bdcbbaacbabcbaabaccbdbdddccbabdcbdabbcdbadccabcdaabbcdcdbbdcdbdaaabbcbacccaadbadabcdacddccbacbbcdabababdcbbcaddcdacccdbcadabbdcddcdaaadbdbacdcacbadbdcdcdbabbadaabcdddbbcbbacaadccbcdacddcbcabdaacbadbdccbcacaddbddadcdcddbddddacbaadcdaaabaabadccddbaabbadacdacabaccdddbbbacccaccadacbbccdddbaddaaaccccbdcabcbdddbbbcddccbabcabaadadbbcbbabaaadbcbcdaccaddabadcbcdcccbadadbbbacdcacdcbcacbcbbcaabacdabcbbbcddcbaaadbadabdaaabadbbbcddbbacacbbcdadcabcabdacbaacbaabdbbcbbacabbdcddbdabbbcbcbaddaadcddbaacaaadaababdbbbacbdbdccccacbbdcabbbcbaaaaadbabddcaadddcaacdcdbdaabdbddcbcdbcdaccdbcdbbdddcaddcdcbadcbcadbdbdcaacbdbcdcaacbbadadcbbaccbaadbaacacdddbcbadcccddbbbdaababdbcdcadbdbcdaaccabbcdbcacdbbcadcaaacbacdaaaadbdaadbcbcbdddacbbcdbaaddbbadadabbdadabbbcacbcbcccccaddaabdbaabbbdbddddacccbddadacbbddcccbdcdcccbacaaaccaabdabaacadcadcdcaddabcbabacaadaaccadcbddabbdddbabcacaccabaaccbaababaaacdaadabbadbdcbddcbbbcbbdcacacaadbcbdcaccbbacccdaacaccbcababcdcdbdddbacdaddcaddbdccdddcacccbdcbbddabbcbbbdddbddaaadacaadaaababccbcbaabcbbccbbdbbbdddcdadbdcccbbcbdddbdadcdddacdccacadcdcbcddcbaddacbcdcdabcaaaaadcaadbadbddcccbaddccbbacbbadddbacaddacdcaccababadcbabccdcddbabbdcaaabcbbacabddcdbcdcdacacdabcaadacaabbcdbdaacbbabbcdaadaacdcbddacddcccbaacbbcbcccdadbcddaccdcbbacabcdaaaabaadadddddcbdcabddabdbccbaccbacaddabdaabacbcdabacdacbcbdbdccddbdabbcacccbabbadcdcbdaaddbdbaccacdcbbadabbbcdacadcdbbacdadbdaaccddbbbccbbdddabaccbadcdbabdcaadbcaddaaccabacdabdccbaadcccdcdadbcbbddacccadddcaddbacdbdcbcccabacaadddbbcbdabdbabdcbabdabbdadacdadddacdcadbcabcbdcadbbbccdcdabccbcbbcadadabbacbcadcccbcddaacdcabccdaccddcbacdbaaabcddddbadddadbcbcdbababacdcddbbdacbdaacbaddbcbabbbadcadbdcddbdabddddadcadccadacaddcacbadbdcdaaacbccbbcbcdcbdaaaaacdbcbbcdaacddbcbcadbcbadbddcabbbcdcacbdddcdaaadbbbbbbacaacbccbdcddbbacccbadddddabdbdbddadbdccabbdcabdaabdaadcdaadddbbbdcacabbbcbbcbbccacaccbabadddadaccdbddaaabbcbcbdcbcabbcdabcaabbbccbbcadacddddbddcaabcadacbdaccbbdbaddcddcddbaacdddbbdadcadaddacaacacccbacdbbadbbdabccabcdddcdcdacbbdaccdddcdcaaccacaaadcdbaccdaddaaaaadcbbcabaccababdbcacababcccbbacccdacbcbcbabdcbbcdcbcddbbcaaaccabcccddabdcaacdbcccaaddaddcabaadcacabbbabbbcdaadadadcddacddadabccaaaaaacadccbddadcccabccbbdbacbdcacddadcaababcabbaacdabdccccacadddcbdccacccdbdcabccaaddbdadaacdbaccbcbcccbacabbbbabacdabcaaccaabbcbdcccdcddcadcdadbcdbdabdbadddaacacbccbcbcbabdcababaddbddadbadacabacbacccacaccbcbaaabbdcaddaacaadabbabbcdabbbbcacbdaddadbccbdcccbabddaaccddcdaacdccacdaccdcadbaaccaaabdbacbbcdadabacabdcdbdbaaddabadbbaacbdbcddaddbccddbadbdabaaabbccdbaabbbbadddbccbbaadddbaacccabdbccaaababccbdbabdccdbdabbadabbaadcdddcdadcbaddabddbacacabdccbbadbbadbddaabaaabbbdcccacbaababcddcbacdcaacbcdcbaddacdacbcaaacabbccbdbcdbabbccbccbadaddcdcbabbdbcadcbaddacddbaabaadbbabbbdcbbadbdcdadabdcbbcaadadcbaadadbbaacbddacbcacbbccaacbdaccdadadbbbbcccbbaaadcadaaadbbccabadadbcbbaacbbbdbdbbcaacbbbacbaaacabbabbcaadacadcbaabacbbdcdaabbddbadacbccbcddbbbadabbdadbbdcccaabbcdbbbbdbcccddacabcdaacddcbbdbdddddcacddcacbbcbcbcabaadccdcbaccaacabbdcbdbcbaacbbbaabccadaabaaacdbbccddbcdbadcdadbbabbbdaabddbaccdddbcbadbbcbcbaddbddccbdbadcbaaddcdcadadaccdbddbbdacbccdacbadbcbdcdcbacbbbbccabdabdcbbbcbbadbcaabcdcbcbbaadddaadbcbbbcbaabdabdbcaccdbaddbdacddbcbdadcaaadcbdadaccbcdbddaacadddcbdbbdbcaddbcdcdbadcbbdddcbbadaacbcccabddbcadddddcccadcdadcbbbbabdaaccbbbcddaaaacbdcbdcbbacbcbcdaadaaabcdcccbcbbbacbcbdabacaacabbbcbcbadacbcccabccadbbadbbabbadbcaadbcaacabdadddccaccbbcadaacbccbacaccbccbcdabbbdbaaabadcbcddbcbacabbdcaacbbcbabbadacdadcddbbadabccdacabaabbbbbcbbbacbaacaadbdbaaaaaabaccadbdbcacdcbbccabcacbccdbcbabdadabdcadcbaabbbccddcbdbddbdababadccaabacdadbaddcdbadcccbbadcacabddcbabbccacbcdabbcbdacddbdcbaaadbcbaccbcaddbabcbdcabccbcdadcabdadcaacaddabcacdaaadadbcaadbcadddaaccabcacacdaaaccaadbddabccdaadabcaccbacabcabbddabaadaaaccadccaaacbbcbdaacccbaacbdadcbddaacaccdddcbadacadbccccddcddcdccbcdbdccddddcdcbddcbabadabdcddacaddbabcaaabdcbdbabdbbcadbbbcbcbbbcaddcbcabbcbdbbabcdababbbbddbddaddcddbcacdccacacdcaddaacdadbddbaaddccccaaabcdaccbcdadacbcbcbcbcdcdbdababdcbdbccaacdbbaaabbabacabddacbbccadcdacabacddabbaadbcbaaaadcbddabadbbabcbadbdaccccabccbddbdbbaadccadbbddcabcdcbbbbbdddaaabcccadcdccadbbcbabacbbabbbccacccbdacadddddbabdaaddcdadcdaccbadbdcccabcadbbcaaddddabdacabcddabbcabadbccdbbbcbcacbacaccbaacdcbbabdaaaadcbdcddaddbadacdbcdbbdbbdaadadcdbdbddddbaadbabbbbdcbababdcabcbccabbaddabdddcdadccadbdaababbccbbddcbcacaddddbabaacacaadabaadbcbabbaacbcccbddaadddddddabbcccaacabbdbccddadbaadbcdcbccbabacdbdbadadbbaacdbaccbabdaadaadacaaccbcaaadbadacadacabdbcccabdcdddbcbabbdcbcabdcbddcbabdcbcabdbbadbadabbddcdbdabadbcbacbcaabaaabcaddadbccccdbbaabadcdcddcddcbdabdcdbccbabdcdcdcabccaaadacacbacadccdccbcdcbdcccbbbdddbdbcacadbadbbbccadcdabacdbabddabbadadcbbcbcbdcdabbaadabcdaddccabcbdcacdbbccbcbcbbbccdddbaaccccbddadaaadbabbabcabacaddaabcdccddcdabbaacadabcdbaacbaacbbcabbabdbabaccdcbbaabcbddadcbacccbbbcbaabcbcdddaadcdccdbaaaccbdbcbdccbbdbaaccdbbdadcbdddcbabdbaacdcddbbbcbdbcbddcdbdddaaabacbcbbaadbbcdabddadadcbccdaddaaaaddcadabbbdcccddccaacddbbdabdcdaacabbaccaadabdbccbddacdcaaddabcbdabcdcbcddaadddbacacdcdbadbbbbddbdbbcdaabbcddbaabdcdbdadacacdbdccacbdaadadbcbbbcdcbdbacadacdacbbdbdbaacdaabbcabaacbcaddababadbcbbcdbbcdbbcbbbcdbabbccbddccacacdaabacdcbaddbddbbddbbdccccccbabcddadbacabbcbcbaddbcbcddadadcbcdbdcdaacdaddbcadbabcaadccabccacbddcadbcabbbbcbaccdcbcaccdcccbcbaaddbbcaadbbdadbbddabdbdcdddcbccbacaacdcadcdccacbdbccaccadcdbbcdabbddabdbddccbabdcabdadabddcdbcbccaabacabdadccdabdbbaaddbbabdbcccacddbbcccbcacdccbdbdccbdbbbaaacaadcccdbabaadccacaaadabbaaadccabddbcaacbbabcdbabcaccbbcbbabcdcddbbcbccbccbcbccbbbbadccacdcdadadbdaaacbddcbccddddabbbdcddcababccdabcaccccbaaadcdddadcaacccbbbccdbadbcdcaabccaaddbbbaaddbaccbacdcddadbadadaababcacccbcdddabcadbdcadabbddabbcdccdaabbabbcdddabcbdbccadcbabdbdcddbdabadbcbbaddbcbacdcdacddcdcdcddbdacadadcddccbdaacbdabbdbbacaacacaacabbadcdbcdbcbaaacaaccdcaabcbaccadcbdcaaccaadbcddabcddaacacbbbacaddbadccabacdbdcbbdccbcacdbcccdbabdabacbaabbbbcccbdabcdccaaaacdabcbbcbaacbcbdddaaadcbcacddcabcdcbbdbabadbbbcbdbcbdcbbbbbbadaaccdbacccdcdbcbdabbbdacdcaccbdbcccdabcbddcbbdcbcaaadaaaddaaacccbddcddbaaaaabdcddaacbbbdbdbbdcbdadcdcaaccbcbdcacddbdacbdcbddcccbddaccbdcabbcbddaabbbdacbddbcababdcbbabbbcbbabacddbcaddbccabcbbdadbaddcbbbcbbdcaaadabcaadbabcadbcdaccabacaaaacdbadabbcbdadcadddbddcdbacccccdbacdcbddbccdbddcbddbdcaadaaaccbbcdcacacdccbacbcacbdaddabcabbdcaacbadadabcaccaccbdabddcdddccbcbaabacbbaaddbdbcbcdbccdbcdadddbadccbdbbacbcbaabbddbbbaccbaccdbbaadbccbccdabbddbdcacdcadbdccbbbbaddadbccbbcacbabaacaacaaddddabaabababcccdcbaaabdabadbccadbbaaababdbdacacabaaabddbaccbacbdbbcdacdbbcbddbbdddbbdbdccccbadaabdbcbbdacdcbcdccbcbabacbccbadcdccccbadcbcdadcccbaaddabadacbcacadacbaadcbdacabcacbadccdadcbdaabcacbbcadddccbaccccccdcbbccdabbccbdccbcccabdbbaacadabdcccacaabcbcaadbbdadbbdbcccbcbabddbbdacbdacccadbacacdbdbbacbcdaddcddadbccbabcddbacbddddabdadbcdbbbdbbdcbcadcbadbddadcbaddcdddaadcdbabdbcccadbbddcaaccdbbbbdcdcadccbbcbcccaddcdaaacdbccddcbbacddccdccddccbcdccbcbabdbaabdabbcbabbaccacbadacdadbcaacabdcbddaadbadcbdbaaddbccbbadbddabcccbbadcabdabcacbabddcccdbccaccacddaadcbdaadabccaacaabbcdacdabdacdaccccadbdabddcabccdcbddccbbbdaddbbcccdcddcdadbdcaabccdccdcdcbcdaaccbcbbacbccbcbaabdbacdacdcaddcbcdbdcbdadbcddadabcbbdbbdbcaccdbcdcbbdadaabbabdcaacdbadbdbabbcbddabcbabacdcaddcbbddbcccacbcabadbbacadbcacdbaacbacdaacdbbaddabbddbcbabdadbbbcbdbbbaccdaaabcaccdbcdbbcdbddababcdbbadcabddbbddcadcdcadcccdacdadbbdbdcadbabcacccacdddabbdacbdcabddddbbadcadbadddddbbcadadbcbdacaaaaccbdbccbbddadaaaacaadddacdcddcccadccacdaadbbbcbaadddbcaaadabcdbcbbdaddacdadbbbacaccbdabbbbcdaacaddcbbcbaacbbdcdcccdaaabbaabadbabcdbabbccdadddabcddcddbcabaadddcbacdbacaacddbdaaacacacddbdbaccdddccbbdaccadbbaacdadbabdbdadcbcbcbddbcdbcaccdcadaabddaaadddbbaaddbcbbabbcdbcbacaabdbacdddadaccaddcbdddcbddbcdcbcccdddbaadcacaddbcdbabadcacdbcacbccbbaddcdbdbabaadbbbdcdabadbbcbdccbbbdcdbbdcbcccbadacccbcddbcbabbdacbcbbadccdcbdbaaddddcbdcaadadbacbddbdbdddbddcdcdabbaaabbbbaadcdaadbdcbcddccbdaababddabccaababaaaadaabdacccbdcadbbbbddbabdcccaddcddaaccbbccaadbcacddacccbdcaadddcacbaccccbdbcaccbcbaacbdcdabadcbcaaabcaacbaaaccdddccbbbaadcddccabccabdaadbacdcbcacacdacabdabcbbadaaabbaaacdbdadcdcddddcdaadcacabbbdcdacadbddacdbaaacbcdacccbadabdbdcbdbdaadbcadcbddbdabbadaadbcddbbcbcbbdaacddbcbbabdcaddcbaaacaddbbcdaaccaabdcccbadcacddadcdadcdccadddabcccaccdcacabbaccaacbcbbdbcbbcaacabcbcddaabbbdaddcaabcbaabaccddbbaadbccccdbcbaadcbbddcbbcbdcabdaabcaaccacdcabaddbdbdabcbdbbbaabaaadddccaaaaacacdcbbcbaaaddccbddaabbdbacccbddaddbbdcccbacacdccacdaaddccadbacbacbabbaabbbbbabacbddcccbbbcabadbccddaabdbabadcabbacbcbbdcbdbdccaadddbdbabacdddccdaacaabaacadcbccaaabadcdbbbacbaddcabcdaddcdaaadacdbacaabbcbcabcabcbaddacbcabdcdbcadaddacaaacdccadcacabdbadddcbbaadbcbbbdbaadacbcaacdcbcdabacccdadadadaddbacabaacdbbbacbcccbcdccbaccddbbdacbbdcbaaddcabdcdabdbcbbcbbcabdaccabdacbaddbdaabbdaacccdcccbbababbddcabcadacbddbaabdbcdcaabbbdccbadaddabdcbbdcddbcaabcadcccccdcdcacaadadbaabdddbcdacababdaaadcdccdccccdadbbcdbaabababdbcdaaadabaacabaabaacddcbbadbabdcaaaaadddbbbaccacabcdddababcbcadadcccccdaacdabbbbcaacbabaccabbdcacbccacccaacccbbbcbabadccacdabacbacaaddcaabdcbbbaccbccaaddcabdbacdddcccbbcacbdbddcbcccddbdbdaccbddddacbdacdddadcdacdcababcddabbbdbbbcaddcbabbcdddcacaadcdbaaccbcabbadccadbbdcabcbadadabbdbacdbbcccabccddddbdbadbbbabdbaddaadcdbdcaadabdcbcadabbaddccaabbddbacddddccdacbdcdcadabdddbdadcdcacbcadacaacbddbabdbaaaacdbdcdddcbdacdababbbabcccdcabbaaddbcaabcdcbddbabbadbacdadddacbacabbcdbdbbbccdadcacbdadabdabdaabbcbacdaddbbccadbcdcabdddabdccbabccbbbddcccbacdacdbddbccbcbbcbacdbbcbdadbcddddaaabccccbcbdccdcacabcaabbaabacbcddccddcbaccadcacbcabddcdcbaaddaaacbbdcbccccabdabcbdbcdccababcbcabdabddabadddaddbbbbcdcdcaaaaccadadcaccdbcbdcadaccccbcddbbcbadacaacdadabbaaadbbbdaabdaaaacabaaadabbadbbacbcabacbcadadbbcddbbcdbbcdabcbbabbdccbdddbcbcccdbadabcbdbbadcbbcbbbbcddbcaaadcabbddcaddccdacaabcdbbbbccbbcdbabbddacdbdaaadabdcbdacacacccdaccdcaabcbcdbbcaadcdccccccaaabaabbbccbbbdcbbcadbdadddcbbcaadaccdbadcccbcdbdacdcdcacbcbbdcbbadbddddbdcdbccbdadbadcccdcddacdbcadcadbccbcddbcddccbdccbcabbccabbcbbcdabbcccbabccabbaacadbacccdddabaadccbacbccddaadcbddacbdbcaaacdcdadadcccbbccaadcbaaaadabdbbcaaccccadddbdbbabbbdacddacdacccaccbdbbcdabccaabbbccacbcdacadaadbdddcbcddbaadcacdbcbadaacbaabdddcbbabdabdddccabcabbaccdccbdadaaacbccbcbbabcdbababccdccbbbbdddccbacdbdbbdcdcbbbdadbbacadadbdacbddcbcadaccdcdadbbaadddadaaddcdbcdcbaaadacbdccabadbacbacbcadadaacbbdbcbaabcadcccccaabcdbdacacbaaabcbabbcdcbaadacbcdccbbdabdacccabcbccccabcaccabbabcabccbaacbcdbbdaaacbdcdbdcdbccdbcbaadabbddabbddbbcdaabbccadacbcadcacdabcbcaddaabaaabacacccdcbdaacdbdddccaaddaaddddadbdcbadadaaabacbccddcacbdabdcaaadcbaddadbddbbcbcbbdbaaccdcbadbacacaddccadcdcadabcdadabccddcbdaaaaabccbabdccaacbcdcaaabacdbcdccaccdcbacdacadddbbdadcdbbbaccbbabbdacaacccbbbccaddaabbcacddbcbbbdabdaacbdaccbaacacbcbcbdccabacdbbbaddacccabcacabdabcbbbbabbdbaabcbbbcbdcacaddcddabcabbbacdcbbbdcaccabbdaddbdaabcabbbccbcbacdbddbdaccadbcacadbcbdcdbbbcaaccaddaababacaccacddbcabccbbcbadcbabbaaccdcacbacaaabbdcdaaddaaddcbbbacbbccbcccacbdbcbcdbbbbbcadacccddadaddbddddbdcacdbdacaaaccddcabaaabcaccadaabbdbbaaaacabdccdaddbcdabaddabccbadbdbbbcbbbcdddbcdbbdccabbcabadacccddcdabbbacbaabadadacbabdaccadcdbcdbbadadbbbdacbcdbddabcbdaabbbbcdabbaabdcbbcbacbacbdbcddbddcdcddbdcbaddccdbbcbbddddbbbaadbbddbdaadddaadddcbcbacbbbdacdbcccccaccccaddccdacdadaccbcbccbddcccaabadcadcbbababdbabadbbbcddcbcddabbdbaaadabadbbcacabdbcaddaadbdadddaadcacaacabababdcadabbadababadddbdbcbcbabdbcbabbabccbaaadddbdcdcbabbdaccdaccaaaadbbadaaccdabcbdcbaacbaadccdabaccdbacbacacbcbbacaaabdaadcbadddbdcbbadbbcbcccaaaccbdbbbacacbabccbdccacccbaddaaaaccdacddbccbaadbaccdbabcbdddcacdcdcdabbdcaccabddadcccabbdaaaaababacaaccaadddbdcbcbcccabadababcbbddcccabcbbbadcacdbaddbdaaababbdacadddadbdcdbcbdbcddaaacbdadbcdcaaccadddabbddcdcabaaaacccdddbabdbbabccddadbbaaabaddcbbbddbccadabbcdbdcdadcdddbacbbddcacddcdadbbabdddbddcccbbccbdaccddcdadbabaadcadaabbccbcaddcbacaacabbcbddbccdddbbbcbbbdbdcabdbaabbdacbbbcddbbdcdbadaadacacdbabdbdacbbdcddacacbbbdcacbbccddcabccaddbcdabbbcbacbcdaccbabbdacbbabddcabadcbbddaadcdbacdbddcdbacdccacbaccdbcaaaaacdcdcccacccdaacacaabcdbabaadabbcdadaaaabadbcddaacbaccdcccbbcdabcaddbdcbabcdbadcbacdaccaadbcdbbbabcdbdabccacdcbdcabacbccbcdcbabcbcdaccdbbbdbdbaabadbabbcbbadbdaaddadcaabbaacaacbdbaacdccaaddbaadacacaccbabcacbbbbdbddcbdccbdbcabdddaaccbbbabcccdbcadbccccbcdacbcdbaacaabbbddacdadcdbbcadbadbbbbdadcddcbbdcbcbccacdacacbaddddbacbaacaaaabdbdbdaabcabbcbbbcadadbdcbbabdacdaabaaaabddcacddcdbaddabbdbaddbabcadbcccabbddbacdcddcdcabddacddbddacababdcadddacacccccacdbdabdbbddccbacbddccabadbcabbcbcbadadabbbdbcdabbcdacdbadbbbaabcacdddaaddcdddaccbaacdacccdbbcdaadabddcbabbdcbdacccbbaadbacacbaaaadccbaddaccccccaaadcdadaddcadbdbacaccbcabdbcbdaddacdccacddcdbcdcabbccdcbcbbacbcdbdbbaaadcbcdccaacaaadabcbbcabacccadcaccbbbcaabcabbbcdcbdbdbcccbbdcbbbbcbaabbcbbdccaaaadabcdbdcacacacbaaacccbcbccdaddddcdbcdbbdabbbdabccbaadabbadacdaaaddabbaadacacacdbbbacbbcbdbcaabbdcccdcbddbddacacbbbccbaddabbabdcbbaacdcbdabcbdbdbbadcabddbabaabcbbdcbadadbcaadcdbdbbbcdbcbdcdcbcccbbddbdccbbbbadcdccbddcbbcbbbbbcccabacddacbdbcadccacacdbaabaabdccaadaadacacdacdbcccaaaaabbdbcdadbaccbadaadccacdabacdaddbacacdbcdddabdbbabadcbddbadcddbaccdabbcabcacdadbddabbdcdadaadaadbbddaccbaabddcbcababacccdccbdddaaacddaabbddcacdacaadccabbabbbbdbadddbdcdbdddcccdcaaadccdaccdbdccdddbadcacabdcbdbabbdddadaaacddbdbbabaccacccaaadbadbadacbaacacaccadaddcbadccdacaaadbadbccadddcdcbcdddbdcccabbddcbcccaabcabaacdcdacdaacabdcbcdbcdccaacaaddccdddabadbbabbaccabcccdcdbdaadbabadddddabbdcaccaabadaccaaaaacdabdbdabcdaabacccdbadadbdbbcbbcbdcaccabbadaadddbbdadcbabccbdcacaddddabcaaaacaadbbcabcaadbbdbdcdcdacccbabcbacdbbcccbbadbaadddcddabaadcdcdddaacbaaabccbcbddacacdcbcdaccacadcdcdccdbcdbcbbddacadcbcaccadaadbbbabcbdbbcdbbccddadcbdacccbbdbdbadcbabdaabacabcbddbbbcacdbaaadcbadcdccddccbdbcdcbbabddccccbdaabbbacbbacbadacacadaddbaabaabccaabbcdbbbadbabcbcabdbdbcadcdbbccccadcaddacbbcddbdcbdadccdbbaaabaddbcbbbabdadcbacbbacdabddccbccdacbddcdcdcdddbabdbaabdbacdccadacaddddaaadcaadacbaddbddcddcccddabdbbdadcadcdcbcccbcaabacdbadcbbacbbdcabacaaccdbcbcdbccdbdcccabccbddcdcdbbaacdbaaaadadabbdbbbbbcaabddbccbcaccacaacbacbaabbcacddbdadcacadcdddbdabcbccbaddbadaaddaccadbccbaaadcadcaacadcadacbbacddcaadccdcdbcdcbddacaaacbcbcbbacbbbdbccabbbdabddbaabddbcdbcdcbdabccaaadcccbdbaddacbccddaaadaccbadabcbcbbcabaabaaddddacadddaabbbbbbcbddbaaadacdbbabcdbcacccdcbdcddcdcabdbbdbcbaccdcdabddbdcabcbcbacddcadaaadaabdbbacbccdbdbacdadadabcdddaabcdcbadadcabccacaddacbdbdbaabcbadbabcadaaaddcbadbdbaaaddcdcbabbdccdcbddbbacacbdbbccdcacbaacacdacdcbaaccbdbbacddabaabacdaaddaacbbbdadccadcccdddcaadaacaacccdbabaccadbdcabcbabcbdbabbbbcbdddaaabbdacaacdbcabcaccbddbdddccccaaabbdcaaacbaccdabdbabddaabaaccbcabdccddaddaaacbacddadaccbcddadcbdcdbdbddccaddaddcbacabcbcaabddbbabbbaacdababdcabadbbcbcacacdbbdadbdbdcddbbabcadccbddbcacadaacabdcabaccaacccabbbcbbddbdbdbcdbcdbcbddddbbcbabdaaaccdabcddcaadbabdcdaaaabcbbacbcdcccdccbabcdbbddbaaacccdbaccccdbadbbcddbdcbccbbbabdacacbbdcabbbdbcadcdbbdbcdddbacbacbcbadbbacdbababbcdacaccdbabbcbaabdcbabbbddcdcadaabdccdaddccdbcdadbcdaccabdbbcccadacdbacbbdcbcaababdacddcdcdcaddbabbcdcaccabdbbcccaadcdcdddbaaacbbcbcdaaacbbaaddaadbabdabdbbcbdcdbbcbcabccbacccadbbddccbdcabccbdcbbbdbdcaabacaddabbbdaccbbcadddaadaaabdaaadddcbcdbbccadcbccbcaacacccbbbdbbdaaddccaabddabcddabbccbabcbacabaaaabdadadabcddaccbbaaaaabdcaabcdcccbcbacadbbdbcbacaadaddbaaadbaadcbcbdcddccaacbbdcaddcaadcbdbdaccccabaacbdaccbddcaaccbcdbadcbbdacbddabadddadcadccbacdcdcbcabcdcccbdadacadabcddcdccacbccbcaabaabcdcdabbdaabdccaadacacdddbbbcddadbcbcbccabcabcddbdbdcadaccbabcddaaaabdbdcdabdabdccbcddbdaddbcdbddbadabaadddbbacbdbdaddadbcdbcadbcbcdddccabcabccadbaaadccbbbaaabaadabbdacbdbbbdbdbbababbbcaacdbbcdaabdddcbbdbadbbbaacdbccdcdbcdbbbdbdddcadcbdbdbddcdbabcababdbcbdaababadcbbbbaadccadacbdbdbaaccdacccbacbcdddaadaaddccbcaaaccbbaccccabcddbbddaccdbcadcccbcaabbdbbcdcdabdbccbabaadaabacacbaaaaaacbaacbcacaccdcdbdcaabdadacdcbdaccdabdddaacaabaaadccaaddbbddcddcaacbdcbacbbdbaabdcbbaabcabcbbbadadadcbdcdcccacbaadddbcabababcdccbdcbcbcddbbccdbcabdbccbcbacdabaacdbdadadddaddabaaccbccabbddaadaddadcbdabacbccbddcdddcdddcdccabcbbbdddcdbcbcaaaacaccbbdbcddbabcdadcbcadcadcabbdddaadddddcacaabbcaadbacbabcacbbdccdbdbaabaacbdbdcaaadcbdcbdcbbcccbbdcdddacbbccdaccccbdddcbcdaaaddbbaacacabcabbabddacbcbdcabccadbddbcbcbabbbabdbabaddbaaadbcdaabccddcaabaabcbbaacbcbccaaacbdbadbcbdcacbadcbdddcaaddbddddcdadcadcabdaadabaabbdadbcbabaacbabddacdabcbccddaadabaaadacbcdbbdacbdbaabdaacdbdbaddcabadbdaadbcdbcbadcbbbaaabadddddcaaccabcbdabacbdacbccbaacbbabcaacdaabbdacdabadbccddbccabbaadaadadbcbdccdccabdcdcdcacbdaddccbcbdabbbaadcdadaabcccbcbadcbbcacdabbbbbdcbabbdbcbcbbaccabccbcadbcabccbcdcbadabccacabbadbcbbdcddcdcaacbcacbdbbbcdcbabbcadbcbcbccaccaabdddabdcdbdadabcdbdbbdccbbabcddcdcdbacaaccbbacbdadaddcdcbacacddcbacdaacbddacaccadcabdabdccaccddbadcbdbcbccccccddccbadcdcacabbcdabcacbadbcaabdacacbdbdbcdccdabcbddbbcbccbbaccccbddbacdabaacdddcbccadbbdcddbdcdbadacdacdddbcdcddbaccdabadddddacdabadabcacdbabdaacddcdabaacbacbdcdacdcacbadaddbadaabccabacddccbbbddddcdddadbdbcccbccaccdcccbadcbbbbadabcdadbbdcbddabaccadadcaaddacbbbdbbddddbaaddacdbcacacdccddbacbbbaacbdbcdcbddbbcdaacbdcdacddccbdacabdbdbabccdcdaadaaddbcdcbdbacdabbaaccbcbbcbacdabbadcacdaccbcacabbdbccdaadabacdccbdadbbdacbbddbdcaccddbaabcdaadbcbbaabddcbbaacaadbabadbdabbabccaacbabaccddaabbcbcdbbbdbbdbbdabdbbcbdaabaaccaacdcdccaacdabdbbcbdcdcbbcbbaadbcddddcddaaddbdbaaaadcdbdbadcadaacadcdcaccccbccdbadcbdaddcabababccdbdbaadabdbaacbccabdacabbbbaadbaccccbadcdcaccccccbacaccacaacabcdcdbbcacdacacdcabbcccacddacbabdabbdbcccddbbcacbaaddccacadcabcdcadadabadbbbbabdbdbbcbadadbcdccaccccbaaaacddcdbcddaddcaaaabaacabcaacbabdbaabcdacdbdaccaaadbbdcaabdabcccaccdddcbdbbbdbaddcdcbccccdabbaaadacddacbbacbbbbabbdaaabbaabddabacaacccaadddbbcdcacabdccaddadcbddcdcabcaadacccbdaddbdaaabbcbdbbbddcaadcbcdabaaacbbdabccbbdcaabcbbacbccacabbbdbdcacaaabbccdcbdcbdcbddbbababdccddabcadbbbccacdcacbcdbdbbbbdabbbcdacddcccbbaababdacdbcabdbaccbcbdabbadcabbbdccbaccbdaaacdbabdcdabacabddaaacdadcbcaacdbaadcbaaccaccbabbbdbacadccbaccdcacaddccdadddcdbcbdabdbbbdabbaccdaddccabdbdcccbcdabbbbbcadbdddbdacacadcaddacdcccdbabbbdacddacaccbdcdaaabbaacbbccdccadadbddbbddbcdcddcdabbccdccbacdbcbcbdbcbcccddcdbabbaadaaaccbddaadbcdacbcbbbbbdcabbbdcbcbbbdaadbbddddaccacaadaabbbdbddbdbbcdaaadcadbadaacdbdcacbaacaaabbbabaacacddcadcdccddddbbdccbabcadddccbacbbbcdbccdbcdddacbccdbbcdaadbddadaccdbcabdddacaacbdadaadabaaacbcccdaaccdccaccdcaaaacbaaaababdddabcbdbbadcaccbcddcdbbdcbdbbcbadcccccadbcbaaddadbabaacaacbaacbcdaaaddbddbddacdbcbaaccbbacbdcabbdadcaacacdbabdaadbbacdcbaccbdadbacbdddadbaaccaaabdcdcaddccdbcabacbbabbccabbadaacbcbbcdcbcaacddcbbbcbbcddbacdadaaaddadccaadddadadadbdddacabbcdaccdbdacdacadcddabacadcddcadadbaaddccbbbcdcbdcbcadacadcccbccccaadcbabadbccddbcaaaaabdbaaacbcadaabcbcdcbbddbdbcdcddbccaddddcdbbdbcdacdccdccdbaddccaaacaaadcbaaaabadacadbcadccccdaddadcdcddbcbaccbadabaccabdcbccdaaadbcbbadacccbcadbcabbacaddacbddccbccdabcbbbadcddacadddbbdacbcbacbaccdcdddabaccaaacddcbaddaabdcbcadccdddcbacccaaadddcabbacccbbdbabdbbcbdccabcccbcbbcbabbaaacdbcadadbacacccbdbcabdcbabccddcaaacbdcdbacabbcdddabadadbadccdaaaaaccbbaacdcbbcbcbdcbbabbdabbcbcccabacaccbaaddabadabdcabbcabccbdadbbdccaabcdacccabbccbcdbdbbbcaacabdcabdcacbdcaadadcaaddbaaacddbbabdaccddaaaadcaabbbaaddacbddcdcabdbcacddacaaacbacbdadddaabcdbddbbabbacdaaabcabdcbbbcaabccbaddabbcbdacdabbcbbbcbacaccccbdbadbababbcddaadcccaabbdbbadabdbbbaaabadbccadcbbcacacdccadbbaddaabbdaaaaabcdacbbddcdddcccddbddadaacbcbacbbbdbcabbabbbccccabcadaacdcadcaabdbbcbbdbdccbbbaabccccacccbdabbbacbbabdddbbdadcdaaadaabcdbbddbcadbcaadbdcbbddddbbcdadddcccddadcdddaccacbbadcbbcccdcbbacbcabcbbccabbabdadcddbadccabadbbdbdddbacadbaacaabbbbccacdacabacadddadccbcabbdbcdacabcbbcccdcdadacddccadacacabcdadabdbbcdabbbdcdddbadddaaccdabbadaccddbcdcacbcbbbdcdacabcdacbcbbdbdacdbddcbdaddcacaabbaaccddbbdcadacccccbccadbcddacbbbdbcbbcacaddabbdaaaccaddcaabaddaaabdbdbdcdcadddbacbbcbdbdcababaccacddbaaccdadcadcbabadaddabaddadcdacabdaddddbadcccdadbdbbbbaabcacccabbdcbcaadccabcdaabbdacdcacababbdbabdcdabddbcccacdbdddddcbbbaaacbaccdacdaaccbabdbaacadaccbbbcbbcaabdaacdcddabaabacbaadbcbddabdbacddcababbcaddbbccacacadbbaaaccddcabddbcbdbcbdcdcbdcadbddacbbacaadabcdbdbdcdcbdcdcaaacdcdbaaccdcbcbbdaaabcbabddccadccddcabdbcaadbdbbcddbadcbbcdbdbadbcdddadbacabcbccbcdbbcdadadacbbdcaacadbbddbacaadabbdcddcbadcdbdabdbcadbdbadcddbdccbccbddadcaaaadbaacbdbadcbcbadcaabadbaaddcddbbdadaadbabbbaccddbcabbcbaaaccdababdccbacadddcccbadcbaaaadccbdaacdacdddbaabbbdaaabbdacbdbddadcbdaababaaadbcbacabadadddacaaddcdbbaababddbbbcccaacccbadcbbdbcabcaadbbcdcdccbdccacccbabbdadbbdcccaaadbabccddcdaababdddacbddaadcbbadbacddbbddbcdababbcabbacbcaaccdbbbccdcadbaadcccbbbcddcdaccbddccbcbddcdcabdcbcaddcbddadabacacdadbccacaabdbadbbadadcdbcddcccacdabadbddbaacbccdbcbaaddbabcbbddcadcbacdcbbbdadbdadddbdbabdaddddcdabadaccdddcbdbcbccadabddaadcacbcdadcbdbdbdacaccddbdbbcadcdbbdbdbcccdaacddacdadbbdccdbdaabcaadbcbddbddcddccbbbcdddbcabddcaadadacdcbaccdbabdacccbcdddcacacbbdcaddabbdddcdbdcaaacccacdacacdacbdabbbbaaabdcaabddcacaacaddcddaadaadcbdacbcccdcbccbcbccbdcabdabaddbddcdbccabbdcbabdadaccbdcacdbcbcaadbcddabacbcdacdabdccbbadaddabcadbcdacbcbacdadddccccabbcaacbdccadbbcbadcddddacbdbbadcdcbbcbbcbbbcbadbdbacaabddccddcbadddadddddddacadbdcdddcabbacadddbdadcbabcbcddbbcdddcbbadaddbcbaaadcccbabcbadbbcdbbdbbbabcbaaadadbdbcdbdadaaaaacddcdbccadccabcabaddadbcbdabbcbcbaadabcadabaddaaccabdbbdabbabdcdcaddaadbdcabbbddacbabcaccbbaddcaccdadbcaddcddbabbaaaacdbccbdbdacdcaadaacbdabaccaddbbacacdaadddadacbacdccbdbddbbbadcdadacbdbaacdababbbcbcdbdbbbccbadcaccbaacbadbbbccdbabacbdaaddbbbdddadbcdaabcacdcbabddbbcdbbbddabccbabaddbcaabcddacabadcbcdbbdbbdbabbccdbcbbbbddacdbddcbabddaaacbaacbbaacaccabbcaaaacaddcadabbcadbcbddcbdbcaadcdaababbbcdabcbbcbadddacaccbbdcddaadccacddadaaccddbdabbdbdbcabddbbddabadcbacbcddcbcbcbbdddccdbbccccabcbbadadacbdcaacdbacaadcadbbbcacdbaddadcbccdcdbdccaccaabcacacccddbcbbbcadddcdbcabaaddddcdbcadcccdccccbdbcddbdcbbaaccdcacbbbdccdcdbaabbbbddabccbcbdcdbdadcccadcdbccdababbddcddcabadcdaabdcbcdcaabaabdbabacdcbadaddddbcdabbaaddbabcbabdccbaaacbadccbcaaccbcdaddbabdcbbdabbabddaaabbccbddccabddaccaaabcdccddbacddbdbabddabbdbbcdadaabbcdcbddbadbddcabacddbabdbbaadadbabddbdaabadccddbdcdccabcabbacbcccaccccdcadacbdbccbaddaaacbbdbbdbdccaddcdabddbbccaaddabcdcabddccadabcabaddcaabadbdccddcddadabadabbcddcbabbccccacddbadbdcacbcbcdcdadccabadbdbdbbdaaaabdbddacadcddddaacccbddbbdaabdacabdadbbadcdacccaacdcdddcdbbdaacdbbddadacbaccacabbabdabdbcaacbcbabbdcbddbbbaacbccdcbbccbadcdabcbabbacdadbbacacaabcbcbbacacbcccbcbbdadacdcccabcdbdaddaaacdbbdddcdcbccdbcccccaddabcacccbcacadbadbccccbbaacdcbddbabcadbdabbacbcaadcacccdbbcaabcbcbbbcacbcbccabadadbaddadabcddaaccccabbabdaadadaacccdacddacaacbacdcccddabdaaabbbbbbabdccadddadbbcdbbbbdcdbcaabadbcdabadabbaaaaddaacbacddadccbdddbccaacacbcabcbbdddadadbddbadcccaabaaaabbbadccadddcbbadbbdccdaabcbbcdddabccdbdaccbbabaddddcacaacdcdaccdbdddacbdadbdcdbbcdaccbdabbddadddccaacadccbcbacbdccabcbbccbbdaccdcbdcdaddccdcbbaaabdcaadaadacddadaddccdacdacadcbacdabbaccdcaaaaadcbaaaaadddcdbddaacdaabacaadbbdaaadbbbdadcdccbdcccacbdcbbaabdbcadaaaaabaabbccabbaaddababbdaaabadbbbcdacdcdbabbbcbababdaaccbaaaaacbcabcacdabbdbcccaadaccddbdccdacbadcdddaaadcacccbbcdadccaaccbabcdbddacbddaccdcbdbacaaaddcdbcabacbbcaaaacbdcaccbcacabaaddbbbcdacbbcdcaadaabbbbdcbcbcbaabcbcdaaccdadbacbbbcbcddbababadabcaacaccaaddbabcccaccdccabbabbabbbbbcaccabbabadadbdbdadcbdcdcbcdbabdacbbddbdcdcbabbcdbbadcadccccdbadabdabcbbaaadbaaacddcddbdddbcdcabdbbaddadadcdbdbbcaccbbbcddbacdccbddcdacddbdbabcbddaabdccadaadccbcaaddbdcbdadcccaccbcbbabacdccdcbaddbcaddaadadddbccbcddcbdaabbbbbbdacacadbbbaacccccddaaddbbddccaaadbccdabadcbacadacbbdaaccdcdbadcbbcacadadcbdbdaaddddbacdcdcbbdbccbbdaadccabbbabbbbcbddaadccabbbdaabadcddbdaaaccadbaabbdcbcdcdadbacbadacbadabadddbbddaabbbdcbccbcaccccbdddbdccddcaabacbdccdbacbdddcbababdaabacdccbaccbddbcaabbbbbbcdbcdcbacbdbdddcbaccbccabadbbdaddacbcdacbdccbcaccdbadbdcadcdcdddacdbdbcdabccadcaacaccdaabadcbcddcababccaddcbabbcadcdddaacdbdcaccddadcdacbcdcdcbbabbaadcdcdbaacdccccaadcaacdaacacdcacdbddddcaacdcadaccaddbaaadadbaaaacabbacddacaddddcabbbadacdabdcdabbdaddddbbdbccabddcabddcbcdbaccbcdcbdbacbbccddacabbccaccaabadacccaacaaadcacbbdbabdadbdccdcdcdcaabcaacdaddbddbdcbadacacdbcabbdbdadaaaddaaacbbcaabadabddacbabcadbdcadddcabdcaabcdbbbdbddadccaccaacbbddbbdbbacadabcbabadcdcbcbcbadbdbbdbcbcdacddddcacbaccadccdcdaacaabbcadcbaccadbcccddcabbbdbbacacbcbbcdbcbddbccaabdbbcbbabbccacaddcadabdabcdbcbcdcdbcbacacdbacbaddddabacccaabacdbacbbbdcaddbdccabcddcaacaadaaddacbcbcbdccdbbadcbabdbadcaddadbbccadaabcbaadccbdccccdbdaabdbdaddaabbbabaccaaaacbbadacaacaaddbabdcddbccdbdcdacddbcbaababcdcadadacbadabbcbddbbbcbababaaabaadadaaaadbdcbacdaadcddbdbcaadcdbcdbcdbacdddcdadbadcbddadabdadcababacccdbcdccbbaaadadbcbaddcbcacadbbbcababcdbcadcadbdaccddcaddbdaaccbdacadadabdbbbadddcdacbdbbdacaaccdcdddddcbadbdaacccbbccddaccbbcdcdbbaacdaacdddbabaadbbbaaccdabbbbcdacbaadaadbbdacbbaaaabbbbdcbddcdcccbcccbdabadbaacbaccaddcaaccbadddcaddcaababcabbccbcadbcdaaddbcdbcdcaadaccaadcadaabaababcdabdaccbacbacbdbcbddbbdaaabcbacdbbdaccddbcbddbcdbadbcabddadabbccdbdcdccccddbabacacddbdacdbaacdbccdddddcbcbadcdaddcadadbcdacbccbcbbccbbbccddbbcdaacdabaacbdbbaacccccccaabdbabbaacaddcdcbcbdbdccacabbddbbbacacdadabcbbcabccdbdcaaabcaddadcddcaacaccbbcdbcaaacacbdbddccabcbabbbdddbcacbabcdacbdcaacdadbdacdcbadbadaccdaababbcabbaadddacbdbccacadadddaacddbabcbbacccbbdadbcbccdccaabbaaccdbaaddbdbbbcdbbacaabacacbbbccbbadadaadadccacbdbdbbdabbbcdadaaacbbabcccccdadbabcdcabddbaadcbdbdcdadcaccbcaaabbbdcdcaadadadbbccdddbbcaccccaadbacddacabccccdcbcbcbdbacaccdbcbbbccadabccbcdcddadddcbbcdaccddbcbabcbcbdacacbcdadaccbdcacaacdabdccabcabaccadbdccaaadccbaaddbddaccbcacbcdaabdbcadccccbcddabcadabdbcdaccdbcbccbcdcccbdaabaabcabbcbdbacbcbbbcdcacbdcbcbdadcdcaabccdbcbacacdcccccacdacddbdaccbbabdbcdbcdddbcdccbaaddcdbdabcaaccddcccbdacbadbdaddccbbadbbcdcbccbbaccdaddcbbcabcbcabcaaccdacbbcaaacdacbabdbcacdccbbdbadadddccbdddbccbbbccbacaabcbccbaaaacddcdccdaaaccbbdbaacbadbacdaccbdcbddabdcadbdbabbccdddcacaadbbcdadbddddaaaccaccdbbaddbdcbddddccbcdcdbdbcadcabbabbdbbdabcaacbdaacbdbcdbdcabcccbbbddbbdbbcabbabbccddcdbdcbcbaaaccbdadcdbaaadaddcddcabdaddabcaabdabdbcaacddabccbdbaaacbcdccdcdcddcbccbacbcaaadcadcccabbcddbddcdcbaabacbabcabcabbcdbaacccdcddbbdacbccdabbaaadbacacccadddddbacddcdcadcdacdaabdddbdbacbaacdbacacabbdcbbccccdcaacabacadabbdbbbdbbbdcabdcbcdcbadbabbaadbbdbdcdaabcabcadccbcdadaabbbbabdbddccabbcdcbabdadabccdbdacaddbccabdcaaadcadcddcacdcdabcaabbaccdacbadadcdbaabbdccabcaddbbcaacacdadcbabdaadbddbcbabababbccadcdcbabddcbdaddabcaacbbdbbdccbdbdbabdccbdabbbbddbdbdbccdbbcdaaddddadbdddaccccdccaaacdddabbbdacccbbbabadacccaddbadacbadbcdbbdbcaaabaacbccccdccdbcbaddacbbabcbadccabadbaccbabbcdadbcbbcababbcccbaccbadccdcbcbbcbbabddccddcbbaadccdcccdadcbcabcdcaacdbaddacabcabacbaadabdacbbdbcacacdbbbbbadcbcdbcddcbaacccbddabbbddacbdcbcabccabbaaacadacaaccadbaccaaccdbbbddbbcadadcabbdbcbacbccbdabcddcabbaaddcdcbddaccdabbcaadaadcdaccacbbaddcacbdcbbcddcdbcbbcadcddabbccadccdaababcbbdbcacbcdbbbcccbdcdcdaaaccdcbcadbdddbacdcdbbacaabcadabddbabdcdabbabacbbddcdbbbbdddaacdadcddbacacaadacacddcacbabdddbdabadaadbdbcccbabcbaadababdccccdcbdabcdcccccdcbcabbbddcaaabdadcaacdacbaddaccdcdaaacdbbabacaccdbbcaaccacddbbbbdaccbadbbabbaddbdbdbcaccdacaabcccdabbacaabddabccdbbdbcdaacabacabbacdbbadabdcccbccbcabccabacbddabadbabdacdaacbddcbddaddabaabadacaacbbcddcbacabdcdbdbccacbabddaadaaaccbdbaaadadbaabbdaaaabbdbcddacdcdcdcbcddabbdcacbaadcdaabaddcaddbbbbacabcacbbcbcaddcaabbbbbcdbccbdcbacaacadacddcbacbbbbdbdabbbdadabcbdcdbaabbbdadadabdcdababcacdbdbaddbadacaadbbaaadcccbaacacdcdccaacddcadaccdcacbdbcbddcccccbcdadbcbbcdbbbaccaaddadcccabdbbdddcacdbababbaabdbdccccdbcadaabdabbddcdadabcddbacacdbdcaddaaaabaacccdacaddaabbbddbccbcacbdccdabccbaacdbdcbaacdadabccadadacaddaaaadccdabcadabbaaddcdabcadacbbcdcaccaccdacdadadcbcadaacbbaaabdcdadacdaabcadadbbcbcabcbbddcabbcdcacacdbacbcccadccdcabaadbcdcdbbdbadbcdcbaaadcddbcddbdcdddbcdbadaaaaaacbcacaadcabbdbaabadcccccbbdcdbcaaccabdbcbdcabcaacbdbdcbcdacccabaddcbddaaccccbaaabbadddbbdcabdaabbcabbbbdcaadcbdddcadddbbaccabdbadaaabdbccadaadcbbcccdddcccdbdddccbcdbabbcbdabababbddabbcdccdabdbabbbdbbbcaababbbadbabbcdbbacaabbccbaaaaadabcbbbdccdcabcdcddcdddbddacddddacbcadbacadcdcabbcdcbbacbbacbcbcdbcdccacddbbcccabbdabbadcbbaaadcabcbcdacddbaaacbcaaaabadcbdacadccadcddcaccbbabcbabcccdcdbcbadabaadadbdbcdcadababddadabcddcdbccabaaddddcaadacdaaaddbabbbbdaadcbacbdadcaccaabadbcdddddadccbbcdbcdabaadddbacbbddbdcdbbbccadcdccaacdcadacdadaabdcbabcdcbbabacaadccaacdacbbcccdbdccdadababdbdbccbdddcaaccbdacccddacbdaddcdcdccdbaccccccbbbadacbbbdcacacdbbaabdbdcdadadbdaddabbbbacbdcdabadadababadcccaabadbccdadbaaaaaadbacbbdaddccdbabbcddcbdcaabdcbcdacddaaccbcabbdbcbbbdbbaaccbcbaababaaccdadabbacbbddbddbbadbabbdddccadccacccabadcabcdcadbccadcdadcbdacbbcccbdcaabddcadacabdbcddcbadbdbcdbdbadbcbabbbabdaccdabcbacbcdaacbabcbccaddcaacdccbdbbdbdbcabdaccacaccbaaacbabbccbbbdaadbcccabcaabbabaaccacacacaaacabcdbabdbcbcaaddaccabccbdcccdbaadcbdcbdaccaddacdccbaddbbbbadccccbcdcdcaabaddbdddcbbbcaddaaacddbbabbcbbadadadbcbbabdcccddddbbcbdbcabbabbadabbccadddabcacaddababdbbadbcbadbddaddacbadddbabaaddddaaacbddcacbdadbdbcdbdcaadaccabbddbabbcdaabaabaddcbdbbbcbcacbaaabcabccaacabacbadaccaaadcbbdbbcadccdaacacaaddbcbbbcacbbdbbcdddabadbdcadabacaabbbdcddaddaaaccbdbbcbaddbbadadcbdccdddbdacbccddacacabdbdddadcacbdcdbadaccdbcbacabccbdcbcbcabbadadcabdbcddbcdcccccdddaaaabcdababccdbddbcabddaccbababaaacaddabababbccabcbcbcdbdcaacaccadcaaaccdcddcbbaaadabacacdcbdadccabdddadaaabaaaccbdabcccbcccbcaaabaabbbabddabcadbddacbbaabacacbdbcaadcdcccacbabcbcccbdaaabdabcdddccbcccccabbccccdaaabdbdccccadacbcdbbccdccccabdddcaadccbbaaaacadcadadabdccddbbcadcccbacbaaccacaddabdcbdcbcdcbdddadcacacaaadabbacaaccbdccbbbccbdcadbcbdadaacbddacccbadcadabbddaadcdbabcdbabdddaaadddcbabcdadbdbcdadacbaddbaaaacadccddabcaaccbaadacbdabdccddccacccccdcdcdaadbddcacbbccaccccbbbbdbbdbcbacadbbaadbadddababcddacaddbabbdcacaabbcbdbadcbcddbdcacbcaaacacccdacbdcccabccdbaacbcdcdddcbaddacbdbabccbcbdacaacddaddccacbabdbbddddbdddbdcbadcdbbbadaccccdbdbcdbabccaaacacdcdadddbbacccabcaabdbcaddadadcbcacbbcddcacddadacbcbccdacdbdbbbbdbbcacbdcdcabdcadadbcbcbcaacdbbcdbcccbbacbbdccadaaccabdbcacaddbbddcacbcdacacccbaaabdccaababdaabcbbaabdbbddccbccdcddacdbcbbacdbdddabdbabddcddcbdaaaadcdbadddcacddcaccdbcdacdcaccaddbdbddbccbbaadddbdbadbcdccddaccdbbadcacdbdcbaddcbbbbcaddbcbcbaccdacccaaacdababbabbdaabdcaddbccddabddbdacdcaacbbbbdddabcacacbdabbbabaccccadbdababddccaaddcbbbdcccdcbdaddbacbadabacbbccdaaadcbadbbbabbbabcacadacccdbbaaadcdbbabcdcdbcdccaaadcbabaddacaadbdccadadaccadcdcdbdabccddcccbabcdbacdacabccdbcbcbaadcbbadbcddcccabbddddcdbbacbdacbccccbbcbdddcbbdbbbbacdacdaabccaaabdcdaaadacdbcdaadabdbadddcdcccacccbbadcdbadddbcabccccbababaddaadccdbabdadbbbbaddddbddccdbcacbadcbbddbcbcccdccdccdcbcccdbbddcccbdabaabcadbdacbabcdcadbacaccdccbaaadcbbbcbaaabadabdbadaaacaadacbbacccbcbbabbcccdcabccbbcbaacbaccabdadcdddabadacdcdcabdaccbdbcdccbabcbdacbbdcabcabdcdaddabbbbbbdbadcdbdcbaaaaccdaaaacdbccaaaaacddcddbbbbacaabbddbccdcddadbadbadbbcdaacbcacdbcdccdadaddcadabbbddadaabbbdaccbdabbcdbcbdccbcbaaddbbcacbcbabbbcaddcccbabbdaadcdaccadacccdaddaacaaaccdbdbcdbdabdbbabbcbddabbbacbbbbdbcaacababdcabccbdcabaadbddababacadbcddbbdadbabbaabcadacaaacccbbbaddddccbcaccabcbdaaddbaaaaddbccdbbaccbadbcdddbbabadcaadccbcbdadbaadccdccddadbdddcccaabbdccdbdaaccaadacbcabbaddbbbbaababcbbdbdbdccdddbccabcaabcccbbcbacdaaababcbaaccacdaabcdacabdacaaaaccbbbdbabccdcdbdaabcdbdbbacabbbccaabbbccaccdddddcddabbadabadaabcaabdcaabadbacdcaacacadcababbbaacccadaabaccbaaabcdcdacabababbacaaadbbaaababadcdadbbcbaddbccbbaaccccadcdbccadbaabdbbadbcaadadbddcaaadcabbdcabbddacbaccbbabdabbcdcaabbdadddaddcaabbcdcccacbcdacccbadaadcdaabbddaabadbbcdbabdbcdcadabcadaabdbaccdabbdccbccdcccadbdbcdcdbdbdbbccacbbbbcdcccaadbdcabaabcdcaabdadcbbaccddbacddcdcdddaacacabcddcadaacbcbcdbbaabdbcbbcacbcaccbdcdacaccbbbbccbaccdbacaadcbaadaadabdcbdcccaadcdadbdcabadccdcdacbabccbabcccadddcadcadadbaabdddbdcdadacbbbbbbadadcdbbccdddcadbcdadaabbdbbacbadcaaaddaccadbaabbaccbcbdddbdcaaabcdadabaadadaabdaccdadacdaabdccbaadccdcacbadbcaaaaadccbccdbadddccddaccabbcdababccdbdabaacbdbaccbacbabbcbabcaddadabdcdbbaabcaadcbbabdccdccaccacccbbdadbcdcacddabccdbacaaaccdddcdcddbabacaccbcaadccdacdcbdcbdaacacddcdccbbcaacadcbccaacbbcddcccacddcdcbabdcdbbbbdbabacccacccdcbcabaacddcbdbacbcbdcdbcacaacddddbacbbdacdbdbabaddacbddcdacdacacaadddcbcbbadbbaaadaabdcaccbbabaaadcccbdcbbdccdbacbbabaccdbbdaccbbdbcbbccacadcabdddcbaadbabcccdbadadacabdcdcacdbdcdbcbbdabcaccdbccbdadbbcbbccbbabaabccbdabbcadbacdbbadbbcbbcacbcbdddabbabaaaaccbcbbdabbdaccdbdbcaabacbbadadccbbdbadaabdaaccaddbddacddaaaabccbdadcdbdacbddadbdbbbdcdaabbbbadccaaaacdccdbadbdbcdbdbdbcabddcabbccbbdaccaddacbbcbcbddcdcbadcaccabbabccbaabbdcccdcdcbabadbaaaacacbcaaccadbbcadadccccabadccabcbdbbbcbadcbdbbccbadccccbbbdbbbbcbcccdaacbdbdbcdcccadddabadacddbdccbdaacbbcaabcbdddbbcababcaccccddadabdacbdcddaacacbaadbadbcbacadddaaadbcdacadcbcbaacdbcbcadabbdddcbbbbabcacadabdddccdbcaddbccacadadadbbbbaaccdbbaadcbdbbaddabbbbbdabaadbddbdbcabbadacadaaaadacaddbddddababdcdbdbadabcdbddddcdbbabdacaccbccbcbaabbbadaaabbadbcaaaabbcdaadcacddbcaaabbcbcdbcbbdbdddbcccbcaabcaddbdacacbbddaadcdcacbdbadacbaaabddabacabcabdaddbdacadacaccbbbacdbacbbbcdababddaccbcbbadbbccaadbbbddddcbccaccaccdcaabcccdaccdbcaadbddadccdcacbacdbcdbdcdcbcbcacbbccabddadbddcdcdaccadbcdbddabbdcbcdbbdbaddcbddadcbdbddadaaacdabbbabcdccbbbcbbbaadbadccbcddaacccdcddcccbbddbdacccbbdcddbdbdbbbaadbbbbbddbabccdadbaccbbbbadcccabbddababbaadbdadadbcdcadcdabdbdbcaaddaabcdcbbddddcaacabbbcacadbbadbabdddddccccbbccbcccdbdcdbbbdbcbbbddacdbbaaaccaacbbaaddcccadcaaacbcbcaccbbdacdcbbaaaaccdadcddbbccddddddbaacbbbcdcacccabadbcccbacdcbbbbccdcbcbcdddbaaabbaadaacdabbbcdbdbbabbdcbddaacdcbcabbcbccbcccbdbbcdddbaddbdcddbccacbbdaacdbababcdbbcdacadabcdcccbaacddabdacbabbdbddddaaacaacaaadddbdbacadadaabcbdccbabdacaaadcccbdbbaaabcbcabbcccbbbbbddcdcddbaacddcbbbcbaadbcbcdcdcbddddadbccbdbacccaacccbabaabccbcbddaaacbacaddddaaacaabcdadcabaddbacccddbbdbdbaacabaabcbbacdbbacabccadcddadcbabbbdadcaacdbcacdddbaacdddacdccacbccacbadccbdcdddcbaccdabccdcbdddccadbcadbabcbaaacddacccdadccdabdbcadbbbcdcacbadaadbabcccabbbbcdddbdbbcbcadbabbcdabaccdcdbbccaaaacabbccbdbbcadbbaddaaabacdcacdcbabdabbbbabbdcabdbcdbdacabddcbbbbdcdbbcacddccaaadbcacccbbbdcddcdaabdbaddbabacbbbbadaaaadcaddddbccbdbdacaabadadccddaababddbbccbabddabcdacaccccaacbcccddccbbbccbbcacbadbccaddbaaddbdbbacdcdcabdaababbbcaccbccbcdbbaadabcdbbacdcdbaadbacbcaddacdccbbdbbbbabadcdcadbaccbbaabddbdbdababbddcbddabbbacbcdddbbddabdabadaddcccdbdbdcacadaddddbddddcababaddcbadaacabcddddabcddddaccbcbddbdbcccbdbcacbaccbacbdbdcbbdadbdccbbcabdcccaabbbcbdacadabcbacbdadbbdbaddbdbacabbddcbbbcddbcdcdbddbdbaaaccbbbbbcbdbaadacbabcadddbcdbaddbacdbadbaacdcadbaacccdabbdaacdabaccbadddbdadcdcbaacddadddcbdbaccbbbddcdbcbcabbbabbdcadddbabdacaadcbbdbdccbabaccdccbcbcbadbbbbaabdadbaccbdadbcccaaaabacdccdbcabbbbbaccadabadbbcaaccdaaaaddaabccaccbdbcaaaabbbddcddcdbcdbddaccdbcdbdcdbbdcbacdacdcacadacaaaadaabddcadcdadadcbdbadcbbdddbacaabcbbdbddccbadabddbacbcbdccbacacbbccbddadcdddabcdabbabcbbbabbcadcababadcddcdddabddaabdcabdbbdcddddacabbbbdcaacdadadcccdadcdaaacababaacbbdbcdcbcbaabdbaddddadbadababccddbcbcbcadabdbcbacccdbbddcacadbbbcddaddbdccbdbcacaddacccbcbcbdbacbabbacddaccbddcaddadadbdbdcaaccdaabcaabadbdadbddaadaabcdabccaacddcbbacabcbababaccddaacccababddbddbbbabaddcdbaadbbbdaaaaacccccbbddacbaacdadcadbbdabddaadcaadbabbdddcadbbbdaaacbcacdbcbaacdddcabaccdbadaddccadacadbbddcddcbcacadbcdcdaacbbddddcdaccdcdbbbbddadbcabbadcbabdabbcaacdcdbcdabadbaaccbabaadbbadbddddbbcbcaacdbcdcaccdabdaaacccabbcaaaccabdacddcabbacaadbdbcadbbcdabddcbbbdcdddacbabbacddcabbcbcdaaaddbbcdadbddaadbdcdbdcccbbaddbdccbacdcbabaadcadbbdcccaacabccacaddababacbacdddaaccbcdbbadccdcacabcccbccdaddbdcadccdaabddbdbbbdbbcaccbadaaaabdbdacbdcdbcbcdbaddccdabcabbdddaddbbbbdbdadaacdbabcdacabbdddbcdddccadbcbaacdbddaaacabbcdcddccbcaaccccbddbaaacbcbcbbbbadcdddaddcadaaaabbcdcdccaccaabbdcddacacbdcbbabdaddaacdbcccaaaaacdddaacdddcbdbaaadabaaaccdcabcddbcbbbdcddccbbcdabaabdbaddcaabdcdccbcdcdbacaacaccddbcbddbbdddcdabdacbddcabdaacbdadddabdacacdbadbccdbddadccbdacdbcaccddbbbacabddbadccdabcdbddcdcbddddadadddacbdcaaadbcdcaaaddbabbbbcdadabbcbaadadaaddbaaabbcacbcacdcaabbcacadcbbbbacdcadaacbbbdbabcdcadbaadbddabccdbdcabcaadbdbbdccbbddcbaaaaaabbbbbbbccccccdcdbccccbbbadaaccaacbbdcdbaadbdbccabbcbbdbcbcdcdbdbbadcddbbbabcbabaabdbdbccdcbcbcadbdbadcdddbaccbacbdcbabccababcdccbaaadaddadbdcadbcdccdcddadabbdcdaabcccbaccadbdddcbccbcdadbccddbccbbdabbbcbbcdddabaabcdccdccadcababdadaacbdddabddbcdccacbabbcbccdbbbcbcabcdabdddcaccadbaaabcbdadbddaacdccbacacbaaddaaddbacbdcbdbdacddcdbacadcabcdcbdcdccddbbcbcbadcaadcdcbbcabcdbaadaabdadaadbacadcddcdbaabddcaadddddcaccbaccccbdaccadacdabddcccdbcabdadccccdcadbbacabdbddadaacbbbadacccdddbbbcdbabbabaabaadcbcbadbbdbdcddbdbdaaaacacadcaabaddbbccbabcccaddbdbdccbbadbddcadbcacddbaabbddcbcdcabdddcababdaadcabaddcabbbdbadaddcadcdddccccbaaadbabdaacaabbccbcdaacabbcacbccccadacccbacaacaaacbcbbbddcadcaacacbaaabcabdbadddccddbabdddadacddcbadcdcdbbaacaaccbabdadcaadaabdbbddcbcdadddcbbcbdbabbbdaaaccddcabdcbabacdadaacbcdabdacadaaacabbacccbddabcbbcbdccdcbadabbcddddaacaabbdcccddbccaacccbdabdaabbaaabbcaacbbdbdcabaabdcbacbdaccabbdbbdbcbdbbcbcacbcbabadddabdadccbdbddcbbdadaddbadddbaccbacbbdbbbaacccadaaddcddcddacaabdcdaaabddbdddacdababcbddbcabadccddccdcbbccbdbdacabbcdddccaddcacacddbbadbbdbbbdcbbdbaadbbadcbdcddabdadabaaccbbbddddbacbcdbadddccaabcaaaacbacbdbcbabbdcacdbcacdacabbcbcbaccaddaaadabdacacdcccbbccbccacbbdccdccabaacbdcdbbbbdbbaabddbabbdbbdcdacbbaabbbbbdcadaaacacabacccccaddabbbbdadaacddacbbababdacdccccadcadcbcddddddbabdaddcbbabaccaccbaddbddcadcbabbcabbddbbddbcacdcbccbcddadcbadcdbdbdddcccbbcdaabbcbabcbacbbbdddddbdbcbdaadcacdbadaadccacadbbddbababbdccaddaadbccdddacbbcddcdacaccccaaccdacdcbbcddabccbbccacdabdcacaccacddcaaccbdbcddcacacabdcdabddabbcaccbadacdbcadaddbaabdcaacbbbcdcaaddccccbacaddbdbbcccaabadbbaabcbaaadbdacbbaabdcbcbaacdcddaccacabcddacccddadaddbcabcccdaacaabadcaddccbddbaadaadbaababadaabbaabdccbadbddaccbbbcbbbabdadacdbadabccddbabacadccabdcaccccdbaabbbcdaaccaadccbabcadcbbcdbabccbcdadcaadcbcbcbcddbbdcbbcbdaadbbbdacddbacdaccabddbbadbbacbcbbddbaccddcdddcabcaadcabacccddacdbccaddbabbbadadabccabcccaacdaaacadcdbbbaabcbdadaaccbbbaadaddcccbacadddaadacddaacddccadddabbdbacbdabcbddbadbdcdbcabbbadcbbbabcdddcbdabdcadaacadabdacaadadaadbccbbbdbbcbaddcaacddcacddddcccbdcbaaadcdccbdbabdadcbbcbabbcbddbacaddacdcbaaaabcddbddddbcbccbdababcccaaabacbcdbdbacdaddadadacbcabaabbabdadbdbcdadbbbdbccacaccbbaacbbadbdadbdbbbddcdddbabbdbcdbdaccbbdbdcaddbbacbbccaddccbdccbbbaddbbcddbacabcbbcdaadcdcdcdadabcaabbcdaaaaaabbdcaadcbadacacddbbabddbacaaabdadcabdddaaaacdccbcbadbcbbddabbdbadbbcdbdaaadbdbcadacaabcddcacbbdbbadaacddcadbbadccaddcaddaaabcbccbabcddbbadbbcdbabddcacacabdaadcacdbcddbdbbadbbbdbacdbbddbabcdbcdaccacdbcdddcbcdaadbdbcbdaddddbcacddabdacbddadcbdababacaddbdbccddddadacbcacbbcabdacbaadcbabcdabdbcacabdadccacbbbcdabacccbaababbcdbdbbbbacdccddabddcdacabbcbadcabbddcccbcdccabdcbcaaaccbaacdaaaaddabcaccabcaadddbbcabaaccdaccaaadddacaacccdbdaadacbbbdaacaddbaddcbcddbaadcbddaaacacacdccbaabababbaddcdcddacadabbbabdccabdadbbccdaccbdddcdbdcbbcbbaacbbbcacbbdbacbbbdccdbacadcdadbbccacdaabadcbbbbcabbbbadabdddbaabdddbdbbccbbbadbdccbcdadbbbdbaababaaaccdababccacbdaadaadabadabccaccacccdaadcdaddaccddcadabaacdbbdbcacdabcccabdcadabaadbccaddcabcbabacacbcababbdadcaaddacccbadadcaadbaaadcbccabacacadbcbacddccddabaddadbdaadbadadddbcdcabbbcdbbccbacbaaddbbcddabccaaddabccacdadbcaacddabcadadbddcdcbddaadbbcbaadabdbcdcbcbddcabbdcaabddacadddbbbcaabdbbabddbdbdbaccaacdabcabaccadcbbbbaaddddcbbcccccadbabdccddaadacadcccaaccabdacbcadacdcaabcaacdbbbbacacdacccaccddddcbdcacdbdbaaaabaaabacaccbbbdbdccddcbbadcdcacccdaacbddcabacadadbcaacbadcdccdadcbdbdccbbdaccaaccadbcacbacbdddaadbaabbacabcbaabbcbcadbcbddbdcbdbbabdcbacabddabcadacacddcdddcdaccdcacdddcbaaabadbcdbdbaccadcaaaacaccbbacaccdcadadcaaabbccdcaabdbddbacdbbcaccdbcdaadbadcacabdbcdcaacaaaaccbcdbdbaccdddacaadbbdccabacbbbbacbbabddcbadacdcdcbabadbbbcccdcdabcdcbacacddaabadbbccdccacccdaaacacdbdcaaddcbdaacbbdcdddcaccdadddabcdcccaacbdabbadbaabdcdcbccccacdacaabaadbdabdacdddbcbdccdcdbdddadcdaadaaaabdbaabdbbddbdbccdbddbbdccbcddaabdbdabccbdcabbcbdaacccacdcdbdbccabdbbbdadacdbaaabbcdcaaadaabbdccbcaacdcbccbaaaaabbacdccdcacdcbccdcdcdcaabcddcaababbbbcaaadbbdadcdcacbbcadcbccaaabaddbcadbdabbdcdcabddbdaddbddaadddbbaaaaadadbabdacbbccccadacbbacdabdaccdbabbbabaacbaacbbdbacdaaacbadbadaccbdbddcaabcbbaabcadbdbbcacdbbabddbddbaddbcdbbdcacbcddacdbaacaccdabccbbcacbddbbccccdcddbabbbacacddddbdbdcdabababbccddacdadcbababacccacadcdaaaadbcdddddcaddcabdcbbbcababdbdcabbabdbdcbddacdabbcdbdbbabdcadcaaddabcddbaaacbcbccbcbcaccdbccddbbdcbbbbbcccbbdadbdadcbddacbabbdcadbcdbddaaacdbadcdcdbdaadaccacddbaaddbcdbbbcaacbddccbaccccbadacbdbadddbbabdadabcbcbddabdadccabcddddbddccabdbbbabdbcacdcbbddcdadcbdadcaddddccbccacdcbcaaddcbcaaaddddbbdaddbddbabaddacadacbdaddcbcdbadabddadaddbccdcacbbdaddddaaacadbabdaacddaaabdaaacccdddbaabbbccadcabbcaddbacbbcdcadadbbadbdddacbbcdbaaccddbadbacadbbbcbcbdaadcadbcdbbcbccabbcccacacabcacbcaabacbaabddbccdbbcaabadabbcbaadcbccdadccddddccbbdcdcdcbccdadbaddcdadcbcbbabdcbcdcccaaacdcbadcdabdadbccdbdbbdaaadaabadcbaaccacbadbcabcdabdcdacadcccbbdbccdbbcccdcdcacabacdadbbcddaaaabbbbccbdadcabadbcaabcbabcbcdacbcddcacbadadcbdbcbbdbdcddcdcbabdcbabdcbccbdccadacaaaaabbcdccdccddaddbdcabcadddaccabaccbdcbacadbcaadcdabaaaadcbcbbabdbabdbdaaacdbcbdadadaadddcdbbcdbadadacadcaacaabacbdacdabaadcaddcabaacbbdddacabbcbcbdbacdabaacdcbdccdadacbadddadbcbaaccdbbdadcbbcbadabcaaddcbbdabdadaccaaccdababcbbdddabcabdbbbadddadbbccbdbcddddccbcaabdcdcdcabbddaacddbaaddddaacaaccbccbcbadadaabadaccbdddacabcdbccdabaacccacbbcbacaadbbaddbbbcabccdbcccdcacdadabaaaabadddbadbbccaabacdaacbddcaddcbcacddabbcbabbbcaccbaaaaaddcdbaabbbddddccadcdbcbdbccbbdbbdbbacdbbdccaccaccbacdcbddbababccabcaddbdbccbdabbbcddbaabbbdacbbddbdddaadbdccadbdadcadabadbddcdbaaadbdcadabbaacacdcadadccadbabcbababcdbdbacccbaadbadabbccbbaaccbdcdbdcdadddbcacddbbbacbdcdadabbcacccadbaaadcdccdaccacabdbcbdabcbbbdabaddbbbadbcdbaadcbaccbccdbccacaabbbcbddaddbadcaaacbabccdbdbddabcbcacdabcdccaaadaccddccccbaaadacbbadccccabbbddacbacdccdcbabdbadddaddcbdbbadbbadcccbcbcdcdcadbcdbbbcdbaaddcacccadbbdaccbcbdcbdbbdbbdbabbbbbcdacdbcabbbbacddbbadddcbacbdcdcdccdacbdadaadabbccaadabcddbccbcbdcadadaaabbcbaaabcadcbccbcdcbcadaadddcbcddbdcbcdcacdbbcdadcddacbbaddbbbbcdccdccacdaccbcdbdcbadadaaccacdacbbaadcdaacdadacddbabbdddacbacaabccaadccbcbbccccaacacbdcaacaaccbbbacbaaaccacaaaadbabdddaaaddacdddccaacaccdaaacaadbcabcacadcdcacabbacaccdbdbaadbacdcbcdbdacccbabbcaabaddacacdbccaaabdcadabbbdcaaaadbcdbcbdccddadabcbaabdbbaddadccdaadcbddaddbabacdbccdcacdadacacddbdbaadbbcaabacbcaaacdbaabddbbcbccbcabdcbdcbaaaabaddaccbbdccdaabcdcdcbcbdccbadcadcabdbdcbbdbddcbbdcabdccbdcaabbccbaaaadbccabcdbbcbbadacbcaaaddacbddbbbaaaddddabdaabcbdcdadddacacadbcacdcbbcdbdbdbabadadbcbaddaaaadccbabdcbaddccaaacdbdbbddbddbddadcbabaababbdbccdbcdbcabddddcabbbacbccdaadcdbaabcaadddadbacbbddabcdccabbcdadacbcccacdccadaadddbbcddbbbdacdaabaacbabcbadccadbcaccdcddcbacddcbcacdbdddbbbacacddabcbcabbbcdbdbbacabcdcadccaccdcbddbcdcacccdaaacbcbcdabdadbdbaaaaadaaacbcbbddbabbbbddcadabbabcdaaaccacbdacdbcdabbabbdaabacbcdcdcdddbdcdbcacaccaddadcacccbdbbdddaabdbddadddcacdddbdbbacbaacacdaaaabcdbddcababacacaacdbbdaaacdbbbccbbddcbadbcaacdbaacabcbcbbcccdacccbbcaadabdacbbdbdcdddcaacdbbabcdbccccacbdbbabbdbdcaababcadbcbbabaddabbaccddbdcddbbbdadacccdaaccadaccdbacbcadabacadababaadaabdbacddcbbadbbcbbdccbadbaccdbadcacaccabcddbaaacdcdbcbddbbdbddacccdccaadccabcaadadaabcccbcccdcbdddbaacbdccdacdcaadabbcdabcccbaddcdcbbcdacabaaaadadcbbbdcbccbdccdbcdcbbdbabddaabdbbcbcaddcccddacabcadbbbbdabcaababadcbadcaacccbcbbdcbddddcddcddadacbbbbbaacbbbabaacdadcbbadbbbcbbdaadabcdadadccdbdcdadddbdccbbbbdccddacadaaabcdaabdcaccdaabadabbbddcccbdcbccdbabbbccadcbbbaacadcbadabadabbdcbbbabdbbbadaacddaadbdbccccaabbbdddaccbdbbbccdaaacadcabddbbbaccccbbcdcdaaccabdcdbcccbbcbddabcbacbdcbdbadaaddcabdadcabbddcccdcaacabaddaddadcbacccccbabdaddbaaaaabcaacbacdcbbaadcbbbdadbdbcdabcccaabbbccaaaddcaddccbcacaacbdbcacaadcadddabadccbccbcacddbaaacddcdaddbbcaaabcdbbbbddcdacbcbaaacabbbadddcccaabdccaacababdddddcadccbaddbbdcbbbbdadcddbcaadadddccccaaacbbaabcacdacdddadbbcaaccaadbbcbdaddaadcbdbcadbcbbacabdaabbcaaabbddcbdadbcddbadbcadcbccabcacdbacccabcddacabcdbaabcdbaccaaccdddabadaccaabccbbacccabcbbcbbdddaaabbaadcdcdbbbbddcabdccadadbbdccdbcbddaacbddcbdadbcbaabaddaabcddbddbdccdccdabbdbbbabaddbaaadabdcacaabacbaaccaadaadcddaabbdbacdaabcdacbbaccbacbadacaacbaabdabbbcdaccabaabcbddadcddbcdaadbccbcbdadcbbbdcacaddcdbbbabbbabdccaddbdccddbcbbbdbddbbabcadcdabddbaddaadbcbdadbcabacabbaaacccacadcaabbacadbadcdacccacddcaabbcdcdbaabcabacdbcbbbdbacbcdbdababdbbaaadcbcbacdaddccdbdcbbdbccbadcdbccbaacbbdaabacdddbcdbadbdcacccaddbacddaaaadaccdcbaacdabdadbadccbccccbabddcdabcdacababbdcccadcadaddbdbcccaabbcccbabacbcccbcacaadddcabcdabcacbbacadbaccdadddcddbbbbdbbcdbbbbcaccbbadcdababbbddcbcbaabaacbacddabcdaabacabdcccaadacbcbcacbdbcdbcbdcdddabaaaacdbcbdccdcbcdbbabcdababdcdbaaadbcdbcdbdcacabdbcdbdccddbdbdddaadccccdbbdadcbdadccaacbdccdaddaabbbdaabbdbcbbccbbcccdabadbdcadaaacbaccdcdccdcaddcabdabaadaccbbcbdcdbabacdcdbdacababdcbdbdcdaccaabadcaccabdbdbdcdaaacbbccddbbdacaaddcccbdcbdacbccbccaacaadbdddacabcccabaaaaccccdadaababcbccdbdbbddcbaabbbbadadbcbdcdbbdbdbcbacdabadadbbdbdcbcacbaccaddadbbcbcabcabadacddbbbcabdbddcdcddcbdbccddbadbadbddbbcddbaccabcbcadddcabacccbadddaaacddbccccacabaacacaaadcdbdcdbabcaaccbbddadbbdacdccccdddbcabadcaccadacbddddbabacdbbccabdcabdcdacbdddaacbdbcbbacbdccaaadadddccbbcbaacbbcccdacddccbdcabbacbbcdbacbbcabcacaddcdbaaccacadbdbdadaabaabadabcaaaadbbbaacdddbcbbcbcdcaaaccdddacbababbcacdcddabddaacadaddabcdcbbdddbbcaaaabcacaadcdccbabdabbdabdbbddbcbcdcddcabdaabbdddaadaddbcdabcbdbabbcdcabbcabaaaadacabcccadcabacbdcadbabdaacacdbcbbacadddccbbdbaadccddbdaadcdaadcacadbbbbdddcaddaaddacbdbaaaaacadaaddbccbbabdbaadadcdacacaababcccbccadbcdbacdbdccdbdcdbaddaabbababdbdacdcbddbdacdcdbbabbdabdbbddaccbbcdcacbbbbddbccaddaddadccddcbcacabcccdbdcdacbcbaabaaacbbcababcabbbabbdbbccccbddbadacadcabdbadddbcbbbbbdccdbcaccaccacdbdbacdadbcdcbdbcdccbcbbccbccddbbaddaabbcbcdccbbdccadbabdccddcdddaabcacccabbddaabcccabadccdbbddddcbdcabcabcbaabdddabbdadbdcdabbcddabaddbbbcaaabdcaacddaccbdbddbbbacaadcdabdbacaadbaacddbddbadcaabbacbdccabbbcdbccdadddbacbcadbaabadadaadaacbabdaacddcdabbcdaccbcdaacddbbccdabadaacacbacdbabaaaccdcacbbbacccdacbacacaabadaacbbaadbacccdaabdddaabadcaacddbbbaacdccdddccccabcbdcccbcbcdadcbdbaddacaabccabcadaabbbdddcbbccbadcddbccacbbaaacacddbacaabbbbdccdacbcdbaaacdbacdadddcdbccaacdbdbbdcbcbbdacdddbcaaaddbaacacdbdccabacaadbcdcacaccdddacaadbcacccaadcdbccbdcbbbacddbcaacacaacdcddaacaaddddcaadbcacddaccadcbabbbbbcbdcbbabdbacaaadddccbcabcacdbccbccadaaadbdacdbbdcdbaadbacddbacbcccdcccccbcacaabddbddddbabcacaaabbdabaccdcabaabccdabccabdaababaabccbcabaababccbaddbddaaadacddccdaaadbcdbcbbabcdcddbddccaacccdcbcbbbbcabbdbbaddcaadbaabdbdadbcacaaddbdcbabbbaabcdadbbabccacadadaddbacdadbdcdaadadabdcbdcadaabcaddabdcaccabacdccacbbcccbaddacdddbbddbadbbbdaddcaabdbbaabdacdccdcadaaaaccabcbbaccaadadcdcaaacdcacddaabddccdcdabadbabacdbddbcbcbbacacbdddbcbbdbcbbcaacbacabdccacbbcabdccbdddaaabcddcbcddddbdcbbabdabdbccdccbcddbbabddcbdabdcdbacaabbdbcdcbbcdcdccdbcdcaacdabbdbddcbdabcabdcbbccdaabdbcbddbaabacbdcdacaccccbddabdddccddccbbacadbbaaaabbdabbbcabdabbbdccbcbabababbddabacdaddaacbdcacdcdabdbccbbcdbbbbbdbcddbbaccbadacddcaadccacccbcacbddcdcdbabddcdddacdccddabcbcddbdaacaacadbcbbadccbccdbacadbbdbcbdccbdcbacbbcaaaddcddbcabbccddddaadccabadbbcadacbcababdabaaadaadbadcdbcaddccabbaaabcdbaccbdaababcaaccabdbacaccadcdddbdadbcbbbacbdabcccdbcacbaccacdcdbacbacaddacdcccadacaadaadccbbdcbbdbbbacdadbdbdbbbaaadcdacabdadacadabbcddbccdcadabdcabccdcbdaccbacdbbdddbbcdaaabdaaaabadbbdddadaacdacdcdcacadcbcdaccbdbbbbbcbccadbcbadbbdcdbadccabdcbccbbbadaabccddbbbdccdabdbbcabdcccaccdacdbabddcccadcccdddccbbdddbcaddabaadbababaacdddaaabdcacaddadbddccbaabaccbddbaccbdcdcaccccbdbdbbbadbbbcaccaccadcdbaadcadcaaadddbccaacaadbbbbbdaadbdbadbbbcabdddcdababddddbbbbadcdcbacdadbdcddadbbbcbddbddbcaacadbcdabaddcbdabbbadabcccabdadbacaabdaddbadbacacddabbdbcccccbdddddcdabbadadcbcaadababbdadcababdbbbdbdaaadabbdbdccbdccabdddbdcccdbbdbbbaacbccabdaacbddaababbacabccbbacdbcddbcacdddbcbcaddddbdaddbbbdddbdabccbcbcadabbacdbcddcaaadbadbaadbadabccbacbbcbaabcdadcbadcbddaddabdbdaddcddacbadbcdacaddabacacdcdaaabbaadaadcdcbddbabbcdcddcaacbbcbdabddbcaccadababdcbdcccabcddadbcccbddbccadcccbbccdbdbbbbbccabbcccbaadacccabdbdacbcbbcbbaaacabcdadcabcabbbbdabdacddcadaabaccbbbcdaadbbbbbabbbaabccabbdadbbdbdadcaaacccabdaaadaabdddbbcccccbbdcbabaddcccbaabbbcabbdcbaaddabdbcdabbbacaaaddbbbbcabddabbdcbadabbbddbccddababaaaaacbbaabbcbaddcdbcdcabaccbcddaadaabacdbadbdcbaadddbdbcbdabbbbaadabaddbdcbbadcbdcacdadbabaadcaddaccbabcdcbbabdbacddbdccabdbcabbbadcdbbcaaaabdbdddbccbcaacbcadabdbdcadcdbddaccddddbcdcccbccacddbddacbdccbdcdacadbdbdcbbaacdddccdcccdbccaddaabbdabcacbaaaddadbabadaccacdabcacdcdabbadaacadaacdcbcccdbaddbdccadddccbadbcddccdcdbabadabadbcdbabadbabdabbdbacbadbaadacbcdcdcabdacdcadaaccabadbdbcaadccbdaccababbbabddabcacacaabbcbabbccdcabaababcaddddbdccabbcdcbbacdadcacdabbbdbccdcaadbaaaaadccbdbdabadaaabdbabdbdaaacbaddbdaabaddccaadaaadbadddddacbddabbaadbcbacdacdcacdbaabaddcdbdcbaacdababadbbccaababbadccdaacabacdbcdcbcbcbdccbbbbabbacdbddcbbabdaddccdbcadaabddadcbabdcddccdabcbadbacddbccbadabdcbbbddbdbbdcbdbdbdabccdadaacaabadddbaddabcacddacbcdbddadaababbaabbabccdcadbaabbccbaaaacacababdaabdcabacabccdaaaaabacdbbaabadcacccdcabccabbbbaaacdaabbdcdbccdbbaabdadbacbadabadaabadabddababbcacddcddaccbbcdcccabcaccabbbdcccdccdcbccdbcbbddcdbbbcacadbcacccddabdddbdaacbcdbcddbbbbdbaaaaacbdbcabdcdcdabcacdabacccacadcaacacaddacbbdccaadabaaabbaaddabcdabbcaddbacabbbaddcbcaacabdadcccdcacccccbbbcddbbccadaacdcadbccdbaddcddaacabccccccdbdccacdacdcddccbaccbbadbcdbcdddbbacdbbacaccdbcbaaaccbdccabadbdbdbdcdababccdabbcdccadcdcbbbcdccaaabcdccacbababbbdcaccadcccbbbbabdaabbbbdacbcbdabbaadcdbcabacdbbacdabaabdcbbcccabbcddaacacaaacdbbbcbaacdbbbaaabacdbcccacdbcbdbbcacdabdbccbccadbbaddbbbbdddccbddbdccbbbadacdccdacbaccadcdbdbcacdbdcdadabdccabcbbdddaaaacdaaddcccdbdcddbdabcbbdbdbacbdaabbdddcadbbbacdbbdcbacdbaaadbcddbdadadadabadcacbbdcadcaccabdaacdabaabaccbdcadadddadddaabdbbdcacbcbdacccbabdcaaddcbbcdcaccaaabadbdcbbcaadcbacbaabcdadacddbadaabdbccdbcbbbbbcabcbadcadbccbabdccadbdabbdbbddcabccdcbbddcdacbddabcbdcbdcbdabcdbbdbbdcccbccdddddbbddccaddcabacbcdaddbbccaabbcaaddddbaadcbccdcccbdadabbccadcaccadacbdcdadbbaabacccdcbdacdaaadcbdaddbcbadcccbcdaadcabbdcacdbcdabaacdaababbddcdcdaddddcbbabbdadcccbabcbccddccdbadaccbdcbacabbcacaccbdcbbbbaabbdbdcddcbdbddaaddbccbabdcdddaccacbbcaccabdddccdbcdaccbbcdcbcddcbdadbaacaacaaddaddcbdbabaddabdabdbdcadbcbdabbadabdbbbcdababcadbacdabcccbcbacdabdaddcacbccdcadcaabadbccbcbabcdabbccddaacaabbddcccaacbadbcdbdbacacccaaddadbcdcacbdabbcaaddbaacdcbbccbcacadaacbcccbacbaaaabbbbbacdadcaadcacaddcbcaadacdadbabddadaadaadcbbddabccbbdaaacbcddcabcdabbbcbddddaddadcacccaaacacbadccabbbdbaaddbdcccdbccdbcddcddcdcdadbcaacbacbcdbcbccadbcbdaacbdabddbdbacbbddaddbadbdccbcbccbadcbcdcbbaccbdbcadadaaccadadbbabaabbcccbbbaadcdcdaacabdbcbacadadcbdddacacdaddcbabdcadabbaabbaaddaccbdbbaabcccddccbadcdcaaaddbbbbaccbcacacdcadbdbadbaabddcaadabcaacababadabdbcdbacdcaccacddbdccadbadadaacddddadbcacaccbbabdbadcdcddaaacdcbadbbacaaaabbdacccaacccdbcbccdbdcbaddbabbcacbcdcacaabdcbacdbbabbccdcabaaddaccdbcdbdbcadbbaaddbabcbdcdbcdcddcdcbacbccccdcdaacbadcbcddaacddabbbabcdcaabaaccbaadaaddccbddbcabbabdccddacbbcbddbdddccabcdcbcbdcdccbdbabbccaabdbdcadabcdbbbadcccbdcdabdcbdadcabbcbcacddcadcddddadacaaabbacacabcdccdbccbdcadadbcddbadaaacaacddabccacddddabcdddbbbabaacdcdacdcdbaabbddbdabbcdabbabbadcdadadbdbbdbdaccaddbccdbcbcbabcdcadadbcacbdcdbcdaccccbdacdcddacabbabdbbcdcbccbcbdabbdaabcbabcaababaadacaaaaadacdaabdadccdddddaddaacaacabcdadbbbdcbdddbacdbbddabbbcddcbacbcdbcddabbbaaccdacacacacaabcbddcbabdccbacbcdabaddddaccdcadadadbddccbbdccacdadacdbbadccdcbcbbcadcdadcdcccbadadcdbacdbbddbbbaadacdbaccaaacdacabdddadcccdcbacddabcbcabaadaccccadcbdabdddacdbbaddcaaabdabddbdbbdcacddcbdbaaabccacabbbadcdcbdddcaaccacdbadbbacabadcdbbdcbdcbacdbcbadabbcdbbcddaddcaacbdadbabbbadbbccbdbbbbdccacdabcbddaccddabbcdadbdbbddabaacabccdbaaabbbcbabbabadadacbdcdaaccbcbcbdaadaccaaccbadcadcccaaaddacbbbaaccccabcccbadbacbcbdaaadbccaaccddddaacabdbdcbccdbbdabccdcbcaaaacdbaccbbdbccadaababbabbacdddcacbcbabdabdddabddccbaadbcdbbbbbaacbddcdbbadbbbcbbaccbabbbbcdaddcbbddabddbadacbadbbbbabcbaadaccbbdbcbcdadbbdadccabdacbddbdaabbdacddbbdddadccbbbdcadbbbcadbdddaacaacdacbadccdcdadcdabdcddcaaddcdddddabacbbddaabdbddbbacabdadbacbabdcccdadcccdbcdddbbcbacdbacbcbadabadbccbbabbbcbaddbaaabcdcdaabcdddacaadcabacbcacddaccbdacbddccdadbaddbacaccaacbaadcadcadcdcbccbcdcacabcadbbcaadacccacaddacdcabbbcdcacdcabdbdbabccdabcbcadbabbabdaddbdcdabbdabacbbcabdccdacdadcdbaddcbbdbddccbbaddabbaaaadabbabbcbaccbbbbbdadaddadbaacbbdaccdcabaadbabbccdddaadcdcccccbcbadabadccdcbddbdbbbacbabbcccabbbdddcadacbbdadccbbdbcdaddbaccacbbcbbabbabadadaaddacdadaaccaaabbbccbccccdabdcacbbacbaccbccacccdbcbdcabccdcdbccdccaaccdbdbbdbdcdabcaaadddabcadbcbbbdacbbcaccbacadbccacabddbddcbabddddacabcaacdcdabadbbcbdbbcbdcacbccdcabdccdcdadcaacbdbccdbacbabdaabbdccabdacdcadcadbbcdabaaacbadaadccbcdaddcbaaacbccabaccaccccaaabbdccadcababdbbcaaccbbdbbaaddacbdadbaabbbddacdddacbdcdbbdabaaacbbccbabaaccddbdaddbdbabccdaccbacbbbdddcddcdcccadddddddadabcddccbbdcadcadbdcdcbcdbaccbabaaabcbbcadbcadcdaadcbbbabbbbcbcaaaabbacbdcbddcbaaadbdadabcdbbddacbdddabdbcbdcadcdadddcacdadcbaadcbcbbacdadadadddccccabcdadadccdddaabddaaacaaaaacdadadaddaaadcbcdaadbcdcabaddaccaaabaaaabbcdbadcabcaccdaadaacccdbdcaaadacaaddddddcbcdacabbbbcbabcdccbdccbccacaadcbaddacddacbcccdddddcaddddccacdbdabaddacadadadcacccacbcbdddacabccbdabcabcadbddabacbacacabdabccddadbadbbbbdbacbbcdaccbdddaaccddacadbbababbbacdbcacbcbcaadccbccccdbdcdadcacbbabdadbbbdcccbacdbabdacdacbddabbdbbaaadbcddddababdacdcbccdbacccdabbdccbdcbabcadccdbcdbdcaddaccbabdbbbcbcacbdcdcddbaccdabcbaabababcadbacbbbcbcbbdbaddbbdadcabdcdbbadaddbbcdbbdbdaaabdaaddcbcddacababbcbbaabaaacaddbccaccbdcdaaddacdbabadbacbdbcdabbbcbddcbcbddbcacdaacdbcccccbcaadccdbdccadbcabadacddbabbcdaccbaadbdbcbaddcddcadbcbccbbccaaacdaadcbabdbcbdcbccaaddcdbbdadccbddcddbdacabcbacabbaddadbcbcbbcdcbadbbcdcccaaaadbdbcadacdccacabbabcbacddcaaadbbdcbbaddbbacdcacbdbdcaaabacbacddaaabaccdcbdabbabbbcacadcbbcabdabcacdbaacbaabbadcaadccdcddadbacdccadddabaaddccbaacaaccccbaddcccbdaaabcdcaaaabccdcabdddaadcccbcaadccddabacbdcdcbccdcbdaaaccadcdbddaaadddbaacdcbbbddadbdabdcbbbcbbcaabcaacdaaddabbacbbaccdbcaddbcbbcbcdcdbcadbccacacaaabcbcaadadcadcbabdadcabadccbdbaccdcadacdbdbddcbddcdababdcbbbbbcbbcacdaaadbcaabddbbdbcbdbbacacbabdadccdcacbacabadbcddacadabacccabbdaddcbccdadaadddbbcbdadcdabbcdcccdadbbaccabcccccdddbccdabbadcbccdbcdbcbaadacaddcaadbabcacddabcdbabcbcccbcbabdaacbccadabacdbdbcabcaadbddcdbdaacbbdddaacbdcdadacdcddcbddcaabcdbdbdcbbaabdaddbcdbcccdddbbbcddcadadbbddadcbcacbbaaccaacbaaadbcbaacbacadcabbababcdcaadddbdacbadcccbaddababcccddacbabbcbdbacacbbbbbbcbaccbaccaccdbcbdaaacdabacbabacccdabaabbdaababbbaccbcacadbbcddddabaacbccbbaddabbdcdddadbbddbbbdcadaacbccbbabdbdbbaacbddbcdaccaabbaadacadadcbdddcccddcadddadcdcbdddaaadcddcdcbcaccbddcacbdbaaabadbcdbabdcdabccaaddcbddbadbadbabadbddaccdacdbdcbbbcdbccbbaacacdddabbabcddbbaccbcdbcbcacbacdacaadccbcbcacbcbbabdbcadbdaabbadbcbcddbdbbcdddcbbccbbdddcaabbbdacbabccaadacbdabccddadbbadadabbdaaaaddcaccbddadacadbccbcccdaababbcdddbccbcabdbabcbcbcbbbbcaaadadcbadaacdbbcadcbcbcdaaaacaaaaccbbbdddbaaabbdabadcbccadacdbcdacccdbadbbdcccadbdaadaaccbcabacadabddaaacddcabdbacbdbdcdacdadbacdddcdbbbdcdbdbccbcbdabdabddcdbbbcbdadbddcbaaccbcbccacdcdbbadaacddabadaabbbdcadbbaccdbadadccdcccdccbbbdccaccadadabbdcccbabcbaadacbdbaddbacddcbccdccdadadddccbaddccdacacdbbcbadbbbabbabbbdacabdbabaacbbdcdacababadcdbccdbdabdbacaccaababbccccadcdcbbcaaacdaccddadbbaacbdbaddbcddabdbdabaddcdcdacaaadbccdcacbdbdbaccdabdcbdbddabcbabdbbcacaabbacdddabcbcbccccacbdabacaadadabacbaaadcbdddbdccadadcbddbcdbbcdadacaaccbbacbcbccdccbbbddaacbcbbccbbdddcdbbcabccbaaaadacdacbaacddccbdadacccbdaaacabddabbddaddcdddbbacbdacbadbadaabbddcaadcaccadadcabcdaddcdcaabdcbdabbcabcdcabddcbaccacadacadcdbaabbdaddbdcbcbaddcdaccadaaddcabcbacaaccbddaabdabbddddbdbabacbbdacdcdbbbcbbcbcdbaacdaaaaddddadbbddaaabdbbabccbcabbddcbbdccccbbaadbacacadcabcaddabdabcbbadbdbbbdaccbcbdaadabdcaccbadaaacabcbabdbcdbbabcbaacaabbbbababdacdabbbbcaccdabadccccaabacdbddcbacdddbdccaaaaaabacabaaddcdabdbbaaccadbdbcacacbcadcbcdcbacacaccabccddaaaadbdbccddbcbdcbbacdbabdbbbcacbaddaadcabbbcabdbaddcaaddabdccbbbbdabbdddbabcabbaadacdacccadcdddccddcbbaadbdbacbbcccdaadaaababcacdcbddbaaaaacdabdbbaaddcabdcaadcdcbaacaacdcbbbadadbbbdbabbcaabcbdbabbcaadaaccdadbcababaaccadacaddcaabbabdadccabccdbccacdadacabdccddadbcdddadbdbcabddcbdbbccabcaadbcdabcdbacbddcbdbaccdddbbdcbdbcacacacdacbcccbaabaaacdabdabbdadaabaddadcaaddbacdbbacddaacbdbdaddcdcadcbbaaddadaddddacaaddaadbccddccaccdddadabbbdbacacddbcdacbdcbcccbbcdbadbbaddadbacbadabccddcacacdcacbdbadbcbcacdcabdcccddcabbcacaccbbcaddadbaccdabbcddbbdcdcbbbddaddabaaacdaacbbbddcdabcacbdaaccdbccbcdadcbcacdbbaccbbcaaabbcdaccdddadddccccbdcbbbdbdbbddddcacabbaddbddcddcbabaabacdbddddaaadcbcdcadcbaccbdbdddcabbacbcabbcbbacacaadbddccbbccdcaddcaaccdcdcbabadddddaabddcbccddccadacddccaacddbccbabddcdaacbccccbabacbdcacabaaadcdddaadbadabcdbbcabdcbbccdbbabbabcccccaacabcddbdbaacabdcddbaccaadadcaaccccccabbbbcdcabdccbdbcdbccdaddccddcbdadcbcddcbbdccbdcacaadbddbdbacdcadcdbcccacbdadaccacdabbbccccbaababababdbabddacbbdddbadabccdcbaddcddabdcabaacbcabbdbbadabddddadcccbacabcbadabbadcbadcbdccaabaabddbacadaaddbccbbddadddbcabcaadcadbcbbadabdaccabbdaccdaaddddaabbccacdcabbbadacaaabddadbbabdcbcddccdbabcbaccdbabbbddcdacccdaaabbdbbbddbaadcdacadbcabacacbdccbaacdaddababcdaccabaccdbcbacacdabaadbaaadbabaaaddbddbcdbdbbaacdccbcddcdcadcadcbabcdacbcaddbbbacadadadadbdbdcbadadababcaaddcabbbbcdbdadadcacbccbaaabdcdcbccddbcbacbccccdbccdbcdcccacbababdadbcbabdbccdddcdacbcabdcdbbbaccdcacbcadaadaacddbadccdbcbdbddbaaabaaaccaaccdbdacdaadabbadbcbdacdbaddbdadddabcdaadabadcbcddaacccaccbabdaacbbacdcdbdbbcbbdbbaadadbacbdbaaccdcaccddbdababcbdcddcacaddccaaddaaaacbbbddaddcbcdcdbabcbbcaccbcadbaacbbdbdbbcabbbbcdbdddbbcabadacaacacacbadacbccbdcbcabcbcaabdbbccbadcadddbcbbddcaddbdcacdabdbbddbdacbcabddbadcbcbbaddaaabcaadaccdbdcbcdbaddcadbbbcdcbbcaccaadddbaddbbaddbbbcbabadaccbdcdcbddbdcadadcbcbacbbccbdbdcbaddabccaaacadbbccccbdddabacddbdcaaccabbcabdcdbabdbcbcdddcccdcaccdcaabcdaccabcdbdaaaadadcbdcaaccaadbddaabdadcddbddccadcbcbbbcdabadcaacbdbccabdbadbadddabcaabcdbacddddddabbbbaaabcaadacbabacdaacbdbcababdbdcbbaabbbdcccadbcadaabdddccbcacbcccdbadacadadccaacaddadabbcacbcddccbaabaaadcacddbacbddaddbbdbbbbaabdcababdbaabbdbaccbdccabcdbbbddbdcddccbcaacbcbcaacacddcdddcbbcabcddcbcacdaacddbddcbacbdddabdabdcbbbdcaaddcdacaddcbaabcbbbbbbaaaaccdbccdbbbbbbcdbabbccdcddabacddccbdbbcbadccadcacbaccacbacdddcccaddbbcaccbabbacbcccacaacdccdadccadddbdcbbddcdccdbbbacaccacbbbbddccdbaaaabcddbbddbcacdcacabbabddbbcddccdababaaccdacccabcccaabaddccadabaccadbcdddbbccddbbcbbdcaadddacadbcbbabbdabacbdddbbabbbcdabdaacacdacadbbdbbacbccbadddcdcbbacabcccadbaccdbddcabcdccaacdabcccaacabccbabbacabcbaccacadbbacadcbcadddaadbbabbbdccdcdaabdddadaadcbcacdbbdbbdbdacbddacdabacbdcaacbcbbdbabbcdbbaacacbcdcdbabaabbaddcccabdddbbdadcabdbcdbacadbaaabaaacdbbcccddcdbaddcaccccccabaabcaaaadcbccbaadabbacdcaacbdccacacaaddcbddcabbdabbcdbddddcdaabcbcccbdcadbacbdbdacbdbbddbcbccddacabcdddccdadbdbcdbdcbcacaddddbbacdbccadbbdbbccdddcbacdccccaddcdadddccdbccdaacbcbdbdbcccddbabaaacaadbbbabdbcdcdbaaadbddcdcaadadcddccbaadadbadcddabacadcbbcabbdabcabddbddbbcbadacdcdabbbaadaadcbcddcbddcbbbdbdabdcccabccdabdbabaccbdaadbddbadbadbacdbbdcacaaaddaadcbdcbdcbabdcddccccbaabdcacccacdbbbcccccccbdadbdbddbbcccacabadcdcbbcccacabccabbbdcbdcdadadcabcbddaaabacaaabacdbcddadccbadabdbccaaaadcaadbbccdcabcdcbacbdacbaabacbabcaddbcdbbbbdddbbcdaacabbddcddaadbddacabcababaaabbccbbcabbacaaacddadacbbbcdddbcddacbbdabadbcbcdaabccdacdcbcdaacbcbbbdbddadcaabddacacdddbbbdcadbbacbcdabacacaaadccaabcbddbcaabdddbcdaadaabdacbabadccbddbcddcaacdaddabddbadddbaccdacaaddbbcddbddcabaaddccacddcbcdcabbbcddbdbaadabdcdbbdcdacddacbbadbdccacbbdcacadbccdadaccdaddcddcdaaccdbdddabdddddabdcbbaacccabdcbdbaaddacdbbbadacacdbbdccccacacdbcbacdddbdcbcabbcbccbdbbdaddcaacbaaadabddadabddbdcabcbdbcccaccbbbadbcadacbaadaccdbaaddcbcbcbbabdaadacdabcdcacaccccdacdddbcdbdcaaaacadbccaddbaddbcdacaadbacacabccbdacabcbcccdcadabdabcabaccccbbcdcabababdbbbdbddaaababaadcabcdadabcacbaacdddacdcaacdcacdcdbdbdbaadababcbaadddbbbbbdaaacaccdccdcacbbdcabdaadabbcbcdadbdabcbbdbbadccadadaadbbcbdadddacbbbdaadacdabaddcbdcbadabbbaaabcddccabcbdcddbdcccbcccdcdddccadddbcddbbddbdacacdcbaadccadccdcccbccdbdccccddccacdbdbccdbcbabcabdababcacbdbdbcadaccadaaddbdccdcacadcdabdaaabbdccbdbadbcaadbdcddccdadacbcadbadbccbcddacdbbdacbbaccaaadddcbdbdcbccdbdabddbbabadbababbdcdbdadbbcbbabddcbbabaacbbbccbbbcbcadacddcddcbddcabbddcddbddbdcccaddbddcbcaddbabdadaabbcabcbcccbbacbcbcdbbbbdddbcccdababbbddaacccccbabbcbaabccddcddcacababacccddaadaddbdaacdaccaadaadddccaabbdccacacbccbdadaaadddbdbbacbddddcbabaccddccaccacbbdbababcbdababbaadbcbddbbdbaaacbacabbdddddabddaabacabdbbcdcacdbbbccbcbaaadccabbddadddbaddbbabbcdaacabcbcbaddbddbabdacacbcabcccbadaaacabbcadcccbddaacddacaccdadcdcbdbbbcabbcaabcbcdccdbccdaabacccdbabaacbaabbbbbdbdaccdbaacdaadddccdabadbacabababadaabccdbdcbdbdacdcbbbdddbcbadddcbacccccdabbaddacbcacbccbdbdcdccdccabddadddccddadccabddcacacdaacacbbcdcabacacbccaadbdccbcabccbbddababcdcdbadcccdcaabddaabacccdcdaaaaaadadbbabdbccbbdbbccbbaccabbdbadcbdbccadddbbbacdbaabbcbbdaabadabcacdcdabacdcbbcbcbcbcadbdaacbbbdbacadadbccccadacaadbbccdcadadaaacccbbbdbabbdcbaababaccdadbdacddcccdbdcdaadaacdcccadaccbaaabadbbcabbbbcdadddbbdbbccaaccaaaaacabdcdadbcaacbacdbabcaccbabdcbadaaabcadcadbadbbaaaaabcabdcaddbadabcbdabcacddbdbdadcbcccddccddbcdadabdcbdccdbbcdcbbaccabaaabbcccbaacdcdbcabaaadbccaccadcbcabdacccbaccdbaddcccacbbdcbacacbdbdaacdcdbcadcccabdaaaabcbcbababaadcccacddaabcbcdcdacaaccadbacaccbacddcddbcdabcdaadadcddbadbaaaaaccadbdabacbbcbcdbabbbcbbacccdcdccabdbcccadcdbbddbbbcccbadbacdccbcbadcaadabbaccbcccadddcadcdbdcbccccbbabaadbbddcbcbdadcbacaacddcdadcaacdadabdabaacacdbdcbbbdbacdccacdcadbbdabaabacbbcccdaddaaabccccaabddbbbaddbaccaabddaacbbcdabbbddcddcbbacdbaccbbbcacbaaabbdcccddcadaacccdcdabccaaddbbadbcbbcadadabaccabcbabcbabdcdabdaccdbcbcccabadabaacbddddadccbdaadacdbcdccbdccacdbacdabcadcabccaadbaabdbaadddcccaaadbbdbbadddacddbcaaccabcbdaaddbcccdabdbacdadbbbbccbcddddcdaacbddadbadabdaddadbcdadbbdcbadcdcdcacdaddacdccacbdddcdbddaccbaabdbbbcddcddbbdcadaaacabcaabdbcbdddccbbdaacdaabdbcbdbbdcccacddbcaddadbaddcddcbbcdadbddccdcacadcabdcbcdbdacaabbbbbcaacccbccddbcadaddaddcacaacaabbabcaaacacddbadabbbcccbdbccbadcbdaaacddddbcaddacccdbdcbbacadcbacddadbcccacacbaadaddbadadbadaadaaacdcbdccbabdbbbbddcccdcbaadcaacbddcadbbcbdbdcbdbcabadcdaddabbcbcdabacbdccdddddcdabbcadccdcbdadcbcadbdbabaaddabcabcdbaacaddaddadcbbcaadbabcbddcabccbdacdbbcbaaabbdadacddbdcaaabccdbbbdbacacbbaadcaccabccdabbddcdbbdccbdbbadbcacbdadbaaccddcacabdcdccaadbbdccaacbdbbdacacadacdbdabadcdacbdbbcdbdbcdabcbbbddaddccbcbbaababddacccdadcccdcccacdacaccbcbccddcacbacbcabbaaadcdcddbbadaabaddabaddcdbbcbcccbbdbbcaaabaddddbcdccdccacccdbacbacbcabababbbdcdbdbdadcdbcdbbcaadacdaddcccdbabddcbbbccaaccdadccddadbbbbcbaaadbcccdabbaddbddadaabbbbaadcdbdbdddcabcbcbccbabdadaaabdbadddabbcbcdaacbacdaddbdbddadacacccccaaabcbdabdddabaacdcdccbcadbdaaaabdbcbbbabdbababbadaacaadbcbbdccadbbcacbbbccdbdadacdcaabdbdabbabbcbcbbccbdbdccabbdbbcacdcdacbddabdadbaadbcaabccbaddcdddcddabaaccbaadcadcadbdcdabddcaccabcbadcdabbdaadbdcaabdccbdabacbcbabbbbbcdbcaabacccdaddcbbbcabcdbbbdacabdcabcbbccdbbabccabdbdcaaccdbbcdbadabaaacbcbacadcddaddadbaaadccacdcddddbdbadcaccacaadadadcbcdbdbbcdadaccdabdadcabaaadbbcdacdbbababdaabcbbdabccbcdbadbdbacbbcdadbddccdbdccbcbddcbcbdbbbdbdcbdadabaaadadbbacbabacdaaddccddbcbbdcddbdbdbacdbbcbabcbabddabcdaaaddbbcabcadbcccadbdbdbaacacbdbbacbbccbaaaaaabbaccdccbaacdaabdbdcccadbcadacacbdbabccabcaabbbbccabbdcdbcccadcbbabdacbabdbaaaddbcbabdbdbcccacdcdbdccdcdabacadddbabcbcadaddbdddacbcaddccabcbbbcaccdacddbdcaababadcdbcaacbabcbccbcbdddbacbddbddaadbcacababccbbdbabbdaaacdabbdddcddddddbcaaadacccddabbccbbcdcdadcdacddbaadbbbdcdaadcdaccadbdaddbbdabddabcdcbbbadbcabdcddadcaacbcbcaaaccacadddbbacacaccaccdbabdaddbacdaacddacdadbdacdbbdcbbbddaddcdbdbbbddbbacdbdcdbaacbdccccbbbbbccaccabcdbadbdabccbaaabacbbbddababbadabcccbabdbccccabbabcabbcdbacbbcdbbccacccbbdaacccdcbdabacdcadbaacaadcababbaadcbdccbacccbabccdaadacabbbcbdcdcdbbacdabbccabaaabaddcabbccadddcccacabaabaadadcbdaababccbddbdcaccbcdbadbbdaacacddcdcddabccdddbbadccdcdbabbccbddaccacacbdbabddcdccabdbbccccabcccccddcdddbbadacbbbbbdbabbbbdbadacddcbbadcdbadbdcbdadbcacbccacabbdccdbacaddcbccadaddbccabcccadadbbbbddacdcddcdabdbdcccbcdababbdddcbccaccccbadcbcdbbdcabddcbcbbbdbbbabacabbcbcbdbabbabaddadbacbbbacbcaddddcadadabdbcacacadcaacbdabbbdbccccbcdccdaccddabccdbbdadadcbcbcbacaaadcddadadbaabdaddbabaadbabaabadacdddddabcabbcabdbcbcacbaccbaddacadbaaadcdabbabbaaccccdbbacdadcaccbcdacdcccabdcddabbadabcdcbcbdccdadcbbddbdcbadccaaadacdbdbadbddcabbdbbcdcbbcbcdcdddbcbadddbcbccadbcddaccdadbbcdcdcbbaabdccbadcabcccdccbdabdaddbcacabcbababaaadbccaabcdaaabbadddbaabcccbcaddcbcdabacbcdacaacccbdaaddcddbdabcbadaababcdaababacbacabaccaadbcccbbbcabbddddbcdbcbddbbcddcaaddacacadcccbcaacbdacdaaacaaabcbaccccbbccdaaacabccabcbcbacdcbbbcdbdbbbdbadbacaabdddadcbbbadbddddbbcbbcbcdabcccbadbbdabacaaddddcbacccacbccadddbddddccbdbaccaadcabcacabbdbdcbadccccbcccaaabbdddcabaaacdbcbbacdcddadccddcdcddbdcccbcdcdbccbacbbbbacbadcabcdbdbabddabdbaabbbccddbbbdcbdcaadbadacbbddadbdadadccbaacbacaaddcabbadaddccbdadadaddcbaccbbacdbbbbcdccbdbaaccbddddbddbccbbcdbbdcabbcbcccbabaccbbdaaabcbcdcacbbbbbcbdaabcdabdbdcbbdacadcadcdbadddaaabbdbdcbccadbbdbdbcbcccdadbabaaaccaadcddcdacddcadbadcdbddaaacbabcadccbbadbbadbccaadabcdbdbaacbdbcbdbddcabababbadbdacccacdbbbdccccaacbccdcaaacabadbdaadacacccadddcabbdcaaaddcdabcbbbacbaaddddcdbbcabccadbbaccabdacabcabaacacccddbadcbaadabbbbddabbcaabbcddbbaabcaacabccaaabcdbaacdcccdccdcaddcaccccdadaaadacbbdcbccadaacbaaddbdabadadbbcddcabacabdbaccdbcacdacbcdbaddabdcaadbbcacbcaccababaddcabbabcbdbadcddbcdbacdabbcdacacdabacbcbadddaacaccdccaccbddcabacdaaccccbbccdacccccbddaabbbccadddcbbddbadaaccdabddaaadddcacbaabbabccabadbacabbcdbbaadbcccdccadaaadbcdadcadabbbbdcbcdbbacadccdbdddbbcbaaacacddcabadcabababdbaabcaabbaaacccbbcccdbdbdcacdcaccdbbcadbbbabcadadcbbabddcbbbcaddcdbdacbdabcaacacdbccddabddadababacabbaaaddaadbacaaaabadccddccbdcdaddddabbcccdbacbcccbcabbdddbcaadcdbabbbbcdbacadabbaddaaddbddbcaccaacbbdddcdadcbcbabaccbcacaddbcbddcabcaaaabccbcdbdbbbbbcbdbabdddcbcccbdbbccabcabcaadbcadbaabbcbbbdaaadddbdccddacacbbbdcdcaccacbbabdaabacabdcdbcddaccacdbbccdbaaddaddbabdcabaaacdcccddbdbdbbcddbbddbbbbcccdcdcbbbcaaaddacdcdddcdcccbdbcaadadaacddcaccddbbbdadbbaddcbdbdbbdadcbdababcbbcbddbcbcbabccadcddbdaabccaabcdacddbddbccbadcadbcaabbadacbaddccadbdabdaacadddbbcddcddddbbdabddadddcbdcacbadcccabcccbaccaadccbcbddcacccdadbaacbdcdbccddccacbcadabdddbdbbcbcddacabccdbaccdbdbcdbbbdbcabddabbbbdcdabdcbcbaddaccddaabacbcbadcccdcbdcadbbadcadbdacadbadbbdbddbbdacdcbddbacbcdaddaacdbdbbbdbdbbaacacdddcdcdcccbcdabccdddacdccdacadbdbcadbccbdcbabbbbbbaaacdadadbadddccbddcbcadaacbdcabddbaddbccdcbdcacdcdcccdbabadbadbabcbdddcabbbabbccdccdcaacabdccccbbddbacbbdbbccccbbbaccdcaaabaadaacbccccdccaabdcaadddccbadbbadaaddabdbccbccacdddacbdcdbddccbaccbdbbcbbaccbcadbdaadcadacbcccccbdcaddaaaaddbcccabdaccdcdabcdbaccadbbddabbaacbcbaacbaacdbaabcdccccadbcbbdddccbbdacabccaabddcabaccccbaaaaccddacbbbbacdcbcdbbcbabcbbccccbbbcaccdadddacdbadddbcadcabdabbbadbcacdabcadccccbcbacbccbdabcabdbbcdbacccddcbcaaadcabdcaaddcccbbdcbdadaaccbbbcccadcdcaccacbabdccddbadacdabadaabdbcabdacddcadacbdadaacbbcbdbbdaccbcabbbbbdbcbabbaddcddbbacadcbbcdcadacabdbdbcdbbcabbdacaccbbdccdbaddadbabdbcacaaadbaddbccddccbdccabcdcdccbdcddabcccbacdaabcdcdcaccbbdcccaabdddddaadddbddcaabbaccccdaabacddadadacaddacacbcaddcbbacbdcaacbdbaabbacddadcbbbdcbbbdbddaadccddaddaddbacbaacbcbdcbbabbaaaadcdcabcdadbbbdbbdbbaacaccdbdbddbbbaabacdcadddabcacdacdbdccbcaadacdabdaccdbaabbaaccccadbbccdcdbdbdaabbbcdaaabcbaababbbdabccabcbcacaabbbbcddabdcababbcbdbaddbbbbbbccdbabcabcbcddcaaacbbbbbbdddcaccbdbcdabadddbbcccccaadaabddaabcdcddaddcaddccbbdcacbbbcadabcacaabdbdaadcdbacacdaabcdbdaacbcabaaadccaaadccddbbcccbdaccddddcccddbdcdcbbaaacdbabccabddbbddcddaacaadbcacbbabdcbcdbaabcbcabddccccbcbbbcbacbbcbbcbabdacdbcbdcdcaaadcbadadcbcadbcddabcabbacbbbbcdcdbabbcbdbccacadabccdbdbbabccacdadbccacabddbddccccacdddcdddcdccbcbdacbabcadbbdadbdccbdabaaacaadbcaddabdbbdbdbbdbdbddadadbcbadddabacbadacbbdcadaabdcaaccdbcabdcabbdcadaadcdbdcbbbcccbaaadcbacbcbbbacbbcabbbdadacabdbabbcdbaddaadcdcaadcaaabbbbcbababacabbdccdbabcabdcbcaadcadbacccbadbbdbbdcbbbccaacabaaadccbbcaaadbadbbdccbcbaaacacbdcdabcaadddbbbdbcbbacddcbdbbbccadcbcdabdacaadbbcaccabcbddccabcadaccbdbbbcbbcdaadbbcbccbcddacdbababdcdbbdacbdadaaadbabbaabdbcdbbbcddbadbdabcdacabcaacdbbdabdcbadddcabbbbabcadcadabababacaccdcaddccbbddabacaabadbddabcdaddacbacadcdabadbcddbbacadddcbdacadcbcacdabacdadbdaacdccbddddbbdbaaaaddccadcddcbccccccdcadadaaabccddacaddbcacabaddddbcdbadcbcdcdabdbacabcbcdadaddadbacccdadcbdabcdcccbcabbadacdadcbacccdcaadbdcddcdadabcbbbccdbddbdbddcadcdddadbdcababaddcadbbddcdbcbcacabccdbacbdcccbddbaacbbdaaccddbccadbbbbacaabcccdcddababcdbdcadadaaccacbdabdcaaabcadabcbabaccaccadddbaddcabcdddaaddaaccdcbacccadbbadbcabdacdccabcdbacabbdadbbcbbdabdddddccabbcaccbacabadbbcabdbadbcddbbcdcacdbbaccadaaaaacdbdaabaaccaadddddcbdbacaadcdabacacaacbcbbabcdddabbbabbbabbcbdcbcaaddcaccbaacbbcbabaddbcacbcababbdcccaaccaccacccbddbdddcbbddaaacbcacacdbbbddaaadbdddacdbcaacbcdbbcbbbdaacdaadcdddcbbcbababcccdadddbaacacadaacdccacacacaddaaaccadccaaccabacdadcdbabcbbbaabbccbbdbbddbdddbcbadbaddaabddcddacdaacabbbbcbdacaaadabbdbadddccdbdaabdddbbaccbabdbdddbdcabcbbdbadcbcdbcdbcbdcbdcccbcabbcbcabcdbdcbddbabdabaadbadcbabbbbabadaddcbccccbcdcdbacabdabdcadadadaaccddbadddadbcdabddbddccbccbdccbddddadbadbdacdbaaadcdaacdcbcdadbadcadbdbabdddadadbcbbcbacbcbababbbaccbbcaccbdcbbbbacddaabdcdbbcacdbbbdbbddabdabbabacaaacbccbccdddbbdcbbadbacdbcababbddbddcdcbbdbbbbbbabdaacacabcddaaadbbcbacddbddaabcaddbdbdddaadbaacddcdcccdcacaccbdaaddddacbaccbdadacbcbdacadbbacaacdbdacddccbaddbaadbccacdadcddbbcaabddcbddaaccdbaccbaabccccdcbdddadddcdcdaabbbbcacaadbbcbdcacbaacddbcdcccabbaccccbbcacabaccbdabcbcdacdbbbcbacdabccacdbdddbabccabbdadabbadcdbbddaccadbdbcaaaccdbcabacdcbbbdcbcdadaacdcdbabdcacbbaccacaadcacdaabbbcdccaacbccdabdacadbadbabccdcacdacbcacaadcaabbdcbbccbdabadadbabdccacccadbcacdaacabbcdbdbcddabbbddadcaaabddbabccbbbcabbaadcacaadadaacbaadcabaddddcddbdbbcdacbbcbdccaacddbbdadccadbcabcdbaabcdbcabadaaaadcbddbbccdbdbcbdcaccbaabbbbcaacbdabacabaabbdbbdacdbddddcbaacacbabaaaadcdbaacaddbcbadddadadbcbdbaddcaccacbbbadcdbbdcccddcccaaddbdcdddaadababaabaaadbbdadbaadaacbacadcddbaddabcdaaddccaddbcabdbccdaddcdabbadbdcaababbacdcbbacddddcdadbbbcdbacaaadaabcbcccaddbbadddabcbdadacdbabdacdcbabddcbbdccdbaaaabbbdbddabcccaadadbcadadadbcbadacbbddcbbacddcbbaabdcdcbddabbbdbcddacbaaaaabcbcdadcbabbccdaacacbadacacadacdcccdcdcddbdbbcbdcddbdbccdbabacdcdcabdaaaaababdbcbacadbbdcabaabababcddbbbacacbaabdabbcdcccbcccbbdbcdcbaacaaacaadcbabcddbcccdbcacadbdcbcbccadaabaacdabdadbcdccaabdacbaacdbdbcdaadcddcbabbdddcdbcacddbccaccdadbdaacaaaacdbddddbaaadddbdddabbcaabbbdadaccddcaadcdbadccbdddbccdcbdaaccddaccaabbdccadcbccacacacbacdabddabbbaddcdbbdabddccbbbbcabdacacdbddccbacbbcbabbbbbaccabdbccccbccbbdaaccbbcbbbbaacddbdabadcacadddaacbbcbbbccaadbadddbadbddbbbbabaccaabacdaadabcbaddbabbbcdcaccdddabaaabdcdbaccccaabddccbbbbcbbaaabbcbabaddcbaaacbbadbddbcbbacaacbacaaabaadcdcbddcdccbbaadbaabccbccabccadacbbacdbaacbbbbaaacbbacbccdcbcdccbcccdcbaacbddbccdccaccdacbaadaccddadcacdccdadbcdaddcacccaabaaadddcaacaadcccccccbbcdbbadbdbbaddacdabaadbcbbdbaaccdadbcdbcbaabccddaaddcadadabdcccdbdcadcabaaaddadcdbdabcdadaabcbababbccdbddacacdadaaaabbbbcadbdcdcbdcabaabadbacbbccbaadbdacddcdbccaadbabcbdddaddabacacaabaaddbddbddccbdddccaaccdbcdbcdbccacdadddacacddbddcadabcdccacabbdbcbcbdbaabccbdaccacacdabdcaddabbbcdbbcdadbdbdbbcaaaadcccbabbbabbccbadccdadcaadaccccaacaabdcaacbadabaadddbddabcdaabacbdddbdccdcccddadbbabbdcaaaaabdaaacbacddbacbccaadbbbbddbcabddbacacadcccccbbdddaacddadddddaabcbcbaccbcdbdbccabdddaddbadabddcddacacccdbbddcbaaadcbbbcabcbcdabccadcabdcbcacddccadacbdddcbbcdacbacadcbadbcdccaacdbcacdccacdcdabccbbdccaabcaaabbdcccddbdaacdccbbaccbaabcaacaacccadbcccdcdbacdaacdccacdaaaaadabbddcbbdcdbacacabaaaaabacdcacbdcabdbbddbddcbbbbbccbaccdcddbbccacdabdcabcacddcaddcdbbbcbbdcbcbbdccaccabddddaacddcacabacbcaaacaabcdbbcbdbccdbadcadababbdccbbaddabdbddbbadacaaaddadbbaababaacbccbaabcdddbacaaabdcbbaccddbaaccadbdddcbccdcddaacbbdabdadcbdbabcacacbdcbbdadabbdbadadbaacbacabbcaabccbdcbdaadadcbaaacdbbacdaacdbccccdcacacccabdadcbaaadcacabacdadbbcbabaacacaddccbbbaabccdadcdbbdabaabbadacbdaacdaacbadcddddcaccdcabdbcbcbbdbaaddcccdbdabaadaccbaabbbcabadcbbbcbaabdddaabcadbbacacacadbcaacdccdbdbdadbddbbaadbaddcdbbdaacbdbdcabbacbcdbdbaadbadbacadcaddacddccacbbadbddcabdbdcbbacdbddbabcdadabcbdcbabacbbcabdadcacddacbbbaccbadcbdcacddabdddadbcbbadcabdccdcbdabbadaddbccabcccbbbacadcbbdcbdddaacbaaadaaaccadcdcbdcdaddcbbbdacaaaddcabaabaacdbcdddbbaaddbcacbcabaacbbaaaaddaacaadacacbddbddbabdadbabbaccbbcbccabbadbbbdcacdcbcddaccccddadabcdccaabddbaabbcababcddbaaccddddbbcddaabbacdcaabacdcddcabbbcdaabcbbacdabdcddbdbbdccacacbddcadbcaabadaaabaaaaccccdadaddadbdbcddcaacbcdaaccbcbdbacaaacdcdadcdadbcbbdddcacbbdcdacccbcbaaaadbacadbddcdbddbacbbdbbdaacadadcbddacabcdbacadaccddcacbbaccccccbbccacbbccaabccaccbaaddbdcddcbcccdcabcccabbadacbaaacbbcdddbcdcdacddbabcdbcdabdadabbadaaabaccbdabcdadabccddabdbdbcbaacaabcabbabdcabdcacadacdcaabdbcddddadadbdcdabbdbcaacabdbbdddacadaaddbccbdadcbbabbdbdccbaadcaacbcccccdbaacdcbacabbbcdddbccccaccbcdccabadabcccaaaacbbdbdbcdaaddbbcbbbddcbacbadbdaababbdacddccbbbbbbacabaddadcbdaccccddddddddcbaaaabaaaccbddbcbaccbddacbcacdadcdaacaccddcaacbbaccdcacadcddabbbcbdbaddadabbcbcbadaddcbcbcdcdcddcbadddcbaccccbddccbbddaacabaabbcaddaabdcdbbaacbbccdbbaaaadbbbaddbdcdbddbdcabddbaddaadbbbcbacbbbbbdacdcacadcaccbadcccabadcddbcaddaaccdaddbaacabbbbcacbcdcbbdaaaadbddbaddabddcbbaddcccbdbaccacdacbacabadcdbcddbadcaadcbbdccaaabacdcccdacbaacbddcdabaddcbaccbcabddcbcdcddcbaadcdaaacbdabccddccbdacdcdacdadbdbabbbddabdccdaaadacacccdcbacacdddacbbcbbddccbdaccbdbcddbbaaacdbdcbaccddabcaaacabdcabcbaacadbcddcadcdaadcdddabcbaaccabdbcbbccbbbababdbdddacdcacaccaddbabcddbaabcaaabcadbdadbbdccbddddacaabcbcaababcaccbddddddcbdbdcaacabdacaacdbacdbbbbbdaacddbcacbbbbabdadaacbacabadcbcbacacdaacadadccccdbdaaccdbbcccbcdcadaabcdbbbdddbaaaaddbabddcdabacabacadccbddddbcbabadbabbcbcdbdccbbcccadacccbcababcacdcbbbcddcabadcccdcccadbbdcddbcbaaaddacdabbcdbcdcdbccbdbcddcdcabadccbdcaabbbbbabcbacaacaccaddccdabbcabcaddddbccaaaadcaacccdabaacbbdcbbadcaddaacccbdaaadbcbbbbbabccdbdddcddacbabdbddbdddbbdaabccadaccbbddcdbadacbaadcdaccccbaabbdccabaddbacdcbcdbbdcadcbbccaabcbacdccaabdcbdacdbbcbabbcaabababadddacbbcadccdadcdddacaacabbdddbdabbcdadddccdcadccaabddbccacbbbaacdaacddbdbacaabdbdbbbbcbabadcbbacbdbdbbbadacbaacbcdbabbdbdbacbdbaaaddaccadbacacdbdacbbcbaccdcccbaacdabdddbdbabddbbaadacacdaccbcdccacabcccdaddadbbdcadccdbccaacbabcbddbaacaccabccbaabccdaaccacbbcbbdaabbcdcdabaaadcbabdbbcacaadddcdcccaaabccccdccbcddadcbbabdabdcacdcddbcbadacbddbadcbabccdacccdcddccaacbbcdabacababacadddbadadabdadbddbbcbcaacabbbcaaabacaacdcbaabdadbdacaaddbcddaadbaadbbcbcdcdbccdaaacbaabccbcbadddddcbdcbcdccbbcabacaabbcaddcaadbacbbaabcdaacbbccbbcbcadacbcabaccabcbbabadccacbadbcbbccadcaccccbcaacdacabdadbddbbdaababcdcaddcbbbaddadccaddbccdbddccbcbdcbdcbbcadbacacccbadabbbdcabbdbacabaddccbdaacbcddbcaabddaddbbacbdddddacdaadadacadbdaacbaadaaadcaabaccddaacaddcbdccbdbcbbaaddbbbdcbcdbdcadbcbaddcddcaddddaccdbbcaaddabdccccbccbabbacdccdbabbbcaacbcdddbcccacddabdddbdcddacdadacccdadadccbcccdcaccccacaccacbdcabbddbadcdacdaacbacdaaaacdbcddcaacbabacddabbcaaddcdbcddbdabcacabdbddcbacadcdaaacaaababcbabcacccdbcbdbbbabcacbbdcadcbadbdbdccdcbcaaaaabaccdadbadbaacddcacddadbacdacdbddcabacbbbabddcaabdabaaddccbddccdbcadadddcbccccbccdadddbdaaaadbcacadddcbbbcdabcbbbbdcbbbcbabdbabbddcabddbccdadcdabddcabcbbaaacdababbdbbbbaddcbaacaabdbbdcdbcbabdacbdcccccbdcbacadcdadcdababcbdaadbabdacacacccdaddbabbcbdbdddacdcccadddacabcbccbdcadcbccdbdacacdccbdcbcacbdcbbcbbbddbcbbdadacbacdddaacacabdabcabcccbcaabbbdbacaabbbbbdbcadabddbdddabddbbdddcdddcbcabbcdddbddbaccdbcdbdbbbbbdcddccdabadbccadddaddcaabcacacbbaaaadcddcdccaadaaccdcbcaaaaadcbbcbbdcacdbdaddacabdadcaaccbcacbbadadccbbdaaabbccbdddbdbaaabdacbdacacdbadadbbdbcdaaacbadbccdcdbbbcbadacbcdcababadcadbbbbbcddacbcaaacdcabaadddcadbbbddcbcddadbddbadbbcdcaccccddcdbdaddcccacdbabadcdcaacbcaadbdaadaaddacbdabdacddaddbbccaccaabdaaacccdbcdddadabdacdabacdbdbbbaacaaddacdddbdcdaabaabdcbacbdbccdbabdbbadcddacaadcaabaabdddbdcadbdabbbdccdaacacccdabccaacacbdcbdbbcadcaddcccdbdbcdaddacaaabbddaaaddaacbcdcccadcbacacbaacbcaabcadbcaadbacdbddbcbccbbbcaabaddddccaabcadcdadbccababbbbbbcbbaaacbdacaacbcdcbbabdbbdbadddddacabbccaaaddddaacbbdcaadadbcaaabcddcaabdbbbcbbcbdaccadacccdacbaadbcddabacaddbbcbccbbccabbbdacdaacdccdaaabdcbdadbaaccbbacdbdbcbdcbdadacccdabdaddaacbcddaacddcccbadbccaacdcdccaadacadaaabcabddcdcbcacacdacdaadaacbaddadabddbbddadadcccdcddcacbcdbababbbaaadaddaaddbbcbaaadbdadabcbccabcabbaddcaadccdccdaccddcccaddabcdacdbbdbcbdcdbbacdddbcccaccababcacbadddabaadadccacbcdbdaabdcdbabdddacbddcacaadcbacbbbbbadbdaadccbcadcbbdbcccdaadcddaddddcddbacababbccdcacccdaadbadbacbdabbdabaabdbcbcdcdaaabacbabbcdbcacbbbbbdccacabdcbbabcadcbcddcaaaccadaddbcddaddcbbccaabccbbdcabbaccaaddbaaddadbbddbbaabbabdcbbcdaaaccdbddbdddcbaabbbbddcdcbbdadddabaacbcabbacdbaabcbcbdcabaddbbdbcbbcaadbbaaacdaabdcdbcdadadddaddddbcccaadcabccadcadcaddbdcacbadacddbbaadabdcdabdcdbcacbcacadcbadbbcccbbdcdccdaaacabaccadccaaaabbddbcbdacbacdccaacbdbddcbbabcbaaabdabbacdbbbdaadadababdcbcbadabcbccacbdadabdabdcbaacdbbcaacaaacdaccaccddcababaccdbdacccbbccbabcbdaaadbacabdddbacdabaadbaabbcbbcdbbcbdddcaaccadbabcdaaaaaccadbdaaacaababaabaadaaabaddabcccabcadbdbdbccbddaddcadbbdaccbcbcdacadbdcacaddadcbadcabbccbaaddbbcbdcdabbabadbbcaabdcbaabadbddbcaddadccbacbccdadabbddbbbabdcdbdaaadcabdcdbaddcdcadbadbcccdbddcdcadcabccccdbbddcddccddbbcddbdabdbdcdccabbbdcacdbddbaddcdadcdbacadbbcbcbdaaacdacadcdbcaaadcdddbbabbcdccbcacdbbbaacabbabcacbddbaacccaadabbabccbccaaaccbbddabcdbacdccbbcabadccbcabcddcbcacdacdcbacbddabccacbadadccdacaccaadcbcadbaaabbadcbddccbcaaababdcadcdacaabdacdbacadbcdabccaddddabcdabdbdbdbcbcacdcddabacbcbdcbdccadbcaadbabbdbdacabbdbcdddcdcdbbacddadcacdacabdcbbabccaadcbdcbbcbdcadbacdabaaacbcbcaccacbcbdcaaabcdccccdabbccdbcbabacdadccbbbdbdccbcbaacbbbbacbddbdaabcddabadabbbaacdabaddacbbaccadacbbcdacabccadbddbbbabbddcccddcabaadcdadcacaaabadcdbdacbbbaddcaaccbcbbdccaadbabaaabbabdcddcddbadabcbcadacdabdacabbddabccadcaabcbddaabcadddcdbcacbccaddcbabbcdaccbcddacbcccbcabbccccdcbbdddaabdcdabbdaabccdabcabddacdcccabccbccdcbcabbadcabccbdbaddbbdccbdbcaaadddccadcaadaabbcbbbcabbababdcaddaddbdaaabbaccabbcbcbcbacccaacaababcccbcdcabdccccaccabbbdcbbdbcaddbbcacbdbbdaddabacdadccaabccdbcaadccdcbdcaabadcbabbbcbbbdcabcbddadbbbdabddcddbcbcbbcddaccbbcaabbdcddcddabaddbadccacbcadccbababacdbaaaccdcbadbadcdaddabaabccccaabbcbccdcaabbaccddaadabcddcadcbccaccddacaccbbaccdbdddcbdaaadcbddcaccdcdbbbdbcbaadbcccddaaabbaccdbaacdbdbabbbcdaadccbdccdabcddbbccadbdcacbadbaababdbdbbbcdacbcbbcaadccbdbccbddcadaaadcabcdbddadbdcddababdcacddbacacadbdcacacbabbbaacccbaadcbbddbcacbdaaaacbbdbccabddcccaaaaaabbbbdbcdbaacbbbcabcbbddabadcdbbcbbacccabdcaabcddbccbcccdcaddbadcabdaacaabdaadbdbdbbabcbbbddabadbabcbccabcaabbdabcbacbbdadcababdbcadbadaadcdbadbcbdadbdbdaddacdaaabbdcdcbbbaaccadacccdbacbadcbbcbccccabdcbdbabbcadaacadcbcacacaabbcbcdbdcadddabddbccabccaabdcdddbbddccadadbdddbcbadacddbabccbbbdbcbdbbadbbdccbcbaaadcaccbdbabccadcbdbdcdaaacaaadbcdddaaddabdcaccacaacabcbcacdddaaaaccaabccdbabddddbcdabdbaabaacbdcaaadbbdbddcdcdcabbaadbddbabbdaaaadbdbccadcdbbcacdcaaabbdddbbadcddbbdabcaaaacbacaddcaababadabcbdcbddddbccddabdbbccdbbdadaaadddbccbcdcaccdbbbdaccdacdbbacacadcbcddbaddddabdabccdabdacdbcacbbbaabdcbddacaccbacddbdabbbccbcacdccabacadccaabdbadcddcdcadbcbdbbcaadadaddbcbbaaabdacdcaacdccbdcaadbadacddabccbcadbacdbcbababbabbcbbaacacbccdcabddccbaabddabbadbdbdcbbbcdcaadbbabbdcbccdccbcaacdbbdcacadabdbbbbbabcabbbbdcbacdccabcaabbddbcacdcbdbacccabdcbabbdcbaaabdbabdaccbcccdbdacaaaacabbadcdcdbcdbacbbbbdbbabacaddbdacdbcccccccddacaccaccabcdbabdddaaaabadababbcdcbbbccadacbbcaabdaabadcacddcbabdbdacabbbbcdcbccaaabdbbbdbcbcdabdcacbccdbbdddbcbaabbadbabddcacbabcabbbbdadbacbbcbbabcccbabbcdbcbcaacaddcabbbbbcbacadcbbcbacddaddcdcdccbbaccbbbcdbcbadaddcabcabcdbdaabdbcdabcbddbadcdccdbdcbddbcccdabcaaadbbddacdadadcadbcdaaabbdddbcddccaabcaacbcbaacbcdadbaaccddbcddacbdbbdaaabbccbdcbaadabdbbdbcdaaacbabcbadbabccdbbbdbcdcdcddbbabaacaddaaaacdacaddbaccaadddcddddaabbcbbdcaabcbcdacdabdbadccbacdcadbaacadccacacddabacaacbbbaccbbbdaabadaccdcaadaaccbbbadadadcbdbbadacaadcdacdbcdcbadbcbcaadccbdbccbbbdddacccddbbaabdccacaabbbaaabaacbddcdbcbccdaabdabdabcacbbbbdbddbadbcbbbddbbdbcacaadcccbabbddaacbdadbacdbddbbabcdbdddbcbcccadbbdbdccabbadaadbcacdacbcbbdcdadabcddacbbcbdaddcbbcdcbdccbadadabbddcbacbdbbaadbcaababbadacaccdbbddaaabaddccabbcadadbdcbdddbbcccbbdbacdaaddacdbbbbdcbcaadabcbcddaacdaacbbccdbbdcbdcdcaadbbbbbccadacdaaddbcabbbabbbcddbdaabdbdbadbadddaaddaccbaabccddacdbcabcbbcdabdadaabcdcbdbabacaacbacbadbdbcdbddcbdabbdaacaddbadaddbabddbaadcabdaddbccaadcdacabbbccccbdbdcadacbdcaddabaaacabadaccbddddadbaabcadcddbcabaccdaadccdbbccdbdddcabcccbbcbbdcdddacacbaddcadbcbdbabbdabcccdacdadbcbddaccddbdbadcadbbdacbcbdbcdddbcaddaaabdabccccdbcbdadcacaccbdabccdddabdbcbaacdcdbcbdcacdbbabacacbaacacdbbbadcbabbccdadbbdcaadabbdbcdcddcabbbbdaadccbdadabddaabdadbcdddbddccbdbbdaaadbdcadbadacddbddcdbddcadcbdadbacaabadaaabdadabacdaaabdcbcddbdbcaddaccacadccdbbcbabadbccabacbabdcbdbcabddacabcbcdabdcdadddadadbabcddacadbbcbbbcbadbdccacdddaadabdbcbddcbdcbbcacaaabcbccacdabdddacbbbcdabcbccdbababdddcddadbaddcbddbadacbcbacadccbdbbaaadadaccacbacbcdbaaccacabacbbabbcbacacbddbaacadbbdabcdbacaddaadcdadcabdcabbabdbccdbbbcabbadadaaaadccacdbcabdcccbcdccbaccaabbababbdbabbcddddcdbbcdabbacbcbccadcbccbaccdbaadacccbcddcaabdccabaaacadacbaabaccbabdcaaabddadaddaabdddcddaabdbcadddbcbcdacbbbcaccabdbadacacbcdbbcbdddcacddaccabcdcabbaacbdaddbdccbacbbbbcbabaccbcacbadcddbbbcbccbdcbdccbbacdbcaaccabacdababaaaddccacdbbccdacdcbdcdbabdcdcbcccdcccbcabdadbbcabacdadabcddbaacdcaccdccbcdadcacbaddbdbadcccabbbbbcdbcbcdcadccaaddbccbdacdcadbbdbaacccdadbcdbdcccddbdbbccbbaaddcdcacadbabcbcadddbddcabdcdaccddbddccbddbbcdccdbabadcbaaccdbcccbaaaccaabccbdcbdbbbcccbcbbbcddbacadcbbbacbacdbbadabcbdabdaaccbdcddcdabbdbcdcdccadcbcabddbbdbbbdaccddcbacadbbabdcbadbbabdbcacbdcadcddacbacadcbddbbacbabdbcbbbabacddbdddcdbaaaaddccbbbbdbbccdacaacccdddcacbcdccbbdacacdadcbcbdadcaaadcacdaabbbdacacbabcdcaadcabcbabdcabdbcbdacaccdbaddccbabdbbdacbdcbdbadbadbcdcabdbdcacbcaaacabaaabadaccbaaabdcbaaadbcadcbbabbbabddacacdabacbbcacbdbabcadabbacdbaddbddbbacabbcbacbddcbbdbbaaaaccccbadbdcdcbddccccbbbccbabaacabacaddddcbcbccdabbdacaddacaacbdaaddcdcccbcaabdbbcbddcbcdcbabadcadcbbcaacdbbbcbbcddccdcccacbbabddccaccadbcbcbbddabddcbcbaaaccdababbdbcababddddccdbdbaddaabccdcbdcdcbdabbbbdcbdbcdccbbbdabcbadbababbdbdbaabacdcbbdccdcdbabadbadabbbccabbcadabaaaaadbbdabbbcaaacabdbbbbcabbcadcbbdbadddbbbcdcadddbcabdbdcbaccadbaadabbcbbcaaacbcccdaaddcbbddabccbdadbdcabaacacadabadacaabaabdaaddbcacdccdcdcdaacaddacbabadbcabaacdadacaddbdcdccacbaadcddbcdcdbdccaadbbaaaddbbdabbcdaadcabadbdccaacaabcabadcdbcbccbbcacbcbdcbbcdababbcdcabdbaccbdaaabbcdcaddbbbabcbccabacbadcdabcabcdbcbdccdacdbaabdaabccaacccbdabccabddacabcdbadcbbdbcabccdbdcdbcdacbbdcdaddcdbddbcadabbadaddcdbcdcadbdbcadcabdadcaabcaaddcaaaddddcbcddbdcacbaaccdaadacabbabababbbcbbccbadbadaddbcadcbcaddbaabcdbdbabddbdcbddcbbcacbbdacbdcbadadcbdccaacacaabaadabadbaccbbcdcddbcbdbbddadccbbbbbadcaccdbabdbbcbbcddbcbbbbacdabccacaccdddcacddbcdabadbcacddaaacdaababcdbdaddcabacdcbcaaabdacddcdcdbcbbadcbadbbbdbcbdacabbbbbdaccbcdabbccdbcacacdddddbcccddcbcddbcaddacdaacaacdbaccacacbbabbadabbdbcddaacccdabbbdababbaaabcbaccacdbccacacbabccdcddcbbaabbbdcaacadccacbcbddcabccaccbaacbbbdbcbdcabddcadaddcadcbdbdaddbbabdbdabbdbcdcbaadbcccddadadcacbcbdbcaaaccaacbaabbdbcbcdbcaddccddcbdadabbcaabaccbddbaadaccbbcbdcccdcdcaacaabdbbbaddadabbcccbaccabcabcbdcacddbcdcdddbbbcdaaccdaccccabdccacbdcacbaacaabadcdbacbccdcacacabcacbcababbbacbbcbdabaaadddcddaccaaaaddddadcdadadcbcbbbdbccddbaadbcddacbbbdaadabcaccccdacbbaadccddabbcdbcdadcbbadaadaaabccaddcbbcbacbcbcbdcbcadabaaccdaabbabbbcaaadbcbdbddadaaadccbbdabccaadbbacdbdadabbddbcacbbaccbabadaccadaaddacbbbabbbbbcbabaacbbbdcdcdccbbdabdadaabbadddddddbdbccdcdcccbbcdbccdccdacbddcaabdaaccaddcabbcaabbabdbcdcabccbbabdacabcbcddcbbcdbdcbdbddabbcbacbdbdadcdaaacbaaddcbbaaacbddbacdaadbbaabccacccabaabdaadcbbbadddcabaacddcaaccacdadacbddabdacccdddaddaaadabdbcbdbdcabdbbdbbaadbbbbadbaabbadddccddddbbbccadacbdaaabbcdbcdabaabdcaabbcdbaabbdcbbccddcacdbddbbacbdbbcacaaabcccdabbdbbabacbdbabcddaaddcaadbbcccadaacabdcbdccdaddadbbadcdbccbacdcccaaabdadaabbdbacbaadcbccadaacdbdccbddcbdacdabaaadddbcdbacbbdbaadcddcbadcadbdcbaadadbcbbddacbbcbadcddcccdbbabdbbacdbddcbccbdbcdaddaabbdcdbddcabbaadcabcabcdccbacccbcaadbdaaadccccbddaccdbbcdadbdaaccbbcdcababddaaaaacbcabaadbcbacbacadaabcdbabdaadbdbbdbaddccdcbcaddadbaaddbbbbdabcddbdcddaaabbddcaccbaaaccbddddddbdccabcaadaaddbdbadadcacbcdccbbdaabacccdddbcabcdcadcdbabcdbdacdabbbbbbbacbcbcabcdabddcbbadaadbaddbcdbdcdcaddcbbacadcdcadaccddcbbdcdbddcabadadacabaaccdadaddddcbbaaacababdbadabccdbacddddbbcdbbcaddccacaccbcaccddbdcddccbcbcdccbbbaddbbbbbcbcbbcbbbcdcbcdadcabdcaadbcbabccbacbbcdaddaaaaadaddabaabbbcbcadddcdbbbdbcddacdacdbddcbbdbcccdcaaadacbdcacddbabcacdbcadaccabacaababccdaddbccccbcdbdaddadbdbbdcdacdbbaacbacaddabbdadadacddcccaabcabdccadadadadcbcdcababdbdcabcccccdaccddacddbbaabdbddbddbababbbbabddcabbccaabbdddbcbcbdcaddaaacacccbdbcdcabaabaabccbcdccadddacdabadaadbcdddacbadbccdabdcddcdaacacdbcdacbdcbacaadbcaccbccbcddcbcabccbddacbdcdcacdbcbbddbcadbcccbabcabbbdddbcdbcaaddaacbabacbabddbadcddcabdabbddabcacbaacacbcabbcbbddbdbcaadccdcaacdcbbcaabccbbcccdabdbbbdcdacbcbcbbcaadccdcbcaababbddaabbcccbcbbbcdddbbaacabddddaaadbdaabdddbdcdcccbdcbccacbbaabbcdbdcdacdbddcbcdaaaabccabacacbccbdbbacabcadccdbbccadcaaccddccdbbbaacbaadabaacddddcaadddcbaccaaadbdadaabdcdaaaccbacbdaaadcbcbbaddabcabbbbbcccdccdbcdcbdaaabdbaaabbccbdcababcccbcbadaaaabcbccabddacdcddacababbadbdabbdbdaacdcdadddaacababbadbadabbacddaadcacaacacbacdbacdacdaddddabcaddacdaaadabbaaadddcadcaadadaaccddcdbbddccbdcaaddcdccdaddadcdcdbbabdabbbdabdbbcccdcbcbdcdcbcddacdddbddbdbbcaddbdabcbcaadabdcbdbcadccbdddccdccabbdccccddbbbdabadacbcdddbdcccdabbcaddaaccdaacdcaabbcccddbdcbacbdadbdabaabdadaccacbbdcabddcdbadddbbcabcdccbccbacabdbbdbcdcccbcaddadbcccaddbcabcddcdcadbacbdbcbbabbbcabcdadcbcaaaadabaaaaaabbbdcbaadbcbabdacbddacbdacadcabdacdbabcdbbbbbbcdabdacabaddcdbdbddbdbadbcabacdbbabcccacadadcacddddbdccdcaacccdccbbadccddcadcaaddcdcbbdcaabaaacbbabbcbadcddadadaabbdccbcadaccbcaddaadaabbcacdcccbdbccdaabddddcdcadbdbaaabdcdadcabcbcaaaacacadcbcccacdacccadcbcbadbabcbabdbcbcabdbadbddbacbdcbccbcbadbdacaaadaabdccaddaabbabbabdccbccbdadbcdbddadcabdadcaaabbccdcbcbcbcbcdabcbacbbddabcdaabbdaabdacdcdbdacdccccbccaadbdccbcbadcdabcddbdabcacadadbddabacbadbdcbbdbdcdcccabcdbbcccadccbbdbbbbabcccadcaccbddbdcddcccddacabcdaccbacbdcadbdaccbacaddcacacdaaabcbbcaddbcccadabcddabdbddbccaddccddaabbbabadbbacabdbcbdaabaacdddcdcccaddbdaccaaccccabbcdcadcddbcdbbadabdbababcccaaabdaabadcdbdbbcadacccdcdddddaccbaabbadbdcbbaddbadacaabccbaccaadabcdcaaddabdcacaaddadbabcdadbcdacbaccdbbadabadcdaaadadcadccadcadccbabcdacbdaadcbadaccddcdcddddbdbbbdbbaacaaadbdbabcccaadcbabaccbbcabbcdccacbdccacdaccbcddbbcbbabbbdcddaaacacdddabcbbdaccadadbabbaaccbcdabbabcbcccdbadaddbcadadbbbdaacbbcdadccdbcddcaacdddcaadbccaaaacddbdaddccaabadaddbbbbbdddbcbdacdbbcabbdaccdbdbdbabbabbbbcbccdaaaccbacdddcbacddaccbbcadbdacbdabbcbabadbabddaadcddadaabbabaccdbddcaabdacccaaddccabaddcbdbbbbdabdcdbdaadcbdaddacddccccadbbccdbccdbdbbbabddcbaddbddaacbccdcaacddabddcddadaaabdaaabbaabcccacaacbaabbcbdaaaaadbcbbbdaaabcccdadbaaacadbdddaadabbddcbcbdcacddbddddddadcacbacddcdccacdddabbbdbadaddcddddddcdababdccadbacabdacddbddbbabdcacadacbbcdbdbaacddbbaacadacadcadabccacccbddbbbbabdacdbcbccdcaadbbadbcaddddbccbcbbacadcaacbbbdaddddbdacaabadcdcddaabcdcbcabcacbbdcbcdcdacddbbdbbbddcdbbbadcaacbddcadbbddcdbdadbcbcacbcaaaacbdbbbccbcdcbdabccbdbcbbabddbcddaadbddbbbbcbadaccaabdaaadbdacdabbaccbbcdbcbdbdcdccdcabdbbddccdbdbdcbbccbdcbbbcabccbaacbaccdbaabacaccccabcdcdacdcadbaadbdcaadacadbacccddabbdcabcbaacbbcddabdaaadacddbbabaaacaaababacdbbddbaacddbaabacdaccccdababdabbbbaacccaaccacabdccbdacaddcdadcaabacbbdbdbdccccbadacadccbbaabcbcbaacbbcacddbcadcdbccccbbcacbacddcdabcbdbccbbadbaaadddaadbdddabbbadbccbadbbabacdabdbaadaddddcbbdcadaacbcdbdbcdaacbdcadaacdaaccbbcacddadcddbdcbdacdbbbbdbddcaaccaabadbbccdbcdccbdddbbbddbcacabbcdccabddadbccbcbcdadcacccbcbcdacabdaadccadccadcbabcbdddbddabcbdadadbdaccdbdbaabacddccddadbdabdbbbdcaddacdadcbadacccdcacacdbdaadbcdbbccdcacdcadababbcbaadacbdcaddbdbccbcbaccacdddbabbbbdacddccbdbcbbcddbabcdcadcabcccbacdbdcbdbadddbcbacaaadcdcadbcdbbdbccbbbdbacbaacdbccaababbbdbbcbccdadaabbdbcaadbdabbaaaacdacadcdcbdcabaccdcbcbdcbcddaaaadbdcdbacdacbbdbadddbdabbcbcdcdbacccbdaabdbacabdabacddbaddacddddadccabccacadacdcbbcbcdcbbbcdcacaacaddbaacdabddddbddacdbcdbbccabdadaaacdadabbcbcccbbdabdcacbcbbacccdbddabcdbcddaababbdcadadaaaacdacbbdcacbcabbbacdbcbdacabdacabdabdabbcacdbcdabccddbbdcdadcddbdbaabdcbcdaaaddabcdcadddabaacbcccbdaaabcdcbbaaddcadcabcaacdcbbdbcaaadccdbaadbadcbbdbbbbadbcadccbddcbcbcbcdcadbaabdabbcccaadbdbaabdbddbcdacdbccdcadaaccccaacaabdcacdcdcabbacadcdadcadbabcabbdcaddadaaadaaaacaabcabcaacbcbcbcdccbaabdcbcdcdbabdcbdcbddaabaacbacdbcdcddcadcbdaddbdacadcbdcbbcdcdbaaabdacbccbabdbddcaadbbcabcabdbcadadacbcccdbbbcbaacdcabbacacdbaabbddaabcddbbbacddbcddbaacabdacbacbdbadcdababdcddddacaabdcddccbdacdcabdabacabadadadaacabcddbaaaadbdcbdbacdabbbbbccaacabacccbdccdacbccbcaabbcdbdaccbbcaddbabaabacbbbcacacddadcccadbdaaadabcdacaccacccadbddcbdcaaddbbaaccdadaacbdbdadadbcdcaaddadcbabdcbddbcaadddaaabbccaccbbdbcabadbacbacdcabdbccbcbbaadadbacccdaddadbadccddbcdabcdabdbccddcaccdcbaddcdbcdcbacdcddadbbaacddcbdaaabdbaacddbcbcbacbccdabacadadcadbabcbbaaadcdacabcbdabbbbdaadcbabadadbdabcccbacbbbbdbdacdacddbdddadbacbbcadaabcaddbdaddaacabaabbcbcddddbadacacbabccbcadacaacbbcdacdbdddacdcccaacacddbdbadabbdacadddadbcaddabbdcbcaaacdabaccbdcacddacbdbaaaabcaddcddaabaadbadddccdcabbbaabbabbbabaacaacbaaccdcaccddbddbbccadabbdbddaccadddaadabbbadcadccbaadbddcbcabdadabbccbddacbccbcacdcabdaaaaacddaaccbccaaccccbbdcadbabdbccdadbcbdcdcbbabbadbddabadddacdbacbabcadcacacbbdabbdbbdabdbcdbcbcaaadbddcbcaddababccccaabcbdbcdacbdadabaabdabbcbddcbabdcccdadacacdbacbcbdcddddabcbdcbcccadbacdddbccccdbbbdadddccbdacbbdbddddaaabacaccbaabbdbcdbabbbbacdbdbadcccbcccbcdbabaaddddabddbdcbabadbccdcadbbbdcbdaaaabdaddccddabddacabdcdbbabbdcdaddbdbaaaaaccccdabdbdadcadcbdbcbaddccbdbdaaadbdadcbcadcddbacaadcbaccdacbacbbcacbdbaacaacccababadddcaddbdadccccdaabcbaabcadbddbabacbbdaaaabbcddcbdaaacccdadaadacccaabdddcadbddbadbbddbcddbcdcddbdbddadadadaacdadbcddbbdcccbbdcadbcdbcdcbabccdabcbbabcbdbdaaadcbbadcbbaacdbabdbdaccbbadddabdaabccacdbcdcaacbaabdddabacacbbacbddacddcbbabadcdccccdaacacdaadbadddcbcbbbabdcdaddabbdbacdadcbcaadcccaabacbdababcabcadaadbdbdabdcbacbbbbddcdcadabdcaabadcbabaadbddbbbbacccdaaaabcacdadbbaccbcbadaabdadcacbbdbbddabbaaabcaacaddbababbbaccbdbdbbccabcacdbdaccbddaadabdbaddbcbddaabadaaccbcacbbcbdccdcabbbbcdabaacdcdabaaabbaadaabbdbaacdbcadaacccccdcccdddadcbdbcadbacaabaaccddabacddcaacdbddbdcaadcddcabdcbaadaabcdabccdddbdcbcaccacabddbdcaabdccadcdbbdbadaddcadabcabdbbcbbdcacbabaaacadbcacacccabbaaddaccbddacccabcadcdcacacbbccdaacbdbabdabcbbdaccaddbdcdaccababccaabcdaaaaabbabdcaaacdbbdcacabacabcccdccbccddbddbbdaddbccccdcdddbbdbbdcdccabaddcddccbdabcadacdcadcdbbbbbcbcddaccbbadaabcabacbccbdcacbbdaadbadbdccbbbcdabdcccccccbcabaaaddaabbbbbccbdddadbcacadbaddacdbdddbbdacacdcbabbbdabcbccaccadbdabadbabbdbccdbadcbddacacaaaccbdddcabcaaddddbcbdddabcbccacbbdacddcdbabaaaabcbabdbdaaacbaadcbabddccbdbbaadbdbcbbddaacbacbaabbbadacbbdaddcbbadabccdcadaddbddbcbaaddcbadddacbbbacdaddcdaacaacdcbcdaaabcaacdbacbdcbbcdaaacadacbacbacbddbaccdaddbbbbcbcbadabcaadaacdabcdbccbcddcdcdacbbbdbccbbdadccbaabddcdaabdcdadccddbddddddcdbadaacaaccabcdcaadbacaadacacadcacbbbbaadcdabdcabcbdadcdbaccdacacaddbdaabddcccdaadacabdddcbdabcbcbbdbbbaacbdbadbbcadddacdbadaaaddacabcacbbaadcdcbaacbacaddcccacadbbacdaabadcabbabaaabcbdcccaaabbbcbbaaacccbabdcdcbdbbadbcbddccbdbacccacdaaabccddcdacbbaababbbadccdbbabadbbbbbcdabcdbcaabcbccabacdbaacaddcabaddbdaaaabaadcabadbddacbadccbcabcbbbdddcbdcdbbbabbdaccabdcababbbcbcdcbdbcddccdababdcbaaadcccdddbaaddbdcdddbabbcaccccdbcbdbbcacbdadbbccdabdbbdacdaaaddcadbdacbdababcbbdcbcbdbbddcaddccaaccaadcaaababbdbdadaddbcdbabcabcbdbbabcdcbdacbdabbbbbbdcabadcaddabcadcdbbaacaabadcbbcdcbddabdccccbdadbcbbaaacacdaaaacbdbccdcacadabacbdadadcabdcaacdaacdcbabbbcbbdbbaccdcaddbccbaacbccdbaabdddabbbccabcbacadaadbdbcdcbcccaaccbccbcdcbcdcbadacbaccbbcdbdacbbcbdddbadaacdddbaacabcbdcddaabaccdcbccdaccbccdcdcbbbcbbbcddacadbccdabacdddbccadbbdcacacdacbbbdbcdabddccaacdcddbddbabdbadcdcddbbbcbbbabccbdaadabdacdacbddaaadbcccabccadddcabddadababddadcbbadcddbcccdcbdacaddbcbdbbaddcaddbaadcbbaacadbdaaadbbbddbadaaaccbbadabbbbcdbbabbabdcbbbcccdabaadcaccbcbdabcbacbcbbadcdcddbccbadddabbabaddbbbccadcdadccbcbddcadddacdbccdccaccbaadabbaacdbacbaadaadbabdbbadaccccbcbadccdbccdbdbacccbdbadcabbcabdbccbadaacaadcccabcaaacabbbdaabdddbbcbbaacdbccbacabbcbacbcbcaaabddaaddcdccaaaaabcbcacddbbccdbbdadaaaddcdcabdadcadbaacbdcdccaaaddbcaacbbcabaabbacbddcdbddddacbacddbbbcdaabdacadccccabcdddcbbacbddacbacdddddadadbcdcabdbcbcadabcccbdbbaaccabadacccbacacdcbdccacadcadbcbdcbdbdddbddbadccabbdacabaadaccccacdcbbcbcdadaadbdaadabbbdabcdbadddcabccdbcbddaaaaddcddccaadabbddcddadadbdccabacbbbddbbabcbbbccbdcdbcdddccccbbcccbdbdddabbcbccbdcacdcabdddbcdadcddaaacbddbbbbabaddddaabdbbcdcbabdaaddaabdbddbbdaabadcbdcbcdddccdcddcdcabaddcbbcddcbdaabaddcbdbbabdcbbdaabbbdcddabdbcbcccdcadcbdcacacdcacdccdddbdacadcbbabbccbdabdcbdcbdabddccbbcaaadccbacbcdcdccddcababbbcbcbccaddcabaadacbcdcababcacaccaadacdddcbcbbacabccaababdbccbdbabddbcdbabdabcbabcbdcbccbacdaccadbdbdcbbcdcacdbcdccdaccccbaaaabbbbabbcdccacdacdbbdbbadcaacddabacdcdcccadbadbdddbcbdabbbbcbdbcdcabbcccadddccbabcdabbbadbddabadccabadcbcacbaaadbbbccbdbcadbbaddacbcdadcdccabacddccabcbbbaabddbdbadcabddcacbdcddcdbbbbdaccdadbaddbdcadddbdbcbabdabdadaddccabaabbdaacbadbcbaadcdaabbacacacbbacacbcdbddadacaaaaadababadabaccbcbacbbbabbdccccdaddacbaabbdccbbabacacdbcabdbddddcccdbadabadcaddbcbddabccbaabacbbcbdcdcaddbbbdddcbbdaccbdaaabaddcdbaccbbcabdcabbddcdaddcaaccccbcaccccbccacddbbdaccdbacaddddcabbcdbacadbcadbadabadbcacdbccdccbcccabaccbdbcccdcccaadcdbaaccabadabcabbaababbdcdcabbbcbcddaacabacaacbdabdbacaddabdabdadbcbaaddcabdcdcadccdbbccbdaaabbdbcbabcbdcbaddbcbcdaccacbbabcdabdbacccbdacddcbcdbdadaacdadadadbdadcccbaaadccaddccbbacdcbdbadbdccaabbdabdcbabadcbbcadbccadbcdbbdcddaaaadcdabbdbaaadabdadcdcacdaddcdbbbcacdddaddacaadacadcaabdccaddacbaadbabbdbaccdabbbaaabccccaacbbbaaddcaadcdbadbbcbddcbaacdcddcbbaabdcbcdbdcdbaadabcadaaadbbbabccabcaabbcbbdbdcbcccadcaadcbbcbdddbccaacdbacaabbbbcabbcaacaddbcdadbbcbbcaacabaabdcabcccdabdcbcbabdbbaadbddcadddcadaccdcbcdcbadaabdbaccdcaacbbcdcbbdadccdaaaacdaaadcdcaddcdbadacdabdbbacaccdccbddbabbdbbdddbcbdaccddccbbdcaabcacdacdadcababcbabbbaacccbdabacdbaaacbadcdbbccbabdddabdaabaaacadbdccccabcbdbaccbacaccccdbaaccbadbccbbabdcaaccbdbcbbaaaccacbbaaacbabbbbcbacbccbddbaaabbdbaddccbdbaccbcaabacbbabacddccabbccdcabbdddbaaacbcaaacbcaddbcdddbccdbdcbdaddddabbabcdabcdacddcadbabcacdabbacddadacbaaabaabcbbcbcaddcdbdbbaccabcaaabddbcdbcdabdbbaadcbdcdbbbccddbcaaaccadccbcbddbdbbaddcbbcadcbbdabcaabbdbbabbabdcdaddbaaaaccaabbcdccbabcdaabbbbdaacabbcaaccdbbaaabbaabbddcaabdddcaacdbcbbbdbdcababbbbbbddcdcdbcdbdccccbcadaddcddabbbadacbbbbaddbbbaaddcabcacbadbcddbabcbcaddddaabdacbbdcaadbadabdabccabbcbacacbabdacabdcbbaccabccccabbddbacacbaddcaabaaacdadccaaacddcbcaccbcbabddcadcdccdcadbbdacddbcadacaacdcddbabbcbddabcdaacdccbabadcbdccacdccbcbbccbadbabbcdbcbadcdabbabbabcaddbaaadaadcdbdaacdbddddcbcacdaccbdbabcdcbdddcccccabddcbbabcdcaacddbcbaadaccabccaddaabacabbcbdbbcdcdcabcdcbabbabacacddbacddccadcadcdacbacdbdbdcdddcbbcacdcdbabbbcabacaadaaddccaaaacdbdccbadcdccbbacacaddacadcabcccdacaddbbaadabadcacdbabdadbbbabdaabbacbdacadbbbccaccbacaaadaaabcbabaabdbbcbdbcdcadbcbcdadcabdbbaabdaddadcddacddadbddddcdabccacbdbbaddcddabbbbbacdcbcdabbaabcadbccbcdabbbcbbbbcbbbcbcaaddcaccbbacaabddccddbdabcabdbaccbcaccdcbbaacccbacdbadbcddbdbdacbacccadbbccbbbbdbdadbcdcbdcadcaadadcbdddacbacdcccaddacdabaadbcadacaccbbbcbdcacbadadaabbbabbdcbbdabdbdbbdcbaccadbbdadacbabcabdcadbdaabdadabbacbcddbadadcbadbabacadadddcbbabbcabcbaabcadbccdadcddbaddabdbdacabadccbdabddcdbddcaaddcadcdbdccaadbbdaddcadcccddbddcaabcacaacbdddbdcccaabdbbbdbcabcadcddcddcaccbdaddcadcbacbbdcbabdcdbdccbbaabadcbbdddccccbdaababbcddaaacbbabccdcaadcbbacdaaabbddcbbdacbbdbbdcdddabbbcbaccbadccabbdbacdbcccdbdadcbbdaddcabbcaadabdddaacddacbdaadbadcccaadcbabdbccababbababddbaaabbcccbddcddbddcbbbcddcddddcaaadbddcbadbbbdacdcaacdadaaaadcccacccdbacaddddcadaadbbbcbbdabacadadcbabbaabccbcadacbaabbcaaabaacbcaaddcccbacbddabbcadddbcabcccbbddcdbddbccabcbbdcbadbabacbcccdbcbadacdacbbcdcbabcddddcddbcccccccbacbbabcdacddddbbdbcadcbcdbcadbaccbddbdbcadcaadaacddbbcdbdcaacadadbacadbbdabcccbacdbdbaacbccaadddcadcadbdcbadcbdbcabcacaaccdaabaacdbbcadabbacaacccaddbcddadcabbadbacdaddabcabacbddaacadacacaccdbcdbaadcbadcacaaaddbaacbccabacbbdadbdbbdcbacccbbacdbbdcaaddbbbbbacddadbdcabbcbbcaacacccababababbcddbccaaabdacabddcdbcdddadacdacdacddadacddadbdbdcccdaacbbdcbbbddccacabdcddbadcddbcbdcdadabcdaabcbddadbcbcdadddabaadbcdbaacbadbdddcddbbbdabbcaacccadabbccaaaabbbdbbcbaccaadbcaddbccbccacdcacbcddcdbdbcddaabccdbabccdbdbcadadadccaccbcdabbbdabbacddccdccaabbcabccddadbbbaddaaabbcbdacbcacdbbbcdbbbddccdaddcacadbbcbbdcbabaacbabcdbcbdcbddcdbcabbbbabacababbcaaacaaabcbcdbdcdacbbaacbadbcbdbddcbdddaddcaacdbccbacaadccbaacbbcbbddbdacbcccdbcdbdddcabdcbbdcbdcbaadabcbcddcaddddbaddbbddbadcbcdaaadccaccddbadddcbaabdcccaadbbaacbaccccdbaddcabbccdddbcbdcbcccdcccbadccadbabcdaabadcabcccbddbbbadccacaacbdabacacadaabbadcbbccabbcdbcadbcacaaacccacbbcabbdccaccbcabcbaaaaaacbdccacacdbbaadbbacadbbdccaaacdabdabdccddbccbdacdacccccbbdaacaccbbdddccbbdcdcbacbdbaaacacacdbabccbaaccaaacadabddcccccaaacccdcdabbbdaddddcbccadcdcdbacdbacbacacbaaccabbddabacbdbbbdacaadccbdccadbadcaddcccabaaddcdcaacaccdcadadbdcbbcbbcdaabcdaaabccbcabcacdcdacacdacdadbabbcbacdbcdabddcacadadadbdacccdbbcacdcddbbaabbabbaadcaddacbabbcdaaaadaacaccbabbcabdacddcdadbccaadcabcddcccacddddcacdaddddddbacbddadbdbdcaadbcddbdddbacddcdddbcadbbddabdcacabcdbacabcbbcbacddcadbdcbccdddbdbadcbbbaacdadabdaacabcdadabadabbdadccdadadbdacddbcddbbdaadaaacaccabdaddccdbdddcbbbaaddbdbcdcacadbcdaddddddbcbddddadcacbacdabadacdcddbbdacaccdaccbcccdabbaddbaadadbcdadbadaaaddcbbddaddbbdccccbcdcdacdabacddbbcaadbddaabbcdbccbaacccbbcccbabccadddbddaddcdcbdadadaacdcbaadbcbdcddbaabcbabbbcaccbddabbbddbbaaacacdcccadddabcddbadbdbacadcddccdcbabacaddabaabbbabbbaccdaadadaadaaadcabcbccdacbcbbcccaaabcdcbaadbbdddaadcbbcbaddaabcbdbdcccdbbbaaccdcdbbbccbaacbddbbbbcddcaddaccbbddaacdcacddbabbbbaaaaadbbcdadbacdbdaabbcdcbbdbddcbaccdacbdddacdccbbdaddaadabccdcbbdbaddabbbdcddddaddcbccdbbccccdbccbcdbdcddbacddadbbbbdacbdcacbadcadabcbbaacabaaadbddbbbddaacccabccccaaacacbddbbcbdaddcadaddbbccacacdabcaacdbbcccbbadadaddbaaadcacdadbcccadbcaccbcbccaaccdddccadbcdcddddcdabcdadacdadbbcbddddbbbbdccacbdcdadbdcddccdcbacdddbdbadbbdcaabdaacaaabcdcabaaaadcbbacbaadaccacadcdcbdddcacaabaacbcaacbdddababaddbadcaaadbababcdbdaaacacdabcabbabcdadbddcadadbdbdcbabcabdbacabaabdcdabddcddccbdcbdadccccccddccbccdddabdbadadbccaccbdcabadccddaadbcdddbacbadddcbdcadddcbcdbdcddaddcbbdcddabcccdaadbbbbdbdbacccbdcadaadbbbbaaaaddcaabacdadccdddcadcaacbbadcbbcccbabccbadcacbabddacadbaadbcacbdcbdbdccbbddadccabdcbbaccbacdaabcacbabcaabccccabcaaccdaccbaadbcbaddbbddadcbadaabddcbbccabcbdcbbdbdbdbaadadbdcbacbcbddbaadccacacadbccdbacaacacbdcbcdbadadcabbacaccccccbdccadbdacbdbbbbccbdbcddcaabbabcbbacaaacbcdbcddcabcdcccbbacbcddabbaabbdbdcddcdaaddaadaabcddadadbbcaadcbbbbbdcbdbaacbbbdacccaddbdbaadcacbadcbccdcdcdcbabcaadccbbcacdacabbabdaadcdddabcaabbaacacaacbbdbbbbacdcbaaddcacbacadbdadddcaccbccadcdcbdbdbbcdccacbdabaccddcacdcacdbaaacdacaacbaaacaccddcbadcdbdcdcacacdbbabaabdbcacbabacbacaabbcaccdcbbdcdcdcbbabbbcbcbbcbacbaadcaacbddddabbbaaddbddbabcbacbcacacbbbcbcacddcabcabddcabcbdcaabbcbddabbcdcbcbddcdaaaabbababaaddccacdaacdbddddbabbccdcbbdcadccaabcbdadbcdcdbbaadccabcdccdbbdadcbcbabdccccbadcadacbddbcadddddbdcdcccdcbacbdacbdcababbdbcbadddadbacdaadbabbcabcdaccabcdbcaabadccbcdaabbbabbadbacbdbbbadcbcaccccddabbbaaabcadacabcdbdbadcbdcaddddbbbabcccddbbbabaabbcbdbbdcacbbcadcaddbddcdaccaaddaadbcbccbabdcdabdddbcbababbadaacbdcabcdcbccbadccbbbbaccdbabbdaacbcdccddcddcdcbddbccbadadcbbadbcbacabaabdacbaddccdddaccbccacbddbdadcacbaddaacabdabdccdcdddcbadcbcbddbddbbbdbcaccabcbaaaacdabdcccdbdcdcccadccdbbaccccccddcbbcadddacdcaabcbbddcddddcbaaaaccaadbdadabcadaaccbdbbccacbddcadabdcdbccababdccbababddcbdbbaacdcbcbcdccccddabccbdcacdcdcabdbdbacdaacaccaccbaaccababddbcacdacadcdbdaccadaacddaadaababcbacdcbdaabbbbcacadaaacbabccaaadadcbcdbaaabcbadcaaabddadcdcdaabdcacaabdaccbbbacdccddcdaadadaabcabbbbdbcaacdbcabbccccabcabbbccbdcbbbddadcdcababacbccaccbacaacdcabaaddadcccbcccbcdcdcaacbdbcbcacbbacbaccaadcdbbdcacababbccbadababbbbacaccaaabbbabcddcdabaadddbccdbdbadadcbbbcadbdddbcaacaacbaabcaccadaacabcddcbbcddbbcccdadbabdbbbbddcadbdcacbbddacdaaaacdcddccbddcabbbbaddadccaaadbbdbcdbbddacdacacaddadbaacbdcccbcacddbabbddbdaabdcaaaaccadbbbdcbdacbdaddcdddabbadcddddbdccbbacbcddcbdbcbbccdddcdaccdcbabbbadcaccccabbadbcacdbcabbbabcdadcbcababdaabaabcadccccbdacdaaacdcababddabcbbddbbbbbadcababddbdcddaadddddbaddcbcddcbbbbbdadddcccdcdddbbbbaacbaacaaacbacabcbcabddcaaacbaabcabbbaadaabadccccdbdaadcbdcbdbbdbadddaaaacddcadcdadbadcdbabcddcbdbaabaaababcbacbababbadbddcbbaabcaccadbdbbdacadccdadbccdcbdaaaadcddacdbacbdbbdabaaacdcbdcabdacbdaaccdcabaacacdacabbbbacbaaaddcdaabcdbdbacbbacbababadaddbbadcaaadccccbcccbbbdbadbcaccbcdabccbcaaacbaacacaccdcbdbdacacbdaddcddbbcbddacacccacdabccdccccbaabaaaaadbbbaddcbcadadabdddddbdaaaacbbabbbdcaccaabaabdcbbcddcbcbbcdcccbaddaacdddcccbabcbabcbadcbbaacddbdcadaadacaaadbcaaacccdbbbcacabddaaabacdddbbdcdabdabcccbcacacddbaadbcccdaddacbcccbcaddbadbcaacaacadddbcbaabbdbabbbbaacdddbdcacccccadbcbabcacdbcbcbbdcdddcaaacdaddcdccdcabdcdaddbcdbbacadaacbcacacaacbcddbbacbacacbaabccbadddddbbaacbbcaacbdcaacbddadbdadbabbdbacacacdcccbaadacadddbcaccabbbddcddddbbacbccbbbdaaddccbbdcdcacaacddadabdddacbaadaccdbbddddbddcdaadbcdbbdaabbbbcbbccccadbdabbdbcabdaadadadaabadabdbdbcabddcabcabaaccaaccdbadbcbadbcddcbcbbaaadccdcdabaaaabbdacbcdbbbdcccbbdaadcacbbbddcbcccbdbdbabcccccdaaacbaabccdbaaddcdddbaabddcccdcabcaaadcdacadcdbacccacdddacdaaabbdaddcbadbabbbdacaccddacccbabddbabccbdbabbdbcbdbaaaadcddbdadddddcccabbacadbbadadddddadaddbbccdbadadcbccacccaadaddcbdddacdbbdadcabadcdcbaabdabbaacaabcbdacdbaacababacadaccbdbcbabcbdadaccbcccbcbacaabbaadcbbccddcbbbbdccaadddccacbbacadcbcbdcccbadaabcdbcaccdbcabdccdbbbaabdadbdcadcabbddadbbbadbbdbaaddbbcadbadabdaacddabaddabaaacacdcbadbcbbbdccacbdbdabdcccaababcdaaddcbccaaddaacdbcaccdbdacbcbaacbbabbacbccadcdadbabbdaddadbcabdabbabcaabadddcabcdaaabacabdaccdaacdbddbababcccdadbdacaabbdbdacbbdcdbacdcdabbcadabcadcbcadcddddbdccaabbbbbbcbabdcdbabcbaaaacddbacccdccbbcdbaaaaaddbbcabccbacacdbcbbcadaadbbbadbbabcbaadaabdadbadbdbbaaacbaadaddbddbbadabcaccbdaddcdacccbcacbccaccbcbdcadabdaaaaaadacccdccdcdddcacbaabacbbbabaccdbabdcbbaaabcaddbbaccdbbaabdbdddcdaaccdcbbddbcbbcddaccbcbbcaacbdcabdadbbcabcdadadcdaddbdccadabcbccccbabdabbdacbabbbbddddbdadaacabdbbbaccddadaaaabcacdbbdcdbdcbbdbcbddddaabbbdbdbcbadbdabddbccdbbabaddcbdbbddccdddabbbdabccadacddbbddbaacbadccddbdddbbddadcabaddbdacdaabddccadcbddbcdcaacbddbbbbcacccadcddadbddaddcdaabbbbbaaabababdcccbdccbacbabcdbabbcaaabdaabbacccadbbdbdcbcbcbddbdabcbdbadccacdccbdcbdcaaaaaabdadacdaabddcccaccdddcbdabbbcddaccabadabcbacdccacdcbbacacdcdadccdddcdccbacacdcdcccbcdadddcdccccbadabccaccbabdabbbdbbdcdcdacddabaaccddacabddacbbaccaccabcdaabdacadbcbabdbbcadabdbbadbcbbcdbacbbdcacabcacbddddddcadaacaddcaaabbdaccabaabddbcccbdcbcddadcbaaaaccdcaababddcddabdccbaaccbcccacbcbcacbbcddcbddbcbaadcdacdadbacadaabaadddbcaadcbabcacdccadddbaacbadbadccccbbadbbaabdbcddadbcbaddcbbcbcdbcdddcbabbcbbbacccaccdcdacddcaacadddcaadaadbcadabbbadbaacbdccbdccadbadabaddacdbbcdabbcaacdddaccbdbbcbcbcbcbcccacbbacbccbabdbcadbddddcaaadcacdccbadacdcacbabdbcdabbcaccbcacdbcccdbbdcddacdbccacaaaddcbcdbadbbdcccbccdaaaabcaaddbbcbcadaccbaacaabbcccbbadaaaddaabdbadbcacbbdbdacccbcdaccaabdcbddbbcbadcbcdaadbbbbbababccaabdbcadbdadbcaadbdbdabababcbbdcdcacaadbdcbdcdddabbcdbbdddddddaaaaddaabaaabcaaaaaccbacbaccbaacacabcbbddbcadbadcaaadcbcacbcadadbadbdacdddccdccbbbdcaabbdaaddbbcddacccbdbcabaacbbaabccdbddddccaaabbabccbcddddbabcbbcdbaaabbbbbdcaaaccbdbaaddabcaaabbbdbdbbacbcaddabcdcacaabcddbcbdadbadddddcbadbadcdaababbbdaddadcdcdbcbcdcbccaddacbbddacbddbbcacbbcdcdddadcdaaccdcadcbbdddbaddcdcadcaccbbbccadbdadaccbbacacbbacccbccaabdadbcadbdbacdcaaacbcaabcdcbdaacdaaaadaaddcaaaddbbbcdcdbaddccdcabbdacbcdadbccccabbacacccaddcbdabcacbababaadbdbabcaddcbaddabdcacbacbacdacbbacdaacddaddccddddacacddcdbbcaaabccbdaacabaabcbbdbbbdcbddddbcaabdaacacbbdabbcaddcdbdaddddbcdbaddabbabbacabcbaddbcadbcddcbbdacddacbbcccdadcdcbbabcccdcdaaabbcbaddaabdddbabcbcdcacbddcadaddccdccdbcbcacabdaadacdcabbdccbbdcaabdadaadacbccbdabdccbcdcbacccbdcbcbaddbdaacdccabbbabcbaadbddbbdbcacddaddcabacaaadcbaaadaadbbacacacbbddccabdccbcdcdadbabcaddcdcddbdbddcaacbbdacdccdcccdcbdbbcddaabadaadcddbcababbcaddaaddcdabbbcbdcacdbdbaddddccbdbcbdddbabbdbcbbabcbbccaccbdbddbcdaadabdbdbbbadccbdacaaabbbabccbcddbddddaccbabdddacbbdddcbccadbcdcbbccdbdaccacddcbddccaabacbaaacadbbbbbdddabcbcbccbacacdcbbccdbdcbcabcddcddbacdcbbbcaccbaadbbaaacbcbcbbcdbddacaaacccabcdcaccccddddbaabcbacccaaaacaaacaadccccbaaccdaaddaacdcbbbddacbccbcdbbbaaabdbdaabdacbaacddcaabdbdcaabdddacacaabbcdbddcabacbaaadabdbcddaddcbbdbabbaacbdbabbababbaccaadccdcbaadcadcdbadbbbcbbdddaddabdabadabaddadbbaddcbcbbcacdddddbcdbaccddcbdaddacbcbddddaaabbbdcdaccddcbbbacadcbddbadcddcadcdcdcbaacbaadddbcbacbabaadcbbaddddcdccdddbdcdddaabababcbdccccdcdaaacadadadabcdbcdbadacbdabbbccbdadcadcaabacdbaababdaabbacdbadaddddbcadbddcadaabdcbccbcdcddabbcbabdcdddadcccadbadbcddbcaccacccdddadcdbadbdacaccbbaaaabcbbabbbaaccaccdacabdcacaabdbdcaddbbdbaaaacddacadadacaacbdbbbdccdaabaccbcabcccdabcdbdccabcccddcdbbbcddbdcdbbdbbdccbacbcbacabcddbabbababaddabaacadddacccacbaaccccdcaaadccccccbdcbbddbddcdcbdcdddabadacdadbccdabbbdcbaadccabbccdadaabaabdcbddccbbbdbdbdcbacbcdabbdaaddaaadbbdcbbbdbacdaaabdccbbaabdcdbbabbabddbbbcbdbdabdccaddbacacadaccbdcabbaccdcbaddbbaadaabddcdcbaaacaabacddcadaabddaadbddaccdaacdcadbacdaadbcbdbdacbbdabdbddabcdbcdbbcbdacdadbdbdaccbaacddbbddddcaddaddaddbcaddacdbdcddacdddacbccbcbbcacacbdacccacaabbbcbbaacdaadcadbababaccdadccababbcbddccccbbdabadcddccdccdbdccdbccaadaddcbddadcbcaccccabaadcbdbbddbccbccbdccbbbcbcabacdbddbabcdaddacbddacdbdacbcaacacbadacccdbbddcacdabdccacbccbdcdabbccccbdccbcbdbbdddcadcbccccbaaddaacbcddaacbdbdadaabbddaaddacabaacbbcdcddcaabbbddcdabdadcacbbacaacdccdbcbcdcddcbdaaadbbbabacbacdbabcabcddcbcddcdbacdbaaadacdbbbdcbbdbdbdbcbcdbcaccbaccddbaacdadbabbdbbcdcbabcdcbdacbdcbbcaaadadcbbabdcbaddcdaaddbcbdcbbdaccaabccaabacaaaaaacddbbdacaaacbddccccbcdbcadbacaacbcdaadcdddbbbcbccdcccbbddbbbddadbcccbabbcbdcabadbbdcaaacdbaddbabddaabbabbdcbbdbadaaadccadbdcdddcbabbbbccabadabcbcddacbdabcdbcdbbccdcacccaadaacabbdbbabddcabbbbcddbccdcddacdbbdadddbbaacdbcabbcaabbbbdddcabccddadbbbabddacbddcdcdbbdbacbcaacadbdbcaddccaadbacaccdabababccdbcaddaabccbbdcdbcbcbbacbbbbcbbbcabbbdccbbdadcabcbcdcccbabddddbbabddbaddddbcabcbdbdccbbbaaadabbcbcdaabdbabbaadbcdadabadccacccabdaddcbdbbdcddaaacdbcbbaabbcaacacccdacaabbbcbaabdbcccdcbdbcbadaacadddcaaaacbcbbcadddcbcddcdbcbabdabccbadacabcbcbddbbbbbdbadbddaccdbabacadccccbadddadaabacbbcbbabcbbdbabdcdbbadaabbbaabcdbdacabcacaccdabbacbcdcddddadcccdcaddbacabdbcaabcbbdcccaaccbccdaadcdbabbdcbaccbcaaaabdcbbcbabcdcbadccbccbcddddcadaccaddbbcbbdcdacddbabdcadabbbddbbccdcdcacbcaabccdcadabbddbbbdbccadaabcdcdbdaaacdbcdcbdbccddcdbccabaabbcdcbbbccbabdbabcccabdbbaaccdbddaadbbcadcacdabaddaaccdacddcbcaccabddacbcbcabcadcdcacdbbaadccaddcbbcddabdccccbcdbadaccdcdcbccccdbddacadcdbacacdadbccbbcbcbaccaadbbbaaaadaacaaaccdcdbdccbdbdbbdbacddabdcbbcdbbaccabbcacadcadbcdbdabdcaaaaaccbabbbaddbdcdbbbddacbccadaaaadcaadbabdadcaacabdcaddccadbcddddcdaddabdbdacbdbbaadddabcbabccccaabcacbccbcdaadabbababdabbbabbbbaadadbcbbccbccdcabdcbadadbbacbbacbaaabbadacdbddcddcdcabddbadacdacaccbbddcbdccabadacbadddcbccacbbcbababbadbbdbcabaabcababcbddbdbdbbabacddacbbdcdaaacbacbbdbccbaabccdcbdbadacaaacbbddbabdababababacbdcbdbbabcacbaddbddaaddcaabadcddadcaddbadbccabacacaabdbcdabadbaadcdabbdcabaabbbdcdcdcbcdcbbbbbcbaadaabbcaddcadbcaaacbccacbdcddaccabbcdcdcbacabddabdcabcacdbbcaddaacaabcbaadadaddcaabbcbbcddcdbbadccaaabacbbddaabdcdbccbddbabcddbbbacbdcdcdabcbbddbccccccdcbbbbdbabbdaabcbbbdaabdccdddcacbbbbdcbbcddcbbadcaaacddbbbdbadccadcacaddabcdcacdacbacacdbdcabbbcaabcacbbdbaadaadcaaaddbdcccbdbdadaddaaddadaaddcadabbabddaaccddccacdabcbaabdcdcdbdacbddabbaaadccacdbadcbaccbdcdaaadcbdddcabcdddadbdddbbaddabbbadabbaaacaaddbabcbcdbdbaaaaadbcababdcbbcbbbcbdbbdadcacddcbbdcddaacabaabbddabddbcaaaaadcbabdaaabbbabcdbaabcdadcacbbdcccbaddbdddcdcbbcdbadabdbdabdbcacaacccdaacdccccbbbbbcbdbbdddbbcccbdbbbabbabcbcaabcccabcabcaaaabdcaabdcddadcdbdbacddbcacababcabaadacdbccabcadddccdaadcdccaababcbcbdadcacdcdddcdcdabdbababdbbdbddaaacddabbdbcabbadabdcbdccabaddbdcbdcbdabdcdcbabadbacccbbadcbbababcccacadaccccaaaaaaaacbcdbabacbbcadbcccabadaaacdcdbcabdcdadbcbbbcacacdabdbbcddabbddacadabcaaadddbbcdbbbbcbddcbddbddcddacbbcdacdbdabcadacaddbadcbbaccbddbacbcbbdcbacdbbddbbcabacaadcadbaabdbabacaabbaacaabcdcadaddcbcbbabbcccbcbaadabaddbdbccbdadcddabbabcdccdcabdbbbcbdabdddacdcabbbbdbddadcdccdaccaccbbacdddddaaacbcccbdccbcdccddccccabbcbaadacdaabddcdcddbcbdabdacdccbcdddacadbcdbdddccddcbadbccdccadadaadcdbbbdcdbdbbaddcbaadadababbcbacaacdcaccadaadcccadbbabcddabcbadcdbdbabcadbdaaddaadbdabbaaaaddbcdadcaccccabababcbdcbbbaadbaadbccaadbbbcbdbbddbcdadadadcccadaaddbccccddaabbbcbddadacabdacddcbbccddcdabdcbcbdabcbadbacbbbabccacccababaadbbacddcddddddabdaacddadcacdbccbcdadacddddbdbcbabaddbcaaccadadaabcbddaccadcbdacbcbbcbdbaacaaaccbcababddabcdabcaaaaaddcbacdccddcbadccabdbadccbbabdcdcbcaddbdbbaaadababaacaabdcbcbaadadabbcbcccbdcacddbcacaabcbbcacdcdddddcbcabddbcbbdaaccccacabcbbddbabaadacdcbbcccbcdaddbbadbbadcccabadbddadabcdcadcbdddcabdabaacccbbbcaabbcbcbdaacbcbbbbabaadbddbabaababaaadcbbadbddbcdccdcccdadcbccacadccccbbbcccabacdabcacaaababddcadabdacdacbbcbaabddbabcacaaddcccdbadcacaddaccdaacabbdbacdabdcbacddbbabaaddaaadcbbdaddabbadbbaaddcdaadbccdbccaadaccdbdbcabdcaccadbaccbdcbacccabababbaabbdccaaccabddbaccaaccdcbdadbaacbcadcdaaddcdddbbdcbdcdcdbbbbdbacdcbcbbcddcdddbcbdbcccbbcbdabadbdcdcccacbabdddadbbdacabbabbbabccbbdbaccbabcdbcbdbaaccbbdaccacddadadbacadaaabadabaabcdddaababaddacdaddbcbbaddbcbcaabadabdcdacdbbdbdddbcbaaaabcdcaccaaaccdcbccddabdbcbbdbcdbcbcbcbacaaadcbbaaaabbcadcddbbdddadacdaccbbaaabdcddabbdccdcbdddcbbcbacaddadcaccbacbddabcadbdaabdbadbbbacbbccdabdbdacbdbbdcadbdcadaadacbcbbcbddbbbbaacbbddaababcbaadcbabdaaabaadacaabbbdbaddbdcdbbdcabccdaabaacbccdcddbbccbbaaabadcddcadcdabbcbadcbcdcbdadcddcbdbcbaacccbadddcabcbdacdcacccaacbbaddaddaacbbdbbbbaaaabbdcdcaaadcadbdabcadbdddbcbcdbaacbababdcbcdaabcabcaacdbdccbacbbccbaddbccacdabddcabbcccbcbccadcbddbcbbaddabcacccccbabbcbbcbcbdbabbbcadcccdcadbbcbcbccacdbcdadcccbbbccadbabbbcaccababcdcbdccabcbdadbcdadbdacacadbdcacadbbcadaddbddcbdaacdddddacccccbdcacccbccbdcdcdccadbbcacbdacdabbbcdbbcacdabdcadbdbcadccbcccbabbaddddaccbdaaddbadabcbdacbdadbaccccdabccbbdadbdcbbaaadddcbadddcabacddbdbdbbdbacabbaaabbdababbbadadcddbdababadbbaaacdcaaddbddbababcbcbaabdccccabbcdcdabacdbcdacbdbdbdcaaabbadbcaacadbcdbbcdabcabbacabbbccbdacbadacbbccccdddccadccbbcddbacccddaabddaacacccabaaacdadbdccddcbbaabaaccacabccaabadcddabcccabccbddabdcabbcacddcbabbbabcacabdaacaacdbdcdbadbcdddbdccabbdbbabbacacacdacdcccdbbdddccccabddacbddbcccacacacdabaccbbbcbabcadbaabdbdbddcdddccacdbdbbcaaacabcbccddcaabcbdaacddacbdacaabbdddcdbdaccbacbbabdbcaabddabbbcccadddcddbaacdabbbcccaaaadcdacaadacbaadaddbbaccbaccdadddacaabccabaacddcdbbcababaaadbbcbcacdbdcadbdbddbabbcbccbdccccbccdabadcdbbadaabaaacddcbcdbcabbdadabacdcadccdbabaacdadacadbcbadbabccaacbcbbbddbabbbbbdcabcdacaabbbdddbcbcadadbcbccaaabdbacccdbbddcaaddbbabcccdadbddaddabbcddcdbacaccabadddbabbbcdcababdbccddabbcdabacbbaaddacdadaacdcacbdccbaacacdddbdbcdcbbbbadbccdcdcadacdacdbcdddaabccadcdcdbdacdacccaadbbdabcccddabddaacabddbdadbcddcaacdcbbaabcacaddbbadbcbbbbdcbaccccdcadcddbbaccbdbcdbdbcdddbbbdbabccccdccbccaadbbabadcadddbcdcdbacadadabdcabdbdcbcabbcaabadabadaaccbaadddbcacbbaabbdbccadaccaadcbadbbadbcadaccbcdadaccbaadddcacddbdaadacccacbcaccdabacccbadadbacbdcbcbaacdcaddabdabbacddcbaabadcadbbcbdbadcbdbdccdcadbcbabcdcdccdccbdbabcbbdbcccbcddcaabcdbbaacccbbbaadcddacbdcdcabdabaadbadacbacbcbccdcddaabcaacbcbdacbbdbdccccbacacbacbcbcdbcddcdabcdbaaaacbacadccacbaadaddddadacdbbacabccaaadddddbaacbdccdacdbadadbbbcdabdcabcadaadbadbcbccdadcdcdbbccbbabdbccbcdcdbcababcadacbddadccaaddbbbbcbadbacaddddddcdbaaadcabcdbcccadccbbbbbdbcbaabcbdbcbbdbdabacaddcccaaacddabbdcbcaababdcdabbbbdacaaaaabddcbddbdcccaddadbccdabcddadcbccdcbbdccbbacdcccbabdbddbccdacddbddcbccbcccbcccadadcccdaddaabccddbddbdbccdbcdbacbbbcbbabbdddbadcdacbcaaabdddddabacaaaaadabbbaccaadcabcdbbbbadaddcddbccdaabccbbbcccadaadbcccababbddabaabcbaaddddcdacaadcabcdcacddababdbcdcdbabcdbcbbabdcabbcdaacbaabbdbdaaadabbddbdcacbdacbcdbbaacdddaaabbcaaddcabddaadbdbbbbccbdbbddadaaabadacdabbccbcaacbdbcdadbbbaccdbacacaddcddcccdbbbbcddcbcacbdddccbcbbcdbbdbbbdaadccabcdbacbdcbbdcdabdabbdbdbcadbcacacabadcbbdcddbbcdacacddbdcdcaddcdaacbdccbccaabbcbcacccaadbbddcdbddbddcddcdaaacbdcccbbabcdadddddacdddcdbcadaabddabdbacdbdbabbccbbccadbaaabdccdacccbbbcabcdcaaaacbdabccadaccdaadbacbdbabbdaadbcabacbaaacadaaabbaaaccabdcdcbdcbdddbacabcaacbdcbdbcdbbcdacdcabcaccdddcdacdbcbddddcbcdcadacbdaaabdcccdbbddaccbacccbbbdacdbdbaadcbadadcbcdaadabaadcdcbbacaabccacbcabdaddddbaddadcbabcabccaacbacdabcddbbcccadaacaadbbaddcdadcbbcdaaccbdaacdbacbccddcdbcdcadbddbbcbcbbbdaabcbdabbabbbcaabbabbbcbabcacdabcdadcccbadbdbbcabdbabdadbcdcadddbbaaaaadaacaaddacbcbaacacddadbcbccaccbaddabacbbaaacbcadacdacbdbadbaccbddbddcacabadcbcabbbcbbddcadbacdcddcbdcacbccbadcbabddcabcdadabbcacabcbbdbdbaddacbdbcbccaadccadbbccabaacdbcbcbaabdcacdcbacabbbdbadacccacacadaaaaddbacaacdbadaaaddcbcbcbdccbcaabbbacbcdbdbabaadadddaadddbacddccaacdbbabdcaddbcbcbcadddbddbabddbbdbbdaadbddabbdabbbbdbcabdbbcdadbdbbabaddbacadbbcbdbbacccdddccbacbcdbcdcdcbaabdccdaabdabbaddcdbdcbabdddbcbbdccdcdcdbdbabaabdbbdadcbbbbadcddbdbadcdddccbdbbaddbbddbdcbbaaddcddabacabbcdbaadccaacdaaaaacadaadacbbdcadcacadbbdababacaddddcdddcdbccdcccacaddcabcadcbdbaadddbcdcddbcddbbbbcbcbccddccdacddbabddccabcabaaccabdbacaccabcbccdcaacddbdbcdccbbddacbcccdbbbabacdbdcddbaadcdcbbadaaabadcbdccdcabdbdbacdddddbabdddacdcdcabdbabcddcadbbbdbdcaaddbddcacabccccbdccbabadddddcadadcaaabbbdadbdaccabccbdccbcadacacdacccdcbaaccadbccddadabacddabadabbcccccacabddcdcbcadbcdcacddcbabadccddabadbddcacdabbcdaabdbcdcccabcbdaccadbcbcdbdcabbbcccabbddaaacacdcabbddbaddbccbcccbccadabdcabdbbbadbbaacbbbdddaacabacdbacbbdbbccaaddcccdbacdabbdbcdcbacdbbddbabdaaccaadaacaabaaddcbcccbdddcdaacabbbdbbbbdbcbdbcbdbcaadddbdcaabbbbbdaccadccaacbcdcacabaddaadbacacadddcbaabbcdbaccddbbbaadcadcbcaababacddacbbdbccbaddabaabbdddacabddacacdaaabcdbbbdaaabbcaddbacdbbddddabdaadbcdcbbcabaaddaadacaaaacccdacadcdacdabdcdaabddbbdcaadacaaadcaabacbdddabbbcacdaccbabcdacddccdccacabdbcbbbadbdcddcaddbadcaacaaddbacbdabdabcddddcdbabbcbcccccaacbbdbbcaababddcbbdadaadbbcbbbdddddbcaadadaaacbcabbdaaacbaadabbdbaccdbdaababcccacacadcdaacaadbbcacdbdaabdabbbccddbabcaaaacdadbbaacbabdcacaadccadabaccdcbadbacdaacdbcacccccaabdabcaccadaacadbbacdcdcabcbddbaaaaccddacbcaccbaabccaccbdaaacdabaddbacddcbacdbababcbcbccdbcadddbbbabaabadcddbacbbddabbbccbaddcadcbaaaddbdaacbcbaadabbcdcdbddbddbaccaacaddcddcaababbabaacdbaccdbbbdbaaaabadbccbcdcbadbabacbbaaaaddacccabcdbbdbbdbdbdadadadadbdcbdbcdbdddaadcccdbbdbddbacaddcdcdbacdcbbaabcdadcadbdccdaacbbadcabddddabcaacbabdcaabbdbbbbacdbaaaddababbdcacddccabadcbcbdcdcbccaddadbccacbbddaacddbbbacbddadccccaabddcdbacbddbaccdddcdadaadccddcbcddddadcccacabdbdbaddbcaabbbdddababbcacbbbbbcddbcccbcaadcdbdadddaccbbbdbcabcadaabaccbdcdbadacbdbdcccacabdddcdaaacbdbdddabbccbbcaaabbbabacdadcbccabbbcaabbcacbdaddbbcccbcddaaaabbacaadabaaadbbabdbccadbabcbaabdcdbabdcccdbbaabadaccddcabbbbbadacdadcbdccbbcaccabaddaabdacdbcdbdbbdccadbaccacaaaaabcbddabdcdddadaacdddbbabbbbdbbccbcdcdbccacdbadddacbcacacaaddbdbaacbdcbbcbbddacbaaabdcdaccabcbcabbddddbdddacaaaadcaadabdcdaccaabaacbbabadabdbccaacdabadcbaabaadbaacdcabcbabcadbccbbcdcabddbbccaccdcccccaabbdddcbbcdccdccdddadadabcdbdabdcdaaaccacadabcaacbabdaaaadbbcdadcddbcdadadabccccccdcdcbbdbbdcbbacadbacacdacabdcbccacaddcdadccbabcdaacbabadababcccababadccddcdbabdaaabbdbbbdcabdbdcccbcbcbaaddbccdcbbdbadcaccbccadcdbcbabbdbbaccababccaccacabacddaddaadabbcbcdbabaddaadcbdbcddcacdbdcbdaacdcabdcdacabdcdaacdcababbddbdacbdcddacabcdbaabbccddaccdaacaccdbdcbbbcddcbddbcbadaccacbbddbdbcdadaabcccddabbcababadaadbdcacabbddbcddddbacccbdcdcabbdbbabacdbcaadadcdddbdcbcadcabdcaaccaadcccdbdcacacdbdbacddcabbcacdcdcbdcacdcccddbdddbcccdcddbcdaadbdacbadbacbcdaabbaddbaacdbbdcdaacbdbcabaccbdbcbcbacbddbaacbdccdacadccdacabbccaabbbbdabddbaddacbddcdaaccaacadbdaadabcacddbcdbdddcabaababbcdbcdbacdbdddbadbdcdcacbbbddabbdbdcacddcbacddbbadbadbbdddaadbcaadadbdcbdabdadaccdccdcbcdbdccbccbbbcdcadccbaddbcdbccccbcbddadabbbdcbbaadbbcddccbabccbcbdbbbacdcbaadbbbddbadcbdccaaababcdcbbdbbddadcddaaaccacadcbcacaccdadacaababdbbbcccddaaaacaccddbcdabbbccadddaacaabbbddaaaddaacbdbadbadbaadbdadbbabbbddaabaddcbbbbaadbbbdabdbbadcaddbcadabdccbcddccdbdaaddbbababcdddcaaabbaaaaccdcbbacccdbdcccbcbbdcadadadbddbdadbaadbbcdbbcbcbbadaaabcadcbaadcbcaddcbdadaabbaaccdaabdbcccbcbbdcdccdadbdaaddadaabbddcbcbabcddababaddcbbcabdddbbabbabaadbcdaaacacacacbaccbadadcddcadaccadbbddcccbbaaddcdbabddcacccabaacccdadaadaadadcdcdadddcacddacccbdacbddbadddaddccacddadaddbbbdcbddbdbcacddcccdaadbdbcbddabcbababcbbabbaacacccbabacbdacdadaccbbddccdaddbdabaacddaaadcdcabddbcbcddcdcbbdabdaaabcabcddabdbddaaddccabdddabbbcdaddcdabdadbdcbdbddabbdacbabacdbacbadbddbbcaabbcdbcdadbbdcbcdbcbddbbccdadadaadbdbdcaddcdcdabadbdbcccbbbbcaadbbbdcbcbadbdaabbdcaacbdcdaccdbccaabbcbacdbaccccbbbdaabacabdddbabcdcaccccdbdabaddaababdacaaccdaacdbcccbcaacddddacdbddccadcdcbcdcaadbcdaadbcbbabdbccdccacbbaaccdcabdabccbadcdbacadbbbccdbdabdbbdbacaacdcdcbddbcdabbdbddbbbdaacbdaaacdabbbabdbccddccbaadccbdbadbcdcdcdabdbabcccbdcdbcccdbbdcdddcabbccdbbacdccbbabbbdccaacadadbadddddbcacdcbbddabcddcdcbcbbabdabacbadcbdacadaddcbdadacbddcacadbbabcccdcaabcaaadbacbacddbdabaccdadaccdaaaaabcbbddcadbdcacbbbacaaadacdcbabbadabddcbacccdcdcababbaddbabbadbccadaddacdcacadcddcabababcddabacaadacddaaadbbadccdbadababaabcaaccdddcbadbcdbbdabaabaaacdbddcccbbdcbaccaaddacddddddcbaadddbccadacbdcccdabbbcadababacdcbdbbccddbddacbdbbbbccccdacabcccadcaccaadbcbdcaccbcbaaddcdbdbccddbbabaaadadcdcccadacadccaaccbbbabadbbbdbdacbddcababcdacbbacddaabacbdcabbccacbcadabdbabbadcbabadcabdcdcaaabcbbbabbbbbcaabadadacbdddcddbadcbddcbbacbaadbbccacaabdddbbadbcdddcdcacbbcaacaaddbcbccbbddaaaaaadddaddcacaaabcaddbdbcacaadbcacaaadacdddbcbcbcadaacdadccabccccdaacadbcbbddadbabcbbcacbcdcaaddcbdcdcadcdcadcbcdbacbddcaabcdadabddadabdadcbabbaacccdbacdddddddddcbdabcddbcacbaddbdcddbdcbccdaddaaacaacacaaddaabbdddbaadccbbdadbacaaadcbacabaacadcdbddaabbdcdadbccaadccaddcabccbbacdaddcddbaccdbbcbcbcabddabbdccddccdcaaadaaaaccdacdcdadcacccccbcdccbadcbdbacdcbcdbcdcccbdbdcaaadcdaabbbacdacccbbdddabdbbccdbcabadabbacbabadcbcdaccddbdbabccdabadaaabaaccbdbccbdbabbdcacaadbddbcccdaddccadabdbabbbcccccabbccacabbcadbccdaccabaddcabadbcccdadacccbabdcaadcadaababcaacaadaccdcdccbaaddbbaadbdbbcdccabbbbcbaadadddadbcdccbddbccadccbccbdacbdbbcccacddccdacccbdbddccdaccdaabaccabdddddcbadccdbadabbbbabcdbdaddddaabdaaaabbcdaccdcdcadccbcbaaadcabbddccbadbbabdcbbdbccccdaabdbcaddaaddcacabbddacbdadcabbaabadbbbdbdddcbbbbddcabbdcccaabdabbdbacadacdabadacdcabaaadacbbacbbcdcccddddabdaadbcbabdbcaacccdcdabacdbcaddddccbdbcadbdccaadbccabacadacdbabccadaaabcccadbcbbdccdaaccababbcdbacbccccacdbaabdcdbbacbadcdcacdcdddcacaabbbcaacccccaabcbccbbccadaddaabddadbabccbcbddbacdaddccddbbcabccdcaadccdccccaddcacbdbcdbdadabdaaaadcbdaaabdaddbbcdaccbaccaddacbdbbbddddbcbdcbbbadbbbbddadaadadcaaabacdcdbbcbbcaaddcccbbccaaacdddbaaaaaaddaaabcbaaabdcadccbdcddcbbdacaacaacdaaaaaadcbdacaacccbdcaacaaababadbccabccaaacdbacbdbddcbabccbaddccbaadccbaababadcabccacdabcdbdbbabbcdadcbddabcaababaacdabcbcdacdcccbbcaccbbaddccaabddbdbcdaabdbccbcaabacbdcadcdcbddaccdaccabccbcbccdabdcdacabdabcbacdcdacbdbabbacabadbbbcccdaacabadbaacbbbbaadcdcadaccbbbbadabccdbdbddcbdddcbbdbaaaddbdbcbadcabacbbcbaacbdbcdbabcadbabdccbcddbdcdabbbdbdabbcccacbdbbaabadabcddbbccacadcccbcbaacaacbcdbdaaabcaadacbccbddddadbbdccbdacacbdbbddcbbbcbbcbdbdbcddaddadbbcacddcccddddcbccbddcacbbabadcacaabbbadabbcccdcddcaabbabbcadcadcddbaccabadabaacdcaaddacaccdbbcacabbacccdcbdaaacdaacccbccaaabddcaccaaadacdacbbddddbbcbbdcdacdbcdacdccadcddccbccdbadaacaccdaacdcbaacabaabaaacbaaddadbbcbccdabbccadbcdaccbaaccadbacdbccdabccbaabbddddcbcbcacadcabbacdcddbacdcabcacaccdbbbcdaabbbbbbabaddbbdcbadabcabaaabcddbddaaaaccdaddbddaabbbdabbbcbcbbcdcbbadcbaaaaabaddbbadbcbbacabbdabbbadcbddbcddccababadabdcdccbabcbdcbabdbbdbbbaabbbdccdaadabcadaacaaadaddaacddbdaddaccabdcdccdbaaaabddbcdcbddaacbdbadabcdcabcacabbdaaabdcadbadccabdaaddaccadcbaaddabddbcbcbababadcccbcbccbaccdbbbcabdaaacaaabdabcddcabadcbbaaaabcddbaadcbcbcdaabadbcdbccddbcacbbddadabdbaabbaacbcacccbaabbabadbddbdbdcabcdbdcdabbdcbdabbbbdbcaccbccbccbadcdcbccaabaddccbabadacdddccbaddcaccbadcadcbdaabcdacdbbdddccccadddbaddbacbadcaacadabbbbbdcadbdccbbaabccddaccacaddabddbaddaacbddacadcabdbdaccabbbcabcdbacbabccabdbddbcaadadbddaacccdaaccbaccacbdbccccaacdabacdaacdabcbddbacacacabcddabdbbabdcdcdbaacbccabbdabacbcdbababcbdaadcbdadbbcbaacabcdcacacdbacbabbadbcabaccadadbacccbbbacdbabaabacabcbcdabaacdccbddcbbdddbcdbcccdadcddbadddbbbccaaaddbaddabdcdadbdcbbdaabcadbcbaabaddcbddcbdcdcadaccabaaacddaaadccaacbbdbacbbabbadbdabccbadabcdcaabbacbabbddabdcdcbddabddbbbadcacbbcaddddabbcbacbcbcabdbabccccacdbbaddaabcbcdbbbaacbbacabcbdcacbbdbbabdabdddbbbabadddacadcbcaabcaddabdccadbccbccdddaaaacacbabaacbddbdbbabbaccbddcaacabdbcacadbbbcccccbcdacdbaaadddddadddacbdabddccaabdbabcdaadbaaaccbddbcbcbddcbdbcdcbadbdcaabbacaacbbabcbcdadbdbacdadccccbbddbdadbccbadbdcddcaadbdbbabddaddcdbabcabbacadabcbcdcdaaddabccccbaadbbaccbcbacbddbadbdacadccccbddababcdadacacbaacaaadbaaabddaaabdcdacabdcdbcbbdbacdcabccabcdcdbccbbbadbbcbacccbdcbcadcddaacaabaacadbdcddcccabbdcaaaabcabcadbadccbcbcabcccbbdcacdccbdccabcdaaacacbcdbaabbdcbcbbabdcbdbbdccbbaaacdcacbcdcdabbbccabaccdadcccdbbbbdbbdddacccabdadbaccaccdcbabbbaaabdabcaadcbbccbdacabdbcccccbccadbbbdddcbcbcbbaabacbcadddbdbdddbaabbcaabadbcbadbcaabbdbcbbbcccdcbcbcabbbbdbcdcaaccacaddccbbdcaabbdbcdccdbbdccacadddbdbabacaacddbdabcbccdccbadbbaadacdabdcbbbdbabaddbacddcadbdacbadbaacdbacaacacdddacbbdabadcdbdadbaddbadbaadbaaabaabbaddbabddcdadacacdaadbddbdcbabdabccccbcccdaacdbaddabbcdcbacbacdabbcacbbccccacbdabadacaccadabbdcbbdaaacbabdbbbbdddcbadbcbabaabbadbaaddbabbdccbcabcaccdcdcdacbacbacbababadddddccbdcbcdbbaabacacaabdaddcbdaccacdbbdbcabbabaabcdbadcddccddadbdadcccddaabdcccadccbacadbdcddcaddbdcbabddacdcbccdbdcacaacacddccadbabbccdaddbdddacddcdddbcddbbcddbbacddaabcddabbbccdabbdcbdbdbcdcbdcbacbdcaccdbcddbdacdbabadcadcccbcdabacdbdaabbbadacadcdcddaadabbdccddadcabcadaddcaddcacbdaaadbdcdaddcdadbdbddbccddadbaccacdacabdadcadacbbdadaacadddbcaaabbbdcddacbdbbacbcccbadcdaadadcbacddadccbdcddcacabaaaccdbaabbbdcddddbccadbdbacaddccddbbdcabacbabccbcabdcaabbdccdddcbdbdacabaacaccbadbddbaccdadadadbcacadaadcdaaaddbdcadccbdcababddbaadbbcbaccbdcdddaabacdccdcdddcbaabdadaacbbbbadbabbbcccddaabbcbbbabacacddcacdabddcdddbdacaccddadbacbcdcadbabbcdddaccbaabcbaddabcdbaccdaadaaddacbcbdcbdaacbddcbcdcdcdbddbccabbbccbadacdbddcccdccabdcbbdacbccbdaaabdabacbdaaabdbbadacbdcabccabdcdbbcaaaddadddcdabdcbbbbacabcbddbaccdbbccddcbbbcccccccbccdcbbcbcadddcbcacaddcdddbdadcbaabbcdcaccbadbaccabbbbbaabdadbaacacddaddbbdddbdbbcdadcddcdbbaabaddadaccbaadadabbcbadadbabbaaacabaabbdcaadacbadbdddbaabdccaacbcaacaacdbbbccaadbdddbccbabbadbadaadadbcdcbabadccbadaaaaaddddcdaacaabddabddaadbbaadcbccdabbcdbbcccbaadaabddbbdabcbdcbbcbddadacbbddddbadbacbbdcbaccbaabdddaaddcdbbccbcdbdbddcddabbbcdadababcbbbdccdabdadbccbcddcdbdcacdbddabaccadaabaaabcdcdbadbcdcaacabaddbdbbddcbbccacabbcbbaccdbcdabacdbdccbddcadddacdddcbddbddbaadbcaacdbabcddcaddcadadbbabbbacdbdcbdbbdabaacbcadcdcdadccddbccbcaccbdaadbcbdcadabdcdddccbcbddbddabbcbdbdcacadbddacccdabadcabcaadabcacbccdabbdcaccdcddbbbbacddaaacaacadaaaabdcdccbbcbcbbcbdcaccdddcbaabaacdbcabddcbcdcbbbdcbcaccccdbcdbadabaaaabbcadabcbaaccdbabadacbbddabdabbbadddddabacbddcabbbbdacccadbbdbadacaabdaadcbaccacacbaababcbbbcabdbcbccbdcbbdddccdaddbdbbcdddadccbaabcdbbcacadbccbbbddadaacbcdaccadacbabcdbddcbadbdaabdcbdabdbabccbaacacbabaadccabdbccdccdcbbbbbcabdccbbdcbbccabacacacadaddcddbddcbcdbcaacdcbdababcbdaabdcbcbcccdddadadcbbabdcdcbdbddccbadddbdccbaabbaabcddbdaacdaaccaaadcbcaacdcbadcdadbaccdbcddbcdaddbccabbdcdcbbdabcdaabdccdbbcabdcbabaaaabbdccdaddcabbcdbabacdddacccbaddcadcdacdaccccccbaadbdccccdaaccdbbcdbbaaddbaacabaddcbddaaadcbacbcddaadcbbdcddccadadcabdccdbcbabacbddcacbdbddddabbabbbbbcbcdccdaadcddbbbacdaaaddbaddddbdadaccbbccacddaacacccaabcbcacbadcbbdcbdcbbcdcddaadbbacdaabacdacaadcacccbdcabcbdaacdcabcdbbdaabdadcdaadabcbcadcacbddddcadcadbcabdbdbadacddacadaaacdaabbdbdbaaccdbbacbdaddccbbacacadbbadaaadbaccababdbbbbdcbbdcbdadbccaaaddabcadadaadcadabbacccccbabaccdcadcdcacdcdcbaddccdadacccdacddaabcbcbbaccbbbaadcbbdadcddaacaaababbcddbddbddcddddcabaccdddadccacaaabcbbcdbcbdcdcbadddcdaacbcbbacddcbdacaaabaacabacbaacadbbadaadacdabdadbcbbbadacccabdadddcbbddbdbcbacddabcdbcdbbbdbdabdddbcdbcbcabbdddadbcbdbcaadddcbccbccadcbcddcaabbadcaacccabdcbbcaabbabbadcacddbabbcddbddcbdbaacadadabbccaacdabdbaadcdbabdcdbcdcdccddbcabdbacbdcacccbccdbcbabacbbbcdacdddccbabcbbcbcbbdbacaadbddbdddbadcbaabdbbacabbdddbaabdbcbbcbdccdddaaacaddacddbbaaacdbabddaabccdddacdbbbccbcdabdbacdbcaacbddacbaaadbbbaddcaadccbcccaadddcadcbcaabdccdaabdacddcbabbbaddbabaaaacabcaccaccbabdcbcbcdaabbdddcbaabacabdbdcbbbbddbaccbaadbddabcccbdabdbdbdbdbcddcbcadbabccbcbdadcdbbacbadacddbcdcbcdbacbccbbbbabbddaaccbbdddcacbbcdbaacdabcaadcabaaaaaabababbbdacacbadcacdcaadaabcacabcdbdccdcdddaabdbadacddabcbdcbcbcdbadcdaadacddbdcdcbbddddddbcbddaacccbaabddaddcadcdbcdcaccbcddadaabbcdaccccbdbbaababacdbcadabacbacbaacadbdbbcbcadacaddccabddcdcaddbcbadacdddcbadbbbadbabdabcdbacbdcddbbcdadcddbcbadacdcbcadbaaabdcbdbaabaddcdbcadccabcdbbccbcbaddadbcacabcccababcbacabccaaabaaabccbcdaaccdaaaaaacaacbcbabaccacadabbcccbbcabcbbacabccabacccccadcabaddcdcababdcdcdbdbcaacadaccbddbcdbaadbddcabadbdaaccbbbdbadadcabaaacadccbcddcdacaaaccbaaccbdbadcdbdbcadbdccdacccacbbcbaaccccbaabacbbcbbcdbaaaddbacbabbcaadcbcdadbdadadccdcbabbacbdcabdccaabbabcdbbbbdcdcadbacadbcadbbdadcaccaadcacacaaddcbbbadcddcaddacbddddcacacaaacbbabdcacdcbbcadccacbbadaddadddddaccabbbaacdabdbcddbdadacaabcabdabcbbcbbaaacbaaabcbaaaacccbababdbaccccacbaccddbbbadcbcabcacacabaccdbcbdcacbabdaddccaaacddccccdbcdddcadabbccdccbcacbacbadbcbbbccdaabadaddddadacaddbbdbcbbdcccdbcbcbacaccbbcabcdbcadaaacdccddcadadcabadcccccdaddbabaddbcdacaabcdcdbbdbdcabbddabaadadddbdbaabcddcbbaadaadbacdbbbbcaacababbdacbadccaadbababcbdbcdbddcaadcbbbbdbabcbbccbabdcadadaabcdaccbcdcadacbcbbdabadabdadcccaaacdaabaadcadabaaaabadddbdbbacbdabbabbbbcddaccadbbbadbdaddbcadccbbddbdddbcbdcbbabadbbbbadbccccaccacddaacacccbdabcbcccdabacdababcacbaddacdcaaaadaadbadbacbacbadaddcbccccaddabbabdddbccacadaccddcdcbcbbbbbbaabbdbbacdcbabadcddcadbdabadadacabccadbdabdcacdbcacabdadabcddacabcddcddddbbaacaddacacbadacdbbcaabbdaabbcaaddabdadabbcbaadabdabacdbabacbabbcdaadcababcbcdaadbacdbbdcbcadbadcaabddbabacbbabbadcbacacadbbdadcbccdddaadadacabbdacbabcaccbaacbdcbbdbadcbdcdddcaddadddcbdaabcbaabcaaabcabbabdcabbbbbabdddbcbdabccdddbdacddcdcdcdbbccbdddcdddcdcdbbbcacababdcccabcaadadacbbaabdbbadcbcbbddcbadbccdbdadcaaacdaaccbbdbbdddbbabdcdddddababcbbaddadddbbdbdacdbabbcdddaaccccbaccbdddadbacabadcdcacdabdcddddaadcdbdcaacdacdacddcbcdcdaccdbdbcddbbbbcaacdacaddccbabcadbbbcbccbcdcdccaddbaccbbaddbbaccabacdcccacadccacadaacbcdacacaaadacbaaccacabcdcccdcbbadacaaaaaabcaacdbdbabdddccbaaaccaabdadabcdabbaadbddabbcabdcdabcacdcdcdaaadbadbbcaccdccbadcbaddabdcbbdddbbabcdbbdabacccccabababcccbaadacacbcacacadddcbacdbaacadbdabbbcdacabdccbbadbdacaabbdaccddbccadadabbcaddabbdcdaadcbbbbadabdccccbddcacddabdcbabbaddccaacaadcdcdcdbcdcdbcdacccabacddbcacadddbbabbcbddccccbabcdaaccdadbdadbaadcaaacdbdbcadaccaaccbcbcbccadddaabacbadbcdbbcacabbdbccccbddcdccdabacaaccaadccbcbbcacabbaccadbdddacbcbdccbbaadbbabddcdddabbdcaabbdddabadcadadbacdbdcccdadbdcdbcdbcbacbaccacbabcaadcdbabcbbdddbbaccdbabbbcbbccbaccabdbcacdcbccacaddcdcaaadbdddddccddbbbacbcababcacdbcdadacccbabadbbdbdacdcaaadadbccaccccccbcadabdaccabbaadacdbbccbcbbcabacacabdcbbdbdcabcaabdbaccdddabcadbbccddcabdddcbdcccbadbbcdcbcbbbaddcdbbddadddbdcaddcdcabdbabddacccdddadabbdabdbdddacbdadaadbdbaddbdcddaccabbdbaaccadcbabcbcbddadbadaddabcbaddaadbcdbacaaccbcaabdcdbdaacacabaadbcadbcdaadaaccbbcdbdbcbbdbbddadcdccdcbbccbbabbacccbaadbabdabdbdddccccabdacdddabaddadcddbbbaacdbddbccddcccdbcbdcbbbbdbddbdbadbbcbabaadacdacaacbcdadbdacabdcdbabbacaadddaccbdbccdbabccdabbcaaccbdcdcacabbdcdddabdcbbccccdbdcaaddcbbcccccbddacaddcbadaaddbcdacdcabcaccdbbdcdcbdacbadcbbcabaaddbbdccccccbcdadcbadaaabdbacbaddaaacaccabcadbbbabaccbacbccacadbdbbacccbcabdacdcdddbccbbbdbaccaabcdcbbaabdcbcbdbdccadacaacbcabdbbbacbbdccddbcbadadabdabdbccdbcdbcadbaabadbaaccdcabbbddcbbcadbcbacacacabccbbdddacdddcbcacadbcbccdbcabbaabdbadcabcdddddbaccbdbcbaccbddcbbcdbbdcbddbbaadabdaadddddacaadcbcdddcdcbdddddbdbbdacbaddbbbccdccbbcbbcccddbccaababddadbdbddcdbadcbacbcbadcbbddbbbdabbdbdabbcccaccbaccdadacbadccbacabacaaadbbdbbcaacdabbaaccdbdbbaadcadaababadcadadacdccbacbbabdccaddccbadabbcdbaaabadddcdcdcdccbbaaabcaabaccaaddbdccdacadcbcccbcadabadcdcdcadbddbbdbbcaccdbcdaadcdadabddcdcdbadcabcadbcbaccdabdcdbadccacadbddadcddabacbddbdaddcbdadacbbbbddaacbaabdadacdbccddbaccbadcaddbcdbcabbccccaaacdcaabdbabacbacccabdababbdcddaccdbbadaaccaabbdcbbbddbabdacaacddabaddccbbcabcbcdaaaabcaddbbbaacbcacdccdcaddddcdbbbaddadbabababdbaabbcbabcadbbacbccbcdddbbccabbbaaadabbacaddccbbadcdccddddbbddbcbaabcddccdbdcddcbabacbddbaccacbabaaacbadbbcdbdacacacbbdaaadadccbcccbcdccaddaababcdabcdacbbbdbdabcbdabbadbddbcacddadcadabadddcbdaabcdaacdcaabaccadbbaaaadcccaadaddadadbacddccbdbcbaaccbdcadbbbccaacaccdadadcbbcadaddcbdcabdaccadabcacadccbddcadbbbabdbbacdbbacbcabbdcadabddbcddacccddcdadbdbdddbddbbcadaaacddacadaaaccbbccabbdaaabbccbcacbccccaccbddcdadaacbaaabaddcadbadcbccacbababacbddbbddcbbdbbddcbbdaccdcbcdcbdabdcdbcbbaaadbcdcbdcbcadacacacaacadddbbbacbaccddbaaddabdddadbadbaccabbdadaabcccbdcccddaacbadabbbbbacacdcdcbaaccaacdbbcbcdbacbcadaccddddccacdaaadcbccaaacdcacdbbabcabdbdcdccbdaccbaddddabbaccccadbdabaacdbdbdacbccdcbacabdcddbacbdbbaccaccdbbbcdbacbdbbbaaacdbcbdcdbcbbabbdbcaaccababddbbcbcdacabddaaadccabdabacbdbdddccbcaacbaaaddcabaadaddadcdcaacdacadbaddbaababccdbdcdaaabcdacbccdbaaacbdaddcdcaadbabbadabdacdbbaaaccccbccadddcaabcabdbaddadbdbabdaddddbcbdabcaccdbbacdabaaacbdddadbdcccabbdbcdacbdcacdadababcaacddaddbabbabccbaddcadbbcddbacbbcbabcdddaacdbddcabcddbaaccdcaacbdccccbabccadbaccbbbdbbcbbbddcbdccdbbacacaadaacacddddbacbaabbbcdbddbcbdadccdbacbbaadadcbdcdbbadaacabccaddcbddaccdccbbcdcccccadcbcbccdcdbcacadacdacbbabaddcabadcbabcccccadbbacdaaabbcbabaaadcdbcdbcaddbabdbadbbadcabddadacbcadbdbaacdccabcbadbcbbbdbccbaadbcaacaabdadcdbcdabdbadbbbaabdcddcbbaddcddcdacabdbcdccccababdcdbaaccbabdcdbacdcdddadabbdccdbdacdbaddcaacddbcaaadcddbbddadbcccadbbccbacacbddbbaddadcbbdacaddcacbdbbbacaaabaabddbbdcaccabbbbccbdccbcbdddbdcbddaaccdabcababcdadabaacdacdaddadbbcddaaadcbcbdbbacdacabaaacaacbabbbddbdaadcdccaccdadbcbbcadccbdacbaabbdcacbcdcbaadbdbbdaabccdaaabdadcdbbbdcabaacdcbcdadbdcdabaadccacbbaaaacdadddbaaaabcdccddbccbaabcccbbbdddccbacccbbccacbdcabbcabddbddcccdcabccbbacaabadabbbcdcbcaabdaccdaaacbbcbcccbccdacadadbcbbcdadcbccbdcdbcbcacdbdcbdcaccaaaabccaccddbdbacddcdcabcaadcbdcacabbbbabcdbbabccdcababbddcbbbdbbcbcadbcccacadbbcdcaccabbaadbccbcadaddbaaabcabbbcdcbcbbadcdaabccdcdbcccdbbccaabbddacaaaacbccddbddcbbbcbccddcbaadddcdaaddcbbbdcbbcacabddcaabbcdcdaaaaabcbcaacacccbdaabbbbccabccdbbddddbdaadadcccabbadbcccdcabddcbbbabccdbadcbadacccacadcababacaacbdcadcbdbcabaccbbabacdbbdcbcbdcdbdbdbcdabbdbbbdcbcddbbcddaaacddddbacddaacacabbcbacabcbccbaccadcbaadcbabdccbaabcdccabddbabccacdbbccaadbdbddaabbbbaacbaadcabddaccbbddadcbbaccdabadcdddaadaadbcbcbbcdaccacabadcdabdcacbddacbaaabcbcacbbddbcbcacbdbcaaccddbcabacdaacadbbdaccbdddabccbdcdcadcdaccbcdaaacbbbccdbaabddddadcbcbaaadaabadabbadcabcadaddbacbcddcbdcadbdacccbcbcbaccabbcadbadcbddbcabaabcadaaddcdabbabcdaaadaadaadbbbbcbbdbbdcddbddddcdbbbbbbbaddddadcadabbbbcbdbbcbcadddaacdbdccddaaaaacbbcccdbccbcccacdcaddcaddbdcabbabccdacabdacaacabdcccbbdadababccdbabcdbdbabdadadcbbbcdacddbcbcdcbaddddabcabababbbcdcbccdcbdbcabccbadccbdccacaddacbdadaddbddaddbbddbabbbddbcbccccdbbbaadabbcabdcbcaabdbcadcdddaddbdacacdbccddbadbbbbabcacdbaabdababbbccddacdcdadbbbdbcbdcbacdaadaadcdcbadaacbaabbdcbacdabcbdacdddccbbcacabdabbcbbdbdcdadabbdadaaadcdbcdadccbacdbaaabdbacdcdabbabdaacccdcdbcbbcdbcccddddbbaabbbadbdadccdbabcbcbdbddbccaccddddadbbbddbdcccbddbbbddadbbaaaabbdcddbaccbcdbbddadaccdaabcbaccdaacbadcdcaddbbbbbdcccbdabaaddcddccccdbdbccabaddbccbaacdbccbacadaccacaccbbdddcdacbacbcdcacbbdbcddaacbbbbdccadcabcdbbcaacadacacdaacbddcadbddabcbaccabbabaddacbaaadbbaddcccabcdacadacdbbacbcbacdbcdacbdccbdacaacbdabacbbabdbdcdabdbbabdbdcabaddabdddbadbaabbcabdcbbdddcaabddadacbabcabdbccbbdddbbabbccdbccdcbcadaadbcdcccbabaccbccdddaacddbcdaddaddaadabbcccbdabcdacdddcaaabacadacdcadabcdcbddbcacbdaccbaadcadccdaaaacbabddbacdadcccaddcdabbdddbbcbabcdddcbccdcacbaadcdbaaddcdbccabadddcbbccaccaabababccdcddaccdbbcabbbaacddbcbadccabcddbdbdbccbcaccccccadbbacccdaddabbdadadcadacacdabcbddbbaadbcadbdaaaacccdacdbbbccccabddabddabacccdcadbbcbbddbcaccaabcbabbcbdddddbcbddaabddabdbdbbaccccaabdaacbcacaabaadaadcbddacacaddbbbabdccbbbadddaabdbadacbacbbbacbdbbcadaabbababbdccccbbabddddcbacaadcdbbbbcdacdadcdddcbbdbddbddddbacccdcabcaccdbccabbbdbadbdcdaacccdcdacacacaaacdcbccdccdaacdcacaaacccbcbbdacaacbccabaadcbbabcbaadbcbcdbbbbdccbdbbacadadaaacaabdbccbaabacdccdabbaaabbdbcbdcdcaacadadbdbbdbacacdacdcbaaaaaddccbcbbccaddcccadddcddbcbaaadbbcaccaadbcbcbcadabaaacbdaccbccbbdabaaddadadcbdbacaccaaccaabbcbacddccbaabccbaabadadbcadbababdcaaaaccdbaabccddbbdadabdcadaaaadbccdbadacaacabadaddaadaabbdcababcdddbcdabdcbadbadaddcadcbaadadaccadcbdbdabdcadbddbcaddddabbbabadcdbaccaabbbccaddaddcadcdbcabbbbaadbbaaacdccbcdcdbbaccdadcddabacccddbabdbddccdcaabbdcdbdcabbaaabadabbaadcbabdbbddadababcbbaccbcdcabbcdacdabdbabddcabacccbcadbccbcbbcbadaabaaaacdbccadaadcdcbdcccdddbacbcbcbdcdccccadddadcabaccbbdadcdddcbaadcccaabccaadbcccdbbcacbcaacaaccaddccbabcbacdbbbddccaaaabbdddcddccdcadcdbbdababbaacddaadaabcabbabdcbbdbccadbcabbcbdabadadcddaabbdddbadbddcbdacbdbacdbcdcadccacdaccbbaccaccaddcdadcdacdacdbaabcccbbdddcaabdcdcabcbdacddbcaaadbbbaccdaacddcabbbadcabdddadcaccdbccbccaccaacacbbdbaaadddccbaadaadaabdddabadcdcddcbacdbdcbdabbaddcbdccbdacdadddcddbbbdcdcdaadbcbdbcbdcbcadadcaacbdbbdbdaadbdaabaccababdaddbcbabbccccbdaaadaccabdccdbdcdbaaaabacbabcaaccccdaccccdbbaddcbdabaabcabbbbcddadbbdadabcabbcacbcdbbabbabbcbcdcdcdcddccdbbdbadbbbabbdddcdbdaccaaaaaadbcdcccbaadbabaccaddcaabdddbdaaacbbbcaaccbccaaacdcdbbbddddadbbdcbdbaaccbdbaacbbddcdbdaacacdcacaddaacbcbabddabcbaccacbababdbadccdbddcbdabcdbcacaabcdbcddbbaababcbaaadcbcbcacdaabccccbdddadacadaccdaddcdbcaddccdddbdacbccbdccadcaabcbdabadaddbbddbacbdbabbccabccdbdbdabaacdbccdabbbcacbdcbcadbbabcabddaacabddddbdabaddbbcdaabcbbdcaccbdaadcadabacbbddbcadbccbbcdacdbdabcddcbabcaddbadaddacaaaabdcbabdbadcdbbbbbbbcdaabcaddababbdbbcbcbacabdcbdbbcaacacbabbbcabacdbddbcadbcccdbdacbbdbddbccadccabdcbcaacdaabcdccdacddcacaaabadcabcbcdbccbbcacccacbdcaabaaadacdaabcbcdabaabbadccdadccabdcddbdbddaabbddaddadabbdcccadddbdbddbdbacbbbbddacccabbcabaaccdcbbcbbacccbabbabdcdcdddddbbcddcbdaddccaaaabdcdcdcadabcbbccbbdadacbdcbcbdbbbbdcaababaaccacddaccbccaddcbddbddbcbbabcbbcbcdbcbdccbdcabdcccbdbdcdaddbaababbdbdabbaddbdacacccabbcbabdbaddccbdcbbadabbcaabadbdbbbbabcacabacabdcddbccbadbdcbcccbcdbddaacdbdadbcccadadddabcaacaacdabdbaadbdcbbbacbacabadabcbadadbababcdcdccacdcaacdadbbadbcbddaabbdbcadadcbbdcdaabacacbabaddbadcadcabdaadcdabdddabadbbccdababcdaabbbdcccccbbbabdcbacabdbddddbcddadbbabbdccacddbaacdaacaadacbcdaacdabbbdcabaaadacacbcabcdbdbddbdbaabbdbcabbbddcaabbdaabcdacacdaaacdcddbdaccbdacbbacbbdaadabdacccbbcbacadbccacbabdbcddcdbbddbadddbbcbdcddccaccabcccdaacbabddcabacdacdbddbddaddaaddbdbadccccbdbaddaddcdbcdcaaccadaacabcbdacccccdabbdcbbabbbdbddababbcdccccabbdabaaaddcdcbcaaabdccaaabdcacbcbabbaaacbbacbbdaabbbbcaadccdccbbbdbaabbccacccdaadbbabcdadddccadddaddbbadddcddbaddbaadcdaacdabccacdaacccdcbabcadacaacccacadacadacaaaadcbaabcccbbaaadcabbdaddccaacdbddaabacddbdddababadcbdbacbbbaacdbbcbbabcbdddcacaabbadcacacacddcaddacdbaaabcdcbbaaabdacadbccbbdbadcdacccddcbcdbbddacbbddaddbaabdddabbadbabcbaaddaabacadbaaabadcbaabcdabaabdddbbddbcbdcdaacacadababdcadbdcabbccddadaabdadbbccdaacaacacbbadccccbaddccacaadbccaddbbbdadbaababcdaadcdcacadbdcddcabccdbbcdaaadaadcbbaccbacccbddaacdaaadcacbcddbacacdccacbbdbccaacddbcdbdbbbcddccddcdadcaccddbbdacacddbacdddaddaddacaacbadadbdbbcdaddbacccadbdabcbabbdbaabdbbccadbaccbdaccccacabcdabccbbcbcadaddaddddabadbddabadacadcdcbadbadcdbbbcbaddaacaddbcaacccadaacdadcabadadcbdcdcdbaaddbbacadcaccaadccaddacccbabbabdbdadccbbcaabbdaaddcbdacdabbcbbbabcadaacbdadbdcbdbdcbcccdaaabaaabdccbabcaaddbcdadbbbcdaccaacdcccbbcaabdbdbbdbaaacaaadcccaddabcbddcddcbbadaaababbdbacdabacabbdbcbdadbbdcaccacdbcaacadcbcccdbdcddacbbcadcadddacaadbcbcbacbaacadcccdcccaabcddadcbcadccccadaddcdbadabdcacccababddaddbddcbdbadbddbcbbdbdbcccaadacddddbccdbbacaaabdbbacabbccdaacddcbabcaccbdaddccddbcabdcdabdcaabdbcbbccddbbaaabcbacdbddbdccdacdabbcadadbcdbccaaaacacdbcbbaacacbcbdbdadbadcbcbbdabdccbbabadcacdcdacaccbdbdcdbbcbadcaddbaaccbdbabacabdbdadbbdaddadacadadccacacdaddabdccbcadbcdbabbddccdbdcaccabdbbccacdcbabdbbaaccccddbdccbdabddcbabcccbadaabbcbbbabcadbddababbcacdcbaacbadcdcddbbdcadcbdcbdacdcddcacbdbbccdbdadbaccbcabbadcadaaabddcadcddbdaadcbccbbbbcccdbbbdbdcccacdcaaaabcbcdddbdaddbbcadcdaaddcbcdddcdccccbaddbcbcddddddbdcbdbbcabbdadccdacdbaddbcadadbcaadbbcbaacbadbcadccddbbabcddacbccabacadbdddbddadcabcdbdacddabbccdcaccdaaacadadcbacacbdddcbcbbddcadbdbddddbbbcacbcddabcbddbabdbcaadcdacadbcdaadcdbbaaadcdbcbaacccbaddaccbabdbbaccdcaaadadabbaccdbddbacdddbdbabacbbdbbcdbcadddabccdacacadabdcbbdcacbcdccdbaccbbadaadabdccababdddacaabbdaacacababbcdccbabdcbcbcbcbdbdabacbadbbbddaabbbdabbabacdbbbadbbaabadbabacdddcadcccccdadcdccbadbbacbbadbacdcabacadbcaddccbadcccaabdabcbcbcacdbbdaddbcdcbaccadccabdadabddcdbaddccbdbccddcdcddbdbdcdcdadbadbadbbbbbcddabcbdbaabbabaadcddabcbdadadaccddbcacbdddaccababdcccbdacbabcbcbdaaddbbdcabdcddcddbbddcbccbcaaacbdddcadbccaaddbcbadccccbdaadcdbcbabdcbabccaccbbacbccdcaccaccabccadcbaabccbdbcdbaadabcbacbcbdaadcaaabcccacadabccaacacdcddbbbadabdbbbaaaccdacaaaacbcacdcbbcbbbabbdddbbbabdbcaddcddbbccddbadabdbdbbaacaaddbadabdadbbbcbadaccdbbdccaccabcbbbacbbdddabdcbdbcbbacdaddcbaccccbbcbadaaadbccbaabaadacabcddbacbbbdbcaaacbcbbaddbbdbbdccdaacdadacaaabcdaadbaabddbcbdbdaccccdcdbadabdbbcaddcabcabaacaacbbcabdccbaddbdaacbccabdbdaddadbbdccbdabbcaacbacaacacdddadcbbadaaddccbcacababccdcadabbaacaccdcaabacdcadbdcbaabcccbdbcdabadbababdacacdcccbadabbacbacdacaccbcbcaaaddbdccadcbdcbdbbbabdcaaadbccbddaccdacdcdbccdccbaddbdbcacabaacbadbcbccabcadbacbdcdbbbbaaadcaaccadccabdbccbbddcacbcdddbadcccdbbcdcbbbbdbbcbdabcaaddaabcbacdabbdcaddcaababcccdbbcbadaccdcadaaabddbdadadaaaccadbcadabbcaccadaadddcaddccdccacbaabcabbbcdcdbcbdbdbbcaddddccdacbaccadacdabbcdadaccddacbbaaccbcdccdadbdaddcabdbbadbddbbdcacbabadbdcdbaddbddacabaadcbacabdadcdcbbcccbbabbcbaccbdbccadcbdcbaabcbdabddaabdbbbdbcadbdaaadbcccaccbbbdbacbabcadaacaabdcccbdabcbdcddbddcacabaaadbadbbbabdbaacbbdbdbbabcaadacdcbccddcaaababdabcbaddacbacbdcbdacadcccdacbbcaabaccaaaaaddcccaadccbaaabddaccabbdbacbcbbdacbacddaacbaaddbabbdbbabccbbadcbdadabbcadcaacbaabbcabcdbacbddbcacbabccccacddcdccdcdbddbccbccbbbdadbcbccacabdadaaaadabdbbbadbaabdddcaddcbbdbbbbddcacbbcdbabbacdabddcdacadbddcddbdcaababbaccccdaadcddaaaabababdbbcddbbabacabdbacbdacbcaacbbcaababcddacbaccbcbbdadbadaaacbdbbbadaacdbcdabcddbaadabdcccabddcdbdacdbcabdaabdccaacdacabbdbdabbcadaaabdbdbccdbcbccadbbaadaccbdddccdbddbcabcdaccbcadcaabcbccdadadabddccbcbbcaaabcacbdcdbcaaaabcbbdbbbabccdddbbddcbdcbbbcadabcdccccdaadbcdadabdabbbacccbaacacdabaaacccabbbdbbdabaacccacdbcdacaccadacdaababbbdbacbaccddddabdddcabdcadbacacbbbdabdbbabcccdcaaccaabbccacbabbdcbbbadcbbaaacadabcacdbcbacaadbddaacbcababddaacdddccaddaddcbcaaccbdaccbaddcabdaddaaccacdccbcdcdbcadbcdddbadabbadacddddaaacabcbabdabaccadcaabbcadcdaabaadcacaaaabdcdbcdddcdcabacccbacdcdccaabacdabdbcdabdcadbabcdaabccccaabddbdadabddacccbdadaadaddbadcccaddbdadcdacaabbddddabcccbbacaaaccbdaadcdbccbcddcbacdbccdadcbadbcccbdcbaaabdadcadddcdbbdbbababdddacbadaadabcdbcdbdaddacddadbbbcaababddabcbdbcdcdddbabdbdcccbccabaaddbddcabcdacbadbcbddacbcaaddbcbcddbcdadababcbbaabadddbddddbadadbbdacccacaccabadaadccaccbcdcdbdcddbbbbdddbbabcdbdaabbaaadccbcddaaabaabdbbbabbdbadbdbcacbdacccdccdaaaacdbdadcbccbcaaddcdabbddadcbbccabbbbbcaddbadddcdbcdcdaccbcacbcdcbacacbadcabbdcdcdddabcaacbbcbadccdcddbccbdcabbdadcadcccdaddbdcdabbcdabadddabacdacddbabdbddccdcadbccdccccacddacabacacdcdbcbddbcdadcbabddbbccdbcdcdabcacadddcbdbcbcccbddcccaacdcadcbdcaaabdadbabbaccbabcdcdacacdaacaacacbdcdabcaabcacbdcccacccbdaccdcbbdcabcdbcbacdaacadaabcadacbbbbbdcccaaadbbbcbabdcaddaacbadbbdacccdbcabbadcbdaddacaaabccacccacabcdcbccddaddadbcdaddcdaabbdcbabaddccaacabcbbdcbbbcbadddddaaadbadddbcaaddcacadbabcdaccddaacadcddbaadbacddcdcadadacdaadccbddacdcbbaabbbabbaccccabdadaaddabdcaadbccbaacdccddccaadcbdccbdbadddaadcadcaadabccdcbbacdccbdbddcbcacbdcabbbacababbbdbabcdbbadbbababcadbdcbdcbccabadbdcdbbbabdcbcbbbdbbabdcdcccaccbdadaababdadcacdcddaacbcbdbbbcadccacbaadcdaacdddbcdcbabbdcbaccbbbdcadbbbdbdcbccabaaaccabdacdaaddbabbddbdcacabdbddabddccdccacabcddaacccdcbcbcdddabaaacddbcdccadcabbdcaabadaaabdacacdaabbbbcaddcddcbdccbdccabadbcbdacdadbcdbccdadaddddacccccacdbddbcdcadaaacccbacccbdacbbbacbbddcddbacaddaaabdbccbccaddcbbaaacbbbaaaacaaddbcbbadcbabadcdbcbccdbcccccccdbaadcdbbdcbbbdcdadacdaccdbbbcbccadcdbdcbbdabdabbcbdadbaaaddacdaddbcdaaddcdccbbdacdccbaabddcddbcdbbaaccadacbabbccbddadcddaaaccadcdaadcbcbcddaacddddbabdccaaddbbbadacccdbbcdbaccbacacbaabcaabcdaabbabcddacbbadacccbdddcaadccdaacbacadabccdddcaaaccbcbbccdccaaddcabadcaaabbdccbcbcccddabccacbadcdcacbbdadccdbbbdcacaaaccbccadbcbaccbadcadbabcdccdabdcbbdbbbddcacacdbaabbcacbacabbbbabaacbdbdadbabbcabcdbcbaaccccddcbadbbccdcdbabdbbcabaacadadabaadcbbdcabcdcabaacbaababdcbddbcbbbabcbcadaddabbbdbdbaccdbbdabaaabdcbbcccdbadbcbdbcbccbaadcbccbaccbdcabbcbdbdbbabbdbcacabababcbbaacbadabdabdabadbadbcdcaabbbbcadacdcccdcccdcacabbdaddbdcdcdadcdacbddccccdadbaccdbddaabaaccbbabbaccbbccaacdaacddbcddbacdbdabcbbbdbbabadbabababbcccabdacdadabddccaccddaaadccbcbcbbadbbcbbbccabadccbcbbabbbbbdaddabbbbabbaacbbcdbbcaabdbdbdddbaabbbaccaddcadcaaadcdaabcbdbbabdacacbcbcaabaccaccdbdbcddcaaadaadabdcdcaccaaadaaaadcabdccddaccdcbdbcdbcbbccbaadcbdcbabbcdddabaddbdcddbaabcdaabcdccaaaabdcabcbccdbdcdbccacbaddaccdbadababccbbabaadaabbddcaabcccbbbbbcccacbdbbadcabcdbcadbbdbdadcacaabcbabacdbaabcbcbbaabacdbbadcddabacabcbcddaabbbddbadcbcaddbaaddadbacbbadbdddabdcaddccbbaddbcadcdbbdaccacabdccccddcabacdadadccccaacbccacabccdbacadbcaddcbbcdabcccbdcaaabdadaabddcabbbaacaccacabbdbdbdadbbcbaaadaaacbcdabdaccdddabccbbcbdcdacbbddcccddccaccbadcdbcdaadcdacbbbcacbdccbadbdabdbcacacbcddaabbdbacadbacddccdaccbdddaadaabaaacbddaaccbddbadcaddcaacdddcdcbdcaaddbdcccbcbacdccbcbccbcbacabcbdddabaddaacdcdbcabcbabbdaccbaadcccbdbacacbadaacadcabccacdacaaabaabacaaadabbcccadcdbabacdcddcddaabcdbbddddbcbccdaaadacdacabdabdbacccaadabaacdabcbabaaaccbaddddcbbdbcaaadddaddbbadccbadacaaaddacccaaaaddcddbdbcadcadcbabbdadccccdcbcdcdbaaccdbbbcabbddddcabaccabacddbdbdbbacaadbbdcacaacccadaddccadddbcbcaacdbcaadccabcbddcbbddcaacaaababcbabdcdccccadacdaddcbadbddccabacbbcdbabcaadbacdccbbcbabbbbddabcacaabacaadbbbddaacdccdaddcbddccdcabdbbdacabbcaacbaaacccbccaddddaacbaaccbbccbdcabdaaacaabdaddddcbcdbbbcbacadbaccaaabbbddbacadbacadcaaddacbdcbabdaddababaacbdddadacadcdbbabcbcadabdbcdbcbabaddccacbbdabaaccbacbdcacabbccdcbbabcbdaccdbcbaaabccaaabdcbdacbdddaccdbaccacabbdadaddbddbadddbbbbdaaacaabbcbacdddabbabdddcdbdbdadbbccdddbccdbbbdadacadccbaaacbbcbababdbcbadbacdbabdcdbaccaacbbbbacaaabbadbbbdaaaadabddcbbadbcddcbabccadcacacdcbccadaccbbcbdccdbcabacbdddbcacbacabbbdbaaabcdacbdadbadaaacdccdddcabbbcdbadadbddbbbcbaccbaddbcdaadbbbdacdcabbabddbabbacdbcdadcbccccdcccbcaabbaacdbcadcbabbaadabddcadccbdccdbbabdbcdaadbacddaabbddbacaaadaadacaaadccbdbdabcaaaaaaabadacbcdccdaabdcacccbbcbccdaccabdabacdacadcccddadbddbcaccbacabbcacbdacdcbbbbbbbdbdaaabbdcbbbbbadcdbdabcdbdbadbdbbcbacbbbdadabddacbccbbabbdcacaadbbbcccaabdababdcaadbccaccbabcadcbdcbddaccacdabcbacccbdbddbcbbcaabbadabcdcccabaacbdaabbdddbddaddbacdccbadccaacbcaacdbdaaccdcdaaacdadadcabbddcadddaabaacaaabccddbbcadbacccadabdaddbccdbbddaddbaababcaacbcaacbcccdcabdbdacabcdccbccdbbbbdbdcbabddddcbaccbccbdcbdccaacaadddccbccdbadabcabaccbcddacaaddddddadcdddcabdcbaaadbbdbbcadddacccdbbaacdbccacbabcdabcaadacaabdcbcbacccacadbaddbddacaadcaaccadbbcddaaaadaccbcbdbbdcdacabacbacacccadcbcbacbcbcbcddcaacbabcbcdadbcdcbadadbacccabccdcbbbccdaabacaddddabbadadabdccabcddcdcaadcdbaaabdbcdddbaccadbbbaaaadaaacdcccccddadacabaddccadcdbdadcccdabacdddddacdacdaaaacccdabdaadcbcdccbbabadcdadabacbcdcddbcccdadcbaabcacbdabbbadbabaacaadbbacccdddddbaadbcddaaacccdcbbdaacbbddabcdddadadcddcdbdcbacacbaabbcbaacddabccabbbdacacdcaddcdcabdcbabbcccbbccdabaccdbabddbcbdcccdbdcaacacdcbbabdddaabaddaccddbcbcbaaaaaabbcdcaadbbdabacdaadabcddbdaccacdaaaacdbcccabaadacadddaacacaabcddccdddddcddacbadbccdbabdbcbaaabdabccbdadbadaadabcdcbcdabcccdcbdcbadccdbdbaaabacbaadbdbbcbbdccaabaaadcabcbbacdcdbbdacdcaccdbcbacabcdcabdacdccacdadbcabaccaadccdcadcaddcbabaadaccbcadddaabaadcddcbdddabcbacdccaacddcdaaacaabdcdadcdbabbabbdabdaccacbdbaccbbbbbbbdcbdaaadccbabcacdddccdbaccdccdadbabacdcacccabcdcdbbcadddcbbbdbdcdcbccbdabcadcdadbbacabddcaabbbcbabaabbdadbcdcbbbbcbbcccccdddbaccadbbadacbccdcbabbdbddccdcabddccbbadcaccdcabacbbbcdacaabdcaaaccddbcdabacdccdcdaaacbcdcadcadddbaaaccaadcccadccacbbaaaadbdcababdaadbbcdababbabccbbaccabbdbbcdadabddccdbadcbbbbabdbcabaccbacccbacdbdbbcbcacadacbaaadabaabbccababbbcabaccccbbdbbbdacddccadcbcdccabbcbcdacdacabcabaaaaddddddbcdcdacaccbccbcccdbababdcdccccaadcbcdbacabbdbcddacaadbccccbadacadcbacbddadcbdbaaabdbdccdabdcabaaabbdbabadaddadbddbdccabcdcbdddbabbbacdcddaaccbdbcbbbdbcbabcaadcddadabccccadcabcaaaadaacddcbaaacacaaddaccaaacbbcbbcbdcabadbadacabacddbaaabbacbbbdbccaabdabaddbabbabbbcddcccdaaacabdbbdabdddcbcdddbabbdcddadcdddaddccacbbdbcbcccaaccbacabdcacadcacbbcbcaacbbdcbdcbbcadcbaccccccdddcdccdacbcacbccbbadcdbbaabccdcabddccbbddacdaddbddbacabbaabacadbcddcdbcccbcacdacabbadacdcdbadabcaddcbcddaaadcaaddccbdcbbddabccbbaccaabdcddcaaccaacacacaaaacdacdcdaaabdaddcdcbcdbddcaccaccbbcbbcbbbcbbdccdadaabdcbbdaccbdcbaadcabacabbdcaadcbbabcbcadaddcdccaaddbdccbdddbacbacabadabbdadadccabdccbdcaaaadcbabdaadcbcacaaddbbdcabbccccdabccbacaadcdcbbdaadccacacbbcccbbacbcddbdabaddcbcadcbdddcdbbbcdcdadccbdbdddacccbcbbaaccbdadcaaccbaddcddabcdaddccaadbacccabacaccbdcabbdbcadcaaacddcdaccccaaabadcccbadcbdadadaacccabdcbcaabacdadddcdaaaacdaaababcdadcdbbbdacaccbcbcdcacbaaabcbcdcaccccaacbdcaddaaabddbacdaadcbbbdcbcabacdbbacbbadccaccbccdaabcbbabbaaaaaccdcaccddbacccadbdbdadbbdbcbbbdaabcbcbabddabbbbadcbbdbaabbaccbbbbaccabdadddbacdbabcaababaddaabaabaacddabcdabaadbaabcacaaadcabaabdbcccadcddaabdccdcbababccbdbacccddaacbaaabddcddbaacbaccdcbcbcdabcbbdcdcaaccbbaccaaccadcdddbddacddacdcddddcbbdadcacccbaccacabcabdbbccacddddccbbccdcdbadcbabbbbbcadcdacaacdddbdcaaccccbcdbabbacdddacbcaacdaadaaacacaadcbbdbdbbdababcccadcccabcbdbacadddaaaaabdbcdcdaaaacbababadbabbccbdaacbabcabddbccadbddbbcdccbabaabdadcbdaccabcaaaccdacaadbccabbadbababdbcaddbabcabccdccbddccacabaacbbcdacdabcccdbbdccbbdbbdbbaaababaccaaccaccaaabbdcddbbbcbcbbbccbbdadcbcbdcacabcbdaadcdacdcbcadbcdcaaacbbcdabdddabdabacbcbbcaabbcaacdbacccdadbccbbaabcbbbccabdabaacbccbdddaccdacdccbdabcabdabbbdbdbcaaccbcdacabbdbcbbddcdcdcaccdcbdabbbabbacddbcacaacdbaaacdbbabaddaaaacdddbbccdacbddccddadadcaccddabdadabcabbcdbdbabcccbdabacaadbacdbdbaddcadcadbcbdbdbbbdbacdabaaaddbadddbbbbcbacdbdcacabdcbddbadbcdbbcbcaabccbccacbbbddbccddadbbbdcaaadcabbadcbadacabcbccadccdcbbcddbdbcdadaaacbacaddbbccabbdccccaaadabababbbadacdcabdabaccadcbddbcababbbbcdaddbdbddacddabcadcdacbddcbdcbcadadaabdadbbaabcbacbdacddddadadabdcddbccdcbadaaaaadbacababcdcacadddacaaaadcdabcbbcadaddddacaacbbcbcdbddcccdcbcccaccbccddcdcdadcaccdbacddacdbdcdcbbcbaccdaaccdacdcbbddccbacbbaaacbccccdadadbbbabbaddcadbaabbacdcaabcdbacbadcdbcdcdbdabbdcdabddbdadaabdbbabbdcabadbdaacadbccaacbdcabcbbbbabddcdcbadbbcbabaaabbbcaabddcddbabcacdadaccbccbaacbbcbabacabacababccaccadabbdccbabaddddaddbbdbcdcbaddcacdadcddbadadcbcccdcbcacddaddcdbdbabbadbcdcbadcadddacdbaabaacbdcaaaaaddadaadacdbdcdaccbdacbbcacbdaccdcdbdaddbcdbadabacdddadbbbabbccbcacabddcbbcbcdbbdacdcdadddaadcaccabbdcdacdbdcccdbcaddcadadbcccdbbcbcdcdbaccbcccdbaaddcbdcccddddddacbdbaababcaacbbabbccbcccbacadacaddabadcdacadbccabcddaacdbcbbddccadcaaaadbccabaccaddbbccbacdabbcdbacdadccccccdaddcaabdabdbbdddcccbbadcaddabaaaadddcadcccabcabcacccccacabadacdccdddcabcaaadbdadacdbaadddcbdcabbadacccbdddcbbdccbabadddbbcdaabccbcbadbaacaadbbcddbbabdcbddaaaaaaabacdabdbdbdbbbbacddddaaabacdadbabdcddaddcbcacabcdbdddbdacadadcddddbbdcdaacbddcbcddabbbabadbabcdcbababddbacdccccadcdabbadcabdddcdddaacabbcaadbbaadcccabdbabcdbbdbdabbdbabacbaacbbaabdcacdcbbcdccccbcaaacabdbaaaadcabadddccabdbcadcadddcbcdabdcaccdccabdadbcaadcdcacdbcdabdbbdbaddacbaccbacdccdacabadaaadbcadaccaadaaacbbaabdadcabcddcababbcadddbdcdabcaababcbabbbcbaccccadddabbcdbbdbaabbdacbccadcaabbbaddbacdcccacbbbcbcbbdbcdbdccdaaaaadccdbdaacddacbbadcbcbbbbcbbcdbaadbcacbdbdccbddbccdbdbdabdcbdacdacdcddbcccccbbcbccccdddadcbdadddbcccdbaaccbdbdacdbdabadbadbadccdbacabcccbcbdccccdaddacdbababccaabaacccdabadbdccaddddaacddaccbcabcadadccbaaddbdddddbbcbbccaabbccbcaccacaabcacddbbcccdbadcdbaccccbababccdcaadddadabcabcddacbdbcdaacacabacbbbadaddadcccdcaaaacbcddbaabaccbbadababacbbccbdcabcbadbbddaacdbbddadbbadabbdccbacdabddbdcbcadccbbcadddbadddcdacdcddbddcccdcbdbaccbacbbbbacddabacccbdadbccabbbacdccabcabacbdabcabbdacbbcacbdabdccabacaddadcccdaabaccdcdacdbccbdcddcabbbbbcbabbbcaadbadacbbcbdbddcabddcdbbaadbccdacddcbabcaaaccbdaddcdaacbdabadacabadbabbdbabaabdbddcbbadbdbdcbaddcbacdbabbbcbbacbbdabcaadbcacdcaccdbbbcdbabbaadaabaabdbcddbddddbbcccddcdbcddccdacddcbacaccccabbcaccbbcbbbddccdbcadcdbadbcdddcdbbbdcbdaacabccacacabacadcdbcaabbdcacaabbbccaaacddcbabccaddcdbdaaabcaaadddddbdcdbccdaacbcdaaaabdbcbbadadcbbcdbbcabcbbdbccddbdadcbaddddbccaaacccdacbdbcdbcacddccacbdbcccacbbddbcbabbbdddadbdcadbacdddbddcbcaaacadbaddacccbaadcbccbdabbcaddbbcdaddadbdddabacabcacbbadadcccabaadcbcdadbdddbacbcaacbcbdbbacdaaaadaabbcabadacbcdcbddcbaaddcabacacbddcbaaaacaabacbbbbadccccbacbdbdaddbddddcbadbaddbbdadbcaadcbadbcbcccdabacbaaaaddcbdbcacbdcbbdcaccddccadcadbccbdcdbddadccccaacdbdcccbcabccdddaccabcaddaaacdadaccbcadcaaabdcabaacaccacdbddbccaaadaccccbacbdbbcbacccbbaaacadcbdcbdbcbabdabddbdabdcbbcbdcdccbcbbcabdddbbacadcadbcabadadababddbdbbccadabdbbddabbabadcbbcbdbacadcacadbacabcadbacabccbdbdcdbbcaddcaadbcbdbaababcabbacacdcacadadcdcbddddcabbabdcdabdbababdbbadcadabbdacbcdcccbabacdacdbdcbdbbdbbcddadabcaabcccdabdcdadcdcacddddbcdbabccdadacdacabddbdadaddcbcabbbbbbaabacbbbddbbdcdbdaacdadbcdaabcdacdcbcdababbabdacababbaabadbaaddbaaacbaccbdbadddaacacbabddacbdbbacdacccabcacccbacddbaabadaabddccbadacdbbcdbadbdcdbbacaaccaadacccbbcbbaadcbbcaaadddbcabcbabbcbabddacbbbbadcbdaabcbbaaadddbdbadaabdbbcdbaabbbcccbacbdbbabddddccaaaadacbcdcdbdacddbbbcdbabcaaccadccaaadacbdcbbaabbbbdbbacaadacabbbdcbcccadcbaddbabcbcdaabbbccaadbddcbdbcddbaacddcadcbdbbcbaacdbbbcbdcadcdcdaccadcbdbacdddbbcacabbbcdcdbbddadacdcddbbcccbdabacbdaacbdcbacadbaabcdbcadaacabbbaddccbabacadabcbbdbccbdbcaaccadbdbcacddadbdddacaaaadccacdcbbbbcbaaabbdacdacbddbbbabdbbbabcbccbdbcabbadcbaacabcbadbbcccbaddaccbccbdbcdbadabcbaddababcacbbbdabcadcadbccddccccbcdcaccccbcbdabbacbbdcadababaadabcaacdcbccaddbccbdaaddbdbbddccbdcadbdbaccadcbcdbdadadcbccadbbabbccddddbddddaccaacccdcdabcbbbcddaacdcdbccbaaaacaadacdbbdbbcbadcbaccdcddadaaacddbdadcadbaacadccbbabdaadabccabdadbaddcdcccbabdabddcbaaccacacabdddaadabaacddbbbdcabaaadccbddbdbbbdbbaabdbcdadaadadddcbbcccacdcbddaaccbaadabdcbccdbabccaadadddbacaddbdddbdbcdbabcdcadbbcddbbddddbabddbabbbbbcbdcdbdbdbcbabacccddcdddabcbcabaaabcdcabbcabbdadadabdbacccacbbbacbabdcbbadabbdccdacccabbdaddbdccacccbccdbddbbadaccccbadaddaccaaccdcabcdddacbcdcdcacccdddbcbaccdbcacbaacbadbcaccccddbcadcabaddaccadcdbccbdddabacbcadcadbbcabadbccbaabdbbddbbbaccababcdaabbcaddcccbbadbcbadbcbaabcbcacbbaabcddaacbaaadbdcabbdcdcbaddbdbbbaabddbcabdbcaaabadbbcabddaabdcacdacbdbabdccddadadaadcaadbbdaadbbabbdcdccdcbbcacdcabbbcaabbccdacbcacacabcaadbaddaaaabacdcaadcacdbadccdbcadcbdcaddcbdbadcaacbcaacccbbbabbadacdcdddbcdcbccbbbbddcaaadbaabcddccaaacbdaaaaabcbacccbcbadcdcbabdacacaabddaacbcdcdbdadcdbcbcddadbcdcbcbddccbcaddbcdbbbddcadccddbcbbdadddbcaacadacabcbcbcbbbcabcadbbadabbaacadadbdcbbcabccdcdcacbdccdadbacbccdcbdbdbacdabddcdcabaccdbbdaaadbdaaaaaaccccdacaabbdabaddddbccacbadcaadcbbcadcdcadcbaabcbcdddcbcacbdbdaddbbddbdbdcabacdcbdbbbdccabdbbbdbccbcaacaadddcadbbccabaacaaaddbcbbaacbdddddbddacaadddcacaaaaddcbaaacacccaabacdccccdbaddacbaaaabbddccdbbbabcacaaaaabbadcbaddaccaabacdbcbbaccdcacaddbdadbabbdcacdadbbddaaabddbadbcbbbaccabbcaabbdbaddcdbcabcccdcadbcdaaadbaabaddcdacacaadabddddbaadacbbcacbcdaacabaadbdabaaccbcdcddaadcbddbbdccdbaacccbccadbbadcacbdadcdbccbbadacabdbcaadaabbbcacbabbadaacdbacaddcdcdbbbacbddcaacaacccabadbbaccaaabbbcdcdabcaaacdaccbbdabdbcaadabdcdcdcdabadaadbacacbbccaaccaaadaacbbaaacdabcbddccadacbacbdccccbaaaaddaadbbccaabbdddcbbcbdbcbdacbaacbbbdbdcaadbcdbbdadacccacdcbdcbdbbacadcaabbcddcdbdadbcadcdbdccbcabcbadddababaacbabbcddaaddcacadbccbababababdcccdcbddcabddbadcaabaaddcbddaaacbbdccbbbbacdaddcdbacabddbdababbcdbaadcddbcdadbcdbdcbddbabcacdbabbbaacdccdcbbbcdbcabcbdbadaaaadbbccdadcadccabbcadabbaadbdddccbadcadcaaacbbbcccaddcbacccccddcaaccddbdcabdadcbdbbdacdaccaadabcadaccaaabcaaaaddcddbadabbacbaacdbccddbccdabbbdbdabdcbbcaabbabccccdcacbcabadbccbcccdcaccaadcaaaadbcadddbbbbbcdcbaacdaabacaacacaacaaacbddabcccbabaacabbadddaadacaccbaccccbcdabbdaaaaccbaaccdbcbaacdddddbdbcbabdadbdccdabacccbdacbadcdbbabcbbadaabbdbdbdbadcaabccdbbdabddbbccdabdbdbbdccdacaadcdabddbdcddbcbdcaaaadbdcbdabcbaaaaabdcddcabbdaacadbcbccbaccdcbaabdccadadcbdccdbcdadcccddcdaccccacaaaadbcccbcdbaaaacaabaabccdbadacbaabbacbaababbacaacbdbabdaabbaddddadccccbcbacadccdcddbbdcaadadcccbacaabbddbcbcdcdddddabcdcbacbabbabcaacadccabcdbcaccaaaacbaadcddcdbaacbcbcaddddbbbdbcadacacaccaaaddaacdabacbacaccdbdabacdaddcddcbdadcadbbabcdadacbdbaadbaddaadbacdcadbadbcabcaccabcccddacdadaddadbcccdcbbdacacbbababadbadbcbbabdbbdcdaabdbbabbdbcddabdcbdbdabacdaccbcbdbadcdcdcacdcabdadcbdcbbacdabbacabcbabccadbdcdcdacddabcbddbdbcbcaabdacdacbcdbbaacbaccddddbaabaadddbcddccadcbcaacbcadbdabdacdcdbbbdadccabacbcbcbdcabbacbdbbcadcabacdbbadaacddbdddbbbdaccbcddacdccaabbcbdbbdadbddaaddabadcaccacbaddacddaaadadacbcbdadaadaabccccdcabdcdbcaadccbddbcddacbcaacadcabdaccccacccddddddbacbcaccdacdccdddddcccdbbbbbdcabbddabbbccbddadaabcaddadbaaddcdddbaddcdbccccdddabaadbbbcddbabaacabcbdabdbacacaddbbbaddbaddcbddacddbaacacccbaaabbaaddbbacacacccbababcacacaaacdaaccbaacacabcdaacccdacccbaadcbbcdaccdacccbbacddbaddbddbcddbddcbaabbbacabdaccdcdbbabababbcabddbbabaddcbccdacacadddccdacaddccdaacbbbdbadcdddddbbddcacdcadbacccacddcacdabdcbbbdbdcdaadddbbccbcbbbcaddbaddcdabbabadbccacaacbdcbddddcbccddbddadbbacbddcabdcdbbcbdcdabbadbbdddbacbadbdabbabaabacdcbdbbdcbccdcbacdbcbcaaaaddabaacabcdaaacdabcabbcacaddcbcdbcadcabcbababdddcadaaabbcadbdccacbaaccbbdaaadaaacccaaaccddabcaaadccbcadabbdbcacbaacbaddcabbdabcdddbddcbabcabbcdcacabdddddccabdadbabdbcdbddcddcabdbadadddaaabbaaaaddabbdbcddadaacbabaacbbbcdbbcdbabcbcacccbadacbabadcdabbbcacadcddadbbbabbdbbbcccaddcccdddddabdcbbdbcbbbcdccbdadaacbacbacbdcdcdbcadcbacbccdacdacbcbcdbcdaaaccccdccbccadcdaccdacbacbbbdcadcbadbbccbbbbcadbadbaaaddcdadcddabaaaabccbadaccdbbacdadddacacbcbddadaadbccadccddabbcbdbdccacbbcccdcbdacabddcbccdaddbcbddbadccdcdbbddddcbacabbbcdcabdabcdddbabcbcabcbaacbadcdcbababcddadcbabcacaccababaabcbbadccdcdabbcdddbcdadabbaabdcdbdbccccdcdacdabdcdcbcaadcdcaabdcdadddcdbabbcdbbabadddacddbcccccbbcaadbbbbbaddbdbacacaaccabddcabbdcaaaabccdcdaabaadcdbabdadccbbcbccacbdaccadabbcbccbdbabbdccbcbaccbaadabddacaddcbaadcdabadbdbaadcddcdacbdcadccbcadbadbbbcbaccbbaacdcdcbaaabdaaaccabaabbaaaaadbcadbdadadbdccbacbbcbabaacabdabbcccdaddadcdbdabddbadaccccadddabdbdbcdaadbdccbaddcabdbcdcddbbabbbbdabaadbabdcddbbdcdbbaacbcbbbdcacbacbaaaddadaaadabbcbcacdabcadbaaaabcbbdaccaddbdbabbccbacbcdcdcbbccaacdcbcaacdcccccdbdbaabdccadbbbddabaaadaddbbdbddcaadbadcbdacadaddabdacbdbacdabcdbaccbccbdbbdaaaccaaccbdcddbabccadbdabdabaacdcbabcacbdbcdaddbaacadabadddbacdbaacdbcaaccddcaabbacdccddbcddbcbcdcaccdaaccaaaaacabdbadbabbadbabcdcbdbacbcacdabadddbbbbabbdbdabcbbcaacaaaababdadcadcdccdbcadcddccbdcddadbacdacdcdadbbbcccaacdccdbbbbadcbbacaabcddaccdcbacbddadcacdabababddcbddaddadadcaabacdaaaaaaabdbabccaddbbdcadddcbaabbabbcacdccbddaabbdabbcdadbcadbacbacacabccabccbbcddaaaadcdacdcbbdbbcaccbaacdcadcaaaacbabdabdcccbcbccaacbacadcabcacbbacbacadbcabbcbbdbdadddabdadaccbdcadaaaacbccbbddaacabdddcaaddaadccccbbcdcdadabccacdbddcbacdccaaadaccdccdcbcaddbcbcddcdcdbabdbbaacdbddcdabdddbdbbdbddacdabdabadbbadcdbbcbbabacaacadbadcdaaabaddaddddcdcaddbdababaccaccbadcbcadcadcabcaaacaabbbcdbbbbaccdccbadabccbcdbdbcccbcdddccccbcdbaadbaaddcabacddcacbaddbbbbdddadcbcbcaabcbdbcabbdcadcbcbbbacccadcaacbcbaccbdbbcdbbddccacdaccacbbdbbddbddccbabcacdbdbbaadbbcdbbadbdacabccabccbccaabcdaaabddbcbabddacdcabdababcdbcbccbbbdbddcacccbaccbcdccdbaddbbcacdaadcccdbadccbccdbadddaaccdbbdcacddadacadadcabbcdcdcacacabaaadbbadddacaacbcdacbcddbdbdbccaddadadbcddacbdabaaadadabaadddaabbddbdcccddcbdccdaacdcdbadaacbbaacaabdcbbbabcbaabcbdbbdbcacdbcbdbdbcddbbbcbbbdaacdbcbaadcbdadcbdcbbdcabaadcdcdbcbccdadcabadccbbabbdcddcbcdbbdbddacddbbdcdcabdacdbbcdacdbacaacbbaaccacdaaabdddccccbddcdccdddaabddabaabababbaaabcabbbbcabcaddccdbdbaccaabcbbcadacbcbcccccaabbbbdddbbccabdabacbadcbbdadcaabacdcbacbaacacbdcbdbdbacacdcbaacdbddabdbdcaabbddcbdbcddcddacaaabaaaabccdbaabbbddbcdccbdcbcbaddddccabacadbcadcdaccbabacbaaddaddbabbddcdacddbdabccbcacddabaadcaaacabcbdbdbbcbaabcbcdbababdcccabbcbcabcabbbacbcbcacbdbbddaadaaaaccbbacdddcccabddaccccbbddbcccdbcabccbddaaacddacacddabdcbcaacadcbabcbccdddcccccdaabbbdcaabdabcbbadbbcdcdacacadbbbabddbbddaacabbdacccbdbbdcaacddbacbcdaabbcdddcacbacdcbcdabbcbccdbdacbababcaaadcadcdabbcaccdbccdbaaacaccbcaddbcbccadbccdcdaabcdbabacbacbdcdccadcccbcadddbdcabbaabdbdbdabdcdbddcbdbddbcddddcbbcbbdcdbcbadbccababacdbdbccbdaccdadcadcabdaddacacbbbbbddcdbcacadcdacbdddcdddcadcaccbbaabcaaaaddddbadcabadcbacabbbabccccbaacadbccabdcccdbdcdddbcababcddcdcdbaabdbbcadbbcddbdcdbadbdddcccacaaacdabadccdbcabcbccbcccdbbacccacdbbbcabacbdbbcdcacaccdcdddbbdcdcbdcbadbbaddaaaacaadddbaaadabccdbdbccdbbaaccccbabbaddddabbbaccbccdcbdbcccbbdbbcbdadcddabdbbbaadaabcadbbbddcacbbaaadbabbcadddadbaaadcbbdcaadccbacadcdbcadddcbbdbcdadcdbdcdaacdbdcdacadddbddbbacdadddabcbbabccddcaabcdadacbdacbdbbcdcbcddcddbdbaccbbccdcbdaaddcdddddaddacaababddbdcdcdacbaaabadbdbcbdddbddbbcacaacbccddccdcadadbbcaaaadcbdbbabdbddaddaaddbadaabdabcaabdabccbccaccbddcdaabccbddccacabadadcacbbbdbbdcaddbcadbbdcddaccccddcbdaccdbdcdacaacdcdbaacabbddccdbabdaadacacccbbbadccddccbdddaadbabcbacdadbdcacaccbbbdaabddcbdacadbacabdbddcdcaabdacbdcadadadbccdabcbdbdadccdaacccbddaabdcdccdddbaacdabbbaacccaddcdbdbaddbadddcaccbabdaabdcbbcaccadcbddcddadbdbccccbdbcdcaacdacddbdbcaaaddabddcadcdaadabcdcbdaaabddccbaabbaccaadcbdaadcbccdcacbdabdcdbccaacabbcbcbacbcccbababbdcabacdaacbadadbcaddbcdcdbaddabbdcbadacdcabdbadcbdccadccccbabababdbcdccdddcdabccaccddadcddabbdbccbabbaddcacdbddcbcaccababbddcdacddabdccabdcacbaacadccccdcbabdccadaddddbbbccbddacdadaaccabbacbaaadadcacaddaabbbdbdcbbcdbdbcdcddacbacdbcbaabaadddccbdcdbaadcacadbaabcdadcbbdcbdddabbbcaacbccabccbbaddaabcaddcbdbdbdcdbbcddbdcbdacbacddabadcbbcacbacbbabdbacacacbcddaacbaccdcadbccccccaacabaccccaccdbcbbbbddadabadaaacbbddaccbccdadccdadaadcacbdadaaaabcaadacabdadbadabcbddbcabdddbbbdaddaddacdbbaaacaccabbbbdcadaddbaddbbcbbcdcbdbccdcbdadccddacdcacadbddbcbadaadbbcbdbacdddddadbacdcbcccacdabdadcdabaccbadbbbbbaacdbbaacbbdaccbcacacaccbbdcdabaddaccbacdbbddcccbcbddcaacbdccccbbcabdcbdaaddaabacbbbaaadbdcddcdadccccacbacdbdaaddabdbdabdbdddabcaaabcaaabbbcbaccddcdbbadabcacabacbaaadadabcaabddbcaddaaadcaabdddcdbdbaadbdddcdcbdcdbbbcccabdbbbbabbdcdadbadabcdbbcbacbdddacbadcbbadabcabdadacdbcadadcdcdcabddcabdbdcaddacbbbcddddcbdcacaabcabdcaacdddaabdbacbabbdddcabbbbcbccbbbacddbadabdcaabaababaccabcaabaacdbcdaabccbacbabbcdbddababdadccdacbcdaaaaccaabcdbbbaacbacccbdccbdabdcbabacaccbcadaabdbbabccbcadcabaddaabbccddacacddcdbddbbacdbbbccdbddbdadbccadbabbbdbdddacadabdddddbdacbbacacaadddbadccaddadddbaadcdabbccdcadacaadaadbdccaadbccbddaabcddcaabcbbdbdaccacaccadcabbbbcdbccaacaaaabbcdddaaacaabdaddabbacbabadcddddddbdbdcdcccaabdabbcbbccccdbdcabacbdcdcbddadbcadacdabcbdddbbdaccadcdcadbbddaadbdbcadbdcacbcddaacbccbdcaabbdabbcdabcbcddaddcadcaabacadaacbbaccaabdbdbaaabdccacbbaacbbabbcbdaddcdabcdcbbadcddbdbcccccabaaaabdabcdbddbddaaadbbaddbccabdcacdddbcbccbbbadcbdcccbddcdacaaaababbcbcdbccbdcbdccddcccbacbdddaadbbbbbdcbacdcdabcabccbcccdadcbcbddbdddbdadabdbcbaadcabacdbdbabbcdcbdccbbccbcaaaacacacdbacbdcbbdaadcbadbbcacbbbdacddbbcbababadbbdadbacabaabbdbcbabdacadbbadaccdabcacdbbbdbdbdadadbabccdcaddcdbdbaadddbaddacaaabdacadabaaccaccbcaaaccdabcadccdabbdbadadaacadabdacdaddaabdababbaccdcbcdbdcdccbdbdaccbacdbabcadcabdddaaccdaabdaccadaddddcadcbaadbcdabaaacbbabdbdcaabccdbaabcbbbdbbddcccbaaabdcdcadccbadbccdcbbcccabbccccccbdaddbdcdbaddaadaccbddbadacdaacadbdcdddddacaacbcbbcabdbcbddcdcbdbbbbdaadaccabbcdcaaabbbadcadbcbbdcccdbbbcaddddabdadcadcabaccbcccabbcbadbababbcababccaacbddcdbcabbadcbaabcccdcdcbbcdccbdbabcbacbaacbaddcbdadcbbcbdacabccadccabcadacbabdaadccaccabaddcdcaaddabccacaabccaadacbcbdbcaacaccbbdbbdcadcadaddcbcabaabbadabcadacccacaabacbbdbdadbaabdaccaccbddbacccccaddcddccdbcbcdabcabdcdccccbcadbdbcacbadaaabdcaadbbaacaccadaacaacdcbbdacdbbadcddcabbcdbbcddadbbbdcbcccbdbaaacadcabdcbcbddbabdbaababbbaccccbaccbdacbbaddddadadacbbadbadcbbabadddcaadaaccbadbbdbbddacabddaadbdbbacadacddbccbbabdacacbdcdabaaacccaddddadcbcbdddddaddbcdcaacdaacbaaddbbbcccbbbabdcabcbbabcdcdaccddcbadabadaaddbdaabdbbddbbcdbbccbabadacadbbacddcaaacdcdabbcccbbdadacaaabbbdbdaabaddddadbbbaaadaddddccccbcdbbaacccdaacbaabacbbbcdbcadbbbbaccddcbaaadacaacdadccdacbbdadbdababcababcdbddbcdccbaadbdcbdaadacabbdddcbdcabcadaccccbacbdddababbccbcaadaccaaaadaccdadabbccaabddddcbabdccbabbbdadcbcbaadcdcacbdcddcbabdbcddbcacadbacadcacaadaabdcdbcdcccabaadaaadacacccaacacaccdcbaacadbacaccdbcacbbaadbddcabaaddcdcddcdaabaabcdcbccdcadbcbdaccbcadddbdbdbcaaddbccdbabdcdcccaacdbcdcabdabbbbdcaaaadbbbcccbababacaabaacadaddbdbabbbbbabdbdbbdbdaddcaadbcccdccbbaddcdbaaaaaaabdcadbdcacbcaddaadbadbadddcbbccacdacccdbcbddddcdabddaaabadadacadaddacbcadcabcabcbabcccbcbcaadbbadbacccadcadcccacdccabbccaddccadacbcabcdaaaaadcaaaadacabbcacbadddadadcccbbccbbbdbcdaaacaacacbaacbdbddbcbbbbbadbbcbcbbdadcaabbcbbbbbccddcbbdcbadbcdabdbbdbcacdabcbdccbcabdcadcbdcddddaadcdcdaaabddbcdcbaabbdbbbdcdbdbacdcaccdabdcadacbaacccddaddbcdbbbacbaacdcdadabcbddacabdcaadacbabaaccbdabaaadcccbdaaaadabcbbbcdbabadabaddccdcdbabdcbadbaccbdabdbbccdbdbcaabcbbaacbabbcddcaaaabbabccbddbdcbdbaccabadacbccdaabadbacbdcbcabbdbbbabacaccadbcdcacccccdddbabbdbabbcdcabbcccccddabddabbbdcddbdbccbdbccabcacbddcacdabcaccbabbacddaaaabddacabbbdcacaadbccdccbdcaccacabadcdcdddaacbcdaddbbbbbcdcdddabdddcadcacdadccccabbacbcbbaabadccadcadccdcadabcabdcccabbbbdcbbbdddadadcaaacadababdcacabbadcbdbacdcdacacabdbacdcbddcacbbbbbcddcdccbdaddbbbcaaccbbdbdacaadbccccddaabdcdbdbaaaddbbdddabbaacddacabddaccdcbaacabdcaabdabdcbbabaddabcadbcaaabbddacdbbcdbdbbabadadddcbddccadbcdacbcbbaadbabcbbddcabbddadacacdbbbcbaabcaacabcdbccbccabbccdaccbbacccdcdcdbbcbaddabbddcdbdbbdabbccbddcbdddaddcaccdcdcbadcdadbccddbcacaaaabdaccdbbdbacabbacaaacabddbbdabbbaddccacaababbabdddcdbadaacacbabbdacbdbaaabdcacdcbcacbbdbdcdbbddddbcbaddcdbaadaaadbbcaaabccbbbaacddcddbdcdbacaddbbcbdcdabbabcdabccdcbabcbbccaccdcaccbbdacccdadcddaaaaddcaacacbadcaaaadccbdcadccdcbcddbdcaccbbbbaacbbdadcccabcadadacadaaadddaccaacdbddbbcdadddaaaabddbdcacdadaababaddacccdaadcaacabaabaaacdaaddadcbcdacbbabdadaadccaaddacaaccdbcadddabcdaacdcaaddbacdbbdabababbddbbbbdcadcbdbbcbccdbcacacadadcddddadcadcaccdaaddadadbbbaddddbbbbadbccaaabbdaddbdddabdbbdabcbbddbadbbddaacadacacdbcbaadacdadadacacadaaadadccddccdcdbccdccbaccadddadbcbcaaadbdadaddacbbaacadcaabdbdccacbbbcbaadbbddbdaabbacaaabadacbccdbdcabaabddcddccdbcccdaddbdddcbadccbadbbbcbacdacbbadbddcddaddcdbccbcaddaadccaccdbbddadbdbcaccadbababccbbaaabdcbdbaaacaacdbdddbacdabadbbdaaccdbbdcdaacdbdcabcdabddbdacbacdabbabbbccaaaaabadccdaabcabdddbaadbacabbabbddbadbaddabccacadbbdaddcdbcdbddbabdcdabaaccddadbbbaabccbddadcaaccbbbcddbbbdbbaacbdadbdaaadadaaadadbbadbacdabcbbdbcdcddbcadccbdcadaacadabaabcaccdcddddbabdbbbccddabddbabdabccbddccbacbabdbbcbbbccddabccacccacabadbbddcdbbbdcbcadbbaccbbcdbcbcbccbdacddbdcaaabddadcbadcaccbabdbabababacbacbadbacdddabcdcabccbdbcccdbdccacdbbcdcbccadacccaadbabcdbbbdcbcccbcdddccacacbbacdcdaabdadcbdcccacadddddbcddbdaccaddddbbadadbdadcacddccaabdbdcbcddcdaddddbddaadaaddcadbaccbcccaacbcdabbdcacdcadcbcadbabbbacbaababababcbdaaaddcdbaaacdaccddadacacaaadadcdaaccaccbcbbbbcaabaababbcaacccdcbbbaadabaacbaccdcbabdbdaabcacacaaddabddaddadccbbdcbbbaaccdcababcaadbaacdbdcaccbddabbcacacbdbbdbcdabacaccccddacdbdcaddcdabbcccdbaabbdbdbbdcdcbdddcabccaaabdcabadbcabbbaabddaddccddcbbabbdcacccdacdbcdcccdacbabbdabdcdaadbdbcabaabacaabcdabcccadbbcabcacaabbdcccbdacbcaddcbccdcaaaacbdbdadaaddbadacacabbabbadbcbcddcdddbdaadbbbbbabcadccddabdbcabddbdbdcdaaaccdbbabddcbbcaadbdccccdccdacabcddbdabcddaadcdacbbdbbcaccdbaabdccdbddbddcddbcccacddccdabaadcddbbabdabaabaddbbdbddcbdddbcadcdcdbcdabadaaadaaabdbcbcadcbdbacdbdacaccdbadbdcdabbadabcdabcbdbcbcbdaccdcbaaddaabddabdcdbaaadcaadcaccbaaadaadbcdabaacaaabddbcacddbddddbacadbbababbabbaabaacddcbcbacdadadbcdcdccbbbbaddbbabbaaaaabdddccddcdccadbabbcabdbabacdaddbbbbbdddbbccadccdaadbdbacaccdaadbcbbbcbaabaacaacdbccabdbbbdcdadddcdcbbdbdbdbcdbcccbbcddabdaccccaddbdbcbbadccabcbbdbccaabaabacdbdbabbbcbadaddbabcbcaddabcbccbabacabbbabcdbcdddbdddbadccbdbbddaccbbcdcdcdcccabacaabbdbddccdbcaddadcdcbdadcaadbabbaaaccaacbccbccdbdcbddcabacdbbdddcdbadbddcdbccdabbaacaaadbbcdabcdbaddacbaaaccbddcbbaacdacdbcccbabcabdbdccadbdacaccbcabcdcbbcddbbabdcbdabdacdbacabdccaaabdabababdcbbbdbaabdbabdacbaddcbbdacccacbbbdccdabccabbdcabdccaadcbddadabbccaadacaabddcdaababdabdbacdacdaacbdaadabcdbadcabddabdacccdccbbcddbccbcccacccbbaabbcdcbcdabcababdaaccabaabadbbdddaaacabcbbcdcacacacdadbdabaadbdaaacbbcacbcdbcccaabdbdccaabcadcdadbdcaddaabdabbdcdccababbbdcdaaacadaacbabddaccbdbbaadbacacddaadcdddcbabcbcddacddaabbccdbdbbbadacbbbbbaaccccdbdbcdbacaacccbcadabaacddbdadbdcbdddbccabbdadcdcbcacdbdacccaacddcddbbbabcaacadbdbdddabaddacdcacddaddbccdadabaadcbadbabbabcbbadcdddbaddabccabaacddbdabdcaaadcbbbccdaccbbaadaabddcadabcadbbacdbaddaaababbaccdbcdbdaacabdbcdbacadadcdabaacbcbbccabaccacbcacddcdabcbdadbcbdaaabcacabbcdabacccadadbcbbbbbacaadcdbabcbcbbaabcddacbcdcabdccdccdbaababcacdbaabbbcadbcbaaabbcbdcabcabcdccaccdaaaacdacdadbbcaddcbaadddacddbacbcbacccdcdbddcaadbdbbbaabbccdccddccdbcdaccdcbccbbccdaacbacbdcddbadacbbdcdabcadabdbbdaadccbdbdbbcaddcdcbddacbdbbacaabbdbcdabdddbbbdddbdabddccdcbabccbcdabcadcccaabaddbaccdddddcddadbbabcdcaddacabbbbaacbacaccaadbdccbdcdaaaaaacadddbdadcbbddbaccabcaaaddcbcbbdcdcccdadccdccccaccadbdbdbabccaddaddacddbaacdcccaddbcbddabbddbddcacdcbaaacbadccabdaccbdbaabbbdbbaadbdabbbddcabadccbbdbacdcdbbcbbddbbcaadddcadadacbdddbabdcccadddccccbcabaabbabbabdbaddabdcbcabcdbabcbdacdbccaaddcbdcabccdaabdbabccbdcccbcdcdbdaadbdaabadcccbcaccbdbbcadbdadbadbdacaaaabcccdacddcdcdcccaadadaccabdaadaabaddcbdaccdcccaddbbbddddabbdbabdbdcbaacdcdbcbccdadddbccdbdcccbacccbdaababccbbcdacbbbacacdbccddaadcbcadacaaadaccdacaacbacbdddabcdcdaabaaaacbcdcbcbdadaddccaaabdcabdbcabcbaabccbabacaabcaddbcbcdbababddbcabbacdcdbababcbbdabcadbcbdbbbdbdadcbdcabcbcccbbcddbdabdddadcaaaaacbaacaacdaddcbdcccdcccabccdabbabdccddbbbdcadacadadaabcadacddcdbcdbadaccddbddcbbccdcdaccddccdacaddacdaadadbccdadbadcbabcdcabbbbbddcbdddbbcdddcddddadccadabadcdabdbbbabdacbddadabbbdaaaaacccbdbcdaccabcadadbdadcabacbbacdddbacbbbaadddcbbbaddaaccbbdccacdcddcbdbcbcdcaddbcbadcacaddcadaaccabbcdbbbccabbabccddadacdababcdbbcccbdbbaaccbbddabdcbccababbdabbdccbdaacdcaccaddbdbaabdddaddadcaaaadcaaabddbacdadadccdcabbbbaadbacbaccdddbdbddcdcdacdddcdbaacdbadbaaacdcaddbddbccbaddbcacdddaabbddbcacbadbcaaadddaaccbcabcdcaaacdabcdbdbddcaaabcdcabcaaabdabbbabcdcacbcaacdcdadbaccbddbcddcbadbaddaddcaabbdbbbbdbacaabbcbdbdddbbdbdcbabdaaddadccadcadcbbcdbddaabbddaaccbacacbdbdcbaaaccbccacdbdbbdccadabbdcaacbcbcdaadbaacbdbcdcbacacaaddcbcaddcbdcddabdbddccadbbabdcadcacbaabbddbcaabdcaadbdbbbabaacabdadbacbdcabdccddaacdddccbabbcacaadbdccdcdacccabbcadbdabdbcdbbbbbbacdccbbdcdcabaacddacaabccdbbacccaacdbcbdbccacccaabbadbbdacdaabbdbccccbadbdaacadbdbddbabbbbdbacddaccdacdccbaaabbaacbbabcdbbbdcacabdccbcbbddcccabacbcddacdbddacabadadbdbbbacddadbaacdbdcbdadbadcccddabcaaaaadddaaccccabacbadddcbbbadacbabddbacabadaabccddbdabbabbbacaacbdbaabbbcaabbccbbbcbcbaacdbbcbaaddcbbcddbbbabcacabbddcacdabcbaabddcdcccdadacdbdcdddcaaccdbbaadcaccacbbdbadbbcccaaabddadaadadaabcccbdccdabacbcacbabcaaabababdbbbbbcacddbcdcdadbbcbbbbadabbcdddaccddacabcbacccdcbabbabbdcdadabcbdabcabbdadacabbdccccaacbddbabababdcdbdbddbdddbcddddcdacbcbdbacbbabcdaaccdaabddcbbaadddbcdccbbcdbbadbbadaccbacbaaadddabbaabdbcabaccdbccbcdadbabaadcbadaccadddbbcacdaadbacaaadddaacdaaccaccdbbddbadbdddcaddbcbbcadbbabacbcccaaddddadcdcbbcabdacccdacacbadcbacbcbbdabcccbbaaaaaaabcbbbcbacdadbdbaaaddddcdababbcccddddabbbccddcccdcbbbaadddbbddcdacccacaababbccabadaaddcabdbcddcbbdccbccbdacddcccaccbdbbacdaccdbaabaccbabbbaaacadaaccbaaacddbbcddabdadbddadbbaadcabccbddabdcaabbcabbdcddbbacccbbadadcadddbcbcaadbccdcdadcdabacaabbabbbdcadbcadbdbcccdcbdcadccadaddadadadcccdacdcddbbcdaaabacbbbdaababdbbcbbbdddbdbbcaccdbdcdacababbaddccbdabbaccdaaacdcaadacabaaabbbbdbdccacaabaccbcbddcbadbabbdbbbabddaaccacaabbcbdbbbdaaddbdcdbbccacbaaadcbacacbabbabaadcddacbbdbddcbccaabdaaccdaddaccddaabcdcdbccccbbadadbbcadbcdcbcbcacccbcbcbbdbadddcacbdbaddabcabbaabccbcabdbdabbadadcbdaaccbddddacddcabccdbabcdbddadccbbbddacbdbdaaadcdddbdadbddcacdccacaddcabaaccccddacaacbddbbccbadccdbcbcdbcdcbbccbdadacacaaabbbbccacadcbcdbdadadbaddacbcababbbbccadcbdbcccbbadddddacbaaccbacbaccadabcdbbbcdaabaabddbbacbbcaddacddabbbdbadddaabbdccadcabbacbdbcabdbacdaacbaabcccacaccbbbadbacdcdbdbcabcdcdabddaabadacbdddbbdbddbcdcbddbadbaaaddddcbbcdadcaaacdadadbaaacbbabbbdccdbbbcdbbcbdacdaddcdbcddabacadccccbabbdbdbcdcadbdddbacdcbcaccbabcbddbdbcbdbcaadbbbdacdbdbbbdaddcbcdbcbdcdadacbaccacacbbcdabacccdadbbdcadcaadbccaabdcacccbbcabaadcaadcaaddabcbaabdaddadacbcbbbccddadabaaacddaabbcdbdaaadbcbabbdcddcbcacbcddabbdcaabcdddacbddddcadccbbadcdaacbcbcddbccdbcabdcbdcdabddbbabbdbdaabdbaaacaabddcbacbdccddbcccdadcddaacdcbcbcaaacacbadadbbadbddddcdaaabddaccbbdaabdbacbbbacdcccbbdbcaababadbcbbabbcabddbccdabdadccabdbacdbddbbaaccdbdadddcdbddbdcdcdacadcabacddcdbbdcddbddbadbacabadadcbbdcbbbacdcdbddbbddaacbdacbcccccacaabaaabbadbccccbdbacadcbcbbbadcbdbdcddccbabaabcdccdcacdaacaabcabccddbddabccabddcdadcdadcddabbacdaabdabcddcababcabcabcbbaadaddcbdddbbdcacdbaabdbcacbcddbbbadcadacaaadbcabcabcdadccbcbabbdaddadbcadcbcdcdadbadababcdcbaaaaddccdacaabccbbcdddbcaccbdbabcdcaabcabbcddabccabcbdbcbaaccdcbbbccbcdcacdacbadccbacaccdbcdacabddcbbabdcdddbcbbddbadcbccdbbbdcbaaacdbabcadcaaacacabdddadadcddbaddcdccddbacdcacbccdbbacbbdacdbbabbabadddbcccaadddbaaacbababbadccaabbacbcabdcdcaababbacacacbbdcdbbdababdccddcbddcdcdbdcdcdaddbbcddcdcbbcdcacacccdbaddddaddaacadbcacbdcbbdcccaaacbcbcbabbaccaabcabdcbbbbcbbcccaddcaacadccdbaaccccacbbbdacacdadbdddcbdcadcbccbdbbbbccaddddadcdcaaddabdbccbdababdbcbccbbdcbddabdddbbcbdaaacdcbbacbbabaadbcbdacddaddbcdddbbbbadaddaadcbcbabdbcaaadbadcacaadddcdcaaaabaccccbcbdbadddaabcbccbbddaddcdcbdbabbadcdbabaddaaacbdcbababbabddbacddbdbadbbaccdcbbdbabcddccdcdadabdcdbdccbdbcaaababbabbbdcdcbabdbadaabbddcdaabbdccdbdddddcaacbabcaccbaababbbaacabcaddcabddcabbabbbbadbccabcdccadddabbacdacdcdabcadcdcdacbccdaabddccbbbacadbcdadcdddcbdcabbaccaabdcbbbdcccababacbcdaccacacdcbaccacdaccbdbcaabddddcddccadcabbccadcdbabdadacdcabdccbdbacbdddcbbbaaadacbccdabcacababbacaccaabbbcdddabacbcaabdcaabaaabcddaadaddabddccbcccabacaabdbdbcdbdabbadccbbabbababdbddbddaababcadcddadbcacbcdadddddbbccdaadcadcddbabcdcdaaddacddabddcddbcbadaadbadcdbcbccaabacdadbaacacdbbccdddbacbbadaaadcccccabbcddaccaadadddcdbccacadadadacbbcdbdcbbbcaccbcdadadaaadacaabcddbcabccadbaaacacbabcadbccdabddaabaacaccaacbcbabcdcbacbbbddbaaaaddcbaadabcbcbdcdcbcbcdaddbdbccaaccccbaacbbbccbbbbabbdaabaccacbbadcdcaccbdddbcdcdbaaddbacbabaddcaddccddbdbcaadcaaddadbacbabdaabaabcddabcabcbbacbccadccbcbaaaadaadaaddbcbbdbdcacdbdbaaabaaababbcadcdcdbcadcdccadcaabdaddbdcababcccbabcccadcdaddbbdcdccddadacbbabbacbababbcbbdcdadbababdbddbaaaadcbdadcadabcadcabcccccbbaccadbbbacabdcbaabdddabcccdaccddcddccaacdccadbbccbdddbdcadcdaacaaaabbcababcdbaccabcadaabcbdccdbdbdbcbbcccaaadddaadcbabdcdaabcabbddacacbcadacdacccadbbdcdbccadbcccbcbbaadcbadbdaccabcbacabcbaddbbbaadcbacccaaaabddbcadbbdddacdadadbddbaaacdccdaaabbcabbabdccacbbadddbbacaacdaacbdabaddbdaabcbbbcadabcaacacbbadacdacdbbccadcdccbaddddbaabdccabcdaacdcdbacacbddcbacaaacdbcdbbdccbbaddbdbdaddadbcccaaccbccddaccadccbadacaccbacddddbacacbccbaddccbdcbcdcbaccccddcaccdcddcccadadbacdcdcdcdcadabdacdddddbbcabcaddbddcacbcacbadddbbbababbcbbacaddccbadbdcadadbaadcadccbcccbcaabdbacabcddadcdbddcbdccaaabcaccdadbdccabbddcacccbabaddadcddadbcddbbabbbcbdbabadabaddabdcbdacaaacaabdacbdacabbbacbcdbbbbddbbacddbacdcccbddaaaaadccbaaddbaabcaaccacdacacddacdddbaadcbbbddabbabddbdaddbbbcbbbdddcacabaabdabccbcbbdbccccbddbcdccddbcbcdbcababaadbbcbcbaccdadbdbadacdcacdaaaababdbabbcacaaccbccdbacaacbbccdbbcbcabdbcabdbdcaabcbcbbdbbbccdccadbbdabdccdbcbcbadbdbbaabddddacabaaabacdbdaccbdcdcdbadccdddcabbbcbcbbbaabaaaadadbacacaddcabdbababbdcabadcdacdacddcdaacaddddcdacdaddcbdddabbdabcbbbbcadabcdabcaadcdacbbccdbacbdbcddadadacbaddacabdadabdbbaacbddaccbbdcdbdadcbcdddaddaccdcbcdcdcaabdbcdcccdcaacdacdbbcdaabaaddacddacddabaabdbbdadddcdabddbacddcacdcdddbaabbaaddacbdbcdcdcaacccaabbbcaadbcdddcbbacacacdbbadbcaabcdbccacbacbcaabaacaadbdbdbabbddbbbbccccdbcdaabbcbcdadddabaddadbdbdddbdcdabdcdabaccbbabbddaccabccbdabcbddabdddbaaadaccdaacbccbdaccaccdbbabbadabbdbccaccccadcdadbbbcacabdacddbaaccdcdabcdaaaaccbadbddbaaabdccbadaabbcdbbadabcbcabdccbcabdccacccdcdbbdcccccadacbcbacbddbcacddbadcdbadaababdbbcbdcbacbbcacbaaddabddaaaacdcbdcacbbcdaabbcbabdbcbacdbbccbadbdbccddccdbbdbdcadabcdbccabccaadaadaabccabababaaabdbcbccdcabaaddaaaabcbabcbabcadcdabacbcabcccbccadaccbcdcbbaacbdadaaddadcbddbbaadcddcbdbdbaaadcbbcaadbbccbcabcbccbcbbddbccbdbcccabbccbbdbcbbaaadddbdccaccdddabbbbcdbcbdaaaaaccaddbbbcbadcdaadcdcbcccaccdadcdbdabdbdbbaacdcdccdbdbbdddbdbdcbaaabdcccbcaabddbabdbcdababdaabababdcbadabaacbdcbdbcbccdbdcdbbdcabcbbddbccaadcccbbaabaacaadbcbbbddcccabbbaadbadbcccccbbadcaacbcacbbdbccbaddddbbbccdbabaacaddccddbbcbdadabbdaacabbadcdbcddacabbbcdaabcadabdaadddbdccddbdddbddcdacdbbabcddacabccdaaacddcdbbadbbdcacaacadabcbcabcccdabcacdbddcccbbdddcdccdbdbdabadcaadbcddacbdcdbdccaccbdabcbbcacaadaddbcdabdabacadadbabaabadccbddbdbbcdccdcacbdcdcbdcadbccddcbaaccddaabddbccbbcbdbdcbcacacdacaaaadccadaddccbcbaaadabdccddcacbabbcdcbbddababdabdcddcdabdcdacdcbcacaabbabdababcdaaacddabdaaccbcaadaddcabaadbbcbbddaacacacbacbcddabdcabaadccaacccdbaccccaccdcadccccdbbabccccacaadbdcdcbaadaccaacaabbccbaacdcbaabddacbbbaccadabbdcdbbabcbbacddcdbddbcbbcbaabbdbddaaaccaacabacbcddcbdcaaddabaadcacbdbbbdaddabbabccdaadacddcdacddaccaabbadbdaabcccdddcacbdababbaadbccdddbaddbcbdadacccddcadcddcbbbdadcccbcddacacbbcadddcdcbbbcdbaadbdbcdbbcbaabdabdcbbadddbadaccbacacbcacacadadbbdcaaccaddcadcbbcccaabacadddadddbdacdcbcbaaabddbbcadbdcababcabcaaddbdbdcccddccbbbdbbabdcdabdababdbabaccbdaabcdaabbbabbaabdbccccaaacdcacdcaaabadacdaddcbcabdaabcdbccbcaabbcdaccaaddbaddcaccbcdaddddbbdbdabcadbabaacaccacbadadbadbcbcbdcdabdbccadddaaabdbaabbcdbcaacabbaaacdccbcbbdbbaaaddcbcdccdddbdddbabcbabbadacbadcaddccdaabacacdabbdadbccbcaaabaddcddccaabbbddababdbccbadddaabdacaccbadccdcdcccdabccdcccbcddcccaaababbbaacacbadaaaddcccddcabdcbdadbbadadcdbcdbcbaacbacaddcddcdcacdbbaacbaabccdcbcaaccdbdabcdaadcdddcdcabdbbbcdbabbbbccdbbaadacddbcbbbcacdbdbababdbabbbdbaaaabcbacccddbcbdaadccdaabadaaaacabaabccbbbbdcbcccadccaadcacbbdabbccacddaccabcbcbbdbbbcddbaadabacdaccccdcbcdcdabcbbcbcbadcaccdcddbbbcccbbaabbdacabbbcdcbbbdabddcadcdbdaccdabadbacacacccadacddccdaabbcbaadbccaacbccdbacabaddcadaddadddbcccdcdbadacdabbacbacdacdcacbbdcaccddddaaccadddbaacbbcbddccdbcbbcadbdbdbbacacdbaddcccbcaccabbacdbbcaabccdaddabcabadcdbabaacdacbbdacbbbdabacadbbcacddcbbdaaacacccdbadadabdadddabacbacdcbabacddabddcdadcbbacadbdbbbcacacaabbacdaccdcbddccddbbcbddaaddacdaabdaaacacadaaabababbacacddaddbcabdbcddaadacbcabccaccaababcdcddabdbbcbccccbabcdcaacadccdabbaaaddbcdaaccbcdaaadaaaaaadaddddabcdbacbbccdcacaccccdadccccaadadaccbcdbcbcdaacdabccaccdbcdcdbddacacdbcbbcaabdabbaabcbbaaaaabcaccbbbddadabcadcdbbddadddcdbdcdabbdcbabcdbdabbcdccdaccddcbbaacddbabdcbccccaccdccbddddcaaaacabddbacdaddcdcaccdaabdddbcbdadbbabacacdcabcbbdcbacabddaccbbbbcaccadcdabaadabcbbdbaaddbcdadbccacddbacadbdadbaadcdabcadccbbdddaadcabdbbdcdadcaaadabcaaacbbcdcdddacdccdaacbdbaadbcbcbbaacbdcdcbbdadcbcdaaaccbbccdadcbdccccbbbbccdaadabdbaabbcaabadbbadabcddccbbaaccabadccddacdbcbcabbabdabdadacbadcbabbbdbbdabdcbccdabadcdacadcbcddcccaccaabcabddddadcddddbccccccadcbbcadcdbddbcbaaaacdaabaacbdbdcbaadbbbdacddbdcaaddacaccbbdcccaabdcabcacacadddddcbaacccadbdbdcaababbaddccadbbdbaccaabadbddaaaddacbaadcccacbcabdaadbbbddbdcadcbacadadbcdbaacdacdadccbacdcdcddaacddbdbbddbdbbcccddcbdccdbabcdaadbdddbbbbcbbabddbdbcacccbabadadadaadaadbbbdccaacabdddcdabbabdcabaacdbdcababcdbcdcbccabcbdbbbabcbddccdcacbdadcaababcaaaabcaaaaccbcbbddbbacddbdccbcbdbcddacbadcddbcbaaddccabcbbabdbcbdaddbbcbccdcadacabdababcadacacdcaacdbccbcbadbdccdadddbadabdcdabdacadaaabbaababcacccdcbaddccadbabdadabbddbacbdbbddadcbcbcccbadcdabddabbcddaacabcccddbacccccaacdacaacccbbdbcdbbbaacabadbddadbbbccacaadacbcaddadadcdbdbbdcadddaaadddddcbcbbdbccbaabcbaadcbaadacccacaddcadbdccdadbbaaadcbcaadcddaccdcbdaabdcaadbcbbcbdadcbbdbbcbbddbdacdccadcacccacbbaacdbdcbcdbacabbaabadbcabacbbabcbcbaacabaddcbdcadbdabccdbbbdcccacabccdcdddadacbbadadbbdabdaddcdbbcabacadddbcdaaaadbadbacdcccbacddadccbbbbacacdddcdabbcbacbdbaaadadcadcccabacdadaddabdadddbdcccdbbaadacdcdadbddccbcadbdbdddbccadbaabcdbdaaababbabdbabcaccbdccbbcaacdbaadddacbbabcbbababbcaaccbdbdcdabbcbbaaddddaddcaaadaabbdddacddbcdddaacdacbccccddcaccaadabcadaacbcdcdcdbcbcadbaddacbdadbaadbcbbaccbabbbabcdbdcdabbcddbbaaaadabaaabbadcaaabdddbccbbdabbcbbbacccacbcabcbacbdabdcaaccaaddcaccbcacccacbabcacdadccdbbadbaacadcbbcabbbaaccccabbbcbddcbddbdaaccabaacbbabbccdaaccbbccddbacbdbcbabdabbbacaddacbadbcdaaadaaadaaacbdbdbcacabaacdaaadbddcbadddbbdccbdcbdbbacdacbdcbcccabaddcbbbcdddccaddbcbddcccacdddcbdddccbdbccadaacdbbacaaabdbbabcccbbdaddbbcdbcddcbcbbdbddbbdccddbcacdaaadcbabbcdaacaabaaacccdcaaccbddabbbbbcbaabbdbcadacdcdadcbcdbcacaddaabbcdaabbdadbbdcaacbdcbbccacddbbacbabacbbdbbabbaacaababbcaacccacbcbdddabbddbcacaaaccccaccccacbcbcdcabcdabdaddcbbadbbccbdcbcbaabcccbbcdbacbbaacacdcbcddbababcababaddabcadbddccddbcccdddcdcadaacccaacadbcdabdbaababbabdbbddaaadabdcbbdcddacbbcaacdcbadcddcaadcbbcdadadcbcaaaacadbaabbaabaddaacccbccadbbdcdaaacdaadbcbabcaccabaaaddcbbdcaabddcacbaacaadbdadbbbdbcadabcdbacbaaddcadadabddbccccdbacbaacbaccabacdbdadbadbcaaabcdadcbdabbdcbddbdcdbaccadabddbccbbdbbdcbdcdabaddacaadbdbbbccaadbddcabbdaabdcaadabccccabadbddbbdccbcaddaccacaadbccbcdaacabbbcadcaccadbacaaaabcdccdcadaabbcbcbcacabbddbbbcdabcbddcbcadaabbdaaadababdbadccacbcddbbaadcadcbbbcadccdaaadcbddadcdcccccbbadabdabcbbbcdaaadbdbaccdbaaddcdcbbdcaabcbcbcdaabaaccabbdbadbbccabbbdcaccabaaacbaaacbabbaabdcaabcbbdacdabbdbaccbdbbcbccddcbbbbcdadcbbadaaadbadbcdcacccabbaddbdccdbacacbdbccbaacdccbdddcbbdbaccbcabbccdadadccdcbcdbbccdadaddacbbabccacddacccdbaabcbcdddbabdaacabadccabbccdbacddadbcaddddbbabaddbcccbabadbcadcdcadabbaaaadbcbcabcbbdbbccdaddcccbbdbbbadcabdadccbdbbababddabbbbadbaabdcaaadbacaaddcbddccdbcbaaaccadbaabadaaddbdabbbbaccbcacdbadabaccdcbdcbbbcdbadabcabbabaddabadaacacdbbcbbaddbdadbacacccbbdbdcbbbdbcddddbbaabaadaacdddbdbacdaacccaacadbcdadcccccdabcbdbcddbcdabcdbccbdcccdbdcdbbabbbadbdccccdcdccaacdbcbbddcdccaadcbbdcbaddbccdbdcbdbcdcdbbbaddcbcadbadacccdcdcdacbacababbaacaddadaabbaababbacacdaadacacaddddaadccbdccccdabbaaddabcbcadcccdaabdddcddabdbcadbacccccdadacbbacbdddbddabdbbddabbcabbdbacbadcbbdddaddcaaabdbdabdbbbbbdcdaaddaddddcbbacbaddcabccbdaaaadabcccadbcabcbbacbddddccdcaadadacbcacabbacbcaddddccdbdbbcbbabcddbccacbcbacaddaccdcaddaadacbdacbbbbddbbdbdbabdaddbcbabacacbcccdcdadabbcdcacbacbddcbcdadbdacccbbbcbbdbbcddacdbbbadbbbbcbbdbdaccddaccdadbcadaddddbdddcbadbaabacbdddbccdbbbcadaaaaabaadcacdcaddabdcbdddbdbddabdbcbbcbbbdcaaacbabddbddabaccadddccabdaabaccaadbdadaaabaaacaacabbdbaadccadccdabbaadbbdcaccaaaddaaaccaaababcbbbdbaddcbbabbbdbcbbcdcdddadbacadaddbbbccccacdcbcbdbadbdcbcabcccdbccaccbddbacabadbdbcbbaabcdbddbdcabcccbbcbaacdcadcbaadcdbaadbaabdbccdbcdaaacbabadbcbbcabbdbddacbcbadbaccccdbcbdcdbdcaacddcbadbbccdacbabbbacdbcccbbdbdddccadaacdbadadaddaacaadcbacadcaccdacacaccbccdadababddccdbcadbddbdccbddbdddddaddddacccaaadadbbacaabbbccaabcbdadbddddccdcdccaaadcacabdcccdbbabbdaadcdabbadadddbcbbdabacaadcbadcbdccbccbaaadddccdabcbadcdbadcbaaaadbdbdaabccadccbccdaccddbacddcbabdbbaddabccccbdcbabbbabcbbdddbdabbcdaccabdaddababddadabbbcbaaacddcccbccabbbcaadbbcbbdccadcabbadadccbdabbaaaabbacacdcccdaccaaabbddcaadababccdabbdccddacdaddddbacbdbbcbccbbbcdcaacabbdcabcbcdddacdcadaabcbdbabbbdbdbdccddcdbdaaaacdadccbbdaadcccdcaddaccbcdaadaabcbcddbdacccaaaabbcbccccbccbddccadabaccbdbcababaabdbaaddaadbdbbdabddcdacbbccdbabadaacdacdccababdbdccbdcabbadaabdcccccbdabbaababacddcabaacbadbdbccbcccbddaccaccdcddbddddcacddaaadccbaccddcdbcacaabdbdbdadccbcabddbccabdbbbbbbbbaabccaaacadcbcaddaadabaccaacabddcddbabddbcadacadadabadcdacdbbbdacaadbddbbcdbdbaabcadacbdaabcdbcdaadccdbbcabcbbbcbcdbcaaadaadccdcacbbdadccacccddcaacbdbacdcbacbacbaadacccabbabadcaccbbadabcbbccdaacdbcacbaadbdaadddabcaaacbabdddaddcabdcabcdddcadbbdbddcdbcbbdaddcdadbbaaaaabbccbbddbbacadccdddbdbccbcaadaabdadcbcbbdcdbbdbbbccbbdbcdcbaccabcdddacbccacddaaaadcadbcbdcabdacbcccadbaaccbcdaabbdaddbbbcbcadbaacbaddaddadbddaddbdaabdbbdddaccdbddaadbcdccbcdbbcccdbacddacdbddbdaabbcbcddadcdbcbbcbddaaaccacbdcabacbdbcdaaadacaacadddbaddccddcacdcadbbbabdddabdbcddbcdabbbacddcadbcbbbddabbbcbbddbdabcdcdbaaddaabdccccdabadabdbbbbcddaaaacdcaadabacdaadaacaabcbcccccaabacabcaacdbabacdcadcbadcbacdccabaabbaaaddadacacbdccbdacbbaaaacdcbadadbdabdbbdddddabbadbdcbdbbabacabdcddaabaddbadbdabaccbcbddacccdacadcdbcaabcbabbdcacdcabbbbdbbddbdcdcccdbcccabbbdacbabdcaccdccdabccdadabcbcccaaacaddbdccddddbaaccbbabddddaabadcaaaadaaccdbcddcbaaddaabcacbccdaddaaccbcbcbaabaccdccccdbcccbbcbddaabcdddbdcdbacacdbdbbdacccaabcaddbabbdcdcddbadddcddaabbdddcabbaaaacabbacabababbbcabacdccdadacabdbbbcdbdacaaabcbdcdadbcdbdbdcbcadbdbcbcddacabbdaaadcbcbddcccaadaabbccdcddcccbdcbbcbbdbadbadbaababdcdcababadbbbadddccbaabbbaabccbadbcccbbbabdacdbbdddaacbbccdbbabcdbbacccbbcabcbcbcdaddddcbcabcbdbbbdaaccaabacadaadccbbdcbddabbdbdcbdacaadbdaaddddaaacbddbaddaadddcaccadccdacbdadadccadabbbdbdbbcabbbbcaadbcccdcbaabaabaccacdddbddbbcdcbbbcbabadbdacbbacdbadddcaacabdbabdabdababdcdbadbdbabacbcccdbaabdbdacbdcddbacdabdccdccadccaaddbbdbcadcbccbcabddcbaddbdadbcbcdadcaaadbddcdbbcccadddaacdbdaddadbabcdbacdccaacbbbbacddbcacbbccbbcdcbbbdabcabbdcbccabbccbbaccbbacabddaacbcbcdcdbabaaaacbbdabcbccdabbdccccbdddaccbdaaacdbcdbbdbbdadadabbdddaadbdbddbabcdbbdadcaddbddadbcabacddbabcabcbccccddcbababaacdadbaacaddccaadbbacdbddacacaaddbbdbddbabcaddadcbdcddaccbcdbabccdcacbcddccbcabcbbbbabcabcdabcbdbaccbaddabcbbadbccabbbbbabdbbdaabacdcddddaacaabcabaaccbaddacccaacaacdaacddccacbbdbdcbabbaadacddaccdbbddabaccdbddacdbacbdbbbcbdaabcacbcdacaaaddcdcddddbdcbdadabcbcddbddacbcaabcdadbabcddbddacadbadcabadccbbacdaddaadcacacdcdcccddbacaccdabddaccdbcbdacaaccaddacdbddaadcccabdbcbbcdabcdcbbcabddaccccccddabcbbcbadbddcbacbcdadacbbaabadadbccdbcabdaddaccdcccddbccdcaccbbbddaddbdddcaccdabaddaabcbacbcacbdcaacbaaddddcdaabdbabdbadcabdbdcdabaadddddacacbdbbbbddbaaaadbabacdcdcbbccbdbbdbbaccbcabddcdbcadbbdbdbbcccdbcabddccddcbcabdbadcbacbdaddbdcbadbddddbdacbbbddaddddacadaacdbaddaccdddbcacdbaabdbcbcdddadcccbaaddadccbcdabbaccddcbcaaddabdbdcacbcdbaaccaccdaddcccabaadabcbccaddddcacabcabadabcdcbbbaadabcccadcdbddccbcaaaadbcacbcdcccdabcabbbaadabbccadcdbbaacdbcaabcbabaccbdabbadbacbbdcdcbacbbccbccbbbccbbcccdaaaadbcbbdbdbabdaacbcbaabddbcbbbdbadadcddbddcbbcddabacbdcbbbbddcbddcabcdcbabcdcacccaccdbddbbadbbbcacbadcbdbcbddcabcadcbaabbcdacdbddbbddadcccccbacccaddbcbcacddcdabdcacacaaadadcadadbcbbcbbcacbaaabacdcaccdbbbddbaacdcbbbababaccdbbbdbbabaccdcdababbbdcdbbdaaabddaaabcbcdbaabdbbbbdadbdabcbccbbdaaadcacdacabcdbacdbadbdcaddcbbdbadaabbadddbaacaccbcccdbabbbcdaccdaabaadadccadbdbacabdddadbdabbdddacbcdacccdcaddcbaaadacadccbbabcbdbddbbacbbaddbcbabcdddcdbaccbdcacabaabdbabcbddaadcadbcabbbbddbdcdbabbdacbddabcdcccabccccdbbacdcbbacddbacdbcdadbccdabdccddbdacdaaaccbacdaaabcbbbaaccababacccadcacabacbbdbaacacaabbcbcddcaadcbbaddbacbbbddbdbdcbaddaddbdddaacabdcdbacabbcccaacdabadddcadbdacbacacbcacacbbcddaddcbcadccaadabcbadadaddddadddbcdcdcdacaaccdabbcaacccbdcdcadacbbdbdacbcdccbdabdbdabbdadcbbbadbaadcbcadcaddcbacdaabaabaaabddbbdcdcabdaccbabdbccdadacdaaccbdbdcbcdbdbacccaddcaacabdbdabbaaabcbbadbbbaacdcadcaabbbcdbcbacacdbddddcbbddcadadbcbacdbababcddcdbccaacdabdcbcbcdccddcabdbbbabaadbdbbabdadcdbaadbaddbbacdddaccaaccdddbbaadaaaaadadbabbdcaddcddabcbdaaadbdacbbcadcbabaaaabbdcbabdbaccbabcdcbdbabacccaaccbbbabaadbcdacdcbdcdbbddcbbbdabccdabbcaadddcbdccdbcadbdcccbacdadcabcdacdaaacddbccacccabbcbddcbbcccbdbaabccbabacdccbdccbdbadaadbcbdcccdbdaadacaaaccbbdcdaccbbdcdbbacdcbccacabbbbbddccaacabdcaacdbcdddbdbcbcbbabbbdbadbdaababcadcbcabbdacabadcbabbcaadbbcaccccddcccdcccbccbcbdddaddbabdaababdcddddcbaadaddcdbaaccaddccdababcdcbabdabbadcbabdccbbdabdaaabdddaabbcbbadbbdddacdabccaabddaacbbdcdbddaabdcdcbaadbcbbbbdddcccabccdcabcccaaacdabbabbadadcbdbcaadddabadcbbacddbcabdadcbabcbdddadadaababadaabcaacdabbcbcbbadbcdcdbdbacbbcbbdabacbabdcddbaddcdbcddaccdcbdcacdccbabcabdadbbdacdddcdbcbbdbadbbdddcbabaaabdccbcaabbadcaadccdacabbaccdcbdbcdcccddaaacaaacabaabcddbbadddaacadcdddccbabaadacbdddcacddbacadbcdabacdcacdcdbcdacabddcddaababadbddbdddaaacccbddbbcaacdcddcdcddbcaacbbbdcabbdacbbbabdddbaabaadbadbdacbbabdabadabdadaacdbcdcabccccbbbbcdcaddbcbccdddadddbbadcbabccddbdbdacaaccccbaabcbadabcadabccdbacdababdccdadaabbaccdbccaccdaabbdccdabacdaaccdcccabdddbbacbaddcadbddadddcbabddabbbcbadbcacbbcbaacbaabdcdbadcdcbbbcaaddddccbadbaddccdacbaabdcbbcbcbabdbdbadaadbcabdacabaccaaadcadabaadabcddccccbabaaabadcdcccdcacddcadacacbcabacdaddcddbbacdcacbdbbbaabdbbcbddcccdbaddcbabacababacdadbaadccaacccbdbaaacbcdcaadcdbbbbbcdcdbcddaadaadcbdbaacbcbbdcdaadccbdbdcdbdaddbdcdaacbdbabcadbaacddcccaacadbaacdddddaddababadcdcdbbacdbadcbaadcbbaaacabdbabcdcccdbcaccbddbbbcdcbaadcbdaaaadabbbccadacadcdcadcbddbcbaacbdacdbbddabdcdcdddbddbbbaacdddcdcdcbdababcdbccbbbddbbbcaacabcbadcdbbbcbadcbadcaacaababacaaacccdccbdcdddddcbbdddbacdbbcabdbaabacacadcbdaddccdabcaadbdbbadaddadcaddbacdacbbcaabbbcdbbacdbacadabdbdccdaddbbaabccddadccadabacdbdcdddaaaacddacccbcaacccdaaadddddbdacabcdbcbdddbdcdcaccabbdacaddcabccabdadddaddbdbbccbbdaaaaaadbaddacdaddbddcdadbbdabcadcadacaabadabbcdbbcbddacdaaacbddcbadddbaadbdcabbcabaabbdbbcabbabdbcaccdcdbbbdbcbdacbcaaadcbddbacadcddbcdcdadbdabdcadbccdccdbacddadbdbcbdcbcabdabbdcbdcbacacabcbdaadacccabaacbacddaccbccabdbadbaddaadcccdbadddbcaaddcdbcaddcbdabccdcbccadcacbbbdaddaccdccbadacdbbbacadabacdbaadaadadadcacdaacaabddcddcbbcababbaaacddbcbaccbdcbdddcbbadcacbdaaaadabaaacdaadabbadbccdbcdcbadbccccdcddbcdadbbbabbcbcccbacdccadbcadbabcaacadccabcddbdcaaacdddcbaaccbdcdcacbacbbccddaadaaacdadbcdbaadbcaadcdcdaaacddabdcbabbbadabbdadccdbddbaaabbbacddadbbbbbddcbbcdcadcabddbddacacbdacbacaccbcddbcbcdbaaaaadcbbcdcbdcacbbbdabcbaccbabcdaccccdabbacbddacdadbdcaaabcdabcbacdcbabcaccddbaabcbbcbcbcdababcbdbbbcbcdcacaaabdbdccdbdcdcaccaacccccbbcbcacbbbbaaabccbdadbabdbbbdcbddccdbcddcbdaababcdbdccdabbdadcacdcdacdbccabadabccbcbcdbdaabddcadbadccbadbcdcbbcabdbbddaabccdcacbadaccbadbadbadddcddbbacaacbaccaccbacadcadacbdddddbdcbcccadadabaddcbbaadbdaddaccccbcaccddaddcbdcdbdaadabcdadaacbccdcccabbcbadabacdbdabdbabaaaaadbdadaddaaabbadabddaccddabaaaabcdbdadaddddbbccbdcdbcdabccbcbddadcabddabdcadbbbcdccdacabddbbdbbdbaabddbcabbccdaabadddcabbdaabdbdaadaddccacbcbcccacddddddddacacdcacbacbdcaaaadabadbdcaaccdcccbaaddabacaddbdaabadaacbbbbdcbcadaddcdabcacbcddacacddcccaadbccbbcbaabcccadadcdaddcaacdcaddbdcdaaddacaddcabbcbcdbacbdddadbbdadccdcbabacdabcdbccbdabbcccbbacbbdddbbbbadbbacddbbacabcaddbbbdcbbcaabadbaacdaccabadacbdacabcabbccbcbcbdccabacbbdbbddadccdbdbacadbadcbdabacdbdbdabdbcaaaababacadbacabddbbaaabbcacbdbdaabbdbacbbbccaadaccbccadbcdcaadcaacdcadddbcdbddabaaccddbcacdcdbacaabaabadcccdddcadcccacabccdbdadbdcadcbbccbddccbababbcadcdcccabcccdabbcbdacabbaabcdcbaadcdcddaaaccaadaacaccacdddcccdbbabdbabbcbbacdddcdbabcabbddaacbacbabdbcbaaaaadcabbcdcbacccbadcdbacddaaaabadbbdcccdddaccbcbdbcdabbacbdbcddcaddcaacaacacccdcdbdbabdbbadacddcaddacddbbdadbabaabbdbaddbdcbacababcdcdababcccaddbcacabbacaccbdcdcccbacdbadbcdbacbabcacacbdcbcbbcbcdbbddbabdddcccdacabbadbcababacaccbacddcdcdadddbbabbbcdaadbaaccddacdcdbaccbabaaabadcbbddcdcdaacaacaddaabcccbcdcdccadabcacbacbaaccdaabdccabbabbdbadadacbccabbbadbdcdcdbbbbdadbbcbadbadcbacaaddccadaddadbbbbdccbdcbcbabbdbdaaaaadbcbaabaddbbadcccacdaadababadbcaaccdcccbacabcabbabbbcbbaddacddbbdaadcddbbcbdaacddbccdccabbacdabbdcdccbacbcbadabddcbbabcdbaaccaaddbabbdcddbcdaabacabcbadddbdaabdaddbbbcacdbbbadaddcdbcdbcccacacadcdabcaabcdabbcddbdbcdcbccdbabbdddadabcadbacaacbaddbdcbaabbdaadccabddcabbdbbaccdccababbaabdbbdcbdcbbdddbacbccdbbdbccadcaaabcdcbccabcddacacddcccccaabdcbabdcccabdadddbbcbbbacadadaddabbcacdacabacbbadacdacacbddcbcaadbdbbdccacdacaaddccbcbcbbcccddbddbbbddaabccdccbadbdabbdcccbccbaddbccbadddcdbbbaadabcabdcabbbacbacabdaadaaaadbadcddddabddadcccabacccddcbbccdbddaabbbadcabbccdcbbabcaddccbbbabdbdcddcaccbacbcbcaddcaaddbcdadbaccccccdbbccdcaabaaadbccbcddbbdadbcaddbadbcabaadaccdabbbbdcaacccbccdddadbcbcaddcababaccbdccdadcbcadbadbbbcbbdbbdccaaaadcaadacdabdcdddacbcacaacaabbddddaaccbbdccccaabacdaadbcacaccdaadbcacdccaaaccdbdadabcbbaacdcdcccadabdcabadaccabdcbdcdbcacccbdbdbbdabcadbbcdddabbadaaadacaaccaaaacbabdbdacbdbdddaddcbccccdccbbcdcbaaadcbbaaccddabdadadcccbabbcbdadcbbabcbabbdcdabbbbaddccbbdcabbaaacaadbacadbdbbbdabdcacbcdddcdbbdbdababaccdaddcbacbbcbbbaccdbdcabcdbdcbcddaaacbacbddadadcddcbdccddadddcddaabdcdabaddbabdbcccdddcaacbdabcaaddcacdbdcdbbdcbabdadcdddcdadacaccaddbdcaaaaaabbbdcabcaabbdcdcadcacdcdcadbdcbabdbaddbadabbbcccccaddcbadbdadddadbcbaabaaddadcddacbadbbcdabbccadddbbbaaadbbaddcaadbdccadabaababacaaddacbddbccbbadabcbbdbbbadababcbdbcbcccadadadbbbddbcbdddcdbddddcbbadcdcdaadbdbcdccadcabbcbaabcbdbddabcdcbcbabdcaccccdbbdcabbaadcaaaccddcddcbbcdbacdabadbccbbbccccaabbcbdabdabbcbabcbdaabdbbdbbbabcccbdacccbccbaacaaaddcddbccadbacdbbbdbcabbcccabdbdacaaacadcccabcbbbaacddbadddbbbbbddbdccdbacdabbccacaabdcbdabcdccdadcdcbccbbdddcaacdccdaaaadaaddddaaccddbabcddbbcabaadabbcccccdbddcbcbbcbbcbcadcabaaddcddcbadbddccacdcccdbcacbdbcdadbccccdadaaccbcccccbcbacaaaddbbcbbccaccaccbbccabddaaacccbcccdabdaaabaacdbdbdcdaabdcdbdaccabcbadaaaaacadbccddbccdbbbbdddadbccdabccaadcccadddcddcbbccaaaaadaabddcdcacbadabbdacdbaaaabbccccacadbdcacbbbacaddbbcadadccdcdcbddccadbbcaadaabbdbcaabbaabbbdabaaddbdbdaabbdbcbcdacadcaabadaaabaaaabccdadcddcbdabbdbdcaabaaaabbdaaccdabbddabaaccaccddabccbadbabbdbbaacdcacdbdadccadddbabadbaacbaddbbacaaadaddcaaaadccbccabdbbacabadadcddccbcaacdacdddabbcdcdcdbacbdadccadaacabcdaaddddabaacaaaddaaacabdbcccdacbdaacdabbcbabaadadaaccacbcaabadddaabbacddbacadbaacbadcddabbdaaacbacbdbcbbaacdccadcdbcbabaacabcccababbaddaaccaacaaacbbdaccbcdddbcaccdbdcbcddcdbddabacddbdaccabbdbcacbbacdcbdabaadbccadbddcccbdccadacbcdabdcdbabcacddabddadacaccacdbaddabdbbcdacdccdcbbbaccddbdbcabcddbaabdbbacabbccaaccbaadacdbbbbbaccbbcccbbcadcabcdbacacaadcacdcabcaddacbabdabbabdaadbbbbdccbbdcbaabbccbaacbadaddcabdacdddbaddaacbaabbcadddcbdaadbadcccabdbbacbacbadddbbaddacabcaddddabbdadcbcdaddbdbccbbdaaccababbacccddcbbacddacbacbacddcbbdbdcbcbaadcbbdbccdcbcabcdddaabaadddacadcaacdcaccbcbdbcbcdacababcddcdbbdadccbdacddaddccddcbbccdcbbbcaabcdaacabcaadabcbbdbbbacdccbdcdbdbbabcdbcccadbadddaaaaccdcdacbbbaddcaddaccbcdcadcbdbacdcdcabdabbabbbdaaaddadccdbbdbcadbabdacdbbaccbdcddadcbacabbbaccadadbdcaacbbcaaddbccbbadbdbdbaddcddacccadccddcadddcdbadbcdadddcbabaadbdacdddcbbadbddccdacdcccaccbdccdcabdbdaaacabdcbdddbaadadcacddbcadddcdaacdbbcbbadbabcabddabbbbcccabbdbbdbccaccaadcbbabcbcdbaaaccdaddaacbcdbcdbcbbdbdccaacdcadabddbccbbddcdaacdcabbdacbcaccaaccadacbbbbacbbcbaccdcababddccbabdbcbcaacdcbbccddaddbbcdbdadabbdddcbdbdcadcbbaaadbaaaabdcccbbdccccaadbcaaadaaccdcdcdcabbabcabcabdddddbaccaaddcdaabcdcbbcadcbcaadbcbdbacadaccbcabddadbbabddbdbbbdbcbbbabdabacadcbabccbadacaabcbbbbbaaddcdbbddcaaaccbccbbcadbaabbacaabbccadbadcdaddccbbabbdaaddccabcabacdbabdcbdcdcdadadbdabcdbcaccdcabacbdaabdcdadaadccbaadadcaaaadcccbddcaacbdacdabccdbcbdaddabbccbaacaacadadccbbaaaaabcacbcbaabdaccdccbcbcadddaddbcdabbddddacaacabccadabaaabbacdcbcadbcdaaaddbabbcbaddcccbdcaddcaccccdcbdbdcaadacdcdadcaabbddabcccbaddcaaccdcbccbcabdcdbdcaadacdccdcdcacdaadaaddcabcbbcdadcbbcddcccbbcbcddcaabacdcdbbcdcdacdddadaabaddacbbdcccdbccbcbaaaccadcabdaaabacdaabdaabaddcddbbddbbdaabbdababcadcdadcdaaccdbdbcccdcbbcacccacdcadcdadabbcbaabbdddbcdaacdbccdcdcccbdaaaabadaadcbbdacababaccbccccbcbbdabbdacaaddadcacbbbcaabdccdacbcbcdbccdcddacabcacbbbccacbbcdddcbaccabadbdaddabaadabdacbcabddbbdcbdddcdacabadbcaadbccabacadbbcbadcaccaddabadaaccbcabcaddaabbccbbddcdcdbcbbcdddcdbbccdcbadcdbbbadcbaaabaababdccabbbddccbabddabdbbadcbababdddcaabcacaabbdbabbabacdccaccabcdcdacdccdacadbcdcddbbbdacdccddbdabdcaacdccbbbdadbadabcaacdabbbddcaccdbcdbacbcddaddadbaccbcaaabbdbbdddabcbcaaaddaaddbbbabddccddcabdacdbdcddbacddbdabddbddadbcdcdddadbdabdcaabdabcaadadccbacaddacbbdbcaaacacbbadaadacabcabbddabbcbddcccbbcbbdaaaacaccddbbddcdccabcdabdaaabdaccbdbacdbcaabbaddbacadbdbbdadabaabbdcccaacadbbbdadcdcdbabacddbbbcacdbdcbcdddbdaabaadacbcdddaccabbccdadddbcabccbbdddddabddcccbdabcbdbabbdbdddaddddaddbcdcbadcdcdaabacadababbabdbadadaadaaababddadcacadacaabadddcdcddbddcadcdcdacacacaabcaddcdddacbcacbacdcabccbcddcdabdacadcacbdacdbacdcaabbadcdaddbcabaccbcdbcabccdacdacabdcdcdbbddbdbbdadbdaaacadbdccacdaddcaddabbaacdadddadddbdaadbbcddbbbbcdadbcbdbbbdbcdbcdccbbadbabaddabacbbbddcbadbdddcddbabccdaabbcdbbccabcbadddccdccbbdadccaccabadddacababadcbacbdccdcadcbcbcdccddcaccdaccbcabcbdcddaabdacbaaacddacbdaccaaacadddbbbdcbbbabbdaccdacaddcdadaccaddcbadbdacacbdbcddabddaadacccacacddabdddbabbacbdacabaadbbcbbbcabbabdcacbcadbddbcdbbadcbabdaddccaaaddbdadadbbabcbabcaadccdadcbadccacaddcabdaadacdcddadadccbbccdcaaaadbcabdcdbaddaaddbabbdadbbbbcabbbddacaaddabbcdbcdbacdacbcbbbaccbddbdaddbaacaaaacaabdbbadbcddabbdbcdcacdadadbacadaacabaaacdbddcaaadcaacabaaababaaaaddbadabbdaadccbdcdbdccdbcbdabcbbbcaccdcacaddbdaccdadacbdcbcdcdcacbdbdaaabcababccbdaacbaacdbaddbcaabdbccbaaadadcdbdbcabccccacbcadbaaaacddaadcbddcdcbdbdbbcddcbdabbdaabdbdcdbcbdbbaccddabbdcbdbabbbacbbbadbcbbbddababbcabaabcddaaaaabbbbdacbaabdabdddcdaaddcaaaadcdcabdbcabbccdbdcccbdbbdcdddbbcddcccbacbcbdcccdccbdddbaabdadcbbbbbacccbabcdadbadbbbdaaccdbbcddddaddcddbdbcadadbdacaadcaabdaabcdcdacdacbdaaaadcbaccbaaabcbacdcbdacabdbdacccdbcdbddbbbdacdddbdbbccbdcddbdabddbbcdcdbcbdabdbdcadadbcccdadbbadbcadbdbdbaccacbbdbcdbbbdcaddacadcccabbadcaadadadcbddccdacaabacbbabcbcdcdbbbcbacdaddbbacbaccaabbdbaddbdcabbdcdaddcdadaabbcbbaadbaaaaabddddbdcdbbccdbbabcabbbcdadcaccdbaccdabddbdbbcdccdbaadcbbacbbacbcadddaaacbcbbaacbcbbddabdbbacbccbadbdccaabbdabaacabccabcdaadacddbdcdcccbbdaabccbabcdaadbdbdcbbdcaddacdddbcdccdabbcbdcdcbaaacddccdbdcabbdcbbdddaccdcdacbaadbbacaadbcaaaccbadcbdbadaabccbddaddcdadbdabdddcadbaabbbcbabaaacdbccacaaabdcbaaddddabadcbbccddbaaaaaadacbbacbbdacabbdaadddaabdccddbdbddadbbcddddcbdcbddcccccdccbcccacacbcaacadddbbdcbdacbdbdabccabcdbbbaacbccbcacadabbdccbddcaacdbdcbadbadcccddbcacbbbbbcacdbbbbcadbbdadcdcbcadadadacdbabcddabacbcbbcdcaaacdacacadbcbadcacdcaddccaaaacbbbdadbbadcbcdaddaaadabcddcadabacdabacdcbcdddcccbbabbabcbdcccdbbcabdcbabcacbbdbbdadaacbbbacdcaccababbbdbcdbcccadcadaddbcacdaddabbbbaaadddcccbdccdcdbadabbccabcbcaaddbcdcdabbbbbdbcdddcacbcabadbcccccaacdbabbadbcaddbacacdacccaaaabcdbacccbdbdabaabdcbabcddacbbddcdccbacddbdcbabcbbdadaaaadbadaacabbdbbabaccdcdabaddcaccbabcbbdabbdccabaabbabcaabccdbcaddddacdabbdcdbabaddcbaddabacddccddbaaaacbcaccadbbcdaacbaacdbccacdadadaabddbdaacaaacdcddadbdbabddbbcaacdcdaacaaabadacdabcdaccbcabadbadcacdbacdcdaaabdccaabacbabbccbccdcbbbdadddbdbcabcbcbbadbdcdaabacdacadabdddcbabacacadabcbdcbacacccbdbaaddcbadcbaccbadbbcbcbccccdabcbcbadadbcddbbbbabcadbcbdbcbcadacbbacdbcaabccbcdaaadbbbcdacdddaacdbccdbdcdddbdcccbbbdccbaacbaabaadbaadbcdddbdcccdcabdbcabcdabaaccbcdcbcbcaddbcbbbbbcdbdcccddacccadccdcbcadbadbcccdcabaaabccacaccbacdaabcaddddcdccdcacdbcbcdbadbacbdbbdaabbdbdcaadbdcdddbcdbaccadccaaadbdcbcccaddabbbbcbcccdcabbadbbcdaddabdbbbdccbcccbabbddbbbdddbcccccbdccdbcadcdbbabcdabcddddabbbaddaababbabbacbcccdbacacbcbdbbdcdbbbccdadccdbdadcdcbdadddccbcadacbbdbddabddacabbdbabbadcbadbbcdcbbbbdabcabdaccdccbccbddcbacadbaabbdacadbbdadacbbbdcbdddabbbabbcadddbdcabdcccdcabdcdcaaacdddacbaabdcdcbcddbdbdbbdbaacbaaadabccccdcccbbcccddcacddacdacbaaabdbaadcabbcccaabacbdaadabcdbbabbdabaccdacdddddbbccbbcadaccadcdcbccbdbcaaadccadacdbaaaabbdabdadcbbcdbcccdccabaabbddacbadabddcccbdaaddbabccbaabdacdaadcdcbdbbcbaadbcdcbbadacddcccaccaaacdbaccdbbdbabcbbbbbdddcabaaabbdddcaddabbacacdcbccdbbcddcbdadbdbaaadababaacaccbcdadacadacabddddbacadbbacdadacbcbadabbdbcacccbcccaccbcbccadddbbdaaacaaacbacabbccccddcbcddcbccbbddabccccababdbcbdaadbbacadaaacbccaacabbcddcdcadabbadbdcbbdadccdacdcdbdbbccbbadbbbcbadccbbadbacccdaaaaadabcdabdbadaabdcddcadddccbddabacbaabcbdcdcccaadabaadcddbbccbdcbadabcadbcdcadadcdddaaddaaccabcdccbcbdbabcaccbcbadbaabcdbbdccbdaabaccddacccbacaaadabdbdccbcaabdcaabdcdabdccbbbbacadbdcddccabaccaaccabbbddbaadcaabadbbcaadadcdcbabadaadaacbdbbbbdcdaabadddbcbbdbdcadaccbbbbbbcddbbdcdcacbbadbdaaaadacdbcdbdcbccbddbbdddbccacacddbaccbcbadccbbabdaacadddacbcacdbcbbcadaadbbbbbadcbacbcacbaccdbcdbcbbcbddbcbdbdbdddcabacbaabadccbccbccabaacdccddbdddcbddaadcbacacbcbddbacccabbbbcabcdbbdbbbdaccbbddbbcadcbdbddbbbadccdabdbbbaadacabaaccacabdacbbcbdbcabbaddcaddbcbabbbadcabdcccddbaccbcdcbdaaabbbaacdbbcbcadabdcdbbdbcdcdddaddddabcbaacadbbcacdbbbccacccdcbddcaabacaccdbaaccadbcdbdababcdddbdccbcadcbbddccbddacdaddbacddabbbcaadbabcaddbdcdccbabaadbcbdbdabbcaacdbabccaaabdbadbdacddbaadbdaddccbddacbbcbdccbacbbbccbcbaccaacbcbdaabcabdabadacdccbaacbddadadcdcabadaaaccaccbdcadaaadcdaabadcbcacadaabdddbcabcbdadadbcadcacddabdadcaadbabccabdbaaadddcbbbadcbadccbaccbadbaabcbbbcbbcbddcbbbcadaaadcbbacdbacbcdbadbddbdbcbbbcadddbbdbcddacacdbddabdadacdbbddbcdbdcddbbcadbbcbbdaabdaacabcdcbdbcdcabcacdaaacadadacdddccadccaccddbabaabaacddadbddaccdcdacbdbbdaadbcaabcdbbbaabbadaadcddaaaadcabddcddbadabaaaadabdbbacbaaadcdbbbcbcbdbacddbddccddbccccdaaacbddbbbbccddabcdccbdbcdcbcdabccdabdbcbdddccdbcbddbbaabacbaabdcadbcdbacabadbaaaabbcccddacaddcddaacaabdcbaaadcaaadaaaaccaaadacaabdaccbdcaccccbadadcbbdcacddcddadbacbbdddabadbacadbbbdbadddaaccbcaddcddbdbacbbbcaabcbbabbbcabacbcbccdaadccbbbcaccdddddcccbcdddbcbaaccdacdabdadaaccabaabddadaddcdabcddddaabcdcaccabcabddacddbabaadcbddbddbbbbddcaddcddccaaacddabcabccbbadbaddddcadcabbabdbbadbaccdbdababcbbdcbbcbdaacbbdaccbdacccbacabcddbbbbcbcaddcdbccbbdbabccabaaabccbccbaaccbccbcdddbccddaadbadaaabdbadabdbabacddbacbdddbabddaaccaabcdacabcabdcbacabdaacdbabbbdcbaccbcbdcdaacaacccacbcddcbadbbdcccbdabababbabbddcbbbbdddcbabdbcdcdadcabdacdccadbccacdcbcdabcccabbddccaaaaabbacbabbdbbdbdcdabbbdbbccaabdacadcadadbbddbadadabdbdcbdccbddbccbbdddcddcbadddabacacadbcacaadabbabccdbabccbbcabaaadddaabbcbacbdadbcdabaabcadcaacdcababaadbbbbcdccbbbccadbdbcadaccbdadcadadbdbaccdbcdbbdbdbdcadbcbcddcddbcbbabbbdbaccdabacddcadcaddadcacbcddbacacdcdaaddbcdbcaacabbaccacdaadcadabdababcdbacccbcdbadaaaaacabbdaadbdbdcaddcdbaaacdabccdbdcccadadbacdcdacadcdddddcacdddcbccbbdcaacdccbbcdcdaaaadbcaababcabccaaaabddadbbbcaadbddccbbcdbbdddaabcbadcbdacdcaccaacbaaadcbacdaadbabcdbbdcbdbbacabcddbbadaabbccacbdaadccdcabcbbbdacaccdbccccddcbabadaddaccdbcbbdadddbbcccbaaadcbccddddddcddabddbdcbcbacabddaccbddacacbbddbcbcdddabbdbbcdbbabadbbabbabadcdcbbaacbadadaabdaddbadabdaacccbcbcdddcbbdbbbadbaacdabdddccbcbabdadbcdbdcabdddbdddadadbdcbccabdbdcdcbcadbcadcadadcacacacddccadddcbdacbcaaabddcdbddcbcabbaccdbacbabbcdbababbdccaaacadbdbdcbaabbabaacabbacccddcbacdadabdabdbbdaababadadadaabccbbdcacacbaaadaccaccdaccacbbccaddadbababcdcbcbddccdbddbcaccabddacdcddcabddddbcacaaaaddcbcabdbdcdcaaabbbccddaaabcbdbacbcaaddabbaacaaaadcccacbbbcbadcdaacbacacbbabacacaccdbbbdacaabbdbcdbcdbaaddddbbaaccdacbbbcdbadacaddbacbacaadaacbdbdccaadaddccabaabbdbcbadbdacaccdbbcadaabdccbadbdadccaccbbdccaaacdabaddbcbcacbccddcddabccbccbbcaadccdaccbcdadaaadccbbbdcbdbcdcddbacbddcbdccdbadbcbbcaaacaacbaaddacacaddccdddbcaacdacdcaabccbabaabcacdcdaddbadcdbcdabaabdadbbaadcabcabdadcadcdcababbadbbccbdcdacbcaacbcbcccbdabbcbdadbcbbbbbccadacbccddbcddaabadacbbabaddaddddcdbaddbccddcbabadddaddacbdbabacbcacacdabbdcaaddaccdbcdbcacdaaadddaadcacbcbddacbdadabbbabacbbcabbbcacaccaccbcbdcdbbbdabaacbbdcadaddbadddddcabbadcbcbcbcabccacdccadabcbbbadbbdbcdacbbadcccbdadadbbcaabaddbbbccdbadbdbcccdbdbccbdacdcacdababadccbcacbacbdabaaabaccbacdcacbdbccabcdcbcdaddcdbabccbcbddbcbacaadbdddbdddbabcbcbabccadbbdbabacbbdbbabdcdcdbcccbadcdadbcdacbcdbcabccbacdaccdcbdbbbbaaadacaaabcabdaccdcacbabbdbbdcbacaabddcbbdbdcbbcbdaacccdcadbcdaadaaabccbdabddbdbdcbbddaccaccdbcadcbbbccdabdccbabaaabacbbcbacbcdbacbcbdcacadccbaccbabcbadddcdccbdcaaacbccaabbacadbbaacbacdccbbacaccdcbacbcadddddbcccdcbbbccbdcaacaabcddbcbcbdabdcaadabbdbcbaadcbacaadcabcddbbdcaacdacdccbbbbdaabdbbccbcadccbcbdbcbcbdbaaaabbdaacbaacabccdabbdaddbcbdbbcaccdccbabaabdcadadbbccccabbdcaaabbadccaadddabdddabdcbaccdccbabaaabdacababdbbdabbcaaccabacdbdbdcaaccdbbabdcbaabbcbbadcddcbcbbbdcbaccadcaccdcadcaabbcbacddccbcccdaddbdaacbdacdbbbdaccabcddacddbcdbcbcdbacdaaaadddbdcaadbcbabdbcaadddcdddcbbcdbcabdbbaccbbaabcbaabaabbdcbbbbbdcadcabcdcabaadbaaabacdbdddcadddcbadcacbcccaaccabbcdbdbaddbcbacdccbddcaddacbdbddccddddbdbcccabaaaccbccbacbdcdabccaacdccbbbcccddbabdcbbbcabbcbccdcadccccbbaacbaabdaaaacaaadabaabaabddcdadcbddcaaacadcbcddaddddbacaabcbadcdaaddbddcbbcbababdbadccccdcbcdacddcadcdaacccdcdbaadcbbdcccaddccccabdcabcbcbabcdbcddaadcabaacbcdaadcdcdbbbcaddcbccdcacdcdbadbdaacdbacdcdbacabcadaddbdbaaccaccdcdbcaddaabbacbdabbddcadaacbdbbadddaddaaadcbdcbbadccddbbcadbbdcbadbdaadbabdcdacddccbabcacbbbaabddcdadbaaaddaccdaacdccddaabaadbaccabccacbccacbdbadbcbbcdcacaadddccdaaaaddccdbbaaaaabdbbcbcbbbdddaabcabdcdcbbdcbabcacbcdacaccbdbcdcddcaccdacccdcbbbacabacacdaadbddadacaabdbdadcbbbbbddbbacbccccdcdbadbbaabbabcaaadcdcdaabcbbacdbcddbcddbbbddabaabbccddcdcacbabdabccbcbcbdadbdccbddcbabddbbcbcbccdbdcbdbaddddbbbcdadbadbadadbbbdaadbbdaaacbcdacddbddcbabddaccbbabdcabccdcadccadcdbcbadbddbbccbdcbbcacdbdacacacddaadcadaabaabcabacbadbddbddacabacccbabadbaccdacbddbaccbbccddbcbbdcabdbcbbaadaddbbbdcdbccbbdcccbdddbdcbbccbbddbddbdadaccababdbcaddcdcdbaadccaddcdadababdbaadaccccbbaabccbabcdcdabbdadaaabcbabdaadcaacacdbdcdbdbccaadbdddcdbcbdcddacacdadbbbcbbcdcccbdbbcddcbabbdbbcbaacabbacbadcbbcbbdbcddcccbaddbdddccbccabadbbcdcdaddccbabbbbdadabadbccadaccbaaabadbcbcdcadddabdccccdddaabbcadcddcdddaaacaaddbadddaccdcbdbdcadadbabcdcdddbdbccbdddadadcccaacaacbcacbccbcadaaaddbddbbbcabdbbbbdbdcbabacbbabddcdcddcddabaaddcbcacdbacabdcbdbbccccbccddbdacdddbabccbbdbbbddbaddaccbddbbddabdacbcabddbaabacabdcdcbaadcbbdadddbddacabacdccaacbcdabbcdcddddccdaadabdaabcabbbccbbdadcbbbddacacccabbaadabbcbdcdbdbdddcdabadbcaadccaabbadabdbbdbbbdadabbdbadaadcbdbddddbdabacdcbbadddbdaadbdabbacdbdcbddbcabccbaccadbabadbbdbddcbcccacaaadabdaadbbacabbbaccabcddbcadcabaccdabdbcbcdbadcabdabdacdccbcddcddabddbadbbcabddccdbbbcacbbcdbbaccdcbacadccbddbabadcabadcbcddcaabcbcdddaabacabbdccccbcabcbbcccbabcbbddabbadacabbdcbdbcabcdabbcdbddcbdcbdbbaddaccaccdcbcacddaabbbbadaadbacbddacbdcaacbbacbcacbcbadacdcccadddbdccbdbdddbcdbaabbbbcabbbdacbbcdaacadbbddabcadccadabbcadacacbadabcacdddcbdabdcddabddabaaddababbccbcacaccdcddbaaadaaaaacddbacadbbabbbdadbbadbbdadaccdddbabcadaadacbbdadcdcdccbcccadaaacabcdbabccaacadbaadccabbcabbadadbabccddcbcacbddcbcbcdcdbdcbbbcdbabdadcddcadabcaccaadaccbbadbcabbbabcbbbaaddddcccacdcaccccaccccdaddbbbaabbbdbbacabbcbdabbbaaabdacbadbaddcddccbabddaaccbabdcacddaaccbccabddaccbacaabbbadcdabdbbddbdbddaadbbdcabbcbaddacbcddcdcbaadadcacadadaccbdabcacacdbbabbcbccdddcddaccabadcddbddbdaacacaaddbbaccbdcaaabcbbddbddbbcdaabacccadccbadbdccbccdacdcbcccccbddbaabdddaacaacdddaccdcbdacdaddcdbaacdaadababccadbcdacbcbcbcabaabbbdbddbcaccdabccaabccdacbbacbcabaaccaaaccbcccdababbbdacbddaaacbdbbacdacadccbbbcabbdcdcdaabcdbbdabadbdbcbdcdbbabcbbdcaacddcacacddcbdcbaadddcdaabbcabbbbdaaddbdabaabbabbaacbbdbbbdabaaaabdbabbbbddcadddadbbdbabcaddaacdaaaadcaacbaadcbbdbcdcadcdccbadbbbdbdbaacddbcdaccbbadacbcbaaababbcdadbdadcaddbacabcbccbbdacbcdcbbaadacdadbaaccbadaccdabbcccbdaacaaddcdaabdcaaadaabbbcbaabadcabbdabdaddcdbadbbadbcabcadbbbdbbdadbcabbccdcdcbcbacaddccaabaacdbcabdbacdcadcbcbdacbaabcccaaaaddababccbcadcacdababcabcbdbcccabdbcbbcccbbadbdcdabcdcbabdbcbabdaaabcdacbaaddcbcaacadcbcbbbaddacabbdcdacbaaccacacaadbdacbadaacdcdcadaaacadcadbcbbcaadaddabcbdabbabcaadcabddbbadacabccbcdbdccdadabbabdbcbadddbbdccbcdaaaaaabadaababaadacbbabdcaaddddacdacacdbacacaaccbabbbdcdddababdcacdadbdcbdacabdccdddbaadcaddddbadcdcacdadaaddadacbddcbbabcdaccdadcaddcccbadbcaccbcdbaadbcdbdddbddbbadbacacdcccacbbbcbdcdbddabdcbadaaadbccdccbcdbcbdcbadddaadcadcddbdcacbbbcacbcdcbdbdddcbdcdbdbcadadbdcadbccacdbbaccabdbbabcabacacdaacadbaaabadcddbcbdaddcbbccbcadcbcbbaaaaaaccbadddcbaaabcdbdcaaaacdcacccdacdcbdccdbcbadcddadbacdabcddacdbacbddbadaddbbdadabaacbbdadccdbcadabbbbdadcbcbcdbcbcccddadbddcccabcbcddaaaabababbcabdaabcbacddcabaddbbcdbbdddcadabcdbcbadcbcaadabaccdadbbbdaaaacdbbcabdccbbabddbdcdabdccaacaabbbddcadbbaaaacabadcdabcabdbdcdbcbcadbcbcabbdddbacdcdddcabcabbdbbabbbacadbaddbabacadbbbdbbaabdbdadccacaadaaadacdbddabdaadbbcacbacbcccabcaaccadaaccaccbccaadbbdbaccdbdbaaccadccdaddccdbbcdaadcccccabcabddacabcbbdbccdbddcdcababacdbcacddcdadcaacbbbddbadabcdbaddaadddddcdacdbcddacbabdccddddcdddacacaabdabbaaadbbdadccddabcacdadcbbdbbdbdaaacbcdbbaacbaaaacdccdddacddaddddcadbcdabbdcdbaccddcacccbbdbdccdcdcacddcbcadabcddabbbacabbddadcccdccccdbadacdcdcddbcaacbbdbbccdbadbdadacccacdccddacbabcbbddcbccdbbddacaabbbddcbaabcbbdcacadcddbcbcbccddcbabbcabbdabadabbcdcaacaccabdcadcabdabbcccbaabbbcdbaaaabadcacaddcdcaadbdabacabdbadcbbadabbbaaadadcbbddbbbadbdabbadabcbaccadcccccdcbdbcbcadcccaabacababacdcdcccccabccbbbccadcaaadaaadbccccdbbaaacbcadaababdbbddcdccccacbdacdcbadaadbccdaaaddbcddcacccabacdaadccabcbdaaaabbbadbcddadcdbababddbccdbabbaaabadabadbcbdacdccbbbbbbaabcddcbadcbaabbaadddacbabbacadbcbadddaaadbdbcbdaaadcbabcbbcdbcadbdccbdbbacaaaadadbbbacadbbbaaddadccacccbbababdcbadbcbbdbccddccababbdbbdcbdbacaacbacbddaabaccbacacdabddcbadaddaacbdcbcbddabbcbcaccacccbaccaccbbcddbdbbaadabccbcacdaccdbcbabccbdcdacdbbccadcbadaacdacbcdaadcbadbbdcbacbdbbcbdabcabcdaadcdaccbaaaddbaccadabddbcdadcccbcadcbdcbadbadcdcabcbadcdadadbccbbdccaddacabbbbabdcaabacdbdddddaadabacbccaabdcccbbbaddcdaabacccbbcacdacbadddddddbdddadddabdbaadadabdddcdddacaabdddabdcabadbaacdcacaddccacddddbdcbbcbdabdcdbcacabacacadbccbcbcdaabcadbddbbaacccdcccdbbcabbaaaadbaccdbcddaabdabbbcbbcadaaddacdcacddbccacbcbcbabbcadccababcacddadaabbccbbdacddacacbdddbcaadcccacaccdccdadbaddbbbcddcbbaabadbccbdcabcccddcaccacdcccaccccaabbdbaaadbbcdadcdcbcabdbcbcaadbdbacddcccaaddddcbdcbdcbcdadadcccbabadabcaadcddcddcdbadccdbbcadbacbbddcbcbabbdddcacabdbaabadbaccdacacbaadcbcaadaaddcbdbcddacdbacabbcbbdacabdcbdddaabddcdaacaccaaccbbbdddadabcddcdadbddcdbcacdbabbcaccabdbacbabdacadcddddcbbcdababcbbacddaaabccccadcbabbacbbdbdddbcccdacabacbaacdbaddadccddcddaababdbccaddacdbacccabccabaadbaabcadddccdcbdaadcccacbcbdbadaaadabcdddcbcbbadccaadcdaddbdbabbcccadbadbadacbdbdbbaaddcbbdddccacbdaaccbcdbcadbbbcadaccbadcdacadbccaddcddbbaaadbcacdcdbaccaacbcccbcdbdacabaddcddbbcbabaabacabcddababcaadbcababaacdbbbaaddacadcbaacddbaaaddcdcacbacdaadddbbabcadacbbcccbbbabbdccbbbccddddadddaaadbbbdcabccabdcabbaaddbdbcacabadacbcbcbabcddddcdcabaccdaabcdaabccbdcadbdbdbcaadbcaadbcddbbacdcbbbdcaddbcaabccdbdbaccacdbacbcbcdabccabbbdddaabadaddaaccbddbcdcbbcaadbaccadacabcabacadbcacbccbacbabaacdcbadddabdbbdaacaabddbbbaddbbadcccdbabddbcdbabbdcbaadaabcaabbddabdbbbacaadcbbacbabdbdcababbddbdabddcaaacddbcdcdbdbacdbcaadbddbaccdadbbccbcbadcadbabadcbccbcacddabdbabaaaababcbaacddccbcdbdbdddadbaacbacbcadaaabdccdbacdbdbccddabdcddddacccbadaaacccdabddcdddbdacdbabcddcbdbcdbdaabaddbaacccbcbcccabcdacdcbabdbcdccaababdbabcadaaaaddcadbbaaacccbddbbbdbaddbcdcdbcdbbdabcaabbbabdcccbccbcacbaddabbadacaabcddbbaaccbcdcbadddcdabacbabdbcdadbbcdcbccdadddacdbcacacdcbdcabcaadaacdccccbccaddcdbcacccabbcdccaddcbcbbbbdccaaaacccaabdbbacbcabdbbbdccabcdcaaddccdcaabaacdccabdcdbbdcababbacddbbddacbbbcdabdaabdbccabddcdcbaabccabddddccacabcbadabcccabdbbcadcadaadddcadddcdbacccbccaaabcdabdbbdbbbacadbdadbacbcdbbbddccdddcaadbccbdccaddaaadbdabcddcbddbddbbcabbcccbbaacbacdcbacbcbddcaabbbddcacacdcdaabdbbdddacbbddacadaacdcdbcdabbdbaddaacadccbaddcbcaaaaaadcdbdbbaacbabddbbccbaabdcabddcdbaadbbdcbcbdcacaaccbadbabbccbdbdbbbddbcaddccaacdbacbdcacbddcbaddbdcabbabccabcaddcbdaddddababacabbdbadaabbaacaaaadddaaacccbddcaaadcdbdddbdcccaacdccdcadcbcdbcdbacbdabdcdcbbaabdbcbdcbcbadddaabdbdcacbbbdcdacabccccdaddcbdbcdcbacbdabdacadcabcbdacddcbdcdbbcbaacbcdcdabbbaddcdcbdadcdbdddcbdddabdbccbacaaacbbcbbddbaddbcdabdcbbbbcbbdabdbccbbcdbaaacacbbdaaabcdcbdcbdacaabcabbadccdcdadbdadaaabbabbccdcbbccddbbbabacadaaabacddbbddadddacbbababdcddabacbbddbdcbaccacbcbdbbdaabddbdcaccdbabdaccdcabdbdbbbabcbcaddbcddddcbbcddccbbdcabcacacbaddaacacbdadcdbcdaadcaaaadadddbdbcbdcadddacccdacbcadddaabdbcbbaadabbdbaccdaabbcddccbacccabddacaaadadabaabdbcddacacbacaababadbdcbcadccbddaddcaabbadaaaaabbdbaddbbabbdbcabddacabbdbacdcacddcbdbacdcdbbdcdcabadcbbddacbbadccccacdbdcbaaaddabcdcdcbcbaadadcacdbcbaccbcddccdbbbaaddcabbcddacdabdacbbaabaddbadaabccabaaadbbacbadcdcddabacabbdcdcacdaabacaddaccdbdadbbcabcdaabccdbdaddcbaaccabcaccddddaaaccdcddacbcbabcadadbcddbdaabdcbcbadadcdbcadcbdacdabadaacbbbadcacaadcadbbcbbbcbdddaccdcbaadcabcbaacacaabddbbbacaccabcdabccbdaaaccaacbddadbcbdddbcadabdcabcdadabbcacbbaabbabdadadcdcadbaaccccccbccdadabcabbbccacccccaccddabdaadbcaabacdaaccacacaddbddaddcdcabbcbacdaaccdaacdcaccdbdbbcaccccccdcabbacdbbcddbbddcbcddadddbdaadbbadcbddcacdabacbbddbcbbddadaaaacddcaacbacdaaabadcbdacbdaaccbdabcddbddcbacdabbbddbaaaaacbababbbcbacbbbbabadbdcadadaadaacccddbccaaaacbccababbdcbdbbbcbbcdccbabbabddcddbbabccbdacbaaaaacdcadcdcabdbdabddcacdabaddddcbacabddccdadabdbccabcbaaabdbdcdabcaacbcbbbabbabdaddccdcdcadcccbdbddaaddabbcdcacbacabaaaadcdbaaddbbaacaacacdbcbacccabbaaccbbdcdbbcdacdbacadddcdbaccaddbaabbdcccaacacdcdadbcbcabbccbbdaaddaabaccababdaccdcdbadcdcbacbdbdcacddcbccadadcadacddcbbcacdaccdaaaaaaacdcccaadadabbbaacccdbbddcbbcaddaccbcdadbaccddbaabaccdcabdbbbcabacadabbdcdaababcbadcacddcabbdcabbadcddacdcbcddccddcabcdcaccadabacacdbbdaabbccadbcccadcbaacbabdcabbdbdbcaacbccbccadcacadbcdccdcbacaabbacaacdcddacddbdabccddbddccdbdcdacabdbcaacbbcdbcabbccadcbdcdcdcaabbccdddcbddccddacacdccdacdccdbdaddbdacbccdcdcbdbbdaaadcbabdccbbbacddcdbadcbdbcadbcbddccbdcbbabdcacacabccaadacbcbadddddcacacdabcbbbcbbcdabaaaadabaaadaacdbacdbbbadcdcdbddddbbccbcbddbdaabcbcdacaaacbddbaabddadabddcbddcbddccbbddddbbcdbdcccadacadcacacbdadaaaaacadddbddbcaacaaadadbacacadcaaaacbbcccbabddddccbabbcdcdcabcbbbdcbcdcdddddcdcdbcbddaacabbcdabbdacbaaccbbcdcbaadbbbdaadddadadadabbadadccbadaddddbbaaacddbaaccdddadadaddbdddbcdcdcadaabbadddabbacccdacccdabcaadabbacccabcabdbddccdccdacbdaacabcabbdaaddccacbdbabdcabbcacdddcbaaadcbaccbadcbabdcbdadccdddbbcabaabccabaadadbbdbddbbcdbdbccbdddcacccdbaadddcaabbacdcabacabddacabbdbbdadddbcdbaabbbbdbadbbbdddddbdbbdcccbadbddabcacddccdbccdacbdbcadbcdcdaacbddaaddbdadbacaacadacaacbccbaaccbbcdbdadaaaaabacdbcddacdcaccadcbddbcacdacbccaccadaabacacdbabbdbbdcbdccadaddcdcdabbdcbdaadbaadabdbacddcaaabdcbccdcccbababbcbbbbbcadabcadaacbdbcbdbaaacbaccbdddabccdabddcddaddddbabccaabbaacbcdacbbbcdbadcbcdbbcbadcabcdbbcdacccdacbbcddddbccbbcacccbcdadccacababddbbdcabbbbbacbbdabdaabbbcbdbadcdccbdbcbcbdbdbcbcadaadaaccccdbcacbaadabcbabcdcbddbdabcacbcabaaddccadcbddaddcddcacbabccdbaadcccacbcbadcbbbabddbbcabcbbbddbddbaaccaddcbadbcababacadbdcadadbdddccccaccaacacaabacddbbdcbadccaaccdadccccaddbccacdbcddaadcbacbbcdabababddadabcbdababccbcdbaccbaabadabdbbccdadcacddcdadcadbccdbcdabaacabccbbbcabdccccdcabdcadaccdaddbbabddccbdbabcadacaabdaccacddcbdbbacacaabadddcbbaadabcacbadcdcacacabccdbdcaabadbabcdcadbdacccdbdddbadabcccdbadabbbbbcddcaddaadaadaaababcaacccaadcadddddcdbbddadbababccabdadcbadccbccccdccdccbacccdacdadbcabdcbcdaaabbabacddddddddbaacbaabbabcabbcaccadccacbdaadcaabcadaabdbcdbadbcccdbdcddcdcccbbaacaacdbdcccaaaabbabbdbddcdadbdccbbccdddbddadadaacdabbaaaacbcaaaddcaaccbdabbddcdbacabadaddccbbcbbaacbcbbdacaddbdbcdccaccdbdcadbbbaaadcdadcbbdabbdaacacbdacaaabdaaabaacdcabdaccdccaccabccbccadbcbdcabcbdadaabdbdaddaaccbdccdbdbadbdbccbaadabcbddbbddbadbbbccbdadadcaddabadbcaaabcbcbbddaabbcadbabbccbaddddccbacabbcadcabcabaddcbadaabdaccaacdcdbccdcacacbaaabddabaaccdaadabadbdbdbaaabdacdbcccbbdadadaaacadcbcddcbbbbdcaccbdabdcabcdacadbdccdbccdbaabacacabacbccdcacabcbddbacbbacbacbaaacadaabddcddcddabcadcbabbbbcccabbddddcacadadadddadacdbdabdcaaadcabcdbcdcacccbcbcbdaadacaacaddcbaadbdacddabddbcbdddadbbcccbdcaddcdbbcdbdddacdcadaaaacabacaacaddbbaadbbcbcbddaccdbabcbadadabaaaccddbcdbbbdcdcbbbadcbabddacaadaaabbdaccadccdbcbbaadbcaacdbdddbcadcdaaccbbaabcaddddbddbdddaaabadcaccdacbbcdcabcbbddcdaabdcdabaadabadbbadadacacdbdbddbcbbcddadabbacdaadbbbcbcdadadaabaddcbaccccababbcdddbabcacacbabbddabcadcadabbcdbdbcabbbdbdcbbcddabccacbdddbddcdbbbcbdadccbdbaacabcbbcddbadbadababcdcbcdbcbdcaddbdabcdccdbcbcdadccbcdacbbccdcadbacdbbdbaacababdccbadbcbddddbbcddabaabacdbbacabbdddabdbacbabcaccbbacadabdbcbdddbbdccbaacdccdbbcabcdcccbaabdcccdaddcbcdddbddccbcdbddcbcbadcbcdbaaccbadaacbbbdcbdbabbaadacadcacdcdabbadbddcdbbcbdbaddbdbdcadabaabdcbdddbbcabcacbdcddcdccbdacdddcbbdbbcdbcbcaaababbdcadcdbdbcccbdaccddcdacbaaabadbcccadbcddcdbcddcbcbaabcacaacacacdbcbdabbcdadbdaaacccaabdcccacdcadcaabacabcdddacdcbaaacddccbbbccadcdbcaabcabbaaabbdddbcdaabdbccdadadbaadbcdcdbdccaccbbbbadabcdcaacbdbccddbaddbbdbdabbcbbbacdccabcbdccdaccbdcadbdbaaacddddcadcadbacddcbcdaacdbacdbabccacaaaacdabdcbdcadababcdaddbdcbcacabacabbaabadaaaacbcbbcbccbdccaadabadbadaccacdacbbabacabbddacbdaccdababbdcdbdcbccacbaaadbcdbbdaccbabaabacadccbdbdbccbdcdccdddcbccaacacacacdcdbdcbaddbddddaccadbcadadaacdadadabcdbabadcdcbccaaccadccdacdcccddbcaaabdbbbcacabddacdbbbbabdccadbbccdcabcaabbccdbcaaabcacacdbdbbcdcbabadcdaddadddbbbcabbbbcccbcbddacdbbbdddaaabbbacaddbadbbcdcadacdcadbdabadabbddabccdadbdddccdcddcacbbdbdabacabadabdcbcdadcaadbdadbcaccaabcdbdccbacbdcbaaddbcabddbbadbbcccdbcdddcdacddadbbbdabacbbbcdaaacdddcdcbdbabdcabcddabbbadbcbbccadbadadabdaccdcccaccdcdcadacabcdcbdaabcbdaacacbdcddabbbadbabbcbadcbabbacadaacdbdddbbcabaccbdcbbccdacdbccccacdcbabbbabbdacdcbdaabcaaaccdcdbadcacadccdabccacddbbababddcabadcbdacbcbdbdcadcddaaabdaacaacddaaadddbcdbaaacbddcaddcbdabbcabccacbacddccbbcbbaddddbdadaacbdadcdbccadcccabbdacbbccdbcacaadcadddabdcddbbdadcddcadcddaaddcbdddbbccbbabbbdbccaddbdcbababbbbbbbbbdadbaaaccabcaddbcaadccacaaccdbadbdbaddadccadcdbdacadbbcdcaccdcccaddaaccadacacbdacbbbdadacadcdcacdbdcdcccdbddcdacbbddadbbbabcccadbabbcadaacccbbdcddbbbdaadcbaacadbabcaadadabcabccccbaccadcbadabcddabbbdcbbbccaaabcaabbaaaacaabbacddbbdbcbababbcaddccdabcbacbdabdaaadcdbcddcdbaabccccbcababaadcbabaabaacdadbacacbadcaabadbacdbdacbcbaaacbccacbbaddccdccbbaabccddadccdcbbccbadbaddcbabdabcbcbccddddaabbacaaacdbcdcbaddcddcbdcbddbdcbbdacdbbacabdcccadadbaadaaaabaddcaaadcdcbdcbbacaddbbccdaaacdbcbaabdddadadabbcaabbcabddcabaddcbbcabdadbdbbbbbbcccadaabbdcbbdcbbddbabdccadcabbdadbbcdbcdbccccdccacccddbadaccbcbcccdbabccbadadcccadbcdaacdacccbbbbdccadcddaccccaadacbdaabbcdaabdabcbdaacddcabadbdccabbbbcbadccbbddbddbbccdbdccdadddbacdccbbddcbadaaacddbacdbdbdbcabbccbddadddcacdababbbddcbbccdccdcaadcbaadaacccdbbbdaadbdbbaabbdccdacbbcdcddbcbbabaddcbdbdbadccabdddcbacadccdabdbddbcddbaddcdcccabbccadaadbabbbdddcddcdacacaaaccaabbbaccbacdcdcabadcddddaaaaaaddccacbbdadcdbcdbcbbcaadacadcdaaabcdcaadbdcdadcbddcddbbbabddcabbdcbcadbcdbacadacbcbbcbadabadccbabaababbddabcbacdcacabccaaaadacdaadcdbabccccccadbcbacbbcbdcccbbbdaddbbdaccdaccbbddcbddaabdbdccdbacabcbadcdadacdabbbaddcadbacadddabbdbacddddaddbddccadadbaabbbabbdbdbaacbdddcaacddbbccbadaccbcbadabdcababbcbdcbcabdccbbaacbccacbbacdcdbbdcccacddddbdacacbcbadbabdbdaabcbadbcbbaabbacdbdcbadcaaddcbdcdcababdbbacabbbdcbacdacacddaaadcbdddabadacabbccddaacddbccaaaadbabddaaacbbdaddbcbddccdbcadcabdcacaaaaacdbdccaccbbcddcbbacbdaccbcaddbbdccdcbcbdbbbdbdcbbadabdcabccdddacdcdccdbcadbaccbbcccbddaaddacaacddaabcbdacddabbcbdaccdcbbadcbacaccadadabcadbdddcbbbaccbdcbabcccccbccdacacbcddccabaaddcabbdbcbdacbdaccacababddbccccacdacdbddbbcddddadabbcdcadbddcdaabacbcbadddacddaaadbbabdacbbccccadddacaccbbacbdbcdccadcbaadcbdcdcdbabbdaddcddbaabadaadacaadadabdbdbbbcdcbbdbacaaaaccdcadbababaccdccabaddccdbcababacdbaccbaacccbcabbcdabaabbdabcadaacabdbccadcbdccbcaaddccabdbcddcbabbdbbdbcdbaddbacdabacaddbccbdbddcbcbdcabaadccabdbdabbccccbdadbdcaaccabbacacacdcdcadbbdbbacdcdacdbbadacdacbdaccadccccbaaaddbccabbaadcabcbccaadaccaddcccccaabdcabdcbacadccbdbadbdadcdbcdddcbdbadbdaacdabbcccabcacccddddcabdcccbdddbcabddbaadaaaadcdacddbcacdddcbbaaaddabbbdbbcccaddcadadabaadbbbcbadacbacbbcbabbdcabbcadcdacadcddcaacdadbbbcdaccddcddbcccacbdbcacbbcacdaacbacccdccadbabdbabccbacaabccccddbaadbaadcabaabaaacdcaabdcaadaddacbdccadadcdadcadcccdbcadbdcbabdcacaccbdadcddcabbabbbabddcbaddcbadbdbadbbaadaaddcbbbadcdaaaddcdbdccabbdabcddcbdaabcdacbdcbbaabaaadabcdbdbccbcbaadccbccccbbdadcbdacacbadadcdabdadaabaaadbbdbbacccabdcbadcbbddabaadbaaddbccbdcdaaacbaadbcabdbdbdcdbaacabbacacbdadbadbcddadbcacacacbbbcccbbccaadadccaadbabdbaabddaccddacacdddbcbdaabbbacdbaabaddcdbbddcdcbacbbcadcaaabcacdbcaabcdcbccaaccbbcddbcbaddddcbabdacdcbdbbdbccaaddcbadccccdbaccacaddaacacbadadbbbacbdcdddcddabbadacdcaabdbacaaccbddbddabdbbdbcbaabbdaabcdcdbcbcccbdddccbaabaaabaaadbaadbadbbbcbcadbdcbcbdacabbbadbdbabddbddadcdccdcacbcbcaabdbbcaaababcabcacbdabdcbbbcabadcaccadcaaccbdbcbdccadaababbaaaaaddbccaddcbcacbbdcdccddcbdacabacccbdacacddddcadcbcdcacaddacadaabbccbacadccdadcdddadadbbdcdccdadadbcccccddabcbccbdadcdddbddcdcddcaaccddbddbcbcaacdbcadcaaddcadcdacdbbdcbccdadbbaaadacbbbaacbbadaccaccbbbbdadcadacbdbcaaabdcdbdacddbbcaacbccdaaddbddaaadabcabccdbbcabddacadcadbcbdcbbcbbcddacaccaaabbaaaccdcadbbcbcbdaddbcccddcbdbaaddbcadaadcdddcadccdaaaaabcddbcdabcbaabccdbccdcabacaacbdcbcddbdababbcadddadaadbddabbabdadbaacbaddaabbbdccbdbacbdbacddababcbbabacaabddbbdcccbabddacbbadccbabbcbbdcaabcacaaccabadddcbaddbdaacaabacdbcbccbdcabcbbacbdcbbdacdcbaddaaccdbcaadcbabccaaaddacbddabbdcdbdadddadddadddccacbbdababccabbbdbcbaaabbbdbbcbadbbabcacdbbaadddadccccbcbadabbbaccdcdbcaccadacdabacdcacbadcdcdadcadcbbdddababababaadcbdabcbcbdccaaaabadcbccbbbcdcdbbbbbbcddabbcbaababbcdabccccaddaacbddccbcadbdccdcaccacccdbdcacdadbcbaacdcdaacccdcdacaacdabdbcbbcadcbbbdabcdccacacadadbddacabaadacbacbbacbaadcccacabacbdcdbadbbbcdbbcdcbcacabbbbddcdcaabbbdbbabbdcbcdaabaabbbbaccdaadcbddcdadaaadabaacdacdcabdccacacdbcddccccccdbbbbbadabbbdacaadbaaacacdbabbbadbdbcdadaadabdadcdaadcbddadbaacabcccddbdbdbacdbabddcbbacdccbabbbabacabbadbacccdaaddbbabddbbacadcadbbcdbbaabacbbdaaaaaadaabbbaadabdbbaccbaaacdccbaadbaaacaacdcaacbccdaaadbdbacaadbcbadbabcdaaabbbccbcadbadbacccbcccbcbacdccbadbaacbdaadaadadddcacdcabbbccabaccdcbaaabbcccacddaadaabaddbacaadddadccddbcadccacbddcbbaaccbdbbacdaabaccdacdaabadbbcdaacdbcadacabadcbcbaabcdbbacabcabdddcdddbbdcddbcdbbcbcbbdbbddaccacdddbbbdbacdbacdadcccaadbcbdcaadadabbadbdaabdbabddbdbbdbababbbcdcbdcbcdadcbbccabbcbcdbcbabdbdcdaabdddbababacdcbbacbdaabaadccaacbdbacbcadaccccadcaddbcdbdcddbddbaadccddcccdaaababcdadabddcacacbaaddbccacccbbdaccdacadaccacadcaaccbadaacadcaabababaddaacbbccacdcbacdcacabccacbabaaaddabcaacaccbddbcdcccddbbbcadadddccccdbacaccdcbdddacbacdcdadcdcbadbbbbdccbabcccabdaccadacdcaddbbcbbccdccabbbbddcccacddddbbbbcbbdbbcdabacdabcdccadddbbbcdbcbcaddbcdcdbdabbbdbaacdbcdaadaaaacacdcccbcccdabccddbbccaaaccbdddaadbbdcadcabcaaccaddcbabdabadbaaadddbcdaadbbdddccadbcaddaaacaddbbbdddccabbddbaadbbadbbccddbcbdbdabbdddbcdddbcccccbacdaacbdbbacddabaacddbddcaddcbcaddbabcddddadcbbaabbccadaadcabbcdddabacbbaadcadbbaabdbacccdacbddddadacadbcabadabaabddabdbbbddbbdbdaccacccccabaadcadcccddbcccdaadcbadcbaabcacbbbddcbdadabdbacbdbabdbcacdbccdbbbddbddaabacbdbdbacadadbbcccdcaacdbbbcccdbcdcabddbddbdbcdbaadddcaadadbcaaacdccdddcacdcdddddccbcdabbacbaabbbcacdadcdacabbdcbdbbdaabaaabaacdbbcbabdbdbcabdbabaccadabbdbccabcadadaabdaaaaccdcbddbbabbdbccabaaadaddbccbbcabdcddbdabbbbcbcbacacdadaacaddbcccdaccbcadaaadbabbbcdabadbcadaadcccbdabacdccbadaaaadbddaccdcdabccbabccbaabaadcadadcdcabcccdcbdcaacdcacddbbcaaacdccbbbcdcacccbcabcabbddcaccdcabbaadbbbdccdbcaabaabdaabbdaacbbabbdddadccbadcbbbaccdbbcbdabaddbadcbabcadcdbdcbdcccbcdadbacababdccacccdbddabbddbaabbbdacacadaadaabbacccbbbabbacababdccdbcadcbbbbabdabcaddcabaadabadaaddadabcbacccdbbbdbacccdacddcbabbcccabaacaaddadadddcbcdbcbddccbbddcdabbabadcbdcbbaccdbbcdcddbbdadbadaadcdbdabdcbbbbdbbbabbbcbaddadcabdddbadabbbbddbbaccccaaacacaacadcacadccccdaabacacabdccabdbdcdabbdaacdcbbacaddbbbcaabcabaddcbcacbbcddaacabacddbccdbdbdaaddabdddbcbcaabcbdbbcaabdbcdddcbbccbbcdaaaddabdcadaadabcddcbbddaacaacbcddcdddcbdabcbadadbbcbdccbddabccdaaacbcaccdcacbddabadaaccadbdaaaccbacbbabdbabddcdcaccacccdccbdcdacddbdccbacbcbcadccbaacccacaccdcdcbddcdacddbcadcacccdadbaaacaccdddbacbbcbcdaadbadbbaddbbdccbbdddddabcbdddcadbbacbbbabaabcdbcdaccdcaddbdbcacddacdadbbcccbbdabbdcdabdbddcbbdcacdbbcdbcdadabbabbcdbddbccdddadcadadddaadacdcdaadcbbbbdcbbcbaacacddcbbaabdbbaccddcaaaacacdcbddcddccacccadbbbacabcdadaacbbadcabaacabdabdcdabdcbbdadbddddacacccbcdabbbbdcbcdbaaddccccdabcdbacbcbcbdcbcbcccbbdcdbccddccbccccaacaaccccababcddcaadccccabacbdaaaacdbadbbaacadbadaabadacdabdadbbdbadbdccaccbbaddbcdcacabcaabcbdcabdadacccbabaabadcbcddccaccabadcbcddbbbbccdaacabdddcdacdadaccaccbdadcddbaccaadddbababbcddcabaaccacbdbcbaaacbaccaabbcdbaadbbbdacdcabdccddabacddcdbdbccddaabbdcccbcbccabccdbcbaccbbbdddabcacdadbcbaccbabdccabdacaadcdbadabcbbabbdbdccbcabbbaabbaadbcdabcabddddbdbaacbbbcdaccccadbdcbbddadbbaacdacdcabcbbdaaaadbabbcdbadbadcccbaacacaaacdabbdacadcbadacdccbbaaaaabdbadbcccadcbabababbcdabdcaddcaaabcaddabaaadbdacacccdacbaddadcaccccaacddadbabdbdaddabacbdacbadbabdacbaddabadccdcbbacaddaadcacbbaabccdcbcdbcbcccadcdddcadacdbaacddcdcbdddabacbabdcdbdbcbddaadadaacdbdddaabddccbdbbcaaddbabccaaabbacbccccdbacbdcbabdbcdccddcbacbabcdcbdbdbacaaacabbdbdcbbbbaccabbbacdddddcadbddabbcaccaabdcdccdadcccbdcdabaadbbdcbacadcbaddadcccaadabadabcdcadacacdbbdadcabcbcbacdabadbdadabcbaaacdddbcadccacddcddabadacdcaabcbccbaaddaddaddbaaabdbaaaabbbcdcddabaaddcdbadaabbdaadbccddbdcbddabdbdccabaacbcdbcbaabdcdacccddcdbbbadaaaaabadababbaaabacbcbcbabdaabaabadddadbbddabbcabbddbcbbaddaacaadcbbacbbddcddbadbcddbbcbacddbabdddbcdacdaaacabacddccacbdacabbaabbabdcacdadbabcaddaabadccdbddbddacbaabdbbcddaadbacdccbaadbcddcabdcababaddddaabddbccccbdbacbaabdbabadbbdbbcdadcbcbcdbacacacabdababbbcbaadbbcbbaccdcaccdaaabcdadcdcdacadaadababaccdbbcaacbbaaaaddbaccdbdcabddbcabbbaadddbbdbadcbdbabdcbbcccbdcacdadbbaacdbccdacbcddcddadadcddcbcbbaddcddbccadabbcbbaacddabddacababcbdacddbbbacaabbcbaadbbdaababbadbbaabbbaddadddabcabbacccdbdacbabdbadadadcacacadcbddbcdadabddbacddcbadcacbbbddcdbcddbbddaddabdcbadbcbdacdcdbbbdcdcbaaaacbbdaaddbdbcaaabaacdaaddcdaaadcbbcaaddccbccdbcdaccbcdbcdcbdabbccbacbbcaccdccbacabddcbcdbddddccabdabaacaaaadbcaaccccdcccbcddaabcabbabaccdabdcddacaaaacabadbbabdcbdbabcbaacdcddccbbdcabbadacacbbabdbaadbababababbaaabdbdbaaddcdaadcdbaaaccadbaddbacbdbbbcaadcdabcbaaacdaabccadbdcdcacaacbdbcbabcccdbaccddccaddbcbbddcddaaccaccdacdaacdacdcccadbacbadccbcdbbdbdcabcadacadaccabcacdcbacabcbabdacbbaaddcbdcdccdbbabcadbdadabddbbacdadbbdccdbcdbdbabcdccadbadcaacdddcbbccabdbacdcdcbdbbacabbdddbcccbccbaddbdbcccadbcdbbbbbaacabadcaabccaadaddbcdabccbddbbacadccccddbcdcaddcccdcbcabbccadaadcdcdccacaacbbadbacbabcbaabcaddababadddccdbbdcadacdbdcaadbacbccdaddacdadadabdcacbdaacbbcdbbdccbcdbbbbcacadccddabddbdbaababccadbccddbdbbcacbdbddcddadacabbaccadabdcddbbdaabdabdbbabcbcbdacdcccbbaacabdacdccaadbdcababbbddddddcbbdcacaccdccacbaccdabacadbddbddbbcdccbabdcccadadaaabcdcaaabcadadcadcbccdaadddbdddbaaccdccdccadbababdbcbacdcdaaadccababdbcbbaadacdcddbacabccacabcdabbbdabddcccacbacbdbbccaaaadbdbaddacbddbbbaadbacbadcdddabdbcadadaccaabbbdbddaababccbcdacbacdcbacbbacaabdccccbdbbccdccbddaccbadcdcbdabacbcddcbbddbdbbaabaadcdccaabcacdccabdbdcacbcbcaccacaadbacbdcaabdcabdadbacdbbccbbccabaddacdbdbcbbddbaadbddacbaddbaabbddadbadadcdbbccaaaadbbcbcccacbbbccbaccacacaadcccdadadcbaddbdcabbcdaddbdcdcccddcadaacbacbcbdaccddcddcababdadaadbadbbbbcccdcaacabcbcaaadaaadaacdbadccccabddbcaccbccaabaabccbadcccccadabbcbdcdddcbbcbbccabdabbabaddbaaaacbdcaccdadcacdddaacaacddcdaddbdcdbdcccaabacadabdddbcabcadcbaabdbddababcdcccbadbbbababccadaccdcbacdacabccaacccccadabdacabaaabdbdacadbcdcccdcaadbbcdbdcacdbdccbcdddbadbccdbbaabdabbbcdcacbabbadbacbbccbabbccababacdacbcacbddcabccdcabadaabaaababcccddbccdbdddcbbcdacdcbbcdcadabbbcbbdcbbbddacbcbcbbddddcabccbbcaadaadabbdadbbdbcddcaadabcdbacdcccddcbddaddbdcbacdbabcbcdacbaccacddaaccdcbcacdccdaddbbccaccacabcdcdccbbbcadbadcbcddbcdbdccdccddacdadbcadcaccbacddaadaadbbddbaaacbdddaadaddcdbbbbdbbdadaadcbcaabdacabdccccbacddccaadddadcddcbcbbadaacdbcbdadcacbbbbdadbbcabaccaacdababbbabdaadcaaccbbcdaacdacbcccddadaccabadaadcdaadcacbdbabcbbcbabbdcdddcaadaabcccddacdbddbdadcabbacdddbdcacbdbccaccddccdccadacbdbdaaccbbabaaacdcdcdbadababcadadbacdbbaabdadbbcacdccdcacabbdbaacdcddbccccaccbdaacdcdbccbcdbdadbdcdcddacaddbccdadbabddabbabdbabcdbbdadbdcddddbccddcddabcaccdcacddcacacacdbaabddcaddadbabbddacabadcccacbbadcdbddccddbbacbbbdabdcabcbdacdbddccbdccabbcababbbdacdcaacbbaacdacaababaddbdbbacdbaddabcaadbcdadadcadddacaaacbdadbadabcaaacdbadaaadcbabbcacaabcabdaacabdcbcdacdcacbdbdcabcdcacaadccccdcbdbbdcbdbaaacabbabacdadcdbcacdcabddcbbccccacdbcdbbdbcbbbadcbbbcbdccdcbaaccdcbbcbbabadaaadcddbadbddccddbdacaddbdaabdaaccdcbcddcdcacdaacabbacbcadccabccabcacdbabcbbbdcaccadbddbbaaaaacccdcdbdcbdcabcbcdccddbaccccdbdacadbbcabacbcddabccababbcbbdaadbcbccccdbadadaddadbadaabaabaaadcdddbbbcaccaacccccdaaddcbddaddacccdcbbbdbddabcdcbadbdddcdccabbbacabdaadcaaaccbdbbcbdbbadcaacadcdbaccbbaadadbbcabbadcccdbbdacbaabdaacdcbbaccddbccbdbccbcdbacacddbcbcbacddaacdcdcbbdbcdbbacabdbbcacbddaadccbbcbadbbbdacdacddbcbadccdbcacacbbbdbdbbbbbbbaabbbbadcbcbdcbbcdcadbbccabbcacabbacbbadcdccdacbcccdcbbbbaccbcabcaaacacbdbdcbcbbdbbbdbbdcaacacabccabcbaadcacacadbaaacdabbadbadddcbcdddccccbbbabcbdadbabaabbccbbddbdbbbadcadbdbcbacbabdbdddcaadcabbbcdcbcbbdcbcdcadaccaabdcbdbcddcacaccacbbdcddcaaaaaccabaacbdaabaacabbbbbbaabcdcdbaccbababbabbbacdacacbbddbbabcbacbbacdbcaadcbbadcabababadcbbcbdaaabcccdddbadccadbaddccdcbadbadcbdcaacabcdbbccdcccabbbddcbaadabcdbaddabdcccabbacaccaabcbbccdccccdcbabbbabcacddadcddcdddbccbbcdccbdbaccbbddcaabccdbcdcabbcccdcaaadcdccbaacccacbbadadbdbcaabcaacdbdbacaabdadcbdddacdaadccbbaadcadcbcccadcdbaadbadadbcdbbbabdbbcbcabacccbdbdbdcdadbabdbcccdadcdbdcabaaadaabddabcdddccaadadbaaccdbadcabcdaadcdbbaadbdacdbcadcabdbaacbdcbacacaddadcdddbdcadbbdabbccbdaddbbdadbcdadabbbddadbcbdaacacdcccdbcbbcbcdcdbbcadccbaabcaddaddcdadadbcdcacdbbdaababadabdaddadcadaabddbacabdcbccacbcbdabbcacacbddaaaacbaaacddacdcccdcaaddabacbdbcddacdcadbcddbdcabdbddbdddadccbdaccaabcdbaaaddcddaaadbcacabdccbbdddccaacbccbbdcbabbadbddaccbabdabdbbcccccabcddbcddcccacadcaddbdccadaadadcaaacaabddcbcdbdabccdddcdbdccccaaaddbcdddacdabbcaccccccbbbacccbacbbcadbdcccbdbdbaabcdabbcbcdbdcdcaaaccacdcbbbbdccdcddddbccbadccdacacabdcccbcbbdcbaababbcbccadbccdcbabdcbadbabcadbcccdcaccdbddccaccaadbcbbddbbaabcabdadcadcddccbcddddbcadcacdbdbdbccacdcdcadbcddbbbabadddaacbdcacabacabacbaacdbaacadbdabbbbaadbdbaabcdcaabbcacdbdddaaccacabbbcbdacdcacdbabaacaccbadbcddcdddcdaccacbcdccabbbccadbdabdbbcbacacdbadaccabaadadadcdabaaacbbcbabcabbdbaabadaddbadabbdcdadbbcbccaadbbbaacdacccbdacaddbcbdbbdccbcadbdaddcababddbababcbaccdddcbdbdbcaaddaccdacdaccdcdddbadadbbccacbbdabbdcdcabbdccbaabcbddcdabddcbabdccaaaadcccababbcaddddabdacbcaddbbdbbddbdcbacdbbccdcbcdcbddadcbcdacbdbadbccdddcbdbaaaacdaadabcaccdaccbcdcabcaadcbbdbcdccbabddbcaacbdadcbabbcbdcbcaddcaccbaaddaaaccdaccddbaaccbbbdabdbaaacbdacbbdcabccacabddaddbbbdbbdcbbcbabadcbdadabbaabdcbbacaaccbbdadbdccabdcadaabacddbdadacdcaababcdccccbbcddadaaadcdbbdaabdaabdacccdabbdaacdbdcccdaacacbccbbccdadacdcdabccbabbababcddbaacdaaaadababcbdcdacbdbdbdabacbdcaacdddbabcdabaadcbbdbabcdaabaacbdbabaacdcaaadbbdcacbaccdaddabcbbdadbbcdbdcadbdbbaabbaddcdbaadacbdcaadccbdabddadcbcbcabadabacbaadabbccaddbdcacbdccababcbddddadbccaaadddddcccdccdcdabbdbdacbcacabcacdccbcdacbaaddbbccbbabbadcadccabcaabcdccccddcdaaacbcadabadabddbcdcbdababaddbaddadacbacaadabacbdddbabdcbdabcccdaadacaaadccbadadabddbdbcaadbacdbcdcddadbabdccccdadbadccbabbccdadacdadbadcbdadaddcdcbbdcccaabdabbdbbdcdcbaabbcdddbbbcbddcbcbbbdbdddcdacaddcdccadcdacbbaabbddcbdaacabdcacabbaacadbbabdccaacbcadcacbbbacabaaabdcdcbdcbdbbbbaddaacddbabbacbddadbdcacbdbabbadcbacccdacbddaadcadabddcdabadcdcaadbcdbcacbcacabbaacaacdabbcadbdbdbddccaaabacadddacddccdbbcccaababbaabbaaacdbcdbbdcacdaabbdccaaacacbbcbabbcbbaadbacdddbbcdacbcddabcbddcaaadcbcddcdabadddcaddbbdacdcabcdcdaaccdbcabbbcdacabacaaaadbadbbbcdcddbdabccccacbabbbdcbaddaabcacdadccbaaccdbdbaacccbbadabddbabddaddcadbbddaabadccbcacbdddccbcdddbcdccddadbaadbabcddaabbbdbdaaaadadcabadbcadbcdccabccbabbccdbbdbabccaacabcdcbbcdcdbccdacaadbbacccdddccbdacddcbaabbbdaadcbadadabadccabcdaacabdcacdacbdaccbdaaddaddbdacabaaabadabbaabadaadcaadccccadbbbddaaddddcdaaabcdcaccacaabccaabdbaacccddbcbdadddbbdacabdaaabadaacdbaaadddbdbcdaabbaabdaaaaaaacbaadaccbddcbcbcbdcdccbddbdddcddbdccbabdadbcccbcbbbabcbdaabdacdcddbacddaddddcccbdbababbccbcabbcdbbbcbbbccdaabbaddccdadaaaadcbddddaccbbdaaaacdadbbccbadabaaabcbccddbadaacadabdccadacadddabdcdbdbbdadabaddcdddcaacacacdddcdcadbbbbccccbcdacaadbaacbacdacccdbbaacddddadacbdaccdcbcaccdcdcdadbadddcdbabbccbddbdabcbbcbabcbadbbacddcdbadbcbbacdcacaabbccbcbdacabbabacccdaacccbcbcddbbaddbcacaddacccdbbbadabddcabaddbbbcbbdcabbbbbdccacacdcdcccdadcccabbacbdaabbcbcbcacabaaccadcadbadccccacbadcadbccacdcbdabbdacdddaacbaaacddadddadbaabcbbcaddbcaddaaddacbdbcdbabaddbadcdadcdaaccbbdadcbcabdbdbacaddbadccbccbbadadccdacbcddcbccaddbddacdcadcdaaaccdddcbddaaccbcdcbbacbaadcbbdacdabdbdddddaacbbcacddcadcaaddaccddbbcdadcbbcbccdbbaccdbbdabdadadadddabbcadacbdbccdccdccbacccbcacaddadccdcddadabdccdbdbbdacbdaaccdddacbddcbabcaddbbdbcabdcbddbdadabddddddbcdacbabcbdaacdacadddaccbdbddadbaaccacbbbcbacbbbbbadcbcdabdcaabbacabacdcccacacadbbdbccdcbdccdabbacdbdbbbbcbdcbabdcbdccdabacdacbcdbbaddbcdcdbbdbaccadadbcadaccbcdddbadcacaccccdddaadccbcccdcacabdbaddadbdabaddabcaaadacaccbccdcdaddaadcbddaaccaacdaddcddababbbdbdcacbcbdabcaabadabdaaccabddadddbcadcccdaacaccdbbcabcbdbdbbacaddbdcacddcbcbdddbabccbdccdaabcaaaabcccacaddddbadbbdccbabcdbdbabddcabbddcdcccdadbccbbddddbaddcbababdcccacabbadababdbcbbaddabdaaacabaaadaccaacacddaddadabcdbbdacaadaaacbbccacdacbdaccaadcddaccddbcdccaaabbddbdbcdadbbbaabaaabaabcbaacbccacdbaaccadbcbbbdcbdcdbcabadbdbcbdcbdbbadadabddddbbddccacdadbcddddaadacdbbbdaadcbaacaabcbaaddacddcdaadbdbacdbcabbabdbabdbadcaaccdaadbdbbbbdccbaacddaacdaaaaccbbaabaabcddcccbacbacbadcadbddabaacdbbbdccdcdddccdacdcbacdadccacdbcbcaadbcbcbddbccacbbccdbcbadbddcbbabaacccdaddcbbdaacccadabdcacbdabcbbacbdcdccbdbcadacdbadababbabdbcccabacbacaccaacbdcacadccaaccdabbdddaaaabddbbacdddaacbdabdbdddbcccbdcbacdadccabacbaacdcabdbdbbcddbadcbacacabcadbdbcdbaadcdcaaddbaccbddbbaabacdcbbccabadcbcbcbccaacdccdcadccacbababbccaabccdbbbdbcdcdaaacdabbaccbcdaabacbbadaabcaddcadccbdddddbadbabaacdadbbbcbbdcbaccdddbcabcdddcbacdcbababcddaddabcacddaddccddaacdcabcdcaadbbadbacccbdabdaaddadabbbaadcaaadddcdaddcccbccaabdbbdbcccacbadbaabaaccdcacdaaadacbadadcddadcabdabaabacccccccdbabdccabcabdcdcbbbbcdccdcbcdcdbddcbacbcdbbadbdbababdbdccdaacbccbbdabaaacbdbcbaadbaaaacabddcdbcdcdbbdabdbcdbdaccadaabcbcbcbcdddcbdcbaddacaaabbadccacbabbadddbaddbddcdacbcdabdcdcbdbcabacbbcdcaabddbdbabddbbadcbbcccaaddabddadbaaaacbcbaccadcccaccbcadabcdadbcdddacccdadcdaadbcbcbddbbdccbaaaadadbabbadbadddbadaccaddbbbdbbaacbaacdadadccadcddacdccadbbbddbddccdcacddcccbbddcddccdbcabdcddddbdaddacccbdbddcbadadcbbcbcbcbcacddcdbcdcabaccbdbcabaccdaccdbcbbccbaabddbbadccdbabbaabbdaddbcdccdadbdadcaddcdbdbcadbdccaaaacdaccdbdcababcabbbabcaacdbdacbcbacddacababdbdadccbbdaacdcbabdccacccddbbdbccdcbcadcdbcdcbcdaadacbdabbacbabaaaacabaabbdddcabdccadaabaccccdcdacadaabdccdbcdacccdcbbccccbbdaacccbdcccadcbaccacadcaddaaabdbbbcdacdaadaabcddccbdadcdbbdbadbcbdadccddabcaabcdbadcddadccacdbbcaacabacdbdabbdadbdadcccabaaacabdabccddbaacabbcbdddcbccababdcccabcbcaaaacbaabbccadbabacbabbbbdcbbddadbbcacbdbdbbaaaabbdabccbbdbddbddbbbcabaaadcdccddddaadbadccbbbaddbbcbbdcadcdcbcaaccdddbacbbaaadbadacccbdbdcbabbcabacbabbcabdddadccacddddacaacaccacbbdadaaabcacabaacdbcbdbdbbbccdbaccbcddcaabdbbbddbbadaabbdddadaccddcaccbbadadacccccabacbdcacddcddacdaabddabcccacbccaabccbbaadbdddbdcbcbcdacbdcadbbbadaacbbdabcaaabacadddcdaaaaaadaaaddcbcbcbadbbbddcbddabadacaacacadbacbcbdaadcccbbbcdcdcbdcbaddcadcdbbddbccbdbbcabaadcdaabcabbaadcbdccadcddcddcabacbabacdcacacadadbcbcbbbcbcabcdcbaccdbbdcdbaddbbddbaddbcdaddbabccadcbcddcccbacadcacbcdadcacacadcabbdabbadcdaddcdbbacabbcaccddcaccdbcbbdaacbccbdbbcddccaacdcbbcadbdcdbbbacccbcdaabdcdcdbbababcabaabacacddddbaacacaaabbbbbacaaadacbdaccbcaccacbdcaaabbbdadadaddbbbbbbdbcdbdbabdadbdcdbbbdacbbcbbcbcddacbbbbbccaddbbabcdabbacabdcddacbbaddddaacdcdaadaadbaacaadcdaccdcaadbcdaddcbdbdabcbbcbbcdabcbdbbdddabdddaddcddaabcbdcdadbcccbbadabbcdbbaabdcbaccdbbaabbbadbdbbbabbacbcabadcbaabbcadacccbdaaadbababbbaccaddacbbcbdadbabbadcbddcdadadacaababdcbabdcbdbbcaaaccddbcabbdbbcabbaabddccdacbbdbddcacdacbcdbbcdbacdaccadddcddbbcbcdddacbcaccdaabbacaaababbbaadccdcaabbcbadbddadcccaaaaabdcdbdaadaabbbdbcbdbbcbcdccbaaccdccbcdaadbcdcbdccbbcbcbbbccdbabacbabdccadacbbadddaabadacccddcdcdacadadbdabdcaddacdcadcbccadddbdabdcccbdbdadacdbccbaacddacdbbacbcaccbbaaabdddbadaadaadaadbdabcadccbcaccbacacbcdadbcadbcccbcacadbcadccdbcdcdacbcdbdbbbdcbddabbaccdccccddccadadcabacaccbabbbbddaddbaadadcbabdaddadabddadaadcabcbbadcccbdabbaccdaacdbccdaadacbdcdcdbcadbdccdbbcadabdaaacacdadacbadbadbcbcbdbaddcabbddbbccacccbbccbabddccabdbdcbbdbbacbdabbbbbccadddbccbbdcccadcacbcdbabaabadaacddddbdcdabdaadacaaadacdcddabdabdcdaadaddaadbcccbdcadadacddbdaaddababbbbaabddbbbcacdaabdbdbddccadaadcbaadacbdbbbadccccacabaadcacdbbbcdccccaadbcccbcbbabacabbcdaacbbbccbabbcaaabcddaacaadbbcadabccababdabacbacbaccadcbaddacaccccadacbadbadacdabaacabaadbaaccbcccbaaaabbdbddcdaddbcdbcdacacacbbbdcababbadbaacccddbadbbcbbabcdaaccadbdaaaccccddabcadbcbdbcbdaabcabcdaaacbababcabcdbacaadcbdcabbabbcdcbddbbadcbdaacdddaacddcdbcabdbaacadbddbaddccaabdcddddbcaabdaacdabbdaaacbdbbbcaabbbdbbddaddbccdbacdcabaadcacaabddbadccbdbadcdaddbaabdaadabacbadcbdcdbadcbcacabdadbbdbcbabbdacbcdcaadabacdcccdaddaddbbaadccadccdccccbbbbcdbcdbdadcdddbdcdadddcccdaccbbbbcacccddcbbcabdaabbbbccababbdbbbccdcacbcbddbccdcdbacbddbdcdcdacbadabdaaaccabdcbadcbacbdcccaacdbdbdabbcddbbbcddcbddbadbaaacbcabbcbbbbdccadcbbdbdabcadbbaabbbabcbcccdcdaccdacdbcccbccdbdbccadbdabaddcccddddcbddddbcdcacabbacbdbdbcbbbcdbdcabcccbdacaadbadbbcacbabdcadbdaddcdbcaccdbbdabddbcabacaabcdcacdcbddbcccbddcdaddcbbacacbcbadcbccccabbcacdbdbbabacdbabdcbadaaaccbbacccbcddbddcdacdcabcdbacccccbbdadbdaddccaccacbdbdcbaaaaacbdadaaaabaccbdcadddadabbccbbcbbbbbdcbacbbcbadbcabdcbbccbaabdacbdbdccdbdabbcaddddcdaacabdddcbaadbbcdcabbcdcdccbadddbcdbbcdcddabaacaadcabbdbbadcdddbbadbccbcbcccbcbcabcdddacccaaabccbdbbacdcacccdabbbccabdbabccbbdbbbcdddbdbadbbdbacbbbbbcdadbaccbcdccaaaadaddbcdcaaacacdcbcadacbdccbcbdddadcacddbbbbdcabcdcdccbddcddabdadccaaacbcbbacbddcdcdabacddbcbaddddaddcabbacadaccacadddacaddbdbacbdddccacacbcbabbadadcbbbcbdabcdcbbdddbdddcbcbdadbcddcdbbbdbcacbaccccaabcdccadacabacdaaacbdcbaaacdcaaacacbcacccaccdbdbcaddbcccbaabbbcabbcabdadcdcddcddcddbdabcbbdbabdbbabbcbcbbdbadbbcbccabbbbddcabbccaabcdaacaddaaaadbccacacccdcadbcbdddcddbcdcbcadbddabcabdbcdbaddaddbccbccdbccddbddbcdbddacaccbabbbcdaabbcbdadcaccabbccddbabaabccbddcababdbccabbddcbbdbdcbacbcaaddcbdcdcbdaaaaacddbccbabcacabdcbbdcbaacaadbaddbbdacddcaaaabbcccdbcccabacabaaaacdadcbbbbaddbbcccacbcadcbbbabbaaadbbcddcacbcdcbbcbadabdaddaacabdddddcabdbbbcabbbdcaaddcacabcbacbbbbdbbcdcbbcccbdbbbcbcadabccbdcaccbdbdbbcbbacbbbcccdbaccccddbaabddcabcaadbbdcadccacdbdbcccdaddbccacddccbaadbbbcaacccbcaaccaddcadcacadcabdacdbccdccdddbcddbcabccccbcabbbddbcadadbadbabcaacdbbbabadbcaccaabdbabddddccbdcccbcdacdbbdbcbbcdaadbdaaabcbbaaadabcadcaaccabbabadcbddadadbddcdbbcdaabbdcabcdddbabbcabcacacccbbccbcbdddddbcbdcbccdbabdabdbacdcbcaddaadccaacaccccbcddbcabaaabaaaadaadccddabdddcaaaabbacadbccdcdbcaccabcababaccdcaacdbbbdbbacbdccdccddbcabdababdcdccacbddccaaabdddccbdcbbcccbbbcbcbbacdbcbcadbdccbacbaadbabcbaacccddabbccaccdccaddacaacddcbaaaaddbbacbdbdcbdbccddccadbdbbddadaadcdddcbbdaadddbdcbcaaaddbdbccbdcbbacccaabcbccbcbadcdcccbcaabbacdbadabcbbabdbcbbbccdccbcccadbbbdcabcbddbcacddabaadadddbcbbcbabaababdaacccabdabacdccaabcacdcccdacacabadacbaaccbdcaaabcccabbcadacbaccacbccbccacbcdbdbacccbddcbcdbccbdaadababcdbdbacbccabcbacbabcdcacdbdbbaaacdacdbaaaadaddaccdaaccbabadcccdabcabaaddcbdccdcdcaabaacadadabbcaadbdcdbbbaababdbcccdabacaadcbddddcadccbbccbbabcbbbdcbbdadbdcaaaacdaaddbcbccabbbbbcbdacaadbaddbcbdabcabdbdbadcddabadbabccbddddbacbcdbbaddcbcadbbbaadcbbcbcdddcbbbbabdbdbbddbadcbabdbbcddbbdbdddcccacddbbbaacbcdacdbcdadaacdccbbdccccdaccdcacdabacdabadaaabdddbdacbcadcaabcadbaadcbccadabbdccdcadbcbcddcacddcdbbdddadbddadcddcbcbbbbdbbcdcbababdacbdcbbdabbddbdbbbcacadacadddbdcadaaabbdcdaddbcaaddcbadbaadddddbaddaadbacbdddbcabbadccbacdbabcbccbcbcabcabcbccccacdabacacdaabcbbabdbbaabaacdcdccaddbbddcccaadcdccabddadbcdbaddababadaaabdabdcdccdacccdbadbbddaacaddddaddcbbacbdcacccadddabbbbcbabdbdbdbbacadcccddbaaadbcacdbcabdbdbacbabbccddaaddccbcbacbacdabaacbdcbbbccaaccbcacaccaabaabcacacabbdbbaccdcdcdbaadcabbbbcdddcbbbabdbdbbcddbadbdcdbdcabaacdddddbdcadadbbabcbdaaaaabbcbdadadcdaccbdcdabbbbdbcaaddabdbbbddcacabbbddcdbbdddcabbbccbcbcacbbdddcdcdddbcaaabcbdaadbdadaddcdaaacbabaacdcbdbddacdcbabbdcdcccbacbcdbbabaaaaccadacbdcdbdccccbbaaadddcadbaabbdcabcaaaddddccbadcbbbbdccaddaaabcdadbcdcdaacdccbbccadbccdcccbdcabcbddbbbadbabcdadadcdddbbcaccdccdcdddbdaccabccbbabbadbdbaabdccadbbdcbabbcadbbcadddacaabcccabdbbccbccdddabcbcbbdccbdcdccaabbadbdbddcbbdddcbaabcdadcbcccbacbbdccadcccbacbacabbddbccdcbaadabaadddaabaccbdddcbbbdddcccbadcbbcbacbcabaddccabbbcdcabdcdaabbbbcdcbadbdddaadccddacbbbcbbdcbcdaaaabbacbbbdddcddcaacaabdbbbbcddbcabdbaabbdccbbcaaabdccaaabbbcbcabddbdcbdbbbddbacddadcbadbdbbaaacadddbadadbaddbadbaacabdcadbdbdbacdcbdabdccbcbbbbdbbccaabcdcbaaaaccddcabdcaacbcddbbdbcdabbabdababcabddabbddbacbabdacadabcaabbacaddcbaadcbaacccbabadddcbdcbccadadabbdcdcadadccbbabbcabcdcdddcdcbcaadabcabbbbbdddbcababaabacaabaccabbadcddcdbbdabddacadbbcdadcccbbdbbddbcaadbacacdbdbaacadddcdbbadbacbdbddccbccabbdcdcdbdaabccbccbdbdaaaddabcaaccbcdccbacdcaacadddbacbacdcddbdcdddcbacabaccacdbbcadbdadadbadddddbbaaccaabbbcaadcccbbcbdacbcbbbcbbaacdaacdabcddabcbaacadaacdbacdaddaaabcbccadccbbbacdccbdacccddbddcacbdaacdbadcdcbccccbbaccdbdddccadbdcdacbcbbdbddabcccabdcabaadddcacdccddacddbcbabcaaacdbabbacbcbdabaadbdaccbbcbdcdadaaababdddbddbccdcaaadbbcacaaaadadddabdcbbaaadccaaaaaddcdccaadadcaadacbabccdbaccdabaccdbccbbacbadbaadabcdbbccddbbdacdaaccdbcadbcdcdbbbbdccccccadccabddcbddcbdbdabacccccaabdbbddccdcabcdbddbbaddaccabcacbdabbacddaabaabcabbdcdcdbdacbcadacacadcdacdcdcabcbccccbddaaccacacdacbdddbdbacaccabbbbdaacdbccbdccbcaacaddcbcadbaabbbabcabacbbcadacccbacdcdbdbbbdcaadcababdbaacabaabbbaabcabacddacccddcdddddcdcbaadadbcdbbaddcaaadccbbaccbaabcdbadcddacaccbcaacbbdadbcdaccdbdbddccbbdaaacdabadbdbadcaddbbddccdbaabdbdccaaccccbcbdbcbbddbccaadddcaddabbabbcddaaddadbdcaadbdaccbcdcbcdbcdbdcbcacabcdadaddbbdbbddbbbbcabcdbcddacdacbcdcdbccadaabaadcbcdccdbddbbcccabdbdbdddcdabccdadccaddddcdaaaacbbbacddbcaaaddddadccbadddbaabddddcccbccacaadcdcbdaabdadccabbbcaadacdabbbaaccdcbdacddadacabacdbbbddcacadddcdcddaccbdccaaaacdbddbcaadbbaadbccbddccdabbacadbabccaabcadcacdbabddacccdbbcddbdcbcbddddddbddcaaabbcdaddaccdcaaabcdbcbbabbdcacaadbaadaaaccdbbdbbbadcabdcccdbcdccbbabccbdadccbccbcdcacbcbdbaacddadcbbdbaaabcbcabacbccdcbdcaacdabccccbadcdbcaadbbcaaabbbbbcaacacdcabbbbabacdabdbcacbbdbbcbcabaacbcbdbdbbaaccababcbaddccdaaccbcaadcbbdbbbdbbabbddcbadadcbbacbcdccabacbbcdadcdbacdbddddadcccbccabddcbcccdcbcdbdccbcaddadabcbcadddccbbabbabdbacdcdbbdccddaccacadadcbbcaacaaddcdcbdbdcdabadbdacbbdbabcdcbabbbddacbccdaaacadcbdbaadaddaaabbadbbbbccbacaacbacccacdbdaacacdacccbcddcdbdcdbccdadbdbacddabbcadabbbbbdcdcaadbbabdabcbcaaaaadabbadddadccdcbaddcdaaadbabcacaabccbddbadccaacbbaaacdcddbdcbadcdaccddcaaabaaaabcabdbacbadbbaccdcbcabcbaccaaddbaddabbcbdcbcacaadcbddddabbbdacddabcdabdbccdbbcdbccbdccbcaccbdabdcaadbbbbbaaccbdbabbdaccdbdcaabdbaccabcdbbcabdcdbacacddabbbcccbbcccaabbccccdbabcdaccdbadcbadaddccdabbbacbdabaabcabccadbbdcbbdbbaabddbaadbadadaaadbaabbbcdcddcbcdddcabdcdadaaadcbdcdcbbacacaaacdcacddbcbbacadaddbdbdcacbbbcbdcdcdabbddbabacddcdccdcaccdabcaaaabbdcacbdbdbaaddbdbddccacbadccdcdccacdcdbaccdbdddbcdcacdcbccacccdacabbcbbddcbbcdcabddbacccaabbbcdbdaadbadddabcccacacbcaabaaadcbbddaaaacacaacdcaacccbaadabdcacdabcbdbcdabdbdabbbbbbabccdbddbccdcaadbacaccbbabcababadcccaaaacacdddcaccbcbabaacabcccbcababbbdacbdaddbaacbaadabbddcabccdcbcdcabdbadbcbcdadbabdcacdcdcbababbdabcbbcdcbbbdaaacbabcbaacddabddaaababbdaccbbccabaabddcddddcddddbcabcaaababdcbccdacdbcdcdddccabdcddacbbcdbcbbdcadbbbaddcdbdadcdccbadaabdbcdddcdccaabdbdacdcccacbbaddccccbaadacbcdadcccbcbccdacddbbddcdaadcdbcbacbccdaabadbaccbcdccdaaacdbcdbacbabbadbabadcbcbcacaabadaadaaaccaddcdbbccdcaaabdcbdbacccccabcbccddabbbaaaadcbbdcbdcadadacbaacddadccdbddcbdcbcbdbabdaccbbddadabdbabbdabdbdacabbdaddbdbdcbcdabacbcacbccbbaabadadaacadbcaaaccbdbabbcbdbcbcabbcbadccacbacccccdadbababcddbcabaabdcddabaacacbcbccddbdcadaabbbcbbbacbcbbdcddbbbdcadbdbddcdaaabaaaaddacdadaaabcbbabdccacaabcabacbbdbaccdcdccbdaabbbccadcaaadaabdbbdbcdacaaabdacdcabbdbcbddbcaaacccddbdbcdbacaccbddbdadaddadcbbcbdbbdbaacdcddabacbaddadcbdabacdcbabaaadbbabcdaddddbcbbdaaaccddbcddabdacdaddbbbccbadccbbccbadddbddcdcdcabddcabcacbdcdcabaabacacbcadbcacaaabbcaadbccbdbcbadcaadcbbcdcabcaccdaadbddbbdaacbabbcdabccbbadbcacdadcdcacaacacdaccdbbacdbccbdddaaaccdcdcbdacdddcabdbcadaacdabababbdaadacacccaddbdbbbdbcdabadabcccbadadddabcbbbcbcdabdcadcbdbaddcdabdddbbbacbadbcaddcdcdbdadacacdbbdaaabadabcdcabaaddcacdacacbdccdaadbddcbadcccdccdaacdbabcbadddbdcdacaddabddadddcdcdbdcbcaddddacbdaababaadbbbbdabcaadacdccbbcaaddcadccdccddcdcdbacbacbbcbcdacdacbdbdadcabcaddaccdcaaaacdbddcddbcbaaaacccbaccccabbdccbbcdddabbbbdcabcccdcbcbbdaaccacbddcbdabbaaddcaabaaaadddbbabadbcabcaacbddabababaacabadbdababcccdaaadbdbaaddabdddbccaddccbacaddcaacbcaddccdbaacddacaacaaccabccdccabdbdbacaababbbbcabbcdaccdbacbbbaddcaabdacbdabdddccbcbbbabbabdccacbddaabbaddaacabcabdabadcbcccdaddbcdacaaddbaaadcddbddabdabaddccacbabdacabdccaddcbbbabccdadbcabdaccdabbcabacbcdacaacacbcdbdddbcdccadbbdabdbaabccddadabaaacbacbbacbdabdcbcababdabbabcddbccadadabbbaddbabbcbbdacdcaaaaddadccbacadcbccbcdbbccaadcacabcabbaabccbcadcaadcdacdbcbdcdcdaaddacdcddaddcaccccaabaabccdccabcbbdaccbdacdacbcdbdcdbdacadcbaaddbbbcdcbccbadccbdcaacdcbbaddcddddddcbdbaaccabcdcdbdccadcdbcddaccadccbbbcccdbbabdbbbdbdadbcddccbdaacdbbcccddadaaabddacbbcdcbbbcaacaacbddadacbcccbacdacddbbdccbabadccbbabbaacbdabbccdcdaddcaddbcbdcbaacaddaacdabbadaddddadbdaddaccdbdbbadddccbcaccabddddaadaccabdcdcadcbaaacadbccdbbbcbbcccadaccaacabdcccbabaaacabbdaddcdcbbadabbdacacbabbaaddcaaabbbbdcbdcdcbcaaabcadabcdcbcacbaacadccbbabaaddacaadaadbabcadaddbbbbadacdcdbddcddddabcbcdcaadbbaabcadddabcdcadbabbcaacddcaaadbabccabdbdadabaccabdcabdadbdccbbaadddadcdaadbadadcbdacbccbdaccbdbcddaadcdaccbbdabcbbdabbddbdbaddaabcdccbadaaabcddaaaddabbdbbdacbcdcbcccbccaadbcccaccdbcaaadbaddbbcbbbaabadbdaaadbacccbddcabdbcbcbdadaacbdaaccbadbdcacdaabbcaadbcbbabcaadcaacbdcbddaaaadbadaabccbdcdabccbdbabbdcacbaddbcbaabaabccacdbbbcbcddddadacdadadabcadbccaaaddacbdcbcdbddadbccdadbbcaabddabdbacbddccdcdcddcaabcdcbdcbbacbdadcabdaaccbabbaddbbbacdbdcbcdadbccaddaddccbdadbbcdadcbabdaaabdbddaacaadcdcbbcbbcadbcaccccbcbacacddbabddccdaadcddbbccadbacdddcadbcdabcbbbbaadaddcaccacccacdcbaababadccdacbbdcdadcbccbdcbbdaccbacbaacadabcdcadcabddadddcbcbcdcdacdbcabcaadcbaabbacdbadaddbdaaddacdbbdcbcaabdbbaabbaaadaabadcaadaddbcacbabdabbbdcacaabdbdcbbbadaacacaababacaaacaccbcccabddbaaccbbcbadbccbdaabacddbcbcdcbaaadaacdcabbaddbabcbacbbbbcdcbaaadddccbbdbaacdcdcadbabadadcbcbccddbabdaaaacdabccdabcdcdcbabcdbcbbbdcacacdccddaabdbcacadaabdaabdbbdacaaadaaaadbbbbdbccddcbddabacdcbbddbadcdcbdcdaddadcbbbccadaddadaacaaddabaccacaabbaacadbcdbbdddbddcdadaadabacdbccabbadabdcbbdbdacdcdacbcdbdbdcccacdccbdddcaabdddabaacacaadbbabdcacccddbdacdcdadbabadcacddbdbbabbaaabdaabcaccbbbddccababbcdacbbaadaddaabacadcabbabbbaccabcdabbcbddaaaabdccddcbadcdadaaacaacbbcbbcbaadbdcaddbcdccbcdabbaaaaaaacbacdbadabadabddaacaacdcacbabbbabdadaddacaaddbbdbdacdadbcccbcccddbbdcaaabddbadbacdaacdadcccccaddcaaacaaccdcdaabbaadddbbcccaddbcdadbadbadcddbadacbbdababdaaadcddccadcaaaaaabdcadaaabbcbcbaabdbcdaacdccbaddbbbddabbdaabacdddbbaddbbaddacccdcbdddcbbbacdbbaaacdbadcccdcdccbbbbdacdbbbadcbccbbdcbdccacadabaaddaacddcbcabdadddaacddababaaacdcddcddacccbcbddbbdcbbbcabdbcbbcdacbacdbabccbbdaaaadbacbdabcbabcbadaabddbaacdbdcdddccbbdabddadcddadbdaadabcbccabacdcdaccccbcaacdddcbcdcbbbcdaccdbdcdcdbbcbcbcdacccacbabbabdddaadabaaacadcbaabbabaadbdacadcdcdabbddaccdadbcadacdadbdabbdcbbcbadddcbbccdbabbaccbdabbaaddbcbdcbdadadadbbcbaddababbcddaacbcadccababddddbdbddbbaccacadaaccbdacadaccccadadacbadacbddacdadaddccadbabacdcaaaabddccdbccdbdaaacacbdabcbbcadaccababddbabddbcdcbaaddabbbddcadabaccbcdcdaaacccadddadbbbcaadddbbdbaddadccbcbbccbcabbccadccbddddbadacccbdacdbdacababaacdbaccbdacddbbdbdabbbcdcdbbddadddccbcdababdbbabbdcbcbacccadaacdddcabdccabcccabdccdbbcacbddaccabababcacadcbaabaacdcbcbddaccdcbdacabddacabdbdccbddddcbcdcadcaabdaabcbdaaabbcbccdabadbdaacdcaaccdbbbddaadbaaacadbcdabdbcbdbadcaabcdbdcacdbacadbdabadccaddbddbadcdcaaacacdcdacabdbdcdaccccbcdcbabdacacbdaadbddacbcaacbabdbbcbbadbdbdadddbcabbabddbaaabbccdcdcccccbdadcadadbddaadccdbdacbdbbadbbadcbcdbabbaabcabcbcbabcbbdcdacacdabaaacdaabbcbbcaddbdbcdbbabcaddccbacbdaaadbcbcddbbdacbcdbacdbacddddabddbbdbbabdcaddadcbadcbcdadcabccbdabacadcdcbcbbccbbcabbcabbbbddabacdcbdbacbbbaccaccddcabcddddaaabcaaddccbaddbbdbbbaadbdddbaacaddcabddddcabaaabbddbdddaababdddcdabadbdcbccdcccaadadcbddbabccccdabdbacdbaabcaaaaaddccabdbbcdcccdddabdbbdcbacabcbadcdaccabdcadcccadbaccdccddccddbdacaccbdddcadbcbcadcacdddadaadadabdcbcddabbaccccddbbbddcbaccacbdbadbacbcdcbdcdacdadddbbbcbcbaababdccdccbcdcbadccdbadbcabddbcdddccdcdccbbbcccaaddcaacdcbdccddadbccadadccbadacccbccbdbaadaabdcacabbddddabcaaabcbabbcdbdadbadaaaacabdcaddbdbdccbddbdcdbcbabcbddaccabbdcadacdbcadbbdadddacdbdcdcbbbbdddacdcddbababbddaadabdbbbcdbdadacddbdcaacccbbdccadadaadccdcbbaccdacababddcdaaccdcadddbccdccbddadbcbdaabbbdaaadacbcdbbbaacccaaaacbacadbdacbaadaabbcaaacccdcaabcbccdadcbbaacbcadacccbcdcbccaadacbaadcbcadcbaaddacabacdddccbdddbdaadcdcbadddddbbcbcccccdcaadacabcbdacdcbaddcababdcabadcaadcbadadacaaaddbddbdcaccbdbcbddbcaabccdaacbdcbbadbbbbcbdbbdbaaccdcacbdcdaaadbbbaddddcbcaaaacccdadbdadcdccdacdcdaabbbccbcdadabbcaccabcbbcdaddadaaabccdaaaddaacbddbdaacdaacbcbdbdbcaabdcdcbdcbdccabaadcadcbbbdabcababdcdbdcabcadaddcdcdcbdbbcbbcacadbaabcdabbddaccdbdccddbdcaddacbaabcbcdbbbcdbbcdbcdacbdacdccaacabbcaaabaaccdbccbcbddaddcccadbcacdcddabccddcbddacddcaccbacacbbdcbcbbacadbdcadcadcabdcdcbcdadaaccbcddadcbdcacdbccbdbbdaabbcccbcdbdbbbddcdcbdbaadcbcaabdccbdcbdbcccdcbcdcdbadcabcbbdbcacadbdcccddacaccaabbbaccadbdcdcdcccadbbdaaaacdadbbcbcbcaabdacdcaccccdbacacabbabacbcacbdabdbabcbdbdaaabcdbccbbaaaccccddbbaaadcccdcbbdbbabaadcbdcabadbcddcbdbbbbbdcdbbaadabcdddaacdcabcacdabdcdaaabaabbbbabababacddbddbbadcdbaddddbcdbbbcdcbdbddddbccadaacaadcbaaabddcbcbbbddbabbcdabdbdaaadabcbddadccdaaddbadaadbaccabbcaabddcddbdbaaadaaabdbcdddbdbadcdbbddadcacbdcdbaadaaaddcbdaaadbdaddbbcdcdbdabadbdcbacacaddbaaccaadddbaccdcabbccabccddbacbbacccdaadbcbbbabcaabcbaacbbccbadbaadbadbabaabbadbcbdcacbcacbcdaaddbddcaadbbdcaaccbabdccaabdbbbadadadabddcacbbacdcbdbccdbddbdccacacbcdbabadbccaacabdddccaddccbdabbcdbdcbdbbbcccbbccdcbccabacdacdddadabadddaabccababbcadacabdbcdbdbbccabdddadcbcadabbdbbcbadbdbbddadddbdabacddcbcdbcabbdbccbcbaccacdbacdcacdddabbababacbbcdabcbbcbdbdbccadbcbdcddaccbbcbccbbbcdbacacdbcbbdddaadadaadaaccbdadcbcdadacbdcddddcbdacccbddacababbcababdcdbcccacdcdaaccbcacbdbccdcaddabcadcdabbcdaabdbadbbdcccbcacddacdcddabdbbdcabaccbccddccccacaadbdbdccbaaaddbdbdbdcabcabdbabddadccdadcacdbdabdbdcaacadcdadcaddbbbddcacacdcabdddadbccabccadcbcbcbbaaddbbcabbbbbcabdbccabccdcdbdbadadcdadbbbdacaccabccdddbabbadbdbbacdbcbbccdcbbacbdacababcdabdbbbbcacddbadbdaaaddcdddcdabbdadcdbddcddbbaaadacbddbacacbbcacdcbacbccdacaabaabbdccdabacabdddbbabcaaacdcadbcdbdcadaccbbccccabacccdccaacdaaaadaadbcdadacccdabddddaddbcadbddbbabbbddacddbbbadcbbbcbcdacdadbcdddcccddcccaacdbaabacadddccdbdabdcacaaaddacbdbcaacccccdcadaaddacaacadcaaddbdbdbbbcaabdacbdabcdabaacdbcadccabcccdacdcbddabccbcbbaaaaddcbadcadbaadddbcdacaccacdcabdbcbcbbcacbadcdaddadbddbdddddccacbaaadaadddbcddbcbbcdbadababbcbaddcaddddcbcbbcbbabcbdcaaaddbcabbccaaccdcdddacabbdccdadccdaccccddcaacdbddccbabbdbbbdabbcbaabdcbdbabaadcddabaddadacdaadbbcacdbbcddbcccbdcaadbcaddbaaabbbcddadbbddadddbbaaddacaddcaacbadbbaadbddbbcbbcabcdadbacdaabadbccdabdcabbcacbddbccdbcbaaabbacdcdbccbaccdadabcbdaacccaacccabcbddcaabbddabcddbbacbbbddbbadcacbddabccbdcbcabddaddbdbbdaacdddbacbdaaabcabcaacacddaabdddaadcccdbaaabdcaddbdbdccbbacbcadcdcacbaaabacbadadbbbdbacdadcccacaabbacccabacdbddadadadcadabadddcccdadccacbadadbcbbbbbabdbbbaddddcdcbcccdcdccbbdaddbbaccdcabcbbddabbbdcacbcbcccbddadbdabbdcdbcacacaddabcdccbadaadcdadcbbaddbadbbdbadadbbdcddaacdacbdbbdcdccacddaacdabbbbaddddadacbbcabdbccabcddcaddcdcbaabdbacacddbaabcbbbbbacadadaacddcaddadacbccdaccaccddccdbdcdacabaabdbabdbbbbccacdbcbdccdbdbaddcaccdbcbbbccbbdcddbdcbdcacbcaccccadaccccccaadadbcdccaacbcbdbcabbcaaadbdbbcabaaaabcdcdbaaaaabcdcbbcaddaaccdbdabbdbdbaabbdabcccddcdbacdddbcbddabcbacaaacdcaaacdcdbadcabaccbbdccbabaaacadddbcadaadbadbabbbdccbdbcbdabdccbccdccdcaaaaacdababdccbbbdaaabacdbbdbddcacbcaacbadabcacaacbcdbbddcdaccaddaaaccdbbacaaadaabcaccaccdcbcaaddaddcdbabbcaabdbdcaabdddaccdbcadccddadcdbbbbcbdbaaabcdcbadcdabacadbcdcaadbdbdaddadbacaabbabbbbaccbbcbddddcacdaaaabbccddbcaaabdcbdcbddcdcacdaaacbacddbbbabdaadbcbcdccdaaddaaaaabbcbdcadcbbbadbaaabddcbbbbadadabaccbccaacaabaaaadcabbcdcdaccdbcabbaaddaadaabaabbddcdccdaccaddacccabbcacabcccbbbaccbcbcdcdabdadbbaadacdbcdbbbccddcacbabcabbdcabbdcbabcdbdadbbacddbccdbcddbdddaacddbcdbaacccdbbcbdbabdaaadacdbadabaaadabdabbcdbadcbadcccacdaacccaccabcdcdaabbddabdaacccbbcacaacabcdbacddbddcaccddbbcbbddcdbbcdcddadaaccaaacaacabaabcacdacbdccadacaadacadcacdabccbddcdbbabdbbaddababddcaacdabcddadacaaabadadccdccbaabdacbbbcbadadaaacacabdaaddbaaacabbabbadabcdbaaacabdcbcbccadaccaddccbcdddbabbaabbcbbaaccdcbccddbbbcbacbccacacacbdbaabdaacbcbadcbaddadabbdaddddaccdbbacbbcddbdabbbcaccaccddabdddabbcacbadbddcbbacbadcbbcddbadaccacacccbacdbaabacddaddcacccbbbcdbdadbdbcbabccddcdcadcdccdacdbccddcdbaccddabaaabbbaaccdcadaaabdaabcdbbcadcadcaadcbddabababbadacdbadabdbbcccbbdcaccccbacddbaabccadabcdbbabddbbcacaadccaccaabdcccbaaacdbacbcddbcbcbddaaaadbcabacabcadacdcadddadccdcabacbcdacdcdbbaaccbdaaddccadbcabbdddcdcdbbcdcccdccccaddddbcaaadbdbcbadbcadccdababaaddddcdcddacaddbdbbadbcabdcdcacddbbadacdddabadabdabbbbbabdbadddbdcdaddbdddcbbdbabbadbcacbaaadaccabcbbddbdbbdccdbcbcabcbabdddacbcdbddabcdbdcaddbccbadaadcadcdadccabdcccacccddbbbbadbcabdaabccaddaababcdaddbcccbcbbdcccbdbaccbdcdababadbbdbbaaddacacababbbcccdddaccbcbdaaadaddabaaccacbdcccadaccacbbdacbdbdbbadbcbcccbbadadabdaccdabdbbcaccdbadbcdacccbbdcdaadcadbdcdacdaccdcacadddaacabdbdccbcbdbacdacaaacddddcbdaddbcdaccbccccababdbaabccbdbbbaacdcaccdbadadaaacbddabdbbcccadbbadddbaaabbbbccdbbacacaccacaddcdbbbaaadccccabbaccacdddacdbadcbbbdcbadbdcbddcbabbaaacbbbaccdcdbaacbacacbdbcddabdadddcabaaabadbaadcddccbcacdbacbdcaccaccadcaadcdddabaaabdcddcababdcdbcadccbacdacbaadabdddccdddcabddabcccdaacbcaabbdabddccdccdbaddccdabcbcdacccddcdbaabdcaacacddcdbbaabaaacdbcababdadcbadadbccccccbdccdaaccdadabbddabacdacadacbbabdbdacdbddccdcbddbcabbcbdbaaaaadbcacddbccbccbdcbdcccdbaabccadcbccbabcccaaddbaacadddcbbdbacdadccbdcdbdcbbcddcaabddccbbcaadddbcdabbacbaaabbaaccaaaaaabacdaaacdcdcbadcdddbdabaddcbdcadaccadabcacaaddabbcaddbabbccdbddbdcddbddaacaabaaccdbbcbcdcbddbaaaacacccaccaaacabddabbcdcadaccbbacaddcaabdbccdcccddbacbaccbdacbdcdbbadbcabddbadbabcbcbadacdcddadbdbbbbcbcaaadcbdbaddcdbddadcdcdcbdbadadabccbbcddcabcbdacaaacbccabbcbccdaccabbdcbdcdbacbccaccdcdcabadcbbcdddbdaddadaacbadbcdcbaaacaddbdddacbadbdcadbbbcdaaabdcaaccdcccbcdaabddbbdadcdbcaaccdcbacbccbbbbbdbcdabcbbbaabccddbadddbacbbcddabaacbbabbabbabcacdbcdbaabdaccadcacbacbacbcdbbbaccabbcbabccaadcbacbdadbbbacccaaabcaabadcaddbdccbacccdcbbaccddbdabcaadbbacbabcacacdccbaacdacccaabcbaccadabdddbacdaaabccaacdbdccdabcacbcabdbcdadcdbbabcbbacacbdabaaacddabddaddcbdabcdddbdbdbadaccbcbadbcdbacacaccadaddaaddbaacbccadabddabaaaaaddbdccdacaddaccaacadcbdccadaabbdbbbdbcbbcacbaddbdacbacbbcabacdbbcabccbaddbacabdacdddbabdbdbdbdcbbacabcaabddbdccdbabacdcdbdcacbbdbdaadcddadcabadaaaaaacdaddcdcbbcaaccbbcadbcaacacccbcbbdadbaccbcdacbbadacdaaacbbcbcddbdddbdcdaacbbdadddbbddcdcacbaabdbdcbdccbcccddbdbdbcbacadadbdccaabcdaaacddcdbadcbccbccbcbdbdddadabcaaadcdbcdcababbabcdaaccdacbbbcdcddcbacdadcbbadcbddbddcbabbdbdcbcdadcccdadabacbbdacdcbbdadaaccaaaacccbbddbbdbcdaadaabddccbcdabdbaacddbbdadbccaacdcdabcdaaacbdacbddbcddaddaccabdacdcadaadbbabdbdbddabdcacddbbababaaabddacbaaccdacbaddbadcbcdccdcbcdbcabaacdcbcbbbbbbdbbaaaacaacbbabcbabdcccbdbaacaddbdcbaadadbcdcddcdacbaabadacabaddbdabcbbcbabbadcbaabddabbcabbaaaaddccbaabacabcddbddacabaccabdcaccbccdabcacaccdaccbcbdccaaccaaabdbdacbbdbddcaaddcbdddabdabdcdcacbcacadcbabbdadaadbaaccdabacbbccaccbaccdbcccbbbdacbcacbabbadddccbcbbdcadbdcbbddbacdcadcadddcbddbadbdaddbadbacadacccacbcbabcdacbdddcccaabdbacbcdacbdbaddbdbaadcbdbdbddbbdaaabccbdbcaadcbdddbcbdcdbaddacbbccdccbadacababcdcdcacaabdadbababadcddcabaaccddcdcabcbdcbbbdabcdadbbccbcaabbabbdcdadcadbabacbcabcdddbcbcdbdbccadcbadaddbbddcccddcaadbcdabbcbdadbdadbbddbbdbabbbcacbcdcaaccdbabaacccdccddacdacbcdabbcbaadddbbbcdbdccbaabbcbcacaaddddaabacbacdcdcadcccdcbabdddcddaaaacdadacadcccaacabcddddcdadcdbcbbdadcdaacccbabbcbdaccdadaccacdcabdddbdaddbbbdaadbbbccdbcadcadacadaccbccabcdcabbdaaacaaccdcbdacacddabbacdbacccdddccbdadbdaccdabcacbbcddaccdaacdabdbdddaccbccabbccccddbaadaacacdbbcabacdabdbbbbabbaccbcdbccacbbcdbcadcdbbddddaddaabdccbdadcddbdddcadccaaacacbacabbcadcacdabccbdcdddbccbbcbccccdbcddbcbdccbdbddcbadddbaddcbabaccdadaabccbadbbccdddbcbbbacddcdadbbcadddbaddcbccdcacdbcaacacabaaadaabcddbcabbddbcbcadabbcdcbdcddbbccadbabadddccdabbbababdacadcbcdbccbabbbcaaddcaddcadabbccbcbcddddbbdbababacdbaaaaaccbdbbaddbdacdbdbacaaccdabcdaadcbcaacbcdbdbccbcbabadabcdadaabcaaaaacdabbbcbddcddccabcbacaadbbbdabbcbdbdcbddbcccbaabdadbbbcaddbddabaacbaacdbbcacddbaadcaddcabbdcadbaddccbdcaacdccacababbcdbacadcdcadccbbacccdddbdcdcbcbcbcbdbdbdcbdccbccbcbcaacadaaddcabbaabddbbddadddabcbbbdadbbccdabbccddbdcababbbacbdacabaccdccbadddaabdbbbbabbcaabdaddcdabbcdcacbbadbbcaabcbcbcbadabbbbbccaccddabccbbadbdababbcddabaaacdbddbdbcaccdddbcaccdbcbbbccbdbadbccbccadcbadaaabbadaaabdaacaaadaabababbbdadcdabcbcbbdaabcdcccdadcbccadddcbaacabbbcacbdcdcaccdadbbaaacdadcbadcccddbcdbadcdbaacacbddabdadaabdadcdcbbbacbdcdcaadccdadaccabcbcdcdddaacbdcbcdbcddddabadacabccddccddbacbbbccddcccdccbacbdbcbbdcdcdacdaaacaacdbccccbddbabdacadcbabadbcadacccbdcdcccbbaddaccbabbdbbcddbdbcaddbdacbabdaaaaccbcaababacaadadcabdabaaabbcbadcbdaaabcabcccdaacbaabdcabcbdbdbacadabbabacacdaddcaacbdadcccbbdbbcddccdabacacdabaaddcaabadcbdbdaabdacddcacdaccdaaabdaccadbaaacbbbdddaaaadcdabcdadbbcdacbaaabdacbdbbdacbbadabdcddbadbddbccbabadcabcbbdcdcdcadadbbcbdccbdcdabdcbabdccdaadaabbbdcacacbcbccccbcbacbdcbdacdddacdbcdaccadaadcdccbccdbbadbaabdabcadadbadaaacaabccabdabdbdbdbacddbbddbadabadbdacaddaabdbaaccdddadcdabcccbdddcabaddbddcdaacaabacabdcabcdcdbbcaadcadccdcccabdaacddddbaddbadcabcdabddcaacaadccdcbbddaaacdbcaadcdcdbdaabddbcaaccccccbccddbdcadcbbddcbdcbccbcddcbdcacccddbcbcbcccdacdbbbdcbdccacaaaabdcdadbbbcadcdacacddbcaddbaadcdadddbaaaadaacaadcbccacabbadadbaacdacbcdbdabadbdadcbddccaaaacdcbcdddbabdcadbbcbaaacbbdaadcadcbdddbdcbcaccbccdbdbddcbcaababcddaadcdcccdcccbdbcdbbdbccaaaaaabcbdccadaabacddaacabddcdcdbcaddacaccbadbcbbcaacdaaadcacaddadbdbcacabbdbccdbcacdccdccadadcdcdbbdbadaaccbaadacdacaaddcdcbdddcadddcbbadbcdbaaddacbdaacadcbbdbaadcabdcbabccdababadacaaaadbadcadcabcbbdddcbbbbbadaabccdaacabadbbbdadbbaacddabcdaaadabddcdbaabcccdcdadbadaaacaacdccdcaabccbdccaccaccaddcdcadbdbbaaaccabbddbcbcacbacdcaddadbbccbadcdddbdbbdbadbaccdbccddcacdcbbdabddacdcddaaaccbcdacaabbdadbadbaaabdadbaadacbbabadcadbbdadbcbbccbbdcbaddbdaadabaaadacbbadccdacdbdcdcacdcbcaacdcbcbacdababbcacddbcbccddcaddcdbadcaddbadaaaccdbccadbdcabbabadacbbcdbbdbddddcdccbaadabbaddccbabaadccbdaccbddaddaaacaccccdcdadcaacdbdcdaaaddbbbdccbadbdcadddcbcbcbddbccdababcaadbbbdddcbadbacabdddacaabcbcbdcccdabbacbddababdbdaacabdbcdaddcadcdbddbdddaacdabdbbdabbacdbbcdabcbacbbaacaddaddadbaadaddabdccacababccabcacccbbdbdcdbdbbbbaaadcbadbbaacbccbcbddbdabcbbbdcddbddcbddaaadbdcaadacaabbbadbbdaccacabbbbcdcbdccdddacaacdbddbddcbadadabbcacadabcababbcaddbaabdbaadcccdbbbbbadddcbbbccdcaacccccbdbbbdcbbdbcdcdbcaacdcddaccbdbbbbddcbccbabaadbdbacadcdcbaaadbaaabbbbdadababdcdadbcaacadcdaaadcbdcacbbadcdbcccbcdbdbacbaadbccaddbbcdcbadacacacaccdcbbdacdaaadcacabadccccbdacbdabaaaacbcdadcddbabdcabaadabcbbcccddcdbdacbbcdcadabbacbaaabbacbcddadbdcdaacacddaddbddbdaadcadddbcdbdddcbbccaaabdbadbabdcccabbcaaccadaabbbabbacbbbccbdcacdcadddbadbbacdcadadccadabbdcacddadaacbcbccacdacbadbbacdadadaaabbcdcbbbacacbbaddaccbaddbdcabbbdbdbcddadadbddacaccaadccddbabcabcaddacabcabadcbabdcbbbcddbccdbdbdcbccdcabcbabccbdbdbabadcbcaaacadbdaabbdabbaadccccadddacccbddbacdddaaadbbdaabadbccacdabcbdbbddcddcadbbadadcadbcaaabcaaacbadbcacdbaabcdcbcccbbbddbcdabccdccddbdbbdaabbbadaddcbbbbbcaddcabcbcbabcbbddcadbcaccacbdbddaadddddcbbcbdcbbdcddbaaadbbdbbbdcdbcdbaadccbdbddabbaddcaababcacaacdadcdbcbcabbcadcdacbaccdbcddadccabacbaccdbbadbabbbacabcbcadaadddccabaddaabbadbaabddbabddabadaaccbdabdddcbdaddddbbcaccaaaadddaccadadadabbdcdcaabccdcadbbabcdcdabdbddbaaabdacdabbabcdbdadadbccddcaacacacdbdacadaccaadddcdbdbaaaccbaabddcdaacccbadcdddcaacddccccbbdcaacdcacadbcbabbabbcbdadbbdcaaadccbbbabdabaaacdbadbdcddcadcbccbcdacddcbdbbbdddddddcaaadaddbddddccbabaddacdbbabccadcbddacaadccaadbcaacbcddbccadaddcabdadadccdaaadbaabcadbbbcaacbcadaacccbbccdddddccddabcbbdcabcdabadaddabccbabbbbbdbcbabcaaaaadbbbdcacaaddddcdadabdcabaddacacdabcbacdabbbdabdbbcbbbbcaadacbdcddbdddcbdddaabbcbccdddbcaadccabddbbcddcacabcddbabababccaadbdbcaaaaddbdcddddbdaddcbdacccddadcccdadcbbcadbbadbdbbdbdbccddbcbbbbbadbbcbdbbadabdbcdddbbabbadcdababccbcbabcbbdcdabcbcbccadbadadabbcddabcbdbbdbadbaabbbdbccdbdbccaccdadddbdadcabdcccaabcaaaacbaacdbadbbcdbcacbdcaaaccabdbcbddddbccbdbcabdcaabbacabcdcbddccccccbdbdacbbcdaaddbbdaadabaadcdabdccbdddbddcabbabcbbbbcbdabcaacdccacaddcbdaccabbbaddcbacdcabbbaabacdbbbdbbbcdccaadadccaddaabccddddbcacbcbdcccdbabddcabbdabbacdcbdabdbcccbcdcdcdbbadbcaadcacadccbbbbdcccbcbddbdabbddddbabdcddddcadcbaccdbdcbcaacadbdcccaaabadbbcaddaabcdabbaccbbbbbaccacdbbdadcbbacbbcdcbabaabcaacadddbadbbaabdcababbadcaccddcdbadcdcbdbabbabcbcababadccdababababaabaccccdccdadbddbbcbbbadddaacdadcbcbdadcdaaacddadccaadbbaabccadabbaddcdbdabdddabbcdbbbaddacbadbaacdbaabacaaaaadbaaaacdaadaccddcabbcbbaaabbbacbacddaaaddbccdbcabdadabdbbbbacbadbdbcddadcaccacbadcacadcbbabaaddaccdcbcbdcddaddabcdabdbdbbacaabadcbcadbdcbddabaadddcaaabdddadcaccdacdabbdaccdbbdacbbcacbbddccccbacdbcddbdbbbddbacadaddccdcbdcddbbacccddabbbabccbbcbcaccdbddaabbacbccdbdbcbddbabaacdbdddccdcbcdbdbddccbbdadacaababddccddbbcbdaddbdbbcbddbcbbaabdadbcbddbaaaddbdddbbcabadabbadacbbdccbabbadcdbcbbabcadbacbaaabbbacacbcbcaaadddadbbaaadacdcdbcdadccaadcdbcbddaccbaadcbddbcddbcaacbacbbadbdbddadacdbccccccbbddbcdddaadaacddccdcddacabbabddacdcbdcdcddacaddcddbdbbcbdaadadbbaadccbdbaacdbaaaaaacdcccdddaaaaaacddcacccdbaaccdbcdabcbdddadddcbdcdacaaddbccbaababacdcdabcdcbdabcdbdbbcbabdaaacccddbacbbaddddbadbacdbadaddddcddaabdaadaadbccddbdcccadaccacddcdacbabdadccdabdccababdbdabaacbdadabddbbdbadbabccadccaadaacadbbccdaddbbcbdbdddaadadacbddaddbdacaabcabdadacccacddadbdbbbabadddcdddabdbbdccadbacdcaaccbbccbcacadbdaacbadcbdacacadbcbcacababddddcccabdabdccbdacdcadaddbdadaadaacbcbcdccbaacdaaaabddabdaaaaccdcbaaaccbbdaabaadbdbaaccaccbabbababbddcadbcdadddcdadbcddddbccdaacadbccdbadabbcdbcbccabbbaaacaadaccabdbbcbcdabdabdaacbdcadaddadcaaacabbcaaacbcabacbbccdccbbcbcdcccddcbbdbadcbcccccdccccdaccdcadbaabcacdcbbbdbabccdcccadbcbabcbabdaadcbaddcbabdddaccbdbdbccdadbaabdacacbcbbbbcbaabacabaabdbccbdbaadcdbbaccabdcabbcdbaabaadbcaddcddddcbdacaddbcbcbadcddbadadacdccdadcadcabcaacacccacabadbabddcdbddabacbcdbabcbabdcdccbcbbbcbdccbbbddcdbccccbabbbadbaccbcdbcdaddbadbbcdcadddacacdaadbbbccbadbbdcbbaaddbbddcaadbddbbdbbbacbdcccadbdcbcccababaaadaadcdacdbcdcdaacbadbabcdbcccdbccacacbccaadcdcbadacdacabadcadcccbcaabbcadccbcaaaddacbbdbaabcddcbdaabcabcdcdbddbcadddbbdddcaccabdccdbabbaaacdcabddcccacbdccadbbdcbdbdccadaaddbabdaadacdabaaddcccbdcbbcdcbcacdcbcdcdcabcacacbadddadcbabbacaaabbcbcddcccddbbacadbbdddcdbabacddaadbaaacdcabccbcaaadbdabcddabcaaaabaddacdcacddcddcddbcbcccbbabdbadaadcaacabbaaaddbbdabadccbbbcbddbbccbcabdcdcbccbcaccbdaaabccaadcbdabbabbbadbaddacbdacccdacbabbbaccacaddbdbbbdabbdddcccadbadcdabdabccbbccdadcdbabdcbcbdcdddcdbbbbabbbdccdddbcabaddadbcbbbdabcdadbcacbdbdbcdcacacadbcdcadcddccdbccacbdbacadcbdabdadbddacdbaddacccaacaabbddbabadbbbddbcccddabbbcaaacbbaccbadccaddabbcdbdcdabdadccbabccadaccccdbcacbbbbdccabbddabddabcdbdcddacabcdcbaabbabdccdcaccbcacddaadccaabaddccccdccabcddbbabacddbccabdaccbabbaadccbbbdabacdbaadabccaadacccdbcaaccccadaabdcbaaaccabcdadcbbdadaddabdabcddbdbdadcadccccadccddcccdabdadacdccbccdaabacbdcddccbbdabadbbcbccaaadadccddaccdaadbbccdcacbcacdbdadcdbaaccacdabacbadbbdbcbcabaaddacdcaabdadddcbccddbbbdadcbaadadddacbaadcaadbbcbbdcaadbaddcbcbcabbdabbdbdbabbbbcbbcbcadacdcdcacaabddbbccbdbbbaacdddbabacdccccabdcacbcacdacbdbdabaaaccbadacdcccbcbcccddbcdadcdbaaabcdcbdcdbbabccbdabbbacbcacbdccbbabccdccddddcdaabdaaaccbbabbbcacbcdcaabcbbbccbcacbbdaabaadacacbadbbddacccabaddbddddcadbabddcabadbdcbcbcbbbddcbdadbdbdddcdacbbabdadabccdcbbdadadabdaacaabbbdccbadaacaabacbdbbcddddadbbbbddbabdccddbdcddbaddacabccccbcbdcbadbabcccdabbbbdcdbcaccdadcbbcddcdcdbbadaaccabdbcdadbdcbacabacbbadacbbcdbdbaaabadbacbbdcacbdacabccbacbcadccddbcddbdcdbdbddcbcddbbdbabdadaaacdcacbbacccddbdbadcadadaaabcccdbacdcbaabbcdbbbcbbcabadcdcbbdcbabddaabbcdadbccbcbcbdcadcdacddaabbcdbaaaddbaabddadbdccdabdbdcbcdcbbacacababcdbcabcacddbddbdbdbdcbcbbacbbcabbcbdbccbaadbaabcdbbcccccdcddbbdabcddcdcacacbbdbdbbdccbaaccccaabddabdbaaccbaccaabcdddbdacccddcadacdaadaaddcbcbcdcbdaaccccbadcdbcabcbdabbbdddadadbadcdcbaccbbcbaddddcdbdcbdccbdbdaadccaccbbadacdaabcadcbaacadbbdabdbbdcaacbcdbacadbaddabdccbbaccabcbbacaaddbdcbdaacbcdcbcbcaadcdadcccddbbabddbcbdacccbdddacdcbdddbabdacccccdcdaccbdbadbdccaabcabaaabddccbcddbabbcaadadaabaaabadbcdcadaabbdddbcbcbabbbcbbbbbbabbdaadbbccaacbdcdcaaacbcbcdabbcdccbacbaddacdacbbcbcbdadaabbbaaddbdbcbdcaacbbbdcdaabbcacababdbdcbaccdccbddacbddbdacacbadccabdbcbaccacddacbbcdbaaccbabacaaacabdaaaaddbcabddabccaaadccabdaabdababcbdcddaadddbcacaabcdbbdaacbdbacbdadacdcccbbdcbabbcdaddaccaacdcddccbaabbbccddbdaadcccabbcccdabcaaadaadacccdbcdcaaacddbccadaacabddcddddadaaaaacadbabdcacccadcaddddbbddacaadabcbcdacaddbcddccddbbacccbcccaccbdbcdbadcbcbcdadabddcdbccacbdcdaacdadcbbbcabdcbccaaaabacacaabacdcaacdbddddcbcdbdbcdadcdcaaccdcdcddacbdbdcbcddbcbdacaaabaabbabdbcddacabdddabbcccbbbaacbdcacbcddcddbbabacaadbbbdbbddbccbccdbbbdabbbdadcdbbabdcbdcbaddcccdbbbccabaaddbcbdcbccabadacbcbcdaddbaabbadddcdbcddaaaaabbbdcdaabbabcabbacaddccbabccddaccdaacdcbddcdacabbdcdababdbcdbadcbcbaadccabbdbdaddaacabbcacddbcdadacdccbddadcbcdddabddabcbbdbbabdacbcdddbddbcbadbdaccbabccddcddbacbddadbdbaacdcddadcddadacbcbcbcdccbbbacdbabacbbbabbcbcdadbadcbbdadbabcccaacbacabddbddaaccbabaaadbdaccbbadbacacbdaccbdbcdacadcccdadaccdabbaabdcaadcadbbcbcdcaadccbccdccdabdbddabcdadcbcacabcbcdddcdbdcddcbdbbcabaabdcbbadbbabaacdabdbcbdccccbccddbadabccdbcabcaccbaababbbdacbcbaabbabbaddabdbadbdacbbbbdcbccbdccccbdbbbdbcbabaacdabbbaaabdcadbacabadbaadddabbaaabdbdbbbbcaccdccabcbadbbbbbdabaccbbdbbbababbbddbacdbbdbbaacbabdcbddbdcbbaacbbbbdbaabdccbbdcbbaaaddddcdadabdaaadabbcdbcaadbcabdcdbaadddcacaabbacbadcdcdaaddccdbccaddbdcbababddaadccdaaadaacacbcaadbddbdcbabbcbcdbcccbbdaadacaacbaccbdaabccbdacbbcacabdbddddddbdadaabababbbdacdcbcccbbdabbcdbaccbaaddcdcddaadddccbccabbacddcdaacccdcdbdaccbdcaabadccbdbbacdbabaacabdacccbddaacccbbcbbbdbccadcadcbadddccccbcdddababdabacbbadacadaadcccabbadcbbdbcbcdbbbccccbaabbbbbbacccbacbacaacabbcabbbabdabccbaadcddccaadacbdbddcacbccbddddadccbcdbddaaddcaabbbadaccdabcdadbcccbbbabbcaccabdbcbbcdbacacdbadbbdadabdbadcaabbddccddccdccadbaadddbacbbcabbdddbbccaabbccddacdbcdcadddbddadbaadcccddbcddcdbdcbdcdcdaadccabaadacbddadccdbbcddbabbdbaccbbbabbdbababdaabcbadbddbababbccbabbdadabdbcbbacdddddbddaadacdbcddbbaadabacddcdcdabdbbdabdaaccadcbbcddadbdadddcacadddbbadcdaccccacaabccaddcaacbaacbdcaacadbbdccbddddabcbccdcddcabccbabcdccacccaccbaddcbccbcdaddaacddcbaddaddbdbdccdbdbccacadbdcaacdadbddbbcaddadbaabbdbabdacddabdcddbcbaddbcbbdaababbacadbadbaadadabddbdabacdbdddcabcddaddabbcbbadcdbcbdcbdaddabbbbcdbcdabcbdcbdbcdcaddaccacabbacbacbacbbcbdbaaaddbcacbabbcddccbabcbcbacabdcaddcaaadcacadcbcadcdadabcccabbbbadbccadbcacadacbbddcaaddbbcaabddabadbcdabdcbcbdadcbaaabbacdacadacaaadccabbcabacddabcbdccbbaabaaadbbdbadabcadcdbdabaccbbcdbccaaccccabbcaabadcbbdcaabcbcdcbaddcdadbcdcddabababcadcdabbbdacddacaaabaaaccdccdbdaccbcbdddddacdadabdcaaddbbbdddabccccccddabbbaadbacbcdbdacabbadcadcddacdcbbadcbaacdbaadcccbdabdacdccaccbdadccbbcbcbabaabddacabaabbaabbcacbdacdbcaaccccdcbccadbabaabdccaadddccdcbbbaddadcccaaddbcdaabacadbdacddcabaaacdbacadaabcbbdcccbcabbbdbacdbbbccacdacbccaacdaddbcaddbcccdccdcadbacbdcadccadbcdbabdddbbcdbdbddabbdccdbacdabccaddcacdccddcdbdccdadbaddcdbbccacbdbaaababdbbacbccbacddcddbadaaaadbdcbbbccaadacaadacabbbdabbcbccabbccdacddcaddccccacdddcacbcbdcbcadbbddddcabbdabbdbaccaabdcaabaaadddacbbbacbacaddcddbdbadacababcdcbccaaadaddacddaabaccdcbacbdabacaaabddcdacacacbaacbbcaaacdddcdadbcbaadddaaddabbccdbcdababdbaadccdbdbcdcabbaaaadaddbdccacbabdcbcbcdddccddddbabbcddabcdacdcacadbddddbbbdaadaadabcdaacbdbbadaaccacbdabdbabdccabccaaacaadccaaabadcacbacdcabddadadabcdaacabdaccbbddcdcbdddacbabaaaacdcaadabaaddbcabadaccdbdbadbcdadcaaddaabbdddcbaaaadacdbccacabbddbbabbcdacdadaaaadabdbdaadcbaccddcbbbccaadcbcaabacdddcbadaccacbaabbdacdbabcacaabbbabacabbddbdaadcddbcbccdddcccbcacacaaadbaaccccbadacbddacddaaccccaaacacaaaaaaabacbcbdabdccbbbdaddcbbccdcbaaacbdbcbcabbcadcaacabcbcacacbdbbddccbcbaacacdabdbbcaddbdcabbdbdcdbddbaabdcaabcacbbcdbbcdbdacbdcccacbdbdcadcbddadcdbaabccabdddadbcbcdabddbbbbdaabaadcbbcadbccbadcdaccadbcddaacaaacdcccbcaabbddbdadbabdcdddccbdcccaaaacdbbccadbddabcccdacbcbbdddcdcdcaacacbddacbcabbaccadbbcbdcabdcbccbbbcbbdcccdbdadacdbdaaccdacaddcbcacdbdcbbaacdbdabdadbbbabbbdddbbdcabaacaaacdddcaabdcbadbbbdcdcdabbccdddbbdccbbacdadcacbdaddbcdaaabcdaadcbdacbaacacbbcbbadbdcaadacbbddbacbdabdbcdcbaaccadacadddaaabacabcbcadabacaddacdddcacdbbacddaacbbdadbbcbaaabdbacbddadccddbacbddbaabdddacccbbacaaaadaadcbdabccbbbcbaadadbabcabbbaabdcbddbbabdabaaacbbcacdbcadccbdabbddcaccbdaabbdcadcabaacbaabcbddcacbdbcbccbcdcdbbabdaddcadbcdddbcccadbdbbbdabdabdddabacdacbddbccaddccaadbbacbbabcabddadcbbbcadbcddcdcccaccadcababcabcaccaccbdaccdaadbbaadccadbaaddcbcbbbaaacbdaacbdbbdabcddadbcdabbddbdcadbcaaadcacaccabbccabdbdbaabacbabaacbabaccacbaddadbdbbabaadcabaabdbacdbbabdbbabbdbcaaacacdcbdbdccddcdabcbbdbddacaddcdbadcbdcbdaccaaaacccadbdbdbcabdbccdaabdddcdacdabacdbcbabcbbdabaccadbacdabcdddcbacbdddbdcccbcaddbacdaddbdbaadddbaacdaddcaadcdabcadbadbbdacaaabaabcbddcaadccdbcdadaaadbcbcaddbdbbdbacbbadcacaaccdcacdbbdcbdcbccdcdcddcaddbbcadabdacadacdbbbcacaabcbadccaaabcbbdbcdbdbaabcdbadddddcdbbaddadabcbcbddcdacbadbaaaaccadbbaacaaccbbaacdccabadaaacdadabbdcdbabbcbabdabbdadccbbaadaababbdccdadadbcbcbcccadddbabacdcaaabbbdabbdddcdcbddaddbcaacdddcacdcacaaacddaccccaacbabaadcbdbbaacaacaddccbadabaaadacccdcddbccaccbdbccbcbabbabacdbcbacbdbbabbdbbdbdbbbccbbdabcbccaabdaccbabcddaaaababbdacaadbcdbacacdaadbadbbaaaabdcababbbbdcbbddbaccbbbddcdbadaacbbbbaabdcddacbabbaddcdcccabadbbdabddaaaaddadccbaccdddbdcdddbdacadbbabbcddccbcbdbaacdacabbbbdacccbdcdadbcbdcbdcbcbbcdccbcacaddcddbbaacdbcabdcadbcadcabaaabacdacddaabaabadadddcaabbababdbbabddbaacbbcbbadbabcdbccdccabacabaaadbdbdccdaabcddabcbdbcacbcaabbaadacbdadcdbccccbabbcadcabcabdcccbdacabdbcccbbcdbbadbdbbbbabbcacdbccdddbcddcdcabdaaaadbaadbdadbdccbdcaddcddcdccccaaccacbdadcabaadcacdcacbcacbdcabbacccbcbbccbbadcccbbadaddabbabbcbababcccbaaccabcbbabcbddaabacdcccbcabccaabcdadadcdcadaaacbdcacddaaabddaaaabdabcdbdacdaacccbbcbcadcdbbacabdaacabdcdcbdcddabccbcbbdbdbabbbbdacbabdbddbcbcaabdaadaddcdcdabdbdcacaaacbbaabacccaaccddccdcbcbcbbaaccdccacabaadbcaccddddbababcbbbccbcdcccdbddcbbdcbaddabcdacdaaaaaaaaaaadbabdbcadccbabbdbcccaaddadbddcaddcdddcbcdabbbaabdaadbcbadbcccadbdadcbcddbcbccabddaccbbbacadabaacacabbcbdcbddbcdaabbbdacdcbdcccbbbabaabbcadddaddcccbdbabdddddbdacabcbbadcdddcabaadcaadddabcadcaababadabdbccaabdbcacabacbaaacadbdaacccdaaaabdbdcbacbabcaacbabaddccddcaabbbcdadbdadaccddbdcadbcabbbbabcaccbdbbbcccbdabacaddaacdabdbbddbdbbadbbabdbacaadbcadbccaabccdccdaacabccdccccdadaccaaacaaacbcabbadcccbcababcdcbbadabbcaabadddbcbabddcbacbbbcbaacccabacdddcbdcdbcbdbddddcdacbbbdbbcdbcbbdbbcccccdddcdaccbdbdadbddaabaddbccbacbcdbdcabacdaacbccbdbddabdaccbaadbdcbcbaacadcababdccaabcdaddadabadcbabbaccabbcacbddbdbacabaacabddacadbadcdaddccbadbabbaddccaaaacacacabacbbdbdbcdadddcabacbbaccbbcacbdcacbdbdbcbbdbdbdcbbabdabdbcbdbcaaaadccbcaaacaacdcbcdcacadcbdcbdcddcaddddaacbcaddcadcccaddcaaacabdccadcbdbacabdccdbdabaddaaacadcddbabdcbdcbdacbcacadaabbbbacbaddccacbbdbdcadcbbacaaabcbcccadcacbccbcabaabcabcdcbbbacdbdbdacbbaabcaccdcbbccdcbbbdbcbacdddbdcbbcccbbccbbabadaaadbdabaaddbdabdbddcdabcbbcdacadddadcddbbdbabcbaaaabcdcdbacbbbcbbacaaddbccaaadacbcaccaacbdbbdaccadaabbddccdbbaaccddddbcbabbcadddccbccbdaddccdbddbccacdbccabbcbbcabbcdaabdacccacccaabbadcdbacaabcccbbbabadbacabcdddbbdbabbadacbcccdcddcacbdcabbdcccdacdcabdcbdbddbabdbbbabcddaaacaabccacbdaccbacdbccdbbcbacadbabcbcccacaaddbccaabbbabcddbbbabacbdacddccbccddbbaccdccdabdbaccacacdbddaccdbacaddaadaccacbcaaaacaccbcbbdcccdccabbaabcbaaabbdddccdbddddabaccaabdcaaabddcdbcdbbbbabdcdadbbacaaddcdbcdbbbbabbbadabbacdddcaccaddbaccccabddaddbdacabbdbbdaabbcabdadaadadbcdbcbcabdaddbdcbcbdcdccabbadcaacaaddaabdacccdcbbcacacbcdabdccadcadddbcabbbdaaddcbcddbbadccabccddbccdaabadbacdabbbdcdbadcbbdcccdbdcccdbbcccadbcdbbabbdbcbdabaccdbbcddadccdacddccbdacdcdadbbcddbbaabdbdbbdbdbbadbcddacdbdaacadabcbaaccbdadacaabababcddccbcbddbaccdadacbcaaaabbbdabaabbabbccdbdabbdadcabaadbababddbbbccabdddaaddbdcbdadadacdcaaccbacbcdbbddbaaddcccbbdcaaaacbcbdadddbabaaaaaabcaadbddcbbdbbadbdadbdbcdddddbbaccabbcacdabcdbabcdadcbaabadbcddccbcbcbccabdccdcadcdbcccdbbcabbadbbacbbcbdcdbacbcdcdcdaadbdccdcddadcbdabddbccacbbccdcbabbcbcccbbbbcbacddcdbbbdcdcddacbddcacaaccaaabcbbaccadcaabbacddcdcbbbbbcadbddadccddddabddbcccdcccddbddabdcbdddbbddbdbdadadddcdbbadcacdbaccbdcbbbacbbbbbbcbbbadbbaacbaaddcacacadcdbbccdaadbaacdacdbacacaabdababdaddddadabacdddaccabbcdacacadbabcadbdabacbacbcbbdbabddccaacdcbadcacabbcbadbbdbacdaaccacabbaacabaadacdabacbbcadbcdbdcdcacdcdaddbbddbacaacbbcacbcaacbbaabadabaaaaccdacccbdbaddbccbcaaadbacbbabcddccacbadbcddcaaddcadcbbdcccdddbcdacbdadbbacddbadadacdacdccacbccdcdbbcdcbddbddcbbcccabacbcccdbcbabbdacbaddbbdcccbbcbdadacdbaaaadaacaabcaddccaaacccdddacacaadccabbcddcbdcccdacdbacdcdaadbbbddabcdaacdcbdadabbcbdcdaadbdcbcdbddadccbabaacabddaccaabbdbbdaaadccbacdaddcdcbadaddbbabacaacaabccdacaaccdcbcdbacbcaccabcdbccbadaddacbaddaabcbccaaabacdaabbdbdaaaadccadabaabbacabbaaabaddccabccbaccdbbaabcaddadbdcaadcdddccccdaadacbbbbacaaadbcbcbcbdbccacdccccdbaaabadddabdacbacddaabacabcadbdbbadbdcbcadcadbbbcdbdbbabbbacadccabdbdcaacacdabcdbbcdabaddccbadddccabbdadbbbabbaadadddccbcdcdbaabdcacbcdcdcbaabadcbcbbcddcbababadabaaccacbbaaddabcdbacaccacaabbbcadbaddbcbdbbaaaddbcadbbcbdbbdabbccbbaaabcbdcbbddcdadbccadabdcbdaccaaddddcabaddccdddbbbcdcdbcaabbbccadddbaadccbbbbccddbcdbaaccbcacabddadbdcadcdacacbddddbdbbaacdbbddaadcabadabbdbbdcbbbdaacbaddcbaacadddccaaccbcbbdddacbdbbcababdbdabbddabdddaacdcaddabbccbaababacbbcbcdccccaccabbbdcdcaacbccaddcaabadaaaaadabcadddbacccbdacabcdaacadaddbabbbbbadbdccdbcdbacddcdbdaddbcdcccdbabdcadbaabadaddbdccbadddadbbdccdcdabbbbcddcbbdadbdacaaabcbdcdcccbabcdddcbbdcdcccbaccdccadbacbcbcbaccdbbcabcadadabdbdddcadccbabccdcbbbccaaccadcdacaacaaaaadaccacbddbbbdaddbcabacacbccdcdcdbbdbbadaacdbdccbdcdbccacbbccbbcacbbdbcdcccbdacdcaabbdaaabcaddadbddacbdaaadbacdcabdbaccbcaddcdccdbccdcbcabdcbdbbcbddddacdcbcadcbababdcbcaadbaddddadadcdcdaabccbccacadcbbbddabbbdacdaaddcbabccabadacdcbdddaddbbadbbabadaccdcbdcaababdbcaaacbabacbadbddbbabccbbdcaadcdcdadbadaababdadacdbaabccbbacacbdadddaaaacccbadcbcccadbbdddacbabaaddbadbccadbccddacdbacbddbdbabcacddaddcbadabcbdccaabcbdbdbdcdacdccaccccbaadccccbbaabacdbbddaaaaaddbdcdbcdadabddaacaaadbdaccddcdddaccdbbbbabdbabddcaaabacbcacbbbccabacddaabdbdddadcccaacccadbcdacdbcbacdbcadaacdadddcaabaacdbdcabdaaadbdacdaaaacacacbcaddaaaccdcbdadabcbabddcdabacdcccacababdccaccdacdacabbcbcbadbccabdbbaddbccbabadabbdbbdbdcccccddcaccbcaaaacddbacaaddbadabbbbdccdcacbcaaadcadcdadccdbdadbddabbbccdddcaadcbbcbababbaccdcdcbcdcbdcbacccbbbabddccbbddacbcbcabdacdbbbaccaabdbbcddddabcaccbbbabaaabbcbdbaabdbdcdbbabababdacaaccdccbadcdacaccacccbdcbdabcadbddaaaccaccacacbbbbadcbcdbccddbdcacaabdcdabbcaddccbbabbcdbacabbcddacadbdbddddacddbddbabdacadadbdddcddcaaaabcacccbddabccaabaaddcbacddcdcaadcacacadbdbdaccacbcdacdbacbaaadbacdbbabcdccdaccabdaccbcbbdddcbaccaaaacdacdddaabdabcdcbcbababddadbacbdccbdaccacdcdcdcddadbbabcdbbccadcccaaddcccddcbaccbacbbbbccadabddbaacbabacbadcaadaabaddacbddbbdcadbdcccabccaccacbcbcdbbcbbccdaacadbdccaaadbaaadadccdaadbbcdacaadcadcdccabbbaaadcbbdcdadcaacbdccdbbadbcbdadcacbbaccddcccbadadcadacdadcdccacdaddacdaacccbadddadbcdcdbcdaccdddbbdcddcbbbaddddcabcbbcadbdcddccabcaabacdcaabcabbaaadbbadaccbabdbdddbcbbaabdcdadbcbcccdccbbadbbcbabbabcdcacbabcdddbdadcabcdcdbadbdadbcbadddddddcbabacbdabdaadbbbdbacdcdbdbaadabcbabacadcabddbdddcadacbbcbbacababccaabddbdccbbabaadcacbdcdbccdcbdacccdadcadcabdcbbcbaddadaccbdacacbdbdbdccddadcdacccaabcaaadcaadaaadacacddbbabdbccdcaccdbddbbabaccbdacddabaadabdcadadcbacbcadbabacbcadacabacdcbdccacccbcddadcbdcccabbccbcdbbdbacabaadcaadbbbcdcccdbcbabadbcdcdbbcbadbacbdbcdbacddcccabcdcdaddaddaaccbbbbdddabcbaabcbdbdabacacabbdcaacbccbaadbbcbabcccbcbcdbacaaddacaaddddacccaaaddbdbababcccbdcbcbbcdbbcdcccaddcabddddabccdabacbcabcbdcccbaccaacaccdcaadcaadabbcbabdbdacbbabdbcbdbdccbacacabdcdaaacbbcbcabcdbdbaaddccdbcbababacdcaacddadcdccaabdaccacddcccbcddddcdbcbdbcadabbabccbcbadbaadbdbdabbcbdabacdcaccbcbdaadbccbbdcbbcdbaaadadccddbbaaabcaaabcccbdacbcdcddbddbcdbbccbdbacdcadbdacbccbbaababcbadadacdddbddbdaabaddababbbdbaabcdbbbddccbdabbcdcccadcbadcdaaadccbbdbbcacbacddacbdcbabddbbbbddabaadccccbaacbdcbbcdacddcaacdacaabbadddaaaddadababadcaacccaaabdccadbddadbacaadbbcdacdbacaabcabcabdbbaaaacbdbbdcbbbababaccabdabccbddaabcbbabbdadcbbcdcccaaddabcddadddbcdccdabdaadaddcdcccbbcddbadcdaaabbcdbbbbacaaaadaadbbbdadabdadddbaacbccdacadbcaacbdcabcbdcaabdaabcbcbaddabbccbadaacbcbcdbdcbbbaaabbaabbbdaabaccabddcacbdbddacdcccdaadacabcacbbacabddccabcdcbdddbabccccddcdacccdbabaaabdbacdaaccabdcbcddddbcaaaaacbcdccdbddcccacbdcdbcadcdaaccbdbacdcadcacdcabadcadddcaccdccadddbddacdccbdbbbbadbabcddccaababbabdbcdccaabacdbdabcbdbdababaacaaadddcacaadaadcabbdcbacbcdadbdcdddbccaddbcddabcacdbbdccaacbcacabaacbbddadbabdacacbadaaddcacdbddbbcbdaddaadacddbbaddacabdcacadcbcacdcbdcabccbadaddcacdadbbcbbbbdcaccabbbacaabdadcabaddcbbdbbdabddddbcccdadacacbdbaabcddcaaababababdaacccacadddbbbbcddcbddcccbbbbbadadbbaadbdabaabbdbdcacdcbaadcbdcccaabdaadbdbbacaadddcdbdaaaaddcdaabbabdcdadcaabbdacabcbddcaabccacacabddbbcabbacdadacaadaadbbcacdddcbdbcdddcdccdbaddccbbaacbadabdadbbdcdddcdacbcddcdbbacbcabdcbcdbbdccddbcdcabbcdbadbddabcabababcdbbcacbabdbccaacbadddcbbcaacacddcbddcbdbdaadbcababbaabadcdcddabdbcaddcaccccddabcbadcabdcddabaaacdadbbcdabcaaadcacdcddccbaabbccbbcdacdddcccaadbcbdcdcdabaccbadddbdabdbcddadbbaabdbbaacadabccacbbacdadbcaaabadbaadccdadacdacdacdbdcbdcbbddacbcbcaacbbbabdcbccdccdbdacbcacdbbbbccabcdaddcccbadcdbcabaccdadbccbabcacacbdcbaccadcaaccaaabccadabbcbccacdacbcadabcccacaacbcccccbacccacdacbdcbdadadadcbcdcbaaccddbddcabbaadcdcdbccdaddbacdacadbdaadbadadddaabcdbadddadacbadcabbdaabdadddacabdbbbbadbbdccdcaadddabacdbddadddbbaacdaddbdcaccdddcbdadabbadccdcbbddcbdabbcbbcdbcacabacdadbdcdabaacdcdaaccccdaabcbddacbdaddcdbbcccdabbbbbccbbbcbdbacbdbcaddaacdadcbaccbdddbdabcbcadbcabaddddbdbddbadbdaabbcddbaaacbdcaaddacacabbbdadbaabaddaacdbcdabbbbadaaacacbdbbacadcadacbbcbbbaaaddbbbbdbacdcdbbbddbdccdddcddcccdadbcdcccdccbcadabbadadcdbbbdcabbdcadbbdbbacdbadadaccadbbabbddbcababbaaabacacccadabbadcdbabbdabdcdcabcadddaabaacdcabaababddddbbbddaaacbbcbdbcdabacbababddddacdcdcccccbacdaccbadbdccaadddaadddcccaacacaaacbcdadbdbdcadcddcbdccadbaccacdcaddcdddaccaddbaadcbdabbccbbadabacdadbbcddbcdddaccadbadbdaccdbcbacadadacadcddaaadddddaccbbdbdabddaaccacaacacbbbadaccddccdccbdcbcacccbdbdacbdcdbddddcddbadcdcbddddbbbdaddddbbddbaaccccdcbaccddddbbaabaccaacbccbacacdcccbbbadcbccadbaaabcdcadcabdbdcdbdbbccabbbbaabbdbccacdcdcdadacdcaabbdbacbbadbdcbcbaaccdadabbabacbccbdbadabbcaabdcbdccdadbcbbaddaacdbdbabaabcbacbddacbbacabacaabcbacdababbccabccdbbdbddccbcdcbdbdaabdaccdaacbbcccdcddaabcadacacccdddbbaadaccdbaaacddbcadaddbccbbcdbcaccbdbbbddaabadbbacbadacccacadccdaadadddbdddcaabdbaaaddacbdcabcbdacdcadcabcbbadcdbdbdbcbbdabbdcaadbcbcddacaacdbadacbbccbbbdacaaadddbdcaabcadcbaccacbaaccccdaccdabbccabccdaddbdddaabdbcaabbbbacdaabcdcbbacbdbcdccdaacabacdddcababaccddacacabbbcddaccbbdcdbaddadcbbbdbccbcdcbcbbaccdabddccbdadcaccbaaacbbdcbdcabcbcdbaaabdcccacdcaddcddadbcdaabccbcacadbbabcbddcbaabdbdccbddcaaacdcdababbdcdddddbaacadbcdddabcbbbddabcddcddccaccbbdcbcbbaabcacbdacdddbadbaadaccaabbbcadbbcaccbddacbdbcacbbcbcaadbdadcdccccbbbbcadbdbdadaacbacaacaccbabdbddaabadacdbcdbacdddbbcaacddcdcccdbccbbbbdacabaaacccdcaccbbdaaabcddabbcdbddacbdcbaaacbaacbbadaabadbdccadbaabcabbcdcdddbacdcbccbdaccadcbbdcdcbabcdcbaadadcbacacacdccacaaadaddbdbbdabbbadcbadbadadcacdbdcdbbcdccacadcaddbdbdabbabcbcabcdbbbdacabcabbcbadbaaccaacbcdbabbcdbbbdcbdabddbadcccbcadddaddadadddcbcadbbcbcabcbdcaddbadaddadcddddaabcdbdaaadddccccabdabadabbcdadbacbbccdcaabccabaaacccadaddabdcacdbcabcbabbcacbbcbaadbdcaccdbbaaaacdadcaadbdbcbaadaaacdcdcbadccddcabdbccaaaddbccbbcabdaaddabcbdbaaabbdbbccbddcadcbaacdbdccbabbccbcbadddbacddbcbaddcaaadbbcbddaabadcaaacdcbacababccbdbdbdcdcccacccaabbdcaaaababbbdcccdccdbccdbcbbaaabddabdcaccccaaadcbaccbdabdbabbcabaddccacdadbddbcbabaaadbaabadcaddbdbbdddbbbadbacbcaaababacddaacdcdccabbaadbdbaddbbbaaddaaabcccbbcdadddacdddcdcacbdcbbbabcbabbbbdbddcbccdcdbbdbbddbabbdadababcdcaccdcbaacdbacddbbadcbdcddadddadbdbabadaadcddcdadddbddabaacadbdbdbdcacabcaccabcccbaabbaacbbbbdcdaddacacddaddbccbacbbaaaccabbbdddccdddcbbadadbbcbcdccabbcdabccbcabbbaccabbcccadbabbabdacdadbbcdddcddcdbcabbccaadccbcaaaaacbccdddcbaccababdbcbcbadacadcdadadadaddcacdcaacbbaaaabddaabdabbcabacaccbcccacccbbbcacdbadddadacbdbcdadcbaaaaccdabbdaccccaaadadccbaabacdbddcacbcacbadddcbbbccadddccbddbdaccabdcbdacbcaddacaccaaadcdadbbdadddccaacdddccadaabadbcbcdbccaabcbabdddaddbcdccbaabccbcdadadccdbaaaddbdaddbcbccaaacdbdabaddcdbadbbbdddccdaccabaabbadaabdcdbabcaaccdacbccbdadccbdbbcbddbbdbbaddcdadacabbbadcdbbaabbdabddabacaaadbbdbcbdccddbadabdacacccacaaabcdccdaabcbdaadbbacabcbbbadcaccccacdbdcdbbabaadbbdadbababbddcaaaababcdadbbadacdccaaaacbdaccccaabadadbcadacacdbdbabdccabbabcbbdbcbbdbccdcdbaddadbbadadcacacdaadcbbcdcbbbdbcdadcccaacbbdcddddadbccdabaacdbccbadbddbbdabbbabcabaddaabbcbcbcdcbbbccaddabddbdababacbdbcccabdcddcbcddccdbcdbcddcdabdbcbccbcababccdaccbcbcccbabcbaadbadcccadbcbdddabcccdabbbabaababddbbcbdbdabbcbcdbbcdcabaadbadbabccaacdadaaabccdbaacacacccaababadcbddddabbdaacbbbbbbbccbbadcbabcbabbcbcbddcddcaccdbbcabcbdbcdbbdccbccabcacccddcbddaacddacdcddbbcbccdbbbacaccdbbaaabbacbdbcbdabcbabaaabbbbaabddbbabbabccacadbccddccdaabdbbcabddddcadbbbbdbcadccbababdcddacdcbbcbadbaacadcadcbccbacdbbbcccdbdaccaccbbdacbbccbdaaacdbcbaccbbcdcdadddcaabbbbaabdadadadadcadbaddcbacdadbccdccdcadbbaabcbcaacacbdaaabbcccaaaacbadababbbbdabaabaaccbccbcadbbadbabadabbadabbcabbccdaaaabdcbddbbbaccccddacbaadadcaddbaadacddabdbdaccdaadadddcdcdacbadaaadcbdbccdbabbbaaadbdbaacddacbcdacaabacdbdcbcacaaaccdcbddaadadbddacbcdbbcaddbaacacadabbccbbbadcbbaacacbabcaddcaaaabdbcdccabbadbdbcbaaaaddcdaadaadbcddcbcdbccdcaccdbbbbbdbbcdadccdcbbcabdccaccbbaddaadadcdadcbdabccadadbdbaaaaddacbcdbcabdacccbbbdacbdcdbaaccabdbcaaaddbcaacccccbcdcdbcbabbcbbaaccbbdbdaaaddddbcaaccbcabcbaaadabadadbbdabdcababcdccabbbdddaddcbacadadbbdaddbdbbcbabaadddcbadaabcddcbaabbdbcaabdaacbaaabdabaacdbabcdccacdddcbaaaaddccabcdabbbacadbcddddbbcbababbabcdcbddaacdbcaccdacabdbbdaccdabbcdcbbcdddbdcdcdacbcbcadaaaadccdadcbaddcaabbcabdacdaabcccbadcaaacdaacdaccbcddbbbcdbdcdcaccccabaaaabbcccdbacdcabbbcabaabcabdaccdbbcaababababcabdbabbcdabcaabbbdcbbadddbdbdbcbdbddabbbcdbadabdbddbdaabddcddabdbacabccdaccdaddcbbacddababccbcdcbadbbcccacdcdcacdcaabaaadacdcbaaddbcbbacbaddbaadcabbacacadcdaccabbdabdadcbbcadabaabdabdbccabcabdcdaacabcdaacbaadddcdacbbbacdbcbdadadaaddaddbdccdddcabbcadcabdddcdacacaccbaccccbcadbcdcbbcdbbcbdddbcaaaadcddcabcbdaadcabbddadcaddbbcadadcccbbbbaabadabcabcbcacadddcadbdadcdcdbcbdcbdbaaaddadbdcdbbabdadcccdddbbbcbddacbaacdacccbcbcababaabacadcabababcddbdcccabddddaababacdaaabddadcbacddbcddcccabdbcdabadcacabcdbbcacaacacabbdcbddcbbadadbaddcbdbadacccadcdbcacccccadcbdcbabddddbadcdcbcacaccabdcadddaacddcbdcbbadabcbdaddddbddbbddbcacdcdcdbabbdadabbbbadaaaabdabacccdaaadacdbddacbcddbcbdcbadabcaddcaacdcdadcdaadbbccdadadddbabbaccbdbcabcdaddacdcbabdbcaddddbdcaccdcbdccdbbaadbdadcbdabbbcaabbbbacaacbcbaccbddbcddbccccccadddbabbbccdddbbdcccdabdbddbcadbdbdaddccddbbabaacdcdccbaaabaacdcdadbbacdcbccbccdbbbbdcbbaaccdbdddcdacdbadabdbabbacddbbcabdbbabcaaabdccabadcadcbdbccbbabcacdbdbbcbbaccbcbcbdbbdcacacbbcabbcdacbacbbbdcddbcbdbabdcbadacadddadadabdacbcdbcdbccddbcaaddbaccbcddbdcdaaadabdbcbcdcbaaacbabaccdbbcbaddbbadcbbdcbaaacdadcbcccbbbdbaddcbacbcabbbcbcbcdbddcabbbbaccbcbbdbdaaaabdadbbccdcacacaabcadabddbdacbbddbbcacbaaadbcbadabaadcaaaacdbdcabdaacddcccbbaddbddaaabdbcbabadabdddcaaacaaaadacdbbbcbdbbdcabadddbdbacccadbbbacbabcbbcaacdcdabadcbcbabdaddccddacdcadacdcdccbbcdbccbcbacdabcbcabcacdcadbddabbcbadddcdbdbdbdadccaadacacadcbabbbaacaadadccaadbbbacdbcbaaacbbcdcdacbbadcadddbcbabbaaabdccbdababdaaaddabbacadbbcdccbdbacbacbbdacaabcaddbcddcbadabcdaaaccdaaccbbdbdbbcddbadcdaaabbabbababccbcbcacaaccddcccdacadbacdcbdcaddbaaccabadbcbbbddcbbbdbaabbbadbdadadaddcaacbabbbaabaadbbacdababccacbccdbddacbabbdbcccdabcadcccacbdbaddbadbadbdbabaacbdcaabbccdcccbabcbbcdaaadbdadcddaadcdbdcacbcbccbbbccbdbccbaadbabccadadccbbabbacbabbdbdcdccbcbcbddcdccadbdabadddcaabcbdbaaacbbbacbdbcaddcdbdaddccbdddabadbccdbcddcacddbdaadcddbadabcdbbbdacbbbdbbbbacabbdcccdadccbabaadcccccabcbdabadcbcdcdbdabccadcabbabbadabbccabbcacaccaddaddaccaddbbcabdaabdcacaacbcacabdcccbcaddbabbadaddccacabcdccdddbababbaadcdaccbabaacddbccdbcdcaadbbdaabcaacbdccbdcdcccdaadcccacbdcbadbdbddbabbcadaddccdcddabcbdcccbddbdddbddcdbcaacdcbbcaacdbddadacdcbdadcaddcdaccbddbdcbbdcbddbcbdadbddbdbcdacbcddcabddcdbbadcacbbbdcaccddababcdacabbaacdbdddabbbdddabddbadcacaddbabbbbdbbadadadddddbacdadbcabadbbaccacbccccaacdccaaccabdacadbabbdcbaddacddbbdbaacabcbbdcdacacdcbdbcaacbbaabacdddcdbddcaacbdcbbbcabcccabbddacccbdaadadbbaadddabbbadccabcaaabacdbbbbdbccabddacdbddcacbbbbdccbbdbacaddaaaacbcaddbddaadabcabacdbaadbdbbcabcdabdccdacadabdaadcacacbdbacdbaaaaddccabcacdbcbacdaddbdacbbdcbbdcbaddaacbacacddbaddabcadabbaacdcccbbbababcbadddbabababcadabcabbbdddbbccaabbadacbbddcdaaadcbbdcbdbccdacaabcbcaaaaadabadacbcdbaddacacdccbccadbdbbaddcadcaacabacaadabadaddcaaacadcabadabacacddbddddccdbcdcdcbbbabadcadaadccdcabbdcbdadcabdcaaabadbdadbddabbbdacbccacbccdcbccbcdbbdaddddcabdabbccadacabdaacabcddbcdccbccaacabbdcdbbcbbccbcccbbbccbddbdbadccbabcdbdcbcabcbdcbdcabaabcbbdaadadabadddcddaacadddacababddacbbddddccdcdaabcdcabdbdbbadcaadacdadbbdbbbdabcdcbacddbbcadbccdcdbcdbacccdbccccacbcabcabdabadbbcacdbabcbdbbbbcddccdbbbaddcdcaadadbbbbacdcbcadadbccacdbaabcdbdccaababbdcdcacbbaaacbcbcbdacbcddaccdbbaccdddadaadbbcdbcbcbaddbbdbaabdbddccdbcbadaadbbdbaadbbdaabccadcaaccdcbccabaccdaaabdadccadaaacdddbbdbdadbcacbadddbcddcbabddbbbdcaaacbdaddadcaaddcacbdcbbccdcbbcdbacaaabbbadbbacbbdccabaabdabdbbdcdbadaacbadcacbbdccadbddbbbdccaadcdabdaacddbbacddadcbdabcaddcbcbbdacdcabdaacdabdcacdcbdbbcbdcaabddcbdaccccbbccaaddddbcccbdcdadbadbcccabcadbacdccdbbcacbaadaaddddabbcdbcdcacdcccbacbbaabcddadcbcbdcdddbdbddcddbbabbdbdbccddacdaddbcbccaaddbcadacbdbaacbaaaddabbbdcabbcdacccabcccabaabadddcddbcadabbcdaddadcacdaaadcdaccddadcaacbbcbcabdcccbccbabcbcacccacadbccbcdcddcccbcbbbbcaababdacdccbbbadcabcbdbdacdcddabdaabcacdcdbddaabdddcabbbcdddcaabaaaacbdcdbddaaabdaddbbaaaabcacdcdbbbcbbaaababbbddaddcbbbcbacaddbdddcabadacbbbacbddacadbcdbcaaddcabadbcbbbdacbbaddbbacbdcadcaaaaaadacdbdcabadbdabbbabbbddbcabccdddadabcbbaccbbbcbaddcdcbddbccccacdcaacccaacadaadcdbbadbababbdccacccbbadcdadacdcdbacbadbbbbdcaadabbdacccdbaaddcbdaddbcbddddabbbddbbdbcddcaabdcdadbbababacdcddbddaadcadbbcbbadbbbdcdcdbccacbccbbdbaaacbdaaccdaccbcdccadccdbbaddbdcccaaaabdbbadabbbdddcbaddbbadabaaacaabadccdbcbbcadbbcadbcdccdacbbacdacabccccdbacdbbabbdcaadabdacaddbccdcbbcabadddcdaabddaabbdddbcbddaddbaddddaccaacccddacacbcacbbbaaaddadadaadadbcbbccabcbdabcdcddbccbcadddbadbcababbdaacbcdbdcdcbddabdcdcccadddcbcccbccdaacbccdcbadaababcbbbbcbcbddbabcddcadcddaadcdbdddabdadcbcaabcccaaddadddbdaddddcddbaaccbcaddacbbcbdabdddddabaddbbbdcacabbbdbbbcccbbbdaadbbdabcbcabdcacdcadbcbdcbddacdabbbddbbddccdcaabbbbdaacbcdccdbadacbaddccabbcbcaaadcaabadcbabbaddddbddbdbddbbdbdbccabbcbadbaabdbcadbccddcadcbcdddadccabcbcaddabbdcbbccdadcddbdcaaadbccdbcacadddadcdcaccbdcabccddcbbabaaccbdbbddbdaadbadbaadbbadbaaccdbacbdaadbaaabcccbdaabacbbddbddaddccdcabdaabccacbbbadadbdbccbbdcbbcdbabcdbbabddabddcbcacccddcabddacacdbdadccacaaccabdaaccbcbacaaccabaccdcaaaabbbaabbdaacbabbbbddcbdcdbaaacbaadbbbbdccbdccadabcbaacbabbccacbabdadbdcacdcdbcadaccbcaccdcbbcbcbacdaddbabbaadbabccbcacbaaabccdbbababddbdccbaadabddbddadcdddcdccbdccdbaaaabccccdcddadbaccbddadadbcdbbcdccbdaddcddbdcbacddcaacdabbdaacbabccdadabdcaccdddcadcdaabcaadbccbbdbcbabdcbbbbdcbccbccbacdacbacddbbcddddadcdaaccadababcabbadddddcbcddcdddadbabbdcaccdcabbabacaddbabdcbbccddccbbcbbcaabcdcbabaccddccccabcbddddacacbcdbcbcddddadbcbacdaacbbcccdbdcdbbabacccabbdddcbdacdbdadccaadbcbdcccbacdcacacccccccdddcdbdabbbbbdacccccaccabcdadbcaabacdaabababdaaccaabcadbdddccbaddbaddaacaaabcdbddadcadccaccdaadbdaaaddbbaadacdbbdbcbdaabcddaacbaadbabcdddddacabbbdaccaadddbdbdaaddaadccdcbcadaccacdccbdcdcbbcbbddcbcbaddcacbcbdaabbadbbcaccbcbdadcdabbdadaaaddcaccabbcbcababdbdbacddabcdcadacdcacccacadaabcdccdcaddadaabdccddcbcccbbdcacdaacdaaddaacaddaaadadbabcacaaadcdcabbdcddcabcccaadbcbcbcccdabbdadbcaaacabbcadacabaadacdaddabddcdccadcbbaacacbbccdbaaadcadadbbbbbdadccabdaabcdbcabadbccadcdabadbdbdaacbbabdaacdabbdbbdcbccbcbcaacbadadbadcdddaddbadacababacdacaccccabcadbdaaabbbaacbbcadcbacacaccdcdcbccdcdccbdcabccbcddbcaccaaabdddccabbbdcbddbdddccbcdcdcccbacdbacdccdcdccbdacabbcbabdcacbbadadabbcaadaccdacbabcbbbbbddccadbbabbddaccddacadcabbbddcdccbdadcccbbcdacbccdbabccadddcccacbaccdccccaacccddbcdacbbacadcbddcdbdbccadbcdccbdbbcccaacdaabbadcccabbcbbaabadcdcabdabacbcadbcccddabbaabbacaabaabbdcdabcabcbaabdcbaccadabbdbbbbaadcadccbcdbabcaadbadbabacdacacaccbbdacacabadcddcdcabbbdbabacdcdababbcaaaabacbabcbcbdacdbccbdaaaacaddaccdadccddcbbbacdababadbacbbbbcacbadcbcdbdabcdcdbccadaadacddbdbcdacccdbddcdcccdaaaccadbbbdaaddacdacaacacbddddaddbacacaddaabbddaabdbcbbdabdadabcbaadbadcbacbbbdbabdbcadadaaaadacdcdbdbbbdacdbbdcbcdddaccaadadbcbbbcdcdcaadbbdabacadadbcdbadabddcdcdbbddacacaabddcacbdbdabaaaadcccccbdcdbdadbbcdbccdabdbacbcdcddbbcadccadccbdbcbaaabdabbbbdccdccbcdcbbdbbbccbcccdcbabbbaabaadcaddbddacdccaacdabacbdaaddbabdbdaacbbbcdbcddbdbbbbdcbccbaaacdcadacdadbbbbdcdbaadbaadaccacddcbddabacadbcdacdcbbcbaabdabcddabcbcaacbdcdccdabcbadaababacaccdccdbcbacaadaacdabddbcccdcabaddadddcdadaabcbabbabacdbadaabadbcabdbddacbcadddcadabbacbacccabadbcddcdddbcacddadbcdaabcbcaaddcabcccaacbcbdddcdadabddbbcbddadcccdbbbbcbdbabdddbadaccaaabadbdbabbddddacadaacdbddacdddbbcbcbaadbddbadcddabbcacbcddbbdcadbcbbcabadbdddabcabcbbdccbaccaaddccbdcdbdcabdcacbabadcabbbdbdcbccbadbbdadbdcabdabadcaadddacdabbbdcbdbdaabddaaadacdcdacbccddacabdadbcccacdcdacddcdabcdddaaccdbccacdaaacacbdbcbcbbccccdadbcbbbacbdbbdcadbbacaaaccaaccbadbcddcacddcbabdaadadbcabbbaacadbcdccbaadbbbaddbddcaadddaabcdbacdddabaaaabdbddabbddabcaacbbdcaaddcdcabacabadbcbaadabaacdbcbcbdcdababaadbdcadcabadadbdaabcbacbbaddbdaabbbaaddbbadcdbddbcccdbbabaaddaccdcbbccacbcdbccddbaaacdbdbdabddbbdbabacdcdddddbbaabccdaabbcbbbcbaaadbaadcadcdcdddcacbabcdbcbacadcccbdbcadbaaabbabbbacddaabbbaaccbabdcacdcccccbbdcdccdbbdbcaddcccccdcacbaccaabbdbcdabcdbdacabdacadbccdaabbbdacbaaddaadddbaaadadcbbacdcbaaaacaccdadcddbaadbdadcbbcdabbddbddcddcccdddabdbbbadcdcdbcbbcadadabaacbadcadbbcbcadbaaccacaccadbccbcacddbdbddbcdaadcddabaabcabdaddacddbdcdbddaacdcbadbacbbdccdadcbbbddcbbdadcdacabacabaabbdbbabacdacdddcbabadacbdbabbbdbbbaadcaaaddbcbadddbbcbbcbdcadddcdadabdbadaadacbbcacbbaadbcbaddabcbbabadcacccbbbccdddadbacbbcdcacadacbabbbbcbdbbcadcabaacddaccadaaddccdbadbcdccdaabdcccddddbbbccdbadccacccbacdcabaccdacbcbddddddcdaaaabbccabdbcdabaabacbabcaaacadabcdaaabaddbabbcadaddadbbbbdccdabbcdbbdbbccdaabcdbbbadcddccdccdcbdabbbcdabadcbdccdabdcddacbdadabbabaadadbbdbbcbbccadadddbccdcbabbcddadcadcbccccbdabcddacbacbcbccbdabdaadadcabccdccdddbbcadbbdddbdcdaadcbcbadbacbcabbbdbbaadadcbadcbdabadacddccbbdadbbdbaabdcdbdbabbddbbaddaccbcbbbdbbbabbabacdabaabccbaabccccccabdaabacdcdbbdacddcdaaddcadbdbacadaaaaaaddccaadcdcbdcbddadcbbdcccaaccbcbdcbcdcbbdbcdbbbcaadddcabdbdbbdbacaabdccdadcdcbadcacbacbddbdbddadaadadcbbdcaaddabbdabbaddbddcdacadcbbdaaacbdaccddaadccabccbdcdaadacacdaadaacacdbabadcdbcbcbacddbbdccdcbcaddacbddcccdbcdacdbbdadcdcdbcbddbacddacdddbadbaabcaaabbdaaaddbbdcbaaabcbcdddbcbcbacdaccdaddaadbccddcaacdcadacacaccbaadcdbcababcbcccdaabcaddbbbacddaddacaabaacdbcbabccaacbadcbcacaaaaacbbabdddccabaaddbddbcdccabddcbddacaabdadadcacabdddabbcbadbccaaacadbabbaaacacacabbaacdddcaacbcadabcaccdbdbabbdbdaccacdbdbbbdbccddbaccccabbabadccdcbbaaaddbddccdacadccbddaaccbdbcdbcadcacdcbddcbdcaabccdbbdddbdddaaadcccacdbacbddcabbccaaacdcadddabcbbbccacbaadacddcdadaacccddcabacddbcbbcdabddccbcbbaaaaabbadcbabcdacdbddbdccdabaccbdcbcddddbcdabdcaacddbcabbcbdabddcaddabdadddbaadbcbccdaadbccddddcdacccaadddabbbbccddacacbdaaacaabcadbdccbadbdbbadbbbadbbcacbbdaaacdbbaccdcacbbbaaabddaadcabddabcbbadddcadbabbadacbbbabcaddaadaccdacadabacdaadbddbadacdadcaabaddcbacaaacaacacabddaabadbcbacbbbdddddaadcadacccaadabababadcbdbaadaabccaaacbcdcbbbddacbddaadbaaaabcddbbaaccbbabdaccccdbaadaacadddadabbcaabbbabaadabcadabddabdcccbbaabadbadabdabbacbacaadbcbabcabcddacccbdbbcbdccbacdcbddcbcbddaaabcadbdcabbccccbddddacdcabcbbbbddcdcdbdcbadbbaacbabdccabdcdbbbcacacddaabcccaabaaddcaabdccbbdadcbbdbabbcdababddcbcbacbadcadbdcadbcbbbbcdadabddcdbddbcdbccbcbdbcddbacbbdbdaacdbdabccbadabacdddaccaaaaccbcbccbccdbcbcadadcddcbccddddcabbabacadabaaacbdbaccbcbdddbabddcabbdcaddabaddddcaaabaccabcdabdcdbaacbdbbabccaacccadbdcddcbabadcadbadaadbacadabcddbbcbcadbacacbabdbacbbcbacbadcbccaddcabbbcaabbadbbbdcaadcacadbdbaddcdcacacdadbbcbdaddcbdccdcadcbcaaadccbbcbccaadbdcbdaacbdabbcbdbbbbaaddbbcacbcbabdabbabdcacabaddcaddbaabddcbadbbbbabbacbaddbaabbdccaabccccbdcdcddbaabcbdbbcccbdaabbbcabdacabaddbbcabadacacbbcaaabdaacdcbbaaddcadbcbdaadcbccdabbdaabdcccbbccabcacadccadaadddccdbddaaadcbddacdcdddabddbddddccddddbcbaddaaacdbabccccacbdbbbcdabdaaacddcaabcdddcbacdbbddbcdbaabaaadbadaadbbaacbbdcbcbacbacbabbadacddcdadddbacddbbcbbaccdadccdbbdadcacadbdacacacbacdbbaddcbcaadcadabcccbccbcbcbdabbcddcccadabadbadcccdcdbdcdbcadaadadacbcdbdacbcdabdcbdbdadadcbadcdbdaddcdccdcabddbaadcddcdbaccdcbddacddcdbbbdaaaaccabbbcdadddddccaaaabcbcddacccabacbcdccdcbddcaabcabacccbccababcaccdbdcdbbbbdcbbddddbbcacbdddbcddbddababcddcccbcbbacabbdcabacbabbcddaddaadcbabacaccdacdbcbdadbbdddaaddcbcaaaacddaddbdbacdcbaabcabdaaacaacdbccdccacdaccdcdccabdbbcadaccccddbbdadabdcaadacadcccdbbdcbbbabbadcbcbabdccaaabdbadbcbacddadcdbdbddbbcccbdccbcbaaddaabbcdcddddbcbdaadcbdbbaacaacbbcdbddadbcbdaadbcccbbabbaaaccaccbcdccaddcbdabdcbbbbbbacabaccbbaadccdaacbcaaaaacdabcacdddcdccaaadcbbcbdcaddaabccdbcaccadddaaaacbadaacbccbbccacdccdbcbcbbddddcbbcdddcaabbddacdccadaccdaccadddcdccdacbdcadcbdcdddcbcccddbcabacacdcabdbacbadcccdcdabadaacaacbcddbadcccbbaaddbaadcadccadbbcabbdbdadbcbbadbabadbbaacbbababacddbdcbacdcbcbaaabaccbbdabdbaabcabacaddccabcddcbcdddbbacbbcbabcaddbaadbadabbcacaabcbabaaaaabacabdcbbabbcbbbdabbddacadddbdddcbbbaaccdbabaadaadbbcdbbcbbadccabddacbadcacdcdadaabccccbbccbdccbbcaccddaaccaccbbadacccccdabbbdbababaaaddbbbcabcdacdccdcdbabbdcddabcbdcaddaccccdcbddccadccbbcaadcbccbdcaddabdbabbdcadcdbacccdcdacacdbdaadbddabcbbabcbcccaaccbddaabacdbbbbbdbcbbbdadadbaaccaacaddadbadcbbbddaabacadaabccbbcbbabdbbcacccadcbdabcbaabbbdddadbdbcddccdbdbbdcbbdacadbdcdaabaadccccbbbacdaccdbcdcbaccaccbabaacaabdbcccdcaddadddabcbabccaacccddcaacdbbaaadabbcadaacbbdaaabcdcdbbbaabaacbdcdadadabdbaabacaccdcbaddccbcdbbccadbabbbaacddaadadabaadcddccbddbccbbcabaaabcacdbbccdbcdcbaabdccdbcbbcddbbcdbcbacaaddcdcdbbdcbbddcadaacbbccbcdccadddbbcdddbaccadadabdacbdaacdcbbbdbdbccacbdaccccbcdacccaaddbdcdbddbbcccddaacbdcdccabcbdddbdddbaabbdcaadddbaacacadbbbdbcdbaadcddbbababdacabdacaabbdaccdaaacbcdaccdacccdbbddbddacabbbbdbddccbaabbcdcdccbdadccdddccabdbcccaaddacbaccddccaacabaccddddaabbcaddcadddbccdacacaaacbccbbdbccdcbaaaaacaaacdbdcccacdccbccdbcbdcbaadcbbbdbbddddabdacaabcdcbccacccdcadddbbdaaabaadcadbaacabdabdcbdaabaaacdaccabbddbdabccbdbabdcddbdcabaaaaddccbcaaaadbdbaccddbcbbcaaaaaabaaacbbaaacdbcacaaabadacaabbbdaacddabcdddabcbccbdddbbcbbcababacbabdbddaabddbaabbbdbaaadaabdabbbcaddabacdaabcadbadaadabdbcdbddabbbcdddcbbcaaddabaadcdbbbacabcbddcddadacbdacbdcbcadcaaddbabaaadcdbadcadbdaddadbacbabdcaadaabbccaaabadbcbbbbbcccdbddabdcddadccabaacbdbcccbbababbadcccbdddbaadcaaabcbccbbdbacccccccbcccacbddbdcdbddaccdbdddbdadbaabbdbdadbcdcdacbbcddadbcaacaaabddcccddddbdddcdcdddcbdbbbdcccadaccbbdbaccdbdadadbbadadaccadabaccbcbbdbaabdacbaadcacdddbdbadacbcadadccdaaaccbdbadacccdacabcdbadbdadbdcdccbbdacbcbaccbaccbbdacdddcbccbcacbbccbcbddbdaccbddabcaddaaaabbddbabbcbcbbbcacdbdaddbbcbacaabcacbbdbacabaaddbdadcaccbcdcadbbcdbddcbaddcbabddadbcbcbabadbacdabaacabccadddaacbbadcaccbcbcbbbaaccdbdacbaadbadaadbbabdcbcacaabcaacdcacdaddbddbdccbcdbbbddbbbaccaacabcadbbddabcbcbdaccdccacbcabdbcbddccbcdbdcaaaabbdbcbaaddddadcbbdaddbadbccaadadcccbacaabdcbaccccbaadcdadbcadacabddcbcdbdaabcddcbccadacddccbbadbadbdcdccbbcabbcabdacbdbabccaadccddcdbddbaabcbdbabacccbaaaccccbdbddcbdaabdbcdaddcbdbcdbcbddbbdbbaaabadaaaabaaaadaabcabbdccaababbcbadbddcdabdacabcccdccaddcaaabacabadbacaadcdcccabdcaacdcdadcdbcbacaadbbdbdbbddcddaacbddcccabcbabbadddbbdcadbcadcdbdbbdcdaddadbcdcddabcdadadabbcacacbadaaabccbdaadbcccdabadadbaabcacbcdaacbadbbadbcbcdaaccddccabbddcadaaaaaadabdbbcbbdcdbaaaabbbadbbdbccbdcadccddaabbabccdcaacdcdcbcacaddababdcdbccddadcaddabdacdcabcdbdbcbadcccbcaaabaadadabcaacacbdbadcbcbccabddbcabccdabbdddbccabdaabddccbcccaabccaaabcdcadcddaddbdbdadbccbaacddbadabacdccbbdddcddbacdbbcccabbbbcbbbadcaacdbdbcdaddbcbbddddcaabdbbbacdcbdcdddaccabdadbbdbddbdbadacabaccdbabbcabccbaddbbccbbabdccdadccbcdcaadbdcaadaccacbbdbcccadcbdbdcdccbacbbbccabcacdddbdbbbadbbbabaccbdcdbcbdcbdcdacbcacbbcdcbdabacadcbdbdccababaaabcccddbddbaddcaccccdccccdbbadbabcbacbadabcacdcdcdacdccabbadbbccaddaacacbacdaccbdacddacdccdcccadbdbcaacdbcccbacadcabdacbcaacacacbdbcbcdddcdbcaabbabbabacbcbbbaaacdbaccadaaadbddccccacbadbacacadccbbcbadbdcbababddccacabaaacdbadccdcbadcddccdacbcabddcaccdadbcddcbdcccbbadbaaaaccccccdcaccbcdcddccadcacbcabaccbbaabdbabbbbcdcdcacadcccdddaabbbaadbdccaccacdcadabcabdddccabbbccdcdbddcbacbbadbaddcaacababccabacababbdbaddddadccccacbcdadaacbaaddbdadaabcdcbabbdddcacbdddbcddabdadbadbbcbcccddbcdcdccdcabcacbcadcacbbadadbbbcdabdaddabbbcabbbbcdbdddcabbbbcbadadccbbcadaaaccdccbaaabadcccbcdbccaacdabbbddabacadcccdacabbccadcadbbdaccaddcdddcccddbddaadcbcbacccbdadcabdbadbdccbbcbabbbdaacbbbbcbcddabdabcadabcccbbbdacadbbaababaabcbdbbaabdbddcbccbdbbbbadadbcdcddddcabddbcadccddbdcccbbcaaacaddbcbbddcdccdabdbdcbccacacccdadaaabdbcbdcdbccbaccdbdbdcccacbdadabbccdcccbacdbaccddacacacbdbdacbaabcdaaabdbcbcdccbdcbdccccaaacabcadcabccaddcbcbbcaccdbdbaabccdbaaacbbcbaabbddcacddadbacacdccadacbccdbdadbcdabdbbdadacdcbbbabaddbdcbcbbadaaacacbabddadbacdcabadabdabccacaabadaabdbabaadbdbdcdddbccbcccdadabbbbbcaadadbbccbcbbcdcdddbccbddcabbbdcabddacbabbaacdbdaccdcbcdccbabbbcbaaccdbadaaabcaddbadcdaccdabaccbcdccbabbabdbabbdbddabdbdcbdaddbabdbabacbaaabadcdbaabccddaabcdbcaabbbbaaddaddaacbddacbaccadadabbbbacdbabcbccbddbacdddbbaababadddbabdadadbcaaadbbccbbcbbcdbbdcccbbddacccddaacddaacbcacaacbacabadaacdbccdcabbdccbacbabcaccddccbcadbccdbdabbcbaccdaaacaaacabcabcddbabdbabdbdcdcacabadcdbbacacabababcaacababdddbdadddccbddabccabcdcbdbacdbdbabcdcbcbabaaacdacdbcbdbbabbbaddaadcdabcdbbabbdddacdcdddbccaaddcaabacdbdcbbcbcacccadaacadcaaaccddaddacdbdcaddaaddbacdcddcbdddbdcaddbdadbbadaabdaaacccdbbcbcbcacdadbcabdbcadcddabbbaadbdcbbdcbdbdcabdbdbccbacbcdacccadddacaadbacbbaccdadbccacbbaadcbddcdbbbabdbbdcdcbbcdcbdaaccdbccabccdcaccbbdadddccbcddcadacdacbdbdcbaadaadadbaaddcaccbccabdacdddccddccdacbadbadaddcaddcbbacbaacabdbacccdbababdcbddddcabcadabcccccdbbddabbcdabddcdccaadacadcccdcbddcdcabdacadaabcbccbaabdddcbaacdbcaccabdbcdaaacabadcacccccbccbabaabbdadcaacdbadadbabbbdddbabcbddddbbddbaadbccdbbdadcbdcdcddcbbdddcabccdbadacbdcbacaadbaaccadbbdbddababccadbbdcbbdacaccbbbbddcbbacddabbcdcdcddabddccdadadaadadabaaababddbdbadcabddcdcaccadccaabbcbddbdaddcdcaddacaaabdaccdadddadaccbdcdbcdcccadbdccdbddabbbbacaaddcccddbbcbaccbbacbcbcbbbbcdacbcdddcbddccdcbbcdbcdbbbaadcbadcadbdbdacdabdbbbcaddccaccbaadbcacaadbabdaababadabcddcbadbbdbbdbaadcdbccccacbdabadcdcddcabddbaacdacddbbbbaababdabaddcddcabbcabadbadcdcaabdbadaddddbbabacdbabbadabdbbdcbadacbbcccbabadaacabcbcccccddcbcaabbaaadacccbaaddbbabddcadabbabaccdcccbdcdbdacbdcbcadadaddaadcaccbcdcaadbdcadcbacaacbcbccaddbacddbcccbcacbcdcaabbdcbbdbbbdabdcdbdbbdcddcbdadaccdabbabdadcdcdcbbdcbacccdabaccddadbcdacccacbdccadaaaadacdbdabcacbbbccdccaccadbdaadccbaadbcadaabbaaabadbcaaadcaccbcdaddccadccccbccdadbadaabbcadbdbdbdbcccbdaadcdbdabadbbdddcdcbaccdbadadcddacdccddcababbaabdddcccdaadcdadcbbbcbdbccdabdacdadcdbacbaccbcccabbbacccbbdcdbabbadbacccbdbaabcaacddbddcaadcbbbbbbbcadcabacdbbccbbccacccaaaabccbdcaddabcbcdccdbaacabdcdcacadacbdabaacbccbccccddbabdbcddaccdadaccaabadaaadcccaaaacbccbdbacbdacddaaabcadbcbcdbbabcacadcdaadbdabdaabdbacdbbcbdaccdddaccbcbadcadabbbdcdddbdbddabbabddaacccbcadccdcddaccaabbacdcaccbddaacabccccbaabcaacbdbbaccdcccbaabababccdacbbddcadcabdadbadcdcbabcadaaccaaddcaadbbdcaabdcbbdcccccbcaadcbaddadbbcdbdcaddadcacbdaaaabbadcdbbababddacbaddaaddbbbbaacdaadaaccabadbacdbddaddaddcacdadaaadbdcdddcbacbddcbabccccdbdacadacadabbddaacdddacccacccdcaaacbbccaadcbadbcdcdcaaccaadadbadbccbdbccacddacdbbabababddccacdbadddbcbdbbcacccdcccacabcbbcbbabbadbcdabdacdaadaaadcadacdaddccbadcbdbacaddcdabcadddacadcdbbbadabcddbbdcdbbdcddddaababcbbbababdcabcbbabaacddcaacaabaddbdabbabcaadadbccccadcbbccabadcbabccbacbcaaaccdaaadcbdbbbddbdbacaabbaadaaccaddcaaaacaaabdabccbbccccdbdaacbcddaababbaadabbaacdddcdaddbbddbbddbaabbdbcbbdbcaadbbddaccddabcbbaccbdddcccadacdbabbbbddcbdbcbcaabacdbabcaacdbdcadbadbcabdcaabacadddadbcddcbabccdbadaadddddadbbdbbdbcccdacdbabcabcadcadbbddadbabaaccddcaccbbbaaadccbacdcaccadbbbababbdcbdbbccaaadacadbbcdabdddbbbddabbddbbacbaccdaabddccadacbadaccbbadbbccdabcbabdababcbbbaabaddddbbbcbbabcaabcdbdddaabdaccbdbcbbdacbbcbdcbdabacbccdaabbaabbbdbcadabdadbdacdbbaacabbaddcccbadbcaacdabacbddcdcdbacddddaaadbbacdaabccbdbbacccccdbdcbbbadbadacdbbdbabcabbdadcabbcdcbccbdcddcadbcdbbcabacbdbabadccadabadabdadaddccabbacbaddcbbbdadcdcdcabcbdbddbbbcdaaaaaacbdbdbbdaadcddcaadcbdccaacabccdcdaacdbccbadadbccdcccdbcbcbbdabacbadadbdbccabaccaccabdcbadcadcaabaaaaaadadacacddbdcbcbcccbcabaadbccabdaadaacadcaadadccbdcadabbcdbabddaccaccabbccdccdddbbadcddbabddcbbababccdadaabcaacadbdcbabcabbcbcaaadadabdabdacbbcbbddbdcbbbadddcaddbcddbddbdacdacbbddaabdbadadbdabdbbbcbdcbcaccdaddcbdddacabdccacaacddadaadaabdbdbbcbbaabbccbcbccabcdcddabaaaddbcddacaaccbdaaccbdbccabbddcbdaaddaccdbddabbababcbadbbddaabbbbbcabaaabdbabdacddcdabcddcbabbadccaabbabdababccbdcdacbdbbabcbabbbdccbbdbadbbccdddddabadcaddddbddbdbaadcdbbdbadadcaddaaabbdbbdbddcadcabacbdadcccbdcdccccbccddababdcddbaaccabbabccacacddbbbaadbbacbcbcaacdbddddcdbbbccdacabcdcacbaaadabcddaabcbccadcbccabcbabccbabaaabcabaabcbbdbbbccbabcaacbbddccaadacabaacaadccbcccdcaacbabbddcabaaabcddccdccdaaaabccbcabdcdbaacbacccbabaacabdcddaddcddbdcdaadacdaabadcabbbbaacadccbbdccbbdbcabbbdddcdbcdddcdabcabcaddcbdbcacadbbabdadabccabcdddcadabdaadaccbadcacbccbdcacadcdaaaadbaadcabaccabdbabbadaddcbcdabacddaabcbbddabdacdadddabbadcbaacadabaaabbcdcdaabddbdadadcbcbcbbbaacabaadabccbacbcdaabcdbbacaacddddcdadddbbcdbbbabdcdbccdcbdbadabdbdbcccbdccccdaabbdcacbaacdcaccabbcdcababcdaabaacbaddadbccccdddccabddcbbddaccabbcbcdaabdabacbacaaaaddddacbadacbabddabbbbbdacbddbdbaddbababaadcaccabacabacdcddccbabbcadcdcbdbdaabdabbbcbdadacdcacdabbddbaaaaaacdbaabbcaccabcaabcacadcadcbabdcadcacacdbbdbacdacccaccbbabcbaaadaacdbcadddcbacdbcaaadbbdcbdbbdcabcdcacdcaadddcbdbcbadcddadaaaaadcdbcbbdabbdcdacadddcdbacddbbbabdbacacaacacdcdbadbdcdabcbcbdbcbcddbcbcdabccdadabcbcaaadddacbbbdccdadabbaccaacbcbdaccdacddbaaabcacadacdcddabdaacccbbbcbdccbabdcccaabbbbccdcaaaccbaaadddaddbaddcaaabcabcbbccbcacddcbdcacddcabadbcadbdacdddbbbcbbabdaaaacbbbadbccadbabaabdabadaccdadbacdaccabcaacdbaabdccaaabbbbdaaaddadccabadddddbaacdabacabadbadbacaabadbbcdbcbbbcacabaabadbdbddddcdccdaabdaabadccccdddbbdbcabdcaaaddababcaadaddaabdcddcddbbdabdbdbbacdacaabcaaaabcadbabadbdbdbacbadaddbbdadbbadbcabcaaddaacaaccadabdadccbabbdbcbaaadbdcbaabadaabcbdacbabcdddcabbddaabdbdcccdabacbabadaccdcdccccbaadbbdacaddbbbcaaddddbcaabaacdadacbcdbabbdcdddbbccdbbccaaabdddadabcddccbbaacbaccbbccddbaacbddcaccccdcdadcacbbaaababdaddbdcccccccdbdaacbccbacaacadbdadbdaccabbbadbcdbaacddddcadcadbaacdacabbadabcbdbcbcbddaadccbdcaaabbbdadcaaccddcdacaaacdcbaadbadaddcdcaccbcaacdcdbadaaddddccdadadcccadbabdadbaadcdcabbcccccdabccabdaaaacccdaccdcadcbaacabbdbcdccbccddddcadbabdcbbcbdadadccacadbabbbaacccacaccddacddbdbdbdbcadbdabccabcaabdcbaddabcbcddbacacbadadcabccbdcabbdaaddcbbabbcabaaadbaabdaaadbdcbcaccaacabbcaaabcabadbdcdacbaccdbccaabcddbdcdaaabcbbbdabbbcdabdacaadabdbcbbcdcbdccaaaccdcdcadacdbbaadbcbbbaccdcdcdcbdcadadbbcbbcadccbadabbdabbaacbdbacdbbadaacbdccbaaabdaabdbadadcbaababaabbaabcdabbcbdbbabababcbaabcdbabbadbcdcababaddbcbdcaadcaadadaccbdabacbcdbbdcddcdbacabdabbddadbcabccacbcacacbdcdbaddbbaadcdcbdaabaddccccbbccadbaaaabdbdabcbadcaddabbccaacabbadbaadcdcabcaccdcadabbacdbabcdccabdadaddcbbccdaabcdcaadacccdaaadcadacbdaaadaddabbbcdbdbcdbbbaadbccdabdadbaddacbdbdabdbaccbbdaddaccaaabdbccabcdbacabddcabbcabcbbdcdcadaacccbbcadadbccabbccabbcacbcbcacbacbcababbaadacabdbdbcacdddddbcaabbaccbdaabcaaaaddacaadbbdacdbacddaacaccbcadbdbcbcccdbacbdcccdcaabcadddaacdddadaddbacdabcbbddcddacabdaadcacdcdcccddccbaabbdcbaccdcabdcdbbcbdbdcacaadcbccdbccdbccacdbccccacbcaacbbadaabdccddabbadbbcabaaddabdbbcbccdbccaaabacddccdaababbcabccaccddbcabbbaaccccabbbcdbbdbabccbdccdadadcdbabdacabdbbdcadcabacbdadcccbbaaabcbcbacadadcacdbcddccdbcaaaabaccdcadddbabbcacacdbcbabbddcdbddbbdaaadadbacbdccadcacdcaacccaacbbaababdcddaadadcaccbbbcadbcccabccbabcabacbbbccccdcadcabdbbdbadabccccbbdaaabaaacdbdccdcabcdacbaadddaddbcbabbadababddccabdaaddbaddaadbccabdbdaabaababbdbcaddcaccabcabdbdaaabadadacddcddbbbaadcbdcdcbbcacbdbbdaccadccbbcadbabbbbabcddcccdbdbaadbaddbdbcddaccabaaaaddbabcabddbacdcbccccdbbbccababababaaabdabadddaaaabdaccdddcdadcdcbdaacaccdcdcaacadcacacdcabcabaabdbcbcdabbcccbcbadbabccbbadbbbbccdcbddcadbadddccadadcdaadbaacabacdadadacaccdcaabdcadabdaacddaccdcbaddaaadadaadadaaabdbaddabbbddadaaccacabdbbbbcbacbbdbcacbaabdccbbbdbdccbbabbdcbaacbbdbcdbbcbbbabaacbcbdcdabccccaadbadbbcccadbbaccdbadcbacacbccdbccadcbaadaabdbbccabdacdccacbdbaaadbaddccbbbaabdabbcdbbdbdbcabcadcabcdbbaabddadbcbdacbbbdbcbadddaabdbbaacdcbccbbbacdaaccacaccadbccbbdbcacaaabcabcccbaabbdbbbdbbcdacddbcbcccbaaabdbdbdacdddacdbaadbbddccabccddbdadbaabcbccbbcdbdddadddcdcdccaddcddacdaabbccdbbcadacccaddadbddaacadddbdbabaddbbccbcbbdabbadaddbddbdabbcbdacbabaaddcdccadacdadcbaacbddccddcddacdaaaadcbbbcbaccbabaabdadcbbcddccbbddbabcdacbaacbacacaccaadbcccbbdbbadaabbddbbabcddbaccddadcbaccddcdbdbcacbadacabdcabadabdbcdabaddddbbdccabbccddbcdcbcbacdbcdbadbdbadabacaddbcbdcdcabbadaccbabcadcaaadccdacddbccccacadcdcbcbbccdaddcdaddbabbdbbadcbddaacadbcbbddbcccdaaabbaddbdcaadaadbbbbbbcbbdbdbadbdddcddddacbaccabdddcdddadbdadadbddbcbccdacdbbccdaabdabdbababcddbadcabcdcbccdaadaabbbdbbadabdabdcbbcaaccaaabcdbcabdcdacdaccbacbcbacacccacdbbaacbbaabccbddadbdabbacabdcbdbdbaccbcaccdbbdcdadadcdbdcaaadaabcaabacbdabdccaaaddcbbcdcdaababbdcdbbbcbdddacaabaacccaabddbddbbbcaaaacbdbcaabbaaacbcbcbcddabbcdbabdbdcbadbbadcbbabaabcbdabdadcbccabdbbbddadbadaaddaaadbaadbdaacdddbacdcdaabccbdbcbbabbddadccdacbbabadaadbddcaaadccbccbbdbacadadacabacbddccddaabbcdbbbcdacbcabbbdadbdbbbcdddaacbdcbbdcccdaaadbdbaabdcadbdabdccabccabcdbdcdcbdbddbbababbbabbaabbddadaaddbdddaddbbdccabbbbcdcdbccccabcdabcbbccbacbaadabdddabcbaaabcabaccbdaadabbbabbadacdcdbcdababbdcbccbadcbbbdabcdcdcaacdccaccbdddaccdbdbcdddcaccdadaddbdbaabadacdbddaaabcbddddbdcdbcadabcabdaadcacaccdddccdaccdbbdbcdcabbcbccbadddaaaddbcbcabddcadcdbbbddccdddadcdcbadadcabddddbbabbdaabcccdaaadcccbbadbdcacdcccbabbddcdcddabccbaacccbddcbabbdbcbdaabbcacbbcdcbccaaaadbbcbbbaacbadcacbadbbdbaadbcadcbcccacbabbcaaaaaadbdbccadadababccbbdddcccbbcaabbbcaccaacbcbdaadbdadadcbcbdcdadabdccdbcadacdcaadacdddcacdddcbbbbcdbcbccabccbccdcbacacdbbbcccabbdbaacbcccdabbbccbcaccabbabbbbdcaccbabdaddddaccdcbcddbabdbabbcdbbbdacccaddcaadaccddccdacaadbdcbadabcdaaaaadacdabdabbacadccbadccabbbddaadbaaadacdcacdbcdacacacbabdcaccdaaddaabdaabbbcdcabdaaddabddbcbccaabbbbddaadbcbddaaccdcddadddaacacccdcabbcddccacacabadaacaaddcbdaaabdabdbcccaabdaddacdabddaacadaaaadaaaccaccddbdbdccbbdbcbdaaacadddcdaabbadbdcacadaacccbbbaaadcddcdbdbbcbcdbaabbcccdbdbadbbdadccdaacbddaccababaddbbdbcbcacadcbbdcabdacbccccbadbbcbbddaacbaccbbabcbbccbccabababcbacddbaccaaacddbcbccdcddbaabbacddcaadaabbbdcaabbaabbbdbcbddadbacccbdcaccdbdccbdacaacbaaadaadaccddbddabdabdcbabbddddbcdccccbccabbcbbcbacabdaaddbbdaaadcadbdacbcdbddcbcbccadbaccabcdadbcbdbdbdddccdcdbddbacbcbadcccadccabbdbddbcababdbaabccabccadaaadbcabcaaacbdacbbddaddaabcadcbcbcdadbadacacbaabbbbcaccaccbbabccacddddaccdcaccdccaaabcbbcccccbdcdcdaadaccaddbbcabbdddcccccabbcbacbcdbcbcaadcbbaacababcddaaadcabbddcaccdadaddcbdcdaabcadadaddcdbbcbdddadcbacccdbdaacdbbcddbaaddccaddabdabaacdaaadccabcdcdcbbdaadaabbadbdbcbddddbccadccadcddadbdabbabcaaadaacdcaddcbdcccdadbdcacbddbabdcdddcdbcbbaacccdcdcddaabacaadaccddddcdaddcdcacbddabdaabcbcaaabbbdbbccdcbbdabcabbadbdaddbdaccbdcdbaaddccddbcbcdbdadbcdadbabaddaccbccaddcdccdadcacacdbbbdacbbadaaadbadabcadccdbcdbcbdacdddadddcdccccabaadbccaadabaadcdcddacabcacddbbdbddabcbcaabcbadccdcddbcbacadbbacbddcbabbdbdccaaaaacbabbcaacabacaccccddacdddcbcdabbacaabadacdbcbdcdaabaacbcdbcdabcbddaaabbdabcbcbdbcbaaddbbccabaabcaaabdccccdcddaccdbccdbddaabbdacbaddacbbabdabcdaaabddcadbbadcddabaabdbacdbcdbdabaabaaaddddbadaabbcbddddadacbcbccddcadcddcddddbccbcaabacbbdccabdaccbbdccdadcccaacbcbabadabbcddadadbadaccdbbabdddbdacbdaccadcabcdcbddccabdabbbcdbbabacbbdabccacbdbccddcdcdbdbccabbbdbadddaacdabcdddaccdcaabbddbaaddbcaaadccacccbbcbadbcbccddacddbbbdddcdbcbcbacdbbbcaccaadabadcccccbcdcadbdabcabdabdccdbcdcabdaabcbabcbababdbdbbcadccbbddaadaadccdddbaacbaabdcbddcbccadaaabdbbbdabdabbdbbbacbddadcaaabdcabbabadaabbbccbcddcaaaaaacbbbaaaabdccddcacaaadbddcddcaccbacaaabddacaadddaddaccccbccdbcaacdadcbddaccdabcbabddcbdcadcdbbcabddaaacdcbbcdbcddbcacbbccccaabadbadbadbccccbcbbdaadcdcabdaccabdacbbcdcbdbcccccdbddddddbaacbaabdacdbdabcaccdaaaddcbabcaaadccabdddcaabcbcbdacdcacdcacabaadbbdadaabbbaaaabcbababaccdcacdcbadaaaabadaabddbadbacddcabcacabaacdbcdbcbcbacdbabbcbaddbdbcaacddbbbbdbccbbaadbccbbccabdbabaaacaaacdcacdbbcbadddbdabddcabdbaacacbdbdbaadcbcacbbadacdbaaccbdaabaaddadddaacadccdbaddcdbabcaaaababdbabaadadabbcacdaddddccdabbabddbdbdbddcbbbdccddaacdbccbbaadbddbbbcdcbcdbbdccdcaadbbaacccdbdcbacacbaabbbddacadccdacabbcabbcabababdaccbccddaacacccbbadaadbddcabdaadbcdccababcaaabcdadddcaacdaabdacddabbdcabdddbbbcddcabcbacbaccacdbabdaacbbcbcadbcabacdccdddadbccaabbddcddddabbcabaaabcccbadcdaacaacdbaaaddddacbcaabdabbacaccacddbcacaccadbdccccbdcacdcaaacbadaaaadacdabbcddcccbaccdabdccbbbabbdcddaabdabcdcbbbadcabdcccaddadbadddcddcdbbbdcacbcbdcbcbdccccdbdaabcdcabcbbbbbadbcddacddacddcabdbdabbabcabcbbabcdbbdacaabcdabadcaacbcbcbcabadcdcdbddbacbdadabddccaaabcbcdddcdbabdaabbacaabbcddcccbcdbabacaaadcbbacdcacbbababbdbababaddbccbdcbcdcbaddcbddbcdbdcbcccdcadbbdbdbadaddcdaabddaddadddcaaaddadabbbbbdbdaabdbcadabcbabbdddaccbccdaadcdaaadcdaccbdaacbbcdbacbadabdcdbaddccabccdbcaddaccadbaaddbcaabccabbdbbdaddcdcddbdbdaaddadaccadaaadabbcbcbccddabbadababcdcaabcabbaccacbcdababaabcdbcbacadadcbbddcadddabbcaacbdbaddcbabbcbbccbacaacbdcddaadcdbbdabbabbcadbaaaacacbaaabadbbacdbadcbacdcccbaccdbaaaaddaadbbcbacabacadbcdabdbacbdacddcbabcabacbdbacccdcbcaabcdcdabcbccdbaaddcdabdccbdabbbcbbbadcdcabcdbcbabbcccbdddacaaddbccddbdcabaacabcabddbbcadcbaacaccbbaaccddbdbbbcbbcbdddbadcccdddddaaaaddcabdcdcacbadacbbcaaacacccddcbabaddbdadccadcbbcbcddbcbacabbcbcadcaabcddacaddddacddbbdbdcdbaaddaddbddccdbdcdadbcaccdcbbacaabdaddabbcdabcccacbdaabcbdcdbdaaccaadcbcbbddbbddccddddcacdbabcababbadcdaacbdacaadbbacaccacbdbadddbbccdbadadbdbbdccdcabbdcbccdcbbbccdbcccbdcabacadbccbcccdadbdbcbcbcabcaadadcadcccadbbcccadcacbdcddaaddcbaacdccdabcdaaabcadbbccdbaaadcdcacacadcbbbbccdbadcbbcbcaacbcdcbdbcbababbdcabbdcbbdabdddcbaadbaccadccbcbcacddccdddabcccbadccbdccbbabdddcbcccccbbbcdbdacbcacacbdbccbbdccacdbbacccccbccbcacbcacabbdddcdadbcbbcaaabcaacbacdcdcacbbddaccbdabcacdabcbbdbaccbccaccadddcacaccbdaadabcacbcddcacdcbccaabddbadccaacdcdcdadccbdcbdcabdacdaddacbdaaccaccaccacbdbdabbbbbaacddbddacddabcadddbcbbadcbdcdcbddccacdcbcbcbacccdcbbcccaadbcdbdabdadcacbcabcacacbdcbacadaaacaaacddbdccaabddacbcadbabababcababacacddddcbaaaadddacbcbbcabdaacbacdcdbdaabdaaabccaacbabcccdacaabdbbcbaddadadaababcaadbacccaadacbbccbdbbbbabbddbbadadccccbaaaddbabdbdccbacbaabcadaccaaccacdbbacbaabdacbcbddddabaddbcccaadbcabbcabddddadcadacadaadbaddacaacdbcbcacdcddaacbdbddddbdadbcccbcbbcccdaababcccacbddbbbbaabaaabcadbcbbddbccdabcaabadacdabbdcdabbcacabdbacbbbcaabcbbcaabdbbcaaabbbdddaddadadcddbbbaabbabddabbaaaccccdbabdbabccaddbabcbddaccddcbcadbcbcbadcabbbbdaddaadbcacbdbaacacdaacadacdbcbcaacaddbbaaccddccaaadbbbcbdbcaaaaddacddbbcaacadbddddcccdbbacbcdaccadddcbddabdabbcbaaabaaaaacdaadbbabadabbcdbdbcaaababccbdbdbcccdacbaadcbdaaccbccabbcdccdccdbbbcbcaaccccbcabdcbcbcdbcbadadbbbdcadbcbaddbbaabdacbdcccbbaabccbdadbcdddbcdcaadbaabdacaabbcaabbdaddbcddbbdbddcabacbdcadbddcbacbcdbbccbaadcbabababadababcccbaaadbcbbaadcabaadcdcacbcbdadddaccadddcccbbccbccbccadbcdbcaaacaacbbbddbacbccddbdbcabcddacbaaaacaabcaddaccbbbcadbbcaadbdbadbdaddccdcdcaccadbdcbacaccbcdbaacdcbdaaadbddadbcabaddabbbcddbdaabaabadbdddadbacbadbdbbacadcabdadddbdcdacabbadaaddcaadcddcdabbabdbdabbbbbbabccabaddbbbdbbdddaacdadcabadabddbcddcbbbaddacacbaacabbcddaaccbddbcdccacddddadacdcdcbacbcacabcdcaaadcbbaacdabbdacdbbcbadacbddacccabddaccdcdbbaccdacdbcdaaababbccabaacbdbabdaccdbcacbabdaabacbddcbacababaadaccbaacccaadaaaaabbcadbcbcacbdabccacacbdabbbaabdcaacaacdddaacdaadbaacaddbbbabdaadcbdacccadbaaaddddbacdaaaabaacdccccdcdcdccbcabdadadacdbccdabbcbcdcabcadcccbacabaabacbddadbaaabbaaccbdbacddcacbdaaaabbbadbddbabbcaabddabbbdcdbabadccdbcbdcbaabccdaccbdacbcccbbccacdbaabdaddcabbdbdbccaadcbbdcaccaccaccbcaaacaadbabcccbabbcacbdbcdbbcbadbbbbbbaacbccbdcdcdbdddbadabbbbddacbbcccddbdcbcbbbdddccaadbcbcbcbababdacbabbacbcbcccddbddccccdbabcdddbcdbcbdccabcdbbbadcdabcddbadddbdcdbdcaddadbbdcabaabccdbaaadbaaddabdcabdbaaabacadbacaabcadaaadddcaaaacdbbcaacdccbbacacdbdcacaaabaacbbdbabbbbdbcbaccaddccdbdabadbbdbcdabccabbdbccdbcdbbcbbdbdbdbcbcbdbbcaccdccdadaaccdaabcbdddaadbaaaddccdabaaacdcacdaaaccadcbcacccacaaadcdccaabbbdbdbdaadadabbcbabbbdbadbbabcadbcbdbbacadbaccbdccccdcdcaaacbbbbbcdcbbbddbcbdaaddbdcbddcccaabcacaccadaabbdadccbacdbbddbbdaabdaadacaddcadbbdaccbbadbdaccddbbabccbbbdccbbcdbcaaddaadabdcabcbabaaabcccbcccacabcacddadcbbcdbdbabaccccababccaadabbcbccaaccccbdadacddcabacdcacdcacddcacbbabbccabdbbdddddbcddadbaadbbaaaadddcaccacdbdacadcacadabdcbdcabbcbbdddaadadaaadaddabaddcbbbbccbdcbacbdabacdccddacbbbbaadaacbbbccacbbbadaaacbcdbbacacaacbbdcbcdcbbdccbbbbcbadbdccbadadcbacbaaadbbdddaddaacacbcbcbbbacacadbcdddadddbbaabacbaaaaaaadcbadccccababcdddaddbdccabdcaadcccdcccbaddbdddaadaabdabbadaadaabbdaacbbddaddbabaaaaaddbdbcabbcdacdabcccaadabadadbdbdbdcccbccaabcdacabdcdcddcacdcdabdcdaccdcbdaacdbbcbcdcadaacdcbccdcbcaaccbdabcaabbacbbabdaddcdabaacddddcacabcdbdcdcbadbddaacaaabbbaabdcacbbbdbccbdcabdaccaadabadabcaaadaccbcaacbbbbababbcdbdaacbacccdabcabcadcbdbbcbabadbacdabdcbaabbdaddadbbdcabcddaddcbbdcdaacdbcdbcbbbdcbabcbdcadabbbaddadabdccbaccaadcbdddabbdacacaaccabbbadbadddcbdaaaacaccdbabacabcaccbadbadccddbbbbcabbaabaaddacbabdcdbbdccddbdccbbcaabbbcdcbcabccbacaddadccabbbbacadbdbcdabdaababaabcccabbccacdbabbbbacadbbaacdaabdadadbbdbcdcdcadacacddbbaaacccadcaccccaddccaadbccaddbabcbcabcbcabbdababcaddcbaaaccacabbbacacbcadadcacdcadcbabacddbcbacdbbacbacddabcddbbaadbbdbcbcabadccbbdbccbbadbadacacabcbdddaaccacaaabaaadcbcacbbccbacabcdccddcddbccbaacbdabbbacabbbbabbdacabdacbdaddaadcdbbcdbdbdcccdaccaaadbdbcabbcabbbdaccaadaddcadbcbabbaddccbbcabcbdcccdadbaaddcdbbabcbbdbaadcaadbbcbddbabbcccbccbcbacaababbcabdacdcabbbbdaccaadbdbdcdbcdddddddcaaacadcacdabdddcbbdcdbbdddbaccbdddbcdcbadcdbdabdcccdbbdadabcabcababcbdacbdbdccbdaababcbccdaddbcbbbcdbaadadccadacccabbacadbaddcbadabaccbacbdbacddddbdddbacccbacdbaaccddaaaccadcbcacccaddcacbdcacaacadaabbdcdaaddabddbdcdddcaddabaccdbcabacabdaddccbbddbdaacccbcadcaadabdcdddaabcdcbdbbcaccdadbabbadcaddbbddcadabdbadabcbccbcccaddabcaccaddddcdbabaadababaadcdcbcacdddbdadaccbaabbddcbadddaccacdaaddbcbcbdbabcaaaabbcbcaccacabddacacaacbbbabcbcdbbaacdbbaabbbdbcbacbbabaccdacbabbbbdabbcbbabaabccbdccccbbddbcbcbccadcbabacbcbcdbcbadbbdacdcabdacbacabccbcddaabbcdaadccdbccdcbcbbbaaabdbdaaadaddcbbcdacabaacaccababacccddacdbcdbbacddddcbcdbbdaabaacdbcdaddddacaccdacadccdbadddccbacacadcbbabacbbabdddaadbdaddbbadcdaacddbcaadbbcaddbcccbbaadccbbcbadbadbbbaddaddcdccadbdddcdaddaddcabaacbbcdaddabaacbdacbcdcabadccddcdcbcdaadbdccbdcdbdaadabadaabcabcdbadcadbaadabdcdccbcadcaaddabdcdaaacacdcadbacbbcdcbcdbdcbcabbddcdbabccdadababdaaaadbdbbcbabdbdaaabdaabaacbdabcccabbcabccadcacbcbdbadcdbcadacaacbaccadbbcacbbbcdaaacacbdabaadadccbcbcdbccbbadacbadbccaabbbabbcdddbcdcbdacaaddbaacaacdcbabcabbbbcdcdadaabaacbcdbbadadacabaadcdabaabbcdacbcbdbbdbadddaddbddcbbbcadcbdbadbbdacacaabcbbacbaabcdbadacaadbabcdaaacaacbdddaddbcdbacbbdbccbdbdccdcaaabccacaccdadbdbcaccdbdcaccdabdacaddbccacbdaccaccdcbdbdbddaabbabadbdaadabaacacadccbcbacaadabaabcdcdcccabbcbcaaaaaacddabbaccadaccacabdccabdabcdacbadabbcdbabccdcabbcbbbddaacbccadcccadaaacddcddddcbdcdacbcadbabcdccddabccdacccaacdbddbbcddbacdcdbabccdabccdbbaaddbdabbabbcabcddbbdaabbabbaddcbdbbaacccccacdbbbcbddbbcddccbdbabddddddcbaabacdaadddccbccaabbbbbcbcaadcbdddbbcccaacabaabdbccccbdbbabaacdabbacdbbdaccccdcadcbadccaccbbcbdbaadbbcbaccbcccadbdaabaadbadabccdbdaddbdddacddccbbacbcbdaccabbbbdabbdbbcdbadacccbdaccdacdbadbabcdacacdcbcddbcbacbaddacccdbcbabadbaadcacacdacbccabadaadbacbcbdbdddcbdcdacabaaddadcbdcbabdcabbdcadccaacddccdddacdbdbacbabdacdbccccacadacabaacbadbdcdddacdbaddcaaabcaaacbdcdbdbbcaaadbacbcbacbcbbbbcdabadaabadcccbbdcadccbcbbbcdabbbadcdcdbcabcddccdccbcbbccacbaddababbaddcabcbbcabaaabccbbcdaddccaadcbbbbaabacdcdadabdbbaddbbbbddaddccccdddbbcadbbdbcbbbbadbbdaccddacdbadbddbabacacbcbdcccddcccbdaabcbaacaddaacdabcdaadbcbccbabbccccacadcddadcdcdbccccacdadacbbbcbbdbbcbbaabcbabcdddbbbdabdbdcdddcacbcdadaaaadaacdadabbadcadbccbccdcdabadbabcacadcaaaabaacabdaddcbddcddadcacacabdabbdbabacbabcddaadccadaadacbbdcddadddccdcbdbbcbaccabbbbbacbbabbddbccadbcddadcacbadbcaddaaaacdddabbbdabbbbdbbddbbadcabacabcabdccbcaabdaabcaaaddbdccbbbadddaccacdcbaccaababdbadbcdddbccdbadcbabcbbdbbcbcacdbdaaadbcabddcbbbcabdbbbcdbdadcaccddcaddabadbcabacdddbbcdbdbddcacacdaabaddcbadcdbaabacbacababaacbddbaaabdcccdbcdaacabadbaccdadaaacacbccaabaccaadddabdabaddbdaabbaddbdadcabcbcbbbcadadbbbababdaaadbabcdaadcaabbdadabdcbdbcddcdadbccbcdacbacbadbbacaccbbbcbcbdcbddbcdacbdbaaadcdcbcddadbbbadbacabbaaaddddaaddbdcbcdadaacbacbbdcbcdaadaccbadaccccbccabbbbcdacdbcddbdcdccdcdacbacaddbadacbcddbdbbacdbcccabccdbaadbdbbbccbbadbdbacdbbbacdcbbcaddacccbcaaabccdcacdbadcdbdbbcddbcbbcacbcddbbcababcdaabdbacdbadacadbdddbdbbadcdbcdcbddbaadcbacbdcddcaaddbcbaddbcadcaabcdcdbddbaadbabcdbcbdaaccddadbbdabbbabbabaccbaacbaadcdbcadaddadcdaadbcaccccdadaccabaadacbbbbbcbdbabcbadadbdbabddcbcabbcaccababcddccaadbbbcabbdbdccdbddcacadcabcaddcdababababdadbaddadcadacbbdadaaabcbdcbaabdbadbbaabcccbcddcabadcadcacbddcddcabcccadbababbddbcddddadcdbdabddadadababbadaddbacbacbbcbaacadacbbaaaaddcbbaadabbcdabbbcabbbacbbacaadaddcbdbbacbaaccdbbcacccaccbcacdaadbccdbabcacdddbdcbbdbbcbabbabbdcabacbdbcaccbdbcdbaaabdbcbddbbddbbcaabddcccbbcababadaadaabaabadbdaabdadccbcaacdbadcdccacacaccacbbcbccbbacdbabcaaddbcbddbbaacbcbbbcaddbacbadcddadcdcabbacbcabddcadbadcadddbbddcbaabaadacabbbdbdacbaacdbadbbcdcacaccadbdcacacdcdacbadaddddbaabbcdacbdccbbacdbcadaacdbddabacdbbddacbaabcbbadcaccdcbacaadadcbdcdabacbdcddbddaaabdcbbbbabdadacabddccdcbcaacbdbdbddadaccbbdbcaddccddbabdccadacabccddbabdacbacaabccdabcabcbccdcbbcdbdcaddbbdbbdadcacbdbbbcdabdddcddbbcbbaabcbacadbaaaaadaacbaaaccdcccdbabcaacaddddccaaaaadcbbdacdbbbcddacbdcbabadcdcbdbdbdbaabbbabacbbcbddbddcbdddbabccabcbacabadbcbbbaabcdccddddaaaaacacbcbbbcddbaacdbabcaaacbadddabccbadcbbcacbbcdccccdcdbbbbcbdbaadccbdddcabbccbdbaccdaaacacabbcabbabcabacbdddbddacaacddcbaabbdabbdcdbdbddadbbdadcdadcadacdbcbdcadcdadbcaabcdcbadadcdcacbaacdadbabdbdadabdccdddbcdbbacccdbbddcbbcbbbddbdbcdaddbdbaadbacabacbcaaacbddbcaccaadbdadaacdaadcbdabbddbdacbbccadaccccadcbdacdbabdbcaaaaadcddcacbadcacbabddddcadcbccdbdbacdcbcbbcabbbaccccdddbdaccbcaaabdabacaabcaabcaaaaddabcbcbbdccbbdbbabaabcbabacbccbdcdcddadcddcccadcccbdbaaaccabcccbbbcaadbdcbbabdabcabacdaaddaadbaccbabbcadbaddcabbbbadaabdcabaaddbbbbbbadcdbabcbabcbbbcbbdaddacbdcccdbdcbbabcdddddbbdbddcaadcaabadaccbcabaaaccdcbbccdadccadddddcabbdcccdccccdaabcbbdbdaababcbabdadbcdccddbbabbaddaddcdaccdccbbadddcaadccddaabbaadabcbcbddddbaddabdadcdbcbbadaabdbdcdbdadcabbbadbaacbddbbaadcadbcadbdddbdddadbaabbadcbcdbadbdbdbacaabdadbdddacacdadcdaaaddababdabcacddbbbaacdccbadcdbadbcbcdddbacdddddddbdcbaabcccbbdabaaddcbdacbbabacddacdabccdcddccabdabbddcbabcacdddbadccadcaabcdbddaaabaddcbbaddaacbaabbcccdbadcabccbabbabadddaccbdabdbcbbdddaadbdaacbcacbacbababaabdacbccdadbaaddbbcaaadbaaacbaaadbcaacdaaacbcdccadaccaacacaaaaaabaabbaaaccbacadbaabbbdaacabdbcccbabdccaacdbbccadbbbddabddbbadbdccbbaabcacdbdabddaaadcdcadcbdcaabdacacbaddbdacacaacddacaddacdcdbcdaacdcaccbddbdcbdadabbbaadaadccaacabcacbddbcdaccddbcdcaaacacaaccaaddddccccabbadddbdababdcbcaaaadcdccabbccddcbabcbdbbaaddaadccaabaaadcabcdbcadadacdaaccccdaabbccbcddaccadbabdadcbadbcabbdbbcdcdcbdaaadbdbddcbabdbaaaabdcabccacbcdbdbacddbccdaadbccccbadcccbdaabaddadaccbdcbdacdcbdbbdbabcdadcbcccbcdcbaaabddbccbaacaccdccbdcdacbaddcccccbbcaccaddcdbcaddabdcbcbbcdbbcaacdcbbccdcbccadbbdbcdddacbadcddabbddcacddddbbdbcddacdcbcbaaddadcdbaabadadbdabcccdbbcbcccdcccaddacccbcdccbbccaddadaabadcdcaacbdbaabbbaabcabacddabbccbcdaabacdcbbabbbddbadaddadaccadcdadcddddadbaddadabbaadcbbacacbbdcbdbacbddbaabbaccbaacbcacadcadbdcdacaacdbddcabbabdddbdcddcabadabbcddcdcdcbccbccdabdadaabbdbbbcadaccdaacdabaddbdcababcabbbbbccacdaabbdabbdccddabdacdcadaabcccddaccaadbadccbadacacdddababbcbbacbbacababccbcdbcbacdbbacddcdbabdadabacdbaccacabdddbaccadacbcddabbddcbacacaaabcacabdccbddcdbdcdabcbaaddcbaddcbbadddbcbcccadadcadcadacaaacdddabcabcccdcccbddcacbcddcacdacdbbbbcaacbbdacdbccabcaababcacacbabcdcbbbbbdbdcaaaccaadcacbdcddcddddbddbdbaaaddaacdadcccbbcdccbdbddbaadcdacbabbbddbaccbbbcdaaaccacabacccdaabbdbcadaccbbadaabcabcdabcccadbdcbcbdbcdddbaaadcdbbbabcbdbdbaabbbdbcbcadabaddbacadadadbddaaaabccaaacadbdbcddbbabaccccdbaadcaaddcccbabdbaaddacacdacccbcbccaadabbcaabdbdcdaaaaccdabdcbcbbcdcdbabccadadaaddbcdccdddababdbdbcaccadadaaddbbdbabdaacdcbbaaccabddcbcbcccddbcdbacacbbdacbcdbbbbaaabadaaadbddbdbcbcbabddcbbddccccbbbbbbadccbcbcdacdabbaadacdcdddddbdabadbcabdbbcadbaddccbadcbdbcbabaaddabddcdacaaadccdbdaacbabcbadbadbbbcbcddbbaadcdaccddacabaaabcdbaabbbdcdbaacdbdbaabbdbcdcbaddcaadbbcbadabcddaabcacbcbdcacbacccaacdddadbccccacdbddbbcaabcacccbacacbabadbbbdcdbacbbdbadbbbccadbbbadcacbbaadadcdbcaacbdddbccabaaadbccddabacdbbaaddbddabdacdabcdbadaacdbcaabddcacdabbcbdbbbdbccabddcddcbadbbcddaddbcdbacccaccaabbccbabaabadacbcabababcacbdcbacacdcddbddddbbddaddcaaaddadbbcdcdbdaabccaccbabcbcadccbaddabbdcbcaccccdbdaabbabaadccacabdccccacddcbdbbabacdcaabadbdccaabdccdccabdacbbaccdbabacccbcdaddbbdbccdabcdacdacabcdbabbabdacdbbaaaadbbadcabadcabbadbaccbabbadaccabacdacbadcdbcbaabcdaaddcabadbbbacdcabdadcdbaaaabdccdcbcbcbcbbbbabbcadaabdbbadadbdabcddacabacddaddcbbdaacbbaccbbdbabdcccdabbbdaaabdadbacbcaacabccaabadacaabbbbdacacbadcddbdbbcddcabbdcdcccbcbcaccaabcbdccbadbdadddbdcddadccacbbaacdbdaddcadbbabccbddccaaabdcdcdcbbabcabadadccbbaacccdbdbcbbcdcaaddcbddbdacadababcabbbcdbccdcccacabbbabddbcdaaccddccaabbaacdbdcbbdbdaadbbbbaccbcdbbdabbbbadbccbddbdcbcccbbadbaaccadcaacdcaccabcdacabbcaabbacbabadccdbccadbbbacacacaaddaddcbdabbdaadbadcbdbbbabacccdcbbaaaacabdacabaddddcdbbcadcdadbdbbaadbcdbbdcabbacdabbccdddbcbbdcaabbdacccbaccdbadaaabdaaaabbabadbabaaadcdbdbacabdbdbbbcbcaabdddadbaaabbbccbcbacbbabdcbcdcabdbbdddddddabbbcabaddaaccdccbbaacabbdacddcbadcdabcbabaacddbacadcaccabaacacacdacbcbbcadacabadcabbacbababdacadcdcbdcdbcddacacdcbabaaaadadbdbddccccbcdcbabcbdcddacbdaacdbaaadaadddccbccbdaaddcdbbcddabbccccabaccccdaacdaadbdbbbccbaabcbdbbbaaccdabacdbdccbbacbddcbcaddadbdabcdcdbbbbdadabcaacbaccadbbbbcddaabcbabcbacddbaaaadaddbcacdbcbdacaabcbdcccaaacddbaaccbacbbabddaccddbbaddaaacdccdaddcbdabbcadcaacaccdaccbabdadcadbaadcaaccabcccdaadbcdbbddcdbdbcdbccdaddadbcbcddcdddcabcaabdcabccbaadadcaddabbbacbbaaadadacacbcabababaadbdbabdbadaacaababbbbaccdaccdcbbaadcdbdbcdcdacdcbbcadaadcccddabaaacaddcbbdacadcddcdaddacbddccadcdabccddbcddcbcbdcccbabaaacabaddcaabaddcbbbcadadbbddaacdccaabbbdbcbbccdaacdbcaaaadbcabcaacabcbcdaabccddddbccbcccddadbaacdadababddbaacaadddcddcddcccadcdaccabcbdbaabcccddacdabadbbabddddacaaadbcacccadbcabacaabadccaaabaadbacacdbcbabcbdbbcbdddcababdbccadabbaaccaddcccbbbdabcddcbbcdbababbdcaadbcabcbadcadbadccbadaccbdccccadcbdaabcdadcbdbadacbddabcdcbcddcacaccabacbcbabcaaadbcbacdcbdacaddabdbddddccbaaaccabdabcacdcbcabcbdcbdcdacbcbaaacbcaaacbcbbabddbcdabdbccdcdacbacddacacacbacaacbcdccacdbdbdcbaadaacbbdaddaddbbbbaacdadccdacccdbabbbdcbbbabbbdaccacaacbbcdbddabcadabcdbbabcdddbbdabddbbbdcaddddadbcabacadbddaacbdcabcaaddcddcabbaddcbccabcbcdddbbabdcbbdcabcbdaccacdabcbbccbaabcdaaadbcacddcbaabdacbcdcabdacdaddabacbbaaaacbaabadcaddadbcdabddcdbbbdacbbdabdababadcadddcbabcbbddcdccabcbcbaadaacbbcdcdacbadbdadbadcdaccbaababbccadabadccddaabdcabcdddabdbdddaaccccaaccbbbdccacacdbccaacadbdcbbbdbadcddcbbdadcbadbdcadcbbddccdadacdabcabcbddaccdaccdaacaaadabaadaabcbcccbacaabbdbcadbbdbaabbbbaccbdbdadcdccddbdccabbdcdacddbdcbcbcddbaaddcdddccddbdddbaacdaacdcdddabcdbadbddccaccabcaaaccacaadcacacbbacbdcdcbbaaddcbaabbdcbdddabdaadccbbacacbcadbdbbddbcbacdacaddadacddbaacabbbcabdababbcadbbccbdcacaacddababbdabcadbddddbacdccbcabcccabdacdcdbdddccdababbbddccdcccdbcaadcbdbdadcccbdabaacdabdbaccccaaacaddadcdddbddbabdabcbcdccbaacbddccdbbccbdbbbcdaadbcdcbcacddbdbcdaddbbadacdabacaadacdcbddabbccbaaccdbaddbbaaaaababcacbdacddbcbbbbbcaadbdddcacaaccbabadabbbaaaadbcbaaabdacbbdadbacadbaccacdbcbcdcbbcbcdcbccdabbcdbdaccbbdbbdbbbabddacbdbabdbbbcdddacdddbaacbbdcdbacdddababdddcdcddddcacbcdcdcdcdcbdcbdccacaacaacbaccdcbdadbacababdadbcacddddbacccbbabdbacdddddddcdaabdddbbacbaacbbadaddbccabcbaccdddbccdbcadcacddbaadbbcdcbadbabbdbdbcbcbdccadbbbbbcbaddbbcbaadaaaccddccbaccdddcbbdddcdddcdccccdcabdbbdbabcaacdaccdbddcacabddaaaaccddccbccaadbbbdcbaaddddcaddaacdbdbaadbbdcdaaabbabbbacaaccddacdcabcbabdbdadbdcccdaaccdadabadccdaddacabdddaaaacadabdcdbcbccdccabdddbdcbcabbdcaddbaaaddbbdcbdbaaddcbaaadbddbbaacbccddbdbccbccddcdabccdbacbccdbbcdcadabdbddddaaacccbacababaabacccdbcbbbbcacdbdcaaaddbbddbcababbbddbdcdcddababbcdbbbdabbabccbdccadcabccacbabacccbacbcadbddabdcccadaddbacbabadacacbcddbddabbccbbbcabccbbadadbbccbadacddbdacadcccaabddcbbccbbaccacdbdddacdcacabbcbabddaadbbaacaadbbcdbccabbaddaccbbdccbaacccbcaccddcadaccbdabdccdaadadbaadcbbcdbdacdaacdadcadcccbabbdcabcbacbcadabccbbdbdcdccccddadaacccaccbbbdbaacaccbdbacdbdcacdababdbccbaaadaaadacddbcabcdbccbdcbcabdabbcbddbdadbdcdddbadbacbdbddcccabcdbccdacbcdbbddadacabcacdaacccdaabdddbbaadcadbbbccbbacccdbbbadbcbbbbabbbbdbdbabbdcabdacdbbcdaadbdbabdbcabddbaaabddbbacacccaabbdadbddadbbbcdadaddabaccdadadaccadbbacdccdcddcadddbbdddbaaaadadbcacdcccbbdbaccacdabadcccdacbcabdacabbcbcdbdbabacbdbadccdcccacbdabddaadbaaaaacdddccddadacaacccdcbcddbbdababbccddcbdaaabcdbccbacbcbbdbbdadacacbbdbdbdcccbdacababbbbbdbcdaabbdcbbdaabccbdaabddcbdcdbcabdabddcabbbbabaccacddadcbdcbadbdddbadacccccccbadccbbdaaacdccadccaaadcdbacbbdaaaabadddbbddddbdbdcdacdbacbdcdaabdcababbcaacbabdcbccdcaccbdbacabbdcdccaacbbcabcdabbdaddcbdcacabacacbaaddbdaccbcbcdbbdbbadaddbcdbaaaaadbdacddcbaddbacabddcaacdbbacaaacabdbcbadaaddbbbdbbcddcaadbccadbdbdbbdbccddcdcdadcdcdaacbbcbabdcbaabbdbdcaddabbdcdcddbaddcdccbdaabaadabbabddabdcdaccdcbdccdddddbddbaaadaacaddcacbbabcbbaddbbcdadbabccacccaaddabbdcdcdcdbdadcddacdcaddcaadcdbddbabdbdcddbbcdbdcbddbbbddbdbbdbcdaddacdcdcbccbbacbbdcdacddbddaccdccaddcaacbacadddbcdbaacbdadaadcccbcadaabbadcadcabcccadbcbbcdddbbbcdddbdcdddcbbcabacabddbdadddaccaaacbaadccaadaccdcacdcbbbdcbdcababddaccacbccddaaacabccbdbbcdcbabbddcadbbccdcacbcbaddbdddbaabbbcbabcbbddcdacbbdccbdccabccadddaacdbcdaaaccbbdbaccbdbdaaacdcbdaaabbdbabaacddacaadaacbdbacadbdcddddcdbdddcaacdabcbbacdacdccabbdbcbddddbaacacdaaddabcaddcbdcddcabcdadbcdacbcbbddbbadaaaabbdadacbcccaabdaacbacabaacdcbbccaacbdbdbddbbabbacbabcacbcbdcdbdababacadccacbcaccdadbdbabcbbcacdaaabdabaccadbabcdacbddcababcbacbbdadaddbbaacdbabcabdacdbbccbccaacbaaccdcccbccadbccbdddbbdabccdaabaabcbdccddddddbbacbaacdcbdadababcaadccbaabbaabdccdcdacbcccaccaacbacdbbaadbadccbcccabdaacdbcacbaaccbaddcaacdbdbcabccbcabbbadccacacdaaccdccabcdddbabdddaabdadbaacdabdccddddcdcadadcbdacddbadaaaddacababdccacccdbcabcccbadcddaaaadadcdbcddbaddcacaacbcacdaacdacddacbbbcbcdccacbcadaccbdbcbbbaddcdbdbbbbabdcabccbadcbdbdbbdcabaaadaddcdcdabcadabbaccccdaddacdaadbaaacbdaacbadbdbadbbbcaaadcdadcdabacacadcbddcccdccdacbacdbccbdcccbbbaaababddbcadbdaabdacccbdbbaccbdbabdcdabcbbabacbcbbbcdacddbbcdcbcddccbabbcdcccbcababacbabadddadddbacbadcbacccbacaabdcaccdbbdcbacccaaccaaabadacbbdcbaddccddabbdcdbbdbbddcbcdbaabbdadcacdddbdcdcbdadaacacddadbcacdadadcadddddcbdacaaadddadbdccdbbbdbccbdccdadadccbbadbcabccddcccabcaabbddaaadccccdbadadbadcbbaacacbcdadbaccaacacbdabcaadcbcadbaabdbbbdccabdacddaaabbababcccbcacabdbaadaabcdcbcccddbdadbaabdaccdadbbabbdabbcbdbcdbcbbbdbaddcbaabbcabdabadaadaacadbdacbcaaadacdbbcdcabcabcddabcdbcbbcabcaadcbbdbabbcbcabadaddbccbdaaddaabcdcbbdcbccaddaadbddbacadaccbcabdbacabdcabdcdbaadddbdbdaadaddaabbbcdbccabcbacbdcccbcdacbabdbbabbdaccaccadacbacbbccadbccaccadbcdcdccabcbaccbcadcabddadddcdbdaddbaaaddccadaccdbcacbaacdbbdcbccbdabdddbcdddaadbbbacdbdaddcbcaaacbbbbabbadbbccbdbccdbaccbdcabbbdadcabddabdbdcdaccbcbbbaccabcddccbdbacdcabbaccabdadbcddddcccacacbbabbbbdcddcdbdbccabadacccabcaacbadddcadadcbdabddabdaadccacddbdadbbdcdaabaabcbaddabaabdaddcbbacddddaaadcdacccaabbaccdbabbdbdbccacbbcacadaadadcabcdddcbbbabdadcadaabdabacdacaaaadcabbbbadcbcbcabcacadcacaaacbccbcbccacdaabbcccddaadbdccbcccacaacadccacacbddaacbdaabcdcdcbcdaccbcccaadabdbaadddcadacddbaddcdcaabcbabdbbabdcaabdcbbdbcdccadacaaccdacbcacaddccbbbddddcbaaccdbbacdcccbcbddacccaaccccabdccabbabbadacadbdacbdadabacbbdbdabcaacdadbbbdcbbcaadcdabadccacbcdbdcaadcacbddabadcdbbcdadbacdbbbadbbaaaddbcccdbcacadcabaadabdaacbdcabbcbaadbbdbadccacddccccaccbacdccdddadadababdbababdbccbcccdaccdaaaccaadbbbdbcbbacbdaabacacabaaadcddaccccdbbcddddaaaacddbccbbddbccccdbdbccbcddddbdddbbcbbaabdbdaccbacdbbcdbaacdabccaacddcdabbcaadbdabbdcbdcdacdadbcdcbadaaccbddcdbcbabcaacaccabdaccabdabdacacabdadcacadbcdbcdabacdddadaaccbbdcbcdbacddaccabaccacdabbbccaabbcaadbdddaabbabbacadabbdabbcadaaaccddcbdadadcdcaaadcacdcacbbdacbacddcbabddbabaabadaaacabaadbbabdbccddaadddcdaacccbbddcdcdcbabcacbbcdccadbaaaaadcdddbdabbbddadcacdbddbbddbabdadbbbdcdabdacdcbadddbdcdacbbbdcddcbdbcdbccddcddbbccddbcabbbabbbdcacbdccbcdcddacbaabbdabbdaccabccbdcacabbcbccaaaaabaaabcaccaddacdcbcaadcadbaddcaacddbcbbbcadadbbaddadadacbdadccacacdaccbaadbabcccbddddcccdbdaadaccadbcdbacadaadadbababbaaaadbdcdadbcccaccbcdaaaabcdddddddcacadcddaaacdbadcbabdcdcdaccaccaaadcdaabddbcadacbabcaccdbadbaaaddcbdadcbdcacbacdddacabacdadcdaacadadacdbaaccddaadadadbabdaadcaadccddcbcddaaddabbacdaabcdcaaadcacdaadabcbbbdddddaddccabcbddaaddadbccabcbdbadddbbddbdbaabdcbdbacdbcabaaabbadcbccbacbdcabdcdacccacaccababdabbbaadcadcabcdbddbacabacbcccbaadadcdacbadbbcddcadbaacbcbcbdcbababaddddbabcdcbbadabdcabcdcbbccaabaaaaacbacdcddbaacddbddcdccaacaacdacbcbccccaaddaaadbbadacaccbbcddbcddadbbbdbcbccaddbdaacbaccbbdddbdcbbbaadbdcdaaacdbbcddadddcdbccdddabbaccbacccccccadddabbdcabaccbbaddcadbbbaadabababacabcccacccddcbdaaaaabbdaaddbabbbbadcbdddadbccbcaadbcdcbcadddbdbdbdacdcdccbddbacaadabadbcdbbbcbddcddcabcbbcddbddaadddaccbbcbdcccbabcacaabbacbbbababdabbaababdaaaacaacbaabddaacbdccadadaaabcdcccbaaacdddabaacbacbbbbadbbddbbacdddddaabcabbabdcaddabcddbbdcbaaaccabdbabcbbdbccbcaaaabcccdbccabdcbcbdabddcacbdbdaabdaaabaabccabbbbbcddbbaaadadbaacdcbbacbabccccbbabbdaabddaabdbdcdbcdccabaacccbdcbdabbaaaadabbccbdbacabbdbcaccbacddbccdadbccabbcdcacccbbbdadddbbbadbdabcadaacbacbacaccabcacddcddabdcccdcdbdccdbacbadcccbabbbaaddcaaaaabadbaadadbaabadbaacabddddbdcadbaabcbcbadcbcbcacccdcbdccbbacbaddddadbadbbccadabbcbdaddcccbbcdbcaacabccadddbbddaadcbcbbdddabdcbcddcbcccadddbcddccbdabacbdcdbdacacbaaadcbdbddbaabaccccdabbaabbbccbccacdaaabdadbaddaddcbcbcabbaaaccadacadbcdcbacdadaabdddbbacbacacbababbbaccbdcbbabbababccdbcbdcaabcbbdcbbaacaabdcbaaacaaabbcddaabdbdbbdddbbaadcaaacdcbcdccabddbcbdbbabaaadbbdbacdcbabccdbdaadcccbddddbbdaaabbdbbacacdccabdbbbacadbdddbadadabddbddcccbccacacdbdddbccadabadbaadbdddbdcbadccdaacaddababacdbddcaaabbcacbdcddcbaacbbddbabdddcaddcdbaabbbcbbaacbddcbcdbacddcccbbdbddcbccdbbbdacdcbccddcbcaaddbaadaacdbacacddacbacdcbabbadabcaddcbcaaccacadbcccbccaadcbdbcbbcbbdcbdaabcadbbaddacdacdbcabdcccaababdcacdbcbddcacbabbccacdcbdbbbacbbcbaddcacbdadacacdadacaabcdcbdcbddbabdddbaacaababacacadaabbbcbdbaaaaaaccdcaacacabacdddbbacadbbdabcbcddccdbcdaaadccaacacbbdaaadaabcddbacddadaddbcaccccdcadadcbadadabbbdccbbcbbccbabbacaaaadcccbdacdbbdacadcdbdbcaadcdaaababbddcacbccdbdcddbcddddbbccabacdbcdbbcbacdcdbcabbcbbaadaabaaacacadaabcbdaabccbdbcacccaddaaccbcdbbcdadcaccaadbadaccccdbbbcdcddbdcdbaacbcbccdcbbddaadcdaddacaabbbbcbcaadcdbcdaacbdbdcddbdadbbabcabcbdcadddbabcacadbdaaaababacddbdcdccbdcccaddbaccdadacdbdddcbaaddacbcbddbdbcacacbdbcacacdcbabcdadadcbddbbcbdabadcddbddbbbcddaccccabacddcdbddddccabbdbbdadaccadbacadcbdcbdcbcdabcaccbaacdcccbbddbdbdbcbbadacaabaaacdcccbdadcdbacbbbcdbdadaaabcbdbccdbbdadbdbdbdbcabcbaadadbcbcddaabdcccbdbcdacababddadacbdaccccddaddbacaaaabacabdacaadadaacbadbabbbbbbdbbadbdcaaccdcaaabbccbbccaddbabbcabdccbcadabcbcabdbdcababbcbdadadbbadcddbdcadabddbdadcdbadccabadaaacacbdcabbcaacccbbdadcdadcdddbbccbbccddbbbdccbadcadaddaaccdbdbcabbacddbacbbdbadbbaabadcaadbddcbbaaadbbacadadbdaaacbbdbaccbcbaaccadcccdbbddcdacbbbaabaabdadacdbdadcaaacacddaaadbcadbaadaabdbabddababbcadcbadbdddaccababbdbacddacaddcccaabddbcacaacaacbabdbadbbabddbdaadbabcbbadccaadaddabcdcddccacacdbcaaacbabdabadacddbacccdaaccaccaaaadcbbdccdbaacaabadbabcabaaddcbdabbddacccbbcabbadbbaaaabdccacdcadccaaaddacbaddadbbcaaccdcbaaadcadbbbabaddddabcbdbddbddbacccaaacbacbcacaacdbbadabccabacabdbbcadaccccdcddadbbcccddbbcaabccbabcabbadacadbbabadcaccdccacccbbaddbdcdcdcbbdaabcaaadcaaaaacacdaaacbaddabdbdbcabbacbbaaaaabbddcccccbcaadbacdccacbabbaccaadabbabaddcacbdcccbdacdabaacadcadbdaccaadbaacabbcbbaddddaddbdddcdbbcbbabaaababbbbbcaacaaadddacdabdbcabcdbdadddaaadbccaaacaaccdbabdacdbccbcbdcdcbdbdddaabcbbcccacbddbbcbacadccdacbadadaabcdabbaaacddcaabbccbdddbaacbddcbbaaaccccacabbdaaaccdbccacaacdccdbaddcabddcadaccbcbddbbdbbbcadbcbadddddbdbbbbdcbccbddbbcadbbddcccbbcbbbaddcdbdbccbddcddcddadbbdbdbddddcccabaaadbcddabccdbccbabcdbadbbdddaaadcdabaacbccccbacdddadcdbdccbcddacbaaabbbabacacabcbcccccdaaabaaaadadcbaadababdcdadadaaaccdadacdcdddadcdbdbadcddcbdacdabbdcbcbacadcddbdbbbcdabcccdaddaadabcbcaaadbdcbdcaabacdaabdbbbaccbdaccadcbdddbbacacddaaccbdaadbbdbccbbbcdcaddbacabaaabbcbcbcbbcddaadbbcbddacbddcbccacacbbcdbcacdcbadaddcabbdbdcabadabadcddbbaabddaadcaadaccabbacabcbadbddadcadbdbaaaadcadbadbcdddddabaaaadabcbacbcbbcabacadacddbdadaacbaacbcbcddcbdbdbbbbaabadcdbbdcabaccdacdbbbdbacababdacbdbacaccadbdcabdbbbbaadabbdddadcaadabdcdabbcdbcadabccacbdbaccabbcbbcbbbbcaddaacdcddabbcdcdcbbacbabdcaadbbddacabddaccabbddcdcbdbdddcaadccacbaddddbacddcdbbbcacadabbbabbcbdbcaccbcadcaabbcbbcbaccaacbcbbbdddbacbaddddcbcdccabcbdacbaddcccaadccbbcbdcacadbcbdcdbbdccbdbaadbcdaaadcbadbbcbdcbadcccccadccdcaacabbcccabbcddabccdbbbcbccabdddabbaaaaabacbbbcaddbdcabaadbdcaccbbbdaacdaddccdbbdccbdccdcacddddbcbcabcacdbaddbcbbcbabcdbcdcdcddcccbbbcacacbbcaddbdbadbdaaacadbcbaaaabdbabdabccbcccbbbddcdccacdabbddbcbccbdcccbbadbdcacabadacacaaabbcacaaddaabdcadacaadadbdbaaacabcccddbdaacdcbddddaaccbacddccbadcdccbabbabdadddbadabcaacccabbbadcbbbadbcdbadbbabcadabaaabccabbcdbbdbcdddcccbbdbacdcbdcbbacdddbadddaddddbdbdbccaccdddabdabbdccacdaaaabddcadccddbbadddbbacdbdddcabcadccaddbccdacddccdbcadccdcdccbabbdacbadbdacabacbdcbaabddccacacddcdcbccdadbcabdbbabbacdcdacbdccadadcbdccacbdbabbcaabcbdaaacdbabcccadaadbcccdcdcdbcdacdaababddcddaccccdaddccdcacbcccdbacbbbdabaaddadadbcbcbddbcdbddbbacdddddccbcbbbdabaaddacbddddddacdcddabcdcdcdcdbdbbddabbcdccbadbaddadadddcacdadccdabaacbaacbccbddacbaccadddcbcdddaddbbdccbbdcabaddcdbbdabcdddcaddbbdbacaacdcabcbbbcabcbcccabcbbabbcacbacccacccbdaabbacdabbbadbbcadcabbccdcdadccadcbaabcccabcdadaadbdcdabdbaccaccccdbcdbbcaaadaabccdcaabcbabcabbccbcdcbbababcdbdcdcaabddbbdcaccadbabbadddcaaacdacdbadbcbdcadbbdcbdbdcbaabcbbbccbaccbdbccaaacbddcabbcdaccdddacacddbacdccaaaddbddbccbaadddcaacdbcabcbaddaabbbddcccbcaaddcdcdcbdbaddaacddbaabdcabacbdabdadaacccdcadcddcaabbcdabbcdccbaadadccbaabbdccaadabcddddddadbbbbbccdbabcadbaadbbcdbcdadacbacbbdaaddbbdaacadcbdaacdaabcbdbccdddbbacabcabaadbdaccddabdcbccabccdccabacacdadbcbdcbbabccdcaacbccbcbdcbbcccaccacbadcbccdbbdcadbabaadacacdadcdccdbaddacbdadbadbcdadbcbdbbdcabbabbacadccbcccabcadcccccdbaadabacdaccbcdddacaaaabbcabbacdcddbcdabcbdcbcadddbadabcccbabcbdbcabacbdadcbbdaddbdccdbdabdddabbaddcddcbdbddcbddabcbcdccaccdaaacdaadacddcdcbabacadbdbbaadddadabdadbcadccccbadacbdcddcbbbabbacbbbbddccdbadababdbcabddbaaccdbcbcacdddbcbcddcacccadbcbcadbacdbadbbddccdbacacbbbcdbdbbaabcbcbbdacbdadcdbdddbabdddaadabcaadaaaacdbbddbaadbdadcadddcaadaccadcadcddcacbabccbbdbbccccdcdcdaadadbbddaadacbabdcaaccbaadbcadcbcadcaacabcabacccddcddaacccacabdaaabcbcdbcaddbcbdacbbadcbdcdbacbddcaaacabcbabbacabadadaacddaabacdcbddadcddbaacbdccdbadaabddcbbdcabaddcccddbadacaadddbdddbbdbbdbbdcdbcbaadcddadbbdbcaccaddddbccbdccacdcadadbbdccccdbcddcadacadbcbbcbbdcccbddddaccdcddbddabddaddabccacdaddddcbbbccccccddcdbbcaddabbcdcccdacbcbabcabcabdccacacaacbadbddcbdbdadcabdbbdcdddddcccabadcccaddccdbaabcbdbbbacacdacabdcabccddcadcdddbdaabbdacddcaadabaaadccccdadbcbdbaaaabcbaabbdcdccabbccacbcbaccdbdcdadaadcdaaaacccbadcdbadcacdccbcdcbcbdbbbdbbdabdddaddaadbcabcbabbacbdcbbbcbccbadbdcdbdadbddbbaadcbabadadbbabcdababaccbdbabacddabaaabbaaabbddadbacbbddcdadaacadcbdabbdbcddabacdcbcbdbddddbddcbbdcccbccbaabcaabadccdbdbcdbddbdccbdcdddbdcbbdbaccabdcabaadcacdaaaabcbbcbcadbabccadbbbddbcadcbadcdddbbbcacacbabccbdccddbadbcaccbddaadcbccaadbabcdcaaddacaddacaacdabdadadddcdababbacdbcabbaabdadcaaaadbabbcaadcabbbddbbbaddcaaaccddbcacbcabccdbdcdabcbdcdbddacacbbbabdacddddabaaccdbbdabbaadcdcadcdcccddacdbabbddcacddddaaccbbdbabdbcacdabababaddacbacbdddabdbcbcaddccadcbccacbcdcdbadcbbbcacbacccabcacaddabcccdccbdabccabbadbbcdaaadabdcabbbaaddccdbbaccabdabcbdcabccbabbbaadccbbdbcdadccbdcbcdbcbddcbdacbbaaaabadbabacddcaadbbaabdccccddbdcbadabadccaadddcacdaadaaadcddaaacccadaddbbbaddbbddbcdaadcddaabacdbacbbbdbadacbadbbccaaabddddcbddacdbaaaacacaacacdadbdadcbacdbbbacdcacbcbaadccdacbccccbcbbbdadbcdbdabaabbaddbaabbaabadacacabdddccdcabbadcbcabdcadbdabbcbddaddbacacaccdcaabbcbabdbbdbcdcbdbcbdacdcbcbcdbbccbbcabddcacbddacabddbddcdabbdadaccbaabddbdabccddbdbbbbacabccaacbdadabcdbbbcadadbaacbbdcddcaddddaabddbbbabdaddcadccbbdacdddabacabcacadcddaaadcddbabccccdbaaabccdabaacabdcaaaaabdbcaacccbdcdbabcacabccdcccbbacccdbdcccbaddaadaddddadcbdcadccddbbdadbcadaaaabacbabbbbcadbbaddbcccadaadcdcaadcdadabcabbbcccacccbaadddbddcbcdccbaccccdadbdddbbcaaaccdddcabdabccbdbbcaccdcbddcbcaccabdaadcdabacbddddbcbdaadcaacacadacbccabbcdbbcbdaaacccadbcbcdcdbdaadcbcbcddbdbcbcdabbdaaccdaddaabbbaacdcddccdccdbdcabaacaaaabadcccadcdaddbadacdabbbddccdcbbcabbcbaaadbbcaadadaacbadddbdbadaabcccbccacaaaacbbcccdcbaddddccdaadcddadddacccacbaacadcccacddbacbacaadababbbdadbcddadadaccccabbdcbabbbcddcaaacadbbdaabcdccdaddaddddadccaaccdddacbdaddbbddaaababcacccbabbbcaabdbacbbcaabddbbacdbdcbbcdcdddcadbdccbccccacdaccacbdcdddbddcdcacacbbaccccacbcbaacdbbabbcdcadbacbddcdadbbadddadacadadadcbccdcbacaddddaaabccadcbdadbbdcadbacddbcaaabaccbbbddadbddbaaabccbbdbdbcaabbdabbbdbbbbbaacbcaccdcbacddcccbbcdcddadcbdbadbbdcabacccdcabbcdcbdcddabbbcbdbabadbdbcbadbddccacbbbaddbdcbcbdaababababaaddadbcabacdcaccbadcadcadabacbabababcddbdcdaaacbdacbddcaaacaddccacabdbabaacbcacbacacaccdadcbcdacaddadbbcbbdddcbbdbdbbbadccabcacaddcacddaacbdadadacabddcaddddaadabcccdbaadcbdccbcbcabccaabccddbbcaccdcdcdadcadbcadcabdcabbbacdaaddabcccbacababbacbcbcabbdbdacdcadaccddcaaccbadcdccabdbcacadacbabadddcdbcadbbaacddabdbbcbbcacacdcddbacdcbddbaadcbbcbddddcccbadaaaadcaacccabbdacdccbaaacaaddadbbcacbbacddaaacdaaaaddbbbabadbdabbacbadbcabccaabddaddbdaabcddabaaccabdaaadbaaabbcbddaaadcdcbddcbbadaaabaabccdbabaacdcdddcbcbcbdcddaddadccdacaccdcaabbbdacddcdcabbdaaaadaccdcdddbabccaabdcddadddabdccabbdcccdbacbdbdacccccadcdccdabbaabcabbdcdddbbcaacacdcacdcaccbcacdddbcddccacaaaddabccdadccccadccdbccadabdbbabbadbdaabccaadbbbcaaacbadabcacbcdcacdaccbabdddacaabdbdcbabdcddccdadbbadcabbcccccbabaabccbadbaacabddcdbbaacdcdcdbdabcaabdaaaacccbabdbbaaaabdacdbaaccdbdcbcacdabacadcddbadbbbdcadadbcadaadcddbbcaadadcabdaadbcbdabdccddbabbddcbadddddcaabbabccacadcabbccbcdacccdcacadaabdcaccdabbabcbcdaaddcdddabbdaddcbaddadccdaacbbbacdbbacdabcdaddccbcaddcbbcdcaacadbdbbabdabcdadcbcabdcccbabadccaddbaaddbccddacbbbdaacabaaacbbcdcdbbdbddbcaddabadbbbdacbdbdaacccaaddbbbcddadccddbbdcbabddcdcaaabdcadcdcacdcddddbcabdbbcacdcdcbabcdaddcabbcbdccbbdcccbcabdbcdadadabdaddbacccccddaadbddacbbcbddadaaddaaabacabbabcbaaddcabadcdbcacdbabcacadccccabaaaabcacbbdccacbbcbbababbaddbbbaddddcddbdcadccccdcbacbbcccadaccccddddadbbbbbddbccabbbbbcdaccddddbdaccdddcadbbcacadddcdcbbbdbcdacaabdbbbddbadcdcaaadbbcbdaabcbdccbddccaaccbadcacadccbbacacbdcbbcbdbccdddbaccaadcdcccdaaabacaaacbaadbcabbbacdaaacdaddcaccdbcdadcdddaabddcdadabdcdadadbdbbcbaabbdcaccccdabcbcbdbcbcbadccdbccdbdbddabdcadbcddadbcdabbccacccaadcaaaababdbacbbabbbadcdddcdacabdccbcddcbdcbdbdcdddacabdcdbcbaaccadadabcaacbabbbdddddbaacbbccdacccddaacaaaaccababaadbacbdcddacabdadbcddaccabbbcaddbacbadbacbadaccbbdbadccdadabdaabbdabcdbbbcbabbccccddbdadaaddaddbdcbacddaaadaadcacbabcdaddbddaaadbabdabdbcadabcbbaaadabbaccacbdbdaaaaddcdbbccddbbdaccdcdbdaaaaabaadcbdbbbdbbabbbcaaadcabbccaccabbadabbbacabbddabdbdabadcbcbbcbdbdaaabcaaabcbbcbdddabaadcbacaadbbddaddbdcbddcaccdbddcdcdbccbaddbbddbadcccabccbbcaaabcbcbcacbccdccbcdbcdddbaacbdabddaddadbdacabdaaabcbcaabddaccdaabacbbaddcbadbbbddbcadbbbccaddaccaabbbbbabcbdcddcdbdaccdadaaacabddaddbcaccbdcdaddbcbaabcabccbcdcdcddabdadabbbbacbccbdddabdcdbddddaaaccbcdcacddabdcccabcabbbadbbadbdadbaccbaadbabdadadaccdddabadbcdcdbcbddcdcddccbccbccdacdadccdbcbddcaaaccaaabdbaabcbadbcbdaaacdaadcdacabddbbdcbcbacbccbbdcbaddcbdaabbcbaddaddcbbbbcacbaddbbcbcbbdddcdbdcacdaabdaadabbadaddcadcdbbacabaccbaacccbabaaabccbdaaccdcaaabbabdbcdaacddbddbbdcddbdddadaccaacddddbbdbababbdddbdbaacabaaaabdcbccabbcacbbcbdadcddabacaacddacdbcabcabcdcbdabaaddacbacbcdaabaacddacbbcabbbdbabddcdbaaadcdbbcacadacbdabccdcddacbccbbbabbbccdcadcbdcadbdacaaabccaaccaaccbbacacbbbcabdcbcbddbdddababacccbcddbabccabaaabbdadbddbbadaabcbaaabddbbcbacbbcbdbbdaadddccdcddbbdbcdbadccccdacccbddaccabdbcaccbcdcbbdbcadcbaaadbdacbbcdaadabcaacadbcaaaabdbddbdaadcbbdbccddacdadacabdacadcdcacdddddccbbabdcdacacbcdacddccbcdcdcacadabbdbaacaadadaadabbadcabbbadaaacabddcadcabbcbbcbaaabdbdadbbdddccbababaaadccadcabbcabacdbdccbbbbbdbddccddddcabdbabccaccbaabdbbbbcadddddcdbdddddacccadadadaddcbccdccacdaddaaddbcaacdbcbdccccbbacbabcdaaaacacbdbdbdddcbadabbbdbdaddcbabccacadbabbddccbbaababcaddaaaaddcbaacdcbabaabcdddbaaadcccabbbabcbbabacaaaddcbadcbcdbabbbacaacdadcbcbdaacacddccabdddbbabbcabaccdccbccadcbcbdabadadbbdbadddcaaadabbcdbbddcaacbadaadabaacbbcdddcbadcdadcdcbcadaabbcdabbdacddbdccbbcabcbaaabcbbbcaccbdbcbbdaabcdcbcdbbbccccddcdabdaccbcaacadccdacadcacabbacaaadaddabacbddccdbbcdaadadadccaabcbcacdbadacacaadcdcacddcbbcacbcdcdbabbbbccaaaaadcdccbccaaaabdbdcbddbdcdbcbdcccbaabdacdacddcadbbbaadbcdbbdbdbcccbadbaddcdbbcbdddbcaaadbdccbcacdacaaadbdccbccbaaacdaddabcdcdcacadbcabdcdcbddccdaaccdbcacabbbddbbdacbdcdcbcaabdaaabbdcaddbdcdbabaaddbcccdbcccdabdcddbccdbcabacbaddabaaaacadccbacdbcdcbcccacddbbcbcaacdddbdcadacadacdaabdcdbccbaacdbbabdbcdbacaaccaadaabaaabcacadbacbbdbbbbbdacdccbdbdbccdbbcccdbcabcaaabddbdbdacbabdbacabcbaabdbccabcdcdcccababbaccdcadcdcbccaababadcdcbbccbdcdddddcddddabcbdcbcbbabaabadacbdaacbdbabbbdaacddabaabacdcdbcbdcbdccbdcddadccddccddddabccdccbdaabadcaacddddbbccadacdccbcbaddcdabdcdbaddbcbaaacaaacdcadbcbbadbbcdbccbabbcbabadcdaadabccddccbbaaddcabbabbdbbabbaaaccccaaaacacbacddbcbbdabdbcadccbbbdbdcabdcbccdabbabacdcaddcbdbdacdbacabaddadaababdcbdddbabdacdcbbcbdddcacdcbdbbcdaacdacccdddababacabbbddccccdcbacbcdcbddbcdbabdcdcdaadbacddabaabbaddaabadcabdccdccacdcbdabdbbbcdbadcadabacddddddadcdabaacaaadaabbbabcbcddbcdbcddbddccaccacdbbbccaccbbbcbbddcbabadbcbdbbacbdbcabadabdccccdbddabddbcddcbccddbaadbcbbacbcdadbacdabdbcacaddbbdcdcddcddbacbdcbbcbbddbddaadbdddacccabadcdcbdbcbbddcbbcccaabcbccbdaacdccacbbbabdaddbabccbaabcccabaadabbbdaacbdadccbbcbcccbdccdabbcabdbdaacdbcbdccbdbdadadddbbacbdbaabaabccdadaaadaaaaadcbdcbccacabcdcbddcdaabdcccabbccbadabacdbbbddaddabbabdadaaaddccccacbbcddccaaaababbaabcbcdbdacdcccaaaccbdabbdcbaaacbddddddccdcdbacbbdbcaabdcdcdddacbbbaaacbaccbcaacccdabaaadaabbcaaabacaaaaacbdccbccacabdcbaabcdaadbcaacacbbccbddbddabdacdbacbbbbbcbcdddaacdcacdbdcbaacdbddcabcadddbadcadadaddbdcbbcacdabcaacbbcdabbdcaddddbacaaaddcababaabcddbadbadddbbdddacdcabaabcccccadbcbbddbacacbcdcbcbaddcabbbcdbddddacaacaacacdbccbbaabacadcccdcbddbcdddbddaddaaabcdcaacaaabcbcbdccdcdbaccdcabadcabdbacccdccdcbaabcddacbbcbbaddaadcbadcbbadddbdbbabdcadcddaaabbcbdacadcabbddabcabcdcbbcbcccdcaacbbbcdcadbabccabbdbcacbcdaadccaabdbabbbbbbdcabcaadcaccdadbcbccdacbdccadddbaaadbddcccdabddbbadccdcbdcaabaaadcdddcbaabadaddcdaccacbcadabdbcbaccbaacdaadaabccbcaacadbcdacbcdaccdadaddcbdccdcbcbdadcbacddacbbadbaddacadabbbadbacbaaaadcaddcbcacbdadccabcdccdadabccbdabdbcbbabbcdddacbacddaadbadcccaadaabbdacbcadcaacaabcbcdcbdcbbbbcbbddabcbbabadbaabdacbcdbcaacdcabbabbaccdbadaacbcbbacbcabcbccabadaabbcabababbbbbdbcdabcacdcacacdbccbcbccddadacdcabcdaccaccaababaccdccaddcdcbddaaacbcbdabddaddcbcadacddabdadbaacddbdbddcccbabbbcabaddbbddcaacbcbadaaacaabbabcbaacbcccacbdcaabcbbbcbbadaaacdbabcdbdaccccabdcbacdacbcaddbbcbbcacdcbacaacabdcbbdadbbdcbdadcddcaacabddddbaaabccacbcbaabdccdabacaacadcacdddcbccbcbbacabcdbbdaddaadababbabbbbaacbdcbbbbcbcccaccaaacbbddcaccabdbdddacbadbcbccacccbcbaddbaacbbabdcacccacbbdcaccccbddcdccdaaccdaaabaccdabcdaacdbaacddadcbbadccddcbbacdcaacdccabbdbcabaadddbadabccbcbcaddcbccdcaaabbcddbacdcbdcdadddcadadbaccabddcaacccbccabbbbccacbadccbbdabdcdbdcccbcbddacdccbddcbaabacabcbcbbddaabdcadbdabddbabdbdcbdcaacdaccdadaaaaaaacdaacdbaadcbaddddbdaabbaabbddbccdabdbbcccccaccbdccbbbbcabddbdcbcbccbadaddbdcaddabccdabadccddddcabbabcddaccaddaddbbaccdaaacacaabcacacddbcccaaacdcddbabdccbdacdbbdbadcacbacddcddddabccacabadabbbbdbdbbbdcbdcdcaaabcadbdcabccadbbddaadddadabcabdacddbbadddddacaaaababddccddbdaacbddacadbbabddddccbbabbccbbabdadbbbaababacaaadbcdbabaccaaabadaadaaccdaaadbdcdcabddbbdccadbbcbbbcadcacbaccbabbbcccabddbaaabbbbbdbbcddbbadbdaaaabbdcbadaddbacaddcbddcdaacdcdbacdaccbbcadccadccaadddbdddcbdbadaaacaaabaacbdccaabbbbabadbadacaccacdaaddaacddcaabaadbabbddabaababbadbcadcaaddacacdbdabdddabaacdbacacbbdcadacaaadcdaaabbccdbdbbcdccbadaadcdcabadcdabdbaddcddbbcaadaddabcccccdcddddcbadcbdbcdcdcdcaddadadcdcdabacacabbddadcacbaccbbcdadbbbcdabccdbaacaadaacabccacaabdabdbbabbaaaaaddacacbdccdcccbcdabbbadcaddabacadabdddcbbdabcccbcddbacaadaabcdccdcddcdbddabaaabcbacdbaccbcbadbdaabccbbabdbdcbdbdddbaabdbccadabbbcdcbaacacdcabbaccadbdbbdaddccbbabcdadcccbbbadabcdcadbcdcdaabdabacddaabaddbddbbccccadadcbabbbbbbbbabbdbbbcaadbacbdcaddacddcdbbccbacdabbaaacdccbaadbdacdbbdcbdabbcdccdccdadcdaaadbdbadddbbaddbcacccaaaabbddabbdccddacdadacddcbdbcbccabbabcdbddbaacaaacabddcdccbabbaadbcdaccadacbcbcdbadadbcbccaabbaabccccbdbabaddddbdcdcddcacdcddbdddaadbaabdddbaaadbdcbdbcccabaddbadaabdadcbdbcbcbdcabdbabcacbacbddbdcccabcbbbabcabdcaabacdacdddbaadacdbdabcabcdbddadacdbbcdaddabaddadaccbbbbaaddccdbbaaabcbacddacaaacadcbccdbbbcadacabcbbbcdbbbadccacbdbaabadcadacacdcaddcabdcbaababcadacacddbcaababdaccaabaadacdbaaaaddabbbbacadcadbbaadddacccaacabdadadaaaabaacbdababacccddcdaaccaccdabaaaddcacbccababccbdacdabadacccacdabbbdbabdddbbcadbabacaabdbbbccdbbbcddaadbacbcbddcadaddabbccdbddbbdbdbdbaaabbaaabdbdbdbdaabddaccaaaccaabacbbdadaacdabcdbaddbaabbaadcacbddadbdaaddbccddddcdbaacdbdbabbaacadadcacacdacdcacacaabcadabbdbccbcdccbaabcaaabaaadaacccaaccaabcdcdbacbdbcbddacaaabcadccacccbbdabdadabcaababaddbccabadddcabdcaccddcdbcaacbabdadbddcdaacbddcbdbcadaddbbdccbbdddcbdabcadcddadbccccddabbdcaccbdbadacbcdcdbbabccdacabdcbcbdccacddbdabbdcadccbcdbbcdddcaaaddbcbcccdaacdadbabccaababbadcababdcbcbaabacdcaccabacbaacdccccadbcabbbadbbcbccadadaaabacbadbdccbbcdabdadccbdccbddbbbabbdccdcabcacbbccadddaabaaaadaacacdccbbcccdacadccadccaacdcacbabdbdddbcbbcaaaddadddadacdaaadaaabadbbadbbddbbcadcddcbdbddbbcdbdddcaadcdacdaaaaadabbdbcdbcabddbbbcddaaacdbddbabddcabadddcaccbbacdbbdacdcadbcccbcaddbbbaaadbbddcbccbbdddbbcbadabdcbdbdccdacdbaaabdcaaabbcdccdacbaadddcadbaababdcdabbbcdcaadcccdbcaccbacadcaadddcbdcdacdbddcdbddaabddabcbadbbcababbbccccadabbbcccdaccdccbcdccdbdbcaadbbbabababcaddbacbbbaddaabddcccabadbabaaccadaccbddaddbdacdccbdddcdbacbabdaabddcbcbbbdbcbabcacbcbcddcabaabbcaaaaacdcdcbddcbcaabccbdabbdbaddbdaddbabacababdbccbcdabadbcdcbccabccbaadbbbcadacaddbcdbabcbbcaaadacddaadaabaadaadbabdddccabbabbabacdcbdadacdbbbabddbbdcabcaddcbaacaacccdddbdadcacbacdabccdddabadadadadaabcbddbacbdcacabbdaaacdaabaddbcbddddbbaadadbbabdcbbbabdcbdcdcdacacaabcabbdbccdcdbcbcabdbddbabaaaadaaccddddcbdaaddaddacabaaaadcbccccdaadcccbdbddbcadcabbdbbaadabaadacabadbdbdccabbadcbcbbbbabbbaccaddaabbccbdaddcacaccddabdaccbcbddccacadaadccaabbabdabbcadabdcbddadadbdaadbadabdbacbadabddadaaaadbccbcbccddccbbcaadbddadddcbddbbdbaccaacadaabddbdcdaddbaddaacaaadababcdabdacbdbbacbbdbdbddabddadabdbccbbdddbdcabadbdbcdaaabcacbbccbaaccbcadacdbcbaccdbcbccaacbdbddadccacbddcddcbcdddbcbacbcbbbaadccbddcaaccbbaabccbacbadddcbabcbcdaaccdaccaddddbcacacbcdccccdbdcdbcaabaadbbdccdddaaadddbadcdadcdbbbabcdbcddbcaaacadbbbacdacaddcddccaadcaababdcdabaddcaddbaccbbcbdbadbdababccbddbcbcccaaccbdddbdababbcdaadabacbacdcdcbbccadccbcdbaaaadbbababaaabbcbaacaddcbbcdacacabdcbdabbddabdaacacbbbbbdbaccbadbadccccaaadddbbdabcbaaababdccbdbbdbbbbabcdbdabcadccbccdadcaadaddbbbbadbbbcddccddcbdbdbaaadbbabcddbbaadaadbaacdccdadccbcbbdabbcbddcaacddbadaddacdbbadcacdcddbccbcddbcbdbacababddadaadadddaccbcbadabccdbdcbaddbccabbcdcdbadacacdbacdddacbacdcacdbdcbabacbdcdbacdcacbddbbddcdaabddbadcbcbdbdddcbadcbccddababddababbcdbbbbdbaaaadddabdcbbbccbcdbbcbccbaacdaabbcaaadbbacdcdbaabccddbccaabdaaadbbdddabadcbdaaabbbbcddacbadaddcbadacbdabaabccccbccaaadbacdadcadcacaacaddbcdbdaaadbdbcbcacaddbacbbdacadadcdbabdaacdbbcacccabcbbbdddcdbcdcbcdbaacabcdbdbabcadbcadacddabcaabdbbacdbcaabbcbbcacbdbbcdabdcdcbdcadbacdbbbabbddadccdaddcadddaacdcadbbdcbdbdadaacdadabababcacdadaaaccdbbcbbbcabaddbbacbaddaadbbaababbcabcbdaabbbcccaccdacdadabdbcabcdcbdbbabdbacacbaabbbcaacaaacccbcaabbcccbcddaabbdccadaddacbadcbccdddadbdcdbcbbdbabbcdcacabaacccaababcdbdcabacacccdbdcaadcbcccdddbabddaabbbdcbadacbabaaaacdbbbbcabbbacacbcadaabddcaadcdcabbaabbbbbcbbbaacbdccbbdbcabcbaadabcddccdddcbbcbdabcddadaccdccabcaaccabcddcabbcbcadbaabacaddcdbbaddaabaddabdabddadcbadbcbcabadccbcbabcbaccadadbddcbaabddadcdacbdcdbcbcadbcbbbccaaabdaabcbbbcdaacacadabcaabaddcbccaabbdcdbccdabaaabcaccddadcaaadbddcbdddcbcaabbdcdbdcbcbacadbddbccdbdadaadbdbadbcadcabdbdabccaaacbdbdcaccadbdaaaccacabdddcbaacadaaadcaaddbbdcaddcaacccdbaaacadddcbbdbabadcdabddacbbbcaabcbaacbbccadcdcdabbcddbcaaacdcbcdbacccbcabaaabcdabdcdacbcbcbaabaaabbbbbaccaadacabcaabbcdadbdccdbadcacaddccabbcddbcbcabdcaaaaabddcccacbbcadbaaacdddaddaccbaaccacdbcdcdaaccaaabbdbabddcddddbacabaaccacbbbabdaabacdabddccbdcadcccacacccabadabaccdacccdcdbcdaababbcbddbdadcacdcaccccadcdbbdacaacabddbaabcacbbcdabaddbdaabdbdadadbcacdcbdabcbccbddadcdbcababbdacddcdbdcacabdbddbdacabdcabccaaadbbcdadcaabcbaaaddacbddccbacbdddaadcaabbdbacadbacdddaabdddababdbccddbbadbcbcabddcdbcccccddcdcbcaddacccdccdaaacaaaabdccddcdbdbbbdbbbcdcadabadabbbacdccaabbdcabdabbadbaccbddbcbdbcdbaaccaadbddcaaaaadababadcbaaacaadabdddacdbabadbccaddaddcdabbcadccaadbbccdccdccaabbabddbdcdcbbcaccadcabaabdcccbdcdbbbadbcadcadaddddcdaabbcbcaaddaaacbaacabccdcdabddcacbcbccacbaddacbcaddabdaccaabdddbcbbccdbcaadaddadbbdccdccbbbcbadddbcdadbabaaacbbbadaabbaacdaddcddbcdacddacaddabcccdaacccccdcbcdadadddaaaacccbcdaacddddaaabdddbdabcbcccdacdaababacdbdaccbaacbdddcccabddccaabbdadabacccbcbaccdcabbcddccaacaddbddbdadacbcbdadccdbccbacbabbccdcbbaaadbbddabcaacabbbddadcbdbbdaaaababadcabacadbcbcbddabccacbbabacdacbadcbacdabacbbadcaabbbcbbaabbaaddabbdcdababbbbbcddaaadbabacabdacdbbcabbbbbacddadbabacdacbabbbbabbdddadabacdadbbbdbcddbdcbdccdaacddddccbcdbaaabcbcddbbbbacddbccbbbcdddaccdbbacccabcbdcabbcbadcadacaaaadcbcaaaabcbcbdddcdcaabdacbaaacadbabccaddaabbdddcadaabadabbddabdcadabbddadbaaaccddbbaacaddbccdaacacddcaacdbbdcbabadadaaaadbbccdbbbbdbbcdaadddccabcaabcdcccabccbcdddcdbdddabdcbabbddccacabdbadddbbabadbddacccadcbabdadddcacbadacddaacbaaddddcbddbcaddbbabdddbaaaaaabaccdabccbbbcacacbcbacddbddcbdcbdadbddccdadacbadddabcabddccccacdaaadbbbbadadbccbcbcbacbcbbdcabbbcdbdddddbbdaaccacaadcaaccbabdaddcdbdcabdaaabbaadccbdaadbbaddccadcddaadacdbdacdbabddbbacbccbbacadbbbaabaddbacccbacacadadbcbcadcaccadaccbcaacccaabbddcdccaccdbdadcbddcccabdaadcbadbcaccdcaadbbbbabdbbbcbcdddaadacdbcacaccdcdcbbbdbcaabbcadbdcacabccdabdcddbdcdbadbaacdbaabaaaaacabdaacadadadcacdddbadaacbabddbbddacddaabdcdbbccbbccdcadcdcccaccbacdcdbbdacccddabddcbbbaccbccdbcbcbaddbcdbcddcacbaddacacabacdaaddbdbabbbcbccabcaadbabaacbcbaabdacddcdbdbccbbccdcdadbdaabccaaadaaadcdbabcdadcbacdbbbcdbcddaaaadaadddbaacccaabddbccadbbcaabcdaabaacdadcabccddabadddacacbbbadcadabadcbacbdbddbcdbdbacddcdacbadbcddccdbbbcccbbdbbbbcabbbabbcdcdccdcbccdabcadaccccbdacddbdcbcaaccbbdbcdadccdacdcbcbbcbbdcbcbbacbbbbcbccacabdcaccddbadcdbbddbcbdabbbbcddbcccbacadabddccdddcbacaacdddcdabbcacdbcdcacacacabcdcdabbbbbaaddacbbcbddbadbdbdbaacabbdcdcccbcdacbdbdaadaabddacaaabddccdcbcabbdbdacacbdccdcaacbcdcbaaccbdccbacaabaacdccacabbadabddcaccadccbcabaacacdbcbbcddabddacadbbcbbcbccdbbacaadacdbbadadacbddbabdaacaddbbabaadbbbcbadbddabdacabdbabcadbcdabaacddddbcbcacabbcdbdabcbabaacbddabcccdaccaabaabadbbcbbccdbdbbdcccbadcaabaaacdbdbdddddabdcbdbadaccdaababbbdacadcbadcdaacdcabaaacbaabcaccbddbdacdbbcddddbbbabaabccbccddcbadcaabbddccdcaacdcbcdbbccacadbabaaabbbaaaaddcaabaccdccdabcbbcddcccaabcaabcaabbdcbdcdbcbacadcdaacccbdaabdbdbbbaccdabdabaaabccccdacbbabdbbadddabaadbddbacbcadccacccdadbbbbacbddbaddaababccaadaaddabcddcdcbcaabcbbabdbccadddcaccbcadaaadccdaccdaadaadddbccddbdcbdcabdcadddbdbdaadabadcdadcdaddaabcadddcdcdbdaccdadaccbdabccabdcadbabbadcbadcdaccacaacacbbcbaadacddcbbbbdddccbbacddcaaaadbdacdddaaddaaacbababccccbcbdabadaabbcbabddcdddcccbaddbcadbdadcdcaaaacacbcaabcddadaabbcdbddadbcdabccabacdadbacdccbaacbabccbcbadbcdbacadbcbddbbddcaaaadcacbdabdcadadacdddbdcdcbaadcdaabaaacbddcdaacabbbababbadbbbbcdbbbcbcbbaaaabbadbbdcacbccacdccbaadbcaccacadbbccdacddccbcbcbbadaddbddccdaccacbbddbcabdbdbbdcdaabdbdccbcacdbdbadabcadaababaaadbdbdabcbbbbbccbcdbcadcaabcddadaccbdaaaabbdacaabcddacacdcabbddbbcabcddabcacdabbbccdcaddcbabaabbaabdaadcdaadaaaabcccdbabcddbdbdbcaddcacabcddcddadbbaacdbaadcacccccddadbdccabcbbdbccdabacdabdccbacabcbdbacacaabbdbdbbaacddcdcccbcbddcadacbdbcbbbcdcaccdabdcadadcbbaabbacccdadadbddddbaccacbbdaccbddbcaaadaaadbbaadddcccacbcbdacdcacccabddcdcbdcccbabdbabcababdcadcdbccccbcccddacbdabbbbcbddccadabaacdbacddbbdbccadbcdabdacbddabcacbdadadbdddbadbabbabdcaddcdbcdbdddbddddaabadbcabddbabdcddadbbcdbabaddcddcdcdcadcbbcdaacdabadadbdaaacddbddaaaddaabdbdbbdbadbccbdabadddacdbcaabdbaddbbacbdabbbbababdcdaccbadcacbdaadaadccacddbbdadbccbdabaaaaadbbbbcdcacbbddabccabadcddbbacacdabaabbcdbdabbdaccdcadbbdbbdaddbddcdbacabcbdcdaadcaabbbddbdcddccdaadabddadddaddaccccadcabbccddccdbaaccabccdbbccabdddcabdbddcbbdcadcddbddbbccbdaaddbdbdbaddabddbddbbcddcdadbabcdcacdbcabbbcbacdadcbaadaccbcadabdcaabbbcbababcddddccabcabaabccaacdcdabbdcccdaaaccabddcdccdbdbcbcdaaccbddbddbdbbdadbcacdaddbbccddbaabaadbabbbabbddacaccbbacacbcbcbcddcccbbcbcdbdbbdadcdccbdbccddcabdcdbdacbbdddccdaabadcbdbbcbacdcbbaadbbdcbdcdccaadbdbaaacabbdaddcaacbbdcacbabaaabbcababcadcdaacabadaaababacaccdbbcdddddaacbabbdaababcdabacdcbdcccaccdbcadccdccdddbccdabcdaddaccdccddabccbcbbbcaacaadbcdacbcbdcbdcddbdadaaccddbbaaccdcbabbbadddbacaaddbbbbabdcbbccbcdddcbcdddbacbcadccdbbdcadadbcaababadcadbabdaacadcaccbdccbcacbacbddcdddbdbaaabadbdbbdaacdaabcbccbbacabcdcadbadbabddabbbdddbdccbdaacacdccbcdbbacaacbddcbacaabadaadddbcbcdddbddadbcbadaccadbabcbcdadabcaddcbddbdcddccababdcbabccdcaadabbacbdbcbacdcdcabbadcdadbcdcabccbccabdaaabcadaabdbdaadbbcddaadcdddcdccabcbbdbadcbbabaadbabdbcaaaacbccacdccabcadaabbdaddddabaabcacbacbaaccccbcdbbbcccadcabddbbadaccadbbacbccbbacdaabaddddaaddadadacccccacabaccabaabcabcbbdbdcbcddcbadaabacdabacdddbabccdbbbacdbdbccabbaddcbdaddcccbcadcaadbcabacaacbdaadbaccabdbbbcdccbcccbadcdccbddadcaabcdcdbacdcaacdaaddaccabdbbcdaaddcacbacaabcccbbdcaacbabccdbbccbaddaabbcbabdcbbdcbaccddcdadcddbdaccacbcbddddbdacdabccacdaabbdacddcaabbbcccdbdccbaddccdcadabaadccaddbcadbbadcabccbacccbcdadacbdbabdddbabdaaadaddddcdcbdcaddbbbbcaadccaddddaaabcdcbaddcadbdcdcbcdadbbdddbcdcdbbcbbdbbccbcdbaaacabaaaabbdadcdcaadabbadaddaaaddccccccbcbcdcddccdcbcdbbbdbdbadbdcbbccabaaccccccaacddcbdacbcbccbbbdcbbbdadcbbbccdbdcadacabaacacbbcbccacccbdcbaddcbbddcdacadadbaccddcbccddcabaccabbbabdaadcacddbcabcdadaacdcdaadaddbcaadcaccdbabccdadbadbcdacdbdabdbccbdddbbadddaaddbaddaaabaacdbcbcbcbdcdabbaabaadaaacdbbbdabdadaccddacabbabbbbccabccabbbbaaadacbbaadaaabcbdadcacbabcbacbabadbdbdcbbdbcadddaddbddcbddcaccdaaabdbcddbaadabaddddddbaccdddaadbbdccbcbaaadcabadabaaaccdccbcddbdabdcbacccbaadadabaccdaadcdacbaccadcadbbdcdddddacdaaadbddbcdbbbdbbabbbdadadcccbbdccdccbdbacdaacbbcabcadcdcddbcbabaadcdccaaddbabbdcbdaacaadcccccdcabcccbacddddbcdcbddabbbaddcbdaccaccbcccaacccdcddcbabddcddabbaabdcdcbabccbcdabaddcdccdbccbdadabaabaccacdbccabacbccdccadbbbabaaddadcacbdccabcccdbbcadddbbccbdbbaaabcbbdddadbdcaacccdddaddccbbcbccbbdacdddabdcbdabdabcbbdacabcbbbadcddcbbabaccbcacbcbdbdaccbacadbacaddbccaadadbbbaccaadddbbcbcddcbdccddcdccabcaccdcbabcababccdbbabbdccaaabaaddbabcbaccbbabcabcaababaaadcbacacacbdabbcbdbadabaadbcbcbcdcbcbabadcdababdadddcdabdacbbbcccdaaaaabbdbcadddcdbcdadcaabbcaddcacabcdcdbcabcbddaccbdcadbbdcaccaabccdabdbccdadabdbddbbbdbbbbaadcbaddbdddbbdbddaccadabccdcbcdbaaaaabdcbabddcababcbaacdadbdcbddbadddbcbbbabddbdcdbadcdbcbccaccaccacbbbcddccadddabaccddccabddbccbaddcadccadacbdacdcdadddbbccadcadbaabbbdcaaadccbdbdccabdcabbcaccccbcbdbdbaadddcdaaaccadadbabcdcabbddaaccabdbbbcbdcabcabababcdcacacabccacaacdbddcdaccdaaccdbdddcdabdcdcabaabbabcddcaadcdbacadcdcacccdacdaddacdbccdbdbaacacabdaccaddccdbdacdbbcdbcbdddaaacbaccabaddcadbbddbaacbdacccdcdddcdaddcadabbdcbdcbcddaabcdcaacbbbaaddcaaabaabbcdbcaddcdddaddaacacdbcccbdbbadbbdbdccaaaaacdccddabccaccddccddcbcbcdbacbbdbdcbcabccddcaddbcbddccadbacaccbdcaabadcacdcaabadbabaabbbdddaddacbcadbdcadddbabcdbababdddcdbcdacaabdadcbbadbaacdcabadcccccdbdddacdadcdadcadbbbadbdabbdabaacbacbadbbbddcdcbdaadadaaccdabddccbdcaabbabdcacdcbabaccdccccaacbadbdbacbcbcabcacdcbbadcaadcccccbcbadacdbcdcaddaabdbbadcaccdbcccbdccabdacacabdbbaaacbcdadddbcaccdabccbacdcdbdbaabccbacacaccdacdadcadaaddadadadddbdcbcabdaacdcabbcadcaaabcbabdabaacaacaabbccbdcbcabcddacabccabcddddcaacbcdaaaacaccaaacdbcdcabddabbdbbdddbadcaacdbbabcccbdabadaabddbbdabacaccdddcbdbcdbdbdcabbcacbcdbbddacccddcbbaaaaabdcacabcccabddaabdadcddbcbcbdbdbabdcdbbddcdddabccbbcbadacacddbbcccbbcaadacccbacadbddababbdaaaaacbadbddabbddcbdcbacdcabdcbbadaccddddcdaddccbacaacccddcababbacbccacbbbabaabddbadcdbdaadcaddccdcddddddcdabcacacbdbcdbdbdcdddadcbdcaaaaddddcacdbcdabbbaccadcadacbaccabaabcaddaabbacacdccbbcdacbccbbdabccadadcbcabacadcaadcdddbddddccbadcccbccdadddbdaaddbaabdcbdbbcdddbbbcaabdcccbabccbdcbccabdcbabcdaaabcaabbdbbdccdaaadadddacddaadccbadaccdaabdbbcacbdacbbdadccbdacabbbdaaabdddccabacacdaacacbbbadcaccddcdbdbdbcddabadacadadccdccddbacadaaddcaacabcadadcdbddbdaaacdbcccabcbcacbaaacaadbadcbbdbbddabbccdddbdabbdaadbcbbbaabcccbcbacdacaabacdccbbddbcbbbcdbdccaddbcababcdcabacccaadddcddaabcdbcacbdbdabccbadacaaaaccacdacaddcdbcadacdddabdadbdbbcabdcdbdaabbdbbdadabcdddbdbaacadabacbcbccccadbcbdbddabdbcdaddbcbbaabcabacbdddabcdaadcccccdcaacabcdbcadbbbdabcccdadbaabdaddaaddadacabccdacaccccbaacaccbccdabdddabbbdddcdbdbbbdcccdabbddcabccbadbbacdcbbdbaadbbcdbdbcbcaaabcbddbdaacddbdbddcacdcbccdabaacbadcaaddcbddabdcaaaddccdbddacbdccdbaacddcaccbaaacddaddbdcaaaaaaadaaacacccaaabcbbbbaaabccdcaddcaaabcdcabbadcaadbbdddddbccddaabbdbdcaaacccacabdcabdacabaacbcdcbcaaacbbddbdadddccdddddacaacaabdbbcdbddaabddabacddbcdbcbbadddbcbdbbdcddabddabcccccacdbcabdcbbabdddddccdddabcdacbbddbdcaddcbcdbcabdbbcdcacbacaacbbadcdbadddcaacbbbcdddcbbddacdcdbadddcbaaaddabacdbbbdacaacaddcdddadbaaaabdcbccddbadaccdccdcdadbababddbacdabbcbaadbadcccdaaabbbcababdadaaaaaddcaaccdcccdccbbdacbccbbbdbdbdddbccbaaaddcbacbbcbbdaacbdbcdbbbbbddadababbbbccdcabdcacdbbcddcdbcadcadddcbcbbddbcdccdccdcabcddaacabdaccbacbadbddbabbcddbadcacccbbabcddcbbdcdbcbbcdbdcaadaaaadacbbcbdddbcaacbaccaddbcdccddcdadbbabdcadabacadcbddacabbbbcabddddabcadadccddadbaacdbbdcadbcddaadbccdaaadbcadabbcacbbccdababdbbcdbdaccdcbbdbcbbbaaaabcbaadcdbcdcccbbdaaddacabcccacaabbdaacdcacbdabacdadddbacaabaacdddbbbcccddccdbacddbcaabbdcbdabbccabdbdbabbbabbbbbdadddccabacbddabcccbddacabddbdbbdcbdabbdbcbbddacbcaccaaccadadccbbabdabdbccccccccdaaccaacbbabbcacccbcdcdbcbbcdaacbdcbccacdabaddcbbdcadcaadcddcdcacbddcbbabaabddaadabaacddbcbadccdaadcadbdcaccbbbbadcbdadadbbaaacbcdcddccbbacbaddccacdccacadacdacacbadcdbcabbdcddbbbcdbdcadcbbacddbacdaaabacddbababbbbbcadcbacccaccbadbadacdadabbcdbbadbddcacdacccdacdcdacdcbbcdbdabcaadcbbaaaaaadcadaccbbcdcabadbdcabdadacccbbbdddcabcccaccbaddcaaaadaaddcabaddbbbabdacbbbcacddcbbcbaddbbaaabadccddbcdcccaccbcabbcbadbcdadbcccccbbbcbaaadcdaddabdbdaacdacbdbcbcbbcadcbbaaccacbaaacadcdccabaacdccdbaaabcbccbdbddbdbcaaaddcdbacabcdbdbabbacbbacadacbddbaaddbddcbbdaacadcbaacadbddcababccbdbaadcddcdcababbaaadabdbbbbbdbabcbabadcbdbbbacccabcccbdcccbaccdcaccacdbbcbcdcccbbccdddbbdbbddabdbadacaacccbdcaabcbcbcaacadbcadbdadbccadbddbadbcbbbaababdccbaaaccdbadbadbdcccacbdddbdcbdadadbbcdacdadbbbdbcabbadabcbcbbaabdbadcbabacadccdaaabdbcdadbcdbbcbddddbbdbbaacaaaadbdccbbadccadbddbacbbbdbcbbabaadbdbbcbbcbbacdaaccccddcccbaabdadddbaaaaaabadddaadaaddcccbacbdbdaabbccbdadbdbcbdaadcaacacdadaaabdcbdaddcaabcddcdccbabdadccbccbcdcbbbcdbbcdcbbccbcababbbdbacddbcbcabadabbcdabdcdaccddbcbadbbccdaabcdcdccdaabadaacdacdbddcdadcdddddaaaacdcdbbdaabadcaaaddcdcbcbcacbbabbbddbdabdbadbacbadddaaacccbcbcbbabddbbcadadbdcbbdcadccdacbcbddacdcdcbcabbbdbadacaddcbcdcdacdbddcbccadcdaaacccadacbbaddbbcbacdabcbbacdcdcbcabadcdacbacdcbdadddddabcadbbaadacccaaaabaacbcbccdddacbcddbaadddcbcbcbcabcadadbdbcdaacddcdabdcbccdcbbbcbdddddcbcddbbdcbcaccccbddccaadcaccadbbbbbaabbadadccadcdacdbcaaddccaabbdddadacadcdbbabdccdcbdaadcddccaadbbcbddcdcbbababcccaacbcadbadabbcdcbdabbaadbabbddbbbacbaaddaaadddcbadcddccbbadcdaabccbdddbcadabccbdadbcccbacabadcaadbacacadbbacacddbabaabaccacaabcacbbacdccddccaabcbbcadbdbcdaddcccacccdbabbddacdccbbdadcabcaadcabcdcbcbababdadaccbcddcabaccacdbadcbdaaadadcbaadcccddbcbbbacddacabbaaddbdcadccaabacccaccdddbdbacacbcaddddadddbaddcacbdbabdcbcbbdcaacbcdbbdadccdbdcdcbbabdcbacacbabadccdcccdbacccdbdacdddadddabcaccbcabadcbddbcadbdaacacaddbccacdbbbdcdcccdbccdadcccbbcabccdddddbbaaabddcdaadadccaaacddcdbbbdcbcababdaabcbbdcdacdaacabbbcabdaaadbaadbdacbaddbacbbbcdcbbaacdddacbcbdcadaabdaddcbccdcbabbaaaabbabcdbaacbdddcdccadabcbabcadbddadccbccbdcdbabcbabcccdbbacbbaaadacccdbcbabdcccbbaccbdbaddbbbbbcbccaccaaddadbacddcbdcabaacabdbcdbaddbdbddabddacaacdbdadbbacccdacbbacdcacbbaadbcbbabdbacbdcadacbcadbbdbacbcbdccbbcdbdaabaacdabcdaabacbacbdaadaacacadbdacbcbcadddccaadcdcaadbddbdcbbbcccaaacbdddaddbacacbbdabcddacbcbaabbadacaaccbddcbccadddcaaabcadabaadacadbddcbddaabcbaaccddcacadcbaabcdaddaabaaddddbbccdcccccbdbcddabaadcaddcdbccbccbcdddcabdadbcadccabccbdcbbdbcaadcbdacbbabcdbbadbdbcbbadbadadbccdabcdadaaddadcdabbbabacacaaadcbdbaddcdcbdbbaadacdcddbacbddcacacdccaccabdbbbbaaaaacdadbccadcccbbacbdadddcbbaabdcbabaccbcabcdccabdcddabbacbdbbdcaddbabdcacbdcccaacaaadbbacaddabbdbacabdacadbbaacbabacdbcabbbabcabadaacdabbbdcccadccabdabdcacccbdacbcaaacbcacbbdbdaddbdaddcdcbbbbbcdaaccaadcadcbcaccdddbcdaabbbbbdbabbbbcabdcaaaaabdcdabcaacdabddcadabbadcdcabccbdcacbbccbbdcccdbdabacaccacddadacdcdaadbddbbabbadadcbbdbddcddadbcdaaacaaabdaadcdddaabacdabcbcccbdbabcaadbdbdbaabccdbcccabadbbbadbcdccdbaaabaccbbbbbdacbadaccbbdcbbdcdbcddccaddacbacccdaaaabadcdcbdaabacadbcabcaccccbbbbdccbbabdddbdadbcbacabadbdabacccdbdcbcaddbadacaabbdcaddcdcabcaacbabbabdcbcadbccaadadababcbdbbbdbbbcbdcccdaaadaccadbcbbaabacdbccbabaabdacccadcdcabbbcacdcdbcccddbbccdbcbbadbcbabaabcbdccacacdabaddbbcadcbcdbbdcbddbaaaddaaabbaadcaaddcdabbbcdbcdcbcabcdaaadabcbadabacbcccdbbbaaacdacadacddcbaabcbddbacddbaaacabacbdaaabdbcaabcababdaaabddcbddbdbcdcdbcacddccdadcadaddbbcbadccdcbacabcdadadbccbbcabbaabccbbaaaacacabccaaddbabdddacccccddbadbaaabacbacaaaadbbcdbbdaccdbcadcbbccaccdabcacdaabcddcdaabdbaabdbadbcbdddddababdbcaaadbcaaacccdbabdadaabccbaddcdacccdbabcdddcccaaabcccaaccccdabddcbabbdaddaabadabddcdbbcbaddbccbcbddaccbdadaaaccadbdcaadcaabcadcccdaaccaabadcadcacccaadbccadbacddddccdaaccbabcbbcccdaddcccacddcabaddaaaccdcbacbcddaadabcbbdddcadacdcbbdcdcdcaddaaabacbbcbcacdadaaacbbcbacbbcdcbcdddbcddcacdcdcbbacacccaaddcbcaddcdcabacdbccabadcbcbaddbacccdcacccabddaccdbcbaabacabbbdbdadcdbcccacbadcbcdadaaadadddaabadcbcaadaababcbadabaccabbccadcadacccbbacdaacddbbbaabcabccdbaadacacdacdcbcccadbdabaccbbbddadacbbbcbdccdabddacdaaccbadcbcacdabdbdbabcadbbbdbacbbacdbddbcadcaabcdacadbadbccdaaaaccbbbadacacdbdcadcdabdbdcaadaadbddcbcdccdbbdcbaccbccdacdcdcccdcdbbdcadcdbcdcaabadcdadddccdaaddbddcbcbcbadbdabbacdadddcbdcbbadacabcdcdaddcbdbcddbbdcdaaabaabcdccdcbcabdacaacbddddcacdbdccbccddcbccdbcbaacbdacdcdacadadabcaaabddcbcacabbcbcdbaddbdbcbccdabcdddbcaaacdaddadcacbaabdccdccacacbaddacbbbccdaddbcaaadacaadbbbdaadaabdcbcadbdacccdcaabbabbcabccaacabcdbbaaaadccbdabbdaccacadacdaccdcbccbccdcadadacbbbabcabbadddbbbabcbdadbbcbcccdddddabdadbccccbbaacddacbcbbdcabcdadbbcaaddbabccadcdbccbabcadcddbbdbbbaaccbbcbaaadcabacdbcbdbcaddcddcccbbdbacddccbacabbcadbabbbabbdbbcbcbdacaadaacbbbcadddbbabbcdbdddccbccaccbdabadbbddbcbcbbacdadabdbbdddcccdcadccaaadcacddccaabcbdacbbabcbacbbcaaadbbcbddccadbcbaccbcadbaddbbdbbacaccddccdcbaaadaddddccbccabdccdddcaddbacddadabbbadabaabbdbadadbdcbaaccaacbbbcccbdccbadbdbdabbbdbbbcaabbcdbabdabdbbbdbdacbcccadacaddcdbccccddbcddbbaabccccaaddacadddbccbbaadadccdbdcbbbdacaacacaccbdaaccababcacccbaccccbbdabccddccacbddaccbacbbadbadbbddaaabdbbbbaabdcbdbabaaccdcbcdaaacdbbcaabdaadabcdbbabccaabadaddaaadbcdcabdcbccbadcbabdccabaaadccccaabcbddacbcdadddcbcbbabaacddccdbacbcbddddaddaacadcbabcacbccbabacbbccbcdadbcbdadbcddcaadddddbdbccbbdbdcaacabbdacbcaacbcbbbbcaccbcaddbdcddaabcadcbbcbdaabcdaaddbaabdbdabbcdacdddbbcadccbcdbababbbbccbbdaddbcbccddbbdacbaaabbdccaabbdaadaacbccddaadcadbcaabaacdcabbcbbadcdabcdbdccbbdabdaaadabcabdbbddabbdabdbcadbadbdbcbaabacacccadabdddaddbddcbcaabbcddabaabdcddaaddabcaccdddbcdadbbddaacadcaccbabcddcdaccdaadccdbacdbdcccaabaaacadbcbccacadabcbcdacbcacbcacdbcabacadbabccaacdccaaaddbdddabbbbcddcadbccccbbdbacbdcbddbdbdddcaddcdbabddaaccacdcaaababdbcaccabcdadccbdbbcbbdaaacadcbabdbccadcdddcbcbbdddccbddccbcdcdcbcbacbbbaadbaabccbbbcacadccacbdcbdbabdcdbabbbdaacbcdcdccbcaabdbdbbbaacbcdccabddabcacdadacabbaccddbbbadadcadabccaccbccddaadacddadacddadacacaaacdbaaacbddabdbcdadacdcacabdcbbaabcdaaabbdbbdacaccbbdbbccbcddacccaaaccbcbccacbbccdbabddaadadbadbccdacaacbdcaabccdddddcabdccaaddadadadbdbdccdddadcdaddababbcdccacaabacdcbdcbcdbdbdbadcbaaddacacadbbbbdbabddcddcccdcbaaabbcabcbdaabddccabaacaaababacaddcdbbbdcccbccbccccacdaaaccadcccdcddaadbcdbccbbbacaadacaaccbdcbdbccdbccabcaccbadccdcbdcdcbabacadacdcabacbbaaabcdcaddddcbdcdabdddacbacbaddabcbbddcdcbbbaaacdcbbcaabdacdcbcdddccdabbcddcbbccaddcdabbbcdbcddcabbaccdbaaaaddabccadcbdbcddcdadddadbdbdaccacbcabbadabaabccbbadcbbdcdcdbbddadccabdcdbadbdccaccbdbbccbdbcddbdccbdcbdcccbbdcdadcabdaddbbbcbcacdacdaabdcdaaaacdaaacbdabdaddcccccadccbaddaddbdacbabbccadabddbcadcabddadcdcbacbbccddbdcbacaaddcababccbddabbabcaacbaaaaaabcbacadcbcbaabdacbbbdcbdcdaacddaabacaabadacdcadbacacbdadccddcadbdadccccdccddcccadbdabaaababbbdcabdbaacdbaabddacdccdddcdaadbdcccdbacbbcddcabdaccdacaadcbadaaacddbbbcadccdbaddccadcddbbadcddabdaabbcdacbacdadadbadcddbcbdbccacacdaddabdbbcddcdbadabbcacddbdddbddddaddaccdaaddbbbdaaabcdabbbdabdcbbddbccdadbbcdbddcdcdcabbccdbcaccacdabbabdbbbbdbcddbbddbbdabbdddddadbbcdcaabccbdacdcaadaadbbccdabccbabccbddcbddddadbabcbcbbcabbcbcbaddcdabbadcbadbdadbdacacbddadcbcddddccdbbccdcccaabbbcddcaabcacbddbdbdcabddddbddcdcacadcbbadccbdbcbdddabbcacaaababbdccacacaabadcbdadcbcbabadbbdddbacabcadccbbcbcdacdaccdcbaaccccabbdacdaabacadadabbaccaaabddaaaddcbdccbbbabccaaabcabbdbbbdaabcddacbdcbcadcbdacbdddbcabaabdabbccbcdddbddcbdbdaaccbacbcbdaccabbbbdcdabdccbdabdabdaacccdccddcccabbbcdbaacdcabbbbdcbcdbdcbacdbdaacdbcdacdadbdbabcbacbccacdababbaabbbbdcdbdbaccdbdbaabbdcccabadbcddcdbbbddbabacbbbaddbaabcbddcbcccbcaddccbcbcbabcaacbdacdaaaabcbadcddbacabaaabbddacdcbbcacadcbbbaadadbbddacbbcdcadbbbbbadbdaacadcdcacabdcdabbbaccdaaacdbccdbbcdbccdcbddabacdbdddacaabdbbcddbabbbbdbbccbdaccdacbcdbadacacaaaadbbadbabcddacbadddbbaabaaaaddbbaabbbbacaacababcbbaccaaacbbdbccbadddaadacccacbabcbbdabdbbdcdcddcbbbcacdbcbabdcdbacadbdadcbbbcbddcdaccaddbabbbaccabbcddccddbabddbdcccddaaddcdcbbddcdddacadaacdbdadabbabbdcababcdbdbaaccabddcdaddcdbaabdabdadcbabcadbadbbacccdcaadacadaabbaacbcbbbbddbbbaccaccddaddaccdacbccccabbdbabbdbacccdbdcdcaacdcddbabbcabaccacbdadabadbdacaaddbbdcbcbbdbdccacaaddadcbbbcacabbaabbbdbbbdabbbcdbacccdbaaacaabaccdadacdbdacaabcdccacabbadbdacbbdddcbbcadcaddccbddabdccbdaabadbdabcadbddacbddbccdbbbdcbdadcdddacbaccdddacddcaddbccaacaaaacbadaacdcbcbdabbdcaabcadcacabdccaabbcbcaaddadbbcbdbaddbcddbdcddbcdaccbccadcdcbdbbbdcaaacbcabcbbaaadbccccbcaaaaaaccbcaadacbacddcbbabcbaddcbcdbbcacaabcbaadbbbaadcddcdcaaacadaacadbddccdddadabbbbcdbbdaaadcbcaabbcbacbcccbabbbcdcabcbcbcdcaaacbbacbabcaaddcccbabaddbababadccdddbddadccdbadcbaabbcaccbadddddabdbcadcaabcbbbabbdabbbcacbcdcaaacccddcdcaabaaacbaacadbcacccddadbabadaabcccdcbaccdaddbdcdaadbabcbccaaacdcbbcacadbdcacdddddabcccdcbcbcbdbdbbddcbbcddabdcbacdacabdcadbacdacaabaaaddcaacbaacbabcabcdbadcbcbbadcdaddbbbdcbdaacabcadddcacbdacddbbaacbcabbdccdbccaacaaccadcadcaaabbbdbcbbbdcdabbccbcddccdacbdacabcddabbcdabaddcbabcddabccaabacdadbdcaaddbcdabddadbcdabcdbcaaadbbcdbbbaadbabbdaddacaabdbabcaaabdcccdcccaddddabbabbdadaacddcadabcaaabacdacddaacccadcabdaddddbcabdbdbacacbabdcabaaddadbbadbddaddcbbddabcbdbcbbaccbccbcaabbccdccccdcdcdddbbcddabdbbccdacdccdacbbbdbddacabaddadccacbddddbaccdbadccbaadbdbccddbdaaabdbaacddcdcbaacdacaddaaccabbacdabbabdbdbbcdccddcbccbcbbbacdaaaddccbbddaddaddddacbbabbbabdcccaacdddbcdbbbbacaccbacdbacdacdbdcdaaccbbaadbaadcbbdaaaacadbdbabcbcbccdcccdbadaaaddaadbdabcccaaadabcabdacaacccbccbcddbddcbddcccccbdcabddbdbbcddcdbababdcabbbcbcbdcbabacadcdacbccabdccadcbdcadbacaabdbbabdcdabaabcbdbacbccbaccaadbcacddcabacddadaddcaabccbacbdacbbdaacdbcdbaacddbbacdbdcbccbcccbdbcbdbdbcdadcddccbbcddaaabadccbaadbadadbcddacddadacabcccabcadbabcccaaccdabcbdddacaaaaabaaddacdbbaacaacabcadbbcacbacabdaacadcddddcbdcabbbabcadcbdbbcbbcbdaacbadcadbbdbbbccbbbdaaadaddacccbdbdddcdcbdaababbadadccdcbaacbcdbbbcbbddcccacbcacdaddccdcacbbdadbacbcdaabbccbdaacdcacacbbadbaabcadbcbabcacbabdcbbdcbbcdbcbdcbcaaccbcddbddabccddcdbbdbcbcbdbbbbcddaaaadcdaabcbccacaabadbdbbadbcabadbaadcbdbccacbcaddcccbabcdcbdcbcacbdacccbcadcdbcabaaadcbbbdcabcccddbbbdbddcddbbddbbddbccbbcdbddaaccadadddccbbddadabadccadbbcdcdacdbacbccdcdcdbabddbabccacdccadacaddaddcaaddacbdbacbaadbbcdacabbaddcddabcbccaadbdaaaacccbcbbcbcbccdabdbbdbaabbabcaadbacdacccaabbccbcdaaacdadbaacdccdaacbcbacdccadaacadadcbdcbdadabadbcbdbdaabdccdcaaccdbaaccaddccdabccddbacbcabdbbcacdccdcdbadacdbdddaacbddbbacdcdadddaaccbaadabbadbbbcbccaddabdcbabdaddcddabbbcdbcddbcdababbabcdcaaadbbabbdcdbbbcbbcddddddddcddddcddddadaadaaadbcabdabcccbaccdabbbaaccbddbadbbaacbcdadddcbbbbabcababcbbbbdccdcdbcbabbadcbbbdccddbaabdddddbbbbcaddbccbadbaacbaadabaaccaacabbdbcbacddabadbadbdbabcbdbbdadabbcabacddcdccbcdbdcdcadbcdcacadbdacacdbcaabddcaccddccbdcddabacbacdcccbbbcaacddaabcdbcaacbadbdccbbbbacdbcbccbaaaaddbbbadcacbbcaddbdbcbaabacaccbccbaccabbacaadadddbdbccccdadccbabcccbcbdaccdbaaacbdcadcdbbccdddbbdbcaadcadaababadbabdddccddaaaabadddbadbdcbdbbdabcbddadbbcccaddcbdaddccaabbaaadbdcbadbaaadbadaadcacdcadbdcbbdcdabdcadbccdcacaaadadcdaabcaaaaccaabdcccadcdddcadbcdcddbadacabbcbcddcbcaacdbbcbcbbadcdaadbcdbccccabdaabaccacabbaaddbdaddcbacbbbbacbaaddaabdcdcdcccdcaddbacdbaacdcbadcabdabdadbadbaaabaccbcbbdcbcdcaccdacacdcccaabadbdccbccbdcbbacdcbccdbcdadcbdbbaacdabdcdacbbaccbbdcbdacbaabbbcddcccbacbabbbbbcacdbacadcbcaddbccbaacabaaacadabddacccbcabaadcbadddbbacbbabbaddbbcbbdcbabbcbcacadbbccdbcadabddbcdaaaaaccbdaddcbcbccbabcdadddcbaaddbcbacdcdbbcabaccacacbcadabdabbdabccbabbdcdaaabadcbdadaababadbcbadadcabdabcbbccdadabadbcadccabaccadacdcabaddaaaaaadcbbccbddcaacaaddcddcccdbcbccbadaccccdcbddbdbadccdcdabacddbbababddaddcbbcacdcbbbbcdacdabddcadadadaccccaddcabdcbcabddbcbabdaadcbcbbcabcadabcbbdccdccdaaacdcacbcadddddbdbddbbdaacbddaadbbcbdacdcbddbbabbdbabdaddacaccaabbadacdddbbbaaaabdbbdcabdacaadddadcbcbbdccbccdbccacdcccbabacccccaccbccdcacacbdbcacdcacabaddbcaacbccdcaddcdcabdacadacdabbadbbbaaccdadccdacddadbacbbaaacbddbcaddbddbdacacbaabcccbaadcacdbdababbdbccccababbcbcabddbdbccabdabcacbcaadddbabddadbbbcdcdabcabbaccbababbbbcccdccbabadbcdbcabdcdaccdcdabdbddcddccabcaccacaddbaabdacadaccabcbccbcbdbaddbaacccdcbcbdbbaacaabaccdcbcccadaabbbadabbaaaaddbdcaddddcdaabbbabdacdaccddbbcddbaccadaaaadbcbdbddccdadbddadcabdadcacbcaacccbbdbbaddcaadcbbcbccdccdbccbddaabcbbdaccbcbbdbaacdcacdabcddacbcdcabdcbdadbdbdabcbbcdddaabdabbdadbcdadaddaacadaaabddadcaacdcccdbbdbddccdbbdddabadabcacdaaddbbbacccbcaaacbacbddbacbbaabcbdbcbbcccbcbacccddcaccbdcacbddbaddacbadcccadbcdbcbadbbadcddcbdddddcaaaacacaddcdbbcabdcdabcdbbbaddccdcdaccbcdcbdcbababadbbabdccdcddcbacbbadadbcdacaaabbddcbdaacbbcdbcacabbbbabdddddbadaaccbaacddacbadccdbccccdccbbdacddbdbaccbdbbbdbdacccbbdacacbbdcdccbbdcadcdcccbddadcccbabacbdddaadbbbcddbdaaacdcbbcbabdbddadacabbdabdbdaaacbbaccaddcaddaabdccbcbbaadaccdaadbaacadaddbaacbbbcacaaaacaacdbdacbbdcdccccababcadbbaaccdbbdbadbdaaadcddcadbcdbcddbacabbcbabcabaadacccbdbcddaabcddbdccbcabbbaacdacbdcbbdccbccbbccdabbbabdabddacaaddadbccdcbaadcddcccacdcbaacbbbbccacaacccadaabdbcddbbcdccaacdcdcaccbbddbadcbdacbdccdbcdcccbbbcdabcadddddaaacdcdbbdbadbaabbdaccbabbbabdbbdcadccdbbccbcbbbbbccddbdcbcadadbbbbadbcdcbcdcbcacadcacbdadbcdbcdccbbdbdbaaacaddadcdacdaaabbbadcbadddbdddcbabdbbcaacaddbdbcdaddcbbabcccbcdbccdddbccaabbddabcaaccbaccccdacbabaacabdaabaaacabacaaadbbbbbdaccbdbdacbcbdbaddaddcbcbababdabbddabcbdcddcddacbdbbcddbdbccacabbaacbcdbddaabbbbdccdaababdccdbababaddbbdacdacbbbacabbbbdbaaccadcaccbabdddacbcbbccbbaddccdaacbbbcaabcaddaddbcdbbdcabdaddbdbacbabcabcbdadaaccabbdbdaaabbdcadcaddbbcdddcdbdbbdadabddcdaabbcacccccacdbbccdbdccccadcacadcdbcabaaadcdcaacddccdbaabcbbacbcbbccadabcdadabbcbcdcaaabbcbadcbabcbbacaddbacbbbcadccaaadccaadabddddbbccccadbababdbcdbdcdabaabbbccdccaadcccdcdbcddcbabcadcbbcbbcbacabddadcaacddcdacaaacaaabcdbbcaaaacccddcddcadbbbcbadadcbaacaaddabdaaaacccadbbdbdbdcaacbdabdbaabbbddcbdabcdcacabdbdbddbddccbbadabcbaaaadbabccbdccbdadccacdbcccbcdaabbcaacabbbdbbcabddadcaddadcdaaccadbbaccbdbccbdcbdaaaabababbadcdddbbbabcaaddaabbcdacbcadbdaabbabdaccddcdcdcddaaaabdcccddcbdbbddaabbbdcbaddaccaacaaccddbcbccddaaaacadbbbabbaaacbbdbdabcbdcbcaccdcdddccacabaddddadaabccacddbdccbdbbdaccaadbcaadbdaacbdbadccddadbdadacaddabaccbccadbcdabcbdadbcdacdbdcbaaddcbaccccdcdbaaaccbcbbacacabdbacaadbcdcddcabbacddddbacdddccaadbdacabddbdbababacbabbacdadccddaabbddccabcbdcdccabaababaddbcbccbabacadcbadcaabadcbcdccbbaaaddcdaabcdddacaaabcacacddbcbdbdbbabccdabbbbbdddbddbdcdcdbdaaabbaaacadbabcccddaabaccddcdbdaaccbbaaacadabdcadababbcabbbddadcadbdcbdacdaddccccbbbbdcbadcaccaccaabdacdbcbabcbbdabddcbdbcdaadaddbbbdcadbcdbabcbbdbdcbbacbbccbadbcddcddcaadacbcabdcbbccbbdcaacbdcdcadddbdcdbbbcccacbcadabacbdaaabcbacdcaacaaaddbabcdccdbaaaabaadbbbbadcacccaaddadcdbdabacccbcbbabcbdcdbcaadabddbcabdbbcbaadabbddcdadbaabaaabaacbccdaddaaacacdcddabbdabacababddbdcaacbbabddbaccadaaadddaccdbbdadcbcdacdabcbbabaccabbabbbccadcdccdddacdbaccbbcabbddcadabbddccdbacbdadacaaadcdcdbacbaabdadcbcbaabccdbbddcadbbdddaaccadcdabcadccdbcacbdbbbddcdcccdccaccdabacbddabcbdcabaddaabbadcadbddbcdbbcbbaacbbaddbacacbcdbdbcbdddacccadddbabadadbdbdbddaaacdcaacddcdadaddadcddacbcbdddbcbaaddadcdbbdcadbbabbbddababbcdbbbcabbcacaacbdaccaabbdbacccdccbdbadbcabdbcdacaaaacbcbcdabbbcbcadbdbadbcacdddbabaddddddbdcccddadadaacabcddbbbacabcbacdaccabaacbddadcbbbaabbbcdcdccdccbdcabdacbabbbccbddbbdadddbacaacbcbdbbccadbabdbcabdabddddcbdbbcbcdacbabaabbdacabbadccbbbdabbddddabcbcccbdaacbbccbcbddcddcdcbabcdaabcbadabadacddcdabbdaacacdcbcabdcaddddbdaadbbaacadaababcddaaabdabdcacdccdbbdbbacabbcccdaaaabcbcddbababbdacbbdabdababccddbbaaaabacbdbabbcdcaaacbacbbcdacbadccacacdbbcaddbbacbbdbcbdaddadbddaddcdbdadadbcaacdbcabacbcabcccbadadbcaddbabccbbaaddcaabaabdadddbcbcadbdaabbadacccbdcdbdaabcabbaabddcabbadddbbbadccbbcddaaaabbcbadcddccdacbcdccdadacabcacdbabbccbbacbcbbbbacbddbcbbcdcbbdadcbbdcdaccdbbcdabdaaabcdcadaabddbbaadcacbaddcccbdbcdacbbdcadcbcbbdcbcdacdcaacbccabdddcaabdaccccdbabdaddbaddaababbcadddacdbdaacabbbbdaddabaabadccdadccbcdbbccccbbbabddbcccbdacbdabdbcbdbabacabaccaadcbcbbccacdddbbdcacbaccaabbbabdbbdcbdbbdbbbddcdddacaaddadbcabaacbdbaaddbbcbdabdadacddbdbdaacdcbdbacbbcdabdacccbbbdaddcdbcabcbaadbabbbbbbadadcabbdadbdbcdbaadccccccbaadbabbbccdbbbccadcbaccdaddcaaadcabdddcdacbabdbadadbcaacbacbaabdbdaaadbbbdbcbabcadaddcdabddddbbdadbdbcdcbdbcdccdaaabbabcdadbcabcaaaacddbbdbdabcabbacccccadcadcbdbddcadcdccabcbcacbbaaddcabadbbaccaaabdcaabacaabcabaacbacabbbabbccbbcaaaddacacaddbababcdbcaccabdbdddbdaddacbbddbbcbabbdddcdbcbcbcdbbbbccddbadddcbddbacabddaaaaadddbcdbbadbdbcaddcbdccaaddcbdbbdaddcbbdcdbbcadbdcdbcbcabcccddbacaaccdbddaaaabccccacadbdbcacccbdbdcbbddddaaccacdaddbdccabbdadccddbbbbabacacbaccaccadcddddadacbbbcccbbdccbdaadabcaabcbdcddadbdccacbcadbacadcdddaddddcdaacabaacbbbcadbaccdacdddbaababccaacddabddcbacdadcbabbbdaabbdcacdaadabcacaacbdaccbcaaaddbcdbdbaaabddbdccdabcaadcaadccdbadbcdaddabddccaccbdcccbaabcbacaaaaddcccaaaccaaaccccbdbaccdacaddccdaaccaabbaddaacbbccbaabdddbbaddbcdbcadacbbccadcdbbdbcadaabdcccaccdbbbacbcddcacdcdabcbdaabcdadadababdabbadadababcdcaaccbcacdbbdbaacbacadbbdacdaacdbdcbbcdbaccbcccddcaaabbadcddaddbbcdaabcabdbccddcacdcbadddccbbbaccbbcadbbcacabaddabdcaccadcabdbbdcdbcaadbbbbaacdddccaddcdddcabdbacccbcacbacbbbdadbabbbbdbabbdacdbbacababdcddcbbdddbbbcbdcbbddbdbabdadccbacdbbcddaadccdcbacbcaabdaaadbdddadccdbdcddcbdbdaaccdcacdacbcdbbaadabcbdccabddadddbcabadddbaccaabaadddcacdbdddbdabbdbccdacccbcdaddbaccabbcbaadcabacdcbbcababdaabaadbdaacdbadaacdcbcadcccdbbdacbbabccddabddccdddaabacdacabcbcbcbaacabccccaadcbaccaadbcdcbaabdcccdcabcddcacbdddcbaababcbddaabcaacbbcbaacaadacbcabbbcbccdcadcdbcddacbabcbdbabcdaacaaabadbdcccccbaaabccbdcaaabcddddcbdbbacacbdabcabbbbdbdbacaddadddbbaaaaacabbcccddcbabadcbaadcddcbdcaadbddbcacbcdcbbbabdaaababdbaacbbbacbcbdcdbdbbbcaababbbcabddabcbdaabaddabdbdadbdacaccadcdcdabdabddcdcadbbbaacabddcbdaccbcbaadbdcbacadacbbabbbaacdbaaacadcbcdccbbddcbdaaaabdbadcbaabbadbabdcaaadddddcbdcbbbacacbcbaccdaaadaadcbdcbdcacddaadcabcabaccbdbbcdacabccbdabaacbaadabbcbcccddbcccaabddcddaadbacdabcaaacddaccadccadacccbdddabdabadadacbaadbcdcbdacbbdacdcbcbbbadabdcababbcbacbbaddcababbcbdaadbdadabcbdbdabcdaadbcaddccaaacbddacbddaddacacaccbbddacccdcbacadcdccacdddaccbabccbddabddddbccdabdaabcbbacaadcbdcdcadcaababdbaaaabbcaacaaadbdbcdacddadbddabdbacdccbaaccccbaacababdbdaaaddbdbbaabcdaccbbaabccdbcdcadddbccadcbcbaddaabbabbdbcdadabbcaacabbadbabcdbdadacaddcbccddddcdaddbbcbaacabbbcdbccdacdbdcdbbdadbacdcbbaacaadbacbbcaccabacaaadcdbbcacdddddccdadacddcddbcddddcdcaabababcdacbccdaacdaaabcabdbaaacacddbbcbacdddbaabbcdcbcbaabccccddbaabaacdaaacdbdcbbacdcccbbbaddddcacbdcadacbdbdbcbbacbabcaaabddaacddddcbcdcbbbccbdbccadbddbadcddbdcdbaddadbcbbcacddbcbbaabbcbdaacbacdbdaaccabaccbaabdddcdcadadabbdbcdcbcccacbabdbdaaaddbdbcdcadcddccbdbcdaadddbcdbccdbdccddcddbbddcbddcdbcbdacdcbdaaabaadcbcdbdbcdabbcabdbbabdcbabbdacacbcddbcbdcadbcacacbccdacdadabdbbcaaaccdaddcaadaabdababbcdcadccdcbdcccdbadbbbcbccddcccbcccbdcdabccccbdcbcdcbcbabcbcacbaadbbdbabcaacacbaaddaaabbabddbaabcdacdaccdcbdbcdadbadcdbdabbaaaabcddabddcdcdacdcaaabdcbadbdaabbacacabdbcdccaddaacbaabbcadccbcdaacdabccacbcddbcccddddcbcdcdcdadbaacbddaadabdcbabdbbddacacbdcacbddcbcdaabaabbdacacdacbaabdddcacadacbbdbaabdcabcbccaacadadbaaacdacbacadadbabbabdbaccdbbcddcdcaabaadaccbadaddddcddccbadbadbcacbbbdbbccacacadabccdabdaddcbcdaabbabbdbcbdaddbcbacabcdddccbbbbadbcdcadabddccdadcadcbaaddbcdbbaabdabbbdbcdaaaddadacaaabbbabdbaacdbccaaaadcabababbdacbaccbbdaccdaddacccaaadcbdbdbabbadaddacddabdbcccdbbaadabcacacdccadacacacacdabbdbadadbabcbcbcdcbddcaccbbcccbaadaaacdadcccddadbdabcddabbdbcccadccdcacbcddbccbbdabacbdaddbadbdbbccccbbabaccbdbdadacaadcccbcddbcddacddadbbbabccbccadadabbcabbbccadbdadacabccadabaaccddbdcacdbbddbbbcdbbbaabdddabdbaabdacdbaabbbbbbabbcabcaaacdcdcaaaabaaababcaadacbadaaaabdacacadbdccbbbbbbaaadacbcdcccbdbbddbbccadaaadcbddabdcdcdcacdacdabaacacbacdbbabbaadbdbcddcabaddcdacddacbaadaaabbbbadbacacdbcbabcddaccddbabbcabcadbbacbaabdbabbcdbaabdcdadadaabdbbbdbbbbdaadccbcbcaadaaaaadbcbbababccaaaddccbccbadabccbccaadbcbbbabddaaabacabaddbbddddabdaabdabbbbcbbacccbccddcdbbcabadbddcbbbdaadbadbdddcccbdacdccccacdabddbcddbdddbcccdcddddbbabaddadaccbbbddadbadcbbcccacadacdbddcacbcacbaadcacdaaacbbbcadabdabcacbcbdaabbbcddadcaadabaabdbbddcbabdabacdadccbdabcdadcbabaaddccbaccadcdbacdcabcbdacbddcdcbccdbcbcdbccbbbaaaaaaadcaadbccbacdaacbacabaccbddadaabcccbababdadcbcbbcaacaadccbdaccbdcacbddddcacddbdddbdcdacadbcdbcdaacaddcacdaddcdabaacbacacdcabacbbbcadcdbdddadccacacbdccabcbcbacbccabadcbccdbabbcddbdcacacabcabacdccaccabbcdcdbbaabdbacbabbddddbbbcbcbdaaaaccadabaaadbadcddbbccdadacdcabaacccaddcbcbcbaccaaccbdabbbbcddcdcbabbcddabbbbdcdccaccaaddcccaaabdbaadbbdcddabbcaacbbccdcadacddbcdccbacccabaabdbbddcddbcaaaccabddbbcabdcdccbcdddbbaccddddddddcbdadaadbddcddacabdcadbcdcabadbbaaadbbababbcdbabbbcddaccabcdabcdacddabbadbbbbdcbbcdbaadaabdaccbdacdcabdbbdabdcababbdddbaddcaaaacbcbdaadccbdaacbbccaddcdaadbdbaadcbdcbbbdcddcdaabcbcbcccbbdcbcdaaccdaaccbacbaaacbdcaadcccaaadcdcbddccdbacbcadbdcbcdbaabbbbdbdbbccabbaaccbabababddacbabbdccccddbdacdbcadbccbcdaadbaabdbdbdbdacccabcadbccbbbdbabdcbbadaabaababccadbdbbbcaccdbbdaadcdabadbdbbbcdddadbbcaadabdcddddcdddbcacddbddaabadaaacaddccdcdcbbccccdcbdacacdcdcccbbbbbcbbadcacbccbaabcbbabadcdccadccbddccbababbbabcbbdccdbbacaacbcabaaccdadbbdcabaaddaaacbaaccbdacdcccdbcaaacdadcbbddaadacddccccaddbaacdcccbadadcccbadbcabaddacddcaaadaadbdbabbbccbdbccbbcaadbdddcbddbbdddcdbadbccdbbaacbcadbcdbbdccbadcbdaaabdbcdcbdadcdbbcadccadbbcadcdacdbbbcaabdacdcdbbbccbbbccaacdccabccdcdcbadcdacabbbcabccddabacadccbbcccbadbccbbdaacdcbccabccabdbdcccbbddaaddbcbdbcccbccdcddbabdabdbaadababdcabcadbbacdbabbaccccbabcddbcdabdabbbacdababadddaacccbbdaccbdccadadacadbadaabbcdcbccacbcadcabcbbdaccbbcddadcdacdccabdccacacbbbcdaacaabdddddcccbdacabcbddcdbcbddcbdbbcabbcbdbccbbaacbdddcbdcabcaddbbbbbcccdaccccbcdadddcadcdbaabccaabacacaaddbabdcddcaabababbabbdcdcaacabdbbababbdbdadaadcbaaddacdaadababaccbdcccabcacdbadccbbccadbcdbadbcbcdbacbcbaaccadcaabddcdadddcccdbaadcbabaadddacacdbcacbdabdaaabcaadadcdbabacdccacdadcadbcccaaabbddacbbdbdaaababdabaaacdbcbdcdcdbccddbaaadabcbcbbaabbcccacbdabbdadbdbbdadadaaadddbabbbbddbcdadababaaccdadcadbdcdaccaddabaaccdadcaaabadbbdddabcacdcddcbaddadddbabbcbcbaabadcbbacbccabdbbcbdcacaabddaadacaccdaddaccaddadbbacdbbdcbbaabcabddcbcadbbaddcacbaadcacccdabbaccbbddadbbbacdbdbdccacdbaccdcbcccdbbabbdccdaaadcbaccacbcbddcdcaaacdddabbcabbddadaccdbadbbbaabdcbdccdadabdbabdabbccadabbadccdaccbbabdaaccbaacabcacabcbbbdcdbcbcddabbdcaabcacacabadaaaaaadccdabadcdcbbbdcabadddddcbadbddbacbaaabcbdbaacaaacccbdbddbbbbdcdabaddadcbaaaabbdabcbacdcccdddddddacabbabccabdadbdaadcdbabcbcaaabcbddadbbcdbdbabccbaddcbcaaaaacccaaccdcacccbbaaaabadbdaadbbdacccbbcaabadaabbdadddddccadbcbddccaddcdacbbaccbccacdabcdcbdcdcbcdcdabbcaabccddaadbdbacbcbcdbaabdbbcbbbbdbdddbcdabbcabaccbbacaaabaccddbaadcbcdbbccddcbbcbbcdcbccababbddbcdbcdcddbdccadccbcadccbcdbdbdbdcabaadcddcbdbbadbbcacaababbbbbacccabdabacbdbdababbbddccddcbdaacdaacaacaadbcdaacdaadbcdacbbbcbbdcdabbbbcbacbdbbacadcdddcaddabdacabdbddcdabdcdbcbddbdcbacbbdddbdaadadacadbbdbcbaaacabaddbbddcbabbdbacbabadbdadcbcacbcddacacbcdbaccaaaabbaabbcbdcdadcaccbaaaacabcaadbcbabddbccdbcbdbaacadddddccbbbdbbbdabcdbddacbaadbbbbcccdcdddadcbbdacbcddaaabbacccaacddaaddacdcadcbdbdcbadccdcbabcddbdcbdbdbddbccbadadbcbcbcbbcddcadbdbdadcabddabcbadbacbbdccdacdacbaababbadbabdddddbdbdcddbbcdccdcaabcabcaacbddddcbacdddcbddcdaacddaadbdadddcabadcdbaabcddcaacadcddcddaabbbdbbbdcbadbadcdbabbdadcbabcaaadacdccadcbdbbccdddbaadbddbaadadcaadaddcddcbcacbcbdbabacaabcaacdcbccbbbaabcbcadbccccdbbccadbdacccbdcabbbcdbbbdcbadacbccdaadddcaacabbbbdaccabbcbdacdbbbbddbadddadccbcabaadcacdccabddbadadccacccdacdddababaadcdddbbbcadabbbcdbabbacbbbbbbccabcbcadddcbddcadcbcccbadbddbbbdadddadbaaccbaacabacdbcbcbccddaaccadcbbaccabbdabcbcbdbbcaabbcdccddddddbccbcadddbaddbcaaabaaabbcdccadacbdbdbcabadbcdadbbddabcaddcdababcbdadbccadbddbbaadddcdabcdcddabbaacadbacbcadabbddbbbdcdbbcbdbabddbcadaccadbcdcbcbaababdabccbddaaadcacadccdcdacacdcbcdcccbabcdcaacdabaccabbacaccbacaaccdbddccccaddabcddbbadccabbccadbbaccdcaccabdccabadaaddccddbadccccbacacadabbbcccbaddddbcdacbadbbadccaadabadcbacbbbbbcbcaddacaacdddbaadbccdcccadbdcaccbccaadbbcccbcacadabdcbdcaaaacacdabaaabdbccdcccbcdabdcbddccadbbacdadcadabcdbdbdddcaabddaddcaacddcdadbbadbacaaaaadbdccbccdccbacabbdadbbbaacddbdbaadbcacdbdaabccadcddabdaadcbbddcbbabccabddcaddbaaaadcbaaddaabddddadbbbddbadccdbbcabdaaacabdcabacddcdbbdadcccdddcdcaacddcbaabdddbdbbcbbaacbbadbaabbbbccddacdddacdaccaacaadbabbcddbbadaaacdcdaacdcadbcbabbaccdaabdccdadbcabbccddcadabcdacdabbdddcaababbcccbadacabbbbabaaaccbadabdbcdbcdabdbbdcdcddbdcbabccdacdbdcbbbacadbabccddadcdbbcaddbddabcbdcbadbdbbaaacabbbadddbaccabdcbcbcddddbdbdaccccbccbbccdddaabdcddbdcdbcacbdbcddcadcbdabcbcccbaacabcdabdcabdaacdbdcddcbadddadddddbbbcadddaaacabcdcacdccdbddbacdbccbaddacbdcbccbcdccbabbbbcdbdcddadcbacabacacccdcbbaadbacaddacddcccccccabcabddcacdcdcbdaccddcdcabdccbcbaccacabccacddbccdbabcbaabadbdacdbbcadbbacdacdadbaaccadadacbbdcaaaacdaddddccbbcdcddbaadbdabdbabcddaabbaaddbddabccabadbdadcccbabbddcbacabbddabdcbbbcccbdacbadbbddcccddaaababdcbbabbddbbccdbddcadbcaaacddbbadcbbabcddaabbcacdbddcacacbddddacddaaabaaaacadbbddbdacbbbccdbdbbabdabcadcdccabdddccdddacadcabdacdacbabbdbbcbcbbdcbcbdbbcdcaaccdabddcbdbadaacbcabbbdaabcdaaaadaadaaddacacbbbbabdaabbaddddcaaaabcdcacddccbbdcbcaccadbadadcdcbadacabcbaabadacccaaaabcdbadbddccadcdbbdddbcbdadaabdbadbdbdbdbabaaacabaaadddbbcccbddbccccacbddbacdbcaabdcbbbdacdacabdcccccdbdbcdccaddbcabbcabacbdaadbcdabcbbabbdcabbbbdbcdbdbdaccbcbadddcbadaadbabddcccccaacddaddaacdcbdabaddccabbccbbadabccbbcdddbddabdaaacccaabcbddbdbdcbadacabbdbccaabcdcdcdcbbbbabcacabbbddabddccadcacddabdcbbcbcbcccbcabbdccdbaaccdcbbcbabacbabdcbaacacadbbddababccbccdacaaaddddacbddadbbdddddaaccaababddbdcbbabcdbcdcdadadbccdcbdcacaaddaabccaccddddbabcdabcddacbcacbcdaabaccccaaadcccacbdababcddbabdcdbabacddddccdacccbbaddddbdcabccbabbdbaddcbcacbcacabacbbbadbbdccccbdadccdddadcdcbddddabadbaadadcccdbaaadcccaaddddcbdbdacccadbcadbcccddcddcdcdacdbbdcdaadddccaddcbcaccdcbcbcddbbccdadbabdddabdcbddabdaddaccbbccbdacaaacdbabbdbcaabbccbaadcdbcbdacaaacddbcbbccbcadbacdbcbddcadcaadbbccbccbbabcdcddabdbdbababccddbdcccabdcacadcbbdcdacbbddacbaccbddadabbbbbbccccadcbdcbdcadaadbbcaccaaccadbcbdcbdaadadddbcddbadadbaadadadacbbcbcbdddcacddabbbbdbcdbcabcdabbcdacdcdbaddbdccbcabddaccbaacacbcccddccbcdccbdbcccbadcaabaabbbaadccadaababaddabacdabaabddddbdbdbccbcbcdaaddddadbbcdddbdbcddcbbccacbbddbbaddadaacdcbdddcbbdbbaabdbdccaabbaadcbadbcbcacdacdadacdaabcbbcdadbbcdabacadcbcbbbdbddddcbabaaacacbbcdccaadddadcadcbcdadcdadbbaabdaaadcbacbbacbbabdddbababaccdabccbbabdbbaaddbabcbdbcadcacbccbcdcdbdddaccccacbabbdbaddaaadaacaccddbcabddadbccbbdbbcccbcaaaadadaadbcbcccdaccdadacdbbacbadbadcddbabcdddadcbddddbabadaadcdaddcdbcaabbdcdbccccbacaaacabbdcddcbabcabcbbbdbdcaadabccadaabbadbcddddcbbacacabbbdbabacbbbdcadcbdbcdcbccddbcacacddbaababcbcbbabbbdccacbcacccdcddbcccbbddbcbcabadacaccacddadadcaadcaaadbcbabaacbdddabcccadbcdbcbccacdbacbbaabadddcbabcbcbaccacbacccacbcbbabcccababccaabdbcadadbaaaddbbdbadcdddbcdadcbdbbcbdadcccbcaccbccdadaddaadadcbdabacabbcddbabcccbccacbccbbabbdaddcdacdbcdddadbbabcdbbcddcdabccadbaaacdacbbbdaacaaacabcbaabcdcadbcbcbdbcbdbdabbdbdbdacaccddbbbcabbdddbbacbcdddddbbaacdbbcacbabcaddacdcccdbbccddbcbadcbcdbaaaacaadbdaabcadbbcccbbbccdddcbbadbcaaaaddaddaaaaabccbaacdabddddaddddadaaaaddbacdcbaddadadabaaccbacbddadaccbddadccabbcccdbdbdddaabdcccccccdbccdcbaadabadbcabcaacdbcbaaaddbbbbbabdaabcbddcacabddabdcbbdbbddadaaaccbbdbdbbbccbcddaaadbcdcaacdcaccddaaabbdbcdabbdbcccdaddcbabbdbbdbbabbbcdbabbcaabadabbbdbcadcccbdbdababdcbccdcdbcadaadacbdacdddabbaabbcbdddbaaaaaabbdacadbdacdcbdbcaadbdcbdcadbdadddddacdddababccdcdaddccdcaaacdcaadddcdcdccaadabcdaccddddbacadcdcccdacbcbcadabbbbccbccacccdccdbbaabababbaddabaabcaaaadaddbaccdacbdcbbadbcdbbcaadbccdddcdcccadcccbbaaadcabbcccdcabcabbacacdacadaccaabddddadddddadbbdcabcabaadcacaaadababccacdbdadaccbbadabcaacdddbdccdaadbbbcaaacbcccdbcabbdcbdbdacbdbbbadaadcdcddcddcbddcacaabdcbbcbbaababcbcbdbdaabadcdcdcdaaaacccbdbcadbdddaccbdbaabbadbddbacdabaccbbdccbabdabccccdcccbbcadbaaacbbcbaaddacabcddddbaddcbddbcdacbaccdccbddcaacaaaddbdccbaadaabbbbcbbcddcbaacbcbcdcbdadbddcabcccdadddccdcdcccbadcdbbaadbcbccdacaddcabcddbaaabbdcdcbcadcccaadcadbbdbdaaccbaadabdcdaaaccabbdbcbbcdcbbabcacadcacdaaaabcbdbbddbcccdbbcadcbaacccddbcbcdbbdadadcddabcbdcdbbabcccccdababaaaaabdacddaadccccbdbdababacccaacbdbadbcdcadadadcadbcccccbddcbacaaadbaaadacbaacaddccbddcbcdbbabcdbaabdcbabcbbcbccbbbcaccbdcdadcbbcbcdacbddcabcaabbadddccaddcaabdacdabbcbcdccdcdcacdacdbaddacbdcaaccbabcbcbdddbdcdddcbbacaaddcbddabdadbddccdcdabadadddcacabbcbdbacacdbacdccdcbdcbacbcdcccbcccaaaabddcdcdcbcacaaadbdacdbadccbdaddbdaccacadcbacaabadbaacbdcaccabbdccaaccaadaadcaddaadbcdcaacccdcbaacddcbdddbcbdacccbdbdbbdcbaacccbbddccddcccaabbcbbdaabbdddddbdbcbabbbbddccacdbdacdbcdbdbddbbadcacdcddccbcaacdcddacddbacdbbdbddbbadbddbdadacabcccdbbdddaddaababdcbdadcacbdacbadabcdbcabadadcdcdadcbbadcbcbcaabdbddaabcddcaccbdacdacbbddbacbadadaddabaabddbdccdcdccdddccacdbdbadbbcbcdaaccaabbcccdcbbbccccaabbaacbdcaaccbdbdadbadbdbcbbaabccabccbdccacadccbacadabacadaddbbdccdaddaaaacbcacccccbabcaadaacccacabacccabdcdaaaddabbcccdbdbcadbaaadcdbdcbdddabddbbbadcbdaabbdbcdaccccdcacdbdcacadcccbcacaccdabbdbbcbcabaacaabddbaaabcadbcacaacbabcbcdbcddacbbadbbbbcbaadaabccdadbadcccbbbaaddccadcccaddccbacbaadcdbdaddaddaaabbdbdadaddcbdbddddddabcddcccbccdddcddaacddcddcdcacdcacaaabccbbabaccdcdcbcdbabbbcbdbdbdaacaadcdddadccabdbbcaaaabadcaabdadcdcddbabdcdbcdbacdddabbbbacbdacaddaaddbbdaacdbbbaccbccbacbddccdabcacdcdabacacdbabbaadcccadbcdabaabcbdbdaddddadaccbddddcaacbcbcdbccbdbbacbacdbbdadcaadcaddabbdcdacbdddadbcacabbbcacbbdbccbcdcbcbbbcdcbbcdbccdcdaadccbdcbcaaaaaadadcbddddaaabdbdacccbaabbbadcdbdcabccddbdddadbaaaddbadcdacdbcbcbcdcbacacbbaadaadcdbbcbdacaacaccbcbadddaaababbbddddababbacdadcdbdcdbcbccaaacccdcccbccdaadbbdccbdbdbaadbaddbbdcbacdadaddcadcccbabccddcdddcdbdabacaaaabdcccddbcddbccbdddaadaaacabcbcaccacdacddccbbabcacddbccdbacbadacbdadadbbdaadbdbcadccdbcaadddaaabddcbdaddaababadaddabdcadbbcadcadbacddcadbdddabacbaabdbddaaddcaabcdadacdccadaaabbabcbabcbbacdcbdcdacbcaadcdddcbccaacdaadaadaadcbdcbcadadbdaadacbbadbddccbccaabccaaabcdadadcacaccbbbbcacbcdccacdbdaadbccabaabbdaacddbbdbdaaaaccaddacdbbabcbbcbbaaaccdbacaddbababcadccadcbbacaabdbdbcdbbcdbbcbddabdadccdabadccaccacdcccdbacbbabbbbaaddccbcdbabcddaddbabdcaabbacaacbdbbaabdacdacaaccaccbdbcbadddcbadccadcbbddbbbadcddcdbaacaaaddbdbdcbcbacbcbccbbacddadccccbbdbadbdabbcdbdadaabdbbdccaccdcbddbaddadbbcbcbcbbcdbabdbabcabcadabababbdbbddbcacabbadcdcacdbddbababbbbbcabbccdbcaccdcaabcdacababcabdcacbdaaabbcddcbdbbcaabbbacdbbbacdbaacdbadcdaadbdddcbdcbbacdddcadbbaddacaabdbbbdaabddcadcacdbacbbdabcdababcbbaabcdaddabdddbdccccdaccbabcacdcbaccbdccbaabcdacacbdbddaabdabdccbbabcdbccadbcabccbcbccbadabdaabcacdababaacdbbcbbcbcddcadacacdbddcacadabdbdacbbaadbcaddbcbaccbcbbdbadcbaaadabbaabdbdbbdccbcaacbcbbddbbdbbccbadbddacccbacccbcddcbbaddbdbbdaaabbabbbddbacaabdcaadcadcbdacdadbdbdbdddabbccccadabcdaaaaabbadddcbcbcaddbcbbcacaadbdcdccccaabcdcdababaabaaadbddbcbbbddbcbccbbaaacddabcccaaaccbdcabbcdcbabbcbdaacbadabdcabbcddbccacdddaadcdabccadabdddabaabacabccdaabbbabbdbdacdaccadadcbaccddbbbbcdbdacbacdbdbdadbacbbcbbdcdacddbccbcbccbabdbdbdadcccabccccbcddbbacbcabaaccabdddaaababbbaadccbbbbbcbcacdbbbcdbdbdcdcadcbcabbbabbdabdabcdabacaaadcdccddcacadbcbccadcbbcccacddbcaadbdabcddaaabbccaadcbbdbcaaaabcdcdcababcdbddbdcdadbcacddcaabdbaaaccdabadcabbdcabdbabddbcabbbddadaddbccbcbabbbbbbbaaacccdcaabbadbcbacddbbbcabbbdbddcabbcbbccbbcdaaccbadbdcacbcdcbbacaccbbccbddcacaddcadadcabbcbbaddadccbcbbcdccdcbdddcbcbccaddaacbadbcabbabcdbbbdabcbaacadbacbcddbdcbbcaddbbcdcbdbdaddbdbdabdbccbdcbbbaccddcaacbcccbbbdcddaabdcbcdaddbbdccddcbbdccccdcbadaabcaacdccbbdcdbabcddbcdbadbcaddbcacbbcdacbbaabaddacbcdadcdadcccbcaabacbabddddbcbddcddcabcadaabcdacbccdcabbbaddaacadbabbbcaabbccbbbaddbdddacbadbcaacacccbcdaaaabdbaddbbdabacaacddbdadaabdacbacacadbdcbcbccbabbdacacdccbddaaccdacabadcddbcabbdcaabbbdccdaabddacdbdabcdaddcccabcaddddddddccbadbbacccccbdbdaabddcdbadcaadbcbdcbbbabdabbbcbbbacbdbcddabdcbacabcbacbbdbcadcdcbdaaacbaaddadbaacdbbbccacbcaadaabacaccbbdccadaaabbbababcadbcddbabddababacdbbabadccaaabadbababdccdcddbaacaacdccaaddacaccbadaacbbdcbcddcaadacdbdcabddbdcacbddaccdcdbdaadbcdcacbbbbaaccdcdcaaddcaabaabcdddadddbabdaaadcaccabbdaacbadcbdbcdbcaadacbdacaaccbddaaadbbdbdddbadadaaccbcacaabdddabcdbcaadaacbcdaaacccabdccbadcbdadcbaaabdbdbbabacdacbcabbbdddbcbbdddcbadddbcabcbdbadbcdcabaaadbccddaadaaabdacddbdcbccccacccccaabcbdaadadcdbadbbcdaacbccccadccacddadbcccabaadabbaaabddcaadbabddcabcbcdcdccbdaaaaadcddddbbbacdbabcdbacaaabadcdcdcaddabaaaabbddcbcaabbbdabcaabdadacababaddddccbcbbdaddcdbabbddcadbbcccaaabadabacbbdddbbbddbcababdabbbaadadabbdbdddabbcdadbaaabbdcdcbdcdaababaddbcccbadbdbdbcbdcddbabbbbbdcbcdbbaccdaacccacacbdabcadccccdadadbbdbaccacbcbdbaadccbabbcadabcacdcaadacddbdbdddababaddbbacdcccacdddadcdbcacbbacddcaacaaddcaccbccdcacacabbdddcadddaabacabddccbddbaaacadabcddddcdcccdadddcadbddadbddadcaacabdaabccdccaddbabbacbaabccddbccaccbbbcdacdcccadbbbccdbbadadadcdcbddbbbdaccbccaccdddbcdbcabaadaabacbaaadcbdcbdabcaadadccbdbdcbaabdddbddcacbcbbcdcaacababbdcccbdabbcbdaaabdcdbacacbddadccacadcaaaacbccdcaddbdbdadaadcabbbdccbabacbccaaaadbdccbabadbddcadddadbaaabbccbdadaacccdccaddcacdabbacbdadcccdcbbabaacacdcacbbcbdbbcbcabbdddaaaabccabaababcddbddbccbbccaddddbdbdadddcacaadcbdbcbacabbbdcddbdcacbbdacdbbcdccbabcdbccbcadcdadaabaaddbaadacabdccbddcbbabdbaaaaadcccacdccadabddbaccaacdcaddccbdbbaaacaabccaaccdccbbdbdabcdcadabbbdcbbabcdbadaacaabcaaacaaaddcabdccdcdddacdcbbcabaacdbdacaccbbbadcccdddbdcdcbacbddcdcdbabdddcacbcabcbadcabbdaabcabdaaaccdcdadccbbbbcdadbabdbcdcbcdddcdaabadddbbcadddacbbbcbddcbabaaacacdbbdacddabaddadabcddaaaaaabcddbcbabaadabacaddaaaddddbcaacbdacdbbdcbdacdaaacdaaabbabddbabdbabcbadcaadcdcaaacddbcdabcbcddacdbaddddcaccddadbdddaabcbcbacaadcbcdcdaddbdbcccdacacbbbccdbddaccdbcccdcdaaddbbacacadbbcabdddccaaddabbbbabccbccabacbbabbbbdbddbadabcaabcccaccacddbadaabadacccdbdabdddbabdddcabcadbbaccbcbdabbddbdbaddcbcbddddbaaccbcdbddbdcdbbabcadadcdbbdbbccddabdcaadbddcaacbabbcbbcccccadaabbacdaacadacbdcdddabdbaababbacdbacaabdbabbaacabccbbcdbbcabcbacaadbccadaaaccaacbcbcadabbcaddaaacababcdaacbbcabbccacbcbdbcbdbacbdcaddbadaadbbcbabbcadaacadaaacdaaacddcbcbdcaaabbdcaabdcdcaccbadcddddcacbbcdadcdbcdabddcccdacacbdbdbbabdccbcdacbcabaacdaacddcaccbbadcabbbbbcabaadacbcaabddaabccddcadcaaddaaddabacaddbabbaadbdbbaabaddbdaaccbabdadddaacdccdaacbabbdddbbacdbcadbbcacdddbbccbdbdabacaabbccbdccdabbdccaddddaabdcbabbbdaccbadadabcbcbdacabcaadddcccbcdacbaabcbabbacababdddbccddaddadcbcbbddacaaacbcbdaaacdddbdbbdbcbdddbaabdbbbadbccaddbdbbcadbbabdcdccdaadbbbcaabdaababadcadcaabddbdbacccaaabcadaaaadbdcbbbadbaabdcadbaacccbcadccabdbbcccabbbddcddcbcdadaadbadcbbbacbdcccaacccadaadddbccbbabcdcacdaacdadcabdcaadbabbaacaacbbbcbdddabadcbacbdadccbabadbcdcadaaaddcdcdababbbacbcbcddbccbcbccdcdcdcacdbcdbdaaabbccdbbcbaabcbaacbbbaacabaacccdcbabbddcdcbabdcdbdacabdcccacdadddddbcaddacbdcdabccbcdaabaddaacaadadacaaadadbabddbbddcaacdcaabcaadbbdbbaabcdaaccaabdbdbdcbccdbdbddaaacacdabbadbddcbcdcdcccabdcbdbbccddacccbadbcdccdadbbcbcaccdaddccbaddbaddbadcadaddddaaaadbabacccdbccbcbcaaaacdacaaaaccacccccdcadbabbbaccccbcbbdcabcccbdcccaabacdacddcdabccdccccdacbadbcbbcadbccabaabdccbaddcbacacbdbbdccbdcbdcbbcacbdbaabcacbcabdabccdbabbabdacddbcdddaababbacbbcddccdcbdcddbabcacabdbdbacdcdbbccddbcbddbadccdadbdabcccadccbaacdbccdbbbddaccdabccccabcbccabdbdbbaaddccdcddddbdbbddadbaacacbdbaaabcdbabdbabbdbcddbcddbbbbbccdbcadbcbabdacabcbbdcabccacbdbddcddbbadadcaabbbdacdcddbcbbccbacbccdcabaabdbaabdccbadacdddcbdccbdbddccddcbbdaabbddbbbacdcaabdbdbbbbacdacddaacabcacddcbdcbbbdaadabdccbbaacadcaadbcdaddabccbbddddcdbcdbccccaabbbaadddabbbbcaadacdccccabbadbcbbbcabcabcdbdadcbddcdbbdddbadddcccbcbacaaccabacabbaadccdbcabacdacbacdcbddbbaaacbbdbccdaacaadcbaabbdccdcbbcadbbadbcabbbdabdccbddbacbbbcaababcbdcbbbcadddccdbddaabbbacbdbdbdaddacbdbcadaccabcbbdbcbbacacabdacacacccbdadddabddbadadadabccdcaabcabbdcabdabddbdddadaaadccddbbdccbbaaabdbcdaacccaacacdddabbcbbdacbdbadccadccbacacbdaccdbdbcdbbaaabbdadcbaaaacbbcdddcbbaadadaadbcbaacdcadbcabbdddbcddcacdcbcabdabccdbcbaabdbdacaddcdbcbbcbdadaaccccddabbbbbcabbdccbaaabbbabaabcdaacddaaaabdcacbbaaaaaddcabbcabdbbcdddbbbddcabdbcabbccddadcbdaadaabbbcadbcbadaaaddbcdbacacdcbddcadacbadbbdbdddbddcbbdcabddbabdcdbbcbbcddccdcbdbbaaccbacadcbcdcccdbdcdbcdcaaacbbcadbaadbaaddaaaccacddacabacccaaacbddbcbdbbbdccabbdbddabcaaaabbaabababbdabccdbabdbbabdcbbacdaccbcadbcdcbdcacddcacdcacdbbccdcacadbbbdcabddcbcaabbdaaaccdbaccbbbabdbabcabacbabcdddcbccbdcdabdabaaccdbdddddaaabcdacdcccabddadbaaaadbddbccccacdbabdcacdbbdbbcdddacbacabcbababcadbaddbdbabaacadbbadbbcadbaddaddbdcdbcccadcccbdddbdadbbccacdbdcdaccacbbcabdaaadcbacbcdaddcabddddccbdcaaadbbccabbbbabcadcbbabbdbddbdbaccabbbccacbbdabccbcacddbacaabbcaddcaddaabbbcbcbaadaadacdaccddbccbbdbacadaacaccdbacbbbabcabcbdddbbcdbacccbcbbcbbbbdbbdddbabacdaaadaadbcddbdcbdcaaaabbbaccdaccaacacdcabddadbdaaaaabcbbaadcbcdcaaadabdaacdacbabbccababbccbabdadbdbdbddadacdccdcabddcddbccdbddadaabdddacbbdbdbaabdacddaadbcacddacdcbaaabdbbdbacaaccbdaabdddaacddbcdabdddbddbaabcbdddaccbddbaacdbacdbbdaccdbaadbcadbddcdbcccaaadbdbdabccdbcbdcdbdccacdbbdabcbdaadcdbabaaccddddaabcccdccdcbcadbbadccdddacadaaabaacbaabacaadbdadbabbdaccdacbddabbdaddabcbabcbcdcaabbcddddcbbbdbdcadacbbdcbaccdbabbdadadccabdadcdbacaaacbccabcbacaabbcacabdbbaccbaccbabcadabaadadddacabdcadabccbadbaaacbcbacabaccddbccabcdcadabdcccdbccccddaaaabccababadcacdadabbcaaacaabbdcaaabbccddcbbdccababbbbdadbabcccdbdbadccbdbacccbdcbdbdddabdbcccddaadbdcdabdbdccababdcbcbdcaccabbbccbaccdbcdbadaadadbaabcbcdaccdcdabcabcbaabcdcdbdbddababcbabdddbcccdcdbdacdabdaccddbaacdbcdcdcbaaccdbdacbdcccdabdbbbdacbacabbdbddcdaacdaabdaacadcaaacbcbbddcbbaddaadddbaacaaabcabdaaaaabcdcbddbadacdabbcacddadaacbabdbaaccddacabbcbdbdbdaadabdbdbabbadadcbcbabacccacdabccdbbdbdcdbbbdaacbaaccdcdcbbddcaabdacdbbcbcbadacacdaaabbdadadccdccabcdaacdbbdcadcbddabdadccbbcdaccdcdbbcdaaadabaacccbdcddbcdcdcccabbadcdabaaddaccaabaaccdacbaaccdadaddacaacbccbbcbdbddccbbbbbdbaccdcddbcdacdacbbdaaadaccdcdbacbcdbaacddcdbdcbbbdccabaddcbdaaccacbbbabbdddcadccddcdcbdcaababcbdacabbdadbdbbbcdcccccacacaadbcabacdbcabbabbddbdbddaadacdbddabadcbadaacbcdaabdcbbcbaaacbdbdcaddcabcdbadabadaacabcbddbbcbcabdabdccadbbdacacaadbcbabdbcabcabdbdaaccaaddacdcaaaddcacabcbbadaacdbadbbadabacbadabcbcaacddabbbbcccadcddadcdbcabbddabddbcbdcabdccddcadadcdadcdcbdccacdcdddcbcdddabbcbbbccdcccbacbadbcbadaaaabadcddcbbdbcddaaacbadbdcddcabaddccadadaaddbcccddcccbbcddbcbbacabcddaacddddcacaddacabbddbacaacadddbcaadaacbaaddbdacabacdaabbdcbbccacdacbddabddadabbcaddabcdbbabcbdbddbcbbdcccacbacacddbabdbdcbdbabdadbcadabbdcccaccbdcacddbddaabdcbbaaddcbadcbcbccadaccacbbbbacacadddcdcacdbdbabbcdcadabbbdbdcbaacdabdacdadbcddccdabbcaacbccdbcaaccbbccdbcacbdbbbbdcabccadaacadadbadcbdcaddbcdadacbbccaadadbbbbbabdbdadbaddaadcadbccbcddcabbacbadccddcadadaddcddabaacadabbdcbabadbcaacddaccaddbdaaadbbbcacadccadbdcccadbcaddaaacbdacbabddcbcccadbabadabbabbcaddcacadbbcbcbaadbdaccbaababaddbcabacadadbbdcdbcaccccccaddcababdabbbdcbdcdcccbddcaabdbbaddacabdcdcabdabacaadbbbdcbbaaddabacaadadbdbbbdbacaddadabcbdccadcbaadabcddbddcbcdaaccdccdacdbbcccccddbbbccbbbacdcddbbbccacbbdbacddcddbbbdbbacbbbcbdacddcadaaadccbcabacbdbaadbdcdcbaacbcdbabccccccbcdddbdacaddbcabbbadacaaacdcaddbddcbccddabcbdccbcdaacccaabccdbccbbccbcadadcbabbdadbbccaaddadcdacbcadacccbabbdadddbcddbcaadadabccdbabbdddbcccdaddcbdacabbaddacdcbbdcaacadcadcabdcdcdbaabbbbddbdcaccabbccdabcccbcdcdbacdbadadccbdccbccdaabdaddbbadddcbcbacccadcdddccccbbacbdbbbbdacbbbaabbbcaaaaddcadbbacacaabdcccddcbddddcbdcabaaabcaabadcdbdaadccaaabcdadcbacabaadbadbbbdbccabddababccbbcdbdccdbdacabcbcaaddcccbcddccaabbadacacbccabdacdcccbcdcbacadcdcaaccaaaaccbbacbcbcddcbbbadaddccaabbcabcccbacdabbcdbadadcaddbcdacdaabcdcbdbccccbacabbcaabdbabdabcbdbdbcadddcabddadccabaaddadcbababdaabccacbcacdbcddcabaadccbbdcbbacdcdaabcabbdaaddbdaccbcdacdacadcdaddddbdabcdabaacdadcbcbbbacdaacadbabdaacccaccbbddccaaaadadbcbcdbaddcdacbdbabdadbbcbdbddbaacccdadccdabddddadabbcabacbbddaddbdbccaddabdadddcccabdddbdaccaccadacdadcabccaddcbcbbcbbabccbadbdccaabbaaaacaabaabababbdbbcddacacdcddadaaddaacdcacdadaabbaacdadbbddbcaaaddcdddcdccaabcbacabcacacdbacaabaccbdabccbddadbacdcccadcaacabbdacbcddcdcabcddcabcdaadddadbddbbbcdcdadbcbccdcabcdaaccacabcbcacacacbbaaccbaacdaaaabddccacbabaadddbbabdbcdaddaccaaaaadcaadaacbbacbdcddbcbdcbcacddcaccbbaaabaccadccccabbbccccaddcaaddaccdcdaadbdbadbbcadbcbbacbdcabbbccababbbdacbbdcdabcccaaddccdbababcdbabacdcddcbbdcdcdaccadbbabaccbabccbbddbcacbaddcbcbcbbabaccccadbcadbbadccdbbaaddaccabcaccbdccdddbadbacadadabcabcabbaacaacdcdbdbbbbdaacbcddaaccbcccabccdccccbcacaadadbcdaabcddcaccadaacbccadbccabaadbcccadaacbabadbbaabcababbaaabcccdadbaaaadbcddcdaddacddddaadadacaaabcdbaccbccccbabcbbbacdcccdcdbabacabdbddabdcdddaddcdbabaabadacbddcbaacddbbcabdcaaddbacbbbaaaabcdbdbacbddabbaacddabbbbaddcbbdbaadbadbbadbdacdaaccadadbdabcbccbdacddacbadbbaadbddbacbcdabaaacdaccadaadbdbcbbcdabccacbdcdcaaccbdcabddababbabddbdcbddddbaccbaccdcacdcaacacdbdcbccbbabacdcbbdadadabbcaccaabaaaddcacadabbbdbabacddbbbddbbbbbccacdaabbbdcacaccbbbaacdbccacccdabcddbbdbddccdbbbbcbcbcdabcaabaabadacadbcababcaadcdcabdbccabdddacdcddadacdadaadcdcdbcbcadcddaacadbdcbdbbccaabccbccdddacbbdbdbdacdabbadbbcbbaadaacabdcaacdcbbacbddbdadcbddaabdbccdacaabcadcacbbbddddcabbbdbbadcacbcaaccbcbccdcdcdbbddbbbbcccbcccababcdacbdadaccccdaaaabdcdadaaacbdabcbbddcdacbacdcabcdbddbacadcdccadaadcabbcacbadabddcadbabcbcbbdccbbcbbabdacbabcbdcaadaabcaddccdbabcadadbbbbacdcbddacaacbbbccdcdbcdcacabddbadcbcdaabcbcdcacbbddacccbbbddababdcdcbddcaacacdcbccdbbcbdcccddaddcabbacddbcdbccaabbbbabadcaaacbbaacbaddbcadbcdcdabdaaccbdcdaabbbacdbbbacccacccdbdbbbcccacaacddbcbaaaddadccacbadaabcdbcbcbcdacaaabcbaabbdadbcabcabadabdbcbddbbbadaadbcdcaddbcaccacaccdbaabccaaaaaaadddbabdbbdcdbcaddbacababbcbbadcccabcdbaababdbcdacacaabdccbbcdbdccdacdbaccacaabaddbcdddddddabcadaadbbdccbbdacbccbdcadaadbdacddadbbcccbacdbcddccacacddabcbbabaddbcbcaccbddadadabadaadaccabacddbbdbcbcdbbabcbadbabbcaadadbdaacccacccbcdcdbdabbbbdadddacccbdbaabbbbbcadbdbbdaaadcabbbcdbbadcccacbdacabddbbdcdcacdbddabcbbbcdcdacdbbadcacddabaaabbbdbabcbbabbdcabdabbbcabccdbdbdadaccaddabbbdbadccabddabdadabcdddabcddddbbacaccdcdcadddddaaabccaadcbbbdabacbbbddaacbddcdabdcdaabadddcbaddbbbbdaacdbbbcddadcbaddbdabcbdddbdcaccdacadadcdddddcaadbaaaddcdaacadbcbcdcdadabdcabdadcdccddcdacdaaccdaabdacbbdacbcaaacccdbdbbbdbabcdbcacbbaccdbbbdccdaadcbacabaddcccdaccaabbbdcaabcbdadcbddacbdcdcbccaccbadccadabdcdbdbcadbddadbcbbcdbbdbbddbabaccbdbbbdabccadbacbcddacbabaddcbdbbccaaacccbbbbcbbbbacadcbabcccdcdcddbcbbacbccabaaacbabcdcdabcadbadcacbababcabbacadbcddcccacdcadcdcabaacddbdcbbddcbadaacdcaacddbbcbdddbadccaaacaaacbcabcbacaadbbdcdbdbdacbccabbabbdbcdaabcaabaadcdcadbccaabaaaaacbbaabbcbcddddccaddadbdbcaaadcbbcacccdadbcbbbacadcbaabdcbcdaccbcdaacadaabdbbdaccbdddccaccdddbcbacbcdddacbdbcadaabdabcbbcaaadadddcaccddaaccdadadbbdaadacbbbccdccbbcaccdbaddabdcbdaaddcddacabadbabadbdbadcadabdbadcdbaacbacbaadcdbabbaadbaabccbbaadaacdbaccaadadaabbddabbacddbaacadbbcbaabdcbaadbdacdcacacdaccbaabbdcaadcbccadacababcdaabaabacbcbbddcabaccdaccdaadbaacdbdcacdddbbcabbdcbdbcacdbccadcaacdabbacaaaacabcdbbbbdbacccdbbaaacacdbaaddcdccddbaddcdbbabcdcdddccaaddbcaabcdacdacbbbddabdabadbabdbccbacbabdbbdaacbcdbccccacddbdbdbcdbdabbbadadddbdbdaacccbdcbabacacabaadbddbccabbbcbabdbdccbabbdbccbbddcddcaababaadadabdbdbababbdaccdadaacacbbbadddbdbdddaacabdacdbbdbcbbbacbaaaddaddaddbaadccccdadccddadaadbcdccaababcacddbdddbccdaccadbcabaabddcccbaccabdbddbbbaacadddddbbbcaaabbacdbcbcbdbbaccbdacbadacbbcdbaadbcdcacbbbbbbbccaadbdbbbbaaaabdbabbbbcddbcdbcbbbaaccadbcadbabdcaddadcabbcbabbacaaaabbcadcdbdaaadabbcacadbadbdaccabbabbcbbadacdcdcacbbaaaddbbbcadccadbbaadbbcbdadcccbbcbdbbdaacdbabdbabccdccababaaacaacacccadadccadadddaacdbbccbdcbaddadbdbbaaadabaddddddbdadbcadcacdcdbdacbdaabbabbcdbbbdccccddacdababcbabddccbcccccdcbbdcacdadbdcbcdabcabcdbbaacddbababbcacbdbbbdbccaacabcbdcccabccbccbdadcaaabccbbadbadaaacbabddadaaacdbaaabccdcdaacaadacdcaccdaabcaaabdaacbcaccbabacdbbbabddbdaabdaaabacbddabbdbcdaccdaaadcdcacacacdacdcccdcdadbbbcdaacacccaaabbbbabcccdbaccbdabcabbaadaacaabbabcbaddabbaacbacbbadacbcdacaaccabacccdcbbabccdbcaccacddacaccabcccdcdccddbcdcaabcaabbccaddbbcadcdbddabaddbcbcddcbdbcbdbdbdcccdacaacacbcaccadbadcccacdbbabdaadbbcddaacddaaddaadcbdcddaabdaddbdacbdccddbdbbadddccacbcaadcbabbdcdaabcddadbcaaababcdabbccddaacbbbacdbacaabbbcbcacbbdbadcaaccbbbbaabacadbadbcdabcdbcbccaddbbdbcbaddacdacacbcdadbaacccbbbbabddcbaacdcdcaabbabdcdbcdcddaccaccaaabcadabbbdabcadabbcddaddcbbcdadbddcaacccabdbcbcbabaaccdaabbdddcaddcadcbabddccaddcddccaaddddcbbcadaddccdcbbdbacbabccdddacdbbbddddcbccbcbdadaddbbcdaadbdcbcaccabdbaabbbbadadcbcadbdcadcacbaccbbdadcadbdbadddaadcaadcddadcbbbcdcdaaaddbacccdcabccabcaabbcbdbdbbabbadbbaabadbcdaadddbcccdddbaddcaababaddbcaadbaadddccaadabcbdcbdbaddddcbbbabccdbbddbaadbdccbdaddaaccacacccaadbaaaabbbbddbcdbdabacdcdcacacccdabdcddabdcbcbadacbcabbdbcdaccbabacbcddaddabbaadabdcccbbcbddddbadcaaaaadababaaddccccccaddbdbcaacbbbdadbcddaddcadcbdbccdcbbddcddbbcccbddcaadbabdaadcbdaccbdabbcdaadcacbbccdbaadcbaabbaadaacabdbabcbcdccbbdababaaddaabcdddcaaacdbacacbdbaadcccbddbababbdcacaabbabddcacbddabcbdacadbccbbbcdcbadbabdbaacccaaabcdccdcddddbadcdadddbbbbbcacadbadbcaaaccdaddddcbcaacacbadbcccccaadcaaabdbacdbbbdccccdbdadaacdbcadadacdcacdbacdcdbcbdcdddcaabdaccaaddbbbbdadaccdccddddcccababdbcaaaddcbcaadbbbaddbbbbcbaaccaaabddccccaacabcddabaacbbacbabdadcdcdbdcdccabaccbbbcabcccdbbcbadcbcdabdaadccdccbaadadcdcbcadccadabdbaaccdbabdaccbcadcccdccabdabacbbcbabdcdaaddcacaaacdcdabacaacdcbabbddcddcbcadcbbaadbcacadadcbbaccaddbbaaddacddcdcabbddadcabaadbbdbbaaacdacadabcdbaadbbcdcbbaccbdaccbabdccadbdcddcaabbaabdddddaaccbabbcbdaaddcccbddcddddbbcabdcbdabbbbdbccccacadddcaddaccddbcbdadacdcadcdadddaddbbacadbcbbbbbdbcbababcadbacdbcbddbdabcdcbcccdcbbcccbcdaaadadadadddddcadcbcbbddbabbaadbdddbbcbbccddccadccdaaccbaaaabaacaacaddabdddddcdccbcacaddddadbaababaabdcbbabddbbbcbddabbcccbdaacaddabddcbdbaabbcbddbacaadbaabdabaddacbcacdadabcdcbadbaaddbacdacbbccdaddcbabbaddbbdacdbdacbcdabddacddacdacdbddccdaadcaabbbadaaaadacbcddbcccacabaacbaadbbbcddaabaacdbccabbdacccdaabcdddbbaabbbcabdddbcaabaabdcadbddbdddccacabdadacdccbbcbdacbacbccbaadbddcddcabdbaccbabcaabbacdabbaadacbbbabacaacbadabaccdbabbcbcaacabaccdbcddbdaabdccbcdccbbcdddabcadcdbbdacbbdcbbcaadcaababdccdddcaadcaadbbcaabccdcabdadbdcabdcacccbcdabaadcdcacababcbdbdccdcdbcbddbccbbddbdadbacccbaabbdbacddacacbabcccbdacdababcbadcdbccccdccacddabcbcadccabccdbacdbdcbacdadcdcadbbacbadbbbdabcbcadadbdabcddccbaabdddbcdccbbdddbabaaccbccadbbdddbcdcccddbaabdccddbbccadbcbabaccbdbcbcadcadddabdddbcdbaccdacbaaddccbbddbdbdcddddcbccdbdcbdcddacaabaacababaabccbcabbbcaaabadbbaacbadbdcbdabcdaabdaaacacbbaababbabbbacacbbbddabdbddbaccccbbdddbdbaddadaaaddadbaadbbdddcdddbbdbcbcdacddbbabbcddbcbaaababbdaccaccbcdabdababccabadbbcbddbcbbcccabbacbccabcbbcacbdaaadcdbbbdbddddcdddabaaccdcdcadaabdcdacbaadcadaabdadaccdacadccaacddaacacbcaabcabccaddaddaacadadaaddcbcabbdbdbbbacdacdcdbddcaabbdcbaadcacbcabddaabcbbdadbabcdcbbccbdbdbcabccaadbdcabdbccdaaddcbdadcdcbddcddddbdcbadbadacacbbadccbabcabccbaddcbddaccaddaadbdacdadcccbadcadcbdccbcbbcdaacaccacbdbdabbaadcdbbbbcbcaaddadbdcbdcabcddbcdbabcabaccacdbadcbbaccbadaacbdadbaabdabcbcdbadcbbcbbabacbbcdbdadcbbadadbcacdcbaddbcdccccabdcbcccdadbabbbdaadadbaadbdbdabacccdaacbabcdaccdaadabbbddcadcdabcacbabbbcaabbcdcadbcacdacbcccaaabaddcccacaaadbddcbcbddacddcbadaddcdbdcdddcbccbbbadccddbcadbcbbacdddbcbcbbdbccacacadcbabaccdccbdadbbccdbaadadbadbccbbdaddcccabcddaaddcaaddaaabbaaabbaaddabacbabbbcadadacadbddcacdbcbcdcdcacbbccacbbabbaadcdcbaaddccbcadbcbadbbbbacbdcbbcbbddccadbdbaddddcaacaaccccacdaaaadaccdaacdbbbaaaaaaaaaaccdadbcdaaabadbdadbadbdbcbdbddaaaaacddbddcdddacdaadcaccbaddbddadaadaacaaaacacacadbdacbdcdbbbcdbddcacdadcbdcaabdcbbdaccdcdabdddbdcacdcadbcaaacacdddbcdddbabbddbaccaddbbabcadccdbacaddadcddadaaadbbcdaacbdadbcbbbabaadbaaaacbcababcdccdadbcdaccccdcdcdbdcccacadabbaddbdbdcddccbabbbdcbcccdcccbcdcccadbadcbaaaacddcdccaccaccbcacdddadcbcbddcddadbdacbdbbdbaadcaccbcaacdbddaddddadcbdbadadcaddaccbadddcdadaacdcdbdddcbbdcaabdbdddcddbcbcdcadbdbcabcbdccabbabadbcbdddbdbbcabbaabaacdcbacbaacacbabaacabbaccbcbabdcabbadbcacabaccbabdaabbbcbdbadddadbdcccdabccdcbdacbdacdadababcdaccbcaddbcddcbdcdbadcaaadbdadbcbbbcacaadabdcccbccdcdbdbacabbdcacddcdcbddbdbdbcadcaddbabbbcddcddadbcaaddabbcbbadbabccccabadddccdddaccbaabcabccdcbdbadddcddcbdbabcabcdbcccadaadbadbabdcbdcadcbadacacdbcccadabccddacdddacccbddcacdabcbaabcbbccbbabaaacdccabdbdcbcaadabbdbdddbbccbbbaabdadadadbbccacbcabaaacdcccdbccaabdaaaacccbcdbddabccacbbbadcbcbcbddbaaddacdccbddbccbadcadbdadddacaacadbccccdbcbdacacdcddbccdaadcbacacbcacbccbacbddaabadcdcdbdccabbccbdbdbbcbcbadcabbcaadadadcbdbaabcbadaaaabaadbacabdddacabbadaabccdaddcbcddbbdacbccdbbcdadabcaccbdadbacaadbabccbcabaccabdcbadcdcbaaaddbcdddddccbbabcbcadbcddacdbdccbdcbdabcdababacabdaadbcdcbddbbcbabbadbcadaccacddddbcabacdaacdbddccccabccbbdabdbdbcadbbbbabacbaccbabcddaabccadcbbdddccdccdacdaaabbdccacdcdcaabcaabdcaddbcdddddbcdddccadaccadcccaabcbadabadaaababbbccaaabccaaddabcdacdbbabadcdcdbdcbbbdbabbdcbbbddbabcabbcbccabcabccdaabdacadacacaacbdcbcadaddcdcababaadaaadcdbcbbdddaacbbaccacbcaabaacbdcdabbcddbaacdccccaaadccdbaccbdddbcdccadcaddcdbdabbccddaacbcbdcacdbbcbcdbddcdbccdbbbdcbccaabbbdbcdabdcccdbdaadadbabdabbdbddcdcaddabadcccccdbdccddbacacdaadcaabcacbddbdddbdadabacbaddaacddbbaccdcaacaacabbdbcbdbdaaacbaaaaabbaddddcdaaaaacccaadabaddacbabbccaaaddccaacccacccaccbdccabacdbcbabdabcaddbadadadaddcacaadababaccbbbbdabdbdddbacbadbcbacdbcbbcbbadbbdddadcdaaadbbbaaabbcabddacacadacabbdccacccdccdadcbadbbdcadcbabaacddaacdaabcdaadababbbaacadbcdbacddcccdadadbbbdcdcaadacddaadcabbcbdbbabcacddabbdbabbddabbcddcddabadcdabcdacdcddbcddbdbccdcdaaacdabaaaaaadbddaaaccdacccaabaadddbaaaaacadbdcaadbddbbdcadcdcaccdcdbccbccbbddadaccbacadabbadbbcabbcdadabcbbaadbaacbbbbccbccbacadcababccadbcbcccdccbcabddbaaabbdadbcdbcdcadaaddaacdddcccbaaadaddcacdacdabadaabbcacbdcdbbbddabcddbabcdcacadaadacbdabdaaadaabaccaabbbabbccaccabdcccdbbccdddaabcacaaddaabccddbcdadaaaabadabdbbdddabccbcaccbccddbaacabcbdabacdcdcbbcdabcabadccacbacdaabcdbadccbcbbcabbcbcadadccccdcbddadbdadaadaaacdbdcacdabccaaacccbcaccaabbddcbabacabaabcaaccabbddbcabcccccabbbcadbcadbbbdbcaadcbdabaaddbdabaaaadbacccdbcaccacbcbbaacbaabbadacbccacaadcadddbccaccabbacacbdabcaccdcccbbaabbddbacacdaacabcaddcabbcdadccdabbdddbbddbbbcacbababcabadbabdbddadcdcdaacbcbadddadcdaabdddcbdbcdbdbcdaacbbbbcdbccbbccdabaaabbabbdcdcaacbdbdcabbabcbbccaacbacadaddbbbddacdbcddcbdbbdaccaabbbcaadacaccbddadcdacaadadbdbabaabcbccdcbcaddacdddbdbcdcbddaaaaabddbdbdcccddadccadaacbaacdbbdacaadaadbcabcdacbaabdbdabcdcdbbccaabaaaacbdbbdcacbccdaabddaccdccdbdaaddcbabdcdabbdbcdbdaddbcbcaacaabbbcccddadccdbadcdccdadabacbdcdbabcbdcadbddbaabbbcbbcdadadabadcccdbcabcbcadbaabaccbddccdcdcaaadcabbadadcadabbccaabcdccacbbdaabddccbddddabaacbaddaddccacccccadcdaaaaaddcaaadcaccdcdabaacabdcbdbccaddbbbcdaaaaccbdbbdaccbdbccbbbbbdadbdaaaacccdcacbcaabccabdbadabcacaaacccdbcbddcccaddadbcbdadabcabbdbadbdaaabcacccbbbadabadbacdaadbcbdabdbaabbacbbcccadcccadbdcbadcadcbabbdbbaddddbcbaddbdabddcbcacdddbabccadaaccdaacabcbbddcbaabaacabdacdcbbcabaccbddbadbdbdcccbaaaabbdbbcccddddcbbdddabcddccbcdddccbdcdaddcbaacbacbbdbcacdbbdbacdddbdcddcbadacdbaddbabbabdaaaabcbaaadabdbabcaccbbbabcdaddcbdabdbacabbdcabbabdbdbbaddbcacaadbabaaddadaabcccbcdadcbccbccdcbabbdabddcbbdacbaacaddccadbacbddccacbbbbcbbbdaabccddcadccdccaaaacaacdaadbacbccdcacacdbaabdcdaaaaccadbaaddcacdccacdcddbdcdcdbadcbdbcaaaabbcabdbdadbdccddadcdbbdcccccccccbccaaadbadbaabdaddddccccdacaacaaddbaadcbaacaaacadcabdbcdbcbaddcadacbabccccabbadcbcdadadbddaaddcdbaccbbcadbdbccadddbabcacbcdcddcadbcacdccbdcbaacabbdabccdaacabbacbdcbaccbacaacddacdbcdabcbccbbabccdbbccbacbbccbbbbbacbcacdcabddbdbdbbbbbcabbccbddcddacadbdcabccdbaddddbbddcbbabdaaacdadcaddcccbddaabdbdcbddadcbcdbacdaababbccaadcacdbddadddbbdbdbcccdabbbdaccbabcadbdcbcdabbbbdacdcddbbdaaccbcadbccadbcdddadbcdadabcbbacadcaaabcccabbaddbabcbaddacdaabdabbdacbdccaaccccbdaaddcbbcadcdabcccabdcaabcbdccbbbcbdcbcabdacccccddcdaacdaccbbadbabacacacbbddcccccbacbcbabdaddcdbbdbbdbcbbcdcbaacbdbdbbdbbabadddcdaacdaddbcababcdcdcacbacabcccbacbdbbbcbdcbdadbaaacabcdbadcdadbcdbdaacbbaaadaabcbddbbcadbabacdbaacbbbabbaabbcaabbccabdbbcaddddbbdbccddcbaadabadaadacccbabcdddbdcbdccbcabaacbccbcbaddacacddbcbdaabbcabadcadbbdbdbdcbbdadacabcbbcaaddcdcabaccaddbbbdacdbbdccbccbcabdccacadbcbbabbbacacbbcdcbccccaaabbcddcbbadbcbcdbcadaddacaaddabbcdcaabaadbccbbddcddbaadcbbbdcbdacdbcddaadcadabccababbccbababcdbbdaacbabcdacbcaccccadccccbccdbcbccadcddbbcbcdddcdcabcbdccdbbcabdaadbacbdbbcdbcbdcdbddbcadccabcdaccbacdcaddcacabadacaaaadaddbaaccbdbbbaddccbaadcbbdbcdcabddbacdbdbdacddabaacaacdaacdbabcdddaddbddddbdaaacbdacacdbbddabbbbdaabbdbbbcbccbcbabbbbaacbdcdcddddbcacbadabdbbdbccacbadbdcccabbdbaacadcabcbbdbdaaaabdadacddcbdadddcdaacddbdbcaaccabcabcdddccdbcbccddaacbddacdddcacbabbbbdcdaaabbdaadbcadcdaabbaacccbcbabdbaddadcdcbcaddcbacdcbcdbdcaddcbbdddadcbddbabaadbbcddbacdcacddccbdaccadccbccddccbdcbccacabdbcdddbdbaabddbbbcacdadddcabdbbcdcbabcadacaabdccddaddbbcacbdbcadababdcbddaabcdcbdacadbbcbcaaacccadccbcdadbdbbbcbabcdbcccacadddaaabcbbcacdcbacdcdcabcacdaddadcdadbddaadbcdacadadcacabbcbcbbabdacadbcadbccadccbcaabddcababcbccbaaadcbcaccaadcbbbbdabddccacbbdcaadbdbadaccbacdbadddabbacabbcddaadbdababcbabbaddcabdcdbbbcacddbbdcbcddddbbbbccdaaadccbacdcdcccbddcddabdccdaabadbababdbccdbbbdcbacadaabbbccdbacaaddbcbcaccdccddbbddacdaaadacdddcabccccbdbdddaabadddccbabdacbddaccdaaadcbaadadbbabdabcbbcdcbccdbddbcdbacdaaddabbdbdbaaaacbbbcccccbaabacddccbacbddcbbdbdcacacabccabaadbcddcdbbdccddbdccbbbdabbccaaccadacbdaaacdbbadbaccbacdadacaddddaadbbcbcbcabaaadaacccbbbdbbdbbbcaababbbdadbdbcbdacadbdbbccababaadcadcabbaacbadccdccaaacaacdbadaccbcbdbbcdcbdacbdbbbcddaadddbbbaadccdabaabcaaccbacdccbabbccacaaaaabbdbccbdbdacbcbadbaadddcaadaaddbdaddbddaacbadabdcabbacbbdacbacdbbabcbcbcbcddacadadbdccacccdbdcdddbcbcccaabcddddbddcacdbacaccdccdcadddbcbaadcadddbcdadacadbbbadbdbabccdcacbdacbdadcdaacabadbaaddccdcadbdcddcacacdaadcbbadcdcddcbcbdabbdbacbcdbdccaadaadddbbadacacccbddddabacbadaddcbbaccbadcbacdcccdbbabbbcdaccdaadddadaabadabbaddcdbdaddcccbbbcbdaabcdaaaaadccdcdaacabdcbbdaaccdddaabdaccddbddddccadaccbdcdbcdddcdacbabcddacdabbdabbcdcbdacbaabcdbdccacdcbbcbcbddaaaacaacabdaddcadabbddbdcdbacacdcccadabaaadacdcdddbaabadacaacbddddaaccbcbbbbcabbacdbabcdddbacbbbcdbcbacdbdaadbbcbabbddbdaacdbbbabbdabcadddbbbcbabdadcbbcacbcbcdadbdbcadadbccddcdaaadcacdcbdbcccbcccaccdccdaaccaccbabdabbdacccbdabdbadcbdabadbdbccbacdbcaaacbccadcbdcaabcabacbbabbdbcadbcdddacbcccbaaacadccdabadcbbabcbbcaaaabdbacbaacdccacddbccbdbbbddcbdbccdcadaaccdbcbaaddbdcaacabadcbcbbdabcabdbaaabaaccdcacbadddbbadcdcbdcbababcdcdbdddbcdcbbadabdbddddabdbabacbdddbbbdbdddadcdcdcabdbcbcacbaadbdaabdcdbccdacccccaccdadddbdabbccddacacdcdcaadcbcbbbddacbbddaaccbdbddadcaacbcabdddbbaacccbdabcbbabadccadddbcbbbccabddcbdcdbcbacbcadddcddcaaccbadacdbcbddccdbbbbacabccddbbdcabdadcadabadcdcbbacaccadacdaccbcadcdcdbbccadaaabadcdadddcaccbbddacdacdacddbccaccbdbbacabdbbabadccaacabcbbdbbaacbabadbbdaabaadbcbbcdadddbbbcbabcddbbcccddbabcabdbdbaaddbabbdaacadaaaddbbbaccaaacccdbdaaababadbcdbbcdccaccbcccbcbdcbdccabcbcbcbccbbbadccdddabadbaacbabbcaddccaddcbbdaadcadbaaddcbaddbcabdcdbbadcbdabccaabbabadbaabdadcbbcbbccaaaabdbccdabbbbadbaaddbbaaacacbabdaaaadcbaccdbcbaabdabadbbdcbaadbcbabcadadaabbdccbbdcbdcaddbabbaaccbacdacabdaadcbdabbaaaaadbbcddababadadcaaddbdcbbcacbbcabbadcccbcadddbcacbbccdbdcadcadcccbdbcbcbddccacbbcbacbbbaddbccabbdaaacdcacbdccbddadcdaaaabaadbbdcdcaddddcaacdccbcbcabbdcaaaaddcadbcbcdbbcadabbdcccdadbbacacadbaccabaddbddbcacaccbdaacabaccdbbbaddcaddadbabdabcdababaabbbababadcbbacbbcbdbbabbbbdabccbadacbdbaadbadaacacddcacadbcaababcdabdacbdcdbdcccbacabddabbbcbbdbaaabbabdbaccdaadddccacbbbbdcdadababdddbcccadddcdaadabaddaabcdadabcabaaccaacadcdabdbcdaabccdcdadaacbcbccbdaadaddcdcddbbaadcbbcabacdaaacdbccbbadbadaabdbddcbbdabacdddccccadbacaabaacaddcacbddcbbabacdcacdaddcadcacdaddccdabcaaacbcdabadabbadacdbdbbbdaaddddbaddbbabdcbbbcbccbdabddcdaaccccdcadaddccdcabbabdccabbabacddbdbacbddddbcccccbcddddbbcacabccbadbabcbdcccccbababdacbccccadcaabbcccbbbcdccbcaddcbdcabcaaaabccaddabdccbcbdcbaacabddcbdbddbbabcadccadbbdbdcabadbaacdcaadcccddcdbaaccdbdacbbabcdaabbccdbacdbbaccdadbbbcbacdcbdbacbaaaddacabcbbccadcccbdbbdcddcabcddcbcbbbdbadaaaaababdbadcdddabccbbcbdcccbabcaddbaadabdbbabcbcaddbcadbbddbdbbbdcddbaadbdaacddccabdadddacdbddbbcadadaabbbbccaaaaddccdcbaaacabbbbaabccacbbbdcdbacadbbbaddbcdbdacabbcdbbacdaacccbbbacdcaddbbaaaacbaaabbbabdcdbbadbaacbbbaadbcddbdacccbacacbcaacabdacccdaadaadcbbabddabdbdcccdacababdddbccbdbbbdbacddbbcaadbbdbdcacabdabbcaaccbabddccaacdbaccdcacdccbdcbadabcadabaaabaddbddcdacbdbcbbcabcadcbbdcaadbacbbbcbacddadbbaccabddabbccbadbccabdbddabbbdcccdadcdadcdaacdadbcddbabdbdbcdccdabdbcdadabddcbdaacaddcbacdcdcccdcbdbbdbadbbdbdbdbaacacbaacdabcccacadacbbdbacdbccbdcadadacdaddddaacaaabbbcccabbcaacdabbaacdbbddbbaaabdabdbdaacddadabdccccdddbaaaaabcdcabdaacdbcaccadbabdaddaccdabddaabacdcdbcbbdaaadddacbbaacbdbdadbcddcbacbdccdacbcdaddccabbbbcabccccdddbbcadbabddcaabbdacdadcbadcbcacbdadccacddbbdacbabcbbcdbdcaaaacccdaabcdbcababdcaadddaccadadcdbbbcdcbadbbabacdbbadbbaccbccdccbacccabcbbddbbbabcaadacbabbbcbbccacddddaccbbadccbbaaabbbccaaacadcbdcaacdacdbcbaadbacddabcddabbdabbcacaddbddacabcccdadaacddacdccbcaaaccdcabdadcdbdbdcbbdacbcccadacddaacaaddbbacbbbddabdaacddcddaadaabadddbcbbacbccddaddadacaaababbbcdaddadbadacbccacadabccadacbaccacdbddccadbbaacdacacdbadaaabcddbccdaccacdcbbbacaabbbaaabdbbdbdbadaddcccdcaacbdaccdbcbcddadaaccdbbdbbccababababdcddabadaabacdddacacddbccdabbbcddacdabdbcbadbadacdbdcbbbbadbbabcbcaabdaacdababcccbdccaabdbdcdadccacbbbabbccccdbacabaadbaccaccabbbcaacaccabaddaabdaaaaacaaddabbabccbabadbabccccccbcdaccacdcbadddabdccdcbcaccababccabbacaabbbccddccabadcdaabbbdcaaaadacdaadaccbaaccbacdcdabbdacdaacbcccacddbccbadddadddddcddacaddbcacccbabbcdbcdaabadbbacdcdaaddcbabbddcadcabcdadcdccaaccabdcbabbddccaaaacbabbdddabccabcaabbcdaacdccaccaddadaccaccbcaaacdbaabdacacccacdaacabdadbaacbdcbcabdcbbcabbbbbcabcadabcbacaabbacaccadbbcbdcdbbbcdddaddaaaddcccbbdbaadabdadadacadbdcdbbdcaccacbabbbcdacacadddcaaaccabdddabccaccaacaacccbbbcbacbadabbadaadcabbadcbacabcbcadbcacdabadaabbdcaadbccccdaabdaacbadacdcbcaaabcdbbdcabaddbbbaadbadacaadadabbdcabddadaadbdddaacabadadabbcdaacccaaccabcccbdbbddcdbdbdacbbbbcdddccdccdccdadbdacdaddcaabbaacdccbcbbabbbadcbaabadabdbbbcaacddcbbdbdbaaabccaaacbabbbcdadccabbcdacbddccbabccadbcdbaacaabbccbccccdadbaddbbcadabccdddbdabaccccaddcdbacadaaaaacbcbdabbcdadacbdbbacdadddbababbbdbbdddcccbabcaccabdcdacdbdbabbbbdaaaadaabadadaaadaaabcbaabbccacadabccbbccbcdacdccdcbdbccdaccdcbdddcacccddbddacabbbccdcabddccbcaddddbabacbcadadaadabbdbaabacddccbcacacadcaccbdcdaddadbdcbdccccdacbaacacdcbdbacbdddbadaaacaccddacbadcacdbaabbdcaaadccccdbddabccbbccadacaaddcdbdbaadbadadcdbdaddbabdddbbddbbaabcacabaccabaacddacacbacabcddbddbaadbcccdbabdddcadabdaddcbadcbbddcdacbdbbcacbcacbdacbcaaabbccbcadabadabcbcbacdddcbbbbccbadbdbdcbcadddaadbbbbabaabdcdbccccacbbcdaccacadbcbadbbdcdaacaabbdaadbbbadadaadbdbdaaddddadcdacbabbcaacdcdddcdcccbddabbbccbcadbdcbcdacbcaaabddadacbbccaccdaddddacaacdbbacbcccacdacddabbdddbbbcaadbdaacdbbaaadcbddadacccbadbbddaaababcaacadbcdcaaddddccddbbdabddbdbcbbdadccabcbbcacdbaabdcabaccddadbdcacadbcbadaaadbbabdbddddccdbcdcbdadcdacdbccbcacaadddbbbbbabcdcddbbabbddddbaacacdcdddadcddcabccaabacbabbcccdccaabacaadbcabacbdbcdaaabcbcbcabdbbbadddcdbbaddaadddabacdcaacccabcdaaccddbddaacbabcccadbcbcddbbcadababcbddcbaacdadadcdacbabacddccddcbaddbddabcadcadcddabadbcaddbadddcccacbabdbcdacaddddaacbbdaccadbdaccdddddcbaaabacccddcdcbcbdabbdcbdacdcbdcabdcdccdcdbddaaccadaaadabbcdddddabccacbccbaacbbbabadddccacadaacdbadccdacbaacabbdaacbaaadbabdcdbcbddcaabddddcacdddaaaadbcabcabbddccbdaddbbcacdacdbdbabdccddabbddaadcdccabbdcdcbdbabacccadcabdadacdaaacbcdadddacdacdabbdabcbbabbaacaaddaacddccdbaacdaddadcaadaaacadbaacbdcaadbabbddcdabbcbabddbcddbadcdbbddbbbbbabacadabacbbcabaabdaaacabdbcdccdcdddaddbdddadcddcdbbdddcaacacdbaccdbdddbacbaababbaccbcdaaabacaaacdbdbcabbdddacabdcbdcbddacadabaccccddaccacdbbacdcdaccdcdccbcabbbaddcabadaccabbaddacdcdccbbadbdcaccbddbbabbcdbdbaccabacaabaddddaadbbdcdbdcbcadddaaddbabaadcdbcbbbdbabbcadcacdacabcaccaddcbdabccbbbcabadcccbcacdaabdbcbdacdbdcbcadcaabccbcdbdbdbdadcdddcaadbcbbccbdaacdcbcbcacbbaddabaddcbaadccbaadacadcaadcabbccdcbcdacbdadabcdaabcdacddcbbcaaadadabaadbaaaadcddcacdaadbcddadcaaabababbbaaadbbbccabcbdbcdcdcccdbbcddcccddcbddddcddddcdaaaaaccadccdbbcbbbbcbdbcdbadbcadddcbdbcddbaacdaddaccdbdcddddcadcbacaacabbacadabbccacabdddddbcabdabbddbccdddadbbaabdadccabadabbbaacaabbbcbaccaaaccaaabadbacdbdadadcccbbbddcccbbbabdddcaccdadcdabcddaaabddbddcacbbcdbdbcaabddbabdbacbbbbccacdacccbcbddbbdadadcaadbbbccaccadbbaabdabbcaaaadcdcdabdbaabaaaccadcdbccdadabccdbdbbbaccccbdbbcadcbbcdcabacbcaababcddcccddbccadaaaddcacacdbdccbbdcdccdcabbbcccbaabcabadddacdcabccdbdcabacdcadccdbacdddcdcbcdccdcbcdcbbacdccddadcabbbabbdadaaadacaacdbbbcbbabaabacdbbddbbaddcbcdcdccddaadabbbddacccccbbbcdbcacbccdbabcbcabdddccadadacdacadbcaccccccbbdaccabdaaadbaaabcacbddcbcbbbbdaddbbbacaacccbbbaadddcdaabccccbacdaadabdabbbbcbddaacbabaccbbbbdddacbdccbadaddabdaddcbdbccdcbccdbadbcdccbbdbbcbcccbacadbddccabbdbcabddaabcdddbcdbabbcbdcdbcddbdbdcccbacaaaddcacdbadddaacabdbbccbdaaaadbddbccdaacbbdcbcaaccdbdbbaabdbddaaadbdcddabdccabbabadbaabacbadcdbbcaaababbbbdbdbacdaabaddcdcccdaabaabbcddcadaabddabadaddbdabcbacbcbaaaabdbbddabbabcdacaabdbccdaaaddbcddccbdaaadcdaaaaaaadadcccccabddbdacdcdccbccdbdbacbdcabaabcacdbdbacabbddcbaaababbdbcccaabdcbadaacbcaababadbbaddadabbbaccdcbdbccdabbbacdbcbabdccdbadadbbadadcdaabddcbbdbdbbaaabddcbddbabababaaaadccabbdabcddbdcddcbcadcabacdbdbbabbbdcabdddbcabaccdacccdbdcddcccbccbddcbadccaddccadbcadcdbbdddaaabddbcabaddcdcccaacccacaddbccdbddbddaaddcbcdccaaabcacdbcdbcbabcacaddabacaddabcdbcdbdbcbddbbdabbddbdadccbaddbdcacdcacbdbacabbbcaaccdbdcabccdcabdbdaaabdcadbcadbdbabadcdddbbdadcaddcaaddbbbdadbbcdabbccbabaaccdcdddbcabbbaddddbcddcadbdbddbdddbdbbbdbadabcadbdcbcccbbdbbdbacdacacbbacccccbbcacdcaadcabcbbdcaddcaadaccbbbbbcbaccbcacdcadaadbbaacadbbdacccbdcacdacbaccddadadabbcabacadbbaabaccdbacbdcdcaccacbacdadddabbbdddcabacbaddcbcacbabccbcbadacbadaccbcdacaadacabbdadcccabdaabaccadacaababbdbcbdbaddaaddadabccbdccabbcadcaacadabccaacddacbdbaaacabbdccadbdcbbaaccabbabbdcbcdaabdbcabbcdcaccdcacdcbcbbdccdabbdbcbcddabdabadddbdbdbdbcdbbcdcccadcdcdcccacddbbddbcbcdcccdccaaccdcbbaaccdabcdccbaabdabacdcaccaabbbabcddbcddaddadcdddcbbcdacababcbbdbadbdabbadbccabdcdbcbcaacccbddddbabdacbacdcdacbcaccdaddbdccbdcabdabbaddacdbadacbabbcbdcaadaadcdccacdcadcdabcddcbaaaacddddbcdcccadcbacaaabaccadcaaacaadcadbbbcdbcbaadaaaddbccbbbaacabcacbbabdcdacccdbacdcbccdbbbabaacddcaaaaabdaabbdadbbadcaaddcdddbabccaacdcaaaabcdacaabddbbcaabbdbdbbdbccabacadcbacbddbcaabbaaabdbbbbcdacaacbadaddccbbbbdadccaacbbbbadcccacbbcdcbcdabacccacdcccaadccbaccbddcabbadbabaacbcbabdcaddabbcbabcdbbadcabcddabdaabaadddacbbddbdbadadbbaaddccbbdcdcdcabbdabbcbcaadacabdccccbaccbcddddbaccbddadccdabcabcacdbaaabdcbbbcaddaaccacadbabaccabcccacadcaadaaaabadcdcddcaacddcbcdbacdacddbcaccdbccdacccdbcadadbbbdbcacbbdcdabaadbdaaaddcddbcadbdabcdddccbababaaabbadccbdcbacdcbadbccdadcdbbadbbabacabbbcdbacaaaddddcdacabdacbbaacccbdacdcadacdadccbcbcaacababbabcdaacbbcdaadbaabcaadcbabadadadddddbabccdccadddadbbdccddccacaaadccddaacdbdddbccdcbdbbdcbdcddbcdabcdbdbaabacadaadadbcabcaaddacbbbbacbdcccbbcacadadbaadcbacdbbaaaadacdacdadcbddadbbcbccbdcdbacbdbbcbdbbbddaccadadccdbcbabcddacccbadddadaaacadbbcdcdabcbaddcdabcadcbbadbdabaacabbcbccacbbacdcaddbaacacdcabbabbbbcbdbcacbabdcbbdbaccbaacaaddcadbdacdddbccdcaabbabcbadabdbdabdadaaaadaaabdbddabdbcdadbdcbbdbdacddacddbaabccabbddddbacaadababaacdcdbcbcbdcddbcbbbadaaabcacabdbcccbbbabbdcaaddabadbcadcacaabbdcbcdababcacbacddbbaababbdcdcbaaadacdcdddccdcabdbcdacccabdaabcddbddaadbddadadccdddccdacbdcdbcbdbdddabbcbdaacacdccddcbbccaaadabacbbdaddadbdabdabcadcdaddbaadccabcbccbccbacbabdaccaaaaddbbcbdbaccdaaaaccadaabbcddcaaccddcacdaccccabdaccbbabcdaacabdbacbdadddbccaaaacaddaaddcabaccdbdddcaddccadbddaacccaccdbbacccdbbcbbdbacaaabbbcdadddccdcccdddddbdcadacddcadbdabdddbdaaacabbdacbbdbbaabcbacbcddcddcdcdcdcacdbcddacdababcaabdcacdacbddaaaacacccdbcdcdddadaababcabdbbdcadcaccabcaacacccadbbcdadddabaacbdaddbccdbaaacdaacdcddbdcbcccbbcaadabdaddccccbdbdbdcbbabacdccbababcabbabcbccabccaabbbaaddcbabcadccccdddbbddaabcbabcaaaadcbcabcaacdbdbaddacbccacaaabdbabdddbbbdbcbaddbccbbccbbdcdbcbaadaaddadbbdcbabbcdaadabbccadbccccaaccbddbdbbbadaacaaccdacabacdbbcddadbabdadcadbcddbdcbcccccbddbbbdbdbcaaccdddbbdcabaccbcabbadadccaaadcadbdcdaabdddaacaccaacaaacacdcdadcbadacbbbdaacdcabaddcdcdbcdbccabccdacadbadbdcdbbbccccbcbadccdacbcbcdcacbbbabaccbacbcabaccaadbdcbaddcbbbcdaabbdbbadbcaacaaddaadcbdbddacdabdbdccdaccbdbaacdacaccbcdcbabddacdcbdccabadbdcbbadbacdadcbcddddcdbcbacdccbacdcdbbadcbcaddbadadabcabbadcdddbbaddccadddaddcbddbcdcdabbbcddbbccbcdddcbcadaddbdadccdcadabdcdaacadbbbdddadaddcdcdbcdbcbbccabadcdcccbdacadbcaabddcabcddaccabbdddbbacdcbccaccccddaacbdcbabbadcbbbdbdccccbabbcabcccdcdbbdaddabbdcddbdadddbbbaabbcbccbadbbaadadaccaaaccdcbaccaaaababbaabcbbcbbbdddbacccdbdcddbbbbcddcbccbcdddaaaacccaadcadacdcbbbdbadcdaadadacacbcdbabcbbcadcdbcabdadbacacabccbabdbbabdcaddbaaccdbcdbaabbbcacdaadcaabcdbcddbddbadbbbdbbdcccbcbcbbcbaddbbdbdabcdadadacbabbcddbcbbcacbaaccbaaaddbcbadcdcdccacbcdccaacccaaabdcaacbdaccbddadddbcddabdacddbaacadbddcbdaccbcdbbcbcbabbdcddccacaaddcaaccddbdaadadbbaccdacdcaaccbbccddcbcadacbdbabcaddacccbcdcccaaaaaddaabbcdccccaaddbddcadadccabccbabcbcdbaccadcaabcbdacbcbbabcacbaaacaccdabadcccacbcdccbbadcbbcdcbdddbdacdccbcdbcccbabcddaabcaababbbcdbddbababbdaabbcbdddabaadccadaccbbadcacdccddbbabddcadbacabadaddbbbbaacaccacdccaddaaadaaaccdbcdadabcaadabcbddddaababbcbacadadcbabadccadaaddaddabdabbccdbadabcdddaccbaddbaccbdadaccaabdacbaaaacbbbbbabcbdbdaaacdbdbbabbacbbcabbacbcccdddbcbadbcdbdadcadddccbdaccbcaccbaacadcdbcbdbaacdabddcaccbbddacaaadadacdcacaacbacbcdccdcbdcbdbdbcdbcdcccbbcccdcdccbcacaacbabbddcdcdbcacbaabcbbabbadadcaabaabdadcaabbbcdbddcbcadbaddaadcccccdcbaacacbdcdcbaaaaccdbaacabdcbaaccaadbbbbadbababbddabdaddbbdbcbaaacbbadbcbadabbccacbcbbccccaacdcdaddcbddacbcacddbbaadaabdacaaccadbabbbcabbbacbabbcaadbaacacdddbdabdcdbbbcabdddcabddcbbcadcdcdaababbcbacbcaccbabcaaabbbcdbcaaacadadccadabbcbadbaaaababcbdabacbdadabbcabdabbacbcbacdcddbbdcabcdccbbababbbdabbacacbdcbcacadacadcaddbbabdababddabbcbbddcddcbcccbbdddacccdcdbcaabacbddaabdadaaaabdcccdbdacadccccbcadbbaacdbcdddddcdddcddbdabdccddbbaacaabbaaccbcadccacaadaddbcbbdccdddccdadadadabaddcabdbbbdccdddacbdadcbcddabaadbabdbadddccddacaccbaababadcdbdbcdaadaaacdbbbababddcbbccdabcdabcdadcbcaabcbddddaadddadacbaacbdcbbbcaaddbbbcbbddbabdcbaaabbdaaccaabddacdccdbbaddaabcbdcacbaacacaabbadcbdaabdadbccbadccdddaaddccadabcacbbadcaadccbcabacaaaaaccbbbdbcabdcbbcddaccadaabbcdbbcdaabbbbbbdadddbcbbcbddbbbadddccaaccdbdcdcccdadbacdabdaabbabdbbacdaddaaccbcbbbaccadacabbbadcabbaccbaccaadcdacadacaaaaddddbbddabcbacabbddacbbccbbdccccdcacacbdcaddaccbdcdcbaccabcdcbcaacbbbccdbbdaaacdbbcbcdcbdabdacbcbbcccacbccaddaabccbdddabbdabacaaccbdcdbacabaddbccdcdbaadacbdbdbacccbccdbadbbcdadaabcbbacacddbadbbbcacacdddcbdbbccbcabcdbbaadcaccabaccbabbcbbdcbdcdbdbcbbdaacbddcaacbabbccbbbadccbcaadacabaacccbcdacabbddbdaccdbcdddbddbbbaacdbdccbbdbcdadbbbddcddcbdadaddabccadabbdbbacacaadbaddbaaaadddacaddbcbcaccbbbdabdcdcabbdabddaaaabababdccdcbadbaccbdbcbbdabbababcdddcbbdacaacabdcdacdccacabadbabcddcbbabbcdbbaacabaadddbbddabbbacadacabcccccdddbacbadcabcccbbddaabdabaabbabbccadadcbbdcacabbbccbabcddbcaaababaaadbcadccbbcacdddddcaddccdbaccacbbcbcbacdcdadddaaadbdadbbdadcbacbcbbaaccbbaadcdcbdbbaccddccdbdcbadbbcacccbbbdbbdacabdbbdbdaadabdcaaabbdaaaaabcdddbddaccdadcdbbcdcbabdbddbccbcdddbbbdcdaacccbadccdaadddcadcdcbabccdbddddadadbccbacdaadccbdcacdbcaaadabbabcdbadacadbbcbabdcaabdaccddbbcbbbdadbacadacbbcccacdddbddccaccbbbbbbdadaadcadbabadaadabaadaabbdcbbbcbddbcddbcaadadaabdbdccdbcbcabbabaadadbdacadcdaccbdbabadbdcabadddcddacaddbcbddabccaccdbdcdcbadddabbbdbcbcaacdcbcbdacaaaccbdaaadbbbabaaadaaaaddcadccdcbcbbacccabbbbbcdaccadbbdbaccadcdaaaccdbbbdcaaadadabbccabdcaddcabcbadaabbdbdcaadbdcccbadacbaaddaacbcbcabacbacbcdbadabaabdacbdaadbddbcaacbddbcbddccdccdcddbadbbcbddccddadadcaabcdcbcdcdaaddcbcbbabbccbdcddbbcdcbcdadabcdddacbcadbdacdacbbacbcccccabacbbabdbbbdddbbccdbbdcadcabbcdaaccabcbcbcdcbbaadadbbdaabcbabdaabdcbcadbdaccbdcbddabdbbccccdddddaccaacbcbbcbbdaccccabbccaccbddabcaaaadccbabbcaababadddccaacabccdbabbbaabacbdadaadbbabcbabdbbabddcaadacabbcadbbbbdccdcabdddcacddbabddbbacbbadbaacdddcbdcbbaaacaddbdcccdcddbdadbcbbadbbbbaadacaacacabddbaadcbdacbcdcdcddccdccbcdabbbacccdbdcbcddcdadbcaacadabbddbbcbacacdaacbacbcbccacbacacbabaaddacbdddbbbddccbcbbdbbbadcabbcdbdcdcaabbcadbacbdadaddadacabacbbdcabdacddaaccababaccaabbdcdabccdacdacccdabbdbcccdccbcabdcbccdcbacccabaabaabdbcadabbabcdbdbabadacdcdbbddacdcdcdbcdcaaaaababccccddccdbbbacccadcaadababdcabddabcbaadabcccdcbddbcbdbccbaacbcaabdaacbccdbaaadbcacaabcdcdcdbbbcaaaabdcbaacccadaaacaaadbbbcaadddddddddacbdaacbadccdbbbabcbdbdbbcddcbbaacccaabacccddadbbbabdacbdccdcbcddadaadbdbbbabccbcbccdccdbbbabcbcbddccaddcabdaccbdbaddadddcbcdadabcadcdcdddadccadbbddaaacaddbdabbcdddcbaadcbdabddababbadacabacbccbbdcdabbabdcbacdbbabdccbcbddacddccbbbdddabbaababddacbccaadccacbcbdcdbaaadabbababcddbadcddcbdacdbcbddbbddcbaaddbabaadaadadbbbbbdcaabddcbcbdddbaabcdcaabddbbaaaddaabdcacbdcdaabcadaadacabbbbabdbbdcddccbadbacbccddddccbbadacbbcbacdbaccbbcbdaabdaaccaabbdabbdadbccbcdabadbcccaaacaaabcccdcbbbccbaabddacdbbbddabddcacbcccbacccdabbbcbbbacdddcaddabbadaabbabdcabaacbcbdccdbdccbadbaddbacdacbcdccaaacbdbdcbabddcdcdaddaddcccbcbbbcacdcabbdaddbdbccbbaaababbbdaddbbabdbcaabaddcaaadbcabadcbbcdadcddabdddcaaabbcdaaadccbddcbaadcccbdbcdbcacbaadaabbcbbddcddcbbddbddadabbacbcabbbdbcacabcbcbabbaacbbccccdcaabbbcaabaccababcacbccdcdaacbacddbcccacaabdcbdbaddcdbdbdacacbacbddacacbbddcabbabacbcbbdaccdadbbcdcdbdaddadbbcddaccaacbbdcbdaacaaabaccbabbccccacdaaccdbbaabdcbddaddbbcabacbddaabbddcdaacddbacacdcdaccbbcaacacbadacaadacaadcdabdccbbdacbbadcbadccadcccdcaabadacbbddcbbbcacbddccdaaccbadccdbbcbbcbacabdcbcbcacbdbdcbbdbbadccbadbcaacbacdbacadcdaabadcdaddabcccadbcdaccbbdbcacadcaadcbaccbbcadaabcbcdbddbadcccbbcdddabaccdbacdcadddcbabbccaadabdcccbdaddbbddabdcabcbaccabccbcbaaaaadbadbbdbddaabadaddabdbcacdbcbccacdaadacddabcdaadaabbbabacbdcddbdbcbacccbbabcacbdccdbdbcacdbbcbbbdccadcdcabcddbbdbabccbbacadccbbdaadbcdbbbbabcbdadaaacabcdcbbdbbbacdbdbadccdbddabaabbcbcdabddbaadccdccbbadddcabccddbbcadbaccbcdddacaabcacbbaaadbabacadbbabaaabacbbcabcbbbcaccabdcbdaaaccaddcccddacbddcbbcbbdddbcdaacadbadabdbdddbcdcdcbbbcdabbccaaacdadbacdddadccbbddbdadbdadbdacbbadbdabaaccaacdbcbabbccadaddbdccaaacdbdbbdddddabaabdddcaabcabdbbcaabdcadbbcddbdddadcacdabacbbbbcbdbaabbaaddbccdbdcacbdbcdabccadbcbcaacbbbbbcccbddcccbcccabdbbdcddadacadcdccaabcaabcbaabacdbdbcbaabddcbaadbdababcddcbacdcbaddbbaaadddddbbcaaaadcdcabadbbacbccbdccbdaccaadbbbcdcbcacaccdcabdacdacbdabcdbbbdddbcddadccbdbabccbabaadccabdadbcbbccabadcdcabcaccacaccadacabacddacbcdacdbdcbabdacbddcaaccbcdaaccdaadccaaddcbaaabcacdbcaabadababdcbcdbcdababaabcadbbddcdcccbcabcdccbdbbcbccdbdbacdcaaaaabdbacacdbcbaabbbaadabacaacabbbabdcbdaacadccddaddaacddabbdaddabbaacbcabadbaabadcccabcacaccccadddbbccddcaaabbdabcacbddacbdbabacbdaccdbdaccbbcddcadaaadddbcaabbbdbcabbddaaabaadbacadaadabadadcbabdcbddccddbabbccdbaacbddcdcdbbcdabbcdbbabadabbbbbccbddaaabaabbcbbadadaacdddbabcadbcaadcadbdccaccabdbadabdcddcdaadcbbadacccdbbbabacbcbcacdabccabbabbddddcdadadccdbdbbbbddcbbbcabcdbcbddbdabaabccacbaadcdcbdbdaddbacaabaadbbdccddaacabcbdcbccdcdadcaadcdbbddbcbadbcabcdabdcadcccaacdaadbbbccdaacccdaaabdaddacbdcbbcadcbbadbbdbbccddcbaaabdbcacbdbdaacbcbcddbcbadbabdcbadbcadacbcdcaabaadcbbcdcddcbdbddadaccdabcddccaccdddbdadabdaccdcaacdbaabbdadbcdcbbadddadcccdbbabacbdcdcdcaddcccaabbbdaacadabdbbabcbbdbbabbbddcaabdcaaccdaadcdacbcdabaadadcaddddacabdbbadcdabadbacbdcbbbdacdcababbccacddcbdcbdaddabddacbbccacbaadbbbadcbadaccdbdcccadcdbabddccbadbbddccddcadddbbaabdcdabcadacddbadbddcbdccbcdcdccacddadaaddcdddcbaababdabccbbdbbdbcbddcccbdddaadadaadcdcadccbacbcbabbccadddbcddddaccbaadcbadcddabadcbccccccbcbbdbcacaadbaddacbcdaabdcbcbabdbdacbbacbacdccbaadbbaaaadaacbcbbddddcbcdbcdbcbacadacbaaaabcbacacdbcdacccdabdacbacdaaadcadcdcddcccbaddaaaaaddcddcabdcdadccaadbcdddadbaccabcdaddccbddbaabbdaccdcaaddadadcbcddbadaccbcacccdaddcccbdacbabaaccccdcbbaaccdadbccdcccbaddddbdbcbbbaacdaaaadddabaacdcbbcabacbbcbbaaabcbcdaacbdcccabbdddacdbcadaacdbddadcccaaacaaadcadcdbaadbbcdaaadcbcccbbaccacbcdabddcbccddccdbabcbaacbcbcaaddcdaadbaabaabacbdddcdbaadcdbdbcbacacdbdadaaadcaaabcacbbadddccdadbcdbdbdddabcdbcbdcbdcbcabdccababbcbadbcbcbdbacbabbcddbbcccadbbddddbcaddacaabaaaccbccabdacacccadcdadabcbaacdbbbdbccccaaaadbddaaddbaddcbcadcabacacbcacbccbbdbddacccadcddaadaadaddaaabababdcdabdacacbddabbacdbdacdcdaaadbccaddbaddbbbccadbdbdcaabcddbbaaccdccdbacabcabaadadddcbacadbabbcdcbbabaaccbccccacbdbabdcbcbbbdbbccbbacdbbdcabbaacabdadcdbdabcbbaaabacbbbabdbbaaaddccadbbddcccdbaabdbbbcacbcbdcbbaaacbacabdcacaadcbccacbcbccbddbaccbaadaaccabdcdcdbcddbbbddcadcdbdcdaacbbacabbccaacabcdadcdcdcbacdcdcdcdbdaddcdaccbcbbaddbdbadbcadacbcbcdabacbacaaaabadccbdcdccddbbcccbaaabacacdaddcddcccdacccaaabdabbddcacacaaddbbcdddabdacacadcabddbdbccdbadbdadbacdbdddaacbcabadbbccbcabdccbcacdacacbdabadcbccdadbbcdccdbaaadddbdccadcbccbddbcddaddaabbbdcbbabadadcaacbcbabbbcdbabbdddbbbdbcbbccbabbacdccbabaaccccdcdabdccbcabcdddbcbabbabaaaaadcdbbacbccdccdbcbbbbacdcaaaababcadbbcccdccacacdcbbdbbbbcacaadcdccdccdcacddbaaaaacacdabccacbbdcacccadbababdcadbbadacaacbdddbbccddaacbbacbadbbabbcdcadbcdbbcdabcddabbbbcadccccdcabbbaccbdbcadbbccdddbadabacddbbdbbabaaddddcdcbdcbbcaaacbdadccdaaabadbadadacadabbccccbdccbbabdaacaabbcbcdbbcdbbddcdcacbdacdbacbcabdabaaaadadccbbbbaccdcdbdcbbdaabcadcabdbcbbacbaadcbbbdddaacbcddaddbbdddddbdaaddaacacadccadbabddbaadaacdbdbaaccadddabaaadbaddddbbadcbdaaaddbcbaacbaacdccbdbbaaadcdabcabddabbacbdcacaccacccdcabdbcbababccccddbcbbcdbbcaadbaaccbdbddadcdacdcabbbcddadaadacdadacacaccdcccddaacdacdddcbbbbacccddbbaabbaacaabcacbadddbbcbabbdbcacccbbdadbcbcbadddddccadacbabadbcccdcbabadcbdbddaaabcddbcbcccbdadbcbbddcccccacbadcacaabbcccccbcbdccbcdccddddaabacabbdabcddababbdbbadbcdccdccdcdddacacccdabcbaacddcddcbdaabaccdadcaabdcccdcadbbbdcddcdbbdadadbcbcbacbaaccccbadcadbddddbabaaacacdcaaababcaabdbaaabadbdbbaccabacadaddadbdbbdbbbbadacbcadcdadadccbccddcaccaadadbdabdadccadddaaadcadbbadbbacbbcbdababbcbaaccbbaccdacdcabddddddabbcabadcbbcbdbdcdadcabbbaabacaacddcdbdabaaaadbabccbabcabbabdaddcdadacccbddcbacbabcadbdbadabdadbdddbccacdbbcabddbcdcbbadadcadbaadcbaddbddacbccbaacdaaacadcbcccdaadbdbcbbcccaabddbcdddbcccccdbacbdbbabbcbbcbbdcdbadadcdddbdabcdbaaddaabcaccbddadaccabcaddbaacdcdcbabcbcbaacbddabadcdcabbcbdacacccadabbabbddacacdddcdcaadcadbababaababcadaabbdbbdadccddacdaacabbdbbdcbcbbddcacdcdbacdabbdbcccacdbdaccabbadcabbaabbaddaadbacacabdabddcdadcbcbdcdcbdaababbbcacaaddabacccdcbcaccbadccddcaacaadadacbbabacbcbdabacdabbbbabadbbcbbbababaddbaccacdabbbcbccadcdbcaddaadbcbbbacdbbadcddccccbabbbcbdbaccdadaadcdbddbdcadbddacbcbcbccdccbcbccacaddadbabcbaabbdabdbbdcbbdaccdbdcdddcbbbbaddccdbdbbdaadaaabaacccccddddaaabdcbaddabacbadbcdabddacacdbdabbcbbacbbcabcaccbaccccdcdcabacddcdddbddbccabcdcadaabaddbabcbbadaaaddadbdacbcaaacbccbcdbbbcbdaabbacbcacacdddacbcadbacbadbdcbaadbabccadbdadaaccadacbacbadabccabbddbcddbaabadcbcdbcbaddbabcbabdcdcaaddddddccadabbbcbddbbaddddadbbbdbcabccadacbaccbababaccaddbbbabcdbdddbddbbdbdbbacdbdacbbaabdabcdbdcddbbabbdbcabdbdabbaacbbdcadddbbabdacdcbcbadaaddccacdcabdaacdcdddadaaababbbadddcbcdcabaccbdccacaccdcbabbadbdcabdacdbbdabacadbadacadbadcbdbcbcddcaaadcddbacdcccabdcbabddacacdaaaabaccddbbdaabcabbadcdcddcbacacdaabcdcdcdbbcaccbaaacddbcaababaddddcaddcbdbcaadaadbccbdbaddabbabcbbcadbcbababdababdcbcbbbbabbbcdcddadbcababbbadcbaaddacdaaddbcdbbbcdcbbdbadccacbaaaaacbcbdaadddddadcdcbdbbbcccabaacaaaadcababadcccbbbaccacbccabdbdbcdacabdbdaddbbcdbdacdbddacbcccdcdaacbaaabccabccabccacaccbacdadcaaabddaabdcdbacccbabcbbaaacbadbaaabcbddcadacdadcacbcabadadadabacbdacaccccddcdcadbcaaccdbccaddaacbdbdbadbbdddbcbdadaadadadccbbabdddcacbcabcddababadbbacadaabacaccdaadbcddcccaddbadcdacaaabadcbdbbcdabbabdabcbddcdcaaacdacbdcdbdadbdaaaabacddacbdabaaadadbddbdacacdbcccdbbaccabaaaabcbcbacaadcabdbcbbaaccacdcbdccddbcbbcbbcccabadbcddcaddcbcbdbbdcabaccbcbdbaccabacacddcacccbdaccbdcdddbcbbdacbddbdbdacbddabdbcdcadbdadcdacbbbbcdddaadbcddcadbaccdbdabaaacdabaddbadbabcccadaddcdababccbacdcaabbadbacdcadadddccddbaddccbcaaaddcaacdabbaddcbdcccdbcbabcbadcbbdbadddadccdcababbbcaadcbbbcaddbadbbcdbbdadadadaadadacaacbdaacbaadadcbcbacaaccbabacdcabccbdcdccbccdddbdaabcdccbaadcabbddaadbaccbcddcadaabacdbdbcacbcaddabdbcbdcbcabccbcdcdabccacbcbddcaaddcdbddddbdaccababcdaddaaabcdacdbbccacadbbbdbcbcabcdcaadbaaadaacbbdcadaabccbdddaacbaacbddacdaddadadccbadbccbabbcadbdbabbacbacccadcadcbcdccbabdbadbacaabccbcaaadcaacdaabbaadcddcaadcadabdcbdcacbbdddcacaddabaabbacdbabacacbacbabcacbbbcdcdaddbabbbcddcdbaaadbcddbbdcbadabcddcdbacdadbccadbaabdaabacaddcdbaadcddbbadbbdaabcdacdaaabcaaacaabbccaddcddcddacbacdbadbbacccbaccbdabbcdacbbcaaacdbacacdbdcddbabacbbcbbadbcadbbcbdcbdbcabaddcdacbbcdbbbddcbcddbdcbaaadaacaddaabadbababdbccbdabcbababacaadccadadddcddbcccacdcbdcdccbbbbbaadcddbbddcaccbbbcbdbddcadaadbcddbdcddbaadacabdccdbadbccabbbbadaabcacddccccabdaadbdabbdccaabacdddabadccbadbcadabdcbacdbcabcddacbcbacacbaddaaddcaadacacbacdcbabacabadcacddadcbbdbbaaaabacbbbccadbaadbbccdddaaadcdcccbcadbccadbcbbcbbcbdccbccadaabaccaaacbccbbaabcddaadbcccddaaacaaccbcdaadbcccabdcdaaccddacdbdccdcbdbccddddddbabbaddcdbdccabcdddababcccbdbcbbbaccdbaccdcbbdcaadbcccbcabbadadcdbddadbbbcdddbaabaadbdbbcaadcabaccbcbccadacabdadabbcbddcbdddadadcdaddccdddccdadacdcbbaddabbaccadbbbbdaadcbcdddddcbaccdbaaabdbddbaddccabababdacadadbbbabbdddacdcbdacadbdabbbacdbbddbbaabcbddddabbcbcdddcdadbddbdddabacbabddaaacbdbcbaaaccdbabbdbaaddbcddbbdbababdacadbbbddcbbbbbcadaaaacdabddddbdacbdcbdcbbcdbcdbbaaacbdabaacdacabcaacccbaaaabaddbcaaabcbdddbdadabbcbddabaccbcbbcbcabcdcbaaacdbadbbbdbdcbbdbbdbacbabddcbcddcdccbabbccbdabaabbadbdcbdcbadcbadacacddcacbddbbbccccabcdadaddbdccccddaccdabdbacacdbcacdaccaccabdcabbdbcbdbdcabacdacacaacccccbcdbcabbdbbcabddcccbcacabddcbbdbbabcddbdcaaaacadcacdcbadacaadbbbbcbacacdadddcaadccdddcabcbcdcabdabcacbabbddccdaabdbdccdbdddcdddcdccddcaccbbcabaabaccabbddbbacdcdababaadacaddbbcbbadddccabccbddcbcaccaabcacabbcadbcbabcbbaaddbaaddcaabbbdbadbdbcdbdcabdaacdddcdcbcbbacdaccbbacdbcddcdcbcdcdbabbcbdbbacddbdbcddbcaccbbacdbdcaaacbbdbdbbacddcdccbaacbbcabcccaccbbdbdadccbbdadbaacacddbcbdbcacdcacaddacdccbbdbdcbdcdbadbadbcbbccdccdbbbcccdacdabdddabaadbaadbadbaaabddcdadbdbabbdcbababddacddcdbbcbbdaaddbacbcaaaccacddaabdabcbcdcbdaacdabbcccbbaacaddcbccabbbcdcadabaaaaaaadbdaaddcbcadddacddbbbbbbbacabbccbbdcbdddbdacbcdbadacabbbccbaddbcaacbbdbaccbcacaabdacccbbabacbcbbbddddacbdbbaabbcacacbadadcccbacbdcdadacadaaddabbccaadadaaadbccadacacaaabdbbbbacbbcbcdabcdacbbcccbdabdaddbdcaacbcbabacaadbbadbdcdcaaaddacbdcdadaabdcbdaccbbacccdccdbaacbcbbccbdcaaccbaccbbbbbaaadabbbcbddaaaadccabadbacbccbbaddbaadbdacabcddbadabacdacccbbacbdadcbadbaaccbdaccbaadbadccbbaabddbccadbcddacdbabdcdabbcdbbdaccbcacdddbadaadacbbcacaddaaaacbbbbaddbbacadabbbccddcbbbdcbaddbdcdbccbddbdbcdbbaccddddccaaaddbbcdcaaacdbddbadbdabdccdacdbddaabadbcccaddaadbcddcabbdaccdccbadbcdacabaddddadabbbdddddcbdddacacabadbccdcadddcbbabbbccbdcadadbbcbadddddaaadcdabbaccaccbdbccbbbdddccaaddcdaacadbaddaccddbdadccdadbcadbbccabbdccaaaadabdaabcdbdcabcbcbcbacddacdbacdabccddbddbbddcddbdcbbacadbcabbabbaacbdbbbbcbaccadcccdacdddccabbcdcbbabaccbcbcccccddaccaccaccbcccbbddddacaaabbddacdacddcbddcbbdccdcabccabdaddbdaaccabbabcbddcabbabbcdabcabbbdaddbcbabbdbbdbaddbddacdaddbdbdbaacabdbccbbcadcadaabccabcdddabbcddadcaacbacdadbbddaddcabbaadbaddaabcacdcccacdcdaaccaaccdabcddaaddbbbdcacabbbbddaddcaacdcdbcccacbccdabdacacbdddccaabacccaadbdbacbaadaaccaadccadcbabdbbddddaccdcdbddabbadcccaadbcccdbdaccbbccbddabbcacdadbddbacbacdaaacbdbbbdbbbdccabdababdadbcdbcabbbcddbcaddadddbcbbadddbcaaaccbbbbcbcdcdaadacdaaaacabddbcaabbaacccabbbdcdadbacabccccabbddcdadaabcbadcbdbbcccbdbcddabdaaabbababbaabcbacadcbcabbdcbbcddccdabaadcddcacdbdadcadbbcaadabcdcaadddcdaacddbaabcabcbdadaddcbcbcdbcbdbdcdcabdcaccaacdbbabcccabbdbdddccdadabadbaddddcccaaabaddbaadbcdbccaccbbdaacbdabacabdcdcadbdcddcdddcacdcbdccabccbbbaacdbddcbbdbdabaadadcdaaabccdbdbdcabbabddadcccdaababadcaacbbbbbbbabbbbdcbaadbccdbbccddbcaabdccdaadbacbaacbbcbbbbdccbbdddaddbcabbdcccbaaabccbdcdcbddcaaccacbddaccbdabacbbccbcccdcdbddcacddcddddcdccddbcccccdbbcadbcdbdbdaadbcdccdcdbaabdbaadbdabbabbbaddcbaacbdbbbdcdbcbaddcdcbaaaabaddccbcbcbdbbacabddaacbcbadaacddaabdcbbbbabdcdadbcbabbacdddacbdbcdcbbddcaabacbadccabdcbcbcbaaacdcabdadbadaadabbddacbddacaaccdacdcacaabcdcaadabaddaddddddcadcddaccdbacdcbabdaabbcccbacbaaaddcbdbcdabbcdccbbdccaabccbabcdbbccadbdccbcdbbbdbbdccdabccbacabbacdbbbababbcbddaccbdcbddddadbdaadcccbdaacacacddcccbcdcccdbadaaababcbcbdcccaabbbcacaddabcbacdadbcbdbabcabcaabbadbabadbdbcadabadcacddbccbcbadadadcaaabcbacbbcbbbbcbddcbcadcbadccdaaadbbdbdbcbaadabcbdccabacdccacbcacabcbddbbaaaddcaaacddbdabbdbacaababdcabcdbacbbdcababaacdcabcccbcdacabaabbbaaadaaaddbbbdbbdbadacaacabbadcbabcdbbacddbcbdccddaacbaaddcacbaabbccdccbacaabbacacaaabacccdbdadcadbbcccadcdbaccadadbbabdadabbccbcabcbbadbaddabaddaccdbcddadbcddaabbbdcddacabdbadddddaaabcacbbcadccbddaaddadabbbcdacddbbbccbacdaaaadcbcbcacbdacddaaddaddbddabaabcdadccdddcaadaabcacbbdacdaddabdddacdddbcddbadbcaddabbadaaadaccadbddcdcabadbbdadacaaccabadcacdabbdbdcdcbdcacaddbdbbadcaabbccacccdcdcccdcbbdcabbccccdbddddaccbadaabbcaddbcdacadddcaacabbdbbbdcdaaaddabbabdcdabbdcdbaddaabccbcacdbbbcbacddabacccbbccbdacbacdbcbcacbacacdaadbacacaccabadbcccbdcdacbccddccddcacababdaccadccbaaaaacdbbbddccbbddddbdcababbbabaaddaabbcaabbccaccdadbcabbabcabddcdccdccdccdcacbccbaaadbdbcbadcabacdbacddadbcdcccbabbddccdcdbdbdaaabbaaddbabdababacddadaddabbadccaacdccbadcdacddcadbbabbdcbcdbddcbbabccabcddbabbdcaaaaaabcbdabbcccaadbabcbdaadcbacbbdaaaadddcabbacbbcaacadcbacbdcbddcaaccddabdcacdbadcdbdcaaacdbcdbcaddbcaaabdaacadddcacdaadaccbbcabddbbadcbaabbcadaabacaacbbaaabadcaddcbddcbcabbdbabcdcbdcabdccdbacdadddacdcbccdbcabadaadbcaddbccbacdbadaccadbbdddcdacbacbaacbbaadccacdaabcacaddbadaabaaabbdbabbaacaccdcdcccdbacacbcabbbdbbbcbcdbbdadacbccbadbcdcddddccbbbbdaaaadccbcadbcaaccccccdaabcdbbdbcccbddaaacacddaaaccaccacadcabacbadddaabaadacadcbcdadcabbccdabcdbbdccddbcdababcbacadacdadbcbcddadccbaaabcacbccbaddabdadcabbbdcbbbabaacacdacdabcbcbdbdccbbdadcacbaacbdbbdbdccdcbacddadbabdccbdacbbcdbadbbcbddbcddaddaacbcddabbdcaaccdccdbdaabdcdaccdaacdbbbcbadddbddaadddbdaadcadaccbabacaadaddbaddbabbbabccabbcadcbbaddaadcacbaabdbcbaddcbcbbccdadcdaabbaabacbdcaababdacacdddbadaacbccbcabdaadabdddbcdbddbbccccdbdadbbaddccaacbcbddacdbadddacbdcabbdbadcaccbbdbabbdbcdabcabcdabbccbabdcadccadabbccabcbdbabcbcbcbdcacddcdccbabbbdadddabbacaccbcbaaddbbabbbbaacdbabababaccccddacbbadbdbdabddadbaaacdcdbbcabddbbddbcadbdcccacdbadbaacbaddddcdaaacbcabcabbbdbbddaaaddaadbadbbaccadabdacaaadaababcbadacddabbddbdbacaabcdbbccbabbacadcbadbbdbdcabadcbaabdbccbcdcadddbacdbdcdaaacbccaccacbbcaadbccbcdaaddcccdadaabcbdadadabdaccbbaaddadacacbcccaacacadcdcdacdbcbdbcbcbbbcacacbbccbcddcbcdaabcacccbbbddaacdcddabddacabababadcdbaccccdbdddadbcdbcaaabdbcdccbbababdcaddaabdddadacbcdaccacccdadbccdbbadcbddbdaddcbccdacbaacddcadbcdbdabbcdcaadcacabbdcdbbacdccbcbacddabdbddaabdabcadbdadaacbadadcabbdadbdccccdacadacabcacdabdaaadacbbbabbabdcaccdddccdbccbbccabcbbddbcdcccdaddaddbdbbddaacbdcdbcbadcaabbcaacbabaabccbacdcdddcbdbabcbacccccccacbdabbacdddcacbadabababbbbddadbdbcbdabcdcbdbccbbdababdcadaaabbcbbcbbdbaabcaddabadbcddbbadcbbddccdaaddcbdcdbcadbdddbdbcbacbdcdcbadcabcbbbabadbbaababbcbdcbdccaccddaccaacbdbbdcbcacbddbcbccabadababdbbbbbbabcbdabdcaabcbdccacdadcadacbccddddcbccadbacdcadddcbbbbbacaabaadbdbcabbdabddaaabdbddbdcbabbbbabcaaadabdbdbaccadbbbbabcbcbcdccdbcddbcbddcabadcddabdccbbddbddaccdbcdbdccdcdcacccdbcbdbccbaabdbccdbdabbddbbcccdcbddaddccdabaacadcdbcabddadaddcabdbccdadacbcdccacabbcccdbdcbaadbacaaacbaabdcbcadaddadddbcacadaccddbdcacabbcdadbaaddbaabccdccccdcadbcdbcdaacbadcbcdacbccbdbbcbacdcadcdbbdbabdabacabcdbadddaccbcbdaadbcdbdbabbaccdbbaacdbbdadaadccbadacbbbbdcaccbcdbdbbcacbbbacaabadcdbbaadbbbadcbacadcaabcacdcdbcabbacaaacaaabdbbbaacbbcbccbcdaabbadbaadbdabdacbdbcbabbdcaabbbbbbaaabbcacabcadcdcbacadbbdabbcdacbabadddbaccbbaaaabbcccbcbdbccccdbdcbddbbacccdbdaccbcbacbdcbcbabcbcdddbcadccaddcabdddadadbaddaadcbbbaddbddaddaadddabcdddcdabdaddcadadbdbabcacdacddcabbdbcbbdaaabcddcbabccdbcdbbbdcccddddbcdcdcdaccacacaadccadcccdddbbccadbbcdbaacdaaabadddcaddaabdcbabccbdaddaccdbaacbacaaccaacaadbbabcaccaaaabcbcbadbbaccccdbaadccbcddbaabcdcccaccaabbdbbcdddadcdbdaadbbbbbdbcbcbaabdddadabbbbbdcdbcbcdcabcbccddbabcbcaddcbdbcdddaacdbabccadcacccbddccdbbbbddbbaddbaccababdbddbdbbcadddcdabacbadabdccbdbcbcabbadddbbadcdcdbdadcbbacdbaddcacdaabdbacacadccbcbdcbabdacdbddbdaadcddaaccddccccabbcdbcddcdacdbdddabcccbdbabaadaccabbabaabcaaabccdbbaadaddccaadbdadabdddabaddbddbadbbcadababbaadacdacabbbcdabcaacadaaaaddcbddbbdcaaccdaaccaabcdddcdbcaaccbbddadabbcdadcddbdccddaddadbacbccadccabdccdcbdcdabacabaddabaacbaddddcbbbaaacddadcdbdabdacaababbdbdacaabbcdadacaccaaccadcbbccadcadcbdbbcbbcccacaaabcadcbccdacdcbbcadbddabbacacadbddcbddcccdabcdaddcaddccacbbaaabadaabddadaddcacccccbbacccdccaddbcbabcdddcbabdbadcddddacadddaddbcabdacacdddcbadabadddaddcdcbcaadcdcbdcabcbdccbadcdcdcacbdbadacbbdabaadacabbbcbdaabdbdccabcabdaaabacacdbcdaacdcdbddcdbccbdbdbdbaaadddcccdcccdbbdaccdacacbacddcdbbadcbaabdccccacddbadaaaadbdaccadccbdabcddaabbdddacaccabacdabdadacbcaaadacbccabccbaaaadbbdbbddbbccdbbbdcbbcaccdaabadbdadcbdcacbbacbaddcabadbcdbbaabdcdddccbacdcdababcacbcbbcbbdbbcbacbbabdaadcdcdadaccaccaddbbdbbdcbddcabaddbaaaadcaaaaabadcabddcdaacddbcdcdddbacbbdddbccbdaabaabbbbcbcabdbdcacccdbdcdaccdbbdbddcbbbbbacabcabbdbaaddbbababcacbabcacdaaabdbadacbcabcdbdaaadbbdaccdaaccbbaadcccbbacbbadadbdcacbcadcbdcdcdcacbcbccbdaaacddabaccadcbbdcbcbcdcdccdcadaacadbaccbaadcbacdbddbdccdabddbadbddacadaacaaacdccdadabcddabdcbaaabddcddbccbbcacdbaadbaadcaabcdcaadbdabdccccddaccbcbbbabaccaddcdacccbcaadaabbcaacbacdaaacacbbacdcacaabaddcbdbccccbacabbddababddbadcbbddbaaaccbbcbbadccbddbdbdbcbcabcdcdcaadccbbabccaccddacbbdbadcbdbcaacdcbdcdcbcdcbaddcdaddcaadddddddabccadccdcdbaabcdaacccdccbdbacaacbcccbaaaacadccccbccbcabdbadcddadadcdacbaccaabaacbbadbdcaccddccdaaaabcbcacdddbadbccaaadcddcdadcbaddadddadbbdbcbdccacbcbdacbadcbaacbdcaccdacaabdabbccdabacaaddcdbdbadbaddabcadddcdbcccbcccbbcdbbaacdadbcdadcbccdccdaccbdcbcaaddadbcbdacccbadabccdbadcdcbaaaccaacbdcaadaddbcbccbbdbccacaddbbccdccacddadcbaadaaddddccbbbacbcaaccaccabaabcaccabaabaaacaadabbacaccacdabddcaabaadadbddbadddcdabcbddcbdddbbddbdaabadcabdbdaaddcdcccabcccbcbabccdaddbacdbcbdcccddaaaccdacbcbabaaacddbacccbdbbbcaccbddcbdcbadcdaaddbdcbddcdacdbdabadabcdabbadcbadbccaabbcdcdadcbdddbdbbcdccadbccadaddabaccccbdadbaadbbabbdccacdbcdcbbdbcbbbabdddccadccaccadadaaccadacaaacddbacadbcaadacbaccbdacdbbccbadddcdbbdcbbdacaaadaaddacdacaccacbdcbbbabbccadbdbacbdabbcdbcaaccbccbccccbbccccbbccbbbdcdcaaabccdcdcaabacdcbcacacbddadcdabadbdbbbaabdcccabacabdaacbbbddccdaabbcbcacababadccbcdabcacadaabbccabdabdcadccacdbdbbcabcbdacdddbbbcadaadcadcaaabdcacacaacabdacccdbabcccddbddacbcddcdadacccdcdbbbdbbdcbbbddcaddcabcdcddcacabaccbcbbbbccdddabcdbaddccabacccaacccdccbcbacaccdbcbcaaaabbcabcdacdbdacdbbbbcddabdcadabadaaccdabbdbbcbbadcacdcaaaccdcbcadbdcbbdcbcacbccddcddaaddaabcacbbcbbacdbbdbccbdcbacbddbbadaabcddacdbcaadddadcbbbbcabbdbaadaccdbdaabccddcdbcccadbcccaabacaacadbbadbadbbdcbcadabdbcacacbbbdbbcadbdcabacaadcacdcaadabbdabaaaabdbaabcbaacaabbbdddbbdcdabccccccdcbdddccbbdadccddcaccabbcdabcacbabcbbdbcbdacdacdabcaaadcbaadaddcaaabadbdbbbdadbccdccbbbddaadacaabbbacbacbaddacdbddbbdbcadccabbbdcabccabdadabcabddbddaacbcacabdbbaaaacadbcacdbdcddddddabbcdcddabbabadbcbcdacdcabdbacdcbdddbcabacacdcabacccdbaaabccbabaaacdacdbaccccaabadbaadcabaabadbdcdadccdbbcabdbdaabcbabacacdbccbdbdcdbdcdcbaccabbdcaadabdbcaccaddddacadabcaadbdabdabadadbbabbabccddabcbdabbbacbaacbbbcbbbbbbcabbcaaaaddbdadcddddbcdabadbaaaddcddabdddabdabccdcbcbdbbcdaccdaacaadacaaabadbacbcbdadabcadcddddddccbbbdacbabadabdabbadbadcbcbadbccbadaacdcadcbdcbdbaaddadbddcdbbadbcadaacccdbbdcbbbaacbdabddcbbdbcdaaccaadddaaaabdbdbdccdaabcacaadddccadbadacbaaaaaabbcdcabbacacaadcdabcdcdbccaabbdadabddadcbbdabaabbaddbcdcbbcbbbdbaabcdbdcbdcdddbcbdaaccdcadcabbbcdacdbcdbddaabdacddadcbbdcdbcddbaadcaadaabdcbabdacbdbdbcaadcaaaabaadbdcacaabaaccbaabddbdddcdaddcadabaddcbccaadcccacabbbdbadbdababcadccbdbddcaaaadbbbdaaadcdcadbacccbbbaaccbccbadddaabccacaaacadccdabdaddcaaabddabaabaabddadbadccbaadbbbbcbcbbacacdddcadabbcdbacdbbdacaacacccbadcbbaadccdacdbbdadcacdcabcddbbcdcddcbabbdddddadbbdcbbdcaccdbacadcddacdbaaacbcbddbcdacacdbdcdcbbcdaaabbdcdccbcbbaddacbcdabdcbcbaccbabdaccbddbbdbcccccdaadbbabcbcdcdddabbdbcbccaddadaddabbacddbcdbbbccbcddadbabdcadcbdddddcccbabbabdaccbdabcdabdddaabdaccbacabdddcaccbdbababbacbdbbaaabcdccdccccdbbabccadbabddcddbadbbdcbbcdbacacbdccbadddacbaaddcbdbaacdacaaccabadcbdbaadaacdcacbddbcbbccbbadbdacdddbccdcbaaabbabbbbaccbcdbbbabdcdbcadbcabdabbdbbcbacbdddadbccabdbdcaddcadccaabccbcaccbaadcdcbccdacbabcbdcaccaacbdaaabbadddbbdbabdcabbdbbbacacdbbcccdabdbabdbbbcaaacaccccabccbcdabbbabcacdcdcccdccbdcadddaabccaaadccabcabcccdaaaddcadbcdacdddacdbcdcdcabbddcbbddcdccdbcbbbacaabbadddadbadcbccdbbaacbbcadddaaccddaabbbdcbbacbbccbddcccdbdddddadbaaacccccaacbcadaaddcaddcaddbbcdabddcacdcbadbccdadbdbbbaabacdbdacbaabbccdaaadbddabdbdbbcacbcdbdbbbcacdacdbbcbbaddbabaadaadabbacdbbdcbcaaadaaaabdbaaacbadababbbddddacabcadbabdabaaabcacbddbabcaadbcdcccdcacddabdacacbbbaabaccadcddcdbaaddadbaacabdbbcbbabdbbabccdabbdbdbbabbcdbbbcbcdadbccabaccabadaaacbadbbdabdbdaaacddbcdbcadbdbccbbbaaaccdaadcacbdcbbcdcdacdcaacdacacdaccbddaaadcaddcaaddbcaccadaaaccbaadabbcabcccaacadcacdbdacacabadadaaacaddddabccbdbabacadcbdabadcdadacbcddddadacbabadcddbcdbbaddddadcbbdaabdaaacabcddccacdcaadbabcabcdcdadaadcbddbdbacdbaacbcabaadbcdbadccabbcbdccacddccbddaccbaaadbbbadcccbadadcbbcadcbbbbbadacdabcddcabaddaabdbbbadadcccacadaacbcccbbacdbbbadbcadbdcabacbbdddabcddaddcabacdababcccadaacdcccacaaccbddabbacdcdcdabaacaabbaacbabacadcccbbaabcbdbbdbabcacaabccbbcadacabdabddaddcbbbcaddcabdcbddcdbadbadbdacaababbaaaaadbacababdbddccabdabccaaabcadcbdbaadcabddbdcbbaabbcdbcacbabbbccacccadaaabaadcdcacddddabaabddadcdddbdbbdddcddbdabbabcdbdcdcddcbaabddaaaadccbabbccabbabdddbbcbdacbbabbccdacacdcdabdcaadbdcbdddbacaccdcddcddbbbaadaddcabdbdaaccbbdcddacadcabcaccbaabcabdcbdcaacbdcdbcdacddaccbdccbbaccacadbbccbbccbabdccdbababcacaddbcdaaddbbdaadcdcbbbacdcbdccadcbbabdbddcddccadbdacaadbcbcbaaaaaddddaadcdaaacbbdbadbbbbcdadcbdacadcdaaadcbacdacaddadcbaabdcaacabdadaccbbbadacccdcdbccccdcbbdacbbdbbbbddadbabadddccbdbadadbccabbabccacdcbdbdbdaccadbdaddbbadbcbddacdccbddcdbabbabccadbcadbcaadabdcdbacbacdccabadadcbbcbbbbabbbbacaddaadbbbbaaabbbbccbdcacadddaccaadcacdcbbdacbcaadbdabcbdddbccaddbdbbddbacdbaccddcddabcdcbcbabcdcdbbadaccadccbddcbbdddddaaccaacdcdaaddcdadbdbbcdbbcbbbcbcbbdcbcddcdaaccdabddcbdccaddcaddaddbadbcbbddddcabbcccacaacbacbcddccbadcbabccbaacdaacadabdccadccbbdcbbdbdcdcccdbaadbaaaadabccadaddcbcccccdaadcacdddccdbcadabaccbcddddcdbcbcccbaacccbcdbdddacbcaabccabddcbbbbabdacabcaabbcabddbaadbdaacaacbdddcbadcaaaabddaccabbdbbbaacbabdcacadbaacbbadacdacccbbacabacaaabdacadadcbcccddcabccdbdbddbddcdbacbcdcdccbbdcbaacadaadbbbcdccaacacddacdddacdcdacbbcbaccdabccdbbdcadaacccabaabcdabbbbadcaddcaaacccdbaccbbdaacbcdbadcacababbcbabdadccabdbcdbddabaccadbaabaacacdbcabaacbabdaabccbadadbbdbaaddbbddbcdaaacdcabacbddbddbdbcdbacaacaaddcbaacbcbbcaccaddccdddcdbaccbddcdcbdaacddcbaacbacbaddbacdcdbabaddacdbaacbdcbcadbdbcabccadcacaddcbddababcdddacdddbbbabbddbabddcdaddabbbdadaddaacbcddbcacdaccacbacbcaacabddcbabaccdbdcaddbcaadcaddcadbdcadaccbabaadadcbbbdbcccdabbbbadddbacdcdbbddbdccabddcbbbacacdaaabdbbdabbadbabddabcaddbddcacabccdcbcbbbcbaccacabaccabcbcaaddaadabddcbadaacaaccdcadaaadadddcdcbdabacabdcddccabdbacacababaadacacaabadbbcbaabacabbabcacbbdaacacbdbacadddbdaaacbccbdaccbddcaccdabaadbbdbadcbcdabbcdbbcdabddbbccdaacbbabadbaabdcabbcadddaacccaadaacccbbcdcabcbccbadbddcdbcbccbdaacbaccabacaabbaabadcaddddadcacbdcacbdbcdbbbccabbcdcadbdaadadadabaabdacacadacdccaacdacabdabadcdbaaadcbbbddcdbdbacdbdaabacabddadcdbacaaabdccdaddcbaacacccdcaacacccdcbdcaacacccadadabcddbbadccbcbadccdacbccdacdddcccddccdaacaaddadaaccddccabcdbdabdcbbdbccdbcacabdacbaacbaabacbacadcbbbadbcabcacbcdbadbcccbabccabbdbaddadaabdbabbdcbcccbdcaadccdbcdacadcadabbdbaadddbbacbdabbdbcbddbcadadabaccbdaaabdbaddbcadbdbcbdbbcbabbbddaadabdcbbcbacaabbbdadccdcdcccdacadbadcddccadbcdaadaabaaccbbadbbaabaabacadcaadbbcdcdcbaababaabcbacdccdddbbacbcbbacdbcbddcaadcadbcdaadbdcacbbdbcbaabadacbabacbaaaddbdbbccbcacccccacabacbccabcccadbddccdbaadbdbacccacdcabcdbabadabbdbadabaabdbadbabddbdbbddcaccbcaadcacacadacabbbabbbadcccbbcaabadaddcbacdbadabadcccaddaccddabdbcbabacbdbaaabaadcbbddbaaaddcaccabcbddccaadcbbbcdcddcdadbddbbccccddcdadabdadadbcbcdacadadbaadacdaacdbdbdbaaabaabbdddcddcdcddabdcdbdaadcaccbadcabaddbabcccbadbdcddcdabaddddacddbcaabbacddbcdabbacadbdadccadabaacccacacbbadabddcdadbbbcbadbdacbaacbbaddbadbbbdcabadacaaacabbcccdbdaabaccacdbaddbbcbdbcbddbadcadadacdaabadabcabadddbcbcddcdacdbbbacacbaccbbcdbbacbbdbaaaddcdcaddcbdbbbdbcdbacadcdcdaadacacabcccbdddaaacccccddabbccdbdccddbdacddddbadbbcdaddacadddaaaaaabbdcdbadddcaabdbcdaccdababdabcddbdaaaadadadddadcddbabadbbbdadcabbbdcbcbcabaadcdbbadacaaaadbcbabdaabaaccddadbcbbbddaccbaabdcdcbccbddddacaddadcdcaacdcdbbdcbbbcdabddbadaaabbaccdabcadbcdaccccddaacccbacdabaaabdccdbbbadcaadcbbcddcbbcbdccaaadcbadbbbabbacaadcdddadaababbbccacaccdcabccdaccbbadbdaddabbacdaabbbddcbdccaacbbadbbabaccadcbbcdbcaddbdbbdddbcbccddcdaddaaabbdcadcdbbdaababbcdbcdccacabbdbcdbdaccabccdadcadddbaddddbacdbaabcddcbccdcdadadbdbbcdbaaacbbbcccdddcacbbccdaacbcdbdccdbcadbddbdabbdacdababbbccbdacaddddbcbdcacbcadadabcccacbcbdccacbbadbdbcbdbcacaacadbcabdbbaddadaabcacbaaacabbacbaddadbcbadbcabbabababbaddbbdcbcbcacdcbcbacdabdabdcdbbacdcbdcabadcddccbbdaccaabcbcdacadddddaccacdcbddcdadbdccdaaccbccbaaacadddaddadabbcdcabdbcddacbbcbcabcbbdacddbbacbbaacccdacaababacccbaddbcabddbaaaadacbbbbabbaacbacdbaaabbcbcdbccacadbcabaabcdbdbabacdbdbcabaccdadbbccbdcdadccbabacaaadcdbdbccbadcadaacbddacacdadcdbabaaabcccccdcaaaadcbbdabdcbdcbcbbacaacccdbdbcdbcbdaddbaaadcbcadbdccabbccacadacaacdbdcdddaaadcbddddcccaabbcaccbabbdcdacccccdacdaadadababaddcdbcbcabcbbdbbabbacccacabdacacddadabbacdadbcadaabbbcdadbccbbcbadadcbbacddbbbcbcabbbccbcbbdcbbaddbbacdddadccdbcdcddadcddbaddcccaacdcdbcbadbbccacacaacabdddaccdbacadaadccbacbbddbcbbcccabdccaaadbcccbabacccbbcdbdbbddbcdddadccbcbdaadddbccdbaacaacbcbbbbdbdacadbaccadacaddcabaabbacddcddccaaaaabbbbccdcadcadcabcabdcbbdaaccddadaaaadcddabcdcabbdcacaabaddcacbbaacbbbabadbddbadcbbdbdccdccbccbcddbcdbbdadddcadbabadadadacdccdcadbcbbacccbbaccdcdccadabbbccabbcdccdcbbbcabadcaaddcdaabcacccdddadccababddbcccdbacbccbbbbadbaadacddbcddabddddbcdcbdabdcaacabadacacacccddaaaccbdcbaadaccddbccdaadbddacbddddadbadbbcadddaccdbdcabbbbdcbadbdbaccacbcbaccbcadbdccccddcbbaaacbcbbdcadbacbdadccabbcdabaaadadaaacbddcdbdddddaabbaabbbcbdbdbdbbdaccbcabcccddbbdcdaacccbbbbddaaacababcadbabccbdbcbbbbaababdbcdbacdcccdcbdddbbacaacbabcdccbbadcdaddcdacdcabdccbbcdcbaabdadbcbbddbcadddaacbccabdbcbdddadbabbbdbaacccdcacaddadcccbbbbaddabddbaccaacaccdaabcbadbcbaaacdadaaddbdbbcccabaaaddabaccacccbaaadaadaabdccaaacaaacaabbaaabbcaadbcbdacaabbacaccbdccbcbbbcababbbbcbbbbdbadcdbaacddcadabadbdbadccddcddddccbbbbdbdacbccacccdacadcddcbbbbadcbacbdaadabacadaabbcbdbbdadccbcbccbddddbabaaccdcdcaaaacbbaadabdcabbdbdcbddbbdbcaddbadccacddbccadbccdbdddcbbacacddaababdbbdbdabadbbdaccadcdbabacaabdcabcbadbcaaabbadbbbdbaddcdbacbdacabdbdabcdaabadaadbadbcabaccadddbadbbcaacbddbadcaadddaabbbccacbdcbcadbddabaccaadaadabbabacdddadbdbbaabcaadbabcdaadbabbababbacdbccbaaadadbaccdcaacadcaaabcddbabbdcdbbcaaddabdadcdcadbdadcabbdbdacdbdcddadcdbddbdbcaaaaabacabbacbbdabbcbadddddadacddadabcdbddabcaacdacababbcdcbccacbbaddbdabdcbdbcadaddabbdacaddbadaaacadbcbdccabaaadddaddcaabdbcbcaaadbddbcaadbbdcbbaccdabaddcdaaabbddcdddbbcccccdddbddcaabaddbaabbadabacbdddabaccbcbbdcbcdbadaccdbbcdacccaccabddccdbcabddbddddbaabdcbccbbcbddccdcddddaddaabbbdccbabccbaadccaaccbcdbccdbbaacbddccadacddbbcdbbaaccaadacccbdcbbaccccbbbabcbabacaaacdddcccbaddabbacccabcababcdccbbcbbaccccabccacdcaddccdaabcdbdcdccacdcdbccbcaacabbabdcadbbccbdcdadadbdadcbadbaddbcccbacabaccbbaaaddcbbacdbccaaadcabcbcccdbcbbcccbcacadcdacabdcdcacddaccbbaacbddcaabcdbadbaacccbabcbcabbcddcbacdbabaaaaadbbaddabddccaaaacadbcabbbbbadaadbccaaacaadcaaccbbbaccdbdabbdcbadbcadcdbcdcaacddbdaddcadbbdadacdbdcbbcbdaaadbbdcddbdcbbdbdabcccabccaabbbaaabcdcdbdccdaacbbaababbdaddacbacacabaacdaccaccacabadbcbaddabaadadddddcacaddbbdaddacdaaacaaadcdaacdbacdaadcbcdaabddabbdbababcbddccbccdbabdcdcaaddbdddbacccbaccaaacdadbaccabadddbdcbaacdcbcacbdcdaaccdbaabcbadbdbdccddcadbbbaadcbacbccddcdabbcabbbcbbadadaaadacdcdbbddbcbccddaabddcdccdadadddddcdbcbcadaacadbadcccaadaccabdbccabdccddbdcadcdcbbbdbcaaccbbcddbccddcbabdacdcddaadcdadcbcaaacabbbcbbbbcbcbbadcdabdcbaaabbdcccdddcbbcdabbbabbabbdddcdacbacaabdacaaccdbccbaddccababcbdcbbaccdcddaccabbdccdcabdabccdbbacababbacbbcdbbdaadcadbbbbcaddbccacabcccabdbbadbdcadddcccbaacbadbaaccaccabaadadbaadbdcacddbbbbddccaaadccabbbdcccacacddaadcccbadcbbcbcdcdaadacdaddaddcadbbadccdcbbccadadabadaaddacadddcddcbabdadccdcbacacbdaacdbbbadbcdbcacabcadcbcbabcaacadddbabccddabaccbcdcdadacdbdbcbcccbdccdbddbbaaaaccadbddcbacbddaccbcacbccdaaccbcaababddccbbbcababbcbdcdabdddddccdcbcacddabbcccbbbddddbacadbcadcbccdbabdddbabbcccdbaacbdaddacdddbacadbdaaadbdcdcaaccbcdcccadbccabdbaadbabcccdbcbabadabcdbadabdabdccdbadddaaadbdbabdccadddcdcddbccdadbdbbbbbbdbaddcacaaacacdbcbdadbdacaadcbbcaddbacadbcdcabcddbcaabbcccdaadcadbcbddacaaacbdadabadbacdadabbcbcbddcdaaddbdbddcabcdaababacdcbcccadaaabddaadbbadaabddcccbccaadccabacccaddcbbaadbdadacabbbabbcbadadadabbddacadcdccbcccbcacadbcddbcccbcdacdddaaacbddcababdddcabdabaadadacdcbbbaddadbaacbbbaacaaccdcbdacaacdcaddcabcbdbacdcbdcadabbcdbdbdacbaacacbbbadadcddddbaccddccdbacccbdddadbdbbacacaabdbcdbcddaaacacadcbbadadbdbbcbabbcaadbddbdabbacaddbbabccdadddddaddbcaadccdbbbbbdbabdaabddddcccbabaccbdaaacdddbadbacacbabadbccadacdbbddadddbaccaccaccadccbdaccbabadabcbbcbaaadcddcccdcdcaaddbbabdbddccdcbdbbbcdabababadbdcdbadababbdcbaadcbdabaadadcdacdbbdcdbcbcdabcbbacaabaacadacdbcbcdbcbaddcbdbacacddbabcabdaadabcccaaaaddabbabddabacbcdbacccaacdacbadbacbcdcddcacdaccacccbbbaccabadbaacbdbcddddabbabbacccdccacdbdababccbddbdbdabbacaacdbcbddaadcadabcccdacdbbcbadacabaacccbbabbcdbbbcacdcccabaaadaaddccaaadddacbbaacbddaccaddabcaccddbccddacdbabaaaacdbcabdbdaaccccaabbdcbbcbcbbcdcadccdabacbcbddbacadddcbdbcaaadcccbcaaaccbbbdbadddaabccddccbadaccbccbbabddacbbdbcdddbaddbabaacddaadcdcbadcadadbacddcccdbabcadbdaabbabdccdacbdbdccacaacdbdacbbccccdbbbaaabcbdbcccaccabaaadbcacdbabadbdacbcbcabccbcaadacdbcadadcdaadabcaaabdadacaabcabacabccdccaccabdcddbddacbcadaddadacdbacbccaddddddbdcaacbbcabbabaacadaaddbabcbabbcddadaadadbcdcabdbcbcabbccdabccbcbacdcbbcabaadacccabaccbbbbbddacbbcaadcbdbbdacdcadcdacbabbaaaaaccccaabaabcbdbaccbccaccdabbabccbcaabadcadccbccacdcabaacaacbbadbaaabccdbdcabbdadcbabdababadbdadbccdbbcdadbadcabbddbabcdcbdbbcaccaadddcccdbdbcddaadbcaddbaaddcdcdbbbdaccdcbdbacccccccadbbbddcdccbdbccbcbdcabadabaacdddbddbaddacaccaddbbaddadaddbcdacbacddbdaabaabbabdcdadcbcdaacbcadbcdbabdabbcaabdcdbbcadcbdadddccbcbcaadcbaddcabbcaadbccdcbaaaccdcacabccbacbcbbcddcaccabbacbbdaaccccdbabdbadcbbdadcbbbbbadbbcdaccdcbbbbabdbbbcbbadbccbcbcccccabbbbbbdadbbddbdcabadacaadadcdbddccacbdbdbdbddcdacabdbbdbaadadbbbbabcccbcaabdcbadbdcaadbdddaddbcabcdcccddcdababdadcaccadddadccacabcacaabddccdbdaadabacbbcdaaaadddaadddbcbcaccadbcbbadbdaccddccdaccdcdcdbcdbbbaabcdcaacadabdacbbbadabcddcdaabbaadcbabadcaacbdbbbcbbdabaabdddabbacbdabbdbdabcaabbccaacdbbacdbcacabbabbaccbcbbcacdbdcaacbbddbcbbbacbdabbbcdcbdaaaacaacdcbcbddcddcabdabdbaabbdddcaacdacbbacbcdaaaacddbdaaaacdbacdacbcadbadabddbcbbbabbbcbacacabdacabaacbaacdcbbacdabacaddabccadbdbbcbdabdcccacacaccdadbbbddbbdbdbcabdddcdcdcdbacddcbbdbcccaccadabadccbdaabbddbabdaaaddaaccbbcdbbacdbdacddbdadbababcdadcddadbdccdabdbadbadcdabacbbdaddbacdcbacbabbadbdcdaabdcbcbacccaacabcacdaadcbdbabbacdcaaabacdcbbdcbdbdabdbbdadcacaccbbdbabdabbbcddacabbcaabdbaacbccaabacddccbddacacadacaccbdddcbababdaacbdaabbbcbaccbadcbdccdcbbdaddcdaddcadbdabcdbdddbbcaacdaabaccaadcabbccdacaaccbcadaaabbaacaadcdccacdbdcbcdddbdbbbbabaccddcdbacdadccdadaaacccaddbdbabbccaaaaabadaadacdbcdcaabddabdbbbaccbccbdabdcbaddabdabcbcdddaaaccdbcacbbddacbabbaacbdcdddadababddbbaadbbbddadddbcaddcdaadbdacaadcbbacddbcababdadcdacacdcbbaadcccbdcccddbdadbbdcabaabbbcbabcdbadabbadccaadccaddbbdcddbdbbaabbdaddadcdabbdacdbbddaabbaddaabbdadbbabcabaaabdacccbbccbbdbccdcbcdcbacbabdacbbbcddaddbbbabbbbabababdcddabcccbcabccaacdabdabbabaddbabbaabbbabdbabdbbbccbcaddcbbcabdcabbddccbabcddbbbbcbadbcabcabcbddbdcdddadadaaadcabaddbcadaddacbabcaaccddbaccbdaababdbcbcbbcdbabababbcbbabdaccdacdbabcdadbadaccdcabbabcbadcdcaaddcdbccdadacbdcbddbbabddadcaaacbabbaccddaabdadccccbacacdbbcbacbaaabcdccaadadcdccaccbdcaaababcdcbbdacabdcbbbcdadddbbadbaababddccbaaacacbcddccccbbbcdccaddadadabcadddabdccbbbacbbadadbabcdaaabccbaabbaddabcdbcdbadccdbbadbaabcddcddcbcacdcdcdbbdcddbbcaaacbbddcddccaacccccbbbdbabcacdccdadbbadaaccccaabadbbbbaabcbaaabdbcbcaddcddabdbdbbdcaddccacddcdbcbcacadcbcbabacccdbabacdaaddacdbbccaccddbccdcbaadbddacbcdaaabbcadbadcbbdababdbcdaddabcdcbdbcabccadbabccbaadbbbbdbbbbdcdcccadcaddbabdabccdbccaddddabcccbcadbdadcbcdddccbddbdcabbddaadabbdbbacddbdabdcaaaacacabaabdbdbdaababbbbccddacababdcdbdbdbcabdcadccaabbaaddabacddddccdcaabdadacbaddbadbcdacbadcbbdbdaabaadababdddcaaadbacbddcaccdbdabbbcabcdcadacddbccacaaabdacbdaabddccaabccaacdddcaacdcbdabaccbadbbadbdbababdbdbaaacbaaadcaabbddbaccbddadbbcaababdbccddabdaccbbddcacaddbcdcbabcbcddbacadaacabaddbdaacabcaadccbabacaacccddaaaaddaaddaadcbcbbacbddadccccbddcabdcdbbcadcaccddacbaabbccacbbbccdbdadbbcddabacdcacbccccdbcaccccdcaccadacbbaadbcbadcdccacbbababcbadabbabaaabaaaadbdddddaddaaacddadacdadabdacadadbbaccdbcdbdbaacacdaaddabcadadbbcddbccacbcbdcacbcbcdcccbdbbddbcbbdbbbcbbbccbcaddcbbaddbdaddbbdcbdcabbdcacabcddcbadadbbcadbccccccddbcbcbccabbabccadbccdbbabcacdccbaacdadbdcccddccbbdcbadbaacabbddcbdbaaacbcddcbdcbdbdbdacaccdbcacacadcdbabbbabcbbbbbcabadcbccddbcbdbaccbdabdbcbadbbbdcaccacbaccadcaaccacbdaddcdcadccddcbcaacacbdbaabaabcdabdddabdaabcbccaadabacdcccaabcaaabbacccdacbcbdaadadabdbdcdbbaadaddbddbcacbdbdadbddbdcbbaacdaadcbbdaccaaaaadddacbbdabadbacdcccaaccbdddadccbcaaddbbcacbcbadbccaaaaabcadaabdaaabbbdbabcdbcdddcccdddccbcbbcdbabdbabbbbdadaacaabaacbaaacbddbadcbcbadbdcdacacdaaddddaabdadaabbdacacbaacabbacccdcccabaccddbcaccbccbaabbdddccaabadcdddadaadccdbadcbcdbadbbacbbcbaaabacadaaadcdcddddbaacdddabdddadadddaaccbabdcadbababccbddcbcdcaaaadcbcbcabcbdbbacbdbdcbbdbcccaaacbcdbcdcdcacdbcadadccaadaadabddddaacacddbbcdacaccaaabccacbdaabccdaccdcdbabbbcccddcadbcbdcddabbbbbacaddabaadcadccbacadddcdcdcaddabbcacdcdcdbdcdadcbdcbccbaabdaabcdacbcbcbdadadbcdbacbdccacabbcbdaabacbdaaaadcbdbbcbcddcaccaabadbdaaacadbadadbdaccbcbcbabcadddaadccdcadddbbbabaabdcdcddbabcdbdcdabcbdacbaabdadcbdabadcabbccbdacbaadbdddbbdabcdddaacccddddbbcadacdbccccccbddcbccccccbdbadbcdcbddbbbbdcbcbcbddddbcaaaacccadcaabdaccaaabdaacabdcdcbdcbadaaddadbcbddbdcacddddacdbaaaddcbdcdacacccaacadaabacaabdcdccbddadcbcaacbdcdabcddddbccbbabbcbbaacbdddcdddcadddabddbadbbddbbabbbdddcdbbadaacdbdcddccdcdcdcacdbddacbbbacaacadadcbcbcbdbdacbaccdbdadaabbcbcccabaadaabbcdcaccacdbaabcbccbcbacdaabdabdabababdabdcabbbdbcacdbccadcdacacabbcabbbbadddcaacdabdaacdbabadcccdbdbdbaadcdaacadbbccaadcaaccddabacdcccdacabcbbaaccdcabddcdbabcdbababcaabdabcbacbdcacdaacadcbccaaccabdcbaadcbcdccaadcdacdbbbadacbabababacbddbcaccbccbbcdcbdaaabbbabadbbbdadacdacaaadaacdcdacaacdacbbdcdccdbcdabbbadacbdadcaabcbacabbbdbabbdacbaadcaaddcddcadaaaacbdbbbbcccacbbcbdcccbbcbccbbbbaabcbbcacccdaababbdadcabacbaaccacadddaccacbbdbaddcdccdacdbcdcadbabdccdbcabdadbddcacaccaccabadabdbddbcbbcbcacdbbadcddcdbbaccccbdcbbcdcadaadadadcaaacbaaccbbaadcbbdabbadcaaaabdbabdaaacaddbacbbbcacacbbcbacbdcccdddbdbdcabaccbddbddadbaddbdbbcbacabaabbbabdbddaddcbdccbbcdaabdbcaacdccacbdbcaccbbdcbbacdccbbbdbaddaddcaabdbccbbdbbcbdccddadbcdcdbadacdacddabbbabcabcaaccabdcaddacaccbbcdaaacdbcabdaddaaadbcbbcbbcbddcaacbbabdbddbaabbbbdcddbcbaccadabaaadcbabbdadcaccaadccbbbddbdadbcabdadbcdabddaaddcaababdcdbaabadacbbbacccdcbcdabcdbbaaccbcbadacbdbbdadcadccaccabbabbcacadadabadddbaabddabcacdcaaacdbcbadbacbdccabcddadabaaabcaadbcdbcadabdddacabaabbbdccadbabcbdcbddbdacadcaadbcccccdaddddadabaaddbddbccaaacbaccdbcbdbddbadadccddcacabcdcccaddcdcacddbbbbdbbabadcabddddbdbcadcbdbcaadcdcbddbcabaccbccccabcbdddcdcbbdcbdcccbacccbbdbcbaccdadbabcccaddccdbabbbbdaadbcadcbddcddcccdadacaccbadbbbcbdbcdadcbbdbabdaacacbabcccbdbdbdbdccdbcacdbcacaaadccdcdddbdabbddccdddbcddcdcaddbacccbbcccbabbcbbbaacbdaaaddbbacdbbdbabdcdcbcbaabccdddcaaacdbcdccaabaddddabcdbcdabcddcbddccdaccaaacbbbcbdcccabdaabcddabcbcdcdbcaadcbddccbbdcacddbcaabdbcdbabcdaccdaddbbbddabbadbcbbacddbbbdbadcdcaaddbaddadcdaabdccbbbddacaadcdacdaabcddcbadcababbdacdbaddadbadaacbaccdabbcbbccacdcccababbcaaccaccadbbbabcaccccbabcbbcabddacaaaaacbabddcaacbcbbbbbadadadabadcbbdadcaacccddcadbbabbbbbacbaccdabbccccbcbbcbbdcbcdbacaadcaadccacccbabcdbdccdbcdddcacacaddaddacbccdbabaabdadccdaaadbcbbcbdbadcbabcbddbdbbcdcaaaaccdcacccddddabbdbbaccabccacbbacbaaddabadcdcbabadccdaddddcbaacdbcdcddccbddbccadabdcaadcddbdbabccadddabcccdcdbabdabdcccdacddabbaccccabdbbaaaddbbcdcabcdbcaddaaaacabccabcbcabcadaadcadadbaadadaacdddbddcdabdcdadacaccbadbadaddbbdaacbbbbdcdbccdcacdddcdaacdaaadbdccaabbdcbacdabdaaadccdbcabcadddccbabadcbccbadddccccadabdadccbcabdbccbabaadaaccbcbbcdbbccabcbbcbabbbdcabbdbabbbadcccbadabcbdcbdcabdbacbabaccdaabdbaaabbbbbbcdcccccabadabdaabaddcdccaaccbdadbcacdcbadbabdcdccbcbbbaadcdcbacbdacbabbddddbdcdaacbdbacaccbbbdcbbbdddadccdcbbacbdddcaaaccadbdaddcacaacbcaacacddcbdddddbccaddcbabadaadcdcbdbcaabdcadacbcddcddadcbbacbccababdcbbccdadbaddcbddabdbacdddaadcabbbaaaaabdabbabdacbdcddddaddbccbaaacddaccbaccdaacbbbddccbbddcdabacdaadcbaabbddddddbdbdaacaaaccdcbbdcabaaabbaddbddadabadcddccddadadabdcdababaaccccbdbddcbcbcbacbbcbbdaaabbbcdccdccccabcaacccacccaabadcbcdcacbcacdcbbabccbbbaadddaadcaabccddbddcddbadcadbbcaacbbacabccdbcdbaabbbcccadbaacbbdcdcbbddccbbabbabaacabbbaaabadbcdbdcbcababdbbcaddbbaadaabcdcabadaadaabccdcdaaaccdadbcabbbcccaaadddbbacabcbcbcbbdcdbccbcadaabdcdddbbbccdcbaaacdcbbdddacbddcdbcbadcacaacccbadcbaabdcadaddaacadcabdbbaccdaccbdbcbbcbbcbdbccdddaabbbadbccaabcbcdbadacddadaadcdacccaddbbcabbacadddacadadbdacacdbbdcabbdadcbdcdbcddcbcbdbddbddbacccdccddddddacccbaadcadcbcabbcbbddccabaadacaabbbccdccaabccdabcdbdcccbaaacacaccaabbabddcccbbcbbbabadaacbadacdccdbcadcabacbcadaabacbbcabcbbbdaadadbdbaaadcdaadababddcbdadcadadbdacdbdaacbddabcbacccabccccaaabbdabbaaadbbccbdbcccdaadddabadbbbcdbcacbcbcccbcddbcacbdbdcdaaaaaacabaccddbddabdcbdacbacdbcdcddaddabccaacbbbbaddbbdbdcabdbdbbaadbdaccbbccbbacaccaacdbbcdacaabcbadabcbbbcdcadabddbdcaccadcbdddaaaddccbbacbcadcbdacabcdbacbccabddcbccbabbddccdaccacdbabbaaacacadacddadbcbccbcbabadcdccdddabaabbcbcddaacddabadcdadadcacdacacbbdcacbdadaabaccccabbcdddcddadadbadbbccbaaaacdadddddabbaabadddddcbdbdbbbacbdacabcadaabcbddcdaabbbadcddbbddcddcabccabccdbaacabccccbaadbdddcbaadadcbadcbaaaddcdbccbacdaaaabaaddaababadcdbbbdcaabdbacddbddccadcaacbbbcdcbcbdccabacacdacaddcdbacaaabadcdcbbabdaaaccbaabcaabbdccdccacdcdbcbdbcbbdbdaabdacdcbcdcdcdacabccdaadcaccdaddbdbbddccaabaddabbcaabacbcdbbbdbadbcbbdbdcbbcacdcbcabdabcbbadccccabcdadaaddaaddcdbcbcdbabbcadddaabaabaabddadbcbadcacaaccbbcdccbbdbadaccbabcaacccaadabbcbabcacbbabadccadbddcbaacddcdcbabddbcdbabcdcababaaacabcbcddcdaacbabddabbddddddcdadbcbcdcdcbbbaacdbdcdbbacdcccdbbabbddacaccaacccdccddabdcbbdacbbacbccbbdbdaccddaabbbdbdaaaaaddacaddddacdabbcccabcbaadadacdbdccbcbabdaacaabdacccadcccabdcaababacaaadaaaabacdacabdbcdaabaccaacacbbaaaadcbcaaaabdabcdcdbbbdadacccabddbdbdcbacdddcbbaadbdadaabddabcaadddaccbbacdccccbdabccbabbabcdcdcdbdddcbabaaccadbabaabbaccdbcaddaadacddbdbcdbcccaadaabbdacdbdcddaaccadcdccbbdaddaaadabbddbcadadbcbadcbcbbccbaddbddbbcadddddcdadacdcccbddabcccababccccbbabdcdcdbbababbcbcaaacaccbbbdbbbbcbbaabadaacdcadbcdbdabdacbddcbccddbaddccabcdddcccdbbddccabccaaabaaabbcbcbdbddaccbccdbcddbdcdcadbdcadaddcacdaaadbdadcbcbaaacacaddbbdaccbacacaccbbcccccabdbddcccadbbcbcadcbcdcddcaabdbdbadbcdabaccaccdaddcadddadbbbdcbabbaddcacdcaccadbcdacaadcbadbcadacabcdcdbcdbdcacbdabbabaadcdcdbccdaccbdacadadbccabbdccccacaadabbabacbaadacbcbcabacbcadcdcadbacbbdcaabbdcdcbacbaaabccacccccbdddcbcadaaddaaddcddcbbcdbccbdadaabadbdbcccddadccddbbccbacdadcdccbdababdbaaabddaccdbdbbabcadadaccadddccdbdcadccbbcbdaadcccbdbbcabddbbcabddbadcdcdaddbbbcccabbdccdbdcccdcdbadacbcbbbdbccccbddbddcbadcbbdbdacdbcaddcbaaaadcdcdadbbacccadcccbddaaccadcddcccbdddadbdaabacdddaacaacaabbbbcbddccbcacbcdbabcccbdbdabdabacbaaccbbdddccaabdccaaadcabbdcacabcdbcbcdbcbabbadccdbbbdbacabdcababbcbddbdbcadcbdbacddabadcdaacdccbcbacdaabaacbbcbdddcadcdbbbbbcddcacdbcbbacbdcdddbdbcbdbccbbddbdcdccdddbcaabaabcdbccdbdcbdcdaaccbbcaccbdadccccdbcbddddbdcaaabbccaddccddbdcdddbbacdcddacadbcabdddccbbcadbdcdcbdbcbcbbadcaaccaadaaacaabdcbddabbabbcdcbbaadadbaaacadcadaaddbbcaccbdccadcbabaabbdbbbbcddbbadcbcbadacabbbdaddcccbaacdadbdcddacbbccccabbcdbacdaccbcdbbaacbdbaabadddddacbdadbdcaddabcbababcbccbcaadcddcccabddadacdacaabacbdbadbdbbccdabacabcddbabcabacbaadcbccaccdbccdbbdcacccadbdbcdcdaccdacdcacbdbbaadabbacccdccdcbddaaaababbdcbcdabcdbccabadbdaccbbaabccdcbcbadcbdcacacdaadacbccddadbddbccddbcdcccdbdcbdccbdddbbccabaabccddddcdbcddaccbbddccbdddaccabcdadbcddbadcadbaadbbadddbdacacbcbaddbddbdccbdbddbddccadbacdbdaaaaccbcdaccdcbcdcbacdbadadadbcdaadbaadccccbdbcaddcbdcadbdcacbaacacdbdbcbbbaaadbaadddccadaccabbbcabbdbcaaaabbbdddcdaacbbadabbdbbcacdaadccdbabdaccbbdddcbdcccdddbaaccccccdbaacdabbbaabddcbccccdaadaaccbccaaabaacaaccbabbcddbbbbccddabdccacccdddabbbdddaacdddccadcbcddabbbcbdcbddaabaccacddccccddbadbbdcdcabcdbdbdcdaaadcbdaabbdbbcbdabcadbbccbacddbdcbccaaacbbcbabaadcdbcaadbacbcaabcacddaddbdbabadaddddadcbbbbcdddbbaccdabdababaaabcbcbccccccbbbdadcdddaadcbcdddcadcbbabbcadaaadbccddaabdbbcbbbdbcbaacbabbabaacccbcddbddcaaadabadaaaaaadbacdcaddabdddbccbbccdadcdcbcdabbcddadcbcdbbbcbacbcdbbcbdddcaaaababdadbbaaaacbaabaccbbadcddadaaaaccacbaacbcbbcbacdcdbdddbccabdccdcacdaabaaccdddbbcaaabcabcbaccbadbabbaabdddbbacccbabcbaadbbccacabbaabddaabbbbdbaaddcdbabcabdcdbddabddabddabcccacaabdcabcabcbddcabadbbdbbdbbcacaabcbaabcbacbdbdbbabbdabadcaabdbcbcccddbbbdadcdcbaadccbdacacadbcacdaadcaccbcabcbdbcaccbadddcbcddaadcdcbdadacdcdacbbabadbbbadbbdaaddcaabcbbaabbcabcdcabaaccbaadcbbdaacadabcdcbbcdcadbbddbcaddcccdcdbaadcadacbbbccccbbdccdddadcdadcdbabdcbcbabccdcabbbbdcdcbddcbbbabbbacaaccbbbcddbddddadbaaabdaadccdadbddabdbdaaccdbcaccadccaabcabaccbbbbbbcadadddcaacdaccbbdbcdccaccbbdcbdbacacddcaddcaadadcaddbabcdbbbbbcccddddcaaccdbddcabddddadabbcbccacbddccaccdbbabbbdcaddaddbdadcbccaddbdabcbcddcbccaacadddabcbbaaaccbcbcddbadaaacaccaaccaaabdaccbcbbdbbcbccddababcaaadaccabdddcaccdbadaacbbccddadadccdcbaddbbdbcacadbbbbcaaadcdcadabdbbbbbcacdcbbadaaddbcbcdadcacadbbacacdcdcdabcdccbabbbacadbdbcddaabbcdcbccbbcbabbbabcbcbddccbccaaabbdacdacbabcaaacdcdbabcbbadcaaacabdcacbbcbbcdbdabdccdbabcadcadcdcbbdcccbcdbabcddcbcdcbcbcaadadaddbcadacaccbaacaacdddbddcdccbabdaaaabdadaaacabdabcbadcdcbcdcabdadaaccdaccdbabdbddcbababaadbcdaadadcaacdbdbdaddbadcbaddbdabbbcaccbaacadcddabbaabbadacdbaaccddbcccdcbaccabcacdccaaccadbdccddbabddccddbcbbcaddbadadbdbabacdccdcacbdbdcdbadaabbbbdcaaaddbaccbcddcaabcdbddbadcaccbbdacaaabcdcddccbcbabbacdcdbdddcacaabdacbcacbccacddcabdaaccbadcccbccbbaabbaaadccbadcaaddbdcbbdadcadbacbbacabbacbbbccdbaddddbbcddaccdbaaacbcacbbdacbddbadadaccaddbdbcbdbdbdbdcdcddbbbaddbdaabbabbdbdbcbbdacddbcccdaaaaadcbbabdcddbcdbdcababcccdbcbbbbdbababadacccbdadbabddcbccaaaadcbaaabcbccadbcdadacbbcdcadcbcbbabccaddcaacacdaadaccacbdbaadbaacddbbaaaabcacbaccabbbdbacbdaabbcdcbaacbbcdacbbbbdabccdbdaaadaadcabcbdbcadccabdadadcccdbdabaabbcabdcabdbacdadbdcbdcaadbcbaacaacaacaabdcdbacabcaacdcdaccbdbacbaaaddcdbddaacbbadcdacdaddcbdccaadbdbcddbaabcccaddccabadcbdbbdbbdccaccadbcabcbdabacbbbdbbacacaccbaddccacdccabaacccdccccacdacccacabbdaccdabdccabdcadccbcbcdaabaddbcbacbcaadbbadbbbbaccccbcabcacbcccadcabcddaaabccdbadbdcdccdbdadbdbbdacbbadbababccaaaddbdadbccaaaabcbbddabccadbabbccadcbddbcdacdaddbabacccddcbcbdcbdccdbadbbbddadabdadddbdaddcdcbccaddcdddbcdabdbbbdccacccadbccbadacacabcbcdabdbcadcddcbabbacbcdacddaabacadbacddbcdabbdbbbcabbabcbcdccacbbccddbacbbacdbcaaaaacbadaacaacddadbadbabdcabcbbcbcddcacbadabcbbabcdccddbadddbbdcadcdbbdbaaadddbbbdbdadccbababbabcccacdbbdbddcdaaabadabbabbaadccaadbbccbbaaddadcbdabbabcbaadcbdbddbdbbabaccbcbdddcbacabdcbaddadbcbadcbdbacdbbadabbbcababddacaadabcbacaabddcdabcdcbdbabcaaaaaacacbababaacbcbcdbaaaddbddbcaddcddbbdabcccaabddddddabbbcddadbcabcddcdcbbcbcadabcbcdcababcbdbbabaacbaddaccbaacccdacbadbdbbcabacdccdcabbabacaaabacdccdcbcdbbcdadabcaaddabacdbacdcdcdbaabbbcadbbbcabccdccccabdbbdddcabbabaaabaadcbbbdaabaacbcddcdababddbbadccdbbbccdacbadcdbcccbdbadbadbdbbadabcdcaacdcbbdcaaddcdbbdcbcddaaaccbcadbcabdaccdaccbcbacbbbacbadadcddaadcdacadadcbcbcdacddbdddddaabbadbabbcbadabbbddcbbbbddaacdcbdadcbcdcbabdcbbabddbdcccbbbacbcbcaabbdcdcddcddbcdaadbbdaacbbabadbadaadbbdcddaababcdbaabbbcabbaadcacddacbbadbcbbabdacaababddddbdbcdbbcbbaaddddbddaacdabcbbcdadcddcbdddaabcdabccccdcbbbdaddcaacdcbcabbcdbdaaacbaacddacacbdbcadcacadabdbcbcddbbccdcccdcaccdddaaccdcbdbabbddbacaddabcdddcbbacadbdcbadaabdbbbbdadcdadbabdbcdbaaacbdbbcccaabbbadbdcbcabdadbcccdadbdacababbcbcadccdacbbccdccbdbcddcdcbdaaccbdcbbcbdccbcacbbbdbdcbbadcadbbdabadbbcabbabadbabdbbcabaabcaabaccbadacbbdacadaccdcacbdddbdcdadccdbddddaabacbacbbbaddcdcacbcdabdbaaabdadbdbddddacdacabccaacaaacdbcdacdcacadacbcddbcddabcddbadabdbbdbdbddddcaacbaddcdbdddbaaaaacbbcbbaccbcdaadbbbcdcbcccddddbdbdcbcbdcdacdccaccbbabbcbbddcccbadbaabdbbbdabcabcccbcaacdabdcaaabdbdbdcdcbbacacbddabbccbaddaaadbabadcbdccadbdddccbabbdcabdbadbbbddcaaabccdcbabbccbaaacdcaabcbdccbbdcadcdbbbccadbdcdabbcddcdaacccdadacbcadccbbcdcdcbcabdbbbdadbccbcbccadbdbabbcbcaadadadaabbadaadacbdccbdbbccaaadbdcccbaadbcdccaabcbcbbdadacdbdabcabbaaadbdabbacbbaccacadbcdddbbbcddbbbcadacadccbdbaacbbaaaddcaccddbccdabccdcdadcabbccaadddccdcdaaacccaadcbddcdbacccbcadcdbddbaaadccadbbacbbbbadbacdbabdbaddcddcccbbaabbabcabcdbdbccaaacccbcaadaacacabdbbcccdcbcaacaaccaabbaccababaabacdcadbddbacdccdcaaddbadcbcacccbbacaaacaccbbcbcbbbcccabdaabddcccbcacdbcadcbcbadddbdbdcadcabddbaadcbddbcbcbcdacdacdabdcbddbabbcacabdcaddbcadbaadcddbcabbccdacbcabddadbcdbbabdabbbadacddddbbbaaacbacbaacccdccbbbaccbcbcaaadabadcddabbacccbccdacccccaaacbcbbdddaacddbabbccdcacabbddddcdcbdbabdcacbabdaacdcdbcbbbdbdaaabadbbcacddddacccdcaacaddccddabbdbbadcbaddcaaacdbcaddbbdabcbabacbdbbbbdbbdbbabbdcadcdcccccdbaaccdbbcacbbaddbbbbdbbbbdcababccbaadabcddbaacdbcdbddbdcacdadcbbcdabddcaadcbaacaabbabadcaaabadacbdbdbbdddacaabbaacdaaddbccacbbcacdbaddbcbbbabddcccdadaadbdcbbcdbbadddabadcbddabcdbaabadaccbdaccccccaadcccdcdccacabcddbbcccbbdbaccaabaddabcbaaccdbbbdadbbadacaaaaabadbdacdcbdcccbcbadaadabbcdcdabbbadcbcbcaddccdacbdbbabbdbcaacdabaccbdadcbbabdcaaaadcdbcdcbdbacbdadadbcdcacccbcdcbdbddbacdaabababbabdbacaadcddadcacbdcdacdabbaccaabbcbadcddaccdcdcccaccdcbccabadccddadbdabbaadcbdadadabdbaacccbadaaccaadbbabccddcabaacadaaddabdcdcbbccbbccacdbddaddbccddababbcdadadbdacdcbcaabdddbbbbbabaccbdcbaddddaabbdbdcbacabaccadccbcdacccdccdaacbcabdadabbcbbbabbaddaacabcdbcdccbdccabbaaddbaddcdddcbddbbcbdccaacdcbcccccbcbdbdddacdbddbbddbdadaccbadbbbbcdbdabdbbbcabcacbddbbcdddadcdcdcabbdbccbbbdabacdabbccddccacadacbdadcccbadcccaadaabcdbcdcbabdacdbccbcdcbcadaadacccbacdadcbcbcddbddbbdddcbbadbccabcbcbacdbadbbcaaacccabdaacbbbbbddccdbcadbacabacbdccdacbcdccabadacbbadcccccdbbbdcaadbcabbacccacbbadbcdbdaccbcdccabcabbdbbcabbaadbaacbddbbccaaccbddabccdbbadcddcdbbdbbbcddbcdbadcbadaccdababdbdaadbbccdccadaabbcdbcbaddbdbaaddbbdbbcccacaacacbcabaaccbccabdcabadbcdbabcddbabdaabdacdbcdccaddbccbaabbcdcbddcbbdabcddcbdcdadccabacdcabbcbddaaaddbadcadbcbbaaabddcbdaaabcadabdabaadbbadadcddbbaccbdcaacabdcbabaacdbdccacbaaaaddabbccddadadaadbbabbccaaacdaaadababbbbacabbccddabcadadddbccbcddbabddbdccaccdadcbadbacacbcdadcabbaaaadbdadabbaacbdaddcdcbaabccaddbdcbdcabbacbdaddccdcbdaabaacbaccbdacbbddbbcaddcbcadbbaadaddadadabdddbacaccdbdadcddbabcbccbabaaaabddcbbacbaddcabdbccbcaddbbddadbcbbbccbacaccbadbcbccbabddcccdbcaaabdddbcbbabcadadbcdcccbbbcadbcddaccadaddbcddaacdaddacbbaccabdaaaacddddbacbadabcbadbaabadbcdcdcbbabcaabdbbccdaaddcaacdbdaaababcaccbdabdbdadcabdbabadacdcabcccabacdccdcacbddcdbdabcddadbacddcddddbdbcdbdddcabcaacabbbcbdabbbbacbccdcddaabdbadadcbcdbdddaddaaacaaaacbadadacdcacbcbbabaabadbbdadcdbbaacaddddcdbacbcbbdcbcababaacacccbcdbdbbaddabaddadabcbcdbcadadbbdbcbcccddcaddacdcbccdabdcacabbcdddbaaabbcbddbababdacabdbbaabbdcaabbdadbbadcdcbdccbdcbdadbabcccbbcbcbabcbdaabdabaacdacadbcbabacabccbcbbbdcbdbbacbcaadacbadacaaababdbdbbdadacbcbaadcbdadcaaccdaadadcabbdbacabdbdbbccadaaaabdcaccbcdadcdbaacddcbcbacbccbaddcabddbbbbbbcccdaacbddbadbbdabcdcccaccdacacbdacbbddcbcbabcbbadbdadcbcbabbbbaabdcabcbaadbbadbbbbadbabbcabbddacbbdddbbbaadadcbccbcdacaacbbdadaabccdbbdcaacccaaccbbdddbbaaaacdaaaabadbcddbaccbdcabdbabcccdbdaabbcdbdbdbbbcccbddbcaaaacbbcbabcadaacbdacdcadaaabaacababdcddadccdddacdabcdabaddabdcdbbcdcddababdbadbcdbabcadadaddaadcbbacdbcbacdaaaaadccbabdaabbaabbbcbbabcaabdadaccdbdaaadbdcdacdadddaadbaabbbabdaaccaadbdadbddaacbaaccddbbcaacbaddddbbdbddabcbbbcdaabcaaaddcbdbdcbcdccbbdaacbcaabadacaacbacccdbdcbbadcbbbbddbdabcbdccacbccaabcccbacdacddacccababadacbcbbbadddbaadbaaacccaccbbdcccddbcadadccaababaacdddadadcdaddcdabcdbcabccbdbdccaacbbcbbdcbccadcddcdcadcbadcdcbdcaddbbaababbaaabacaadabcbaccdbccbbacbbcbaddaccbbddcbaaadcabadcbccbcaabdabcddccbadcabdddcaabcaadcaccdcdaacdcdcdcdbadbdbbdbabddcaababaabccbcadcbabadddbbbabacaacaabdbaaadbacdcbadbbbdacadbbdddaaaddaaabcbcbdbcdacaaaaddadacacbbbacbaacdaabaaaaddabbcddbdbdbccaabbcacbcadcdcddbbbbdcdabbdbdccdccabacabcbdbdcdcaccbdbaadaaacbadabccaccabbbbaddccbacacaaaabcdbabbaaddcccdadbbcdcddbbcbcaadcabdccddcadddabdcbdddbacadddcdaacbaacaddadbdccabbdbcddacacbbbacacbdbbaaadcbdbcccbbccdaccddbadcaccabdbcbcccaddacbdcdcdababdaadcadcaadcdadabacbababbbcabdbadcddbcbbcaadadacbabdcbbdaddcaaabaacdaddaabcbaaacadbbbaddbcdccdaadbdbadcdcbcaadabacbcccddaadcbbcdaacdcabaccdabdacdbcccdbccaabdbaabcbacdacbbbdbbbacbdcabcccbaadbaccbcacbdccddcdbbcddbbdbaaadccacbacdbdabdcddccdbadaacaabcaacadbabcdadddbcbcbbbccaaaababbbbcbbabacabddcabcbcdacbddddcbaababcccdccaabcaabccdddbadaacaccacbaabbbaccdcbddbdacbbaaaccdccacdcdddbdbdbddbbcdadaabaaccaccddabadbbbaaddaaaaabdadbbdbdacbcbabdbccdcdabdaacdcdddbddabdbdbbbdacdbbdbcdabcabdbddabdaadacabccabdddbcabbcdcccdddadccccccdabccbababddddccbbbbbcdabbbaacbabdbaabccdddddaababbbbcbdddcccabacccbdadcdaaaaabcdbdbcdcabaadbadabbdcdbddbccbdbdacabbdbdccabdbdbdabaddaabdcbadbdcabcbacaadbcdcbcdddbdcbaabdbcbaacabddcbdcbacdaaadbcbdaccadabdccbacdaaddbbacbbbccdcdbddccddddbdababddcccddcaabcbddacbdddaddbbabddddaabbaabdcdcabacdabaacadadacbdbbbbbbabdaabccbdacabbcdbdaacdcdcbdcbadcbaabcaaaddbcccbaacacdcabbbadacdbdbcaddabddcdbdbdcaadcadcbabccdbdabddabaaddbbbdaccbaccbcbbdbcabdbccddabdbcbdcaacacbacdaabccdbcbaaadbdcdbacbbacadcaccaacbcbccadbdddcdabccccdcbbcaacadadbbcacdacabbcdaacdccaccadaaddabdccdaccbacaabbcbbadadcabcbccccbcccbacddcacbbdbbcdcdcdddccdcadbccadacbbdcbaadbdaadddaccddddcacadaaabcdccaadcdabdccdacdaabbdccbbbaabacbaabdbbdbddddbdcdddcaacabdbaaddcdcbcbbaaddcbcadabbdccbabcbcbcdbcacdadacababdaaacbadacbcabdcddbabbaaccacddaabbdacbacbcccdabbbbbdbaaaabacbabcbdabbadccdcdadcbcbaddbcdbddaaaaabccabcdaacbbabdbbbabbdbcbddadbadabcadaabccaabacdcbcacdbcdaadabdbbaaddaaadcabbbbddbbddcadbddbbdbcacbadacdabbdccdabacaddddaccdaadbbadddacadadccddbdbcbcdddcaabdabcbabddcabbdbbcadbcbcbbdadcbabccaccacbcbbcbadbabcddcdcdabddabcabcabbcddcdcabdadbddddbbdbcdbdbcdcadccccccaadadcbdacaacbaaadadadcdacbcadadcaddbddaccbdcabbcadddbacaaccbaacbcbdacacbbacdbcbcddccadbdcdcccabbbbdaacbcbacbcdcabacabdadcaaddccdbbaabbacacdbadbcdaaccbbadcdbabadadacaabadbcccbccacbabbccabbcdbbbcbcaaaabcbaabbdaddccdcddccbacdcdbcbbadcaadbbbdddbcccccddbcacdbddcdabbcccddddcddcaaaaaddaccdaccaacddbdbdcadbaabdaadacabdaabaaccdaabbbcaacbcbbcaabacbcaaccdbaaaaadccbcaccbdaddcccbadbdbaabadddbaabbdadbdcdcaacbbccbdcddbdddccaaddbddaaabbdddbbcbdcbadccdaaddcdbbacaddadadcadaccbbdbccaadcdcddaacbaddcccdaaabaddbdaacabaaacdaddbadcbbbbcdabcbdddbbdbccbacddacccbbdcdbddbccddbbabdbddadacbaabdbbaddbaadbccbbbbbabbdcbabadbcaddbcadccbbacaabbaadbcbddddaacbbcdacaadcdbdbbacabbccccabcccaacbdddcbddcaaabdabacbdbdcbcddbdbdcbdacaabaaaadbcdabdcbcddbdacdddddaaabdcaacaccddbdabbdbbbadcdddcacdbbdacccaaadcabddccadaadbaccccdcdddcabcdccaabdbbbaabccacadcdbcaadbaaccdadacdabddaaacbdacadccdccaadaccaadaaacdaccdadcddaacabcaccacbddbddbdcdbdbaacbcaaaccdbbdbbdddbcbaaabddbcdaccccbabdabcbaddcabddadcbcbadbdaaccbabbbccbbddacdddcaaacddcacbacabbacadbaaacccaaddbcbabbabaadbbcabcaadbcbbbdccccddbccbdcdbccaacabccdadbaddadbbbaccbbcdbdcbaabcabcacdcabdddaadbbdacbdbacdbcdbdbaabcaacabdacddcbccaccbaaccaaaccddadbbcabaaacadcdddbbddcabacabaccddbadbcbcadbbadadbbbdbddbdbdcadcbacbabbaabbbbaddadcccadddccdadcbadabaddbdcdddccbdcbbbbcddbbddabccccbcabcacadcbdbdcbbdabbbabcabbbdddcddccdbbadbcdbaabcaddbcbcabbdcddbdaabacdbbabaacbccbcdcaadcacabdcdddbbaaacccacddddacbadccabcdbdabbacaaccaaadddcaaccdbabcdcaaccdababdddadbabaaacbbbdbbccbcaacaccbaaddbddadcbcbbcbaacbcdccbacdccabcdadabbbaacaccadcbabbdbbccadcccdddaaaccabaabcbdcacdbaabaaabdabbcaccdcbcccdbddacabdddbbaccaadaabbcadddacbbcccbdacbcbacdcdbccdcadddbbccdbcaabdcadbcacbbcbadaabdbbbcacbcaadcddcaccadccaccdbdaadcbddcbaacddbccacaabdccdcbdbdacdbabddadbbccddbccccadbcbcaabddacdacadabbccddaacdbadccadabaadcdbaaccbbdbcdaadcbdaabcdacddccadbacddcbaccbcbbaddbdcbbbbdadcbdbaadbcdbcbbadcdcaabbbcddadcadcdbdaabdabddcdcbbdbdabdaddabbccadadbbbcdacbcbccbbacacdcbaccbbaaaabbbcbcadbbdcaddddaacacdbddaabaacdddacdbabbddbdabaccbadacbbabdbbbcdbabdaaacacacadadaabdadccaacbdcacdbbbcdcbcccdbadacddcbddaacabaacdbdbabbdddccdbadccacdcbdcccacdccbbdcdadcdbbbdcdadabbddcacacdbbddbaaaccacddccdbdcdbdbdacbcacaabbdadbdabbcbacdbabcabcacbcccddcccdabdadbbcabbdbaabdcabbddbbcbcbacbaadaddcbcbdadcbbadabdbacbbbbacbccadbbcaccbdcccacadbcbbbbccabbcddbbabcbabbddabcacdcdcaccaddabdcbdaacdabddadccddccabbaacdbaabcbcbbadcaadcbabacbddbddccbdbcaabccaaaddabadddacddacbacaabdbdddbccdaccbcbbccbdadcccccadcadcdadaaabdccdbbabbaacdacbbabdcbcbcbdcbacdaadcdcdbaaabadbbbacbcbcbaabcaadadcdcdbddacbabcbdbcacaaadddddabdadabadccaaacadddabaaacacccacbdadbaccabbdbbdacddbdacdabacabacdcbbbcadcdbacbcaddaccbaacabbcaadddcdadcbacdcdcaaadbcdbdadbaddddabacbcacccabcabddadadccaddadccdbbacddabdbabcdbcddbdbbcdccbbdbccbdbbbbbbbabdddddaccaabababaabccaacccbdaddbdbabbdbccbccddcdccbccdcaddbcccbadcbbaabbddbcabdddccacaaaadadbaabcacbabdddabcbcbbacdcbcccbbdcddacddbdbaccdadbacccdbaaddacddcddaaddcccbaaadacabbdaaaaaadbcbbacabdbcccdacdcbbddbddcdabbacdddbddadcbdcbdacbbdddacccbbbaddcddbbdabdbbbbbbaaadabdaabaadbccdcddcbaadaccadbacbbcadadacdadbabcdddbbaacdbaadcdacdbdaccacabadbdacbaccabcdddaaccacabcaadbaadbccdccaacbccdbbbdbdddbccdacccbacacacdaacdbcadaaacadbbaaaabdcbbaacbbabbddbcbdaccbcbadaadabdadacaababbbdbcaccbabacccbdadbddbbdcaaccbcbdaaadbbcdbadaccdadccbbaaccbcbdabdaddbdbcbcaadabddbdddcccdcbdbadcbccaccaaaddaadccbcbdbcdabbbabbddbcbaadcbbcdbdcdacababbccdadaabbcdccddbdddcbccdaadcbabddaabdbacdccdadabddabbdbcbdbbbddbaabdbbcdccddabcdcddaadaadbdaabcbcdbbddcdcacabdbcbcbabccdbddbdccdddbbcaaadbbdbdcdbbbbacbbaadddabccadbcbdadbcbdabcbdcbaddbbcadadabddbbacdcbbdbaaabbcdabcadbabccdcbcdbdccbdcdcbdadaddbcdacbbbdcaabcddcbbabbdcaaacaadcdaaadaddbccdadcabdbacbbaaabaddbcccccddbcaacccbdcadcaabbbaddadacaadccbdcddcbbabdccdabaabadcabcdbadbbadcdadcbbacaacaaccbcdadcbdaaaaddbbaadcdaddcbacbcdaddccdadaddaabcdccccdadcacbbcaaabbcdbbbcbbadacccccbdacacbbcadabbdcccdabbaabcdcccdddcccdcbdcbddadabaadbcabbddcdbcdbbcbacccbacbabadbddcabbbbdbaaaabaccaaabbbcbbdbdbddcadacadadddcbbadbdadcaadcdaacbaababcadbddbccbcacacdcbaadcbaaacadbddbababdcaccdbdaddcbadddcdbdaaabdccdcaacbabcbcdccdbdbcabccbdadbacacabcbdcbdaccdddddbccbbdcacbdaaddbbdaadccdbbdccddaccbbcbbaccbbdaaabacacddcaddabcdbcaacbadbbccccbaabcccbbdcbbbdabcbbababdbcacdaddbcabdadbcddadbcbccbbabcaccbadbcbabacbbbdaadcddcdbccddbccdbbacaaccbbdbacbbddbbdbaaadddbaaccdccaddadbcaaabddabaacbbcbbdcddcaccccdaadbaddcddbaacdcaacbbabdbadbadbdadacadbdbdccbcadadabccdbabadbdbcdbacbaadaacbcaacbbdcadcacbbbdaccddbabdbbbaabbdbcabaadcbcdcdbbcbdbccdcabdbbcdbacddaddbcdcabbbdbabcbdddcdadddbaacdacbbbacddbbdbdbabbacddbcabbdbabadbcdacbbcaddbcacadbbccdcbbbdbcbadddbdddbbddcbadccdaccdadddbaccbdbbccdbcbddabccadcccccacabbdabdcbbbacbddddddbcadaaaaccbaccddacdccddaccbadcdcccbbcbbacaabdbdbdcbabacabdbbdbbdbcccaadbddbbddbacbacddadddcaccbddccaaaaccadacdbabadaddcdabdddbaadbcdbabdacbaadccaaabbabdbaaacacbddcbcabbcabbabaaadaadbacdaabdbacbadbdcccbaacdcbcdcacccbbbabcccabaacadddbbbdcacabddbbbccbcdbbcbbcbdadaddcbabdaabdbddcdabbbadbaacddabcbcbcaaccabcdaaaababbdddcabbcbaadaabbcbddaadcaabdcaaabbbaaadbbbdcbbabbacadbabbdabdbadadabdcbaabcaddabdaadccdbcadbbaadbbadcbdcacdaacbbbccbcadccdaacbcaacdbdcabbcbcbadadabcaaaadcdadcbdaacdbdabccddccccccccacdbbaccbddcccdcabbbddcabcdcddcbcdcbbdbdddacbcaabaccaccbbabdacbbddaccdaaddbdbabdcbcaccbcacbcddddabcabbddcdcccccbcbdabddcbcbdcbccdcdaacccaddaaabacdaccabccbccbcabacccbdcccbbddacdbbccdcbbadadadddcbadabacadacdcbbbdbaddaaabbcbdadccaacadcbdabbcbdddbaaadddcadccabbbbddbbbcbbdcaccddacbcacaacddcbacaddccbadaabbccddaadaddbbbdaacbdadacdaddbbacaadccaaddcbcccdbabcbccdcddcccbccddbcacbcdacdbccdacdabbcadccdaadcababaccabcdcccaaabbbbbcaaddaccabccdcbbaddbbccbaccacadccbacbbabadaaccddbbdacabbcbcadbddcdbcccddbcbaacddaacadadaabcabdddabbbacdcdccdcbbbacdadcbcaaacbddabcccacccbbaddaabaacacbbcddcdbcacbaadbcbdbcddbcabdcdddacbbdacdbdcbcdddddbcbcbdcaaadbbdaccbbdabdadcbccbcabaacbddacdbaddcdccbdbcccadccacadadcbbacdcbdaacaababdccabbdbaaabacbbbbcbdbdabacbddacacddacadabdaaaaacabccaccddadbdaaababbccdbadaabddcabcadcddabccbddddcccbadcccabddbdddbbcdaadaadbabdcaaabcadcbaadcdcadccdcdcdcaddacbcbbdbccabbddaaccdbdcbbdddcaadcbdacccabdcadcbacadcaaadccbcccbbcccdbdbcdadbdcacddbcaddbdabaaccdccdbadcbcadbbbdcadbcccdbcbaaaddbdabccbbabdbcbbaadccdcccbddbddacdcbbbbacbddbaadbaccabddadacbcabaaddbbbdddabbdcbcbcbcaadbdcadadcaabadabacdddccbbcadaddadcadddabdcacababcbdabdabbcbaabcccaacacaabdbbcdaaaaadddaccbaacadadccdddcacbcddbadccbcdaabcbcaaacdadabccaabcdabaadadadcdbbdbccbddabbcdbadbcdabdabaaccdaabadacbddbaadbddbbccaadccaaababaddcccadbcbdabdadccdbbabbabdccabbabbadcbdddccbcbcddbdaddbcaaddacadaadddadccaaacbcbbaccddbcddcadcbbaaadaaccdaabdbacbdbddacbabddddbaaddbcacddcdacdacddbddabdaadbdcbccabdadccadbcbdaddddbdbdbcbcdaddadbbdacaabcccbbdccdcaadbbaddaddbcabcdddabdabcbacdbacccabaabdacbdadbcdbabbbdabcbccaaabbcbadbbbdccddccaaaddbdcdbddbdbcdbdddbcddcabcaacbbdabddaaabbcadacbddbcdbcccdaaddcdcccdcdcbabdbbcdccbccdbaaabbbbaabdddcaaccaabdabacccdcaabdccccccccbaccbadbdbcbcaaabaacdacbbacdccaccaabbcbdadbcdaadbabbbaddaabacccabcbdaaabccdbddcdbcbbbddcacccacbbcbbbcbcdbcbadbaaabacbddbaadcbdaccaaaccbadcdcacaaaacdccbaacdadbddbccbbabbcbbacdcbcbacdddbbadbaabccabadbcdadabdabbcbabdbbddaccbbdcabcdbabcabbbdbadaabacaabbdbccbbcaaaadbdabaacacbbadabbcdcdbabbdcacaabbbbcddbbdbcbcacddbabcbdccdcbaaadcaccbdbcadcbbbbacaabcbdccbabbcbaacbabdcdadbabadbcaaadaacbccdcdacdbbbdacabddbaacbbbdacbbbbbabddbcdbacabdbdbaaabcacabcbbabdcadcdcbcddaccaacadadbcdbbcdacaabaaaadaabdacaabbcbccbbbaccbaaadadbcccdbcacbddcbcdabdcacddacaaccddbbcaaabcadacbaabdcbbabacdacddbbbcbcdbbbbbdcbdddcbddbaaddbaccabadacdcdbcbdbdcdbbdcbaaacdacadbaaabdbbaccddacaccacdaadcbcbcaadadadaaabdcbdacacbdabacccadcaaabbccaddbddacdccbbdbddbadaccabbdcdacaccadbbacbdbaaabcabbcaacadaacbbcaddabdddadaadaacdabdacaacccbaabcdccddcbdbdcdcbbacdcaddddadabdacbdabbbdadabcabaadbddadbdddbccdaccacaaacbacbacdbcbdbaacccdcdbabddaadccbbaadcdcbaadaaaabcbdacbcaababddbdbbcabdabadddadadabadbcdaacaccaacccdaccadcadabcacbcaacbdbddadcdbcdaadbabcdbdcbabbacadddacbabadcccbdaccbcdbadbaadacaaccbabdaaadadcabccdbabaacbcccdcdbddddcbbbbcbcdaddbbacadcbdcccbccbaaadaaddacacaacccccddadacbbabbcbcccaabccddccacaababcbcbcddddcaabaaabcbbdaadbddcbcbbbadacbbcdcdbadabbbbdcbbdacacddbaabcbacabbcbdababdccbaacbbccbbbbdddcadddbcadaadddaccbabacbabcbbcccbaccacadabacacbbadddabcdcacbdabbdccdbddcacbddadcdcdbcdcbcbdcbcadcbdbbbbadbadacabccbdbcddcadaadcadcdcdbbdcadddabbbadcbdcacccbdddadadddabadbccdcbaddbcccbabdaddddbcadcbdbcdcdcbbcbabcaddbddcdabcdacbcabaaaaadcbacabdbbbdcaadcbccdaccbbddabadacbbadcccbdbdddabbcabdbbaaabbcdaadbbdcccacdadddbacacbcdbcaaadddcbcabadabbdccbccddabaacbaddbccdacccdddcabcacabdaaddbbbabbaacccacdcbdbcccaccbbacbbbbcdaabcccaddacacacadadaaccddcadaccabddacadbccbcbbdbdcbbddcbacaaaabababdadaaadbbbadccadbbadaabcababacccadbdacdaabccaadbaddcaadbdbdcbcdbccccccdaddabdabbacccacbbbaaddccddbdabcbbddabdccaddccaabdcbaaacabddadcbdababbccdacccadcacdbaccbddcdbdacadbddbdbbacdcaddddcbdcbdcbcaabbbcdcdabcbddccddbccdbadaddcccaacdbbcacabadabadbdaaaccbacaababacdbacbccaaaacbcadacdabdcabcacabdbdbbcdcccbbbaccccdbddcaabbbcabaadbacbdcdbcbbbdcabbcbdacddbacdaadbacaabaccabaabddadddbdcdcabacdbdcdadbbbdcddbabacbbddaadbddcccbacadccbacdabcddccdbbacdbdabddbbbdaacdcbbbaabdbdadaaddbcadbbdadcbabdbabdabcadbccacadcdcdbadbbababaaaddccaadbadbdccdcacbdbabbccccccddbbacabbdacddbacdbcddddacbdcdbcbaabbadabdaadbbabadbaaacbadbdacacacdbbdcababcaccbdbbbcbddbccabdbbbadbccaabbcddbbababaddbccabcaadaaccbbbccbcabbadacbabddccdbbdcabcbacbbabdcbabbbbabcdaadcdcbaadcdddaadcbdacbcdaabdbcbcbdaacdddccbadddccabadadbcacdbaadbddddcddcddcccabdbcaccdcbcbadbddacbbcbcbccababadcdbcdcacdadacbaabdccdbbcbdacbacdbbabadcdbbccdddcbbadcdacaddcbacbbcdaccbcadaaccabcadbabaadabcdaacccdddddcacdbcdaaadbadddddddddbbcdabdaaabdaddcddcdccbaadddadabdcbaddbcacdcabdddcacabdbbdaabbcdabbdbddddcbaacbadadcbacdccbcdabdbacbacbbacbaacbdccdbbcbcadbddcdcdcdaccabdbddcdbbcdbdccbcbbacdbcaccbabddacaacddbabbaabbcdbbcbccaccccddbddadabadbaccbccddacacadcddacaddababdbabbccdaccadcdaddbacaabcddcaaaccccacaabacadcdaddcabdabcacddabdadccdaccaccaaabbabdcdddbdcccdbaacdabaacbdbcdaabbdccdaccabdabdacccbaacdacaacaccbdbddababacbbcdddcacdcdbdcabbcdbddcadacdcadaacbbdbbcabbbccbabaadbbbbcaabddadbdcbcbccdbccccabdcdbcdbbaabdcabbacaccbdacabdcdcdcacbbbadcacbbcddbcbdccddcdadccadabadcbbbddbdbbbbdcaaccaaabccddccdadbabadbddbdacccabaabccdadccaadabcbcabbcddbcdddddabcdabccbddcaabbadccadaddbbaaabadcdbccdccccaddadcaadaaddaaacaacadadaccdbadbbaccbdbabddadddacbbaccddcddacadaaccbadbdacbddaabdcccbdadbddddbbcdcabadddabdccbdcdadccddcadcdcbdbadacdacacacadbbbcccbadaccccdcdaccdccadbbdbcbaaacadbbbcaacccbabcdbdbaabbbdcadddadacacddccbaacdadcdadcadbcccbccdaacbdcaaaddcbccddcdaacccdbdbaabcdbbdbdbcadcdcdcdcaaabcddaacaadccaaabbadbdcdacdccbcaababadddcbbddcccdcadbdaddacdbcaaddcdbdbcacbabbccaacabaabdcadabcbbabbbbdcdbbbbacdacdcbbcbadccdbbadcbdcaacdacbdcacccacbbabdbbcadadcbcccacbcacdbabcbaddcaccabcdbccacbbacbcbdaabbddbcdbcaadddbaddddaabaaaacbbccacadbccbabcacbaabddabbacabddadaacdacbbbacaccdbbcdcbdcaaacbbaabbbbabdbababbdabbcdbbaccababbacabdcacdbdbcaccbabdbdadccaacabaccddbacbabaadcabcdacacaccccbdaabcbdaddbdadaadaabcaabbcbbcdcdcaccddddacbbacbabaacdbbcddbcacacccddbbaddbabbbaccacadbbdbcbacabddbdbcdacbcdaaacdddabbadaaaaaaddbbcddaaddbdcccdbadcabcaacdacdbcccdbabdabbbcbddadadccddddddbcddccdccddbddbdaabababdacabccdbabccccbbaacdcbcaacbbccdddacbaadbaccddacdadcaddbabccdddddbcbddbdcaacacbbadcbbdadadbdadbadacbbbcddcdccaccbdcbdbabadadbbbdacbbacbdbbcaadbcbbdbbcccccbcabaaddacddcbadcddcabdaadbaddbdbbdaacdcdddddabadbddcaaccbcbcacdbbbbabbbabcddbcbbbbacccacadbdbddcbbdbbdadbadbaaadcaccddbccdbcaacdddccdbddcacaccdaaaacdbbcdaabbbacccacabbacccaaaaabbbbcdddbdaaddccddbdaadbacbbccababaccddcbbabccbdbdcadbddbbacddacbcdaabcaddabbbacbacbddabacbdcabdbbcdccbdcaaadacdbcbbdaabdbbadcdbcacabbadbcaaabcabaaadccabacdbbaacbdacccbadcccaabdccaaadbcacbcabbcaccccbdbcbbdadbbccdacdbaabbbddccbbbacdabbccddbdabdcbbcbccddcabaabcadbaadbbaaacdcacacbbacdaddbcabadbddbabdacaddccdcdbddacbcbabaabcbdbbbcaabadaddbdcaadbdaadbdaccccabcdddcbabbdacbdacdbadcacdcbdcbabccadabbddddaabcbbddcdaacbbaaddbcacaacabdadcbacbddbcacccdacdcaabbdbcbbcbdcadbbbadbabdbadaddacdbacbacddbcacaadabaccddbbcdacdccdbdbcaadcbddbaacbcbdbddabcbbaaabaabdaabbbdaabbbbaadabdcdcaabdbbcbaccabdccdaadadaddcaabaddbabbbdbdcabcdabdcccabdaaccadbccacaaaacdddadabaaacbcacbcccbbcdccddcadcccaaaccbdcbcbabddadadcdbddbbacaabbccdccdddadbaababcbbabbbdcabcaadccbcdacbaaaabaadddbaddacadbabadacdacbbddccaddccdacbaabadbabccaaaccccacabdccdaacbbdaddbdbccdbabadaaccbccddcccbcccabdcdaaaaabaaaacbdcdcbdcdcaacabcdabcbdaacacadaadccccadaadadaddaddcccdcaabbcbcbbbacbcabcdcabcbcddbbccdccccdbaabaaccddadbbbcaabbbabaadbbdcdbadcacabbccabdaacdddacdcbbbbcdaaaccdcbbaaadddaddcabccaccbaabacbbabcbaadbacacaacbccbdbbdbbdbaadabcadbaacdcacaadadbbbcadbccbacadadcdaadbdcbdcadaadadaacaacdadcdddcacbacdaaabdaaabcaadadcbcadcaccabbdadabbacbabcbcdddacadaaaccbcbdadbddacbddbdccccbccdaccddcbcdbdbddadddabdbdddbbbccaddcbbabccdcbcacbdbcbaaaadbcdaaaacdabcdddbabbadddaabbaddaddcbabbdcacbddbdabababccdbcadaacdacdacdbdbcabacbabadacacddcdacacbcadacaacbcbbdbadbabdabbaaaabaadbadaacbdcdbcaccdadbdbacaaacaddbbaacaccbbbbdcabbcadbabcdacbdaccacbdbdddddadbbbddabdbaaddabcdcdccacbcbcddcadaadcacaadbbcabdcdbcaaabadccccbddabbbaabacbcadcbdbccdaccbabcdaabdddcdaadcaabdaaaadacdbadbcddcbcbaddbbadddddbbadbacbcbbbcabbcbcbdbcdbcaddbaabdabaaadabddcdacacddaadabddddcdcbbcbcadcdddacddabbadabbdbacdbabadcbbbdbcddbcdccbcacabcbaabacbacbadcadabcadabccbaabdaddbabbcaacadddadabbdaaccbbdadcdbddbdcbbcdacdabdbbacdacaadadcbbbcdbddaaacdacabcddabbcbcbadacadabdcdbcaccadccbccaddaddcbacaabaccabbadabbacadaccdbdcbbacdcaabcddcadacdcacbaadbccaddbcaaabbcbdbdbbacbacabdccbdcbddacabbccbdddaddddcbcacccbacccdddadcddbdccdddbddacddabaaddadabcbbbcbcbdabcabbbcdbcadccddbcdccdcabcbaddbaabbacaadbabacbcddbbdccddcbaaacadbababcaabbabdcbddacdbdbbaabadcabdaccdcdbdcddbddbabddcbabdaddcbbadccbabdcbbbdccbbacddcdacabbdbbcddbddcaacbbbbdbbbadabbcbdacbcbcddaccadbbbdbcbdbbccdccdbbbadddbdccbdcbbaaddcabbdabdabdcccaaacdcdccadcbababcddcddbabcbcbcccaaddacbddbcbccbddcdacaacdcccabcdbcdadcaadbddcabacadabadbbddcdacbbbcbaabbcdaaabaaababcaccbbbdabdadbbadbdcccbcdaadccbadcbabdbadacccdcbabadabacddaadbbcbcbaccbaddadcbcbcddacdacccdbdbadacaddacaddbdccacbddcdaabccbdbcaaabccbbbcdaccdbcddacabacdbcdbcaadbdaaccddddacdddcadbbaabcdcbbcaaadccdddabaddcacabbbddcdadbacadbabaadaabbadcaddabacaababbcaacddaabcaabbccbdccdcddadbaacdbaddccbdabadcdcdbcdabcaacaaddcabbdacbacaadbcdbccdcadaaabacdbcddabdbaaddcabacadcbbdaddabaadcdabcbcbcbcbbcdacaddcbacbccbcdccacbbacbccbbaabdcdccccbaaaccbcdacadadbcdbaacaabbdabcbdddbcccadbdcadababdccdbabbbbbddddbbadabbbaadcaaccbcbcaadbbcbdcacbadcdacbcaddababaacdaacbcdaacaddbaacbdbadddcbcdddccaccbaabdadaddddbbbbacadccaddccdadbbcccddcbdccddddbacccadabbcabaaababcbbbdabdbbdacbcdbbcabdacabccdcacabbdbaaddddabdbbcbaaabbcdcdbddcdbcdcabbbcadabdadddcadddbbaabcaaaadbcaccdabacaccbccbadadbbcababbabdbaccdaacddbaccaddcaddabcaaabbaadddbcdabaaacbdadcdacadbddaaabcdcaccbaadacdadadcdcbacdacdcdbbdbddcabaadbdcbaddccbdbcddcabbbadadbacbccbdaaadabdaaadacccabbdcccbadabdcccdabbcdabcadcdbcdbdbdbbcdbcbdbadbadcdacddbadbacccbdbdabdcdcdaccbccbabbcaccadbccaccaddcbbacbaababadcdbbabdcbcbacdbbdbbccbabbabbddddbaabbdaddddccabdcabcababbbdbcdcacbadacdbdbccacbbbdbcbcbcbaabcbbabbbbddcaccdcaadcdaacbbbbcdadbdbcacdcbdbaaacdbadbacdaacacbacbcacdbabddaccbaabccdbabbaacbcccbcbdbdcbdadddacadcbabddadbddcaabdcbccabbcbbaadadbccbdcbadbbccbabbadacaadcddadabbadaadcbdadccabcbcdacadbcdacdbadcdbcacaabaddadbadbabbddcddccbddbdaddbadbadcadadbcdacdacbbacbcdacdcddcbdcdaaaaadcdacdccdcacbccbbbaccbdbcdbccdaddadcaabbbccbabdabdbaabbcadbacdddcbaabddddbabbcbcabddcaadddcacdbdbbaacaacbdbabbcbdbaccadbddadcdaccbdddacaaddccabddcbddacadddbcbccacddbbdaadddcbcccdbbccbcdcbaadcbcbccddbbccdbddcbcdababaacababdddcdbabacabadbcbdbbbbacaaabcbcccbdabbabaaadcadcbcadabdbcccccbccccccacbaadbdabaadaacabaccdaccaaadbbdaadabbdbdddddcabdbcaaaccaccbbccbcbbacbbbacbdabbdaddbdbacdddbcdcaadcadbabbccbcdcdabbdcbccbcdcdbbababbadddcdbbbabdbdabcddcabbbaadaadbcdababbbddababccddbbcadacdaaadacddbbccdaacbabbbcbbccdbbbdcacadddbabbcaaacbdcdaacbbbcadcaabdabdcbdcccabdbbcccdbabacaacccdcbbbdbdbcdbaddbdbbacbcbbaccccbababddddacdacbcbacabdbccddabbabccbcbaabaacdacdcacddabcacabbdaacbdcbbdcabaadacabcdababdddcbdccdddcbbdaacadddbbbcaccaacabaacdaaaddbbbaabcaacdbbccdadcbddcddacdccadcaacaadaaabbbcdcdadbdbcabaadcdabddaccdbabbcbcddcdbbbaddaabaddcbcbcaddabbdadcdbddadbbadbcacdbacbdabddaadbbadbcddacbdbacddcacbdccbaccbdbbbbcbabcdbdaadcdacdadaacacddccccccaaabadbbbbbaadbbcaadbddcdaacdccaccbaabbcbbddaaccdadbbbcdcddcabccbdabcdcbcabcababddabdcdacdbcdadbacccccdcccadadadbacbbdcabbbcddcccbcdaabbddcdbbcdabcccccbbbacdabbaacaadbddddabaaddddaabadcbdccaadaadadadababdbacdaaacdaaddcacabbdadccadcccbacbbdabababacdddadcadcbccabcccbabdbbbbbaddcbabadbcdddcbadabbbbaaabcbcabdacccbbddbdbbcbbdbabdcaadcbbdbdaabbdcddbcddcddcdaaddcbacdbcdddddcbcccaadababaaadadccddbbdbdcaccbccdaabacddcaacacbccbcbddbabcacadccdbbbdadacababddacdccccbcddbcdacabddacaaacdccdadacbbdaddcaaababddadabbddbbbcddddbaaabbabdaaaddbddbddcddddbaabbdcbbabaddacbbabbbcaabaabbacacbabadccaabaaadadaabcaadacbbdaccccbacadcabbaacbccbaabcbaacbdbadaaaacbbacbdaadcbcbcbbdcccbadcabccdbdcbbcbccbdaabcccbadabcccaddcdcccdcbdbaacacbadcacbbabccccaddbddaaaadaacccdbdcbcdcbcadbbbbbcadacaabbbbaccaccdbcaadbcbcdbabcbcdadccbddbbccaaacdbdbcbcdabbadbaddcbdcbabbcabbddbbdacddbdadadbdcbacccdcaddabadcdbaddbdbabcdabdacaacddcbcacdacbcddbdddbdbacddddcbbddabdbcdddadbdacdccbbbcbbbbbcbabbbacdddcdbccdacabccabcddadbddddadadacdbaabbabcdacaabdcacaabdddacaacaaadbccccacddbdaddacddbbddbcbbabdadbcaadbcbbadacccdacbaaddcabbcabbacacabdcccbaabbaaaacbdbcabccdaaadddabdbbcdcadbbddbadbcbaccbcacbaacccbacddabdadabcaaddacaacadaaaadaababaaadccbbccbcddabaabcdbacbadccbbaddbcddcccddadbdccbdacbabddccaacacadabbdbaabcabdbdabaddbdcddcdbaccbdcadbaaabbabbaaaabaaabadaadcbadbbdcdabccbbbddadabbccbdbddbdccdaaababaabdcaddbaaabbddabbacdcdcbdccbdcddadddcdaddaccbdcdbbaadaaddadbacbbbababdcaccdbbcacdacbcccbacadadbaaddbaadddbcbaadaccbcdacaaccbaddbadbbcbbbacbdbcbccaaacddcdcbdacdabdcaaccabcdcbdddbaabaabbdaacdbdcdabadabdcacbbabdbbbcbdddcdacdcaaadcabaadcbbcaaabccaabdadcacaaabaccdaabacbacabaadbbdacdcbabccbaacabcccbdaaabaaacccdddaacdccbbcdbdcbbabcdbcaaabddcbddaaacbacabdbcddacabddccbacdacbbdabdabbaaabcacdcbccabdcdcddababcdbdabbbdcdbcbdbaadddbcdaadcabcdccdcddadccbcddcbaccdcbbdddcabbdbadaabdaabbdaacbaccbcaadacdcadabdbcccdcccbadaadbdbcbaddcddabddcdabaaccabcaacabcdacddcbbccbddabdcacddcbdacdadcccaaabaadbbdbcacbbaaddadadadcbdcdbcacadabbabacccddaacaadbaabaabbbdcdccadcbbaaadbacbaaaaaccacbabcadbcdbbacbaabadadbadbdbacdbabdcbbdcbcccdcdaaaaabdcccbaadccdbcacccdbadbbabcbdbbaaaddabddcbbabcdaaacccddabacbbbbddcddbccaacaabbabddcccbdbabbcdbdcccacdbdbbbcbbcdcaddbdbcbdbabccbbacdcbadadaadcaabcbbccccabadddaaccbdadaaccbacdbcaacdabdcadbbdbdacdcbacdddadcbcbbbbcccbbadcabcbdacacaccbbbbcbddbaabbabcbbbadabcdbbacdbbadbabbcddbccaadbccbcbbacdaccdabcdbbaccbbdaacbaddcabcbddbabbdacdabcacccbaccaabacacbddbaadcdddbdcddbaccbccadacccbccdacbbdabbdddbccdddddccbcaaabdacbacaaabcdabbcdcbccaacdadadadbcacdabcaabbbcdcbdcbdccddcbaabdadbbbacbcdbcadaacbacaaabddabcaadacadccbabbddadbccdcbacbbdbdacdaaccbdbbcdbbddcdaddcdcdbcabddbdaccdacbbaacadcabaabcdbccccabcbdcbcdbdbaddadbacbabdbadbbbddbcaddaadbcbbdbbadcadbdadbbbbcabddadabcbaabcccbccbacdbdcabacdbdbbdbdcdbbdcbbdbbabdabdaabbdaaadbbddbcbaccdcaabddcabbaabcccacddcccbbdadbdcbddbdcbacadbaabcabadbabcabdbbccdbaaddbcdaaadaadbbcbdcaaacdabbcaacddccddcbbbcbaadaabcbbaadbbcbcbddcdbcccdbcbaabdbbcbddddddccbccbbaccaddaabadaddabaabccacabcbccdccbdabcabadcbccddcadadcbabdcacdaddbacababddbcbabcbaaaacdacddaadbddaaddaacacbabaacdaadaacdbdbcdddbdbdabcdadaabbabcdcbacdaadbbcdbaddaaaabaabcabaccaabcaaaddcbdcddadbcddbbdbbdcadcacdcdaabcadccbdcbdadddcdaabdcccccbdbbabaadcdddbbcdbbacddadadaabbddabaddcdbccdcadbaabcdbccaccaabdcdcdaaaddcbdcbabdcaaaadbcbcdabccadacabdbddaadbdadbaabbdbabcbdbdabaccbddaccbddcababbbcdadcadddadddacdbdaaddbabbaababdcccbdabdcdcbbbcdadacbaccbadacbbcbbadacabcabcddddcccbdabdacbdaabaddadacbbbbcddbbacadbdabdcacbcbbcbabbbcaacbccaaaadbddccbababacbbbdaaabdcddcbabdbdaccdacdbccdadbdcbdabcccaaacacdcbacaddcccadbacabcaadddbccadbcdcaabccbacbcabdadbdaaddaddcacbdccbbabbdabcbadcadcdadaddbdccdcdcabcacadccaaababbaaaabbdacdacadadbadcbaccdbbccbaabcbbaaccddbabdbcabddbdabaabccabadbdbdcadaacbccdbccccabaaadabbbcccaadcaabcbdcbbdcbdbadccadacaacbababbbcdadadacbcbaaaacdbccabaabbcdaddbcbdbddddbdddaccbdcdabaacdcbadbbbbdcabccaacbcddcacdaaaadbbdbaadadcabbcaddcddadacdbdcabddbabdaaaadadaacabbabcacdbbbdbacddbccbdbccbdcdaccdddbacdcbbacabdbbbbaccadbcbbcdcdabdbdccbacccbbdaacbcdaddbbcdbdbbacdbccbddbbcdcccdccacccaaddbdccdabdbcccbadccbcdddddbbaacabdacdbddabccbbbddbbbaabcbbdadddaddbcacaadabdccbdacadcacabccabdcdbaaacdcadcccdccacaabbacacdaacddbcbacdbadddabacbcdbcdabcbaabccbbaabaaaabbdbacdcbbaaddcaccaacaadcadcdbdcadcacabdcbdbacabdbbacbadbdcdbdccbcccdbdcadbdbddbabdbccabccbcdabcdaaadacdbcdabccdbbdcdabcaccaaccacdbdddcdcabcaacacdadbdcbddbcddbcabdaaaabbccdadccbdcccddabcacacaadbbabddabdcdacddadbcccabbcdcadbadabbbacbccabddcacaabccaaabbdcdbcacbccadacdadabbaadabdccabdddacddbcadacdbadcaddddbacabbbdcabbccbdbaaacdcbdabddbabbbdabbccdaccbacbdddbadcaddbabddbaabadcccccdaadcadbdcdbabbcddaadbcddbcbbdbdbadbacadbbccdbdcaadccbccddcabbadcbbcbcdbbbcdacccabacccdcadbdbbcccadaaacabacbdbdbddddacbbababbdddccbacbaddcdabbbbbaabcbcadaaaadbadabdbdadbcbddbaabbbabdbaccaddcbaadadddcdcbacbcbaaabadacadcdddbbabbdcacabcbdcacbcadaddabaacdadbdcbcaddbbdbaabdbabccabacbbbbbdcccdaddacadcdacdcbaabdccabaaadcbabbbaaabdbcbbddddcbabbdacbbadbbabccddbbcadcdbaddcadcabccdbbaaddaaddbcaddcddaccbccbcaadbcbbbaacdddaadcaacdabddabccabbdccdbadcbcbaaaacccbdccabddccadaccbdadacaacacdcbcdbabdbaaaadadccbcccdcbbcacadadaaadacbccaaacdbdcacdabbacbcdcddabdacdaccdabcccccdababbdabbbcdbcbbcbaccaaddcdaabddddcababaaacdddbdabdbdadbcbadbabdcdbdbcdaacdaacdadbacdccbacdababbcdadccbdaaabdbbcadabdbcbbdbdcdcbddbabdadcbcddccacdccbabadcdacddaadbdadacbbcbcdcadabbdabbbacacbcdbbaaaddcbabdbbbaaadddccaccbaccddadbcddbbbdadaccdcaddabdcddccbbbbbdbcdbacbbccbadcbcbaaaabcadadbcbdababdabbdaddddcbadbacccddcbabccbcbabdbcabbdddacaaaaabaadabbadddbbdbdacdabccadaaaaddacdcbccdabaddababaadddcccbcbdccdbbacacdccaaaabdabadddccbaccdbcacbcbcaaadbabaadbcddcbadcacadcadacbdcccccacddbccdcaddbabdddcdddadcbcbabbdcbacbabaaccdbbdddcadbcbcbbbbaadccdaaccbdbcdbbabdbcdcddcaadacbccbaadacbccbabcdadbbbbbacbadcaaaabcbbdbaccabccccdccadbadbabdbcbddbccbaddabbabcbbbcbccdcacbaabacacaddbcbbccbaabbbaddcabbcdcddbabbcbcdacabdabdacdaaddacaaddbbabdbbbdcdbdadcbddbcdbabbacaccdacddccbacdacaaaccbdbcdcddaacdcdbccbabaccaaddcabacbcccabdacbbadbbbddaccdbcdaaccaccbabbbaddaadcbbadbbdcbbbddcbcbdbbbbcdadbdcdabbabacddcadacadddccbacdcacaadadacaabdcddacabccaddbadbaabccdddabdcdcddabcdacabdbbaaabdbbbadcddacaabacbdacaabdcbcadbbcdcdaddbdacbbdcbcccacbbbbdbbdadaccdddabdddcacbaacdbaacdbbdabdadccdcbcaddbdcbcdbadcccdbdbbcdcdbaabcbbdcbbccacabcbaddaccdddcadddaadccbabbacabdbabdababbaddccbcaadacaddbaaadcbbaabcdccbacdcaccaddddccbbcacacaddbdbdcbbcaddaccabadaddaddccbcbaabaccdccdadabababbdadabcabccabaaabadddbdcbbccdadabacccabccdcaacbccabdbcdaabadcabccabadadacadcaaabddddbbadcdccadbadcddaacbdbabcdbadcacaddaaaccdacacdccddbbacbcbdbbdcbaacccccabbdabdcdacbaabccbabbbadbccbcadbadaacbcdabdddbcbacdcdbbcbabaadaabbccbbbcbcaaadbabbcdbaccdddacbdcbcbcdaaaccacbabbacbccbbddacabdacacadcacadaaadbcddcdbdadbdbcdcdbaacacdaccddabadadabddabaaaacbcbaaaababdccabdaabcbccdbdacbcccdddadacdbbdadbcdaaddcdcbbdadbdabdacbbadbbaddbbbbbccbabdcdcabcdbdadddddcbaaccdcacbaabcacabdcdcccccabcababcddbaababacadddbadcabcbaddaadcbcacbddacacbaabadbdddabbdadcdcabbdacdcbccaddabbdcbabaaacdcdaaaaacdacadbaabdaadacddabdbaabdcbbaccdadadcbcacddbbdccdbbdacdbcdddadbdcabaabdcbbabaadacdabdcacaddddbaddaaadabdccccddbdabcaaadbdbbdcaacdcdddabababccbddcbacdbabdbbdccacdbdddcddadbabbabccacbcdacdccccccbdabdbdccacbdacaddddabbacaccaadbaddcbdcdcbdcaaccacaabdddabadabcadcaaddaadbabbbabcbcabbbaddbdacdbadaaadccddbddddacacbaadcbdcdccbaacabccaccccdcaddbcddbacdaddadbaaaacadcbddcaddbbbdbddcaabdabccbacacbaacabcdaadcabadaacadccaaccaabcaabcdcdacbccaaaccccddddcaadcbaadbccabbacbbdbbaaacbbabbbabcdcbdaadcbbccdbabdccabbcacdcadcaadbaaababbcdadbaacbadbcdcadcdddadacbbcbabbcdbdddbcbbaabbdcaddcddadbdcddabdcccdcbbababdbcbbbbcbcadcbbcccbaadcddcccbbbddbadcddababdbaddadacbacaaaabdabaaabcaadddcbbaddcbdbadbdbbdcbbdbddaddacadcdbdccbabdacacbdaabaacccadbcaabcddadcabbdadcbabaaabacdcabbbdcdbbccaadccbbadaddbbacbbcbcccbabdccbcadaadcccdacadcbbcdbccacdcaccddddcbdcdbcaadbacadcbccbabbdcddcacaadbdaadacabbdcbdccccdcaccabdbccabccdbacabbcddaacdcaabbbaabccdbdcccbbbcaacccdccbcaddacbaadbbdadcacdbcacdaaacacadabaadccbcbadddbcadacacbaaaccbddcbccdccabcbbddabaccdbabddddccacdddcbabbddcdcaadddacdcacaddadcdaaabbdbcaacdcdaccddaccabdddbacbdbbbaaadadbaccbabacaccddbdadbdabbacddccaabadbacdcbacacbacbbcbadbabccbddaddbcbbddbcbcaccbdccacdbdbbbdcdbacbdccbacdddbbbddacdaadcaabaccbaddbabcdadaabacbdbcbcddddccbdbbdddddbcbcbbbcccdbddbddbdddacaadacbdccbaddababdbccbaadaadbcdaabdddcdbdabdbadbbadcadabcdbcccaaccdaaadbbbacccababcdcdcbaaacabbdaacaadbdacdcdbabdcbddddbacaaadbdddaaabacdcdcdadccbddccacddddbcaccaabccabbbbcbbbaabbaddcbcdaadbbbccdcbdbcacbdadacadbcabbdcddccbcaaaddadcccbbadbcacdcaaddddcdcdcaddcbcdbdaccabdaadbcbcaaddcadbcabdcbadcbcabcddcaccddcccddbdabdbddcacaabddddcbcdbbabacaddaccddaababcadaadbbdbabacbdcdbcadadabacdccdbcdbddaadcdcbabcdaaabccadcadbddaddcdccbaadabaddcaddabbaddbbcdcbdcaabacbdaddcccbbcabbcadddbdbdaccaaadaccddacababbdddabcadbdabcccdcbdcbddaccdadddbcbcdcdacdbabdcabacbcdbccccbcdcbaabadbccbdacdaacdccbacdbabddabcadacabadaddacdbddaadbcdcbbcccbdcabdcadaadacbbbacbdddaabbdabbbadacbadaacdabbcaacbbddbbdaabdcbcbbdddacbddbacadbccabbabaaccddadabbdcaaaadcbdccbcbabccacbcacbaaacccabadbaacbcbabbbbdcbabcdbbdbcbcadcbccabdacbcbbbbbbdaaadaccbaaaddbbbccacabcabaddaddcdabaacbddbdaddaaaadbadacbbdaababbcbccddaacaccacbcdbcdcbadaadadbcdbbdddddcbbcddcbbaadabdaadabbbbbbcabbccbbbcbbddbcaaccbdccdcbdbadcadccabbccbcbcdbbbabdaacdcdbdacccbccdbcaccdddaccdacdcdbbacdcdcbacbdddcadcadcccbdbbccdbaadbdabaacbcccddcaabdcddaadcabbcabacbbbdacadbadcbbcbbcbdcaabcdcbddcacccbaadadaacdddacadadcbcdaddddabbdcbbdbcbdbacbacbdaddadcdabcaacdcbbddbdabcbcaadcaadddbcaabdccbacabbbbaccbaddacbbbbbddbaadddddcdacdcdaaadddacbbaabccdcabdddccbcddbdcdcbccbcdccdddbbbaadabaadabdaddbdccddcccdaddbdbaacdcdaabcccbbddbdaacadacadabccbdcaccbabbdbccadbcddcddddabbaddabdbccadcdabbcacacdbdaaabdbacbcddaaaccdadccacadcdbbadddabbadcdacadddccccdaaacbbdbcaadddbabbdcccbdbddcdaccbdabcddcacbbabcddccdccddcbdbadadcbdbaaadcccadadccabbbbdcaadbbbbabcdbbadbdddbddaccbddcbbdbcadcaabcbdaaacdccbdaccccbdccddadababbdabdbbaabcddddbacbaacaadabaaddabcbccaacaacacacaddccadccdacddaacdcbadbbaacadcdaccbcddcbcadbbbadbdddccdddadbdcbdacddaaaaaaddcccdcddbcdcaabdddbaaccabaaaddababcbbbbaaacccdbaacddbbbbcddcacbcdbaccdaabbcdacabbccacccdddcbddcdbcabbcaadabdcadbbbdcbacbaabcadcdbaaaabbccadbadacacbcabaadbcddaadbbadccdccdcdddbadccddbdabddbccadaabaacdbadbcddcabcbcdbbccdccaaadaacbbbcbbdddbcbdabbbbbdbabdcdadbadcaaadabbadabcccaddbbabbbaabddccdbdddbccbbaaddbaddcbccddcbcddcaddcdabbddccdbbababbabdcaaadaabcccaaccddcaddbdadbbddaabbcadaccacbaaacdaabdadcddacbaaacdacaabbacbdcbbdbabadcbadcdbbddbdcbdacdaaacbbaccccbbddbaadadccacdaacacbcbbbdbaacaddacddaddbaddbdddbdabaaadaacdccaaadaadcccabadddbdccaccbcbabbadcccbabbcabbbcadcbdbcdddcdcbddbabcdbbaaabdaadcccadbdccdbbadbaaacaabacabdbdabddaaccbacabcbaddbdbcbaddadbbadccbbaaccbdcdddacaadbdabdbcacbccdbdabacccabaccbacbbdddccbddcaccdacbbbdcbbaaaddcccbcdddbbabdabcdddcaaddcdaccbdcaabddbccdbacdbdcacbabccccabaabcbaabbabadbacabddcaacaccdbcdbccbbcabdbdcddcdcddddaacaacaddbcbaccaaccadbbbbabaaacacbadccddbbaddcbacccaddacadcbccdbbbcbcbadbaaddbbddbdbaaacaacdaacaacabaccadbbcccddbdaadcccdddabbdacdcdaadadddcaaacacacdbdcaccacccdabcdbddcbdbcddcadbbccaddddcabbccddbcacdddaaddadcabdbdbcdcccbbddcdbaabcaaacddabcbaaacccbbbbddbbbdaacbccdadddabbcbadbdcbaabbcdcbdcacabbaabdaccaabaddcbbacbadcaacaddcdaacadbbaccbcdbdbbcacdbcaddadaacaddacabcddcabcbbcbabbaddcdbacddcdadaddddaabcbcaddcddddbaabadacbdbbdccddbbbcbadcbadbbdbcbabbdacbacadbdbbcadbdbdccbccbaaabdccbcddcdadbbdaabddbbccddabdcabacccabcadcbbadccbbbbdadaddccdcdbdbadcdbddbbaacbdddbabbbdbbcaddcaaadcdbaccbdccbabbbcbbdcaddcaddbadbaddddacdccdbdbdbdacbaccbbbdadddcbcbbacdadcabadcdddcabacdacccccbcbcbabcdbaabcdcdbaabaabacdcbabcabcbcccbacccdcbabbccdccdccdaaaaacaacaaaabdabcccdcdbdaacbdcbabcdbbcddccddcadaaddcaababdbbcdcbadbacdacbdcdccdbdabcccdddbbdacbcdbbacdaadbdcccdddacbbbdbdcbdabacbcbadcabaadbbdddccbcbbcbacabaacddcdcadbdbaddcaaaaadcabbbaabbbdbabccccbcabbabaddbccadccaaadbacadcccbacadddbbbbaabbbbcacdddddddddbaccaabacbccbacbbbbcdbdabcdcaddacdbbbcadbddbbcbdcbcbaacaccdabddabcbdcbdcbcccccbbcbdbabcbcdacbbddaabadacdbdcacadadcdacaabbacacaccaacaacbcdacbaddccaccaadcacdbcabbddadabcbdadccbcdcbcbacdaddababcddbddcabdbccacbcaabcdcddaaacacacaccbbbaabbddcbaadcdccadbcabbcadbbacaadcacdbccabddcdbadabcadbccbcdbdbadcaccdcadddbcbcdabaaabddcacadcbbabbcadddcdaabccaabaadacbdabcabcbaaabadaaacdcdcbbccadcdccdacbacdcacbbabcbcdbbddddadcbdbdaccbdbbabcaadccabccdbbabbabbdbbcdaaddcadbbbddbadcacbaabcdbddabcbacaaadaddcbaaaaccbddddadbaaabacbbdabdbadcbaadbbdcbaabaabccbcaadcaaadadbbaccbcdcbacadacacbbccbdcbcaacddcdbdcddbdbbddcdcddcbdcdabaaddcbbdaddbccdbbcaccbddcdcbcdadccacabaaadbacbbbacccbcaccdcdadbbdccaaabcbabcbcbddcccaabccdbddbddcbbbbcdddadbbaaddbdadbaadbdcbcacacccbacccbcdabcbcbacdadbbbdacbcaddbbabdbaaccadadbdcbdabaacccbbaaaacadcbaabcabdbbbacdcbbdcdbdcdbbdacdcacddbadccdddcdacaacdccbdaacdbdbccbbdcacaaaaddcbaaadadbbadaabbcabacbbcccdbbaacbdddabbabcbdbacaadbbbaaacdaacabcaadcddddaacdbbccdddcaccccbddbcabcabdcaccbddcbacbbadddaacbcbdacbaccbacccddccbdddabccadaaaaddbcbccdbbcbddbacbbbcacabadabdacabcdbacadcbccccbddabcadacbdaccbadcabbbdadbbadddbcbbdcdabcbbccadddadccdaabcbdadacbaaaaccbcdbcaaabaaaadcaaadbcababdacadddccdacbdcbabdbdaabcddcdabacddddccdbcccacbcdcccabbaddcadadabcbbacaaabbcacdbacddbbadadaabcbdbacddcdcadbbccadaabcbdaacaaccbdddaccbccacdaaddcdadcbaccaddbccdcbbcbdddacbccadbadbacadcbdcccbcbbcdaccdbdbdabbdababddccdbcbdababcbbdbaaacadbcdbdabcbdbccbccbbbcbcbdccbadbbbbaabdadbdadcbbcddbdddbbdadbcbcbcbacdbdabadababacaaabbaabcacbadcabdacccacdbbcbbacbcccaacabdbcdddbdaaccbaaacbbbdaacdabdcddbcbaacabacaaabdacacdaabdcabcbbbdcbadbdbcadadcbcddbacbddbdbaddbabdbdbabbcdacadbacdbdbdddbcbcdccdaaaadddcccdadbbcdbdbdddbdcccdcdcbcaaabdcdaabdbccdcabdcbbaaaababdbdaaabaddbdadbdabcaccbcacaccdccadbdbbadbdbababddcddcaddcacccaddcbcabbccbaabcbccddccddbacabdccabdddddaaaccaacabccadbacdcbbbcaadababcbcdaddcabbbcacbbdabbcdbaadddaddbdcacacbdcdbdaccddcbcbacbabacddcdacbdcdcacbbbccacbdbdbdabbcadabcababaadccaabccbdaaacadaaadadccdcddbaacaaccbdcadcaaabbabacbcbccadbdddabdabbdbcdccabbcdccddcccadccdbbadbbbddbbccdbdabadcacdccaabadaaddbaddddddadbbdbdabcbadbccdcbcaddadccdcdcacdacdbbccaabaadacdcdbacbccadaabbaccccbaadbabcdcccdcacabbdccddbabbcaddaabbdbdbcbaaddbdccadcabdbbcdadaccdbdcabbbddadbbabbbdbdbbddacbadcabadbaaabbbbddadccacaccbcbacbaccbdcabccbdbbdccabdddbaabdbddadbdccbbdbacabcaddabbbcdaacdbcbabcdadabcdccaadcaccbbdcbcbbcabcddcddcdabccdccaabcbadcdacddbbacdadabccbdddbcbdbbcacadddadbabdabdcadbbcacbdbaaaaddbdcdbaaabacdddbabaccbbbbcddccaabcaadbabdaddaccabbacdbadcddabcdbdccdabacddbbddcbaacabdcdaadbbbdbabcacaddaabbdbdbcddabaacbdbcadacabbbdcbbbcddcaaddddabbbdbbaddbadaddaaabaabdbababcdabdddacbdbabbccabdcccaabcaddccdabbcbddbcccddcadcddaaddcaccacaabdaacbdbcdbbccbcbdbabaabcdcaacdbbbcaabaddaaacaaaadbbcccbbabcddbdadcbdcbbdccadbccbbccabcbcadacadaacacdacbdbdcbbbbacccacdabbccaaabcdcaddcbcbabddbacdbabccdcbbdbbababbcdbaabdbcacddcbbddcadbbbcabcacdccaddcdbbcdbabbcddccbabaddaadbbddbbabdbcbddccdddcbdadadbdcadbdcccadabacbdbaddaddcaadabadcbdcaabcbddbbbdcddccadbdabcbacddddcdcaddcbabadabbabbdcdacacadabdddcdaccddacdccbbbdbdcadbccbbdabdcccdacdadcbaaacdcbbbdbbaaddbdcacbdbacabbddbbccbaaadcddadbbdacbadcbccaadcdbacdccbacacbabcabdadadabccbddddcbbcbdbabaaccacdcabccdadaaaadacdbaccccdcbcadbbacdcdbdaaadcdbddddcacdbbcbbcabdbcdbbbdadadcbbbccddccdbbddcabbdcbdbbadabdbdadbdbcddcdbddddadccdcbbaaadcddaacdaddabbacaaaaacdbababddccaccabadbddacaacdbbddabadacccdcdcdbdbdcdbaabbacabcbdaaaacccdcdacbbdbdbbcbdbccbabccaccdadcdabcbbabcaabdcaacacdaabbdbcbacadbadddccdabbbbdaacbcccbaacbbdcabdbcdbaaababbacbbabcacbabadadbdddabbacddbaccdcdbabdacbddbadcddbcccdabcbabdcbcdbadcbdccbabaddaccddcbacdbcabbcddcdbbcdcdcababcdabbdcdbabbbddbdcbbdbbbbbbcacdcdccaccdbaabccdabaadabcadbabbaadadddddddbbdaaaacadcdddbadcdbdbcaaaabcbabbbdacaddadbdbadbcbcbcbccdccadbaccbbdaddccbacabbdcadacbbdcbdcaaccddbcadcabaccdaacadcabadaaccaacdccdcdaccaaadacbccacbbcdbadbccdbdcbbacdaadaaadaccdbacaacabcacacccaaadaccdbbcdcbcddadadcabdcbcaabcbabddbbdaabcadcaddbcdcbccbccdccbaaadaaacacaddccccaddddbbdcdacbbcdcbdbcadcacabbaddddcdaaddaabdbddbdcdbaabdcabadccaadbbcbcaadacadcdacccaadbcbdcdddabcddcdbacbabcbdbdaabbadbdddddbbbbddacbdcabbddbaddbbacbddabcabdcbdddddcdcddbcaaddccdddbcaacaccacdbabbaaaaddccdbdaacbbbcdbcacacdccdbccadbacaccbbbcddaaaddcadcbcaaabadbbcbacddcdccacaacdcccbdbbbbddadcdcbbdbcbcbbcbcddaaccdbdbaabbdacddadadcddbcddbadbbadcccbdcbcbcdadaddddadabacdccbdbabbabdbcdcccccbbbaccabdbdadcdaaddcdbadacadbbdcbccdabadccadbdcccdcaddadabacbabcaacdcccbabddadabcbdcdaabaddbcdbadcbbbcbdaadbbabdcadaacdbaabacbbcacbcdadcbdaaddadbbaabacadccabccaccbbbdbbadbabaabbccaadbbdbdbadcacbcdbabbadbddaaabdcdbdbbabacbdaaadbbdddbcdbbbbbaddbdcaddadcccddccbbccbadbdccaddbaccbcabcabccbacacdbabbdcdaaabcdbdbbdcdcccdccaaccacacbdaadaddbbabcadabbaaabacaacddcabacccadaaddccdaaacddcccbbaaccdcbdbbbaaaaccbaabadddaaabddbabaaacbadbccbcbdbbdaccadcbabdabcdadacbbbcbdbddadbbcabbbacbbacaddbdcaaaaabcaabdbabdbcbacbaaadcbabaabaaabcbbdccdbaadbacaccabcdaaadadaaaccabbbbaacdbcadcbcbdbdddabbdccdabdcdcdbcccaddcbddccacbadddcbccbdbbabdcdbaddaaccccabbbbcaaaabdbccdaaaacadadcbadbcaababcaacddbabdaaabbcaabbadabacbcdaaadaaabaabcdbddbdbdbcbdbbbbabbbddbcbdbaddbabbdbcabccabdabcbccccadcdadccbddccddbadacdcaabbccacadbbbbdccdbaaaabccdbaabbadcabcccabadccddaacacbcabbbadddcccadcdacdcabdadadccacbbcacdcaadbbaddddcdcdacdaadcdddddccbcbcbaabbbbabbabdcaacbbddbcaadcadbdaddadbdcbdbbbabaadcdcaaaaccccdcaadaddaccdbcdbdbaddbbcbddccbddcdbaaadbbcbdbadcddbdaddbdadbabaadcacccabbccababcbadacbababcbdbcacdbbdcabacbadacadccabcabbcddbcdbddbddbaccbaadbccdcacadbabbddabaddcccbcabcdbdbdaaccddaaccabbadbacdabbbdcdbdbcbddbdabbbbabaaddaddcbaaabdbadcdcbdacdacabcaacacaaabdbdbbdbccdbccbddbabcbcbbbbdbbcdadbacadccadccddacdddadcdbabcdbdbcabcaadbbcadbaadbdbadddabacdcbdbcbcdbadbdddbdbaaadddcbcbdacaabbcdabbbbbdacbcbddacabdacbcbccbabdccacdabcabacdcdbbacdbcadbbcdacdaabddaabdbdaadadddccacdaddacbdbcadbcbaaacbbbdaacdddccdcacdbdadddcbbaabbbcdcdabdcdbabbcccccddbadccaadbcdaaabccdddccdbbdbddbbbcdadadcdcbbcdacdbcbcbdadadadbaaddadccbcdcdcdbbdcbccddacbdcbdbcbcccddabadbaccddcaaccdcdbddbcaccaacbaabaadddcbdbccbdbbdbdcacddabddbcdbdcaaadbddbbddabdcdcdbbcccddcccbbcaaddcccaaabccdcbdbbbbddcabacdcccdddabdaadbaacdbcbcdddcadddbcaabadbbdddbaadccabdbcddccaabacaadbadcdcbddbbdcbdcddbacaccddcddcbccbdccdadcdaaacdadddaabbccdccccbdbadadcabaddacaccccdbdbcdcadbcdbbbbbcadcddbcbbdcdaadcdbdbacadcbbaaaccdcaabdacabbddbccaacaddcbabbbccdbdbcbbabcaadacaaaccbbddaabddcbcbacacbccaaacadccbabbdbbdcdbabbadadddcadadbcbaacbccddbadadcdcabaaabdcdaabdbdbddcbccaccabadadadbbaadbbccaddaadaccabcbadaabcdaadcbacbdaabccccbaddbbbadbadcbdcbabddbacccadbbbddacadabdaaababdbddcbabbacddbbdbbcbcdadbabbcdddadacdddbdadacbacdbccdbddbaacbdbbbcbbbdbdbdbdaaaabcccbdcadbdbbdddacddcdbadccdddcabbadddbddabcccaadddbaadcddddacacaaacbbcacdadaadcbdddddcbdccaabdccbacdbaccbbbcbabbddccdabacbdddacadaaacaacdddbddabdcacbdbcbcdacbddccbddbccdbbdccabdccdddabcacdddcdddaabbbdbbdadbcadbdccbdabacadcbddbddccadbadbbaddadbccdcaaaabbddddadbdbacbdaaabcaabbbcdacbadccaacbcbbcbabbacccaadccabaaaabcbadbbbcdcbadcbbddbccbabaaabcaabdbcbcccddaadcccdcdaabccaccbddaccbbbcdadabbbacaccbabdcaaacbdcdcabadbdddbdababadacacacbcadcacdccabdabadaacacddccddabddbbabaaaccbbabcdddccdaadddbbacbaccabcccdccdbcbaacacacdbadcdacdaddbdaddaaaaadbccbabdabcddddaccbcbcdacabdcaacbbccbbddbaabcdaccbcacacdadbabddacbbaabddaccbadbbcdadcbbcacabadaccccbddaaccbbabdbbabddddbbbcabacdbbdababbadaabdbcacaccdabababdbddaddbabbbcdddaabbcdbbccbcdacaddaabccbdbcacbbaaabccadcbbcbbaacaaacbaababbdabbdaacadabddcdaabdaabbaadcadcabcddaddbbdadaacadcbcaccbdaabdacddcbbdccdcababdacddcaaabacbccadbdcaaccadccdbcabaacccaacacddcdacaadcabbaabaaccddddddccabbacdbaaaddcaaaadaabbabdcaacddddcdddacdcacaddcdbdcacbabdcbddacdabadcdcddadaccdbcadadcbddbddabbcdbbbddbbbbdccdbcbcdadbbbdccabacbaacdacccdabdccaabcbdcbbdacbdabacbbcabcbbacccccdacdacaaabababdbdbdddabdcbbdbbddbdababbcbbcacbdbaacbcbcacccacccbaacbcababddbcbbdabcdcccbbadbccbaabacdadaacbddcbaadbdcccbddcadadcbbbcbdbbddcddcbcbdbbbaaacbdddccdaccadcadcdcdccddbadbcadaacccccbdaacabbadaaacbdbdadcddcaddcbddccdddcaabbddadcabcdbcbbdadbcdccbcdaacabbbabcabdbccdbaaddcbcccaaddcacddcadcbbabbcaadcaadbbdbbcacccabcdddacbcdbaabbdbadbbbcdbababcdbcacaadacabbdbbbcdddbbdbdccbbcccbccccccccdddddcbbddacddcabcbaadbadacbccaadcbbcbaddacddaacaadcdabccbbcdcabcbdabdacbdddaaaaabbdadcaccccaadbaadbcbccdaccbadadccbddbdccddcbbddaaabaddaddccddcbdccdabacdcabbdbcabcabcacdaabacaadbccdcabaacdccccadadabaaabcaaacdabbbbbcababdbdcaccaadddcbdddbdcaddbacccdbdabcbbcbadcdbaaacaaaddcdbbabbaabcdcdabcdaaccacabbdbbbbcbbbbaccccabaaddbccbccbacccbdaabddbaaddabcbbcbccbadbbcddacbcdbaaacaabbbdbdcadaaaccccadbabcdbccaaabdacccddadcbcaabcbbdadacbccdbcabcabdcdcdbccabcdacdaaabcadadaadadadabcdabbbdadcbcabddaaabacbdbacbddbcabcacdcaccbadadbcbacdabbaddcbdcddbbacaccddcadddcccccacbadbbbdbcdacbdabdaacdbcdbcabaddcdccabcacdcccbaacaabaabccacaacdddcbdbdccbdcccbcaddcacdbbbabbbaccbbcadacddcdddacdbcccddaccacbdadcacbacbcdbbdddbccbddbcdbccdbadbdabcaacdacbbccccccdbbccddbccabdccddcdacddbabadbdddaacdbddabcbdcccaaadabbdcdddbacbbdbbbcbaccacdacdbaaaabddabcccacdabbcaacadadacdbaddcbabcacaccddcdbdadacaccbccdaadacbbbbcddcbccddccbbddaccbbdaaadcbbcbabbaabbcbcbacadaaccdbddcadadddddcacbaccadabdbdaabacabbbccbaacababbcbbadcacbaadddbadcaadbdcbcbcabcbaacadbcadacbcabbccbbbcadbaaaddbbccdababaddbcbcdbcbddabbdadcdaaaabddbbcdadaaddbcababdbbacbbaaadccdddcdbdadaaabcdbbcbbdbccccdabcccdccaacdbcaaddbacadabddaaacccdabaababdbacaccbdddcbbdaabcbbaacacddbbcbccddacbbddbcabaadbaadaddddbdcabadaddabcccbdcdccacddbcdcabdbdbbcaaccdbbacaccbcdddabbadadacccabcacbcccbabdbccddddcdbbddccdcaaabbdbdcabaccbbbcabacdcdbdcdddadbdaadccbcbdcdcabadcbbbaacddbcdccabbbabbaaddcddbdbbbcdbdaacdbbabaaabdcaadbbabacbabdbdbacaccbbdbabccdcbdbbcbadacacaadaaacbcbddcdbdbbbbdcbddccadaadbbadaabbbccabadddcddadaddabdccbaddbbddcabaadcdcabaadbbabcaddccdadbccdbdaaabdcdcbbcaddbcddbdcbdadaabcbdaabdabddcdcccadcaccddaacddbbaabcaabbcbabdaaacacbacaabdcadbdcdddcadabdcdabdddddbabbcdddcbdbcaddbadbcbdccaaadccadacacdabdadabaababbcadbbcdaddcacddaadbbddcaaadcccbddddcbccccacccccaaadaddbcdbaacbaacdbadacdbdbcacdabccabbddacbbabcabaacdddbacbadbdcbddcdbcddcabdbbbbdbcbdccccdddcccdacddbcaacaabddcbccbadacdcbddaaaabcbdcbabbdbbaddcbddcaadcaccdaaacdadadbcddbaadbbdddaddbbcdcbbcbbbabdcbdccccbcccdbaccaadcadccdcbddccdbaaddabdddddbadababcbbbbcbaadabaccdcddccbdaddabdbadaccbbbcadbcbdbbcabbdcddddadcabdaacbaaddabacbdcaaabbccaacaadcddccbddaacdbbcadbabddcdddcdddcccbaabdabcddbadbaccabdbbcdcaabbbdcaaaaaabbaddcdbbcbccbbbddbcddddadaacbaaabddddbbcccccccaaddabccbdadcacabacbdcbbcabdcccccdcdcbdcdaccabdbacddbdbcbdcadcadbabdcacbbaaacabdccddbdddbacbbbadcdcaabaabbbaaaabddbcabaaacacbddaabdaccbdddbbacacbacbaaddbabadbccdcdacaabdbcaabdadcbdccbddcbabddadcadddddccdaabccdbabdacaadcdbbadddcdabaabccdcddbbbddbcdccabcacabcbadbcccbbddadaddbdccbbbdacaadcadbcccaaabadbcdcccabbdabdaccbaccbaadcbdabcbdacbdbbaccbdbdaabddcbcbbcdcabcdcdcaabbdaadddacababaaccdbcaddccbbbbaddaacdcddaddaacbcbcacbccdcaabdcadcabaadabcdacdccdcbadcdbdbccdddbaccdadbaadadbbcbadbdadbdbabdbccdaaccdaddcbaaacaacbbddddcdccbdddbaddaadcadbbdbdcdbacdaabdacacddcdbcdaabdccacbcbaabddccabdacabcddccbdbbabdacbbbadddbbbccaaaaacbbbcabaccbcccbddbbabcabcddccbbbbccacbddbabdabdaaadbbdddaaccbbdccabdcacdbbcbaadbcccadcdcbaddcdcbbaabaabaddbaccccaaacbcbbddcddddbadabaacbcabdddcdadaccbbadbdadbadbdcaadcbcbccdbbbccacaaacdbbddadcbcdcccbdbadaabacdbccdcbbcddabbacacabdbbaacbdcbbbdbcadbcddaaccbabdbcbdcbacaddbcccadacbbccdcdbbcacabbaacbcddcdbacdcdcbcddbcdcdcddccabcacadcbbacddcadaabddbdbbddbccdcddccabbdbacbbbbadcadcdbccabbdcadacbbbddacbcadadacdcbdcbadbbcbccdcdddacbdcdbcadbabbcbaddbdddccdcadcbbdbbdcbccbbbcbabdddabdabbbadacacacbbaaaadddbaccbddcdbbabcaaabcababbcadcbdcabcbbcabbcabddccdcbddbaacaccdbaaabaadddabbdccbcaacbdbaadbacabbbdcaccbdcabddacadcbbddbdbdccddbbcbccbbcdacdbdabcadcacddaaccdddaacdcdabacbdcadabacacaddcacaccabbabbbadacbaadcadbacdcdbaaabacdcccdaabccddbddcabbadccbcdadcdcdacdababdccbbabcbcacdbabcabacccdbcacdbaddcdcacdaacddddbbcbbdadbdcacccacdbacabbadabcaadccbcadbbddcdbcdcbaacddcbaadcaaabadccacbdcdbdbdadbbbccabcabdaccbbdccbddaaaaddacacccdcdabddbdddababbaabccbddcbdaadddbbcadadccadadbbaababacadacdadbabbcddddbccbaccdccccdbaccababdaacccbbaabbacdcdacbadcdcdbcbbcdacdcdbbccdcababccddcaabbadacbcccbdcbbddbcccccadbddcabbdddccdaaabdaabababbacddbddacaddaacdcdccdaabacbbaadccccccbddadaadcabdabdadcdbbbbbcbcdbddcbaddbbcabbcdbadbbbacbbdccdcddcdaccbdaaacdadccbbdaacbadacdbddbbccbdccaabbdcadcbccabcdbbddadabaacbcbaaaaddddcbbaabbabdbdbcdcdacddadcbdcdcdacacdabdcabdbcadbbddadbbbaacaacdbacccacbaddcdcccadabddacadcdcadbabdaaccdacdbbbdcbadaaaccaaabcaaaddccbdaacddaaabbcbddcbddccacdadddbacadaaaccbcacbbacbacdccaccdabbbaccacbcbcdddddbdccdbababbbdbbdacdaacbbdbbbbdaccaccacacdbbdcaaadaacdcaaabdacddddbcdabcbbacacbababdacadbdaaaddaaababbbcabdabacdcbacacabcaadaaacbddacbddaccbbcdabdadadcabbdccddcacacadbdcacbacacbdbbcaaaabbbddcbbccbabcddaadbdacaccddbbcdbdadbdddaacbcbaddcababbdbbaddaaccccddbadcacacbbaccdabdcbbbaabacadcaccbbdabbccddaabbabcddbdaaccccbcccbcbdccccacabccbdbaccdcaaadccaccbcacddabdbcbcbdcaaabdbabbdcacbaddbadcabdcbcadbababdddbaadcbcddadacabbcadaabdcdaaaadbcabddabcaacabbbbcadddbdddddcbdbdbaacdaaadccdadcbcbdcbdbcbbbaccddcbcbadaabdcbbcdbbaaddcdcdaccdbdaaacbadccaadddddcddabaacdbbbacdadbdcddaccacdbbdddbbcbbbdcccbdddddbddabdbcaaadbadaabccbddacbabacacadbcccbbccdbdbbcddabcccbacdbdaccdddbacccacacdcbcdbccdacaaaacccabdbcbcbdabddaddaddabcadaabcbadaacbbbaacaabcddddbaaccaabcdbddabacaddacccbacadbccdddbcbbcbddcdcdbbdcbbddbdddbcbcbabbddbbcabaaddcabcdcbadacbbbccabcdaddcbddcbdddcabdbddddacbacaabcddbbccadcbcdadcacbbdacddbccabbcbaccbcbadbaacdcacbcabbbbdbadabbdddcbbadcdcccdcdbaadcccccdcdcacbbbdbbcaababdbabbaaccdadddaacadaaadccbbdbcddcdbcbccaacdbaabcbbdccdacccdcbbdabdaabccddaaabbcdabccdcdbccaadababbbddabdbccaabcdbdbaadcadbcacadbccccdddbcdacaddcddccddbddbbdaabccbdcaccadddcbacacabcbbdaccbdbacdbdadcbbaababaacdcdaadaaacacadbdddccbbcbacdcadacdbcbaacbdcabdaabddddbbbaadcdaddcbcbdabbacdbcdbacbddaadbcddccbbcbdbcdbcbdaaacdaadbbbbdbcdacdbccdbdbabdcacbcbcdcbcdaaddaaaccccbbbaccccdcadacdccdcdbbbbadcbcaacbddcbbaacbacccadddcadabacbdccdcbcabccabcbccdcdcccddccccdaddcbcabaddccaccbcccbdbbadacbbbbdccaacbcbdabbbadacbaacabcdcadaccabdddcbabdacbdbddcbbdddadcdbacacbadcbdabbddbbdcadcabcbaddbbbacbbdcccbbdcadcdbbaadcadaabddcababcaadcdaadacbcadaccdcdaabccbdcabcccabaddcbcbdaabdbdbdbadabadadbccccccabbddcabadbdddadcbadacddabaaabadbaddddcbbabcdcabcaddabadaaabccddbcbdddadcaabcddadcadaaaccbdbcacbbbdcabdbbddbbabcdaccbaddbcadcabdccaacbadbddadacaddabbabdccdbaabbacbbcbdaaacccabcdbcccacaaaaabddabacaacabcdcdcddddbccccbcdbcabcbacdacbbccbcaddacbbacdacaddcbadabcbcabaabdcacabbbaabbcacddcdcbacccccaaaadcadddcdbaacbacdbbbacabccabdddddddabccbcabcccadabbdacdcbdcdacaaacdabbcddbcdbbdbbcdbbbbccdaacdaaadbcbacbbbbbbdcddaabcbabacdbbccbacccaaddcdcccddabdabbbccdadbacbadcadaaabadccabcccbcddddddddabcddababcbaddddccdadbdaaacbabcdacdccbbadcadbcbaddbabbabbdacbacccacdcccaaaabccacdabbadacabdaccacaabacbddabddbabbcdaaabcbadbbbcbadcbbaababdacaacddbcacadbbacccbbbcaaddbcdddbaaaaabcdabbdbbbabaabccdddabaaacadccddccdbaadbdbbbdadcbadccacccdbcadaaaabbacacdabaddddcddddddacdbcbadcbbacbbabdbdddbdaadcdbcabdddacccadbccacdbbaaacbadaaacaccdbcabbcccacbcdbdcbdadbabdacbbdbdbddaabdccbbdadcabcbbadaaabdbbbabbdbbccddbcdbadddcabbcbaaadcdcdaabbcbcbdaadcbcdbdcddaadcaddcabcdbadcccadabbdbcbadadaadddbbcaabcacacdcccaaccccbbaabbdddbbabcbbccbdcdaddbbabadbccdadacabadcababbbcabcbdcdbccbcdcdbddbbddbacbcacadcbacdbcdcbdbddadcaddabcdbbcccdcadacbbddaaadccdbdbbbaddcdcbcabcdabcdbcdbbaaaabcbddbaaccbacddadbdaccbdcdcdabdabcadbbccccadbbabdbadbacaabbadddbbbcababbadcdcaabcdbabadccdaddbdbabbacccaacbddbadbbbcdabcbdbdacbbbddcaabcccbbdcbadacbaaaabddaacacabccdaadcbdbcabddabdbacdcacdbbbbacdcbbcabacabbcdbdbadccabaadbcacdddadaaccadbdbcbaaacbdbababdabdaccadccabaabbcaaacbbaadcacdadcadcbdcbabaabcbbddcdcbdaabcbaadadcbabcbcadbdcdaddbbcadaaaabcdadcabdcddddaaddbbdaacdaacccdbaaccdbbbcbccabcbadabcbadbdabcddadbbbbcddcacdbabcdbacbdcbbbcbbdbaccbcaabadadccdcadcaadaadaccdddbdddadbaaadccbdbcabcbcadccaccbddbbadacadaccccadcadcccddcaacabadcacaabbdcdabcbdbabbcadbdaddabbbdbbbbddbbbbdcdcddabdcbabddaabccdabbbddcdacaacabbaaddccacbcbddadcdbdcccddcccbbdbcbcbbdbbbacaacadadbcabddbadbddcbdabbcdadacbccaabddabdcccaabadababbdabaaddbbaabbbdcbaadbcccaabdaacbdadaaddbdaccaaacacdabddcbdaacabbaaaadbbdbcacddabacadbbbbbaacccbcbdabaddbadbcabdadacacaadcdcaaccccccbdbaaccccdcccbbcdbcaddbbdbbcababbbcdcdccbaacbbcaccbcbadbdacddbaccdaaadcadbbddaccccdbddadabdbcccdabddaadabadacadcabccadbdaacbdbaabbbacdcdcdabcccccbabababcbadaadcaaddcddadaaaaadddbaabddbddcbbdaaddbaadaabadacacbcaaddbaadcabdadcbddddcddccabcddbdbadcaacdaabaccdbccdcbbdadccaccddaabdcbbbdaaadadbcbbaadddcbbdaadcabacbaabccdadbbadbbccabcccbccbcbbbbbddadbdbadcdadaacdbcabccddcdcdbcaddbacadaadcdadadacbabcacaababcdbdacdadbbadbdacddbaacdcadaaacdcaadbcbcccddaadaadcadaadaddbbdabbdcdcaaababaaaaccccaacdbbbcadacdcbbddddbdcabcabbbbdbadbcaacdaadaccbbdabbadddaadbcbcacabddcbaaaacacacbdbcccdddddddbdcbbacbddbccdcbbdadbbdcdcdbbbbacdcbcbddabdabcbdbbbdcaadbbbacbbdbdbbdcbbaabaacabdbccdbbdcbbcdabbdaadaababcadaddbabbdcdadccbbaaaddbccbcdadbbccaccddaacccbdcccbdcacdacddccdaccddccbadbcaaddcdcacbcacccadbcdbaabaccdcdcbdaacadcbcbdbabbacdadadcacaaaaaaadcbddcdbcddbdcadcbccdabdacbbdbabbabcbccddcdcbddcbddcbddccbcadcbdccbdcdcdaabdcadadbdaddcbccbbcbdadcaaccbcabacdbbdcbdcdadbbacbbcbcbdcbcbabacbdacddaaaccddcdbbbadcdabadaaabccbbddbaacabacbbdaacdbcccabddaadbcbadabbbcbbbbcdcdadbdaaacabbabdbbbdccbbacbacbcacabbddccaddabaacdcbdddbababababacbbcbadbdbbdacaaabcbabdbbcbdbaaaabbdadbaaccbccdabbdccdabbbdadcddaacddabacbbdbcaddbcbdadcdcadddbcbbdbaaabdcbbcbddaccdbaaddbbbadaddbaccabcdabccdbbccbaacdbbbcdcaaabbbdbbccccbdababdbaacdcadcadacaddccabdacbaddaacbcaccacdacdbbbcaadcccadacbabbbdcbcbbddaabcabccddbcadaddccbccddccdbddccbbdabbbbccabcdcabbadddaddddcabdbccaaadabbbadadcbcbbdbbadccadbbdcabbaddbbccadddcdcbabdcdbbcddacacbacdbacabbacdcdbacaddcbcdddacacdbdbcdbaddaadcdabaaabdbdcdbabaadcabdbdbbaabbdbcacaabacbabdccdaadaccdcacabbbdbccccdcacdcdbdacdbadddcccbdadbabacaaaaacaaddbbabddcbccdddadcbccddaacbdabbdcbdddcbabdabaacacbaadacabadbbbaadcaadcdbbbdccacbddbacacdcacbbdbbcdccabaadbacdaaadabaadcbbdccbadaaaacbbababbcabaacdcbdcdbacbdcacbacccdcddccbbadcdbbbcdbddbcbbccbdbbcbaacaaabcbcbcddadddcabddcadacddccbbbadbdcacccddbadbdbdbbcbdbbcbdcdcbcdabdbddbccdcdabbbdacbdaccdbdbbbdbbddabdbdcadacaacdbcbbdbbdadbccbbaabddddabccbbcbcbadcacaccbcdadcdaacdbdaacbadbcaadddddcdbcccdbaabdcbbdadddbbccababbcbacbbcdbbcacdcaddacdabcaacddcaaaccbbdaaddcbddcadaaabdaacbcbdcbacbdcdcbacddadcbbcbdbadddcbbabdbdcadddbcaddccbabbcbcbacdcaacdbbabccdadcacccbbbddbaccdaababdccbbabdddddabccdcdcbcdbadabbacbaaacbbccbbdddacabdadcbddbbdbbcdbcdcbacadaacababdacdbbdcdbadaaddbccdcabaaababbdbcdbcbbacadaccaddcaacdbcdddcdcdcdddcbbacdcabdabbbacccdbbcbbacbbdcbacacaaaaccacdadbccdddadbdccdcadabbabcdcbdadbcbaaccbcdadcadaacbcdadaddccaddbbacdbddbaabbadcbcdcacdcacaaacaddbcdbccdbbcbdaacbbdbbaddcdbaaadaddcaccaddbabbaaaacabbcdcbdcabccdbabdcdcbacaadadaddcaabccaddddcbbdacdcbbcccbbbcdcbaabbdaccaaacccdbabbbbcdddbaccaaabbcaacacdbcbbcbcbadcaabaacacabcbccaccdddbdddcbbdbbacdbaaddacdaadbcbabacbadbdbddbcdcadcdabadbabdccdcabcbabbdddcdbcdabcbabdbdddadcacbaadaddbacccacbbaacabbacdaacbcacabdbdadcbbaaccdcddaadcbbcaabddadababbaadabbdadcadbcabbcdacdcbbcbbbcadabaddccacdcdcbddcbccadcababaacbbdcadaccaabddbcccbaccbadbbddacabbbcdbbddbdcadadccddabddbdbacddbbbbaddcbacdacacbaddcadbbadadcbcadccccbcaadcdbddbaaccbbcabacadadbbbabccbdacbcddadacaaddacbcadbbbdddbbbbbcbddbddcddbaabcdbddcadbacbbdbcadbdcbcacbbacbbddccdabadddaccdadcabdbcdcdcdacdbbcaacdcacbdcaabcdacbcdbdacbbdbaccccddbcacadbbaccbbcbcdcbcdbbdadddbacbcacbdbaacaabacbacadbbccbcddabadcadbbcbdaaadbbbbcaccaddabdbcdacadcaaaabcadddddcaaacdbdcaacbdcadabccdcccdacccaaccbbcacbbbdabdbccdbdabaabdacadbadbccddaddacdbadbbdcddbadcdbababdabcbdaadccdaaccabcaccddadacacabbbddbcaacdaadbcdaacdbabbdbcdbddbabadbbcbcdbbdbaccccbbcbccbcdabcaddccbcbdaddbdaadcbcbcdbaaddbbbcccbacbbdbdbccdddccbabaccabbcbccaaddbbccdcbaccbbadbccbadaacacacbdacbcdcbccdcbaddccabdccbaddbaddbccdddcdbaadbdcdccdacdcadcdacaaaaaccabcbdccdcdabbbacacadabcdadbddabdcdacbaacaddcdadbbddcacdcaddaacdddccccabaadabaddccbdcbdbddcccacbbddbbbcccdcacadcddbcbdccdbcbddaadddcbccbbddbdcdbbbadbbcbabbbabcdcdcadbbbbcabaaaccaaaccacaaaaccadbdcdbadbbcdbacbaabcbacaacbdcbbacccaaabbcaabccadaaababbcdbdbbbadbacdaddddcdcbbcccdbaddcaababbabcdbbcbbbabbcdcbbaabaabddabacbaacacdaacaaccccbbbddcababdabccdbbaccaaccaaddabbbbbcbcddacdbccbdbadaaacccbdcacbdcdaccdabbabdccbaadadcbdabdcdbaaadaaccaadaccdbcbaabacddadcbccdbbcdddabccadadbaccaaddcbadcabcaaccabdabbacbbbbdbcbcabcbdbcdcdbcdcdcabcbabbaadabaddbbadacbbaccabbcacccbddaddacbdadacbaddacdbdccbbdcbdddcdcaaddbccacbbdadcbabddaccaaccabbcabbcdabaaadbacccaaacbcbcddccacaccbababddcddddddccabddccaacacaccacdabdabbacbbdbacbcacbbdaaccbcaccbaccaacaabddadddbdcbcbaabbcbdbdcdcddbddabacdcdbdccacaadcbaaabbacacbdcdcabbacadaccbcaadaacadabbbaacbddbddcdbdaacdbcadbaaacaddcaabbdbbcdbdbbbbccaddbdcccabcccbdcaddddcdbdbdbadbbcaccababdccacbbccddcdbcccbaddcbbddadddccabdccadbdcaabcaaadddcaaabaccbabdcccadbccdabbcaaadbbbbcdabcadddadadacccbbdbcdabaddadbdddacbaddbabaaaddcccacabbccbdbdbddcddabacababdabbbaaaacccccccddbcdcaaadacddcadbaadbdcabdddddaaaaabdaabcbbaabbcaccbcbbaadabcdccdacaacbbbcdbbabddbcdaddcabacdacaadcbcbcbcddcbdcaababbadcabcbbdcaddbaddbaabadcabacdbcabdcdbabcdbbbbbdbcdabcbcacdacababcabbcdcadabdddddabccdcdcdbdaadcbababaccacadcadcbbacabacbdbdcbbdadadddabacacaacdadbdadabddbbcdcdabaddaabddcabbbbaaddbaacdaaaadbdccaddcbdccaacdaddaaaaababddddddadbbacccadadbabccbdaacadbadabcbbcbabcbaacdbaadcdabbcabdaaadbcdcdaacdaccbaaabbaadbddabadacbbabcbbcdcacbcadcdadcdbbcacbbbbdcdcadaaadcbcbababaddbacacbadaaadbabddbcdbbadcadabcdcbdcdddbccaacdbcadabbabdbcbbdcdadcbacbddabaccdacbcdccdbbaabaccdbcaaadcacaccbabacdcbdbacbabccdaaccbacacbcababdaadbadcadbcbcddbabaabddcaabbdcaaabdadabcdcdadaddbbbbbcccdcddadbadacbbcdabdaaaabbacbbdcadbdbacbccddccadadaacbabbcbacaaadcabdcaadaddcacbadcadaacadaaaaddddbcababbacadadccacbcdddbadabcbbbcdbaccbaaababbbcbaaaccaccdaabadaaadaccabaaaacbbcadcbabbcbdcaabdadabdbcbdddcaaaadababaaabacdcddbbddcdbdadcaccabbadabbcbcbcaadcaabadadcdabccbccadbccaadddbadaabaccdcdbddabadbadbabccaadaddbabbbaaacdbbdbccdbcbdcdcccdbcccabacccdccaadbcaddaacbbadcdadddcabccddddbadaaddcccdbbcaaacbdccdcccdaddcdcbcbaabdcaabbdbacdddccadbabbdbbaddcbcaddddcdddabaccbabdcbabcbdbdcbabcbcdbaccabdbbbdbdcdcaaccdcabdadbacddddcaaacdaacdaadcdacbbacbdaaccaadcabcdccadccaadaacabcabddcbccdaccaddbaccddbbbbaadbcaabacbaacddaacdacddadcdcbadddcdcbdccbdddccddacabddbdbaadcdcbcdbbcddaaacadadddcaacabadcbaaabdabaaacbabcdadabcddbccbdbbccbbcdaadbddcdddaacdcddabbccdddcbdbbbdcbbacdcbccabadcbcadabccccdaabcdcddacaccdadadbddabbbcadadddaabaaaacbabacbabdbcbaddaadbacbcbaccddbccbbdcdcbbcbcabccadddbdbcbccddbbadcbacbcdbbcacbbabbcacabdddbacaccdaaaadbddacdcaabddcccdaacddcadbbdabdbdbabaaabdcabdcacddaadaacdddccadcabdbabaacdddacbbcbacdadbbbdbbbbabcbacbddbbcccdbdcabadccacbcbdabcdcdbdaddabdddaaaacccdcabdabccbaadaacbcbababcdcdaccbccbbdadddcaccaddcbcbaabddadcacbcbbabacccaaabbdbcbabccbcdcbbbdcdbcababcadcaddbdaccbcdbcadaddbbcacdacddcbddccbaaddddcdaaaccbbbbbbacabddccddcabbaaccadaabdcdadccaddacbadbccdcdbbbbadbacbddbbaddacdcdcccacaaddbccbadccddbbbdddbcaacdcadaacbaabbbddcbdbcbbdabbdbbcdbacbbcbbadcabcddbcacdabddabbababacccabbcadcbddadddadbdccbaababddabccdabcadbddcabacddbdbadbadbbbdbaadaacaccaadacdbcbccddccaddcadbabcdacabdbccdbcdcdbbbbdacdcbbdabacddacadddbabccccaabcddcddddccaacbbcbbbbbbaccdacbccbdabbccbbaadccabbaabbcbcbcacadabaddbddacddcaacbbbcbdaaddbbbdcddaccadcbaccbdacbbacdcddcbbddaaccbaadbcbcbdddcadacbbadaaabbcaabcccaaddabccddcacbdbdbdbccaacacbcdadbdbcaaaaadddaddaccccbcbcbaacdccccabcddcbdacdbcdacadbdabbcbcccaddcccabbccdbabcddaddacadcdcddbccccdbdbaabbbbbcdaacbddcbadcacdbacbdcaabbcadcddbaccaaabaaaaaacaabbcbddadcbdcdbcdbaccbbbabccacccdcdcacccaacbddadcacdbbcababddaacbcccccabdbdbbdabbdcdcabdbdadcbddbdbbaddbdcadcdaddbccdaabdaaadccdddbccaaadddaccbbbdacdcabbbacdcccbcadabdddabbbdabacabccdccbbaccdaccccdadccbdbacdbabaabdcbdcddcbaccdbabaaadbabbbabbcccddacbbccdbdcbbabbaaaabdababbddbabbbbaddcdbbbbdabacbdbbbcdcdadcadbaadddacbccccadddbdddabdccabcacaccadbcddbacadbcaccbaccbbaddcbdaadadaabcdcdabbdbabdbbabaccdbdbadbaaabadddcddaaacbbbbdacddcbdddddcbbbdabccccdbabdddacccbdcdbbbadccadcbaabcdccbaaccdbdacaccaabdbcbcdcaadbaaabdabdddddddcbdddaaccbdacdccdadbbdbcdcbadcabdccabbabcdbbaadaddbadcbacdcaccdccaabddcdbcaaabbdbadabdbdaccccbdcccbccaddddbcbcbcdcbddcdadaadaaadbbabdcdcbddacdbbaadbabccdbabcdcabccbdabddbcdababddbdadaaaadabcbbcabcbbbacdbdacdcdbbaaccdcddcadcddccbdbddccabbadbadbbdbadadaddddadcaadbccdcbddacbccacdddddcacccdcdccdbbcdcdacaabdadcdacbdbdcdbcbabddabdbccaddcbbbcddacbdbccbcbddbddcdacbbcbccabacaadbdcdbdccdaaacdabcbaddcbacabdcbdcdaddcbccabdacabddbdaaabadaddaddcacbccbbdbbcccdcddcaacbdbbcdaabbcccaccadcccdaaaaadcbddcbbbdcbcabcddddddbbcccdaccdcadbcabcdcbcdcdadcaccdaaadadddacbcadbbcadbcaaddcccdcbababccbcbdbcdbdaddbbbcabddcdadcdbbdaabdbcbcaadbcbacdbabdacddbcaadacabdbcacadbdccabaacbbbdddcddcaacabbdccaaaabdcbdaaabbcdacccddbddabbdadbcbacdabcbddbccdbcdabacccdddabbcdccbdcdddbcbbdccaddbdcbdddccbccbadabcbccadcbdaccbcbcaabadbacddbdbccccddbdaadcdaadcccbbadbbaabddddabbcccaaababbbccccaacaddcdccaacdbcabbadcabcaabdadbbdddabdbbccbaaadbdadacaaddcbdbbdccbccabcadccabdbaadadbbdcdcdcaccdcdadddcaadbbaccbdbdbabbaaaabccdcaacddadcbbbadadcdddccddacacbaddbbbccbdcbbabcdcadcabdbbbdbcaabdcccbcdddcdcbabcabdcabbdbabdabcddcacdcccbbdbbdcadabdacbbadbcdcabcbdbdaccdabcacbdccaaabcaccadabaddcddddddcbccdcbbdcabaaaaabbcbcdabcccdcdaadbdacacbdbdcbadadbddababcdbcadbbdcadbbbcabcadddddcbcdcbbbddcadadabcaabcbcabcbccabaccaaaabdadbbaabdabcdbadcbaadbcbbcbbaddbbacadcbaccbdcbcbcbadcddbbbaacdcabbaccddabcbcdaacacdabbdbaaabbdabccaccaddadbbcbacabcdacabbadbbbaccccbccbdaadbdbaaccaaaccdccabbddccbacdbcccdaaddcabbcbabdbacdcbcaadcabaabcdbbbdbbaaabdcbadadacadcabbbbaabcbabddcababccaaccacccaacdbddddadcbaadccbdcdcbadcbbdcaadcbbbbbcbcbccdcdcaaccacdbbdacddabcaaaadbbaadbbbaacccdabacbbbcbbbcdaabbbbbadabaadcdacdaadbadbdcdadadabbabcbbbdbdddccddabccdaccaaccacbbcbcbcabddacadaabbacdacacccbaacddbddaaabaccbccacabcdddcacdaaadccaaabadacadbcdccabbcdddaaaababaacaabaacdbcbcddbcbbaccccdccbdbbacaaacaccbcccbdaabdabcbcaabdddcdcdbadbbdbbabbaccaaaddbdcaacccbbcabdccbdcbdcdabdadadaabdbbdabdacbacadcaccbbaaacadcdcacdbcdababdabadaadccabdbcbbdcaaaaccccadaacbaacbddccdabbadcbddbadadcbbcdbcddbaabdaacbbcdcdcbaabbdddcbabaabcbabbddcabacdbbacbcaacbcbdcabdccacabdbaababdadcaacacaddbabbccccabbaaccdaccadcdcddadbbddaacaccbcbdbadbdcbcaabcdccccabbbdaaacbdbabbcadcdcadaccdcbcdcdccaddadcddcdacdacbdddbadbacaaddaccdbccdadabdaadddbbcdacaacdddbdbddbcbacddabacdddacaacdbbbbbcacdcdbabadbabbcbaadccaaccaccddccacbddbaaaddcbdacabdbbbcaadbbabccaaaccdcdaccadcabdcbabdadbabcabbdaabbdaabdcaaaacaadacbacaaccdabcbcccabcbcdccaccacddadbcdcccaccbbbdabacadbabdcacabdcbadcbdcbcccbbcbbdaaccacdbdcdcbacdabaacacdcddabcadaadbabbbcbadbccbabbaacdcccbdaabcaaaddbcdaacccaadbabdcdacccdaabddcccacabcdaccabacbbdbccbbbaacbdddbbbcbbaacbdbdacadcbccbbdcccdbcbdcdbbbbaaddcbabdbbbdbbdabbccbbdbbbbabbdaabacabacbbdbcbabacababdcdadbdbdcdbddabcacaababcbcdcbcbdcddcadaccacdaddaccbcadbbdbadbdbabbcdadbccdbbbabdcddddbdccbcdabadbdbbadddabbccaccddadccbaabacbccddabdcbccacbadcbaacddcbaddbcdabdcbadddadddcaccbabccdcbddccbbbadbcbadbccdcccdabcbaaaddcdddbabbabbdbdcccbaabcbaacccdadcccdbccbccdbdbaacacaddbabbcabdddbddadaadaccbaddadddadacaccdbbabbabaaabccabacdaadcabbacabccbaddbaadcdaaccbacaaadbdaaddabcbddcabadabddccdaaaacabacbdadcddaaaacbacadccabaaacabcbaccccabcabacbabaabdbbdbcbdadccddaaddabcdacbdbcccbdaadddccaddabacbaccdaaddacbcadbbcdcdadaaacadbbcdcadddaaabddaadaaaacbaccaadccbacbabddabdddbacccabdabbdcbccaadcdbcdacbdddbcadcddbbbacadcdbdbdcbcbbcdddaddbabdcaccaccbdcddbbdbbbdcbaaaadbdcadcbcccbaabbcdcbbbdacadaccbbacddddccbdacaacdcabcbadacaaddbaccbbdbbabbacaadaddcdaabcccccdacbbdbbddbcaabddbcbcccacacbaddddbdcccdbdacbaabdcdbdacbdbbbdcccbcdbbbddbccaccdaacdcaadabcbbbdbadcaadcadacdcadccacdccbbcccbcaaabbaabbddbacdcbdabadbbadcdcdbdaccbccbcdcbacdbdcadbcdcadcccbdaadbbdcbadaaacabcdcbdccadddbccabadcdcbacacbcddcabcbaddcccdbbabbbbcabacbabaadbadabbdbdbdcaaadacbcccccdbbbbdbbbbaaadacabdabaabbdbddddcaadccaaadabdabbddcdbddacbdddddacbaddbcdbcbcdacdabaaaacdcdbbabbbabdabbacbbccabcdcdbbbcddbbaaaddbcbbdcbabddaddbcdabcbcaaadcbacbabbccddddcbaaadcccdacccbaabbdaadbcaabababccdbacbccabbddbcabaadcdcaacdcadcbbbbbcbbcbddbdabdddcdaccddaadcaabbcadbadbdbbadddadadbdccddcdbcdccdacbbccacdacacadcdcbcddbbcacabdadabbcbacdadabbadababdcdcbcadbdcdaabdbcdabadcabacbcbbbabdddbabadcdaaabccbbcababdccaaacaadddbcbcdbacbddddadacbdadccabadaabaccdbdbdabdbbcacaabcdaacadaacadddcccbbabbdcccbbbbdbacdcbddabdbdaaacbddcbcbbcacaaddbaddacadcdadcbaadcdbdbcabcaaccbcadbbdcabccccdacacccbccbacbbdcdcccbaacdbbddbdbddcbaccaaabccacdbacdbacdabcdbccadcdaaddababdacbcddbbdadbaaacabbbaabaadcdbcbdbbbbdcbccdbbcaabbaaaccbacbbbaaadccbbadcbcaadabddcdcacabbacdadddcddacbdabbdbcacdbdbdbaaaccabdcccaadadcbddcddacaacbbcbccaddacdbdbcbcbbcbdddabddaadacbcaddcdadbcdbcaabadabaaabbbabcbacbabdacbcbdbcbbcbcdbcbabacabbacdacbddbbdadbadcabcabbaccdbacabaaaccdbddaccacbbacbdccddadcccccdbbdbcdaabdbdddaabcabadbacdbcadadadddccbbdbbdbddbcabdcbdbdddbcaababdbccdabbaacdcbdccbabaddbcbcccaccdaabadcbccabbabddcdbaacadaddcdbacdaccdabbcdaaadacdcbdbdacbcdabdabbbabaadddbabdabccbccabaabcdbaabcdddbbacccacbbcbcbbacdcabcbaaaddccadbdddbbdddcccbacddbcadbbdbadbdcbccacadddcabdbbabcbacacdacdcdaababdacdacaddbacbacddcbaacbbddbdcdbbcdacaaadcabcacbdadcddaaddbcabbddacddbcabbbbcabdccddbcacdcbabdcbcccddbabcbbabdcbccccaddbdadadbcddbdbccdbaaabbaabbbbbbbadbaaaadabaddabccacacdaacaadbdacacdbbaaadaadabbabdddcdbcbccdddccadcdacccccddabdddddbbcdabbcdbcdddacddacdacbcaccadaaacdcbadaddbadcabcbacddccddababaadbcababcdacabdccabcbddbbbbbdcdbabddaccbadbdaabcdabbdacdbaacccabccaccadbaabcaddbbcabdcbbdcbcaadcaccdbabbaadddacddbbdbbcbbcbbbaababcccaabbbbbbdbacdaababbdbdcacdbdbbdbaaacdbcbbddddaaaabdcbababddcdabcdcdcbbdaccbdddaddbdacdbdbadabcdbbcbdcbcadaddcbcdcdbdaacaddacbadcdbadcdacadbdbdcccaccbdaadbdcdbacadaabbccbdcacabaccbabadccdcbccabdbddddadddbdbabbcddccdbcbddaaabaacbabaadbbaddaaccdccddbbabbaadacbdaabbbbaaaadbabcddbabaadbaccdabccddaddbdacabcbdddbbdbbbcccddabddbdbbbadacbcccacbbacccaccddadbcdaacdbacbdcbabdadbbbddbcaacabdcaaabcdadddcaaccbcaadbabbdcbddaaababababccbddbccadddbcdabacacddddbcdcaccdcdddbcbabbbdbccacdcdabcbadccbbbaacabcaabcacdbbdcbcbbaaaacabaddadcdcadadaabadcbabcbcccdcbbcddcacaaaabddbbcbdaaaabcbcbabcdbbbcadcbabaadcdadcccbccadbdcdacadadccdadbabccdbbaaadbdbcbbbbcdcaabddacabcacbddddacabcbbcaabdaacdcdaadaacbadcabdabbcbccdaacdcbdabbdddabbcbaadadbcdcdaabddbbbbdbdbcacccadacadcccaacbbacbdbcbcbddcdbabaaddcbaccadabadcdaacccabccbbcddbcccabbbbccadaabaacadcadccbabcddcbbcdbbdaabaaadbbcccaacddbbbdbbbdbcdbaacdbbbaabacaaadaabbcbbbcaadbbdabdbbdbdadbcbdbdddabaaccdcdbdbbcbccbccacddbdcddacbadbadbddcdddaddccdbbdcddbddcccbabcccbadcdbddbbacddaabdabdadbacabadabcaccbddaadbaaadabccabdccbacabaaadbbcbdcdbbbcaadccdbbddddaaabcbdddcbccbdbdacdcabcacbadbcccbbcdabadbccaccddabdcacaaccbbaadabbcacbbdccbdddadbbdcdbcbcadcdcbddbabcbbbcadbbcdbdacabbababccccbcbbbbcddcacacaacaddccacbaaddadcbbbcbcbbaccbaadddbacbcdbdbaadacabbddbadcabdbcccbabcbcbccbdcadcacdcbacdbcaacaddacabacabbadcbdaadcbbccbacddacbddbcdbdcdcbcaaaabbbdcaccbcbacdcddabbbbccabacbcbaabccaacdcbcdbdbdddacbbbdbccaddaaccdccdadbccaccdacdbcbbadcbcbccadccbdddbbbaaaaaacddaddccdadbccbdbadabdbacadcbaddbddddcabadcaacdbbcbcadbadaaadbcbcabddddbcdcdbdddccaaacdbddccdcdcdbaabdcacaddcadbbbdbaddccdbcccdbacbcadccbadddbddadabccdcadbbbdbacbdaacaadcdabcbaadbbaacaccdddadabbccbaddabbaacdabbaacccccabbabbbaaadbadcddbaccbbdabacadadbcdddadcaacababaabcddbadbdbbcadddabccbadacabbbacbabbaabcaddbdbbcadbadddcbbdbabdccacaacccaacadcabdabbdabbddcbcaacdaabbabadaddcabcdcccababdcaccbacdaacbacbdcccdadcaaaddadcdcdcacabddaabddbcdacbadcaccababaaabaccccdcadbdcabdcabdddcbdadbacddcabdbdddbdbbaabcdccbddcdcbbcdbdcbddbdccaccbdaabdcbaadbacacbbabcbccbbbadaaacacaaaabbbdacaadabdbaacddabadbacbbbddcbaaabacdcbbbcaccbdbbdccdccddbbddcbcdabcabdadaaccdbbbbcdcddddaabccdcdadacbcbdcdabdbdbaacccbccacbbabdbdaaaddaabdaadcbccbaacaddcdcbbadbdccadadbddcadbbcdccacddbacaddbbbabbadaccaacdccabacbddcbdddccbdccbdadcbbccbdcbdcdaaaccdddabbacabcbcbadadddaacddcaaadabdadccdbcaabcdddccaddbaaccbbcabbaacbccbdddcbacabbcadbdbdbcbccaabadcccdbdabbbacddcdbcabcabdbcacadcadbddcddcaccddcaabcabbdbbcdaaaacccbaacdcbadaacbcdacddbbdcbaabbbcddaabaddddbcddbabdbaabbdacabbbcddcabacdcbabadbccdabdcdbcbbbccacacbddcaaabcbdabccdcadcadbddccddbdddaaabccbddaccadbdaacddacabadcbcaddcbddbcbccacbadcabaabdaacccdacdbacacbbcdcadccbbabaaaaadaccbbbcdaddbbbdaddaabbbbaccdacccbdccaabdcbdbabddbbbababbbccbbddbdadaabbbcdcbdbaadabcacabcdabacbacbbccdccabdcccbbaadcbdaddccbccbabdacbcbaaadbbaaacbcbcadddacbbaababbcddccbdcdadbaddadbbbaacababdaadcdabbdcccbccaacbadccabcccbaabaabdbaccdbbdcccadacdaacdddcdcccabbbcbaabdddabbbcddaaabaddadbcbdcdcadbdcdaacbcdcadbabcabaacbabacadbcbdaaccbbdbadcdcaaaddaadcbcbccbadcbbdccadaccbcbacbcbdbadabadcabdbdcdbbbddadbdbbbabdaddaacaaaadabdcaaccdbdcadcdcdaccdbbccdcbacdaacbaadacbbbdbcacdaccbcdbcbabacccdaddadbabadccbcabadabdcddadcbaadccbabacadbdcbdacaadbacdbaaddbbbadacbacabddbdbdadcdbcddbbabbccacbcbcabadacccdbcaccbccacdadcacabcabdbaddacabaddcacaddabadbdccbdbdbbddaaadabdaccdcbcacbdddcccacdbcaacaabdbadbcaadbacbbdcbcbaadcacaddacacbbcdababbabbaadbcabbbdddbcacbbbcdcabcdbbacbddaddbbdcaaddabdcbadbadaaaccbdcbbcbcbdccdbcbbdbcacbbccddabbbbdbcaadbddbadbdabdaacddacbbcadbccaaabdccaabbabdabbaadbcbbccacdcdbabdcdbcadadabbbabdccdcbadcdbdcccddaacdabcbbbbddccdacbdddcdbdcadbbbaddabaabcbcacacdcdbcbdbdadccbaacdcacacbbdbccadbbabdddaacdddcccaaadccabbaadcddcddaddbcacbddbcadbbbddbdcbdaacaacbadcccdbcaddddbcbbbacaadbadbbbcaacbabddadccacdbacbcdbcdbbddaadddcbadabdddbadcdacaaacbbddbaddabddbbcadbacabaabdcbcdaacbcdbadcadddadacacbdacbdbdbbcbcabbbbdacacadadccdcbbdbbabbadcabbaacccbcddbdbcabcaadadbaccdbcacdbccadcacdccddbdaccddbdbcaabcbabaacaadadbdadccccbaaabdddbdcbddddcddcccdbaccddbcdccdbadddbdacaddcbaacdcdaaddabcdddbacaadcbddcdadccabccaacddadacdabacdcddabbcbbdccddcabacdbbccccdaadaadcccadbbdbcabbdaadccccbdaadbbcdadcaabaccdbdaddccbbacbcbdbccbcccdabaacddcbcdacabcbdddccdbcbddcabcdaaaaddbaabacdcbbaccccaacdabdddbadbabddabbadcdcccadadddacccdbdbdbddcbdbbadcacbbcbcdaabdabdababcbdbdcaaddaddccdddabaacbaacadddccbcbccddaddabaddacbcccccbbcdcbdbbacaabccbddbcbccadbddbbabdccabcdcacaccabadcbbdaacbaccdbbccbddcaccaabddbcaabbbacdacaabddabaacbcadabcdadadcddbcdabbaccdbbcdaccdaccdccccdbbddbdbabdcbdcdbabdabddaddddcdadcaaddcbbbcaabaddcacdcababcadaadccbaaddccbdbabcddbccdbaddcabccbacbdcbadccadaadcbcacbdbcdcccadbbdbbacacbbbbcbddadcbcaadddbdaacdacdccdcbbcccadaddcbdaadcdcabbcbcbccaadaaabbdacbcdddcaccaccacaddcbbacaadcbbcdbdcdbddacdbdbaaddcbdcaaaaddcdcdbdbcbbabbdaccccbbccdabbcdccbbdbbbcbddcbabdaaabccdaaadbcbddaacacbddadcccadddcbcccbdacbdcdccbdababbccabdbcbdabadbabaddccbdbdaaddadacbbbdbaddadbcabbabbdcbaabccbcdcadcdcabdaddbcbaacddcccdbcabdccaacbbbdaacdccdbdabbadcacddadbcaababdbdcddaacbbcbdccbbbbabcddccdcbacdbdacdbbccadcaadabdbadcaccccbddadcaaacbaccbbabddacacdbdacbadbdcabbaabbdabaccdabdcabdbcbbcacbdbaccacabdaccdddcbdadbcadbbdabaddcddcabcbabcbaddabdbabcbadabdbcdaddaaddcdaccaccabbadbdcbcccdccbdbabccbccbbbadadadcbdacccacadddabcbcbbbdbabbcbcdbdccbacdaadadabcadddbadbdccadbddcdcdddddbaacbbaaaaaacabacacadbccbcccbaadabddbabcccadccbdcadcbbcccdcacbcbcdaddadbaacbacbccabcccdbadbadaabdaaacbadcbaacabdbdddcdbacccbcddccadbbcdddbdaaacdaddccdbdcaddabaacadbcddbdbcaaaadaaccdadcadadabcabbadacabbaaccdddbaadbcddbdbccdaacaacdcaddbaacadbdaddbaccbbacccdbdbdbbaadddbcdaccdaaacdddadcacdaaaababbacadccddcbcbbbcdcbdacaabccbabdbdccbdacbcadaaabaadccbadbdcbbaddccccbcdaddbaaacaabacdddaacdcccdabadabbdbdabcbddbcadacbbdbdaddcdadbbdbdaddbcddbdcabdabbbbbbcddabdbbaddacbabddcbbacccacaadbcdacdddddbbdcacbacbcbddaddbbaadadbcdacbdaacbcdcaddddabadaddbbcdccdcaadcaddadcccbbdbccddddbaddcbdaddbaccbcdcddbaccddcacabacbaddcbccdbbbcdcbddcbdadbbbbbbbbddcddcccdbdaabbaabbcaccbdcbcbdcbdaaddbbcabcaccdacbcaabacacaabcaadacddabccaacdcdcaacaaacbaabadccabcdbadcadbdcbbbcabbbdccccdccdadaadacbdbdddcbaabbcacccddacbcccabdaccababddddabbdbcabaabbcaabdabacddaddacbaadabdabadaadddcdadcbcdcdacabaacdaabaabbaddacacddadddbdddabbaacabaabbbadacbdacdccdcdcbcddbbcadaddacdcaacddaacaabbadbcdabacdccaccbdcaadcccbdabaadddcbdcbaddcaaacdcabdcbbbdddccddaccaabcabbcdbadadaabddabaaaabccbacbbadacccabdadddbdddcbaacdabbbddaadacbdadababacbbacbcabbabdbbbddaabccbdacdddbcbccacdbbbcabcadcadcababcacdadbcbaadcabdabbddbdbdbcbcacdabddcdbcddbcdddddbddbddbcadaddacbdadcbadccbbdbacacacaaacaabbbaccababdbdccbdbdbbbbaccbccdcbddbcacaaddbcbdddccbbbabcbaaaddccbbadaabaabbadddadbcaaadbbdbabdcdcbdddcdbbacbbcbacaddadddddacaabcacdadbaccbccbbcababbbacbaaaacbcaabcabacadbcccdbccaaccdcbbcbcccddbabddbdadaabdcbbacacdbabdcaaacadcabcccdcddbbdcdcaaabbadcbcbdbadcdcbdbaddcaacabccdaaaaadbcdacdcaaddddcdacdbccaaadacacdaadcdcccbbaacbbcaacbdabcaaddadbddbcaacabadadbccbccccbbbbbccccaabbbabbbaddcabdddbdbcadbddaaabacdbcdcbabddcacdacbdcddaacbcadbcbaccacddbddccccccccadddbcdbcbcdbbcddcddacacbbadaaadaabbddcdadbabdddbacbaccadcbcdacdaaaccabdcdbdcccdacabcaadddaaaabacdadccbdabbcdbdbaccbaabaabdcadbbadcdacbaddcbdcbcdbccbdcddccddbdbbbabaadabaacbababcacdbcaadacdcaaddbdbdaaadcddabcbbcacddacddacbcbccadbcbbadcddbdddcacadbcccdbbacbcbdbcccaacddacbadbbbacdcdacdccbdaadaccbdadcaccbacaaadcababbdddcccadcddbbabcbcbbdcabdcdadbbacdccdddcbccbaadabbbcadcdbacdddbacaacdadbcddacdbbcddcbbddbbbccdbcddcbdddcbcadaaddbaddddaaddccbaacdabcdbbdabbdcccadadbbbccddbadccbadcbabcabccabdcddacbbcaadbcccaccabbbbdccbccdcbbbcadccdabcaadbddababdccbdbdaadbbbccbabacababacaabbadbccccabaacbabdddbabdcbddababbddcacdabdbcbdcbbcbcbbccbaaacbdadcaccbddadddabdbacaaaaddcbdacbadcdaccccbcdadbbaaacccacaddcddabcbacdbbbbcabddbabbcbbbdacaabdbdabcacabadbbbabaadbabdbbbbaacbaaccbbbbacdbaaabdbddcbdaabdbbabcbcaaabdcbccacdbacaacdcdadabdbbdddacdbcaccaacaddabcbadbcdadbbaddabccbbddbccdbdbbbdcdccaaacdaccbadcdcbcccdbabaaaaacdbcbacaadaddbdbbbacdbacbbcacccadcbccdcdacccacaabbadaaacdcdddaaacdbddabbcdbadaddddcddccaadcbadcaaccbbcddabbcbdcddccabbdacaadaddddcbadcabbbdcbadaadddcdcabbcbdacabdaadbcbddbaadcdccccababadbdaddddcddaaddaaadadbddcaddaddbdcbbbaabaacddcdddabcdcacddbddcdddbbcbdccaddbdacdcacaddddbdacdcacaddadccacdaabdcaadcddaccaacabaabdbdddbacabacabaadadbcbadabbddbaaabddccaadabdcbcadadbbbbcddabcdccbbbbdabadcbaddcbbacabdbdbdcadcbbddbbdbbabddbcbcbdabbbbbbcadcaddadadaddbababdbaccbcdadaaabbcabcddadaabaaabcadbdccdcccdacbcaaaddbaddccacaddbccaccacbcbccdaabcddbdcaadbaaadddbbcdacdbcdaddaacdaaccdcbdcbbcbdcbbccbccaadbdcbcdabbdaddabaaccaadababbdaadcabcdbabbcadcaabababbcdaacaaabcbbbabcaaddaacbdaacbaadbddccaabdcccadcaacdabbccadcbbbdbcdbdaaaabadcbdadaaacadacaaacbbadddcbddbdadddadcdbcadcbbdcadadcdacadabdcadbdcbacbaccadaaaaabccdbccacdbbccbdccadbbbdadcabddabbcadadadabddcaccdcabababbabaccccbcabbcdbccddbccaacccdcbdbabdbdaaddcbbadddcbbddddaadcdabbdcaddbcacacccdbcbcacdadcdadadadcdacbddabcbcbbdbdabcccddccdaacaccdcbbadabcdaacadacacbcadddacbaaabccaddadccdcdccabadaddacbdcccddabccacdbbdadccbbcccbddaaaadabddddbaddaabcbcbaabdccadccbbbbdcbbccbaabbbcbbdccbddcabdadccbdbdbcdbdddabcbdbcddacddddcbbbdcaccbadcddbdcdcdccddcdcdccabbaaadaadadbcddaccacbbddcccbabbbbdadccaccaaccdbcbabcdcadbcccaacadbaadcdbdaaddcbbcbbadbccaadbdcabbcbccddddddabcddaaadccbdccccacbbabacabdaccdbcdbcaabdaccdcbcccccccadcbbaacaaabbddcbcbbcadddabdbccbdbbbbacdddaadcccbcabdadbadadcbcbcdabdbdaadcbbcdcbcbaadabcbbaadccdcaaaaacbccabaabbbcaddddbcaaddaacacbaaacbcdccdcccbddabbabcbcdaabbdabddadcdccbdcbbdcabadabdbcabbbbaaaababbdacdacccbdaddcdadbcdadbddddacbdbdcccbbccccdcdbcaacdbaacdbadcacccbaccdbacadbabcbdccbdbaabdcacbadcbbacaacdcbddbcbabdbccaadcadbbbadbdaabbbbdadadcccdbacbbddaccacdcadbaacbbbdcdacacbcbdbbbdaddbadbacbbaddbdbcadadaccaccdcbcccadbacabcbcacbdabdbbdcdadbadcbabcdbbcbddcbdbbdbdcdcbdbacdccdbbdabccbacabddcbbcadbddcbdbdaabbcdcaababbaccdabbdadccbabdcadbbadbccbddaadadbdacbabbddaccbddaaadbddaccabdbbabdaaccdbcbadbaaccbdcdcdbdcddbbdacdcdabdccaaccadbdcbabbcdbdbbcadcdacabcabdcdabbcddccdbbaddbbcbddddacadcbadadccabbcdbbabbbcccbcccddadaddaaaadaccdabcdccdbaacabcbcabdaaccbccaccbcccccaccabcbdbdddbaccdbabdddcddabdccbcdbabaadddbbdcbcbbdbbbbabacdadabbbacdabbcdbacbdadadccaccdbcbdcadadacbbdcddaddbadcbadccbcacdbdabadabdacccbcbcadbabccdbbdcdddcbcacaadabacdcbaccadacbabdaccdadcacbcadadbaddbbdbdaddddbbccadcbabbaaaabbbababddcdcbcbdabdbccaaaddcacdcacbbaaccdabdcacdcbbabcabcccbdbcddacdbbcccaadbcaaadaacddcaaccacdaaabccaabbbdaacadadcbbaabdadcadadbcdabbdaaacccdccbdbadabbdccbbcdbacaabddddcdadbdbbabaabccddbabddcabdddcddbbdcbbdacbaabdbaabacddaaabccdccacbcdcdaacdcccbccbcbbddaabbdbbbbccdbbbbbcabccdbcdcacaaddacabdddcddcddbdcaccdbcddbbcddbcabbabdbbdddddbcdcacacbacacaacdbaddbdbbabcdbaabccbdabbbaabcbaddbdadcdcdaddacadcaaacddcbccbdbdacdacaacbcdabccddaccbdbdadadacdcaddabaabdbdabdaaccccccbaddbabcadbbbaabdacaabdbbcbadccaaadbbdccdbccbcbcdbdccdcbbccaadddabaacddbdbdbaaaddcdbbbaccbddddcbacdddcdadbaadcbbdaababdbddabdadaadbdaaadbdcbdcdcacbacbcbbcdaacddadbcbdbabbbbbbcccdaddbaadbdbcbdcbccacacdccbcbadaacbccbbacabccacccdbabaacaddbaaababacdcbdbdbaccdbdccddbbacbacdcddcaccccccccdccbbdcbbcaaaabdcaccbabacbdbccacaabbccabbbbdcdabaacbcbbabbcbcddcdcababdbbadadcdbdccaaaaccbbbdbdaddaccadbddbbddcbdcacaacdccbbcddaabcbcccadcaacbddbcbadacadbdaaddabbdabadbadcbaadacbaddbabbdbddcdababaccdddcdbaadabcccadbabcddbcddbdcbaabdddbdacdbaaaaabadccaaccdcaadacadcdcbdabcbbccdaacbdbbccdabcadababaaccccbdccccbbbccbcadbadddccadbbabdadbbabcbdcddbdcbddcdababadcabdbabbbccccddaddcdcacbdbaaaabcdaadccdbbbdcadadadbabdcddbbdabcbbbbccbaaadcabbcccabcdaabcccbdcccbbbdbbdbbbbbbbbdacacbcaabdcbacdaddcdddaccbdcacacbdbbcbcadddbddabdbadbdbdbbacbcbabdababdbadcbddaacadbacbcbcdccdbddbdadbdaabbddadcbcbddbbbadbcbbccacacccbbcdbddbaccbadabcacabbaacdadcdcbdbcccaccadddacacbdcadabbdccdbbddcccccdbdacdcdaadbaabccbdabdbabcbcbcdddbcdabbdcdacbdbddbddbbdacabcabbaadcababadcbddcadccdbbcaabccbbcddababadaabacaaacdbdaddabdbcbaddddbccbdbabbacacaaacccddbdcadddadabcbbcbcbddbbaccbcbbbacbaabaabacbbdaaaadbdbcbdbccbaaabaccaadadadbcaabcbccbdcdcccadacccdbddbabbdbcdcbbdbccbaadbdcdadbcacbabddacccaaaaddadcbdabbdbabdcbdbdaabdcccabdbcdabdaabbccdccdacbbcbbbaabdaadcdbadabaddacacdcdacbcaacdddcccbbbaddbbaabcddabadbbcccbcadbbbcbbdccdbbdacbbdcabcbdbbabccbabacbcdcbcacdddadbdacbbcdadacaacabbcadcadabaddbdcbadbbcaabddddcbadacdbcccdccacbbadcbcadbbbcddbabbcaaabadcdbababbccdabacacaabbaabccccddbabbddbcbbdbbbaccbdadbaabbabbabbbbaabcbcbaaadabcdaaaacbbdbbbacdbbaaabdbbddadcbbbdadaddcaddcccbcbadadbdcbdcbacacbdaaacaabadcabcdaaacddddccabccdccccbddbcccabbdcacdcdbaddacbcbbdcdbbbacaacabcbdcbababcddbbdbbbbdcabaccbbdbdaccdccddbcaabdbdddbccdadacdabdbaabbabddabbdccbccdcbdbbbccdddbbdbccbbbabdcdbbcabddddbbcbcabbccdabdacdbadcbadaaababbbdcddaadbdbcccbcccbbdbdadbcdbdcdbbaddccdbcdbbddaabcadddadacdabbbcbcaaccdcdbccdaaaaabcdaddcbdabddbadcabdcbcdbdccaaabddbbaabccabddabdcbbdabcdbbdaacbadaadcbbbdbdaababdcbcacbdadacaabdcdddcdababaadccdbbbacbbbdcdcddcaaabbccbccbbddcdcaabbddaccbbadccdaaacbdbcaaadccabadabbdaadddaddddbaddcccacbaddadaabdbbcdcbabdabadbdccaababcdcbaabdbabcaccabccadcdcadcdcacaacadbcadbdaaaddaabdaddbcddbbbaccababcdabdbbdcbcdadbbcddddbdadadbbdcbacdadccbcadddbccdbcbbbbabdadbdacbdaabadaabcacccaabdcbccdadaabbdbabddacbdddabdaadbadbbbbbddbdadabadacdcaaddabcdcaddadddbcdcabadaadaaabdbabaabbdaddabbadcddbdbabdaaacccaccdbdccddbdcacbabbdbdbbcbcacdcdbdbbcdcaccabadacabaaabcaabdabacdacabacdddbcbabbabacbcddcacacbcbadcbaabaabbabbbbddbbcaabccdbccdddbcbcacaacbdacdbadccbcbacdcdbdadaaaabbcbcbbdadbdcbbcbdabcbdbdabcacdbdddccdacdcbacddcbaadabadadbbbabadcbdcbbbdabacdcbcdcaaadcbdabdbbbdddcbabbaabbcbdabdcabacddcbacddaddcccacbbccbcccdadadbaabcacdaddbdcbddaccdbddccababacddccbcbdbcdbcbaacadbacdccacbbdccbddbdddccdddacbabddbacbdbacccdcdaaababaddccabdabcadacdbcacccbcacddbcbdaaabcdcacacbbbbadadbbbcbbbbcabaddacbadadcbbadcabbadbdcacbabcabacdaadbdcbaacbbcdabbaccbadacccbdcbcddaddbcabdacdbbbddaacbaaaabcadcdcacdcdddcdbadaabcbbdbbcbdacdbbdbaccbbaccabbacbadbaccccabbacddadbacabdaddbcccabaacdbcaccaaaddbcdbacbaaccdaababcacbabacdddbddababbdadbdbdbdaadcabdaacbbdbdbcabcadccdddbddddadabbdcdcbddccaaaaccabacaabdbcbdbabdabcabbcabdcadcdaddaadaadcdcdcabddadbbcbacabbadabdbbcbdbabdbdabcadadbdcbcbdbacbbdaadcababbabbbbbaacbbabbdddcadddddcadbbadcbddddaadddbbbbaabddddcaabdddaddcaaabbadaaaccdadadaddcbcdddbdbdcdccdcddacdcaccbcdabbdbbcacababbcbaadccbcdbadaaaadbadcaacbaadadaadbdabdabdabdacdcdcbcacbcadaadbbdddbdbdddcbcbaddccccababccdadbbbdbbbdacbbcacabddcaaccccdbcccabbdccccaadcbdcdaaaaadaaababcdddcccdaabdcbcbaccbcbababaacddcabacddabadacbddcbddbbaccdbcbbcaadccacdddbdacbdccbcaaaaabcabccaacbcaabbbcdccbbcadadbbcadbbdaccdbbcdbaccadbbacdccadaccdaddbddcbbccaaccdadabaacbabcaadddbdbcbbbcacccccccadcdcccbbddabadccdcdaadbbbcabdadbccacdcdabadbadbdcdabdcbdcdabbaadbddccbaacabdbabbbbadbcacacdaccdaaaadadddbabbacabbbcdcbaabaacbaddbdcdccbadcbdddcdaccbbdaaccbbaabdbbddbbbddccbcbcadbabbdacbadbdddaadacdcbbabacbababcbddbbcabacbbabdbddadbdadbccbcccbaaddcdcddcbdcdbcbcacbcababcddadacdabdcccaaaccdbbcdcadacbbdcddcbbcddacccddabadcaacbabddadadcbcbbadbbbddddcdbdcdddcddbdddbcadddbcbacbaaadbbadaaaaaadbadbccdabdddaaadccdbcaabababcddcadacdbcaaaabdbdabbacddbaabdddddcdddcaaaabcdabbdbababbdbcacccdadcdaabcbbdbbdbdddbdcddbcccbdcbbccbabdddcdccddabdcddabcdcccadbddcdbabbdbbcbdabcaacacbdbddccbcdddcbcbcbcdaccddccaabdabaacadcbcbddcccbbcadcacbdbaacdabbdcbbdcbaddbcacabbaddbbacdaaacaddccdabdadadadddccadccbbdcdabccdaacdaccabcdccbaaadbcddbdbcccdbacbccdcbcabcabcddcdddacbaacabcadcccbddcbbcdcbbcbccaadcbbbabbddbababcaabdadabccccbacdbdcbabbcbdbccdddcdabbdaddbcddacdcbbadbaadacddaaddadadadabbbcdbacddbddaadbbbaacccccbbcabacabdabbacaacabacdbcdabadbcaddaaaaadbbdbdbbbccbaccadbcacdddabdbbcccabcdcdccdadbcacbabcbdacbdababcbdcbbcabaacccdaadccccbacddcdcdacaddcaabdbaccbbaddcadaddcbcdacddbbabaccadcaadcdcddbaaacabdcbbdacbdbddacbcbcbddbccababbdacbbcbcbdbcacaabadddbbcdddcddaadbdbdaaababdacacddccbdbbdaddddadbdcbccabdacadaddcacddcbccddbacabadccbbdccbbcacdbabddccdcbacadddddabbcbdbabbbbadbaabcaaacbbddbadbbccccdadcaabcbbbcccbdbdaddcdbabddaaccbabadbaccdabaddbbbddbddabbbdcbcbdbdbadabdbccaccacbabddbabbbaadbddcbbbacdccadcadabdcbbcacbbadadacaaccbbdbcadcccbaaadccdddcbdaaaadaaaabbbdcbadbacbaddacacdcacdddcbbcbabdcacdaaacdbbaacbbccabdbadaddabdcdadaddcdbbbdbccabadadccdcdbcaaddccddaccccaacbcccbbababcddabbadabdbcaddbbbacddaabbccdbcdbbdcddbabdcacdbbbabddabbbabbbbdbcccdccbadbaaaabcaccdbcdacbdbcdbbbabbbccaaddbadcadcdcdcddaadbbdaadccacccbdbdbccddaacbbddaaadddabcaabdacdadbbdacdcabbccbcbcbcddaaaccddbbccdaccbdabdbbbbbaaacadaadbabdbcababbdcdcbcabdddcbcdddbcbdcbcccdacbcdbbaabdbdcacaabcdbcdbcbdbbddabadabcaccddbabddcabccaabddbbbbccaabdaacdbcdbccddcccdcccbacbdcccbbdbcbbdbcdbcdcabbdbcddcaaddddcabcadbacdcbcaabbbcaaddbcaacadccbabdababacccaadbcdcdccdabbcaccdccdbbbbabbbcbbabddcdcbaccdbdcdbcdbdddbcbbadbbaccdcabbddcdddccbacdaddaddccccddddbbbadaacbbddccadcbaaabcdbcaabdccccbabccaaaacbdcabbaadcbadbaacdbbbccdcbabacaddbabbdaacacaddcbccbadaabcbdbcadbadaacababadaaabadbbbcdbaabcdaccddddddabbcdcaabcdbbcbdcdaabbdbcdabdbbdddcacdbbdcabcbdadabaddbabdcaadcacbccacbccdbbaccaaddacbadadaacdcdbdcabcaaaaabadaabcbccabdbbacadbbdbddaaabbbbdccabccdadddaabaacaadddbbcbcacbcdcbdbddabddaaccadccdccbdadacbdadbcbcdccdabaabaaacbabcdabccaaadbaddaadccabbcdddbdbbbadaaccdcbdacbcdcbdbccbbaaacdcaabacdcddaccdcbacacacbabbaabacbbcbbadddaadccddccdbcddbccdbaabcbdcddcbdbdcccacdacacbccbdccccbdcccbaacdbccbcdcdddbbbaaddccdbadbddbabbacccdccbcbdbddaccddcbddabacacdadcbdbdaabcddbbdcddcdacbcccabbbdcddddbbbbcabdddbccdccacddccdcccddadaabdabcbccdbdccbcbcbaaddbaadabcbadcdacabcaabbabbbbbacdbbadaaaccaccadcdaacbbdaddbaacbadabccbadaccbbdbabcaaabdbcddddbabccabcdccbdacbcdbaaabccdcadaacdaaabcdddbadbabacaccaddacddaddbcbcabbcbabadabdbacacaadbddbccabacdaaadbacadddddadabccdabaaaccabcccddbcdadaacddccddcabdcccadadcaabcaddcbbcdccacdadcaddbacacacdaaddbcccaaabddccadaccdcaccdaaddcdbabdcbccacacbcabdadabcbbbadaadcbcdbbbbcdcbcbbbbdabacdcdacbdcacdadacacdcbcacaccaaababaddaadabacadddaacacbddaabdddbadcbaabacbcdbdcbcbabbdbcdddbdabdbdadcadcaacbbdcbbccaddbdabbadbccabaabaddcbdbcdcdbbdadccadadcdccdaddcbdccacadcaaabababdbccbaadbacbcbdcabccacdacadbbcabaadddccbcccbdbbabacadbccdabdadacdacbaccacdaabdadaddbbbaaabcccacccaaaddcccddacdbbcddbbbbadaabadcaacacdcbdcaddaaccabaddababbcdddabdabbbbbadbccbbbcbcbabcccbadbddbbcaddddccadcdbdbbdaccadbccdbbbaabccbcdcdcacbbdbddcdbbbccddcbddababcbadccdabdcbadbdbcadddcdcdbaadbbacabddccabdbddcaabccbaaccaabaacdccdadbbbcccbccbabbcacabdbbbbdbadcbadbcdcbacddcbdaaadcadacacccbdcacdcaacbdacdaacdcaabbcbdbdcdcbddcaabaacdbddbaacddaaabcdbbaadccbaacddabcdcbccdcccabcbcacbdbaacbabadccdcdddcaabbddccdddcdddcbaadbbadcdbcdbcbaccdadabbaadaabdbacdbcbababacdcbbaaaabdbaabdddbdbcbaacacbccdddccdddcbdddaacdcbcddbccadcdcdccddcabcdbcbdbababccbaadcdabbbbadbcddccacdddcbcdcaddbacdcdadcadbbcbdcadcbbcccacdaccaddbbadddacbccdcbbdbcaccbccccbbdbbddcdcacbdcbbbcdcdcaacbacbccabaadaddcbdcaccaaadaadcdcaddbdbddbadcdaddccddddbabcbaaccddddcccbdddacddacdadcdcabdbddbababacaabccbcaaabbaddcbbcaccbaadcccbbadccaaadabaacbccbaaaccdacbcbcddcdaddccdbadccaddbdbaacaabadadbcabbdbadbddaddbddbbcacabaadcccabbbdcbdcdbdbaadccbdadccdddaddaacdcabdabbdacbccaababdbbcccdabaabbcdbcdaacccdddaddcddbabbadabcabdacadddcddbdcadcdddddaacbacbdbcbbaccadddcdcaacbddaacbcdaacadcdcacacdadabdaacaaaaadacdccadbdcdbbcabcdbbacbaaaddabcacdacabdaaccaaacdbdabbddcbdcbbadcbdacbacddabaaddabcdcadbbdadcccdccbbcdbadadaddabadbacbabddaadabcbddcabbdabccaaccdaaadaaaacdacbabbdbaaabaaacdcdcddcdcbbbdcdcddaddaaaaacbbacdddbacaccabdbcbbcbbbdacdbcddcadaadbdccabbaabaabddababcbbcdbddacbcbcdacbbadddbdcaaddcbdcbdbcbcbddcdccdaacddccadcaacdaaddabdcbbccadcbcddddcaabcaccdbaacaccabbdabbddcabaabdcbdbcccdddbdcdbdcabbaddacbcddccabdabbcacbdcdabbddddcacdabcaaadbaaacadacabddbcdacbbbbbcdadabaddbacccaddccddbbcabbdcbbabbadaccbcbabcacbbbdbaddbbcacbccdddcdabcbccddadcdddaaadaaadadbcbbdbbccaadbbdbacdddddacabdacaccdabadabccddabaaacabbccdbcccbabdbcbabacccaaaabbdabadbdbdbdaaccccdbdccdcadbbbddabddcbbadadadabadccbaabacaccaaabdcddaabbcabbbabdadbdadaaacaaddcbabcbddacabbccaadbbababbdaabcdadbbccabbaadcdadcdcdaacacacdbbdbcbaacddddbbbaaabbdbbabcbdbaadaababddcbcaadaacdbabbabcdcccadbaabcddaddaaacbaccabbdddcaaaaccaabcdddcbacdaadbbdbbaaaaacadbbababbdbadbaccddbabbabcdabacaacaababadcadababdaccdbddbdbdadddccdaabdaccaadcaaacddddcdcdacaccddbdccbbaacdadadbbbcdcdcbabaddaabcbccdadbcbcbdddddadcddbadcbbbdbbcdccbddbdccdcadadbabbddabdcccbacacadcbbcbbcbcccccbbdaddbbbdbadcbcdccccacbaccbcabdaadaddcddccdcdcbcacbaddbdabccdababcdbaddaccbdbcdaacdaabbcaadbaccdddaabcdcdddbabacddadcdaaaddbbbcbbadaaadadcddabdcbddbdcdcddbbdcccdcabbabcbcdcbacbddaacabcdcbcacbaacbacbacdcaaadccbddaacbbadaaacccdddcdadcddcdbbaccdaccdcccdcbbcbcdbabbdbbdcabdbddbdccadaddbbabdccbadbaacdbadadcadadadcddbdbaddaacdaaddbbadaaabcbbbaacabcadadaaaabbcdaddcdbbabbbdddaddcbcdccdbbaadadbcbdccdcdccbdaabcbcadababaddddacacacdacdbbbaadbdbaddbcacdaabddadcacbadcdbccbbbacabcdcbcacccccbadbbcacddbcccbddccdddabcdbdadbaacddbbcabbcabbbabbccdabcabaccacdaacccddbbbaaddbcadccddddbdacbacdcadddcdbdddaccbbddcbbdcdbdbdaacadcacccacdcccaccccacbddbdaadccabcdddbdbdcdaabaadcacacdcdddddcbcabacaaaacaacdbdaadcdbadbacadddcbacbccacbcbabdbddaadacabbaaaabcbbadccacbddcbcbcbbcbcbbdbacabddcaadcccddaacdcccaabadbbcbcbbbddbcaacbbdaadbdbdccabdddbdacaadbcbbccbdaabbdcdaabaabdcbcaadcbbbdabdcccabbadaaaabbdbbbaaaccaaddcddbcbaaddbdddcddccdbbbabbcbdbcdcadabcacccbcbacbaddacaddbddaccddacbbbdccbadcddbdcababbcdacbacbbcdcdcbacabdaacacbadcabcddcbcbcbabccdcdbacdbabacadababcdbcdaabbbcadcaddcaccaadbdaaaadabaabdddacbbaddbbaabcbcbcbcdabcaadccdccddcaddcdaacbbcbdcdcbbbddcaccdbcdddabcaabbdabbdcadacabccbccacabdbacababcccaacaabbbbddddcbccdcdacadddbdbdcdcaaadbddbdbbdabbdbdccacdabbbabbdddccbadabcaaacabccddcddddcdacbaaaccbbcdbcccadbabcaaaaddcddbaacbabcdaadcaaddbdacbbbaddccbcbbdbdbddbcbddddacdddabbccaaaacdcbccdbdbcdadcabbcbdccacbbaddadddacbbcbadacdccacbddabbacaddcddcbaccccdccacdbdccdabdccdbbaaabcbabcadadcbcdbddaaaacbcadbbbcdabbcaccabacdbacddabcdbaccbccdaddcaaaccbdbabaabaccdbbbdacabdcbcccdacacdbbabdcabdbcadabaabdbdbcbabcaccbdddbabbbbbdbaacccdccbdcabacbccbbcdcaabbcbbdabdadbbadbcbdcdccdcabbbaccaddaaddbddaabdbbabcaddbcdcddcaabccbddcabcaaabbbcaddabacbbabdcacddadbcabaccddacdcabcdcbaccbbdbcdcddbacdbbaaaabaabdaaadbcbdbdcaaccbaddcdbcadadcacbaacbbbccdccccaddccaaddaadbccaccadbdaaadbbdacaaddbbcbaacabdbaabbbbdcacadadcaababdaadabadcdcbcbcccaabcdacabddacdaadacbbaacacabdadaccbaaaaddaaabcbdaadbdbdcccacbcacbdacaaabbbadabacbaaadcdbcbacbaddbbabcddacaabcdbdaadadacbcbdabbaccbaadadbddcccbdbdbbccabcdcacbadcadccbcacadbaabaaaccbddbcacaddabaccbbbadccdccdccdbcdbcbbbadcbccbcaccdbcbaadadaddaddbdbdbaddcbacbbabbcdcdbcddbccdabccbaddbaacaccadaccaabaaabadbdbbddbabcadbaddcbcaaacbbbbdcacdccccbcccbcacdaccbbaccaabcacdccbaccabdbcdbbdabcadadcbccdbbabadbcdcbbaaaaddbcacaacaabcdaaacaaccdbdcaabacbdcbbdaaabadaacbdaaddababbdcddacacccaadaaabdaaaddcdbbaaacdbdacbababdadbbaabaaabcadaabcaabcbbadabbbadddbdcdacbbcddabbaaaaddaddbdccbacbadccbcbdbbbcddacbdddbbbdbbbdbbadadbdaaddcbacacccbadbdadbcbbdaacaccacaaddaacadaadbaabcdbcbbdbabbcbabbbabbbacddcddcdbabdccdbaaaaccacaacdaadbbdccabccbbabcdcabcabacaddcdaaaabacdcaadcacdbcaccccbabddcadccbcdcacacabdbaaaabcbbbbcdcaaccbcdadcbadbbbacadabcdbbbaddaabbccccddacdabdbbadcbabbaababcdaddccadddabcdcbdcbbabcccdbdcbdbdacabbbdbcaacbbaacbbbdcdacddacabbbacdacddbcdcccdcaddbdcbcabaddaacbbdcccbcbacbacacbacbadaabaadddcaacccdcdcaddaaadbacbadcbdcbccddbbcddbccdaadbdbbcdadddabadccbbaadacdddbdcddcbadbccbccaadadbaccbabcbbbdbcacddccabbbdbadddcddcdaaacadbaaccccbcacbcdacacdbaccbaabadbbabddbdcbadbcbdacbabdabccacdbcbcddccacccadaabbacabdbddaaccbaacaabbcdccdcabbdcabadbcaadbcccbcbccabdbcbcbddaccabddaccdcbbbbaadccbdccdaadbccbbccdcdaaaadcbdddbbcbacdbaacccaacdbadcbdaaddccabcabadbdaddbaabdbacbcdbdcabcacadcbbbbcbbbcbdddddcacbbaaddcbbadcacadcbccabdbacbbbdcaaabdbabdbdaabdabdcdcdcccacdbdaabdacccdbaadbdbdbdbcaabbadcaccadccbdccbaaabbbabccdacdbbbbacccddadaddbdabddcdabcacbbbababcbbccabcacbabbdabbbcabbadccddbdddddddbcbccddbcbbaccdbcbcbabbdbbabbcbddddaddccababbddbcacbdbbaddacdcaadcaaddbddabbccdbadbcbbadbadbababbcadbdcbdbcdabacddddccbcabbcbcababdbacbabbdabcbcddadbdadcddddabbabdbabcacdbdcdacddbccdacdcbbdabdaaddadadbddcbbccbdcacbcccaccbddbacacccaababddabddbabcbbbbbbddbaccbcadccbdcaccccaabdbccdddcbdccdadcdbcdadccaacbdddccccbdbadadbddacdbacccacbccadaabacaadbccadabcdacbddaaadabaccacaadbbcacacdcdacccbbdbdbdcdabbabdcbbaadadaccbcbaabaaccaaaabdbbdababcbacdacbdcbdaaaaacaacdccbcabbdbdabbcadadcbdadbdbadccdcbabcdbacbddbabadacdbbbcdbbcaaaddbccabcabaaacbdddcaaccccbacbaccbabdcdddbccbbadbaadbaacbcadcaddbdcaaacbbaadcbccabababaddcbdbcdbccaadacdbadcadcdddccbdbcccdccaaaddacdbcdaadcabdaababaacabcbccaddccabbccbdadbddcabdaccadcdcbaabcbabaccabbcaaadcdaaadbacbbacbdcabcdcbcdbcbbdcbcdbdcbcddbbdccbdbacbcbabdbddbbccdacdaaabbcdbdbccadabbbbcaabbccadacaaababacacddaccaccddcbbabcbdbcccadabdddadadccabaadbcddddadcbbbdcaddccaddcdcdacbaccdcbbddcdcaadcadbbaaddbbbdbbcdddbbadaddaaabcdbcaacaabaccbcbadcbdbaddabcbdcacabbddadbbbadbbdacbdbccbcbadabbbdbaaaaccbbcbdcdbbabdaabcdbdaaddadccacddadcbabcacadacadbcccdbabcbababdabbaadadccddadcccdddcdbaadbdbbacaabdccbadddaadccddadccacbcbcabbbbbacbdbcaacddbcdccadbdbccbccdcdbcdddbdcddbcaddccbbadabcbabccabccbbddcababcadabcbdcbabdcbababccababddddbdcbbaacbbababcaccaacbcdcccdcbdbdbccdadcdbdcdabacabdabbcdadadccbbdadcdbddbcadbdadddcddbbaababaddddacbbdddbbcabaabddddbdccbddbbabacddbbacdcadacbccdccaabaabbcbddaaddbcdbddabcbcccdacbdccaabcadbcddabcaaccabcdaaaacccbcdaddaadcaaaaccdddaadcdbdaadbcaaacacbdabbbcbaaddcdddcddcbbbdaadabddbdcbbcdaaddbddcbadccbdacadacbdacadadaddabdaaadcbcbbadabbcdcccbcabbdbdcadabbddbabbbcdcdbaabdcddaadcddcaaacababbbdabcbcdccdabcccdabcbcacabdabcbadcabccdbbdaddacbadbcaadbbcdabbcdcabcadcadcaaddbdababadaacbcbcbdaabbbcbbccdcdccacbaaaaaabbaaccdddddddbacdbcccaaabadabbaaacabdcaadcbabcabbcbcaabdbadcccacdcbadabdcdbbddaabdcacddadccbaacccccdaddcaccbbbcdbcacbadcaadadcdddaacdbcddabacccbcaaabbabaacddbdcdcdccacbabdcbaddacaaccaccaccdccccccdaddbdacdbbbdbdcdbabdcdadadddcbdbcdaacabbbabdbddcdadcdaabcddadaaadbcbcbdcabdabaddacbbaccbcaaaccddadbabaadbadcdbdadccaccacbdacbaacbdaccdccbbabacaacbcaadaabdcddbdcdbcbbbaadcddaaddbabcabdcdaaacabdabcdbacbcadbbbdcdaddabdbaacdaabcdaccbddbbacbdadcdbbadbcabcbdcdadababdccbabbbdbdacbbaabaaccccaddaddaadcbcbacaaddbabbabdbdddacadadcaabcdabadcdabacbabdabaddcaaccdccbdcbdcacdbaaaccddacdcbcaddcadcbdcadacdcddaacabdadbaaccacacddabcbbcaacccbdcbbacdacbdabadbacdaaddcbcadbbbbbbcdacbdccbbaabccacdbadaadaccbdbaaabdbbdbadddabdcbbbcdadccbadcdaaabadbcbadddcddbcbbdcccabcbdbdbdcdcaadbcdbcaaaacddcbbacaccdcbcacddbdcdbbaabcccbbbbacbdadddcbaaacddadbdacdccbddaadcccccdcdadbadcacabadababbaaadbccaccdcbdccadadbcccbbdcaaccbdcdbdddabaacdcbddadbcacddcabccccadacddbddcbccabdccdcbbbddbaccdbccdbcbbacbadbcabcaddadcdabcdcdadbaddcbaadbbbbadddddabcbcdabaccdbabdbdbacdccbabcbccdaccdaddbcdadccccbbccabccdacbddabbccababdcaaaacbcdbccaacaacccdadccddbdadddabbccadcacbacdaabaabadabadaacdcdadbbcdadadcdbcdcacbbaddccaddbdcbacddbbacbdcabbaaaaacbbaaacbcddcababadabcaaabcbddcbdadbcdcdcaaabccdcbaacabdacddbdbbccdaddbadcabaadaacbdbbabbaadbaccdababbadadccaddcdaacabaadbbcdcccdbabcbcbadbabbdcabcccadcacdbaaabbcacdabccabbcababbcaccaabcdccadbcbdccacdaabcbbcababdacbdcadabccdadabdccdabcdcbdbdbbbddbcaaaaacadccdabdbddabccadaccadcccdabadbaacabbdcdabacbaaabaadcccabacdcbdbdbcaaacbcdcdadcadbdacadababcbcbccbdddacbcadbdadabdddbcadcbaaadaddbcaaadccaaccbbbcbddaadbdddaddabaadadbdbabbdbdaaaaababaabbabccdcdabbcbbdcabbcdcbabbcddbabcabbadadcbacadccabaccbdccdbbbabbdbbbddaacdabcbacaaaadacdbaccbaabccdccaacaaabadbababbabbbdaadbcdaadaaccbcacaabbdacadcbccdaadadbcddbccaddadbdbddddabdaddadaabbbcacbacaaacbcbbccbbdcbdcddabbcabcdccdaaacdbddaadcdcddbcccbadaacbabdccadadcbaccbddacbbbbaccdbdabadbaddddbbbacabcddbaccdaadaddbddbacbaadabcadbccdcdaaddadccbbbababbadadcadbbbcbaaddaabbdcccabbabcdccdbcabacddcaababcabdcabcbddabaccccdacaadcadabdcbbabbbdcdabbcdbccdddcdbbabacbbddaaabcdbddadcdcdabcdbbabbacbaaaabadabbacbbbbcdacddadccdbddcacbbaaacbaaabddbddbcacdabcdcdbabcbbcdcaaacbcdaadbabbccacddcabcabddddadbaadbabcbdaadcaaacadbabaaddacddaabddcdbddcbdbddbaaccbdcbcbbccbbcdaaabcacabbbcdccdbadacadaadadbddacddaabcbbababddbdaaacdddbacbdbbbccdbbbdaadadaacaddbdcbadbdbcbcbdcbcdbadbadcababdaacbcbdcbdbbcabccbadacadbacddaddbcccbbbbacbcbcbcaaabadcabddcbddabcdaadadadbdaddadacddcbbacadccbdbacadcdddcbabcdbbbbaadcccbdcacbccdcadcabacbcddbdbabbcadbcbbccdbbacbabadbaddddacababcabcccddabdbddbbddbdbbaaaccaaabcccabccadacbccbadbdacccbdaddcbcaabdbdbdaacbddaccdcbdccaddbcaabdcccbadbcdcacaddbcbdbdabbcbdcccdcbabdabbcdbcccbbbcabbbbcacdccbadbbbbbdbacbcdaccbdabdaabacacbaacaadabdccddaabbccbddacbbacacdbddbcadddacdbcaccadbdabddaadcdadddcdadacdccabaabcbbadbdbabcdbcdbbdbcbadbbddaccdbcacabacddbcddcbbdbadcaddadaadcabdcbdadabadaddaacbdcbcaaddccabcdcbbbdacbdbbbdccababcbdddbabcbbbdacadbdaccdbbbcbcacdacacaccbdcbdbdbbcdbabbdccdcccdbbdcaccccbdadcbcbdcabbdddcbabcbacaaadbdcbbbacacaacaccbdbaddacbcbbddabbccddcddcbabbacacaadaccbddbacbbabdbcdddddcbdcddcccccabccbcdaaacbbbabdacbaccbdbccaddaaacabbbdaabbacbdbcbbcdcbabcbcbcacdbcabbadaddcabddbbabadcdabbbbcadaadbaaaddcacddbbcdddacdddadacdddcbbbcaabcbadadaadcccdccadbcbbcccdaaabacaabcdaaadcdabcccbacbbdaabdbccdbbabddbdbbbdabaccdbbbadcbdadbddbbbcdbbbacdacddcaaddbddbbddcbdbbddcabdcbdbdbbadbcdbaadddcdbcaabdaadccbbaaaccdbdacacccdddabbbdddacddbacbbbbabdcbaaadaaaabdddbcbdbdaacabcdaaaaddcabadaddcbacabbcccdadbbdbdbbbbacddddccdbaabcbccaaddddbaaccbcacaadcaabccabaacdadacdadddcbccddadbaccacaaaaaadbacdcdabccadacaddbbbadaadaddcaabadabbddabdcadccbdcacdcbcacacdabcabbbdabbcaabbbacbdbbbddaacbdacbcbbbbadcacadccccdddccbbbcaddddcddddbbdbbccdadbcbacdcdcabdcaddbdbbbbcbabcbbbcacdacdabdbccaabcdabaabbadddbacbbdbcacccacacdabcabcddabbdbcabacdaacccbbdcaacccdcbaccbcdccbbcabcddddbbaddccdcbdbbcaaddabcdaacbcaaaabdbddbaddbbdaddbcdadbbadcabdddabacadacddbccbcaccbcdccbbccacccdbcaacabdbbdcbdcdddabaaaccabacddcaaabcdcdadabdbaaabadcaadbabadababdcbbabdbcdaacabaccbddacbcbcadabcddcbbbdddaaaabbdcbcccdbcdcdcbcdabcdbadbdaddbcbdbdbaacaabadcdbaccadcccabbaadcadaacdbdbddbcabaabbdcaadbadcbaaddddcdbadcabddddbccaabbdbdcdddbabdccbccdadaccabbbadbabbdabbcabbcacdacbaccdbddaaaccdbacbdabbabbacaaaddaaddcdbacbcccdbcadcaabdbbccccaabdbacaccdaaddccabaddbcdcaaabdcaacbbabaacdcabbcacbbacadcbbdacdcabacdbccddcdbdaccbbddcababddbaadbdbdadbadbcdbdbcabababccaaadcabcbcdaadaccbcdacddacadbbbcabccaacadadbbddcbddbcbaaadcacabbabcaabbcdcbdacccababdbbddabacbbcaccbadddbbdddbdaaaccbcacbdcbaddcbacdadaabadbdcbbddbacdcdbcbbdbcbbaabccdbbaadddcdbadadaddaddcdbbbacddbbbbdcccdccddbbacccdcbcddacadcacababccbbcaddaadbcbcaadcdaadccdbaacccabbababccaababacccaabbbdbddbcaabcbbadddbcabcddaacdbbaaabaabbcdabdaccbababcdbbacbbbcbcdbcacccbccdbacacccddaaacdbdcbdcbbdccddabccdcdaabdbddccbbdccbbbdcabcdbddacacbccddccbccbddbaaccddccaabaddadbcdbcdbbcbcbbacdabdcbbcddabcbccccbdbcadcccadbdcdddabaddadbacdbdcadddabcbaadadaaccbbccbadaccbdcdcacdcdabbabbdabadaaadabbbdddcdddccbddccadadaaabacbcaabbcbcaaaaadbdacbabdaddbabcaaadcaacdadadcabccddadabbabcdbcdbacdddaacaacdcaaabadcdbcbbcaacbaccadbabdccbbbccccadbcabcdacbbcadddccdaaadddccdbbabaabdbbbbcddddabdacdcbbdbbdbbaaccadaaddcaccbdacacabcbcdccccaadccbdcdddaddcaaacddbcbbabdabadbcbdcbdddcdadccabadbcaaccacabddbdaabcaadcbbccdbbaabaaabbacbcabdcdaabdbcbdbcdaacdcabaccabccdbcdddbccccabbcdadacbbbadcddaabcccddcbcbbdcaaddccaacababcacbdcdcddcbdaaccdadbaabddddaaddabbdbabdcbcaccbbbaadbdccbdcbdcccadcdbaddccabdddbcbbdadadcddbaddacaadbaaaddcbcbcaccabcdadcccbbdcdccbcababcaddababcacabcbccbbabcbbadaaccdadcbdccbdabbccaabdcbadcdddcbbddcdddcabbcbacbccbaacddbdddcbbdcbdcbcdadbbadabacbaadcbcbcddbddcacbccbcdbadaabddaacdacddbcdaacddbabaadccdcdaacabaaccbdcccdbbccaabdabaddbaaaabdbcccbdacddabcbaabdddacdbbcdbcdaaabacbaaddbcbddbbaaadaadbbccccdabaccbbbcdbbbaacaacabcaaddbabdacbbccbcaaabacdabbdcdaabaccdaabbcabbddaaddbbdccddccccdccdaddbddabaacbbbadcadaacacddbcbadcccbdaddbabdcbdabbabbdbdaabcdbdabaabdbaadadacacddbcbbabdaccacababbccddbabadaadbdcbdaddcbdaccdbcadcadbaddadcbbbabdcaadaadadaaaccbcbbdcdcbcbacbbcbaacbdaccbabdcadbaabddbdabbadbcbbcacadaadbccbbbddccaadadbdaccaabababcbbbaddbdbadbbbdcaccdbcacbaccdcbbbabbbbdbbaabbbcacddddababbcccbddbbbcadccccaacaddbbcdcdacddbbccbcbaccdaaccabcabbabbdcabcbdaadabadbbcabddbbdaaaaabdcdddddcddacabbcdabbbadbcbdaaddcbadbbdaabdbabdccdacdbabddbddbdccdacbabdacddcbadddadabcbdbcaabbbacaccddadbbddbdabcbabbabacbbcacabacbbcabcdaccdabccaccdabcbddbcdbdaaccdbadbcbcacbcbdcadcdacdaddabcdddcdcddcdcddcdabaabcbbbdbbbabdcbcdcccbcaddbbdbccacbadabdbbadcadadbdcccbdcbbdddbdccacbacccdcbcdacaaadbdbaccaabbacbbacabcccdddaddcccadbbaaaddcddccddddcdbdabbbcabdadcadbdbbbdcbabdaacaacdcbaacaccdbadadacbcdaaaddbabaadbbaaaddcbbacbdbcbcbccbabbdbabccadbbbbcccadbcabacabaacdccbbcdcbcaadadbaaaacaddbbdbacdacdcccbabaadcadcbcccbdbcadbcabccddddbdcbdabababdababddcaaaaabbbdadcdddadacccaddddbadbddbbbdabcbbcbcaabdccbbdaddaabdacabbdcaabcbcdcaddccdaadddabdabdbbaadaacdcadcccdaaaccdacdcadacbdccdbbcbcacbacbbbaaaaddcccdacddcccdbccdadddadbacdbdaabbaacaaadcddddaaaddacdbaadacdbccadbbadbadccbdcadacbcccadacabbdbbdcbbaabbdbbbbcddbbcdbdddabbadacbdcacdbbbcadbaaccbadbcdcbabcaacbabcaabdccdbadbdaacccbdcbcbcbaabbbcbbbabaccaaaadddbdbacdcddaccabcdbaaddaaadcdddcdbbcbcacbdbbcbabaacbdcadcbcdcddcbbdccbcaaacaadbbbcddacbccabacbbaddaabcbaaddcbdaadcccdadbccdbbccccaaaadaccbccaddbbdbadcdddbbbadabbbdacdddadacabdabddcbcaaacdbadadcdccabcbbdbdbcbdabaadaadadbcbbbcabadccbdbacadaccdbbcdbaaaadbbbbbbbbbaddbccccdbaccadacccbcdacbaadcaadadaadbcbccdadddcaadadbcadbacabcddccbcccbdbcbaccdcdbaabbbcadabababadbcbcdbddaacbcccddccbcacacbabaddbbdaddcccbdcdaaacbaacbdadbdaaacaabbccbdbdbcddcaacacccbcadaabaddbadaaaabadadadbcabbadcdcbccacdcadaabbbdadacbcdbcbdcaddacaacddadcaccddbccdbbccbaaaddbdcbdcbaaccaccdabcabccccbacbdcdcbaacabcbcabddddbcdddacbddbddadcbbdcaacccadcbcaabaadddbcbcacbdbcbdbbacadcbbaaabaadadbadbdcabdadcabdccabdcaadacdbbccadbbdadcabaacacdaaacbdaabbaaabddbddbdaabbabdcdacdcbcaabccbbcadbaadacadbcadccdddbcaabbbcbadbacbcbcbbdadadaaababbaacdcadadcccbcccaccbdacddbdadccdcacbadaadbbbddcabcdadbaabbdacbbbbcdcbcdbadddbadaadbdadacacaaabcdbcaabcaadbdccabbdbbcdbccbdaaddbdadbacacbaadbabbcadacbacbdcbcbbcdbbbbaadaadbccbddccaddcbaccccadbcbddadbacbbacdcabdcdcbccacaacabbabbdbcaccdcdaacdcdbbcdabbdadbabbbbdddbbabcadccabcbbcdbbbdbddbaccaabbbbddccacdcbdabddaaccadbdcbdcadcabcdccbcbbdacdccacbdcacbcbccbaaaaddbacbdbabbbcdaabadbabddcbdccbddbabdbcababbcbcbbdcbcddadbcadbdccaabbdabbbcbbbdcadccccdcdcbbdbbdcdbadddddadcaaadccdcacaacababdbabddadcaddcbbadbdaadbbbccabddbbdccabcabbccbcbbbaadabccbbbddddaaaacabcdbcbbcbddccacdbaacdbbbbcdabaddcdbdbaadacdcdddcbadcbcccbdacabbdabbccbadbbccbbbbcadacaddccdccbdbabccaccacadccbcccdcccdabbadbabbbabcabacddabbbbccdcadacccadcbbcbbcbaaccabdacdcaaaaccadadbccabaccdcacaacaacddbcbaacdcacabdbbbadccddcbcaddddacaaccbadbdabcdabadbabbacababcbabbadbcdabccdacdabaadadcbcccadadcdcdcadaccbadadabbacabddcdaccaacabcdbbdcdcaccacbbaccadbccccbcdaddbbacdbaccadaccaccaabcaddcaabdabcdddbabcbbadcdcabacbaacdabbdbbddcccdcbccbadaacdaaabbdbadcdbdcbaddbaaacbdbacccacabcabcacdaaadcccbacdcabcaababacbdaadbcbaaddadccacbdbcbcbaaddddddbaacadbaddaaccaccbadccabcbdbcacabdcdabadcaabacabcdcaababbadbbcbbcadcdbdbcddacbacadcabbaacdacadddadaabacbdbdaddbaabcbdbbddacccaaacadddadbdcabccbabcacbdcccbcdbcbdbccbdabdcbdbbdcbcadbbaccbcadbbabddcaacacdcbbadbacadbccdbaaabddbcccabdbbdcbdacabbaaacaaaadcdabdbaddbcbdaabcccddcaacabbacdcbbcaabccddbbbabaabaddabbadadddacbdaaabdaacdcbbdbadacdaddcbdbacadaabdabbbbabbbdcacbddadcbdcbddaadacdcbacdbcdabccababcbcccdabdacabacbaabbcdabcacabdccdcdadccbadbcaacadbacccbbadabdaabaaacaadaacacbbabacdcddbccadcdccadadcbccbddacbacadddbdaabcdaacddaadddcbbaaadddddabcbcabaabdadcbabdbaaddbcbabdaadababdcddbacacdbdbdddbddadddbcbbddcdddbccdccdacdddbbcbcbaddcaabacbdcdabbbccdbaccbdadddaaabdcdaabdbddccbdcdacdbdcbbcbabbcdbcbabcabaaddaadbccadacacdddbaadcbabcddcbddbbbacddaacadcbdcabcacacbbdaaaaaddcabdbcdaabdcaddabbaccdaaddbddaaabdaddbbdbcdcbaacbabcbbbcdaacbbcdcbdccccccdcbacbabcbaacadcbccbcdccabcadbaddccccadadaaddcbcdcbbbcdbcbbcccaacdabddbcccdacddcdbcbcabdcbbbbddbbadbbdcddbbdabcbdccbdcacabbdcaddddbdbdcabbccabbcaccdbacdbdabcdccbcdcccaccabdbbbabcbbaaacabbcccddbbdabacbddcacbbcccdababacacbacabbadcbbdcabadabbdaabdccdabdddbadcabbcdcddbdaaacdbaddaacbddaaabcaababcdbdbdbdbcabadbcdadcdaabbabcacabacaaadbcdadabdbaaccddbcaaccbbccdadaadcacbabdacccaabbaadabbbbabdcccdadcbbacccccbccabddcbbcadccadabcacdbcdcbbbadababbacadbcaabbbbdbcabcbbdacdbbbdbbdbbacbbaccbacbbcaadddddacddbdbbaacbdadcbdabcccaabaadabbabddbdbcaababdaaaaacadadccbbddaddabdbabbbcbabaaccabbbadbacaaadaccbdbadcbbadbadbbdcccabbaacadddadbcbcdbaaadbddddcaccadcdcbcaddddbddddaabdaabbbadcccccbdbaaaacacabbdbdbbdbcddbcbbcabbaadbdbcabdbdaddddbddbaaadabbcadbcdaadabbaaacccdbcccdbbbbddbaabccbacdddccadbcccaadbccdbcdcaccbcabcacbdcdbcccdcdbbcccaabcaabcdbcddaccacacaacbcaacbcddacbbbbaddabacaadabcbbcbcdbcccaddcaabaabadacdacbbbcddcddbaabccbdabacadaaabdabcbccdcdbdcacbcabccdcdbcccadbcdbcacadbccdccccabdcddacddbddadcabbadbbbccadddcbaaaccdddaccdbdbacadababbbbccdabddbacaccaabbcabccdbddcbbddabcbcccddbdcbdddaaacaadbabcacdcadcdccddbbcaadbadadabcdabcaadbabaaddcddcbdbdcadcddabaaacdabbccbdbadaccabcacaaadacdbccabcaacbaddadadbccbbadcabdaaddbaaacdbccbcaabaabcddcdddcbdbccdcadddbaddbaadadcdcbddbdacbbabdcbdbcdbbcbabcdababcbabbddaaddbbcadbdbbddaadbaaadababcdccdbbaacacbbccdcdbbbdcbdacdcbabaacadbbdddbdcbbbadccdcbdcbdbdaccabbdadccbcbabcaaabccbcbdacaddacddbddbadcbdabcbabcdabbaabbdcbbbcbccdddadcbbadcdabbdaddbdbdbbdadbbabcdbcbbcacbbbbccbbbddcdcbdababdcdbacdcbaadcdbdcacbcabbbbdddaabcaabcaacaaaacacccbbcadccadcdcddbdcddbdcbabadacadacdadcbdcdcaaaacccaadbddaadadbbaaaabadbcddcacbdbbbacbccdbdbbdadbabdcacdbdbacaaddbbabadddbbdddabacabdbcbdbcbbccdadcadcdbacbcdcddcccbccdcbdadadabaaccddbdcabbbcadbaaadbcabacdaaacdaabbbccabadcaaacddcabcbaaccdaabdbbbddaadbaddbdbaadcdddbadccaddbaccadccdbaaccbdcdcadaaccdcadcdcdbcbcccbabdabadcabdbddabbdbabdacbddadbdbdabbbcdadbbbabcbbbdbcdbbabaaccbbbdbadcdbabbdbccccddcddbaacadbbccbdcdaabdbadcdabacccddddacdcadbdcccdcadbbaabaabbabcddbcbcddacddbbccbcbcbdabbcbbcddcdbcbcabdcbadaacbccacabbadbdcdcabcbbcaacaabbbcdaadbdadacbbcdbadbdcbdcaaadcdddcdcadcccacccadbbdcbbccbaadcbbcbdbcdcaabbbdcaccbcabccabadcbdaabcbdbcccddaabacbbbadaaddadaccbdabbabccdcabaadcbcdbdcbccacdbbddabdbdcbccdaabadbddccccbdbdbbddbcbaabcbddcacbbcbadddddcbdbdbcddbcbbabacdbdbdbddbbbadcbddcdddcabcdbbaaccabbbbcddbcbaccaacccaacaabdcbadabcaaabcbaccadbbdddadcdbabbcbaadadacddabcccaaccbbacaabcdbddaacdbdcaaddaacdbaabbcbcbcbbbcbcdbdcdaccabaacbaddaadaddadddcabddbacdbcdbaadcccbadabbdbdddacccdaadbabbddabcbdccbddcbdadcacbcbdcdabccaaccdccdbaadbdcaacbcbbcacbdcbabcdcdcccbbbaddbdddccdacdcbccddbbdcdaddaadbdcaccaaadbcbdcabcdcbbccbababdabbdbbcbdbddbacbaaadccaaccadcddcdabbcacdacccdadaabbcbbbcbddbbcbbdcbcccbcaacbccaacabcabbaccbdbccbaddbdbbacdccdcacaacaabacbccbabaadadcbcabbabdadcdcadacbbddccbbdbbbbdcbdadacdcaaddbcacddaaaaaddbcdbbbccaaadccddabdbbccdbbcdbaabdcdcadabccccdaaddbabccbbdabddcacabcabbdddaabacccaadbcaaccadbcccddaabcacbadddbbdadcbaaddcbdbadbbbbbbbbabbcaccbbdbadcbccaabaadddaacadddaaabdadcccbdacadcdacddabdcacbcadacbdadcdcaadbbacabbaddcbabbaadbadcccbcdacabaabcadcbbadaacccdbdbdbcaddcbbaddcbcaacbbcbaacdaddcabcdbdaaaccaccccdbdabaddaaaaaaabcdabbcadabacbcaaacbdddbdaadcdaccaddbcdaaadddbaadcabaadbbddcdcbdbaadcdadbdcaacabbdccdabcacadcdbdaabababdddccccbaaadcacaabcaadccdaacbbaacbcbdadadbaddcaacacacccaaadccbcdbccabcbcdacbddbbcccccaaccbcbbdcccbddadaadacddcaccabbaacaaabbcdcacaaccaacabaabcdadcabcbacbacbdbabcbbbbcadbcaaadaacdbdccddadcccddadcbaabbaddbcacbbdbdddbbdadbdddbbaaadddbcaaccdccaaaaccbbdcccdababbbdbddabdcddacacddacccbcbabcbdccabdacbbabbcbacbbcbdddccadcabbccddcdcaccddbcbdbdddcbcdcadabdcccabacbbbcbadacccbbbdcacbbaddbddbcddcabcdddcdacacadbaaaddccaaaddbcdabdcdbcadbbdcdaadaacbcdccbcbcdacbdbdacaccaababcbccaabdcbcdbacccbdabadcdabaabacddacbbaabddddddcbbaacbcdbdacdaaabbccadbaaaaaccdddadaadbbabbcccacbbddbbacacdcbbadabddbcaabdacddbabdbcabbbcbcbdcbccdcadcbdcabadcacdcabbacbcdbabaabbbcababbbcbcbcbaaccbbdadbaddddbcbadccbaaccccadddabbbdabcddabbdbcdcabaaabdbdbdcadbbdccabcdacddcbcdaadadcbcdbbadacccaacdaabbdbcbbdcccbcbabdaadacabbccdaaccdaabcdcbddbcddcabadacccbbccdddadbbcaacdbcbdaddadbdbbccdcccadababbacbadadcaacddbaadabcdddcacccdbcaacbbaabddbbcbacdbccadbabbcbadbadaacadcddbdcabbcdbbcaaadbbaadcdddbacacbbdadbdaccbbccdbddcbacbacacdcabbdddabcaabccdcdabbbdbddbacbbccacadadddbdaaccbbcdaccaaabbcdbbadaddddcbddbcbaddabccddbaccbbdaddaadcbbbabbaaaaaddcacdcabcdadbbdbbdbaddcabadcbddddbdbcadadbbacabbabdcbdaadbabbbbaddbcdbdccccdcdbccccdddcdabcbbbcacdcabccdadacbbddcacdddadcbcabcbcddbaacaaadadbdcdbcbbdcbbcbaabcbdccaabbbcbbbabcadbbdbcddddbdddccdbbccaccdacabcbddccaabbabcbacadaddaacaabbdccbccaacabddcadaccdcadbacdbdcddaddbcaccbaaababcdbbdbdcbdcbbccccbbadccacadadbccbdbbadcbdbbbdcccbdacaddddcdaacaadcbcbcbbdcababdaccdbaadaddcadacbcbdbaacdcaacbabcdbdcccddacaabcadddabadbcacbccabbaaabbcaaccabddccbdbbaadadaaddcdaabaddacaaacaacddaacbdaccbcdaacbddacacabaaadbdabbacacaaadabdaacdadacbbabaccbcdacccbbdccbcbdcdddbdadabbacaadacdaabadcdadddaadbcbbdadbaccabaacaaddbdadbabcccbbdcdccdbbbabdabdcddbddbcdacbbbbcabcdbacdabccacadccbcbcadbbabbadacdbcbbcadaadabcacbcabbbcdadacadbbddaaabdbcbddbddccdccaddaaddadaabdcdabccdbaacbbcdbadcaacbabaccadadcaacabaadcbbcababbbcabbdccdbbadaaccdabcbaaaccabbcacaaccaabacaabaacdbabccdddadcdccacbccadbdcbcbccaadccbaabacdbdabadcddbbdadabaaaacccbdccacddadabcccbabcabcbcaacdcddabcaadbbcadbaacddcbaccdabadbadbcdbbbbdddbbbabacccadbdcadcaccdcbadaadabdddbabdacdadccaddbbacbddacacdbaadddbcddddcbbcdbcbbcacadbcdacabdbdaaacdbccadddbcbdccccdbbcaaccababdbaadabadcdacbacadbdbddacccaddacdcabbabddcbdbbacdcbdabcabbaaccabbacdadaaacadabaaaaddaabdbcdaadbccbaadababcadaddcbaaccdcadcaabcbdbddaccbdbddcabbdbadabcbbabdaaaabacdadbdabbccaccbbadaabbcbaccbdbddbbaadaccbddcbcaacdaaddaccbdabdaaabaaaaaaccdbdbcadccbadadbdacbbcdbaabccacdddccaacbbdcdbacbbbabadbbaccdabbddcccbccccabadddbcdadbbccbcbbabbcaabcdbdbbdcbdbbbcdacbcdddaadaacdadcbadbccbbdacabbacccdbabcdccdacccacddbcccbbbadbacdcbcdabdaacdadaccdabbcbcddcaabdcddbacaccdcccbbabbdbababbdddbacccbccdabcddcaaabcaaccccdaacdaadcacbacaaaddbddacbcdccabcadcdbdddddadaabbbababbaacdabcdacbcdddbdaabdacbbbbbcbdbbaabdadccbcbbbbbababcdcbbbbbacddabbdbbacbccbdcdcbababdcdcccbcccacbcadcdaddbcaaacaccaaaadbdcdcaabddaccbadcabcaaadddcddddabbdbdcababaaaadbadbacbdacbcdaabbdbadcbcabddadcabddaabbdccbabcbacaddcdbdddcdcddcaddcbcabacbdccdbbdabbcddbcabbaabdbbbccddadbcaaabcbbbaccbccbdbbaccbbaacbdabddbbcaaaccdbbdbdcdbdabadcadcccbcabbccabccaaddcbabcaaccddcbdabbbcabbbcbbdbdccccabccadbcdaacadcdaacadcaccccdbcbccaacbcbdbcccabacaadbbcaacbacbcdbddbacabdacdcdcacadadbabdcdbdccdcaaacacaddcadbabaabacbbacccccdccbdbbbccaababadcdccdcbacbaccbcacddcdbdcbcddacbddabddcdbbacaccddbddbbbbaddaabbcdcccbcaaacbbdbdacccabdcbabcddbaabbbbbdddbcccadabbdbdabbcabadacdadaabbdcbbcccddddacdcdbdddabdbcbbdbaaddbdacabdaaccbaaadbcbbcdcdbcbddcaacaabdbccbaaabbbabcdcdaccbbababbbccaccdbcacaabaaacbabbbdbbbbcbcbcabaaddaccbbbcbccacbcdaaccbcbabdcdcaadddabdcbcddbcaddacbcadddccaacaccaaacbaddaccbbcabcbbabcbdadbdccbbccddccabacbdaacaadddcbbddbacacaabbddbbdcbbacdaccaabcdbbabcbdbccaddddbdbbbbadabcacbadadabcadcdaacaabbdbaccaaadadbbdcbbcdcadccdbcdbbbacaaadcadcbbabdbccadcadabdabbddbbadbcccdbccbdacdcdabadaadadcbcdacdbbaddcdcbbdabccadabcddbdcdddcdcdaabaccbbcbccadabcdbabbaaababbdabcaaaddbbbbbddabdabdbadbddabcdbdcaacbccdacaccbccbcaabdcbcadbaddcabaccdcccaaddacbacccdcccccccabbcbcabdcbaadabbdddbddbccbdcadacaaaaaaaaccdcdaddbbaddcbcbcdabdbaaaaabbdabbddbacbdadbccbdbaccdbbbbcdabdcbdccaacdddbdaddcaadcadbbcccbbaadacbdacbddbdabdccbdbbabdbcaaaddacaccccdadbacbdccbaaaaadacadbbbbbbaacadaacbacadbababddccabacdaadbaabcacaddbbcababdccdcbbcccddaddcbcabdabbcaddaabddaccbdbaabadaabdcbcbacbbcdcaabbdbbbaccdadccadddbadcbaabdddcdbdabdbabdacaccaadabcdcdbabcccbcbdcdbddabddaaaacadaadcccdbcddcdbbcbdadbddabcadddadacabacbdccaaacbbaadadbccbcbbdaacdbddbdacdcdbcbbcbaacdabbaaaacadcaddbbddcaaabbbbcccabbacadcaccbcaadcabbaadabbccdddcadbbbbdabacabcdabadadadaccbccddacacbccaabdbcdbcaadbdacbaccacbddaddacaabcdddcbacdcacbabcaaddacbbadbbbbadadaadcababbcadcbbcddccbadababbabacddaaacababacdacaddcdacbbbdcaadacababdccccbbcbdbdbcbacadbbaacccdacabdaaddddbaaaaaabdcbdacbddcbbdbdbadabdbaadaccbcaccaacbccbcbccacccdbcaaaacbcdcdcdaacdddbabbdccbbbdcccbbcacdccadbcadacbadbadcdadcbdcadbaccbcbccacddcacdbdaabcbcccdabdcbddacccbaccbacbcddbdbccbbbbdbcbcddcdabbdbdbdaaddddaddcdadaddaacdbddbaccaabccdbcccbbaabdbbbdddcdcdaddddcbcbabadddbddbacccdadaaccadcbcacacccdcbadbddddddbbdbdabbcddcccdcabcbccdbabaababaaaaccaabbadbaccbaadddbbdabcbcacabcbdccababbdaddabcbdadbacccaaadabccbdbccccddaabaddcbbadaadbbcdddccbbcdacdbbdbaabadbbaacdabdaddcdadabcbbcddbcbddbbdddadddadbbacbbbcbcbcaacacddbbdbcddbdcbabcccabdababcabacacadaacbccdccdbcacbdbddcbdbdabbdbaabcaabdbdaaccacbcccbdacadbbbbbcaddcbdabccbdaddcaddccbbaacdacdbbaacbbbccddbcdddbbacccddaadaaaacddcddcaabcacccbcbccdbcadcdacdbabdcbdaccbadcdcdcadabdcdabacabcabaabdcdcaddbdddadcbaaddadcbbddcbbddbaccbcadbcadbadbbabcabdbcdaaaadbabdccbbbacadccbbabacbdabbcddbdcaaaaddddbbcdcdadabcdaabdbbabdabcaaadaacabbdbdbbabaaabdabdbcdccccddcbdddbbabdbdcddbddbddacadddacccbcabbcbcccdabdacdacddccddbdbcabbdccbccdcadccbabacdbcadcbbbddbccbccccdcbbcbbaabdcbdbdbcacbdbdcbcaccaadbccbbbbacbdddddbbcaaccbbadacdbddaabbcbdacbdbcccdcbadcddadabcdacbaabaddbaddbaadccaaadccbbcabccbccdcdbbccbdbdddbabcdbdbbcdbacccbbbadaaadcabddbadbbccabbaaacaaaddcaddacdccadbdbadbcdcbbcadcbcaddaccaddadaaddaddadbacadddcdbdacdbcbcdcbdddcdbdccadccaaabadbcbbbbbcdddadbbdaddccccbcbadbbaddbdbcccdccacdbcadcbccbadbbbcaacadbddcbbaccaddbaddddbaabdacaadcbabccddcccccbadaacbbcbbbaadbdbcbddccaadaabadbbbbddaabddbcdcbaaadccbcadcadbabbacabccadbdcbccbabbdbdacbddbcdccabaccaaabadabcaabdadddbaccccdababbbcccdcbadacbdbdbadcdbcadccacbccdbbccddaabbcabddbcbaaadccdccbacddaadcbacbdbbabcacdaddadcabbdcaccddadbcacbdccacabbbcccdcaccadabbcdddccaccbdacdacbdddaabcccdaabbdddabaddaacbababdbabdadcbbdbdcaacccaabdadacaccdccaccbacdbcaabdcbbbdabbacaaabdddbcdcdccaccddcbbcbabbccabcdcbcaddbdcbbaadacdbabaadaccbddcacccabccabacbadacdcbcbbbbbcbbddbaaaddabbacddacdadadddbbaaccadaccacdaadbcabbcdbbddaacbcadbbbbabbaabbbdbaddaaacbadcddbbdbaaabdabbaabbbcbbabddbdbadbaadcacabbadaddcddcbbbbacbaabadadabdcdacccdaadabdbaaddcaabbaaccdacbdcdbcacaccadbabcabcdcbcacdbabccdbdcdcddbdbaccbadbbabddcbcaadcbabdbcdccbdcbaccddbdbaadcbabbbbcacbbdacbcdcccbccdbbcaccacccacadccacaadcaacbbcccdbdccaccaabcddccbacbacccdcababdabaabdaadccddbdcbdcabcbbcdaababcaabcadbdbbcbaddaccabdabdbdabbcbbabbdcdcdbcbcabbdcadbcbadcadbccacbccadadcdbbddacbdbbabbcbbdccacdbdacacbdabcabcacbabbddacadddcabcbabbbbcbcddbaabcdababddddaccddacccaadbacbcadacadcbdbbdacbaabcddaaaaaabddcdbacaddacabaaaccdadaacbbadbbbcbddcbaabcbabdbacbbdcacadbdaccbcacbbbadaddbaaabdbabacdbaaadacdcbdccaaaddacdcaaabbacbadccdacaacaabcbdbcaaddcccabbabaccccdccabaccbdbbdadacdcdaadcbadbdddcdcdabccaccbbadbbcabdadabaabdcbcbdcbdacadcdcbadbcbcacdccdaccdaddcdbbbdbdcbcbcbaacadaabdaddcaccbdbdadbccdbcacaabdccadaddccdacabadadbabdacccbdcaaabbadabadacdaaddadddbddcbdcdcddadbccacbcdacddcdabdcdadbabcbbcabacabbdabcbdcddccccdbcabdcbababaacbdbadabdadbaaabababcdbbbbbddabacadacabccddacbaabbdcdabccaabbdbdcacacabadbaadcdcccbcabcbbacbabacaddbacbccdbcbdabdddacbbabcdbddbababadacdacdccbccabaddcbacaadbcbbbbcdadcccaaaccdbaaaaddddcaabacbabcdacdabcacbabbdbddbadddbcbdbbccccabdbbccccacababccdaaaaacaccccbddcdbabcbccdccabaadabacdcbccadcbbabdcbcdadddcabbcbabbccccaabbbdadcdcacbbbdacaaddabcacbadacbadadddcbacaaaadaccdabbacccccdcaabaaaacbdbdcacddddddabdddcdbbaabcbbacbcaddbbaadbcbdbcccadabbdaadbadacddadadaaabbacdaaacddcbdadccaabdaddaacddcbaabdcaaaacddcbadadaaaadbcbbbbadbadabdaacbbdcccdccbcbaaaaadcccbcdbbcdcadbbdbbdddbdadbdabaddaaadaccdabbbcacbacdadbbdcbdacccdbdbacbaacbbaccbbcbddddbbcbdaadcdaababacaaadbbdadbddbcbccdadaababbbabbbaabaadccbacbbcbaaddabaacadacabcacdcbcabcbbcdabbbcabbdcdacbacaaabcbbbdbbdbabaadbcdbbbddbbbcaaddaddbacdacddabcbdbbaddbacbcaacbbdbdccadcccaacddccbabdbbdaaabbbbacbcdbaddccdbcccbdddcdbcdbddddaddaacdccaabbadbddddccacabdbddbbccbcdccccaadbddbdbabbdbcaddcdccaacbcbbdbaadcbdbbdaadcbddbddbbaacbbcaabdabaccadccabacabbddbbdaccdbbabadbadcbcdacbcdcdabdddbdbddbaaaadcadcbbbacddbccdcbabcbcaaabdbdbdbdbabadbcdadcdbcaadccddbdbdabcadaaccddddbddaccabdadcdbabaabadcbbdbcbcdbaacdbadccadcddaaaddabaacbbcbadcdbdccbcbbaadbbbbdabcbaaddaadcacbdabbdacdccdbcdadadbcdcbaddbadaacaaddcdcaaabacbadcbdbbbdcbcbcaabdbbdbbacddcdcbbbdacddadbcdcbbbdcbabcdabdcdbddccdbabdcabccdbbdadbcdaccbccccddddccbabacadddbdccbdaddcabddcccbccaaabdccabaccdbaabdbadddadddbdcbbbcccbbcdadcaabdccdddbaccdcbbaccbcadbdcbccbdacabcbabbbbbbdadcdddabadacacaadcdadaaadccdccdbdbacbddccacbcdacddbccdaadbbbdbaacadabddbdacadadaaacbacbccdccaaacbcabcdcacacaadcacdadcbbbdbaabaadbabcdadbacddbbadddaaaccdddbbccaccdbdbababacdcddddcdbcbcdbadbaddbcdddadbbbdcbbcbbcadddadbabbcadaaddbdaccccdbbaccdacdcbbcabbcccadcdcadcdacaadbdbbccbbbbdbadcdadcbabaabaddadbaabbcbbddccdbccdabddbdaccdacddcbaadacbccaccbdcdcdbcdaabababaacbaaddccaaaccacaaccbcbdcbbcbcbcdcbbbddcbcacdcbaddbadbcacdaddabcdcbaaadddadbbdbadcaaddcbbbbadbbbbacacbbadadcadcddbdabcccbbacdabdbcdcbacbdbdacaccabcddcbddcccdcddabbaaaccbabbbcccdbaadbdcdaaaaccdabbbbdccbabbadbcacccdcaccacdbdbbbcbbcdcdbbabddbacccbdbcbccbcdddacdccddacbbaccdadabcbdccbabbddcadbdcdbbbdcdadbaddbacdccbccbdccbbbabdccbbdabcadcccbdbcddccbaacdabddbccacbcbdcdbbbddbddcbdbbcbdccbbbcacdaacadcdddabddbcbdbaaaacbadcadddcddcdddabadadcabcaaabdddbbbaaaccaddbaddbbddbbcaccddcaacbbabadcdcddadbaacaacbbaabcaddadcaaaccadbddaaacbbaadbbbdadccdcccdddbbacadbabdcbdaccbacaabdabbcbbcaccdcbbacacddcbbaaadcdacbcabbcccaacbbababcabbaadabcaacbccabcbacbcdcaabcccbdaddbbcdaabdcbadbbcadcbdaaabbaadcaccdbbbcdabadaacdcdbbabaacdbcbbbdbcdacbcdabddbaddcbaddcaabcbcdacbcbbcdacccbcdcdcadbabdbddcdcabcacbccbbcdddbcaabddbccdbabccbcddbabadcaaddbcbbccbddbcbbdcaaabdaaadacccccbadbaccbbcaabdcdabbcbaabddcccaabccdcbacbcbdaccbccccdcbdcdbaaabdbbbddcdcaddddccbcadcbbccdbaaacbddaddadbdcbdcdbccbddbabcacabaccdadbabacbccadbdaadbcbaddcdabcbdbccbbbdacccbacbadcccaadcdacccddaccacbaabdabbdbdabcdccbddacdbcbdcbccaaacadadbdbaccadcabdddaccdaccadbdbaaccababacadbdddaabbabbaaaabaddaadbbcdadbaccabadbccababdaddbacabadccbdccdacccababccddababcbcaddaabadcdcdbcdbacadccacbcbbcbccadbaacbcdbcaabbabcdaaaddaaabddbbbcadbccaabdadcbcdddadadbccccdbbccacacacdadcbcbabcdabcaadaddcbddcaabdacaccaaddddccccdadcddabcbaacbdccaadccabaddbdccaddadadcdbdcdcbbaaabdbdbbbcbadcdbadbcbcccbbdacdcccaacdddcaccdbbbccabbcacaacddaabcacadddaadddcdcaaddbaaaacdacbbbcadcdbabcbbaddaacdddacddaaabbcdcddbbddbddcddaccdaddcaadcdbbdbbcaaddaddadacbbadaaccaacccaaabdcdbdcbdbbddbadcabcdbcdcdbbadbdaaddccccccdacaabcddcbadcdcbabbdacbaaacbdabdbaabcbaabcdbbdadccbdbacbabbbabdcacacbcccbbdcbccdbabdacbddbdbbdadbbdbcadbadcadadaadacabdaaccdbdbdaddddcdddbcbcbdadbdadabdbcdccacbdabbcbdabdabbcadacabbddddabdbacbaaaaacbbcdddacadcacccccbdbadddaabbbbccabaccccacdacbcccadbdacbdadbdadbabaabcaaadaddbdbbbbbcaacdaacbcacddcbdbbacbddbdcccabcbddabbabaabcbbdbbbccbbbcdcadcbdabbcccdccaabaadabdabdccccabbaddddbbcddbcacbbddccadaaaaaacaacbcdbcbccdbabbbbcdbcbdbcdddabacababdbbdaccaccaabcbbbacbdcacdcddbbabadadbaccdbcccdcadbabbdabbcccdcaabacacbcdacbcdcccdabbdbccdaddbbbcdacdadcaaaabcdbcbcbbacbacdbbcbdcdcbaadcbaaabdabbdadcdbcdcaacadacbccacabcabdccacdaaaddacbdbdabbcaacbbcdcaccbaaaadcaaabbcaaacdcacdbacacadbdcaccdddcbbabbcdaacbbcadcbbcddbaccdbddcbbcbbccaaccaadccaccbbcccccbdbabcadadadbcddbbbdadcdcbdbadaaaacbcadadcdcddcbbaddacbcccdbbbbcccaabcbbdbadbaaabbccddaacbbbccdcaccadacadbcdacbcdadcbcbcdbadacbadabadabababcbcbdabdadbaddadcbddabcbabdccabdcaadaddbdabacdacadbccdbbdcbcdcbddabbbababbdbacbbdacababacdcbcbdadcdbcccadbcadbaaacaaccbabbabcbaabdddaaacaacabaacddcadadbdabccaccacdcbbbdbbcdbdabbddadbbbdcadcabaadacaacbadbabcbcaddaadcbacdacadbaabacaabcadaaddabcacacddaaabbadbbabdbaddcbdcccdddbdbddbbcbbcddbcdcdcaccdcdcdbbbadcabcdddcaaccaacdbaadbccbccabdbbcbadcccbdabbcacbbdbdcadddcadbcaacbdabacbacaadccabaaaadbabcacbacbccbadbccbabcdbdcbccdbdcbaaaadcddadbcbdcddcdcdbdccbcabbddddbdccabcdabdddacccbcdcbcabbbbcdbcbaabaddddacdcdabacdccacccacacadccdbcbabaabdadacabbadcbabbbabadabbcdadbaddddcaccbcccaaaccadcbbbddabbabdadcbadbacaacacabcdcbdbdbbbbbacdcaabbccbbcadbacccaabbddbcccacdccacaabaababacaadddbcdcdbabcabdabbabbabcdaababbbaaddaaadbdabababdacbddacbaddabdcccdcbbadcaacdcddacabcccacdabcdcbddbaaacbcdbccdabcbdaadcbccabbbdcbccbdcaaddddacbcadadabcbbbdadaadabbadddacbddaabccbaaacccabbacdcdbcdadcdacbcacbbcbddbdccbccaadacbddaacbdacaabacddbddaccddcaaaaaaadddabdcbcbcdcabdabbccbccabbcbabbadcbddcdaabbcadabdcdbdbcabbcdcacacbcacdbaccacbdaaabdbcacdbbabbaccbcbcadddabbcbacdabbbdbabcbbdabdccaadcdcadbbdacccccddabddcccaacbaadbadddacaccabbabcdbbabacdbdbcdcbcbdcdcaaccccbdacadcababcdcbccdbcdbabaabcdbdbdbaadccbddabbdbcddcaccbaddaabdcdbacadbbdaabcbabbcacacdbccabcabacdacadaaddcaabbdddcdcabacbcbccaddaaaabbbbbbcaadcbcdcdcacbadbcdaacdddbdcddbbcaccddbbcacdadcdbcdadcbbaaacdbcbaadabcddabcadacbdbdaddbbccdcddcdbacbccbbdcbadbccbdcbbcdaabaababcbcccbaaccdcdcaddccddcbacdaccacdbabaccadbadcbdadcbdddcbddaaccddacdaddcadacabdbadddabcadababaadacccaccdddbaaacacdcbbcaabdacddcbcacacbccdabcbdabcabccbbdcbadccabbdcbcacbccdabcdcdacabbadbdcacdccbdcadddabccdcdacdabaabbbbaaadcccdbddadcdacadacbacaacbdcdbccadacdbacbaadbccbbaadcaaacbacbddacddcadbcababcadcadabcabdacdacaaabbaccadddabdbddcdcbdcaadbacbcbacabcbacadcbdbcbababcdcddacbabcddacabaccbabbdccdaabbdaaaacddbdabacbabcbccdadbbdcdcdddcddddbaaabbcbdbcddddcbdbdbcbabbaddbddddabacadcaabdcaaacdbaaddcdcabadcbcbdaaacadabbbbdddcaacaabcaacdcabdddccaddbbbcdccccabcdabbadddcdacbcbabacdcdcccaaadcdacbbbcdaddbcabbaabdbcdcdcccccaccadadcccbbaadcdbcccaaccabaaacbdddcccadbbabccdadbdcbbbdabccabddcababddcccbbdaadcabcbccdaacddddaadbbcdcbabbcddbbacabdcaaddcdddacbbaaccabdacadabddbbaadaacbdbdbcccbbaaadaccddddcbbdcbbddabdacdcbcddbadcbdaccacaabbccdcbbdcccbcadadbbcbcadbcaaccabbbbdccabcacbaadddbbacbaaccaddddbbdcccddddcacadcdcdbdacdadbabbabdaddaacbdbcabbbaaaddacdbddbaddcbbbadaadabddbdcabdccaabdccdcacabdddababbaacadbaccdbbbaaaaaabbcaabbdbcccbbbbddddcccbbcaadcdaacbabcbbbbcdcdcdbcddbaccaacbbddaaddcbbddbdcaaadaadbcbcdbaacbcabcddadddbdcbbcbbccbaabacbbcbbbcaaaddadaaccaabcbbdcdbbcbccadbdbabdccdddcbdddcbabbbadcabbdbddabdabcadbdccccadaacabbdcccddcccbcdcccddaacbcabbbadddaaadcaccbaccadbbcbddaacdabdadcbdbaccadcabadaababacdddbcbbcdcddacbdabdcabcbbadacabccbadcbadaaaacaddadbcaaddddbadccbdbcacbbdbaabbccddbdadaadbdacadbdbddaaabbacdcdcdbabbccdcabcdabdaaadcccddcaccdbadddbabbdadcdccadaddaacbcdbaccddbacdabcdbcddabdcdccabaaacacbdbababbbbaddcbabcddaadbababaccbaccaccbbbccadbdddcbdcdbbddbddbbdabadccccbcbadcccddbcdbdddcbbbcbdcacabadcddaadaaaccabaadaabbbabdaddbadbcaaddbcbdbdaaddcadabddbdcdcabcadabaccdbbadcdbdcbaaabbaabdcbdbdaaadcdbbdccdcadabbcddcdbacddabadbabdbcacbddbabdacabcaddcdaccbccbdddaadaaadbcbdbccdcbbcaacccdbacdcdaabbdbaaddacccbddadaadcdddadacdaddcbdcdbbbbcbdabcabcbccadacbccbddcccabcaacbacbcdbdbcdacbcbbcbcdcdccccdabaaccbbbdccacbcdbadbaaaaaaabcbdbbbbadcdbddadbacdadababcbcadacbadcabbabcadaacadcaacabcacbddbacbdbcacaabcccabaadbbdcdadacacaaaddbbadddabbbcaaabcccddbbbbcddacccaabcabbabdbcdcdadbadadbdaaddacacbcdcdbcaabdbdcabdbcdaabbdbdddbaddabcbbcbccabdddabbbccccacacabbdbdaddcadbbcbbadadaddaddbccdddcabbcddabddabcdaabbabbaddaaccdbbcbadbcdbbabbbcacbddaddaddcccdacabdddcdacbbbdbbccabddabdccccdcbacdaaaddddddacbaaacbdabcbddcddbcaacddbddcdcadabcbcacbcdbaabccdbccabcdbddbdaabdbbadbdcbbadccbcdbcacdddbbbbcacbaccabcbdbcdaddcaababaaadcddaababbccbbbcbdbdacbcccdbddbcadaddcbbdbcbdccdcbdbcabcbaacddccaabcabcbcadbdaaadaccccabbbaacabcddbbddaaabbcbdaddbccdcbbaddaaccbbaadbaccdadacdaaabbbbaadccddaadadaddbcacdaccbacdaaccbbcdbdcdbbabaccbacdbbcbcabccbdbaaadabdccdadadadabaacaddbccaaacdabbbadabbdbbdcddadadbaaacadabcbdccbaccbdbabacaccccbbdbcdabadccaccaccddddbbdcccaaaadacdcbdaabadbdcbbcacbcaababdccdcccbabbbdcadcbadacdbcdddbbdcabbcaaadcbccccabbcbdccdcdcdcbbcacaccbddaacdaaabdadbcddcbabaddddddcacccbcbbacadbcccbdbcccbcabbdabddaababbabadcabcddabccabddddaaddddadbabcaccadcccadaabbadddcdaaaadcccdcdbdbabacbaacdcccdaddbcddbcdabcdddbdcdbbccccdcdcddcbcbcbadadddcbcabdbdabadcbccbbbcbbaacdddbbdacaccdbbccbabcdbcadccdcdcdcdaccdadcbcabccdcbbbaccbdbdbcadccbabcddcddbbbcabadbbbabbddbdcbccbcadbabadbdaabdddbccbbcaddcddbaacbacdcddbacbabddcacdddbbbddadbccaddbdacdcadbcdaabdcadcadbacdddbbdbabacadbdbbababbcdcdbacdbdccccdbdcaadbcdcbbbcdbaaaacbcccacbddabbcaaabcbacadbcabccacbaabddbdcaabcdacababcabbacbddcabbaaadbcccddcadbcdddcbcddcdbbbadadaabbbcccbabbdbbbacbdadbbbabdcccbdcdacacaaadbbcadbdccbccbadcdddbaacadabbdddcbdbbdadbcaccdcabbbcdcdcbcaccbaaaaacabbaadacdbdcdaabcccbbcbacdaaccaabaabbdbcbdbcdcddddbabbdcdaaddacacbcdabbcbdabcbbbadbbaddbbddccaddbabddbddddccabbdbcacacdabdaadddbdddbbcacaacbbbcbcbdbbccbcbaadcdddccdbcddcaddccbacabcbadbbdaabcddddaaadadbaaabcbccaddaadbacbdbdaaabacdabbbbcacabbcdcccbccdaadcdaddbbadcabababcdcadbcaadddbdcaaacdabddbaabaacbabcabdbcddcbcadccacbcbabacbadcabccabcaabccbdcdddcddbdbcbabdddcaadbbdccdbbacdbdabacbacbccabcabbdadbccbddbddcdadbdbccbabddbccbdabcabadabdcdaadddcadbaadbcaadccbbcacbcbacacdbaaaacaabdddbaddbcdbdbbbcbbdddbdcaadbdacabcabdadacccdadbccaddbcdabcababcacbbacbaaaacdcdaadacbcdccbdcbdabadccdaabaddbdccaddccbacacdadcabddccaabbbbbabacbccdcbbadbbdbaaabcdbdacaacccbaddbabbcbacdababbbbbccadcdcbcdcbbcbadabccdbbdbabacddbaaaacaacccaadbbdcadddcccaddaadbcdccdcbacdcacddacddacabbcbdaaaacadbacabbadadacdbabdbcabbddadcddccadadcdbcdcbbddbcbaacdccabddaaddcbcabcdaccbdabbbacaccaccdaaadbbabdaabbbdaccabacbaadbbdaabddaaaaaaddadaacccabdabcbcbbcaadabdbadadbcbabdcaaccabcbabdcddcadbccbacddbdbdbcbaacddbadacabbbddcbadcdbbccbbacbddbdcdacddddaaddabdabbdbabdbacddddcdddbabbddcccbcaadcacbabccbacabbdbbcbbbacaaccacddacaaacaacddccbadbbdaabdcccdbdbddadcacaabcbdaaaaabbabaacdcbcacccabadabdddadbcccaabcaccbdcabbbcabbbccccbcbccadbdbcdaabddcbadaaabbdcdddbbdcdaaddcbbdabdbabdbdbcaaadcaaaddadddbbbbddddabccbbbbadacbbaaaccddabbcdddbcabaacdbbcbbbcbdadccccacaacbaabadddacbdcbddacaabccddbdcccabbddbdbdcbbbaadbbdcbbbdacbbcddcaabcccbdaddabdcbbadccdadabacadbbbbaddcaabaaabdcacacbbcdcacbdbacddbbbbcccdaaabbbabacbbbcbaacbacbcccbcabbbbdacabcccbbddcdabdbbabdcaadcabbacbbcbbbbabcdadccaaaddbbabaabddccadcbcabcddadcadacbbbdbaabcbddddacabdabcabbdddadbddabdabdcbacacabdbdccabadbabadbcbaddaddaddcccbcadddbcbadcadbadaadaddaadddbadcdabbaabdbcbcadaacbcaabbbdbaccadacccaabdcdadaaaacacabcccdccadaabababbabbcadacbcaabacadbabbaaadbadaddbbcbbccadbbbadcacccbdadaadbcaadabacbbdccaadbbbcdbbdacdadacddcddcabadaababdddccadabbcddbcaaaaddbadbcddcddbdbdacddaddbdacabbcccadadacdcbbacbbbcdabdcaacadddbbbadbaacbabadddbdbdcaddbdddbcbbbadbadccaccdbaadacccdaacaaddcdbabddcdababddbbbbcdbdddccbcabdacdcbdcdccbcaadabccbdbaaadbdaaddadddbcdcccbadaacbabbcbbbdacccadcaacbdaaacbaadbbcdabcbabadcddccdbaaaaccbcadacbaabcbddbbbabbbcccadadbbdacdcabcccadbbabdccdcddcddbbdcadbcdcddbbdababbaccdabcbdabacabccaadcbadbcdbbbdbcbbccdccabdcdcaaaccdacbbbddbacbddacdbcaacbddadccbbddbbbdddaaaccaadcbbcabdacaadcbcdcadaaacbbbaadbacbbcdbcdbdcbbbacbcccddbddcaaddcbcccdaaadabcddbdaccadcbaddccadddbabcbbaccaccddcacccccccbbddbadbbdbcdadacaabacabdbacbcaadacdcbcccbbaabbdaccddacddddcdddbdabcdbbdaddaacdabaabbaddddacccbccbadcbaabcccacdbccdcccccacccddbccaadadaddcadbabbdddcbbccbbccabcbdbdbbabddcabbccdcbccaacdbbbbdaacccacaddbcccacdccbdbdadadbacaacbacbdcdbbcddbbcbdbccbcaabcddcdaadaabdbdbcbbdacaaacbacbddcaacadabbcdadccadcccccbbccbdcabdcdaaacacbccbdacbdcacdabacccbaabdabdbdccdccaccbbdaddabbcdcacabdcaaddbddacabdabddcaccdcbddbcabdbbbcbcbccddddaaddddbdccbdcaccccacbcabccbcbbabcacdbdbdcdbaaddacbabcdcaaacdbbaaaaaaaaccbddbbdababcabdacbbdcaccadcbdcbbabaadcbdcddaabdccbccadcbabacdabbbccccdbbcccdcdbaabbdaacdbcdcabdbbadadbcdcabdcbbacdbbadadcbddbcadbddcbcccabacdcccbdbdaccdddadcdcabdcddccadcdbcbddbacadbbcbbccabcdadacdbabdacccdbddbcbcaaabcdcdaccabacababbbacdcaabcbabbddddbbcdddaabddbacccbadbbdcdcdccbddbcabdababacbbadcaaaacabbcdcdcbdaddddbaadbadcbcaacdadbccddbdbbadabddbaadacbbbbcaaaacacccabaaababdadbdbbcbccddccabbababaaacadbccadaacddbbdcddacdbdcabcacadccdcacdbdcaadaddacabbdbabddadcdccbcbaabaadcbdacdaadaacdacddabccabaaddaababbabbdbccbbdbbdddbbccadddadabdbabccdcacdccccdbbdcdaabbcbadcbbadcaadaadaabbbadbaabaabdbccdcdbcaaadcadcbbccadcacadaacadccbbabcdddbcbabccacdcbaccbdcdccadcaccacccbaccccdbadaaaabacddacdbbdbcdbcdcacaddddbddcccccadddcbabcbbbdbcabbadccbacddabadacdabdbdacbbcaccbaadbbcdaadcabbdcdacabbacccbadccdbbdbcbbcdaacbadabadadbaabbcacbcdcaabbcbbbaccbcbcbaabbdbbcbdcaacbbbdaadadddccbcadaddcaaddcdcdbdbbbcaadcbddcadcbadccdcbabcbacbabaddddaaccaccddbcadbacabdbbdcccbdaddcabdccadabaccdcbbdbaddcbcdbcadabadccadbacaabdbaacdacccbcccaccbacbccababacddcdbdaaaddadaaaadcccaadbcdabadadbccbdadddccdbadbbcabaddadadbccccacbacbccdbbdacbbccccacbdcbbaacdabbaabcccddcabcaddbddbdcdbbddbdbabcdbcbcaaabdbbacdcbccbddaddadabacbaacdbcdbacbaabcdbbaabdbbbdbdacacaadbaddbaddccbcbdcacbabcdcdbdabbacdabdcbbcbcbaddacdabbbdabbcddbaabbcaabaccdddabbbbdabbacdbacddcaddcdadddbdbcdabdcabaacdadccadbdbabaaccbababdaabdadbccaaabcbaadcdaccdcaddcdbaaddaccdcbbbbbdcadddacacccbdabcbddabbcbddcbbdacaaccdaabcdaddbaacbdbbbbababcbaaaccadcdbdaacbbcabcbccbdadabbdadbbddaaadadccccdcaacdacdddcdacbcbcbcababbacaacddbbdbccdcbbabdabbbbcdcbcadaabdbbcabdbbdddbdbcbccbbcbbdbadddabddddbdcadbdbddadacdbbdaddcdcbbadcbddbcbdaaacddcacbabbccdcdaacbbacbbbbcacddddbaabbdcaaabdbcacbaacbccdbcadabdccbbbabbdbdbdbabcacadacdaadaadbdcbcdbccdcccaadcbcdcbccdadbbbabddbddacddbbacbbcaccacabbcdcadaabddddaaccacabadacaabcbbccbdaabbbcaadddcacdadadccdbadcdbddacdccbcdbcbdcbaaadbadbbbadaabdaaaaddadddabcbadadcaadadaddbdbbbdcbcdadbbcccdbbcbaaabcdbcadacbcabbcccdabcdbcbddcccbdaddddbbcdaacdbdbbbbaaadbbbdcaaaccdcdacdddcaacdddaadddbcdacabccbcbbadcbccbbcaaaaacadadadccbdcccbaabbcabdcadbccddbdbcbaaccbdcdbbbdbdbdbcdbbcbaddbddcbdabaddbddcabcbacbbcddddaddcbbdcbbbdcadccbadaddcccccdccaccadabdbbabdcbdadddacbbbdcaddbcdbacadcdacddcccdacccccbdcabbddcbddddcccbdababbdcbdbaacaabcdbcdcacabbbadaccdcaaacadcbaabcddcacbacdcbbababbadadbacbbbdbcdddccbbabbbcdacaabdaadcdaaaaaaaacbccddcaadaccbaaaddcbbbdbbcbbdcdadddbbabcdaaccaaaacacadccccbbaccabbabaddcbbbbbaababadddbbbbbbdbddcaabaadcccaacddcbdacaaacabcdbaccbbbabcdacdbcbaaadccdaccaabacdbabcbbbbdcbbccbcdcbcdddddbcdcacdbdacabadbaabcddbbabcbbaddbbcbcabbdbbdccaaaacbdcaddaabccbccdaccacbcddcaaacaccadbbaabddbdadddbadbcbbcabacdadcacbccbcdbbcbaddaabadcdcabbbdcdbadbabbbbbdbccdcccccabbdcbcaacbbdbdcdbcadbccbbacdcaabdbcbacbadbaddcdaaadbddcaaddcbcaabdaabcbcdacacdccccddbddbbbabdddabcbbcbbbdcccabccabcacbddddcdccdcadaaabbbcbdbcacbccaadaadbbcdadddcccaddacdcaccbbdccaaadcdcdaccaccdcdddccdbbaddcbaaddabbacaadabcbbbacbcdbcdbacaccccadcbddaadbdacdabddcddddabacddadcdacbcddbbcdadacdbcbadadadadbcdadbdadbbdcccadbbacbbcbdbdddaaabacbbccdbbbdabcddccacbbbbbadababddddcaccbbdabaadadccabbbdcbdbcddacdcaabadcaccacacdbccdaccbacdadabcacccadddcbdddccabadcadacddcbddbcaaccbcaaddcdbcddabdbcdbcdccddacababacdacbcbdbcbddbaddaccdabddccccdbdcaacbbbddcbacbddadbacbdabadcabbcabbaacaccacdcabcbacabbbbadbdbabbaacacdcbcaaabcbadbadcbaabbdaaabbbbcdcdaaabddbabdccbddbcdabcabbadbaddbbcddabcbcccddadabbacbabcbaaccbdbacdbbcbadcadccccbbadacdbbdcacdbcbaaabdcdbacaccdbacdaaabcdccdccaacbadcdbccddbdbbcabddbdcbabdadcdcbbcbbaccaddacabcdacbbaddbbddccabdadabccbbacbaadcaaadcaabdcbddaaccbdbccccacddccbdbcadaabdbbbaacbbabdcdcdbdbbbadbaacacddabdddaccbacacbbbdcaacddddcaabaabdcbcddbbdbdabbdbdbacacacdcbbddaccddaddbdcdbddacaccbdbbabacccaadbbdbdbbcbbcbaadcacaccabcabbbbccbbbbcacaddccddbdacdbdcabcddcdbdbbdbbbbddabccccbcbbdaccbbadaaaccddccdcadcaadbacbaabdbaaddaaaddacbdcbdacbaaabccbaddcbaabadcbbbdbdadbaaacaddadacadccbdabbbdccbbadbbabababbabbddbbaccdbcabcbadcaaccbdcadacadbcaccadbbdadabccbccdcaababcdbdcccabcdbadbbcccaddabddccabdaadccaccabcdacaddbdccacbdabcabdcdcbdcbddbdaadbcadacaabcbabddcdaaababccbdaacdcdbaadbadccdcddbdddddadcdabcaacdcdbbccbddadbcbcbbbcbbaacadccababdbabcccdabdcbddacbaabadcdcabadcdbdcdccbbdbdbbdcabbbbdbaddbccadabdbdbacdabcbbdcdbccbbadaaacdabdcadaaaacdcddabdbcbabdddabbdbcadcdabbcabbddbbdbcbadcdabbabacddaddbccadadcbacabcabbdacddadacdbabbbcbbddcaddabbbcccddddcdccbbcabaccbcdaddccbaabbadcdccabdbdcbbabdcdabdadbbadaaacddbbbbbddcbbdacccdaddddccbadadbadbcaaadbbcbbbbcbdadaabcabbababbaacbacdbccddbabbccbbbaacccdcdacbbaddbbddaacaccadabbacbadbcdccdcbbadaadadcabbdcccababbdddcdbbbbdacdcbabadcdbccacddddaacbbddcdbcaabdbaddbcbcbbcbdbcbccbbdbbabbbdcdcddcdacdbdadbcbcdcccaabdbbdcbaabcaabaaadbadccbdbdbbccbcaadcbcabdddabbdbbcaabacbadcbdcadadabcabcbcadabbbacbacbdcdcacbccddbbaccccddcddcdddbbabbbdabbabdaacaaadaababdbbbcdaccbcdcdacaadcbcabbaaddcdabaaaddabbbddbbdbbddbdaddcacaccddbdcccdcbbdabadcddbadaaadbbdcccbdadccaaabcaaddbcbdbbabbddabcbbbcddbdaacbaddbacddbcccabbabbdcacddbddcddbbcccbccdcbbcaaacbaadacbddcddabbdbddabcddcbccdaccadbbadcbaaababcabdbabccdcddcdaaccdadabdccbddcccbcbddddbccacacbbabddbacdacbbdcabbcdcabacdcddcdbcbdbaccbbbabcaabbddabcabcbdaabbdcdbdabbdaadaccabcacabbdccdaadccadbbaadbbddadcdaabbbccbddbdbccaabbaadbbbbccaaaadbdbcbbddbccacaadcdaaabcbabdbdddaddcadabbdbcaaacddcbccdaadabbbcaabcdcacdbdcdbcddbbacdbcdbcdbcdaddabaaccadaddbdccbcaccbddcaaadaccacabcabadadbacdbbcbccbdaaddbabbacbbdccacabcdddbaddadbcbcabaaaaabadbbababcacbcadcabcccddbbbddbacdaccccdabadacbbbbbaabbaddbabcdddcacbddccccdddbcccaccbbcacbdcdbbaadbcdbcacdaadcdcabbbbaabbabccadabaccbacdadabcbcaadcbcbbabdaacdccdbcadcbaddbcdadbbdccaacccadcccbbababcdbdddacabbddcabcaaacbdbcbaabbbdabccbdcbdcbdccacdcbacbccdacdabcdadcdbbabadacbacbcaccbcababbbdbdabbcdabcaaadbdbbdcbabababccadbdccbbcccbbabdaccadcdbdcdcbdddddccaaaddbaddcabccdaccacdadcddcbadcbabbbddcccccdcdcdaaccadbdacdcbddddadaddcabbbccbccabbddbadbabdbbbbdbbcbacbabdbaabbcaaddcdbcbcbdbbcbddcbcacdcccbddbcaabdcdacaacbcdcdccbabdadcdabbaccbabaabbcacbddbdaaacaaccabbadbbdccabbdadbabcccbadbbcdabdcdabdbbdccacbbddddaadddaaccabccdaaacaddddadbaadccaadadacbbddcbbbdcaaccabaababbcbdcdbbabdccddadccabdbcaadbbbbbdacbdabbaaabcaccbcacdacdcdccbcbadbccaabdaaadcddabacdccdcbccddbcbbdabdabdacbcbcabdbadddcdbcacacdbacdcbdadbdbcddbdbcabacbccabcbabdddbdacbbaaadbbbcbdbbbcbacbaadaabcacdbccbdcbbadcdbdabbadbdcadbbaabcdccacdcabadacbdcdaccaddacdabcbbbddacdaaacbcabbbbaaadbbddabbccbbdccaccdabcabcbbdaccacdaabdcabcdaabbadbcdabcdacbbdcbcdddddcccbdcddccdbccabbdcdbacdbccaadcdabcadacccbddcaaddccbddaadacccdcacbbaddccaadbabbddcccccdbbcaacaaacdbcabcbdaacbbbbccdddbcbcaacbccabdbcbbbdbcaddddcaaddabbaaddcdabdddaabadcaadcbcadbbaaadacabdacdaabcbdadcdddcbcacacbabdbdddbbaabcaacbbbccbbbcbbbabaaccdcbbbbacacccdaacdcaaacabacbddadbbbabcdbbcdbcaccdbdbcdbdadcabacccddbbdacbdccccbbcdaabcaadabbadaadcaaaacbbabbdcddbadddaadadcbbdbcabdadaacccbadbadbdabddaaccdcbabbdaabbaaabcdcacaadbdbcccdadaabcaaaadcbbcccadacccdacdcabbdbcdccbddbbaccabcaabccadbdbabbdcccbddabcaacaaccbccdabdaddcdcacacddbdaccdcbccaddcdccdadcdabcdababacadbbbbbbddbdcaddccdbcbadacbdadaacdabbadacaccadddcccdccbbacddababbabacccbbaadbdabcbbacdbbdcbacdbcacbccaccbbbcbdacaabdcccdcdcdddabdcccadcdadabbdcbabacdcacaaacbcabdcabadbcaaddcaddcbccddbaabbabdddabcbddcccbcbdaddddbbcdcdbdcddabcbcdbcabbcbbcbcbacdbbcacbdcaacabbcbcdddcadacbaaccbdabdabbcbacacadcbabacdcbcdcbdbcabaaccbcbddcdccaaccabaabdddccbcaccaabaacbdabdcdbddbbcccbcdcbdcdddddaccbbcadcaabadcbdcbbcdcababccabdbaacdddddacbacdabcddaabdbccadbbcadbabbbbddbbcdbabbccadcdddbddcaaabccbcbccddaabdcccacddcdddbbcbadccbdbddddbdbbbbaaaaccaacbabdbdbdaacadcccddcdacdbdbadaabcacdaaaabdaddbaadabdaaadcaacababccdabdbbdbdabcacccccbdbadaacddcbbcbccccdcbbabddcbcbccdcbadaacdaaacbbcaaadadcaccaddccccaaccaabcbdadaddadbbbcccbabcbadcbadcacdaacddcbdbcccaddacdbcbaccbbbdabddcabcbbbdcdbbbaabdbdbbccadabadcabdaadcbbabbcbadccacbcbddbddccbbadabbaccbccbccacbddccabccaccddadbcccbadbbddbbdcccccabbadaccacdbcdaccdbbdcadbabdacaabadcbbacacdbaaadaadbdaaadaaaaaabccddbdcbcbadcdacabbddaccddacacdacacdabbdaacbdccbdbbacbbdaacdcbdacccacdbacabdccccdaaaddaabbcadabbaacaadabcdccabbddbdcbbcdbadbdabccdcbdbdddbbcbdddbdabaccbdbaccbcabacdabddaacabddbbabdcadbaacbbcaddcabbdddbaacbabddddccddcbddbbadcadbdccbdcdbbcaaaaaabcbccdaabadbadbbbdcaacbdbdcccbabcdbbbcadabadcadcaababcdbdcdcccaccddbbdacabacabbdcbadacccadaacddccdccddacbbbbacdccadbcacaacbccadddbbbbcaaabdbcbdaacddbcbcbcaddaadbcbdbdcaabdcbddccbacaaccaabbdadaaddddbbaddccbcbaccbbdcdccdccdbacbadbcaccdcccdcddbacdcbdabdbbcdbccababcacaacaabbcbdbbccbdadcabbadacadccbbaaabdbdbcadbacbbcabaadccababddaddcadccdaabbcacdaaccacaaaddcccabbbcbddbcddbacbaddcaddadcdbadbdddddbdcbdbdddccaddcbdccadcdbcdacbbdbcbdbbaddbbbdbaadddcddccbddcddccaadbbcdbdcdcdcbbbcabcbbbaaabdababaaabdcccabcbdabbdddccadaccdbdbddaadaadbcdaaccdbcdadcabcabbacbbacaaacacdacadaacdaaaadccddddcdabccadbcdddbcbdccadbcddbddbdaabacadbcaaabaacdadadcdccaabbabddcbaddbbabddabdacbacaadacacbadaadacdbdaabddccccabacaacaadbdaaacdadbacccdcdbbcccdbbbddadccadbdddcbdddddccdbccccdabdadbddaadcdcadcbdacdcbcdcacbddbcacdbcdddcbabddbdcddaccadbdbcdbcaddadbacbddabbdbabaaaaabaacaadacbccbaaaaddbdcdbcbcabcabcbbbaadabdbbabdbacaaccbdccdadcbcdbaddbcaadbdabaaddadacaacaadaddadbcbddbabcaddcdcdaacdcacdbacdbcabcbbcbdaaacabacadaacacbbbaacdcabcaddcadccadbbdcacababadbdabadddaccbccdacbdddbbbdddccbcccabcaacadbaaacbabadaaadccccddddbabccbabadbddcbcaaabcdaadaccadcdddbcaccdbdbbcbbaaaabbaadcacdbbcacaccacbddadcadaaaacaddabaabacacacbacabdabbabdbacbdbdbbabadbadcaaacaacdbccccbbdcaaddcdaadabcaadaabcacccaabcbbccdaccaadbabdadccdacdccbbaadcccacdcbbadccacbddbdaadbcdacdbadbaaadddcadaadcbbddbbababaccbbaccdcbaaaaacaccbcccdcabbcaaddbcdbcadbbabdbdbbaccaaaadccdcbadacbddacaadaccabbbdbdcccbccdcabcddbcdababccdadccaacabcacacabbabbcbabbdbcdaccdcbcbabdbbccccddacdcacbccdccadcbbcdadadcdbadacddaacadacacdddaadbadbcdbadaaddbdcdbbbdcabdacacacdaaadaccbbdbacccabdcaadbaddcabbadcbdcbaacabcdcdcacaaaaddddaacbaacbabcdaabdbaddbbbbacbacdddccdbccdbcaabcdcaddbddabcabccbdcacacdcccccdbacccbccacabbbacbcaadcabbbdcbcdbcddbbacaaccadcabccadcaabcabbabcdadccaabbbddabbabdddbacddabcbcccdcdbbdbbbddaddcbbaadaccdacbbdacddabacccddbcbacaadbdbcbbbaccaadbbabbdadbbacbaccaaacabddbcdcbaacddbddcdbbcdbbcaadcccabcabcbaaddabcbbdabacbcbcdbdcbddcabcdacbbdbaaacabddccadcdcccccbcdcccacadabcaaacaaddcdadbbabddabacbacddcccdccaaaaccdadcddcbcbbaddabdbbbbaccddcbddcbabadddabaacabbdacddcddcdcaccaaadccccbacacabcaddbaddabdabacbabacdbcdcabdbdbbcbaabccbaccdbcbadddcddbaadcbbbcacbabdaabbddabddbccabbadadbbaabababdbcdbaddbcdaccbacbbdcabdcbdabdcdbcdabadadddaaabcbdbdcdbccacbcacbcdbbdcdaddadcdbdbbbcbacbabddbdbacbccbdacbddcabbdcddcdadabbabacdcbbabbbcdaddcdddaccddbddcdadbdbaabdaacadbbdabcaadbbabddacbdaadccbabcddddcdcdbbdabbaadcdabccabdaacbdccbaadcabbbbdddbbbcbbaadccccabacadbcccbbbabacbadadaadccaddbdbbdbdbbbaccaaaddddaabcbabbcdccbaddaabacbabdbcabbbcddcbdabcbcdbacccbddbcdbaacdbdcbdadbddcdddcdaddabcabbcbaadbbccdbbcdadacddbcdadacddcacacbdcabdabacddcccddabcbacdcbbaabaadbbdadcbacbccadaabdcdccabccacccbbbbbabacaaaaacacaabdcddcbbdaccaadbaacaadbacaabbcbbccacdadbdbaddddbdadbbbcdcaacddcdbadccabcddabbcbbaddacbccbddcaaadbdaabbbabadbdbddccacddbdcdddbccbbdcbcbaadbaddcbdacbddbdbaabdabcbddbaccdbcadcddbddbcaaaccddabcaccddaaddcdbddbcaaabdacaaddcacbbbadbadcabdadaacdadbacdbbbabdabcddccaabcacaacacacaadaabbccddbabddbacdccdcbbbdcddaabbcacdcdbadcbdaddcbcabcabcdcaccbcccacddcaadabdacbabcaaaabbbcdbbbacabababcdbdcbbacdadacbcdcbcddadacbcdcccbabacbabdbcddbbdbbbbbdbacbddbbababccddaddddacbbbbbabaabddcbcdabaccdaacdbccdbdbcdcbbcaddcaccadbbcdcddadcbbdcacbbcabcacabcbdccbcbbdcaaacccaaaaaadccacadcddbadadaabbcddabdbadacbcacacdadbdbccbbbaccacbcadbcabbacbdacdcbbddcadbacdbdcacdcdbbabcbcbbcddbcdadddacdadababbdbcddaddadababaccababaacabcbbddbbbcbbaacbdddcddcacbacdbaccddabbcaaaabddadbdbdbacacabcabbdcbcadcdbbaaddaadcbccacddddbbbcdcbaaaacbabbcaddabdbbdcbcbbaaadccccaccdacadadadbdccdaaabdabbcaaabccbdabadbccdcbadabbdcadbcdcaccaadadcabcbabddddacdbdacbabddddcccbddbdacadddabdcddaacaabcdabdcadabcaacbbdcbacbacccadcdccdddbaccbddbcadddbaadbabbcdaccccacbcdbbabcaadaccdccdaccdcadadabdcadbbbcdabbbcbcbaadabaacadbccdcbabbaabdcaadbcddcdabdabaacacddacccaccddcbdaacbcdaabcdddababbbabadcadcdbabdaabdabababdbcdccababccbcdbdcabdcddaddbbcdbabcdadbddbbdadbcbcabbcddadcabbbbcbddccbaaccbbbadaabadaaacdcbadaaacdacbcadacabbdbadabdbcaddacbaadaadabdacaabdabadcbadbbabbbddddcdadabbbdaccdcaacbbbadabdbbdccdcdbaddbddbbdaaccacbcbcdcbcaacccabdbccdaccdcbaccbbcdcacbccdcbccaddcdcaabcadadaddbbbdccdcdbabbbcaaabbabcabaccdcddaadcbcaaaacdddcdcadcddbcacbdabdddbbaabccdbbbdabbcacbdbddbbcabcaacacdaaabdcbbdbaaccdbcbbdabcbadcacdddbbcaabbbaadbabbdddbbcdacbbcbddaddbddcadddcaacdddbccbcdbabdcdbbcacdabcbadaabdacddbadcbadcdcccbaccacbacbadabdbabbdbaabdbbbbdbddbbdacbbdcbbbabcdbbbcbaaabdccbccdddaaabaaacdadadcdacdbddaabaabdddcbbabaaadaabdcaaaccaabdbdacbcaacaaddcdaabbbcbddccabbdcbbbbbdcacccccddadacaddddacacabdaaccbdaddbdacddcacbbdacddcaacbcbcbabbcccddabcddadcabacbaaabaacbdcdcbbdcbbaacdbbdbbaacbbdbbdbdcccabababbbcbadccddbdaccacadbcdbaccbadabcacaccddaaaadbacaadbddbbccbcbacabcadcadcbdacbdbdcbbbabacdcaacbbbcddacdaabbddddbdbcaacbacdaabcbbbcadabccdcdbddcacaacdddccabbccdddabaadbdbbbdadadcacaacdddabcdacddccdcbddacdddbbbaddcddadbccbdcdcccadacabbbacbcabdccabcadbaccbdbbbadbccbdabcdacdacbbadbccbdadbbbcbcdbaadccbbabccacbabbaacdabdccbcddabdbbacdbaddacaacbaadbadacaaaabdadaababbacbbcbcadddabcdbccbbbbddaacacbbdcddabdcdbaaadbaddbdbabcadbdaddbbdcbdbcabdddaacdbaabbdabbcaccbcbbddacbbdbadabaacabcabdaadbbdacbbcbabddddcddbdbbabacdbddcdbddbdcccbdcccabbaadaabbddadbddcabccbbbbbacccdbdaabbababaabcaaadacdbdbcbadbcbccdcbdcacbbbbdbcaaaabdabdaaabcdbaccdaacbdcbdcddcadaddcbbcbcacdbcadadabddbacdbadccacdacbaaaddbbdadbbbbdcbbdbbcbcdadcaacdbbcabadbadddaddbbdadcbddadcaabddabacbcacddaadddcbdcdccdcdcdaaadddcccaadbbccdbcbbacddbbacbcdbdddccbcbcdbdccccbabacdbccbccbdddacdbbcaaacaaabddadaaadacaacddcaccabdbcdbbcaaadbaadbddbcdcddccddbcacbabdcbdbdbccdccbaadddbcbddbbccdbbabdcbcacbcdbdcaddadbcccbbdbdabdddabbaacbdcdddacdcabaaadbbcadcacdcbddbacbdcbdabacabbdbaccbcacdbdbaabadbccdcbbddbddcaadbdddababbbbcabccacabbaccbcdcddbdabaddcbcdcccbadbacbbacabdaaadaaacbdcbdcdbcdcabcabdcdaaddacaccddcddadbccdcbacacbdccaaabadbdbbdabccccdbaaccdcdccaaacabdbcbccaabdabadccbccbbaaaabcbcbaacbcbccbdbdddaabaadacbbacaaaaabcadabcddaacddddbbbaacacbcabbccaabcddabbcadbabcbcdaddbdcbdcadcbccbcaccddcadbddbacbdccccbddbccddaadbdcbabdcabdacdaaacadabcbcdcbaaccbdaaaabbbbcacbdbcccacaccbbcbabcdccaacdabaadbadbabadbcdbbdddaabcabcbdcbcabbabbacdacdcacbcbbdbddbdaaacdababbdbdcdabccddaaccddccaabcabcbbacabacadbccadbabaacbbdcbcccadbbccbbbaaaaaccbbcbbabbbaddadcdbbcabbcbccadadcbddddabcadaacbdacdcbbaaccaabdcdbacdcabcaacacbcdbcbaababdcbdaabccbcdbabcbdaccbbcbcababdbbcbdbbbadcadcdccdbbcddbccbcbdbcbcdddcddcababcdaddbbbbcdabcccbcccabcaabdaabadbbbdcaabbdddbadcabddaabddbccbacdccdabacbcadadccdbacdaabbcbdaaacbdadddabddabdbabbdaacadbddaabbacabbbbbddaadcacbcdadbbddcdabbcdbabcbdddbcaddabacbbaccadcdadcbcbbcbdcdcbbcdbabacdcdaadbbcdbabbbdcdbcddcacbcbabcdcbdcbaadcdccdbdccabbbaccacdcabacbcbadadadcaacacbccbdaacaddccaacccdcadcbddababbcbcbcaccacccdaaadcabcbccddaccacadadcacddbcdbdbadccbbdbdaaabcdcbcdaadabadbdaacdbccabdabdcbcadbaababababacbaccbdcbbacacbaccdbdaabdcbbdbcabaccdaacddacbbadabcbccddadcbabbcaaaababadaacdbccbbdaddbcadcabdbadbadaaabdacdbdabdcbccccbaddabbdcacbacbbbbcabddbcbccbdcabadaddbdaddabdbccadacabacbdbadabdabbadbdbdcbcbdcaacbcadadbcabddacccddcdbcddbdabccbcbbcadbcbcaaabaabcdddbadbbdbabaacbacccbbabdcbddabdcdccaddaacbbcbbcbacdaaaaabccccabcbcbbabbbdccddaacddabcbaaabdaadbacadddbcbdbacacbcbdcbbbccdbdcdcccaabccacdddccabdbacabccccbabdabdddccadcaccdcccddcadcabdabcccabadcddddcbbbcccddcacaabdacadcdbdaccdbacccdbbcddbdddaddaadbbaabcacbdcbcdabcdbbaabdbabacbaddcbcddbbcccdadacbdcbacdaabcdbccbaaaabdabbdaccbdacccbcbbcaaabbcdbadaadcaaabadcabbdcaabbdaccdbdbddcdcccaabbadbaddccdccdcbacaaabdcccbcccbaaacbddadbdabdbaacddbdbcdcbacddacbadccbdddccdbacbbcaabbcdbddbcbddbcaadccaaadcadbcdabccdcdccdbbcddaddbbbddacadaacaaccacdddabdacaabbbcccadbbbaaaccababbbbbabcdacbbcbabbcbbbdbbcbcdcabadaaabcddadcdbbbacbcaddcdbacaacddbcabcaadbaccddcacacaccacaaabbacdcddbbadadccddacbdbdddbabadddbcadddbbcdbbbccdabcadbdbdcdabcccaaabaadddbbabbcdaccddabbaaadbcdcdcbaddccdaacabbccdaabbbcbbdaadabbbdabbabacddddbbbcbcddcbcadadaadbddabdbdbabbbaccbcdaabdadccbccccbadcacbbabdaaabaaccdbdaaacbcdabacdabacbdbdaaddbdcadbdacdbcbabbdaacdbdbbbabaaaadabacbbbcdcbbaadddabbddbadadbccdacdbacbccbdcbdddadabddbcdbdcbaddbbbbbacdaabbbdadbadbacbbaccdcdddccdddcbcbdbddaaadaddcbaccdadbbcacadccddcbccbababcddcbaabdbdaaabaaabdcbaccabadacdcdabbcaababdabccccbbcacbbcdbbddabdbbdabdcabddccdcdddbacabcbacbbbdbdddaddddabaadbbdccdabbcaaaacbabacdccbcabadcabaaaabbdbacbbcaaacadccddbcbddbabccabcbbdaccddacaaadabacbcdacdcbaadbdbadbcaadbccdbacddacbcdcaaabacaadcdddbbddacaabbbdadbbdbacabddcddcbaabddaabacaddacdacdbbaccdddbddbbabacadddbdaabacdcdaccdbaaacddacbbacdbddabaabcdcabbdaaaaabcabbccbcadbbbadbddbbcdacccdcdbbbdccddabadacaabdcabcddcdddadccaacaadcbdaadbdddaddacdabdccbbbdacadddadccbabdabcdcacabcddadbdadaacdbdcacccabacdbdaadcdcbbdcbbbaacdccbdbacbdddbacbaaaabadcbbccdbddccadccbaadddddadabbbaacbbbccdccdbdccddabbabdbcbbaabbaaaaadcbbddcdbcbabdbccacabcdcacbacdcabacadddcabbabbadabcdbdbadcccdbaaabcdbdcbacaadcbacbadbcdddcbdacccbbaabccbbdcbcadabddbdbcbcbbbdddccddbcbacadacbdacdbabdcdcdcccbcaaaabcddcadacccddccdaadbdbbbccccabcabdaccccdddbdaadadbdcbdbdbaabbbdbaaadaabaacadbabbbbcddccaabcbbbdabcaaaddaccccacadcaadcdbabcdbdbdaaccccacccbcaddacaabbacaddcadaabbdcdabcdbccabcdccdddacadacacaacdadaccdccdcabaccbaadddcbbadabacaddddabdddcbbaacabaddadbcbccbbcbaccdcbbaabdcacddcbbdccdcacddcccdbbcddbacdbccabdadccacdddcbcccdbbaabdccacacbdcacdcbdcabcdcadbabcddcaddacbcdcddaadcddcbbdaaccaadcaccabadccabbcdadadccdcbabbaababbbdbbdaccdbbcdcdbaacbcdbacabbbddabdaaaddadbaabccdacdddbacbacbbddccbdddabdcbcbdcccabbbbbadacdcbdcabdbbccaaabdbbcdbacbdadbaddccdcaddabacbabbaddccdcdbacccbbdbdaadcdcbbbcbcdddddcbdbccaaaddcdacbaddaadcacacdddabbbbdadcaaaddaadbaddcddcdcdddcbadbbadddbdcbdccbdcbaacccbddddadadbbddbcdacddbdbbbcdcabaacadcdadcdbddcbacbbbcabdddabdddaabbcadcadabbdccabcbdbbddcababacdcccddcbdaddbdcbadaacdccacaadddbdbccbccbcdcdbcddcdcaadaddbabababcacbabdbdbbacdbbbbadbdacccdbdcaddacbadabadbadcbcbbdcbcaccccdadbbabbbbcaaabadcccbdbbabcbdcaccabbdcddddbacbdcbdcbdabcbadccabcddadcdcacaabcabcddcdddbcddaadbacbbaaddcabcabbccaabbadddacabdacbbdcabdaaccbadddcbbcccccbabccabaaabdcbbadcbadacbccadcaabbddadbacbdbbdabaddabbaddbabacdabbababacdddcddabbadabdaddbbdbccbbcbcadaaccdcccdacacbccdddcdaacaddacccdadadcdbdbcbccdabdbacccdddbcbabdcbadcbdaddabcccbdcacdbbdabbacddbdddddbccbddaacbcbbaccbdcccabcaabbbccbbdabdccbdaacdcbcddcbbcdcdbbabcdacbdabadadabcbbddaabcdbacdaadddccdbcdcdabbcbbdadcddbadbaabdcdbdbabdbccbbbccdcdbcbaacdddbabbddbdcadcbbabdccddcbcabcadcaddbcacdcccaacbcbcaccacdbdaacdaccccabdbdbdcdaddaadccddbdaaddaaaabbabbaaacbcdcadbcbcdcacbdbabdaddadccdcdbaaccbdbadcadddcccdcddbccabbddbbaaadaacacbadbbcbcdbaddccacbcbdcabaaddbdcacadbaccbcaacbaadabbddaabbcaccdcabbcdcbdcbadcdbaabcaccaddddbbcdacabdbdbdacddccacddbdaaaacacbabbdccbbacccbcabdbbadccbbdcbddacadcabdbdbadcaabadccaccabcbddbbdcbdccdcacdaccaabdabaaaaccdacccbabdbcbababadbcdbcaacabcacabdadccdacbddaabbddddcabacabadbaacbdbddbdbbadbcbbadbabbbbbaaabdcaabdbcacbabdacdaaddbcacaccdadadcdbcbdbbccbdcdccdbabcbcdaadbdbdbddbacadcdbdbbdcadbbbbdbdaababcdaacdbbcadaadaabccababddbccbdcdcbccaabacdccdcadbddcbcbcbccdacdabcaabadacaaddbccddbcdcddabcdcccabacddbbbdcbccdaabadaaabcadddcdaabdbcaaabcbccbcbbacabcdadcdbadbccdcbbdccccccacbaccabcdcadabcadddbddbdabdbdccbcabcbacdcabcadcdddacbdaacdbbbdcdcccaabaadcdcbdbbcaaddabbdabbbdaacaabdbdacbccdaddddacbbdbcaccbacccbdccaaadabbbaaaabcddcbadcccacbbacadbcccbadabcaccdbcdabcccaccccddbdadbddbabcccdccaabacdbdccdaccacbcbabaadbaadccacccddbdcbddcbcaccddaaddbbdbccddbabddccaaccccabcabbbdaabcabdabcdccbaadabadcdacbdccdbbdcacbcabcbadabbddbbbbbccadaddbabbbcdadccababdadaacbacdcdacaabddcbbaacbbcabbdbdaabcabccbabbdddabadcdbbddaddaaacdcdabbcdcbacbccbbcadabaadbadadcdcaccbcadbadbddbdadbcacbcadbdcbdcacccaabacbabddaadcbdaaaccbccbaddadbbcdddbcddbbccddabcdccdcccabacbbcadcdacbbbdddcddbaabbcacbcbcdacdadbcddbdcccabdbbaddcdbbaabbadacaccccabdbbcbaabbacdaccbcdbaadcccdbacaccdbdcbabdcdbaccbaddadbcdadbbbaaacbddbdcdadaadddddcddbabcbabddaaabccadcbbbdabdcabbcdcbcddbabcbbadcdccabbbccbaacdadcbacbdbadcccbbcbdadbcbabcdcdaacbcccadcdbaabbdcdadaccdabcdbcabdbaacdacaaadddaababbacbdcaaaccdabdbcbcbaddbbdcbacadababddcdbcbccdccaabadaaccaaaadbbbbdbdcbdcdbaadbcadddbdaaabbbbaccaacdadbdbbdddcccadacdadcbdcacdbdadcbdadcabcbadabdbbcbccddcdbbdbdbcdaacdcbcbdcaddaabbdcbbabbaddbacdaacdbdccdaacacadbdcadbcacaaacddcaccbaccccadbacdaabacaccbacdcbaddddbcbcbcbaccdcacabcdddaacdaccddbdcbdbdababccbabacccdccacdbababcaaadddbbaadaccbddbadacbdabbcdcbdbbbddbaccbcddadabbdaadbcdaacccbddbaacccadbccbbdddabcacaaccccdcbaabbbcabccbbbcacdaddaadababcadbacabaaacdddcbacdcaccbadbcddaadbadbbdcbcccdbbcaaabbcbbcaabbbddadcdcccbacabbbcdabdcabcdbcbabcdaddcbbbbdddacdaadadabdbcacdbdadcaddbdbaccccbbbbcdcaaadbccbdcbccacaccadadbacccccddadbbaccccacbabddbcabcdaccdcbcbbadacaacddaccacababccdabcbcdddddaaaabdbcddbacacdcdbaaaccbcbdbaacbdabdabacaaddcacbbdbbaccbdabdddcdddcacbaacacadaaaacdbbbbcbabcbccabaabaaadcbdacbbbbcbbacacbccbdacdaaccacccabbbababbcccaaacbacdacadddadcddbccdaabcabdcbadccbaadbdacbaaaccbddcdcdcbbdacbdbdccdccccbaadaddbdbbbababcbbbdbdccdbaddcbbbabaabcadddbadabcbadccdadacaacdbcbbbdaacacdbabbbadcdbbbcdaaccdbaccaacdcbdbadcacddcadccbdcbdaaddaacaaacbddbbbbcbdbdbcddbadbcdaccaacaacbacabbaaadaaccddcaaadbccaabbcdbcbbaadacdbbbbbcaddcdbdddaccccccdaddddbbdaabbcaccbcaaabdcccdbadaacacbdadacbbbcaddcbbabcdaaccdbdcddaaabacdbcbcacbcbdadcabddbccbcabddcddcdddcbcbdadcadbcbacabbcdadadacbabccbdaacdbbdddadbcabacabacdbabcaddcbaaabaddddccdaadcbaaacdcdcaadcdaaadaadadbcdbccbbabcdccbccccabbaabbccdbdabcccaddccaddcaaadaccdbbacdcadcdbbcaacacdbcbbdaaabcaabacadcdcaddddaccabcabdddcbdccaccddcdadddacbacdaccbdbdccacacbdaadacdbbbdbcccaabdacbabdbdcaccabbcaacbddacdabaacabbdbbbbbbbcaabbccdccbccaddbaabdbbabcbccabdbddddadcbccccbdadccacccadacdbbdbcbcccdcbacdcacbdaaddbdbbbacdbaacdbbcacbbaaaadddbccddaacacdddbcbbbaaaababbcbddaadaccadbcaabacbacabdadcddbabdccbaadadbdccbccababbccdddbbbdbbbccabbdcaaaccacdcddadbbbddabcaacbcbabccacabbaabbaccbccddcdbaddacbcbddccbbadddbbacabaddcdababddcabbccdcacbcddbbcaccdacdddcbbcbcadcbcabccdabcaadbabbbcbbabcdabaacacbadbcbcdaabaacdbbdaabdbdaddddbaddcabbcddbabcdcbacdcbadcbbacddcbcccbacacdccadbbabdacdaccdbaddaccdbdcdcbbdbaddcabaddbabddaabdbccaaddbdacacbdbaccbbacdbdcdbacdabbddcdadacdccdabccabababbabaacbadabababdacbcdcbbabcbdccdaaacddcccadaddbdacaacccabaddaaacdcadccbbabbcdcadcdcbabbadbdbcbcbccdabcadbadcbccdbbbbdabcbacdadbbdbccbaaaddabacbcccdadaadbcddccabddbbadaccddadaacaaddadaccacaccbacbdadbbdbaacaacacaddcbdbcdbdaacbdbadcacadbcdccadbcbdcacccbaccdcabbcccccbaccacadbbaabcbcaaacadacaacadccdcabccdddddddbbcadaabdcdccdccbcdcdaacaccbcdcbaaaccaddbdbccdcdbcadaabdbcabaabcbbaabdddaddbaacabcabddabbadabbcacaccaacabcadbadbaacddddbbabbdacaaadcdadbbdaaadaddacdcccabddddbddccbaccddcbaaddbabbbdbabbaadcdabdcbcbbddddadddbbdabdcbcbbdddbddbddcabacbbcaacccdcbdbadbadcbddcddcbadaacddbcbdccddbcbaaccbdcbaccbbdbcdbaaacdcccdbddbcacdcbdaadacaccacdddadbbbdbcddcbbcbdccdbccabcccabdbbdbbcdbdadbabcddbdacddbcbdbbbddccadbcacaddccacdadbacdcabdadbbabaaabcddcdbddacacbcbbaabacddabbbacacddccacddaacaaccbaabbbabadccaaccabbccbcdacbbaadcddabdcaadbbdcabbcbbbcadbdaadbddcdcabaaacdcbcdddcddadbcabdaddbbdbdbcdacbcddbcacdbbacbbbdcccdbcaabcbdaababcacabbadcaacdbbddabbcbbacdccbbbadbbddaacababcdaaabadcdaabcddcccdbbbdaadddbaacdbcdacabdaaadacaaddaccdabaddbccbaacaabbbbbbdbaadbdaddadbccddbdabbdadccddbddcbcbcababdbaadabcabbdaddccbddcbbaadbbbdbcbbbababcccccdcadcccdccacabdacdbbadcbaabdcbbdcabcacacbbaacdcbcdabbbacbbcbadbccccbabaaadcdcadbdababcdbcbaaaaddaaccbabdacbabcdbbacddcbaccaadcaaabbdbaccdbcdcbcbaabbbadabdacadcdcdadbcccbaaddddbaaadcacdbccbaccabacaaccabdadaadabcadcbcabbadaaadddbabaccbcadddcdbddbbcbbacbddbcabccbccdaaabbaccabbbbacadbdaadcdcccddaddcbbdbcbdcdacdcbbbbbdabcabcadbacdcacdacadcbacdabbcdcaaadadccdcadbdccbdacaaacdaaddbccaccadadccdbcdcdabdbadadadbacddaaddbbadbcbaaddbaaaabbdbadcbcdcbdbdaddccacbccdacdcccdaccddcddcbabbbbbadbdbaddbcaccbdbbcbbbbcdaddccbbabacacabccbbbcadbcabbdadbdacccbdbcdccadaccbccdbcbacabcabbcaccbaaacadadabccbbcadabcdcbddbacbbcbbbbacccadddaababdacbaadddbbcbbbbcccadcddabbacbdccccaaaabbcdcdadaabcccdccbcacaabcdbbabbdaaabcdbccbddcddabbccbdbaddcadbbddacacdddbcbdaddaddaddcbccbaacabdabadcdbbbcaaddacbcdddcbbadbaadbbcabbcdacbabaabdabaacddacacadbcacbacaababcbdbdcccdbadacbbdbcdcbdccbccaadaaccadbadadaccdabadcbbbacbacbaabdabdcdaccabaaacbbddbadcccadacbbcbcbbbdcbbbadccbdabacabacabbbcadcbbccdcaabbabddbacaadcdaadabaddbcaabcadadcaaccbaddcaccddabccccbbdaabacbdbdaccddcdcaadbdaabddadbcbabbaadbdbdaabcdabdbbcdbaababbbcacababadbbbcdbbdaaabdcabaccdbbbbddaadbbbdaabcabcccaabbccdbbbcdccbbdacbaaabbabbbabdaadcadcaacbbdbadbadcdababdabdcababddccaddadbdaddbbdaaacaaadcddaabbaabaaddabacaddaccaabbadabaaadbbcaadaabacddaaacddbcbbabdbcbbbacbacbddabcddddcddcdaaadbaadbbbbcacbbbddadbadcbabcbadbdddcdcbdddaabbdcabbcdadbcacdbacccbbcaadacbcdbadbabaddbacbcbbbcdbbddbbcdcbadbbacbcdbdcacacbbacadadbdccbcaaddabdaaaabdaadddacdbadbcbcacbbddcbbdbdbcccbdccbbbddbdacabcaadabdbccacacdbcdcbddaabcbadabacbddcdaabdbccbadcdabcbcbdbbccdaacbccdddcbccbcdadadcbddadddccdcccdaaacaddbbdbaddacddaaccdacaddbcbcccbcdcdaaccbaadccacbddccbdadddbcdccddbadabcacdccdabbccdcaacddcdacddcaddcbbcddbbadabcbcbddcabcdbdddbdaabaabdcccbdbaaddadabdacaccbbbdcbbccbcddaadacbbaaaacbadcadbdbbabcacbdbbaddccabccbbdbdacbbccadccbccbcababcabaadbcaabbaadadccadddbcdcaadcacdcdabacaddcadcaabcdcbbbcbddadbccdbbcccdaabacdadadbdabbabddabaddabcabcbcadbddcadcccbddddbbbaabdaaaaccabdaddcbdaabcadabacadbcbddacdcbcbbdbdaadcbbcbdacccccdacaacdcdddbdcbbcbbabacabdacddcdcacbcddacdaabbabbddcaddabaadcdcacadbddaabacdacdcdbdcacacbdaddabdddbbcbbdccabcbbadbadbbcdadbdbbabcaacdccdcdcbccdacbcabcaadaddcdbbcabdaacbbbcccbaadcdcbbaccbddcabdaccaabbcbbdacaccdcddddbdaddcdbddbbbcacacbbbabccabaadbcddbccbaaadacbbbccbdcdddbaacdcdccddbcaddcdbbbbbdaaacdbdbdbcaacaddcbbbbabdddbabdbdccddcdbbcdbaccaabadbaabddaabdadbbccbadaddccaadaccbbadbdddacabdacabbddabdabbcdbdcbacadcabdbcccaacadddbccaacdbcbcbbaadbdadaccabadcaccabdbadcbdddbbdccbaadaaababdcdbcadbbadddbdabddbcbcdbcacddacbcdcbbcdadbbdccdcdcababbabcacbdaddaadaabddaabcacddcdccadcacaaabaccccbbdcdcdbcbabbccacdaadaadcccbbadccddddadcdbacadabdcabddcbbddbbaadabbadccababbacaddddcddcaabbabdbbbddddacdbdbbbbaacadcbccbadbddacbadbdcbadacdccbdbdbadacdbcaddbaabdcadcbbbadaabdabdabadcacbdbccddbcdbcddcdccbdcacbcccabbadabcbdaddccccbcbddabcabcbcbaabdbcbadacdddbadabbcdacccadabcbdddcbcddadbdbdbcadbababcddbaddccbdaacbccacacabddcbdaaabbdccaabcccadbdcddbcdcbbddbdcbdaaacdbaaaabddbaccdbcdacaababbcdadbcbcdacbdcabddbabadadadabdcbcbadcadccaacaccbadabcdbaacabcdcaabdccacbcbdacdabaddddadcacdbadcbabaacaadaccccacaabbdcccdcadadcdcdcdabadbdacbcccacdcabadbdbcdaccaaaacbdbdbabbcacbababdacaaabcaadabcabdbabbdabdabaacabbcaaacdbabbdbbadbacbbbccbcaaccbbbaadabbbaacdabbdddddbadacdccdacadbddbdadacaababddbabaababbaaaadbbadcdbcabbcbcabaccbcbcbabcbccddbabcdbaabddabacbbcaccdaccccbaabdddaaadbdcabcdcacadbbddcbacbbccccadabacdcaddbccdacaaccccdcccacbcdcdbdcacacdbbcaabddbcdadbcdbbdcddbdcddddaaabbbcadaddddcabddcacbccbcadddccbddcddaaacacbacccccbdcccaabdddabcababdcbdddcdbdacacaacacbbdbdbcbcaadaddcdbbdbcdabadaabddcccdbcbccdddacbbddbcabdcccddabbddbaacccabddcddadacbadcdbadaadbcbcdddbdadbbddddcadbdccdaddbdbcdbcccbdbbdaadcacdccaadabaaccbdcdcdababbccaabababdcdbdddccdacaccdaccacddcbdccbabbaadbddbccdddbbdbbbacbbbbcccbdbbdcbdbcdcacaddbbadbbbaabcadcbaadccdbddacbbbbcdaaaddbdbcadcbcacbbcccbdcacddadbccaabdcccadbdcbbdddbbbbbabaacdcaaaacbdbabbabddbacabbbbccacbabdddbcccbdbadddaccaddccaabdadddbcadabcabaabadaaaccabdacddcaaaddbbbdcaccbacabddccaccacdaacbcbbaccdbddabcbaacababdadddbacaaabcabadacccaabaaaaadbabaddaccbbcdacbdbacadbaccbcddddcbcaabdaacaccabdababbbcacaddccdbccbaddbdcbcdacdcabaaacadbadcabcccadddcbcbcbdbdcbccbbbbbcbdbcdbdbbaaaabdddaaaadcacaaabddadcacacadacbabcdcbcaabbcbbaaacacbdddbcdaabdbaacabccadcddcadababaaccaacdbaddccdcbdddabbaddabaccdbbdbbbcbdbdccbaabaccdbadbacbdcbdcddbacbbbbbcbdbcdccadbadcdddbcdcbbdadccaacbacaaacbbbcadadddccacbccbcddacdbaaddcdcacaacdbccabacbcabacddadaddbacdbcbdaadacccccacacbcdbaaaccbcdcdabadccaacbdaaddcdcdabbccccadabdcbcccdbddcbdaddbadbddaaaddadaadcbbbcaabaacbbadcccacbadabddacaddacabbcccbbcbcbddbaadbbcdaccccddcbddcaadddadbcddaaacccdbcbbababbbaddccdddcdddcbdbdadcbcadbcaccdcbdadcadcccdddaddaaddbacdbacdddbaddcdbcbcacacdddbcccbdcadaaacabadcabacbaddcbbddbbdaabdbaaccaaabbdcbbcbabccababbbbccbbdaaaabbcbaaadcdabcbbdcbbdbbddcbbacaababbadbdadabdabcacddabcbcbdabbdbddaaaacaaaabcdbcbdadccbcdbcbadaddadcadbdcdcbbaaabbaacadddbaaaadbdaccabadaddaadbbcdaabcdccccdbcbdcacdaadbdddadbbcbcadadccbdacbdbdacddaccdcbdcabbbcdaacbdbbbbcccadccbdbbcbaabbabbabcdcacadcbabbaacbaddcacadcccbbcbbbbbbaacdbdaaddcdbacbcbadbdbdadddacaddbcbbcbacaadccdabcacadadcccbdabdcbcdccdddccacddacdcabbabccbababcdcdaaadcbcdbbcbdcadcbdcdbabdabcbdadbbdadccdbdbdadcbbaddabbcbabacacaabcacbaadcabbacbadacaddacdabcbcadadbcaadaaaddbcccbccbaacbcabdbcabddbdccdbcbddaacbddcccdadabacabcbdcdabbccacbbccacbcbccacdcbdbbbbbdcbabadbdbaabdbdbdcbbcccbbdcbbddbbccddadbbaaaddccdaaccdadcaadcccaccababaaaacababcadaacdbacaaaabcaadccaaddadbadaadabacbaadabdccdacdbddbdddbddaadbabbccabddbccbaaabcacaddcabbcdaaadccddacdbcaabcacccbddcbbaacdbdacdaadaddcacdbbddbddbacabaccbbdabdcaddbdacadabcccbddbbdddcccbbdadddabcbcddacdaddcddcabdacddcabaddabcddcbbdcadacdacbddbdabbbdaacbdbcccabbacbbdacbbccaaaddbcbabddaaadacdccddabbaccabbccbddabdbaddadcbbbdacddbadacdabcaadbaadadaccdccdbdbacdacdbcbcbcbbcccccbbcabaccdccdddbabadbcddbbdbacabcdbbbcacbdaadcadcdbaaadccddadabddabcddddbbdcbbddbaabcbadababbbcbcdadcdccddcdccbabacdadccadcddcdaadcbadddbcdcddabbacadcbabdbcaddaddacbaddddabcaabddcccdcddbdbdbbdbbbdacdbadacdcdaacdbdcbbccaadacbaacdaccbcacbbaccaddadccacbbadcbdadbbadbddcaabddbcacbbdbddbcbdbdadbdacaaabcccbdddabdbcdcbcdbcababdbdcccbdabdcbbcadbdbbaadbadcaacdbdadddccbbcaabbddcbddbcbbddcccbbcdacdcbabcbaadbbadccacddaaddbbbbccbadcbbdcbbccbbbdacdadddcccdcbcdbccadbcdbbbcbbdbbdccacadddbcbaabccaccdddbcdaadcdcccabcabbabacdcdccaccbccacbccbaabbbbaccccadbbccdcbbcbccbbcadacbabbdadadcbabcdccadbadbabdcabcdcaaaacabdbadbdcbbccaacbdabdbbcdcccdcdbbdaddbddcbcbdbbabadbadbacbbdcccdcacaaabdbbbbadcdccdabcbbcbadccbbabccaaaddbdcccdabbaacdcaccadbcccbbbbbbdbbcbcaccbacadcabcdcbccabcabdbabdcbdabdacdadbbadabbdbacddadadacbabbabdaddbdbbbabdbbbddcaacdbdadabddbcbcdadaddacddcdbddbbabcbbbdbddbbbaccdcdddcdaacdbdacaabaacccdbccababcddaaacbacaabcdbddcbcbdabcccbcbabadcbdccaccbaccdcdbaaabbcdaabacbcdcbabdcbbcdbbaaaabdccdbbcddcccdcdbccdadcdccdccddcbdbdddcbcbadcccdacbcadaddadcbaaccbcbdadacbbcabdddcdbbcacadbcdcdddbdabdacacdadbddcccdddcadabddbdaacddadbdaadcdaaddbdabcaaddcdcadcabacadadcddcaacccddabdabbcdcbcbbaddcabacbaaadbcdbbdbdcdcccaacaaadbbaccbbdddbaaadcccdaadbbdaacacbdccbbbdbdbbdadbcacbcbaadcbddbdcbbdcdaccddacacddaccddbabbaabbbbdcbbaabbcabcbdcdccbdddacacdabccbbcddacbbbaccddbabbaabcadbbdbdababadbbbcdbdbddadaaadadadbacabdcdcbdcabddddccaaccadbabbabbdbaaacdcadbdcacdcabaddacbbdacdabacabdbddbbbacbbdacaaccdcbaccdbdadacbcbccdcbdcabdabbadcbabbccdcccdcccbddadadbdcdbddbcddbbdcdddadcaccbdacbcabdddbbbdaabbbbccdccbdccabcbadcdcaadacccbbdbcbccbddacacdaccbadaccbbcabbccddbadddbcddabdccbabbdcdaaaabadacdddadabdbcabdccdddbbcdcbcaccbddddaaccababababbdaddabdaadbabbbaaccdbcdccadbcaaadaaddaaacdcabaabbabbabbcbdaaccacbbbdbaaaacacdcbabdadcbdddbbddabacddbadcbbcdbadddbbcdbadbbdcdabddbacbabbdaadacccacdbbaadacabcbbdcddcacbcacccabacddbbdadabbbbaadbcbdabababcaccdcbbdcbcbcbdcdaddbaadacbaacaadbabaacacddbcabcadbaacbccddaacbbacbbcdbbdcccacbbddbbdaaccacaaddcccacdbbaadacdbddadcbaaddadcdccdccbcbacccdcdaaddccacadaaadbacdcdbcdbdcbaacbdacadbbbbaabadcaadbadbdccbbcabacdbcbcaccccabbddcbbbbaaacbabaadaacaccaaccbadcabbbaacbcddacbcabbabbbabacaacacbbaadbcbdbcdcadccdcbcdcbdabacccdbcadcbddcabcacbaaccdbabddadbdbcdbadabdbdcccaadcaccacccacbddbdddbdccaadcbccdcdcbbababaddadaaadbccabdaccbacbbcaddacacadaccdaddcbcacadccabaccbacadcdccddadbcbcbcabacdcdcccadcbbdcdcbcbddacabadabbbcbbbdbabacddaabbabaacdccbbdcdbcbbbabbdbacdbccdbddcbddddbccbbdacbaadcddcabaadbcccaaabcdcabcacaaaccdabbdbaccdcdabdaabbdddadbdaccacddadacaaaccbdacbaababcaadbacbdcabdbabdbbdacdcccabcdbcdcddbbdadadabbdbbccaadcdbcdbddcdcccddaccaddbcadcdcadbaadaabcbcbddbdddcdacbbccddbdabcadbbbbdaaadacdaacabbddccbbacadccddbddccccacabbabbdddcbdbcbabbaaacaacbccbadcbaccdbbbadabdbccaccbdbbbdaddbdbdabdbcdddaddcbcdbaaccbcadbcacbbababdbcacaccacabbabcbbaddccdcdbbcbdabdbaaadbabadcbdadcbaababcbcbbbadddbcadaccdbacbabcbaccdabdbcbbdbcbabcaddbcdcddbabcdaaccdbabccbadccaaaabcdacaacccbdbccddddabadabbccdbdcaccdacacacdbdaddddccacbcaaacbcbcdaadcbcbcdaabdabbddccaaabbdcddbadadcdaacdacdbbcbcdaaadcdabdcccbbddccbaadcbcadcdccacdabbcdaaabbddadaabccaddcacdbccbbbcaadacaddbbbbddddbdcdcdcdbddbccdbbddbdcababadbacdaadbbdacdcbcdbbddbccbbadccddabdddcccadcdacddddbabcdaccccdcaaabacbdcabacdbcaddaabbdccddcddbdddbbadadddadadbdbbddccbadddddabdcbacdccdcccaaaddcbcdaabdcbccaccbbacbcaadbdddbdcdabbcdadccbadbadbdcccbdcbbdccacacbbdcccadadacddcdcacdcdcbcbcaaccdcbbababccccaadbabbbcacbbdbdabaaaddddcdddaabcbcaacccabbbcddcaddcddadcacddbdadccaabcdddcdaddbbcaaacbacdaadabccccccbccddbddccbacbacdcacacdddbbbbacabaabdbcbdcbaccbaddcbdcdadccacbbdcbccbdadabdddaabdadddcabbdbaaaaabdddbdacaaaddddbbbdaabaababadddddcbbaccdccadadcdcacaaddacaacbccdbbdbcadabbbdabcbaabcbcaaccdcabbacbaddccabcccccbdabddbaacbaabdcaaadaadcbcdaddbbcbbdccbaacbadbdbddcdccddccbabdcdabdbcccddbdcdcbcbbacbbcbdbcaaddbdccccdaccadcbacabbdadbdbdccadacbcccdddaacccbaadadddadaaaabacdbdaccaabbdbaddcdddddddcbdbacbbcbdbbdddddcacdcdbdbbbacddabbacabbadaaacdadbccdcbaaaacdbdcbabaaadadaddcbbdabbbddbcbcdcabacaaacbadbdbdcbbccbabcccbcbaccdbaaadcdcccbacaaccbcddabadddaabbbcacdcdbbccbacabdaacdddbcadbbcbddbbcbcdcdccaaaaaaddbdcccddcaabbadacacdbdcacbcbaddacdccabbdccbbdacaabdbbbbdaccbaddbdaaabbbacddbabbccdbaadaaaabcdabadaadbbdbdcdabdbacabcabdcaaacaabddcbdbabccdabacdbcdcddadadaabdbdccabcbbdbcdcadbaddaddcbdbddbacdbabdcdbccdacbabdddddaaddbbabcacaaabcdaabddcaaccabcbbaabbddbbacaccccbdcbdcacdcaacdabccbacbbdcadaabcbddaddccbcabcaaccadbabadacadccbcabcacdabcdcccccccaddaddabbddbcdcaccaaacbcbbdddadadcddcccaaacbaadcbbddccacbdbabdcdcccbcbdcadcbadcadcacdcccdcacdcddbdcdabddadcabccbdbabbaaccccdbdbdcabdccdaacdccaabbccbcacbadabcadaccaadacaaccabdadccbcdcaddbcaddddaddbacacdbaabaddcacadacccbaddacdacddaccbadaabdacccdcdcdaacbaddaadabbcacaaddcccccdadbacacaabcddaabbdaabcdbdaadcadabcabbbccdcdabaabcdaacbdcaddcadcbaddbcababbdacdbbdcdccddbaadbdcddddccdaabddabbbccdbbabcdcccabdbbcaccdbdddddcaacbdccdcbdacaccbcaacbbaaaaddcccdbbbbadbcdcbaacdbabadcdabcbdddbadadbabdbdddccbbcbcadcdadabacddbabbcbbcbbbcbdbaabbdaddcdbdacddabcaabbdccabadacbabdcabacacdacddcbabccdbbddbcdbbbcdaaadccdcabbaaacbabcadaccbddcddababcdbbdaaccddacccbcdbcaacdccaddaadbabddbbddccacaabcdbcbdbbcdaaacadcabccbacbaccdbbbdaabccccaaabcdbdddcccabcaddadddcababcbddaccaacbdcacacbbdacaadcaacccbcbddbabacdbbddccacacccaccdadcacacccadddcabdcdcadadabacddbbadbddbbbcaabddbcdbacdbbbcdbcddbbcdacbbcacbcdbbcaccaaabbcddcadbcbccdcddddaddcbadddbcccdcbbbadbdcaaccbbbcaabddadbdbcacbabacdbbdcacbbcaadadaccaaaabbbdccaaacbcdbbdadcddaaddabcacbbcbdbaddbdbcadcdbacbbbdcacbcabbaddcdcdcdbdaacbaddabbbcdabbbaddcccbdaadddcdbadaccadbaabdcdabdabbacbababbdddbbcaaccaaacbabdccaadccabcacabcabcaaccadbbbcbcbbcbbbabbaddcddabdbacbcddbcdbcbcacabbdcaabbbaabadbcbabbadbaaadbdcaddabdcccbaccdddcddbaddaccbcdaabcbddbadabdcabbabdbacabbcdcdbdbbadccbbbcabcaaccaaaccbbcccdddbdcdbbbaabdcbccdabccbbacbcaccccaaaacbddbbccadcbcdbadabddcacabcdbcbccdacbbdcabadcaddcbddacacdbddcddbdccaabcabdabdacabcdabdbcccabacdcdcdddbdbacccddcacdbdaadccbccaacaacddcaccaadcdbabdbabadbdbcddcacbbdaadcddbdadcdacddabddaadccdbbaccccadccddbacbccdbcdcbacaabaacabdbdbaddbccbdddcbbdbbabbaadcdccacbbddddbddccccbdaddbdcbcaabbbcbacccddbbdbbbccdcbacabaabdbcabcddbbaabdcdcaacaccdbdabbaabdaadbbcbaabbddbcaadbacccaabacbcccdcbdbaadcbdbaaaaabccbdadaccadcabdccabccdccbbabdcbaddccaabdbaddccababcbadbdbcadacdadadaabaadddcabddddddbbadcdbbbcbbdacccadcbbdcdbadcbbccadbbdddbbcdcdbdcaccbdddbdccbcbcadacabcbdddcaadbdbbcdacdbaaacbdadababcaaaaccddbdddcabbbadbbdadcdacbdaaccdbbbbcccbacaaacbaaababccabcadbbacbdabdaaccacdbdababadbbadcccbacbbdcccbaccdccdadacaadabccabbadcbddacdbadbdbbddcdbbbabbdbdccaccdbbabbacbbddcabaaadbcbcccccbaddaddaacabdbdacddaadcbcaacaaadbbdbdcadcaabbabbaabacdaccddcbaabcdddcdcdbccddaadcdcbbbbcbbccdcbdcdacccdccbaadcbbbbccaadabacacabbacbcbabbccaddadbcbbddbcbaaadbddcddbcababccabadadbccdccddcdbbadbddadaaaaddacdaccdbadacdbacbdccbabbdbacbddcccccabcdcbabbcdcabdddcccaadbdbdbcadacdddabcadbadcccbdabadcbbbabaddcdccbdbdcddcabacbdaaabdbcdcaaabcbccdcbbdbdadaccddbaadcabbbdaabdcbdcacbadbbcbcbbaddacbdabbbbbcacdbcdacaaabcdabcacbbadacccdbddadccacaddbbbdcabababbbddacccbbaaacdbcaccdcacbcbacccdadbadccbcbcdbacbcdcaccccacbadbbdbcadbbcabadbabadbadaacbacbddbbbaddbdbaadcdaaddbbdbababcdaddbbddddcabbabdacaabdbaddcccbcaadaccbaabddaabdbcacccabadbadbccdbabdccbddddadaddbcadccdbcdddbbacdabccbbcbcbcbddcaabcbdcdcdcabdbbacacdbaddddcadbcaadcdccabbcacbddadbcdddbbdcccccdcabbdabdacccdcddbccddcbdbabbccdcddbdccddacdaacbaccaddabccbbcbcaaaabddcaddcdaabcddabccbcaddabcbcbadbcbbdabddabcabbcbddabbbaccddabbadabcaadbbcabccaaadcbccdabcdbbccdcbadaadadbddcacdcadbddddccacaaadaadcaddbccbbbaacdbaadcddaccabacdadcddbdbcdaaadcbccdbdccbbcddddcabdcbdbcddadbcbabcaddcccddcbbcccacbcacdadbbabccbccccbabdabacabbbdcaacbdaddaacddbbccadddcbaaacbbbddbcdaaccbcdaaabcbdddacbaddaddacbabdcdcaaadddacadbbbdbcaaaacddacbbcaadbbacdcccdbddbdadcdbabdbaacdadcbdcdadabdbbdacccbdbbbbabdaaacacabdacccbdcabaaccaacaddbdddbdbcddbbccdcbbdabbaaddcbbcaaacaadaabcacccbccadabbbcccbbdcabdbbbcddbcdbacdcdbcbaddccdadddacbbbdcbcbdcdcbdcdddccaaaadbdabbbbcddcaaaadabdbdbccaabdacacdacadabbbbcbaaddbcccbacadabccaccbbdccabacdbdbdcadbdacbaadbcbcdbabddcaccddbacddabcaccbddbcdacbdbdcacbabddaaddbabcaccbabccbcbaabccabdbdaacbccbbabcaabdcccaddbbdabbdbdbaccaacbbdacddabcbaabcbdadddbacabbdbcbdbdcabbcbbdbbbbaadcbbddcdadddbabbbddccabaccabdcbbdbbacdabccdcdccdcdcbabdccabacccabcdaacaccbdbacaabdbdadddbaacdbacdacdcdcabcdaddacacbbdbcdbdadccabdcbacdccacdaabcdccabdbbccccabbccbcdccccbabcccbbaabaddbdacdbcddcdbbdadbbacabdbccbdccabcbcbdaadcadadadccabdabbdbcaadaacbbdacbaacbbdddaddcbbbaddbabbbbcdbcddacbcbcbdddadbabcbcaccdbcadacbdddbbcaddacbdaabdabddcddbcdcccbcdadddbacbbaadabadddccbcaabacccaabdddbcdcbccadababacabddbdcaadababcddbdcdddbdcdacdbdadabcccbccadaddaacaddddcbbcaddccccbbcabddbbbcddabaababddacddcbaaacdaabcaddcabddcbddacbdbadabcddccccccdabbccaabacdadcadbaacdcbccdabdbbacdbddddcdabacbbacbaacbbacccdbdbcdddcdbababbdbbbddadcdbaaddcdcadbcdaaadcdbccbcbddbbbcbbaaccababcbacddcbcaabcdccadcadadcaadbcaabcbdacbaaccdabbbbacadbbcbdcbdddccbbbdcdbddbbddbbcacaacbbdabbdaabdbbcbabadbcbcabcbbbdaacadbdcacdaacacabacbdcdabbadcaaddddcdbdcbabbdcdbcbbbdcacadddaabdcccbdbbbccacccbabcabbcabbbbcdabdbbdbabcbbbbbbadbcabccadaccdbbbdbbcbacdbcaabdcdcadcaabbacdbddbaabdcdcacdbdbcdbbdabbdaaacdcadacdcbaaabddddacdddccaabcddaacdbccbcccddddbbcaaadcaabadbabaddccacdbadaabadbaadbdaaaabbdbcdaadadadcdacabaaadbcbabaddcbbabadddacddddddcdccadcbdabbdbcdcbadcaaacdaabbbcbadcdbcccdaddabaccbbdacbdccdaddaccdccdacdbcbbbdbbcbcdadacaccaaabddabbdcdacadaaaabaadcaaaddccbdccabccdcaacbabcaababaacadddbdccbadddabccbbaaacadaccbaccdbdbadcdaddbaaccaaacbbbccbacabdccdaaabbbddabdcccadbbdcbcbbbdbcddcdbabbdbcaccbddaabcaabbcacbddbdcadddabdbdacdcccccdaddacdddadacdccccacbcaaabdadcdcdabdcaaacbccddbbadddaadcacbadcddddaaacdacacdabcabdddbccccddcdbadacbaadbcaadaadcdcddcbcddcbabdcdacbbccccaacccadacdbccccbccbabdddddacdbcbbaddaacbbdbccdbbdaaadabaadbcdbcacbdcbbcaabbbbaaabaddccdbadbbcddcbadddacddcdabaabccbbababaaabacbdacacbdbaadbbdaddadaaaadccdcbbccbbdadacbbbccddcccdacabccbabdddadcacbbcaaadbbdbddacccacccbbcabbbadbbdbcbadaaacaacdabadccdcadacdccdbcadcdbdcacdabbcccdbabdccdacaaddaddaddbbabcdacacbbcdaabbbdbbdddccbdcccabdbabdccbbbcbbbadabddbdbbdccdabcacbbccccabbbbddabcadabcddcadbcabddddbcaccadddabadbdccababcccdabdbdaddcbdbabdbbbbaadccdccbadcabcbccdddacdacaccccbcdbaadcbadacbddcdacbaccdbaaabcaaabbcdbcabcccaabdcacacdacbdaadaaaabcaddbbddadcaadddccddbabccbacbddbdacaddcbacaaaaabaadddcadbddcdabdadcabcdadcddcbdddbddbcadbaaaccdcdacbcbcabccadcacbdcdcbadacdbccdcbbdcddbbddaddcacabccaacadddbbcbaadaaccabcddccbcbddadacaaddbabbbcadcbdaadcbbcabacddbbaccddcbabcdbdadcbacdcdabbaabcaadbabbbaddbcbbdcccdbabbbdbaaddabdbbddcdaacbabababdadbddddacdaaabadbacbccaaddbadcdccbabacaabbcbbaabbcbadabaaacbabcacbcdbbcdbcddddbcbbadacbddacddcdbdcddaddcaabbcababbccbcdcaacacbcbabbaabddbabbdccbacdddbdcbcaccdaadddccccbcbdcbbcaddcdbaabbccbcadbbcabccdabbbcbaddaddbdcdbabaaabcabbabdaddccdacabbcadcacadbdcbbcbcccbadcbcacacccdaacdcddabbbcadbcdbdddacabcbcdcdadbabcdcdbcccdcddbbacbdadbddaadbdabacabbcaddcccdbddadadabddbbcdabcdabbdbbbbcaabaacaacbadbddbabaaaaaabdddbccdabbdaaabbadddaaddaccbcdbacaddbaccbccbaabdbcacddbddabaadcdaaabbbbdbadbacaaccdcbbbbcadcdbcadcadddadbabcbddadbdbbdccdcbabadabbadbdababacdabacacaaabdbddbcbdaabacacdbcbacbbcdccbaccaaabbdbdbdacbccdaaadcbdccdbdcccabbbddcbcbcddcababaccacdbbbddcbbbaabadacdbadaabcbbbcadbaaabadbbdadadcbbdcbcacadbdadaacbccadddcbbdcbbccdcdcaddacadcbadcbbabacbbcbcbacabbdbcbcadddcdabdbdadcadcdcadabbcdbaabddaaacddadabcbcbbadddddddcdcbbcbbbdbdaababcbbacbcdadbacddbcccaacdcddbbabbccbdbbadcbdbdbcbcbdbdaddaccbddcbaababadabacacdaaddaaaddacaadbccddaadccdacdabdbbdaaaacbddaccbbdcabaacdaaddddadadcdaccbddacabddbcbbbcaacaccabbcdaccbacaacddabbdbccbcccbbdbbdabbacbabbdaabadabdbcbbbbccdbcbcdadacabcaadcccabcbdadbacccabaaacabbbccaabbddcaacdabdcadcbacadacdacdbbdaccdcabdcbcadcabccbcdccaaacbcbdaccaddbcadbdbbdacacbbcbbbcacadacbabdbacdbdbaccbabbbdccaaacdaccaaccdccdccccdbcddacaaadacbcccbdadaaabbdbccbdadbaadbabbdccadcbaabaccbcbaccdddbaadccadaaaddbdcdbcbdccacbddcddbbcdaabccccdacadcacdddcddababcdcbddddaabbabdbcbdaccdcabdabdcadacdddbbbcdbdbbaccbbdbdcacabbaacdcabbabaddbdacabdaaaddaabcbcabbadbaacdaaadbadbcccdabacbcccbddcaddcbaaddbdbcdddbaacbaacaccdabacaddcdadcdbbddcadadbacbbccabcdabdbbaccbddbbaaaddbdabddcdabbbaacdaccdbdcabbcabccbbcbacaddbccddbddbdaacccccadacabccacdbdbdcdccdaddbbbbbbadcddddcdbbccdcbddbdadcbdbbbbaddaddcbaabbaddaadbbbacbbcdaabdbcddcabcbaddadbacdabbadcccdcaddcbabbaabadaacddbdccabcdabccdcbcbbabcddabbcbabcbbdababcbadaccdaadcaaaacbccdbccddbdddbdccbbbcdbabbbbaacdababcbbcbbcddaaacbccadbdcbbbaabddbacbccbbcdaadcabdabbadabaaddcdabbcccabaacbbaacbbbaababaadbccaacabdddaabbcdbcbbccaddbbdbcccaabbdbbcdcccdaaccdbccaadbabaddadcdacbbccdcdadbbcccddaadabacbbacbaacdadacbdddbdbdacabcbbccaacbabbccbcaabcacaacaaacdbdbbddcabdbbddaddbdbcccacabcccadbbbcacdcbaddcaabadcadaccbabaacaddcbaccdbcaacadadbddbbdcccbaabbbddbbdddabbbbaaaccbacbdbccbabddbdbbbccddbcdcadcdcaaabbaddabcbdbcccabbcbcacbcbacbcdaaccdddcdaccaacacbcbcaadccccdcaacdcdabddbaabcbbdaddcaadaadacdbadabcbcddbadbabdbcacbbcacabcabadaaccadbabbbacdcbccdbbccdccdabadaacbcdabbcacabcbbdaacaccbbaabdabacddbcacbcbccbdccdcadaabaccbdbddcaddbbdabddccabcdbabcacccbadcdabaddcbadcccbcacaaaaacadbaaacbcadcbaacaabdcaacababddcdcbacdabcbccbcaabcacddbacbcaadbbbbccdbbdaccdcdbdbacdbadddbcacacbacbdadbdbdbadaaaabdbcddccaaccdacbcbcddbcaabcbccbacaddcabcbdbdccbcacbcaddddabbbabbbacaabddacabbbccdbcddadadabadbdcbadbaaacdcbacdcaadacdadabacdabbbbcabcdadadabcdcbdccaddbbaacaaccacbacaacadaaddabaadcdabdcdbbaabaddcbdddcadbddddccdbbabbddbbcbaaabcbcdaaadadcbbccccbcbdbbbcbcbacadddabbaabcabcdcadaabdbdabaaaddaadbddacbdcdccbbbabddbcbdadddcbdadcacbbccccddbbbabdabacbbacabbddbbddcbcbdacddadddabbbabdcddcdabcacdccbdbabaccddbbcdbdaccaddaccacdbcdbdbddccddcccbcacccbdcbabaddacdbdacbcbbdaaccababddcdbcbbcbadcdacdcddacdadbdbabdddacbcdbcabbbbbabdadbadbdbaddbbbacaadababdbbbccbaabddddbbcdbbccddcbbccbbcaddbcdbacdcddacdabcbdaacccaacbabcaddcaaccbbccbbbbcbbdabbcdcdacbbddacdddcccbaccdaccbdccddbddadaacbbdcbdcabdccccbbdddcabacccbcbbaacabdabbdcdcccbcdabccddbaccabcaaaaccabadbbbcbbcbbaaddbaabdcbcbcdaccdbaabbcdbcabbbccdcdacadbddcbdccaaaaccadbcbbacabcdadabbbddbdbbcaaddbadadbddbdbbcabbcbddcddbccbccbbacdcccaaadcdbadcddbdcbbcbaaaaadadcaacccdbbaadcdaccbbbdbddccabdadbcbacdddbdaabaddaadcddacbbbaaddaaaccdccbbdbdbbaddbbcbbbbccaaddabadacdddcacbcbcdddbabacabaadcdbcabcabdbcbacbdcbaddbbbcabddaacbcbdaacdbdcddbaddadbacbbbbdbbdbbaacbbcbccddcbabaaabaabcdaabbbccbdacccbbbcacaabaaadcdcdcacaccbcdabcacbdcbadddbabbbcdcddabadbdaadddacdcadaacbdbabcaaaaadbbdaadaadadcadcadbcaabdbacbcbccacbadacacaabdadcadcdccccbbdddabdaabdcbbddbdbccaadcaccdaccbdcbccdbbcbbcbccbbadcbcdccdabaaccbbbdbdbdbcbaccbbaadaaccdddaccbcaaddbbcdccdccdbcaccdcabacbacddbdadabcbcacbccbbcbcdbdabbdcbdccccbddbdcadddaddacabdcbaaaaddcbdbcbadabddddbabccbadbacdbbddbcccdadbccadabdcdbdabbabccadaaccdacadcdaccddbddbcdccaccddbcbbcacbdbbcdcbdccbdaadadbbaaacbcbdcddadcbdccabccaabbddbccbabcbadbbacbabbaacdcbaaaccdbccdacbcadaabaaddaddbabdadaaddbdbcacdddaabcdadadadcbccbddaaabdbacddcddccaaaadadcacdbdccbabdddccaabbbcbdbadcacdcacaddabcbcdbcabacabaacdabcdabbcbdadcdccbddcaacaaabbaaddbcaaccdaccaabbdddbaaaadaaabbbabaadbcdabcbababcbbccbadabbbcddbabadccccadcbdaabaccdbdacbddbabdccabdddddbdbacdababdacbccddcdbbbbccbcaabdbbdcdadccdcacdccacbbabadabdbbccdbdcbbbbbcddcdcbbabadcbabacbcbcabaaddcbcbdbddbadcbadccacccdaabaccbdcdcbcdbabbbcbddababccabbddaacdaadadacacaabcbabdacadabaabcbbaaaaddbcaacbdbaaacbccaccbcdddbbcbccbabcdacddcaccaabcbdaacdbdbbcdabbcaabadccabddddbdcccabcbbbcdbabbbdbccdcdbdbdaaabdbdcbaacbddabddbdbacdcacbdcacdaabccdbadccbcbdadcacbcddabcddddcddaaadaadcccadcbaccacbbabccaccabbdbbdaccabcdcabbbbacaacbcbbbdbbdcdcadbbadbacbcdabbabcabccdbaddcccacdcaddbdcabbbaaccdccddbcbbbccdbbcabcaaadbbaabbaaddcaadcdbdcabcdddbccdacdadbcaabcbcbadcacdaaccdcbcddbcdddcbbaacbbbccddcaadbbacbbbcdacccccbcaddbdacadcbacabacdcdbcabaaccccbabdcbbcaaccbdaadcdccbcccdddabbacacacdcaaacbbcddccbddbacbdcadbaaabddcadbaaaabaadabdcddbbabcadbadacdcaccdadcbcaddbdcccdbbaacdccaadcbaccbcdbcaabbaacdbbcccbbccccbbccabcaadcbabcdbccabdaccadbabadaccbdcdaaadcacddcbdcbcaabbadadddbbccaabddbdcbabcbacacdaaabbdbbbabbddababbcaacdaabbabbcbabcdbdbbccccbcbbcacacbdcaaaaabbacabcaabadadaacacbcdbcaccbcdabacbbbdbbdddbbdbbddbdabccaadbbddbbabacbaacbcbadddbccaacccbcaadaaadcaccbdbbccdbddaddcdbaabccbacbbdbbddcbdadabbdcbaddcaabddabddabaccbddddbbdddbbddbdacaacbbddadbdaabdddddbbdbadbdcacbacabdccabccaddbbcbbcbddddbcddaaadabaacbaddaabaddaacddccbdbaabdbcbbadbbadbdbaaabcbcbcdbdcadbbcccdacdbadaaadaacbcdbadbabaabdbaaaaabbccaaadadbdccbcccdbacccacbabbdcacacdbcbdbbbadcadddbbcbbdbbdcaabbdddcaaacabadddccdcbaddcabddbadbcdcdcabdbbdbbccdbddddcaaaabcdbaacbcbcdbdbcccdbadcabadcabccbaaddaabaadabadbaaaccdadcbddddbababdabbcabbdcbdbcddcbdbadacdadcdaccbcbcdcdabaacaddaadbbcacddbbabcbbcbdacbccbbcaddacaaabaaabbadaccdbdabbbcbbddcccabbddaadcbbccababbbdbcddcddacababddbddcbaccbdadcdccdadcddcdcadbbcdbcdbaddcacbcbcbdaacbccaacadbdaddbdbacdcbcdabdcdbdababcbacaacdddbbbddabcdabcbdddbacabcaacdaadbdcdbbaacdadaddbaaccdbcbbabddabcbdcacbbdbdcccdaddcaacacdabbcaadcbcdbaccccadcdabcababcbccaacacddcdddaaadbdddcbaadadbababdbcadabdcdcadbbdabbcdcacbddacabddcdaddadcababdbcbacbcddacabbaacbbbaddcdbbaacabaadbabcbddccdadbbbbbdcdadbaaacdbdccaaddbdddbcaddbadcabddacccabacbdcddacaacabacabadcdbdbabbadddbcdbababcbbdbdddbdbabbccaabbacdbbdcccbddbddddaddccdcbbbaabcbbaacdcccabaaabbcabaabadbcbbdddcdaccdcbcaacadabccdadcddccbdbbdadddbbcbdabbdaddddadabdccabdacaababacaacacbbccccdcaadacbbbbbcabbacbdaadddcdbbcacbaaccdcbcacbbdcbaddcdaabcdddacbcbbbbaddbabababddddcccaabbcbaddaacbbcabbcadccabccbcacdcdbbdbdbbcaabdadccbcbcdcbbcbaccccbccbdcbdbccaabbadbabaaacaddabbcdcdcabbcbbaabadbbdaaadaacbdbcdcaacddcacaadbdddcadccbaccaccaaabbdabbadaddcaaaddadddbabddcdccdbacdaaddbcbcbddacaacacbacdcbadcdaddaacabadcabcbdddabdccaaacbdbcbadaaaabccdaacaadddabacacbaddacddbbbbdbcddbaccbcacacdcadccabadaaabcdbdadbcccdcdababcbbadacdbbcaacbbaadaddbcddbdccbcbdbaabcbbbdabdcddddaddcaaacbcdaacaddbbacadccccbbbbaddabddddcdabacbddccbdabbabccdcddaacbadcdbdcbbbccdbaccdbcdccddddcbbdccccabaaccdabdcdcacdcbcccabbddabdcdbcdbbdabbdbcbcdbcbdacbbabacadcddcaaddacabbdcdddbdabcadadbbbbbbddbdcbabbcdbdbbbdcaaddbabcdacdbbbbdaadcdaadcddcdcddcdbdaccdddabacbcddbbacbaadbbbccdadbcddadccbbcdbbcdccbaacbddbbcacccbadddddaddcaddccbccdbacaccccbacdbdcaaaabbcadcddcabccaadbbcbbbadccbdaacbbabddcacbbbadddaadbcdbcadbcbdbaccadabdbcbcbbabbdbdabccabbdabaccbacdbbabadadacbbddbaaddddadcabbcadbdccbbdddbccbbdbcbdadbbcdcdcdbabcbbcbcadbacbdbbbaabbbdbacbcbaddbacaccdadadbcdbddbacadadcdbbdabcaccaaadabaabadccabaddcbdcdcdddcdaccdcbacdbbccbcbdcbbdcbbdbababaaacadddcccdcacdcdacbdabddcccacaacddbcdbbcaadaaccccbdcddadcddddbbaaabcbdaccaacdddcabcbbacddacbdcccbcdbdbbbdbddcbdabbdcdbdaccbadbaddabbabaddacbbdcaabcabbdaaabaabacdcbaddbaacdbabddadbbcbabdcabcccabdcabaadadacbcbdbbcdacccbcaaabdcddcbbcbabcddbcacacadbbabcbddbacbccaababaabbaabbbababcbbccddabbcbcacccaddbabbcaccdbabbcccbdcadccbdddddbdacdadccaacacbabbbabadcbacadbaaddaaabddcaaadccddcacddacddbbbccbdabdcdaadaacaaacabbccaabddbdacbbadbabaadbdbccccbbbccbdaddabcbaabbbacbbdadccacabaadcabbddaaaaadadbcbaadaddcbccdcbbdcdcadbacdbabbccdcaccdcbbadccdcdcbacadcbdcdccdabadbbcbcbbbbbabdbcaabccbccdcccaadcdbcadacacadacabdbddadcacbaadcdcaabdbdabcdabcaaaddcddacccbbaddcaaacdddbcccdbddcdcacbcbccbddcbadccbacadacddaddadbccdbaabaadaddbdddbddbdcbcbbbabaaabddabdbdadddcdddbdbbcadbcdadabbcdcadccbdcdcacadabcccbcbbddccccdddbbcdadbaccbbccbbdbccddbadaabcbbbaadcdcdaccabadaacadddbbcdadacdcbcaddbddaaabbbbdbcbbbdaaaadadcdadbbacbbbdbabcadacbbcdbbdcbacccbbbddaacbcabbbcbadcbaaccbcddcccbdcdbbacdddbaccadbdaccadacadcdcbccdbabcbccddcadbaddbcadaddbcccdbcdacdacdabbbacdaacdacacccbbbccbbcbcdadbbcdaabcacdbabdadacbabccddcdccaccbcbbacdbbdcbbdbdbabbdaaccbbcccabbaabdcbadbcacbadcddbbdbabbdccadaabcdbcacacddddabdcbdaddacbaddbdaddccdcacadcacbdcadaabbcaaadbacdadcccbaddcdadcbcbdddaccbdccdabbbdcdbabbbbaabcabcbabdcbdbcdcdcddcbdcbbcaabdaabcddbabdabbacddabccbdbbdbbabccadbdbabdabcdabdbcbadaddbcdaadccaddacdaaaabacaadcdadacbccdbabdcacbdaaccadbbdbcadbaddbbbdcbbaacbbcdaacdbacdbcbbaacdbddbddaaabcaaaacbacabcabcdcbadccdcacaabbccadaddcaccaaaaadbbbcaaddbbcdddabdbdbabadccdcabacadabddcadbdadbaabbbbdbbaddacbadbbdcddccadbdbcddacdaddbcadcdcbbacbdbbddabbaddaacdbdbaacdacacbccbbcbbaccacddbabdadbbbacbcbabbddacabcbdaaadbcbabacbbadaaadacdbbbbcbbcdacbaadaabaabacacbbacacbccccabbcadcdacbbcaccccabdadddcdbbaaabdadbcbbcbadababccadbdddcbdabcadacdadacdbabccacddbcbcbdddbdddbdcaaabadcabdacbcbcaaabaabdadaacbbcbdaacacdabdbcbcaaacadbbdddddddacadcbaacddaadcddabdddbaaccdabbaaccdabbabbcbbbbbdaadbaddcbaddcdbaddcdbbabcddcdbbbcbccaadadbdcbcccadacbccaaabddbdbdcbbcdbddbdabdcbbbcbaadabcacbcdbdbbdabbcbacbaaacbaaadaaabddbccdbacbcdababdcbbacdddddccdbdcdddaabbbbdbacdbcbbabadacbbccbcacacadaaccabccbabcadaccbcacdacaabadadaaaaadcdaaadcaadbdadcaccbadcbdbbdbdcdcbacabcdabdddacacbcadaccddaaaccbabaabbddddbaadbadbcacbddddabcababdcacacdabdaabcbbdcbaabdcdaabccdcddaaddbdddbaaaadbaabaccccadaabbbabbdaaacbdccdaaddadacaacadccddabcabaaaadddbdacbbadbcababaabdbbaacadadbdabcdcbbccbbbadbdcdcacaabdcbadbbbbdddddabacbcbadabaacccbbbbcddadbadddbdcbcbdbcaabcadcaacbacbdbbdbdbddbcaadbdbbaabaddbadadcbcbcccbbacdabbbbcbdaddaccacbdbacabccdabbdcbbcacddaadaabbadcdaabaaccdbdbccdbdcccacdcaacbbabcabacddbbadaddabdcbcadaacdadadadbcdbccdbbccaaddbbadbdadbcdbdbdaabcaddcaadccbaabcabaddccbaabbdadabbbaacbccdbdcaababbcdacccdbaaabdccdaccbbddccdaabcadacdccadcdacdcccbdbbcdddbacbaabadcdadacabbcccbcbbdbdbcbdccbcbbbdccabbbcbabbdccdadabbcccdcddbcabcbaaaacddaacabcdcaddcccdbbdbccacbdccddcacbdbbbccacccbabdcbbdcccadabbacaaadacabdcacbccabadbccadcbcaaadadcbccdccbcbbdadacadaaccbccbbdbcacdccdabacacdcbabaddbbccabccadbbbbadbaacaacccdbbdcdaacbaaabbcaacdabacdcabcdbbccbddacaadbbaaacabcdcabbacaccacadbdcdacaabcbdccddcabcadddacddbcddadabacdabcbaadabaddcacbdcabdaccbcadccacbdcaabdcccddadbbdabdadadbccbacbddabcabacbdcdcbaddbcdbcddabaaaccaacdbbabcaabdbabddbccabbaddbcbdadbbaddabbbdaccaaacddadbcbcbdccaadbccaabddbdbdccadccdadacdcbaabdacadcabcccbbadbacaddbccbddcacdabddbdbcbcddddadbdbaabccaaadcbcbbdcadbdbbadabbadcdcbcdbbaabbdaddaddcdddbacdbcddaaccdbadbcbaabcdcddbcbddcdccaaababdbdddbdbaaccdbadcbbbdbaaadbcacbaabbdabdcacadcdcbacbcbbaabddbbcdbdadaccaccadcabcbdadcddcbaddcdcbcacadbbccbbabccdbadaccaacdbabcababadadbddcbbabddbcbddacbbbdacbcccbadbacabadaddadaddaacbbcaadabaaddabbabbabbdddbbbbdcbddbbabaddbcbbaccbbcacbadcaccaccdbacbacdadbabcdbaacddabaaabccdacbcccdbbadcabbabcaddabddbdbacadbcbbcdbcddcdccaddcccddcabbadaadddbbadbbcadddaabadcbddddccbabcbdddacbcdcdbdbdbabaababbadadabcadaabcabaaaccaaccabcddcbcddccddbabcccdccaddaccddaabdabbabccddacdbaadbbcdbcacabacaccbbabbdacdcccaddabbbdbcdddcabbbdbcbdbdacacdddbacbbdadadacdcbdabdbdabbcccaadddbdddbcbbabcbbaaadbbacccdacdabacaacddbcadddacbccabdacbcbaccadaadbddadbcacbddbdccbadaadacbbcccbbabccbacaccabddcbdbddcacbadcadcdbcaccbdcdcaddcaddabacaadadadbddbadddcadcabdccdaaabbbdbbcccbdcddccaadcaacaabcbcdbddbbbcddddcccccdbbacacaabbdbbcabdbbbcdbabcbacadadabdbadcdabcbdacbbccbcbbbcacdbaddbadbddcdaacccbdbdcbdcdbdbdcdaadabcabacbddabdcabcbaaacbddcddcbbdddddabaabdcddcdcbdccccadddccabbddcbdbabadaacaadbadbcddcbbbbaddbcdaabdacccdbabdadcdaaabaadccddabbcdcdcdbddddddbbbaadddbbbadccbadacaadcbbdacdbddabaabcbcdaabcaaddbccdabccccdbdddbacbbddbaaaaaabcabcabddcdabcbcacdaabddbbbcacbcacddbdddaaaaccaacccddbcbcdcccdcbbacaccaadddacaabbbdabaccaccacbcababacacbcbbadcabaadbadcaabddccbacabcbdcddddcbbccaabcbbaaaacbadabcccbdbcbdcccbabdadbacddacdbbaaacbcbbcbdbccadcaabdaaaaadbbbadacbaaacadddcbdbcdcdcbbbcacbababcbacbcaaaadbbaddcbadcaccbdaacabacdacdbadccbcbcdbbccadcbdbdccdcacdccdcbdbdddbdbabbcadaaabacccdbcaacaccdbcbbcacdbcbbcbbacaadbdcdcccabaaababcadbbcacbddccdbaabcdaabacacabbccbddaccbacaaccccaadcbcabaabcddbaacbbacadadacdcadadcdbabdacaadabdbcbddbcabdcbbcbdbaccbbccbbabbcdddbbbacbccbcbdcabddcabadbccbdaabadbaccacbccaacdbadbcdaccadcadbbccccdccddbacadcabcaaadbddccccdbcdadbababcaaaccababacbabcdbadcddaabbddbdabbbdbcaacbbcbcbdbddadabdcabbabddddaaabccbbdaabcbaabacbcbdddbaadcdcbacbdcbabbdaadddccadbdacadbdaccccaddcabcbcbaddadcdddbabacadcbcddacdbadbadcdabdbaccddcbadbcbccbddadadddbcdaacbabddbdadbdaacddddcabbaaababadaadcacddbdbdadcbaccbddadbccaabccbcbcddbdaddbbdcddbcccacdbcdaaddccbccabaacbaaddabacbbccabaacccbdbbccadbadaaabdcbbccdbdadcddccabbcbcdaacbcbdcabdcddabbbacbbcccaccdccaaaacadbccbcadcbbacbcddbaacbadbabdccdbbbcaaadabdadbbbacdcabcccdcadabacddaccacdcdcacabccdcccdabacddbabacacadcdadbcdaadcdbdacdddabbaaadaccbdccbcccdcacabcbadcbacdbddcdcdddaddccbaacdcbcccdbaccbddbdabaaadbadabddbcbddbdbccabcddabccbddcbadbddbdacbbcbbaaaacdccdcdacaabdabcadddbacacabdccdbdbcdbcddbddbbbdadbddbacbbccdbaadccdaddcaadabddcbaabbbbadccdbccbdacabddcbaadbbacbadababbbbbabbcbaaccbdddabaddddcacdbddcdacdccbbacbcdbaddbaabdadaaaacdcdbcdcdbadacdaabcabbcccdbbcbcbddcdcdbacdccacbbdbcddbcbccacdaddddcdcdddaccddaacaabbcbaaabbcbddcdadaaacbbcdccdccdbaacbacddacbcbbddacdcaaacacbbbdbaaaaadccbccaccabaadacbbababdbbcddcdabccacbadabbcdadbbbacdcadabcbbabbcdacddccdacbabdbabcdacabcabdbddadbaaadddbdcdbaabdaabbdbdbccdabdabddaabaddbbddcabbdcaddabddaaaadddcacddacadadddbaddabdddcbabbabdbcbcaabadbaabdddcaaaccdbbcaadbccabddcabbcabbdbadbabbbdddcbababcbdbcadaacacadacdbabbaaaddadbbdaddadcabdcacdaddbaaccaddadbaaacccbaddbadbcbcccdaadbdcacacabdbbdbaddadadccdabdcaccaadcadabbbbdaddbdabacbcdbccddddbacbabdaccddbcadabcbabacdaacbbbabcdabcddddddabddbaacdabaccdcdbadababcadacbbcbcbdadcadbabaabaacdbcaaadbccdbdddcbcbcbdaadccdadaacaccdbdcbbbcbddbdddbdcbadbcaaaadbcbdcbdaaaddcabdcacadcdbdaaaadbbccdbdaaaaabdccbaabbdccbaabdddbacdbddacaaccaddcaddcbbcdbacbcadcdacccbdbabddbccacdcbbdaccbbcdddadabadbbacdcabcdccbacbaacdbcaddddbccbcbbabcddcbcdaacbacbbdadcaccacaaccacadcdbcdabddbcbbaddbdbbcbdadacacdddbacbaabdbbbcabcddcacbdbdcaddadaabacbaacdbcbdacbbccbcaadaaddacdccbcbabcddcccdbaddcababbbaadbdcddbadbbadddbccbadcddbaccabaacdadbddacdcdbadddbbdaccabacbdcbcbcdabbbdcadabdccbaabbcddadcdbdaadddbdcbccabbcdccbcaccccdabcdabaacaddaaaaacababccdcbcdcbbcdccaccdbcdcbadaabdbdbbcbdaacadbdabddddabbaaddbcddcdacdbabaabddbcbbdcbcbbacdbbaadcaddadcaacaaddabcaddcbbdcdadbacdcbbdccaddabcdaddbacccaddcdbcabddddbdadbacbddadccabdcdaadcacccdacdccaddcabdbaabaaacbbaadcddadabbcbabdacdacaaddcbcbbdcddddcabddbcbdbcdadccbaaabdadadbcdbacacbccdaacabbdcbabbddaabcadccadddbdcddaabdbbcaaddaacadcacdcdddcdddacbcbdabbcdabbbbbdbacdcaccaaccbbcbcbdcdaaccccbbaacdcabdcdbacacadbcbabddccddacaabddadaaccbbcabbdcdabaabdddbacccbdccccbbddbdbdbdbcabcbcbbddccbcbdbccbdacaacbbdaabddcdbabcbdbbdcadcddcddddbbbadcddaccabcdcbacbbdccbdadbbdaaaaabcccabccbcbdbadddccaacbcaacaadbcdadcbacabcabbbcabcabacbbdbcdbbdbbccacabcaababddccdcdddbbcabdddcdcaacdcccacababdccaaabbbccdcbacbddbcdaddcccacacdacdcbcbbddaadbdbaaadcacacaababccacabbabdbdcaabddadcbcccbdaddcaddcabbccdbccbdddcadcbbdbabcdcddbbccbbabacdcdabbcdcdbabcddbcdbcbbabcbccdbaddbcaabddabcaabacabbadbdacbbbdcbbdcbaaabcddbaacccdddddbbbaacdabdbdcccdcccdddddabadacddadcdabddddbbdabdbaddabadbdcaabaddbcdccaacdaccddbdbcdbabdbdbaddcbcccdbacabdddccbcdbbdcddcddbcacadcdabcbdcdcbcadbbdaadbdcacabdcbacdcdbaccddbaddabacbbdbcddbbcbbddbaaaaacdbbabaabbcbbdbcacaabdcbaababcadabacbcddbdaaabbddacddcbaccbbadbccabbcccaabdbacbbbbcbcbabccaaacbadddbdadbdcaadcdbbcddcccdbacaadaababdddbccabbdccaabcabbbbddacdbbdcbbabccaaddbcdcabaccaddddbaccdddababadacabbbacaaabdaadacbddbbabcbbdacdcabbbacddcbaacbabcaabddbbdbdaabcbacbcccddcacbadbaadaacdaadaddbcddcaabbbdddbcaddcdaadbaddbbabcbcdaabcabcabbadbdcccaddbcacbbacbcadbbaabddcdcdddaddcbcabcaccdbbbaabcdbcabcbabccdbcbabacadaccdbcbaabbaadbdbbbcacbcabcbdabcaaccababbbdacdcdabcbcdcbbdcbbbbabcccccbdbbcaccdbacdbbddbacccbbcccbadcaaacabbbabaadbddaadcdbadddbbdbbdadddaabbccbcdcbbbcdcbaabcbabdcdabdcbbdcbbbdbaadbbbcbcbbcbcadaddbdbbacbdacaaacbdcadcbcddadbcbbdcdacbbccbbcdacabcddcbdccbbaadccbbcbbcadddcccbbbbdcbcbacabbcbbadcaadaaccbaadcddbbcdaddacadcaadccbaaccaddaaadabccccbaddaccdcdaabdacaaddbadbcaadacabdcacdcccddbabdcacdbcacddaacccdacdcbdccbcbbdcdacbdcdbbdccbaabddcbbccbcdaccacccbcbccaadbacacdadadbcddadccddddbdcabbdbbdcbbadbccdbacbccbdcdbbdaacdadcdddcdbdbcacaacddddaabaacdbdaaadcaadcaaaadbaaddcdcbccacacbdccbbbbcbdabadccbccacdabdcdbabdaadadcbcbddadccaccbbaddaabaabdabaadaacbacdccaccabacdbbcdadcaaacbbccdcabadbcbdabdabadadbdcadbcacabbbcaddcbdddabbcdabbbddbcbdcacacadcacccbcbbccdcadcdbbbccbaacbdadaabaddadcbbbcababdcbacdcddbcccccbabbbcccdcacccabcabacaadaacdddbcbbcbdacabcabbdacacdccadadacbddcaabcacadaadcabbbdaacbdbdabaaddadcaadadccacdccdabdacbaaadabbbddbdcdcbabdcdabdabbaacccbabaccddacbdccbdacbcbdaaddbbccdcbbabdabbcadbaaabcaaacaddacbbaacaccdabbabbcbcbabcadbddaaaadaacaaaadaaadbbcdbdadadbdaddbbaaddcabcbdcddbcccbbadcabbdacdbadbdadccaccabdbccbdbbdcdaabcabbcdccbdcadadccadbcccbddcbdcadacaccdccdaaacabcdaacbdcbaadabcbcbbabdabccdddacaaccbadddddcacbbcaacabdaccabccadabacbacbbadadddaddcadaccccbaddbcdaaaabdddcbabcaadacaadcbddabbbcbbcdccddbadbccaddbacbaabdddcbaaddbddcbcccdadaddbaabdbdbdababcabdcacadbddcbbaabaadabcddcccbbbdadcdabddcbcbcabbbbbdaabbaddddddacabbacbadcbdbbbcadbbddbbadbbdbccbcdbbadcddbccdbddccaabaaabdbddbbddacacacbbacdbdbccbdccddadbcbcabdccdabacbababdcddbaabaacdcbccbbbdaddbddadcabcddcaaacadbaabbcdcbdababadbaadbbbbdaadcbdddcddabcdbbacbdabbaaacdadcbddacdadabcbcbdaaaadbabcbdbbabaaadbaaadbbdcccbccbccdbbccddacbdaccdcddcbbabdcdbacaaccadcaacbcaadabcdaddcdcbcccbbaaaadddbadcdbcaddcdabbdcccddacaddbdcaaabdccdbdaabadccbcbdbacaadbcabdaccdaccddddabcdccddcddadadcbacacdaddbadacacaacacaabacacbcdcddbabddbddadbbdabaadabbbddcacbaddcccadddbdcccdddaacdbbbdbaaadcadbdcdaaccccdbbdbbdccadcdcdbdcacadcacbaaaccbdccddddbadbbdccbcbaacacdcddabddacccdddbbdacbbdabdcbddbabbacabcbaddbcadbdacabbaacadadcdcabaaacdcbbacaaacaacabbdccdcdcdcabcddacbabdaabacaaaababaccadcdaabbddababbdbccbdccbbdcccbdcbabbaadcbbcdccdcddabaccddbadcccabbcadaaddcccadaaaddcabcdbbcbacadaccbbddabddbbccddcbbdbaaddcbcdbbdbbadbcbbdcdcbdabbaadaccdddbaacbcdacabadadaacbacddccccacaaddadaacbcbbdbccdacbadacaccdccddbaacbdadccdbbaacddabaddbbadbaacbbdbcacacbcccbdbbdbbdbbbcbbdbbbbdccaadcbadccadbbbbccaccbbbccdbcdbcacddbbadccdddadaabacdddbddbdccbacbcabaaaaddabcacbdbadcdabdadadccdcbbbbdacdaadabdbddbbcdcbdcbdcbdccbbddcdacdcacdccdcdcacbdcbaadcaadbbcaaaabdacdbadcbbdadbbadbbbcbbbcabdcdbdbcccabbdcdacdadbbcbacdcccaadbcdadbcddddcdaabcbacbbbcbddcccacbddcadbbdaaccbbabcadaacccdcdcacdacabbcbdabbdadbcbddaacabdcabcdcaabcdcabdbaabdcccddbbdbddcaadaacbacabbdabdcdbddcbbdcaabbbacdbcadcdccbdbccbbbcabbccdcddcbccdbaaaaadccbbacddcaacbabaadcaadcdbdbccadacabaacabbddcbccaccdbdbacaacdacdccbdbcaaddaddcacdbdbacbdadbbaddbcbcbdbbdcabbaabcdbbaacbcaaccdcbabacccdcacbaadccbabbcdccbddabcdacaacbbbdcddaabbaadcdcadaddbacbdbabdddabcabbdbaadabbcdbcbabdbabcccbdcccdccbababddbcbddabbaccdabbdadaacddcaadcdbbddcccaabdbcaabadadcabacddddacacdabddccbababbcddadcddbcadbbdccbbbbcaaccaddcdabcddaaaddabcdcacdacbbddbbcbadcabadddbaddcdaaadcaabddccabaaaddcbbbccdbadcbdabcbcadaccbcdabddadcaaadccaadccdcaddabdacabcdabbbbaabcbddbbdccaaccaaaaaccbcbbdabbcdcdbabdacdccddcabbdbddadabdcbaddaaabdcddaaacaadcbdcdddcbcacdbdcabcdbababdcadbdbbabbaacccdbcbbdcadabdbcbaaddbcccaacacdacaaccadccaadcccbcacadacccaabbcbabaadcadbbdcbbcacacbcaaacccccbaaaabacbdcccbabdcbdcbcbdacccadbbbbbcbadbbbdbbddabddbacaadccddaabbcababdacdcaacdbcacdcdbcdadabacdbacdbbdcccabddcbdbbabaaacbccbddbbcacbdbbacaacdcbcabddbaccbdabddacddbacccbdaccbbcadcabcdababaacdacdabdccbaccadcdccbcdacbcbbcbbaaaccaccbabbcacdbadaacdcdcaddcbcdcccaddabbcabacccbcbbdcdacbccddbbaaabbccacbcacdbdaccaabbacddbbccbcdbdabbacadbadabbddbbadbcabcabdddbacbabdbacaddaabcadaaaccaddadcacdaddacbcabbcbcadbaaacbabbdbcacbcaaacabdacbaddbbdccbcadcddcbdaaacbdacbdadaabdaddaabcdaaadbdaabdcbaadcccaacacbddbaaabbaaacdaacccabbbadbccccddaddcdabdcbaccdbbaddbadbaccbdcdabdcbbcadaddccdddcdddacdbcddacdcccdacccadcdcccdcbbdddabbccaaacdbbccadbadddbcdbadbcaadccaacbcdddacadbccddbbcddddbacacbbcbcbabddcacbbdcccbccdcbbadcbbddbadbccaabdcadbdcbdacabbbcccbaccbbdddccdaacbbcbdcdbcadbaabaddccddcdbddbbdbdaadddbbbdcbaacddcccdbaaabdcbccacaacabbbdacddbdbbbcaadcbaddcdddbdccccdbdaddcbccddabadbaddddbaaaacdbcbdbdaccccddcaddcacdddbaaababdaddcbdcadcdaccabbcaddcadbcdccaacbcadaababacbbabbdaaabbdcdabbcadbdcaaaaabaaacbcdabaadaddadabdabaacaccbbababccccadbbdabcaccdbdbdcadccacaacdcbbcaadaadcdacaccadbabccbdbadacadadbabbddcccbaabcddbbcdbcdabbacbddabcadccbcaaabdcaddcbaddaabadadbcaabaddcdddabbbababadbcaadbbddcbcccdcacabddadbddaaddcbccdcccdcdbaabacbdbcabbbbdcccbbabaaddddadadcdaacbbadbdacdadadabdaacccccdbbddbabababdbaccacbdbdccbdccdaadbdcaaaaaaabbcbdaaabdbdcadcdacddbacdcadddbdbddacbdaddaddccdbcaaababadddccccacaacbabbdabcadbbababaddbdaddaddbbcabdbdddbdbcabbddcbaddbbbbcbbadbccaacbbaadaaaabcdcdaabdbabbcabacdaabdbdcabdcbbbcdaaaaabacabcabbaabcaaadbbacdcbacacaabbbbcaabaaabddcbdabcbaaadcbadaabaacbdbbcdbdacbacacabccdbbccbbccbdabdcdbbbccbcbcbdbcacbbbcdadccacdcacbadcdbcdaacacbaaaabdbccabcabcaccabdaadacdbadcccdcccabacadcdaccadbcbacdabbbbacaddadcbadabdadccbbccdcbbabdaaaabbacbdccdcbaaabbabcbadccdcdcdcadabadabdacdcacacdaccdcbccaacdcdacabdacddadcdadbbcdbbbabaaacbbadccdacabaddbdbbaddacbdddcbaccbcbacbddbddaccbadddbacdbadbbdaadaccdcbadbbacabcbddccddbcadadddbcdaaccbadbdacdcddaaddcddcacbccbabdbbdabbbcbcaaadbaaddbbaaabcaddbccacadacbaaaddccbadabbcbcabbbaacaddacbacccbcadbbcacbbabdadbabcaccbcacbbcddddcbccdbddcabdbbabbabaadadacbbbbdaccacdbadddbcddaadddcddbdbacbcabddabbcacccbbcccbccbcdbaadbaaccabacaacaddaccbabadcbdcbdbddbcdbacacdabcbaddaaddbbaabaccabaadaaabcbadcddacbdabdddacbbbcdaaaaabdcbabcbabdddabbdbcdbcaaabdddddbcbdadccbacbadacdabccdbcbccdabbabbaddabdcdcdbcabaaabacddaddbaddcbccccbbcbbdaaababbcbbcbcaaaabacadbabdcccddccadcdccaabcbdadacbaaabbdadcddaacbdcbcbcaadacadaccdcbddbcabaaadababbcdabdccbcacbcdcdacdccabbdadccccdbbadacaaababddcddabbadcbbcabddbdcbddadadccaaacbcacaadacdbdabbaaaabbddcdddddbbbdbddcbbdcbabddbdcddaaaadbdbccbbbcadaaccbcbccaddccdaddacacccbccbaabcbbadbabcaadcacdadbbbbbddbabdcaacbcbcbbddcbcddaadbabcdcadbbadcbbababdbdbaacdacaabbdacdbdbdadbabcacadabcbbdccdcaababacdaddbbdadbdaaadacbadaabcbaddbabbcbcadbabdcabaaaaacbcbaabddbdbcabcacbbbcaacabbdaaabdcacdabaabdcdbaabbacddaaadcbdbddabbacbddaacbbaccababcadaaadabdcdbdacbbabcbabbadcdddcabdabaddbbcdadaddbbdbdbcddbddabbadaccdcbaddcacbaadcadbaabaadccdccdadccdbacbbdbcdadbaacbaadcdcddbdacbdaadbbdbbcbdcaacccdcdcdddcbbacbddcbcbaaccbabdbdcbbdcaaaaaadcdbbadcbcccdbacdbdbbaabddabcdaacdccddbabdabdcacbcbdbcdacccabaadcccdcbaabcdabdddaabcbdbcaabbdadcdcdaaddcabdabcacaadaadbabcaadbcdccbbadddddbdcccbcacbcbbdcadbcabdcacdddddccbaacbcbccbccacdccadacbccaccbabccaddbaaadacddcbcccccddaacacbbbadcacdaddcaddbabcaaabaabbbbadacdacdcdbbacccddddddcddbbddcbbcdddcacccdcacadbbdaaccaadbccbbdaabaccdbdadddaadcadabaabccabbcdddbacbdcaccabacadbbcdcbabdbcabbadcbdcabbcbdcccaaacacabddbacdaaacbdbcdabbbddbbbddcdcddcdaccadabdadababdabdacccadaadbbcdbaccabcaacdbbccbbdcdcbbdbcbabacbaabcbdcaddcdbddbaccdcbcddacbbdddcdbdccaabbdbdbddaababdcccdaaadabccacabacccdbcabcdaddabcdbdcacbdcddbbdadadabdcadbbbddbabccdcddcacdadacdccdbaaadccadacbdbcabcdbcacccbdcbbdcbbaddbbbbbbdbbdcccdbcbccaadbacbcbbaabcdacdbcbabdbbbcdccdccccbbbdbdaaddcbdcccdcbbaadbadcbcddbaccbacaaadacccadccbcbadbbcaaccddbddcbcbbaabcddadaaabdadabdbbbabdaadcdaddaadabadadabbdbddbcaaaccdbababdcccddadbadbdcdabdcbdadabbbcacbdcbbbcddbbdadbdcbcbcccdacdcbcaaababdaadbabcadcbbbadabbdaddcadbabdcaadbaacccccaddbcacbacabaaadacaadddccbcbcabaacbacaaadadcbbbabcbccadbbcaccadddddabbbcaaacaabddcbcaccdabcbcabcbaadcacbdaddcccdbabbcaabbcbacaaababccadcddcccdabcbadddcbdbdabcccabdcbaacdadbdabdbbbdabbbcbaccdaaccaccadacdddbdadccccbcaddaacacdabbdaadcccccabbacdcdbdcbbccdcdbbaaddbcbcababdcacadbcbabbdcbaaddaaccdadbbddbcbdddbdcaddbddadaacdcaabcbaabdaaddabdccccdcdabbadbdbadccacddcdbdacccabbaaccccabbaddaacbdcdcabbdcbbdacacaaaaddacccddaabacddacdccacccbdcacdbbabdbadaddccdbadadcbdcaaaddbdbbdcbdacabdabddbadcabdddcbabdcaccdacdcabbbbdbbbbbddaaacddbcaddbcaabcccdddbdccbbbbbbdcdddbbdaccdbdacbdacadbdaaacdabcacdbdcbcccaabddccbcdacaccdadccddcbcdccadbbcbcacdccaacddadbaadaccaacbccadaaddddbcdbbdaabcddbddcdbcbabcdbacdcdbcddddbdcbaaadbddacbbcdccbcabbcccacdcbdbdccbbcbcababccdccacdccaddddaaddbcacbcadccbaaadcdbcabcacbabadcdaadcddcccbcdbbbdacbbbddacbcdccbbaabdcbccdbdddbbcbcdbadbbaababbcabcaddaabcdbabccabcbacdabcbdabaacbcddcaabcacdaccbcabaabdbabddbddcdbcbccbddddbcbbaacddaddabcdcaccbdccbcdddbccaaccccbabbaacccdccadbcadbcdcbdbdacdbbdbcaacdbcddbbdbcddbadcabaadabdbddccdbbbcacacbacdcaacbacdacdcdcadbabddbcaccacccdbaaacbcbbbaadadbdcadaccbaaddcacaabadddbccdabdcadbdcdccdcdcdcddbaadaabbdacaaddacabcbdbaabbadacbcaccaabadbcacddbdadadddbcbcdcabaddbcdddaaccacdababcbbddbbbaadaaadbdbaacacbcbbccbaaabbcacbbbaddbcdcbbaadadbbbdaaadacabddadadbccbdaccbcadcaaacabdcdbddcadbdddbbabbcadacaabbcdcacbcadaccadbccadddacadddcacbccdddccbcacdcbacbbadcdaabababbdcabbcdbbddddcacdcadadddadbddaabccabaadbdbccbcacabacacdccabacccbdacaaaccdbcacaccbaacdbdbadddcaccdcadcbbcabcbcaabadaadccdddbdaccbaadcacdcbccbdcbcbaccbbbadbdcdbcdccbbcbddcbaacacccdabbaaacadddcaaccdcabcbabccacacdbbddacdcddcbdcaabdacbbbdbcbcdbaadbcddbcdddbcbaccdcacccddddccbdbbbcbbbdaaaddcacacdbcadbcaabcadbdacabcdbbccabadcacbabdadbcaddcddbdcbbbadaddbaddcaccddcdbbcaccccabcbdbcaaacccdcabaaadadbbcdcccababbabbcbddccabaaaadbccbbdbdaaaaadbccbbcbdabcbcadddcddcbcbdccadcdbdabbcdcababbccadbdccbdbddaccbaddcbbacdadcccaddadaccbacacbbaaddaadcadadcadddaacaaabdbbccadaadbdbabcabbacaaaccbcbacdacccaccbbcdaaccbacdbbbabacbabcdacabbaaacdacbbabcccdcdcdcdbbcadbaddcaccbbcdbadbbcabccbbabccabcadccbccdaddbbcbadccccbabadacacccbdbbaaaaaaccdabbcaadbcbaccbdbaaddaabdcdcdcbcbdcaabadcdadbcaadccaacddaaadbaaacbccacbaaaadadcbccaddabddbadacdddcacbbcabcccbaabadbdabcdaabdddbdcbadbacaaccdaadddacadcbabbdccbbbbbadbaaddaadddabbddddcbcdddbdcadbcdadacabdcaccbabdddcbddabdbbcdbdddccadcbbdbbddabcacdadddcddacabdbcaaaccdaaacaacdddccaabbddccabdcbcababdadbbccbcbddabbdbaacaacbdacdbbdbabdccccbadaaccacbcdbabdddbcaacbabbaacaaccbcccdaacdcbbacbcdbaacadcabccdcbaddbcddbdbcabdbdcdcadacadbccbabcccdadadabaaacddababcdcdabdbbccadadbaacaaaaadabababbcbaddadddcdcadadbadbcacdccbccabcbcdbcdddabaabadcbccdcbbbbaaddcabbdcddaddacdbacdcbaaddbcddacadccbccccdcbaddbcdabcccccabbcdabdccdddccdcbcccdaccccacddaddbbdadbdcaccbccabaaddbddcadacdadacaaccdbbbadcaaaaadabdabaabcbccccbbadcbccabadbcdcdabadbabdcbddcbacbacbabdaadababcdbacdbcbcddabcabcbaddcaddabadddbcbacdbcaddbbcadcbdabdcddaacabbdcdcdaccbbdaddabbcdcbaadcaadbbdacadbccbdcdabbaaccdbbcaaaacdbdbaabbcbdcbbdccdbdacbaacddcabbcaacbaabbcbccbdbcccbddacbdbabaacadcccbaacbabcdacdbcbccdbddacccacadacddaaaadaadbbbbcaddbbdbadcddddaaaabbcbaccaabcddaaabdddaddcdbbbccbbaadacbaacadaaddccaabaabdbbcddaaabadbccdcbbbddcccddcadbcbddcabbdcacdcbdbcacacccbcdbbbcccbddddbddbdbccdcaaabcadbddbabbacdacbaaabcaaabccdbabccadddcabcacdddbdacbabbccdaaddcdaaddcbbaacaaabdcbbcbdbcaddbdbbdabddcdcbdacdcacababbbabbdabcbcadbcddcbbccaccacabcadcdbdadddabacbbcdbcbbbcaddcdaabcbcdadcddacddadbabadcaadbababaadbbbacdbddbbdbadaddabbcddcbbdcabbdddabadbacacddbdcbcbbcbabbcddbddbcbdcbcddbdadbdaacbcaacacddddbcbbabddddbdacdbdaaacbdbbcdaadbcdbcdccdabaadcaacbbcbaaacdcbbbabbbaddddbdbaacdaddaacabacdbcdddaadaccacbbbdcbdccabcadcaabcccadddaacdbcbddacaccbabbcbddddcdddadacaccbdaacbccdaadadddbdbccabdccbbdabbadabcaadaabadcdcabbaacbccbaadbcaddbcacacbdaddbcdcddbdbadbdccbcdaccbbcaadddddbcbdddddbbadbdbdbbbaabbbbdbdcbdcbcacdaddddaacdbddcbbaabdbdacddbbcadaaacabcbaacdacdabdddcadcabdbcacdbadabbbadaadcacadabacccabccbadcbbaadadcbcbaddddaacccccabcdacbbbcaccdbdbccdabacacdddbdcdacddbbbbdadaacdaaaacaacabddcddadcadaaabbabdaccbcacdadbdaccdacdddbabacddbbbaaacabddccabccbdbbbcbcddcdadbdcddcbbdcdccacbbbcabaabdcabcdaadbadccaccbdaaddbdcacdacdbcbadadbdbaccaababdbccddbadbaabaaddcbcbddabababacbdbbccaccaddaaacdcaaddbddabbccccabaddbaaacabcdabdacbadccadabaddaabcdbadcbcaacbdacbbadacddddccaddaaaaccaaabaabbccaadccbacaadddbabcbbdddcadcbabcbbccbacdbbaaaadaabacaabaadbbabcaadaabdacbdacddbaaaaaadbaadacacccacaddcbddcbdbbadacbbddbbccccaaaacaadaacbdadccbcaaacabbbabdacbadaccdccddabdcdaadcddaadaaaddcbadaddaaddddbddcdadccdccabbcdbbddbbbcbcaaddccadbdbdadddbacdbcdadaadaabcbababaadaccdcbcdbbaccadcaadbdacbcddaabcdbbaacadcbcccccadcacacbcdbdcddddcbbdacccdacadacaadabdbabcdbbacddbdcbacabbaabccbcadbdddbdcbacadbbcccbccabacdabcdddbddbbabbcddcdbaaababadbbabbcddadbdccdadddbcbdbbacbadbbbccbdccdbbadccdbccddcbbddbaacbcabddadaaadadaacdabdacbaadbccaadbcddadaacacdbdaadbdcdbbcccdbcbcddcdcaabdabbcbbaaddcabbacaaaddcabcbadcdbaacbadcdcacaadabadcbaabddabbdabddabcccaadcdccbbacccabbcbdaccdaddcabdcbaaaddcbbddcddadadbcddabdbacbdbbadbbdbabdcbbdcddbabcbbbccdbdcbdcadcbadbdcadddcaccdcacacaaabbcbbcdbadccdcdcaccdbddabbdabdcaaddccbadbbddadaadcbbabddaddbbccccbbacddcbbccdbbdacbcdbcaaccccdbdadaaccccbbacabcdabcbbccaaadaacabaccccabcdccbaacabdbcaadaaddacccdacbcdabbddcaddaaaacabddaacbbdcaacccbadbacabbdabadccabaccacdacacdabadcdaacdcbdacdbcccbcbdbbbaabcaccccadaacabbdbabcbdbaaaaacbbaaabcacccbcadaccabaddcbcddcdcbdcaddbcabbdcacbcbabdabbcaccabacaddadadabaabccdbbbcddbbababcdacbccdaccddbbdacdbbdaccdbadcdcbcabacabdbabcbcdcacdaccdbbbcaaacdccdccacddaadcbaaccdbbbdcdaaaddacdbbadabaabddbbdbbdcdcacccaaddabdbbbaabacddcbcaabbdcdaccbcbaccbaddcbaddbacaabdcdaadcbcbccdcbcbddddccbccbbdcddabaabbdbbabdbccdcbacdacaddaabcdadcdadacabccdddadadabaabcdddadabaddbdabcdadbadbdabadbbcdddcdababcccdcaacaacdcaacaaaddcccdbcddccdddcddcdbdbcaadcbccaabddaadbbdbadddaabaabccdbddabbabddbcadbaddaadbbccacdadbccacbcdbbcbcdbbddaabacccbdadbdbcabbccdaabbbcabaaadccdcbaccbacdbcbbdbacadadabddcaadcacdccadabcacddbdcadbabcbbcadcbcbdcdacdccaaadcaadcdacbcaabadcdadccbaddaccdbcdccbaacdacacbddcbdaddbdcdbabcccdddddbacabcbcabccddccccaadacacababadbabdddacbaacaccccdbdacaabaccdabdacaaacaddbdabccbbdbcadbbadbadbccdddbcccbcbcccaababcdbbaabbddbabcbccdaaacacdababdabcdbdcbbbbadbcaaddbccadcbdaaccaabbbddbbacbcaabadbbbaddabaadacadcdcbadacbadcaabaadcccdcbcdbadacdacadcbaaabcdbcdcabddcdddcbdabdcccdacbdccdbcaddbbddabcdadbbacbcdbcdbcadcabadbabcbaddbcdcdbbdaacdaccddcbdabdbabaacacadaadacccdccabadbcacbacdbddbcadabdbdaacbcbdbcbdaccbbdccacdabdabbaacaccbbbdaadddccaabacdaabcbcdccdabaaadbaadaccbcabccddcddbdcddbaaccacdcaadccbddcbbaaccaacbbcdbdbaddbabcadcccbcaacbacdbbcaabdbcbcadaacccbcdacbdabacbddacacaccabdbabbbaacbbacacbaacacdcdbaddcbdbdbcaadcdbacaabacbbccdbccbabddacddbbcaddadbdababcccccadbcdcacccadcbadbdbacdbabccdabdddbadccdbbcbbcacaaabdadccbbdcbdcccbdcddbaddbcbbbaccdadccbcdcbaabbbbdcccbddcbcddacacdcabaccdbbccbbabbaabbbabdcddddbaadabaadbdaabbbbccabcddadacbabcbcdabacaacbcbbcbcddccbcacabaadbaadbddddccdbacdddaccbddabaddddddbabbacaacccbdbbdaaacbbbddbdcbdbacaddcbcadbdaaccbbcaddadcdaccbbccacbbbaacdcdbbadbdbbdddddccacdabdcabbcdccdabbcdccdddcadbabacdbbddacccacbdadcbabcaabcabcaddbdbdcbbbcccbbcbadbcdcabdabbaaaacaabbbdcabadcbdbbcacacbaaabcaadddbbcbcaadcbbcbbbadcbcaacdbdddbccbcbcbabcdacabbbbabdddaadacbaaaaaacdaabccbbdcbcddddabbdabdcabcccdcdbbaaaabccddbdabdabaccabbbababcbaababccdaadcadbdcbcbdcbbdbbbbccbddabbccbbcdaaaabcdcdabaabccdbdccbbbbdbacaaabbdacddbbadccbbdbaccdbbbaaadddbbcccbdcdcacabccbadacdbaabbacbdddaddbcaabacdaabcbccdddacdcbdcabacbbccaabbdaacacbcbdacaaccbdcbdbcdaccacacbbbcadbcbaacbcbacbaacbcbacdddddccccbddbdbdbdbbadabadccccaabaddabacbdabbbddccbcdacdcabdccccbcbbdcddbcacabdbaadaaabbcbacdaddabcccbddddbbccdcdcccacaaccbddcccabcdcadcbdcbdbdbccbcadaababbcdcdddbbddcccbaaaccacccacacbabadcbbababbcdccabdaccbbbbaababdbbaabbadccabadcadabaddbbcacbaadaabbcadbdcccbcdaabbcdabbbdbcaaadbddbcbdbaabcbaaacddccbcbcbadbaccdbbaaaccddbaaddcadacadddbabbdaccaaaabadadbdccabbacdcddcddddbbadaaacabacdaabcaacdcacdccbdbcdcddbaccadcaabdaddabcdbdacadcbaaaaccadbddbbbcabcdcccababaabacbaababbabaddadbdcaabacababbbcbdacbcaccabbcdaddcdbabdbccbcaacbcbdbdbbababaddcbbbdbbaaababccacacddcbcbbdacacbcddddbdbcdbbcaacadcddcacccbccddacbdbdcacacacadbbccddcaababaccbadbcdabccacbadadbdbddacddacbbddcbbbcbaadbcddabbbbcdbadaccadcdbcabdcdaccbbcbcbdbcdcbbaddcbabbcddccacbdbaabccaacadbdbdbbccccaabcdaaabbcbcbbaddcaacadaadcdcaabdbbadbccbcabcdacdbccdadcdbadcddabadaccabcbbccdccacdccbabdcadbddcdbcacabcdacbcdbbbdbabcacaadadbcacdcbbaddbbbadccbcabbdbbaadacdccaabddbbcabcaddcccdccacaacdbabadadcddcbcadccbbaaccdccccdcdcdbcdbcaadbddcadaaddaddcbccccddaccddcaacccdccaaccccaadacccabcdacaabacbcbaaddadaddabacdabdadaaddbacaacccdcacaaababaabaddadccddabbcaabccbcaadababacaaccccabaccabdaaaacddaacbdcddcabddbabadbaaabbbacdacbcaaddcadddbbdabcbbcddcbaacbbdcdcaddcbddddccdcddcbdbdcbbacdcbdadddbbcdaaddbdadbbbcdbacdaddbccacaddddbacdadbabdbbabcacacbadccdbcdbdbbbcbcbddaaadbcabbddcbbdcabbdadcabccdbddacbadcbccaadabcbdbacacabcbbaccdcdadbbaccacdcbcbcccbbbdacbdadccbcbbdbbaabccdadcbaaccdcdccadccacbdddacbabbadcacacccbadacddcdcdcadaaadbdbccabbbddccdaaadbacdbcabcaddacdcdadacdddadcdbbaddcbcdbadcbccccddcbbacbacbccbcaccadadbdcaaaaabddcabbbabcacdacbaaabcaccaacdacdddaacaaadbcdaaadaddcdbabccbabccacabdcadaaabbddccdccabcddabcbccbcdadacbadaccbbddacabacbdcdcbbdaddccdcdabbcdbcbcdadcbbaaadaabbadddabbadbacacadaccaabadadcbaaacdbabcdbbddaabdbcaadbdacbbdcaadcbaabaaddacddccbcdaadccaaacddbdabacbddcdcadacaaadacddaabdcdccdbbcbcdbbcbbcbddbdacdaccabbabdadadcbcadcbcbcdcadbddbcabdcaccccdcaababbbbaccaadadadcaaddbadbabcbbabbbdbccbcacbbadbccaccbcdacaadcdabbaaaccaccacabcbdbadcabccdadaccbbacdcadcccabbbcbbcdcdbadbaabbdbacdddbccbcccbcaabdbadddabdabaaaaacaccbbbcababdaccbddacccaaabddaaacacdcbdccdcbbcbcbaaccdccdbbbacddcccddbbacbadaaacabdbcaacbdcddcaabcabbdbacaddbaaccdadbbdbccddcabdddbacdabccdbcbcadaabadbadabbdaadbccadaababaabdcbacaabbcdcbaccadabaaadaadcccbbbddbdadbdacdcdacbbbbddcdbcdccbdcabddadcadadcbdabbbcdadbddcbdcddcaadbcbdcdbdcbcddccbbbdccaacbcdcbbbaaccbacbbddadadcccaddcabccdbccaabaacbdcdccbccddacbdbbadccddcdbdaacbdbadccdccdaabacaabadabbdcbcadaacabccbadbcaacccaadcacbbaabbdbdcadadbaabdbcccdaabcccbcbdcdaaaabbbddcabdababddcbbdcaaaadbbbdaabaaadaccbaaabccbdaacadbabcbccdacadbcbabdcdcdddcabccbbbabaadcbaadcdababbdacbadcaacacddbbbdcadbcdcbcbbdcdbabcdaacdabdaccbccdcbaaabcbaabcbcbbcaadbadacddcdbcaabccdcbddcdcabcdbdabcacadcabaccdcabcbdacdbcbccdacaccbccaababcaabcddcadbbccbaddbaddcdbccbdadcbadcbcadbdabbdbbddbdbaabddacdabadcbbbbdbdbcddcbadcadbacdcdacababcdadccdaadcbbdbbabbdbcdbbabbcaabdddcbcbcbdcadbcbabcbcbbbbcbcbcdcbaacbabbdddbabbdaacbbaaabdcdcdbbbbbcddaadbddbcbbdddabbabbccaabcdcbbdacdadbacbdcdbcbcabcaaacdcdabcdbadabbcbdaaadddcdcbaabccbdababdaaaabccdabadcbadcacbdababadaabdacaddcdadabbccddbdaddacbcdcbaaacdcdababadaccadbbbdadddccdbdbdbcaddbabddacdcdabcaccddaddaaddbbacdcddbcacddbacabcddbddccdacbabbacddbacbddaaacbbabdcdcabbdbdccccaddbddbabbdbbbcbccababcccddaadcbbccddccabbcbdabcccabacbadadaccbbdddbcdcdacabadadacbdbcddacaccadbcbbdccbdabbcdcccbdccaadbccdaaacbdcadcdadbcccdcbadacdcdbbbbdccbabdcdabbddbdacbdcbadaaaadbdadddcbdaabdcdccdbdcddadcbacacccccbdcabdbccabacbcaadacbadcadbbcccdbabcacdaddadcabcddacacacbbdababbcaacabbccdddbcbaccbbacddcdcaacadddcacbcadaadcbbcdbbdbadbdacdcaddadcccababaacddcbbacadcbacccbcadabacbabdcabbdcdbdadccaddbbaabcabdabdcacbdadcaaabbcacbbadbbaddccaaaccaabadddcacdadbdcdadcdacdcdbdbdddaacbcabdadabcbbcdbbcbcabaabddabcacbbbbcaacbadbcacabacbccdcdcbdabccabddcddacddbdcbbbbddccbbbbdcadcabbbdbadbbadbbdddcadacadcdbcdaaadbdccdbaddbdddadcabbbbabcdcadaccacaccadccdcacccddabadbbddddaadbbbbacbabcbaabdacabcacbcabcbacbacdaabbadbcadddcaabaaddbdcadaacbdacddbdabcbbabdcaacbabacbacbadacaaccbbabaadaccbbbddacbbbdddcbcdcdcadaacbddaaaccdaabcdabbcbaadcaadcaddcdbbbabcdcabbbdbbbbaccbacdbdcccacbbaaabcabccacbdcccbccbacbaddddcadabdcbacdacbdbacbbdcbcbcccdbcdbaadabaacdcbddcdabdcbddcbcabacaacaabbcbddcdcdcbdaaccacdaabdadcccaabaccaccbbabdaccccacbcabddbdcaddaabcdbcaacccacdaabddabdadaacccddacccdaabdbdbcdccbbcdcccddaaccdddcbaadadcbabddccaccdaaaadaaccaacdcdbaabbdddcbcccdcadacbaddacdcdccabcdddddbabdcdbaaddcadbbabcbcdbbdaababadbbdddccdacdabadcbdbccbcccdcbddabadcccacdbcdbdabbbaadadaccbbddacaadacaddbcbcdccbbaaccddbbbabadaabbdbabddacbcbadacaabbabadccdacccdbdddcdccabcaadcbcadcbbaaccbcbddbbadabddbdcdddbbdddbcccadaccbbcdbbddbbcadbcbcbcaacadaacacdcddbacaabcdabcacdabbdddcbadbabccacbcacdbcdbbdbaadbcdcdbdcdddbcddcbdadcbdcbcacbadcaadabddddbaadddbcbdcddcacaadcbcbdbddcbabacbdacddaaddaddbbbbccdbaddbabcdccbcbbcdaddbddbadcbbdaaaaccaccbccadbcdddbbaccacdcccccdaaccacaaabbdcddaaabaccdbaccdbbdbddbbacdadcadaaaacbdccddbababdbccbacdacbdbcddaaacbbcddddbcdddababacaccacababaadacbdcbbadacddaadcdbcdadcdcddbccaabaacacabdaaccccccdbaadbabcccbbbbccabbccabcabcaacdabaabcdbdcbbcccaaadcbabadbcadbccccdbbbdadcacdaaddccdcbaabbbcdabaaaadcdacacbddadacbddabaabcbbbbdaccbdbcddadccddcacbbbccbabcbcdcadbbdccbbcbccbdcacabacbccdaadbdbdbabdbddbbccdaccacabcaabbabababdcdabcaccbcdbdadccdcccdbbaacbddabccbddddadbcbdccbabacbdbccdcbbbacadadbacacacddbbaabcdbadbbcccccacabcbdbaaddcbbbacacabbcadabacccabbcdbbabdbddbddaaadcdbcbbcaddcabdcdccadcadadadccbbddbaaadaccbcaddccdcdadacadbadcbcbbcbbbbbacadccdbdbaaccbdacdbbccbadccdbacdadbbcabbcadbdbcccadcdbbdcccccacdcadabdcbccababbbbcccccbdbbddacbabcdccadcdbbbbbdccaacaabbbbcabadddaadcadbddbddaddcaaddbadbdcbadaaccbaccbdaaccaacacbbbabacddbbcdabcabcbcbdcdcbddabbbabadcccbbabbbabcdbbcbabbcbacbabddbcbcccacaacbaaabacacabacbbdccabaaadabccbabccdaabbacdbccaddacbdcccdccdbdbadcabbadcbccbabadabcdaaaacabcdbbdbacadcaadddabcbcdcdbccccacabddbbdcdcdcbcaccccdbdbdaacaabcbbcbcdcdbbcbcccdddbcaadaaabcacabccddcbcccabdcacacddadbcaaaaaabbcbdbddabccccdbacbdcacdbadabccbacdacabdccdddcbddcadcacdbdcdbacdcbccacabacacdbbbbaaaacdcbddacaabaadadcabaadadabddbacccccaabcddaabddadcddcdcabadbdddadbdbbddabdbbcaabbdcbaabbaadcacbcadbacbdadbccaacabdddbabbcbbddcaacbcdccbadbcdbccbcdcbbdcaaaabddbaabbadadddbcdacbcacbcaaaccabbaacadadabaabcbbccbadccaaddbbddacaaddbbabbbcbdadcccdbbbbcacaabbacadccabbbcadaccbabaaacaacdcdbcdbaccdbccbdabbcbaddaaccdcdbddcdadcbadbccbdacaacbbbdaddbcabcdbccbbabddbbcacbbabbcaadddaddaaddabdacdcbaacccdcbdaabababddababbdcbcbcdaababdabaaccccbacbcddbcbcdaababaddbbbccdbcdadbbacbacbbadacddaadcdcbcdaddbccddbbbacacccbddcacabdddddbdaababddaccbcbacdbdbaadbdddddcbccaadbdcbbcdaaccdcaacbaababaacadbddccaddcdabdbcabcabcdcadcdbdbcbbbbcbcdaccbdbdddddbbcaadabadbcbdabdabbacbcbdaaddcddaddbacacbddadcdcbaddccbabcaddbdbcaacddcbdabddaacdbdcaacdcddabdbadcbddacbbacdbddadbbbbcadacbbacaabbcdbbbdbccbdadccbabdaddbcaaacbddabbabdbbbcbbdcaccaaddcaaccaddacadabddbadcdadbadabdbadccbdaaaaabccdbbacdccbcdbbabaadcbcdadbcdbbcabdcbbcacdadcadcdbccacdbcadacbaabdbbdaacacacbcbbccababcbccadcbbcdadadbddcbaccbcabaccbabccbbadcccaddbcbcbcbdcdcdcaccdacdacccadadcdccabaaacaaaacddaadbcaddccaaacbaccdbabbddbadccbdbddaadaadddbdcdcdcdcdcbccdbaabdbbacadbbacdbbabcdcadcbbdaaccabbbbbcdaadccacabbbcddabbdadbaadacaabdcdcdddbbdcddabcdabababdbcadadadabcdaccbdbddbacbbbcbacdcdabcdabbcaaabbccddcbbadcddbdccbbdbccbddbaacacacccccacdacbadcbaaaabdabcacbbcdbcabddcbbaacbcbcdccdcbcdbcdbcdcbaacdabdaaaacdaaccdbbbbdcbbdcabcadacabdcddbabdabbaacbdcdcccaabcadcccdcbdabbbdcdabcdbcccbdccbdcaacbddaacdadacdcddacbaaaadbbcdbcbdbcadbddaabcabccaaabcdcdccadcbddddcbdacbaaccbbcdcbdbcbaccabdbbdbadcbdaddccddabccdaaacaabdbbdbdcdcaaabcbbaabcabddccacabcdccbbaabbacccababdadbcdcadabaddbadcdadaaadcdbcbccbdcbddcbdbdcddbacbcdcadacbbcdaddbdbabcacacbdcbcddacddddaacbadcdaadccaaabdbcdbabacccacddbcdabbccadbddabcdddcabcacbbddaddcbddbbddccbcbdbdbcddcddbcdbbabdcdbacaccdbbbddaaacaaaccccbbdbcbccbbcbbadbdabbddcdbaccaddccaacbdbcbaadbcdaccbdcacddcaadbadbdbdbdbbdabadabcdcbccdbdcddbaadccccbcdcababddaadcbddbbdcbdbbadddacdcbbbacdcbdaadacdacdaddbddcacabdabdadbbdaaccbbdcdbccacccdcabccbcbcbacacbcaacbbbccbcaaaabaccbaddcdcdcbdaaabbadbbacbccccbbaddcbbdbaccbaacdbabcbadacbbadbbddcaccddbabdaacaacbbbcdddcdabddabcaadcbaccdccccdbbbbbaccdcaaddcbdbaaaadadbdccdaacbbcabbacbdcdccaaabdabbacaacbcacdccdddabccbbbbddcdddacbadcdcaacdcabaccddcbddadbbdabacacccddcabbdaacaacdbbbbbcccdcabcdcbaddbabaddcdadbdbbdbaaabbcdbaccbcdbccdaabbacbacbbaabacddcaacbaabddbcbaadcbdddacabcdccbbddbdacdbabbcadcccdcaabdcddbddaaaadcaadbacaababddddcacbcbabbcccbccbbaccbdadcdbbbbdadaddacbcbaddcdcabbbbdabacddbacacaddcaccdabadacdcdccccaddbdcddcbcaccaadacddbddcabadcddcdaaddabbbbddcdbacdbbddcbacdddcddacccadaadbbdbdcdaabbadadcabccacacddcabdbcbdbacdbabbdccbbcddbcdbacccabaaddaadbbcdabdaababcbabadbbcbddbddabcdadacacddbbdacddabcdbdcdbabbcacadccbbbcccacbccabadaacdbcbcddbdbbdbbacbdcaabcccbabbaabaacccdbcdccaabbdcabdcaacdbaaaaababdaacdbdbdcabcdcacbabbccccbccabbcabadadacdcabbdcbcdbaaaccababbaaacbbbadcaacaddcbdcccdcaccbccaadabdacbddbcccabdbcadadcbcdccaacdadbbaabcddaacccddaadadbadcbbdccdbbabbddaabbbbbababdadaadbbdbaccadcbbcccadbbccaabaadbcbcdbaabddccdddabbaccbdbcabadcbbcacbbcdbbdbdadaadcddbcdbdcdbdadababaaaabdcabddabbddbdbaabdbbabaccccbdcdadcbdabccaddbdddadcbcccccbcbcdbbcacccdaccbccdcddabddbccadacdddbbdcddacbadaadddaddbdcdcadddcbbdbdcbadbccdadabdcbdacbabadbcadddcccabcbadbccabbadabadcccbbacaddabaccddbcbdbaaabccabcadaccdddababdacbadcddadcdccbabaacbbacaacbabdbcbdbbbabccacbcbbabcbaadddddcdabcbaadbccbcbdbbbabdcbacabbdaabbacbaccdaadbaccdababddcabbacbbddcbdadaaadbbccdbbabcbbabbabcdcdddabcccaabaacdacdabccbdbcbcdadddcbaacadabdbbdaaaabccbddbccabcabddbbcabadcdbcbdccbcbabcddaaadabbcbddccdcbacddbbbcddddcabccabccbbccaccddddabdaaabcbacaddadbabbbbcabbbbbadcdacddacadabdbbaccaaccbcbcddcdcadaabcabbdddbaccacacabcadbccbcbddadaabcaddccdabccbcccacaacadccabaabbbcbcbddaddbdbcacacbabbbbdbbdcaadaaadaadaadbaaabccdcbacadcadcadbabdaabccdabbdaacacdbcacaabcbacbcabdabccdcccccaadaacbbaaaccacabbadbbcdbbdbcccbddabcbcdacadadabccbbcdbddbaacbbbccbddcdbabcacbacbcdabacddacbacbdcaddabccbabbaaaacadadacbcbdbbbcbdaabbaaabadbbcdacbaddadcdcbbbbdcbcbbcdcdadcaabaadccbbabdcccaddabaabdbbbcbdddbbccaccacbdbadccbaacaadaaccdadcbcbdacabdbbacccbaccccddbaccddccdaaabdcbbbcddadaaadbbdbcbaaabacadaaadbdadacbaaaaacccdcccadaaabcdbdbccbdbdabcdddcbcadbcbdacdcaccdcdcbddbbabdcdbdaaadccaadababcadbaaddccbccaabbbbbaaaabdcdbbcbcaaabcbadbabbadadbabbaababacdbcaddabbccdcbcabddacacdadcdbccbdccddadbadbbcaaadcbaabcadbccccdadcadaabbbadcbdbbcbacdadcbdbaddababdadbcdabacccadddbaaaadbbaaddcbbadbaabddbabacccdddcdacaabbbadbbaaccbdddbaddabbbaabdbadcbbaaacabdbccdcadadddbbcccdcabdbbbdcdcbcbccbdbadbbaadadaadcddccdcdbdbdacdddbacaddddcacdbddbaabaabdbaaacccbacaddbbacbbbddbbdbaacddbbccabdbabcccaaadddaadabcbdddcdcbacbbdcbdcddbdaacaaacacbacababddbbdcdbbdddbbbdbcddacbbadababbccadcbdddadcaaabcbddadabccbbcddbbdbdabcdbabdacddbddddaacdababcdadbddaddcadbccbdadaaacbccddccaacdbaaaadacbdacccacbdbabbcbbbbddbacbcbcacacddaddbaddddbbcdaacbcabcccaaaadcabdacadaabadcdccbdaccdababbdbbcbabaacabccaabbaadaadbccccbddaccdcdbcdcddaadadbcbadccbabbabcadccaaacdbaaddacddbdccdcccbadbdbdcbacdaddbccaaabaacccbcddacdaadddbabddaaadcabbcdaccbbabbabcbdcaaacaccbadbcdcbcddabbbcaadccdabdaacdcbacdddadbacdcdacccbaccccbcaacdcdbbbbaddbcddbbaaaaacabbaaddbbcaabaccccbbddccadcdbdbcdddbbdcaddcccbabcbccbdadcadddacdbbdbbcbbbcaabadbccdccaaacccdbbcbaadbddbdacbdbddbcaabdbdabaaabcddaddcaaaadabdbccdddbdcdabacddbadbcdcacbdacccddcabdcadadbddaacabdcaabadadbbdacaacddacacdaadbbabaaacbaaccdbcbacdbaabdbcbaabdbaabdbaaaabcabcdadacadddcccadbcccbdacdabdcabcacbdbaddabdabdddcbcddaddcccabaaadcacdaaddbbbabbdaadbadbbbaabbcbcbadcddccacdccdbaadabbdbacaacaddcacdaccacbacacaadbcadcaadbcaacdacbaacabdbadacddbcccabaddbcbdbdcccddcabcbaacdbdddcdbcddadbadbabcbabdaaacdccbbdacbcddaaadcbbbabbdaabcbcdaaadcdaccbaadabdbcdabacddbddbbaaaabbbbbdaccdcbdaaadcccdcbacadcddbaadddcabaaababcbabdadcccbcaacdbcadbcbbababadcadbcdacdccadbcababbcaccdccbaccddbbadaacbbccaccacdaddbdcbccdcdadbccaaaddbccccccbaadbdcbacbbbbaabbdacdabdddbcddaaabdccdcdbaddaabbdccbdbbdcaccabbccbddccdacccdbbdcaaabaddbacbbdcbdcbcaadddbbaaadadabbddbababcaccddadaadaccbbdcdddccddacbdbdaddcbadaaaacdabcdcbdcacdddbcdabdaccbdcbabaccbcbacccbbbcbcbcbacaadcddddbdadbbaabcdbaddcbcdbaacdaddbbaacabcdaccbbbbcabbbbaddbddacabbcacaadababadcdadbddcddcdbcacdabbdcdbcabcdcbadbadabaaadcccabdabcacbdcdcaadcdbbdabacbbcaaadadcabcdcabbabdcaccbaabbcbdbcacadacdbdbcbadcbcbccaabbcdaddadcdccbacabccccbabdacbbcbbcdaadbbaabbbbccdcbdabbccbcbdcabbdbdcdcdbbbabdbcbbabbbbadaacbdababdacabbcdcccbbabbabcaddccbaacbaccddbabbcbddcaadcbcabbdaddcdbbdcdbdbacbcdadbccdcdddcbacbbbcaaacbbabbccccbacbddcccccdbdacaccabababbaaaccdbcddacacccdacdccbbdacacbdabacbcaabcaadbaaaabbbcdbcaabcbdcaaaacbcacadddbaadcaacddddaacddaccadbdccdcaadcddaacdccbddbbaabdcdabdbdabcbbabbaddcacbdbbcbdbbddccdabdcacbcddccacacdadddbacbacdccdcdaadccddadccdaaddccdbbcbbdadbdbccbbbdaaabaccdccddacacbdaccdddbaabbbdbcaaacacbdabaccabbbaddddccdbacbdbccdbddabcaabbccbdcbabdbcbddaacbabadaacbaaacadadadacdccdadcbbcdddccaacdddcaccccdddbcbdcadddbddaccdaaaabdddbaacabadcabcaccccddbaabbcdcdabddababdcbbabbabcdcaacaaddaaadbaaaaaacacbcbbcdccccacbbabcddbaadaaacabdcadaacccbddccdddacadcaabdcbadaaaabccbacccbbccdbbdccabadbabccbbbdcdbcadddbacbbdabcbaddccadbaacadabcdbcccdbabcdbdbdcdadabbbabacaddcbacddacbbaaaacbccbaacdcaaacbdcdccaabbcbddacabccaccbadccbdacdabbdccacacbccbdadacbcdbbcbdcaacdadbcaadadaccbaaddbcbdbdbabddacdcaaadacacdbbbddcdbcdabdcddbcbbdacddbbddadccbdadcacadbaddcdadbdabadabcaacabadadcbbbdacdcccabdcdccaaacacacaccaadddddcabbcababbcbcbaadbccaccaadacdbaadbadcdacdcadcacccbcdbbbdcdbdadcadcbbbabacbdbacdcbdcabbccbdacdcaddacbcddadcaddadbdbbdcaaadcdbababadcabccdbcadddbbdcddabacacabdadccdcbcdcbcdbbbdbcbcccdabdcbaabcbbbacadcbaaabcacacadbbddbbcdbcaccbbabababcacacdabababaddabababddadabcddaccbdaacddcacabbdcabdcacababcdbdbdcdbdcccbddbcdcaacadcdaaacbbabbccbaabddaddcccbdaabbcacbdbaddabbdbbcacacadbadbbdcccdcdbabcaabcabddbdabbabccbdbccdbdbbdbdbbabdbbdbbdbcbcdcdcbbabbadbaccadbababccdddbcdddbbccabaaddcdbadbbadcccdacacaabcdcbdbbaaaaddddacbdcbaddabbcbdcbcaaddabcdbdcdcaacbaddabcdcdacbcabccbcdbdbcadcacdbabadbdbbcdcabacabcdabdcccbcddccbaaacaaacacbaacdaaccccabcdabbccdadbabdacbdbdcdbdcabcbcabbcdcbccbcbacadcbdbdbbbadcdbaccadccbcdbcaccbcccbabaddadabdaccdbccbbccbcbcabdbcbdabddcdbbddadadabbbbdacbbaabbddadbbdcbdccbccbdbdaacddcadcbccdbcacaaaacacbdacbabaabaccbdbbdacbbbdaddabbcacbbdcddbdbbbccadbaabacdccbaabccdbbbcabccbdbacddcdbbaddacaccdabddccdaadddbbbbaacabbcbdcbdaccadacdcddbaaacabaddccbadddcbddacdcadacddcaacbaaddadbcddcaacaaddaadccaaaddbdaaccdddacdacaddaccddacaccbcaddaaacaabdaddaddbacbcddcaaabadacbcccdddbbbdbddaaabbaadccbcccddcabcababcbdcacdccdacacbabdbdbcdbddacbddddaccaabbbaaacbcdabdcbddabcbcaabccbdcdadcbbddbcbdadaccdccdadbdbbdcdbcbaacbbcbdbbcbaadaabadbcbbcccddbacadcabbaccdcaddcadbbcbbbccbddddcdbacdbbdddbdccaaacbcbbbaaaaacbdddbbddcdadbdcbdddaccdbacddddaccccdbddbbddcabccbdcdcbdbbabacbcdbdcdddccdcdcdacdbcbaabdaacbcdacaababcabacacaabaaabbcdddaccacbabddabacdcbddcbcdcbbcdabbdabbdbcdaadabdbbcbdcccadccbddcbadcbdcaddaaacbadddcabadabccadccbcadbcbbbbbacbdabbcacababcdbaabaadcadddaabcaccabcdcdaccacdbdbacadbbdaccbbaccbbaaddcbcbdabdacddaabbbdbdbbadbdbcdbddcaaddbbbcabbdbabbdadddbbbccdddadaddaacbbbcbdcbcadadbadcdcdbbbadabbccdbcccdbabcaadaabbdbbaccacddbacadbbababbcbccbacbcaddbaacbbadaaaadbacadcdbbdaccdccdabcaddabbdcabdadcadccbddcdcbcdaacadabdbddbadcdddacaddbcbcdbdabcaaddaacadabadcdcddcdbdabbcabcbdbaddacbdbbbacaaaaacaaabddbcacbaadbaddccbacbdcccddbabcdbdadcdbaadbbaadcdabacadbbdbdbdbccacdbbacbdcbccddaacdbbcadbdbbacabadadbacabcdacdcbdcacdcbbbabbbcacadbdacdacadcdbdbbcbbdabadbdaddcdccdabddaaadbdcbbcadbcdcddbbdabaadddcdacbadaddcabdcbdaaacadabdcdababadabdcdddddcaddbdbadcbaabdcbabdcaccbdccaaaacacbdcbddccdcbdbbdacbabbabbaacccaacacbdddbdbdcbdaadbbdcdbcadbccdbbdaccacbbdaadccbaaacacdabdbcadcbadcccbbadaddacaddcbcbaabcdacdbddbadcbabaabbabddacdbdadcabdcbbbdbaaddcdbcdbcddbbdaaddcdaaadabbadadbcdcbbbabcddcdacaadadbbddbaadadbdadabaaddcaccdbcbdbbdaadacaddacdacdcdcdaadaaabcdaaacabdddadbdddcbcbaadccdcabccbdbdcaabaadbabdaccccaccaabdccdcbacaacdaabbdacbaadccbdbabbcbacabadadcdbacdcdbacccaacdabbccdacaddbacddadadaaccabccaabaabccbaaadbacbdbdacdaacacbbddbddcbaccddbdccbcbbadadddaacdbcddbbacacdbddcaccdaddbbdccdcbaabadaabcdbbacdcdcacbdbdcaadbcccbcdbcccbdbbcacbcccbaddcabacbbcdaddcaabbcccbdbaaacdaacdaddaabccdbbddbcabdddbaccabbcacdbdcbbdccabcbccbabdccabbbbbdddcadadacbbdbbccdbacabdbdddadcdabbdcdcdaccbaccccbadcaaabbddcaaabddcabccccbcaccdbacbdcbcadbdccaaababbbcdcacacdbcaddacbdabcdcabbccacadacbcadadccadaabcaadbbbbcbacdbadcabdbacbcdbbdcdcadcbcdaadabdccdbcdaadcddaddbbdabcabbaadacdbbabcdbaacdcdaaacadadbcabbcaacdbddbbcbbdaabccbdadacabcddabdbdcbcccbabbbbcddabacddbaccadbcdcbdcccbaacddbbcdbdbababaaaadddbbdbcccaabaddaabcdaacbcccababbbcbaddddacccdddaadbbacccdbcabacaccdcdaadacdaadbbcdabcbcbcdaabbbdbbbcdaaadcbbcaadabdbbbbcbcbbdcbdbaccdbbdabcbddacccabaadaacbcadbcccaaaadcbdbabbaacbbcaadbccdbbabababadbcbbcdadaccbacadaadcbbabbddcadbcdcccddccbddcdaadaadacadaacacaddbaadcdbbdcbcabbddbdcdbcbbbaccbadcdbbcabaddaacddbbbcbcacdddbcbbdbabbaabcbccbdbbaadaaaabbadccbccbbaadcaccddbcabbbdbcbbdaaadcdbbddbdaaaddbbbaaaadcbadbbbdadbdabdcbaacbddcababdbddabdcabbabbabbadbaccbbbdcabcdbbddbdabcdbbaabaacbdadccadacdbabbaddbacaccdddbccabacdbcacbddbdaabdbdcdbcdababbdbbadabbcadcaddbacabdbcaaacddbaaadbadaddcbbcacdcadbdadabaadbdcabbccbbddddbaadacabbbdbbccbbbccabccabdcddcabdadddcbdabaadaccbcabbccaaaaaacccaabcbdcaadcbdcdaabbabcabdbbcdcddacddaddbdadddcbddaadacaadbabdabddabdbcdbbadbcbabcaccbabaabbdbbbcbbcccadddcdbbbbdbdaabbbbaacccbcdcacdadbacaaccddbaddcccaacccadcdabdcdabdcbaabdbbdabdcdaabcddbdaaccdcaaacdbadbdcddddbccbabaabaabbddcdcacdcababbcaaddbadbbaabbdcbcaccbbdacaaccdadabababcdacbaabaddadabbbdbdcdabcbcddbaadacacdddbcbbbcadbddadadcdddabddcdbdddcdddddadcbadbdbbcdcdcadcbcddcdaddbababdcbdcccbdccccdbbabdddacacddadcbccaabaaddccdabbadbbdbbccdbbbbbbbbbdbbbbcabcadadcabdabcadbbcbcaaacddbcccbadbbcbbadccddbabdaadddcbdcacbabbbbcdbbcaddcabadabbdcaaaccacccdcdaacdbaddadbcdcbbbccadbbacdadcbabbcdbbbaabbdaaccbadbdaadacccccbdbddcbbdcdcdacacadadbbbdbabcbdcaaacbddbaaadcdcdcaacbcbcdbdcbbcdcccdddadadaadabbbcdccacadaadabacdcdacdccdcaddbcbdcadbdbdadbacdddbabcaadcbadacbbbcddbaacabbccdbdaacdbdcdabcaccbbcbcddccdaaaddacdcdccbddccbacabddaddccbacabbccdbbabddbcabacddacbdcdbadccbaccbddaabaaadbaabddbbbbdbcdcacccbbbdabcaaaccdbddbdcdccbabddccdccbccccddbccbdadacdcbbaacaabadabcccccbabccaacdcccaaadadabdadadbdbbddccdccbcddcddaddddaaddbbddabbdaccbacadbcdaabddcbbddcaaddcbacccddbcccaacadbaadabdcadabdcbcdddabdcadcbdccabbdaddcdabaacabaddbabdbabddaabaaddaddabcddcabccbcacddccbbbbdbaccabccbcbcaaaaacbbdcadcdcacbbcbbcdccaccbdbaccaabaabcdadddbcbdabcccbcdcdabcabbcbbadacbdbcdbabcdaabccacdcacbcdbadccddcaaccbdcbddacdcadbadaaabdabbcbbadbdababadccccacdbcdbcaadaacdadccbddabdaaadabbbbddacacbcdbadbadcdcbdacbbbbdddadbcaaddddcdbadacccddaabaaddcbbcacdcdcdabdbcccddbbbbdabddbdaaadadddaacadcdaaaacdbdaaacdddbbacbdabaabdacdabbacbdcdbcbaccdbcbbaaabccbddacabaaaaadaacdacdbacbcbccbacdacccdbaaacccdbaababdbdcdadbbdaaacdaadcdbdbbcacdbbdaaabdcaabadabbcaadbdaaddacdcbabcdbbdaadaaadaadbacabaccbbddadbbbdccdcabbaccabdbbabcaddbcbadddcdcdbadbcdbacbcbbcccdcbcbbcccdcbcadbdaccaacbcdddcccbabacacccbadadaabbbbababccacacbbadabbdbccdaaccbdddacacbbaddadbdacdbabcccbbccddabcaddaabdadbadbadbaaabdadabdadcdcbdcaccbabbcbabaadbbdbdccbacbdbdddbdacbbbdabbbcbacabbbdaabcabcdbdcbcbcaabbdbdaddccdcccbbccdacdcdababddbabdccdbbabcddcddaaabdbddbbbbbdbcbdbcbaaddbdccacdbbdcdadacbaabcdddabbaacdcdcbbdbbdacadcdbcbacbacccdacbbcabbacdbdbdbbcdacbcadbadbbdccdcbbbacbdbbacccbacddcddacadcddbcbcabbbadabacbbaadabbaaccbcadaadcabbccbbbdbadbacccbabdbcabbbbcdacaddbbbacddcacddccccbbaccadcbaacdccbcdbdcbbacaaddddccccbacdbddbbabbdcadbbaaccacacbbbaadbacbcbccbddddbddbdabbcdbdcaaacdbadcdccdcadabaddacabbbdcacbabbdbdcaaccdcbbaababaddcbdbcdaccaabcdddbbbcdddccbdbccdbbcbbbdaddcbadcdcddcdbbaccbcddcdccdbaaaddbcdadbccdacdbbadcadacdcbbcddddcdcadaccbcbbddcaabababcaaaddadcccabdcdbcaabddcadccdcdccdadccdcdaabbbdadabdcccdacbbddbbdbbccdbcbbacddbabbadcddddddcddababbcbbabacdbdabcbcdabadadbabdccacbdbcbcaaaaaccabdccbacbdcdaadacdcbdacdcdbcbbbccbdccaadddbbbabacbbcacacdccdbacddabaccabbddbbddcccaaaddcdbccbbdabbbbaccbdbdbbaccbcbacbbadbcbbadcaabdaddabbacddbbaaccadbacaddabdbdbccabdccbdcabaabddacdbbdadabddbadcabadbbcbadcdddcbbbbbdadadddccbabadbaccacbaaccddbdacbbbdadaaacbdbdccaacbdbbdcdbdaacbbdcccbabcccddbbadcddbadabbbdbacdadaccbabbdaaacabaccacacacbacbcbacacbcadbaddbbadbabbdbbccdcdadbbcbadccbadccdddcdabbbcbcabcdcabbdaaddbcabdbabcdcdadbddabcdbddcccdaaaccddcabccadaccdcddadacabbdbdbccbddbccdddbdcbccabcbdaacacdacadabddaacbcdcabadaadcdccbbdcabdbaadaacdcdbbadcacbabcdbbddcbcdbcbadbaadbcabbacccdcbdabccbabbdcdbcbacdbaddabaddbbbdacbbbdcaacababacbaabdbadbabdcaccdaadcdcaaadbbccbbbcbaabdcbbdbabbccbbcdbcbaabddcbacdbcaadabddbdadcacddbaaddbacacdbcccbcddccacdcadaadbbabdddbddacacadadaaddaadccadccaabbdcdcccabddcdaadaddddabddaccaccccacabdddacddacccbbcdcdbddddcbdbacccdccdbacabccbdcccacbbdabaddadcaaadaacbbacadbbbababbbcaadccabcbcdaacabadadbadbbcbcccaddcadcaadcdacbdbdabcccddcacabbcacaccddadbbbccbacaacccbdbaacccaadbcaabdccddccdcbbdcbbdacdbbbacdccbbcbcdcabaaaabbacdcbdabdbdbbabbcdaccccddcaaccaaacababccdaddddbaacbaddddddddabbbdadddaccdaddbccbddaadbcccdacdbdcccaaccbdcbacdabcdddaaaacbcaddbbdcbbcbbddddaacbadabccbcbabdddbaabcdddabdccadaaaccdcdcadbdcbcdcbabdaabdaadbaaabdcdaadbdbdbddcabadcccabcbcbbdcdbacccaacaadccadbccddddbcdaacdaabcbabcbccdcbdcaddcaaaccaccdcbbccabcddbbaacbdcbaaadbddccaccabddbacaaabdbccadcddbdcbaacacdbcbdbaaaabacdabcbdabdbcdcccbcabdaccdcaaaccbdccccdbdabaacbbcbddbdcbcacdcccccbdbaddddbadbaddadbbaadccdadcabbbacccabbcddbddbbcbcddcdcbdaabbacbbdddbabddcabccbadcaccacdcdbbbbcabbdabcbcaacbbdabadcabccbbdabdbadaaabbcbacbbcdcabddbaddbaccbacbcccaacccacacbbdadbadadabcaabadadaadacaaadacdcddcbabbaaacacddaacadbdbbcbbdaaaabdbbbdcbbccbacadbbbbadbaababbbaccdabadcbacadbccaccbdbcabccdcabadddacdbadccdbbcdbddcbbadccabaacbaadabadcadddaccccbbadbcacccbbadbddbdcdbdbcaaaacaadabccdaddadcddaacbccadaccdadddcabcbdaccdacdccaacaccacddbccbdbddcccdcabadaadcbbbdabadadbdcdbaabddaacadcabbccccddccbacadcbdbadadbccaaccddacbcbadddbdcbcbadcccbcbbbdacddccbddcaacdcdbaaadaacadccabaccdbbabacaccabadcbddabcbbddcbbabcaccddaaaabddbdddaaacdcccaaabadcbcacadbaadcaadddbabbaaccaabdabcccacdcdbdbccbddbbcbcdcbbaacaddbbddbdbddbbbabbbaadcacbbddbbdcbcaddaaacbcddacbdbcbdcacddcaccbcaacdadbacbadcdbccbdadabbadbddcaabbaadcdacccdbaadccacabdcdcacccadabcbddacadcbbaacabcaaaadcadbaccdccacadddcdbabcacaccbacbbddbccbccadcbcaaacccdddbcabdcdbbbabdbbdbdbbbdabdcbbaccbbccdcdcbbbabaabbbccacbcddccbccaabdaccdcbdaccccadaaabcdcadbacaacacddcdbccadddbdaabddadcabacdbbbbbccbbababcdcbcddaaaadadbabcbcbcadbcabbaccccaacabadaccdcbabcdadbababbbbcbbddabcbcbadddaddccaaabdaabddababdcaddaddbacaacabcdddbbbbaabacbbadbacdbdccbdbdaadbddbdddacccdaadaabacbababdbdbaddcaaadcabccaacddbdddbdaacabcacdbdcdadbabbccbdababacacbadcaccdbcadaddbaddbaabdaabacdadbcaabdbdcbadabdcabdbcbdbdcadacabdcdaddacacabadbdcdbaabcddbcaddbccdbacbddcaddcbadaaaabaabbbcbdbabaddadacdbdadaddcdcbacddbbbdacacbbdbbdbaddabbbaccbacddbbbcddcdbcdbccdbdadddcddabbcbaabcadacdcbcdaaadddababbaccadabaddccacbbbdddbabbdcbdaaacdbddcdabcbdbaabdcadbbcdaabcbbdbcabbcbaaadbbbacdccabbabdccbdcbbbbbdddcadaaababaddcbdbadaacadbdbcaadcbacdcbbacaddabdabadbdcbaabcbbbdcdcdcaaaddbcbacdbabbabdcdbdaaabbdccaaabbbcbbbdaaaddbdbbdabbabdddbadabaaccbacbabddaadcdbdacbdbbaddcdcbdaaacbbcdbcccdbddbdcbbadcdbdbddadbaabdbbdabcdbddbcbccbabdaabacababddcadabaaacbccbcaadbccbbdccadbdbbacadaaabcababdaaccbcabcdbbacbabbbadcccddbbcbccbcccdabbbcdadaabbdbccaddcbabbbcdbdbcbbadddcabadbadacabdbaabbcaabdcdddbcacdbdadcbdcdabcdbbabcdcbddcdcccaccbaddbdacbdcbbcdcbcaadbcdbcaccdabcbbdddcbbcddcbcdcdcccacbbccaddadaccabcbdaadaaadcadaacccbddbbbaadabbacbbbcdbadddbabcbbdcacbdbccbabbbdbaaacdaadbabbbcdcbbbdadadbbaabdaabbacadbaabdcacccdabdccadccddbbadacbdabdadcbcdbdbbcbdbbddccccdbbacacbcdcaaabbccaababcacbdccadddaddaddbabdcaacdbadcbadbcacbaacdbbcdcadbbcbabcbcddcadccdaccdbaadaaaabcdbcbadcadbabdbacbaadabaabdcacacacbbdbacaacaddadbbbdcbcbbbdbdadbcddadcdbbbacacbdbcdacccabaabdbadaaabbdcddabcbaabacdcabaababbabcaaabadddbadbabcadbabdcdbbbbaddcbcdcdacccbcbbdbcaacdcddadcccdbacccdacbdadacbbdcdcbacaddadabdaddddcdbdcacccdbaabddbbccbdadbabccbaddcdddccaabcccaacaddbbbacbcccacbdccbbbdbdcddccaccbccaabcacbccdbaabbdbbbbacdabadabaaabdabcaddbccbcaadbbacacccaddaadbbdaacdccadaccbddbadbaaaacbccdddcacbacdbadbcdadccadcaaacadaccdaaabdcdcaacbbbbbdababcabbcabdbbcabddcadcabdaaccbabbddcacadddababcabdcaddbddbaabbbbdabbcbadaacdbbddcacabcacacbabcacaaabcddddbaddbcabacdbdbdcdbdcaccddadbbcddcbdbbbbccbdaacbcacbbbddbdbabccbdddbbddbbbddccadcdbdddcacbddbdccddcadbacbacddcacdacbabcdadbbbabbbcadcdaaaaacdbdadacccdadaacdaadadaddbdbacbcbbaacacccbcacacacaccdacabccbcacccadadaaddbbaabacddbcbdbcaacddaaddcbaabccdcdaaabdadbaddccbdcdcbabdbabcabaaddbbcdcdcbcbaaaaacbbacaddcbcdcbcdbadaccaadbddabbdcacabaaaccddadaadcbdabdbbccbdbddadbacccadcccbbaabdacdacaccdacbccdabababdbdbbbdbddbccdbdacadcdbdbcbccacddbadadbadddacddcdbbdcdabcccacdacbaaddbbdbadaaacdcdadcccacacacbbbcddbaaccbbaccaabcdbbacdbaddbcbbacdccdaacdbccabccdacbaaabddbadbcaabcdccbdbddadaabddcaadccdacbbcbbcdabdabaabcddabdbbdcdccdcadcbabccdbccbdacaaadabbdacccdccbadabaaacdbdabcaadbbadbcccacbdccdbaacbdbacaaabaccdbdcbdadddadbcbbcdacdcaadcccbbcaabcbccbccbcabcdadaabadbdbaddaadddabdbcabbdbcccdbbdadcadbcacdcabaaacbabaddbbcdbbcbbcdcbccbcacbddbbacbdaadcccbcaddbacbbadadabadaddbaabdbbcaabacabcbcabcaacaadddadcdadbdabbccbdbdbdacbaccbdbcbccdddadbddaccabbdacbabcdacabbddcbbcabdcbcbcdcababcddacbcbdcddcbbccaddbcbdadbbaabccaaabadabddbbdbbdbaabbdcbbaacdccdaadbdaccbcaacbcddbcadaaadcdcdcacbbacbacddddcddcbdcdbbbacaadcdbabbbdcbcbdcddbdadbdabcbcbbdcbcbaadddaabdcadbaddbaddcbcbdacdabaddcbabadbacabbcddbacacdacaddbcddcaadabdbdcaaccdadcdbccaaddbaccdbbaabbcbdccaddccbcdccddbbbabddbddacdcadbcdbbacddabadbdccaddcbbdcbadbbadababaadacaabdbacccddacdacbdcaadcbbacccadcdbbabcadbdbcbabbcabcabcdcdacacdbbbadddcbdcaddbabadbbabccbacccddadddbdadabbcddccaadaadbacdddcdddabbdccdadaacacacaccdbcadbbbdbcaaddbcccbbdbbdaccaadbcbdbabdbaaacbcabababbddcabbabbbbdcdbdbccdaaccbbbcdddcbbacaabccddadadcaadabcdabcbdadabdbbbbccdcbdcddbaccdabadcbbadcbbcbaaabacbacabbcbaaadaabddbdcbdadbccdccdbaaccadacdccdbcaacdbcddaadccabcbcbcdbbcccacabdaaddbdadabbbdcaaaacbadaccbadbddbbbccbcccdabbccbacddbaaabdcddadbaabddbdbcaabcbaaabcdcdaadbbdcdabcdaddcbcaacdcccccbcdcbcdbdbbadbcdbbbcbbcadbcbdacbacdaaabdbaacdbdacccdcacddbabcbdacbbdabadccdbbcacbcadbbcdcacadbabcadbcbbcabbdddabcdacdbabadcbadbdcadbabbcdadbdabbcddcddabbdacbbaccdbccbcbdbcbacdbbcbabcbadddbdbbbdbaaaabadcbbaddcbaaddbcdcddbaabdadbabbddcbbadaadbdbbcdadbdbdadccbbbccbbdccddbadcdbdcacdadccccdaadbcbcacccadadaccaabbadcdaaaaacdadbabcbcaddcaacbdccdcbcbbaaabdcdacadadabababcabddbdaddacaaccbbbbdacccacaaabbabcdacccaabccdbddbadcdcbdbdbcbabbccddbbdcaaccbccabacabaadcddccdabaacadddcaaabbcdbbabddcacaabaadccddbbaadccdbbdbcaadbddbbcbadadbdaaccddccdabbadbdaaddcddcbccdbcacacbbbaddbaccdbcbadaabacbbadabaabdabcbbabaacdcbdddabbdbcaabdaadddddabdcaabbbcaabcacabbabbbbabddadabdaabddcacdccbbdabbadbabbbbcacdbbbcabcbbbbacddcddadbccadacdddaaadcdbddabbdabbaabbcaddddacabcdbdcbbbcdbdaddbabddddcbbababcdbdbbdcbbbcccdbddabacabbcbabbbdcbdabdbcacbbbcccbcaabdbdcbabcabadcabcdabcbbdcddcbacadcbbadcadbdabdbcdabbdbcacdcabbdadaadacbcdddaccdacabacbdcaaaaaacaaddadbdbcbccdacdbabbadacadacbccdabdbaabcacddadcbabddaacddcaaddccadcdbabddbaaaacdabadccbdadccdcddcdcbbaadcbbccabbabcacdaaccbdbbabababbdabaababddcaddcadcbabcbaacbbadacdbdcccadbddcbbccbdadcadddccdacccbcdabdbcbddaacadcdbcaddbbccadddbcdcccbbbbbbccadbbdaabddddbbacbdcbcacccbbacaaadbccdabbdbdaddbbcdabdbdcdbdabadaadcaccdcabbcccabbbcacdddaacbbdbcbcbbcbaccdbbbccbadabccbdbcbaccadcdbacdddccdabcdaaccddbcaadcabadbadbcbcadcbaadccbdaacabbdaabcddcdcabbdcbbbdadccbbabcbbabbababdccddbdddacaabbcbadcbadccdadcadadbdbbabccaccbbcabdcaacdaddcdccdaabcbcaacbacdcdcadbcbbcddaccddadabddcbacdaaacccddabacbdcbacaccbccdadbabbbdcdbbdcadacabbadbdbbddbaccbddbddbdccaddbbdaacdbccadcbccababbddacccccdaadadcabbcbabcccdbdccbdbdacaababaaaacaccaacbabaadcdcbcddbabdabddadcccbbdddccddadbddcdbabcddadbdbadaddddabdbadcabccbbccbdbaadcbcbcccaacdcaddbccbbbbcdcbcdbcadbadacdabaacbdcccacabacdaccccaacadbabbdddadbcccabcdddcccddadbadbaddaacaaadddcccdbacbcaacbbbacddcccabcbacbcabbbcbcbaacacaddadddcaadbcadadadcdbddaccbcbdaccdcdaadcdbabbcdbabbacacdbcdcacbcaaabcaabdbbbcdabcdbcccbcbbdacacdbacdaabdadaccaaccaaaabdababaccdbdadaaccacccbcaddbddcddcbdaddaacdabcbdbaaddbbbcabcdaadbcacaccbcacabbdddadaaccddccdbabcccbcccbcacdaaddcbdcccabbacbcddccbbcacbadcababacacaadbcbdaaacdbdddadccabcadcadbadbbdcdbdcdddacdddbddbbbbcccbbbcddddabacabdbaaaacadabacdbabcdcbdccddaccdaaaccdbaaccbcbabcddaacbaddbadaddccadbbbdbacbdbcabadbcabcbabddbcaabbccdcacacadcacdcababadadbcccdabcdbacbbcacaadcadccbaccdcbcbdbdabbabcabdbaacdcbdbacbbabbabcaabbdbdcdbdccdadcacbcbcadadbdddadcbcadbaabccabdbadaaabccbbacdcdabdddadbdbbabadcdddadabcabcabdcbcbccbaadcadacddcdbbadaaadaddabdcccdbadabcbdcdcdaabdbcbdbbaddacabddbabbccdcadbcdbdcaaddadddccabbaddccacbdadaccdcabdcbdaaaaaaadabbbcdbbccdbcbdadccbcbadabcabaaddacabaddccacdcbbddbcadbdaaaddddbccdaaaaccdacbdbbcacdcdaaccadbbdacddaabdcaccadbcbccdadaabbdaabcacacdcbcbacbabaaddabcbbbddaabbdbbcddbcccdabbacaadbbbbbcbccacaabbbdcbbccadaccdadcdcaadacdaadaadcaaddcbbbdbbaddcccdabccaabcaaccdcadcbabcbbcbcddbbadbdbcdbcddaddbcacdbadcddcbdaacabcdaaaccbbccdaabccbccbbdbdcdbaaaacbbabbccacccdcbabcccbddadbbdbacadbabdbbaccbcaacccbcbdadcdadbcdaaccadcadbdbddabaabdbbbaddddacbcbabccdddbbbdadbdadcaadbcabbdaabcdcacbcdabddcdbbdbddccacadbdcaabbdddbacbaccbbcdaacddadabcaaadcaadccddababddacbadbcdabcadcddcccddabbccaadbbbdcbbbbdbbdbcdacbbadcbcccdcddbadabdddccdabaaacaddbbadcbddcccdacbabadabbbabcdcbcaadabbbacbdaadacaacacccabababaaaababacbbabacddbdbaaccdcadcabbcbbbcccbdacbdcabacabdcaccacbbaadaabdcacacabdabdcbbdcacaaaccbccdcbcacddddaddcbabacbbdcaccbacbddabaacdbbbbcaacdcdadbababbdaadadbdcbcdadddadaadcbcbddbcbddcbaaccabcaddddabdbcdbdabacdadcddaddcddadcabadbbdabaaaaacaabddbbaaccaccaccdcbaaaababcadaccbbaabdbccbaddbabbbbcddcdbbadcbbbdddcacaacddbabbcaabadddcdbadacbaccabccbcccbddabdabccdbcababdcdccdccbdcabcacdacbcacacaadaccbbcdadaccdddcdcbccdbccdcbaabddbaabcadbabddccdcaadbcbdbcddddabcabaaabdaddacccbcbddbbdbbcbbcddddabcaccdabdbddcbabcdbbdabbbdabaaccbdcdbacaaddacaaaddbbadbdccaacbbadadbcddbbaddbccbabcdabdcdaccbdbcccabdbbddaacddccbddbdacadabcbdcabdabaaaddadadcccabacbbbabcdcabccbccadacaaadadbaaacbcdcbdaaacbcdbbbdcdaddbbdbbbabbaadbdaaacdcabdacabbcbcbaabaaddddaacadcbdbadaabccdadccacbbccaddbabdddabdaacaacabdabcaaacdccaadcdbcccbaadbcbaaaadddbbabacbaddcdcbcdabadbcbaddcaddcaabdcaaddaddacacdcadaadbaddccccaccbbaacdabdddbacccaaabdbabdcbdaddacadcddddcccdaddadccdccddbbcdbdaddcddbbabbdbddcdabcbccbabdcddadcdbbdbdaddccdbaabbbcdacaaddaadcbdaabbbcabbdaddbaccddcbbdbcbcdbbcadbdbacbbccdbcbaaabcddcbaaacbbabbdbdcdbdcaabbdcaabbdaadaccacddabbddcbdccbdccdbaacdadbdcbadcbacdacadadbadbbdbccabbdbcccabddadccabdcdacadabccbcbddabdbccdcaadadadbbbbbbdccbdaaabdcacdabdddcbccdbddcdcdaadbdbcdadacaadcddccabcaddcbcaacbdabcbbdaddcddadcbdbadbdaaadacdddbbbddccdddcddacdbaccccccddabbcaacddbcbdaddccdbbacdaccdbaddbbddabcbadbadabccacdaaacacccbcddabbbccdbdaddcaadadccccaadbadbabdaadcbdcbcacbdaabbbbdbadcbbacccdbadcacbacbaccdaccccdbcbdabcaabbcdddcdcacadcccaababdbacdacdbbcacdbcdbccccdbdbdbbbbbcdacdddcabbbbcddbbbbdbcbddcdbdbbdaaaaccccbdddbcabcbdcaddabbddbdcdcacacbaadcabdbcdaccadcbddbbcaddbdbbcdaddcbddadaddabddcdbdabddbcabcbbbdaccbabbbcddacdddcaababbadaacbcdbbbcdacdbadaacdcccccbbcbcbbdbbcaabcbdcdaacbbddccccacdcaccbbddcdadbbaddbcddcaccacddaacdbadbdbcabcdbbbbdccaabdaabbadccabdbbbbdccccccaddccccbabbbacbaadbacabccadcdcbadbbaddbaadcbddcaddbbdbdcbbcdbbdcddabacacdaabccddabbaaccccadcccbcccdbadcaadaacddccabcbddbadbddaabbcbddcbdbdcbaabdcbbbcccdcaccbcaadbddadbbadcabaacdcbbdaaddadccdcdacccdcaaaabccddccddbbcddcacbabbdcdacabcdbdadcddcbbcbbdcdddcdacdcdabcccdbccbcbbdbabddadabcccdacdbbcddcbaacacadbabbdbbcadbbdcaabaababbdacccacdcbcdccdabcdcbadcbdadbbbdadbccbdaacacbbacaaacaaacbcbabaaadadcbabdcbcddbbbbacbdcadcccbcaccacddaccccdcbcaaadaaaaabdcadadbbbdbcccccbcdcccbccdaaaabdcdabccdbbddbadcdabaaccccdddbacdcabaccbbbcbacbdbaacdbacccccbdacccaadadabaabcccbbcbacbbabdcbbababcdbbcdacdbdbccccbbddcbbdccacbccdccdbcbbccaaccccaddaadaacaacaaabcaadbcdbabcabacdaabbabbcabbddbbdacacccddcdbaccbdbcdbbadcaacbbadcbdbcabbbdadadccbbdcabbdddccbbbcdacbdbaddbadcdaaabdbdaaacaccdabcaddabbadacbcbacbcaacdccadaababddddbddbddbcabcabdaabbabdaaadbdccbbaaadddccbacaaabdbccadcadacaaaaababcdbdaaaabccababcbbbdbabdcbddcaccddbccccbabddcdaaadabbbbdddbbbbadccbdcbbbdbcabcdcdcbcaccadddaadacddaabacacbbcdcdcddacadccdaadbdccacaabcdddcabbabadbabccaadbdbcdbbdbaabdbdadadbbaddcbddaaaccaacadacabbdbdaaddcdacdaacdbbadadbcddbccbacdacbcacaaacbbbbbcaddadabcdbcdbaddcbdbadcddcbdaabbbdbdbbadddcbcccadadcddbdccbacadcdbddabaaadcdacbdcaaddbadabaadadcbdccdbdddbcdbddcdccdbdcadbacddcdabcdbadcbbcbdbcbdcdbaaabdcccacabddcadacdbabcbaabaacbcacddcaccddcbdadbcaadcacdaaadcbaababbaddbbcdbadcabdcdcdcbcdbadbdcadbbababcddabacccbdcadddbabbadaacabdcddbaabddabdcabacdccadbccbdbcacdcbbdacbacbcbcabbcadaabbbbcbcdabdacbbbbbdcbbdcbcdbcdbddcbbdbabdbddbccddcbdaaadccdccbaadaaabbadacdcddbaddbabbbbaaabcccdaaccdcdacbbdbbdbbbbbbcccbabbccddbdbdddadadcabdadbabbdcacbcdddbcaadbcbbbcbbacdabbaddbdbccaadcaabbcaddaabadbcccccbbccbcbacbddbddabaadcabaccacaabbbbbacbbdbbbdbdbbcbdddacdbbcbbabccacdcaddcbbaabcaacbccdbaabcdacabbcdaadacbcbaadbdbccdcbbccdabbbadcdbbddddadcdddbbcdabacbdbbbdcbdacbccddadcdaddcddcaaababccaddbbbaabdcaaabcdaacbbddbdbaadbadacdacbaaabcdcbcdcadbbcbcddcbbbcaadabbdccddccbddccabcddcabdbbcddcccbadbbdbbbbccdcdaacbadacaddabbdccddbabaabbbdabccbabbbcabaaaabddccaadcbccddbcbacdbacaccccacddaacbaddddbbacadbaaaabcddacabdacbcdabcdbccdccadbbdddbbcabadddcdbcabcccbcdccbdcbbdcdcdbbaadbdbdadacaacbcbbbcadcdabccdbdacbacbcdccdacaacddbdcbdaaccacabbdcadcadbaaaacbdadcaadbcccaccadabccbdaadbddbcdbbacacdacccbcbdbccdadcccaccddacbabcdbbaabdbaaabdbbddbaadbbdccaccadaccbdbbbaabbbbdabdcbdcdccaddccbccbcdaacbacdcaabbbcdadbddacdcdbbabdaaaacacdabcdbcdadcdabadccdcbbdbdcdacdbdbcbbbbccbccbccddaabaddbcadbddcaabbbcdccbcbbbaadcacbbbbabdcaddacdcbaabcbadbadadadcacdabcbcdacbbbcacccdccdacadbcdcbbbcdccbadadbdabddcabacabdadcbbbcadadbdbdcccaacdbdadadacbddbccbacbbdbdadbbaacdcdabcdcacdbccaacdbccacbbbcadabddabbaaddacaaadcaabdaddcdadabbbaabdbdadddcacbbcdbbadbdabcbdabdddbbacabaccdadddadbcbbaaacdbcaadadacaabdcccdddbbcbbddcadaacbbabbcdcddcbbbcbcdcaabdadbadbacdbcdaaaccbbddcaaaaaadcbbccaddcddccdddbddcbbbaddaccdcbcccdadaadacbcacbbbdaddddbaddccbbabdcbacbdbcccdabddaabbbdddccacbdbacdacbaddbbbdbbabcaacdbacacaaacbccaaacbbccacabcbabdcdcbbadcbcadaddddcacbdabdadbdbbcabadcbbbbacabcdadbcbccbccaddccbbdcadaddccadadbdddcddbaaaccaacacccdcaddddcccbaaaccaccaacaccdacbcaaddbacbddbcaaabdaddbccdabdddbbbbbddadacdbabbcddbcddcbdaddddbcadabdcaddddddbcaaacccdccdcaabcaccadbadabbcacccaddcbbbccaaccddcdbdcbadcaadadabaddacbacdbabbdcacddbdddcccdbccabdbacbaaccdaadcccddaabdbbaacaacdbdbaccaabaabdaaaaccbbbcbdaaaddadcddaccbadbddcaabaabbdbbdcbbddabcbdbdcabcbdbabbdbacbdddcdcacaadcdbcadccbbabcaacadacadbccdabdaaadadcadcadaccadacbbdcdbdacbdddaadccabbcbdcbcccdabdddadaadddcccddcdcdacbdbdbcbadadcacdbdbdcbaddccddacaabdcddddbbbccdcddbaacddacabdcdcbdbccccddcaccaabaaadcbbcbbbaddcdabbbdaadadbcdbdabbaabbabdbdabdacacabddddadbbbbddbbabdacccbacbabcddacadccbadcbdacadddccdaaabaaccacbbdccaabbdacbbcacccbdaadaaadbdacdadbcdabacbabbccbacabbadddaacadccaabaccdcadcdaabccbbbcbadcaacbdcabbcdaaaccdccdabbaccdabbddacbaadabdcabbddabacbbcdbbbccccacccccaaabdbcadbccccaabcaddddcdcacdaadbdaccdcacaabaadadcdddacaacadcaaacbadbccdddcccdbbddbbadcdbaaaadccbaaddaaaaacabbaddadadcbbadabbbdbdcbadaccbdbaaadbcacbaaacbbbaacdcdbabcccddcbabccbdacbbacbbbbdaccaddcbadbcbbdcbdaddbaabaadcabdbaacbbabddbbccccaacddddabbdbdcddcadcdcbbdcdbbcbabaaccbccdcbcbccbdcccddacbbbbccadbcddbdcdbbacbadbbaaaaddddcaadbaabdbcbaaacdcaaddadbaabacbbbdbbadccbcccbccabdabaddddacacaddcdcaacccdddabaaaaaadaabbadcaddddbdbadbbddcadbdcbccdbcaaddaaccaacaaddccdbccbccdbddddccaddacdddbbcdcbcddddabdcdcddbadbbacdaaacddabbabccbaaaaccccbdbababdccbaacbcdccbccdccbbbacbadcbdcbabaccbdbdcabcaaacdbcadbbdcabadaabdabdaccababddcdbbadaaaabdbccbaadabcacbcacacdabdadbdaaaadbcbdcdcaddacbdbdbccdadbdaaacbdcdbcabdabbdacdcdbbdbccdbaccdabcbdccdcbaccdcdbbaabbdcdbcaabacdbbbbcbadadadacddbacdbbabdadbcbbdcaadadadabccbcbbcbddbcdacbdbacbbddcaacadabcdbabaaccccdadccdcdacbccbdbdbdbdcccaadacccbbcdccadcbbaabaacaccabcbddcddbcabadddccbbdbcadbcbdabacddcbacbbabbbabdccacdbaccdccbadacccdacabaccdadddacbdabdbaccdcbcdbdcabbddacabbdaacbadbcdddcdbbaaadcccabaacadacacaaadcbbdadcbbbbccbddcddbdcbddbcddcadbdadddccaaabcdbdbddabcdbdadabddbbadcdbbcddddddbbdcdaacacddbdaadbbbcadbcadbdabdddadbbacabdbabbccbdbbbbddbadaccbbacbadbbcbdacdcdaaacabbbadabdacbbbbccacbacacbbbbccbdcdaacdbbcaacdbdbbbccdcaaaadddadacaddddcccacdcdbdccacbdaccccbabcdacaabacddbddcdbcadcbadbddddaccaaabbaacbdbddacbabdabbcbbccbaacdacdabdbbabdcaadabdbcaccccbbaadcaaadcadadbdcbaabbaaadbbbdcabbdcbabcbcacadbcaccdcdadabcaadddacddcddddbabacadcbbbdbadbdabaacadabcddbcabdcbbadaabbbcacddccaaddadbbcbccdbdbccbcaadcacaddcacabcacadabddadcbdbcbdbbadcccacdcabcdaacdddaadbbabdddcccbdbabbbadccbabdbbaadbcdddcccdbaaacadbacdbabbdadadbbdcadbddbbdcddbcccbadccadaddbdacbbadbabbdbbbbcabdabcbdcdbbcdadbbadaccbcccadcbbadccbbdaddddadbbcbcadccaaccdbcbcadbdadccbabcbcacdbbacbadaccaabbcdcaaddcbcdddabbccdaddccabcbcbcbcadaddaabbdcdccddbdbdadabbaaadacabbdaccdaddaddacdbbbadcbccbccaadacbacdaccabbdaaaccacaababcbbdddcbadbdcaadddacbcbdcadcacbaccaacccccaddbccaaacddacdacbbcddabbbcdacdbbcdbdcaccdbccbbaabcdcddcbbdadcaaaadadaacbdccbddaaddadcbdbbdbdcadddddbcacdbacbddccadddcbccddaddbcababaddbacbcdccbacdaaadabdadbbbcacaacadcaacdaacdabbdbdddcdaaacbcbcbdcabdadcbdbbbabdddbbadddbcadbadbadcbcddcaabcddbcacdabdcddabadabcbcbbdcdabbbcabcdacbccaddcddbaccdbbbdccbdabddadaadaccaaacbdabbadacdabdaabaabadcabcccdcaaabccbdbccaacadcbcbacadaaaabcaaadbcbcddcabadcbcdbcbccacabcdabcdbdcabbdaccacbbbdbcbddcdacacdbdcddbcabaaadbaaadccbdbcddaaccbccbdddbacaccabdbdacddcbadacbaddbbadadabdbbddcacccaadacbdadbcdabbbcaccddaaaaaadabbbbccdbccaadcdddbadcddbbadacaadabcbaccbbababdadcbbcccbdcaaccadcdcccbaaacbadcdaaadccdacabaddbcccbabdbcacddbacaccdbcccacdabaaaadcabcbddadcabcaacaccabbcabdddcbcaadbcbabcdbcdaaacccddabacbcdabcadabdcbaddcdabbaaabbbbccbcbadcadabbdccadcaacbccdaccacbaadcbdacdaabdcaadbdcadabdcdbcbcbccadbdaadbabbcbdacccddacdadccacdcababaaddabddddcacadacbbbaddccaadbadbabbbbadbcaacdbdaddcbcbdbbbcadddaccbdcbbcaabdadbbdacbbcbcbabbdbcccddcacbbbdaadddbdadbbcdadbddabbadcadbacdcbadbabccbadddababacbadaaaddbabccbbadbdccabdacdadcbddbcbbdccacddabcadadabddccaccbbacbadbadadcacccadbbcaacddcbdaaadcaddadadcccccacacddcbacbbcddcbdbacbbadadcddadbdacdadbdabacadcadabdbcacccdddccdaaddccbcbaddcadbcddadabcabbacbbbdaccdabccadaccaadcaccbdaacdbcccdcadccacbbccbbbccdcdccddaadccacaddadcdaabdcdbdbadcdccaaddadcddddcbaccbbbdabdbdddaddaabcbdcaaddcbcbaddcddbaaabdadcdbcbcbaabcdaaccdbbaaabcbdddbdbbabaabdacddbdccbcadabbcccbdcbadacbdcbdcdaabdabacadbbbbdbccdcdadaacbcbdacabccddbcadadadaddadabddabccacdbcbdacdababbcadacaacabbcccbbaadbbcaadabaabdcdccddcbbdbbbabaddbdcbbdcdcabbcbadadddabababbcdcbbacdacbacbcacbdcbbbbbdbddaacaacaadddaadcccadbcccbadcdbcdcadbdaabcbdabcbdbcaaccaddabcdaabddbcadabcdaddccdacabcadbbccdadbaddbbdbccdbdabaadcaadbaabcdcdaadbcaacddababccccdbabacddcadcadbcacdbcbcbdcbabdaaaabbacbdadaddbccaccaaadbdbcbbcacbdbdbcdacdaddddbaaccacdbbdbcbacdcaaaadacddbbdcddcccccdaadacccdabbaaaabbcdadbccadbcbcdbabcdadacabbcacbaddcaabddbaddadbcaadcdbddcbdacbcaadcadccbcacdcbbaabccdddabddacadadcbcbaccbaacbdcbbabbcaacbadbcdbcbaccdcbbbadacbbcccaadcabbdbacabddcbbcdacddacdaadbbddabcbcdbccdadcacbdbbdbadaaccacdcdcdadacddaaaabcadcadcbdddccabdbdddbbadbcdadccddacabdacbbaaababbdcdcdddcdddccccddccdcdddabdaaccbcbdaaacabcadadccdbbccacabcbdacdacbaddcdbaadcccdadcdabccaddbdcdbbdadadaabdcdaaaadabacbadbbdbbdcbbaacbbacbccabdcabcdaaadcdbaddabddbacdcabbcaaccdadaddddaacddadadacccacbbaddddcabacbaccbcdabdccacbaddabbdbdcadaacadbcbbbbacbdbcaacbbbdabaabbcdccacbbcaacddacccaddcaaabddabdbadcabdbddbdaadabcbadddbcdabddcacadbbabcdbacdcddbdcdacaabcdbbadbcababadbcaacddaacddcadacdababbababcbbdadbabcaaccacdbbadbacbaacbcbadacbbacdddbdbdbdbdbaaaababddbbdbaddddacacbcadadadddadcdcbbadcadddcbadabadcababcccadabaabdcabaaccddacacbbaaabddabdcccdbcdbcddaadadccabbcbcadcaaaaddadbaaacdcabbcadcdbabdddddcccdabdccddbcbbbaaacaaccaccacccdbccdbacdccabdbbbccbacbaddcccacacdcccccbacdbdddbddacaddccadcbbddcbbdabdcdddddcadccdabdcdccbddcacaccbdddcdaadddbcdbddbddcacbcdbcbabbdabbddcacddcdcbdcdccddabacbdcddacbbdbdaddddacabbbbbdabadadcccaadbacbdabaadcdcaabddbdacddbabdbddaacaacaddccdabcccaabddabcdbdccacbacbaddbaadbccaaccddbaacdcbdbbaaddbcbdbccbdbcccadabacbbdcbacacdcabbababbbcdddabbcddbbaadcbbcbadaccddddbaaacbcdcccdcbcdddacdbcbbbbbdbdccdcbbadcaadbcbbabbdbaaacbacdcddbadcdbabbbbccccbdddcacaaacbcbdadddddbdaaabbaddaccacbbacabcacacabcddbcccdcacdbcdadaacdcdbdddcaadcaababbababaadbcbbbbaadddaaaacdabbcdaabcdaadabddcacdadbdbaabdbdabacadbacccbacabaacdbddddbccccddcccaaabaaacdbaaacdbcdbcddddbacdccacaccacacababcaabccbbbbbdbacdcdbbacabccddbaadcdaddbcacbccbacbbbdbcbcbcddcaabadbbcbdbdadcbbabcddabbddddbbbcabbaabadaacbacdbcabbcababddadcbcabcaacdaacdbacdbbdabcaaaccddcdbddbbdbaadcccdcaacccdabcddbadcddbbacbcadddacaccbbaddaacaccbbdcaadbbddacaaabcacadbbaabbbadbacdbbccbadabaacbaaddaccabdabacccccaacabdcbddadbcadacccdbbbbadadcccacbacccdddcabcccccbadcbacacaddacdbababaaaadddcbcadabcbcacaddabadcdddacaccbbbacddaacbddbcccbbcbbbdcabdcbcbaaddbdbaaabbccaadccbadbacdccaddddbdbbcaaaabdbcbcabcdbbabdbacadabadbcaacbdccbacbcdbaddbcddaabbcaadbbabbacdadbaddadaccbbbccdbcccbaacdbbccaaaacdbdbcbcdbbadddddcdbbbdadcbbdbacbdadbdcbccadcacbcaadbcbbccaabacabdaaddcabacbababdcaacccbacddcbdbdccaadbbdcdcacabbabcdaabcacabaccdcbbbbdcdcbcddaccadddbdbdccccaaacdbacbdbbdddabccdacdaadcabccddcabbcbcbbcdbabaadabbcbbdbcccacbcdadbabacbadbcabdccbbcdbadccadbcbababbcdbdccccaddddcbdacbaddbcaacbdacbccdbdaccdbabdadbccbccbcaddcdddcbdbddabddbcdbddbbacdadbddcbccdbadcadacbbcaadcbcaaccdbddadadadabcabbcabcabddcaddaabccdbbdcabcdbcbaadaddadcddacacbaacbdbbdaacdccccdaabbdddcbabdbbabcdcdbcdcabacdcacccbddddbadabcadacbccbdbbbccbcaaabadcccddbdddbaaddbcbacadbacaaccadcadbaadcdcacbadbabbdacadbcdbdaaadaaaadababbdadcadaacaadbbacaadaccbbbcbbcdabdbabdadddccbadcccbcccacdcddccdadbbddacbbdaccabcbbdacababbdddbdbccddadbccaacadccabcbdccbbddcdcbdadbddcdbbbbcabaaddccbaccaccaacbbccdaabbcdbadbbcbbddabaaaddcccdcddbcbbbbdcadaacbbcdaacbcaabbccbcbdacbddacdbbabbcbadcbbbabaabcbdcacbdacacddbadbccdacccdbccaababbccdadaaaccadddbcccaadabddbbdbdcbdbdbabdadddaacbbabdadddccdbcdabbbaccabbdaccaaadabdcaccddaabdddcabdcddabcccbdabbadbbcabacabbdbbdbbdbabbdbdcbdddbcabdbcbdcdacdacbbabadbabbacbddababbdcadaababddbdccadbcdbbdcdbdabcaadddcdbdacdbbbbddbabdadcdbbcabaaaddddcadabcdadcbbcddccccddaccacbcdddbcdcccbacbacbbcbbcabcddaaadadbadbacabdaadbcdbcbbabcbbabdddbbacccccdbdddbbdacdbddaccadddbcbdbabaababbbdaaccbbcdcdbabbddccaacabbdbbcdbccbcdcccddacdcddcbabccbbdcabddbccaddacacbcbdacbbdabdcdaadabbadabbdcacaaaccbacdacbdbdbddcddbcbaadbddbddccbddbcaaacdddcaacbcaddcabbccdbcbdcbbbcbacabddcbdcbacaacdabdaaabadbcbcdabcaacdaacbcadddbcacccabaddcacbadddbcadabdcdabacddccaabdcddddbdabadcbdaddadcbdbdcaabbacbbbaddaaddadbdaaacdadcdababcddccabbbdabacccccdabdddacaccbcdaaaabccbccddbacbcdcdadcbaccbdcbcaabcabbacdcaaadcabbddabdbccdcacdadbacccbbdbdabccbaccdadadacaddacbcabbadcbcddddabccdacabbcdddbdcccaacacacddcabaaddbbddbaaaccdddabaaabbbcddbdacacccdadcdbdbcbadbcddabdcbbbadbcaacbbcdcdbabadacadbbcacdcdaaabbadcdacccabddbdcddaddcdadacdaadadadbdbbccdbabbbbaacaccaabacbadcdabbaacadbddcaaadbbbaabcdbcbdaabbccbccbbcddbababcdabbbddaabcdbcadbdbcaccbadacbdcbcbcbacacdccbadcaaacddbacaddabaabccaaddabcabacccbdcadcbacaadcdcccadddccaacdcaccdaaadcabcadabdcddccdcdcdccdcbbaadddacbabcbbbdabdcdadcdacbdcaaacbaabdacaddbcbcdaccaadacdabcbcdbbadabacabcdcddddabbdcdacdabadbbcaddacabbcbaabadccccdabcaacdababbbcccdccaaabdadaddbcdbdaaccddccaacbbbbddcacbadbcadababbddbadbcbbaacdbdadaccaaadaddadcddbababbdddbadaaccadcaadbbdccbdbcbcbbcbdbddaadacdaaaabdcaddccbacbcbcbdbaddccbaddcbbddbaccabbdadaaabdcadddbcddabccbbcddadcdabdbcaaabcccadaacacddadbcbbdbcbaabbabaabbaaaadadaabcdbccbbdabdadddbaddccdbccaaabdbddbddacddabdbaacdacadadbccccaddbdcdcdbbadddcbaabdabdcbdddcbbbcbaabcbccdaacbbcacabaabcbabbddbcdbadccdacaaddacaadbddccdbbcadabbdccdacabcccaccdddbdacccccacabcbcabcddbbacdcbcadcddbdbbcabbcdabbdabccaaaacbccabbcaabcdabcbccbadacaabcbdbabbbaccbbddadaddcdaaaabbcccaabcbaabdadaacbbabadbbadddcbaabbcabbdcddbdcbbdacbdcccaabdbbacbbbcacabccdddcccdacbccacbabbbdcddcccabacadddadcdcdaaabbccdcacabbcaaaddcbaccbdcdbaacbdacaabadbccdbaadccbddbbabbbbbdadcbaacdadcabadbabbbccadadbbbbdbdbddbabdbddddbdcbccbadcbdcccbccdbbaaabdcdbbccbcaababaaccabdaabddcbbdaacdccdddabcacdadcbaaaaddcdddbaddccaaaaaaaabcbccccadddbcbdbdbcccdcadadbcdccdacabadaccdccadbdbbacbccabdadaddccaccdddaddcaccdcbbcabacdcccdcacdccbdcadbabdbacdccacbacddbacdadbbcbdbbcaddabcdbbbaddabdcadbcabacaccbbdbcabdbdabbcddcbbabddabdbccabdbccabbcbdacbdaddabdbcadaadaddadcaacacbaabdcbabbbdbacbcdbbbcbccbcdcacbaddabbcddaddabadadcbacadcabcddbcbbabbacdaabcdaaabbacaaadacadbccccccabcbdcdbdcbaaacddbadbacdbbddbbabbcaacccbbbccbbdcaacbbbdcdbacabbccbaadadbcacbddbddddadcdadddaddbbdcadcdabdbabdacaadddcadadcadddabbddaabdbccbdbccccaccdaddbbcdddbbdcdccbccbbbccdaabdaaadbddcaadcbacdcdacabdbadabdcddabdccdcdacabdbccbcbbacacaddddadaaacbacbcabacddabddbbdbbccbaacadbadccdccbbcccddbaddaabadbaddacddcacbbaccddbdbbddacdbcddcaadbaacabdddcbcadddbbaaddaddcbaddbcbbcaacccdcbabacbbabccbcbbbddacbbdbdcbaadddcdbadaddbbccdcbbbdddbdcdccaaaddcacbcadbbdabcccbaacdccbbbababababbccbcaaacbdbcdbcdadcabdcdbdaabacbdbbadcccddbdacaacbbbaabbccaccbcbcbbabbbcdbcabcadbccaaabbdbcbbdaaabcbbdabbadcdaaabcddacddbdcddbdaadbabccbdadbbbbcdbadbbaabacacaaddcabbbcaddadcadacadcaccdbabcadbccbcbccbcddcaabdccdbcabbbcccaabdaaabdaaacbaddaddbcdacbdaaadabbcdbabdbdabdaabbbdbbcadcbbdacadbabddaabdbdbbbcbcdcbdbbbcbbadccabaabbbccadcbbccddbbcacabbdadbaccacdcbacddcdccadbadbacdcaaabacabbccddddaacacddccddcdbbabcdcabadcdbdaaadcaacddbbdccbccadbcdccdcaaddbccbdcbcdcbbdadcbbbdabbabbddccdaddcaaababadaaddaaabdacdcddcaadbcaccabcbcdaccabbdccdcdaadcdcaacaacaabaddacddabadbcaabbcddabdbdbcdcbdbbbcbadccdadcaacbaaadcdabadabcabdbaabcbcabcaddbadbdaacbabdaabdcaaababcdcbcaacdbabaaccbadcaccccbabcbdbacadbdbddbbbdacdcbbabccaaaccabddbbcbbdadbccacddcdcbbbbaadccbcbacdcbaacbddbbbccbbabdbdbcabdcdbdcbdbcccdbdddbccdadddcccddcdbcdbdbabcdbdbcdbdaddcadacabbadabbbabacbbabbdbcbabadadcdbcbbcdacbbaaaccdcdacdbcdcbbcdddabbacdcdadadbaaccdbccbabacbbbbbdddbbddabadbbddbbddcccacbcdaabcbcdcdadcdcbadaadddbbdadddabccdbabdbbaabcccbcbbcaddcddddacbbadbcacbcbbbadcaabaabcacddcdabccdaaadcbcaddacbdcdbdbbaabddbabcbdcddaaccdabbadbbbbdbddcddaacdacbacdbaababdcabaacdabdcadbadccbcbcbdabaddbcbbbccabccaacbdabbcadadbccdacbadcabbcbdbcdcaadaccbcddcbabdddbdbadcdbdbbadcaadbdcbbaaadadcabbacdbdbcabdaababbddbcaabcbabccdadbaabbabcdbaaadddcbacbbbbacbdcccbcdbcadabdcdabcbdbdbaadcbdddddbcdbaddbcdccbacdcbbdddaabddbbcccaabbdaacddccaadbddbdbddabbdddadcbbaacaabcbaabcbdbcacdbbacccbaadcacacacaaaddcdadddaaccbdbbbaadbaabbaddcacbbcdbacbbaccadacaacbdccdbacabbddddadaddadcbbddcccdabcabddaadbcadddacdabbacdbbaddadacbbcacdcccadbbddabaccdabccbdaddbdaadbabcdaabcabdbbbddddbcabaaaddcdaacbbaaaacadbcbaaadabadcdadbdabacbacdacadabcdaccdbdaaaddbbbddbdbccdaddcddcbdcdcbccbacaacbcabdaaccadacadaadbbcacdddabccccdaadddbdabdadcaabaddbbcabcdcdbccacbbdcccdabcdddbcdabcccddcacaabccacbccbabbbdaababbcadadcbdcbdcbdbadcadbbcabacdaabbbdbcabdcadcdcccddccaccbddbaaaaacbcdccddbbbcacdcbddaadccbddcbbbdcbaadaabdadcacbaabccbaaabbcddbbcabacbdbdabaacadcaddabcbcacadcbcdddbbcccaacabbbcadbacbccbccbdcbabcaaaacbddcbaaaacdbcadbdbccbcdcadbadacddbccbadbbaadabcbddadbadadcbbbdcdbbbdccacdcdabadadbadbbdaaabdbcaddabcdabbdaabadcbcacaabccbbcadcbadbbadccaadccbddadcbddbdacaadacdabdbccdacccccabacaabdcdabbdbbaaabbdacbdccdbdacdcdababdaadbddbdbbbccdacdacabcbbabccaacaddbcaabaacbdabbccbaaacbdadbacccabdaabadcdcaadbdbdbcdcadbdcaaacdaddbcaaadbcacacbcaadddaddbdddbacadcabbccbdcbabacbdccdbbbaadabccabcdabcccbbacdddadbbcdddbdaacacbacdcabbbddbbbaaacdbbaccbcabdabdacbbbdaadcbabccbdacadbbccadaccbcacbccadabdbdcdddadcadbdbccdbccaacbcdbccdddbabdbcdbdddccbcaaabaaaddcaacaadbbcaddcacdcaccdcaaaabbbdbcaacdacdaabcddccccbdcddccdabbdddaabbdbdddacbdabdcaacaccabaadbabdabaccbadacbddadacadbaddabdcbbdababbbdbcaabacbaadadcabdddbbabacdbaabbbababdcadaabcabcbbbbbaadcddbbcdcbbbdcbabbbdaddabaabbbbcbabddbcddadcbaccadabccdcbddcbdbdcbddccacbdddcdccaadccaddcacabacaccacdcdbbdaaccdadaccbcabaabacdabbddabacddacbcabcadabbdbbaadddabbdcbbcbcbdddcabdcbdcccbaaaddaddbbbcdabbacbbdbbabbccccbbbcbccdbaccddbdddccabbddcccdaaccacccddcabcbddcadcdacbdcbdccbbacadacadcdcdabcabdcbdcddadaddbcdaccbcababbccadbabdadaccdbbcdbdbddbbddcddbaadcacacadccdccabaddccbaabdbdcaaacabbdbcdbcdbaccbcacbbddbcdddaccbbbbdbdcbdbadbcbbbcabbcbcccbcdccadabadcccbaaddcacabcadcdaaabdcbbccdddaadadddbcbdcdddcbaacccdbbbcccadabbccbcbbabcaabbbdcddadccbdcdaadcbddadcddbacddcbdcddbadddbaabadcaabbbddbdbddcadcbababbdcaacdddbdaacaccaacbccaaddabccbbbadbcdcccbbdaddccbaaabcdbdcacacbbbaabbbbdadbaccbabacbcdbaadccbadacccacbdddbddcabcadabcdbcdaccbddcabcbacadbcccabaadcdaddcdbbbacddabaadcddadcadaadccdddbbcbdbaaacabbbbdbcbbdaadbccbcbaabbaadcbcbcdaacaddcdccdadaacbcbadcddadaadcaacbbadcbbcaaacbbbdbaababaaaaabacbbacbdcdbaaccabbcbcaaaddddccbddcdcccadaaadadcbaacdbadadcccbcccadacdddaabaaaddddacdcaadccbadbadadbcbaccdbacddacccddababcbccbdbadbcbbcdacaadbcaddabcbccaaacdbcaadcdabcaadaddcccbbacadcbbccddddbddcbccbbaccdcbccbcbbaaccddcccddadddccdbabddbbbdccbbdcaadbabbcaabdaaccacdbcbbcbdcddaccbdadddbbddcbbddbbdbabdbbddbcabadaaddcdadabcddadbbabaaaabddbdbbcaccdaadaaaddccdbbcabacbbaadbacadaacdddcbcbabaaabddbbbcdabcadaddcdbadcaccbdbcccacaacdbadabcddbdbdbbbdbddaabcadacbdabdcbdbadaabcdbaaccbcbbbaaabbccbbccdbdbcbdbaacabbbaccaabadddadbcdcdabaaccbcdbbdccbddddcabbbcbaaacccbdcabaaacbdacbdbdcbcadccabddcabbbdaacaaccaacacaaadcbaccbbcdccdccbbaadbbadcdccacaddddbaaacbacdddaccbaaddbccccdbddddbcccbdbbbbbccddabadaddddbcdbaacbbbbabcdddcadccaacdccbaaaaaaccbadbcbcdaabccaddcdcaaccdcadddbdaddccbddbbbabccdaaddcdaccdcacdadbbdababcbbcbaaacabdbdaabcccaacdbcaaadabacaaccacbdadcdcddcbcccaaaabababbbccacadccdabdabcdcadcbbbcbbcbcdabbdbaccbbbbacdcdbaddcddddcdacdccbddbbdbabdcacaabcdcdbdcbdababbadddbdabcabcccbdddabadcadacaaadbcddddcdabddcacaacdcddacaadccdbcaaaddbcbcdcbdddcacdcddcbdbddccacacdddaabccddabacdbcbbdcbbdcdccdbadcdbaccadccdcababdbdccbcdcbdcbcbbacadbcadbbdbaacacdbccbbdddbccacdacabacabacddccbcdadaaddbdacaccbccdabbdacaaccabbccbbbccddababcadccbabbabaaaaaddbcdbcdcbccbddadddcccbdcccabdcddaacbaadcdbcabacaadabcddaddbdcaabdaadaacbbaddabccaabdcaaaacaaaaddaccacacacdadbccdadbcdaabbdcacaaacdcaabcdbacdabbdbcacdbdabcbbccaccbdcddacaaddcdcaccabadacbbacacccdaaddacdcadbaacdbdaccdccbdbaadbbdcddaccdbacddcdcacbbcbccbdbdcaabcbdddbaadbbbdbadbbaacccccbcddbcadcddbcbdadddccabbdbadabbcacbbadabadbbaacccbabbdccaaaddbccadadcdaaddaddbbddbaabcbaaabdbadabcdadcdadccabdcadabccadaddbaacbcbdcdcbbadacbbaaacbaddcbdccabcacccabdbbbaabbdcacddcccdddbccaadbcbbdbbdddabaacbcccbacddacaabaacbaaaaddabccbaccbaaaaabbdccbaccbbdabccbbcdadbbacacaccbaddbcbddbadabdbabbcbbbacdadbbbddcbcbabadbbacbdaccbadadaacbddacbdccbdccbbbabcadcabcbdbbcabaaacbbcddaabdaaadabcbaadbdbdcacbbcacbddcdbcddcdcdaadcbcddabbdabccacbbabbbbbabccabdabccbdbbbccdbabbbccbddaddcbcabadcbaadaabbcbbcccddccabccbbcadaabddbdcadddddddddcdddbbbdddcbbdabaddadbcbdcdabdabcadaabbbbadbbcdcdabadddcddabdacaaaacacadcbbcbdcaabdcdabacaaaacbdbcacacabacbdacabadcadcabdcacbdabddddbaaddcdbdccaddbdbdabbabbaaddcaaccbacccccbcdaadccdcaabacdabdbcaabcbccccbbdbdcacddaaaaccaaaddbcdaadcacbbccdabdbddddadcbabdcadbbdbdbbabadbdbbbbbaacdaccdbacbcddcccbdbcaadcdcacbbbdddbbdbcaaadbcbaaacdabbdabaddcacddcdddbdddbadcaddcbcaadcdcbcddddabdbccaccacbbdbdccdbdabdaacbdcadbdddadbcbdaacaaddbabcaadccacbccabcbdbbaabccadbcbbbdccaccbabdbdbbcbaaabdccaccddcbcabcddabdcaaddababaccaabccaddbbababcdbcdcbbbbdadbddbcddbacacaaabbcdaddbdddbdacbdccabdddcdadadbdddcbcabdaddaabcdaacdcadaaccacacabddccbbacbdbabbbcbbaacdccdbbcdcbbaabaabddddabcaacbbbacdddddcdaccaacaaddbcaccbbabbbdacacdbadbdcabddbdbbdbdbbacaccdbbcbcbdccbcbaccacaccadaaabbcbbdadbabcbdbdddabbbbccdbbadcbbbcbadcdbbddaddbdbdaadabadcacbacadcadabcaabadcdadcaddccdddabdacbaaddcaadaabbabcacaccbdabbddadacbabbbabbabbaacbcdcabbddaaaacaadababdaadacdcccbdaaaccdbbadcbadcbbdcddabbcdddaabbdbbddadbababcacacbbabcbcddabbbccaaadadcadcdddbabbadccbabdbaadacdaddaddcadcbdcccbaadcbbacdbbddcaadccbcbdcddaadacdcbadabadddbdbabaaaababbcbaacccbbbaccbcabcaddbadccdcacaadbccdabbacdbdcbadbcabdcaacbbaaabbcdcabdacacccadccaabacbaaaaabadbbaccbbacaaaddcccdadddcdcbacbdabddbaabcacdbbaabcdbccaccaccbdbaaaaacddbdbbcdccacadaabddaccbdcdbbcadabcacdbbacaaaabddadddcadaabdddcaddacbcddacddcaabdadcdcadbbabacdadcddccbcdbdcbaabcdadbbccdabccaabaaadadbcdbdcdaacbabdbdbacdaaddcbbbbbbbcacdccacbbdabcadcadcacdaacbbcccbabbdbddaccbaaddacaaccabbacabdcacadddbbbacbccaacbcdcaabdadaaddbbddbcaaabbdbabdddbdccdcbbddbbadacbabaddcddaddddcdbccdcacbadbbdabaadbdbdadcdbdccbddddbcabbbabdbdbbadbcabbabbcbdbcadbdccccbbcbcaaaaadbdddccccdbabdacddacdcbccccaabbacdaacaaddbbaadbbadababdaacdbabbabdbbabddcddcbccdcabdcbcbdccbcdcaacbbbddbcddcacccddacaaaadccbbadacbbadbcccdaaadbbcbdbdadbbcabcabdbaaabccbdddbddddddcabdcababadddadbdcabcaadbaababaddcdddbddaaaabccadcbaacdcadbbadcccdcaabdddcdaabccaddadacdbddaadddcdbcbcabaabcdcbccdacadccdcbabaacddaccddcbbbacaaccdcaabdabcdbadbddcabcdcbadaabdcdbbbcdadccdaacdbdddacbdcccbcbdcabbdabccadacbcbdaaabaacaddcdccddcbbdcdcbacdcacbacbccdccbbddacdaacacccaddbccdaaddaaacbadabbbacaababdcadababdbddaabadbbccbcaacbbbbbcddaabbcbbbcadccbcdbabacaccadcccbdcbcdaddbabcaadcddcabdcdbdaadddaadbbbdcbcaaaabbdccacadcbaadbdcbaadbaccaddbbdadddbddcdabadadaddbabbabadccbdbbaaabacadbdccbdbbbbbdaadbddccdcbcadbbdcbbabcbbdabbdbcdbcacacaadbddadcaacbdadabbdbcbcbcabaddcddbbddabbcbaadbcbdaacdccabcbccbdccdbabacacbbacdadacabdbcaccbbddababaabaaccabcaababdcadbcbdbddbddbaacddcbabdcbcabbdbdcbacaccbcbddcaabaacdbadacabcadcccdddadbcabacabadacbbcdbadadacddcaaaadaadbdcbdddddbadddaacccacccbcbbcdaddbccdddccdacaadbbddcbdbabbaabcacddaaadadaadddaaaddcccaacbdbcadbdddcbbcaacbaabdccbddcddbdadcbaaabbaadbbcaacdbcdaaaddccdddbdbadbacbdcdcdcbdbccccdcaaabbacaadbbdaaadcadbbaabdbddbbdcacacadaccabdcbccbdddcdadcbaabcdbbaccdaaccdbdcdcbbcbadbcbdaadcbdcbacacbbbaddadacdcbcacaacccaaddcacdddbdbcccbcbabcababadbbdabcadabdcadbaadbdacbbcdaddddccccbbbabccbdcabddcdbaaabdddbbcdaacacbcababadbacbadcadbbdcbbcabdcdbaaaddcdcabdcdcbbbaaddaacccdbddacbaadbaabcaaabbcbadbbdabbcbcccaadcdccabddaabcdbacdccadaacdacdacccbbcbaccaadddaabbcacacbbccacdadbaabacddcabdbabababbdacbccdbcddbababcdbdabcadbdaabbdadcbbbdbacabacaaaddbdaddbbbbbacccadabacdbabaabacbdadddbcdabbcabbbddcbaadbbcaadaddcddccdbacdbbbcabacbcbbacccaabdcdbdbdddadabccaababcdbddddadcbaabcdbdcbabbbabaadabbbdbabddcdbbbbbabcddacdadbaddbbbcdbbaccbacbaacaddbddbadccddcbdcdacabbcaabcabccbbaacddcbcaadacbcdccaaacdaabbccabbcbdabddbadcdaddabadbcddadccdbacbcbdabdacadbccabcbcbaaacccbdabdbabacdaadaabadddcabacacaaacdcaccbabcdbcaabbdbbcdcdbcbdccddddbdadacbbbbcddabdcbccccbdcbabcbadcbbaccaddcdabaacdcaabbdadabcbbadadaadbadaaaacabdabbdbbabbbcaddabaacbccaabccaacdaabcabbcacabdaaccbacbaddaabadbcacdaacbbbbaabcaabcdddbccbbdabcacccabdcddacddddcdcccdcaacddbbadaddbdbdabdadcbccaccddcdabdadbadbacdcadadbccadabbdaccbcabdcddabcaddbdbbdccdcdaccbdadccbabddcdabdcabcacaacccdabadadadbbdddcaaacbbaaabaacddaaacdaccaccdbabddcbcccbaaadcdaacaaadbdadcadcdcbdadcabadadcbbccbbabddccdcbdbabadddabcbdacccacdcdaacccaadcabbcabdcabbccbcadbcdbadacababbccbcdbcdaacccddadacbdbdbccdcabacbddadbaacaabdbaaadaadaabdabdaabccddbbdccbbccddddcdccdaaccaadcdaccabcbbbadbdccadcddaddbdbaacdcddcbaacaabddacdaadddbcbcacdcbbdcbacdcacadaadaaadabbabcbdbaabbcccdcbadddbbabbaaaaccbabdacbddcbdacaacccdcacbbbcdacaccbbddbdccbddaadbcbadadcadbacbcaccdabacabbabcaddbbdbbdabcaadccbdbddcdcdabbababbcdadbccdbccdbdcdbddaabccdbadbdbbcbabbbadbbcacdbdaccacaabaabdbacbbbaabbcadbcddacdddcdcacddadbbcbcabdacadaabcbcabbbadcbaaddbcdddccbdabcdccacdbbbbdbcdcdaccdbaacacbcacacbbdcddbcbaadaddabacdacaccddaacdbcdbaddcdcbbaddbbbdddbddcdbdbddaacbddadabdbabbabbcccdababbaabcabacccbabdabdbbacacbdcbcacbbdcbbdbddbabababacbcdbbcdcbcacdcdbcabbabcacaaabbbcacdcdaccacadcacdddccdabdabdddaccddcdbaccacabcbccdcbaacabccaadadcaadbbaacbaccdbcbdddabbbddacbbadcddacaccdcddcdbdbcabcbcadcadadabaaccbccaccbcdbbacccdcbacbdddabaaccadccccbbdcbcaccbbbdbadbbbcbadaacbdaddcacdababbbbddbcdccacbcbbccbbdcdcbacaddbddcdaaadcddacccddbdaddadddccbddaabbddaadbcaddbcbbdabbacdcacaddaabcaccdcacccbdbbcaabbbaccbdcbbdabcdbabccbabacbbacbbbacdbadcbbcacccaacbdcbccacbadbbdabbbacbbcccabbdcccbbaababbacbaacbddbdbaccbaadcdadabbbbbdabbbcbbdbcabaaadccbdacacbcadbaaddcdaacadcbaacccdcbdcbdcbcdabbddaacbaccddaaccdbdacccaccbdadbdbdcbdddddadcbaabccbccdddaccabbacbbbabdabccabdcddbdcadcdabccbbdccadbaabbbcadabdaabbabbacddacbaabdcccbbcdadbdcbddddcaaddcddccbbbcbbbdcbdacaababccdbadccbdcbaadaaaabbadbcacbdbaacdddbccddddadcadddbccadaddcccacaaabdabbcdcdabddbccabcaaadbabcbdbccdcaabbbdacbddcbcaaccccaaddbbbbdddaddacacacbcccdcaacdcbccddaabbcbabcaddccaccccdbccbaccdbdcdbcdabbcabbadddcadbdabaccddacbbddbdbdbbdcdccaacabbadcbcababbdcbdddabadbddcdcacbabbcdbddccbddbccddbcdbcbcacdacbbaabcaabbacbbcdbccabddcdddcbccaadcddccbbdddbbbabbdbabbcbcbcadddbcaacbabcdcdabababcabcbdcababbdbabaabcabdcdddcbccbdcbbcaccdcbbccaacadaaddcccaaccdbddbcbbcbabdacdaacababbcacdaacbadbadbaddcbccccaaccacdccbcadabcbccdbddcadabcabaaabdbbbccbcaaadabdadaaababcccbdacaabdcbddacdaaacdabbcadbbccccdcdcddbbbdbbdbbabddcdcbccacddccdbacadbdccdaacdaadcdddcbbadadabaabddbccccdaabbbdcbbbdbabcdcdbdccdaabdaaabcbacbdbcbdcadddabbcddbbccbbcbbcccbaacbddcaabbdddbdccbabbcaccbadaccbadabbaabcacacdbaaadbaabadbdcdaabdcbdcdbdcccbdcaccbdcdbadabcabadaaadabcbdadcbcacaadcbccbbcdbccaaccddaaccabcbacbddccadbacdcdccddddaadcaacdabaacbbabbdaaddbcbbadbddcdcbdcbaabbdadcbbdcaabcbcddcbdcdbabacadbacbaacbdbaadadcdadaccacbdbaddddbbccbcdbbddddcdcdbbddcdabbcdacbaddcbdbdddbabcaaabdcaaaddbabcbdbabdbbadbaccadacabcdaccaacbdbacadabadcbbcccbbcabddccabcacacbbbcbaccacdaaddbbaccdacaccacaacbaddcbbdcbbabaadbcdccababbbaccccddbaaaddddaaabaadacdbbaababbcaaddcaabcaadabbacaddcbdcbaacabcaadddcccbcbbbdcbdbbdbbbdcdcbccddacacbdbcddcbbabdbcbbaacdabddabbababddbbadacddadacacbdddbdacddbdadbbbddbdacdaacacadacbcaadcdadbaaddccacbbdcdcabdbdddbbbbcabbdbdcaadbacdbbdaccaacaadbabcaaabdddadaabcdbbdccccbbbcabacbbcacbbbbcbdbddbabdbcbacaccdcbacbdabbbcaaddaadbddbdbabacadaccbcdbddcaaacdbbbcadddcabadccabdaabbbbbccbdcddcabadbbcbabbccccdbbdacadcaaabbddcaacdddbbdbacbbccadaaccbadaaacacacbddaadadbaabbcbcbddbbdbbaddcdbaaabdbcbccbaccbabaddacddcadccccdabadccdadbcdcadbddabcbaaddbdabdababadbdaaddcaadadaacacbdcabacdbccabdabcaddccbaccdbcdcbccadcacadbcbdbdacaccccbcacbdadcbacabdddcbcdbcacacbaccddcbcccdaadbdbbcddacccaaddbbcbcacbaaaccdaccbddbabcdbcdbbccacabacbacbdbacbdcbcacabbcdddcbaaabdbcbcabbbbdcdcddddcdacbdcaadbdcaacdacaccdbbadadbbdbcddbabdddcdadbdcdcaabccbcabdbaadadccadabbcdbcbaaacdbdbabbcaacdcdacadacbbdcabbcdbacaccbaadcbcbaabbdaaaccdacbdcabcccadcbacdcacddbcbdaabacabcacbddabbcbcdccadddabaddccbbbdbbcdcacbacabdadcccdbaadcbdbbbbbbdacccaddabaabaaccbbddacbcbabcbcacddbcabddcbbbabdaababddbacbbbcacbcbbaaccbabbabbcaddbdcbacacbdabacbcaccbaabacdacdbddbcbacccdcbacbcbacddcdbdabccbbbbdcadbdaacddcacaadbbbdabbdabbbcaadcacadadcbbbdbbcdacabcaacbabcaaababaabcdbaacacdabdddabddbbcbdaabccddbcddddcabcadcbdadccbbdbdcacdacccdccdacaaadaccbddbcadbcabbdababddacddbaacaaaccdddaddabddbacbaacadabadbbccddacbdccbabcddbbaacdcaaabbcbdbcbbcacabdbdbabcddbadabbbdddbabdddccdacdabcccbaabaabababadabdbdddcbcdadcbbabaabddacbdadaacdabdbdacdaaddaabaccdbbdbaabdcdcccdbbdccadaabbaacbbcaabcddaaaddcdbadcddadbdcadcbddcbbcbccaacbdbbdabcaaccbaaacbacbaabddcdcdabddaabbbbddcddbbbbbbdabbdaacdcabdccbcacdbccbcdabbadbbacbdbcccdabcdabddacbcbcdbdcdbaddacacdcdbdcbbabadcacacaabdaadadadbbbdbbddaacaaaaddcdcdbdcabcabcdbdabdaacbdcaccadddbacdabcbabbdabaddacdcabacabacbcddcdcdadddadacbcccdbcbdcaddcccdbbcbcaaacccbaacaccdcbccbdbdcbbccadcbcdbddddcaacaaaabbacbdddcabbbcdccbabcddcdddabaabccbdbcbccdddbaccadabaddbcbbbadbbbaccdddacacbbcbbaababcadbcbbadbdaabadbbbdbcbabdacdbdaacacadbaadacbabcaccaddbcbcddcadabcbaccadddbbcaacabacddbbacaaacbbccbdcbddcbdacaabcbdabbcdbcababaddaadbcdcbadaaaaacbcbdbabbdacacbadbcaccbcaabcbbcbddddcccddbcbcabbdadbbdccbbcacddadcbbaacbdaacdcdbcddbcabacbdbacabaacccaadbccaabaaccabaadcbdacbdccddaaabbdbccbdcacdccbcaddcdcccddacbdbabbdbdbccaccdbabcdbaaacbbdacabdddcdbbdcadaddabcdbbaacabdcaadbdaddaadcddbdbdadacbdddbcacabdddcbacdbdaccdaaacbccdccbacabdddbadadabaaabcbadbcccdbcdddcadaccdbdbbaaaabcddabcabacaaacbaccdaabdbbddbddcbcbdddccccdaaaddcaccdbddcbaabdcbdaaabbcacaadbdaadddbabbdcdabcdbbccdcadaabaadabcaccbbacaccddcadbdbbcabbbdacddcaacddbbbcaabaaaadbdccbccbcbadbcddcaacdbbacbdbadddabdbbdbadbdacaacbccddddcbaadbdbbcddabdabdcbdbadaabcabccdcaaccbcbdcbdaddaadbaacaaddadbbbbcdcddcddccbdcdbdcccdbccbdbaabbbdbcddccbcbabaaacdcdadadbdddacadccadaacdccbbddbadaddbbaacbbbaccdccdcabdddbdbacdbbbdbdcdcadcdcbbabbdacdcbaaabbcbdaccbcdcacaadadbadddcacaabbadabaddddbcbaabddbbdaabaccdbdabbdbdccbccdcccaaacacddaacbcabbaaccdadabccccbbacadcdcaddbccdddabddcbdadabdacbadbcdabacdbcbbcbadabdddcacddbdcaadbdabddcdbaadbdaccbcbcbbcdadcbcaddadbbdabcbbabbccbccdaccdaabbaabaddbccbbacacbcdbdbbdcbccdbcdbbcdabcbbcddaadadaabadbadadbcdbdbbbcaddbdaabaacdbbdacccddcdaabdcabcbacddcdabaccbdbbdadabddadabcdbaaccacdcaabdbcdcdaabcadabddccacababcbccbcbbcdcabaabccbabdaabdbcaaaaadcdbbadcaddabcacccabbabaadcdaacddddccaccdcbabbcccaaabadddabdbcbdbdbdbcdadcbdbbacabbdcbccbbcabccdbbbbcddacaacbbdabdabdcbdacaccbbcdbdabbadcabacaaaadbadaaadddacccbaaaaddabdbccbcddacbbbadbabbcdabdaabcddacbbdcbbcbaadcabbdadbbaddbdabdddadbbaabcbdaccaddcdbdbbcdabdbaccccbdddaaabcdaadaddabacbdadcacbbaadcbcabddcabbdbcddcddbccdbbbddcccadadabcabacacacabdbcdcddabbaadcccadbadddbaabcabcbaabadbcddbbadccdcbabbbcbbcdbacbddbacadbaacdaadabaadbcadbabbddcaccadccbbbddaccdbcdcadaabbcdddcabacdbaabadbbccadadbaabbbabbbcbaacadbdcbbdaadddbdbdbaaabcdcbbbcdccdaacbabaddcbbcccadbbbadadcabcddbdbbcbdbbdcdbcddbcdbdabadcbddbaccaacdcccdacdcaabaddaddaaabdccdbccdcdacdcdcaadbdccbadaadaaadbabdccdbaaacbbccbccddccaaacadcbcdbbdccdcadddacaadbdbadcbaacbbdbccbbdccdcdbddddabcddcbbcbbadaacadacabdaaadccddcdaabbdbdaddbdbcdacabddcccadbdbabdddcdbdbdbdcbcaddcbbabdacbaacadcdacbdacdcaabbabbbababbddbcdbbdbadcbbddccacabcbbcbbdbcccbbbacdbdcccdbbcdbcbbdacacbacabcbdbacdaaccacaaacdacbdacdcdcbaadcaaabdccccdaabcbcbabcdbbcdadcdddbcbacbabaaddcdbbacccaaadbdbdbdadcaddcccddacccbccbcabbaacccadddbbacbadccabbbccbadddbcbccdcacacccaddabcacdaccdcbcdacacadcddadabbaaabcbbdaabbaaccdbdcdababadcbbacbdaaabdcdcacbdbdbbbdccacbbdcbbddacaabbdbcbaaaacdbdbadcbbacbdccacdaabbadbdbdacdbbdcdddcbcccaabdcbdcddaadadbdcbdabdadbaaddacbbbcaabddcddddbdbdbbddadbbacddaddbbdccadddcbcbcdaacdbbacdddbcddddcccbdcdcbbccdabcbbcaaddcbdbcaddbcacbdbbcacdbbbbdddacbccacacdddccaaaccddccbcbbcccddbabdbaadaabddabcacaaabcadbddbbdcabbbcadbdcabbbadbdcdddbababccddbdbddcbabdcbbcdddadbdcdabbaacbbcdbccaadcdbbaddcabcdaabbbddddcdabaaddbcaadaababbdbbccbdddbabcddbdacbaaccdadabccccdbbbaacbaddaaabacdbbdcdaccbabcadcbacbccabddbcdbbdabdbdaccbddadbbabcadbadcaccadccaddcabcddcbbddccdcbbcaabddadcadabdacdbcddbdbaddbaabbcbabcbaacbdbacdccccbaaddddabaabddcddcacabbaccadadadabbcacacbdabaaccabdcaadbcaccdbdcbdaaadcdaddbcabbdcbacadcbbdbaccdadccddbddbbcbbabdddcdaaabacaaacbdcccbaadddabababdbccbdbbdbbadbdabbbbdbbdbdbbddcbdcdabbdaacdabdbabbcdacdcbcbbccdabcddbccaccbabbcccddaadadbcdacaabdcbbadbdcbaadbdcdaadacdbbaaacbacdcbbbadaddcdbbddccdbcabdbdcdabcaccbcacbccacbcdbbbbadbccbdcdabbaaccaabbcdbccbadaddbdbaabbbbaacdcdcacbaddbcdaddadbcbddaccadaddadaacdacacaabadbddbcdcbadacbbbcbbbddbcaaddddccbbcbabbbadabdcbbadcbcdaaaabcabccdcacdbddbccddababbadcaaccbcaddddadbcddddcdcacacdbaacbabbcdabddbbbbadcdbadabbdabacbbbadadddddabacdbdcdcadccadbaadacdbbdbcaaabdbabcdaadcadcbccacacccabdabacabdacdacadcdabdddacabcbdabbbbccddcbababdbccbdadcdbdddccbdacbcabccbabdddbbccabdacddccbdbabbccdbcdddcdddbabdcdadbadbacaaccdcacdabaddcababdacdcbababddbcabacbcbccdbcbdabddabbbbdbdcccdcbacdabdbccacabccaaadaddcababdbbdcccdbddadaaadabcbdbccabccabacbcccbdabdbdbcbdbddbaacdbdaabacbcdacdcaaccbadbbcaadadcbcadbccbdacbaaacbcadabaddabccabbaaddabdbbcdbadcbddacaabacdbccdacabcadbaaadacbbacaacaaacccbcaddbbdcddaaadcddabdbaaabdbadcaddcdcbdacccaabbbddadccabdddbdabdbddcdadbcadbbbadcbdbccdbcdaaaabaddadbddacadddbdacdaabbabaaaddcaccaccbbccbccbddcabccabbbacdbabcabaabadcadacabadcddaddbdacbdcaddbbadabdccbddddcccdaabcaaadccbccaacabacddbcdcbcbbacdbccadbddaadcdbcbdbbbacbaaaaadcacaccaabbadabdaaacbabaacadccbcddbacdbabdacaacddbacccbbcadddccabcacbcaccdccddabcdddccbaaccdaadbabbabaabdaabcabbcbbdcccbcacacccdbbdacccaaddcdabaabdbddcadcbddccbadbdcdadbaabadcdbcccaccaadbbbccccbbbaabbdbaadacdbbadbdcddcddbcdbacbdcdadabcbdadabcabbcbccaddccdddcdcabbcddaccdccdbcbbccadbbbbdcaabcaaabadddbcdbcadacbaacccbddabbdacadaabbabbcbdcabddbabddcaaddbcddccadbabdabdcccdabaabdbcbbdaadbabbbbaddbcabdbdadcbcaababddcacacdbbbdbdaadaddcdcdaccabbacbbdbddcbbbddaaabdabbdbacbbcdcbbadabadbbbbdabdcacccaacbbbccdaaaabdbcbbdcbabaadcbcadaacbddddabdbdccbdaadccdadcbadcddddcaabbabaccbaacbabcddcbbaabdbcbadccabdaccbdcabbddddbdddcccdbbabaddbabadcddbdcbaaccdcaaaabaabaadacaaaabaaccaccdcdbbabbcaabbbabaabcadbdcabdcdcdcccdccaccaddcacbccbccbcaaadccaccddbabaccddaaadbccabdbddcbcbcbddadcccddbaddcbaabbccbacdddcaabadcddabcbbcdabbabdbaddbaaadbbbdcbbbbdccacbdbddbbdbdccaaadadaacddcadcdccccaaddcbbcbbcdacbcadacccdbbaccabbcbdbccacbbcbdacbbcacadacccadacccdcccabbcadbdddbcabbbdddcacbbdabcbcaabdadcaaabacdadabcdacacddbcbdbbdcbcaadddddadabaabacaaadabcbabcbadbdbcbadbbbdbddcabdcdadcaaccabbcadcdabcccaaddddcdabcdaadddadadbddadbbccccacacadabcdcbbbdbcbaaabbcbacddacbdbcaccddbbaddabdbbabddbcbadadcdcbcdddadddabdadcaabcbddaccdbcacdbacccbdcacddcabaabadddabdccdbacbaabdabbcddaadbdbbadacaadcabadcaaccdcddcdbacdcacacaadcdacdaadcbbacbbcdbacbddabdcdcacdbaacddabcdcdaababaccccdabdaddcccdbabbadabcdcacccbbddbdcbdbaabbbcdbdadabbcadaabadcbaacbadcbbdbdddadcbdabbcaaadcabdbabdaadadcbbdadcaaaaaadccbcadabbadcaaadbaddddadbcbcbadbdadcddcbaaadddbaadaacdaabbbabababbcddaaacdbcbabdcccccddbabdcaabdadbdbbaabaacccadabcdcadbdccaadababdcadbabcdadccdcadddadbddbdbcadddacccdaaaabbbdddbbcabdccbcdabbaddadbdddcbccbdbaaaddbbbcbcabacccbcccaabdcdcddbbcabddccbbdddaabaadaccacdabacbcabdddaccaccdcddadcdbacbdaacbaadcdcacccccabbcaadadabdbbbabdccbccbbaabadaacacacdddbccdcaabacccabdcdbdaaddacdabcadacadbbadcaaadaccbbabbcbbcabcadbcbcdadacacbdcbdbbdcddcbdcbadbcddcbbbdcdbbaacddddaaaadbaaddadaaaddbccaabdccbdabcdcbcccccdaaaaadddaabadcbbbddddbaacadaabbbdcbcbacdacdbccdcbcdcbacbbabdababadaabdccbadbdddbdcdaaacccbcdbcbbbcaddcddaaabcbaacbaadcaaaddccdaadcdcadbbcaccdbabcddaadcaaacbcaabcadbbddacadcadddbabcbadabccbccdccaadaacdcacbcacbccacacdcadddaadacabdccdcdadcbcddbdaabadbaacaaaaccbacabbcdaaacaabbbaacaaabdcacaddbdbaabbbdaacadbdcadcddbbcabbddbdcdacbccbabdbbddcbcbdcdcbdbcccdbaacacddacbdbddaacdbababbcccccbdcdbddadbdddabddbacdbbccacbbbcadddbdbbdbcccbaadbdcdbddbbccbcdabdadacdaadbbaadcbdbcdabacbaccdabadbaaadbdbdaccbbbbbaccbbdadbbacabccddbbdcbcdcdcdbadcaaadcbbcacdcdddcbdcddbdbdbdacdadbcaddbdcdbdaddcbdabcdcdadcdaacacaacababcccaadccaacccbccaaadbccbacacabdbacbdcacccaacddbdddccdaddacaaaadbdccabbacccbcadacdbadcbddbadbadbdabddbaddcacddcddaaddbbabdcdbbacadadaddbcabddbbdbdddbdcbabdbbcacacbadaadadabaddcdacadcbccbbcbcbbdccadcbabcdcdaaddbcdadababbbbbcadbdacdabaabcdbdcaaaccbcbcabddcddbacdbbccdddaccabbccaccdbdabacdbdaabdadaddccdbcccaaabacbdccaaccccddcbaccddcacabbbdadddabacacdabaaacccdbcbccddcccccaddccdcabcbcbcbacadbadbdacdbbbdbdcbccaadcdadcccddabbdcdbccdcbacbbcbbbdacbaabbccbbbaabcdacaccaaaacaccbadcdbbababcbbcbacddcbbdabdccabaacacdcbacbcaabbdaacddadcbaaaaacacabaabcbcaaabcbccdccaddccdbaaadbbcadddcddccaabdacbbcacbcdcababaaaccadbacabdbcbaabddbdaadadcdbaddcbaabbbaaaaaaddbabdacdbcdcdadadddcbcdddcadcacddcaddbdacdddbdabddddcbdadbcdacbaaaabbcbcadaacbcbdadccdaaaccdacbcadaabcacbbcbabdabccdbbbaabbbaaaacaaadabdcdacdccdbbbbdabcabdaabcbaddcacbcbbdaabbadcdacbaccadcbbbacbcbbbcbddaabababbddccaabbcdcbccbbcadbdadccbbaadacacddadccccbcbbcddcccdbddabbdbaabbaabdcbdbddbcbddcbadbbadabcbadcdccbacadbabdbcdccdccbaaacdccbbddddacacbabadacdbabbccbaccaadbbbcaadabcccadbbcbbaddbdadacabcadacddcbbcdbbaddaabcbcdabcabdbbbbbdbcbcdaabccbcccccdbadcbcbcdcdbacaadaccddccaccdaacbbbbcacacaacbbbcddccbbabbacacacdcabcabcaaccbadaacdadcbadbcbbbcbdacdbdbcdddadabbbaddabddcbbcaabbdcbaddadcadbaabaaddbcadbdaacdbcccbcaabdbdbdaabccbcbcdcdcbbcababccabbaccaacbbdcaaabbdccbbdbddccaccbdacdcbcbbadddadbbadbcbccddaaadcdbbaacacdabdccbcadddcbcabdabbcbbdddbdbccbbcdbbccadbabcdabccbccdbacbddcbbabdcdaacabbddcbdbbcacbbdacdcccdcbaabbcbadadcdabdaabacaabbcadbaabcbddbcdbadddcbbcbbccbadadcaccacacbcbbdbccdaddaabdabddddbdadaaacaddaacbddaccacddbaaacdaccbcacccbbdccbaccbcdccdabbcaabcabbbdacadddcaaddadaabccaaaadccdaccdbacbabbdccdacbbabbcaadcdabcabddacdacbabacbdadaaabcadaabdddacdcbabddaccbccbcdcddaadadacccdbcadabcdadcdbbdccdccdaadababdadcabadaabbabaadbddbaccdcaddacddddacdddaacdcccbaddacbdcaaacdbaddacabddacaccaaadabaddcadacbdcdbbccbccbaddcacbacddacddcddaccabdadadcccbbadccdacbddacbcdaddcddbcbdcdcacabcbbcabbcadabbcaaacaabaaacbbdbdcaaadccbbbaadbabdcaaaacbbdacdcbbdcaabdadabddbccbbddbbacbcbbbdbbbcbbaadddadcbbccdcdcbabcdbccdcdbbcbdacabdbdbbadadcacacadadbcdaaccaddddabcdcaacbaadacabadbdcdcacccdbabadccbdcbdbacaaadcdcdbccbdcbabadbaccdcccbcbddabdacccbaaadbccbcbbabbbdbbaddacbbcbbdaaadcbaccbbddbabddcbaaabdbcdbbbacaaaaccdcccccbdcadcbdabbaaadbaacccaadcabccddcacdbacbaccaddcdadaabcaabbccacbbbdddbadddddaddadcaaddacacaacaccdbbbdccbbbabbcabdbbcacaddcdbcdbaccbcaddbbabbcdcdabccadaaaabbbaabdddbbdccdacbaadbabaacbdadccadbccdcccdbccbbbbdaaccdaacbcdbaaccbaddcdabbdbbccccccbbcadabbadddadcabadcacdcbadcdaccbbbccaadcaabaabdcdcbcaccbdcdcdbbddcaaadabddcbcbadbccabdcbdbdaccabbbbbbcbbbabbaddbaacacccabbaadbabbccdddbdbbcaacaaddabacccdddacdbdbcbcccabbccabbadabaadbcbbcbdbcaabbaccbcdacdbabbcadbcdbbbbababbcdccdaaccaadcacdabdbbadaaaacdbcabcacdbdadcabacbabcadaadcadacdcdadaaccccbbdabcaaddbbbcbadbadbbddabdcddadddaacaaababddbabdcbabcbdcddcdcccdddcbcaddcbcddddbbaabdddbacbbababdadcdbabbcdccabcdabbddbbbbadbcdbbdcabcdbbccadccbadcdbdddbadadcddddbbcadbdbaadcacaddabcacaaacbacbaccdbbbacbbabbcadcadbacdcdcbaadcbdbbbccabcccabccbccbdadbdbbdadaadcbcabbcbacbcbdacbdcbcdbacdaabbdabdaccabacbdacabbcdcabbabdadcbcbaddcbacadcacdbaabaadbadbccbccdcbbdbcdbccbbcbcabcccadaccbaabcbcacaaddcddcbcaccbbcdbccbdaaadaaacccadcacaddbaacacadcccbddbacdaabdcaadcbccaaccadccdcacbaaccbcacbaadbddcdcaacccacadabbccaccdbccbacbadacaccbbcdbcbdabadbadcbcddcdcbadbacabdbbcaadbdabdaddaadbdbcbdbbbdcbcaacdddcdcdadbdadbacbbdcaadaccccabddcdacccddabacdabbbbdbdbacabbddcdaadbbabdbcaacbccccccdcbbbbdcccdbdaddcabdcabbcaddabacaacccdbddccaacadbbdcdaabcccdccbdcacabaaaadddddcbcddcbcabcbbaacababbdcdddcbdbddabcccbaaabbdaabdbbacaaadcaaaabdcdcbcaccdbccdccabbdcadcbdabaccacaaccabadccddabbbabddacabadddcbddbbacbaddbacaaaabaaadbbabdadcccabccdcacbdabdbbddaaddaccdababadbbccaaddadadaccdabdaaaabdbabbdbcadadbbabbcadaacaabbbbababbdbddddaccaccacbaddabdcbccbbaddcbdcdcbbdccacddccabdadbcddcadbdaacdaabaaddabbaabddccbbcadbabaaccdabbdaaacacdababcaccaddadcbcccccabcbbbbbbccbacaaacbacbdadaaabdbbdbdabbccdbadacbddbdddbbdddadbdbbcaadaccabacbbddcaddcdcaaabbadcabbccadcddbcbdadbbcdbcabdabdaddbdaaccabdbddcbcbdbbadbdabdcdbcbbddbabbdadbcacbbbcdbccdddbadacaaacdacbacbcadbcbaaddbaacabbdadcdbbddcacadbcaccdacdbbaccacbcbbaacaaaabadddaaabaabacdbbdddcbbcadbdbcabccddcabccbbcbacdadbdcdddbabdddcacddcbbbbabbddbdbaababdbbaabbdcbccddadaddaaaabacccccddbccbcbadbdcbdbbcdadbabdcaddaccaadbdbdadabccaccadadcdcccdaadbbaadbbdcdaadbbadbcbcadadcabbaaacbbdcdcddddcddbabadbaabbcbbddacadbbadccdcbcdcdddccdcaaddcbdbddabadcddbcaddaacdbbccadcdbacdcaaacdcbccbcccaccccddddabdadbcacabbacacdabccdbbaadaabcacadbaddbaccbbdcaaaabccdcdabdcdadcddccbbcccbbcbacacddbbccdcbdacdbcbbddbacbcdbaddbdbddbdaadadacdbccdadaccacaccdccbbadcadcdbcabaddcdbcacacdadbbadcddbaccabaccacbdadabdbdcbabdbadadabddccdcacdcabdbdabadadbaaccbdadbabacbcdbaddcdadcbaacdbbcccbaaabcabbddaaabcdbccbbabcdbdadddcbccaccccaaddbbdccbacadbbcabbaaadacbaccabaacabdcddccbcbdbabcadcaabaabbbbccdbadacaddcdbcaaddcddbddbcdabaacbbcbcbadddaabddddadaaabdcaccdcdbdadddcdbbcccbaccdbbcbaddabcbddaddbdaaaaabbcaabdacabbdadcabdaabaadddddaaddbdcadcaacbcaaaabaccccaabadcbabaddaacbddaccbaaccacbbcaadddacbdacdabcbcccdcccbddcdcacdccdcadcadbccbcadbaabbbdaabbdcaccaaabbbadcabdbadadddadcaccacbdbabcaacbccccbdddabdaaabacdcbdabcaabbccabdbbbbcbccccbbbccdcadbdcdddcdacbabccdbdbbcabbdcaadaaabcdbbabbcbcaddbcbdccbdcabadadcbdbbcddaabdddaadcddadbbcbcaabcbbccdbadcdddbaacaaddbddaadaabbcdcabcaabadccbbddbacaaacbaaacddccccbaccccbbbaccacccdadcdacbccbacacdddbbbbcadcccdcdaacaaacbcdbcaccbbadbbddadacaaddbbaccbcbacdddaddcbacacbacdabacbccbdbabdbbccdcdbcbbadbcdaccbbbdbcbdabaaccbaccdcddbbcbaaacbbccdbabacacdccbdaadcddbdaaabcbcadacccbdcbbbacaaababbbabccccdbdccdaaaabcabcaccccabcdddddccccddcaadacdcaabcdcbaaaaaccacbccaaaacdaabdacdccadaacaaacdcabdabbababbdbacbdbcdcbcbbbbdcacacaabdddcabbbbbaacddacbddbacbbdabddacbbaaaabaacbbdaaccccbbbbaaacaaaadcccbbbdadddcbcdcbbbaacadcdadbccbaccdddccccdabbaaccbabaabaaddaddccbdbabccccaddbdbcaaadcdddaababcbbdcbbabcdadbaabbcdddccdddabdcdcaaacaabbbdbbbdaccdccaaabdbbcabcdcababbadbdcdcbcaabccabacbaccadaaabcccdbbdaaaabdacbcadaacdbadbdbcaddddcdcccadadabcbadddcbadbcbbddccdbdcbcdddaaddadcdcacbddabcbcadccbcddccdcbdacdabcacadccbdccdbaaabcccbddabccabbccacadcbadcbcddccbbaadbabcdcdaadaadccabcbabacccbdbbdbbccbabbbdbacaccbadaaddbaaccdabdbabacbcbadadcaaadbbccaacbbccdbccddadaabdcdcddcbdaabdaddbdabdddbcadcddbddbccdbdaddbdcdbbdbdcabcdbacadaddddaaccdbacbbdcacadddabbbcddbcdadabaccabcdcddabdaadcbccbbddacaabddcdacadccadbacdbcadaaabacdbcdccdabaacdcbccaadcbadbaccdbcccdcbbaddacacbacbacddbcaddaacdcaaaabcbbdaadadcbdacabdcbaddcdbabbdccbbbdddbadbadcbdcacadbbcaaaacbddadbcbbcbdbdbbdbccacbaaadadacddbabccbbbabdbabdbccdcdbcccdbaaaddabadadcbacacabcdcdbacdbcbbbccbaacdabbbbdccbbabaaadddbaabcddacaddacddabdccbabacdbbaaccdadcccdbadaccdacbaadacddccdbdaccaaababbadbcdcaccbbdbbbbbcacadadaddbccbbdacdabddaadcdacaadbbcdaadbdccaaaadaaccbdbbddcdabbadadccacabbaaabaccadcbcadcacbaadccadcdbbdcacddccbcccddcaaaaccdddbbbdcacdccabddddbcddcdaacacbdbaccacbcbdbcbcbcccbaddadadaddaadaddabcababcadbdcdccdcbddbbdbbddcbbdcabbabbacbdbbabdddcddcccaaacbccbdbcdcacccbaabddbbddacccdacbbaabcbaccccabdadddcbbcbcabaaaabbddcadbcdabbcdaacbaddcadcdbbdbddbbcadbdcbdcdadbdcacbadacbddbaabdabdcccbdabbadccabbadccdccabaddbdcbadbccdccacabaddddcbbbdbbdbadcaabbacddcdddacbcbdbcccddadbdbdcdddadbaaababcdcddccdbcdcdcddbdabaddbbbabbacdcacdbdcbabcccbcbbacaccdcbacacabbccddaaadbadbccadddbbbcbacbcdbdadcdabcdbacadbccaccaaadbccaacddaabdcbdcabbddddbccabacbddbcabcbbccabdabcdcdbdbcadbcaddcabcacdbacbcaabcaacddababadcacbbdcabccdccccdddbddabbcbcadddbddadaadbaaadbbbaacadbdadccabbaccdbbbcbcdbcbaaaaaacbbdccadbcacbcbccdaddcdcdcacdaaabbccccdbacdabadcdcbcbddbabbdcbdaaadadbcdcbcbcbccddabcabdbdddcbbbddabbddddbccbbababbbacbdcacdbaacaddcadcbbadbbdddcaacccdabadabacbbbbcbacaddcadaccbdbbbcddaccadbccdcbacabcadbadbbdccddcccbbcbdccabcccdacbddbadaaacacccdcdacaaaddbdcadddddbaacdadccbdbcbddaaddaaacdcadbbbdbbbdcbccdbbbbccabcdddcbcddbbbcbcabacbcbadbcaabccbbabdbaadabbcddacbdabdbbdbabcadcdbaabaccaadddcbbabcbbacbdacacbaccdbdabadccadcadccadbcdabdcccdcbccdbcdbbcccbcddacddbcbcaddadcdbdacddabdbcabcbcbdaaaddadcdaaadbbdcbccaccbbbcddddabacddccdccacacacdabcdcccadacddbdcabdbbbaaddabadccadabddaacadaccddbdcbcccccbbdaaadadaabddaaaadacababbdbcbcdcbbabcaddbccacdbbabaaacadadddcdcdacabcaacddcacdbbbdacabbccadacadaadcdbcccbbbbaabbaaaadcbbbbbcbaadaddacdcddddaadbcacaccaccbcbdddbbbdbcaabcbddcbbbaadabcbabcddcdccccabaddacccdbcdabaadbbbbbbcadddbddccdabbdbcdbbdaabdcdaddbdaaccdbadccabcbbccdbcdaddcadccaacdcaccdbbcdadbaabccbccdacabdccbcbdddbababdbdbcbbabccddbdbbdcbcccccacabbbdbbcbdaadddcadbcccbadcbccdadbbbbadbccacdcadcdcddaaabccababadcabcdacacdbdddabaddcbbddbbcbacbbdabbdaaddaacdaddcdacaacdcbdbaddabbdacdacdcccadacbdaaddbcbdbcaddbccabcbccbadbcbcbabbadaabadbcaccccbbdbbcdbddaddbbcbbbadddddacbddabadbdcbacdbbaabbcacaddcccabacadcbadbcbcccbcadddbcdaccbacddadcdabbabbcbcdcdbdbadbcabdadaadbccaaccaaabcdddbcacaaccaacdbcdddaccdcbbdabaadccdccddcacaababbbacbdaadaaadcbacddddaacdccdabbabdcbddbacccccccaadbaacadaabcccbcaccbaddbacdabcabbbcdabcbdcaabadaccacaccacbcabbabcabbcdcbaabadcdacdddadcdacbabcbdcccaaaccabdbccdaadcadaccacaaadbcdbdccbddcbadbcdadacbccdbccbbacdbaccabdbdcccaadcdadadbaddaacccdbaadbacbdcccabbdcbccdddadddacaadabdddbdacddcadcdabcbdcbcdbaaccbdacdbacbbbbccdcdbacdbcdbacbccbcbabbcdcbccbbbdbbccdbdabaacbbadacbbddbdcbdbaabdddbcbcbdbccaaacbcccabcbddcdcbbdabbcadddcdbaabdcbaaaccdcbadcbbadcccdabcbdddbcacbbcabacadddddbbbacdadcbdddbbbcbcddbdddadccdacddbcdbbccdbadadbcddccddcdddbaacdadbcddadabccbcdaabcbddbadcdcbbadcdaaacdcaadbbdbabcdaabcaddbcdbddbbcbadaaaacdabccdacbcccaaddacbbcdcdcdbababbdabaacbabbabadddcadccbcbabbddcbbaadbabddcdbcbdabcabbdbcbacbdddabdaabbbbbaaabccaabdacbdcbdacabcccbadadbcdaccaddcbcbcdcbdcabcdbdbcbdccbadacdbadaaadbadccdbcdbcdcdbcdcaaddbcdbaaadaccdaddccbaadcdcaacdbcdabddadbddbabacbdaddbbdbcbacdbacabaacbdabbcddbdcabbacbcaaaaabccaadbacacaaacabccdabbadaccbaccdcaadccadbbddcdabdcabdadbbbddbbaaadabddbaddacacabcbbbbabbcdbcdcbdabaabcdabbaadbdcaabcbccdccdaadcbddcddababbccdccbccdcbaaadcdabbdadbdacdbbbaddbcccbdcadccadbdaaccaabdbaddcadaddddbdbddcbaaadbdccadcbcddadacadbdcdadcdacbdddbbcababcbbdaadccbdbcdddbacbcdbadbbacbbdcbcdacbcbabacacacabcaaaabcdcbdcaaddaaabcccddccbbcdbbbbbacddaaaddaddadbcdadaddbdcdadbddacbaacadbbadbdccdbdaadcabacdbbbcbccbcbcaccccdddbcbdcddaccdcbcdddcddbadadbabbddcccccabadddabcbbdacdaadbadcdbdbcbbdcbbdaccaaacbbddaacadbacbdbdaaaaabbbdabcbcccbadaabbcaadaccccaaabcaccacdbcdccdacaaabbddccacaccddacdaddcccbbdcdbadadaaaadcdcdbcaddddccaddcbddaccdcadbdacaddcdbcccbcdacbabcdbcabddbcaabbccbbcadbddbcabdbcdaacabcaadddcdacbdababdbcbdcccadaabdcdabddccadddccbcabdbbdcdddbdddcdadddccddcbbcadadaadabbaadbcbaaaaadbdbcbabcbacadbabbbbbabaabdacccddccdadbaaadcabdbdadacbcdaacccdcdccbbabcabdcdbbddcbacccbacbcdacbdbcddddbcabbbdcbcddcabddaddbcadacaaddacaabcdbcaabbadaccacdacdbbbddadaccadbdcbcbdacdcbadbccbdccbdbcbcdbdbddcdaadbbbdbaacaaabbadbccbcbaabdcdccdaccbdadbccabcdcdbbccbadabacccaadcdccddacdaadbddabbdcdadcbbadbcadaaccadaccdcaacccbbabbcbaccbddcbccbacaaaccbbdcbdbbcdbbbabbaaabcdacdabaabaaacbdcdacbbccdabdadaabaacaacbcbcaaadccabdbbccccbdcbbaabbdccadcccbcdbccbbacdcbbbdacbaaddcdbcdcacbddadcdaccccdcdcaabbdaacadcabcddadabbbdcbaacddabaabbcbabadabbccddadabddbdacdabacadaaaddcdcbcaaacacdcabddcadbcddcdbadcbdcdbaadcabcdcabbdbbaacbdbcbaaabcbdbcbcdcabcbdacbcdccccaccabbbbbabdbddcacacadadaaacbaccadbbbdcabadbcbabaaaadadadbbcdabbddcadbadbcbbcdbdbddbcdacddbabaddcbbcacccbaacddbadadbbacdadabbaabaaddcbddbbbdbacaabbdcccccadacbbcbbbcbdacbdbacdaccabbdadbbbaabcbcbcbcddbbbcdadabcaabadaaabddbbcabaadcccbabcdbccbbcbdddbdadcbcbcdbaccacdbccbabbacddaaccdaaddcbccbbccabccdadaadabcacdcbbcccaddcbaddadbacabbbdabbddaaaabadbcccadaabbbcdbdabadadbcaadbccacdcdddabbdcadbdbababdadabcaaaaaccadbcbdacbcdbabdabccdabdbdbcdacdddaadcccdbadcdbbacbadbabddddaddabbdbcbdbcbdbabcddaddadadcabaadbaadbacdbdaabcaddaadddccacbaabcdcddcaadcbddddbbcbdbacabcdddbadacddbdabadbdbbadabaddaabadcacbddaadddaadaacabddbcabbacbbdbddcaddbcbbccadcbcbcccbddcbdcbcdaabdadcaadadccdbcacdaaaadadbbacacaddbbdadcddcdaadbddaccaadccbdcababdabcbbccaaccacdcdadbdcdacbcbdaaaaaddbcbbdbbddbccbabbdadbcdaabdadacbacdbbaaccabbabbacbbdcdcaacaadccaabaadbbabaacccbbadcacbcadcdbbdbbdcccbaabaaadacbadbabbdbabdbabbababcadccdbadaaccbccbdcdbbabaababccdccaccdbbabaadacacdadcdbacbbcbcddcdadcdabcdacacadbdadbcbaddddcadacccacccdbbdbadcdacbadacdaabadbcbddaabcbababcbcdbadabaadadaaadabdcbaddbbcbaaccbaddbababdacadcbaaccdabdaccddddbddccdddacbbbabaccaaaaaabbaccaacbcbddabdcdcabcaabaadcbdcbcacdadabcccbdbbccbacbbddccdabbdbddaacdcaacbbadcbdcbbcdaccbaacccdbbdadaadddbbdcbdbbdacaadacaaadddddbacaacbdbabaaacdcbadcdbdbcdabbccccbcaadaaabdbbcdbddbdcabcabdadbdddbcccaaddbbcdadbccdcabdcdcbdddaddadacacbbbacbcbcccdabcdacdbdcbabbbdcbcadacdcabbaabdbcdbcdcacdbbddccdaabdbbabadcaadacdacbdaccbbbabaccdacacbadbbbdcadddaabdddbdbbcbaccddccaacacdaccadddddabcaaababaddabbabaacacdabbbddacadccabdbcabbcbddcdcdbcbdabaacbdacbabbaacaccbdbcbdcddabdabaabaacdaccadccdcccbcdbccbbdbaadadddddbaadacdaadcbdcbaadcdacaacbaabbbbdabccaddcbadbbddddbbdcbabadcdadacccabdaaabbdcddddcacddddcccbccdcbbbcccccacdabcadcbbddbddacbccbbbdaccbbacccbdccccbabddadbccdcadccbccabbdbdcbaadcaccaddbbaaaadccdcacabadbbbbdcbddbacddaaabcaaaddadcccacacbbcdadacaabcddccdccbaadbacabaabcdcaadbabacaccbcaabbacabcabddaacdabbbcccbbcccccaccddbdddcdcdbbbcccdaddcddcabdabdadadbbbabdddabcaacbaaabacadacccaccddddcadbbcaccabcaccbcdcabbbaddbabccbcbacdcadaaaacdbdbbadddadbccadbaadbbdbadacdbcababaadaccbdabcacadbadbbcbbcdccdbbbbcccdaabcdbddcbccabcbcadacbcdaaddccabbcbdcccdbddacdaabccbdddbdaadacadbdacdcaaacbacadbaabaacdddadbaddbcbcacddadaabbdcddacabddbdababdbbbccdadcdacccadcbcdabcadaabdaaccbaaddccaadcbcabaaddacdcdccccbaadadcadcddacccdaddabaadbccabdcbcccdddbadbaddcadaadadcbcabbcdbacabadcaabacdcddabbdbcaaabcabbdbdabcddcdaaadcbdbdaaadbddcbdccdabacdaaacddcdcdaddbdbccddacaabccccbdcadacccbbbaaacbbbdbbcadabccdddcadadcbddbccddddcdcaccdccdcacdaacaadaadbcdddcdddadcccddddacbcdcdbdaaaaadcacdaddadcccbdcacabaddcbcabaadacdcdcddaaddbaaadbadccadbbaabadbaabbcbabcbbabccddcaabdbccbcdaddaabdacddcddbadbaccddddababbcaddacdbddcbbdaccadabadcadccbdadadabcbdbdadddbddbababccaccbdbbcbccacdaacbdbbdbacbaadcdaaaacabccacabcddcabbacbcdccdccbcdddcbbbdbcaadbdadacddacdcacbabbddbbcdcbddaccddbcaadbabbbddbdacacddbdbababadbbbbcbccccbbdbbaabbbbcbbccabccdddddacaccabdacdbbabdbabcdcdbbcabadbcdbdacadbbbacdbadcdcbdbdbcbacdadcdbccccbbdacddbdbbcbcccbbcdbddcbdcdbcdddadaccbccbdbdbccabdddbaaccdcabddbadaacbbbdacbbcaccaccccdbacdcdcadcabcdccdbccdcdccbdacdcccbdadddaaccadcbbdcdccbcabcccdbaaacdaccdbcddcdbbaabadcbadddccbcdacbddddbccaabbaaacbccabdcbcaadacdbaaaadccdbbccaaadcdcabbacdddbcaddcddbdadbdababcadbcbadacddadbabaabdcbdddcbcddacbdbdbacbdbcdccdbaccaadccacdacbabaddcddbbbcbdacccacdadacddcdabacdbdcbaccbabaacdaddbccbdaacbbdccdadcbdaadabbacabcbcabadddaddabbdbbdccadcdbdabcbccdadcbcbadadbcbdddbaacaddacadaaaaddbbbdbbaaccdbbcdcbcbbabababbdbdcacacbdbaaaaaacadaddccbaadacccdbbddcddddaacbdabbaaacadddddcacdcdabdccbadabdddcdaacdbdddddcddbdbadccbbaaacdccbdaccaccddddadbcdbabdbbdcdaabaccdbbbcbcbcaccaadcbdddadcabbaacdbdcbcdbdabaaddbdcdcabdcdbbccacdcdbbbaacadcdcacabcbacdddaccaccccbbcbcbacbdacaccdaabacbbdbabdbaacacbdaaacacbacbccbbdabaacbdddddbccccddabdaddcacabacbbccdccbbadbcdaacbadcdcbbbcdcbccddddababbdddddcabccadacbcdcdcbdbddadbddcaaacbcbcadbcbabcbcddcaababacaddaccdadbdbbbaddcbdabdadccdcdcbdbbcbdcccbcadccdbdcdcdbddddcaccacabdbacbdcaccdddcdbcbdacdcbdbabdaabbbbcabbbdacddacdadaabbcabaddddcbcdacbcdbbbabadbcacbbcccdabccccacdbdcaabacacddcccadbbbaadabbaabbcaaaddccbcacdcddbbabaddddadcababbcdcdcadaccdcacdabcaccaaacbcbbbabdbbcaddccbbcbbccadacdaccbbddcdbcbcbbccacbbcdbdcbdbaccaaabacacabaaccddddacdbadadcbdcbcaccaaababdddcccbcbbdbadbcbacddadaaddddcccdcbdbcbbadaccdccadbccbbadbbadbbdcbcaccddcddccbbbbabaacaabbccabcdcbacddcccdabccddcbabacccdaadcbbbdcdadbadabacacccccdbbcdbdbbddadbcbbcaabcbccdacaccbcbccacbccbbbaddccacdacbacdcbbccdccabbddacddccddccdbcbaccccbcbdaabaacccbcdcdcdaabddbdcbadbaccbdadddcddcdaccacaaccdbacadcacaccbccbccdcbccddaacddcccbadabbcadddacddadcdddccadbdacddddcdbcbbaabbdacbadbcbbcddaabbddbaabcaabdcdcabbbbcacaadcddcddcdbbbdccbcacbbbdaccbadcadabdbcbdbcacddcccccccdcbdbbbaccbbccadaabbadbbabdcaaacbdabcbacbddbdcabdbcabadabbbaabaadadbadcacaddcbcabaacadddaccccbaacbabcabcdbbbcdababcbcabdabdcbbddcbaadcbbdbacdaddcacadbcbdbadbadacdbdcdcbbbddbdacdbbbaddcdacdcbaacaddcbbcbdadadcdaddadaaacbcddcddbdcbcbbacbcdcbddddccdacacbbbcbccccabcacabbadcaddcaacdcaccaacacacddddcbccdbdaacbaadabadaaaccddbaaacdbaacdcabdabcaadcdbcbbcdadaacdbdaccdbadcdbdccddccacddabbcdadccddacccddccddbddcbadbbabcadaddccbdbbaaccdbaabbddcdadbcaccbbbbaadccccccdadaaadcdadcacaaabdbcdbbaccbacdbdcddaccdcbdbcacadabbdcdaacacbabcbdaaadaaabbdaaaaacbccaccacddcbacaccdaaacadcaccbdbaddcbadddbcbbccdacbcbdcbdcbddccdabcdcabccdcddbaddbbacaacacbbbacbcbbaaabacdbbaddcddbbdabbdcabdbbaadddcadacbbccbabbdbbcdabdcbdcacaaaacbaddcccdbaaadbdadcdabddddcbbdbdcacdbcdbddbcccdadcbdddbacddbdadbaddcaabcabddabdaacdacbcbacababaaabddadbbaabdacdbcbaabaccdadbacabddadadbabcbcbcbaabcabddccbacbbdadcbbbddcbaacadadbabbccabccbdbaacddddbbcdbbbbbcdcbbaaaaabdbbbacbbccdbddbaadcaccaaadbdbdcadcbbbbcbaabbcbabbabdbcdacbbabdcdaadaadacdaaaaabaddacdbbcbddcdaaabdcdbdbdddaccaaddacaccdcdabdabdaadadabccbdbbcddddccbcbccaabbdcadadcaaaccaddadacdcadcabcdaadadbadbdcababdbdcccdbacbbcbdcdbdacbdcddacdabddbaabbddbbbccbdbcadbbabaddaacacadbbaccabdbbacbbbabdbaccadddccbbbbabccaaacbabaabbcbcdadaabaabadbcdbdadbdddddddddcdddccabadddaabbbddccdcabbdcaaadaacbabccbcbadbaabcbabcbcbdccaadaddbbbcccaadbadaadabaaadaaddcbdcbacccbbddacddbbcabdacbbcdbdabdcdabdaccdaddaabccdaddacaddcbadcddbdbcccddbdbddbbcbbcdaccdbabdbaaabcdbadcbddaddaadacdccddbccdacbbabbccaaadbccdaacdaaadabddaaaaaacabaababdbaadacacdaadabadcdbdcabdabcacbbbadcddbcadcbaacddbbaabddadcbbddbbdcccabbcbdacbbdbdbdcddbdcdddabaaadbdcabbcccdbdcadadabccaaabdbcbbbacdbdabdcacdcbdccadacdbadcabdbddbbbcbbbadabddbdcccadcacccabbbbacaaadccddcacaadacddddabaadabdacbadadcbdcadbbaaabdbcdcabbabacdadbcbbbccbbcabbacbdabdcadabccbdbbadcccabdcbdaddbcddadbdccabbbcdbbccbadacbbcabccdcbcccbaabdabddddbdabdbabcbaccddbabbdcdabacabcbbbbcbbabbdabbddbbcadbcadabbdbbcccbcbbdcbcbbabcddacadabbacbbcdbccaabadbacadadddbcdbbddcddbdddddccadbdbabadbbccbbacccaccbabccababdbcaabdddacabccddccccbcbdccaacccadcacbbbabdbccddabacbadcddaddcadadaacdabbdcacdacabdbdcbabdddaaaabbcddbacadaaacddbbabddbbbdccbccaaddbadaaababacccacbbbdacdadcccaabdbabbbacbbdcacddacbcccdcccdcbdbcabbbccbccbdcbdaababddcccacabcdaddbccacdaadabcccdcadcadcccaaddaddcddacababccdddaadcaaaabdaadbbbbdaddcdbcbabdbddcdddbccaaabadbacaddaddbcdadbadbaccbabbddcdacaccbaaadbcbddabaabbbbdaaaabbdaadbaccdcdbbddbbaaccaacdbacdddaddacbdcaabbdcbdccbbdbbbcacbbbcaadabbcaaaabadbddcccbbaaaddcacbcdacabbbababbbbdccccdbcdacddcdadcbbcdacbcbbbbbbbacccbcabcdbbcaacbccdccadcabdabdbbcdddcdaaacdddddbdaddacdababadbaaacdcaabbaaadccbbdadbcadaabbaccbacabccbccdaaadbccddddcbdccdacacaccdbcaacdbccadbbcbddbbadbbcabbbcbccdbdaaacaadcbaabcabaaabdbcbaacdbdbbcabdaaabbadbacdddadaccacddabbadddadaccdbdcacbbbcbdacadabbbbadbabadcddababcdcddacccddbcdababbabacdaaadbccabaccbadbacdbccdbaadacbcdbabdaddcdcbbaacbdaabbcbdccccddadadcbadddadadcaabacbbcacbbbdacdbdaadaabdcdaaaadcabaccaaaccbdabcadadbabadcbacbbddbdcabaadacaacdddbcadccbbcbacaabdaaacdcabddbbbcaccddcadcabcbdadcccaabdcabcaacdcdababdbcbcdccdaadbabddaacccbdaaddbbccbaacadddbdacbddcbcbcbbdbddcbaaaacbcddcdabbdcabaddadccadccaabcabdccbdbdacbbdadbaabbbbddbbabbbcdbbadacbcdadacacdbbcddddadbcabcdcacdddaddbaadcacccabcacbdacadaacdbacadabcbaaccababaacdababbbaabbbbaadcbcacdadbacabbbabbdacccadcdacdababbaabaaddbccbcdbacdcdbcbcabaadbacdbddcbbdaabdcdccdbcdacbdbddacbaaaabbaadacdcccdcaddcaccdccadbbdacbbcdccccadacdcdababcdddabbabacaadbaacbbcaacdaaadcdabaccdccbdbcdabcbacaccdcdcdbcacbaadbaacddbbdddaaaaacbabccbadbbcbaaccbdcccdcabcdcbbaabbadabdcacababaccdcccdacdcbdcacbdadabadbbcccbdccbdcaadacdccbbcbdacaaabdaadabccccbaabaabcbdbdabdbccadbbabcaddcdadacaacbddbdddadddbcbadbbaadbbaccccdccbabbbbadaaaaabadcdbaacdcdbbabcdbddabaccbbdcaaacdcdabdabbbcbcbdcbcbdadbdadbcbdcccadabdbacdabaaaabadcdcaadcbcdcacddbcabdbcbddcadcbcaaccbaadbcddaacbaabcddcccabdcabacccdbdcbaccbbabdacbcbbbddbbbcaadcdbbbcbbddccdabcdbabdbdcacdaadaddadcadcbdbdcbdcbbbbccaacacadcbcbabddaaaacadddbcabdbccadcabdaccbbcdbddbabddbccdcababbdaabaadabcdaaadbabdddcaabaaadccbdccaaaaaccbbbdcdccdddcababadcbbaccdacbdcdbaddbdbadcccdbcddaacbdcccaadcbbbbdcdacbbcbdcbdcdaacdadaddbcdbabbadcdcdccaaddbbdcdddddadcbaccdbabdbcdadbcaacbaaadbccddcaadaccaaacacddddbdbbaaddcdbdbcbaccadbaddbcccbbbbcbcdbddcdaacaadadddcbbadaabdaddbcdcbccccbcdcbdcdccbdadcbccbaadabdabcccccacdabaacdadaacdbaccccdbacbddacccaddacdcadacbaaacabadaabccccacdbcdbdcdddcaabdadbcabcabaddadddcdddbbbdbadacbcccdddacadbbdaddcccaabbcbadbddabaacdbbbabcadabaabacaaabdbcdabdacababbaddabbbdabdccddbababcbcabacddcabadbcdadaabccaaacccbdacadaddcbbadbcdbaddaccccdadbcccbbcbddacabaadcaacbacdabdaacbcabcbaddbdabcbcacabcdbababcccccbadaabdadacadaddaacccbadabaccbdbccababcdbbbbbdddaccbaabbbccabdaacaababcbaacaccbcadaadbabbbaddabcaaccdbccaccbbaadbbbaacbbbaabdacbdbbdbacddbcbabcbaddadbcdcacbabdabbcbaaaacaddcbdbabccbaddddacbbcaaccdccdcbddaddbcdaddddbdcdadccddddccdabdcabcacbbadbbabcccbabcadbbaadddcdabbbdccacbcabbdcddbcbdccabddcadcddddaabcccccdabcaabccbcacbccaacddadcabdbdbacbbdacccaaadbbacbcaabbddaccdbdacaaabdabbaaaabbcadccbbdbdcbabadaddbbddcabadddcabbbbdacbaadaaddaccbbacdbcdbadadabddccbcdaabdcbddaabbacadaabcbdddbcabbcbacbcbdaaababdcbbccaccdabbacabbaaabadbacdcbbcccddbbdccacdadaabbddccbbbbacacdcccdddabdbbaabddbcdddcccaadbabdadcddabbaaddcdddcbbabcddacdcabdabaccccbadcdadbcaddbacacccbdcbbbcabcccddbcdcacbdabddcddadbcbbcdabdbabadbbbadbbbbbcdcbdcdaadacabbccacbccdacdaddcaabcdaadbbadbccdaadbcbdadabdccaabcaaabddabacbdaaabcdcbabdbbcaccadbacbbabcaddaadbcbbbdcdcbbdcacdbabcbaaacabcdacbccbccbbdccbbdabdbccabbdacddddddbcbcadacbbbcadcdbabbcdbcabccbcabacbadcbdcbbabcddadcdbaddbababacacabdcbbaabccbcdcbaddbbbbabbabdccbaaacdadacdccabcbdaadcdaaccdadbcacbbdabbcdbddbdaacbdadacdddaacccaccbcbdbdabcbbacdbbbccbdcaaadcbbaddabbccccabccaacaabcbbacabaabacadabdbbaacccdacccacdccbbdaaddadcabbacddbabbbbdcbdbbcddbcbcabcadcdbbcddaabdbadabbdccaabdabcbacaaaacccbbddcbacdcdcccbaabdbccbaacdcbdccdbbacddbccabbdaabbacbdadaccbccdaaaabcccaabbcabcdbdbabdccbdddbbdcddacdbdcddbaadacababcdbcacddaccbdbabcdddaacbacddbcabbadbcdddaadaababacbcbbdaddaddbdadcddbcbdaaadababaddcaaabbdddbcbdadcdaccbbccadaaabababddacaadabbbaacaadbbccbacabadbbbdbadcdccadcadacadaccccdaabdddcdacdccdbacdaccccbcbabbabadcadccbadcabcadcaaacccbcbdccdbacbdbbdbbdcacabbcabcddbcddbbbdddabcabbddcbdaabdccdabaacdcabbbbdaadcdadbccabbccdccbcbbdcbabddbcdabacacbbcdaaaabdabdbddaddacbdbddccccbaddadbdcbbbaaacaccbcdacbaccadacbbdddcddbbcadcccaccacdcdbbdbccdaccbdbcaacbdbdcabdbbacddadbbcbbccaddadaacbacdbccddccbdbcbcacbcbbcbaadababbcddaccccbadbccacdbbbbdaddabbdcccdccdadbacddcadabbcbaaaabadadbabcbccdcbcbcdbadcaddcdaabcddddccbabbccadddaacdbdcbcaabaadbbbbaabddadbccbccbacadadbabddbcdadabddcccabbbaccbddbddbaadbdabcadaaabcadaadddcdcdbbabdbaccdccbbcbcccbcdbacbcbbabdbbdaccbacbcdaadacddabacbbacbdbbcbdaddcddcbcbcdcbcbbcdbdddbaccdcdabbaddaacabbddcdbbcaaabbabdddcddcacbdddbbbccbabacabaabbbcbbdaaabbacbbdbdccabcccdaabaccbabaabddaccaccccaddbddaacdcccbacabbbdadddaaabbadadbdcbbbcdbcbaadcbbdbbbccdccdcbccbbcacdcbdcdddddcbbacdbabcccabbdbbccdcdbbbbbadbdabdcdbdbaacbaccaaddcdcabacbdccaddbdcacdadabcbcccdbcddcccacbabbcdcadaaacaabbddaaccdbcabacddbbabbcdddcadbaccbbacdcbadaabaccaadccbbdbcbbbcaacdcbaadddcdabdbbcbacbadcdabbdcbaadadbbcccddacbdbbaadabccbbbaacabcbabdabcdcabcbaccdbddcabdaacbbddcaaacdcccbabdacabbdaacddbaacaaadcbacaccdcdbcabcacbbacbbaddaccaaaaabbacdbbcbdcaccaadcccaabccbcaddbcddccabcbadbdccdccaadcabacabdabcbbbddaccddaccadcddabddcacddbbbaadbccbddcadadcbbcdadaabdbadbabbcdbbacddabbadddacbdcdaababbbbddccbcbdbacdadbdbdcadbacbaadbdbadadbcbcdcbddcbabddcdcadaabbcddbadddaacbdabcddacddbdacdcabdbdbcbaabdccaadbdddbadbbdccccabdacacdccaaccdcbbaadacbcccbacbacccbdcbcdadadaaddbbdaddccbadbccbcbbacbbabdacdbadbcbdbdbccbadabbccbcbcdadbababbabcbcdbcccbcaddacdcccdbdabdccabacdbccacbaadddabdcaaababcaabcbdcbadabcaaddabacacacbcbaccadaaadaabddbdbabbaadcbdbabddacbcbcaacbadddaabcacabddcbdabaaccdacabdcdadaacabcbadbadcccabaddacdabdaaccdadbdaccdddaccbcbadbbdcdaabbaaccadbbdcbbddcdbddbdcdcddcabbbccacaacbcdcbabaabccbdccbcacccdbbdcbdbcdcaabdacdcabddaaadaabbdbbdcdcdddadabbdaaacccdaacddacaadcabaccccbcbbdbbddcbbbccbcaadacbaaababbdcbdccbdabdbdbbdbcbcddbbdabdaacacabaacbadaacaadbbabcdacaacabccabaaaccddbcbcabcccabcaaccdbaaadcadadcdcbdacaaaccadbcaddbababddccbbddcbdcdddaaddaaccbdccadbbaabacdcbacbdabbaaaaaccacacbdaabdccddccbddbdcaacadbbbbadcdcaabbadaddcaadbddbbaddcbcbbddcbccbdbbdbbacbacdcbdadbdcbadcadbadcdcdddcaddbbadbdccbacbcbdcbbdcbccdccddaddbabbbcbdbdbccbabdbaabbcccbbabbaadddcdaccdbacbdadabaacbdabcaaccdcbcabadadcaaccdaadacbdcbcaababaaadcddccdcaaaccdabbadadcadaaadcdbcbccaaaabbddcdcddabaaabbdaadadacdbcddbccbababcdbcbcbbdcbbcaccbbcbccbacadacaccdbbaddbdddacddbdbadabbababcdccbcdcdabcacabacdadcdbcaaaccccbcddacaaabcbaddcddcdcdaaaacabbacacdbcdbbbdccaaccdddbadcbbadcdaaddbbbdccdcbbbccbbaadadccbaddcccbcaabcccacdcaabbdcbdaadbabdcabdaadacddbcaccbabaaacddabcbdbcdaacbbaaaccbddcabdacbbdbabdcaaaccbcbabcacacaaacbcbdcdcabdddbcbcbabcbbdabacdccdaacbcdbbcbbcbdbbcdbcacdcccbbadabbcadccdbadadbdccdcdbcaadabcabcacadcaabbacdbdcbbdcbbddbaccbcbcdadcdbaadbddbbcaacbcadbcbdcdcdacbbcdccbdcadbddbabbacbbdbabddbcbbddcbdabdacdaacdcdbaabacdbadabccadabdccbdadbdcddcbdbbabaaddbacbcaaddddcaddbbcdbbdacacdbccbdabbbacdddcdadbdbbbabbdbbccdaccdccadbadcdccaadacadcababcdcdadcdcdbcaccacbccdccbadbdbcbcdcaadaadcadadbdacabdcbcdcabbadccacaddcacabadaccababbcbcbaccddcdddcabbccacbdcdbbcabdcadacdadaabaaaabadbdbcaaabdcbacdcccdbcccdaaddddcbbbbccbcacddcbbcccbcdcbbadaaddccdbadcaacccbbbbdbaadbbdadbbbababbbdbbdbcbbcadacddddbbaaaacbddcdbbbbcdcbdbcccadaabdcdbcaddbcdabcdccaabcbabacabadbdacdacabdcabbdbcdbbabbacddbdddadbdcccbcbbbabcdddabcbbaaadcbdbdaddcdccacbaccddcddddabcacdabdcadaccaaadbdbbbcaddacabbabcacbdcdccaacdaaabbcaadcdaaabcbcaaccdabccbaadcdcdbdadbbddcddcdcccadbcddcbbbbdaabdccbccbcbdaccacacbbbccaabdbdcbddbbdadabcabbdbcbdbbbbcdabdaacdcaaccabbdccccdbbcbabbbadaccadbacabcdcadbddbdcbbcbaabbdcdbcbbdbdcbadbadcbdcdbdacdbdaccdcccbcddccdcabadcbadacdaccdbabdbcadbcbcdddbbacbabccadbddcddaddcacdccaaaccaadadbaccbbbabccbcdbbdaaadcacacaddbbddddacbabdbbddbadadcccdabcdbccadacbaaddacbdbbbcdbddbdabaddadccadbbdbabbaacdbdcacbbaabcbdcbbcdadbbcdccdadddaabcaaddacbcbbbacdaddabcccbcdabababcdbdacdbddddbaccdcdcacbdbdcdaaadbcdaaaaabadabdbbbacbabbacaabaacbaccbdbbcbdcdddbdbcbacdabbabddccccbdcadadaacbbdbbcaabccdccacaddbddbbdaaddbacddccccdaaadbbdcbadacbabbcbdbbacbcaabddadabccccdbcdcadadcccbbbccccadbadadcbddcdcbdccbcdabddbdcdaddbcabdccdbaaababbabacdcadbcdcbbbabaacccababcbcabbbbacbbabaadadcccdadcbccacdccabcabadbcabcccdadabbddabddcdbdbdddabdcbacbbdabdccadcbabaaabddabbddcbaaccacbcbdadbbdaaddadbacaddcdbddabacddcccbdcbcbbdbbdbbddacbaaacbcbccbbacbcbdabacacabbdcbbdabcbacabcdcdaddbabccacabcbaabdccddcaaaadbbcdccccdbaabbcbbccbdacccbcbaddbcaadcadababcdcbaadaadddccadbddacddccdacacdbddcbbddccdcbaacdadaacbdbbddbabdddaddddddbadbacbcbbcacaabaaadcacacabddcbccdbacbbadadcadbaababdacdddbaabbccccabbddccddacdbcbaabbccbadbadadbddccdabbdddbdbabddcaabbbbddbbaaaabadcdabccdbddccdaababccacaddbbbbbacdccdbcdadbaaabbcdbdaacccbdadbbdadabdcadcbcbddabaaadddcddaabbdacbcdbbcccccabcdbccadabdadddacdbdddddcbdbdcabdcbccbcaaaccbcdbcbabbddacccabddbcaababbcabccbccabdadbaaacadbbcaabbddbccccacbddbcbbdbcccabbaccbdbbbaccdbabadadaaacabdcaacdcaaacddaadbcbbdaaaadddbaccbbadbaacdaabddbbbddcdbabcaacababcbadcddddcbbabdcdcdcdcaabbacdccbcbbbcbddcdbcbddacacddcbbbdacbcaccaccbdbbcacaacabbabbbdbcabaddccabdcbbccbdbadcbcadbbcaabbbbacbbbbcbcacbcdccdaaacbcadcbaaabccbbccaccaadccbccbcddbabcbdbacdcdcabcaccadbddaccddcdcbdddcbbbaccacadcacddcdddbcccbacabbaaccababdbbdaaddccbadaaaddaadabcaddddccdcbbcacddbcbabcdbbbbbddbcdadbcacaacbbadacbaaccaccbdccaccabbbadaabbdabccadbccaacdbcabdddabbadbcbbcbcabaabaccbddbcadcbdacbadbcbbcacbcccdaadacbbcccbbabbacdbabdcbaaadadacbacddaaddababdacabdbbccbdcbdaacaaccacdddcbaccddbdcadbcaabcaaadcbcbccacacbdaabbdbcadadbdbddbddabadabbaddbbcbaaadacdabcccbcadabccbacbacbacaaadcaddcbbccbabcccbdadaaacccdcbacdcaadabcbdbbbaaaaacdccadcdcbabadccaaabcdbcbcdadcdaaddbdaabaaadcdacdbcccdadadbbbadbcbaabdcdcccaacbdaaccacdccbbbbacddcabdbacbcdcabacbadbbbcbcdddcccbabddbbbddcbcbabdaddcbcadbdcdcaabccbadadcdbaadccbbbabbcacadaaaddbabcbacbcabcaabcdccbbbacbdccbcadcdbddbaacdacdaabadabdcabcbdbdadcbcaaabcdbadcabcdccccbadcbacbcbcbabcdadcdcabcbadcaabdcbccbaaabbbdbbacdacaaaadacbcadbacbaccddcddbbdcbaacadbcadacdaacccbdcbdbcbaacbdcdbddddcdbbdabaaabbaadabaaacbaaabdabcdbcacabcdddabcbccabacacaadcadacdababccaccbcccdcacbddabcbbaaadcbabadbadddcbbdadaabcddcadcdddabbdadaadbdadbccbbdaacbcadadccbcccadaccaabdddcbbcadcabbaadacaadddccddabbdcdacbddbdbbacdaacbabdcbaabdcbcaccdcaabdddadcdaadbcbcacdcdaccccddabacbacbdcdbbacabacbbdabcaccdbccccdaaadcdbbdccacccdaddaaadbbcabcbcccbdcacbabccccddbcdabdadaaacbdaabdbadbbaaadcbbcbacbddddacbdabadbcabaadabbccadcdbaaaadacdbdacbbdbbaaaaccdbcbaddccdbaaccabdcbcddccaddadacdabdaacdccccabddbdcbbbbbacdaabaacdcaaacccdcdababcbadcdccdadddacdadcbbadabacacdbaaaaaaccadaabbacbccdcdbdbdacbadcadcaaccdbbbddbbcaaabadcdbcdcbaabaacbaabaaabcadbbcbdbbabccdbddbbccccdadbdbbbadbabcaaadbccdccbcadacaaacbcbbbbabacdccbacdbcbabaadcdbaadcaadbabcdbbaabdbdddabaadcaccacdcacccbccbdbddbcbacbacdadaacbbbcaabdbabaaccbcdaacacbaaadcacbcbaadbabcddacccbdacabdadaabbbbabacdadcbbddcacbddadcccddcbaddbbbadbcacbbdbcbdbccabccbacbdaaaabdacabbcdaaaccdbdcaccaaddaadcdcaccaaabbdbcbddcadcddccadcccdcdddcbadcabbadbccaddaadcabbdaacabbadcddcaadbdcbcadaaadacadadbbdbdcbdbadcbcbdcacbbbcbbbcdbbdddbbbcdcdccdacacdadbacbdacbbbcbaacbdccbaadacbcaaccbbbacccddcaaacdbacbacdbbcadbccacdaccdcacabbbdadbdbaaabbdcbddddbbcdddaddbdbbbabbbaababaacdcdacccccbadaacbbbddcdcbaccaabddbcdbdbbcaddabbdcadcbdbcbbadddbdadabddbbbaaadacdbaaddcaaabbcbabaaaccabadcabdccbccaccdbacccddbacdaddabbbbaaacbccdccdaaabccdbcccadbadbddddacabbaaadbbbaacddbcaacccbcdaabaacdbcadddbddccdbcccacdbbaabacaabcccacddabdbabaabbddcabbcccdbdccaccacdddabadacbdcadccdbadbbacbdaacbadccbcbacddacaadabdcaccbdddbbadabababaddacdcdddcadbadcacdcdbabcdcbccacbcaddcbbbbdbbbdcbbcbbbbbbabaacbcdbcbbaccbcacacbbbdaadcbadbabcabadccbbdcdbdcdcdacdddbaccccabadaabcaaabdbddbacadcbcbdccbbcabcdbabcbcaadadccdccabbacadbbbaacbdcdcadabaabaabbadabbaabdaacddadcdbcdcbbdadbabbccdbccbcabbbdacddbbadcdabdcddbaaaadababaccccccbabaaaabcbdccbbacadcaabdcbbabababddadaadccaddacaacaaadcdababcaacdadadbacbabbdcddabdabcdaacbbcdcbadcdbacacbbdbdabbbbcccacddbbbbbbdbcccdbcddabdccadcacdcaabdcdcacdbbbcadcccdcbddccbbabddaddcccdaadccadbdbacdcddcaacabdddccabdaaccbbabacdcacbaaadaacaabcbdcabcccdcabbcbddbcbbbdbbaaddaaadacddadadbddaabbdaacbcbdddcddbaabdacabbaddaccaacbcbcddbbcdccbaddacdbdcdcbadcabbdaabbcbaacadddbcbcabbbbadbaaddbddbcdbcadbdabcbabbbdcadaadbccddbabbcabdcbaadadcbadccbaddbcbdababbbdccabbadabadcdacabacadbcbaaccabddadcabcadcbacbdcbbadbcdadcbaabcbcdabaabdddadcabcccdbbbcdbbbbaddaaccaabbbcbdccacabadbaccacaacaaddddabddacadaacbabcacaacabdbcdbccacdcbdadccbcaddaacacbabaddacccccbdcdddacdccdbcaaabcdbddddcddbdcabcabdbbbdbccbdbaddcdadccdcdcdaadbbadabbcabbdaddbababbcbadbdadccccbcabdbbbabbbdcccbadbcacbacadcccacabbddcdcacbccaccbbabbbdddacbdacdadcaabccdabbbbddabccbabcdadbdabdcacbddacaacdcbccabdcacdbdbbcbdddcbdabdbacbabcaacbddabbabdccababbcccaaddcccddbcdaddcaacabaabaddbadacaddbbaadddabaddcadcbbcbbcbcaaaacdacccddddabadbacbdaaadccadacdbaacaabbaccacbcbadccaaacdadbdbbadabacbbcddcaadbbdcddcabacdbcacbcbabcdbcaddadbcaabcdabbbccbbdbabbbbbbdabbcacbabbcbcccacaaadcbbbbbcabcacdacbdbcccdcadbdaaccaabbdbdabdadaddbcdbacdcbbaacbbccdccabacbbbdaabccdabbbbbbddadcccbaacddbdbddaadddbdbbdcdbcbaacbbbabbadbaadadcddcdcbbcadbcacacdabcddadccacbdccdcdacabbbabaaabcbbcbbbacadbaccdbcbdcbbcabcdcddcdadccccaddcccccacabbdcaaadccccaacaadccbbdcbacdadbcccabdddabddaabccbcdcbdbaddbabccabdbaadcbcddacacaaacbbbdbbdcabacdbdcbbccbcdddbbcbdcbaacddbbbdcdacaaadaacbaaccbdbddcaccacadddcbcbcbbbabbcbacbcdcaaadadbcdcdbcddccdadacdcbbdddbbbdcbacccbdcddcdbacabbbdabcaaabcaaddbcbbdabbdcbccbbabbcdddcdcaccbbdabcacbbaabacddccdbabccccaaaaabcdaddbadddcccacbaccdbaadddaaababdbbaacababadddccbddbddbbbbddacadbacdddbccbacdcbdabcbdaacdbcadaadaacbcacdacababbbbadcccccbdbccbbbbabcbddcdabbcaaccadcacbcddddaadbbbcccaddbdbabbaacacccbadaadabdddccdadcabadcbbbbaaaccabdaccdaabdaadcadbbcadbabcdabbdcdbacacacdaddabcdbddddabbccdabdcbababaaaccbbaabddadadcabdaddbccddbabbdcbdbbaabdaabcddddcddabdabdcbacdcaadabacbbcbabbcabdbdcdbdbdcddabadcabacaacddcdbaddaaacdaaacbabbadbdbadbcdaabdcdacccbabbbadbddbcdbdabdcddadabbcdcabbcbbbddbbcbddaabaddcdbdaddbadccbdabbcabcdbcbdabbbaccdbdbacbabadcbaabddacacdcbdaccdcdbcbcaacbcccddbdcbbccdabcdadbccabaaaabbaacbbbaddcabbccbcdaaacdbcdaddcbbadbdbcdcdbbbabcddbdcdbdcdddbaccbbcccaabadbbccdbcbcdbbacbaabbcaacdddabdaccdccbacdcbbaadadadabdcdcccccaacbdbbbadbbdabbbbddbaddccadaddddbabbbddabaccaddcdbddabcbbddcbaccaccbbcbaddcbaacbacdddabaaacbaaaddccbdbadaabdbacacdbbbacdcbcccdbcccddcacddddcbdccaddadadcaaccadbccdccddaaaccbbdbbbacbcbbcbddadbbbdacadacbdaccdbaabbccdcadcbbacdccadcccdabbbadcdbbdddccccbdacccbaddddbbaadaccddabadacbadbbcbbaddcdcacdcdabcbbcbabcdaddbbbabbaccbdddcabbdcadabcbbbbcddadacadadbcbbcbacbabaacccaacacbccdaccddaddaddbbddccbdcdaaacadacdbaccbcbdabdcdcbbcdbdadcdcdbdbdcdbbcbaadcaabacdaaaddbbdbaacccabdaabdddacbdddadcdbaacadcbbabdaabdadcabbaadccdccbaacbbbcbbbbdbbcdacccdacbabcbcbdabdadbadddbcddcdbbcccbbabdcadcdbccbaadbbdcadddcaaddcddcbcdcaababbabbbbbbbcacdaaaadacaadbbdbdadabdaaacdacbdbdcdccdcdccdcdbdacbccddabcddaddbaadbabbbdbacacabbbadadabcdbbbbcbabaccbabcdabaccdbbcbdbaadcabdaadcddcbaccdcadacdcccdcdddaadaaabbadbbbdddbacabacdbabababddcdbaadcdbbadabdbadddadbccbccbddbcaddcabacabaadbaadbabbbbcbdadaaccbbcaadacadbadacdbdbbbbadaddbcdbbaddccdadbbbbccdcbdddbcbcddaccdccbaddcdaabacbbaacacaddccadbcacbdbdcacacadabbdccaddbdacccabbdabadbbacdbcdadbdcddaaacccabadbdbadcdabbbdbbadaaddddcacdaaacaddbdbaaabcabccdbccdabcacccbbbcbddcabcbbddddbdcabbaacaabcbaadcdbcbbddabdcdcccdbcacbdaaaacccdcabccaabacdcaccccdabababbbacabadadcddbabbaadabccadbacacddadbddcccaadcabbcbaaaddbbbcddcbabdbccdccbdcabbaccadccaabaddaccdcdccabdadbdbabbbabacadaaddadadaabadbccaaacacbbcaccbcadcacddbbabcdcabccccbdabcccbbcdcadddbdbbcdabcccacbabdbaccbacacabdaddadaddbdcccbbccacadddacbbacabacbbddbcdcadabaabbcbdcccdbcaddcbccbdbddbcbccaacdbaadcbddddbaabadaadbabcaddcbbcdbbaccabcadbadbbadcdbcadbdcbbbcaaabbcbcbbcacaabbdcddbbdbaacdacdccdaaacddadbbdbddcaaadbdbbdcacdcaaabbccdddcccacddbdabbacbcacadacabdabccddbaacbbabadadcacbcbbcbaaadbbadabdcddabaadbabcbdabcaabaaadbdadbacdacbbcdcbbadccccdcbbbcdccbdcdaadcadcbbaddcdcbcdddbdcdbddccbacaabdddbddaadccadabdaccbabddddbcdaabcdadabaacdacaacbdaccbbbddabdbbdabdccacaabbdbacadcdaccabdcdddbcabbbbdabadbdbbbdccddbddbbacaddddcbadabadcaadbcbbbbdabaabccbdabbcdbaaacadcabdbcbaabbabcadabbbaddcadccccdbcadcdccbcbdcdddbcbbbdbbbcacdcdacddccadbdbcacdcaaabccacbbcabbdacbcabccacaaddadaaccccddccbcabdadbdccdcbadcbaaadbbdcdadcbdbdddcaddaabbdacababcbdddbadbbbdcbccbdccbacdadbcdbddbddbbdaaaccccccdbbbdccacccdccdccdcbaddcacbbcbddbcbccdbdcbacabcbabbdabbcaabdcdbdadadaddabcabcaacdbdbbbccbabbacaadcdccababcbcadcccabbaabdbadabddcaadabbaabcdabbbbcbcccdabaabacccccbcdbadabacbdddaabdaabdbdbaaaaccdbbcdabdbcbaccdbbcccdcdddccaaabcdbddcbdbdacccccccdbdadccbaacadabcbdcdcaccbadbbacdcabcababaccbbcccdbdbcdacabbcbbdbdcdadbacdabbbadcabdaccaaaadabacddcdcbcadacaabdccaadbacddcabbacccdabcdccbaccbacaaaddbbcbdaaccadaddcdbcbcdbccddccadabccdadcbaccacbadcabcacbaccbdbadccadcbbdbcbbdadbaddcbaadddacbdaaabcbbabccaacdcdcbdacbaadbbdcaacaccdbacddcdadaddbaccccaacadaabcbbccabbbaaddadbbdaddccbacdbbbabbbabddbcaddacccadddbdcbcbaddabbbbaddbddbcbdcbccbbaadcabaabddbcdbadcbcbddabcbaabbdaadbdacacddbaaacabbcaaddbdcdbbcababaddacaadbaccddddabdacbdcdbbacbbbbbdcdaadabdcdccdcddcacadbdcaaaacdabadaadabaaaaddbcacaaabbbdcaccccaddddddccdcbdbddacbdabbbabcbacadbadaacbdcbcbdbcaabadddbbabbaadcadbcdaddcbddbbadabaccbccaaabacdcdbbadddcddbaabcabddcdcbcdcbacadacbdbdbccaccdddadbcacbbdbbcbaabcdbbbcdbccdacbcbccbdddcaacbbdbccbddadcaababbadadaccaadabbadadcdbcaaccdbcaabdccdcccbcbaccbdabddabadcacbdaddadaaaaaabcbcacbcaacabdcbaacdcacbccccacbadddcbbcdcbbacacadadadbaacbaacccaabbcadbccdaaabbdacaadcccdcaabaccdbdacbcbcacaadaabcbbbccccaddbcbcdcabdcdaacacbcbaacacabbcddabbbdcbcdbccccabbbabdaadaaaabcccaabdaaddadaadddadbdaabcacbbbbcccabbdacbbbdbdcdddcabaabcbddcbabaadadaccbbaacccaacbbacaabadaabaabcbbddababddbcaaadaccaddcbdcdcdbabdbcdaacdacbcdacacbcaaccabadcbdabadcdbaadbdbadababdaadddcdbdadcaaadbcbbddddbdcacacaccddbadaacaacdcadccbadabaadadadcdcaccdbabbcdcbdccdcccbbcccdcccdacaacacaababdaadbabccbcabaccacdaaccbdbdbdcdcbccbbdbbacacabcbadbcaddadbadbaaabdddbcdcdcdcdcbdbdababbcbcaaacbbccaaccacacbdcdcdbdbdbbbddcccdaaddbcddadbccaccadcdabcbcaabaaaabcbdcccdbbbbdcaacadbbaaaaccbbacbadcbbdcddcdcbcbddaaccabdcaddabbbbccadbdbbbccdbcdacababddccdaacdabcdaaaaddcdadcdcababbbacdccbabbcdcaacabddcdaccccbadbaccbaaaacdcbaaaaacbbacaaacdabaddacbadbabcbadacbdadddbadaddccababaacaadadbaadbbbaabaacadcdadddcdbcbacccbdaaabdacddcdabdbbcabdbcaddacaccacdcbcdbcdcacabbdbbddcacacaccbdccaacaacbacbaacbbcbacabcaaaabadbdadcbdccadbcdbdcdddbabbacaccccacddddccaddbddddcdcbbddccacddaadabaabddddabadbdbbabacdccbabaaddaddbcacabbdbdcdbcabacbcacaaaabcddcbacbbbbbcccdaacaabdbcababcddddaacccdcdabbbcadbccbcdccdbbccbdddccbbbccacdabdbdbdabdbddbcbbdbdbcdbbbacbcddccdbbbbdbbcdcabacbcabcddabbacbcbbaacabcbcacadacddddcdabdbbbdbabcddabbadcabacdacddbcbbbdaacddcbcddbabacbdadbcaccaadcdbdddacdbcadbccccbbdabbbbdcbaacdbdcdcddbbabbdbddadbdcdccbcacccbbcccdcbaccacbaacadcabdaddbddcababdcccbcbdddacabdbcbcadcdbcbccccadbddabcabddbbacdabccabadcababdccabdcbbbdbcdbadcccbbacaccabcdcccbbadbbbccccacbbcabababcbaaccbcaccbbddddacbcaaabbcdadccbaaabbadddbbbdbbaaacdacaadbcdabccaddadcbdddcbaacdacabddabbdddbcbaaacbddaacbdadabbcddbddacddbbabcbdbbaaddddaaabdcadacddcdbdcaadaababacbbddbaccaacdcdadadbbadabcaaadbaabddaddadccbbdbcbcbacdbdbcbbaabbadaaaaccaaababacdadaabccbdbcaadcdcddacdddaddccdcacbbaccbabbcddccdcdcabbdbcdddbabcdbbabdacaaadcbcbccdddabaaccadcdcaadcdbbdaaadacbdaaccccdadaaaacdccdccababcacbcbddcdcddbdabadddcbdaacdacbcddabddcacbcbcdcaccbdcacbaaaccacccadbbbbbccddcdbaabcdbcabadcdcbbcccbccbddcacdcdccabdabbadbdabccdbbddbabaddcbddcbbdadbbdabacbcccbdaddacacbacabadbbdcdbdbdaadbcbcabaaddbdabbadccaaaadccbcddbcadbdbddcdabdadbaaadbcddddbbaaddbadcabdabaabbbddaacaadadbabdcadadccababbdabbdcadbcbdcddbacdbdadccbcbbcdaacdcdacacdbadccaabdacdabadcaababbcadaaadcabbcdcacaadbdabaadcdccdcbbbdbaacbcdbbaaadbbdbdcadbbdaaacbbcbaabacdabbdadabcbaaddacdddcccccdcadadaacaaadaddccddcdabbdbdaaacdaccdacbcadccdbdbdaaabbcdcbbabacbdaabccabddbacddaabbabdbdaccdabababcbccaabddacdccbdaaabcabddcccacbabaaccbbacabadcbaabdbbbbaaddbaadbaacddcaaaabdcbcacbbddaaaabbbbcacaaaccabdcbcdcabaacddacdabbadccbaaccdccaaabbdbaaddbdcdcdddbaabaaaddacacbbcaadbdaacaabdaadbbadabadaaaabccabaadcddcccccababcaabaabbcbbdacddbdabcbaacadccabccbbcadaccbbdcacdaacdcbccbacaabababcadaccbcbdaaccabcccbdadcacdadbdabccccddddaccbacaaacdaaddadbaaababbbadddabbaabdaddcddcbddbcdcdccccddadbbbcabddbbbbabaddcccaacddddcdbbbabcdcdacaadbaabbbabccdbddbddcdacadcddabdabacaabcbdcacabddadccbdaacdaabcbabdddacbbbbadccbddcdbdaacdabbbccdbbacdddccbdaaabcccaaaacdddbdcdcaacacbbacdbddbdcbbdcbddbaccabbadbbdbbdddcdddaddbbabddbccababadcdcbcdaaaabddcbcbdddcccbdabcbcddddacddcbbabcacaadddacacabbdccccaccdbcaaabdabcdddccbacdadbbdbbccabbdbdcabaadccddbccdacbadcdddacdaddadadddbbababbdbbbbccadbcaddcbcbbabbccccaaddccabdbbbbdbbcacdbbaabbadbccaaabaddcadabbbbacbbdcacabdbdcaaddcdabbaccdbaaddddcacaaacbacaaabdbcacbbdbbaadadbbaaccdbcdcaabbdbdaaddadcbabcacbadcabbadccbddbdccaacbbcdacdccdadabadaaccbcabcbbcdabdabdcdcdddbccabcaaadccbcaccabbbccdbdbddcccbdbadbddabadacdaaabcdbabdbaaabcdddbbdddcbdcddbdcabdcbdddadcabacadbadbddbdbaabbdadadadbcaadaddccddabcabbabccbbbcdbbcdbabdabacdccccbbdadabdaaddbdddcacbdddcddabddaddcccaddbcdbbabdcdccdaacdcbdaccdaddbccbbcaacdbddaddbdbcadcabdadababcaacaddcadcdbdbddaccabaacbadadbbcacdbdadcacbcadbcdaadcddacdbdadddaccbcdbcadbdcacdbbbcdbdcaaabccccaabadadaadcaddbcccccccabdddbcdbcbcbbaacabcbcaccdbacababccddcbddccadabccbadaadddcccabcbbccdbcdbbbcdbccccdacbdabbbdacacadbbcbbbbbcdccddcdcccdbabacaabbdbacbadbacdacaabccdbbdbdccdacccbcbaacbbbacabbababbacadcacdaaaabcadbbdcbaadcdcbbbbdaacddcdcbbdabbdadbccadcbadbdcdcbadcddcbdaabbbdccaddbddaadadbacadbdcadacbddcbdccacccccccacccbabcbacacbdaaadbaacadaaaadbacbdacbaaabbbdddadccbddbccbbbbbdddbcacccabaaabbdadccadacddabbccccbabdacdcbadccdababadbbbdabbbabdbdccdcbcbadacaadcdddbacdcacbddbadcddcaccbcdddcadacccbdbbdbcccdabccaccdbdcbcaaaaaacaadcbbdbbaaaaaaaabcdacdddbbbcddbadbcacbadadabacbdadbbcbcbdcdabacbabdaacabbbcbccccbddaccabbadcbcdccddcabacbcdcddbcabbddbcbdaccabbabdbcadaaaabbcddabadadaabbacbaadccdcdaccdcbdacdbaacadacdcbcacaadcacddaddaaddcabdaacbabadaccccdadadaadcdaabdcbbadbbdddcddbcababcdbcddbddacaabdccbaccbdbdcccbaaddbaddadcbacddccaaccbbbdabccbaddadcdddcbcdaacccaaabbdbbadbacbdaacdbcbbcbcbddbcbaaccacdcacbcddbadbacdbabcbbbcbacdbbcaabaacccacdbadaccdaadccbdcbbdcacbcaddaaabcddcaabdbddabbddbddccddddacdcbbabcadaaccdcbabcbdbacddaadabbbdbcacbcbabbaccddcbdccaabaccddaacccccdbabbdbdabcdadbddcadccccddddcbcdcdbccccbcdcdacbcbdbbcabaccaabdcdcbddcdbdddbbacdabccccdadacdaabcadadbacbaccbddbddcabbabcdaacdacbbcdcccbaabacccadcdbadbadcbbbabccbbdacabbbabbcadbaaaaddbdbcddacdaccbbcadbcddcbbcbaadcbdbcadbdabcadddaadaadbdddcdbccbdbbaaabcbdbdddcacbacaadaaabbbaabdcccaababccaadcccacabbccddcabcaacdbdbdcddbdbdcddddddbdccacddcbcdbdacdcccdcadabdcacadacddaddcdbaaaddbacadbcacacccdcadccdbbaabdddcdaddbdaaadccbdadcbbdcbcddaaaacccabbaaddbbdddbbddbcaacbabdbabdbddcdaaacdbadaacbdddbcbacaccabaacdbdcadacacaabbabcadcbccbcbadcbbdadcbdcddcdbdacbadcacdbacacdabdbaacbdaabcccbdcbaadbbbbaaccdbcabbacabacddccdaabbcaccdcbcabcdbddcadaaccabcadbddbcbbcbcccbcabcacddababdbdccbddaabdaaaabdbaaadacabbdbaaccdbcadacbcdccbaaddcacdaabdcccadccaccabbadbbcdaddbddbbaddcbbdaacbccdabdccacddaccadbacdddcdacdbababcccabaacacacabdcabcdabdbdcaacdcdcbacbccabdadbadabbdbccbbbbccbcddbccaaaadabdabdbcdddaacdccabdbcaddcacccacbabacddabccaadbcddbbbcadcbacdbcbabcbbbdbdacaadcbdccbbcdaaabcaabdaccadbbdacabcabbbccddddaddaabaaacbabcdaadaabbdbddaadbabdcbbadadcbbbbbdbabbaccccbdabbbbdacdbbacdabdbccddadddbacbcbcddbdadcaddcbacbbdbbadbabcdbdadaccbabaacadcbdddaabbdbbbbdcbdaabcbaccaaaadaacddbcaddddcccddddcbacbcdcbbbbdbbdaaacbaabdacdabbbbdbadadbacadcacabaacbdbbaaaadcddddadbdbaaaadccbaadcbbbdbbcaaacacbcdbbbbbcbaabbdacaccbacacddccaccababbbdbdbbaacaacccbacdbbbbdbaaabdaacbcbcccdbbbdcbcdddbabddbcbbbcbcaddcdbbdbaccdccbbaddbaacbdabcadbddcbcbdabbacdcbbcaacbdbddccadaadaabaaadadcaacbadcbcdbdbbcbccacbccddccbbdcbadabaadcdbcddadacaaccbccabacacccaaabdbdbabbaddbaacbbcbadaabaacdcbadbadbbdccbabadccdbbbacabaacabcdabaadcbacbabdaccaaaacdccbbcbbacbcddcacdbddcdabbccacdbbabcbcabadcaccbccdaaccadadbcbaacbabaaadbcabaddaccccbdbccdbdbdcaccdadbabdbcddbbbdcaacadbaacbdcabdddcdcdbbbabbcbcabaaddddbddddaabcccdccbcbdcdbdcdacbcbbaabbdaccbaaabcaaaaccdbacccbdabddbdadadaccdcabaaaabdbddaccaabbcccdcdccbbcccdcbcdccbaccccdcbdaabcbacaadabbbbbbccbdddacdccaaadaaabdbadcabbcdccacbddacccddabaadcabddadbbbcbbaaaaccbcdaaccabbbbbddbdcdccbbdbacaadcacdbddcabdddcdabadabdcdbbcddcaabbabbbcdcadbabcbaabdcaacdbddaadcabcbdacbcdaccacaddcacababbcacdcbdddcdbabdadcdbbbcacbadbbbcccbbbcbccddadbbbbbbaaadaacddbaabbccbdccaacababadbadccbdcdbbbbaabcadccccbdaaabdabddbabdaabcaabcdbcadcbdacdccdabccdcdaacabbcbbdaacdadabaaacddaadbdcaccbaaaddddacbcdacacaabcdcbdbcadcbbdbadacbdadcbdccbaacbbbddacadacccabdabdacccbddcbbcdabacdadbcccbdbaccdbdaadaadcaabbbbbacaddccaabdbaacbabbabdabcdaaadddcbabbadcdaaabbdbadaddcacdbdaccbcddbbbacaaaacccabadabdabcadbcbddacaccacaaabdacdabcbacacacdbcbcdcabbcccddddbbcaadcadbbcadcadcdccaabdacbbbacabcdbdcbdbbdabdddcccaadcbdccccdcbcadbdddcdbcacbbccbbdaacccbbbaadadddddacdddcdddcdbbccddaabadabdabbdcbcbdbacccdbaacababaacccdcccacabddbdbcbdcadcdcdbdcdacaabccbbcbbbbaabdbcaddbaabdbcbddbaccddabbdbdccabcbbbdaccabdaccdbcacdaabaddbdabcabdaadbaaddbdcacabbadbcaabcdabcbadddbccddabacaaaaaddbcdabbdccaacdbcdabcaaacdddbdadccbacbcdacbddbadabdbbdaacacccbacbbbdbbbcdbcdddbbacacdbccbddcaadadacdbcacaaacbbcccbdcdabdddbbcbabdaccdcabcbbcccdbabcaabadbbbbddbccbdbbaaadacdbcccababbcdbaaabacabaccacaabbdaadbaaddccbabbaadbaaabbacccaaabadacbddbcaccdddcbdbbddbddaaabacbdaadcdccbabddbbbbbaaccbacacbcacbcdaccdcbbcacdccdcaacadabdddbcdabaaaddaddaaabadcbdcabacabaadacabadddbdbaaabcccddddaddadbccababccdddbbbdbccccbccbdddcdbdabcabccadcdbccdadccbcdbcbbcbacabaadabadcabacacdcdbbcbdbbdcdcaaaccddcdbbabcbdddadbdcdacbacaadacadabdddaacbaccdaddababadcdcbdaaacacbcacbdabdccddcabcbadbbdddbaabadacadcbaaacabbcbccaddccbbdadbdcddcccacabaadcdaadaddbadcadbdacdbdbcdbaababbbbcccdabaaaadbcadadbbbccbbdbdddabdbaddcbbdccbbadacdddbcdbdadddcbbddddddbadccdcdcadadacdadbcdaddbabbaccbbbdcadacabcadcccaabcabaddddbdadbcdcabdbbbacdacaabaaacbbcdddddbbdccbddbddbbcdbccaabdbdaabbcacabcbccadaadaaddabdcdcbbcdccddbccbcacccbabaadbbbbabaadadcaadcbcacdcddbbdcdbdcdaadabadbcddbacbadcabbdbcabbaaadbaccabaccacccddbabccaddabdbbacbacabadbacbcbdabbddbbcacbdbdbccaccbbddbdabbbbbababacbbdcccdddddcaacabbdabdadbbabdbbbacdadcdddddacdbbbdddbdddaccccbbabbccdddaddcabbdcbcbaccbbacacdacdcdcdbadcacaadddabdddabadbddbcdacaaacbaaabbddacbbbccbccdabdcaabcdcaccabcaddabbcadbdaaddbabbdbdcdacaabbbaadaccadbcbabbdbdbcbdcdaacacdcadccddbdbdbaaaaabbbcdaacccaacdbdcccabcbaabcbadcbdaddadacdcdadaaabbcdcadbbacabdadcaadabbaadccdacaccacbcdaaddccaaacabcbadbbbcbbbbaaacccdcdcddabdcacabdaacbbbadabdbcdabcbcdcbaccddccbaacbcacbaccbdbbbbabadaabcababacbddcbbcdbdaabaccacbcdcdabcccdcabaccacabcdcbdbbbdabbadbbbaadabbabdcddccdaadbdcabbbddaadadbdbbdcaaaaabaacaccdabdacdbbbabcddccabbaacaadbadcdacaaccddacccdababbabcbcbcdbcbcdcbdaccbdadbcbadccdbccccadcadbbadcdbbaccccaccacbdacddcbbabbbddbdbbdcdadbabbcacababccaddcabcdccadcdcaadcdcbadcdbbbcbcacbcbaddadddbbddddcdccaddddacbadaaccdbbcacdccabbddcdbaccbbbccdcbcccabdbabbdaddaddbccabcdadadddbdcaadadbdaaaabdbdcbbdaadaabcabddcdbbadcbbdabdbadaaaadcccacbacbcbdcddacbddcbaabbcadccddcaababdaaaaacdbddbdbbdabcabacccbcdcacccccbbcaddadbddbdadcccccdcccaacaddbaddaaadcbacbdbddaccbacdacaabcbbacdcccdadbbcbaddbababcdcddacbccbcdbacaacbaacdbabbdccbbbdcaddbbcccccbbbaacbdabbaaabaaacdaacabbcdaaacbcaaaaacacacadbacbbadccaaadabddbbabddddbdabccaaabcbbacbacacadabcbddcbbdcbdcbdcbdbabbdacadcdacaccdccddbaddcdaaabdadcbddccdaacbbcbbbcbadcccbaaabdacbdddcaacdbcdcaacaddbacabccabccabadcaaaccbabdacdcabdaddaddcbaddcbcdbcbcbbbabcdadcabccdadabddabcbcabacdcbbbbdadbdabacbbaacadcbbbddbbbdbccdccdababcdbbadbcdadcbcbdbbbcddcbdcaccdbccbddbcddcabacdcacbcdcacaaacdabaadcacbbdddbbccccdadbcdbbbcacccbbbbabccdbaadababccaadbcdabdddbdbabaadcccdacadabbabcaddaadadadbbcdacdcbdbddcddcacbbbababcbbaabaacabcadbbbaaddadadcbbcaacdcbdcababcabccccddadddccaadababbaabdbddacdbadbdccbdcaacbaacdacbabcbccdadacbcdbdbdddcdacdcdcbddcaccbbddbbbdacdadacbbccdbbbddacabacbdcbdbcabdabaaccaccbdaadbccbbadaddadbbbaadbabacaacdddbacabdbbaabdbadbaccadccdadccacaaacbcbdbabcbcbdcdabbdaccbaddbddabddabbcbdaacbbcdcdcacbadcbabcadcbbcbabcbadbcbbccbbbcbbabbccbccddadbddadcabdcdbbcdadabadccaabcaababbacacdacbccbcddbcdaadadaaccccbddbdadbcdbabbcdbaddbccccbaaaddadbaddbcbbdbabddcdaadacabbbcbbcadbcbcabbddabbdacadbabaaaacacaaadbabaacbbbabdabddbcacacbdcbbccaddbdcbaacccbdddadddcbbcaddcdcbcbaddbcbadbaadcddcbcdccdacbddbadbdcaabdbadccccbbcbdcbcbbdaaccdcbabbddbccccbcbdaacdddcabbbdbdaddcbccbbcbbdcaccaccadbbbcdaaddbcddcaadadcdcbcabddbcbadbdadbdbdcbddadbbccddcbcbaacbdabcbdacdacababdaadbcabcbdacadaccbbccaddaccbdabbabadbcdaaacbcaabbbcaddcdbdadccbbcaaccdadcbabadabaacabdddaddbbaaddcaadcabcaadbaadbdbbdbbddbcbbbdabdbdccbdaaacacdbdacbdaacaadbdcbbaacddbbbcabccbaaddabdcaabcadcdacacabdaadaccbabccbacabdcbcaddcbdddbabbdbcabdacbdcaddbaccbadcccccbccbcdbadaaacccaadcabccabbccdcbaaacaadabcadcbdcddbbacddcdbddcddcbbcbbcacabcbccaadadcdacadcdcbabdabbacccabdcdddbbabbbacbadaddbcddbdbacdbdcccdccabcbadbaddddabaddddddbdcbaabdddccdbccbacababcdbaddbdbcdabdaabbaddbbcccdbcabcacdacdcbcdbcaadbdbadaadbdbacaccbaadcabdcbbcbccbbccdcbdacdcbadddbbadcdacabcbaacdaabdabadadacdcddbbdddcbadcbcbbadadacbcddaacaaaddcdaaaccdcbcabccdcccdbcddccdcdcdbabaabbabacccababcacdccdccdddabadacbbadadadaabadabcbcdaacdbcacbcdadaaccdbdaaccbbabbcacdbcbacdcdaadcccbabcbdcdcabbdacccabbbaabccacccbddcaadddbcdbbabadddabdcacbcccbaabaabdcaabdbdacaccadddcccabcbadbcddddcdbabbcbcbcdadbbabcbcaddddcbcadbdbbcbacbdbabaabacdadcccabbdbacdcbccacaddacdcdcdaadcacdabcbacddaccdcddbbbbcabccadaabdbbbcbbdaaabbaacbcbddddaccbbbbabadaacaabbacbbacadabdbbcaddbacddcccababcacbcbbcacbcdbadacbbaadbdaccbbcbacadabcadbababdadbbbaaadadbdacaadcabcccbbcccbbbcabbaccbaaaddccadccdccdbaabcaababddcdcddabaabbbdccbaadbcbddbddcaacddccbababdbaadccaaddccabcdcccddbbdbbddbccbdacbadacddbbdddbaccdbbacbacaacccbbcccabacabcbbcccbadacbdcbcbdbbdadbdbddbddcabdddabbbcadacbbbadcbddccaccdbacbadacacbcdbaccdbcdbcabbdbdcbbdaccdabdbbdaaabbdabbaaadbcadddadacbdbaaadcbdccbcddcdcbdbabbddbcaacabaaadbdbcacacbbbbdbacbbcdacabbdbabbdcacacadbbccdacdacbbcdaabdcbabdcccbbaccccbcdadcabadcaaccbdaadaddaaaabbbcacdddaadddcaacaccdaaabbabcabdabcbaaaabbacacacacbccadaaadbcabdcbaaabbadcbadaacccbdaccbbbccdabbdddcdccdddddaaaaabccabddcddddddabdcbbbbbbcdaaaadbddadaabbddcddcbabbdabdadbabcaadccbaadddcdaaaabaacaccadadbdcdbdcbabdddbcaddbcdcdacdbdcbddadacbcbaccccdadbcabcdbaadacdcdaccaacdabdabdcadcdabbbdaaacbcadabddcabbabdcabccbcbdcaccdcbcbccaabdbacaccdadccccdbbcbcaacabbcdbaadbabccdbacbbabcbcadccbdcddacdcdaaacdaaccdbcabacdabcdbbcadbcabbdaaadddbbacaaacddbbcbabcbcdddaadbddcdbabbabaddabbaacbbbdadbadbbbbddbdabddadcbbcabadbbdbadababbcaddbdbcbdaddddbaadcacddccdcbacdadaabcadbbcbdcadbddbdaddccbcacdcaacbbdbcabbddaaadabccdccccddaadccdcacdcbadccdaadcbaddacaccddbdcacbddcccaacdadcbcbdccdbaacdccdabadbccadcaadacabcbabcabacdcbcbdabcabcadbcacbaacdcddcdacdcdcdaddbbacdcbdcadaadbcdbccdcdbbacbabaccdabcdbdcbdcdcdbddcaabddcacbdbcaababbcbdcdadbcdccacbdacaadcbabdadbdacbacbcabcbbabacbacbcccbdaddddabbaacbcababdabaababcddbbbbddaacbcdbdbcdacbdbdcaaddadcdadcaacacccabbadcbbcaccbbbbbacacbdccdcaadcbcccaadcbddaaadabbaccbdcaacddbcdbbbbbdddccccdbcbccacddddcabbdbcddbbdbdbbcaccbbbddadcdaadcdabccaadcddddaaaacbbbdabcbbdabbcbcccdddaacabadccaabadbaabadcaacabbcbcbaabadbbdaddabcccacbadabaacbcbcdcbbadbaacabcaadbdaabdabcdabaacbddcddabbdccacdcbcdbdbbbbbbdccdcccbadadbcdccbbdcccbbaadaacaaccdacddadbacababaddbcddaaaaadcbcaabccabbabcaaabddbacadabdcdbdcadcdbabadaddbcbdcdbbbbbdaaacaabcaaadddabcbbddacbcbbadbbccccaaabcbaccbabdccddacdadacbddcaacdbcbbcaddcdbdaabaddacaadacabdcacaaabcadcccacdcaadacdbbaadcadccbaadccaccaaddcaaccdbaccabcabbcdbacbbdcaaacabcabbdaadccabddadbbbdbbcacdbbadcabbcacddcdcbddbddbcccdcdabdbacccdaacdcdcdacbccddbdbabdaaaaaacbcabcacbdbadccaababaacbadaabcabdbddbbcccadbcdabdbabbcaacccabadbdcbcbcaaacbbcadabacbdadcabdbddbbadddcbdbddacadccdbacbdccbbdcdbdcdbaababbdcbaddcbcbccbbcbbcadcdddbdacacdccbadcaaabacadcbabcbcadcddaadabdbbaaaccddbbcbdabbdaddbcaccacbbbbdaacddcbdcbdcdbccbaabdaacbacddcdccbadbbcadabbadcbcbddbbbdcadbddbbcbbacdbaadccbabdaabdaadddacbbbdabdabcdcdbccbadccdadbdcbbbbbbccddbbddbbbbbaacbdababbccddaaaccbaaddcdabcbdccabdcadcaccaaddaabbdcdbcaaadbbcddbcbbbcbbdaacbdbbaacdacbacdcaabbcbbcacbdccabdcbbccdcdcacbcdaaababbbddbbbaadadccabccddabddadabcddbccdbbbbdcbaabdcbdccdbaaabaabcdbbdbbcbcadbcbdbdbcadaadbbdaabbadbbbccdaddcbcbaadddacbcdccbbddcddabcbbcaaabdaccbcdcbbbdacbabbddddbcbcddadabdbccaabbadbddddabaacbabccbbdadacabadacdcadcdccbaaaadcbcacbbabbbabbbaabdcbadabddcadcadcaacdddacbcbbacddadadabcbdcdadcabbabaaabaadddcbcacdabdcaaaaaddadabdccaaddbadcbbcdabdadadbbcaacbabbabaccbbdddcdaadbaddddbaaadbbabdcbacbcaacbbdcbbadabadbabaddabcaabbadacacdbbdabdddcadcaababddddbbbacdacbccbdbbbcbcbccccddaccbdadadaddccddbddaaacabadaddbabcdbaaabddbbcaadcacccacdbaacadcacacdacbcadaddcacbacdacbdacbdbbcbaadbcaacabbacbcadbcbaabcadababbccddbcacacadddddadacdbbccdbbaadabcddbdcdadcabcddcaddccdacccccabcdbcbacaaadbabccdaaadbcdcbcbbddaccaabccabaacabcdabacbbbaadcddaddaddaabaccadbcbbdbacbbbbbbcbbaaaaabcbcddbcbadbabaabacdbcddadbcacdabcaabdbbabcdddccdddccbbddbdddbcbcdcbbcbaadbacbbaabbdcbbacddccaccdcabaaaccdadaddcbdbadaccccddcaadadaccddbbdddbdcaadabbbbadbbcbcaddbadbdabcacaadcdcbbaaaadbcdbadbddcaacdcaabdbdddcdbaabcbaadcabcbdbddbaaddbdbcbcbdbddcadabbbbbdaacadbaacabbdcbbccbcabadaccbdccbaadcccccaacbbbdabbabbababcbdbcbdbdbdcdaccdbbbbdbaabdccadabadbaadcccbaaddcacccdbbbaddddbbacbcbcbaabacbabaadccdccacbdcbabcaabddccaaacacacdadabbadcadddaaaaddbbbdccbbcbaaadcadbbbdaacddbbadaabcacadbaaaabaaacbdcdaddaaababdcdabdcddbbabbbbdbbacdcdcabddbbabbcdbdbbaccadcdbcbbadcbabdddbbccaaabbcdcabbadcdcbbaabbbbbabbcabdadbaddbbdbcaabbcaccbbadcccbcbdabddcccdaadbbcccbcaadabcdbacdbadaabdaaadbdbddbbbbcbacdacbdbbdbcdbcdddccbdabbdaacbabdbcabaddbdcddcbabaacbbdbaabdbbcdbadabdacdcddddabaddcaaacbacdadddadbaddccadbcdadacddddcaddcbdbdddabadadbbdcaacacdaacdbccbccaadabaacbbacddacadaacbcdadddccdcdbccdbbaacacacbcbbcbbdabddaabbccbbcaaabcabdbbaadcabccadbdabdddbadacacadccaadabbacadabbadbabbdbddccbbdbbbcadbacbcbdbaaaddbdaabbddaddcdbcbbcadcdbbabdaababbdcdcbcbbcaadaccabbadbcbdbacdccbddabdbbcdcccbbdbcadcaddcddcdcaccccdcbbbddbbccccbddbaaabaaaacddabbcababbbcdaaabaaabcacbbaddacbadbadcdddbcccdcbddddcadccccbabaaacdadcbcddadadaddbccdcbabbdabbaddcdadbcdbbadacaddabdbcbdaabcaacaacadabbacbdcbacbcaaadaccaadcabaadddcdbbbaddcdacdbabdddcdbaaddacddabadcaaaadacaabbbdbcdabbdadddcbdadaabdbcdacddaadccbabcbdbadbcbacbddbdddbddccbdadadbdaddbcaadadabcbbdcacbdcadbbdddbaababbcadcaadcbbbccabbabbbdacdddbdabaaabdbbccdccabbacbbdabbbdbbaacbcdaabdbbbbdbbacdacabdcadcbabcbbdbbacdacaacdcbaccbaadbabcbaacbdcdcddbaacbbcbcbaaaaacabaabdcbadabbcadbddbbddacabbbacdadbbdacabbcbddcccbbdbbdccdbdbddbddcabbdadcadbaccdbcbaabcadaacdaacbbcddccdbdbddbdaabbdcbbdaaadabbdddbcdabccdccdaccabcadbadaccaabbbabdbdbccaadaabbcacbcddabccdddbccbaaadddcbdcdccbbdaccdddacdcbabdcaacccacaddbccabcababccdcdccdbdcbacaaabcbbccccbcbbdbbbdbcaadbaadcabdcbddbdcaabbaaacadddbcaacbaddddacaccdacacadbbbaccadbaccadcadbcadcadbdcaadacdccdcaaaccdcadadadadcbddcadcaaacabaddadbaabccddccddbbaacdccaacbbdaacbccacadbddcdbaddcdacabcaddacddaacdaacbbaacdacccaaddabddbbcaabaddcaccadccbcaddbadccdbabbdcddcdbabbacaaacbdcaadaabcadaddadcccdbbaccccbcccbacaccbdcdaabacaabdabaadaacdabaabdcbdcaabbbcccaccddbbdcbccaddacddbddbbabccaabacddabbcbacdadddbdcdbddbcaaccddccadadbbaccbdbabbdccaadacbbcabdabacaaccbcbadddacdcbccdcbbadcccbabaababcbbcccaccaabbcbbdadadaccddddbdcadbbbcbbbabdbbaadadbddbcdaaaaccaababbbabccabccbcacadcccaccaacddaddababdabaabaabacdbccddabdcadcabdccaabbdabaddbaccbadabbbadaadccaacacacdcdbdbddaacddadcbbadabcdddabcbcacdccbbcdacdbbbcdcbcbcccdacdabbdaddcbdccadbacacadbbadbddadbbccdaccbbaccbccaccabbdccadbdabacbcdbcaadbaaabbdbcabbbabcdbabbabcbdacacaaaabadacddadacbbacddcacbccbdaaaabcbbcacbccabaddcabbdacbbbdaaabccccaaadbbadacdaadadcdabcdcdbcccddadacdccdacacdadbdddcbdccacccdadaadcddddbabcbaadddbcaddbccdccbccdaabccbbbcabcccaacadbadbccdacdcbddadcdbdcacdcddbbbcbcadddddcababbbbaabaaddddbcaabbaadbaddaaadcbbcdcdacabababccdbaaddcadbcbcbbccbbbacdbcccdbabdabbbbababadbbadccbaccdcccadbdcdbbbabcccdddcddadbadbbbdaabcabddccdccccadcbdcadcacadbbbdccbacabaccaabdcbacddbdbaaaaccddcbbaddddcaaaadabbbdbbddbcabacdbdcadbabaaadbabbdaaadcadcacbacaacaccbaadbabbcccddcbadcddacacaacbddccbbadacbccbdbbadcbcbccdbaddbddadbdbcddccbbdcaabcccbaaccbaddbaacadcbacacacaadabaabcdbdcccacabbbcccbddaababacdddcaddacabcbccbdcadbadbadbabbbbcddcaaddcbdcdbbccbbadbababcaddbadbdcabcddbbabbbdcdadbcbabbaabdbacdcabdcdcaccaccbabdcabddbcdcdaccbdcddccadccbaacdaadbcdcbdccbcabdccdbbdabbaacacbddabdabacaddbcdbdcdaddabbaaabbdcbcbaaccbddccdcccddacbcdaaccacaacbbcdcbaccbdddcadcdbcacdabdbcaaccabbaacdcbbdaadbcccabacaacdbadaadbddabcaacbbccacacadbbbdaadddadbaadabaadddabcaccbabbbacaaaadaadadaacbddaddabbccaabaaaccbbaddcabacdcbdaaaacdadbbcabddadccdbcdaccbbdccaddabbabdaaaacaabaaacbbdbaccbdabbbdccbbbcdabcdbabbabbdddacccacbccadcaccdadadcbdacdbdbbbbbbdbbddccabdcabcccbbabcbdddbabcbacdbbbdbcbbcacaabcbcccacdababcdbdbccdadbbcdcabdbdacbbdbbdaaaacabadccabcbddcdadcadcbbbcdbcbabddcbaacbdbddcacaaabdbddcdbbdccbbabbaccdacddccdcdbcdacbccbdabbcdadcdbdacaabcadbcabaaddbabacbdabdcbdbddacbddadbbbbcaacbdacdaadccaabdbddccaabbabaabcadadccbbaacccabcabcabcdbdddabccaacacbbadabdbdcccccacdccabccbaadacaabbbcbbcabbacaacdcbbbacdacadcbbbddcbcccccabaccacaadbccabaddccdddabadbbacadcddcdadabbccaadcbacdddbccdadcccdcdbccbaccbaccdbbdcbcacbbbbaddcbddcaabbbdadacacababbabcbdacbacabbbccacabadcaaaacabbabbabbcbddcabdcdacccbbbdcdaaddaabcacbadadcacdcdacdacbaaccddbdacadccbcacddccdddcbddaacbadbbbabcdcadbaabdabbaadaadaabcabdcbcdcaaadadadaddbcbbddbbdaaaaadcdadacacddddcbdcdccbcabbbcbcdbbaddddbdddacbacbcabacdddcdbbcbddddcdcbdaccddaaabbccdaacdbdddbacbccadcccccaaddcddadbbacdababccccbdbababaddddaadabcdaaacbbaaadcccbaddbbcadbabcbdbbdacdcdbdccadbadacbccccacdbacabdddabaadcaccacdababccbabbbddbbbdcadcbbdaaadbcadcdbabadabadcaccbbcdbaabadabddbcbabddaccdcaaabdacadcdcbcdaabaddcaadacdbbcdddbcabaddcaabccaccccdbcbdbbbbcadbbacaacdadbbccbdcccdadcadbbbccabcdccbaaccabbbdcdacaabdddabcbccbdacdccbbbdddadcdddbbacccbabccddddcadccbabaddddacacdcbdcabbabcacaddbbcacdaccadbbccdbbaccdddcbdcbadadcdbadaddcadcbabcccddcabbcbdabcbcbaabdacdbacaadbdcdaabcbdbbbdadccddadcddbcdaaccdccccdccbcdcabdbcbacddabbddcdbcbaadbacbdbbbadcdcdbcbdbdcccaabdaadbabcadaccacaadacaacbdbdcbdcababaaaabcccdcdabadaabcdbbacbaddbacbcccccccdbbbbbbdddcbdcaaddbdbdcbdabcbadccacadabcdbcaacdcacacbccacbbccadabadabaadddbacbadddabdccccbbbdacadaaabadcabdddcdccddbccaabcdcdbdadccccbbbdcadbbaacaacbadadcccbdbcddbaaababdbccabbbcddbcbccaabccbcbcabcabadacbdbddcdbdaaadbbbdabacabbbadbdcdbddbadbbacabcdbcbcbddcccdcbbaaacdcadaddadcbdbdabddaaddbddcaddabbbddbbddadbdbddcccbcaabacbaacaadbbbccddcbaacdadcaadbaadcacbbdabcacccdcdacaabcacdbacdcbaadcaccdbcaaddcaabbbbbdacacccaadccdacaadaaabcabdcbcaccbbbbcabacccddabadcaaadcbabadabaabdccdaccbaadbacaaddbabdadcbacbaaadbcdcbabbbcccbcaaccacbbcaacbabbbcbabaababaacadcadcdadacabbdccdddbcdcbccaacaacbacacaadabcaabcbccdcabadcadcbddaaadadcadbbcbdaabdcdcdadbaabdcbcabdccaabcbababababadbcabdabcbcdbdbbcdbabdbdbadbbdabbabdddacacccbdcadadadcdbbbbddbdbdbcabcaacbcaacdddddbdabdcdbccaaabccbbdcbdcbbbbaccabacbdabcddcabcaacbdcacbdabaacbacbbadcbdcbddbbdbabddcdccaddaaaddcddbbbbdcaddabbbadaabaddcacdcdcdabbdddddccbdacbdadcccacbacbadadbcdccbacadcbddbabcabbcaabdddabcdcadccdbbdccabbdbdacbcabcdbacaddbacdabadcdbdddcadcaddcdddddbdbcdbcaabdbbbddadbbbdaabadcccbcacbbbcacbccccddbaabbdbbbdbacbaabddabacbcacbcadddbdcdaddddcddadcbadcdaaddddbabdcaaccadabbbaabddbcabbdbccbbcbbaadabaabbcdddbbddbcadbcbcbaabdaaabacadddadabccabbabdacaadaddcaccdbcdcbccbbabcbbbbdcdaacbbbacabbcacabbdcadbbcdaabbdccbccdbdcabdbdcddbccddbccdcccdadbdabdcddbccbbbbdcadcddbbabdcdadaabbdbabacdcbdccdccbbaaacccdadbbbaaaaabdddacdcccbbccccddcdadccabbbdcccabdaccdcabbcaacccdddcababcccddbccdcbcdcdbaaacbcccacdbdbaaaadcbbbbdcdcdcbbbcdcdcadcbadaabcbadcbdcbaddbaccdbcccdcdaddbdbaababddaddadbabaabbacddadcaadacddbbbcddbdbadcacaaaaaabbacddddcbabddabbbdbbddcbccdcdccbcdddcdccbbbcbaabcbdbabddbdbabacbdddaabbdbdbcccbabbbacddacaaaabbdcaabcbabbddddaababcccccbcbddcabacaddccadbabcbadbdbadccaadddabdcaadcaddcbbbacbcabaacbadcdcaccddcaadbdbccbcdadccbacaabdbaadbadddabdcabbdbdcccddacdbbbcdabdaacdaabadccabddabbaaacbbbbdbbdbbdbcccadbcacdccbcadcadddcddcbdbbbbcdbcdccddcaccbccbbbbbbabcaabbcccbadddbdadcdbaddcdbbdbadcacabccbdccdadacaadddaabdbbaddcdcbbddabbbcdccbbbcbcdaccabddcdaacacbcaaaabbdddcadaacbdccaaabdabbabddabbbaddadadbaacbcabdbdaccabcdadddbbcdbcaaabacddbcbbbccaddadbacacadabccbdaccdabcacacadbddccdcdbabacbaacbccdaaddaccacabcacccdcbddacbdcabcdbcbdbdcaacaaacabdabcbacdcdcdcdcbbcdcabababcdbddbcabbcddcbdbbaaacacabcdbbdbbbcdbcadadcbaaaabaadbbbadcdabaaacabccdcacdcadabcdcaacabddaaabbccbbcbdddcdabcbbdbbdcdddaccabccdabddcdbbcdbddbaabacbdcbcdbcbdbaabbbdbaccaddbdcbacddabddcabcdccacbacbdcbaabacdacaaaacdbaabacbcaaaddccadcabcbabdabaadbcdcdbacdcadcaddccaacdbbdcdacdcabaccabcbbcbabdabbdbbbcccacabababdbcabaadadcbaaacaabaddddbdbbbdadacdbabddcdadaddcadccbcbdacbccbcdcabbdbadbcaccbbadbbbbaaaabcdadbabdcdacaabccbabcddddbdcbdbcddbbadccbddaaaabacdaaacbdaabddcdaccdbbbbcdddcbbdbadcdcadbabbabaddadbcdabdaddcbbccdccbcacbdabbaabddbbbbaabbbccdbbbdddcaabaccdcdacdcbaacdcdabaaacadacbcadaddddbbabcbbddcbcaccdcacabcbbbaababbdbbbadcadabdbaacbbcbdccbadadbdcbcbacaadbcbdbdacddbabcabdbbdcccbcbdaacddcddcdaccbdbcddbccdbaaaabbacdcddaddcdabbbdadabdccccbadabbababdcadacadddbaadadadbcbdbdbcdbccccacbcbdddacccdcbcdabcbcacaaddcabbdaaabbaddbbabdacdbccaccbacacdcacccddacdcccbabdadddcacbcdcbcdbbabdcabbdcbaccbdbabaddaaadbcaccdddbaadbcddcadaddadccaabdaacdacccbcccadcbbdcbaccdbcaccacabacbbdbaddadbccccdbcddbdbcdcbdbabaccaccdccccacdacbbcbdcabddacdbacbdcacbbbcdcdcdbbbcbcbbadadbacbabcbbaabbbdcccbcbbaddaacbdcbcdabaccadadbacccbacdadcaabadddcbcbbcacbddccabcbbaababbddccaaacddbaadcaadcbacadbccbdddbacbccaddbbbbdbddbcbddcddcdcccccabbbaddcbacddbdcaaddcabcccbccabdbcaadddbcdcabbdddacbbdaaddddabaccddcbacbdcddddcdbadbbabcacadabaccacdaaddaaddddabbbabddcdcdbddbccdaaabaaabbcdbabcadaddadacdbbcbacdcbcadaccbabdbbbcbdaabccabaccccccddccabcaadbbabdcaadbabdbbcacbbabccbcbdddbadcdbabdbbcddcdabaaddddcaccdbbadbdbcdcbcaccddbadbbcdcdbcdcacbccddcbdcacdcdcdadccdadaabdbcdcaaaaaabaadaabcdcdbcdbcdcbcacdddbddaadadabaddbcacdddaacacabcbcaabcabdacbdddddccacbcabcdaaccbaaaccdcbdcdbccdccddddcdbcbbccaadbbdacccdacbacddbdcaddbcbabcabcccdaddbaddadcccabbcadbcabbcddbcccaabdacababadcbccdcabbbcaccddbbbbaabdcbdaaabcbcccdbbaababacdbadccddccdaacaadadbcbccdbadabaccbabaabcbdcacadaccaacaddaaaadaccbddaadadddcaabdddbbdbabadbdbaabcaccadcbdcaadbddccccaddabbacdddccbcdadcbaabdadcdbdbddaabcadabaadaccdcaddcddbccdaccdaaaadddbdbaaddcbdabdadcbcaacaaabcabcdcabddaddccadcbbaaaddcdaabdabbaaaaccbbcacbdabcaacaddddbdabbcdccaaabcbaabcdbaabbbcbdbabdbccadacbbbbbdabbcdacdacaabdacabcacbdadbbadbbaabdbbabcaaabbcdbaccbadbbaaadbddbbcadabdaaccabbcddbcdbdbddcdacbccadccddbcdacddacdabacacddbdddbdbdddcbbabacbabcdaccdcbddabdbbbadcaaabccdbabdabcdcbbcddadabacbabdbaabbaacacdbadbadadbdcdbbabbacabdbbcdcccddcbcadbabddaaddbbcabcaddccbdcdadaadbdbbacaddbaabadcaacdcddbadabababddcabbbbdbddbdabcabcdcbcacccccddacdbddabbccdbdaaddcdadddadaaddbdbbdcaddadcbbabadcdcdccdcbacccabcbaccdaabbcbcddbdabcdadccbbcbcbbabaaabddddccddbbbcaacbbbcccbabaaacdbaabdcbdbddaaacaadbbbbcbdabcccbbbcdcbcaccacacadccddabcaaabddbdabbdbdbbcadccaabacdacabaabbbcbabddcbaadbbbbaaddddbcdacbdabbddcccabcdadadcbacbbccddbacbbdcaddaacadcaadadadacccbdddddacbbcddccdadccbaacdadadacccbcbbbddbcdaddbbcddadbbcbcbdcbcbdadbdbdbdadbdbaababbcdcbbadbbdddaddcaadddbcaacaaddcbbbcdaccdacacdbaabcbcaacacdbdbabbaacbdcbadccccacdddbdcccbaddbcabccbbaabdabaaadbcaccacccdbcbaabaacadbbddadcaadcbbccddbccdddaadacbbddccbcbadbdbcaadaadcbddddddbbbbcadaaaaacbdcdbbadcacbdcbdcbdabbbbabdbddacabacaacaccddcddccabcbbbdbbdabddbbdacbcdbaaabbdbdaddacdbcadbcabbacddddbbadabbaddaacdccaabcbdcdcbcdacbcacdbbdabbddbcddacddbaddbacdcccccadaccdcbaddbbdcddaddbcddabcbcbaaaaaadbdcdccccdaabacbaaacbaadabaacbacaababcdbccddbdabbbccbdcbdacddbdadacbccabdccbcadabcbdabddbcabdabdddbdadddbaccaabdddbcdbbdbbcdadcabcacccccdcdabbdcacaaabcdccaddbbcaaddbdbcbaccbbbcdaaccddcbbdcacccdacccbddaccbacaacbacddbcdabcbbcdddddcacbaadabcaaadcaaccdababadbcadbcdccbdcddaccdaccacacbbbcccddccdbaddabacbadddbdcaabccaacdcccbdbadcdacdbacbaddacccadbcadbabbbcacccbcddbcbcbcaccdacdaccbcbaacbcbdacccbcbbbbdbadbccccabcdadbbabdbbbcbacccbbadadaaaadaabccbdaccaddbaadccdadbccbbbbddbbccbccbdbcabcaabccabcbbdbabcabbdcacdddcadabbbccdabcccdaaccbaaaddcdcabaddcdddcccccbccdacabcbbacacddbcbdcdaadcdbcbbdbbacbabcbbcdcbcddadbcccbbccaabdcaccdbdcdccabcdabccddbbdcdadccddcdcbdbcdbaddccdbdacbcaadbccabcccdbbbacabadadcddcdbaadadabbccbdbcdbccddaabbdabbddcdcaabacacbcdcdabcdbaccbddcbcdcddbdaabbabbbcdadbabbbcdbaccbbacbccdbdcaaacabacabdbcbdcbbcadbcaadabdbaddcadccabdabdabcacbbcadccdaacbdcabdcdcdaabaaccabcacabbabaccdbaadcddadbabadcabcacabddcddddaabaddcbbcaabcaccdaabbaccbbbcddbbbcabdbbdbcbaacdcddcddcaabbcccbacabbaacddddcacddcaadbcdbdabbaabdbcacccabcdbdbcbdddcdccccccacdbadccabcabdddcddcbbcddbacbddcabbbcdcaabacbbccdcbcaddbadbddbbbadbcccbaaacddccdabbcdaadaaccabacbbdcaddbaddaccdaaddbbdddadcbadaccbbdbacbddaadddbbbbabaaacadcbbbadbaadadbdcadbbcdbcaccbabdcccacaddbdbcacdbacdcabaadbbdbddcaddcbbbdbbadccdbcabdccaadadccbbbdbdccddcccbcdaccadcccdaadabdddabccddcccadccbcdabacdbbcdccbabddcbcaddadbaabdcccadabdaadbacbbaadddbadcacbbdacbbbdcbbdcabdcadcccbcdacabdbaddbbcdbcadbabdbddcddadbbcacdbabbacdddaacddcccabcddcaccbdcddaabcacbadaabacbbdbbcddcdadbaaabcdcaccccadcbddaaccbdcdbdcccbbadadddaabdbacabccabbbbacccbddabddbdacdcabbdaadbacadcdcadabddccbacaddddcddcbcdccabcdbabdacaaadcabcbbdabbdbacdacbbddadbcdbdaaddadddccaddcdaaadbbdbcbbdbbbdbdcddcdbaaacaaacccadbbbdbcdddddaccbdddaaabbbcdcccdacbcadcdacbdaacadacabdacddccadddacbaddbcbdabacaacbdccdbccbdbadcccadbdcacdccabbddbabcddccaabdcdaabacddbdcbabdcadbccbccbabbcaaadddaccdcbbbbdadabcacaaaaccdbcaacdccdbacddbcaaacacdabbbabddccacdbcbbaccccccaaddcbaadbbccacddccbbacbcbbabdaadaabdabdbdacbcabcbbbdcbbbcccabcdacbccacdbcaabbaaccdacabbaccaacadddcabbcccdccadbabddadaadcddbabcdbddcbcbabbdcccdccadbdacbddccadacccccccdcbcddcbabdcbabbcdbbdcbabcabcccaaaabcbbbbbcccaaacdadcaadabddbbccdbccdaadcaddccbabdaaabcacbcdaacacaddaaacacacbaabdacacdcdcaddbcbaabadddbdadccbcbadacabacbcccdbdbdcacdccbcbbadaabadccdcccadbbaccaaacaddbacabccdadbaaddcdcddbbbdcacaacdcdcaaadabbcdbcadbddbbdbdddacccbcdadbdbccddbddcadbaadcacbdcadbacabdabaacacabbbccdccdabcaddadbdbabaabbababccbddadcdcaabdcbbcbadbaabcbcbbbbbbbabcabcbcbbadcddcbcdcccbcbbbbdcaacddacaaacdbbaaadbcbdacdcabddbbdaabcbaccacbdbacddaddbcadbadbdcdcadddbcccccadddacddbdcbaaacddbdcdcbbbdacddcbbbdadaaddaaabbcdcdadbdddabcdbbababdddaacbacdabdbbcdcccaabbadacbcaadacdabdcddbdcbdacdcbcaabcdddcccbcabbccabcadbdbdcabadbbbabdaaaddcdbbdccacbccaadbcaabdbcadddbccdbaadacadcdaadcbadaabcccadacbaaacccbbcaddbbdcabcbccabbcdddacbdccabadcbaddddbcbbaddcddcbdacaadcbbbbcdacaddcddcdabadcddabdbacbbdcbccacacdbdddababccaabddbdbacdcacccdacabdcdacbddacdacbddadbcccdabacbdbcaadbccdacaabbabdbaaacbbbadcdaddbbcdaddbdbaabdccdddbddbcacbaabbccbbacacbdaccabddabcdacdadcaabccbcccabddaabaddcdcdadaabcaabbbdabcbbdcacacaabaaabccbaabbbdcdcabaacccbdccbabddacabdcaabcdbaaadadbbbccbcdcaccababaabbcdccbababadadabadbbaddbdbddccabdccbcdabacbccbabbcaabbbddcddbccdbbaaadbbddcbbdbabcaaddcaabcaccbbabaadcbdaabaabddddccabdacdbcbbccdcccabdaabbdcbcbaadbbcbaacccbaccddcbcdcaaabcbabcdcbdbaaacacadcdabdcaababadacbbbbcbbcacdadcabbddbbddbbddbdcbacddaadcbacbcdccdbcccaaacdddcaccaacbbabdcdaaabccabdabcbdacdbaabdddabdbacdbbbabcbcbcacabcacaccccdbabdcabdaabcbbcadbaccaaaaaaadabdadcacbcacdcccbcdddaadbbcbcbbdbacdddcaaaadbdcbcdbdbcdacaddacddacdbbdcdaabbbcacddccdddbacdddabbcddaccccacabaccabbcaabdcbaaadcaacccbabcdddbcbcababbbbbaaadbbcacbcacbcbbdadabadddcbdacccabcacddabcbbadcabdcaddadbaabaacbcbbdaacacdadabdaabbcbbbdbdaddbccbaabdcccadccabcbbbadadcbbaaaabcddacccacdabbdbcbcaabacdaaaabccbdaabddabcddbcabcaacdaaccadcadcddcdabaadacbcdbccaccadadcbcdabaaabcbdcdcbcaababbdadcdcdddcadabdbcaccbabdccadabddbacdbcacaabdcabdccdbdccdbbdaacbdbbaaacdbcccbabcbbbabddbabccacbbcdbdacccaabadbdacabaabacddddcdcbbbbbabbcdadcbbdddbbbbadaddacddadcddcdddcbdaacaaacbaaacaabdbdddbaacdadcdcabaacdccaadddcdaaccbaaabccbddcbbadcbbadaaabbdacbdcabacacbaaabadaadbbcbbbcbbaacadcccbcdaadddbcddcaadadacbbbdddcacacdddbbadcadcdbaadadbdbdbbccbddbbcbbdbbbccbabadabddddbcccaccadababbcbbacabdabddcbdbdcadbdacacaabbacadbadbccabcaabbcacddbddaaddadccadccadadccacbdaabcdbcbbbcadbbaccbcdbbacdccdcccccdcbccbaaacabbcacbdcdbaddbabcadacaccdcacbadadddbdbbccacacabcbccbadbcdbbcadcbbbaacbaabcadabbcaaadccaadcbacdabdcabbbcbbcdcbbbaaacddacbcadbcdcaaaaccdacbadcaccbbcbbbacbadaabdccbcacbadabcdbcbdaddadabaabcbddabcccbbcaaacbbdbddcddcbbdccbacbccddccdbccabbdcbacaacadaccadcaaacdbcddddcadbacddcddbdbdbdcacabaddbacbddaddbadccddaddaaaaccbdcbadddcdbbcaddcbbddbababdcaddbcdbabcaacccacaddcadaadaddabdbbaccccacabcbdcbbcbcaaacdacbaaabdbbcdcaaddacaccdbcbdbbbbdcadacbdabaaccdcdbbdadaabccaabdaadcddbbccbcbccdbabadbdcadabbbddbbddaacdabababdcadbcddddaaaadcdabaaddcdcccdcacbbcdccacbdcbacaadcbbabcdbabdcbaaccdbcdbcdbabcbbdadbaccabbabadbbccddddcadcaccaaacbbdccadaabdadbaaabddadbbbbabcccbdddccaccbccabbdbdcdadabcddadabbaadbdccaadcbaccabbcaacbcdadabcbbacddbcdbdaabdadabbdaaccbbaabbcccbaaabccbaccbbaccddbbbabccbabdabcaddacacbcbdcdbacbddbcbbacdacdabcbcbdbbbcbdcadbbbdbdcacbcddbdbdacaacddbaacbaabbbbdacbcdccbdaccbcdddcddabddadcbbadcdccbccacdbaacacdadbccddbcbaabaddaddccccddcdadacccbaccabdaccddddadccdbcdccabdddcbcacbbdbacbacdcccbbdddacdbccddcbcbccdbbaadacaddbacbdbccbdadcbaabcddddcadcadaabaddcbcccdaabdababaccbcaddacbaacdacadcbddbbccaaccdacdcadcbbddbabaccdaaadcadacdbccdababccbdcccabccbcbbccaaadaacbcacdbacabaccdbacabccdcdcdaddaadbdcbbdcbdbacdbaabdadbadcabbadbcabbdddacacaadabbdabdcdabdcbbcbcdcdbdccaadccddddbbddaddbcabbdabdbdcdbbcbbcbadbbacabbbacdadcdcdbbaaaddbcbdcddcaddcccbddcabaabcdaddccdbcdcccdbacbbcccdabdaabcaddadcbbadbcbbacdcdddbdcabcaaaaadbdaabdacccacdababbaacaccbdbacabdcbaddbbbcdcaccdacabbaddabaacdccdcbaccbbbdcddccabaadaacadacbbaabcbddbbaddacbbabcacdbcbbacadaccacccabbbdcbbdacdadaaddbaccdabccbbccddccabdbdaddabbbaabcadcbabaabbdcbcbacddbcbdabacdbcdaccccdddcabdabdbbccabdcbbcdccbdaddacbadadcaccacbcdccbdbdbabadacddcaddcaddbaccadddccdadcbbddbbadadcbbdcdaabdacabcdbaababcbcdaaabbdccacacbbabbbaadbcabadaadabdababbcaadacabcccbdaaacbaccbabdbbcacbaadabbbadcdccbdbbcddddacbbcadbbddaaccbccbccbccdbbdccaaabadcbbabdcdaabaaccbdbcccacbddadabaaccdddbbadbbdabdccbbacbadacbdbabcbcadaddadcdbbbdacadbdadadbcccaabbabaabcdbcbaadbbbcabadaddbddaddbbccdadccabbaccbccdadcababacaaadaacbbdccbaddacabdaddbadcdcdacddcbbcddadacabddabbcadbbadaacaabdacaaacdddcaccbdcaaadabbabacbcbdddbccbbcaaadcadbaabbcabdadcadcbbdccbdbdcbccbddbaaccdabdbbcbbcdabbbdbbdccdbccbbaabdbacabadcbccddadbcbaacaacbccacdababbaccbaacdbbbacadaaabcdaaabddadcdbaaabcdaccdcdbdcbaacdaacaccbadaddbbaabddabcadddcadbbddacddbcaabdcddddbbbbcabadcbabbabcaccabcccdbdbbbadcbaccdcabbdbdccaddabccbdadbaaddcbdbbaddabbacbabccaaccdacbccbbabbdbcbcdbcdaaccdcaaacccabbccaaaadbbcbacddccaabcbbdcaacaabcbabddaaaaadcdbcacbcdcbddbbbbacbcbaacbbabddaabdacdaddcbbbdcabaacabdabcbbabadddbdcdddcdacdbcdabbaccdbdcbbaacdaaacacaaadcccbdcccdcccccacdccbdbbcbbadaaddbaabcaacaabcacbbdacbbabaabbdaccabadccdbcbadbbbcacacacbbabbdadcadbcaababddcbcaaddadbcbbbbcdcccabacaabcbdbbcccacbdabddcddcaccaccbababdcbacddacdcacaacbdddcbcbbdcaaccabccaddaacbcadddddccdccdbdcdcabbccddcbaababdbdcabadbabddcbdcaabcccbccbccddabcbccadcabbddcabadccdccadbacccbdbacdbddcbbcdbcaacabaaaddddbadabddcdbacddcbcbacdccaabaadccaacbabdbdbdcbdacabdcbaccbbbbbbaabaccbbabadcacabcbdaaabacccbabbaaabcaddacbcdcccaadacdaadbdabdbdccdccdcdcdbbbbdcacbbacdcadaabcbadcdddcaadbabcdcacdcbdbccadbbdbabccdcadacadadacacabcaaabdcaacbdbcdacccbdbdbdbbdaaccacbcacccbccbbbacddabcacbdcbccbaccbadcabbbadbaabddcbbcdddbacacadbbbabcabbabdcababcaaccacabcddbccbdadcadbbabbcdaaaaddbccadddadcdaabacaddaaaddadabccbddbbdbdaacdbccdbabbcabacdbbdddcabaaaacdbcacbbcdcaccadcabcadbacddcdbdbbbbadccbcdbdbabbbabbcbbacaaddddcaaabacbdbdccbacbccabbccddaccacdcaccaaddbdcbbbaddcdcaaadaabdcdababdabbacbdbdadcbbdaddacbbaaacadddddacacccacdabdbdabbdbabddcdddbddcddabdbcabadcbbbdddcadcbdddbadbbcdcdcccdacdddaaaddcabdabbccbbcbaacadbbacadaacddacddbacdbbcbddbccdddbdddcdcdbdbddccdababdaaddcdcabcabbbdaaabaaddbbaaadddabbcbdbabbbcdcbadccbbcdccbbcaadbcbaadddaddcbcdddbcacaddbbbddadcdcbaabaaaccbbcbdccbcbababddcabadcadcdcdabcdbdcdbdddcadcdcccbccaabcdddddaabadabadabaddccadabddbdacadbbadcddabcadbcdadaabdadddbaaacbdddbbdbdadccbddbabdcddbadaacbdcacdcbcabdbabccabdaadbaabdccdaccacccbdcbabcbdbcdbaaadacbaccbcdaddccbbbccadabdbbbabbbdabbabddbdbabcdbdbaaadabcdbadaabaacaadbbaaccaddddbdcdbbaabbacbdcacbcdababbcbbabdccbaccbcacdcbaaabadadacbaacdbaabbbabdbbcbabdbbcbaaabcccddcabadcdadabdcaadadacadacbdabddabbcaaacddaaaccbbbdccdaddbadadadaadbcbaccaadacaaabaadccbadcaddcbdabdbaabadaddacddbabdadcacdcbdaccacddbbbdbccacadbbadcbbaadcabadbddbbdbbdacbddaaacaccdbbbccabbbdcccabaaaacddcabcbdbdcadaabaabcaacbabbadcdadacaadbcdcbcabdbacddcaacdcbddcbababcbadababcabdddabdacdaaadaabcadddbdbbbdaabaccddacdccddaccbddbbadcbdbbdddcbacaacbcdaaacddabbcbdbddaabccbbacbbcbbdabbaadaccbbacbdbacdbcaaacbcacbbbabdbdbcbdbcdcbccdcacacbaaddddcadabdbddbaccbbaccdccddaaadbacabddbaabdcdaabacbdbdbbdacddaacbcdaccbcddbbdccbcdcaaccadccdbbddccdccdcdcabdcacbadcdcccdacacbcbdbbdddacbbcbacdddbaaddaacacdcaadcbdbbdacaddbabacdbbdccbcabdbaabdbcbdcbdcbcacbcddabdbbdaabbcaddcabbcbcbaabcdabadaccdbcbddabdadbcddacadcabbcadddbcaabcbdaabadacccadadbdacbbdbaaabbbcbbbcdbbdcccbadacdbbdbacdacaacddbabcdbccdbcdcadaacdaaabbbdcadaddabdacdcbbccaaccabccccaabbdddbbbbcadcadacadabbbaaccbabccadbadbbdbdababcdcdddbbcdbddcbddbbcccaabaaacbccbaddaddabdcbabdbabddbcbbbcdbadaaccaababbccbacccabbbabccdbadddbddddacdddddbaccbcdcdbbbdbdadddcdaaddbccbacbcbbabcaaddbbcacdaddacaacbaddabcdacccdbbcbcdcdcacaaabdcacbdaaabbbcbccaadbbbdcdabdddbcdbccccbbdbcddabdabbcccbcacdbbdcbaaaadcadcabcabbbdaaabcbddabdbdbbcdadddbbdcaddacdcadccccbccbdcbcccbabcdddbaaaacbcbbcadbadaccdbddbbcddadaabbdddadbcccdaacadabcdaacdbadbaddbccbbacdbacdbdbacbacbdbdddbcababacbdbcccaaadbcbbdaaadcbddbcbdccdcccdddbacbabaccddbcdababdacddcbcbbaccbddbcabaadbbcaabacbdbacaabcaadacddaaaabadcdacacaacadbddabdcaaddacbdbacdadadabdbbbabcbabbdacacbcdadbaaddacbdbdcadbabcbbdbdbdabddddcaacbdabadadcbdcaabbdacadccccdacabadacaacbadabbcccddbccaadbaddddaaacdcdbcbacbaccaacaabadabadbadaaabdbaabdaaacaadccdbabadccddcadadbdbbdabaaadddadcdaabbcbcbdaddddaacadadbbbcacccbdbddbdccabcccccddcdaccacbbcacdaddcbdbcbbadbddaacddcbdbacdcdacdbabccbcdacccdbbddacdbaabdcadbdccdadaadccacbabaaaadadcdbddacabdaddcadddacdcaabcaccdbbccbbddddcbaacccdbbadcabbccadadbccadbcbadabbcddacabdabaccaacdadcbcddddabdcbdacabcbbbaababdbcbdacbcadbcdcbcadbdcadbdbacdcaaddbadaabddddbcdcbbaccdcbcaabbdbaaabcadbddccdddcbabdbadcacbdbcccaaabccddbcbdabbbadbaaadaacddaaabdbcadacccabcabbbcbccaddddbadabdabcdcaabaddacadaacdaabaabddbcaabdcdbadacaddcbddaaadddaccdabacbdaddadcdaabcaabbdadbdadcdbdabaddcdddccdadbdcbddddbbcdcccdaddadabadbbaddddaddbbbcabdbadccababacdbdbbbcaddcdbbaabcddbdbcbbbbcdacdcbdddbddcadaddacddadadaddaccbdaccaabbcbbcabcbcaaaddcdadcabcacccddccddacbcddaaaddabdbbbbdbcccbddcdbccccdcadbccadbbdddacbdbdbabccbbbdaddcbbdccacbddacccbdbdcaadbbbbabbbadcccddbdbcdcddbddacaabddcbcdadcbbbdbcabacbddacbadbabcbccacacdabdcbcadddaacdbabdbbaccbcadcabddcbabaadaaaacbdacdbdabdbdcbdcdbcbbbaccaaaaaaddcbbabacaddadbddaccabdcccabcabcacaabaccbdbacbccdbbdacdcaccaabcdbaacbccdccacbdbbdacbaaaabddbdccacabcadbabbdcbacbaaccadcbaddadaacbdcdccbcbabcccdcabadccccdaccccdadaacbacdbcdcbbdabdcaaaababbadccbacdcaaabacadabacbcbbadbbadbaadcacdcacbdddaddabdcadbdaaccbaacaddcaaacbacabadbbdadddbbcadccdbcaccbdddcbbaddccdababbccabacbcddcddabddccabadbbbadbbaccbbdacdddbbddccddcdabaacdbdddaabbddbcacbdcdccdbaaadcbabbbcabddbcaadadcbddacbcaacddbbdddccbbbbdabddbbcdcaacbcbaadacbaccabcbdacaaaacaacbaaacdacadbbccdbaaacabccacbabacabddbbbcacdbaaaaabaadadbcdadbdbbdadbbbcdddcdbadcabcbaccccdbdbccacbcdcdbdccdbbbbaaadccacbadcdbbbbbadabadbababcdcbdbacabaccbaaddcbcdbadabdaaadacbccabdcbcabdbdbacaababcbbcdccdcbdbdaccaaaddcacdcacbbdcbbcdcccadcacadbabaddacabcddccaddcdbdcacacbbaadccdbaddbccacbbaaabbddbcdabbaadabbdaaadbaabaadcbbacbacddabbbaaddccbcdcbbcbcabdccbbcdccadccdbaacaddbdbcbcbdabddacbcacadbbbbdabaadccabababdaaacbcccbdbccacddacbdccabcddbadddbddaccdddcbacdbbbadcaabcbddadadacbbcddadaddacadbadbbccccdcddddbaaabbbadcbaacdbacbabadbcabadbcdabccadadaaddacccaadbdbaabbdcaadadddbdddabdacbcdbbcdcabbdbdbbacaabbccbaaabcdaabbaabbdcacbcccdbddbdbdbcccaabcaddcaabbcacbacabacbdacbabaadaabdbbabdbabaacdabdbadcabbacdcddbbadcaacacdcdcadaabcadcaadbacbbabdcadbdcacbacbacacdcccbdcbaadbdcacbcaaddaabbbccabbabacdbdadddcbacaadbabddcdaadaacabadccacbaaaddcdbddbbaccdbccddbcababbcbdadacdcddbdcbdddaaadcbcbcdbbdbbbbaaaabbdaaabcdbbdddadcdabcdbaabdcacdabdddabdddcbcbddbcaccdcccddbbacdaaacbcddbbbddcdbbaaddbcbdddcdbdcabadbdbdccddadddadaaadcbaabadaabcbccdaadabcdcacddccaddacdbccdbbaaaddacddbbcaabacabcccdbccdcccaaadccbbddabdcdccdcdbbcaacddcbabddbbacacbbcdadaccbccadacdcbcbabaadbbadaccdbcacdacacbcadaddabbdccccabddabcdcadaabbbdddbbaadcbbdbdaadbcccbaaaddbdddcabaaadaadacdcddadcddaddadcdccadcbbdabdccdccbaccccbbdcdccbdcadcdabcaaacccbcddaddcbcbbcabdddacdbcaaaaadbdadbbdccaccdbbabbbbddbbdacaaccdaabdcababaccdbcadbcdbdccacccdacdddbdabacacbcdaddddacacadddcbdadadbbbaacabbcdaadcbccacbcbbcccbbcdcbbcbcdacbbcccbbddcacddbcbccdaabccdadacdbdcccdacbabbbacaacabccdbbacbacdacbdcccabcbbdbacdbdcbdcadccbdcadabcbdbdbbabaccbacbaabdcdaaabaabdcaacbddbdacbdccdbdbbdaaabdcacadbdcdaddccbbddbbcaabcbbbbdaadcaddabaacdbcccbdbbcacddacdbcacdabdabdcbcdbbdcdcbcaadcddcbaaccdcddcdbbddbabdcadbbdabbdaddcabbdbddaaabdcaaaabadadbbbaaadaadabacdddddacbdbdddbaabccdcdcaaccabcbaacbdacbaaabbbdbcabcddcbcbbaadbadaaaaabcdcaabccddadcdcacdcddbaadaabcbaddbdbaccdcdcbbdcdaadccbcbdaaacbdcbabcbcdbacbcbaccddcadbadcccacbadbbcbccabaadacdccddcdcaaabcadcbbcadabbbbaddabaaadbcdacdaddcccdadabaadcdbbcdbccbbadccdddccaaddddcbabcdddabaaaccaddddccdadacaddcbcaccaddabcbbbcdcbcbbdbbdddcdbbbabaadddcacbacbddbcbcdbbbcdaaccabbdabacaadcbaaddccabdbacbadbcdbbddcdbacbcacddcdababdcddddababdbadbababbbdddbddbbcaccdbdacbdbccaddbddabcacbbbdcabddccbabdbdabcaddcdbddacadaacbbaaccbbdddbdabbccbccdabdabdaabbadcdbdccdbbadbdabccdccbccbbbcaaaabcdbdcacddadadddccdadccbbababbbcdbacccaabccbbbabdacbdabdcddcbdcdcdbbdcaacbbadaabbbacbbcaaabbcdbbdbdbbbaddddcbacdcadabdadacadaddbdbaabbbcacaaddcbbdddccadcacacacabdbacccdbcaacbaaddbdddacdadcbddbddcdbbcabdbcbcaadddbacccbbcdbdaaaaadcbaddacacbbaaadabaccdaccaabdcdaccddadcdcabdcabccbbbdacbbcbbaaaacdacdbcbacdaddcdbcbabdddbcacacdadccbcbdaddccbdaccbabaccdcadabaacbcacabbcbdabdbdabddbbbaddddbddacbbdadabbcdcabdddccadbbaadaacdbdbadbbaaddbcababddbdccbdcdccccdcaaccbdbbcbacdddddabdabcdacacacdaacdcbdbacdaaddcbcaadbaccdabbcbdbbddadabcdbddcababdabcabbccaaacbbccbddbaaacadbbbcadcdaccddbbccdbbbabbabcdabddcdbadcbcddabcaddacdbccaadcddadabaccbcbbddacdbbabbabbcdddcbdaccddbdddadaccbbabcaaadadbcdcabbbcbbacbabbcadcdaccabbdcdcdbccaabcadadbcaadabaacbcbcabbdacdddcbccbdadbcddddbacaddabccaabbcdacaadaacdcdbbcbaadabbaabbdcccccaabdddcbdcabadadbaddadabaadbbcbcdcddacadadcbcccdbdccdabcaccdcccbcddacadccabdaacbadbcadcddbaabcacdadccdbaaadcbbdacaccdbdbcbcbddcbddbadacbddcaabcbcbbbdcdbabbbcbacbadbdbcbdabcbdcccadabddddcacaddbcdaacabaaddcadbaccabddaabcdbbaabbabcbbbddccacbddcbdadcdbaaccdcddbdbbdadadaddbadbaacdddbbaadbdbbdbbdcababcaddacaaddbdbcaccaaddcdcdabdbdcdbbddcdabccdadbbdddbadacbdcaaddbaddccbaacacdddbdadddbacbcbbdacbadbdcbcacabcdddcdbbcdbaaababdaaadcdbbdacdbabbadcbaaacaaaddbdcbacacbbbacadaccaaddbdcbadadacabbdabdcbcddddcbdbdbacbdaddbdaaabcbaadddacdbacdadbcaadbacbdcbdcbaadacbdcadbcdddaddbbcacccdcbcdacccdcbcaddbadadaaddbdbdacbabbacbadbbdbcabbadaccddbabcccaadacbdaaccddccbdddbabbbdcdccbaacdabbcddabcaccdcdabddcdacbaadbbddcbbbccaddcdcccbaddcdadbcadcabacdaababbadbadbaaabccacbcdcbcdcabcaabadbbaabcacadcdabbabddcadbaababcaadddddcaddcbbabcbcbabbaacbaaddbdcbbdddcdcbacbccdadddbbabcddbcabcbaacaabbddadccbadbbbabbadbadadbcbaacacabbcddcdbabdaaaabdcbabdcdacddadcbadcbcbbcbbdbcbbbadcaacbadbbaddabdabcccdccbbbbcaabcdacdabadabdbaddaababcaddccadacaccccccdabcaaccbcaacbbadbdcadbdbdbdabcaddcaccbbdccdaddcbacacdaccabccbdbcdabcddcccbbcabadcdcbddcccddadbabcdbcbbadcaddcbababbcdbcdcacbdccaccbbdcaadbcabdccaddacbcbbbcaccadbbcdcddbdbdbadbbdbbbdaabdbccadbacddbdadabcdddadcdddddddacacdddbccacdcdaaddacbdcccbcdbcaabdbbdbaadcaccdccbcbcbbcacbdbddbdbbcaadcaccbbbdbdaaabbdcddcdbdcadbcadbdacdcbbaabccdddbacdcdddccbdaddababbcccabadcbbcaabbcbdbcddbcabadbbbbbadcccacabcdcacbbcbabdcacbbbdcabccdcdcaaacadadbddabdaccbccddcbdcbbbdabcadddbabcdaadcadbcbcbdbaadadbccdbdcdaadcadcbadaaccaaabcaccbaaadccdcbadcdddabcacaacdddcacbcbcacbcdabdbcdbcdbdcddcdddcabbbbbcbbcdbbcbddbcdaaabdcdaaddadbccadddccbababaaabdbbbdaaadaacddccacacacbbdccdcacbabbbbbbcccdaabaaaaabdabcdcdadddaddbabdbdcadcabcbbdcbbbccbcabacbaaaaaadddddbbcdaacabbbdccccdacacddbdcbbdccdbdbadabaadaadddbbaabbbaacdabbbaccbbdcdddbacdbdaadbbacbbadaaddbcbdbbbcccabdcaacbcacaccaccbadcdbaaabdadbcbbdbcdbcbdccccdadcdcacccdbdcaaaaaaadcaaddbabddacdcadacdccdbaccbbacddcdccdbcbccbddcbadbaabdbbaabbcbcdccaadddacccdbadccaadbcbdcbbdaabdddccdddcdcabddaacbbacbaddcbbdbddadcdcbbccdabdcbcdcadadabbcabbcadbcbadcadcadbcacdcdccdcdabadabbddcabbacccdaaabaadaddbabddccbdcddddbaddbababbbbcbabadcbcccacdbabcccdbcdcdbcbcabdbadbbdbbabdbdabdaadbacdcccddcbaaabdbbaddbabadcbbccabdabccccdcdbacddacdcdddbbdbacddadccdbaabdbaddaacacbbbcbbbcbbcacbdbcccacadbbccbcdddcdbbabdddcbadddcdacdaccbbbbdcdcacbbdddccbabbcddcbdbacbcbbbadbdbbaadaaabaadcaaccbdcdaaadddabacbabcadcdcddbacbbbbddcdaadbbbcddcbbcdbbaaabcdddcdbccdcaadddccdbacdcdbadddcabadcbcbcccbdaaabbbbdbbddcdabcbbddaddaabbcccddddbcbaacacbbccacabddaccbbccbaccbdaadcbabdcbdccdbdaccdddcdcbbdaacbdaaadaabbbacabcdccbcaaaacadbbaacdaacbaabadccbaacbcbccbadcabadcdddddcbddaacccdcabdcbbdcabdbbbdacaddbbacabdbcdccabcbcbcaadcddabadcaccabdbddcbcbcaacdbaddbdadcaddabababbacdaacbdabadddadcbdcaaaddbdbcbccacaddccccacdddcabddadbdcadaabdbdcacaaaacdcaacbaccbdbaccdbaaddbabacaabdabdccbccacbaacbadddbdcdadcbcdcbbdadaabaabadbdacddcdddcaabadabbbbabcabbcbadabcbbabcdccaadcbbdbcbcdaccddabdccdcdbbdbdcbaadbaccacdcddcdcabcdbdddbbcabcbdaddcbcccaddcddcaccdcaacbcabdcadbdabddababbddaddccdbcbdacbdaababcdbbdbcbbcdcdbbbccabddababbcdacdaccdaaaddccbcacabddcdaacbdccdcccadaacaddbdaadcaabacaccacaababbcbcddabdbdccbdcdcbccbdabadbcaabdacbcabdccbdaddcbadcadaaaabbddbddcaaaabbbddbaabcbccbadabacbbddacccbaacbbbbdccaacdacadbcddddcbdaaccacbdddaaaccacbabbdcacdaaccdccbdddabcbccccbcbcdaaadcaadbccdbdcbdadbccddaaccccdacabbacabbccbdddcdaccdbbcbcabdabdadbddbbcdcaadccabccbdcabcdbdcadbbcabbddbbbacccdcccbcddaaaddbaddddacbabacddcaacbcccdbaacddcacadcdcbddcacdaddccdbddadabaadacdbdcbddddbcdaddadcbcabcdbbadcdbabbacdabcccdddbdabcbdcacdcbccdbbcdcadddccacbabcdbbdbbcbcdcaacbccddadbbcadacabbabdcdacabbabadabdbdadcdcaccabdacbbcdbdadcbcaacbbadcabadccdbddbbbcbacaccabcbccccaadaadcddbabdcbcdadbdcbbacbacabbccabaacadadbababddaabacaabcbddbcdcdbcbcbabbcdbddabadabdbdcdcbccaababbbbaaacaacacbadaadbcbbcdcbcddbbaacaccdbbdaddbbbbacdabdbcaccaaabadcdbdccaddcaaadbbbbddcdbcdadcddccbbcadccacbddbbdcbcbdbccacbdadadcdbcacbccddacbbdcbbcbddadcabbbbdbdccbbdcbaaaaaacbbcccbccdbacdacabdaadcdaadbbaaadcaabbdddddcdbcdcaacbaadcacdbcdcdbadabdabacdaacddbadaaddaaaaddddabaaabbbacccddbccbddccacdbaadbaaaabdbbcdcbdbccccdcdabadababccaddddaaacabdbcaacbbbacdbddbbbcdaacddaaddbdcdcaacacdccdadaccabbbccbdccabbdbdccdadabcaacdbacabbdcabdbdaabcbcbabbacdacdcdcabcccbcdbdabcbbbbaacdacbadcbabcbdbaacccbacaabcbcaddaddcbaacacccbacacdaabccdaacbaaddadbdcbcccabcabbdbbbbddbddbbcdabccbaadbcadcbcbaddabcabccbdbcaddacdabcdcacabdacccdadaddcdbcabcdcbbadbbcabcbdcdbdadabbbdcccaaabcabbdccbdbcbbabacddaadddddaadababcaaaacababcbadcaddcccadcbbdbdbcccdcababbdcadbdbbaabbaaccadbadcbababaabbdbabdbaabbabadddddbdbccccbadddbcaababbdbdcabbabbbadabcddcddacabadcaddacbbacaaddabbdccaaaabddbcdbbacabaccddddbcbbdaabdbadaccadbdadbdadacbcdbbdccabadccdbaacabdaccbdccdbacccaddabcbddbcacccccabbaacdbcccaaaddaddbcbbbbbbddcadbbcbbadddcdadbdbcbbcdcbdbdcbbbcdbacbacbbdbdcdbccabcbbdbccdcbccddbacaabddcacdbbcacaadbbbbcaacbcbdddaacadbdcacaccdddaadddcddcaacbaadbdacabbcaddaadbabbbdacdcbbbdbbadbaddddcaaacdbdcdbdabbbdcdcdbbccaaabacbddabdabbbadbbcdadccdccadbadbbcbdaadbdccdaabdbbccdababbbcacbdcbcacddcadbcbbadbbcdbccaadbcbccbbcccddacbadacdddabcdbcaacdbbcdcdccdcccacbcbcddadcaddabcbcbddbbbbbdddddbacbbbabadcdcdabadadcacddbccddcdddadcdcaaaccbcbacccbaabaaccdbddbbcdbbdbbdccabbbddadcaadaddbcbbacddbaadcdabcaadacbdacbbdbdcaaabbdaacbcaadcadabbaaddbbdccbbadbbdbaddaccbbbbddbbcdabcccdcdbaabcbabdacacaaabadbabdaabcbddcaacdaccbddcaadbcadbccbdcacacdbdcdcbcbaaccccabcccacacabcbaccbaaabddccbabbdadcccadaaadaccbbdcdbcbaddbdbaabccbadabaddbacbbadccbdcdcacbcdcadcdbabdacdddddabaadcacdbcdddcaccbdaddcabdacaacddbddbcacdbdcbacdcdcbbcdcdcabcddbadbcaccbabdacbadbbaccddaaaccadcccdabddcddddbdcddcadbaddbabcabbcbdbbbdcabbbdbaacaaaabdbcbadbcdbabdbdccadbdaacabdccaacdcdabdccdbcabacaaacdddbbbdbbbdcbabbaccbaabbabcadcccdbbddccabdccbdbcabbacddcccabbcabdbcacddbadaccbabcdbadcbbdcbadddbbcccbbdaadadcdccbbcbdbbbdddbcccaddbbbdccdabdaccaabdadaaccababbbcdcacbcbabaadbaacbcdacbabaddcbbaaacabdaddcdcccdcdddcdaabddbbbcdacddbdabcdcdacabccbcbabccddbbccdaaacbaccbdabdaccaddcdaadbccbbcbbdcbcbdabacaddadcbdcbadacbcabdccddcaadaabccbbddcbcbdbbbbdcbaccacbdbbcbaadaaccdacbaacdabdcccabcdbaadcbdabbcabcbadbbababcadbdabcbbdcccbdbabcaccaaabdaacaadbcdbdcbdacccabdcbcbcbbdababbbabdbdddadbddccabbddbcdabcdcabaadabbcaacbcacbbdcdbaabcbcccadbdadacbbccaabcbaddaaaaaaaddaabcbacacdbbdcbdaadbacccbdbdadbadacbacdacaccacabbbabccbcccbccbcdbaddddcadcaabdddbdcadcdbaaaaddcdaadcaadacbcadbdcbcccbbbbbddbadcabccabbcacaadabacdaaaacdcbccadaccdaaaaabaccbcadadddbabadbaaaadbabbbbccccddcdcbccccdbaabcabdcbccbbdbbbbbcabcbdbabbdbcbdacbdddacbaadaacbdddbdbdcabdbbbdabbaabccbcbabbcdbbadabdbcddbbbacccbdaaabcdddcccdccdadcaddacacbdddbbbacbddbabcdbdcdbcbacbabaacdbbdbbccacdabadadcaabcdcacaabdccaaaabbaacabacdacdcbadbcbdcddadbcddadabdacbbdbbbddaacccaaabcdccabdcadddaccbcacdabcdcacdbdbbcaaaabcbdbcdbcdccdbdddbbaabaababbcbabcaccdaadbbdcbbbbbccdcdcbdaaadcabcccdaccdcdddcdcdcdcdcbdbcaabadbcbadbdcdddcdacaabdacdabdaccadbcdcccbacddcddcaadadaacbcbdbdddcbadddccdbdddaadbadadddabbacccbccbbabbacdbacdbcbdddadbccdbccdbddacccbbabadcdbdadcbbbacaddcbddacccadbccaaaaddcbacbbbaacbdddcbcdacacbbcdaacddbdcdcbdbacdbadbbccadaaccdbdcaddbdcddddbbacbaabdddaaabbcabdaabccddaccbdddcccacddbdaadbccbdadabddbccddccbbcaabdcdcacbdbdcabddaacadccdcbdbadacbcddbadccaabaacaddcbbbcbdbadbcbccbabbcdcdabacdcaabadadbcadcadbadadccaaacdddcddccbddacaaddacbdababddbdaadbdccbddcbaccbbdbbbbaaacdaaccdcbdbddbaabdaaabddbbaabbcaadbdcdbbbacddaddabddaddddaddaaadacabbcbbbcdbddbabdaaacdcbccdbbabddddddbdbcaaaccabdddbabdbbcdcbbaabaaaacbbabcaadaddcccacdcbdadaaddbcabaabcdcdbdcbbadbcbcdcabdbcaddbcdbcdabdcbabbccdabbcbccbdabbcbdcdcadcccacccbbacddaddadbadaadbcbbdbcccabcbaddadaacaccbddbdbbccbcabcccccaaabdddabccbcaaddabddadaaddbcdcdbbadcdcadbccaadbacdcadaaddaaabcadbabdbddbacaaaccbcbcabddacdbbdadcbdbaddbadcdbbdaaaadbbbabddccccbdbabddadaabbdcccbddbdcccadbdbaccbdbcaabbadbbaddbdabdccbdacbaddddbacbcaabbaaddbabcbbdadbadaddabddbbadcbabddbadbabaccbbcadbddbcdacadacbccdadcdddbadbbbdbabaadacadbadcbcccaacabadbdcbdaabacdadbabbbbdcaadccccacabadbcacccdbcbbbddaccdccacabccdaccbcdbdcabcdbcadcccdaddddadbacbddaabaabcdbdbdbcacadbdbadcbacdddbdaaddaddaaddbcbcabddaddaacbaabccdbbdcacaabbaabcdddccadadbbadcbbbdccdcccbdabdbbbcbbdbbdcadadbcdbcdcdaaadbdccbabaacbccadcaabbaccbaacbabdadcaabcdbccaaabddbdcabaaddcdacccabbabbcdbaccabcacdbdbaaababcbdcbcbcddcdabaadbabcccccaaddbddbacabbbdabcbdabdaaacbccdbdcccbccddbccbcbccaadbabadadaddddaabbaddbbcdaddcadddadaadbaaaccaadcdbadacacbbdcdbddabbbabcbaaacbcbabadcabacacabcdbbbdcaccbbbdcddabbcbabdabaaccccbdacadadccacabacbacdbabccbacabcbaacccdccabbcabcdbbddbabadababcdbaaabadcadccbcbaadcdadbbbbdaaccaddcddbcbcbcdddcdccbaddddbdcbccaacbaccdacbcbbbbbbdddadddcbbcabbcbbdabddacbaabbadcbaddbbbdadcadddbbccbdadaadacabcbcaaacdcccadcbdbcdbabaadddbbbdbcbbadacdacaadcbdaaccccbbddcaaccdbbdacccdabddbcaaaaccdcadcbbbdadcdbcabcbbabacccdaadcabcbdcadccbcddabaabdccbbcbaadbdcadbdcdaaaaababdcaaadddaaacbdcaacbaadddcdbcacdacbcbadccccbacabcdbdbdbcddbbddacadadacbbbddbbdbdabaddbaabadccbcddadcbdbacbacacaadcbdccabdcadbbcccdabdbdabadbbadadccaccdacdccdbcdabacbbaddabaaaaddbacaacbdcdacddcbaddbcaaddbdbcabdaaacddbbcbdaadcdbdccdaddccaddbabbccdbccdacbbdbdabadbdcccbcaabcdabcddcddcbbdcbccbdcaadddcbbaaadccdcbcddbdbdbacbaabdbaaabacadbcbcccaaaadaabadabaadcddaccdbbbdcdcbcbabacdbddacaadcbdcaabccdbadcaccccdaaabcccddaacdbccdcaccdabbbccacccbcbcabccdccdcaabcacaccdccddcadadddccdcbdbdbbacccbadbcabbbcaaabcccdcaccdbabdbaccbdacaacbadddabcbaabdabaacabbcdbdbadbcddbcbcaadccabcbcabbdcbaabcabdcaccabccacdaaabccaabbbdddcccbdcacacbacddcabddacdaadcdbabaadbabcccdccaddbadcdbccbacdaccddbccacbbcbaaacbabdcbdbcadbcbcbdabaccdbbbbcdcbbacdbdbbabbcdddadcabacacbbcbdddbdabbbdddccbabbbbbbabdcdbddbddaaaddaaadccdbaabcbccdbdbdbdddbdacacbdaadaabddbabddabcbbcccbbcdcaabcaddddccaabdabbbddcabdcadadcdaacbdbaadbadccdbcdbbaccbbabddbadbcdcdcdbcaaadacbccdacadbbbdaadccbabbdbbcdadadccabdcdccdbcaacbaacdabddcdabadababcccabcabaaccdaabcbcdbbdaaccddddccddccdbabcdddbccaaaadacdaaabcddcdabacababcabdadbbdbacabdbabacaaacdbccdddcbabcbcbcccbbddabbdbbcbadaabccddbabcdbcacbdacdcddcaddadbddbaaaddadacdbddddbcdccbddaaaadbaabbbdbaacbbcdccaaacbaacaccbccddaabcbabbaadbadbdadcbbbcbbcddccbddccccbcadaaabdaaaccbbaabbabdbacccdadacbaaaabcbdadaddbbbccdacbabaaabddadcadaabcdadcdacadcbdccdcbcbbcadbcaacabddcaddcbdcddaaabbcbcbccaddbabcadbcbaacbddcdabcbcbbdbbbdcbcbdcadbbcdbbdbddccdadbbdbcdccbcabcaacddbdbcadacdbcbddabbcbbbdcacbdadadbdcdddcdaddbaacdadcaabaddaaaadbbbbabccdbddadaddaccbaddcbcbdcaabbddaaadadcabdcabdcdbdcadbccbdcabdbbcacdbbddadddbbbbacdddacccbccdacccbccabacdbcbaaddbaadcbaaadcdaadbbaabadabddbcabdabbdaddacbabdbddabbccbbaabcdccabcddbdaabbbcdcccadacbadcdcccccabcccabcccbaccabddcbdbbbadcdbbadadbbbbaaddbcdcdbddabdaccccbaacdabbddadcaccabddadddbcabbadadaabbbbaaadbdacddbabcadadcbadadbbbadccdbddbccaaacadbcababacbcbcaccbaaccacdcabbaaaccdabcbcaabdacdbbdabacbdcdbabbbaacacbcbdadacbcdbabcdacdcbcaadbccbcdcccaadbdaacacacdacbbacaaadccdabbababddbadacdadbbacaadbbdcbadbbdaabacaadbaccbdccbacccbadabcbbcdbccadaabdcdadadbcbcadccaabdadcdcdbcaaddbbbbdddababaadbcbcabbbadacaaadbdabcdddacdaacbbbaabbccabcbdddcdcbddaabadbcaccdbdbbddddadbabcbcacccbbddabcdbcccddccabadbdcaabcacbccdbabbdbaadbddcddcbbcbbababacdaaacadcbcbccadabdadcbcaabbbabdbacacbbbccdcccdbaacaaabcdddbaaddacccdbdaddbcdaccbcdccbbaacaddcbbcabaaccdacabbcaddadbabbabccbcdbdadcbddddabccccabbaadcdadcdcaaacadddcabadbcbaccaadcadbcbaddcdbbdcaabcacdccaacdcdccddcabbdccadbacbabadadbbadbaddbbcbadcdadadcbacadaadcabaadbbdabbaabcbbaddcdbaabcccbccaaddcdcabbccdbbdbddbcccdadddbdbddabbbcccadacdcdaccbbbcabbbadbdadbcddddcadadbcacdcdcabbbbccbccdcbcadbdcbdcadbcdabbcdccbdabbcbabadcbdaabdcacadbdbbbacabacbbbcbdbcabbcddddbdddaddbcbbaccddcbacbaccbddbbdadabddcaaaccabdbcddbdabbccddcccaaddbabbbcbdacabddbaadaadadabaccaacacdadacbbcdbacbcadbabcdccbbdbadcbdcaccadbadabacdcbabaddcbcbccacadbdcbbaabcdbcdaacdadcabcccaaadbadbbbcbddbaddcaccadcaccdacbadcbadcaabcbbcabdbbcbbacdacacbbcabbcbbcbbcdcadbbddcdaabbcddabbadcdacbdcbbcbbadabcbdcddcbcabdbacdbcaadbbbdbdcbabbdcdaddabcaabaacdbbcbcccbaadacbacabbcdcccabcddcaacdcbdaadbabbdbcddadadcbdbbbcbcdbaaacabbcacbdbddcdbbcabacdababdcddbdbbabdbaabacaaabcbcbadcdbdbbbabaaddadcaaacdbabbaadbdadbcddaadadaaddcaccddbcdbbcbcbccbcbdacadbdcbabadbbdacdbbaacbacabddaaccaacbadadadbaddababcdcdbccddcdcbcdbbdcdacbcbcbbdcaaaacbaaacdaadccabddcdbcdcccccdddcdbbcdbdacbdccbacacbdaccbabaabbccbddcbaddbbcdbbcccbdaddadcbbcdaddabddbadacdacaaacbccbccbbbaaacabddacdaababdbabbdcaaaaaddadbbbacdadbaadbacddcbdbcddcaabddddbbdccddcacabcdcdccabaaabdcaccdaadbbdcabcbcbdbaadcbacbbdabdccdcaacabaaddccaaacbddcaddcaabcadccbcbacaccdbcdbadabcaabdadbacadabcdcccbcaddbbbacccdbcabacbcddddcbbdacacaabaacbbbbbddcbababddadbbacddcadddbabadaadbcbbcbadaadbbcbdbbcbaddabdabdccbcaabbaadbbbddabbcbdddbaccdbadbddcacddcccabbadbdabbbbadcbcdcdcbdaccddcdbcbcdbccccabbcddabcaccddccbdddcccdbdbbbdbcccadddbbbbbcacbacbaabdcbabcaddabacbadcbcccbcaaccbcaacadadadcbdddbdddadbcaaabccadadbdacabbbcacbcdcbaabbbacbababbabcdbcaddcbadbcdacdbcccadacddcabdadabcdacabbacbdcacdbabcacdcdaddadacadcddcaacdbadaddcdbcbcddacbbacbddccbdadcccacbacabaddcaccaddbcdbccacababdbcaddabbbbcbbccaacbbdadcdaabbcacaccdcacbbbcdcaaabdbadccababbcccbbccdabccacbacbacbaaabcdbacdaabddcbcaccbacabddabbaadbabcbccbdaacdcdbbcadbbcdcbcccdabccddcbaadbadaccccaabdabbbbdbaaadacbcccbdaadcabdabadcbbbddccaacdcabbadacdcabababbababbbaabaddbbcbdbacddbaadabbccddccdbddccaccabddbcabdbbdbdcadbadbbcdcccddcaabdbdcbdcbdacaacaaacdcabdbbbbcadbcddcbabdccabaaabbcbdaabddacccdddddbbaabaadcbdacbbcbcacaccbbccabdbacabccadaababccbddcddccbcdababcdbddccababbcbabdbccdcadcadaddccbcbcddbadaccbaadcbaacadcbdaddbbbaddabbdabbdbdccbaaabbdadcdbbbdacbadadbbbaadaddcdabadcbdabddbccdbacdacaddccaaabdaccaaabdaaaabbdabdddbbdaaacbcbbccaababdcababbdabccbccbbccabcdcbbccacdcdbcdccdbadaaacdbcddcabaabcbbbbcadcbadbcaacabdcaabcbbaddaadddadbabcdabcdbdddcabdcccccaddbccbaadcaacacbcbbabdcbccdccbbddddbabdacdadbbdbdadbacdcbcbddcabbdaddacaaddadbdddbdcbdcbbcbcccccadacdbddaaddcdaaacbdbddaddbabbcbacbdaccbccaadcabcbbadbccccdbddaddadbbabbccbaabacbaabaaccccbbadaaadadacdaacbdadadbabacbcbdddacaccccddaaccaaacddcaadcdcdcabddbaccdbdbabcccacbacbacbbacadaabcabbddcbcaccdbbddbbbcdacbccdcabbadaaccadaaaaacbaababccbbadcdccdacaccdcccabddbbaadbdbcddcdbbdadbccccaabacdbbacaacabcbdacccdbbadddbddbdddaabbdabbcbcaadadddabbdadbcadabbaacddabadbbdccbdcacaabacdcdadddcbbcbdcaccbacabddacdbccadbbbdbaddbabdaccdabdaabcaacdbcbddcacbdaddcaadddaddaccdadadacdaacbccbabdbbdadbaccbaacadccbdadaddbacabbdaabccdbccadcabcadbbcbddbbcdcbbacccadabdccddccdddbdcdaddbbcdcabbaaaaacabaaaadaddbaaccccccdabdddcddaaacdccddbbbadbacccdddacbcccaabdabaaccdbbaacdbccbddbdaaabbcacccbddcdcdbdaacddbabdcacbbdaddcccadcabcccbcccacbacaabcacccbadbdadcdaabbaacdbcadbcacdabddaaadabdbaddcdacaaacabacbddcaadaaacdcdcbadbcdbbdcacdabbabbcbadacadcbcdbdcbacbadababbcaabaccacddbccbcbbadbdbabacddbbcabbabaaadadddcdcdcbcdccaadccabdbcdadbbabcddacabbcbdccaaaccaaacaacdbbddcdacaddcbcacdddcbbabbddaddadadacddcbdcddccbdccdaddccaabccdbadadccadcaccddbbcabddbdbcdddddbdcadcdacbabaccaabadddcbdacbdbcdddccabcddccddbbcabcdbbcccbbdaabbcabbcaadacdbbabcdabdccccabcbddbdbbdbdbadccabdaabddcabdabcdaabbadaadbdbdadbcbacddbbbababbdccabdaaabbbcbabdaadaaacbabdaccaaacadcdcccabaddccdbbccacabacbdbadbbccbccdddccdbcdcacacadaabcdadccababbaaadcdcabdacadbbadcaabbdcddacbccaaacccccbcdbabaddaddbdbddabdabadbbcabadacbbabdacbccdbccbbcbdbdccbccbccaccacdbdabcbacbcacbcbbcbaaddaaaabcababdaabbadcaddcaabadabaaccdcbdbbbacbbddacbaddccdaddcbadbbcddbddcaccacadacdbddaadabaacaabddbbadacaddddcddddddbcdccacaabbcaddadaabbadbcdabbccccddbbdaacdabddddddababcaddcddacdcbdabdabbccbbcabaaccdcddddcddcdbabbacbaabcccdccdccbcbcadbcccbcddaccacbaabacdbbabdbbbadcbdbbccdacdddbdbcdbdabbacdabbccacbbdbaabcddababbdbaccadbaacbcccacdcdddcbbcadccaadaabbaadacbdcacbbdaadacdcbbaccccacbaccdaadaaddbacbaabddbbbcacbbccbdbccdbadcdbdbcbbacbcdcabdbdbbcbcabcbdcbacaccddaaccdccbbddbcccccaaddaaccccaddaddbbdbacbbbcbadacbdbadcbbbbacdcbdacabcbaabcccadadacadddcbbbacacbcccdbdaaacccaadadadabdcccbcadbdcadadacaacabbccbdbbcbdbaaaacbadddcbddbdcacacbcdbccabdadaaabaabcdbbabddcadbbaaaabcacacabadabaddcdccdabaaacaacbadbbbbcdccccabbccbcbbacdcacacccdbcaaddbbbbddcbadddbaaaaadddabdccbbdcabccbcddccccadbbcdaddacbabaabababaabbabadbbbbcdacdbbaaddccadadcbadadabdaadccadcbbdacbadcdddddaacbdaabcddadbbacabaddccddbbacacaacdccddbddaadbbdcaaadccbaacabbbdacdbadaddaaaacacbcdccadccdaacacdaddacabadcddddacbacaabaccdbaddbaccacdabadacdbbabddcbcddbaadcbbbcaccddaccaddbadcdbddcddcabcbddcccacaaacddcbcdabbadadacabbaccabbcdbcccbcbccbcdaddadbccddbccacddcabaaccccddbdccdbbcadabcaaacbccccaacdcdcbadaaccdbdcdbbbcbaaaacadbddbccbcabbbcdbaabccaaddcdcbcddcbcabacddcaccdbcbdacdbdbdbdccbabdacdacbddbabacabbbabaababdacbaddaacaaddaacdbdacccbcaadbdabddacbdabadcabdddbdccccddabbbaaadbcabbaaaaacdababdbbacaacadabccdbaaabddbdbcdadbccbabcdadbdaaaaabbacbaccdbcbbbdccdbadcadddaccaaabbcccaccdbbbacadadcdbbcdccbaabbddcbcacadabbabdcdcddbcadaaadaaaadabdbacadbbbcdadccaccadcdcdbabadbaccbabababbacacbbbdbabaaadbdbbcaadbccddcadcdabdbdacbaaabaabdbdbcacacbcadabacdddbcabbbbcccaaccbacccddabbcdacbcacdaadaaccddcaaaaddddddbbcdcbdbbdaaddbaaaaaadadcacdcddbdbccacbaabbccdaaabccaddbdabccdabdcacdccabaccabaccabbcccabcaacaaddbcacbdbdcbdddaadaabaccbbacdbcbabcddacbdabdbcaaddaabaacbdaddacdcccaaadcbccbadabcdaccacadaccaabdccabbbddbadccdbdbaaddaddadbabaaabbacdcadbaaaadbddbdaadbcbbbccacdddbaddacbbdacbadbbaddabdbaadaabbabbccbcbccddbaccdadcdacbabacdcaaaaabdcbbbdbdaabbbccdbadacbbaadbaddbbbcadcccbcbbabbdbbdcabbadbabbacadcccaddaacaddbccccacbbdaabcbccdcacdddbdbcbcddcbbaadcadcdddcbdbcdcaddcdddcbadacdabcbaaccbddcddcadadbaabbcddbccadbbacabbabcbadaddbcddbabccdcaadddaaaddcadccccadacbcbcaadbacbbcabdaadadacdacbaccdbbcbbccdadddddcbbacaacdbbcddbcaccaacabadacabbdcaabbbddbdcdddbddccdcbbaacbcadccddcbacdaadbdabdaaacddcdcbcbdbbddcbdccaabcaaacacaacdcdabcbcdcdacdbbadbacdcdcaccdcbacccdbacdbbcccddacdaacdaabdcddaadcdcddbbbddadbddbaabcdbcdbabaaabdbbacbadacbcdbcaacacbacddcbabdcbcddbaccccbbccddbcbcddbcdcacbdcaddbadcaccbddadcccdccccbacbcbbbcbbdbdddcddaddbcccdbdaccdbaabcbdbddaadbbcddbcacbacaaccdddcddacbddacabaaacbbddaacaababbcdccaccbccaaaddbadabadaabdabdcddbbacacdaababccaccbcbbbbbdccddccbddccdadcbcdadaabbcadabbabdcadacccddbaadcbdbddacbdcbbdbcbdddabcbdbcddddcadabbdccdddcdcbabaaddcbbbcdcbadbcbbacdbaaacababbccbcdcacddcadccccdbaccadcdbdbdccaaadcabdbcbddaccbacacdcadabdbaadadadcacaadbbaaacdaddcacdaccdbbacabdadccbdaacdbdcbddbcbaaaaaacacdcadcbbccdbcdcacdcbaadaccbdbadcdacdcdaacabbacdabcdcccddbaadccbabdaaccabacbccccdbaadcbdcdcddbcaabbddacdbddcdaaacabccdadddcdcacbabbdabdbabcadddbbacdabacddabcbbcdcdbbccaaabbcbabcbabadacabbccdccddadcbcaddbacdccbdcdbaabddcadacddadddbcbdabcbcbbcbccadaddcddabdddcaacddbaacbbbbbcbbdacbbbdddcbaddabdccddbdadbbabaddccacabdcabdadddbdbdbadaabdaadbadcbdbbcbdadadbbbcbcbbbacbcadcdbbabcacbaddccbbcdaccccaaaccaccbadacaaacdcadaabcbbabacddcbcbbabcdbdccaadddcbbcdaacadcdaaabaaddadcacccbadbbdaaabcacaacadccbbacacbaacaccbdbdbbaaaccdbabdacbdadcbaddccadcccccabcdcdbcbbdbccbccbdaddbdacbdbcaabcdabbddcbbadccbaadbccaaaccdacddaaddddcbddadcaacbbabbcccdacaaabadccbdbccbdacddbbaabcdaadacadbdaaacabddcacdabcccdacacadacacbbbabcdccaacdbdbdabbdacabdbabcddbbdddbdcaacdcabddbcadccdbaddbdcbdacdacbbacbddbaddcadabccadcdbbcddbdaadaccbaccaccabadcaaddbcbbccbaaaaddbcaaacaadaacdbbdcaddacbcabbcddbddbbddacccdcbcabbbcbaadccccabdcbbccadabdabcdcaabddacdbcadddcbdccdbbbbbaaacadaadacaacddadadcdbbacbbdbcddbacadaddbdbddcacbaabcadcdabadaabddaccdbcaacbddacbaabbdccdcdbcbbcbbcadababcadaadddbcddbcbbadacaaaddcaddddbddaddaaccbdbadcbbadbaabbaadacdacbcdacdaddbbcaabbacbcccadbdbcccaaddbaacacbaaabdbaddaaadcacbacdcbbaddbbacdbbcddbbddbdccabaaddbdabbbdaccacbadbdcddabdcbbcccadbddcaddbdaaadbbbddbbdcbdadcbddaccbabdcdacdcaaccaaabcbddbbdabddbbddcbbddaddacbccbccaccbaaccaacbddddaadccbcadddbbadddddbcdbaabdddbdccbdaaccaaadacccdcadbdcbdbaccccdcbbccdddaaacdbdcadcccbaaccaaacabaaddbdbbccddaaacdbcccacaaacaaddccbbbacbcbbdacaadddacadaddcaadabdadcddbdabdaccaacdbcbaadacdbdcbbcbcccaaacddcdbbddbacdaccdcaccddbcababddcdddaacaabbbdaaaadbbddacbadbdbcabbbabddbdaccbbdddacdabaddbdbcaaabdddcbaababdcbbbcbcdddacbdcdcacbccbbaaddabadddcacbccbaaacbaddcdabadddbadccdddadbdbacaaaddbcdcdcdccabcccbadabbabcadbbbbdabcdbabdaadcabdaddbcdaababddabcbbcbdccbaacbbbbdbcddabdaabbdadcdbccdccadbbdacbdccdcbadabaacbbabdbbabababcacacaaacbbcccdcacaadbdbccaddabbadadbaccbccdbcccddabddbbcdbdcaadacdddddcbbacbcccbbbcabdabdcbbcbbcccbabdadbacdcbacdcccaadaaccaabbdddbdacbabdddccdbaaacaddaaaddaddabcbbacacadaaccdadccbddbcdbcbcbddacbdcabaddaacadbadbbaadcacbdabdbbbbacabdddbcaabbcaddcdddaddccddccdcbddacbdaccaaaadcdcbddddbaddbbababbcdaabadbdcbacccabacabadddbdcdcbdccdaaadcaadaaadaaddcabccabbadccdbdcdddaabaccdcababcadbdaddaadacdaacdbdbbadbbbbaabbcabbbbaabadbbccbdcdbbddcdcbdaabbdcacbacbabbccdacadbddbacadbdaaabbbbabbacaadbbdaabbadcdcabdbaccbbabddbbaadbaaadbbacbbaccacadbcccdccaadddddadabbbacadacaadbcbaddadcbbabacacdddbccaaabdcdaddaacddabbbcddcdbabcccbabdcdabbbddabcdabcbacaaddbcdddddbbdadabaaddbbabaaccdadadbdaacbacbbcbaacbdaabccbcacbbbdccbccccabbaaadbccbbbbdddbadaccabacccccdcdaccbaadbcbcabcbcdccacadadaddbdcbcdabcbabdbbdacaabddaabdddccaabdcdccdadacaddbcccddccbcbcaaadccbbbbacbabadbabdcabacdabdabdddbaddacdbdabbadbdacdaaaccddcdbbbadbdcaaaccbdaabbbbadbadbbcaddadddcdcdcadaaabaddcdacdbbbbccbcaccdcbdcabaacabbadbabcaddcccadcadddacadaddbacadcabdbddaabaaccadccabbdbabdcdcadaaccadadcccdddbbbbdacccbacabddbbcaacdaabdacddbdbccddcdabcacbdadadacdabdcdcbacdbdbacdcaaddaaacadaabcdbaadcaacadcbdcabddacbaaaadbacaccadbcbcbacccbdabdabaacbbcabcdbaddcbcbdaabcddacdbcbacdadcddacddcddcbaabdbdddccbdaddbddccababbbdcddacdacccaacdccadaaadcacccbbadcbcbbdcdcdcacdacbbaccbaadccdaccbddcbcaabccdbcccdbbbddacacdabbadbbaddddacabbaaddbacccbcccccaddddbcabdcbaabadaadbbdacbbdbcacdbbadbabbdaadbdbbcbcaaccbddbaccdddcdcdcbcdbbbcbcbcdaddcbbcdbdbdddbbbbcdcbbbadbbadaadcaddbcacdcbbabcadddaaadbbcbcbacdacccabdbdbdaddcdddaaacaacdacadcbbbddadababdadbaccbaacccbabbbabcdacadccadcddbbaacdcbbdccbbbabdcbcacbbabddbddbaddadacdcacdabdaacadacabbaabdddbabbbadbcddcbaabaadcabacdcbcbaabccadcbaacddbabcbddaabddadabaddcdbabacbacdbcddbdacdccdcdababbbbdcccadabbbcabcbcaabdbdbcaddbbacacbccdddddcbbbaaddaaabcbcdcdccdccaaccbadccdbaacadddbadbdccabaabcddbbcabacaddaacccccadddbaabdacbdaccdaddbdadabaccddcaaccbcbabddbcdccbdaadbcddadbbababcacdabbddccacbccbabbabdcabddabbbadbbbbdacabaddaabddbadccdaaacbcbccadbaddbbacdddccacdcddaddcdbbcddbccabdadbbabcadadddddcdddcaaaabbddddbdaddbbacdaccacbccdbcddcacacbbcbbdcaaaccdcacacbddbcdcaaadacdcbdcbabdacacbdcccbdddacadbaabcaaabababcacddbaaccddbadbddbabacdadbdcddaaccdcaabacdaccdaaababddaacdaaaacaccadccbbccdbbbbbaacacbaddcbabdadbbbbadacbabdbbcccaddbadccdcbdcbcdbabbaabcbacccaabbcbacccdbbbcccbabcccddacaddabaaabddadacbcbaccabcddccdbaccacbbdddcbabdaacbdcddbdcdccddcbbabaaabaacabddcaddcdccdbcdcdaddcabddcadbcdbcdddbcdbdbcdacbcaadcddbabcdbbdbacabbcdacacbbdbcbccbacbddbcccbcaabcabcddadabcacdcacccdacaabadbcccdabdcbbabcdadcbdbadabaaacadbbabcacbbcdaddadddcacdddccbccabccabadaddcbcddbcbacbcaacbddcbcaacbabbdbcbaccdaccdddbbbcadaddbcdbcaacbcbbcdaababaabbddbcaaaabbdadcbddadbadddaccbccdbadbabaddaacabbdacccaaddbacbcbcbdbdbbabbdabcaabaacaababcccdbcddabcbbddddbddbcaadbdbddadcabcddadccaadaaadcbbabcbccbbccbbcdbacabbbddcbabbabbbbdcabaaccbcbdcaccbdbabbacbcccdbababaccaabbcdbbadddacdaababccdddbacdbcacaddcaaadadbccbabbcbddcdccbdcbbacaadcdcccaadaddccbdcdbdbacbccadbabdddcdcacdaaccadbcbcdabbcbbcaaabacbaabbbbbacacdbbabbaddcbcdbababccbacdcaaadcaccdbcaacdaccdcbacaddcbdabadbdabdbdbcbaabbdddcdcdbcbdcdaccacbadcbdabaadcdabbbccadcdcabcdaacccdbddaaabddcdbddbcbddcbacadbccbbbbccaaabddccdaddacdccdbccdbdacbabbddabbbadccdcccbbbacabacccdbadcadbcbbbbbcbdacddacbbadcbbddadcadcbbbbadddadbbcabbdcccbbadbcbcdddaacdabbabbcabdbddddcacdbbdabaddadbcbdbddcccaabbaadabdbbaaddcdbdcaacddadbdbabbaacaabbdacadabacdcaacdcaccccdaacdbadddabdbcbbcbcccdaadabcbddbadcacacbadcdbcbcacdbbbcabbdbbdbcbcbadcbbdbcddacccbddddbaaadacbacdcabcacbabbcdcdbcaccdbbdadabcaaabcccdabdcacdbaadaadadddbbcbccacccbaabcbccdddbccabbddcccaabbdcbbbcbadbdbdbbacdbcbdccbadacbcccdcddadcddaccadcbcaddbbddcbbaaaacbdacadabbaabaadcadcaaccaaccdaccbbbbddcdcbabadbbabdcdbdbdaadcdcbdbbaaaaaaacadabcddcbdccbcbccdbbaadbdddbbdbcbdaadbbabaddbdddcdaadccbdaaaaacbabdbcabddbacaaabcabdddadacbacbcbdabdbddaacbdadcdabaabbcbaabddbddcbdddacadabbbaacbcbaccadadbcbddababaacaaacbdcdcbcbbaddcaaadddbbacbddbabccdcddcacccadaacbdadabaaddcbdccbcbcabcdcadbcaddbdddaaaccddadcbabcbadbaaadbcadccbdababcabbccacbcabdbcddcadacadadbcbccbcbdaaadbadcbbcadbccaacccdbcbdabcacaadbabdcdccbaadacbbdabddbbcccbcdddbabbccbcaaadcbaccabdacdcadbabbcababdbbaaaddcacaacdddbbdcdacacddbbaabaabaaabcbcdcbbbcabbcaadacacaacdabcdaccddbcdcbddcccadadbcbcbcadccbdacbbbcccacdaaacdbddacccaacccacbddaaabbbdbbdadcaaacbacaaccdbdbbaacbbbacdaccaacabbbbbbcaaaababbdbabbddddcbcbdbbddbdccbcaabdaccbdcabbdabdcbcaaddcbabddddbcdccaaaddbddbdcdbbddabcdcddabddccbcbaccdcdbbbcbcabdccbaabcdccddcdbdabcacdaccaaacbdaabbcabbcacbbcadabdddccbbcbdddbaabcbcacdbdcbbcbaabbbdbaaccaccabacddadbccdddcabbabcababbbbcabdacacdbdbcbbdcccccddbcdadcbacdabbbbcdbdabbcaccbadbdbcbbbbcbadacadcbaadbcbcbabdcaacdcdcbacbacbaacbacdbabccbcdbbdbdcaddbbbcdbcacdcdddcbaadbcabbcabacabcaabcddababdbacdbdcddbdacbdbdbbbcbadaababdaaacaabccbdbdcdcabccccdbcaccbccabcaacbbcccddbdbbdcdcacbaacdaadcdcacdacccadacbbddccddcdacdbdcaddcabddbacccdccaacbacdabccdcdbcdcaabcbcaadabdccaabdccdddadbcbcddaaccbbcccdcaaddaacbbdcacbbdaababacabcbabcaccbdbbbdcbbdcbdcdacccbaaaaddbdbadbcadadacdccbbcbdcdbdccbdadcdbbbcabacdcdbcdcacbabbababcacacadbbcdcdadcddbadbccacadcabdadcbdcddddacabddaaaaadadabccdcdacbcddddabdcdcacbcabbcaabdccdccdbbcbcbbbdaaddaddaacadbaabbcbcdddbbbbabcbddacaaccacadacbadcdddcdcbbacaaabddbdaaddddcccbababaaaccdacccadcccadcddbdcbcabdaadbcdcdadcccabaabdaaabcacabdbaabacadcdbccbadadbccdacbbbabdaabadacdcdacbddcbcbacacdbccdccbabdddaccbcdaabbbbaabaacdbbcaaabdcdacabccabcaddbaadababddbcbacddababbdaccccdcdccdbaadaddadcbcbccdacbbadcbabbdddadcabadbadddaabcabcbbbdbabccddbdcaddbdabaaacdbbbcabaccadbdaddbccadabdcbcdaabdcdcaabdccdaabdabababdadbcabdacddbddbaacbcccbaadbdcdacbddbbabdadbabbbddcdcbaaaadbbadcbdabdbcddcaaabbdacddadbbdbbbcadbbbdadaadcabcbbbaccababbccdcdddadaddcabcacbdddbabbddcdbbbdbbacbabbbadbdcbbbbdcbbcdacbabdcdcdbbadddaaabacacaaaabaabbabacdbcbcdaaacbabbbabddbdcddcabdacbadbdacadddbbacadccdbdcbaacaaaadacccbccaabcabcacaddbbbdaccbdcacdcdbdacccdccddcdacabcbbaaadbcacaabbcbcdbbdbcbbdabdbadbdadcbaaddbbddccdcaaadcddcacdabdbddbaacbbddcbacbabdcbadccccbabcabdbabadcaddbcccbdabacdcdcbbcbaddadacaadcabcccaccadddddccccbcbcddcbddcdacbbccabdadbadbcdcdcbabbcaaccaddbcdddaccbbdcccadcadbbacdcbdcddbabbbccbadabcbcdbcbacacbabdbdcabaddcdcacccdcddacdbdbccccabaccdbddaccadadbdadabccabddbadddddcccddccacdbcadadddbccabadbaacabacdccbacbcadacbbcdbdaacadcadbaddabbcdacaddcdbabbaabaacaaadaaddaacdccccbbacdadbdcbbdccaddddabdddbbcacdcdcddcaabdccdabbccabdddbbcbdcddbbabddcbbbaabcccbdaabbbdcccbbabaadbadcadcbacacdbbaadcbaabaccbcdbbbaaccbdbabdbcbacbcaacdcdbdabcadcdccaadacadbcacccdbcbbcbdcacdcdccabcbccbabdbccaaddbaacbbbabccdbacdadcbacbaddaacbbdaadbdcabcacddbdcdccdadabbcabadcdabdacadacdccdaabcdcccabbaddcdcbdbbbbccdacdabdbdbaadadccdaaccddacdabdcbbddbbbacdacdcaadabcabcbcdababddcbdbbbbccccbdbdaaacccadccccbcdcccddcccdcadcabdccdcccccabbddaabcbabbbdadbccdbadcdabdcbdbabbdddacdaddadbbdbbcabcaaabacddadaadcabadbcbdddccaadbddbacbababcacdcddddabdbccdabdcaabdabdabacbbcbddddaacdacdcbdcacbadcacdcadbdcbbbdbcbdabdabbcddcdccbaaacaddcbccaccdcdbacaaaccbdacdaadddabcdbaccacaadaaaddadbdabcdcaaaaccccaccadcdccddcddbcdcdbccddbaccbcaadadaabcbdcbddddbddbdbaacccbbbcbcccdddabbadcbdcdaccddbddcddacbaadadbbdbdbcccabcbabcbdaabbcabadaddbbdcdcbbacdbbcccadbcaacbcbacccbdbcbaacadccdaddcdccccbccbdacaabaaacdcbbacccbadcacdacaccdbccbdabaccccbcabbcacaabcdbccdcdbcdbcbbdcdcdbabbcabbdbbbbbcbdbbdabcddaaddccabaccabaacdbaaacacccbdcccacccdadbaaadadabcbdacddcabacdbdbdddbaddccdbababbdabcdcdcaadcbabcaaddbbcbbaadbbdbdaccdbbccadcddcccdbcbbcabbcadddabdcacaaacdbdbcadacddbbcdabdbaacaaaacaaadadadcacbbcddbdcdbadcdabbdabbcaccbdcbbdabdbaaadacbadaccabbcdcacaadadbacabacbabbbdbddbddadddbccacbbadbbcbcccbababccaddadcbcdbdbcdbcbccbdbbdcddbadcbacadadcbabbdcabcbadadbdbbbccddadddacbdddabdccbccbddaabcbddabcdbdbcabdccbdadbbcaabbdaaddbaaddaccdbbadbacbcbbccbddbdaddbddaabacacbbdbcdcabbdcdbbcbaaababddcbdaadbbacabcbabcaddadccacbdcadadddacdbbabcacdaadcddcaadaacabbbddbbacbcabdbaacbabbbdbdcacabacaddbdbcdcadcbdbabdbdbaabbadbbbccbdadcddacaccccdbcadbbdbccbbaaacdacbbcabcbdcdbabccdddcabcdabccbcddacccbaddcdccadcbdddccdaaabbaaadadcddbbcccdbcbaaacadacbacadbadaddcdcaddaabbbbcbcccadccdbcddacbbbabdbacabaddbaaacddaccbcbdcdcccbabdcdcbbccdaacdabdbddabdcbcbacaaaacbccacccbdbbccdcdcdddcabdbbdabcdbbabdcdbdcabdadabbbaaadbbbbcccbcacadbdabaabbbdccaaabccccaadaabddbccbcdccbdccdcaacdcaacccbddcbdabbdcdcaabdaaaadddbdccccaddbcbbbacccbbccadbcbababdabdddddcbdbbcbbcbcabacaaddccaaacdbdbcddaddbcddbdbccdbdcdacdcaacbaccdcaabcbdcbcbdacccbbbcabbbddadddcddbdaccccdbbbcccddbddcbdbabcbcbdddbadabdaabdabaacacccdccdcaccbabdbddabcdccacbdbdccdaccbabacaadbdcacccdacbabdbddcbacabcddcddcdccaddbabaabcbacacddacdddabdcaaadbcbcacadcdabbadbcadbdbcaaabaccdabcbbdccdbacdcbdbcdacadcdabcbcbabcaddddcabadbcdadddbdabbaabaabcaddbabdcadabaabaadccabacbccaaaadcbbbadabbabbbcdadccdadddcdcdbccdbdcccbbabaaddbbabdbbbcabbaacaccbbbddbcdacbbbbcaadbaccaaaacbbbbcaaaacbdbcbaddcbbdaaabdadacbadcddbddcaddddbbcacadccaadcbaadccbdabcbbddcacccbaacdbacadabbccaddddbddbdccbabcccdbcccbbabacbbddabdcabcacddddbddcccdddadcccdaaabbbddacbcdbdbbbdabbbdccaabbdcbdbcacdacacbcdacbdccbcddaccaadacccbbdbbbddcbbdacbacbcdddcdacdaadbdbdcddcadcacddcddbdcabbabdabbabaccccbbcbadbaadbdcbddcddbacdbcddcbbccdbbadaacccabcbcaaddcdaacaadcadadccbbdcabbcccadadadadbddbbaccaccbccbdabdcacdbacdcbacbdccadddbacddbdaccaabbadacbcbaabdabcdddbccbdcbaabaacddaabcdaaddccbacddaacbbdabbccdbabbcdcdbbaabaabbaacdcabaddacdcddddcacacdcbaccddccabbbdbacbcdaccddcacacbacddabbabcdcaabbccdadbbbcbcdcbbcadcdbbcaadbadbbbcccccbadbdabacdcabadcdbddacacccaabadaadbacccdabacadccaadbbadbaabbabadddabbcdcdddbbdacdccbbacddcbbbdddaddcdbcacbccbcabacbdbccdbdaccbacbcadbacddcbabbdbdbbcbcdbbdadcaadbacbbcdadddbbbdcacbadbcdbadbdcbcabbccabcddbccaacbbcbbccabadbcbcbbddcdcabccddbaabccaddcdbadbcccbacbabdaddbcbaadacdaabdcdacabbacbddaacbdabbbbcbbdccbadddbbbcddcaccaacddababdabcaccccddccccabbcdbcdacbcdbddbbbcdabaaacddabadabaccaccdcbbcaaababcddaacabbacacaccbcbaabbadbaaaacbddcbddabbcbaadcdddbbbdacbcaababbdcadababdcaccbbbdbaabadaababbaaaccdddcaddcadacddccacaacdacdccbababcccddbaabcdababbcbcddbcadcbdcddccdcbbbccabbacacdbadaccdcacdbccbdbbbdadcbbcadadaddbadbddaabaaacdaaadbacbbbbabbdccaacaddaadccbbbcabcddbaabdcdcbdccbccaccbabbbddabaabcbcbcdbaabababbccabbdbbccdaaabddabaddccccdabcaaadcbbaababbbddbbaddabcccbcabbdcaacdcbaaabdbcbbddabbaaabbababcadbdbdddbdadabaaadbacbcacdaccbdbdcbaaadacdbbdddddaadaadaacdaabbdbbdcdcdbdaddddcdadbbddbdcdaaaabbbbdbcadacaacddcbbdddccaddddccdbcbcccbcddddadbcccbcbaccbcaabdabdadbdbcdbdbaaaadbdbbdcaddccabdddadbaddcadaddccbdacdbaadacccbcaabdaaaaababbbddddbbbdcbadbbcbcdccdabbbcaacdcbbcbdcaaacbdccdcaaacbccaaabbbdddddcdcbdadddccbcbbaaabaabddbdccdbdadccdbacabbdadaaadcabadaabbbbaddcbdadadddacaaadbdcbaccbadaaddbacacccabcbaacabdccccccbdaaadbcdbdcacdcbdaabcaddaadddbcdddbbbcdabbcbddadadcaaccaccddacdaabbcdcadddcddcbaacdaabdacbbaadbbcdabbaddbabaddbdccdcccdbaaacbcabbccbdcbddabdadacdabcbcbdddaabacbcddccbbddabcddbcabcbddbbcdadadccacbbbcbdabddbbcacccabdaabbcdbcdadabbbadbbcccccddbdcdcdddcabbabbaaccddcbcddbabbcdccadbdabcdabcdcaddaacdcaaacdcccdcddcdddacdccacaddadaddbbdcddcccdaadbcaabcabbcbbabbcaacddacadaabbbadddadbaacbcaadacbdabbbbacddcadaabdbaccbbaaccaabadcbcdddccababdcddabcdaabbcbbcadacbdcababbdaacdccbddbcdaabcdabbaaadcacccbdcbacdacdadcabaadddbbcabbddddcdcaaadaccadddcddbaddadbcaaabcbaaabcbccbacbabaabaddbdacdcccddbdddbadadbcadcdccabdddadadbdccbcdbbadbbaddccabacdbbcdaddcabcaaddbbbcdaaaccbcbbaccadaabbacdbbcbdaadbacdbcaacadbbacbbddddaddabdbbddddaadccdcbdcacbaadbccadbdaabbbbccbcbdbdbcbbadcccddcdcadccbddaaacbdadccbcacbdbbdadbbbbbbdadcbddccddbdabbbcdbbaccabdcabadabadbadbdbcbbbadadcccbddddbccaccaadbccbbadbdaacadcadcdcacbbbbcacdcaabddabbcaadcababddbdbddabaacdbbbacbcbdcbdcabbbabacbdaacbaacaadacdaccccbbaacbacbbcadbaacaccdbdacdcdcabcacaadabcadddacbaadabdcadbcbacbbddbdaaccbbdbdbacbabbdaaccdcdcaaaadbbcadcadcbdccaacbcbdaccaccdcbbacabbbcacddcbccbaadaaabbcacabccabbdbddaddbdcbaaadbcbadbaccbcbadaacccbdbdaadbdadbddccdbcccadbacbbdaddbcccbdccbadddbcdcdcababdddaabdabacadcbdbbbaddbbbbbbbcdcdbcdbcccddcdbcdccdddcacccabddcbbadabcdcdcbcacdddbdbbabdcdbdaccbcdddbdccbacacdcccbcccdcccbbbcdabcdbdbdcddacacddcacdacbaadcbdaadcdabacdcabbacadaaccbacdaacbaadddacdddbcccdbabbccdadcababdaacbdbbaddccbaadcccacdcddcccabbbabcdcbcbdabbbcdddddccccacdcdbbddaccdabbcbbcbdcaaddaabbdbcdbbbcbcaaaacbacbdcaacaabdcbdddcadbcbadbaaadbaadabadcdbdadcaadbbdabbbccbbcbcbcdcdbbbdacadadcadbbcbdcabbbdaacacbdaabcdbccbacbcbbaaacccdbbdddbbbcbcbddaccdcdadbaacdabcbaddbadbddcbdbdadabdabbabaabdddbbacacacccdadacbbcbdccdbbbbccaaaddcadcabbaacadcdcbdbaadcddaabccddaddcbbabcdcdbcadcacbacabcabdbcdaddcccbdbdbccacacaaccdbabccdcabdabadccaabaaddcbccbbaaabadcdbbcaadbbadbccccbbddcadaadcdadbadabbbadbccabddbcbacbbabbbcbbddddcddcabaccabbadcdddddadbccdaddccaaabddccdacbddddddacdcabdaabccbdaadcabdbcdbaaabddabaddabbdcddcbcdcbcdbcbdcbacdaaadacdcbcadabdaadbcdcccccadacdcabacdabdadddbdbbbcddcdcbacabbbbabadaaddacdcbbadbadaaadbbccadcdbddaddaabcaaacdcddcacccdddbcaaabacddcbdbaddbacaddbdcbbddddaaddcacaacabcbcdddccdbabbccdbbcaddaacbbdaddbdabccddacacddbcdcbbaddccadbaacbbacdadddddcdcbcdadaaabdaabacacdaaabbbaccbcdddcbddccabbbcacadbbacdcacbabcdcdbcccabaaaddcacaddbbacdbccdbbcabccbbbaadcaccccadbcadcaabdacaacccaccccadbaaacbbacbcbaacdaabdabacdabaacccacccaacddcaacdcbcdbdbadcbddcaabcddcabddbaacadcbdcddbcdacadaccabdbdccdbacacacadbdcbaccaddbdaacdacdccddaaccaaaaacbadddbbbadbbbddbdbaccdbbbcdaacabbabcbabaaacadabdcbbababcaccdadcddbbccabcbddbcdbdaddbddacccacbabbddbaabdddaacbbcccadddcaabddacccdcbbbdadbaccbdabbbaddbddabdaaddcadcddbbdbdbdaacccbaaadbcaaadbbaabddadadccbaaccccdacdbbdaddbaddabcabadbbcabbccadadbcddcaccabbadcdbdcbadddbdcdbbcdacdbdccddbddccacdccbabccadccddadccdbaabccabbdcbbbbbbdacbddddbacdacddcbdbbaaadbbccccdddcabcdcbadadbcacccbcadabcdddcbdbdccbacbabdbdbcaabacabbaaacddcdacdccaacbcacaaadccbaabbdcabdacaacbaabbcdddbcabadaacdcbbbabdcaaadbbdadadadbdbcdadcaabbcbbddcacddddbddcbdcbbadacbdacbdbdbcbbabacbcbadaaddacbaacbbacaaacdcadaadcdbdbdddbaccabcbdcabdbdddaccdbcacccabdadaaddaddccdcadcdcbcdcaadabacaacbbdbcaadbbdaddbabdcddacdcccaccaabdcdbdcbaddcbcbddcabdadcddcddccdbcdaaadcdabaacbccddbacbaadcbacdabbbcbacacadbcccccdcbdddacacdaaaccddcdbcbcaabccccdddbdbddbcbadcdadcadccdacbdbddcdabcbbccbbabbcbabdadcbbdacaddabadbdbaaabbcacacdbccccbacbddcabdcdcbaabaabcadadabdaacdacbdbdddacbbbbbadadabdcdcabdabbdcaadcacbdbbcbbbacaccaadbbdaccbcaddbbadbabdcbdcabddacdccbbcaadccacabccbdcabdcbaccddcaadbadddcbccacaccdaaacdccbdbbbbaaabaabadaddcccdcdaddacbddccbacadcacacbbaaccadcdbadbbabdbdcccdcdaaabccacddaadcbbbaabcdbbdabacccddbadbbbbdbbadcbcaddaaabbaddaadcbdcccaccdcabddadadbdcbcbbdccbdacdbbcabcdbabaaacbdbccbbaacddcabdbddabadbaacddadaaddbdcddabbbdaabdababcbdabbcbbbdbbdbccdacbcbcddbbaacacaabdbbdadacadbaccadbadcbaabcbccbadccddabdbaabdcacadddadbbcadcbaabbcdbaddacccdbbdabdacccbdaaaacddcbdbccacbadbdddaccbdcaaddacadaadcabcbccbaddcacaaccccbcbdaabaccaaacbbcaacbdddabbcbcacbcdaaadabdddadbcdbbbaaddbbddacabbcdcdabccddaaabbadbaadcbcbdbcbdcdcacaaabaaabcbbaacbadbbbbdaddabcbddbbcabbabacbaccaadacbabbccbbddddcbaaadbdcdabbdadbaaabcaccdbadcbccabccbaabcbdddcaddacdbbaabbccccdabaabbbaccdcbcadcabdbdcbddbbcbcdbcdbbaadcaddccbccbcdbacaaccdabababbbcdccdadbadcbdabccdabcadbcacdacbdbbacdccccdbdbacaddbdbdcdcacdacbbbbcaddbcdbadbcbdcaaabccbcbcabdacacdaacaccdbcddacddddcaadacabcacdddaabbadbadddcdaabdacddaaaacbaaadadbcaacacbaccabbbabcccdacadaaadcadddbacaaadcbabcbdaaccdccaacbabbabcbddcaabcddacbdacdcabbacccbacadcddcbbdaadadddbbddbacacdddbdbbcddbabddcbababbdddacccadbbbabbaabccbcaaaaacbdbdbdddaadcbdbbcccbacbadddbdbdabacbabdaabddbbcbacdacdaccdbababdcdcdaadbdacccccabcdbbacbcccbabaacbdbdbaacaabccacccdcdaacbaddcbcdbdbcbabaadaabcacaddbcdbbbddaabcdacaaddadadbdbdbccaccbcbcbadbbabbabdcddbbcdcddcbcccbdddadadacaccbdcaaddaaabaacadbdbdddcbdaddbabacbaaabcbddbcadcacbddaaccddbaccbcbcabcbdbbaadaaacccdddcddcaaccbccadcbacccaacbbdcbaaccadbacdadadadabbbacabbcabaddbdaccddadbddacddbccdadadbcbbaddaadcddbaacaddccdbbabdcbcdaaabadacbaadddaddcbbacdbdaddcdadccdbccaadcccbabaabaadbdcbadababdbcdbcbdaabbadcbcbacddbcbadbddcdbbcdccccacccabddccabaccbabcbbacaacccabddaaddcbacdacadacbcbbadbacbcadbacbadcccabccaaddddddabbbcddbbdadbaabadbadadddaacabadcbdbaacaaadcdbcdbadacbdbadddcdaabdbcccbcddcaaabbccbacbabbacaabadaddacabcacddbbaadcdccadbcccdababbcaabdcddbaabcaabbbcbaccbadbaacdbdbaadacbbdcbbaddbbdcadcacbcdcacbbcabdbbbbbdaccbcabcaabdbbdcbccbddadacaaadddabcdadaccdababddbdbdccacacddcadacccacddabaadaaabbccadbaddcdbaadcaabcddbddbdbdbdbcaccabdcabcabcabadacdbdbaadacdadaacadccdcabbadcdcddaadbbbacdcdacabaabbdccacdabbdabdacbdaccbbbbcaacddbadcdaacdddbdbabdbbacdbbdcdbbbbbccbddcacabcbaccddcaaddbccdbddcbcbdddcbbdddbcbcbabddadbcccaaddabbdbccbcabbcbcaddaddbdaaddabcdccacdabaddcdacabddababadadaddaaabbbccaacbbcaadbdbdbbcddbbbacdbdabcdaabcbacabcbadacdaaaaadcdbdccadcadcbdcbccadcbaabcdcadbabaacdbbbdaaccddadbcdcadbcaccddcadddccbbcbadabbcbbccdcbcddbadbdbdacabbddcbccdaabaaacdcaabbbdacbdacbbaacabcdbcabdcabcbcaaadbaccabdadbddbbdbabcccbbabbcdbddabaccdbbacadbabcdaddbcdcaadadcbdccdccaaadcbcacdbcadbacddadbdcdcbbcabbdccacabacdcaabddcddababddbdacadbaacddbbdbbcdcaababccbbaadbbbbaccbdcdbccaacabaabdddadcabcdabdaddacbaacdddbbaabaadbabccbbbbddbccdacdaadacdabcabccddddddabdaababcacdccacabcddddabcdbbdaccbbadbdbacdbcbaabbcbcbdbbaabbccdcadaaaabbdbbcababbabbcbccdbbcadbbdcddbddadababcbcadcbbcdbbcdbddcbcdabdcbbccaacaaababadccacdabcccddcacccbcabaacdbacbadbcadbcacddcbcbbcbdabbbbcaddbdacbcdccadcccbbabadbdaccdbcdacaddaaacabccbadabcdbdadaccbdbccbdacbbbbdaddacccdacacdbcaacadcadaaadbaaaaaaddadaaadcbdbadacdccacdcabbcbaadbbaaccdbbadbdadddbbcbabdcbcddbcadbccbcbdcaacbdabddbabdbabdaccbccddbccdcccacadacabbdbacabadddcaddbcccdadccbaaaaadcadbccddacbdacadcacbdcddbcccdadbaadabdcaaabadbbdaabaabadbaddaaccaabbcbbdddbbcbdbbddbdcbcaccaaacbdcaaccacdadbccdcabbdacdccddcbcddccbadacdbcdaadcdccdbacbbcbcbbdcaacabbdbbbadbdbadbdbaaddacacdacabddbbadacaadcacdabdcacbbdbcdadbadbbbaacbaadcacdcbcdaadbdabdbdcbbabcaacdaccaccbabbcddabacaacdbcddabaabaadaacabadabbacdabdcdacbcbdbcabbdbbddbbddcaadcdaacbdbcbabdbcddacacdabbaaaccaaadbbabaabccdbddbbbdaabadcbcacbcbccabdcabdcbbccdcbdacaadbcdcbbbddabddadcaacbccbddaddacccaacadbdabbccababbacdbbcbadbacadbcddbdabcbccaabbcdcaacabccccbcdbbdacaccddabdddddcbddbdbccacbcaabbbbcbabacdadcbdcdddacbcacbadcabdbacabbdcbbbcadbbcbcdaadacacbcaadbbacaaaaaabcdacdaccdcaaddaacbabaaababbdabbbcbacabbcdadaddaaadadddbacbaddbbacdaddcccbaccddbdacaadabddbdacddbcdaaaacccbddbddadcdbaaacbcdaacbbbcacdabdccdcabbabaaccccbabcddbacbdbacdcaddcbcbdabbdbabacdccabaacbdccaabdaabbbbbbccbbccdcdcbdabbbadbddabbbdaadabbdaaccabcaddadbddccaddacccaacdabbbcbbabdcdcadbaaddcdcdbadcdcabccbbbcaaabbcbbbbdbcadbcddddccbcadccbdccbabbbccbdbcaabbaccdddbabbaaddccaaacddaccaaccaccdcabbbcbcdbbddaccbdbccacbadcbabcdcddabdadcdaaacbddaaacbcdabccdadcbcdadacacccacccabdacdcacccdccbaaabddabcdabdccdbbcadabddaaccbacbcbaabdadaccadbcbdbaddbaddcdaddcbaabcacccbdcaacddbcbadccabdbbdbdbbaacaababacadcbbcadaacbbdbdcbabbbccbcaabccadcbaddbbdacbdcdbdcbabcccccddbcbaacadccabdbbddbaacdaacccbbbadabdbdadbbaabbbdcaadaaadbabdabdcdcdcabbcabacbdcbccdddbaacdcbcdbbdcabbdcdbaacdcddbaaddadbbcdabdababcbdaccaaadacddbdcbcabacadabddadacdadcaabaaaadcabbcccdabcdccaaddcbccdcbcaabaabdabaddcbdacdbdcabcbcdddbbadbcbbacabccdbcdbabacdcadadacdcbcbdaabbdbbdccdaabadacdacabbaabbbaddadcbbbdddbddaddcbccbddabdcacbcbbaadcadacbbabcdddacbcabdbababcbcaacabcbadbbcacdcacddcdcddccabcdabcacdacadccbcbcdadbcbdddadccaadaacadaacaadacabbddbdbaccbdccabaadadbbbddcdddacabdbdbdbbbadbbccadbbcadaaccbcacdddbdabbacacadcacbacbadccbcccabbbaacaaccdaacbbbabccbbbaacbbabbdadabadccbbbbccadbddcbbaabcbbabbacdccccdddcacadbaaabbabcbdcdbdbbbacaacaadbcbbadabcdbadcbdbcbababcdcbababcddbcbcccdabacabdddccbcbaaaccadadbcbdcdbdaddbbdadbcbbbabbbaccacbbbdbbbdbcdcbbdacbcdacddacbbaaabbadaabdadacbdbbddaaaddcccbbaaddddbbdbcabccacabcbacacbcbcddccaddcdccdaadbbcbcabcdcadccdabacbbacdccdcadcddaaccccadaccbcbdbccabdbadbccccdcacbccacbbcaddcabaaadadbbcbbddccbcdcacbdcddbcdbddbbdcccdcaddacdbaacaaabaddddacadbacbabdcaabbccdcaadabbbadcbcdabdccaacacbbdaabaaddcdbdadddbdcacbbdaaadcaabbaadcacbadaacbabbacacdbbadabbcdacdddabcaabdbdacbbadbdbcbbbcabbbacabaabbbadccddddbccacbbacbbbdcbddbadaaabcdcaddbddccdbadbccacdcacccdcacddcbdcacadcbbdddacbdcdaacabccdabddccdccbbcbbdbadcbbddcadadbcbbdbdadaacdabccdcbdabbadddcbdaddaabdaadbddcaabccdcacccccdcdbacaddababdcacbabccabccccbbdabbdaabcabbbabbbaccaadabdcbacdcdabcbcbbdcbccddacbcddcbcadbdbdbcccaacbbdbdadadbcabdcbbbcacbaaaaccccbcdddbbcbcdcdbacdacbbaadcdccacbccddaadddabadccaadbccbacbdbabcabcccdbbcdbcbcdbabddcabadddbddbaabdaddadbbdbcccccdbbaaadbdcdacdbcbdcbcdacdccccacbcacbabaccbbdaabcacccbbcbdacbbbbdcadcacaabcaacacdccbbdbabbbabbaddbdacaacbbbbaddddcbaddbaaccdddcacddacdbabaaddbbdcaccbccabdaacaddacdcdddbcdabacdadadbccbcdcbaccaccdbdaaddbcabdcccabaadccccacbbbbcdddaacacabdcdddadaadddcabcaabaaccbdbdbbbcacaaacddbadcddbaccbbdbccdabdbacbbddbabacddcbaaabbdcdcdacacdbdcabcbbadbdddcbadccadaadbdbaabdbbccaacacdcbbdbbbdabacadaddadcdbbaacacccaaabbbccbbcacacadbaaacaccacdcbbcadbcbacccddcdbddcccbadacbabdcbdddaabbcacacaddbdcccdcabaabbbdbbbbccacbadbbadddabdcaadbbcbcbabbdacbddddbcbccbdcabbcbbbadbbbcdabcbaccbbbaccabbdabccdadbbcdabdbdbcaccadcdacbcaccdacacadddabdccdbabcabdddaacaaaacdddabbbadbdbaaacbddddacddadababcacadcdaabcdabccbdbdbdbddccaabcbddddababdabcdccccaddcdbddbcddabcccccdcdbbcdcdadbccbdaabcbddbddcdbababdcccdccadabdbbdcdddcdbccccccdaaccadbcdccbbbbccbadbcadaadacabcccdacdaabbdacbcadadddaccbdcaaaccbbbcdddbbbbdccdbcdbadbbbddaababbbbcacdccacadbbccdcdcadbcbbcccacdbacbdaaabccabcaaccccbbdcaadadbabcbdabdcdccadbcdbbbabdbccdccacbbddacddadccadacacccddbcddbdabaabbabddaaacaccddbcdadbbaadbbccddabcacccabbabbdbdbbaacadddcabadcacaabdcdaabaadcacdabdaaccdccbdbaacdacdbcddbccdcaadbdcacdaacadabaccdacbdcdbdacadacbabcccbacbcddcbcccaaaccadddaaacbdbdcbacaadbcacbaccdcccabdbdcdbaccbdabaaabdabadccaccbdbcaabcccddaadabbacdacadcbcaacaacdadbbbcbaaaadcbcbcbddaaadccbdaccbaadaccbbbdcbccccddaaacbcddacbcbbabbbbdabcdccccbbbcabbdbddccadbcaabbacaaacacadbabcadadadaaacbbadcacccabbdacbddbbddacbccacbbddcbdcccabacabdbbdabadcbcacadbbcdacdccdcbccadbabaacaddbddbacdbbdbdccbbcbaccdbbbdddbbcbdabcaddcbdbccadccbbcdaaccbcaaaccbcabbcaadbdccdbcacbddacbbabbcdcdadcdbbbcdaccbacbcaaacbbaabacccbcbdcbbacddbcabbcbcbccbdacbcccaacaaaccbaccabcaadcbdaabdcadcccaadbbbabacbaaccadabcbbbdcabbcdbacdbdcbacadbcccddabbbbdacaaaaaccacccbabcbbadcacbbbdaabcabcccadadcaadbcabbbcabaabbdabbccacddaddaaacabddccdbbcdbacbdbbdadaaabadbccbacdcbcbbcacbabcaadbdddbaaabccabaabcddcdaccbcdbadaacdcdbbdcbdbdaddcddcbbdabbcddaabcaccccdaddddcacdcbbbacacababcbaaccbccadcdbacbdaaaaccdddabccccccbccbdcdddababdbdbbccabaabddaadcadadbcdccdbaacbacaacaadbadacbdacabbaddbcdbdbbbaacadcdaccdddcbbadacacbcabaddccccababccadbccdadccababcabaadaccbcdbcbababadcbbccdaabcbcbacabdcadddbaabddcdbabcbabaadcbccaadadbabbdadacbdbacddacccdadacabcadbbabccbdabcaaacbdadadababbbdbbdaddbadbaacbadddddcbbadacdcdabdaccdbbbdadaadcdaddcdbbbcdaaabadaacacbdbabbbcdacdbdbbdbbddbbdbabddabcaccddadbdbaacaddcbdbccadcdcbbabccbdbdcadbacabcbbadbaacaacdcabbaabdaaddcadcaabdcccdaaddcbcaaacacadadddbccccbbcabbccdbbdbcadbcabdabdbdbcbbcdabbaaabdbcabdacbcdddbdbabdccbdadabdccbbddcdaccdcdaacbbdbaacaaababbdcaaddcabbdadaddcbabaddbaabdcdabbcadbaabbddbbbdcbccddccddcbdcbddbadbbabcabcbbbdababdaabaadcddadbccabbbaadcbcdbcbdbabbacdcbbacacbaccbdaddbcdaccbabdccaacbbacbabdcccbdcdacccbddacaabdcbdabababbbcaabcddacdcaacdbbbaabdbcabadbccccbbdcbacbbdacbabbdbbdcaaaaccaabaadbaadbbaabcbccddadabdabcdaccbbcadaaccdbbacbbdaccaadacdaccababcccabdadacccaaadcccccccddbbccbbbadadadbaacaccabaadddbdcbccadaddcdcdacbcddbcbdcbbabdcbbabbcbbabcadcbdaddcbddababccccadadaaabadddddcadacccaaadccccbbcccccddbddaaadbabbbbadadcbdbdaacbbbcccabcdcdaccdabdbdcadcaacabcdbaabaacacdcadabacccbdabbababcadacabdbadbacbbbadacdccbdbcabbcbddaacdcdbcadbcbadaacdcbcdcabcacdabbccdbadadcacabbcdbaccdbdbbdcaddbadabbbcbdcdccdaadadccdaccbabacccccdbdccccdccbbbcbbbbccbcbbcdbcbcacacbbbadaacbcbbdabddbcbaddabddcaccaadbabbdaaddddacdacdccdcddcdaabdbaadadccdbbcdbacbddabbdacbacdbaaaccbbbdcdacbdabcaaadacabddcacddcaaddbcadacacacadabbabacdabbbdabcacdbadbabccaddbadaacdaacdacddbcbdacdccaadcabbcbabaaaacbaaccbdbdbddbabddcdbcdbabddaccbadddbdbbacdacdcaccdacdabbcbaaadbbbacaddddaddbacccdaadcabcdabaaabbddbdcdbadacbcdabbbcadaabbdccaccdbdcbacabbcddadbbbcacaabcabdcaadccdcadadaddcccabddbdabcbaccbcbcdcaccacdcbaadbaddaacdabbbaadbaddbaadcacdccccaabdbacdacdcaabcdabbdbaabbdcbdbadcaacabdcdabcadddacabbdddbccbbbbacbbdbcaabbadabcabbdddbbcadddcbcacddccddaacbccccdacabbbcaabdbbabdcbccadabcbbaccdcdcacdcaccbacbdacbbbdaabdccbaccbcaadbcabdabcbccccdadcdbbabcbadadcbdcadddddcbadcbabacbbcdbbcadbcabdcdcaabcadaccccacddddcaccbbccdadddcabdacddbaccbcdcadcbccbbbababbabbbcaccbaaaacaadcadcbadbdadcacdacddcbbaabcddacaccbdcdcacccdddaacdbcdacdaccbaddbdbcbbdbcbababbdababadbcbbacddbabdddabacddbdcbcacbdacccaaaadaadabaabbddcabdcdbdcbaadccdcaacbacbbaacdccbabcdcbcccbbaadbbdacbbadaabcabadabdcbccdbadaabbaaabccbadcdccaccaaabdbaacbcdbcababbccdbdcbcbadbababaccddbcacabacadbbcbdaccabcbbdadcaabacaabbcccdcbdcadaaccdbbddabcacbbccddcbaabdbcccbbdbdadbabbbcbadddbaaacdcdabdbdabaacbcadabdcdaabbddddabaadadbadbdcbaddbbbdabbcdbcacbddbbddbcabbabcbddadbdccbbbaddbddccbbdaccadaddabacccbcdbbacbacabccdcdabdadbcacaabcadbcacdcbadbabbdabacacdaccdaaabaacabbbcdacdaccaabcabcbadcdbbbcadcdadacadbdccaaacdbbabaddbcddacdccdadadbcbcddacdaaaabdaabbbadaddccbbdcdbbdbaadaabcccabdbadbbdcadcabdcdcbcdaccdccdcbcacdcbcadacbccabdabcbadbaccacadadbccabdccdaacdbadbccccbbcbadccccbdcaadccdbabdbbccacccbcdaccbcabdddbbcbdcdcddaabcdcbdcaabdbaccbcbbbcddaabaacbbabddacaacdbcccacbadbacabbabdccbcddadcbacbadcccccadcdbddddccdbcaaadbcbbdadcdaacdbcbacbcabddcabcbdddcbcbcbacdaabcacdbadccdabccacdbbdccccbaccdaddacdacacdcbabcaababcbbccadbacabcadcdcabbcabacccabcddcabbadbdcbddbcacbabaaacbbdddbdbaababddadbbbdbccdcbdaadaacadccabddbabcbcdbcaaaabdccccbcdbadcaabbbaacaabaacacabbabbdaaaccbddddaabcbbddcdacbcaadbdabdddccadadaaddadcccaadabcbdbadcabdcaaadcabdaaabdbbaaaccdaadcbbcadaaaabcababaacbbdaccabddbacabbddacddccdabdadabdcddabcadcdadcdaacbadaaccdaccccababdbcaababbbdcbdddccbddcaabdcdbababddddaabacbcbbbacccdbcacadacababaaadddaccbaaaacdbaccdaccdbdbcacadabacdbbbcaabccabcaddbcbbcabdadcbbddaddbaacdaccacadbabbaccdbabbacccacdccaabadddaaccccbbaaccddadbcbddcdccbcabddaaababbadcababcccddbdcbbcaabacabadaccadabababacccddcbddbcaabbdadcbcbabddbdcddcdaddabccccdadaccabbcabdadccaacdbdbcdbabacbcacdcdbaadcbddaabcaacdabacacaadbcbccbcacdabbccccdaacccadbccdaaadcdcbabdcdccddbaaabcbbaadaabaaaacbdbcaaacdbcdabdcbdabdbbbbdadbaabaddbcdbdbbabacbcaabdccdaabcdadcccdcbdaadcabcdcdddddcbdaaadcaabcabddacbaabdcdacaacabbccaacdcdccdaddaaabddddbdacaddccbdbdddbcccdcbbcbbaaabadcbbccbcadaddbadcdbadbdcbabacacacbcdcbcdaadbbcbcbddccbdabbdbdadabacdbcaabdadbccdbbccbaabdbdacabddabcaabdabcddbbdadbacacbbddbdacbabbccabccabbcccabdbabdbbcacbcdcbadcddccacabbdaddcbccabcdcbaaabcddabbbdcaadbacdcddcccbdaadddbaddccdcbbbbdcbccbadbdcbacbbccadaadcccadbbcccdcdccdbbddcccbbddccadcbacdaccbaccbcbdccdacaacdcbcaaaadcabdabdbdbddcdbdbddadcbbcbbbadbadddbbaababdcbaaacdcbaadcbbdacacbbcaacdddcccbdbddabcccdaddaddbbbbccbaacabdadabccdbbbacacddbdbdcdbaccbdcbbaabaaabdbdddaccabbbaccbcdddbbabaccdcabacabaabcdbabbadbbcaabaabdcdcdabccbccaaccadccacddccbcddcabbaaccabcdddbbabbddadbccbbcccadcabcaacbabbabacacababccdaaddcbacabcabdbabcbaabbaddccccbabadcacdaabcddccdacabbcddbbbcbcbbabbdabadbaacbcadcabbadcbcccaddddacdadddbaabbcdbcaaaabaddbbbaabbacccacbcaaadabbcdccdadcdabcacaabcdcdccccbbdddabacdacbdbabadbbdabbbadbbbcacbdadababcddbbaddabccbdbbbdcdbbbcddacddacdddcdbaaabdbcaddddbdddcccccccacdbdaccaaddcbccbcdbdadbdbddaaccadddcabbbbdcccdcbcbbacdbabcdbbbbcbcaadddccabbcddcababacacbccacdddddaababbcddacdaccdcbdcaddbaccacbcccdddaacadbbbacabbcdadbabcaddaacacbabcbabbbdacdccbbbbcabdcccbcbaacbdbcbaacdcacbaadbddabcadadcaabdbbcdadcabccbabacdcbdcabadbcdbbabdbcbdbdabcdcaabccbaadbadcbddaadadcababbbacddddbcacdbddcbdacbacaabdcdddbaacbacccbddbccbdabdcdadcbabadaddddbdcdddddadcdaddababaabbddcadcbacbcbddcbaccaddadadabadbadcdddacacbcdcbcdacddbbacbcacacbbddbddabaaaabdadcdaddabbbdacccbdcbdaddbbabddadbdacccbcdcaaaabdbbbcbbcbdcbbdcadaccccdababacdabbababdacbcccdabdccabdccbcacadabacdadccbbbbcddaadababbaccdbdbacbaccadcccdacdddadddadbdcbababcbdcdacccbcbcccbabcbdcdadaacbacbabdccabcccdbbcdbaccccddaacadcdccbbbddccdbdadccdaadbabbcabbaaaaabaaadaadcdbbcaaaddbdddbabcbadcdadcaddbabdbbaabbccddadadaccdaccbabdcccadddbbcacabadbbaaadccdcabacddabbcdcaccddcaddcbccacdccdcacacdacadcdccbbccdddabdaacabdbbdcbccbddbbbaccdbcdbbbbcadacbccabddcacbacacadbbaabcbdcdbbdcabbcadddabacacbbbccdbcbcdabccadbdbdcdacdabcabddddacdbcadacdcdaacacabccdddbddaadcbcdadccbcddadcdaadacddbcabcbaabcdddbcbcddddacbbdacccddadabcdbacbabdbbcdbacaaccabcacacdbcacddaccaaccbcabccadacdccbacbccdaacbadbbbdbcbbadbabdaccdadacdacbbadbdcbdadbabbaccabacccddbbbabcabacadaaaacdddcdbcabcdbdbbdbdddaacdcaabdcbbcabcbadcdaccbbabadbabdabdbaddddadadacdabcbcdabddcacccaccbadbdcddabddcacccbcabdabbdcddcdcadcacbacbbcacdbabbddddcdccabaaabdbdaaaadbabddccdbcabbbdcbdbaddddbcadabcbdbbaabcaabdcdcccccbcbbacccccbaadcbccdbabcdccbccaabcabaadaddcbdaaabbbcaddbadcbadcadadbcacbacacdccbbaccabadaaadadcdaabacaacdcbacbabcbcdbcbbacddcddcaccdbbbbbbbbdadbabbcbabbcaccacaacaabdacaabbadcbbcdbcdccdacbdccbbccdaccadcbdddbdcdbcbdbbbbabbcccadaccdbddccbbaadcabadabaabcaaaaaadabadcbcaabdbcdbbcdbbdcadbadadaddcdccbbdabbcbabbbadadaddbcbddcccbcccdddbcaacccabcdabdadcaabdaabdcbacdaacdaabbbccaccddbbbcbbaadabcbcacdaccccccbccddcacaddcbdbbcdccbccddbdcdccddadcddcdbbaacadbabbaabdbcabcccccdccbdaaabcdaadbcacabbccdcdbaccbbdbdbdbaadbccbabaacccbcdacaadddabcaacaaccaaacbaadbbadbadbcbbcabcaccacddbcccbcabaacdbddabdcbbddbcddbbbddddaddcdaaaaaddddccabbbddddbdbdadbdcbacdabcaddabcadbcccccdbcadbddcabbababcdacbaaacbdbdbadbacacbdbccaadbbbcbadcdbcbbaddbbabbbccccdabbccaadacabdbbadabacbccbdbdcbbcdbcbacdadadcdcacddddbbcadcaadddadcabadbbacadbababbcddcbbcadadcdaccdabcbcacdadaacdcbabdacccacbadbddbbdcdcbddcadbaccddbcbccaaddbcbcbccbdbcabadddcacddbabaccbbcaabaabbaabdbdbdcbdccddabbcdcbdccbdbbaabcdbadccabcbcadaacadcddabbaacdcccaaaccbcacdcccbbcddddcbbdcacdcddccaaaaaabbbaaccdccdbaaaccaccbcaacbadccacabadabdbcaaccbccdabadaaccacbbababcdbdccabadabacccbdabdbccacaaabddbcabacddaddaccddccbcccdbcccbcacabbbcbcccdaddbacaddadacbcdbdcdaabbabdbdcccbcdacdcabdabddcbadaadcbabcbcacbdacdcbcbdcdbccaaabcbdcadacabbdddcbccaadaccccbacadabbcbcadabadbbbddcdcacccabdbdabaccaccbbdccdbddaabaabbdadbdcbbbaadbddcbaadddbaaaacdbdcbaabdaaabbcddbccbdbcbbbccaabdabbbcadaacbccddaabcddacbddbadacadccacdbccaababadddbadaadadaacbadcccacdbdaabdbcdccbcdcabdbdadabbbcdcdccabdddccabdcabdccbbcdccddcbbbddabbaaabdbcbabcddddccdcdaccbcabbcadbbacccdabbabbbbbacbdddbbbcbbabdccaaabdaaddabdcdbbbbccdbccbabadacaccaabcabdcdbdbabadcdccbbdbbabaadcbbaccbccccabdacdadacaaabcbbcabaccabcdbddbddcdcbdaddbbadcdabccbddaddacdbabdbdccbcbacdcaaaccabbcbadaacddaabbaaacdacacabbbcccbccabaaaabcaacbdbdacadacbdbadddcdcdbcdaadcbcaacccddcaabcabddabcbbccbbdbadaacddbbcaaabaacacacaabbbbcdaddaadbddbcabdbbabbaacabcbdaaccccddcdddbcbbbdddccdaccdacdbbdadbdbcdacdddcdbcdaadacadbcdbcbdddbcdaddbaddabbcdddbbbaadcabadadbadcbcccabbdabddcacdbcbdabdcdacbbcdbddbdcdcdbbcbdbcdccccdadddcaccbdcadabbbcccbabbcddbddabdbdccabaabcdaccdbccbdbbaaaabbdcaaadadbdddabddbaddcbaaacbcbabcdcaaadbbbbbdadbbbbcddbcacabbccbdcadaccbcaaccccdbbabcdbaaaddbcdcbdacbaaadacabcaacbcacabdcabaaadcdddabccdddadbbadccaaacbdabcadcbdacdbbbddaacaadbbbabbddadacbbdcbbcdcacacbdbaabcdcadadbbbdadaabcacdabbbdabcaaacdbcdcdaaabacdbcdccbbbbdcdbbdbabcacccbcdbcdabacdccddbdbbadbdadbdaccbbdadbdbdbbbbccadcbabaadacaadcbdcddcabacddacaaaadcababddbbddabaadcccccdddababdbccdaabcdbdcbadbbdaccaadcbaacbdaabbbdcdcbaadaadbadcacbaccaddbdcdbbaaacdccccdcbbacaaadaccaadcbbbddacadacabbaccabddbcbcdcbaacaaacadccccacbcbacaacccdddddbbcadbcddcbaacabbcaaaadcababababaacccbbbbababbbadbabbcbcaaacbacbcabcdbdaccccdcabbacbbbabbbacddddbdbbddaabcabbacdbabcadccbaadacadacbdccaccaabadbaddaadcabbadbcabbcdabdacacabcccbcbcaaacbbcbccbbacaacbabbaddccdaabcdadacbcdabddbdbdbadbabdddbcdacbcbbbabbdbdbdbadacdbdcddabddacddcccdbcbddbddddbacbcbdbccaabccdbbbcacabcaabcbbccdcdcbbbabcadcbccbbccabcaadbbddccdadbbadcdcaaadcddcadabddbbccddddcdcaaabbdcaddbcdcbdbdddacddabcdcbacbcbaabcdaadcaadaadaacbdacbadbbcbdabdacdcdccbacdadbcdbacdbacaaddcccdadccbdbcdaddcddcdcdbdbadcbaaadbbaabbcdcbcbdadbdbbbadacaacbdaccaacbcbdccacdbcdadbdddbbdccdaccddbadacccccccddcabccdacddbdaccddbcbccbbabcccadaccccdccbbddcbbdccbbabbbdbdabcbaacdcbccddddcbbacbdadbbabadacddaaaccaaaabaadacacacaaddcccdbbbdbccbdbabbabbdacbcdaacbacbdddccdbdbccabddbdaabacbcdadbbadbddcbaccbbdbcbdadbabaacdacbdcbbbcbbbadacbccbdaabcdcdcaaccbccaddadabbabadbabdacdbddaacaabaacddbcdadcbdadabadabbacddddaabdccdbcbcccaccccbdbaaddbdabbbabcdcaddcbcabbabacabadacaaddbbbabdadabcdbaddbbabdacdcaaaadcaddadccacddcbbdccaadcdadccbabddbcaadaabadddcdbbcbcbdadacaddadbacabcaddbdbddcbcadcdacbbacddcbbdaabcdcbcdcdbcadbbdabaadbbdcbccacbbdbdabacbcdadbcbdbabbdadacaacbcaaddddddbacdcdabddacbbdacdcaabbcadddbddccbbbcaaccdaadbacbdaacadccddcdcdacbdaabaadbcdcdcaccdcdabbccababaaacdaacdabbbbbbdccbaccccdacabbcacdddccddaaaadcccdcaaacdcbacaccdaaadccabdacbcbdbcacbabcbcdbcdcdbddbdbdddddaaadcacbccdccbcbaacaacbbdbdbcadcdcdddaaabbaddcbaccabcbcaccacaacbdaddbbbaabbcacbccddbadbbbbdcbdaddccdccbcddcbaaadaccbcadccabbddbabbaabadbdbddddddadacdbcdcabdddacddadadcbcddccdbaabaaaaccbdcbccbacbdabcbbaacbabcadcddadcbacccdcbccabcbbbaaadabaacaaaacdaaaccbccbcdbaabbaccabadacbddccdabcacddcaacacbabbadbcdccccadcbcadbacbbdbdaaacdbcdaaabbabdcbabbacbacabcbbabaddcbbadbabcdadddcbaadddbdddbbddbabbdadbacbccbbddaacadcdadcabcaddabcbbbcccbbadaaabaadbbadbccdcadbbddadbcabbdbdcddadaaadbbdddadadacadcabbaacabaadcbaadbcadbabbbbdccbbccdaabdcbccaacbdabacaadcbcbdcadbdacbdcadbcbbdddbcbcaddcdaacaddcbaaadababadabacabcdacdadacbdacbacbaabcdcbbdcdaaaccbcdbabbcbdddabaaaabcdddbacbababccdadddaccdaddcdbabdbdddcdacaaddbdbcaadbbbbdcacbbbbacaadccaddcabcddbcccadbabdbacbccdcdcaaccdbaabaacbcdcdbacbaaabdadbbdcacbdcaaddbcbdbaabbdbcabdbaacabbbaaaabbaacbbdaccccbcccadadaaabdadadbccddcaaabcdacbadbdadacaaddacbcabcadabccdbdacbaadcddcabdabbcbddabdccabccdbbcbbaadbcdbbcbadcbdbbbddcbdccdbcaaccadcddacccdaabdcbacdbcdaaaabcaadcbcdddccadbdcdabcbdbdcbddcabbdbaabdcdaacddccdddcccbbdbdcbdacacbddadddccccdaddcddacdabbcbdbbdcbbabcbabadabdadccacabacdbdcacadacdcabccadcdcaabaaabdcadcadbbaccdadcdaddaddabbacdbbdaadddbadccbcdabbdbaddacadcccaccdcabacbdcdababdabdbbacbabdbbbbdcbaaaacbbdcbdcdbdcbdcbcbdadbacccabcccbbdacacdcdcbcdcdabccbcbbabdccbdacdbcddaddbdabbcddbcbacdcccbcddbabbdcbcabdcddcdbbbdbddbcbdabcbbbadddbabcaddbddcbbaaaabcdcccddadbbdcdabcdaccbdaaabbccacacddddabaddddbdbbdddcabdbaddaaaababbbdcbccccbadabaaabbcbbadccdddcbaaccccdddacccddaddccdbdcdaacaacaacadccadddabbacbabccadacdcdaadbbbbadacbddbdcacabbccccdbdddacaacddbcbddbddccdadcdcdbbcbabdbabbacbacaddcadccbabacddccbcdccdcacdbdabcdccaddbacbddacbdddbbacaabacdcadadabdbdddccdaabbddbbddbdcdbdababcaaabcbbaaacacabbcdacddadddccacdaccdcacccccbacaacaadbcccddabdcacdccdccaabbbccddababaadaccdcdaadbccdabcbdcaadadaaddbcbcdddcadbdbdbdccbdaddcdabccbccccddaaabdbbdcbbabacbbdccbbaaabacccabccdcabdadbbaadaabddbcacdcabcddbdcccacddabababddbaaaddbbccdbdbddabadbaadbcdaaadbcdbacccccdacbadcbacddaabcdaaaddcdbcccbcaabadcabcddbbccbcbabbcaabbaabadddddcdbdabbccadacadbbbdccdadaaaaabbcbdbdcabccdadabcabcadccbdbbdacbabbcddaacdcdccaabcbabcccddccaacabcaacacbdcacaaacacddbddbadcbaadbdbadddddbbaabbbbcccccacbcbbcbcbdaadcbbbdbaccbacbadbdbbdabdbdccbaaabdbadcaaddabcbbbcbdcdcacbbbabcddcbbcdabcbabaaabbaddcbaddcaccadcbbdaacdabbdbcacabdbcacbcdcbdbdbbbccdabdacbbaabdbbdcdcbcbacdbabbcbcccbaaaadccacbdcdcbbdbcbbacbcabadccaddddcbadcabbbdccccaaccdadbadbbadbaccbcccdcadcdbaadcbdcbcdddbcdcdaacacdcdbccaaaabdbacddcbbcacddaacbdddccbabdbcbadaccccdacdbddbdcdbaadabbadddbbcabadbdaabbcabdbcbbaaacaacabacdcccaacbcccabcacddbcadabcaadbcdbabcbadaacdbbabaadbabbccacbbdbbadbbdcbdccacddcdbcccccdcddcadadcdabcababdbcccabbbadbddbddaccadaacabdcbcacadabbcbcdccabbbadccacdaacbcdbbbdbbbcbbbbdaccaaaddcbbaaaccabacaaadabcccccddabbaccbbadbacbddddaaaccdbadabbabbddcccddabacadacbcdbbccabcaadcdbcdacaccaabccccdddddddbacbcbcbdadcdccdbabbdcbabbbcdbccbdacccbcaaacadbbaddacadcbcbdabacddaddabbcddbdbdcadbccdbabdcccddadddbdcbdbdcababbdddcbddddcddccbccdbcbbaaaccbcbdbdcaccdbcdbccddbdbddbcaccdbdcbccbdaddabbcbacacbacccadbbbcadbddacacaadcbacdacccbdbbacabdbbaccbccbacbdcaaccadbccddabbcacdadacbbcdcadbddaacdbddbbcddcbadacdbcbdabdcbbbacbadacaccbcbdaabdccbddcbacaadbdccaabddcbdbababcbabbbadbddbdabaaacdccdcdaacadcaaadaccdaacbdbaccabdddadddcbdaadaddabdcabaddcdcaaccccaddcdbcccbccaccacbabbbcdadcaacbbadcdacdabdbbdcddcbabbccabbcbbabdcdcdbacbcbaabdacacbdacadbdbdaacaccaaabbbccbbdadbacdaadbcbdbadccabcbcbcddcadccdbaadcabcbdbdabccbbdabbccbbababcbadacccccbbcddaabbcccbbbbccbbcbcacaddbcbcdadcbaddaaaccdacccabacdaddcbbcbaaccddcbccbccbadbcbaaaacbabbdccdacdbcacabaddcdbcacdccbacabdbcbdaabcdccadadbccdadbdddadcbcbbcacacdddccdabdacbabccbacaaaabacaccdadcccccaadcbcabdddacadaaccbbccbbbbcdbddbcbccacbbcdcaabcbdcbcaddbbdabdccbbbdabaccadababdaabbbacaaddcaddcdaaccdacccdbbcabcaaaababacbcadcddabcccadbaadcbcddcddbcdacdbaaddabcbbbbddcadccadbddacabdcacaaaccaababbaabdbdbdcbbdbbaadcbdcaabdbbbaacddacadbdaacbcaaadaabaabddacccbcbddcdcdaddcbdccccadbaddcacdcdbdabacdbddbabbbacadacdadbddcdacccddacdccaddaaddcbcdbdcacbddccbaddabccccdabddbadccdbadbccbbcacdcdaacabacbbcdacbadcbdcbcddccacdcccdbbbcdbdcadadddcbdbdabacdccccdcacbabacaaabbcdccacbacabbbcadabadabdcdcdbdddaacdcbbabcbbbdcabbccaadcadbdbacbadbddcbdbadcdbacbddbbbcbbdbbabaacdbcccbcabcbabcdbddabacaabbbddcdbacdadaacbbbadcabbbababadaccbaadbdbbaabdcccacdaddacabbbbadbbddddaddbcaaadaccabadcddbbabcabddbabccbcbccdccacbaddccadbacaadddbcbdccddbbaaaaadccbbbbdcbdadcbabddcbadadcbbddddcababadabccadbddbacdddaccbbbcacaccbbcbaacccdacbdbabaabbbdabcbdbbbacbabcdacbcbabccaadbcdbaccdaacbbccadbaddbbacabaddaacaaddabbcbbaacaacbcabadacaabbadbbcbababbdcbbdadabbcddbbddaaaddabbbcdbbbcaabdcdcdbccaabbcdcbbcabcbadbccbbbcacccbbcbadddadcacdacdcacabddbdbbaadcccdbdbabaabbbaadccccbadcddcdcbcbbcacdbacaadaaaadddcbabadbcacbaabcccbccaaddbabddcbdabcdbbdabbbdcdaccbdaadbbcaadabbbacaaabaabddbddbcdbabcaaaadcabbadbbabaccbcbcdbcbbdbaaccbbdbdaadaaadcbcdcdcdbbcccaddaddcbacabdddbdddbadbaaadaaaaaabbbcbaacacbcabcddccdbbddcdcbbdbaddcccddacadaaacaadbcadcaaabcbadccbbabdcccddbddbacccccbbabadbdabacacbdddbcbcacbbbdaaadbbbccaacbbabdcccbbabddbbbabbbabbabdadccddbcacbbcdaccddbcdcacabbabcabddcbdadabaaaadbcaacbaaaabdbbcdcabcdaddcbcdaabcaaddaaccaaaaaaaabaaabdbabcbdbaacdaacadbdcbaadddaadbdbabcbccbbdaaacbadcbaccaddcdcddabbbbacbabddbbacbbbbccaaacbacddbdabccbddadbbdabcbccabbbddbbabdacabbacbdadbccdbdabbbbbccdddcaaabbdadbddcadadcbadbdacacaacbcbabdaadbaadacacadaabdccababadcbaaadadbadabaaaadbcbddadaccddbcacbbaccbddbaccaaadbbabdbdcbbacadcacdccbbbaccabcbabcddcadcdcacddcabcdcbdaddbdbdacdcdbcdaadaccacbdbadadadcacabbbbaaabbcddaddddadcdcbcabdbcaababcbcaadaacacaccabdbdbdcacccabbcbaaaacadadbcccbbdcdabccabcdaccaadcdcdbbcacddcbcbabcdacacabdddcbbbbbaccaabdaccaacdadccaacdbbcdbbcbddcdbbbccdbbbadaadccbcddaccabccadbcabbaccccaadbacdddcbadabcaacddabbddcaaacbcbccdccdadcdaccbadddcacbbcbdacadaaaacddbabbcbddcdbcbbadbabdbbadadccabaabbdcaababadbcbaccbdddbbddbbbddbacdbacddadabdbbcacacbddccbcbccadabcdabccdbccbdccaccdcadddccdcdbaccaacdbaaabbabcdbddcacadddcaaaacdcdcbbdbdcadcadcdbdbbdbaccaacbbdddacbccdcbbbaddcaabaacccadcdbcaacdbacabacbbccbadaaddabbabbabccbcddcabcbbacdbcacaacdadcadbcbacdbbbcccdcddcbcbbbbabbccadcdbdacbbabccacbcdcdadcaccdbbbadcddddddbdccbaadbaabbbadbaaaaddddabbadccbbbbcabbddbbadaacdacabbacdaddcdaadddcaacaabddcddbdbdbbadacddbbbdccddaddadbbbbadcccbbdccdadcdaadbcaabcdcbabcadcbadbaaabcddaaccdddadaccbcbdccddddbbcddbcbddbbbbcbbbabddcbcbccaaacbbcccdaaacccdcbadcdadaaaaaacdbacccacbaccdbbbcccbcbdddcbcacbbbccdcacbbdaaacdddbcdbddcaddcddaabdccccbcacdacddbdbcccddaacbadaddcbcddcaccbcccaadbdcbdddddcdcdbbddbdbcbcacbdcdccbabbdbdaabbaaadacbcddbbbddaddbddcbadcddbbadcddbaacbabbbdcbbbcbbdbbcbbbadbcacaccbbbdababbbdcddccbaabcabccccaadcbdcdcdabdaacddcabddbcacadccadacccabcabacdbbadaccbaaaabacabadcbbcdcdbaacacdddccaaacbaacdcabcbaaaabbbcaabcabbdadabbaddcbcadccabaadbcadcdcccccdccacbaabadabaaadbabbaaadbccbddcaadbdcaacbdaccaacaccaccbccababdcbbdabdddbdaacddadaddbddbbdbcbccabbbbbddbbdaddabdadbaacabdacbaadbbbbbccccdddbbacccadcabbbacadccccdbbabddacacacdbacdbaddbcbbdbcabbdcaddaacaacadcdcacdcabdccbabbdcbccbcdacaabbcdbdbbdbbcdbcbcbdbbacbdcdbadcdabcadbdcdcbaadbbdbdabdbabadbccbbabdbcbddaddabdbbdcdadbabadbbbccdbdcddbcbbaadddaddbabdcbdaaabcaddabcadcddacbcaacdabbdcacccbbdbdcacbddbbcdcacaddbbcadbdbabadcbbdbddaccdbabdcbddabdadadcddcacbaddbcccadddacddabadbaabcbccbdabaabcaacadaaaddaaabdadabdaccadaaaddbabbcabcabaadbdccabcadbcbaadddbbaadddaadabcdccbdbddbdcaacdddcbcababadbddbcbcdcbaddbacddcdadccabacdbdaadcdcdabbabaddacbbcdbacabdcaadaddaaaadadbcccdcbbbcabaccbdbdabcbdbbdaddcddddbcbaadadddcdaacbccbdacccbdcadcbddddbccdbaaadaaaddacadcddbbaddcddabbcdcccdcbccbcabcbabcabaccadaaaadbbdcadaadaabbdabcdcbacbabccccbabbcaacaacddacdddacccdbabbdbbdbacadbaaddaaacbbabaadaaadabcbadbbccbbccddcbdbdadbbcccaccbbbcbbaaadbbccaccbdbbbdccadbaacdbbaabadabdabdccbdcaadabaccddddbbacaaaccccddadadaaccbbcbadbcdadbdcdabacdcaccacbaacbdcbccbadcdcbaddcacbcbbabadababadbbacacbbacbcccbcdccbbccaabcacddaaaaacdcbbdacbabacdccaabcbdbbbacdbadacaccdbadccbcaccabdadcabdcbddbdbcccbadddabbbcdaaadbaaaadcdbcbdbcacacbcdbbbcdccdbbaacbbcbbbddbaabaaccbcdcdddabbddbcbdbddcbacdabababbbdcdadcabdcddabdbabdccadbbdaacddbddbddaddccaaaacacccbacabbddddcbadbcdddddbbbacacccabbcdcbbabaacdbdddbcbdbcbaaaabbbbccbccabbddcdbcaadcccbdababaabadccaabbbccccbdddbcdbbbaadaaacbddcaaadabdccadbbdbdccacaaaabaabcdadcbddbddbbccbdcbbdbadcacadccabbdccacbcdaaaacdbcbacaadacdaccbbaddddabbccddcddaababadcdccaadcbacdbbaddcbdaccddcccbcacbbbdabdcbccddbacbdbcdabaddbcbcbbccccbdadcdadacbcdcdacbccdcaaaacbbdaccadcaccbacbadaacdaccbdbdcabbbbacdbbcacdaabddcbadcddcacbcbbacddbcccbbcdaadccddacbdaaadbcbddcbbcbccccaaaabdcbacdcaccdbbbadcccdbcacdbcbbadbbdacddcbaabaddddacaccdcbadbaabababaabdbcdaadcabacbbaadabcdaabbbbcbbcadadcccbaccabccbabbbccacbaadadaddbdddaadaabccdbbcdbbbcdacadaaaddaacdbabbcabccadbddbdcccacabcacbcbadbdccadbddcbbdcbdbacbbcaabccdddcbacadccadaaacaaccbcacdbcbaddadabdaadaadabdddaabcbbacddbdcbcbddddbbaaadaadcbbbaabddccccbcbcdacbbdbbdcabccacdbdcacaaabbcacacbabccaccaddbabdababacdbccdcbcddabaccacbaabcdacbbaacbbabacdabdcabcadbdccabdbbccbdcbdadccbdbdbdbadacbcbbbcdbdbddaacdbdabbcdcbaddbacacadbdcdcaadcccbcaacaaaccddadccabdbcccaacabccadacbbccdabcabdccdaddddabcdacaccdcdaadabbaacadabaacdadabdcaabccabaacdcbddabbdadbdbaccdcacbdcdbccdbbbddaddbbdadacdccdbacddaddcadbababaabdcccdccbcbbcdcbcacbcbabbddacbdacdabcdcbbcdcaabbacbdbcbcdbcbdcdccdacdabbcdbdddabdadacbbcbaccbcadbbbcbdccbcdaababdbcdbabdddcadbdcbddbdbcbbddacadaadadcdbdadcbbacbcbcdcddbdddcacbbddbbcdaaacdababdccabbccbdbbababaadbcbccbdcabdcdbbabcdbaaddcacdabcdbbdaadbaadcdddacddcadbbbadacaddcbdadbbbaaacdcabcbbccdaacadcabbddbcbbcdadbdcacddadcdbacddacbacadbdbbbcdbdcdacabaddcacacccbdabdbddbbaccbbbaccadacdacbbddccbccbbcadaacbccdcaadbdbcacbdccacaaddcdbccbdbbbcdbbccbdcdcbddcacdccbdddadabaccbdacabcbdddcacbaccaddcbaddcaabddbbddaccbbacbdccbcbdcdddbcbaacacdacbbbbbdacbbbdcddcbababcbbbdddaccdbcacdcdabcdcbcbbcddcdbcdacdadcccdccccbddaddbaddbdbdcacdddbbcbcabddbbddddadbbbabaddccaabdbdccbabdaabdcbaabcbabbbdbdcdbbbbabacbdddcbdadbdccaddbdccbcbdaabadbbcacabbabbbabdaacbaabacddcaddbabadacbaadcabbbccdaaadbbcdbdcbadbbbcccdddddcacdabdcabadccadadaadbacdacaaaadbababdccabcbddbbbcbbccdaadddaccbcbcdbdacddcdaaacaaccaadbcaadbacaaccdddddccddbaccbbdbcbbdbadbcdbcabacbcbcaccbdadddbdcbacbaabdabcaccdccddddbbcbabbddbbdbbadaabbaddbadcadbcdcdaaabddddddadddccbdbbcddccdacaaddbdcbcbaacbdbdabcbbabaabbaabddbabbdbdcbbcdccbdaddbdacaaaccdcdddcbbabbdadcaaddccaababaccdabacbdadaccaacabbdadacaabdbadaacdbddadaacdcbcddaaacbcabdbcdcbcbdccaadccbabcacacbdadcaadbcaaaadcacbbcacadacbcddcbbbcdddadbaacbcbaadabdbdadcbaabcdaacccbdabaacdbbbcbcdcbccbbacbaccaacadcbabadaadbdbaacdadccbaddcdddccbabaabbddccaabcdcbadcdacabcdbdcdcaaddacbccaaddbacbcdadccdaabbcdbddccdbccbbbadbbadcaaccaaabccdcabdcdcadddcccbacdbdcbdbaddbccaaaccbbcaacddbbccdbadbdddacdcbadbabaccddddccbddabaccadbdcadaaacccccbabbbaadbbcbabaacdbdcdddddcabcdaadababbddbcbadbabacdaccbabddbbddadadbcbabcacbcbddabbabbcdbdadbcaddabaacbddadbccdddabdbbdbdcbbacacdadbdaddaacadbccaacaabdcadbadaadadabababacdacbddcabaddbdbcaadbdabddcbbbaaaabbdbcabdaccdbcdcbdacadadaacccdbccabdbccadbbadaaadabcddabbccadbaddbccdabbdccdcbdcaddbabdbddabaccadcababbadcbbddaddbbaaaaabbcdabcbdaabaaacddddabdbbbcbbbbdbbcdcadacdccdccbaaaabbacdabcdbcaccdbbbbacbacabbbaadbbdbbbcbacdbaccaabbbcbbdcccabcbcddbbcdadbcaaccadcabbbcdbdcaddbcdaabbdbdcbddbbbbcaacbdbaadbbddbbabbdadbbccabdaddacbcdcbaddcdacdbccccaccbdcacbacbaaddbbbbcadcabbbbabcbccbbdbcdaaacccbddbbaadccacdadcbbadbabcaacddbacdbdbddbdcccdcbcadcbabdcbbaccacbbccdabdcabdadcaddadbccbdbdaadbbbadacdbdccaccacaddaccaabdcacadacdccdbdcababbcddbadacbbadadbdacacabddbddbddbabdacacbaaadacbababaccacccadbcddbbbdbdbdddbbcdacaaaaacbcdadaabcaabbdcdddbbdbdcccaadcddacacddaacbabbbbadcccdbddcddadcdcbbcdbbbdcdbcdbabbaccadcbcddbdcdbddbbcbbbdbacadaaabbbdacddaabbbdbdadbcaccadadbaabdbabdbaadcdabcddcaccadabaccacdacbddabddabdddabccadacacdddcbbccdabadabddadbcabbcdbadbbccaccdbbbccdadabbdccbdbdaadddddcdabcdcdadbaaabdbabdcadcbaacdbbdddadcbbbddaddddcbdbbdadbdddabbddddbcadbdcbcbdddbbcdccccbbdbcdabbbbdbddaacabdabbadabdaccbaadbdbbcbddbcbddddadbabdbdbcabacbaabcaaadbcadbccacccabbaadbccbdddbbbdcadacacbbcacdadbdaddbcdacdaadddbacabcabcaccdddcdbddadbacabdbcdcccdccdbcdbccdddbbaddbcaccdabddabadbbcccacbcbaddbccbddadbdccdccbdbacabcdbcdabdadabdbcccbdbdadbaacbabdbdccabdbcaccdbcdcaccdcbbdcddababcbbbcccbdddadbddacbcdaacbcbcccdacabbccadbbacbadaccaccbdbdbbabddccbbdbaacbdaaaacbbddaabadccdbbdacbacadbdddcccdcccdaabbacbcbdaadadbabadbabcdacccaaddabdcccadbadcacaddbddbbcbcdabaabdcabcabcccbbadaadbccbababcbadcaabbadaccbabcbacbddcabadcdacaababbbaddadcdadcbccabbdaddbbccbcdbdbdaccbbdbbddbacdbbbcdcadabdcdbcbbcddabadaadadcbacaababbdcddbacbcabaccbabccadcbddbdaabdcabddcbcaaccdbcdcbdbabccbdcccaabdbbcacbccabdcaaacbccbadbbaddacbddbadadadadccacbddcddbddbbdadbddbcbaacbabbcbcccbbcadddcbdadcdcdcdababcddabdcabdcabdcdcacddcadbcbdcccbcacababaccbcacdbbccaaabdbdbdbaabcaccbdcabaccbdbcadccadacacdaddcaabcdddaacccdcbbacbababbadcdbdcbcddbadaabcadabadaaaacdadcbdbacddbaaccdbcbbdabddbaacdbccdcbbbdbcabdbdacdbaadbacddcaabccaaddacaccaddbdbcccdccabdcabbbccbbddbbcccbccbabcacbaaddbcbdcccbadcbbaaacdaccabcdaacadaabbccdbdcbdccacddccacaaabccaccadcbdbdadbbbcbdbcacdbaaacdbcdbcacaccbadcdbccdbadbabcacacdabbbaababbadaabcbbcccdcaaaacaadbdbabbbbbadadacdbcabcadaccddcdcadbacbbadccdbadcbadadbcdabcccaaaadbdbadccdcccaaccacccdbcddadadacccddbcbadddcbcacbadbabcdadddccbcbbbcadbdcacaabcabbbdcccaacadaccccdbaddcbaccabdcbddaddccaccbaabcdbcdcbdabcdbbbbadcbadbcdcddcccababcabcaabaaabbbbddcbbaadcbdbdaaacbcbcbaaacacbdaadbccbaccaddaccdcdbbbcacbdcdabadacdadbdcdccacabcbcacbbdadbbcacbbdcddcacccbbbbdabaacbacbdaadbbbcbddaaaababcccddbdcdccbbabaabdacadcddcdccaabbbccadbdbacbdaccbdcaddbacdddbdadccdcdacabaaaddddbcddcaccdabcbacbdbdaabaacdddcabdcbddaacbcbbbbadbacbaacabaddddccadadcccacdbacddaaababccddbabcbaabbddccababbaaabbbadbbbddcdddaabdcdcbacacabdcacccdadacadbabbbabacabbdddadddbbacdddcdaacabdaccdbdacabbcabcabacdbadbbdadadbbcbddbdbaaaccdaabbdabaddddbdbbcccdbbbbaccbccddbbdadcdbbbcbcababdcbbbdabcdbbadaadaddcbbccacdbbbdbbcbbdcaabadacaaabdadbaabdadcccbcbbbaaddadbddddbbbccdddaabacdbbcbdcddabddacdbadaddbdccdbcbcdbcdcdadadaddddbddaacaaabbbddabbdcddbdadacaabaadabcaddcdadcccacbbcbaddbbcdadaaababaaaababcddadbcadbacdcddacdbabacbccdddccbdcbcaccbdacdadbadbdbcaabadabacbdcdbcabadbaccacdadccccaaccdcadaacccbdbcbadbdaadbcbbbbbddbacbbcbdbdcbabbcadaabbcacccbabbbcaadcdbcbdddaaccabcabbcacaadcabcbbacadbcddbbbacbdbcddadddabbdabadccabbddcbccdaabbcadbdcbacbdcccbdbdbbbdaabdabdacdacddbadbdbcbbcadacccdccadacacbdcdddbbbddaabadacaaabbbaabacadcbdbcadadcddcdbbcbaaaddbcbadcdddabacacbbabccdaabbddcbddbabbbcacaddacbcabbbaabaadbcbcddbabcbdaaaadbbccbcbdcddcdcbbaaccbabacdadbbdacacccbbdccbddbcbaaddadbcbcbadbabdaadcbcbacdabbdcbccaaaadbdaadadcabdabbdddddaaadbcaddabdbadbacbaaabaadaccdcacdddcaabdadacdbcacadbdbbccbdbcddaddbcccbdbaabccdadadbbddcbacadccdadcbccccbdadadadccbababdbaacbccaaadcbdacbbaabbbaaabbadcadcdddcccdbdbdcdccddcadbcddccadcaddcadbccabaaaacddcabacbbdcddcbcbcbbdcbbadcdcdcccdcbcaaccbcbcdccbacbcdaacadcdcccaacccbcbabcbbaadbabccbdbbcaddcbaadcbdaadadaabdcabaaccdcbdcbbddcadccdbcadcbbbdacbabddddbcaddcdadccadcbdacbdbccddaaccddcccdbddaabcbbacbaddbacdadcbccdbaddaacccbbbadcbcacabaacccacdbacaadcbaddbaabbaddacbaacaccdcdbddcdacdadaabbddbcacbadabcadbccaccabbbdbcccddcccbaabdadabaacdddbaadbcdaddcccbcaadcdbddcddaacadadbdbcbdddbddbdcaadbcbaacbdaddabdbccdcdbabacaaaaaabbbacacbdcdadbcdacbbaacabccdcbddaacdcbdaaabcdadcdaaacdbcbadcdbdabdbcdccaabdbbcdcdcbadbbddabcaccaddcdabbacdbbbccddddadcaaadbddcbdcbcddabddbaabcbbadaacacccdcdbcbbbacbdbbcababcccbacbdddddbcbdcbcbadcaacdadbdbddaabbcabbbbcdabbaddbdccabdaaadddbaabdcaabbdcbdabccbacdcadcabbbbbccaabbcdcdbbbdccabacbdcbbbbbadbdddabbddddacabbcbacbcaddddcacaabddcdcbdacbcccddcabadcabbdcacbbccacabaabbacacddabbccddacdaaddddbdababdbbbdcaaabbdadbbabcccdbdbdcacababbbdccabbdbacabddbdcadabbcaabadcdcccdbcdddbcddadbcbdbbbbdccdbcdacbcccdacdbcbaaadccaacdccdabcbdcddbdadcacbbaccdabddcabacdacbaadcbacdaaaabaccacaaacddddcdcbbbdddcdbabdcacbddbdccdaddccccbddbdbbbbaaabdcbbcdbdbcbcddbacaccccbacbcaacdaacaddbcdccbdacbcccaddbdbabcaadddcbacabbddbbdcabaaacbddacaacdababcacbdcbbccabcadbcadcabbccdcccabdddabbadddbbbabdccddcdadacdcadcabaaabaababadcaccdcbaaadabcdbcddadccdbdacadcbbcdbbdcdbcbcbbbacaccaadbbccdbbaaccaadbccbcabcdbaccbaabddbaaabcbcccaddcacbdadadcbbadbbacaaabcbccadcacaaadcaccdabdbcddddcaabddbbdacdaaabacadadcbbbccaddbaacaadbacababdbaadaabcbaaadbdbbdabaabbcbdbbabccccbdbbdacabbaaacabcbacbacaacbdadadbbddcbccdbbddcbcdaccadaadabdcdccdbabcbbddcdbdbbacaabccbdbbdbcccdbcabbdcddcabcccddcddacccdcddbbdabcdbbbcacbcacabaaddbcdbcdcdcbabdabbadcbabaccaccaacadbbcdaccabcddcabacbacdbdccbdababcbabdbcabdbdbadaadaccccbbbbdadcacabbdcbadacccbadacaabaaaaddaaaadaddabcdacadccadcdbadabcacdbdcdddaacccdacbdcadacddbdcbadabcdabacaacccbccabcbadddddbcadccbaadcdcaaccadaabaaaddadbdddbabcabbadaadbcdbaaabcdcdadcbbbbccbadddaccdbcdadbabdbbaddccbbdcaadccaddcaabaccbadbacdaaabcbbcabcaabcdabbdaadaaaaabccbcddacadbcbbbabdccdaddacbbdccacabcadadbdbdbadaabccdbccbcbbccbcacacadbcdacadbaddbcdaaddabbddccbccdaccaaaaddbbacbcbcccdbcdaadaabdabcbaababcbcdacacbdabbdaccdbddcbabbbacddcbdacaacbcdcdaddacddddabbcaacbdcccadddbcdddbddbadddaaacaccaacbcdcacdbdadadddababdcaddddcdbadddbcdcaccdbabbbcaccdbdaabcbcbdcddcdbcbabaddcbaaaaacbddcacaacadccbdaccdaabdacdddbaadbaaaacbbabbddcbbcbccadddabcdcbbddbaadbbbacdabcbdcdacbbaaccdabdddbddadacacbbdcbabdbbbcdcdbccccbaabdbdbcccdccdbdddbcdcacddaabdcccaccbcdacdbbacaacdbcdcdcaaaadabdaddcdbdcaddacaaadbacadaddbcaaaadadbdaacaddcdbdcbdbadbbbdcddcacadcdddcadcdaaddbdaaabbcbcacadaccdddbdcaabbdadabbdccdabbdcbccacdabcacbbbababcdaadccaabbddccabdcaabcccaabdacccbdcdcaaaccabbdcbbbabcccbcdaadcaaccbabdaacbacadbbbcabccbdbcbdcadcadcadcbdbabaabdcbabacbcbccaabaadabbbadbabdbdbbddadbcbbbdcabdcdabdbbcbababcddcadcccaaaccccccdccbacdcdcdcdbcbaacddabcbcaaabadbabacaddadaaabddaccdbdcacabddbddadccaabbbadadabcdbdccababdcaadbbcbadcbbddadabdabccbacdaababbacadaddccabbccdacbababbdaadbcdadcabbacdabcbbdcdddcdabbbdacbdddbddbbbcbcdacbbaacabbadadbadddbacccbcbdbbbacbbcbaddddbaccdcbbcabbbdbcbcbbabbccacbddbbbaabbaadddddbabcbbdddaddaabbdcccbabbccaabcbbdcbccbcdbdcdabbaccdbabdbcddabbdcbaaccbaccbcccabbdadadbdcaacbccdcadcdbbddbaccbcaaccacacdcbaaaaaabababacbbcacdbaadbdbccdaabadabadaaadcbcdcccadacadaaabbcbabbddbadabddacccaacaaaacabcdcddabaadbabdbcaddbadadcaabcccbddcddbdbcbdabdbbacadbcabbdadbacbcdabcdddcbadabcbaadadccbdabdbcaabbaccbbddccadbaaacabcbbcaabacaaddccaacbcacbddacbbcbcaccabcbaabccaaddcbbddbdacbcbbbddaacccbccbaacdadacdddbaacbdaadbdbabaaacbcabcbbadddccadcdcdcaddcdadbbbaaabbdbbbacdddcccaaabbbbcbcabdadbcbdabddddabbbdcccbccbaccccdbcdaabbbacacbcbadbcaabbdcaacacdccacdbdadbdacdccdcabbadcbbbccdbbadaddacddabaccaddbbbdabadccccdaddbddcdbbdbaadcbacccadddcccbdcdbdcdabbcdadcbcdcdcbdbaaacddbcddaaacddadbaacadbaadbdaabddadbcddbacdbdbdbdccbdbcddabdcaccbdcabdacccacccccdbbccbbaadacdcbdcdbdddaddcdbbbaabadaaccbcbbaaaaccadbaadbbadbcbbccbdacddbdbcdcbbdccdadcacbdcbbdbabdaabaadcbbdbbbdbdcadcbccbcdaaccdbcddbacccccbbdbdbcdbbdabdcddccbbbcadacabcaacbabbdbbcbaaacbbbcdabdccccdcdaddbbdccccbbcadcbbccdddbbcbacacdddddcadacacbddcbdddbbdbdcdccdbcbbcacccdbbbddabaabbdaaccacbdbaaddccbcbabbacbcbddcbdccdaaadddbadbcbcacbcbcacaddababcddbbdcaacaadabcccccdcbcdcdbcbcddbacbdddcbdcdcbbddcacacdbadbdbbcaccbabbaadbcaddadbbcccdcbddbddabddcdcbccddbaaaaadbccabaaaccdddadbbbbddaccdaabbadadcccacdbaabddabdbbbdddddcacbdaacbacbcaadcacacbdcbabddcccaadadbaddbccddcdacaaadccdbcacacbcaaccddaadadcbdcaabbbdacbadabaccbbaccbddbaccaabccdadacbacdcbccdaddbccdaccaabdbbcdcbdaaaaccbabbadccaaccdcdacdcbaaabdacacadaaaabccccdddbaaabbdbcaacdcabcabaaacaaacbadbbabdbadbdccbccbabdaccadcbaaddccccabbacaaaababacdcdadccbbcabbbcbbddcbcbbaaaccabaacdccacabbddcbcbdaadacacabdcccbdddbbacbaadcaacdadadadacacbcbbabacbdccccdcadbcddaddaabaccdbcdbbaacabbcadaadbbccbdbaddaccdddcbbbbddddabbbacaccdacccabddacbabdcbcbdbcbcdabdaabcadddbbadbbbbdacdcadaddcdacaacbacbbbddccbdaaddbbccbaacadaabbaacaccdabaaacbbdacabbdcbcdaccbddbddacbdaaaabbbbdbcabbdddddddccbbacbdabddbdadcbaccccdaddddcdacccaabbdbaabaaddbbdabbabdbacdbbcaacadabdabacacbdccbbddabdadddbaddababbaacbcbaaabdccccbbdbacaaacdddaddbdccadcdbcadcdcdacbcdababaddcddbccdbddacccabdbbbadbdbbadcbbabadcadcdccdbbcbadbdaaadacadccabaacaaadcccddaacbbccbbdabbddcdadacdddaaddcbabadcccbcdbbaabacbbdddddddaaadddcbdddcbcabbbdbcdbaacabddadbbbdabadaacdddaddcdcbbcdbcaacaaddcabaacbdbaaadabacbdcadbdacaddcacdbbbdbdaaaadcddacbbbabddddaaabbacabdbbaacbcdbabdcdcbadbcdccdaabbcccdabbdccacdcdddbdcdbcdaaccdddbdbdaacddaadacbbcdddcacbcdaddcbcdbadbbccbbaaccabadacbbbdcddbcaddbddaacadacdabaadcddccccddccbaaddaabbcbdcadabbadcadbbbacdccadaccdbadbccbddbadbbdaacdcababcdadcbacdcbcbacaaddaccbbdacbdaaacbbacbcdccabcaddbcbaccbacbcdbbbaabddaabbaddabadccbdbdadbddccadbbbbddbbcdbdacbcabadaaabacdcccaddbbbbdbcacbbdaccbbbdbbadbdadbdccdcbcacaccbbbadaadaaaaadaadabaaacbbbbcacbabcacddbcaddaacddabbcbbcaadcddbacacacacacdccacdcdddacbbbbbcdbabaacdabbaaacadacaabbcbaaabcadacbdbbbcaaddcbacdddcacbabcdadcddbddbcaacacabbcabdccbdddadcdadaadbcccdacbdbbcadbbabcadcadabadaadbdbddcaabdcbcccabadbccabbbcbdcdadaddbaccbdcdbddbadbddddaadaccdbacacbcdbbbaadaacddacddaadbcbdadcbbdcbdbcacdbadadcdddadacdcadabcdcabbcbabadbbdaaaadabdacabacbcccdabcaaabbbbaddcaaadbdbddccccacdbbacacddbaabcdbbaaabbbaadcaabaacdaaadccadacdcbdabbbbdaddabdcabbbaabdbddbcbacabccdbdbcadbbcacbdbccdaddaaadabdcabbdaaadccadbcdaabddacbacdcbadbdbaabbcdddbbcdbdcaababbdbdbdaababbbcadbadddcaabbccdbcadaaddbbbddadaadcdcaababddacbaabbcbccabbbbaacdbaacabddbdaddacbaccdbaabccdcdcdddacccccddacaabadadabdbbbbcbbadbbdddbccacccacbbaacdbdbcdcdcbddbadbbaddccccdadabcadccaccddbdbdbcdadadcadcdccbddcbdbbcbbccccdaaccaddabbcabbdbcdacccbacbcbbcabdbadabbccbbbadbbccabaadabacccaaadbabaadaaabcbdaaabcdaddbaadcabcdbcdaacabcabbdbdaacccbcbbccdbdcaadcadbdacccbccbbcddcabcdddbbbdacdbcaacdbabbaadcccacdabadcbabacabdcdaacaddcddcbaccbaccbcccdacbcabdcaddaaacbdacabbaacacdbadbbaaabadbbacbadbbaaaddadcabaabbdbddadcdbbbadbccabaccccaacdacdddbaaabacaaccbdbcacadcdcbbbadbccddddaaacaadbcdbbbcdbcabdbdcddbcbbbabddbccbdbbbbbabcabddaccddadcadbbdcbbdbdaccdddcdcbbbbbccddddcbaccbddcccbdbabcccddcdddaddbabbdabdccccacdaddaacbaaabaaabacccbdabdacdcacbbaadbddcbacabdacdbcdbbdbdabacdbdcccaddbdadadcdccdcaddacccbcbbcbdbccdbacddbcdddbcbbcacdddbacddadbdadbacbdbbdccbcbbbaccacccaaddadaddbccaaccbbbddabcdaddcabaadaadddbccabdbccbcacaabaddcdbbcdbadbcabcccbbcbababdadbcdaadbacbbdcabddbdacaddaacdddbbadcbccabcccccbbacdbdabbcccaaddacbaaddcabadbdbbcdcbaabaadbcbbccabccbbccdcbbcbbdcdadbbbdaccbdbadbbdccccacbacdcddadcbcbbdcbacadbaacbbcaabadbacaaabdaacbccdbcbbcdbddcdccbcbabcabdccccbbcccadaddbacbcbcbaccbccddcccbdcbacdccdccbddacacacacbabcacbbcbbabaaacaabbabcdacbabcabdcddacadadbccacdbccbcbcccadcbdacadcdacbdbabdcdabacbbbdcdacbcadddbddacacabccdadddcabcdabbbbccadaacaaaddabaadcccbdbbbbbcadbccbbcabcdddbadcdcdacacbcacaddabbacdcabdddacdadacbaaadbaabdbbababbcbaabcdaccbdbcaadacacdacbcccbcbacdbdbdababaaaddbabcbbadabdbadbbacaddbcddaadcbaabbbdcaabddacbadbbdcbabacabddabbacbdabbbadccccddcbbacbaabddbbbbddbcdddadaccbbacdaacabcadddcccbabcabacbaccdbcaabcaadcbdbbdbcbcadbcdbdcddccdcbdcaadaddddaaabadddccbdcdbadacccdbdcdcaddadabbdcbaadbaabcbdcbdccdddaaabdbcaabbccddacddbcadaacdacbaadbaaababbadaddcddaccddcadaccbcbbdbadaaccdcdaaabcddabccacbcacbbbbccdbcdaddddbdcacaddabbdbaccadacacbdabddbdbcdbabaadcabaacbdbbdbadaddcdbbcdbdbdbcbaadbccbccaaddbcbbdbabcdbdcbdbadbaacbabababdabbcadcdcbdbdaaabacccdbcdddadbbabadabadccdbcabdacdddaabaaaadcdbcdaabccdbdaaccbcbaabcbbdcddbdcaccdbadaccbcabacababadcdccccacacddbabdbababacdcddcabccbbcabcacccdbcbbcadcdbadacdbdaaaddbaddddaddcadbbaabacccdbcbbdbbcddadcacaabdadbbacabcdcaabccccdaabacccacdcaddddaaabdbbabbbaabcadbabbbcdccaadccbcbdbcacdbabbdabcbcacdacdadabcbcdcdacdcdabcabcbddbdcdaadbaaccbdcdcdbbaadbdadaadccababcadcbccacccaccddcbbdccacaadccaadbaddcdbdabaacaabaddbaaaabbddbadabbddbacbaacadcbcbddadaddcdadddcdacbacabbacdaadaabccbaccbacdacdcbbaacbdddabcaddaacdccdaddabdbcbcddcaaacaccddbadcbcbacbddcdbcbddcbbddabdbdcaccdbcdcccbdccdadcccdccdaababdbcaddaacdccacbabcdacbacabacdaddccadcabdadcdbbcbbcccdbdbddbccbadbacaadadbcdcaababdabaccddaabbabbbbacdcbbdadadaaddaaccaacccdccadbcacddbaabbdcaabdcaddcacdacbbddaddccccaddddcabbbdaabcdbacddbacacbabcdababbbcdbdddabcdcaacacddcacdbcbabdccdbccaabbbaaabcbbcccbbbacacccdaabccaccbdccbbdddcbaccbdbbcddbbcdcabaccabababbddccccdbbccaabdbabdcdbacdaddbcaaddcddbdbdbbbbbdbaabaabdcbbcabdbacaadddddabbbcbcbbdabcaaacbacdcdddbdaccbccbdbaaababbabbcaaccdbcabdbbacdbdabdbbdcabdaabcadddcbcbadccaaaccddccbbbbaaaaabbaccaadadddcbcdaaabccaadadaccccbcccbaabcccbadcbaaccbccdcabddcdbdcbdaacbbadcccbbadaddcdaabacacbaccdabcbddbdbdbadddbcacbaccbcdadaacdaccdccabccadacaabbcccdacbcbabcbdddccbaadbadddcddcdcaaabdddadadddddacccbbacaadccdddcbdccacdcdadcdbbadaaccaaddcdbaddbddcdbdaaacbcbbbcdaccadbadbccdaaadcacabaaadccabdbddcaabdabcbccbbccddccbcabacabcbdbcacaccdbaaadbbccaabdccccbaabbbdabdcbbdbcdacdbccdbbdabaabbbddcaddabcbacdabbbcacdddcbbdacbcdcdacdabccbabbababbcdbadaccdcdbdcdbaaadaddbcddadadcabcdccbddcbbbccccbcaabcbdbcaddbbdddcadaacbbacbcdcccdcaacbcbaaacdddaddadbcabbaaabddbdcaddaadbcacdbdaaabaabbcbdabbdcbbbbaccbbbbabccbdacadcbadaddcdbbabcaadcaadccdaddbbbdbacacbbbbbacabcbaaadbbabddcbaaccddbcccadaaacacdbccdbdbaccaccbbaddccabadaddcbbdcbdbaaccaaaaddddbbbaaabcbabcabcccacdacdcbbcbcdbbcdbbdcbacbbddaabcbbccdacacacaccbcdddbacaabdbccacdacdbdbdbbcababdcdcbddcbdcabddbbbbdacabbcabbbcccaadcbbbbcacdddadbabbabbbcabdaaadaaddcbccabcdcbcdaccbdbbdcabadcccdddaaadbddbabdcaddbbcaacddbcdbbdabaccdccdadcaccdbabadbabbdababbdcaabccbccacdaddcacbdbcacdcbbccbbcacadbadbacbadaaccaabadccdddacaddaddabddadcacbabdaaababbcdddcccbababdbbcdcdacbcacbbbbadddacdcdcccbbcbcaadbcccbbbcacbdcacdcdcddbbdcbdbbcdcabcaaaabbdccdbbabdacccdaddbdbdbdbddddcaddbccdacbbdaaabaabbbdbcdbddbcddcbdabdbcdcbadbacdbddacadbaabccaaadaaddbaaccdbbbbababdbcdaadabadacbbadabcdcbccbbaddbddacccdcbbbdababbadcbccbdbdbdbddabadccacdcdbcacdbcbcddacacbabcadacaabacbbaaaabdbccacbadadcadbccdcbddadbcadcbcbcbdacbaadbbccccbacdadccdcbbacbaaaaddabbbaabbdcabdaacbacaaabdbcdbadbabdcdbaabaabbdbacdaaaccbaabddcaacdaaccabcadacaaaacdcccbaaccacaabaccadbdabbcdbbccabacaadbaababddbbdbbcddbbaacbcaacbabcbcbbcccabcdabdccddbbbdbaabdddaaddabbcdbabcaaabcadddcbcdcbcccdacbbdacaaddddcaadbdbdbadccbabbacbcbbcacacdacadaccaaaaccabcdddbbdaddbbccdddbdadccccdddddcacdbbcadcdbddcaccddbbddcbadadbbddacbadbcaddacdadadcdbbbbadacdaaaacaabcbcdcaaacdddabbccdbabdddcddaacddddacaabaaababdabcbbcdbdabacadaabbdccbdaabcadcbacbddddcabcdadddaadacaacbbddcdbbdaabcdadadabbddacccaacbbbbbadaacbdcdddddabbdcbdabbcbcdcabdaadccacacddccbacbcbcdbcbcddbcdabaabdcddcbdddbbbddccabaacbabbbcbdbdbaaddbdbbdbbbcbddadbccdbbbadabacbaaaacdadabaddbdaadbdacaabbbaadcbbddccbcbaddbadbcdbacbcacbbadaacdddabcabcbbcbbdbbaccacbcabacdbabbbcabcdcbcdabbdabdbadcdbbdbadadabcabbcbcbadadcdabacaacdcbdcdbddbaadadabcdbcddbcbdcbbcabcdabcddddcaaccbadabcdbbcbadcdccbcdcabdcabdaabbccacaaccacbbcdccadbddaadbadadbabdacccbcaaaccddbdbcdaadadbbbcabadbaadbdadaaccbcbdaccbbadbdbaacbacbaabcbacacdbdcacaadcccabcdcbdcdcaacbadacbadaadcadccccabcbadadabcccdacbdabadabccdaabdbaccdccddbccdaaabbbcdbaacdbbadbcaadbaabdcacdaccdcabccbbcdacbcdaabadbcaccbdcdccbcbcbbdbaddcccaadbbddaaadbaaabcacbbcdaabdddcbcccaabdbaccaadbcbbcaacddacbdcbcbdcdbadcbcbdabbbaabbdcacddbadabdacddbcabdacbcbdccbccdccbbddbdaabccacccbaabbbbbbddddcbaababaaadcacadcbaaaacbbbbcadbdbccddddacadbdbbcacdbcbabcbadbacddbaacacaddbccaabdcaaacbddabbbdbadcccdacbcaabaaddadabcdbccbbbbbadacddbacacbacbbccdcbcabccdbccccdbcaaaabdaccccdbaaacdcbacbaddaddcddcccbdddabcbdabdddbbcdaabacddddaabdacaacccadbaaddcadcabdcbacbacaabdaddadcbbdbdcdabcadbdcadacccdadbaaaaadbabccaabacccadaaaabcbdccbabdadcaacdbadbdbdbbadcbbaddbdaadadaadadcbabbbacdaabadcacdccaacbbcdbbcccccbdabababdaccbdddccbcbdaacddadcdadccbbdaaaadbcaddaabaacddacbcbaaccdaacdaaabcabddddccabbdabadddbbdbbcaacbadbddadabadabdcabcdadaabbaaddbcddccabbccdccddabbbbdbaadbcdcbabbbdcaaaabdadccbabdbbddccadabcadcbaabaabdcbcdbaacabddddacadbcdddccbaccbacadcaccdbaabccdddcaaadbdbdbdaabdcdabbacbcdddaabacbccdcbbcccdcdbdcddabdbdccbacadcaabcbbddaccddbaccabdcaaaabbcadaacdcbabcacdbcdaadcaaddbabccbdbbbacbdccacdcdddababddcabdacccadcbacccdddcabadabbbcccdaabcbcdcbbdabadabacdacdbabbcbccdbcabddcaaddbdbbbcddbcdbbbbcbdaaaccbddbdbddcdcbdcccababbbcbdcdcddacaacbddddcaadbdbbbacaddcaadddadcdbccbcdbcdbbbbbccccbdcbddccbbadcddbcaaaccdcdcddaddcaaadbcccdccaaacdaadbadcddadbacddadbcddbdbccbcdcdadbcadbdabccdbadabacaddcababaabaaccbcbdbdbcadbdccbccbdbbdcdacacbcccdcccdadbdbbdbcdcbdacbadaacdbcbacabdbbbaacbcdcadcaddaaddbcdcbdcdddacabdaccaacaddadccdcbadcbddbacadabddaacbcacdaaaaadcdabacabaadbbccabdabdaacabddacdbadabacccaaacdbdddbddcdbdadcdcaaddacbbcadbdcabcdbcbcaaaccbcbdacbdbabcbcacdadabcbdabcdcadcacaddaddacacdcabbdbacabacbddbbdbddbbdacbbddcdcdccaddabaacdddccbbcddbbaaacabcbdacadaaddbddcbcdddcdaacdcdcdcbbcbdbacadccaabacdadacacaaaccbadaddbacddbbbbbbacccadacddcbbbbbbbcbdcbbdaadbadcabdbabcbbaadacdadbadcaacabbddadbdabdbbaddddcdccadccabccddcabbdadddaccbacbcbdcaaadbcacaccbcbbdcbcacabbddbbbbddbbdcadcadaccccacbaddccbdcccacbdcaaccabbcabbbddcbdabcbcddbcadbabdbbdabcdcbbdadccbddbbadcdabbcadccbaabdcabaccdcadbbcccccbadbbbddbbabaaabbbdcaabdaccdddabcacaadabbddcddcbacadaccdaadacacbcaabdaaacccabacddddabdcdbadcdabdcdbddacdbadaabcccbdadbcbcbcbdcdbbbabaacadbacddadddadacadbcdaabcabdcbcbacabcabbbbcdddabddcbcaabdbcbddabaddbddbaacdbccadccabbbcddcabababddbddadcadcdccccdbcdbbcaddcdbcbcccaaddaddddaabccdbaabddcddbabaaabbcdbbbdbbbbbbcbbaccccdcdddbdcbbcbdabacbcbdacaadaaabccccbcbdabcaaaadddabdbdadcccbcaddbdcacbabbccddcdbababbaaadcaacacbcbdbcdaccccccddbaadbccaaadddbaaabdbdaddcbcaddbdbcdaccabcdbcaaacdacbdabacddddbccabbabcdaadddadbadabaacbcdabdbcbbacddcbcbabacacabacaacdcdbdbddccbdaacabacaddbcaadaddbaacabcdbbadbdccbaadacaabcadabbddcbaaacbbaccabdaccccaadcbcacaacbaccaaacbddbcbabbddddadacbabdbdbccdabadbadcbcbbcdccdacdbabaacadbaacbdabcddaddcaadbbaabdabdcdbaccacbdcabdbdbacacbbccbbbccccacabbcccddbccaacbabaaacbacdbddacbbbbddacdbdaaadcadbbbcdddabbbcccbccccdcaadacbcdbdbbdbbddabcdbcaaabdbdabccdbbcddcabcadbcdddabcccddbdacaaaccbadcbccbadabbcdddcccbbdacaddccdcacdccaabbadbbbdcaaddabaabaccbdcaabcbcbcbbbccddbaadaaaddaabbbcbadbcbacaabdbadbbcaadbccdccabaddcbdbbbdadbdcdccdbbdcbdaacadbbcdbcddacabdabdbdaddbbabdacbbdaacaddccbdbdbdbdddaccdacddbdbcdcadcdbbcccdbbddbaaababacadcbbdacadbcaccccdaaaadbbadbdcdddabadadcaaacbccbabaabdbaddcaadbabcddaddbddacbcaaaacbdddcaaacbdaaddbdbbcccaadabadacccacddabcddbddbabacbdbacbbddcbdcdacabdaddcdddabbbdadcddddcccdcddaacdabaadcdacbabbbbcbbcdbacabadbcdabaadddbdbbccddabcdcaaaccbcdaccdcbdbacacbddddacbdadccaadabacbcaabadbdacaddcdbbdccccdabbbccdaccdcbdaddbbcaabbaddcababdcaccbbbcabbaaaacdabddcaacdcccbccbdaccaddbdcbddcadcddacdbbbaccaacabdaacacccdaacbbbddbbbdcdcaaacdcacacaadabbcdbbaacddacdaacccaaddbaadddcacccbabcccdcbaddccacaccbcaadbaabdaaccbacddcaabbdaccbcdddaccdbddcbbaddbaaccbabbdbcdddbbacbbdcabaadccddddababccadbadcbdcbcbadbdcccdcdaaddacdacdbbabbcccabdcdddbaadcdcbcbcdccdacbbbcdaababcacaccbabccdcddbabcadcadaaaddacdbbdcababcdacabdbccccbdcbadcacbbcdcddbcbdaaacdddbdacacababbabdbbbcdaaddddcadccbcdbcbcaadcdabddaadccbccbddcbcdcbaaabcdaacccbaadddabdcaddcacaaabbdadddadcabcccabadabbcaddadbdbbadbdcaaccdcbbddaacddbabbdcddbdbbddccdbbbcbcaaadbdcbcbdabadabdddaccdabbadaaadababadacabaddcabcbbddbaabbbdddcabacaccaacbcabbbbcadcbcbaaaabccabbbabcaaccbdcadabcddbcbcbbdbddbdcacbdcadbadcccbbabadbdcddcadabbdacccaadbadbabcacddccdbdadbdabacdadbacbbcbadbbbdaacbbcdbbdddbaaacaaaccacbcabaaabbaaadddbacbacddbddcbdaadadccbbcbbaabdabacbaaaaadddccdddcddbccacdcbacbdddaddcbdbccdcddbdbcabbabbccbdabcadccdbabddbbdddcbbabbbbacbbcaaddbbaadccdadababbacbcabcaccdccdadabbcdccddabdabbdbaadabaccacdbbdbdbbbabadcbddabadcabaabaadadbcdaaaadadbdaccdbbbddcacbbacddbcaadadbcccbacdbacbcdddcdabdcddbadcdacbccddcaaaacbddcdbabbdcbccbcabbcabbcdcbbacddacdbdddbcccadbccccdcdabcabcabdbdacdddddbdaabcacbcddcdcbcabbdaccabbddadcabdcaccddcdcccadabcbdbdadabcabbabdddcadccbacdbcddacdccddaacdcabcbdbbacbdbddccccacaaadddbbddbdaadcbccdabcbabdcbccbbdcdcbbcaddccbbbdbcaaabddadaabbdcdbcdabcaacdaaadbbcbcaacdcbbcbdbabdcbdcaccdbbcaadcdaacdacabaacdccdbcccbbcaaccccdacdadddadddcdbbddcbbaccdadbcbcacbddcccacbccbccaadccddbbddadadbacdaacbdbdabaddccbadbbdbbadaddcdadcddbdcdbcaabcaaccbcdadcbbdbcdabdccbdbbcdbdcbaddacacabaabacdccccddaadbacbdbbaacadcbdcacadbdadbdccadbacdaccadcccadbddaaccbaacbadcbcbdcdbcaaaccaaaccbcaabdbaacddbaaaabbdbcbccbbcdbbdadaccdcabdaadbabacdcadacabbcaabadbdccbdaaccbabacaababbaddaadcdcddcdccbbdddbbdaccbabcacbdcddabddacddcdbaddcbdcacbdbadadaaacddbcdcdddcadacdaadbdaacdcbbabcbcabdaddbacaccdcbcbcabccbdbbbcbacbbddcbdbbdabdbcdccaabbdacccdcdbaddccdcabbdadcaabccdbdadcabddbaacbcccbdbddddcdddcbdcbbacabcdaddbdddbcabcbdacaaadcaccdaadbbacdadaaadcdcbdacaddbbdbccbcaadddcbdcdccdcdbbbbcadaaadbcdcccccddaaadbadcdcdadbbbdaacabcddcacdcadacddbbcabadaadacdcaddbcdbcddbccbaccdcccabdcbaaacdcbbaadaacbabadcadcbcabdacbccbdccbaabcdcccddddcaaadcdbdddbadccdbdcdbccbabdaabbcaaccbbddbbbabdccabaccbcbcdccbccbdbbdbadddddccaddcdcccaddbcdcdadaaacbdabbcdccbabdccaadddcabacbadbccabacbcaaaccadbcaabdacbdabcbbdccbcaddddacaccddddbcbbdbbabbddbadadadbbcbacbcdcddbbdbcadcdaccacaaacddabdbcdcdcabcddabcbdaddcccaadccdcaccddcdabadbcacdbacdcddbcbcdbacacbdbbbcbacddabbbcaabbcdddabbcdbcabaddbabadbbacdaadaaddddaacbbaadbbcdacbdbbbaadbdbacbadccacbdcddcaadabacdccdddcacccbdaadcadbddadbddcacbdcccdbaacacbcaaaacabccaabccbcdabaaaaacdaacbdccccdabcbaccaacbdcbbabccbbbadaddddccbaacabcccbbaccabababdacadcbddbbabcdabbbbaaccbaaccdbddddccccbaaabaccdcbdcccaaccbdccbaaabddbbdaadaccadcadbaacaddddbabbdcbcaddcaaadcdbbccacdbcdcbbdbddaacacccccacbdcbdaacddcdddaacbbaaadbdcaddabadccaadccaccbdccdcccdbcadbdcddbacbddbdaaccccdaccaddbcddbbbaabaaddcbcaadbadaaabbccccaccccdcabcdcbdbbabaccdcababcccbccbcdcbddbccacbcdabcadccccadcddbaabdcabccdcbacabaabbdcaacddbbddcaddadbdaaacacaadbcadbaadcdacbacabbacbbbaaaaaaaabbcdddadbbacadbdddaacacacaaadcaaddbdbdbadacdaaddcbacaabdbabbdcddcaccaccbbacaabbabbccaabdcaddddcdcbabdcbbdcabdbbaccbdcbdadcaddaadbcccdccadbabccdabadcabbaabcddddabdabbdbcbbccacdbacabaababdadbdcdbbbcbdccbcdabdbaacdcbdaccdacaccbcccbdbddbaadcbcadbbadabcdbabbbdcbdacdcddcbbbccccacdbaadbaddcbcaaacbccbdaacacdcacdcccbbbacadaaacdcadbcacbabdadaadadbabdccbdacaddacaddcdbcdcddabdccacdcdabdcccbbbcdcbdacdbaaadccabdcccbbddaabdbbdabaaaadadabccabbadcabbdacddcbaabbcbaabcaaaaccbbcdcabaadccdcbcdabdccccbabdddaaaabdabbcdcdadcddbccbacbbdabaccbbdbadddcabdadabcccadddacbbadcdbadbdcccbccabbabbcddbcdbdaacccdbbdcbabbabacdcbbaccaaabdbcaccbcdaadddabcdabddbbccdbbaacabaadaabbcbdaabbdbcccbcdbaadbcbcccabccbcbacaabaabcbabbaabaadbccabccbaacaacbdbdaadaaacadadabaacbdbbbbcddcbddcccadbdaddcdcdccbbcdccdabaabdcddcccaadcadacbbbadbddbdcbbddbbbdbacacdbcbabadcdbadbdaabcabcdcddcacdadbcadddaccbdaacbdacdccbbbdadadadaabbbbdbacabaabdcddbbccccddaabdcbabbcacbaacabbacbbcdcbcacadccabdcbbadcbadbaaaccaacacaccdccdcabdadabddbcaccccdddbabcbabbbcbaacbaddbcdddbdbcacddabbbcdaaabaabcadbcbabdabbbbddacddddcbcaaaabccbcdbdaaabdcbdacccadacbadbddbdababaaaaaccdbcdaabbaacdddaaabadccccbdcbcacdcacdabccccacabbbdadabacbcddcdacbccaacabcacadaadbaabccdadcabcbcdcbbdcbdabdcbbcaacacdbadbbccbaadccdadcbaabdcccadddabcaaddadbcdbacbcabdaadbacbbccdbcadbaabcddadacdbcdcddbddddbdabdcaacbcbbabdccdbaacabcdcaabdcbdadcbdcdabaababcacbcabcbcdabdabaabccacaadadabdbbdcbacabcaaddbacdcabbabcbcbbbaddbdcbcdadaaddcaadacadcababddcacadccdbbaabdaabcdcbcdaababbdbacbcccaabccbbbdaaccbbcbcdcbadbbaccbddcbabadaabaacbddcabbbccbcddddcbbbcbcddbbabbdadabbcacacdbaccadddaaadacddcdaddadcbccacdcdadbadacbaacbddcaaabacbabcaabccbabdcacbddaaacdccabccaddccabccaadabccaacdbdcdddcdcbabcccbcdbdabbbcdcadaacccdaadcbbbbdcdbadabdcbcbbabadcbbbbcbacccacbbbbbaccbcdcdcbcdbcabcadccaddbdadcdacbaabccabccadbbdaccdbbcabcaaaaddaacdacacabcdaddcababaadcadbddcabcdbadbcddbcdabdcdddbcabbbcbddcacbccaccbbdcbbdabadbbcdbddbdadadbcddbaccddbbacbababadbccabdcbbcbdbcbddbabacbbdabccbbaadbabdcabadccacadbcdacdaacdcabaadcbbacccddcaccbcbaadcbdbacbbabdbbcddabdbccdbcdccbcacdbdcddcdadddbdbadcdbaadddabbbbcbbdbcbabccbddbbccacdaaaabadbadadbcdbddccaadbdbcdccbbbdbddacadacdbccbcccccdcacbbabdcaacbacccababcbbbcbbdacaaacdbcaacbabcbacbabdbddbdacdcddbdbddacaddbcbdbbdadbadbcdcabdacbcddbccbbaadccdbdbdbadadbbaaaaadacbcacbccbcdaadccbcdaccbbdacadaabbbacccaaabdbbddbaadaaaabbabaddabddacdbbddbdbbbbabdcbcdccdcdbbcbabcbcdcbbddbbcddbdabdaabdbcdaadddddbdbbcbbbbddddacccdddcdadabdbadacbbdbbdddccdbbbadbadacabcdabaddbdabbbdbdbbccaaacacddccbcdadddadbdadcaabbddccbbddbbbbadcdbcdbdaccabccaddadaabccdabdccaaabdbaacddcabbcbbcbbbbcbcbbacacacadbadcaddadacbcdbdcabbaacdcacacddccacbbbbcdaadaacccabccdbbbbcacbaddbaddccbcbbddaaaabaabadbbdcddbbadadadcaaaadadbabbdacdabaadacbbdccaaddbacddbdbbddabbdddacbccbcdbadddbcbcbbaaabbbdabbdddaacddcaabbacabadddcadacdadccddccbdccdbaddbccdaaadbbbcdcabbdddbdbcadabcccbdddaccbabcdddaabdcdbacaacbabbadddbacacdbbbdcdbbbbbcbccbbcddbbbbadccbddbcccaaabaaacabdcdaabdddcacaddbbdbbaddcbcbcdbaaababdaabbdbdcdaccdddbacbcdbbdaaababddadbbccaccadabaaabbbdbaaccaaddaddcdacabbaabcaabccdcbbabbacbbcbbaaaabbbadcbababacbbdaddbabbabccdcbbcbabdbdcccdbdbcaadccdcaaacabdddbaddddbcacccdbbaabbcbcaaabadddbcbdacdcbdbaddcdacbacbadcbcdaabbcbcccbacbabbbccbdbcaaacdbacdddbcaaaacbacacbacadabbacadacdcadacabbcdbddcdacdcadacbccdccbababbdccacdbccbcccdcabbbacbcdabdabcaccbacadabcbdadbcddbddacabaaadbaabbdcbbddcadbcabbcaabccdcaaadaadbcbbccbccccadcacabaddcdacbcadddbbccacccdcdbadaaaadbbadcdbdbbbabbddcdbaaccdacddaddbbabcdddacdadaaabddddaaacacacddcbdbabddbaddacdbaadcbbccabdbddcbcdcabcaaaadacddadbaddcbdabcdddcbdbbddbbcbaccdaccccdbaadbdbacadabadabcdccdbbaabcdaabcbcdadbdbdabadcaccbddaaadcdaddbddccacbcbcbdbabaddabcdbddbbcddadadbadccbdbcdcdcaddccaaaadaacaddbadcaddadaacddcbbcbbaaaaabcaabbcacabaacbacbcbcccbacdacacccbdccadddabbbaddccdbaaddbbdccaacadbdadddbcaababcccbbcabbdadcadabddbadacdbaacbadaadacbdaacddcabbcaddccbcdbdcaadcadacaccbabbcabadcbdbadaaacbadcccdccccdadadbacadbdbbcddddbaddadbccacbccbddbbbbcbdbbcddcaaabddccdddaadcaadadcbdccbcabbaadadccdacbdbbcbdabcaabdaddcbccddbbacbddaacbaaaadbdddacdbacccdacddbcbabbabacacdbcdbbbdbadcdaadcabcbbdccbddbcdbdcdaadabaacabbbcdcacbdcacdbccddcabcdaddbacbdbddbacadcbddccadbccbbdcacaaacaddaadcaddaadbbababbaababaacbbababcaacddbbaadabdbbbddcdddbadcabdcdbcdbcacacdcbddbaccbcbcbcbbccccaabaccbacacddcdbabdbbccddabbbcabbaacbabcdcbdccbabcacdbabddcacbddaccbbaacbdccdccbdadabbdbaaddcaaaddbcabbdacdabadcccbbbbabbccccbadbcbcdaadcabbbdbbbddcacbcdcddbabacbcbbadadddabbcbacacabbdbccacaaadabcbddaabcbaababdcbaaabccaabcdbcbcdcadccdddaacbbcbbaddbdaddadddaaadabbcadcaabbdccaddaccdcbcccabdbbcdbbbadaadbbbdabaacabaaaaacdddbaacccacdabbdbcbbddbbdbbaadbdcccbddbaccdddbbabbadbbacdaabcbadaacadcadaaddbbacdcbacaddaacadcabaabcabcaabccdabacaccbdbabdabdbbdcbdcdbacdbabbbabbccabdbaacbcaabddcabdbacdbababcdcdbdabdbbabbdbabacbccdbbbbaacacaccbadddaabaabdcabccddbccadaabaacdaaddbcccbdddadbdacddddcdbdadcacdccbaabbdadbdabbdadcabacadcdacdbbdcddbbbaccabcbcdcbaaacaaaaacdbbbcbabbcbaabbcaddbccbdaadccabadcdbbcacbacaddadddbaabaabbdcbbdcddddaaccccdcbddcbccaaaccdaadabbaaaddabbccdcdbcbccddaccbbcacdddadcacbdbbcaccadddcdcabaabcbddacbbdbcdbddaaabdabcbaddddbdabcbbbadacabbcdbabdadadcdbcdcacadadbaccbcabdaadcbbdaabdababbabbbaddadddabacadadaccccbbabccbddddcabdacdddcbcaabaabdaacbcaaddbadacbcaaaabdccbadcaabdadbcbabcabacaabbbdbdcaddaaabacbddabddacbdcdbccccdaddbdcababadbbdbbccccbaaccbbdaabdcdbbaaacbacabbbbcbbcaacccdadaadaaacbcdaadabaaabddcdcccadcdbbacaddbbddcdacbcbcabdcdbcbcaadcbcbcadadbbbabbdccbacacdbcccbbccabcabccbdaadbdbcbbacdaadcacbcbabcbacdcbcbcbaccaccdacbccadbdaccbaaddddbbdaccabcbdbcdccddbddcbdaddcbaaabaaaddcbbacbabbdcccccdadabdaababcaaacaabdbaccbcddadcabddcadcddababcbddaddbacdcadaadaabcdcbbbcadaaabadaacdaaaaacacbbadcaacbddcaaaccadaddaabdabcbcbdbbccbcdbacccbacddacdabbbadbadbcbdbdbcbddcdbdabdabcacbcbabdbbbcdbdbdabcaccaadcbccdbadaacdbddaddccacdabdaababcccdacdaddbbcadddaddadbacbdbaddbddadccdabcdddbdaabcdcccccbbababadbbcdaacddbadaccbdbcbbcaaadabaddcbccdbdabccdccdadccacbcbadccabbaaccbccbaaccdcbdcdbcbbbdcbdbadbdadaadbcbdaabddbacacabbbdadbadcaddbacabbcbabdbddacaccacbaabacbacaddaccdbaabcdbbbbbccddbcadcbcaabcccdabdabbadcccadadabdabdacdaadbdabdbcaaaababbbdadcbddabbcaaabdcabaccddabcadcbdcbdcbcbdcbdcbaaaccbabdcabccadadacdbcbdabddddcdcabbabbcdcaadccabcaabbcbccccbddddcdacccacbcdcaadddcbccdaacdddcbbcbbbbadaaadbdabbccdbaccdcabdadbbbdaccabbaacbabdbabccacbbdabcaacacabcccbdabdccbcbcbaacdaddcacdadbaabcdababbacbccdadacbccbccabbdcdbabbabcacdcbacababbdcdccddbdddcbcaddacbcdbdbdccbdcccadaadcaddcdcdccdbcddaabcbadcabbdacdddaccdadabccababcdccaccbbdbddaabcdbcdcdbaadbaaaabcadcabbbabcbccbbcddaccbcaaaabbbadcabacbbdcdabbcbdaaccbcccdcbabcdbdcbdaaabadacddbabbacddcdacccbdbbcbcbabbababaacacdcdbbaabdbadbcbcacdccdccaabcccddbacdacbbacadaacccccbdbddbcaacabbcabacaccdccabbdddcbdbdddbadbcddbcbacbdbaabbcabbabdaaadababbaaacdbdbadacdddabbcadbacdccbacbbccbbbcabddbabbababbacbbbdccdabbbacabadacdabddbdacaaabcddccaadabccbadbaabddbcdcbaccadbbbbcddcaccadbabbabdbcdaddcaacadcdccababbbdddabcddcdabbacbbaaddbbdacaadccdbaaabacbbcabdbdbbcbbcbcbadbcabaddcdaddabdadbbcaaddabccaacbcbdcdbbadcddbcbadbcdcbcccdaabadbcdbdddbcaaccbdacdaabdccaabbddcdcbaccdaadccdbacbcccbccacddadccddbcdccccddbbdbadcddcbadcbbcaadbaaaaccabcdacabdacbababaabdbccaaaaccadbcaadccbbdcbbcbabbadaadadaaddcddcdabcdbaaadddcccacdadbddbbbdaccbdbadaaaacbacbbcccacbddddaababcbaabbabdbdbadcacbdbacddddbbdcddcddcbdabaaccbdbacaddadababbccacaabdbbbbbdccbacbdddadaddacbbaddaccbcccbaadbbbddaaabcdcbbbbcbcababbbbcbabaabadbbddbadbaccbbbdacccbcabadcdabaadabdaddcaaaabcccabacaddbaababddadccabcdbbabccadacddbddddccdaadddacbacadbccccdaccdbbbcdbababddccdabddcaaaabbadcdbdbadcdaaacbdadddbdcbabdacdbbadccdaacdbaccbbbbaaaccdacadcddadbccacbddcabdccacabaaaadcbaababdbcacbabbdbdcccdcadacacddcacdbacbddaddadccbcccdacadbcabcabadcdacddcadaabbccbddbadbcacbaadbabcbabbadaababadcdcbbadcadabddacadcaccaccaacbaddabbbdcdcabbdcbbcbaaaaabbacbbdacdbcadbadbacadccaabdbbbddcbcbccbaccdbacadabadddadacacddddddcdadcdabdbdadabddbdcbcbbcbdccaddccdccaabaaadbbbddcdcadcdcacbbacaadccaddadbbbcbbacabccddcaabdbdcccbbccaadaaacccaaacdbaabddbabaaabddabcdcabadcbccabaaadacbcaaddaadbdbcbcbbbcbaabbaabdbbacdcbbdaabbbdbadcccaaaadbddcdbcabccdcdddcacbdcacdcbcaabccbcabbcdbbcbcdcdcdcbdcdabdcabbdbbcbbdcbcabaadaccccabdcdccbbadcdccbddbcbbaddcddbaaddcddcdbcdbcadcaaccccdbcbddcbdbabccacbccdadbcacbadcaabcbabbdcaaacbdcdbbccacddbabababcacdcbcdcccdcbdccbccdbbdadacdccaabcddbbdccacbbdcccbcbcadcdadadddddcccdcabddbaaddccdbccaacdacbccabbccacddcaacbcdabddadbddcdadabcdcccaaccdcdabbbacbdccccadddcccccdcacbaadcbaabdadadaaabdbabdcbdddadcbadcbdacbababcccdccdbabcaccdcdcccdbacddcdbbbaabdddbcddacdbaddddbbdbcaabdaccacdaacadddacacdcadbacbdcaaccdacdbdddbaaadcacadbbcccbcdbbcbbccabcdddaccdadabdabcbccdccdaccabbbbddaddcaabdabddbddcdaabcddbcadabbacddabcbcdddcdbcdacaccbabcacccababcddbcdddcbaaaabbdabccddccdcbbcccadabbdadbacaccbddcccbacdbbbaadcbabacdaacbcccacdaaabbcdccbcddbddbddcccbccbdcacbdbdbaaacbadbabadacbdaacabbbdaddbccadcbcaaaacbababcaabdbbdaaccddbacbdccbbdbccbcbdbabadbccaddacdbdbbdddaccddaddcabdcddbcdddddbdbcabaaacacdabadbaaabcdbcadbabbbacbdacccccabcacdaabcadbcdaadcdcabcaacdacdacaacdcbaabdbbdcaddcdbdbbcdcdbabddcbdabcdcdcdddadbbbaabadbccabdbbacbbdacabbdbccbccbdcdaccbabcdcaaddbccadccbabdccdcabccdbbcadcddaadabaabdbcdaadacbdacabdbbaababbbdacccbdbaccadbabaaacdbcaabaccaabadbadabbccdbddbcdcccdccccccbbadbbbadbcbcbcbcbcadccbbdddcdccbbdccddaabdcacaaadbccbdbbdbaaacdcbddccadaacadcdccabcccccabcdcaacbbbccdcadcaadababbababccbdbdccdaccdcabdadcabaadcdbaaacadcbaddbbccbdddabdcdadadcaabdddbcddacdcdccdcbadbbcbcdbcbcdacbaccbdabddadabbcdaaaadcdcadacabddbdadcbaddcbbbdbdbababacaababcddccdaadaabcdabbcccbcccdbcbdaddcbccdabdbadcdbaacbaacbaaaaddabbcddccadbdabdcbcbdbddcdccbcbcadbdbbbacadcbacccacabccacacdddacacbaaccdbbbbbbccdacacbaabcbaacacbbbabbaddbddadcdbdaddaabbadadbabddaaacbabadadadbbcacbbabbcbddcdacabaaaccbcbadbabccbccdddaddadcacbabcababdbdcaadacccdbbaddbbdadcacaacdbbbdddabbbbbbccbcccbabbabdcbdbaccadadccadbadbcbcabbbbcabcdaabbccccdadcbbcddbccccaaccaccdbabcabcbcbbcbccadabacbcdabdaabbadbabacbbbababddabddcacdcbbdccbacbdabbbbcbacacddabdabdcacbaadcbaadddcbacabdabddccbdcbdccdccbaadcdccbbddaabdcbddbccdaacbabdcdbdaadccaabbadbcbbbbddadddcabbaadbabdcdacbcdcacccbdbaadcaddbabbaabbbbcaacaddabacdddaaccbabbdddbdaacbbcdcbaaccbcddabababddcabacaadbabcdbacadbddcababadcabaabacbcabccacddadccbcaacccababccdcaadcbbdacbaadcbdcbcbdacbccdaddcbdcdacacadcaadcddadbadbbdccbcbcaacacbccbdaacbcacccababdcadcdbbbcbdbdacddbbadbabbdbdbabbcaaaaacbdadccaadcccabdcdbacddcaaacdaccaacdabaaaacbbbcccddcdbbdccabdaabacadacbbbabddbdcbdabccaccdbacddabbdabcddbbcbdbdabbacddccdcdaabcbaccdddbadbdcdbcdaadddacccdcbadddabddbbbccdcccdbccddddbcddcbccacabccababbbdabbaaacabbaccbdabdccadcadbaddacacdccdcddccdddcbadbcddcbcbdccccbabccaadaddbcbccdcbbdbdccadccccbacccddacaaadbcccadbbbbabaadbcbccbbccbdbdaacccdaabdbbbbdcadbcabbbccdabcbbbacadcabacadcbcdcdaabbcacbddabdcbcbcbadccadbccadbbabadaadcdccaaabdcddcababcdadcbbbbabcaabbdadabaddddadbbbdddbbbbcbdbbbadaccabcdcacadbaddbbadcdabcaadbdacbacdcdbccbbdbaabacacbaaacaddcbadcdddcadadcdcdccbccbbcbccaccccbaddddcaaabcddbaadaaddcaccddabdddbcbadadbbdbccddcdcdabacadabcdbbcbcccacbbbababbcdccadaacbdbbbbbbdccddcbabbdddccdcbcbcddcaadadcdcbbddaddbcbcabaaaaccbadaacbaaabcbcbadccdbccdaabbbddbccdadccbcadaddaddccddbbdcbdacbdacddbbbbcdccdbddbadcccaddbbbaddadaadcacbbbdbcbabddcbacaddbabadcaacbdbadccadcdddabcababccbdbaccababdcaaadccbbddaacabbbaaacdbdaccdbbbcddcaacccdbacaccabdbdbbcaaadcdacabcdcdbdbdcccaddbadcccaabacbcaadbbbacdbbadbdddcadcdbdaacacdbdabababcacddbcbaaccddababcaddcdbaabcaacbaccadddccdcdcabdababcacaccdaaaacdabcdccdbcccbbbcbcdaadbadccddabdddcdcbbccbbacbcbadddbcbccbbbccdaccdbaadadddbbdadaadbadaddbbddaacbbbbbadddacbddacdabcdddbbdbcddcdaacacbacbcaabbcbadcddbaacbbbaddbbdcaccaabbbcbbdbcccbdbbabdccabdbadbbbddbdcdabcdcadddbdbddcccbbdcdbbcacaddbdcaaddabacccacbcaacbcddabdacaaabcdaadadcdbbdcddddbdcaaaacdbadaabcdabcabbadcbaadbbabcbbaaaadcdacbbbcdadadcabdcbabaaaaababbcddbddabbacdccacaaadbacbbbacdbddaccbadcbdcbddddbbbcddbcdadbddddbcdbdabbbcdddababacdbddadbbbbbaddccbcaccaabdccdbbddadbabdadbcbbbddaadabcaabddddbacbccbdbacbabdcbdccdbbbaadabbcddcdbcbdadbacbabadabbaababddccbabadaaaabddcccabddaacddabaacaadadcadbdcddbaddddbcbaaaddaaaccbcaddbddbcdcaaacabdbdccdaccadddddcadcabddbadbcbdcbdaabcdcbbdabcdcdabdccdacddaddbdaababccaacdddcabcccadbdadbcbcdcacdbcdabdcacbcbddcbabdabbcadccbcadaadaaddadccbddccddbdccaccdaccadaddadbaddbbbbdacbddccabadcbdaccaaadcbcdbdcabcaacbbaacdbdbccaddacbccababdccabdbbcbacdbccdaabbbcaadcaabadcadccdababddaadbadbadccccdaabbcbbcbdacdbacddbbbdadbbdddbbddbcabaaacdbabaacaadbcdcbcadbaadbcddaaadbddacbcdbccbccdddaacdacbbcbddddddbadcbaaacdaadbbacddadddbaaacdcccabbdcabdbdcdbbbbaddbccabadbcdacddabadcdabcbdcccbdbdccdabdddccccdabddbabbbdcdacbaabacbdcdbacaddbaaabadbbabcabdccbcabdbbcddcdaacbabaacccddcacadacdbdbdaabcadbdadccacbddcbdacdddcadabbadbbbdabddabacbadbbdabbadbcdacbacdbbcbddbadddcbababbbabacbcdbbbbaadbdbacbbbccadddcdcabdcdcbbdcaabdccbdbcbbdbbcdcdabdadadbcccbcabbcdaadddabdcdabaddabadaadcacdbdcbbccbbbccbadacccccacbddbadbddcdbaaaccbddcdadcddbcccadddadbcddbccdcddbcabccdbcccadbdcacadddbdabcdaabcbacdcaacbbcbcdacbbdaddddacaaddcbabcbacdcbbacddabdccaabaadaacacbddacabcdbdbbcaadcccdcbbcbbaccbacdccdcccddcddddbbdbdbacaccbbbcaaddadbbcdcdbadaaaadccdabbdbababadcccbadaabbbacacdcccddaacdbaabbddcbbaacdddcaadacccddbbcdbdacdacaabcadcdddcbaacdadacbdcccaabadaaccdbbbcdbcdcbcddcdcbccabdddadbdabcddbcbaccacccddddcdddbaabcabaddbcabbccbbcacbddabdddcbddbcacddcacdcbdcdbbbadbcdddacddbcddbddcaccdbcbcdabcaabbddacdbbbabbcacbbabdccbabadabcaacacddabdcabddacbacbbaccaaacbdbcccabaccdcbcaccdcdddbabaabccaccaddbdcdbadcdbccbbcbaabacbbaaabcdacaaccbcdddaacdacbadccbbcaabacacaadabaabaccaabaabddcdbcdabcbabbcdcccdcbaacdcbdddaacbbcdbbccbcdbcaccadcbadaccdcdddcdaccbbcdbdcdbccdaacbacbbabbcbcabbccadcdcbddbdccccacdcaacdbbcbdaabaacdcbdadcacbaaaacaacbcccccacaacbbadbcdcddbcaadcabdaabddcadabcadbdcadaaabbdbbcdbbddbccdbdbbdbaaadbbacbaacaddcbbaddcccbbacabdaacccabaabaabcabbdadbccdbbcdbddbaaadadbbbcccdbadbcdacbdabdabddcadcdddadbcbabddaacbacbcccccbbbbdbadcbcacbdddcddddacbdddabbdacbbadcdbaaabaaaadddbdacabdaaddcaababaacbaaccdbbdaacaccaadbcddbccababccbdadadbddddccabcbbbbacaccacbabccccdcbbadacadabbbccccbdacbdbccddbcdaaadbbaaccdcaabddbcabbaccabcdbcbdbbccacdabbacabbdbdadbcbdacadcbdaadccabdcbcddbdabcdcdbdaaaccdbcdabacbcbcbdcdaaccdadccbadacadccacdcadaaadddcbaabbddaacaaaabacccaccbcdbcaaadcdadaccdcdbbcdaacbcababcbcdbadccadcacdcbcdccaabdababaddcaaacddcdcdbcabdbaaddabbcbddabdcdbabdcdcabadcdaccccdddcbabadbbbbaabbdaadcdbbbbcbdacccaaaaacbaacdaabccabbaadbddbaacabbaacdaabcadabbdacadcbadbaadbabdddabbdddaabccadbadcdccddacabbabddbadbbbddabacabdacadbdcbadbcadbacaddddaacbbcbbbcbccdbbcacdadcdaaaabacacccbbdacaadaadacdadabbbacbbbdbaddaabcadcbdbdbbcacadcdddaddabbccaacaadcddbdacacddcadaccccbdadacacdbaaadbadabadbadcaaabcbaadcadaddcdcbaabbdbccbbaadcaaacdccccbddbacaacbcddcbdbbcdbbabdaaadbcaaaddcbdabacbabdaacacadccbadacdcaabbcdabcdacdbbcbaccbdbcdbbadacccbabdabddbbdabacdaabbadbbcdcacdbbbbbdbdaaddcbdadacbbabdbbaabacddcddcababdcbcbbcdcdddcdacaadabdaccddccabbbcaaccbaccbdbbbbdaacbdcbaaaadadccacdabacdabadcbcdddddcbacdcccbcddbcdddddbccbabdbdaadbdbccdcbbdcdcbcbcccacbbaadbbdccdcacabbdaddabadacbbbcdccbccddaddbbddccaacabcbbaabbcdbbddacacaaabdcaadababaacbbadbdcbcbcbbdaddabdacaabbcabbaccbaadcddbccadacaddaabdbacbccacccddbcdcdaaaabaabbdbaaaaddbccddcabccbccbccdbccbdaddbdcaabdabbcbbadbabababaabdcbdbcdcbcbabccbbcbdcaddaabcddbbcbdaabcccdbcdbbcbbbbabbccababdcbbbadcaccccbdcadadcabcabadcccbbdbabaccaccbadcdabaaddbbaabcddbcbbbaabadcbccdcdbbdbdacbddbdcdcdbcddacdcddddadbacabaadabbcdbabcdbddccabcbadbabacbbbcdadcacdadcbdabcaccbdbdabbaccacccbdbabcbcadabbabaaccacbdbcaaabadcbcccdccbbacabdabaacacccddbbaabbbdddbccaaacbbdcbadbbaabbcaacbdacaabbababdcacccdabbdbdaadbabadbddcdaaaadacddabadaaddbcabdabcbdaddccacaababbadcbbcacdddbccccdcddaabababaadcbaaaaddabcbcccaaadbcbbbaccadcccdbcbbcabcadbcccbdcaaaadbacbcdbaaddbbcaddcbadbcacbadaccaddabbadcdabccbbbacbabadddccadbcbdcbbcadabdaccaaadbcddbaaabbbdadadbdcdbcadbbccccccbbccdbcbcddadcdbbaacabdbbaddbdbbcddbdcdbcdcbcbcdcabbbcbacbacaaabcbaacdacccddcbcaaaadadabcadaaddaddbccdbacccaacacccbabaacbadabdbcbbcdcacacdcbcacabdabcdccabcabaadcdbdbaacdcbdabaadbbbcccbacdabaacdddadabaabaabdbddbdcdacbdcbdbadaabdcccdbccdcabbbadccbbbbccbaabdacabbdaadaaaaddcabadcdbccbccdbdbccabdbbadcbcacdbacabdcccadadcacaadabbdacddcccbabdbcacaabcbaccddbdbbacdacdadcbdccacbbcaadcaadbbcdbdccabdacbdaadaccdcccdddbbcbbbbdddbbbaddabdbcbdcbdcbdbcaccabdbbcdadaddbdbdbccbcadbcadbadcdbbccdbbabacbaadadaaabbacdbaacbdabbcadabddaccdadcaaadbbaabbcbdbcababbdaadaadbbccdbcdadcdcaadccbbaddabddcbcbaaacdcbdcadcabaaaabdacccacdbccbccddadddaacdaadbbadbbddcdaaaacbabcabdddabdabcaddaccbdbacadaddccacacdbbddadbdaccbcccddbdcccabcdbccbcdacbdabdcbabbdbccadcaabcbabddccbaaaacbbcadbdcadccccdddbccbdcdcbccacabbbaccdddcccabcbabcabdaacabdccadcddbbacbadacaacabadbdabbbcdccabdbccbdbabdadbaddabadadbbdbbcabcdbacdccdcbdaabbbaadadcabacdabcabbdbbdcbabbddabbccaddbcccabbbacccddbacbbabcadcbcdbcaccadcabcdccccddcdadaacbdcbcadbddcabbbdacbaaaacdcbabaccaddabccbaaadacabbbbbbacaadccbcbccbbadbabcabaaadccabadbbcdcbdbbbdddbcdbbcaadbacaaababaadbddcdcbcdcbdcadbdacbacadbbdbcdacbbccaacabaabaadbacabaccdddccbbdcaacbbdadccdbadbcddddabdbcbabbadacdcbaacbdbaddcacaccbddccbacadcdccddcdbdadbdabdbcbaabbdcbdabadbccbcdbbaacbaabdaaddbcddcabcbddbbdacabacdabccadddacdddbddbdadbaddacddbddbbddbdddbcccdaadcaccacbcaaacddacdaacbccabaadbdcbccacdccbbdcbcccaababbccdacacbbcabbbbbdaadbaadbcbdaacddaabdbcaaadbdadcacccdcdccbabbbccaabcbbbabacbcadbdacabacbcaccccbdcaddbadabaccbbbbaabaddaacccbdaabadababdbadbdccacabaabbabcabaabcaacccccabcadbaccacdaaaaddbdbddbbcbabaaadcdbdccbdaacbdacbccbcaadbaaccdbdcabaaacacccdabcdabcabaccdaaccabcdcddaacacdcacadaadbbcacbacdddddacbcbadcbcdcccdbbdddddbbbdacccddabcdbcbddcddacadcddaaabbccaccaccdcdabacadaddabaadcbccadcabacccdabccddbbcccabddbbcabbacdaccbabadccbdbcadcaaddadcdccacccbadccacccaaadbbcccadacdccdaccaddbabbddabacddddcacddbdbaabbadbddccdadcabbddccbbababbadddbabcbdadbacaacaaabbbdddcdcdbcbcbbabcddbdcadccccbadbdadbbcbdbabbabdbddbbbcdaacbddddaadcbbadacacbacaaadaacddcbabcbcccbaddbabdbbdddcccbbaababccabbcddacbcbcabdcbaacdbbddcddccbacabdcaacaddabcadcdaabbcdccdadbabbaadcbbabdccdbdaaabcacddbdddcbdcbadadaaaccccdbbacdbdddacdcabbcabcacdabbaccbcbbcaadcbabbcabaaccaadcdabcccbaaacadbaaacddccaabacbbbadaccbbdbadabcaabbcdcdabccbaadacadcccdaddbddbcccccbbbbdddbccbdcadacdabaacbbcbdadaaaacbddcdabbcabcdacaddbbbbdabdadababbabddacccabaaccaacabaadddcdabcdbddacccdbbadcbbabdabaccbbbaaccbadaaccacccadacaacdcaacdacaacdcccccddcbaddbaaaaccddbbbbcbdabcddbdcadbbbcbcbdaabadbcdbbaababcabacdbadacaddbadabdabacadcdbbcdbbdcdadacbabdccbdacbcaaaacacadbcdbadbccacdcbadaccbaaacacdccabdbabcbdcbaabcbcbbcbbccbdcadddcddacbccbaabbaabbccdabbccdcbabbbccacadaadaababbabacddccddcdbaabbbcbbaabaabadccdddcbaaadbddcabdbabcdcaacaacbaaadcaadddcaaddabcddbcbabccbdaabcccaaddcdadbdccabbcadcdbdbdbcabdabbadddbbadbdbbadbdababaaddbaaaddbcbdbadcbaabbcdccbababdbcadaaabcabcbdcdbaabcaddaaccddaccbcbdadccaacadccdbccccaccbcaadabbcbabcadcdbdbccbdcdbdcbdccdaadcbabbdcabbdcaadcccdbaacdbdcadbbadaccdbbcadaddbdbbadabcacdcddaccadcdcdcdbbadbcadbbdaaadcbdbcdbcacadacdbcdbcadaaadbdcaadaccdbadbcbdbccdbbccddaacdcacbaabadbbadaadcbbadaccacbdaddabdabcaaacadadcdbbacdadbabbabbdbaadcddcdddddcbbcbabbbabbdbaaaddaacadcacbacdcdaabdbcdcccdbcdcbcdbdbddacbddadcadcbbcbacdaccadaabbcccbbcbcdbcddbcdbacddccadaccaaddbbcdccdcacabcdddabdabddadccdbcaadcaddbaccdcdcbccbacdccccaccdcababcaaddddaaddbdaabbbaaccaabaccdacccbbcddaddaddcdaadddddabcbcbccccdabadadddccccdaacacccdbbaaaadcccdbdadadcaaabddabbdbbcbdbdcccdccbdcbaadbaadaccdadcacbabccbbdccabaccacabddabdabbcbabaadcdabcaaddadcdcaacabcbabbaddbcacdbcbbbaabdacdaccdbdbabdbddacabaabcacdddaaabadacadccdccaadbadbdbabadcbdbcdbcbacbbcddbdcadcddddddddbdccabbabbadaacbcbadbbccbadadcacddccbdaadbbddcdcbbaabbadadccaacbbddcdcaabddbaccccbbcdccbacbdbdbccddaaaabaaaaccadddcdddccbbacbcbddbaccdaadccbddadbccbcdaccacddccbdadcaacbcaccaacacdaacccacabbbabbacbbacddbdbdaabdbbddacacacbdbdbbddcdabbdcbcccdbadcdadbbabaacabacddcddcabcbcddccbaaabaacdddbccbcdccabcaadadbcadabcaacccbbdcbadbcdbaccaccdadadccaacbdbddacacaabcdbaaadcdabaddbbbdaddbdcdbaaabcdbcadaabdcacccdacbcdbbbbcdcaacbaacadabdccbadadabdccccccccbaaaacdcdbaccbcadbbacdaaabbadbadadacacbbbaaaadadcbbcccbaddaaaccdcadbddbbbcddcccaccdcdccaadcdbcccdadbcdbaccabccbaabcbcabaacaacadcbcaddabbdacadbcaccddabbbdacbdcdbbddaacaacbbbcbdbbcddcadcadadacdbccbbcbaaadddadbacddcbddaaacbccacabdadacbddbcbcdabdbbaadcacdabdabcaccdaacbdaccdabcdababdbccddcbcccbaccadbadadcbbdcbbaabcdbbddddbdcdaccdcbbbcdadbddabbbbdcddaaadcbcccdbdcdabcdccaacdbdcacbadabcdaabdbddaadaacccbabcbdbbbbccbaabbaccdbcccbcccdbacbbbdcbcccdadbbddaaaaacadcbdbddacabcacdcadaaabaadaacaccddbacbcbbacbbbaaaaccddbaccabcadcadaaccdcabcbbddacdacbbbcabbcdcbbbcdcdbcccccacdddabadcbcbbbcabccbcccacdcbbcabdacbbacadacdbcdbdbdaacdabbabacaccbdbdabdacbdbbdbccaacdbddbaaadaacbbdcdcdcbadcabaccccddbdbadcabcdcaabcdcaadacdaaaacabbbacacdaabbaccabcdcccdcacbcabccabddbcdcaccbdbaadbdccbdbdcabbdabdbaabdbaddadacacdcdaccabccddbccccddbbacbdaabdaaacdcbcbabcccccbbabcaccdaaadbbdbadbbcdabcbbbcdbbbaaddddcdbaaabaaadcadbdcabccdcccbddadddddccbbaabaddcdaacacaacaccbbacbbdbadbdbcbbacadccddacadcbaacdbddccbddabdcbdbbbccdaaacabcbcbdcdbadaacccaccdccabbacdbaadacbdbccdcacababaddcaccdabbacbccaabaabbbbdcdcbacddccbadccccbacabdbbbabacdcdbabcdcbacabcbccadadcdcdbabdcbabcdcacccddbaaaaaacbddbadcadacccccaccacababacaabcbbdcdbbacbdbacdccaaddbabcbcbadcddadaccddcabdacabaccbcdcbacacddcbcbadbbdbbadaaddddcdddcccacccadbabbcacdbcadcbccadbdcabcbbadbacdccbaadcdbdddaacabcdcdadadacdbcbcbdcddbdcbcbbadbaaacdddcbdcbbcacbbbbddcccccbbbdabdddabaaabbadcbabbdbdacbddcabbbbaddbcddabbcbbdccdcbbaaddcacabaaabababacbbdcbbaacddcccdacbaadbdacaacadbcbbbdbddabcbbccacbdcdbbbaaadbbbddabadaaabbbbbdcdbbaabaadbcdcdcdbbdbccbbbacccbbdaccadcbcbddabaaddbcccaabdddadabbbbacbbbcadddcadbcccdbabbddbbacddcbddacbabaadbdacdababdaacaddacadcaccccbbadbcbaadbabbacddccbdcdcddacbbbdcacabbcaadcddacdbabbbadbcabbdaaaacdcabdabdddcbcbabaaabaaadcdbcdcdabbdbddbbcadacbbbbcddccacdbbbcccacababadbddcaccadabdbdaacbdddadcbbbbabcaddbbcdbccddcaddccaddbcccdbbbabddbddddcdcddbdbcdcbccdadacbaddddbccbbbdcaddbdaccdddccadbcbbcacbddbcdcadabddcddabaabacdcdbdccbcccbdddcdacdacddcbccbbacaacbcadabbdaccdbdddadbddbdacbcabaccbcdbbaccbcbaaaabcadcdbacbabbcaddcbdbadaccccccdabaaaacdcbddbcaabcaabcbbbbbdcacdadbbbbcaacbbbbbddbcabbbdbcdcdbddbcabbbcdbdcaaacbabcdccadbcadcbdaaaaacaaddbabdddcccbddacbaadacccdcaacbcccdccdabcaddcccbbdbccdbabcccacacdcbbccdcbabaabddabdcaaccdadcabcccdabccbcadcbddcddaaaabaccbadccbddcacadcdbcbcabcbabbdcbbcbacbddaadbbaccdacaacddbdcbbadabdbacccaaabadcdabbcbcbbacbbabaccdddcaddcbdbbbdbabccbddaabbcccacbcbcbdccccdabbdcdaccacaddbdbcbcbccaaaaccacbdcaddbbdacdbdcadaababdacabbbbccdcbcbbdaaacabdacdddccdcdcbcadddacdadbabaddcaaccabaddddbbcdcbaddcaaccddbbabdaaaccddbaacadaacdacddacbddbccdcababbcabcdbcdbabacbcdadadbaadaaadcaacaddadccddbdbdadbbbdddcdddcadabbccbbbcaadcdaddcbbadbcbcdbddadadbcbdcbcabdbdcadbddacbdcadbcbbcdcdbcacaddbdbaddccbbccdddcabbdcccbbaacdcdbdadbabdaaaadbbbbaaaacabdcdccbbbbacacbcabbbbabdccacdbdadddcdaaccdddacaaccbddcbbdddadbbbbccabdcbbaabbbbcdcbbcabdbbdadddadbdccbabcbbbbccccccbbcacbdbdbdbbdcadbcdbbcdcaccababaaaccdabcdadddddcaabdbcbaccbddcabbcaccacacddccabaddaaccccdaaacbbcddacbcaacddcbbadbaccbacbccbcbabcdcbcbaaaddabbabadbccacdddbaadcaddbdabdaddcdbcadccddcbaacbbacbadacbdacbbcbcadcdbcadbbbaadadbdacacaddccbcccbdaccddcabbaabbaccacdcbdaddbbddddbbcbdbbbcddbadbcacbbbccdbadbddcbcbddcbaaabdbdccbabcbbadcdccdabadacdbacccdbdaddbcaacdcaadaababaaabcbdbbdaabdbbcbbdcbbbaaacbbaddbdbbddddccadacccbabdbcacabadbccbdcaccdaadbdbdccbcbacabbaabadcbadaddbcbadbbcbcbcacabcdcdadadcacbbddaccdaabaacbbbcbadcbaddabbbdaccbdbddababadabbcaddcddbbcadbcbacbaaaacabaadcccdcbacccccdcbcaadbcaacbbdbdcadbbbdccbdcdcabcdadcbaabcbcccdaacbcbddacbbcbbdaababbaaabdbccadcdbaaaadcaddcadcdccbdabccaaabaabcbabcbbccdcccbbdbdadacdbccdcdbaaddbcaaaddacdaaaabccabadabcdbadbcccccadbcdccaddcadbcbccbcadcdcaaaabdcddbadddacbdcdaadddbccbdddcdcacbacbbdacdccdcdcdaadaaaccaacaadbadbbacbdcadcdabcabbbdaaccdbbdcaaacaabcccabbcbabddcacdcbbcddddbddbabdccacbdcdaadacdbadacddcbabdcbcdbdccaacbccdddbaaacacddddbbddbbdcbbaacbcaaabcadbbbbbdbdcbaaaccdcaabcbcaaaadbdbbabbbcddddcabbbdccdcdcbbdddaaacaaccdacdadbdadbacbcccbcbcdcdcbdcacaccbacadaaaacccddcddcdcdcdadccbabcbdbbabdadddadbadadcbdcccaabbdabdcdddcbdaacddbcdbadcddccccbaaacaadccddadbaaddabaaacbcbbdccbcbcacbdcabdcdabadbcbbddccabcadacbbacaaaabddcbdbcacbbcadccdddaaaacbcbcbdabbaccabaccdcbbcdbcadcdbdabbdccbdbdccacadcabcccddbacbcadcacababdcbcbbbdbaaaddcaabadacbcbbdcbddbcdcbccbdadbcdadcdaccacbbcbcbccababdabacadcbaaacabbbabcbcbdadadcbcddbbbdabcadbbbaaabcddacdcbabdacadbdacdaabbcabababddcbabbbacbbdccccdbaccdbdabcdccaabdacbbdaaaccdcacaaaabadadadcbbbdaabcadcbadaadadadddbbbccdccddbdbacbddabddacbddcccdcabccbdcabaccbaddcdcaaabaaacdaddacdddacbdbcbdbabbaddcadbcccacacdcdabbabdbaddcbabaddbccddacbbdacadcccbcbdbcdcaadaddcdbcbccabacccbbccaddabcccacccdadbdcbdcbbdaabcdabdaacdcccadadbbcbbaabdababccaabcaacdbacbccbacbbdbcbdbcbbacccadabbadcabcdbccbbbaddacccabbdcdbabdbbcbdacbcbccdccdaadbcaababdbbdadbaaddcabbcbcddddaddaacaddbccddabaaaccddcadaacbdcbdcbadddaacbcddbadddcabdcbddaaddacaaadcadbcdbddbbcbcbadcbadbccabcdccddbaaddadbcdabdcdccaddcbacaacbccbbbcbbcbabcaaccdbbacdaacddccbdbaddaacbbbabababccadcaadcdbdbbaacbbbcdbbdabbcdadcdcadbbccdabbccbcdddcddccddacbcdaadcacadcccbccdcadbcaaaacbdacdcacabbaccdbcdbccccdbdcbbcabbccddcccbdcabdabaadbdaacadbaaddcacaaccadacdabdcbcaddbddbdcdcdbcdcddbdabdababbacbbdbacdcbddbccaabdbdabcdaabbdbadcddcadadbbdaadcacaccddccdaabdbbcadcacaaaaadadddabdcabbbdbbbaadbcaaabbaacdbddadcccddbbbcbddbbcdddcdadddacabdbaadbacabbdaacdadddcccccbdacadbdccbccacadddcaabadcdcdbabcbbcacccaaacbaaacbcacbbacaabcbcbbcdbacbadbdacacdcaacdadbbdbbddcdccdbaabccbbabaabdcabbccaccbdbccddabdaddacddacabddcbbbbbaaddbcdccaaacbaabcdcbdbbcdccddbcbabaaaacccdabcdbbaabaccbdcdadabaabacbbcbacbbcabcaccaddabccdcbbcabdbbddcbbbaaabdbacbcdacbdadccbdaddcbbadccbdadbdbbdcaddbdbdbdadaddabcbdbbadccddbdbcdddbcdcaacdbbbcacddccbacbbadcadddbddcbcdcbcadcdcdadbdadddcbcdbdccadcacbabbdbbdbacaabadccaaaaacdcddcbaaddacbcdcddbcbcbbacaccaccbcddccbabaaccdcaabadbbccdcccabdccdacdbbddaddacdcaadbbbbddaacaddddcbcdbbcbaabaddccdacdddabdaaccccccddcabddaadbbcbdcdbcbdabaccddaadaabdcaaaccaadbbadadadaacacdcbddbdbaaddcacbddcddbbaccdabdbadbababccdaddbcdbadcbdbaacbcdbbacbddbaadcdcabbacbbabdbaaabbdddcbdacddaddbdddacbccaccabdbaddaacabcdbcdbccadcdbacddbddbcdbbabadbcbbbdbbbbadcbdadcbdadadbcadddaabddacccaacadbdbcbbcacbddcddaddcbcddadbacdabcdbabcdcddcaabadcccadbacbcadcdbcaacbdabcacbacbaddccdacdcdcddbcbabbbacabdadcabddabdacddabccadcaabcaadbbbdacdaaadbaabcdacaabcddbddcaccbdbccdabdcbdbcbaadccdacccddaaccbbdbdbbdcacbacabbddaaddcdbaccbdabcccabbddbdaabacdacbdbcabdccbadddaddcccbabacadcadabddddacddbbbadcaccdbcbcadacbbbdabaadcddccbdbbbcbdbaacdbdbbcbaccdccbdbdaadbacdbabdddcdcdddbbcccabbbdabcbbdccbcabcdcdbadbbcbcaccadcaadabdbaacccdcaaacdbbdaacdcdbdbccccabcbdaccabbadaddadddbaaaadbdbdbcdbdadbaddcabadccabbabcbcbaabacaaddacadcacbacadcbccacabcacbadccacabbccbaacbcadddcccccdaccdddcdbcdbbccaaadccacdbabccaddbbdddaccbdccadaadbabdbddddbdbcdcbaabdccbcdddaadabcaadacdcaacbbcabcbdcaacadacbcabbdaddacdcbcbdaabbddabdbbbacdbcbcbccaaabcbabaaccaccabdaccbcbababcbacabbdbaabbbacadbaabcdaccccaabbcbaacbddbcaacacbddcdbaccbcadaddccdbdaabdcbcdaaaaadcaaccadbcdcdbdbbcadbaabbacdbaabbbddcadbbdccbbdbabdcbdbcaacbbdbbdbccbbdcbddabdcdadccbbdbbdccacbbbcbaacbdcbcaacbacabdccaaacdcabbdcdcaabdbbabdadbccbddaadcbdbdbcddaaaccdaccdbdcaccbaccabacdbabbdadddaabcbddbacaabcaccacabdaaacbcdbadbcabcaaccbddcbbacdbacacddabcdccbdddadabacddbbdadabcabddcacdbdbcbbbccdaadbabdbaabccbbcbdacaacbccbcdcddcdcdcdbccadbccabbbaccadbdaddcaaddcccaacabcdcbcdbddddabddcaacdcacdcaacaccbbbbbdcdbdccaacabddbcdcdacccdbccaaddbbaacdbbdabcaadccaacbdbcabddadbaacaabcbacdbcdaddaabcaccbdcbbddcddcaacdbcadbbacdcabbbcccbbdbdcbcacbadcaddaccbacacccdcbacdbbccaaaaccbcdcbabbcaadbacbdcacdcbdadaaadabccabcccccbaaadaabcbbdbdbaddabcdcbbacaacddbbdacadaaacaabcaacbcccadddcbacbbcacbabbbbbbccaadcdaadbcdcadbadcbbbcaabbccdbddcbdbaddbbcdacbbadbcacddcbaaaddbdcdbbacccabdabbaadbdcbbbbbdadccdbaabbcaadcdcaabcaabbdababadaabbaaaabccccaccbabadacddaacdbcdcbaabdccbbaddabcaccdaddcbcadccccacacadadbccabdbbbdcbbccccbdcbddcaccaacacbabbaaabbbacddacdbbdabbdabcdbadaaabcdcdcccabbdccabdbbddbdadcbcdabcaabacddbabcadbdaccdbaddbaddddbccaccacbcdcbacccccadadcccbbabbccbccbdabccdabacdcdbadbddbbacbabdadccbcbadbbddaacdbddbbbacbbddcbccaacbdcdbacdddbcbbababdaacbaaaaddbdacddabdbacaaaacaacaacaccbdbcccbccbddbcaacdbcadbbbcbdaacacaaabccaabbbaacababaccccaddbdccbcbcadcadcbcdddddaadadacbaabdbcaddccabbbacbcdddbbdaacaabadbcaadabacccaaddabbcacbcbbaabbddcdbddaccbaaadbdcbccccaaacbcdacaaabbddcdcabdddbbbddbcbdacadbdcadcbabbacdbcbdabaadabcddcdacdabaccdbcabaaaddcdabcdadbdbdbacbdcdcdddcdbadbadacdccadbaddaaccacbbdbcccdcbcbdcbddbdddcbdbbdcbacdaabacddabcdcdccdababcbdabbcdbbbbdddcdcbdbbddabababcbdcdadbcabaaaabbabacbcdadbbbabdbbccbbcbbaadcadddbbdabbcdbaccddbdbbcbabadadbbcabbacdadcdbaccaddabdccbbacdbcbadacbddabacbdcdcaacbadbdadaaccbacabacabcdbdccddbaadcdddabdbdaacddbddcaadaddccbbdaacdbbaaadcaabcddadcabdddbdcaacbbbcbaabdbacaacccaaddbacbaaddaabacddddcdadddadadcabacbcbdcbdbabcadcacdbacacdccabadcaccbbcadbaddbcbcaccadadcbbabdbcaccbdcbcbadadcaccadbbadbabbdcbdaacacccaccbdcaaccbccbddcdcbddaadabacaabacbacdbdbccdcbaddbcbcabacaabbdcadbcaabbbbbddaabcdbddbbbdcaadbdbbbbbbabbcdcaacbcacdaddbdbccbccabbaacbddababbadcddbccadcdbdacddacbdabdcbcdcbbcdaadcbcadacdcdabbbabbabbaddbccddcadbbbcbaacbadbbbdbdaaaabddadbacaddbccaaddcddcbddbdbaddbdabaaaabcdcccbdbaabccabcdbbcaacbbcaacccabbacdaaccddaddaccccccdacdbdadcbbacabaaabaadddaacdccaabccbbbcabcbdbbdadcdcccdaaddbaccdcacaccdbccaddbcbbdbacddcabddcbdcadbdbbcbabbbaabbacabbdcbabbdabbdccbbdcccacbdcddacabddddaccabdaabacccabacaddbabbddbbcabcacbddabcbdbbadbbadbcdaadddccadaccabdccaacbbaabdbaccdbaabcccbcacaaadccadadbbcbaabccdccadbadcdbabcdbadbadcbcdddbadabaadbaaabdadbacdcccbdcdbcdcdddadcbdcccdddbbdddbaacdccccdaabbbcbcbccbabacdddcbcbbccddcdabdadbacacdabcacbdcdbbacaabadcddbadcbcbdddccbadbbdbcaaadbadacbadadddaacbabdaadabcbcacdaaabbbaacbccbcadacbdcbcaaccdcbbbaadbbdbdacabcbccbddabcacbbcbacbcaadbbdaabbdcbddaaccaddcddaccdbcdaacdbbcaddaaaaccbccdbbdbdcabdddbdbddcacbcddcaacdcbbddaacbdcadcdcaddcaabbbaabdcacabddbdbababbbcbcaccccacbdacbacbadccbbacdbbdbaacdadcaadaccddcaacbabaccbccccdbdcaccdadacbccabdbcdbcadcdbbbaaaacddddaadcacaabaabcddccddddbbbbacbccddadcbbdaaadbbbabbaccdbbdcbbcbbabcabdbddccccadbbadacdaadddccbcaaaabadcdddcdbacbaadbbcaaadabcdaabdaadcadccabbabbdcdaddddcbbabadbadcccdbbcddcabaabcccbacacbcccdacacbabbddccbcacbbdddbcbbcabcddbbcbbcadccdcdbabbdbdcaddaadcaadbabcddccaadbcdbacaadadbbddaadadcdcadbcbccbcbdccddcdddbbdbdbabcdccabddaacbbccabdaabddccdcccdccdbaadbabadbabcbcbdccbdcdbdadabbbcdcdbbadbbccaaabcdbbbbabdadbabbcadcbcaabbcabbbdbdacbbdcdaaabdcbabcbacabaadaddbcaaddcbaabbdbdbabbdbbccadacbdadccbcbccabcdcbaadddcabdaadcaacdcdbdabcddcabdadbdadddcddccababaaacbdbcbbdaacdbcbcbbddbacddddcbcdccbadcbdcdabccdbbacacbbadacdbcaabaccabdbbdccdcaadccdbdcbbddacbddcbdabdaadabacbdaabbbdadadaabacbbabbbdddcadbdbbdadbaddadbdcdaddbdccddabababddccacaacdaabaacaccbccdcdddcaabbabbdaddcdcbabcbbdccbcadabbbabcaacaabacdbccddbdcbabbabbbacaaddcabacbccabbbbabbbccaddddaddbaaddaadddccbbbcccbaadbbacadadabcccddbbadcdcaddcbbbcdbdcbabbbdbcacccbaadcbacacbbdcaaabddcdcdddbbbaadbdadaddabddaccdabadabadddcaddccabdaadcbaadaddcbbbddcaabdbcbbaaadaaccabaccabdaadcabbbcaaadddaacabadbaaaccbdbcbdcccbcbacddaccdbacacbacaabddaabcacdbaddcacaaadabdcabccbcacbbbbcbcdccddacbcdadcbacaaabbcbacdbccbcbdccddbbbbabdbbbacdccabcbbbdaacccabdcccdcaaabcbcbacbdaacccacbbcddbcbbdccdacdddbddbbdbaaacbcaaaccddcbbccbadaadccccdadaacdadcddcccacdacaddcddbabbcbdabdccbaccccbabacabbbcbcbdbbaacddbcddbdadbbcbdcadbcdcaaccabcbbcbcdbcababcdcbaddbcaaaaddcddbdcbcdabadcaaadcabdbcaacaaccabaccabbbddccaacadbcabdacddabbacacdddccdaacdcbdbabccabaaacbdacdacaddacbcddabadabcbdddbcdaabbbccaabbcccaaacdcdcbaacccaaabdbabaddbaccacbaabacdcdcddccacbabcdbdcbdbbabddcbdbcdddcbbddddbabcdbdbdaaccdabbcdbccbbdbddcbcdabccadbcdaaaddddbddcacbababdccddabbbacdcabbacdddbcaabbdbbdbabbacbbcbadbabcdcdbdadbabcdddabdbdbccdacbdbbbaacdabdbcdcbcddddbbdadbdbdcdacabbbddcadacabacdabccdbdabdddccaddabcbdacbadadadddacdcdcbcabdabbcbbbcccdcadddacdbadccdaccdbcdcdacddbbbcdcdadadbcaadcdbdccacaacaaaaadbacdbccbadcaadadcabcadaabadbcacaadcacadadabcddaacacdcaacaacddacdccaacaaaddabccacdacdbcccadbcbccbbcbbbdaddacbabaaacbdbcbdaaccbdabdaaadcaccddacbacbbaccbdbbdccadabbdcbbbcaadbcdadadaaccdccbddacbdadccaaddbdabcccbcbbbddcbaccacdccdddbdabbcacdacdbacdbbcdcaccbaaddabcadcaacbdbbcbbcccabaaadcdadddddcadcabaccaadccbbdabcdcaabbdbcbacdbbcadcddaabddccbdaabccdbbdbabaccbcbbaadaaacbbdbbcdaccaaacbabcddddcbbbadabccccadbccdbbacdbbbdadacaadaacdacacbdbdbbbcacaaacccacbcabdbdbaccbbbddccbdcadbcaacaacababaddcadbacbaadbadbdccaabdbdcabbabddccabbdaddbdbdbdbadbbdcdbaacccbbdbccbbccabadcbccacdacbdccacacccbcccdccbdcacddcddaccbcadbdbcdccbbccbcbbbbdcdbbbbddcacdaabbbcdadacadcbcddaadcaddbbabddabdacadcddaaaabddcdbdbddcdcdcdcbccacddbdbddcaadcccdcdcacbccaadbbcccbdbcadbcabbccbcaabadcacacdbcdcaadaadcdcdddaccddcbdcaaddcddcbaadcbbdcdbcaddbcdacbccbbdbaddaccbdbddaadbdccbbdbcbddcbbcaadacabbacaddadacbccbcccdaabaadddcdaadccccbccbdacbbdbddabbdadabdcbaaacaddbaadddcdabdbcbabcaadbcbabdbadadccacbdcbdbbbdbadcccdbcdbdbbaaccbcaaadbdadbacbdddcacbcdcbddaaaaddaabdbaccddbadaddcaadbcdbcbadcdbdaaadabbccbbdddccdccbababacbdbddbbacabbdbcccbacbbbbcdbcddccaaaddcbbabbaccbadadbbbdccadcabcacabbacbabcccadadabcccdddaaddccabaddadaddbacbdbdccdababdadcbcabcaaaabbddcdacdaccdbdaddccabdddcacdacbaddadcbcabbacdcbccdddbcbdbcacaaaccabaacccaccbcccabbaadaaabdbaadcbcdcbaadabbbabdabaababbdabcaaddadbaccbdbaadbcbdccbdcdbbcbccdccdacccdacacccbbdcdcdbcbadbccbdabaadaacbccbdddbddbcacdbbbabbbcadddccadbdbbdcddadaaabadaacbdcbccaddbbaaacdddacbccdccbcacdaadabdccacdddccacbabcbbccaaacccadadcbcacabccccbdaabbdccccdbdccdaccccadaacacdaddbbcaccbdaddbdddcddaabbbacdcbdccddddccacbdcaadbbcbaacddddbbcccdcbddbaccbaccccdcddaabaddaccccdaccbaaccadabdabddddbddaadcdbdbbdccabdaadcaacabddaabdccddbcbaccaabaddbbcabaddddddacbababbcbabaccbcccdddbddbbbcdbdddccbabdcaadacdadddccacadacdccdcadadacadacabcdbaaaaadccbaddbaacccacadbcdbabadaadcbbcbcbabadcaabcdcaccddbabcccbcdaacaddababbcaadadcbcddcdcdddacabbcbdccadddccbbaccdacabbacddabddbbddbadaacbbdbdaccdadaadcacddbababcbdbcabccdcaaadaabacbabdbacbabbcaabdcababdabdbcdaaabbdbaaddaaccadbcadadbbccaddababcdabbbacdcdabdddbbabcbadaaddbbdaabbdcdcbbdcdbbcbbddcbaadcaaadcbbaaaabaaccbacdbaddcacdbcacbadcccccabbdacadaaaddbaccbabdcacaaddacbdcdcdbdddadcacdacadcabbbbdcdcdadddaadadbddbbdbadbbadaadccabbababaacdcabdaadcbaaadadbdcadbbbbdcacbbabaabaacabacbbdddcbbdaccdbbbcadcbbddadddbaadbcaddbdabaadbacdbbbadabbdcdbbdbbbcbccccdcbcacbdbdaccddadadabaadbabaacadaccbbccccdddccdbccaccbbdacbbddcccaababcabcacddadaaabbdaabdabbdacccacaddddbdbdcccabdbdccbccacccdacabbdbbaacbcacbadddbabcdcdcbabbaacccbdbcddddccbdccbaddbababcccadbdbcadbdabacddbacdbbcccccbacacbbadbdbcdadbacbdbddbbdabbaaaabcdddaabbdddbaabacadbdadcaaabbcdccacdaabbbbcbbaddaadbbcccddcdddcdbcadcaccccbabbbbbbcbaccabbdcccbccaddacaacdddbabaaaddcbcdabcdbcddcaaddabaaddcaddbbcabdbaaadbabccddadcdbadadacccaccbcbaabdbadcbbabbbbacbbaccacdbdbcdbcccdaadcdaccccbddacaabbcccdacaacbbaaddbdcaacdddbbcadbdabdbaacccaaacdccaccbbaacddcdacbaaddadaacaaacccbdabadadcbcbbdbbacaadcaabccdbbbcbcdcaaddbabcbbcdcdbbacdaabdddbaccbccaccbbdaacabcacdcccdccaccadbccbbcdbcbaddccaaacddadccddaddbdacadcbdadbdaaaccdbcaaadcaaccbbddddacaaacaabbdabadbddcaaddbbdacbcbbaaaabcbccacaaacccddcabccdbbbacaacbcbbadbcbcbccbacccdbbaaacdadccbccccdbadbcbbbaacacbdacbaaababacddcdaabccdaaddadaadccadcbdbbbaddcdccdcadbbcccccdcbbdcacadcbdaacddaabcaccddddadccdbcbaacdcaaabacaaccbcdbcacdbbabcacadaddcbbbacdadccbcccdbabcdbccaddadbcbcbbdbcdcccdbddbbacaccbaabbdacbbbdacbadaddbbaddddaccdadbbbdbdcdacdbaaddadaadbbabbbdaddbddcbcadbaaaaadacabbaddcdddcaadddbacdbddbbdcbcccbbdaabbdadbbdabbbcdbbaddcccbaaddbbbdbacdbcdacdcbcaacadccdabddbbcdbdbacbaaacadcaabacddddaaabdaaababccccdbcdcaddbdadcbacddadbcbcbcabdbabcdabddbcadcbccaccdabbcccaaaaddcbbcdbabbaddbbaaadbcaccdcdbbaabccbbabadabbdddcccbaaccaadbdaccacddaacbbcadadabddcabbdccbcbbddbdcbbbdbdbcbdaaddaaaadddbdccbadcacbddbddacdcdcabcdbbddaadddadddcbccddacbabbddbaadbddccacdadadcdcabcccdccdbcdcbdcdcaccdacbdcbdadcbcbdcbcdcbddaddacacbbaaaccbccccbaadbbcbadddabdabdddadddccbaccbabbbabdbcaacadcbdbaaacdacbaccaccbddddcbbbcdcaddbcababccacaddbddcacabbbabdbabdbbdbaaadadaacdcdabbbadbddccccdacbbccaaadccaaaaababbbdacddcccabbabbdccbcccdbdcadbdcbbaccdbcbdadcacaaaccbcaccbcdaaadcbbbcbbacdbcdcdbccbbcddabddbdbdbdbaadadabaddcababadccdddddccacbbabdacbcbbbacdbbccaddbaaddadaabbcbdbcdbdbbbbacbbaadcbabaddbaddadcdabcbbbaaaaaadbbdcbbbbadddadcacabacbcbbbbbcccdcaabddcdacdbdbdbdcabddbcddacbddbccabcadaaacbacbaabaddcddbaccbbaacbbbaaabcbcdabcbadddbabbcdbcbdbaccdacdcaaaddabdcabadabbcadaaadabccaabaaaddacbdbdacabdddbcacaadaaaccaadbcbbbbbdccaabbbacbcbcadbaccbbdcdcbbbbbbadcbadacacbbbbaccaccbcaccaaccacbdbdbdaddadddddcdccddbbbdddcbabaacabaabbdcccdabcdaddbbdaddbbabbdcbaadcbcadcbcaabbbbabdcbdabbdaacbddddacbbbbdbbabbbdcbccabdcdacadcaddcabbacccbcdbbbcbbddbccabbddcdcdaccddbcabdbcbaabddcaabbbdadcdaadccbbdcdcaaaabbaaccacdcddadccdcdccdcabdcdabaabdacddcdddcdababbcabdcbaaaadabdaddababccddaaddcacabbbadaaddcccbbdadaacccbbbccadddbaaadaabaccdccbcdbcbaccaadbbbcbdaccbadbbdbcddcdadbdadcdbdabadcdbdbcaacdacbddddbdcbaadabddaaddbbbbacabbabdcaabdcbdcdbbccbcacddbdabdccdccddadddbcddabcdababdabbcbbaddbadbaccbccbbbdadbcabcbbabaccdacbcbcdbcdabbdccbcddddaaabcbdccacbccdbdccacdbaccabccdabddbbdbabcccabdbdbddabbbdbbabaccdddddbdccdcbcaabbcbcdcaaccdabcbaccbdddbbbcabddaccacbdbcccaaabbcacdddcadbdcadcaddaababdcbcbdaadacbcbacabccbabcacabcbddcadaaaccbbdcaabbbcbbddcdbdaabbaabadcbcaabadccdacdcdccdbdbcacdccdacaddbbabbbcbaacacbddaccbcaddcbcddbbcbadabcbcaacaacabdaaaacdddbdadcacbcaacacadbbcdaabcbaacbcabdcbcadadaabadaccccdbaccabaaacbdcdcacccccbbbddacaabacdcacdbacbccadbaacadaacdddbbaadbbdabdaabcbbbacaadcccdcbcdddcaddaddbbacbacbcccabbdddbcacbdbcdddbbbaaacaaddcbdaacbacdbaccdaacaccdbadacadcdadddabbadcdddcdcbdcbdcbbabaaaaacdacbaaaabaaabddbbcdcacabbcbcabcdbbbbadbdbcbbdcbaccdbdbbccbddbbbdbddadbbdacaaddbbbddcdccabdbddaaaacdaccdbdccbdacdaddcddbaccacdcdbddaabcddcabdcbdcdbcadabadcaaaaaabbdaabaccdbbbdbaccccdaacabbbcdcdbacaadacabdcbbaacbdadcdcddddcddaadaacdacbbabbbbaacdccaadbdccddbcbdcbdbbabbbabdaadbdbbccdcdaccdaabddcbbdbdcbacabddcadcdcccccbcdcdbadbddaccaccaccdbadcababdbaddbbadaccdccacdacababdbacbcbbbacdbcaabcddbadbbabccabcddccddcbdabacbacaddbbacaacacbcabbdbdcabdbcbaabbddbbcabdaadbdaaacddcdadbaaabadbbdccbcaadbbbbcadbdbcbadbbbabddbcccbdbcadbaabcacdcdcbabdcbcdbadacbdaabbaddbaaadbbabdabcdbdbcbcbaacbbacacabdaadbbbcdacccabbcccbbccdabbbcacaaaacabbccadadddbabbdcbbccbaaccbbdbaacdbcdddbdbbccadddcadcdbcaacccbaabdaddcddaaabcabdaadbbcaaccddbccababcddbdbccbcacaaaaacabbdbdcbccbadbacbabaaaadaaadabdbbacdbaadcbbcadbbadbabccdbdcbdbcaadcddcddbdbdddcabadadacaacbdccbabbaadbcbcccbcaabbcbcaccdabbbdcbcccadaacbbababacaacbadbcbacccdccdbbbcacddcccabdcabddcbacacbabbbdbdbaaabbbdbccabccacbdddbddccbddbaacaaabadcacbccdbddaadbbbbddddacaabddadcbbacddadbaacbadacdaddcbabdddcbaabcbadcacaccdccabbcaddbcdbdcdcbdacbbbacabadccbcdcdababbaaacdbbbdbadbaabaccaadadbdcadcdacbabccbcadadcaabbacbddcdabdabadddabdadcdadbbdbcbacbccdcaacddcdbabcbacdacdcaacdacaabdbcbbbabbcbdadbbdacdddbbcbcacdbdbaacddadaabcacdbdaabdabbcadcdacdcdcabddcccdabaccbdbdddcccdbcccbaccadaacddcbcabccdadcdadcddaadacddadabacbaabaacbddcaccbbdaaadcadadddadbccbadddbabbacbdbcdccacabccbadaabbbccabcaaccddccccbabbaccbcdcbcacdcadacbcccdbacbcadacddcbabbcbbbdbbdcbacbddbdcacdddbabcdccaaabbadbccbaaacddbdadbbaaddcddbdbcdacbdcddbdcbaadccbcddaabbdbbaabdcbcdbdbdbababbbddddabaacabdbbacaacddcadacacabaabbcabdccdbdaccaaacacacabdbaaabadbbadcbcaccacbcacbbabdddccaabcaaaaccdcdbdcaabcccaadcbabbaddbdddcdcccdabbbcadcbabbdcadbdcaccabccccbbcbaaacdcbdcdddcdbdddcdacdcdbaacbcbbcabaddbdcdaadaadbcbddcdcddcdcdcbaaacdcabaaccaccaacbbacbbdcdddcbaabdacabdacccbbdbdbbaaaacadcdbdbdccaabbcdddacbdddcbdcabaacadcdcccdadaadbaabbcdccdaabccbddadadbbcbbdcddbcdcaadbbadcccbdbabbbbddccaabacccbcbcbcbadacdabdbdaddbccabdbabdbbbbadbcbcbbdaabaaaaaccbaacbbcdabacdabbcbbdcbbcdbcadbdbbdcddbddbabdcadacdbbadabbdbddabbaabdbdbbddddbbbdaaacadbaccbdbcbcccdbabaadbdadccdddcabaddbdbbdcabdbbdddcdbcaaddcdacabcabcbaadbbdacdbcdabaacbdacbdcbbddbcccabcabbcbccbbccabcbabcaabbcbadcabdabbddcbcdcccdbdbbbccabbdcbdcddccaccaabbdcdccdcaacdccbbccccccbbbabacbcdaccbccbbdcdcdddabccaccccbdacabddaabdcabcdabddddbaccacddaaaacacdcdadadbdddabcdcacbdcbbbacbbadcacccdabcbacccabdbaacbcccddaadaababccacdbcccdddbbaaabcacacdbbbbaaddbbcbabaadccdbdabacabbaaddadadbaccdacbbabaadccdbddcdaccbddacdcddadbdcdbbcbdbcbbbbdabdacaaaabcabccdcaaabdabbcadbacadbcacbaddbccddccdbddddbbdbdcbcdbdcccddbaadbbbcbccbbcaddbdcaabbccabaabccbdaadbdcccbbdccaabadcdbbcdabacdbacacacddbdddccaaabaccacbdacaadddbddabacdcdbccccdababbdcadcaccbdcbbcaabdacccaaccbbcddabbbddcccabbabadbbbdbbaabababddabbabcddacbacdbbcabccababcbcabccbdbbabaabdddaccdbcbccaacbcaacddadcdaaadbdcbbbabdabcbbddaadcccadcadbdbaaadbdcccbdbabadbcacbabbaccadabbddabaabbadaabdddbbccdccbbdddcbcccbbcbccdbcacdbacdbbdbbacdbbadcdadbdcaabdacddbbaaddcbaacaadbdbbdbbbdacabbaadbbcdccdccabdadbaabdcaabcaaddaddacbaaabdbbbbdadcbddcbcdbbbddcdcddbccbaccdcddabcaccadcdabcadbccdacbddaabccbacbbdbaacdcdbcbacdbbdbbddbdcadccaadcacbbaabcbcbcbcdaccdcbddbacbaccacacccccbccdcbccacbdcaabdcdddcbacdaacccabacdddddcbbdbdcccccbacdcbbabacddbdabdccdcdadbdbadacccddbcaddaadcbdbbadaaabdddacbbacdcccbbccdaaccbabbaabbbcdbddddccbcacccabcbdbcaaddccadbddcdccbdbdddadbbbcaccaddddcbddddbaacddbbbbacbdbbdbbccbbacbaabccabcbcddddacadcbddddadccbbbbdbbaacccdbdcdbadbadababddcaccbccddaaabbbabdccabcdbcccdadbdbcccbaadcdccddcaabcbabdbdddabacadacdadaabdcbcaccadcacaccadddabacbadbddcdcbadaaaddbcccccbdbdacaaabbcbabbdbbdbdbcadbacacddbaadcddccaabdaabbcdadadbccdbabdaaccbbaadabdbcbdcaadbabadbbdddacaccaadbdbdbdbaacdddbcaaabaacbbcaaabdbdbddaddbbddcbbbdbcccdadbbabacacabbbaaabacdccdcacdadaabaaaaacbcbdcdddcabcbabadacccbdacadadcbbdddcaaabddbabaaadcaabbdaddbcdcdbbadaabcdbabbbcbaadbaadaddbababcbdcabdddccdadbdbcbdcbbbabcabaaacaccacdbdcaacbbbbbccbacacdcadaccddcdaacdacacabcbcccddbcddbdadcdddadaccaccbbacdccbaabdbcdcdbbabcbcadbbdddbdaacdabadaadbddbdddddccbcccdabaacbdddbcbbdbaaccdbadbcddcacbbccababcadaadddbaabcacdaadccbaadbbacddcdcbbbcbbdaddccdaacaaacdabdacbaacbbaabdbabcbddbbccadbbaaadbcdadbbddbdcddbccdcccdacdbbdaabaabacccacdcdbdbbcdcaacabcbbddbbdabaaadcdacdbdadcbccdaaaadbdadacabbacabcddbbdadaabcadcbbacbaccdbbadddcbbdbbaaacdababddaddbadcdcadcaccbbabbabbacaabbadadccaabbcbbdccbbcdbcccaadbaccbadadddcbcbcbadacdbbcbcbdbdcacdaaacccadcbccacbcddbcbbccdbdcbbbadcbaddccbcaccbacaacddaaadaddcdbcbbdccbadcccccaabdbdbcacabbbaddbdbbabcbddbbcaadcdbcaccdcabadaddbabdbdcabdadacbbbbadddbbcbcbabbbcbbcbbccacddaccddabbcbadbbaabddadcccbbabadcbcccbbacdababccaadbbdcccbadbaccaaabbaccbddacdbabdaacbbaabcacdcbcbcdaddccadbcbcbcbdbbacabcabacadaaadacdaccddbbacaabcddadcaaccaddddbccdbacaddccbcaaadcdbcccdaaadcdcdbbcbacdbbcdbdacddaabcbdbbbbcdacbbabcadaaccdabcdbbdbadaadddcbcccddcadaddbcaaacaddcccaddadacabaadcccaaaccaabcbcdcbccbddbcdbccaabadcdcdabacabbadacbbdcbbaaaccdcaccdaabbccaacdbdccdbdcbbdcbcbccbabcacabbabbcccacbbaacdbaadabbcccbbddadbbdcdacbcbcbbdacbbcbacaabadddadacbaabcadccdcdabcacbbddaddabcbbdaabbdcdbbccddaaaaddcbdccdaabcdccdacccbddcbdbbaccbcacdbdcdaddabcccbbbccddbdbbaddddbdccbdacdccbcbcdcdbddbbbaabbbaddacdcccadcdcadbbbbaabbbcdbcbdddadbabdddcbaaaddcdccdcaadbdccbdcbdcdcadbddacadcaabcbacdabdbbcabaaaaddabcacdccdddbaaaccabacccdcbcbdacdcbbaccbcbccdbdbbcdbadbadacabaaaabaaaccdddcbcbcbcbdbcdabaccbacddcccddcbbcaccdcacaacbbccaadcababbdbcddbabdcaccbbdbcabaaaaacdcbccaddccbbccadaccabccdbaddcdbaabbbabbcccdabaccaadbbcaabcbaaacbabbbdcccadccdddbaaacaaaddabbadabdacdaaababccbdcbccdabbbddbbccdcbbabcbacaccabbbbbddcbacabacaabcacacddbbabadbdbdcdbcaaddddbdcbcabbbbaabbdbcaacbacabdabdddabaadacdacacaaabcacdbdabbdddbcaaddccdacdabdabbacaabbadddcdbabbdaccddabbaadddbaabbbbacabadcddcbbdaddadcbbddbdacbcdcababadaababbabadbbacbbcbabddcbdbadcbbbbcbbbdbdcbcddcddadbcacdacccdadabcbcbbaddbabbddbadbaddaccaabdabbdcacbbcbaddddadcbccddacccdcacbbcdaabccbcaccdbadacabdcdddaaabaaaaadccccaadbabaaacbcacdcacbcddcacdbcddcacabccadadbddbbdddbddbabdddbbaccbacbbcacdcdbabccaadcabacccbcbbababbcddcdbadabdabbabbbbcbbcdadbccdcaccdacacbcbbbadbcdbbadadcbabbdabbcaabddcaadbddbadbdcddddccdcbdddcbcbabdcbacaabbbcaabbbacaadccdcbaacbbbcbccacaababacbcccbdadcacdbbaadacabdcabbccbaacbdcaadabdbacacdaddadbbcacaccdbadcbaaacccdbadacccdadbadcddadbacabcadcadddddbdccbcbcbbbcbccaccaabddabcbddacbbaaaabcabbddaddcdbbaaaddaaacddabbbdcbcbdbccbaacdcabccbdcaaadddcaccdccdaaacdaabadbccbbabaacacabbaaaddbcdaddbccccdbbbdcdbaddaacddcdccdacacbdbbdacddbacbbcccacbccadbcdadaddcbbaabdcddcaabadcddbdcddababdcbdabbcbbbcbbcbbddcdbaaaacdbdbacabbccdbdcdabacdcbdadbcbcdbacbaabdbcbbadadbabdcadcaddaadaacbddbdddcdbdbadcadcbbcbbbaadbdccdacdcbdaddbacadaddacaaaadbddccacbabdabcdacacbcccbbbdacdadcdbadbbbadaccbbaddcaaacdaacdddcaadccbbccadabadaacabbbcadbcacacadbbcccddccdbacbbdccdbdadbbccccdcccabbdcccbdbbaccbacacccacaaaccddaaaacbddababbbccbaddddbcbdcbbbdccabadcbccdbcdbcaadbcbcadaadcdcdbbbbccdcabcccacbcdabcbdbbdcdabaaabdacdcbcdbbaadbabdaccccbadcdcbdbcabacadbaccabccaadddaaacbcdcbcacacadddaaaaabccaabdbcbcbbacbbaccdabbbadddacddbdccbddbcaabcdddcbddcadbacaadcdabbbcaabacdbbabcbbccbbdccbddabadbddcdcaaadabcaabbcaddcbdadacbdaddaacadaccddbccccadddbdadbdcbcddabadaaaacacdbabcbbbbacbcaccbcbbcaabcbdddbdbbbbddcdbbbbabbaabcccdaaaccdbdcbdbaaabaddcddcbabaaccbdbdaaacdcadaaccddadccdbadbcbcaadccbbbbccdabbbbcdcccbbcbcbbaacbabbaddddacdabbabbbdbadaaaadbbabdabccbdcddacaacbdaccadaacdcaacdbabacbabcababbdaaccadbabbbacabcbcbdddcccacaccbdbccadbbddcccacbdbbbaabbadabbcabddbccaacdbaacacddbddcaadabdbccababbccccbdddccccdbddbadbcabbbbddadabbbacaccadacbdbacaddbbbadacdadbbcbaacdccacbcbcadbaaacdadadccbbbcbabcdabddaacbaaddaddcdbbabdccddbcdadcccddbaacabcdbabccbcaddbdcdbcacadaddbbbcaccabdcdabddcbdcdbadbbbbadbcaadcdcacbccccaaabadcbcbbcadacbbbabbccbcaccbcddcaccbccdcdaaaacdccbbcccbbdbbbacabdddbbdabcbdabcabaadcdcadabdabddbccbaccdbbadddccbbadacadabbbdbdcbaadccbaddbacaddabbcabcbacbbbdcaabdbdcdcdcadddbddbacdabacdcdabdcadcacacabdaabbdcabadccbdcbbdadccbaabccdaaacaacaacdddaddddbdbaddcacdadabbddccdabbbcdaccacbadbaddbccdbbbbbbbbadcaccbddcbdbbcdacbcaacdaabbaacdcdcdddddcbcabbbabddbabbacdbacdbabcdaddccabaddbcaadddacdcababddacdbdbdacbdaadaabbbbbaddbbdcbbcbddacbaaacbbbcbbdacccaaccadddddbaadccddcdcadadddbabbacabcacabbbbdacdadbbdbddcdaabbadbaacbadddbbadbabacabacaddcbdbaabcabdadbdcbbaccdccbadadbdbdcbadbbddbacbddddbbdcbababdcdbacdbabdabbcdabcccadaddccccccdacbcacacabdbacadabbadadcdcadcabbaababdabacbcccacbabccccbbbacbacadccdcbdddcaacaadaababacaccbddcbdddabadbdbccabdcdbbabcadacadbcbddccadddcabbcbcadccddadadbddaaccdbbdcadcaacccdaacdcdbdabbadcdaabdbbddddbcbaccbbccccdddaabcadbdbadcbcdcbcadaddbcccbadacacbddbdbbabdaaddaabddabbcdccdacdcbaaaacdddccacdaaccadabcacaaddcaddbcbdbadabbbdadcacdcbbaacbcdbdddbcddddbacbbdcdbcddaaadabccaccbddcbcbbdbadbbcabdcbaacbaabdbacacacdbbcaadcccbabacbcdcaacbbdacbbbdadcbdabbdcdabcaadcdadaabbcbabcccaccdbcdbabdcdabcbdaddcadcabbcbacacabcbdcaaacbabdcdcbabddddbdaacabcbacbbdbccdcbbcdabbddcbbacbbbbbabbbdaacbdbdbbddddaabdbbcabcbcddaaabcadbccadbbcdcadcccdaccaaacaddcddbcabbcbbabbbacdccbdccaabadbaacddbcdbbdcdbbacccdddbcbabbcdcdcacbbbbdcbccbcdccddccddaabbabbbdbaabddbaacdcdabbabdbbacdaadcbaaacabaabdccccdaddbdbbacbacddabccdbcccabddaabbcadbacbdccdadccbadabaaaaaacddaaddaacbacbbbdcadbdadccbdcbccbcdbddccadcadddbcddacddaaacbbdaadaaadcdcbabcbcbabbabbaccddbddaadbcccdccdcaadbcccccadccbccacdbabdcbdaadcbddbddddadcdbbddccbdaacdabcdcddcbdaacdbadddbdddbcadaccdbddbcabbdbbaabacadccdccbcbbaccccadabacaabbbadddaaabbdbadbbabdabddbccddccccbacbbcaabbbbdaadabcadcaadaacdaababdadbdcbcbbcdbbbddbbccdbcdbdddccdbcccdabcbcbdaacdbdbcdcdabdabcbcbbadbcabddadcbbcdcbabcdccacbddadccbadcacbdddbcababcacbcacabbdbaadacbdabbadbdcadbbcacbcdcddbbdaddacddbcaccdcdbacccbdbddcbcbadadccbbcdaabdddbdabacdcbbabdacdaddcadbddccdadcbdadcccbcbaccaaaaaddcbcbccaabcadaabaabaaadbdababdcbbaddaabdbbcdbaaadbbdcbcdadcbccabddaacbdbccdadcbcbdabbdababbdddabbdaddccacbaccacdbbbdbbdabdcadacbdbbacbcabbbbbdbdadcbbacbacbcbbbbcbbcbdcaadbbabcacbaaabacaaaacdaaacbcccbadbcdcbdbdcacacddddaaacacdabcaabdbbacdacddaadaaaadacaadacbdacbbdcdadadbabddacdaacaababbcdadaaabdabcbdbdbccaddabcdcdbdbbccababadcbcabbcddaadacbddcdbadbddbcaabdcaaccccbacdadcabacddaaddcbcacdccacacdbcbadcdaaabadbcbccabaacbbdbcadbbccbcbabddbabcdbbdbadadcdccbbddcddabdbaadbbbccbbccdcccbddacaaddaabcbcabbbaccddbbcdcacabdbbadaddadaaadddacccabddcccdaccabcdaabccdaddcadaabcadcaacdbababadbbabbcccbabbacacbcacabaabddddabcbadaadccdcacabaccdcdaaccbdbbabcbaaacdcbadacbddcdddcacdbdaaddbbcdacdcababcbacbaabdcbcccdaaaacdbcadacccdaabcaddadadbccbdaddaaadcdadbacccccdbcdaadccdccdaadddccdddbacaaabbabcbdaaddabbddacbbdbccbdaddaabadadcadaadbddabaadddcadacdcddbbccccbddcdddaddcbacdcdbbbdcdabddaaddddadcdaadacabdbcdbaaadadddbaaaadcdddaaccaacaacddbbdccdabbdabacddcbdcaabbabbbdaccdacaacbdddabbbcbacdccdabccbdaaaccbcdccbaaaccdcacaccccaadaddabbcababcbdababdddabcaddcbdcdaddddaddcaaadaacdabbaccbbcacabccadcbcababcdcaabcacbacbaacacbbbddddcaddbbcaadacdbabccaccdddcdbbdbcbaabbdadbddacdcbacdbcdbcadbccdabdcbccdbabacbaaacddcbddacdaccdaabdbdcdcaacbddbddcbbdcdccadbbdcaccaabbcccbacbdddbcccabcadaabddbcacdddbcbbbbbbbdaadbdddcdccaabddddbaddadcadbdacddcdbcdbcbddbdbbcbdaacbabbadccaccacdddadaccdbaddbcbccbabcdddcbdcbcacccababdcbbabdadcaddbabddbacdbbaadbdcdbbaadbccbcdbbbdaabbbadcadcccdcbaddbbbddabbdbbadadbadabcdddabcbabdbabcaaddaaacbadcdadcddbbbcccbbcbcbccbbadcaddccdbaccabcabbcdacbbcccdaddddbadbcabbcaaaddcccadaddbaaddadcbddaabcbbdaabbdddaadacdadcadabaccaddabcddcbaadabdbcaacdcbacddacbacdcacabaacddacddabdaddbadbbababbddcdadaddcadddccadabadbddccdbcadbcdbabbdcbcccabdddddcaacdcaabddcbbbcdacdaaabdbcdadbcadabdaadcdbdaacacadcdcdbbdcddaddbdbabbabdbadadbdccdcdaabcdbcdbdbaaabbddbcddacadddaaabbbbaddcccbdacdddcddabbbcbcbacabdadabcdacdccabcbcbcbbaaacaadddbbbcbbcdbdcbbdcddccdbdbacadcbccbcaaaacbcbacdcdbbdabdcbbbbabbbcdabcbaadddacdbdaacdcbbcbaaaadccaadbdbdcdaaadbbaccbabcccdcbcbcbcdadcdbdacdacbbacccaaadadbcdbcdcdbbbdccbaccbbdaddcdadabbbbbbabaaabbcacacbcbadcadcddbcdcacbdcddccaaaacaabdabbdadbbcbdadadadccdacbcddbaccadcdaaccbdadbcdbbbcbdbaccbbcdcdaabddddbdcadacdbcccdaaadacbadddbabdbbaaacbccbcbdcddccaacabaccadabccbddccdbabcdcbccbbdbacbcdaaaccdabadbadcacccacabacdaabddabbcacabcadaabaaaaacaccbbdaccdbabbaabbcbdbddcdbbdbaaddcbcadadbccadccacdbdbaadbbccbcccddbaadcdcccdddadbddcabacbadaccdacbccaacbacbbcbbbdcbaaaabbaddcdddbcdbcbccbdcadbddbdddcddbdcaccabaabaddaaabbaaddcacbcdaacacdcddddbbdbacbdbdbcbcbbdcdbbcdbacbbdcabacdcadcdcdacaaaddcbcddbabbdbddaddadbddacbbbbaabcddbaaaaacbbaadbcdaaadadcccccaddbccbddccccaabcbbacdaabdbbadbddccdadabacccdacaddadbbacdacaccacccbdaddcadcbdcabcabdabbaaccddabadbcdadbadbcbadacbbcaaaccadcdcaddccddbdcdbacbdcbcddaaaaacbbddbdaddbdccccacdcabccdcabdbbbacbdbdcdabcdcacbbbcacaccddcaddaabbdacbaacacaddadadaddcdbcddcaabdddadbbdbdcdbcdbdddacdbdadadbbccbcaacbdbbabcabdabcdcddadcccadabdaddddcbddabbbbabdaaadabbccbbcacbcaccccdabcabdcadccaabdbcbdcddaccdbdbdadcdbbbdacaacacdadcbaacddcdbccaabaadaddabbdacacbdbadbbcaacacdcaaadadbccadbbabbdcbdbdbbbbbcdcdcdaaabacdabcdaadcbbdcdcadbdbacddcabbddaabbabcadacddccaaaaccaaccdcdadcbccbbcdbadadbdadddbbbddabcadddabbddacbbddbaacadbcbccbbbcabbbbbbbdbcccbbcbddaaacaaaaaddcbdaaabaccddacababdcccbddbcacccdadcaddbbdcadbaadadbaddaddabdccaadddddddcbbccabdbdbbbaacacbcdcddcdddcdcacbdddbdbdbdacdcababdcbcacbbacabaaaabdabdcbcbcdbaacbdaabbadbccbadcddaabaccbbcdbcbbbadaabbdbcaaadbbabcbcaaaabddddbbcbcabcdbcadaadbbddcbdbabbcaadbacdcdabbcbcbdcdadcccacaacddbababaacaacabacbcdddacbbbaddbbadcdcdbadcacbadaabbcacdaaadadabcadddbdbacccdddddbdcaddcabcaacdbbbdcbcdbcdcabbbabcbdaabbaddaacccbccaadbadaaddcbcdcbcbabacdaadcbcdbbabacdbadabadccbbdabdadcbaabbdccbbdaccaacdaababdacdddbddbbdadbbdacacbbccabbaabcdadcdbcccdcaadbbcccbabbaacbbddacacadbcaabbbdbddbadabdbcadbbcdbaabdcccdcddcbdbbacacbaccbacacabcdacadbdbdcbadbbbccdabbcabbcdadbbdacaadadaccdbabcdccabcbbdabbdabcdcddbacddacaacdadcccdaabdbbcadccaadaaaabcadbbdcbabadcdddbdacddccbcbaabbabbabdddbcbabaccccbaddccbbaabcaadbbddacabddcbaddcbaaccabdcbcdbcdcaccbaaacbdcdddcdcaccadbbddbbdccdbadabbbabdbddbcaacadbdcaaaaddbaadcabadcbbacbbbadcbcdabddadbddccdacdbcaabacdcbdaccbbacabdbccacccbdcadabccadbbbdadadbbbbcdbdadbcdadbbacdaacbdbabacdcdabadbbcdccccdbccdacaccbdaabbccdbbdacddbcccbdcaccaabcacdaacbabbdaddcdabbbbdccaadaacdaadacabbdbddabccddcdcbbbcbcaaaadadcdcabbaddbdbdabcdbadccccbdaccbdbadcbadbabaddddcbddadbcacdccccadbbabbcbbcdadbdddcbabaaddccdaddaaaddbbcdadcccdacdbddbbddbdccbadaacbbacbdacbbbbaaddacdcadcacabaccbdacbcbdddccaddbacdbdccccbacdcaddaddaabacaabbbdcccdbbadddcadaabaabcdbcdbabdcaccdcaccdabacaccdcbcbcaabbdaabdcdaacaaccccaabdbcadababddbaacdbccacccdbcbbbcadabbcccaddaabdcaddddbdbcbbddbbcbcddccbaddcdacadddbbccacaabcacbcadbadcabbbcbddbcaaacadabccdbcbbcdcaacddcacaaadcbdbaccbbaaaccaabddbddacaabcaadbdcdabacdaddbcbabaaacdadadaccdbcbbaabbcdcbbcaabaabddcbbbcdadcaabacaaacacbdaccaaadcaccabcbadcbbddacacaccbbdabcacdababdddbcccdccacdabbdaddabcbabdaaaadcaaadacbdabcbcbcbabbbddbbdbadbcdcbacbadaccbbdbcbcbbddbbaaacccbdabbabbaaabcddcbdaddaddbadbabcbddabaccadcccbcbaabcbbdbcdbacbdbbadbacacababbbddbcabcbabccddccccacbdcdbbdbddaabadbcbcbcbbdccbbbbddccbcdcbcbbddadcabdbdcdcaddcadbadddabdaaccbadaacaabccccccdacccdaaabcbbacbddacbbcacccbbcbdbabbbdcbdaabacbabbdcacddcbabadaadbadabaacbddcacbbadccdaadbdbcbbdcabcccaaaddacbdbddcdadbdcbccbdccadbdacdcbbbdcddbbcbadddcdcbcbdbaccabbbabdbbcabbbdcaabbcaacbaacbaaccaaaabccaadcacbdccdbacdcaaccdbbbbdcdbbdcdbdcdcabcdbdcbcdcaccbaacdacacacaaaacacdabdabacbddababccaacccaabddaddcdabadbcabdbbbbdaabadcaccacdbdabddbaadadabacdbcbabcccdaaacdabdaadcbcbcaacaaacddadbacccaadacddcaadbddacbdcadabdadcdcbddbdaccdbdabbccdccdabcdcbadcaacaaccaccbaddaadbbcaddccdccbbbcbacbbdaaaddddadddbdadadbaddcbdddbaabbccbdaabbdbdadcbabadddcddbbaccabbdadcbdddcdaadaabbdcbbbcdabcdbcdabbaadbdbcaacdaabddddddccacaddabaadbbaddacacbdabcddaddddcacadcbbbabdddbcdadcaaadaddccbaaccabcdbdbbcacabcbdbcadcbbadadbcbbdbbdadaabaddccdccabaabadbdccbbccadadcabdadbdbbbccbacaddbbccaabbcbbadbddbabbdacbbaddadacbbbccbdabcbbcdaacdacaaddcbdbacdddbabbcacaddccbbccdacdabadabccddddddddabbccdaaacdabddbdabaabddcdacbaccdaacaacdbddabaaadbdabbdacddaabbddccbaaabaaccbcdabbddbcbdccadbbbbacbcacabdddbaadcabbdbbbddcacddaacbdddbcaddbbbbcacabcaddaadacaacdcdbdbacdacbaccddcdbbddadccacdcacbaddbdccccdcbacdccdcbdbbdcdbccdbbbaddacacdabdbbbbbccabbdbcaaabdabaadbcdddbdcbcaccadadaacbaabcccdacdabcacdabbddcabdcbcddbbcaacbdcdcccaaaaabbccbbcadaddababbabbabcacacbcdbbadadaadbacbcbdaaacabdadcdbabddccaabcbacdccacdaabcdbaacdbaabcdbcabcdcbcccabbbadabcccbdababcbdbdddacccbddadaccbadaddbddbbccdaadbdaacbacacaccaacadccaacaddabdabaaddabaddbbbccaccdabdaccaddcbcdbccccdbbbbbbcdadadbbbccdadcacacbaababaaddaacabdbcadcabababadabdaccccaadccdadaaabcbbdabdcbcbccbdddcdbdccacbcbdacbbacdbcddccccacabdbbbbdcbbadcabadddacaabdbbdcabdbbddabcccdaaddadcdacaacacadbabdbabbbaaddccdabdabccbabbbcaadbcbcddabbaabbdcadcaadaaddccccabdddaaccdbaadbacabdcbdddaddadccddbbdacbadcccbcbcdabcbcaccdacabdbbacdaacbdccdbcdccdacbadcbaadbccacabcdbccccdcabacbdaaadddddbdadaabdccaacdddcadabdbdbabbcacaabddcccdbbdadadbbdcaaadcaabadcdcbdcbbcbdbacdcdcddaabcadaccadabccbcccdccbdbdbccabacddcbcbaaccbbabbabbabbadaadcdacddcbabdbbcccdcababcbdccdaaacacbcccabbdabbaacccbcdaaabadcadacabbaadabadbbacbaacdacabcbacbbacabcbbddcbaabbbdadbdbbddbbbbccdbcdaddbaaaacaacacdcddaddabdbbdbbaaabcdbaabaaaccacdcaaadadbcddbbdddcadadaabcbcdbcacbcbcabbdacaaabccbdadbacacdbadcccabaccbaaababbacddcbbbdaccacaabacacbccdbcaacdcbdddcbaddbabaaaadbbadbbaacbbbaccaadcbbccbabdaccdbddadbdaabddacbcdddccbcddbababcabdabdcaacbbacaaaacddddccbaacabccbbaacddccbbaabbcabcabdadbaaabbdccacabbcacdcaccdcbbbadabdaaccbcabdabddaaddcadaacdacdbaaabbbadcabdddadacbbcadbdbcdabdbaacdadabdcdbcdbddcdbbdcbdbdbddccaddcabcaadaadacacbcabdddaadaacdbadbdbcaadccacbcdbbcdcbbbacdaaaddcbbcccaddccbcdacdcaabaadcbdbacbadbbcacbbccbdbacabdbdbcbadcdcbbdabacdaccbbddcabbcddcbadbabbddbadbabdbdabaccadddcbaaabdbcabbdcdcadadddcadddddacdacddcadddbaaaaddbcbcabdcddbdccddacacbbadbadccabcbbbaaddbcacccacbbdcacadadcdccaabaccacbbabdaaaadddbcbcacdbcacaccbcdabdaacaaacccbccbccbbdbcdcbabdbdcbacbaabddaccbabaabbbbbadadcabcbaabcccdccbaadadacbbccadccddaabccdaacbdcaaadadadcddacabdabccdabbbadbadddcbbdcbcdcbabdbacdcbaadbddaadcabadacbaccacacdbbcdccdaddadbbcdcddaabaacbdabdcaabbcddacdacabdbcdccbadccdccbbabadddccbccbacabccdbaadbdcabdbdcdcaaaddabcdbcaaccabadbbbdcabccabacbbccaaddaaccaaddcbacbdbaccdbbacdcaddbcaaddbdbaccadacddbbaacdbbacccdddbbdabbcdcacccbdcadbccbcbabaacddbcadcaabcbcbadaadaabbcacdadddacbddabdadbddcdbaabaddaabccaaabcacdcddabcddbbcdbabcacdbdbdbaaaabdaabadaadccabaddcdabdddabcdbbdccddcdccaddbbccdabbbacbabbbaacddabaacaacdccbcadddccdcbcccbabbacaaadadccabcabccdccdcbaddcdcaadbccdbcbdbaacddcabbccdbbacdbddcdcdcbabbcabdaaacbbbddacbaccccbbdaadabdacacbacbcbacccccacacadcaddddcdacbbdddbcdcaacbcdbbdcddbbddcdbddccdabbdadaadcbcccccbdccbcbabbcbababcdbdbbacccdcacbcacccadbaccdccadbdccacabcccadadcdcdaadcdabdbcddadbabddabcaacacabadcdddbcdcbbbddbdabbcadabcabccacadddacccbdcdcadcddccdcabaccaadcbbcdcdcbbdccabaabdcbaddcdababcdaddaddaddccadaccacbdcabbcdccbabdcdbacdaccdbbdabbcadbcccbaadbaccaacbacaaabcbaccaabcabbcaddadabbdaabacbcacdaccbaccbcdcbababbcbadabcacadbcadcdcbbdaacbaacddcdbcacdbdbadddddbdcbcbddaccdcbaadaccacdcacbdcacddcadbccbdbcbaabaddadcbbacaabacdabaccbcadaacdcabdadcadccabdddadcbbabccdcbabaabcdcdbacbdadbcbcdaccdcbaadaddbabbdddcaacdddabdcdadababacdbbaacacbbdbaaababcddadbdbdddccddccdcdaccbdcbbaddbdccbabbcbadbbdcdbabcdbddacadcbdbaabacbbadaddbbcaccccdbcbdaddbacdadabadcadabbabacacccaacdbccabdaacdaadadaaccdcdbdadaddcaaabccbacacdadacabcdccbdbdbdddaaacdabbadaaccddabadcdbdbcbdcdcadccaabaacdbccbcdadbdbbbcbcbbacbbcbbabcdbbacaabadcbbbbabddcaaababbbaabcbcadcdaabacdcacdcaccbcbcddcdacbbbddaacbabbbcdbccdbddadbddaddabaadccaccaaddddaadcaadadcabddcccddadbcacaaadcbdbdabdccabadabcdcccaadbbccbbcddbababbcdcacbaadddbbdbbcbddcdabcacbbcbbbdccabbacabcadbbcbcabcbccbaadabcddcdccaaacdcaabbcdabaacbcaadbddbcaaaabccddacbaddcdbadadcbcdcbabcccaacaaccbcdcdbbabcbdcadcbcdbaccbdddccdabddcacacdccbbabbddbdbcadaacbbcdaddddadcabcdcbbbbbcdacccdddcaaacbadcddacdaaccdddddcdacacaaadaabdbcaabcbccdcbaacddbcdddbcdbaacdcaabadbdabcdabcbdbbdddcdbaaadbdabbbcbacbbddcbabcbdcabddbdbdababbddccbdbcadbbcaacdbacaabbccaadbacbccbbadbaadcacaacdbccdddbbddcdacdcdaacbabcdbcbdabcacdabbabdcbacbdabbddadbcadaaddaccdcacabacccbdbadccaaddbbcbbbcbbbbcdcddabacbbadcccdabcadacaddbdcdbbcaabcdcddacdadbcdcbdcdbbbbdadabdabbbadacaaacabaacabcacadadcdccdddacdbacdcbadbbcdbbcbabbbdddabadcddbbdcbbddabbcdcadbcbadbccbbbbaaacbdbacbcbdcaddcdaadcdccbcbcacabbaaccdcbccbcaabdaddbdadacbaaabddbcbabbdaddcbcddacdaabadbdcbbcdcdddaddbaddbadcbdcbbacddaddaddbcbccddacbdbcccccadccaadbccddcbbabaccdcbaadddbcabcabaacdcdacaabcdcaaccbadadbbabcabdcddccabacccbcdbcdadcbacaabdcdbbbdbadbcdddaddadabdaaabaabaacdddbdabdadccdaccdbdcabdcbbcbabddcbababddabccabbddddddcccbcaaaddcbbcaccbaacccabcaddbacdbadcdbddbbcdcbdaaabcadabbdbcbadaabdddddcbabcbacacbbddbaadcadadadacabccabcabddbcbacbbaccbabbddcbcdacabdbaaddccacddccccbddbaaaabcbddccdcdbbaccacaccadbdadbcbbadbcaddadbdbacadacdbacacbbdbdaddacdaaabdcccaaadacbdddcdcacbcacaadabddddadcadacabcccaadadcdabdcaaacddbccadbbacbbdabdabbcaaabdabddabdcccaacbbadbacdcbdbdcbdcacbdbbccbdaacabadadddbccbbcddcaaacddcdcddabadccbcacbbaadadadcabdbabcbcccabbcccdcdbcdbbcbacddcacdddcabcddbaaccaddaadababbdaacdbabadcdcaacccabdabbaccabbadbbdcacdaaddbdcbabadaddcbddbdabcacaccaacbbdcbcbcddaacaadacbbbcdbbcacdbbdcddcaaddacdbcbdacbbaaacdbbcbddacbbbbbbccacacbbadcdccbbaddbbdcbdbaabbdddaabdbdadccabadadcbdbbdbbdaddabacbccbcddcacddcbccabbbdababbaddbaacdcbacabcaabcbdadddaaadbaaaacadbdbbcbdabdddcddbdcbddbbacaadddabcbbdaabbbcdbdcdabddadbdcababccdacdaddadbddabcccdcaaddaabbbcabbddacdcbdacbbcbddbbaccdccdcadcacacdcccbaabacccacbddabddadbcaadabbbbdaabbbbadbddccaaabcdccbbadbcbdcabadbbadadccaaddacbdcddcdaabccdbbacbacddbcddbdbccdadadabbcdbcdaacabbacccdbbccadddbacabadabcbacaabdbccccccdbbcdaadcaddabddbcacbbbaccccbbdabbbdadddcdbccacadaaddacdbabadbbcaccbbbcbcdadbbadaacbdaacccacbdacacbbbcdadbcacdbbaaadccacdabadcbdbbddbbadbbbbbbddbbbcaacabccdbbbbbbbbbddbccdcbbbddbccbdbbadcaaacadadbbbabccabacaddcbaadcaddcabadbdcdbdaccadbddcdccbabddbdccaddddbbbdbdbdabcbddaadcacacdddbccbbcbabccbaaadcdcaacaddabbdaadabcababbccbccadcbbdaabcdadacaacdacccbbcdbdccaaddbcacaadcdccbcbbbdccadaabaabcbbacddabdabccdaacdabcadddabdcbdcdcdcacdaadadcbaaaddacacbdabaccccdddadabdbdaabbdbbdcacddaadabddaccdbdddbadbaabbddadccccddcadaadccccbdbabdccabdbbdadcbbbabccbdddbcdddcabadccbcdcaabddbcccacbbdcdcddbcbdcabcdacaaaabbdcddcbcbddcdadabcbabdabbdcbcdababbdcbadaacdccddcbcccabccaadabcacbacccdcbcbddcaabddcaabbacdcdbdcababdcaadabdbcbadbdbdaadacbbdcbadabcacbbcadacbaaababababccbdcbcbdaabdabdcdcbbdaaabccdccbbaddcbccddbdacddaaaddaacbcdcdcdddbbadadbcadcdaabddbaccccaddbdcbbcdaaadbcacdbadddcccabdaddbacdaaabddacdddcccbccbcacbcbcdbdcdacdabcabadbddaacaaccdabadddcdabaccacbdabbdcbcbacbdbdaddccbaccdacababaabcddbdbbddabcddbabdcddabbacaaadbcdcbabaabcaaacbbcbadaaaaddbdacdbaadbdbaaccadacbaccccdccdaababbadaacdbcbbcabbcabaddcbdccadbdccbcdcdacdabcdbabbddaddccdcdbbcdddbadbdbabdacadbbdababcccbdaddbdaddccddccdaccadaacddcdcbcbdacbdcbdcddcbaaabcbbcdcbdadcdacbbddbbdcdbcbdcaabcaaaadccbccabdddbbcaabddccbbcaaccadaccaaddcaccddcabcddadadcddcccbcbbbddbaadacdcabadbbdaadcbddcdcdbcdbbccdabdbcabddbaccaddbacbaddcabaaccccaaadbbbbbcbbbcbddcbbddcadcdbcaacacacabbadbaacdadacdbcbbcddddaabcdacbcadabdbbbccababbbabbcbdccacddbdcadabcadbaddcccababdadcaabcbdbbcddadbaaaabdbcdaccaacbcaadccbcdadaadcbbcadbbddcaaabdcccbcabbddddccbcbaadcbacbcbacdbbadbbcdcbddbdbcdccaccddcbccddddbccbbadccaddbdbacdcbaadaadbdbcddbadbaddcdbaadaddbddbdadcdaabcacdbcdbcbbbcbddccdbccccdcadaddcddabbdadddbcbaacacdacdcbadadddcdbdcbdcbaddcccccbcacabdbabacdabadbaadcdacacbdbadccbbbbbdabcddaaaacdcdcbabddbababbbcbbabcbcacbddbcadbccbaccdaccaaaabcadcbbaabcadbddccbbbcadbaacadacbbcabbdddcdacdacbdaacbcbbbbdbaabcddddabbddaadbaacacdbacdbbdabaccabaddbbdcacdabccaadcbdabbaacadbbbbdcbdbbdbcabddbcbbdbabcdcdabbbaaaacaababcdcbdbbcdbbddbdabadadacccbdaaddbddadcbadaaadbcbbcddadddcdadcaadabdbbaaacabbcbdcadbdadaacbaadbddddbacccacadabbcabbabdccbbcdcdacbccabcccbababdbcbccabcbccbcbaaacdbdbcaaaaadcaccbaacdcbbbadcaacddddacdbbaaabddccbcdadabdcaaacbbbccdcdbaabaabcccccdcbcacaacacacbbbbbaabacbbdbcbaadacdabaaabdbdddcbddbcacbaabbddbdaadcbcbbdabdbcadababcaabbccbbcbbbadcbdddddaaddccabbaabdcdabbcdbacdcddacbccbdbcbbcddccaacbdadcacadccddbadcbaacdbcddcdaccbaadddbcdaaddbcabacabadbcbcdaddabbdcacddabcbbcbccbdbcbacddcdaddabacadbbdcabbccadcbcdbbbcddcaabaaabbbccdaaaddbdbbaacbdbdcacdabadbdbccdbaadddabcccaccbadadcacdccbcbbdabcadabbbcaddcbdaacaacaacddacbbacccdacdcbdbcbccacacbabcdcadbccdbabcacdadbcdddabdbbcbbddcbaaacbcccbacacbbddbacdcaabbcabddadaddaaaabaacdcccdbcabcbdcabbcdbbdbbddbbdbcccaacbdababdadbbcadbccacdacbccdabddbcabcabcbbabdabacdbcadabbcacabaddcdbcbddadcbdcdcbbbbdabdacacaccbdacdbdcbdbaababdcccaadabbcaaaccdbcbbcadbadcadacdaabaccaaabbaadbbccdaabadcbcbdccddaacdbaaabccdbabcdadbbbadcadcaadcbbbdaadacbaccbbdcccdadabcdaacbdbbabbdddbbdddbdabbbdbdcdaacdbabbbadaaadaccddadcbbaaddabaaddbcadcbbabbbdbdddabcaaaddbdaaabdadbdcaabbbcdabcbdddadcdaabadbcdbddddbcccccaababbbaadddacbcdcadbbadcbdadddcaabcdaddbcbdaddcddbccbbaccbcbcadbbdbabaccbbdcabcacdcbdccacadbabcadccccdbdbdbbcdacdaabbabbaaadbdbdccbddcabbaacccacdcbacadccdaabcdbcababbdbdbccdccdccdaaccccbbcdadaabcddadcabccbcabcadddaabcbacadcdcdbbbcacddbdcaddccbaddcdabbbcdbbdbccccaacdcbdbdbbcbbcbacacbbccdacaacbdaabccadaacdccadcbabaabbbdaaaddabdddaaabbccbbcbbbcccddbadaacacbdcbbdcabaccaabadbaddaccbbbbcadbadcabbbccabccaabcdabdacaadbbdcadcbbddaabcccaaddddcbddcdadccdacbcacdadcadbdbaddcbbabdacdcbaccabcbabdbcddddccacdcababdcccacaabcdbcbbcbdabdaacaddbdcbcbacdbdcbabcaacdcaadabbabdadbdacbdaddacaacadbabaccdbcbadddcbbccdddccdbcdabdccdbbbcddacadccaadbcbdabccdaccbbbdcdcdabbbabccaabbbbccdaaaacadcbbcbaadcaccbcbbaabccbbaadbdbbcacdabbddccbcbaccabdcbacacdddaaddcaddcccdadaaaccaaccdaddcadcdacdcbcccbaadbaccdbddcddbddcacbacacbaabdaadcdbbdcdaccbbcacbbbccbabddabadcccdddadcaaccacacbabacbcdcadabdddbcdcbaacabbabaaadcdcddddabdccacaacccbcddcdacbacccacccbdabbdaababcbbabbdacabcdaccaabdacbbacbdccdbdaacccaaaccbcaababaddbcccaccbbcbaccdccaaadaaddaabbadabcbcbdacdbbbbcbdbbbadadbbccbcabdcbbcdcadcadcbcccaadbabdbcbdccdcbbbadbbcccdbdbbcabcbbcbbbacbdbbaccabadccadadcbabcdbaaaccaddacacdbaacddbdccbabadabaadbbbabccbdccddabdbbbdbcababbdaaaaababcbabcdccbbacdadabaccabbaccadcabcbddbccacadcacbbbddddddbadcaaacaaacccbdacaacaabcccacddbdacaddaacabcbcbdcacabadbddcabddbdcadbddcabcaaaabcbabaabcaabaccdaddddabbaacadacaaadbbbcaddddbdadcddddbbbddddbccddcddbaddcdcbccadabdadbbddcbdbaacdbaacdaaaacdbddacaddcccaccadbdbabdaabdbccdbcbcdabaccdddacadcdbbdadaaccbaddbbdcdbddaaaacbcddabdcaacbbdbaaadddcdccbddabbcabddaccdbbcccbbbaadacaccadaccaacccdbbcccacaadaabddcddbdcbbcadcbacaccccdddbabcaacabbbcbbdabbcabdbaabddbcbababcbdcccdacbcdaddacbcabbabcabbddaadaccccabcacbdbacbccacdddddbdddbccbadabddddddbbccdddbbdaaacbacdacddbaaacdbbcbcbddabcdaccaadaaacddddbccdbbdccbaabdbbadacccbdcaccbcdabbbbdabdaddcdbaccddbdbcbbdccddacabcbccadddaacdabcddcbacdabcdcbabccabcadabbbaaacbdcdcbbadacacccaadddcaddbadacbccbcdcbabacdbaabcdbabcdddaacdaacbdddcacdddacbcbcabadcadbddabddcccadcaabcabcacaaccaabddcabbaccbabcdbabbccabcdbdacaccadacbcdadcddacdadaaadacdddcbbaacdbaabcbcadbcaccaccbaaadbccbcacbdbcddcbcdccddbbddbbcdddaabadbcbdabcdcccbccbacadcbdccccdcaabcdbdccbaacadbacdbacddbadbbdabadabcccdadaaccabdcaababdbdacabaabadcbaaaacddddaacadabcabbbabaaadbddbaccadddcbdddabcabbaddadaaddddcbadadadbbccbcdadbbaaadbacbabcacdbbddcbdadacadbcadcbcabdccacaadcbddcadaddbabbdbdccaabacaddcacddcdcddcbabbcbdacabcaddcbadabcaabccdbcbccbaddbcdbdbaacdabdabbbbcaabbbcdccdacacbdddbacabacaacdcccdddcbcdcdbccbcccbbaccccaababaaaaabbabdcadacbddccbdbadcbccddbddcbaaaaaaccbbcbdccbadcbbddbbaadaaacadcddbabcadbcddddbbccababbcadddacdbbcbddcaababbbcccbacbcabbacbccbcbdcbdcabcdbaacaddbddaaccdcbadcdbbbbbbbabadcabaadcddadcddabddbbadddabddbdcdabbbbccbaadbdabaccadabbbcbbccccabdcdadaadcdcbadccacbdbbbcccaddadabaaadadbdaabcdbabbbababccbacbbaabababccabaccdbccdadacdcbcaddacdcbdadbcbadbccbbdaabdbbabdddcaabbdbdcdbbdbbcdbcadbcaaddbaaadccccaccdbbddbdaaadbdcdabcccabcadabbdabdabcccbccbbabccabacabccaadbbbabcccaddadabdabdccbccdbddaccdcadccccbabdadcabcaccacaaabdcdcddddccabdcbacacdcbaaccccccadbaabcadbabcddbdcdcdacdcdbbcacccbaacaddbcbdcbddcbdccdcbccbbcbbcdcbacadccbbdabcabbcccadbadcddabcbcdabcbdacaccccddacbcadcaabbadccaadbbccdacdaccabcdbabcaaabcabcddbdbdadacbccddabacdddbdccbcabbaadadbcdddcbbcbacdcbbbbbabdcabdaaacaabbddacbcbddabccbaabdacabaacbccabbbccccccddccddaccaabdddccabbacdcabbdbcbdbcddccbbabadbcccbcaccdbbccabbccdabdcdaadccbbbacadbddccabaddaadaccbaabbdbaaabcacadbddaabbadabcddabcaaaacdcadbbbdbbdbaddcadccbdbddadcdbcdbaddcadaddacdbbddadbadacacbdcbcbdaacabdddcaaaddcdbbddcadbbbcaaccbaaabbccdccbdadccdddbadadbcdbaccbcbccbdabcbddbaacbdabcbcbaabbacbdabbbcccccbcdcbaacbbaaddcdccddaaccbdccdabdcbdbaddaddcababdcdabbacadadadcdaccadaaadacdaaadaccabbcaabcbddbdcdbdcdacabadaabdaddcdbdadcbdacaabdbddacaadbaadaabdccccadddbbaabbbbabddcbbbaddccddcccdaacabacbaaabbbdbdcaabcbbdbddcaabcadccbbdacdbddbcddddadbdbcacbabadcdacccabdabbbdbbcabdcaccacaadaacaabadcdddddacaabbcdbcdacdabcdbabcdadccbdbabccaabacaacacadadccdaaabacdcbddcbacdacaacaaaadaadcdbadddcddbadbdabdddccbdaddaaadbacbbdcbbbbdaaadabdaaadacabcacbdcadbdccdcdccdcbaccbdbdcbbddcbdbcaddcbbccdadbbaacdcdccdcaddaaaadcadacdadcbaaacacbacbdaddbcdbcbdabbdbcddbacbcacdbdcddaddcacacbaadccbaddbadcbdadbaaacbacbcdcddcbacdaaddddbdcdcbdcaacdabbbcccacbdcaddadccdcabcdcdabcdbccbdccacdbccddabbccccccabcadabaabbccabadabadabdadbcacdadbccacabbcdaabdacadbccbabbdbcabbccbaabcbdbccddcdbccabaacadbbdcbccccbcccaaccccacdbbdabdcadaaddcbaacbccaabcbbdabdbcbaabcaabdccadabbcdbcdccaaccddcababbbaddaadbbcbbcbdcbaabbcbccddbbaccbcacaccccaccbdaaacbaabbcdbbbbbddcdddabccdcadbcdcccdbdaacdbabdbdddbbabbdaccaddabdcadaccacaccbdcdbcbacdddbbbadbaacccbacdbaaadaacacdcbcdaacdacdaaadbcacbbdcddbaccdddbadbaadcbabbaacbccbbbccaaabdaddaccabddabacaacdccdbdaddbbaadcdaaabcccccaaaccdaaacbbddccdcdadadddbaaccbbcdbaccccbcbadcaaabbacbbbcacadcaabadabccdbdabadbbbdababdacbacaacacdbcdccdcabcdadbccbdccdddcacdcdbccbcdbabbbdabacaaaddcabbacabbbdcabacccccbadacdbcdccaacbbbbdabcdbccabdcbaabcacbdaabcdacdbcdcaacdbadbcbcdcbbdbdcccdacadcadbdcbdaaccdcadcdabbbcaadaddcdcdbdbdaacdadacbaddadbacddccbcbbcdbbddbaaccbaccdadcddadcdbbddccddbcbcdbdcbaddadccbabbbacadaaadbaadcdacbcdbdaabdaacbdadcccaabccbbabdabacaccbbdabbbacabbbdcaaddadbcdaaccbcdaddcaadcdccabdcaddaabddabddabcddacacbbbcbadbdaccbdabbcccdacacdacaaccabaddadccdaadacccbdacadaacddddcaccacaccbcbcbbacbdaddaadbaaadaddcabcbaccabaaaabcbccccdabdaddacbbbcdabcbccbcbbadcbbcacccacaadcdbacdcdddcdbacdcadadabcdddcbaacccdcdadcdbddadaddbaadcadccadbdbccadbdbcaaccccdadbddacadcbaabbccaaacacdcbaaadaabdddcdcdbdbadbacaaddcddcbcbabddcabdadaccbacdbcbcdbabddbdddcbcadadccdcaccdcdadaddbaacaddbddbddcdbbccccdcdaabcadaaadcbabbcbabcdadaabbbccdccbddaabdabcaadbadbabbbdbbddbbcabbacacbbacadadbdadbdaadcdbccabbdbbbccaadaadaddadccdccabcabdcdaddbaaddbddadcbbddadcbbbdccbdabbabacaccbcccbdcbbbaaaadbcdddbcdcbdadcacdaabcbcccabdddacddcdbadbddbcdbcdbdcdbbacdddcdbaacaacbacabaadadbdbbbdcaddaacbddabccdbbcdababdaacaadbbadcdbaddcddbbdccabdbdabcdcaacbbdcddaccbdccdcbcdbadabbddbdcadaadddbcccbbcabaaccdddadabdabddccbbdabbcdddcbcccabbaaaabdccdbdcacbbbdbbacaadcdabbdaadccbcbacadbaacabddcbaaadbcbabcaaacdadabbcdccacdcbcaccccbcbcbcdadbcccacacabbcddaabdbcccdddbbabaaacacaadccadcbbdbbbbdddacacabccaccadbaabaacddbbddadacccabcdbcabaabddccaddabdccacbaadcbbcdcacbcdddadccdabadbbbbcbaccaadabbbcddcaacbcadddccaccdaccabcaadacddbbddcbcadbbcbccbbccbbdbcbdddadadaaccdbdacabbaabcababddabbaabdacbadcdcdbdbdcdadcbbcadcabbbbbccbbcbabbadcbdbccbcbdddcccbbdddbdccbacaadcddddcacacadabdccddbccdbacbcbbdbcdbbddcdaacccccbcdcbacbddbcddbaadbbddbaaacabbbddcccdcaacbcddaacddbcbccbcaadaacabaccddacbccddadbdddaabbccdbbaacbcdddbcacaccdaadccaacbbdccbcccababccdcbcadabddbccbcbabddcbcdacaddddcadbdcdaddcddcadbdccdbbaaabdabbdabcdaacbdabbaaccaaccbbdacddbbbababbacdbcbbbcdcdddcadabddbacaadcbaaaabadccbbbabbccbddacbcbcabcadabcbadaadabcabadbcddbbcbccdadadddbbdabdcbcbacbabdaccbdbaabdcabdabcdbabbbbddccbabcdbddadaadcdcabadcbcccabbccbbbabcbadcaacabcabbbbaacbbdcddcbbcbdabbaddacaddcaddcccdddbbaaccadbccdbacdaabaacbdbbdaccbabbddaaaadcddbbaabacdbcbcabbaacdbbcbccbbdadbbcbddbdcacacaacaaccbbbbddabaaaadbabacdcadbbcdbcaddccaacadcdddbcbaddbcdccdcdacaacacbbbaadbaccbaadaccdabdbabcdadbccdcdcabbcaaaabdbbcddaadccbacddababadccbdaacabdbabbbbcaccdcbaaaabdabcbccabccbbdcbdaddccdabadccdcbaaccaabcacdbbdcbbbcbbaddadcabbbdaabcbddddaccdcacbbccccabadcabbabacbcbbcacdccadabcbbababdcdccbadadccadddcabdbccdddaadddcdbacbcdbbddcabbbbdcbcdbccbdaadccabdccbcbbdabcbcbbadcaaacacdbbabbbcddccccbaaddabcccdbbbbbcacbbbdadbcadcbcccadcddcbccbdadccbadcdacddcaddccdabcddddcaccdabcdabcbcabdadcadadbacccbcaabccdacdcdcccbdddacadbcddbdbdabadddddaccdadcccabbddbdabcddbaaddbbadbdbddccabdccbdbbabccadbcdddcadbcdcbdabccdbacdbdcabcaabbccdcdcbdacadddbbbaabbcdabddcbaabcabcacacccaabdabbccadbadbdcbbadaccadbbcdccdabddcaddbacbbdbdbbaaacbcdccacaccdcdadbbbaaaabbbdcbcdcddaabbbaaaacdadbaabcdaaaccadacbbbbbabbcdddcabbdccbabdbddcdabaacaaccbaadcadddbacdababaaddcacdaabbddddbbdbbcaacacbdbdbbdcdbbaddaddbcdbcdcbacbdccbcbcadbadcacbdbbcdadbcaccbabdcbbadbcaaaabbccbdacbbccddcbdccacdccbccadaacadcacbdcbbccdaacbbbbabbdbcbbccddcbbdabacbabaacdddbbbcadccbbaccddaadcddadcacacbddbdbbdcbddbabaaccdbbdcbcdddbabbbaaaaaabbbcacabaabccabbdbbdbcdadbddbdbdaddacdcdaaacaccbacdbaccddabccbbbcdbbabcbbdddadcbaabdcdcccbccdddbdbdccccddcccdbbcabccddccacdbaccadcacbcbccaddaddbdadbaccbcbbddbacdadbaacaccdabbbbcdcbaadddccccdccdddccddabaaacdddaddacccdccaacccabbacbbadcdcdbddddbdbcacabcbbccdbbcbcdcdadcbbadbcabcdcaccaaadbbcbbccdddabccbadbdccadaababdbabcacabadccabdabcaadbdbabbbcccabcdcdadadacaacbcbcaaaaaddaaccacdaccabbabbddbbdccaaccabdabcdbdbcdacccddbbcddabdddbbababcabbbabaadddbaabacadaaacbccbbdcddcdadaccdbdaaabbccbacbbbbcdbcaaccbdadadbdcaddbdcddcddacbcbccadacacabdaacaabcdcbaacbbcbbabdacdbddccaccabcadcbaacccaabbccdabdbbdabacdbccbcaddddadbcadbabbbdbabdaaddbbcdcacdbaaacdaabbcacddbaacacddcbcaccadccbcbdabdacdcdbdbbbccbcacbacbcccccbcdbbbdaaaabcbadaaddadccbcddccdcadbbadcadcbacbdaaccdadbddbdabccbbdbddaadcbcaaadbddaaddcdcadabcbdbaaaaccbadcadcbcbabcbbaaadaacdbbbdbdbacbadcbbaccddbaddadcbbdcacddaddcdcaccdddcbccdbacdbbbbdddbdadbbcbaaccadaaacaccbdbbbdbddbaccddddbccaabcaabcbcabcaddbbccabcbcbbabccadcccdacadcdbbddacdaabcbaacdadcdbccacdbcbdcadbbcadbdbccdbcddbbaadbaddcbacabbbbcddcdbcabcabcddacbdcbcbabddabacccdddcbdaabcadaabbaaccbabababaadbcdcacacbadacbadabdabccbdbdbbcbaccbdccdabadaddbdcbaababcdcaaadabdccdaccbdbbcbdcddcdddbdacdadcdbbacdbdbdbbcbbacbddaadbddcbccacaacbbccddbabcadaaabaacdbcaddacdaacbbbcbaacabaaccddcdbddbccdcabdbabbacbacbdadadacadcacdadabdaacddcdccbbdabbaabbbbcdcdbbcdbaddaddbcabbcacbbdbbccccbddbdcddcacaabaccbbbcacacabccbacabdcbbbaaaaccabccadcbacaacdaabadacadcbaaaaaaaacdacbcccbacbddbbabbdadcadcdbacdacdabbbcbbadbddcdabdbbaaccbbdabdcccaadbcabdccacdacabdcdbaaacacccbdacdbbaccdbdcdcbbaaaabccabbacaaccdbaaaaaaddcabdcdcdcdbbbadcdcccbbccacccdcacacadbaaabbdbcdacacabcbcdbcdccdcdaddbbbaaaacbabbdcdbbadbdcdcadcabbcccbabacdbcabcdbcddacbbaddbdaadabbddcbaadaddabdbccadaccbbcdbcdcdabdcbdadddcdbcbabcdbcbadadaaabcdacbadacacdcbcbcabbbaddcddcbbadddcdadcabdbabdacdcadabbcddaddcdbdaadadcdbbbaadcccdbccaccccbccbbccacddbaadcbdbbbababcbdacbabbadadabccaacbdaccddbbbabbadcaabadbadcccadbddbdcaacddacbcddcadadcddbbccabadbdbbcdbacbaabccadadcbdcadbbccdaddbbdcddbdbcddcdbabddadcdddacdbcdacddcbccacbddabababdabadbbdbbbdddccdacddbcccabbbddabdacddbdbaddcadacdbcbcbdadabddadacccbacabcddbbbbddddbccaadaadcbbcbdbbabcddabcacbdcaccaabcbbacccaacdbdbadabbdaacbbadacdbbbbdacbcaaabdcccdbbcdcbaaaccbdbdddcbddcdcdabcbaabbbbcacdadddcbcddbcdaddaccdbbccacbabadccaccbbbdaadaabcbbdccbccbdcdcdbacddccabbbbcccbcdaccbcccddabdadcdcacbddccdacccdcadcbaadbadabdbadcbbacbdabadcdccdcccdccbddcabccbadcdbcaccbbccabdcaaaaadabddddaaadbadccadcbabbdacdcccbbbadddacdcbadaccccaaacdabdcbccdddbccbaabbccaccbbbdddbcbabadacdbcbbcadbcbaddbdbabcccdcdbbbcaadaadbdcaccbbbddbcdccdaaaadabbcdcbaddbacaaabdbdbcddbccbacaabcaababcaaacadcababbabcbbdabacdacdcdadcbaadcaaadababbdbdbdcccaaccdbcdbcbdabbcbbbdcddbbcbaaabcccccdbccacaadbbbdbcbaacbcddaccddbddabcdbbbabdaccaccddcdabddbbaaccbcacdbcacbdbbabbcdcacdccbcddaccbcdbadabacaaabaababcaacdbacbabdacabdbdacdccdddbdcbdbdcbccdaacbbadbddcdcbddbdcdbccdababacdbabdccbadabbdbbdbbcddbbabdacbcbcdccbdacddaaabdabacdbdadabcbdbbddbdacbadadbddcbdcadcdaadabcdcadddcbaaacabcaddcbbcdcaadcbabababccbacdaaabdddcbaabdbbcccaaabcbccacdbbdbaacaadaacbbbdcccdadbbccabbbabdbccdbcdcadbacddbdbbcbababaabccbddcbbdbaabaabcaabdccdaadccbabacbabbbdbbbbadbccdaacbaadcccadbdbbdbadcbaadcbdccccacabcbdbacabdddbdcdbabcaaaadaaddcabaabbdaadabbdaaacacaddbabcadadcabdabddcadcbcacacdbddbccacabcccaaabdacdbcddcdccaaabcdcdbbdbddcadbbcdbcdbabbbdcabbcbbadaccbaccdcadbabaccbcbcccdaadbdbdbcaddacbddacbacadccdbdabababbabacbacbaadbacaddbbccabdbdbbdaaccdabcacdcacbdaccbadccdbcbbadbddccadbaaabcdbddcacdaaddbbacbcdddbdbaaaabcabccbcabcbbaaddbcbcdacaccbbcbccbccacccdbcccccdbbdaaadddbcbcdbcbbaadbcdbcacacabddcadcaddadadbcbccabcdbbcccddcdcbaaccbdbdbaaacdaadbdbaadccbddbcaadcbccbbcdbaabaddcaaabbaaccaddcabdbdadbbdddaddcadaccdbdabdaabdbabbaadddbbbcabbdccbddabbcbcccaacaccddccdbdcbcacbcbddbabddddddcdbcdcaaacdbdbcdbbdabaacbdabcdcaccadacbaaccdabcdcdbaadacbdbdbacbdaaaddcccdbcddbdcdacaddabcccabddbacbdaacdddbccdadadadbbacdcbdadbadcaddbbdddcbdbcbddcaabdbacddbddacbcdadcddcabcbbcdcccddcaabdbdccabbcdddcaacdacacdbbacadadababbddaabaddabacdbabddabdbbbabababdbadcacabcdacbccbdadaaaddbcadcccdbccddbdabadadccadacaaaabddadbacdbcaaaabbacddccbacdaacdcdbcabbaddadbbdaccabbdacbcccdbdabddbadbadabbddcacaccbbcbcaadaaacdbadbccbabdcbddbadcddcdcdacdadcaaabcbabaadadbdcbdcdbdddbdbbdabbbcccdadcadabbccadbbdcbaabcddcabbcdaacbccdcdbcdbdcdadddccdadbdadccabcccddcdccdcdccdcacbcdaadbaacadbacdbdaabbbadbabccdadaaccaccdadbddbdcadacbcaddbdcbbadbbbabdadbcbbccddbbbaddcaaaacdcbcbbdabbdcadccbcbccdcaadcaabaadccaaddbccaabddaabdddbbdbdadcddbdccbcdaaddddcdacdacababdcccabdbdddddbbcabadbddaadcbadacdcaddbddcabaabadcdccdbacadddbbacccaaaaccbcbdbdddddcbaccacdbbddcbbaaaababdbaddabdadddcdcccaaabbdcabdcbacccadccacdadabbbcdcaaddccaadaaccdddcbcbbddaacbccddcdcaaaacdbbdbbdccadcbdcbcabadbaadcaaaadadcdcdadbbbbcaadabacbaadccaccdbdadaddbdabadaaacdddcddbddaddcdcbabcdbcadccdadadcbcacbabaddaaabdabdbbddcbcaadcaadabaccdbcbddabbcdbaddddababbddcdcaaabcaacadabacacdcadabdcbcacdddacabbadcddcadddcdbacaddadbbccdbcaccdbbaddbcbdacadbbdaddbddabaabddacabdbaccdbbdcbcddbbbaadddadbcacdbbddcbbabdddaaabdbaabacabcbcbabadbcdcaaababccbbdccbcccbcaabcaccbaccbcccaccbdbdbdcbdbbdabddddbcbccccdbdaddacadddbbbcacabbbcabacbabbbdcbddbcadcdcccacabbaddddbadcaacaacccabbdcacbbbdbdddcacdcbbbbacbadacaacadaacdccbaaabaabadcdcddaadacccdcbbacbaacbdcbabdaacdacdcbabadddbdbaacbdccdacdddbabdacadacbbadbddccdcccdbbdcdcdcbadacdcdbddabcdbabccbccbaacbcaadbbbccddddbabddccbbdabaabddbdaacadaadcacbadadcccacabcddbdabdbabadddcaabdcaccdabacbdadaddaacbcdbaddbdaaddbbcbbdadbdccbadccadccaddddbcaccddbdbcacadaddbbacdccddadddcbdcacdcaabbbcbbaddbaaadacccabddbccaacaadcbacabcacaabdbbdacbaabcdbbdcbadaaaddbbdacdbacbcdddaddbbbddabadacbcbbddcdbdcbbbaaacaaabbaddbdbabccbbdbbaddbbdcacbbcaacccddbddbcabdcbcacabbbcccaabdabcdabcbcaadbaddbcacbddbaddccdbdcdaadbdbdcadbbbbdaaccacbabdabdbbddcaaacbcaadcacbabbbadcaaabcaddbcbcccacddacaadddcaacadbaadddabcdabaacdbcddbbccacccbccdaaaaadcccccbbaacddbcccabdbcaccaabbbbdbddaacbcdacbddaabbacaccdbaccbccbcabddbbabacdcabacbddaccbcbdbaacddabcdcdbaccadbcbccaddcdaacbccdcbbdbdadadacacaacacdabadacccdadadbbbdaaabacbdacbadacdadbcadcbcdbdabdccbcbdaabababdacadcdbccbdccdcccdbddcbccadaadcacdbbcbdaabccacaadbcccbacacddbbdcbbbcbadbbaadbcdacdccacbabddddcbdcdbcccabdcccbaccbcabdadcbbdbacdabcaababadaabdbcbbbdcacbaaaccdbdacdaaaabbdbdabbdbacbdababcaadacdcbbbcaddaaabddcababcaddcdbabbdabccbdacccaacdcadbcbacaacabbcbddaadabadccbaabcbaacacbbccdcbdadacabbacdbbabcbdccabdbbcdddcccbdaabdbbbaaaccbabddbcddddddcadcbdbbdacccbacabcddddcdbbdbbbcacaabbdadaaccbdcdbdcaabcaadcccadcdcccbdbdddaaadbcdcdddcdccccccaaabcddaaccdbbadabdbcaccabbabccdcdacabdaacabdbacaaddaaabdaaadcaddbaccdbadcddcbbdcdddcadcaacdadcddccddbbbbacdccbddbcbdaccacadccccabccaddaddbcbdacdcccdbddbcaadbabaddddddbdcbbbdaadcdcaddcadcdbdddabdaadaddaaacadbdcbcbbadcdcacdabbbcbbbbdabbdcbcdacddcbdcaccccdcababaccadbcbbdabddcababcacabcdbdadaccdcccbdbddbdddbcaaccacbdaddccaacccdaddaacbbbcadbddacdababaacccdccbcbbbbdbbcbdacbacdaddacdddbdadaccddabcbcabddbbccbbcbcdbdcaddcbccddcaabcdaaccdbaaabbcacccbccaabbcaadddcbddbdbdbcbcabddbcbdbbccdcbcbbddcbcbaacaaaddabcbddaadabbcbaccaccbdbacbbabaacacbbaabccbabcdacdaaaadaddbbadbdcbbbddcccccdcacbbdbdcdccdaacbcaaaababbcddabddbdbabbaaadbcdbbcadcaabcbbbaabadacadbbbaadcdbbacddbbcaabdaddbbacbbcccbacaaaabcdddbbacdcdbcbacccacccabbbbaadacdcdccbdcbbbccdcccdabdaaddcbddaabcddaaccbabbbcdcccadabdcccdbcdaaadbcbbadbcbbdbbbbcdbbcdcbdcbbdcccadadbcadabcdcbccdddcabbcdadbdcdbcabdcdacbacbcadacabcadacbbddcccbbcdccaddacbdcbacadadaadcbaacbddcabdcdaabadacaadddcbadaaabadaacdbbabbdbddacdacbbcddcbdddcbcaacbacbdaccbabaacadcacaddddcaacabbcdcccacaccacdcbddbbdccbbdbdbcbaadcaddbdbbbdccacdacacbacbbbdbabddcdcacddbcddcdcaacbdbbaacabaccaccbdadcabbdcdcbdaabdadbacccbdddbacbdabcdbbabdcdbcdcdadbddabbcccbbddaddaccbcddbcdbdcaaacacdccbcaccadadcabcdbadaacbbdbccababcaadcddbdccbccdbbbddbabdcacdabcdcbcababdadcdddddaacddcbccdacdcbcadaacbbcccacbbbcaaaddcbcdaabcbcbcabdbaabdbcacddabdbbaacdadadaaaaccabcbcdbcadbaabcdadcdbcccbbcbbabbbccdcdcaabdbadaaaabaabadbcdcdcbaaadabbcddcacdacacadadcddddcaabddcadcdcbbacccdadddcbacbcbaadbbdbdbdbdadbaddddcbabbddbaaccaabbdbbbaddccababadccacbacbccabddadacdbdcbdadacbbddacbdacdccbcacbdbbcdaaabbcaccdbadbdabbacbaadcaddaccbbadcbcabaabccddacccaaabccccdcaadaccabcdacdbcaddadddcbddcdadcaabdcbbcdcdcccadcbcddbbacbdccbcabaddbdacaadcaddccaaabdacdaaaaadacadabdaadadcbdddadbaadadcbcabcdcccadddcbaabbdabcdabdddaabcacdbdddaadcaacbacaddcdccacbdcbbaddadaccdadadccaaccdbaccbddaddcccbdbdccabcaabacaddbbcadbbbcadcccdcccaddcbcaadcaaaabcbcabbdacaabbbacaddaddbdddccddadddbdbbabbbaccbdbccaddbcddbcaababaaaacaddabcaaabbdcbddbbbdabdacdbdabdccababcdcbcbbddbbdcdbddcaddabbbcacbbaaddacbabdcabadaadbcdddbccabbbaadadbddbbbccaacbbcbcacaaadacabdcabbabdaccdddccacabbbcddcbcdbbbbdccccbcdcdbbccdcbcbabddcaacbaabadaadbbaacbabbbacbdaabacadcaccacadbdbacdaacbccccbadbddbbbbddccbdcdbbcbdbaaabbdccccadbcadbcbdbbabccdabdacabbbcbdbccacadbcabacabbaabdcabcccbbdcaaabddbdbacdbcbacddddabaacdadabaddcbdabdadbddadabcbddabdbdadcdcbbddaccaccabdabbcacbacabdbbbbabdcdbbbbcddccccdbaadabbcccbbbbbabdbbbbcdbaddbabbbacbbccaadacdaadbddbcabbbbcccddbdbbbaabcdacaddbdcdbcdcadcabddddcacaccacbacdbcaaaccaddcadbcccbcdaaaccddbdbbbdbdbddaccbdbcccdcdabcdadcdabccbbbdddaacccdcdabcaccbdbababbdabcbdaacbdcaabcbdcdbbacbbbaacdacccacbddccdbbadbdbcddccabddbcaabbaacbbcdddddcddbaabbbbbcddbcddbdbcbbbbbdddbdadcbacdadacadcacbbdacdddccbcdccacbaacadccddbdabbabaaddcdaacabddbadbabbbbcacdccbbddcbcbdcacabdcbbbddbbddbaadccdccabbacccabdbdbcbdcaaccbadbaccacaddccbaaaabdaadabbdddccacbaddcdbcaaacbdbcaaddaaddcbcacaddabbbddddcdadbaaaadbcbdcbbacbcbabdadbbadadccacadcccabcccdbcbaabaadcdcdacccdcbaaadcaddcbadabaadacdbdbcddccaacaaabbcbadcdadddcadbcdbacbddaadddbcdcbccbaaabdcbcbcaacaddcddbbbcabbbccdaaaadcacacdadbacddcbabdbbaadbcbdbacbadbbbdbabcabaaacabdcbdacbdbbcdabaadcbddbabcabccbaddccbaacbbcabddcbbdabdbaccddadbdccbadddadbabdccbdddaacdbdccdcbadbdabcabdcdabdccdbbddaacdbbcbdcdcacacbbcdcbaddbccaacaababddbdbcaacdbcaadadbdabdccaabcbbdbccccbdcdacaccabdbdcaccbccddcabcbadcbdbadcaccddddabcbdbaacdbcccbdbbccdacbabcccbbdacabccbdaadbbbbcbddabdcdabbdbbaacacacacbaadacddbdaadbbdaaaddacccabdcdabbbccbbbdcdadbaddaababdbacdcccabdaddcbbbcaddcabcdcbabcaabccdbdaaaabbcbdcddccbbdadbdaadadccaabdadbbaabbdbbabcddadbcbcdccadccaccacddcdcabbabdcbdbdbdccabbacbcdbdcdccccacbaadaabdcaccdbcdacdaadcbcaddabbddbbaacbddbaabbadbdadbdbddcbbbdccabacdacabbacdbddbcdabcbdaccaaabbaabbdbdcbcdbdcabccaabdadddccaabcdabbaddcadcdbcdbaddcccaddccacdddbbaababdcdcabddadbdaabadcbbacccacaccdaaadbbcacaccbbbbadabbcbbdbbbcaadadcbbbbbaccccaacacbbaaaabadaadabacccdbcccddadabacabbdbcbcdbccaccccdbdaaabdaccccbabbaacddbdddddacbabddcbbabacdbbcbacbabccdacadddacadcdbbbddbdbdccbadbcdadbaabccadcadaddabdbaabcadbcddbacdcdbcbbcaadddccdbabdabaababaabbcbbbddcadaacccaccbcdcbaccdcacbcbcbdaaacaddaababbdbadbaacbdbaabaccbcdccbcaddddaacadacbabaccaabbacabbaccbbccdbcbadacccbbdaabbabababbbdacdbadbcddddaccbbdabcacadbbbdbdddddaacabdadbcdcdcabccbbdbcaacbcbbdcdaccaaddcdabddbdaabccadcbdbcbacccadbcdbdcbccbbadbdcdaddcbbaabbaaabcbacddabacbbbbacbdbcabdbdbdaacaaacbbddcabcbccdacdcdcaabcdbcbdbcbabacdbdbddaddcaccacbadbaababbdcbbabcdbaaabbddadaaddaabdaacddddacacbcdadadbbaaccbbcabbddcbbcdbcbaadbacbaacacdcdcbcaddccddddbdaadcadadcddccaacbcdbacccbcaaddbcbdddcaaccbcddbbbaabadddaccadcdbcbdcacdabadabbdcbbaabbddbbccbabccbdcbadbccbaddcbdbcddaacbccacacdbcdbbbacbaddcbbabcadbcccdaadaaccaabbadcbabaddcbdbcaccdbdcacaadacbcbabdddacaaacdcacaabacababcaabcbbbbcdcadcdbaabacdccccadabcadcdbadddbcbadaadcaaabaccbaacbbbdaabacdcdcbaacbdcdabbaadbcbdbbbacccaddbbbdccdbadbcabdbaaaabacdbbbdcbbcdcabddbacddbcbdbdddaaccdcacdbddbcbacccaadddccdcadaadcbadabbcbbcbddbdcbdbcaadbdccbccdacbccdbabbdcddcadaacaacbbacdbcbbaadbbdbdddcacbbbbbbdaadddaaabcbcccabbbdadbdddbbbaadadaacbaadcbdbcbbabcabcddbcbcacadcbcdbaddbbbaaccaababddbddababcbddaacdaccbbdcbcbaccdbabaaabdcbcbbdbbcbadcadcabbbbcbacdcbdadbaddabdbbbddadcdcbbadbcbdadaaaddadaccaaacbcdbabbabcbddddbdbcbbabbabbbaadbdadabccbddbdcacdbcadbbddccbadabcddadbccadbadccaccabaadaccbacddcabbcacabbbbddabcddadbaaabdcdaaccbdbdbaaadaddbcaabacadababbadcdccbccbdcbdcbacbdbddbdbadbabbdcbdbbacccdddcadaababaacbabbdbccacdddcadbabcabbcabacbbabaddabbbacbcbabacadaddbaaabdcccadcabdbbbacbacaacdbcccabbaddabcccddadbadbbdccaccaccccdaddcbabaaadbdbccacaabbacbacdadcacbabdbbdabbcacadacacdcbdadcaaacdbaddcddadcbdadbcbbcbadcbbadcdabbdadddddccbbbdaacdbbcbcddddbabbabcacdadcaacddcacbddcbcdccdbdabbdcbcadabbbaccddadcdcbacbbddaacacdbccadbbcdabbbcdcbcaddaaaaaabbddcaadcacaccddbbcbabbcddcabddacadaadcccaacacbdadddbbdcdadbbcaabdaaaacbbaddacdbbbacdbbddcabbbaaabdcdaabbaaacdbbaccacdcdbcbddaccccddaadcbabbbdddacbbccddabbdcccadaadcbbabddbaadcbcddcbaaccbcbaabaaadcdccbabccdaaabbbbbccbbbaddaccddbdbcbcaacbcaadabcdadbcccaacaabdbbcbadbcdaaccbacbbcabadcdaddcbbcacdacccbdbdabdbdcbddcbbbaabcbacbcdbababadcdbbbcdddccdcadbccabaacccabdbccdbbadcbbddaacbadbbbacbccadacdbccdcaaadddbbdaaccbcdbdababcabbccbcadbbbadbdcccacbdabbddacbcbbaccabccaadcbcdcadbdcdbabbbaddcccccdcddbbbdcbddababdbaccbadacadddbddadabdbaabaddbdcbdaacdccddabbcdaabdbbbdbddaabbcabdaaaadddbccdbdaddcacbddccbcddabbaccaaadddbcadbdccccbaabbdabadcbbdadcaddddccbbdddaddddbdacadadcadcdacdbbcdcdaaaacbddbadccddcdabcdbcbdcadcbdcbdaacbbabddaabaaaabbddbccaddcbbbbbdacabcbccdcccacadaccbbdaddacbcaaaddddbacaccccbbdacbcdcadaacdbddaaacddbaccdbaacabdccbdcbdabbdbdbbaccccbcaddaccaadcddacdacddbabbcdbaddcdbacdaadabadbcadbabccaadbabadcbbbacbadacdaacbdcaccddddccbadbacaabcacbbcdbbcabacdbcabaadbbcbcdaabddacdbdbdacbbabdbadddbaccbdddcdbbdbcaadbadbddbdaaacadbaddadaacabccacabbbdaddababdadbdadaaacadabdacbbbcdcbabdaabbcbdbccaccabbdbcaccaadcbcdadccbcadacbbbcbdcbaabdbcadcbadddbabcaaabdcdaccbbccacabddbaacdabcdacaccbcddaadcadaccdcbcbbbdbcdcdddccbccdcbaadddcdacbbbabcbacdaccdbadaddbcbabccdaddddcbcacdacbaccbadbddcdbdddaabadbbdcadcbcdddaaaccbcdbcaacdadccadcdddacdcdddddbacabcbababbddcbccaddddaabacbacdcaddbdaccddbabbddbbbadccdcdcccabbdaadbcdadddddcdcddadcdbcabbcbcabddddccdddaaacacddccbdbdcbbcaacdbaccdccaabbcdbbaadddaccbbcdababcdadbddadcdcbddcbddbdaacddadbadcaddddccdcabccdcacbdadbbdbacdabcdbaddbadadcdccdabcacdbdbdbcdbadabdcbcbdbbbaabbdbbabdddacdbadbdbdddcbccdacadacbbaaddbdbbcccdbcabcdbbbacdaacaacadcbabdacdcddbbbdbddabddbcadcacbbcaacbadddbcbdcdaccccabaacdccacdbddddccbddaddacddcdabcdcccaadadcdcbbdaacdcbccccdddaddaaddccbcdbbbbdacddcdbdacdaadbddacaadcaadadbaaaddbbcddcbdabcdadbacabacbbccacadbddbadaadbadcdaabdbbaaadcdccdccaddbbdcabbbbcaacbacccbbaaadaddbcbadbacbdcacabcacccdbcabaabaadbabdbcabaaccdacadbdaabaaadbdcbdabcacbcadcbcbbacabdacbcdcddcaccaacbbbdbabbdbccaccbcbcaccbcabaddddacdaaaccaddcbbabccacadccadadbbabcdccacbaacddcabacdaacdaacaadaaaadadcbacddabaadabdbcdbddddccdbbcbabbbdcddcbbdddbbbabddcccadaccaaadbacaccbbacabdaadbbcbbdcddacdbbdbaaddbcbaddadabacacdbcbacdcdddcbaaadbabacbbddaadbbadcbccacdbacadacbdbcbbcdcaaaaabcbddcbbaacbbaccddcbcbbabdcccbaabbccaccdcdcaacabdbaaadaadbadcacccbadabdadccbdccbaccadbccdcacdddaadcbdabbcbbdaaabcadccbdcabcadabacabadabacccdcccacdbddaaabbcbbaddaccbdbdbbaccdcacacaccbddbccdddcccdababcbdbcccbbaabbdbabcdcbbcbbdabadcdacadcdaccdbdddbdaaadcaabcadaddcdcbcddacadacccddbcdaadacdadcbdccbcdcbcacdbaccbbcbdabbcbcccbdaddbbaabcaadbabcacbbbcdbdddcbdbddacdaaabaddccabbddadddadbdaaabcadaddaadbdaddaaaddbcdcbadbdadbaccaccdbadaadbbddaddbbbdacdbcacdaabbdbacbdcabcdbcaccbabadddbcaadaabddcdddcbdabbcdbcadaabaabacbccdabdbabdddccdabdbddcbbdddacdaaacbdaaacaaababcdacbacdcddccabaccbcaccbbbadbdadaaddbddbcbccdcababbbaaabccdcaaaacddadcdabdddcdddbbaacbdadccccabdcdadadcadbbcdbdcdccaababaaaddbcbdabdbabcbabdddbcdcacdbbcbdaaadcdbaccdabddaadabbdbcbccdacbbdadacbbaaccbbbccddcbdddddccabaddccdbaaacaaddddaccdaacdbddabcbddcddbcabaadadbbbdcaaabbcabdcbcbadbdddbbacaaaabcbcadbdcbbacdacdbccbdbbabdcbcdbdbbabdcdcddccbdbddcdbaacddbccbcbaabdbbbabababcdddabaabadcaddadabccdbacaabccdccdcddcdddbccbaaddcdccbddadaadaddcccddadacdbcabcabbaaacdbcabadbdadbaabcbcadbdabccdbdbcccadaddbddcdcabaacbbcbabdcdacbcaaddbadacaacbbdcbbdcdddcabcacbddcaaabcbbabccaddbaabdbabaddccccbcbbbccbdacaaddcaacbadbbabccdcccadcbdddbbbbabccbdaabbdaacccabcbdbaadcaccdbbdcacadbbccdacbddadbcacdabbacccaadacaddcdbaacbdadaadbadbdbccdddbcbcdabbacadbcdccdcaabacabdbbcccbcbddbabcbdbccbcbdbdcddbacbdabadddbbacdaaabdcaaddbbcdacdcababdaccbdbbacacadacbcdbdabbcbdcbcbdaaccdbccddacaccdbbbaaddbddcdbdcbadccccaaddadcddbddddaaccadccdabcdcadadbdccaaaaaacdccdcdaaabcdcdacadadcdcdcdcbbdacdaaacacabccddccdcacbdbbdaabcdbadcdccbcbadadabadcbdadacddcdccccbbcadabaddcbbcbbadaddbaabdcccabaacbaccaacbabaadbdaaddbadbacdbbdbacdbbacacbcabaccccbcdbdabdddcdbacdcabbddadaccadbcbdcbcbbddbcbaadccdadccbadbcdabdaaaabaaaabcddcabbdcbcccdaaddaccaddabdabbacdcbdadabccabaaaaacdcbdccccaaabcddcccbacdcccbdbdbcabacccaaacbaabadbbaabcbcbbdabcbdaabcccaacacacabdbbdacdabaaccbdbbbabcbcaaadbdacddddcadcbdcadaabbadbbacacbbbcaabcdabccadbcdcbbadaacadcdbbadcacacdabdcabbcaabbdbcdbbdaabdacbcdacdcadbccbbdbacbcadcdabddbcaaacaddacdbcaabdbdbbbccaaddccacbdbcaadcaaccdcdabcdcaddcaabcdcdaabbcbcbaacadcdaadbcbdaabadcabccdcbddcababaddaabcdcdacbdcdbdadaccdcbcabcbbabbccaaaccabdddcddacabcabbbaaabdbbccbcbdbdabaccabbcaacbcbcadadaddcaaccbbbabbcddcabaabddcacbdcabddccbdccbacbdacaadaddddaacdccddddccccacacdcdabdcbcdbbbdccbaaaadcaadccdadcbaccbbbbdaaccbcdcddddadddacadabdcaccdccccabbddbbbcabdabbbdaddbbcdacdcaacadcbdbccabaabbadcbbaddacbaacaccdcbcbcddabaadcadcbddbadbbadbaddddddadbabbabbbdcdbbcbdbbdabadbabbbcccbbcaaddbadcbcdcabababacbaaacabcbddddbaababccdbcccccadacdcbcadacdcbaadccaabddacdcacadadbaccbcaacbabcacaddabaabbacacddbbcddacaaabcaadacdccaddabdcbcabcbbcbcacccbbaadbdbacacaabaadbabdacdabadbabacbbdddccabdcccbcbabbdbdbbdcabddacdadadcaddcdbbdbaabacccdcadbabcabbcddccbdaacaabbacddccbbddacadbbbaabbbadbddaacbcdabbbcddbacdadadcbadbcadaadaddbcbbbdabdaabdbbdadcdabdbddbdaccbddbaaabbdbddacbbbdcbdcbbcccbadabdabcdbddbadaaabbcddbbbdddaaacabddbdadccbcdbcabbbddaacdabbddcdabcabaccadcdabaadabacbadabdcbdcbdacbccddbdbbababaddbadadaadacacaababccdbdcaabdaddcdbbbadababcaaacacdccbdabbbccaacccabdcbdcadcbbcacababddbccaabdbbabdbabaacacbbbcabbdcadadccaabbcdbcccdbdbdccabdddccaabddaddbbdcabbababbabcbbddccbccaaccbacdaccddabacccabcbcabbcddbcccacacdcbbadbcccddbcbcbabdabdbbdacdcbcbabaadbbabcaaadccbcddaaacbbbdaabcbdbdcbdccdccbbdcaabbdddccacacccbcddbdaadddaccddcbdbaadbccbacbccacabacaacbcacddacddabdacbababdbbaaabacddaabbdddcdbbaabdccaabcaacccaababaabacaddacabbacbccabaddacacdacbddbcdcdaaabacaddadcbaddcabcdcddacabbcacdbdbcdaccdaddacccaabdbdaacdcababbdabbcddacacaabaaadbcbddbcbbdcbaccadcdccaddcbdcaddbcddaabaacbcbbdcabddcaaaddcdcabdbddbdabdabccaabbabcacacaabaaacacadbdcacccacbcaabaccaaccacdccbbaadbddacdaddaabacdaadbcabbdcbbbaddddadbcdcacccbaddbabbbaddabbaaacacabaaacdddcbdaccaccbaacdcadaacbbadcdccacacbabaaccdaaacaacaacbbdcacbcabdaabbaaddbcbbccdcacdabddbdbdcddaacabaaadaacdbabdaddcabdacdbcddbaaadaccbcabcccbcbdbbcbddddacbdbbaabaacaacacdaccbbdcbacabdbbbbacbaddbbacabbaaabccdcaaacbdacdaaaabbccbbcaccbcbbcbaaaddbddbcbbbdccdddaabbcacaccbbacadbdbadadbdbabaacbdadbabbdacbdbdbaadcadccbbaaaabdababdbaabcdcbaaccabcacabcadadcbdbdcccbddccabbbabbcbadbacdadaaabbabbcdbadaccddcbbcdabdcdbcadcbaccaabbdcddcacadccddddaccacbaaadcbdcdadcacbcaacbabadaacaabdcbbcaacbcbaabcdbdbdbcdccbcddbbbdcaaacacbddcbacdcaadadbcaabcdacbdccabacbaacbaccdcbcbcbcdbccbadadaccabadaababaacdbaabbccccdcaadaadbaabbaaaacdacbbbadabbaabcccccdcbbcddcbadddcabdbdcbdbccbdbbdcbcbdabadbccbcdccdbddddbbbbccbabbcbcccabcabdabdcaabcbcdbcddbbadaacbbbaddbbadacadcccdbbccbdccbdcbbacdcbbbbbccdcdcddbbaccbcadaababaabdacdcbddccbdcbadaaccaabdacaacbbcbaadaabaadaaacddcacbccaacdbdcbdcddaccbccdabccbabcbadcdccccabcaaaacaaddabcbcbacbdbdcadadcdbbcbbddbadaccdbacdcdccdaabadccdbdcabcdbacbaacaadcdcbbdcdcbcabccbbacabdddadcdbccadabbbaadccaacacaaccabccbcdacbddcacadaddaacbcdbbacaacaccdaccdaddbcabcbbdbabccbdadcabcbcadbcdababdbcbbdcadabbcdbbadaccdbbabbacbbabddbbcbbcacbddaabbbddcbabcaccadadcdbcbddaadcdbcababaabbcdbcddbbcaabdcabcbaaccccadaccddbdaacacabdbbbaaddabaadaacaccddadbaadbdcacaacdbdddabbbbdcbacdadababcdbcdbabbbbbbddaaacccbcaadbaddaccbddcbdcddbbcabacbcbdccbabcddcbbdbdcdcccdbbcbdaadbacbbbcdccaaccdcccccbacdabaccbdcddacbadddcccdbdabcccaaadcdbbbcdbabcaacaaadababbbaabacbabbaccdbacdbbdbcdababaacabdddcacbdadcdbdcabcbadcadbacadacdacabcacdbadddcaacaabddcabbcdddcadcdbbcabdcbbaacdaaadddbbabcadaaabccddcbdabbcdcaaddcbdacadddacddaaadbcdbdccccbdaadccdaaabbaaabcaabcdcddaadaadccbaaabcbaddadbaaacacbadacaacbdcbdcccdaacbdcbddadcadcbcadadacdadddcbbccaadcbadacaddbcddbdbaaabcbbddbdcbcbacabcaadcbbdacaacacddcdbdbcbdccdcacbbaacdacbcbcbdaacddabcbbaabcccbababbaddbdddbcbbbbdbccbdddcdcbcabbbbbddacaddaabbabacadbcdaacddcabccbcaaaadaacbbbdbddabaacaccbadddcbbcbbccbacacaaabddbbccacdabddbbbdcadcdbcbcadcdddacbaccabaccabdbdcacbdabacacaaccabbbadcbbdcdbbdaadbbacaccaaaabaacbddcabdbdaabcbcbdabadbcadcbabdccdcccbacaaadbbddbbdccbccdddacddddccdbdaabccaddbabcbbacbcacaacdbbdddadcacabbbbbaadbdcaaaacbdadaabcdbbaacaaaccbbbdddacbcdaabcabdaacabbacdbcadaddbbaaaddaaaaddddbadabdbbbabbcaaaacadccdbaacccbbcbcbbaadbababcddcdcabdbabcbbbdbdbbccbccccdbccacbbcbccccccddbdbbbdcacdbaddbdbcadacbaaccaaadbbdcbcdccaaacbcdaabaccddbbbabccabbbbcacacddcbbbbaabacbabdbbdddcddbbcdaabdabdbaadacdbbddbdcdadbabaabdcbacdbabccadabdcadcdbadcadacbcbbaaaaaacabbbdabbacaaacaabdcdacbccbbabcdaaacdbcacccdcbccccddddadddabbaaaddbadcaabdadabbdbaccdadaccababbccaccdbdddbcbbbcbacdadcaaaadbadabcbcaaacbccdbdbaacdcdababdbdcdcdcabaacdcccccbcacbdcadcbccacbdddaabbcacabcbdbccdbccaccadacbdababbbbdbdaadcdadbbccdacbaaadadccabadadabcdbdbbcdcddbdaabaddbbcdacdddcccbdadadbaacadcbaccabaccdbddddcadbccbcbababbaabccdabaddbabadcaadccaaccbddadbcadadccbbbbadddcbcbacccadabdbaaccdcbabcddccacdaccabbcdbcccadabcbddbadddcdcbdcabcddbbcbadcaabadcdbbcdccccacbabacbbccdccaaccabdaadaabcbcabbdccccdabbacbbabdbddcadaabdcaaaacacadbdbcdbdcbdaddcddbdabccbbabbddcaadbacbaacdadacbcababbabdbccadbdcacdcdbbaacdccbadaaaabdccbcdadccababbcbabbbdddaabdcdadaabccacccdbdcbbccbddddcdacdadcbacbdacddccbdadadabaaccabdbacdbddbbcaaccadadddddaddacadaccbbaadccccaccbddbcdccbcdbacdbddadabbdcdbbcbcddcdbbddacacbccbbdbabcdbddbcdabdbcadacdbaaacccbdcbddcbccacaadbacbbbbcdbacbcbcbdcdadcadbabcbddabdadacbbbccabadcbaacbdbdddbabcdbbbbaccdbabdbcaccbdcabdcbadbbbcbbbacaacacaacddcdcdabbbbddcccbdcbddaaaabaacbdaccaaadabbadaabbdccacacdadbcadbdaababddcddacabbdacacdcdbcacacabdabcadadabccdbbabaacbbddaaaadbdacccabdcddccbaadcaccaccbddbabaccdbcaaccbdcddbaaadcbddaddacbdabacabbcabddddbbadcaadbdaadcacdbbcdbcbbcccdcdaabdacaabdbadcbccaadbdbbdabdccccccbbdccdacdccbbdbaccdabdaccdcddaaccaddacddbbaccdacbadcddcbddabbabcbddaabccaaccbdabaddbaacbadacbbbbdcadbdbaaaacbbdcbbcccaddbdcbcbdacdbaccaabdbaadaaaaaddacabbadcbbcbccddbddbddcbabdaacccbcbaddcdababcccaccbdaadbbbabcdcdbbcbadccadbaadbdabccaacabbcccacbdcccadbbcbcababdbccdbcbaddddabdcdacacbbcddaabbaacacbbccbaacbcaccdaaddcdccaaacccccbaddbbddbadabcacbbaabccbcbaacaacbdddcdacccddacaabcadcaddadcbabcaabcaccbacbccbcadccdbdbcbddacbccdcaadaccbaddbbcbddacdbbcbdabdaacaaacdacaabbdddabbabaadbabbdbcaaabdcaccdcaaccbbacbabdcadbbdbcccaccaabccbdadccacbdaadcdabcdccbdcdacbbabccbadcbcaacdcccadbcbcdadababcbbcbabddadacadbacbbadacbaddbdaabacabdcddcbdababbabcbbdaaaaaccbaccdacdabbdacacaaccbbabdcbcbccbcacdbbbdacddccaaaacacdbabbcabcaabacdbccaadaaadbddcacbbdbbababcbdbbbabbbbdaabaabbaccbcaaccaddaadddbabacdabcaadbdddcaaacdcabdccaccbddabbdadbbaddddbcbbccdaadccaabdbddadcbbcccabbabcaddabcdcaabdbaacadcbdbabcaaddcadacdcddaccbddaacddbddbacaabcdacadababbdcdaddacccaccdcbaddbccbabaabbacddadbbcccbcccbbbcbbadccbabcddccdbbcaddcddcccbcaddbdabcadcbdbadbdddbcaadddcdbaddadcddbadcdcaabbdbddcaaaccaccccadcacbbcaaadbbbaadcccbbdcbcbbacdaddccbcdacabcbacdaccaaacabcaaacacbdbaadabadbdddddbaccbcbaddcccadcbadcaaaabdbbcdcabcdbcbaacacdbdaaccbbcddbbbcadcdddacaccdcdadcaddcccdcddbdbbcdcccdbbdbdcdccbbacaddbbbabdacddcaaaaccaabbbbccddcbaccbbdbbaaaaaaacbcdabdcaddbdbbcdbddbcacdbdcccbacbddbcacdabcbbdacbabdaddbbcdddddbaadcdbcdcbbcacbdcadadbcddcdaddadacbcccdcddcddbcadaaadcddbabaccacccacdacdcaacdbabcbcabbbbcbbdbcbbcdcadccbccabcbacabcdccdbccbaadccdadccbbadaddcbcacdabacddcbbaccababcaccbcbdacdcccabcdccccdcacaaddbddbabcdcabacbbbdbadacacdcabdacddbdcabcadaacacdcbbddbbdaccababdcddcdccaadbbddcbbbacdbabacaabdcbdaabbbdcabccbacccdddccdacccbddbbaacbccdabbbbcdcdaabbcdcdcdadcbdbaccdaccaddcacaaadcbccdcabddabbbcddabccbbdabbaaddcaddddacddacdbbcbabddabcdabaccdbdaaacbdcaaaaddcabbdcdcbbbcbcbddcbaadadbaccdaabadcccaacdcdacadaacadcaccaaaaddccccadbbdbccbcaacaaacdccadbbcbaadddbdddacaacabccacdbaabcbaacabaadcdbbcaddadbaacbaacbcccbbbaaadbbcbcdcddadbccbcbaccbacbddbbaabcbaddbacdbdbcacaacaabadcabbbaabaadbbbdbddcbdbdcdadbbdabdabccdbbbdacbabbccdadbadadcaaaadcbbcbaccbbcabcadaaaacdbacbdddaabcbdbbcaacbbaccbcbcbdacaacddadcabbadaaadccacacadddaadacababaddbaccaaabbcbcaadacdbcbbbccbcaaacccddabadbdacadcddbbccbbdbbabaaabacadddaaadabcdbadacdbbccdcaadbbbccdaadcbcabbbbadbdcababcbdcacddadcccabaabdbacabccbddadacdcabcbcdaaddaaaaacaccdcadcbcddbcacddbcbcabbddabcbabccdaadabcbbcdcdbccabcbabbdbcdbcdbcbddbdccccacbbdaadcaadbdacdbaddbccbcbabbbdadccbbaddbcadddccacdbcddacabdbbbadabcdcadbbbccbbacaddbddddcdadccbdcacddcdddbbbadbdddcdaabdcccdcaadacdaacaccdaaddcbacaaaadcbddccabdaccbcbbadcbdcacbadacbddcbdcbabacddbcbdcdabcddcacdcdbcbdcdcadaabccacccdcdcadcbbcacdaacacaabccbadcdaadbdcddddadcbbdcabbadaaccbaaababbadadcbaaaaacbcbbddbbcbdbcbdbdcaabcdcabdcadbadbdbcdacbdacdabaacaaaacdbccaadbaadaddaaddaaadcbcacabcaabcccbcdcaacadadbabdaaddcccaadcbcbbccaadaaccdcaacbbdbbccaccdadcdcddccddcaaaadcdaccdacaaaaabbdacbabadbcaacacccabacaccbbaaccdacccdcbcbbccaaaaccaccdabbbdbadcdccaadacbabadddddbacddbadaccbbbaabbabcbbccbdadbbbbabcbccbcadcdbdaabdcaabccaadddacadbadcddbadddddccabdbcaabadbcadabddcaaaabbabddddbcbcaccccbbcabcccdbabccaabaabcadbdddcbcbcbcbddcbabadabbbdbcbbcdbdcccccbcddbbdddadbddbcadbccabbcbbccccbaddbcddbacaaabbbccdaacabdddcccbabcaaacbcdacbbdddbcdbcccbcdadccdadbdcbcbaddcbbdaacadcdacccaaadcadcababdcadabcdddabaccddbbcbbbabcacddcaabdbbbdcddbaadbdbbdbcbabdbababbcacdbabdbdbbcbbccbadbccccbbacadbcabdccbddabaabdbcbaaabacddbabdddcccbadbccadbacaaaaadddaddbaddcbbbcccdcdacacbadbcccbdbdadbaacdacbbacaaabbbddcbabbccadaabbcdbdcddcccdbbddabcbadbdbadbcdbabbdbbddccbcbbbabcbbdbdabbcbbbbbccdabbdadcdaabccbbdbabcdcccdabaccbccdbdcadccdcacbbdbacaacdcdbcdddaabccacddbcdabacaddcdbdacdbaddcbcdbcbadcbccadccaababdcdcdbbcabdbcbadccddadaabcadbcdccdccbdadacccbcacadbdadcdabdbbbcbbacdcbbddaddbddcadbcdcabdacccadaacacbcbadccacdbaacccbbbdbadcdacadacbadadbdccacccdbddadaaabacabcabdcbaacdccdddbdaaaacddbaabcabbadadcbbdcdbadbbabacbcabccabdacdaccbdcbdcbdabaacddbbbccdcddadcccaacdabdbbcdcaccacabacdabbacabdbddcaaacadbcabbacababdadbddcbddbcdddbcaccbdbdbbcadbcccddbaccbcbcbaccaccadcccbdccaacbdcadcaaabcabadcbcdccddcacbaaaadcbbbcccddcadacabadccdbaadbabcddacdbccaabddabbbbdbccbaddadbabdabdbdadcbdccdddddbcadbcabadadddcdcabaccddaacdbcccacdccaacdcdcadbdbdcccacbccbbdddbcbcdbcdcaaadadbaacadccacddcaabbcabdabdbcdacbbdadbabdaacbacccaccadbaadbabdcdbaccdccacbbaccdabcdddacbdacdbcccccbdccbbdbbabcadcbbadcaaddddcbbbacadabdbcbabadcaabdcbdaadddbbadcbcbcddbcbacacdcabbbabdabacdcbcdbbddadabbaadddcddcbdbccacddacabdadcccbcbdbdcccbdbbbdbbdbbdcbcabdbdcbbaaadacaaaacacbdcadbddabbcaaadbbdbacaabbccbddadaccbcddccbdadabadabbcbadcaaadcccbacbdacacbbbaabccbdbbaddcdbabcbabcddcbaaacbdcddddddcbcbbccaddddbcdcbbccbdddacbdcbaaccbddbccbbdcadbaacccbddbcbcdbcbdaadabadcdacccacdbbdcbbaddcccabadaaddaabdcccadbdacabdbcdbbcdccacbdcdacaaaacbdbdbcaddcdbdcadaccbbbcdacacdcbdbdbcccdcaacdcbbbacccdadcadddacaccaccddcbbdccababcabcbbcbdcbcbddacddbadbacddccadcbbbadaaddcbbcdadddcdadcaadbdbadadbadabcdacccaabcdabcbdbbcacbaaababcdabcbcbdadacdabcbcbcabcdccabaccddbbdbbaaddcaaaadcbbadccdbaaaaccdddabbcdabcadbbcdcbbcccabbdbcbabccbdbccdbcbcbabcadbaacabbabbcbacaacdbccbadaddcdddbdbaccbaabaacbdbcdbbbadccbdcacdbbbacbcdabbdddaddbbacdcccbdaabadaadbddccccbcbbdcbdacbddaadaddaacadbcddbbbadccdcaaddbabaccaabbcdbbdcdcbddcacacacacddcadbdcccdaccbdacdcbdbadbbaabacacbcabbddbcaaaaaccaaadbbaaabcbdbcaaabcabaadbdaacbdccabdddcdbabdaacadbbcaccadacbacdabcdaaacbcdbaaccbcabcacabadbdcbdcbdbbbaddbcbbdabdbbcbdcbadacbbadddbcacdbabccdcbcaddccbdbdbbdbaddbcbadcbccccccbaabacaabadaacbbbdbcaabaacaddddddaccacddbdcaddaacabbcdbcdbbaadcaabcddcabbdadcaaddaddadaaccacadaadccdbdacacdacbdcabcabaaccdacddbdaaaaadbabcbcdabaaaccddbdbabcbbcaabdbbbabdbccbacccbdbbcdbbdbbdcdccaacbaccabcaddcdababccbddadbdddadcdcbcbacadbcbaadbddbaccbddbcdbddbadbddbdbaacddcadcdaddbddcbacbbbdcadccdaadddaacdbddccdadbbdacaddadbcbcdaadcccabcbdbcacdcbcbbdbcccdbbbbacdcdadbcbdaddccdbdcaadbabcacacadacdaddcddaccbdcdadcddacdccdadaadadbaaacccddacdccbadadcbcccbaabddbddbcbbcbbdadccdccbdbbdbaaacbdccbddbbbcdbbbcdddabccaadbdbcadbbbbdbbbbacbcdcbacddbadddbabaabacbadcbdccdcccaccbbbdcdbcddbcbddcdbddaabaadabdcbbacbdbddbaccaaabbcbcbcbdbbdabbdaaabbccbabbddcdadcbccabcdcaddcaacacbbaccbbcadbcdbdaccadaaacabdcabdcdbddbccdccddaccbadabacaaaacaaaddcdaccdccccbadaaadddccabdbddacdddcdcccbcadcaadcbdadadcaaabddacbcacdabadddaddddcdbcddacbabbbdbbcddddabadccbadcdcdcaadbaccdacbcdabacadcdbaacbbcbdabbaabaabdaabdbddcdadbacaabcdacadbbaaabcaabaddcccbdcbcdaccadcdaacadbcbaabadcaabacabdcacbaacabaababcabbadbcddbadbddcdbbabadbccaccaaccccbacabdccdbdcabcccddcdbaccaaaaabbccadcbddcaaacaaabbbcdcabbdbbbbcddbdcaccccaddbcbbcacccddbbcbdcabdaccabcbcdbaabaabcbadcccddccdcaaadaaaabbabccbbbdbdccddacbccabbdabdcdaadbacadabaacabcdadcbcbddbdbdccbcabccabdcbbcacdacabaddcbaadbcbabcaabadbcacbdaabddadbbaacaccbabbbdddcadbddcdcbadacaddbcdcddbcadbbbbdaadacdbbacddbcabcdabcacddcadbdbabdbccacddddcbacadaddabbabbdbadbcbcccdbcbbabccbcccabdbcaaaaccbcdbcabbcaddadcabdcdbbbddacabdbdbbdababcbcddccabddacdcbddcacababdcdbccbbcccbaaddcaacbbcdbdbacbbadddbcccdbbbcdadcdaadddabbbcdbbdabdcdccaabdbacbcabbcddabdabccdabaadbaadbbdbbaacbbccdbcddbadcacbdadbdacdbbadcddadabaabbbabbbdbadaacdaaacdbaababccdbbabcdddbcdbccbccaaadbadbaadccccddcdaacaaadaddcdbdcbbbdbccacaddbddbcbacbdbabddabcbbbdcadcdabbbbababbcbdddacbdbcbdbdccccbaaccadbccdcddabcbaabacadcadddaaabbcadcbddcbcaacacddabcdccabbabbcadbbaacdcbdcbddcaabbdaccaabbcddbdaddcabccdbacdadccbcdaadddcadccbdbadbddbcbcdcddcbaacbdcdcabddcacbcddcacdadcdadaccdbacbabdbaababaccdccbdbabdbaaaaaabcaaabbaabbdcbbadaaddadcbabaccacdcaccbbddbddacbcaddcabbaaccbdbaaccbccbbdbbadaaabcccaadaadcaadabbccdbbcadcabdbacdcccacadbbdabcddccdddbcdaacdbdccbaadbbadaccacdcbbbacaacdcadcadcccccdcbcbdbcadcdadaadababdbbccadaaddacbdacdbaacaddadbcabdbbcbcbcaacdaaddcbbcacacabbbcdcacdadcabaadaccdacdabaabbbaccacabdcacbcabbadadaddabdcdbbcadcaaddaaccaabcbbccadbaccbbcdaacdbdbbabbaaaabdcdadacddbbabbdadadbaabddaaadccbabcbcbdcaadbbdcbbdcbdabbcbbcdbdccacbbccbcbaaadcaabaacbadcbbddaaddabbdaabdbbdccbcdadbbbabaaaaacddacadaadbddccbaacbdacadcaaababacadcdabcbdcdbdbbcaabcccbcbbcccacaadbadadaddcbcbbacbdddbbaabddadcaccbbacabadcabdddcbdcabcbaccddddcddbbddbcdddacbdaddbbadbcdabdcaacbcbadabaadbadbccddaccdcbbbcbacacdbaacabaadbaadbcacbdcaabdcdcaacabdaccadabbddbbdcccbbacaaaddccacdddabcaacdbdcacddbcdaadddcaaacbdadcdbacabbbcaabcdaaddddaddddaadccbcbcacbabdbdbaadddcadcddbabddbdcbacabaaacacbbbbaccadbbdaaddcaacbacbdccabbadbdbbddbbbdadabadbcbdacddbcaabbdbcadaabddccaabccaddcadaaddddacaaccdaaaaaaabbbbdbbddacdbdaaadcccdbaabcbacbbaabdcadcbaabddacccaabccaaabcdcbcacdcabdcacddabbbbaaababcababdcdccbadacdbbcadccdaacacbdabbaaaaaacadabacbddcbbbbadbccdadabadbbdddaaacccbdadabaadbaccdcabccacaddacbaabbcdacaddbacdcbdbbbbbccbcdbccacbdaabcddbcbaaccacacbdcdbacbdcabddbccacadbcadbddbbdccddcccdccddddbaaaadcdcbcabaadcbbddacadcdacccadcbabacdaaaabdcadbdcacbdcaaadabbadabdbcbbaabbcaccbaddbbabdcabbbcadaacdbdabbacdddbbdbacdcacddddccacdccdabadaabcbaaacdadcbdadbbbcdaddbadcbaccddbccddddbbbadcadbcadcdcbadacacbbcdbbbbcbbcddabbaadadcddabcababadaaabaacacdabdbdcbcadcacbadccacababadbddcbcbcabcbcccbaacbcbddcbddbadbcbacabaccabaacdbacbadcdaabacbabdadbdbaacaadadabbddddbcbabdbadabddcabcccbccadabdacaaadbaacbdccdcadacdabbadbbcdccccccacbacadaadccdadbbdaaadaacbadadaabbcadccadcddabaaddabcdbdbdaccdaadccbadbdacddabdbbbbbaccbccacdbdabbbdcbbbacddacabbaadbcdcadddbdcdadbacbddacdbbdacadadbbdabcdabbcacddadcbdbaddabbcaadbdbbbccacbcdbaacaacadacaaccbaadbbbbcaaddcbdcdabdbaabdadbcaadcabcccdaaacacbdcacccadbdcabbbddcbbbccdaadcdaccdbbdbdbbadbabbdabdababadabcccbbbcabddbbabcdccacbcadcbdbcdccbccdbccabadbabbbbcaccccbdddabcabbdddcbadaabccccbacbacbaabdddbbbdaddbcddbcdbccbddbdbccbdabbbbdcbccadcdcbabdbdbcdcbabccdbcccdabdabdbbaabacacddbcdaaaaabccacddcdaccbaccadbdaacbddbddccbaddbcdbbbcbdbbdbbdcbaddacbbbabbcbcabbbbdcdcccabacdccdaadadbbcbbbaaccccccaabcaaccccbcdbbbadcbbdbaaccdbbdbdadcccbdddbddbacbbbcbdbaddcdbddcbaaaabbcaaacbaabadbabacbbccababddccadbcaddddcdcacdaaaadaadaacbbdcdacadcdbbbbbccdddaabcababbdacbcaacadacbccacaabbaaaaccccacbdcabdddccccdadcdcadbbacdacdcadabdbcbdcbccacbabddbddaaadbcbcbbdcbbbcdabaccdbabcadbcbbdbcbddccccaaccbddadcddbcadcdabaccdddcdadaaabacbcdcbbdabdcdadbbbbcddaccbcdbcbcaccabdbdcabaaaddbdabdcacabdcddbddbcabcbcbaabbbbacaaddcdccabddbcdbadadbcdddddcbddaaaabbbddcdddcdacacbdbacadcbabbcadcbabcbcbdadbcacbddadabdabaddaccbabdbccddbdcdaadccccbdbcbcbddccdccbddddbdcdbcddcbabdabbbabaaabcbabbbbabcbdadacccadbbcacabbccbdaddacadbbcabcabadabbbbabaabbaadbbbcdbbbddbaccddadbbcdccbdabdbacaccbbaaabbbcdbddcaaaabacddbacbbdbabbbbddaadadaccdcdabbdacdbbaaccbdadbaabddcccabbaabcdbcacccdddcdddaadbdbccabadbdadcadadaaadbcdddbabcbdcbcacdbaddddcaddcdcddbabcbbbbabbcccbbdaaacadddcdbcbdbbcadddcbbdbcccdcddbdaacdacdacccbdaadacdaabbabcaacbcbdbbdaabcbcbcbcadbbcddbacbbdacbdbdcaddddbaaadcbbabbbbcccdcbbdabbcacabdcabbcbabbcdcbdbbccbbaacccbbbaccadcbddacadcaabccbccbbdbabbdccccdccabadcaadbcadcabcbcbaaccabcaabcaacbcdabdbccdbdbcaacdcdaadacabbccdddbcaaadababbdddbccccabccadbdbaacbadcccdcdbdaacbcdbbbaacadadbccbdbdccbdddbaaacacacbddcadccabacdbddbacaaaabaaabdadcdadbadacbbddababcbcdacddccccdabdacddcadcaddcddcbaddddbcdabbacbbdaadaadbccdaaccabaadcdcbddadbbbbadbcabbbacdabdbbbdcbbabcbabccdbdccbadcadaddbbdacdcabddadccbabdcdcbcaadabcbcdcabddbcbccdaaaacdbcbcbaacdcababbcabdcaacdbccadbaddddcbadbbcccdacccbbaadaabcdaacdcacdbdaadabbaddacddccddddcdacddbbadaccbccadbcbaacaccdbdcbaaabcdabcdbdccddbccddbccdcacadbdddcbbcadbcbdacbbdcbbaaacccabccbcdacdbbabcadbbdacbddbdcabcbcdabcbcabadddbcabbaabacbddaaacdcacbabbddcaaccaaaaaacbdccddabbbdcaacabcdacaadcadcbcccadcbabcccbdddbcbcbbabddbcacbbacbadbaddbccccdbcccabdbabadbddddbdcadabbabcacadbdbbdaaadbcccbaddaddabcbdbcdbcdcadadacaddbccbdaadcccccbaccaabcacdcaaadccdaccabcbbbdccddcbbdacdacabcbcaabcbddabbaccaadadacdcdbabdcdbbdaddbbaacadaadccbdbabbccbbcdacabbdacccdcbacdccbdbadcababdacccdaabcbdccccddaaacddacbdadddcbcdadddddacddbddccbdaacbacbcababdbdbaacaadadaabcaacaabcaccaddabddcbdbcbbcdbdbdbddacdabcdbccabadbdaacccdcaacdacdcbabacbcdcadccbbaaabbbcdccdbdcdbbabaacaabbcadcdccccbcadbacddbdacbbddbcabddaacdbdacdadaccdabdbcccdacabddacbbbbcdaabcaacabddaddbaacdccbaadadcadcaacaabbbabbcddbbabcddcabaabbdbadcaaccdbadaabaaaacdbabddcdccaddaaadcacdbccdccbbcadcabdbdbabaadacdbbacdbabcacdbbbadabdcdaacddadaddabddbdaddbbabdbdcadbbcacbccbdadcaadbcbccddccbaacbbbbcaadccbdacddcbbaddbadbdddddabddbacdbdbadacbadddcaaccbadcaabdcaaaabcbaacbcdccdcbdcccaabaadabcdbccdaaabadcddcaaabdcbabdccabacaacdcbaabbadcdaccbddadcccdbbadaaccdbcadbddbdccadbacddbcccddbddddbdbbbadbabddadcdbdcbbbdadcdcbbbacdabbdcababcccdbbdcbababdaacbacadaacbaabdbdbcdcabaddccacccacbbccdbaaaadbdbdaacdcaaddcbcdbbadbcdddbbcacaaaabdbaadaabbcbccdcbbaadadbaddaabaadacbadbaacbcdcdabdcabadaddadbadbdcdadcdaaddaddbddbabcbcdadbaabcdcdccdccddbbadacdbcbdbdcdcbcccabbddcabaacaabadcbaddbbcbaadddadacccbbbddcabdcbddbccbbbbdaabddcdbadadddaddbdbddaaccccaddadcaaadbcbcaabbcbbcdcbcbcdbdaaadcbacddbccacccdababdbdaaaaacadccabaccacbcdcaddcbddcbbcbdcaccbdcaccbdbccabaaaddaacddcdbcbbcacbabdbdbdcaccdccbaddcccbbcaaaabdadadbcdbbbdaaaaaaccdbaaadbcccbddacdbaccdddcadccdadaddaddbddabccabdcabdbcddcddccbacdbabdadbbdacdddcbdabdcbccadcdbdbbbbccdbbcabdadadcccadcdcbcccbcdcdcdddbccccadcddaddcdbadccabbdabadccbbdabcdbdabaaddddbaadbaabbadacbbcbcadaabcccbdcbbdbacadbbaccdabbbaccdcbaccabdddccddcdacdaababacaaccbbbbaabaaaaaacddabaddbbccdabcaccbbdbbbcbabccaacaaadccbcaddcaaabddccbbcabbbbbbdabcdacbcadadabddcbaacbcacccbbbaaababaacddadcbbddcaacddddccabbcdbbcabccaadabbabaccdbaccdaccacacacbccabccccddddcbcaddcdaabacadcaabbdaadbbdadcdacaaccdacdbacbcbddabcdbcdbbabdddaaddcdaaabaacddddbddcacccbbdccadccaccdabbcbbaabdbdcbdaabcbccacaabacadcbbacabdbccacdabcdcdccdcdddbbaabdbcdacbccbdaccaaabbbadccaacbbccbcaaacaadacdacbaadaccccccdbdccddabdbddddbbbddbaadcadbdbacdadbbaacdbabacdbaaaccacadcbdcdacddcbaabbcaddbdaccdabacdddaccbcbbbaaddacabdaddcdbccacccbabcadacddbdadcccabcdaaacccaadaccbcacdabdcbbaadcacaddaaaadbabbabdcabdaadacabbcacbbdbdcaadabdaaaacaabadcbabccaadadbcdccdcddbbddacdacbcbabdbcdbdbadddccbbdadcabddaaabbcbcbcadcbdababaabbbbcacabbaaabbacadbdccdbbcbbcbddcadddbabccdcbdbacdccbabdadacaaddadccccaaaadacbcadacbacaaadadbbddbcbaacdbacaadbdacdbacddcdcbacdcdaddcbbbddbcdcddacdbcbcacbdcadbbcbcadcbdbddaccdbdadccaaaddcdbbabdaaddccddacdacddcddcdccbcccababbcaadcdbacdccaaacdcccadccbbacaaacddcccccbbacbbdcbdbcbcadccbdcbccaddbcadabddccdcdcadbdcdbadacabdcbdbdacdadcdcdcbadabadccbcbbabcbbbacacabcaccbdbdbaacdadabdbdbccabaccdbbcabbcaaabbbcddcbccccddaadaadcdccacdcaabbabcdaddabcccbdbcadaaacbbaacbbcdcdcdcacdccbcaabdaaacbaadcdbcdabdcdabacaabddcabbbacbdacabaddcaadbcadbcddbadacaddabadbddccdbacbbaabacdcacabcacbcbabdbaacbbabcdaadbacbaccadacdadbcddccdbbcaacbadccccdcdabdbdbcadcccbbcbcdcabcdbdbbacaaabccadacaadbaddcbcbacbcccbcdcbaddbbdccabdbbcdccabcbbcaaaacaddcabddcbbcacabbddabbbbdcbadbcdcacabbaadddccadaaabcbbadbbdbccabcbaabdbddaaddddbaccabbdaaddbbaadaacbddadaadccdacacacadaabdbcbcccabcaaddaacdaacabcadaaaddbdacbadaaacdaadaabbbbcdbbddbacdcdcacaaabcbaccdbdbacacdabaddddadcdbccadbcdacadaacacdccbccabdcaccbcadbcbbcdccdbccbdaaddaddbbabbdcabbdbbcbdabbddcdbccbdddcaabccddaddbabddcccbbcddbdaaacbbbdbccddbdbbcbddacdbacabcaaacadbabcbcaddcaababcddaadacaddcbdcbbabdddabcdbdcdcdcddcdaacdccdadcdbdcdabadccbaabdcabbcacbdaccdababacdbcbacbcdcabbddcddbabbcbdccdaccdbdddaabdadadccdbbccbdbbabcddbbbbdcbcbadbdcdbbabbcacdcacbbabcdbbcdacbdbcdbdadcacacbccbddaaadccbddcbbbbdacbbccddadcbdcbcaabbdcabdccdcbbcacccbacaccbcdbdcbcccababdadcabcacdaaacbadbccadaadcabdccddbcdabcacddcdabdadcdbbcdacaaacacbdbccaddcbcbbcaabadacbcbdacccdabdbbdabacabddaabdbacbddccacdbabaccbbdbcbccadcaacdcdacbccaacbbdcbbacaacaababacabbdcbdadbabdaaaaaadbadccadbaaaaaacbaaacdaabaabbdcbdbabacabadbccabaacbbcacadcdaccbaabbbbdcadddcadadadabcbcbccabadaaadcaadcadcaccddbcabbdabdaabccdbacbaadddcabcbababcdbaadadaacdbdbdbcaaddacdadbbbcdadcbdabccdcadadcadbbabbcbaacadcadccbbdddcaccacbcacddccddbcbbdcddbdcddcbdabdcbdaaaacacabdcddbdddbaaabdadbdbbaaaabcdccbbaabaaadabaabcdacbbccdadaacccaaaaadbcacccccaadbddbdcddcbcaabcadddbbcbaccdbcadcacabbcbbbccbaadcbdbccdbcbcdbaaadacaddbbcbbbbbcabdadabcadcddccdcbacabdcdbcbdcadbcdcbbdcaddccdaddddacdcadddbcdcaaccacbdbbdddbdaadaabdbadbcbaaabbadccadcbbbacdadacddaddabbdadcabacdcadddbccadddccdddbcaacadadccdaabcbdcccabbabbdddaaadabddbacabbbdadaacddbdbabbdabdbcadbdbdcaacdccdccbcaacbabbabdbdbbdcbcddcaaadcddcbbbbaddbcdcdaabdacdcdbcbaadadadddaabbcdacacbbcdbcbaccacbacdcdcddcbbdcddabbaaccadabcadccdbcdcdcccdacbdbdcaaccdbdbbacacacabbcdadbcdddabdbccbbdbbbcaaccbcdbbbaaccdbbaadbcdadaccdccacddbdaccbaadacadbccdcaadacdcbddabadabdbbcabaadcbdbcdccacabdadadccabccdabaaaddabbcdccaccbcdbbcaabdbbabaacbcbcdabbbcbbbbbbbdbaddcadcdccbdcbdcaadacbacbdbabdabaadbddbcbdcacacdcaaccabaaabbadbdaabdacdbccdcdabdaccbcbbbaabbccdbaaaaaaaadccdcdbbbbcaccadddbbbaaababdacaddacbcaddacdbdadccabbddcbacabcdddbddaddaaaacabaacdacbdbabadcadbcbabddabdbacabbdbbaccdcaacaaaccbdaaadbddcbbddadddabcbbbbbaacacddaaaaccbdcdabbabadaabbcdbbadddcdabadbbcbbbbabccaaddabbabcabddcdcdccabccaacbadacdcadcddbacdbbadbadabbbcaccabcbbbbaababcadcdcdcdbccccbdbcdccaaabbdaaddaabcaddabbdbbbbcdadbbdcbbdbbbbadabcacbbabcdaddbddbdbcbadcdaccccdcbcbdadbdbaaacccccabbaadcacacdbaadadaccddccbdcdbbaccbbdcdcdbaaadadabcacadbccaddbccbccdcaabbbbcdccdddbccbbdacdccaddaacccdbcbcdcacaacdabdaaacdcadbdddcdcbdabaddbdacccdbcabdacccbcbaccbacbacadccdabbcdbcaaccdbcbbaabdcbcdbdccbacbcacaaaaacbabbdddacbdabbabaadcdacbdabbbbbbbcadcabcbbbcddbcaddadaadbcdbddacdbbbbcbbaaadbdbabcdaaacaadacbaddadbdbbccdaabbdaaaabbdbcdbdbabdbccaabadacccacacccadaccbadddaabcbabcbacdaabaaaabaaddbbadbabcbabcdbccaaccadccdabbdaccabadadccbcdcaddcacddacdcccbbdccdbacaaababbcbdcbaadcabdaaaaccdbabcdcabbdbacabaadbcbcabacbdbcbcadbcadcdcaaaddbbbcdaccdbacbacdccbcaabbacddbacbadaccbccbcacdadccdccbaddddbbdacdbdbabaaddadadcccdddbddcdbbdabcbdadacabccbcaacabdbbdcbcbccdbaabcbbacddcbbaabadbbdcccdccbcdaadccddcadcabbdadccbadacbdccccacbabcdbbdbcabdccdadbcccacaccadadaccbabdababdccdcaaadbbcbcdbddbbbccdcddcccccdacdbbccacdabcdadabacbdcccdbbdddcddbbccaadadacbdccbaaccccddcdbbcddccdcaacacdacccdaddabbcccdbacddaddbadadddabcdaaabaabcaaccabbaabbbcaddbbdbbaacdaabacacccddbddcbbdcccccaddcbbabddccaadabbabbdabdddaabdacbcbbacdddbddddabdcbccbcadaabcaccacdabbbcdcabcadacbdaaabdcdccbbadddadbcadbdbaccaadbdbddbddddaaddcdabbcdcbbbdccadddddbbbcbbbcdbbddbacbdadddadbdcbbaadbadcdbcacabdadcbabcddcaabddbcbacddbacaaaacbaaadccbabdbacccabdcbdaadddccccbdbaacddbbbacdccaabcbdacdbdcbaadccddaddabccbcdadcabcdabbadccadadcaaddbbabaabcddacdcdccadccadbddddddcaaacaaabbadaaccbcadadcdbbabcabbbbdbadacdbacbacacacdaaacbbcccccbadbbccbbbddcbaaaaaddaddcddaddddabcadbdcdacbbbaccdbcbcabaabbbadcaaacaaacabcbbbaaaddbbcdcbaabbcccabdcdbcccabaadccadddcabbbbbadcdcdbaddbacbbbbaaaddaaccbcccbbadbcbaacdacdcddbddacddccdddddcabadabdbcdacabdacaaddaabdcaabbbbacbddccbbabbabcdcadccbadccbcaccbabaaccabaacdbcccddaccccadbddbbbbabbbbdbbcdbdbbbacbbdbcbacadbcdcbcbddbdacbcaccadaadcdbbcddbaaccabbdbbcaabbdbbbbcccccdcdabbaccccaabaaaabbdddcadaacadcabadbbcdaaccdcbcdcabdcbbbbccbbaaacdaabbdabbabcccacbcdaacdcbadaacaadcabbbcccddcdbbbbaaacdadcabcdcabccdcdbababddcaddacdbdbddaaababbddcaddcbbdbbbbcdcbdcdbcdacabdcaccabbbdbaaccbadbdbcdabbaaabbadbbdcadbdddbaaccbcdcadadbcbdaccaabcaadcccdbdcccbdaddddadadbbcddbadaadcbaadcbaaadccadcacbbbabdcaadaabcccabcbbdaaababaaaadabcdabbccbadacbacaaabddbdbddccccbdbdddddcdacdbcbcbccbdacbdaaadcadbaabbacbcaaaaadaccabaccbbbcbbaabcdbabccabddbbbbccbddbddddbcbdcbdaddbdbadbdbacddbabcdcaaddbbaaddcbcbccadcacbcbdbbbcabcadcdbacbddccccadcdababcbdbbaadaacdabdccddccaccbdbbdbbbbbaccbaaacaddddbaaddadbdbcabbcacbbdbaccdbcdbdbbacbabacbbcaacbcbddacddbdcabddcbcdabccdcdbabdbabdccaccacdadccccabdacccaccbabacadbdacccccdcbccabcdbdaabbdcbbcbddccacdbcacdbdadcddadcacabccaabadbbcabadabadcbbdcadadcabbbbbdacaadabdcbcdbcccbbcaadcabcdaadbaddbdbaadcbabbadbcaabbaabadbcccbacdbbcdbdaadcdbadcbacaddddcdadcdaabbbcacabcddbbbabbaaabbcacbdbcddabdacabcdacaccdbbbbdbdacddcccadccddbcbbcccdcadccbddccacaaccbcccaabaadacdacadbdbcdcbbddacdabbdaababdccacacbaaacabbccabacbcccdcabbbbacaacaddbabbddcaccbacbbcddaaaabadaadabcaaadbbddaadcaadbcbddcbbaddccccddacbccbadaabdabbacadbcbaaabdcaacbaacdddadaddaddcdaddaccaaadcbdcabdaddaacaaadabaabdabdaadbdcdababcacadbbdbbdbcbbcdccbdcabbabcdcadadcadcdccdbcbbacabdaccaadacddaabbbcbdacaccdacbdacbbdddadbacbaccbbdbbabddacdbdabdbbdaaaacddccdabbdbbddaadbcdcacabdbdacbddcdbcabdcdccdcbccbcddbccddaacbdaaabdccacdcacabaacabaabcaccabcccddcddcbdbddbaadcbacacbaabdbbbabbabdaabaabadbbadbcdacbcbbbbadcbcaabddcdbabcdcabdbabbccacaaacdbccbbcdaacbddcbddadddcddcbcbddccacaddccaaddbddddaaaaddcacbdbcaaacbdbbdcabbbabbcbbcbaabbcccbbcbadcadaaaddddbcddcadbbbaacbabccacccaadbdcacbabddcccbaccddadaabaddbdccbbcaacccabdcbabdabbbbdbaacbbbbbdbdbcbdbcabbdbcabccabadcdacbadaadaccdaddcaddccddadbddbaaadaccccbdadaaababdcccddaddccdadcaaaabdadaccdbbcabdddbabbaaacaadcaddcddaaaddcdadddbddadababddaacdcdbdaccabbabcdbccdddacdcdaacbbbbbabdcabcadcdabadbdaababadccdcdbddaabdacdbcdbaccbdccacccbcaaacdadaaabdcddabadbbddaddbdbaaadbccdacabdacdbaacbdbcbcabcdbaccacabdbcbccadbbbaddacdccdbbbcbaccddcbddcbabacadacdcbcabdcadcdacbbacadbaaabdbcacdccaddbdacadbbaacdadcdcadbabbadbdadddddbdadaacdcbaadddbaadacddacccbcaabbaaaddcaabadabdcddccbcdbbcccdaabbcbdbdacabdbbccdbdccadaadabdadaacbccacaabbaadccbbddcbcddcbddbccadcdbdbcdbdcbdbaabaadbcdcdaccabaccddaacacdccabdbcdbcacabcabababdbbddcacabdcdaacbaaabbcdbadbcdddbabbbcdcccacbabbaabcaaaccbdbcddadabbcdcacbcdcbdbadccddcaacdbcabbccaabcdaccaabcdadcbcddccdddacaddbdadaaddcbaabdcdcadddbcdcbccdbaaaccbddcdaaadacbadaddcaaaaadbcbbbdccbbdacbadbaacbcdaacbcbacadddaacdbbabdcbadbcdcbbbbddccbaccdcdaabccaaaacabddccdbaabdbcbbaaadbabaacddbcacbbcbdccdbbadbbcacbdcacaababacbaacbbcbdbcacdddabbbbdcaaddcccacabdaddcacdccdaccabccbdaaccacdacccbcbcbcbbcbccbaaabcabdcdbbbcdcccacaddddcddbabacadadadaabdcbbbabdccacaddcdbccadacbaacaddadcabccacbdbabccdabaddbbabacdcdaadddddcdabccbbacaaacdbaccbbaaaacadbaddccadcdaaabbcbcabdaadccbbacbbbadadcadcaaddccbdbbacaaddcacdacdbdabcacbaacacaaaaaaabdcbabadabaccabdddcbaacdbbcbaddccadbbaddbccabcdcadbddbccdddbddccabccaacacadbbdbddcabbadddadadadbdabcaccbcbcdacabbdcbadccacbcbadbbdcbbbcdddabdadaddbabddbabdbbbdadacdabadbdbaadabdcbbcccccabdabddbbacadddbdbbcccddaacaaabcadcdbbdaddabaabaabbbddccbcccabadbbdadcdbcbdcaddaadbadbccdccbaabaabaddcaacabdabbbcadaadccbcabbaabccaacbccdcabcdbabdbcbcdbdccdbbcddcbddadcbbbcbbbabbdcdccabbacbccabcaccbdabdcbbdccbccdbcdbabadaddcbccaaacbadcbccaabbcbaddcacdcacbdbaccabdddbdaccadabdccbbabbcabdadadddbdcbdabbabcddbadcccdbdcbcbaaadbbacacddcbcdcbddcbdddccbadbdcdccbdaabdacdbabbdbadbadbdcbbdaabdbaddbcaddabbcaaabacddacddcbdaddadbbcdccddbaccaacabaddadbbcadbccdbacacaabdaabbbcabbddaadcccbcacdaabaccccccacadcbcabbdcacdddbcadabbdadabcddcbccbabbbbabbadddcddbadbaddcbdbccabadbbbccaddabbbdabdaccdcacdcdcdcdccbcdcbbdcbadbbabdbccbabbadbcbccddcccacdbccbccacbcdacdaddaccbccbdbcccbccddbdacdbdbdcadbbccaabddbccbddccdbddddacabdbabdccabddcccdcdaacdcdcdacdcbcbccdabcdaaccbbdccbccacdcdbbcccbabdccaccbcaadaacacacadcaaaaadaaddacdbbbbbccbcccbcadbcdcbbdcaabadccabbadabddaddccddcdbbcabbccaaaccadadbdcddaabdabbdabcdddccdcdadcadcadaabcacacbbaaadbdcacbaaacbcccddddaabdacbabaaacbbbbacaacdabdaaaddabbabaaccccbbddcdddcccccdadadbdacdabcdabbbbdabbbbdabbddbabcbaaacadadcdcbdbadbcaacdcbccabdbacdbcacadcacdbaabbaabcaadaddcdbbbabdbaaadddaabaaaacbdccbcaacdccbbdcabdddbcaddbcbabbcacbbbabdbdbbbadcccadcacbcacadcbcdbcbdcabbdbacdadabcacacddbadddccacbcbaaccbdadddddcadabaddbcbcdaccacccbaddabbadaabbbacdbccdddbdabddacdacbcbaadbdacbdcbcdbaadadccbcdcaccbdbcadaabbbacbcdbdcacccbbcbdacaadadcbaadccccddbaddcddddabcbbdbaccdcdddcbbcabbbddaddacdbddaabdcdcabcaddbccdccadbddbdbcaababcacbddbcdddadcbdacdccabbccbabbccccabbaacbabaacacaddabbcaabacaaddbacadacccdcbcaaaddccadbacbbccdabbdadbbbcdbcaccbbcaadcdacadaccbdddacabcdccadbbdbcbaabddacaaddaaaccaabbcccabcdbcacabbcacaabbcbbbcaaccbcdadaaabaacdcbddcdcdbbcdbbaadaabcacadbdddcdddcdbbabbadbbbbabdcbbdcaabcbdadccddaabaadbabcbddcbdccabadccbcacddbcbdcbcdcabdcbcdcbdacabbdccadbbcabbccabdbdcdddcaaadcacdadabaacaabaadaddcccabaddbbdacbcbadbddccaadbdcdcbcbaadaacaacbaababcddaaacbbbddaccadcdbdddabdcbdbbcbcadcdacdabbdbaacbdcdddadaabcadababbdbccdbdacdacaabdbbccddcbabdbacbcdaaccaabdcddcacbbdbcdcabaabbcbddcaabdabcbbcdbcccdbbbdbdabadbbcabcbddcacdcddcbcbcbcaadbaaddbbacdcbdbddbacbdbbcaabdacccdadbbdbdbdcdccbaacbbdacccabdbaadddcdbbacadcacaaabaccabaddddbdaddcaadacdcdadbbabaaacacabbabbbdcddbdcbaaabaabcbacbacadabccabbbcdbabdababcacbbbcdccabdbaadbdbaacbbdbbcadadbddacddbdccbdccbbdbcbdcddcbacaadabbcaaddcaacaabdaadaaadabcbaabaacbdddccbdddcdadbabacdabdddccaddbbaddaddadddbbcbcdbacadccacdacacbbacdccbcbcdaccbbbcabbbaddcdbaadddabbdddabbcbabddbccaacabbbbcdcadddabcbcdbaabacabcbbaacddbcabdbabcbcaccacccdcbcabaabaccbccacacddadaddccdbdadcccadbdadcbdaccbdcbaccbabbdaddadbcdcbabcbdbdbbacdabddadaacdadbdbcdbdbbcdbdbdbcdaaccaaadbadbdadcbdcdcaacacbdbaaaaddabbdbacabcbbacddbcabcdcddadcbdddabdacaacddbabbdddabbdaddcabdbdbcaacdadbdcbddbdbaaabadabbdaadcbddcabacddcccbccddcbdaccadbdcccaabacdcdbcbabdcadcdabbccaccdcaadadcdacdbccccaaddcbcbbaacadcdacaddaddacaddacbbcbdcbdbaddbbcbbdbaddcaccbbbbaccdcddaacbdbadcbdadcbdcaaaccccacdbcbaddadcacaaaccdacccbdadcabbcababdcaaaccbdbddcadcdbcdadbbacababdbdbcacbdcddabcdadacaadbcbbabdacabdaccaaaaabbabccdccabcbcdbcbbcbbcbddcbadacdacbdbcdddcbababaddaddaddabcbdcbdcccbcddaacaacbdbdcccabacdbcbddadcdbacadcccbdacabadabbccacccbcaacbdbdbbcacbaabbbcadaaccabbcdcaccddbdbbbdbbbccaaacddaddcaacbdaadbdabbbbaccccadbbbdcdabadcacaaaaabcdbdbadaccadaadcdddadcabadddbcaacabbdbacadcacabcadbccbbdccaadbddcbaaabddaabbdcddcadbcdbdaccadccbbbdaacdddbbccbddadcddbcbcdcdccdddcbdcdddcbabdcccdbcbddaaadbaaadaadcbdbbcbaacdcadddadabcccaadcdcbcacaddbcdadccdbbcddccacbcadbbaacbbaadbadaccdaabbbcaddcdbdbbaaadcdabbabcabdbcbdacdcbaddabbbacddcddcdaacddabadcdddaaccccbdbaadcccabadbacadadaccbcababdddcabcbadccbcbacbdbcbdbbccbbadbcadbadaabcaddcadcdbcccddcbadaaccdcaaccbbdacdaaadcabadccbadcabdddaddcbcadbdadcbbadabbadabddbbdadddbbddcbacaaaaaddcbaccacdacacccdacddcdcbdddbbacdbaadbadbadcbdaabdadabdbdaaaabccdcdbbcbcdbcabcdadacacabadddbbacbadbabaadcbacbdaabcaccbcccbaadccddaacccaaaccadabadbdabcaaacdbdcdbbacbcdabcbabdababadaadaddbacdcbccbdbbacacaacbcbdddbcaacdbcabccddbcdaccacdadcbaadaabacadaaabcddccbdcaadaacccaadddccdadcaaaaacbcccdbacbbcbdaaaaccdbcabbabbbaddaacbbdcdaccdbddbcbaddacadacbdbbdbbdcaaadbcdcddbbddadacbddcbabbaddddacbabdabacdbaacabadabbaadddbdacbddddaacbdcdaaaacdccbcccddbdaddbbabcdbbcdbdbbdcddcccdcbbcaacbbabbbccadddbdbdaacdabdadcaddbabbdadacdbddcdbbcacdcbbadccbcdcaabdcdbabcacacacbdcbbbbaaabdaaacadacdccdbbabadcbbbabacdacddcdbacaadadbbcdddacddcacddadaaaaaadbbdddaccdbabdaaabaddadbddbaaabdbdacdaaababacacdabcdbadbcacbbaabbbaacdadaccdcbccdcdcabcdabbcdabdbdcdcdccdabbdacdadbdcaadddbadccabccaacbdccccacbaddadccabbbadaacdbbabababdbbcdcdbabcdcbcbccabcbddadbaddcbcadddbadacaacdadcdcddadccacbdbccaaccabcccbbadbcdccdbcdbcbcddbdbddbdcbcbcbbacddbdbcbaddcacdcadacaddacacbbaacacdbaabbcdabdddabddbccdbcbcdcbcbcbcbbbbadcbdbadcbcbadddaccccddddddbabdacbdbddcbbdccdcabcbdaddaabbbcacdccbbbacabdcaddacadcbdcaacdabbcadbaaddcdbdcbccdbcbdaddcbdcabcbcaadacaaaacdacdccbbdabbabddaabacbcdcbbbdbdbdabbdcccabcdcdbaacbdddcbccbcbbdadbcbddcdacdcbbbdabcdccbbddacccbbaaccdaabadcabdcbdcbbadbdaaaacdaaaddbbccbacacddcddccabcadbaaccabbabbccddcadaaddcbdccbccdccdcaaaacbbdcbbbbcbbcabddaaacddbbbbabdcaaadbdcbddbcbccdbccbaabaccabcacddddbabbbcbdcabcabcacabbcdbaadccbdabdbdaacddcbaaabdabbdbdcadacbbdaccbacdcacdacccbaaccadcccbcbcbcdbdabbdbcdddddbdbcdbcbdcaadbdddbdcaabbbcadaddbddbacaacbadbddbadadbcaacacddddcdaccabbabcdcbbaddbbaadbbaacacbacacccdcaccbdcddbbcbcadabbababaddbdbdbbdadcccdacdcbbacabacccccdcddbacadabccadacbcadbaccbabdaacdcabcaaabaacbaacdccaccdabbbbbacaccabacdacbacdacaaddcacbcdaadaabadcbadccacdacbccaabbcccaadbbadcbaabacaddccdccbacdcacddbdacdaccbcccdbacadbbdbddbdcaaccabaacbdbaabbaabbdcbdbcbbbddaddaaabbbadcdddbbddaaaccbcbbacdbadbabacaccdabcddbdbcadabcaccbcdbcbdbcbdcabcbabacacabbabacbbdbdbacddacdadadbaaacaacaccbcacdaddaccddddcbbacdbdbdabcbadbdbaaadbbdccccaddbcccdbacdddcddacacbbcccccbcadcabcadbccadccbdddcbaddbbddbaacabadbcdabaaaaabbbbbdacccbbdcacbcaabbabccddbddabbcbdaddcabcdbdbddcdcacbaadbabccdacbbadcabdabcabdaacbcabdbccccbcbdcbbabacdbcdbaaadcdadccbdadddcbcdccdabcaadbabdcaaacbbacaccbcabcdbbababbcddcbdadacdcdbaacaccddbdaabbaaddccbdccbdaabaababbabcdaccbddcbdccadacaddcacdbbbacbabdbadcbdbcdcadbabcabacbbcbacacabbabadcacbbdcdbdaccabaaaaaaadbdbadbadaaaacbaacadcbccadacaacdddbdacbdaccddbadccdbddacbbdcdcbbbaaaacadddccdcdabccaaabcabdadbbdbabbcbbdcddbddcbacdabddacbdaadbbddccacdaaaababaddbcdacdbddbcacbbccadccbcdcabdabaaabddcddbbbdbbabaccccabcbcddccbaddbdddadcbcbabddddaabbbdccbdaaddcabcdcdcaaccaaabccbdddabbabaabaacbbadcacbbaabdccaabdacbdbbcccacddbdbbddacdddaabbbdcaccbcddaabababbbbcbcbbacdaccacabdddbaadbacdbdbcabddddddcbcacbcdbdbabaccccdadbadddacbbdacacddbadddcbabbabcbdadbccbddbdbaaabccdbcdddcaddbccdbdabccadcddcbadacbbbdbcacbbbabdcadbacbcdbcbacbcbbdaaadaacbaccdaaaddacacdcbbbdacaaddccbadcbbaaacccdcbdccdacbccdbbccbccdbbddbbbcdcababdacdaddaaaababaabbbacaabdddbcbcbbdcacccdbabccaadbabaaaadbdccbdaadadbdaacccddcdabacdbcdbbccabadbbaadadbcaabcbbbcabbbaaabdbacbdbbdbdbdddadcbacccadccaaddadcadaadbbdbaacbadcddcbbccadcddbcaadadadcbcdaddbbbaddbacdaacdddbcccbcbcddbcdddbcaddabadcbddcddadadadcbbadcdcdbdcbbdcbcccccccdcbabccacddcbddbbaaadcbabcbbbadaabcccbcbbcaadcbdcdabbabddcadcadcadbcccabcdcbaadccaabcadbabdbddadcabcaccbbaaabdbdcbabcacadacdcdbcbcabdcdaccdbccbbdcabaccacbccabbdccbdcccdcabbcdcbcbcdcabdcccaabadbddabacbabaaddbdcdcbbbcccbccdaaacbccddcbbabccbaadccacacbdcddddbbbabadaccbaaddacbadcbadacabdaccbaaccccbaaccdbabcddbcacaddcdbcadbdbacadabdbacacdddcdbacdcaaaabbccdcccadaddcccdbbbaabcabbbdbabbcbbaababbcbacbabddcaddaddbbbbadcbcbbcdadbcaabdddbdbbcadaddcddabcdbdcabadabaddcbccaaccacabdcaadcbbadddccbdbbbbccbcdbdacbcaacbcdbdcabbdadcdccddcabbbcabdadddadccabacdaabcdabacddbcdcdbdbcdcaaaabdbbbcdaadadccacaaddcddcaadcccccdccbdbacccaddabdbdcddabccbcabaadcaadcbabdaadbbdabdcbcdccdbdcabcddcadabdddbdddccbcddcdaccbcbaabcccbdcbabbdccadadadbaabacabdccdaacbbaccbcbbacbcbcadbdbabacdcaabdbbcdaddcdcabbaddcdaddccaadacdbbcbbdddbdbdcbddbccaaaddddccdadcaacbbdbdcccaacaccaabcbcdacadcccbadcddbbcbbcdbccaddcadaaccaaabdabcadddacbbdacbbdbadcdcddabdabdcbcabacaacabadbbcdacbdccadabcddcdaacbbbcdcdbbdddacdababcacddaaabaacacaaccdddadaacbcbdbdbdaddabcddaddbdaadbbdadcdcdcbcaaccdcddcadadababdbcadbdbbaccabbaacbccdcbcbaddbcdccccdbaacaadddaacbcacdbccacaaabdaaddaaccadcdaaabaccbabbadabdcccbadbbddbdbcbdbcbcabbababccdadbcdbaccbadcaacddcabdbaddbcbbadaabbdcbcdbcdaaababdddbcbbbaadbdabaddadacadbbabaacbcbbabbbbcbbccbcacccbbabdbacabbabadabadadbabbbdcccaacaddbaccbabcdbcdabbbcbbcbcbadaadcbdacbcadcbccbbdcbcdcccbdbaadaddcbbddabdadbbbccdbcabdddcdcbcdabcbdcdcacbdabdccbacddbcabadcabddbdaadbdabaadaadbdddccbbcaddadcbacbadcabbcbbbbaaabbdbbababcbbddcdbacbddadcabccbcaccdabcbbdbaddcdbddbdacaadcbaccdbadacdbdaaabaaacacaaaaabaccbcdacbdcbaaacbaacabdbdcadacdbcdaacbbbdaadcbaadbaccccabacabdccbacadadcababaaacbadccdddcdddaaadcbadcbaaaadabbbdccaabbbaacadacaabdcababaadbbcddababcdaddbdaccbccadcbadbdadbccdbaaacacdbbacabcbcaaacacabbcdbaaaadbddbcdcadcbccccbdacadcaccaccbaabddadbaacacccaaadacbbcdabdaacdcbcabcdaadabddacaddababbdbddbabccaabccbcddaacddcaadadacdaddadbadaacccbcaddbddaabbdcdadbacbaadbaccacaadcdcbccdbdbdcadadaaacaabddadcbbabcbbaaaccacbcabdddbbabdcbbdbcbadacacbbddbcabacdadabdcdcabadbbcacdbcbcaacdcdbccbbbcbababbbbadcbccbdbccacbddacbbdacbcadacaccdbbcabadcbdaccaacccddadcbbaacaacdadcbcbacbdabbcabbdcbbbacccddbaabcbbbcbbdaccadbadbacaaaabbacadabacbcdccadcadcbbcaacbbacdcaaddddbdcaddddbccabcbbcdcbbacbcbcadbddcccadbadbcdadaaabbcbddacbaabbcbabdacdababbdbdabdcaaacadddbbbaddbdccdbabdadbcaabdbbddabaadaddddbbbabcdcdccabaaaaccdadadcbbadcdadaacdbadaddbadadaccbdacabdacdcbabccdbdbddbaadcaaaaabcbbbdaacccbacbdaddbbdbcbccabdadcccdddbabaddbadbcddbddaabbdbddcadbbcddcbcabcbcaaaadcdbcadaaaddcdaabcccbaabcccabababbbbdaaccaadddbddbdccacbcdbcabcccaccdccaabbddacadcbabbcdbadaacbbcacdcbabcaacdacccaccacccddbdadbcadadaccbccbbddaaddcbbcdccbbaaacbdacaacbbcddaccbdcdcbdcdacacccacbacddaddcadccdbdabcaccaababaababcdabcbcbbcdaadcdbabbcdbdbdbcdbdadaddcabaddccadbaddcdbabbddcaabcdadadbbcaddbdadcbbccdbbabbdbdbdccaadabcbdabaccdddbadbdbaabcabcadbaaaacdbdadabdddbdbdccacddbaadcbacabddaddacacdcacdcdcbbabadaacacbdccdbccacdcaaddcdccabacadbcdddcaaabdbaccabbaaaabbbdcaaacbabbaaaabcbabbbaabddbcaaddcabbddbccdbcaaddcbdabadbdcdbbadaccbbbdaacacddbdcaccaddadaadcdacdcdbbaabbdccbddbcbcaddaadadcbadaadddbcdabcacccbadabbdbadadbbbabbcdbaababddaacccdcdbdacdaaacbdabcbccabcadddadaddcbcdcaabadacdcabbbababbdbdbddadadcddcbdcbdbbaabbbbabdaddccdacaddabcdbddadcbaaacbcaacdbaccaccacbcacaadadaaabdbabdcbabadccdbbcaccadddccaadacabcaabcadbcdbdabdccdcaddbacadadcbcabadcdadbdbadbadcaaccaaabcabdcacacbabbaacbadddadccacdadcdadccddcacccbadbdcaabbbbbaabdabcdcbdcccabcccacbdbaacdbbbadcbabaddcddbddadacabdabcdadbbcbcbdbdbdacbabdcaccacaccbcdddccbaacacbbbaaaaccdcacccaacabcaaaddabcdbcbbbbcdabbcaaddccbbcacdaaccbcbccddbabdddabaababddababdbcdadacdbcabcccacbbbabdddcdccdcccbbbccdcccdcaabdbbddcadcccacbdcdddbddadbaccbcbcabbbabbdbdcdcdabcdacbbdadbcbcddabdbbbbbdbdabacbdccdcacabcbbbbccabbdacaadbdbbacddacdbdabbcaccacdbbcbbbdddacadabdbdbcaaadacbacbdabacdaaaadccaccdadbcdccdbbaaacbcbaabaddcdaaadacadcdddbcbdabbcccbdcdabccadbcabccdbbbabcabdabacbcdddbbccbbbcbdcbabddbddbddaadbbdddccbcabcdcdcddaccbbcbbbcadccbbcdbbaddabcdcccbbcbaddabddbcddccccddbdacadbbaaccabdacaaabdaadabdbabbadadbaccdddcaababacdbacbacbbcbbaaaaacaccbadcccbadddaddcbdaacbbcddabcddacdcdccdddaaaabddbbaacaadabaababcbaacadcdacacdabbbcbddcdcbbdcdbbbadcbdcddcabdcaccdabacccbdcbbdddaccddacccbdadaacdccccdadcbdccbddcababcaabdbcbbddabdddadccadbcbddccdcbacbcbbadbcdbddcccbadbabdbbdcaaaccbaddcacacdcdabbcdacdbaacdcaadbdabccdcbcbdcbaabadbacbbabbbcdddcbdbbcabbccabacddaaabcabbbdbddcbcddddbdbbddcbdddddccbaaacdadddbcacbdbcbdbbcdcbcaacdaccbbcbbddabcbadbdadbacadcdcbbcaaccabadcbddbcdbddcdbdaccbddccddaddaadcbdcaadccadbdabbbdddcccbbdaadbbaaccabbdddccdcbcdacadcaddacabdadbbcdbbbbabacacdcabbcbdcbdacdbccaabcaaddddbdbbacdbbbcbbddccdbbacdbbadbadaabacadcdbbacdccbdccdcdabadbbcaabddadccbdddcddcbadaddcbaabdbcdbcadabdbdcbadcadbbbdcaadbbbcaaaaacacabdbabcacbccabbdbdddbaadcdadbbcbbbacbbcadccbaaabdaaaccddcdccadbbbdbcddbdcddbabcabcabdcdcdbdcaaddabdcabbdddccddaabaacbbdccccbaaddbdcabbabbacabdadabdbbcbcdadcddbacabcdbaaccbbbdbbaacabbbcbbcdbdbabcdcbdaabaacaccaccacbaddadabaaadddacbacccaacbbabbdacbcbadbaabdbdcdaaaadbddabcbadaadbacabaabddcbbadbbdcaaadadcbcdbcccbdcbabbcbbaadbdacdccdbdbabbbddcadacacdbdadccdddcdcdbccdabbbcadddbcddbbcbbbdcbaaddbbaddddaabdbacdbbadbcacbddcbbdabcdbacddaaabcdcccdccddbdcdddaccacbdccadcbbbdbddbbaccdcabaadddbbbbcdacccacdcdaadadabbbbbdacddcbcbabcbacbaddcacacabcadadcdaadaddccaaadcbbacbdacbbcddcdcbcdcbbdbccaccdddccacaaabbdccdaddbbabbaaaabbdbdcbcddacadaccacabdaccdabacbbaabcccaadccbdbcadbcdaadadadcdaddaddddcacaaccadbbdacbadddacaddbaccccadbadaccdaddddbabcbdaccdbbbdccbcbdacaadcdbdcccbaacbddabdcccdcaaabddabcdbbbddddacabccaacadaacaabdabbdcbacaaaccdcdcadaadbaaabbacbcccbbabdbbcaccaabbbcdacacdddbbddadaaaadccbbaaabcadbbaaddbbbaccdbcbcbccdaabbaddbbadbdabccaddbcaddcccdbdbbcdccddbaadbccddbcbabbdcbbadbbcaacaaddadacacadcdcababddaabdbacadbcbdbdacdcaaccdadbbbbbabdbabaccbbdabacbbcdbcbcaadbdccdaccdacccdddacaaaaddaadcdabdbbccbcbbbdcaacccdcbcdddcabdbdccccddcbcbabbbbbbdcdacbdccbaccbabdadacadbdcdacbdacdbbcadbbbabdddbcadaaabcaaaabbbabdadbaabbcbdcdcbcbadcbccbacdcbaccaabcbcdaaadcbcbdbbbcbcdabcaacccadccbddccbbdbddbacadacaacaaadcacabbabdcbaaccbbcbacbbdcddacdabadcacbbcdccccbbaddbaadcabdaddbbbddcadddadcbcabdbaaadbadabbdccdabdddcbabbcacccbddacddaabbdbbdddadbcabbccabcddadbadadcabddcdbabcccbcbddabcdabcacbbbabcccccbdcdadacbbddbaddabbccdbbcdcbddbaddbbdcadddaccacaddcbcdbdaaabbabcbbadbccddcdcdbccddbbbabddbcadaaabdddcacbbacacbbdadacacbdcacdbacdccdbcbcabddabbcdabdabdccabacbccdddadccccacbcabbccacacaadcbacaddaccbbbabdbcacbcaabdddcbdaccccabaadabbcacdcaddbdbdbcacdabcdcdaccbdacadccbaadcadccdaacbdbddbdbddadabacadabbcaacccccccaddacadcaaddddaaadccbbbcaddadbdacdbaabddbaaabdcacdabddbcbdabdcbabacdcadbbaacacdbdcdccdbdaadbbabdcbbdadaddcbaccaaadadaddabcaabdbccaccacbaaccbaddcaabcdccdcdbaacdbcdacdcddbdcdadbddadaaaddaadbacdbbabbabacacbdbcabbdcaaccbdccccbcbbddcdadcadbcbbdadacbbdddaabdcbdacbaccaabccbdaaacbdccadbacdadacadbcadbacabdbabccaddcadbabbcabcdbabddbcadbbadaacddcdbcbdccbbaccbccdabacabcbcbabdcdcdbaaaabaacdaddbbddcbdcabbdabbaabcadabdbcabacacdadacaabbddddcdadaaaaabccdbcbadcdacccacccccddbbabcbcaaadbcdaccaaacdddcadaccbaadabdcdbabbdbcadcadddbccdcabdccaaddcacadbbabdcaabdbbccbdbcbabbbbacbdaccbabbbbdacccdbabcadbadbdcabcbbbbcbacdcabcdaacdbcadabbdddbddbadbdcdbccbaadcaabbbccddbcdbacaddcadcadccccccbbcccdabcdccbbccdcbbbcacdcabadabdcdabcaaacaabaaabccdcadaaddbadabacbaccaddbdcdacbdbdcdbbaacbcdccdcbcbacaaddaccbbacadbabcdaddbcbbdcbdbdbcddbbcbbdbacbccbdbaaadcdbabdabbbadddbbbbabaabaaacbdadccababdbbddbbabdacaccaaccbaccdaaaabcbabbbaddaacbbbcabadcdacddaddbbbacdcdbcdbbadbccbddcaacaabadddddbccbcdadcababaccbcbadccdddcacdccadaccdbadbaabbaddcdddbdcbadbbacaabbdddddcbbddcadccdcadbcbacbadadbadcbccbdddcbacacbccdbbadcbccbcadabdcbdbcdabaadabbadbbbaababdccbdbcbcbcadbbccdbbadcdbacaaaaaaaaabdcabdaddbdddaacacdabdbdcdabcdddccdcbdaccbaddbabcdcaccadbcbbcccaddbacbdbaaccacdaddcacdcdcbbccacbbbbbdbbacbadccacbaabcaccbccbcddadbdaaabdddcbabdaddcbbbbacbdbabcabbbacadababacaaddccacaaadcdadcaacbbcbbdbcccadbacadddbbdadadacbccdcadddbcdbccbcdcdaccccabadacbaddcdbacbcdbaccbdbcddccaddbddddbdbacbddddaadbcbacbcdadcdaaddddacbbbdbcddbdcbcdcddaadadaaababbdadcababdabcdbcbdbdbbcdbacccdbdadddbbbbbdbbaddacbbcccdcacbdabbabababbabdccccbbcaabdcaddddddcabbcccdabadddbddaaacddbbdaadccddcddadaadabbbaaaaddcadcabbcdcdccdbbbcaddcccdcdcdacddacdcdabbcdbbbbccccddccdcbdbdacadccdbaaaddaddcbdccbccacbbcdcbdcaabcbdbbbaaabcbbacdcbcaaacccbabadbcbdbcdaaaacddbbacddbbaadcbddccababcaabddbdacbcbdddbbcaddadaddbcadacaabacacdbcdacabdbcdddbcbdcbbdadababccbdbcdabadacabcddddababccbacbcacdcadbdbbabcdbacadcbcbcddadbdbccccaaaddbbccdabbbcaacdbabbdbdbdbabddcaaaaddaaddcaabcdbcaccccbbcbcbbbacabbcabcadaacdcbdabdbdddbdaaadbdacabdcdddcdddbdbaaabbbaddbcbdcddbbdbccbcdadbcaabbaaddaabccaababbcdbcabbdbcaaabbbabacccacbaabadacaadbbdabbbddddbbacaccaadddbbabadaddcbabdabddbccdadbbcccddcbdabacdcdddaababaddbcaacbaabdccccccdccdabdbdcbadcaabcdabbdcaacabbbcbadcadbbbabacbcaadcaddaddcddbbbabdabbbdcbdccbcadabbdcddcdadcdaabdabadbbccdaddbabdcaaacbcabbabbdaabbbdabadbdabdcadbcaddcdcdabdaabdbcdabacabdaadaccdabacbcccbdbbbbaabdadcaababcbcdbccbbabdabdbbabdadddabacddbcacbacddcaacbccbacdcbbbabdbacdcabaddcaacdabbbaaadadbcacbbbcdcdbdbabdabcdcccadaccdaaabcdaddadbddbdcbadadbbacbbddccdcbadbbdacacbbcdbaaaabdcbbaabdcdabaccbaaddcaabbbbdcbbacbdabdcddbdaaadddcaaddcdbccbcabacdbcdabddcabcdcbbdbdaacabaadabbadbccbbdacdcddddadddbdbdddccbadbcbbcdddacdcbdbabbdaacdbcddcabdbacabcbbccdcdcababdacdabbddccadacabcabdcdcacddacabacdcbbdddaacdbacbdddccddbabbacddaaabdbacadbcddbcdaaaadbdbcaabbbdcddbbdbdacbbdabbdcadadacbacaabcdaccabcadbabbdccddddcbccbccdddaccbaccacacadddcaabaaaddababdaacacbcddbbdbabddccbcaddccaacdaadbbadabccdcaccadaaaaabbaddbdcccdabbdabcbacaadaacbbbbddabccdbcccacbdacddbabacbcacabdabaabbddbbdcdbbdbbbaabccddacbdacbdcdbddcdcdadcbbabdbadcbbcaadccabcbcddadbdbccabccbbcbdaddbadacbbcaadccdaaacbcabbbcbcbcbccbcbaaaacabcabbcdcbbadaabccacccadcaccadadabdadcaaccdddccadbddccabdcdbdaaabacdacbbacbacdbbbcdabdddaccbdaacbbbabbcddaabdbbcacabddabbacabdacdddccbabbabbbcaabdccccdcbcadbbcaababcdbcabccdcacdaddddddcabbdcadbcaadbbabcdcadbbcbacccdddbaaccdbcaadddbcdcdcbdcaaabbadbaabcbbcdcaaadbacddaadcdcadcdabbbabccbbddacacdbbcbaaccdccacdbaaccbbabadcbabbbacdacabcaaccdddccababdbcddaddbbaabcbbcaabadcbaaaddcaabacbbcabcdbbbabbcbdcbbcddcdbabddccdacaadaacaddaccaddcdaaaadcbccbbccacbbbadcbbdddddacaaacddaadbaccbbaabbbdcbaaddbabcdbabadbdbbdcbcdccddcddadacbadcaababbcbbdddbbcdacacdbbaadcbbccabdadbaccddcbaccadbcbccbaccdddbdbccaddabadddcabdbccdccabaccadccaccbbdacbbbbbcdadddbaddacddaddcabadaabbcacbcdabddbaaabcdcacadaddacbadcbbcdcabbbddbbacdcdddccdddcbaadbcadcaaabbcaacbbabadadacbbbdacbbcaccaabccdaaacccbbaadbaadbabbdcacbcbabbdccdcdcaabdabddaccabaaacdacacbcbdbcdcacdaaadcaadabbcabbcabdbadbbaaaaaabbbbdacaabaccacabdbadaaadcbdbcacacbabdccacdbddbcbdcddbddcddaacaacddcacaddbbbcbdbcaadaacbdacaddcdbacdaadcbcdbcbcaddbbccadbbbccacbbcddbbdbcbacabcccbbabcaabaccdcadaaaaccabcddbccbabadbdbdaabdcbcbcbaccacdacaaacaaacadbdccdaabcbcbbcbdaccbcbbdccbdabbcccabbdcacccabdcbbababdabadbabcbbdacdbcdadbcbcbaacaddbacccbbaabdcbabbddacadcddbbadccbbbadbcbadcadbddbabcbdbadcbacabdadbaacaaadbcaccdddddababbbdbcbadbccbbbacaadbaaabcdadccbbacdccbdbbdccdbaadabbcacbbbcdaabcbdccabcbbccccccbbaddccdcbabccbbcdbbdccbadcbdbbdbdccbaaddbadbacabdbbdbacdbbaaabbcdacabbcabdcaabaababadaacdabdaddbcaacdaccadcddcbccababdccbabdbaacdacaabcccadcadbbaacbabccbcadacccadcbadddbabdbcbbdaaaaaadbccdbbddbcbcdabccadbdbccdacbdbdcbdcacbcacadbdbdbbbdcabbaacaabddabadbddccdbccadacbaddbdbdacaddabcaadcbdbcbcbbcaacaacbdadacdbbcabdabdbbabdabdbcacccbdaaccdccacbababcbbddbbbbabdacdccbdcaddbcadaadadccbbbbdbcdcdcddbbdbbcabaacdbacadbaadbdacadaabbaaabcbbccdbabdbdbbdaacacaabacaaccdaddbddadcccbababcbdbbbccddbccbacababbcaacaacdaabdbcdaaccacabbbdcbbbcaaacdbdbddbbccbaadbdddbcabdcaaaddbbbcbcbcbcbdbdbbbccacbabcdbcdabcbaacddbddcdbddabbcbddccaddcbbcdadacbbadacbdddabbaccbadcbdaacbabaabadbcadccaaacbacdacddbddddacadddcdaabaddccdbaaccccbdcdbccbdbcdbcacbaacdbaccbbddcdabcbaaddabaacdbccadcddcdaadcdcdbaccadbdbcbabcbaaabbbbcabbddaadcbddcdccdbabddddbdcaacccddbcdcacaddddaccacadbcddbdbbbdccdccdcadadbacbcdcbcdcbcdadcbbbccacddddabccadacbbaaabadcbcbaaddbdaadacdddbccccbcbcddaaaccdacadccbcadddccdabbaaaddddcbcddbdbcacadcdddacdacdbcbdccbaadbcbcbcddccaddacbddcdcbdcdcbaccdbabdabcadbcbcbcadcddadbabbbbbdabdaddcddddccbbadccdcdcaaddbbdddaccddabcbaacbbaaddcbbdadacccdadddcaacadbcbaccdcdcbdacbcdbacccbbddbdbcabaabaaccdcbabbdddababccabacbbacdabcddbacdbbacbbabdddcadcdbcbcbcbdbdccbacadaddbdadddbbbcddbccbabbdcaddbcbbacbdadbaddccdbcaacdbacaccbcabdadadadccbaaadbccddacdcccdbaacabdcadabacaabcabcdadacccabacadabdaddbbbbbddaaabcbcbaacbbdbddadbaddaadaccdacadbbbabccacadddddabaaaabbbcacddcdacaaaacccaabbdabbbacbabbddbaddbdcdbcabbdbdcbbccbddbddbdcddadadcbaadcaadbbcbcbdcbaadbbbbddccbdcaabccdbbdbbbabbadcbdcccadadaddcdccbdbaddabcbcccacabdbdbdadcccaadabadacaacccddbddbdbdbbbbadabbacbabaddbbbbbbdbcbabbcdaccdddacababadbabaccbcadbcddadacbddcdaccbdbabbdcbaccadccdabdadaddcdcacabbbcdacbcbbdbcdadcccadacdcdaddabcabcdcbbaadddbacbbbdcdadacabdcbdacbddaadccdabcaaadddccdbdbccacbccbacbdabccabcacdcbddcaccabbdaacddbcbbdabccacbbbcdaadbcdbbddbcbcbbaccaacbbcaddcbcadddbbbacccddbcddacaaacccbbcbcbabdbcbcdababcbcccddcdadcdacaacaccadcbbbacddcbacabbdabdacbbcacddacadadbbbdaccddcbcaacddccbdddbacabdbddbccccdcacacccdccbccacddbbdaddacddaabaabbbaddcdccabbaadacabbbbccddcbbbcddcdabddbbaaadcbbdadcdccbacaccbaacabaaccaaaccccdccccacadddbbcbaaccdbddddccacdcdcbbdbabdacabcbddcbdabaacdcddacddadcdbacabbacdcdddaddbcadbdbacccabddcbbcabdbdcdccbaddcadbdabbccaacaccaadccbaddbcdbcaabdbbbacbdadcbdbcbbadcadcbdadcbbcbdbcbaddaacdddadcccabddcdcccbbadbbaaabcaababbabdbdbdaadcacabdabccbabddaadbcabdddcdbccdccbcbdacbbccdbaacacadadbbcbddcadcbacbccdacbbacaabbcddcbaddacdddbacbacccbcdacbdcdccdbcdacbdbdccbcbdacbbabbddddadabcaabaacdadacaddddaaaddddcaaaadadccdcaadcdcacbdcaacdddccbdddbddccbdcddacddaddbcadacbcbbcabbcaaaaadbdbddbccdadabaabcbcaadcbababaccdcacabbdcabcbddcdcbccdddabbcaadababbcdcddbbddcdbadddcccbdacacdcddacdabbcccbbbcaaaadcaadbdddabdbdccccababdddcdadccbcdbcdaabcbacdccbbabbaccacdddadcdbcdacccbcabaacbabccbacccbddababaddababcccddbabaabcadbccccbdbbbabbddcbbddcdbdbcdaddbabccddcbadbacaadabccdabcadcdbcdcacaacdbaacdcbdbabbacdcacbcabdbbddccdbccacacabacbbaaaabaadabacbdcacdbbbbbabdccaaaccabadbacadccdbbdcbdbbcbccbcbccdddbbbbdaacbbdbcdcbacadaacbadaabaacbacbaacaddcddcccbcabdaacabbcddbbabdcccddaadabbabcacdddaddaddddcbccacadcacbbcdabbdacbaabacadbcbabdabaabbcdaddbabdacabdccdddadbcadabbdacbbbabbcbcbbddbaabcccaaccbbcdbbdaadbbbdbbddacaddacabacbcacaadbadaaacaacbbaddbcdaaadaabbbdadbdbaddcdbddcdbcddababbdabbccdacbacdaddcdcbbbbddddacbacacadacddcddcbcdabaccbcaacdddccccbdcccaabbbdddaadbbdbdaccccacbdbcaccdacbabdbdccbdcbcaddccdadacacdbacbdacbcacadbddcbdccbbdcbadadccadadcabdbbbabcbdbdabbbccabbbcadacdbddbdbbddcbacbbddaddbbbcabaccbabaaabbbcdddabbbbdddccccbdbdcccaddadbbdbcadcbbccaabcdcccccddcabbabbaccbdddabacdacbcacababbcccabdbcbdbbbaddcacacddbadcbbdddbdcabdcaacabdcaddaaaaccaacadacbaaccaddcaacbadbadbaddbdadacdcdcadacddbbddaccaacccccabdbdbcadcbdcaccaacbcbdddcbaacaacbbdbbcdcabdcccadcdcacdddbcdbbadbbdcadabddabdddbaddacaabddbcdcacadccaacbacbbccbdcbaaadddbaaabadcbaadcacbbadbadccbdcaaadcabcbaabbcadacbdaacccbdcbaacdcccabdccdcbabaacddccaccbcbcdccaadccbbabdddbdcaaacbcdcbcbacaddbaddddadddadcbccbcbcbdcccbdcbdcdacadaabddbdabbabdbdccbbcbacdcbabacacacacdbdcbaadbbddddcbacababbcaabaadddbaadccacdccaccdcbdbdadbbadbaddbbdcabacbaccbcdbdcbbccccacbddbacbadaabdcdbcaabcbccaccaccdcacddaadbbaabcdbccdadabccdbcdbaabdbcbabddabcbdacbcdadabaacabbbddddacbadcbbbccbbbccacccaabbbabadbccabdccccbadbbcadddcbdacaaaaadcbaacdbabbcadbcaddcababbddbbbabdddbabbbbabbacbcddacadddcbabdadaaccaacabbbcbcbbccbbbaaccddddbdcccdcdaddbadcddddabccbcdbccdbdbcaccbdcabdbbdaadabbbdcaaccdcaddddcadccaddbaaadcabdbbdacadadbcbccbabddcdddbdbacddadadbbabadcccdbccacadcadbcdbdbcabadacadcdcabddaddccdddbbaccccddbbabdddacbdaacbdcdacccbaadcbdbcadcaaadbacabdabdadbaaacddacbaadddcadccddbbabcadcbaddbcabbddbdcadcacbaddbbbcbddadccadcdcbcdbdddbbdcdbdaaababcadddcabaabcbcadccabbbabbadabaadaddadaccdabdcaaadbbdabbdcbaddacbabbcdcbaaccbabccbccddaacbccdcbabaccadccacbcddbadbbacbabdcdddacaacbbbadccbccdabcddbddcbdacbbbadbdbdddcdbaadbbdbdcccdbbbbbddaaaccadbbbcdadcaaccaadadbcbbcaabdccbbadbbdbbdbdcacbbcaddabddabbcadcabaccaccccaddacccdccbabcdcadbcadbdbbbdbdaabdcaaccccddccabddccdccddbaddacbbcddbdcbcabcbcbadddddbcdbddbcbcabbcacccacbbadccbddbdcbcaacdacdbbcccdcadddbcacabdbcdbadccdabccdacdabccbccccabaabcddcddcdbdcdbcccadaaddadcdcbbbaadbcbacdccbcbbaaaacdbabcdacdaccbdbabbadcbcabbcbcdbbccbbbbabdcdcbccdbddbbaacdbcacbbacddabadaabcdbdaddcacacaabccbddcbaddcabdaadabdccbcbcaddabdcadaabcdcbdabbbbcdcabbadaaabcaccdbbabdcccbdcccccaaabbababbdcbadcacdccdadbdcbaddcbddabbbaccccdcdaccbcdbbcacccbcbcbdaddccabaadbddddbcdbdbcadccbaabcbcaabaaabacbcbccbaadbcbcabaccbdddcabaabdacbcdbcbbdacdbddbdcccbdbdaababaabbbbdbdaacaabbdbaddbbaacddcbcccccaabccbabbaadabccdddccaccddbbaabbbdacdccaadcbdbdccacbbcdadabdcddbadabdbcdabccabbaaaabbdbbcbcdccaabaadadbccbaaadaaddacccacbcaacacaacaddacabcccbababbddbcabbadbdbcbbddacadaabacacbaadbaaacccddcabbccbccaabbdacdbbabbadbadadcdbbbdbddabdbcdbbbccacbdabddaadcaddaccabdacacccdcabcdddaadbabcdcacaabbbcabcdddbccaaccacdcaccadcabdddddbccdbcdaacdccbdcbdadddadacdbabcababdbdabaadbcbcdcbaabbbadabdcaacdaadbbaddbbbcbdcaabdbabddddddacaddbabdabdccaaabdbbabaaacbdbdcaacbcccbddaabcdbcdcbccaaadbadacdccbddcbccbdccccdadccbcaadacaacdbbadabdddcddcbdcdaaaadbbdccbabccbcdbacaabbdadadabdabbabadacbdbdaddccbddccbaadbbddbbcaaaddcaaadbdbabcbbbbadbddccccdaaabccbacddbbdbcbbdcddccaaaddabbaddcbbabdbdadbabddbcbcaadcabacababdaabcaadaddccbbabcaadbbbcabdcdacbbcbcddabbdcaccadabdcbbadcaacdbdaacdbaddcdcabbbdccddbbbdabdcddccbbdadaaabbaccbadcdabaaacbbddbcbadcddbbbcaddaabcadbddabddcbabbdabbddaaccacbbbdbbdacbaadbcbacbacbbbacacaabdcccddcbcbabbbbbcbbcddbcccadacadadcaccbcdaaccdccaddbabccaddbacaddaadddbbcabacddbdbcccccccdcdadcccacbabdaacacacabcbbbdadbaddaadacdcaadbbdadabaaaabdadacddcdddbbacadddbcdddcadccabccdcaccdcbbcbcaabaccadcbdbaccdabbacdcadabaccddcabbbbaaaccaacddcadaaccadddddccbdbcbcdaaaaacacbbcacabbaddddbdaaddadbbacbbaadadbccbccdacbabacbabddcdcaabaaddccadaacdbcacdabcdccdcadcaacabcaddbddbcbacdabcccdddcccabbcbbdbbbbbbaaabccbdabccdabdddbdabaababdcacbcddbbbadbacbbccadbdbacbabdbdccdcabbbacadcacbdbdbacababdddabcddadcbcdaaadcddcbbcbbbbbdadbcabdbcccabaccababdbbcaadbccdbadbccaabcbadbddcaabccbcdbbccaaccabcccddcbccbdcabbdcbcddbbaddbaacccaaddababbaacbcbbacdccbadcbbbdbbaccbcdbddacaacaacaddcbadccabadbbbcddaabbacbbbddaccbbbdcddccccacccdabccdaabdccbacdcddcabbbabddacccaccdadbbadbdcaadbadacbadddbaddaccadbadaaaddbdbdbdcabcdbdacdcacddadddbabddcaccdddabdbacbadacbcccacdddddabaadccbcadaacddbadacaacccbcaabaaccddccbadadadaabdbcbbaccbaadcdbcbbcdbbdabaadcdccddbccddbadbaaaacbcbcbdaacdacbdcacdacdacdccbdbbcdbdccddbddbdadbbdccbccdabdbbdcdadbbcbbcbdcadcdaabadddcdbdadaaadbcdaccaddbbdccbabaccaddcacacdcabbaabcbdddcddddbbdabcbadbcabbbdadbddabcacdcdaaccdbdbdbaddccdcdccaccbcbdcbccbaabbcdabaabccacbccdaccccbaabdcdbbadddbcaaddacdcdddbcbbdcdaddcbbdcbbaddcaaccdaddaacabbbbcabcdccadddcaacccaabacbaaaccbcbadcabdcadabbacbbcdbbdccdddabbdaacabbbcbaacacdcdadaddabaccaaadacadcdddcaaddcbccaddbdcabdcbccabbccbccbcdabddbbbbcddcdaabadbbcababccbcbbbdddbaccaadcdadcacddbdccbbcbcbcddbdcabdccddaddcbadcbcaadadddabccdbcccdadbadbcacdcaaaaababadacddddbbabbdbbcbbaadbbaacbadaaccbbdaadbadbabbccadbdbdbdbcdbabdaaababbcadcbaadcabbbdababccdcacabdddaadabbbaacdddbbacbcbdcaadadaadbdddbdcdbcbbddbaccddbdaaaabacbcaaddacccabddadbacdacadabdacddcdbbdccadabdbbbdaabbbbaadbcdcbbacccabccdaabbbbabdadabdbdbcaabbbdabadcccdabcdddbcbadaaaacccacbccdadbdbbbbadacbbdbdaacdcdaccbddbbadcccaddaadbcadadccbcdcdbbcbacdddcbbcdbabaabccccabdcdbbadcdaaddbabcabbacdbccbcbaababcacbdccbabcabcbdbcdaccbadccdbdcbbbbbbccaddaacbccdbbccadcccdcbaccddaddddbaccdaccbccacccabccddddbccabcdcdacbdaacdbbaadabbacaacbbadddacdbacacbdabdbabbbcdadacaaaaddcacbbdcbbcbbabddaacdccbcbdabbdddbbdadbdcdbbacbcbdccdccddcbcbdcacdcdbdddcbcbcadbccabbdadacaaacdbcddabdbaaccbaabdcaccbccdaaaadaabbcddaccccbabdbdcbcdcdbbcbbaccccccbdbdbdbdbdacabbccdabccaadbabdcdabaadcaadcaadaddccdadbadbcbdadbccccaddaacdbacbdabbddcdbdcacdaaaddbcacaccbbcadbbccbbddddbacaacdcaccaaadabcbddabddbcccacddbadaacdacabaacdddddddbacadacdddbcbdccaaabbdbdbbacdcdabdadbccbdabbbcbbaabdccbbcbbbbadabbaabddbadacddbacabdcbbcbdbaddbabbdbcabdcccdadcadbdbcdcdabaacbbccbbdddcdbbbdaadbcdadbaddbdddadaaadbcccbacdbbbdccdcaaaaabdcbaacababbcaaadacbabdbbccbccaabacbdbbbcbbddcddbabcbacbcadacddccaaadbbadcaaccbdcbacbbaccaadaddbbdbcbbaadaaddcacacdbacbcaccddbddbdccadcaccbddbababdcdcdbadabbdabacbbddccaabbbbacbcadabbbadadcbccadaadcbbbbaacdbbdccbcdbcbbdbbccbbaddcbcbbadddbbbacacacdbacaadccacaaaaddadabbddbccaacbdadacccddbacbaccadaaccbccdcacdcacbdddbdcddcddbbddccbcdacccacadddddbbdcdacbbcadcbcbcabaaaddbaacdcdcadbadbbcccdadacdcbbdbbccccbbabdcccaccadcaacabcddbcabcbccbcdadbaacadaacddbababaacbddcabccbbaddbbcbdbbbadddabaaacdaaccdccdbbcbcddbcabdabddabcdcdcbdcddbabadabbdbdbbacaccaabadabdbbcaaabcdbbbbdcbabadccbbbddcccabbbddbddcaddbddbaabcabadbcaacbcadcbbbabbaadacccccdabbdbcdcddcbbdccbdcdccdacccbdbcadadbacacdbdbadbabddcdcaadcaddaacbababdcdabababddcaababadacbbbcaaccbdcbabbacbdcadbdbbaddabacccacbbabccdadababaaccaddccabcadbacabbbccdbbbcddadcadacaddddbdcbcbdbcbdbacdabbcaacadbdddbadbddbcdacbaaacdcdbdbacbaaccbbcaddabdbaaaaaccbdcacbcadddccacdadbddabbbdacdacdbcbadabbccdbbacdaabddcdcddbabcdbaddbccdcccaacdadcbdbcacaaadabdcaddaadaddabcbbbdbaadadaccbbdbbbbbaaabbadddbdbaddddacacdcabdbccdabcbbbaddcbdacbccbbdabdcacbcbcabdadccddbbbcdaaddbcbdadcbbcbcbabcbccabdadbbcdbcdabddadaacdaabcdcdbddacdabababadcacdccbcdaddccdccaacbbcaabadcaaaaaccacdcbbcdbadbcddabbcacacadcaacbdaadcbadbaadcbcdccbbacbcdbdccbadcdbddcbcdaacdacabddbaabaabbbcbaadbddbcbbaccbbcadbadcdbcdaaddaaacccadcbcdbcdccaaabbbdbcccbbccdbcddccdcaccacbbacabbbdaabddbbdccbdbadaaabcbbabcacdbdcccbbbabbaddacabadcacddcccacdadcbdbddadbbcdbdcaaacdbdadcaccbbdacbbbbadbbcbcbabaddcadbbcadbdacaddbcacadddcddcdbaabcddacbaaddacadbcadcdccdddcbbdacbbbddbbcacabcbdaadacdddcbdcbdddcbdcadcbacbbbbdcaaaacdaccdcabadbbbcbbbdccbdaddcabdabbbdabcacdaadcacacddbbacadadbbbdbdbababcddcacacaddbabadcdbbdbbcbcccaacbbcbaacacbddadcddabddcacbbaabbbdbbbcdabcaccaddbaadcabdabdadcadcbbcdacdbbaccaadadbdddddbdbabababaaadacacbbbacdabdcbadbcacccbccbabdcaccbcddccbdabaacdcabddabadcadadcbbbabddacddbdccccbabcdaadcdcccddadbccdadbaccccdacdcaadcbcccbbcaddbbcacabaabdcabacabccdbbaababadddabbaccdbbbdcbaadbdaaaadddaabacccabbbcacbcabcaccdcabbdbbdddcabbdbadabddaccabbddaabdcdbbdadaddbddccbccbadbccbccaccbbcaabbcdccbdcbdcbddabbccddaacdbaabbaacacbabdaaadabdabdacbcdbbdaaaaadcbccbdcbdbdcdbbbdaadadcdbbdaaabbacbaabbcdbbdbcdbcbdbcadabddbadcdacbbcccdacbbdaccbbddbddbcbbacccaabbbbdcbabacccbcabbabcbabbadccabaccdcbcbadabcbacddcbacdddcdcccaddbccccbababacadcabbadbcaacddaadbdbcacaadbccdcbaaadbaaaaabbabdacaadbbababaadddbaacacdacddadbddcacbabbcdaabacbbcbacbaababccbcddbdaddcabababacabbdccddabaccbbbdbdcccabbacbbdbddabdbbcdbcbbacbabdcbbbaaacdcccabcadcdbabbacbbacddbcbdbbbbccbaadabbacdcdadbbababadacccbbdcdadbbddabacbcccddcdcbbdbbbcacddaaaacbddbdadadddbbbabcbbcddccbcaaddbbbbbbddabadaababbddaddbdcbbaadcdbdbdaaddcbddccddcdabaabcadaaddcabbccacdbdbdddabcbaaddcccdaddddbbacaacdbdbddccddacbacbbcddadcadbbbccacacbcbdaaaaacaadadccaadcdacbcbadbdccadaaadaadababccaabbbdbaacbbcabccdbcdaabcaddaacaddccbdaccbabdaacdabbbbacddcbddbaadbdabdbbbbdbcbbdbdbdadacbdbaccdbacddcdcdbdddbbbacdddbbbadcdcbdccbdbcccdbabddcacacbcbcaccaccbccccdcddcaaddcdadddcadccbdbdacbbdacbcddbabcbcdacdadbacbdcaacdbcdcbdbcdacdccabbadbcabcbadacbbabadcddccaacbdaaaccbacaccccddabcddabbbcadadbccaaabacccddcdbbaacddbdcccdddaaadabcbbcddaddbbbcaabdbdbddcbbbddcaaccaabbcaddddadcaddabbbadacdbaaaaccdbcddbdaaabcacccbbabbcadadcbbaabdaadabaccaadcbbccabbadcdaacabdabbdbacdaaadabacbdadbddabcdbabacdcaabcdbcaccccadcccbbbcadbdbacbababcadabcbbbdccabcacbdacddacaacbddcaddcadcddbbadccaccccdabdcabcdcbbcbddabdcccaaadbacbcbadacabbdbabaaddaaacbccbbcaaccbbdccdddbabccbcbcddbacbdccccaacbdcbcdddbbcdcdcccbcddaabcdbbccbdaabaddccbaccddbdcacddbcbcbdcdcccdccdacccbdcaccdabdddbbaaccdcccadcddcccdccddcbddabbbadadcbdabbbdcdaadbbadbcdcaadcddadcadcbcacbdcbbdacddbccabdbaccabbcbbbddcbbbbbbaabdacabadcbbdbddddbacdcbadbcdcdadcdbadaacdcdddcbcdcbaadbccdacdbcabbbbbbdaccbbddcbbbdaabcbbadabbbcaadddaadcbabcbcdbbbbcadbbbdbcccaddadcbdcdbdacddacddcccbbacdcbacbbdbbbcccbcaadbbbcaacdababaacbcbbcdbcbacaaadcadbcccdadbcadbcbbddbbdbdcbcaaabcbdddcbbbbbcbdbbdaababcdaddacdcbcabbcdcadcdcabcbadbabbbaadbdcdcdaacdbdadadddcadccbbaccdabcdbdcbcbccbadadcaaadadacdbadcbcccdaacdbdcdcabdddcabdcacacbcadcbccbccccdddbbcacddbdbdcdabcddcacdccdbaabbdcbbbdacdaccdcabbbcaddbcbcdacdaddddddcaccacddddcadddcbdcaccccadbaaaaacdbabcddacaaabbcacbddadbabaccaaaabbbdabdacadbdddabdcdbababcaadcbaacbcaaccdabdaaaabcbbccbabaaacadddccdcbbcadabbdcbcaaddbcdddbbcabbbdabccdcbbccddcadcabddcaaccadababcadacadadabcaabcdbcdbdadacbaadbadabcbabdbcacdbadcddabdaababbcdaccdcacaaaccaaacbbcbadacccabdcabdaadacccbbddbdadcaccddddaabdacacdcabbdcdabddccdbddccbcbbccdaadcaabdcdabaccbabadddbdcdadabdccbdadcdbbcdcbbdcccdcdcbbbddacdabbadbcddddabdabcdbbacbadbadabaacadbacacadccaaddcddabcacdcaccbdaaddbbbcbcbaadabbdabbdbccdbdbbbbadddadabdbcdcdcbacdddbabdcabcaacacdaabbbbadaabbdcdccdcaabccacdcadabbdcdddacabaadcadcbaddaabdbdbdabdcbcdbbbabccbacacdddbadbbdcdddbdbaaccabaadacababcaaccaabdacddcaddcddbaabbcaacabcacccdbbdddacdcadacacaddbcddbcdadbaacbacdbbdcabbbdabaaaaddcdbacadababccdcdccddaddcddccbbabbddcddddacdbdaddbdabbdbddbdbaabbcbbabccacadbbabcbcddcdcdcdbaacddbddbdbdacabacabbdbdaaabbabadbaccbacdabacdababbaddadccadcccbbcbcbccdcacbdacbbaabbbdbdcabbdcbcdadcaddccdacbdbbbaaadcccbcdccabdadaadaacdcbcbabdddddaadcdcbccadaacdadabdbaaddbdbabcaadcaacdacbccacbabdbdbcbabdacacadbadacabddaadccdbbbabacacbdbaabddddabacbbdccbaadbaababbdbaaddacdaaddacaaacabdbadccadcbaccaaabbdbdbbaddbddbaadaddaaddbadcabcabababadddbdabdbaabbcadbadddcbbcaacabdbdaaabbbbcadbcccbdcdccacaddababababaadabbbdccadaadcacdccbaccddabbcadcacbdbaadbdcccbcadddccaadcbcdddbaccbbadbacbbcacabdbcacbbbcbcaaaddcbacabacbbacdcdcabacdcccbabdbabcabdcbbddbcdcbbbbbbbcadaccbbacacacbaccdaccabacddbaaaaacdacccabccdcbdcbcccddbcababddcbadcaddcaddddbcccabdaddccdabdabdaabacadaaaaadcbcbaabdddcccdacbacdcbccdacbddaadacbacadcccbacadccabacbabbcbbbddadcddbdcbbdccccccadbbbdbbcddccdbccaddbcaacadccbabcabbaaadaaddaabadbcacdbdacadbadccbacbbdcdbccdcadababbddddbbdddcbdbbbbaadbdccddbbddaadbcbaabbabcbddddcbcaabbdaddacabbdccabbcdabdaadbbdcdbadacbabdbdabadacccbcaddccbacbcbccacdadbbdbdababdabbdcbdabddccabadbccaabdbdcdcaccabaadbbbcbbaaaddbcbaacaddcdcddacdcdabbcadacdccabcbdcbcbbbaaabcaadcaadcdcbbcbaccaddaddacbadbbaadbcdaadacacdcbadacbcabdaccacdcddacbbaacdbcbbcbdbabccabcccdadcadcbccccbabcbbcdacaababddacccbbbaabdddadbcdbacadaaadaacdbbadcbcdbcbddbbdccbadbaccbbabaadaadbbbcadbdccbcadcccbdbadaaabccdccacdccbbdbbaaabaddcaadbaaabacdbcabcabccacaddbaacbccaacabbacaabcddcbacbbacdbddaaabbabdbcadccaddaacadcbdbbbdbdbdcdcddcbcccdcaccbdabbdcddbcacacbaddadcdddddaaaccbababacbbbcddddacbdadcabdacadabaabcdbcdbddabacbabbdacddacbdadcdcdddcadcabdbaaacdbbabbadacddaadccdbbbabababcbaacbacdabbabcbabcadcdcabccbdddbcbdbbcadaacdddbbcdaadddddbddcadadabccadcdddcdbaaaadabcbccddaddcbcabddaaabdccccdcaabaaccabbacdaccccdacdbdabcbbbccdabbbaddcbdcbacbbbcdbaccdabaabaccdbadbaccdacbbbbcabbdcbabddcacdabcbabbdbbaaabdaccbcddaabadabddbccabdabcadbdabbaadddadadadbbcaaabbdcdbcbadaabbcdddaabcdccbbbcbccdddcacbdbbddbbcbbbcbccadcbacbcbcbbcdaddbdbaaacabdabdadacccbdaaadaacdbdaaaabdcacddbaabaacdcabaccdddaababcbccbdbbaaabdbcdbbccdbacababbcdcbcbadddacacbadacabdbadcddbcacabcdddbdadcaaadcaabbaccbcabbdbbdcadaddbabcadbcdccdabaaccaaabcabbbcbbbcaabdaadbccbabcdadcdabdcbcbabbdccdbcbdbbcbabdcacdccbdaacaccadaabababccdcdbbbcdbaaaacacdaabbbccacdbbbdbcdcdddbcbddbabcbaccabcadcabdaddcddcdaacbacbbddaacdbcbbddcbdbbbdbddcdbdaabdbadaacaaccbdcaabbdaadbddabcadcbbcacdcddcadabdddbcbcacaaccdddabababcccdcccbbcaacdbcabdcdbbdacbcbbccaabccdcccbacbbddaaaccbbdcbadaabdbbddcababdadcadbacddbcddccddcbdbdabdaccbdccbadaaccbbccdaccdabbbdbcdbaaaaadaaadddabcdaacadaaadbcaaabcdaacacacacadcbcdbdbcaddcdbbbbbddaccdadddbcbdbaacdadaabcdbaadbccdcdbabbaacdcaacccbccbaacaacbcddadaaabadadadaccccddcccbcbbcbdcbacbadbabbddcaccaacaababdbbaaabccacccbdbdbcacabaaddbabcccccbdadadbaadcddaadadcaadbcaaccaaddbddcbdbacddcbccadcdddcaddbdaccdcdbaabcdadbdcaabdbaabaaacdddbbcbddcdaabcbcabbdadddaddcaaaabadcaadaccbacabcdabddbbdcbcdcccbbcccabdcaadbbcbaddcdaddcbadcabbdddbdddcccdadcabcaaddbdbcacccbabcddcbbbdcabcbbbadcccddcbdbaacabbcbcdcdcadbcdbbdbdbdaacdddadabadabccbdcbddbadbbabddbcdddbacbcbdaacaadbbbaabbbabdaaaacbdacbcddaabdccccdabbabadbaabcccaddaacaadbbdabaaaabbddcbbadbcbbcabaddaabccbccdabccabdaacaccabdbadcbbdacadcadbaaacbbacdbbddacdbadddbdadcccddababcbdddacaabcabbaccbadababacabbaaccabdcaddabdaacdbcbaacbbabcbcdcaccbcabababdbcaacddbdaaadbdbacadddbadbbcdcccadbabdccbbdddcbacaaadddcabcdcdcabcbbdabdadccdbcdaaccdabbbacaddbdcacdbcddcddccbaadabdcacdbdcccdcbbddaaddbababdbbabcdbbababbccdbcabcaabccdccdcdbaadbcbbbcdaabbdbdbcdcbdaabcdabcbaaaaccdcdcaadaddaddaadcccaadbadbccbacabcadddcdcbdcdbcbcbdbaddcaaaacaabbcccdccaacabddabbddcccadaddcbcacacbacbbadaacaaacadcdcaadbdbbdcabcccbcaabbcaadbacbadcdcadcaaddbadacddcaaccbcababbdbacacbcabccbaddcbbccbacaddbaaaadccdaaacccadcbadbaadaadadbcccbbaabaabbbcddababdcacacaadcacbcadddacbabdbcbdbddbdddddddddbcdadaacaaccaccbbadcacdbbbcbdcdbbacacbbbacbadcbdccbdccddcbacabcbdccaabddcddbddbcddcabdbbacdcabbacbbacdddbdccaaadadabaaccababddacdcdbdbbdbbcdadbdaadccaacbacbacdbabadacdccddabbabbaadabdaccaadcdaccadccddcdababddbaaaccdaadbcbccbcbadadacdccbcadbcddabacbaababadabcaccdddbbcaabdcddcacdaadabdccaddbabdaadbbadcdcdcaaacdaaaacddbbadcacbaccbaacddaddcdadddacacbdcdbbbadbadbcbacadacaabddadcadaabbdcbababbdddcdaadddccbcacaddadcabcaabdbccdcccbcdabcabccdcddacdcbcdcdaaabaadddabddabdbacccbacccbbbdaacabddcdadbaabbacbdbcbacacdbabdbcccdccdadbdcbbcbdacaaddcbbcccbdcdbcadadcaaddaacbacacdddcbabaaaadcaccbacbcdbbdcbadaccabbbdabcdaabccbababdcdacbbabcddabcdccbcdbbaacaabbabdaacbcbcdabaabaadaacdcadcadbaabaabcbcadbbcaaacbddaaccbcbdabbdabbbbdababbaddbcdbcaaaaaacdcdcbcdddcaddddbdddaaabcbbbdcaacbbcddbdadbbdbcddadcbcbdadaacdacdbcbdcddabbcbdaddcdddaccdddacbadbabacabbcadbcacdabccbaccdaacbcdbddcccdcaaccaccaacaadabdadcbdadcddabcdcdaacacdcbaabaadbbdaabcadaccdbacccbaadaaddccdbbaacbadcddccaccdcbddacadcdcbccbaabcdcdaabcdaadcdbddaacddcbdaaddbdacdbdaddadaaabbbadadcbbdbcdbbdcdbbbbacbdaddcccbacbdcdcbcccbcadbdbdcccdbcaddcbcddbbcacabaadccacabcdadabbbbcabcccaadbbaccdcddbbbbdaaacddaabbcdabcbddacbdcbbbddacbcdaadbbacdddadbcbcaabbbadcbccdbbcbccabbbddbaadbbcbcdbcccccccadbbccbdbdbdabbdddcdbbbbbdaddcdacbcbcbadaddcaabaaacbbcdabcdacdbccacacbbdbccabbcbabdcbccaabbadcaabadbbddcccdddaacaacdbaacddbcdcdbddcadadbdccaaabddabdcacbcdcaddbdddbcdccdbcdaaabccabdcabdcccacdacacddcdccbbcabbadddccaddbdccaabaadacadddbcbaacaccaaccdddadacaadcacacccbacdabdadbddbccdacccbdbddadbabccbdccabaacbdccbaddccabccbbbacbaacabcccdadbaccdaccbbcbccccddddadacbdcccdbccbdbaadbdbdcbacabdabddacbbdaadabbabaddcdbbaadaabcacaaadcbbcbacdccabddaaacdacaabbbbdadbabcdcabdaacacdddbdaadabadccacbbbdcacdaacbaabcdccdbddadcdbabbaacacadcdbdabccdbccadabcccdbabbdcbadcabbacbcaacaadacacccbcbcacdacbdacbdcacccacddcbbbbcabbddbcaccddaaddbbccbbbcacdcdccdccbdddcabcdbadbadcbbcdbdcacadcdabcdbaaaaacabddcddcccddbbabdccbbdccdacddbbcdcccaadcaabdadddcbdaccddbcabbbbcdbbcdbbdcbdabdaddcdbabaadaabaccccdbaddaadcddcaacdbbbcbddbbabcabcccccdbddcdabdcccbcbabdbbcbabdccacdadaadadcacbbddcaacabbabbcadbdaaddacbccbcdbdbaadabacabcabaabdcdccdaaadcdcababbdccabcadbbcbaaddccbcdbcbaaacbcabdbdccddcbcacbccdccddbbdccddacabacccccacbdacbaacbcdcaadccacbbadcbcaabcaddaccabddcacdbbadbcabcbdabdbdabdbbdacaacaaabaddaddccaaaddbabcaaabbcdbcdddbbaddbdacbacaadbaddadadcbcbaabadbabbacdbbccdcbbdcccbabdcbcccdbabacaadddcbbaabbcdbdcdbccbdababacbdccdacbccdcaabaadbacccdccbaacdbccdcbaacccdbcbcdcdbbccabbddabadcabacdcdcccdddaddbbbdcacdcacabcbdccbabbadadcbcbcdbbdbdbddcbcbdccccccaacbbcabccbcbcadabdddaccbbcabccadbcbdbdcabacbcccdbdcabaaadadaacaccbacbdaaacdcdcdbcadcccbddadabdbbddbcaadbdcdacdacdaccbdaadbdbccbacbbccccccbcbdcbcacbddcddbbcabdaacdbbdbbdcacacadaabadabdcbcbbcabccababbcadaaadcacacddbdaddccccddcaabbcdbbbadddcbcadbdabacdaadddabdaabbbcdababccacadacbddadddcacabdcbcddacbcabbccbdacdbaccabccbcccdaccbabcddbcdddddbaccdabcacbcddcdabcabaabcccaacdbbcbcacbaadcabccaabacdbaddddcbcddbacdcbddcdabacdcbbbdadbbddcbadbdcdaaaaabcdbccddbadbcbaabddbbbabddaadccaccdaccbcacbdcdccadbbcaaccacbdaaddacbbbdccdaddaccaacdbbccbbbdbbabcdaddccaaacacaadbdcaddcbddbaadbcdabcdccabddaabdbdcccadaaabbbcbadabccbcdaaabbddcdaacddcadaabcabaadbbdbaabaadddbabadbdcbbacaadaabbbacadabbccaaaddaaaddaaaabaddddbaacbbcbcaddcdbacbcaadaacdbaddddcddaccddacbadacdcbbbdcddcdbabadbdabbdbcbbbacbbaabdcdbdcdddbddcadaadcccbbaddbddcbbadadbbadacdadbcbaadacaccdaaadaaaccacdabadbdaddcbbdbbdcbcccadadbddccacdccbadbbadddbadbaabbdcdcbaaccddccbadccdbbcbdbddcabcccaadbaadbdcbbccbabbdcbccacbdacabacbdadaccdcdbcbabdaabddcddcbabcdbabbcddcccbcccccaadcbdddaacbbdccdcddbbcdbccbabccbbadacdbaaacdadbabccbabcccadbadcddacbcbbbabacaddcddaabaaaddbbacbadbcaaabacaaddaaabacadcbcbadcbcadccaddddcabddadddbcadcabadbbaadcdaadbabbbdadcdaadbbdabdabdcdbabccbccccdabddddbdacaaadbaadddddcdbbaccadcbcadbaabcbbdbcdcddadabdaccddaacaddcbcccccddcbdddbcbbdabadadadacccdbabcadbcdbabddadacaabddcbdbbbddaaacdcaadaacbcadbddbbcababacdbacdadbbbaacaaacabcbbbccabbbaaabdabccaaaaacdcddbdbdbcdbdcaccccbcbcaacbabcabbcbaccdadadcbaababcaabcaaddcccaadcaaddcdddddbdacccccbddbbcbdabcbacddcbabbaabbdcaabadbbabbacccadbbcccaaccacbdccabdaccbbaddbdaadbccdbccbddbdbbdbdaadababccdbddbcbdbdaabcbcdcbbdcacabbbdabaddbccaccddaccdccbcdcbcccacccadaacaadabacabddbacbcacdddadcbaacbbdbdacdbddcbbbbcaacdacccddcbdcaacbdbaccddccdcacdbbaadbacbabddddbacbdabcdbaccacccadacdccbbacbaadcdccbababbbdcdcbcbdbcabaccadbbccdbaccddbcccdbddbcadcbacddabbcbadcdcbaddddccbbcbaaaaabacdabdadcccbdbaccadaaabddbcccccabaaacbacddacbbbccdabbaabcddbbbcdbcccdbcbdbaabddcbcdbacabccbcdaaccbbadaadbdcabcabdaccbcadadbdddcbdcadacbcdabdbbabddacdcabcbcadcdcdaccabdacddcbbcacaccacddcccaccdbbcbbcbdbdaadbbaaccabcbbcdcaaddabaabbddbaadddababadaddccabcccdaaddcbdbcbaddabdaaaddcddccaacacbcbadccbaddaaabbbdddcbcadbcadcbcdccbaaddbddbabdcdbdabdccccabcbcbcdbbcacdcddabbadccacaabcdaaaddbacbdcadbddcabcdcdabadccccdadbbcddccccddcddadcacdaabddbdabbadcdbadbdadcaaddddcccccabacdddabdccdadaabbadbdcdbbcacbbadccdaddddababbcdccadadaaaadaabcdaabddcdbabcdbdacccdbcccacdccbacabcabdcdacdaaabdccccdcdddddcddddcbcdadccdddbadabcdacdbadcabcbcacdbbdaccdcddcbabddccaabdbdddabadcbadcadcaacddbadadbbccaabccdbccdabadddbcccdaccbabacaabbccbcabacbdbdabdcdbadbcabadbaddaccbaacbbdbddadacaaccdcbdccdbabcbdbccdaadbcddcabdbdbcbdccdaabaadccabdacdccbccaadddadacbababdabacbcbbbbdddccbcacadbcbaabababbbdbdbbbddcccdadaabddccacdcdccacabbdbaccacacaccddbbbbbabdcccadbddcaddccbbbddaacbacbabdbddacccacaacbdcdbccaddabdcdabaadcadcacaccbabaacbabacdabcdbabccdddacbdddabadccbddabcabdcdbdddbbcbdddabccbddddddadbacbbcbcddbbcdbbdddacbcadaaaaadbcbacaabbacdbacbaccacbaaaabdbdddbadaddaabbbbbdbdccbdacbaaaadccbcbdadbaabdcddbdbbadbdadababdcbdaadbbcdbbacdccbdddcbaacadbbdadaaccababdbadadddcaabaaddbadddcbdbcbbcbcacbaccaabbbaaabbbbcacaaddbcddababbbaabadadbcbcbbbaaaaaadcadabcabaaacbbbaaaaadcbddcddacabcbacccdbaddccbdaccbcbdadbbbccaacbabbcdcbdccabbbcbdbbabbbadaacdbdcbcbacddacadbbbdacadbbbbaddbcabbcacbbbbbcbbbccdcbabaabbcdcabbdabbcacabbbdbcacbacdcbdabbdbbdbddcdbdbaddaadddccdccccddacabdddababcbcbacdcbabcbcccaddbaddcbabddcdcdddbdbcbdddabdbcbabbabadcbcdcbcdbaaccabacdbbdabddbcadadbabbccadbbbbbadabdddadddbdcacdcbbcdcadbcddcacacadbbbabcdcbaaccabbbaacacdababaabbbccddcaadbcccddbdabdabccdbcdcaaadadcabbcababacdaccbbdcadabadbdbcccadadcddbcdcbabbbbbdddacbbaaacccadcbacaacabcdbbabcbdcdaddbacbabdddcbcabacddcbdbcababbcddabbabdbaccdbbbddccdccdddccdbabcdbbaddcccbdbaacdaabbdbbdddabbcddbbbdababbaaabdaccbadbcbcccbdaddddccdcdcbddcdcccddbccbbcbbadddbdabcaacbcbabccaadddabbcddcbdacacdbaddadabadbccbcbcbddbbabbddddacdddcdbbcbddcbaaddadacccadbbcbaabdcaabcdccbacadabbadaadaccdbcddbaacccacaabbbbbdbbdbbaacaddcbbbabcabdbcbbdadddcacdadabdcbcbbadacbadcdabadcaadabaaacbbdbdddbacaccdaccacdaaccacabbdbdcbcbdadaabbbacccaacadadbbbcadaaadabaddabdbbccdddabaabccddcabadabdacbacbccaddadbbdbbcabbbdbbdcadbcdccacbadabbabbbdaddbcccaabdcdacdcbadabdcddababaccbdadabcbacdbddccbaccdcdcbdcbbbcacdadacbbadadbdddddbbdbbaadcdccdaddcabcadabdbdbdccacaaabbccbcabddddaabcddbcabaabbddacacbbdbabcacacbcabcdbcabbabacbbaacbcacabcacdcacddbddccccadbcbddacbdbbcbdcacdcddccdaccdacdbcddbcabdadaccbbbbbaddccbdbbcdbbdaddccbabaababccdbaddbacaaddbabadbaacbdcaaaddcabacdacddcadbddcbacccaadcdbdbaabbddccaccbcdbbbadddcaaabbbbbbbadbbaaccccabccddacbbbbbbcbbabacadddabdaddaabcbbddccbcbdccdcccbdcaadbbaddaaadbbcadcdbabacccbccacbdbcaadbdaccacdcaacdabdadbdbbcbccbbddcababacdaacbdcbbcbacadbabaddccdabcbcbdbdadcbdacbbabaddbdbcbbabcadbacbacacbdadbcaabbcbddbdcadaabadbacccabcacbcabcdcccabbdbbabccbabaaadaacadcdccdccadddbdadcbddddddcbbcddadccabbbacaaaddadbdbcddcadbaaaadaacbcccadcaadddbaabbcbcbdadcababbacbdcccbbacbddacccdcccadadabbbcabccdddadbbcbccccccdbdbcbbddcdcbbaaccbdaaabdcbcddbcababacbbbdddddddbaabcccbddcbbcbaccdcdacddaaddcabcadbacbdadcbddbadcbaabbbacdccdccaaadbcbaaaadcaccdacabbcdadbdccbdbbddabaddacdcccdbccdddcdaabaaabdcbacbbacdbdddcadbddcddaccdbbddacaccadcbcacbbdaddbbabacdcbdbcdbabccacdbddcaccabbacaacdbdcbdaaaddccacccdcadbaccdbdcbbdcccbaadddcdbccdcbadccdcacacaabbaabcbcbcabbbddcaaaddddbdaaaadcbacbccbcdbdbbcdbabbbcbbcbbddddaddbabdaaacbcbadbcdadaddacadbaddddbabbccbdbbadbdcbdcaacdbbcdbbacddabdabbddabddccbcccdccadadbadbcacdcacbdddbbaddcdcabaaddbcbdbbdcbdcbbdcdaabbddadcdcacbacdcbaacddbbddbccbabbaaddbcbdbdadacccadcdcbdccbdbaadacdbdcacddccaaaaaabbccabbdbcdbdacccbacbaacaaddcabdaabbdaaaaccdcabbdcbdcbaabbbcdabacbbacbdddccadbbbbbaababbabccdccaddabcaddbaddcaabddbdbaabacdaaadcacabbcabbdbcadbdcacaabcdacdccdcddcacccabbccdcdadcabbaaadbcabaaabaacddbcadbaabaaaacddbbaaabcabbccaccbccacaababcdcddaccdbdadbcdddcdadcccbbcbaddcdcdcdacdbaababacdddbaccdbbbcabdabacbabddbccdddddbdcbadabacddcacadcaabcaaadacacacccacdcdbabbbccadcbdadbbbacdcbdbcadccdccbdbccddbacdcdbdddcacbaaadabcdddaacabdcaddbcaabbccddddacbcaccaaccbdbdddabdaaaddddddbdccadddabccabaddcbcbbbdccabddacbbcdaabcbacdcdbabbbbbdbcbabcbdcccaaaacadaadccdaadbbaaadcbabbcbcddbbddcaaadbcbdddacdcacdbacbbaddadacbdaccbbacadcccadbcdadddcabbbcaacdacabcadbddbabcadcababaccbbdacbaadcbddabdbdabcaabdcddacbaaddccdbcdbccbbadccddccbdbcddaaccbbdabbbccaaddaabddcbccccadbccbacccddcbbaccccddbdbdbadacbbbbddccdacacdcabaaacddcdbbaababcdddbdbaddabaabbdaaabbbabbbcbdaacccdabccabcaaccdbdbbbaaddddccababcbbdbadadbdaabadcaccdbbdccdbddcaccdbcbbccabdcbcccddddacddbddcaadbdbdaacbaadacaccccaddbdcaaccabbdacccdcacbbccbaabcddaabdcabaabaacbabaaccadcaabdbcbbabcdcbcbccccddbaddcabbcadcdadbdacbbbdcaabbcdcbcdbadccbcaacababbcaadbaccbcbbadbacbdadcdbaacbbcdbddbabacaddccdcaddacabccdccbacbcdbdbcbbabdadbcbaddddadacabacdbacbadabdaadaacccacbddbcbdcabbbbbadcaadcccacaaabacabbbcbaaabacdddcdbdbbcadabaadbbbdadabccababbabbccaaacccbbdcddbcccadcbcbbdccaaaabcccbdcdcbcdcadaabccabacbdbdcdccbcdcddbccabaabddbdbcabaabbcbbabcbadddbabdbcbabbabdbccccbbdcdaccddcacbaaddcdaddccaddccdaaddcbbcdbcbcbcabbccbddcacbbdaaaacdcccdacdcbbcdccbcbbdaddbcbddaadddbbbdbadbbbbcdbbdcdbdcbacaacdaddbcbbcdaadcdabaaaaccabbdaccabddaabbacbbdacdcacbcadacbbbdcbccbadbcbbaaddaadadddaacbddcccdddaddcdbdcabbbbbbadcdabcaccdacbaacddcaccaaacdaadaacabccdbdcbaccabcbdbcccccadcbdacdbcaababccdacaccabcdbcabcddbccccddbbcadcbdcaaabdabddacddabaccddaababcbbacbbabdadaabbabddaddcccaaddbacccdaacbccadababdbababdccacaccccbbdacbdcabdadcdddacadbcbdabacbbdccdbdddbcccacccbcdbccbcbbdcbadcadbdadcbabbccccddcbcbabdaacaaddbdabaddbdbbabbacddccccbdabbcccacdbabcdcccdcdbddbdcbacdddbadcccacccaccadacccbcadbbdcaaccabccbcdccdcadbbbcbcadbcdaadbcbbaabcbdcbdacddbbdddcaddbddbcaaccccababccadaaadddabdcadabaaadaddaccdacbaabbcdbdaabdacbaaccbbbaabacadabcdddbcacddaacbddbdaabadbdddcacaacddccabbdadbabdddbbacbccdaacacbadcddabaabadccccddccababdcccdcdcdcaabdcbcbadaababdbbdacabddbdcccaadbcdddbbcbbbbadaccacbadabaaaddbabbadadddcaccadbdcbbbbbcabbbddabdababbacbcddcacababbcbbbcbcadbbbadcacaadbbddddcddadcbdaacdbacdcbdbcdccbbbabddbcaabbdabdaacdbcdbdcbbbaddbcdbcdaacbbacdddbbaacacbcdccabccbabcdbdbdcadbcccaaaaddbabdcbcdacadadbdcadccdbaaabbbabacccbabaddbaabababdabcacacadacbadbbdccdcbcadbdcccdabaddacabadcbcabdbdcbbbcbbbadcccdbdcaaadcaaccbddcbbdcccccbbdaccaaddabdbdacbbaadbbabcbcadccbcabdaabadcbcdacaacaddcaddcddccaacbabacbddbadacccadccacdabaccaaabbbdcdacccbaacacadcdcaacabbcbaacdcccababbcbbbbabcdadcbdbccccdbbdacdbbdbcababcbcacabcdacddbdbaaabaadacdaabababbbcbbaadddcdcccdbddcdacadcdcaadcadbdcbdcdadacadadcbddcaaccdcbdbacaaabacdabcaaaaddbdddadcccadccbdbcacbccbbdbcabaadbdbcadbbbdcadcbbdcddbddcaacbbaadbdbddabdaabcdcbdbcdbadabaccdbcdbbdbaccbcabddbdccadaacbccacadcacddcdbbaaabdabaaacabadabcbcbadadccdbaaaadcadccabddccdaabadabadbcbddcdcbbcbccdcdbadaabcbdddacbabcbacacdadaacdbdcdbcacdcddabaabacacdbaadcaabaaccaaaacbabdbacabadbdbadbadcbdccbbacccbbbadcdbbdacdcdabdcdadbbdbdbdbdcbbdabddbccbbacaddaacccbcdbbbbdcabadddaddacddcacddbdbadbbbacbabcabbcdcbaabbadacabdddaadbcacacbccabccaccddbacdadbaacacdbbcaddaaddddcbdcadbbddcbcdccabadcdbccadddbdacbabccdcdabbccabcbdddcbaacacddcdadadbabcddbbaaaddcadacaabbddbbddbaadddbcbadbdbbdaddacbdadcdadbcdabbbccbdadcbbabdcdacaadbccbacacbcdbcacdaabdabadbaacacdcbdaccbdaaabaadbddbacdcdbdcdccddbabcddcaadbcabaddadacbddcddababbcdcbcdbaadbcbadabbddcbbacaacadcbaddbcbccdbdbdadcaabbbcabbcaacadcbcddcdacdabbcabbabdbcbaddcabbabdaddcddaddcbbcddaddaaabcdbccabaddddddbccdcddadcbcbadaaabacadaacdccdcccabcdacabaaccddbcacccbdadcdbcadcacacacdadaaacdccbcacbadcaaadbdababaadabacaddaadaadccdbccbcbbbccacddcbbcdabacbcadbcdbacbdbaacdacbdcacbbbddcabcdccdcabaddaaacaacccdaccddbdbbdbbadbadaadabcddaccbbdbbdbddcddbcaacbdaddccdbdadbccaaacadadcbbcdcbccadbbdcbdccdcbbadbbbbcbbcbcbcbdddbdcabccabaadcbbabdccdbcdabbaadaacdbbcddabbbddcbdababdadbadcacaabdbcdabdcdcdcaadbaaacdabbdabdaabcabccaadbdddcddcddbbcacddddacaddcbcababcdcbccddddabdcdddccdddbcacccabccbccabccadcdaccadbcdadababccdacccadadcccaaaccdbcdaabddddabbbcbcdacdbddabcdacbacdaddacaabdabbccccbbadddbccabdabbabdbadbddcbbaacdcbaadaaaababccaaaadbacdadbcadbbbdcdccaaabbabbddbbabdbacccadbacadcabadbbcccadcdaadadcdccbccbadbaaabdcbdcacbaaadccabcbbdcaacabddcaacdbdcbabcdaacabbccbbaaaabbbcdbbcaaabccccdddcdccddbaacccdbbddcccdbccdbdcdbbdddaaccdaacadbcdccbabbcbcbbbcbdddddcabbbccbdadacdbcbbbcddddabcacdbacacaccdaadbaccdadbdcaacaaacbbacccdcddbadbddabdcbcadbccbcbdcbbdabadbadddbdabadbcdbbabcccadccaabccabccbaaadcddbccaaaadddcadddaaccadbcdbccbabdcbbdcdbccdddcabbdabcbbdddbbdcdadcababddaddbdaabbdcdaaadcabdbbcdbacbbdbbbadaaddbdadbdbdcadddbcbcadaacdacddcabbdacbdbddbcccccdbdccdcbdaabbdbcbcbdccdbaccdccaaccdbbddaaaacddbccbdbbdaaaacaccabcaaaddccbaadbbacdbcccbcabaddbddccadcacdacbccbdcbdccbbacaadbcbacabacdababdcaacaccacbbcdddbdbaddacbbcabbcdcdccbbcbbbcacbbdddaadadddddddcccadacadbcbacbcdddadbdacdbcabdcaadcdcbbacbbabaabdcccbbcdadbbbcbbacccbaddcdaadabdaaacdddabcabbacacdcbbbbdabbddaddcaadabdadcdaabadbbabccaaaaccbcbdadacccdacdcdaadbccbacccdaccdabaaacacbaacccadbcadbcdaddabbbcbcbaadcacbddccbbadabcdcbbcadbdcbbbbdacbccdacdcbcdcdbdddcddcdcdbcabcbdddbaadcbaaadcaaacdbccdaddcdbcaacddaadbcdcdbbddbbdddbbaddbcdacaadaadccbcbdcbacdacdadabcddaabcdaadabadbcbdccbdddddaddbcccddaabadbbbabaccadbacbcdddcddbbbaabdcbdbcccabcacdbabdcadddbbbaaaadbccabcacdbdcdadabadcdddaabaddacabbdbacdcbddabdbbcaddbbaadcbdcdddccabdccadcdbbddcbaddabbcbabcbadbdcadcaaacdbdbbbdcdddacaadbdddddcccbabbaccdbcbbdccbcaadbadcccdddddcddaaabcacdacdbccdccbbaacddaddadcbddddabcdccdbbcadccbcbdcbccddacdcbaaacbbcccbdddcdacdcaaacdbaadadcdccccabbdbcdbdadddbdbadaabaaacddbbaaadabbbcabccabbcddaaacabadddaddadaaccbacdbccadddaaccabbcbaccbcaaadcbccaccbabbccbaabacaaacabbcaddbbcbaaddbdccbbdbbcadbabbabcabcbdcdadaaaaadaddabbbdbaddcaccbadabcabbcaaacaadaacabaacccabbddbddccdddcdaadaddaacdcabcabaddbccacaadddababcbbbaccccdbbbcdbccbaaacdccaaadcdadddbabccbabbdcbccabbdccacacddaabaacadadabaaddccccadbddcaaadacdcaadabcadcbdbbdbacbbbbbbaacdaddbbdabcabaadcbdbdcacdbdccdacddcbbcdcaadbbbdaacbdbdbddabcabaadacddbccabbaddccbadddadcaababacdbcdbdbabcabbdcadcccacacccaacbdabdcaccaacdaaddbbdbaabcdcbbcbacbababdddbababbddcddabdbbaadbbcaacdcabdbdcbdbdcadbbcdaabaadaccdcdcacdddacdbacaccdbacaabcbbdbdacabbbdccaacddbbdcacccdddbabcccbccbbdabcacadaacacbbabcdbbaadcccbcaddbacbdcbdabbcddcbccaabbaddaaaccadcbcbadaddddcadcbdcabbabcddbddabbaaacbadbdbbbcccccabacddbbadbbdccabbcdcdbdbdadddbaadbbcddbdadadcdacdacabcbadbcbdcabccaabaadbdddabbbacbdcabaddcaaadcdccdbcaadbdbcbdacbbdababbbadabadddaccdbacdcacabdcdcdbcbdbaabdcddddadddbabdbcdabbbddbddbdadaadbbaaaadcbcabddbabbdcabccaaacdbacacdddacbdccdddbcdcdccbcababcdbadcadbbbbcabaadbcdccadaaccdadbabaabacadbdcdcdadcccbdcccddbddbccdcbdaccaddcdbbccdcabbccbcaaabdabdbabdcddbbbccdaacbdcacddcddabcadcdcbacccbcbabcdbbaabdcbcdbcddcbcdaabbdaaaccbbbaadadadccabbbdbdcbcddbddcaccdbdacbcaaccacccaacbbccdbabdbbcdbcbacddcdbbcddcbbccbbdbaccbabaadddbbcdddcadaaadccbbbbcbcbaadbdcaaddddbbdcdbaccdaadabdbddadcaddaabbbaaacbaddadddbaadaabbbddacaacababcacbdcacbcbaccdabccabcdadadcdaadaabbdddbcadacdadacaacadadcbacdcdbddaccccabdbdbdcacaaacdacbcbdddcbcbddccccbdccacccaabdaddcddcdcaddcdacbcbadbdcaaabbbabbacaccdcbdabcaaaaabadcadadbdacbbcdabbbcdcdbddcbaaddccacdcbacbbccccababaaadbccbbddcccaccddacccababdabbcdbddcdbcdbcdadacaccdadbddccbcaaaaccccabbaabbccddbaabaabcbcadbbddaabccdddcdadbcbbbdacbadadcacabdacdbbababdccbdbddadcabbcadadbdaabddcaabcabbcaddddaccabbadbdbddacbccbbadccbdcdacbcbaadacaabbacaaadbdcabccbdccddccbcadcdadddbbbbbbbbdabaacaaaaacbbbbdcacdadcacbcbdabcddbdbddacdcdcdbdbdcddcbbadadaacddcdbacdbcbbabcaccabcccacabadbaacbcabcbbdcbddbddbdcadaccdbdcaabcbcdbdbcccdddbcacaadabbcbbcabbdacaddddccacddbccadaabcbbacdcccbcbaaadcaddabacadbbccadcaccbcbaccbcacacbbbcddbdcddbddaacacabcddbbbbcbabcbdbbbddababdadabbcdcbddbdacacbcccaddbdcbbadbbddacdbdccdacbddbdacbdbdbcbbbbacdabddaacdbcbabaaaaaacadcbbcdbdadabcbbaaacdbcccbcdcdadbcddbdadaddddcaccdcbbdacaaccabddcabaccaabbadaadbadccaaaccccccadbcdddacadacddcaacbcadbbaacdccbddbcbbbcccadbcbaaaacdabbdacacdbaacaccdcabbddcccdaccddcaaabaaadacdbcacdaaaacaaabccbcaabbbdbcdccdddacccaddcaaddbadcbbbbcdacbddaadadbbacdddcdaabcbbdcbccdbdbccbccadaaccccbbbccbaddaabdbccbddcdcdbaacaabcccccbcdbcacbacaccdddccbdcaadcaadddbacbdbcdbabaaaccdccaabcdadcaacddcabcadbddccaacabcbbabbcdcccbadaabbddaaccbbbbadbdacbbdaddddbaadcaabadbdadccbcbaaabcdccabacbcbabaacbcacdaacdcdbdcdbcdbdbabdaddacabbccacbbabacdccbddabcacdddacddbacdcddbdaccddbccbbabcddacddbbaaddcdbbdbcbccbaadbddbaaabbdadbcccbbbdbdbaaccbbaddadbdcddddcaadddadcaadcbadacdcdbacadcbccddacacabaadbcbaacacdcabbdddbabbdaaacddccabdadacabcbbbdbabcaccaacbdcbcbababacacadbdbacbcdbadcabadcdccabdcbcccadbcaabaacdccccdcdbcabdadbcddbdccacaacbaaccbcddacdccbaccbcdbbdaddbdaacabbaaacccabddaacaadcaaacdbcccacdabdddaaacdccdaccbdddcacbadbabbdbcbdcabbdadbbabacccbcbabcacbdcccdddbcccdcdcdcdabaccbddadaabdddaabdbdbccaacdbbdcdbcbaaaadbdbadbbbacacabbbdddcbdbbcbaaddaddbadccdbdbabcccaababddbdbcccbccdbdcbdcaaddcdbccabddacbbbddccbacddcdcabccadcdbabbccccdaabcbbdddabaabcddcaabbaaccdaabacbcadddababbbddbbbcbabddccabaacbacbcddacbdddabdcaccadadaabbcbbdaadbccbbbbabaabbabacaabccdbcdcababcaddaaddacdbccbabacaacbadacccccdbdcbcddbcbbacdddccdacbabadabadccdcddacccaaaadcabddcbdbbbbcdcddcbdddbcbcacabdcbcccdbabbbabddcabcddbcbcbcdabcdccccccccbbbadcbbdcaacbdacdabbccbdbcadbcdabbbddaccbbdbbbcccdbbbcbdababdadbcacaadbadbabcddbbcddcccaddcbbcbabcaaccdbcdcabaacadbacccdadcadcaccabbbadbcccbaacadcdbacccbcadabdccbcbbabcdbcbdadccaccdaadbcaddabdbbcbdbbdcacbbaaddcadbadcdcccddcbbdddcdcaccbbdbacaaccbbcabcaddcaaababcbbdcbadabdbbbbddbabbacdacbdcaadbdbdbaacabbcdbdbdcabaaaaaccaadaacdbdacdbbdaccbcbdbcadacabcaadacdcbcaaabaddcaadaaabcdbbddbbbacdbbcbaccbacdbbbdcadddaaaaaadaacdacaccaccbdacbcdaadabdbdaacdcdabaccbdccccabbdbbcbacaaddccbddcdadacdcaddcadbbabcdcacbdacdbcadbddcdcbbdddbadaabbacdbabcdacabdccccbccabbdabbaccbdbdbadccbbbaabbbdccccbaccbcdcbaccdbbbaaacbacbaabadccdbcbadcabcadbbbdbcbbbbccaccddababbdcdcacaacddbbdbbcbcbdcabbacdccddccbcdddbcadabbcadddbbacddcdcbbbaadaaacbdacdadbabdadaacadbcbabccbadaddbaaaaacacaadadabcbdccdbacaddbadcdbbabbdccbbbacbbcabcbdbbadcccbadcdbacdcacbadddccbbacbbdbcababcaadbbbcaaacbaabcaabbddddbadbccddbddccabdcaadddbccbbcddadbdbcccadaaddabbbabbdcdcdadabcccabcaabcdbbaccadcdcbbdcbcdddddddaaacbcddbbcbabddcdbcbbcbbbaddcdcabcdadcccbccbbccccdbdccbbcdccddaadddccdcbbbadddcdccddadcddaccdbdccadabaadbacacccbdabcacdccdbbacadcdddcbcdddcdccbcaaabddabaadcaaadcaabbccdaacdbdadbdddabadacadccaaadbccdabcadadcccbcaacddaabbbcaabddcbdcdaabdbdaddbdcbaabccdabbcddcdbdcbdcdcdccdbdbdccbbbbadccabaaababdacdcbdbbddcabaccbaacdcbcbababcddcabbdadadcbdbacdaccccadcbaabcbbccbaacabbaabcdacdaccddbdddaadbdcaacccadbdbcadabdbbdbbccbbcbabaacadcabaacbbdccaadacbabddbbccacccaaadbacbadbcbacbcdccacdbdabcdccabccaddcbcdbadbdaaaadabbacdcababdbdcdacbaccaddbcdbacbbcabbdcbaaddaadbcbccdddabbcaaacdcbdabacdbbdabaccbddabbabcbcdcbbaaccbdbbcaaabadbdcdcbadbcaadbaddacddaaacdcaaacabbbabbbcdadbccbccdcbaaddcdcdcbaaaaaccabddaddaadbdbccaaaddacaabdbbbbcdaaccabdbbdbdaddcadddcdcbabbccdcddcdccccbddddbdaababddbdbabaccddccdccaadbdbabccdaddadcdcdcdadddaacdabccabdbbddcbcdabbacdcbbdacbbdbaacaacddbccdbdbcdbcbbccdcbabbbaaabcaaddddcbcdadcdacdacbacaacdacabacaacbcccdbadaacabdaadaccddadadbabdbadcbdcdbcdabbdccbdadaabaabadcadcdbadbbabbdabbabdcdabdbbabacbdbcaacbabcddaccbbdcaaaacbdccbdaccbccbabcbddcbbbcbdcaccbdbcaabdbdcbbabdcacdcbddacaabbcddadacadbadbddaddccbdbaadaccbccaccaaaaddadacacadbaaddbbcbbdbbcbacabacacdaaccbdccdadadcddbabdaaaadccbcdddcaacaabddcccaddcacbbbbcddcbdcbaccbcadbdacbdbbcdacbabaababccdaddcbcbdbdaadbdddddaaaccdabdabdbadabcadcadcdcbdddbcabadddacbddcabdbbacbcbcacdadbdddbbcddcbbddcaabbaabcdcaccccabaacccabddabbcdcadbdcddddabcddbddacddbcdbcacacaacbaaadacddcdacdccbaccbbcaddabcbaccbdcdbaacbbcacdccccbbacbccacccddacabbacbcaabdbdbadbbcaccaccbaacbddcddccdbcbaddccadadaadacaddbcdcaadaccabaaabcbccdcdcdbdcdabcdadcddadbbcdddddcdddcddacdbccabdacadcadddbcdbdcacddaaaddcdabbdacdcbcbbadcbacdbbdbddadcddacadccdcadaccbdddaaacddaacaaddacbbdaccacabcbcdacbcdddddcaacbdbbaabddcdadbcdbcdcdadcbaddbbaaaadadbdbcbbbbdbaaacaadcdddbcaddabdbbaacbbcacadbcaabaacddababdcabdddcadacbcbbddbbcbbdadacdddcdabbacbdabcbbbadbddbdddabcbadcdadbcabbdbbdcccaacbcdadbccbbcabcdabbdbacacbacaccdcdccdbdbcabccabbcaacdcacccbdaaaddaacaacadbbdaadcdcbbdbaaacbcccabbbcbbddcabcadddbddcaabbdacbaccacdbdbaddbccbbbaaabddbdaddabcbdadadadddddaabbacacccdbdbaaaccbdddccdaccccddabacdaabbcaaaaaacdccaddacadccbdaabcddacdcdcabdacbacadacadacaccaabaccccccadbaabcadcdccadcbcabadbcadbdabdacbacdabaccddcdacdbbadaaddcddbdacadcbcacaacacbcabbdabacdacbaccaacddabcaabaaddccdbdcaaaccbbbdaaacddcbbbbcaabbaddbaacdabddbabcbcaccbbbdbabaadbabdcaccbaaacbdcddaaaccabdcdcdabbaccdddabcabdddcaddbdcdcbadbaacbaaacbdbdadabcbcadddcbcabdcdcaddccdbaccaddddcbbdbcadcbbadcdaabccababaadbadabcacbbdaadcccdaccdabcaabdaadacbdabdccabaddaacbdcadccabddbbcbadabbbdbcaadcbbbbacdbcaaababadbcddddabcacbddbacdaadbacabccbdcbbacaababbacbaadbbdaaadccdccdadbbadadadbbbbddcababccbccaaadadcabaadddabdbcdabadcdbadccabdcbbbacddaccdaadbadccdacbbaabdbaddbdabbbcbbcbdabdccaabddbccdaabbaaaacbabccacdcbcddbcaaacbcabaadaadcccabbacbdbacabaababbcbcbcaababdaacadbdadacbdbdadabdbdcddcaabddaccaaacaaccbbabddbdbdcddcaabadbdabcdcabddcdcddabccadacabbcccdbaabdabacdcbdbdababbbadbaabdccbabaaaaddaaacacdabdbacdbdbcbdcbacacbdacbbbddabbadddabbaddaaacbcbbdddbcababbaadccabaacbcdadbdadcccddaaaacdaaddcdacbdccbbdbbbbdbadddadcbdabacaadabddbcdaadaaacadababbaabccdadbdddbdbdbbbaabbbbbbbdcacddbcccbbdbbaaccbbaddadbcacbadaddcacaaaabcddaaaadbbcbbbbbdbcbccccbabcccacccdaaacbcadcadcbaacbccabcacdaccdcacbbbdbddccdbcacddcdddbbaabacdccddaabacdabacdcdbccddbdbbdcbadcaadbababdabdadbdcbbddddbcdcbdbdbaccaaabbdabcccdaccdbdbdcccddccdaacdcdcbdbcacbdbcddabaddddabcdcacacadbacbabaadadadcbaccdddddbcbacdbdddcbaaddccdbbaadaabaabddddbcacaabdddabbdabbddcbcdabacddbcbcbabaababdcccabbcbcadccaddbdbacbdccbbbbdbdcbccbabdbacacababadcddbbccadddbcddcddaaccdcddccccdbbdbdcbadddbbcdccbdcbbcababdbcaabddadcabbccdcbdbcbcdccbabbadbcaadbddbbdcabbcaaabdcdaacbbdccbaacccbdccdabbbdcdcaddccddacabbbbbbcdbbbdcdabbabcacbbbdcababdbabadadbaabbcbdbddacbbabbadcaaacbabdcdcdabcdadcccccadcdcddaccabcbdcbaaddacaaabdcdcadabcdadadbbcbadabacbcabbbaabaaabdbdcacbbbdcccaacbbddbbcaacacabbacbacdccdadbbacbcbdbadbacdbccbccdbabcdbbdbccdddbddcabbaadbabaddacabdbdacbcdcdcacbccbacbacacbaadbcbbcccaadbabaadbdccaacaddaddbadaccbaaaacbdbbbdbdaabdddabaacbbbcadcddaaccacdaaadcbdcadaaccdbaadbbbaadbaaaababbaacbdbaadccbacbdacbbcccdaddacddaddabcacdabbdbcbadbcdccaacbcaabadcdcbdaabbbccaadcabdbcbcddcaacdccdaccccbcbcbccbcbabaddcabddaaddaabacaadadcccdadccdbaabdaccccabdbdbadabbabcdbadbabddcdcbbadacbccbbccdbddcddccdddadadcccbabbbcadccdcdcbaacdcaabcdbadbdbdacbddbaabadcdcdaabacdddbbcccaadbccdacccbadcbbccbabdcbdacccdcccddabbcdddbabbcdccbbaababbdaaddccbddbccdbcabdcdbbaccacadbbdbcdadddacaddaddbabdbaddbaacddaaaadddcadabddadaabaabacccbaccbdddbcaadccddaabbcdbdcaacdadbccccbacdaaccdcdbcbacdaccbbbbcaddadbdacaacdcbbcdcaaaadabcaabdcaaabbcbdcdcdabcccbbcbdcdcdacabcacadabbcadacddaabbadbabadacbdcadaabdacdddacbdbabdaccabaddbbbddbccdbaadcacdabddbcddddaaadbacaadabdcbabddaaadbddbabaabdabcddaadcadcbccaddcdbbbabbacdccdcddbabcdbcababadbbdaaccddadcccadbabdbadbddbbbaccbcdccdbdababbdabdcbddcaabacdbcaacbbdcddbbdbccbdbdbabccaabcadbdbbbaaadbdbdbbbabacaaadaabbcdcdbadbbacbdbbbcdabdbbbbcabadcdadaaddbcddadabcdcabcacadbabadbaddadcdbdccbabbcbbcbdcadcddadaadbdbdababcddcdcdbdbadbacbabbbdcccdababbdcadadabdbbadccbbdabdccbcddbacbcbdabaddbcbabaaaabaccdcadacbaaddcadcdbbaadbaddaacdbbaaabdbbbddccbabdccddcacdacbbcddaadadbdcdadbabdccbcdbcadbddbbdbcdacbaabaccccccdccbcbaadbbdabadcdbdbacaacacbcbbccadaaabaccbaadcbbcacccbbbcbaddacbacaacaaddddacbbcdaaadddcccddbbdbdbccccaadcaccbbacbdaacabdbdacddcbdcabcacdddcbbbacaccbccdbccccbcdadbccdcacdbabcbabddabdcacccbbcacdcbdbcdaacaaddbdcacadcbdbbbacbdaacccdbabcbdddabcaaadaaaabadbddbccbdbaadcdacddcccbdacaacabcdadccbddddcadcdacdacacacbcbabccbbaddbdbdcdddaaadccdaacbccaadaaacbdbabcdbabdcddccdcaddddcbcdcdcbbdbaabababcdcadbcadadcabcaadcdddbddbababadabdacbbdabbbdbdbdbdddddacbabcbdcabdbcbbcaacdcaaaccadbadbbbacaaacaaccdaadbddbaadaddccbaabacbbdacccaccdbbcadcbdcabacaccbcdcdbdcddcabdbcdccdbbdadccbbbcccbccdccbbccdccbccdbbbadaabacdbdddbaaccdabbdaaaccaacaccbdacbdccbddbdcdbdcabcacaacababdcdbdcdacddaadcddcaaaaccbadccddbbbbccacabdabadddcadbdcaccdabcbbdccddabdbbbdabacacdcbccaccccaacdcaabdadbbbcadbadacdbbaaacabbccdacbbadbbadbaccaddddcdcdcdbbdcddadbbbacdbadaadcdbacacbccbbdddbbcdacdaccdddddcccdacdbdcabcbbdadddabcbcacaccdbabcccadaaddadcdddcacbccbdbabbacbcadddbabcddbacbcabdbccbdaadacbdbbaacdccbbccaaacadabdabddbbabdcabbbcacdaaaadcddcbddacdccbaadacbcbdaccdccdccaadcaccaddadbbbcdbbcdbdadbabcabcbcbcdccbbabdabdbcaabcaaadbdccddbcdbdbcbabdacdaddddcbcddbbcccbcccbdcccdabdacbaddbbbcdaccddcbaccdadccdcbabdbcbbbadbbbcabcbcdbaccbdcadaaddcbccdddcddacbaddcaaaabcccbbaacabbdcdadcccbabbbbdabaadddcdbdacacacbcbbaccdacabcddcacabddaadbdaadcabbcabbcbdcdabacbddbbbccabddbbdbdccbdbdcbcdacbacdcdaabbcccadcbacdbcaadbdacbcaccbdaaabbcadaabcbacabdaaadaabbcbadccdbcacbcbcaaacbcbdacacdacccbddcbdabdbadcabbdacadacdccbaccdddcdadbcaddcaaadbabdcabbaddddaccacddaccdabbbaddbcbddaadbbbcdabacdaabccdcdbaaaacbcdcabadadbbbddccacccdddbabdcbcdcaadddbabdcbdbacabcdbddbabdadbabaabbdbdddacdccccccbbcccdaccadbccacbdacbdcdcbccabcbaadbcadabddaaacdccbacabcbcbbbbcaadacdacacddbabbdbbdbcbccdccbcdbdbabbbaadaadbdacdbcdbcdbbaabbbbcbabcdabbdbbddbacbdabdbdbdacacdccbdcbddadabbccdbaacdbaacadcbcccacdabcddacccdacbaacdccdcadcbcabddbadbcbbadaccbbdabbcabddcbcccddacbddacbbabacbbdadddddcddaabbcbdcdccdcdcadabcabcbbdbabbbcdabbddbacdaababbbabadccdbcabcbcabcdbacabcdbddadbacdbdcccbabdbcaccadbaabbcbdacadcbbaccadccdadbadacbccdcadcbbbddddcbbabcbdaddbacbbcbaddbdbdbbdccaaccadadccaacabbbddcacababddddadbddbbaaacdcdcbccdbccdacdadcbbaddbabdacbacdccaaacddadababbcbbcaabdbddbacaccbaaadbdbaabdadabdcadbbcacacbcbaaccbbbaddabdcdbabcdaddaabbcbcacdddddaddacacbcddaacdaacaddcacacbcbbaabaddcddcadcbbddbdbbcadaaabdccccccbbbaababcbabaaaaccdadcbdcbabccddccaacbdaadadadacabdabcaddbcdbcbabbaabcdccabacadbcbdaaacaaaadcaddbacddddcadadcccbcdbbcabdbdadcbcdbbcdbddbcaabccdabacddaacbacddbbdbbbcccadaaaacbddabdcdbdaacbbbaabbbcddacaabdbcdabddaabacdddcacccbbabcbadaabaccbcabdcdabbdacbbcbdbcdcbddaabccadbbccdabbcacaaddcbabcbadaccabcdacdbcbccababcdaccbdadabbddadccdcbadbcacabadaabcdacabacdaabbadadabbdbcdccacdaabbbacdabbdbbacbdcbcbbbcabadbdccbdadbbaabdcdcdcdcdccddbdadddccaacbaadcbddadbcbbbcbcddabdbacbdbbdcbccbdaabdadabcccaaaaddadcccdcddadbcdbadabbbcacbcdcbbabbcaacadbbccacdccdcbaccdcbcbcbcdbcbabadbbddbdbbcadddccacaadaaaaaddbddaccbdababcadaaacaddccbccbccbacccaaabcdacdcccddadddcdaabadccabbcccddabaabdcddadccbddaccacdaaccbcbcdcbcbcabcbadacadacaadccadabbaacabaddbcdadbbcbcabbdbdbaddcddbdbdcdadbaacbbbdaabbdabdccabbdcddadccddbbcbbabacdcaaadacbdcaabbccbdadacabbccbdbdccbbabaddabdbadacddcdadbdcaabacbdcdaddabcabbcacbbdadacdaccccdabddcabcacccbcbccdaaacdbdabddbccddacadbdbccabbcddaaacbcdabcdbdcadbadadadadbbbdddaacaaacbdbbdccbcbaccccbbdbacbbbaabaabbbdcaadddbccdcadaccbccddbbcacbbdcddbbdddbcccaadcdadacadcbbadaacabadaaccaababdddbccbbaabccbddaddccdadaabaabcbaaadbacaabbabcddddacacdcabddcdacddbdadcdddddadcacccdcaccbbabcaaaaaddadabdabacacaddbbaabdacaacccabcddddcdcacbddbddaabbdadbaacdaaaabccdbbcdbddacabbddaabbadacbaaacdcccbdddaaacaadcddbabcabdcbdabbdadaadcbccbcabbdcbddaacbaadcdbacdaaaaddccdbdbdadccdbdcaaabbbdabcdbdaadcbacbacdcaadadbbbdaaaccccbcccabbcadddccdbddbdbbbccaadbbdccbbbcbababddbdbddaddcacacbcbdcbddaacbdcbababaadabaadbcadabbdaddcddddddadcdadadadaacbbaadccbccabcdaccccbbdbabbdbabcddacdbcbbddbbacbdbbaaaccabbdadbdcbaddbdaaacccbcaadaabcccdaadccaacbddbcdaacadbdddbdbcbabadcbcdddbaacdbbbbcbddacdcabcdadacdbbcbbadcbabaabacccdddcabacdcacdbbdccacabcbddaabdddabbcacddcbdbbbbacabbacbcdcbcdcdcccccdbdabbdabcadaddccbababddbaccbdddbbcdbacdabbaacadabbbcbacddabccadcccbddbbcbccdabbcddcbcddbdbbdbcbbdaaddbcabdacacabdbdbdbcaccacdacccdaaccdcadbaacbbdaddccbcbbaabcdccbbcbcaadbbddadbdcdadbdabdadddccdbaddddbbddcdccadbbbccdaddbbbcccadbbdddccbdcbbaddcadddbcbbcabbcdbccaadbdbbcdbbadabdcbbcadbdddaddcaadbcccdbcbdbaddcadcadbaacccabbadbbddbaadaddbadbcdbcabadccbdbcdadcdabacbbcdbadadaabcbaaddcbcadaccbcadbdcddabcdbaacaacaaddcbdacbbddcbaacccbbadaccdbddbacdcdbbadbdabcccccdbabbddddaabcabcbcadadcacaabccbccdcbbddddbaacaaaacddcadaccbaccddbccdadbabacdadadacdcddacbcccacbadbbcdbdbabdcbbbbdaaababcdcccdacccacbabdabcaccbbabccdabccaaccabbcbadbbbcabddbccdadbbbcaadabdcccdcdaaacadadbdacdaaadbadcdcccbbdddddbcacccdadbbdbddddbabbabdaadbaaccdcdbdcdbbdbdcbbcdcdbdabdcbdbcbadbadcdaadcabdabacadcabdacdaaaadbadaaaddddcbbbbacccccabdacbbccdacadbacdcacacbddcacadbbabccddccaaadbacdcbcadcccccabbaaaacadbbcacccbdcbdbddabcaadabcccabbbcbacdbcbacdcdbadaacdcaacbabcaabccabaccddbccdbdbbaccacacddaaaadbdaabbdcacadadcaccaabcaadbcddcacccbababadbaaacdacabddcadcadbddbaddcaacddacabcddcdddcbdcbdddcdaaadadcbdadaccdddbbccadcadccbcdbacdcbcacbccbbbaddbaccdaaacbddbcaabdaaabacbacdaddaabccdcdacccdabaccbbaaacdbccaccbbbcacdabdbcacdbdcccabddcacbddabacabcaabadcbbbacabbcbacaabbddadcadcadddccbcabbadbbdbbdabddbdbccdababaabccbacbdaddcccdcbcccdcbaabbcaddacbbcbddbddcbbcabcaacbbbcacacaddabacbdbccaacbbcdbdddcbcabdcabaadabbabdcbacddbddabbbcdbbdbacbdbcaaaaadcccccdabbaaaabccbaaddcadbbbdadcdcbadadcabbaccbadabdbabbcabacccddaabdcdaabbbbbccbdaacacccaaadcbccbbdaaacdcbccdcdbbccbcdccdcbadbdaccacbcadbcaaabccabbcacdcbaaddababaaccbacbbcddcddbabbdaccbdbcbbccbbdacaaabadadcbaadccbcaaabadbdacacbdccdcaddbbdcabbdddbaadbadcbbadbbabaabcdaabbdbcaddcadbcabaabdaaaaddcbdadbbdbcbdcabcccbdddddbdddbbbcdcddbddadaacaacaacabcabcbacbbadcacaccbccbbdaadaaddaacbdbcacdabadbbdcdaaaacabbbadacabcdddadbacabccadccacbcbbbcabcdbacddcdcabbababccabacadacdaaadddbbddabcdccadcdacacacabbadcadaabbbcbbbcbbcacdbdadadaabdbcdddcdadbcccaaadbccaadccaaddcddbadccbdabcbadbbacdcbaacdbccdcccdcbaddaabaddbbdacccadbdbabbdbdabcaadadabdbbbbdcdcaabcbddacdbcdcbcabdbabcbbcacaabdaacaadaacabbadabbabbcdccabcadadbbdbdccdcbcaaadcbdddcabbccdacaacaacadddcbaadadaacddbadbccddcbccccbccadbbbbccdaadaacccbaaccdccaaccdabdccdccbdbdbcccabacbccbabdacbaabdccdcadccaaadddcbacddbcacdababdcaddcdbccaacbcdadccddbaaacaacacbdaaabcdbcabbabdabbcdcdcdbacbbccacadcddbbcddcbccabaddbbaadcbcddacdbbccbbbcacdabdbabbabaaccaddaccbaaddaadacadadddccdbcacbdaaccddcaabacbbadabbbacddcaadaaddbdbadadbabcbaabbcaacababdccadaccdbdacbcbcabbcbbadcbdbccdcaabadccdbacccbbcaccadcdbbaadaccdaddbaadaabcabbddacacbbdcdabcdbcdcbbdcaabcbddccbcddaabbcccccbddbdccaaccbdbaddbacbbbdddadbdababdddacccdacdbcabaccdaddcbdcdbcabbbbdacdaaaadaaacdbcaddcbaaccaaabcddcacccadccdcdcaadacdccadadadadbdaacbbdaabbbcbdcaacdcaaaacbbadcbcbcbabbacddcabaaaabbddccbaacdcadbdddaacbdbaddbdcdbbbbacdbaccdcccdaccaaabcccadbdbaaaaadbddbacbcadbccdccabcdddcacccbabdacbdababdcccaaccacdaadbdaccaabbdabbbdcaacbdbbabaadccbaaabcdddabdcdcccbacdbacabbaccbcdcbccbdabbbdabdbdbababbacadbbcdbbabddccbddcaaabcbbddccccabaabadcbaaacbdbaddcbbddbdbcdcdcaaadcbcabbbbbacdcdcccaacabdddadddaabcddbcadabcbbabcabdaddcbabbbbdcbacacbadcbaddddccdbadabbadccdcccbddaccbdddcadcbabcbcabddbdcddccdcbcccabccdacdbbbdddbbacbaacdacadddbbdadacdadbcdbccccabacdcacacacaccdbacbaccdaaadddcccdbbbcabbacacccbccbabcdbcbcbbaacbbdcbcdacbdbdbadcdcbaaadadaccdccdbdaddcaaccbaadbacadaacdcbddaccddbcdacdaadbddddcbdbbdbdadabaadaabaddacddacbaabaccbdcdcbcdbdbcdadcadabdaddbadbacbccadacbaddbbdaddddaaccbadcbcabaccaabbcdbbdbadabdbdcadaacbabaddcdbdccbdadbdbcbbccacadbcbbbadbdaddbbccbdbdbbbababbccdcdbcdababcadabaaacdddbddbbbccdcbdcbcabbcddccbcbdbcbbcdaccbddcbdbbbdabbacdccbddadcaadbbdddbbcadadabcbcbdbaddbabcacdcdaccdbdacabddbdacacdadbaabdbacdddabcdbbadbbbbdcaaccbdaabdcdbbdadbddcbbbcbaddbdbbadbcaccdcabaccbcbacadbcacbacababacbbddcdaabccdddaacacdcaccddacbdbccdbdcabaadcdddbdddcaccadddbdbddcddccccdbccaaccaacdcdbcacbdccccaaddbbabdcbcdcaccddcbcbabbadbabcdcabbadcbadcdcbbadbcccbccbdccbbcbcddcccdcbdadbadbbccdccbcbbacbadbbdadaadabdddbababbadcbcdddcabaadaadbccabbbdacccdbccaacbcdbccabdaddcccaccacdacadaabdaacacdabcdbaadbbcacbcbbacadbccccbbccbbccaaabccccbacabbadbbddbaccaabcbbddcacacabadcbbacbaddbccbdaadcabbaaaadbddbadcbcaaaacabdbbdbbbdbccbddbadbadddacacadcbdcbdaabadcdaabdcacbaaaddcacaacdaadbcadcacbaadbbdbccadacbdcaaacadacdabbbdccddddbaddcdcbdbdbabccdaacacacaccbbadbbdcddabbdbabcacabcbaadbdcbaddadcdacdbdaadcbdcaaaabdbadcbdabbccbcbbacadbacacbddadbadccdcdcacbbadacbadbaccabbdcabcdbabcdbdddccccdcaddcddddcddbcddbdcdbcbdccabcbddaacdbaaddddacccbbcbaadabacbacbcdbcbabdbbcbacadcbdcbdbdaadbacabdbababacdbbcbcacddbdbacaadacbddabccccbaccdbddcaabdbabaadaabdbccdaabaddacdcbdaaadbddcaaaddbcdadaddccbadadacaabddbbbdbcdccaadaabbbbdacabcbcccabccbcccddcdaaadaabccdcaadbcdbbdbdbbbdcddddaaacabacbcbbadbbbadabbdcdbbcbcdccbcabccaadbbabcacababddabcadbccbbdcdbaddbaddbadccccbbabaccdcbdbccdbbddcbbdaaddbaacddbcdbbbddbdbbaadcdadaaccdbcbaabdddbcbaabccdbbaadcbdbaccddbcaccccbaacadaaabcacadbacdadabdddcbbdbaadbccadccbadccbbbacbabdbbabbaadcdcacbbcadbddccadacddcdccadccddbdacadbbdbcabbacddaadbacaacdaaddcddabbbcaabdaccbadbcbbacdaadddacadcbabcdddcadbcdcaaccdbbcdaadacbdbccbcaabbddbdcddccbbabdccdccabdcadbadadbbdddadbbddadbdabbbaacadaabbadaaadccdcbdddcadbcbcbbcabccdcdcdcaabdcbddcbaadddddcabdcabbdcddcdcdbaccbbdbaabddbbddcccdbddbaaddcdcdbbdbcdadbbbbbaccdbabbddcacddbbdcbccbcdaddbaacbacbdaddcdbdadddddbbccadcdaadadbcacbadcaabaaaadadaaacbbbbbdcaacaddcdcddcaacdcdadaadcccbcdcccbdadddbabcdbcdddcddbbabbcadccadaddabbdacdcbcbbadccbcbdbabcbdcddbbaabcbdaabbdbddbbdaaabdabdcddcaaabddccccdabcadcabdbbcbbbbccdcbbbbbbccbcbabdbadbabbccbccbaadaadcacbccbacccbddbcccbcdcddacdddcbdadabacbaccabcababaccdcdbcdbcdccdaddccddbcacdcdcadcabdcbacbbadabadcdcbcdcddbabbacdbaddabdddbcccbccbabbcadcdbbadbabddcbacddccadabcaaaabbcabdbccdacaabdbbddaabbccbadcdacddccbabbcababbdaaacbdcadbdacbcbbaddbcbdadadbabcddbbcaaacdccddbbbddddbbabbdbcbdbbccdaccacdbddcbddacadddccbdddacaddcaabbbddddbddadbdacdddcacacacbbcbaacbabbdabdbbccabccbdacbdddaddaadbabcadcdaacdcababdacddbcbdabbcddbabdbdbacdcbdddbabddcdaabbacdaadaddcaabacacbaacdbbdacbbaabddcddaaadcdaabccacabbcddccbcadbcdbcadaaaabcbabaaaacbcdcabbadcaddddcbbbcaaddcdbbcccccbadcddbadcbbddbdaaacdbadcdddcaccccdacddbdddccddcddbddbddbdaaaddbcccdcaccdcddbbdcaddacdcbcadabbbdaccaaddddabbdbccbadaaccbcddaaadbacbddabcbaadbdcaadccbbdaadabbadbadcdacaaadabddabbbbcacccbabaccbccdbdabcdadbcabbcbdbdbbaadddacbcccbcdadbaabccabbbbddadcbacbccdbababdddbdaaaadababdbcdddcccccaccbdacbcddabcbddbadadbdacacbbccbdbbbdabadddccbaddabacadaacdbbabadddadbabdbcaccddcdcadabdbaddbbbddaccbadcaabccdccdabdabbadcabbaacdacbddaddaddbadacadbaaadbddbbdcacbcbcdadcdddabddaddabbacbccaddaccdbbcabdababbbdddbaabdccdcabdcabaddcdadbcababcabdcbababcddddaddccdcaadcacabadaaacccccaadadbcbadaccadcdabddbccadcdccacbdcbaacbbcbbbabcbdaadcabdbcbdddaddaacdcdcabbccdbdcbdcacbdbbdcabaaabdbccdbcacaaddbdacbaabdacdcdddadadcaccbbcddcbdacdccabcabcacaccbbaccaccdbbcbbbcbbcaadaaaabcdaaaabdbcdcccacabddddcacdbdadadcdbbdbbabdbcbadcbcadabaddcbdaccadaddbcdadbcadaacdcddbccabababacbabdcbaadacbcaacdbadabaaacdadbaaaabddaddbbbbddadaabdccaacbaddccdaadbbdadbdddcbabbbddcaccdabaccdbbbaabbaaabddcbddbabcbabbcccadabdccccdbacaadcbccccccababcdaddcadbbaddddabccadaadabadcbdbdbdcdabbacaddbbbaaadaccbbbbbdacbdaabbccdccadddabbdabbccdddcccaadcbccaaddbbbcaddbdaaabdbbaddbbddaadbbcbccaddacbacdbbcbacbdcbacdbdadddbbdacacacccbaadbddcaacdadbacdcddcabaabadadccdcbccbdacaaabbabccabbcbcabcbddbaadabdbdddaddccabdcaadaaacddbcbdddcaabdcbbcadbcdacdbddbcddcdadccdcaddbdacdcdcdbaacdbadcbdaabcabcbcddccaadcdbbcabaacddbdaddcadbddcacdbccadabdcbcabbdabbcbcbaacadbbaabbccbcbbbadcadabccccccdccbabcacaaddbdacdbddcdadcbbbcadbbcbaabbacbbbdcccbacbaccdbdcdbdcdcbaaadacdcababbabcbcddabdbdbdcaabdcabbcdcaacaacddccaddacaabaaaaccdbbbaadccaaddbbbcaaddddabbcbddcadabddacdbdcccbcabdcabcbacddcdcdbadcbcccbcaabccbdccababbbdccccccaaabaabdbbdadbddcbbdbbbbacaaadadddcbabbcabbcabacbddbdbdcbdacbabadbcbaabbcbaddcdbadccabaaaabadbabbbbbbaddbbdcdabbcdccbdcbbddbcdbcddabcadbdcaacabcbadddcadabadaaabdacbdbdadbdbaaaadacddcdadbdcbbcbacaaaacbbbcbdadaaddddcbcdaadccccbddacbdacabdccccaddadbaaaaadddabaccbcdddaccdccdcbdbaacbaadbcacbcbbbbbbacbabbccabdbaccadcbcbacbabbdaccdcaddbbacddacabaabcbbacaabcbdcdbbcaaabcdbcbbdaabadcaccdaacbabccadcbaacacacbbaabdbbdcdabadddadbdbcddbdcdadabdccdaabcdbaabcbaabbbccadddddbadbcdcbcabbbdcacddcbdcacaabdddabcaccaddacdcbbcdbcbacacbdcddcaabaacacccdaaabadaadbbacdcacddbcbbbdcacadcabdacdbbdaacacbcdacabdcccacdacacaabdabcddbcadcdaadadbbadcaddcdbcbaddbacbccbabddbdaacdaaacaacccacbadaabaaaadaaacdbdabdcaccbbdcdadbbddcadbdabdacdaaacdcbcabdcdbadbcdacddaacddabdadbacbaccccadcccbdddbdbabaadddccbbccaadaadbccadcaddaabcbabdabbaddbaadbabacbccbdadbaaaacccbadcddbdcbcddaccadadcbccdcaadacdbadbddbaadcaabcdbcaddcaccbccbdabaabaddbdaabcaaddabcdabddcacdadccbdabbdadaddacbabdcbcbadadabcadbadccbacaccccbbcbccacadbcdabcdcbcaacdcdbbabbdcaccbbdbcabacbbcbccbdbbdddadacbbbcaabaabcaacaaadaaaaabaaababdaaadcadadaadabdbacbaddcadbabcaadbddcbaaadbdadccaaddccabddbbcadbdcaaaacccbcbbdddccaddacdabbadccccaddddabbcabcabccccddcadcbabcdcdbccddcdcbdcbbdbbdbacdaaddbacccddbdabddccbabbadddcdbbadbdcdacaababbbdcaaddcccbbdbdbaccbdcabdcbddcaccdddcabcdbbaaadbdbaccdcdcbabaabbccdbacabbdbbddcccaccdbcbbdcdbcadbdccaabbdacaadadaaaccabdccdacbdbcadaaaabdabbcdbbdbcdbbccdcccbbaaaacdabddcbcbdaaacaaabbabdaadccadcddcbadabbdababadbadbbcbbdcbbcabcdcdadcaccdbdbcaabbdbcbdcbbbaddbbbbdaccddbadaacdddcdddcccacbacddcacdadcbcadcdadccdaadabbccbddaabaabccabcbdcaabacabdccdaabacbccccccbbabddacbcadccddbcddcddcbcbccbccabcbddacddcbbdbadddbadadbaacabadccddbacccbbbdcbdbcdbbbdddccbaacdbcacadacaadbdddbdbbacbacbbcaabcbbdbbddcdcabaacddaddbdcbdddbadccabcdcaaabaccdcadabccabdadcdadbbdadbcaaddbdcbcbbcdbabdbadabdbbdaabbbbccaaacaccbdbcccdcbdcbdaabddabddadadcbcaabaddcddbabccdadadccbdddadccbbbdacdbcdadcccdcaaababaaadddcdbcaaababcdbbdacddbdcacabbcbddaccbaabadddcacbaadbcdbacaacbbbccccbabcbbccbcdcbdbababbdbbbaacaddcdbacdcbcdcdbdcadadabbcccacabcbacadaacbbbdbadcabbddaaaddcaddbdccbcbcdbadbcabdaddcbbcbdbddcbaccbabbcaddccddbbabbdbcbbddbcdbacbaddcdcbddaddbbbbadbcbbcabcdcccddbbbbaacacbbcaabbdbbdbbcbcabcbacbbdaabdbaaacbadbcdacccacbddcdbdcbadcddddbbacdbcddabbcbdcbddbcccaacaabcbcbaadcccccdabdabcdaaabbccabdbdaadbdcdbbaddbcaaccddbbcbccbdadcdaadcbccccdaddcabcdddcabbbdddccdabccbbbacbbdbabadbbcaadabadbcbaccabbcdabccbcadccacbabcdcdcdcaacabcaabbdacbaacbbcdbcbcdacbabcbdcdabddcdcdbabccbcdbcdcaddcccabaacabccdcbbbbbbaacbbcbaacbcacdcbcdbccbdccbabacbabdbbbdacbdcdacbbccbbaaadbbdbdaabadcddaacabdadcadcdcddadccccacdbaabcbcbbcdabccbcddcdccdccaaadcdaaccaadcaaaabbbadbcddbadababbddcccdbdbcdcacdadaddcbbcaabadaabbbaadbbbabbbccbddcdaadbbcddadabadacabddaaadcbbbddbccbadccadababbacaadaacbcbbadacbcdbbaadbbbaabbccdaccbcbccbaabaaacaaccddddccddabbaccbdcadbadabdcadbdcaadcbddddbaadbccbbcabddcbadbddaadbdddcdbbbbcaddcddaccdaaaaadcbaacbadaadaadbccbaddcaaccbadbbabdbdcddccddcdaddbdcdddbdddccacbbbbbdadbbaaaccbdccccddcdddbaadcdbacbababbbdcdddaaccbddcddaccbbbacbdcacbcdcbadbadcbaabdacaccdadbadcbdccdcacaadacddadcbcdbbcddbdccaccaabbccacaddadcabbbdbabbddaaadaacbbcbcbccdddbbbddcabbabaddcbacabcacaadccbaabacccdcbcdcbaabcbdbbbacbcdbadadbabbbdadadbbddccdcbaaabdcccabbdaddcccbbabbbabdcdacdddabdbcabbccadcdcacbcbdccddcdaacbcbddbaaadaccdcaabbbccddccbdaaaacabddcdbcaccdbaccccacddcadcbbcdadcdbbcbbdcccacbacbccabaabdcaaaacacccadcdaccdbdaaccacadbcbdcbadcdcbcadaccbcaddcbbdaccadddbcaadcacdabdbaccdbadaaaadcacddaadcdacaccddccccdcaabcbbbbddacbcdbbdcbdbddadcdddabbdaaccadaabbccddccadabbdacdddbacdcdbdcaacddadadbdbadcdadcbdcabdaaaaaacbbbdbdcacadbbbccdbcbbbcbbbabadadcacbcaabcbadcdabaacacadaaabbdaddaddabcdcaacaacdbbcbacddcddbacabbdabcddbbddcbaabbaadcaccaabdbcbdaabcbdabddabdbdbdccdaabbdcdacbdabdddabbcabaacaaabdadadaddadcdbddaadbaaabbacaadcaddacddacccdaabadbabbdcccbabbbcadabdaacaabbddacbbdbaadbaddbacbdbdcbaacbabdbabbdadadbaacadccdcbcacdccdccaadcddaacbacabdacddbbdaaabbbbdccdccabacdacacbcccabacadbbdbacbdaaddcbcdabdacbcdadddcbdaaabbccdbbaaccadacddacdbaadbbddaaaababbcdcbdbcdcbdcadadaaaadcdadbadabaacaccdaabdcbabbdcdbcaabddddacdcccdcccadccdbacddaacdbaaccccadcadddacdcdbbbaabadbbcdacacdddadddbdcacddbbbdbacabbcabadbcdbdbcabbcadadbdcadbdababdabbddaacbccdbcadbbaacabdabbcbddcdaacbcccddadbcdcbbaabadbcdbdbadddadacccccbabddaaddaadcdadcbbbbdabcbbcdbbbbdbbdccaabcaabadbaacdddaabccdcbbcdabacaddbcabcabdbcdbccbcbdbdbddaadddcbadaabacddbabcbabccabcabbddaadcddbddbbbbbccadccaddcbbacbdcbbbcabbcdcbabcbbcbcadbaccdccababddcbdbdadccbbacddabdaabaaccbdcbabacaccdadbddbaaaacbcadccdddcddcaadbdcbcccdccdcbabdacdcadccbaaddcbbcaaabdcccbacaabbdddbdbdbcccbacaabcacddacabddbaaaabcbacaccdbaccaddadabbccacaaccdcdcaaccddbaccbacbddbacbacaacbddbadbcaabbaadbaaadacaccdbddbacdddacbdacccadadabdcddbaababbadbaacdddabcbccadcdabdbcdbddcdbcdbabddbcadbadadddaabcabdcbbccbbbddabbbaacdcacadabbdbbaaccaacabdabbdbbcdaabbdbabdbdcbaadbacbdaaacadbabcbabadaddccdbdcdccddabbdcbbbabbacabadaccbcbabacabdabbcbbadcaaabacdbaacbdbbccdcdccdcbacacdddcbabadcabaabbbaabbddaddbbdcacaacdbbdacabcdcadaccaabaadcbacbababcaaccdcbaacddbbabacdadacaddadaacadbaacccdcaccdabaaabbaacbcddacacbabbabcbcaaacdaddacbaaccadbbbdadcccdbcaccabddaccbddcbcabbddacdcbbbcacbdadbdbbacadcaadddbaddcaabccacacadabcaddaadcbacdbdabdddbacaddddadcdaadcbdbbcdcaabcccbdcbabdddcbababdbbbdbcddadddacbbcdbacbbcdaaaaabadbddbbaccdbacabacbabbcbdcbdbcdacdacadbbbacaabdaacbdabdddbbbccadaddcddcabbdaaddabaacdbabcddcadbddcadcacdbbddcdcdcacdaddadbbbdcadcbdaaaacbacbabdbaacdbacbaadababbbbbbcdbbcabcabbaadadabbbccbdbbabcbdbcbacbcbbcdcbaaaccdccbcadadcbddcbabbadcadddcbaacaadbcdbbadddaadabbcaaacabddaacccdadddaaabdacddddbcdabacddbbbaccbabaccdcdcbcabbdbaaacacbaaddccacbbbccdcacdddcdacaaddcdaabcdbdddcaabbccacbcbaabbcabbdcbbaccdabbcbdbcacbcabbabdccbddccaccbdbbddadbabdbbbadadcbdacbabdbcaccaadabbcacbbbacababacadccddacadbdbdbdbbacbcdddbaddadcaadabadaaddbdaacacbbbcbabcaacadcdaaacadcbcccccdcabacadbdacaabcbdccddabaddcdbaacbbdbadbdccbacbdcbddacbbbdabcbbacdacdbbaaddbbabbadadabaddcbdddcadccbbccaddcdaddcaaacbddadadabacdcadccdabadbaacdaacbddaddbabaddccdbdcbcadcbdaabbbadabacdbccddaccddabccaddcddaabadbaccddabacbdbcdabbcdbdcbbacadcbdaddacdabbddcccbdcadadadcdadbcbcaaabbdacdaccacddccccbbcabbaacdcbcbaadcbaaddcddacbbaaddabdabcaddcbbbcddcdbadbdaacbdaabcbdccdddbaadbabbdaaabaadacacdcccacbdbaddccbdcbcdacddaadacacdaddccabbaabddcadcbbabbbadbbbbdadddbdbbccdbabacdccddddddcbccabbdddcbaddccdcdbabbcbaabadaccddbbcbbcdacbccccacccbabcdacccdbaccdcabcdaadbabdbddbbbbaabddbbcbdaaddccadacbbdbaabccaabdcadacbadcddcacadaaadcdcdacbcccadccccdabbabcdcccbbcadbacacdcbadaaddbbdbacdacadcaccacccbacccabcaacabcbcccaaaaaaccbacddccdcaadacdcabaaacdbddaabbbccbcbcdadcaaacddadbabbabcddadbaacacddcadcbcacacaabacaccaabddcdcccadcdcbbcddbbcddbcdacbbcbddadabdbddddcbbcadcdbbdadbaccdddcbccacadcbbdadbdbaabadbbadcbdbdccdaccdacdcccbabcbbccbdccbbbccdabcccbcaabcccbcacacbdcacbcbccacadbcdcacabcccdadbddccdbbbbabadccaaccbbbccccdaabccddadcaccdadbabaddacacccbddbcbcbbabaaccdbacaaccbadcbcdaadbdaababccbddaacabbbdabacacbbadcacbabcdacdaadcddaabcaabdcddcadbacccaabcbbbdcaabcadcbcabcacabccdcdcbbcbbabcabdbdaddaddadbcbdddccccdaadbddccddccaaacdacdbbbdccccaaadaddbaddbcbbbcbabdcbbdaabbcddadcaadababacbcabdbbaccbaddaccdbacbbababcccdabdadbcdacdbccadcbdabadaabdcbcdcbdaaaccbacabaadbdcbddabaaabcbcbabdcdaccdaabdccdddbaabdddacbddcadccdadbacddcdbaacbaacdabbbccdbdcabdcabbdcdbdabcaddadcccbcbdccbcadcbacaddaccaabbdabbabaabcbcdbaddcacaccbcccbdccaacdadbdabacabaaddabaccbcdabccadadbbccdbaabbcbccdaadbbbabaccbaaddcdadbdcbdddacaddaacacbdbcabdcacaadaaccbaacadaccbaccadbabdababcabdbbcbdcacbdbbabbdbadcdcabbdcbddbdddbdabaabbbcdabbdaabdbacdccaccdcadbddddcbcddaacabaaadcaaccdabaccdbbdbbdabbacacbdccdbdbcbddbcdccabdddcdcdaabcadcacdcabbdcccdbbcadddadbcbcbabbddbdbbdabcbabcadbbcbacddbccbbabbbbabadbacaccdcabdcabcdddcbbbcbbdadabbadbbbbdbaadcdcbbbdcddbddcabdddadacacdbbdbbbadabdaaaacdcbcbbbbdbdbbdacbbbccabbcbaabcdaddccdccaddbcaadaabccbbcbadbbcdabcbdaddddabdcbaabccbbbbdbbaaabdbbbdcdcbaabcddcadabcdcbcddacdacacbbacadbcdabccdcbcdcbdacbcdccdabbbbbaadbbcbabccdabdadadaddbddbcdcdacccbbadbdbbcccdcbdbcabdcacacdbbddccbcdabcbadabcbacccbccdabaaaccddccacdcdacaabdaaabdbacbcccabdbddbaabbbcdbbbaccddadccaabaadbacbdadcbdaadaaccaabadaddbbcacdadaaacdaababdcaadbbcdcdcdcdcbabacabcdcabddadbacaccbdbdbdbcdddcadbcbcddcadacbacabcbbcaaacdbabbdacdbdbbabcabccaabadddaaaadcbbbdcabbacddabdbadbbdaacdbddabbcbddbbccacdaadaacdcbabbaaaddcadcbcbcbcadabdcdcdbabbcbaabcbbadcbaaadbddcaadbbdadaccbbbddcacadbdbdcddadacaacbaaabababccadddaaddacdbaabcbcbccbdadccbbdcccdbadcbcaacccbdddcbaaadabdbcbcbdbcccadcaabcacdbbbdccaccacaaabcdacdadadacbbbadcddabccdcabacbdcdcaabccbadcddadccccccdbdcbabbbcddbcdbddbbddaccddaacbaaacccbabdbccdbacacbaabccdadbcabdbcbaccccbbabcdbdbaadaddabdaddcacdbbaaddadbcbadcddcaadadaaaccddbcbaadaaddcdcccccccabdddaaadaaabcbabcabccbbabacbdbcbadbddacabbbdcbdabbababaababccdabcbaddcbcaabcaabddbbbaacbdbcaacddaddadbabcaaaacababdcacbcdddadacaabaadabbbdbbbadccdaccdaadcabdcbccdbcbdddddcadddabddadbdccbdbddcabbbcccadddadabddacababdcacaadacbccdbabdadcacbcdcadbacbcbdcbdddcaacbccbbabacacbcdcddbbaadaabdbdabdbaccadaacabbadabcdaaabbabcccaccccdaccdbdddcdcaadacccdacacabcdacbababbacadcdbdcbabdcddbbbbbcbbbadbbdadcdbccdcbbaaccbaabbbccdcbcbdcbadddccbbacbbddaabdabdcdcadccdddcbabbabdcbdcdbcbddabdacacdaabaddbcacaadadacdbddbddbabadbcdaabdbcccacdcadbbaaccdaaacaaacbdbdccdccaaadaccccaadddcccbbaddacdbdbbbdadabaddcadbcdcbdabadadbbdbcdbcdcabbcadbdacddbdcbbdcadbababccdcacddccbccbcccbcccdaabddaaddbdcbdacddcbbaaadbdabadbaaaabadbbbcbadbbadababaddcbccddcdbbabcadddcacdcbddadddbbdbbbbadccbdbccccaddcacbdbdaccbbcdbaabacbacddbaccabbcbdaddacdbdbbbcddccdaadabaacdddcdddcbcaacbbdbbabddddabbcddbccadaccadcbbaddbbbccaaabaababacbcbdacdddaadcbbadabcbcdbacabbdabbcddbdbabadbccbbacdccbabbadccabbbbbbccaddadccabacdadbdcbdcbcdddadacbbcababcdbcbaaccadddcacacbabddcbacbabdcccaaacbaabdccacbdbbddbabdacaabaadcbaddbbcccccaabcbcbdaaaaaabdbdabbaccdbaddbbdbccadadaccbabdcaaaccbcdabacbcbcbbccbaddcabcbacadabbddbbbdcdabacdccdbbdaacbdbdbcbbbcaaababbcbabadadbdcacdcbadcadddcadaadcadbcbccabacdbbaddddcaacacdddccdccabcbbdacbdcdbcbacadacdbcbbaddacdbbddbcdacbbadacbaacccccbcaacabbaadaadcbdadcbddadcbcdcdcabccbabdccdbbddbccbabbbcabbcbbaaaaddabbccadddbaaadcddaccabbddccdcadabaccbddadbabcacddccacdbbcdadacbdaacacbbbdcbcdaddbdbbbdbaadaaadaaccbbccbccdaccbaccdccdddccabdddadbcddcaaaadcadabdbcccabdbcdddcbbabcdcccdbbbcacdabdbaccdabcdabcaaabacacabcdbbaddaacdbbbcdabccaddbbdabacddcbbbadddabbacadcaadcbaacccdaaabdbcdcdcabddccbcddcddcbdacbcbabbcbcbabcdcadbcacdbdcabcaaaabbdabbadbaabacabdacabbdcaacdadaadddbbadccdbcdbdbbbbbbcadbbcdddbcbaccccbcddbbdddaaccabadaadcaccbcbdcadacbaccacbcbbaddbbdcdcbdcdbbddbbbcabccbbbbdcddbcbdccbdcbdbdadcbaaccaaccdabdaadaadacbdaacbbabbcccadcacbbabbcaacaaacbcbbacdcbacdaccadacccbdcdbbcadddcbcccadbbdbbaacbadbadbcdcdcddaaddbadadbcacdcccbbabcdaadbadddadccddacdabbbbcadbbbdcdadbbabcdbdaaadbdcbccccaababcdbaabaddabdacacdbaadbacccaaddaddcdccabaddcbbbbddddbccbcbaababcddbcbcddcdbdccdbcbbdacccdadcdbacddcddbddccadbdbbcbdbcbcdcaddbcdcccdddaadcbdcddbbdacadbddadaccdacbbdaadabcbababaadadccacacdbbcddcbbccbaacacabdcbabcccacdcbcbbcdcdacbdcbcdcbabcbbaacdacadddddccbcddadbddcabbacbbacbbacabdbaadbabcbcbdbbacdcbabccabcadbcccadbaccbaabbbaccadacbdbdccdddacbccdbcdacadddbbdababdaabaabdcabcbbcdabcddcdaccbcccadcddadcbcaddbccbdadbdbaccddabaaadcdbbaacacaabbbdadabdabcaddcabbdbbdcaaaabbdacdabaadbbacaddaadccacddcbdbccdacababddbbcddcbcbabcaaaadcaabddcddcabdbdacabcdacbaadbabbacbbbabdcbdccccbcdbddcaadcbcbdaccccddaababacdacbadaadbbcccbbcccdcbdcdabcacbbbaaadacacdcbaddcabbcdaabacbcccbcbbcaddbacaddbcccddcaacbaabcdbbbdccabcbcbbaabddcdbbbdadcbcbbbccbbcdddbdacdcbdbdccddbdaddacdacdccbbdabcbdaaadbabaadddcdaabdacadabbccbabacadacbbdcbcdccdbcdbdbbbdbbdbabaaaadacdadbcbaccaadbbbbcdcbbbbdccdacdbdbcbcdcbbcaaadbbbbabbdbcbbddbaccadbcdabbacabaccdacccdabcddabacccbbcdacdcdddabbbbaacbdbdcdbdddacacaaabbbadadbddcddcdccacccacbdcabcbacadcdcbbcaabcaaabbabdaacbbbbabccdddcddcdababadabacacbbdacddadbbaabcaadddbdcabbabbcbcbadbbdacdbccddcdcbadcbbbddcbbabcdbccadcbcdcaaabbcdbbaaacccbbbbbcabbcbbdcbabbccaccaacababcbbdbcdbcdadcbacacbbccdabcabaadaaabddbdcdbdddbacadbbccbbcaaadbddaaabacadcdcbbbcabcacbbbbdcdcbcabdbacaacbadcbdddcdacadacadcbdbcddadaddcdddccccbbbacaabdbadcccccbbcacbabcbbabccdbccabbaaaadcdbabccbbdacbbabdabcbabacccabdabaadcaaadcdaaddbdabbaabbacabdbaabbbabdbdbcdbcdccbabaabacadbdcdcddabddbdbcacccdcbcdcaccacaacadbdbaaabcdbcabbbabdbbcdbdbddccbacbddbcddaaacadbcacbcdcbdbbccbaabadcbcaabaacbacdabcdcabbdccdccabcbcadbccdcacaacdcadbcddcdccddadadadcaadbdbcbadcdbdccacbabbaddaccdbadcdabbacadabbddbbbbdacacdabdbdaddbbacbbadcaabbdddacbabaadabccaaccaaccabccaadadaaddabbdcdddadcbcabbcdacbbddbdbbcabacbccbbdbccaacccddddbdcbbcccdbbdccacbacacaaaacdcdbddcdbbcbabddcaddcddaaacadccadbcbcabdbcdcbaccaabadaadacbcbdabccbbdccbaabdaabadbcbcabaccbdbcaaabadaccadccbabdabdccacacdcbadbbadbaaadbbddababdabbbbabaabdcbcccadddccdadacdcacadcabaccacbaaacabcadcbddcddadbcadbddcdbbacddaabcadcbaddcabdcaadccdcaadbdbcbbbcdbbdaaadddbabbdaaadbdccabaaddbdcbbacbadcdbacccbcaccbddcadcddcbcadcacdcaaadababddbabbadaaaccaaddabbcbdabaadbbddccadbdccccaaacadbddacadadbabacdbbbbcbabbbababbbabcabcacdbdcbbbdbabbadadbdddaddacdcdaabccabdaaabbdbadaaccbccabddcbabcdbdbccbacacbdacddcdcbbbabddaaabddddadabbaabdacdcbaabddbabacdcaccddbabccdcbaccbdbaaabbcabddbbcaabadbcacbdbdcaabacbbdadbbadabdacbcbadbaddadcabcbdddbcaaababccbbabadcbcbbcabbbbbdabacdaabdaadcabdaddccaabdddabbbbdaadbcbacbbdabcacbdbcbaaadccdabbabcaadaddcaaddabccaaaccbcaabdcdbddcadbdacdbddadbddacbbabcdccacddaadcacbccccdcccbdabccbacdccbadcdbcddbcdadabcbcbadcdadddbbcbbbabbdacdcdbbabcdaadacadcdbcdbabaddcbddaadbadddbacdcbdbcbcacaccbdbdadbaadccbacaddaaabaaaabbabaabbbcbabbcaadbabcdbdcbaccdbacbcaacbddaabccbaabbcccbcdcdddbcadccbcddbabdcabcbbcdcaacbdddaccabbaabccbcbcbaaddacdcadacdbccabadadcbcbdabaabacbdbddbcaadcabbabacddbbdbbdcdbdadacdaaabaaabcbadcbababcbccaabccdbaaacbcbcaccccbbaccbdbcdbcdbbabdbacdababaaaccbbbacdaaccbcdbccbdcbbabdbccdbacdacddbaadbcbcbdbaacabcdcdacaacddaaddbdccdcaabaaaacddaababbacbcddadbdddcbadbbcadbaaacabcdbdbaacaddbbabbccacbdbbdcdcbbbccbdaabadcdcdadcbdbbddcbdabcdbcaadcbcaabdaabbbcabbabadcddadacddadcdbbaacbbdcbdacbcadcbabbcacccbabbbbdbdbcadacbabdcdaadabaaaabcdbdbbbcbcdddcadbacaccdbdbbdbdcbbcadddcabcddccdbbcdabbacdbcbadadcbacccaddcbdbadddddbadbacaacbcbbabbccdbdcadbbacdcabccdcdaabacbdaaabacbadacabaadbaccbbcccbabbbaccabaccdbcddcacbbccbbcddbacbaaacabcccacaabddbaaddcadacbcbaccbcabbbaaaaacdcabcbdccabdadbbccbccaacddddccccbadccddabbbbbbbddcbdbdbaaaaddadaadcdaaaadddaadbcbdacdabcdbbcdaacadbacaacbddbccdcbdccccaabbbcbcacdbdbcaacaacdcdcabddddbbcdbbbcddbdddabbccdbacdabccdbadbbabdbbdddbacdddaaddadaaaddadabcdbadddbcabcadbccdccdaccbabbdcaccbabdaacadaacdbbcbbbddcaabaabcdcacdabbbdcabaabbabdadaaabbdaabcccbdbbadccbaacbbdcdcdabbbabbcdbdcbacdcbaaadcaababadadabbabdcbdbcabcddccdcbdcaaaaadbadcadcbddcdbaabacadddcadccaaadccacbacabbaacbaadacdbaabdbbaadbabbdccddcbcacbdcacdbdbacbdbccbbaabdcccabcdcbddadaaabdcacdbbadadaacdcbbbccdcdcdddcaddbddaddbcacccaadbcbbacdddaabdaddcadddcddcdaababcbbabbbabdbdcabdbcbabaddcbbdbacddcdcdaddaddabcbaadabdccabdaadcbcbdcddabddddcdcacbbbabdabddcddbdbacbddbbcbbacdcaabcaaabcaddbabccdacaddccaaaacdadbdcbdcaaaddaacccacccbbdadadcabcbcbdadbcdabccacbdabaddacccadbcddadbbbaddaabbaaabbdcbbddcacaaabdccacabdabdbdddcacdcabaaaccbdcabbacdddbaaabbccdbbbdbcdcdbddbbddacabbddbbbaacbabcdcbbccbaccbddddabbbcaaacccaccbdaacdbbcddadbdacbadddbddbbdccdcbdddaacaddddbdacabaabbadbdbbbbbbbadbadadbccdccbaacacdadabcabdababbbcabdaccdcbbdcdccdbcccadacbdcbdbdcdbcccdddadcbdcdaaadbccaababbddbbcddbddacbacdcaaacadddccacaabdadacbbbbbaddacadabcdabbcaccadcaadbabddcccddcabcbbbcdcdaddcbbacccdbdccddbcaadbcadccdadcbbbbaddbaabbbdccccadbcddbcbccaacbcabdcdcdcababccaaaddabdcdddbdadcccccdbdbbadaccccaadbccbaddcbccdcbacbbbdcadadaaacbddacbdacdbdbcbdbdbbddccbadcccdaacaddbbcabbbbcddcbaadaabaacbcbddaccabdddacadbcadcdddcdaadbdcbbddbcabccdbadbbabcbddbaccbcccbacbbbabadcbbabdddabdcdccbbbdbaabacabbbcacbcbaacdaaacbddcbabbcadcaabdaacddacaccbadadbbdcabbcbacddadabdacacabadcdabadbbcadaacccddbcaddabaccdbbbbdbcdbcdacadcddabdacbaaadcbadddcdccdadbadbcadbddacdabbcdadbbdbbccdbbcccccdadcaccdabdacdabccddbabcacbdbadabcbadacbabcacadaadbabadacdcabbaadcbbadbadbbccdcaddadcdbdcbbcccbcbcbdcabccbabbbdabdabacacadbccdcaacadbbdaccababacabcbddabaddcadaaadbbdacbdddcabccacaccdbbccccddcccbdcbaadaddbdbbcacaaddcdbcdbcaadcddbdccddcbaabcdcdaaaddbdaadadcddcccbaaaabacaabaacdcaddabccaaadbabdccbcbacababdbdcdaaaacdbddccdbadaabbbcddcadbddbbcccacadbdbbaabbcaddbbcacbcbcaccbcabbbbbdcacddaacbadcdcadcdadacdcdcbccadabcacdaaaabbdcaccacccaccadccddaddddbcbcadccdcccdaabacbdadbbdbbbddbaaddaddccacababbdccacdcbbddbbdabacddbdcccdbadaaabcdccdbbcbdbcabdcaaabdddcbaabcddabacbdacbcaaabdbcdcdadadcbbabcdaacdbdabcccdcacbacabacabdcbbaaabacbbbabccbcaddbcbadbbaddcaadacccdadaccabadbbaddacbcbabbbcdcabdadbbdccacddbacdddabaccaccabdadcccccbbdaacddaabcaddbbbdbcbcccbacbaacccadbbadacaadaabccadbdcdccbbccaddbacccdacbddabccbacbbcdbdbcddbaaacbcbadbbdaacbcaddacdbccbbabaadbcbdabbcdbdabccbaaababdaaadddbcdcbdcadbaccdddbdcddcbabdabddbadcbcacabbcccbcbaaaaacabbdaabbbcabccaaddcabddacacbddcdaaccaccccbbcabbaabcbbcabddabdbbcadbdacabadccbcbcaacdabdaadacaabcbaddbbcaadaabcddaacaadababbdaddaccbdccdddacdbbaaabdcddcaaadccdbcbbdabddaabbbcbbcdacbdbbcdaacbbddbbbbbcbbcaaddabaccbadcaaddcabaaacdcaabaabadcabdabccadddcaadbaaccbabacdacabadababacdccabdccbbcdddcbbdbbacddcabcddbdaaadcdbbdacddadbdcdccdacbabbdccdcbaacdaadbbbccdbbcaacbdacabdddadcadbbbdbdbabdcadabcbaaccadbdcdcdcdcbdababdaaaacdddcddccaaacdbbdbbcdcabacaddcadcccaaabbdddbbcaabcbccaacdacabccbbdacabbdcaccbdcbcdbdabacddaaccaddbbacbdbcbbadcdaaabababdccacadabbaaabcdddcbdaaabadadcabccbaacdcaccaabcdacbbcbbccdbbadbddabbdaabcdbbbbabdddcacadddaacabcdbbadcdbbdaaddabddcacacbcaccccabbdccddcacadcbdccbbdaaacacdcdbcbbacadbdbaaabadcddbddbbaacaacadbcdbabcddbcdacbadddcacddabcdacbaddcccbdccbbabbabdadbddcbacaccdcbcbbddddcdddbcddabdaccabbdbcddcbabbdcdddabdccbbdbdcadddbdacccdbaadbbcbbabccbdbaabadacdcbabccbddcbddacbaaabababaaaacbbdcbdaabcbdacbcdccbcdaccabbaccdcdacbacbcadbbcabbdaabdbcdabdbcbcdcdbdccdaabddcbddabbabaaaaadbcddbdaaaadacadcbdaaacacddcdaacaaaabdbadbcdbddddbbcdcdccddacbcbbcacaadadcbabcddbadbbddbacbddadddcaaccbccbddabcdacbdabaddacccbddddcdbbabbdacabcadcadbcddccacadabacaaaddcbcdbcdaddcdcbbbdbbdcbbdcadabcdcbabcbcdddbcacbbacdbdbdbbcacddbbbcbddbcbabddcdabbcacddcacadaddbdbbddcbbcbaccbabcaacbabbbaddcdacaccbcdacccbbdadcdcaaaabcdbcdaabaababbdbddcdbbbdbabcdbcbdccbaaccadddabaddadbcbccccbaabccdaadbabdcaabbbbcbcbcccddbabdccbadcddcddddabcbaddbacacbcadbbaddddabcadcabbcbabadbdaddbbcddcddbdadcacbabbbbabcdcaabdadadccdcdbccdaddadacacabccbccccadbadacddddddacbabdbabbacccbddaacbaadddabbcdcabbcbbacdaccbabdcbcbababcbdddbbdcdbdabcacbcbaadbcdccacdcdcdacbcdbdbcdcbdddaabacaaacdbbbacabccacaabacdbacbabccaaababcdcddccbddbcaaadcaddabacaccaccaccccbddbbcbaacaacbbccaccbbccbadbaadbcccadadcbdaababcbabdccdadcddbcccbcabcbaddcdcbdadadddcbbcbbcdacddabcddacbabdacdabcacbccaddccbabdbadcdbabbbbcabcaccddcbadbcbaddbdcacbdbdccdadacbdaacdbcbbababccaccabbbbdddcacdbccbaacbdbdaaaaadbdaddabaabadbabcbbaccbdacaccadcccdacbbdaacacaddbbababaacdbbbcdccadaadbdabbabdaadbdcbacccbbddcdcbbdcabcacdaacaaaabcdddbadadabcbaadbbbbacccaacbccbbdaabcaabadbacdadaaaacdccddabcbbadbcdccdacdbccadddbcbcccbdacdacaadddbdbddbacdbbcacabcdcddabaccbabadbcbacdbbadcbcbabddcddcaaaddbaacdcbbaddbbabacbbadbaabaacaccabdccadcddacddabdddccacbdbbbbbbddadbcbcbccbcbdcadcddbbdcadaddbcabddaaabcccccddbacaabbdbcdcbabdadccdbcaaabddababbcacdbcbaccddadccbcabbcaadbbacbddcdccabbaaaaabbcaaacadcdcbacdadbbabcbaaddaaccabadcccccdddcbdcdabccaacbbacaadcdbcddcdababaaddcccddaadabcbddadcddddcdcaccbcbaddabcadcbabadbadcccadccdcccbacbaabaabcdcacdbbaacdcdbabaddcdcaaaacbdacdcaabdddbcbabbdbcccadddaccbcabdcacbdaadcdbdbadadacadcdbcdadbccdabbdbaabbcaadbabbabbddbbbcaabccbcdcbbbaaadabccccabbcaaaccbdadadcabacbdabacbddcccbadbabdddbadaacbacabaabdcdbbbacacbdcaabbdadbbcbaddddcbcbcadcbcacdbbddbccdaabbccbbbacbbbbababdddbacdaabccabbbabddddcddacbcbaaaddcabdaddabbdbdcbdcadcbdbcaacdabcbaddcadbdccbdccbcaacddadddcbacbadbacbccadcabaddaaaccaddadcdcbccbacacaddcadbcdddbcadbbaccbbcaadadaadcdcadcacadddcdbcbbcbbbabcabdacdaacbcbaddabaacabcdcabbacbbcbbcabcbcccddccdacabdddadabdbcadadccbdbbbabadcabdacdaabbdbdadadcbbdbbaabccadddadbaddcbdbcdadbcaabbbdddacddbaabbaadacaccdbcdcbdbaccbcabcdabccdbbcdabdacdcabdddbacbaadbdabcacbbbcabbaacbacdcbbddbdbabdbbbddcaddadcabdaaaccabaccaadddabdbabbddabcbaadcbbbcdbcbcdaadbcbbabccbddcaadbdcbacddaaaaadcdbacbcbbdccabcaaabbdaccddbbdacabccdaccbcacccdbaccaaddacbdccbbdbabcbcbcaddccbdacbcbdddddcddabacbbddbcdbcdaaddaddbbbbabaddacabddcbacaacbabdbdcaabbbbbdddbdaaaacddacadadbdabddaaccaddaabccdaaadcbdbbdcadacaaaddcdccbadbcaabacbdaaaddccdabbacdacbaccabadbbaacbadddbcbabcaacbabbaadaacacaddddbcddcbaaaadcbbaabccdaddabacdabdcadcbdbcbbaabccaacbbacadbabcdbccbbaacadcbacdaabcddddcbadadaabdbcabcccbdbdaadaaccbbabbdbdbcaacacbdabdababbbaccacbcbddddbbaacadddcadbddbdbcdaacaddbdaacabbaabcacdcdadcaaaccbcbaccdddddaddbbaddddbcabbbbdcacbacbbbbacddddcaadbdbcdbcbcaaadabadbbaccbbacaaacdadadcbadacbbbdbcbddaabddacbdbcaadbdbaaadbabadbbcaddbabaccaccaadcddabccaddbabdbcaaccbdabbcdcccdddacabaacbcdbacdaababdacadbadccabdbaabddaddccddbabaccbbcaabbdbbdabcdcabddbdabbdddacbcdcdddcdcdabaadbdacbacaddbcadaabcaaacdccbdbbaccdcccbbbaddbdacacabbbadabdbcdacadbbdcabdcacddaccdcadbbacdddbdcccdcdbdcdbbcbcabadbccccaddabdabcbdbabcacdcdbbbabccbacddabccdbcaaaabcbbacabbabacbcccbdaadccbabacddbcbaaadbbcbabbcbacdbdbddaccbcdabccaabbdbabadcdcabadbbddadcdaaadadacabacacadcbcdaacdbcbbdabccdbdcaaabbcadbcdadcbccdddaadddabdbdcddcbccabddbbabbbccaddbcdabcaacdacacbadcdbdccbdbcadcaacdbaccdacddcbbdbbdbcbbadbadcccbdaacdcddbaadaccdbbacdbcacccaabacbdbcabdbccaacccddbabbccaacacdbbccbadddcabbbdcbaaacbdcababadbaccadcccbdcbcacaadcdabcbcacdbbcabbdcaadddaaccdbdddcaabbdcdbdaddbabbddbddcabdcdddbdccabdbbddadaadabadccddddccbbcdcdbdbbaaddcbdcaadaadaabacadbbdacbdbbdccccdbbbaaddbabbbacddacacccdbbaddbbcbaaccddccbbdcabcdcadbdacaccddbcbdaaccddadcdcdbddaddddadbdcdbaaabcdccacbbcddacdbadbaacddbccadadadcdbbddabacbcccdcadbbbabccddddbdbcaabcdbdcbdcacbdbcbccddcccdddcacabcdddddbcdcbcacdadabcadcbacadbcccdbacabacacdaaddaacdcbdbdbadddddccbcdacdadacdacacabdbdaccbabbdbdddbabddaddabbdbcadaaccdddccbadabdaddabaaadcdddbbaaccbcddbdcacabaaaadcabcdccddacdcacccdabacabbadadbdabcddadaccddabbcdbdcccbbcacbcbbdcadaabcdadcaadcdaccddabcccdbadcbbabbcaacabbbbbddddcccdccacbbddbbccacadadbdabdacdbddaadccacdababbaabdaddcabdbdbcbbccbcbabaaabaaabcccaadddcbbccabbddcbbbccddbcaadacdcaabdaacdbdbcdccddbcdadaccaaabcaaddbaaccddabcabddacdcdcbdabcababcdbcdccabdcccacabbbcbadaccdbcbccacddcdcadccbddbbdccadaacccaacbadbdacbcabcdacdcbddddaadaddbbcbaadbcdccbddacddacbdadaadcaababcdcccacbadbcacbabadaaacccbabddbdcbcdbdbcccbdcdbcbaadacaccccbaacadbcccbcaabccbcbdcdcaccdcaabbbcbadbbabbbdbbdbaccabdccbaacacccabaccdbcaddcbbaadaadddbadaddbcaaaaadabccdaddcdccadacabaacadbddacccbcccbaccddcbcccadcdbccccbbadaacdcbcdacdcbabbabaaccdcbbcadacabacabbbabbaaabacdcbaccbabadcbadbcacddccaaddddbadccabdacbadbccdcbabacacbcbaadcdbcadddcabadbdbbdccdddacccdbdcdccbcabdccbaacbbaacabbcbbccbadbdcbdbccccdacacdbadddbdcbbcddcaabccadccddabaaaabdddacbcadabbbaabccccdcdabcbbcddddcdabcaaacbaaaacdabdacbbbdacdabacdbcbadaabcbdadbdccdccadccabaabddcdcccadccaacaadadcbdacacddddccdaccbcdaabacadadcbabaadcbdadaddcbbaacdbacadaccdbcbadbdacadacabdaccccbcdabcdacbbcbdaacaadbddcaabdaabcdccacbbbabdabbdbcddadaaadddcdddcbbabcddcdaddcdabacbcbbbabcdcbbaabdccdadddccdbbbcdbdaddbabadadbdcaacdcbcbcbaddbdddcdabcabacbcadbdccdbdbcbddbdcddaccdabbddaadcdabdbdadcdccdbbccddcbcdbdbcdbcccaadbdddacccbddaccbacbbcbdbdcabdcbabdaacadaacbabccbbdaaacdcaaaaddaabdcbddaabcddcbbdcdccbbbbcdcddaccdddacbabaccaadbdcdadababdacadbaddcbaacdddbbbddbccaabbdcccbcdccdabacbbcaaacadccadcbccaadadacbadcaabdccdcdbaabbbdabddbbacbbcabbabdcdcdbcdcaccdbcccdbccccacdbcbaacaacaddbbdbacabddabddbdcbaaccadadadbcabadadccddbbcdbcccadadbadabbbccccdadbaabaacadcadaadbaabdbddadddbbacbbbadbabbddcccadcbbdaabcccddbabdaaaacbbabcabdbbcbaddcacdbccbcdddbdbbcabddbcdccadbbaddcabdcaabddbbadcadcccccdcacbdccadcababdbaaddcbbbbdacacdcaadccaababcdabcadadcbacbdcbdcaacdbdcdcbcbabccacadbbbdcdbbdbccaaaddcdbacdaadcddccbadcbdbbadcdbbaacdadccaabdacbdcbcabbcbbbcaccdaaddbddbbbdcddcacddbbdbccbabcddcbcccabdccddadbbdadabaabcbdadcbdbdddbbaabadbcdbdbaabacdbdabbdcaababdcbadcbcdadcadcadbcccbcbabacbaadccbabcddbdcdbcabcbbcbcbdcdacccdabacaaabacdbabbcacdbddaadbabccdbadabbdaccddcdbcabdaddbaddaadabdacbcccbbdbabdddbbccaaccdcbccbbbcbdcbaacbcdaadabcbcbddccbbbccabbccdbbdbaacdbdacabbbddcbdacaaaadddcccdbbbbccadccdccaabacbbcdbaadaaabaaabccdacdadaaabcdbdcaaaaacabdbdbccbdbaddddbdbcbcabadbadaadddacadadabbbdbdacbaaabbaccbbcddbaadccccacccdadabcdddcddcbddccacbcaacddcdbaabbddbbaadbbdadbdabbdbccaddacbbcbaccacacbbccadcbacdabbbdbadbcddbbabcacdcadacdbcaccbabdcddbbdadbbbdacbdaadbcdabcdabbaccdbcdcbddddaababdadbaccaddabddcdddbcadcdbcaababadbcaaabbbdddcbcabccdcdadcbdcbddbcbcddadcacdaddbacaaacabdddbcddadbbdadbaaaddabcaaadadbbddbbcbabaaddcddababbabbbabaaabbacddccbbacdabdddcdbabcbacdabccbdbbcdacdcabdacabdacbcbbabcabddcdcbbdcdccdcddadaaaadcbcdcdccacaaaabbcacacbaddbdbbbbadaccbdccdcadabdbdcabbbbdaabbcdcadcdcdcacacbaccddabbbbbdcccadcdbdacaacdaccbbbaabdbaadbdaccbddabcacacbacbdccdbcdddaddbccddcddcbaccbddcbbbcdbccaacdaadbdadccadabacdbdacadacacdbacbdcddaccdbadbaddbcabaaccbbccdccbbcdaaddcabddcddcbbbbdacdcaabdacaacdddddcaabcbbcaabadcacadddadacccbdbabcaccbdbdbbbdcbaaddbbdbdbdbacaaccbaabacaccaddaccccccdcdccdacbaccadabbddaccdcbaaadadcccacabadbbadbaccabdccadcdccaddadcbbaccabcccccdaadabccddaccacabdcdddadcddbbdccaaccbbcbcaadaaadadcbccddcacdaaadbdabccdccbbcbdcdcbcdddcbabddaddddcdabddadadacdbbdaabdacbadadcabadadaddbdbcdccdcdbabddcadbdcbbcccbccbcdaddccabbccccaccadbbdadddbddacbabcccbbaabacbaabcabbccbbadcdadacacccddbaccdadbadcaacdabcdccccbadacbcadaaabdddddccdddcadabddabbaaaaddadaaccdccadbbdbbacdcdcdddbbdddbcddcaccacbbdddcadcdbdaaddcddbcabdacdccdcdabcaaacdcccbbbaccdcddabdaaacbdacabbbcbbdccaccadaccbdbcbcccbbbaacabccbbabcaaccacbddaacaaacaaddbdbadbbccaaabcbacaacdddddcaababccaadbbabccabbccdcadbdaccbddcbcacbcacaccabbbaabbbabacbacdabaacbccbabbcddbcaacbbadbacdcabcddcbddddbdbdccbaaadbdcbbbccbadcbabdacdabcbcdddbbabbabbabbaddbdbcabbbbbaaacdabccdabbabcabaaabaddbbcbbabddccbbacdacbcbbcbaddadbdbbddbaadcadbababcbdcbddcadadbadaadbdddaaccdbcdadcddcccadbbcabbbdabbadbcbdbdacbbbaacadcabaabcdcdaaccdcbddadaaabdcadbacbcabcddbbddadabacacddadcbcbbacacdaddacabdadccbaacddadcdacdadbbccbddcacccdbbdaadcdccaaccdcbbbcdbbbaabdbdacddbddddaababcacbaabcbbcbabdaaababcbcdcbaaacdbddbabdccbcdbabcbcabaccacbacbccbcbdbccdccccadaaaabcbaddcccaadcaacacbcbcdccaacadccdccbbaabdccbadbddbaabddadcdbbdaddbaabdbbbcdaadbabbadccdbdcaccbabbbddaddbcaaabacdbabddcbadbdbaccaddacdbcbddcadcabddbccccacacdcabcadbbcccccbbacdcbcdaaddccabcacddcccccbddabdcaddadcaddbadccbbccdaaacdacdcbaccadbcbbdabcbadccbaddaaacdcacbcbcbaadbabadacbabbaacadcdccaaaaacaccbccddcbabccadcaccbdbaaadaccddacbcdbbdcbddadcabcabcabcdcadbddbacbbdbdacbcbbccbcdddacadccbacaacbdcbaacbdbbbbcacbbdcddccbcccdcaaabbcdccbacbabcbadccaabaadbddddcbccdbdcbdbccbddcaabccbacddcbdcadaabaadadbcdbdaddccbadccaacabaacdccabdadddbdabbdcabcadabdaccbaacdcbcccacdbcbddaaadbccacddbbaadccccacdddaaadbccaacccabadccdadbbadbcaacaccbaabdcaacdbadbdccbddcdbccbddddabacbabdbcbdacdaccbbdacabbbaacbdcacbacabcaccbcabdaddcbabcdbdabbbbdddbbdbcdcbbbdbaaccdbdabbbcdaaacaaacddbcacdaaabbaadcbddbbccbcaddabdcdcbcdccabadcaaadbcacbbadcccacbacacddaabaaddcbbbaaaacbbbdbddaaccdabddcabaacbbbbcdcbdaaadcdcccbdcbacdbaadbabbcabcbbcbabdbacccdcabdccccacaabddaacbcadcccdcbdcbacaabdcbdcdabadbcabadadcddabdbbbbccabdaccacbababbbdbbdaccccbcdabcddacadcababaddadacddbdcdccdabcdcbabbbbcbdaacabcadacaddddbdbacbcdacdaacbbbbbcddaddcaacabacccbbddbbdabcbacdbcbadaaaacdabbcdbabcdbbaabdacbcdaabcccdbdcaccbaaadbaaaacdbadbcbaddbbaadababccacabcdddadcccbbbcaccbaaabccbbbbdbdcbbcbbcdadadddbdddacbbcaddacccababcbcacdacddadbcabdbbcbcbcbbbabcbbadcdacdcbcdaabdcddbbcbbdaacbadaaccbbaaadadcdcabdadacabdababbdcabababcaccaccdacdaacdabdadcdbbbadacdcabcdcdbabdbcbaaaacbbdbbabdcaddaddcdcbbddababcdcaadbbccaccaccccbbbaacbbbdbbbcdcdcdbaadbdaaacdbbdbbbbaaabaacddabbacacdbdbdbdbbabadddbcbaababbddcaabdaacdabadadcbddbabdaacaadcbabcbdabcdbdabbabdddacbacdcbdbadaacdcacdabdbdadaabbcaaacbbbbadccaaabbdbbbccbbdbcdcddccdcddbdbadbcdaaadcaacbcddcdcdaddbbbabddbabcdcabcccdbdcccccaadccbcbabcaddbdddbabbdabcdbbaadaaabacdaacacbcbcacaaccddddddbcbaaacdadcadbdacabccaacaadabbadacdbbaddddbcadacddabddadabdabcaaabbbaaaadbbbbbdcdcdbcccbdcbdddbdcabbadbccabdbcbaddadacbbccdbcccaacbccbbadabbadcbcdabdbcbddcdbdddbdabbccaacadaaabbbcbdddcabcacaddbdbcaabcacadccaabdbcdbdcddacbbdcdbacdbcacbcbdbbdacaabddbaddaabaadbcbcccbdcddaaabdcaacddbbbbddbdabaadbaddbbddbcdcaacddbdbadddcdccbccaabacbacbbdddbdbdadccdcabaaacaaddcdddaadbdcaaaccbabcddcdadacaddcadacaabdacacccaccbbdbaabddbabbccbbcbabbbdbccdacbadcddccadbdacdbaccbccccacddcbadacbcddabaaadaadbbccbccbdacbbdbbdbaddbbcdcbacddadbbbcaadbcdcaacaddcbcaaababadbddcdccaccbabcdccaabbdabdcbcaabacdaaddabaacdacacabcddccbabbbabcdbcccdccdaccbadcabcdaacabbbddacadbbdaddcdabddcbadcbdccdacbcbacdcacdbdaccccbbababdabdaaacaddabcabdabdadbccdddddccdcdcaaaddddbcddccbdacbabaaabbbbbacbaadabdbadaaccdaccdcdbcdadccabbabdaddadbdabdcbbadaabccdaacbbddabbcbdabbbaacdadbadbbdaaccdabbacaaadccabadcbcbcddbddbabbdcdacabacadaddbaacaccdaaddddabbcadddcbcacddbaadcdabbcabcabdbaadcbcdaddbadabbaaadabbbaacacddddcddbcaabbdbbdacdccabddbdaaadddaadcccadcbbbdaabddadaccdacbcaabcccdabacacaaddcacdbddddcdabaabbbabbacbcddcbcaaacccabdbadabbbccdbdadcdbaddcdcbcbcdcccabaddcdcbaddadcaadbcadadcbdabaddaaaadbabdababbbaadcbaaadacccddcacbbabdcbbbdaacdbdbdadaaacdacabacbdbcdbbdccabbaaddacddaabccabbdcbbbaabdcdaabbbabcdcddacadaddbcbcbdbdccbbaaadbdcbadbdbbbddacbbabbabdaabdaacccdabdcadbdddcbcdadcadddcccddaaccbbddbbdaabcadadbaabcacbcdcdabcccccccaaadcbbcbdddbbdaabccbdcccaadddddaadddbccaddbaccddadbacbcbadddbdaaabababddcadbadbaccdcaacbbbadbcdcdddcbcddcbccbcdacbcbbaacdddabccabbacadddccacaadcaccddbadbcabbbcbaabbcdccaadccdbcbabccbbdbaddbdadadccbbacacadbcabbacbbaabbcadbbacadadababaacaaadbdcbdaaadbccadbabbbcabcacabdddbacbccaccabdadddcabaddaaacadadcbdccabdccbdbabdcdddabdacacaaadddaadaabbcddbcdbcbbbacbcabccbddbcabcdddaacccaaacadbaabdbabbacaccddbbadcdddaadcdaddbacaabaabcccbccbcaabdcbadbdbabbddabdcdaacadddaddbacbaacacababcdaabdabdaabbcbabcbcbababcccadabdccdddcddbcccacdabacccbbddacccbbdbcccbdabbaccaabbdcbadadaccadddabbadbbdccacdacabaacabccbccadcdcccccdbabdcbbcaaabdcabcdabcbbccbacadbbcbbccccadddbdddbcdadbdcabdbbddbbabcaadcdaccaaddccdaccacddcddbbdacaddbacdabccbcdaadcbbcdbcadbadccdbcdabccbdbcaddbcdcbcdaacaaccdccbbbbdddcbbbbdcbaadccdccccbbdbdbcadabdddabdcaccadcbacabcdbcbdccdcddbdbcdddcaaccdccadcbddbdbababaddaaccaaadaabaddcbbabccdbaaccbdbbcabcadbdbadbabccadcddcdcdbbcacdbacbcadcbcacdbbcccbdcdcbdacbaadacddaabbbdcaccddbbacdbacabaccdbcbbcbbdabddcdbaccabbcaaadbcdacdbccadcbbcbabcadbacbdcadcdbcaadadcbccaccabbbbcabccbdccabbbddabadcbbdacacbddcdbadbadbbcdbbdbccdbbccdacacbabacacccbccbbaadbdaacadacaaccababcdacaddcbadcaaabbabadacaaddaabaddccabddddbddddcbdaaaabcadddacdcaaadddccdcbbccddbabccbdcaacbcbbdbccabbabdbdbbccbdbaaaddddbcbdcadcdadbdbaabaabddddbbdadcbddbacdabacbdcbdbbbcaadaaaabdccbabddbccdbaddbaacdadcbacdcbacdbcacacdbdaddaaddbcbdbccccbbaaccdcaabaccddbcbaabababadbcabcdaddccdacabdcabadbdabbbdabcbdcbcdcaababbacbcdaabdbddcddddaadddcbadbacbabbccbdbdbacddbabcdaaaabdadcdabbbadabcbccccaccabaacbdadabdcabacacdabcccaadadbabaddccbadbcbddcdabaacabaacdadabcddcaadabbcbcadbdadadcbcbddbbdabddaacbcbaacaaacccdcaccbdcaabdbbaabcacaadbadadabdcdcbdabcdcabcacdcaddcaddbccabdadabcdcbdaacbbddabbdaddabbdbaaacadbababaaaaaaaccbdbddcaabbcbaddddcbadcdcdbcddaccacaddbbdcadbbbcacdbdcddccacccabacbbbcacaaccadcdcdccdcacbdbcccaadacccbcadddddacdaccdbcdbdaabdddbbabbcbbbdcdbbdbddabbdaddcbccccddbbbaabcbabcdbacccbcddabbcbcdddadbbbcdabdbaabbdcbabdcbbbdadcdcdddcdadccdcccdcddbaadcdddadbcccbbddaabdaabdbbcbdcbddccbbaacbcbbcddbbdaadadddbadccccabcddbdabadabbccbbcabcdbbabdaaccdbbacbacbbcabadcabbaccdddcbcdcdaccacdddbbddccdabaccaadadbbdaacccdbadccacabcbcbcadbddacadcacddacacaabccddbbacbbcbcacaabccaddabccbdbcdadadcdbdbdabcbdcaabbaabdcddccdabdadbcabacacbbbcbbbdadbbadbcddbabddadcbabaabdbbcaccbdccbcdcdbbddabbbdaaaadddabdbcbddacabbbcbadaaabcacbbddbbdcdcdbdddddaccdbcabcdbcaacdbdddcaabddaadaccbbcbddaadcccccbcbdbddaabbcaccdcdacaabcdaadabdbccddabdbbbbbaaabaabbaabddddddccaadbababcddaccbbcdcdabbbccdbcdbcdbcddddacbaabddcaaabbcddacdaddcdadcbccadbccdabdbcdcacbcadbcacdacadaddbcabcbbcbccaacbdadbddccdbdbdabbaacbbbadbdcbcaccbdbbadddcdbcdcdbcacbcdabaabadcbcdccddcadbabcbaccdadcdccbbcadddcbacddbbaadadcdaabaaccdacbddcdacadcabddaaaadccababdaccbaddbabbacaccdadcdbaddbbbacbbddaaccddbaaccbccdabcdbcbcadcccbbcdabdbbabdbcdcccaaaacdaadbdcbbbaaabccccacbbbbbbdbcdcdddccbccbbcdacddaaadaaacddddccabdcdabcabcbdbcbdcdbdcabbcbdcdcaccdddbacddbcdabacdcbaddbaadaadcacccdacdbcadabaccccaaaacccbabaddbbaabdcbddabcaccabaacddcbddabbaabbdbadbadccbabadacbddabcdabaccdcabcdbdccdbbadddaaddbcccdabbdbddbcabddadabaabcabacdbadddccdddaddddcbcdacbbcbaabddbcbaabccabcbbbccdadbbacaccbadcabcaabcbbcdcababbccdacadccdacabdaadbcbddadadbbddccdcabcdbdbcdcaaddbccdcbbccbcbcadcdaadbbcccbcdbdbcbbdbadadcabaccaabddbbddbddbddbbacdcdcbdcdcbdbbddabcabaabcabdacdddcbaaddbaabaacbcacdbabcbcbaaabbdbaaabbabaaadbccccbddabaadccdabbddcccdccabbdaccdbbacddcaaacaabdbadacccadacaaadcbdbddbaadbdaaacabadcabbbabaaacabbddaadabdbacbacddbbddaaaadccccdcaaadcabaccbadddbbcbcdcabccbacdbdbcbaacbdddaccabbcaaddcdccabccabbdbadaaccabcabbbacbcbcacdcaabcabdabddbabbcdddadacdbbdbcdabcdccacbbdbbdddbcbacdddbcabdccddaacbbcdabbabaddadcdbaabdccacadadbcbbbbccbdabacdabdaaaaacccaacdaccbaaddbdaccacaddbdddbccccdcddbabcabcaccadbbadbbaddbcccbbbabcbadbbccdbadacdddabbbabaadddaabddcccdaaaadbabccbaccadaacbabdadcadabaaadbacccaddbaabcbcadacaadadbdbacccbccbbbbacdacbbadbcbbcbbdccbdaaadacbaaaaaaddbdadacdcdacbcabaccabaaddabcadaaddacaccaadcccacdbbbcdbddacbbcddacdddaaadaccbbadcabcabccdaababdbccbbbbbcdbbdabddabcacdabbacaccdcdccdcccabbbbadaaaccccdadbcbabbcdcbcacccabbaadbdbbbabcabbcdbdcacabcadbacbcdbaccccbdacaabcaccaadddacacadaaaddcacacaddbcdbdabcdcccdbccdababbaddbacaacdabdaccbdcbaddcdcdddacbaaaabddccacdcddbcacddadbccadaabcdddcbddcadbdcbdaccdbcccacaabadadcdcdacbcaaadbccbddaccdccacaacdcddbaccbaaadcdabcdbcadbbdacbbdaddaaaabbcbbacbdcdbbbacdcacddbdbbaacdabaabdcbbaddbabcddacdbcaaaadbadabbcdcacbdbcbdccbdaddbaccddcdacabacbdbcddcbaabdabbacdaadbdddddcdabacbadbaddaaaadacdadbccbdccaddcdcdabbdcdcaaddccbcdbcdbbababdbabddbccdcacbaacbcddcbaddcccaddcdadacbbaabbcdcacbcddbdcdaddddaabcaaaacaacdcddddcddddababbbccbaaddacbbcbaaabcdbcbbabaaadcdcccccddbccadbabcdacccdabaacbdabadabbdcabcdaccaadcbbbbdcbdacdbcabbdcabbdbdbaacacbabdccbcabcdacbadbcddbabacbcabbdabaaacbdcabdccdaaabbccaadbddcabdbabbcccddabcabdbabcbdaccbbbadccaacbbcccaaddddddcdaaacaccdacbbcacddddbacdcbbdbacbbbcabcdddbdccacdbcdbdccccddadaabbddcaaadcddabacccaaacabbabacdacdabcaabccacbcbabacbaccbdddbcadabbbaadadbdacdaddbdbaabdcabbbbacbbaaacbbadddbdbbddcbdbcbdadcdddbcbccaaaadbcabaaacadcdcdcaaccccbdaadbcdbdcbcbcdcbcdcaabcadcadabbbaaabbabbcbbbabaccaadacacbbbdaacdabbbadababbabcbabdccdddaaabdacdbaaccacdabbdbccdcbbadddbdadadddbaaaadbbbcbabbadbabcbacacdbaddacadbccdbaadacbacdabaabaaddbdddcabbbccccbadbdddbdcbdccacadbbcadcabadaddcbacccdbdadbccabaacbbaabdcacaabadcbbccdcaacaccdaaccddcdabbcdccabdbbbacdbaaaabcdbbcbcbdcbacbaabcdabcaaacdcdaccbcaabcaabbaacbbbdcbadabbadcccacaacabcdcccbadddcadabccaddbbdabbdbdabdcacdcdbcdabcdbcdddcccddabdaacddcdbbdbabcdbdaccabacccabcdcbbcddcccaccababbcbacdddbabcbacabcbadbdcbaadabcdaacddddaacaabcbcaccdcabdcdcaadcbdcdddcbcccacacabcdccabbbaabdaaadacdcacddbddbbdccacbbbcacddcbadbcbcadacbabcbdccaddcaccccdcddabaadbccddbcdcbacabdddbabdcaacbccbaacdbababbdbcdcbacddaacdcddddacacbddaccdcbbbadaacbaaccdcddaccdcbbdcdabcabdddddaabbbbddccbcdaaaddbbbcaddbadbaaccdcbcaccbdabdddddcddaadddbccaabcadbadadbbcaddbbdcabacbdadbdccdadcccccabdbabdbcccccbacbdbacbadabdabccccdbabcbccdaacdbbadbbddbbbbccdccbcbdcbddcdcacababbccdaacbdbadbcabdddcaccbbbaabadbbbaadcdccbcadbbdacccdbcadcbdcacbcacccaacbacbaadbdddcabaacbbdabdccbcacddabdadacdcddddddbcadbadbaacdbddcdbcbbcdadcadaddaabbcdbadcaabdbbccaccbaccbaadabbabaddcccadabdbabcaaaacdccbacbbcbaddcddbbcdaacadbcbdbcbbcadbabcadcaccabadcdaddccdadcdbacdaccbbdbcadccadbbabadaaddbbdcdcacabdcacacadcacddabaaabddbbbddddbcbadbcbadacadcacdaddcbbdadcbadbadacdcccaccaccbbadbadcdbbdbccdaacccdcccccddddaabbcdadcccbbcdcbdcbacbbdcdbdcbddabdabdddccacacbbdbcddbdbadbccaadaddaccdbacbcdbdacdcbabccbcbbdaacaddcacdccdacabbadaaadbddddcccccbdcbabcccabaababbdbbcacdaaadcacadabbbcabdadbbdddcacbadbdadcadcdbabbadcddbbcaddacbadadabbbabbabbbbddbdabccbddbcbaddadcabbaacccccaabddbbabadcddaddbaaddddabbdcdbdccbdccbbacdbccdbcabcbaadbacbcdbaccabdbacbacabdbbdadaadcdaccdaaddddbabaccbbdadaadacdbbccbaaaadbccdbbdcbabaccdaccdacadabbaaddabaddabbdccdcdabcbdabadbaabccbbbbdbcdbacbbccdbcdabcaadddbabacbcccabacbaaddaaacdccaabdbdabcbaabaabbdacadcbcdbbabccacaddcddbaabdddaddabdcdddbdcadbddbacdddacdadcbaacdcbbdabcabbddcbaccccabbdbaaaaadbadacabdddabbbcacaaaaccbdccabbbabcaaaabbcbabdbaddcbbdddaabcdbccaccacdcddaadbbacdccddaddacadbabbaddbbcbbddaccbabbdcdccbacddbddcccaabdacddcbbbabbbdbccddccbbbbbaaccdbaabacdbdcacdaacdcbbabbaaaaccaddcbcdcdbbdbcdabdbacbaaadadbdbdcadccbbdcbbddbadcabbabbbdbdbdcdbbddcadabdabaccdbaaadcbbacabbbcbcbbbccabbbbcadbcccbbbcacdadacbbccbdabddcbccbcdccacabcbaadbbddbbbcaccdbadcbcdddaddccabcdbbbacccaabcbdbdcbadabddcbcdadbbadcbadcbaddcbbdbadabdabcbdcbacaadababdbdbbacabbccdabbccabaadcdbbcacbdcaababababaaacddbdbdabdddcbccbababcbddbbbdaabcadabcbaaddcbacadbbdabadcdbdcacdbdcaadbcddccbbdbccdddcbbcdaabaaaabbabadacdbccbabbbaaaaadbacadddbaadaccdcbdddbdccdaadadbcabacadbdddddbbdbaacbdaabbdbbdaaaacacdcbabddddcdccdaabdcbdddccbddcbcaaabcdcbbcbdccbaccbcbacadcbcddcdccbabcbbaaadcaaccbbabacbdbddaccbabdadabcbadadbcddcdaacbabbdbabbbcbcdaaccdaddcbddcdacbbddaacbbddacbdabbcbddcbddcbdacabbadadcaddbaddbadcbdcbaccdabbbadcbcbacacabdadcabbdabbcccbcddcacdbbdabbbcbababcbbbdbaabaccbccbbabbcccdcbacddcbcbadccacdaccdbcaddcaacaadacdbaabcdbaaddccddabaddddaacaddadabcaddabdbababbbdddbacccacabdbdacbbbdabbbbadbaabdbcbdababdbabbcdcbbadadcccdadacddbaabcdaccbdabaacbabbcaadddadbcccdbbcbbcabcbdbcdcbbaddabacabbdadcccaadadcadcccbabdccbbbadcabccbdcaacdbcbdbcbbdcbdaadcbdbdacdddabaddddabcabaddcbadddaddccddcdbaabdbcdaccddcbaadcadababdcaaabdabddaddbaccccacdabcbcbdbdcabdadbddcdcdacabccadcbaddcccbbcabdcbbdbcdadddbacadabcacaabddbabbdcbddbaabcbaadcdaddbcbddaccddcabcdbbbadddaabcbaabadddddabcbbaacaabaacbaadbcabbdaaadcabcbcabccdadbbacdabddbccbcaadadcadcdbbdadaaaccbbdadcdcacccddbabcdbabbcbbdabcbcacdbbadaadcdcddcbdadcddcbbdcacdcacbbbabbcdcdacaddabacdbcccbcdabbcbcaddcdbabcccabbbddadbaaadacdaccaabbacbdacadbadbcaaabccddccbcabbcadcacccddadcccaccbcdaacbcdccadadccdaddcdacdddbadbdbcbdbdbdacbcbbdcdbaaacdadaadabbbbdcbacadabacbcdbaccdbcbbcbcabddbbbbdbdddacbdbadaacbdcdbdccddacdbbcdddcddddcbbabbbbcbbabdcaacbadcddabdccbcbcddbadbbdabdccadacaadbbaaccadcbcdaacccadddbbdcabaccbcadcadcabbbadaaaabdcabbcadcdaccccbadcbadddbbcbcaccdcbccccbdacdbcacbcaadbdbcbdcbaabbddbabbcbaaadabdcccccacaadbcccddbbacdadbbadccdcbbdbcccbdbbaadaacdcbddadccabbcccdbacacaddbaabcdbccddbbdddcbbbabcccbdcbcddadadbdcdbbdcdbdddadaabadabadabdabbbdcccdbdcdcbddacadbbbabcbccbabcccdadbdcbdadddddadbcdacddcdbdcacaccdcaccbcaaddcadbbcdaacacdbbbbaacbdcbbacabcbacabcccddacdbacdaadbbdbdbadaabcbdaaaaddadcdaccbadadaaababdcccbcddabaadbbabbaaccbcbaccbbbdaaacbbdaacccbbcbdcbcbcbdaabbadcadbcbcaaaaaaadccabccbbaddcbddbdcacabacadbccdadbbdbdbaaccbcdcdadbddbbdcadccdbacbccbbbdbbccbbcadbddbdacbadbbcaacbcaacdcdcdcaccadddaaabadbccadcccaccddbcbdcacbadacdabbadadbabaadcbaadbbccbbbdadbcdbccadcbabdcbccabccccacbdccdbbacccdabcdbabccdbdcdcabdaaaddbcdcacbdcdcadcbbbaaddacaccbdbdddcadcdacdcbbbcdbddcccbacddabdbcabdbbdccaccdcddbbcadbaaacbcdccaaddacbbbacabbbbaacbdaaacbdccccdabbddbacbcddcdcdcbdccaabddbdaadbcbbbcacabbacdccdcababbcbdacbdbadbdbbdacaabaabcaaaabbacadddcaacdcdacbaddddbccbbbcbadcadcadddbbbabbdcbcaabadacbcaadadddbadcddddbccbadaacbbadacacdcbcdaaaaadacaddbadadcccccabcdcccccababbcbabbccccabccdbbcbabcabaaabbbacadbaaaddbbcbcabdabbaaaadcdcdcbcadacbcaabcccdccadcbaadbccddadabcdababbcbdcbaaadccdddabdcdbababcabbcbabcddadbadcdcdacadcaabcdcdddbbbbbbdabccbcbbccbaabbadbccaadcabacdbdccbcbaddbdabdcbdcbadccaccddabdadbdbdcadccabdabbbbcaccabdbbcccdaacdcbcaacaaaadcaacddbdaabdcbbbbabcdacbacacaacbcaabdccaaaddcddcdaabbbcdadbddbbcadbbaddbaabcbdbcadcaadacbcaccddabcaacaaacacdaccbadbdcccaacddddbccdabbdbcdabacdcacabbdbabbccacddadcadbbaaabbbbddbccaccaccbdbadcbaacabbcbccdbdaddaaccbbbdacbabacbadcbcddabcabdacbadddccdbadddacdbaaaaabaadcdcbdcacddbbdcadbbcddbacaadbbbcdaacadbdcaabaabdbdcdddccbabadacbabbbaccdcbabccaadabaaddcaccddcbbdcbdbdcdacbdadbcbadccdcdadbcaaddbbdbcbbcabbcbccaacdbdbbcdcbddcbdcbbcddcbbdbbbabcbacbbddcbaabacddcdbcadaddbcdaaaabccbbbbbcacacccacdcdaabdbcaabcbaabbbddcbdacdcdbdbbcbbdacdbaccdccaddcdbcdaabcbacbdcaadbabcbcabccdcadcabdbdcbdbbdbbdbddbdbadbdbbdabcacdbcdcbbdaacbadcccaadcaaabcbbababbddbbdadaccdccdcbaabdadcdbbababaadcbbcbdbbbaadacacaaccabbaacddbacdadbbaaaccabbadbadccddbbcdbccbcdbcadbadddcbbddbabbcbdabcabdbcbccbabbbcbdaaaabaccddaccbbcddbacbaccdabbadcabddcbddcccbdadcbaddccdbcbdccbcaaaaddcbcaacaacdcbacbadaacbaccdabcabaaccdcbbaacabdaadabbcbbadcbcabcbdbdbaaadbdaacaadacbabccdbdabcabbdbbdabcbabbccccbddcaaaccbbbcdcdccccdaadbabbbbbbdbdbdaacadcacdabdabccbcaadbbababcddbaccaaddcccccbaabbcabdaaabbbbdbaddbdcdadadcdcbbacdaadbdaaabdbddbdaacacbdbdbdaaabdbddadcccacbdcaabbcbbaadbcabacaccbdbbcbcdbbdcadbaccccdcbaccbbaddaddcabcaabbbddadadcbbbbabbcabcdcaccbabbabbaaccabdddcbdbbccabbcaadcbbbcbdadbbccadbcdbbcccaccccdabadabcacaabacabdabaabacdcdddddacbdaccbddcbdabdcbacdcdbcccadbdaaccaddbcacbbdccadddddccdddbcadacdaabdddbdbdbdcdbadbbbacccddacaabcaadccabccdcacacbdabaaccaaadcbaacdbbaadadbcacdcbccbbdccaabdaaaddcdbaaadbbdabadadbbddcdbcaddbdcbddabcaabaddaadbaccbbcaadbdbadabdcbbdabbcacbcaccdbdacbbdcbcaccddcaabccabccabaadbcccadbbbaabbdbaabdaaabadabcddcdcaadadbcbabbdcccddaadcbadabdccdcdcaddacdccdccaaaddcccccbcbdaccdbdabcbcdabacdbbbacddccdbdcbabbdbcdcdadcddcdcddcdbdaaccabdcdcbbcdbdbbccadadcbbccdbdbcdbccadadcbdaacccbccaaacdaaddbdcadaaccbcaadcbbdccdbaadbdcdcdcdaabbbdcdbcaddcbdaacdcabbabcadcddaabcbacadacdcaccababbbcaacbbbdddbadddaaaaacbddddaadbcbccbbbdabcbdbbdccadbdcdcbabdcacdabbbadabbacbbdacbdcaaadcdcbabddbcacdaacbbcadbaccbcbbdabddbcabcabdccdcacdbdadacadddaadbacdaadbcbabaabbbcaaaaaacbaacacabdddbcbabdbdadccbbadccddbcccacddbadbcdddacdabcdabaadcdabcdcabcbbdddaaacbabddcaaadbbcbababbabcbbacacdadcddcbccdaabcdddcccacdbadaabbbcbdbcbdadbdbabadcbcbaddaddbadbbdaaacdbdaaccbadacbbcaaddccdbccabbaccbcccabdbbabdabbacbaabdaabbbabddbcdcaaacadacdaadadaaabcdaccdcacdbdccbaabccacaaaaddcadaadcdddadcadaadcdaacacdcbcadbcdcababacbbbabacaddcdcccbbdcdccccdaaaabbaacddccbabcccabbbaccccdaadadddcbccbbaabdcbdacbbccaaaabcdbcabacdaadddccbbbccbbdddbabacbcdccdcbbddddaacdaaaaabababbdcbbdcbbbcdabaaabaadaabddbcbbdbdbbccdbcadbbbbdcdbcadaaccdccdccdddbdbbabcaddddbdadacabbcdadcbcabbdbbaccbdbcbbbdccdddcbddbdcbccbccdbadabdbcabaaabddcbabcaddadbbbdcbdadadaaacccaacaaadbdddcdacbdbabdaabadabdccdccbbdbaacbbaddccbcdbdccabdcadacaccdcacddbdcbcdbcccbddcacabcdadcdacddbdbbcabccbacbcccabadaacdcdddcdcbcacadbbdabdcbdbbdbcaacccaccddccdadbcadabaacbccdbaddabadbbcddcbcccaaaccdbadddcadccdadadcddaadadbcdabbccdbabadaccacbccadacdcbbcbababcabccccbdcbadddcacbdcabdabadbbcdcdccdadcbbcbccdddddbacbcddacdcdabbdccccdadadacbcbbbccaaabbbadaaacccdccccdbdcaaabcabacbcddaaacdbbdddddcbaabddbdbccdcdccabbdaddaabcbddbbadcacabddddadbcccbbadbbcbbaadbaacabcaacbdaacadbbcdcdcdaacccbcaaaabdbacdcadddbbdabbdcacccdcdcaaabaaacdacacacadcbcddbccddacccdadbdbdadbadddcbaabdcccbdacdbbaabcadbbcbcaccddaaddcbcadcaddacdbbcddadaaaacdadcabbcaabdadbdcdadbababcddaaddbacdbcbaccaccacdbbdbcccacaabcccaddadccccadbbbdaccabcddacbdcaacaccadabbccccdcbbdbadbcbdbdcbbcccbabccddaacadbcaacacdcacdbaadccdbaddaccdcddbacaddadadcbdacbdabdacbcbaabddbcbdddbcccdbaccccbaddcdcdadbbbabcdbbcbaadcbbbcaccadabbacbccbdaddbabdbccaacaadbadbaababcdbbacbcbddbdabbaabdbdabccbbdbaabdadaaacdacababacaabacbabccaabcaadcadbcdddadccabddacdbbbcbaacabddbaccbdcbaaaaacdddcdbacdbcbddbacacbbdacbabaaadcdabcdddddbddcacdaacbbabcbdbbcdaddaddccddbaddbdbddaabdacadccbbbaaacccdbdbbbddbaacddabdbacadbdbccdddcacbdbdcabdabbccdbddaaaaaddddcbcaccbadcdcacabbbabbbaabbcbcbabcccbaaccccaacddaddcbaaddbcccaabbcbbdbabccdcdaddaaabacbdacdbcbccbdccbcbdbdbdccdacacdaacdaddbaccbbabdadabcdbdccabbbabdddaddddbaacdccddbbcbcddacddcabdccaaadcdaddbcccdadaaddaddccbaacbdbdcbbcddadddbcdcccdcdbdbccabcdaddabadbaaabcabcdcdbabdbbccdabddddccbbaaacdacaacbdbacdacdadabcbdbccbcddbabcbbcabcaaabbcdcabdaddaadadcbadcaddbbabccbcdcabbcbabdccddbaabcdddababbaadbcbcabacdbdadaaccddccbcddbadaaaabdccdbcdcdbbadcdcbdcabcacbdbbcdcbdcabbddadbdcaccaaddddddcbcadcaddabbaaadcadacddbaddacabbcabdacbddacabddaddcdadcdaabccacdaabdddbbbbbcdbcbdcbadababbdcaadbacabddddcdbccdabacddaaacdbcababddddcdccbabcdbdbcadcddadcccbccbaaadcdbcbbbaabdaaccbaddddabaaaabbbcbdbccaaadbbabdbddacdcbdaabadaddabacabdacbcaaddbbdbdcaacaddbbdabccacddaadcccdccdcbacaddcdaaddacabccaccddcaccdbbdcdcabcacadbbbbaababababcbcdbbacbdbdbbadaccadccadddbdaaccbdbcababaaaacababcbcabbbbadddbcbcbcaddadddbabbdbcccbadbbbcbbcbabbadccbdabadddabaacccdaaadabaddbccddbcacabbcacabcaddbdcaaacccaaadcabdadaccbabdacabccdbcddbcbccbbcbdacddbbcadabdbccadcadbddbccadcdaddcccbbbdaabdccdadcccbaadddcddbdaacbdaaacbdabcdbcdbadbdddadcdccbbbbdabaccdbbbdcdaaaabdbbcbcccddbddadadcdbccaacbdbddbdddbdccbcdadcabcacbcbaaaddaadaccdaaccdbacbacdaacbaaddddabaaabbcbdcbdddbcdbcdddccbdbbcbabcbaabddadbcccbaadbaddaadbddaabbbaacbabaadbcdacdaddbcccdbadbbcdbcaaaabdccdaccbbbacdcdcccdbbbbbdbbcaabbbbdcbbdbdcbaaaacaddaddcdcdbcaadccaaaccacbdcdabdadaababccddaddccadabadbbdccacdccacbdbadccdbccadbdbbbdbabdbaabbcdacbaacbbdcdaccabcdacdbcacbbbccacbbadccadcdacdcbdddddddcdbaddbbcabaabdccdccbdacdcdcacabdbdcccbdddddcbaddaddaacdcadcacaaabcbddabdbabdacabadadaacaacdcbccbbcacaddcbbdadbcabadcbcdbadbaadcaabcdacaacbbdabbacaccbabdacbbcaaadabcaacbbcabdbdcbdcbaccbdccaacbbbcaaadcdaabdcbaabccacccaabbacddcdddbadcbadcddaadcccdadacadcbbbdcdabbbdbdbbadddcabdadcadbbcdcdadbcddbbcacbabddadcdabdcdbdcaaccacaabccdccaccbdccbdbadcadababccadaddcdcaccadbccdaccaccacddccaabdaaaadbadcbcdcbddbdddcacbadabcccdaaadbbbccbcdbbbcccbbacdccbacbdbbcbdaadddbbadccaadcdddccaaccadcbaababdabadddaddbaaacdadbacbcbbbddcccbaddcacacddcbcbaddcdbbabcabbdbdaabbcdacacbcadcbccdbaaacdaabcccaadaabccdaccccdbbcdccaadaadcbcbbbacbbaddaabbbbaddcacacdcacbabacdcbcaccbadbbccdbddaacdccbacabdbaacccbdcaaadbbabddaaababaddccdcadcbabdbbbdcbacdddddcbbdcacbaacbbbacdccbaddbbaccdbadacabcdbbbdbaccbacddbbadcacccbacddcadcbcaacbccbbaaadabdadbdbadcdcaacdbbdbbdaaabaaadcabadbcdbbdcdbabddaddaaacacacdbbacbdbcdbacccbacbaddadaadabbbadcdcbaccdabacaabaccdbcbcbbaaccbdcdaaccdcdcbccdaddcdadbaddbbadcddaaabdcacbabdcdbddcadacdcccaabaacadbdadaaaaacdadbcdbcbcbaddaadcccccbbcdccdbadcaccbaacdaccabbadbbcbcbdbabbbcddbaccdbdbdbbcaddacabddabbacdadccdcaacbcccaddcdccdaacadcacbadcbabdcacdadbdccbadacbadabdacaadcbcbcddadbccdbacbbaddcadbdbacdccbdbacaacbaabcdaacaaaaaabdcaaddcdbbdcadddbddddbdbbdddbcdbadbdadaaabcddadcdbaccbbbccdbcdabdcabdcaabbbcabbcddaccbbaccddaddddacccdcadbbacadcdaccabaaaaaddbccdcbcabbbcacbcdbbbcbcadadacddaabddacaddbbbcccbadcacdaabbabcbaaadbdabbbdddadadabcbadcccaacbbdbbddaadaabcdabcdbdcbcbcacdcdcbadcdbdabbbcbddacaadacdabccabbabbbbbbccdccbcabccadbbbaaacbbdccadbacbddbacbccadababcccdcaddbcabcacdddccabcbccacacccbbdcbdbdbbdbdccdccdaadadbcacbdddacabdbbadaacabaaacabaabddbccacabcddacbcadbdbadbdaddcabdabdacdacababaaaaacddcaabacdacdaabcbbdddaabaaddddadaaaaaabbddadddcccbbbcbaaacdccacdddcadcdbbacacdabbdaabbcadaccbccbcddbaddaddddccbcbababcbcbcddccdabdcddcbdadbbaddccbcbacbcbdaabcaadaaddadbacddadbabbdaaaaccdbcbdacddbcdbddaddaccbbaccdbdaddabbbacadbabbddabdbddbcadacdbdcbdcbabdaabacddddaccccdacbdabaaadccaccbaaadbdccbabcadaacccadccdcaababcaaccbabdccdadcbbcbcaccdbddacadbcddabbacbaddcadbbcbbbdbdacdcaaacccdabababbaabbcaaccadacacbaccdbccbddbdcabbddbdbccbabbdcdbcdccabdbcabadabcbcdaaccbdcaccbabcadbacabcccaccaacddacaaaadbadbcdbdbcbddaaaccabdcabacccbdcbabdaddacdaccbadccdbdadbdbbabdddaddcdcdaabccdaaacdcbcabaabdbbdddbdabadcbcbbcbbddabcaccdbcbadddbdcdbbabbacacdacadbbcaaabdbbcabcdbbcbcbadbdaabdbdccddddcbbabbdcaaddccbdcdacdacdaccabcddddabddcbabcadbbbabaacabddccadbdacadadbcbccbcbdbccccabadddacddcbdbdabdcaabdbcbcdcabacbcabaacabccdaabacaccdbaabcacbbcaaddccdcbcdbdaababaaabababcdcdbccabcaabcdadcbdccaccaccabbccdddbddabbccdcadacccbaababdddddacccddababdcbacabadcdacbbacabcbcdbbabdadacccbdacdcbbdcbadcbbcbcccbbcabbddccabbabaccaddcaabcabcacbacdbabddcbddccaaaddcddbcabcbacaccbaacddaccbbdaccacaadcdaddbbaddcddbacbddcdcdaaddbcdcdccaacdbcccadcbdcacaaddbdbcdabbacabcbadaabaddcadbacdacbababbcccccadbacadcccdabddaccbcbbadbbbccbaaabdcaaabcdbdbcabcdbaaacabadcaabdaadbbdbdccdcabddacabbcbbadbbdbddaaaaacddbcdcbcdcdacbababaadaadadacccbaacddcdaadddbaaabbbddbdcadddbabcbdcaacdaccbcbddadbabbaadddbcdaababbadcacbccdcacaadcdccdabbacddaadbbaacacbaadaddabcadbabcdcbcccabadcbcbbddaabbdbbaaabbdcdaacdccdcdcaddbbdbdabdcabaddbaccbabcbcaaabccacabacdabdddcdaabbacabddbaabcbbdcaccddcdcbccddcdccaaabcdabaacccdcccbcbcdcbcdbbcabadcbdcaacaabcdbbacccbdbbdaacadccbdbdccdaacdabdbcddaccbaacbaadababbaacbdcadbddbccacaadcabdcdcbacdcaaacacdddbadaabaccbbbbbccbdcbcbcdacccbabbabdbcbdbbbcdbabdbbbddaccdddadadccacaddababcddccacbadbabccaaddbacbccdacbdbdbdddadddaccbbdcacaaaacaabccadbbbabcccbaaacdcdcaaaddbcacacabbcbdbaacdcbbbcccabddaddaaabcaabcdacbadcacaabcbadaabadbbacdbadcdadcaccbbcddabbdcdbbdbdbdbbdabddddcbabcddbabbcbaadacaabcdcdaccacdabdabdbbbbcddcbcacbcacbcddaadbbdbccacccadbbdaabacabadaaacbbcbcbbcbccdbcabdacccaababbcdcdacadabaabdadcbbccbadcddaddcccdddacaacccacdcbddbccdcbcdadbbaabbbaccdabaacabbdbdcdcadbdaacdcbcdaadbcaacbabdbabdbddbccabddbccbdbdccababadbdaccadadbdddcbdbccacbbcbdccacbdbcacabacacadcaccaddcdbacdbabbbcaabbaadbdaadbaaddaadcbcdbaaddccddccdbabcbaacbddbacccdbacaddbdcdcaababdaacbdacadadadbdaaabcabccdaaddbcbaddddbabadabddaaddbccdcdadaadcbbbbdcbcaabdcbccadacaabbcdccbcaccabdcbcacdcbdabdcbddbcbacadabbbbcbccacbdbbaacbabddcdadcbcccdcaaabbadbaaccabbdddcbaadcacbdbbacbbabcdcddddacacbbdcabdabbabacdcbbbcbddcacacccdcabbcdbcaadacddcadcdbdcadcccdcddcdaddbbcbddbbbadbcdbadaaddbbdbcdabccdcaabbbacbaacbbbdaaccdccabbbbaaaabcaaacbdadccdadcaabaaaddbdaaddaaccabbbabcadcaaaabaabaccabdcbcccddbdaddcaaddbacdddabbadacbbdddbcbcddcdddbacadcdacacbaaddbbbbaabaabacaacccdacdbbbdddabaabdabababdadabcccdabdcdcbbaddadaacddcbadadcdddacbbdcabbaadcccbdcdbaadcbdadcadabaaacbcddbbbbdccbdcbaaadabbcaaccbccaacdbcdcadcabddbdbadcdcbbddaabdcbcaaabcbacbaadcdacbddbdccdbbccbddbacbcadababbbabcabbdbaddcacacbacbacadadadabdbcdcbbaabbcbbaaaabcbdcaddadcccaaccbdacdccacbbaddadcdbbbacaabccdabdcbacdbacacdcbddcdadabdacdaaaabdcabdccbdbaadcdacddcabddbcccacbabdbdcdbaacbccccdcdcbdcacacdbadcbabccacbbcdbcbcaabbabbbadbacddcaabcdacabdbbadbddcbcadcabcdabcdbdaaddcadcddbccdcdaaabdaadbcadaadbbabbdbccbacbbccaddcadccaadcabddddadcadddbcccdccddddbadbbdcbbcbddbaabadabadddbdcaaaaaccdddddbcdbbcdbacbccccdccdcdbdabccdabacdddbadbccdcababdcccadcbcdacdaadcbcbdbbddddacccdcdcbbccababdcdccadbacabbdbabccaaadbaabadcbdcddbbdaddccadcccaddbaacbcaadadacbbadcaddaddcdbddacdaabdbbcadcbbbdbadacccbbccbdadbccdbdcadcbdbbabbaccdcbbdcbacadadcbabbbaaccbccaabcccdcdaccdcdccdbaddcccbbbbccaddcbcbadaccbcddcaabcadacdacdbadbcbbbcbcbdcaabdadacdaabdcadabcdbcdabdadccdcadbddbddaaadcbcacccccaadbcbcbabdaddbdccdcbdabbdcdcaacdbadbbbbbcdbadbcbbcaadddababdbbabcabcdbbbaaadcbcbcddbaacacbaccaddbbdccabacadabadbdcccadcccaccadcbcbaacdcbccabacdcbddccbbcdcbbdacaababaccabbcddccccbcbbbacbcbabbbddbcbdbdbcbbabdbbddbbbbacacabcdbcdbcccbabbcbcbbddddacabcdaabcbdabbdcdbacbadddddbadbcabcadaacaabaccabdacbbbbbdbacdabbdbcaccaaaaccbcadcacbddadbaadabacdabcadccdcacdbdbcbabddbaaadbccdadbbcdcdbddaadcbbbcbccdadcdcddaaddbaabacccadbadbbbcccadbddbdddabdabdcaabddbbdaddcaddcabaaddcccabcaccdcdbdcdcbcbcddaaabaccbdbcddaacbaaccbaadddaccdccbbaadbbadcdbaddbdadabccddddabadcbadcdbbddacaaabaabaccabbdadbddcbbababdadaddcaaccbbcbdadaadcdbcbdcbcdcabbccacdaabbbdbaacabbacdadaaacacddaabddbdccbbcccababdaaacddcbbabaacdbabcdbcbcdabbacbcdbcaaaacbcbababaabbacabadcdacaaadbcccddbaddcadaacbcabdbdccbdaaddcbadadbbbbacbcddaabcadcbbbacaddbaccdadcbacaabaaccbaaddaaabcbbbdbbbbadbbddcbccbbaaabaacbcaabddcbbabaaccdbcddabbdaacbdbbbdcaabcabdbcddbaabadccdbacbaacdcdbadbdbccccccbdbabccaaddddabcbaccccdabaddcbbdabbbcacadadbabbccbcacbcdcdcbdacbbcccdcccbacbcccabbbadbdcaccbbdbcdadbbbadccbcbcdcdadbabdbcaabcdbcdcacacaddccdabbdcadcbcaadaacbcbdaccaacdbbdcccbbabdcbbdadbbaccacdacadbbacbbddaddaaddadbaabcccaaacdadadbbcbdbddbcddaddddadacbcdcbccbddadacabdcddccabcbdbcaabccddbbacbdacacacbaabcbdcbcdbccccccbbdaddcccbaadadbacbabbbbaadbadaaaadaaccdcbadabbaacccadcbcadcaccdbcbbdbacacdaadadcbbdcacddbddaaccccabddaadbdddabbadacdcdabddcbadccddcbdacbdbccbbccdaadacdcbbbcbbaddabaacabcccdaddbddcbacccbacdaaccabbaacbcabdbaacddbdcbdbdbdabccbbdacbbadcacbddddbdccdbddccaabbcdddddbaabaddadabcdbbcbbdccdaabcddcbadcddddccbddddcbdbcaddabdaccbabdbdbacdacddbbdbcdabddbaacabdabdbdabcddbcadacddcdabccbccadbccdacbdccabcaddbdaadaaccbccdcbacaacbdcddabdcbabaddaadcbaabbbdaabcddaacdadbbcbcadcadcadcdddbbbcdcaabdadaabdababbabdbcaccaadbaddccaacdddacdbcacabdbaacaaadbccbbacddaccabcbacdaccbdbdacdbcababacaccccddccbbabacbbbdcbaaacabbccbcbddcbaddabbbabbcbdabcdbccbddbadcbadcdddbdadadbbddaabddcdbdbdacdbdddccbccdbbacbcbabacdcbdcdaadcbdaabcbbdccbbdababadbbbcddcddcdbdbcabadaabadaadabacaacbccbbdcccbbcdacdbbcbcbdcdcbabdbccadaddccbcaabbbadbcbcbbbcbadcddcdadddbbcbdcdbabbaaddadbccbbbacacccddbbccbcadddbbcadbbacbdaccbbccdcdccbddaabddadbbdacaaaacbcdccccbcdcacadbddbcbbbdaadacbcacadbbacbdaaacabadbcbadcacdabbbbcdbcdbaaaabbdabbcaadcbaadadaaaadaabacbaddcdbaaadbadcadaadcaaacaacabbabbadbbacbaccdadbcdbdddcaccdadaaddabbdcabddacbdaabdbbcbdadddadddadbccbadcaaddbcaccdcccdbbbdbdabcddaabdcdaccacdbbdadccddadaddcbacadddcbbcadbdcccbdabdbddccbbccbadcccbddcccbdacdcbbbbdadcaddcadbdabcaaacccadbbbdcabcabdbcccadadaccddcdabacccdaaaccccdbdcbcdbdbbdbaacaabdacdaabbacaacbdcddcdbddccbabacbcdbcacaaabbbaddcbddadbdcbaabdddcabcbacbdbcadbccbcbcaabcdcbaabacdbcbbcaaacccbbbaadaddcccbabcdcbcdccdaadadbabcbbbacdaccbdadcdaccdcadbadcdcbaddbccbcdbbdaabbddaacdccaadbaccbcadabcadbbbaddcddcaaabbcbcbbbcbbcaddbacbaddbacabbadadacbccdbcccaadbaadcdaaabaaccbdadacabbcbaadbdadbcadadbddcccbbcdabcbdabddbbddccbabcbdbacddabdacbcbdcaccadbdcabaaddbbcbabacbcabdbcdaaaacdadbdcdadcacdbdbcddacbbabccccaabadabaabbaadbdcbbabaaccabbdbdcddcddcabccbaddcaabaacdbbcbbacddcadcbcabbcacccacbcdaddcbdacddcadabdabcadadaddcbbdcdababadcbbabcbcbaabadaadcbbcaadbadacbabdbbddcacbadcbbdbbabadaacabaddbcbbbcabcbbabdcddccbbabaaccbddbdcddbdacbdddddcaadbaaadabacccbccbabdaaabbddcddabcacbcaddbdcdbdabaccbaaaacdbddadddbcbbdbacccdcdddbadbcadbaabacddacbbdcaddbddabcabbaaddcbdbddabcccbacadbcaacbabccabdadbadccaabdcdcabbddbaaddbacbddcbcaaccacdbcacdaabaaacadaaabddcadbccbadbddcaddbbcabdabbcddcbcbdbcaacddbdcabcbcacdbcbbdddbbbcdbcccabcddbdbdcbcbcbddcbaacbabbbbbccaddbaccdbbcbadbcddddddaadccbbacbacacddaaabcdcbdbddccdccbabcbaacaccbcbacadcdbbacbccbccbdddbbcdcaddbbdaabcdacbbdbcdccddbcccbddadacabdddadacaadbcccabbccbccbdbaadccbacccabbacdabbdcdbadacabdababcbaadddabbcbcaaddbaabdcbcaaaadcacdccccdaaacaaddcdddcccbbbdbcdccdcadbbddbdbbbcbdcdacaacddaaccbabacdbdabbbabbcdcdddcbdbadcabddbbacdbcadcdcbbacbbdbdccbdddcaacaaaabccacababcdcddcadcddcbadbcaabdcbbbcbaddbaaddaddbaddbcaccadbcdccbaabcbcadabaabaadcaadabcdadbccdbcadcbdaaadddaddbacdbcababdadbaddacccdddacbdadbccaccdbaddcdadbabbabdabcdaacdbaacbadabaabbddcddbabcdbdbcbcacbacdaabaabccaacbcbdcbbaacbccaccbcaabcdbabbdcadabbdadcabdacadaccadbacccaccdbdabccaaacbcbbdaacdbdbcbbcddcddbdddcdaaddbdaccbbdaaddccdbccddbcccadaaacaacbaacddabbcdbacdacaaddbcabcaaadabaacdbabbdbbbcbcbbdadacbdcadbbbdadaccabccacbbcbccdcbcdccbacacdacbdadacabcadacadbbdbbbbdabbcdddddccbdacabccaadaddbbbabbdddcbbcbbbbdbdbaadadbcdbcbaacbbaddbccdddddcaadbbcdbdaacbbddcdacbaadacdddcbaadbcbddacdabcdbbaaaabbabdbddddabaccbbdbcaacbdacadcbababccdcaabacacbdadccaddddccdaaadabbaabdadbbdcabababdbbcacbaabcdcacddaabdcbdaabddbcacabdcdcddabdcddcabbabaccdabdabcabdbcccdccdabcccadbbbbdbddbccdddccdaadcbbaaadcaabbdabbbccbdaadcdbcacbbcacdcaaaabcadbcdbacddbbbdaacadbacbdcddccaabbcdbcbdcadccbaddacbdddcabadadacdabcddbddbbcbdbcababcaaccdccdccabcccadddbcdbbbdbabccddcdacbdddacbaacabbbbaddbacaadabacbaadadcbbbacbbccbadcdcdddccccdabccddacaddbbdbddcdcbbbdaaacbdddbcdcddadadcdbccdbdabcbcddbaadbbaababccbacbdaaccccdbbdcabbadbdcbddbaddbdaddcdddddbabdaaadadbcddbccbdcccbaadccadaccacdcbacccadbddcbdbabdccccadbaddcaddbbcaddccdcdddaaddadacbcaabccbabcbbdcbadcccaadcbdcbacaabcdcccdbcccacadadcbabbddaaadbbcaacbbcbbbccabbacddcbaabadaddcbcdcabdbdbabcbbddaddbccaaddccccbabacddddddcabcccdacadcacadbaccaaaacdcccbbbbbdcbdadddacbcbdababcaaccbadacacdcacdacabbbccbcdadcdadbddcdbddaaccddccaaaaacbacbdcacdbbbddddccdcaaaccbcbdabcaddddbcbaddddbbcadadcbbddcdbddbbcaccddabcacabbbadcbcbabcacaaddcddbbbabacaabbaccdcdbadbccdccbdcccacaacdabdaadbbddbdabaccaddcabbacadadbbcbdbaacadcacbbbdaacadcddcaabddbccaddccdaddbdacbcdbdacddbadddacddcabddddacabcddcdbcaddddbcacbcccacdabadbddadbdcaccdbcbcbacbadbcbacbcbdbdcdbdbaacbadbbcbcadbbcbddbbddabbbadadddbdbcccacddabdcabdccddddaaadaabbdcdcddcbaadaddccaacdbaaacbddbadaaddcbbcbbbbabacabababcbbbdcccdbddcdbbdcbbcbcccddcababcddbccdccbdbbcaabbcddcabdabbdadcdbbdadcacadadbbaabadacdacdaddbbbdccccdabcaacdbaaaacaaddbbbadccdddcbddabdaabcdbbddcbdaddbacdcbdaadbcabdcdcaacccadcbccddbdcddcabbaddacdddadcccbbcbbcabbdccbbdcbdacbdbdbbbadaabcdacccbbccbcdcacbacbaddaaacdbcaadbccbdbccbaadbdddcccaacddbdabbadbbabbccacbdbdadbcbbbdabbbcdbadacaacdcbcdddcddaccbbcbbdacabacacddacbaddaadcadcbcbabdcdccdbaaaadcaccbddcbadcdaddcdaaaacbdababbadddcddbccbcbacdddccbbbaaadbbccabbdbcabbbcadaadbbaadbcacacacdaabadddcadcdaabacadddacdacacbdcddcccdbcbbbcadaabcbabbbdbdcbcbccdbaabadabcabbadcabcbaaadccbacbdcbabbbcccbcdddddcacabdbddacabcdadbdcabbbacaaddbcbdbadacabaabaaccbbdadadcaadcbcabdabbdccacbbdbcddccbacbaccdccccbdbaddbdbbbacaaccbbdabbadaaabcabcccddcbacddbcdccdbbbbccbbcaaddcdbdbabacbadaacdcbcdaaaaabbabdcadbadbdbcbabcdacadacccbdcdcbdacbadadcaddabbaabcccbbbbdabaaadbbddcdcbbaabdaacaaaaaacaabbddddcdccdbcbaabbabbcbcadccacbabaabcadacaadbdbbaadccdbcdaccdaabcbbdaadbdbdcdadddbabcabdcabccdcacbaddbdadadbacacbaacaddcbabddbcadadadbcdbccadabbaadcdcbbcdaddcddbddadbdaccbddaccbbbddacddcbabdcdcdcaaacdcdaaadbdaccbbdcdbbcbadacccbdddcadddbdccadadccbacabbaccbdccaddadacadddccddabbaccdbabcdbcdbbdababaccbcdbdddcbcbbaabdbdcbacccaadcbcbadddaccbdbcccdddacaadcbdbadcabcababcdbabcaaccbaabccdacaabcaccddaddddacacccddbddbbdbadcbccaacbcdadaccddbbddbabdcddcbbdbadbbbdbbbdbdddcacdcacbbdbccaabacdacabbdbbbdaaccbaacacbddbbabccbbdacaddbcdddacdbdcbcdbcdbdadbdababbadcaadbadbcbdddbbddadadcacdaccadcbccdadbbcacaadbcccbcdcddbcccccddbcdbdcabdabcacbbcddbdaccdbbdaddcadabbcdadbddcaadcaacddcbdabbdbbcdabbaadbbacdcacacdbdbdbdbdcbccabdcbacbcbdcadcbdcbdbaaccbddcaaabbddabbcdcaadabadaadaadbcadbdbbdcbdbcbacddddaddbbdccbdbbcbaacabcaacdadccadbbcaabdbabcbdaabbcabaadbabcacbaadbcbbcbdddaccddbdbcbdacdcabaadaddcdadaababcbcdaacbbaadbdcdbdadbbbcadadbbacdaaaacaddaccabcbdbacbaccbddbbabdcdabcddaadddcadadbaabbbddcabdddacadcadadacadacaabbccbcbdbcccadbbaaacabcbacabdabbacddadcababbabdcbbbbcadbaabbacdaadcbabdadbdcaaddacbdacabacdcadaddcdbccdddadaacbdabbabcacbaabdcdbacccbbbacccdabbbdacacacdabdbcdaddcbacadbcdcdcddaaccddabbbbbdddabdaabbadbbaadddaabbadcbbdbbdaadbdbbdbaccccdbdbaaccdadcdbccccadccbaccbdaaadccdcdbbacbcacaccdcdbbbbdbdcbcacdbdacadbcdacdbcbbdcadbddbcabcccdbcccbcacbadbdacdbdacdcaaccdccdddcdbdbcbcbbccbbbccaadbabbdaabcbcbacabcdbbccdbbbcdadcbbbdabacacddbcddabadbadcddbcdcdddbbbcddbdbadcdabddcdccbddaddccdacdcddaacbdbbccbacccacacbdcacbdacbbdbddcaaadbddcddcbabcbbccacccdcabdcccbdcddbdbcaddbccdccbbbdccbadaccdbddaaddaccdcdcaaabadbdccbcaabacdabacbcabbdcaddbbbbacdbbaaddcaacdbddcaacbccbdcbadcaadaacccddaccbdacdcadbbbccbcdadbdbcbabcbdbadadaabababccdbbdbdbaddacddbcaaaaadacdcbacadadcaddcacbccdbdcadbcdbccccacadbcacddcdbcbbbcdacbcadaaabadcbcbbabcaddbdcdaccadcbbdacbcbddadacabdadddddaabddabadccaccdaaadcbcccdddabcccddccdcdccabbcccbdabcbcaaabdcbcabcdaaabacbacadaabdadccdabaccbddccdbdacaddbbdbddadaabadaddabbdddadbcbacbadcadaddabaccddcbbbdacddaaacdbbcacabbbcdacddbdaabacddcccbdcacdbacdccbcccbcccbcbdaacddadbbbbccddbabadbabcbdcdabaddcbcdabdbcaddccbbdaacdadaddbdddcbaacbabacdaacccdbaaacacbddccabaddbabbcdbcbccccacdcbdaaabdacbbbcbccbddadbdbcbbbbcdbccdabdbbbddacdbabcddbcbbbcdbcadbcacbbddddcaaacdacaadaacbbabaccacbbcdddcdddcadddacbccabccdcdcddcabcadadabdbaacaaddcbcbddaaddcaaddbdaaaccdbdccacbacdbcdabacdcbdcbdbdcbdbcacbcdbbaabcdbccbaabcbdadaaacbdcddadacccbacbdaaabdbbddaaaabbdacccadbabadabcbadccddcbaacdccdbabddacddddbcadbbdbadaadcabbaddbcbdbabdccaaddccaababdaacbddbabccadbcddbccdddaaabcdaccdbddbacbcbaabacddaacbcbaabcbbbbdbcbabdbdddbabadddbadccdcdacbcbbabaccbccbdcbacaaddaddcbbbabadbcadcbadcbdddcaccdaacaabaaddbacadabdbbadcdabdababcdaabbddaacbaccbdccccbbdcccbbddccabcbabbcabcdbdaaaabbcddbdcacbdabdcddcbacddacccbcacabcdadcdcacbbcaaaddbacbcaadaccaaadbcdbbacbbdcaaabaccccaccababbcdababccbccabcacbddbdbbccbcdaccbaabdaaabdccbbabcdccabbaacbbcdbcdcbdacccabddcacabcddaabaacabbaccdccbcddcbaddbaaccdddadbaccdadbadcddbcadcaabcaaacdccbdcbbbdadadcbacbdaaccbbddabacaaddacddbbbcdcbbbcccadbbbcaadabacccacababcbddbcdddbabcdabdacdcaccbabcabbadcadbcccaabcccdbcccccdbdcadbdcdbadcaadcadbdaaaaaddabdccaaacaacdbacdcbaacbbcddcbbaccbccdbddaaadcadcdaaaadddcbabbabbabcddabbcbadadbbcddadcabaddccaabaacdddcccadaabbdccbcbdbcbabcbcaacdabdcbdbdbcdcdbbccaadcbcaccccabddaaabcbabbdcdcbbbdcbbadadddaabccdadcdbbcdcbbaaddabadddcbcdcdbbbdbcabdcccbbbbdbbadadaddaccacbddccbdbdcadcadddcaddccdbacdbaaabcdbaadbccccabaddccdbbbdababadabdaacacddcadaccadacdabbcaadadbdcddbdcadcbccaddcccddcbadcdabcacdbddbcbdabbadaccadbbdccbacdbcdbbcaabbadcbbdbddadadcddacbadbbaccdcacbbaaddaadaccbadabbcbdcccdaabadadaddaadbdcccbabadaccddabbcbacdabbaaccacbabaaadbbdcdbdbbdbdaccbbcabcbadbbacaabdcdbadbadcdbcdbccbccacddcbbbbaacbcbcdacabdccdbcabbcaddcdbddadcccadacbddbabccbcabdccdaabacbacdcddcddcadacaadddacbbababccbadcdcdccddccdbbcbbacdbcbbabadbbbbbadcbccbdbddcbadaccbdbcbbbdcdaadcddccbbbdddcdcacadcbbbcccadbcdadacbcdbaabcdbdbbcadbddccdacbccdbdddadcbadcdddcdbaddbbdbddbabadbadbccabbddadbaacabbcccbddcadcbcaaaccbaacbcbabcdcadccdcbbbbaaadcabbcdcdbbadcbdbccddaccabcabbabbabdbacddadccadadccbdccacbaabacaacdcbcbacbbaaccdbabdbddbbdbddbacccbdcccbddacdababbacbccbdadaadacdccdacdbddcbbacbcdccdbccdadaddbabbdbacdcbabcdbcabaccccaaccacdabaccdaccdbcbdddccdddacbaaabacdcbbdcabacaacbaacdabdbdabaddabcbdbbcadcbbaddbbcdadddcadadcbaccabbdddaaabcbcddddcbdcbcddbbcacdabacbbdaaabccbcaadcddadbddbabddbcaadadadabadaccddcababbadddbaacdcabcddabdadbdaaddbdcabdabbbabbbbbacbcacddcbbbdbbaabddbadbbcdddbcdddbcbcbabcbbdbdcdbcbaaccbdbbbdddcdcadbaacadbbcccadbbbbdccaacbdaaadadcbbcdaacdabccdccbcacdcadbcacdbbccaacbababbcdcacccacaccaddcbcbbaabbbccbacbdaccbdbccdbabbccbdcddaaaccacadabdbbabcacdacdacabccbadabbdabcdccdadaaadcabacbbdcdddbcccdbddbbcdadadbdaaccdaacaccaaacbdddbbddcaacbbcbbcccdbcdbddccacaccbacbdadccbdacbaadcbacabcbdaadccadbddacccadaabaadbcabacabccddbdbbabcabdcaadbacbdcdadacdcdcadadcdcdabbdcabcbbdacbadabcdddbccddcbbbcadcdadbbbaabbbacacdccbcaacbccaccdbcadabbbdbaaacbbdabacccdccadbcbdbbccccdbcdaadababbabdbbdabdaacccbdccdcacabcbddaabcddbbdadbbbcaadddbbcaacadabaabababaabbdcaccacdbdaaaabbabcbbcbccdbddcdddcaaccabaacbacdbbbbadbbdaacccdcccdbadbababbbabdbacabbcbcabdbbcdcaaddcbdcbdcbaaabadbabbbacbaaaaaacccddddcbacbabddbdcbbbdcdadddacbccdbdadcdacddcdbdbabbbdabddccbcbdaaacaccaabddbcbbcaddccaacbbbaaccddcbdcccaabacacdcadacbbbddadcdccbbbbddcdccabcacaaadbdbadaccdbbabdadcdbccddddbccbaccccaacabbdcdcacadddcddcdcbcccddababbabbdaacdcbcddcadadcaccbdcccdcdbaaacbccdabbdbddccdaabdadcdcbbccddbbcacdaadddccbdaabbccccccacddcabdcacaacabcaacdadcdbccbbbbcbdaccbcbacaaaabdaabacbdacaddabbcacaccdbbbddbbabaaadccaacdacccadcaadbbbcdacdbadacccaacabadbdacddbaccbdadbddbcdddadacdcdbbcadcddcbcdddbcbbcaacaddaabcdadacabcdbcdbdaacbdbddbbccdbdcccdddbddcddddcbaaaabcddccabdcadcabbddaacbbdbcccbbabaaacdddbbbdcddacabbacadcacddbdbadacdabbddbbddcdcddbaddbcbcbdacbaadbaadcdacbbddabadaddacccccccbbddacdddccbcbadddaccccbaccdaccbbaccaddcaadabcdccbbbcbbbbdcacccbbcabcdbaaabaacabdcadbabdadbcbbcbdbddacaddbacddbacccdabbbcdbaccdccaacbcbcbaabdbbbbcbbbcadcdbacbbdbbbdacccbadcdaadccccabbbdacdbcdadadacdccbbaaababcdbabdacdaadcacdadaccdaccdcdaddbadcaacaddacccacacaddcaacdbddbdbccacaacacbcddcbcdcdddbadbabbdcaccddbbbcdbbadacbcaaaaddacdbbacdcdadaababadbdcccadadbbccabadadcdbddbcaadbbbddcbccdadddbcacbabacccdbbaccadaacdcbdbbbacdcadbabcadaaaadcbcddbdbbdbaccbddadaccbacdaccbcadccacdacbbaadccbaadbcabddbccdcabdaadbccbddbbadddbccaadccbaccacbdcdbbcbaaacacacadcabacccacdcdacddbadcbcbdaccbbabadcdaacdccdbacaaccbcdadbcbcbdaabdbbccbdcacabbaabcddcaccccdabddbdbbcacccacbbbbbbccadcdadaddadcbbbcbbadbddacabaaaaabdaccbbdacadcdadbdbabccbccadcaccddadbabacacbdaccbadaacbcccdacbdacdabcdbbadbacbcccbbccddcccbbcdbbbdcccdccdabaccadcadbacacdcacbdcdadbcacddbbdbbaadcdcbcccaaacdcccddaadbababddddbbdbbccddbcbbcccdbbcbbabacbdbadacbbbddbdddbdaaacbadbbadbbbcacdddddbaaddddcabccdbccbbacdccbdacbbdacdbbadcdcccabaaabcaccdcbccbabcdaacadabddaadadcadccdccdccbcdbaabbdbbaabdaaabaabbdbbccacabddbabcdcbbdadcbcddacdbddbbdcbadbddccbdcdbdcdaaddaddddaadcadcbbadcaaccccbcbcdcdabdcbacaddabcbccacdadbbabbaddccccaaccbabcacabdcdddbccddcbbdccadbcbbadabbacbabccdadbbccadaabcacbccddaaabbbbaccdcbdadcadccabcadacbaaaaabbbadcbacdaabcbbcdacdaabdbaacababdadbbdbadbccbcccbbcbcdbcabacbcdddbddbbabbdccdaddbbdcbcdacdabcccaaccdcabbdadbacaabdbbbdaccbdcaddbabcdabddbaccdaabbbddcbacadadccddbbbbccbdbbcdbcdaacabbcdabdccdcbcacbbaaababdbdcacdcccbdadabcccbddcbbadbccdadcbdcdadaadddcaaaabccccbdbbbccbbccdccdcbaabdbaccbabaabcdcbcddaaddbaacaaacbbdababccdcbdcbadabbccaddaccdabbaaddbcdbcadcaadcacaccadbaaaacdacabdccadabdadaabbabcddabbbbddcbddbbabbcddbadaccbacbdddddcaabccbbaabccbbcaddccabcbcdbaaaaddcdbdbdccabdbadaaccbbdaacbddaaaddcdacdbaddddbddbbdcbabdbccdddcbdbacccabdcaacdaacbbbcbdbbcbcbddcccbacabadbdcaacbbadcaabaddcbadcaccbbbdacadcbdaacdacaadcdabbbdbcaccdbdbabdcadacdcabccacddcccbdbbbaacabcbdacbbcbdacadbcabbadabdcacdabaddbacdcdcabdcdabbcaaddbaacabdacaddbbdaabcaddbabaccbbdacbcdcbbcdccaabcdaccbcdbcadaaddacbabacabcaccbadcabcabdadbcbbdcbbbdabbbbacaddcdccaddbbbbabadddadbcacdadddbabcbcadddbaadcacabbadcdadcadabddcdbbadbabbdcddcaacaaabbdcddbdbcccccbdbcdacadabbabbbcbbddaadcacdaaaabdbabadbdddbdabcbdcdcdbbbaddcbcbdcccddcaadcbbaccdcdcdbbacdcdcdcccdacacabcadcdddaabccdcbbdbccbccbdbbdacdddcaaabdaacddccbaccbbaaaccbbcdbcaadbcababdaacbddccabcbcbdcccabdbdbdbcaadbabbbcdcddbdadcabadbacaabcbacbcccbaacccaababdabacbdcbbbccdcadacbaabacaadcdaacbcaccbcacdbaacdbbbbaddddcabdcccdaacaaaadcdcbaaddddbdbccdcbbdacbdcbaacaadaadcddcaabaaacabddacccaacbaddcabaaacdbaacbabcddacabcdbdcddabadbabdcdbdcddcbddcaabacaaacddccaacbaaccccabdddcdcccbdaaadcaccbcbccaadadadabccbabaccbbababadbddcdbccabdcdabdacbadadbddccdccabadaaaacbbabdbdbdbbcabbcbadbbbaacdcdacabcdcbaccdbbbbdadadddaacdcadcccddbcddcdbbccaadbbacaaacabcaabccbabdbcdabaaadacbaddbccabcbcdddacdaaadcbabadcbbadcbdbdadccbbacccbacbdacbdacbaababadccbabcadcdddbbbacdcdabbaddccaacadaabdbadbccddacabdccccbbcdbaabdbbdaccdcdadadcadbddcacacbdbbdabaccaccbaadaddccacbddbcadababdcabbabcddbcbbadadabdacbbdddabddbdccabbbdddcbdcaaccddaccccbddbabbacdcddbacdcccacdcbaddcccdaaaaadbdbbcddadbddbdaacbdaadcdccabacdadaaacabbbdbddaabacddbdcabddbbabcacbadbbbcaacadcbbbdaccccabbadaaaccbddbbabbdcdbdbbbbbadacdcadddadbdcaccbbbcdcbcaaddaababaabadabdacdcadacaaababddccdacbcabdaacdcccdcacacccbadbaaaccaaddabdbabdcdacbadcdbccacdbbabcccbccaaaccdcccadbcdddddbbdccadaccacdbaacaacddcadcdacbdbaddbdabdbadccbcdaaadbadbbabbdcbacacbdaddacaaaddacbcdbdcdbabbbadabdaccdcdcacadcbddbbdabaccbaadcdacbcdaccbaaaacccbdaabcdbdaaadbcbcdbbadbabbddbdadbbbddadacddbcdbaaabccdaaddcbdaccccadbccddbcbdbddbccdadcccbacbdbddaadbacdbbaccdbcbacdaaabbaaaaaddbacaccdaaadcadbbccaadccbdaabccacadccacbccadcaadbccabbbabbbaaccbdaaabbcddabacbddabbcaccdbddabadcbacdbbdcdbdcdabacabaccbadbccbcabccbbdcbccaccbdbdcabaacbbcaddbabcdaababcabccaabcbbbcbaacaadcbbccddbbdaddadbcadcddcabdccaaaddcbbacaaccddbdacbaacbcdaccbbdaccacbbcabccbcddcbbbcbbbbbccbacabaddbbbdadaabacaaddbccaadaaaacddaddaccaacbdacbabaaccbccccabbbbdbbbbcbcdaddacaaacccaaaddddddbcbaccaadbaddbcbaaaccacdcaaaaadaaacbcbbdcbbadbbbaadbdcddcaaadcbcdddccadcdbdbcbacbdbdabbbcdbdaacaadabdcccdbdccdcdacaaacdabcabdaabccacbaadabbbcacdbaccbaaccdddcccdbbababbccccbadbbacacadbababacbcdadbcbcbaaddacaaacabacabdcbcccbcddaadcbaccbccddaacabcdbbccbbdacaaccddacdcabddabcbdcdcdcbaaaaacdcdcacdabaacdabdcbdcbcbbacbacdbbadbdacbddccacbadccccaacbbddbaabbdcdaccdbcbabbcdbabbcddbaadccacbbdcacbabcdbdbcdbdddbddaacbbadacdabacdcdbddccdbadcdacdbcbbcbccabcabccbdaaabccadcdbadcbbcdbbbdddbcbdadadadaababddbcbccdcdcbcabcaddabcaaddaddbdddacdcdaccbbcaadbcabdcaaabccddccdccccbddbbdacccadbcdcbbdadbbadbddccdbcbaabbdaddadccdbcbabadcdbccbdadcddccbbdbabaaddabacbcabbbcabcddaabaccdbdbadbbdbaaabdbaadcacbdaccccccbdadbdcccadcabcbaabacbbbcdcdbdbdbaabababcbbacdccddabddabbcddbdaddadccdcccaddbdadcbaadaddcbbbcccdbacdaaadcdbbacddccbaddcdbdddbcaadccbbcdddbaadbacdbcdbcbdacccccaaccacdbddcdaaacbbbaddbddbdcabcbddacbbaaddccbcdbcaccaddccdcbdadcdbcdcadcccaabcadcdcbcbcbdcbdbacdbdaddbbcaadabcdbdaccadcccccbcabbdbbddddabddccdabcdbabacccabaabdbaacccdacbaccaddccbbccddcbbbaaddccccaabaabbaaddcbbcbdacaccccbabbcacccdbbabdacbacaadbbdccdbbdabaacbdbcdaacaadbcbacdbcdcacccddccddaadccbabaccdcacdaabbadaaddaccbcaccdadaadaaabbcacdabdcaddcdbddcdddcbdcdcbabaaabcdacabcbadddaaaadddcccddbadbdabddabacccddaacccdbcabadbcdcdacbabbbccbbbbabcaddacababdbddaaddbcaaddabbbdadbddbcdbcbdacacdcbbadddbdcabbccaabadcabcabaaadbddbbbdbadaabdabaacbcacadccaaaddbdbbaacbdbacbacaabcadbacbcbbabcdbaccddccacdcdbacbcaaccbbbdbbdccaaadccdbdacddadadbdabbdcacdbcadddcacaccaaacccdcdbaccbcbdbaabccaaaaadbdadacacddcdddcdaadbadcbadbcdbaacdacdbcdaabddaabcdcabadadddcbcdbbaaaaaaaccabcaddbdcaabaaaacadbcbaddccabcdbcaaaadacccdaadadbdbdaadbcaabdcacddddabcaacbddbadabaacddabdbcbbdaaccdabccacadaddaacdabadbcacdabcbdcaadbaabdaacdcdccbcadbabbdbaddbcbcaaaabddbcdcdabcdbdabdaccbadcbacaadccabacaabdabcbdbadbdcdcbddbdbaadcbdbdbdbdbcbcccbdbcbbdabbcadabdabaadbaddcadbdbdddbcdccaabbbdcccadcbabbdccddaaacbbacabddbabbcbccaddabaaccccacabaacadbcaaacacdadcadccabddcaacaaaaddacdcbadbbccbbcaababcaabbdaabacdbbbcaccdacbcacaccdbbcacacdbbbdcbaaddddbcdccacccbaaccadccbbccddacdabaddbdcccdaabddcbddbcabcccabbabbabbbadbbaaadcddbddbbcbadcdbaddcdddccdcdbdacaadacdbddcadccacbadcaabdccdabdbbbddcbbadadbadbbddbdcdddccdbacadcbdddccdcdcacdaacbdbdbbabaaadcbacdacdaacddbddbcbdaddcdaddaacdcdddcdaccadcccabaadbdabadaacaacbaacbcbdcabcabbdaacacaabbdccddccdbbccaabcacdbabccabcaacbdcccbadadaadddadacccdcadccdcaccaddbbcaabbcaaadcbadbadbadbbabdbadbdaaacbddacabcadabdbcbadabadbabdddcdbbdbdbbdcbdcaabcbbbdcdbdbaaabdadabbabadcddbacaaddaddaccddcaaabbbdcbcaccbdcaadcdadaacadcbbabdadbdcadcbaaabdacdcddbdaaabbcbbcacbabcdabbdbddbcaaacacbcaadbcbcdacdcadcbacbadaacdcbdcadacbabbcbcacdacbbcbbccddbacadbddaadccbddaacaaaaddbdbbdaddaddcacdadbacbcdbabdaddbbbbacdccbbbcbcbcdbcacababbabdacbacbbdacdcabbcdcaaadcbaadadbdabbdcdaabbcdccbddabadcdddbadaabbabbcbdbbcdbcbbdbddbbbdcacababdabcabbdbdbdcbcccdbacddaabccddbccbccabcadcabacaddddcdadabbbbaabaddcbbcdcccacbcabdddacabbcbaacabbccbccddbbcdaadcadcddccaacbababcdddcbacaddbccdabccddcaaaadaccdbacdddacddabbaabacaadcbdcadcdadaccddcbadbaabadbdbccbdcdcdacaabcaababbabbbcdbaaacbaabadbddbacaabdbbcdccbabdbaaddbcdabdadacccbaccabdbcaaccddddacdabadddaadadcdaabcabcaadadadbcccddadccacadacbaaaddcdbcdccdbbcacaaaacbdbbdcadcaaccdcdcadcbdcaaacdddddaddbbaacdaacdbdbcadadaccbdbcacbcbcdcaaaddcbbbbdcbabbccabaddaaacdbdbcbcbdccddbdaadbdbabdabdcacdbcacabcbbcbddccdbccddccabaadcbabdcaacaaaadcbdaacbdabadcddcccabacadbcadcabbacaabbdacbddbaabbcbaacbdacdcaaacbbaadbabbbaccadabbdadddbdccbbddbdbdbbccddbbcbbdddcccaaaaabcadbcadcaacaccddadbbcddcdbdcabdbcbdadcbccdbccbdbaaabaadbacacaaccaabaabadadbaddcccbcdadcaabcaadcaadccdbcacdadbbaccbddcdaccacdabadaaaaddaaadcbddcaccdbcdbdccdcbcdadccaabbdddccbdcdadccadcacbdcddddcbcdaacacddabddadabcabcbdaadddbcaacdbaabaadaddbcdccdcbaaadcccaadbabbadcadbcccbbaaadcabadcbbbdcabbccddbdbadddcdcdabcbbcacadcccaadbbacdbddaadbaaddaaaacbdacccbbbadadccdbdccabbdccadcdbaadbbbcbbaaaadcbddcccdcddccddadacacccbddbcbacbababaacbbdcdbbdddddaccdaacaddcadbccdbadbadccbaddccbcdddbbabddabdbadaadaacacabcbcddbbaddabadddbcddbddbbbbdbcadbcbbbcccdbabaadbdadbdbcccaadddddaaacbabaddccababcabdcdabdbccdbcdadcbbbcaaadabcabbddccbadbdbcdabbddbdcdbccaabdccbbbabdbacdacdbadaaccadaacdbdaadaddadcbaccbdacbacdbccabbbaddbdddbdabbabdddaaadcbdbdcacbddccdabcacbcdbcccabadccbcdcadbdaccdbaadcaaddbacadaccaaaaadaaaddccaccabbdadabaabcdcdccdaacbdddacadcbdddabbcdbdabddddadacaaddcabdbddaddcaacbaacdbabdaddccaccddcabdbcadbbabaaddbdadbddaacbdbbdccbbacbbddcccacccaccadaddaadaabdbdcbbdabaaccaacabbbdbadbaabadbadcbbbaddbdadddaabccadabcdbaaababccdbddbddbadcacbddddccddabbbcacccbaaccbbacdabcddaaadbaaacddbcdbbacbdcabbcadcabbbaabcaadbaabdbdbaddaddcbadbaadddddddaabadcabcabdcbbacacbaabdabddbbadabaabdcccdabadbcaadbdcabaddbbbcabadddaddccbadbdbbbaddaacacbdcacacadbbdaabaddbdbcbdadddddddbdaabadabbaacbbdcdddacccdbcbadcdcaacbdabddcdadbcabcdcbcaccdaacacaabdbcbbdcbdbbaacdcaabdadaaadaadcdbabbaabdbdcadbcbbbacdcaccaaadcbbdbcbdbdacaaaabbadcaacbdddcabadbaaaaaddbacccbcbabcbbabdabbacbdaaaadadaabcaabdadadcdcacaadbbccdcbbaabbdcadaabacbdcaaacacddcbaadcabbcdaadcccabddcadcbbabbbabacbdcbadadcabacdadbacdddabdbbddcbcaababbcdbddaadabadccdaaaaaddbadcdcdddabdacacabbbbabaddadccbabcdabddbdbadbbbabbcbaadccaaaadddabcbdcbdbabbdcccdbbabdbddcaabbadbbbbcbdadbbdabcddbadaaacaadcdbdcbccaaaaababcbaddcabdadaaaddcdcccbbcddcbaaadbcccccdbbcaacdaabbdbccadaacadddbdaddadaacdbcddbcbaaccccbcacccbadbcdbcacdacabddabcddbbadaaddaacabcddadbcdcdaadbccdcacadbddadbdacbdcddcbaaddacbdddadbddccbcacaddacadadaacddcaabbadaacccbddbabdabcbcdacadbbbacabbcbbcaacdcbacbbdcdbabbaaabdabbcbdcabdcabcddcbbbcbbddbdcdacdbdccadbabacacbaccccabaabddaaacabcbbddbacaacddccdabdaabcbdaccbdcdcdddacabddbdcdddbddabccdabbadbaababcdcdcdcabcbcadabdcddaaddbacaabdaacdcbdbcdbbbdddadbddbddcdcccabbdccdddaacdacbacdbabaaccabcdcddadaadcbbbbacdcabadccaabaccbaaccadacdacdcbddacaaaddccabbcbcdcacbcaaababadacbababbbdbcdaaabbdbdcbcdbdcabdcaabbcabadaadbcadccabcccaabbbbcbcccaddbdbdcbdaddbbabbaddcacaabcdccccaddccaaacacbaddaddbbcbabbccaadaccbabbbccddcdcdbaacabbbcdaaacdcddcbcbbcacdcbbabdbbbcdbaccbcbbbacabababbcdacaaaaadcbbcdadccbdbdddabccdbccadabadbbaabcbbacadabccabddddbcdabdabccbcabcaddbdcbbdcbacbbaadbdbcccadccdaadcbbbbccbbdaacbdbcbccaabbcbbddbcdaddacddcdadacaadaadcbdbbbdcacbbaddcbdabdbdacadabbddbcdbabddddbcabcdcdaddacacdbcccabaddbdabcdcabcdbcddddbabbbdbacaadcadbbdbbcaadadbccbacacbbccacdcdbdcdacadcbcaacbbcbdcbabcdcdbabdabbcbdabdddcbadbddccbddbadcaddccbdadaabdbbccccaabdccdddabdadbddccbbbadaccacacbadcabbbbaaaabcaacacabbbdbbbaaadcddacdccdbaaacdbdabcaabdcaccbbbcabacdccadbcaaccbabbdddbcdddabbdbdbdabdaabcadbdbcddabdbadacdadbccdcbacddbbdccadccaaacabbadcdccadcaaacadbcaaaaddbcbaabadcaddbadbdbbbcccacaddcaadddaabdaadbccadcbaabddacaccdddbbabddcaadaccbcdacdaadbcadbacbdabcbbccbdcaacadbcddbccccaacdaadbababcdcbddaccbacbdcbdbbcdacabdbdabcdaabcccacadaabbbddbabaaabdccdbcccbbcbdbcadbacdccdbbddcbbdaaddccddbaddacaacabcdadcccadbaddadbdbdcacdacadcdbadacdbcaaacccacabdccdbbdbcddacaabcabbdbccabcbcacdabdddcccdcadbbaabbcbdbccccddacccdcccbdabdababadaddadcdbaaabacbdbaacdcdbccabbaabbdcdabaadaccbacadabdbadaadaccbdabddabcddddbadccadbbcdabddabacbaabccbddcdcbcdcddbddacacbaadbccbbaadccaadadbbcbacdcdccdaabaaadcadbcabcccdadbacbabcabcaabbbbbddbdbdacaacdbddbbbbdacadbcbcddbccbacaaccddcaadbbbcdbbcbadbccdbbddcbabccdcdbadddcdacbdaabddadacdacbcccadddddacaabcaaababdadddbacbdcccaddacdabdbdbcbcbcbdddadcbbdccaddbdbaaddbdcabbdaddacdbdcdcdadbabacdbcdbbccddccaccaccaccbadacdccdcbaaaaddadbbbacbaccbcaaaccbdaadbbadbbadaacdbbabbaddadaacdcddcdbddbcbdbcdcbcbacdaabdaddcddcdbabcaaacbdbbbbcdbdbcdcabbacddaddbcdabcadbccbacaddadcbdbdadaaaaaaccbccdbaddbccbdabddbbbdaacdccbcdcddaacccbddabdadddbdcccaaaabacdbdcaabcbcacbadabaddaadddacdaddaccacaaadccabcaacbbcbbcabcbaabdadbadaccdcbbdbcdbdbddddccdacbccadbbdddbdbbaababcdacbabcaaddcbcdbdadcaddcabaaaaaaccdbbcaacdaacaadcdabcbccadabbacbacbabddcabccabccccbcdbdaddadcdcaabbbacaacbbabbaaabaaaacacacddbabcdbbbddbbaadacbbdccddbbbdddbabbcddadbbccacbadabcbcabddabcdaddcbbddddaabadbbdbbcccdcddadbdabdddbadbaccbacabdbbcdccbcdaadcaabccdacbcbdcbabddbbbdcbabccbaacccadbddaabacddabacbbdbabaacdbacdabaaaabacdbacdcccdcddbadcddbacababcbccaaaaccdddccbcbcaaaaaadbcbddddbcadbcdcdddcbbdcdcdadddaabdcbbcddcbbacaadcbcdaacdcababdaaddabcadaadcccdbbdbcbbcbdbbbdbabacacbbabdabaadabdaccccaccacccbcbbabbdacbcdcdcbdbddabbbacbabcabdcaaadcaaabaccabdaabcccdcbadccdabdbaadbbdaccaadccdcacacadbabcdbccabbcabbbbaddcdbdcaaadcaacdaabbabcdcbadbccaaccddbaadcddbddcbddccbdbcdacddadcdaabddbbdcdbbcaadcdaadcdbbcbabadbdddbcacaabaddbcdcbdcbdabacadcbababcdcbdcbcacdbddddbaabcddbbabcdccadbbabaacdadaaddbabdaccbadcbadcbbadaaddbbaacbcabbddcbdaaaabccdcdcdccbbdcbbbdacdaadbcaaaccccccbabbdddbbddddccdabbbcdcddbabbcdadbddcbacdbbbdbbcbcbcddcdcddadccabaaaacccacdaacddabbcdcccbbdccbcadbdccabbabbbaaabbbbdcbbcdacbbddccacccabbacbbccaaacbddbaaacdbcdddddbdccbadcccadadbdabbacbdbbacbcbabbacabddadabadabcacbcbdabbbbbdccabdbcdcbaadcbaacadacbdbcbbdbcdbcddacbcbaddaaadbccbadcaaddaaccbaaabcaadbdbadaaddadacdbdcadbcbbadddbcbbcccbdcabaaccbddadbbdbcabbcddaaadbcadddcdbccdabddbccccdbdbdacadcbbdbcbcbdccbbbbdbadadacdbcbdddcacabcbccbadcdccbacddcdcbbcaacddcdcddcbdacadbddddcccdcccadbddbabcabdbdcacddbbabcdcdaaacbbcadbcadcbaabdaadbbcbdbcbddadbdaacbaaadbccbaadacbcdccddaddccdacabddcbacbccdccddbbbccbbddddadcdbadddbaccdccdcbbadababddbbdaadabbabdcccaabbcdddabccdcbaaddacdcaddbaacbadcdcbbaabaadacbacdddbbdbaaacdbcabbbcbbdbcbdcabdaddddcababcaaaddacbdcbbcbadcabdbbcddcadcbcabdcabdbcbbaabddcdaacbaadbdbccdbbcacabcacacaadcddbddccdbbacbadcbdcccccdbaacacdacdcdacdaadbbddbacdbadbacddcbdbcbdbaaacbbcadcabadbddabdbaccadabccdaaacacabbbdbcabadddccbaabbadbaddcbcbcddcaddccaadddccbbdcaccdaccabbbbdaacbaaddacbdcabcacabddcadddcaaaacaccabcbccadcdbccbbadddbacabdabbbbacbdabacabdacaaadbcbddccbaacccccdcbcccbbbbabccddbcaaaacbabddbacbcadbbcbabbbaddbbabcddcbcdccccaabbabaacacaccabaccadaaadaadabcabdbadbadaaadcbcddccdcacaddcacaccbababaacacbbadabdabaaabdabbdbbddcacdbbacbdcbdaaabdcdabacacdaddddabbaadccdbcdcbadbbdcaccbdcabdabadacdccbabcabcacacbbcccbdcddbadbadbcdcdbadaacaabcddaddcdcbaddbdbcdacbdbabccdcddbbdcaaaaaabcbcabaccbcadababcdaadaccbcaacddabbaaaddbcbdacabaabdabddacbaaacaddccccdbbdddbbcabcbacaccdbaccdaabcdbaacbdaaaccdddbbacdbbcadacdbbbcaccbdcdcdaaabdaaacabcacdbdaaccbccccdccbaaaaaabaccdadababdacacdbbaaacabdbbaabcddacabadddabcccaaabbdacbaddacbbbdaabdbbddbbaabbacdaacbdbbcbbdacacbcaaadcccbcdddaadcbbbcdcdadbabaadacacbbccccbdbdcadacccadaaaddbbcbabddabdddaddcbaabbbccacaaadadcadacbabcbbaabbbcdcaacaadddccbcdcbcbcdcbdaabbddabdcbabdaaaacbccccbcccbdbbbadcaaccadcadcdbadcbddbcacbbbadabbcbcdbcbabcacbbccbdadbddbbdabbbbabdcbcbbadbccdccbcdccdcdadbccbacbacccbcadddacaabccabdabdddcadbcddabcdbdbbadddbcbbbcaccbdccdbdbbacbccdddbdccdddccdcaaacdcadcdadccddabdcddbbcbadaaaccddacbabbbbadbccbaaadccabacdcccbdadbdabcbdcaddcbaaaadaadbcdaabcacbdbacbdaccccbbbabadbadaaddaacdcddaadbddbabadbdbadccdaabbbbcdcabcddbacccadbcddcaadcccaadcdacbcddbbdcadcbdaadbcdcdabbacdacdabcbddbccbbdbbbadbabccadbccabddcabcacccdcaadadcbabcaadcbaabddcbbcadccaacdababcbdbaccbacbababcddbcacbccdbcdbabdacccdbbbddbddaadddcbcabbdcabcccacbbbadbcdbaabcccaacaabcdabcaddbaccbbbacddabbababcacaacddacaddaccacacabcbddbcadbdbdaabdcaabdbcacacbaddcbdcbdcdcaaddcbdcaacacbbbaacbbcabacdddbdcaacccaabadcbcdbbccadcdadcdcbdcadbdcbcabdbadaccddcababccbbbbaadabcbcbcdadabcabdbccaddadcbcdcbbacbabbbdbdcadccbcccccdbdccbbddcadabcadcaabcbcbbaacbabbbadcdadcbdcababcccaacdbdacdcccbacdbdbbbabbcdcbcdabbcbbacadbdabbcaaaacbcdadcbbaacabdcddcaccaacadabdaaccadddcabbbbabbabdaabdcdaccaadadbbabdbcbbcaadcccaddcbabacaadcbbbbcacdbdbddacbaddcbdcbdbbaadbbddaadbcaaabbacbbdbcccaabbcdaddddbaacbcdcbaacdddaaaddddbbdbbdbcbbcacadadaddcbcaaccbaacbadacaabbdadabadadaaccaccabbdabcddccacabdccaacdcdcacddbadcadccbdbdddadabbcabbdcbcacaddbacdbaabaddcbccdacbcbccadaadccaddaddabbbbbddbaaacbdcacddbdadbadbaabcdaccabcdccddcddcdaaadcbdbdabadcabcccdabccdbdccbbbbadddddbacacddaddddbaabcdcaadcacbdccabadbbabdcccbccbdbdbcdcdbccabdadbcdccacabcabdccdadcacabdddaaabcccbbcddcbbdbcdabcbccabdacacdcabccbacddcabcacbcaaccaabbcadcaaadbacbbaaaabbadcccbcbccbadbcccaababcbccadcdbadddaadcdaaabdcaabaabbbcdabbbdbdcbacddabbaadacccbadddbddcdabcadbdbaccaccaadddddaacdabccacdacabdcadbadabbaddddbaddcabbdcdcacacdcddbadcbcdddddaccbdbcaddadbbbacaccccadbabccaadbdcbacdadacbabbbdabaaabccabcabbadcaababadcabbdbabddaccdbbdddadbbdddcddbcacdbbabacdddccacddbcaaabdabcbaaccbacdccccdbcdaabdbacdaacddcbaacabaabdaaadcbacababcbbdadcadcacaddbcdbdbcdcbabdabcdccadaddbbcadcabcdbbbaadaaaabccbaacccbcdcbcbbdcddcbcbaaabaacbbaacaadbcbdcabbdbacbdddadcdddbcaddabccdcdcbdaabdcbcdcdaabdcdcbbaabdccddcabbdcdbccadbbdacbbbbdacdbccdacdcabcddadacbcdaacdabddabaaccbddbadddccccbccdcaccbaacddacbcaccdcaccbaaabddddadcddaccdbbdbbacbcaccaccdadcaaaddcadbddabcacdccbcccbcbbbdcbddacbcddddcdcdbcdbacbcacbcacdbaadadbcbdcdbdcabbdcbbccdbcdbcbbdccdaaacbbadbaaaccacdddabcbbcaaadbcdaccaadabadbcadbbbdbcbabdcdbddcbddbddadacdcaaabacdaabddbdbabbcadabdcdbcbddabccbdadddbdcbbbadadabccbccbdabcdcaadadacdcaabbddbbbbdcdccadbaaaaabdddddbbacadaaaabdbbabacacdaadabbadccccabcaaccbdcccdcabcacdccabdcbacbdbadadbddadbaacbcdadaabdddabdbbcbcbbddbccdbdbcadcdcbbdbbbbddbbbddbccbccdddbcbddbaaabdbbbccaaaadbdaaaddcdbaddacabdcccabadccbdcaadbdabbbdcbaccaacdcdcaddcaaadacabbddcbaabdaacaabcccacdddcbbddcbaddbbaacbbbccbcdcacacddbdcbbdcaccacbbbbadddcbddacddbdbddbadadaaaaadbdaabbbcdbabbabaabaaacccbdbddadbdcbadbdadcbdbbaacaddaaddcbddbddddbabbdcbbacdbdccdbdbcdadaabdabbbcbdaacccccdbddbdbdcabdbbacdcccbadadcadbbacdbaaabbadacababbcbadbbdaadbccdbcdaaccdacbdbcdbdbccbbcccdbcbacbbbbbdbcddbbbcaabdaabcccdcdaadcbbdabbdadddbbccabbdaadcacbacadddbadbdaabddbbdbbbbcacdbbbacaaacbbacdddcbccbdbdaadcdaccdacdddddbabbcacdadcdadbcbdcdacbcacdcbdcddbabcdabddccbacccbdbcdbcadabbdadcaababcdcbaaaddaabcccaaccdadbdbacbbdbddaddacdbaabadabdcadacdbcaaccdbdacacdadcadcdacbcbcdccacbddddccadbdcacacaddbbdbdcbbdccaabcacbcdddbdbaabddbadcdaabacabccababbbadbaadcbdadddacbdcdabdaccdbcadcadbaddccdadaddadddbabacbcdabcacccdddcaccbabaddcaabdbacaddaaadbcdaaabbcbdcbaadcbdbcbcdaccdbdcbadcbccbcaabadacdcbacdaabddcaabacdcabdcaacbdaabadcaadbddbadccbdaaaadadcddaccdbaadccdaccbdbacbbdbbacbabbcadadddcacacdcdbbcdbcaddccdbdbababdbcbdcbabddbbddaadaacdabacccadccbabbbbbbdcdabcbbbdbbcbadbaabaacbccaabdcaddccbbacaabbcbdcdddabdaddadacacdccdbddaccdbcdccbaaccaddadadbcbcbbbaccdabccbbdbdcbbbaddaaaaaabccdbcdcaaadcbddbddcdccbcabaadaabbacacccbaacddcbadbbddbddadbaccdabdcdaccaacaaadadacdaabbacbcadadbdbdcdcdbdacadacbdbbdcdccbbaddabbacdabcbdcccabacadbadcdbacbcbacdcaaadbdbcbbddbbbdccdbadcccacaddadacddacabacbaabaaaabcdcababddacabacbabcddbbbbcadacccbdadbdcdadbabacccbbcccacacddaaaccbcbbadbbdcaaccbbbbabbccacbcbacccdbdaddabdddaddccabcbadbaacdbbadaaadcdbbdbcbdbacdbadcdbabcabdbdbcdddadbabdaddcbddabcacccaabbbadcabbacdcddadbcddacbbaaabdddadcdabadaadcccdadbdbdbcaaddddccbaabccabcacbaaadcdabdaaaccabccccaccacaddbacbabdabbdaabaccbaddabccbbabddacdadbbbbbbaccccadccccbddbaaacaabdbbbddcdcbbdbdbbadbcbdadbbbacccbccdabacddcbdcaacabddacbaddbcbbcabadbcdccabdadbcbcbaadcdbcaccbccdaddbbddccbcacbabaaaaaaaadabdbdadccbbaacdaacabadabcbacaaddbadbcdbaaccbdddacbdcbbbdccdccacdacddbbdadbadbbcacdbbcdcbdddadbcbccacddabdcdbcbbcbadbdbbcabccddadbccbbabdbcdcdcaccacdbddbbbbaadbddbbaacadccddabcccdaabbdaaabacacbbbcdbabbbdbdadbcaabccddcddcabcccbadbabdcbbbcacbdbbaacccbadbcddaddbacbabdcdaaccddadcbcaadaabccddbddbcacdabdbccdbacdcaaddccacddbbaccbbcddabdcdbabdaaaaaaaaaadbcdbacbacdcbddbdbdbdddcaaaaccdcbdacdddbdcdcbdaadcdcacadcadcbbbadccbccdcbdcbbcabcacbdaaddcbbabbaccbcbadddcbbdaaaacddddbacaaadcdbcadddabbbadbacaaabcdaadacbdbaabdacdcdddcbbdaaacbcdbdaddcaaabdddbcaababdbbbbbaabbcdbacccdcacccadcadcdbabcbcccdaadcdacadccbdaacccddcdaccabddbbddbdddabdadcdccdddaadbdcddcdcabbdbdcbdddadddacdccbcdabdcdcccbcdcacccaddbdddabbabdadacaddacacdbadddbdbcbbccbdcddacbddbcbbcbdaadabbabdddddcbcddcdabcacdcdaddcaaaccdbbcaabcbcccaaababcbacaabcbababadabcbacadcbaacdbccbdcddcabdabcadacabacbdcccccbbadadadcdccbbbaabcdabcbddbbaddbacbacbbababccbaacdcdcdbacadaaaabaaadcabbacdbacaddcdddadabacbddaccdbcddabbdbccdbbcdcdbacdccdbabcbaabdbccbaaabbdababcbbdbdbaabbbdadcabadbccbbcabadbacbbccacaaccddbbdaadbcdbdcdbcadabacdacaaccbabddabcbcadabdbbadadbabbccaabccbabdbdbddadbccdbbbcabdbabacbaddcddbbbcccabccddbbbdbcccdcdbbdbbcbcdcaacccaacdadbdcbcbbbabbbcdacbccaaaabaaccbbdadcbdbdbbcaaabaaadacddddcccccabcccdcacbcaddabdabaddcbaccdbccdabdcdcacccaabadbaddbdbdcacaacabcbaaabaccbcdcddacacddacdbbadcdccadacdbadcbaccacbccbaabbbbacadbcbabcabdcadcbacbbaddbcabdddbcadbdbcbabdabaabadaaabbaddaccdcccbcaadccacdcabcadbcccbadcbaabddbdcccabdcbbdbbcadbbaaacdabdcdbbacdccbcdbacdadccaaaccabbbdbbcacdbdaacddabdccbccabacdabadbbcabaabddccdddcabdbbddbdbbbaddbbbcddbcbaabbdbabcbdcdddcddbcbdabdaaacdadadbadbcbdbcccacddcdabcabcaacbadbdbcbaacbbdacbdcbcdcacaaacdacbdcababcdbddadabbdadbacbccdcbccabcbdcdccabbabdbcabaadccadaabbadddbdddcadbbaacddacbcdbcccbadccaadaccbcbbbbdccdbcbdacbcdbcadadbacdacbdaaccdabcccdbdbcdddddacbdacccddadadacdbcbadbabcdbdbcbabbbccbaaabdcdccdbdddcaaacbabdccddcadbcdbbbcdcdcbcbcaaadbdccaaccadcbccddbcbaacaababbcaaabaaadbbacadcdddbddbdcbcddadbdbbabaadabcdabcdddacaabccddaaddbbbcabaccccdbaacbccbabddbadabcdaabcddabbdddabcdcbdcaccbabbadabaacbcbbaabadadadbdadaacadbddcdbbdcaacaabbcbccdabcbdccbdbabccbabbbdadbdbbdaacabdcaaccadbcaccbbbcabbaaddccabcccddddcdaacdaaadcbaadacdbcabaaacbacdccbdcbdaccdaaacaccbabbbcabdddcdcdabcdacdcadbabadbdddaaacbcdaacadaabcabacdcccbacbdcadbbbcdacadbdcdabacadddcbadcdcdcdcdcbbdaaaadadbbaddbaddbddbabcccddbbaababcbccdcddccdaadcaabaacdccbaddacaabbbdacdcbdbdcbdbbbcdabbdbbdbbdbcddcbcacdbcbbbadbcccbbadcbabbccabadbaccdabaccaacdddbbdcbaccbbbacadabaadcdcdaabbaddadaddacddbcdcddcaacbcdddcccbaabbdbabdadbdcdcabdaadddbddbbbccbadabcbbcdcdbcbaccbbddacacdacbdddbadbbcbabbbbbaddcaaaaddaabbaccbddaacabcbdaacacbdccbccaaabaabddbbdbbabdabbdccabdababaddbcaddadaaddacbdcadaacacccaddcbdcadcbcadbaabbdcaaddadcbbddadcbdcabcaabacbcdcabbddccbcbccbddbdbdaccbccbbabcbdcaccacdcacbbcaabcbcdaccadbdbbbaabdcddbaadddadbbcdabababdbbbddcabddadaaacacabcaadbdcacaddddbdbcccacbdacadcadbdadcbbadabdbdadacccadadabbbbcaabcdbbdbbdaabdaadcdcacbdabbaadcbabddbcbaaaacdbbddacdcccddaccaaadaacaacbccabcbdddacbbdabbcacbabbbacbbbbaccaadbcddcadccdbbaabccadccbcbaadaaaaddadacdbdbddddaadbdacdbddcbbdbaaccccdadbbbaabdaddabbacbbdadacdabcabcaacbacbbbdaccdcccbbddbdbbabcbbdbdcbdaadccaadabddbcacaabbabaacccccbddbdbbbcaadddcaacaccabbdbdbcbaaaabccbdbcabdddbbdbaadbdcbbdbdaabcbbabcdbddcaadbbdcbdddbccdababbbadbccdbaccbbbaaddcacdbcbbdbabaaadcaccaaacabaacdcdcbacabadbccdbcddadcbcbdccdacddcdaccdbddbbbbdbcdbbddcadbbdaaaacbabbcbdbacddddcdcdcaabdbabdbbdbccbcadccaccdcacbdbdbbbaccabdbbcaaabcdcbdbbdbccbddaabdbddabaccacdccadbbadadcbdbbadbcababadadcccbddcbabbaccdcacddbccdbacddccdcaadaccadaaababaadcbcdacdaabadbdccbbdadddbcadcaaacacbbdddcadbdbababbaddcbdbdcdddcdcabbdaababdabbbbabaccbbbbadbccbbbbdccdcdadacdababacdabddddabccddacbacacbdddbdbbaacdcdacdccabdddbbabcabccdcadbabcdbdbdacbdcdbccadcacacacbadababdbdadbaaaccbadbcdbcbbcaadcbacabddcdaddccbccacabdcacadddacaccdcacaddcdcbdadabbcdaacaaadcbaddabccdaabaccbddbbddccdddbbdcccdadcdcacbdbcbabdabcadadcdccdbccbddabdabbbaadccacbbbcaabbadddcabbdbbcbaaccababacbcbcabadaaddcdbaddddbbcdcdccdadddbaacbddbcdaddcabbbccbabcbdcabcacadadabbccddacbbcbbbccbaddcdbbbbcacdbdadcbbaadadccaaccaddaacacbddacaabbcddddaddbadcdcbcddaddbbdbdaadaaabadadddaccbabbbdcaccdbddcdcabbbbcbadadbcccddabcaccbcdbcbcdbadddcbbabbabdcdccdadccbdacacdcadbcddadcbcaaaccaadbdbcbaddbadcbbbcaabcbabdcbcdcbddacacccbadaddcaadadcbaddcbcbbdcaddcacdbadcbcbcccbbacbaccabcbdccbcabbabdacabddbdadddddadcbdacddccccacdabdadbdbcbcaddccbbbbcbddbaaabddbcabbccacbbcddcdcbdddccdaaabbabacdabbcacacaacbdaabcaccdbcaadcbbddbbaabbcadccdbcbcdbbccaadaadcaccaacbacdacaadcbcbdacdccccbacccdcadabbbbacdcdbdabbdbabcdabdadccbaabbdcbcdacaaddbabbacdbdccbbdccdcbacbdbcbbacdcacacccbbcbaccccdadbaccbddbbcadccacbcddaaacdccbcdbaaadbaaacdaaadadbacccbabcbabaddbacddbddccacddbdbbddaaaaaddbdcbaccbcbcdbbcdcdbdbbbababbcadaabdcaabaccdbaacdacdabdccdadbadbccdbbccdbcdaadbadabbcbddaccacbaaabbdacabbbbcdbabccdbadabaadabbadacbcbaaddccbccabcabdccbbcaccacaddbcabaddbdbcacccdadcbdcdacadaaacacadbdcadaccdbbadcdadadcdaabacbccbbdbbdbcbacccadabcbcbaccadbbdaccaaadbbabbaddbbadadabcbdaacccdaadbdacdaddbdacbdabbabdadcdcaadcdabacdccbddbacbbacbacbdcdbdbbcdadacbbbacbdcdabddbcdccccbdbaacbcababcdbaadbbaadadacaaaaadcadabdbcbbddadbbbccbbabcccbacbaadaabbcabacbdbdaadbaaabdddbdbcaddddacaaddacdcaddbcdaaabdddadcbcccbacabdccbdabcbdbaadaaaadccaccadddaaadaadaadbcacaaaaaccdcabaabcbadcbaddbabdbddcadadbdbaddcdbbadacbcccdbbcddaaabcabbbcbbadcdcababbcacbbabdbabdbabbaaddadcabbdccacdcbdbacbbadacaaccbdadddaabbcadacaadaacbaccbcadcdcadddadddcbcbddbcaaadabbaadaabbdbadccaacbacdaadbdbbbbcbbacdcadbadadaabcccbbacdaaaaaabcaabddadcddbdaadbcbdccddccbcbdacbbbbbbcbcbdcbdcbdaadaddaddcbacbdabaddadcdacdddabbdcbbabdddbbaddcbbcdccbdcbabddaaccdbaadcabdcdadabdabcdabccbcadccacdbbddbdadbbdbbcbbbadaccdbdabcabdacaaccbdbaaddcddcdabbccbdaacbadabdaaaccbdcadacaabcaaabbcabcbababdccbddcdbaccbdabccaccadbdddddabdabbbdbdadbabbadcacdaadabcbcccdacaccaabbabacccbacccadccabdabbdbbccdadcbaabaaadabdcaddbdbaaccdadbacdabddcdcaacaaccacdbcccacaaaabaccbcbcccacdbddccaadaabadcaaadabacbdbadcacaaddbdcaccacbddaaabdbbbbaddbcaccbbdcacbdbcdadbbaaddbadddacddacdcacbbaccdcbcbcccdcdcdddadbabdcbddbaaccdadadbbbaacabccaacbcddbcdadccdccaccbabdbaabaabbcadaccdadbacadaaaabaaacbdcccabccdbbadcbdcccdcbcabbddadbcbcdbdababbcccadaaabbacabcbbcdaccaadbadccdcbadadaabadcbccbcdabdabdddddbcdaddaabbababadbdcbcdbccacabbbddbbdddabdcadbbaddcbcdbbcbcbcbbcbddccccadaddbaaddcabbddacabacdabccbbcacdbcccabbabcacbbaddccbccdcadcaddacbacaaaddbdbcbddabababacadbaaddcdcdaaadadbdddbadaccbbbcddcaacadcbbacabcbbdabbcbbcccacddbccdacaaadcbcaaddcbcdaababadabccaaabacadbcbcddacddacacdbbdccabaadbbbaabdaacacddcccadadcbbcbcdaaabcabcabcddcccbababcaaaaaaccdddbddbdcaabdccbdadacbbccddccdcdabbddccdbdddbdcbcbbbbddbcaddbcdabddcdccbadbbdbacbddbdbddbacbdbadbabccadbcbdcdcdcabcacabacbbdbacabbcaabcaaacddbddcadccdadadbbacdddccacddbddbddbadcbdacddcdddccbabaddaccdcddaacaacabbacccaaddbdabcbccaadcdbaccccdcbcadbdaacbbccacbcaaabbbbbdcaacdcdacbdccbddbaababbbccccbadbcacbdaabaddadbdacddcaaadadccbbadacbabbbcdbbbbbbdcabbdcddbcacccbccbbbaabcbcaaaaccadcaabcdbaabbabbddabcabdcdcbacdbaabcdbabcbaacdbaacbbcdaadddddccbaadbabdccabcacacacaacbdddbdadccaabddaabaaddcabdabbacdbcaacabaddbaaabdccbaddddacaacddbdaaccccdadbaababbbbbdaddccdadaabccdaddddbadabccbacccbddcbcbacdabbbadbbdbddbbbddddddbdbcadbcbcbadccacdddbccdddaaaadcbadaadbcbbbcbbbaccbbbbdcbbcacaddbbcabddaadddcdabbaaacdbbbabddbccbccdccacdbdbddcadbdcdaadbacbbdabcddbadccddbdabbaacdcbddddbbcadadabcccbabababbcabdaaccdbaadaadcaaaacaaddcbccaadacabcdcdcabacbdbbcdbcaabbcbbdbddcddcadbcbddadbdaacabdcaadbdddabaaacdbdcaabcbdacdddcabcacddddcdadaaccbadacdacbadccbdaccddaaabccacaadaacddadcbacacddacadbdcacabdabbbbaabddbcdcadabaadaddbbccabbdcdacdcbdacaddacacdbccadddaaaadaaccdddbcbadacdddbccadabdbaccaddbaabcddbcddddabaacdcbbcacdcbbbcdcdbabacaddaacaaccdadacacadbdadacdabdbcabdbbccbbdbddabbcdcaaabadbdaaaddbbcddadbacaaacabdaabcccbbbcdcccddbaadcbdccdcdabaddcddacbbbdacaacaabbdddddcdabbaaacbbadbadccdadbcdbcbcabacdbbddbdcdabaaddacadcbdaddabccddaccdccbdbdbbdadbdacbdbcccacccdabbbbdadddaacbcdbadabbacdadbcccccccaddadbaadddbcdccdcbcbbcacddaaabcabcdcdabbbadcdbaadacadcacbbccdbbdacabccabdacaacadabacbcccccaddbbcabbddacaddabdaabdaccadabbddddbbaccbdccadbaacdbdadddbaccbbdacbadcacadbacdbddbacccbadbbcbcccddadddcadcaccbddddcaabdadbcdaabbcabccddcccbcddaadbabcbdccdddddacbcdbcabacabccdabbbadadbbdbadbbacaabcadbdcddaadcdcaaccdbdcabddcabcacccdcabdbdccbccbddbcabcbabdcccbccdcbbcdbdbbaaacacadbbdbaabbaaadcbacaccbddbbdcbbbadccadacaddadcacbabacbaaababbbccbbacddbdacaadbdcddacccddbacdadcbddaadabbbcddaccdabcdccdadbccabbcbcdcccbbbcbdadbbacaaddbdabcdabcbbaddcaabddcabdaaaadbcbbacabccdcadaccbcddacdbdbdcdcadcadbddddccbacdcdababccacdaabcabdabcbdcbbbbaddbacdbcaabbdbbccaacccdcdbbbabaabcacabababcbaccddcbcbccbbcdbbdbcccbbdaacdcbdadbddcdcddaddadcbccacccaacdddadcddabaabbaddacaacbcabacbdaaacdcbcaacadbbbaccaadabbdaabdbdadabdbbdabdbabbbcaacdacdadbdbadddddddbacdabdbbccaddcccbacdbacbdbdadbdcaddccadaddcbbbdbbaddacddadcbdaddacddabbbcacbbdbcaadddcabbccdcabacddadacabcbbbaaaadadcdaaddccacacddddccbcbddbbbdaccadaccbbaddacdbdacacdcbadbdbcacbbaaadddbccbccdbdacbccdaaacdabbccaabddbbdcadbbccaacbacacabbadccccbddabaabbccbccddbdcdacbabccbbbdbdbcacadcccbdacddacaaacdcbadaabcadcdadbdadbbbdddcdbdaadaaddcdcddddbadbbddadcabbbbdacabcbabbacacbadcddbdadccdcadabaacaddcaadabdcbadbccaaabddbcabddddcdacbbdddabadbbbcbcabbbbdbccddbaabaababbcdbddcdbcdcbdadccdcbdaadcabbdddccbbaaccbccaddbadaabddcbbdcdbcbabdccdbdbaaadbcacacddbdbbabbdcbcccbdcaddabccbaddddaaabbdccdabadcbacaddabcdcccadbcaccacdddadddacabadbbaadbcccdccdaaddcdbadcdcabacdababaadadddcacbbaabbbdbcccabcdddbbcbcccacacacdbcadacddcbbcaadccdbcacccdacddbdddabdacaacddcadbbddddccbadadbdcacaacbdbddaaacbadbcccddbbcdabdbcadcacddbbbcbbbacdbcbbcaadabaaaabdddaacbdbdacbcdadbbcabcadcdbbbaaadaabdcadbdbcbccabbabcabcbcbbbdadadbdadbbbaddcdaddccdcbcdcdacabbaabcbbaccbbaadaaadaabccdcdaababadacdabdcbbcadbcbccadcabdbdcabccadbdcacdbccdddacbcdbdbbaaabccdacbbbaacadacbcbdabdcacacabcdcbaddcabcdabbadcddbaacbccccaccacdaccbabdbdabbbcdabdbbcabdcabcbbbdcdbbdbbbdcbdacdbbbcccbabbbdaddbacbaacbbdacbccbabbbbacacabcabacadccbdddbaaabdbadabbabcadddaaadabcdcbddbdcdbaccaaadaaadcaccabccccaccbdaacddbddbdbdbcccdacbcbadbcdabbbabcccdcababccdcbadabcdcddcccdabbadadaaddbadabdacbdbdddbbaadabbbdbccbddccacbacadbabdaaccccadabbcaaccbacadaaccbdbabdbbbbadacbccabdcdaaaaaaddaddcabdddadaaabbcddcbdbacacdccbdccbbabcadccdcdabbacabddccdaddbaddccccadcdcdccdbadbcdccadccbcbababcbbcabbcbcbdbaaddddaaccdcccadabdacdaacdddcbabcddcbdbbbcdccabdacdbbdbbcbcaddcbcccdadabccaabcbaadccdbbbccbdaaabaabccbdcdaadababbdbbbcabcadccbccdccacdbaacacdaacbacbbadddccabadaadaaacadddbbddcbcadbddddaadccabdddcdadabaddacbbadadacbcddabccdcacabddbcdcacbdbbabbabaabadbdcdccbbbcbbaabcccccddcbbbccdccaaaaadbaccccbdcabbadaadaaabcddbbdbaacdacaccddbcadcdbdddccaccadbdabbdadbabdcddccbbdabdcabadabbabacbcabcaaadbdcdbdbacbcddadddbccacbaabbbdcadcbdcdcabbdbabaabacdacccbddbccadabbbbbabaccabacccadbaaadbabddcdaddbccdcddcbadbccacacccabcadbabcddacdcdcacbccdadbdacdccbddccabccbabcdccaabcadcbbcdaabccadbdbccadabbaacabadddacbbadbbbbdccbccddabbcddacccbacbbbdcdaddaaccdbbccaacacdbcbbdddabbcbbbdcaaacbabbcdbadcbbacbbadbabcddbcaacddcccacaabdccbcabaabccadbcabbabacbabcbcabbabbdccddadaaabaabdcdbbbbcdacbbccbccacbccdcacbbcbddacabcdbdacdadbbdddbdcdbcdccbddcbdddaccadabacbacaababbdcdbbbdbdcddabdbdcdabaacacabbbcabbdbcdcdbbbddbbdaadcddabdaabcacbdabaacdcddbbdaddcccabbcdcadbbbaacaccdacabdacdccdaadaabbcadadbddcaadbcbbababbcddbadacdcbcdbddabaddabccdabccbcddbcacacddcacdddccbaabbacabdcbdcbdccaacdbdbdacadbcbddbccdcccacddacdbdccbcaaacbdbdbdcdbaaaccdabdabcddacddcbaccbcdcadaaacbbadcddbdadbacbdadacddabacdbabcccbdcacccbbacadddbbaabbdabcdddabbcbabcddccaaaaabdcbdadddaababdbabbbadbcbbbbbcbddccccccaaddcbcaaaadccaadbcdacdaacdbbbdbdabdbacdcdcddcabbabaaaadccddcaaccccaaaccadcddabdaadcdaadcdbdbacabadbcbdbddccccaaddcaacadabbaaccaabdccdccbcacccaabccaabacccbcbdbaadadcadbacaaacddbdcabdaccaaddacbbcadbbabddcdaabaacdaadbcaababdcababdbbadbbdbacbdccabbbbcdacabcbcaabadbddadddaadbdccdbabbcbddabdbbabadacabadcbcdbdcbbdbaacaccaaadabdbabcacbdcbcaabbbdcdcbabbccccaddccdbabcbbcbccaadddbaaddddbacccdcacdbcddcbacbddcddabcaaacabbdbcdbddacdcacdacbcbccddbdddadaabddbcabbadaaaababcbdbdadadbbcbddbbccaddadacccccbabbbbabbbcabbcbcbbccdbdaccddbcdcccdaabdbcdbdacccaaabdcbccddcccadadbabcdccdabbabbcccbdccbcbddcaaaddabcbdcabccbddbcddddbbadcbaadccabccbbddbbabdbccdbaabbbddcbcbaadccbbcdcbacccbcdddcacaabccbbccdcaacababcacbbaabbdbadabbabcabdbbcbacaabccdddbabcaabaccbdbadbabaaadccccbbccccaccbccccbccabaddbbbdcabadcdccababcbadacccbcddcbdabbdccaacaddbdadacddcdcccaccdaacbdcbbcddcbaaccacdccdbbdabddabbbdddcbccbcdacbaababdbabaaddbaacbdcdddabbaddbcddabacdcaadbdcbbbcbaccaabbaacaabacdaabbdadccbacdcbaabdbadcddaabbccbddcbaabcabcdcaddabbcdcbbcbccbbbbdcccccacdadaaaacbdbcaabdbaccbdccaaaadbcccdabbcdccacddcabdddcaaabbbcbbdbadbadaccbababbcacdbcdacbcccbdadcccabaadacddcdcddcdbbdbcbdcdbcaabbabcbbdbacdbdaddcbbcdcddcbccdddcdbdcbccadaaddbbcbcacdadacddaacbdcdbdcacaaddbcccbaaccccbacabcbdbbddbdbcaabccbcccdcdbddddaaadbdcacddbadaddccbcccbdbdcaabaacbaacdaacccbbababdbcdacacadaddabdabcdbdbababcadaacbdbadbcacbddbbdaabbdccbdbbabaacdcbcabbbcbddadcdccddbddabcddcddbadcabdccbcaddbbbccdcacdabdbdcbacddddabbdcabdbbcccdbccdbcbcaddadabbcacaddacccccdccaadbdcbdacbddaccdcbdbadaacadccbcbdcdcaaabdaaacbacaabcaabcdacbddbacddddbbcbcbdbcaaacbcabcddbcbcbbdbabbcaddbdddbdacddadbdcdaaddacdbcacacdacbbdabdadabbacbabcddcacccabddddbbcdadcacbbbbadccadddbabbadccbbbaacdcadccdccbadbcddccddccabbbbbaacababdcccbcaabadadbadbacacdbcbcaabdcbdbcbccddaabbdabbbddadbbdacdddccacbbdadbdcaacdcddccaaaabacbddbddbccccdbaacbccddcbddbbbcddbcbccadacbdddccbacacbaadbacaacacdcbdbaacbccadbaccabcbaabbabdcddbdbdcabdccdaddbbddbaacdbacdccddcdaaabbcdcacadbcdddadddadbbabdabacccdaacbbaadccbcbdcaabbcabcbcaaddccdabdcdbacabaccdaaaccaadcbbbbacbbccbddbcbcbadcaaadddcacdabaaabcbdccabbddacccadabbdadcacaadaccaddcccadbbacaadcbccacaacaccabdddcdcbabdbdbbaaccbabbbcaadbcdcdcdaddbcddaabcdabcaaaaaabbbbadbddacabddcaddbcadbadabccbdaaadcabaccccabbdddcdaaabdbbdcdcdcddadddbacabcacbdcacdccaccdbdbbcdcdacccbbbbdabcaccbcaadcaddadbdbbdccadddabbbdbbacabcddbdbbdccaacbaaabcadaacbccbaabaddcbdabbbdbbdbccddcddacdcdbabacccbdbbaddabbdbaabbadcdcdcbdacbadbbbacbbdacabdbcdbcdbdbbdaabaddbaddabbabdacccabcacbadaabcadbdbbcbbcbdaaaababbadacbdbcbadaddbdacbcddcdcacbbcddbadcddababcadcdcccbcbbdaabdbccdcbabcaccabdcddbbbbbbdcdcdccdcddcccaaddabcadbdcdbbcdbdcdadbbccddacdabccdccaaabccbabacbdbdcacbaaadbcbbcbbaccbaaabadcbdddbbadabaacabacddacbddcdccbbcabdbcabcacbdbccdbaaccbbcdacbdccdcbdccaccdadbbcddbbcddddbcbccbadbaabbcdbcabdacbddaabbddccabdddaaddadbcadabdbbbcdbddbaabbbbabbccbccaccabcabcacbcacbaacddadabcbbcdaccccdccacccbaddcbdccddacbbccbaccdccdcbdcdbdcbdabadbdbcbbbcbcbcbaabcbbaddacaddcadddccbaccdcaaadbcbbcacaaacadcabccddbccddbacddccacdabaabacaddcbcddaccacdbbbbbdadabcddcaacbdccddbdacdcbacbcacacbdbddcbacaabbdcdaadcbacdbcbddcdbcbcacbdbdadacbbbabdcbccaaccacbbaaadcacacaadabbaccdbbccaadadbcbbdacdcbdbabbcaadbdbaaaddcbabdcbdadadddbbcaadbdbabbccacaacdbcaadddacaaabacdbbabdbaaaabdbcdbddbbbdbdbdddcaccdbddccaacddcdaadcbdaabbdcacdcbbcbaddabacbabacacabcacadddbbcdbadabaacdcbaaacbacbabaadadaaadadccacdaadbdbadacddcbbbcddbbaddccbbcbddcdbbbbababbddbabdbbcbbbbacccacdabaaabcbaabcadcbabaddaaabaddbcadcdbdbbaabadbdaaaaabaacdcbacaadbababbaacdbdacbaddaadbcdccaadbabadbaccdbabddbdbdbbaccacdabdabbacbdbaccaaabdacacdcbddcdcccbcacbdbbcbacdbbacbbbdddccbcbbacacbccacdbdcacdcadccbcbddddcdccacadaccddacbcacbbbcbadbcabddabddadaccaacaadabaddaaddabdddcbcbccacbdbcbddccccbaabacbdbadadcadbbdaabaddcbdadbacccdbacddadccadaaddaabbadabbabccbddbbbcbbbbabbbabbccbacdcbaccabcbccbcdbdacdbddbcbabbdabccddddcacdbbccaccabdadccdadcdbbdcadbbddbadaaddacdbacababaadbdacaaabbdddbdcacdbbcddbdcdbadacdbdddddcbccbaaddcddbccdbabdcdcbcdbdcadbccdbabbccccaabcccddccddcdbaaacabccbcbbdbaccaaaabddcbdddabdbbbddacaabddccdbaccdaccdabbdbdcbcbbababbdcbbcdbcbbabbbaddccbabcdddcdbacddbdbaadcdadccaaaaadabcabadbdddcccbaabcbabccacacdaabcacacaadbdaccddddbddccbbacbbbdaddaddcddcbbadddbabcbbccadbdacbdcccdbbdcbaddbccbccdccbcddacaddcdacbabcdaacbcaabcdbcadbabcddbcaacddbbccbbdccdcddccdcabcbbcbddaaccacbaddaacbdaabdcbbdbaadccddacaacbdacabbdcbaadcccdcadabcdabadadcacacadbdbddbcddacdcbbdcdaaacdbaaccaacdaaadbdadadcccccbbdcbbdccbccaddcacaabcacbaccdaddbbaadbddbcdcadbabcdababddbcbcdbdbbbdbbbdbaddbabcbcdbbbadccddcabdcabcdbbbbddacddcdcaacdbacbcdbdccbaadabaccbcccccadbdcdaaacdaabaadadbacaccadbbaadbabbccbabbbccaaccbccbccbaaacdbbddaccddaaaabddacabdabdacdbccadcbbacacaaccddbdbcadbcccaaaddbcdbddcdcccbcdababddabbbcdacaabddbbbaadddbdbcbbaccdabdaddacbabbcadddccbbbbdabccaabdccbbbdaaadccdbaacccaabdadbcddbbaccbdadabdcabbcbdbdbccdacbddaadaccdbbbdddddcaabacdbbdbabbbdbccabdaccbcbddaacaccbbdabacbdabacdcbbbdcdadccaadabbbbadcdddcbcbddabdbaadadacbcbbdbdbbadcbcccadddaaaabcddbabdcaacdcddddacaaadbacccddaddbddadadbdccadcaaabacdbaaaddaadaddabbdbbdbccaccabdcdcccdabcbadcccdcddbacccbdccbbbcacabddcdbbaddbcdacaaacacddccdbbaadbcaccacbaddbacbacacddcccbcbbabaddadbddddabbddbbbcadabcccbbddcaddbddcaaddccbbcaabbbbbcdbbdccddbbdcbbadbbbbdacdabaaddbbbbbbadcaabbbbacdabccdcbccdbbaabdcaaccbbadcdcdbbbadacdbcacaadadcbcdabaadcbbccccddbbdccbdddabadbddcdbabcddccdbdbcbbdddddcaabdbccbcacddaaaadbbabbdbbabccabbabdcaabccdbccdbbdcbabcbcdbbcdbbddcccdacbdcbbbdbaabccdacdcddacdbbcdabbddacdbcadacbabbacbdadddddcaacdbacabccbdccacabbaacbddcccbdcbcaaccdbaacacabbadabcdcdbccbdcacacbbaccaccbcaaaddbacbcbddbdacccabddadbdbcdccccbccabbcbaacbddcdadddbabaddbdcabbbadbdaabbcdbdabaccacbcdbdcbabccbbaaadcabbddbddbaabdaccabcdbdaaaaabadbcbacdabddcbabbacbaaabdbabdadcdacdbddacbbaabcbbdbcaccbcdabdcabcdbcaaccabaddbadcdadbcaabaaaccadbdbcbabccabdddbcddaccccccbaaaddbadbadccddcbdbbcaacdcbacbcbaaddbccdbccddcaacdadbcdadadaacabcdcaadbdccacabbabcadcdcacbbcbcbaabdddababdacacbddddaaaadcbcbcdabccbdddcbaaacdbadbbdbcbddbbadcbdabbbccaccdcdbddbdadbcbbddabddacdbdabbbabbadcddcaddaacbddbdbadbdababccaccdcdcdbdcdbddaccabbaabbbadacabacddbcdbcacbbabaccbabacdcddbccccdaaadcacdcacddbcadcadbccdcbbbdabcdbaccccbcabccddbdbbbcadbabcbadadadbbbbadacadbdbcbdabadbdccaacabaacaadcddbdadcadaccbddadddaaddadbacdbccddddadababacddccdcabbdbcbcccccddcdcdbbaabaadcabacbbbabacdaddcaaacccdbdbdaaaadccbdbaabcabbadacbdabdcbbbaddbbcaddadcacbbbdacabdcbcdcadcdbdddcaddddcbcbdacbbcdbbbdddabbabcadaddabddbdbbdddacbbbbdcdddbcaabbadbabccddbbccbcbbababbbbabcbadababcadccddbaacacbdbbdbccbbabddacaccddbbbabcaacbbbbdacdaacbaacdcdcddcdddcbbddcbbdcbbddcccaadabcadcbcbcbdbcbddadaabccbdbcbbadcddadbaddcccadbdddcbdaabdcdccdbabcdbbbcaccbbdcbaabbdacaadccbadcaadcabccddacdcbcacdbdadacbabcccadbbbcaaabadcabbaacdcbcacacadacacbbcbcdadbccdddcbbacdbbbcddcdbcdbdcacdbbccbccdbbbbacdacbabdacdcacbbdaaacabaabdbbdbbaabbdddbaddabddcadaacdbaadbbdddddbbbcabbadbcdbadbadbddaadcccbbdbdaacdbacdddbbaababdddcaadbbdaadabbddbcdacdbacccbcccbbccdacdcaaddbababcdccbdcccbaddcdbbaccababdcbdddcbdccbabddbadbbabdacabadaccbaaddddabcbcbbdaaaccdddbcaccabaaadbddbbcbccdcaabbabddaadacddacdbdbbaabdbbbadbdabaddddacdaacbbdcadcaadddccbcdaddcdaacddcdaaadccdabcdaccdddaccbaccdccacdcbaacadadaabadddcbbcabcabbcbbbdddcdabdbabbccccbbbabdddabdcddbacdbdcbcadccdbadacdbadcaaabddbbabdacbadbbbcccacccdacdbbddddaddadbbdcaaccacabcaddcadccabadbdbbbdccacbacabacaadbaddcbbddbdadaabacbdaacdabddcdbbdbdacaadcddadbcbaadadbcadcbcdaaaacbbbbddcdccddcacbaacabdacbbaabbbbbcacdabdcaabcbccdadccdbdbacdcadbaadbddcbdbbcaabcbdaccbbbcdbddabddabdcabacdcdbabbaabbcdcbdccdaddbacbcdcbacdddcdddcbaaacaadbadccdabacdbdbbdcdbccbcbbdbdaacdcadababaabdccacccbbaacdbdcbdcccacdcdbbdaabcdaddcdbdbbcacccdcbbbcccdcbbdadcdaadcbdcdbbdaaccbcdbabbddbdcdaadacddbbccddcadbbdcbacbcdcddbdccddbbbdcbdcdddabaccbcababbcdbacabccdcdacabbaccccbcadcbccccbccccacdbbdaddddcccdbdcbacbbdabdadadcdcbcbbdbcddbbcbccabaadddcbcbddaaddabdabbcdabbddcddbbcaacaabdcabacddcbccbdcccbcabbdcdcadbaccbbcbbdcabcbaaacdadbdbaacbaadcbcbddacccbdcbbaddaddcdddcdadbdcdbdbcbdbcabcbaccbbacabaddcabbaccaacbbcadcbcacbdbccdcdccacbaabdbaccabcccaaaacaddcabacbabbcaaddddcbcdcbabdbcadbbccbbdbcbcbdccbddacbdaadaacddccbdaabccbcbacbbcbcbadbbccbdcbbccadbabbcbdcbadbcddbabddabccabaabdbbcccddbbccadacacddbaaacabadccbacdaddaabbcbabbcbbccdcddadaadccaaaadcbabccdbbcaaccacbabbdcbbabadadccbadbaccaaccdcadcddccacbbacadbacbdabadcbaccbabcaddbccabbbacdcbbbababddabdcdddbbbccddacadbddbbbaccccaadcdddbabcbbbcdaacaaddbcbddccbaabadbdcbdabdcdddabbacadacdabbcddcdcbbbcdbdbcdbaddabdbddcbdaabcaadaddcaabbaacaaddbaddabcaaddaabdcbddaadbbbacacdbbcaccbcbadbacdbdccccdbcabbbcddbdacdbdaabadcbdcdcdacdbbdddaaacadabbdadcdccaaabbbdddddacbdbcbdabcddadbdabddbaabbdbcdcccadcbddcaadabadcbabaaabdccadacdbdbaccabdbcabaabccbdacbadccbcbaabdaccaaaacdabdbaaacbdcddabacbcddbadbabbdacdcdacadaacdbdabbdaccbcaddbbbaccdadababcadccaabddcccabaaccaccbbabddbaaaacbbaddbdcccacacdbcddbcbccddbbcbcddacacbdddccbbadcdbcbbbdcaddccbdadbaabacabdcbcaddccabcbbbddcabacbbbbdccdbabbababdbaadacabcbbcbdddcbbbabbabbcdbbdacbaabcbaddcbdbdabbbcabababbbdcababbccaddbcababbcacaabcccbadbdcbdbadadbbdbbddbabbababddadccdbcacadcbcdddaddddcabacdbdcacbadddcdaddacbcbababddbcabbbbbccdbbbcaadbcdbcbcccbccacccacdbcaadaabdadbadaabccccbcdaabbdacbdadadcddbbaadabcbdcdcadbdabaaadbcdcabdcaabdbcddbcacdddbcaaaaddabadddcccccaccbaaabadbbcdccdcdccbbddddbacdcdbcddccbdacbdcdaccbabadacaabbccddacccaadcccdbadbcddccbabcadbddadaaababccdbddbadbadadccaababdbaaddacdaadddbbbcdcccdddabbacabbcaacadbddabaddcacbcaacbccbdbcaddaaaaaaccdabdaddddbccbbccadaabcaabdacacbcccaadabbbbdddccabcacbcddacdbadaadabdcbabcccadcbacdcdcaacadaddcccdbbcababaadbbcdacddaaaccbdcddbcdaabaaabaaacaacacccddadbadabbcdacbbbdbcabbadabadbbcbacaabcabdbcdccabdbdacdaadddcccdddcabcadadadddabdcbaddaadbdcdbccbcaabacbbcadacdbcbcdaabcbbaadcaaacbdccddccbbbbcccbbbdddacacbbdaccadbabddbcdcabacabdcbccadbccdbbabbccdacdcaabcbbbcbdbbccbdcaadcbbacdaabcacabdaaaaccccbbcbbadbbaacacdbcadcdccbbadddbacccdcbbdbdcbaaddcdbbacadabbadcbaaacbdcbaddaadaccccdabdabccdcaaaabbcbbdbccacbdaadcbdadadccccbbaadcccaccaccdaadadbcbcadddcadbadbadbbbdbacdaddbcabbbbdbdabcaabcdacbcbdcbbbdbdbacdcbcaaddcccdadccdabacacadcbdadbbdbcadbdcdacabcdbdabacdbddbdccbdbcbbdddaccaaddcdacaabccbbcbbabdaccbdcabaaadabccbadbbcdadcdaddddddcabcdcaadcabaccdaacdcdadccdadbbdcbabbcdbacaccabddadbadbdddabcbbcdaddadaacbaaadabdabbbcccddddbddbabdbbbccadabaacaadcdbbccdcdbddbbabcababbbddbcaddcbdcbdbaddcdbcddaddaabbcaabaccdbddcbdbcaddcaccdacacadcadbbbcccaddaaacddbadaadbccbbdcccccaccabddbacbaccdcdadbbccdacdacadccccbbabbbaaaccdaaccbbacdbdcbadcdcbacdacbccdbdbddbbdcbddbcabdcadaddcaadcbdbababdadcbcdcacbdcdbccbdddbadbbaabbdcabbbabdddaaadabdadcbabcdcbdbccaabccdcaabacdbdbbbadaccbabdccbaddcdaaddadadbdcbbcddabbddccabbcaaaabdbbabaabdbdadaddcacdcaabaccdccaabacbcadbadcbcdccdbcdbdabdadbbdbdbbacdddbcccabbabacdcdaddcabcdaaacbccabadcbccabcbdcaacbadccadbabdccabbdbcaccddaadbadbcabddcbdaadbdbccbbdbbdcdacbbacbaaacddddccccacccbdabadcddaaccdbbbcccdabaacbcbaaacddddadcdababcabbdbbdcaacccdacddbbababdccccdbbabacaadcadbbabcaaadadacbacdcdadcacbbccaaadadcdbaaccacacdddbdbcacdcbaabdaadbadbcacdddacabadaaabcbaabdcdadcbbcaababcbcbdddabadcccbbabdaccddbcccbbcadabddbaabdcaaaabdacdcbadaadbcddcbaaaaabccacdadbcdbbdccbabcaccdbdabccbcacdddacdbbaababdbddaaacaddbbbbbabbddccaaccaadcddbddbcdbcddcbcacbbbbababbcddacccddbbbdabbabdcbdbcabcccbddddcbbcdcdabbcdbdddabbddddbacaaddbbadabdbbbcdacdcadbdcaaadacccccdbcdbcadadbabadcddacdbddbdbdbcbbcbbcaccaaaababbbbaacbdccdbcbbbcccadbcdcaccddddbdccbadaabaaaccabbadabadcbdbccccacdbdbaadcddbcbdbdbbbcdbdddacdddaccdacbaddadcbdadaabdabbdacdcbdcbcdbcbacdbdabcbcccccdcddcaaadcacabbbdcdacbaddcaddcdcdbbbdcdcbabdaadabddaadccccbbbabbccdbcacbcbadcaaadddddcdccbbbbbadadadaabddbbbccddaccbdbccbdcdbdcddddcccadccbaadbdcbacdabdacaaccbdbabcccbbdcbbacdbaddcdcdaabdcadbadabdaabddbddabcbacabbbddabdddacddaabdccbbdccdcddbccacabaddbabaacdccbddcbbcbccdbccaabaadacabbcbcdbdcaababadabdcbaabbcacababbdbddddaadbddaaadbbcdbbbbcabbbbccabbdadbacacaadcaaadacbaadbabcdbbacadcaadccccddaabccdbbdcdcbadbbddadacdbddcaabbabadbcdddaabdbbdaacbdccdccddbbcccddaabdddcdadbcbcccbdaaadcacbdddcbcadcdccccbccbcbdcacabbadaacccdabaaaaabbcadcabdcabddaabcbbabdabdadabadcbcdaadcacababccbcaccacbbbbcbbdbddcabdbadccdbabaacaddccacbcbdddbaacddcdbdcabccccdacbdadadbbaadabbcdadaabbadbdaacbbcddaccddadcbbdabbcbcdabaaddddabacbbbabdddadbaacdddcdaabcbacdbbdadbccdabcdcacacbabaadabdbccdadbabcdccbddacbdbaacbbabbbcacdcccbadbcacaadabcdabbcbacddabcaadbbaddcacabbcacdbbaadbadbbbdcbacadcbaaccdbcddcbdbacbabdddcadccccaccddbabbdbbbdddbadabbddbaccbbbdbdadadbaabbccabcddabbdaadacaadbbacacdabcbadbcbabbaacbcadddabcacabbbdadbbcddcabcdadbabaddddbcacadacddcabadadcccadbddbbaaddbaadbcadcadaaddabbdabcaacbadccbcacaacdddccbcdcbbbbabdadbdcbdaddbccdadabcbdbacacacbaaadcaacddbacbdabdaaaaabcdbcddacaaabbcddcbadcabcbdcaabaacddbbbbddcbdadcbbadcaabccbcbdacdcdcbdaaadbcdbdcbbcbacdcdababbacaddddcccbcbbaadbabdddadaabcadbadacdccdbcccbdbacccacaaacaccbbcbdbaddccccbabadbadacdcccadcbdcccadaacbabbabcccdaccabadbaacbdbbcbcaaaaccdccaccddddcdcddccadbbbadaabcdaddcccadcdcddddacbbbabbadbcbdccacacbdcdcbdaddacccdbbddaccaccbddcbcddbddcddaabababdbdabcbdcaccadccbadcdddbbcdbbacbaaaadddccbcbadccccacccaaccacacacccbdbaccdbacaccbadcbddbcbcaacddabdaaccdbdcdaabaacacbaacbbbbadddacccbbbddcabaabadcdaacccbbcbbdadadabdcabdcacdadbbdbadaabbabadbdcbcacbccadcbabcacccccacbadbdadbbcbabcaadbccbcaadabadaacbaabbcadcdbcdacaaccbbbcbbcbbbcadbcdbdaccbabbcdbacdadccadabbbcddbcacacbcbccbabcacacacdddddcdcabcbcbcadcabbcacdbbcdccabddbddcdbdcbdcddaaadadcadbbcccbbaacabccdbcabbbcbdcbacbbddbdbdaaadbbdaacaccbadbcdbadcdbcdccadddbadbbbabbabaabacbbbddcbdabcccbbcdacaacdbcadbdddddbabdbbbadcdcacacccbbdbccdaccacadddaaaccccadcdcdacdbadcacbccdcdddbadcbcdddbcccccadaaabdacccdcbadccbddbccdbbdcaddaccdcabdcbbdbddababcddacbabccdaabadbaabaacdbbcbdcacbaddbdbdbdcaccbadadccbbddbbdcbdbcababaaccdccaaaacbcccccbcaaccacacbadbbacbcccabacdbbadcbabdcbbacaaccdbcdbdccadaccccdaccdbaccaabcdbddcddbbcaadadbdccacaddbccbdcadcadbbddccdbdbddcbdaccacaabddaccccbaadbbaccdbacababdbcddbacaabadabbcabdbbddccdcdbcadddcbbcabdbadadaabcbaabaccbabbacaaddbdbcdaabccddaccccdddbcbcccdcbbcbadcacbabdadbabbacaacadaddbdaddacdabbddbbddcdbdbaccdbdadadbacabaadacacaaacccbdbdccbbaacdabdabdcbbacaabdccaddcdcccbdbbbbcdcadddbaddbcaccbcbcdacdbbcbdcadcdaaacbaccabaaabbbcabdccaaabbdabbbaacdadbaaddadbaacbcadbbabcdbdddcaabccabccadabcbcddbddbaddabdaadaacbcdabddcbccaddabbcbbbdddaacbbdddaaccbdbadabdccdabdccdbbbaadcbcdddaccbbcbdaccbbcabcabbddabcacdaaadbabadbcdcbbbadacadccbabbcadadccdbaccdbbcdcacddddaccdcccbcbdbbbcbbcdadccdbacacbdadaccbbccdbdbcdbaaaaabbcaacbdbdbbaacadaaabcddbadaddcbccbbccdcdcdccadbbdbcbaabdccdddcaadcdaddddbdaacadaccdddddacacabbbabadaadacccdccccddccccabddbdbacddcbdcdccdacdacbcdadcaacbdbbcdcbbcbcdacaabbcbcddcbcdcbbbcdddbbaaaadbdacccdcbabbdcbdbdaaaaddadaabddbcdadcbcadbbbdbdbadaccddbdbadcabcdaaabbccdbccdbabadbcacacdbcddaadadbbcdadabcaaacdacccdddbacadddccdaccddaadacbbcdabbdbcadaddbdaaadbbbbcdbdcdcbdbdbdcacbcaccaadbadabdcbdccdaccdbbddaccbcbaccbdbcccbcbdabaadddbcdddaadbddadabacbcbdabddacbcdaaaaccadbcbdacacbbacbdddaabdcbdbabcaaaaadbbacccdcabcacbadbddcbcbcdacbcdcacaabdcaaaabbdcddcdddbdcbcacddddccbacbbadbbdacabddccaacdbaaadbbaacabdcdbabbbbbbcdbacbdccdccbcbcaaccadabdcdcaabcddbbaaaadacccdbddadadccdadbccadcddbadccddbdddcdcbdcdcabdaaccaaccdbdabdbccacbbcdcacbcaaacddaaabdccdbbabaadcdcbacacbabbbacbaabbddcbbbbababcbbcacddbaddbabbccdabaccdcbbbaccabccabbbdbacaaccdddaadcbcabbcbbcdaacacacdacaababcdbbbacdbcddddbcdbdcaddbdbbacbdabbcbdabdabcaccdbacdcdaddadccbdaacdcdbcaadaaadbbdbccdcaadbcdbabbababddcadddacbbbdddbbdbbdcdadbcadbddbdabadcbbbcdaacddcdddacdcbcbaccdbdccabbdbbddcdccdadbcdcbddadcaaddbabadcbbccddaaabcddcdadaaacabbaddaddabcabddaccbadbaddabcdaadbabaabccacaddbccddcaaaadacdccaddbaaaacadabdaccaccccbbcbdbcbdddadbcdacdacbaacdbbddccbbbdccadadabcadccdbadadaaabddabaabdccbbcabbbaddbbaaabdaabdbcbaacdadadbcdbcbbabbadaccbdadcaaaddcdbacbcbcaddcddbdcadadadbdbccbbdbaaaadaacdbbbdccaaacabadbadcdbadbaddbccadccdcbacdbaabbcdccaaacbaabdcddbdbadcabcabcbcdbdbccaaaccaabdaaddadaabadcaccaadcbabccdabbcdcdccabbdcaabdabaadacbabaacddabbacaaabcabbbdccddbbcbaaabdcbadaabaaacdbbcccbadcbaaabaadbcbcbccdbdacdabadcdcacdcdccdcabcbadcbbacabcbcbdbacddcaaddbdccdbadbdcccbbccacadacccaddbabcdbcbddcddadbabcccbddabdcbacccaddcbabddbabaccadaaacdabccddcddacddaadbaccacbbcdbbabbbadaccacbbcabbabbcdacbdbbaccaaddccaaaaddaaadcbdacddbddbbaccbccdaacddabdacbbacaaddadccdaccddcaddbbcdaddaacbdcabbcacdbcacdabdcdbdddbdccbcbcdaaaddaadcdbdbcccdcbbcbabcdbdddadadcacbdbddbdaaababdabddbacbaaaabadbababbbcddbdaccacabadbcdabbcbdcaaccdddaabbbadbaaabbabdcdaadcadddcdbdaccbdbaabbcdaacbbadcacbddcdaddcdbdbbddcaccbcdbbdcbbdbcdbcacbcdcabdbccbacadabcacaaaadacaddaaacddabbabcdbabdbacdabaacddddbbadaadcccadbbcadacaccdbabbdcdcabccbbaacaabbabbadbcaaabddcbcacdabddbabbcbbdbdbcacabaaddcabdbdcbabaadbbcdcaaabdddcaabccddbddcacacabcbdabbacdaaabbbbddddaacbbbdccaadddbdabadcddbdaadbbddacccabcdcbbabbaaabbccabbacacdcadaaacccabdcabaabbabcbbdbccaadddbdcddccdcdcacdacadaacbabbaacdadabacbcacdbcdcddcccacddbcacbaacbccddbaddbacdaaacaaaabdaacbabadbddcacdcabccaaaacabbcccdcadcacdbacdadcdccacdacdbcbcbaaacdbcaaaaaddbbcddcbcccccdccddaabddcdbdabaacddccdbcdaadaadcbbbadadacbcddcbadbbcdddbbacacacbaadcacbdbbdbbccadabddbacadaacddbbdbdcdbabddbdbbbaaadaacacaadaacbbacbddcbaccbdcbcbbccbbbdbbcaaadcadcddbdccabdbdadbdcabbdaddcbccabdabadcadadddadddccbaccbaadbdddcccddcbdbbabcaabbbdadcdadcbbdddadcccadcdacababccabbcdacadacbccadbbbdcccacabaacccaabccadbcaadccdbbbcabbbcdbcbbccbdaaadcaadababdbabdabbdcdaadbcbbddcbaabcddacadacbbcadcdaddabbcadaddcbcdcdccbdccdacbdcaabcacaaccdaabbcdaabcadcdabacdcdbaaccdcadbadcacbdbdbcacdcbbdcddabdadabdbbccadcdbdcddcbdbbbdabcbdabddbdbdadaabacdcbbdbdaacbaacaabddbbaccadcababccccdcacaadacacbddaccaccbbcaaaabcbacbcdaaabbbabcbaabacdcccbddddcdccbaaadbacabcbaccacdaccbcbbddcdccabcddbbcdaabaadcabbcddbbbbcacbcccddddddcbcdabbcbaaaabcdbabacbbaacacacacccddddbdbbbaaccdaaabadabaddaddbcccadbcabdabadbcacdbaacaddbdccbaddacaacdabacbccdbacbabcbaacaadaddbaacbbbdbaacacddcaddddbabcadbaacadabdcdacdbcdccbacbdadcbdbdbbddbaadaaadabaadadcaddbccaabbaadaacdcacdcbcdddbcacadcdcbdbddbbaaacbababbccccbbcbcaabbadcdabbbcaaddcdabadbaacacaddadcdbcacddbddadbdcdddcdcdbdcbcadccaacbbcadddccccadccadabcaaddddadbdccabaaacabddddadaccdaadabaddccdacbadbcaabcccbadadadbcaaabcdddacdccdbcdaccabbdbdcadddcdddcaddbaacbdadadccbacdbccbbbcdcbbadbabdcdbbdaabdbbccabadadccddcacdaaddddcbacbddabddccdbddaccdbadcbdbadcbdbdccdcdbbbadadccdadbacccbcbabbcadccabbbbcbbadcaacaadcadbbcddcdcccbbdaccbdbcbdbadddbacbbcdbbdacaacbaaacbbdbadbdbdcddddddcbcdaadcdbabdbbbdacbacdddccccddbacbbbbbbccbdbacbbbcbccbabbbdbabadbcdcbdbdcbcadddccdddbabacaabbdbcdbdacaddbcaaddcdbdcccbabdbccbddccdcbbcaccadcabadadabddbdcabdbadbabcabdaaaccaccccabccdccadaddbcdabccadaddcddcdaabdddadbccbaacccbcdabadcbcdacbdcabdaacacccbaddabddbcbddaadcbadccaaabcbdcbbcbaacdbdadacddcacababddbcacdadbbcccdbdbdbbbaabbbddddcacaaaaccbacdabbbdcadbacbbbcbadbbdabadcbdcddadabbcddabcdcadabadbcaaccbbdbbcccbddacbcbabdccbabdbabdbaaabdcdadaaccabdabbacacdbabcdadbdccbcacccddbdbbcaadbbaddbcbacdcdabadadccacdcccdaacacbcdccccccccaddbdaadcacbbdbbcdccacbbdddbdacbabbddbdbddbbbabccbacacbcabaccabcbbacbcdcaadaabadbcbaadbcbaddbddcaacaadabcddcaaabbbadaacdccaaaaabdbccdbbbdcbdcbcccbcdaabbadaccccccdbaaadbadaacaccacdccacaddccbbdcbbbadabaababccacaacbadbccbbbababbadacdcbabdabaacbcaadbacbbbbacdbbdbbdcccdcabccccdbcbdcacdbcbaadcadaddbbdcaacbdcccbadcaddddddbdabbbdacddbbdcbdcaabaccdcacccbccbbcaabaddcbddaddcaadbbdcbbccddcbabcddcadcdbabdcbadccbababddccdbccaccacaacdcbcbcbacacddaacddaddbddddcacbcacadcbbcbacbbccbcbdbcddbcabbbbdbbdcdcdaacdcbcdcacddddacbccbbbcbcaacbcddabcabcadbbbbccbabaadcddbaadcdddddbdaaabacdcbbdaccbbdadaccccbadbcddaacabdacaacddcbcbdadbcaacaccadaabdbdadbabcdcccabdbcbbabccbccababababbacaaacaddbabbdadadabcdcbabcdcccaacdcadccccdabacadbbcdcccbdccdcdbddacbadadacdbaabddccbcaddaadacbaddbdbdaaababacaabbbddcabdabadcbbdcacddcadacdbaaccaaadabadcbcdbbabddbcdbadaacdacbcdcdbbbcdacbbddcbcbbcdbdaddabacdaaddaccbcbcdbadcacbabaaadcdbcadcdbbdcadbbcdcbcabbacdaabcbdbadaacdbddaabcaccbbcaacacacaddacbdaaccdaabbcdbaaadacbbcabaccbdacddcbcaabbdbbcbaadcbbacbcaddabaadcbacddaacbbaadaddabbcaabcbbbcccaabdadbcbaccabacbaccdbadaaddcdaaddbcadccdbacbdbaabdbcacadcbbacdcbdbcdcbdaaaadbcbdaccbccadaabdccccdbcaaadbdcbbabadacabbadcccababbcadbadbabcaccaddcbdcbcabbbcbcbbbccdddbcaacabaaacbbaaaadccdbbbccccdaccbcadacbdcbdcbbbdccabbdaccbbdddadaabbdbcacabdaaadbdddaabbacdcdcdbacabcddcaadbbddccacccbdadaabdacbcdabdcaabdcbaaacaaabbabbbdbbcdbdbdaacabdadcdacdadccabaacbbccbabbddbcbaccaaaacbabcadddcdddcadbcdbbcccbddcbdbddabacadcbacddacbbbccdaacadadadcddcaadbcacacacccbdddbbdbdcbcacbcaddddadcbccacbdddaaadcbcdccbbddaccbacddcccabcdbdbdabbdccacbdadccbbbddaadbbdcbbbbacccadcbbbcdbbccddbabdbdacaabadacacdbcccaabdcadcdbbadbdcaddcbbacdbbcdccacabbacbdcaddcddbbaddbcbbcdabcadaaadbbbdcdbddcbdcdaddabadaaababaacccdbddbccccdadadacdccabbabacabddaaacddcdacaadccbddcbdbaaadbdcdadcaddcdddabbbbcaaaaadadabbabcaccdaaadaadbadcdcdcdbaacadddccadcccbcaaaaabdddbaaadaabbbabcacbcdcdcdbcdcdabaddaabacbaabdaabacacdbacbabcaacdaccbbaaddacbaabacbabdbbbdcabcccdcabcbadbcdddbbaadddbccacbdbbdccdcacadbbcdddaccdbbbbbcaaccadbccdcaaaadcadcbbddddbbddabbaacccabbbbbdccddcdadbbcccdcaabcbdddaccbccddaadadabbbdacdadbbcbbbdbccadddcadcdbdbcbdaadcbadddbcdcccacddadbaaabbbdcbcacbbbccbcdacadaccccdddbdcbcadbaadccbdaabdbdcbbcdbdbddbdcbbbbadaccaccadacadbabdadacdcbbbaaadbbcabcbdbcbbdcdbdccccabbbdcccbdadbbdcbbbbdccdbaaacdcaadbcccdbbccccacccbcadbaddbacdbaaacabdbcbaaacdcccbddccabcacadbddbbbcbdbaccbabcccbdaabbcabcbbbaaddababdbdadabdcabacbdbddbbdbcadddbcdababddbbabaadabaccbbbcbdbdccaabaadbbcbdbddcbadddbaaccdbabcbaccdbdddcdddbaabbbbcabdddbaaacbbccbdddddcdadababbdcadaaadabbbdbabdadaacbacbcccabcadbbaaadbbddcaaaddbbdddcaccbaccdbbccbcbabddcadacbabdccaaaaaacaaadcaacaabbcacdbdbacadbbdccabbabbbaccaccdcbddcdcbcbcbacbdacbdaddcadabcdbbdacccbbbcacddcdcdaaadcdbcbabbddadcbdbcbcbaddadcccbccddbbacbbdbbabbbddbdaabbabbbcdcccbcacaacdbcdcacdabdabdabbcddcdbcccbdbdaacccdbbaadadacbcdaddcddcdacaccdacdcbaccacdadbbacddacdbbdccadcaaabcaadddacaadadbcdcaabdbaabddaabdcbacaaddadbbcbbcdbbbcbddaddddcdaadddabdbbcadabcadbdbaabcddababcbacccaacbccdacaddbdccaabbbcacdaabcadaabcaabdcbdabdbaacbbdcbcacccdbdcabadbcaacdbacabbdaabbaaaabbcaabdbcdddcadddbabcbdccbdaddddcdbbbadcddccdcabaabbbabbcbdbbcabbabbbbcbbdbcccaddbbddadaaacadddddadbccccdaacbacbddccababddacbbbddbbbcddddccbaaaaddcdbddacdcccbabdcbdbadbdbcbadcbdddbdbdaabaaddacdaacbbcdddaadcbdacaacaccababdcdcadbbcadbcbcccdbbbdccdcdabdcadcdbcadadcbdabdcdcddaabcacaaddacbcbcbddbcaababcabbbaabadcbdbdcccaabaabdbccddbdacababaacabdabddcdadbadacbdadbbdccdbcaaddbcdccddcddcddcccbcaaccbbdbbdcdaccbbccbcabcddaddcdcdccdbdcbcbbadacdcccbdcbcccdaacbabcdaccddabddbdddabddaaabadccbccabdabdccdbcdacccbdacaaadddcdaaadacbcbcbbcaaabbbadababcbdabcabadadbcabadacadcdbabacbbcccaadccdcbcacdbbcbdbcbccadbcdddbdddaaababdccbdbadbccbdabccbaadcbdbbdddbdccdadacdabcbbacbdddbdadbdadabacccbbddbbbaaaabbdbdcadbbabacbacbbadcbaabbaccbdcadcccbbacababaadcdbdbdbadddbabdccacdbaacbbcdadaabcbbcabbcbbbbccbbcacdcabadcdbcdbdbbdabdccddacdaadbacbaacccbbaacddcddbdacacddccbcdcabdcadbcaacaaddabaadbabcaccdaabdcbccdcdaaaadcddbbcacddcddadcaabcacddddabacbdacbdadcaaaaacdabdaccabbbbbadadcbcdbabbcccbaacaaddabbbcbbacacaaabbabcbdbaadbcdaaaadbdddcbdcabbbcaccacaabbabcaadbbbacaddccbadbbcbaddcdcadcbaddaadaabbdcdbaacdcaddcabbacdccbcdcdddbbddccababcadbcbdacaadaaaadcdcbcabbbaadbbbccacdcbcdbccdbbbddcdddbbdadaacbccccacabcdaddabdbdddabdbddadbccdbddabaccbaccdabbbbdcaadaccbccdabacadbcadbcbaddcbbaacbcaccccadcabbcdaccadacaacabdbbcababaaccbddacbdddcdacbcbbdddabbddacbbacbaacbbdcdaddccbacccaacabbbbdbacdcbabdcddcabbddcbbadccadabcacbcdabcaabcbdacadcaaaaacbcbbcdaabdbcbadddbdbbcbcbdddadcacaadabdabddadbbccaabbdcaadcbbadddbbbcbcbbaaabddbddbbdcabdacddcbbbbacbccbbdcabbbaabcadabbcbbdcaccddcddabbadcabcdddbbaadbadbdbaabcaaaaddbbabbacbdcaabacbbdaacdcdcbacbbacbbcbcadbdbcadddddddcdabbdbcbcddaadacbcacbbdabddabaccccdabdbdabdbbccbdcccbdccdaababaaadabccabcacdbdddabacbbccbbbdaacbddadabacaaacadcdccabcbabcabdbcaaabbbaabbbcacbdcabacccdcddaccaaaabcdcbabbdabbabcaddddaadccaddbcabcbcadcdccccbccccdadbbccadaaddbabcdbacabdbdddcadbddabcaccaddaaaabddbdccaddccacbaacbbaacaabcbbdbddddbabacaccdabccabaaadadbddddbabbaabbdccbbccdbcccccabdaadbcaacdabbaadbbbaaaabbbccbcdbacaccdcdbcdaccaabcadbccdcdccbacdaddadccaabdddaddccbcbadbaacccdbccdbdbaaababdaddadaabbaaacdaabdababbbabcdcdcdaaadcbacabdaadababacadbadddcbacdbaabbcabddadcccccbadaadcadbdcccdccdbacaddbbaddacadbbbcacaddadbbdcbaccadcdcdadaaacbcdbdabdcabbccaaaadcdcdccadacacaccbccbdcdcdccacadcdccbcbcacbcccdaccadaadbbdccbdbdbcdabcdbaaacbaacbacdcdcbdabbcddcaadbdbcdbddacadcbbcdcddcaadbdbaadcdaadbccddbccadcabadbaddcadbccadcaaddaadaccdbdbcbddccbdabbdacaacbcbdcacdddacacdabbbdbbacdaadbadbacccadabdcdbbcccbdaabdddacdcaaccbbbdcdcaaccdddabdbccdbabcacdcbaacdbdabdccdcccddcddbbcdbcdbcdacadbcddaabcbdcdbbaadcdaaabcabccaadbbbcddbbccaadcccddcbbcbcaabbabbbbcbaacaaadcaaaaadcbbddddbadcaddbcbbbacaaccdcbaadabaddbabcaaacddcccaaaadadbdddadacacccdbccacadbbcdaabdcababaaacacbcbcbbddabbbcddbaaaaccacabbcbcbcdddbcacdcddddacbcddcaadadcbcddadadbcddcccddadbbddbcbbcddabacaaabacaccbbababdacabcdcbdccbbdbbbccacabdcaaddccaabbdabdccdbcbcaaccbabcdbbaadbbcabbcddbdaaababdbaddcddbacabdcbbdabbddcbdbbaadcbbdaccadadacadddbdabbbccccadaabdacdddbaaadbacdbdcbadbaacbaaddddbcdabaadabbbccabbabbbcccbdbadaabbccadcbdcaccaccabdcddaccabacbdbaadcabcacbbbadbdbabaddcbbcdbbabcdabdccddcddcdaadbbcbabbcadaddcaaddbcacacdddbbcbddcabdbadbcdbbcacaadbacdbbcabdddbdadccaddcdbdaacadcaaccdcbbacbdaccbabccacdbadbdccaccaddbcacdcdccbaadcaabccdbdacbdbddcccbcdabbdbdaaddadabaadbddadccaaadbaaadddbbcbddcbddacbadadbbdbacbcccbccbdadcccdaabbbdcccccbcabbdadcbacbdaadbcbacabacdbcbbabcadbdcccaacdaabbcccaadbabccdddbdccbbdbbbacdacacacabbbcbcbbbddaddbcadabdddaccabbbcdadbddadbcabbbacababacbbaabbddcddaaadcaadaabaabdaaaadcbacbcbdcdaacdbacdabbcbdaccabbbbbadcdbadaaabbbdacacdbdabbdbbcaabdbdcdacbbbdddaccbcbdabdbdddbbaddcbbbdadaaabadbcbcaacdbacdbbddabcbcdcbaccaccbcccdcbadcddccbdbccbcbaabbddbcacdbcbaaaadaaaaacdaabbdccdbacadccddabdbccdaaacacacadccacaadccdcdadbadabdccacacddbadaccbbbcccbcdadbcbdbadadccddbbbacbdddbcaccadacdcbbddacbbaccdccbaababdaaacbdbbabbbbcbadccbccdaccbbcdbaacbdbabaacdcabbdcbadbddcaaadcdccbbddbacdcabdcbcbbccbabcbccdaccaacdcaacbdacbccadacbacabbbcdbcdbcabdcbddcddcaddcddaacadcdbdbababbacddbccdcbccaaacabdcddacdabdddcdbcdbbbcbbdaaddabddcdddaadbbdccaabaababbaacbcbdacadcadcdbbabbacaddcabcdddcbcbadaddbcaddaadbacaaabbcdaccabcadcdbbdbacacdbbcbaaccccabdcdccccdcbaaaaadadbaadcbcadbaacbcacbbcdbabdababbabcaccaabbccacdcadbcdcbddcaddacdccaddaadcbbbcadcadcbcabaccbdddbabaaacadbcddcdaabaadbccccbbbdbbabcbcdccabbbccacaabcacaccaacbacdcccbcaacaaccaccacdbabcdcbbacdaadbcbdabcdcbabbcbccbdbdccbcccccddcbbaaddbbbddacddbdccdacacdabccbcdaddccdadccccaccacbbcdddaaddcbadbcabdcdbadadddbdccddababcccbcaddbaadccccbbbccadaabaaacabadddddcabdcdbdcdbdcdcdbabdbbaabccdcddaddcbadcabbaaacccdcacbabadbbddbacaddbbaccacababbbcbbdddadacdbbddbdadaaaabdbdadaacbccaaacdbaadbcbcadacadabdcbccadbdcabbdbdccacabcccaddadacadcdbcabaccabdcccbcabbaadcbbdbaacbcacbabccbcaadaababdbaacdbdaaacbcddaddcbcaaacbbcbcabccaadbbbcbcbdadcabdabbdacbdcaadaccbcddbadcdacbcccccdadbbadbcabcdacbdcacacaaabbccbaccabbdacdbcadcabdadbbdcabddbccdaabaccdaaaacccdcdcccbccdacacaacdddbbadabddbddcaddbacddddcccbbcaaadcdbcaacbbabbadddcdcacbdcbabcbacadcbcdcdaabcabbdcdadaabacadbaaabcaadaabaaabcdbacaaaccccddaabbccddcdbccbabcdcaadccdbadabaabcdcaaadcccacaccbdcbddbabadaaababadbaaadbcdabcacdbadccbdbadbcabaadcadcdbabbababccdadbadaabadbdbdcddcaabdadcaabcbbabbbdadbcccaddacbbaaabcdddccacbacaadaddcaaaacbdbdbadaadadbcbababbaaadbbcaccacdbdcddbbbadcdcccdcdbacbddaaabdbbbdabcaccbcdcabbdddbdbaddbabdbaabdddbccabddbdccaaccbabcbacccdcadcdddccdbabdbdddddcbdbbcabddcbaacdbacadbbadbcbadddcdbcbcdabdcabaaadcccccccdccdaaadccdadcadcdddcadadcbabcbcaccdbabcddadcdadacdcbdbbcabcacabddbdcadabdcaadcbcacbadddcadbcdadabdaccaadbbbdacbdcdaabadcbccbddcabaacaabddcccadbbbbbaccbaccdcbaaacabcadcbbbadacbbdcabaacaacbbdaacddbbcddddcdcdcbbbcddacbdaddaddacabadacbabaaadccbdddcabbbabdbaaabddabcdcdaabbacabddaaaddbabbcaadacdaddbacadccdccbdadcbcdabdbabcaccdaccaabddcccbadbbbbbbaccadcdccddccaacbdcdaaaddacadbacbaadcccdcbabadbbabccbcaadbbccaacddcaccabaddccbbbadbbbdbdbbbdcbcabaadbdcccbdbcdbcadadadadbaabddddaabbacbadaababbbabbdacdabbcdbadadaddbadcbcdcbdbcbaaaadbcdcccdddabddacdbcddbcccbcabbbbacbbacbdbdbbaaadaaabbcadddbadddabbcdccadaaabbabccddacadddcddcadadcdcaabadcbbdaabdcaacccbdaacdaccbacabaddddbaacacaabdcaacdddccbbccabbcabadddadcccdaaddcbdcdacbbbdbcdcaadbabcddbacababcbbcbdbcdadccdccdbadbaddbbccbccdaabacbddaaaddddddaabbdacdcacddccadabcdbdddacadbcbdadaccdaadcabddadabdadadccdaabdbccddbccbdaccbcdbdabcbbbbdacadabacaaacdabddcdcdaadacdacbdcdcdbbddabccbbadcbadcacaacbdbbcbadbdabdabdcaabccaccdbaadbabdccacdabdcadcddcbbcddacacdcaabaddbccbaabddacddaaddcdbcdcbbbbddabbcaabddbbbcadcdadbabbccbcbbcbaaddcababbbabbadbababdddadbaabbcdbbdbccadaddabacaaadbccdbbbbaacdbabcbaacddcacdccbaddababcaaacdbadcaabdaadbbcabdcabbdccadbababbbccbaaaabbdcabddcacbbbbbaabcabcdadbdbbaaddddbdaddcbcdcbbaddbddccbccbbbcdbcbdacbcdcbcbdccdcccdacddbadabcbadaaabddabbbdddcdababbadabbdbabccacacccacadbcadccccbadbaadbbbcbacddcdddbcdddbdcbababaaadabdddbbdadbdbcccbdccdbababcbbcadacbaddcabcdbadccacaaccadcddacccaadcdccccdacaaaabcddbbadddbabdbacdaabdbbaaadaadccccbabdcdbcaadabccddccacbdadcdcdbcdacbabddbbcbcccddaddbbcdcdacddbaaaaacbadcddcbcadcacbdcddccddbbcbbdbbbbbabaddbacddaadadcbbaaccddcccaadabddcaaaccdaadcddabbdaaddbabbcdadadbdacbccaddcbbccaccbdbabbcbdcccccbabaaaabdbabcacbbcabdbdbbdddbdbabcddbcdcadaddbccccabdbccbcbcdadaccbcbaabbabaabdcbaadaadabbaaacdbbbdcdbcaabcddacadbcbaddabacdacdcadbdbacacccbcaccbaccbdbdcdddbccacabdbcbbccbabdcdddadbcdbdaaccddccdcaaaaabadaddccbaababdaccbacccdcdbbbdaabdcbccddaaadccdcaadccacbddbbdadacdddbaabbcabddbcdadadaadadbdbbaaaaccaaacdaabdcdddbcaadcbaadcbaddcababcabacdbbdcbabdcaaabdccdaabbbcbcbbbaddbbccbdbbddcbddbdbbdaabdcaaabadadcccbacdcacabddacdabddabbbddabccdbcdababbcccdabacdaacbacbbaddaabdcaccbadcadcbdbdadaadcaacbaaddbccccdcbabccaabadccbbdbdddbcdbccdacbbdbadaddbdddaddabbddcaddaddddbacbbcaaadcccbadbaabbdcdcbcadcadcabddcabacabbbbdcadcaadcccbcdaadbbddccbaccbcbdbcccadbbabdbbcbacbcbbbcdcccdbbdcbcbbdacabbddbacbadbbabcdbddadcddaccbcbadddbbbacaddbbdbbabadbcabbabccbaddbbddbcdbdadcccadaccacbbadcbacddccbacbccabacabdacbdaadccacacbcaddddddaaadbaddabadaddcbaaaaacdbadbbddaabadbbbbaaabbccabcbccbcdacccbbadabdaccabbbcbaadbdbdcbcccdacdbabacdadadabccdbdccacbccacddabdcbcadddbddbcdadbacdaddcaccacbcbddcbbccdaadbadbccdbbdbdcdbabddbcaaaccadaccccacbcbacadacddbabbabdabbaddcdabaaddcbcaabdabcdddbdadddcacdcdaababdbadaccaccdcabdacdbbcdcdaaaabdcadabadddbbbcbaadbabdaccddcacdbcbdbdabbbadcbbbdcbdddcbccdaacbbddacbddbcdacdcddbacaccdbbacbcabcbacdcaddbadbdaabbabaaabdacaacbbcccbabdbcbbddbabdadcbddadbabbacdbdddcbacdccccbbcaadbbadbccaabcdbccbcdbcddcdabbddadccacdcbacbcdbbcabacbabadcbbcdbabadbbbbbccbcdadbcbbbaaabcccdcdadcbddcaccddabadabbacbbdddaaaaaabaaaaccbadcdbbdaaacdaabadbcbdaadcaadbcdcccbaacaddcbccdbdbaaddbdadadddcdaccdbccdabaccbdccdbabacbccbdacbaccaabcdaddcadaabdbcabccbacbccabcaddaddadadcddccabaaccbcbadbdaddcccdbcdbddcdcdbdaabdbdbccaccdddbdcccdacacdbdcabaddcdbabbababbacacdddbcbcbacabdadbbdddabcbaacddddddccabcdbbcacacacdadcdcbbadabacdabbabbbbccbdcbbababbbdaacaacdbcbdacccddbbcbacddbddabbbcaabcdabccbcaacbcbdaaabccbcabbcabddbbacaaaadbcdbbddbdcdaaddadbbcbbaacbddbbdcccadbadbbbcdacbdabdddabaaacccaccbdcbdcbabdcbaddbdcbccbadccbdccddddadddcddbdabbbcccacabacabcadcdabdccaccbccbdadddacdbcbcdbbbcdcaddbdcabcdbcacacaabbddcadbacdacacaccddccddddadadabadadbcdbacbaabcabbcdadbadcbccabdaddcbbdddbaabcdcdcdbcbccabaacdcbabcbcbcccbbaccbabccddbbbdcbdbcadaacadcadcccabaaabbddacacdaaaabccdaabbbbbcbcbccdadadabbadcaabdaaddbcaddbcaaabbccacbbabbbcdcabddbdadbdabccbccaaddbcdbcccaaaaadbbaaddadaccbbacbaacddbadbcbcdcccabccddcddaccbdddddccdacabcccccbdddacabbaadbdbccadcaddcccaccdbbcddcddbccadddbbccabcaababccdcdbdbdbbbadbacddabdacdadcdabbcdcdbbacdbdcbcbdcdaccbdaabdccabcdccabcdaaccbadcabdbacacdbaabcbbcdbacbcacbaadbcaaaaaaddbddbddabbabdadbcbcbabacaabccabdcaddcbbbdbcbabdcaaacabbddbdcdaddaaaddbcdddbbbabdaabbcbbcbacbbdabbcaaccdcbcbdbbcdcadbdacdbdaabaabdbcbcaacaadaabbbbcdbcdbaabcacddbbaccacdbddadccccddccbbdddcabaababcbccdcaaddccddadaaccdcbddbccaaaaaabddddbaccacbacadddcccbdddababcaadacadbcaddcdacbbdbccadcaaadbbababdabdcbabcacdaddbacbaaacdbcaccabbcbbaddacbaabbacccdcbccadaabdabadbacadacccbacbaabbaccaccaccdcddbbdbddacabcccabbccacdacadabcddbcadaadbddddbccadabcbddcbdaddbdddcdcbbbbccbbccaaccadadbdbdbdacaacacddaabacbaddbbdbccccccbbbbddbccaacaacdccdcbdccadaaaadbdbcbabacaadbdddadbabdacbcdddcdacdbcdddccbdddbccaadbcccccbcccbabadcdddadcdbdcbdabcdaadcababacacdbcddccacacbbacbbddabacacaabcabbcbdaccabccdcccbbcabaaacabdcbbbddccbbccbabcaccddbacaddcbdcbddcbddcadbcaacaccbcadbacadcccbbbccbdcccaaaddbcdacaadddddcccdbdaaddabdbcbdcddacbbadbdaabdadddcbcbaadaaccbbcccbcccbbdcbcddaabddbccaadbdcdadcddacdbadbdbcbaabdcbaddbbbdbaddadbabbcaaccdabccdcabbddcaaabbbbbbdacdbdbcbdaccccbadbbdacdacdbadccadaabcddacdbacdcdbdadbbababcaddacbacbdaddacddaadddbddbbbbcdaaddcdddbbadbcbdccdacbcbaaabcaadcccacbdcbabdcaddaaddcacdadaacbdddbdbccacbbbbbdabaddabcaaaabccabdbbbcdabbbadbcadacabbcdbaaacddcdccdaccbccbabbadabdacbbdbcbaabdbbcdcbcdcabacaddcdbadbdbdbcacdaabcbadaccbaaccacacaacbbbcbdbcaaddbaabbccbcbcbabaadccaabbdcdaaababbdaddccdcdbdbacccdbcbcdbcdaccbbbaaaaadacccdddbcadbcacdbdbdcdcabccddaccbcdaddcaddbdbcdcaccbbbacacdabcaddaaadbabadcabaabbcdbcdbccbcbbcccdbcaddbaaaaadaaccbdbdcdccbacbdbccdaccdbbcddbcbcbdabaabbabadaddacdbcaadcaabacbbcadadcaacacdddcaddabacadabcbdbcabaabbadcdbacdbcccbbcbccbbcabbbbaaadcdbcadbabcbabdbaddddacbbcacdcdbcdaaddcabdacbbbcbcbaddadbaadddaabaaadccdcaccaaabcadacdaacdaccdbbaaabdddcddabdbcdbcdcbdbbcdbccadbabcadbadbabbbacabccadcdcbbccbcaccaccbabbddabadcbddccdbddabaadcdbaaaaccadcbacbaadbcbabcacccdcccbaccccbddccbbccddcaaabbcbbcdaabcaabccaddadcdcaaccbcabbaaacbbdbadcacbdbbacbdddccbcdcaacdcaacdadacbdddcacdacacddcbbcaacabdaddabccbcdbdcbdccaacdcbcbaccddaaabadbaacddcaddbadcbbdbdacbdabaaaacabcbddabdabbadccdbdcdbbadddacaadadbbadabdbbaddacbcaacdbaddaccdcdacabadddaaaddabddcaaadbacadaddadbcbcbbdbdacbccbaacdacbabadcadccbadcdbdadcdadcdbcdabcdccdabddabbabdbcdbcacabbaddcbabdcaabcbaabddcabcbcdcccdbcadaabbdaabdccaacbaababcbacacdcdbdadacbccacaacadddbaaaaccbcddbaabbbaadcabadbbdabbdacddcabdacadddddbbadcbdbbdadbdddbbbabbdbaaadbbddbdcbadcccbccbdcdddddcccddccbaacbdbaddbbadadbcbcdccabadddabcdadbcbacccdacccddabbacdacacbdcbbaccadcacabacbccbbdaddabbacbbaadcacadbbaabbcacbcababddddcbddbdbaddddadabaabbbcbddbaddbbbbdcaadcbcdadbdbddbbbacadabcdadccbababbabbbbabdadcacaadbbbdacdcbdabbaddcbaacabbacbdbadaaacdbbacbdcadaabcbcddcacaacccbdadabbbdbaacdabcdabbabbaaadacacddcbcacdbbdddacadccabcbbacdcbdbdccdbcddabacbdcbbcddadadcabdbdcdadccadaaacdccddddbbcbdcacacbbcadabccabddadddcbcabbccacadbcbbddbdcadcbcddcbcaacacdcbacacddadbccaaccdaaddcbabcdcccdbcabacdabbcadcbcbccdbccabbdbbabddccdbcadbcdbaaabccbbbddabdccadacdabcbadcddadaabdabddbdbbddabccbbbabdcbcddaabadbdadcbadcaccccdcaacacbaddbbdbbadbdbbcbdcbbdbaddcdababbadadaaacdbcaddbdbccccbccadcadadbccdcccaadcabdcdccacaacabbdcbadcbdcbdaacbccbbcccacbdabaacdadbbddbcabcaccdcacdabdabdbdbccaabccacadcccbcbcaddcbdacbccadbbbcbbdccdcadbdccbbbbbddbaaabdcdbccddbaaccbbaaabbadaabdccacccdadabdbbddaacbdcaccdbabdbdbcadddcabcadcddadbaccbdcbcaacdbadcbbcdcadaccbacdbcdcdbdabbdcdbaaaabadccdbabdddbaabbbccadbcbdbbccbdcabbcbbcdddacbbaccabdbcdaacbadbdabdaabddaadbbbadabbbadbcaabdaadbdcdbbbbccacdccdddbdabcaccdcccbbadaaaccdddbdbcadadcbdacdbccdacddbdadccdabacadcccdabcccdcabbbabbbadbadaaadaabaddaaaccdcdacabadbccdddadaacbbacbadcdbadcacbcabdabcccabbbcadcbbcbccbbaacdbddddddcdadcacdbadbaccbcadacbdaacadbddbbddcbcdaccbbbaddcbbbddadbbcbbcbbccbcabaddcbadccaccdcbddcccbccdacbabaccacdcaddbaccaacbabccdaabbacbcccdadaaadccdacccadcdbccdbadbdacdbdabbdaaadacaacdcbacdbcbbabadabaacddcbcdbcadacbabacadbdadbdabbbdcbadcbbaabbaaccccaddbcabdcdbbbbbdbbadbacdbdcbdcbaddbdbbcbcbadcdaccbabcbcaabbbbdadacdbacddadcbcaddaaabdcccbababbacbbdbbcadbbabbbbbbbcacddabbbbabbcadacbccdddcaddbcbdadddaacbdddbbdabdcbbbbdbbbdbccbbabdcdbbcbbddabdcacdbaaabababccbbcabbcdddacccabbbbbcacbccccaddbcccaddbbcbdccaabcabadddccbbbcbdacbcacbcbaddadbacdcaccccbaabbbcdbbcbadaabccababcbacbcdddcbabbdcdbacdaaccbcbbcacbbdcdabcbabbdbbcadbbabddddcdabbddddbacccccddadabacdccacbcdaabbbbbdcacaddccacdbbcbaacbddbacaabbdcbbbcdaaacdccdbbddcaaabdcddaaadbbdadaacbbcabaabadabcccbccbbcbbabacbdbdcabdbcbdaddccbccdcaddccccddbdbdbabddacccbcadddadabcdddbccdcddccbbbcadabbbddaacbdaacbbdcdcddbadcbcabbddccbaccbdbabbbbddacaccaacbddddbddcdbabdddbcbaaadbbdddaaadaddcdcbcdaacbcbaaaadacaadcabaababbdcacdaddaccbabdbccdccdaccdbadcabddcbdcbabcabaccbabdccdbbbadcadcdcddbbbddaacaccbcbadcddbcaabbdbcadaccbadbbdaacdcbcbbadacbddbdbadaaadabaddcbcdcdcdcabdbacaaccccdcbbaabaddddbccdadbdcadaccabdbbbbdcccdabdcadbdabbadaddaaddcccdcbbaddbaccabacdadbbbcacddbdbacbddbdbbbacbbadbddbccdcbadddcaaabacbbcddacccacaaabadacccbdabadccbdcbcdaccaccabbddaaabcdacdbddbccdbadbbabcacacbbcdbbadaadbaaacbdaacacadbcdacadaccbddbdaadbcabadcbbbcddacbcccdadddbbdbcadbbbcddccabdbbbadacbabbcaaabbababbbaacabdcdaccdaadcbadbcbadbcadbbbdbacdaccbaabbccbcadabdbddadcbdbcdaaaabcddadaaaadddabaccaababbaaaacbcdbabcccbaadbacbaaadbdaacacbcddccbbbddadaadbacacacbabbdbbacdcccdacdbcadbbabcbcabdddabcaaabcddcaddcadcabdcdacdabcdabddbdacbccacbddbbcaaddaddabbaabdcdcaddcddacdbaacccbbaacbbdcddcabdaababcccccadcdacdccdcaddcdacdaddbabcbabcbabdddabdacdbdbdddabbcccdbabdcbbaaaaadcbaaacdcdadabddbcbdaccccadcbcddccabbaadbbcbbbcdcadddbdbaaccbbcacaacdabbbdbadbcdacbccdcccacacdcbadbabddbccdaacaccdbaaccccaaabdbbddcddcbadcdbabcadccacdcdabbcbaaddaacdbabcadccbabddcccbadbbdaaabdbbacdbaadbbcbcbcddcdaabccabaacbbbacbbbbcadbbdbdbbbdddabbbcbbaabbbccdabdbbcadaaadcdddbabcbcabbabaccaddaaddabbbcacadbabcdbbddaabdddbddcdbabcdcdddddcddcbbbcbbaacccacabcccaddcbadadacacaddaadcbbdbccdddaddadddaabaddabbbdacccadadcdbadcccbbcabdcdcaadbacbacbbacddbacabccdbbbddaacdbcddabdacbbabddcbacaadcbdcdabdcaccdabacbcbaddcbdbacacdacdacbcbadcbacbcaabdbbccbbadddbbcdbdbbabdaccdcdccdacbddabbabbbbddbcaadadbadadbdbcabaccccbddcabddcbccadbcacccbaabadcdddbccdaacbdccbaabddddaaddcdcddcdacbccdbdadbbbbbbcadaccdadddcdcbdbdabaddadabacadcabbcadcccaacbdbbaccddaccacaaaadcddabcccdabbdccabbdbbcabdddadbbdacabdbbbdacdabdccdaabcccccacdbdbbdbcbddacaabcaabbbbbbccaaabcdbdcddcadbbbacaaddcbdbdddadaddadadbbaddacacaccaaabbbbbcccdadcaccabddadbbcddcddbbccadbaddcdbdabbacdccadacadaddcabbdddbaddbbacadccabccdcbbbddccdddbcbdacbcdddbddbabbadcdadbcbddacabacababcdbccaaaadabdbdcdbbabaabcccbbbaddccdccbcdcdbaddadadbbbadbdadacbbbdaddbadababbcadcabcbddbbdbacdaccdbdccbcddadccaacabbcdcaadabcaabbdcdcdcccbaabcdbbabcaacbabdadcdbbcbddabbadbbcaccdcbddacccddaaabdcaabacbddddbcbdbbccccaaddcbcabacbaabcabbaacabdbcaaadbbabbdcbadddbddabcbabdcbbddbabbbdccabdaddcccdbcacbadbaaaadadcbdddcbddbbbddabdcbdcaddcadddbccbdbabdcacacdababaabdddabaaacacadcdcdbdcddacabcbdbddaddbbbccccabcdbadabdddbcbcacdaacabbdcddcadacbdbaabddbdcadbabcbccbdbcdbdbaddabcabdacababdccaaadbbddccdddbdbababcdddddcccdadbcdbcadadcbadddddbcdacbcbaaaacaacdaadbcddabbaaadcbbdcacacdbaddbacddddbadabdcbbaacbbdbcbddaddaacacbaaadaddbbddaaabcacccdbbadcbabdcdaaccaadccddadbcacaddacdbccbbbdbaccbaabddcccbcccbcbdcdacdaddbdbacaaaabcddcbdbdbaadadcddcdbacbcbbdbbdbcbbddddddcabaacbbbdbbddbacacaaddcdbbcbccbaaaccacdcdcaacbdbbcdabacacabdbaadadacbdbbddabbadcddddabaaaaacabdcbbdcbbdacaacacaaaabccdadbddcbdbdabdbadacabddaadaaadcddacaabbbccdddabdccdacccacddccdbdbbbadcdbbcadaaddbabbcdaadddadcbbaaacdbabddbdcadbaaaaccbbdaacbcadaaabdcbbbdcbcdbccabbacbaddaabaaccdbcdaabdcaabdbccdcabbbcbaddbacaccdbbbadacbdcbbcabdbadbbddbdabdcbbbcccacbbacccabacadcaacadaddaaddbddcbaccbaaaacdcadcbacbabcbbacddbdcadbbbcdbbbccacddcbccbdbbccccdbbdaccddccdcccbddabcbcabcddcbdacbaadbdcadccadbcdddcdbabdbccdcccacabbcbaabdbdccbbadbaacdaddadaacbddaadaaadddacbbacababdbdaaccaacbabdbaabdbccdcaddbbacbcccbcdddccdccabcbbcccbdcbbdcbcaabbdcaaaaaccccaddaaadccbdaddbaccddbdcbcabcddcdccbdbddddbcbdacbdddcdcbbccdcbaddbdccbbbcdcbbcbaadcadcabdddbaaaabdabdcabdbbccaaddbbbdbdaccbcbaabbccbdcbdcadbbccdacdaddacdbadbbadcccacaaaabcbbbbddcbdaadbaaadabbdbcbdacadbcababbdcaccdcadcaadbddaaacabdcddbbdbcaaadbcaddabbdbcddacaacdbbbdadaaaddcaabdaaacacdbdbdcdbcccbabbdbbbbbdacdcbabcbacadbadbbdddcdddbaccacccaadcdbcacccdddbcdcacbdabcddcdcdaccbdcbaccbbbbcbbdbbdccccaddcbcadcbdbaccdaccdabbddcbcdbadaabbcdcaddbdcdcacdbaaacbdcacdacbbbcacdbdddabccbcacabcadcdccabacdcccdabdacabaaabddabdacbddcaadacaacaabdcbdabbcbdabdddabbccdcccdbcdbaaadbdbbaaadbcccadbbbaaaddcbbdccbdacdabbacaccddddabbbbbbcdbbadcddacbbdbbbcadcddbbadcbddaccbcadbbaddddcbdbaabcdcbbbbddccbbdbbddcdaadbddbacbabadaabdbcbcbccdbaccdaccadcbbabaadcacaabdcaccadaaaaababdddcbbaadccacaddcbdbdbcacddbcababddddaabadbdcbddaddcdccdadadabbcacdbccddccacbbcbcaddbccdddccabdaabcbdaaacdccbabaadbaaacbbbcbdbbdbdadabdaacddcdadcaacadbbadbddbbcbddcddcaddccdaabbbaaddadbbccadabcabaccaaccddacaaddadabaabdbdbabbcacccadbabbbdccbacbdbcaadbaacbdabaacbdccbaccaaccdddaadddbbcbdbbabddcdaadddbaabddccbadaaaaaabdaabdcbdbbcbadbccaccabbbabdcadbdbdddcadacbbdcddbacabaccacbaaacdcadcabcccdddacbbbababccaddddabbcaabcbcbbcbddbdbcbaacbcbcdabdcbcbbdaacbaddcdbdcbcaaacddbbcbbababdddacadbabbcccacacacccbadccccacdbddccdbadacbabaabccbadddccdcccbcbbacaaaaaadbaacaadcccdbcbadacbbbaccbccbcbadbcdcdacbbadbaddabccacabbdcbccddbdacaaadacdbdddddabbaddacadbcacaadddbcbaaddbbcdabbdcdaccdbbabbcacbacbddcaabccbadacbadcbbabcabbdaabaacabdadddcbbabbcdaacabcdbbdcbbcbdacbdbdddadcaacdadbbcccdbaaabbdbbcacadadbcbbbbddcdbbdcdabaadcaccbaabccddabbcacababdbdbbaddadcbadbacddcddcadddaccdbaacabbaabdccadcaadbcdbbdbdabdadacabaccbdabccababbbdddcaabbaadababddaadbbccbcadbcaddbabdcabcadadbdabbdabcbdbccaabaccacbcadbadcdabbcbcabcddbacbccbcbabacdcccbbabcdddcbdcbdaddadbaacaddcdaccdaaabdccadbbcaadadbbadcaddcdbbabdbcbdbccccbabbbbacbbcadcbadaddbddcaaccdccaddcccddcabdddcbabacddcaadbccbbbdaacccdcaabbbacabdbbaaccdadacbaabbccbddadcccacddcbcdcbadadcaddacccabdaaaaaadbbcadccbcdadcbabaaddbbaaccbacaadaacdccaadaabadbadbdabbcabdcccacbacacacadcbdbbdabcdacadbdbaabcddbcdbddcbbcbdadbcccacacbbaaccdcddcbcdaabccccccdaaaadaacbdaacddbddbcdbbbddddbcbbddbadabdbbdaddbbabbadbbdcbbdcbdcdccccaaccdccdacdbddbdbbbbcddbaabacdbcadaddbbaadcabdcddddccaaddcadbabddbbdadadbaacacabdaaacababbddacbaacadcdacbacadabccaddbaaaaccadddaabaccddcbbcbdbabdbdbabcbabcacaddbccbaddcccdaaaaadbbcdbaccaccbbacaddbcbbacaaaddacbaaabcaacbccdbbbddcbabdcbcadbcabbcbdabdaaaaadcbccdddaddbaaddabbcdabdddddacdccccabcadbbcbcddbadccadbbbdbccbccaaaccccbbabaccdcadbcdacbaaabcdaabbddbccacdbabadbdcbaacbdbbcacccbdbdacbbbaabbaccbdcdbddccaddabdddbbbabdcdbacccadbccabacadddaddcbccbcccccbbaabaccddccaaddcadcdbbbbaaaacabdbcbbcabaaadddccbbbddacbdcbddaaccdbacbacbabddddbbddaccdaccbbbaccbbbdbadaadaacccddcbabcbbbabaababbbbdbaabacbdbbdcadbaacaabdaaabbcccdcbbddcdbadbadaabaabcadcdadbbcdbbbdadbdccccdbdaddbccbcaacacccaaacaccadaaaccabccbaabcdddabadababbacaabccbcbbcdacdbdccbbddaddadbbadcdacddababaddcbdabbacddcbdabbdcacadabbbbadcbdcacabddcddbaaacdccbcdcaddadccdbcbcbbaaabdadccacbdddbcabdddcacbcabaddaccdbccccaababdcccaccddbacbbabcdacbbcdcdbcbdddaabdbcbabbbcaacdbcbdbddbbcabaccdbcdbbccbccabbdbabbdbdbcbbbbbbadcdbbadbccdadbbabdacacaacdadcbadaaabcdcddcccdabaacaaccdbbdddadbcdcbabcdcccaacdabacbcabcbccacccacdacbcbbbadbdbdbaacbdacbdcccbcbcdcdabbdabcbcadbbddacbcbdadcdbcbadbbbccdbaaabdcddbabdcbcddbababcadaaadaabdacacdbddaadccdadabdcccaacbaadddaaddddaddcbdaccdbdacadcaabbbaddbdbdddabbbaaaaacabbdabdddbcbdadbbbdacdddddaadcaaaacabaacaabbccababbadcaadbdcbacaabbdddcbbddcbbcbbcbacaddbbaabbdcbccbcbacaabcaccbdacbddbadbbbddcdbdccddcadacbbdbbbdcdcdbaccddbadcbdcdcbbbacdbbcdbcdadccaabaaccbbcdbbacbcabdcabaaacdbadbdabaaabbcbadaadbdbdcaddbcabddccbaacbabaaadcddccdbcbdcdcbdbddcdbaccaaacbabccbadbadcaccbcbbbacacbabbcabbddabdbbccbadddcddbbcbdcaaccbaabdaddbdccbbddacaaabdcccdabaaacccdccdaadccabaababcbacabcadcdcccaadbcccadaccbbaacdcbbcdcaaacbdcacaccbaddcdcdaacbdcccccdbcacaaccdbabcddcdacbbdabdcaabdbbdbbbcccdcaabcbcaaababdbbdcdcbbaaddcdcdbbabcadcbbcaddbccbdaaaaaaccbbddaacdbdaacacdcbcbabbadcdaadacacdbadbccddabbbcccacacbdbddbdcbddbcacdbcdbaddcccdccaccbcdccaddcdcdddbaccadaadbdcbddbdcacbcbbccddcaabccddbdbccbabcbcbddcabaadbddcdccddcdacaadbbcbccaacdbdcbddcadbbddcbccaddbccbabacdcbbacbabcbcbaddbadcadcabbbacbaddaccbddddbddaacaacccadaccbadcbacbbaacadcbaaccaadadccaccddaadccdccacbaacdcacdbbaaabacaaacbaadadbacaaabbbdbabbdbaabadcdcddcdadaabdbabcacdabbbdbcacbccabbccaaabdbcaddddbcbacbccccbdaddaacbcdccaccacacbcadabbadadbabddacdbdbcabccdbbbccdbbcdcabbbcbdacdccadbdadaaccddacabbbbccbdbbabbaccdddbdaddbaccadaaaddcbdabcbdaddddbcbccddcbdcbdbadbdbcbdcbaadabdaccccbbdcbdcddbaabbbcbbaaccaacccccbbbadcbcaccdbcddcbaabadaadcbaddbdbaaddbddaadadabababcaacbabbdadccbdaacddacddddcccdbcadcdddddddbdddbddabadbaaabbbdadcbcbccdbbcdbbcabcaabdbabddbbcabdddbcccdbdbdbcbbdbacaadcdcdcccdddbadbddccabbadbbdabccdaaabddbcdaaaaaddbbbdbddcbaadcabdadbccdcaadccbbaacaadaccaabcaddbccddbccbbaacdbbdadccdcacabbbdbaddbcaaccaacdbaacccdabadbdcbddccabbaacbcaacdacbbbbddaadcddbcccbdadccdcaaddcaabcdacdccddcbdacdbcaccbcdaadbddddccbddaaddadbaadaacccdabddbdcdbcdddbdbbcdbabadccccdcabcadcbdccacadaacdadacacadbbdcacbdacbbacadadcddbcabcacdaabdccaadabbaccdacdcddbaccbabadddababbbcbcddadcddadccbcadabdadadbaabcbbdacbddbdabccbdbdaadcacdbddbacdbdaabdbdaddcbbdddbbbbabbbcabddcdbdbbabbacdadabccaacccdaccbdacbabcdcdadacbdbdadbdbdacbacdcddcdbcdabcbcacbdaaaabbabcaccccdbacbbcdaacdcaccdacabcdddaddaddccaddcbdbaaddaabbddaaccbbccdabddaabaabcbdacbabcbaadbacadbccadaaabccbadddaddbbdcacbdccdabcacbbaccbabbcadcaaaccadbcabbdccbdbcddcddcdcbddbcdaabbaabdbdaccbcacbbaccdacccadcbbdaabaacdcaacdbdacabadaccabcbbdccaadaccabcdacddccccdbacddbccdaaabcdcbdbbbbdcbccbbbdbbaccabdcdaccccdbbacaadbbcaccccaaadabaadaadabdabdabdbadcdbdcbababdadababddcadbcdaccddadadacbcdaaabbacacdddbdddddbabdbcbbcbdbdbadabbbdcadbabbdcdaaadaabbcbbbbddaacaaabccdacddcdccabcbdabcdbaddccbaabdcaadacdbdbbdccbacbbdddddabcbcdbcdddccbcdbcdccbaaacaacadcbdbcabbbdcbabaabdbdabadccaddcabbadbbbbcbcaaddbbbcdaaaddddbcabddadcbdabcbbaccbbaaccbdbaddccddbbdbabdbadcbcaadcdddbbcbdbbdcdaccbcbacaadcccccddddabbabbddacadacabdcacccadcabcccddacbcbcbcaabccbcaabcdcdcdadacaaaabddbdbabbcdddbdaabdccdadbdbbbccccbddcdcdcdabbbddbbdbbbacadddbdaddddddacbddbabdcaadccddcadbaabcddbaadaadcadbadcababdcabdbbbcccbcddbdcbdadacdcddacdbdadcbadabadcdddaacabddacbdbaccbcbadbadcaadadcdcdadbacabdabbaaacadadddacccbcabbdabcadcaadcdcdaddccbdaaacbdaacacaabababbddddcadbcaccacbbcbbadbbdcdbacaaabcdabbddccbbdcdabbabcdbdbdbddbbccccbaddacbaccabcccbaadbaccaaaccccadcaacddaccccadbbaaacdabddbabdbbbbcaaaddbcbbaacdbabbcbaddcacddcddbbbacaccadacacaabbbcaadcbbddddbdbcabacbabcbbbbccacaccddcadaddbddbcdbbbbbabbcaddadbdddbddcacbbbdcadcdbbdcabcaaadcaccdccaadbcdcaccaacaddbabdbcbaabadbaddbdadccbdadccdaaaccdacaaadabdacdcddaaaaccdccdcacbdcadabaadcadabacadadbbcddcbacbcbdccdcbaaddaacbddabbbbdccbbbcbacdbadbbcaabbdcdbaaddaadaadaadaddbadcaaabbaccaadabcccbbddaadbcccaccccbdaccbcbacabcddadcccaddcbacaadcacbdadadbdacdadccaaaacadddbadbdccacabacdacbdbabbbcbbbadadcbcadcabacdabadbadabdadbbabccddaacaaccacdacbaaccbaaabaacacdacdcdadbadacaddacaacccbccbaccadaccbcbdabcddaabcbbbddcbdcacadbdcaaddbababcccdccdbdbcbadbdcaccbdabaadbcbbcdcabbbddbccdbdabcbacdbcbbbddaddadacaaacbcbaaabacbdcccdbaddcbcacdccaccdbbdddcbcbdadabcdcbdddbaacdbaadbdaddabccabddabcabccabcdccbbadcbbbacdbbdcadaddcdcccdccbcddbcdcbcdaccdcbcbbdabbbcccddccdacdadbaccbcdcbacbadaddbcccbccaacccaaadddababaacbcdcbcbbdddadaaaadcbbbdbdacdbccbdcdacabdbcccbbcabcaddbbcbcccddbbbcdcdbddaabdcbadbabbdbaaababadbbacacdbccdbabbadbdbbdbbcbacddbbcadcbdadaacbadbcabdcaabacddcaadadabcdbcddbabcccdbdaadacaaaabcbdabdaababbccbcddbdaadaaadccbdcccbacbbadcdddbccdabbabbbdabbbcaaaacbaddcdbcdcacddcdadadbdbdbbdabcabbcabbcdacadddcababcdabcbccddbbbadaccbbaddadbbcbcbacabdccbddcaadccddbdcdbcadbcaccdabadcabcddbddbbabcdabaadccdbadacbaaadcdabccbbcababddbbadddddcdbcadabbddabbadcaabddbdcaddabdaddadbccaabadaacacacadbbcbcdaabdabddddaacdbdbccabddccabbbdbcdbbcddaddaaccadababaacccbcbbbcbbcdccdcdbdcbcccaacdcdbcbddddbabbcdbcccabdbaddbccbcdbddacbbadacbccbcccbdddadaacaabcacbaaccdaabbcddcddbaddcdbaaadbccbabbccaacadcabccacdcaaacdaacabcdddddbcdbadcaddcdbccdbaadababbababacadcddbdadbddbbdcacddbcacadddddbbbcbbcbdbddadcdddacdabcaadccaddabcacdbabbbadaacbbadadabddadccbabdbbdbccbdabcbdbccabccaccdabbcaddcccbbcacbdadbcbcbbadcbccbaadbbbdacaccdcbcaaccbacadccbcaccdccaadddcbaabacbabdcaaacdaaaaabdadbcdaddccbdddadbcbbbdbdcccbbbddcdccbcabccdadbbbdacbaddabcbcacdacaaccbbdccbabaacadbbdabdadcacdcaabccdcabddbcddbdabdbbadcbdabcdaabacbcccbcbbbbbbbccdacccbdabbdbddbbaaadcaccabdcbabacddaccacabdbddbccdbddabdbacaaaabacdbccbacccdcadbcacddcdbbcdbbdbcbbbaaacbdddcbcdddbdcccbaddaabcabacdabcccbabccdaaadddcaddabaacdbdaddaaabaacbcbaaacdbbccccbbdaddcacdabcaacdababdbcbbbbbddbdabdaccbbcbcbbcadcbcadcddaabdcabdddcabadddddaaabcccbcdaccacccaccaabaddbbbddddbacbadcacacadbbbdcbcbbbdcdcdadaaaddadcbccbbbcabbcbabbdbacbbbcaaabdbaddacdcbadcdcdaacbdcddbacbbadbddbbccbccaaddcdccddcbbadacbacaccdbddacdadaccbcdcbbaaccbdcacbddabcaaccbddcbadbbaddddbadbbddaccbdbddbdbddbbcadababdbdaaaabddacaddacacdbcbaadabadbcaabccddddadbdaabaccbcdabacbaabbcbcabcdccaddccbbaccddbdadccbaaadbddacccccabdddcbbadcacdacabaccccbadcbbdabdcbbaaddddbccbabdbabbbbcbadaaabdcbababdbbcaadbadbcaccaabaacbbbddddaaccbdddcbcddadbbdabadbddbbdaabbadccbdbaccbaaacbdcbbcadbbcadbdbdbbabddaacdddacbacdbbbabdadcbbdddddbadcdacdaadddcbbbdbddccacdcaabcbbdaaaadcaaddcadaaddcabaccccbbdacabaababddbdcddbbcbcdbcbccaacacaaaddaabaadddccdbaabbbabbcdaddabdaaddcbdbbbcdacdddcacbbdbabacdccabbddbddaadabaadbcdddcdcddcbcccccabbbdaacdbbdcacabddbcabcadbcaacbcdaddccdacbddbadbcaababdaacbadbadbcacdaadaddcccabcdbbbdccadadacbbdbadcbbdcddadddcdbcdbddccadacabacccbccaabddbbccaccadabbbbcddcaddcdddaddbaabcddbabdbacadadcadacbcbadbbdddbaddadcbabcabbbbcbdcdabaccacabbddacaadadaaaacddcacdcaadbcaacdcdbcdabcbacbdbcdbdcaaabbadbdcbdcdccbdcabacdbbbcacddbbccdbabdcbcbcdbcacddbccdabaaabcadbaacaadccacddddccaabadaadbdccbabddcddbbacddcabcabaaaabadcaabcddacdadabcbbbcdaacdbddbaabccacadaaabcaaadbbbcdbadccaaaddbcddbacadbcccbdabaaadacdcbcdacbacbcaaaccaccddacaaaaddbdacaccccabcbabcbaacaaacbabadbdddbddbbabaacbbbcbdabacbadcbbcdcccbcabcbcbdadbbbacccbabcaadbddcaccbcaaadababdcaadabcbadacdcddcdabbbbabbbdddccbcddcdbbdbabaabdcccbdbcadaccacccacdcdacbdcadcdabdacaaacdbbcbcbdcadbddcabadcaacccddbdacbcababcdaadcdbdbcdcadcbccbabcaccadadacdaababccaacccacdbacaabcabcccbacdcbccdbabababcacacdabdbddcdaaaacdbdbcccaaaaabbdcadbcdbbddbaacababdcadbcbcbbbbcaccabdddcabcddbbcabccadbadcaacbccabbbccabbcdaabdbcaaaccacadbbdacbbcbcbcbdcadbbbccadccbbdccccdcabbabcbcabaabaddadbdbccccdcaddbbdcdbddacbcacacdcdadaababadaaddcdbdcaccbcccdabccccdabcdccdcdadaacadadabdcdcbbadacbbabbbdabccdcbbbdaddddaddccdcadbcbcdbddaadcbdbadacbdbddaddadbadccbbdaacbdddcadcddcdbbacbccbdccdddcdcbbdadbbdcdcdcbdbbbddbdaadcabbdaccababcacbccdbaccaabbdcacbdbcbbaabddadcbbaabbcaabaccbbbadbbacbccdaacdabcdcacdacbcdbcdcaadbbdccabbbbabdaddbdacccaddaadcbacddcbdcbddabcdaaacbccabaccabaddddddbddcabcbbddbdccccabbdccddacdcdbddbbcbcbcdddbcabcdcbdddbacbaadaaaddbbacddabdabcdcbdbccccaaabdcbdbdbcdaccbdabccdcaddbdcacbbbcaddaccbbcbbcacdcdcbcbddbaaabbbcdccdbbbdabbdaababbcaaccdbcdbbddbcdcbdbcdbdcbdcbccdbbdacacdbcddcdcbcbacbbcaadadbaaabddbbadadccbdbccadbaddbdcbababadbadbdacaacccdaabcbdcacddbbdbcddbdcbabbcaadbcaccbacaacacaadbdaacbcacacbccccaaddcbcabcbbaadadcbbbbcbcdbbdddaaadacbcbccabbcaabbcacbdcaacbdaacadcbbdbaaacabcadadbaadadcddcdbaaaadbadadabadadaddbcddbacacdbdddbcccbaababcbddbccabaaadccccdcdabbadddccdaccdaccdbccacdcabddbddddbdbdacdaacccadbcddcbbccaaaaaadababdbddbcbabdbcdcabbdbbaaaccdcacbaddbcccbadcacaaabdbabadcdaccbbbdacbdbbadccdaaadacdcaacddaaacbadcdddbbaaabdcccbbacddacababadcabbbccaccbbbcdcdadcacdcabcdacadbdcdbaccacabcddcdbacdaacdddbacbcdddcdbadbdbbadcccabdcaadccbbaaccdbcdbddadaccbdaacccadddabdccccbbdbaaacbacbbcacbcdaabdbcbcddacbdaadbbbadaaacabbdbccddabadbdacadbdcdbbdcbdcddddcdaaadaadbbbcddabccddcbcdbddcddaddcadbbbcbababaccabbddcddbbccccabbadbbaaddbabccddaadbbcabbcbcacabcdacccdbbbccbbbaddcadaadcbcddcbbacbdcbbbccdadabdddacaacababbbccbabdabadacccadddbaacababcacdccdabdabccdbcaaddbbccaaacdabbdddcbdddcddadbacddddcdabbabacdabddcddabdadddaacdaaabaabadccacdbcdcccbbaadcccabbadcaaddaacacdbdaadabcbdcdcdaccbcdacbbddaaabcaabcbcbdcbdcaacacbbcddbdcdaddaabdbacbabdcaaaaacbbcbbadcacababbbabbabbbbbcbdaadaaacccabcbddcbddbdbbaacbacdbdabadbbddbbdbcdcddbccbbcacbaabbadbdbaddacadacacabcaabcbdcddababddcabcdccbbbaccbacdadccadabacbbbccbcaaaacabbdabccbacddabcadaaccdcccdcdcdbccbdabdbadcadbcacbaccdaadabacccdbdabbdddccabddaacbdaaccbdaccbabdddcabbdddaaabaccaddaccbbdcccbbcbbdaccacaddacdccdbbdcbcbdcdadbbdbcbcdccbacbabbaddacdcbabadbcaddcaaddccacadccccabbadbaadbabddabddcaabaacccadddcaccccabddccccdacabbddbcaabacbbaddabcbbbadacaccadababdaccdbaddcabddbbdaccbdcdacacbdcaaaccccccbacbdaddacbbdbabdcbdabacabcbacbcadcbdcabdcdcaaababaaabaabbabacbbccbacdbaaaadbcdcaccabcdbaddcadaacaabcadbbbabcaccacbbdcccdabccbaccccddbbbaaaadccdbabdddbddacbbddaccbdbbcaccabaadacdbcddabacbcccacdbadadcadcdddbdbaadabbcbbdccaaacbaadabbcabbbdbdacbddaababcacccabaaadaacacbdcaabaadbbdcdcabaadcacbdbabdbdbddcadcddabdbabcddaaadcdcdbcdcbdbdddadbbbbcdaacaddadacbcbcccdcbccacbaadbcacacbaaaababaacddaadbdcbbbdbcddacccddbbbccdadddcdcbcbcabccaaabcacdcaddbbbdccbadbbdaabbddaacdbbcdabbcbccddccdbbabcbdcaaabcdcbcbddcaaaabdbadacbadcaaccdacdbddcacbddcaddacccddbcbbacdbbcabadbbcddbdbdbdddcddccaaaaddabcbdaaaabbadaddcbddadacbddbcadabbabbdddaaaccbbbbaabdcabacaaadabcbbdcacdcdaccaabbddcccacabbcdcbdcbbbdbddbbdbabbbbbbbdabbbcbcacddbbcbacddaaabddbbacabaccbccacccaccaaddbcaadabcdcdacccbdadcbabdcbdcbabdcbcbadbdbcbccccacdbabddbaadadacddabbddaadbabadaacccaacadbcaacccdddbadaadbbcdaabaacccddabacdccbcdcaabcdadccbdacadbcaacaaaacdcacccddcbbdaddacbdbcdabdadacccaaaadcccbbccccbddaaadbaadcadcaabddabdabadadcadaddcaddcdbccdbaccbdcdccaddadccddbadccbcccdbdcbabdcaacbdabadadadcdccbccacdcdccdbdccddddccdcdddbaddcabdcdbcaaabadaaccbcaabbadcaccbcacaacaccabcacbadaddacaadbcabcacdcdccbbabddbabaacadcdadbbcaabaddadbddabcaaacabaacadcddadaaaddabcadcdabcaccaabcacbaacababcadbcbdbdcbbdbbbaddabcbcbcbddbdabacdbddbcbcbbacbcbbccbcbdadbcacddddddacdddbaababbaccccdddbbcbdabcadaadcaaccabbadaacccdbbadacacbaabdacddcdbbdacacdbbdbabbdaaadbbbcdbcaddcdadaadbbbbddabcdcddbcaadccddbabcdadbdbdccbbbabaccccaabacdcabdcbdcbdadbcbdadcadaddacdcadabaddbcbcabbbdaccdacdcadcbacacacdbbcadcbacbccdacbaccbdbacbdbcbcdacabbabacbcadabccdcaccccbaddbcbbcccabbdabbabdaabcdcbddcaddaaaadcacccccdbcbbbcbadbadbddabcbcbadcadadaddacbcddcdacdbbcadcbbdccdcbaccbcbdcdddccadbbacabdabbacbdbcaaabccdbaabbcccbacacacdccdbbcdcacaabaadbddccacdacacabcadbcbaccbdcababcaddacbbaabdcccdcaacccbadddabcbabbbccccdbaacabdbbddcdcbcbdaabdcdbaabdcabaabddacabbacaddaccadadadbccabdcbacbcbbdbcbbcdadccabadbabdabcacddcbbbaddddcbddaccaabccbadbccabdbbbccaddcbcbaacbacbaacccaccacdacabbaabcabcddcbbbddcdbababbbdbcdbdcdbbbbaaadaddcdbcdaaddddadbdaaaaaaccbbccdcccabbdbaddbcbacccccbaccbcacddcdbaaabababccbadbbbddbdddbdcabbcbbdaadcdcbdcbbccaddbccdcbbcccdbcbacaaddabdbbcdbbddbcbadacdbadcadbbaccacddbadbcbbdbaadbadbdddbbdbbaccbdccdddabdcdbdccbdcbbcbadcdadbdaaaacdabacaadabbddadddacaacacbabccadcccaabaadbcdbdcbdaddbcdbdddaabcbdcabadacabaadabbbadbaddaddbbddadddcaadacbacbaabcbbacaacaabdadbccaabdaddadbbbadccdbadaacaaddbadadcccaddcadbacbdbadcdbbdaabcdadbcccbacbcaccadaddacbabcadabbcbbcbadbadcbbdabdcdacddacdbccbcbbcdccccbabaddbaadbccbadbaacdcccbbdbabbbaccdbbbddcdbbddbbdbacaacdbdcddccdddabacadaccdcdaacbaabccbccadaadbbcdcbabadbadddbdcbbdaaddaadcbdcccbadbdadbaabbccdcaccacaacdcaaaadcdbcdabccccaadaaabddcbadbadcadbdabaadacadbdbdcababbdcbcaadcbbbdcdcdbaabbbcbcbcbaaccdabaaacdcddcbbbdaccdaaccaabcbbbdbddbdcccbbbddbcadbbbddadcccbaccbbadbcdacdbddbbadaabacaaacdadaddbbbdcabdabdcdaabadadcadaadccbdcbdabccddaadddcdddabaaddddaabbcbbcbaddcbbabaabdbadcbbcadadadccbbbbbadacbdcdcdbcdabadaaabcbccbaddccdddcccabdacdbcbabadccbdcaabadaabdadbabcdbacdaaaaabcdadccccdaaaaccbaabbcabcaacacccacdcdccdadabadbabdacdbcaadbacacbcaaadcdacdacbcccddccbdadacabcacdbcacbbbbdddbdabcddadaaacacdbaaadcabdaacabbadcccbabadbadaaddbadbbbaabbcaacbccdbcadbccdccbdaacccbbddabbbbbdacdabbcddccccadbdddcbccbdbcdddcabbbcacacaadddbdbabaaccadbdaadbccacbdcaccbbbcbbadcacbcdcacbdbdbdcdcdbbaddcaccbcdbbcacabaadbbadabcccabccdcadcbbbdcdcddddadabadbcdaaacadddddcabaaacaaabacdacbbccdbcccbdcaddbdcacdccaccdbbcdbbacbcacdabdcdbdbdadbacbddddaccdaccbcccbcacdadbacadcabacacaaaccbdbababcadcdbdcbddadacddcaacbdccddbabddcabadbcccbdcdabaabbaddbdbbbbcaabdbdadcdcacdccbccdcabbcbbbadbabccaabdcbbcaccaaadbbaadcaaadcbdaddcadcaddcdbacbaccdcbbcddbaadadcaadbdbcbaabaccabbddcaabbcaabadabbadabdcaabdbbacbacdcacaaaadacadbacccbdcdaaacdabacacdaddaabadcabbbbacbccdadbdddddddcddcabdcccacbbcdccbacbbcbcdbdabbbcadcdbadaccaaadbddcaabadacccbdbdabbbabbbbbdcadadcdbacdbdcdcdacabdacbabcbabcbbbcddbdccddcaaaacbccbdbcacaabbddcdcbcbdcadadcddadadabdadadcbaabbccbdadadcacbdbbdcaababccccabacbcdbaddcbcaaabaaacdcbcbabbbabcdaccbbbcbdcdabadcbabcdbbcaacbadbdaddcddcdaadcbbccdccadaccbdbbbbcbabcbddcbcbababdaccaccdddcccdaaccacdbaaabbcbdcbdbadbddbabdadabdaccdbbaaadacdbacabcdbdcacacabcdcabadcacbdabcabbaaddddabaaddccacacccccdaacddbcbbddbaadbdadcdcabdbbcbcccbbabdcbaadbddbcadadccacabbbabddabcdcadcdbbcccddcacccccbabbbbabdcacaadacbcadccdbbbaabdbdcccbbbccbcbacacbdaabbbddddbccbaaaaaadcaacbcbcaadbbbccababbdaabdbdccbabccadbbbccabcadcdccaccaabdadbddbcdddcdbdbdacbbbabcdabaddddbdaadbaaadaddcbccaadbaadabcababcdacdaabbadacddbdaccacabbcbabcdaacacdcdbacdaadbccdcbabdbbdccdccdaaccaabaddddbbabdadccaacbacacabdacadbadccbdcdbcbaacadadccdcaadaddbccdbdbccaaaccaaaaccbaacbdacccbccdcabbdbbbccbabcdbcabbababcdacbbdbadbbcbacabadabaababbdcbacbbadbacabcbacbadabacbdcbdbdcddbcbddccbacddabddcadcddcbddbcaaaadddabdaabbdcadadadcbdaacaabcacbddbbdbccdcadddccdbcddcbcdcddbcdcadbdcaccdddbcbcaaccdcbbdcadcdacbddddbdbbdacacbdddbcadcabaabccaddbcdcdcdcccacacdbdbcdddcbaabbcadddbcdcdddddacdbbcbbdaddaaaadacbadadbbbaadbaabcacbbcacabaaddcbcaacbcadbaddbaacdcaaaababcbbdddbbdabacdcaddbcaaddbbdccbdddaabdacbaddcbcaabcadcacbbbccdccbdcadbacdbdacdcdcddaacdbabcdcdcdcabaddaacaadbcacbdbcbbbdddcddadddddabcbabccccbaaaabdcaddbccbcacdcdbdddbdabddcbcdbdbaadabdabcbdcabcadddaddbbbbbdcccadddbdbcaddbdcdbbbddcdccaccdcbcabaaaddabbbbdabaddaabbbddabadcacaadadcaddabdcddabdaacaadbcdcbbdcaddaacccbccaabbbddaaabdcdbdddacbadcbdcccacbbaabcbbbabbcdcaabaaaaaacacbdbdccadaabddcadcaddbdbbaaddcbcdccdacbdbcdcbaddbbbbcbbcacbadcbaddcabbdaddcbdccaddbaacdbdbcccabcbbbbbabcababbddacadcddabddbbdcbcabddacacddddcbcbddbaccbacbbcbbcbcdcbccaccadcdbacbbbcdddcddbddcabccacddbdabdcdbdacbdcdcbcdabdcbbcaccbcddcbbbbbacacabbbbddccadbdccababbaadacabcdddadaabcbcbabaddacbaddccaaaddacaccbbbaccabdcbdbcadaabbbdcccdcbbcdacbacaddddcbcacdccbdaaddcccabcdcbacbadabdcbbddabdadcdbaacabbdbbabbccbbacacdbcbcbddabdacbadbdcccbacbcdbcbadacbdabdddabbabbdbcdcbdbcbbaaddaddabaabbaabaddacbadaccdcaabbdddcbaacadadcacbcacbdbaaabababcccabdcacbabadadbddaccdabbbaddcaaabdccdbabadabdcdbdaaddbbcdbaababaccbaddbaaabacadbdbddccdabddcccdabbcdadbddaacdcccacaaaccbaaacabbacccbbbbbadccbddabbdcabbbdcadabdaacacdacacbacadbccbbadcaadacbabbaacdbbaccccabccacacbbbcbcdcacdadcacbbcbdadbcaddccaccabacacabdbbdcdccdbdaaadcaacbbdadddcaadcddaddcaddbbdbdabdbadbcabdacbbdcddaaabdcddbaaccddbddbaaacbcaacdcbccacdaacddcbcabaccaabccddddacaccdaacacbdcabbbcddcbcbbddccbccdcdadcacdadbbcacdacbdadcadadaccaccacddbccddccbcaacaabaddbabdadccbbdcadabdaddaccccdddcbdbccdbbdaadddbacbaccddcbabbcaddbddbbdbbdcbacbaababbddabdbaaabdacbababbacadcbaadcbaadbbabcdcacdbaddbddacacbddacbcadcadbcaabbbdcdcbcbcccaabdcdccbdbaaacdadababacbddabdcaaacddcbddaabadddddbbdadbacdbaabddcaccabadabbcbdbadacacddcaaadccbdaaddccccdcbbcaacbbcccdadbaabbabaccacaaddcdaddacbdabaaacacdcdddbbcbdabbcacbdadcbcaccdcaacacacabcdddbddaaccabdabbbdccdacddaaabbadbcabcadcaabacdbaddccccaabacaacacabddacccadcbdbcabbbaabbacdbaacbbdbdaccdadbbabdbcddaacddbbacaaaadbbbddddbaabbcacbadbcadbaacbcbaddbdacabbddbadbcdbbdadadbbcacdabbdbacabcddcabdacddbababcbcacddbadbabbdbbccbbbbbabddbaddacabcccacccbcbacccbcbdbdccbcababdbbdddbcbdccbbbaabcddbaaaccdaacacbbacdcaacbccaccbbbcbbdabaadccdcddbbadbbcccbcbdbbbcccccbdbacdbadabcbbaabbbbccdaddcbdacacadbddccbdcacacbdddcdcbccddaabaabdccbcddddaabcdbdcccdcdccaccddcbbaaddbbccaddbabccbdaaacabcbbcadaacdbdacbadcabddaacbcdcaacbccadcaabadddabbabdbadcbabbcbcbaabdbbbcbddadbcbbcdbabdbdbbcccdabbacbbbcbcbdcdcddcbabbadcabbdcbdbcbbaadabaabcbdabdcbdadacaccdcdddcaabddabbcabdacabbaddcbadacdbacabadaddbcabadcbdaaabbacdcdbccbdcbccbadabacdccaaadbaddcaaccbbcaabbcbcdacbcdbbacbacadcdbdabccbbbbbddabdabcdbabdaccbdccdbdccbdacdadcacaabcdbddadcacaacababacbaabddbdabaddddbddadcddbababddcdcdbdbcdcdcdcabbdadcbcaabdbaddbddaabacbadacbdaaccbbaaaadcccbbabcabdbcacbcddcadbaaccccaabbcddccbdbbacddddacddadbcdbccbbcbcadcaccdbcabaabadccbcbcbccabcccbccbcbccbcdbcabbbddcadddbcdcacccaccbaababbadbdddbbbadcacdccabdbdbbcccdbabddaacaadbbdbcbabddbaddaabcabbdcccacdbaabdbcdaaddbbbccbbdbcaddcdcbbbaaadadcaabcadaadbbcdddbccdcaaaccaaabadbbacddabddbdcabbcbacdacadaacbbcaaaddacdbbabbcabbdcdadbbcdaacbbcbdbbbcdccddbcbcbbdbddbadadbdddddbcbabbbccdbcddaccadaccacccaccababbcbbdbcbadccadaacddabaddbdbcbcdddacdacddddccbbcbbcdbaacccaddddbacccddcdacbdbaabacccaadbcaccccadcbccaacdabcbcbdcaabcdbdaddabcacaabdcbaaaaaddddbbdadcddcdcdbbbaddbbbbdccbcabdcccbddadaadcbbcbdbaadaaabbcccdcdcbdbddadbbdbbbcaccbcccacbdcbbbcacaadaacbcacbadacbbccccddbabdcbcdcbdcdadadbdbbdadbcdcdcacbacdbabdbadccabbdcbdccaacbdcdadbadbcbbcdadcbcbdabbabdcdbdacdbdddcbadadbcccaadbddadbbaacccbcbcdbacabacabadddabcabcbabcbbacdccdadcdbcbddbccbcdacbcacbdbaacacccbbdcaccddbddbbdadcabdbadccadcaaccdddbbacbaabbcdddabbddabcdbcadbbdcdccacbcdddcbcbbcaadaadbdddcdcdbdbcbdcbaaacaccddacddccbbcbcbdabcbcbaacdcdadbbcbaadccbcbcbaaaaccdcbadcdbacccdbdbddcbbcbcdddabbddaacdadadcdbdcdaadcbaadaadabdaacacabbacbccaaddbddccdadbabccbdcddacdcccbcbadcbdabcbadbdabddcdaaacccdddacacbcbbdbcadcbbbacbaaacaaddbaddddbacdcabaddabaadbaddbccaccadcccbbdaacabdbbdacccbaccddadadcdabadbdbdcacbcbdbdccdaabbbdabacdbbaccaabaaddabccadbdaabababcbddbbcabbbadbdddbcbdcddabbadbccddbabdccccdddbdaaadbdadddcdaddcdcddddbbdbbdbadbbdcabbbbaaadbddcbabbacdabcbcacdbbdcddbdccdbcadacdddbaaccbccdcdaaaacabccdaaacddcabcddacbcdccabccacbabcbdcbcccbacdacacddacddbabdaadacadbdccadadabcdbccbcabcdcbcadbaacabcaabcdcbbaaacddbbbdcbabbdddbacbbdddacbbdacadcababcadbddbacdcababcdaabdacbcbabbabacacdbbaadcccbbcbbbbcacadcdcdcbcccccaabbdadaccadbdaaacdababddcbcdbbcaacccdcdccccaddccaaccdddddbabcbbdbbcbcdacabaaabcdbccadcbcacbcbdacdbbccaadbbabbcbaddabbbcaababddabcdccddacccadadcadddaacbadaddcaacdcbcbbbcddcadabadbadcaddadacdcbcaccabcdbcaacdadaabaacddaacaaccbcddaadabdbaaddcacccddcdbddbcbaddadbbdbbcdbcbcbcaddaadabcdcbbbccbdbbcadbdcaddcadcccddabaccbdacaadadbddddcbbbaabbaacddbabadaaaddaddbccdacdbacbddcabadbcccddaccddacaccadcdddcddbdababbccccccbaaadadaaaadcccbbdabbdcdcaccdacabbcbdbccbaadbcbbccabdbbbdabdaaccbaabcaacdacabcbacabdbdadbcccaccddcdaaacdddabadaddacbacdcbbdabccbadccdacacccddcadcddadabdddbadcdcdaccddcabcdcdbdbbabbaccddccdcaacccdbcaabaabdbcabbbabdcccaaadbdcdcbabdcdabbadabcccccbbaaacabbdcddcbaddccdbcbaaacababcddbcaccaabbbbdbbbbdadaccbdbbdbcacabacccddddaabacdbbdadcbdbccdddbdbdaabbbadadabbcbdbbbdcaaacdcadacbbcadbabccdddbabaacbdcdbdbcdbbdaaadaccdaaacbbabbaddbddcacaaddadcdddccbbbbdbdbbcadbbbccabcccbbabbcccacbadbbcadccdcbadadaabdaaaccabbabbaccaaddadbaaaacdddccbccdadaaccbaacbcaacbaaddbbabbccabacbaccbaabcabdbdbbdbcaacacdbccbbabbcdbdacdaacbabdbdaaaacabbbbcbcaabadcccdbbabdacbdbccdabbdabddccbdabddccccbadabdcdaaddcbdcaddbbdbbddbbacbabcbacdbbbdaddcbdabcccbdaadadacdbacbbdbbbcaaddcddddcadcbdccbbcdddadbcaaaccdcbbabddcbaccccddbccabcddacabddaaccbadaddbddaddaaaccaabaabbaaabbcbabcbdadddaddbcababcaccbdaadaadaccccdaacdddbaaadbdbbcacdbacdbaaabbadbcbaabcdccbbaddcbcccddacdcdcdcdcbcadacaaccdccbaacbdbdbaddbcacdacddbbdccdcdcbbcbcabaaddbaababddbbcaabbcbadcabacbaccbadcccbcdcbdcbdddcaddcddaadcdcbccbaccdabcababdbdddcdacabbaaaddcbabdcbbbadccdbdcbddbcaadccddabadbaaccbaccdabadcdcdcccbdbdaddcbacddcabddaccacaccdadcbccaaccaabacdbacdbacccabadaacccdaabdcaaadaccaabacbadcddddabcaabdaddcbdccbcdbcccdcccaaddcddcaabccabcdabbbdccbddbbabcdcdcdbccdaccdbdcbaaabddcaddadcadaaccabaaaacabbdaacccaacaaaacccaacbbdaccacddbabcabaaccabcacaddcdcaacdcadbcbdbcbbcaddbcdcdabcdcdcccbbdabddcdbbabdabaaacdbddacdbdcbdaadcaadcbcdabdbaccccbcbbdcbbdcdabadaadadabbdddbdabcdadbccaddabdcdcdcdcacddcdaccccbbbcaccccddcbdbaccbdbbcabcabdbbdadabacababbbbaabbbcbabcbcdcabaabaabdbdcdcdcbbdcbaadbccbbccbdbdadcacaccaccdbbcacbdddddaddbdbaaaadddbdccdacdbbadadaaddbdbaaddddabaacdbbcabbbdbcddadccaddabbcccdaaaacbbadbbbaacacabccbacbbbaadbdadcbbddcdbdbccdcdbaabcdddadddacacdbccbbdbcbddcabbcdaaabbababddbaadbdbbdbddabadacbcddaadacdbbdbbaaccdacaacdbdacbadaccbdddabcaabdcacdbccbccdcbddacdbdccddbcadabcbddabaababcbaadcbbccbaaabcbadbdccddccabacbdbbabdbabbccbdcccdcdacbbddcabbaaaccccbbabcbddbdccbabcdbdbccbccdabdccbbcababcbcbcdbdadcbdabdbbacdcdbdcddabcddcddcdbacdaaacbdabdcdcdadbbabbdcabacddbddcabcbaadcbcbbccabaabbbdbddcdbdaaccdadbcbccbbaccdbcbcccbbddddbccdabbbbacbccbacddbbcdbbbddbaddacbddcbaddcaacabbbcbbbacdadccadababdaacaccbcdaddcaaaaabaddbbcdcdbccaacaaadbabbbadcddabddcaddaddcbbadcddcabbcaadcbbccabdcacdadbabbacdadcabbabababcbdadccadbcaaaddddacbaabdcbbdbddacaabaaaddacaabcbbabaacdbadcadcadccacdcaaadadadaccdccbbdbaadbcbdbbabbaadadaddbbbaacbbbaabdadabdabacbabaabbcbaddddbbcadbbcdcbcbbcbbbcbadcdabdacaccdaccdccddacdddbdacccbbddcdccaadadacbcbdddcdbdcdcbadacadbddadcadbbaabcabadabbacaccdbabdcabcdbbaddddccdcdabcadddbdabcaaddaaadcacdbbcddcabadbabdacacccddddddaacddacbcdcdbcaddcddcccdbaccadccdbaacdbddbbcacbaadcadaacbccdcaddbbbbadbbcddbbbaaacabdcdcccadbcadcbcadcbbbcddaaabcbcddaabccdddaadbcaabacabdadddabddccdcbbdaccccabdadacccdcddcaaadcccbabddbaccddccaaddbcbddcdcbdabbbacabacdccabadcacbbbbbbcbbddadbabcaacddcbbcccdbbbbcadadcddcacddabbbdadddccdbdadaacdacbcbcccaadbdadccadcaadbccaabbccbdacabbaaabdadbccacdcbbbadcbcbaabbdababdaccaacdbbbddacaddaddcabadbaabcccddcdbcddbcbcbdabddcaadacbadbdcdacaccbddcbdbbcadbdaccdddaccbdbacbabcdacacddbbbcccaadcdbadbcacbcaacbacbcaaaaabdbaddaaaaaaddbbaaadddcddbdddcdadbbcdaccbaaadacaacccbaabcdccbdcbbbabcadadbbcdcdadaaabccabadacddbbcbdbbadaababbdccadbcbbabadabaaadbdcabdcaccdcbdcadaabbbbbdbaddddabbdaccccbbbdcbbbddacaaaaacadcaaaaaddacbccacbdcccdadbadbcdbbaadcadabbbcdacdacaabaabdbcbbacdaadaccbdccbbcacbcaabdabccadabbbbbbbbccddcacaddbbdaabbddaccaadbaacdadbacbaadababdadcaacadcdccbadaddaddaddccbdbbbdbdaaabadbdddbbbccacdcabcbdcddcdccabdaabbddadccadddddbdbaabddaccdbdcaaabdcccadcbccbaadaaccbbbcdaddadcaddaadaaaadadabadbcdddcdbdccadddacbdbadbcadaccabbcccbdaaaaabcacbdaddabdddcbadacadbbabbcbcbbcbbaababcaddacacccacccddabaaabcaacaabbadddcbcbbadccdadbaacdacabcdaabacdcadcdbddaabadacacabcbadadabdcaadbdacdabdbcaabadccacdbbcbbbaaaaaaadbddbadabcbbcbbadbaadccddcacccbccdadaddaaccabadadccdaaaadcccabadcaaaddaaaabcabdbadaaaccdacaabaadacacabdbbadadabcbbcbacdbbbbbbcacacbcaadcbacabdabaaacbaabdcbbcdcbdadcddcbbbaaaabadcadbacbacdcaddbbdacacbcbbbadbaacaaacdbbbccdaddaadddbbbcacbadcdabbdddbbaddcdcadccbdaddcdcadcbaccdbacabbbdccdbddabbadcdcadacbacaabdaddcaddbaaddabddcabadbcdaddcacbbbacaabbccabbcbcbbdcddbbcbcdddbccccdddcadadabbcdcaaccdaabcadbaacadaddddaabbbbcbccddcdbbdcbcabbaadbaacacdbdbacaaccaadbbacddabcaaaccadabcbaaacabcbdaaacbcdadbcccacbabadcdabdcadbcddccadbddcddaacbbcdcabbbddccddbbccadabbbdcdcbadcbdaabcadcbcacaabcbaaacccabadbdaccaacabbcabcdcacacdcbdcdadbacbadccacdbbadcbdcbcabaaccbaacdabcccabbbacbbdbccbaaddaadccaabdacbdaaacacabccabbdbdbcbccdcbdbaaccadcdbadbcdcbbcdbcbdaacaabdbddcaabbdcadabbabadaaacdbdabbcbdcadcacacbdbbaccddcbbcdcdbacbbbadacbababdccbcacaddbdbacccabbdbabcbcaadbaccdacccdbadacaaaabacdbaccbdcaccababdbbccaaccaadbcdbaaadadcdbadcdaadcddcabcaddaddcbbdbacdccdcbbddbadaadaabaacbcddbaacdbabbddacbabbccabcabcbcbaddbcdbcdbccbcaccaccbaaccbcabaaaddbadabccabdabcbdbdcdaacaacadcdccdadcbbbccdccbccdcabcdcddbbcdbabcdcddadbccddacddcaabbabbbdcbcdbbaddabacaaaaadbdadaddbbcbabdbcdcdacbdbdaabcdbcbcacabdaabbdcbabcbcaddcacdbabcacbbdbdcccabbcdabaaddcbbddaabaaaadccacdcdcabaaaddbaaddbaabccbcdcccbccaddacccabdacadddcbccbcdbcdbcadbcdbcdbcbdddaddbbbbbbdbaccbaaddabcdaddddbccabbbbaacaabcddcdcbdbcddbabbbddbdddadddbddbbdbcaccbbcadcbbccbddabaabcabaccdabbddbbcdadddbabdcbdcbacbbbcbadabacaacddbacbcdccaabcdbacbabcdaaaddadcacbabdcadbdcbcbccbbcdcbcddaddbcabbccbcdccababdadadbdbcbaacbbcbbcabbdddabdadcbbbccdaddacbabbdabcccbaabdbabbbacdbbbbbbaabacbdbcbccaaaadabaaadabaaabaccbbdcbacdabacbbbbdaadcbdaadabbccbbadbaaddddcdbdacdcdbcacccbacdbbbddaacadcaccdbbdaddcbcbbaccbaabbbaadbabacbdbcdcaaccaaccddbcddbbacdcaddcadbbbabbbdcbdddaddccbbaabcbcaadcadaddcdbbabcabccabababaccdcddbaaaacbbadbccdaddbbaddbbdcabadabbabbabbbabbdddadacbdccccaadcaddbbbdcadbadcbdaacbbaacdadddcacdddcdabbccacbcacaddacdacbcdaddcacbabdbccbdcdacddcdaaddbbccbcdcbcdbccacccdacccbddbcabcddadbcbcacbbcaacdccbdbcbaadaaacbcadadbaacddcddcdabbdbddcdadbbbdccbbdacbbbabdadacabcbaabbabdabaabdcabdcaacbaacccbbadbcbaccdabadbabbbaadcaacacddccdccbabcbbcaccbadccaadcdbaaadddcabaabbdcdcaabddbccadbdbadcabbbdcdcdcdbbdbbcdddacaacadbdcbcddaaaadbdbaaabbabbdacacdabaccbccdcbcccccadddabaacdcabababbcbbdccbcbddabacaaaadabcbcbdadbbccbbacbcdaccdacacccdababcdabaacacbababbbcaadabacdddcdacdcadbdcdaadbbaaaddbcccddbaadaadbccbdadbdaccacdbdcabcdddbbabdacdacbbddcabddcdabdaddddccacaaadcdbddadcaaaccbcdbaaddadbadaadcccbbaccbaacdccddcbddcdbdbcbadabaabcbbcaccddbdcaacddcdddbbadbcadccdddacaacacbbdccaaadcccbcbdacbcdabdbabbcaddabbcaccbdbcbaddddbaadcddbaabdabbaaadbaccadddbaabdaddccdcdcbdbdcbbcbadcbbaabacdaadddcddbaddcdccadcbdadddabdbcbccdcdcdcdddbbbaabadbdababbaddccaaaaccaddaddaaddbaddbcccdbadbbdbbadaabbdcccbbdbccaddaddaacdcbacddcbdacabbaaadacbcdbbcdbcdcadabddddcdcbdbcdadcdbdbabcddbcdddbddccbcbbddccbdcdccbbdaaddcdcdcbcdddcbbbdbbaccacdabddaccaaadccbbdabdbaabcadbadbddabccdcdcdddbbdbbdccababdbcccdacccacccbcbddddacdbbdcdbbdacabdcbccadabdbaadccdddcaaacadacbddcddbadaabdaaaacbddbaabacccbdaabcacdcaadabcdbbdcdaadbbadbcacadabdacaabbcccbbbcdcddcbdcdcacaddadcbacdaddbacdacaabccaadbcbbacbbabdaddacbbacbcbddbabcabadbcacbdbbdacbabbabbdcbabccdccbcbbbcaadbddbacdcaaaaaadadbbadabccacabacacbdbbbabcdadcdbccdaddaabbdadcaabccbabcabaaabbcdddddbcdbbddbccbdbbccdbcdcbdddbcaaaabacddcaadbabcadccdacbcabaacbaaacbabaabcdccaccbdcaaabcddbbcadabcbddcacbdccbabddbdbdbaacdaccddbdcdcabacabaaabbccbbadacdbdccbcdddcbabcaadbcdbccddbbbbcbdbbbbadbdbaadabadcdddabacccbdaaadbcdbcdaccbabaaccacbddabbdbbdcadadbabacbdaaabbaadbdbaadadbcbbaccbdcbdbcdbcddbddaaabcccaababdcdabaacaadabcbaccbdddddbcbabbbadcdabccdbaccabdcbcbbcaccddccbbbcdcccadddabbdaddadadaacdcaacabababdcccccccdcabdcccacdbddadcadbbddaacaaccaabbbaddccddbbacacbcababbdaccdbdcbdccbdaacabccaaaacaaddbcacaddadaabccaabdabbcdcdcbbdddcdabaaadbacbcddbbccbdcdaddbadcaaccdabcabcbadcbcdbabbcacaaccdacabacbccddcadddbaacaadcabdacadabcbccaddbdbacadbaabbdbdbddbcbbaddcbcabadaacbdbcbaaccacdadbdacccaabcabdbacbacdddccdbdcaaddbbdadbdbbaaaddadccbcdcdcbddcbcdaabbbcacbadddcacdbabcbcddaccdadabdaabadbdbacddcabdcddccdbdcdcaaddccbacdcbadbaabdcdcabcabacdbababaccbdccccdaaabcacdbcaadbbcaacdbbbdadccacaabdaaacdaaccacdddcdbaadadbccddcccabccdddaddcbbdbcabdbccdbadbcabdcbbccadbbdacaadaabacabadbdaabbdadabcbbbabdcdbaadabcaddadacdbcbcabdabcabcbcdacdcdbbdbcacbadbdbcddabcddbddcbdcbdcccdcbbccdcaaaabcbddbabbabccbbabbbcdbcaaccbdbbabdcdccbcabbdbbbcdabcbaaaddbcabcbccddbabddddbbccaaddbabdabadbdcdcaaacdbabacacbaacacacbadcbbcadccaaaddbaddbdaaccbcbabdacadbcaadaaccadabbbcadadcaabdcdddcbddccaacbbabdaacdccaabcdbcdcbbdccdaabdccbbbccdaabddaccdbcdcbbdaabdacbabbaddadaaadcdcdccaadcacaaddcdaabcddaaccbaacdbaabaddaccbcbddbdccddbacccbcbcbabcaabdababbdbdbcddabacdacdcdbdaaadddbdabbddbbcbadbacdbbbcddadddbacbaadbccdbddacdcbbbdddcddccbaabacdcbcdaaddbcacdacbddcdadcbdbbbccbcdacbccdbdaddbcadddaadaaadbbccbabcbacdbbacccccbcddbaabbaabddddcdcabbdddaccdccbbbcbaaacbbcbaacadcbccaccddaabdbdbbbabdddbabcbbabccdabaacbbbcbcdacdddccacdaaaabbbcaddbbcdbcddccccabbaacddccddbbbbcbcdbcabcabbadacbbaacbabbabdbdaacdbddabdbdacbbabacaacddbbdddbabbdbdcaacbddcdabccabaccadcabdcdbdadbaabbbacbbccacdbbacdcaabaddbcadcdccdddabddbacbaccdaacbacbacdbcaccaddcaaabbcabacdcaabbdbddccacdbdacbbaaadbdbdbbbccdcbddccaacbbdabbbcdacbcacbadabcbdbdbcaaabaccabcdaddcdbcbcdbacbccabbacddcccbaabbadbaaadabdcbdacbdbaaccdbdcbacbbddbabaabdadcbdcbaccaacadccacdbbbacabdccacbdaadbcccaaacbdabaccdbaaacbcbbcccbbcacdddcadabcaadcbcacbdddcadbaabbaabdbdccabcbcaacaaacbaacccbbbcaddabdacabddbbcdcbcacaabdddaabbcdcaddcaaacbbdadacbbbccbcdcaccdcacccacdcdbbcbbdaccbabdddcacddbdddbddaabbabdddbcaadbcdbaadddadbbdacdbbbbadcdccbcabdadbbcdccbdcaadbcaaacbcbadaccdbccabbaccbbcbcddcbabdbbadccdadddabbddbabcbcddabdcbbbacdcbdacdbddabcbcadabcbbbcdacadcdcaababaddcabbcbccadbadaaacbddbbbadbbacccaccdacdabbdbbcbcdaccccbaaabddbdbdbdcdaccacdcabdcccabdaccbdabcccccbadaaadaadddddaaadacacbdcbbbdccdbddddbdcaccaaaababcaaacbbabddbcdcaacbbddbadaaacccddabbacbadaccdaccaababccdabaacdbaabaccdacdddababcbadddaaadabadcbbbcdbccbdccbaccabacccbbabccbddddcaddbcbbccdcdaabaddcbbaadbcbabdbabdabdddcdaacadcdcdadbcbaddabbdabcadcbccdbdbaaccbbadacbcbdabadccacaacdacabbbcacbbcabcadbdbdadcbccddbbdbbbcdcbadbdbdacbcbacdbcaaaccdbcdcbbacdbbcdccdbaaacadbcaccbdcccbbddbaaccacaabcbacbbcdcdddbbcaaaddaaadaaabccccacacabacdccabdcaacacbbbdaaadcbccaaddadccbbcdbaaacccadabbabbcccacdccbbddbcabdccddcabbddcdbadbbddacdbdabccacdddacdcddaddabbcaccabdcacbbbccaacaddacbcadbccaaccdbdbbcbaaaaccccdacddabbddcbbcbbdcdcbccbadccbccbdbbadcbbdbcdddaadcbbbbbdbdbabcacacacccabacbccdddaddbbbccadaacccdbdbdbbddabdccdabbadbccadabbadcaabaacabaabcbaadabcbcdcdbbddbdddbdbbbccccdbabaababdcbabdbaddbbbabbccaaddabcdcdcbdcaddcababbccaadddaaaabbcbaddaddcdbcaddbcbdddcbddbaccdaabcaadaccbbccaabcddcaddbabaabbadaaaaaddabccaadabdbbabdbdcadcdddcccbbccdabddbddbbbabcbbcdbbbcaadbddbdddcccdcbaaabbaadbaaccdcbcaddbdbcbcabbbdccdaabdadbdcadccdbadbdccddadacbbccbbdbcabadcddcaaaddabdcdbbbdbacdccbccdddcdcddcdcdcbacdadbcdbbcbcabdcaabddcdbabccabdcbabdbbbcbacaaacddcbabcdaddbddbacdcadadcbdbbdcbddddadacaadbbbaccddcdaacbaacbddbcdabddbccadbdbdabcbdaacdabbdbabccadcdcaddbdcadcccacaddcbdadbabdcbbbacaacdddbdacbcabdbcbbddcddababacdccdaacbcdccccababbbdbdccabdbbbdddaccbacdaddddadbcacabcacaacbbcbadddbadabbbbdcdcbdbbbdbdbacdbddcbbacdcacacbaaabacbbdbbbcbdaacbdbdbadaccbbbcbdaaccaabcccdddddaabaacabbadbabdcadabbdddddddccbdaccbbddacaadcddcbaabdbdacbbacacccdadcddcdbcdcbcdbbbaaacbadcbcbcabdccccadcdaadbaacadbbcbacdddcccbbdccddbbbddddcbdaccbbbbaabdcccdddccacacacddaccaccadcbacabcaaccdcacaadbccaacabdbcbabcdddaadccbcdbdbdcdaccccdbcbaadcadaaabadcbdaacbbcaaadbdcdbbddcccbdbcdabccdccaabddcbbbcbdbddbbdddbcbcdaddccbadcbbbbdbdbdcbdcaabdddcadcdcacabadabbccaaaddddcbddbbbcddccbbcccbddbaadabadabddddadccadcadbaaadbadbdbcbcccbdacdbdddbbccbaaadcacacddbdcacbbdddddaccccbcdddabddbdcaaccdbaccccddbbdbccacdcacbcccdacdbbadbdbadcbbdcaddbacbcadbcdbbcbcdadabccaaaabbbabcdddacacabdcadbbbddccaaaccbccdbcaddcdbcdddacdccdadcdaabdcbabbdcdcddbadbdccbdaccbdbcadaddaaabaccdcabaabcaaaabdbcdddcccbaacaadaabbabdbbdbababbddccdadaaccbdbdcdadcadabbcacdcababcbbddcdcbddbccccccdbdaddaaadcddcccdbcbadaaabaaccacbbacccaaccbcacaddbdadacdacababbbabcbaaddbbcabaabdccbbbbdbcaccddcabccbbbabaabacbddcbbcabbabbccabbbbdaabadcdcabdaadaadbaddcccabcbcadbcbcddbbbbaaaaaabbbacbbbdcbadbabcddbaddbadbacdaccdbcaacbbdddcccddacadbbbcddbdaadbaadccbaddadacaacdcbdaddbacaacaaaccdcbaaddcacbacdabadaaccadabadbbbacddbbccbbabbacacbbacbbadcadcbddcacacddbbddbaaabcdadbddacbaabaabdaacadbbbdadbcdbcaddbcbdcdbbccaadbdbacdddbbccdbcbabcdbbddadcbaaabdcacdacdcccbbccdbcbdcbbddbccabaabaaadabdaccdccdddddabcbccacccccbdcbbdcadcdabbdcddcccdadcdbcdbbaacbadadadbdcdbacbbbbddcbdbcddcdacdbcddddbcccbdbdddcaccacacdbbdcaccdadbcccbaaddacaaadddccdbbbaddccbbddcbdddccabdbdcaacbcbacadacbbbddbaaaadccbbabddadabdccddadbbabccddbbcbcabbbcdcabadaaabdcdcbbaabbdcacbaccadacbaddbbcddddaaacbbdadbcaddbacadccbdbaaaadbdacacabdbaddabddabddaddaaababbadbaadbaaadddbcdbdbabaaabddccadbcacddbdcaaccbdcccccdbbbcbdbacbcbcccaaabbaddaaacbbbcdbdbaacabbcadabcacabccbdddbccddbabaacdbccabadadbcdbbcaaabcbbbddbccabbbdaacbdadabbadcbcadaddcabddddcccdbbbadbdbdabbbdbaacddcaacababdbcdbdabccdaccbaababbabbdbbcdadacbdcabcaccddbadaaccbabdacadadbaaddabcbbaacdcadcdcacbdbacbbbabcabdadcabdbdacdbababaaccbcacdabbbaaadbcabbbdcaacddcbcbcabaccbabbcddddcdaccabaddacacdcadadbbbcadcdbadcbabdbdacdaaccbbcbcbdddcbbdddccbbcdbcbddcadacdcdcacdcccdadccddcbcadacdcdadaddcaabbccabcbaddabdcdcbcaddbdddbdabbbdbbdbbcaaaabbdabdcbdacbcdadbcdcdcadcadcddbbaadaaabbadbbbddcbaabacbbacccabccbdbdcbcddccadaacbcccaabdacdaccacbdadaaccaccbbacacbadccdadbdaacdbbcdbcbbbcddddbdccdcbdbdddaccacadbcdacbdbdddbcbaabacbacdccdbbbababbadabdbcbbbcdcdabbccbcbbdadacbcddcaddddddbdcdacccdcbbdaaaabbcbaabcddcbdadbaabbcacccdbddcbbcbdbddaacbccccabaccbdadbcacdbacbbbabdbadacaccbcdbcbbbcbcaadcaddbbccbdcabcabdaabcabbadbddbcddbbdadcccdbbbbabdcadcadddabcdacdadcddacadadadcdbaabcdacaaabbacbcadabcccbaaabcbbadbcdcabcaacbcadbcccdcaaccaabdabdddabdddbccbdcdaddcaccaadddcbdaddabaabcddbacbbaacdabbccabaacbaccbbacbcbdcbcbacddacabccbadcabbdcabcdddabddbcaaababaddbccbdbacccabdcadccbabddadbacbdddcdaabcabcdcdbcaccbdbbadcdadaddacbcadcdaacbdbdbadaaddddcbcababdbabacbabadddbdbdbccadadbbcdcacdaaacdcacaadccbbccaabddcdbbdadaccdccdadcbaccbcacaabadccdcadddabdbbddcacadabddbdaabaaaaacddacbabdbaacacbcbbdabadcccbcadcadbbcaabcaaccdabccccccaaabcabcabddacacddbdbbadabddcbbccbacacddbdccdcccacbdddbabbbccbdbcdbabdcdaddbbbdbddbabbddbcbcdcbccaccbcabdbdbccdaaaddbcacbddccbaabcbdcdbbaabdbbabcdbbcacccacbcabdbaccdcdbcadbabdbcbaabadcccdcbbacdcbbdbbdbcbccbbcccbcbdabaadaabcadaaacddddacadcddaaaddaaddbcdbaaabadcbadbdaddabccaadbddabaaadbbdbaacbbdbdacdcaccadadabdabacbbaadadbcbbbcddaacddbadcccdcaadacbddcddbacdbdddbbcabbdcbdddbadadbddccaaabcbabcdbbaaddbcbaabbcbbbcacaabddbcbdcabdacadcdbbadcaaacccabccabaccbbabcadbbdaadbdbacadbdbbaadaacacbcaacdddbbcabcbccbcabbbbcdabdbccbcbbcdabccbccdcaabbcadddbdaddabdbdaacaaccbdadccabccaccabcadbcbdcaabaabbacddcdbcbcccdbadcabbcadbcdcadabdababcabddcbccdbcdbabdcddcbbbaabbacccccbabcdccbbddbaaccadbccdbaadadbdaabcabbdbacaccbbcbacdbdcabcddbcaaabaabdcbdaabbadbcadabbbcbbcdcaccccadcaaccaaacaddcaacdcdbacacbaccbdcdcddcbbaacddabadcbadcdbabcbacbcaddccaaccaccadcbbabbbaddbcbbadbcdcaddccdcdbdbaabaddcddbdadaadaddaccbcabcaccacabdabacabbabcbddbbaabddcbbacbadcbcdcaccacbdbddcbdbdcccbcacdcabbdbdabbabbcabbccabdaacbbccabcadccacdcbabcccbaddadcbacadabdaaddccadabbabacddddbaababbcbabdadccddbbaddbdbbabbdcddcbcdcaccbcbdabcdbdbbbababcbabcabdcbadacdcaaaabcbacabbaaddadcddbaaabbacbdabbbbbabaaaccaaabbcbcbdbaacbdbabbdabcdabbabbdcdaacadcdaaacbdbacadacaacdbddcdcacbccccbdadacdbbddbdbcbaacdcbbcdbaadcababbaadacdbdbaacadbdcdcddaaaadaabbcccdaadcabdcbacbdaaccdcabbdbcbabcacdbaddcbccacbcdbacdcdbdcddaadbbcbccadcdaadabdabcadbcaddabddabddcbbdcdcadbcbdccbdddccccbdcbcacaadddbccddcdcbcddbaccdbdbdbdbaaaacdacbadbccccbaabadcacaacbdcbdadabaaaaaaccbbcddbcabccddbdccacaddaaccdcbdaabcdcccccbabbbbdbacdbbbabbdcacacdadccdacdccbdacdddbbcdadabbaabcbbdbbbdadccbbdaaccbbcbcbbdcbbaaddcbdbcabddadbddadacabbbdbaacddadbcbdbdaabbadaabbdbdcacbbaaacdbcbdcccdcabdabadacbbdcdbcbaddddbddaddabaccabbcaddcacdaaacddcdbdddddcbacbbcbcbdaccccccdacaacaacbdcbabcadadcdbbacdddabcdcdabbcdaaaacdbdcacbbdcbdaabbadcddadbaadcdbaaddcbbacccbddaacabaccdbcabcbcbacccddcbcbbdbdcabdcdaadcbcdccaccddcaccdbcddababbdcabddcddcbbddcaacadadbdadacadacddaccbaccbbaaaadcddddacaacbcdbaaabdaaadcabddccdbbabbaacaddabcbaccbcddbbbbdddcccbadbcbaddadbdcdbdadbcacbbbcabbaddcccdadbdcdcacababcaccdbbadcdbbbcbcaddabbbcaabaddbacdccbbdbbdabbccdbdabbcccbbbbbddbcbdcccabaabbbdabdadbdbdcbcaaaccbdcbabbbadddcdcadabadbbaabbccbbaadaaaabcdaaabccdccdbdccddcbbbcdadcdaaccdccdbabadbddaadbdabbdddddabddddcbdcbbdaaccddacbcdbbaadddcbdbcadcbbccdadbdbbbdccabcdcbbccdbbddcccbcbcbaadbcadbbcccdaaabaabadbbddacabbbbcdccbcddcdcddbaabcbcbbaabaacddbbabbbcbcbcbbacdcdcccccacccadbdddbdcdaddcababcbbcccbdddbbddbdcddbcbcadbbbdcccadcdbabdaccdccdcabcbabbbccaddcaaccdadabcddbadbdddddbcbdadabdbbcbcdacdbbcbdccdabdddcabacabaddbacbddddcdaacdbcacbddabdddbabdbaaaddabcdccbbcdccdbadabaaccccccddacabcbcbdaacababddbcdbdccabdabdadbabaabaaacdcbddbbbacdacddddddbdbbcdbaddacddabdcadcbcdacacdaabbdbdbbdcdadabbcdaabcadabbabcabbbbddbcbbbaccdbbbddaacaadccbbdccbddcabbadcaabdaaddddcabaccabcaadbadddcdaadbddcaccccdcbcccbababddcaccbaaccbadcdbcbaccdaddacacadcabddbcadacadadccbbaacbbadbbdccbcbbdcdddabbdabcacccbbbacdabcdccdbcdbabdcdcccdcabaccadccdcbccabbcacadbcddcdabcabcdacdbcadbcabccaddccbdbdbdcdadcccaccbbaddcddcbdaabcadacadbbbddbccbccdcdbdccddbaacdbbddccacdbdabcdbdbcdddcccdcdcacdaddcdaddacadccadddccdccbabcdbadbbcaabbddacaaccbcbcdacddcddbddabddadcbcadadbbadbbaabcdbccbdaadabcbdbbdddcbcacadbbdddbcabbabdddcdbbddcdadbcdbbcacddcbadacbdbbbabcdbbccdaddadbbccacaddccabbadbdabdcccbcbcdadacabdbcbbdbbaccabcdcddabdbacacaaabcccbdcdcdbdcbdddacbbcadbbccdcdbdbbdccbcdbccaaacdaacadcccdcddbdaccabcdbccbddcbdbacccbccddbdaddbdcbccadcbbadaccbdddacbcdcaddcaaaacacdadacababccdddacaaccaadbccdcaacaccbcbaaacdaccccbcbacdcbcbdcadaccdbadbdcbbdababbbbbdccbbbadbdbcbaccbbabccaaaddccbddcbbbaccdbccbcabcbaadaddcccdbbddaabcabbbaddcdabddbdbbcbadbbcbbbdcadcabbcacdbbbcaabbaabcccdcddadddaddddbdbdbaaabbcabddcadbddbabddbdabdbbbacbabaababbbdabaacdcdbbcdaabcacdaccbcabbaccbbdabcacacaddcaacbadcbacbdcabddcdaaaaccabcabbcddacbdcccdadccccdabbdbddaddbdcdabccbdcbcaaaabbdbcabdccbbcadaccdbcbbaccdbcdccacdcdcaabaabcccadbaacadbbcbddcccddbabddabbcbbbadbcdcdcbcbacbabbcbcbacbdacccbbddbdcabcdaddddcbbbccdcbdcbcbdbcbcaaccbcabbadbadaadcdcbcbbcdaccccdddcddaaacaaacdddcbbcbbacddcacddacbabdbddcdcdcbadbcacbcdcccaccacdcacababcaabcaacbdcabdcbbbbbaadaddcabbccacddadcbbaadddccadccbdbccbddbbcbdacccdbdaaabdbdabcdabcaadcbacacadbccdacaddbaabbcbadddaccbcdaaddcdaaacdaacadbaddcbdbabbddcadbacbdbcbcbcdcbddcaabbabadddcabcdababdbaadabcddbdacdadbccbddccccadacdcbbcdcbabdcdbabbbdcbaaabadababbccaadbddbdaabdbbbddabababbccbdbdacadabbdaaccbbbccadbcbbcbbbddcdaacccbaccdbcddcdadacaaacbbaaddbbddbbadcabbdddadadcdcadddcdcabdccbacaaadbdcdaadadccacadaabcddbabcbbcaabaaddbdadcacdabcaddbdacaacccdbbcbdddadccccbcccdbdbcdccbdbabdadcdbbbacbdbbbacdaabccdcadabdcacaadddcdabcdaabdddbcdaadcdbddadcdbccdbcacbccaabdabddcdcbadbccbcddaacccbdabcabdabcccbbccbdadacabaababbcacbbadacbbbcaccbabcccbcdbdccadacaddaaddccadbbcabdbcccddacccdacddccaccdaacbabdabdccdadcbdcadbaabdacdbbacdbbdaddacbdaaaacababcbdaccaddbbbccadaacccbbbadacccbbbcbccbcccaccadccbaadacccddbbddcabacddaabdacacadadccddcadddacddcbdbdbbddadcbbcabcacdcadbadcbcadadabdbbdcbaddddabdbccccadbcccbdaadbbacbaacccdcabddabdaabbddaaadadabcbbaadcaaabcccadadddbbcadabcbccbaaacdbbbcabcbababbdbdcadccddcbbddcaadbdddbaacbaadccbdbbabbddaaccabcccacbcdccacdcccabccbcabdbcaadccdabdbdddccbbcdccacccdbccddbcaaccbccacaaabbcbcabbaccacccacddadccdabbbddaddcbabdabcacaddcdadddaadacdcdcdbbcbcddbccbcbdbdabadadaadcddaddbadbdbdbdababcbcbbdcbbcddddabbbcdacbbcaabcabdabadddbaaacdcbcbccbddcbadaacddcabdabdcbbabdcabdadbbaddcbbcdaabdcaacbdaadddbbadcdddddcdaccdabaababbbdddbcccacbcacbbaddababdabcdaadcadbcbbbaabadcaadadbbcdcbadacabdbcaaacbaccdcccbccccaaadabcadcadcabbbccdacadbdaadcbacaadbdcdabbcaaacccdddbacbbccbccbbacdbdbccbabcdbbcdcbdcacdcaadcdddccbbdbcccdccbaddcbabbccbbbbdcdabdddacdabadbddabdbbdbbcaabbbcbcdcaadddcdccacbccacbcaccaccdcaaacbcddcdabdcbcadbcaccacacbadbbcbbaacbccddcdbacabbcaaddccaaacdbdbdabadddcdcacbdbbcdddacddccdccacbbbdcdbcacccaaddcdcbccadabdbacdccadbdddbccacbdadbcbcdcadbbabbbcdbaaaaaaadccbdcccbdcaabdabaddbdcadbbbacdadddcdadcdcadccddacdcdaddabadbaddabccabadaacccbcdddcacaddadbdbdaadcabbcccbbdacdacddbdadbbdabddbbcadcbcabbbbbccccacbabcababbcdabbbdabadbbbdbaadccdbcaaabaabcaabcadcddabacdacadabcbdacdcaddcabadcdcaadcabbccdbabcabaddadbabccbbdabcacacaaacdcccbaadcabdcaccbbccbadbcaccdabcbacdbabddbabacaacaadaaccabdbbdaddaacbbccbbcaabaabacdccabdcabbddccaabadacdadadbaacabbbcbcddaabdabcabbbbccbbddccababadabbdbdbbdcadcdcacabcdaacbdbdbcdabccdcdbdbabbbdadadcdddaccddcccbcaaaccddbbbaaccccdccabcaadbaaadabadbdcbcadbbbbcdddcaccbbadccdabcdcdbbdccacabacdcbabbadabdccabdbaadbbabbbddbddcbbbbddbdddbccdcbaabbbbacdcaacbadabbaadbbdcddddcbccaccdcdacaaadccccacccdcabcdbcbdcddbbbcdcbdcabdcdcbacccacadcdcadcbbbadddaccdcbcbdbdbbcdbbbdcacbdaacdbcbbbaaccaccbcaabcbbcdbdbabbcbcaacdaaccbbacaabcdadcbcccdabdbcbcddcadcbabaaddbdcddcaacccacddbdbbadccadbbcabbabccdabcdcbdcaccacccdcbcccdbddadbadcbcdcbcadbcbccbbddbbdcabbdabdccdcaaccddaaababacdadbadbddbdaadaacdcbbbcabcabacacbcaabdcbabaddabaaddacbdbacacdaccaaccdcddadbbbcbabbbbacbbaabcbddcabaccabbbcdcbbcabcbcdbabbacaccdcdacaabcddcbcacabdddddcdabdbcbaacdabaabbcabacdbacbbcaddcbaabdccabacdcaaabbbbcbcadbcbacdbdbddbbcacdbaddbbacbbbacacbcbdcadcbabbdbbadcacabacbacbadbcdbcbaadadccabacacbbacabbbddcbacbadaacdcdcbdaaacdacadacccddbacdacbbdabdcbdacacdadbbcbcbcdcaaddbaabadddbbbcdcbdddadbbbdadcccbddcddddabcdddbdacabbcddbdbabcdcccabddaabbcadbdbdbcbdbddbabdcbbbbdbbaadaadbdddbbbbbabddddbbaccbdcdadabcbabcaaabbbbabbddaccabcbcabbcdcdccdbcdbccbbdaaaadbbbabcbdcacaabdddbcdaacbaaaddaaabcbbbbdcddbadbbbaaabcdadaabadbcbcbdbabadcaabbcdadccaacddbcbbbdddccbddbccbabbbbcbaddccbcbcdaccdddabcdcdddcdccddcdbaacaaabbaddddabaaddcbbbbdbccbbaacbaccbdacdbabcabacbabdccabdaaabadccddacbcccadbcbaddbbbccadabcdccbdbdbddddbbddddaabbabbdaadabddcbccbbcacdcaccbdbccabddcbbcaadaddbbcbcbcbaaadddbcdcaddcabccbadcacacadccdaccbbccdbdcbbabddcabaacaabaacbadacddcaaadaabbabcaadbbdccdabadaaacaccaccbbacbccaaacaddbbacbaacbcddcdbabadbadaccbcadaaadcdbbbcccdbbcacaabacbaccbcdcbddaacaabaaaddaacdbcdccdaccadaddacacdaadcdcacdcdbbdacbcdcccbbdaabbdacdbbcccbacaaabbdadbbadaabdddccababdabacddadddcddccccddccdaadddbbbdacaddaacaadbbbbcdcdcdbdaacdacdcdcbccdbbdbaaabbcbbdcccabbccadbccaacbbaaccbdaabcbbbdcacdbcaababbddaabddaaaadaabaadbdaadbdddcdccacddbdadbcddbcbaabdcacacabaadadcccbbcddcacaadcbddcabcbadacaabdaddbcdcabbbdacaccbcadbdddccbcabbbdbbdbdcbdbdadddaaccbbcabbbcdbbdbbdddaccdcbbaadbcabbddbcaababbbddbcddbddabbcdccacbdbcbbcadbcdbcadaacddacbbdadcaadadccadbbbacbaddbddaadcaabdaadbdcccacaabbbdbabcdcdcacacaccbbddacadbcbbdccdacaaddcaacaacabcddacccbddbccddabbaabbbcdabacacadbccaccabdddaccdbabdddccacbcbbccaddbbacaddabdddcccccabcaaacbdadadbcdaddcaabddbdccaacaabbddbaacabdbdcbdddbcdcdcdadaddacdabbbcaaadcdacbbddacbaddbcbdaccddccdbacbadadcdabccadaddabbcccbcdbacbdccdaaaaadcccdadddbddcccdbdcbcbbbadcccdbcdbdcdacbabadadacdccabaddabdddcbabcacaaadccababddadbabbcaaaccadaccaadabddbbbbccbdcaaaabaddbcddbbacbddbdbbbbdddbbdccabdacaabbccbccbdabdbcacadbcacbbbbbdacaacbadabdabcabdbcbaddaaddcdcacabbbacaaccbbdddaddaddcccbbacbcdccbddadaaccbadbdcaabaaabbdcddadcaaacccdddbdbabbabadadaddabdcbdcdccabacdbdccbdbbaabadbadcdcccaaaddabddcbabcaabddddabdbcaabddacdbbccbcdbddbacdbbaaacadabcdcdcdacddcadbdadbadabdccdddcccdbbdbaaadbabdcacccadbaddabbbcdbbaaabdbdacdcbbdccaccbcdaabddaaadccbababbadbadadcadbddcccacabdbdcbccaccaadbbaaabadbdbabbacdbdcdacdccadaacdccddbcdcccabcaaaddbdbbcdaabddbdcccabcabacbbddcbccabdbacadbadbbbbbbacaacbdbcacababbbdaadccbadbaacacadadcabddbdbcdcccddbdcabacaaaadaccbddccdadacadadbccdcdbcdaabdbcbaddabaadcbdbaadadcaadcbbacbcdaaaacdbbbddcdbdadaccaabdbabbdddabcaadbaddcddcbaadbccdbacaabcbdcbccaabbbcaddbcdcadbcdccbadaddabdabaabacccdbbdbaadcbddadadbdabdbccaddcbacbbadcaabddbbdaaaacbcaaadcdbdadbbcbaaddbabbccdbcddabacabdabbcadaadabadabcbbadadbadddcccddabbbaccbcbcbdaaacbdbbcdcbaccabbdcdcbcbccbddccdcadddbccbdccddadbcbbcbdcbbacbdaadbacaddddbddadddacadadcdabcadadcabdbbaabddabaadccbcdadabacaaddddadccbacccadadabacbabacabddbccabaadaadadcbbcdcbcadcdcdbbdaaadbbabbacbbcdaaddaacddbabcdddddbdbacacdadbacccccaaadccdccdccbccdacbbbabbbdbacbcabcaccaaccbbbbccbdbaababcbbcadcacadadcaacdaadabcbcbccacccbdcdbbcccbcacbdddcbaccbcccdbbdbcdcacccacbcaccaabadcbbcacdcbbcccbcdddbccacbbdccdabaadcbaddbcadbddccbadabbdaadcaabbdaaadbbaaacbccdbdbdbddacacaddbaaccccdccbbdbacabcdaabdaccccbdcbcacdddcadcdbaabbbaadcdcaaacabaaadabadaddacbdbcbcaaadcaddcdaddbdbccaddaabbcaabbdbcababdcccdbcccdbbddbdbbadbcbcacbaddbadccddbcbaaacbacaacbaababbbbbdcadcbcadcaccdbbacbabdddccdbacddcbdbdacacaddcaddbbdadbaabdcadacadcdcaacacbbdadabacbacadbdccbcddcdbbcaaaddacccdaacbacaacdcccbcdddddbddaddddbacbcaccdcbaaddadbbacdabdddaccacaddbdaadabbbcaabbbdbbdbacabcbabadbbabbbbcccdcccddcdabcadcdbabbdadaacbdaddcaaadbbdcabadcacdcdbbcbabaaaddaaacbcccabdbbabbabcadbcaadbacbabaccbcbaacddbccacaacbacddbbcdabccbdcacddaccbcabddaabcbbbccdbbabdaaacadbbdcacbdbbbbadadcaacbbaadccadaccbababbaddadadbcbaddbcbcbbabdabaaabadddcbcaacdbaabcdaccbdabdccbcdbdbbdaaccbbccdacabbcbcbcbaaabdaabdccbcccddcababbbcbcaddaddcbacaaabcacbaccadcdbbabbbbcaaaddbcbdaadabbaaabbaabddcdcdcdaadbdccacbbbbcaccacbdcbbccccbaaaccccdbdaaaccdcdbccdbbadbcacabbabadbdadcbdbadaaacacbbcdcbbbcdcdcddbcddbbdbccbadbacdcdbdabcdacdcaccbcbdddbbabcacbaabbdbcdddbcdcddaccbacbcaaaaadabcbccabbcbcabbbbbadcbabcbaaacbabbcddabccdbdcdcdacabcccdbdbdaabdadddabccdbbcdadcaaaccbbadbcbdaaaabbcdacadbccdbaadcbccaaaadcdbadabacaacbccbcacbaaacbdadccababdcbbabbbbdabccdcdbcbcaaadbbbbabdccccdcbdbbcbcbaddddabbccccdbdaaccbbccbccacddaabddaddbcdbbcddbadacacdcadabacbbadcabaccddcccbcdaadddadcaccbccdbdcaabbbcadbccbbcbbbdbddddaabddddbbcaabaccdabbacddadacacbaaddccdcbdccdbdadbbcabdcaaddbbdadcbacadadabcadbcdddaaaaabddadacbabcddccdcdcadadcdbccaddbdcdadaccccacbcbaabbacbacababaaabcdaabcbbbcbaddabadddbdcdcdcbabccccbbadaadddccdbdacccdabbdabacbdcaadaaabcbdcdabdbaaaaaacbacdccbccacdbbcbcaaddababbaabbbcbdddcdadccdbbabbacdcbaacadddbcbbbcdddddcdbdcbbdacbddcdccbcccaaaadbdbcabbdadcababaaacdacaadddbacdadacdadbcddddcdcddcadbaabadbaccabacababbbdddccbdbcbbacaadacacbdcacadadccdcacabbddabbbccddacbccdbdbccddbddabbcbcdacbabababcaababdbbdcacaabdcabbacccbbdabdccbdacaabcdcccaccbbabbdaccdbddcbddadddcbbccddaccaddaababbdbbcbbcdddcdddbcbccdbaabacdcbaddcaacacdccadaaccacadcddaacddbaabdccdddddcaacdbbdbabdcacdcccabccbaabbbaacccaaacbcbaddaadbadcbacaaaabbabbadbaacdabbbcaaddddcbdcacbaabccbaaaccaccadbabddbbcaaddcdabcabdacddbbbbdbbaaaddbdbcdcaadddcaddabbccbbacdacbdcdcbbacdbcdaddabacbcbbaaacacdcdddddabcaabdadcaaadabcadbbabdbaabccdbcdabcadaacaccadddccbdccabddddbbcbbcabdacdaaaaaccddcbbdbadbcbcaadbcccdcccddabbacbbdccdacacbcccbabdaabbdbadaabacadbbdbcabdaaadacaaadabbacccbdcadbdbabaddadbbcabadbcbdabdaccbddccaabcdbbbdaccaccbccadddbacbaabbdabccaaccdcbcaacdbbbdcccbdcaababadbcbcbacacabdacbabcddcbadabddabdcddccccbbbacbbcacaaacadcbadbbbcbcadbdbbdaddbbdbcbcdbdccbbadbcbbcbbcdadcdbbabddcdbcabadbdbbcdbbacbbadbbcbadbdddbaccbcdbaabdcaadcddbcaacdcbbbbaabccabdbadbacdcdcbdcddcbadbadccbacccdbcccbabadcaddddabbdadabdcaddcabccddaaabbdaacdbacccdcbaddbacccbdaaaadcccccadcadbdacccbbdcdbddadacacdaaccaacaccdcbcdbcaddbbdbdacddccbdbabcccdacacdabcadbaddccbbcacadcdcaabbbbabbccaacabbbdbddddcbbdbbcabaabbcdcbcacbaaaccacddbcdbabadaadabbaddabdaabadbdadddbaddbbabcbcdcdbbbbabdccbaacdbbacbbbccdccaadcaddbadadbabbdadcacbdcabccacccddaaacbddadbdcacacdbdbcbccdcaabacdaacdacdddcddbaaadddaaaadddbdccbbaacbdabcdbbbcbcabbabdbcddaccbbbcadbbacdbdcbdcdccbbccdcddcdcbaaddaabcbaddbbbbcacaaabdbbcdbcbadbbdddabacdcabbadbddddaaddbdcabcbccbbbcbabaaddccdbdbbababbddcabadbbcdabacaacbdbbddbdaddbcacbadcbadabbdcbbbcdcdcaabadccaacadbacaddadaaabbcbcaabaddddabccbaaacadcaaaacddcabaaadcdccdababdbcbbabdbdacbccabacaacbadbdbacdcdcabadbccbbbdacddddacdbbdbcbdcadbacadacdcbdcabbdddddaddabbcabaccbcbacaddaaacdddccaaaabcacbbaabbdabbbdbabdbdbcddababbdcddacdacadcbccbbcccdabaaabaadccacccaaccdadaaaadddbadddbbdaaaacdcabbdcbbddcbccbacccabddcdacbccdcaadbbbddbcdbdaadccdbadbdddacdbdddcbdcbabbdbcbcacdcdbaddbbdbdbdcbbdabcadacbabdcbcdbdaccbadacacbacaaccdddcdddacdbadaccdccccdbaadacadcacbadabbadabbabdacbddbcbcbaabcaadddccaaccdabdaabdacbccddabdddbaabaaacbacdbddbacddcbbbcababcdabcdadacaabdcdabbcccbbcacbdcacadbbdcacccaccdbcadadaddcbcddadcddcabbbdbabcdcddccccbbbcacadadbbcbcadaabccdcbaabbccabcbaadaddadbccccbbddbbcbdbdbcaaaccabacabcdcbdcadddaadacaaadbadcababbddbdadcccabaadddbbbdcdccddddbacacacdaddabbbababaadacabbaddaabcbdbcdbdcadcbbcdbbbccbbccaaacbbdbbbabacbdbaccacccabdbbacaddbcabccacbbcbdabcabdcbbdbaaacabbcabcbbbbaadaadccdaddacbcdbdddcbabddbaadabadddcaaccdcaddbabdaadacbdccbbcdcaabdcdcddaabaacadcdbbbbbaacdbcdcbdbbcbacccaabacaccaddbacbddabcbcbadabdbbacdccbcbcdcabbabdbbdcaacccacbbacbdbbabdbddbbbcdbbcaadbaadbbccbbadbbdbbdaabbbdadddbbcdcbadcaddcadbbabbbadcdbdcdbcdcbbdaacddaaddabbdaabbabcbddaaccddbdabacbbbbcddcbdcabaaddbdbabbdcdaaddcdaabcbbacddccacccddcbadabbbaaacdcbdddbcdabacadacdbbbdbdbcddabbacaadcbddcbddbcdbababdacbbbcaabcccdbbdccbdaddbdaacbcbcddcadaddddbdcaaadcbccbabaadabcdbcddbddcacccadcdcbabdacdacbdcdaabbccbcaadbcddabbddcbabcbbcaccdcdadccbaaaaaacccadcccacccdcddcdadcdbcacacbbcbacdacaabcbcaabcacbdccbbccbcdccabbabaaacdddddbbdcabaddbcbbcabddccbadcdbadcddddbdccddacccbddbabcbbbbadaadbcacbbabccbdbabddbdccbbacdbdbdcbdabadaabacccbcabbbbaadcaaacabccaccbdacbbcbadbbbbbcccacdcacdabbbabcbabbabadaccbccacdccbbbadbabdccaacbdbcdadcdcbbcbabcdcacabdbdadddccadccbbcccacccabdbadcdadcbccbdbdadbccadcdaabaabbdbaabcdbcdccbcccbcddcadcccdbbcbdaabadaccbcbbcaaaddddbcbbcacadbaacbbaadbaddbbdcaddadadaaabcdacbdbadcadbbdadabbddabababaadabdbcaabaaacbcddabbdbacbdcbccaccdcdadbcddbacbbcaccbcdcbcdddbdbacbbddbdabcbabcadacdcabdadcdcbacdabcdcbbcbdcbaddddcdcbccadcdadcbbabcbdcacdccaaddcabcaaaddcdbbddbbdccdbbbdbccdadcadbaddaaacdadbccadddbdcbabcadaacdbdcadddacccdacaaacadaaacbcbcdbdcdadbaaadbaacaaacabcaacabacdcbccdabcdcabdcdabbabcdaabbbbacdbdcbacacbadddcccdbbcdacabaaabbbbabcacdaccccacbabdacbdadbadddabacdacaadbadcabaaadcabcbcbccbdadddbcbdddaabdcdaddbdbcbdcbacdababdbdddabddbcbbcdbccbdbabcdbbcdbdcabdbdaacccbcccabcccbddbccdccbcdcccaabbbdbcbcdcdabcdbabddbaadacbbbddcabcbdaddabaadcccbcbabbdbabadaaaacddbdacddabaadcbabdbcddcbbbbbbabdcacccdbbdbabaddabddadbcbcaddcabcbbadccbdaddbdbbcdabdbbddbdabcdbacbdcadbbcbbccbdccdacbacadddaacabadadccbdbabadbcaccdbdadccaadbbaacacaddcbdcdabadaabdcdccabaabdcdcbcbddcadcbaacacabdbaabbbdddaccdddcaacccaabbadacbbccaccbddbaacadcbacaccbddcbcdabadccbbddabaabbbabccddccbadcaaaaaddbcbbcaabdacdbbbbaaccacbabacbacadbacbdbddacccdddabdcabbadbcabdccbbdbddacabbcaacdacaaccbdbabcdcdbaddcaacabbbdbdcdaddbcdacaaddccbacbbacadcabdbbaaddcbcccdcacbcbaaaabbaacbaabcabdcdcdababccccaddaababdccdaddbbdcdadcadaacdabbdbddcaabbabcbadccddbbdcdcccaddcadccaabdaddcccdaacbcddadbacbcaddcdcbdacddccbbccddcacbdbdadcbdacdddbacdcadbcacbadcadaabcacacccacdcaacdddddccbcbadaacccdcabaadccbaadadbabbdbaaddaacbbddabbbcbbabdcdacacaababbbddadbaddacaaacacccbbcabbdabddbbccdbcaccaacbadaabdbabaabbbabdbdadacccdacccdbadcaacabdadcbbbcabbbacbbdcbdcbbabaaaddbaacbccdcbbcbaabdbdccacaaadbbcdbcacdcddccadaaaddacaabcddbdbcaabbcdacbcabbaddadbaaccccccbbaacacabbdaaabcddcdababdbbddacbaacabdcbccabdbddbcaacabbcbcacbcaaadbcdbdadaaddbbbaddcddcccbccabdaaaddccdababcdbabdddaabbcababdddabdbdbabbdcbbddcbccccddaddcaadabcbabbbdcccdcdcddbbcddddbbbadddbdaabbbddbabdbadbbdddddbddaddaacabcbccaaddacdbccabaabddcdbadaccddaadadcadbdcdcbcdcbbbaacddaaaacadbbaabbddcdccbbaadcaaabbbcdadadaacbcadddcdcbabacbccaabdcaabdbcbacdacddddcbdddabbcaabccbdcaacaccdbddaaccccbbdcbbbdbaaccbcdacbcbbdcadccddcbadbbdcdacadbaddbddcbabababddabcaaabadddbababccabcddabcddaaccabcbbcbbccdbababbddadbabcbbdddaccaacccaadacbabaaacadbbadbcdaabdccadddbaddcdcabcddadaaaacabdcbadcdcdaadadadbccbbddcbcddccbdcbdacdabdbbbdabbddabbcaaccbaddbadabdddbcdcbcbbccaabbdccbccaaddbcccdccaadcdbdaacdababbdcdbbcdacacbbabacbdcbbddabbbcabdbbbbddabbbbdccccddddaadbbadacaabddcddacacdddbadcdadadaacccaccaabaccaccbddabbdbacccbbcbaaabcdcabddbacabaaaacccacaaacbaacbaddbbcccbabbbacaacadadcdaaddbadbaaabacddbdaabadadccddccbadbabbdddbabbcbcdbcbbddadbadccaabbabacdbcabbddbbdbbaaccddcdaadaacccadcddadbacaccabacaabdddcabdcbcadccabbcccddddbcbddcabcabddcaccbbcadabbdabbbbbbaacddbbacaccabdbbbcdcadddcdabcddbbbacddcdcdcadcabccddbabbbcdcdbacdcddabccacbaccdccbccadcbcccbadbdbdabdddcbbaddcbcdadbadcddacdaaaabdcdccdaabbbadcbcdcbdcabdcbcacdacacabadacddaabcaaaccdbaaadbcdbaacddbddaadbbcdccacbcaddddbcacbababdccccddbcbabbacccaacadaacccbcaaabdaabbdcbbaabcaadcbcadddabdbaaadcdadabbdacbbcbbbcdbdbccdcbbccbabbabddabbacbddababbabaacdccadcabdaacbcbbbacbcadbddcbadcddbaabbccabddabcdcbcdcabdbccabaabccccbccbdaacacccbbadcabcbbaacddbdbbcddcadccacbbbbaaaabbcdccdcddbabbaacbbcbbcbaabbabccacbbcdcddadcbbaabcddaccdabdcbaabcdbbbacdbdbacdcabddadccbcccabaccabadadbddbacadbbdabbabcbabbaaadabbacdcccacbcabbdbdaacddabacddcacbdabaacccccdbccabdbadccdabcdbdbaabbcadbdcbcbbacdbcbcaaccccbbaaacbbddddadabdbcaaacdbcdddcddadcbcccbdbacaabacbdddacacbbddcccdddbcdccdbdbcddddaaacccdcadabcabdaadbdabddbdbdbabcccbccabbacadddddabbbbdcccacdaacccccddcbdabaccacdadabadbbcdddbcdaabadadabdadcaddbacccbaacabcabbdcbcaddbbdaadddddaddadcaaabdddddbcdbaadccaccccdcaaadbacbcadadcbdacdcdbdaabdbcccbacabdbccadbbdddbaddbacacddadcdadccbaadccadddbadcbabadbacdddbcbcbbabacdcbdcccacbdbcabccdbbcaaacabcdddacbaaacbbbadcbcabaadaddcbaaabdcdbacbdacbccccadbacbabbdababbccaddbdcdaabbcabadbdadbcccbbbabcacaadaaddbdbbcadcadcbcbddadacadcdaaddcabadcdddbccaaacdcbddbcbccdcdccbbcdccdbdcaaccddccbaabdcbbdcdccaadbabdababdcdcdccdddbddaadaddcbcdbdbdbcbabbaccbddddcbdbccdddacbadcbdadcdbcdddcddcbbcbddacbacdbcdadbcbcaaaaacabdbadaddabdbdadaabbbbcdbcbcacdbbaccddccbacabcacbbdcaaccdccabacbdacdbcaacaddaabcdbbccddcadaadabcacdadcaccababccdadbadaccabcacddaaccbaabaaddabbcaacdcdbbdcaaddbdbccdddabbbdccaabbcccbdcadacbaddddaabcacdbcabcdbbddacdcdbcdcdbaadadbbaababaddcdbaccbddddbccbbdababccaddabaabbacabccdabaccccbacabcbcbacccddacdacabcaabcbabdadcdcbddcdcddaadbacbbbddaddccadbadddddbacdbacbdcbbbabcbabcdbabdcdcbbbddccddacddaadacbcaddaaaabcabcdbdbbbcddaccdbcadddabcbcdccaabacaadcdacbcadcddadadddbabbbcadabcadaaabcbadaaacbaddbccacddccacdcbcaacbcdbdcdbdbabbbadabcdbaadbbadabdaccabccbbabdabcaacadaabaabbbadbbaaaccbdcdccddbdccbbdccaaaadacccdbdcabcdcdaabaaadaddcdbacabcbcbadbcadaaadaacddcbcaccccaaabbdbbbccbdbdaacbdabdcadbcbdacbdbaabbababdadacdacddcdcbbddbbadadabdcbbacdddcdbbaabddcdbdabbaadcddaaadccbadcaabccbdabdcabdccccacccccdccbaabaccdcddcbadddddddaddbaccaddcaddabdbdabadaaaadccdbabbdbbbaadaadadbaacbdabccdddbabdbddacbbdbbbacbabcadcdcdbdddcbdbdacabddbdbdacbcdddaaddadbbdccdcbccbbaacadabbaddcadcdbabaadacaacddcdadbbddbaaaddccabbdabaacabdbbbdcaccacdbdbcdccbbdadbcbaabbabccadaacaccaccbcbbbacacdddaaacccdabcaddcabcccdbcdaddaacbbddcabbadacbcabdaaababacacdabcabdadbcabdcddcccdaccdbcaacbaaadadbbaccaddbbbaddabcadbbabadbbcabaddadcdbaacacacaacbcabacbaadabbbdacbacbbddacbaabcacbdcaccdcbbacabbcbbbbbbabadbdbddddddcbacadcaaccdcaaadbacccabbcabbbbcbdcaaadcdddabbbaaaaadcbcbcddacadbcdcbbdcbadaacabdbbdcdccbabdcccbacaaabbdaacdbbaabadaabddddccbdaddcbabccaaabbdabddcadbccccbdddbbbdbacdcbcabcbcdcbcddaacdbcadbaaaaccdcbbdbcbdabdcadbdacadacadbbbdbbbaddacaccbbdcdbacbadcdccbaddccccacddaddacdddbdddcbcccbccabcadabbadcbbdcbadabddacacabbddacbdbcddaaabbbdcdabdcacbaadcbddbabbcadcbbbdaaabacadccbaaabaacbbdcabacabbacadabcdcccbdabababdbadacccbbdccbcddacdbadacddcaabacaaabddddbcabccacbadcdaccbdcbadbddabddbdabdbcdbddacaaccaabdadcbcbbbbbbcabadcacdabbcdbcbcacdcabbcbbdacbbddbccddbaadbaabbdddccbaaaddcdcaadcbbabdcdbaadbabcaddcadbabaccbbcadadbcbddbbdaaabacbdadacdcdbaacadbbacdabcccaacdcbabbcdacaabbcbcadcdaaadcacbcbbbddbcaaabbdccaaddcacbcbcccbcbcaaabccbaabdaaacbaddcababbacadbdbbddadbcdbbacdccdababadcbaddbcbbbaacacbcbdcdcdbabcadbbbbaccadbbcbababbaaddcdaccdbcdddccabbbcbccacadcddccdbcbdbbccadcdabbccbbbbaacdccccdbadbaabcccaadbacacbadaabdccbccaadcdacaaaacbacaabbdccbaddbcbbbbbbddaacddaadacdddbcbddcddcbaaadccbdcaddddcdbccabbbccbdcdcdddbacbcacadcbdcdbdbcbacbcccbccccbbdbcadcbdcddccadcabbcbaccccbccbbabbcbcabacaaadbbadadcdbbbabaccadbcabddcbacadddbbacbcabcacddaaccabbddccabbcbdbddcbaccbadccdcadbdcdcdcaddaaacaabdcbdddcabbccbcaddcddccacbdbadbdcccbdcdcbbdcbddccbbaccadcdbadadadcaddcdccdbcadbcddcccddadcdbbacccdaaabbadbdcddbbdadcdaabdbcbdbbdcacdcbacbdddaabadcbcabcbabdbbdcdcadcbdcdcacabbcacbcbddcbdbaacacdcbdadaacbadddbdccdbbacdacbbcbddbdabbdaccabbdadddcdbddbaacdccccabaacdaacdabacaabcdaddacabcbdcaddccaabdacccbdccabaaccdcccdcaddbacbdbcccbdcdbbbcbbddbccdbdcaaacccdadacbacbabdaabacadddbbcbdcbcacbadcaacaddbddbdcadbccadbccabddddabcbcbaaddabdaccbcaabacacbccddbddbdaabbbbbcccbadadccdcaabdaaabbdaaddabdcddabadccadbbccbabbacccdcabadbcccccacaacabbaaaddcddacbcbaacacccddbbabdaaaacacdcdcaabdcacddbbadbbdddbccabaaacbbbabcbbcbddacbbaaabbcccabdbbdbbdcbddddbdaabbbcdbbacccddcbbccabcddbdaadcbadcacaadbddddadbcbadbcdaaadabcacabcacaadbacbbabacdbcbbbbccbcbddbbdbadbbcbaaccbbccdbcdcbdbdcdbabdaabbabdcddcbdcbbbccccdbdbccccbababaaaabbaabcdaadcbbccadbadcccbdcbaaccddadabccdabadbabcbcbddbcdcdcbdbccaabbbdbbbccabddcddbbabccddacabdaadabcdbdbdddadbdacddababddcabadcdacaddcddddbbadcbaaabaaccadabcbaadcdcbcbdcdabbdbcbaadadbddcbddcdbdbadccaacdaadbbcdcbcacbcadbcabadcdccaaaaacbabbdcacbccbdddadcacbaaabddddaddaaadacbadddaabcaabacabcadcbdccacdaccadaaccdcabadbaacbdccdabcdcbddcbadbbabdbbcacdcbcdbcddbddddcdbdbbcdddadcaabccdbaadbbdabacaddcdcacbdbdcbddbccbbbbddaacababacbaaccdbdccaccccdbbbdbbaacdbbbcdacbbaccacddabacdadcdaddbdaadccdcdcadcbabdbcdcabdcacaaaaaddacddbdccccdaccccabcccadcccdbdadccbbdaddbdbaadcdcddccccddaaadabaabdbcbcbdaabcdcaaacbcccbadcaacadcdcbbddcadbbdbcddbcabadbabdbcaabcddacabbbdaabddcacdcadbdbaadadabadbcabaabaabbdbacccacddcccadabcbddabcaacbacddcaacadaabdbababbcabdbbbdcadadcacadcbddacaabdaabadcbcabcdddcbbccbdaaaaabacaacdabbbbbbddadabdacbccaaccbdacabacabdcbabaacccddcddadabdcbabbbbcacabacacbddadcabadcddbbdbdccdddcbbbadaabcdbdddcdbabcccdddbdcacabaacabbdddaabddcdbbaddbccbddccbddaaacacadacdbcdadcbdbbbbacbccbbabcdddbddaaacbadcbcabcbbdcdabdabbaacbbabcbcacadbcccbbabaadbcabbcbbcddccbadccccdaccddccaacdaacbdbbaccacdccbcbdbdbaacabbaacabdddabcdddcddbcbccbbbdbbbcdccaaaabdccdadbbdabcddbabdcdaadacbbddcdbabaaccddadabbdcccaadababababdbdacaccaadcddcdbcdabdbcacbdaababcaccbacadacabaadadbdaabbaaaabddadaaaadbabbcbadacddddccdcddcaadadbbdaddbaddcaaddcdabbbdadacccdbcccbddaddbbcdadcaabacbccaabbcabcaacdcbbcdbaaacacabddbcdddcbdcccddcacdbdddadccbdcacaaddaabaadaadaadbcaadbcdcbdcdbadaadcbbdddbabababacacaadadaddddaabcacdaacdbaadacbddacbccbabaaddacccaaccbdcdbdccaccbabdaacbcdcddadabcbaccbdaabcbcbdcaabbdcdabbdbdddbdabdcbdcadbacadaacdddcdbccddbadcbcdcccddaaccddbdabaddabcdaaccacbaacbacabbccadbdadcabadacdaabacbbbaabbcabcbbadcbbdbcdbadabcbacbbdcddbcdbcaaccabcdaaccbdcbbabbccccaccbdcabcbdbbdbcddbdbbddcbcdadccadaababbccbabdbbcabbdbcbbdbbcddcbadbdbcbdacadbdaadaabdadbcabdbadbbbcadaccacbcbdccbbdbdcccaaaaaabbbbbbddadaaadbabddbacccbdabccacacdbdabaaaacacabcccacbcbcadbcadcadbdabcacddbbdddacadccdbdbbbbdadccaaaadcacbbadbcbaaaddbacbcbbbaacadcbdcaddcbddccbbaccdbcaacdcdabcbdbcbcadddcccccdddbbccbaabbaabdcbcacabcbccbdddbdaaaddaddaabaaccdbddcdbdccbadccdbccddcbaacbadabccbabcacbbacbdaddbadbbcabdbcdcbccbccbacabccaabddbcbcbcbaadacdbbabadaabdbadacbbcdaaacdcdcbcacadacabbcbbaaacbaabbccaadcbdcabacaacbdabdadcaadabbacdadcddbddcdcaaadabaccacbbccaadcddbabcbbacbaadbdabbcbcabddabbabcabccdbbccdcdcabdacccdbcdcdccdacbdbdcdbdcacddbccdbbcaacbcdddadbcbabcddbccadadcbdcacbbbbadaaadadcabacbabacabdccddabaaddadaaacbcbaaaabacddddcabaadcabdaacbccbdcabdcdccadbbbbadcadcdbdcbbbdddcdbbdbcbccdcdacbaccdcdcddbcddbbbddacbdddabbcbcaaccccdcbbdccbbadaaaacbcccbdbcdaabddabbbadaadddcdadddbadbbdbbadbcabbbdcccababdddabccddaabadbddaaccabadbbbddbcddbaabcabcbcbcbcaadaaadadcdddddbbadabadcccbbaadacaacdaaddbccabcbacbccdcdadbdbbcdcddaadcdbddadadbddbdadcacbbbbcbadaccdacbdccdbaaadadbcdbaddcccbdaaabcdcdbcccbcadddcaaccbcdadbcaddadcdbdaaccdddcddcbadbbaccadbcdbaccaccccbbbdadbbcbdcabcbcccaabbbbcccadabadaabdbacbdcaacbbcdcacccbdaaadcdcdacadabdccacadbcadcccaddbababccdabdcdbadabcbacadaccacdddcbcdaaadbbddcdddbaccdcdbadadcaccdaacbdaaacadadcdacdbaaddccdacbcbcadccabdcccaccdbbcacccadadbbabbcbbddbaabaccbababccdbcbcacdaaccaddcccdaaaabdbaddbaadddbcadcbdacbabadbdcbbdbabbaccbabdaaadcccddadaddcddacdcaabccbcadacacbdcdaccaaddabcaaccddcddbcabdcbdaaaabbddbccdbaccdcbcabcccabdababccbdcbccdbdbdbddcaacaccabacbbddbccacdcdabdbabbdabcbddcdccdbbbcadbabcdbbccdacadddaacadbacdadddacbabbccacabaacaacabbbabaadcaaddbabcddcdbbdacbdbbdcadcccbadbcdbacddbdbbddbcbddbddaacdbaccdcccbdbdcddacdacbdadbccbaacbdcbdbcacdbcbadcdbbbabaadbaaacdaccabccbaaaabaacacbabacddacdbbdccbbcbddadcdcbbcdbddbbcbdccccccdbbabcdbdacbcbdbddadabadbccdacadccbdccbbdadbabcabcaadbbddddacccbdbadacabacacdaccacbcdaccaacbaaabddadadbaddbdbdaacbadbbbdbacdcbdcbbabdcbdbabbbbadcdcbcdbdbdbbcacadaccabdaabcabddcadddcabaacbdbadcaabbcdcbadbdcbabbcdabbaaadcbdbdbabddbddcacdacadbbdddccbcbbcadaadcdaccadbccbcdbaabbcaccaaaabbbdcdaacabbbbcaacadacdbacbadadcacddcadbbbdbcaaddbbccadbaddcbabdccabbcacadaddbcdddbbbadacaabbbcabbcabadbdaadcdabbadcbadcdcbacdababddddacdcdcabaacbddabaabcbbbbaadbbbdaddbaccaddbdbdccacdbbbcccdddbbcabdbacbccdbcaabcadccbbadbdaaddaadbddccbdbaccabbbabaaddbcdbadbddbbbddbbccabacbbdbabcbaacbdbaccccdadabcdbdddccadccbdcbadccababddddbcbcbadccadbabadabababbcaadaacdabbaccabcbacaccdbaccacacadaccadaccdadcbdcbcdcdabbaaaccbaabcabbdcabbdcbbdcdabaadcabdadadaaddabbccbdbbaaddacdaccdccddcddcccdcddacabcbaabbcdcdcdccbadbbcbddaaabacaacdbcdddccbdccaaddcacbcbcdbadcaaaacdbccbddadaccdbdbbabbbcdcddbadadbdabbcbcacadddbcdbdbdbadaadbabbdcabcbaccdcddddaaaacdadccbacddabacbbbbcddabcbbabcdcdbbaacdbbabbcaabcdbbdbdcabcbacbcadbdadacbcbddbcbdbadacacadcbbacdaaabaaaddbbddabbabdbbbabaccbdbadaaacaabaadcdddcdcbadadabbadacbdacdbdcdbcddacadaacddbaadbbdaadbdcabbaaddcbcddacadcacdcdcbadbcdcccbbcdbacaaadcaabdddbcdaabdbdabccbbadbabdbbdcddcdddcdcabacbcaddbdddcbcbcdcddccabcadbddabcabbcbabbacaddbdccddcddacccbbdbdbbdbcbaabbadbcdbabacbbdaabdacabbacbbbadaddbaabaaaacccacccbcdabaccaabacddddcdccdcbccbcdaabddbabccbadbdaadbccbaacabcdcbbcdccababaadadddacaacdaddbabdaccadbbabbaadccadcbdacbbcabbaadbcbccbdaaddacdaddaccdbdddcbdcddbbcabcbcdacddabccadcdddccbdaadbcadadbdbcdcaacabddbbbcdabddcddaabaccccdadcddbcdacbabcccbdbcbdaacacabacdccccdacdcdadbacbadccdbabcdbadbaabcddaabbcdbccdccadddbbddbacabbbcababbdcddbaccbddbcabadbdaaadcbdbbcadddcdaddcbbcdcccdbcbacdacdacbbcabacabccabbccbacddbcccacacadcdcbacadcdaddccbabcddadadaadababbccadcbdbabdacabcaaddddddddaddaacabbbbdcbaabcaaadbbadcabaaccdbbbabaababdabbacdddabdabadcbbdcaddbbddbadbcaabcdbabccdbbbcdcdddadaddaccaccaacdadcdcbaaddcaacbddaaabbbcabccbdccababbbcacbcddabbdddbcacdcbdcbdacdcdcbaddccadcdccbccbabcbbcbbdacdaccdcbabaddaadcdbdbabdcabadacabacdadadbbcdbadaacbdcacbcbbdadabdabbdccaccddbbcdcaaccaacdbcacbccdbbdbdcacccacaddadadcabccbccbadcdbbadaadbababaabddcadcdabddccacbbdbdbbabdbbbcababbaabadadaddbddacbbccdacbdabbddccddbdaddbdbbcabccaddbccacdbddbbaccabcbaadccbddacdaaaddadadabbcbcaacccbdcdbbcdcbdbcbcdddbccdbdacbbcacddcddbdbccbdadcbadcbcdbdccccddbdadbdccccdcabacabaddabcaacacdadadabdbbdacbaadbbaaacdbdcddddddbbbbcddacbbabcaccccbaabcbdabbdcaddadcbcacccaabddddbdacdbbbbbaaababbcbaacabbbcabdacccbaacbbbbcccdadcaaccbaccbbcddcadddcbbbaacacddcdadccabddbdabccaadcaaadbccbccddbbdbbcacdcbbbccbddbcbbadbcbccddcbdacbdacdbcccadccabbacaccdbacacdbacaaaaccbcacaddbdaddcadcbbcbbabccbdadabcbcaccdbdacddbbbabdadbccddbaccdababbacacddcaadbdbcbcbbdccdbaccacccdacaccbbbcbddccbcdbacbbcccaccaddabbbdbdacddbbbdaabdbbbdcbbdabacbadcbbbdbbdcbccaaddacbcdcccbbbacdcccdddaaccaadbcabbadcdabdcacccdbbbbcbaaacdcccbccdaaabbddacadadacbccadcaadaccdabcdcadbbbcdcbbcaaccbcdcbdcdbccdbdcdcdbdadccbcccaddcaacbcddabacabdaacbbabcabcdccbccdaabaacdacacddccdcbdcccbbdcdddbacabbaabddacadacccadbabdccaccaaccaaddbcbdbcaccabddcbbdabaabccddcdbdbdadaacbbcdaadbdbcbabbabccddacabdbaaccabaacbdbbcaddcddadaaaadbdddbcdbcaacddbaadaddcacaaabcaaacadabacbacbcaabdacdbcabddbdcbdccdcddcdcadbbadbddbcbbdacddbcababccccbdbacacacddcbbbddaacddbbabddcbcaccccbcadadabbabaadcbdacdadcacdbcbcaaaadacaacdabcbbdaccdbcadacacaacbcaabccddadbdaaddaddbaadbccaadadcabccdccdcbddacaccacbbaccbabbabbbcccbbbcbcdcacaadbcabddccbdadadaccdbbcbbaccdbdaddaaadbabccbaadadddbacbabccbbdbcaaacdabcccadabaaacadcddbabaddaaacbdbaadbcdadbbaabbdcdbbbaaddadbaccddadcdccbdcdaacabadaccddcaabdcdbcbbcadbadadaacdbcbbcaadbbabbbbdddccbacbccaaadadaacacbbabdacaaaddcbdacddaabdbdadaddbddabbaacaaccccaddbadaacbbccbcbaacdddcdacaadabbdddbdacaabbdbadcaddcbcbaadacaaaacbadacdabddaabcdccddcadbcdcdbdaabcbcaaadcaabddcbbaaaabcdcacabdbabddbcbbbaaabbcaaaadddbbcdacbaccddbcdbdcccaadbccabcdbacbcbbdbcdbbadbdddaaccccbbcaaadcddacaccdcbdbadabbcacbaabaadabdddacaacdbcddcaddbaadbccbacdbabaabaaccdbcbcbbdddabcdddaaccbbcdadbbbddadbcbadbccbcaddaaddcaaaaadcaacbdaabcbcbdabcaadcbabbddcdbbdcbabacdaacdbcbdcadadcaababbadaadbcbdcbbaddbbdaaccddacbadbcbbbcdacbaddbdcddddcabcabccbccabddabdccbbbcdadacbccabcdacddcbacdddddbdcdbbcbbddbccabcbdbaacbddbcbacbddbaaacbbbbbacdbddcdddaaacddcbddcbbbcddcbddcccadddbbaababcbddcdccbbcabddbcabaadccabacccadbdcdacababcdcccdddaadcddbabbbcdcdbdbcbcccdaacdcacbbabbdcdcbabbaaaaacddabcdcddacbdbbcaadddbbbaaaaadcbcadbbcababaaaabdcbcacdabdcdbcdcbdbabddabddbbdbbdddcabcadaccbbdcdbcbbdbddddaccbbdadcdaddbccccdbacadbbaadbddabadadbadccbbcbbbbabdbccbddbdacbaaaccadacbdddbacbcbabdbadcbcdccccddababcaabaabaaacccdacdddaaacabbddcdadcdababdbccdbdadbbbbcabbadbacadaabacdbdcdcbbcddaccbcbdcdabdacbbacadaacddaacabcdcbbdcaadddbdadbbaaccadabadcbcdcdddabcdbccababdaddcadccadddcabbdcaacbabdbbacacacadaccadbbbdcbacbbddcdbccccadadaddccddabcccaabdabdaabdacddcbdcaddcbdabdbddcccddccbdbaadcbbcbccdddbadbdcbcdcbadcaddbdcbaadaabadacadbcbaadaabacdadbccccabbabdbaadcabbbdccbdbcdbcbcacccaabacbdbbccdccbccbadbaaaacabbcbcddbccbbdabbcccdbdccaaababbadadbacaaddadadbcdcacbdcdcbcdababcddbdbdacbadcaaccbccdadcdbaaaaccbacbccdcbdabccddbbbaadcccbbadbaabddbcdbdacbbabcdcacdbacbddddbacaaacbaacbabdabdaadbcabdbbdbbcdbcdcabcaaabccdcdababacddccacccadbcbadccaddadacabddbdaacdabddaacbdbbaccdcddcbbbacdddcdbabbadbabdccdbabcbdcdccacccaacdcddbcddcbdaabbbdcddadbbdcaaabbdcdbdbcbadccabdadbddadcdbdbabbbcbbcbcbaabddbcbbabaaaaccdacacdcdbdbabdadbcdccadaacdadbadcdadabdaaaaaadcccaaddddccdcbabdabbbbdadcdabaaddcacdccdbddbcbacdacddbdbbddadaabacacbbabdbbaadbbdaddbccacbbaababadbaccdbdcddaacddbcaaddaaadcccdbadddccccbaaabcaccbbccadcdbacbbacabcbaaacdcdddbddddccaaaaabcabbcddcdbcddadbadaacadadbacdcabbddbacaaaadacdabaaabbccddcdbbdbbdcbaddbaaadacbbcabadcbadadbadddcbbacabbcdccbdccbbddbdacdaccbccdcabcdaccccdadcdbcddcaacabacaadabadadbccaabccccbacadbabdccddcbaddababaaddaacaabdcdbbbcbdbcbcaabbdbcabdbaddccdbaccddccacbcabdaacbccccddbddcdcadaacbccccbabbcaddacbddccdadbcaccdacbababbacbdcaadabcaccdcdddbaadcaddbbccaaccabbccdadcdbcbaabbddadbaaddcccccbddbdabadddbbbdcdabddccdacababccddcadadddacdbdcadabbdbbcccbadbadbacbdbcbccdcadcdbdaabcacdaccabbabcadaddaddddbaaccaadbbadccaaabcbbacbdabdbdadabcadadaddaadacabddcdbcccbcdcdbdbaabacdadbdbccabccdbabbdbaababaacaddcbdbadaaacdabadbadcbcdbdbacdbcbbcbdbaaaaadabdddbacabdcddcbddacbaababccdbdcbbdbadcadccbddabbbccbcdbdcabcbbaccdcbcbcadabaaacadacdddabccacadbdcddcbadcabddadaddcaababbdcdcdbbbccbddbddcacacbcddacdaaddbcdcbdaccccaccabbbddaaaabbdaddcacbabdbcaaaddcbaabcbadbbacdcbccddacdcbcdcacdcabdccbabcbdadbcadbaadbdbcbbcadccaccadcaacaaccbbcdccccdcbcdaaadaccdabacbaacabcabddddbccddaabcaacddbbaadcacccccabcdbbbbbcacdcbddcbdabaddccadbcadbcdadaadaddabaaddbbdbbdccdcdcdcdbabaaadccbaaabcabdcabcacbdaaaaaadcbccdbbadcbcaabdbcbaadaaadcbacaabcaabbddbcddadcbabbdbacbbcbababbaccabbbababbcadcdcddbdacbaccbddbaabdccaadabaacddaccbdbbbbabccaadbcacdddaaaadbddbdabdbdadadddbcacbbdacbccbaaddcadacadaddadbaacddabaddabaacbddadbcbadacbabcabcdcadcbdddababcadccadbbcccccdaabababcaadccdcbbcdcabddddddbbaaabcadcccbbdbdcababcdbcdddaccdbdbbbbdcacadabbccbdadaaabdbbbaaaadaddadadcacbabbbbdbdcabadbbdcaaaaadaacdabaabaadcddbadbcdacdcdadcbddcabadbcaadbaabcdbdcbaaadddcbddcbcbddcaaddccbacbabcbbccdadccaddaabbcacdddcccddcbcabdaddaadcaabcdabaaabdcdbaaacacaadbcdbbdddcadccdadaaacbddcbabbcacabacddbcbdcbbaadacabddbbcacbdbbdbacabccdaaabdaccdcaadcabcdaddadabbccaaabddaccbdcccaaacabcdbacdaabbbdabccbbacccbcacdcbddddabbcacabdadacbbbcbadbdcdbbadcacdacaadbcacdbbbbbacbbccdadacabdddadbbcadaddcbaadadadacadbaddbbaacdbadaaaaaacacdacbcdacababababadcdbcdacdabbcdbacccdbcabdcddbdddbbbcbabbbcccbacdddbcbbbddbbbabaadbbdccccddbdcaccddaacbbcabcccbbadcaddbcaabdddbcdcadddcccddcbabccbbcdbdadacbcdccdadaacbaadccbcddcaabaababbbcbdabdddcaccdbcbacaadcacddccccaaacdcdabcddcdabdabcccbccabadaacdadcacddccacbccadbabbbdddaaddbdddadaaabbbddccbbdbbdbaabbbdbacbbaccbbdbbaadbbbbcadcaadcdaacdbaccbcddacdaacabaaacadbbabbacddbcbdbcdccdababdcbddacdabdcbccccdaaabdcccdbadabdbcdcddbbdbcdabdbcbcdadacadbccdcbbbcccbaddacbaacabababdcbdbccaddbbcacbcacbaabccdbddaacaddaddbcccdbbdcadbbdcdbbbacabddabdacbadaaaccacaaaadbdbdadabbcddccddbddddbddccaddddcbaddbadcbddcabaaddbccbdacdddcabcdacdbbbcbcdcbaaccbbbadccccbcdaaabcadaabdabbabbbadcbaacaacaacaadbcdcbddccdddccadbddddaccdcddcdcaabadaacaaaddccabdbacbaddbcacbbacdcbbbacdbbcbcdabbacdcabadbbdbaaacdbaddccdbabdddadbcaddcdcaaccabaddddcabbbbbdbadbbdbdacddcbbdbcacadbcbbccbadbadadbdbcbbaadcccbadccbbdcbcdcbabddaacddbacdcaaaabbcdcaccdcdbddbbcabdabbcdbdddcbcccabddbdadadcabbcdddbbababbbbcbacdbccdacbaddcccddbbadbbaabcbbcbbbcdbaacbbbccbcdacbabddabaacccdddbbdcaabcbdbbdcbbcdadcbdccdbcbcabbbacbbabadbabcadbbbbcacbbdadbcadadccbabbdccbccbacbbdcbbdaaabcbaddddcccabddbbbcdddabdaaddcbcbdbbccbbbcbccdddcdbdbcabbdddbddacabdbccaddcacbadbabcbbbbaaddabaccaaaaddccabbbbbbcbbbccdccbddcdaabbccacaabacdbdbbdbdbdcddacabcaabcdcdbabbadddccdcaacaddbbbbdbbddcbccbccacbddbbbbcdcacaccacccbaabddcaddcdcbcbccbaccdbcacbdaabcbabbdbdcaaacdabbaccaacaadcabbacbcbdddbcadcbacacbabdabccabcdcbbaaddaadaacbcddacdabbddbbbdcbccbadcdbbdbddbbbdbccdbdcbcadbcbbdbbaadabaddadacdddcdbbddbaaaaaccdbccdcaaaaccbbccbbbabbdacccababadcbcabcdabdcdcdccadadcbbccaabbaddababdbcdbcdaadbbdcccdadbcddcacadcdcadddbbbbbcacbdbcdaabccadbbbcccbdddccabcadcbbcccccdbdaccadcbdddbaddcdbdadcdddbaaddcbdddcacaaacdccabdcbdbbadabacabdaddcabbacbbbadcdacacbbbaaaabcbaaababacadbcddbacbddcccdcbadccabcaacdabcdcdcbdbcacddbadbdabaadccccdbbbdccbacddabccddbcadabadbaaaccaabdcacbacbcccbbcadbbdbbbdbdddccddacddcdadabccccccbadacbbcacbdcdbdaaabbdcacbbabacadbcdacacdcdbdacbcccddadcddabcbddacaadcbddbdcabbdccabcadbcadbaaccbbbbdbdddddbbaccbbcbdcaaccbcbacaabbcdcbacdbdbcddccadadacaacddbaadcabbacbabcddccabdddddbacadabbaabbdccaadcbdbbacabdcbabdddbbdbdadabbdbcdcabcbaaabcdabcabcaddadbbdcbcdbaaadccaaccdcaabbaacbddccadaddabaddacacacaaccddadbdbbdcdccdccdbbdbdcbdccccdbbddddcbabccdcbccddbddcaacccaddbdbcacacdadbbbdadacbbbdaabcdbbcbbccddbbbacbbabbcbadbbdabdbbcacacaddaabaccdbdcaabaaabddabdbbabdabdbbacbdadbcdaaabdccdabcbccabdbddacadbbddbababbcabdbddbaacccbdabbdbcaadcddcaadabdadbbbdbcdaadcdccdccabaccabaadccdcdbcbabaabaacdacbaaabcbabbcccbcccbcaddcaccbcdaccccacabdcbbaacaacdaadadcddbcdcaabccccdababdcabddababbbdbbcddbdbcddddcddcadbcddadbcbaccddcbabbddcdbddddbcdddaabadcccbcbdbbbddbacdbdcaacdbdccbaaccbdbcaabaccadbcaccdbcaacccbbbddbaaaccbbdbcbdacaadaaacccbcddcadbabcabdccdbdcbccadadcbbdadbcddccbcdcabaccbbdcdaadcaaacdddacdabacbbcacaadbbbabcdbcdcbbccdcdaadaabadddddbacbdbadaabdbbbbbaacdccaaaacdadcbdcacdcadadababdbabaccacccccddcbbaaddcbbbdbaabdbcadbbbbccbccbbaccdadacdccddaccbadacbbbabbdbbddccacbcdbadbbbccccaccdadadaadcacddbbaacadcabbdbbdbbbbcacdddabbaddcccdaadcacabaabbccbdacbbbdabdacabbdaddddccdccacccdbacddcbdaccaadbcaaabdacddcbbccbaaabbdbbdddbbbbcabdbbbacacbddadaacdadaadaaabdccadddcbbaabaddcaadccddacdaabcdbabdbddccdddcacabdddcbdcddccbabbbcbbddddadaaaaccaabbdbcbddbadabccabdcdcbabcaaacbbadbcccacbcccbdcadbbabdcadaabcaccdcdccabadcdcaabbdccdaacdbcdbbbdccdcbbbcdadadacbaabdcbcbdbbbccbbcdbcbcdbaaddddabcbcaaaddbddabaacacaabcbdbdcaccabccacbbaddccbadcbdaadbcadbdddbdaadddcbdcbaaabcadacccbadccbbdbbdcaabdabcccbdaaabccdddddddaabacdbdaaabdcdabadcbaacabdadacdaccccdabbbabaaaacbdabbaadcbacaaabaacbcabbdcaabdcbbaaabbbcabccdbbabadddaabbaabdbdabcbadbbddcdbcccdcbdbddbcabdbddacaacbbabcdcbcdcbdadbcdabbbdaadabdbbbcdabddccdbacccadcbbdbaadcdbbaadacdaddcbbbaaabbddbdbccccabadaadcbcbbccdbaccdabdcbbabbcaaddbbccadaadabaaccdbbcabbbbcddbdddcacddccabbbdcbcacadddbacbaabdcaaacdbcaabccbadbaabcaaaadbdabbabbccccdbaccccbddabccdcdddccbdbbaabcccdcbcdddbacbdbddbbcbbbbbcacdbdbbbcabcacddaadaacbbaadaabaccdbabadcaaacbddbadcabdacacbadccadcacaccddbcdabdacaadddacdacaddcadcddabdccbcddabcbbadbcabcadcbcbcbacaadddddddaddcbbbaddccbccdddcddabccbabdacdabcbbbdddcdccbcbdadddbdbbbbadddabbbbbcbdadadbbbcaccabacccaaccbdabdadbcacdbcbccaaadabdadacdaccdbbbaddcadcadccdadbabcaccdccbadabddadbdbdcbcaabbbbbbaabdacbdcbcbbcbbdddcbadcaabbbdddcacadbadaddabcaddccadbdabcccddcaddccdbbdcdcddbccdabbccbaaadaabcabdabbaaabccbcbaadaaacaaddbaaabcdbaccbcccabbddccacbdcddbcbdcabdcabbbabcadabdbbbbacaccccddccadaacaacbcccbabaddbbadababaaaabbcdddcdcbbcddcdbccdccbaaadabcdddacbdbabdabdaacbdcadbcabadddbcaaacccdacacdacbabdbabdababbddddcbabdabcccbcacbdacdccbbccbababcdddaadbbcdcaadcbccbabdbacbaacccdaaddaacdaadcccdabcaabbcddcbcdadbacdabccbaadbbabcacaaddbddccabaadddbdacdabcbcabcbbbcdadcdbaccbcddccbbcbbccaaabbccdacbbadadbcdbdbbbcdadcabdababaddcccccdcdaddcbdddadabaadbdcdddbcdbdcbaccccdcbcddbbaddcdcccdcacabacacabdacdbbaabdabacdbbbabdaaaacabbbdbbacabaabcdcadbababbabcccabbadcbcddddabcbcdacdcdddbcdcbacccabbaaaccbcddcadcbdbadaacdcdddadbcadbacaccbdaadcbdcdccccacbacbccddddddaabaacdaadbdddcadbcdbadabaddccbccbaccccdbacadccbccabaddcacbbbdabcdcdcadcaddddcbcaaadacacddadacbdabbbbaaacadccaaaccddcadddbcdadaaabbdbdccdbddcaccbbbbadcdcadbadadcabcdbbccbbbabacaaccaaadaabaccbaadddddcccbaaaccbcdbbbccdabcdbaccccabbdcdacaadacbabacccaaacddbccbbdbddacbbdaaaaddccbdcdbaaacbbbdddbcdbcbbabbadacbdbbdccababbbbdaaabbddcbdcabbaabcbacbadbddbcadaabbbdbaccdcabbbcababacabaaaaabccbdbabdaddcccdbbaabadbbdddcbdadadbcbdabbbbbcaacccadbccbcbabddadaabcdadddabaddbbcccbcbdabdcddbcbdccabbadcbcaabdbbcaacbabdcccabcaaacdbbbdbdddbdcaaacabbddcabcabadabaabbbaaaaacadcddaacdcadcddbacacdccbcaabddcdbccdcacaddbdbcbbbbccadbbdcabaccbccdcbadbbddcdaaacbcdddddbacdcdabbaadcdbddabcccaabadbcbbbadaaacaacbabbdbcbdccababbdadcbbbbcbddbcdddddadcaaacdaabaacdaaaaddcbccdbabdddadaacbaadddaacadbabaacdcacdaacacaabbacaddbadacdddbcadcdabcaadbadbdccbacdbcdcbbbbbabaccdabacaabdabbacdbbabddbbadbdcdcbcdadcaabbdacacacacbaaadddccabbbdbdaabadbcbcbbbcabaaaccadbadbcadbbdaaacdccbadbaccdaabbddccdccccdaadbaaadbabdcbbddabcbadbdcdbcdabcdcabacbbaacdddacbddcdbbcbbcbadcdabdbdadacbaabcabbacbcddbdccabdcbbccabaccabdbbcbdcabaacaacaddbcccdcbacbabcababcbabaacbcaadccbbdabddbcdaccdadcababddabbddbdacbbcdcdddaabadabacbbcaccddaabaaaaccddcbadcbccabbddbbdaadccbddbcabbaaababdbdbbaaaabbbcbdbaabcbbdbaaddaadacdabadbbabdabcabccaacddddddaacccccbacbcacbcdabaadacccadddddcbbbdbadaddbbbcadadcaccddcbddcdabcaccacacccdbacbddccdbdadabbaabcdacccbabaabcdccaaadcddddccdcbadddcabdcacaacaccacacdaaacacbbdcbbbcdabcadaadbbbbaabddbbcdddcabcbcdadaabdcbdcdbdcddcccddacbbbacdcddacacdbccdbccbbcdbaabdddacbadabbdcddbdabaccabbcadaaacdcddcccacbddddcaadbbcddddddddacbbbbcdcbdbddcacbcbccccbbdddcdabbacbacdbabdbcadbcbbbdcdbcbdacbccbcddccaadbcdbbccabbcbadcbbbdbddaacbabdcbbbbbcdcbdadabbcdcaacaabbcbcbaacdacaaadadbcaccdadcaddacbddcbabdbdadabdbdddcbbbddccdbddcababcdccdbadabdbbbbbabcabdcbbacbdbbbcbcaabbccdacabbacdbcabcacdcacddcabadcbbcacdcccdbbdccdabdcdbddbcdbdcdddabbbcddbcccbaaccdbabbabcaabbdbcdbadbdaccbaadddddccdbdcacdccabbcccbcdcbbacaaacccdaaddbdcdcdbcabcaaabddccbddddadacccbdbdcccbadbcbbadbcbdaaacacbddaddcccbbdcdcbbbcbaacabbadbbaaccbbcaaacddccdbacdbcabbbbacddcdcaddcaaaaacbaadbddcbdcabdabadccbdaccacdbdabbdcbabcdcacbddcbacdaccaadacbcddddddbbcdaddadcbcbddccbaccdadcbdadababadacaaacdacdcdddbddbadbbcddccbccbcdabdbcaababacdabcdbababbacaccabbcdbdaccabdbabcdadccaacabbaddcacaccdbaabcacccbbbaabacbbadacbbccdbdcdaadbdbbdcadacaadaabddbcdbcbdbcdcdcddbdbbaabbbacaaaaacbacadbabcabacbddbcadadcdbcaaddbbddbdadbcdbbddbccabbdbcadcbadcabdbcdadbcccdacbcdbdbcddbbdadcccacabbccbcccbdaacdccbcbdcaaacdbbbbaaacdcbccbdadddcaaccabcbdbacababadcbcabaccabdaddbcddbbadadacbcccadacbbaaadbcaacadcddccccbabadcadccaccbadabdabccbbbdbcaddddcabbbdbbbddadbcbabdccccbcbdacdbbbacccbbcbaaaabddacbccbaadbaccadbadaacbaaddacdabbabaaacadabcddacdbadcacdbdbdbcccdccbdaadcadbcbdcddabbababdddbbadbabbadacaabbcacadadcacbaaabbabbcbbdddabcbccbcdbbabadabadabdddccccdabacbbbaabaaabaccccbdcbbcbacababdbbbcbccbccbacbcaddaabbcacddcdcccaaaabbaaaabcdcbdacbbdccadacccabadcaacaccababdcbcaaccddbcdbdcddbdbcacbbdbdabacddddbcbaabdccaabccdabcbcbbddbbcacdabcbcdababaabdbaaaccbbdbdbbbcaadbaadbaadcaacbaccbcdcbdadabbcdcadbcaccdaadcababccdaacacdccdadbabbbcbdbdcccaababbccbbccadbdccddbdcabbcccdddbdbbadbdccddacbacddcacdaadcaaababcdababcabbdddcdbbddcdcadcbcccbbcabaddacaddabdadabbddadcbddbccaccccaddcaabcccbadcddadabaaaccbccbcadabdbbcdaddccdbbcacddbdbcdaddcdbcdaabcbdbccdbcbbdaccabdcbcdccdacbbcdbbbadcbdaccbcbdabcaccdbdacdbaccbccdaadabdaacbdcccbbddcadbbdcbaddaadbbbbbcbbaabcbcaaddbaaacabddabdbaacdaaaddcddcacbaccdadbdbacaacdcccbddcbcccbbdbdccaddccccdcbdadaddbdcccdbddbaacaaababcccdbcddabcccbccbdaabcbaccaadddcdadbbcdbadacdccddcddcdbccbbcbdddcdcbbadadccaaacdcccdbcdbcbbccbcbbdcddadcdcdccabacbccddbcababacadbbccabdbbcaadcabaddabadbaabadadddbbccbbbcaacdcabcbabcdcdacadacbcabdcccaccccbaccdbacbdaaabacbddaababcdcaccdbbdaabddaaccaaaadbadccccbbccbddabaccabcdcbadbabbaacaddddadddddbbbabababcacbbbdaaaaadcaacaadbadbdcddccaaadbdcdbaadabccdccdacadbabdccaacbcbbaacbbbcbbdcadabdadcccaddcacacdabcdbaadcdcadddcacdbcadddadbbbadabcbaadbcaacdabdabcdadbdaccacabcabaaabdacbccabcbdabacbddaaacadadbddabdbbcaacdcdadabbbbabdcdcaaccbabcbbddbbdaabccdaaacdcbbadaadddcdcaabdcadbcdcabbbadabacbddaaaadacacccaccbdaccbcbbcadddacdcdccbdcbaacaccdbbacdbdddabbaccadabdadcddabacaabccddabcbbaabdcdbadaddaaddddcabaadadabccdcbdaaddadcdbcccacdabdcbaccccdddcddacadbcdbdbadadaadabaadababbaacabaaaacadadcdcadadaabacdcdcbbdaabaddcbaaacaacdcddaabcddaabbcccabcdcadcadabacbcbcacabdbdbbdcbaadbcacabdaddabaaaadcccdccccbcbaaddaabcccddaabaacbcbcbdacabbcdbcaacccdcaaacaaadcadddacabdacdabbcdbbbddbadcdacdbbaddaadabacbaadaddcbbdbbdcbabadabbadbcbabccbdacbabbbadddcccdcadcccbcbadbbcadbdcdbcbcacdbdcacacccbccdbbcbadbabaabadadcdddcabbdcbbcabbccbcbbabbcadaddbcdcdabadbbcdddcabbdcdaacdcbadcbcbbbdbcaccbacccdacababcbdcaaabadbcccbadabaadbdcdbbcdccaabbcbdbcacaddccbdbccbaadadaabcbdcbcddaadbcacbbacdacaabbadbacaccdcdabdbbbababaddccbbbdccdbdddacccaabaabdadddbdbbbabbcdbdbbdbbdaacaabaaddcbcadaadbbccaadccaacaddccabdaabacbcabadcdadbbcdaccdbccbbaddddacacddaaaacccbaddccdddadbadcdcddadcdbabaaccdbccdcdabdbcddaadababdacbbbddabbdbbcbbddaadcadbbabdcccdccbaaddcacddabbbacbcbbabcadbaacbaccbbccbbabaabaddccdccadccccdcabbccdacccccadaabdbbbddcbcadccdbbcbabccbadabadabbabddcababdcdddbbdcbdbbacacacbbaadaadccbdcacddbdbcabcbcdcbcbaadabbacdddacdabbbbabbbadabdaadbdbbbdbacaadbaccabdbbcdadcbdadbabccbabbaaabacaacaccacadcacadcdbbadcccbcacabdcabbdbdaddcaadbbdddabbdaadbccabbddbaccaadcdaaacaddbdadcbcccdbdcacddcadccbcdabaadcddbddddcabdcaaaaaddbbccbcccabdbdbaddcbadcabdbccbcbbbdddaaabdcbdcbbaccadabbbccdccddddabbcbbdbbabccacbdbacbdacdaddbadcaabcadaabcdabacaacdccaddbcdabdbcbbaaaddcdddcacabadacaaddaabbbdabdacdbdbdcdadbdbaabbbcdbaddbddbdbabbacabaabadcbadacbaabcbbaaacdadddaabaaddabcdbdaadbbcbbcbccdaacaabaddbbaaaddbdbcbbdabcbccccbbaadabadbaaabdaccccbbcbdccdcacdbcdacbbdbacdabdbdcddaaadbcbcbbabbbabbbbdaccddbaabddadbadadaacbcbdcabddabdabaabaabbcaacdbbdcaadcbccadbbbbdcbadbdbddcdbbccbabddadcbdbbbdcdccdacacbcbabcbaadacbdbccadacbdddacdabdbadddbacdabaccaababbabbbacbacdadcbcccbcbacdbdbdddcabacbbcaadbcaabbccbcdbcdaaacbbcbdcddcbddcadbaaadbcdabacdbdbddcabaadbabdcadadcbaccbdcdcccdcdabcddacabaacdcadbcbcbcdbddbdabcacdbbaadaddcccbdcadcaddcbcbcadadcbbbcdcadcccbcdbaabcbbbbdacbaaddddcaccacdccacdcccbadcbaadccadcddbbadcbadcdbbcabcdaccdaccccccbdcaddcbbcabaadbcccbbcbcbddbddbcdddcacdbadcaabdccabcaadcddabbdbacdabbccaadbcbbaddacddbdbadbadabbcbabcbadadccabaddddcdbcaaaddddbcbddacdaaaaccbcddbbcdddcbccdcadcbbccdabbbdbaccddddcaaaddbaacbaaaccaaadbcadddbdcdcccdccdbbabbccdabddaacabbdabacadccdabddaaaaabccaadccccbcdaccbbadbbdbbccdbadccadaacbdcdacbcbcbadaddabbcbdacaabaabcbdabbddddcbcaacddbdabbcadcbcdccdccaaccacccbdddbbaccdcbbaabbdabdcbacdcaccaccbcdbcddbbacdbacdabaabdbcbadddbbdcdddbcacddddacadbbadacdccccbcacdbccabcdcdccccbbaadbbdcadcdacaaddddaabddacabbcacaaddcadbbabccacacabdcdccbccaadcccabdaaddcdbdaadacaddddccbadbbbadabddcdacacabdbcbbcabdbacacaababaaaccdaddbcaaaabababaddaacaaabcbaadbadcbdaccbcbaccacabcaaacdcacacdcdcdabdccbcbdcaacbdcdaadcdccbacddcdbbaccdddbdddcdabdabcbcbdcdacaabcabadacadbcbbabccbdcbcbacdbccddabdacaabbabdcadcaacbdcdcccddabbdcbacabcdbdaadabcccdddadbcbbddabacbddacdabaacaaacccbadbaaadbbaabbddddbbadcbdcdbbbcddccadcaacddaaadacadcdadbaacbdcdaaccacdcdcbdbabadbdddbcbabcbcdcdcadbabbbbbaddcccdbdaddbaababcaabddbbdccadcdcdabbddbdcacbddaabdadabccaaadadacbdcacbbcccbcacdaabddcccbdcbabdcbacdacaccbcbdddccbbadacbddbdcddaabacdaccacdacbcabdbbbdaadccccabccabcdddddadcbddbcccbaacabbabaadababacbabcbabcbabdbddbddbccdaabcabddbdaacdccccbdcbbbcbdbbdabccaacccdddadbccbcacdbcacabddddbdbbdbcbcadcdccadbcdadcbddccdbacdacccdbacbdbadacbdadbacdcabbcbcccbccadadabbccabdaadaccbadadcbbdbdbbaddabdacacdaacdbccbabbdaacbddbabddbabcdbcccadbbaadbabdabacccbcabadaacdbcdadadccabcadcaacacdbcdaadddbccdbbaacbaacbbcababbadcaadcdadbcdccaaaaacbaaccaabdbddbdddcaaadacacbcbcdadacbdcccabcaadacbcbbadaabcbcbcaccddbddccaaaadcbadbaaabdbcababaddbbcbdabdcddbcaaadaddaabdbbdbcaddbaaacddadaccbbacdbdacdabdabbbcdbadbacbdcccacddbcdbcacabccadbacbbddbdbbdabdbcadabddbaacbdcdbdccdcddccdcdcdcdacaaddacbcbcaccaacbacabbbccdbdcddcdddbbacdccbaaaacabbcbaaaadadbabaccbacaadababdadbbdabadababdddbbaabddbddaabddacadaadbabbbbcaacbacbaacdccabcaabddacacbdadcbbbddbaaccdcdbdcbabbdddbdadbaaadcabadcabbbccbccabadacbadaaabdadcaabbbbbacccdddcdbdccdddddbdacaccccaddbacacacbabccbabaaccabcbcddcccacdcdaadbdcbdababbaadbdbdccbbcacadccabbaaacdccdbcdccaacabdbbabaabccdccdbbcddbaadadadbdcbcadbcdacacadbbabadcbacbbcaadcbccdcbbcbacabacdbdddbaccdcabbabdcaacdcbccaabcdbaabacdbacabadbbbbdaababddcadccdcdaacbdbdcdbcdbbbaccdccabadaaacacdbbbcbaacaccabbdccddabbababdacabdacdcdcccbabaadccaadabbccdbacccdcdaaababaadcbcbbdacdcdbcdbdbabccbbcdcbdcbdbddaaddbacddacdbdbaaaaccadabcaaccabcaccdadcbdadcbcdadcccabddccacddcccadcbacbaaacacabdabcdcadadbcadbacbbaaccbaabbbdcddaaddacdbbbdabcacdbcacacbbcaccdacbddbbdaababadaadbbaddabcaadaddcacbbdcdcdbdbacdcaacbbbbbccbbaabdcdcbbccddbcbcdacdacdabcbabadcbdbaadddabbcbcadbaaddabdcdddcbbcbccbbdbdbcdacddbdacccccbdccaccabaadabdccadcdabdcdcadadcadcbaaadcdbacaabacadabcbdbadbacabcccdaadcccbacccdbacbcbaadccbbabaaaacadadacbccdabddcdbdacdacdabcbcbbcdcccccbacadacaaadccbcbabcdccabcadadcdbabaacdcbadccbacccdbbdcccdbcdbcacaccadcacddcdadacadaacaaccbcacabacdcaacdbcacacddaabbcdcacadcbdcdddaddadcdccabccdccaccccbabbccacadbcdcdcabdcbbabddbdbcbaccabcacaadadadccdbadacbccccbbcccdbcdabbbcbcbacaccbddcccacdddcdbdacdcbcbdcacdcdbadbacbcccaacdaccdcdcabbadddcccacabbbcbaaabdcdbcbbdaacadcdddacbaccbaacccbbddbaaccaaaabcddbcadbbbcdaacadaaddbcccadabaaccaabbaabbaabacccdbcaccbaacaabbbcdbbbacbabcdcbdbbcdcdabdbbcbcabbaaccacabcaaacbdbcbaabdbacacadcacaacdcabbdacaddadbddacacabdadaabccccccdcdbaadaaabddabcddaaabacbdbadbabbccbabdabbdcbbdbcbcaadcaccbcccacdcdadcbcacaddcdcadadcdcddcaabdbdbacdacdbbdcacbaabdaacadaacadcdddbbcbdccddbbbabccccdcbddadababdbadabbbdabbcddbcccbcabcddbaacdcaddcdbaccabcbcbdcdbcdbadccbabadbdbaaaaddbacaadddaccaacadcddaaaaacddcbbbadaaababdbdddadcbaacddbabbcccabcccabbdbbdcaccbacabcabaabdbdabdbdaadadbddacacdcddcbbddadddbbccddbdccccaddabccccddcbdadcccccacdbaccaddcddacaaaacbacdcabbddddddcabdcbddbcbabdaabaccccddbdcbbddddcccadcddabbbcdbabcbbcbabcdcaadccdcdadacacdcbdcbaccadcdcbadaacdcdadccbacabccaaddcabdcdddaddaabcdaaabbaddababcaaadbdabcbadcbcdddadcdbacbbdcadcddddddcdbacadccadaddaabddaccdbcdaddbaacacadadcacbbdcababcaaacccadaabbcdbddabbbcdadccbadcadbbbbddcbddbdbbbcadbbccacbdaabacdbadddacbadbdcbdbdcccbabbbdcccbccadddcdabadbabaddbdadcbccacddbadccaabacabaababcacdddbdacbdcaaaaddabdbcdacdccbbaddbccdcadbcadcdadddaaadaaabcdccdacdacadbcdcccbabababdcdaaddcbbbaabcabbddcaadcacbabdbbbccbbbacbbdddbddbbbdcdcbbabbdcddacaddabaacbbabcbcdbbdcdbadabcbaddacacbadbaaccbabcadbdbcaaacbbaddcbabccdacccbdaadcbcccdddbdcbdadddbadbcdddacdadaccbbaccdbddbcacbbbaccbadcbbcdcdcabcbdcbdaaaadadcacccdadbaddbdaacdbcbcbacaabbcdcabaddaaaadbcabcddddcdbcbaabcbaddddaadddbbccacccbbbdbabcbdabdbcadbbccabddcbacbbccddabccaabdabcabaaddddbbbadbbdcdacadddcdacdabbcbdacccaacabaabdcbcabccaaaadabcdbdbbacbcdacdcddaccdbcabadaddadcbcbddbddcadcaaddaccabccacbcdccbbdbcdaacacaaaccbcbbbbbabbcacdacacacbaddbbcadabddcbccdbabcdcccbaaddbaacaaaaadbadbcbacbbaccdadbcacaddcddcdaacddcaddccbcbcdcdcabddabcbadbcbadadcdcdcbaadabcaccbcbaaabcbdbacacdcdbdaaabdabaacdaadbbacaadbcbcaaccacdcdddbbcdcbbaaadcddabbccacdbdbbbdddbdbcaddacadbbdbbcccadbbbabdcbcbdccdddddcaabacababccaaabcdadbbadaabdddbdbcdddbdcddcbbbabddabbbaacbabacaaccacbbdabbddbdabcabbdcacaddacdbddbddbdabaaacdcdabcbbbcddadaaabadbbcbcacbbcaccccaaaadbadbdaaddccccadaabbbaccbaddddcbcabcdddbcabddbabcccdcccabddabdccddaddcdabbbabcacddbddcaadacacdabcbddccbaaddccbaaadcaaccddbabcccaddbbcccdccadadbbdccacaddcacbdccccaadddbbadbbcddababccbcbacaacaabddddbadddcabdaacbcbdcbdaaddbbdcccabddccacabddbbdcaadaaabaadadccddabadddcbbddaccaddcabaccccdabadabbcddcddcacdacaddbdbcbadadadbcabdadcddabdddabccddcdcdaaacabdbabcccccbcbadaaadcdbbdacbdbcdbabcbabccdcbdcacbbaccddbaacadabacaadcddadbdacabcdbdacbabbaddaadbdbabcccdabcbbbcbcaddccdddbdbbbadbcdccbaacdddbdbaacbdcaaacaabbbbbaacbddbcbcbbdbccadcaababdccdbcbadbaaacbbaabadabdbcadcdddbcbbbddbdbcbaadcaccbcdbcbabdbcbacbbaccadcdaccadcccbaadbdbddcacbacbddbdbbdcbcbdddababccaaaddcdbddacadcbdccacdadcbabcbbcdcdbbabdaabaaaaddaacbbbcdcbdbacbddbaddcbacaabbddababbacddccbdcdbabdaaabdaaaaddcdbbddababbbdacadaabdddcbbaaddabbbadcccdddadbcaddbcddddcccbdaccacdbabaadadcbbdbdbcabadccadaccabbabddadabcdcbcabaccddadabcbbdcddcdbdccddbadbababcaacdcbacaadbdcbacbdaabdadcbdaccdcbbddadbdcabdccddabddbdddbdcbaddbcbddccccacdbcbbddacaccbcbadbabdccdbadaccdddaaabbdcdcbcacddcbdbcaccdbbabbcbabcbdddbbabdbacaaaaacdadacabbdbbacacaadacaacdddacbdddcddabbacacabcdcacdddcdcdbdacadacdcddadddddbbbbddaacdbbaddaabcacdcadabacddacaccabccbbcdddbbccdadcbbdbacccdaabdbcbbbcdcdaacbbdadccaaaabadccdabddcabcdbcaadbdadbbdaacdbaccacacbcbbccdbdcdbbaddaaadadcbcdbaccbadcbadaccbcbacddaadbacdbddacdbabdabbadbdbaaaccadcdaaccbdcdaddacdcbaaadbbcbbadbdccadbcabbbbbaddbbcdabacbbbdbdbbdbcacccaaccdabbdbcbdcdbbdcadcadcbdcbbdbbbbaacadaddbaabbddddbaadbaddaabbacadcdbcdccacbbcdddbccbdbaabbcdbbdabadcdccbabcbbbacbccaccccdbacacbbddabaabadddbcddddddbbddbcdaccaadabccbdcabdcdcaabbdbccabdbbddcdcbcdbadcabababaadbbbcdccbddbaacdbcabbcabcccdbacaaacaaddaddbbdcbdbbdaacacdbacbcacadbadcaabbbacddddabcccbcdbccabaacbbbcaccddbabccdaaabddaabadabaddabdbccccacdbcdbacbbdbaaadcbacdabdccdadbbcbdcddcdaccddcbccaacacaaadbcdcacbcccdbbddabacababdbcdabbccbacbccdcabbbbdbbabcdcbdccacccdaadbcdacaaacaddcaabdbbcbdbbaddacbaaaaadbbcdbdabaccadddadacdbddddaacdbdcbacbdaaaaadadabcbabadddbdbabdbbbddcaabdbbdabdcbddccaddaaddcbbaabcacdcabaabbabbbccbcbadcbadcccbadcddcbcacabbcbbcbabadcbacabbcbbbdddabbcdcabbabaabdaabaccbadccbabacbdcccdbcdacacdbacdccccdbdbbaddcdccccacaadaccadadbdcddcbbadbaaaabbabbdcdadadaddbacbcdbbdbddcbbcbccaddcaaadbabacbbaccbdccccdcccdbbadbdbdcaaccbbacdaadaacbbcacdabbbdccdbacacddccacacddddcadbccdcacddccdcbbdddcadacccacaccbbbbcdbcbbbdabbddcabdadcdddcdbbdcadaabacbcddcdcdcacaddbcabababacdccdbcbdaadcabbbddaababdacbcbbaacdbacaddccdabcbdbbcbaadccbdaaaaabbdcdcdaddabcaadcadcdaaadadbdbddcbdcbcdcdabcdddabdbacabdadddbdacadbdbcdabaddabaadccccbcbcdcbacabbdbdbaadddccbdcbdabccadacbddcabdadcdcdddabdaddbcbdddbadbadacbdbbbcaabbdddbdbaacddcdcabcdbcddbdccbbcccbccccbdddccccdbbcacabcaddaabddccabcacbabaaccbcddddcbbbabacbcdabcbcadccdccdadddcdcdcbcbadabddbadccddadbadcaabcaadadddbdacccccaabdcdaccacbcdcbcaadcadbbddcaacbcdabadccdabaccabddabcdacdbccaaacdddddbcaaaccbcacdcbabbadaddcdbdcddadcdcccbdcabadbadbcddbaccabbbbbacbbcbabbcacdcddadbaccaaabdadbbbaccdbbbaccddabdaccbccddacadbcbacccdababdacccaadbbcbdcddbdacadadabdbbbdbbbadddbbaddbbacbbbcaabccbbddabbdccaaddaadcdccbdababcdcbdccadacbdadcbcadacaacdcccdaabbdabbcaacadcabdadbdaacbdcdbcdcbacbcabbaacdabaddccdacdcadadccdcabbbdcbbcadcdcbdadcdaddabdbaadcacddcdaaacddacdcbddcaabdbcbccbcdcddabcccdaddcbbcddcdbbdbddcacbdcccddaacacabdbaaaadcbaaadabdbcaaaaadabbdccbddaddcabcbcadccadccdbaaabdcdbbcacdadbaacaddbbcbdabcdabaaccccbadbccacacaddbaadbaaacbdcadddcdadcbdbbbddabbdbcdabdbabacadbbadacdccadbcaacdaabcccbbbababdccbabbdddaacddcbaabdbcacdabbcabcdabdccccabcbcadcdabcacdbddaacacddccadcaabdcaaaabacdccdddabcbbbdddadbacacabcbaccddabbacbaabbbbcccddadabcbacdbddbddccbcdabbadabdbabcbcbabbbabcadaacccdcbbaadcdcabddbadcbbabadacbbbdbcbabddbabdcdbbaabaaccddbdbacdbdacbbbababcbabbbcadbcaddacacddadabbabddcdcaaaacdddbbcdbcbddbaacddccdcdabddcbbcdadaabcdbdabcbacddaabccdabccdcadcbddbdcacacbddcccbbcbadbcaccdcbbabbcbccacabcdbcccccdcdbbcdabcbdddcbbdbadcaaddcdcbcdcbcddacaadcccbcdddddacbacbdcccbbbdadccccddabddbcadabbbdaadadbcbacdccddadbdacaaaacccbccbdbaabccddbacdcbadbbcacdaabddcddbabbdccbacbadcabbdcbdbbddbdabcdadbdccaaabccadcdacaadbbbcdabaaaddaabccdcddbbcabaccbbaacbcbbaacbadadcaaacbabddcaabacadcccbabdbaabdbcaaabbadcacaaacaaaaabbbaaabbaaddbdbddccaaaadabbcdabacbbbadcbbcccadcdbbdbabcbdbbcadcbacaccacccbddacacdbdbadccdabbcbbdcbaabadbdbcdcaadbbbbdbdaabacacdadbaddabddcdcbababadbbbdcdaabddadabcbddadadacbbcacaccbdabbbbddcabcbbbddbccddbdacbadbadcddaaadadbbbbbbdddaaadcbcccbdccdadbdbddbabddcacacdabdabacbccacbcbcccdaabddbacadabdcadbbaccbadadddbbaabaaaabdcdcabcdcaaabdababacacbbdaddcbddccdddbadcdcadadaaccacaccccbbbabcadabacccbaccdbbcdcbadcaccdbcbddcbdbdccbbddacdadabaddaacaacababcdbccbddaabdcdcaadaddaadadcaccacaaababbbcdaabbacaadabcdcaacdbdbcddaddbaddbbaddacbcbcddcbcdcddaaddaadbcbcbdacdbcacbacabbdcdabcdbcadbccadbdcadcbadccabcadcaaadcddcddbbddaddbbaaaaabdcbabdbcbabdbbdddddcccbbcccbbdcadccabdbacdddcadcbacadddaddacadacaaaddadccbcaaacbbadabdcaadbcbddadccbacccacdccccdbbbbcacddccddabaabcccaaaabacacadadbbbacbaddddcdbaaadcabcbdcbabdaccadadddaddddaddbbaacacccccbbabdcacdddcbbcaccbcbccabacbdcaccabcbbadbcdbabccccabbaadaccddbdddddcacdddaaaddabaccacadbbccddaabddbacdddabddbbdcaccdcabbddccdcbddbdbdddbcbdbdadccbcddddaabdddcdababbdcddccbbdddcacdcbbcacacaacbaaacdabcaabbadcccdcbdaccaddcadcabbcacbbdbbbdbdaaabbaacadaaaaacbbddccccadddbcbbcdbacbdaaababbdacabbabdbbbcadbccbcaaadbbdabcbdacbbdacdacabccdbababdccdcaacbaabcaaddbdccababcbcbccdcadcaaccbdcdaadcdbcadbbcbdaccbbcdbabcdadbcaddacaaaadadcbacaabcbbacdacabcdabacdbbbccddcacddaabaaacdbdadcbdcadacbbccbadcdbbdcbccdbccabbbadabcbbaddabaaaabbdcdcababdbbdbbbdcdbbccaddcbddcadbbcdcdaadcbbcbddbbcadcbbccbbbbbdabcaabcaadbdddbbdadbabbbbcddcabbcdacaadaabadadabcdbbacadbaabbcdacbbaddcdaabccbadacdcdabbbaadaabdbcddbcbbcdcdbdddbbbdcccbdadbbbdcbcccddaacbaccdcbcadddcaccaadddbaccaaadababbbcdddcccaddabbcdbbabbadadddcaddabcabcacabbcbcacaddbbcbddcbacaacbabbdadcdddddddabbbcdbaaabdccacbcbdadaadccacadcbccddcdccbadbbcbadbcbbbabbaddcaadcdcddadbdccacaddacdbaaaabadbcccdaabdbadccbadbacdaddccdcbcdbadbdbdcbaccbdbaccbcdccbabdbbddcdabdddaaacdcdbbbbbbabcbabaddbdddddbbbbdaccaddbdcbcbdadcccdddaadbdbcadddccddddababbdbcbdadcddcacaccdcdbdbadbacdbddbcacacbbabaaccdbcaaadccdbccbbdcadcdcdadcbcddcaacabdcacadadcacdacddbbddbdabbccbbcdbcbacddbddadbcddcddddcabacbddcbddbccdbbadcbcccdbddddaadbbdcdbdadabccdccbccacccddccbababcdbdadaadbacdbdabaadcabdccbabcdaccbccdbdcbccdcccabaabaadaccbdcdcbbbdbadddaaccdacbaaaaabaabdaacdcbadaabaccadcacbcdbaaadbdbdbdaacdaddbcdcdddcacaaacabdadbcddabbccababacdddbbbaaacbdcdababbddddbcacabccbdbacacddbdbbcbababdacbddbacbbbbabbcbabbcbbacbacbbbccdabcbdabcdbbcacaadbabbaccccccbcbabbdcbcbddacbddbabcccdbdaacabaaadcbbcbabccbaddcaccacdadabbdbbacdbdacdadadaabcdcdcacacdbddacbcacadaccaabdbaaacaadaacbbdbaaabdbccdccbacccddacddabcbadcaadbddadbbdbbadbbacbbabacbdccadbcdddcdaadcbcdacdabbabcaacaadbdaacdcbdabcccdcdbcaaccbaacacbdccccdcbddbcbdabbdadaccccbdbbcbdddcbdacdaabcaadbabccccadacdabbdbcdcbbbbabcbacbbabdadabdadaccbcacbdbcdcababbbbdbcdacacbbcabaacacbacbcbacacbaabcbccbccbcbbbaddbabdcdabdbccddddcaaabbaacddbbdcbccbcaadaaabcbdcaccbdbdcddbbdddcddcaddcddccdbdbdbddcdabdcdbaaacbcadcccadcdddcddacdaccaadaccdaadabbdcbcbdbbddbcaddbbcddcabadccbcaaacbccbbcaccdddaddbabadcbdbdacabddbbcdcdddccdbcdcdcaaabdcaaabddaaaaacdcccbaddcbacbacbdddadddddcadbddccdcdddccacabbaabaadaddcdcdddbbbbabaaaddadcabcbcbcbbbccacadbbcdcbadbddabbbdddcccadcbababccabcbccdbbcabbaabaaaaadbdbbdcdbcddabddcdaccacbacabaaaadcabddadcacccabcabbaaaadabcbdadacdbbadbababacbbcabbddcdcdaacabdaacbacdddddccccdadccdcdaaddddaccbadbdbbcbdddadbdaccdccadccdcabbddbbbdccdddccbcbcadbaababbcdcbdcdabbccbbabaabbaadbaacadbbbbddbcccdbcbdcbadbbcdbdbbadabaabbdcdbaabbccaabadcacccddacbbcdbadbcdcddbcabddaaddbdcbcdaabcacbcbdbddcaacdbcdaaccdcccccccdaabbbbdadaacccbcaccbbddbbbdddcaccadbcaabdccdbbaddabdccaddcbaaabbabbbcdacdcadcbbddabaadbdbdabcaabdadabcbcddcaacabcabbdccabdbbdabbadaacddaacdbdccaaccbdddbccaaacdddcbdbcaacccadcabacddcdacbbcccaacbacccbcbbccbbbbccbbdabdacbadbcaccacbcddcbddaddbdbdbabcbbdabdbcbaaccabdadabcabdcabbddabaddacadaaaacadbaabcacbcaccdbbdacdaadbaabcbbbacaabdabcaadccdbccaddacbadbbadbadbcddcdcccbcdbbbaacbbcdcadbccdaadcdccbbadcaaabcadbcbaccaddbdcbbacdaabcadddcccdbdbddbdccdcdbdbccccdacdacadbdcacbcbbdbbddabbaaddbabdadcbcacbbdddadcddbbadcdccaaadaadacabdcaccdacabbaabbbacbaadacdccadaccdbcbacccbcaadcdabccdcacbbadbcaddacccccaacbccadddcdbddbcadabdbdbabdcbbaddcbdabadbddcacddbbcdbababddaaacbddbdaaabddaddcccbdcbcdddbdacbdababdccbccccadadabcbdcbcabccbadbdbbcbddbbacbdbcadcaccbbbdccccddbbddadbbbccdbbabbcdabcadcdbbbddcaadcabbababbcdbccbddabbadcddcbcbbdbcdbdcacbcdbaccdaadcbdcbdcdcbcbadcabccacbcdaacccaaaacdbdabcacabddbabdbdbcbcccccbbdbdabababbdddbaabcdbcdbccadbacabcdadaabdbbaaaacddacdcabcbabacccccbadacabdaccdbcbbcbbdacdabbbacacddbbcdcbbddcabcabdbcabcbaacababdcabbaaaddbddabadcdbcabdccbddcaadbdabcccadadbadbdddabbddcddddbcacabadabcaccdddababaadbbcaadcbdcadddabdabaddcbabaaadbdcbabbcccccbcddaacdbbdbbdaaabaddbdcaadddcbdcacbcbdcbbdaabbcdbacccbdabcadcdcbbdaadbbadbdabaaadbbccacbabcbabaddbccbbabccdbdcabbbacaabdbccacccbcdaabaadabadbdcbcadbdadadcadabdbbbbbbcadbdbdbcadcaccbccaddcaabbccdabdadddccddcbbbdcccdccaacaddddccbbddcdbdbdaacbddbabcddcadbccdcbccdbcabcbabccaabddaacdcdcbcdadbdcbbcadaaddcdcadabcacdbdbbdbbcbccdaadcadccccaacacbbbdcadbbddababcbdadbbcbcdddcbdaaccddccababbaadddbacbacdcddbcdcdbbbcaaabaacbaaadbaaadbcaccdcadcdcdabddaaabaacdbdcaccbddcaacbdaaabaddcaaadcdddbdcbabadadbbcbcbdbbabadaabdbdbbccdddbabccdcaccacadacdadbbcdcbcaaadacdaccabcddcdbcadbadbbbadaadddaddabcbdabcdcdcabdcdcadcbbccddaadcccdadabdcbdababbdccdbadbddadccabdccabbaadabcbacdbbbdccdbdcbbaacacaccbaabacacadacddbdcbbbdccbdabdbadcaccdddcbabbbcdabcdbccbbbcbdcdbccdcbdacccbaccabbcccbacdaddaaabbddcdcbdcadabcababbbbddddaddbdcabdbcdbdbcabababddcbcdcaabdccddadadacddadcabddddcdabcdbcdaadbbdcaadbbbccbcaaabccbcddcaaccdcbbbbdcabdbbbdbacdddddbcabaccaacccdaccdcdcdbcaadaaccaaababcadcddddbdcbaadcdcccdbaaabcdacdbbdcdbdbcdcbbbddbddcbdadcabacabcaddcdaccbccadacbabadacacdbdcadbdbcabccbbccdabcaccadbdcaabddaadadaacdbdbdbddabbdadcdbdbbccbbbdababdbaddabbaddccacdcbabbdcccdaabcccbbcbcbbcdcadcadadcdcadaaccdbbbadbbdacacaacddadadcdbddddcacbcaadbbcdaaadbdcddcdacdbbccabcbcabbdbbddabbaaabacbdacabccbcacabdbaabadacdbaabdccdcccccbcabaaccbdaccacbddcbcaddccaccdddddabddccccaacbaccdadbbbdcdccdcbccabcdccbdcbaacadbdacdccdbaabcaaabacccabbdaaadcbdcbbdaacbcdbcbcabdbaacddbaacbccdbbcbaabcbbbbacdbbadbbbaaaccdabcacbdabbabbcccdcddacdbaadbbccbacbbddabccadbcacabdaacacccdcdcaaaccbbaaccabbbbaccbbdacbadbaccaabdabaaacbdcbdddbabbbcaabdacdcbbdcabababcdcbadadcadadadaacdccbbdacacbdbcbdcddabbdcadabcabbdadcbbadbacadbdacbbaccadcbdaabcbccdcbbccbdcdbbdabdcaccddcabdbbddbcabddcccddaaabbaadcababbbbaaabdddbdbcdabddddadcdcdbdcacbadccdbdbbbaadbcaccacbabadcdaacbdaabdbcacbbcdadccabcaabcbabcacaccccbaabaadccdbbdccaccdbdcccadbababadabcdcdbcaccbaddbcddddadaacadbcbbbdddcdadacbabdbdabdcbabbacacabcdadbabdbaccbdbcdcddaabbcbacdbbcddabcddddabdbacbbcddacacbcacadbbcadbacabcaccdadaababddabdbbacccccabcdbccdbbacdcabbadadcbadbdacbbadcbcdbcdcccdccdabbbcbdaadbbbabcbdbddacacadadccbdbbadddbcbcbdbbbdcbbadccdacadbacddbddbccbbaabbcaacbcbbaccdacddadbcabadabadacaadbbdadbccdcdccbabacbaddabdccbaadcaabcdcaddadaadcbdadbdbcbadbcaccadaddcbcdbadbccaabddcaabcbcadbabbdddddccacaaccaabcdcccdaacdbddcddcdcaadbddcacacbabbbdcadbbbacaccadccacccdccbacbaacbdbbadcdcbcabaaddbdbddbcddbabcabaaaaadccacdaadbcbaaaabcccbcacacdadddacadccbcccbddcbdccdccbccdcdaadddcccddabcddcadcdaacbcddabdcddddabbcbcbabdcddadbdcbbababbbdddcddbbbdbadcccaaddbcccbabcbabdaaaacaccaacbacbcddccbaababdbabdddbdcbaddcbaaddacdcaddbdcbdbaadcabcbbcdabbcbabcbbadcdcdbaaacdcaddcbabdacdacbabddcbbbaabbdbdbcbaddaaccbdbdaabdabbadacbacbadacbcbaadcdbbcdacabdaaccaadaccaccddbabbcccdbbbcdcacadaacbbadaccaabdaacacbaccaabbbacccbcabacacbdcaddaccaadaaaadadabaacdaccdcbdacdbbdccadcdbcbcaacdcabdbacdabadccbddbaacdcbcbbcddaaddacadddbaddcbaaadbabadcbbccaccccabbdabdcbaaabbdbcbabdcabcbacdcaaadbdddbacbddddccbabcdbcdbdcbaddbcacabbbbcdadbadadcbaaacbbbdbacbadcbcccddacadddcabcadbaccbcdabcacadacddddacbdccccdbdacabaccdabbabdcaabbabdabbbcaaabaddbbbdbcabddacbabbcdcbbadabbabbaabbbcdcbdbcacbccdaadcccacccbcddcacaabdbcdaaaababdadbbaddcdabcccabcbbbddddbdccdaacbbdcccddadcdddcdabdabbacdcdddddbbcbabbdddcdacbaddbadabadcbcdbcaddbdacaabddbbbaaacaccbacccdbcdcdcbcaaccbdcbaaacdaabccabbbabbbbaaabbdccddaaddacddccdaddbdbbccdacdbbdadcadcabdbcacdcbddccaccbabacbdcdbadcdbadabcdbcbdacaadacdcdadccddcbcddbbaacbbcdcaabdaddadaaaabbbdbadbccacbacdaaccbdbadbaddabadbccdabbbbcddccadcbdddcacdcabcaacaacddcbcbbaaacbadabdbcabdddbcbdccdacbaccadaabadaabddccabcccadbcdcdccdaababcaddddabbbbcccacddbbaabbbacddddbbcbaaadabbdbbbdcbbbbaaccaadbcacadbcabacadbaabdadcbdaacadaabbdadbbccdaabdccdddbddcddaaadddacdaddcababbacdbdbbdcacbbddadadbbbddddbccaadacbcccaabbcbcaabbaabccbdabcdbaadbbabaacbcbabaadcabbdcdccaabdcdbaabdbdcccccaddddcaccbbbbcaccbdbadbbbbcdacdbcbbcbacdacaadbacadccccdddcdcacdbabdcabdabbcdcadbccabbabcdaccdbdcdbabadacddaabbacadddabaabddcbcacaabcbdaccadbcadbcdaccaaaccccdccdcadcaacdadacbccadcbabcbbbaaddbdcdbacbadddddccadccadbcbbdbcbbdabcbabbadacdcaabadbbcdbcbbbacbcdbddddaadabaccdadcacbaddbbcacacddccbadbcaddddaabaccccaadacbbaccccabdbdccabacddacdaacbbddccdbbdaadabcadccddcddbbcaccbaabbdcccaadcdaacbdbbbcadcbbbddddcddbbcbbbbcbdbdbaddddadbabdbbdcdcddabddcbcbdadcdabcabbbcabbdbdbaacbccabdbddbcdcbcbbbddbabbabdbcbcacabadacaabcbdacbddbcbbdbcbdcddabddaadbbcccabdcabcdbaabadcdacccadcacbcaabdaccacbcdbcddccbbdcbdcdbaddddaabacbcadacdbbcdbdcdbdddcacccbadcccbaaaacdddaadbdbbcccccabdcbbbbbdbbccddabcaacaaccdbbcabdaaccaccbabbadddbcbaadcdccbbdabcdbccbcbabadcbacadddbbbbdcdabdddacadabcdbacbcddcbbadadadcdbadaccdcdbbcbcaaccdbcbacddbdbdaddabbcddaddabddbadaabbbbababcacdbddbaccddbdcacaaabcacbdcbdbcbaddbadcacaabdccbcbcbcddcaaaddabcdcacacbbaaaccaabbadcdbdacadcbbddaccadbbccdcdbdadaaabcdadcccbdcadccdcbcaabcdbccbbbcdbbbacdbbcbacddddabdadddbadccbdabcbbadcdaacaadaadddcddddbbbbdcbacdbbabdbbbabcabbbaddcaabacdaadddabbdacccaccaddaddabcdbdaaadbabddccbbcdaaddbccbdbdbbdaabdcdbbaacdbaabcdbbdbbbadcaccbcdcbcccacaddaaacbddcacaaaaccbdbdabddabaadacbacadcadbcbdbbccadadcdabddcbcdcbabbaccacbbbaadbadabdcdcccdbacbabcbabdbcdcccabdbddaacbddcdddadadcdabdcaabdbabbdbadcddccbacdacacbcdcaabcbbdcbabbbabbdbcdacdadcaadcccabbdbadacbdcabaddbbddaabbcaadbcddabbcdaadabcddccbbdbbddaddbaddbadaabdcbaccbacdcaadcbcacbdcadaaabbadcdcbdbdadcddbbaccaaddadbbbabbdbbdbbabddaccdacdaabdbadcdaaabbdcbccabbabbcacbbcacaadacddbadadbabadccbbdacabdabddddadcddcbbaadadcccdbccbdabbbadbdabbbabcbcdaaaacdcbbbaabbdcdababbbdbaacadcacdddacbcacadbadadbccdbddbabcdcbbbbadbbcdaabcabbabbbcabbdbabacdaccabdccdcaacdcaaaccccbbcbcdaaababbccdaddbaaaaccdadbbdbdbbaaabbabbdbccccaccddcdbcdabacaacddadcdbddcadcbcddacabbdbacddcbdaababcddabdacdaadcbcdcdaddacacbdabcdbaaaaadcbcbaaacbcdcbadbbcdcaccbcacdbdcaccbaacdddbdccdcadddddadbddacdbdaddbdbadbaccddbddabbbcdaaabbacadaccbddacbcbaadcbcbdbcacaddddddcbaacadbdcbaacccbcdadcadaaccbcccaccbadbddddbaabcbacdcbadadddaacabdbdbcbdadddabacdbaaabddaabbbbdcabdcbacaddbddabbcdbdabcbcbacaccddbbbcaaabdacababdbbddbadaacabdabdcddccdbadcaaadbbbadcacbcbbadbdccdcadbbccbcbaacbdbcbdaddddbdcbaaaabdadabcbcdadbdcaccbdabbbddbbdaaaadcbdcbdbaaaabcdccbadcbaacbcbbdadcbdacaaaabbcbabcabadddaaadccbbcdbbdaaaaccbaccccbaadcaabcaaaadcdabddadbaacadcaabbabdadcddcdcbcbbbbbadccadbadbabaaaddbadaadbcdabbbdaabaacabbdbbbaacadaaaaacadcbdbccadcbdcbaaaddaacabbcacacdbacaacabcadcdbacadacbdacbdcdcadccdbbaddbccbaaccbdbcbbabdcbcdccbbbddabadbaadbbdbacacacccbdccabdbcbdabcbbdccadcdadaddbadcaacdcddaacbacdcbddcbbbbaacaccabccaabcdbaaabacabddacbbaadcadcbacbdcacbddcabcbbdddacbcadbdadcadbbcbcaaaabbdaabcadbbabbadbbcbcdacdaccadcbdabcbcdbdacbdccabaacabbbdbabdcadccaaddaccdaaddcbdadbcbdaccacbccadcbcaaddccabbbacaccccbccdddabbdacbcbabbcdbcaaabbdaaacbdbbcdaddbbabdaadbacbddabaacdbacccddbacbddabccddaddbabaadbabbbcbddbcbcbcdbdaadcddabdbcdbadddddaacadacdccbcdbbdbdbdbdcacccbdacdcacccdcdaabbdddaaabdcdcbcdacabddacacacccdbdbddcbcbabbbbdddbacdccccdbaddccbaaabbcbdadaabbbdaccaccbababcbcabbddcacbbdcbaccddcbcacaacbabdcbacacdbaacaccadbabddbcccbadcabbababdbadbadaccddbabbdbbddbcdaccccdbcbcbcaadabdaabcdcbbaadbdbddcbadacbddbadabbdadabddccddabbdaacaccbacbcadbacbdaacddcccbdccdabbbbbbcdbbcadaabdbbcadababddcabddbccbaddabdcbbaacbacabacacabdcccdcbbcabdaaddbcbbdcbddaccaadccabcbababadbabddddaabcaaaaddccdcaaabccbdcbdbabaaabacacdbdbbcdddaacacdbdbbbadabbaacccdcabaaaddcbcacdaaacabacbbdbcacbbdccddabacbdcbcccbbdabbcbcccbacacddbcccbabcabddbbadccddbadacabdcacccaccddccdbdddcdabbcaaaaacdbcacdbcbacdabcbdbadadaabdcabccddddacdccacabdbbdabbbdbcaccbbdcddcadcbbcccacdbacbbddccbddcbcaadcbadbbcdcacadcabbdbddabacddabbacabcdcdbaabcccbcabddbadacaaaacdadcabdadcdccbdbdacddbaaabbaccdccccdcaaabdaadbbaaaacccacccadbddbcdbcddcbabdcabbbbdacccaacaccdabcaacdbaabacdbdcdadbdcbccddbabddbcdcbdcbabbdcabbbccbdcbbbcadbbbcadcaabacbbccacaacbcaaabadbcccbcdbbccdbbdcbbbcdaaddbaccbdbbdbbbabdadcbacacaddbaddacbbdadcbabcbacccbbaddddbdababdbbdcabbaacdbbbbdbccbbabababbcacabaacdcaaadccaaabdddbbcdbcaddaacabbbaacddacdbcacccaabdcdccbabdccbdccdbadaddbadabaccccababbaabcddcbcacccdbdcaccdbbbbbaacacdbdddcabdccbcdcabbaddcbcbbcaabdbbaadbcaaadacaccdbdbdacadaadabbccddaaddacdcadcbcaaccddaddcdabadaacbdccabbdbdabbbcabddadaaddbbccaabcdbcddbbdcbbabdbcadcaaddcdbddadcdcadacccbccbdccaacadbabcdcbdbbadcccaccaabdacacaddacdcddabdcbaaacacababbddaaadbadddbabcadbadbabcddbccbddbcababaccabdcddddadbddcccddccacdcbdaacbccadccbcaaaaaccbbbadbdbccddbabbbdbaadcdababaccabadabdaaadcadbccbcccccabccabdaaaaaccdcccccddcdbcabaaabdadccbcdaacdadaacdcdbcabbdaddbdbabacabddadadbbbbbccbcdababbdcbaadabccbbbdaacacddcabbcbacacbcaaccdadaabdddccabacdcccabdacbdaabcaadaaacabbdcdbdadacaaaacbccaadcbbcbcdccaacdaccccddddbbacabcabcdbbaadccbdadddbdabccaddbabaccaaddcccdcbcaabaaddadccdcbbacbddbaccbbbcadabdccdbcdcacbabcdddddbbcabcdcacddccbcdcdddadcabdababcbddbadddacdbdadbddbaccbadcbbccdddccdacabaaabccbadbadddadbbcaacaaaddcdbbcbaaacbabdbadcdbadacbaddbcbbccaaccdbdadcbcdbcbcaaaacaabddcddcbacaaccbcacaccddddabbbbbdadcdcdddccdbcdabcacdcdcacbcdacdbbbdaabbddaadcccbddbacabbdadabbdbdaaaddddbbdbbbccadccbccbccdaabdadbcaaadaccaadbdcdbabccadbcaddbdcaadcbcbadcababcbbccbacddacdabbbccabcadbbcbbddcccddacdbdcaacaccddaccaaadbcddadaababbbbccaacaccbcdbdcccadbbdaacbcaaaccdccddaaddbcabaabdbbcdaddbaaacdbddabdacddcdadcbcbcadababbadaaaacdcadabacbcbcdddadcaacacbdddbbdbcbabbcabacbaacbbdccccbbbcddbcadcabdaacacbddcbaabcdcbadcbbdadcaaadbccdaddadabcbdccccbadaacacdabdccdcbaacccdbcaadbabcbcbbbabcacdcacdaadccbcadaacadabaadbcbacbdbcaaddabdbcaccbcaaaddcdadccbdbbcaccdcbbbccabddcacbbdcccbcbccbbbddbbccdaaabccddccddabcbcabcdcadcbadcddcadbcddbccacbbcddadcaacbcaaddbadcbcacbbdbaccadccacdbbccccdccdadbbdabdbdacabcccccdbadbbcbbaadddcbdccbbbbbaddacbccbccdbdbbbacbdadcdbbbbdabbbbccacbbcabdaaddcdccdbaccabadbdddbcddcacabaccbdcddbbaadbdbbdaaabccbccbdbabddbacdcabccacbcbdadcbaaaabdcdddccbacaaddcbbbdccbcddcbccccaadbdacbacdcddbabacdbccbbadacddccddbcdcaadddbdccbccbcbdbbaaddbbcdabbadccddddbbadccbbbacbdbbacacadaadcaccccbacababdbadcccabbcacdddddadabcaabcccbbcbaacabcaacabcbddcadbdaabbcdbcbdcdbccbacbacabaaabdbdbbdbdabbadbaadaadcacbabdddccdabbccbaabddcbadbabcccabbcccacbcccdddabcbabacccdcacaaccadcacbbbdccabadcdaabbddbdbaadbabdcdcbcdddaacacdaaaccccabddcbcdbadbbaccdbbdadabacddadcbdbaaccadaccabbababbaaabcaddcbcddaddccddababcabbacbdccccbccabccdbbcddcbbddbcabcbbadabbcdadaccabdbadcadcabcdcaacbabbaccbdcacdbdbcdddddccddbbacbdcdbdabdbdaadcdbacbcccaccaabcbaaababadaddcabdadcbcdacbbadcbccdccbbbcbadbddabcdbabdccbadbdbdcdbdddcbcdbddaacbccadccaddbbddcabdadaaacacdabadbcbbcdacaaaabcadbaaddcacdcbddddcdcacdddadaadabbacdaddacbdbcdbcaaacbdaaabcbbbabacadccbbbabcaabbdbaccbddbaddaccdddacacdaaabacdadaabaaccbdcaaacacacbcddcbdadacbcaaaddbbbccdaaabaadcdddbdbcddccbadacdbadbddbcbbcdcccbbbcbcccabadbdaaacbabacbabdcdaaabdccadbbaaaacaabacbcabaabdddabbdaaccbaacdbadcadbdccbacabddbdbcccaadccacccbbacbbacdadddbacddddacdbcbdacddbdcbbaadaccbbddadabddaabaccacadcbcddaaddcacbcaacbabaddddacadacbdbaadbbbbdcddbddbcbabacdacbdcdadcbccddabbbaccabaccdbbbddbadaddadbaacaccbccddbabbacbcbcddddbdcadcdacdaccababdacaaaabbbbbcddbabdacdaadbabaaacdcdaacacccccabddccccabbccdacdddbbbdbbddbcaaabbbddddbabbdbcbccddddaaddbdbbcdccbbbdabbcaaacbcddcaccdaccdcbddaccbdcdacdcddccdabadabbbddaaadcacccdbccaaacdabdabcbcabaaabaaabcbbdbcdacbdcbaacbadbdbbbdcdbabdbadddcaaccdbadcaabccdddabdcccbcdcbaddadccabdccbdddbdcbabdccdcadbdbcdbbddaadcdcdccdaccaadcbdcddcbacaddbdcdbddbbaddbbbababcdbcdbaccbbcdbbcdcbbcdbcccdabdbcdbdcaccbcdadcacddcabbbbcddddbcadaddaacccabbdbbddddddaababcccaaaaaacacbdaddbdcaddbabdddbaaaacbbcdadabcdadbacddbdaadddddabadbcdbcadbabbadbdacadabdcaabdcccacbacbacbddcacdbbbacbaaddabcdababcdcdbdccdcbcccbadabdddcbacdbbacccaabcaaddabdddbdbcdbdabcbbbacadcbbcbbdbddcbdadbcaabdcbbaacdcacbccdcdbbaccbccdabbcdddcbddabadaaddbbbdbdcabcdaaddbbbaabcdacadabccdccdabbcdbdcbcbddacbbbcacbbacadddaabcaccccdbbdbbaccbbcbbbdaacdddccdccbbabadbcadaaaaabcbbabadcbcdadbbacacaacaacdcadcdccdaddabdabadcdabacaacaadbdccccdccadabcccbccabcdddddbbddbbaabbdababdccbdbdcbabbbbccbdcbcbbaccbdcbcddcadbddbdbbbadaccbcbddddabcddcddabdcdbcaddcbddcbbdcdabcbbabbcdccdaadcddcacacbcbbbacddccddcbdbbcacabcaabbddaaaaaaaadbdccbbabdccaacabcbaccdbdcbddabcccbbcdbccdbdcbbbaacbababcacbaadddbaadcbbdccacdcacbcbddbaacdcadadcddbdcababacabcabbcddabbcaaddaaabaddbddbdcabacadbcadbcabaccdddcabdccaabdcccbbdcdbaaaadcddccdbcabdbddbacccbcbbbddcbaaccbbddccdddddadacdcaacacaddddcdbbcbbdbdddaabbaaabbbbbabbabdccadbcdbbabdacbcbbbbcdcdcabdbcbcdbbbdcdbbadcadddaabbdcacabaaadcaddcbababbdddabbddcdbaaacdcbdabbbcdabdcbbbdbaaccbcdabacccdddaacadcabdbaaaadccdcbbcddbdabddcccbbaacbaddbbdaaaaacaabaabccdccbbdddbbcbcddcbabbdccacdadddcdbbbbaabdbdbdabaadbcbdbdbbbbdcbbdbabbacdabdcbccbdaaccaaaacacbcbcabbdbcbbacddbaddcbbcbdbcaaabddbdcaabadcbdccddbbdaaaacbbcdaddcbdbddccadabadddccccadbddbccbdbbbbddbabadaadddccdaacabcaaabcbbccaccabcababbcdabdacdcaddbdddaacdccdaccdabdcabdcabacbbcaaaabbbbcaacbbaadccccbdcbbcdcdbbbababcaadadaadbdddcbdbbbcaadcdcccdbacdaddbabddbadadabadddbdddcddaaacbbbdabcbddacbdccadbcaddccbbdbcbcbdbbdacdcdcddbdbbabcadabcaccdbcaadaabadddbaadccdbbcbbbddcccbbadcbdbdbbbcddcadcbbcbbcdacdcbdabacccdbbccabacddaccbaacbbbacabbbcabbadccdddaabaabbdabbccdddbdadbbbdcdbcaadcabaadbbccbbdbdadbabddacdabdddbddcddacadaaacacaababbcbbdcdaacdaadaadbbbaadabbdcddcbcbbcbccccaadabadccadcaddaabaacbaaaabdcddaabaccddddaaabbbcaddddcaabbbccccadcbacbdcbccbcadbdbbdbcbbbbaacbadabdaacacccaaaddaccadcbcacbccadccabaacbdbbcddadddaddbbdacdcdbcaababbccddacdadadbbaacdabbcbaadcbccbdcbcddbcdbcbaabadccdccdcccabccdbbdcdcabcdbbaabcbccbaadbaaabacdacaccccbaacbddbdadddbccccddcbdddbacdbdbcccabdbbdbbdbbbaccbaaaaacadccbcaccbaabbddcbddbaccdbbdadccdbbbbaaddacbacacaaccadacbcacdadadcababcdbccadabccdbaadaaacabdadddbbcbcbcbddcdbbbcdcbbcdabcaccdbddcadbdcaddbcadcdccccaabcdbbdacbadcddadadbdbaacbabdaabcadadbbbadccbddcdadabbdcadbcbdcadacbbdbcdddabdccbacdacdddcbddccaaaaabcaabaddadabbcccadacabcbcddbbbddddabcaccbcabbbcbdacbbcddcbcdabdddcdcddabbcbdaabbcddcadacdcbabadcbdacddccacbcaaadcdbadccacddabbcbccdcaaccbadaabbbdcbbddbcbbbccacbbbbcbccbcdcbcbbacdaaabbaddaadadcccaccaaccdaccbdccdbdbcbaaaaabaabacabbaaaaadacddacdcddbccbddccbccadbacddddabdccdcdbbcacdcaabacdcbdacaabacabacdcbaccdbaadacccbccdccdddabbbabddcddbbcbacbdccbdcacabdaadbacdbcbbcbbcddaadccdddbdcdbacadcbdbcddbdcdaabdcddbadccdcddabdbcbbdabbbbdcbaccddaacbdaccbddcbbaaddadadddbccacdbaccacdcbbabcbccacdabcdaddcadadbccdddbbbabbbcdcbdaadccdaddcbabdcbadbdcdcadccbaccddbabcdcbbcbadcaddcdcbddbbadbcbacccbaadabbbcdbbddcbdaabadbbaaadbcbbbccdbcccdccbabdcbabbdadabacbadddaabdcccdcbcbacdbadccdcbdacdadcbbbcdbcdacbdaaccaadadbbaaccddcbadabdcbcdcacbaacbadbbbaabbacdbdbbadaaaabdbbddbaddacbbaccaabaccabdbcddbadcbdadacdcdddbbabcdddcdbacaacdbcaccabcbbdabcaccddcdbdbadcacabbdbcbddabbbdcabdabadbbbddcacacadcddddcdbdbacaabadbbcdbaadbacaacdbcdcbadcacbadbadcddcbdaccdbdacadbcdccddbaabdbabacdacdcabdbcacdacbccdacbbcaadbdacdbdddcdabddbbbaabcddbcdcbadbbdcabbdbdaaccdbbdbbbabdbacbcbdcbbbcbcccbccddacbaacbaddcbddbaadbcaccbacbdbcbdbbabbadcdbacabaacdcdcbcababdadcccdbccbdccabbaccabbbddabdadbacabaddddccbcabdcbccccadcbacadbddacbbcadcababbbdbdccaadbcaddcabbbcdcbcaacbcabdcbaddcacabdaacacddbcddbdaacdbcdcccdcdbacddcdcddaaccdaaabdadbaadcaccccbaddbaabdabdaabbbcccdcccdaadadabcadbbbdbccdddcaabadddcccdcdaaaccbcbaaaadddadabadbbaacdcdadddbbdadaaccdaadaadaaccddabaadcdcdaaacdbcddbbaabbddddacbdbaaaccaabdbadbddcdddaadcbccbbcacadcdcbbdddadaccaadadaabcadcbacbdbbaadbccdbddcbdbadbaababdbaacdcddccbdabdcbaabbacccdbcbcabbabccbbbbaadabcbaaaddbbcccaaaaccbccccdcdadddbcabbcbdcabaabcaacdabbddcadbaddcaacaddccdaacacddabbbdbcabdcabacbdcccbaaaddabdbbcbdaacbcbaabdbbccbdccadddacabdbabccadddbbbbabbbccdcbacaacbbabbdbbcbcdbccccaacbdacdadaccccdacbbaadabbcddacbcdcbacdabdbbdccbcdbbbdcbcccbdcacacdcaacadcaaabcbbbcddbdcabaaddbbacaaddcbdabdbdadadbabbadccaddddcbcacddbcccccdccdabbadbccbccbdcbbdaadcbdcdaaabaddcdcccccdabdcbcacdaacdcadcadadcadcaadcdabcabaacddadabaabcdadaacccbdbccdbcbcabcccdbcacdabcadaaccbaddccacdccbdbddacddcdbbcbdaaaccbbdcbaddcddcaabaaddbbcddaccddbcdcbbbaabcaddccccbadcbcbdacbbaddcccbdacaaacdcdcccdaccdababdacadddbcddaacacaaddcbbbccbdcdbaaadcbbdbbdccdccbaccdaddbcbbdabbbacaddadbcabccdacddcbccdabdaadaaaacbdaaccdbdbddabcabddbbcaaadcaabbddbddddcbcbcdccdcaadcbadaadcbaadbbadaabdccabaabcdadccdbdcbdcaddccadcdcdaacddbabbadddaadbacdddcdbdbaaaabcacbbbcacccdbaaccbddcbddcbacbdcaadcaabcacccbbbdcbbdcaaadbbdaccbddcaaccacacbdcaadaaadbabcddaabdaabcbcacbbbacbdaadacbadcdcccbdaacdccdbadabcacacbcaaaccbbaaaaddabccccccccbdaacbbaddacddaabacadddddbacabdadaadbcbbcdaddaadcddcdabbddadbbaacbbdcdcdacccaacbcccaccbcccdcbaacaddabcbdcaabbcdddacdddcbcddcdaabcddadbaacacbabaadacdadbddbcddbabbbcccaadbdabadbcaadacdabdbcdaabcdbccaacaddabbcdbdbadcdcacbacbbdcbcbddadbcdabdbdaaaababadddbcbababaaddacddcdbcdcaaddbddadddbccacccdcacbadaaacabbaabddbbdddbdaccadbdbccabdcaabdadacbcdbadcbbdbdbaaaadddbccbcacacdcdbcdcdbddbcbaadbacdccadbbcdcaacccbbbddbbadddbddacdcbdcbddacacaacacabbdcaacadbcbcbaaccdadacacdbacaabbbcbcdabccddbbddaacdcdaabcadacdbbdabbddacbcbdcaadadabddcbcddbadbbdadcaacbaccabbbbaadaaccddcccbdbcbddbccacacaaaabddabadbccaadbddcbaccddbabbdbbbdcbdcbdccdccaddbddbbabdadbadcaaaacaacbbdcdbcbbaadaccdbbabaadbcdcbdbbdabcddbadbbdacdbbbbadaaabccbacdacaadbdacbacddabaccddabcdadadabdbbcdadaadabbbcaccbaabcdbcdcbccacabdaabaacbdcbbdadddabadcdaabaddaddcdcdabbdbdaddabdbdbdabdcdccdaaddabcacdabccdacbcdbbdcbabddacdcaacbaddadcaccabadacbcbcbadccdaacbdcdaabdbccbcbacdbcbdddababbdacabacdddbbcdbdcdcbbbabadcdaadaddabcdccbddcbcbabcdabcdcbaaccbaaabaaaaaabdcaacdabbdcccabcadbddadacdbdcccdbdabbbaaddbbcaddddabdbaccccdacdcdaacdddaadcdbcbcadbabcdcdddacbacbcbdbdbdacdbccddaadbdbdcaabbcaaadcddbdcacccbbdcdccdacaccaddacdcbacdbaccbbcbdcdddacbbabdbadccadbdbbadbcbddbdddaddbaaaccdabacdabacddccbdbdbbbbddacbccdcbdaccdacabbdbdbbcaacbbadbcbddaddcadcdadabaddcddbbbadabcbddcabbccdcbbbbabbcbcdaaaaddbbacbbbcdacbbdadadbbbcddcaaaabbabcdbbcabcccbdabacabbacdddbadabbbcbacbbaadbbdaadbbddbcabcccbbbcccbdaccabcdabdcaaddccaaccccadddbbadbbaadaaaabadaddcccbbcbddadababaddcacccccbbbcbdadddddbcbbbadaabbbadcabbccbcabacbabaaabbccbbcddcacaccbbccbdcaabbcacbacddababddbaabcaaaaabbaaabcdbadadaaabdbddddbaacbcbcddcddbcccccccdccacdcbddacadabdcbcacbbccabdadcbbadcbcdcdcbdabcabbcbcacdbcaadccbbbcdaddcbcdcabdccabbacbdcabbdadbcdbacbbdabbdbdbddcdbcbabcbdadbdbcdcaaccaccddacccbbbacbacadbdadbcababdaaacadddbaacddacbadcdbbddddbbbdcccaadbbadaacbacbaccddccdbdddcccabbccdabbabdacdcaabbbcacbadddacacadcbccaabadbbcaaaacabcdccbacbaabcacacccddabadabbcbadcabdacdbbcdbbbcabcaaaadbcaccbbdbddcdcbdcbcadacdcbbdaccccdadddbacabdacdcdddcdcdddcdcccbbcdaaabbaccbcacaaccbcadddadaaacbdddcccbbcabbcdcdcdabdbdccacbaadbcddbadacdabcdcabbddacdbaacdabcabbdaccdbcccaadddacbcbbddbaaccacadcbacbbdabdacacdbdbabbacaadacdaddbbadbadbbdcdccdacaacbdbbbcabbbcddcbacccdbdbbabbccbaddcdddacbbcccdcbaaddbcacaabaccbddddbbdaddaabdbcbccccdcbcdbaabbbdcccbccadcddabbddcdaccacbddaccbdcabacadbaacabadbccabdcbaabbacdcdbddcccbddcccbacabcbdabdcbdadcccbacdcbdadddddcbbdabcacdcccadabbababdcbaaacbdcccbddcbbabbacdcbabbdddbbddbabdacababcbabddcdabbdacdcbdcddccbabaacaadacadddcadbdabdacdacaaddcdadbccdcccbbbccbacdbbabdccdbabcabbabaabadabcbdbaaccdddacabbdadcdabdbbcadbbbbcccbacbaadbbbdcccadccdcdaabccdabbaccdabccbdbdddcacccdbbbbcacaadcabcacdbbddabcccbdcbdbbacccddaccbccbdcdaaaadccaaadcccccddbbcbbccbddcddbccabcdbbddcdddcabdcdaabaabcbabaacddcacdbacdbbcbcdabddccbbccabdbbccbbbbbabaaabdadcdbccbddbbcbdccaaacadaabcdcbdcdcdcccabcbddcaddbdabadbdcaddccbacabccddcccdcaaccccabdcadbbcdcacbaacdadcaaccabadcdadcbbdaacccbdbccbcacabacadbcccbdaacabbaddaaddbdbcabdbacbbaacddabcccaddcccacacbccdcdbcacabbbdbccacacdbddcacddbddadbccddabdbccbcccacddacaacddbdbbdddccdbdadcadbbbadcbdaccdbbaddcdcccddaaaddcbdaaaaccdacbdcdadbdabaaaaccdbcdbaddabddddccdaddccbdcddbbabcddbdbadbbabcdacbaaccaacddccdcdbbabaacabaaacbdccadddbdadccdaabcbbbcdcadbaaaaadbdbdbdadabccdbacbacbccdadadcdcbcadbcbaaabbbbabcdcadbcdddddaabaddadabbbddacbdbdbcbcaddcddbddcaddbcadaccbdabadbdbaaaaccdbbbcbbdbbcdddbaaacbcbbabccdbcabbabaacaadcacdccacaacabddcadacdabadcdddcacdacdbbcbcbcaaacccadccbdccccbbdbdcbdccbaabbaddcdbbaccabcadcddbcabbbddabababbdcbcacdbdbdcddcdadbcaddcbdbaabdbcabadcabcbdddbcabbbaacbdbacdcadaddbbaabcbcdbccacadadbbcacbbdbcaacabbcdbdaabcaadbbdbacadcdadccacdddabcbdcbccbcacdddbbacdddbcadbabacdbdaabbdadcaddddacabbacbacacbcdcddcbdbbadacabdcaabaaddbdbababbcaccaacdacdbdbbadccdbddabcbccbdbaaddcaaddccbaddbcdaabdcbabbbcbabacbcbdcbddbbdbbcbcbcdbadabbaddcbbbbccdbdcaabcdbdddabbcadbaccbdddccccaadbccbdacacbdabdaaddcbdcabcbddddcdaabdadcbbcdbadcadaacaabcbcdbcaadddaadacbdbbdddddacccbdcbbadabaacbbacbdacdaaddaaacbcaddbbabdbabaaaaccbdbbbccaadcacdcccbdcdbcbbddabbcdccbabdaadadcaaaacacacddcbadacbddcbcbccdcbcabdcdacddcccacdabccdcddaaacbdcbcbbcbbbabbbcaadabbaabdbddadadbbdabaaaabddccacdabddccbdcccdcddbcdaadbbcbdbdadcbcdbbaaccbaddddddbdbbdddcdabacbbdbbbbdaddbcaaddaabccadabbadaaadcdabdbcacabbadcacddbacaacdbabcdbbcacdaabdacdcbaadddcaabaabaaacbcdbbacababdbcdacdbaaddcddddacddddabbcaddacdbcbdcdadccdcccdabaddadabdabcbadabdddbadbaaddbddbdabcabacaccbbdbaabbaacadddbbdbdbbbadabaacabdcbbddbadbdaddbaaccbacacabcbdbbadcbddbcdcabaabaacaabdddacaddaabcabaaccbcdbaacacacabdddacdabacdccbbddbcadcbcddcdaabdbbbcdccbdbaacdbdccaabbbdbbdcccdbddadcaadabcacdcadbcaaabaaabadbaaddcdbaddccdcaddcbaaddacdcadddbcbacaaadbadadbacbbbaabdddbdccbcaddccdcdcdbbaabbdcdabccbdbaadddbabdaacdbddbabbdbacccddcdcdbbbabdcabdcabadccdccbbdcbaaabbbbbcabdccdbbbcbabbbaabcbbcbdadddcdddbcdbabaadbcaabdbcaadbccbadaabccadcabcacaaccaccaaacabadccaccdbaddbcccbbcacbabcdbaacddddaaacbddcbcccacdbddaaacdabbaacadbddcbbddbddccbcdbdccdbcaacddbccdbcbaddbaacdaddddbabdabccbddbaccbdaabcbddbddddaddbabacdcccbacadbabaaccddbbabbbdacabbcaddbacaabccbdbcccccacddbbabbdbbddcaccbdcbddbbdacddcaabdaaabdddadbabadddbabdacddadabbcbbccacbdbbacddbabcdbbbacdcdcaddbcccbcdbbadcbbccddbdadabbdaddddddcdcbacacaabaddacabdcdbbccbcabbbabcdcdacbdabbabaaaacccaddacaadddcbcdccbcbcbdbacbaaccbcaddcbadadcccdaaaaacdccabaaabdccabaccaaadacaccbabdddaacdbcccbbadacaabdcdabbbccabddaacbcdadabcbcdadacdaaacddccadcdcacbabdcaadcbdbbaccabadccdcabbddcbcbcbdcbccddbacdadcbdcdbcdabaaabbdacbcbddaacdcaacdbcacbddbbabbccccbbbbbdcacbddbdcbaaadaaacabbcccbbdbdcbcbbbcbbbcaadcccbadcbccabbacdcddbaabdadbcaddabdabbdbacaadccdaaaabcccbcbacdbbdcbbcabdbdbacbcaadacdccbaddbcaaabbadcddcbbbbbbbccdadabcdaddadaacaacdcacdccadbccdbdcdbbcdacddcababcddbabaccbbbabbbbabcaacccdccabadddccaccbbbcadbaccadbaacacdabbaacdcdbbbdbdcabbcbabddacabcddccacaaaccbbccdacaabdaabbbabadabcbcacaadababdbaccdbdbbcbadcccdccdaddaadaababdcbbbccadcbaddabdcadacccacbdcbaccacaccacccdddcbbacbdabbbdbcadcacccdabaabcaabddaabbbbddadabaccaacacdaabdcacdddbaccabbcbcdcabdacbcabdcaabbbaddccabcbddbbcdbacbdcdbcbbbadacbdaaadbcdbabdaadacbddcbaacdabaddabcdcbabdbcccaadbadcbadcddacaaccccbbdcdbaddbccbdbbaccbabcacbadddbaaadcbdbbdcdcccbdbbadadbacbbdbdcdaddaabbadcbbaabdaccabccacdddabbaaacabbdadbdacbcacbcbbdaadbbdacbdabbadcbdcdcdcbbdcdbbbddcbbcbadbabacdbdcdaaaacabacbaccabaabbbcabcbdbbaaaabaddcadadcadbdabacbdbbabbccdbcbadaaadcdbdaacdacdadddbbbaacdabaaddcaabcdbccdadbdacaababddbcccabddbbdbbccbcabbcaddaadbdbdaabbacdabbcddaadccaacddcabcdaacbcbadbdaccaadabbbbbacdbbcaacaacbdcccaddacbadbacbcdacbdaddcacaaddccddbacbdbdabddcaabcddddbddcbbccccdaddadccabbbdcbcadacabdbcdddaaddbadbbdcadbbcabcdaacadcaaacacbbdadbdbddacbaaaabcdadddcbaabcbcdddbacaccdaccbcdccdccadabcbabcacddadbbdbdcacbdbbbcadcbaddbdabacacabdadbcbcdcbccbbdbccaaacdbdabbdbbdcbbbcddcbadaccaaaaabbdabaadccccbddacaccadadbbbaddcdaabbabbddabcddabbbbccbadddcbbaababbabdcbbabdbddbbbbcbaaabbaabdcbdcaaaaabcdccaacacdbddbccdccdcbbddcccddddcbadbbdcdabbcdcadaaabdbccddbddbcaddcaadddaccacaabcacdbdacbcaabcdcbaadcbccdaacbabcaaaadccbddbccabbbbaccaadbdbbacdbacabacccaddbdbdbbdaacdcccadabaacaaacddcccabdadabdacbdcbbcccccbbbadcacbabcdbbdcdababaabcaabbabbbddbadcdbbdabbababaccccacabcaaccccaadacdbdcdbcddadccacacadabbaacabcccaddbddbdcdcadddababbbcbccccdcbcdaccdabaccbacdbcccbdbbadcbabbdbdbcadcabcbbdcabbacdccbdaabcbbdbbadcbbdabdbbcddaaccbdcdaaaddcbccbcabadcccdbabddbdcbdbccabbcbaaadcdabdbccdbbbabcdaddbaabdbcccdbbcbdbdacdacdaadcacaababbaaabbbaccabdadbbccacdcabcbcddaddddbdabbddbabcccaaadbacbdbadccbddbcbabdbdaacabbbcbdaabadbdcdbdbbddcbbdbaacbdbbaacdbcabbcbadcbcbbadaabadaaaabbddabddaaaccaababcaadbabcabbdaddcdabaacbdadbbbbddacacabbbacabbcbdbbaaadbaaacddabacacbabacaccdddaddbbcbbdbbdaddccadddcadbdababbdbbacdacddbcdddcbbddbbdcddaddbbbdcbaadabcdbcabacdbcdbdbcdddbaddadddaaabadbbdcadabcdccbcddcbaacbcdddcdccaddcabbbcbdadaabadaadbbcbccbcdaacbbcadcbcdbbdcdbbddddbcdcddabdbaabcddddccadbadcbaabbacbcdacaddbbbcbcbdbaaaddabdacabccccbbdcdbdaaadcbdbbacaabbbdacdbaddaabcdbbbcdbdbccadbbdbdbbbcdbaacccbcdbdaabaababbabadcaaddccdcbbbbddddccaabbbadcbcaadbbcdddddadbacabbdccbdacbddadccbaacbabaccadcbbdabbaadbadbaaabacacbbabcdbcabcbaccacabbcdcaccacdaadabadbbbdaccdddaacccadadbbdabbbaddcbdbcdabdcdcbdbcabadcdbadcdbbaaabdabddabaacbaacdbaabdddbcbadabbdadbbcdcaaddccbabbcadaacbdcccddddcacdcdccccbdddccbcdaaaabadcbadcdddbbbbcbbcdbdccaacadcdaabdbdbcdccdacdadaacbcdbdbbdbaabdcdcacbacbbbbcdcbddcacdcbcadbbbdccbbcdcabdbbbbabdadccbdddbabcbdccddcbadbdbacbbdccaccabbbcbdbcbbddabbbdcbbaadddddccddbcbadaccaddabcababadaadbbaacabdaddccdccabaadbbdabcaddcacacdbcdccbbbbbbdcdcacbaadcbdaacabcacccccdabdabbacadbaacccbdcbddcabacadbdccdcdcabdddbcddbcdcbbbcbcbbdcbacdbaccbbdbcadacccabccbdaaacabbcbbbcdaacabcdbbaadcbbdbcbccbcccccdcbabbcacdcacdbaaaaadbdddddccbdddcccabcbcdbdbcbacadcbddddaddbcacdbdccaacdaabacbcadbbbaacdabdccbccdbcbbbdcacbdbdbdbadadacabcdacdcabcbdaaacccccdaccacccaacddcbbaaadbcbbabcbcaaccdacccbacaadaacaaabcadcbdddbbbdbccaccccbbacdaaabaaabbbdddbaacccadcaccdacbbcbdaabbabcdaaacdbbbaddbddbcdbcaccbbbacddaabacadbdbbcaabdaacdbdaabbadcdbdbbcdbbabdccbadbadbddbabbaccbcadacddabcbdbcaaadadadccbcdadadaabcddcbaadbadccdddcdbbbcbaddcdbaacdbbaacbddbcdcadbbbcbadddddccacbbacaaadabccccbbcaccdcacabbbdabdbcaaccdbbcacdcccababaabaaadbabbbabbccccddbbdbcdccaaaacaddbacadadbcacaaaccdbabdbcadabacbcaddcbcacdaadaddaabdbdaddacacadbbbaadabbaccaadaccbddacbcacbbbacbccadaadbbccdaabbaabbcadabaaccbbccdbddbdcdabcdbcdcacdaaddacdccdcdddcbadcccacaaaddcdabababdcadadbbaacddaaddaadaabbaabadcabaaabaabbbdbdadcbadadcbaddaacdabbcdbaadcdbdbdbdbbccddaddcccbdcbaacadabbdccdacaaaacccabaadadccccddadbdbbbadadcbaadccdabbcbaabdbacbdbbdadbbdbdaccacdbdbbbdaccdaadaddacdaaddbbdbabdabbadbddcddaccdabccbcbcabdaacccbcbbccabacbdccbbbcdaabbacadbabbccdabccccadbccdbbbbabbbdbbacacbaabadcaacddcdcaddbbaddbbddbbbadacaacbcdacdcaccdabdabbdbdddbccccdcbdababbccbaaaabdcbdbdadcacddbaddbdcbccbaadddcbbbbaadabadbabbbcadaaabdadaccabacabbdbbadcdcbcacddabbbbacbbaacbdbddacbccdccddcdbcaadaaddabbadbbaacbddacbdaabacacaaccbbbdadcbdbcbcadcccadabcadcaaccbdacbdbdbccdbacbbacbdbbcbbbccddcdaddaaacadaaabdabdddbdcaabddaddabcabddabdbdaadadacdabbccbaacabaadbaccbbaaadddadadaacbbabcccbaabcacbdcaacbdacbddcabaddbcdbaacabdccadadcbacdaccbdcbccbabdcdbccbddaaddcdccbbbaccadaabbacccdacadadcababcbddacaddaacbbcbbddaaddccbcabbaabbaaabcadcccadccabdaacdadddcaddbdcbadacabcddddddadcaadddddaadacabcccbdcbddbadbcdddbaddcadbbaaadcdddbccabbabbcccbdddcabdbacabdbccbabccadddaaccbdabdbbddbcbbcbdabbbbaacacaabccabaadabbbbcbabcdccadcbaaccdcdadddacbaabcaabbcabaacbdbdaadcbccacdaaaaadadacdcabddabacddaabaabaadbbcabcabdccabdcdccabdcaddbbcbdbddbacbabadbdaabbbdbbcadbaaadcadabcccacbbaabbadbbbccdbbcdcdcbaaddadbbddbbccdababdbbdcbbbbabdbcbababcddbacadabdcbacbcbbccbdbbddbdcabacaaabadddaacabccdbdcdcbdccdbdccabbaaacbcdcddddcbcbbdddddcbdbbadabcadcababcaacbddddbbddbbdbbdbbbbdddbbcbbcacdbbcdbaccbbcbdbaadcdbababbdbcbabadacbacbdcbbadbabaabbcabaabcacddcaabddccdcddaaaababaaccdbdbbcdbbccdabacbccabccdcbbdcabdbdcbdabcabdaabbbcbcabccdcccdaccbaddcbbadccababdcabddbadcadadcdcbcaccccbdadbabcbccdcabcaabddaadacabcbcdbbbbcbdbbbdddddcbabdaddcaadbadabddaadcbadcdcbacbdbcbaaacdddaabacbbcbadaabcbdacbbadacccdacbdadabddacdcbcdbccddcccacbcaccacdccabacbabaadcccdcacbccdbbdaadaabaabcdbdaabdaacaddcacbbbdbbcbbbbbdbdcbbdcdcadbabdcbbdcabbcbcdbdcbadaadacccbbdddadabcacddbabbbabbdaaccdbcccacddccadaaddbdcdbaaaccddbdbdbbdbdbdbdbdabcadacccbdbdabbaacdadcdbaccbabcdbccdaccdcdadaabccaacaccaddbabaddccbbabcacccbbacadddaccccabbaaacdbbcadbcdabcacaaacdabcabcbdaacdabaaaabababbbbaacacacabaabaabdbbaaadbcbbbcbaaadabcaabdddaabbcdbccbddacddbbaabcabbdaabdbccbccdbbadcadcababddbdbddccbadaaccbdbcabaccaacaddbccadaacbbddbdbacbaaacbdbccccdacaabcaddcdbbaacaccadacabbdcddabbababaacccabadababdbcababadcbccbdbacdbbbababadabbccddadaacdcccbabccaaaadabbcccbcbdacbcbdcabbdbadaacabbcbbabadcddaabcdcbcddbddccacddabdaaabcabdbacdbdddabbdabaddccdbdbdcbdcbadbcdbcbbaabbdcaddbadaabbaadcbcabbddbbacdabbaabbcccdadcacbdcbccbbadabadbbcbadadaabbbbbccbbbddacbcaaabaccdacbcaabcdaadadcbaddbbadaacadccbbdabbdcacbcdaaadcacbabcaadbdddcaccddadbcbaabdbcbadccddcbabadcabdacabbabadbbbbbdbbddcbbdbcdbbcaaccacaadbaadabaabcaababdbcdbdacdabbadbbdcacacaadbcadabbdabdcaadcaaacbbddbcbaacbdcbbcccabdcdbdbddddaacadabddbddabbacbccdcaacbcaacacaaabcdddbdabdcabbcadacbccabbdacbccaddcabbdbcbcccdabdaaddabbcaccbbbadcdccbcbdacccddcaaabababacdbbacdacbcabbadcddcdccbacaccadcdccdccbbbaabdaccaadaddbcddacacccdcaddbcadadabcdcabdcbadbaacbcdabcdcbdaccbcdddadccadabcdcadccdbbbcbbadddacababddabdbbcbabbadacdbbbccabdcaddaabaaabdaddbcccbabbadcbcddbcdaacdbdccabdabdbacabcacbadcdaacacacdcadbdbabddcbadcbacdbdcccacbccdacbdddbddbbcbaabaabbdacacaccdcdabccbcabdccddacbcdaadcaddbacbaadbcbccdcdcadcadaabcdbcccbabaccdbcacdbdcccccabddaaabccbcacadbaabbbccbdaadcacacadbcaacbbdbbbbdbccaadaccdaabcbbcacadadbdbcdddbccbddcbbaddcdbbddddccbbdbcbadbdbddcacaccbacbacdbccadabddbababaabdadcbddbdbbdccdcdacbcaadaddcbdbccbcbdbbdddacbabcacddbbdcdbbbaaccdabbadbaccbdcbcbccaddcbddacddddaabaaacadddcaadbaccbccbaadaddcacdaabdcbbcbabbcccabdbdcbbadadbbdcdcbbabaddbadcbbadccacbacccddcbcccadcacbdcacdbdbadaabccdabadadacaaadddcabdabccdbacddcbcaadadbabbdbcbcbabbdaadabbcccbbaababcbbbcbddcdaacdbbaabbaddacbcdbbddbdccabaabdabbcaabcdcdcbcbabbbcdbadbdcdbcccbaaadcabacbcabbcbcccddadbdccdbcdacbadcababadaaccdbcaabdbbdcdacbccdacabdaccdaddabbdcbbdcdddbbadbaadcbaacabadbaabbcbacabaccbdabddadbbabdacbdbccdaaccbaadaddbaaddbcbdcdddcabbacdaacdcaabbccddcddcbdccccddccbdaaacbccddacacaabbcadcadbcbbabcbcaabbdcbcbddbddbbddbcadadcbbdbbccacadccddbbbbdbcdbdadcabcbdcccdbccbdcddacdadadbdacbaacdadacdaadccccbaacdcbaaaabbaaadbdbdcadaaadcbbdcccbcccaccaababccdcddcadcddccbaacbabcbdbdcabccaacacbbcdabcdbabadbabacaacacadbdcbdbdbddabdbaacaccaabcddbbbaabcdccbccbddabdbaabcbcabaadcbcdcdccdccaadddacddcdcddcdcdbbabcbdbaabcdbdddbbcbdbaaaddbabbacacbbaabaddddbbaaddbdacacadabdaadaccbdbbcdacadccbadacbaabacccddbcabcabcccababacdbbabdaccacacadaacccdcbbcdbcccbaddcbdcacaabdbadacdbbcbacccbadaadcbadababddcadddaaaabadaabcdaabadcbdbadbdcccddadacadccaabcadabbbbcaaadddcbcddcbdacacbdcdaadaddabcbabbbddbdadbcdcaabddabcdbcbadcbbbbadbdaddccacdaacbbaabaddcacaadbacbcbcaddbcaabbdabdddaadbcbbdccaabaadcabdddaaadaccdaddaabdbbbcbcdcabdbbcccadcdbacdcdcadcabbbcabccbcdccdaaccccccacabbcacccdaddcdcadbbcbacdaadcbcbdcdccbadaddddaadbdbddbdcdbcadbdddbdabdadccdcdddbccabbacbcbcbcbcccbcabdabbdadccbbdbcdccbcbbbccbcdadacacdbbbcbdcdcadacbbbbabdbdddacdcadaccdccdcccddcdbdbcbaadccdcbdabcbcbdaacadbdccdbdabbcbcdaacacbbabbbbdcacddbdacbdcdaaadadababcbadbdddcbbdcdacbdbbbaacddacaddbbccdaaabddbccbbcdcdbbdaddcacbdbdadadbabdbbdbdcabcdacacddbbcbddbabcddaababcbdaddbbacadbdccabccddbbbcaddaaccdccdccabaccbadcabadddcccaddbcccaabadacbcadcddcbaabccbbddcbcdbddbdbaadccacccbddcbadaabbabdaacabcaddaadcccaaadcddcbdcabadbdcddccccbbbabccdabdcdbdcbbaddbcaaadddbdcabbbdaabadbbadadaacddbdabadddddcdbadccccbdaccdacbcdcbbdcabbdcbbdbbdddadacbadacdacccdbadbadcdabdcccdaadddabbdbdadbccbbbcaaddaabcaadadddcaddbcddadcabcacbadcaaadcaaabccdadbaaaccaccbdcdcdaccaabbddaababbbdcddcadcaabdcbcaadbbbccdcdbaacdbbbccdadbcdabacacbaaddcbdabbccdaadcabaddaacbdbdccaddacdbaaabcbaaadbaddabbcbaccdbacadcbacdcccccbdcbabbccaacdcaaddbdcaaaabdccbbbccccbccacddacaaabdaacdccdaabcdcadbccddbbcacbbcbadcccbabcadccacbcdbaccdbcabcbbabdbbcadaadcbdabdbcaaabcbcaadaaadadadbcddbcbbcbdbaaaddcccbadcbcccadccdbdbdbadbcbbaacbbbccaddaadbabbbbdccccdaabcdbbbdbcbbccadacdadccbccbddabbdcaabacaacbbcbdaacccdaaabdaddacadccdadbddbacbddcdabbabdabcbbbaccadbadcbdcccbdcabbaacbabbabadbabcaadacaddddbbabcabdababdabbadbdabaacdcccbdccaaddcaacbcbddbacaacdabcdcbdadacbbaacbadaaabbdabbbbbccdccaabddadaacabcbacdddadbacaacbcadbbbaababddcbcbcddbbddcbbbcbadbbacdbacbababaadabdcdbdcadcbccdadaadcdadcbdabdcdacdbdcdccbbbdcdcbcacbccddadccdabacbdabacbcccbddbcddcaabababddbabcccabaccaaabadcabdaccccbdcaabdcddcbadcdabddbbabacccccacaadaddbacacbcaabccacdcacaadddcdbaaccbabccabbaaadbabdbacdbbbdadcaacadbbaccdbacbcaabadabcdcddddcbcbcbacbabcccaaddbabbbaaaacddabcdabbddcbbdbbdddcccbccbbcbadbbccaabddccddcbdabcccdbdcbccdacaabdbbcdccddddcaaaddbdaaacacbdcbddcdaabccadbcdaadbadccbdcddbaddccdcdacbbaacbcddbdddbabdbbdcbdacbacbaaadcbcabdadcbdbcaababbcbacccaaaacddaacabcadcabbaccaacbbbdacaadabddbddbaddcbdbdbacdcaaaccbadabbbaacddabdcaaaabacbaccdddacadbbbdaddaaddbdcaadababcacbdddabcccacdadbcbbcbddbabadbabbcdcdbabdbdacbcdabdaacacabaadabacbcccabcccbdbcadbabbcbdcaccccabccbdacbbdacddcbbbcdbbdadbddcdbbbadcdabbdcbcdbaacdcabdddadaacabbcaaacabbacbcacacabdbdbbadaaddcaccccddaccabadabdbbcbdbbabbbbdbaadcacabddadadcbacaaaabcbdcdadcdbddbbdcacddddbaccdaadbccdcacddddbccbbcaabbbbaadbbdccccdbaddbacbdabddabaddacbddacdcadacddbcabaaddaacabbdbcdaacdcccdbcbbdabccdbabcaaaaccccbddbbabaddaadbddbbbdbbdcddcaacccdadcdcdbbddcbbbabdcbcdbcdbabacaaccabbbacbdcddbbdaaddccccddaacacacaccbddbcdbaccadcbcbcccabbadbbbbccbbaddabddbdaadddbbdbcaabdbabdcdbcdbbdcadacaaaabcdcdddcccdababadbdcbabdaabdbcbbdadacabdbbcabacddddaaadbdcbddaacdbcabdbbdcaabdabddcadbbcdbccddaadaacabdccddbbaacabbdaccadcaabbdbbacdaaaacbdbbddbcaaabbaadaacacaacbbabddcccdaadbbdabaacdadcddbcbcdccdcadbcbcbdbdcbcdacbccabccbaaacbbcaaccacbadacabbdbcadbcabcccbdbbbbcadcbcbddcbabbaccbdcbcbcdcaccccaadacaaabadbbdcbccbacddabcdcacaadbbdddddbbbcdbacbbbbcdbdadbabadcbbcadbcbcaccbbbbbdccccccbdcdcaccabdcdbbadcddbacacddaaacbccbbdaddabcddcdbdddadcddbcbddbdcdddbdcadccabdbaabdacbbdddcbdcccbdbdacdaddadddbcbdacbacccbdddcadabacaddbcdbaccccccbadbbbbddaaabaacdbbbabdddbbcbbacbddbbbacdbbacbddcdbccbbbbbabccbdccaabcacbdcacaadcadcdcabdadaacdacbcccabaddbbcabaddccbbcadacadaababbcdacccbdddcbdbbbbbcbbaabaacbbdacaacacabdabdddbdcdbcbcddccbdacaadcdbadcccdbdcaababcdcbcbbbdbcbbaccdcddbacadbaabccaaaccbcbadacbbddbddddbdcbacdccbddccaabaaaaccadcbddddcdcbccbbaacbacaacdbbcaaacacbadaadddbabcccbaddabbcbddbdcabdadaaddbbbbdccacbdababccdcbcbbbcacccbdaccbcadbcddccddcbcbcabaabadadcbbacbaaaacaccbbaddddaacadccaaaccbbbccadbccdaaabccbcbabbdcdbbacbdbabbcbcbbcbcabbaccadbccdcabadabcbbabbbbaadcccdcdabccdbdbdcdadbaaaabdccadadbdababacbdadcddaccabadadcbcdbbadacbcbddcbcaabdacbddbdadadcddbbcddabbaddcbbcbdcbbadbabdcddbabbbdcddabbacbaacddddbccbabdabddababaabcadcabdbacbcccdcbbaaccbcddacacccccbdcdcbdbaababadacacaccaccabdaaaadcdabaddadbddcbdddaadcbccdddabcddaaacbbddaaddcabbcdbddcccbdcbdbdaccbdbabbbbadccbabdccabcbcdcdbdacdcadbacccadbcabcadabcaacdbabcddcbddbddddaaacadbcdbcbadbdadacdbaaccdadabadbadaaababcbcccbadaaddacdccbacddcbccbadbbcdadabbacbabbccadbdbddcaadccddddbcdcabaddbdbccbbcdcadcaccbccddaddcdaababcbabacbbaaddddcccadcdacaccbbbdbddbaabcbacabbdccdcacdcbdacacbadbddabbcbabbddcbbcdaacdbaabcbabddcbdbdccaadbacdbdcaaaadbabbcdccbbacddbacbbcdcdbdccbaddababaaadbbbbdbacadbabacdcccccacbcbdbdaabdcccbadaacdbcccbcabdabbdacabbccdcbcbddabababbdcbdcbdcbbbabcccabbcababaadbbbcccbcbbdbdcdbcbcacdabcbbaddcddccacacbbcddbadabcabbdabcbcacbbacccdabacddacbddcdbaadcadabbadcdbdddadbbbcdbbbadaabaaacadccbcddbaadcbdcbbadadacdabaacbaccddbabadaddcabbcdaaaccddcddaacaabadacdacacdbaddbddcaaddccdbacdacdabacbccadcdabccadacccaaacbbadbdbbacdcbbabbdbccaaccbbdbabdcaaacbbdbdacabdcccdddcbdcaadbaaaccacbacabccbcbdbcdcadabcbabbcabbbacddcdacccbacccdcdcbcbcbbcbabaabadaabdbccbaccbacbddddbddbbbaddddaaadabdcdabdcdccbcddcaaaacbacaacdabadcbddabcdbcbbcdbaabcbcdabbcabdcaaadbcaaadccadcbcbcababbddaaccbbccbdacadbcbdbdbcdbbbccaccacbabbdcaacaccbbbbccacadbcbbcbdbcadcdacaaaacdddddaadadbaacbbcbadcdbbdcbbadcacadcbacdaacdadbaaadbddddbbcacbcdaddbddbdbcbdacabbcacddaddbdbbbcddbbabaabcbdbacddcdbbbdadbbbccbdbccbdbaadcdcbcadacbdbbdaababdbdcadaadbddccadbbcaacbcbbccddbbbababbdbdbdadbbdadcddaaccbdaddbcdccbdacccbbdbccccadcadcdbbcbacdababbaddbdddbdcdcdcbbcbdbacadabccbdcbdaabcbbacbacabbbdabababaccaadaaacadadaaabdbbaccacaccaaddcaddacaccaaccccccadaaddcabccadbdbbbbbdabbcadbdddcacbbabccccbcddbdcbcadacdbdbaccacbadcdcccdccaaccdacacaaccbaacccccaccadbababddaaaadaadccbabbabbadcabbbdaabaabcaabdbabaabaaccccbcbdacddcdbccdacadadabdbcbcbddaabbccbaaaaccccaccaabaabcdddabdaccababcadabdbbccdaddaddbdaabbbcdbbddabbadcbddadbbcbdcabccbabcccaadaadddbddbdcbdabdcbcdcdcdadddcccaacddddcdaddcbcdaacdbaabddbcdcdadaadaaddccbcdabdacdaaaadbadbadabaacbbdaaadcccbcabddcdbcdacbccdddbbdbbdaadddddccddbbdbbcbdbdcdadcccacabaccbbaadcbddababbdabdacdacbacacabdcdbdaadbdaccdcbaaacaabccabbcabcaacbccbcbbcabbcbccabadbdcabcdcdcdababbddbdcccbcbabcdbcdcbabdbabdcccaacbcbbaaabcdccddabcadabbbbcccbdbcdabaccdbaabcaadbabbcddcdcdbcabadccdcabacabbdcabbbdacdcbcdccaccaddbdccbaaabaddbdcdacbcacbddbdaadcbdcbddccaabcbacabcadbbdbbdcddddbbcddcbaaabbdcbaaacacdadcbbbcbadbaacdbcacbdaabcacbcbbdaabacdabddabcbccacddacbacaaacddcaccbabdbabcdcccbbddcabaaddaddabadcacbaddacdcbbcbbacddbddcdaaacbaddaddbaaaadddadadcbaddbaabcddacbacdcccccaccdadcabdabdcbadaccaddccaccdaaddddbacbbadbcadbccaadaabbaaadcababbbdccacddcaadbdacddadccdcbccdcbadadcdbdddbcaadbbbcdaabbddaabdcbcdcadcdaddabbaddcddcadabadcabbadbbbbbcbbddbccdbabbbadababcbbcbdbdcbadbcdbabcdbbbadabaaaddacbdaaadaccbacbdbcccbbddbdbbabcaccadccdcacbbcacbdbdaddbbdcabbabacdbdaadbdcdbdadddbcbabcdcccbadcddcdacacdadaacabdbcbdbbccbbdcabdbbbdddcdbabccbacdaaadddbccabbabdcaddcccaacdcbcdaabbccccbabbbadbbaabbacdadcacbcaacdbdccdbcdadaadbabdcacabbcadacbacacadccdbccbcacdbdabbdbaabbdccbbcbcabbaaabcbcbddacdbbdddccccdabdaddbcaddcbdcdbddaaaaabbaacdbccacabdaccddcddbaaddccbcbacaddcaadcadabababaaadbbbddcbcccdadbcabbbaccdcaadbacabbbdadbbcababddbabadabccccbbcbaacbdcadaaddbdaccabbcdcdbdbbadcbdcbdbcdcdcacbabddcbacacdabcddbcdbadcacddbbcbbbacdabacbddbcdaabbabdacdcdcacbcbcdbbbcbaccabdacacadaddbbcaacdcaabdcdbccacaaccbcdbdadccdcbabdabcbbcabaaaacabdbacbdaccdbdcccbdccdbddbcdbabdccadadaadbdacbcccdccbdccdccbcadadbadcdccababadccbbabadbacabbbacadcbbbdcdcddbccbacdabdddccdacddbdbaaaaadccbaccbdbbabddbaaabaabaddcdcababccdadbadaaddadbbddcbbddcbdbcbbadbdcaadaddcbdababaababcacdcdddcbdaadabbcbaaaddacbbcdacadabaabbdcccddbabdcababaacbdcaabbdcbdcadcddbcccdcdcdbdcadbcaabbbacdabdcaccccccbadddcaadcddbddcccabbcacaabdcaabcbbbbdcccbcbbdaabaababaababadbcaadcbabbadbbdcccbddcddccdccccaabcbaacbabdcbadadcadaaaccaacdcbbbcbddbababbbccccabaabadaddacaadbabbccbdbbbbadcccbaaacdddcaddbdcbacdbabbddacdbbcaabacddbdbccabbcbcaacadbdbbdcabbbcdacbadbaaaaadcddcbbadcddddbdbdbacbaabcbddabcaddcdbdbdcabbccddcbcbdcadcbaddccaccaaccbbdacbdbddaaacbaadcacbcddddadadbcadbbbadbbacbaacaabcbbaaadadcacacdacdacaabdabbacbcdaaaddbaacadcbaaccaadcdbdcbcbcbdcbdddaaacaadadbcacbcabcdddcadcbcddbaaddcbdbbbddddcbadbcdddbabdbcaaabbbccdadbcddcbcbaacbbbadbdaaaddbddcabbdbabcdabbddacbcdbaaadcababbccadaacbadbdbcaccdbbbdabbadbcccabacdbaacdccaaaddbbdabaacbdbccdbdabdabbccaddccdbccddccbdcacbdcaaccddcbbbdddadabaaaacbdcbbdcdaacdcdaddbddacccaabcdccbbbbcabdbdddbccabbbadccbbaaacccbddababbaaaaaadccabdcaaadadbcabdddbcadacdcdccaacdacdabbacabccaaddbdcaaccbadbcdcaccaadbcdacddcaadcdbdbcddacabdbddcdbbdabccabdcdbcaaaccdaadbcaddcbcaabcaabdacaadbdcacaaddaccddcbccbcbcdcadcacacddcbcabbcddbababcccbdbaadddbacacdadccddbaadaccacaadbddcbdccabccaccdddbbdccaddaacdaddadacdddaabccdbdbcdcadddbbaadaadadccbacbabacdacbbcbdcacabdabccbddadccdbcdbadddccbdcaabddbccdcaaaacbcdacddaaabbccbaabdacdabbbcaccadcabaacbabcdadbcdbadbbcdbaabaaadbddbaabbabdaccccdccdcdcacddbdcbbbaabccdacdcdbcbbdbadaaababcacdaacdaccbbdbabdadaaabadcaadcdbcbddabdabaaacdbabbdabbbaccdadccccbdbddcbdbbbdaaabbcaabacacbccacccadacdbbcccccabcbbcdadabbbccabcaddbababacbadabbdcdcbcdbcbdabdcddacbcaacbcbcbdabbdadcdbccdbdcdaccdcdbadaabbdbdaccbdcdcadaabacdddcccbbcaacaabcbcddaadccbdaadbdaadadcbbcadbdcbdbcbddcaadaddabcdaccabccdaaccaabbbbcadcddcbaaaabdbabdbabaaddbadbddccdccdbadddcbbddbabcddacacbacbaacbbacccdaacdabbbbadcccacdacadbcbbdcbcccdbabccabbbcccccaabcbcdcdbcacccbaddadccbcdbadcbadacdadddddadcdccacacccccbabadbbabdcbccadcdccccacadcacdddadcacdcbabbbddaacdaddcaaaddbdbaddddabdbaaccdcbaadbbaacacbdadbabdcbcccacbbaaacadaccdcdabdccbcbddacbddcddaddbaddbdcdaacbbbcdadacaaddacadaddacacccbdcaadcabdadaabbbcbbcdbcadacbccbdcccaccbadadccbbacdacbccdaabdcbbcbdaaddaddaacaacccdbabcdabaddbaddcdbdcccabcdbbaddddacddabdcabbacaadcbaaaabaaacabcdbadcacbaccdacabdcbacbbacbbccbbccbcccbddcaccdacdbddccdbbdadabdaacaccddbaaadccdaadddbbdadcdbdddcddaccdabbbdacccbbdcdddcdbccdabcbbcaacacdabbdbccddbbccaccccccdddabcbabbbabdacddcbacacaccdaadbbcdddcadbcccbccdbcbccdccbcbbadbadcdbadcbdbabcaacabaaabbdaacddaadbcacbbcadcdadcadbaccdacacbccdddacdcddbdadabadddbcdbaaabcdcbbcbaacdbbdddadbbcabacdbdacbcccabddabbcdbaaaaacbdcbacadadbcbbbddbcbbdccacdbadaccadbddccdbcdcbacabbdcbcbcbcaaacdbcbcbdcbacbabadabcabcbdadcdcaacbccccabdbdaaccaacbbddabbbbdbacccdbbbbddacdadcbcbcdbcddbacadbacacbcbdabadbaabdbcdbbcacbaaccadbddcbcccddcbddcadaadbbbdabdddcbacbcabcbbdaaaaabccdadabdcdadadadbdbdddabbadcdbaddadddbbcccbcabdcddcacadcbadcbdccbaacccdaaaddabbbdcacdbbbaabcacbdddcbbcadcbabdbbbabacbcabaaddbaddbcbbdccdadcccdacbbddddcabacbccdbaabdbdcccadacdddbcaccaabbadabaddabccddaabcacbcabacbbdcbddadccaddcacccaadcdcbccacccddbddddbabbcddabdcaaddbdcbadbdaaaacccbaaadbbadbabbddccbabbabadabcbcbcbdacdddccccdadaadbdbbbcaacdcbaccadcdbdcddababccaabcdbbcddcbabbaaadabcbdabccdbdcbababcabaaddaabadcadccbcdaabbbadacadcdabbbcbabdcdcdbdbcabccadaddcddabdccddbaaadddbadbbbbdbbcbabcbbdaccacadadacababbacbaacadbadcaacacbddaccbdadbbdbcdababcdbdccddddcbdbcbcaabaddacbbbbcddcdccaacdcccdbaccbbcacddccdcaddbbcbadbacacaddabccbbbacdabbcdacbdccabaddaddcbbabcbdbcadbbdbadacdcbacdcdbbaaabddadccdbadadbdaaaabcdddabadcccbbdadbbbdcbccadbbddbcabaccbadbdbbcbcaccacbcaaaccadbbbbcbcacbddabbadcbdbdaaddbacddaddcbacbaaabacadcadababbccaaaabcaccbbdbaabbcdcbcaadccddbcbbbbddbcccadaccbcbdcbccdbacddadccbabbdccccabccadadcdbdcaadbdccacbcadcbbdbdacadadaccacbcaabbbaaabbadadbbcbdabcddcaacdadbbadbaddbbbacaddcbbaaadbacdbcacaacababdbbdcdbcacdcaddbbcbdabbdbdbddcacdcaddddaccdbbcadccdbcdcaaadccbdacdcbdabbaddbadcddbcacadbccddbdddcaadabbacddddcbadbbcbaacdaccdcbcbdbcbcbddadcddbcbbcbdaaccabbaccddaccbcadccbccbdacdaadbbadcdbdcccddccbdbaaadccbcbcbbaccdabdacacdcdaabaccabacdababddbdcbccacaccbbadcccbacddccbdbdbaccaadacaddddccccbdbcccaabcbdccbdbbbddccddddabdcddbabaacdbcddadcdcbdbbbcabddbcadbdcabbbdcdabcbbacbcdbcaadacddaadbbadadbccbcaaaaacadbdaccbdbddbadaacadaadacbbdbdadcbbddddabbddddacaaacdaaabbccabcbbdcacdbbbbcaacaddbcabcdbbabccddcbbacacbddcacbbdaddccdbbcbbadcccabbdbaabdcccdabcdbdcdbbabbcdcdbbbbacbdbdbabccccdcaaaaadbbdadbbdddcddbdbdaddbccaabbcdbccdbcbdbdcaddcccabddaadbccadaabbcabbcbdcbbcabcbbcacabaddbcbbbdbadabcadcddbaabbddcbdadaccabcabdcddaadaaddbdccbddababbbcbcbdacbccbbccddcdbbbaccbabbcabcdbcbcccacdcddabcdbdabacbbccaadbcddbdcabadbcbabdadbcbddddcddcdaabdabbdcddcdcbcdcdadbabbddcacadcdcadcbcabbcaccccbaabdcbdadcdddcbdcbcadacddbacdacaaaddaccddddbaacdadacdadbaccccabcdbcaddcadbaacaddcdbcdbbdbcdaacabbdccdcacaabbbacadbbbdbdbcbadddabbdccbddbddcbcbacadabdabababbadacdadcbacdbdccbaccdbcdabadddcbbccdbcbbabbddbcbccbaddbaadbbbdcaaccbdcacdcaacabbcadcabcbcaacaddbadaababcdadddaabddbaaddadbdbadadaccadccacadaadacaccbcabddbbaabcbbdabbdbcadababbddadcdcccdababbddabdbdbddbbcdcaccddaadddbcadbbbbbadcbabbaacaabbbbdbcaabacbcbbbbbdbcaaabadaaddabddccbbccddcddabdbaaadaacdbdbcdacadababaaadccdbdcbccddccdbcddaddbbbabbbaccacddcbaabbaacbdaabbcacbbdcbddccaadaaccabcbdccaaabccdbcbbdcbcbbbcaaabaabdadabacdbddcacdcacabddcabbdcbdacaadcdccccacbbacbcaadcaabadcbcbaaacabdcbcdcbbbdbbaccdccbcdbbbcaacaabddcccdcddbbcdcdcbcbdcdcdcdcdddcbcacbdbdbbdaabcacaabcadbabdddcccbbcabcdbbbacadcbadcbabaabcbdadaddbddcccadcddbdacdccbccbabdddbaabdcadabacbcccddaccdccbdbddbabcdccbdaccdbcadccaaacdcaacbccbdddddbddddbcababbbaabbdababbbabaabaccccbacabbcacdcbcaabaadacbccadbcaabbbaccdcdbacacdbdbbcdcaaacaadbabdcccdbadccbaabdbccadadcdadbcdcbcbddddabbabbdcdacbaabdcbacccdbddbbcaccaacdbbabdaacddadcbcccbaaccccdaddadbbdccbcadcddaadcbdabbdcddadbddbaccaaaadbcdbccdacdcccbddadcbadaacbdcddcaddacddbdcdbaacacbdcacbddcbcdccbdbbcddbdccbdadcdadbbbaadadbbcadbbadbbdadbacbdbccadaadcacdabdbbbcccdacababbdaccbaaaabaccabbadbbbddbcaadacbdadcadaccdabbcdbdadcdbbbabbbabbaddbababbbbacdabddcdbaababbdcaaabccdcabdbcaaaadcdbaadcdaddbaddddcdbdcdaacbdddadbdbabcaacbcbdccbcadacadddbcadcadaaabbdadadbcdbdddbbbddbdabcbddabacccacdcbacbbbbcbaccdaaabbbbacbdcbaadccbdbdabbcddabbadaabbddbcdaaddbaddbdccaddadcbcbadbcddcccabdbdabcabbadabdccddaaacdbdbcdaaacdbabccdcbacdcbbbaccddaadacdabddccddaaacdadcccabcaacababacdcdbdbacccbcabcaacbacbcbdabcdbdbccdabbbcbcaaaadddcdacbdcbdbacaaddbbccacaabbaadcbbdadccdbbcacdbadabaaabbaacdcbcbdcdcadbcccacdbddbabaccadabdaaccddacbcccdadbdcbabddbbcadadbacdccccbaaabcdbcbdabcbdcbbbdbcadabccbbbccdcabcaccacdcbacdaaccbacbccbdabcdccddcadaadacaccbcaadddbccadcccbababdcdcabdddbbabbabdcdbabbbacdcbbbccbadbdcddadbadadbddbbdcadcaccbadbaabadabcbbddcbdbbadacbadcaaddcbbddcaddabcbbabdaccaabcdcaaacccdbdbbaacddbabaddadbcbdaaddaccabaddbacbaaaaaaddbccccbacbcccbbcdbaddbadbbabbcddbdaccdaadbcdcabbbbcabbbbccaacccdbbdbbcaccbcaccaccdcaacddbbaadabcdcdbcbdacdcdbadcdacabadccdbacbababbbadccaaacbcdcbacabcacadccccbcacbcadcbcadbbaaacbccaaadbaaccbabbdbabbadbbadadadbbcbcacbdacadcbaaadbdbbabbbdacdbadcdbbdaabadbbaaaadbaadbcdbcccbccbbbabbacacababdabdacbdbabdadcdabbacbdcabddcabdcbdbcbcbcababacbaddddaaabaaccacdcddbdcccdddacdbdbbccaacaccaaddacccdaacdbddcabdaababdcdacbbacabdcbbddcbddddabbbbcbbcccdabbaaacbcadddcaaacabbdddadbdcbcadbbccdbcacabdbbdbaacdabbccdaabbadaaadbbcadacdcbadddcbadacbdbdadcbdbcdcddcbdabdbbcdcacbabaacdaaddbdbbddccacaadcdabccbbabbdbbdbcccdbcbaabdcbccbcbaabcddaabccdabdbcbaddcdabcbbababddcddbaacbbcddaaccabbddcacbbdcbbabdcddadbaccbdadcaabdaadcdbdcbddbdccadaacabdbbccdadaadcaaaaacdcabcadbadbbacaadccccbaccbacdacabcbabaacadcbbadbcbcabacbabccaaaaccddaaccaaacbcaabcdbbababddccdaacadaadbaaadcdcdabddccddcbcabbccdbcdccdabcabdbaddbababbcbdbbcacdaaaaaddccddddadccdaabdaadbbdadacdddaaabaccbbaacbdbcaaabddbbcadbdcdaabddcbdadbaadcdabbdadacddabaabbbbdcccabcdbabbcdbddbcaabbadbabdcbcdcbbdacdbdbacacbbbdbacbcaacdaabbadbdcccbbcdbdaddabcdabcbaacbabbcadbbbabdbcaddadbdabaacddabdcaccdbbaaacabdbcdbabddbcadabcadcdaacabddaaababbacbccbdccdbaabbdaaacabaadbadbcdcbbcabbbcbcaabcbddcdadaacabbabddcbdbdbcdcbcacdbbacadccbaccdbbbbdccabaaacdcdbaccddcaaabdadccddadddcbadbdcbaadaaddccacbaabadaadabacaddbbdadccbdbadbbccacbbbbbabdcccccbdccacddccacbaaddaccbcdcbcbcbcadcdacbabacdcbccabadccaccccbdbcabccddabddbcdabbdbdacbaacdbaccbdddbdcbadbacaaccddbabacbdaddcbaaddcabdaabcbaacabbdcabacbabdaadccbddbaccbbcbdabddcaaabddadbaaacbbbccbcdabadabdcbcbaadabacacdccdbacacccaacabacccccccdcccdcbddabcbcabcccbacdadadaadbaacdabbdacadcddabdaadcccbddaddcbdbdacbdcdcaacddaacbcccdbdabcdbdcdaccbdacdccccaabdbddbbacdbbbcaddaccadbbcdccadbdadbbdbbdabcccaddcdcddcccbbadcccbdbdbbcdbddadadbbaaaaddcaadbcbdababaddacbdddbaddaacbabcbbdabbbdcdbcccdcdadbcaddcdddbcabdcdabdadadacbadcbadddbbacbaaccacddaacabdddbbcbabadaadbbddddcabcadabcacbbadadbaabcdddbcddcadaccdbcdbcadacaaadbddbadbcbcdbadddabdbbdbbbbbdddacbbbddacdcccdddccddabbdcbacabddaabdccbbccadcbdcdaddddbbcadddaaabcbdcadbaabddaccccaddbdaabcccbdadccbdbddbbcaabcdaaaccbaddaccaccdacbcddacdbccccdbaabcaccbdcddbbbaddbabbadbbbdccbdaaaaabbacadcccaccbdddaaaaaaabbacccbcacaccbbadbdadabdadaadbcaadbbdacacbdadccdddadbadbbadcdddabbccdcaaacbaaaacadaaadadcacddbaaccdbadaaabcdacbbcddbadbbcacdacbdaabbbbacdddadadbdbbaadbabdaaccbbdbadbddbdcdcdddcbcdddccaccacadddbcdbacabcbbaddccdcbbddacacaddbcbadaccdcaaaaccdbacbdcbdadbddcbcadadcbccdbddccdbaacbaaabcaaacbddabdccadbabcdadbddddccbabacddcadbabdbdacbacdcccbaaddcbaadaacaccbabdcbbadbaacacdacdbccaddaabcabdaababadcbccdbdddbabdabbacbacdccacbacbaddacaacaacddabbaddbdbccbcbbdbcdacaabbcbcbbbbcdacdcdbacddbabcccccdacaddaddbdcadbabcdddcacbdcbbcaaccaadaabdbbdbababcccbcdccbaccdbcbdcdcdaccbbdabacababadccdbddadadaddbcabaacdbbabbdbcbddddabbbcdbdcbdcdbaadaccadaddcadcacbbccdcbbbabcacaccbaaddacddbabcddadccabbdaabdadcabbdcdacaabcddcaddddbdbdccdaddcccaddddbabdbadbcadcadccabcadbaabdddbcaacdbcabbaddccacdbdaddbbddaddbcabbbacddbbbbadbdcdbcbcababaabcbddadaacbacabbbaabcbadbdcbaacccccabccadbbcdacbdabcdabaadabdcbcdbbbaabdcabdbaddaaaadccdacddcdaccbbabbddcaabbaaccbcdadbaadabdabacbdbbcabbdadacbcbcccbcdadacdddbdadcbcbcdddbbbadbddbbcabacadddcabccdcbaaaccbaacbabdcadbbabbcbcdccadccbcdbcaabadbddbdbaaabccdbacbddabbbabccccadbacdbbcaacacdaddbcdbdcaabddaaaccaaaaddccdadbadcaaacaabadcbadbbbcdddcbcdaacbcdadcccadbbcdcdbcadabbbcccbadccbbcacccbdcbaadadacccabbddccdbddcccaabbccacbbccddaaaaccaacdbdccdbdbdadbcbddaacccaaddddaccaaadbcdcbacdabccbcbdddaccddbdacaddbabcdbbacbcdbdaccbddccbadcdaccbabcbbdbcbaacddcadcddbddaccbdddccccbaddabccbcbdcaacababaabdcbdadbddccbccbadadcdabbdbdacdddabbacddcdbcddddcddacaaccdaaabddacdbabaacdbcadcdabccadccbaddabaadacbdbcbddcbdcadbcacdaccaadadaaaadbcdcbcddbbddcbacabbabcabccabcbccddadbdaddccdbcccccadaacddbbcabacbcadbdbcbbacadddabcbdbaacacbaadabcbbddaadaabadcadaadcdddcbcbdcbadabddcaaacaaacdcacaccacaadadbbbbdcddadcdbdddddadddabcbabdddbaaacdbcbbababbaaaabcaacacddbdbdccaccabadbcaccbabaaccddabcdbbdcacdddcadbabbddbdacbbacabaccaadddabdbccbcbccacaadbadcdcbaadbdbaacbaadbbabcbcaccbbbdbccbadaddabbddcdadbdacbbdbdddcbacadacddcbdbcbddcaddddbbbadaadbdddbdcccdccacccabccbbadaabcdcdcccabccdbcaccdbdcdbcacacaabdbbdadacdadbcccbacbdacdbbadcddbcacdccbabbdaddadaaacbcdcdaaadcdcdbadcdccbcaababccaadbcdcbbbdccddbacdddbbbbacbbdccadbdcdcbadbadddccdabbbbabbaacbbcddacaccdabaaacadbdbcdbbddccdaacbaaacabdaacdacaadaacadbbddddcbdcaabcccbbabcdadacaabdbcacdacddababdcacacbbbbddbbdbcccadabbddccadacdbbccaabadccbdabdacaadddbcbcabbddddbbcacdcacdbccbddbaaacaccabddcadbddccbcadaabbbbdbccdcacdbdbcdcddaaacdcdbbddabccdcbabdccbddddbdadccbcddcddcacababcadddcadcddcdbdbbbccaadcdbcabcdccccbaacddbbcdcbacddcbcdccbbaadabbbcbdcacadcdadccdcbcadaccbadddddaaddabbaccaaacbddccbbccdbcdddbbcdaddcdcaaddcadcbabacbdcdbaccbcaaaccbdcddacbaaabadcbcbddbbccdcacdccdcbacbadcdcabaaaabdbcddbbbddbbdabdddaaaabbbacaabacdaadcaddbccddbaacbacdddbacaacabadbddaabcadbbbbdbdcddbdddaababadbbccbcdcdcbdabcacaaccbcababcbcbabccbbadbcddcddadbdcdbcdaabaaddbacaaaaaaddcacbabcbdbbcccabaddadaddbcbbdcbbbbdcaadbccbbcadcccdbccccadbccbcbddaadbcccbabadcccdbaabaddaabbdaddcdbdbaacaabdbcbcccdbdcbdddacdbaddadbddbbdadcdbdbcadbdbabdacdcddcbaaddcbdaaabcbdbcddadddbbcbabadbdacdbaacdbacdadcaacbdaabdbbcdddacdddcdcddadbcddaaaacdaadbbacdadbbccdaadbdbabbaacdadcdabccabdbdccbdaadaadddcdabbddabaabcbccadbbddddddaddadcaaadcadbdacbcbabddaccabaacbcaacddbdaccdacccdcaaadcaaacdbcbaccccdaddaadbdcdccbbabdbaacbcabcdcbdcacabccacaaabbcaddacabdaadccdcabaadcbcbbdcaadcdadacbaadcccdccabcbddbbcacdbcaaadddcbdaadaacddaaddaabadacabcdadbbcadacadcbbcccccbdbbcbdddaddbbaaccccbcbbcbbdcddabbbbdccdabcbbdadadabacdbcbbdaaabddcccabbbbbbbcadccbacdbbbbbbcbaaccbbcbbbdccbbcbcbcddcbdacabcacbbcccdcbbbcaaadadbbdbcbcdcbcabcabcaaabdaadabbbbcadccbabdaacbaaaaacabcadccaabdbdadbdacbbaaccacdaadabaacdbbdbaabdbadcdaacadcbbbadacabbbcadccbdbcdbcadbbacabdacbbccdccadbdbcdabcccccbdbddcdacccdbcddcbbccdbdbbabbbaaacbaccbcbabcaacbbbbcacaabcdbbcabaaacaccdcdbaccdaddbcabacbcacbcabbbcbcbdcbcdbcacccbadbcdcaadaadaccccdcacbacbabccccdacbdcacbaccdaacbbbcbdbcccabdabacdabbbdccdcdadbdbdddbabdcaaabcbcbcdabbacccaddaabcaccaacdccdbabaacddbdcdaaadbacddcdadcdabdabdbbdcacaddcbccddcbbcdadaacadbdcdcbdbadabbdbadcbdbbadcccbcbddaaddbaabddaddcababdbdcbabccbcbddcbdcbcddbacbdccabdabccaaaacbbacdbbbdbacadbdaaddbddadbdcadabdcaddccdccadacabaddbddbadbddddbccabbcdccccacabcccdbcaadbcaabbcadbbdaacacaabacaababdddbdadadbddddbbdddcbdddcadddbcaabcaaabccaaccbadcddbdbdcbdbcbcdbbcbccbadbbbcdcddabcbccdccabcacdbdaabacbadbabcbbbdabbcaacbbdbcaabdabcdcbbabdddadbcdccdccbbccbbaccabadbcddcbcbacdbabbccdbabdaccadccabaacacccbcdbddddbaadaddcccacbdcbbbcdcbbaccaadabcbbdbadbcbbbdbadbccdbadaaaddcdccdbdddbcaaadaccddccadaaaccaaccccbacbcdccaadcccaadbccbacdaaccdbbaabbabbcddcccbabccdadaaccddbcaddadcdabaaaaddbbcaadcaaddcccabcbacabaaabcdbcbacddabacadaaabaadadccbadadbbcdbbdddcddbcaabdcbcdcacbabaadbbccccadbcbcdbbdcabdbaadadbbcabacadccdcabdbaabcbbabdbdbadbbbaaadabddabbaacaadcdaabdbbcddcaaadbbdaaacdbcbccbdcdababbaddccdacddabbddccabcaddcbacbcacaccbdabbdaabdbaccdbcdddddddbacbbdbabcbbbababadadaccdaabdbdbdbbdbcbbbddabcdcbaadacdbadddbbcddacdaddcbbdbcbdcdcbcbddabdbadbaccaccdaaacadccccccdcbcaacdbacbcadbccacadbbabdcbcabacadaaaaacbcccdbcaacdacbadaabdbcaacccbcdbbacdddaacdcadbdadaccccaaacdabddcadabddcdcbddbcdbadcddbdcdbbbdbbdaddabacdccbcbabaddbbacbdaabaacaadabdbacdaccaabdbabadddaadccbcbbcadaabdbdabbbddbcbbdabaadbcddadbdaacacdcacbaaaddcabccaadaabbbccababcdaddaadacacbcbcbbbadccabddcabbaabcaacadbccdbaddccaadacbbaddbabbadcdcbbbacccbdbadabdcaccccdaacbdbdbddaabbcbdcbdcabadcacaaccbcbdabdbaccbaabcacabdcbaacdbdcdbbcbdaaacbaabbdaddaaadaccbdabcabcccbbcdbccbadbcabddbacbbbbadddddbdddccdbbabdbabdddcacacadcdcbbbbdabcddbdaaddacacbdcdbdaaadacaccaaaaabaccbdbdabdcdacccbaccccaabcddbdabadcdbbcbcdbacddbabbbccdbccbdcbcadccdbcbdcdacdbbbaabbdccaaaabcdaadbbdcddbdaadabdaadcadcbbcabbdcdbccaabdadaaddcabdadbbbaadbbbcacadabdccdccdcccaddddbabacadcacbbbbbdbdbdabadbabbddaadbacaccbadbaddcdccbbcacdacbdccccadacccabaacaacbccadaadababaabbabadcddadbbdddcdbaccbbccbbbdadcbadabbbcbadabacddbaaadacabbddbdabadccaddbbdddaaaadaddbacbcccbcbdddcdaacbcabaccaacabdacbdacbdaaaddbbacbbdabcddbbbdcabaaabbdaccdcdcdccabadaaabccabdadcbdbbbbadacdaddbddacdbcdbacbdcaaabbcaabbcaaaddadccabdabbacdbaddaadbadccddacccdccdddccdacbaacaadbbbaabadabcbdddadbaacddadabcbbcaadbbdbbbbbcbddabcaddadadcabaaabbabadcccbacdbcbdbadaccaabcabcadcbcabadbcacabccbbdbdbabdbbdcccabaaddddadccbdbccbbaaccbcadaccddadbdbcbcaadaaabbcadbacabccbabbccddaccaccbacaddbddddaaaadbbacdddadabdbcccbccadcbcbcdbbcdbcddaaaddddbabdbabadcdadbccccbcbdaaadcbacdbbdddddbcacdbdcccabcdccbcaaaabaabcaabdaabaabcbbaddbdbcbcbccbbbcdacaddbdbbaccddbccdcbabcdcddddcdbabcacaccddadbccddddabccadcccdcccccacddadabdadbcdcbbbcbacadddcddacbcbccbcdbbdbaabccccbbbaacccbddcbcbddbacddcbddacaadcbddccadaddbcbababbdddcdcdddacbdbdacdbbabcdabcbbbadaacbcbbbdcadbcccbadbadbbbbcabddbdbbcccbacccdbdcdbaaabcdcaaaadbccabccbdbaddcdddddbacbdddacccdbdbadddbcddaababdbcbabbcdcbddbbdbbccbbadadbbbdadbdadcdacaadccbacdabacbdbbcdbddbacdabcabdcbcbbcbaabcaabbaaadadbacbcdabdcaabbabbabcbdabcdcbcbdbababadbaacdbabacbdddcdaccdacdbcddacbbacbdbadcdbadbbadaacbdcdccaaacdccdaccdbbabccbdbcaccdadaddcdacdcddadcccdcdccdddaddccacbabcababbaccacdcbddbabcbcaabccbdadccddcccaadcdabacadcbcbcabbbdbbdcaccccdbbbbbcbdddabadbbccbbbcaaaccadcbabbbdcdacaaadabdacaacbcabcbdcccaadbabbcbdcdabbbccbdbadbacbcabbdccacabdcacadabaaaabaddbcdddbacbcdadddbdbdcadbdccccbadcdbcbccdddbbcadbccbcbbcdaaacdccdddbbaacacaddbccaaaabbddacbdbdaaadbdbbbdbcbbccadbacbddadbbbcdaadbadcddbadaabbcaadcadcbaabdcbaddddddabadbccccabcccbaadccaadbdcccaabbbbadccabbbdacdbccacbcadabccaccdaccdddadabccdcacccbadcddcaabcadbcccccadbacadbcdcaaccadadbbdbcdbbcacdbdccddadbcadbdaadccdbbbdcacdabaaabbdddaddcccdadccdbcdacaaababaccadbbabbcacbbcdaaadbcbdddaacaabcacdbcddacdcacacdbcddabdbaabdccbdbbccaacaabadcaccdcdddcabaacdadbddcaadcdacbaaacdacdbccacdccacacbddcacbcbaacdbadbadccdddbccaaadaddadcabccadaacdcbcdcbbacabdddbccabbbcacabbbaccbcbbacddbacdadbadaadbbbdbaaddbcbddbdbdabcaabbdcbdbabcbcddcdcdabbcbddcabbdcaddcbdcacddcaadabdcbabbbbbddbbdbadbdbddbacdbbaddbbbbcacdabbaabacccdccbbbaabdaadaabbcabacbdacbaddaabdcbbcdabddddcbdbbdddccddabccdaddddacaccacaddbdadabcbaacbcdcbacadbccdadabcaacbcbadbcddcbaacdbbbcddaadbccbdbbcbcababdbabacccaadadcddbbcdcbccadccdcdbabcbadbdbcdddadbbbdabbdacaacdbcdaadadcdabccbaccabcacdaaabbcbdcbcdbaaddbdbdccbcdbabcabbcdcddaadddbcababbadaabcbddcbdbbbaaccabdadabdbabccabdbaaccbdbcdaadcdabcdccaaaadccddaacdddaadbaaadbbadccddbdcabcbaaaaaccddcbacbadacbdbabbbacdbcdcacabadcbbddbbdccdcaddbaaddcaacccacdbaddadabbddadbcbddaccccbbddbdbcbdddbbbbccaabcaadbcdcaadcabbaabacaaddaaaddabcccadbbaababccabaaccbccccababccccacabcccdaaabccadddbccbcbddbdcdcbbdaabacdbabcbabccdacbcbabcdbcbaabdccbdddcababdabbaadbbdcaaaacababcddbdcddcbbcadadbcdcabacababbddcacabcacbcdbdcdabbddcaabcadcbabdbdaaccdaadcddbbbcadcadcccbdccacdacccbdcabdbcbababaaadadbddcbdbbbadcbcdbcbcdddbdabdaacadddaadaaaccacddcdbcbadabdccbaadadbdadaacdacbcbadbaaabbddbbcabaddcddcdccaccbdbdbdadcbaabdbbdcbacbdccadccaaddbcbddaddddbabcdacdaccdcdcaaabcccaddcddcbacacccbdbdbdcdbdcdcacddbbdbaadbcacccaddcababcdcccaabaabbccbacacacabacccddbacbcddcddbdcababcddbaabababbcbbddcaddccbabdcacacccbbccdbdbabcbcaacdcdaacabdaabaddbdadbddddbdbdbdddadabcadcbaccadcbcccbdddcddccdaddcacacddcaabdcdbbcbdbcbabbbaabdabaccacddbdbcdabbbbdabddcabcaaacbdbbacdaaccabdcabdabbccccbccbdbcddbadbddbdaddadcacabdabcdbababdddbdcadbbdadcdcddccdccdbacddabbabcadbbcbddaddabddbddbdcbbcaaaabadcababbddbddcdacdcdcdaabbaacaaadcbaaccdacbccdcaababdcbbbaccdbaddcacdabcbbcbaccbcadbdcccbdbcbbccdccbaddcbaccdbdccdabdbaaccabddbcdbbcbadcdcbcccacbbbdabbbaadabadddabdbcaccadbdbddbdabdaddbbdbcacabadcbccdbddbabcbcbaabdcbcdcaccaaccbbbcadbbbcdcdccacabdabbbddcdbadcdcaabbadbbccbdcaccdbadacccdadadaaaddbadaacdacaaddccabcdcadbdcadbcbacaaabbabccbbcbbbcbbbadbccdaabdcccddbcabbaabdaadadabcddcdaddadccaccdcbacddadaaccabcbbcacdbddbaddbbacbddacdadcdcaacdbabddcaadaddbaccbbdcaccdcaaccabdadacbcacdddccddcaadaababddbaddcbdcacadbcccbcddacbbbaadddcddadbcaabbcccacaccaadcbddbabacaccccddcdadccaaddccccaccbadacdccaacbbdaacaddabbdcccdabbdbacaacbccaccacbaccaadaddaaacdaddaacddddbacdbaabadcbdabadaccbcaaababddddcbdddccdcaabdabbbccadacccbaddcdbadbadcbacbacdaccbaccabaadddacabbbcacadddbdbabadccdabbadadabccbbbccbaacacaccacacccbcbccaaabddbcadccbacdbacbaddddcbdcccdbdbcadaabbdcccaccacdddbdadbcbcacbbacccdadbbcbcbaccddbcdcdccbbbdbbcdbcacbcaccbdcccbabcadcbabacbbdaabbabaccabaddbddcabbacdadbabccadbcbdacaadcbbbbadccbcdbbcdcdcbcbaadaaacccddcbbdadcaadadcdbcabbaaddbccaadccdcaabaacbcbdcdbabbccabbcdcdbccddbcbaccbcacbabbacddabccbdbddabdabbccabdbdcaccccddbcabbabababbbdaadcaaacaabbccbdcbaaccdcddbbaabdbbaccadbccdbbbbccadbabbadcbdcabcbddbdcddcbcddcabacdadbcccbdbdacdddbbbacdccccdadccbdcddddbabdaadccabddaaacdccdbdcdbbbdbbacdbcbdbcabadaabcdcaacabbdcacbdccddaaaccdbbbdacaccdadbdbaaacabdbdcbadcdbbdbcdbbaccabddcacbdacddbddbcdccacbbdbbcbabbdadaaaaacdaddddadaaccbdbccacbbdcabcadcdbaadddcbddaadababacbbdbacbbbdcdabddabccdbdcbbcbdbdccbbdacdbdbbacabacabbcacbdaacbddbbcadbcbbcbabdcdbaabababaacabcadbbbdadbdcdadcbcbabaabdaaacccbbbbbbdaacccaccaadbcabddaacdaccbabdccdbccccdddcdcdcbaadcaccbacabcdbaaccccbdbcdacdaaabcdddaaaacabcbabcdcaaaddccccdcccbacadcaccabcdbbcdbdabadbddaccabcdaaadacbdbddbadabddcbbacdddabbbccaacaabbbabcdcdadadadbaacaddaacbabcadccbcbdbaddbbbccbdacbdaacacdcabbacdbcadaccccaacdadcccaabccddbaaaabacaadccccbcabcddabdccaadacbdaabbdbabaaccbcccbacddbabdddabacadcbaacadddbbcbcacdadacadccdcbbbcccacbdbdbdbbbabaacabdadaccbdabcdbbbdcabcaabacbbcacaccddcabaadbbbcbadddbddacdabadddadacbdcccadbbabcadaddbbbbdbbaadccacbdcdaadbaabaaacabdbabcbccaddcccdadaaacbdbabcbbdddcdcaabdabcdcbdddbddcdcdcbcdddabdbaaabdaaddbcdbcbddacdbcddadabbddcabcbddacdcccdbdcdcccddddaccdbcdbdcdcbdcbaaadadabcbbcbdcadbaaabcdbcbaacaddddbaccacccbdaaacdcadbcbccacddcadbaabbdabbbcbdacddcbdaaccdbcacdadadaabcaabbaddcababbcdccbddcbdccaabaccdcabdcbcbcdbabcdbabccdcadcccadccdbadbcbdcddacdaacdbbbbbbcdcabddccacbcdbcabdcccabccbdcdbbbdabbbcdccacadbcddddbdcbcccbcdcbcdddaabbbdadcacdccbcdbbaacaccaddddaacdccabdabdddbdbbdacabccdaabbbdaabadbdddcdacdababdbadddaddacccdcadcadacbaadbcbbbbddbbbcaaabbbdacaccdabacbcccdabddbbbabbcddbbbdddaaccabacbadcacdadaccadaaccdaaccccbcaadbdbbadbbaddbbdabbbdabcbdaddcdcddaacbcbaadbdbbadcddcabdbdbcdababaadaabadddbbbcdccbadaaddadaadbdbacbddbaccababdddaaadbccbdabbbcaabdbbcdddbcbdabbbdaadacdabccadcabcbcbadadbbabddacbcacdcdbcadaabdbadbddcacdcbbbbdcabcddcbccdcabbbacccbdccabcadaccdcacdaabaccbbcccabcdcbdabbccabbbdccbdccbcccaccdbacdcbdbacaababbadaabcdacddaaccdbbbcbdcccccbadcadbacbbbbadaaaddbabcccabdadaabcdbcbddbaccccccbacbaddabbdbacacbdcaddbbcbbaaacaccdcbacbcccddcacbabcbcbbddccabddddcbcbddcdadcabcdadadacadddabbbaddbdbbdaabadddaddcbadacacbdaabcaacccccbbcabcdbdbbacbadbddaadcbaddbbbcbcaaabaadbbbaaacbdbdbaabdabcbabbcbddcbbdcdbddcabdbbdbddbdddccbbdbcacddbcccbacdccddddacadbaabadacddabdbcbddbdaacccbaabaccaabadabcddbadcaddacaddcbddbabcccaacdcdcaaddcccaadbaaaddbdabdadacccadaacddccbccbdddbcacbadbaabcdabbbcddddaddaabacbcbacaabcccaabbbabddcbcaaabbbdbbccadccabddcbbaccbaddbcdaadccbbbcbadcacabdbcbbaccdadbcbaddadcabbbabadcabbbbacaacdbcaaddadbbaabbbcacdbacadcdddcdaaddccddadbcdcdcddadaddccdacdddcbbdcbcbcbadbbcddbcdbabdabcbdbcadabaddaddbdabbddddcabdabadcdacbdacccbdbccbdccbbdbadadccadacccaddcbccdcdabbbcaacdaadcdadbcdccddbbdcdbdbcdabccbcdacaacccbdabccbdacbddabbadcdcddadbdcbacbdacacccbbadbaaadabcbcbddddcdbbccbddccbbcbadacdccbaaaddcdcacbcbabbdcaaaccdcadabcdcdcbccbcddadbbacdccaadbbbdbdabdacaddbddbcddccbccdcccdcddadddcdaadbddbbaacbcddcdcddacabdabbbdcacaccbdbbcdabcccbcbabdcdadaacbaaaacbcdacdddcbacaabcdabcccdbbcdcccadbacbdabdadacdcbadccdccbbdbadacdadbcaddacdabdbadbddadcbbdbddbbccdbcbddbcbdcaccabcadbdbccddbcabcbacddccabdcacabbccccdbbddbdbcbcadbbbddcabcacccdbbadcacddcbbbcdaabcdaabaadddbccbddabddcbdbdabbabbbdbbdbddcabacbdddbaabddaddadaaccbcdcaddacadacccbcbdccdddccadcbaaddddddddcdadabaaadaabccadcdcbacbdadcdcddadbbacadccabcbbcbbddabaacabacdaabbabbdacddcacbabcbdabcdacaaaddbcdbbadadcdbdddabaaddbccbbdbaccdddbbccddcdbcaabdabccabadaacccadabbbdcdacbdabdcdbcbabdbadbdacdcdbcdcdaadaddadadadcbbccdadaddcaadbccbcabaaadcccdadcabdadaabdcbdbaadbadbaaccbadbabaacdadadaacaacdbdcdbdbaadbcbbcdbacddaddcabbabcdbbbccbcbcbabdcddacaadcddbbbacddaadbcadadbaddacdadbbacaaccabdaabccabdbdbbccbbdaaddcdaaadcadabcbacacdbbbbbdccababaadbacacccdcabdccdabbabcbabdabbabcdacdbbbabbddadcadcbcacadddcbbdccdbbccababccbbdcabcabbdacadaacdccaddbcbbbadcaccacaacddaacbcabdbbcbdbbbcdcabdacabaddcabaacbabbddccdabaaabcbcaaccaaadbdacaabddbbabccdcdabacabbdbacdcbdaaadbbbbaccaaabcccdbdcddaadaddcdccbcdcbddbadcadbabdcdbadaababbdddadbbbadcbcaadaadabaacdcabbddcbcbcaccadadcbacddacddcbccdbbdacaababbabcaabbddcbdddccaaddaadbdbacdcccdadacacdcbddcaddacadbcadccdccbcaadccdbbdabdbcaddcbcadbaabcaacdacccbbadaababbdaccbcdbbccddacbadbcccdbabdacabccbbdaadcccaaaacaabccddbbcbadbdaadddcdabcabbbdaaadbddddcbabbdbcbddacaccbacbcadcdccdababbcdbdbcabacdcbcaacacbdbadcaccacdbdbcbbabdbbcdabddcadcbbcdacdaabcacddbbaabaadbcaccaddcadaadadcbadcbbbbccbabcbabdaaaccbaacaadbbdabccbbbbababcaabbbccddbdbbcbcddcadbcaaddabdccdccccbabcccdabdddacaaaadcbaadabddbdacbbdccabcdabbaccdaadaddcadbdcbdddabdbddcccdabdddcccbadbadbacaacadddabaccaabccdcddddbadadbaabddaaaadaabcaabddbcaacdbcccabbdcacaddccddbcbadacdbdbcbcdacbbdaadabaadaddbaddacadaabdbdccadbcbacbabcbdbadcbcdccbacdbdaabdbcacabdcbbbcbbcadcbdbcacadadccbbcabcbbddcacccbdcadcabcadabdaccdadcaacadabaccccaadcadaadbcbbbdbacdcbdcabcccdddaccddccbcbbdadcdbabcbbaadbddbbcccacdabdddbccccbbddadadacabbdcccdbbaddcbacabdbcbdbacccddbdcbccbdcdbbcdcdccbbbdaabbdaaccbcbaddaaaccbbbacabbabdadadbacadcbddbcdcdcddabcdccccdbdccdcaacbabcacdbacadabaaddbbcdddabbbdbabbddbbbdacdbbbcccbcdbcbbcbdbbabaabcacbabdcbaababddddbcddccbcbdbcbabcdcbaaadbdacccdcbbcdbdabcdaaabaaddaaddaabcbddabaaadccbadcaacddcdbcbbbcdcabdccdbcbbbcbdbabacccabdabdcdadccabddbdddbccbccaadbddccbabdadbbccddaabdaccbcbbcaaaaabcdcabcddbcdcbdbadaddbcdddabdaadadadcaddcdacdcbadddddcbbaddbcccdbbdbcddacdcddaccbbdbaabbbadbdbdaccddcddbdbacdaabcdccbaacaadabadccdbaabbddcdaaacaabbaaccacdcacaabdbacacdcaccdacdcdddaadcdbbbddddcdcaccadbbbcdacbbccddadcabadaaddcdccdbcbbcabccdabbcdcaddcbcdbadaacbdcbcadaacdddadbbaddcbcccbacacbaddabdcccaabcbadaccacbaacbbaaacbcadbbbbdccadbbddabdcacbddcaadabcbababcaccaabcbddbcdbbdddddccddbdcbabccababbbcdcbdbbaaabcadbcdcbddcabbaccdddaabcbcabcccadbacbdabbaabdabadcdacbbacdadbdaddbaacbbbcdababdabbabbabababcbccdcdbbbbbcdbdddddccbabbcbcbddbddabbaacdcaadabbaddddbccbbcccabccdaadabcdcadcacabcaabaacdbcadadddaabbdcbbabccacbbaccdcdccdcddcadcdaacbbddabaacbdacccbddbcbadabbbdacdccbaabddadddbcacaabaadbacacbadbcbcbbcaacabaacabccccbcaddbcddaccccbddbcbcdabbddacacacbccbacaccbacadaabbadddadbdcaaccbaddbcdbdcdadbbacccdcdcbababacbcdbbbdcadddacdaccdbbabaccdddbbdddbdbcdcaabddccaddcdddcdabbabdccbddcaccdbcbbcdbaacdbdbbcdacadacdbadcbbdbdaccddbcaabadbdcdbdbcbbddaaccccddaaadacdbbddcbabbdbaaadcbcadcdcddccacbccaacaccbbccdddadbaddaacccadbcadaabddaaaacdcdadbcadbdcbababcabcabacdaccdbdadbaadabbaaccabaccdbacacaaccaabcdadabccbbcccdbccbbaacdaabccacbcccdbcbabdcbcaccbcaadaadbbbbaacccccbbacbbadbcccdccbcbbacdaccadddabdcbacdaaaddcadccacabadacabdaaaabbacdddadbbbcccdabaaccabbbbadadbcabacaadbbcadcbaddccbcacababadbccdddccacbbcccacacbcdddcdcbdaadcababdadbaaabbaaadacdabbcddcbbbddcccbdcadacbaaabbbbddcbacbbababbdcbbdcdddcdcccbaabddabbdcdabbbdcccbaaacdabcaabdbcbadbdcdcadccdcadbbcdbbcdbdbdbabbdabadbbbdddbccaacbaacdaaabbdbabdcdbdadbdadbdbaabcacddaaabacdcaabcabbddbaadbdbcdbdaaacbbdadbbdccbcdbbbcdbcabcdbacdaccacbcbdbbdbdabdccadbdbcbcbdbaaadbdcadabbbbdaccdcccacadbdbacddbdacbbcbbddbcaaabbdabcbacbabbbadcbbddbabbcacddbbaabbbdabacddcababcccdbddacbdbabdbcbaadcabbadbdccdcaadbddaababbaaddcbadadbccbdbdbddbdaaaadbcabcdcbdcccbaacaadcaccddbdccccdcddcccbaadcaabcdacdadcbcbccbaabbadbcbdbddaddbdabddbdadaacdcdccabbbcabbdbadbccdcdbabcacbbacbcddacacdadcccadacdbcdacddcbbcbaabcdbbabdabbadbdabbcabddbdbbcbbacbddbdcbddcbacbbdaaccdabddccdabdbcbcdbdddadbcbacdddbdadaaabbddcbcacaadaadbddccbbbbcaadcdcdbacbdbababbdcdccbaabcdddbddbdbdcbadacdacccbdcbcdcaaacbabdbaadabaadbaabcacbadaccdcaacabdddabddcdcddabdbcacdcbdabbbcdccbbdaaaddadbdcaccabcddcdcdaabcccaacaacdcbddbbdcdcacabbcaacbddccbabdacaabdcaddacabaacbcbdaaccddbbaabbcabcdbadabbbdddbdabbbbcdbadcbcdbadcbbadcbacaaabacbaacabccbdcabdcddbaadbccadccbdadabbcddbbabbcadadabbcddbbbbbacdabbdaaccddbdbdccdbdabcadbccdcaacccadbaccccbbabbacdbbbddccdccdbdcdbbcdbcbbcbdbbbdccdaddbbababccbbddcbaacdabbacbbbdacdcccadbcadbbcccaadaaacdccccdaabdccdaaddcccccdddabbbadabbabbaacbdacadbcbabcdbbbdacbbabcabcdccdbbdcacdacdbbcacbadccaccdcacbddcdcdaaacacddcadacadabddbaddbdbdbcacbadadaadcacbbbccbadcbcdbdbddabcbdbcddbcaddaadbbbbccbbbbbadaacaddabdaaaacacbbaaacacdabdbccaddbacbdadacdbddbcdaddbcdbccccbaadbcdcbacbaccadcdcdbcdbdacdbccdbdbbcccbbdcbbacadacabdadddaccdaddacaabdcbbacdcbcbbaaddaaadddcdcdbdaabcbcadacacbabcdaddacbdacdabbaadbccdacdaadbbbccabddacdaacadcdcbbacdbabbaabaccbaccaaabadacdccdcbacbbadcdddbabcbcacdacdabcbacbbaaaaabaabdbdbbbacbcbaaaaddbcddcbbdaaabaccbadbcbacabbcccaaaddacbcbbadaccbdbbddaadcbcdaabddcbaccaccbbddaccacbbcbbbcdbccdddaacdcdbbdaabcaabdbcdacaabaddbcdaaccbadcbacdbcbccbbacbcbdabddacaadabbbddadbcabddbccbcdbccabbdaccabbaddaabaacbdaddaddcbccbbbcbbaaccbaccbcdadbccbcabdbaadbabccdaddcaddccbddbdddbbcbdaccacabaadacbdcbcadcdcdacbdcdcbdaddabddabcdacdccdcbadcaacacbadddabccbcacdbbdbbabdbcaabdbabacaacadcdbadcbbdcaacbabbcadbaaddaccbcbcdaabbdddcbbaabccbdacdcabcaadbdddbcbddabcbdadbbcddabababacbabadacccddcdaadbacbdcabcaaacdcbcaadbcaabbbbcbbdddcaddbcacadccaadbcaadddcabddbadbcbdcbcbdbadcbcaddcdccdbaacccadacdabadcababdbbbdbbacbcbbdaababbcaadccdaaddcabbabaabadaddbbaadbddbdbccaabbcbdddccbcacadaabaaadbcdadabcbabcabbbbcdbdaccddadcaadaacddabdcdbdbddcadbbbdcadcddaabdbaadbddacadbdadcbbdabbaddbbcadbbbdbcbbbbccdacdbbddcbcdaadaadacddbbaacddcacacbcaccabbcaabcababbadccabbcbcccdcbdaccbaadcaaccbbcbbbdaddacddacbbbcddadbcabbcbadaddbdddabdaccbadbbccacddbccacddbccabdbdcbaccbbcbcbdddcdaadaabbaacacccaaadacbcdcccabccbaddcdddcadbadbdbbdaacdaacbbbdbadcacabddcdabdabccacbcdaaacddbdabbcdbdabcddcbdcbaabaddadddcbabdcaddadbbdbbbcabccccdbcadcdcaabcaddbacbadbbdcabbccbccadbaacbaaadcbaaddabadbdbbabdbcdabdcacdbbdacdbcadadbadaadbacacabccaaccaaabbcdbcdccccaacbabcddddcdabacabddddbbbccbdddcdabccdadacbdaabbbbbadaabbaaddbcddbabbbcbcbdddabacaabcbdbadabadcbaabdcabdbcbcddacddbaabcbbaaadbcdcaccabbcdbdbdcbbabaddcbbaaccbddddcddaccccabcabbcacdabaaaccdabaccddbbcbcdcdbdabdcdacddcdbbcdbaabcdbbacbbacbddaccdacbddbbbaccccccbadbbacbaccdddcadcbcabbbbcbaacaddccaabdbbdbccddaabbddabaaaadbaabdacacaabaccccbbacdaabdcbacdbdbacaccddcbbcaaccbcabdacccbcaabadaacbcaacbcbcbdaacbbbacacadaabacaaadcbbabbcddcadcaccadbccabdbdbabcababdaaadbacaabdbdddadbadcdbabcdcacbdadcbdabddbdaddccdadadabacbaacbbcadbdddcbdcbaadababbdbcbdbcabaaacdbacdcadadaadcabcaacabdbbbbdbcdbabbcbcacdccbabcabadbdadcdbccbbaccdbbcbbcabaadcbdaadcaacaacbcadadcabbccacddbcabddcaabcabcaadcdbbddaacbcbcadadcbdcacbbbbdabdacacbdbaabdbccbcdaddcbdbbddbddbabbbbbadbccdcaabbaacaadbbdacaacbaaabcdcdbcdccacabccacadbacadccbacbacadbbaddcabaccbddcdabccaaaacbbbdddbabbabbbadaccdabacbdcccadcaaddddbdcbbcbaabdbcbcdcabddcdabcbcdcdacbcbabbadbcdccbadbaabcaacdcdbbaaabdcddcccbcddbcdbbccdadccaadcdccbbbcddddddbdcbdaabcbcdcdcbddadbcdcbbadaddbaddadacdcbdcdbdcdddddcadbbaabccaddacbcbdddadbdbcabcbaccddaabbbdccbbbccdcccdabcdbddcbbcacaacdcdbcaccbbadddccdbdbccbddbdccaaacbddbbcbdabcabddadbcadbdcabcbadccdccddbadbaabbbdcbabdbccdbaabcbbaccdbabbbdadbaddcdbdadbaddadbbdcabcddababbcaadbbcddaaddabaaccdbdbbdbbbcccbacaacabcdabccbdbdcbacdcacaaccdaabcacccdabcdababcdaaacddccdbdbbaaadaabcacaabcabdbbadadacbbbbaacabbdddcabbbadbdadbdcbcbaaadaddbccacdbcdbbdcdddbabdcadccdbbddbccabcddabababbcdabbdcabdcbbadaddaadbbbaadbacbcbccbabcacbbbddbbcdcbbccccdbcbcbdababadcbbdbbbacdbbabaabcadccddccacddbcbbddacacccabbbcacacdcdaaccacbaccdabdabadcbcaabbbabccdaaaccddbddaabdcbccadbbdaaccdbdaabdddddcabdddddcccabbdddcddcabbcdcbddddbcccbaaddadddabcacdcabddcbbbcddcaadbabdbadbbaaacdacbdcdcdadabbbaaccaddaccdcdccdbbabcacbdcbabbddccbddaabaabadacabadccaaabdcadaacadccdbabdaadbabcababdbacadabbbcbcdcaabacccacaaacdabdabbcbcacacbbcaacbcbdbbbaacabbbbadbcdbaadcbaddbcdcdabadddabbaddadadcbaccccbbacabdddbaaabbbbadbacbbdddacdbadccaabaccabaabccbbaabdbaccdadbbaddabdbbaaaabbcacccbadbaabadaccabcaadccabcccbadcddadabbbcabcacdddadacdcbabbcbdacabbadabaaaabccaccaabcaaabccddcddcdbaacaabddcbcbdbdcbddcabcccbccddaabadbdbccccabdabacacddcbaabcddabdaacabcdccddadbdbbbccbbbdaaddcabcadcccacbdacacaddbbcabdbbcbdbacacdadaacbacbbabbcdbaaccabcbbddcdcdaccddbbbbbdcbadabbdaddbddddbcbbcdbdcdbbccaacdacbcdbcccddbbccdbbabcbacabaabddcbbccaaaababaccbbcbbacaadccccbbdacbcabaadbddacdacbacdadabaddbdcaaddbbbadacabbabacbdacaccdadadaddcdadcddabdcbaccbaccaabaabdaabdacbdaccdabacaaabccaccdcbdbcdcacbcdbdbadddacbbdccbdacadddbbabbacddabadccccdbabbbaaacccdacccbabbbaaaabbcbdbaaabaaccbcdbdccaaddcccbcbcccbccbddddbdbccadabdddcadacbcbbcdadaaaaaabdacbddbbcbaacabbccbcdabcacadbcdcaadccaacbcdcaadcaaaabbddabbdbabccdcaabacdacbddcabbbcacdccddddacacdbbbacacdbbcbcddcccdbcbddacdadbbddcbabcdaaccaacbabbcdaccaddabdddacbbdcbdadbadadacbccdccbbdabdbcdbcbacadabdbbddadabbcdcddddcddadbaacbcddcaddbdabdbdaabdcabdadcadddbaadababcbdbaabcdaacabbccacadabbbdbabbcddbccaaabdcabdccddbbadbdcddbcdcdbdacdbcdbdcbadcbdbaacccbdddcdbaddcaabaccccabbcababcbbcbaadbcdcbdabadbcbbbbadaabccbaabacddcabacabdbadabbddbaaacbdcbdddcaacabddaccadbcdbacaddbccdbdcbbcbbcabbbaaaaccccdaacadcdaadaabbccbacdaabadcacababababcdaccddccbadcbbccbbdcabdaacbadcccbbcdabbacccbdcabaddbcdabccaadccaccdbbbbbaacbddabcbbbababcabbcaaadbbcdccdccddbcbdabbabcabcadaacdcccddcdaaaddcbacbabaddbcadacccdbcbadabcddccaadbdcdbacaddcbacdbabbbdcacdcdbcdbcbccccccdccbcdbadbbacbccdbbdbddbcbddccabcbbabcdcbaaabaccaccbddcaaadbaacacbbadabcbdcbadbdcacdcbccbbcdbdadcdccadbbbbbabcdddbcbddacbdcdaccadcaaccdcbbaacacdbcdabbacdbbaacdbccccddddcacdacbcbbbcbadccaccddcbacacacbaccccadcdccddcbcbdabdcbcadbccbbbdabbddacbadaaaadddbcabababaccabdcbbbbdabdbdbdaadccadbbccbcbdacbdbbdbbbbaccdbdcbdcddbdccbdbaaccddaacbbccccadcbdbdccacdccbbbbaadcdadbdbbbdabbbcbcbdbbcbbcaacacbdcdbdddcaacbacdaabdddccababbbcdcabdbcbadddbddaabdbaaddbbcdbbbdbcdbbbbbadadddcbbdacadbcacbcabccaddcabcccdcdbbdcbbbdccbccaabbdddaabababbdaaaccbccabcdcacbaadcbdaccaacacbccbcbabcdcdcbaabcdbccbbcdcddaacdbacbddcdabcdcccaccadbdbabdddaabaddbdabccaaabbaadcadacbdadaddcacdaadbcdacbaaabdabdaabcdcadbddcaaccadadcbbbdbcdaacdcdcadaabadddbddaddcabcbbbcbdddadbdcdccbbdbdbcaccbcaddacddcbddacdaadaadbbcacaaadbbccbaabacaabbcbacbbbdabccdacbdabacbddcbbabdaddbcabadbccccddbcadaaddcbbcdccacacacdacabadbabcbdbcbbadcacbccddaaaacabcadbbbdabdccdbdddbaddcbcdddddbabbbddcaddcdcbddbdbdabbabadcdccacdacbbdacdaadccbabdbbdcabdcdbadadabbdcacbdacbbbaacbccdccadabbdaddbccbacadbdadcadbbabaadbcdabbdaacdaddbbaacbabadcbbaddcdcacdcaddcbdddddabadbbbcdadcddbaccdbccadddcdbbaabacacdbacccbaabaacdbbcbaccccbcbdaacacbacccdabdbaccaaddbdcdbdaacaaacdccbbdccadbddcdccaccacbbbacddcdacbaccabcccbbdabacdcbadcaaddddcdbcccbdacbccbdaddcbbcbcbaccbdabacbcaabbccdaddabcdbddcbbabccaccddcbbddcbbdbbdccbbdddcbabcbaddbbbbdadbacadbbabaacbbaacaacbacccdadbccdcaccdddbdabccddacbcadcddabbbaadccbbdcabdaadcadbccadabddcaaadcdbddcbbabbacadadacabdbccdbdaccbbbbbabcbbbabccacbabcdbcacadbcccdddcdddaabdababbcdbbadcbaddaacdbcbcaddcbbcbdcccddbbaaaacbaadcadbbbcddcdddcbddbbbbaadaabcccddbddbcbcbabcbdcddabcbbdbcdbcacbddcbbadcaaabdbcabcdacdacbabcdcaccadbdcccbbdbadbbccdcaadacabdcdbbdcbbaacacdcccacbcaaaaccbabaabcabcddadccacccbbcbdcacbccabbbbcabcccadadcaaddcaacaccdcbcccccdccacbbbbbcbcdddbabcbabbdaadabdbbadaadbbbadbdddcdddddacaccbddcaaaadcddbcccdcdcabaccbccdcdadabcdddaadcadaccdbcabbbdbacaccbdcccbcbbabbbcdcbbabaacadddcabbbaacaaccdabccabdadaccbdddddabcbcdaacbadbdacddcbdcbcbbadbccddaacbcbcacabdccaabdaacddddaadabbadcbaadbdbdcaaaacdcbaaddbbcdaccadbdcdddbaacabddacbdcdcaddddaccbabdcdccdccbdcdbcadbcdccdacadcdbbddabbdbbaadbbcdababbcbbcacbcddcdbcaacbddadaddaabcbdaadcaaccddabbccccdbbcbabcdddbbddcccacacdbbddddcbdcdbdacabacdddaadbcaacdadcaaaaacdcacdbcbcaccbccbdbdcdaddbdcadacadbcbddcadcdcacdbcabbddcaddbcbbaabadddccadadadbdbadacbaacccaabbaadcdcdbccaaaddaacccbbaccaadcbadccbabadbcbddaabbcbbbabcbbabdacbdcbdacdcadbccdabdbdbdacacaacdcbbcaabaccadaddccbbcdccadaccabbbbdddcadaabbbcdddacbdbdbdcdabcbbdbcaabddaadadcacbabadbdcabdabbdacdddccbaccaaacacbbbababadbacdcadbbabbcbddccdccabacbdabdcccaccaccabbbcbacccabdbaaadbdcdaaddbbddacccbddaadbdadcdcdddadbdbaccabcdabdcadacacdcccbcccaabacababacaabdadccbcbdbbdadbddaadbaccadccdbdaccdcabcdaacbabcccaacdaddacddadaabadaddaaacbbbbacdaacbddaadbbcdddaadbcbababbdbdccbaabdacbabdacaddadbdbaaabaddbdabaacccbdcdbcbcabadabcdcdbdddcccddaabdbcbcddcacccdcbbadabccbbdccadddbdaabcddddbaadbdbdadbcbbbdcbdcbddbbbacdabacaaabbcdbdbcbbbcaabccbbabdcacacbbbcabdbdbabccbdcbdcdbaabbbadddbbdbacaadddccbaccaccdadbcdcaaabacdcdccdaaabdaccadcbabddcbcacabbbccbbbbbcbcaddddbcaccbbdaadbcdabdddadbcddacdcbaadbdcaaccadbdcacbdccacabdabcadbccaddbdbabdacdbdcbddbbbbcbcbccaababadcddbdcbaabaccaabaabdcabdbacbcaccaaddbccadccccbbaaddabaabbcbbdcdccacadabacbccbcdbaaabdcaddacccbdddccdacbcdcbabadbabddadbbddbcbccdcdcabddaadaddbcacdbbbadccbddbdcdaaaaaabcdabdddbdcaadadddbdcabadbbcbdbdbccabbdcbdadbaddcdbbbcbbddacdadcdbdabdbcbcacddbbbbbbadcadcadcdcadaaccbddcddadaabaadaddcbbcabaaaaabbdbacadadcbbcddcccabdaabaaddaadcddddbbaabdcbdacbdabddcdaadbbddcddcadcbbadcdabccddddddccbbaccbbbddbdcbadbbaaddacacaadadcccdddcbbaaddaaaacaaaabbaddaccdccaabbccaaddbaabaaccdbccaadddbdaadbacaaaaadacdbcbbbacacbdbcaabcdabdcdcdabbbbddbccadadddbcadaacdacbadbbacabbbbaccdbdcbdbbdbbabbaaacacabbaabbaaccbdcababaacbdacbbdcdcdbcaccddbacacacbbaccccdabccddadbdbddbdbcbbbcacacbdccadaddacdcabbbcabdabcacbdbdaabdaaacadccdcdbcabddbdcddaaabbddddbaabdddadacdccabbcdddabcabcdaccbdbaadddbcabadcddabbcdcdabaabdcaddcdddbcacaaaaddcddddbbbccddbbcdcbcdcbccaddabcaddbbaadcacdcbcbabadbddbcdddcbadcddaddcacbcccadcddadacadbabdbcccabababcbacdabcccbbdbcaadabbccbcaacdbacdbaadacaaccddbacbccbbcdaaaddbcdadabbbbbadbddabbccbdbbcaccbbcabcaccbadddacacbcdbadbacbbcdcbbbcbddcddbcbbbbcddbcdccdbbabaaabcbbddabbdbadbbbccbccbbacbccaabbdadaabbcacaaccbbbadcabbaabcaadcabcbcbcbcabadaadddbcbdbcbdcabdcddccadabdbdbdddccabaaddbcdabddcdadcadbccbdabdddbcbcccaabacbadbdcbaccbacaadbaadadbabaacdcacbddabdadcbcdcdcacccaaddbabbcaccacabbcaaaacadadabdbcbdbacbdaccaccbcbcdcdabbcaaddcabdccbcdadddaaddaacdaacbbaabaadbacddcbbdccdcabdcaccbaaabdabcccdadabaaacaabbaaabbcaababdcbcaaacaaadcacabccbccbcccdadbbdbbacdccbadbbabbbccaabbbbdcadddcdcacdaabdcbbabacbdcddacbacccbbbccaaaddbbbccdadbdcacdbacdccabdaccdaadddacbdcdcdabcacdccaabadacbacdddacacdcdacabbbbabbacbaccacdcaadcbaadbdcbdaccaadbbbadcdddbdbbbcacbbccaddcdcbadacdbcadddbccbcbcbbacbcddacbaddbdadadbacaadaddcaaccbabbcdbaacaadaacbbdbdaccbddbccdcbbacdcadbdbcaadbddccaddaddddcadcdbbbadcbcaadadcaccdcbcbdbcbdddadbbcbdbccddcdacdcacbbadacdbddddadaaaccddbbbbdaadabcaccdaacdacdcdabbaabcdcdddbdabacbdbbabcaaccaaadbcaaadcadacdbddbacaaacacbbcdadacdadbaddaacdadddcbbcdbddcbbbbacabbaacdbdcadaacdbabcdcaadabbbbccdbadaddddbadbacbddaddccdadbbdcdcabbbadcdccacaacadcaaaabdbaccbccccdabccdabcaddcdaacdbdacbbaddbddbdbdbbdbdcbaadcaaccbacabdacbabdbdacaababdaaaadbabbddccacddabaddacaacddbacdbbcbbabcdabdbcdaddaababbbbbbabaadbadaccaccaccdbadcaddbbbdcacdcdddabaaaadccbbdbcabccdccdabccdbbadbabacbabacbacadadacdbcbcacdbdadbcddbcddccccdcaaabcaadaddccbcccaadcacadcddaaacbccbbaaabcbabcbcbadccdcdacbddddcddcdababbcdddcaabcaaddbcbbaabddcdaccbddcbaccbcdddccbabbabdbcabbcadbcbbddbbccaaadcabbaddcdbcdbbddcbbccabbcacacbabbcddaacacacbdabcbdbbcdaaccccdacbbdabbddbabadacdbcdadcdcbdaabbbccbdcddcccccdbcabadadcdcaccbdcccdddcdbaddcbacdbdaccaddbddcdaabcddbbadcbddbaddaddabaddacbbcbaabbadacdabdddcdbadccaabdcdccbbbbcaabbcdacaadbaccbcbdcdbacadcbbccabdbdacbababaccdcaabbcadbaabdcacbccbcdaabbcabccdbbdddbbbbcabddbdbbadadcdccadbcacdbbbdadccaddddcadcdcbacbbbaaadbdbacddbcccbddbacdddccdacccdbbdacbdcbcbcabdbbdbdbddbabbdcbadbbbccaaccbacbcbacccbbadacabbabdcabbdacbacbaadadcccabcdcaaacbadbcdccbdbbaccbbbccabcdbdbbcbccbddcaadbccabddddaddababddcacbdcbdcadababbdababbaaabbcbcdcaddbbdbbbcbadadbbadaabbccddbbaaccadabacadbdacaddaaccabddcbbcabacbdaccadadadadccccbcbccccccaaaccccccbdbddcadacdcdcdcdcbcccbbbaadaddbbaccddaadaaddabacbadcdbbcacdddbcccdacbcdddccacaacdabaacaaadabcdbcdaccaaaacabaacbbabbdbabdacabdcdacccdadbadcbdacdaadabdbbcdcddadbcccbadccccccdcbcdbcaaaaaaabbcdcdabccdcdaacddcbbddadadacabbaabbabadddadabdcacccdbadcacacbbadcdbbaacdcabcdaacccacdaddbadbbaabcdcadcccdccbacadaaddadcbdaabddccddcdcabcddcdcbbdaccaaccabcdacdabacabcccccdbdaaaaacdcbbdbaabaaaddbbcbcacaccbaccacbdbacccddabdcacbcbcbbbddcccabcaaddacbbcdcdaccacddbdddbbbdddadcdacdbbacbddbcdbbaccbbadabddbaacaadabdaaaddcdcbdacdaadbadcaabbbaaaadcdbcddbbabdacdadcbddbdaccddadbdbcccaabbabbddcbcdbacdbbaccbcddcbcbdcbdbddbcbbdcbaabacabaababdbcbcccdbccbbbdacbabbbbdbcaaccddabcccbdbdbbcaaabadddcddddbbcdaccbbabdabcaccddadaadacbdcadaacdbabadadbcaccdabcaabdbacbccddbcbdbdaadccdaccabcbdcdcacdddcadcbbdbacbcadaacaadbdacbddbdbadcbdcdcacdcccbcabdcbbbbaacccdaaacdddcddbbacabccbcbbabacdcdabbcaccddabcdcccaaccbdadaccababcabddaaaadadbabababcbdbdbcbcaaaccadbcdbccaddaccacaccddabdcadccbcccdcbbcacabdcbbcbaaccaccabccdbcbbaabacaccddaaacdabccbcccbdddbdccadddbbabccbccadddcaaaccadabbcbddaddddadabdabacbdbcdccbccadbbdadbaabddcbacaacbacabdcbdacccaabbcaabdcbcdbdcdcaacbaccadadbbdaddbccdaddbdccadccdbbdbaacbcbddbbdbdabbbabcbcdcddbcddcccababacabdacdbcdacccbbbababaaddabdbdcbadcdbbabddbcdaaabbdcdacdddbcaadacddcdabccbaabadbdcbdccbbdaaabbbdbdcdbcccdddcbbacbacbdccbddddbbabbdabaacadbbbccdacadcaddbcaaadcddbddadaabddbddddcbdbcdcaabdddcbadcdddacbdddaacdcabccccaaddcccccddcdbacdcbdcbcbccccbdbcdcdcadccabcdaddaacdcbbbcddbdbaccbbcadadcdcdbbbbbbddcdaababbadaaaadaccaaadccbcddcadacdcdbdcaaabdacdaabadadbbdddcdbaaddacccadbbaddaddbcadabacdaabdcdddacddadaabcdbbbddcbcbdcbaccdbcaabcbbdbbddbbbdbcdaadaaaabdabbadadabbdcadcdcdcbaacbaaaabbaacbcabccdbdadcbdbadbcdbdcbcbadaacaabcdabdbbdcbabdbabbddacbccbaddaddbbacddbcaddbdcaadbabbcadadcbdaacabbdaaccbaddaddadacbbcdabdaaaaddaabbddcddacdddbacacbcaaadabddadcdadadababcacaacdbadaccbaccccaddddcddbcaddaaddcdbaabbdccdbbdcbcaadbaabdcdaddaccbdcaddcbcbbcddbdcdccadbaacbdaaaccbabcbcdcccadcabaccdaaddadaccddbbbaccbbcacaaacbbbaabbaccbadddddaadbbacaaaadaaddabaadbccdcaabaabacabaadacddcccdacaacddcdcdaababcddadabacbabadcdccdcbcacabddadcddcacbadbdccdcdcbacbccbabdaacaaabcdbabbdbdbcddbdbbcaddbcbdadaacadbacbcddaddaadbdbcdbccaaaabadbacccdbaaadaadaabcdcaabcbbbcbdacdaabcaaabdcacbddaaacbcadccddbbcdbaddabbccadcaccccbcaabdddbdcbcccbdbaababddacbcbbbcadcacdbcaaadbbbbbcaccdaacbcadcdacabcbddadbadbbbadcadadcddbbdabcbbcccbacbcacccbaabadaddbbdbbadbddcacddadaccaadacdcddddcaacabbdaabbbccbaabaadabdbccabaaabdbbcabbbdcaddabdcbdadabcbdbbacddccdbdbaccabbcddbabcddbdacdcdbdadbbbdaddacddccccadadccbbcadcdbddaadcbcbccbbdccabcdbabaadddcbadbcbdbcdbcdbcbabbcbaadbacbcbadbaaaaaaaaadcbcacabacdcccabbbaaccbbbbcabbdbcbaadacdabaaaadcbdbabacbcadbdaaccadccdcbaabdbdcdccbabbccddbaabdcbaadacddcbacbaadcddbbdcbaabadcdacbbcdddcdaadacdbbcbaabdabdcdcacdbcdabadacdbcaacabacaddacbcaadbdcbdbbddaacbaabacdbdbbbdbdbccccabbbddabaabcbbcbdccabdcbdbcaadaddcaaaddaacddbcdccdcbcababccddcaaddcdabacccaccabcdacddcbaccbdbbcaddaabcccdcbaadaacddbbacdbdddabdbccbbabbdcbabadbdcdacaccbaadabbdbcbaadbbbcbcbcadbddbabdbbcadadbaaaadcacaaccccbbdbdbacddbcdccbbcacbbdbddcdcbbddabbbbadcabaccbdaddcdccccdcdadbadddbdbabcbbbaacccbbdabbcbbcdaaadbcbbadbabcbdcacbdbdaabcdbdccacbdaacdacaaccaacabadddaacbcbdcaaccddcdbddaddbbcabbbdcbbbddbbadcdddacdddcdabdbbcccbddddacacbbabbbbcadbcdbdbbccdaadcaccdadbcdbdbbaccdbadbcacdadbbbbbcacadbcdcccadccdcadbbdaadbccbdcbabdbacdcbbadbcbdbbbadbccdcadcccbcdbdbbddbabbabdbcddadddbcadcddbbbcaccbddcbdddcaadacdcbaaddbbdddccdddbdcbcdbdcabbdadbaccdacbadcdbbcbbacbbbbbabbbcbacdccaccdccdbccdcccddcdbbcbdccdbddcccbbcaaaadbccbacabababdaabdbaadadcdacdcdacdcacddaadabdadbdbbabcdadcadaacddbcacccacbbcaccdbdadacdadcabadbcbadcbcadccbacbadcaddbbccdbdbddbdccaccdbbbaabaadbadadaababddcbbdaadacdbdbbbbacabcdbcdabdbbdaccdcabbabbdbddcddcdbacbcdbddbbdccbabaadccaacbbaadbbbdbadbdddacbdadccabcddcbacbbcacaccbdddaaadcbaabadadaaddadbaacbadcdabdabbaadbcadbacdddccbcbdccbacccadccbadcbaaaacbabacbdbabbcaddaaaccdddaaccaccbcdccdbcaccaaddbdbccdaaadbbcdbbdbaaaccccbcacdbbbaabddacdacbadaadabaddcabbbcbdbbdcddacbacdcbddbaaacdaabccabdccaccadccddcbdbdbaccdaaabadcaacbadaaaaddddbabaababaddccaabbdcadacbabbbbccadccccdbccababdaaacacbacaaacdcacddcbbcdcddcccaabbccbdddbbacadcaadabdcdbccdccacabcdcdbbcaadabadbaccbbaccbbbccbdbbbbbaaacbdaddcaadcdddbacdccdcbdccbcdcbbddddbccccaccdbabbaaacdabbbdbbddcbbbbaaccaacbbccadcbbdbcdaddadacbcbbdcdccbdaadccacacaccadddadbaabbdcbddcadaadaabcacaaacccdbbddcdaadcdbddcbdbdcaccadbdbacbacadbdaacddacdcbccdaababdcbdcbdcdabbbdbacaccaacbbbdbddcddbccbbaabdaadacbabccadbbcbbdabcacacaacaabbddcaccadcacadbbbbacdabdccabccdacddbcacddddadcddccaadcaacabaabcadadddabadaddaaddbaccdccbbbaaaccddddbdcbdcbcdabddcdadddaaababdadbadacdabdbdacaacddddcbadcdccabcddcbcaadacdabaabadbdccdcaccdbaaacdadacdaaacabadccdabdcacdbbcdcdbaaacdabbaacbbdddcdddbbccbbaadbbaabbcdcdbacadaabdabaddddbccdacccdcddbcaacdabcbbabdbacdcaabbddddaadcabbabbbbadccbddbdcbcbaddddcbdccdbbcdcbcbbcdcbbbcaaadadacaadccbdbbbbaaacdadccccabbcbdcbbbddacdadacdcdbdddadbdbcadcaddcadcbdcacdddcabcaddbdddadbacddaadcaddacccbaacccadacbcdccdccbaacabddbbabcdaadadadabdbaaabdbacabdbbbcbacbdabbbddccaccbdccbbcdaadbabbbcaccdabcddcdabdabbaadbcacdcacddcbcdcdabccbbaabdcddbadaabaacbcdbbadcdbbcbcbcbbadabcbbbcdacdcddaabbacdaccdcdaabdbdccadddbacdbcbbddbbccadbbaccaddbdccdacddcdddadccddcbcdadbdcbbbbbddddbadbacbdccadbccbbcddabcbddacbaaacaacbacdabcacadccadbbabacdcdbbbdbcdabaddcadcccdbadbbbcbbcdaddacbcacbbacbdcbacadadbcdacadcdbbddabbcbbcccbdadaccabdadddcadbbdcbadacdacbcadcabccdbaadbabccbbdcaaadcabcbadbcacacddcaaabbcaacaadbabbaddccdadcaaaddcdcaacccdaacdadcdcccaaacadcbcaadaabadcdcabaccbadbbbabdddcabdbbbddadbbbcbbcbbcbdabaadaadbcdaaadaddbaadddcbabcadbcbbaddbdccddbacbbcacdadccddbdbacbbabdbaaadcabbddabadadddabddaaadbbbdcddddacdbbabacdcddabbaaacadacbcadbdacadbaabbaaacdccccbabccabaacbbcbccdacccacdbdbbaabddbdcbabccccccbadbdbacaaddaddacbbddddbcdabbcddaaabaadaabdccbbaaddbccacadbbcbacbbddbbcabbbacaadcbbccddadbdcdbdcdbbcbacaaadaadaaddbddbdbbbbbcaccdadabddaadabbdcdddadacadbbababcbcabcbdccbcbcdbbcddacbaadabaddbbaabdbbccbdabbabbadcbaacaacbbacdabaadababcbacddcbcdacbdcbabcadcdcddbcbbaadacdcddcacdcdbddaddbdaddccbbdbcacdddabababcaccabbcabcbbaddcbabaaaccadbbcdbdbcdbcbbcdcaadadbbabbadbddbdabbaaccbdacdbbcbacdbdaaaacbaacbbacaadbccacdccbbcbcababacccabcadddadcbabadddabccbbddadabdacdbaddaabbcdadcbabddbcadcbbdccaabdcdacbcacbdcabacbdaabcbddaddaacbaaddbcdbbbacbbaddcdabdadcbdadbcbcaabcbccdddbcddbddbcbbdccddbabdbddbcbabbdcaaadabbcddddadbbdbcdbdbccccdabddccadbbaaabdddabbaadacabaabbbcdcacbadbdacbbbbcbdcbdbabbadccdaacbadcadcbdbaaacbbbbabbcbccdcaadcaddabdabdbbbdbdbaccbacbadcdddcdddaccabaadabbddbdbccadbdaaadccaadbacdbcadddccdaddcdcdbcadcbbbbccaababdabdadcadacdbbdabcaacdaccaabdadaadbabcdcbabbaddcbbbdbadbaddbcbaddadcaddbadcabcadabdcbbbaddbbcdaccabadbadacdadbcbdaacbbbaaddbadacacabddccccccbdddabbbdbcbdadaabdaadddcdcbdcdaaddddacabadcdcdbaaababbaaacbaabbdbdbbdbdccbaaacbddcaadbaadcdcbacdbaddbbabbcbbbbbdbbcbbbabdbcbbbbccbbbacdbcaabdbdabdadaddcbaaaadbdccdbccdbadadbaaaaddbddcabaabbcbaadddadcdcddddcaadadccbbccadbcadbadbcdacdcbcbaacdcdadcaaadccdaadacbcdcddbcdcbaccbbbbabbbbaacdcccddcbaccdcddbaaabdaabdcaabbbcaccaabdaacbaadacbdaddbdcdcdbacbbabdcdddcddadbcaacaddbccbcbacbcbcbcbcbdcaababcbcaaaadcbacaaadbdbcccdbcdabadabccdcadbdbddbbcacaadcbbcaacbbddbacbacabacaaaabbbdacacdddbdacdcacbcbddadabbbadbddabcbacdcbbbbdcdabdadcabaadccbccdcdbbcccccbbcdaccddaaacdcdddbbbcddcabbdbacdcdbbdcbbccdbaaacabddcbadcbcccdcbccccdacabdaaddcbcbdbadbcacccdbcbdaccdbdaccbbddbaddaadddcdabbabbaccdaabbcabbacaddddbabdbadaaaacdbcdacdcbbbcbaaaccbaabbbcdacbbcacdcdccbcdaadbaccdcadbdadbcacdccbdccdacbcddadbbacbdddcbaabcdcadabbbaabcbbcdddbdcdbdcddcabbbbbdacbcbdaabadadaacdcbddacccacadaaaddaacbaaddbaabcdbaadcdaadcaabdbbcbdacabddacdadcddabccaabdaddbcadcbadddbbccddabdaddbabacababdbabacbdcbaabdbaccbbbdcaadbbcdbbbbaaccbccdbacbddbdbaadddbaacaabdbccdcdabbcacabadccaddddadabddacaacdcadabacbbacbddaabacaabbdcacdcddcaaccacdcdcaaaaaacbcdbbbdcccbaacabcacbbdbababbbccddbbdadbbdacaadcacbdadddaabadbbdcaaadbbadaadbadcdabcdddcaaaccaddcdcbcaacbccbabcbcaaddadabccaaacdcbddcabdcdcbcccdccacbdacacccbabcccabcbbacadbcdddacbbbddbabacacdcdccccaccdccaaccadbdabdcdccddbccbcccbadccccabdccbabccbbaaaccabccdbbddcddccbdbcdadabbbcaddaadddccddccddbcdcdccadaadbdbccaccbacbaaddcaabbadaddbcbdbbacabbbbccdcacabacdddadacbbbbdacdbbbbcbbaabcbbcdaacccadacdccaaabdccaccbcccbcabbaabacaddabbcbbddbccbcbbcbcabbcdccabdccbbaaddcbdbbadcbddabdaaaaacababaacbaccdbbaaaabbbacabadbcbbbdddacabbadacabddabacdbdccdbabbdddddddadabcbbbadbdcbdadbcbbdacdaabbbcbdbdacbabbdcaadadaacbadcdacbcccacbbcdabdcbdadbcacddabaaccadcbcbcbcbdbcbbdcaadadbacbcbbdadbdaaccdabbbbdabbacddbaccdadaccdadacaaabaddabbbbadcadbabcddaabbdddbaaccacbdbddccaabcccbbccdcdabbabcdcdacaddbcabddddddccbdbacdabbdbbaacbdabcdbbdaabacdcdddbbbcddaadccabbbadaadabdcabddcdcadaaaaaadccddbaddcabbbbdacdbdabbaadbdbdaacdcdabccdaaccacbcadaabaddbaacccbbddaccbdbadbcddbacdbbbcbbbbacbbcdcdbdaccdcacdbbccadaaacdbdcbcbabccaaacbacbddbdbbcccddbcdcbbaabbacccdcddaaddababbcbaadbbcddacbdccaababdbaccaacbdaababcdddaccdababbbdbbaacbdcaabdcaabcbcbcbcaacccbdadddddaccdbcacaaaadbbacdcbcddadbabccbcaddbbbdddcbcccdddcabbbbdbcdaaadaacccbdddcadbbbdcaacbddbcaddbacbabaacbabaabdddbdabcbbaccacadccaadcaacbcbbcadbadbbaabdaacbadcadbbbbbdbacdbbaaacdaacaabdcbcaabaacbbadacbdccbdadcbdadabaaacabdccddacacbaabcdbbbadbbbaababcabdbdabadbbddbbdbacbbaccaaaccddccdbacbdadcbdacadbdaabadcbabcdbccdccacadbacddccbdbccbacccbdbadaaaacdaacddbdbddacbdddabcbaccbaacbdcdbcdbaaaaccaacabdbbbdbdabcbbcbbadcbdaccaaabdccbbcadbacccabbcdbaadaaccbadccabcbbcddbacacdccaabbbbcbaaddadbccacabcbbdcbccacbccccdbbcbbbcddaccdaccaacaddabcacbaaadacbbdabdaccaabcacaadbdbbbbdbacaacccdacbacbcdcbbbdbdddcddcdccbddacbbbbdbdadadbcbcdcdccacdadddccbaacabdcddcbbbbbbbddbabaababbdcabccababcbacdaaadbcdaccaadaddbadcdcbaaddcadddbdccadabcbdabbbbbbbcaddcdbaddcbdabacbdadbbbbadcdabbcababaacacbacbbacdccbbadbdaabaabbadaccccdbdbbbbbcaabdabddaccabbacacbcdbdddaccacddddcbdcbcaaacadacabdcccdbdabdadadbbabdddcbccadbbbabcdcdddacaacdabcbcaccdabbcabaabdacabcdbabddddcbcadadcacabdbccbcaaacbccbbbddabdabdaabbbbcccdbacdddaadaaddcbaccabdaaddddcacacbacdaabcdaacadadababababbdaddcbcdcbcdcbabbcbbcdbacdaaabcabaaabadcaaddddabaabcbadcadbddabdbddabbbcdaabcddabdcbadabcccaacaabaddaccdabdccbdbdaaaaacadccaaddcbaddcdcadadbbbddccdaaadbcbcdabbcaaddaccdaaddddbbadacccacabdbbaacacadaccbddadcaadacbcdabccbddbccadbdccadaacbaaabdabccbaadcbbadddcadcacaddcbababddaccdacccaaccdbcddbbcabaccbdcacaccbcdacbbcaccdcbddadadaddddcaabddbacbadbcadcdacdababdcdbdadacdbddcaababbbdaabcababdabcadcdaddcadabcacacccaabcdcaccbdacaabcbcadcdbbdabccabccdcddaaaabdbdddcbacccbddaccdbbdacbccdbdadacdcadaacaaddcbcbaaabbacddbbdacccadacbbdcaadbdbcddacdcbdadadaadabdddabcacdbaccbcbddcbccaabbbabbbbdcdcdcbddadbababbddbcadbccaabadadacbdbadababcdabbcdababccccbaddabacabadacbbccaabdbbccacdacdcadabcddacbdbdcdcadcdbdcdddbaabcdbdbcbbacbbaabbcaaadddbbbaabdbcadaabccbaabdabacbccdcdbadccbbcbacdbccabccadabcdddbaadcdabdcdbabccccdcabadcbaddacdccacbdababbcbcddccadacbaaadcbaaddbaadcabcbbaabadccbaccadaddbddddcccbacbacdababbbdcabbddaaccdabdabcdcdbcbccdabdabccaccacdbbbacdababbaadbdabbcaddaaabbbacdccddbbabddbcbdbcabbdcaaccccddddaabbcbbcdcddbbacbbbccbddaaabacbcaccbcdccabaadcacacdbacddcdbadbbdccddbaaababcdbcdcabcabbcdabbccbdcdbbaabdaccadcabbaaadbbabbccabdabcccccaddddabcddcabbcabcdbbdcbcabbdcaababaabcacdbabcbaabdacdbbadbbaaabdabdabccbdadaabdacbcdabddcacadabdccaacadddcaaadadaacabbcaddbcabcadddabcdaaabbabbcadddcadccaadbdaabbbaaddbadcdddbdcabadcadabcacbbbbbddbcbcbaabacbccdcadddabaddacadacccbacdaaccbccdadbdbddcbacaddbdaadacdbcccaabbaaaadbbdbadbcdcdcdddddbbbbbadcbdcadaabbdcbabdddbbaddbdbaadacbabcbcdbdacbccbaaadccdccdccaccaddcadcdbcbbdbbbacdacaabdbcabdcdaaadcbbaccdcaddbcbdacdbacbccccddacbbababbbbacbdabaacdbabacbcdbaacdbdcdcacbcdbbdabaddccddabbcabaacabdadaccadbadbdcccbddaadbcbccbaaddabbbccddadbdabcacabbbdcadbbcdccabdbdcdccaddcdaaadadbcdbccbcbddadbaddcdcabdacbdccccdcbaaababaaabbcbbbbcacacbcdbcbdcbcadddbaccdabcababbcaaadaddacbdccdbacaccbadbaadbcdbcdcaccdcbbdcbbbacabcaabdcddddadabbcabaadbacaadadacbddbdacaabacdadccaabbaaccbccacaddddadcccbaddabacddcaabdbdacabacdcaabddacddacbadddcbcdccabdbcbddcdddcbdadacdaabbccaaccababdabbcbdadbacbcdabdbdbddaacbadbaabbcccaccccacdcccbdbdbadcccabaacbbbddcbbabdccacccbbdacababdadadcdaacbbbcadcadbaaaccacadabcabcdcbcabdbaaabcadbdccbabbbbaabacbaabdbadddcadadabbbaadbaadaaadbcbbbbabbcadbadacbbcdabacbabcbcdbdcaddadccaadabcaacdcaddddcbcdbbbcccaaadcccbbcaddddcccbcbcadccdcadacacaadbaadabddddaaacadbcadbbcaacdcbaadddbccdbdacccccdddbbcbddbbdaacaddcdbaacdbbbaadbacdcabdbacdcacbddcccbdbdaaadcddccaadadbbaadbdbabcbccbcadcbabbcbcabdaccdabccccbcadbacabdbbdadaccabddcbaabdddcbacdbbbdaacbbcbcbcccdcacddbdcccccadbdcbddaacbbccddcbbcdbdaabbdcdbcabadcccadccaabbaccabacbcdbcdccbccaacaddabbbbdbacdbbbcdbcdbdbdcbcccdabccdbccbcbbccbcaccacbcbdcdacccccdbbbbacdbbcccdabbdccdcbbbcacccbdcddddccbbbdcdbbbdddacacdaccacabadcddbdabddccbccacabbcdaaaccbcdbccbdbddddbdbcdbaadccdcaccaadcaaadcbdddbabadaaadbaddabaddbbbddcbcdccdcbbadabcaddacbaaabaadadccadbccabbbccbdaddacaacddccdacbdabdadadccdbdaabdbcdcaadbcbadadbdcdccbbaccacddddaddbccbadaaacadccbcbaabdcbdccabcdcdcaccbdadbcdcdcadbaddbcdcabdcbdcabbbdacaccdbaaccdacdbbacccdcaabcabcddcaaccddcbbddcdbccbdcddccabacbbbcacddabaadddaacdabddaccabbddcccdabbbddbdacbaabbccdaadcaccbdbbdbbaabcdbdcaacdacbdacacbaadcbabcdacddaddcacaaacdaadbdabddddcacacaacbccdddddbbddcdacaabcabcbdcdcabacaaaadaadacacdbdbcbccacdccbdcdccacdcdcbcbcabbabcdbcccbddabdaaaabddddcbbaaddaddcbaabadbcddadabacdaddcbddaaacdcbadcdabbcaabdaaaaaccbdcaaabcbcddcdcbdcddcaababbdcddbcccabbddbdabdcaabaabdbdaaccccadaaddbaacabccddccdabcbddddddbbdcdcbdcbcbadcabcdabaacdabbacddcaaaaaabababdccbdaacddcabdddcdddaabadaccbbbcdaacdbccdccdaaacbbdcbabbbaaddcadccaccbbabbacadacabbbbbbdbbbcbdacadbababaadadbacadbaadcbbbbdadcbbabbcabcbbaadbdcacaaacbabaddddacabbcaaadaadcdcabcbadaabdccdcdbaccacdacdabccbbdcdadacbaaacabcbccddddccdbddcbabdaacabcabaacdaaaadcabccbcaccabadbbabdaabddaabdcccabcdaccddccdddaadcdcdcddbddbbdadabccbbbdabdbadacbcbbcdbddcddcddbacaaccbdcddbbacaacbbbdbacccdddabcacaaadaadbbddddaadcbcbdaaaaccbccadbddcaaddadbacbbaccddbbaddacdabdcdccaccadcaacabbdbdacdddcaddccccabaddadcdbbbaaaadcabacbcbdbccaabbaddacdcbdcdaadbaababbababdddbdacddddbacacdabcabcaababababbdbacbbabadbcababcdbdaaaaadbcbdaadbbcdaaaaababadbbaadccacbddccccccbbbcdbacdbddcaacadabdbdbcdcabddccddbdcccaabbcbdbccbcdcabdcabdddbacabcaacddbaadacbaabcabbcdabacbddadbcaccbbcabdaaadacbcccabdbacacaabaadccacdaccdacbcadadccbdcdbccbddccaaccadcacbdadbaabbcdddacbcbabbaadaddadbddaabdbdadcdccacccbdcdcbacbddcdcbccabbabbabcbdcbbadbdbddadbaadccbadcabbabcbdcbbbdacbbadabadddbbaabacbbccabdaddbacbccdbcdabcbdbcadddddbbdacccddacccdcbcabdacabaabcaddddddacbacbabcdbbbccaaabacbacbdadcbbaabaaaddbbbccabbababbadacdacadccabbdbabbacadbadbacdbacddbabcdbddadaddbacabcadddcbdbddbabcbcbabbbdbcccbcbddcddacccbddbdaaccaabaccccbaaacddbdbbbbcbabbdbdcbacbaddcacdcdacaabccbbbbcbcbcccdaddccaccabdcccbbbbcababdcabccbadaabbcddbbbcadacdcacadabccdcbdcdcbbbadabdaddbadbdbdcddadbddacdddddccbddcaabbabbaddccdcaddcacddcaccabadcdbcdddbddbaabaccadcaccabdacddbcabdbddaadcaabdddadbdcadaacccbcbbbadcbbbaacadcdbcdacacacdbcabcdbbcbcdbcdacbcddcdbcabdbcddbcdcdbcdccabdaacbcadbbbdabdbcddadaadcbddccdaccadadbddbbcdcdaadddabacadbcccbbadbababbbdabdcdacdbdadddadadaaadadbdadcccdcadbaaadbabaacddcadcbaddaccddcacabcdcbbbacbaadbdddcaddbddabdaddccbcbbcbaadccdaaccadabddaaaabcdbcaacbadabbbbbbccaaabcccacdddccadcdcaacaaaccacdbbbabbababbacccaaadaacbdddacaaacaccaccbabbcdcdbadccadddbbdcbcabbbccccddadaacdbaabccdbbdaddbaddacabdbbaddcddddbbcccbcabbdadbcdabdadabcdddbdaadbacbabdabccccdcbcbaacacadabdbddbacacaadadaccbbdaababcadbdcbcdacacdcbdcbacadcdaabdcbcaccbdbbddcaccbaabcdadacabaacdbddcdabbbddaadcbcdabadabccacaccccbcacdcbabdacccabcbddacbadaaabddcaddbacdcaacbacdddcbddbbacacbabbcbabccccacaddacdcbcdcddcaabcbdabbaaddaadaabdacdbdccbbccacabcabdacadcabadbddbabcdcbcaccababbcbcccdcabcdbcddabbdcaaddaabdaccbcdddbccccdbbcabcddddbccccaaaacadbbccdbacacccadddbbddddcbbbbbcccbbacdcdbcbaadacdbabaacccdccdadbcbddbaccbdbacddabcbaccddbabdacddacbaadbbdbbbabadcadcaadbcddaddbccdbdadcbdcabbcaccaddddddcdaadcacbadaadddbbcdddbdbcddcaadcadcaabcaabbbbccbbcbdacbaacbaaccbabcbdabcbbdccaaadcbabbabbdcbacaacaadaadadacdcbbabadbddabddcdadcbcaadacdcabbdaaaadabbdcbbdccbcabbbaddbdbdccddcbcbadbbbcdaacbababbacdcbbabdddbaadcdbaaddcdabacccccbbcddbbdcaddbbddbdaadcddbbadbcccadcdbccbdcaaccdbaddacdcdbcdbdbaddcadababcbaaddbbbccbdbbbdddcbaadaababdabdacbababadadcbcbdaacbaccccbcaacdaccbbaacadbbcacbcdbcddbdcdcbbbababcbacbcbabaabbaccbdcdbcaabbcbdddcdddbbbacdcbacacdbdcdccbddbcadcbbbaddbaccdaaccacbacbcacbabbdacbaddaacadaabdcbcdcbcdcaaacaadabdccaaacbdacdbbaaaadacbdbdbdadacadcaccbababaaaabacdacbdccdccdbdacadddccdddccdadddaddadadaccbdddaacbcaaabacdbcbaaaadbbbdabbcdadaaaabababccababbaccbbacbacbbccbdacddbbadbdcadabdabbdbcdabccdbcabaccaacdcbcbbabacdaaadccbbadadbcbbcbdbabaaddbdaadbabcdaaacdbcbaabadbadcddbdaabbcccdbabbdadabddaaabaaabddcbdcaaabcadabcaccbcdabbbdaaadbcabcdcbccaddacdadddccdcabcaacbbdaacabadbdbacccdbccbcbaadbcbdbcbabcbaacdcbbddcccaccabdddbaadcddbdbadbaddadbbaaddaaccabaacbcacbaccddaccbdcdacaddccbdbbabddacddbbbabcbbadbcbcccaadddabcabcbbccccddddbabacbcdbdddbbabaacbbdacaaabbdaacbacbbabbbdaaadccbaadadbcbababacaddddddbadbbcaddaadbcbdbbccaddbdccbaabcddcddadbabdacccbadcbcbdbbcbabddcccdbddbdbadabbddabcdcdadaaacccbabbadaabdbbcaaddddaabcaaacbddaabddbbcdabdcdbabdabcdbddaadadcddacaddadbaadcbadcccacacdbcacbdcdaacabdbbddabdcdcbbdbcbbcddccddabddadbaddaaaabddddadbadcbbbcaddadbdbbacababccaddabbcabdadcbabcacabbbbcacdadbdadaaddaacaabdcdaadabccbdadabdadbbdcaadbdacadcddcbaccdbbbcacbaddadbcdbabcbcccabdbcbdddcbbcdbcdaabbcbaccdadcdabcbcdacdaadcabadabaccbcbdbacdbbdbddcbcccbbcbacbbccbdcababcdccbdcddddcddcbdbcbdbccbdbbadcccbdbabacbaaccbddbcbdaccdbdbbccdddcbbdbbadbcbabdbaccabdcddcddcaccdccadcbcdacbbcadcdcbcabbcabdccccbaaaabdacdadaaadaabdbbcbdbcbcabcadddaaadcccbabdbddccdbbdbccabdaadcccdcdacdccdcabacaacddbacddcbaabcabdcaabbabbccccaadcdbdcddaaacabaaabbbabbcddabdcccbcddbddbadbddcacbbcddbcabaadabccaccbabdadcbcbbcbbbbcbdcabbdbadcdcdaccbddbbdcbbbdcbbcbddaaadaddbddcdaadadcadabbbabcddabdbbaaabbccbabbccbdccabcbbbaadabbbdbdcadcabbabccbcabcabcbbabbdddadcabaabbccccbdaacbddcbcabbbcaccbcddcbbadadcbddccaabddccdcccbbcdbbcccdbacbaabcbacbcbcdcaccabababdabbdacdacdcabcdadcbaabccdaadabccddcbdcabadccdcccdcbdaddbbbabaaabbaccbcdbbcdabadadcaaaadaacacaddcadbaacaaaadbbdbacaabbaddcddcacabcbccbbdcacaaccbddbaadcdbbacdbdbddabdabdddbcdccbbcaabdaabdbcbdcbbdbabaccbccbdbbacbbdbccadccbacadaacaaaaaccdbcadadabbdbbdabbdbdacdaabcdbdbdbbadbccbdbbdcbcbbadcacacbbcbbcaaccbdcddddaaabdabbadbdbdbbccddaadcbbadbbdaabaccbdbbbaccadccbbdbcbbbdaabcabdabdaacabcbadadbdbbdaccbdadaddabdaccbddcdcccbdbbbbbbacbacdcddbdbcbbdcbabbacaddbcbccdaadaacbacdadbacdccdbcdbbbddaacccaddaccbabcaabddbdaddcdcbadcadddbbccbbbccabcbcdbbddbdddbcbdbcbabaddbabccddacccdbadadabddcbbdbdcacabdacaddbbcbabcccbacdcbdacbababdddbbbcbbbaccdcddbdbaabaccdbccaacbcbbdcbcdbadbbdcabadcbacccadcbadabbabdccaccbcdbbddacacacbdcbabcacddddcbcdaadcdbcadcdbbbcbbdcdcaacabbbadcaadaaccccdadaaabacdabbabccdabddabaabcaacddcbdcdadabbccbdddacdaaaddcadcbabcbcccbacabcbbabbbcdaabdccadabccbccabbccacbbbdababacccdacddaacccbcbcabaacccbcddbdaadaaadcddccbadcadcbbaadaaccbbbbccccbdbadaacdbcdddbbdbdcdcbbddabcabbbabacdccbcbbcbbdccbabdddbadbcbaabdacbacbabccdabcaaaccabbdbdaadbbababcaacadadadddbbababdcbbbdcdcabcdadbcabaccacdabbdacaadabacdbaabddccbbbcbdacabbdaadabcdcdccbbcddccdbdbbbbdadcbdcaaaccdaccadbacddccabbabbcbbdabbcbaddcdabcdaadbadabbddbdcdcbbbabdabcadaabdaddddcaaccdcaddabdcdabbbdbddadbcaadcdadaaddbbdbaacddcaaccbcabdcdbabbdabaddcdbaaaccaddcbabdddcbbbdadcbbccadacbbabdcacbacbbdbaddadcdcaacbacdcbbdddddcbcdcccbacbcbcabbccbadabbdaccabbbabddcdbabcacaddccdadddddcbaabacbbacabdadddbbdaaacbcbcdaabbbdadcbccbbdcadacddcabccabbbaabcdaddcccaacbcddcadbadaacbbdcbdbcaaadbdbccccdbdbcccccccccddbacbcbbcabcdababcabdcdadddabdddbdbcbadacbcdbbaaaacbcdadbccadddcdddcadbcbcbaddbacadacbdbcaddaccdcbcccaadbabaababcdaaaddcaaaabcbabddbbccbbdcabcbcadcbbbacacddacaabbdbabbdbdbcdadbddbccddbdcbdccddbddaddbdacdcbbdbaaabdbaacaabbaddcabcdbcbacdaccadbbcdbdccdbabadcababdcbadbdbacadccdcadbaadbcbddaccccaddbbabccbabdaabdaadbabaaddddbbcabdaacdaaccacabbdbdcbacdbaaaccdcaddbbcdaccbbbacbbbadbdaaaabbcdaddcaabddccdbccabdbdcdaaadbdaccaabdcbdabaccadadcccadcbbbdcabaadcdbabbbadbbdcddbadcccdccbbacdacbbcbcbadcbddbcbbcbbbacccbadbaddcdbabccbdacacbccbdbabcddccbbbcbcbaccdaaddadcabdcccbabccbcbaddcabdddacacbaaacbddddaabaadcaddcddccbaaddabccadcbbaaacbbbdbdaadbbbddbccaaaabcaaaaadcddcadacdddbbccdccbcccccddbcadaadddddcdadbdabdcbbcddddadddadbaacaddbbbbddabbccdaacbcbbcdacbcdddbbbbaaccaacbaabbacbaabbdacbcccbccdbabbadbcbabbaddaccbaabcddcbbbccbccacacddcadbbdcddbbcdadbacacdbdbbbcccdaddcdbccbbbbbcddcccbcccbaadbddcabaaacbaabcbdaccddaadcbacadaaabadbdbacdddbbdcddbbdbbdbdaacaaddbdcbacbdadbadaaaacbcbbbaadacdddddcadbccbaadadcbabcdadbdacaaadbbabcacccbaadcdbabcbddadbcaaadaabcdbbbdbdabdcdbcdacdadcccbbdcacacccbaabaddabaddbbbbbbddadbababcaccbbcbaccdbcaadcbcbaaacadbcbbadabdabcacdacbabcadadaddbadcabddacbdbcbdccaababbbacbaccdbcdbdccacbdabaabdbdbacbcabaacaaabcdacaccdcbdadaabdddcbdbbbddcaabaacbdbdaddabddbcdacbdaacacdddcbccaadadbdcabcadadbccaddbdbbadacbbcacdcadbddbdbddbcbcdcbcbcaaabdccccbdbcdccacdbdbacbbabdcadadadabadccbacccbbbdadcbddabddccacdbdbdbdaddaaabbabcbcccaadccdbdddacdbcabccbdddbaaabdabdbdbdadcabbcbbcadadbadaaabcacccdbcddbbabbacdadcddcdbbaabcdacccdbaaccbcccddcabddbdbdababdddadabcdcacbdbbdbdcdaaacdbbaaaccabbdcbbbddccaabdacacbcbddbaccbcddccabcdaaaabdabcddcbcdbcddacdcbcbddccacddabaacbaabacdbbcabcadbdcdabaaddacdaccdddcbadaaacbdccddabaddadbcdbabcacaaaaccccbcdcbbaabcabdaabcccdbcaaccbacccacacaabbcacacbcccadbaabaadbbaadbccccacdbcdacadaaaabcbabcbbcbaabbdacbccacbbddadacaacaabbdbdddadaddbadcddbdcabdddddbdccdcacadccbcabcdddaadaadcaccaddaaaadabcdbbabacabbcabbcdadbbdbabbcdcdcccbcdbbbbbbdccbbdddacddaacabdadddbdadbbbdaaaabacacaddccadbdbbcbbbcddcdbdabcccdaccabaabbcabdccccbbbdbbbcbcbacabababddcaabbacdbacadbadbaacbadcdadbadaaaaccbdadbcdbabbbdbacddcdccbadadcbcaccaacbabcdcbdcabcdbcbddaabbdbbdcbaabcaabdaadbdcdabdbadddbbbbbcaabcccdddaacbacdcabdbbcabdadbdccbbdccaadddabcaadabdaaaaaadbabbddcabbdbbcdbcdcbddddbbdbdabbddbabcbbdabdccdbbcbdbdabaadbdbcadcdbcddadddbaacdaabcdacbacdddacddacddbdcdaddaadbbbddcdcabccdabbaadbcdcccadbadcbaccbabddaccbcbcbdadbcdbdcaccdaccaccacccdaaacdabdbccbbdcdbadabcdaacaccabcaaaddcddbcddcdbbbdccacdcbbbcdaccaacbacdbcdccaddaddabcdcacbdcbbcbcddcbbbcbdddbbdababcdcdcbcccacbbbcadcbdabdacdaddadabbbcadbccbabdcdcbddaadbddabcddbcddcdbcdadababaabdbdabdaaaddcaacacbbaccdbcaacbcabcacdcacdaddcdcccddbddacbcccabdbaccbdcdbbdddbdabdccdbdbacdacdbabcdaadbcccbbadabaacbcaabbacababdcddbbbdcaabbbbccbbadaddbdaaababaddadbdabbbcdadbbcdbdddbdaaabbadaacdbbcabcbadacbabddbddccadbbddbbbbcbddbdbdcaacdccaabbaccddadaccbadcbccdaadbbbaacacabddabdcbdabccbaddabadbaccabdcbbbabddacbdbcbaccdddcccdbbdcbcbcbccaaacacabbdbdaaaddaddcdbdcbcaddbaacbbcbdcdbcdccdbccbadbbcdbadabcccadadcbaddcdadbcacbabcdddacaddaadcbdcaddcdbacdbdddabbbbcbdddcadadbadcaaaddaaddcddadcacaccabbddcccaaabcdcbbddbddabbbddabaacbcbdaabbabbbbccbbbdbaadcdbacaddbbdccbaddadadccacbcbaabacdcdddccdbcbacaaacbdabdddcdbbccadddabdaaacbddcaacabbbccaaccaddbcccbaacccccbbababdbcacbbccdbddbcadbbccbbadadacdcbaadccaccabaddcddaccadaabdbbbabbbadadcddcacbdcdaadaadddaacabcddadbcbdbdcabcabbdbcbdabdddbbcdbbaabacbbacdccdadcbacbbddbbcdaadacdccbbabbcdbbcaddbbaabcccacdaabcaaadbbdaacadbabacacbccddadacbcacabbbcdcdaacdacbadaadaacdcdacdaabdaccbaadcdaabcabcaddcdcddcddccabcdabddadadaccaadbdcadaddcacadabbcdccacbadbbcadbcbbabddbbbddbacbcbbbadcbbaaddcdcadadcdbbdbcaaaddddbbdaabdcabddadacaacacaabccaaccbbadaacccbcbdadabcacaacddccdaaabaabdbdaaacdadabbadccccbbbadcbadbabcbcbadbcbbbdaaddbddbcbcabcdcabcbddbabcbcabdcdcbcdacabddddabdcbabdccabcdbccbdccccdbddabcccbdcdddaccbdccadbacccccdddaadcdadabacbabaadccbadbadbdabbccabccbdbddadabbabcaabaaabbaddccaccdbaccbdaadddbdadddbddcaacbccddcbdcbadcaaddabdcddcadbdddcbcbdaabddbccdcabdbaacddbabccaabbabbadbcdbbcbdbbddcaddbddacddcbabdddaadbaadddbaacbbbcdddcddacccbbbdadbadcbbbacbbbcdbbcacddadadbbbdbdbcdcbbddacdabbbdbadcacbdbcbaabbdadbaddcbdcabdabbcadaabdbbcbdcbccbdcdacbaabbbabaacbcddabccbdbccbcbdcabbacddaddcdbbaacccbabdaacbddabcbbbacbcbbcbbddbbbaddbaadddcadccbbabddddcaaadaddbdbacaccbccadcbbdadbddabdcadddabadddddcdcbadadcabdabbbbaabbddacbdbdcaddbadabdacccabcbbcccbcddbadabddcacdacdcabacbabdcbdabcaddcbabbcbadaabccaaaaccdabbdaababdacaadacdabbbbacbbbdcdcdacdccdcddbddadbabbccdbdddabaacaacbcdbbbdadccdcbaaaaadcaaccbcbbccbcbdcdcbccbcacacbbaaddcabaacbcddbacbdbdabccbbdadbbbdacdddbadbbadbaabdcdbbadcacabcdccaaabdbadabbbbdadbdcbcbddcdcaacbcdaababdcaaaabdadcdccbabbadbdabaccdcbaabbbaadadbacdcbadadbbbcdcbbcaccdabdbddccddcabaacdbdbaddcbaaacdaaadaadbaccbbdcbaccdacababdddddcccbcabccdcdadbdaccaddacaadbbdbccdbacaaabbdbcdaccadcbcdbcbcbcadcddcbdbdcdcbcbccddcddddaacddaabbcbabddbabccccabdacbdbbabacdbaadbdaadcdbbaabbbccddcdbaaccdcbdcacbaddbbcddcadadbaadbdbccddcaccbbcdacccadacabbabbdbaadcabcdbadddcacbabaabbbbdbbddbcdcbcaacdaacbcdbaacbccdbacdcabddcacbddcbadabcdadcddddaccbbbdbdbdddbcaabdacacbbaabaabcdcaddbbdacacdabbbbbaaabadcdadbaadccdcbacddcaabdbcacdbdcbaddccdbacdbbbdacdbbdccbacacccddbcbdbabbaacbadaaccccaadadbabbdbcdacddcadbdcccdddadbccabcacbcadabbabccdcaabccbaccbbbacccbabdbaaacadaadadacbacadacaacccbadcbdbdaccbaaaccdaaacddbaccccadbcaccaaddadbcaadaadadbcbbbaaaccdbcbaabacbadccdcccbaabdbdbccddbcbbbccabbabaaddcdcdcbcdadbadaacddadadabcabdccbcbbadbbcaaddddcaabacddccccbdbbdbaacbdcadccaadaddbbabdabaacbdbadacddadaddabadddabcdddaaacadaabacbaccdbdbbcabadacccddcaacccabababdcbdcabdddcaadabcacdacacdcbcbbbaabcccdacdaacbdbcbdabdadbbdcddcaacaabcabbdbbaaacaabcddddbdaadbdbcaccacaddccbdcbacbbdcbaacabacabbadcddadacbacabbadcbccaaadbbccadbabdbbdbacbdccadbabaddccbccbbdacdcdbacabacbbcdacdbddbaddbbdddbcbbbcbcccbadcbbdcacbabcacdadbcbddadbbbdbacadbbdbdacadbdbccacaaaddaaaabdadcbbbddbcdbadabccdddbadababcdbcddcccddbaaacccaddbcdadcacbdbaadccbdcdbacbdcbdcaaccbbbcdbbbbcdbdcaacadadabcdddbabbbccacadbccbacbaadcbdaaddddbcababcbbdbbcdcbdddddcdcaddbbacdbaabacdbabbcbbcbdaaadacbdacabaaaadaccbdcbccdadbbabbaadababbdabdadbdabaddbccdbcbdaadcddbcbdaddabadcdbdabbaadcdabaccbdcccaadcccaacacdbbcddcdccddabcdbddcabdcadbacdacdbcddbbaadbdbbaabcacbbcbbaabbaadbcdbbccdadabaacdaabdcdaababcbcbdbdacacdcabdcccacdbbbacddacdbbbbdcadddacbabddbcbdadbccbbcbbdacadadcbbbdcbdcddcdcbdcbdbccaacbbadbcccdbaabadabadaccddbbdbacbbaaccbdabbbbcaadaddaabdbdcbabcaccbbbbdddbbaaccbdccdacddcdaaaacdcdcbbccddbddaadabbbacaadbddccaabcdddbdccccdababcbcccdaaccadbbbbacdaabaaccaadacbbcbccbaabcadaaadaabdbbbdabbbccdbcdabcabbbdbbaabcdcdaabadabbbcbddcbdbccaccbccaabddacaababcdccbcdacdcbdaaadacbacbadccbbddbbadbaadddcbdadcdabbcababdccaacdabacdbabdddbdcbbdccdbcbabdabddddaadaccdbccdcbadddbadcbbdbbadaabacddacddddcbbcdccacaaadacbdbaccaaccdcbadddbdbacbcdbdbcdcabdcdccdcbcdabcdddccdaabcdadcadbdbaaadccdabbdaaabddbbcaadaacbbbcdbbbdcbdcadcbbbbdadccddabdbcddaaabcbddabdcdbbabcdccccaddcdaabbabacbdbdccabccdccbccaabaabaacaacbdabcccaaabbccdabbdaadddcadcbdbbccaacbcdbcaaababdacaddbccbddbdbcbdcaacdbdcadcccbbdcdadbcbaaccbbbdbcabccbabbbdcddddadbdbaabdbadadcdbbaaccbcdddcdcbbcaaadaddccabcdacabbddbbaaacbadddacadbdbbaabcacadccccdcbacdaccbbabcdaaaadaabacccbdadaacddaccabcbacdacccbccbddabbbbdcdacbbcadcdddbbdccbbdbcdababdcbacbbcaaacdabcaabdcbcadbbdcabddacabdbabcbaabbbbabcaddcbdcccabbdccdbcccdbbccabcadbbabaabbbcbdbccbabcbabdacbcabdaaacdaabbccdddabbaccddcadccbcddabdcdadbcdacdbcaaacdbdbccacbabaaaccdddcdaccbcbbbbdcccbcbcabbadbcbdbcddbdbabaabdbabababdbaadcabddcbbacadabdcaacbcdbbbbcbacbadaddcbaccadbdaaaabbaaabcddccaaaadbdcccdbaaddbdaadadbadcabcaacdbacacbbacacccbaccdadcccacadabbdbaddbddbcddbabccbbadacbcbcbbadbddbcdacddddcddcbddbbdcbabbbddaacbcadbbabbdddcdddcbcbcdbaadbcbacadbdaaabccddcccbddccabcbccaadbbcacbbcdddccbaddaabbaaddadcbabbaaabbcbbcdadbddcaccabddbdbdcacdcddcbadadaaaccabbbcacccbdbcbdcbbcdccdabdcddadbdccbbdbcadccccbcddbbbcabcaabcddccdadaabdcdbaccdbacbabcbdddcbaaaaccbdbadaabcbabcdcdbdabaaccadbcbdbccdbbabbcbbbdadbdcdcdddbacdabbccabcdcabcccddbcbccaaabcbdccbcbcbcbabcddbdaddcdabaaccadbdcdacbdbbadcbaadaadacbcbacdcacaacdbdccddaadcdaadbbbdcdadbcdbaadcabaacbcbaacdacabbbbbdacdcbcacdbaacacdbbaddbdbbabaadddddccddcaacbbbbdcbbddbcbbbbddbcccbdcacabdaccabbabaacaccccdddcaccdddcddccdcdacdbbbcbabaadccacdabbbabaacbdadbcbdadaaacdbacccccdddddbbadbbdcabbddaabcbaadcddcdddcabcaccdbabacdabcdbacddabacacadddbdbbbbbcdcaabbadacaccdaddbdbbbabcbcbababbabdbcdcbabbcbabbadcdbdaadbbcabcbdbbbbbdcadddabdbcdacbbddcccddcdcabdcccaacabbaccbaacbdcacabccdcddaccbcdabadbacbbdddbaaddbbdcaccbabdbdbbccdbbcbabcaabdaadacacadbcaccdcddabcdaddabddccaaadbccbaadbbdaaaccbccadbdcbaabbcbbddadabdcbbadcdaadaacddaabcadabcccbdcaadbcaaaaabbdadcaaccabddbbadcdcccbddbdccdbbdadaccabbccabcbadcddbabbbcbcabbbaacbdbabbdcbccaaadccdcaabbbbcccbbdbbddbabccbbabbcbbdadcdbbacdaccccbccbccbcdadaabcacdbdbbbdcabddddcccdaabdadcbbbddaaadcacdacaaabbdabaacadcbaacbaabbddabacaacadcaabddcaadcabcacadabbcccaddadadcccaddcbcaddabdddaccdacdbbacadabdcdbacaccbdbdddcdadacdcbcdadcadbcaddccbacaccdcddababcdaadcbaccdaccaccbadccbcabdcaacddabcdbccdadaabcadcaddddcadccbcccacbbbdbbdaccdaddaacabbccbbbbdbdaccbddcbacacbcdbbadbadbdabccbbcaccbadacdcbcababadcacaadbccaaadbaacacdcacbbadbaaadacdbacaddbbdcddcacaadbddddbbacadbdcadbccdbadacabcdccbdaccbdacbbabaaccbcabdbbacaaaccbcdabadbcdbdcadadaccacdcadbdaaadbcdbaaabbaaabcbcdabdabdabdcdaacbbddcbbaddcbdddccbcdaaadcbaadbadabcacccabadabbadbbccabaaabbddcbcadbacacabacdbacbccdbcacbddcdabccdcadcdbcbbabbbddadbcddabcaaabcdacbbcabaaaaabaccdbdbdbcbdabbbdbbbaadcdbdbcdbdcdaabaadbddbdccbacdbcddbabaddcaabdaddacbcdccbcdcdcccadcaaabbbbbbbdbaababcbdbacbaaacdabadabcbabcbdcdcaaaccddaabddbbdccbdddabdcdaddddccdabacaacdbdcadbbaacadacbaabcdcdbccadddadbabdabcccacbbbacadacdbdadbcaaaadcadcbdaddbdacaccdadccbdcdcadcaddbcacbacbdcacddcbbbaaacacacaadabddaabaaadcbacccbbdbcbcbccadbcdcdcadbbacabdacaaabccaabaabcbbccacccdbaaadcbcaabccadbbbbdaabdddbbcdbcabccccccaabdaacabdbccbcbaabccbdacabbcdaabaacccadbabdadbddaaccdcadbdabbbbcbcdabbbdddcddaccadadcbccdbabcadcbcbdbcaacdcbcddbaccdabacdaacbbdbcaccccdcdacaacdbaadcadcbabdbbcbddcdbaaadabccabdadcacdcdccdcaadddbabbcbdcdcbddcacadbadbdbaacabdbdabcccbbbbcdbcaaabdddcbbcacbbaccdddcdcdbdadcabaabcdbbcbdcdbccdcccadbbbbaabaadadddcacbbcacaadcbdabbadbdcdbcccbbbcaccdabcacaddcbcaaabbdacdadabccbacabcaadcbbaadcddacaabbdcaababacccbbabcaaaaacbbadcddabddbbbabdbbcabddddadadcccdcacccaacccbcdacddbabbcddbacaacaaacbacadbabcaccdccbdddddabaaabdabbcccbcabbdcdddbbbcaacccaabcbbaccaacbcbcbbcccbadacacdbdacaabccaadbacccdccabbbbaacdddcbacbddddcbcdaccdcdddcccbdcdddcbacbbbbbadcdbaccacbdbadddacaaddbbcadbadddadcdddbddbabbdbdbcbcdcadaaacbabcadcaddbcdccaaacdbaababddddaccccbccdbddddddbacbbcdadccccabdbcbdbbdcbdaaaacadabacbdcaabaaaaddcbabcbaaabbbbddcababbbcdcadbaabbacaadccaabdcdaadddcacddddacdbbaacddccbbbcabbbdbcdbdaacaccbcaccabcaacccbcdbccdcdccddbcdabbaabbbaacabbbabaabadcccdbdacdcdacbcdcabddcbadbaabaabcddbbadabdccdcdccddaccabbcccdcccbaadccbacbdabcadbccbcdddadaaadcabbdbacadcabddacdabbdccddbdddddddcaabcdbbdadbcdbadcacdacadaaacdcabbbbcdcabdbadccaaabcabbbacbadddccabbcabddaabbaddbadaaddcbcdbcccaaaccdacdcccadadbbdacbabbbabcdbcdbaddaaccacbaacbbcbcbbbbcababcaadbbacdccdbcadddbabdccadbbcacdabbdaadcbbcbbbaccbbcabdddadadaaacaabddaabddccbdaccdcddacdcdbccddcbdbbbaabbbcdcbbdbbacbbacbcbdadddaaddddcbadacacabdccdcadbdccaddaadbcdbadbdcbdbadcddaaacbaababaadadacccddddcaaabdbaccdaabcabdbddcdacaddcddabdcdbbacdbdacbbcdcbcbcccadcabbadaacbbcbcadbcbbabbcccacdabdbadcacdacccdbdacdddaadbdddccbdccdcbbbabadacbcbaddccaaddddbbabacbdaabbdaadccabcdaadbcdbbbbaaabdddacaaadbbadbdbcabdbdaacddcccdabdbdbbabccbbbbbcddbaacddddbbabdddbdaaccdadabcbcbcddbdcaddcbcdcbdcbbdbdabdcbacdbdabbdddbadaaaabbcdbbacaadbbabdddbadddccbaaddbbcddddbddcadabcbaddcabdcbaccbdbdccdadaadcadbcccdadbacbddaacabbdcadcdaaacdccabbabcbadbdaaabaadabbbbcdbdccbdbbbcddcdabcabdaccbbdadaabcacdbacdbccadadcdbddbaccacddcbdbcaacccbadccdcdcacabdcbdcccbabbccddbcabdababbbdadcbacaadacaccdbbbddcdbcbadabdcbddacbbdaddacdcadbcaddabbcccabaadbcabdbcbbdcacacabaadcbcbcacbdcbacdcbacabddacaabaabdddaddcaaccccabadacaacbbadccabdccadccbbdddbaabcbaaccababbaaacdadadaddacdddcddaabdbcaccddcbacbaddadcacdbadadddbadbcbdabaccbabdbadbddcaaaccbbdadadbaccacdccbbcaaccacbcbabbadbcacbaacdadcbbbdbaaccabcdadcbbacdbaabbdcbdcacacbabadbaadbdcacdcdcaadabcbddacdcdcdcdbbdccacacbdbababdddcdbcdabcdadbbaccaaadcabaaabaacddabbaddddbdccabbccacddaddbdbcdbdabadcdbcdbbdcbbcbacadbccbabdacbaccabcbaabacacbdacbbbcbdcbcddbcdabcbadacddddbcddcdbccdcdaaacbcacbacccaabcbccdbacaaccddacadbbbbcdcaaddadbbadaaaacbacaabdabdddbdcdadbcdbddcdaaabddddcddadbccbdccacccddcbddbacaaddccdbbaaacadabadddddaabbdacacdaddbabdcbdbcbccaabcbabbdabdbcacbcacccbdaaacdaabbcbaccddcdbdababacadbacadacddddbccaadddcbabbcbdbbcddadbddbbadbdbbcbabccccdcddccbbdadcbaccbcdbcabdadbcbdddaaabcabcacaddcdadacaacbacccdcbbbdcccbaabddcbdaabdcbacdaadabdddddddbcdbcbbbaadccdbbcaacbbdaacccbbbbbadcbcdacabddccaaddbadaadaabcddadadccabbadcadbaddbbdabccdbacdcdaaaacaaadccccbccdbdaabbbdbbbdbcbcbddbcacbccabcabbadcbbbdccccaaabbdbccccddbcddbccbacdbbadcaadcbbcdadddcdccbccababbdcbbacbbbdddccdbdddcaaacdcadbaabccddcacaacdbaabbcddacdaccdbdccaaadddabbacabbbccbdccabdabdcaadddabdacacbaacabcdbcabaddbdbbcbabbbdbbddaddcacacaddbdcacdadaacdcddbbbcdbcdbdacddcbcbaccbdbcbdbbadccdccaabcacdccabcacccdcaaababbcaacacbbbadbdbdcccdddddcdcdbdbcacdbcccbaadddbacbdcabbaabbdcdacddccbbbccdcaaacccbcbabdbdbbacbbdcabadacbacdcdbdbbcdaaacaaacddccdcdabccacbddcaabbaacdddcbbacccbdacddbdcacddabcdcbdddcbbcddadccccdbacbcdccdcbcadccbaacdcabacdaddcddcaabdaaadbdcbdccaabdbbbdacbbbbbddacbaabaadcabbadcdaacabacbcddbadbdabdadacaaddacbdcbdabcbaacccbccdbbddbabdbdbacaabcccaadbcabcacdcacddbddbadabbbbaabbbcbddbbcdbddccbddbcabcadaadcbbdbaddabcbddbadcdbdaadcabcdaadcdbaddcbbcaaaacbdbaacbadddcbcbccadccbcbcacdbdacbcddbbabdadaaacdbaaccbbdcbaabbcccbdaddaaaaabdadadcdcdaccbdccccbbacabacdbbdcdaadcaacbbcadbbabbcabbbccdddbadcbaaadaabdbcaacdcabdadbcddaccbaacccbbaaadcadcdabdcbaaabdccbbcbaabbaacddaabcbadababdbadcaabadbbbdacbdaacbbcadacdaaaaadadbdcbbbbabaabcbcaccabccbcdbccacdcbacbcabcabbbbdbcdcbaabadaaddacaacadcbddbbadcbdadaaacdcdabaadcbcabacbbbcbcccbcbdbcdadcbadbccaacbabbcbbddcdbdbaaddbabbbdbadbaaabcccbdabdabddbcdbcbadaacbaddbdbdddadcbcdcdabbcabadacdaddcdccbbbacaaaddcbbbcbccadbabcaaacddaddbddbcbdcdbaaadbbbdbdbcbadccbbaadbadaddadddbcbabccabbdabcdaacacdabccbcabaacaddbbabbaababcabcddaaacaaacbcccabacbcbcdbcbaadbaddcbaacbcdcdcbddcbdadcbbacdbadcaabdaabccccdbdbdaaacdbacaacdabcabaabaaabdbbdabdacccacdcbaccddbbbdaaadbbabaacdbdddccbbdcddddbcddabbdcbccdbababbaccabdcadcbddccbaacbdcbdcbcbdcddcbaacdcdbadcabaaaaabbdcbccaabbacabbbdabbbccbabbbadaaababdbdccbaacbddbbabbcbacbabdcdaaabaaccaabdcccabcaadbcaaadbaabbcdacdcccacbbdbabcbdcaaabbcdcbacaddcaccbdacbdccbbbdbcbdaddcbaadcbdbacbcabcadbaaddbbdbcbdbaacdcaaabcacbaadaccbadbddbccbbdcadaaaacbdbabacdcddaaabbdcacbdcaadababbcadccbcbcbbdacacabcdbdaaacdccacaadababbabaddbbacabbaaddcabdaddbaacadddcccadccddbaccbcabcbcbcccccdcbdccabdbbcaadbdadcbdcddadcdcddcadddbddcdabdabcadacdbacdaccdbbbacdbddcbcbbbdcaaaddbddaaaabaadcddddcbacccbdababbbaacacdcddcbacdaacbddcbcbadcdbdadcadacbcadccbcccabcdcacddaddccbacccbbaabdccbacbcabdbbaddcbbadbacbacabbcacccbcbdcadddaacddcdddbccddcbaccbddcacbddbcbccbddccaaddbdacadadddbaabaacdbdaaccabbcbdddabddbabccddccdbbbaacbcdccbbacddddacbbaadccbcdbcdcaaabbabbdcddabcbbbdbdabbdcdcbbcbadadcddccbcaddcbaaaccdbdaaadddbaccdccbbdcaaaddabdbdbddabcaddcaddbdbbcadabcdbcdaaaccbbcccbadcdccadccdaccaaadbcccaccdacabddaadabadccbadbbcdcabddcdaadabcdcbbbcbdaacdaddbbbaddcacbadadabcddbaccbaabadcadbcdbddbcadcaadcccbbababccbbdaaaddddccdaccbcbcadcaddbcbbcbabaccdcaacaddccadaacbcbdbcbbaabbdcaabacdbabbabcababccdcaabcbcbadadcdccbdbaaaacadabcdacccdadadbdcbdbdddbcbbababcdaabcabdaaaadaabaddbddcdabadcbdbaddddaddaaaccccdbcbbabbdbccacbcdbbdcccbaaabbacbdbacbadaddbaacacababadccbbdbddacdcaaacbcdabcbaacbabcdbaaacccbccbbcaadccdbccccabdccdbdbdbddacadccbdbcaacacbbccbacbdccdcdabdcbdacdbdabbbacabbbadccaabcaddabacdadadbcdddddbacdddadbcbdaaababcaaaccdaabbdaaaabddadaaccadddbaaabbbbabdbdcaaabbcacdcbaccbbddbabbacbddaaacbcaabaddaddcbbbbabaaddaaccdcbabdaddbbcbcacbaabdbaccacdacdcddbcdddadaacadaddcacdabcaacdacaadddcbcacaabbbdadbbdbcddcccdaacdbcdcdccdcbcabdbdaccdaccbddbbacbbabccdbbacdcdcdbadadbcabccabaadbddcbcdddaadcbdaddaaaaadbddacaaabccdddbcabcababadabaaacccadbacbaacaccbaddaddbdcababbadabbbdcabadbdbacbddcadcabdddbdbccbbbadbaaacbcdcabbdababcdbdccaacaccdbbabbbcdcaddbdabbabdcabbcacacddbdbdadbaacabacdccacccaadcacabccddbdbcbabccdaaddcaadcdbbdcdabbbabddcacabcbbcdbbdcdcbddbcbdcbbbbacbadaabccdbabbbbbdcbaaacddbbaddcabccabaabcdccbabdadbcdbbacdacdbdddbdbbddbcacaccadaacabacabaaaccbbcbbaaaacaadaaaaddcabaccddadbbaccdcbdbacacbdcdbccbcbbdcbbbadbbbbddcaccbcbbaabbbaacbacccaaadbadcaaacdddbcdabaaaadadcacddbabbadcccabbdbcbcbcbaccdcaadabbadccabacaacdcbbdaddabbadabbdcdcabcdcacacdccabdadbcaddabbbccddababbabadaddcbdbddacadccaadcbaadbacdcbbbacaddccacaddbabbababdcbcbaccacbcbdccdbbbbccccacabddacadacdcddaaddcddcddacccccddacdaaabbbacdbcdbdbdbbcccacdaabcccddaccadbcbabbcacddbdbacdcbacddcaacdbccbcadbabccbdbdbabcbabbcacbcdccacbccbacabacdabcdbaccaddadbcbdbcdccbcdabaaadabbdddcaacabdabcdcacbdadabcadbadbacacadbbddabbbabccdcbabacbcdacdcdcbddcdcaaccdcaadcbabbdbcdbbdddacaaaddcdaadbcabdbccacbcbccbbaaadacdbcbdadbbdbbabccbabbcdadadbdbdbcbbcbacbacbcccdaddaabbbbbaabcbaadabaddabdcbadadaccdbdbabadabbacbbcbbccdabcdacadddaddbdcdbcbbbcdcbbdccdbbdcdcabaabbaddbddcbdcdcaabbabacaaaaabbccdabddcdccbcdcbacacbcbccdaacccdaddbccacadadcbdaddcbbcbcacadadddbababbdaacabdcddbcccaadddcccbcadadcbcdddbbcaccbaaccbcbaaaccbdbdacdacdaddaccdaacacccdddbcbdacccacccddcacdbaaccdbabcdbcaccbddbcdcaadcccbacbccccacadbabccbcbdadbbbbbdccdcdadcabdbdcacbcbdacbccbdadbbbcadcaaaddaabdcdcdcabacaacaaabdadabbacadabbcbabdacaddaddaaddaacbddbbddbbbcaacbddcabbcabbcddacbbccbbbaaddaddbcadbcabaadccdbabbbaaaacbccdcacdbabbdabdaaadbdbacbbbdcaabbcbdccdbccbbdbbdacbaaccbdadbbbdcdcbaaaabddcbbaacdcddacdbcadddbddcacccccbdccccaaacbbbabdbbabcacddcbbdcbacdbbcbaaddbaaaadaddabcccadacdbccacbaccddaadaccbdabadaaabaaacdadbbacabbcbdabdddaaaddbacaccaabaabcdbadbabacbaaccdaccaabbacbdcacbacbddcbbadbbdccbcacbacaddcbbdaacdbbcdbaaaaccddccddabbadbbcaccbddccdcbaacabccccbcaabaadacabccadababcbbcccacbaaddbacbdcddbdbadaaacbdbabdbaadccbdaabcaacddccbdcdcaddccbdcaaacabbcbdbdcbaaabccdcabbbcbbccdcdcdbbdddaadddccbcacdabbbccbdcbcbcaaadcadbbdbaaadadaddcdcbaadbbddaadbddbaaacdacbbcdbdcacdcdcccdaccacdacaddabcdadcdbddbcdadcacadacdacdaadbddcaccdbdbcdbccdacccccaddbbdcdcdaaacadbcdbbdadcddcaaabcaacccbcdaabcaaabaccddaaabdbbabbdbcbdaaadccccdcaccbcdcdccabbbacbabbcbdccbcaaabcaddbadcacdbdbcabbcbcdddccaaccadcddbbbabbcddcbcbdaadcdcbdbddcacbbcadbdcabbddddbbcbdadccddccccbaacbdacadabbdcaddaadbcabbcbbdbcdabbcadacdcdbaddccbcddbaacdddadbccbabcdbdbbdbbccccbacbacddbacddaabddbcdadaaabbdcbabcdcbdabacbbdccbadabccbbdacbbdddcdbbadbcdcabccbbccccadacdaddcaabbcddacdacbdddbbadbbcbacdddcbbbbabcacdcaacdbdbcadbdacaccdaaacadacdcbadbabcbccdcdacdbbbbacccaabdbddcbadacdddaaaccdbcabbccbdacbcadabcabdcdcbdbcaddbacaaabbcdacabacdcdbccaadbcddbbabdbaccccccaaaddabbdbabcddccbdbddcddababcbbbdabbabbcbddabaaaacdbaadbcdadadbadddccadacbbdbdcdabbccdbcccbabcaabcbabcbabaacbdaabacbddaabacccabdbccdcabbbcadcbdcbdabbaadaaabacdcbccbabdcacbdaadadbbaaccacaccddbabaacccdabdbdcbdcdbaaddaacbccbcddadbddcaaccbdbdcbddacbdcddababacddddaddadbabdacbcdccbacabcdcadcbdbccaccbbaccdcdbbaaacaadbbcacccccabbabcaabcbdbdcccdbdcdcbacddcdacbddacabbbcbcddcabccacbccccbbbcdcadddbbadbdbaabaddbbcaabccdbbaadddbaabdccadacbcdbdaddbaacccbaaadbcdbcdbabbaddacacacdbabcacadcaacdccdcddadbbbcbbddabaccaddcbdccbbbbaadbcdbbccadccdabadcbcdbcccbbccbdaabbabacbbbcaacaaadaacbdbaabccabdcaaccbabdbddbddcbacbbdbbbbcadaadabaddcadddbbbcacbccdaababccaddbabbdcbbcbddddbacaddbadcacdaddbbaaacaddacbaddabaddacbccccbbadddcdbcabaabddbbaaaccacabcababdacbabcbddbcbcbbbaacdcadddcabcdbaccdcbbcdbbaaaddabddbbbbdcccaaaddacadcaddacddacdccbccddaacbaacdabdbdbdadcdcdbbaabcbcbccabaddbacbccdbccbdacdabdaddadacbbadadcdcabadbaacbadcadcbaddbaacdbdbbaadcddbacabacdaccacacacabdcaacdababaabbdddaadcbbabaaacaabadabacbccdaaaaabcdcaabbcbcddccdcbbbacdadbccbbaabddaabccdbdcdbdddbbadacdcccccaabdccbaaababcabcdbadddacdcdacdcbbabaabcbdabacddadbaabdcadccbaabacdbdcbabddbddaabcccaddcabcaddaacaacbacccdccdbdaadbaadadbcddbcdabcacbbccadddadddcadadbdadacaadacdbdadcdbcbdbddabacaccccdababdacdddcdccaababcbbddbbcaacaacdaddcacabddccbabdcbbaccadbaacadcbaccaaccdcdabadbdddbdccdcabdcadcdccbddcabaaadcbdaaadabddbabbdbccacaacadccdbacacaababbdddbadadddccbbacaddcaaaacaadbacacdbbcdbcadbcbdbcdbbbbaabcdddbbccccbaacbcdbdcddccddcbacccddbbdcdcaabababdaadddabaaababbaaadaddddccdcbaaddbbdcdadbaababcaaddacadbaadbcaaccadbbaddbdccbcaccbbbacbccadcdcccaadcbbadcbdbbbcbadbcbbccdbbaabaabaddadaaaaadaccaaadddbacbaadcbcdbbdccdbadcdccaabbabbccbaaabbaddbacaddbbdbbbbadaaadcbcaccdbdbcccacbaaccbdcdacadabdacacdacacdaddcbccbdacabacababcabaacddcbdbddaadbdcbddbbccdabddcbdaaacbadbbdacbdcaacaabdacaacccbcdcdcbbabdcccacdaaaaaaabdcadbbbccadbabbdddbcacccdcaacccbcbdccacadbbadbbaccadcbddcabbbabdccdcdcdbaacadacbbbaaccdabbdbbdadcbbdaccaabccabddbdcacbbadbccddbcabaddcbccbabaadadadddaaabcbdaddbccbdadbcdcdabdabccadddabdabbadcadcacadbcbdaccbdbbaccbdaadcdbbccbdbbdaddcdacbdcbadadbaacbdddddabbcbbbdbdadabddbaddbcddcabddbccaabacacdddaccbadaabddbaabcabcccbbacbddccccbdcbbdabbaabbbabadbbbddccababdbddbbacacdbcbaacaaacbcbaccddacabbabbddaabccdbcaaacaabbabdabdbbdaaabdbbdbaadbdaccdddadabdcadabacaddbbbcbcdcabdadccaacaaabbacccddacbcbdadcdcdaacacadbbbdddbbbaaabcbccabdadcddccdcbbdbcbdbbabdaacaabbcdabaacaddabdcdbbdbdadcdbddaccbacbcadbcddabbdacbddcbbcbaaddcbabcadbcbcabacbbcacbccadacadadcbddccdbbddbaccddcabdadcaacbcdacaddbababbdbccadbcaccbcdcaabccccdbbaabbdaabbccbdcdcdadbadccbdaacadbacdacaccabcbabbcacbcaabbbadcdbbdaccbdcbdacdcdbcaaabcabcbdaacdbcbacacbbaaddbabaaaabdbabddbbcbbabdbcddccacdbbaadcbdbaaabbcbccdadcdddbccacbdcbbbacddbabadbbcdbcdacabacbcaaaccaabbbccdbdcabbbcccbdcbbcdcdaddbadbbbdcddaddcdccbacabbbcddabdcbbcbdbcabbbdcccbdcccbdcdaaabdbbadddddbdcacdadabddcacdbcabacbdbdaacbbbbcbadccbadcbaddabdccbbdaabbccdaacbcdacbacbdbadabbccdaddadcaccbbdbcaabbcdccadcdcdcdcabbdbdcaccbcbabccbdccccbcdadbaabacabcddabacbccadccdcdbbaacdbccdaccdddacadacdddadcadadddcccbacdbbdddaaabbdcccdbbcbbbabbaccdbdbdabadcddccbaaadcbaaabbaababcccabbbabcccdddcacaccabcddbaaabcbcddbaccdcdabbbcaaaddcabbbaaccbabbcdddadbcacbbaadcdcddbabcdddcbdabaacaaccbadbadcadddcdbbbaddacdcadcadbdacaacdbacbcbdcbbdaddbbdcdccbdcabdabdccdcccbabbaccbbbbcacacbcdbabbbdbadbcdbabdacdcaadacabaaddacbdacdcddaacabacccbcbdaadddbabcbddbadcddcddddbbbbdbcccbcbdcddddabbabddbccddddccdccddababbbcadbbacadaabccaddaadcabbabcaabcabadcbabbdbddaacdaabbcccdcccddbcdbbaaaacddaaabdbdaddddcdcaddadcccdcbdccdabaccddabdcddbdbcccadabdcadabaadababadccbabcdbdabacdadcbbcccaddcbbaaadddbabadcacbaaccabaddcbddbdbaccaabbdbbdacddccddcaacdadaabddaccddddbdcdddbbccadccbbbdcadddcddcdbacbdccacacabccbdabbccdbdbcdccddcbdabacaadcadcbacacbccaaabcdcddbccbbadcadaddaaacbcaababadaabcbcacdcdabbccdcdbabaabcccbbccbcdbcabacbdcdaacdaccabcdabbacaacbcbddbccdcbcdaacbdcdabbadbdacdaadacbcbdbbacbabddbbdddddbdbcbcdccdaabacaddabdcdbadcaaccabdbccaaacdbccbadcdbddcdcbbdcbcabdcbaddadaccccbcbdacddacccccbbdababcbbababdccaacdcacccccdcdccaaadbcbaccbbcddcddcaddcccdcabdddcdbbccbadcccbdcdcadddbadbcdadcaaddaddcbbcababbbdbaabcdaddaddaabaaccdcccbaabcabdcadcacbbcbdbbcddbbacabdaccbbddadbdcddcbbdcdddddccabdcddabbaabcbddabbdccdadbacdcaadacdcbccccbdcbcdabbcdcacabaccacdbabddcbabcdaccbdcdacddcbbaccacbdaccabdcdddcdbcacdadbccdddbcababdbcbacbbcaabdcaadbbddadbcbcddababbbbaadaccbdcabcacaabccdbdcbdbdbcdcadbbdcbbccabdbcbdcbbcbcbababcdaabcaabaccaddacccbdacbaacddbbdddbaabcbbdccbdccbbabbbcdcbaddcbdbbdbadcbacacddaccccaaaaaaadcbabddcacbcbaddadbcbdbbcccabdcadcccbdacdaacdcbbacdaaaaadcccbadbaaabcdacddcbcccdbabcdbbccccdcbdbbbccdcddbbaccbaccbccdacaaacbdbdcabcdcbdcacdaccbdcadaddbaaadccbdbadcabdccadbbabbcacddbcabbcccabaaddddbcccdcaaacbcdcadcccdbadacddccacabcbbcadccccccaacbaaaabccddbdbbccabbbcacdcbdcaabaccdddacdcacbcacddbcccaddbbbcaddacccadaabdbdbadccddacdbbbbdacdcddacdcccbcdaccdddcdbcaaccddacbadcccdcddbcabdaadcdcaaddbabccdbbaddcbdddbaadabdaddaccaacddcddabdabcabacabbcaddabacdcbaddbcbadcabcdaccbbcdadabbbcbcdcadcbcddcaccbabacbddbbbdbbbbcdccadbadcddbbdcddbbccbcbdccababadcbdbacddadddbbcdcbbdbdcacadcdbbbddccbadabcdaaaddcdcabbbbaccbaaabbaaabbbbabcbbabbdcbaaaccadbaacaaaabcddcbcabacdabaaababaaadcccbcbcddcbdbadcbaccaaaccacaabbcbaabccbdbdcbbcbdadcdcbcadbaadbddbadacabcaccccabbbcbdaddaacbcaddcddbadcccabcadabadbaaaaabcbdcbadbbddbbbbacbaaccccbdbacbaacddacadacbaacbcdbacdaaccaaddacccbacbbddbdaabddcccbbaadcccacdcaddcddbcccaaaaddbadaaaabdcbcbcabcdbacbbbbcadbabddddcddccabdadccdbccbddccdcbbbbccabacddbbdbadbcbdaaacacbdbdadddacacaadadcbddddccbabbaadcbdacddcdbcdddccdcaaccbbabbcbcddbacabacdadccddbccbaabdadadaddbdacdadccccdbbccddcbdddadabbccaddbcdbcabaadddacbdcddbdbaadabbbaacaddcccbbcddcbacadbcaabdcaacbbacacacdddaacdbdcbbadbbcbbdddadbcbdcbbcbaacccbbcabddadaddccacbabdadcdccaaddbbbacbaddacadaaddbccbbbacbccccdcababccaabdbdddcddcacdcaadabbacccaacadddcddcccdacadbdbbbbcdccbadaddddcdbdaadcbcaddcacdabdcddbbcdaacdbabadbaccaacbadddabcdcacdcaccacaadbbddbcaadacdbccdddcbccaaaaacdadcbaddbabacadcddababccadbbabbacbacdbcbdacdcabcabdbbadbbacbdddcdacdaacbccdbaaccbbdddcbcaacabbdadbdabdddddaaddbccadbbadcadcadaabcbbaccbcaabbbcdcbbcacdccaddccccddcadaccdcdaccbaadbacadccacaaabdcacbacbcaaddbacdcbccabadbdbbcbabcbcabbaddccccbdacdbdccaaaadadaadcaccbbcbcdaccabbbbdbbdbcdddabbbdaddacccaaccaaabcdabdbaabccdbddcbadccbaacabcbaabbaaccbdccdccbaadaaacdabccccdabacbababbabddcdbbdcddbdadaabcbcdbbdabcadccccdaaabacbcdbcacdcbaaabbdacacdcacbdbdcacabcbcbaaacadccabcdacaaacdaccabdaacdccbccdcdbbdcdbdbaddddacacbbbabddabacbbccadcdcddaaadddbcdcdcdbbdbcbbbbabadacabcccdbcbdcbadaccdbcbadccadabaacabbdbdccbbbcbbadbbabcacdacbcaabaacccdbcaabdbcbbabbbabdbdbdaadccdcdaadbddbadcaadcacbaabaaacbbdcdcaaaabddcadabdcccbbcbddccabdcddcbbdacadbddacdbcdcbdcdaddbbabbcdcaccbaadadcdaabcccbcdcbccbadaadccbacbbbaabcacbaadaabdacabcbbcdaacabcdbbadccadabacbddabaddcbbdcbcdbdccbadbcacdddaccbdaccaaacbbbddadaaaadcacadcbdcacccdbdbcdbaaacbaacccbabcacbadbccabcabddcdddcbbcbbdadbcbdaaccddcbacbbadcddbcbdbccccbbaacbbbdadccdddccaccacbcdccbdbbddacbaabcbaabbcbacaacdacabdaccdccacbbcbbcbaacdcddbccdbacadaddabbbaadaddbadabaadccbcabcbaaadbabbbaddccdabcbcaccbcbdbbbaacbdaadacbacacdcadabaabddccdbaabdbbadcbdadabddabbaaabbdaccbadddcadabbbcdadbcacacddadbadddccbcdddadcbadaccaddabbdabcaadbdaccbbddcacbbacaacbddaabaadabaaaabbcdcbddbacdcabbbbaccdadbdacbdcbcddcbaddbdaaabccacbbabddbadbdadbcdbaacbcadbcbaaddabbdadbbcacbccdabcdbdbbbdcdadcccbabddbacccaddbadcabbadbccdcbcdadadbcbbaabccadcbacadadaacddbdcccaabbbbdcaadccccbcaaabddaacdbbdaabbabdabcbaaadbccdbcdbabddabddaddabbaadddabaadbabacadcccdacdbacbbaccbdcdcbcdbdacbbcabcbabcdddbabcaabcadddbdccccddaaaccbbaadccbabbbbcdbacdccbbadddcddbbdcbcbaddcdaccccbcaacabcaddcadcbdabacbcadbdcbbdaabbccaacdbddcdbcaaaddadaccbbdcadbddabacacabbbcddccabcbbaabbcdabbbcdabdacbbbccaddbabdbcccbadcdbcaaabcbaacbcaacdaacddcbabacbaabbdabdcacdadbdbbadddbbbcdacaaabdcddccbabbacbdbdbbdbacadbcbdbabadcaadcabbddadaadaccacdabbdbacdbaabbcdadccadccdbbacadacadbaddcbdcdbcabcbbcccdadaacaccabddacaadbbaccadadacadacadabbabddbabbdcadcacdcaaabcababbdaaacdbbaaaddabcdacccadbdababdcacdddddbacadaaabdccaddbcbbbadacadcdbbacaadbbcbbdaabacaabcbbbdadbcabdcbadabcbbbbccdacdbbbdbdccadccccbdbbbddddbdabdbbcaccbccacacccbdbbccdcacadcabddadcaccaadabaccaabaddbbbcbdcbcccdacadddaacddbacaddccbacdbacdcaaabcaadbcbaddcabccccbdaccabdadaaadbdabcababcdacabcaddaabadbacdbcabbabaaddddcadbdbcddbdadcacccccdbcbdcaccbddccadadbdcacdcdccdaccbbcadabaacbaababdccaccdbdcbdbacccddabcccaacabdbaccdcbdadaaabacabddaccbdaadbdbdabdbcbcccdbdbdcdbadbdcbbbabcacdbdbbadbbdbbabdaadacddccabccaadbcbacaccacdacdbddbcbbdbacdbdddddbcbabbdccdbcbaacadbacadacbbaabdcbbbbdbbcadadbaddcdbbcbaabbabdadbbbcacddadbbcabcabcdcbccddbabaaabccbdbdcdcbdcbbaddabdccbcdbcbdbacbcddcdddcaabcbcccacabaadaadcabbcbcadbababccccadbbacaaabaadbbaacbaadabbcaddccacccccddaccdccdcbcccaacdbbbccabbabbdcddbbbadcaacbcabdadbcccbacbaaddbddbbccbaddcbdbcdbbabcbdcabcabadaaabadcbaaadcaabaaabadbabacbaaddcdacaabbacbbcccdbadcbabcdacaabdcdaabcdbbbcdcbdadbbacacabacbccaddcbbabdddddbadcbbddadbcdddadcbcaccaaaddbabbcbdcdaadcaddacdacdcdbcbbcaaabddaddacaddbaddcadcaacabcaddcacabdcbdcadbadcbcbbdbaadcaababddccbaaaabccbdbdcdddbcaabcaacccacaabbbcdddadabcbcdbacacdaddcabcbcddacdcadadbcacdcaaacdbdcdadaacdcbadccadcdbdbbcbccaddbacabbdccaddabacaddcddaacdbdcdadbdabcbbbaaccdacdbbcacbaddabddcdaccadaacddadadcabdbdaadbaabaddbaadbcadbdcbcbcbcccddacabdbbadccdccbcccbabdcadaaabaadaccadacccdcddaadcccdcdabbdbaddddbbdbaddabdccdddacaacccbddbdccbcddbdbcadcacccaaaadbdbdacccadcccabccabdbdcbcdbdcddbbccbcbbabbccccbbaaaddbcbddcadbaacccccdbdadcabbadcbadaaaabbcbcbdacbaddbccabdcdbdbbdbcabdbabcddcabcbbbdbaccbbaabbdaabbcdacbcaaccacacbdddcddbdabdbacaacbcbaabdcbdbabcbababdacdacadbadbcdbddccacdcddbcbbbcacaaabbdacddbbdcacaddcdcbacbcccbcdabacacbdadccbdbbbddadabdcaabccbbdbddbcbcbdcbbcbcabdadcbabaabdbaabacdcbaacdccdcabbccbdcacdbccdbcadbabadbaacacadaacbcbccdbcccbacdcbaddacdbaddadbdcabbacdddadbdaabcdabdcccdddcbacadcddbcccbcdccbccaddadcabadbdabaadbabadacccbcdabbcccddbabbabdccbbddbccddbdccbddacdadaccbaadbccbdbadadaccbbaabdccaababbccadddccccabcbddbaccbbbcbddaabcdddcbbbcbdacdcadabdccbcdacccccdbababadcdcbcdcacbbcbddcbbacdbdcaabdddaadbadccacbddbbbdcbbccacbbccaccabbbaabcddcdbbdccddabadcbcacccccabdcdddaddadaddbddadcacdddbccaddacaaaaccddcbacadadbbcbacbbdaaacabddbcbcbdbcacdbadbcdaccadabdccbdbcdbbcdacccddaddcbccddcadbbdcccabbbdccbbcabcbcccaddcddabaabbbcccdbaabdccacbdbcadbaaddcbcbbbddbdadbbcbcccccddddadbacaccaacbbddcbbdcbcccacaabbabacaddaaadcbdbbcdaaddbdcdaacaaddaabddadbbbdbbaabaddaadabcdcbdbdcbbabaaaddbcbaddccdbddcdaaacdbaabbcbbacddcdabddbdbbadabddbbccdcadcdcdbdbccacbdabddcbbdcaaddbaadcbbbacbdccacadccddbbaaacabbbbbdaddbaacacdabacbabcdcdddaccaddaadbacdddbaddaadbaaadacccabddccacbbadadbaadbbaadbcbabbcacddcabbcddaabdcdaccdccacaddcbacababccabbcbcabdddadbcabddbcaababadbcccccacccbabaacbdccdcddacdcbddadbbddcdbcabdaddbcddcbcdadddbdcbacccadcddcbcbadcbacdcbaccbdbbcadcddadddbabbcacddbbbdcbcbbaaaacdabaccdccdcdbbddccadddddbcccaaaacabdacacbaabbabddacacbdaddcdababcaccdcdcddbcddaabdbdabcbaddddacddbaadbbcbdcdcccccbdcdadacadbadbccbcbbdaddcbddbbbaddccbcaabbdbbcbdbdcddddcabbcaaddbaacdddcdcbcbdbddcdccbccacadacaaabcbacddbbcadbbbacadcccaaadbabbbabddadabadacdbadbaddbdcdcbddbccbacdaabaadbabaacbdacabdaabaaabcddaabbabbdbdbaddbadbcbbaadabccabbbadaccaacadbbcbdbaabdbbbaccbdcaacdaabccbcccbbdadbaadaddbdcccbbdbdcbadcdbdaccbaacdbccbbcdbcbcbdbdacddbcaabadcdbaacbadcaaacbcbaaababcbdbbcabdcddabccdadacbacaaaabcdcccbdcdabcaaddbaacccdbbadcdadbabdaacacdccdadcadcccacbcacbaadcbacadacbdbaacacbacbbbbddddccdbacbabdbabcdbcacccabbbccaddcbbdbcddbccbdcdaacaaaabbccabadbcacdbdbdcdacbbadcdaadbdddcddbdcabcaabdddbbbabdacdcbcdcddbdcabdadbcdadaadcabbbabaadcdbabbdadbaabadadbdccccbcbddabcacbaddbbdabcdccdcaadbcaaabbabbbaccbccaaaabaacacccbddbdaadcabbccbcabadaddadbbabacabdacabbbacccbabacbdddcdabbcbccbacbbdcdbdabccbabddcbcbdcdcdadabdaddbcdcbbacbdbadbcdbbccbaccddbcbcdcadaacbcaccacacddacccaabbddcdbdcbdadbadccbcaababdaaabbbcbabcddbcbcdcaaaaadcdacbacdbbdbbacdadbcccdbcbadccdbaaccbcbaddacabddcccbdbcadaabddccaabccdbbcadbccddbccccdcbabbcdadbdcdcbbccdbbbbbcadbbbadadbaaacdadbdacdcbcaddacccdbabdbbcdbbdcbbbabbcdaaaabcacdcabbccdcddcdbabdaaadbcaadbcaccdbbcaaacdbcabdabddcddaadbdaadccbbbdaaacacdddacdaaccbdadcddacdcdcdbdacababdcdcabbdabaadbbcdbbaaadbdcdaabcdacccbcaadbbcddccdcdadaaacbbdbdbbbaabcccabdbaadbcadcbdbacaaacbadadacaabdbcadcccabcddddacacdcbbdaaabaabaddbdbabcbacdbddddddccdbdbcddacbcacaabcaacabacdddcbabcacbcccccccdbddccdadccaaacbddbddcabdbcbdccddbcadcbbabacabbbaacadddaabcabddcbcacdcaccbbaccacabbaabdbadbacbbacdddabcbdacddaaddcdabcdbdddcababcadcdbbabababcbaddcbadcdaadbaabcbaaaabccdbdbbdbccdbcccaaababcdcbdbcaacaadbddabdaadacbbacabdabdccbdbabbcbcacdddbaabccdddabcacabadcdcdbdbdadadacccddadcaaccacaccccbdcaddabcdccdccabbddcdddbccdcddbdabddacacccadcbddaccabcdccbbaaadccdcdacbcbabbaabacccaaccbadadacdcbccdcccdbbcccacccadcacadbdbddbaaacaddacdbddaaddadaaaddaaabbcbcccaccdcbcdbccbbbbbccaacbdccadadcccddbdddbdbccbddacccbadcdbdddaccbadbbabaccdbddddaabcdaadbadbcbaaccacbadadbadbabbcccddbcbddcadcdbccbbcadcaccdcabcdcdacbdbbccbadaadddacaabdcacabddadbbdbcabbdadbbdcaaadccbbaacbdaadaadcbaccccbadcdcdbbaaabcdbddcbcdcabcbaadccdbbcadbdabbaccaadccadaddccdcabdddbccdcacdbacaabaccbbbcddbbaabaabbaaadaabdddaaacbaddacbbbadadbabccddccaacdccbbddadcdbabbcbdccacbdadaaaadbbbadbadddbbbccaaacbcbbadbdaaaabcaddadbadcabcdacbdabdccdcbaaabcbdcabbdaaddacdacdccbcbbdbcadbcacdadcdacbbabdcccbdcdcabaaccadcaababaccdcbadabbbdaacaaadbbacdbbaabbdcbbaadbbdacdbcdcbbbccabdbcccbadbbbcdcbabcabbbbcbdbdbdadcdbaacacacbdbabcabbcadcdaccabcbccbcbbdbbccaddbcabcdddababbddcbaabcbdcbadaacabbadbacbbbdcaddbbcdcadaadcbdacaccbacaddcbddabaccbdbbcbdcbcacbcbcdcddcdbadbabddccdcbdcdcacbcdbdaaccccdacbcabaddbdcbcabdbcdbbbaaabcbbcbcaaacbcacacbcabbdbdacddccbcabdabccaadabcdbccbbddacaddbacdaadaddaaacbbbbdadcbacbccbacbbcadddcdadccadadabcbadabcdbcbcdcccbcbbbcbacabadcddbdcbcaaaabadcbaabdbaccdddabdcbacdaaaddbbbbadacddcaddcdbadcbdacbcbbadbababadabbbcdadbacddcacaddcabbadddaacbadadbddddddbccdbcbaabdddbcdbdddccbcdccbaaabbcbbadadbdcdcbaacbabbaacaccdaaabcdbabccbdaaaaaddbbbaaacddaacddbabbcacbdaaaddcacdcbabaabbdaddacacccbbaabaacdaddaadcbbddcbaddbbbbcbccbdbddddccddaadcbbdddcdcbcbadbdbaadcdaacccaccbbcdbbbbdccbbadbadccdacdbddcbdbbddcadabcbccdbbccdbdddbabbbcddbabccccbbdabcdccbdcddcacdacccbcbbaabbddbbdbabadabacbcdadbadbaaccbbabcaaaccccadbadddcaccdcacbbcdbaccdcbbddbbbbbaccabaaacbddaddabbdcdbdbcaaaababcdcddaabbbdaadbcabbccdcdddbbcbabaabbdbcddcabbdcbdacadcdbadacbdabcabaacaddcccdaaaabaacbbaacaaabbabddcdadbaccdcaaccacdddcbdcbcdbcaaabbbabbdbaabcabbbacdccddcbbacbbdddcbbadcdcdacdcdbadddcbabbaabcddadbcdadabaabddaaabcaacadbcabcaacdaabbdaddcdcdbcddadddbbaadaaaacbbdbabaddcdbcabbbaaadabaddcbcbbcdbbbdbabdccbbcdbadddcbcadddacdcabcacddbcdcdbdcbcbccbcaccccdaacadbbadbbacdaabdadaabbdcadbaaddcdcacbbaaaddcddbbcbaaaddcaabaabbddbdcdcaccbbcadccbcbbadddcddcdcdccdcdccacbaaaaaaadcbabcadbbbbcaacaddcddcccbddacccdcaccbbbbbbcdacabcdcbdcbcbabdbcaddadcadbccddabcdabababcbcbaddbbcdaddbbddabcbddcaabbcdcbbdccbbbddacbbbdbadadaddacddbdcadacadcddadbdcbadddcdcbcbcbcdadacabddcdbaddbbddadacacaddacbbcdabdabdcccabcadbacacbdcdabbaaddcdbaccacbcabdbcdbbaddddaabcbbcdbadabbdaabacccadaadbdacbbbadaacbdbccbcdabbaddaddbbcaabaddcdcaacbbcbbaaabbbbacaacbaadaccaadacdacdcdccadbbcdbbdacbccccdbaacadccbdcddbcadacaabadddddcadcdbdadbacaddadadacabaaabdcccccdabdbadaacabbaacccbbcabcdcbdcddcddcaddaccaaaaaacbacbdaccdccabbddbabbdadbbdcabccaccddddbbdcddbdcbabbdabbdacbacacdbbbdcdbbacdaabaadababaadcddcacbbcdcabacbbabaacdaaccbadbccaacadadbbabbbaaacccaacabacaadcbdcabcadbdcbcacdcbcbddddddadcaabcbacabbaabdbcdccaccaddbcdbbbccabadcbbbacacaccaacbccdcabdbcdbcbadaddbbadadbddcdcbbdbccddbbcbcbdbcccdbccbbadddbdadbdbdacabddaddbcacddaababdcadaacadacddcddcadbdaadacacbdcbaddaadbbbcadaccaacaaacdacccbccdbdbacbbbbbccaabacddcbacbcdddbcdcdcbdadacdabbbcbabbccbdccadccabdbdcccaaabaaadbadcddbddbcdadadcabdcccbdddbddbdcbcadabbbbababbadbcacadbcaacaddbddcccdbaadbbbbcddbcddcdbbcaadbacbdcababcbddbdcbbdcddacbdadadbadadacdadacbcdbaaadcbdacacacccbababddcadbddccbadbdcaccbabbdcdacaddadccbadbddbabdbbddbdabcbaaddbaaaadaacaccbdccadbbdbdcdccccbddadacbaacbbcaccbadbadabaabcaaaaacadbdbaabaccbabccdbbbdcddbcbadcbbbbbcbbababbcbcbbbddabaddbcbdaaabdaaaabccbbcbcbbcbdbcdcaaaacaadccbdcadaccdcdccacaaabbadbccccdbdbacdbdcbcadbbbaadcbcdcbdbbbcaaadaaabccdbccdbdaadccbadadcdbccdcbadcacdbdddadadddbcabdabbbbdccbbccadcaddbcccadcadbbbdcdadaccdbacccdbacaabdaaacaaacbadadddbabaddbbcdbbbabdbbaaaddbaaabadadddcbdcdadbdadbabcaaabacaabdaabbbcadcbbbcccaddcaccddbcddadbaadcddddcadabdaddcdaaccadaacdbdaaabcabcabaaacdacbddaaccbbbadaacbcbccdcbaabdbabbbabdcdacabcbaccbcdcbbdcdbdaccdddadbdadddbcadbacdbcbcccabbdccacabccbcccbdccabcacdcacdacdadabcabdccbcacacbbcddaaaccabdaacaacdabccbddbdcacdcbacdacddcdbdcbbcdbddadadaaadadddcaaaacdaacacacadcabaaabbdcaddacadcabddccabdcbcbcccccdddadbbaabbbcdacbdaccabcbbaccddcdcacadcbbbdaabcdbadbdbbcbababbbdabacdbacbcdbacdabccacbcbccadcdcdbdddaabcbdcabbacadbbacaacaabcddcaacccbcdaccccaaacddcccbbacabccaccacadcccdbbbcccaddadaaacbabacddccdbcdcbdaaababbbdddddccbaaadbbbacbdbbacdbdaccbdcbbdacdaacdaddbbdadccdadbcaddbcabbabccddbdcccaabbddddacdddcabacccbccdabddacddaaccbadcdcbcbacbdabaddcbdcccdcabababaddcdbadacbacbdddadcdcacbcacbabaabaabdbacadbbbccaacccacddddbacbabbbbdddcdbabdccbbcdadbdbaddbdbbbabbaccdcabbbcddcadcbdaacaabdaacccabcacbbdcdbabdbbacabdcbacacbbdbcdaaddacbddcabdddaccabcbadddcaabbcbbdbcbcdadcaacaddcbacdacbdbdbbddcbdadaacdaacdccadacabaccbdadcddcadaadaccdabababdddbdbcbbcbbccabcccbaddcbdcbcbcabadbbdcddcabdbaadbaacbbdcbdcdbbbdabaadadccdacababcddbdcabbbabbaabadcbcdcbbdbcbacddbdbdadbbbacdabbbdcbdccaddacbbdbbaaadbadbcabdbbcbbccbddccbdbddddcdddaaabcccbdadcdbdaabbbabcaddabbcdaadbbdaabbbcdacbdbbcdaacddabdddcbcccdacabdddaddaccabaacacaabbdbacdabdcdacddbbcdddabbccbdabbcdcccaacdabccaabacacaaccbbbbcbbacacbaaabbbabbbabbdaacdaabadbcdacdbdddabbdbbaaddaaabdabcbbdaaaacbbbbacadddcbcbbccddaacadbdbdbaadcccadcbbabccacaaabaccabcbdabbaccdaacacdbdccaadbcbaccdadaabdcddadccbdacacabdacaccaadaadbabbbdcacaddbcccaadaabbbbdcbcdbadbcaaaabbdaaaadbddcdcdabbbaabcdbadabbcbccabbbcbbbbaadcabbacdcabcdaddccaabdcaabbbdcdbadcdbcacddccaadaccccbcdaddbcddbcddccabdcacbcaccaccbdadbdbacbdbbcdbacaaccbcaddaddddcdccbaadbddabcaacbbdabdabbaaccddbdccaaddaadadcddbbdcaddaccbcadcddbaaaabdcbaabdaaccabaddcbacdddaccdcbbababbddacbacadabbbdcbcddccbccdcccbddcbcacdcdcdccbbdcbcababaaadbbbcddcbcbcccaaddbacdaddccbbbcababcbacbbbbdcadabcbbdbbadbbbbabbdacabbdbabdabbaabdaabbdbcbdcbaaddccadaaaccdcbcbdbcdacabaacbdbcbbbcbdcadbbddbcacdcccdadddddabdabbdcccbddaabbabbaaccddbbabbbdbdbbcbdbaddabdcdcbdbadbbbaacbbccdbdcadddbddbbbdcacdccbddccccbbbbddcacddabddabbacdcaabdaabbcbdabccadcdcbaddacbbbbacdbdcdcdbbdccacaabcacdddadcddccddacbddabaacbcbcaaadabbcadccdaadadacdccdccdbaadcbdcdbdbacdaddbdbcdbdcccddddddbbcdadccadddddbabbbccacbadbbbccbdbbbbcdbcbddcbacdabdcccabddadadbaddaadbcacddbbcbddbbddddcccdbdcccaabbcbcbddbdadcdbcbdaacdddacbccadadcbbbcacdcdcdbaaabcdccabbbdabdbadadbddbabdbcaacdccaadaddbacaacddccbbcddcbcabdadbdacdccdbbbbadcbdbbbbbbabcbddcbcbdddbaabacbbddcadabbacbcbbadabdababaabdacdadabdacabbaacdbbbcbbadadcabddbbcdabbacaaadcbdcabbdbbcdbabbcdbacdabbaacccdbdacbcadabbccbdabbccdbbbcbcdcabdcabcbbbdaadbbaddbabdacbcdadddbcbbcaddddbbbcadcabbccdcadddaadcacdbcbcabaaddcccdddcccaccdbdcdababbabcbcdbcdbcbaaaccdabddccdbacadbbabdaacbbcbaccabdddaabbcadadcbaadabdababcbdabddbbdbdbdddacaaddaccbdcabbcbccadbacadbadbccddccdbbcbcabababaaaccdcacbdcadadccbcdabadacaacadddcadaddbbdcddabcbaabbabdbabddbcdcbbabcbddcddbdacbaccbbaacccbbdcbddaacccacacdacadcadabbdadcddcabbbbccaacbaddccddbccbdcdcbacdadbadacbccdccaccbbcbcabaddccbdadabccdcccbdccdbcbaddcddddcaaabddacbcbbcdccdcadadacadabcaccaacccaacacacdbdbbcdbbaccbcdadcdbacdaacdadcbcdbaacbaaaacadcaccdbccbadcbdacdabcdabcbddacdcabddaddbddcabcccddbdabacaacbaccbcbdbbdaabcabdbbddaabbbadadcdacabdbcbcdcabcdcdacdabcbcbdccbddccddadbdcaccbaadcdddcaacdddcbbaabcbaddabccccbbdddaacadbbbddcdbbcaabdbcbbadcbcabddbdcdcbbcdbaccacdcccccddadbaaacbbdaccabbbcdbddabbacbcbcdbcbbadacbccaccccdabaaccbbdabdaacddaccbcbbbacacdacdbbaacaacbbddaccdabbacabdbcadbaabaaccdadabbbacbcccaacccacbdbabbcddcbaaccbbacccbddcbadcbcabcacbbbccabcdadaaacabccabacbaabbcadbaccadbcddccabddccaaddbdcbcccdbdbcabcdbbdcddbbdbccaabdccdbdacbbdbcdaadbcabdcabadcdccdaaccbadacadacaacdaaacdcbdacccdaabbccacdbadcdddbabcaaacbdbaddcbdbdacaabcdaccdcddccadbacbbccbbbdacaccbaccbabdccdbcdddababcdbdbddbcddaaacbdacabbdacabacadcbdbacadcbbacbacdadcbcdbbcbbcbbcbbddcdbaddbdadccaccbaddcccabbbbaccdccabdbdaacdaddddacdbdbaabbacdabbccbaccbcabcadaadbbdadddbcabbcbcacccdcadcaaacccddaabaadcaadbbddddbcbbdadcdbcabacdddbacbbddcadabcbdabccbdaccbddaadbabdacabcbabdadddacdbaaaaddadbadadcbbbccbcddbdadcaccacbcddbbdaadabddaddbddccabdadccddcbacbabcbbadabcabdbcdcaaccdbddaddbdcabadcbcbbabcddcccbaaacaddcddadbbabadbadbdacdacdcadbbcadabdcbbbaadbabccacddaaccccbdadbdcddbacbcdadbbdbdcacacbbacdbccccbcaabccabccbdcacacccdcdcaccddddbcbccbdcaccaacbbbdabaadbbbabdadacacccdcddbbadbcadbddbadcacacbcdaddcbdcabcddcacaabdadccccbadbbaacdaacacabccdddbcadbddaabdadbccadabbbdbcdccbdaacbbdcaddbbccbbdabccbbaacdcdcbcbbabbcbadbddcbcccacccabddddcdccbccadbddbdadbcdcccbaacaccdbcbaadbacbdbbbcaabcabaaadbacadaaabbaacabbaacacbbadddbdacddddcbbdbaaacacadbbbdddbbcbcbbdbbacbaacaaddcacdacdcababddccbcabddcadcaacbbbbdababcbabadaaaabdcdccbcdacabdddacbbcdcadbdacadaccdccccadbadaaadbbdacccdcadbccadcbdcadcaacadaababccaabcbccdbdaaaaddacadabbaabbbbddbbacbcdacbaabdbccbbdbaabbcaccccccabbccaadddddacacbabaaccdaaccadccbaadaaadaacbaaaadbdddccacdabddbcadcabbacbcabbbcdadbcbacdcbabccacacacdcacccbdbbbddabacacabdadaabbadbdcadddcbcddabaabcbacacadbacbdbdcccbcbbbdaadcbcddacbcbcaabbaadbccaaacbcdcbcbabacdbbddcdadddbdaddadcbaadaabcdaadbdcbbcadcdcacbdcacbdacaabdcbbacbacdacbbacddaccadbbdcdddcbbcbcccdaaacdcbacbdadbbabddcccaadaadcacdaadacaacaddacbbcbcbaaccacddbaaadaccdbcbcaddababbbcccbbaddcbdabaabacbccadddabbcddcbdcaaaddbdabdcccbccccaabdcdbbcccaaacdadccacdaabbdbddbaccbababdcccbdabadacdccdcdccdbbabdcbccdbcddcabaccacaaabdcabcabdaaccccdaabccabcaccababbcbccbbacbbcdcacacabdbaaabbabbdcdbdacddcacbcaccbbddcddadacdaaddcbbabbaddbadbadbddbbbccdccdbccbabacdcdcdbaddaddaaddcdccabcaccbddbaddaccaccbbdbcdbdbaaccbdbccdcdcababbabbadddacdbabbbdddbbbcdaccdcdcacadbbbcaabacacdcabbddabdcbaaaccabddcdbccababccdccdbdcbdadbaabddaddcddabcddcacaacddbcbcaaadadaacacddbcabbddddccdbbadbbcdcbaddbbacbccadabaacccdbddacabbdccabaccbbdacadddabbcdcbcdbccbacadcdaabcbbacbacbbabcbccbcdcccdbdaddbdcadcdcddadaddbbaccaadcbbbdbdccbbcdcdbaacbccaaaccadcabaaaacbcaccccacbdccbdcccacbabdaadadcaabbbdcccbadbcdbabcccbdcaccdaddbbdbaddbcadddbadacccbbacdbcdbbaacdbcacadcdddabaddccacddabbbbcdadbddccdbadcabbbacbcdacacdbcaadadaccbccabdbdaddacbaacccddbdcaacacbdbddbbabddbbadbabcbbdadbaddcdcccdccddddccaddbabbbaaaaddddccdcaccabdcabddabdaabbcacbbcdbcddcaabccacbddcaabddcdbcacabababdcaacdaaddbdddbbaabbcbdacaabacadddbadccccdbaabddabcabcdbaddbccdbdacdbcbacabbbbbdddddcdcdabcdacbaadbddbccbbcdccdcbcbdaadbbdcbabacddaadaabcaaccaddaddaaddbcddcacccdddcbbbdbdadcdbaaadadbbcbbababdbabbdbadadbbacaddbcaacbbcacacbaaabdabdaabccbddcabccbdcdbcdbcddbabcdcabadbccbdaacdddaddcbddbbbbabacbaaacdaacadbccbbacabddacadcccadbbdddbdcbadadcabaddabbccddccdbbbdddabadddddbbcabddbdaccdabbbdcdacbbbdcacbccbcbdcbbcdccdcccacbbbbacbacaddbadbbaccbcaddbccbccaddbacdcadcdaaaadabbbacddccbaaadbdcaabdbadcbbabaccddbccbabbcbdaadacdbcddbdaaddcbadbdaaabbacbcacbacdaaabccaaacbabdccdadacbccbdcdadacaddcbbdaadadcbddddddcccaadadcdbbbbddddbacadcccbadccddbbdddabadcadaccdddacabcaccdcdccbaccbbbabdacdacdccbddddcdabddcaadccdadbcccadcaaadccdabcddacccccadbaadddbabdbcadccddacadcdcbbcbbcacabcabcdcabcabcddabbdcdddadbaccbdddbbbdaadcacbcdcbaccdbbacaddbdcdbccaaccddaacdaacadacacbacadddcaddabddddcacdbacbbacddacbaaadcabbabcbdbddbdbacbcadabcdadaddaccbdadddcbccbbddaacbbdbabcbababcabdabdcbdddbbbbbbbddccdbabacbbcacdbdbdbbcbaacabbaacbbbdbcddcabcbaabdbacbacaadddddcdcacbbdbdbcaccadacaaddccaadddbbbdcbbabcacaccbdacaddaababdcddbccbabaabbbdabdabdccaccbbcdbddcadbaadabaddcdbdadbbbcbbbaddadbbbadcaaccdcabddccdccdaacdcadbabacaacdaaacbaddbbdcacabdcdbdabddadbaaccddacaacbdabaaaccabbadbdcdacadccaabcbbdbdabacadbcdadbccdadbbcbadadaacaabbadbbddbaccccadbacdbaaabbaabaabcccacbcbbcddccbcdacbadcadccbbdacdcccdcddcbcdbcbccbdbdbccbdccdcaddbdbdbabccbbdbbddbabacdbdbadcadabadbcaccbbabdcccddaaabcadababdacabcacbacadbbbcbdbdbadcababdcbdbaaaababdcdabbbacaaaabdabacaadcdbcadaaacbaccbdbddcdbcbcccdbabaabaacbcacbddabdbcbbbcdcbdcbddaaccabacabddbacbabddaacccaaabbaadcacdbbadaaccbdabdbadbabadabddabadcbaddbdbdcdabacddabbbdbbbccdbbbbaacacddabdadbcbdbaddbddadbabaccddabacabdbbccbacaaabbcbcccdbcccdddbbacddbaabcbbcbbbaacabbdcaabcbcdbdbcdbcbacddcaaacbdbadacdaacacadcacdbcdbcaaabbbbbcdccdddbaddbbdbcdacccacadcccccadcbdbabcddaccdcacadbdbbdcdbcccaacaabadbadbcdcbcddbacaccdbbbcbdcbcbbbdddcadbdcbdabcbbcbccccabacdbacabbbcbdbadccbdadbabbdaacbcbdadcaaacbbccdcacabdbdaccbcacccddacadaaacddccddbcccdadaacdcadbaabacadaadbbcbcabcadcadbcbdbdccccdcaddaddabbccdcddddddbabccabbcbaaddbdddbdbbdbbdbddadbcadbdccccdbaaabbbcbacdbdccdcacbaccbddacdaabcdcbccdadcdaddabbbbbddcccbaabbadbddddccbcdcbdbabacbdacaccbbabdacbdbdcdcbbbdcccabaaabcaddaabbbddbbccdabdbbacadbbdbbacbcccaabadbcbbbaabddbaccccaddddddbdabbdbdadcbbddcccadacaadccabbadbcaaacabbcbdbdbdacbacbbacdbcabaacaddbccbacdabddaddbdcddadbbaaddbaddbddbbdcbaddaadacccbaaaadcdabacdcbbdbbdcabbcdbaadcdcbaddcdbbaddddadcdbcbabcbcdadcadabadcdcbbcbbbbbabdcdcdaddcaccaddcdabdcadabdcbccddaaabcdcbbbbdbabddccbddabacbbdaabaacaddbcaaccabdaadabddaaddacbaadcdccbaabaaabbcaacbabadbdadaadcdbacadadcadaacbacbadadcbdadaccacabcddcbaacdaaddaccdabbdbcbabbcabacccacacaadaaccbcbcbbddbbbadbdabdcdcccbacacdbddbcbacbaddcccdbbcddcacdddaaadddbdbcabdacbacaddbcbdacadbaccdccddbadbbdcbbcdabcccacabddbcbbdaccbdbbaacabcccaadcabbabcbcbdbbabaabbadcadbbabcacbaddddabdbbbaacbddbcdbcbdcacbccddddcbbacdcababccbcacdabdccabdddbcddcaabaddddaddacccaacbbbbcabbbcabaaadcaacdbadbcabbbabcacbacbcadadacacbbbcbcdcdccbabbcddbdddacbcaacababbbaadddcbdbacbcbdbbccdbcabbdbaabccbdcdbdaacaacccdbccaabcbaababaadcbbbaacadcbccabaddaabbbadcddcbcccbdcabcacabdccbdabbacadbcbacdcccbaccddbdadaccddacdcadcccadccbdacccbdbdcdaacdabacbbbdccbcdacadadaaacbaddacdcaddccbcbabacbdbabcdabcdabdbbcbdcccdcbcabcdbaabbbadcbaaaabbddbadccdadbbaadbbdddadacadabcdbdbdaacddcadbbacdcccbbaccabcdcccdadbaabbacdadbddacbddabcaadadaacccbdabbaccdaacdaccbabdddabaddbbaaadaadcbbbddbadbcaabdccaadaadbbaccdabacbddcdaccdbdbbdcadbdcacbccbdcdbcabddddddcabccadbddaddacdcabbaaaccdaddbbadadbccaadcdbccaccddbbdbdbdcbcdbcdbbacbcbbababaddadacdbbadddaabacbbccacbccddbadbaccddbaadbcabdccaaabaadaabbbcccbaddbaabbdcddcacdbdbbaddbddbbdaddbccddabbaacbadbcdacbdcbcddcbdaabcbabbdadbcacdbbbadbcbacadadcaddcdbbadcaabbcadabbaccddcbbbadcaddcdbdacccdccccadbaaabbdcacdbabdbbaacdcddcdbbcbadbccddcddbbcbcddadaaaccbcbcdcbbbabadcdbadcccbabcbcbcbbaabdbabddcbbbdccbbbaccbdcdababaddaabbadbcdacdcbbcaabacddbdaccdcdbaddbdbabdbdbadddbaaadcdbbdacdccacabbadacaadbcbcaacddcdbbcbdbdbbdcacadbccacccabdcdcadbbadacadcddbbccaacbcbcbbcdcacdbddbcaacbbacaadaccbbbabaadccccaddbabddadaabdaacbdabdcbbbcddbadbcbdccaccbcddcccddacaaccbcadddcdcabdbdabccbacabaaabbbdbdbbbccbadcdcdbcdacbcadbdccdbaccbacbaabdddddbdcdccbcdbcdcaaccbddadbabbbbabaaaabbdcdcabcdacdbbbbccaddbbccacabddbcbdcbcccccbbaadaaddccdbbacdcbbcadcbcbbdccbbcadbccdcccccbdcbdddaaccbbdbaaadbccdcabcbddacaaaaaabbaadccacdadbcdacaacaaacdaacdbdcccdbabbaaaacdacbcdbcaabdcaabddaababcaadbaacdabbdabdabcddbacadabcbaabcbacdbbacadbaadadccbddbdcdcdbabdcddabcccdaaddbadcbddbabdcbacbcddcdbadbabacdabcaaddddaadadbbaaaabccbbbaadbabbabdcdccacaddddccdbaddabbaacbaacdcbaaddabccacdcaddcdcadcacaacaadaabacdbcddbdbbaddaccdadbcdaccbdbccbbdbcbabadadaacdcbcdbaabacbcdbbcdccbaadbbcabcaacabaadddbbdaaaaaccacdbcaccadcdacbcaacbbcacdcbdcadcbccbcaaabcdcdddcaccbcadbdaaabccaacdcbdcccbbddabbcddbababcdcbbbbadddadcaadabacdcbbacdacbbdcdadbabdccccacdcabcddcbcccdabcbadaabdcabacabbccacbcdaacccacacbabbcdacbddbbbddbcbcdabdccbcadddbbacaabacbcabcdbdabbcacbbdbcddabbcadcbbccdcbcccaddbdbcbaaabadcccddcababdcabaaaacccaccdddccdadbadadddcabddbacadaabbddbdbaacaaabcacccddcdbababadcdabacbaacdbcbbcdcdaadabbacccddabacadcdcaccbddabbcbbcdcababdbcbbbdccbabbabacaaddddbcdcdcacbcaaaaaabbcacbdcaddbbcabbcacdddadaccbbcdbcaadddddbddcdcdaadaaadaddbacacbacacbcabbcaccccdcbabdadcbddbbaccaadccccddbbadccabdbdbbdcbbddddaddbdcaaabcbadbdadcbcbbcbcbccccbdcdadbdccdcddabcccadbbbdbcbccddcaababcbdcbdacdaabccaabcaacdadbacdaababcbbddaccbcadcbdaaababcbacdcacaddcdbcddbdcbadaabacabccadbadcaddcabaacbbdaccbdaacaabcbadbcadbabcbdaaaaacdaadcbddcdccddadbddcdbdabbccabbdacccccacabbadbdaabacabacbaacaccbbcacaaccbacabaadababcdaadcdbcdbcadbacdccbaaddadbaccacdadcbbdcddcddacaadbddcccddacbaaaaddddddbacaacdcdabcbdabdabbcbcbadbcdbddcbddacccccbbcddbaccdcdcadacbdabddcbdcbbbdacdadacaadbccbacdcadbdbdabcababcddbdbcccddadbdadcbadaddcbcbaaccdcabdcdadaacadbdcaaacddbdbacbcaddadbadcdbccabbdbcdbabcbdcbddacaacaabadaddcdadcbaabaccbaacdbacbadcdcbbadbaaadbddbcbcaaabcdbddaacdccaaaadbacacabdbdacaabbdacddbcabdbcbbdbdcbccdbcdbbadccdaabaabdbacdbacbacdadccbcbacbacddbcaaadddaaaabcdadaaddccbdaacccdabbaababaabacbbabdacabddbadbdadacdddbbbccacdccbbccaacbcdcbbbdbdacccaacbcacbbdcaccdbcbbabbaaacbcbdbccbabddcddccaaddcccabdbccdbaccbccaacbcadccbdbdddadcbcccbbbdaaabcdbcccaaacbacbcabaaacdbbcbcddbccdcacadabdadbdccbbbcbaabbcbdcdabcdbcdcbabcccbdbadbadcccaccbdbccbbbaaabaccadabcddbccdacaddacadcbadbaddbbacabdaadbaaaddddccdccbaaaddadbcaaabdbdbcddbabbdbcbbcdddbabcdcbaadabadbaacdddccaccbdbbdbdababadcadaabbbcdddbdbadddaddcbadbdccbabbddbaaaabdcacaddbbccadcdbbcdbccabdcdcbcdcddcdddcdbcaacadaccbbddacabcabccdcdddadadacbbcaacbadbcdcdcabcbcbcbaaabbdcbcabdaadcbababcbbdcdbccadbbaccaabccdbabdadcccbbcbbdccaacaacbacaacccacabdaaacdaccbbaccadccdcbddbcccadbdaaabcbccbbaaccbacccbcbdcabaddbcdcbbabdcaacbbdbbcbdcbddadbbdbabdabdbccacaaaadbcbccaddacccdddaddbbccbacbdccddcccbadbbdcdcbcbcbdccccbacdbdccdbbddcddcdcadbbacdbaaaabdcbcdbbddddddbcabaddaccdcdbbcaaccbcdcccddbdbdadcbcbbcdcbcdcbcadaacabddbcaabacbcccbcdcdcdbacddabaabdbcaadccdddadbbabdccaaaacbbbddabcdaabccbcadcacbacaadcaccbacdaccccccccdaadccdbccbdcbdadbdabbaacbadcdbcbcbbbaabaadddbcdbddabdababdaccabdcdcbabcbcabbbdbddbdbbbcbccbbbbaddacbccadcaccccabdbaacabcadbabbacbbacaddaadaadabdcabcacbdccaadaadbcdbbcaccdbcbadcddbabbddccaddbdcbdddbbadcccadadabcbdcaaddbbcacabcddcdbddcacdadbacdcddddababaddbadcbbcdacdbaacbccaddccabccbbbadcbcbdccbcbbccacdabcdddddbabcdcaacbdbcdcbcbbcaadadbdbabcbdcbccdbddcbdbadbbcadbaaaacadcabdaddddadbacaaaccccdbcbcbaacaaadacdddcbcdabaaacdacabaddccbaadccccdbcabcadddcccccdbddbbbbcddadcaadabcacbcdbcbcddacbdbddcddbdadbcbdddcaaddbcdabccbdadddadbbbaadcbbcdaccdccabbdcacbcbcacadbccccccadbbbdddbabcdcdabcbcacadabccdbbddcbbdbbcadcdbcaadacdbbdbacbbdababaabcbadcdbdcbcabacaaabbbdacacbddaacdabadabadacabcbabadccbaadcdcadabbccadacdaddbdabdbdccadaabccbbabbacdbdaddddbcdcbbdcabdcbcadcbbabcdbadaabadddabaaccbbdaadcaccbcaaacbadaabcbacdcbcabbccbbbcccbbbbaabadaacbabdbadbcabbcbddaadccaccbbddcabccdccaaadbbccdaabcacdaabbcbcaadbbbaadbbccdcbadccdaaabdbadcbdbbdccacdcaabbbabacbadcababcdcabccaacdaddbdabaccbcbccbdccaacbacadbdadadadcbadbbbabcbabdbaccacbdcbadbabaadabaacadbadaaaabbbacacdbdcdcabbdaabbabbbdbcdbaacbcbabdacaacdddcdbaccaabbdcbbcbbadacdbaacaabddbdcbdabddaababdbbabbdbcdddcabbcdddaabcaccbabddacbbddbbdddabcaaaadbdaadabcaadaccddbcbabbccbccadaccaadcdadbdadbcdbdcacbcbcbbaacdccdbddbbcdadcdcdcaadabbdbdabdcabccddaccadbdddacaaaacabbcaccddaccadadbdbcbddddacbcdbadbcdccaddbadbbbcaacacbbbcadadccbadacdccadbcccbbbabbaacbaddddbcdadcbcabbbaaacdcdbbbcbdccacdddbcbcbcbbddcbcbbaccadabcbadcddaabcaabaadabcccadddadcbcaadaddbdcaccdbabdccbbabddcaddaabbdcbcadddccddcabcabbcbdadcdcdbbbaaccadcccbbccbdadbdbddadbbbdbccadbaacbccccccaaddadbccbbbddbcbcbcdcccdcacdadbacacbbbddccadadaaaaaccccdacbddbcdabcabccbadbbaccaacabdbddaaaabbaccacbddcacdaacccdcbbacdbaaadacaddadddcdadcbacaccadcddbdccbbcdbcccabddcdadadaacbcdbbcacadcadbbcdbcddcdcdddbddaaacdcbcccadcdddacaaccbdaaaadbdbbcbdcbdbdadbdddaddbbbdbdbcbddbaabdcdaaacdccacdcadcddcddbbcdaddcbabccdbbbccddaabbdcbdabbadaddbaddaacacdadbddddaccbbcccabccdcdabbacbbabdadbbbcdbbdadbddabbadaaadaadadbaabbdccacbdddaabadbcadbdddbdaabbbdaaadadadbbddacdabacddadabdabddccddddabbbaabcabddaabddadbdbaddbdbbaaabaacacbcdcccaccdcbacabbadccbcdbccaabbcbcbaccabdadbbbadcdcbdbabbbdabddadbadddcbaddbbbdacbabddbabdddaaaadacdcdcaaacdcbcbbbccbaddadcbbdcadccaaacbddabcbabacaddcbccabdadcddcdbdaabbacabadcbbdaadcabcdabaadadbcadabbabbadacccdacdacddaaabddcdddbddbababcbcbdbbcdcbbbabdaddcbcadcabaaccaacccbcbddcdccaacdcdbbdabdacaaccdbadbccdaabdcbbcaadbadbcbcbbacddbacbaddbadadcdbdbbddabaaabdadbcdcccacdbacbdabdadadbaaadadacabdcbababbbaabcbcddbcdcacddbacddadbaabdbcaaabbacccdcdcbcdcdcddaccccdaaacbdacaadbaacbaacadbabcabbabbcacddaaaabbddbdacbbbaadaabacaddbcbcabbccbbcabcacadaddaabdacdcdcaccbdcacbbddddbaadaacdacdcccbdbaacccbbbcdbbdabddaaabddbaabdadbabbdcbacbcaacbbdcadabcbbaabdbabccbddcdcaccbcdcdadadadacdabcbccadaccacabbbaaaabbdaadbcdbcbcbdaddccbcdcdacbabbbcdddddbaddacbaaaacabcccdaabcbcaccacabbdcccadadcabbaddaddccbdadcbcadaabbbbdabaabcdacbccbbcdaadcbcabbbbdddacbacaadcbbcbcdaacdbdbdaabddddabcbcaaababdbaacababcdadbcbccaddcabcdabbaaacacadcaaccbcacdadddcacacacbccabccbcbdaaadbdaaaaadbcdbaaadbaaaccbbbddbccbbcadcdabbbdccddacabddadaabbccaaabbabcccbbabbbcabcdacdcaadadadbcdbcdcdabaccccaacdddbbdaacbaaabdadbcbbbaaccbabbdccbcaabcabdccaccadcdcacbdacdcaabcbccdbababadbaacdbbacaaabbabdaabdbdddaaaabbdaccbcdbbdacacbacbaccbcbcccabdadaacdbdabcddbcdabbbacddcdadbdabccabccddbbdaccabcaadacdbaabadddcccadadbaabaacccdbaacdaaaaabacddbacbadbadbddbcddcbdcbdacdccdabdabbcbccabbaabbadbdaabaccdddbcdaccabacbcddcbbbddcddbbcddbaabaaaaaddccdcdacccbbdbaacdbbbdcacabbbbcabaabbacbbbaccbbdcbbaccdbaabaddaadddccbddacbbabaaddacbdacccbaccabbcabccbcaccbddabbcaadaccddbdbdabbdacdcbbbcadcbadabacadbbcbaabadccddbdaccccbdaaacdddacdcbddcadbdcbddcabbacdddbadaabddddaaabdaccabcaddcabcadabaddbcccccaaadccbcccadbaccaadbaaccbdcbadbccbcabacbddcabdbabcbbbccacbddcadcbbabacdababbacaacbbbaccabdddcaabdcdcaaaccbdaaadaaccbdbccacabdcabcbbbdbbacbddaadaadcaaaaaaaaabcdadbbcdcacdcdccacadabccdabadcbaddbdddbbdcbccccabccbbbcccbaccbacadcbdbbcaaccbcabacdabbacacccccaaadbdadbdbbbcdaaacdaaaddaacacccddcabcaacbdbdacddcdbbcdacbcddaaaaadaadbbdacacaaaddbcdcbbccddbaacabddbacabccbaabaaacacbabbbbdcbcbbbacccdcbaaddcacabdbabdadadddcaacbbdbbbccccadcbdddaaadcdbcbcccbbccddaabddbaacbcbaadccdcacddccbdbdbcaddbaadbcabddbabdbbbaccabbaddaddbaaabbabdabdcddaabdbdddbbabdadaacccccccbcbccabcadabadccdddaadcbabadadbbcbbcadaadacbabcccadccdadacddabdacbdddcdaccdccbcaddbadacdaccaccbbccdaccbcdbadccbaabdcbcbccbadcbddbcadabcbdcaadccbaddacacabadddabbacbcabadbadbdaabacdaddabcdbddabcadaaacccdaddbcbbaaadaddddcdaccdddcdbabdbdabbbaabcbaaaacbddabbbbdaaadabbbcaadbaabbaddbaaaddcabbabcccdbcdadccdabccccbccaabbcbddaacaababdadaacdcbbcdadaaadadccbbbdccbadbabadbcccbbdbabcdcdcbadcdbcbadaaddccadcdbcdbbadcabbdcdaaabccbdadbbcdbaabbbdcadadbdbdddbabacdbccdcabbbdaaacabadaacabbbdcbccbabccdabdcccdccbbcbdbbddadbaadcaaaddaabbaabbdbbbabaaddbabacadcbbcbaccaadabbdbdddccbbaccdadadacdccdbacbacdacbdcddbbabbbabacdbbbcaaddddcadbcddbdcaabaddbbaacbdbbbcadabbacdacadbdbadcdccbdaadbbdbddcddaacdbbabdcadcbaadbcbcacbcbadcbacdacadababcbbddadbdcacbddbdbaadcadbcbabadadcaccdddaccacbacaadcbaaabaadcdbbcbbccacbcbabcbdadbcbaaacaccbdbbdbadbaccbbdadbbbccadbcbbcccaababdcdcbddcbacdabcaaccdaabaaabadbdcccdbdbbaaaacaddabbcddabbdadadbdadaacddaabcdbbddbbbcbbddcdcaddbcaccbdcaadcacabcbdabbabcdbcabccccdabaccbaddcbcbbacbccdaacdacbdcbacdbbbaacdcaadbbcacaaccddbdacdbcdaacbabbcaaaadbbcccacddbcdadbbaacabbdcadbdbadbacadcdaacdddddbbddbdbddcccbacbacdbdcddccbcbccabcbdcdcbacbdbdbcbcddddcbdddccdaccbcbacbbadccddacccbccaacadaabbdcbdbdcdcbcdabadacaccbdbaabaacdcddbaddcbcbababbdacadabdbcaadbadbcdbcaaddbcdccabaadcdacabbabaaabcadadabbccbcabbdcccdacbaacaddccdadcacdbcabccddddccbdcccdcdadacacadacdcdbcbbbacccdbbcdadcbacaccacaacbcdcacdadddabaddddcbcdcdddacbbbaababcaadbdbccbcbdbadacaacdccddddbdadbadaccbcbbbbbdbdbadcbacddbbddaaadacadaacdcaadadcbabacbbbcdacbaadcccbabaccbcbccabcccbddacddddadaadbaabcaadbacdaccbbbdacdddccdaacddbbabddacaddbcddacdacdcadccdcabbcccaaabadadbccbdcbabbdacddbdcacddabcdadbddbcdadddadccdccaacaabbccdcdcdbdddcddbdcabcbcacdbababbcacdcdabacabbbccccabcbdcbccacbdabcdadbbbbabdaccadbabccadbddddbcabddabcccdadaaccbdcadbbcbcbccacbbcbbdccbcbacddccaaadacabbbdaccdddadababdbccccbbdcddcbbacbccbdcbdcaaacdccadbccdbdacacadbdbbabbdcdabcbdadcaccaccadccbbdccccbbacbdadaddccdccdbddadbccbaababcddabcaacbbadbcbcbdbbbbbcdbdbaabdcbdbcabaddcaabccbbdacdaaacddcbbadbbddadddbcdcaadcdbdcbaccdbadadbbdadddccdabbdaddccbccbadcacbbbacbccadcaddcddbbacbcabbcdbcccaacaabcabadcbcbdadcbbbbaabacdbbabbccddaabdacccbdbbcacccbccdbbbcdcadbacaccccbbccadacddadaccbdbddcadabaaabdcbbabbbabaccddcdacccbbbccdccbbaaddbccbbcabbdddcccacbddcabcaabacbbdbbcdaaaccdcadbdcbacadbdbdbbacbabaacaabddaccdadacdaadaadcacadbdcdabbacbddcbcbcdddcdbacbbbadbddbbbaadbadbdaadbbddbaaddcbdcccdbdddcbabdcccaaccacbcdbbabcddcabaddbdbcdcacdcdaccdbbababcdbcdbcccadccdcbdcdbaccdddcbcbddddabddccaadcdbabddbacaccbacdabbbccbccbdcaddadccbaaaddcdadbccdccbcbcaabccccddbbccbcbcbaccaccaccbacdbadababbddddabadbaacbdbaaccddbddadccdaabdddabaddcddbdaddbaddbbcdaccbaabcacdcacbcdacaadcddcbbbcadddababdcccdcbcdabbcdadacabcdbcdbbacccbcdabbaabbcbacdbacbcacdcadcaddbaacabaabbdabcccbbacaaddcdadadbcbcbbabbbccacbaccaabdccaabbaacabadcadacdacacccddcbaaadcdadcdaccdcdadadcdccadbaddcabacdbbdbbdcaacbdddcbdccdcaccaccccddccbccdacaaaacdacaddbaabccdacdcdcdbdbcbcbdacdddabacddaaacaaddcbacbabccdbabcaaabddbcaacacabbddbddcdbadcabdcbdabacabadcbcacbadbdaddcccbccccddbccdbbdabcdcbbcbddbadccdadcadcddaabccddbbbddbbdbadbcadbcdcddbadbdccabacacadaddaaddcbccbdbacbcdacdcbabcdbadbddcaddccddbacdcbcbbbadbbdaddadadadccbddddcccadabccbabbaabbcddacddbacdddddbdabddcbbbadcaacddcaaaddcdccbacabcdcbaaabdacaabdbdcbbbbdcdcaadbcdcbdcacbdaadcabaadcbcccacabdbcbabccaccdbbbcbbdbdddaaccbabbcddacacdcaabbabbabbdcbddcbabcbdacbccbcaddcabcdbbbbcbaaabdbacdacaacccdaaabdbbadccacddabadbacbabdbbbdadcdcaaacabdadcabacabdbbbbddaadbcadcdadabbdaabbcbacbbbaddbbbcadccaddadcdbbcccddcaacbbcccadbbdbbcbcdbaabcacbdcabbddbbacaabcbaabaddacdcaabacccbbabccddcbbbbbaabbbbbdababccdbacdbbdcbacacaaaabbadadaadcbaddbdcdacabbccbaacdbadacbccdbadabcacababbddbdcaaadbbddbdcaaccdbaadbdcbcabbdbaaccccdbcdcbbaacabbaddcadccccbdacddaaddaabbcdcbdcdcbadacadbcbbbbcbdbcacccdccdbbcadcccbcbcaabadbdccdccadacaccababddccddbccdddaaadbadcbabaccadbdccadabccccabcadcacadcbaaabccbbccbaaacabdbbddacabcdcdcdcbcbbbacbcdcaaaaadaaaacdcaddcbaabcabcbccddbdddbcbadbdaddaabddbabaaabdaaddcacccbbabdadbdbbaabdbdcadcccadddbaaacbbdcababddbdbcaccdcabacdbaaaacbabdbcaadbbcaddbbbbcabbcacdcaadbbaaccbaaabcdbdabbbdcbddcacbdbdabacbbacdcbddbdadddbbbaccbabbccddabbaadacdcdbcababcaaacadbdddcccccbcddadacbaabcdbaacaddabdadaddbbabdadcdabccdadbbaddbbcdcbdbadddadcbabcdaadbbcabbacbaadbcaccaccbaccdaabcdacbcdddabbbdcdaabccdacbbbbccbbdbdbbbbbdbbacbabcdaadbdbabbdbccbaccddddbdbcabddbcadcbdaadcdcdadcdaadaadccbdbcabdbacddcabdccbaabdcbcccadacbcddddbccbadcdcdbbdacbddbdbaccbcccccbbbbabbbbcadbbdbbdbbccacbadacddbdddccdcaacdabdcdadbcdcdaabbbdaabbabacdadaaadaaadcbcdbdddcdccbdaddcabaaaaccdaadbdadaabbcbbbdddcddccbcabaaaccbdacdcaaababdaadbbcccbadbcdccacdcaddaddabdcabdaacdbbbcdddbbcdacdabdcdbbdddbdbdcdadacabaccaacbdcaaaaddccabdaaddbccaccabcdcccdbccbbaddccbccbbaadcbdbadbbcabdbdbaabbddaddcabaabadcdcdbcacddabbbadbdccbddccadbadbcdcdddddaadbdbdacccabcacacdddddcdbcabbcbbcbdbbcbabbcbbdcaadbbddbbaaadbcccdcadbabacaabcdaaacdcdcdbabbbbdddadaabcacdacdbbccbbbbbbccddddabacbdaddaaabddccbaaacbbabddabdccadbddcaadaddccababadddcbcbcadcbcbdddccbcccbbdcabacbdbacdcbacdcccbbbbadacaabbaaadcdccbabcdddcbbacbaacadaddbcadaacdacddbddbbbbbcacbbacbbacdcabdacaadbcbaadcbadadbccaaccadabbabbccbbabbcabcaccadcddaacbddbcabbaccbdacaccccdadaccdabbabadcdcbbcbbcccdddacddccabccbbacadccccadbbbdccbcaaccacbcddabadcbbacdabddaaadadcaabacbaccdbbdbdabccbcdadcdbabdbcbacddcdcaaccacbcddaacbdabcdacccdccbccbacadaaddaabbddabdbdbdaaadbbcdaabdcbdcccacbdbcaaabadbadbbcbbddaccabdabadaaadbdbcbbacbcaccdddbadbcdddcbabdcbccccacbadccabbbdbabbdaabadddabaacacddcadbaacbbdcabbcbdacbdcadbaacdcabcccbcaabbcadaddbadcbcbbdcbcdbcdbdbabcbadabadcbbaadbdadcccccbcaabbabbbabccaabbabadbabccaababdcdcadcbadacbbaddddcdddcacbbdadbadacdadbabbbbdacacccdacaddbacdaabccbdbccddaaddabdcbabbcbabaadcbaddcaccdaccccbdbddbdbabbbcacdcdacddcbbacdcbddaccddbaacbccdbcaadddcdacadbabddbcbabbdbcaabbbbabddcacddcabdcddcaccaaabbbddbccdcbaccaaddcdddbadbccccbccadbbdcdabcbccbcdbcccbabdacaadddcaddbadbabdcdddaadaaabbbbcabcbadabbddaabdaacabbbddadadadbbbdacbbacadbacccccbaddabcadddcbcbcbccadaaababbddddcccdcdbbcddaaabdabcaabdadccbabcabadcaacaadcbaabbcabbdcbaccadbccbcaaacddacadcaaccadabbacaddcaabbbbddcdababaadddadbcdccbcbadcabcdccadacdadacbacadccabdadadacdccdbcbaaabdddddaadbccabdbdddbadcaddcababadcdccbbbcdcacdcabcbaacdbcbaabcadabdccdabbbaadcccbbddcccadbbaddbdacacbdcddbbbccbcccdaadcbdddbdbacbdbdcdbdbdccaaddbcbbdbabadacacbaccbbcacdbcdcdaaabaaaacbadbcaaddbbcbacbaaacddacaabcdddcacabcbaabdbacaddbcaaabddcddadbabacdddddccaccccadbcabcccdaadabdbabacdbbbccdcdbdddcacbdbbadcbbcddddadccdcbcdababccbcccaacbadbbdcdbcadcabdcbbccaaadbddbabbadcbdcddabcbaaccdddaaccabdcdbadacabaadcddbbacbdccdabdbdcddaadadabddcbaabdcacdaddbcabdbaacdaadddbdbabaabcbbdccdbacadcbbaacbbcbbdddcadcbadcaaacbdacbbcacbbcdbddccddcdbbdbdadcdddcdbdcabcccbbbbcadcaddbbddbaaccadabdaddbbcbcdadcadccdcbaccadbdadbcacbabccdcbdbbdbabbabadabdbcbcbbbcbaababbddbcdcccadcdcbbcbbddacdacbacddcadbcccccdddbbcccccabcbbdaadaddcaabbbaaadbdccababbabddabdccacdddbabcbbdbdcdacdbcdddbbbbdaddddcbdaaddbdacbcdcbcaababdcbdbcbaddbccbaabadbccbcdadabddacbdddddcabdbcbadddbdcbbcdadbddbbbabbacccdbdbddbdbccabccaadaccbdacbccdddbcdabcadabacadaaacdbacadcccdaadbdbccdbddbbbabddcbccadbaabdbaccdbacccacdabbdbdaadbabccbdcccaccbadacadbcadbcbcdaaddbdaabadcbaabbbdacdabadbccdcdbabbcdaabbdbbbcccbcdcadbbbbdccdbbbcdbddabdabacdabbaaddacdaacabacdabbbaadddacbaadbcbabaccababbbababcdbabcaaacadbdcacdbcbacbbbacdacddcbdbacbcaadcbbcacacdbcabbabccdbcbadddadddbcbadcbabccbbaccbddbacbdccadbbccbdcdcddbbccdaabbbacdcddbbacacddccdbbdacdcabbaaacaccddabcbacbdaabcdcacacaabbddccbacdacbbcdbcabaacbdbcbdcabdbcadddbcaddbbaddcadddbdbcbcccadadbbcaccdadcdccbbdbddcbadcaabcddddcdaabbaddbadbcdbcaadbbbbabbcbddacabcbaddbbacdcaabdccdaccdaaabaddbaaabdbbbcdddadadbbaaadabacabddabadabadbbacdcadaacacccdbdbabbcaddbbdcdbbccbcbdbbbdadbdabbbbdabbcadabaccabbbacbabdadcacbbcbdcabbcdddbabacdddbbdcaadcdadbcacccacccccaacbddbcaccbbbbadbcabdbcddbbcabbbcaccccddadaacacdddcadaccddcbbaadbbccadbacdbbacdcccacdbbdcbaabcaabbacdadbbbdcdbdccbadabcbabaccaabcddaaabdabbbcbbbaabddbbacdccbbbcbdadbcccbcaadabbcadccbcbdbabbdddcaaaacdccbadaabacaaccddbbcbdbccddbcdacdcbbbdbcabbdacbcdcccbbaabbdbbcdcaddaadcbadcbadcabdcacacdbabdddadcadccccdbabaadbdcdbabaadcacbcadacccadbbadaccdcbcaddadbcabcadacbcdccbbadaacbbbaccbccdbdcdbdaaaadddccdaddddacadccaaadcbbaccccddadcacbdabdccadcdbcdadadacbaccacdaaadabdcbdcacbcccbdbbadcccbaacbcdbaaddcacdacbcbddadbacdccbcaabdaadabbdadababdbaccdbbaabbbbaacabbccdddbddccbaadcadbaadddadcdbadcdbadccdccbbddababccaacbcabcaadbccdbcaaacdbcdbbacbdbbcbcacddaccaaadaabdbddccbcdbadccacacdabddadccbdbbcacacbccccdbbbdbcccbbccddbddacacbbdcdbadaabcbcacabcbccadcdbcacacddbccdcacccdadcdadccbbaadccaacbbadbdbcadbddbcabddabdabacadcdbbdddbbacdcbbcbacdbbdbbddcaccbaacdccbadacdcadbabadaaadcadcabbdccbddddaccccdcbcbdbcdadaabbbdadacbcabbbbbdbaacadcdacaadacabcababaabacbcdbabbdaadcabaaadaddbabdddcddccdbbbbcabdbcdabbcaccdbbbbaadabddcbbaabbbaadacdcbcbbdacbdccdacdcdccddbcdadcdcbcccaaaacbddbacddccbabcdabacbddcaddadacbbbaabcdcbccaadbaccbabdbcccbbdcbbdcadcbabbcbbcddccdacddcaddccbdddcdaaaacdaccbbdaddabacbabbddcddadbdbaaaaccbcdacdbaccbccddddbacccaddabcbbabadddbcbddbbbbadbadaccccdcccbddadacdcaaacbccddacccadbbbaaabbdabacddabbbadaaccdddbccbdbdcabaddbbccaaadcdaabbdcbdadacaabddbbabbdabbbaaaaccddbbbdbbbdaaaadcccabbabacbababcbbddcaaadbddbddabbccccdbbadcdadacdbdddacdbddbcaccdcdbccabdbaabacddccdadbacdcbbacbddcaccbbdcccdccbcdcdbbcdccbdddcccbcdddddcacbabccdbbaabdccabaaacbabcdabbbccccdbbdaddcaaabbcaaabcadccdabcdcadcabcdbaddcdcbacddbbcbadabdbbcbdcbcbddbdcddbcdcacddbdbabbdaadbcbbdbbdcabcbacdbaacbcbddcaaadabababacdbacdbbbccbdddbadcbddbddbaaabdbcabbbbddbacbcbaaacdabbdbdcdaabcdbaadcdddadcabbadaacbcacaacccddacaabcdcccaccdabbddabbcaccbaacaabbbddbcbadacadaddccbcabaddabddacbacdabccabbcbcccdaddcaacabbddcbddadbbbbdcdaaaadaabcccccbabcbbbddcdddcdcdbaccbbacadbabdcbcdbcabbabdbbdbdabcdadcddbcdbddabbdbcbdabdbdccbdaadadabdbacccadbbabbdabbabdcbacbbbaaddaccbbadaaaaabdacbaabaccabbdabbacbdcdacaccaadcbbacdbabbcccbacdddbccaadcbcbdaaddbcdadbaccbacacaacdccdcbddadcdabbddbbbcdbaabbcbdcddbcdaaabdbbcbbacddcdcacbbdccacaacbbddaabcaccabdbcdabacccabcaadaaadaabdacdadabcbdcaabbcddacabadbacdbbbacaccabaabbdccabdcdcaaabddcbccdcdbcbaabcbdcbdaaacaadcacabcbcbcababdcdbbbdcccaaabbbdadabbcbbabbccbccbabbbacbcbabdaccdcdcdcbdaddbdccbbdadaccdadaacdaccdabdbdbcbbccccbbbcccdaacabcdcbcaccbddaaaabbaababdacdbdbdcbdcacadacbdcacbbbdddbccbdbadccbdacbbcdcbadcdaddcdcdcddccaadccdbbacadbccadcabdbdadcdcddaabbbcbcdcdbcbadbbadcbdacabdccddaadcabbbcdcbdcdbabddabcbbcdbabcdddbaadadccddacabbcaaddaacdabaccbcabbccabcdbadadabdadcadccaabbbacabddadcccabdadbbdbabbbdcbbbbabbdaabddadcbabcbaaadbacaaddadcdddaabdbdcabcbcbbdaaddbcadbbbaaddcbdcdadbbabbaaabaabbbbbddcdcadaccabbcabdcddcbdabcaacdbabcdccaacaccabdacaaaaccdadcacdacacccbddabaabcdadabaadbaaacdbdbdadcabdbdcccaaaaaaabdbcccccdddabaabcadadcabcdadbbdcaabcbaaddaaddabcdcdbaabcbccdadbccbbcdbcccccdacbbdaaacaababddabdccdaaadcdaccdcdcbadcccbbadacadabdbadacdbbacdcbccccccabcbdddbabbddabadacbbcaccbddabcbcacaaadadbcbbcbaabddbbdcccdacaabbbdaadbcaccbcccacddaabadabbdabbcbddaabbcbbacbcabdbaddbddbdcbaaddcabcbaccadddaacbbccbdbaddbdbdbbbdabacabbadadacaadcdcdbcadcacabadbcdaadbaabccbbbaddddbcdcadcbaacbddbcbaadacaadbbdcdcbbcbbddcabaddbacdbcbbccdabbdbadbccbabbadbbdbbdaccbdcccbdcdbbdbcadabcabbbabaddbdbdbdbacbcdccacacdccaccaccdbaddcbbacbbbcacabdddbbbdddadbdddabaccbbcdcabddabdcabcbcdabaabaccdababaadccaabbbadbdaddaddaaccccccbcbdbdbcdacdcbdbdbaaadbabdbbdaabacdaaacdacbbccacabadacbdadbdbbdddcbcdabbdadbcbbdcaaabcbbbacabadbcbabcdaaacbccadabdcdccbadcaddbbdddbcccaabbccddcdbddcdbccdbcdcbbbacdbcdcdabbdddcaccdcdadbbbaccacbadddaaaacdcaadbdcabdccdbbdcadaabdcbadcccacbbbbaaddcccdabdbdbcbbdcabdcdddcbadbbddacdbccdadaccaadcbacdbdbcdcccbaacaccabcdadcdbaacdcddaaabcaadcbcdbbcccbcdaccddacaccdbacbabbcacccdcabdcddccbaaabbbdbdccbbcdaaacdaccdbcdacdaadbcccdbcdaddbccaccbccddccaddcbdccccaacbdaadcbbdbdabcdabbacddbcccdbbccaaaaddbaaabdadaadcbdaaccbabdaacdcbbdaccaaacadbcadbaccbacdcddbdacbbbdccdddcbaccdbcdbccdcacababcbbdaaacbadccadcbcbdcdbacddaaaabbbccdaabbcdcdbbbccbcaccbbbdbbbbbccbbcdadcacaabaaadabdcaaabdddbabbbbaacdcbbaacacdbadaddbcaaccbdabcabcdcbaadbddbcccabaddbccccbdcdabbaadcddbcbdccacacccbabcdbbdbcdadddababcaaacddbbbbababaccadbdccbbacdcaadbcaaddabcadccbbbbbcbccdaacaaccdbacadcbbcabaaacacacabcdacbaccdbcaaccaaabbdacabcacdbccbbccaababcdabcbaabaaddbdccbbabccabcdbaacabbbadaaccbabacddbcabbbbabcbacbbabadbcbdacdbadbbacddaacccccbacbcdddabdbcddcdacacbccccbccaccdcbdbccddcbdcdbdaabbddbcacdddccccdbcaddddabdccdccabbabcdacacbadabacdabbbbbaaabdbddaabcbdbadabaabbbdbbaddbcbacdbabddbacaababaaadadbccbbddddabcdccabdcbabcadacdaaaabcabbcdbdabcdadccccbccdaaacdaaadbbdabbadadaaabdabccaacddacccaddabacbdacdaacdbdddbcbacdadbcbdadbabbbcbcbabbcaacdbcaccacbcbccdadaddbccaccdbdabbcdbccaaabaacbacbbcccbccdddacaabaddabcbadbaacdbbdabdccadccdcbacbaaabdaadbbcbbdadbadbbccaaccdbbbdcbcdcbcbaadbdaabdbadbbbccabcaccadcdaabccdcabcbcbdbcdbdcabcccbccbdabacccdadccddcdcaddbcacbcacaaadaadcdcdbacadcbbcbdcbcdaaadddbddbdbcccbdbaabcdcbbcdbcaaccabbdccccdbaccdbbacdbbdcaddcddaccacccbdccacbccbccdcccdacbbbccabbbadddddcbababccccdddaaccaadacdccccbcacbccddbbabcbcccbacbddbbcacbdbabacddbcddcdabbcddabaccbaabdadbcccaabbbadcccbadcaccdcbaaccabbadabadcbbbdbbccdddcbbdbacdccaabbaabbdbdcbcbadcbdacdbcabcacababccccaaabdaadcbbdacddbdddacacbbcccdbaabbdbbdbbccbcbddbcadcbabdaaababdadbaaaadbacabcadaadbbabddbdcdbacabbdcbbacbdacbacaaadaaaacbdacadbbabcbabddcdcddaaccdbdbcdbdacadddddaacdbbcdbcabaaaaabbacbdcdcbddcaacdbaadbbccdbdbbdadcabccbdddadcbabbcdddbabbbcacdbdadadcbcbccacbcdcadcddacddcbdbbabbcadcdaccccdaddcaccbdacdabcdbbcbdaaddccddcdadddcbadabcacbcbaaabaabbddccbdccabdbadcdbdddacddacadabbbcbbadacdbcbadcccbdaaabbbdbbcaadbbabdaaaaaabdbcdadddabcbdcdbacaabdadcccdbaacbddbbaacdabddddbbdbbbbdaddbddcbbacbbaccdcbcdaabdacacbbdcdcaaadddddadcaabacacabbccdcbaddddcacdcdbdcdbcbcdddbcbdaaaaddddddcbcdbdadbcdbaaaabbbaadabddcadbabddaaadddaabdbadcccacddcdadbabbbadcddabdccbbababcbabbbccaccbcabdccbcdcadcabaaaabcbcabbbbbbcdcdbdbbccbccbaacabbacccdbdccbcdcdccbddadaddbcdcdccbaddbabaaacaaaccddcbbacdabaabbdaaadbbabcdbbbabbcdbbcdacddbadbdccdcbaabbbbccacccabddabccaacacdbbdbbcdcbcddbcabdcdbbabddaaaabdccbccbcddbdaadbbbacadadabccaadabbbcbcbdacbabadacddcdbcdcaacaaaabaabbaaaabadadadcdcdadbcddcaaaacbddcbbdbbbabcbbcdacbdabccdbbdbdaaabcaabcabdabdddccaddbcbcdbcccaccdacbabbcbabbdcdcadcccdcadbaccbaddadadbdddadbacdaccccbdadabcddcddacbabcdaadbadbbcaababdcbaaacdbddbaadaaabcdcccaadccaaacdcdbbabcaddcabcbbabcccaccacccaccbdbcbaadbdbdabbbbcdbdaadccbcbdbcbabaaddbaaddcadbbacdcabaabbdabdbaaacacaddadbaaacdbccaaacaaccbcbbdcabccbaabbcddbaddbdabcaacdbbdaaccdaabaabcddbbdcdbbddcbdacbdadcbaccaaccbbdddabdbbbbcbbbacdccbadcbbbdabcacbacbaccadcbddbaaacaadacccacaadcabcbdddbaddcdccdabbaaadddbdaaadabbcccbbdddbabdcaabbdbdccacacbbbdddcdbddccaabdbbdbbcdcbabcdadbcdacbadbccbcdbacbcddcbbdcaabdabbcbbabbbbacbcbcbcddbabaddcbacbcbccccdaabbadcbbdcdcacbbcccaacccbddabacbddcdbcaacbbbcabccdbbdbbcdcadcbbaadbaddaddbbcabbaaadcbbcbcacdabdabdacabdabcdcdbbbcdbbdbdaaacdabbaadcaaaabbcdcccadcaaaddabacbdacdbdcdbdaadacbbabccbacdccaacbbcabbaddadaaababcccbabdaabddadcddbdbcacdcdcdcddddcdabdcddabbbabdcbdbdbcbcdcbbcdbcadaabbcbabbbaabaaabbbdcbcccdabbcbddadbdccdadadddbdbbcdbadbadacaacbadcbcbccacbdadcadddacdbddbbbacdbcaaadbcccabbbbdcddabdaadccbcbddccdacaaddcbdabcbccbadbdcdaaaaccddddddbdbbccbbdadaadadddccdbbbacbddabdccdcdbcdbccdccaabbdcdccccdbcddbabbadacbaddddcadbaabadbdbbbabcbdacbbddbcacdbdddacadcccdbdabaddcbdbdaabcbbaddaacbcbbbaccdcccbbbbcabbdccbddbcabdbdbcbcbaccaacbdcbdbdbaadbdddbdcbcbcadbdcccabcdbacdcdcddbbacccbdbbccdbcbabcbdbbbbdccacbdcbadcdbccbcbcabdcdbbccadbbdbbccccccccbcbacacbdcbcdddbdbbabcdacadcbbbdcdbacbbcabdcccbdbcaddbcdacccacbddbbccaabbcacabbadababddcdaccdbdbdccadbbddcccddccadbaddbaacbcabbaccccdcbdbcaaaabcdadddcadaaabddabcabbbabadbcddbbccbdcccbdaccbbccbadddcccbcccccaaadbdddcdadbdbcbdbbbddcdbadacbdbacaacbaabccbabbcccadbcaddcaabdaddaadddabbbbacccddcbddcaddcbdcbcdbcadddaddbcaacdcbdaacdaaaddcbabacaadbddcbbdccccdccbdcabaaddccaabdaccbbcbdbbaadaccabbaacdabcdaadcddbbabdbcaabaaaacadaddbcdddddccbdbbcbaadcadadcaabccccdcaccbaccbbbbbdddcccaaadacacdbbcaababdbdaadacbcbacacccbaddcdbabaacbdaabdddbbcdacabababbdbcbaddcacaaddbdabdbcdcccddbbccddaacccbcdbddbbddadccadadcbbbdabbaaadadbcbdabcdcadaabcddacccaacbddacbdaddcabacabccbbdbccdacddabdadadbdbddacbcbbabaccdcdbaabddbabccbdbcbbdaababbaccccccaddcabcbadbddbbdacddbaadaaacabaabcbacbcadcdcbcdbbccadbcabbccacbdacddbdaabddcadbbcadcbdbcdbbbcdcddcabaaddbbcbdaacdcacdcbbccabcdccbbdbbaaccbbccacddacadcaaadccdbaccddbbdcabcbdabdbaabdccacdccddcdbdabcdabaabdcdacbaaadbababadbabcdacaadbaabdbdbdadbcdcdbcaadbaddaacccadbbdadbacbbcaadabbbbbaadaccdacdabdccbccdcbcddcbdadadaabbabbbbccbacadcbbbaabaaddaaccacddcbdaabdbacbbaaaaaddcdcbcabdccbaacabadccacabaabbacdbbdaaacccdbdcdaacdcddcddddccabdbcdaddbaaaaccdbaaadabaabdcadcaadadaaccbcacadbcdccabadaadbbddcaddddadaacddbbacbdacbddccdaacabcdcbbdddbcdaaabbabdcdccdddbbbadbbddbabcabbccaddbacaaadbdccbdacdbdcbbdddccdcaddbadababdcabcbabddccabbabacaabadcdadaacbbdcdbcdbcabbabcbacadbcbdcddbcabccbbcaaaacabbcdbbdcddbcccbdbbcbbcaaadaddabacbccdbdcdbdabdbdaaddaadcdaacbdcadcddbbacdabdbbcadbcaaadaccbbdaacbdaacdddbcdadbdcbaccddcdcdaddadacaadbddabbcdcdaacdaabadbcabcbbcbdacbcabdaadaabbdbcdaddbbccbbacdaabbaabdbadbacaacbbdbacddbdccaabdbddcbacbbdccadbcaaaaadcacabbcbbbbbaacabbcacaaabccdacacadaddcdcccddbcaccabbbbdacbadabcccdddadbbdbdccccbacddcdddddbddbaaacadcaadcbcdbdabddabdaccdacbcaaddabdabaacabdcaabccbccbdadddbdacdbcdbccbddbadabddadddaddbdbdbdaddbcaabbcddabddddbcdabaccdbcabcbabcaaccabacbdcbdbbcbddbdbbaadcdadccbddaacdbabccdacbbccadbbbcdcdddbcadbcabbaaabcbdbcaacadaaabdddbdaddabcabbcccdaaaadbcaadabcdbbdcadddbabddccbbaccdcbaddcbddbbdcdaccdabcdddbcaabbaaadbdabccaabacccaaadababbcaccadccabaadccabdaaabdcddbdaacbcccadabcbbadbbbdabaadaccdccddbccaaddaddcdacbaadcadaaaabccddacaacbcdbcbbddbbbdaccccadadcdabcccccdccbccadcbccaacdccccacdcbacbcdbbabbccdacaacbdabdcdcdccccddcccabddabdadbdcccacbbaadbaacbbbbcadbbddadacdcaabaadacacdaaccacdbcccabbcaddbadacbccacddabcbbbdacddcddacaadcddadadcbdcdbcabadbaadbddcdcddcddaadabacaccbabdcdacabdadaaccbcacadbdadcccbacccadabcbbbcabcdcdbcadaccbdbcbddbbdddbaddcdcbdbdacdcbdcdbbbbcdacdbaadabadadadcadbaccbadacbdbdcdcddbdacccaacddbdcdacbcadacbccaddbdcbacdcccbdaabcbdbabbaaaaccbadabbcdbaaabbabbcaabacaadbbacabcbcadcacdcddbdccbbbadbccdaaddccdcccbcbaadccccdacdbcccbbbcbddacacbcacabaaadbbbdddbbbabbdcacdabcbcdcaccccbcacdcdbbcbdaaddccbdaaaabbaacbbdddacadabcaacbbaaabdbcacabddbddcbbdccbcddcaddaadcdbdbaaabcbcdabcddcccdbdbccbbcbadcbaabcdaadcbbbcbcdbabdcbaaadabccabbddcaabdcdabcddaacdbaabbacccbcdadbccdcaacacbdcbababbcbcbdabdaadcaadcccbcaabdccdddbcaccdacddbbbacacbccadcdcbaaaadaccccabcbadcbacccdcbcccdbbdcdbcbabcabdabbddbcabbabcbddbdcaabdabcadcaaacdcdcddabbccbccddaabacbdadbbbdbbabcbdcaddaadcbddabadcbdbcdbcdbadcdbdaabdcdcdaaaadcddabdbcacbacdabdccaccbacdccadcdcaaaadbcdbbabccccdaacabdadcbacdcaccadcdcccddcacdaabadacbcddbaddcbdcabaddabccaaaaabbdbdacadacabbadbcccbbcccabdacddaccbccdbccacdcabdcbbcdadacadccddcdbbabcbaaadbacbbcdbadacacaddccdaddbbcdcbbaaaababdacdbabcaddddcbbdbadadacbddacdbadabdcbdcbddcacbdbbdbcccdcdbdbbcdccccddabdacadbacabccadddacbabccbbaaadcddadcdcccbcddcdbbaadbcdbabcdbcbdacacacdcccadcaddadbccaddcbccccacdcadcbabdbacdcbadbbacbcaccabbbdcbaddacbccdcabcbdbaadbccdadcabadbccaabdaaadbadccadcbadbddbdbbbdacacdaadbcaaabdcadbdadcaacdddcbacaaadaadadcadccacabcbcaabababdabdccaacddaccdcdbcbaacbcccbcaabbcdbbcaacabaaddcbddddccdbbdccbacacacabcbbdbacbaadbadadcbdacdddbadcbabdababbacbaacbcddcaabdaacacbaacdbbababcaddcabbabccdcacdadacaabaccdbddcacadddabcbacaaaccbaaddbdacbdcbabacaaaccbcbccdaacbbbcdcbaccacadabadadadbdaddcdcdbcacabadbbbcaaaddddddcbdabadadcdcbbacabcabbcccadadacdbacbdaddabcbccbbdcbaadbbabaaababbcaadbdabababbadaabdbbaaccbaaadbacdaccadcdabdaadddacdbccbbacabbccaabdbdaabbbaaacaddcddbcbaccddbccbddccadccccdddadadbbacaabbcacbccacdcbcbacdbbaabababadbdabdbcccbbdabaacdaaaabdbbdddcdacdcadccbbadacaaabcbcdaadbcbcadbcbbaaadbddaaaddbcdbccccabcadacdccaadcababccabbcbbdcdaadacccbdddaadccddbaccdbdcababbbacddacbabbbadacddbdcccabdbdadcbbcbaccadcccdacbabbcaadcdadaacacdcaaabbaacccbcacdbbcbbdcabccbaadddcbccddcaadbcaaabacbabadcaccacbadcdadadbacddcdbdaaabacaaaacacddabcadcbdcdcbacaadcbccbdaddccabdbdacbbcbaabcacaccbccdbbdbcaaadbabadadabcbcadbbadadbdbddcccbbabdaaadacdccbadcbaaddbabcdccddbccbdddbbadbdcdcbdddbcdacadbccabdcabbccbbbbdbaabdabbccaacadddbacbcbaacdacbaaaacbbcaabbbcbdacbabbbbcddccbbbdccbabbcadbaccccbdccbbbbadbdbcdacabcccbcbacdbdcbbaccdacbadacadbdcaabccdbbbcaabbcbbbbcbcbabccbdabbadaaabdbaabbccbdbdaccadddddcbdbddadbbabbbabcdccdabcdbdbcddbddacaaaacdbddacbcbadbcdcdbdbabcaabddcbacdbcccbbcacbbacaccddabbaddcbbadabbcddccaaacacabbcdcdccddacddabcacbaabbaabadbcbbdbbcdaabcdcdcccabcbcbbcaadaabadabcadbbbbcadcbadbaaadcbbddcababbacbdaabadaabccacacaccbcbadbdcddbaadadbccdcdccbcbabdadcddaabacdbddbadcbbdadbcdbccdbbccbbdbabdbcadbcdbdbdbccccbcbbbcbbcadbcadcbdbbdbabcabadaccaaccccbaaccacaccdddbdbbbcabbcdaadbaaddddbacadbcbbadbcddcbcbcdcdcbdbaadcaaadbadbdbacdcccddbbadbddcaccdbbdbacddaccbddcdaaddaadbddbdbaccaddbabdbaaacddbddacaddcadbcacbadbbbcccbcbbbcabccacadcbaacdbbbbbdbccaadbdbbbabbaaaaddbddabccadccbabcbaadddcaddbbcbbabdbbcabbcbcaaacbcbdcadcbbadddcccaccddbacbbddcccbadcdaacdacdbdaccdaacabbbdbcdcbdcadccdbbbacacccadacccdcacbdbaabbdacdbcaabcbdbbabbbcdacdbdbadbadaabdaabadadbacdbdddbbcdbaabaadacdcbddccbadbcccdcddcdcdbbdadccaaccbacaacacbdaaddccdacadacaccbaaddbaddcbbcdbdbacbacbcbcabbbddddccdaabacbddcbcddbaadcdcabcdabbbcdccaddcbbcbacdacadbdddbdcdaacdcaaaadcbdcbcacbabbacaabddcdcdccbdcbbdaaabaadcacacbbdadbbdcdcaabdaaaacdccbdbcdcabbdcaabcbbddcddbabbbcccdcbadcaabbdcadababcaadcdcbdcadacdcdcbbccabccbdddadcbbbbddabdaccbdbbbabbcbbdbcbaadacaaabdbacdddbdcddbbdddbabcacddbbadccbccbaadcbdccdbccccdcdcdddbaccabaddbbaaadbcdddaadbbbbbdabacdccdbabadbadabcaddaadbcdabccbdcbcddacbdacdacacacaabdbabdaacccabcaddababbddbbddbcabdabdbcacabadcbdcddbaabbbcbcaaadabcdbaadbdbbacdbcbdbdbaaaccbdbacbcdbcaacdadbbcbcdcdbaabccccbacbccbbacaccddaadabbbccacbdadacaddbaddcdbbdaddabbccaaadacbddccabbaadddadddbbbdbcbbabdbcddabddbbaacdcdacbaddadbabcbdbcaaadcccbccbdcddacacccabbcacdbbbdbacbbbccadbccababaaaadbbccccacbdaadbddadaabbcddaaabaacadbaccdcaaaabcacbbbcbcccdbccddcbaddccbcbbcbadbdbacdaabadcaadcdcdcdcbdddcbdcbcbacdcdaabaacacdabbcaaddbdadabbdacccadbdbdcdaacaabaaabcccacddbdcdbcddddbbbdaadbabbbaccabcbbadbddbdaadbbbcbadbcaddcabbaadcaddbdabdbbcdaabdaccadadcaacdabaaddbdbcdcabbaccbdddabddcccdaaacabbdccabccacddbccdcddcddddcadddbdababcadadcbdacadbabbababccdbaaddacbbbddacaadbdacdccbdbdbdcbcbdccbbdbdcbcdccccabcabbdccddaabbaaaddbdddbbdccbccbcaabdddddcacaadccdbbabbbcdbbbbbdcccadbcbcbcadaacabaddbcacbbccbcbacbacbacdadbdbaabbbbbdccccdddbdadddabccddabbcaadcacdddccdcabaccaacbacccbbdabccbaaabdacbabbdcbbbdcabcddcccadddddacdaaaadbdaabcacbdbdbdcacbdbbdacddbdadccaddbadccbaacaaddccabaabbdcbaddbbcbaccabdccbbbbcadaaadcbdcadadaccddadbacdadcddcdbcdcabdbcaccbccabacabdadbdbbbbcadbcbaabdcddaddabdbbbacbbabbcaaadacadaadbdcabdcbccdcbcdacdbccccdbbccbacdaaaaaaccdbbacdcbbacaaccdcccccbcddcaaddccbaccbacbdddacbcdbaccabbbcdcdcdbcdacbdabaddbacadbbdcabbbcadacaccdadbbbbacbdaddccdbcddcaddabbaccdcdcaacabddddcbbacccbbdcadcdabcbaadadaacaadbcbccbdaddaabcbadcbaddccdcccacdcacbaacbddccbbbadccbbcddccddcddbdabddbacdadddabcddaccddcdcaabbaababcaacadaddcbddbcbadbdababdcbcbccadbbcabcbabbadcdbccdcadcaabbcbadddcbccdbdddadaddbdadddcbdbdbddcddcadcbaadacdaabbabdccbcdaccacabbadccbdbcccbbcbdbabaacaaacbddcdbbdacbaadddabbbabdccccdaaadbabadbbdadacddcdbdaacccdacbcbdcbbabbdaaddbdbadbacbacddbdaabaccaacdcdcbacbdddddbbbdcbdcdacddaaadbcdcacdcbcbcbbaabbbadccdbbdcdcadbbabacbbbaccccdcbcdbddbcdbddaabbbdccbcbccdbccdaabcdaaabbaccbaadabdcadbacbbbcaccacccdbdadccbdbdcdccaabdddcabadaaddcdbdacdbdccacbdcaaabadbbbdbbadddbdabdbdbdacccdabbbabdcbadbbccddbadcbcbccbdcbdaccdbbaccadbbbbcbdacadcaaccaccbacaddbdbadacdaaddabcbbdaaaadbcdbdabccacaccddacaccdadadcccddbdbcadbdacbccbacdbbbdbdaadbbcccbdbbaccccaaadacdddabbdaadcaaddddcaaaacabdbdcbbacdcdbcbdaadbbcabdacdbbdcbaacadaddcdabaaddadbaabaacddadddaddbbadaddcadacbdbaadadadcdcbdddbaddbdabcdbccabbdcdacbdccbacddcdadcaaccabcdccbdabcadbdbdcabadaaababacccacdbcadabcdbbaacbcdbbdbadacbddacaaaacbbbbbddacccddaadabdbdcabccdddddadaccaabdacdaacdadacaaaabccaabcbbaaacabacbcccdbddadbddcdaacababddccbdddcbcbbabdccdacddcdbcdbbcdadcdbadccdbbbcbbbbabbcbaddbbbbdbddacaabbdaaddbcadbbdcdcdcbdcadccacbacdddcbcadccdddabdbcacbdcccaccbcdcddbcdabdbaacbccbbbddccddbbbbadaaccadcddaaabccbaaaddbcbddaabcacacbdddcaaddccbbddcdbdcdccbdcdbbcddacdddddadcccbbdbbcdabdabbdbdbbcbdbccbdbdbcbbaadabcdbbcdbcbaabadadcdacbccbddadcadbccbccccccaacabbcadaaddccbdaacacdbbdcddcbbcbcaabacddbcaaaaabacbdcdaccabacbdacaaccbbcbcddbccbabacdbdaabadbacaddddcaaaacadadacdddbbaccbaaabbccddccbabaacbdbbdbccaadcbaabcddacddbcadddacdadcbacdbaacdbcbabdacbccddacddbddbcbcdadbaaadacbcdcdbbddcdbdadaccddbdcbdbbcbadaadddcbaaccddcbacabbadaadcbabcdabcaabcaadbbbbbdbabacadaacaaaaaacabcbabbacacbdbabaccaadabcdddbcdbdaccbdbdaddabdadcbdcdccbcdbdadbdadddbadacddddccccadcccdabbbbbabaaaaadabdcccccaabcaaadddaabbcaacddadadbccbbcdaacbadbccbbbaccccacccbaaaabacdbbdbaacbcbdaaadbababddcabacdacddddbbadadbbbcccddbcbcabcbcaaabdaaddcddddabacdadabdddacbabaabcdbbdacbacbdcccbbddcbdabbbaddabcdadcdabbcdacacabcbddbabbcbabaaaabdaccbcadcdbacabdabcccddbaacbcbaaaabcbccbadcabcddcddcbdccdbbcbacbcaabacdbccaaccaaddcdbccaaaabcbacadcadcbbdccbbdbddaadacadacaadbcabdcccacaaabbaddddbbbdadcadadbcbbcadddcbcaacacabbcddcbbcdbddbaccacbcacdcdbcaddcdbbbdbadbaaacdcdcccddaccdcbadccdacbcccddacacbcccccadaaaabcddcdabccbaddcadddcadacbabcdbdcdbdcccbbcddcacdbccbcbdcaadadcadddcbccbccbcbccdcbbaccaacabbdadbdaaadbccccdaabddaaacddbcbccadcbbadbdadacccbdccbdabaaadbadbddddbccddabaadcadbccacdcbbaacbbcdbbdddcaaaaaddaaabaadcadaadbcaacbbadccaabcbadbadabbdabdadabacbaddaddbccccddccdbbddcdacbccddbdaaddaaadacccdcbabdbbdccdccddaacbddbbdcdbdbbacdcbadbbcbacbcdcdcbddaadadaadddbcbaadbbbccabaaaadddbcbbdbcbdadbdddbbdcbdcabcbacaddddcadcbdcbddbdbdbabbabbaacacdabcbcdcbaacbaddcdcbcbcdbcbdbabaaddbaddddccabaadcddacddbbbcaddcbbcadbadadbdaabbbcabbcccdbbdbadcadcacdbcccdbabbdddbbaabbcaadaccaddbabacdaabbbdcdacbdadbdbbdabcaaaadacaddcbcaaccaadabcbaccccdcdabdbcdacbacbbadcdbdabbccbddddccadddadbdadbadcbcbdadaabbcddabacaaddccdbddacacccaabdababbabddbccdbbbdddddbbcaccbbabbcaabcaacbdbadbdacbccaaccbabcbacabbbbcbbdccccdadbdcdaaccccbdabbdaadabdcdbacaccadaddacbbbdacdcbdbddddbdddbbbccaadbbdbabcaabdaacdcddccdcbccbbbaadcddbadaacacbdcdcacdbadbdbcaadbabcdcabbccbaaccbddcbdbccbdabbcbadadcdbaadaabbddccdbccadcdddabacaccdaaacbcacaadcdbdbbbbcddaddddcbdacbdbaacbaadddaadddbdccbadacdccbbabadaacccddaaddddddbbcccbbdaabbaccbbaddababccbcdacdaadbdccbdbcdbdaadbcdcabacbacdbcdddbccdcdbbbcdcadbdbaaddcddddbcbababbdbddbabaadccdacdacbabcdddcdcbccbabbdccbdbdcabadccdacccdbabdcaadcdbdabbdacbcbacdaabdcaccdabdcdbdbddcaabddabadaacddadabbacabbcdaacbdabdaabaaaaabaaaacabdabbbccddbccdddabbdcadadcbbbbbbabaacaadababaccdacacdacccadcbddaaabbdacaabdcbcabcadbcbcabbaababdacccbadbbccaccaadbdaaddabcdadbdbbaadacbccaabdddddbaddccbaccdcddcdadcdcadcccaaccdbdddbbdabdbdbcdaaadcbaacbcccddadddbaaccabaaadabadadabccbbdbbddcbdaddaccbccaddbdbdddcddccbddbbbaabccdabcccddaacbaaddacbdcdcdbabdacbbddbcdcbdcabbcdddbaccabbcaaabaabcdcbbcbbcdacbbbccbdcbcdcaabacccbabaaabbdcadddddbacbccdcddadcbdabdbdadadccdabadddbcadabccbdbdaabcbbcdccbdbbbdabdcaccdadbdccaddbcddbacdbabadaacdaddbabbdcddcbacbdddcaadbabdcbbbdbcdcbbacadabcbcaababcabaccddabdbcbababcbccaddacdbddddddbcaddbcbbaacacadabddaabccdbadbbddbddaabdbbcadcababcbadbadcadcdabaabdcdabdabddaabacccdcccbbbcbaaaabddddcaccbabdadccacbadbbadbdcaaaaddacdbabdbcbdcccbdacbcbdbcbbcbcdccbacabcabaddbadbdbaacccacddbaaccbcbabbbbccacdaacaaaabadbbbbacccdddbbccacaaccdcbcbccaadbbccbdcbdacccbabadacbdccddcbbdcadddbcddbddccbabdddacdadabcadadbdcdddbbcdcaadabbadcdcdcdbaccaccccdaddbdbcabadbbcdccbaacdbcabbacbcbcbcaadccbddaaaabaabcdbcbadadccdbaddbddcabdadaabbbaadbdddaadcccddcdacaddabccadccbdcabddddbdaaccaaaaaabdbbbdbbdadbcaccbdbdaaaacabaadbbdacdcadbaaadadcccbbdabccbbbaacdaabbcdcdbbbdabcacabbcabdacadbabcbbddcacbabacaaadccbcbcbdbcddbbabdadaddcbdbbaacbcaaaddbacaacaccddaddbdbcadccaaddbbacacdbcbcbabbbdcbaaacbacbdacbcdabcdbbbaadbdddbbddbcccaabcdcddcbdbbdccdddaaacabdadbabacbdbdaacaaacbcbcdbccabbaacbccadbbaccbbbdbcdbccadddadddccdaaacbbcbdbdddcacdaacbadaadbbaabbbabdaabcbacadadacaacbbdbcddbccdbcbbdcdcbabddaaddcbbbdacbdbdbcdbacdababdbcaabcdcbcaababbbcdadbbbccccdbcabcdbddcaaacabadabcdadccdabcdbcabdbaddbdcacadcaccbcbdccddcccbbbccddadabbcdabacabdaacacacbbaccadcaddbadbbbbcbdcacabbccdcacbcbababbbdabdaddaddbbaadbdbdabcbcbbcaaaddabccaaddbdabddbaaabcbbbcacbccdbacbaaaabdbadaabddbbcdcbbbaadbddbbbccdccbbbcababbbaabbccdadacbcbccbcbddcabcbdbbcbaabdbbdddaacaddabcbadadabccadcbaaccaacbbaccdadcdaccacbbcdbbcbccdcdddadbcaaacaaddadcdcbbacdcddbbdacccaaddddaccbcdbcaaadbdbccbddadbaaabbdcdcbabdabcacbbacdcabaadababccdccaccacbabdddaaacaabcccadcaacdcaacddacdbdabacbbddcbbcdddabacddcbbbbbdbbaacbadaddababadcccddacddbdacaaadacbcdbdbbddbddbdbdbdcaaaddbaabcdbacbadcccaadbaacaaabbdbaacdabdabcbbcdaccadadadbcbbbddaccdccadccddbbaacaacadadaccacbcadadaacccaadccbabbccbbdadcdcabcbbddbabdbdcdadadbccaacacdabcbddadcbbdddadaadbcddddaddaddccdbabccabbdbbabddcaccacacadbccbccaccbbdcbdadccacabccaddaddadaadaddccaabadddcdbaaabacabbbacccbddcdbbabbbddbcaccdacbababbdcbddcccacacbadcbbacadcdcacccdbcbadabccbbaaadbccddbcccdabbcbadddcaaabccbdcadcacabcbbaadcaadadbacbbbababdcddcbcdccdddacabacddabbbdacbdbddaabaabbdcababbbbdacbdbdccbdbcbccacddddbbcddccccdadddbddcbcacbbcaadbaadadbaaacaaaccacdaaacbcaacbbaacabacbdcbcacbcaaccdaadbddcbbbaadbcdccdacbaacabbbcdbcbcbbacabacccbdbdabdababdbccacaaadacabccdacbbdcccabdbbacadcdbcbdbbcabbddaddbdbcdbdabbdacdbbdccabdcaaccacdadaccddcdcaddbacaccaddadccaabcdddbccacaccbdcdabcdaccddbdcadccdaccaaddbcacaaaacdaabcaadbdabadbbbddcbbabaacaaccadbabdaadacdcbaacdabbcacddccdddbadcdcdaadcbdabdbcbaabcabddcacadbdccbbcbbaccdccbbcadabadcaabdddbbdbbdbbcddcbbccdadadacbacacddbaabccddbabbdacbaadbcccadcbaddccabdcbddccdcbbbdbcabcadaacaaaacacababccadcadbbadaaaadddcabaaccdaabdccbdacccccdbdbddcdcbcbbbaadaacdcbbbcabacaadbbadbbbbaacdccdbdbcabaacbabaabdabbbacaaadccdabcadcccdcddbaaaddaccadccbcbabacadabdbbcbdcccbdbbcddbddcadacccabccbcbbbbdaccadbdacabcbbcabbaabbbbabbabacadddbbdbcaaadccbabaacdcbcccabbcbcdccdbcddaddaabbcacbbcbbcaabbaabdddacddddccbbaacbaacbcbabaabbdbcdcaaadabaabdddcdcaadadcdccdccabddccdcdacdaddccdddbccabccccabadbdaaadddccabddabacaacbdacacbabbcccdacaadbdadddbbdcbaddbddacdcabbbaadcaccdaaaaccbcdacbaadbddbdbcaddbdaaababdcdbbaaccdbaaddacbbbbabcabacbadabbdcbacaaaaddbcdabbabcaaaabaaadbbabdccbbbdaadcbdaabddcdbcbdddadbaccbdcabdacbcbcdacddbdacccacdbadaabddbcabadcbbbbbabcbbaddbdabdabdcbabbdcadabdbccadbdbcbaaadddcbbabcdccabadcddccbaabbddbcbdccdacddbcbcaaddbccabbbaadcdadcaabadbabbbbccbdbbccccccccdccacabcabcbadddbddbacbbbcabdaddbabadacbcaddbdccbbbadabcadcabcdcababdbbccddcabddaaddbcddbcdabdbadbdaaccdbbdacccbccaaabdbcddbccbbbdbdaaddadbaccdddadbdbddcadadcddbabbaaaaaccaaacbcdaadddaccbbabdaacbbbbbdabdcabdcacabcbaadaccdbbdcaadbccadccbddaaabddcdbacdcbdddbcdaaabcabddaccadabddcddbcccabccbdadcdadbccbdcaddbdcbdbdabbcbcddadabadbccacdabaaaccacbaaabcadcaaabcaacdddbdcdaacbdccbbdbacdcddccdcbccbadbcbbddcaddadabccdaacabcdcaddcbcbbadabccddcbbaabbbdddbabcbbbadaccdcdaacdaddcbccbaaacbcbbcabaabaddccdbddcdcdaabcbdccdcabddcaadadccbaccabbcaaadcaacccbcaccbbddbbacdcaaddbbdaaaaacbabccddcdaccacaaabcacdbdcbdbccbabcaccdcdbbddbcbbcdacbcdbcbbaabbddbbadcacacbbbcaacbbdddbdbdadbbdacaacbbbbaabccacccddccabdddaaabcbdbbaacadadcbdaaadcdcadddbdccaadcddacadccabdcadbbaadcdcbbdaaccbbaacdcaddbaaccccbadbdadcddcdbbacabdbbbacadadcdaadbbbaabddbcacaabaadaddabcbbcacadaabdccdcdbddadbbaddcdaadababbcacccbdddbcacbdadacaccacbdbabbcbacdccbdbdabddbbabdadbcdacddbabaadddddacdaddbbabdcbabddabdcacabbddcdcbbaabbcdddddadaadacbacacdddcbaabacbdacadbabbbdcbccbdabbcbbcaaaddaabbcbdcbcbbabbdbabdcbacaccddaddcbacdbbacccadadbcccdbdbabcbbabbacbcadadaccbbacaccdbcddcdacaaaccbdddbdcaaacaababbcccbbbacddbddaacbbddcbabddddddcabbcabbbcbbcccabdbcdbcdccddacccdbcabdcbbbbddbcaaabcccabbadcacacdbdadaaadcbccdccdbaaadcdabacdabdacdadddbcdabcacdbccdaaaadcdaabadbaaaccbddcbccaadabbcadbbbddcabadadccbdcaaadcbcddaddbbcaddccdaccaaabdbdacbbcdabccccbacdcdaddaabbccbddddbdbdcbbadccacacbcdbcbaacccbdddcacbcadddadaddccccbabdadcbdaccacbbadcdabaababbababdcdbdbbadcbcbdbcdaabaddcdadddcdcadbbcdcdbdacbacabcbabdbbcbabddbddcddbbaddbcbbdaaabadcbdbbddabccddbbdcbdbbbdadcdddbadddacdbcbcbccccdcbbbcbdabdadcabaccadaabcaccaaaadbacbdcdadcdcacadababdcdbabbaaadadddadabcdddaadddbababcacababababadbbbbbbadadbcdadaacddcdcabbdabbbbcdbddcabdbadcadacacdbcbdddbcdbcacdbccbcbacdadbababcccdbdcdaaabcababbcddddbdbabcacadcddcaddcabdadbcbacdabbdbbaadbddbdbddbbcabdcadbdaaacbdccbdbcdadaabbacabdaadccaaccbcacaabddccbbdcbbbcacbdccaadbdaaabcaaaabddaabdccccdbabdcdbccbadcadacbbcdcbdabdbaddbdbbcddaaadadcadcddcddadacddbaaabbddcbbbbbcbaadabbbdbcdacbaacddbdccddbcbbcaaabcccddcaacabacdbbdbdacadddcdbabaadabdabacbcbcacbadbccdcdacccdcabbbaccadaaaabdaddabccccaaaaaaaaaacbccabaabadabbdbdcabcaddbdabccabbbabcccbccdddaabddcdbcdbdaabbacabddccbabdacddbdadbbadbbbdddbbaccbdbdcbbbccadcaddabaaaabaddbabbdaaacbcccaddacbbcdadadbaacdcccaddcdccddaddabdddcdcbbdcabbcdaccbaaadddddabaccadcaacdbbdaaacbdbcdbbbbbbaccccbaadbcabcdacbbaccadcbdacbadbbcbdbdaabbdcbadadcabddababdbbddaabcacdcabccbbbbacabdacadbaacdaaadaddabdbcbcdadcacdccbdddcdbddccdaddaaacbabdbcbccbdbabcbdbdabcbadabdabdabbabacddccaaaddabcaddccabbdcdccdbccdddaccabdcbdcabacbbadcdaadcbcbacbaaddccdabbabcbbbbadbaadccbdcabbdbdcddcbbdcbccbcacadbbcbcdbbcccaaaddbcccccbccabcbadcdadacabcbbadabaacdbbacdbdabcabdacdbdddacadacbcdcbcdbdcaaacbcbbaaaaaadbaccbdaccdbcbddacaaddbadddbaadbadcbcccadccbddccaccaddcbccaaaadaabaabacddddbacbdcaaddccabddbbddadbcdcdccadcbbcabaabbdbbdacabdaabddcdabcbaccbdcaaccccbddaddaadcddacdbbabaacccdcdadcbcbdacdacaabacdaaabcabacbddaabacdaaaacbbabbbbcbabccdbccddbcabdbaaadabcccbbcacddacdcddccdaaccdcbaddddadddddccabcbcbdcadbabbadabbdbdaacddaddbdcdcadbcdbcacabababbdaacbacbcadbdcbddcabcbccbcbbcbdbcdcabcacadacbdcbcbcbdbddddccbcdaccaccdcaabacadbdcadbbddabbbcdbacbaaddaddabbbaadabdacdbadcacdbbddbbcabcccbdbccdabdddbcddbadccbdcbbaabadabacbcbcaaccccadbdcddcdadabacddcbcdddccbcacddbdbcccabbdbccaccddcbbabccbccacabcbaadadaacaabbddcabcddacbbadbacbdbcdddaacbabcdddbadacbadbadbadcacaacdcccaabaadddcdbadcdaddaadcdbcccbcbccbcbaddddcacaabcdcbdcbabbcdccbdcccdcdadbddbaccaadadbdddadcddbcdccddadacdadbbaccbaabbbdbcbdcbcbbddabaaabbdadadcabbdaccbacbcbcbcadccacdadbddabbadacaddbbdcdbbbdbccdccaabdadacddbadcbcbbbabbbbbdcbaccadadbaadddaabcabbdadcadbbdcdbdadbcbacabbbddacdcabdbacdbbccbaaadbadcaccbcaababbacccbbdabacdacbdddbaadcaddbbcbcdcbdbcbcbcacdbcbdbbdcbdbcaddddabaabdacdbbabacadaddbbdbbcaadddbdcabcdaadddccbcdcbbbaccdbccadbcacbcddadccacdacdbbdcdaadacabddadbdcbbadbabcbdaaaaacaddadaacccabcdaccdbadcbdbbacbacddbcadbdacdccccdbcdbaccdaabbbbaaadadccadbdcbbabbdbbddaaaacbcdbbacbcdcdacadbcdbadbbaacddbbaacbabcdddbcaadddacdcdacdcabccdbcbcbbccadadddcabbddcadcdbdaaabbcdababdbbacbddcbdacbbddacccbbdbbaacdabbbabbabadbdcdabcccaadcdacdaacabadaabcbccadccccdabcbbcbcabacabdcbcbbaababbdaacbdcdddbbcabcbacdddaadaddcabacdbadcdbaccaacddaacaccaabdbdddbddbadbcbabbdaccdcddcbbacbbdacbacacbbcdccbabadcabddbaaaabdbbcccbbaabacddacadbdaaccaaacddbabbbbcbaaddcadacdccdcabdccdbddbddcbabcccdbabccbcdbaadcddbcaacbdcaaacacbccccadaacabbdddddcbdbdcbbbbbcadddadccaacbcbdabadaadcaadbbccabbdcdbdcdbdaacababccbbcdbbababcccbaaacddaaacdbacdbcdbbbbcbaabbbccddbbbbabccdcbaacbcdcacaaccdcdcaabcbcbabcdccaddcacbbcaddaaaddaabdbdbcdbcdbdbdbadbdbcaabcbbacddddabbaccbcbdabacbbbdddabcaacabbabaaccabacadcbaadacccdaccadccdbbadbddddcabaacbaabcbaabacacaaacdcdaadbabddadacdcddcdcbcaccccaddbcacacacadbaddaaabdcbcaddabcdadddacbabcbddbaabaaddccbccccbddbcddcabdbbdacccbaadcddcbdbdaadaddbbdddbbbcdcdbaabacbcbdabcabcdbbcacadbdcbbbcbcabbdbbbbcbbbddacacccbbdccdcbbacabbdcadbcdccccdaaaaaaaddccbcbaacccccaabadcbccaddacacddbbbbadabdaaabcabaccdbcabbaacdddbdcbcacbbdddbbcaabababbbcbaccbaababdaaadbdbadbcdbabdcabcbccbabadbbdabdccdcbabbddcddcaacccdcbbbdddcdbcadcaddaccbaacacddbcabcbcccdcbcddbbcdbadcbbadbbdcbdbcccdadaccacadbbbcccbabccbaadbabdbcabdbcbadccaddcdcddaddcbacbbcaddadbcdcadaabaacdbcaddddbcadacdbcbacadcdbddadadcbddbabcaacdaadcadbaacdbbadbadbaccdbbbbcacdabccacbcaadddcacaccdbdadbacbdcbdbdbaacbcbacaacacadccdcabddcccbaddaccdddcbccabaaaaadcccabadabbcaabdabcbbaaacadccddcdcdadcaaccdaaaaacdbcddbdaaadddcdacbbbcdbdadaaaddaaacccbbccddcdbddbcaddbbdcccaccdbcbbaaadccbcabbdbbcbabcdcdaaaaaadcbabcdccabacdcbbdcdbcbabdbbdbdaacacadababdcaabdccaacdbdddbbdbcbccaddddbbbabadcbacdcabdacabbbccdbbbcaabcdaadcbabadadbbcbbabadbdcbdacddcbacdbacdcacccdaadacbbabaddbcccbcdbaadddccdddccdaabdcacddacacbbbcabbdbdadbbaaaaadccacbbdbadaadaadcddadabbcadbabaabbcbbbcbdbbdbbbcbbaabcbdddbbcabccdbbabdbdcabbadbdcdddbcaabaaddabcdaadbdacabbdcacbdddbbbcdcaabdaaacdbcbcbadcbabddbdbcbacbbbadcbabdcaabaaccabaccccbaaaaaacccbbcaabbcdaadcacbdcabbabaabbcbcbabddabcbacadccacadcaaaacdcdadcccabbbdbccbdadabcdcdaadcdcbdaacacdaabbadbdccacaddddccbaabbabdaaaabcdcdbacdbccaabddacabbcbdbbccdcbcabaadbbdcaddcdcdccbadcabbdbcbdaccaccadbbaaccdbcccbabcdcdbaacbaaddcbdcabbbbddcccacddaadabbcccaacdccaacddbbabacbcbbcdbddbbaadacdabbbaaadcbbdadaccbadacddbdddaddbdcccadcaaaaccccaabdbbddacddaaaabbdadbacabbcbbdabdbabadaaddcdcbcababcbcdccaacbdbcdbdabbccbbdcdbcdcaddccbbadadcadabdddbbdaababcaadabbdbdcbbaccaccadcdacdacababcddaccaccdabbcbaaddaabaddbccbbacdadaadcbdccbdbdbacbcaabbbbcdbcbbacbdacadbadbbcabbcbcdadbabccdaddcaadcacdcbcbbbcbcbcbbbcaadbaddbabadddcbbbbbdbadcdabdbaadbbcaacddabcccabdcbdbabcbaadcddccabcadcdaddcccbdccadcccaabccabcbdbbdbbcaadacccbcccddbbcccdcadbdcbcddbaadcdcddccbdcaadcbbaabdabbbacdadbdcbdbcdacdaddbdaacdccadbaabaccccccbbddbccabbcbaaddadbbdaacbcbcbabbdaaddbaccbccaddaabdcabcdcdcccdadcdcdcdadacdbabcaadaaadbdbdcbadababdddaabdacbdcacbcbccbcaabbdabdcdcdcddacaaaddcdbbdcdbccbacaabaccbabdbcccaaadabbdbbbbccbdacdabccbaabdabdbdaacdabdddcbccbbabcdccbdadccdbbdbcacbbbcbcbbbdaccabbcbdbcdddbabdbadddcccbbdacdcbccdbccddbbabcbcdbccbcbccccabdaabbcbdadbcddadacdadaaaabddaaddcaddaabdccaccaccbabbcaadabbccadbbccabbbabdabbabcbdbaccbbcbbaaaaaddaaddbbdcacbccbbadbccabcdacbaaabbdcabdddaaddcbacdcccdbcaadaaaddcdcbabcdcabcbbadabacbabccccbabbdccabababdcdacbcadbacdabdddabcdabdaacbabbdabaddbcadbdbbcaadaaaacddbcbcaacbcdccbbdcbdccacdadadbabccdbddaddbbcbaaddbbcddabbabcbccadbaaaadacbcbbdbacbacaabbddabadddccacbccdbdabcbbaadbadbbabddbcbdadcbdaaaacbbabacacccdbcdcdabbaabaddaaaacbbbcaabadcaaabbdcddbabcacdcbcaadcaadacbdccdaccabdbbbdabaaddddadddbdddbcccdccdabdbabbdcdaaacadbcddabdcbaaaaddcbaccddcaccbbabadabaabcaddaccdadaadacddbaadbddbbddcadbcddcbcadccccbbbacbcbacdababcbadccdcddddadcbaabbdbadcbbdcdaddaadabbccaddcdcccbbbdacccbdcdcdccaacabacbaadabbbadbaddabbddcabacbbacadacdacbbdbcddabbbdddcaaabaadbcbbbdcdcbadddcbbbdbdbcbdabadbbdacaabdbdcccabacddddcddaddacdabbbdddabcbcaaddaddbabdabddbcbbaaccdabadaccbcbadabddabbbbcdcacabdbbbccddacabdadcaababbbcaccbdbdbaadabccbbaacaababaadbcadbbacadcaaaaccabddaacccabaabbcbdbbbcabdddaddaaaaabcbbcadbbacbcabbaddcababadadbacacadcbcdcdacaccdaabacadacbdadbcdbaacacdaadcaaccdabadbcdacdddccaaccbacabacbdcadcbcaaadaddadacccbdbababaadbdddacbdccaabbbbbcdcbccabcdbbabdcbadbababddadcabacddccdbdbacdcbdadabcbcbabdcbaddcbbcaccbbddbcaaadaabacabcdddadbcddcccacacbabcabbdaadaabddcddcdbadcaacdabacbdcbcacdacdbcbcadcbcdcaccbdbcdcccbaddcacdcbaaabbbdadacbbdaadaccadbbccbabddbaaaccababacccadbbbacdbabbabdbbadbdbdcbbddadacaccdbbcbbbbcdabcbbdadbadbbccabbdbbdacbbcdbddaddbcdbacddccaacadbbaaadbabbbccbcdcdabcccabddaaabaadbddbaabbbdabbbcadabcaaabbccdbacdbababcbdccbbdccdcdbdcbddbcbabbaababbcbdacbcaaabcccadbdcbdcbcbdabbadbccccaabccbabcbcbabbdabdadabadbbcbdddcabcccbaabdcdabbcccacababbabbadbabddabcbaccabcacbcacacdaaacaadacddadbdbbbcadbddadbbccccdcacdaabdcdaccbddcdbcabbdbddbdadbdbbabdacccbdbccdccdacabadbddbdcabbbdadbbdddcdadcbadaddcabbccbacbaacacddaabccabadaacbadcaccaadbbaddccdbbdccdbccdbddbdadabbdbbabaacaddadadbddacadabadcccdddcbacddccbaadcdbacdbcabacdadbbbbddddbbaabadccbabacdbbbaacbbddabadabbadbdccbbbccbbcdbdbbdadbbccadabccacdacdadcbdcdaccbcadcbcaadbcdcbccaacdaadcbacacbacbcbdccbdccbacaddcabdcbaaddccbacabbcbbacbcdaccadcbbaaacbaaadcdbcdcdccdbbddbdbdbccdacbabadacdcabcacaacacbddaacadcdcacccbcabcccadaacaddddccbccaccdacdaaacdaddadddbcdbccccadcbdbcccbaacdcbdbaaddbabddbdbbcdddbdaabbcbbcaacdbddbbaccaaaaabcbabbacdaaabddacdcaaabbadbabadcbaadbacbccaabcdcdacdaabcbbcbcabcbadcbbabacccbbcabccbdcccadccadcbadddcbccbccbabbbaaacaabcbbccacdcbbddadacbaaaabbcbccddaababdbbdbbdcabdcbbbcbdaaadbddddcaadddabccacbcdacdadbbcacdaababbbccbcdcbabcccdabbddddbacdbdaaabddadbaaabbcdbabbcdcacbcaacabacababaaaadddbdcccbaabadbddadabdbdbbbcabaddddacaccbbadbcadbdadcacdddaadbcdddacdacdcbccaabcaccdcbdcaacdddcbbddcbcbddbbaaaadabbccadbadacccddcbbacbdcbbdcdcadbddadaababbacddbbaaaacbcbdabbdcdddccdcccdacdcbdbdaaaccaabacbbdcccbddcccbbbaaaaccddddcdcbcdcbdccccacaddcdcbacbdcbdbcadddbadabcddabdddbccccccbbdadaaabbcbccacddbcdcbdacdbdcadbccdcbdabddabaadddbbdaddbabcbdcbaabbabadcacbdaaaaddcaacdccbbabbdddcdcbbacbbadbdcccbbbdbbdaddadaabcccaaaaccbbcbdccddadbcccbcbaadacbaadbbcaadacdbdaabcacdababbaadcdddabaaabcacbbccaccccabbcccbbdcccbbcbcabdcccdbbdcdbcabdcdcccddddabccbcbdcddcbcadadccaddcccdacbbddabdbbcbdcbcdacbdbbacaacadacbbbbadccccdbacabdadababbbaacacbcdbcdabcdcddadacdbddbacdaabbcddccdcbcbbaccabacaccaddcdbbdbdbdbcaabcbddcbbbdccccadddadcabcbdcaddbccdcaadddbacacdacdbcbabbcbbadcddbddaabbdadbdacadbadcaddacbacdcbcddaccbdacccbbbcadbadcccbdabddcbddbbbcadbbbcbadabddcaaadaccabcddadddabbaacddcaabadaabcbcdcaacdcabbbcadcbabaaabdcacabcbbaaaadbdcacabcadddacadccdddbbdaccdcacabccadddbdbadadbdbaadcdbdaadadbabbaaaadabcbdaadbddabdcbcbcbbddadcdcdabbdcadbddaadcdbdacddcccaaaadbbbaacdaaddbacdaccbbcaaabdcaddcabbbabdbaacccaabaaccdadddacdcbdbacddbcbbadabbbacdcdbaabdcdbadccbcdbdbbadbdbbacbcdcadddbbdcddadddadbccdbaabcbccaddaaaadbcadccacaadadadbcbcaadddbaaaddbcbaacbaababbbbacbdcadacdbdbdddcbacaccacaccdcdacbdabcacccdabacadcbadabbadacaacabbabcbbbdbbbcdbdbacaddbccbbdaabbcbdcdddaaccbbdbdcaddacbddcdabacabcccdbdcdcaadaabdccdabbabbaccabbaaabcbbbbcbcddcacbdcdddddccbabcbbcadaaaadaabdaccdbacbbcddaabaaddbbcdbadcbbcbbabcabbcddbcaadcdddbaddccacbdabcbbcdadabaaaccdbaaadbacadcdccdcbadbaacdbbdabdbacaaccdbaddabaccddaccbdcbddcdddbcaabbcddbaabadadabbabcdbddcccacdcdbcadaadddbdccbdcadadbaaddbddabadbbccacbadabbccaaabdacdcacbdbcaddcaacddbbabaadddadccadadcaacaccdabaadcdbabccbbbaabbcaaaddccbbacadbadbcaddbcabbbdaadcbddaccabdcabdcbdcadacadccdccccddbddddbddbbaddacadaadaaacadacddabaccbcacbaaaddabbcbdbcdabccccddddadadbbcccdbbbdbbbbcddbddabbadcabccaaabdabdccbdacbddadadaaacadcdbdcbaacbcbbbdbcabcdacbaadccdabdbbdbabdbbdcddadcdcdcbbdccabcdbcbbccbaacbcdbcdbccaccbaaabdcddabacdddcbdbcaddddbbcdbbdbbbaccbbdbcaabbbdcdcdbabccaadbaddbacabaabbbcaadddddbbdbdcbadbdcbcdbacadbcbccbbbdbdbcbbdadcacdbdaacbbdbccabcdaadacdcdadbaddcabaddbabdcacbaaabbcaccddacdbcbaccbddcdbdcbcdcbadabaababcdbadccdbbcbbdacabbdbacdbdddabadcdadcadbbdaabbacbdccabccaacbababccbcbccbccdbbbdcdcdbdbdadcddcbbdbcbdabcbbdbbdaabcdcbadcdddcaaadadcdaddbadcbcbbdacbabacaacdabdddabcbaadbcacacdccccdcccccaacbcaaaabaabcaddadcaaaadddbdccccbdbcdaaddacbcbabcbbdadabbccdadacaddbcccdacccaddbbadcdbaacdacaadadcdaccadadbdddaaadadaadcbdddbabbdadbabddcdacccbaddacdcdbaacdaddbbccddbdbadaadadcabdccabcbdcbdacbbdaababaaccbbddbacddccdcaacabdbbabdbaaaadbabaadabadddbdcbaaacadcbcbcccaabbcdadccdaabaccddddbbccacaccdddaacdaadcccadbadaaddcdcabdcdaaccaadacbacbcacbbddddcbbadbacdcbcadccdcbddaadcdacacdacabbcbbcbcbcdbaacacbaccabcddcbabdabbababaadbdacaaabddaddcdbcbbcdbacbabcdccdcdbbcccdccaaacbccbadaaaabccaadbddaaadaacadaacacabaaabbbcdbbaddcbcbcbcadabcdbdadcaccbaaadacbcbbcdbdddcbdcbcabdbdadccabcdddbcbdbadabcbbabbadbcbaddbbdcbbcbcbabcddbaccbccddccadbacdbadcddcdbaaaabcbcbabdabcacaadcabaadcbccdbdcaabbbcabccabbdacaaabbcddcdaabcbabdddbbabddcaabdbddddcdacdcdcabcacbadcbddaadccdcbbadcbcadadcbccaabcabdbdcaccbbdabcddcdbbddbabbcabbabcbbdbabdabbdacaabdcdbdbdddcddcdcccbaccdadcccbdcbcddbaacabdabbaddabbbcbadbbbbaadbdcdcbbabbbbccbbaabcddabadcbddbaabccaaadadadbbdbbdaacdcdbcddccbbbbdbbcbbcaccbddbdaadbdddcadacaadcbbcdaaccacabbbaddbcacdcaccacaaacbabcaaaaadcaaaccabcdbabcbdbbdbdcdccdbddbcacdddcdcbdadddbdcccadadcdabcbdbbcccbadbabacddddabdccbbadbcaaaadbcadbcdaccbbbbbcdacbcddabaadacbbcdacdbacbbcbcddacbdaccddadbaaaddcadaadcbcdaacccddbbacdbcbbccaacccaacdcccabdbbdcbdcccddccaacbdadccccdbcaccabbcabdcbddaddccbccddcccddcdbabcaaaaacccdddccabcbadccbcacbaaacbaddcaabacbddaddcbbccabbcadabcdddacbbddadacddacadbbdbadcdbabacdccdaacccadababbbdccbaaddabacccdbacbadcbdbdabccaaacbddabbcabaadbdcabbabdadcaaabdcdddbadcdcadcacbbdabaaabbdadbabbcdaaabbdbcacbdccaccdabdacdbbddabdbdadddbbcdcaadcdadbdccadacaadcdadbbaaadbdbaacbdbadcbcdbcdabacdadbdbcbdaaccccdcbdadaacbccacacbadcbdacabacdaabcaabdbbbbabacbdbcddddbaaacccbbcadcddddbdadcddaaacbbcbcdcaacdbaaadabdadabcacdddcdcbdaaacacdbaaaaabccaabddbadaacbacacaccccdbbadbdcccadcaadcbddacbbccdbcaaddcddaaddddabbdcbbcabccacbccbaabdbadabaddaccccabdacdbcbbdcaaacbacdbddcbabbccabcdabacdcbcabbdbddccbaccbaccccabcabbbacaaaccbbdaaaaccccbddacabdcbddcaaddacbddbcaccdcaadcdcdccdddaaaadccbbbacbdcccacdcaacbdccdddcaadbbcbbbbccdcadaacbaaadaabbacbdaaaadccbbccbbbcdaddacaabddcdabbdaccdddadcdcacdabccadcccdaaaaadabcccdbdcdadcdccabadcccbbcabaddaacdcdacbadccccadcaabbadccbdcdbdcbddaadaccbaaabbbdddaadddbcdcddacdbdcbdcdddbcaacdbccbbcdaacbdadcacbaddadbddcadbbdccbbabadacbaadadbcccdbabcaadaaacabbbaccdbabdaddcdabdbcdabbbaadcdbbaadbdabcdaaddabcabcabdcbbabbdbdcbcbbcdacbdbadcbcaadcbccbbacbdacaacdacbdadddcbcababcdadccdababdbcccdadccdadbaacdadbbccabaccaadbdbacbadcbbcccbcadcbbacaaabcaddbbcabbcadcdaabbcbbdbabddbcdcbaaaaccabbaaabbadbabbdabadacccdcbcadccdbbdcdcbbdadcacdccacddabcbdbbadaacabddbcdcccabbcbcbabdbacacdbcbabcacaddcbcbbdbcaaddbbadcddabdabcdacadabbbbdbaabbdbcdcbcbdacadcbccbaabdbbddcccbdbdbdcadcabaadbdababcacdcdaccacaaacabbddcabdcbccabaccccdbdaaadcadcbcdcabaaadbccaacabacbdadbabaccdaaaaaadbddccbdcaaadabbdbadaacbaccabcadaddcdaaacbddcbddbaacacdbbcccbdcacdcabdabdddbaababbbaacbbacdadadbaccaaadaadbcaddacdbcbbbaaccbdbacccdacabccabcbbcdbdbbaacacdcdbdcbbdaccccacdbcccbbdadaddbddbcccdcdbdbdcdccdbaabcdacaddaadddaccbddcbccddbcaabbbacdadcbcabcdccaccdcddadcacbabdcdcbbcdbdbcaabbcdddabcbaaccdabacbacaddababbcbbadbdcaddbdcbacaccabcabdcaaccccbbcacbbaccdbccabdaaaaccbddcbadddddabdbabbaddbdcbcbdbabdbabcadcabacdccaadcaddcccadccdbabbbbdacbcadcbbabbbbadabcadaaaddbdaacacdbbdbaccdccdaabdbdacbbbadbccaacdbbbabdcdcdbdcaabcacccccdcacdbcaccdbcdbaddabaabccdbacbcdbadbccdbdcdbcbabdabcdcbacaaaaccdbccdcccdddcadaddaaabbaccabcabbaabcbddcabcacdbccdcaddbcdaccbbdacabadbbbdcdbccddcbabbaabbbdacacdccdaabcccdcadddbbbbadabbdcccdcaacccdacacadcbbdddccbaddbdcccdbbdbdaababbcbcaccbabdddacbabaaddbabdcdbdbbadbacdbadccdcababcaabcbcadddbacaacacabccdcbdbadbbcdcdcadabcaccaadbdbdcbdddccbaadcbcdddbbdddcccadccacbbabbbcaacaabbcbacbaccdaaddcdbdaccbbcdcbcacabcdbcabbadbbddcbdcbbaadbabbdbbbbadbbddaacacdcadbcbaabadbaaababbcdbaccaddacabdaacdccbdaabaabbdcbadbdcbbbbdaaabbcadbbadacbbabaadddadcadcababcacbcbccccabaadbacdcdbcbabdabacaaadddabcdbdccdddbcbbcbaccbaaaddddcdabbbccdcbcbabdbdcaadddcccddabadbbdabdcabadadccdbdaccddacdabaccccabacbacddbbbaabbbacbdbddcadcababdaccaacbbddddbacddbaacbaabdbcadcdccaddbacbacadcabacdcdbbbbbcaaddababcbabcdccccabadaadaabdddcdbbbdaabacadcdcdbcddcbaccacadadabcddcbbbaabdbccbdbddbacdbaccadcabaacdddaddbdbabcdbdbdcbdcbabddbdaacbbccaabcbcbdcbcabacdbccaddaabbcdcbbadbabcdaddcaddbbdbcabdccdcbcdbacccdabdbcddbdcdbabbccbabdcabdcacbbbbccbcbcdddaddabadccaccaabccbddddadcbacbccdabdaaacdcadbacbcdbbdcababbcccbcddaddcaddaacbcdccbdaabcabddacaacbdcdbdaabbdddccaccaccbddcaacbdacaddaacdcdadbddacacccbdcadaabdcabccabacdbacdcadcacdbccaaaadddcadcdbdaacaddbcadbccdcdaabbdccaacbcbcadddadbbddacddabcbdbddaccbcbcbdcbaacbddaacbcaccccbccabccadcadbdcbbbcaadcbbdaadcaaacbddadacdcbcabbaddcdcccadddabacbcaddcabcdbaaccbaaabbcbbddcaadcdacccbbaadbccbbacacaccccbdaadabcdbbccccddabdbbdddbbcdcbbdddcdcbacdccbaaabdbbbcaccbbcaaabddddccbddddacbdbcbbdaddcdcacbcabcabcacbcbbddbcdbbbcadcccdaadbdacaacdabdcddcbcdabadbcdbbbcbbdabccbdacdbcbcdcddcaabadccdcdacbccaddabaacdaddacdacbddccdbbacdcaaabababccbbccaddaabbdcbbdacbaaaabccadcadaacadcbdbcbddaacadcacbacccbbbabaddbdbddcadcccbcbbbbdadcbccdabacdbabdabbbbdbcdaddbacacadbadabbaccadabadbbabcdbabadbcdaabcdbccbacccaaabdbaccaacbdbcadadccacdcabdddacaaccdacdaaabadabddbbbcaabccadcdbccbbcccabdcdbabbcccdcdaabbdaabcddaaadcdbabcbaabdbbcadaacddbbabbcbccaaacdccacabbdacacabdcdcbcbdaabcdbbbbbcaabbdbaaddbbaabcdbdbcbddbdccadadbdcadddaddbbdaddbbccbdbacdcbccacbadbddcbbccbbcdddcbdcacbbdabcaddabaddadddbcbadbcdbbbddbbbccaacddaddaabbcdbaccdacbcacccaadcdabaaccbcbcbcaddaabbdaaccaabdccbaadccbbddabbcabccacdbbabdbddadacdabbabadcdaaccbcbcddbbabcddbddbcaaaccccbbadcddbcaaaaaacdcaaaaadddccdcdbadbccdbabaadbbdcddaaadcaaaaacdbaabbddcababadbbbcaabcdbdcdbdddacbcbbadacbdaababadaddabcaaaabbaabddaacdcdacddcadadaddddbbbccbbaccadabaaabdaadbbbabaaabdcdcccaccaabccadbacddaaaacbadbbbcccbbccddbcbabaadaadcbccdbbbbdddbacbaabbacadacbacdabdcbaaadabddbbbaccaccdcdcaadbddccabacccdcddcbddaccacabbdacacabbaacaacbdbbdcdcbabbaddcaddaabdcccaaabaababdbdcbabaaaaccccbadcbccbcdadccbadddacadadcabbcbdbacbbbcbcbdddadaddabcbabccbacdabcdacdadbcdcccbdcabbaabcdcbccbdcdcbabcdddbccbcbbdbaddacdabacdbadbcdadcaaccadccbbdacadccaadbdaaadacdcbbacddccacaddaddcccccdbddadbbacababcdcddaacbcdacdbadbdabdbcacccbacddcdccddaccabadcdbcaacacccbddcccdabcaabddccddacdadaddccacbdcbbdcbdbbacdbcacabcbadabcbdaccbaddacbcbdddbddbddccabadcaadbaaddcabcbaaadbcbbbdcbdacddbdaddaddacbbbdadaaccababadccccbaaabcaddcaaaacadccbbbabdbcdbcbbddadbbdcccddbbdbdabadbddacabcbbacbcbaaacccbcbcbcdaddaacbabacabcaccacdcdabdcadcaacacbadbddadcbdbddddaadcddcaaabbdabcdbcbdcbacdabacbcbcbccdabcdbcccbbbcaabbbbdcaddbcdbdaadbacbdbadadcaddbadbbbaccdddbcadbcbabaddbdcccbbcdabbdabccbadacacbcbacadabcaccbaadcbabbbbaccacddbcdbaabbdacaccaaccddbbbbdaadaabcccaaccaaacabbcbccccabaccabaadabddacaaddaadbadbccbddabbcdaacadbcdabbddbbbbabaaadbccabdddbcaccddbcacadcdcdbaabbcbcaadcddabdbcaabbcadacbdbacbdabbacbaacbbaabadacdaddadccccbabbcabadcbbbddddabaabccaddbdbaacabdbbbdcdcbdbdadccdcadbbcccdcbbddcdbbcaaabccccdcaabcbaadbccdcddbcbbbaadbbdbdddbabbcaaccabbaddaaaacdcacbabdbaacbdbcdbbcbdacdadcdbdaacdadcadbcdcadaaddbdabbcddcccbcbccddbbdbbaddddadabbbccddcdbaaaccbcacabdbdcaddbaadbadaccbdddccdbabdbbccdcdaaabaaabddaccdcabaaacdcabcdcacbccddbacbaccacdabadacbdcdbdaccaadbcdbbadcabcbdabadacddcdddaacabaabcccdbdbcdacabbabbcdccdbbbcdbacacdcddaccaddcdccbbaabdbccbbdbadbddaadbddaaaabbdacbdacdadaccabbbaadbcbddaadabccadcababdabcdbcaadbaaaccdaadbbcdbbcdbadccdddbbabccddbdcddcbbcdbaccacbbbbbbbddacbabbcccaaaadadbbbcaddccbdbbbaadbcbccacbdcdcdaadcbccdcbbabbbaadddacbdcccbbdacbbabcbdddabcbdbbbcbacbcdccbbbabdcddbabcaccdcbcbacccbbccbbbdbcbcabccdaacbcdbbbdadcddaddabbabdcdcdabdcbcaacdaddcbaabcdddabbdacbabbbadbaddcbdcbddbbbdabdddcddbaadcbdddaddabcdaddadaddcdadacdcddadbabcaabdaaccbcbbcbacdbddcacabcbbbccdabdcbcbaccabbbabccdacdacbaaccabbaaccbaddabcadbddaacadabcaaaddcdcdddcdccdbcadacbcccbcdbcbccabaaaacbbaababdbdcbbcdcbbdbbdcbabacaacddcabdcbbddbcacbdaaddaacddcbcbcbcdbddcaacbddbbbcccaddaadabbdadaddbbccaccabacadcbdbbbcdbbdaddbddaccbaabbcdababaadbdcadcdbdddbdacbdcbbbacddacbccbaaaccdbabbabaabbcaaabadabbbbaadbdddcaaabadbdacbdcdcdccdaddbbcdbdbddbbdbbaaacabaaaaaabdadcbdbcdddaadcddbacdbbccacbcbdacabbcadcadbacbdcbbdbbcdddadbdccbccdadbccdcabbadccadbacccdcbabbabcccdbadbabbdaabbccbdabcabddcbaacdcadacdbaddcaabcdcdadcabdaaabbbdbccbcaabcbdbcbbbadacbbcdbdcbdcbabbcdadcbdaacbbadcdaacdadacbdbddddccaadbcbdaadbacaccbbccacacaaadbdccacbabbdaaabaadcbadcabbdbadbacbbbbaccccacbccbaabdccbcacbbbacdbabbbdbddccbbabdacaaccbcdaccaddbadddcbabdbbaaaacdabbdaaadcbdcdcabcccbaaccdccbdbaaaccdadccbcdcdadbcadccbbcdccbadcabdaabdabcbdaaaabadddacdddcddaccadbcadabccbbbbadbcbcbabbddadbbacdbbadcdacbcaabdbdcccddacacadbcdbdaadbdccbbcdbccbcccbbcdbacadccdbaaabdbacddbbaaddabbdddabacddcaabadbbbcddacaaccdaccccdbcccdaccaccacbbcadcddcddbacdbdccdcdadaabcadbbbddabdbababdccbbaaddbddcdaccdbcccdcccbddbdaadbdddadcdcabcbdbbccdabbccbdcbbdbbacadacaaddacbdcbcccabbdcadbbadcdbaacadcadddbaacaaccabcddabadcddbccaadbcacbadabcbdaddabdbcadabadcdaadccbaacabcbdbcddcbdacbccdbcabdcdadaabccaacacbdbdaabbbabbbbaacddbadbbbacddbacbaddabbabdabacbccbbbbbdcaabcdbcccdbccbdaabbbbbbdaaaabadbcdbacdbacdacabdbcdabdcdbabdaadcddadcadbcabaacdbdcbccacadaacdcccbbaadcccdbaadbbcbcacdbbddbcbcddbbddaddaabccadcabdcdccccddddbadddadcacbabcbcddcdabdcbbacbdadadaadbcddaabacadaaaabbdcccadbcacbaabcacacdbdaadabdbabbcdbacbaabbbcdadaaccaddcbdbabcbabcdbdbcdddccddbcccbcdbcbadcbbdbcabbdcddcbdaabadaacdbdabbbaaddadabaadbccabcdbcbaabddcdbddbdbabbbbcbdbbabddaaaaabaccbccdcbdcddcdccbcccbccccabdcdddacdcdabccaabacbaddcaaccaaababbacacbbdcaaabddcaabccbcdddcccbacaacaabdbcaabaabcbcbabcdbbcccdbdddbcdacaacbbbacaadabdbcbadbddbddcbdaaddccbcbbccbcddcabbdbcdddaabaccddcdacaabcaaadddbddbcddcdbbccababcdaadbaddabddddbacddbbcdbcbabcadabcdcbdddaddbcaccdcbbadcadcddbcccdcdaaddaadbabaadcbdbcccdabcbbbbbacbbbdadbdcddcdccdcadbbbbccadaaccbbdddcdddacacabacbbabbadabdcadcbcbbdabbaacabcadcacddacbcabbcaccdabbdbccbbcabadaabcddbcbccccacadaccbccbdddaabbbcddbcbcadaadccddcdcbaddcaabbcdaaaccaddbadbcaabbaacdaadddcaadbcbcddbcbcdadbbabbaacccaadbadcadaccbdacbcababdacbabdcbcdabddddaaadcddbcabcbdddabbbbdcbaadacbdddcbdcbaacbdadcbcdabbcbdcdbcccabbbdadabaaccdcaadcaccaabbdababcbbdbcbbccacbdddadcddadabdcdabdbbbddbcdadbddacadaccbcaacccdbdbcaccdbbacddbcbccbbcdccdacaabacccdcbdcdacdacaccbabaddbbbdacbabcddbcdaabbcadbddaabcacdcaddbddddcbcbaabacbdaaddbddbcbcdbdabbbcabbabbbbddadcbbdbcccddbcbccbbacbacabbaadccbdccdbaaadddcdccdcaababccbbcbdcdbacaddbcbdcccadcabcdaabbaaababcbcbbbadbddbbaacdcdbbddcddbddbdcbcbcababccdbbbccbdcbcacbdddcaabdaaddcacdbadaddccadbaababbabaddcbddbbbccbabacbbbbabcdadadaccddaddcdabadcdcdbaabdcdbaaadaccbaccabbdcababadcbbbdadbcacbbcbdbbcdcbdbddbdaccbccaccbddddcdaddccccccbbabaccacbcdcacaaabcdacbcdaacbcacbdaaacbabbaabbbdccbbcddbbdddaaadadcbacaadddbbccdcdabcacbcbdbbcacbadacbddacabccabdaadbbbbabbacbccdbddadccadddcbbbdbabaacacaabbbbbcaddabbdcbccddccacbbbdabddaabbbacacadcaddbcbaccdddbadadbbdddbbacdcccbaabcddcddcbcacdcdacddcaadaaadaabcbdcbabbbddddccabcddcabcaaadbacdcadccbccbadaadbacababaacdbcaddccabcbbdbbabaaddbdaabbaddbcbcacacbdadaabdbbccddaabadbccbdadddababaacdadbbccacccdbccdcbcddadcadccbdbbcccdabbdbadbcbaacddabbcabbbabbcbaddadcbcccddaabbbcabcdcaddcbbaddccbacabddcbbcbdabddaaccbcaadaddaaabcadcdcaabcadaaacdbdbdccadaabadcababdbbdacbccacdabbbadcdacbbbdddcdbcbcabcdcbcacacbbcacacbcbbdccaabcbabcdcbbdcacdbcddbabdbbcbdcaccbccdaccbccaadabccdbcdccddaabdcaaaabcbabdaaadbcbcbbcddaddbbabbbaaacdadcccbdacddcdcdbccadcdddbbccbcabddcadacbdaddacbcccbcdaabacdcabaabdddaabbabbbcddacbbcaddbbdabacaadbcadcbdcbdddccaddccaacacabacbdbaacbcdddabacabcadbaaacbcdcaaabddacaccdcdbbacdbbaacadcadcddaabbdcbdbbcabaccadddddcadbadababcbccadcbbdcabcbcacdcdbddcdbabdcadcbaabcbabbadbcdacbacdadbbbbbccdbbbdbddcdddacabddddabdbcccdddcbaacdabbadacccabcccdddbaddcbaddcabdccbddabaddbbdbdaddddbabbbdddbbbcccbabacdaacbcbbdcbaddbababbccbcabaaacbcadbadccaacdadcbabbbbdadddaadbdbbcabdacabadaccaadabbdddcdbcaaacdadbddcacbaddccccdacbdcdaadbaaaaadcdacddadbcccbdbccabdccabadcdaadcccaabcadaddacabaadaaacaabddddbbdabddcccbbbadcbddaacdddcbdacbadadbcbdbaabcacadbacddaadbabcddadcadbabaababccaaabbacabcabaddcbcbbbabbcbbacbccdaaccaacbacbbabdacdbcacbdaaccacbadddbbdcaadccbddbaddbdacadadddaaccbbacddbcdbcadcbcadddcaccccbbaabbdbbcabbabccbbbcdbacccddcddcbcadcaccbcadaccbabddacccacdcaacdadaacbbcbacbcaaddaccabbbcdccacabaccddabcdbdcadbacbbaadadbadbcbdbbccccdcccbdddbaabadabbccacabbbdcdcccaabddaddbbabaccabdaccdddaaacacbddbdadbddacddbbccdcdcdbbddcbadaccaabdaccbaababdaddbdaddbdbcdcbacddcdccdaacddcdbdaccdbbddbddaadbcccccbcababdaabcdcbaaddcbcbddcadbdcbdbccddaadbbdcbddcacaddbccccccaabccabbddadbcdddcacdbacccdaaccbabbbcdabaadbdaabbbabacbdddcdcbcdcccacdcbbcacaacabcaabbadbacabbabbbabdcccabaaddadbddbbaacbdbdbddbbdcccbbccdcabccddadcddbadadbcaabdabacaabaacdcbcbcacdaaacdbcdbabdaaccadbdcbcdbacaaabdabcdbdcaaacaaaabdabddadcbacbaccacdcdaddbcaddbcaccdabbccadcbadadaddadacbcacddcabdccaaacbbcbdbbbdabcdaccbbdcddcbddcaccacbacabacdaabacdabdcbbdaabaccbbcdadccdaadddbdddcdaaddccbdbcacbacbbacbcacdccdcdbbdcabbccaaadaccccdadadacbcadbbacaccacbabaaabddcdcdaddbabbcdddaabbdddbbcaccabbdbcabcccdcabbdaaddaaddddcabcadbbadbbadbbaccbbdacdbbcbabdadcdcdcadbdbcacbccabcbdcbccdbdadadcbcbbcddcdbacbbaaabcdcdcbaabadcabddbbbdaddccdcadcccdccdbacdadaabcabcdbbddacccacabdccbacacaaacccdbbbcacdccbdaccdcbbbdcdcccccbdababddabadddcaadbcaabadbaddcdaccbcdaadabbadbaccbadabbaacdcdababcdcbaadccbddabcadbbddaccdaabdddacabbcbacbcdabccaaddadabccdcbaababbbdcadbadddcbabcbadaacbbccaacccacabcbdcbbcadbccaabbdbdacdcaccdbdbbcbacbdbbbddcbbcabddbbbdabbbbbbbdcbdddcacdaaadacabbcaacbcbcaacdcacaccbcdcbcdcdbadadbbabbacacdccdbcbbbadcacbbaabcaaaaaaddaaabbbcacaabbdbcbbcdadbabcdbbdbdbbabcaccdbadccdccadaccddcbddcbbbbadbbcabbadaacdcccbdcbabddcbccababdadbbbbbaadcadddcddcbbcadcbcaaaaabacacdbddcabdacbbabbdbacdacbaaaaddcccdccbccbcddddadadbdddadbcdadcddbbbababadbcbbbbcabcaccbacabaaaabadabbccbdadcabadbcddadddacddddbdcadbbdcdcdddabcbabbdbbcacabdddcbbccbddadabdcbcadabdabddbbcbbbdadbdcddabcdddbbbadadcdbccdcaccbdaaabdcdaaacbbbaaaaabbddddaabacdbababdccbdadacababbadabdddcaadbddcdddbbdbbdcddaacaadabaddbbaaacdbadaaccababbbabccdbbbbbbbbadcabcdddbccccabcccadcbdcccdcadcdccbadcacabcbdbbabdcbbccddbbccaabdabcccadbdacbbbdabddbcddaadcadbadabcaababbddcaadbdacdbadcbdbaabbabcccbaccbaccabdcbdacaccdbbcaccacaccaabacccddbdddbdacabbcccbbacddcdadbbcaadbcbabcadadbddcdcdcdbcadccbcaadcabdadaadababbddbbbcbcbccdbbadacdabbbcdbdaadcccdbabdddbdaacaddddbdccbaccdaaccaaddbddcbdcbcdcbbcccadbaaaaacbcbbdbbacdacbccabadbddbaaccdddbbbadaadaabcbcbcdadbddddcdccccdcdaccadbdccaababcbcdcbadcbbcaacdaaccbcbccbaccdabbcbaadbbddadcdaddbcdbdbbbcdcabaabddcaabcbaddbbbbacbbaccabbbdbcbccccbdbdcbdbacbdbcabccaacadbabbbacdaacbdabcacbdcbcbdcddadaaccdadbddcadbcbcbacddcadbbcddbdcaddabaccdcacaddcbcadbdcbbbddaabbbdbdadbcbcdbaccbbbccadadcdaccdcabcaadcadabdbadddcacbadcdcbccaaccddbababbcaddcccaadccaddabcbaccdddccbccbaadbcccababadcbdbdcbddddbbabdbaacdcacdbbcdddaadbbbcadabbbadaccdbcadcabcadcabbbbcbaaddaddcdbabbbccdaddaddacccbdbcacdbcbcdaabbbdcaaabcbbaaddbcccdcbdaccdbabcdaddbddccbaadbdaabacaccdbdccacaccabcdbaaadabbcbbdcbdacbcdccabcbdababbaabcbcccaccdbcaacbbcacacacbbacbbdbdbbdcdcdacbbcbccbcbcacaabdabcdccbaabdcbbaccdadccabcaacaadcadddabadbdbbccccddcdbcdadccacbabbbcbcbccacbddaaccdabcabadbdbccbbcbcadbaacdcddddcbcbacbdbcabaaaaabaccbaddcabacacccbccdbadcbcdcdaabcacadbbacdabaabbdccccbcddaaaaddcaadaaabbadacabcabdccabddabdbdbcdccdabbbddcbacbddcaabccdaddbaddbdabcdaacdccdbacbdadbcaaacdcddcdcbbcacbbddaaacbcaabbcdabbcacaabcbddcdccbacddbdacadcbcbbcacacbdbadccabbbacbcaadccaddddadaacccdbdbcabddcaacabccbdcddbbbabcddbdabcadcdbbaddabacccaaaadadaddbaaaaccabdbdadcaddacbacbacaaacbacddcbcaccbcbbaaacadcbddbbbcacdadaabbdbbacbaaacbdacabaabbdddaabdcddadbabcbdacadaacdcacdacbbdadbdbadcbdacdbcdccdbdbacacbbdcaddbbbacabbcacaadcdccccadabdcacdabcddcccdbcadbacadadbdcdccdaccaccadaadcaaccdabbaacbbbbdcadddbbccaddcbacbacbaaabdbcccbadcadccabbdbdcdadadcccccabbcadbbaabacbaaccdbdacbbabdbadbcbbcdbaacddcbdcaabddcdcddccbdaaacabababbacccbbbadcbabcdcbacbbaacddacccabaadabdbbcababdbdaadcacdbdcbdcdbdaccaccdbcbccdcccdacaacbbadcdcbadaacddaabbdcdcdccdaadbacbadbbbcabacbcddaddaaaaaadcacbdcbcadcbbcbdaaaabaacbbdbdaddbdcaddabcbcdadaddbcbbcdbbabbaccbdddbdcbcadadaccbcbbcbbbabbdbaddddbadaabaccacbbdaaddddabbbbaccccdadbdbaaaacdaacbbbddbdacddbdddbcddbbdddbacbbcbcbcabbcacccdaccaabcaddcddbdadcaddaaaabadcccbdadbcdcdcaabcdcdabcdcacbabdacdbcdcdbbbcbcadddcacaddcacddccbcddddddaaabdddddbabaadbdbdbbadbdcdbcdcabadaaacaccababdbbccadabbbbccccbcbabdbacadabbcbaacbccdcbcabcabddccaabcabddbbabacaddadabdcaadccdcdbacddcbcaadbdaaadcdbcccbcdadcbdadcbddacbadbadbaaccbcdabdbcaabdbacccbbcaaddcdaaabbdcacaaacdcabbddccaaadaaaccbadadcbddbddbddaababdaadbddcbadcbbdcadadbcdaaccdbbaccdddddccdbcbabccbaaddaabbbcbbbacabdaaddcccccabbbbddacccaddcbadcccccbcccbbbbbbcdbbddcddabcabbcbaaacbdddaddbbaccccadcdbaaccbaccbdbbbdbcbaabdcdccdcccdccbaaabaccbccaacbdccbddaacbdbabaaadcdcbdccbbbadaddccaacdabadaabddcbbcbbcbabaaacadadccbdacbbabcbdbbcbdacccaccbacbdbbdcdcacdaccabaadadcaacdadbdcbcdcbccadabadcbbabbcddbbaccccdbdcddadbccabbacbbcdacadaddbabbdadaadabcdadbdbcbcdadddadbbbbcdbcbcdbbadcddcdbbaccdcdacdaccadabddcaabaddbabbccadcabdddcdbdcbdccabbdcccbdacbcccacdbbcacaddbddbdbdcdcccdbdbcaddccccbdcacaabbddacddcdbcabcacdcadbddcaadbaccdddabcaabccdbaaacbcabaaadabcdccccccaaacdccddabbddbbccabbdbbbabacbadabdbcacdbbabdacdddbcdddbddbacbddbcbcddaababbcbcbdbbbdcdacaabcdadddaabddbadbdbdcccbdccdcabdcaabadbabcdcbbcdbccbaccbbcdcbcadabbadccbabadcabdccdccbacbdabbbcccacabcccbdcddbacbbbdbbcbdaadcdcabadaadaddcadddadcddccdabcdabadccacbbbcabbdbdbcbcbdcacbbbddccbbcbdbdadcbdbbbdbbdadadbacbcbacacbaddbbbbadbcdcdbdddccabdcbabdaadcdbbcacabaabadbbccbabcdaaaacdabcbdcbbacadcddcbbcbcbacddcbcdaaaaaaadbdbdacdcdbaccbccdabdcaccbbdbdadadcadcbabcadcaddcbcbbccdbbbacccaadcdbacdaadbcbbadbbdbadabdcbabcdddacaacbcdababbccbdbdbaaadaccbbbdaadbcaabbbbcabbcacabdbdddabccacaccaccbdbdacbaaabacaddcbabaadacdcdacadcdacdcadcbcbbbcccadcddbcabdcccabadbcddacbbbcdaccaddbaadbadaccadadaccddadcbacdbbdcccdcbcccaddbacabacddadccccbddcdbdaabbcdcabdacccbcdcabaacddddcaddcbdddaabcdaccadaaaabaddacabdbacbddbcabaddcbcbbacadadbbbcdaacdbbdaabaaccbbcdbcdadbaccacaabdcadccbdcadadaddbcdaabdabacccbaabbacbdadaadcccbaadcadcabdcaaadbacccccdaaabcbdcbdaabbbddddddbdacadacbadabdbaaaaacdacbcbaddbcddddbdcdaddbbaacacdbacaccadcddbcabbacdcbcdccaabcdabdcdcbbdabdccbaadcdcbdccccdabddcbdcbddccccacaabadbaadbddbcacdbdbbadbabcdacccccdadccadbccadcbbcabcaadacaacaadaddaccacbcdddbaaaaddbadcabbbcddbcccabbccaacccabbccddadcaadddaccbbdcaadbacbbbbacabaddaabbadabbabbdbcbdaacbaacadabdadbbbdaaddcccdaaacadabcbcadbbbabccdbcdbbbdbcadaaaacdababdabbbdacddcbbaddacaccbdcaddccaaaacdddbaabadbdcadcbddbbdcbddbbacdabccacbbcbcdaaacbabcdabbbdaccbbcdbadadcacaaddccaadbddbbbcdddcdaacdcbdccdddbccdcbadccbadbcbcbdadcdcbaacbcddccbaddcadddbcbccdbdbadbbccaddadcdbdcdcbacbbcdcaacbabcabdbdaccdbbcbdccdaabdcbbccccdbbdbdbaaddbdabcdccdcbccdaccdcccbdcaacacbdaacdcaaabbdcbbabccddbcacaadcbdcccbbcadbbbdaddacdaabcbccadabdaacbccccacdbacaacddaaaccbcabbadcababbcaabcdacacadbaacdacbcccdbacbadccaddddbbbddaabcbccacccbdddabdabdaabcbbccbacadbadacdabcccaddcabccddaccadaaabbcbcacbbabdacbbcbadbbabcaacccbacadcbbccbcacabbdaaccbcbadbcdcbcabccbcbcbdcbbacbbbcccaccdcbbabdbdabcaccccbdcaddbcbbacdacadcbabbbbcbdcaddbdddadadbcbdaccbddbdaccabadadddbccacabbddcdabdbacddbbadacbdbbdbacbcbcaddccbacbbbcdaabadbdadbcdbdbbbccbaaddbabbdbbbdacdbbbadddcadbddcbbdbadcabdaacabadabdcccdcbaadadddccaabcaccacdddacaaaadadacaaabdbbcacddbabdddaabbcabaaacacccdbbcbddbbbaacbabaacaabbdbadabccbcabddbbcadaadabcadcbdcbacdbbbdabcbbcdacbabcdccabaaccbdaaabadbbdabacddbcdcbddbbabcabacbddcdbcdabcbdbccbbccdbaddabbcbbadbdcddbadddaaaaccaacaabdbbdbaaccadcabcddddcbdbbcbdacacababbcaaacbcbbdccbdddbaababdbcaabadcccbbdccbaccdbacddcbdaabbdbacbacbcdcdddbdbadcadcabbcdbcbaaaaddbbaadbacdddadcacbabacbbcabaacccdacdcbdacbdccbccdcbbbdcabdbcaaccbcdcbbacdcaaadddaaabcbddbacccabddadcdcbbdbadccdcacbdacbabadaadbbccadccaacbaabdbcacbbbbadbbbcbcbbcdddccadaadcdcbabbbddbabcbcbabaaadabdadadccbbadabdbacdadaaabacaaabadcddcdbacdcdacbccacdbaaabccbacadbaddcbdaaddadcbcadadcbcdacbcddaabcadbcbbaaabcabcbdccdacbbcabadcdadbbbbbddbabadcbddbdbcdcabbbcddbbdaaaabdabcaacdcccbbdbaaaacdbdaadbdadbabadbdbcdacccbbdbcbaadcbdadcaddaddcbbccabcbccabbdabdbacccccbdaacacbbbaaabddaaaaacdddcabdaabcbcacaddaaaacbadcbdcbbabcbdabbbccadcadcccabddaaaccabadcaadbbbabbabbcaadccbbbacabababccbbdaddacccbbacdcadbabcacdacdbdaccacadcbaddbaccbbdcaacdaacdadabbacdcccbdcdbdaadcdbdabccabcadccacbaadcdcdddbabdbaadddbcbcdaadbdaccddccdacccdabbdabddbbbcbbabbcddccaacbcdcbaacbdbddccacdcaabdaaabaaaabcbbcdcbcbdcddddadbdaabaaddcbcbabadcccddbdcababccbbbbdddccbbbcdacacdabadaaddbabcdbbdaacbccbacbdbcdabbaccdaacdddccdbaccabdadbcbbabcabbdbdbdbccadaaabdabaabdacbdbbbccbcaacccdcabccdddbcddbbadbddcbdaadbbbddcdadabcbcdaabbaaaccdabdcdbdddddcbaaccaacadaacbdcbdadbcdadbdbbbbbaaaabbadadcdacadaaddcbadcadcaddabdcdadbbcaadbabbacbcacbcddcbbbacadbcbddbacdabcbcadcdcabbdccdccdbaabdcabcabcbbabcccdabacdadddcacdcaabaaddacaacbcbbaaabaccbbacaccbcccbdabdccadcacbbddadcaabdcabbbaabdbddaabacacabcbcbbccbabcabbacbcadcacbddbbbdacabbddcadbdcacddabcddcbccdbaadbaaabddabbcaacdbbabccbbbaccdabacbbacbdcaababdcbadbbaaddbcddddbddadbcddadabcdbbbccddbcabbcccbdcadbacabdadcaccbaccbaacbdcbcabbbbccacdddacabacdaccbbccadcaaccdddaaacdabddaadcccbbcbabbcbaacbacadadcdbcacdcdddbacadbacddccdcadcbccddaccaaacabccacbdabdacddddbdaacadddcbbbadddbccbdacadbaabdbbdbbbaaadbcadcaaccdbbcbcdcbbcbadcdaddbbdbbdaccbbbaadcdadcadcaaacbcdbbaddcbcbddcddcccbdbabcddbddddbaadccaaadddbcbccddbbacbbabaacaaaddabaacaadaccabdcbaabcbbdddcaddbbadcadcbcaadccbadbabddbcbbaacacacabdcddbcdaccdbbaaddaaaabbaaabbbdcadcbdbabaaadcbaddbbcadccbdcbbdbacbcbbcaaabcbdbbddccaadbdbcdbaddaaadbcdccbbdcbaabaddbbadddddbacdbaadbcdcbbddccbaadaccabcccdddbdcabacbddccccdcbdcacaadbbbddcbbacbccddcbbddabdacbadbdbdaabdaabcccbccadbbbcbacdcddadccddacacacaddbcaaaddabcddbbaaaccaccbbcbcadaccaadadcdabacddadaadcccabaabcaaccadacdbbacdbaacbadaaaddbdababbcddcaaddaacbadbdbabbbddcadababbcdadacdbadadbcddcbccaccdacacaccbcbbadababbbadadcaccaacccdababadaccaabdabdcbdabcdbadcbcaadacdccacddadadadaacadbcbaddbbcabaaabccacdbbbcbbaacbdadccdbabcbbcaaccddbaadcadadbcccddbdccbbddcadbdcacddabcadbdcddcdcbaadddbbcccccdbcacdadcbdbaadacababbdbbddabccaadbdbbcbddacaacdcaabbbcbdbabbbddddacdccbccdbdbadaadabddcdaabccaaddbbadcabccbbaaccacbacacdcaccabcbcbccbdbdddcdcbbabcdabbacbacabcccccbdbbdbadbcaaaabdabdabbabadabbcadacccacbddcdbaaabcbaaabababdabbbccdabbccbdcdbbbdcadadaccaddbcacdbbdacaaacdbccdaaaaaaadcccdaabbaaabdcbaddcababaaadadabdaccbbcbbdccbaddadbaadcccddaaabadaddaddbadddaabbabadbadabadaacdbaadaaaabdadccaaddabadadcdbdbcddbccdddaddcdbaaadbbdbcddccbdddcaccacddadccbcdaadaacccdbdcacadcccbbbbadaddcdacbcbbccbccdddbbbacbaddccbbbdbbbbdcccaddacabadaaabbbdaccbabbcabccdaadcdccaccddadcccdadcccdccbccdacdbcdddaddabbaddcccccccdbadadcbaacbcbbacbbdaacbcccaaaacbaabccacadcdacbdacddabdccadcdbcaddcdbbdcbaacdbcbcdbacccbcabcacdbaabddbadbdccbaddcbababdabacabbbcccbdbacbdcccacdbdccbabcdddcdaabdadbcdddacdaccdcbbbbbcdcabbbdbdcdcbbbbdbdcdcbacdcdbcdbdccaadaabcdabddcacadcddaaadcbbbddccabccdcacbccbccdddacacaadccbcabcbdabccbaddcbcbdabcacbccbbcbadcadadaddaccababadcaadcdccccdbbcdaaacdbaadbdcbdaabacacabcabcadccbbacbadbadabbcbbacbdccdbdacdbcbdbbabcddaaacddddabdcbcddaabbbdbcacddbcaababdccdcacdbcabdbcabaddddcbcccabdcccdbcccdccacabbadbbbddaddccacacdbdbccccbccbadbdcdddbbcadccdbddbaacaacbbacaabdabaadacdacccaadcdccbabddadbaacaaadabaaaadbdaddbcacbaabbadabbbdbbacbbadccaaaacadccacdbcabdbccbdbcdcdbabdbcdcaaadccdbabcdbbcbbacaadcaadadcadddbadbbacaacaddbcbaadddadbababcaabcdadbddbbcbdabdbbaccddddcdddaccdaabcbacdcbbdddaabcaccbdabbcacadadcdbdcabdbbdccadbaaacbcbbcacacadddbdabbdddabccaacddaccabbacbaccabccddccacaccbbaaaacccbadccbabacbcadababcabccacbdbdcddcdacbaabcdaacabcccddaaccbdcbaabdcdccabdcbdccdddcdcccabdcaacbacacdbabcabdadcaaaaddbacabdacdcbdcdccadaacaaccdbbdbcdcadcdaabbbaadcdadbddabadaacaabdacbdcbaddbcddcadbccabcbdcaaaabbbccbccdcdcacddcaccbbccddabbacbbabcbaacdbbcddaacdbadadabadaaacbdacbabbdacbbdbdcabdcbdbdbdabdccabcdddbcbbddbccababcbaddccacacccaacacaabbbddaddaababaddbbaaabddccaddcbadaaacabdbdacaabcbbbaddddcbabababadbbbcccccdcbadabaacbdddcabacabbdcacdbcdddbdbcabbaaddbadcbcdadbbbcacdbdcbabaabbaabbabacddcdaaaaaacbcadcabbabdcdadcadddbbdacacaddddaccbcdaaabdcadbcdcdaccbcbbbbdddbdadabbbdbbcbadcdaaabcddadadbcadbabbcadcbababdcbbacbbdddbcbaaccadacdbddccddbcadcccaccbbaccaabcbdbbdddccdbccaabcabaacbcdbbbadcdbabbaccccacddbcdddcabddccddcbaddbdcabdddbdadcdbbabbacadcabadaccbdabcadacdbdbbbdddcddbcdbacadbdbbcbdadcabacadbbaccbacaccbcbbcadaabdcbaadaaddbcbabadbbdccaaccbcbaaadbbcbdbbaacccabbbbaacdaaabaddcbbbcacdabdadabbdbcacbbbadaddabaabddbbdaadcccdbbacdaacacacdaddacbacbddacccccabcbacbbdcaccabddbdacbadacdcadaccaadbcbcddaccccdadccabbcdabcbdbabcbcbaabaaaabcddacbcdbdbdbbadccddbadabdbbccabbdaaacbbddcbbcbbbcadbbdcbadaacadbadddcbbcaaadabcabdabadbbadcacadcddbddbcccaababbbbddcdacbbdbdaccadabadddabadbcabaadadddaadabdbabcbbbadcbcbccadcacdcbadadcabaaabcdbdcccdadadbcbbadbdccdcbbacdbdcadddacaabbdccacdcbabcaadccdacbdcdddccbccbdcacccaddaadcdcbcabbdbbdbcddbabcbabaabaadcadbbdadcabdddabbcddbadacacdabddbddcaaccbbdadcadacbadccbdcbbdccbaaccdaabaabdbdacabaabaaadacaacabcdccddbaababcabadbbaddababcabcddbdccabbcbcdabcacbbdbbcadacdcccbbaabbacccbcbdaacddaddaacacbaccbaaaaaadcbabdccadaddadacbdadbaadbcbcddcdcaddbdaddabdadbabddbbddcdbcbacacacadbbbcababcddaaabacdadddcbcdddcdddbadbccaaadabacdbcabcccdbccddcdabbcbbdbdcbcccdcdddbbdbbbcadbabadacaacbcaacadbcbcabbdaabacbdaadadaddcacbbbaaadbbbadabadbdbdbcacabdaaaacacdddbacbbbbcbcacbddbddcacbdbcadcccbadcbbbbabdbcdabaddacbcbcadbabdbbdbdbbdabccadbcbdbaacddcbaaabcabcabaddaacddbcdbddbaddbbcaadbcbcadbbaddbdcdbbdcaaadbadbbbbcaaabdcaacddaddbbbdbaacbddcdbcdbcdacbddbdccbaaddbcbbdbcadbdbdddddbddcccbdddbbaacddabdcbababaccabbdbcabbadaccabcabcadcaaabaadbddcdaddadabdbccacabcbbcccabdaccdcccbddbacdabccabbbbcaddddbaaabadddacdbccdbbbabcdabadadaddbaccccacabccaddacdcadcdbbaaddccbdddabdbcaacdbbbbdccadcbbacbcbbcaabbbddddbdabdadcdddbdccababddddbabcadcdcdaccaaddddbdbbbbdccacddccccbbcdabcdddbbcaabcabdcadbcdaaaabddaacddcbcbcacabdbccaabcccbdaddcbabddbbcbcadcddabbcaacadadcabadbcadbaaddddacbdacdcbacdabcbdbdaddcdbbbdcacabbbcadbcadadbbccababcacdaaddbcacadaaaacdabcdadadbbcdadaadbbdcddccdbaabdbbaccaacbbdadacabaccabadbcdadccabdadacacacbddbcdaaccdaddbbadbdaddaabbdcbaddbabbaaacdbcadddddccaadbcbcbaaabddbdcbabddbcddcbabddacbaaaaccadbcdadacdbbaadddddabdcdccaadcbbcbdaaabbcdcbabcbacdddbdbdaacadbcdaacaaabacbddcaccaabddbaaccbbdbbabdadbcaacccccbabaadacbabadcabbdaabdbabddadcacaaddadcaadbddcabcddaaadadbbccaadabbcdbacabddcbccdbaccabdadcaddcbacaaadccdacaaaccdbdcdabcdababccadbbdcbaacbdbbbbdddccdcabdbacaccddcadbdbbdccdbcbdbcddabaaaabccadccbccdbcacadaaddbbdbcdbaabdddcbdadaadbbccbabdcaaacadaaddacbcdbdccbacabbbcbcdcddbbaabadaaccdbabbabdbaccbdbaddbdcabaccaaccbbddacccbbabdaadadaababaadbbdbadacdbcddbdddadbaaaddbdcbcbcbbcccdccddbcbacadbbabbabcbbcccdbdadddbadbbbcbbbabdddcccacaadcbcdbbbacabaacbabddddbdcbdcddbbccbcbacabbbcbaaacdbdccbdabadaaadccadaacbdcccbbdadbdbbaaaccbdabccdcaadcaaccdbdaaabbcdbcbaacaaadbccabcdbdbbcaddbcbbdbbbacbddcbbbbcdaaaaddbccbccdbdddcbccadcdcababdddbcdaacccccdbadddcccbbbadcdaaccabcdcbdbabcadaacdcdaccbdcbccbcadabcdbcaadcbcaadbcdcdcbadbccccbacdabbbbcbbdccaccddabdadcbaadbcdaadbbdaaddcbdcbcbdcbdabdcaaaccbbdbdabadcdbbcbbbcbbbadbbbcababbcaadaccacdcdbbcddaacdacaddcbcaaadcaabbbdcccdabbbbbacccccbaddbbdbddabcdaddccdcbbccdbadddadbdbbabccccdbcbdbcdccccdacdacdabdcabbcbcdbdcacbbaccccdbadaacddbbcdbabbdddcddbddbccbccdbbcabdaddddcdcabaacddcadaabaabcbdcadbaaddacdbadbacdaddcabcbaccdadbabcdcacdbaacaaabdbdccbcdabadacbbccbbdadacdbbdbdaaacdbbadbdcdbbdbbdaaddbccbcbaccaaadbadaaddbcacdacadcddacccadaaacabcaaabddaddcbdbdddccbdbccdbadadbcaddaabaabcbbbbbdcdabdcabccabdcbaddaacdcabddaabbadbaabdcacbadbccdcbabddbbcdcbbbbddaabdddacdcdaaabaddccbababcdcdbddcadabdabacdcccadbbccddcdbacbaddbcddbcadddcbcbacbcaabbbcdbccbadcdbbdadabcdababdadddbbdbddadcaddcbbdcacccbdbdbcdcccbbadaaaabcbabdaababbacaadbdbccdacddddaaccbaacbdabbadaacabadcdaccbaccabddcddbdcddabdbbbcabbbddcccccbbcdddbcadbcaabdbacdabddaabaccdaccadbbaaadbddbddabadadccbdcabbddabcdcccaacdcbcbcccbcbadbabadcabcdbbccbbcbabbcbbdcacabcbcdbabddbbbbccdcdccdcaddcabdbccadcabdcbccacddabcaaaccdccccaccdbdbddaddddddbbbbbdcbdbabbbcbbccbaaaaaccacaacddaacabbabbbaadacbccdaacbcccaadccabdaccaadbbddbacdbcddbddccdacadbcddccbcaacbcccdcccaddbcbadadbaccdababbdcabdbbcdcaaccccadcdcbbdbaadcbaaabccabbccabbabacbbdbadbcacabcdccbdbbaadccacbabadabaccbcaacbcdbbabbddcadacacaccdbbacacccdadbadacbadbdcabacdcbdbbdcbabdaaabcbbcddaacacadaacbcadbbabbbbcccbadadcdaaaddcdbacabccacabdadbcccbdbddabddabbadccaabdcbabbdbccbcdaabacdbdbabdcdbacdaddccbbcaadbbaddcccaaccbdadcbddadbdadccacbbacbdbccbcdbcccdacacdadccbabcadbbdbbacbcdcabbabaaacbacabbdcccdcdadabdddbadcccdbccccabcaaabcabdddccdccabacccdabcdaddbdcdcdacbbabbaadadbbccbcbcadbaccbabbddccdbababacdcccbdbdbcbadaddadbcbbcbdcbaccbbdbcccbcbaadcbdcdaabacbcabcdaaaddcdcdbddabbaccadcdadbbdaaddadbbacdccdbdcbbbcdbcadadadbaccbadbcbacdbadbbbbbbddacdbaaaadbddbcbdbabdabbadbbaadadbddabaacddccbddbadddccdbcdcbacbaaccddbcddcadadbaadddddbbaadbaacbbdabcddbdaadbdbbbcacaddacdbcccdcaabcdadcbccbbdcdcbbbcbadbcddadccbcdcbaadaacddccdcaccaacacdaacbaacdbaccabbccbdaabcabbbbddaccaabadacadbdddddcbdabbaddddcbacccddcadcbbcbdcdcddadccacabcdcadbcacdddbddaddaaadaddbaccbbdaadccadbacdbdadbddcadddabaaaddabaababadcabcdacabcccadbacbbbaadcbccbcadcaaabccdcbdbaacbaabaddadcdbbbcbbbacaaddaccadddcbabbccddbdcabbbbababbbccdbabadacbddadbcbdbbdadbddbcdadcacacdababcbacbddacccaccacccccddbcbcbdbdcdddaabdcdcaadcdabddcdddcbdacbbaababcdacbccacccbababcdccdddcccbddcbacacbcdbbdbcdbaacbcdbbbddbbbcabadccdddcacdaccaaadcdcdbaaaababaddaacaabbdabcabcdbbdbcabddcadddbcccbaabdccdddaadbcccbcbbaaaccbaacadacaacdbdbddbabaaccbdbbbaccaaddacbcacdacbddcddbdbdcccccbbddcddaddcdacdaccbdabbbbcdccadaabcbaadaadaccbbabdcbdbddbccbcdacbbbcdcbcbadcabdcdcbbdccdcaaacddbcdcccbacdacdcddadabcbcccadadcbcdadbbccddcbadbccdcbcabaaacacadabbbcadadaaabcbdbbadcdbdbccdddccdcadadcaaacdbdcbaacbabcaddaccdcdbaabaadcddcccbdabcadadabcacccbabdbdbcbdaaaaddadbcdbaaadacdcbbaaaacbddbadbdbdbcccbdbcacbdbdaaacbbcbadaaaccbbbcbcbcdbadaabbabaaddcabccaadddabcbdbcccbbacdbdcbabccdacabddbadddaadcccdccbddddadadadadbbbccdbabacbddabbacbcaaccdadbadbaaaadaabdabdaacddccccadbcaaaccaacabbcaaacbacabaccaadaaaadcddadbdccbcbbacdcdadcbbacbbbcccbaacbdbccbabdabbaabadddbbcacbaabcbcbcdddaddadccacaccccacacaccadaaabcdddcadbbbdcbbdccacadcadcaacbcdbaabdcbabccdcaacbdccdacabbbccccdbcadaddacdbdbcaadccdcacbcbcacbaaccabcdbbccdcddaabdbbdabbadccbccdacdddddaccbacbdddcdaaaccaccbabccdbcabacbbcabdcadabaacaaacadbabbaaabbbcadaddbadbdcdddaaddabcaaaccaaacbddcbdbccdcbdddcdccadbddaabdcabbddbccbcabcbdadcdcababbdbccbdaddadacbdabdbbdccddccabddcacbcdbbddadddaddbdbcacdcbccdcaacdbacbdcadbbdbcbbdbdbcacabbcabdcdaccbdacaaadabcaaccdcbacbbbacdddaaccabdcdcdccacbaacabacacaababcbbbdbbcacbdcccdadbbcbcdcbabcacddaccadabbaccdcbdddcbbdadbdcbacbcddccbcdcaabcdbacacbabacddbbbadcbdacbdadcadbadddbadaaabaacacccbdccdacaabacdcdadcaaaddbbbdbddadcbbbccbdadacdcbcdacdaddddaaaabadaabcbcdaadbaabdadbbdacddacddcbbdcbdddcaddcbbdaadbadbdabdcdcabbdcacbcccadaaddcbbdacdcccacdcabcaccdacbdaabbbbabcadbacbbdcdbdabadadbbbadbacdbcbaccddabdbbbdaaaadacbccccdcdababaaccabcaaadbcbddcdbbbaaabadccacccccaacccbababaddcccdadbdaadabcbacbbddcbabdbacccabbadddcdadddaddcacbdccaaccddbaaabaccdaadbdaaddcadccbdbaaacbacadbcabdadadabdddccacbbdaadbdbbbcdacabdaacaabbcbcdacdaccbaabbcadcddaadbdaaaadbcbbdadcdddcdbbcbbcbcdaaacdbccbdbaaadcacccadddcadacaaabbdaddaabdccbcdcabaacbbbbaacaddabaaacaadcaddbbbcbbababdcbaacaddbbcbabacbabcbbcbdcdacacbdbccbddcdddbcccacadccdcccbdaadcacacdccdbccdddbcbabaabbadddcbdbaaaacacdddccdadbabdbcccbdcacacdbbdaddaacbaccbdcdddcbabbddbacbaabaaaddaadaacacaabccadaaabdadbbabddbdcdcddaddcddbbdcaabdaacacbccbcabaaabaddbabaaaccbdacdddaccddddcccbccccbabcaddbcdbabacbbacdcdbbbbccaaabddabacbbcbdcdacdccbdbaddabcaaccacacdbbbcbabbabbcdaaadbbcddadbbaacabcbdddcadabdbcbaccddbbaacdadadadbabcdbaddcddbaaabddbcabcadcdaddbadbacdcadbccacdbdcdbcbaabaaddcadbbbbdacbbdccadbbdddcaadccdaddaddabdabddcbcddbcabcacdcccaddaaabaccbdadadbabaaacabdcbabbbdaccadbccbaaacbabdbaabcacaaddcadcdaaadcbccdbdcdaaaaadaccddaacccbacdabaabcdddadbaddddbaacbcbcbcacabddbbcdbcaabcccdbbcdaaabbdbbbbadacccacbbbddbdbcbdaaaacdbbacaabdbdcbbdbaabcddaaccbbddbdbdcbbbddababbabacadaccbddaadabdabbdbacacdaccbcacbcdabaaccccabbddacdcdadcadabacaccccbdbdbcbdbdbccdcbdbcccabacdbbbcbadcddaadcaaacaacdbcacbcabacaccbbbcbdcaadbbabdbadbdcccbbadcdaaabcdaccdbbdaadcdbcbddaaaabbddbabcaddaadaddbbbbbbabcadbbaadbbadaacadccbcbacbacaabcdbccacaccccdbcdcccacbcdbacdddcddcbccacabcddbacbddadbdaabdacadbdbdabcaaadbabddddaabcdcbaddcaaccdbddbbcacadadcbccadaacdbdbadcabdacabcdccbbbdadacdcaadadabbccdcdaccdcbadcbbacdabbabbbdbdabddbdaabccddbcbdcbcdabdcabaacddaacdaaccbbbacbaaccadbdbbddaadbcadcadbdcbbcbbdbadaddacabbcabdcddbcbddddbbdddbddadbbbbabcbcdabaadaadbbdaddacdddcdbbcddbabcbadacabbbcbbbaddcaadbddaabaabaaaadaadaadadaacbadddbdcacbcaacabdbacbcdcdcdddcbcdacbccbacdbadcaacacabacaddababdaddbdacbbdaccdcccdbaabbcddabbcacbdcbcdacdaaacabdbbcabbaaacacdaacabbbbbddcdbcbbabbddcccabbaabbddcdcacaaadcccaddddacbabdbaddcccaaaabacdaaddaddccdcbbdddbbaddddcbabdbddbdadccabaababccdbabbddcbabacbacabcadaadddacdccccdbcbdacadabdbabbddaaadcdcaaabaddcbaaabbbdbaadccdbbdacdbadcabbdadaacbcabcddbbcdccdbbdcabbccacbdcdcabdcacbbaccaadcccccdaaadccdcbabbcdddabcadbcdacddbcdaabccaacdadcccadbccaacbbcbccabbacdbdbbdddbbbbcccbdbbbbdbdbaabadabccbccadbbdcacacccacdaadbadbbcdddddabacaccacdbcabcdbacaabaddbdcdbaaaabbbacdadcbabaaabdababdbabacddadcbcdcdbccdabbddddddddabcdbdddbabdcccabddaaccabbcdcababddbbbddabbabaaacdbcbddcacbdcbccccddaacdaabdddbaccdcadadccbbabacaccdddadaabccbbdbcdbccadabaacdbdcacabaaaaaaacaaddcbbbdaccdbbdaccccbacbadacaccababddddcccccccbdadacdbcbcdcadccbdbaaccbddddcdacdababccabbbbbcaabdaccdcabaadaabbcccabcccbbbcbdbabdacbcdbadcdbbddacbdbbddaccbcbdbcbbacbdcbddbbdadabdddabbbdbbbdbbcbabaabcbbbdacdaabccbaadcabacbcbaaabadbcdbabbcacdbabddaccbcabbbdddbbadcdaddcdcbcabbcbabbaddacacdabbdabddbbbcdaacaadcaaccdcacdcddcadcacbdabbbcdbdbcdbdddbabcdcccdddcadadaddbbdccdabcbabcdcdcdcbcdbacccbcbbadbdbcdcdbcdaaabbbbadadcbbdbbdbddaadbddbabacdbaadcaadcddaadcccadadcccaacacbbdaacabdcbaabbaaaadcbcbabcadcccaabdadcbdbdbacbcaaabaabbbcddddbccbacdabdabababaddcabaacddcacdabbacddabbcdadbbdcabaadaccbaaacbaaadbaadcbcdadbcdcddbabaadbcbbabdbaadcabaabbcaccccbbbdccabadddcabaabcdaacdcabaccaccaabcdbabdcbbdbddbbcddcdbddcadbabddbaccbccbddcbcacabbcaabaacdbcdbabadabaaddabaabdabacbadaccabddacddddbbbabababbcddbdabcccbadbdbbcbddaacbcccdaccabbacbdcadcbadccddcdadccabbcadbccbbbdcdddbacacbadcdbaabbacdbdcadadcdadbdbaaabddbdacbbcdbdccdaddbdaadbaddbcacbabaddcadcbaaabaccabbcaaddbacadbcaaadaabdaaabdccbbdadddbabdcaabcbcabbddbabddcbdccbbcdcbcadcbbcbbcdcaaaaacdaaccccadcdcccadcdabdcaaaabcabbcdaadacbacccbcacbcaabcdacbaacaaaccbbbcdcabcbdcbccddddcacbbcdcabacaacaddbadaddacbdcdddbabaddaacabdbaadcabccbdcadcddbabdbcbbbadcadbcddbddbbccabbdbddababdabbcbdadacdabdababbbbccadadbccaaaccdabdbbbacccabccbcdbcdddadcaddcdbdacccdcbaacbccacdaddadbbccbddadbbadcadadddabbdaacdaaacddcbddbabccdadddbaabbddddacabdaaaabcabbadadcdacccadaaaacccbcaaaaaabbddcadaddcabadcddbabbcbcbacddcaadcbdcadccbdcccacdabadbbccbccacbaccbccdcbbddabcacbdbabdadbbcccbdcbabdcacdbacabbdbdabcdcbddbddabcccccbcbbcbcbcbbbccdbbdccccabcdaacadcbdddcaddabbcadadaacbdbcbacdbbbbddadbacabbaaddbcadacccddcccdcdcccbdacabcddacccdcadcccacdbbbccacaddbbbaaccadaccdbabcdddbbcdbabaacbcddabbbccadcdbdcbacbbccbcdbabddcaccdcadcacdaabcdcbbdbdabdddaaaaccdacabbdcbdadbcbbdbddbcdddcdadcccabbaaccdbaadbadbcadacddbbcbbbcbbcccccadbbcacadcabcabdbbdccbbbbaddccbdaaabccbdbdaabdbdcaaadcdabccadcdbaddddacdaaaddbdaacaabdbcdddbcccaacdbababdadbaaabcbacccddabadaddabcddacabbadabaaadddcadccddcccbdaacabcbadbcbbdbabdaaabddabccacacacdbbdababdddcdabbccdddbcabcbcdacbbdbcbccabdacbcccadccbabcdacaabcbbbdddaccaabbbcccbbccccabbdacdcdacdbaadadbbddbabddaaccccdaaddaccdcbdddadccbbdcdcddddbbddddddbcdadabcddcdcacaabadddcbabbacbcbdabcdcbbcdbbbacaadaaabadcbacaadabdacbcadcbccddcbdccdcdddddcdcadddacccaccddcbabadcdaaaccbbcadcbdcaadcaddaacddaabacabaaadbacadcdccaaccaaabdcdbdcdbcbacaaaaadccdbbbcabadcbddacdcaacbccabdaacadadbbabadacacccdcbaadbdcbacbcacdacbdcbacdaaddabdadccaadbadcacacabdcbbccbabdbaccddcbaadaaacdccabdacbcbcaacbbccdacaaaabbdbcdaaaaaababbaccbadcbacabdbdccbccbbdabbacbacdcdbbacddbccdabbdabcdcacaacaabccdbadcbcacdcacbdbcdcabaacdcbbaddbbccdddbcdaaadaccadadcbdbdbcbdadaabadcaabcdbbcadaccabbbcaddcbbaaddcccbdaccbdbadbbdcccddcdaaadcdbbbdbdaabcdcccaccbccacdbcdbcdcbaaabdacdcddcacbcdbcbbdadcdadcddcabccddbbdbdbcaaddcbacbddabcbadbcccdabcdccaccacaadbbabbcbcccdaccdabaddaadaaccdcbcbccabdcabaddbaabcbdddcbdacddbaaabcbccacddbdbbccccdabbbaadbcaabcdbcaaadbbbacdccbcaccabcdbbbdcddddacbcbdabbcccabbdbaccbbaddadbbaccdabdabccbacdaababbdccdacdbbbcdaacdcddabbbcbbcbcadacdbcbbbcabdbcabbdacacaccbcaaabdddccaaadbadacdcdbbbadddcddadccbcdbaddbbbdbcdbadbdacbabdcbcadccdaacdcbdaddcbbddccbddbdbdadbcaacdaacbdddbcabbcbcdadcabcbadbbcaabcaacbbabbdaaadaadabbcdacbccaabaaabddcacccaddbadadcbdadabbdabbcbacaabdcbcbbabbcdcdbccbcbaddaaadaabcdcadbddaccacabbbababdaabcabdadaabadabcbdadbccadaadaddcaaddbcdbdaccbdcbbaabbdbdcbbddbabdbdacaaabaaaacddbaabcdcbacbcdcddcdadddcbdaccabadacbadbbacaadcbdbbdccddadaccadbaabbbbdbcddaabcdcdddcddcabcaacdbbcadbaabbabbabdddcacccbddbccbcbdabdbcbcabbbcbcaabbcbbabaabbcccadbdbcbdacadbccddcdbbcaabcdacdcdcaddbdbacaccadcdbdddaaccacccdbdddadcddcbcddddbdadabccaccdacdaabbabdbdcdacbadbccadbbcbdddadcccddcbbbddcbdccdcdccbbbddbcdbdbadababbdaddbbddaacddaacbadbbdadbcabdcabdaabbcdabddbbbddddbccccdadccabcddddcabddbaccdcadabcaadbabbabdcabccddcdcaadbccbccbbcbacabbcbdcdcacbadbbbacacaddadcccbcccadcbddbddbaccdbadadbcacbcbadbacdaadbaabbdadcdbaabbaddbbddacbabadcacacbccdbccbcccdacadbdadaadcdcbbcdaaabbcbcabaaabdcabbcacbbcdbbddabcacbcddcabaabbdbdcbaadadcaccaaddabdaaacbdabadcddcdbcadcbadaabbcabccdcdbdcabbcccacadacacabbaabddbabaaacdddddbadcaacaacbcacdcdbddccdbcaaccacbbddaccaacbcaabbccbcdaabbaccccddccdbabbabbbbdddadacbccbdabacdcdadaaabdccdadcbbbddbcbdadbaadbdbadadadabbbcacbcdbdcbbccaadddbcdabaabaabacbcbbcbdbccdcdaabdcaadccaadbaacbdbbddaddccdacbcadbaaccdbccbdbcbccdcbbdcccababcbcacbacacbbdbadacaabcbcbcaddaaaacabbdcacdbadbdccbadddddcdbcdadaabdbbdcbcdcacbabdaabcabcabcaacdcbabdbdcabdaaacababbaabbacacabadcbdbabdabddbabdcacccbaaacacccbbdbccabcbaadadcdbdbadadcddbbbcaabccdcababdbcabcbdcaddcbbabbdadccbcdbcdddbadcddbcccbcaacababbccabbacbbbdaabdcdbaabadccbdcacbcddbaaacadcbabcadacabcccbdcdccdddbaddbdbcdaacdbadddbdcbababdcddbcbbddcbbbcbdcddadbbbdbaabcdaabddaadcbcbbcbabaadadabaaddcdaaaabdbccdadaabbaabadcbcdcaadddabdbbabcaacbdababbcccdcadbadacadcdccaabbaddcdbdbabaddbacddcabdcbcbbbaacdadcdcabadcacbabcbddcbbdbbbcdabdccdcabbddbadbdbdbbadcbaddadbdcdbabcdbbabbbcadddddadbcbbdcccdbaaccdbbcbbdddbabcaaaabbcbaddcacbbddaddcbbddddbccabacdcdbabcbbaabbddabcbbdbbdabbacccbabbcdcbcbbcaababdcbadacabbcbdadacccdbdbdddcdcdccababdddbccbaadcacbacbbddbbbbccbdcddbdcbbbbccaaccbaaacadacacddbbcbabddbdcabacbcbadacbcbdabacdadbbabaddbcbcbbacbbdddabcdcdcbdddcbdcaddcddcbaacdbbcadaddcccbaadbbacabccabbbaadbaccabcbddbcbdadbdcdbdbacaadcabcddabdadcbaacbabacbaacbcdacbbadaddbdcccdcbcdaadabbcbbbccdcadcbbcaabdabcaadcdaabacddbddcbcdbadbbbbcbadcddabdcbaaaadbacccbaaaaccdabbcdcbdbcacabdcdbbbbbddacdccccadadadaaabdcbcaaaabddccbacabbccdcabcacccacabaadddcdaadcddddddaacaabdbbbaaabbdcdcdadabdbabbacbddccdbcbcbbaddcbddbabcdabbcccbddbccacbbcbcdabadcacbdacddbbdacaccaabdabacababacabdcbcbcadccbbddadbbdbcccdacabcababbccbdaacdbcbcaacacbcdaabbddddcccbaccccadcacbadabbbabbbdcabdcdaddbcadaababbabccaabdbabbcaaddbdadbaaadbdddabaaaabcbbcdaddacbbbcdbaabcbdabadbadccbccabbcacacdacabcdcddbbbbadbbbaacbbbddadaccdddcccdddbdadcadacdacccbbbcddccccdacaaddcccacddaddbaddcbbcbadaaaccbbcbbcbbccadccaddbbadcdadabcaddadbdcbcdaaabadcbdbaccdcbacbddbaddcbbdbdbdcddcddccbabbddacbbabbadbdcaacdaaacdbadabddacbdcbcddacaaaccbcbbbcdbcaabcdbacbbcbcbccdaddbdbbcacdddcadabadbbbddcbaacdbabcdbccbcdcdccbddcddcddcccaddaaddbcaaddaccaaaccdaabccacbbcadddbbdbcbcbdadabdbaddcbccdbbbbcdbaabbabacdbdcaaabcaaacdaabbdbcbabaabdbbbcddbacbbababcdbaacbbbdcbdaddacdacbcbbddcdaddbddadbcbaabcdccaccabdabccbbcbbbacddacaaccaaddbacdaaababbdbacaddabbbabacdcabbabcbcbaaadacdbacdbcdadadbdacacadbaacaabcaabbdbccadbcdacddaccabdacaddbccbdbdccbabacaacddbbabbdcbacaddbbdcacbacccbddabbbdaadcbcbbabcbbdcaabddcdcbcbdacdadcbccacacccababcbdacbcddaccdabdaaaccacacdcacdddaadcdbacbdbadacbacdcacbcaacabbacaadabdcaccbccadcaaddbdaacadadcbbdcdbdccbadbccaacaadadadbbdcaacdddaadbccbdbdcbcaabbccdbdbacacabcbdddaaaccdadaddcbdcabbaacacccadddabcaadbaabacdccbacaaadcdbdcbdcbccdabdbaddbaacabbcaccdcadadddadccddaaddddbdccdbbccdcbccaadcabccbdbdadbcbaadcacadbbacaddcaaaaccacdaccbbbdcabbabdaababbcdbcdbddbccbbbdbaabdabdcbbcbacdaabcdaaababdbacadaccbaaccadaccbdccacdaadcbbcddbabdddbdcacccbcdbdbddaccbaddaabdcccdcccbaaaadacbccaaabbbccbbacbacacaaabdaadddddcdcbdcdadcaddcdadcbcbaadccabcadbdbacabddbaabbdcbdcbaaabaadbcddbddddadbcaacabbaadcdaddcabbaccbadadcbdbaadabadacbbacacdaabbcbbcabbdccccccaddabaadcbdbdbabcdddaddcbabcccadbccadcbdbbaadbaaadbcbabbcababadcbabcacaddbdbddacacdbdbdccacababbcddacdbabacbbacddacacaddadacdbdacdbddccbdbcaaacddcaabbbcacdddbcacbcddcacabbacbcaabdcabddbbddbacdabddadcbcbdadabacbdcdaddccdbcccbbaaccabcbdbbadcdacdacbacacaddbdcddcccbaaddabbddbbbccbcabdadcbdcbddcdccccbaaddbcbcbaacbbdcadcddaaacccdabaabbccbdabbaacadbbabdabdbaacbbbbdcacbbabbacbadcbbbbbabdbbcdcacdbcbaccadccbdadaababdbbcadbdabcaaccbcabbdacadacabbccbabbdabcaadacbbcaccdbaaccddcdcddddacacabdbcabbaaacdabddabbccddddbbabaacbcacddcdddcccadbbbcbcbdbdcccaddabadbdccdcbdaadbbdcababbaabcabbcadabccddccaddbbcaccdddcaaadcddcbbbcdddcdabdcaabdbbaacbaaaacdbdabbbbacdbccdaacccacbcdddcbabadcbadbbbaddcaddcbadbaaabbbacbdbcadcdadbbbbbadddaaabdcaaacddcdcabddccddabcabcbdadccaadbbbdbbdbdddabcdddccbbccdbcddbdddcbbbdbacdabbbacdadccbaadacaddbbddcacabbdbccdcbdabdabcbcadcdaabadabdbdbabadcadabaacaaacccdccaacbcddbbdddacbdbbdabbcaacdcbbcacabbacbaadabbacbcdddccdaacccaadcabbcbbaadbabbbdddcbddcabbacddaacaccbcdccacddcdacabccdddaabbdbcddbbcbbdbcaddbbadcccdbbcbcdacbbccddbdbcbcbbdccbccdbacccbbdcadacdcbdabcbcbbaadbadbccccddcacccaaaddacbbcdbbcdbbdddbddaaaaddccbdddaabdddcadaaccacbbacbbdbbcbbdbbcadaaadabdacaddcabbdacccdcacdcbacdbdabbcbcdccbccacbbcacbdccdabaacadcdbdbbcccddbdcbdabcadbcabbbdaddacdaadacacaaaaccddbbcbbcdbdcccbdaaadddbaddbacabadddbababdaddacbbdadbddbdbddaaacacddbdddabbdcbccdabcadcababaadbabcbacabbccccaabcccabdaabdbabcbcdcdbadcbacbdacabdddccbdcbddcadcabbcabbadbccbaadbddabdabacdbcbcabaaaaacccabdaadcaacadbddbaaaaccbaaccadaccbbbbdadabadaccaccaccbdcbbcadcddcdcdcdcbaccabccacaacacccabcaaaaccadcdbbacacdaccdcaaacaddabdcccbccbccdbccaabbdadddcdddbaabcdbdbcbdcdacacbbdbdacbcbdbabcababbabdacaadabccbdababbdccaaaaabbcbdbcdbaabcbdcbabacdbbacacacccdabcdcdcdadabacbaacadaccabcddddccacddbabbdccbdcacabadaccbbacaacbcccabbdbadbcdbdccadacadaaabbbcdbdccbcadcbbcdbadaaaddccaabccbaadadcadaacbcccdbbcaddcdabdbbbadabccdcaddbaccbaabadbdacdbabcdacdbcacacaddcaaacaadbdcaaccdadddabddbdbaadcdaaaabbacdabbaadcaadaccbcadbcdcbaabacbadaaddddbdabcdbddcaaaabcbddddabbabdaddabcacbcbddcbcaabbdbddbcccbbddadcbbdddaaaddbdbbbbddbcaaaadacaabccaccabcaabaaabbaabdbdddcadddbbcacbcadbbddbcaccdbaacdcdaaaabcabcdcaaabbccadbdbccdcaabcdacabdddabdabaadaadcddaaaadbbccbdaaacbcaaaccbadbbbbdcabddaccdbcaacbcdbbaabadabbdcbacaaacadaacdcbccdbcabaccdbcddbbaacccbacbcdbbabacbabbbbbcdccbdbabbddaacdbcabcdbbadbcaccacccbcdccdcbccaaccacadcadaadcbcadbcadcaabaadaadcccbacdcdacdbcabacdddbaddacbbcbabbdbaaabcbcbdacacaabdbddbdbadcaaaddbdcacccaccbaaaccdacbcbbadacaaabaaaabaaddbaddcbdddabcbccccbddadacdacbbbbaadcbbaccbadccbdddcaaccddbbcabcbbdcbbaadbbcbbcaddadacccdbbdabddbdbaacabbdcbdabdcbaadbcaaddddadaccddacabadddacaadbabadbcbabcdabbadbdcdabcbcdbadabdbcbcabccbdccbcddcddbbbacdadbcbbdddaccdcdbdabbccdcaddbbbbaabbadbacbccdacbdbcdccdbaadbcdccbaaccadcbabbbacccddcabddabccdbbccccaacacbdbcdbabadcabdaccadcadaacabbbbdbdcaadcadcdbacddbbabbadaccbdbabdccabbdbadaadcddabdabccacdadccddccdbcaaccbbddaabdabbcddabbacabcbdcbbaabbcdcaacdbaaabaacadaaccdcaaacdccacbbdccbbaacadabcaaacaccdcdbaadbabddcdccdbdddddcbcdbabdcacadabaabadcacacabdcabbbddddcdbaabbdbdababdccabdaddbdabcaccdadcbbacbcccaababddcadbadaaccadabbcbccbaacddcdddbbddabbbaddcdcdadacaddbababdcaabbdbadcdccbccaacccccccacdacdbacdcbabcbbdbbcaaacdcbacbbcdbdacdabdcacdbcbdacdababaabdccadcdaadabddccacabaacbdbbdbcadcaccbddcdddcbaaccadbcdaaaadabcccdbbdabdadddcdabbabcddbbdcbdcbdcbabacbdbcddaababacbddaacacbbdaddadddcdcabdcbdbaadddaaddadabcdbccdcacbdccadcadabdaaccbdbdacddcdbadaaacaddbbbcccbcbbbdaacaaddddcababadbbdacdbdbadbdbcdacaccbcabacccabaadccbdbabaadbcdccaccdacbddbdcdbcacdbacbaaaccbcdaddaacbadaddbbacbaadddbcaadabcdddcacbbbcdbaacaacccaaacddcbbbbcddadddbbdbdddbdaadaaaddbabacbacddabdcdabcdbabbbaadbbccaddddbdcadadacbbadbddadcccadacbccdbbdbcaabbddabbbbcdbbaaccdbdbddddaddbcbbdbdbdbbbddaadaacdcbbbdabcdcaccbbadddabaaddbddcadcbacccccbddadcdadcdbcadddacddbbbcbccbcdcbbcbadaadddbcbabcdccaddadabcbabcccabcbdcbdadcacadbcccadadbbbccbbbacaacccbaaadabcdadaddccabbdbcbbaacabdaabbbbcdacbcdadccddaddaddbdccdcbcbdbdcacbbbbccbdddcaaadaddcdddbdddbcaacabbcddcccadcbcaaabdbddcaaddcaccdbacaccadaddddbacadadcadbadddadbadccccddaabbdadaaaccabdccabddacbabcdcaabbcbbccccabbaadaabbdaccbdaabcbcdaddbcdadcccdccdbbdcbdcbababbaadcacabcccbbcabacadcdaccacddaccacdbdccddaacccdcbcacdccabcababbcabadbcdacccdadbbdbaccdbacbcdabadbbcabbdabbcbddacddcccdbcbdcccbbdcadcdcccaabbbacadcbaccbcddcddaabbbbbabdcdbdadbdbaccbccdaacdbbddbcdcbdddcbdccaddaadaadcdbbcbcabccdcbcdcdcbdbcaababadbaaadbbbcddaacccccbdbbcadabddaddcadbbdaadacaddaaaabcbddabbcddbdcbcbccdcddcccbbdcaaacdadbdcabdaddaccbcaddcaababbbacbbccbcddbdacdadcadacaddbacbacadaaacdcdadaaacbbdbdcbdddbacaadabacbdadddbcdacddaaabccddbcdaddacdabacadddcbabdacacccbbbddccaadbdcadccdccabdcadaaaccccdccbcccbbbcbccdcbcbdbcaadaddbacbbaddcbabaccdbccbbcacbdacadccaccadadbadbcdcacbaaabdddcaadccabcbbcdaccbccdadaaabbadacabcbadabbaaaabbddbaadccaaccaacdbaccacbcacacbcdacddbddddcbabdbcdcdbddddbdbbcdcccbbddadbddababdccbcccbbdcdcdcbccbdbaaccbcacabbdcbdacbcdddcbdccbcaddbadcbccccacdddbdbcdcddcdacaadcdbdcaddbabdddadabacadaaadddacacacbabaaddadaabadcaccdbdadbcbaddbbcabddcbbcbbdcacdaddaacadbbcdcbdcabaddcbbbbdadddcdaaccaaddcdaccbdcadacdcaabbcacabdbdabcdaaacbcdacaaabaabaaabbbbdddcdacbcdabbcacdcbdbcadbbbacccdabcbdbcbbbccdacbaccbabdbadbacccdbbcbccbabdbccbcaabdaacabdaaaccdaaabcbcccbbbdaddaacdbacacbbdadccaddacadbadbcacbcdaccbacbaddacdcdacbabddcbdaadbadabbbbabdbcddacdbadadabdbddcbdbbbddbdbddcdaaddabdccacbdddccddcccaaaccccbcaabcacdccdcdacabccbcabcacabadcaaadddadaaaaadbcabadcabbdbccbcdcbcabcbaabcbbdabdabbabbdaaccccbadbcddccacdabddccdadaadaababdddddbbcbbdacaabbccddaabcaccadabdddacadbbcabbaabdbabbdbccbabdcdbcddaadcaaabccbcdbdabacccadcbbadbaaabbddbbabbabbbdaccddcbdbdcdcccaadbdcddbadababbddcdcbdbdccbacdccadcbddabbaddaadaaadcabbdbbdbbbcccaaabdacacaaadabdaddbaabadbdcccabaaacddbdbdbcaccaaabdbdcbddccbccdddcbdccbadddaaababdcccbabbbadcabadbdddbdcdcabcdaaddababdcbdcabddcbbbabbdcdbddddddbadacccbaaccbdbcdadbddacabcbabbbcbbdcbddcabbdbbbbcccabbabaccbcaadccdbbbacbdbddddbdbccacddbbddaaababdddccdddbcbbadccadbbdcacbbadbcdcadbbbccbdaacbaccbadbdddddbabcaaccdddbdadaccbbdddddccdacccddbabcdabdcbdbddccddccdcbdaddbcdacdacacdbccdbbcdaadbcdccbcbaaabbadadcacdbbabbaabbcdcdabbaaabdcbbdacadcdcbdadbbdcdacbbbabccdaadccdcdbdbaddabbcbacbcacadcdbbcadabbabcddaaaaaadacadbbddcccadcbbdcbbddbcdaaadababaddcdcaabbcadbdaddacdbaccbadabaccccbbabbdbbdadacbdbdccacbacbdbcdbbbdccdcdccbcbadbdbbddacaddcdabadddbdabddbcaaaabcdcbbadacccaddadacdabcbbcacbcaccdcbabbbcaccdbbadbdadadabbadbdabdaddccdbabacbbbbbbadbaddbdacbccdabdbdcdacbdbbaaacabdddbabddbaacaaadcdbccabdbcaccbdcadbddadddcbddcaabddcbbaabadaabaddbbcadbaabcbbadbdcbdaabbadabbdbdccadbbbabcababbacadcbdcbabaaacccaaddbdabbbdccddacccdcddcddabbddcdbbbdcbabdadcababbadbdbacddcacabaccbbbaccbcdcccdcdbdcaadabadaaddbbdcadadbcacaadadacccdbcdbcaddcdcaacbcbdbbaabbdcddcbbcbbadcadcadbbadacdadadadaaacccdbbaacddacbddbbcacdaddccccacaddcdabcdbdccdcdaccdcccbabcbdcabcbdcacaadababdbdaaadabcaabbcabbcaccacbddbdadaababbcaadadcacacddadadabcbdbaabccaadacbbbbdbdcddaababbcbbbcbdccdbcaadbcbddabbbabccddcacadcccabaddcddcdbcdaaddddddcbbcdacababddbdacbddaccdadcbddcbddcbbaadbcccbaacacbbacdbdcdcacdbccabadbaccccdddbcbbbdbddaabdbaccdadaddbdaaadbbdcbacaaacacadcaddcacabbabcacadbcdbadacadbaddabbdabaccbbccbbcbcbdbbbcaddacdcdaadccbaaaacabcccddbcddccccdaabddcbddddacccccaaccccbacddbccccbcaccdabacdaaacccbaacbbddacbdabcbdbccddbdcccdaabdbddaaddbabdadacacabdddbbddcdaccabbbdadbcbdacbdddbbabbdcdddadbdcdcbcbbadabaaddcccadbbbabacbbacccbaddabadadbabccaacbbabdcbcacbbdbaccadbdbddbbabbbbdcbcaaaacacadcaadadcdddabaadddcbaddadaabdbcabcaabdccbbccbababccdadccddcdbcdbbbdccbcbacdbbabddcacbdccdabcdddaaccacdacbbcccbdadcddadbdadacbcdbbabadbaadbbbacacbcdddbabddacbcadbcaaaddcaccaacbabaaacacccababcbbccdcddcadcabcdaacadcddadababcbaadddadddcadadbacbccbdaacdacdbcdbccddddacaadddddbcabbcdbdabccbbabadcabddbbcabcccaadaccdcbcbdcaaacaddcccaadcadaabcccccabbabacaabdaabbacbbcccbddadaddbadaaaccdbddabbbddaaacdaccbdddadaaadaccbcdacccaddabaaabdbadadadddcbacbcccddabcadddaadcbbdabbbadbbabdcbdcdcccccddabcbdbdaacbdabbadaadadaacdacbadadabbcdbbadbabbdbadaacccabddabadaccacdccbcdacaddcdddaaadccdcddbacadccabcbdaaddacbdacacbaddccacbbcbcdcadddcdccadcbcbabccaaabdaaaaadaadabaacccdccadaccaddbcddacaacbdcaacaaccddacababaaaddbcdccbbbadcbdddbabcdcdbdbccbddbbdadabbdcdcdbaddaaacbcaadadbcadcdccdddbcacbadbabbabccbdabcbadacdbadbbdabadcdccbdabadacbddabdbdddddccdbdcbbbbabcaddadcccdccdaaacdadbabdbabcabccaddcaabdbbaabcababbabdcbbdabddcbccbbbdaddbbdbcbcbacaabdddcbbcdbcdcbbccdbcbcaaabcbdacbabdbcdadbbacadcddcadacdcaadbbdaddcaccbadadbbbcabaacbcbbabacbdddcabcbcdcbbdbaaadddddcdcacadbacdabcdddbbaaccbabaaacbcbbdabadcabdcaccaddbdaadcdaacaccdccaabaaaacaacbaabadcbaddbcbddbbbdcbcbbcaadbaacacccaacadcbaacabcbbadbabacaadbdbabbbbcabbbcdbbdbdcbdcdacbacdacaacdcaaabbcdbbabaaacacdabddabddcdbcbcbdbadacbabdaadacabcddcdddaccdcabbdabaddccaddddaabdaabcaacabdddcdddabadcdddbabadbaadcbdbadccbbbabddcdbcbbcddcbacbcabcccdaaddcbbabbbcddcaadbacabcbcbdbcabdcbbaabbdaadcdadaddddcacbdddadbcddcdccbcabbdcddbbcabdabbaccaaccadddddcdcbbcadbacaaacdacbcdcadccdccddcaddbccccbaaddbabacaccaccdcdaaabaaccadbbdccaddbaaabddbcaabdbacbcadacbcdbaadbdccbbbbbccadacdbddbabbcbddbccbbacdbcadbccbddadcadacbcbdcdddabbdcbbaadacdaacddbabddddbbcaabdbadbbddccbccdbcdcbdcdbddcabcbcbaccabadadddadbcdbcbdbaccddccabcbcbcbaddbcbabdaaabbccbcdbcadadcaacddcabdabddcbccddbaacccdccaacacdabababaccbbcabbacdadbbddbbabdaacddabdabbacdbbaacbdaacdccbbbddaabbbacacdbbbcaacdbcddadacdaacbaacdcdbbcabcdaccabaaaccaacdbccbaccbdcdbbbbcdabdcadbccccbbaccbabcabdcdabdbabcadbdddcbdcbbdddbcddcbbacbddbdccadddbacddccdcadabacddddddddabdccabbcacadabbcbdbcdddcdbbaddbabcdbccaddccbdcadbabbaacbbaacccdaacaacacddadadbddabbdadcadcbddcccccaddaacbdcddaadcdbcdadabbbbcdcdddacdbdcadcddbbdabadbddadddabaaaacbdaabcddcbaabcbccdacbddcbaccabddbadacadbbbaaddbadcbbabadabdbcadcccbdacadbdcadaacaacaacdbacaaacabdbbbbdbabcdcacbbcabaadbaabaaadbadccaccbacdbaaabdcbcaddbcbaabacacccbaabcbcdabbbddccccbbcaaadbdcadadbcadcbcdbacbadcdbccddaaacccdaaddbdcdcdddabcababbccccbbcadcdadcdcbdbdabdadcdabcaccdcdccbbddbcbaadddcbbcbbbcbbbcccabcabcadccaacbddcadddbcbbddcbcbdaccbacbadabccdbdacabdbdcdaadaddcdddcccddbadadbcddabcddaacccadbdaccbbdbaadcaacbcdddadcdcbbdcabadcddabcdbcdcdaaacbdabcaddbcbacbbdbdababddcaaccbdcdcadaaaaaadbddbbbaccdcadbddbcdcbabadbdcbbcadacbabdbaadbcbbbdbcdcddcccccbccdccbdbababccbddadbbbdabddddbdbbdbdbaacbccbdaadaabcdbadbcdddbbcccdcdcadcdaacababcdbbcbcdbadddcbaabdbcbdcabccbccaaacbcbddccbccbcbdcbcbbcbbcabbbbcbbdcbdabccdaddcbccaaadbcaabbbdaddacccdabbcbacaaadadaaababbbccbaaccaddabdadcacadbcbccccbadaabacbddabaddbdaaabcacbdababbdacbbcdcadbdddbbcbbcbaabbcbdcddcbccadbccdacbabcadadadbcaaccadaacdaadccbbcabbaacbdccacbdbcbadcbddcacbbbbdbdbdbdacbcaddbdaddccacdbdbaabccbcccdddcdbaabbbcbdcddbabcbccabcbbccabcabdcaadcbcbbdbdabcdbdbacacbaabddacbccbdacdacdacbbcacbbbaddcbdccaaaccbbabdbdcddaaccccdccaadbdcdabdbcdbaadababcdbabdabadaddacddbcddcbddccaddadbbbcdbcaddbabcabcadbcddbcaaadaabcbddccbbbddcacddddadbbddcabadadbcccccbbacbcdccccbabdaababaadcbabbabacdbddccdcbbacaddcdbcddbdcdcdbacaadbbadddbddbdaaabcbaabbdcaaaacbbcadbdbadabdbbddacbdddcccddaccababcddddcabccbcdbcdabdbdabbadbaddcbcbbbcbcadcccbadaacdaadcabbdacabcbccbcdbadcddaaddacbdbbabcabcdccbdcbcaacbcdbbdcbbaacdcbbbadccbdaacccbbbbabcbbcadbdbcadbaccbacabbadbcddabbdaddddadabcbdbbdcadabbbcddcaaabddbddbcbcdacdaccacacdddcddbadcdbbddddcacbdbabadccdcddbadbcadbbddaacadbadbabbdbcbaaccdbbbdbdbdadbbacabacdccbaccaacbabbdcccabaddbbabbbacccbabdbaadaaaacdcbdbabbbcbdacdccacbcdcacbccdcdabbdbcbdddbabbcbcdbdaacdabbacccaacdacbccccbbdcddbdacadddcdbbaabcaabacdbbadbbcacbacddcacdcbcabcadabaadccdcdbbdbdbacdabdadacacddaddbbcbabababdccdcbcccdbbbbaaddaabdbbacacbddadcddbdbabadbbdaddaaddcaddaddcdcadbbadadbbaaadbbbdcadddabaacbbdcacdbcadbaccddbdabdadcacddaaaadcdccacdadcccccaabbcccabddccddbdabbacccbddbdddcdbcddaabadabcbabdcbbccbddadccdabcdadcbccaadcadabbbccbaaaddbdcadabcacbcbacdabcdddaabcbaccbddabdabcdadbdabbadaccaaadbccddcadcacddbaadabbbdcacbbdaacadcbaabbbbcaccdcdcbaabbaaabcaccbabcadbdaabbdcdbdddcccabbaabddabcbbbbcabcdbabaaaadbbccdbddcacbbddacadbdbbcdaabacccdaabaaccccdbaccabcadcddcbdbdbbcbddbcccabcddbbcacadcabddbdddbdccbaabbcbdaabbcdcdcadcbcbabbbcaabcccadbcccacdacdccabdbcdaacdadacacdccbdcbdcbbdabbbacdcdbacaaadcdbdbbaabdddaabadbdcbabcbcbcdcbdabdbcdbdaddccdbadcbdcadabcdddcadadcdaddccbbbcadbaabcdccbadadadacdcccbdcadabcbadccccaaaacdbdbdbaacbbcdcabdbacdabcdcbccadbdcbdbbddccdaaccacacdadabbabdccccacbbdddcbdcabdbabddcdadbdcdcabdaddadacaabacddaadbdaacadbcaacddabbbdacabcbacccdacbabaacabcadbbaaadbdbdbcabacbdadacdddaabcaccbcbcaaddbbddadccdaadaacacdcadabadabbbaaacbaacdbbaadbabcbcbdbccdbbdabdadccbabdadddcacaadabbbdcbbccbacdaaccccacdccabcdabccbacccccddccbdcdccbdcbccbaabcdaaaaddccbbdbbcdcdbabbabcbabbbdddacbcbbbbacaacaaacdccbcdababbbaaddabbdcbcabbdaadaddcdbbbdcbdbacdbadcdabcbdcabcbccaacdcbcaabadcbdcbbabdbbbbadadbaaadcadbdcdcadabcddacacbccccbccadcbcdbbdbdaccabbcdcdddcbbaabcbbdaabccababaaaaaaadadbabbcbbaabdbaccddabccbaabaddcdbadddadbcdbacdaacddacadbdadacdbcdccdaaadbcaadcacabddaabbccdbbcbdcacadbbcabcccbbcdcbccaccdabdaadaababbdbbacccdadbcccdcbbbccbbacadaabdbcacbacadddaacbdccacccdccddcacaacbaacbddcbcccacbbacbaadbcdbdadcddadbbbaacaabacbccdcbbbdcdbdabcacccabccabaaacdddbdbadadcadbcdcccabbaddadcccdaaadddaacadbcbabcbccabdabbcdcbadddadaaabacaaabaccacabbadbacbcadbcbbbadcbbcccacdddacdabadcdaccbbcbaddabcaabbcacdaaaaadcdaacaccbadcdbacbaacacbcdbaadaabbcbbabcaacadaccbddcdadacbbdcdbbacdadccddccadbbbbcccabccdcdacdccabdadaddadcbdcdbadbddbcccdbbcdaabbaddbacbdaccdcbabbbaadbcddbddabcccbdaddbbcddaabbbccadcacbbbcdadbbccbdadcbddbdcbbdbadbaacaaacccabacbdbbadbdbbcbabbdbcbddbdcdddadddbbdadbbabdcaddaddcbabcabccabcbaabbdddaabdcabcbcaaddadbddbabdaaddabdacadbcccaaabdaaaaacbccadddcaacacdbadcadbdbbcdddbcbaccaccdcabaadcdaabdbcbdabcabdcacbcdcccbbbbacadaaabadaadcdacbcbcbdaccdbcccdccacdddcaddbccdcbabccccaaaabddbbacbbacdaccabbcadacdbbbcbacadbcacdacadbbcddabddcabacdbccdcddadabcbcbcdccdcaaaccbacdaabdbacddbbabbbcdccababcdacadcadcbcddaccabcaaadaddbdadacdabccbaddbccbccccadcadaaacddbbaaaaadbddadcbaccaddaddcdbdaaacabcbdcbcdadbbbcbdcddacaadbabdbddccccacadddbaaaddbdabcbbcabcbadbbadddbbcbbadbbbbaccbdddcccdadabaacadbacdbbbddcabddbbdbcadbdcbbacaaddbbacccdccbbbaaaadbbbccbbaacabccaccbabbadabddabcbcdadbaabadcacbcbabdbdacaacabaabbaadbabdaadbdaddbdbcabbaabbadcbacccbcdbcbdbdbbbddbadcacdbddbdbccddcbdbacababaaacbabdbcdacaabdbbdcdaababccaaddbacdbccaccbabdbcbbdaccbbabddcbdcacaadacbbbcbcbccccdaaccadadcabbdbabababcaabadadddabccdccdcdaccbdbabbbdbadbcddbadcdbbccbccddbdaaadacabaabdcbabcbbbbcdbddacaddcabdbccdcadcacaacdddbdbdccdadbdbdabdaddbbddadaaabcdbaadaddacccdbaaacdbdcabbacaacbcadcaccccdbbcdbccbbdccbaadbbaddbadbbddaaaddbababaacccbdddabcadddadddabcacdbdccbadcdbcadbbdaaccadabaababdcbccdcaaccaadbcaabcdbcdddbbbdcaacbbcbacaadddaaabccaacabdcbaaaaaabcbcaccccccadbbbdadaacdddbaddaacbdbcbbbddccdbcabbaaabccddddbacabdcddddcdbbdcabadacbaacabaabbbbcbbcbcdbbaddbbaadcacacadabcbcdcaccbacdaadabcdcdbbdddbdbbababdcbbaabccacaacbdbdddaaaaddbadacccabaabbacdccbbadaaadaacdcacbccdbddccaadcacababdbdadaadbacdbbcaabcbbabdcbbcbcbcaacdbccaccdbbbbbcababdccaaddccbddddbdcabacddababaabbccbdcbdcabcaadabcdacccdaaabdcdcbddcbaaccdbacadabddaddabdcbcbdbacaddcaaacadcdcaaccbdbbaddaccddacabbabdcdbccaacacdcbcbdacdcdddabcbdbcdacccdaaccaabcabdbcabcabadbbcaaabbadbcaccacccaaadaacbaddaddbaddabdadabcbbcadccdbacacbaabdddbbdabcddadadaadcdadabccbcaaaacbcdbdabbccbbbbacbbbdabaccbacbcaaabdccddcbaabbccbcdbdcbadabbabddbbaccddbcdadbcbccdddddbbcdbcdcdadabbcdaacbdbadaaadaaabbbbccbacdabdbbabbccadaadbcdbadcbbaacadabaaccadccbbbdcccbbabacddaadbccbccdacddcadcabbbcaaaadaabbdadacbaacbdbdaabaabdddaacabbaadcbddbdadadbbbaaadbaaccdaacddbdbadbdbcacbdbadabcdbcbaaddcdcaddadbacbadbdadbbccadcdcdcccdaccccdbbbbaabbbcbabacdcabcaabccdbdbabccdaadcabadccaadaacacdddbacaaaccabaaaaacddacabdbccbaadbdcdaadadcbcbbbabcbbbcabddbccccbbcaadccabbddbdbbdbbdddccaccddddacdbbdaadcbacbbadbbcaabbcbccadcacbaaaabddddaabaadabdacbdccabbcacbbcbaacaabacbcccddbdddcbdbdcaababdcaaaccacabdaccacaaddadadcbababcddbcbdcbcaabbabbbaccacdadcaccddbbcbbcdddaaadbdbacaccbabacdabdbabababcbcadbbadddaadcabdbdcddcdaacdccacbdbaaadcbdababbdbabdcaacbccbabcaabcadbcdbaccdadbccbbabaabbccbcdacbbddbbacdbbbbdaaaabdddbcbabacbdbababacdaccdcdbbadaccdcdcdddcabdbbdcdadcabababbdddcddbdabadddddcaddbddbbdddbcdadabcccdccbbbdaacdaaaaadcdabadacadcdcbbaacdaccbddddbabbbaaabaadaaabcbbdaabdcbcbdcaabdbbddaaaacabcbababdababbabbdcaaaabacacdcdaccdcccabacbccaacbbcbdcddcbdcbbcbccdcccbbaddddcdcadbabdbdcbdabbaccabcbadadcdcbcbccabbbbbadbddcadcadbdbcadaddcadabdbdbcdbbddcdacbaccbcddbdcaaadbaddabbcbbddbbbdcdbbdadccaaabcdbaaccbdacbbcbcbaacadcacdccccaadcdbbbdbcaddbccdabcbaacabdadcaddbdcddabccaaddbaccdadbabaaacdcdadacbccbabddccbdbcdcdaacacdaabaaaddbabadcacccdcacbadacacdccdacaadbdabcbbdaccdcbccdaaadcbcccbdbdddcbbbcdbdbabbbdadabadbdabcaddccbcbbbdbbabbcdacaddccdaacacaddcaaddbbddcdaccbdbbaadcbdbddacbbacaadccdddcdaccddabbcacacdcaacdbdcdadbcccdcddadadbbcaaacbdddcbacadbcbbccbccaaabacacaccbbbdadcbdcbccdcadbadbaabbdcaadcaacadabadbcbdabdcbdaacbcccdcbcabdacadbddaabbbcddcadbacbdacbcbcbabbbcbaaddbdbdbcabddbbaadbadbadbdcbdbcbdbaaadacccdbbdbdbcbbbdcabacdbbccdcaabccdaccbdcbcbabadddddbdddcaaabdcbbdaadcacdaacdcdbbaadaabdbacaacaddcbdbccaddcbabadddadcdbccbabdbbabbccbaaaacdbbacccbabbdbdcbcdbcdacdabcbacbbdaadadbbdcdacbbcbdaabbdddbcbcdbadacbbacdacdddcdcababcbdddaacdddddbdddddbccadbadacbdbdadacadccdacbabddddbdcaadcbacadbcbadbdcbacbddbacaabcccbdcabdddcbcadcadcbbaadacadacbaadcadddaaabcbdcbbcdcdbdadabdcbaccddbdacbacdccaacbcbdcbcbbcdcbbacdbbddddadddaaabdcdbbcadacbddcbcdbbdabbbdcccbaaddddbbacbbaabdcbdbcbaaaadbdcdbdabdcdbaaccaaaaddcabdbaddcaadccbdbabaaddcdacbdcbcbaccdbbccaacbccdcdaaabaccccddbaccbbabccbccbbacbcdbacddbbbcaadcacbabbdcccdbbcccdddaacdccbadbdbcdcbaadbbcaddcccacdcdadaadcdccacddbcddbdddaabdcbcdabadadacdcaccccbdbbabadcaaabbacccabdbdacbdabbabddcadbaacadddbdcbdacbbcbdcbbbbdaddaccdacdadcbbbbaccdcababddbccaacaddacaadcdadbdaacdbdadbcbdddddbddcdbacddbddaddddaaccddbadbcdacdcdbadbaddccbcdbcacbacbbdccdabbbbcbacdcdcbbadbaddabcbdccdbbbbddbbcaabdddcdacadddcdcddcbdabdcababbdaacbcabbbdaccbbcabbaccbcddbcbabadaabaaabbbbcbddbdbbaaaddccacdddcbbccdcccdaaddddcacdccbaadddbcdccaddccdbcabcacbccaadacacaccdacacbdcccaaacdbcbbbcaccdbabbbccabadbdcbbdcbcabdabaaadcddccdaacbcdccdddbaccdbcdccadaadabadccdccbbdabbdbdabddaadababdbabdccacdccddbccddaabddcbacbdcddddbdaddccdaacbbbaabacbdbadbccdcbdddacdcdcacadcdcbbbddabcbbdccccbbbabcccabacbabaadcbbdaaacdcbbddabbbdcaccadabbdcacbcbccdccbbadcdabdacccacbcbbcdbbdbbacadbadcdccbdaccdbbbcdabadbaddcbdcbccbcdddadcaabbddddbcbbadddadccabadccdcaaacddbcdadcabcaccabadaaaabacdcdaadbcdcbabadabdbcddabbcbbdcacdcbabbbaaccddddcbabbddaaabacdcabbbdcdcccccacbacbcaaabadcbdddcabcdadcbaadbabbaaabacccacaabdddacbdaaacadbacbbcbddcabdbcbcbbaadbcdbdcccbbbabcdbbdbbddbadaadccdbbabdbcdbabbbbcdbcaddacbcddcbacacccdbadacdcbcbdaaaddacbdddbaaacbccbadbbaaacbccddbcdaabcdcddbbaaaacabcdcacbcbcabdddabcacdcdcdaccbcdacbddbcabaddbaacbbdabbcabaddacadaadbbdcbabbdbccbcdcccabbdcdaccdddcadaadbdacacbacacaccdcdccabdcbdccbadaccacaccdacddbaadabbcddbdbbbaadcaacdbbcaddaaadbbdbacbddbdddddbbccdccddaadaaabbbadbdbbcbdbbcacbadcabdccdcdaaaaacbdbdcbadcaabdabdaccababcbbbbdccdacbbaaaddbcbdcababbcbacddcbdcbcdbcaaccbbddbacdbdcabbbaccadbcaacdaaaadddccbcabadddadbcaabccabacacddabcacdddbabacdbdbadccccdaccbbdacaadcccdbbddabcdcbcbdcbadccacbbbdbbbdcaacdddbbbaadaacbaaadccadabcababacccccbadaacaacaaaabbbaddcdaccabaccbcbaaacadbdbbaccbbadacbabcbaaaabbccdddabaabaacaddcbdadbdadbccbaabcdbababdaccbccdbdacaadadadbcddadbddddcdcbdcbadcddaaddcdddbcbbccbaabdccddddcdabdacabbcadcdabcdaacdadcbdacacabdbaadcbbcdcbddbddcdcdddccbabcaacaacdabddcbbdcbbbaaddabbdcdabcaacbbdbddbcdddbdbdccbccbaaddabccbbaddcbaccddaabdcdbaacccdccdbbcccbdcaaaddbadaababdcdbddcaaaaadbbacaccaacaaccdcdcbbddbaaaababcdbbacdbbdadbdddbcdacbbaaaabddbacabdcabcddbbacbccbaaaaccdaabdcacbacaddadaabcaadcbccdbbcacbcdaaaaddddcccbcdcaaddcaccccdddacdcddbaddcbcbcdacaddbaccadabdccdddcbadaaacaaabdadadbddbaaabdacdbcadacbaadbbdbccdadabdbacbcccddbdccbdcdbaaababbacddbcbdacdddcaaadbcbddbcccbaaacbbbdcdcdbbcbbabcabdabbaccacadbaacadbdbcdcacccdaddcbaadbacdccbdabbdbccabbdccacabacdaabcbddbcdbcbccccdacbbcbdacdbdcadadabbddabdacacbdbadbacddadbcdaddcccacbcbbcbcbdbdcbddcacbaaacadbdbaabdaaacddbbdcaaaaaddaaaaabcdbcccadadabdbcaaccdabccdbdaadcddabccaacdddbbaadcbcabbabdcddbbcccddbdcacdaabadbdcdbbcccbaaacddcabcabddcacbdbcdbbcacbaddabccbccacccaaadbdbacaabacadaddbacbddddadcbadcdbcaadacddacdcacbabbbcabcccdabdddddbaccdcbadaabcddcdabdbccbacbbdddcbadaddcdaacbbdcbadbcddcccbacadadbdbccddbcbddadccacccbdbbbdcbbccbbbccabdcbbdbccdbbacacbccaacbcccbbcdccdbbddabcddadcaabddaabadbcacdaaaaacadacdacddcaaddacdcbcccbabdacabcbbabcabadbcdcbaccdbdddcaadaabacccddbccacccacaababccdaddaabdbabbcbbdcaacacbacdcddddaadaaaadaaaacbabbbbdcdaadcbdacaacccdadcadccabccbdcbdaccccdccabdcdcbbcdcabcadbacbbcdccaacaccaadbaaacbadbdcadbadacddbbcaabdabaabcdbacbcdcdcdcdacdaabdbbccabadabcdcdabbddadadbcbbbcccaccccabddaaacdaabccdacdbdddcaabaadacbbacccbcddccbdadccdaadacacaaadabbcbbccdadcdaacbcbbddcbccdadadaddddabcddcadbadcabdcadccbccaabacacadcdcdaaddbabdaddbadabdcbcdcbaddbcabbbcbdcbddbcddacadabdbcdcadcdddbcdbdbdbcdbdcbcbbddcbddcdacabbdddaacdaacacaacbdacacdadddabddacbacbcaabdabcdadcacadcdbbcbcbcbdcbabcdcadcccdcaddbbcbacdbbcddddcabbaccadcabdccabbddbabcdbadbbaaaaabbbcddadaaaaabdbdbdccacbabdbddbdcdabbbadbabacdadabbadbcbadbbbccdcbbbaccbdbbbabaabddbdaaaacaddccacbaaaddbcbadacbabdbcdccdcbdbadbbcbacdccadabcdaddbcaabcbdbcbaccdcbacdbcccdbbcbabbdcaccacacbbdbadadbbdbddbbcdadddcdadcdbdbbbccacddccbbccdddcbbcbabcacbabacbaaccdcddacabaabacdadbaddbacaacbabdbbdabaaacdbddcdbdbccdabccbdaababbaccdddcdabacddbdaabadccdacacbabcdcbdaabcbabccbbcccdabcdabcdacddddaaaaaacbadbcbcacbcdacdcbcacdacdaababdccabcabbbabcbbcdacacdaddcdadbaaddcaddaaaccdddabbbbbbabacabcaabcabcdbcaaabbccbdcdccdcbcdabcbcbbdadcaaacababbddcbabdacbdcccdbaaccbcccdddadacbdbddabddbdacaacddabaccaaadddaaaadccdbdbacdcacbdbbcbaccddbaddcddddcabdadcdbdabdbccaacdaabaccabdbcbbacbaaaccabcdbcabbdcdbccadadadbbadbdbcbacbddddacabdbcdbaccdddbbdabbcdbadcadbaccddbcdcadcacabaddacadccbdbabaabddcbabbadabadacbbbbabbacdcdabdbaaaaadaadbbbcabbbccdbddddabbdcccadbbdcdddbacdacccadcbdccadabbcabbcaadbcabdccbaaacacbbacbbdbdcddbbdbccbbbcdddacbdbcdbaaabaccaaabccaaaadadaaccaadaaddcacdacddabadabdbbaacdccbcbababacbdddddbbdbacdddabbadbdaccdbbbcddbcbbcddbaddbadddabcdbaddccdbadbbbacaabcdccccdbadbacbbbabadccccdabdbddbcddbcbdacbbadcbacacdcbcaacbccbccadcaacbddcdbaadbdbdbddbadcbcbdaddabbaacdcddbcccadbabbbcdabcabdbbcacdbdabbcddacddcacbdadadcdbcacbabbcddccdadcdcacbaccaacbadcbcadcddbbabbacbbaddacccbabccdccaaacdadcccdcddaaaddddccbbdcdccabcbcaabbbaccacccadbdccbddcdccaaacdcbdadcbdacdabddaacbbcbadcadabdacadacadaadbbdbccbccabadcadddbdbacdabccdccaacabcddbdbadabbdabddbbccbdbadbdccaaabbdbbaabbbcdddbcbacbabbaaaacbdaddcadacbccccbaabacbbbdcccabddcddbcbbabadddcaacdbbbbcccbdbcdababcbabacbacaaaaccbddcbbdddbddccdcbcdbcbdabcbdaaaccacacdacaadcdaaadbbdbbcbbacccadaaabcabdbcaaddadddbaddacdcacdcdcbcdbbaddaccdbadbacbdddbccdacbadcaccadcdcacdbbaadabbaadcbcadccadcdcbdcdacabcaaddaabdddbccddadcacbabcbcadbaabdcbdcdddbdcdcabbccccabcbaccdbccbdbbdbaccbdaccdcabaaadbbcadcbdcbdcddaaaabcccadccbccbdddaabadaadbbcbddddacadbbadaadddbabaacadadcbcadccdbdbacbdccaabbcbdbddbaccbbddaacbbaddcbaddcacaacdabcdbdbadadcaddacbccbbaaabddbbadbadabbddcdbbabddccaabdcabbdbdddaadbbccbccdabdabdcbccccdcddbddcacaddbdcadccaddabdabdbdcdcbbcbbaadabbbdcbbbcdbbccdccdccdcbcdaddbcaabcbbdabbdadaacbabcaacbdacbcbaddadcaabccabccdcabcddcbaacaaddadcaddaacbcaabbaaddbaadaabcddddddaadacdbccacbcbccabbbcadccacbbcbcdbadbcddabccdcbdabdcbbcaaabddcdcadcbddbcbddccaccddaaddaacccbdcabadccaddaccbaaabdcdcaaaacabbabccbcacbdcadadacdbdbdadaaddabdccdbccbabdabdcbbabcbdcccbddadabacbaaddaaccacdbcbcaacdcbadaabbacbdaabdbcacdcadcabbbddaabcccbcdbcaadbaacaadbdcdcccbadbbaaddddadaccacdbacbaacddaadcadcbccddddcbbaabcddcbaddcaccbbabdaabdaaadbaaaabadcbcbbababacabbbcdaccbadacaabddbdcadddccbaddcaaacadacdbabcdabccdbdaacddbbdadccbbbbcbadbcdcabcacdbdddbccdcdcaabbbbbacccabdcdaddabdcacdcbdbcbcabcbccbbacaadbacdacdcadbdcbdbcabacbbddadcaaabacbddcdababbbaaabcbadacacddcadaddbdbcdccaaddadcadbbbaaccaadccbcdabcabcdbcbaddcaadcbcbddbdbbacdaaccbdabdbcaaacbcbcbcabcacdbabdddcdbcbadcaaabbbdbccdbbcaccccccdabbdcccdacdbacdccdccacbbddcbcbdcabbdbcdcbdcdbdcbbbbbacacdcbadabacbbdabcabaadaccadcbacbcccbccbbcabbdddababcbbcdbbddbdbcdcddcdaabdadaaababddabbaccadbcadaaacaabadbdbcbbbabbbbbccbacbbccadabdbddbdddbdacbabdddbdddbddbaddbbdadcdacccbddcbbcbbdadbcabbcaaaadcdbdaacdbcccabbcabdaddacdcbbabbbcdbdbbabcddabacbabacdabacbaaaadbaccdacdcddaddbdbbaccdbbdadbbddddbaadadcbcdbcdbbabadcdcddacabdbbbbaaccaddcbabbcbccbbcbacbdcdaaaddbbbdbcaadbaaaaaaaccadbcdcdaddacbabdaaaabbdaabddbabdbdbddbdcdbcadadddbbcaccbdaaccaaaddcaabacdbaacdbaccbaaaaccbbbbdbbbaacbcaabcdadccbddcdbcdcacdcbdcbdbacacaccbaadabacbbadcbbaaadaaddabdbdaacadbdbaddddadbcdacbbaababdbddbabddbddbbbbbcddaadcdabdbcdaaadddbccbbbbccacbbbbccbabbbacdbdcbadcdaaaacccaaadbadcdbacdaddababaabbdabcdddabbbcdbccabdaaadcbadcdbacbbbcbbabddcdacaabcdbbbdacbcccaacdbbcdacaacdcdaaddcdbbccbcbadbaaaacdcccccddaddddbadacccadcaabaccacaaaadcdaabadbccabcbdbbcdccabccaabccccdaacbacdddabbbdcdbbcabbdaabbcabaabcdbcdbdcdbacdddcbdaadadacbbbdbbcbabbcdbaaacdddbddcbbaaccaadccddaaccbdbcdbaddcdcbccbbddcdbacabacccbbbaaddcbadacdcaabacbccdbadbabcbacaccdddcdcccacccbbbaccbdacbcddcaabaaabdaddbdabacbdddbbbacccccccaadbabaaabdaccaadddccbbdcbcdbacacccdaacdbccdcbcbccaaadcadbdbddabbbacdcccdbccadadaccccabaaadadcaadacbabcccdddadddcbcaaaadbacccccaaccdaccacdcddbbcabbdbadcbbacaabcadabcaaddbdddbdbcabbdcdbdabbbbadddadbaccddddcbddbabbbabcddadbacddaabababbbcddcbdcaaacacdcccddcccacdacccdbccdbbbdccdbddaddbcdbccabaacdacddbdbadadbacbcabbaaacaddabddcababdadbabbddabbaccbdcbdbabbddbcdddddbccdccbbacbbcccabcdbcddbaabdbcbdaabccbcaabaddcadcaccbadcbacbadcbacdadaacbabdcbbcddcbccabdadadabbbadccacdcdcbdbaddccaddbddbdcdcacadacccbbabadccccbccbbcababbcabbcdbcaccdbdbcacabaaaaadbacacbbbabbdbccaddbdcdabbddabaacabbaaddccacbdbadabdddbcddaccacadddcbbccdddddbdacacddbadcbcadcddcbadcbddabadbcddbbbacabadabababdaaacdddcababbabbdddbdcdddaccdddbabdcccccaacaababddcabbabdcabaadabcbbdcddbddcbbdcacbdccacacdbbbcbdabbbccdcbdcaabbcccccbdbcaddbadadcabcbbcdcadacacbdacbbccaacdacaabdcdcbdcdcabbdadabdccaacdcbdbadadddacdacadadcadadbaddbbdadddaddbaadccbaacbbcbaccdaaadcbcabbdaaadbbdcabcdcbaaaabdcbadcacbadcdbcdacdadcacdbacdadcdacbcdcaddaababdabadcdcdbcddadacdddcdbccbaacccddccdbcadbdbcbcacaaddbaddddbbbdacbadcdcadaacbadcdbabaadbcdbabcccacabcdaabacaadacbcdbabdcaddbdbbaacdbacbabbccbacdcbadabddcadbdbcbddbdcddadddddbcccacbcdacaadadbdbaacdcaacadcddbdcdabdabadcbddcacabccddccabbaaaabadccaccacbbcabcbdcdacaaabbbddacdcadccbdbbbbbdbcbdacabcabbcddabcdcccacaaacacaccccddaccdaadbadbdbaacbaddabaacccbbcabbcbbdcadcadccbcbadaaddccbbaabbacdabbacdcabcdbacbcbaadbcdacdadadcbbbaabdaaabacbdabbddacdadbadccadbaacbdcccbaacaabbaaabcbabdbbacabadbcbcbdcabcaadbbcbdcdcdcbcdbddadacdcdbdaccbdaccaacdddadbccdbbdcbaaddadddcacaadbdbcdccdbdcadbcccbccbdcabcddcbddcacdaabbcdcdacdabdabbdaabadccbabcadcdcbcbaacddbdccbdcaccacaabbcccdaccadcaddccacdbdcaadaadccdbadaadaabbbcdbdcaddaaccabdddccbcccdadcacdabccbacacabbbdbdaacbbabdbbcbdccddcaccddcbdacaddcddcbaccaaddabdbbbbbabbaccabdaadadacccbcbcadadccdadbccdacadcbcbcdbacdcaaaacbbbcdbdacbdbbabddbddacdcabddaddbdddbcbaacacabcbddaccdcbbcbabdddcdcacdacadadcbbbdcabaabcaacacbddaaacdaabdbbadcdddbcacbddcddadabaaaabbadbdaabcbcacacaddccadcdcadacbcbcadbbabacacacbbccdbbbdbbaabaaadaddcbacadadabcddaacabacdadcdacdbabdaacbbdcccdddcdbabcbdacdddadaabbdddbdddabaddaccccabdbacccadacadbddbccddaaacadacbdcbcbbbabbacadabaaacaabbadcddccbbddcdacdcaaadbddbacdadbaabacacccbccbccaddcbbcadaaadaddbacdddcdddaccbdccaddaadbbaacbaadabadacacababadbcbcbccdbcccbcaaccdddccaccdcacdbadbbcdcabacbbcacbbdadbcbdaccacabdacaaddaddaccaadbaaccaccccbabcbbabdcdbdabbbcacddaccdddcbbbdaadcacaccdcbbaadbbddbdcbddabdccdcbadcbccbdabaacdbaaabbbadcacadaddbaadacbbabbaddddbabacdbabbdcbadbbcdbdbdbdadcdcacabbcacbcccddabcbdacccbbbdccdaacdddabdabdcbcdbaabdaaddadabdbaccabcccdcbdcadcabacadbcbdcabaabcdaabcbbdbdabaadcaccdddadbbbdbcbaabccdacaabcdbdbabbcbdadcccdabaabdacbcdcabbdcdcdadbcbbacdacbccddaccdcaddaaaabaaabcdbcabacccababdbaccbbbccadbcacadbcacbadabdbcdbdbbadbddbcdbddbcaaccbbbdccaaacadacdbbcbbcacbbcdadbdabbdadddcabbdadcdaddaacbbcdabccaaaccbbbcdacdcbddabdbdddcaaabbcbdabcddbaadddbddcbbbaacbdaaccddccbbaabbdaadbbcabccbdaaaaabddcadabbdabdbadbbccaccbaadbbcddadbbddddabaaaaacdbdbadcdbaabbacdabdabccdbcadadbcbaccaaaccdbabadbabcbacccccadabcabbacddbaccdaabadadcacabdbcbdbcdcaabaaddacabbbabbacaabacaadccdcbcabcdbabbcaabcdadddddcbadcacccdbcdadbbcacdcdabbbdcabccdbbddaacbdabadbdcacbdcacbcacbaaadbcabddbcbacbaddbbbccdbbbaaddbcdaddaddbadbadcbcdbbbddabcdacdcddaabbadbbadbcbbadcacadcdcdcadadddaadbaccdcadcbbadcaacacdacaabddbacbcbdbbbbcaabdaadbcdbddabbbdccababadcdbabccbcbaaaabaddaabbcdbcdacdccdabbdcccbadcbcadabbcaaababdbacdbadbdabdbdccdbcbadbbaccbcdcdcbadbabbdbdaccdbddaacccbbacaaccdbcddbdbaadbbcbdcaaabcaaaadbcaccbaccadbdabcdcbabcbccbcbcabdbbcdbbddbbcbabbadcbcbdabddbdbddacddbcdbbcbbbcaadddcdaaaadabbbbbbdbcbaacabbcbdddbcccadbbccbbccddddaadcaccbaabcccbccdcaddaacadcdcdccbdbbdbadbdbaaaacdcbbbbdaabbaadbdccbcdabcabcddbdddacbdaaacbcdcbabdbbcccdacdcacbcaddbbdbcdadbadcdabbbabbddcbdbaddaabccaacbabdbaabcbadaaadbcdacbaccdaabcdbcbcdaadcdaadbddbccddacbacacbbdbccbcaddcdadaaabdbcbbcddcdccbdbbadcccbaaaaddcadabbaccccbdacadacaabaabddddddbddadbaabcaaaabadddacdcacddabadacaabaacccbcdadbaadddadcbddadabcbdbdaaaabcdccacdccabbbcbabacbabbcddcdddddcabbbdaddcaadbcadcadbbddddbccccaddaadddbadbbcbcbdbdbacbbaccbcbadcbdcdcabbabccdbbccdcdddbcaacbdbcbcadaabcdcdddbbbadcddbcbddadcbccbababcadcbddbddbdbcacdccdccaaadbadcabccbdbbacbcbcccbaccabddadcbdaddbcaddcbdabcbcaadcddcdaaabcbdccdcbdabbcbaccdcbdcccdcbbcacdacdcaabbddacaccdbcbdcdbdccdcbcbddabaddcbcddbdbadcaadbcbaacdbcaabbabddadcababbadddabbbbcdcdbabbcdabcacbaccaabcdcadcbbddaccbbbbadbcadcaaacdcbcbbadcacdcaddaacabaabccccccbabcbadcccdadbbaaccaccdbbddacbcdacbacabdaadddbadacdabdacbcadbbbcbbbabbccadaabdbdbacccdcaadcacccacadddcaaabbbbacbabdadbaccaabbddccddcbbaddbdddcbbbbdcabbaababdccbbdddbbbdbabbcabdbcbaadcbaaacdbcbbbcddddccbcbcababbabbaccbbadacacaadbdbcdbccbbcaaddddbbddaacccaadbababdaabdcbacbaabcdccccbaabccccbcababadbcbaadddabcdadcaaaadbdcdcdbaabcdbbbabacaadbddcdbbacbdddccbbdcaaccadbdcbcbcdbadbbbdbccbaadaccdadbdbdcddddbdccdddbdccaabdaddcacbadadbabbdaabdcbbddbddaccbbcadbddbdbddaddbaddbcabbbacabaadccbdbcadabdabdcbdcbbbacccccaddbbcccaacdbdaccbbdaaaccccbdacdbbbcdbddabbbbacdaaaaadaaaddcddcdabcabacdaaabdcaaaddcccdbddaddaccaaccdaddbadaddbaaccccaadacabccbcaabaabcaaabbdacdcaccabacbddadcaabadcaddcdbabbccabbdbdddbcabcddcbcbcbddccbdacddaccccdcbdbbdadbdbbadcbacbadcadcbcacadddcdccadadbddbdaadcbaabdadbbadaccccacbbadccbbcabadbabdcadbdddbdbdbcaccbbbccbabacdbbadbcbdccbcbccbcaddbdcbddaacbcddcdbdcaccdacadbddcbabaaacbcdcacbaacbacccbdcddbdcdabbabcabacaacdbdbacddcbaacaabbcababbbbdbbcbabdaddcdcabbadbcddcbdbcabdbacdbbbdcbddbcbdaddddbdcacaccbdddbacddaaccdbcbdbbcddaabcabbbdaaccdbdcadaadaacdaacbdcbddabdbaacdbcdddcdccbadccdddccdabcacadbdaccccabadaaacbbabbcdabbddddbdbcbbcddabbdbbddcaccdcdbbcbcbbaacbbbabaaabbdcbbbbbdacccdacababbbbaabdaabcaabdbaacbcdcaaadadbdcdccacadcadcbcccbcdcdcdddcbbdbddccacbcdaaddabbadcdbacadadaadbcdcbbddaaddbdacbccddcabdadcbdbbdcbdcdbdbcbadbadaabdbbbbccabbaaaadbdcdbcbbdddcccdbcaaccdbcadcbdcdcdaadabcbadbacbcadbcdbdabaabcdbccdcbadbbaccddbbdcadbbddacccadcbabacddcdcbadbadacacbbdadcdabbdddbaaabbccbaaccdaaadacbddbcaacbcccbbdbdcdcacbcaacbacadbccabdbbbbdacbdbadaddaaddadadabcadbdbadaddaadbcdbcbbabacacdacaadbbbabaddcdaccdbacddbbcabddddbbdbdbacaadbdcabbacabbcccddcbdcbcddcdbabdcdbddcbadacabadbddcdcdddcacaababbccdacdbcadadabadaaccbabdbccbcbcababbbdabcbcccbbcbbacbcdcbcdccbdbaaaabdacabaddadddbadaaddcaaabcdabdddbbcddaadbcbcacbdbbabbadaacdddcdbccddabacadcbccddaadacbcbccbdabbbadccdadcdbabdadbdbccadbdbdaddbcacbddddaccdbabcbaadcddabddbcbacdacabdccbdbacaacadacdbbacdbccddabacccaaaaabdcddcaaabbaddcbccddaadbabdaacbbabdbdcabadbaaacadccdbbbbddbddbddddbbabbccbabdcacdadacbdbcccbdcababcbbbddacdddbcddbdcccbdadcabdcabaaddcabbccdbacccddbdbbaccdbacadcaddddbdadcdcbbbabbacccdacaadadadddadccdabdabbdaddddbbccadcbcdcdcdddcabccbcbdabbaccbbabcaccdabbdaaccacaccbadcbbabadabaddbdbbddbcbaaadbdaadddcdcaddaacbababbabbbdaabcbcdcdbcccaababbcacdcaacaabcdccbdaccdddaacdcbaddcbaabbdadbcabdbcadadcbaaaccbbacaddbcbbaabdcdbddcaaabcdbabdadcdcabacbaacdaccddadacbccbbdddccdccadaacdcbdbaddabadaaacdaabacdcbcadcadadaddbcdcdcdccbcdaaabdadbdbcaadccdaabccacacbbbcadbbddcacbbbcaddccaaddbaabdbdadabadadacbdbbbbbdcccbccddcacdbccbdadadacaadccbabaadddacacbdbddcacacadaaaaccccadabddddbdddbbddbbdcbddabcddabdbaaaabdcdaadcdddbadccdabccabbabcabbbbcdddabadcccadcbccadccaddcbdabaddadacdcdcaadccabbbddaadcccdaaccbacdcbaabadbdcbadaabcbdcaddacddccabcdbababdbdaaccaaadcbabaadbdadbbccdbaccadbaaaccbacbabbabbcbbbcadcdabdbbcaadcdacadbdcdccacaaccdddbdacadbdbdabadbdbababcbdaabbaccaddcaadcbadabcdbbcdabdcbcccddbcbadabacbdaabbbcbacabcbaabcbbaaddbaccccacdacdbaccbbaccbbadddddbabcddcddcbbbbaabcbaacbacadacccaaadcabdcbacadbcbcbdcabcadddaddcadacbadbbbcacdddcbdbdbacaadaadbcaaabccaabacbccaabadcbaabcbadbbaacabbddcaababcadabadaacbdddaadabcaabdccadccbddbabdbdbccacabbacabccaadbaccbcdaabbbcbcacaabcaabadccacbaacababdabdcdcbadbbcbcdccbaadadcbdddcdbaaaadcadadbabddcbadbbdcbdabdddaccddcbdddcacdbbcabadbcdbdbbadaabaabcbdddddadabddcbcdcabcaabacccacbddbaccadadccdcabacbbcdbacdcabccdaccabadcbcdcadbabddacabdbabaddcabbcacbbdbabbacdcbbacadcddaccdaddaccbdbaaacaabaadaabccdbdccdbbbadbaddccbccacdbaaabcabddbdabcccccccbcdcccacbbcaabdcabbdadaaaaddcbadcdadbbcdabaddcdcdcdacbccdddcbdcaddbdbbccdcbacacacdbcdccdcadaacbddcccbdadbccdbcccaddacaaaacbcabdadbdbccadbaccaaacbdcdcadaddcabcbacadcbccbababcbbccdbcdadaacdcdbcbbacabbaaccdcdcabadaadccdbacccbababacbcdabcadbabacdccddacccadaadabbbbbabdccdcadcddbdbcaccacbabbcadcbddcdadcbcdbcabbdbaccbacabbcbdbddacbcbadcccadccaabcababbcdaabacbbcdddabdcdbccadcddccadbbcaaccaadcadaddadddacaacbbbbbadcccadcdbdbcdabcccdaaabadccadcbbbdccadcacdbaccbaabaaaccdacdcdcddcdcbcbccbcabcdadbdbccadbaddaabcacdcbaabccaccaddbccaaadcbdbaddbcdcbdcbcbdaabdcbacdbdccdacbbaacbbcabbaabcacdbcddccadbaccaccbdacdcacdddcbdbbdccdcbaabbbbdbcacaadabbbdbdcbbcdbcadddabdbdcbdcdbadbccaabbacabdadaddbacdcdddcdcbadbddaabdbabcccdbcabadccabcdbacaddaaaabcbdaacbaabdaccacbabcbbdadbbababdcaddbccacddbaddcbccabdcdcacbbdababbcbdacabdbbbbabdbcdacddbaaadddcccaadacadabbbdaddacbadaddbdddbbbbbabdbabaddddbcddaccdbcaddbbbbddbaabcaacccbdcbacbdcababdbdddcdcadacdbadabcccbcbbbbbabbadbcacddbcbbbccddccabadacbdcabbaddbbcabdacadccdcdadcbbaacddaccaaacdddcbabacdcdddddbcaabbdadbbacadbbbbbcaccbcdbbacabcdadcdabcbccdabdbdaadbccbacdaadbdcccbcadcdacaddadcdcbbdcbabcccadbadcbacaddddcdabcbcbcaacdcdccbddcccbdbaacdddbbbddbddcaddbddbaabbaccbcaaabacdcacadbcadcabbbbcabbbbabadccabccdcdbdabbaabcddbdacdaacdddccbaadddbccbdbcdbdbabdaabbbcaabaccddcabbbdacbabccacaacbbcaadbcdacdaadbcccbccddccbbaabcaaacbabdcbbadcbbaabdadacbdaadabcaaaadbbcbbbbcaaacccbadacaacdcdccdbacbdabdcaaabddcaadadcdadaaaccdbabccbadacbacacadbabdbbacbbbcbdbcabbdcbbcbbabadacaadaacccadcdbcdbdbcbadcabdcbdacacdbbbcbcbbdabaaddddbdbcdddabdcddacbdbaaacbbddbbcbdcddbdadcdacdbadcabdbababdaadadabacddbdabcdddcbbabbbdbdcdacbaccdcdddccbcbcddacbdabcbaacbdbbcabbccbcadbbddaabdbacbdbcdddcbddaaaacbcbcaadabbbcdbaddbbbdbaccbcbabcddcbdddcaadccbbddcdbcbccdbabdddaaaaacdcdbbdcadaacdcdbcdababbccadcdcaabbbbdccacadcadbaaaacdbcbcbaabbaddcbaccbbbbaabaacbbdbbcacabbddcbdcdcaccadcccddabddcbddbdadcccadbcbadbbacdadcdbaabbdddcaadbccacddddaddbcbaabcdbbacdbbcbdaddbddbaddabccabadcbdddbcccdadbacbadddcbccccaaddbcddaaddabacdababbabbdddbccdccdbdccddadbcbacaacdcabccbbacbaaaccaacadccbbddaacbadbccbcbddadcacdabcdadcbbbdacacbcaacabcbcbcbadbdacddbaccbbcccaaacccabbbcbbcbbabadcdabbccabaaddbdbbcbdcbbbbdaaccbdabdbabbbaacbddbccbaccbaabcbabbdbdadbaabbdbbadcddcabcdcbcadddbacaadccccdccbdccbdbcdcabdbcdbbccacbabdddbcaabdcdbbaddbccacbccaccdbaacabdabddcaadabcbddabdabacdadbccbdabbdbbddbbaccbcabdaacbacccacbddadaccabcadbdacdaababbbacadccbdadddbbabccdabcbdbddcabdadcccccbacdbaadabccdaddcddbbccddbadbbcdcabaabccacbbccbcbdabbcaaddaaadbbdccdcdbcbacddccdbddabdbdbdcdabdbbbbddabcaaaabdabcbbbbcddbcbbcdddcbbbcaddddbbdcadacaadabacacdcbdacdcbadcbbdddbddcddccadbcacddadabaabbbbcdbbbbdcdddaababadadbbcbdbddadcddabbdcbdddcadabbdcadcadaadabacccbdaacccdddabdbbdbccdaaccadbdbcbccabcbbcabbbcbdbbcacccaaababacabdcababbcbcadddabbaacdbbcdadbccbccdaccbbabdcbbccdabcabdaaadccabadddcbcbabbddbcdbbabaccccbdbabcbdddbadaccdccdbccddbabbbcdadbbcbacbbabccccaddadacabadbabcbdbdabbadcddcaabcddabbdadbcaaabdabadcbbbbabbdbddbabdabddbbcbbbbaaddacccdaaddcbaaaadccbbdbbcacaabacdbacacabacbdacbadcdddcabaabacddadddbbabddbacddbabbbdcacbbdbbdaabbcbbbdbaabdacacbbadaaaccdcacbcabdaddddbdbdbadcbdacccccabcccdddaacbdddcbbcaccabcddcacdbadbcbabcdcbaaadbaabdddbabbdacacacbbcacbaaddcabdbbadaaadccbaadabbddbcdbbcdaddabbaacdddabccacabcbccaaacddbaaabccbcacdccbccabbcaacacdcbbbbcacdbaaaaadbdcddddbcdcdbbdadacadaadbcdddaacaadddcabdddccccaadadccdbaabddbdddcdcbddbadbacbbabacccadbdbabcdbcccbcdabdbbaaccbdbadabdccbcacdcbcddbdccbcdbaaaabbadacbdcaaadacacdddbdbdcadbadbbdcbabcdadabdacbacaaccddacdaaabcdcbddccddbabcdaaacccccabbccabccabcaaacaadadbacccdcddacdbdcdabaadcdbcddbacbdadbcdacdbbaaadbbacabacbbcbacbbcdcdbdbdbaacabbaaaabccddbbcdddadadddbcddaabaccabbdcaacdbcaccabcdccbdcbcdbbccccbcaabdababdbabcbdbcbbaaadacabddbaadcbbadcdabdbdaccdabadcdacbacbaccabcbaccdcadaabbdadcbcccadcaabdcaaddbabbcacaccaaddcaabbddbdbbacbcbaacbbbcccbcacbaccabacbacdadabbabbbcbddccaaacbacdaacadcdbaccccccdbbcabccddacddabbccdaadbccdbdadcadbbdcbcccccabbdbbbccbbabcbdacbcbccbcaaacbbddcdaadbaacdaacdabdddbdbdbaabcabdbbddcaabbdbdddbccadccddcbabbbcbbacdacdabdddadccacaddbbbdadcaddccacbdabdbadabbcabbadcccdcbacbaaabbddcbcdcadbbbbbbadbacaaddaccccabbcacadbbcacaacdabbadaddbbcdbbddadbdbddabccadbcbabbdcbaddbdacaaddaaccbdcacaadbdccdacadcbcdcbacccabcdadddccaabbbcdcaccacadbbadcbcbdbdabadbccaabdbddbddbdbcaabbbcabbcadccbdbdadcaddbcaaccdbbcccaccbbacbabadddbbbccbabdcbbbaaaacaddddbaacbbaaadabbbadaccadaccbcadaacdcadcbbcadbdadddbccbcbbcaacaacabaacbcaadbddcadddadcccabdaaddacbaaabbbbaabcdadacddcbbabacabbbabcccdbbbaabdabacddbcacbcddbaadbadacdabcddbccabdaaccbaadbcadaddabbaaacbaadbccbcdbbbdcdacdcdcccbdadaddadcbaddddaacbcdbadbababdbadacaccbbccbdddabaddbddddcbadabbccdabaaddbdcddbcadddbdaaadcbbbbbbcbcccddcdacbdaddbbdbcaccadaddadddccaabcacbcccccdbccadcabadaaaddddbbcddadabaabdaabcbdcddbbccaabddcaddbdcadabaacacbcadadcccdabddddbadddadbdabaaaadbdccacccabbcbabbadcbbdadbcdcbcdbabdcacdadacdcaacabaccbdcdccabdddbbdbaaabcbdaaccacdbbdaccaabacbddbabcbbabdccdbaaadabcaacdbddcbabbbabcdcbcaaaddcdaadaddcbbcbcccbddaacacdcdbacadcacaddaacbdbabcaabbdcbddcdbbdacddaabdbbbbbdbcbaabdcbdcaaabdabadcdbcdadacdccadacacbacaddaabccdadadddacadbcabbadcbcccbdbbacbddbbbcabcaabbcbbcbbbbddbbccdcbbaabaaccdccdbddbcbbcaddbcbbddccaabaabbdddabaabacaaddbdacccdacacaaacacacdabddcabdddadbbdddbcacdddbdabaabdacbaaadddadccbababbacadadbdabbaddddbbadcccdccdbbbaccddaadcdbcabbdbbaadadbcbbbdcccadbdcaabcdbadbcdbdbdddcadbabaabdabaabaadcaccddcbddbaabbbacaabadaddadddbdbbabaddcbdddcbbddddbabaddcaadadcccababaaddbdbbbcddbdcdbddbdddbcacdaacadaabaaabcadaacdadcacadccabbdacacadccacbcaccabbbbabdbbcdaccdbaadbdccadcabacbcbacbdcbbabdcbcabcdccdacacdbadbdcdcaabbcccdaaabcbdcacbdbbcdbaaccbdcddbabaaccacbcaacbdddbabbbcabdabcadaabccaacdbbdadabbadbbcbccaadcddabaabadaacddbacbbbadcabaadcdabdbdbbcdbdbdbccaccdbcabdbbabdcbdbaacddaadbababcaaabcabdabbccbbabbddbaccbcaddbadcaddacacabadbadcccdcddbdcacdaacaabbdacbbbccbcbdddabdbdaccaacdcbadaaaccddbcccadbdbcbdaaaabdacabadcdbacacacaacaaddbbbadabaadbbcdddbdaabccbaacddabbcddbccbabdadcddbbddbbcbabdcadbccddabbabadcabcccbcadcaabdbdcbdbcabbbabdadccadaadbdacdcbccbbccdaadcbcccbbadddbcbddadabadddbbddcdacdbdabbcacdbddacbddcdbacabcadabbbbbacdacdbbdaabcdcdbabcdbcddbcaaadabbcabdbabdcabacbdbacccabdbaaabcbbcaacaddcacddaacbadbcabbcbbaccddddcdaabbaadaaddbabbbcbcbdccbabadddddabbbaddccbacadbbabdcdcaadbcddbaaabbbadbaddaaadaacacdddcbbdadaaccaaadbaccddcacacacbcdcbbaccbbcdcabdbbdaccadbaabcdcbccbdccbdbcbbacbddabacbbbbadcacbaadbdbbcaabbdabccccacdccbabddaabacdcbbabdcabbdcadcdbbabcacdabccbabcdddacdcccacbcaaadaadcbbaacdaaaacbcacbcbdabcccaccabdcadaddcbdcddcaacadbcdbaddbbadcdaccccbdacbdbdddabbabddddddcddacbadddcadbcbccbabbacbaabccdadbdbcababdccdccdcbbaadabbabcaaadaabdbcbaaddbbacadbdbdddcdbaacabbdabbbcdcbdcaddbdaaadcaadbcbddcbbdcccddddaadacabcdbadaaacdaaccbdabcdcacaabbcbbddcacaabccaaaabcbccbbbbcaddbbaabaabccdabddaaabcaabdaaccbbdcdabbbccacdababdacddcdcaccabbaabdaaccbbaaaaabaadbabdbdcacbcbdbbddccaadbdccaabacbabcabcdbadddbcdcbabdbaaaacbbccabdbabcdaddccdddcabdbacdcddbbadbdbbcadbbdbabcdadbccccbcaddcacaacadcaddaadbcbabdcadddadbcaaadbcdbbbcbddbccbabbccacbdcaabdbbcccccdbbacdbadcacddabcdccddbbcbadbcccabdcbdcacbdbdbdaadbdbadcdbcdbbcccacdcadbcbcdaddbcbdadccbbcaabcdabdbcbacbaaadcabdcadcdaacdcabdaccccacbbbbcadbddcdbccbcbbbadccdbaaccdcdcccadbbabdcbccdadababcbacddabcacddadaadaacdcccbdbccadaadcdbaaabdadcabdadcabaacdaccbcbbbabdaabdcaaadaacccbbbdccccbddbcadabadcdacacadabababbbdccbcccbcaacabbcdacccdaacbbcdccbabcadddabdbbdddaacbddbbaddabdddaabccaaccbcacdbcbdaabbcdcaaccccdbccbdaadbbbbabacdaccacdabbaabdcdbaccacdcdbbbdbacdbdbdddcbcbbaaaadcdcbabbbccbcaadccdbbdcadcbbacdbcccdadbdaccbcbdbcbcbdbaacadaacccddadcbbbbaadabdcbbcdcddcccabbdaccdadcaccacccaadddaacddcadcdacaacdabdcacbdcbbcaabdddacbabadcbadbcaaaddbdcbcccadaabbdbbbbaabcaacbccdacaacbcadddbbdadddacdbdbdbcbabcbccbcbcdabbbbbbabcccabaabaaddbcbbaddbdaaababccaacabcbbdbccdadaccbddbcaaaacbdcccddccadadabdaddabdccbdcdadbdcccabdccbdaabdccaddcadacccbcbdcddaabdbbaaadbddbbacdbabddbdccaddcaaccbbabcbddadadbabadaaadabcdcbdadbccbacbaabcaacaaacdcdcbdabdccaadaaadbbbbddbbbcbcabaaaaccdcbdddbacacacabcbcadddbacacbddcaadddcaadcddcbdbbacdcaadccddddbdacdbcacccaddadcccacdbcdaaccacdaacdddcdbdbcabcbbddadadcbbdbdbbdcbabdabacaaabddaabbbbcabcaddcbabaccdcabbaddcbcaacacacabbbacccbdcddcadbaabdbacdbcdcbdbbacaacacbbcbcbaabcabdccaaccccbacccaacabddddccbcccbdbcbcbadbcdabbdcdadcbaabbccddaaacccdcbadcccaacbdcaacaabcaabdacdcccbbbcddbbccdbcadbadaabaacaabacdcbdbcddbccccdccdaaacdabbdbadabaddbcbdadbdcabcacdbcadabcbacadcbdacdddbdbadbbcdccccccdabbcdcdbbbaaadcadbdbaaacdacadabbabbaccbbdccadbbcddaabaddabaaddcccbadbcbbddbacdcdcccabadbbaacbaabccbdabdbbadbcaaaddbdbdaadbacbbcbaaabdaddacbdddddabcbdcaaaacdabbacddadcbbcbccadcbaddddcabbddabbbbbaacdbbdbddccbcabbbdbbaadcbaabadcddcaaaaccbdadaadcdbcdaadaabdcbddcccacabbbbbadcadbbbaccacccdccccacccdcdaacdaccbbdacdcaabadbbddcdbcdbccbcdabbddabdabbbbdccaccdcdcdbbcadacdbdadddcbaddbbcdbbbacdadacaaabaddbdbdadbcbbbdacbcddccdbadaccbddccaccddbabcabdccacaabdcbabddbbbcbdaacaaabcbabbddbbadadcabdadbcccbcbbbcdbaabacbbddcaadbabbdcabaddcdbaabddcabdcdcdbcdbadcdaccdaacddddccbcbbaccdcbbdadaaaddadcaaddbdabddccdabdcaadcabbcbcabcbcdadbccaddbbcddcaaccccdbbccadcdddddbabddacbbaccadabdabcbddbaaaabcdcddddaacbdcccaccaddabcacdabbacdbabcdbbbcabdbdbccdccbabcbdbadadddcbdacbaaadddacbbabddabccccbbaddbbdaccddbbadddccaabcbccdddbbcdacaadbdabcdcdddaccdbbacbddddcdabbcdbdacccddbdaadddbbacacababbaccbbcccbdcacabacbccbbcadaccacacbadbccdbcacbcccbbcdbaccbabddaaaacaadbdccdaadcaadbbcaacabadbcabbbaaadccaccbddcdccabbadbaaaccbccbdadaabbbbdadbdccbccddbadddadcccccadcbaabcdaaabdbaccccddbbccacccabbbabaaaddccdcddaadbaddabbaddcdbccaddacabbaacaabaabddbbddbcddbbabacaabcacdacadbbbcdbdcbddcabbaaacdadaacaaabdaabaadaacbbbaaddbdcddddddcdbcacadcccabdddcbdcbddbddbbbddbbdbbcbcdabcbcbcbbbbaddbdcadbbbcddbaaacdddaddcbdccbcbcadddcdcbaaabadbbaaabacabaaccabbbaadbcbadabcacacbbacaccbbdbcbccaacaababddbdcaacccdcddcacdbccadddaccabddcdccbababcaacbccbdbabcaddbacdcabbaabadaaadcaadcdcbaddbbdbbaddbcccccbcbaccdcacbddcbcdcccddcbabaadcbbdbcccbadadcbdadbadbbdacdadcbbcdcbdcccabcaadbcdabdbcadaccdbdbcdcbcaccddaabcaadbabdaadcccacbaacdbabcdddacbbbcdaabbaadcbcadbaacbcddbbbbdbabcbadaddacaadbcbabdddaacdbccbdbbbadbcacbabcbcccabbbcabdcbaaccdbdbdccdbabbddbbddcbdccadcacddacaccddccabcdadbcddbbadcaacddacbcbdabcacacdacbcccbacbdcdcdaadbbaadcddcbadadcccbccabbbbcacbbbcbcbdccbdbbcbcdddbbacadacbdaababbcdcccabcbcddccbdbcbdbbcbcaddacbcbddbbdcacbcbabdaadbcddaccbdbbdcccccbabbbcaaabbabbdadaadabaaabdcbcccbdcbccdddabcdcbcddbddcccccdddbdcaadcbbdcdacbcdbbbcccbdbdcaddabdbcdaddabddccbddbcdcdabbcdddabbabbdbaadbccdadcacdbbcdadcbbbccbbbdabddacdcdcadbabdacaccabdabddaddccbbabccdcdadcabacdcadcdcbbbaaaccbbdddbacdcacddcbaddddadadddaaadddacadbbacccaacbdacaaacdadbddadbabbaaddaccbabccddaadadcccbadbadbcddcadaddcbaddbdddcbbbdaaadbbcccccdaaabcdbbdbcabbccdcbbcdabdaccbdddcdbcdadbdabcacaddcdbadbdcacdcacdbcbbbbdaabcbdbdcadbbababbccbcaddcacadccddaadbdbabbadcbbacdbdcbbbbabaacdadabaddbbabbbdaaaddaacaadbddcbadddcbaccbbbdcacabaadbcddbacdbdcccaaaadcdbccadcbbcdbdacddabdbcdabcacbdacddbabdbbdbadbbadccbdbdbbcacabbdaabbcabdadbabbbcabbcccaababddddcadbcddcdcaaaaadcdcaddaacadddbcdacadaccbdabdaacadacdcbbacddccaddccccdcacdbcaccbdbdddccdcaacbaddabccccacabdabbaaacbabccccbddbbbaaabdccdaadcbcdbbacbddccaddcdcdbcacdcddcdaddaacaaaadddddbdbcbcacbdcdabacbadcbabcbbdbadacdbacbdaccbabbccbbcabdcaccaaaddacdcadcadbddabbbdbacbddacdadcbbdbbdbbddcbdcbdbdbabdbcdcaabbbcaaccdcbcdbbcdccabcbdcbdacddbadbabbcdabacdadbdabadaadbcacccbcbabbdcddcbdaadadbbaabdabaaccacdccdcaacbddabdacabcaaccdbbdabaccabccbbdccbabbdaccdcbdcacbcdcbaadcbbbacccaabcacbddbadcaabddbadcbdbcbccabadcbbbcddccdcadbbaddddaddaacdacaaaccddcdbaadcdabaaccdadbccbcccbcbcaaaabdcacdcbbddbbbcbdababcaddbbbcdadccbccccbabdaccccdadcdbdbdddccccbbcbbaaaabbdbbbadaaddcdaddaabcacddbaababcabbacbaabadadbddadbdbdcbcdcdbbcabadcbcacdadbabccdbcabaabcadabdbbbccbdacadccbadcbcaccbaadabdbaaddccaacdcbadcbdcbcbccadaddcdbbbbbabbaababccbdcadcdbadabbddcbcddcaaacabcbabbabccdcacababcccdadbbaaacbcbdcbccdcbabaadcaababbbcbbabccaaabdbacdbcbdbaabdcbacabcadacbaccbcabcbacdadacadbcbbdbbdbbdaadcaabcaadabbabacaadddcdcabaadcbdbdadadabddddbbaacdcdcdccddccbbaccdbbabddddcdccdbcdaaccbacbacdccacddbdacccdbbaddccbaddababbdaabccbbcadddbcdcdbdacabdadaadadbcbdadcbadbacababbacaadcbacadbbdcccabbbdacabccbbbbacaadddcccccddbdbacdddacddcaababddddcdcadaabdbbdcdbdbdcdabcdaddbccbdaababacaacccbbdbbcdbcdbadbbcaccabdbaccbbbdbbaaddddbcaabcadadaacdcbbaaddaacccbabbacbcadaddcaaabcabbbcddcdddcbcbabdcccacdbbbaadaadbaadcbbacbddaaadadcbdccaaacadcaacbcdbbbabcaacaccaacdddaadadcccaaadccbcacddccbbdcbcadcaacbbbbdddbaaadccbccaaadbdacbdddacabdacdddcdbcadcbccabcaacdcdbbcbbcabdbccaadcbbcddbddbdbbcccadbbadccaccccabaabbdccbcdbddbcdabcbbaabccbbdcbdbcdcbdcbadbdaddcbaaabdccbddacdddbcdbbbdacbbbbaadddadbcbcdadacaadaadabcbcbcddddbddbccccbbdddbaacbacaaaadabadbcadddccbbbbbbbdccaadaaadcdadccddbccabdaabdbbaaddddcbbaaaacdaabaabbbdddccdabdabdacababbdbacbbddaadacdccdbcdbadbcbaaccdbadcaaccbaddbbbdaadbdbbdcdcadbabcbdacaddbccdadcadacdcdbdcbdccdadbbcbcbbadddaabcdcaddbdbdbadacdadaaabdcdcaccbadbaabbbbdaacdadbdadadbbcbbabcdbdbdabdadccadbabdacddddddbabddabacdddbcaaabbbbddcdaabccdbcabdabbbbbdcacadadabdbbdaadbbbcaadacbaccbbaccbdddacdddbbaccccddcbcdcabaaaddbacdcbacaacaddcbbddaddaabaabdcaadcbddccdbdcaddddbbccabdbdaabbacabadbddbcaaccccaacbcbcbbdcdcbcbcabbacdabdbdccdcdaadaaaadabbcaddbdabccdccbcaddcdcccadbbbcaaddccbbacabcadaadcbdcccbdddbddcabddcccdabcbbacccbccbcccbcccbcdbcdcdaddddadbcccddbbaadbcdcdbabdacdbdccaccbbaaadcdacbbdaaccbccdaabbacbcbaaaccccbdbbbbadcbbadcbadcaccdacbdccdabccabccddcbcdaddbdadadbcddacabdddcdddbaccdbcadaadbbbbacdcacbbdadbaaaaaaccdbcbaadccbabdcbbaacccbdbdaabaccccdcbacccdacdccbcbabddbaabcacbcaccabddbddabdcdcdaabbadadabccdcaadbbbcbcbaccacdddaabbacaaddbbbbbacbadbabdcbcccadcccddaabbbaacdcabaddbbdaacdbbdaccbddadcaacddababcccdcdcbcadabbcadbddcbdbacadbdbbdcdccbbcbcacbcbcbaacccbbcdabaabdaacdaccaddbcbcdbadccadccddcddddcbabaddbcadcbcacbacadadbbbcccaababbcdbdabaaaabaadaacbdacadcbddbadbddddadaaaaddccdccacabaadbacddaacaaaadbbbbdbccaccdacdaaadddcccddddbcccacbccbdbaddcbddbdaddbdabcdddacccbacbaacdbcdcabbdddcccabbaaadbbccbddbbcdabcdcaadcdccbbcacdcccabbaaacbbdacaabadadaaaadbbdbadbaddbccddcbaadcacabbdcacaccbccbadaabbdabbabadcbcaabbdcdacbdbacdaaabcddbacdbdbbbacbddaaaaabadbcadbcdabacbccdaacaccdccdbdacdbabdcaabbbabbdcbbadccdabbaaccccdacbcccbabdabcbdbcacacadcccbbadcbadacadbbbcdbcabcdadabbbdbadcabcdddaadcdcccbcaccaadaaadabacccddbacbcadaaadcdcabadbcbbdcddbcddcddabdbdcabdadaaabddcdbadbaaacdcaacbbacabbaaaacbbcccddaaadbdbdbddccadbbabbacbddbbacccddcbcbbaabcdcabababcddbcaacccdcbaccccbddaacbabdbdacbbbabaccacacdcccdccacaaaccbaadbdbdcdccccabadcccddbbbdbbacdbcddacbabdcaadcbcaabbdbcdcdaccabdcbccbccabbcdcdbcbbdbdbbccccbcccaaacbcccbcbcaddcadbbdadccadaaacaabcbdbbabdbaccdccaaacdcabbcdbcddcaadbcdbbcabbdacabbddcdbdacdcccdccabaccadccdadadadbaaccaccdbdcdbcbdbbbdddbaadbccbbcadbaaaccccddaddbbddbbdabdbdccaddaabbabadcddaababdbaacddaacadbbacdcadbdabbaacbdcddbdadcddbbadcccddcdacddddbabbddddbdbaccdaaddcadcccdbcaadbacbbacdbabacbddbddbcdaacbcacbbdabdbcdabacbbdbacbbcaadaccbbbccdbbababcacacdccaddaaabcaacdbccadcbbcdddcaabbbcddbbdbcdbbaddddbadccdcaabcbcdabcbdddddcddccbdcddccaabccdddddccbddacacbdbdcadaabddacddbdcdadbbdcacbbdcaadabdbaddbddaabbacdddaaddcccaacbbabacabcdabdbcaadacbdddcabcdbcaabbbcaabcaabaadbbcaacdbddcdbadbccddbaabcbbaaaadcbcdbacbdcabccadacbbbbaacccccccdaccbccdabaacadbabdacdaaaddaaaccccddadadbbcbbcdaccbbbddccbdcddbaaccdbaaddbcccdacabdbdddcbdadbadbcacbbddaaaabcaacaccdbdaacadccadcdbbbabdaadbbdbccbdcbabcdaccddbcddbbaacccdbaacaaaaccdacaadbccbadadaccdaadbddcbacddaacbabadabbddbcadaadbcdbbccbdcddabaadbcbbcaccddacacbbcdccbbaaabccacdcbbaadbabcdccdababcbbcaacbdabcdcabcbcbaddabbbcdcbaacbacadcdddacababdcbadaaacbaacddddbbaaadbaabdcbcddacadddbadaaaadacbdcbccddaacdbcbcaaabaadaaddcbcbaddcdbcaaabcbcacdcdcccdcaaabadccdbbcaaacbddacbbcdaddbadabbacbddadaaacdacadbadcaabbabaacdbcdddbaccdddbabccdbdcabbabacbcadbcbddcaadaaccaadddbdcbdbaaacaddadaaabbabcdbdbbaabadabbdddbacdcddccdcbdccddbadcabdccabcccdaabaaddcabbbdcbbbcbdcdadbacacdaabdcabcdacaabbbbbbdbaacaadbddbaccabbcdabaccbaaaaaadaddbacabdbabdacdcddccabbdabaddaaaabbcabcbacaabbdbabdccaaaadcbcdcbaccacabadbdbbabdacabbacbabbcabbccabacaacbddbaaaacdbddddacccabbdcbdbdadababbdbbadbbbcccdcdcacabaaccbccdcabaddcdbacbdcdabdadabbabdacdbcacdadaabcdbbdbcaaadcaaddbdccaaabdbbacbbacccbdcaadbdbbccdcbbcdcaaabbcdbddbccbabccdddccccccbdddbdcdcaaacdbadabaddccbcccacaccbdbadcbbaccbacacaddcbdadddbbdbaacdbccdddddcdaabdababbaadccdcbdbcccbdacbbccbaddcdcdacbccbaacacbdccacdcbbdaaadcaacccddcdcbcbcbdadcdccbcdadadbcddcdcbbbacbaabbbdcdccdcbcadbcccbaabacadadbaaacddbcdabbacdaaaadccaddbacadaabdcdbddcadcbcaddcdccacdcbbcdaaccacdabccdbcdddacabdabbccbabdbbbbbcacabcbbbabddbbacbbccdacbabaacbbdccdcddacdaabbbbacddbbdcdaabdddadcddddbbcadcdccdadadadddbccabdcbbabdbccdacabbdcabbbabcdabdadadbbbacaabcaabcbacdcdccbbabbbccbacbcadbcaacbddcbbdcdddaabbaccabcabbcabcdccbccdccddbbacbbaabdddaacadadadaababbbadcbcdadbbcadbbbacdbbadcdcaacdcdbddaabcaacbcccbaccbadbcbdbbaaaabbbcbcaaaccdadadcaadbccabcbcaaadacccacdbbbdaddcccbadbcbbdbcacbcccdabcabbdaabcdacdbdccaabbdacacddacbccaabadddcccccbdbdcccbcadccdabacbddbcccdcaccbbbcbbcaddbdbbabcbaadcdbcdaddaaadaaccdbdbcabdacaaadbdbadabbacaddddaabdadccbddbbbbbbbbcabcddbccdaccddbdddbbcadccbddcbbddadbcdcabbbddddcddcdddcddaccbcbbacdabcddaadcbccadbbbdabcdbbdbddccccabdaaddddbabbcadbaadbacdadcdcdcabacabdaacccdabbabcbadbdbdddcbbcddbdbdaadcbddbacabadccdabbcadbbcabcbcbcdbabcddbaaccbdcbdcaaacacbdaaddacdbdcdddccbbaacbbdaaaddddcbcdbdbccadabbcdcdbbbdbdaacdbcccbbaadaadbabaccadccdcadaccaddaabadaacdcdbbdbbbadcaddadddbcbcaacadbdaddcabcccbbbaacdabadbccbbbbadccdcdcbcbcbcacdadbdbbdaccdcdbaaaadbdccadbccbdbdcbcccadbdbabaddbcababddaaacdabcbbdababbbbdaadbbcaddbacdbcdbaacabdcddadaadacccbdbddbdcadbdababbbccddbcabdbdccaaddccdacadacccccbcacbdcbcbadbbaccdabcaabadaaacbaaabddaccccaadbcabddccdbcaadaaddaadccbbccaaccbbccacccbdcddcacbbacbdaabbadcccdaddaccbcacabbdcbaacabbcacdcdcdabaccbdbcacdaacdadbccbbabbcacacbaabcddbdcaacbacaabadcdccbacababaaccbcacdadccbdaaacbcdcacbcaaddccccadbbbacaccdccadababaaaaabdabbacbbcccddccbcbbaacddacbddbcdcbdaabdbbadcccbaaaccdcacabcbddccbcccacbacccdadccabdcddddbcbbcacdacddabaacbbdbbbdadbbabadccdbbbacdcadbcdcdbbbaccccdbcbbdbbdcbbdcaaaaabcdcdbdcddabccdcbadcbabcbbaddcccdaaacddcabbacbcaaddaadcbcadccaacbadcbdcbcabdbcbccadddacaaabaccbbaacbbcaacdcabdbdccbbabcabbcacbaababbcaccbcbaaabcacbdcdbcdddabcbbdcdbaabdbdcaadcdbcddbddacdcabdbcdbccabbcbcdcacdbbdaaaacbdadacbbbbadcbbacadabaabccddadaabdbcbddabcbadabacbbcadcdacbdcbddacbabbbcdbdcccddccacbdbcbddbdbacdbbbcdbaaddaabdbadcabadaadbdcadcbadddacadaaabadcccbbcdbccdabddccdcacbdadbaccbaacadadcaacbcdacddddbacacbcccbbaabaabbbbccbacabaccbdbbddcbdaabcbcbdacaddcddcaddddbabcbbbcacdaccdccdbcadcbacdcacbddacddcbdddddcbdcbadaabcadaadccdacaccadbaacdcaddacccbbddbdcbcddbdbadabdccbbdaabacbdbaacbacabaabbaacccbccdcdbbabccbdcdabdccdbcbacbdaaacdaddcabcddcabacbbbaddbccaaacbbddaacbddbdccabdccbbddddccaacababccaadcdcbcaaaacddcabaaddacabdcbcdbaacbbcaddddbadddcbbdabdbdcbcaaddbadadcdddaacdbcccaaadcadcbccdabcdabbddabbbabdadacdcaccbbaaadccccbddcacadccbbcacbcbbacdcabbacbcccccbddbdcdcdadcdabbacabbbbaacddccbddcbcabcddbddacaacbccbbbdbdbaadbcacbcdbdddcacbbadbbaaaaccaadadbcacbbccabcadbccdbcbdbaabdddcbdbcbdbabcccbabdbdbbbdababbcdbbddaabcbcbaadbbdddcdcacddcbabddacabadadcadcdcaacdccbacbddaccabccddddaabccccbddccdbcaddcadcddcdabccbdbabbdabcadadaddcaadacbbaacbdbcaabdbdbbbcddcbbcaccbdbbacdababbdadababbbbacdcdadcdbddddcdbddadccbbcbcaabadbdabbbadabaccdbbdabadbdcbdbcdabacdbbcbccacbdbccaccdbcccbbabccbcbbcaddabdabdabaacbcdaaaabcbcadbdbcdcdcdcbddcdacdbaacbacdcaddadcdaabadbccdcacdabdadbcccdcbdacdbbbdcdcdbcaddacbdbcbdbdacbcdaaaabcbcbcccabbddbcaabcbadcbdaadcdcaaaadcdabacdaadacdacccbacababcaabddcdaabddcbabdacdcbbaadbadccdaacbacababdbccdddcbaaccdcaabdcbcdddadbbcccaadbbdbbacdddbababcbaccbcbbababcaaccaddaaacbbabddcaabcdcccaaadcdadadcaabccdbacaddcadcccdbacbacdccadcbbdbcbdcadcdcddddbccaaaaaddcdabcdcabdbccbbadadbdadcabababdccbdcbadbaacccddcaddadacdddbccadccdabadaaddaaadacabaabbabcddbbabcababbcadadabddddabbdadcdadadabcacacbdddacddabdabdcaaccdbacbadbdbdaaddbbdcbcbbcaddaadadacccccbcbacddcdbddadcbabbcbbcdbcadabccdbaccbbacacccccccdacabcbbccdcddabcddcaabaabbccbabdbabcbcbcbdddddccbbaddacbadccdabddbbdadcbdcccadababbcadcccaadbdbbcbcddccaaabbabbccdbcddbbcbadacbbbbccbaddacbaaddcabdccababadbbbbdacddddbbbcaccdcbacbacddcacdcddddadababadbabacbacbbbcbcbcbdaabacdbbbdadddddbacbdbccdaacaaddbcddddacdbbdcbcbaaacdcdcdddabdacaacbcccabddacccaadcaccdbddddaaaaaccabbcdacddaccbbacacbbcdcbcbcbabdacbdcbaacbadccaaadccbabacdbcbdcdddbbdcddbcdbbaaabaabcdadbbacdbaadbdaabaadbabaddcbabcbdccbabadacaaacbccbadababcadbbbccaaaddcbdaacbbbbadcdbbdccabddaccdadaddacaacdbaccddbabccccaccdbcdcdcddaaadbaaccdcacadcaabbbaabaddaadbabccaabadcaadbbaaccbabcdbbaaadcdbbcbcbcaadcdcddadaacdadaadbbdbbbbacdcadacadaccdbddbdbacbaaabcaadadcaabcdcacddabbacacbacaddabacadbbbddbbbbdcbbdcddbcabaacdabaccdbdcacbcacbbcabaabbdbaabdcabaabdcbbcccaacdcbdaddbbacacabaaabbdcacaddcbbbacdbacdbadbabcaccdbdaccbcbacbdabcabdbbbbcbcdddbcccdcaddaddadaacaadadadcbddcaadcdbcbabcbcacdbbdaabdbdbcccbabbacbcdaabdddcccdcbdbcbbcdabbbbdbcddbabaccacbbaabbabbacbdadbcdcdcbcbadddbdcdaabdcbbcaabacbcdababbabcabbcbbbbadcbadaccdbccbcbccbbdbacddbddaaaddcdadcdbdabadaadccadacdadbccaabcdadadbbacccbaadacabddabcadcddcbcacbdbccaabadabcacbdaccadbaababbabaadcadccacbbacdacbacdbabcbacdcaddbcdacacdaacbaacddccdcdaabcccaacaadbaaaadcbdddabaddadbdaaccdabadadbbbadbdbaddbcccccbacbbabdbaacabbabbdacbdadddaacdbcabdbbbbdcabdaccaabcacdadabcbabcdbaabdddbbabbbbbcccdabcbcaddbaddabbddacbdacadbacdacbacabbcbbcacbaabdabcdbbaccabacbabbddabdbcdaccabddcbdadaddbadadddbcbcbdcbbcdccddcadcdadccaccaddacbacacbbddccdadccbdbcdabdadbdbbbbcbddbaddddcbdcbdbaadcbcaccdcadadadbadcdaddbdcbbbccdbbdabcbddcbcacadddaccaddaabddcaddcdacadadacddbcadcbcbbadccbddbdbbaccadbcacccaddccbbbbbaacbadabdaacadcbdccbcadcacacabdbaccadcdddaaabdbabcbabcdcbaaacabaadaccbbcdbdbcadbdbaaccdcaddbcaacccccdddcdbacddaccbbcdbcbabbaaaadbacccbbdaaccdadaccccdacaabbbccbcadbaddcabacbbdbdaabaadbbabaaabadcbcbdcdaacddcaddbdabcadcaaccdadcabcbddbddcbcaabbdaaaccddadbcacbacccaaabadcddccdcadabcddbddacbcdabbdadcbbcddccbdbcabcacdbadcdbdacaccddcdbbadadabcdbcdcadcacbcbcacbdccddabcbabbaccaabbcdaabadabcbbbcacddbbaabaadddcccacccbccbbdcdbdabaadabdbabddabbadbdcacaadbdacbaaabcacbbbbdcbbadadadaadcabdcadaacbbacadbbbacccddcabcaabdbbcdbcbacdabadbbdadcbaaddbcdccabcdcbbdbaaaccdacbbdcddbbcaadabacacdabcbcdddaabacbcccdaabcdbaccaabdaabaabaaabaadbdbbaccaacccbbcbccddbcbbccbadaacaaabdcbdcadcaaaccccadcbadabcbbaaccabcbdbcacbaabaabddddabdabacdcacbcbaccdbabddbccdcaddbdddacbdbbabdcbaccbbaccadbabaaabbdbccdbadcbbddbdabcbcbbcccadddccbbbdaabadcccadcadaccdbccdcdbaaabadaaadccdddcadacbdbaddcbadabddcdcdadcaacaadacddbabababdcaddcaaabaccaddbbacbbaddbbbbcbdbbbadcdabbdcccccbccccaaadcdddaacddadbccdadbadbacdcdbdbccbadabdcdbccaaabdacbbddcccdcdadddbddddccdaaccbbdacabaabbbacddadadbcdacdddbadccccdabcaacccaccccaddbdcbdadacdcddadaaaaacbbdbabadacaccbcadacbadbbbcacbddbabddddcbcbcddcaadcbadaacaaddabbcabcdbadaaddaaacbadccadbbcadacababcabdaabaadcbddbcbccaddbcaadcbabbabbaddcaacbabcbcbaadabcadddaacabaababddccacdacdddaddbadcabdbbaabadbcdbbbddbadcaddabddbdbadbdcabbbdadccbbaacaabadadcbbabbbcbcbdbcbaacaabccaacdcdcddabbdcdcaccddbadbcababadcadbccddcccccddcdcbbacbddcbccaaabccacaccacdbbabbbbcacddcddbcddbcbdbdddccbddbbdbdbcbabacddbddbcdacacaccddcbbdbaacbbcabadbabdbcaddbdcbbcacaccccdcbbccdbcaaddcddcbcbacadacabbccbadbdacccdacbcadbcdbbddccccadcbccbdcacdbdacbacabcbbdaadbabcccdcbadabadabcdbbcccddbabcddbbdadacccbcbaaadbaabcacddcdbcacbdaddddabaabacaacdcdbbaacacddbaabcdaaadbddaadccaddddbcbcaabddaaccdabdccaabcaaabbbdccbbbdcbadccabbacababcddbbaadcccdccabaacdcacabbbdbcbbcbdcdcaacbbabadddacdcbbabbcdbcdbaacddcadccbabddcaaaabbbddaadcbadbddaacbadcadcdcacbdddbabbddbacaadddcaadbdbccabbdaabcbdcbdabbcabbcabbcadaddcaaadccdabbbaaadabadbdacbcadcbcdbadababcbbddadcbadddccdddccdaadbcdcbadbddaaacdddcbabbadccbbbdbddddcbcadddcadddacdabdbdcaccddcaacdbcadabcdccdadbcbbcbbacbbbaabcdcbcddcdbcbcacbbbabbaabbbdaaddcccbcdddadbbdbdcbaabaaddadcdccadcccbaabbbcbadadaacbbbbdbddccbdabddcdcbbaaabbbcbaabaccbddacbaadddaabbadcbcababbbcdbaccbccdbaacdcaccddbadcbbdcbdabadcdacdacbcdcabdcbddacababbacbabaaadcaadcdbcbabbacdbbadabbbcdacdbbabdaaaadbdaddbcbbcacbaacaaadbbdccadacdcccdddabddacadbcdcccdacaddabddcbaaaccbbdbcaabdabbddcbccabcbcdabbbddacdabdcbdbddbcbdbbdddabcbccbbdcbddcabcabaadcccdcaabcbccbabccdcadccaaaaadbbbacdbcbcdccaabacdbcbaccaccababbcbdacddbaabdcbcabcbaabbdbdbdccbacdbdcbbbbdaccdbaddcdabbdabdacbdacbcbcaabcddccbccacbbadadcdbbbbabbbdcdccacdcbbcdabcbdcdcccccabadadabbacdbcdaadcdcabdbbaacdcbcddacadcbcddccaadcdcccbabcddabcddacaabcbddbacacbcbbabbbcdbddcbdbbabadcbabdddbbbbcdbdbadbaddbadbaccdcbcccabbcdccadcdcbddbdcdcbabbcbdcbdddbdaacbbbcccbcadaddbacdcacaaddbdcabbcaddaddbbbbddcbdddddadcbcbcbadbdadaabcdcacddcabcbdcacaddcdccadccabacaacabdcdbdcdcbbcacbddddcbbdcbdcbcbcbcbaddbcaadccbacbaacbaadabadabdbddbbdbcdccdaabbabbadcbcbcddcbddaaadcbddbbadbccdabadbcccaaaadddadaacdcdabccdcbbaabdbcccbdbabddcdddcdcdabdadcbdacaadbbbcddabddabadccbddcacbdbacacdacbadccddcbabdabcdbaddccddbbabadacdacbcbabdabbadaacccabdbcbbbadcabddbcdaabaacbddaccdbadbccbababaadcdabadaacadaabddcbccccdaacddbddcddaacbaccdbddcaabdcbbbbddbacddcdbcbadcaaaacadcbcbdcbcddccbaabbabbaddbaabbbbcbcaacbaddbbabdbdbacbbbdccacdccaacdadbaabbadcabacaaabbbddacaddabbdcdbbbbddccdcabddadbaacbccabadcaadbcddbadaadacdadbadcadcccddcbbbcaddcbcbbdbabbbbccacbccbaddbbccadcddcbdcdcdacbbdadcbbddddbaaaddcbdbbddbadcaabcbdcdacdbbbcdaaaacaadcbadbbadcbcaadacbdcdacddbcacacccadbdbacabcbbccdddbcdaacbccadbbbacabbcbdddcbaaaacaddcdbabcaddbbbdacaacdcacacddbbbcbccddbbbaaccaccddadaaaacacaaacbdbbaddabcdcabacdccbddaacbdccbdbacbdbdadacdaadaaabbcddbcddacbacddadbdccdcacbabacdddddacbaadbdbcdbcdaaabcccdabddcbdabacdcdadbddadaddbcbccadbadaadcaadadadaacddacdbccdcdcdbbdcaabcddabccabbbaabadbcacbdccaaaadbcddaddbccbcabdaadabbdcdbabbaabbaacaddcbcdabaacacddabadaaabddabdcdbdabbcaabbbdbdaaadbbbbbbadaacbddbcdbabdddbabcabbcbabbdbadadbcbabbdbacadbcddaccccddcacccddaabacddcdcbbdcdacdcdacbcaaddbadacacadbdbddaadcbdbbbbccabdcbadcbcacacdbcadbadaacdbbbabdddbcacbabbbaddaaccadcdcabbaaabcaaaccacacabaadcbddcbbbccaadddbbbcbddabaddcacbbbcbbdabdbdaaabacbaabaccbccbbacccaacdbadcbbddaddcddacccdaadabddaacbccccdcbdabcbcdbcdbdaadbdadbbacabdcccddbdbbaabacccdbadddadacbddbaabdadbaacbbccdadddcacccabcdcbababccdbcccbcdbccdadaccadcdbdaacbdcbcdbcdcdaadbcaccccadcdadadababdbacccaaabacbcaabdaaadbacbdbaadbbdccbadaaadacbadbbdcacbabddadccaaabdbdadbcdaaabbdcabbddddccabddcacaaadaccabccbdcaaaacbbbdbacdcdbdcddcaaadaccdbcacdacabdddcbadcacdbdcbadabbbcbaccbcaadccdcadaacbadbdbbcadbadcdcacaddbcbbbdccbccbcccdccbcdcdbddbcdbcbcabacbdbacbbabccdaabccadcaaccadccbdcbadbadcaccabcdacbaadbbabdadcbccddcdabcccaaabbbdddbddaadcdcbcaabdddccaddbbccaacbbacdddbbdadbddabddaacbaccddcabbbadbbacdaccdccadbddaddbbbabdacccabdbaacacbbbabadccacadcbddcbbdbaaabbcbdbaabcbddcacabaaccbccaaccddadbbdccaabdbbcbbbdabcdbcdabbdddaadccdbaabbabbdaccbadbbbaacbdcbdcbbbcbcbbacadcabddabcaadaacdcabcbaadadacacccbabcbdaddaadbdadadacabbbcdaacadcbbaababbdcaacccbcaabbbcbabbaddbacdbcbcbacdacbcaaacabdddddbdacddcdcdbdadadcadabdcbadbddaaacddaacbabbcabdbdccadbdcddaacabcaadbbaaaacbcdcababddbaadaacadcdcbcbcaaaacaddadadbbabcdbdaacabcccbadbbaabbdbcabdadbaadbdccadcabdaabcacbbddadbdaddacbabadbcdcaacdaabbbbadbaadacddbbacccaadaacabaacbdabccdcaaccbbbcdabccbacabccbbadccabddadccdadadaadcbbcbaababdabadaacacdcadabbadddbddadbbcbcbbdcbabdababddcaddcbbaaadccaabdbbdbdddadcdcbabcaabddadbbbcaccbcacababddadbacdbcbcaddacbabacbbbcdbabcbcccddbacdadbbacabbdacbdbddacabacbcadbcdddacabcccccdcbdaccacdcdccdbcaacdbacbcbbcccddadbabdccdbbdacbcddacadabcbbbaaaddbcaabcadbdbccddbcbbcacdccccdcbbdbcbcdcacbbbcadcbcdbacbaaddadcadccaabcbdcbcccddcdccccbadddccaaacbddddcdabdbbbcaaaddcdcccdcbbadabdbaaddccaccbdcdbcaddbccdadbadcaaaacbcccabbacbabacabdadbcacbbdadbcbcbbbdccaaacdddcbbbdbbbbbbabaaadbcdcbadacbbbacbadacaabddaccccdcaddcccadadcbacbdacdccdcccaadcaddbcbbdcaccaaacbbacccdcdabcbbcbcdbabcdbdbddbabcbacabaaccdddbddaabaaadcbdbbabadcbaddacbacdccbcdaaabdbbcbbcdaddadacbbaadcbcabdcbdcbcdcbcadddbabccbdbdadabbaccbdbbabdaadbdbdabbcbbcbddadcaccbadaaddbbabccbcddacdabbcbcdacbdcbdcbccbcccdcdddabbdbcabcbcbbaaaabccdccdcccccccaadddadbcccddadbabadccbcbbbbdacacaabccdbbccdabcabddbcccdcabdcdaadbadbcccabdddcadaaacbabbcdcabdabcdaccbaacbcdbdabacbbcdcdbbdbccdacaccbdabcababdbabdbaadccabccbadabdddaabdcdbccdcacdccaabacaaaaaabaadbdcbacdbcbcaaabddbccbbdabddabdcdbcccbadcbccbbdbcadbdaaaabcbdcbddabaadacabdcbcddbbbdbbaadcbbdbabadbbddabcdabcacbbaccdbcadbcdbcdabcbcbbbaaadddaabcaacaabcdcdaaccaddbaaabbcaaacdbcbccbbbccabdddbdbcaadcdbccabdbbbaaacdcbaddbbbcaccaddabbdbddcbcccdaaaccabddacbbababaacdbdcccdbadaacdbabcaaddbcdadbcbdccbbcadbbcabcdcadcaaccaadacdbabdccaaaabaabcbcacdcaadbdaaaddbddaccadadbcabdccbabdcadabccbdbccdbcbdadcbbcadccccbcabaaacaadcadccadaddcbdaabccaabdcdbaadcddacabdaccaababcdaabbcaddaddacddbbacbaabdcbdaabaccabbdccacbabadbdddacdbddbaacbbaccdbcbdcaabbacadabaacdcdcaaabbaddbcddbbdaccacdabacddcaccadcdadbbbaaaadbdccabbdccaccbbcdbbcdcacdbbdcaccadadadccddabbabcdbadcadbabccdbacdababdcddaadcabdcacdbdbdbadbdcadacdcdbbcbbcbbdabdddbacabccabacdddbccbccdccdcacdadddacaccbcbccbbdcddacbcbbcdbdcaabbbccdcdbdccbdbccadbdcadddbaccbcaaddabbdaacbaaacabcdbdcbadcdcadaabcdcdcabbdcdbcaadabcabcacdddbddccdddbdbcdabacbbaddbddadbcbbcbbabdbbcccadbacdaabcdaccaacabcccbaacbbbcabcbcdddbcbaabbdcdddcbbcbdcbbbacacbaadbbbdabdcbaaadccaaacbbccbccabbabadbcaaccccdaabbccadcbbabbdabaddbbbcabbcbacabdaabdbbdbadbbcaabbdddbcddcacbacbbadbcbdcaacacccbdadaccddbbaaccbbadbbddadbbcbbbcbcdaabcbbdbbbbbdabadcdadabccbbababddabbcbddcbdaacdadadbadbbaabbcbddabacdaabcccbdaddacbbbbadcaaaccdddbcdbddabddadaacacbcdcccacdbaaacdbdaddbacdaacacadcbdaddcabadcdbbbabbcadddbcdbcccdccacbbaccbbdaaacddcdbaabdaadcdcccbabbddbacbcabdacbcabcbbaaacbbdabdcabbacddcdacbaabbcacaacddabbadbabcbbacddcbcdbcdccbcdabababccbbbadcbddcaaacccaaabbbcbccdbdcaaacadcccbdbdbdcdbbcbddcbaadacbdcccdcbcddddabdbccbcabbadaabcbcbacadcdcbbaddaacbdccbaacccbdabdcabbbbddabcdaccdbcadbbcacdccbdadbcdcbabbbdbbdcbbbabdbbcbaaacacdbdbcbaaddbcbdadabcddaccccdbcacacdacbababdccbaaaacdaaaadabdabbbdbabaabbaabbcddcdbddbaccdbdddcdacddacdddcddbacabdbadbdcacbbadccbcdacacddccbbbbbdcdabaadbabbcbbbbddadddbdacbcccababcadaaaaabadcbbbdcacacbaabcadacbbdbcdbcccadbddbaabbccddabcdabaaabadbbabcdbcaddcbdddaacaabcccabcacddcbacdaccbdcbcadcdcccaacdccccbadcdbadcccacabccdabdbabdaacbcadcdbbddabbacdcbccacbdcabdbcabbddcdbddbcbaccbdbddbbcddadbddbcbcdddddbacabcbacbacaaccbbabbacbbcbcacaacbddddabababbcdaaaccbaddbabbdccacbddddddddcadccdadccaacdadcdaaccabcabbcbbcaadbdadbaabcacaccccbccacbdbbbaccbbdacdcddaacddcbbacbcbdcccaaadcbcddacdddacbacadcbdbdabbddcadbdbbccaaacbdccdaaadbbcabcdbbcacbddbccccbdbaddaacccdcacbcccbbbccbdabccaaaadcaaadcbbaadcbbdbbddaabacbcabdddacaccacabcdaaddadbbbccababbdcbdcaadabababcadbdadacdaabadbdaabbbcaababcabcbcaacadcdadcbcadbcdacccbbbaaddcdaccbabdadabdcbcdbdaaaaabacacacccabbadcababaccbabbcacdadaccdddaacccdddbabbcbaabdaddabdcabbbdbbbdcdbddbbbabcabbdcabcadadcbbcbcabdbabaddbdbcdcacccabdbcbbaacaacabdaaabcbccaadadaaabbcaabcadbadaaaddbbbdbdcdbbadaacddabccbddaabdababbbaddabdcdabbcabdaccbadbdabcbcbacbdadacccbdccdcbdaacbcdcbdcbacadaaadcdddbdadcacacbaaadbdddacddbadbdabbccdacaaaadacabcddabbaacabdadbaacdbadaabbadddaabadddbbddabdacbaacdadcadccaccccabbdabdbcbbcabbbdbdcdbdbdbabbcdbcddcabdccdbcadbdaaadaabdcadbbbcdccdcadcbbbcddbdadacadbdbcdaaccadbdadcbbcbbdbcccaadbcacccbbacbabbcccbdbdbbbabadadbdbbacddbcaaabbcccbcbcdcaccbddbabaadacbbbccbccbaadacdaadbbaadcdaaaddbdbadbccbacdabdbaadcadbdabcaabdbbdbbabcbacdbccbaccbabadcaabbcaabcaabacdcbccaccdabaaaadddcacadbddacdbbbadccdbdddacbabcaaaabadcddcaadaadcbdbaadcbdbbabdadbbacabadcccdabdcadaabdadbabdddadbcaddaddbaccbaabcaacabacbdbdbddccccccdbdbcaccdbaadcddacbbddcddbdcdababdabddbcdccbabbbcbddbbdbbdbddcbbbdabadadbdbccdbabdabdabddddacadbccadacddabbdaaadcaccdacddbbdbbdabcbdaaaacabcbbbaadaaacbdcabbabbbdacdabdddaddbccdadbbbcdaddcbababbaccccdadddbcddcdbcdbcacdcddbabacddbbabbddbaadcbcaddbcbaacbdcbbaadbaadaadbabbdbdcabbbcdcabbcbddcbbbccadddcdaabbcaaabadcbdbcccbcaadbcbbcacaccdcadddabddcdaadabadbaaacaddacaaadbdacadadbaaccdbdaabcacdcdcdcdccbbabbacdcdbbdbcacaaadbbdabdddcdbabddababdadbbadabcccdbabacbdabdccadccbcbccadddbadbcaaddacdddabacdbdaccaaccdccaadacabbcacddaadacbbabadbccaddbbbddbadabcccabdadaadcdddaccadaadddcdcbaacdbdaadcccabbbacdcdaccddbccbddbabddcdbacddcdddddbbadbacaabbccabdbddacdcdabbcabadacaaaccddbcbbccaadbbdacbbddaadbacacccbdcdbcdacaaabdcaaccddbdbaacbacbdcababdddcccdadccbccaaaaaddaabdbcbabaabcddcbaaadbcaccacdbbbdccbadbddddcdcadddbadacbccbbccddbdbcbbacbddcbabddccdcdcbcaabbbccaacabbaacbbdbdcdcddbadaccdbabdbddbbcaaaabbcadabbaabbaaacbdcaaaaabbdccadababccdbbbbbdbcdaaadcbbddbdcdbbdbacabddbcaabcdacababaabcbbbcdacaaaaddcdabcbbcbcddabcccacddbdabccabdbbaabcbadbbdcdadbaabdddcddcbcadbcdadbabaccdcdaacbdbbaccabbbdddaddcddaaabacdddbaccddcccabcdcaadbbdaccaaabbbbbbbbabbdcadacaacababbdccadabdbdddbdbcadaddcabcdbbdbbaaacddacdccbdaaabddbcdbdbaccaadbcaccdaabbadaabdabdbddcddcbbbbbadaabddacbcbacccdbbaaaccbdbdcbbdcbcadbcdcdbddddcbcccbaabacbbaaacadbbcdabcabadabdcdacddbadbbbdddbccbadabdcadbddaaddacbbbbbbcdcbabadbcdbdcbcdddadaadaaaccbbcacbdcbbbddaddbbdbcaabcbdbadbabbdbbcabdbaddccacbcdaaaabcdbbaddddcaaadacacadcadcdadcddadbaddcbddbbaababbadaddbadcaacdcbbaacbabbcbcabbaadbccdaaacabaaccbaabdbddcccbbbccdccbcdaaabaddbadaacbcccdbdacdacaddbdbbcadaaaaddabacacbbdabbdadddaabbadaaadddaddbbbaadadccaadcbbbccddddbdbdbbcccabdacbdcbbcbaadadabbdddbbbdbabcbacddddcdbbcaacbadcdccbcdccabaacbbbcdcabcadbdcbcbcdcabcacdcaddbcaadaabaacabbdaaabccbcbcacacdcdcaaddbbbccdbdbbdddbbaddddbcacddddccbabcbccaaacdddcbabacbaccabbccbbacbaaaadbcbbcacccdcadddadcbdbccbbcdabbbcdcccabcaddbdbabbdacabbbbdbbcdabdccacadcabbcaccaacababbdbaacaaaababbadbbddaccaaabaddbbddbcccacbddaaaadddcbbccbbdbcacdcbaaccabdccbccabadcdabcacacccccbbdcddbaacadbaadabdabcdbdddadddddbdaadacaaacdccdccabdcadcadbcabadddccdbcadcabacddbbdcbbcbacaadbcddbacbaccadcadaddacadcbcabdbddccdddcdacaaaacdacacccdddbcdbdbdddbcaacddbabcabbabdacccccacbcddbbddcbbbaddcdddddcccdacbbcaabbaddbbacbccbaccadcabccacacadcabaddabaacccdbbbaadbddbdcbbddcacacabddcbdcadbdbcadaacabbdbcdaabcbabdbddabdababddbabccbbababacacdaabccdcdcddcaddbdaabcaaccacaddcabccdbbcdbadccdbbbdbdddaddcdbaabcacbacbcdcbadbdccdbacabadadcabbdabcdcaddcacdacddaaaaaacccbccdcbdcaccbbdbdcdaaabbccbacbcbbacadaabbbbbcbcbdcbdacabcbabdadccdbdbaddbccdbcbabadaadaddaaaacddbdcbbdabdcaabcccdadcadccbccdcdcbdacbbdadacadcbabcabdcacaadbaddbbcdbabdacdcacabccacdbbccddadbbddadabddbaaccaaabdcbbdddbbadbcdaadcbbbcadabcccdababbccbddcbacbbcababcdbccadabbabbababcdcdbdbccdacaadccabdbdbcadcaddbacbcddacccddcbcccadbabcdbdccaabddbddddccdaaacabaaaadcadbadcbbcdbadacdcbcdaabcdaabbaadccddddbdddaddacacbcadcbccdacdacdbacabcdcdaccbaaacbbabbcabadcdddddadcadbacbccabbbbbbdbadddccccacdcbdabdccaaadcccddaddbbbcbadbbadbcacddbccbdcaacadcaacbbabcddaacdcbaadacabaccdadddbabcdcadcbdbabdbacddaacbaddcccdddbcadcdbaddbccadcaaacbaadcbbadcdabcccbdaabadaabbbbdaadcbbacbdcdbaabdddcacdcbcccbaaacccacaccddbcdbcbadcacbdbaddbdacabaccadddcdcbbabaaabacaadddadaaccadadabcccbcccdbbaaabbdbcdcddbacaabcadcdbabacbdabbcdadbdccbabdacdadbbacbacbcbddcbcddcbcddcdbabaabacabbdddcbacdcddddbbaacaaacddbcdbcbcaabcdbbbbbccdddcadaacaabddadbbdcdcacdcabadaaaccadcdaddcbcbcddbbaaddadcbddacccdaabbbdbbcbadbcbaacabbaaaccabbbabddddddbbbdbcdadccdbcdcacbadbbcdadacdaacacccddbdaddddcaacdacbdabdaabcadccabccbccbccabdcadcadcacbbadcccdaaacdabdacacccbaadabbbadacbadbbbadcdaabdaddaddbdbaddddbcbdbbbadcacddaccdbdbdccbdbbbcabacdccbccacbbbbdcdbadacbccccbadadbbddadbddaacdacabdccbbbddbddcbddbbcaccacaabcdaabcccadbcbdccdccdcbcaaddccddaacbaabbaaadcaadcadbbdcabadbdccacaadbbbcdbcdadddbbbacabcdccccbccacacdcbadccadbadcadbacbbccdadcbaadcaadbcbbbcbccbbbdddabcdaddcaaabdbaadaadbcbcbccddbbaaaddaacaccbdbdbcbddbaaabccbaaccdbbcdadbbbbbcdcdbcaddbcdbddbdbadacdbdbabbdccdcddbbdcdccabaadcaabbdcdcdacdaddaaccbdabcbbabbbcaadbbabbabbbadaddcabbcbccdacaddbaadbbadaaddadddbbcdacbdbbddcdbcbbbdcacaabdbdadaccbbcacacbaaccdbadddbdbacdcdcdcadcdaaabbbcbbdaaccddaabcbdbdadbddddcbddccddccabadcabbdccbdbaaabdabdbadbdbdcadbddadaaaaccaaacacdacacacdabaccdcbcababbdadaabcbdaababdbabacaadbdadcdcadababaddaadbabdcacabbcbacadadccadaacdbcddddacbcbabcaccaddbadcccddbdcdbcadcbaaadadacbaacbcaabbadbdaaaadbcbdbdbbdccacabadbdcadbadbabdacbabacaccbcacbcdbccddaadaadcbbddbadaabccdcdabaddbdcadabcadcababadbcddbcbcaddcbacdbcaddabdbcccdbadccddabdadccacbdddacdbadadadcbddaadccacadbdacadcdbbabdadbbdbbddcabbdbabacbbacddbcbdbccccddacbdcaddcbdaccbbaaadcbddcadcddbddaadbdacdbdcdbcbbbdbddcbcaacadbdbbcbaccdcbadbbcdbdadbbccabadcabcaacdabdbdabcaccbdcbcabbcdbcbaddccbbdbccadddccbaadacabdcbbbacaddbadbcbddddccbdddbcaabbccabdbadbcdbcbcbdddcadbabacccbcddcacdaabcdcdbcdbaadaacadbdabacbbacaaabaccaacdddaddbdbaaccbcccddcddbaabdddaaaacabacaadddccddabdcaaabbbdbcbcddddbdaaddbaaabbddaabdbdbbacbbdcaabbacaaabcdcbbcbdaccaacddadaabccdccbcddcbbaaacdbaadbbaacbbacbdccaccbbdddcbbddbdbabdddbcbaadacabcbdcbcdacacbccaccdddbdbbacacddabaabbddabadaabcbbcbcdccbbaaabbacdadcbbacdbacabbddbcdbaabdadcbabbcadaaddcdbccddcccdccbaadbbadcbdadbdaacababcdbdbcccadcddcabcabdbababddabcccbdaacdadcdcaddbcaaabddbbadaccbadbdcacdddaddbaaadbccbbcaabdddcaabbddacaabaacbcaccddbcbacccdabdbdaabcbabdcbaadccbbdabbdbbbbccdccacbbadccacaccabcabbadddcbaadbcaaddbacabddbacacbbdcdcacdddabadcaadbccabacbaddbdacadabaaadaacbadacabbabbddbcbaabcbccbbaacacdacadbacddacccadddcccdabdcbddacbcadaaaabcddcdbdccadbaabaacacbcbcbddcccaccdcaaadcbdabcbcaabcdbcdbdbbaccbabaadcccacbdaaccbbcddadcabcbaadadaddacdcdddbdabadbcaddaacddcdadaacadbbabbddbdadcdddbdcbacbbbdbdaccdbdcadcbbacbdbaddccddaabcccbdacccabcdabcbdccadadadcaacdadddccabacdcdbabdcbbccbcaacdbadbaabbbdbadabcacbdccbbacaaccccdcaccddbaacbbaacdccdccdbdddbcdccdbbadaaaddacacdbbbaddcadddbabdaccdddacdbaddbcaccabddbcbdaadcbbbaaccdabcccabccbcbadcdddbaadbacddbbbdadaccbcacbdcacaccbcbacbdddbadcbbccbbddacadcdbacbbcadcdbbcbadbdbaaabbcbbcccadbbacbcdcadaccbcdabcbcabdacdaabddcddadddaadcbbbcaccbaaccccdacacbaacacbabdbdbbacbbcccbcccbabaabdadcabddabdbcaaccbaadbbcabdaaadcbcccdadacaacaccdcccaadbcdbbaaacacddcdccadcdbdaacaadccbcdbcdabcaabdaddbbdcaddbdbaaadcadcbaacbadcbbccbbbaadcdcabddbbdaabbcccbbbbbddddcbadaabcbcbacbdbbcccdbccdbdbbccaaacbbbbdaaaacaaddddbbbbddaddabcbccaacadadcadcbddbdbcdcaaacabdaddbbbcbadcabbacdcaccdbdbbddbbdabdaccabcabcacbdddaabddbbddaccaadcddbcdabbaddcabadabdaccbadcdddabdacaacdaddacbbbaaaddcacabadbacdadadbdccabbbcdbaadcdcabcdbacbdbdcddbddabcdcccbdcabdbdaaadbababccabbbadcbccabdabbdacabdbaacabbacbdcadcadabcdcdddbacdbaaabcaababccbdcbbbdacbcaccddbacacbbddbcbddabdadaccbdaadadccaadabccabadcbabaadadbaadbddaadcbcacbdddbbdddbabddccbcbcbccbddadbcabdaccdcbddbdbaaaccadcdaabdcbccbdadacadddaacacabdcdbabccdcdbbdacbcadacbccababdddacbcdacabcddaddbcabaabddcbbcacdbabbbdaaaacddccdbadacccadddbdddbacdccaabaccabbabcbbccdaadbcabccacadadaddcdbcabdcddccbdbdcdbabcddaccabdbddaccbbbcbbaccbaaaccabbddbacdbaabbcbbaadbdacbdaacbcabcddcdcbcabcbcadabaccaaaacaaacbbbadabacadcaaccbcabadbbaccaddcacddacaccddacccbdaacaaccbcdbacdcdcdabacbbcabaabdbccdcadcacdaaddabdadabdacdcbdbbbbbdbdcdddaabcccaadacaaabcdcabaccdaaccaaabaabbddcadbcbcbaadbcdccdbadaccdddbcabaabacabbadccaadacdaacccbdbabcdaadddacbadcbadbcdbacbadccaaaddaacccdbcadaccdbdbbccdccbcdabbdcbdcaddcdaaacdaddcacabdbabaccabdcbbddabdbbacaaccabaddcabbcdabdbadccdabcbbbcdddccbdcbdbdabddabcbaadacaacccdaddccaadbccabbcdaacccbcdbbbcabddcbabaccdabbbbbcabbddabaadcdaadadbaababadddbbdbdccbacabcbcddcabbcabbcbdaddcaccccbaadaaaabddbdcdbdaadbacdbabaddcdadddcabcccdbaccdbaabcacdcacddddbbcaaacacccaddbdcddcdcccbccdbadadacdbccdcdbcbccadddbddbdbadbdbdbcbadbacbadbbccccddbcdbbbbbdddddaaaccdcdbacbacacbcddbdadccbbdadddcdbcbbacdabaababdacddbcaddbabdadbddcadcbaddadbabdbccdabcbcccbcdabccbabcdadbdaddadddbbdabccabdcccddccbcdbaadddbcddbdbcaabcdaabdaaadadbacdcbcccbcccadbaaabcaddadbbdacbcaadccadddddbdccadadbcbddddddacdcddcadcbbdbccaaabddbbbddbdbbdabddbbabadaadbbcbadbbcacdcbabbbdbbaacaaadccbdaddaabaddcccadaaacbabcbbaddcdaccdccdcabddccddcacbdacbbdbacccbccdcdcddbadaacbbbaccaacabbddcbcadacaaccbdcaaacadbadacbcddbaabbdacaddccddbcdcaccdbdaacbabbcdbccdaccccaabcabcabbadcddadddddcabbcbaddaaddaadddacbdccacdccbddcaabaaabaaababaaababddbadddabcbddacdbbcaabcaaacbccbdbbacdaddaddbbbabdddbddbbacacadbcacdbdcabaccbdabbcbbddbabddbddbbcddaadaabdcbdcddacadcacdaddbbbaadaddaabadacaccbabadbcdccbacadaadaddacdadaccacaccdccbbbadabdcaaadacddabbadddabacddbcdbdaaacbabdcacdddccbccaaadccbbccabbdbdcdcadddbaddcaabbdbabccccacbbbccbcabaadbabbccbcccaabdcbaddabcacbbddccdcdbdaadadbacacdadacdbbadbbbcadacbabddbacdaabdbddbddbababadaabbdaccbbadccbbdadabaaabccabdbbdadbcccccababbacbcacbccaddbbbcddbacabbdcccaabccaaababdccdbdcaabdbddbabadcbabdbcabaadbacbbdaacadccccacbcdddadaccbddbcdccacacddbabbbccaacbcacdbabcabacbacadcdbbbaccddbabdbdddabaaccdbccbdaababcbccdcadcbbdaccccccdadbbaabddccdbdbcacaaacdcbdcadccbbbcacdbdddcadcdcdadcddacbccbdbdddcbbdacccaabadddabddcdddcdadcbcddababccaadcbaadaaabaaabaaadacaaaabddadccbcdcadccccbcabcbbbbdccdacddcdddcadbccbcaaadbbabcdabccabbadcbbadababcbadbabddbbaabbadcacccbcaabdddcbdbbdcbacaacbabcabdcbcabdcbcabbdbadccdcbaaddabdddcadabaddddadabddabbaccdbcacdcabcddabbdccaddabdaadadaddcbcccbbcdbccbcdadadaabdcabddccaadddbdbddbbbaaddcdaddbbdaccadddcdaaddabbdbdadabaacdbdacddacaccbbbacddccadbabdddaacbdacddacacdddccbcacbcbadccabacdbaaddcadadcaaadadccbdabbcdbddabbbbdbaaadbadcaabacdddacddbbcdaccbdbcacbcdbdcaaccdcccdbadcbbbdbdbdcbcadacbcbadbbdababcbbbcdacbcccabacabbbbcccddaabaacbccacaabbadbabdaddbaccaabddbdacaaacabdaccbadaabbbcbdaacdbcbbbbcadbcdadbbcdbcacdcbbadbabddbbbcaddacdbbbbdadcdbbbddaccddcabbacabcabbbcdccbacaacaadaccdbdbabbdbcddbaaaacddcacabdaddcdaadccaadbadbbccddcdcdcbbccdccddcbdcacdbabcddbdaddbdcbbbacadabaadccccaadacaaacdaabdbcadcbabbdddbaacacbadbaaacdababbaacababcbbbadddadabbacdacabddbdbcadcaaacbbacadddaddbadacdadbdbbabcabccdcadccdadcbbadcbcabdcbacaabcbdabcaadabcdadddacbbacadaadbdbabacaccbbbcadcdbcabacaccadadacdbbbdcbaadbbdbbdddbdbdcbdabcdabaaadbadbccdbcadacdabddacbcccbdabdcdbbcaacbaacbacbcdbaddabcabbaacbccdaaababbdcadcdccbbcacbdcbcdacddccadadcdcdcbbadaadaadccbbdaddddbdccbddbaaabcadbddabbaabaaaadddacdababbaacdbabcbcadaccacbadbaadddcdcdadaddddcaaacbaadaacadbddcddcdccaaabdcdbbaaaacaacbdaddcdcdbbdcacddcabdbbaaadaccbbaabbdccadcbbdbcdabbaccacaabababbdbaddccadddabbcdccbddacdadbbdcadbaaabbddcbddaaddbaacbcbbcbcacdadcabccbcdbcdcaabcacaadabaabdaabddacbadadccaacdccdbcddcccacacbaabdbbddcadbaaacddbbcacbbdccaabccbaaacadbcaaaddcbdbbacccbaabddddadbacbdbddcddbcdabdcddddacabdddbcbcddbbdcdcacadcbbbbcbdbacaadbbabaadbbdbcddcaaabcccaadcdaaaaccaaacddacbcbcadabaaacacbbddbcbdaccdcacaacbdddaaddacdbabddbcbcccbacaadcaadbdcdbadccbdabddabbbddbabcddcdacbddaababbbddbdabcadabaaddcadcaabcdcdcccabdcabccdccbdddccbcccdbababbbcadbacacdbaddbbccddaabbbaabddcbcbbaadaaacbabcbaacdadacccaaababbdcadcccbcabcdacaaaddccbbbcbaacbbaabccdbdbadcabbbbddddcadbdccbccaddbdcbaaadaaadbdcccdadabbaddadbcabdcdcdcddabdbdadabaadbbccacdcabadbbddccbdddacdbbbcbcddbababadabccaaaacaabdcacadaaaaacacccddddbbddbadbcccdbdddbccbdbdcdadcbacdcbdabaddcbacaaddcbcddaadbdabbcdcbacbdcbaaadadbbcabcccccdbbbcaaadbbccacaabbdacddadbabbccbccdcbaabacaacabbdabbbbcdcabbbdcabdcbcadcaadabdadbbdaddaacadcaccbbddbadbcabcdcadbdabbccccddaaabbbcaabddaabdcbbaccbbababccadbacdcacbbbddcbddbdcbcdaabdadbbdcdcbbbdadbadacabcbccddcccaaddaddaaaddacdcbdbadaadabbadcbbcdcdcbbbaadcbddadacbccbdbcdcddbcbdacdaddcdabbbadbabbadccddabacccddacacdacddacbbdbcbababddbbadddbadcaadadbbdabcdcbbcdadddcbaccdcaadadbbabadbcadaccdcadbddcbbbabdadbaccbdcadcbdbddaadddcabadadbaacacddddcbbddbabaabdcbdcbdaddaabccbbabadcabcadcbccddcbbcbaaccdcdaddcaabccabaadaddbaaadaccbbbdccddbdaacadabdcaacbccaadaaaabbacbcadccbdaadcdcacbdbadcdaacaddbaddcbccdccacabbaadbccdbdaabacacbdcacadbcbccdcbbdaddbabaaccbcdbdccdaacaccdabbabdddbcbacdcbabacbbccbdcbdcacabdaabddcccccbdacccddbccbbcbbcccbdbcdabacccdabadbaaabdcbbabcccdcabaaaaddcdcaaaabdbccacabdacbbbaddadcacbdbbacacacadbcadcdaacdbabcaacadcadbbdbbcaabbdaadcaccdaacccbabbbddcdbabcbabcbcccbbcbbbddadaccacbcbcacdbabcdacbddabadbcdcccbcadcabbcccacbbdbbccbbaabbacadbaabadbdbcabccccaddadcaddabbacaabcdacdbbcabbacdcbcbbbdcdddacdccddbbbabacbbabccbdddbbcacbaccaddcdcdbccadabbdacdcbacccbdddaccabcbdddabbadcabdcacacaaddaacdbccbbddadadbdccbbbccaacdaaccadabcccdbbadddbdccbaadcacdacdcdccbbacbbabddacbcbdcdbbdadcdabcacbbdcdadacdbdcadcabadadaddbddddbcbcbaacabacccadbbaadbabdaaccdcdbacdcaacbdacbdddccacbdabcaabdadcdaccaadacacddbdbcaddabccdaacabddddcbbddbacaadbadbdcabbbbdaaacdbbacabdcbdbacdacbddcdbdbcacddccdbcbdcbdaccdcccccaccadcdcabccdccaacbcaccdccbadccaaacacbbbdacbcadcadddbcacdacbacaacbbbabadccdbcccabacccbbbdabbbabbbdcacdcdbcdbcbbcccabdcacddadcbacccccabbcbaadaacbcdcacbddbddadadbbcdbabaaabbacbddbccdccbcbcabbdddcccaacdccbcadbcacddcdacaacdbcaacccbccbbdcdacdddacaaacbdbdadbaaaabbaddccddcbbcbbddbbbdbdbcadcccbdbbccaddaabcdcbdbddabcdadbcccbbaabbabacdadacdaccabcdddcddbabdbbdddbddaacabdcabbdcabdcbdabdcbabdddabcadcdacdcddddcaadadccdbacaadbdbaaabbaacbbbaadbdcdbcbdbccacbbcaacdaabccacbabddbccabddadaadbbaadbbcdbbcbbcacaccbbbbdaddbbdabdcdbcacdbdddccacadcadccccbddaaabcadcbcabccdccdbbccacccbcbbbcbcddadcdcdacbaddbbbddbadcdccadcbcbcbabcddaaaaaacadcbdaabbcdbbadababdbdaabcacbbbcdbdccabcbdbcbbaacbddadacadbaabbddbabddcbabcacddaabddbbcbdcbcdacabbbcdcdaccacaabdccdaaabacddddbbbdaabcaddbbbbdcadccadabdcdcbbbcbadbadcaadcaacadadabdaacccbabcadcbcadcdcabdaaadbabbacddcccacdcdddcdbcadcbcacbcbbcdaabadddcaadadbdaccdcdaacddcaacbbdacbdcaabadbaaaaadbacbadadbdccdccadcdadbaabddccdbbdddadacddbdadcbacddcbcbacbcddacdcdacaacbadacbaccdcddbdbbacbdbdacaabcbadbccdbbbbbccbacbcdbcabbbcbadaddcaccdcddabdcaadcabcccdadbbacbddcbdcddcbcabdbbcaaabcbacbbccaaaacccabdadbdcaacbdccbbbdaaccaaacbccacbaccddddadcdddbbcbadbccbbadbabccbbbbddbbcbdaabccabcadddbbbacaacdbacaacdbcccbadbaaccaabbdbadddccbbaaddccdaaabcdcbcddabacdcccdddabdacabcaaabdbaabacccdbacadbabdccacbcabbccabcdabccbacddbddcdddcdccadddbcbddcbcadbacddcaabddcaacddaabcdbbbccccdacadaacdcaaaaabcabaaccaddbccbacbcacadbcdbbdddabcaddaccdadcbcbdadabdacdadadacdbcadbaabcdabdccdacacbababcccbdbdcdcbbaccccdcbababacbddaacbdbddbcdaacbabcccdcbabcbcabbdbacdadbccbccbddaddacdbacccaacccdbcdaabccdbabacacdbcdbdabddddbdabadacdbbbaaadcadbddbcacbbbcbcbbcaacbcbddacbaaabbacadacddbbdacacccbaaddbcbcbccdbabdcaacddbdbbbddabbdcaddcdbdcbbbbadadacbdacdccabddddbcbdcbbacdddcbbbcacddcbbaaabddaaaccbbbaacccbcacdcabbcbdbacacabbbadbbdbcdacdadadbacdccbaabbabbbdbdcabddbcdadddcadadaacacccdaaadcdcdbcacabacdcccbcabdabdacdbdbaaacbabbcaddbababcccbdbaadcdcdbdcacbacccacddcacbdadabcaaaaabbddacbbcadaabcbaaacbbcdadbbbbdccabbcabbdabbabdbabdbcbbcddbccaddcabacbbccccdccdccbdcbdadbddabdbcdaaadacbcdabdbbccabdbdcadabbcccbdddadabbbcdcbbbdddcdabcdbdcdccdbacbacaccaacdbcbabbadbbacdacdccaadcbaccbcbddaabdddcbadcacdddcbaacabaddbdaabdadddcddabcbbbccddcbadaaccadadddcabbccdaaacabbadbbbcbbdbaabcabbaaccbccbdbcdcdbbdacaccccdabadccbbbbdababcbbccaddadcadbabaacbbaccbcccdaddcbbdaabdddcadcdabbbdddbcbbbaadabbbacdcadaaacdbacabbadccbaabaadbdaaaddaadcaababbdcbdbaaddacbcbabbaccabacbadcbcaabcacccccbbadcadacbddcaaacaabbaabdadcbbbaacddbbdcbaabcbaddcbbcdcdccdbbbaaaabdbccdacaadacdaabdcbdbbaaabdcabbcbdcbbbdddbccbcdacccaaadcabdaddbbddadddcdcdbddaacaaadacaaacdbcbbdbbdbabbdaadbdcbccbdcbadddbdadaadaabcbbdbdddbdbadaaddcbcbdccdbacdddcbcbabddcdddddcaddbcaaabdbabcabaaaaccdddccccdbcababaccadbcddcaababaabadabddaadaacbdddabbbdcabdbbbcdaadbbcdcbaabbdbdbabbcacccddbcddddcbaacbcacbcbacddcddcbcbbadbdbcdbbbbacadadcdcdddadabcabdbaacbccdbbcabdabcbabdddbbbabacdcccccaddadcaaabcadcddbaaddbdbccdadbabbbabdbbabdccdcddadcaababadaccdcccacdccaccadbbbbaabacacdcabacbaaacbabacadadbdabbddabdccabbccbcadcbaacadadacbacacbabdccbbcaacdcbdcbaadadaccdaadcacbddadcbacdbccbccbabbccbbcacccbadaabaaaddbbbbbcdccabcacaabccdbbbdccbdddcccaadaacbdabbabcdbacdddbabcaadbbcacadacccdaaabdbdbbaccdcbaaccbdcddcabadcddbcccdcddbbdacaadbccdadcbabbadbcbbdabbcdbbdcbddbbbacabdcaddbdabdabcbacbdbbdbbdcacbdbbadaadcacbbbcacabcabdaaadcccddccdacbdbadbcaaacdaabdbaadcdbcdccbbbadaabbadbbaaadbdcdaabbbbdbadcbddcddbabcaaaabdabcadaddaaacabbbdbcacdbaabbccacadcdaaddbdbdbbbdccdcdddcabdbbdbdcbbcacbbbdaccddcdcbdcabbabaadbcacbcdcdbacdbcaddadbdcbcbabaababdabdbcbababbcdbabdbcaabbadcdcabdcbcddcbdbdaacbaaadaacdbacabbabcdcbadbaacbbabccdbbaccbcaadcbbcaccbcdacabdbccbdadddddbbcdcaccddbadcadcbcabcdbabcbdbaadacbacdcdbdbadcddbbabbdbbaddcbbacdbbaabbadabcaabaaaaadcdcbdacabdbdbddccbaccabdacbdbcdbccbddacbcccddccadabdbdddcdbbbcadbbbbcddaaccdbbbbcbbdcdabcccbcddabaabdaccaddbdbdabcaabcdccbbdccbaaaaaadbbbcbcabcbdbaccabcaaddadabcbbcdcdbbaacbbabddcaddcabaddaddacddcdbbacddacccbcdacbbbdabaacdbcadbddbababbdbaabaabdbacddcbcbbbddbadccddaacaaaabcacbdadbaddcdcbdacddaadcddbbccaabcddbbcbccbbacabdaddcbccbcbcabbdaabadbcbccdbbbcadacdcbbabbcbdddcaddaacbcacbcaddaaabcaccdccabcdcdcbacabccdcddcadddaadbdbbabaadbbdbbccacbbbbdbccdbcbdacdaddcaabacbdcdbbcaccacbdadbdacaadacccdaacbabadcdcdddcacbdbdabbaccbcddbaddcccabdddbbbaaaccdbdaacdabbdaabbaccdcadcadddccacdbabcadabcddbdbddcdbdccdbaabdabbdcbbdbcbcdbddddbcddabbdbdaabdbcabdabdcdcdccaaaadbacacbdadaacdcdaaaaaaabbcbddccbacdbdbbadacbabdbcbdabaaddbabcdcaacddbdadadaddcbbcbacbdadabbacabdadcaacbadabaabdbddabaccaacabcccccccdacddadccdcdbbbbaadcbabcbcdcccdbaaaaddbddddbaaaacbbdaacccdccbcdabcdcbbbacbbcabaacacacdccaddccbdaccacbdbdbdcbbabbaccddddcbadbbccbdcaadddddcabacaadccadacdcbcbdadbccdbabbbacabdaabdcacdaacaadaabdcbbdadbbddabdacbcdccdcbddabbddcddcdcdbbbdccaabcbdbcababbbacabcadccddbaabadaaaadccddaacacdbadabcaaccadabcccabbcbccbadabbbaddadbaaacdccccaadaddabdacacccbbabdbcddcccdcabdacccdbdbdccccbabccdbaacadbccbaddaacdddbbddddaccabbdbcabbbcccdbddacacbacacaaaddaacdbdaabdcdcdacbdcabdbaaddadcacabbdbddacabcbadbaccbcacbbdbbacbbcbabbbccdabbcacccdcbcdaadcdaadacbdbcdaabccadcddcddcbcadbabcbbdbbcdbacdabcbcdadcabcbdabcddabbabdbddbaadbbaaaddacabdaaccbaccbaddcabddabdbdcbcaddacbcbccccabdbadaadccccdaacadabaadddcdcddbbaadaacccdcbccaadcaddcbbbbbdcaadbabddcbdbbcabbcbaadabbbbadcddcdabcbcaddaacdcbccaddcababbbadccaaaacabbabadbabbcbbcdabbcdbdadbdcabdbabdcbcbbddbbadbcaddccbbbacdcbbbabccbbabbbacdcbdcdcdcbaddcacdbabdccbabcbdccabbcdadcccbcadbabdaddabbbadcadacddbccadabbbcabcdcacdcbccddbdbccdbdacdbcbdccccacdbaaddabbbcbabcbaccdaccbdcdbdccbbcbaaabacdbaddddbbddbdadcbadacddbdaccabcdaadddbdcdbaddadcddcdadacadaddaaabcbbbbcddcdbddbdaabaadbcbabbccacabbdaccbaacdddaababdcbbdcbadabcdabadcccbcdcbacdcbacbcbcabdadddbcdadcccacacdbcccdabdbcdaccabcbdaacdcadddadbdacdddcdcbbcabdccdaccbddcccdacccddbadcacdbdccabdbccdcbcbabdcdbdcabccaaababbdbbbddabdbdcabbbbdddaacbbadbccbdabbbbbcdddbbdcbbccbabbbbabcadcbbaacbcdbabdcabbaaaadcbbabdbcaadbcbcacddccdcbdcbccdccdbadcbcbbbadbadccaaaccbababaccbdadbcaccbabdccbbaaacadaadcabdcccdaccabadaababadaadbccaccdcabdaacdddadddcacdaadddbabcbdaadddbbabaaaadadbccadbacadcbbcbacdcadbccbdbbccaadccdbbbddcaddccdbbccacbccadbaaacaabbacaabbcdcbcacbcadcbabcdbbdcdcabdaabdccdadbddbbbcdabaadbdcadabdccbbcacacddbbadcadbdbacbcbdadbdbbddbacdaccbdaaaacadabcadcddadabdbdcdabdbbadbbadbccacdcadcbdbccaabbabdaadcccbcabcdcacdcadaabbdacdadcacaddadbbcccbdbccbadcdabdbadadabcdaacbccadccadddbcccaaabaaadcbcdccbaacdabcabbdadadcabcbcbdbbaadaacbacadaccdacbccbacbcddccdcadcbbbdcabdacbcbcdcacddbcbaccbcddcbbaaaacacbddbbbbcbcadccbdabbbaaacdbdaccddaaaacbacdccbdcbcbddabababdddcaadadcbbcdbdbddadabcdddbbbabdaddbddddcbdbabdaadcdadbcaaabaddadbbcadbcadbcbdcbadcaacaabdbccaddcbccdbadccabbdbdbdbcadcdadacabbabbbbacbbcbabdaacbbccaabbcdcdcbbcaaaacbbadcbcdbaddbbababbcbdabaddddbcbccdcdbddcabbcbdbadadddbcdcbcadababbcbacbbddabdcbacdbcaaadabadabbddbddbbdaaccdbbccbdcdaaabaccaccacaabcaabbcdcadbcbcabcabcbcdccdbaddaddacccacaccabdbddccaaaccaacbabdbacadbbaadaddacbccbbcadcaabaabdabcaaacdabcdcdcbbdbadcbbbcdbbaddcbcbcababaddbccaaaabdbabdbaddacdbcbdbbbacdabadddccbdccacddccbdccbcddcabbdaacbaccccdcbacddacabdadbadcacbbdabdcddabbacadbbbcbcbdbdacbbaccdbddccdcddbabbbcdbdadacddbbbaccbdacccddbcacabbacddcdacbddaaccdbaaacbbddcabcdbcdcbbbaccdabddcacabcbdbacabdcbbcadacaabbdbadcccdcbcbbbaabddadbcddcdadadaccdabddccadddadaacacdcbbbabbbbcbcddbbdcbbacdbcbddabcccabcacbababbddcacacdddabddcababbcdadaccccbbbcabacdcccddbccbbcdadacaaddbdbcabdadbcabddcdccadaaacacbbcbddaaccbbcaaabccbaacccbdddaddaacabdccdbacdaabdbbcdbbaccacbdddcacdabbbdcbcbbadcbbddddddbabdacbbdbddadccdccdcaacbddcbcbbaddcbcdbabaadaadcabdbbcddbdabdadcaacdacbcdccacdddcacdcdcabaaaadadbbdcacbdccabacabaaccdaacbabdbbdcbdddccdccdabcbdbbcbdaddaccbcababacdcbddcaaabbcabdddcaabdddbbdaddaadbbaacaaccbcabdaccddbddccdbddacccaddcacdbdabddbccabcbbccaababdbabacbaadbbbadcbdaadbbcccddcadadaaaaacacbaccdcddaddbacbdcbbbbacbdbadadcbdabaccaaadddcbadbdbdcaadbcacbcdabdaaaadddbcddcddacdaabdbdddababccdcaaacadbbcdcdbdbacdcabaccbcbdbcacdbcaddbdaadadadabcaacbacdabbaaccaadcccdadcaddabadcdacbdcdacdbcbdbbaaccdbababddabbdaacdbcadbdacccaaddcbaaacbcbddbdaaaccabcdadcdcbccbdcacacaadcaccadbacddcbacbacbbdbabdbadabddbaacdbbabbcdbcdadcdbdbaacbbdaccaacddadabbcbbdaddabcbbbdcaaabcbbcbcacdabdccacbcdaabcddaabdbcbbcaabddbdaabaaadabcbacaaabcbcbcdaaadbcadaabcdcddbdccccdbddbbbacbccdcdddcacbdabbddaccacbbcdcbcbdaadacbcbcddacadbdbbaadcccbbbdabbdabdbcdcbcbbbbcaacbacddbdbbbbcddcbacddaccaaccaddccdbdaadacddcadbadbddcbdcaadddbcbdcbbcdcbcaadcddbbcbccdabdbdcdbabbacdacdcdcdbdadbdddccadbbbbaddbaccadcaadcdcdcaabbdccddaccbddcbdbacccdabdbabadbdabcabbdbddbddadbddbdcbcbbdcaaabaccaabbacccacaabaccccadbabbdabcadcbccbccbdccdabdbaddbaabaddacabdccdadccddbcbacadadbbcaacabcbdbcddcdaccadccadcdcbdacaccbcdaccdacdcabadbacaaadddcaabcbcabaacbdbdbacbacbdbadcdccbaabdbcadbdadcdccddcabcbacbccacaddcacccbbdbcdbbcababcadbbdbbdcaddadbccbaadcdaacdccababdbcadcbbbdcbcaababbacdbaabdadacabcdcbcaccbacbbcbdacdabbdbbabbdaaadbbdbccabcdcdbbaaacaaaccdcbbcddddcaaccddbbcbaaaaacbbdbbdcaabbabdacabcaacbaabbacdbdbdbbcccdaaabddbdddccbcdbccbcdabbbaddbaadadbbabdcddbdcabcacadadadabadadacdcdccaccbdbbadcbddacadddddccdbabcabdaaaaabbdaaabdcaabddcbadaabccccdcbdabbcabdcddcabacdddabbaaacdcdcadabbdaaabbcdbabcbadaccdbdadcbaabcbddcbcccbbbbcddadcdbabdcdbbbdbdccdbcbdbadbcccbbccacdacbdbaacbccacdacaaadbdbbbdddaabccabcdabdaaacaccaabacdcbacaabdababbbdaadbbbabbbdabddcbbcbbcaccaaaabcbdadabcbcddcaaaacabcbaccbbdabcccaddbacbaaddcbdcccabadbdcddaccacadcaaddaadbbcbaddaccaacacbcdcddbacdcacdbbbadaddbaaacbcbaccadacabcaaadcabcacbdcdadbbcddbcddcdaabacbdaaadcbbcacdcaaaacdccccbcdadacdacdbadcbbbcbbdcbdccbcbaacaddcabdcccbccdbdccdbdacccabbcbabcbabbdbdbbccbbbbaddbdccacacaaddbaddacbadcddaaaddbddcbadabadacaadaccbccccbacbbbabbadadacbbddbaccccddcddabacbbdbbabddbddabbddcccdddbdcddbaddadbacaabbbbbcdddcdddddaacdddabbdacbdcddbadbdababdadbddbdbdcbbccdcccbdbccbccbbcbdadbcadbadccbdbbcdbcadddcaabacbabdcdaacaaabcdbabbbadddddacdbdacabcadaccbcdbcabacaaccbddbcbacbacdbaadcdcaccacabdccddcbcbacddabaccccbccbbbdaddbcdaddcdcdcdadccaccdbddabababdaacaabbadbadbbdcaccaaabdacbaabaaddddcdacadbcccddbacbdbbbadbccdbccdcdbbabaaabbccdadbaadbdcaacdcdabcbbaaadaccababbabbaccccbdbdaaadcdbadadddcaadbbcccdccbcacadbaadadcdacbaaabdbbabdbacdbbacbbbbbbaddddaaabbcccdccbbcbbcbdcbaacbccddccdacddbcdabbccdddbaacbaaaaddbdaabbacbdcccbccbadaabccbaaaadaaacbbdcbabcbabacdbcbbdbcaadabdbbdbbddbdbdbbdaddbbbddbbcbccdcaaddbbddbadbdcccaccbdbdcbdcdcbbcbbabcaddabbcbbcbbadadbdabbcacdcbdcdcabcccdcccccbabaacbddbaabcddabcdaccacbbcaaabdbbcbbcccbaaddacacbdcccaacbbbbcaabdacdcbaaabcabaadacdcdccdcdadcdbcbbccbcbbabbcdaccabdbaabaacdccbdcacbaddbadbbdaadcdbacdbabcaaccbdbaacabcdcbcddcdaacbdbacddaaacdcbddbdddbbdaacbdacbbadbadaddddbacbddbdcbcadaddcdabcbabbdddccbbddcacdbadcdadcccabbdaaccacbacdbcadadabbcbabcdcdcdcadacdbdbabdbacbdcdacaaccabdbdadbadcdbadbbdbacbababbdcbaccbadbdabbadbddcaaabddabdbacdccbcbdaccbcbccbdddadcacbddbccbdbddccaaaaddcbcbddbddababacdbcddbacdccacbcacdcaddbbcccbbdabcdbadcccccbddadadcddcdddcbbbcbcaccbbadcbccaadacbbcccbbbcddaabbdbdbcdacbcccbaabdddbacadabbdcacbabadcbbcddcddbcbcdacbcacadbddbbdbcaaddbddaadccbdbabacaaddcdcbcabdbccdcbccbccaabdaaccbaccbcbaccdcdacddbcccabadbdccbccbcbabcaaddddddbaabaaaaddaabaabbcaaacaacadcbddcdbadaadcdccadcabdddbbabadbcabccccccdbccadacabbdbbacbaadbdaadadabdccabbabbdcabcddabbdaccbbacdbbbbccbaddbdbcbbbdbaacdcdabccbaabbabcabbaaddbdcdcacccbbdddbddddabbddabdacadddcadabcaccbadccaacdddbbdbbbddbcccccbaabacabacbdacbadbdbcbccbdbaacadaadddbbcccdcadabbadacbcadaaabbcbbdadcacabaaacdccdadabcdcbbaabcbbddbbdabbdaacdbcbcdcbdabaaaddddabcbdaaabbddbcccacbbddaabaacaddaacdacdddacdbabccacdccdbdbaadddaaacbaccabadcaddcbdbacbbbddaccdcbbbacadaaadcdaaaaaccbdbabacdbcbbddddbabaabcaaaadccddbcabccbcaccdadbcbdacdbdaabdcdbccbbccadcaadbccadbccaadbcacacdbbbcbdbbbbbbddacbadbbcdaabacdacbbcaadcdadaddaccabbcadbcbddacaaaccdcbadcdcccdbccbabaacdbbaccabcbcdaabbcbaaaacbbdbaadcbbbaadddbbdccddadbaadbbccacbbddaaabbbbdcdabdaddabcdaddabbcdaadcbadbbdddaaccbdabdbbabccbccdbdccbcddbdbcaddacbcabbcbdbabdaaabadcdbbabaaaabddbaacbdccaabadbddcaaacdbadbadabccabbcccdddccbbabdacdbdcaabaddbbdadbbabccbacbcaacbdabcdadadbbacdaabbddcbccddbcbdccaddadabbddabbdadddcadadadaabbccbbabdddbdcbdccccdbadaccbccaaccbbcacccabbbbaccbdaaabadbcabadabdbcbbdbcaddacabbcbdcbbbcdbdbddcddadcbacadddcbaabbaddacbbccbcadaaccdbcaabccbacdccdbdccdccdacdccccbacababacaddddcbddbabcddcbbbbcbbacabacdcdbdbbdabccadccbdddcabadabacbcabdcababadaacbbdbccdcdcadddadadbbdaccbaabadcabccbccdccccdddacacbdbcddcacdcadbcabadabcbbdbbdabadcbdbbaddbaaabcacabbbbdcdcbdbdbdbbaccdccdbadcddbbaadbdaabbddbbcbddcabbdacccadccddacddbaacdcbcbdcadbdcdcadbdcddcccccabaadbcabaaccabdbcbbacdbbacbbbdbcaaccdcbbbdbcbccacbcacabcddaaaaadccbaaacabdbdcaaddcbbdcacdbbccdbbdaccadadddbbddddcacacacdcadbcbaccdbaaabdddcbababbdadabccdddbabacbbcdcdaabcdbdcbdaddabbabbdaadabaaccbaaaaabbbdaaacbccdacdaacbaddacbcddbadabdacbbabbacbddbaaddbacbbbaccccbadaccdbbaaddaadadcbdaddbdbbbbdcaaddacacbcbacaccccbacaababbddabadbadcabdbdabbccabcdcaaabcabbbdbbcbbaabcaaaccabaccabbadadcbbcacdaaacdaabbadbcbbdadaabadadaddbcdbddbdcaacacbcddcabcadabcbbdcdccadadbabcbadbddbdaacbdabdadbadcabcdddcdcddaccdcaddbbadbcccdadbdaccdbbaabdcdcbbbbdbbddcbaacbaaaadbbbaaadcadcbadbbacbabaabcdaaddaacbbbbbdbcbdcaabdbbabaddcdcdcbdccccbdcbaadaddbdadcbcdcadbbdcacbbdbadccddccdbacacbdaddbabccbadbbdcabcbbbcaadccaaacbdcbadbacdccbcbbadadbbdacabacddccbcdcacdacacbdccabcaaccbbcdbccbabcbbabbbbdcddbbdcdabaadbcaabcccccabcbcdadccdcadbbbaabddbcbcdcdbadcdabbacadbaadbcbcaabadbbcbcdcaddcbdacbdadbbdcbadddbdcbbbbcbbdcaddaacababdccccaadbcbbbdbbbbaaccdcdadbacddbdacaacbbaddacdaddadcdbaadcbbabcbbcbbacbcdaaadaccdabbcbbcbabbaaaabbbcabdcadabdcbdaaccbbccbbaddbdadacdbddcdacbdaacbabddaaccadadaaaadcbddaacbabccdddaddcacbcdbcccabcdccbdadbddabacccacaccaabcdbaccbabdabddacbadcdacdbdadcacbccdacadbccaaadbbcbcbabccbaaacaacbbbbdaccdcbbcdcdbccbbdbbdcbabcdcdbaadbcaccdbcddaacabbdaaadcbdbdabccbbdaadabdbaadadaacadacbddcbaabdaadabaccbcaddadddcdcdbdbabcadcdaabcadabaabdaaacddcccccdbbdccdcacaabdccbcadbadbbccdbddbccbaacdacccadcdabcbdcdbdbddbcacbacddddbaabbbcdcdabbacdaaabbadccccadbbdbcccbdcaddcaccbcbcbcccabddbaddcbbcbdcaabaaabcdbdabbdaaddbdccccadcbbddbadadbadaabaddbbddadbbabcabcacdcaaabbbbcdbdadbcdbdacbddaacdadcaddabacaabacdacdcbcdcbaaaddcaddcadadacdaabbccaacdabdccbbaaddccacdcccbabdacadcadcdaadcdbbbcbdcabaccaaaaccccbbbbdbdbabadabbddcabdbcdddcbabadadcaabddaaaaaaccbbbcbdabcdaacacaddbadddbdcdaaadccbdcbcbdaadbbbddbbdbbdaadaadabccdacbccdcbbbdadaacdbabacbcadabbdbccdcbbabdcdabbdacddbaaadaccddcdcabacdacabccaddcacacbdadbdccbdaabadacbcbbcadbaaaccccbdddcdcbaddbaddcbdbbcdccddbbcacbacabbcdbddbadabccaddbaaaabacadabddbccaabdabcdaacdddbbaaaddbddabcadbdacbdccbbbbbaabbbbccaabbacadccabaabcadccbddccdcacbaadadbddbcaacabbadabcabccaaccbcdcadbcbdddabdcaadcaadbddacddbccbdbccdddabccccabbdbdbcaacdcaaacabaaaadabaacdddbcddadbcadabadacccbabbacdcddbadaccbadcddcdddcddbdbddacbcdabcccbcbbcadabcbbddadcddcacddddbaaacbcaabbdcdacdaababddddccacacdcccaacabddabacbadcabbdadadcabbadbabbaddccaacbbbcabcacdcbbdbdadbbcacacddaaabbbbabcdadaabacadbdcacdccaddabcddcdabcdcdacccaaddcbcabdbbbbcabbdcddaddbbccacdcdbbcadbdcabccaadbdadbdbaaaaaacbaaacaaccabcaccaccacaabbcabadbbdccbdacdbbbabcccbcabaadbbabdbdcdcaabbdbaabbdbabacddabbbaabaacbbabbaaccacadbbabaaaababdcbaadbcdbbbdaadcbbcdcbaacbacbabdcacdcdccadbddcdbbddbddccacdabbdbbcbdcbabbdcccbbbdcabdaababccaabbccacbcadadbdcbcbadaaadadabccbdcddddbaaacaccbacccdabaddcdaaacbaddccadaacdbddcbaaddbdbadabbdcdbababbadbcdcdcddbcdccabcdccaadaaaacacacadddaacdabdbddccdaddbacbbdccbcacdddbdcbabddbbbbccaaccadbbdcdbabaaacaabcaccbbcbbbdcbdccaddcccccddbcaddaddbccccbcdadaccdbbbbabddcdbabbcabaabdbdacbaabdcccccabacbcbadaaaccddbdddbbccdacbbccddbcbcdbbdbadbaddcbbaabdbccbccdacdcdabbaaaadbabdcdbabddbdbabaaacccacdcabbacddcacdcaddbaadacccaabadcbddaaadacacadddbadabcadbbadbdabbdabdcbcadcaaadcbbacccdcacdaaddbcbadbdbcacabbcaccababaadcabbbcdbaabdbadbcbbcccdcdbaaaadaddbbdcbcccdaabbdacbbaabacbcadaaaaadbadcabbcdcdaacddbdcadddbdaccbdabcdadadbccdcccabdddbbbcdcdabcccccccbaacccaacdbbdbcdcdbcdbadddacdbcabcbbaaaabcaaabccbbbbbcddcddbdaadbbccbbbaaabbbbdcdcaaadaabadbbdbdcdcdaaddabbbcacbaccbdcddddcabaccabaabcbcbaddcaddaaddacdbcdabbacdadabdadbdbdcabcdcdddbcaabcbdccaaccdcaddcdadadbddabbdadbcdcbcbcaababdadacaaccbaacbdbacbcdcbccddaddcadabbaddbbdddaaabbdcbaaccdbbcbbdcbcabdcadbababdccddacaacabbbcbdddcabdcbccddbbaddbdcbadbcdaaaadddbcbcbccbbdccddabbcbcdbdadadccbaccdacddbaaacacaccaddadcabaadccbcbdbddcbcabbddacbbbdcbadddcdacbbacdbcbacdbdcbbdbbdaadabddcdaadcacdcccdcbbdbddcbaaaaccdbbdbabdbddccddbddddddccbabcccabdcaadccbacdaaadcdcadbccbdcccaadcdbdbbbaadccbbbdcdbdcbadaabcbcadbbbcddcccbaacaaabadbadcdbcccabcadcbbadccaddbdaaaccdccdcacadabcadbbbcdcabacaaacccbadddddaccdccddaaacccaddbcccdbaccaccdbacbcbdbabdcbacdbccadcbadaaacbbdaccdacdbccccdbbdaddcdcccbadcacdaacccddbdcadaadbabcadacaaacbddaacbadddbcbdcadcdbbdabdcadbcabdcaaabdbcdbcddbbbbbcdababdbddddcacabcbdbaacabbccabddabdcbbadbacabbbddcbbcbccbbabcbbcdbaccbdabddbcadcabcbcbdabcccbdacdbbcddbdbaaaadcbbcddbaacbdacddcccdccdaaadadcacbdaaaabaadcdbbcbaacdabaabcdbcdbccbdcdbcaabccdbbabbacbdbbdbddaaabccbbcddbcadaccaccdcacdaaadddbdbdcdddbbcbddcacabdddbbcacabbbaaadcabbccabbcbbacbaddcadbbaddbacbbdacaacacdbccbdcdadbaaaabbaababbbbdcadddcddbbbacbccdadcdcbaaccbbdbadacaddadacbdcdbadcaacddcbaacadddcbdaccbacabbbdcdbbadbaadbbbadaabacaacbababdddbcabcdcbadcdcabcccbddabbcbaaacbabdccdbcbabcbaaaadddcabbbcbdbbdddbcadbcaaadcdcacabcdbbacadddcddcdbbacdddbddbddbddcccccdccbddccbabcccccadadbaaabbadddbccdababdabccdabdcdbbdddbcdaacaccbaccadadbaaacccdabdbaadbadaabaddbdcdcdabbaabadcadaaacdccbaadbacbcbbcdccdbcbccdabbbaccdbdbdcccdaddcbbacbdaddbdabbacabcbcbacaadbbccddcccdbcdabacdbbccabaaadaaadcdbcbaaabbacdbccaccdbcabadbbdaabadbccbdbabccddcbaacdbdacbaccaccacabcadaccdddcbababbdcabdbcdbaacacddcddcbdcdcadbcdccadbaacbcdbddaddbacdcacbabcababccaddcbcbbbbdacaaddccadabbabdaaccadbcdabddaabdddcadddcbdccbcbcbadbcddccadccbcbcdbdbaadabcdcabcacdcdcbbbadccdcbcbbbdcdaadbcaadbabacccabbcadcadaccabbcbcdccacddacccbabbbaccacadacdcbbaaabcdbbbcbcacccabbbdaabdbbbcadbbbaabddbccccbcaadbbbdadbaddacdbbabcbccbadbcadbacccbaacccdabcbdacddccaacbdaaccdacdbdcdbbbbabaccddccabbaacaadacaaadabdabaabcacbcadcbbdaacdaaaacabdadbccbdaabccacaaddcabdadcacdcbbacabbaadaacdccadcabbbdccabadbbdabbbaaddcacddacabbccccacdddbdacdaccdcadbadccadcabbdcbbbaddbacbdcbddddddadbdcacdbadbcadcacbbcaaadabcacaabcbccbbadabbadbbbacccddcbbccbdcddbdaddccdddddbccabaadbddbacbcbbbbcbdbdbcacbdabdddbadcacccbacacdcbcacabbcadbddaaabbbcdddcbbbacdaadcbbbbababbdcdadaccccdaddcabadcbabbcadaddcccdbddcaaccdadacabdaabdacacccbcacaaadabaabbccaabaddcacaccbddcddccbdaadcacbdcbcabbbabbacacbbbbadadcbdddaaaaadcaaddaacaabadadcaaaddaacdabbabacadaabcbbbbdbaadbcdabccabcaccaccabbaabcbbbaaddaddbcbadaddabcccccdbacbcbbddadbdbaabdbdcbbcbdabbdcbcddbbaccdbacccbcdbaccaabdbcbddcccacbcbcabacacaccddbcccdddabcbdbccddabdabbbdacabbcdbacabdaadabccdbdddcabbadbbccddccccbacacacbabaadadbbcbdabaccabaccdbcbaacddbdbbacaaadadadaabbddcaaaaaabbabddbbbddcccbabacdccadadbddbcaddbcaacccccbabbbacbdacabddbdcddccdaacdbadddddddbbcddacdacbcabcdbabdbcbbcbbcbbbbbcadaaacdcdbaabddbadddcbbaadbacdcbdcdcbdddbcbadabbcbacaaacdadabbacaadcdadcabdddbdabcdadbacccbaabacdbabaaacbbadddacaaabaddcddbbaacbccddadcacacdcaddabbbbcdacabdabbaccabdaccdbcaaddcdabdcdaddaacbabbdcbdcbccdcadcdcbbcbcccbdadaddbaaabaabcbdbdaaacaacbbbbdaadccdbabbbaaddccbbbccaaaacaacaabbbcadbbadadcabdcdacdabbcadabadbaaccadaccabacbcdbbacbdcbbaabbddddadcdcccdccdbcaaabbcadbdaabacdadaabdcccdddcaacbbbdcbcaaddacbbccacadbcbadcbbcccdcbdccaabaabdbabdddacbddccbddccddaddbabdbbadcdadbcbdcadcdcccccddbabcbccccacdbdbababbacdadbaadbacbdadacbacdcabbdbccdcadcadbcdbbdadadbdaaacaadcccaaddadcdccccadcbabbacbdaaccbbbbdcbcdcdcaccbbdabacbbdbcbccaccccbdbbcaddbdcdadacdacbcbaadccdabdccdbbdbbbdbcacaddaacdcdadcbdcaaddcdacbccdbacbdcdbadcdcaccdcdadbdadbcccdbbdcccaddddbdbcadaaaabbacbbabdccdbaddadbbabcdaabdabbddcccaccdcccaccbcddbcabacbbcaaadadadccadbcbdbbcbbbddbbdcdabccbbddbadacbadcacbddbaadddaadddbdaccdcbbbcbddcddcbccdccababcadcbaaadabaadbabacdbcabcaaddcbdbddbaddaaacaaacabcdddaccbccdcadadcaadaababaddaababbcdcbbdadcacbcdcdaacccbaaddbbdbdbbbcbcbbbcbdacacbdcacadcadabbacbdabbdbcacdcbbbbcacdcdcddccdccdddbcccabcddddabcbdccacbccacdbdacaaacddabaccccabcbbcbcbcdddcbacbbbcababdddacbbcdbcbcaacbbabbbbddadacaaaacbabdcdababbaddabaadbaccbbdaccabcdbadaacdcdbadccaabbbddabadcabbcccacbddcbdcddaaddbddabdddbcdacbacdccaddabcccccaabdbbddabbcbaaaabdbbdacbbdbdcadddbcabaaaddbadbbcadaaacbbbabaccaaaacacdcaadbbcbdcdacdbdadaaccbababcbdaacdbcaadbddbcadcaaabcabcdababbbbcccdadcdcadddadcaddbbaccbcabbcdaadadbcbdaabccaabdacbddcbcddcbadbdadcaadbabbadddadbaaadacabacaaaacbdcdabdadadbdabdbdbbcdcccacccbacadbdccabdbccbbcdcbacbaacdadcacdbbcbbccacbbcccacbabaccbacbdacdadcadabbadcbaabdbbddabbddabcbaadabdcccbacdddcdbbcaadcddbaccddaccbaadddadbbacbcbddacdacbbbbbdbbdbdbdaccdaabbabbdcbbbdbacbbbdcbbaabcabddbdddccbdccbcbdcddaadbabcccbccbbaabcadaabbccbdaaabcbaccdcadcadcdadbcacdabbaadccabdabadddddbcacadcbabbdddcdaadabaaadcbacccadbccacabbaadbdcadadddabadcbbaabdccbbddbcabaadbaabdbdabdbcccbadaccccbcabadcbabbbccdddbbacdcdcbbbbdadadacdccadaabddbccbaadcaaaacdaddccbccabcbcabcdbaddcbaaacbcdccaccddbabbabadcbbdaccccaadddabadbcaaabaddccbcdbcbadddacddcccbdabdaacbadbabbbdcbdcdccdabccaacccbdcabdbdbdbcabccbdddbdaadbbabaadddaddddbaadaddcddaabbdabddbadbaccdcdddddcaddbaddbbcbcccdadbaddddabbaaabdddbdbbdddbbcdadbcbdacbabcbabdacbbccaacdcdbdbbdcbbabbdabbcdbadcabbcacdccdcdabadacbbaabccdcacaacdddaaccdbbcadcdbbcbabcacadbbcdadccddacccbbcccbaaaddabcdaaabccdaaacdbdbdbbbccccddcaaadbbabbdbbcabaccaacbdddbdccddcaabcbdddccbadabacdabddccbdbcdaabaddaddbcccaabddcabdbbbabdbaacaaddbaddbabcbaaacddccadbbcdbabaaaabdbabdabbddccbcccbdcacabdcbcdcbaaccdaaadddaadbbbdacbabdabdaadbbdbccabcddbddcbddddcddcdadbaddcddcdbddbadbcddcdbaccbcabacaacababbcadcacbbacdbadbaacdabccadbcddcbdaabdcdbaababbbaaabacdbdcacbdbdcccaccbacdabbccdbbcdcdbbdabccacbabdcaacbcccababdccbcbccadbcdaccadbddbccbbbccddbccdbaccbbdcccabcacbddacccbddcadbcbcaabddababdacacaaddaacaadbcdccadbbbbcccaccabcbcbbccbaabaccadadddcabcdbbadabbbadcdacacacdacbbddddbbadccddadbcdcdadbdbabbdaaabdbccddaccacbcaadacadacdbddbbabdbddbaaccdcdababcbcdddaddccbcbbabcaddaaccacbccabdacdbaadadcacabcaabbbbddcbcdcaacbdbdcbdcbcbaaddbdcadaddbdabdadddaacadddaadbacccbbadbbbadbccbcadadaddccadbbcccdaabdaadadccdadbdbdcabcaabadbaddcddacccdbbaaaacabbcabdccacdacaccdbdaaacdabddaaddcdbaccbbbdadbaaadbabccbcbabbddcaabaddbbcbdcbbccbbbaadaadaccccbbadbabcbbabdacaddbabacacadcdacabcdacdccdabaabdbaabbbcbcaabbabadabccdabdaacbdabdcaaaaabbaccddabaadacacaabdcdccbbabaccbcddcdcbabdaacaabddcdacbdaccbcaaabbdbdbddcbcacaaaccccbccabdadabccbdbcdbabccddaddddccacbdbbcacbbabdbdadddcbbccbacaccadbcabaccbdccacbccdcdaadbacbddbdcbaaacabaaacadbadddadbbaaccbaaccdddaddcabcccacdccbbadddadaadcacaabcadddbcdddadabbcdabacacaadbdbdbdbadcbddbddbadaabacdbabccdadcbbbacbdcbadcbaabcbcbcbaddbcbabbdaadbcdcbacaddcdcacacaabdabadabadcabbbbabbcbaaccdbdddccbabccddccaaaccaadaacdbcccabbcdbcadbdcaaabcaccabcabacccddddaabdcadcbcadbdadaaddacadaacbaddcbabaddccbacacdbdadbdcbcddddbcbbbddbadcadbdcaaadaccddcbbdbabdbccbddcdbbabacacdbbabdaabddcccbbdbccbbbcdcbaaaddbdcacdddbbadccbdcccbdcacbaddacacbcbddcbbbaddbcbbdaadbbaaddbbdccdaccddddddccdcbbabdbbcbbcdcbabcdaaabccabdacaabdacdcadbbcacdbccabccbabdadaddbbcbcaddabcbabddaaddccbdcbcddccacbdcadaadbcabcaacdaabbaabaddbabbdacbcdcddccdbacdcccabcaaaaabdaadbcbbabdddadcdcddadaadbccbdcdbbbdbbcbbddcddcadcdacdcccdbdcaacbcaadcaabdcaadcdacddcdcabacabcadbaaadabababcdaccabbaccbdbaabadcbbcbabdcbddbdabcccaacbbbddcbbabdaacadacdddabadcbdbadcdbdcdabcbadbabbaccbabadcbdbdccaacaadaccbcbbbdcdcaccbbaddcbdaacccdbdccdaccdabbcdcacdbdddcadcabcbaccdadcacccddadcadaccbdacaaaacaacccddacbdbcadbbcaaabdcadbacbccdccbdcdbddcbabcdcddcccdbaccddabcabcdcdddcbccddcbcbdcabcdbbcbbacbbddcacaaacacaadbbbabdddaacaaabdbcacdcbdddacdbbdadccabbcddcdcacbcbaacbaadadcabdccdbbddbdabcdabbaadbdaccdcdbacbdacabacabdabcccdddaddabcbcaaabcbaaddcdabdccdddcccdbbcddbcaadccdcbbddcdcbbdcccbcdbcabbdbacbcdcababdabbdaaccbaadcabdbbacbbcdbacbbdddcacbccdcbcbbcbcbdcdacacbbdadaaacdbcaaaaacdcddabacdadccbcdaccddcccbccccdaccaaccdbdccadaccdcaaddcddaaababaaddcdabcbccadcbacccbddbbbdccbddbbcbaaabbabcbbbccdcbaccddcacbdbbbadbcdbaabbaddbacbdbbaaaaaddbcdadabacdaccdabcabcaccdcaaddbdacaaccbbdadaabddcbcabccbadacccbdabbadcadabbacddbdaccaddcdadadaacadbdbdadcaacbccbaddbadccadabddcaadacbbcdbacacdbbccacaacdabdbbbdadbcdcbdaaabaadbdccacaadbdaabbdcccdacdbbdcdbacdcabaadacbdccaabcbcadbbccdddbdbbadcdbbdcdaadbdadbacadaddadbaacaccacbdbbcadcbcabdccbacacdcabdbaaccbabadaaabbaabbccccabdcdacadbcdcdcbdabbcdbbcbacabcdbddadacdcdbbbabccccbadbdaacaacabcbadadbadbdbbcbcaaacacdaaaccabadcbccdbbacadaccccdabdaaaddbdbabbbccbaaccdabbbbaddbaddcaadbcdcbcbbdbaadddbdbddabddddacdddbbaadbdabbbababaddadbcaabddaddbacdadcacabbbbdbbacdcbaaddaddacdbaaccbcbbcdadababadbbcaccccdcdabcaadacacdbddadccacbcdaacbadabdccdaaacbaabcddababdaacdbdccacbddbdbddabbabbcdacbbcbaaacbdcaaacbabdaabaccbcadddcbccaccacaaadcbdbbcdbdaababacccdadbabacbbaccbdcaddbbabdbcbccdddcaacbcaadccbbadabdbddaddaccacabdcbdcaacdcdccbadddbdcaacaaabbddbdabbbcccbcaadcdbcdbdcacdcaaaddbdbcbcccddbbbbccbcbbdaccdbbccdaddcbacbdadabadabddcaacadacdaabdccabcccacdbcbcccdcbcbaddddbbdadcbbddacbcddbbdbdcbdcaadbcccbcaaaccccaaabdbbadbcdddabddbadbbadacccddacbcacdbccdaaddacbcccddbdccdabbdbaaabdbdcdcabbdccdccaacbccacbbccddbbbdbccdcdaaababbadccaacaacdbbbcacacddaacaddabbbbcabbbdddcacaccaadcadacddbaadaabadddacbbacdabdccacdabacdbccbcaddcddbbcdadbbddcaabbcabacadbdabcdaadbbabadadbcdacbaabbadddbddabcaacadcacbbaaccdddabdaacbaccaddcdadcdbdabbcbcaacdacdbdadbdccbacbbdbabbadacacbdacaaccdcbabadbddacdbadcbccadcbddbbcdddbbaadccdbdcbcddbbddaccadccabaadabdcbabcdacacdddadccbcadccbbcdbbcdaddbdcccddaaddbcdabcadbcdbbcbbdcadcbdcbdabcdbcbadbbbaabbccbaaddcacdabdcadbccdcbabbdcaccabddddaabddbadcbdccaabdcbacbbbadbccacbccbdbaddcdbadbccbbadccbccddcadbdaacdbbbdabdadbcaaaaadcdddcabaccbdbccbcbabdabbbadbdaadcbbbcdbaaccdcbdcdbccbbbdddccacdbdacddbdcbcaadccdcbabababaccaaccacbcbbddbcaaaabddcbdbcaaaabddddcadbaabddabbabcaadacadadbabdbcccaddbcabbccdbcddaadbbcbaacdcadccddddcccbabbbbbaaacabdddbcdacbcacbadcbcbabbbbbdbccbcabaaacdbaaaadcdbadaabbdacadcabdcddcdacbbddcabbabaadbdbdbdbbbbcbdcdcbbddabddaaddddcbadbdbdddaccccbabdbddabbccbbbababccbdcaaabcbbabcddcbddbabcaaadbbdbbcbdabacadcadadadacadbdcddbbbbbcbcdddcaccabcbcbddbdacdcbbddbbaaabdbcdcdcdaaabcdbdbcbdbacbdccdddcccadcabbaabdabcdbcadbabbccdabaaccbbbdcaccdabdaccbbcbcbadabdccabacacbcababbcdabbbdbccbbdaddaddbdcccaaadbdabddcabaccabcdadacacccbcbcbacdcdcdbcdacaacacaddabdcaccbcbbcdaaabbadbbaabbbcccdbbaaadddcdadccbccbcadbaaadcdddbcdbbbaabacdaaccacabdbcbddabcaddbdcacabaccaaadccabbddbcbbddbddaabdbbdddcdabccabddadcbabccadaabdacaacacaaccbaccadbabaacadbbdbbcbbbbadbabbcbbddacaddcdcdcadccacddacdddcdabbddbacdaaddcabcbdacddabbbbacdbccbdaabbcabdbddddbcbddaacccdbbcabadbcddddcccacccbbbcabbcbadcbbdbcacdcbdcbabbdbdbccbcaacabdccabdbadddbbcccaadabadbcbbdcdbbdadcbdbbcccbaaccbdadbbddbadbabbdbdddbdaddacbaabcbacccbdbbbaabcbdbdaccbddddbaaadbadadbddbbdaadbaaadacaddddbcabbbbbcdcbbccccddbabaacccdbccabdbaaadbbccdbadcaadbdcaadbaacdbdccadcdcbdadbabdadddbbcadbbbdbbcbcacddcacbbcbaababcbdddccaddcdbbcdacccacbadcabbbccdbbbbdcddcbacdbaabdbbbddbdcacbcadbacacccbcdbbccacbccbdaaddcadbadddaabbddcdadcddbccdbbcddbaaadbddadabddbbbbcdadbadcabcaccaaddcbaabbbcdbaabdcbdbcbcdbaddabdabcdbabddbbbbbacddbabcdbddcbdbabcbacdadbcdacabcbacbaddddccdbccdccddbaddbddccaaddbdbadbababdabbcbadaadcbadabaddaccbaacbbcdbaadacccabcaacdcddaadccdcabdaadcaababcdaabccddcadcacdcababddadcabaaaaaaccddddbbaccccadcbabdcdbaadcddbcbbbdbcdbbbbadccbaccaacababcadbcdbbcbbcdbdbbacdbbdcddaaababdaadadbbbacbcaddbbdcccbcdadadcdaaabddaddacaddcddccabdbaacbacabdadaacdcdcabcbdaabbcadbcddbdadccbbdcdaaaddacdbbbbbadaacabcddcbbcdccddccadabcaccbbccdbdcbbcbdcccabbdcaaddccccacbdbbcaadbbadcbbdcaadaaccddbcddaacdaadabbdccbcabbaacbcabcdadcabbbdabdccccadbcbbdddaaabcabddcacbadcbaaaaacbbcdbbaabdbaaabdbcaabaadbbdacaaccbcbbabbabbbbbaddadbacdbabdbcdcadbbcdcabddcddcaacdcdadabccbdbacccbddbbadccababaadbadddddbcbbcbbbccabbddcadacaccbbdbbcbbbbdddabbbcbbaaacccdbbddaacbadadddaccdbcbadcbaacbacbabdbddbaadbbccccdddccbccbadadadbcbdacbbcbbaadbdacbccdbddbcadcadcdbbaabbcdccdcbcccbaadbbacbcbcdababcbacbbadcbabdcaaaabaccadabbadbacdcdaccddacdacdbbbbbdccdadacccdcbdcddbbdbdabddbdabbabcaabaadcbabdaadbcdcbbbbaabdbababdcccadbcccbcbabcaacabcbbbdabdcacbbdadbddabbbadadbbcdaacccaadbbaaadcdcbdbdcacbaabdcaabccabdacccbaabcbdabdcabdcacaaaacacbdabdbdaaababdabbbbbcddbbbbabcbccddcdcbddacdabccdabbbadaabbbabaacdacbbacbbdcadcaacabaccccddbbaadbadacabcbccddcabdbcdcdbdadcccccadbccaaccbaabcdbadbdaaacaccabdcacdddcaabacbaabccbbcadcbccbdbaccccbcddabcabdbdcddcbdbdbbbadbacdaaddbcbbcadcdcbcabacdacabbcaaddbbdcdadcaccdbadadddbcdcaacbbbcdabcbdaddbbbccbcabbbbacdaaadbdaabbaadcbadcccdbbcbddaaaabaabdccbdcbdabdacaddacddbccacbbcdcaabbcacddbdaabccdccbdbacdcaabcbbbddbabcdaadbdbcdabadabacdaccdcdbdaaaaddbbcadbaadaaacaabaddcbbdbbdadbdbcacaaccabdabaaaccddbabdabddcbccbabbdcaabadcdccbdabdabbaacaddcbbbdccccccbcabacbdadabdacccbddacabaadacdcdbddcbccbbdbcdccadbbdbdbbbbcaaacdcbdbdbdabcaacbcbcccddbccbabdcdbcdccbbbdabdabbbddcbabcadddaccdccccacbbdadaacabaacacadcadcaabdcdacbbccccbcbdbbbcddadaadbbbbcbbbddbadcbadccbabcabcddcdbcbdabdacadbbbccaaabadabbbadabcadbabdcddbacdcbdcacdcdacbbddccdbbacccbaabcdacbcdbcdbccddbbddcbabcbdabbccbdbbcabbdabbabbbcdddbbadccddacbbaabdbbdcbacabdaaddbcdcdabbdcbddddacdcbbaaadcbbbadaaadaaadabadcdcacdaacccadcaaaaadcddacdadaadbbbbaabbcadabbddacbababcdbdbbddcadbacabbdcaaddcaddcbcadcaddccadaaccddccdcdbadacbcacdbbadaaaddcabacbcaddabbabcbaadaaaccdcaadcbdbdbcbcadccadaadbbacccbcbdcdbcbacccccdbcbccdbcbdabddddddabbdabadbacadcddccaadcbaadcabcbbcbccbbdbacadbddabbaaadcacbbcaccaabbccbddadccbdbaadbdabbacadbbacbaabdbbbbbabcbbddcdbcbaddbcdaaabbbcabcdcbaabdaabbdabcccdadaacaacbabbaaabadabbacbcdcddbabadaccabaabdcbabbddddcaaaacbdabddcccbabccdcbbdcdadccdbbcbabadaddaddddabadddacdbdcabdbbbbdbacadcdbacccbcbdbabcbbddccbbdbaaacbdabdbcbbdcabdabbdaabadacdddbdabccccabdaaadbcddabdcacabaaccddbbcacbaccacabbaaccccdccbacccbcdcaaabddabdcaadcdcdacbbccddbabbadddacdcdbaccacadcbaadadaccbcccbbaccbcbdbbbadabbcbbdbcadccababbaaaaddcdccccaddbbcabbddddadcaaaddcdcacbcabcdbbccdcaabaaaaaadbaabbababbbaadcdbbddccaabddaddacdddbcaccbcabcccbaabaaacdddcdbcddcaadddbdddcadacaadbcbabcaaadabcadbaaaabbdaaacbbdaacdabcadcacadcbdcbdaacddbdbabdabcaccccbaabddadadadabcadbdcbbbbbcbbcbbbacbdacbaddcdbbbdbaabdcdcdcdcbacbdbcccddbbbcddabadbacddbdabbccdacbddbadbcbddbbcbdcbddcacaaabcadccaabcabacdcdadaccacabcaddbacdcccccbddcddaabbbbbcadccabcbdcaabaddabacacacbdabaacbdddccacbcddddadcdcaacddacabadcdaaccabcbdbcbaadcbdabacbdacabaadaabcaadbcbbcbacbdbddacdbdcaadadbccddcbabdacaaadaaacabcccadacbccbacbdcbbabccbabcbcccbdabdbdddcacacacddcbabcacbcdcccadbbadcbcadbcbbbddabcddaadaaaddbdaacaddbcdaaacaddabaddcabcdbaabdaaadcaddbbdccdbbabaacaddaabacaddcbdddbcbdbdcbabdcdbccabcadaddbbaadbbdbdababdacbcacccddcdcbaccbcddccbacbdbccadbdbadaacccdadbadcdcbdacabbbcbcdbbacacbdbccacdacadadcccccaacdbbccbddaacabcdbbcbdbadccadcabababaabddcbadcdbbbdbaaadcbcacdadbacbdacdbcacbccadadcdbcdaaccdbaaddadbdbabdddcaabdbabdbcbadbccbabdcdcdaaddcbabcabcdacdbddaabbbaddbadaddbccabaabadadabbabcbddaacdcdbaabdccadcdbcdcbbcbbaccccaccccbbcadbdaaaacbdadccadaaacdaaabcbcabbaadcddbaacaabdbbdddacccddcaabbdcadbdbcbbbcbdacbdbbaaabcdaadcaddbdbccddbabaadcadbdaacaacddcbcccdddddaabbdbcddbbcbbdcdaadccdcaabbddaccacdaacbadadcaabbccbaaadbdaabaddaabdaddccdbbadaabdcacaaacabdbcadcabadaacbccadcbbdabdcbccccdcbbdbccdbddababbcaddabdcaaccbcabcbdcdbccbccabdcadccbacacbbabdaabadcbdadacaadbaadddaacabbbdbabcacddbbcccadbbaaabddaacbcbdcddcaadbcadbdddcacccabddbacadcacbbbaccbddbaccadadbbabdbcdcdaadccaacbbaacbcbbdadadbdaddcbdaaddcaccaabccdacdacdcdcddbdacabbbcacacadaacadbdbabdcaadcaaaadbdcdadcaddabcaabacbdddddabcaacbcdaadbaaabbbacacccadabdcccbabbdcbadcbbdcbbdabddacddadbacacbadcbbbccccdddabcdbaaadbdbdacdcdccbcccaacbdacbcccddaaadaccbddbbababaabcabddaaaabacddcddbcdaccdaabcdcbdbdbacabaabdcdacaddbbbbbdaaaddbbabbbddccbcdcddcbaabababbdcdadbaaccaabdbbccbcacbccaacccbbacdabbaaabcadacbbacaccbdadbcaaaccbbaaaccdbbdacddccbdbdcbaddaabcabbdddbbdacbabbabbaabcddcadbabccdacaabcdabdbccbcbadaabbbacccabacbacbbbcadbdbdabccbabadaccccbddbbbadbbabddddacdabddbbdcbcaccbbabccadbdbddcccbbcaabcdbadcaaddccbdacaddaaabaaaaaabcdbbacddaadccbaaddbabdcdbdabdbacbbaccacccbbcacacbbdbbabcabadcabdcdccbacaccdbbbaabccddcdcababaadcccaddadbbaabcbdaddadabbccacbcacddbdbdaccbabdadacddcddbbcacbcbcccdbccddaccdabcdabccbabbbcdbcdaabbadabaadcbacabaabbbbccadccbdcbabbccccbdcdadaccccbaaabdacdbcabbbabaacacbddbbcbdbccccdddcabacabccdabddcdcddcdbbacadcccdddbddbaadbbdcbbcdcbdababdcaabddcabaaabcbabaabbaabadbcacbcadcadbcdcdbbdddbabcdbbccbdbbbbabaaccaadbaccdbdbbbcbbbdacadddddcabaaadcccddddbbabaacdbbbadabddbaabccdcbbcdbcdcdbcbbaaacdcccbbacbbdcdaccdacabaaccacaaadaddbdcaaddacbaadbccbabbddadadcadbaacabcddbdaacdbcbabbacdadacabddcbcdabbccabbccbbcbaaadabccbadddacadbcaabccbabbddbbbdccadacddabbbdadbadddacbbdcbacababbadcdcdccccccbcbdcaaadcacdbddadbabaadacacbbcbbddbdcbbbcdbdbbadbdcdabdccabacbaddccaddacadaaadcbcbdaadcddaaadbbacddcbabacdaadadcdbcbbbcbcdaaabbabaddcadbacbabbbcaadabdbddcbcbdccacaabddbbadbdbcdadabbabcaababbdddacabcdbcbcaccaddccadcbcbddaddaaabdabbbcbccdaddacbbddaaacabaaadaabababcacdcbbbcdbccddbddcdaadcbdbbabccabddbdcaabaddcbdbbdbcdbcdbcacbbabbcdadbddabbcaabbbaddcddbaadbaccdacaabdadbdabcbaabccadbbddcadbbdcacdcbbcbccccdabdbddccbbcccdbbccddabaccdcddabccccadccaababbaabcaadddddcadcddcbadaacbcdddddcdbcdbdaaaaddcabacbcdbdddbbcdcdccabbdcaaacbcabdccdcacbaaacacbcdddadbcacadbacadadabdaaccacddababcadbababbccdbcabacdabcaaabccdabccddabdaabdcdccbddbdbbcdcdccdbdbbbccaabacccabacaadaabdbcddaabaddacddadbbdbbbcbcaabcbdddcdcadbcdcacabcabbacdcaacdbdbbabcbccadbcddcbdcacdccdccbbabccbadaaaacddbbacbdabbdabbbbccddcadacdbdcbbacabaadbdccaacccacaacddbbbaabdadcddbaacbbdddddbcbacadddaabccdacddabddbccbdcadabbccdbacabdadcbdbacbcbdbbbbddcdcbcddaddddbabbacacbcacbcabddaadbabcaaadaacddbcbbbaaacbccbacbaccdabddabcdbbccccbbabcddcdabbdbcacccddbbadbabbbaadcabcdddacdbaabdccdcbbaabdcddacbcccdaacccbdcbaadddbacccaddaabbaadbadddababaccadddbaabbbbcdddadcccbcbbabdcbdcdbcbbbaaaaacbcadccdaaabaabdcbdbbcadadaadbdbcbbacdbddaddbbdaddddbacdcabdcdadacacccacabdbbdbdddcbbbbbbabdddacdaabcccacdcaadddaadaacdcacdbdddbbbdbacbdabbcddaadadbbcabaccaababbabbabdaaccbdaccdccdacddabadccdccabbdddaccdccddaaacbbaaddbccaabcccacdcdbcbbaadbbbdcdbcadddaaddbbaacabddaddadaddbcacbcdbcaabbbaacdcdbdadbacbbbadbdcccddcaaadcbbbacacaacccabcdcbbbabadadcbcabaaaccbdddbadcaddaaadcdcabaccacaacbcbcbccaccbdddadcdccaccdaacacbcbdacccdcddcdcdbddcbcccccacbddbabaaddcddcabdaaaabdacbbaacdcdcdbadaabccbccadcddcbacbdbcaabcaaacdbdcdcbcdcddabdcabbcdcbdbbbccddcbbdcccdcacbddacdabcaddaaaabbcbaccccdccdaddbdcabbbcacbabaaadbcbbbcdcbccddcadcbbaaddcaabbdcababddaabbbdabcdcdcaddcaadaaccdcdbccaadaddacadadadacbbbdbbcdddbbcbddacbdaabbdbbcbaaabdcaabbbacaadcdbdcdcbadbabdccdadbdbadaccdddcabcacadddacdaaccddbaccdaddcadacbccbcdcaadbbdbacddcdcbbabdaabcadcbdbccabdaacdbdbbbddbbdaaababbdddddbacdbccababcabcccdbadddcdcddcddadaccdacbcbbbdaabacbccaadabbcaccaddbbbccacdbdbaaaddbcccbcbdabcdcaccddcdcbadccdbcabbdbcdbcdbabddbdbcabdcbdaddbabcbdbdadcbabdacccbddddaccdddcdadccbdbdbaadbbacaccdaacadbaabcdbcaaacabcababaccabddbaabdbacdddadadccbdbadcdbdcbdbbbdbcbacbdcabddaabbabbbcaacdabbddcadaabadbadadcdccbbccdbbadadaaccbdbdabadaaadcadadadaaddacdbaaddbdbacbadbcabdbdabaccaabcddadcddadabcdadbaaddcbdccadabacaccdbdbabcdbbddddbccacaaadbccaabbdccbcbaddaaaaccadccbbabbddbcdaddbccddbbcabcdbcbacadadbbaaccacacbcdccadaddbbcddcddbacbbbcdabbaabcbacbbbabcccdbdaddbadcbbadaccabbccccabcddbccabbdadadaaddccdcccdbdbcacdaddbdbcccacbbcccadbcadccbaabdddacabdacdaabadbdccbdddbadbdcdcddcabccbddacaacbdbbabbbdbdbacddccbacbddcabdbbcbdadcacdaaabdbdaddabddcbccbdacdaaccbaddcbbdcadcbccaabadbcadcadacabbcbdaabbcddbccbbbacccddadcdabbababadaadbbccacbccbdcbbaacbabdcdccbdccbdbdabbcdbbbadbddbbacdcacabcdccbacaacbaddbadbababcaacccddbdccdcdaadcaddadbbbaabdbcdacbbbdabacdadbbdcaddaaabcccbdbbcdbddbbbaccbcbbbbadaacadbcdcbcaacbcbcbcdbdbabcaadbdcaaddbbabdddaadccdbcbacbaaddbbaddbdaddcbccddcdccbbdddcadbbcbdababddcaaadaddcbdbaadcdabdadcdacdaaadbbbcddabadaaaccaaabcacaaabbbaddccdcadcdabddbaabdaabbacacdbbddcadcddcababdbcdbccdbacadbbbabbdbdddadacddabbcdcbacbddddcacdddbacccbdcccdcdccacabbdcaabadccdaccdbbabbdaacbcaadbdcdbbbcaabbbdccadcbbabdbcbccbaabbcabacbaccdcbcbddddddbbbbadcaddacadaaabcaadcabbbccadabbccbcaddbbaacabcccdddcbcdbcacadbdbbcccbddccacacaaddbcaaacdccbacdbddbadbdaccbadccabacbdcbbcbcbcbcaadbdacbaddddccdcbcdacdbadcccbdbadadbdacbabadaacacdaddabdbcbddaadacdabdabddadbdbabbccdaacadcabbaadadaaadbbdabcadbcbbbaddabdadacaaddbccacbdaabbdbbbacbacbcacaccabadbbcacadababacdcacdbbacabdacadcacdacadbbbbcdddaddbabcbddccdbcdacbacabacbaddadcbdbdabadcdaccccbdddaabddadabbaccddddcadcaaddbbbabdcccabcbbdabcbaadbcdbdccadaabcbcaabcabcbacabacbdbdbcccbbcdcadacabdaacccaadacabbbcabcdbadbbabadacdcdbccacadaccaaaadaadaddbaabdbaaadbbaabbdddabccbbdaaabaabbbdaabbbdadcbcbabaabadbacddccbccccabbaddacccabdcddbbdbddbccdcdbaadcabbadcbdacacacabadcbadadaaaacbccacdaddacbddaccdbbbccdcaabdabbabbcaaaaddbadbbbcccbcadbbcbaadcbcdcabccccdabdadddbbabbbbadbaadadccdabbaaabbccbcdbddadaabbacccbdbdbcdaacbbdcccaadbbdcbaabcaacbbcbdcdacbdbdbaccbddccacbcadcccaadabccacbaabdbdbdbdcadababacbcbdabbbabdadbbaccadcccaddbaadbbbadccabcdadaaabacdcdabddbbbddbdabdbcdaccadcdbddbcadabdbcdaccccdaaacdbbacbabcdcbacadcaabcdabaaccbdadaaccbadcccacacbdbdcdacabcdddcdddadcbdccbbcccadcdaacdcddabddbdccdabddabbcabcdcdbcbdcccadcdacaadaddbbdbacdccdbadbbdbcabdbddcdbcbcacbabadaacabbbdaadbaaddbadccacbdabccaacddacccddddaabbcabdcbbdccadaddadccbacadcbbbcacbdcabcddbcadcddadabcaabbbbbcaddaacdcbacbaccdbdddbbdbaabdacdacbbacdacbadacaadddaddacadbdbabdddcaacdbddcdcbcdcabbbbdbccdadbbbcdabbddabbbaaddbbadadbcbdccabcadcbcbdccbcadbbcccbbdbbacababbaabacddcaaacbbbabcaddcddbabbdbcabcbbdadbbcdcdaacbcaadccaacdbacdacbacbbdbccdccdccbbaaacaccabababccdcaabaddbcbdcabaaababbdbdbacdbcddcddbdcbabbaadcabdccddbdaadbcbacdbcdbcbcdadbabbadccadcbcbcbbbacaaaabdbbabaaddaaccaacabaaabddbaaaadcaadccdddcbcbdcbaadabadbacaccaaaabdccdbdababcabadcbdacccdbbbddbbdbacabccbcdbcaabcaaabcdddbcaaaadbaaacadbbaccbcbddcacbadbddcaccaaccdacaabbabacbdbbdcacdadbdaccaddbdccdcbcdbaaccdbacddcddadbaaaddaaabbbaabddbcaccdcadcbbdbbbcccdcaadbcdddbbbdbcdcdcacbacbddddcacccbbccabdcddddcbbcdacbaabccbbbcbcccabdaadddaaddbbdcbdbcdabacbcbabcddaadbcddabcbcdbdaadcbcabdbbdaabdddbdddbaaadcbdddacdbbcaadcabadcaaddcbbdacbcabcbabacbccddacacaabadbbdacabbbcaccdcddbaadabbacadccdbdabacbcbdbabcbcbbbcadbbcdbbcaabdacaacacaadbdbcbdbbbabdcacabacabaccaababddbbabbabdddaabbccabddbbdbbbcacaabbcddadbacddcccdcbadddccdadcdddbaccabcdcaabdbaaddbadbaabbacadccacbddcccdbdcbabdaaaabaaccdaccadcaadadddcacbbbbbbcddaacabcabcacaacabdccdccdacbcabacccdacbcbdcabdbccabdcacacddbacabbbbcddbabbccdbabdddadddbdadccabdcdabbbbbcdbbbbaadcccabacadbcdbacacbdbbbbdabbbbdbbdddcbdaabadbcbdccbadcabaaabdadcbdaddcabadbdddaabdccbbaacbdddcbcccdaaacabcacbaadccaddcbcaabbacbacbccdaaaabdbabcdaccaacdddaaadbdbcbdadbabcdabdaaddbbdaddcacdbaaabdbbacbacdaabdaabcdddcdaccdcdbcaddbcdaddccccabaabacdbcacadcdccccababbcbaaddaacbbdaabcdbcbaaabdbcdbabdccdddaccbdddcbacbdcdcdccacdccbabcadcacbcccdacbaabbbadaaaaacdbabdcbccabacdddcaccdaddadbcaacbadadadbcaddacaadcdaacbbdabdacdcacaadbaccbaabadbbaaaccaadccdadabacacdcacbcbbaacdbabdbbdbabccbaddadbbddcdaaacccbbcccaaaadbdaacbcdaadcdcbcacbbbdacbddbdbbaaddaababbdadacbaabcbacbaacdbdbabaddabccbbcbdaadadabddacabbacbdcbbadcddabacacacacdcbdcadabaabbbddcdbbaaddbbcabcbccadabbabdbdbbccbbbbbabacbbcdbacacccbbdcadadacdbbcadccaacadabcbcdddabbcbcbcaddbdbdbdccacbbcacccdcdcccdbbcdadcccbaccaccabdcaacbcbacccbccccdcbdcdbcdbabbcaaaabcbdaaccddbbdbcbacbbdabacabcbaddaccacbccbcbbbbcbdaddbbaabbcdcddbdabadcccaaadaacaadcbadaaddddbaaaabadacaaccddbbbbcaaabcdcacacbcdacadadaabbcccbccdbabbdccadaaadbabccdadccbbbaddcdcadaddaabacdcdadbdddddadcccabaaddbbdbbacdcbcdacddccddadbadadddddbcdbacbbdcddddbbacdacdabbcbbaacabbaccddbbbcacbcbbddcddbbadababcabdcacdadcdcbddaacacbbbccdbbdbbdcadbddbdbbccaadadbbcbadacbbdbadbbddcbcbbaadaccabcbbadcabadbacadcdabdbadbdacadccdadbbdbbddaaddbcaababdcbacdacdbaadbdbaadbdbadabbacddbabcddaabcbaadbbacbccacabccccdadabbddabcdaaadbcacbdacdccccacadbbacbdbcabcbbadccabdbbbddadbbdabcbcbddcabbbaaabddacaaccbdbbacbacdaacacbdacdadccddbccdcbdadbdbadcbcddacadbdbbcddccddcbbdddcddcccdcbcdaaacbacbbdbbddbdababdccaaabcaaababdbbdbdaaccacbddbbaaaccadccbdcdbdcdcdadddbcbaccadcdcdaccbbbddcaddcdacbaacdbbdbcadaccbddbbcabdaaccdaadbddcbcdaabaadaaacccbcddbcbddbcdcddddddbdbcaccaadcdaaaabddccdaabadcaaabbcacaacaacadbcbaacbbdcabababaaaadcdbaccdbdbcaadcbacacbbabdadbcbbacbbcacddddcdddbabdbcaadbabddbbbbbaccddadbdbbcbbcccdbcbdcbcaacccdcacdccbaccddcacbaddbcbaaccadbdadadcaadccdbaccbcccdadadbadacaabbcbdaaacaddcbaddcddcbadaadaaadbabbaaadabccbaaccbbddcdcbdbdaaddbdcdccbbcaddbdbdddcbdcdaaddbcababccdaaacbcdaddccabcabcbdcbcaccbaacacbbbcccaacbaddaaabdacbbddddbdacacaaddaabcbacccbcdadcbbdbdbacdbcddcdaccdbcddbaaadbdcadabaadddcabdabddddbdbcaddaabbacbdbcadbbbdacddabdddcdbccddabdcbaaadbcbdcccaaccbadcabdbbdddcdabadacacbdaadbcddadddabbbaddbcdaadbacdbcbcabbbcbbdabacccaadbddaaccdabdcadbccccaccddabbcaacbcdacdabbacdbbdbabcccdbbacaabaabadadbbddbabdbbddbdbcbdcacddbacabacaabacddbcaaccacdbdaccacabcddbcbbdbcdbdcbaabcbbadcabbbbababddddcabccbccaccbabccadccbcbadadbacadabcbcccbacdabcbbddbddbdbbdcabadaacbccaaccdcdabbbacaddbaabacabddbcbaacbbadcddccaabbacbbdaabcdbbdcaddcbddaacaddcabaddacbcccdacccacbdbbbdadbbccccbddcccddbdaccbbabddacabadadbcdcbdcabdcbccccbadcadadddcabbdbbacdabbbbbaddacbaccbbbcdabccdccddadcadccddacbbbacadbdaddabadcabbdccddbbcdbbdcbcdbcaddbcbdcaddbbddccccaaabacacddaadbadadbdcdcdadcacccbcccdcaadcbabbacabaccccddcacbdbddccbadacbcccbabcbcccbadaaacccddadbbbacccacdacadcddabccbdbdcdcaccbdcbbbcaaaaababdddcacacadbdcbbcbbbdabdaacbcdccacbdbccdadcadaadbbdaddbdaaccbdabaccdbdbdadbdbcdbbcbcbabcaadcadbccaacbaacbcccdcccbbbcdcbdbadcddccdacacdaaccbcadbdbcbdbbabdbadabdcbddbddccccaadbacbcadbbdbabcdcdbbdacdbbdccdadacbccdbbdbbdaacdaddddcadccababcadbddbdaabcdbbddaacaadbbbbbacabdbaacddabcccdcbbacdbdddbcbbacbccddacddbabdcbbacbadcdbbdaadcabbaaacdacaaddcddbbddccbdaadbbddddbcbbdacadcddbabcccbccbadbdacbacbbbbddbbdabbadababddbcaacdbdbddadcbcbaddabbcbdaccadaacbcdbbacaccaaccaacaabcbdbaddcbadcdbdcacabaabdcbcadbbcdddacaacbbbbabdcccdacbccddcdbdddcdcaadbdbadcbcbbaacbaacaccddaddbabbbccbcabddcbccdcbbdbadddcaaccdbcdbdacbcbdbaabcdcbabcaacdbbdcacacaddabcbccabdbcbacccbaccbbccbacbbdacacbacddbbdcdbacbadcabaaabaabcabadcccccacdbbabadcdbdadabaaaddbdcbdccbbaadaabbaccbddddabbaadbbcabacaadccbabcccabbdcbaaabadcdbdabbccabdbcccdcbbddbcabaccbbbbcdbbbacadcdbdcddabcbbabbbbdaadcbcdbadabaacdbbddccddadccdbcaadabadaaaddbaaacaacadbddddcbbdaddcbbcaabbabcdcccbdbccbcadacacbdccbbbbdccaccbaabcdbcdadaaaaaaabacabddcabbcbacddbbdaaddadbbccadacabdcbabcbaaccccbadbbddcaacbacaddbbdbcddbcbbbbadbddcaabcadadcabdabddaadddcccdcbbdcbaabccbdabdddaddbacaacbbdbabaabcbabcabadbaaaacbdbaadbccbaacbaabbdacabcbabbacddacbbabaadacaccaddcdbabbbdcccacbdddbddaacabcadacdccaccdcbaaaddcdadddabccbbcdacbaaabaccdbaaabbaabcaadacbdccbddaaadcdbcbddacaddbdacdadbbbdbccddacccabaadabcdddccadcddcddbdcdcaabacadcdabaddbacadbdcdabbdcaaccbddcbbbcdbbdcdaacbaadadaaadadaabbcbbbccdbacbbcbcccabcdccdabbaddcbdcabadbcbadccbbdcbcbcddacccacccbbbbdcddcacbbaccadaabbdaabcbaddadbaacabadcdcacdaddbbcaaacaabcbaddaaaacdadadcbaaddaddbbdcaadbabbdcbbcbacbcbcabaacaaddcdbcbccbbabdddadbcbccddbdbdbdcccaadddbacabbabbccbbdcbbacbdadacbbbaadbdddaaccdabbddadaadacbadddbcbddbaabddbdadaadbcabdbcdcabbabcdbcbdccaacabcbcaddcdbbbdbcddbdbbcccaddbdacaadbabbddcaaabacdabacadbbaadcacdddbccabaabacdcbcdacbbabccddaccbbbcbbddabadacdbbbcbddaabbbdaddbabcddbaaccbcdbbabbdabccbbdcbdaacbcdabbaaabbbacaacbaccdcaabdabbdabbcdbabbcbdabbbdbcbcbbacabaadcabccccaabdddbdbdadaaddccacbcacacaacbdcdbdcaadacadbabdcbddcacadcbacccacaacccccaccdaaaaaccdaacdbdddaadcacdacdbcbbbccccdaacdabadbadadbaaccdbdccbadadcbbcadaacccdbcddaadadadcbaadbdbbdbccddcbdbdacbdbadadbcbcdadabcccacdabaddcbcbdabdccbabdccbabbdddcddbabcbabbaaacadbababcdddbdbadcdbdadbdababbcbdbbaddbccabacacbddadbddcbccccadcdaadbcdcdbbbdadbaacbcaddccacdcdadababcdcdbaabdcdbbbcbbbbcbcdbabbbdadcdbdbacbbcacbabbdcbcaaccdbaddcbbaadbdaccaadcadcdaacdcccccbcccdaaadbcbdabcbbcdbccabbbdadcddaddcdaadabbdbbddadcacbdbdabdcbbbddddbcdbcbdbadabaccbbdbadcdabcabdccdbcbaddcbabcaacbcdcdbaccdbaaacaddbcbbcbddadddbdbbccccadcbcbabcacadcbdbddaabcbcabccbbbadbaccadddcabcdcccdaadbcbbddcabdcbbdabcbbcaddbbbcbaadadaabdadcbaadadddbdbbccbbccaaabccadbabcbcdbccbcddbbcdbadbbcbddaaadbbdcaaccdcbcdbdbcdaccbcdaacaaaabcacdcbbabbccbbbdcbbcbbdacdbdbdacddccccbdcdbbbddcabaadbcacdddcddccaaddadbdddbbacdccabdadababbcdababcdbdcabcbcacdbdacadddbadbbbdcbabcacdccaabdadbdddcddbbbabddbcacacdbaabbbcabbacbbcbaddbddccbaddabbdbdaaddcabdacdabaacbdbdcddcdbdbdccbddabbadabbcbdddbaabbcadccdcdaacbddaacdacbaaadadaacadadcddabcbbbadbbcddcdcbcddbdcbbbccccacbbbbcdcbdccddcadbbbccadddaacacddccbcabbadbadcbcbdcacacdacadbaaaccbdadacabdbacaddccdaccbcdcccccccdddbdcadcbcacbbbcdaabddbcbcaccbbbdadcaadabdadcbacbababaaddbabdddcccaccddbacbbdacacddcdbadabbddbccabdacabddccacbcccbbccddbbacdadcadabadbcadbbcacbddaaddacaadababbdacddabbabcdaddaacdcaadcbdaccdbbadcadbdbdcdbdcabaadcaadccbaabcdaacabcacdadcbccdbadbbdacdbdcbbdbdbdbdbcbabaddcccddbbdaaacadadaabacacddbbdbcbdacbcccabacbccbddcbdbdcbdbccacdbddbcdcdcaadccbadacbbbdaabcbaccbbdbbdabbcdddbddddadcdbababcddcadcabbbacdbdbcdbacbdaaadacdccabcacdcbbdaaddcddddaabdcaddbadbacadadbcabadcacacadcdcddcdbabbdcaabcbaaddbdcaaddcdaddbcddaaadacdbcbcdabcdacbbaabdaccdbacdbbdbadbadacbbbcdccbcacccaacaccdacddbdabccccbbbcadcccddcdcdbabaddadbacdaadadadcdaaccbbaabcacdcbabbdbaabdcababbbbbcccccdbddadcbaddcccacbacadcdaabacabbbdacbdddbcbdcdadddddcccaddccaaadaccabdaaaaddacccbccdbdbdbbbbacdbaaddddbbdaadacddabcbddbbadabbacdaccaccccaadcbabbbbdddcdaabdcdbabaadbabdcbabdabaadcdbaadbaccbaaccddbbbdabbbaacbcbcbadcbababadcbdaddccbdcbdbdbadbcbcbbacbacdbacaaabbcdacbbbaaaaaabadddccccccaacddacacacdcabddddbcbcadcddddcbcaacccdacbacacdbcbaabaacbdbbaabddddadddccbabdbbcbdbddabbbddacdcbbdaaadcdbcdacbabdbddacbbbcdbbdccbbabaaabcdaddaaccdbdcaaadbdbdddbdbcdaacbdbddbabbdbcbacdcbdaddbcbbcbdababaabcadccbddadbbcbddcdbcacbdaacccdaadacacadcaddaddabccdddcccbacccbbbdaccbacbccacbcccdabcaabcadcabcdaabccabdbcdaddacbbdcdcbcdddbcabaadbccbdbabdcccccddabbbcbddabcaadbbddabacaccdacabddddbacbcbcabdbcbdbcbbdcdccbbadaaccdcabaabbbbbcbcbddccdbdbbdaccaadabcbcbcccbddacbcdbcbdaabbdcbdbcacbabcaacaddccaddbbddbbddcccbddcbcbcaabcbdbababbbcadaaccaaddbcbbcdcabcbddcbdbbdcbccdbbabccbbddccdabdbbacdacdbbcadbaabababddddcbbabaadbcccabaabbadbcacccbbbbadccddbbdcaaadaabadadadcacccdcabbacbddbccdcbccacacadacccaabcdbcbbbccdadcabccbacbdbccdbbbcabaaabdcbabcccccdababbbccbcabdacbbbdcdbcbbadbbdbbaccdcbaadccaacbcaabadbaaacbaababbcbddcaabcbadbbcdddbcdaddcbaaccdabbbccccdbaacddddcbabcbdcdcbdddaacbadcbabdabdddaaaaaaaaaaccdbbdbaabbbbabdbbadaaabbcddcacbbdcdaddbcdcdcbbcccbadaccabcdaaababcaaacacdadbddabcddcdaaadacccacdbdaadabcdccbcbbbddcdbccdacaabccbbbcbadddcddcacbbcdcabadbbdababaaaaacdbccbaadbbddbaadbbcdacbcccbcdadcbababbaaabddabadacdcbacdcbabbbcbcddccddaadabdccadbaabdbbabccdbacadcdbdbccbbcccbababbcddcabbdaadcdbbdcbbdbbbdabacdacdbbdadcbcaaacbcbcadadbadcdbdabdaaabdbbbdbddadadadbcddacdbbaabccdcdbbadbbccbbcdacddcccbdcbacbcdbbaacddaccbbbddabdadbcdbaacaccbaccdbcdaadbcdcabaabaaaacadaccbdbbccdcacaadabdbdbddccbadaabdbbaadacbbaaddabcccabcacdbccbbcdacbcdcbbdcacbddaddbadbdaacadccacbddcdbdbdbccbcdbaacacacbddbbcbaaacadddcbbaddcdbacdddaadbbccdbdcccacbddabdbdcddbacabbccdaacdddaddcbcdcdadccdbbadbcdacacdbcdcbbbdadaabacaddbcaaaddacaaacdaacadadbbcbaacdadccbccbabaadabacabddcaaaabaccabdddcadabbcbaacacabcddbccdcccdbaacbbadbabdbdcdaccdccdabcbabcbdabdbadbdbabcabbddaacdaaadadcbbdbccbddcaddbadabcadadacacbbdcdbddabbdddbcdbcdacdddbdcccbcdbccdaabccbcdaadcccbcadddabcdbccbccccadbbddcaabdadddadaaabbcabdbccbbaddbdbbddbabddbcdaccacadcbcbadbaadacbcddabdabbacccdbbddabdacaacdbcdddddbcdabdaaddcbcccabdcaaaababdcbbaddbbabacbbabbcbccadacadadacddbaacbdbbcbccbdabdacadadbacbadabbaabababdadccdaadddabccabccdbdacbbbbccdbbcddadaabdacccdbbdbdbaccbdcbdcbdcbbbccdbcaacbcdcdabddbdbbcadccaacccabdabbaccbdccbabbcddacbbaddbcddcdbbddcbccdbcaaaacaccaadddddaacacbbbbcbcdbcbbabbbdddccdcadaadacdcabcddccabccabdccaddbabbbcabaaaacbcddbdcdbcdbcaddcbbbabadccacadabddadbcddbabbababbbbbbdbddabcbcaadbccccabcbdbdadcbcbaaddacdcdcbbddaaddbdccdadcaddbddaddccbdaddbbcbbaccbbcdbdbccbbabbbdaacacccabcbbaccaaacabcccccacdcdaaccdadaabbdbcbdcbbdbacdcdcbcdcbbbaddaadccadcdaabccbdaddddddbbbbdbbbcccbcbbabbbbdbbabcadbbdbadcccdbcbdaabacdbcaabbcbccbcdddbdcccbbbdcccbabaabcacacdabaccdcaaadaaacdbbcbadabcaabbacacddddcccddacccaacabcdaddbddddaaaaaacaccbccdbaaababdaadddacaddbbbbdaddcaabaacaaccbadcabbbddbcbdbdcadccaddadbcdbdaabcdbaaaccbdcdbbcdbcdabaadddddcdabdcadabbabccbadbdddabdaddcbcdadabdbdbdbbadaddbdbbdababbccbddadabcadcbbdabbadabdbabbdadbcdbcdadabbbcaaacddbabddcbcbcadbacabababbadbbbbaacaabcdcbcccacdacbdcccadaadacdcddcacadacbccdcdabbcadcbdbbcaadabacadbbbbabdabaaaacaabccaabcabbdacaabdcacacdbbadcbacccdcabdcacdabdddbddacccdcdadcbaccddcacadaccbacbabdcbdcddbbacaaaddbddbdaddbcdaacddcbabcabdddaabcdccbabadbdcdabdbacdadaaadabadbcdcadbccbbccdabdbdccadcababbadadbcdcdddbcadcddcdbcdbbcbcdcacbbcaccdadddaacadbddbbbbcbbbcacadbbdccdbaddcadaabbabaddcdaabababbbadadaddaacbaacacdadcdcdcdbcdbbcabbddadabbacddcacadabbdbbcccbbaccdabcacbbdadbabddbcdaccdddabccddcbbcbdacbcbbabcadbccadbadcadadabcddababbccacabcdacabadddccdabbbacabbabdbaacdaabddccdaabddbbddccadcbbbdbdacaaccbdbcabbcaacbbdacdbbcdaabacdaabbcbaccddbbcacbcaaccbccadcaaccccaadbccdbdcdbbbadbadaccaacdbcabcacbbbabcadabdbccddbccccdbdaccccdbcbbcdbcccdccdabaaaaccadddcbbddcdddcbdbbbbdcadddaccbbadbacbaacddcbcddbabcbddbadabbbbdcdddabcbcdabcddbacbbbdcaacbcacadbaadadadabacbabacdbbbbdabcaddbbbdbbbcadbaccdbcaabddbcadbdbdccabcccccaddbccacadbdbacccdadadccdcaccbcddbbcaabdcccadaacbbcaddcaaaadcabddbbaaccbdcaccdcbdcddabacddbabccbbaccccaaaacabadaccdabadcbcccdbaabcbcdacbbddbacddaddbbbaabdcdcbdcaacacabbdbdcacdbaddbacacdcabdabbccccabbbabddcdbaaaabdabbbbabbabdadbbaccadcaabbbbdcdbdbcdacbbcacbcdbcdbbdbbabbbaabdbcaaccbaabddabcaddabbaddbcdcbacdddbbabdcdddddcbaccbbddbaadbabcbcaadbdabbcdbaccbdcaacdddddccadabbdabaddbdcbccdbcbccaabcdcdccccbdcaacbdaadacacabcbbaccaadcdbbdcddbbadddcbbdbbcbabdaccdcbadaddabcaacadddaadbbdcdaabcdbbccddabdbdddbbbadaaabccbdbbdccbadbddddcdcbcdcdcbdcbabbbdbbaccddcbdcbcbcdadadddbdbaabbcacbcdccbabdddadabcbbbabaddbacdacbbbcbbabcadaadaddcccdbccaacdddcdcbacaadabadddddacddbcdaacbbcdcbbadabddddccbdccdadcccbcacbcdacabdcdddbddbcdbdcbddbccacdadbcbbbddbcccdbddbbdcbcdacbcddcbbdbdabcbbdcbaccadbdbdbaacdbccdbcddabaabbcabbabdbdddaaccacdabcbddabdbdcaacbcbdadaccacabadccbcbcbbbbacddcaaccbbdbbbdccdacdacabdddcbcaabbaaadcbcababbbddaccddadabaadbbcdccdaccdbcbbaacdbdccacddaaabdbbbcbbccdcbccdbacddbaabcaccbbcbbaddaadcdcdaaddccdddacccbaaaddbacdddbdbbabdadccdcbdbcacbdbbbadbbadbababcbbdcddbabddddaaaabbbaadadacbbdbaaadbcdcacddcddaccbdbbbdabdcbcdbbbccccdccbbcaaacabcddaccadbdcaadbcaaddbcdabbbaabdadadbbaabcdcabddbbadbbccaccdcaaabdadaaaddbacbbbcbdbabccacdacadaddcaabbbdddddbdbbcaacaaabdcbccdbbcdcaadbcdcaabadabdacdbdcabdcbbbccbdbacadbcddaacbcacdbcaccadbddbadaadaddadbaaddcacbdddbdddbcddbdaddaaaadadbbbbacccddcdaaccaaaaddbdddcaaaccbdbbddabbdacdbcccbaccbcdaaaaccdaabdcbbabdaadcbcadaaacddbdcbbdcbdcbdbcdabbddbacccdcdbacbbcccccddbaaccdaaacbaddbbbddbaccaccabdaddcadbadcdbdbadaadbbbadbbccbcbbcddbaadacdacdddabaadbabdcdaccaddbcaaabccbacbdcdabacadddcdbcaabcdabadadcabbccdabccabaaabdccbbbdaadacccadabbabbdbaaaadabcccdbdddcadabcdadabbaadbaccbdccddabdaddbdacbbabdbdacddcdacdcdcdddadaaddabccdaacdddbdcdaaaaddbbcdbbcbbbcadccbccddbadabadcbccbaadcaaabaadcddabacaabbcdacababbdcccdcccbddbdcdcddaddcbcaccbadbcacdbacaadaabccaaababcbaddbaccdaaadadaacbacbaaabdabdbadacdcbbcbabdcddbaaadadcbddbcacbdbcdbadbcbcdbdcaabcdaadbdddacdacddcacdadcdbcbbcbdabdcbcadbcbbddbdabaaaccabbadcbdacccadacaccaabdbdadcbdbccaccdacbaddaaaaccaabddcacccbbbdcacabdcaabcbdbbabddcbadacadababbaccacbcaacaacbaaddbacdbdcbdcbacdbbadbcbcadacbbbdadddcbabdcabcdcadccdacbadbcaadbdcdcdcdcbbacbbdcbdddcccdcbdcbcabbaacabddcacaadccdcccdbaacacacabbcccabcbbdbbcdabccdcdcccddadddabbddcddcbccbcbababcdaccbaddcdccdadcbbacbabdbabadcadcaacabaabcdbacacbbcabcbbaaccbaccdddbaadcdadcbdbddbdaddcdadbdbdadcddadacdacbddbadcbccaacdacabadcbbcbcdcbadaadacdbdccaaaabdabaddbbbbdbbbacccdccacabdaaabbcbbaaaddadabbabbabcbaabccaabaddbccaadcbdcbaabaabaaccbadccdbdcdbbcaaabadccadbbdabcdacacacccccacdbbddcadcbdaabaaccadccdcbcbbcbddddcbdcbddadddaabdcbccadaaabbdbdddaaaacaabdaabbcacdaddaadabbbcadcdaaddccbccacacacccaadbcdcdbcbadabddabccacbbdbddbdabdcbcbcaaaccbbbdcdcddcbbbaaccccddcbdcdbddddcbdcbddcdbcbccccccacaacaacbaacacdaabbabdbadbabbddbbbcacbbddccdbcaddccbbddcaaddcbcccccaabbbdaaadcdaaaacccadacbcbbdcddaaadccadbbbdbaaababbadbadccaadacbddadbaacbadbbdcbbbddabdcadacadddccadadacbcbcdbbdbadcddccbbbccbcddaaaddaccbccbcbdbcaabdabacdccbbabadbbbbddabbbaccbacacdbabdccacbaabdbbacbddcccdaddbbcccaacbbadbadccbbcdaaccaabacdbabaabdcbdbcddbadcacbbaccaaacbddcaaacadccbddcabcaadddbbcdcbbddbacbcadbbbbbdbadaabccddaddcbbbdadadcbcbcadccccccacacbdbabdabaaadadbccabbbbdcacacdddbacdbabdccdbdcbccbbbbccbbbacadbaabdbabcbabcbcddcbcbccdbdcaadcbcaaaddbaccadbdcbdccbcdcaaaddbbdbbddaabcccccdbdadcabaddbadadcabcaddaddacaabccbccddadbdbbdcbbcaaabdbdbcdbcacbbcadacbdaaadccbbddccdbadbcbcccdbbbcbacbcbddacacaddcdbcdcdccabcbbbbabaaadbaaccdadbcddcdcaabaacbdacbbbaaaadccdcdbbdcaacaddadaadaadbdbbbcbdabbdaadcaaacbabaaacbbaaaadabbddbbcbbbddcaadabdaaaabcddabcdadcbdaadbcbbddcbdaddadbbddbbbcbcbccbdcbabddbaddbbdcaacaacbacbccbbddcdabbdacacbacdacacaacaaadccbacaacabbdadcdbaaabcbcaaaadaddabaaaddbccbcbdddbccdacbbcaaccbddcbabdcbcaaacaccdacbbbadccdbccabdcaacadcdacdbdccbbcdccdaadbccccbbacbabddcccbcdcccccbdacacbcaaddadaabccdbdadcbbccabbacdcacdcdbddacbbbccdcddacadcccbaddcdacddaadbcbbddcddbaabadbbcbcabaddcbddccbcdbbbcbccbcadaacbbbdadbbadaaadbdcabdadabcdbbcbdcdadccacdcccddcccaacccabbaacbadcbacdccabcdaacddacddcddcdddabdddcacaabccaddaabdccbcdcdabcadcadaccadcaaaccddcaacacaccabcdabadabbdcbdddcbbaaddbabcbdaaacccbbbccdacacbbdaacdadacdccbcdadbdbbadbbadccbcaddadbbaadbaccaadbcabbbbacccdbadbdcdbbdabbbcabbbdacbccccdcacdbadcdcbabcddddddccacdbdcdacdccbcabaadabdadaaaccaabdbccdcbbcbddbcdbadbadbbacdbccbbabcbacdabcaddbddaaacdcaccaccddbcdacdaddacdaabadcdcbaaccdcbbddcdabbbcacadaacddbadddbacbaadaccbabbdcabcbcbccdcccbdbcbcbadbcddcdaaadaaacbdbaabcbdadcbcdaaabbcbbabdcbcbabbacbdbcbbcaddbadbbaccdaabdbacdaacaabacccbcbddaacbbaddbcccacaabddcdccababbbcdbbcddddcccdbbdabddabbadaadcacbaddcddabdbdaadadaddcbacdcbbdacdabcbccbccababccbadccccadbcccbbabcacdbbbdccddbbaacaacabaadababbcabadbccccbdcddbbdbcabbbcdaabccccbaadaaccccabbbbcddcaabcabbaaddcdbaaaccacbadbdbdbdcdadacadcabaaadacdbaaddbdbdcbdccdbacbddbabcadbdbbbddbbcadabbdcdccdcbcbaaddadaaaccdbabdbbbdbdadaacaaaaacadcdcacbcccccaddcbdaadadbadcbaacabddbbcabdcacccadddddacdaaddbcdabbcdccdaaabbbcacadbaaaacdbacdddccaccdbbacbdbddddacadadaccdabbccdcbccdcddbbadbdacabccadcadccccabbacabddcbcadbcdaaaaadaacdaadacdbbdacacdadddddcbcadbdbadbdacbaddbabacbdadbdccdaddbcccaaddcbabccabdacbaadbdcbaccbadcccabcadbddaddadcbbdbacbddddadcadabbccccabdcbcbdcccbbcddcabdcdccdaaacdabbacadcaccdcbbcdabddacdbddccacddccdccbabbcbacdccaadadcbabbcbddabdcdadbccbbbcadbbdbabbbdcdadbaadadaaddaaccdbcabdbacdbdabbbcaccadbbccbdddadadacdbccabacaacdadcbabaaacdcdabcdcccaaccddcaabbcdddddccbdabccccabccaddaaabdcacccbacabdcaacbabcdacacdccbdcabddcdaccacdaddbcaaabacbcccabcbddbdbccccdbadaccbcbccbbbcdbadadbabdbbddbccaccddcdaccbdcaaaaaaadbcbacdddcbcdaacadabbdddadadbabbddaddbcaaacaacbbbbaadbdbaadbadccbdcbaaccbddaacbbacbabaccababcdadcdcdbaddbcdbcdcdacabbccdaadbaaabddcadcbcadaadbacdbddacadbddcbbbcadbdccdbdcdbccddadbadddadaadabbddbdaaaabdbbacbddcbacdcccdddadccaacaaacbccdbdaddcacabcdabadadaddacddcbdcddcbcbcaadbdbddcdddcaddbbababbbadcdbbcbbadcbaadbacddcccdabacacdabbcbaadbadcdddadbbabbddaadadcbbdabcbaaaddbaaacaabdbdcdccbadcdacddbbcdaddcbdabdaaabaaabdbcdcbdccbbbccbccdbddaacbbdaddbabadbcccdcaddadbccbaddcdbcbacddbdccdaccaabadccdaaacaaadbbdaabbcbaadccbabcaaccddcbdbbdcacdacdbbbdcdccdbabcbdbcadccacbddccdccdbccdcacbaaccababdacbdccbbbdacdacdbadbbccbbbadcbacdcdcaaacaadcbdaacbacbccbbccddcccdcdddcdbadaaacddbccbcddadddcbcbacccccdccbaaddccbddddbbcccbbacdbaaadbaababbbacccbddbcbcaddaccabacdbbbbbcdacccdaabacacddbdcdddcabcbbcdaddbbdcbcdbbcdbddbcbaaadbcabddbccabdaadbbbacabdcbaabdbadccdaccccabbccbaaaccdbdbcaabdbddcdadbccbdbbbccdaaacbadbbbbaadbbcbcadcbdaccdaabccbdacbbdcbadddcccbbcbabddacbcaddccabcbdaaaacddbddbabaadadacbabccbbdbbbdbdaaadadabbbcabababccbabbacdddbabcccbcdddcccbbcbcaccbdbaccbdbbdbbadacbadcccddabdcbacbdccbcaddacabbabacacdbccbadadbcddacaddbaabbbabadadbccccabbddcbbccacacdabccdacdddccbaccccccadabbcabddbcbacdcdbadaabcccbbccdbdacaadbbcbcccdbdbbabbdbcbdabaaadbbccaddbdddabdbdcdacbccccbbcccabdabadcaabcdacadaacdbaaacbbbadcbdccadbcddadadcadaadabdcbccdccaadddbdaacdcbdbabcaadadcabbcbaaabcdcbdcdbaaadcbacbddcacabcaadbbdabaadacdadbbaabcbdadbabddcababdbdcccadbbbacccccbddbcacddbdcdadcdaccadcbaddcbcbdcaadcdcddbdabddadccccbdadbbbabdbcdbbcadacaabdcccdcdcbbccdddddcbcdacabdccdccdbbcaaadbcaccccdddcccbaadcbbaccadacdbdaabcdcdadacbadbdcaacdbbcbacbccabacdaadbaadabbaadcbcdcdaabbbbbbdbaaabcadcabcdcddbcdcbcbddbacdbcbcbdbadddacdaabcdaacccaacdacbdacddbbadcbadddcbbadaddaaaccaacabdddabdcbbbdddbdbdcbaaddbbdadacbbadbabadccacbddcaadbddbdadcababcbdbcdcdbbcdbcabaddadbbbcdadaacabdbdcbbbdabdbbccbadcbccaabccdbacddaacccdbadbccaccbadbcdddcccddccadccbbcccabbccddccbccddddabcaccdacbdacddcbadadcaddabdbbabcdacdcbaabbcddddcbdbbbaabbdbcabcdbbbdbabababcdadbcbbddddccdaaaabaaaadcaddbbbddacadaddccabcacdcddbabacbcbbbcaacbbabcdabacbacaadcbcbddaadacaadcdbcdadbadcabdacbbdabbaccdddcdcddcabbbadcdacadcbbbdcabacdaaacbdadbdccaacbcabcdcbbcdccccdcabccdcaddccbadccccaacacadcdcaacddaadacaabcabdbbbbddbdccddbdcddaacbbacdacaaabababcaadbacabbbcaaaaddbccbddbaddabdbbdacbbbdbbaddbccccbbabaddbcdccaaadcbdbacacdcbabaadbcdbbcbaacbaccaccbdbbdcabcbdbddacddacaaddaddbdaadbacadcaabccccddcaddccbccbcadadbbacaadabbcbabbabccacbaddadadacabccabbbbccaadcdddcbdbcadabbbcdcdacadcaddccbcaadbcaddcbbadaaaacbddcaddcacacccddacacacddaacadccbbddbbcabdadbadcadbcbdcccadabcbcbcbbcddcbcdcabdaabbdccdabcacadbbccabaadddbcadbcacadbccccaaaabdaadbddabddacabadcbdaadbdcbdabcddbcccdbccacadddbaddbabbacacdccadcddcacaacdcabacdaabadcaacadbabcdbabbcaadcccbbdbdcabccbabbbdbdcadcddaabaccadacaacbdbabcadcccdcdbacdabdbcbccdddabbcbbbcdbcadcdaaccbacdabbcbdcbcdddcbbbacdbcccdcaddaabcabbacbbbabbdcdadcbdaddcbacacaddacbcdbbdbdbcbcabbdcbccacddddcbadcbddbcdbdcbbbbbddabccccdcbabacabbcaabbbdbcddcccddcbacabcabdcabddbbdbabcdbbabaabaddabcbaccdcbaddbcacbcdcbcabadcbdcdabbbacdbbddacadbababbbdcaaababddacdadaddcccdabbaaccbcbccbcddadacaadbccbbaababdababbbabccbdcbaddbcbaaddbcdaddccbdaabbbcdbcacbbbaccdcdbadabcaabcadaaaacacabcdbacdbcaaabaccbdbaabcbbdbcdabbaaadaaddbcddcdabbcdbddbadbababbddcacdacccbdcccdcaabbcddddcddbcbdbbcdccaabccaabcadaaaddbcdacbbccabdbaaacdbaabaabcdbadccdddcadbbbaccadabacbbabcaabbbbdbdabaaaadbbabaccddcbadabdbdcbaadbbaaabbaaacacacacbdaacbababadabcaacacddbcbbbccadaabacdbcccccdaddaacbaadcdacadcbbccbdcacbbacaadcdbdbabbcdcadacacaaaddcaacbcccdbcabccdbbbaadbbabcdddabdddbcddcccbaadbdcddcdabcdddbcbdccbaadaadbcbcbdcaaacdaddbdbabcbbdbabbbaccdcccacaddcabadabcddabcccbdabadccbbabcbdbaabaadccdcbabcaccddcbaccdbddddddcccaadaabcbadcbdadcbbbdacaaddbbaccbcbdabcaaadaabaaacacabddbcdaacdbdabadddaadcddaddcbdaccabbcbcadcdaaddcbcaadcaabadccabadbcdcaaacccdabbddadcaacccddccdcbcdbcaabcdabacabddbcccaacdbcdcccbaadbccaabbcddbababdbbaaacaacbbbdbcaadbabbadbccbadacbabacabcacbbdaccdccaaccaaacdaccbbbadddcbddbacadcddbdadbccaddabacacadadabbbccddbdbbabbaccacbdcababacaaabbddbacacddcaabadbdadccddabcbdabbddadaddcdabbdcbdcbbdbbcddcabccdbdcdbdabbbbbdacdaabcbcdcccdbbbdcababdddbbccabccacccabaaddaaadcaaddacdcbabcbddbcabdacbaabdcdadabcaccccbccaddaaaaacdccccacdbbdbbdcdcdacbabdddadabddadadbcdabbccbbdadacbcdbaababacaadbcbabcadbbdcdaabdbbddaddddacdbacdcbdccbccbccddbcbbaccacbcaacbbdaaccbbcddddabdcdccabdaaabbaacadccbdabbcdabdbdddcaacdcdcdadcaaaacccaaaadbcacacabcaadadabcbbcbbaabdcdabcdcacdbaadddacacabccadbbbdccccbddbadaccaadbacdcdadbaddacbaaadbcdbddbccbadacbcbbaabababbdddddbbddbddacbcdbbbaccbcbcabdbbbcbdacbdcaccaadabcbbbcacbdbabdbdaacccdcdbabcbdcacbcacbbccbcccbcbbbaddabcccbdddbdcddcbddccbcbacaaabcbcabccbaaababcadbbdabbdbbcdabdaabcabddccadcbdccaaccbbdcabbcccdcadbcbcabbcaccbccdbaccacabcbbdacdbaaaccaabdacbbdbaadbccdbbcadbacbcddadaccdcaaccdcccaaccdaaccaabcaadaabcbbacbadacdcbbdbddacbabadbbcdbbbaaabdabddbcdbccaaccdaccddacaccbddcbbcbabddcdaddddddbbcbcadcdadaddabbaccddcddcaabcbaaaaadaadabdbbcccdbacbcbbdcbaaaabccccbbaabbaabbdcadaaadcbdcbccccaabbacbdccbbbacbddbaddaaddaabbdabcabcadbcdbccadbadcdbcbacbcddbbbcadbabddaccbdcdbadbdabcbcaaababadbabcabaabcbacdacaacdacdabdcdccbacdabcbaddaccacbdaadaaabddcadcbccacddddaaddddcdaddbcababbdbcbcbbcbdbaaaacabbdabbdbacdadaccdcbbbdadbbabbababcdadcbadbadaddbaacbdbbbaacadcbcbcbdcadcccadcdbbbababdcabddabadaaadbabdcdcababdadbcbaababccacdaabaabaabcdcaabacddabbdbcadabddccccaacdccdccabbcbcdbdbaaacaabbddadcbddadcabcdcbbbbdaacddbbbdcbcbdcbccabdcdacddbbcbaaddaacdccdcabcdaacaaadbdcdabdadbbbbaadadddabdaaadaabdcabbbabadaacacaaaaddabcacccaddcdbaabddaadbdcbddababadadadbabcccadcbcacdbdbadbccababaaaacddacccdbdccbaddbdabccbbddaabddbdddcaabaaadacdcbdabcbcdbabbbcabaaabdcbabdadabaabaabadacacdacabcadabbdddbddddccaabbcccbccbddcbdcadaaacddcaaabddcadcbaadbbaacaaccdaaacddadcdcdacbabaddcacacadcdcaaaaadcbccabbcddccbdbccdacbcdaccacabbbacbdcdbbbbcdbabcaadbbbbacdbcdbddddccdadddbbdcbdadacbbcabbbbdcbadaadabdcadadcbdaccacdcbbdcabcdcdaccddabcbccdabbacdadbbcbacaddccbdaaddbcadbbdbabbbcbcddccddbacbcadcadbbdcacdaccddabcccabccaaccacdcbbcbdbdbdbbdbcabbcaaaaccddddbaadcccdadcaccddcacaaabbdaccadbbbbbcdaddcbbcdccdbdbbbddbbbccdbcdacbddaaddaddbbbdacdcbdaacccbdabcdbbbadbddbbaaddbabadadaabcaaadbbdbbdbddabbcababdbbcdabdbbcdccaaccddacdabcacacadbdbbbddaddbaacabcdbabdbdbadcccabbcbacaabbbacbabdadbdaacddccadbbabbdbaaccbadddacdcabcdbaccacdbdbabadbbbacdcbbccdccaacabcdbacbbbacaadbcaddacadcbbcbacbddcbdccbadbddabbcacbabacaaaadbcabcccaabccabccddacdacccadaddbcdabcaddacabcaaacaccccacbcbbcacaacabcdabbbadabbccdbcdadcbabbbaaacccabdacbabddcbbbddddaabcbbdddbdbacadcdcbddbcbcdbcbacbaddbcbaaabddadaadccdcbbadabbcbcdcbacaaabbaabaaccbddbaccdccaaccbccbdaaaccabaabbbcdbcdbbbccadbabadbcbbdcbacbdbbbcddcbcaacccbaadbcdcbdccabddddacacdaabbacdddcaadaacdacdcacabacdacacbaaadacccbbbcadcabbadcddddaddadaaadccddcddcaccbcadbaaaadcdbadabbcdbdabdbabdcdbbcbcacccdbbccbacdadacdaacacaccbbdbdcbcbbdacbcbabacaaadadccacdaadabdbcadcbdacdcbbadcbbacaaccdddbdcbacbaddaabababacbabacddbabacbbdcacddbacdbcbaddbcacbbbcccacbcbddcdcddbaadaaaaccaacddbccadadbbbbddabcacabcdcabdccccccbdbacbcabcddbbaaaabbbbaccdaaacccacacdddcaddadacdbaabcabdddbbaabbdabcbcddcdddbdbabdabaacdddcadccdaccbbbcbaababddadbaacddabbadddaaacabdcbadaacccaddcaccacbbcbbcabdbbcddbdcdcdbbaabaddcaccdcddcdcdbabdcadabbccdaaaccdcacbdddadacdcacdbaddacbbdbcdccababaacdadccdabdcabddbbddbbaaadabcbaaabbadcadaabbbabbcdbbcbdabdcaadbcdbcbcdbdcbbccddabbddaadccadabcbbcdbdadcaadaccbcacdbadaacdddbdddaadadadbdcbbabbdcbbcdcccabccaadcbabdbcbacdddccdaccabcccdacacdbbabbbbdcaabbabcdddbabdaaabbadaccacadadcdccdadbddddbaddcbdbdbdaccdadbcbacadaacacadbccdddbbddbbcbbcccbbabdaccabdacaabadcbadcacbddbccdccacccacbcdaccbacdbbacddbcadabbbcdbcddaddddccddacadddbbdaaccaccdacccbdcacbaacabbaaccaddbdbbadcbcdcddcbcbdcdcdcaababbcddcadabdbcdbdddacdddacdcddbdadabdbbaacbdddacbdcddbcacdcccabadccdcbddaaaaaadbacdbddbcacacdcdddcbaaaaadbccbdcbabcabcaabbabaacdbdcbbcabdcabcbaaacabdaaaddcbcdaddbdaabccbdbbbcbbdccabddbacddbbbddcdbdccdcdaacadddbbccccddcddabbbcdbcbbbbdcdadaaaaadadbbcaadacbcdbcabdbbcaacdbbbccbbdadcdddccbdcbbccaccbddbbadbabdbddcaaaabbadaccaabbbaddababbbaabcdcabadbdccdaaabbdbdccbbacdddbdccbcbbbdacaaadccdabbadacdbbbdbdcdbacccacabcacdcddcddcaaadadcdaccdcbbadddabbdadaacdabcbaaaaadaacabdbbdcdcdbcdbcdbcbcaadcbacaddabbacdddcdbcbdaadbcddcadbabbddcbbdcbbdcdcdacccacaddccacdacdacadababdccbccbbdbdbcbadcdabbccbbacadbdcdabdadaccbcccbddbdabcaaddabbccabdabcbcaadbccddabaaabdcbaabbccaddcabbcabbacbbadbcbcbdccaacdabdddcdacccbdccbddcbbbbcddcabdccbdabcbadcabcdbacadaddcbbcbbbbabccbdddcbbcbbaddbbcdcdccbbdddcaaccabbbbcbdcccacddbdbdcbcabcbaccccdacdcabcdbdaddbdcdaadccdcbddddbadcbddabbbabdbdcbbbacdcdaaacaadcdcddbcbbbcdddaaccabcbbadacbbbdbccbacdcacabbbbcddabbddbaacaabcdbbbbbaabbcadbbbacacadcbdcaabbdbadaacaadbbcadabbabcdcdabddccbdcdccbaabdcabbbbaaaaccddabadbabacdcdbbbdbabccdbdccbdbdcbbdbdadcbbdabdbaccabdcabbacdcdcccbcdcddbcabdcbddbacdadadaaadaccbbaabbacbdbaaaaacacdabacbaccddbbdcbddabbbcbccddddcbccdadcbdadbaaaaaacadadabbcbadbbcdbcdbcababbdbdbcddbbabbdbaddbbdbacababbabacaabdbbcbddcbdbcdaadbcbaddccbcccbdabbcadacadbadacbcbcadcddccbdabbbbcadaadcadbcdabcbacdacdadcdbdbacabcabdbdccdcbdbaadddbabddcaadcaaacacdaaccbdcabbdddacdacbbcdcbbaddabdabcbabccddaccdaacddbcdcaadabddabcddcabdaccacccdaaccabdbdcdbbcccdabbaacdddddaabcacdddaaddabadddaaaacccdbbcdbdbbcdcdbcdabbabcbbbbdaabacaddddddbccdcaccdadccbaacadabcbcbdbabccdaabadbbcaadacacabcbaddcdacddcccbbcddbbacdabcaccaadbcacaaddddcdbbadaabacbadbddbcdcdcacabccbacbbadaddcabbdcdbacaacaabbbdcbbbdbdaccabbdabcdabacddaacbcdccbcaacaadabcacbcdddbddadadadbbbddaabdabbddaabcbabaabbadaaadcaaddacdaccbdbcbbbaccdaaababddbbabcaabacadddccabadbdbabcdcdccabccbddadbacccadaaddaddbbbdbcaddbdddacacbcaddcccbaccdabadddcdcacbcdbabacaaddccbdccaaddddaabdddabcdcbbdbadbdaccdadabbaabcbdbcbcbddabbaabdddccabcbbdbbdcaddbcacacddbadcdacdbbbdadcbdcbcbbacddbadccccbddadcdbacccdbbdccaacabcadbaabbcdbddbadaadcaddabcadddcccddbcdcaaacaabdddcacccbdcaadcdaadbabaccbcbadcabbcbaadccaccbcaacbdbadadbcdddcdcdbdaabbbabbcbaaadbcbccbbabcdaaabddadbbadcdcacdbdccddaddbbbdabcbabbaabacbddbabaddbbbddadadbdccbbacdbabbcadabdcdabddabdbcaadbbcacdaccacbcbaadabbadaabaaaaddaaaccdcbabaabdacabaaccdaabcccabddaabbdbcdbbbaacabcbccaabbbcabdccbcadcaadbccbdaacdaababdaacabcacccbabcdaadcdacaddcadcdddacdbcbcbccaddcddacacaadbbbcbdacaabdabdcccccbabcbdcbabdbaadcbddabadbcdadcdccdbbccdddacaaadcbcabcdcadcdaccdbbcaabdacbadaabcbccbababacdabcdbdddbddccdbaaddccdccabbbadccccdbddcadbcabdccbdadbaacdababacacaadcbddabaabbacdacccabbcbaaccdbabbbdbdccaddcdacbbbddaaaaabbdcdbcdcbdaadcddcadabadcadccbcdaabaadbdaabdbddbbbdcbacccdaddabcdbcdcdbcddbbbdbbdddadaaaabddbbdaddcbdcaacdcccbaacaddddccabbbdbbcaccaacccbdddccdaaacbdbbbbbbdbccaabacbdddcbaccbadaaacbadadcdcbdbbcbbabddaccdcccdbccccdbccdcadadaaaccacabdccdddcddccbcbdacbdbccbdcddccbcddcdbdbbccdcabbdcacbcabcacdbadcaddcdbcccbcbdbaadbdbadcdbabdbcacbacbccabcddbacadaaccadcbaaacdbadbdcddacbbcdacacbadbcacbdcddabccaaaaadbbdbacabcbbcbdcadbcaaaabaadcbbadaaababbaaccacbdccbbbdabcaadddacabccadacbacddadcbcbaccadabccaaccbdbcccbaabbabdaadcabbdaaddabacbacadbabbabcbdbcbbdaacbbcccbbdbcadacaddcdddcdddcbbcdbdddaaddbbdacdacbaadabddaddcabbdddcbbcaadcdadbbccabbacacdcddbdcadbbaaaddbcadccdcadaabcbccdacadcadcdaabbdcddbccbddbacdaabcbbdddabbdbabdbdbbabaddacbbaccbcacbbddbbdaaaabaccbdcaabdcaacdbddbccdbaddcbbdcbcdbcbbbcbcbdddcccacdbdbcbbadcdbbddbdacddcaacdacadbacbdcddcbdbdbcdbbcbcbdbcbbcacdbddccdcddddcbcaabdcbabbbbbcddcdcabdddbdbbccaadcddabaabbbccdcabaabcdccbcabacabcacdadcdddbdbbdbcbcdadcaccdcbdbaabcbabcabdbccdbacbbccbcbcadabadcddcadbbdadabbbbdbcadbccbcabccddbaaddbccaabcbdaccccbaddccbdcbbbddaacdcacbcdbaddcabdccbddaadbdbabcbcbdacdabacdacaaddacdccbbacdcbaddbbbbabaabadcdabcdaddcabcabbcddaccdcdccdaddbcddbdbbabcdddddccbbdaacbbdcddbddbddbddccaabdbcacdaabbaabcbbdbdbddbdbdbdacbbbacbcdcbacabcaadcbdcccacaddaaddcdadcbbacbbcdcdbbdbaaacdaccdcbabcbbbcabcbddbbbadbaaddbddcacabaaadcdabcabcdacccbdddbaccadaddbcdcabcccabcaddbcbbccdbacdabcacbcccbacdabcadbcbbbcbdbaccbbdddbabbaaccbcbbabcaaddacbbbcdcdadbdbababbbdbdbbadddaddbacbcbcccbbbbddadbcdabdbcbdbbdbdbccdbcbbcdbbccadbcaabdccabddccaacacbcdadcddddcbdacbbaaaabcbbbacbdbbdacaccdaabdadbbcacbddaacaaacbabccbabdcdbabccabcacacaabaacddccacbbcdddcdacadccbcadabbbdaccbdcbbdbbbdcdbdbabaabbacdacbaccacabaabdcdccaacaaadabacccbcddbcbdabaaaabdacbbbcdcabbbbbdbdddddadadccbcacbbccdacacaaccdaabccdcdacadbacddbaacbcbcbbddadacbaacddcbccaaddcdbdddbddacdbdccbdbddaabacbdbcaaabcbacbdcbccdabccbdbbddacadccddcdbcacdccbdadabbdcccabdbcdcacabbababdcabdaabdcdbdadacccddbbdccbadaacabdbccbdadbbbadaaabaabdbccbdbbbcaabbcbdcaabdcacddbdcbddcbacbaacdccaddbdadbcddabcdcddccbacdcacadabcbbadccbcdcaaaadcddcddabddaaccdacbdbcdcdbcccdcabccbdbdabcbdcbccaaabddddcddbacbdcababbbaabccabacaaaddbacddcabdbbddadddbbbacbaaaadbcaaadcdddcacbbbbcbaacabbcdcaaddacbbbaaccbbcadcdcbddbbcabbddcbccbaaacbcaabdbabdaccabcacacadcbbadcccdaddcdccdaacacbdcddaabdbdbdcbbbcdcadddaccaccdddbdbaacacdbcbcaccbbbaadbcaabbbcccabdabccdbbbccaaabdaddaccdcdbbcbccaccadccbbcacddbbbcbccbabbcbbdadbdddaabcbbdbbdacdabaaccaccbcdabbdcbbddcdbdabcccdbccacdcbcbacbbbacbdbbddcabbadbbbcaabdbbbddabdaabbdaddccdbaacbabadbcbabbbbbcacdadccccdaadbcabdbdcacccacadcdcadbaddddabcbabbbbaacbbbaddddcaddbabdabadbbabbdcdabcdbcbaccddbaadacbcbcdacacabdddccacdcdbcaabccaabccaccbcccabcabdbddaccbdbcdcdacabcdbdcacadbbcdaddbcdcddbdbaddaddddbddbdabadbccbdacacbabbbbccaccacccdbccbabbcaabbbbaaaddaddaaddbdaaabbabadaccbcbcbadcdcabadbccdbcdaacddddccdcadccdabccaabcbdacdcbaccbbcdadcbdddabacaabcdabcddcadcaadcaaabaddcbdaddcacbbabadddccbddbdcbbdabaabcbbbaaabcacbcbaadaddddacdcaabbdcacccaccbccdcacabddcdaabbccaacbbbcbcabbacccacdbbacbabaaacdcbbdbdcaacaaaccddbdbaccbaccadddadadcadbdbcdadbbbcbaadbbbbaddcadbbabadcdbacdaccbdccccaccbcbddbaacbdbacbbcacadbdbcadaacacacbcbdabdccccdabbdbdacdacadcbcdaadaabbdcaaadcbcbbdaadcbadccccacddcacacdddcaacacbabacaaaaccacbcddcabbaadabaccdddcbadcdbbbadcbdcbabaabaddddabaddccdbbcdabcccabadcddcddbcddccabdaabbccdadabacdabcacbaadcbacabdaacadadcaadcdabaddccbdcbbabdcbbdadcacdcacbadacacdccacbdcdbcaddcddbdcabcdddbdbdaacbbcdcacbacabadadddbadbdbcdaabbabaddcacabbdcccbbdcbabcdacaddaacdccbacdabcdabbadadbdccdabbbababbcdcbddabdbbadbcdcbcbbbbaaabbdbbcddcaddbabbcdababdcaaaaadbabbcbccacddaabccbccbdddbbdcdadbddcbacabadcdadabcabcddcddbddbdabbdbcdaabbcaacddccaaaabbbcdcbabddcddacacacaccbcaadbbabdbbccdddbadcabcaaccbababbbaddadcdaddcabdcbcdddccdddbddccabdabcadbaadacdbaccaadabcccdcaacdaabdcabddcdcbcbbcbaacbcddacbabcabdddbdcbbdcbaabaaddcbcacbbadcbbbabcbccbbabbcbacddbcbaababbbddabcabadcccacdbdbaadadcccaacacbbaaaddcdbaaaccadacdccdcadbcbddcacabcbccbabdddabbbbccbbaccaaacabccbcadaddadbabbaadcdbdcccbaddaccacbbcacabddacddcacdbcdbaddcbcbadbbabddcaadbdbaabbacaabdcbadcccbdcccdccdbdabcdadddcdbaabdaacbabccdbaddaddaccaadcccacacddaacbcadbacabbabdacccddabcddccdbbaacbbdaccddaccdacccacdcccdccccdacdbaccbbdbadacadaaaddcbbdadcabbcdddbdaaddaccbdcadbacadddaddadbdbccadcbcaadcbddacbdaadcbcdaaddadcdcccddabcacbcdbaccccacdbdcdbbcaabddababbacbdabcabcdbcdbacdccdccadbccacbacbcadbdcdcacadcddbacddcabcacccccaddccaddbadbdaccacdbbbddabadbaadbcaadcdaabcdaacddbdbddcaaddaababdbdabdcddbdbccddccdccacccdaccaaccdbbaccdbdcdaaaddddbdbdbbbbabcbadcdbdddabadaddbbbacaaacabbbdcdbabadacddbddcbbcbababccddccaaaccadaacdadadbbdaabdcbaaccdaacaabbcabcbabcddbdacdbaaacabbaacbbbddbacbdcadcdabddcdcdcabccdcbdcadbbbbddabbbdbadadcbccdbbccbadccdbcacdbbbaabdabaabadcbdcbddcbdddabaaacabbabcaaacabdbdbcbdcabdadbadaacdbaaadbcaddacdbbddcdababacccaccacbcacdaccbbbabcbbbdbabaaadadabbcabbbaabacdbadabadddcdaadcdbddbabddbcdcbddbcaaddddabbdcbabbcababdbdcaaabbdcbdcdbddccbbbccbdddcbcaddbacdaddbababcdcaadbdcbbdcbacbdcbaadacdbaddbccbcdcdadaddcbdabcbbaaddbbaabcddacaccccadbddbccccdbbdaddbbdccbccdbbbcbbdbbbddabbddcacacacbcdccccbcacbaccbaddcaddaaacaddcacdaccccbbbbcdcaaacddacddaadddacdbdbcdddabdbbabccddbaadaabbbbbaddbbbddcacbddabaccdcbaacdcdcbbbcbcbbbacbadcbbcaabdbccbacaddbbcacabdababbbcbdcaddcbdcabbdabddbbabcdbbdcdbbccbccccaddbabccbddacacddbccacabbaaddabaabcbbadbdbbccbcbdacbcccdaddbbbbdaadbcdccbdadcdddbaabcdbccdbabbbdcdccbaaccddcadadacbcaadbbcacaddbacbacacbadaadcaacacccbdccdbaaadbcddddaadcaadcdcddadacbdddabdccadcccdcacdacdcbaabbaccdaacccdcddacbbcaaccbbddbbdadacbcccaababbabbdcdcdccbcdbbadabcbaaaaddaaaacaaabbcbaccacabcbaaacaccdddccaadcdcdcacdbdccdbbbbcaacdbcaaaccbdcaabcdddddcbabdaccdcbbcdbcdadddbdacbcadabcbadaddcdabbbbcaaddabdacabdbdabdbcabacbcccddbbdbbcbacbdccaddbdadcbddcbdbaadbdddcbadbbbbddbcdadcdabdadbcdaacbccbdcabdbabbdcbbabdbbadabddaccadabcccbcacdacccddbcdbddabaacbacddbaabbccdabdadabdbbadadcbdcadcbadccaadcdcdccbbcbdbbcdbdbbcdcdcdbadacdaaadcccabbabcbdaacdbcccdddccdabbdccdddccadcbadbdcbabcaacbdddaabaddcabcbcbbcbbbdadbaaccbacdbabcbbadddddabbddcbabcabaddcdabcccbbaccadaddbddccdbbbbbcccbccccdadadbbaaadddacdaacaabbdaadaccddaddababadcaabbdaadaaddddbabdcabddddddcaccbcadabbacbcbaabddbbdcbabcabcadabadcbddabbbabbccaabcbdddddcccacadcbbdbdabbcdabbcbddabcdcadbddacacdadbaabadabddcddbcdcddcbbcdbabacddbdcadaacaadbdacccabdbdbabacdaaaddbaabccbaacbddcacabcacbcdddbaccddababccccabcccdcdaabcacadacdaaadbbbabdcdadcbbaddcddaabaccaababdcababbddccadbdcddbabdcbbdbddddcdccdbbadcdadcadbcddbdabbcccdcdbbaabdcbddccbbcdaddccbddbaaacacaaaabaacbcacacdabaddbababcdcabcbcbdaaacccaabacacdabdabdadcbbdabdcdbdadbacddbdcdddabdabddbadacbacbcbdacdaadabacbdbdcbbccbabdcabcdbdbcbdbcdbadcbcaadbdddcaadbcabadabdbadbcdbbcbddddcbcbbcdabbadbdabccddaaaacbddcbbdadbbbdcbcbcbbccaabdcdcaccdabcbacdabccbccdabcdcdadccbbacbbdbcdacbdacacddbcddcdcdcdabbcbdbabaaccdcbdcaadbacbdadccddaadbdcdddbcabbadadbcdaabdcadbbaccccdbbbbabacadabccbcdbacccbdabbaacabbdacdadbcabbbbadddacccbbccadbadddadacbdcbbddcdaccdddccbbacbbdcbdaddadaddabccaddcbddabcbaabcddbccaccbadaadbadadcdbcdddbcaaabdcbbbcbdaccbdbdddcdcbdabdbddcbbabcaadaadcdccddadccdadcdbdacbccdbdacddcddcbddabbabddaaacdadccdbbcdaaaccdcacaacdcabbacdcbbbcbbaacacabaccbcbaccdbcdaddacddcbbbbbccbcdcdacbbccdcdcbbbdbcadababbbadcbbccadbaaadcbcacaaadbdcdadbbdcabdcaacabacddacaaaaccbbcaaddddcbdbbadcccbcbbdacabbdbdaacadddadbcdccacdadbcddbacacbabbdabacbcddbbdddabdcdaaaccbbbcdbbbbabcbccbabddbdbdcdbccddbcadbcaadcbcadacbddabdcbbadcbbacdddcacadadddddccdacdbbacbacdccaddbdcbbbcdbbaadbbcdacbccccbdabaacccccdbdadcdddbbaddcaabbbdaacddacbcacdbdcabdbcccbaaadbbcdcaddddbdabadbbbabdacdccdadbadcbbbdcadcdcdbddcdbbbdbbaddadcbbdcbacbbabaaddbbaccabdbdcabdddbbdacdddacaabdcddccacaababdddcaacdccdbdadcbbbddcdbabcaaadccdbbdcdbbabcadccaddacdccdcdacccbdadcadbcdadbdccabadcbcaaccbaadbcdcdddccbadcbdcdbdccbbaaadabdabbdcdabdbccaaddbbdbadaccbcdabcadaddbccaabcaccddbadacbcccbcbcacbccdacdcbccdbdcaaccbdddabcdaaccbcabdcbcacccdacbcbddcbdddccabccadbdbdacddabbaaabbcbdbbbcdabdbaadbddcbccdadcbbddbbadcdcaacdabdadcddacccadcaddddaababdadcbcdadbbdadbddcaabcbccccbccabddcaaddcabbabbabacdaddabdbcdcdbadbcbdacadadcbdcdaaabbcdbbdddddccadacabcbccbacbcaacbbdbdacbaaaccacdbdabcbddadcbacadcabacbbbacaacaaaacbdbbbbabaaaddbdbcccbabcbdcababbaaaaaaacbabdccbbdbdcdbadcabbabcdcadcddadbbbbbcbcacdccbcaaaccdaaccadcdbadddacaccabacbacdbcaaccccadddbcbcabaacdbacbabadcbacbaaaadbcaabdcbddccdddacdabaadbdaaadabaaabbcbbcacbacadddcaccaccaaacccccbadcbdcdaacbccddbcdadbbdbaaabcdadbccadadccaddcbddaccdacccaaadbdddbccadcbabbbdaccaaddcaabacdcccacdbcddbbadcdcdcaacbddaadabbddbcaccbdcbababcdaacacddbcbbcaacbddcdadddbadacadacbccccdacbcbccbabbabcccdbaaddcbcddcabdcbccbaaacbdcbdcbacbdddcdddabadabcbcaaaadcdbbbabdaabcbccdbbaaadcaaaaacddabbdbbbddcaccccdbddbcbaadbbdaccbcabcbddcadbdaabdcacbacbaacdddbabdabaacabdbcdcbbccccdadaaadbdcabcccabcaadcbacabcbdadaaadbddaaabbdcaaddcdddddccdaaaadabbbadcaddbdcaababacbdbaadcacdbcbcdaddcdbbddcbaabbdbaacdaabbcbcdbdcddcbaacdddabbbdadbdaabcccdcbabadcaacacddaccadbadbbadcdbababadbaadaacbaaabdaabcdcccdccbbddbbdbdccdbbbcdccbbbbdbddabdbacbddacaccccaddbcbbddddabcaaccdabddaaddbabbddadacdaabbdcccdbdcadcbbbbdccbaddddaadbabdaaccaabcdcbbabcdaacbcbabcbddaddcacdcabcabdbabbcacadccdacbdbbbbadcdabadcccdbccabbbdaaccadbcccbcadcbadabccddabbadccdbcdcdbbcabcaaacdcabdbaadabdbbdccccaddbdcbdaadbcaaabcbbcdbaccdbadcbaddbaacabddadbbbdaaddadcadaadcacbbdcacbcabadabbabbbddcadcbcbdccaadbdcdadbbddccabdcadbddabcaadcdbcbcddbcabdadbabbadcccdddadbcaaababdbdaddccbccdbdbdbaaacbbbccbabcacdbcdbacdcabbbbaacdbcdccdbbddddacadddddbbaadcccbbbcbddbdccaccbdcbdcacacdaddabbcdbcddcadadcccdadabacdcbcbcabdacadccbcbdbbabdbbcdaabbdddaaacadacddcdadcaacddcabbcacbbbdcadcaadadcbcbccbbabbcddddcbdbddcdbaaabddabbcaabacabcbbbccbcdddbcbcdccdadcbbabacabcdcdabaabdadddbbcdbacaaabcacdbbbddadbbaccdccbdccbbcbacaacbbaabcccbadbbbdccacbdbdacadabbcacbbcacababbccbbbbdbdbabccabcbdbcabbccacdbadbcabaddcbbdcdacddddbdddbbabbbbbcbcaccaadbabdddacdcdcddccdacacdcaaacadcbbaddddcaabbdabddabbddcadcacbaddbbdaabdbbcbadcacadacbabcdbccdcccaacabadbdacdddddabbdcaaaacccadcdbdcbbcdcddabcabdacaadcdcacdcbbbabcbcbdaaaababcbccabdbdabaabacbcccbccaabccadaadcddcacaccabcaccbaacbabbbdbddbababcbabaccabccbdddacdbdbbaddaddcdbaddddadccacaaaddacbbadccdabdabbcddbbdaadadacdabacaabbbbbbbcacdadcadcaccdcaabbcdadbdacbcabcbbdbaadccddabddccbcdcddbdbcddcccccaabbccaadbcaaccacaaddcbbcaccccdbcdbabbbabbaaaadbadcadddbacacaadcccacccdcbcdbdcadabcbabccdbabbbddbcdddbacdbdabcdbbcadddddddabcaababcbcddadddcbbcdbcaccddadacdccadcaaccacaccaccbddcadbcaacabcbaabbdddddcdbbdcdadbbdbcaccdbacacddbdcadabbabbacddbbbabdddbcbdadcddcdbabcdbbcdcacdcbadbddddadbccabbbcbccbddabaacbccaacddcbdcaabaabdcabcdacaacdacabdccdcbccdcbbdddcbbbcbacdbbacbaacabbadbcabcababaadabddbbddccdadddddcaddacddbcdaddbdcadbcbcdaccacbbaaaabbdbaadcadaabccaddacabbbbccdacbbabcaaabbddaaccbbcadaccaacdbbbcbcdcabcddcbbdcccbdbbbdbdabbacdbbabaddacccccaccbbbbdadddccbbdcdaaacadcccbcbbcdbaddcabdbbddbbdbbabcccdabdadbddaaadbcdbabdabdacbbdaacdddcbdcacccdcdbddbbabccadddcabaadadabadacacabcaaabadcabadbcbcbddcacacccbadcabccbbdbaadadccabddcbcacbbdaadbcddadcbdacadababadccddcbbbabdccbbaaacbbcdabbcbbaabdaadbcaccacbbcbcdbcbbcbdccbdaddaaaabbddcbdcbdcabdacdaacbcdbccdaabddadcacdadbbabccaadbbdcdcbdaabacacdacccbdbaacabdaacbacaabcdadadcabaabbdbacaabcccccabdcadcccacaabaabbcddddbbacbaaccbbbaacbbddbcbdbbcdaadcdacdabbdcaababbbbbdcdcdacbcabbdaaddcbdbcdcdbacdcbadcaabbcbbbbabcdadbbadbbbcbdbcbdcbcccbaabccacadadabbcacbacbadacbdcdbccddbbdadabcbdabdddbadbbdcccbbadbbababccdbbabbbdbadadcabbbaccaccaaaaadcdddcbacabddccdbbbaabbcdccaabccadbacbdaabcabbccbbdbcaddaccbcaaccccccbbdbbdacacacdbbdcdccbdbbadddaadccabdcdabcbddbbbcbbabccdbccdacadadbbdbbbabadbdadbbbacaaccacbdddcdcabcbcaadccabadbdbdbcadbcdccdccbcbaddcbdabccdbaabccaddcbabdccdbabbdbbadcbddacbddabbcccaaccdcaccbdabbbcdadacbdbcbbbaabbbcbcaababbbdabdadbabbaccddddabdadaadaaabdabdcabacabaababdaccdaccbdacbdddabcabcdaadcbddaddddbcccdabddbdbabccaabcddddcbcaaadccadadaadbcdccccaaadaddcdaccadaccbaaddbadbcbaadcdbadcaccdadacdbdabbabcdabdbaadaabaabbadbdcdaccbadaadbccbcdacbbbddacbdaabbbabaacabdcacccbdcaccbcadccababcabdcdcadbcbcdbdaaababdadbbbbaabdcdcadadcdabcddcdbabaddcdddbaddcccdaaaddccddacbbdcbdbcdbcbcaadcbbcdcddbacccbbbddbddbbcadbdbdaacbdbddbbbcbbcaacddcbbccadbcdcccdaabdadcacbccbdaabccdcbbacbdabadddbbdcaacddddaccbccbacbcbaadcbddddbcaccccdcbcccaaddcdcdbccbdbddaadbdddbaccccdcddacabababddbccaaccdaabcaddbcdbbddbbddaadcbbbcbcbdbabcabbcbcadadccddbcdacbbabcbdbdabbccaadaaacbdbbaacabcbbadcbaaadddbdbcacdbccdcabbcabbabcdbbabbcbccccbbbbcaabcdddbabcddaadbbdadcbaabbaddddddcddcaadbabdbddcddababadacdaababddbbbaccaaacccbcbdcbadbaaddbdbbacaacddbbcccdccdbacddcdbbbbdcdcbcaccacdddbaadccbdcdcdcddabaacdbaaaaabdccddbcabcaacdadbdadcdaabdcddbdddbbddabcddacbcdbdaaabdccdabdcdabbcccdaaaaacaacdbbbcaacdcbbacbdcabddccdbcbacbaaabdddadddcdcbacbabbbbccbcddddaabcccbdbcccdcdacaacdcbddbabdabbaddccbbbcadcdcbbdabbaddbcdcacbdcbcabcbbaccbbbddbdcdcacaaadbccdcbcacaacabbddbaabbabcacaccaaaccbbccabddddcbdbbddcbdbbaddbbcabdbdcbbcddababbcdbbabdbadadddbaadcbbdaccbdbdabccdadccdddadadbacaaacaaccbcbaabccbbbcaadaaacddbacdbcacacdbbaaaaaaacdcdbbbdaccaccabdbaadbbbbbcbdcdbbdadddabaacaaddbcddddcbbbbcbdbdccbabdcbdcdcccadbadabddcdbabacbcbbdbddaacbdcbabaadcbadccccbcbbaaacdcdbdbbdbbcaddcaccaccacabbabaadbccadcadcadabddcdddaadcdcdaaccbbbcddacadabacacbcaddcddacacbdccddbabacaddcadcadbcdacabacddbdacbdbdddacadadcbabbdbbadddddbdbcadbdcbcaaddbaaccacabcabbcdaabacddabbaadddcbcbaddabbadbabcccccddabaadbbbacbdaadcabaacdbdbaccbabacabcaccabbbacccbbdaadcacadbddcdadcbbadcdbddbbdbcdabccadaaabcbabaaaddaaaadaddbdcbbacbbacbcdcbaaacaadccaccccaaaaaaacccbccadbcbcbccdcbcddadbdabccadcabcaddcbaccaaaaddbaacccdcbbcabaacacbdcacdabddacadcccababdbdbcadcacbbcbaddcdaacacdcccdbacdacddddbcdcaabbaaccbabadbaacdcdddabdacabdabadccaaaccbcbbdbbadcccbdadcbabdaadbdcadabbbbcdddccdcbbbacaccddcacaabdbbbcaddacdaacccababcadbccbadbabbbdddccbbaacddadbdcbaabddcdacbcbccbcdcbccbccdddcdcbcbcdaddbdaaddaabcbcaabcacadcdbdbddccacabcdcbbaaaacbacbdaccacaaacdccdddcabdaaccbcbcddbcadddbbdcbbbcbbbaacacdcdaadadbdbddccadacacbbcbdddcaabcdcabdaddacdbacdacddbacdacddbbdaaaabcbacdaadcbdaaabcbaaabaabbbacbcdbddaadbbbbdababbacbcdddcccadcddbdcdbbcdaacadabbbbccaddbcccbbbbaacabaddadacdddaacadabbcdaaccbbbaaabddcbabadcabcdbdaadddabdddcdddadcadbcaddccdaaadcbbbdaacbadcbbacaabcaabdabadbbccbcabadddcbbbdbbccddccbccabddaaaabbaddbcbaddcadcdaaaacaacbdcbbddccadadbdaccaaadcacacacacbcaaadabccaddcabbacddcbddccabbbcdccbdaddbcaaddddadcbacaaacdaaabaabcdcddaabdbdbdddadbbadaaabcdcbddddaaadbcbdaaccbacabddddddacabbdcdaccaadaccaddddabadcabddadcabcbdccacbcaddbdbadccdadcdaccbddbaaddcbbdbccdaaadbbdadbbdbcccddaabaaabddbddcdbcadddcddcaccbbdaabdadabcbabcaccadaaadcabcbdddbaadabbabdcdcdcdcbabdbaddccacdabadcdcdcbbddcccccacbaaadbcaacaacabcabbabbcaccacacbbacbbcbbbabaddcdbabaacddbadbdbcccacbacaaddbcbddcbbccdaddbbaaddadcbdddbcdabccbddadbdbaccbbdbdbcdbadcddadacdbaccabbadcbbabdadbcacccbabdcaacdabbbaaabbaddcbdbcacbbbaacdbcccacddcadabcbbbbbaccdbddaaccabbacabbcccadaacaaddabccdaddbabbbdacddabbaabbcdadccdbdaabcdbccbcbacadcabbacbadbcbbdaaaadccbdacbcdcccababdacdddbbdbcadbacddddcdddadbcdcaccddbccacaaacccdabababdcbbbcaabbacdccaadcdbddabbbcbcaaaaccbdbbccdbbbacababbdadcacaacbbadbaabcbacaddcbbcdaaabbcbaabbdcbabdcddbadabbacbcbacddaadaddddbaaabadaaabdcbaadacbbbbbdbaaddccccbabaabdddacddccbdcddcbbddabbdacacbbdaaacaccbbddabdcacaadbbddabdacaddcabbdbdabbcdabdddbdabdcdcdbbdcdcbbabadadcbabddcdaccbaabcbaccdbddaaaaaabbbbbcbabaacaaccdbaddabbdddccadcdabdcbcbaabdaaaddbcbbdcacddcaabcbbdabbbdddbdcadbdaccdcddbaddadadcadbcaabcddbdcaaadcacbdaaaadbaacbcbdbaacdabccacaadddbacddabadaadadccdcbdadbdbabccacbdcbcbddbbacbcbdacbcaacbdcaacadcddaddacbdaabbaaaabbddabbadcbadbddbbdabcdbcaddddacccccbcdcdbbcdbbbadbbdcccdddacaaacdddabbbbccddaacbbbbdbdbcddbdbdcaaaabababaabcdbdadbbaacdbdcacdacbcdaddaccbcabacbbccdadbaaabadabbcadddccabbccbbdadcdbaddbbbaadaddcdabdbadbcbdabcababddadcaabdddcdcacbacbaddbadbbaabdadacdcdcdbccbaadacaaddadabccbadcadbaccddbdcadcdbcdcddbccdbddabdadbbdabddadabbbcadcdcddbabddaadcbdacaacadacbbcbccdbdcbdcdcdaadaccddcdcbcdcabcbacccaacdcbcabbbdbbbadcbdcadcaccbccaadcbabccdbbabbacbcbacbcaadddacaaadccbddbdbcddcababbdddacdadcadadccdbddddbbbdacdcdbbcadcccbbdbcaacdbcdbccbabaabaacddaacdbbadadcaabbcabaddabbbdddcdadabbdbdbacadabacdabbacbcdbadabbacaccbdaaddaaadcdadaccddaadcabdbccdaabcaadbbadcdbbcccaadddcdccccadadcaabbcdaaaddaddddbaaacbbccbcaabcdccdcbdbcaacccddbacadbcacccabacddcabcdddcaacadbbcdddadcabbbbbdacacbbdddddadabdcbaaccbcdabbdcbdcccadcdcbdbaccddaacdcdcdcbbddacabdaadbadbbcddaabdadcdaacadabddbdbabaaccaccbabadddbcbcdbbccbdccbbddaabacdadbcdbbbcadbcaacdadbbdacbaadacbdbaadbcdcbbdadddcaadaaacabddbbccbbadccacbaaddabdabadcdbbdcbdcbbcbbbacdcbbbadddcbdadcabcbddacbccccdcbbccbbbbbcabbccccaacadbbdcdacbadccabbdbdcbadcbacddabbbccaacabdbcaaacdaccdbaadcccaabdaccbbacdcddccbdadbbaadaabbddccacddddccadbadbcdabaaababdaaadcbbbdcbddddddcbdcddbccdcdaddbbadbaddbadabbcbdaaaabacdbbcbadbbddccddacbbbdcbcdaaddbccaadabbccbdbbdccabcdcaaabbbcaacabbcddabacdacdbdabcbbcabababdcbcdaaadddacbabadbcdcabcbbddadccddcdccacdacadbdddbbdbbaabdbbadacdddcbdacabdcbcbcdbadccabdbcadaaaddbabdbbacdcbabdbcdcabccccdcddbbddacbadcdcabbadaadccddccbcbabbadccbdbadaddbbbacabbcbbbccbcbbcadadcaacaadadbacdddbbacaacbabbcdbdadcdbbbccadcaaccbbadadbdcddbabbbbdccbdbaadbdbccbbcbaabbaaadcccdcbdcbdbddddcddacbcdbcabaabdcbdddcbbcdacaabaabdcbcaabdbabcbddccdcbdcbcacbaaaaacbacbabbbbbdcddbccacdcddcaddccbbbcbbaccbdaccdbccdcabadcbccbbadababbcbccadabbcabdcabdcddaccddadcaccabacbcbccdbbbacdcbcddcbabacdabbcaabbbdbcaaacbddbabbbccaadcccabccabaaddbcabcddbbddccdadbccdbabcbbdbccaccdcbadacdaddccabddcbccdcdbadabbbbaccabccbbabdcaccddcabdcaacdcbdadcccccacbccbcddbccbcbddbbdcdbdccbaccccdaadaccccccbabadbbdabaabdaaaabdddacaddcdabbdbdbbacbbabaccdccdbabbaadabadcdaaddbadddcdcdcdcbcdaacdcdcccccdaadcdcbcbbdadbabbbdaadcaadadcaabdacddacbbcbddbbdddbdcdcbbbbadddccdbddadbcbadbabddccdaabcadbbcdcacdddaaadaaadccccdddbbbadcddcdbdbdadacccbbbbabcacbaccaccdbccbcaabcbaccaaacbddadcaccdbaabbddbcdacadbdcdcabbbddbabcbbdbcacabcbbbabddddccddbdcabccadbbaadbcbcacacbbbacccaacdabbbadccdcaddbddadaaabaadabccaadabcbbcdccacddcdcadaaadccabadbcacbbbaddbbddddcdabccacdddbbccbbbbbaccddddadaacbcbbcdcbbadddbcaddcdddaacdddbbcbbdbdccdddabccbabcccdcaadbdbdcbcbddaadcbabaccadcabacccdbddbddacbdcabdabbdcbdaccbadcadddcbbadacaadbacaadaacdadbbcbadabccadccdadcdacadacabccbdabdbcabccddbdadccdddbccdbcaaadcbbbbabbabddaadcbbdabcbbcdbcdbbddbbddcdbcbdaccbdcadadacabdacdcaadbdbadcdcddcbbcbdbdabddaddaaaaabcbbcdabbcbbadbabddadbdacabaccaabdbdabbaccccdcbccabadadddbdcccdbdccbccccdbcaddddbdccddbbacbdcdbdbcbcbaddbdcaddadbddbdddcadcdbdbdacabbaadcacadbadbabbaccbdccbabcccbaaacdacccddccdccbdcdbaddddbaddaacdbdacbddbdcbbacdcbbadbbcacdbaaaaaddabaaaabdbaabdbcbddcadbcacbbccdccdbdddaabcaccaccdabacdaacacccccbcdcacdbcadcccccbbdddadcdcbaddbaaabcbccccadcddaaddccdcbdadcacbdacadddadcdcbbdcdbccbcdaadccdcabddcccbbbcddccbacabccccdbddcbbcbbdcdacdbccdabccddbbddccabdcaaaacbabbbbdbdcadcacdcbdccdcadabbcbacdaaabcacdcddaddddbbacaccddcaacbcdcababadbcdaccccdcaccdbdaadcdaddaadadadddddadddcbbabcbccaccdddcdcabdaddabaaaababdccbabbdbbdbbbccdbabbbccaaaababacdbcdaadcdbdabcacacbabbbbdccdcdaadbcbacbadccbbacddabaadbdddbaddddadaaccbbccdadadcaddcadaadaaaaaddaaccbaaccacdcdccabbaaccbbbacabcbbcababcaaadddcbdabccaabdbbbaaaccbcddaabcabbdcbdaaacabddabaacccaccbbdcbdcbabdaaccbbdcbcaacddbbbcaaabbabacdbcdddacddbacbbbcaadccabadcadacadddddaabcbbcbabdbbaaaacadcdadbbdbcaadbbbddbbccdadcbcadcccdbbcdcaccdaaddbdaddccbbddbacaddcccadabbcacbbbcdcdccdcabbbdaddbccddbcdcaacaabdbbddddbcdbbabaaddadaaccbccdbcabcbaabdcbdcaabadccccbccddccddcbdabcbbacabcaadbbcacbaabdbdcadcaccbbbdcdddcaadccabccccaadbccdccdaabdacaacdabbaccdcbdbbdacccbcddcdbaaddccadcbacbddddccddaaaacbbaacbbabacadbacaadbaaaccddbcbaabadcdabaccbaaadcbcdddcddabccbbaabccabccbbabaddddcccbaaabcaddbadacbcdabbdddddabbccbbbcadbcabbcccccabaaccbabcdcdcdaabcccdcadadbacbcdccabadcbadbbddbdccdbbabcbdcababcddbadcddaddbdcddababaaadabbbbbdbadbdbacdacbabbddcabcbabadacacdadbaddcdcbaadbbbaacbdacacacdbbbddabaaacaadbbdcbbcbccdadcabbabbcbabaacccaabdddcbcbddccdbacacaadaabddcadbdcccdcbcbdbadcbcbaccabacdddbbdbbacbaaabccbbbcdbbddcdbccbccbdaaabbbbddbcccabbaddcbcbbcbadbcbddcacaaddbdbccaaabadbacdadbdaaaadcdccabbadbbadddadadadacaccbddddddcbacaadddabdbbcddccdddcabdbacddadabbcdbacacdbcbdddacccabcdbccbbbdbabbaccabcacccdabcccbccdcaccbadacbddbcdbbcaaadaacdcbbacacacdddbbbcbbbbababcaaccbcbccacdabbabbddbcbdadddaadccacabbbbaaddbaadadccdabdacacacadddaacadbcbdcdbbacdaabdbdddbcacaddbcabcccababbcccadbabbbcbaaccaacbcaabdbccdadbacdcbaaacdcabcdcbcdcaacaabdbdbcabbaddbaddbdcadcabbddadaaacabcbcdabbcadccdadacdddcddacbabdabbbaddbbcdbbbcabaaddabacccdabbcabaabccdcdadcddddadcbadaccccbcdddccbdacabdbdcdbdaddadacddddbdcdadcdbdaabadbbacadddbcdabccababdadbcdbcddbaadbacbdbdccdbcdabccdbccdcdbcccddbdaccddcbddacccabbacdadbabdabadcabdbdddadcaadacccbaabbddddaacbbaacaadbdaddbbadcadcbdabcbacaccdaadddcaacbddaadcadadccbbcccbacacdbbbbaabccddccdbacddaaccbaacbadcaddabccbdacdccbacbcbddbccbcbccdbdbdaababbacdcdbacbdabacbabacbcdadcabadccdcdddadabcacbdcaddadbbcaacbbcddccacadbacbcbcabbccacbbbbdbbbdcddbccbaddadaddaabddbdacaaddbdbacbdaaddcdaaaacbbbbcbbcbaadadaabbbacbbccacdcbbababdccccddbbdbaccdbbadcabcbdddbbccacddcbbddbacabccacadcacbdabbaabbdddddadcaaadddadbadadaccdabdaacbcdcacabbadbcddbbaabbcadacdcaabbccbbabdacdcadbdbadbdbbdbcccdadadbbbbacbbdacabbdbcccadbccbbaabbbdaaddaadccaaaddabcbdbacdabdbaccabcdbbdbccddaaacbdbaaabcddddbdabacdddbaadaddabacbbccdccbaaddcabdaddadcaaddcacaacbbaadaabbbdbcadcbaabddccdbcbcacdcaabddadcadcabddcbbcdaddbaddaaabdbabdcdbcadbddaacabbbdcaadcadacdddcaadacdbabdbbabdbaadcbcbdcbdcddabadabbbacbdcabbdaacbbbdbcaaaaaccdbddcddcbacaddbbadbdabbdaacddcdaddbbdaccadcccabcabbbccccbacdbcabbbddacaddcccdaadacdbabbdcdcdabcbbacaaaccdbbbbacbddbbbaaadcabcdcaadddcbcabaaaaaadccbcbbcacbcbacddbadcdbbbcacbdbcdabacaadcbbadacaadcbaddaaaababacdaccbaabacdcccddbabcacdbddabadbbccaadccdbbcdbadbcccddcddacbbaccaddacabdbbbdbaddcdaaccddabaddaaccbacbbcbabbbabbbbdbadcbacabababacaacdddbcbbcbcaaaacbdbcdbdbdcbccaaddacdaadddbdacadbbcadaacdbccdbcdcacdcabacacaacbcbbcbacacaacadabbccbbadcbbcdacdbcdaaaacdaccdbddaddabadabbabacaddacabdbcbbdaacddcbdaadcdbccdaadddddbadbccbbbcdcbcbdcacbadbaccbccddbbcdbacaacaaadddcabbccbbccbaadaacccbaacaadbddaccadcbcdddcadccbadddbdacaccbcbcadacdbbcccdadccdbaaaadccadddaddaaabababdaacaaccaabbacdcdcbddcaddbbbbcaaaaabacaaddabcbcbdabcacdccdcbaaadbcacccdadabaccdbbbcaddddaacdbacacbdcddbcabddcdbbccddccaccadbccababdcdadcaadbbcbcdddbabddddbbcacadcbdbcaaaccbbbdccdbacacdbddbabdabcbddbacabdbacacdbabcddcacaaacbabdbaaaccddcadadabbccacbcbdacbdbdbbccbbabbacadcdababdcacaddddcdccbbbbacddbadbcaccddbbaacbbccdbbacbbbcaadbabbdabaacbacdbbddcdbaaccbdbbcbaacadccdbbabbddbaaadcbbaadbbabacaccdbabbbdadaacbccaadbbcbdcccabaddcacddcccbbdbbbaddcaddbabdbdbbcddbcadaddabbadccaaddcdbdddbabacbbbcbbcccbbccbbddbacbdcdcbcddbccdbbcddbbbadaaabaabaaccdcbbcacbbccbbcdbcacddddbbdcbadbbabababbdddbdcbaaccddaddabbbcdabdddadbcbadbabddbdabdcddbbadadadcadcddbbccbccaabcabbbabadbbdacaabdbdbdcbccbbccdcaaacabcdabdcdcddbdaabaabbcbcbdbcdbdbbddaccbdcabdadbaacbccdbddbdbdcabdbccbbccaaaccdddccbdaccacdadbcabdddccdbabbbccbbcabcbdacaacbbdcccbadbbbdacbadcbdbbbcacddabdddcadadcaddadcaaccaabdabbdcbbcadaadaccbbbddbbdbdabccddbabbcdacabcbbabddaacbabdbcacbddadcdcaacbcaacddcaccbabbbbcdddddddcadabcadacbccdaabdbddbdadaaaaadcddddccbbcbbccdbddadccbdcddcabbdcadccabbbbaabaaddaadccbbbbbadabdcbadbdcacbcddbbaaadbcddbddbbbacccdcaccdadbdccadbbcbbbbcaaaccdadadccbccddcdabaaddaadcaccadbccbdbdacbdbccbbcbbdbccdcbaddacbabddaddadbdaadbbcaadbdabbcdcaacabdbbaddbaddbacddbbbbabacacddcadaccdbdbddbbbbadbbdbccbbccbdabbcccbdacbacabdddcabdacaccdcbbcbaabbaddbadcddaadaadbcdcdcbccbbacdbacdbccaddcbbbaddcababaaaaaadabdbbcbdaccbdaaabdbabaadcccdabddcacccdbbabbdbcabaabcccdaacdcabdbcbdabaccbadccabbdbabbdacccabdabbbcbbcaccdccadaabbbaaddbddbcdcbbbddcabbbaadcbdbacdddbcacaccdcaccaabccababddbbcbdddcddacadaabcaccddadccacaadbcbcbcdcdcaadacaaccabbcdaabaadabcdddaacaccdaaacbadabccaabbdddcbababdbbdbcadcaaaccadcacbabbcababcbabacddbddbdbcabbadcddcbdcdadcadbaddaaadcbdadacbdccccbbdbdcbbabcaadddbaaadcbbdbacbadcddcdaaaadcadbcadccdcdaaacddbcaccbcaacbcadbcacacadadaddbaabccbaccdaaabbdacabcbabbcbdcaabdbdcbbabcddcdbcbbabdccdbcdcddbddcbdcacdcddccbaaabccabbcbbdcbddddddbadcabaaaacdacbdabdadcdcdbacaadbddaabcdbcbccdbdddadaabdcadaaaabaccbaadaacaaacdbcccaacadccadacdcdddaccaabbbdbdacbdacdcaaddccdbbddbccacabbbbaccbcdaccabbdcdaaccdcccabadcbbaacbcadbadaddbcdacadbabcadaacbbbcbbabadaabbadbcacacbacdaadccbacabcdbcccbbbdbacbdcdddbabcdabadbaabbcdacdccdbabbddaabaadbbacadacaddddcabaaadcbdcdcccdcabbcadcaaacadcaccaccacbccbbbaabcccabcbdbbbbbbaadbdddacaaccadbadcdabdcccbabbcaabbcaacaaccddacacababbdbaddddababbcdcbbbcbcaacdbabccaccbbbdbbdaaaadbcbaadcdcdaaddddddbbdadabdcbbdadbaaacdabbccdbdbbbadbddccacdcdbabbcdcadbabbacadbdabbdcbabbdcbccacacdccacaacbaabdbbacdbbdcbaddbbacddcbbdddcdbbcbccbaaabcabadbbbdcdabbcddaabcdbdbbbbbbcdaadcdcbbbacbcabaddbabcddaaadadcaadcbdabbbacccbcdacabccdaadddddddcdcabcabbbcdaacddddccadadbaaaddddccbcababccbabacdcbdcbaddbcccbbabacdbcbbaadbaaaabaacbbcaaacbaadaabdbdadadcbcccbcaccaadccccacadcddaacbaadccddcdbbbdbabbdcddbbdcbaaaccbabcbbaaaaaabccdccadccbabaccabacaaccabcbdbdaddcdaaaccdcadcbdbbaddccbbcabdbaddbbcddcddabdadacdcaccadabadccacacaaaddcdadbbdabcbbcdbacbadaaddadbabacaccddaddddcbcdcccabcbdcccadbabcdbbdadacabbbddadccccaadccdbddadbcaacadaaaaccabbacddbcddbbbbabcdcbddacbadaaadcbddbbcadbdabdcbbbcddbbcbabcdabaaddbddcccdaccdddacbcccdcdadcdabcdabbcddcdbabbbadadadaccbcdaadcddccdcccbdacddbcdbdddcccadadaaaddbcccccddbcdbdaddcdaacdaaccaaccabdcdbccabdcbddbabdbbdbdddcabcabdcadcbacbddadabbbaadbcdbbabbdadcdbdaabddaadaadccaabbbcaccdaabaacdcddaadbcdadcccacbbcbabcacaabdddccddcabcddccdbdcaabbdddbbdcabbdbbdabaccdcacbadacdadddbddcccbcaadbdcbabadbbbbbabbbccccdbcbdaaabdcadbaddadbbdadcdcccbbddddcccbdcbaaddcdbdddbbababbbcbbbdddbaaddadcdbcbbabaacbadcaabdadbdaaadacbbccbacbdaabddcbbdcacccbbcacacccdbacaacccddcbcddbaabacdadccabbbbaddaabaaccabcacbdcdcddcccbbcadcbdabbcbcdadbdacdccacccbdaddcaddaacddacddbcbbabccddbdaddaaaacadacdccccdbbadbcdcdbbbccbdbabdcabcddbaccddbcadadccdbadadbdcacbbcabccadbccaabbaccdbdcaccabcbcaddabdcadcbcbbabaddddcdbbbdcbdacadccbbbbcadabddacaccdadcdbbccaadccadadaabacdbaaccacbcbdacacdcaddddbbddbdcbbcacabdcbcbcdcdcaaabaadddbbbbdcddbcdcbaddcbadcbccdbaddaccddcbcdcddccdccacacbcaabbacaababcadacdcdbcddcbdcaaabdddddcacabadcdcadbcadacabbacddccabbabddbddadacacaccacdcdcdaadadaabccadddccccadaaddaddbacdabadaadabdadbadbbaabaadabccdbdddcdaabbcbbddadbcadcccaabbbcbcacbcaadcbacccbdbdcccdacbdccaabcddbadadaaacddcdadddcadbcbbaacbadadcdcbabcbdbdbaacaadcbcbbdabaccdcdacccadcbbdbcdabbccccababcddcaaabccaaddcbbdbcbccbbacabccadbaacbbcabddcbbcbdcbcdaadbacbadcddadbacbaccabaabcacadcbccabddddbbadabaccadadabdcabccbdaacdabdbcdabbacdcbbccdccabdadaabdcaadbcdbdbadbaaaadbcbcdcadbccaacccddbadacbaaacaabdbcdcbccdbddaaccbdcbcabaabbcabcccbadcaddbcbcadcadaacdddcccadaccaaadacdadddaaaaacadddcbdacbcbbdbbbdcdbabcdbcbbaaadcbaabdaabbdcbabcccbcccbcabacdaaccdabbacbadbbdbaaacadcbbdadcabbdabbcbadcccbcccdcbcbbcdddacbadbbcacaaacbbdccbdccaccbcadcdacaabccbcdaaddbcbddaddccbbbbccdcbccdbcbbcaacbddabadccaacbcbcdaadcddbacbdbcaaadbabaaadbdbaaacbdbdbccadcbbccbccaacaaccaaaddbbccdaadbabadbabbddcabacacccadadbdababbbdbcdcddbbdcabadaadadccdbcaddccabcdabbcccaaacbabddcaacabbdaadbcacdabcddcdddccccbadaacdccdbdccadacdbcaacdbddcaadcacaddddacbdabcabcbaddddabbccddbdbcdacbdadbcbabccbdaccbabaddabddadaccccaddbdabaabccbddbbbaaaadaccccaaaccddccdcdcddcddbdabbbccbcbcbddcdababcabcbaacdcddcdbbdaabcbdacddccdbbddadcdaabddaaaccbbcdbdbaaddabccadbdcdbaababdbbcdabbbddababbcbadbcbccdabdaabccaddaccadaccbcdadbcbdabacabccccabbddcccbdcdadadcccbbaadabcddabccdddaacddabbabacabbbcacdadccbddcadbcdcaaaccaaddcbbabbcabbabbdbccabbbaddacdcbbbdbdadcacbbcbacccabdbdcadadcdbabbcbddccbbacdaaaccbddbbccbddaddadadbbabadbaaacabdbdcbaaabcbdbcdddccdbbbddbcabdaacbdacbacdaadcbabbbdddcbdaabcbddbcacdddbbddacacaddcaadaaccccaccbaddcabbbacccbbcccddacdaababdccbdaaabcccaabbacadcadcacdaadcdcaccadacabaaacbbddccbaaabbabadbbdaadbdddbcaaddbadcdaabdcbbadbcadbcbcabddcabccbddbdbcaacaadcbdbdccdddbcccadbdbabbabdbbddaabbacdcaccbcbbbbdddcdbdacbcbdacbacdabdbaacbcadcaacbbcbdacabccbabdabadbddddcccdbabcbacdcbbacbacbccbcccddddaabbcddccacbbbcbabacbcbaddcaabbccdcbabdcacbaccadddabbccabbadaadcdbddaaaaadabccabbdaadadbaabccbbabcaacdbaacacddadabccaccbddacdcccbcdbaddccaaabdcdcbaccccabdbdadcabaaabcddddbbadcccbcdcdccaabdbbacbbdddcbdabaaddacabbcabcbddcddcdaaabbbdcbbcbadaadcccdabcdaacddabacdcaaccdcbdbadbcbcbddabdabaacbbdccbbdabdccaaabdabcddacddcacaabacbbddbadadadddbaaaddaacdcacbadccabadbcbaacccdcaaacbabaabcababbbabdddaaddacdaabaaccbcbcbaddcbaacadcbdbcbacdaddccdcbacbddcbdabcaadccdaddcaadbbdbdabbbbbdbbddabccbaacabbcccaabdaadcddabbdbdbddadddaaabddabbdddcabdacaacbddabddabaabbdabcbbcaaaabadddadabbbbbbacaacdabcbadcadddabddcdbbbcbbbcdddbbcdbdddddabaabaabadacacadcaaacccacacddbabbbdcabaadcdcaccbddcddaacbdcbbdbdadbaadbcdacbcaddddcbbcddadbbbacaabccddaacbcbdcdcacabccbddbdbbdcdacacaadaadbcbbcccbabbcbbaccbbdccbbbabdbdadadabadcbdcaabbcbddcdacdcaaacbccbbacbabddadabbacdcbaccdccaaddcdcaccaddacdcdcbcbabbdbccaadbbbcbabbdcadcbdcaddadbbcdaaaddbbdbaaabddaabdbcababbaddccbdbccccbbdcbbbcbdcacbdcbdabccdbdcdbdaaabcaccddbbbbdbabacdbbccbcadbabbccdbcbbccccbbadadcccbadddcadcabdbbdaacdacbaccdcaacdaadbabbaddacacdbdddabcbccbcaaacdabcacbbbcdacbabadaadacadbdacdaaaaabacbdaaaddadbcaaabcdcaccdaadacbcdbababbccddcbcdaacbdadcadbddddcabcaaccdcabccbdbbdbbdccbccabcaccabbbbcdddaacddadcddcadadccddcbddbccaccccdacdbdbdbcdaabdcdcdacaccdacbddbccccbdadbacccacdaccacdddabcccbccaaabccaacabcacbadcabcddbdcbcbabbbbacdbddbaccddddbaabdcbdadccdbbbcccaddcdaaddbbbdbdbaadcabbacdbaaaaadcdbabcbcbbcbcccddbdcabbcbcdbaacbcbbbdbcaaccbcccabdaabadbdababcccaabcbacdacbcbadcacdbddacbadaccbadcbbcbcbbcdabacddbcabcddccacbaaaacbbcacbcaaacaabdbbcbbbacbaabbbabccbbabbcdcadcbadabccacbcdcdcabacbcdadadccdbbababcccadabadccabddcbadaccaaccbcdabdcabcabddbbcacdabcacbabbdbdcbcbcbbbcbcddacdbbddcacddccadbbcbcdadacadaddabdcaaacdababcabdcdcbbddadbabdbadabbcccbabbbbabcacbaaabddbacdacdaddbaadcdacbcabcacadababdaccacdcbbadacbdbdcddadcaadbabbbdaccdcadaddacbdccbdcbbadbddaadcdcbacddacdccbaaacccacadbdbacbbbaccdcbbbbbcdadcaabdadaabddcbadbbcbbdabccabaacdcdcccadaccadddccbddabaccddbdbccbaadcaadbbcdaccabbdadcddcbcddddadaccbabbcbadbcbaabaabaddabddacddacbabadabcbaaabbbbdbbaacbbabbaaaddbdbcddddabdacdbccaccdddcddbacddacdbdacadacbdacdcacbcdabadcacdbdbdbaddbbbacbcdaddcbdddbcbbcdbabdddcabddbbbdaadcaaabdadcacabaddccacbdbcbcaaaadbccabdcacddcabcabaacdabcbabdddbdccaaadaaaabadbccbabcadaccbccabddbdabbbdacbbcadaddaccadaacbcdcbbdcacbababbabbaacbbccddbbcccbcbbaddabadcbddcadbcdbcbddbdbccadacabbddadaaaccaadbbacccccdbbbbcaacaddbbacabbddcaaabdcdcadadbadacbccbcdabbbcdbccdddbaaacdaadabadcbdabbbddcbabbabaddabcaaacdbacdbdcaadccbdacacbdcbacabaacaccdbdcbdbaccabadabbbcabdadbaabcdcbdccccdcccbbccbdbbbdacdadcdacbbacabacbdcdcddbcdabadacacbdbdccbaadcaccabbcdcdddcacbcdbaadbacbdcbadbdcbadaadaabbacaaadaacbcbcaaadccaaabbdacabcbccdbbdbabbdcbcadaddabcbcbbbacaabdaacbdbddbcdabddcbccdbacbcdabaabbddcccdacbabdbaadabbcdcbcdadadccccdbabdccacacdbdacdbdadbdacdbdcbcabbbdadddcddccdbbabadbaddbbdadcbabdbdcdccdacbbdadccaaccdbaabcababacacccbadadddbadbcadcdabaabcccccdddcccacdadbabbbcbbbcdbdaabbdcdcbcaaabaaabbcdbbbaaadcbdbdcdbcabcbaabcacdcacdbcddadcaaacdbacbbcbacbdacddbcccbccaacabbbbcabdaacddaaccbdbdcdddcdbbcddcdcbabcccddadbaabaccdbdabaddcdbccdbbbabaccbbacdbabcaacdacbacccbccbdcdbbdbcbaadbadcdbbdddcccacdbcbdcdbabbbacbcbcaacdcacbdaababcccaaabdbabacdbdcbcbcadabbbaddbbcbddbcaaddaccadcbbccddcbcccddccadcacddcabdbbabcaadbaccdcbbbcdccdcdabdccadcdaccabbdacbcdddddccabcddadaddbdbbdaadaabbbcaddaadbbbaadddccdbadcabddcabcccccbacbcbdacbdbbddddabdabbbaddbdbbcaddbddbabacbcbdababbabbabdabacdcbbcbbdcabbcacdbccadcadccadacdcdcbadcbbacccaaaabdaccabddcaccbadabbadbadddcdbbbadcccaadbccabaadcbdbdcacadacddbcbdadabcbaabddbaccdccbabdbcbcbadabccbcbdbdddbadaaaacdaacdbabbcdbbccddccccbdabbaddbacddbbbbcdbadbdbbbbcbcbbbacbdccdbdaccbcacdbbdbaddacbbaaaacbcddadacbbdddacbdbacbaccdccbccdbdbcabadbbcdbbbdaaaacdccbcaabcdacddacbdabccabbacddbdacdbaacbdcabbdaaadcbaaaadaacbdbadcbbbccccaaabdacddddcbaaddddacabbacddcaacdabbcccdaaacbbadacbbabbbcbbcdbbdabbccbccbbccbdcbdcdaccaaaaaacaccdddaddbadadbccbaabbbbccbcaabdabddbabcbccbdcabccbbacbdadacbddbabacccabcbdaddddccbabaacaacbcbaadbdadcadadddacbabbdbcccdbcaabacaaccabbbabdbbabadabcaabcbadadaabbcabadcccbdbbcabbbcccabddcddcacddcabddacbdddadabcacacbbbcabacbcbbddacacaabcdaacbdccbcdddaadbdccaaaaabaaddbbbdcddaabdbcbbacdbccdbdbdacbacabcccbdaddbcdaadabbccbdcdcccbacccbdbdbddccdcaabbadbaabbabdcdcbcabadacabadaaaaccbaccbcabbcacdddadbbbdabcadbbcbbcadabccddcdacabddcbaddbabbabdaaabccbaaadccdcdcacdcbcbbacadbcdbadbaabcbadbddddccbbaadabdbbbbccbdabcabbadadddbbbdcbaaddcabccbcaddadbabbccbcbdcdcbdbacbbabadaacaaccaccbbaaccbacdaccacabbddbccccbcabbbcbcdddabbdaddbdbcadaaddccdcdcccbcbdddadaabdbdddbdaacaccbcacccdddadacccbdaabcaacdcbdbccdbdbaddabbccadbbbddaadacccdbbdbdcdaacaacbdaacbbcbbbdcdbccabdaaddddbabaabbcdabcbaaadabbccdddbddccadaaaacacbcdbcbacddbccabdbcdcddcbacddaadbacbaccaacadcdcacacddbdbbdbcacccdabbddccbaadabcacddacbbacbdaaacdbbcccbaadbacdadcdbabcdadadbaaccdbbddcdbbbcccacaabcadaccddcabcdabcaaadaababbcbdcadabcaddcdcacaccacdbbcabcddbdcacadddabddaabbcaadbddbdacaccbbaccdbcccccdbaaabcaddcabaccbabadbccbdbadcddcccdadbbcdcdadaadccaadbbbcabcdcaddadaacacdadbdadccaddbaaabdbbbddcbbbdaabdbaabcaaadbbcbddbbbcbbdaccacacdcaabadbbbabcaaccdadddbbdaacdbadcdcabacdbddbdabadcccbaacbacdcabccbdaabcababcdbbccaaabbdaadbcddbaaabbbbcaaddcccaddaaacabbccdcadacbcbbdbddbcdbadacdddaadabbccccbbabaaaccdcdbacdcbaddcdabdacdbdbddcdccdaabcbaacdaaccbbbbbdaddabacdcbdccccdbcccdcdcddbdabbdadbadbbcabbabdbcdbcaadbcddbabacaaabcbdbdabbbcaccabcacacbcdcbddddcdbbcdaadbdcccdcabbdbccdaddaaabdcdcabcbbcbbaccabbbbdadbcbddaddbcbadbccbbbddacadabcbcdababbacbbababbabddaabdaddcddccaaacaaabbbacbcdddcaddaaadcbadcbdddbbdcabcbcadcadcdcacbddddbadacabdcbadcacccaddcdaacaadadccccabcbcacaadbcaccddcccdbadcdccdcabacdccacbbdabbccccadbdadbaaaacbadaaadababcdbbcabbdcaaccbcbabadbcaabcbddcdbcacdacbbdcdabdaadacdcdacaaaccaaddddcccccbddddbabddccbdbcccdaaabbdaccccbacabbdbbacbbdcccaccaddcbddbcdadaadccacccccdbdcddbdccddccddcabbddacbcabcbdbaddbadbbbaaaddcbabbadaaaaaaabcdbadddabadbdbccacbbbbcbbdabbdabcbadcabccadbddbcdcbbbbababcaacbaaaabaaddcccddbadacbdbbccacbacccdabdbccaabaddbcabadabadccaccbbdcbabcbabacabcbdaacdaabbdbdcbabcaccdcbdcddcaacccdcccdacaabcadabdaaadadacbbdaaadadbddadbaacdbbcdccdacbabcbbddbbdaaadbbddcbcdacbbbabdcbbcbddacdccaadbbccbddddbcbbcabdadbdaccdccadadccbbadcbadabacaaaacbabaadbcadaacbbaddddcabcbbaccbbcbccbdddddaccaaabaacbdcbaaacddccacadbddcccacdaaadabdcdadcaadccbdaacbbdadcbbaddddbadcdcbbadbcbabcacbccbdbbbcddcaccdabbcbbcaadcadddccddcbddcabcaabcddccaccbbdadacdaaabdcddcdabcaabbdadccadcaaabbddcdcdadcbcddddccdbbdadbadccbbcaddddcbbacaddbbaddbcccaddabbddbccddcddabcacadcdbdadbbcdaabdacabaaaaadadcacbbbbddabaacaddaadbaaddbabccdbadaddbabddbccabaaacbccadbbdcaddcaaddcadaabccadcbaabccccabbcbbacaaaccdcadddcacabacdcaadcbcaddadaabcccdadddcacacbbdbcccccdcbcbbaacbbdabbadcccabddbbacadadddcacadacabbdcdcbdddcbdcbddcbcbbbdbabbdccddadbadbdaabdcadddbdcbbddbcabdbddacbddaaadaacbcacaaccbcdddaabddcacabadccdcccabdbaacccbcbaadbaccccbaadcacdbcdbcadacabdadadaabbbdaddcabcddcbbdddbcaddbdcabdacbaccccbbbbbbabaccabaadbdbcbdcdbdcdddbcabbccbacadaabbcdbbacccbccccccdcaadabaddddcaabbbadcbdccdaacdadbaddadaccabaadaddccaddababcacaadcddabcccddbaabccbaaabcbdabdcdbcabccddbdaacadadbcaaaadabbcdbbcbcdbdacabbcddbacbbbbbabdaadbbadabaacbdbbddcbbbbdddddacccaadcbadbaddcdcabcdcacabcadaddbcbdccaacbcaabaaaaabcdacacdbccabaccaaabaaadadcdcadabccdaacabadbacddbbbcdccaaadbdbbaddcacadcdcaaabcbbcbddbddcccddcbbacaaccadcaaccabcabadadbdccbcadcbdbdadcbdadcaccbbadacbaccdcabcdabdbcdaadbaddcbbdabdbcbabababdbaadbbddacaddabdacdddcadaacbadacdacdcacadabdcabacdcbadaadabdabcacdcadcabdadcdacbbcbcbbcdcaaaaccaccabaaabbbadcbdcbcdcaddcdbcccddbddcdcbacdbdbbdbaddbbbcccacadadaddbcabcbccdcbcbcabadabacabddbbcdbbacdaaacabdacbdbbccbcdcdaccdcdbcabcdccdcaabbacdadacbcaaabccbccbdadbcddbcbadbcdccabcccdcccadcbcbbaddddbadabccbadadcccabbcacbdaddbabadcadbaccdbbdcdaaaadadbcddabcabadddadbabdbcddddcdabadbbbbaacbdacbbacbddbbbdabccddddcaabddbdcaddadbdacccdbcdacdbacccabaabccdaaacadbddccddcacdcbadcababcbcddacbabbbdbbaccababbbaddcadcdbabcabbdcdbcadcabccbabbddbbcbbdcdacdbcdaabdbbbdccbcaadcaacbcbcdcbcdbcadabcadcaacddcbadbccdbdaaddacbcaabbbddadccabdcbbdadadcbcbcdbabddbbaabaccbaabcbcacccbadddbadcdccdadddddbccbabbbdbbdaaabcdcdddcdcbcbbbdbaccdbcbaaadabbcddbdbcbdabdaccbbbbbbdaadbbbcbccbbcadccdcabdddccadcddcddcbabcbdcddcddbacbdaccaabacdaabaaaabacaddbdcbacaddbcaddccddaccbcbaadabdbdaacbcdbaacdcccbdbbdcdbbcadcbbcacccbadddbcaacdbcddbabddabbaaddcabcbdadaddabcdbacbbacddbcbabacdcdcddbbcbddccbddbbcccbcdccbbabcdddcaacabcddcbdccccadbcdabbdccacbdacdbcccbbcdbccbcdbaabadddbdaabbcbacddccddcbcbaacdcabbabbdddcabdbcbbccaddbaccadcabadbcbcbbbccadbdcccaadbddbddabbbdabcddcaacaabcbbbcaacccbbcdbabacaaccbdabbdcbbaccbaababbaabbbadaccacbbaabbbcdaacacaaabccbdcdbbdbbaabbcbcabaddcbbdacdbdacddaddbddbcdabcadccdbacabcccbbccbacdccabaccaaabccdcbcbbdbadadacdacdbbdbdcbdbabbdccabdbddabbdcdacccdbacacabaababcbbbaddcdcaaaacdddabbcacaabddadcbbbabcddbdddbbaaacbbcaadabbbbdaadcababadabcbbdcadcccdcbbcbcccbbcbabdacbbbdadccdbbbaddbcddacdcbdadaaccbbaaaabddccddcbadbbdadcccacdacdaccdaaccbbaadbbbacdbdcadcbdcbbcddbcacdaacdbcbdacaadbcaaddbcdacdcbcadacbdbabdcadbabdadbadaaadddcdbaadbbbbaccdadaadaabcacaacbbddabcbddcbdabbcccddccbbaddcdddaabbdddabaaaddcbadbdddcdbbccaaddacdbbddbabdaddcdabccaaacdddddddcdbaddcdbdadccaadaacdbaaddaccbaaacbccaccabbbadcdadcddcdbddcdccdbabdbbaddbdbccdccadddaacdadddcbbccbdaacdbdadccadcbdbbacabbaddaacdaccbdcaccaddccadcababacdadbabbbdbadbaccbbabacacacaccabbadbbadabcbcbbbbdcacadaaacccccacacdbadcbdddacddcdcbadddcaaaaaababbdaaacdcbdbadbcbbaadbaaacaabaacbccacdbcbcccadbbaaadadbacbddbddacabddbbdbadbcbacadaaabaaccdadacbaabbdaddaddcaabcadaccabbdcadbbddacbdcccbacabbabbadbaabdcbaadcacdbacddabaccabbaadbdaccdcacadaabaaccccdbdacbcacddadcbcccabdcaddcacaaccdddbddaddddbccacddccadacadbdcbccbadabdbcbcbcdbcaabbadcbccadbcccbcaacdcdbaaddbdccadbbccccacdccbdccabcdbbdccbcdaabddbacbbddcbaaabdbbaadbcdaabbbdccbdbdadbccbddcbbcabcddadbbaaccbcaacacccadbcacaadddcaabcadabcbabcccddddbdaabcdabcccdaadacbabccaccaadddcccdbadbdaccacacdbabdbaabdbddccacdbdbaccbbcbbcacbcbdaadbcbdaabbcdddbcdabbcabbbdaddcbdadaddbbdcbbbcdcabcbddccbcdbdcdaabadbaaabbbddcaabbabbbddcaccbbadadabcabcbabacbdaacaaaacbcadaabcbdbacbdbcbbabcaadacaacbbdcacbdcaaacacdbadddadadcbbcbcbbbacdcaccddccbdbadabdaddbcadabcdabbcdbdcbbbbbaacdacaaddbadabbdabcbbdbdbccdcccadddcddacadccdccadcdbacabdaaaababdcadcbccacdaabcdccabbbaaacbbadcdcccccbaadacacdadabbbcdacabadadddaacbcddabaacdcdadddcadadcdcdbcdcbacbcabcadcbcbabaaccccbcdbaddbaaddcdadacccdaabbaccbdacddaadbdabbdbbcdcbdacadddddbabdbaaadbabbccdddbacacaaaddbdbbdadadddccaaccbaabbbcdaaadaadcbbcaccdbcbdbaccdaaacdcabcccabdcacbdbdcbbbdbbbdccbacacdcbbabbaadabddcadcdbdddacbcabcabbabaaccdddbdaadcdddccddddbddacdadbadcccbaadcadcbbabbdcbcbccbcaccccdabbdbcaaaaabbcdbdccbacabcccbccbaaccddabddbaabcacbcbdbbcadabbdbddbbcaccabcbacaaadbbccacabadadaacbabbdcccabbabccacdcdbbcacabaaddbcadbccbaadccaadcacbacccccddcdadaddbacdbdaabdcdacbccccbbabdbaacdcdcbcabdbbccbdbbaabbacbcadbadddbdbadabccaaadbabbbbabcabacddcddcdbbbbdacbbaabccddbadcdbadddcbadbaaddbdacabdacddcaddbbccbcbbcaabdbddcccaacacabcaddaabddabdbbddbdcabdbbabbcddabdcacbdbbbdaabbbdadbbaaccddaccbbbcadababdbacdcacdcbdaccdbaccbdaadaddbbccccabbcbbdcacaadbdabbbcacbbcbdcbbbcddadaadbbacdddaabaaacdcbddbcdbbcddaadbadbdcabddcddcdcbababcdddaaabbddbadcdddadddbbbcdcaadcbcbababbcadabdaaacdaaacbbccaaaaabaaaaddabdcdbcabddaadbdddcbaaddbcdadbcacbdabccadbdacaabcbdbcaacbabbdadbadbdcaccccbbadacccaabcbbacadcbbbdddadaaddcabaadbbccadbdddcbacbdbaacbacddcadcdbbdcbdbbdaccbdbaadabcabbcbdabcaaccdbaaddccbbcbaaddcacdaabbacdccddddddbddcbacbaabdacbccbdbbaaacadcdbbbdcaaddbacdbdcbacabccdcddcabdcbddbacbdaccdabcbdaacaacbcdbabadbbdbbdacaaccccbdbbcdbadbcdcbabbccddccaccccaddbcdbdcaaddccacbcdcdcdbccadbbdbaabcabdbbabbadbcbcdcaacbaadcabddbacdbcaccacaccabcacdababdbadaccddcdbaabccddadcdcbdbbabaddcadbaddaabcaacdccdccbbcbaacbbbbbddabbbddcabacdadadcddadddcccdadaddbddcdcacdbbbcdccadbcdabbadcadbddbcdacddcdddccbccbdacbbaaacacabbdadbdcadcadabdabcbacdcddddccdaddcdadbdcaabacdaaacbdddcbddcacdacdddadbcdcbcdcbdbcacbacdbcddcdbdcdcacbacaabdbadbdddcaadaaabbcdcdabdbadaadaadacdbdbbdadcacbadbdbbdbbcbadcaaadacddcbdabbacacbbadaababddbcbbbdcdaabbddadabbdabdabadabdabcbcadacdccbbaaddbdbcbaacbacbadbcbbbbbcabdcccabaccbbcccaaabbabdddacbdbbbdaaaadcdbabdcabdadbaacabdddacbacacbaadcdbdadaadacacbdbdcbdacbdcabbbccabddababddcdbadcabaadcbcdcdbdabbdabacccababacbbaacdaddcbcacddddcdcbadcccabdbacbabcccbbbbcdcdbcdcdaacbcaaaddcdacdacccbadbcddcccbddcabcabaaadacbcaccbdbacdbcaddbacabbdbddbcbbddacbdddadcddcaacababacbddbbddadaccddbccccacadbcabdccaabbcbbccadcddabbaadccdccdcaabcbdcaadcadbbabcdddabaabadabbcbdcbbcadbcbaaddcabdacbcdaaccadcbbcbddaccdccbabcbdbcadbddbadaaaccadadccaaddbcaddcdcbcbccabcdbdaabdcdbbdacbdadbdddadbdcaadbccaacbbcbdcdacbcaaddddabdcbbccabcbadccacccbcacbddbdcadbabcdaaadbddccbccabacccddaacbbbdaabcbdccacccaabaadbdbadccbbbbbbcdbdbcabaaaccacacbaacdacdacdcdacdacbdabddabadcabddccbacdacccdbbcdbbdbbdaadcbcdaaadbdcdcbddbbddbaccdcdcaaacaabbadccbabbcddcdcdaacdaddcbccacbcdcabbabaddcadbbcabadddbacbddadadcdbdaaacabddddacacaccaabcabbabbcadcabbaaaddabccdccabdbbabbdbbdcbcbcdadadbbddacaaabdcccdbcdbaddbccadbccccbbdcdccbbddbdadcddbbcaddccbcbddbbbbcacbabacdbaadccbdbadbcbbabbddcadcacdccabddadaaadaaaddcbabbdddabcbacddccbacbabdcccbbbaaadabcddabddbbcbacbcadcdaaaaaddddbcaaabcbdcaacdcdabacbbccaccccbdabacddbcccdccccbddcadcccdbddacbcbdbabddbaacbbdcabadbdaccbcadbdcccacddddadcbbcbdcdddccdbacbcbdbcababaccddacddcbcadccaabdaacdadccbbdcdbbcbbbbdabadaadbaddaaadacaaccbdcbcdadcbdaaaadcbdcabdacdcadaaaadbddabdaabccaabdabdddadddaabcbcdbaddbdcbccdcbdcbdaabdbdddabcbbbdccbdacabcdabbadcacbcccbabddbbbcbcacadddadbccadccaabdccbdabbadbbdaabbcacccccddbccaacddcbcabbdcddacaddcbdcbcccbbcacbdbddbddcadacddadacabccddaadbdcbcdbbcdccccaabddbdbbacbdcbaababdcbdaabcbacabdbccbbdbaacccababababdcaaaacbbababbbbddbcbbbabccbdcababdbbaddaddbbccabdacdbabbabbbdbabcbbabbcbccdcccaaccbcaadbdcdaaabbbabddabccaacabcccaddbaacabdbdbcbdbabdabcdbacabbbcdadcadcacdcaddbcbccddaddbcbbbbcbdbbbdaacdaddaaaaabbbccccbbbcabcbbddbcacabadccdcbdcbccababacdcdbddbaadcdaababdacdddadcbcaadabaacaabdbbdcdcacbccdbdbbbbbcbaacaaabdcbaabbcbdbcbcaaddcaabbacadadadcbdbbdadadcdddcdddbbdbbdbdbccbddaddddaddbddadacddbbabdacacdcacaadcdcbdcbadadabaddacccabacccabddcdacdcccbdcdcbbbadacdaacbcbdaaccaddddccadbbdcdbdbbddabdaccbdbacdabccdbabbdddbaaadbccacdcdcdabccdbddcabcdbaadcacdddacdddaabacaaadddaccbdddbbcdccccaaabbbbcbacdbaaacbdcbaaadcbadadadcaddaccccabbdacbcaaadadbaccdbabcdcddbadacbbadccccddcbbdbadadddbacbcbcccadcbdbdbacadaababddcbbabdbdaadccbcbcacbadccbbdacddbcbbcccbadabcbccbcbcddbdabaddcacdbbddabdcdbddcbbbbccddcddacbbaadaadabaccbcaaddcdbcddbdabcccbddaabbaabadabdccccaacadadabbddddcacccdddabcbcddbddbcababbbcadbbccbbcdbdacbabadcdccbdabcacdbcbddabdddacaaddadaccdabacdbaaacbbcddcadbdcbaabbddcabddcccdcbcdbbbddbcbaabdacbbcdcbabcbdccdbcdcdcaaadbbcacbcccaccbbdccdbaaadadbbbccbbdcdacbacddbdcabacacacccbacbbddcbcdacdcdcaaabdadcdcbdccababaadacadbadabbcbadabcbcdddddcbbcdacbbcdbdddbabacadbdbccdcdccdddcacddbaadcddabbcaddababacbbcdacabbacbdbbddadddcbbaadbacabccdbdbadadadaabcbacdaaddbcddbcdaccbbcdabacbbbaabdbbcdaddcacabbdbbaddcacaacadbbbaabcdacccbbdcdbadccbcbdaadaddcabaddbdcddcbbacdcddbabcccdccbccdcbcadcdddbdbccdbcadcabdaabdbbdacbcbabaaadaadacbdbadddccaccabdaadadaaadcdcbcdadccaaaaadadacacabaaaacdabcbdadaaddcaddbccadacadabdadcaadcdaaccaddabacdbbcdadcacbaadcdbdcabadbccbadddaddacacbaaaabddccadbcbdddabbbddbbcdcbcacaadabbbcdcaccaadbdcbccdbabbadaaacbdacccadcdadddbdcbbabbdbcdddbbbdccabcadaccabacadadcbbcabbcaccadaddcdcaaaabdbbaaccdddcbbbbacaaccaaadaaacacdddcbbcaddbcbdbbaadcbcabbdabcaadbcdbcdbbaddcbabcdddaabdcccdbbbbaccadddcdaddcadddddadcbcbbabadadcbbbacbccbabdcacbbaacadaacabbaadccbacadabddddacdddaddbbcbdcbcbaddbbbadabbaacbcccabdbabcbbbdcdcacccaaadaaddddadbaaaaadbcbaacabcdadbaaababdadbbccaaaadacadbcdccacddbcdcbacbddaadbdabaabccbccbaddbcabbcccdbadbbadccbbddbaadadddcdabcabbddacadbbbaabadcbbbaaacbdcaacadadcbacdbdbaababbdbcbaaaabbbdaacbbcabdbadcacccdaacdcadbbabacaaadcbbddcdabaacbabbcbbaabadbbbbbbdaabacbaddaccccddbadbadacaaabccaaacdaccadcabdbdbabdbabcadaddaaadbcbabccdcbbdbbaaadcdcbcddaabadbbbcbbbddaccdbbdacaddacacddcccaabcaccdccbcdbccaccbdccaddbbdcdbcdccdabccbdddbdaddcaababbaccdbcdbdacacdccbbdaaabcbcaaccaacddabdbaddbbdcdcdaccdbcbbacdcdcccbaaccccdcadacdabcccbddaabcbdcccbabaadcdaabcbbdcdbcaacdcdadcddabcabdcbcbcbaabccdccdcdaadccbadaaabbdbdadccdbdbcdcbaadababdccdcbccbdabccbdcabccdcabcbcabbddcaadabddddabdcbdccadbbbcaccadacbdaabcddddbcbabbbbdcbbdbbacadbcbdcbbdcbcaacccdccdbccaabdcccccaadccbbadcccbbdaccddacdaadcadbdbccdddccabaaccacbdababbbccdaddbbaccabbbccbdcbbccdddbcdadbcdddaacacdaabcdcdbcddadccdccdccdaacccdadbaabcdcbbcadddbbdaabbcacbcbcdaddaaacdadbabbbaaaddccbbbdcaacaddcdbbcbbacbadddbccbdbccbabbaaadbddcdddacabcbddadbddbccacbcbdbacccabbdcbaaacccaadacdaacadbdabbcabccdcdaddabbbdbbbcbcbaabbcbdcbdcbdbdaddbdaaaddaadbdadcdcaccabccbabcdcbdbbabdadbadbbbadddbdbcadababdacabddaadadaaabcadadbcbbacbccccbbddcccabaabbcadacddbcacadcbdacaacabdcadbbbcbbadacdabbcacadbabdacadcacdcbaaadddcabaabdbcabbbdbddbbcaddbdbbdcadcacaadacbadbaacdbdadbbaabdaddbdcbccdcacaabcdcbcabdadcdcaccdbcbdccadbaadaddddabadddddbdbddccdcddacaabcbbacdadaccbdcadbdbbbdabbdcdadaddcbbbccddadbdbdcdbaadcacdcdabbbddddabddccbcacdacdddaacaaacabdbbdccacaccbabcdbbbacddbcbacbdadcabcdbcddabbabcbcdadcbabcdadbdcdddadddacdbaadbdbdabdbbccbddbdbddbddabdbccacabcbaabdadcaccdaaccdcbddabbaddbbbacbbaabdabbdacadadbacbbbdcbcabcacdbdabaaddbcdcddabdcddcabcddbbbcaddcabdcbbbdbdcbcdbdabdcdbdaaadbcdadcbcbadcacccdccdcdbaaddbaadbbabbcaadcdbadbcccdcadacccdbdcccdcbdddbbdcddcaabdbcbcbbdaadddaaaddbbcdcbaccdbcaabccabadadaaaabbabbbdbccadcccccdbcdbdadbddcadabcdbcaabbccbcbbcbaccbaddadbbacccdddccabdcbbabdacbaaacddabcdadcacccbbacdcddacccdabcabadaccdcacbdabbcdbbaabcdcabbadaddbbdcccbbcdabbaddbdbcbbbdbccbcbcadddcddacbdabdadbddbcacdbdabdbdcabddbdccbcacaabcbbbbcccdbbdcdabacddccdccbaccbabdbdaabbdacbaadacddbdcccdddccdcadaacbccbabbaadadabcbdbbdbcacacdcabcbadadbbdbcbdababadadcddcddaaacaccbbccaacddacdbdccbccbbdabbddcabccdcbaabbbddccbcacadaacaadcacdbdcbabdcabcbbbdadcdaddcaccbdcaccdaddabbaabaddaabdababcbbdbabcadbccaabccdacdccbbacddadccdccbdacccbbdaddcaaaaacbddddbabcbbaadaadaaacaabcbdccbdaaacaaadaaccaadacdcbcbcbbcbbcbcddabbccccadadbcadccadbaccacabccabbccbacdddccbdddcdbcaacadbcccdabdbaacacacddbabbcddddaabdcacaadbcccccddbaabccddadbcabadbbdcaccabdccdbabdaacaaaddabdabadaccdabaabcdbbcbadcacdaadaabacbccddbacddbdbcacddaddcdccdaccbabacccacbabbadddbacaccabcbadcadddacbacdcbccbdcccadadcadbdbbbcbaccbccacddccbbcbcabaabdabcdadccdacccadbabcdcdbdccbdcbccbddccabbddbbcbcacccacbdccbadbdbbbaabdaaacdbdabcbacaaddadbaddcccaadddaccaacaadcacbccabccbcacbacabaccadcababbbabbdccbbbcdadcdacabbbbcaacacacdcdadaadbbaccbcabaaacddbadbcccaacbbbbdcbbccbbcdddcaccaacbdcddcbdddaddddaacbcbcadcdaadaccadcdcbcbcaadcccbbcacbdaaacddddadbadadcddbbbbadadadccbaadacbaadcbbbdaddbabbbcbbcdacdaacacddcddcaaadbabdbccccabdddaadddcdbbabaccaacbdaaadbdbabddcbdaddcbbabdbbbcacbdcdbcddadbddbacababaabbddcbdacaacdabcaababdacdcbbcbccccaabaaccadddbbdaababccbdbbdcacddcdabacccaaabcabdcbbdddacaababdcaacbabbaacdaadcabaaaddddabcadddacacdcbacacdabccdacbcaaacdbaaacdcdabdaaadbcbabbcbcbcddcaccdadaaaddbdacdaccabccbabbdddbdcbacaabdddbdaaaabadaadcdabdbabdbdbacaadbadaddbdddbbcdabacddacdcbbaaaadcaacccdadbdbbbbcacadaccacaaaadaacabbacddbcbaadddcaaabbabcbcccdbbbddbaabdbdcccbadaacaadacbbdabddbaaabadaccaddbcddaccccdbaabbdadadbdadddcaddccccbccadbbcdcbbcdccbddbbadcbbbcdbbdabadccddadacdaccbccbbacdacabcbcbdabdcaacbcccacbbbcbcadaabbdaacbadadcbbabbbaaddcabccdbddabbcbdaabbcaaabacacdcddbcbdabdcdbcbaacaadadcadbbbdbbbadbcadcbdbcacaadbbddbabcbdbdcdaddcdbabaabdacbdbcdbdbabdbcbabccddcbddcbdacddcbacccabbaacbddcdabdbcabddaadbbadabbdbcbcaabcdbcacaaaaaadacbacbdbcaccabacaacdacaccdcdcdadbbbaddccdbdacdbbdabdcdacdddacbcdbddaacacdbbbacaddbddcbdbcdddbabbdccbddabbacdacdacdccabddbabbdadcdadacbdcaaaccacdcbaabbdcdbbacddcaccacbddcadddbdacbbbcbcddbdbdddbbcabdaddbbbcdadbabacdccacabcbbdddccccbbccbccbcdadacadabadacdbccbacdbbddcdcdbcaddbdcdddddbdabdbbbddaadcacdcacbadbadcddcadccbacacbbbccccdadcbbcbdbcaddabdbbcdadabaabbccdcbdacaaccbadcbaacdbabbaaaaababcbacccbcbcdaaddcdabccacdcddbaacbccddbcbadacccdcdaacdbadabbbbdddabbddcbaddadabaabdacccaaabadddbbddbabaacbbcbbadbbacabdabbcabddcbbadddccbcbcdddaaacdcccdbddcabccdcabaaaaacbbadbbdbbacbadaccbdcdbcaaaacbdbabcaaacdbcddbddabadcdcabbcbbcccdadacccdacadaddccdacbdbdcddcccadbdbdadddadcbbdacadbdddbcbbaadaccbcacacbdcddacbbcdaabadbdadcbaacdcccdbdbdadbcbdaabccadccaaaaabddabacbbacdccaddbadbaacabcdcacbdbbbdbbcadbdaaaabdbbcaabadddcdddbaddbadcdbbaccabdaabbabaaadaacbddbcaadcccbbbcccdaadaabccddddbddccdabdddcaabbdddcacbcdddaddaddbcacdcaacadaabcddbbddddbabbcdaadabcbdbcacbbcacdadabbbccddaabadddcddbbccddabacdbaaddbdcababcccdabadbaacbaddbbabacbbbcaaccbaadacacdacabaabcddcdbbbabbacabcdadabbddcbcaddcaaaacaabdbaddcddccadcadcdadaddcbaccdbdaaacddadabcbbcdbacbbcccddbccaadacddbcbddbaabbcabbbdaabdaaccdcbccaabcaddbadabccbbacccddababbabcadbbaaaccbaabaadddcaadaddacbaababddabcadbcadcaaddababcbaaaccadbadcdccddcdaddddddadacabbcdaabbdcddaccdaacbcabbcbdcabdcbdcbbdcccadddcbdbbcdbcdbabadacdddcdddadccaadddbdbaadcddaadadbaadabcdbdadbccacabbcbcaadacdccdcaccbabbcccacddddccdaaabacbddacbbdbadbdbddcacbdaddabaabdcbcdacbcadbadadabdacbacbcabaadaaaccabcdbbbbaddbbbcdccbadabccabbccbcdbccddccddcccdbacaadbdaccacadbcbbacaddbabbbbcdbdbbcaccdbdcaabddaabcdbdadccadaabcdaacbbcaaccaacacbdcdacdbadaaccbbcbdbbbcbbbdcacdacadcbcddbddddadaaaabdbdaacdbbbadcabdcbccababcdaaaadabdaccbccdacabadabdadbadadbbabbdcabbdaadcaadcdabdcdacbbcdacbdcaabdbacdcdaadcaddbbcbbcaddacaaabaabbaaacacbababdbadbaabdadcbabdbcdcbccdbdbdccabdbddccbdabbdadbcbbcadabbbcacdadbdcacaacbbaadadcdaaccdccbdbdbbbdbbcaddabcdcbcacdcadaabbcbdaacacacaaadabbccbbaddbdcaacddcbbcacaabdaaabbdadbbdccabcaaacabbabbdabdcbdccdcaddacbccbdccadcbcbdbccdddbbcacbbababcaacddbdccdbbacadbbbbaccdcaddacddbccdddcacabcdacdcdddbcdccdbaccacbbaaabdccdbdbdaccccadcbabcaccacbdbdcabadccaaaaccadcbaccbcbbdbbcabbcacbcdbdddcbadcadcdcadababcaaaaadcdcdacdcbcdadcdbdbccbcbdaadbbaadcaabbcdccdaadbbccadaabcbcacdcdbbdcacdacbcbddaaaaddaadcaacccbdcbcbbcdbdcbadbcabdbccadcdadcdbbcdaddaabacaaccbbabbcbaddddadacaacadabbaadaddddcadccddabdacaacbcbdddbbdcbbbbaddbdaaccbaaacadcacbcddddddcbcbdcddcacdacdddaacbbcbadbacdcccdcbdabddbadcdbaabcbbcccaabdaacccbbdacbccaadbcaabdcccadccccdddabddadcbabacaddddcaadbcadadcdbbcbccdcdbcbaaaaaddbdddbabbdddacaabbaacccabdcbccaddaabdbdcadbccdddccbcadccadbababddddadbbbcaadcbacbbcccddacaabdddacaaaabaccbdbdbbbbbdababacbacdbdabbcaaaaccabdacaadbadabbbbabcdabdaaaabcbadbbbccddccbddbddcbccdaaddddbadbbccabcacaccdacbbaabbdbcbbcddbcadadbacadadbbacccdccbcbbbccddddabbcccbdbadcabcabdbaddbbdcacccacdbccddcddbddabbadbcbbdcbabccdacacbcccaddcdaadbacbdcbadcdabddaabcaacbcabbddbacbcabacbcacdabbbbccbdddacadaacbbbbbaaadbdaaacdbdaacbacccdabcbcbadaddbbbccbbadccbcbadabddbdaadddaaadbdcaabbaaadadcdccabccbbbadcddaaaddbadccbdcdcbcacddbacdbbabbdaddaadbdbbbacabcbbcbdaaacaacddababddaabdacaacaddabacbdccbabaacbbbbcbacdaacabdcacccaaccbdaccbcacdabddacbbcdabbddbbcdcccdadacadcdaccdaccacbccbcadcdbadbcaddddaccadcabdddbcababcdcbdcacabbacaacdbaddbdbbcdccaaddccdaabbadddbcdaddadaabbdcccdddbccabdccddabcbcccdacbbdbabbcbccddacdcdccdcbbdcaadccbaabaddbdcbdbaddbbbacaccccbbdadddddcbcaccccadbdddcbbddaddaabcbadbcbcdbdcddcdcbacddadabddaabcaccdddaccdaadcadaadabdadcdaddcbacaabbcbdddbbccbdadababbcadcccdcbbbaddcdbcdccbbdadddbbaacdddbbddcdadbcabacbadcccddababdcccbcdcddaddccbcdbdabdcdabbdabcbddbbadcbdabcaaabcbbcdadddcdcadadaadcccabdddacbbbbbaddaaabbbabcbabdccabbaabcdbbccacdacadcdabdbcbcbaaccabbdcddaabcddbadbbaacddcdccacccdbcdcbbbdcbaadbddcdbabbcdaaacdcabcdadbdabcdbacaccababdacdbccacacccacbccbbbdabbdbdbbdbaacccaaaccacccbcdbdccbadccadacaabcbdbabddcdabcadbcaccadddbcddbcdaaccdccbccdbbabacdcdccdbcbdcbddababadaddccccdcddccaaddaccabaaaddbadacdadbdabdadcaadaadcdbdbaddadcbaddaaccacbbbdadabaacccbababcbabddaaacdaddddcaadaacbbadadcdddccccbcacaadaccbdbabcccadcddbddcddbbdbcdaaaacaddcbcbcadbdbcbaccbadcbcacbcdcbcbcdadcbbdbdddbcbbcbbcbddcdcdcdbabababcbaaabadadcddaddbaddacdbcddbbaaacdcccbbddaaddcccbadabdddbbadcdbaacacdaaadbaadccadaddabcbaccbaadbdabbbccacbccbdadbbadacdadaccddbbacdacdaadcdabdbddbbbbbcbdbcbaaadcdbdcdcccaaaccbacbbbaabadaadbacccdcdbddccbdaccdcadbaccdbdbdaadbdaaccdbcbbbcbdccacdaacbdacdddacadcddaabdbbaddbbddddcacdccabbdbbadcdabbddcdcccdbaaaaddcdcbddcaddaaaddadcbbbdcccbdddbabcddcacdaacadaabbbdadaabdaaaddbdbadaabbaddbdcddbcadddbbcdcaabbccabadaabcaaddddbacaddbdbcaabdcdacdabcddadcdbdddaddcdbcdccabdbcbbdbbacddadaddbcbdadccbacbcbdabaddbabbadddbcbdbbbaadcaacbccaabadddcbcdadcaccaddcbdcdaddddbcacdbdbdcaddbdbcccaccdccacbaddbbbbccdcbadcbcaadadaadccbcbdddddbcddbaacbbcbbcbdbbcbdbdaaacdbdadcadbcdadbbbbadbccddcbaddbcbddbbadcdcbabdcbbdcaaabadcbacacacccaccdbcdbbdaabcbcbdcbdaadcabbcbacbcaddbbcacdbbbabaaddbabddaaccacbaacdabbcdccbacaacccddcaccabddabbcadaadbbdbcacaacbababcdbdbcabbaccadcacbccdcabbaaaabbcaadcaaabcdbacacdddcbcabbbdcbddbbbcdbadaaddacabcbbdcddbabaddcbbdcbcbdacdabdbbdbbaadcdcdaccdacdabaadcbbabccacdbdcdaadbdacbbadbabbcdbddbcaabdaaacdbddcdadaaacdcdabbdaacdbcdbbcadaababcbaccbcddbdbcaacacaaadddddddccbbccdcbccabcaacdbbcbdcaccaccbdddcbadabcbccbccabccaabcdddaacbbdbdaacbbcbbbaabbaabbaaaccabccccbddadadcabbddbcddbdaaaaadcdcabdcaaaabbbacdbaabacacdcccccbdcdbcbdadbacbbbbccccbbbcabcdadcbbabbdddcdaaddcacddaaaaaabdcddddbcbbbcadaaabcdabbdcbbaabdcbcbbbabbdbbcbabcaacbbbbddcdadabbcdccbdcabbabccdccaaacbacabbcdaccdacaaadadabdbccccbccccadacddbccbdccacdacccbabcaacacdcaddcdadbcbdababacabbcaaaaababaaccddabdaaaaaabdadadddcbacbdacbbdbcdbcdbbdcdaaddbdadbccdbccbddcacddccdbbdcaddaccacbcccadaaccdadcbcabababacccccbbcbbdccbabccacdbbaaabbbabdaccabcdababbcaacccbdcaaabcdbcacbabbbbbbdcabcbadadabdabcaaabbbbddaaccdbbdccdaabdacccbcbdaabdbcadbbaadddcdaaddacbddbddccbcdcccbbacadbdaaacabbcbcbccaddabcdcabbdcdbbabaaacbabddbabcbadddcaccbddbcbcdadcdaaacaddccdadaaddbbadddbdcccbdcbaaadabacbabbdadcccdabbddabcddaaabaccdbdaddbcaadbaddbccbbdddbddaaadbabdcddacababcabdbccaaacacdbdababadbdcddbbabaacbdbdbcaddaadbccbbccaaacdabaaadcbbbaaaaacaadadadddcbdacbdbbadbddccbdabaabbacdbddbddbcdcaacaacadcbacdadbdbbddcbaabbbcadabcbdcbbdcddcbbddcaaaabadccbdabdccbacacdacbcaadbbaccbdbdccacccdaadaddcdcabadaacbcabccdbacbbbcdcacdbcbcaccaacaacabbddcbadcbcbaaaacadaaadaaddccdadccbbbacbacddbdbbacacbdccbbcabbbccbcdabcddaacccbddaaacddddabaaacccaddbcdcacbcdaaaddcaadadabbacaabdacdddabaddabacbdcabcdbcdabdadbabbdcabcbbbacccdcdaabbcabacbbbdcdadbacbdacddbcacacdbdbaaccdcbadacddbbdcbadcbacdadadaacddbdabbbdbdddaacbcbbaabadcaadddbcbdcbdaadacaddcdcccaabaacaaacdbbcabcadddbbcbbdbadddbbaacabacbdccadbdcbccbddccaabbaddccababadaadcaaabcaadcdbddbcabadcaabbdaaadaaddbbdcabbdaabbccbddadcaadbdcdacdaacbcdacdbcddcadcbaaabbdccdaadbddcaaccabccdbdaadbccdbabbaccbddbdbccaddabdbadaddbdcdddbcbaaadacdddabccddcbcdacabcccabdbbbabdcdbabacdacccbdbcdcbabbdaacbcacddccabcbcacababbdccdcbbaadccadccacaccdddabdacbdccbbddabcdabdbcaddabcaabdcccbcbddabdcdbdcbcbabdcdbabcdcabcdbaadbcdbdacbbdbaacaacacbdcddddaddbcbaacbbabaabadcdaccdbccbcdbacbddaaabcaabbacddadbdcdcddcaacbaabcbcccbbbdccbbaacbbaacbccbbadabcacbdabaaddadacadbabbdacbaccbdacddbcdcaadbbdaabdbcdbcabddaccbcbccccccdcdccdddaabacddddacbccdcccacacbacababbadcbbadbbddacbbbdcadaccabdbcadaaddbbbcabaddbbabcdadcbadcadbbbcbdcbdcbaacdcacabdadccdccaaaabcdddcadcbcdddddaabcdbdbbababcadddacaccbdcaadccbcdadcaacaabddbcacbcdabdbbbbdbcadbbcdaadbbbbbcdbbdcdccccdaaacdbcdddabdbbbaddccbdcaacabbcbaacabcbcdddcbaaabcaaccacbddbaaddccdadacbadbccdbbbdbacbaacccddcaacaadaadcbabcbadbacdbaacbdbacaabbdbdabccabbbdbbcacdccddcadabccdcadcdccdcccbbdaaaabdddcbcccccbaccbccccccbccdcadbbaddcbbacabcdbdcbacdadabdcbdbaccadaddcadabadcaabbbbcddddddadbaaaaabcdccbaaabbabacccbaabbaccdacddbcdbaaccbcdbacdaaddabbbadacaababdbcbcbabccaaadabcbdacdbacdcadaadaaaadcaaaabcadcabcbccbbbababcddbabcbadddbcbabcacddaacccbaabaacddbcddbdaccbcdbbbdabcbcdddabacadcabbabaddcbadcddcdcadacddddbacacdaacdadbbbdcadbcdadbbbdbccbbaabddaaacbdbababdccacabacadbdbadccadbdacacbadabbbbaccdcabbdcaccabcadbabcbdccdbabbadbbbdbbcdddcbbbdbbbaadcacddabdcadbbcdacbadabdaddcaaccdaabcaccadcabdccdddbccdcacccdddacbbcbddbdbdbdcaaccadcadcbadaaaadcaacadcdaacbbbdcbbdddadcabbbcbbadbdbdbadaacababadcbadcdacccbadbaddddbbbbbdcdaccdcbacccabcdbddcaabababdacabbbaaabcddccdababadbcbcabddadadaccbcbabaaaadbaaadbacdcaddbbaadadcbcbccbdcabbaabdadaabadadcababdccdabcacdbccddacaacaddbaddbadabaadbabcbbbbadddbabaabbacbcaccdadcbdaaabbadabcbcccbbcacccacddababbdccaddabadabccbbcddbacbccaabdaacaacbcbdcaccabaddbaabacdbbddbadaadbddbcacdcdcdabcbcaacbddcdcbddbcbdccabaddbddabcababbacbbdaaadbdcabbddcaddcccabcdacaabcaaccbdaacdcabbdabaddcdabbdccccaaaddacdbbcababbcacbbaadbdbbdcabbdabadcbbaccaaaaaddcdacdcdabdbbddddadddcaadacdaacabbbababdaddacbdadadabacccbdcbdaabcdacdbcadbababcbbbbcadcacbadcbbaabbaccdbdbcbaacbbadbcbbbcadabdbbadbadbbbbbaddcbbdbaababdaccdccbacaaacdbabcddabacbdcccdadcabddcadbcdccaaaaddddcbaaacacbdacbabdabaddaacdcabbaddacdddcabcadbababaabbccbadcaccbcdcaddacccbbccbdaaadcacbcccaabdabcacacbbbaddbdbaabcacdabaabdaaacaddddadbbccbcbbcdbbcbbabadcbadcbcababacbadbdbccbacabdabbabcaccdaabaccabcaabdabcbcabcbbadacbaccbdcdaaccccbabadababdadcccdabdddadbababadcddaaabbdcbddddcddcddbbbabcddbcdbcadbdaaacaacdccddabdcdabbddddbbcadacacddcababcabdddbcdaaccbcacdccabadabdaadaddbccccaabdacdaccaccbbdadbccbccacdbcdacbadcbdbbcdbabacdddabdadaacaadbbdcacbcaacadcaadcbdccaacabddabccbcabdcccccbcdaacbbdadccbdcdcdddbabaabcdddcddaacadadaacabdaccbbbbcabcdabaaabbcccabbabddabbdbabdbdcdaaabdcbbaccbcdcbcbbcbccbcbcbbbaccddddabaccdbcbbbdcadcbdbbadadbdbcdddadabddbbbacadccbcdcbccaddcacadbdcadccacacbaabbddddcdbdccacabdcadaabcbabcbbacddddcacbcdaacbadbcdbcabcbabaadadbadcadcbbcdacdddabaadaabdcabacddcbadccdbbcddcbbdddbabaadaacabcaababbdadbbbcadaabbdcadbbadacccaddaaaaadaccdcacddbaadabdabcbbbccbccccacbdcbbdbccaccabaabcbdaacddaddcdadadabbacaddddbbcabbdddbdcbcbbdbdbcabddbadcbbabcdcbabbdcabacacadcddddbbcdaacbabbdabcbabdccabcadaabadbaadcbcccbdabacdbbacadbcacdccaaabccbcbdcaddcbaabdcaacdbadcbbcbdcbccdcabdbabdbbccadbccddbbbbadadacacdccdabddbaabdadcbacbdbaccbacbcdddbbdccdbbdcddbdabbccacddbbdcacaaabaabcabadaacacadcddbabacdbdbcdcaccacbbdcadbbaaabdbdacadddcdacaababaadcddacbdabacabdddcabbcaacacccccdbbddcadcdccbccbbadcdcddacaadacaabcacabadaddbbdbcdbbacaacaabccaabdddcdddddddacadcacbadbacdbbdadccbdcaadcbbabbdcbcacbdbbbcbdadbabcdbdaaaacbaadbbbacdaaaadaddabbaaaddbaabdcacdcbacbddadcdaccccabcaaddaccbabbbadabaacccbcdabdcdcbdcbadbddcddcdbccdbbdaadcdbbbadadddbcbcdacabcbabdbadaacbadbbacbbddacaabbbabaddbbbcadadabbddcbdcacbadabbcdccbcccbdbccabbbcbdaccbdababccdbdcddadcbbacbaabadadadddcbbacdbbccccbdcadabacbbdccdbdcaddcdabccacbdcadcccbaccbbabcdacdbbddddcddbbdaaadcdbbbbcabbcbaddbacbadcbaabbddbbacacbadcdbdbccbabccdabbdadacdcbdbcacacddaabaabdadcdbaadaaabbdaadaacaaabdccacaaccabacdabaacbddcbbddbcbbcaaacccccdcccbcaadcbcbcabcbccbbbdddbbcccadabcadcbdbdabcaccddcdabdcddabdbbaddaadccbacaaabdabaacdcddddacaaabcbccddccdcbccdbaacdbabcbbabaccdaacbcabddaaaaacabddddaddbcbccaacdbdbbdacdadbbbabaabddabddadbbababdcaacbccacaacabacaacadcdbdbbaabddbdbcdbbbddcacadacbdbbaccbbdcbcaabdaaccdadaaccddaacddbcddbadcccaabccabcbbaccbabcddaaccdbcabdcdcaaabaacdcccbbdcacbdbcadbccbddcdcabbaccabbcbccdadadbcddbcaddbbadacbbbabaddaadbacacbcdcdaaddbaacaccbdaaaadddcabaaaacbdbcabdbdacbcbcdbbaccdbcacacdcadbdacbcccabaaddccdadacccbccdadacdbadabaaaaccdaababcadddbcaacacbaadcbacabddcbbdadddbdacbdbdadabdbacbacbadbdbaccdbadcacabababdaaaccdcbaccaabcccbaadbddadaaadbbcadccdcbcaacbbdcaabadcacdbbccacbdacccabcaddbbcaabbcbdbcbbbabcbbdababbddabcaaadacdcbdcbdabcdbbcddabacdbddaadbbdddcdcddaabdcbbdadbdbbcdbccdddacaddbdddbcdacddddccccbbbaaacddcbcdcacdaabbabdaaaabdcabbbbcbbdadcdbbbdabdbbacaaccbcbdbdcdcbbcbbdddcddbbabbbbbadbdacdcadaadddbcdbbcbdbaadabaccaaaccbacabddddbddaacdbcbabbbcabadbcdaccacbcdaaacbcdaacdbabdabdcacddcdcddbbddcdaddaadbccbddbaabadcdbbbcdaaaaddbcabdbbccbddbcdbbcdccddbdddccbaacdcbaddcaccacddbbdbcadbbdadbccbcdabdbabcdbaacdcadddddadcaaaaabcbdbbbcbcbddaddbccbbdbcacccbbcaddbaadccabaaccccbddadddaaddcadcbbcbdaccddcaccbaaabdbcbaacacbddaacaddacaddddbaddbdcaacabcaccaacaddbadcbdccaaacdbbcddaadbdbdccbbbdbbaacbbdcdbcbcdaaddcdddadbdaadcdddcdcbcadabacabdbdabaadbcabcbdacccbaacbcddbbaccddddcadcdddbacdbcccbdbbcdabbddadaddbdabaabdaccabbbdaacabbcaccaacdbbbacbbcdccbdcdcdcdcccaabbcabcdcdaadbbcdccbccbdbadbadbdbaabdcabccdcacbbadcdaaaaddacdddbcdbcabaacdadabdbddbbbcaaddacbabcbdccadbdbacbaabcdccccaacdacbadbbcaadcacbdcddbbddadaadbaccbdbdbaabcddddaadaadddabacdbcabadaabbdabcdbbdbddbbabdccbacbcbadddcccbbbacbcdbdccbcbcdaddcabdbccddcaddbccbcadacdacccaadacddadadddaacbacdccaabbbdaaabbcbcadbddccddbbdaadacaadcadcbdbacacdccadcaaadcdcbcdcdcbbbbdadcababaaccdcbaacaddbbdbaaaacdabddcababacdbcbadccadbdadbdaccabbbdbcdccbadacdacadddbbaddbbcdcdcaddcccdadbbaccddbcaacbddabbdbadbcdbbaaccacbacaabcccbcacdaadacadaddccacaacdcabbbbcdaabbcbcabbbccadcaacbaccdbbcbbccaddbdccbbddcabadbaabdbcbacbccadccccdaccbdaacbcabaccabdbddabbdcbccddcccddcddaaababbaaacabdabbbbbddbbcdccaccdadbdacdbdacdaaabaaacadabadddabaaadaddcbddccadcdbcbcdbbdbdaccbcdabdcbcaadaccbdbaadabdbdcbbaaadaccacbcbddbdaaacaccbbbaccbddaccbbdcadaccabbbddcccbcddaddccadcdacaacbbabcbdbdaabbcadbdddadaaddddddaaddbbcbacaccbbcbcbdbdaabdccbdcaaccbdadbcdccaadaacdabdbacbaabdaacddcaabbabcadabbcbaccbddabdaaaccbaabacccdcdbbbdccdbbbddcbbbbcbdbcabddcbbdbbddcdabdadabdbcbabcacdbdacddabcbdcdbdcccccdcddcdacadaadaccbcbabadcbcaababcadcbdddccbaacbdccabbbbbbaddbbadaaaaabadbbaabcdacadaddcccdabdcbadbbcbbaccbdcbdccdadadbddbabdabaadcacddbadbcccccccbbdbdacacdacabdbaccacadbcccbbcacaabadbdddbadbbaabcadcbdaabdbdcabdaabdcbcbbcdbbddcacdadbdaabcbccbaaccbaacacbcbccdaaaabadabbaccaabdbddacdcaadddcacdaacccdcdccdcbaccbaacdbbbbccccbbcbbbcbdbbaaddcbdddbbcdacabdaaaacbbddddbdbbadcccacabddadcdabcbacbccbbbddbbaaddcdbaaaabbbbdcdbddaabcaadbbcbabdaaaabdababcddaacbbcbbaadddbbcccbdcaaaadddcaacaddcccdddaccddddbdabccdcaddaabadcababbadcabbddabcbacbcbcdcaaccdaccaacdbbdabbbdabddacadbbcbdacbddbcadccdabcbdbbdddbaddbccdcddaadbbbabddcabcccadacbbdabcdaadcbddcbdccacddadaaaadacdcbacadccbacddddcdacdacdaccabadcacdccdbbddddaccdbddbacbcddcdccbadaddbddaccbadbbcbcdadbcbdaddbaaddccacabcaabdadbddbcaacaddaacbbadcbacaacdbddbcbbdabccacdbccacadbddaddcdcababbdcbddadddaaabdaababcbcdabaabdbdacdadaabdaaaaaacacababccdcddcbddcdcabbbcadbbbccbbbcaccabcbaddddacdababbacabccadadbaaaaabdcbbccbadabaabddcabaacbbcddbddadaadcaaaddacccbccbbacacdbacadcbddaacbadddbacaabdaadabacaadaaadbdbdaadbbbcbdcddcabbcabcbadcdddcbabbbaaadccccaaccbcbbababadacbcdddbdabcbdccbcdabdabadcbadcccdcdbaddcbcbccdaabbdacdbdcbdaaacdbcdbbaccbcdbadcbbbbbadccabdbadcccdabcabccdcbadadcabbadddbdaabaddadbbbcadbbaacadcbdcdadccbdcbcaddddbbbbbbccabadbdbccacdbcbbaccacbadcaccabcadcdcbdbbaccbabaabbcdcabbbccdbacbdacadbbdcdaaddcccbadcdcdadcdcbadcacabccaadcabcabccaabddabcbddbdcccdbdbbcadcbabaabbadabddaddabbdbdabacbcbcccbbbbbcadaadbcbcabadbdcdabdabbcbbbdddcaabbdbabacddacccbdabdababbddabdbbcdccdabcaddcabccbbbdaacadaadadcbdbbbaaabdcdbcdbbcbaaddbaccbcabddcbbaacddbcddddadbabbbdbdddbbbabdadbbdccccbcacccbbbaabdddadcacbcdbabacdccdbdbcbdbaaccbaacbaacaabadabadbbddcbdaddacdddbdbbbadbcddcdbbddccbcabbdbababcbdcbdacaaabcdbcbadaaaacbbacbddccdaddabbcbdabdbabaadcabcbdddadbbadacdcacabdbdbadaabaddcbdabddbcbdaacabcacbbdbccccccdabbcacbcccdcadbbaabbdccbccbbcacabcdccaddcaaaddaacabbdbcdbbadadbcadcccbaacbcbdbdcacbcdcabaddacbbcabbcadcbcadcccdcdcbbbdbddcdcdcbbccddbaadadbbacdbbddccaccadccdabbcccbdddcabaadabcabdbaaccadcdbbabdbdbccdbcccbbdddacdbdcdbddadadcdababbbbccbaabdcacddbaccbaddabdbccccdbcbabdadcccbbbcccadcbbababdbbdbbcccbaababadbabcdaaadbbbccddbcdaccdbacbbadccdabbabcaddbcbdaabcaababcdcbbcbbbadddacadbacaabbbdbacaddaacabbdcccbacacbddacbacdacbcdcaaabdaccbdcdbaaaccbbcddbcbdadaadaabcabaabcbcbdccddbbbbcacdbbcaadabbacadbddbacddbbbddaabcabaaddccadcbcababccdcbddaadaccadaacbdacabcdddcbaccadaccdcddbbbbaccddcdadbaaaadbdcdccccbaaadccbcdbcbdbcccccdcacbbaddabbaabbdddddaaddccbddacdccacabbbaacbabcacabacaabbcdabcdaabababaccbdaaddcbbbaccbaabbabaadbcabdcccaddbcaabbbbbcdbbcabaccbbdbccabdaddadcdbddadcaadcbbdaacbbacaadddadcbadbacbddcbbaabccdbadcbccadabbdbbaaddadcbdabbcbdcbadccababddacadbbccdcdbbbddadabcabadcaadacbaaadacddadcaaacacbaddcabdbbdcbadcadadabadbbacdbacadbaddbdcbcabbbcbbdbcdaaabadaddadbbaccabdbbbaacdbdbdbdabcdddccadddbcbdbbbbbadcaaaddcdddbbccdcdaaddadccbacabdbbdddbcbbbdadbadaaddbabcabdabddcbbddadbddddcaaadadbcaacbabbddaabdbcdcbdddbdbdddcbacadcdbbcddccdcaaccdbccaacbcaddaabaaacbbbbcadaddaccaadddbdadcabadbaababaaadcbddadbdadbbcabcabbcbabcbdcbcaadbccbdaccccbbbdbbcacbacabbbbbbbbbaacacbadabccbbaccdbdcdbbadccdadcdbbccbabadaabcccadbdaaabcbcaccadcccccadbadbacabccdbadaadddacdacddcaabdbcbdaaadacddccddadadadbddabaabddaaacdbcaddcdadacccbacddcdbaccadbdcbbcdbadbbabacbbdbbccdacdadadbbcabadcdbcbdbdbbccadcacbbdaaddbbddcabdbababdabddbcdbddddcadcaccbacdbcbaddbcadadbcacbdddabcdbdcccdddcdcdbcaaacbdaccaabcccdacbccabbdcbbdaadccaccdadbdababdcdacdbabbdaccaccbbcbddbaababdcbacdcacaaabbdadddaccdabbdcabdbbdbdccdabaabddcdbaabcadabccbaadbbabaaadcddcbababccbabadbdabbaadbaaaaaddbbdbacccdbbbdbdcacbaabcbdcabdddbccbdcbcddbbbdcdbcbbbdbbdccaabbcacbccbcdbbbbaaddbcdbccdcbaabbcadcbabadddbadcbddbacdcaadccccabdbaabbcaaacccbbcddbadaabcbbdacacbacacdabbdaaaadcacbdabbaaacdcacdacadbcabdbaddadbdaacdbaaabbabbaacddadbdcbdbababbcaaabdcbcbddcaacdbbcadacdcdccbabbcdbcdbacaaccddddbbabadddbcbaabccdbccccdaccddadbbaccbabdcdadbcdaacacbddcaacabbaabdccabdbaddddacabdbdababddbbccbbdacdaabadbdcbbddadbabcababdcbadcabdacbdbdbbcdbdcccbbddbbddcddabdbcacdaaddacacdaabccadbcacabaadbadbbbaccdcbcacadbbdbcdbdcabcdcddddcbdbccdbcaadadaadbcbcadbdcbdcacbbacddcbabbbacacdcbbbdacaacdbcaaddccaabdbdcdabcbbbcbbcbcaabbcbaadbdbbacdcabdcdcdbdddabbcdacdddccddbabdbccbbdacabacdccabbaabdaaccabcaacabbccbbddbdbbbbbbbcdacaaddbaacadbdacbccacaddbaccddacaddbbcdacacaccbdcbddaaabccacadbdcbbdccabacddaadbbcbbdddcbdcadbbabcdccdbabbbddaaaadadbcbcbbbdabcccccadaaaaadbbdaddabbacacbbddadddbaacbccccdccbaaacaadcdabaaddbaabdbcddadcbbddbdbbbdbadaaadaadadbdcccdcdaccbdabbbaaabcacdbbaacbcdbcadacbbbcaacacacaccddacaabcbbcadccdcadcbaddbadacdcdbbcddabbaacadabbaddaabccddcccdacbaaadbbbaabdcdbdbbacddaacdcaabddcccabddbdcddcccbbbdbacbdbdbccdbbcdacbbadcbbcdbcdcabbdbbabdadacddbdcabdcbcacabbdbaacdacbbcdccdcbdcdcddcbdaadabccababcadaccbacbaaccbacbacabbbadbdbbbdbdabdcdbabaccdbcadbbccbbccccdacbaaadcccccadbccdcccabcadacaadddaaddcaccddaaadbbaccdaadabcaadbdaccabccacdddadcbddcbabcddbbadbabcaccbdcbaddbadcaadbdabdaadddbcaaabaccaaacdadbaddcbbcdcdddddbccdbdbadcabbcbabcabdbabbcacbddbaaccbbbdbadcddaccbddbcadcbcddbcabccdaaababbcbbcadbbadbdbababbdcbcbdaabacdaacadbbcddabbdbdccabdcccdcacbabbbaaaacbccccbacdcdadabddbbbacbdcbdacbbbcaaabbbcbcdddbadddccadaabacccbadcdbcbdacabcddcadcbbdbdbcbabdbbcaaddbdadbabaacdbcaacdbbabaaabdbccbdbabadbdabbbbacdabcaacbcbccdcadbdbddccacbbcababbbdcabbdbcbbdbdbcdbbbdcdbdadabcdcdccbddccddbbddcbdbcdcbdcaabdacaadcdabcccdddddddcdbbbbbbacbccaacbcddadbadbdcdadccdabcbccdcaccccdcdabbdbcaaacabbccaaadadddacadddadbdbcabdbdabdccbdccccdbaccbdcdaadbbdbccadbaaccdaddbcdacaacddbaaaccbccaacbcabbdbdaaaaacbbbbbabddbabbbbbcaadcabddddcbdcbcddabdaacacbcccaabadaccbbabacdcccacbadcbbcaaacddccaaabbaadcbdbadcbabdbdadaaaabcaadaccdbcdbcaaddcbdbdabaaabaacbbccadcbbaabccdbbbaaccddccddbcddcddbcccadcbabccbdabcbbdbcdbbdcadaccddabccabaddcabacbcddcdadacbcbcdcdccbabacdadadcbabdaaadacdaabbabadbddacabbcabbcddbbdacdcaaccabdbcbbcbdabbaccbddbbbdaacaddbacddbacbddccdabdddbabcbbdddbabccbcbbddbbaabbdbbcdddadbcbcbddacccddadaccbabcbaddcccbbddcddcbbdbabaccaaabdcadbabccdbabcbdbcabbdbbbdaaabbbcdcccabcacbdddaccbabbdcccbddcdcccbacdaadcccbdaccaadacdcbdbbdabdbcabadccaccacadacbdcbbadbcadccdddadcdabacdaabccaccacabcadbcaabadcabacbdbabaacdbbadbbdacaaddbcacdcbddcacadddcccdddacdddbdaaabdbbbbacadbbbdbcaaadababbddabdaaccbcdacccbabbcadaaacccabbbadcacddabacccdacacdbcdddaadadcaacddadcbbaaacdcbadaabcdddbaddcbcccbdaabcadccbbbbacbcdacadadcbccbaaadbcabbaddcbaacdcbacbddcdbcbddaacccbadbbbabadcccbaabdaabdabdbaddbdadadcacdddbcdddcbcdbcccacaabdccabdbbddcacadaaadbdbadddcbcdccbaaadcbadbbbabcdccbaaddabadcacadabcbbcaaadabdbdbcacddadccddaacabbcbbacddbbddadcddcbbabaccadaaacdbcdddccaadcdadcadccabddadacdbbcadacbaaddbcbcdcbbdbacaabbaddcbcaacbcdabdcbbdbaccdacdbaccbadadbddaaabbdbdbcabccdddaacaadccdddbacdaaacaaaaadcdcabadaacddbdacbbadaadcaabaccababddccbabaabbadccbcacbdcdaabadabadddbbdbbddbcbcbbbabccaccdcababcdcbdccdcdcdbcaadacdaaccaacaaacacccdcbdbcbddabccdaadacccccdabaaaacdadacbdccacadddcbcdadacccccbabdbacdccaaddbdddbcdccbbccabdacbddcaacadadbaacdddbcacdbdabdadcdbaabdccacddbbdcabccccdbcaddbbbadcadbdbaaacddbdcdabdddcccadbabaaddbcccddddaadbcccdcddbbacdcadccbcaacabcbacddbabcbbccaadadabadcccccaacbbcabcbdacacdddbdbabcdcadcdaacdbbcadddddaaaaccdbbadcccdccdcadcbdcbbabaabccccaabccdcbcddbcdacdccbdbdbdcabdadabacddaaacdbbadcdaacdccacddabaddabbbcbcdbadcbdcbbcbdaddcccaaadddabcadbddadcacaabbccbcacbddbbaaccdcdddcbbccbdacacdabcbaacbbdcbcbddbabcddccaddbbbdbaabaadbdacaddaaaacdbacbadccccdcccbcdddddbcbcaaadccabadaaacbdbbcaadbbbaccbbcabcbcccdbaabcdcbaaaacaabcbbbdaabbbdcaccbbadcbcaccbbbbcdbacabcadaabaaaadbcbbabdcbbaaddacccadcabcbabbacdbaadccdcacacaaabdababcdcbbdcbcadabbdbbabcdcbcdbcadcbabadbbdcccdabbdddbdbddaacadccadadbbcdacdbdacbdabdddaddacbdbcaccacaccddddddcbacadbadccbbacbcbdcaabbbbddbcaadbccbaaacdbbdcccdccddaaacadabbacdbbcccaaacddaaccdddbbbbbbbcdaacdadbdaadaaaacbadcddddaddadccbbddbdbbacbcdadbdcdabcccccbcdbabcdaabbdabadabbccbcabbcdccbcccddadbacddbbbaddabcdacbbcbaccadbddadaacdcabaabadddcdccdcacaaabccbddccabbdcbbcddbccccabcdbdaddbdbcdaccadcdcdddabbcdacdbdbdbbcdcbdbcabcabdcbbdbbacddaccabbbbabacbcdadbdddabcbbcdadcbbabbdbbbdcbbcdcdbadbabbcbaaaddddaccaddbbbabadacaadbdcdddacaabdaaccccddcbbccacccdbdbbcbdddcacdabaabcbddaaaacdadabcbbbbaccaacdccdacadacdddcdcabacdbdcaddaaadcadcdaadcddbbbccabcabccdcbbadaddbcbdaddabcdaabacabdabdcdcbbadcbaddbdbabccabacddddaabacabaaddacbcbadcccbdcdccadbccdadbcbcdbcbbcadbbbacdacbdabcdcbcccddbdddabddabccccccdbcadccbcdbaaaabcddbabbaabaddaccddbdbadaaccbccaabbddbccdbccdbdadabdcbdbbcbdddacacdbbdddcdcbacbcacdbddabcacdddbdbcbdbadccdcbdabaaabbddccccadadaaacbadabadcddbaccbcabbbcacaababcadbcdddadadaadabccbbccddbbddbacaaddadabbcbcbcdabddbdbaaadbabdbbbcdaddaacacdaccdcacccabadaabaacccdacdcaaadadabbcbddaaddbaaaaacdddbbdaaddadbcdbcbcccbdabddcdcbdbaaacaccddbacbcddabdbbdbbbbabbdcacacadbaadabaccccabddbcdbbbddcaccdbacbcbcddcadabaaabdcabddccbbdadbdcbbacacbdbaacaabdbbcbcbccbbcdddbbdbaaccddaccaaccbcdbdccccdcaacbacbabbdacaadbdddbcdcbdcbbbbcbadaaabdddcadbacccdcbaaaaabdcaaaaaacccaabbabacbdddbbaaaadacbcdabaddcadbcadbddabadbcaadcacdabbdbadbaddbaccadbaadddacaadddabdddacdddaaccdbbbccddbcddbcbddbbbdcbbdcdcabadabcdbdcbacbaabcaacacdbcdacbcaaddbbacbbdbadbdbbabdddbbcdbacddddddcabccdbddcadabadccdccdcaadcdabcadbbbccdbddbcadaabbcbaccbcbdcaccbddbdcdbccaddaaacaddabccddcbbbdbcbacabcadacddbcbbbdbcbbbcbccbacccbacaddbdacadaaddcaccbcdccdaabcacddbaacdddccadcdabddaccadcabadacabcdbcddbdacaccccbacbcbdbcddabcacdcddcbaaaddbaadddcbbcacaadcabcaaadbdabcbcabbaaaacdbbcdcbcadadbccccbbcaabbccdababadabbbcbabbacdbbdddddbdabdabacddddcbcdadacaadadbccdacadcacaababcbcacdccdcbccbcdcabbbbcaadcddacbcbddbcbdaaababbbacdcbbdcbabadddacbddacadbbdbcaddddcbbbcbdacabbbcccaadaaccabaabddadacdacbaabbcdcdbcccdcdcbaccbbcaaadaaaddacbaddacdaccdbcbbbbbacdbcaccaadcccdcadbcabbadccdbdccbbccabadccadcbacaacaacacdaabcdbccddcbdcdccdccbadbccaddbdbaabdaaccbdddddaadddbdcbdbccbdddcdadddcccbbabacbdaaaadcbdcaccccaabdbbcdbadacdaadcccdadcbcdbcbdadbbcdbbdcbaaadcadbbcabdabcadacbaadcbcaccaaaacccadaccabbcabbbbdcabbbcbcbdcddbbacdccdaabcddaccabdcdcababcbabbbdcaaddabbbdccdbbbdbacbcdbcacaaddabdcddcddbcdddddbdaddbccbacddccaabaabdaccbcdddbdbdadbbcdbaccddddaadcaddaabdabcccbcbbcbbabcadadbdadddcbddddbccacbdcaccccbacbcdacaacabbadbbdcacbdadbaabbcaacdcdbbdcdcdbaacadaddcbadcdacdadabdabddbbccccdcaddabdcdabbcbadcdbcccdcbddcdbdababcadbdadabdbccdbacbadabbcdcdadcbbbcacaadcdddabdabcddbddadccddddbabbbaabcbacadbddbaadcddcadbcbabbbadabaacddddddcbdcadcaaabadccbbaacbbaababbccbdccdcadcacbbddcdadbcccabacccbddabcbcaddccccbabdbbaaaadccbabcdaccbcbccbaddbdabdadcbabdabccbbbdbdddbbdcacaccabbadadbacdadcbccccddcbcbdabcdbcacbcddaacddcddbdabbaddcccdadacbdaaaccaacacabcbbdccdccabbccbadcdbcaacacccaccbdccbcbbcaacccaaacdbcadcacbabccacdabbbdbdadcbaccbcdbadbcacbcadccdcbbabbbdccdcaaaaddcbdcaccdccbabcbbacacabbdcbbbadbbdcbdabcdbddaabaaabaabcdcaccdbbbcbdaacacdacdbdbaddccacadccacbaabbabddcbabdaacdbdadbcbbbbbcaddabdabadbcbbdbbaabdcdcadabcddadccaaaccdddaccddcbbccaabcdbdaacdacadcbcdacdabddbcdcdccbcdbaadadacbadcbcbdaaadbdcbcacadacacbcbacdcacabccbaadbcbdbdacadacbdccbbdccaabddbdbacaddccbabbddabacadaddaabdbbcddcdddbcdcaabcaabdbcbcddadcbbdaaaacacbaccbbcbacccbdaccddaddcbacadbbdabcdaddddbadcbdbaddabbbdcbdbabcbcadaabaacdaacaadcadbddaadcdcdcbadcdcbadccadbcbcaababaacbcadddcabddcbbdcbbabbacbbcabccdcdcbadabbabcbbdadcabbaaacbbdbdcddadcbbbccacdbcccaaacadbaccbabdccdacbdcadddbcaaacaccdbbcddbbadbaaccdbbcbddaaddaadbdcbcadbdbdacbadbacabcccdacdddbcadadcaaabaddccddacbcacddcbdbdcdabbbbccaacabdcbdbccacacbacbbbcdcbbdadbbddaddbaaddabbccbabdbbbbadbadddbacddaddddbcadcccbadcdacadcbbdaccdcbabdcacddaddccbaadbbccadcbcdabbdcdcaddbbdbbdacdbabbccdadcdabcacddacdabbbcddabbdcbbbbabdabbaaaaccdcabbcaddadbdaddcdacabbdbdbadcddbddadaacaccbabdbaabababddacdabdccddddccaabdadaababbcbaacdaabadddaacdabaacbcddbcabcaddbddcdbabdcccacabdcddbcdbabcbabaaccddbdcddacdccdbdbdcdbbcbbacadacacddaccbaaabdccaababacacadbabcbccacbddbbdbddbccccbbaabdacbacbcadbaccddbdcccabdacabbcdcddbcbbcbdbdabdabbcddcacaddddcaaaaddbdadcaccbbbcabdcabdbbdbcaabdcaababddbbaabddbdbdbdbbdccaadbbadccacccdacacdcabcdbcdaadabcdaccbddacaccbacdadbbcbdbcaacccbddbadaacadbbacbbddccdadccaaaccabccccaaddcbbaccdbbaacdbabbbbcddacbcaddadccbacaabcdbcabcaababccccaccccdcbcdaaadaadcbccbacaaddccdccacabbaaddcdbccbdaaacacabdccdcdccbbcbbcaabacbcccdabdacbcdadabdbbbcdacaacdcdddadbcaaacbcdabbababbaadcabbbdcbddbbccbdccdbccddbccaacbcdcbcbcdabbcabcbbcbcdddbaccadbddcccbdbcbbcabbdabadbdbbaadbbcbaabdbdaadaccadbdacdbbbccadbaabcdcabacbabbacdcdacaacbdabadaaccaaaabcacccdcbcabdccaddaacaacdbbbaabdbdccbcccbdbcbcbacdaddbdbadbabbcdbddbccadccaadaadbcbbbcccbaacdddbacdbdabddcbdddabadaacbdcadacadaaacdbddbdbabbabdadcabadabcbbbcbbdabaccabaaacacddabbdbdbabdabbcaadadadaaaddbbbabdbcdadaabacbdcbdbacbadbcbcacabababadaabcddaabbcbbccaddabddbacadbbbabaabacdcbacbdbbdcbbacbdcbdccaaddccccdcccaabcbcdcdbacdaacadabbdabaddabacaaaddbbabbccabccdcaadcbddacabaddbaaaadacdabccbbdbabdcccdbcbccadbbbbcaabbadacabdbadcbdccaacdcdbccbaacdccaaacbccbabadddbacbbadbadbcbcbabbcbddcddacdbbcbccaccabdabbcbabcbcccacddabadbccacabacaaaabdcbadacbaadbaccbbbdbbaddbcacddaccbbdacadcdabcbaddddaadbddadcdbadbbbbddabcccccbbbaaccbdcbbadcbcaadbaaabcdadccacccddacaddacdcbbaadcbacabbdabbcbcbcabacabbdadcdcaddcabbdcbcbadddddcabdbcacddbcdaaaaabccddbdadbcdddbaccabdbbbbdacdabcadbcabaddbcbbbaacdcdbddbcdcacdacbaccbbaccdcbcadcbccdbbcacbddccacadbabcdbcddbcdcabcdaccccacdbbddacaddaadbadacabddddaacbacbababdddacbacdbdaabccacbddccacbacbcccaccbbabddbacaabbabddcaaaccddcacdaddbdbbddabcadcdccdadaccbdcccbbacbcbaddcdbbcbaaadbaccdbcadbbdddbdcdabaabdcaadbbdbcdcddbabbdcbbdbbbcccadcbcdcdddaccbbbbcbadccadbabddcbcbbcacccdcdbaacbbccdcacbdbcbdbbddccadcabaadaddcacccaabcddadaaaabaccdaadcdcbccbbdcddaddaadaacacddbaccadaadddbbbabbacdbcccaacdbbcadbdcabcbabbaddbcdabbbbaddcdbabacbcdadbbaacaaabadabbbddbccacbcbbadcdcacaabddbdbcdabcbcdbacbcdaabadcabbabaccacccaacdbcbcdccbbddabcbcdaabbbdcacdacbaccaacaabccabdbcaababcdcaabacabdacbdaacdcbcdabccbdaaaaccdcbbbdcbbdbccadadbaddaccddabbdacccbdbaaaaaddabcaaaabcadcbdbbadddcdacbcdaabdbcbaadcbccadcbdacadcccbaadabacbadcdbddccbdbcbdacaadccaddadcdabbcdddabdbdcacacadccbbdbdacdccbcdbacdaacadcbbccbabcdccbbcaddcdaaadacadacbbaaccbadacadbabbdcbdcbacbcccbcdaccadbcbdaacdabcdccbbcdbdbddbbcaadcdcadcaaaaadddbbbaacdbcabcbdaaabbbbaddbbaadccaadcabacabaabdcdacddcbdbdaacaabbdaccbbaddaddbbbbbccbbcbdbbaabaacbaddbaaaaacbbaabcbddbadcbaaddbbcaabdbabadbaacabdbacddbcdbacccdcbddbccbacbaaadcadacaaccdabaadbcbacccbadcbcdcddabcddbddcdddbaccacbaccbbadcdbddcdccabcdbcdddcbcaaaaaaacbaadbddacacaddacbcccdcadaaaaadcaabdbbdddccddbcdaaccabccbabdcdbadcdcccbbababacdcccdcbbcdddbacdabbbcdddbddbbcccbacdacadccbcacbdbcdcddbabbddacbddadacdabdcbbcccaddabadadccdcbbbcdcacabcccbacadaabcbdbbbabcaaddbabaabcacdbaaabdaabababcbcbabaacabacddddadbbacbdaaacdcbddbaabbbdabacaacadcababcbcdbadcdbcdddadaadccabadaaacacccbcccccccbcadabbbccbacbabbadbbabaccbdabdbbbaccbaacbdbbcadbacadddcccddbcabccaaabddcdabaacadbcbdadbdbddbcdcdcadcdabbddcdbbbbdbbdbcadbadcaddbdcccabaabcdbadcdcbdadbbddbacacbcbabacbddbbcccabcaddcccbacdcbbaaddacbbcbaaccbbbbbbcbcbcdacdcccadddaaaddcbddcacbbcadaddcddbcbbbabbabdaadbaaaacbbbcabdabacddbcdcbcdcbbbdcbcaaabdcbddbbcdadcbaadcdbccbadcdcdcdbcdcabbaadabbccabdabdbabcdbccccbbcbbaadbcdbdddacdacbacacabbadabaaaddcacdcbddcadcddaccbdcbcaddbacbdbcdaddddcdbbdcbabbcccdaccacadcadcdddcbbdbccdbabbbaccbabaadbcbdccdaabcbcdbdcabccddacbccacbccabddacbbcaaabaaaaabcbdbbcdaabdbaabbbadaacadabdabcccdbcadbcbdababadbdaaadcbdaaaccaabdbabacdadcddaabaaabcbcbadcbdbddbdaddcbbbdadabdadabbbdadaccbadcadcbadbdaaabaaaccbcaddbaccbcdcdabdbdcdbddbadadbcbdbdaacbbabbcacdabbdbadccbcabddddcbacdccbcbdccddcddbcadbabccadcddbbcddcaaabbabddbbdaadbbbacbdddbbcdabacaabcbbccbdcadddcbdbcccdadddaadbbdacbdabbcacddadbdddbbadcababbbbadaacaaabccdbadcccdaaadcabadaabddbbbbbdbdcabababbbabcbbcaaddadcdabbdadccacdacdaddcdabaadddcdbadbccdbdbadaaacacdbdddcabdcdacbddccccbbdcdbdbbabdbcbcadccbbbcdaabbcddcbacadadbbdabaacbbcbcdaccaaddabcbbabbacdbabcbbddababddabaccabbcadbcacccaccaabdbbbcdabcadabaaccdcdacdddcddbcbbbadadbadddabacccdaadddcacdabbaddbcbbacbabddbbabaaacbacaddaddabacbddbcaaaadccaacccabadddbbdabdbbbdaabdbbbcadccadbdbdddbcbdcadbbddbabcbbadaccabcbbbcbaccdbdcaccccacddabaabacdbabdbbbbbbcbcaabbbdabccbccabacabaccbcbbbdbacaadddbddcdadbbbbbbcbddbaddacccbabccddadcdcdcbcabdabbbcdbcdcdccaabaadababdccddbbbcadaaacdddbccbcadaadbbccdbccabbdccbdbaaaddbbababdcccdcddbddbbbaabaddaacbddddbbdddadcbdbbcbccdbadbcbaadabbabbddaacbcadacaaddcaddbbddcadbdbcdacbccbabddcdccdabbadadabaaadbccdcdbbabccbbacadccbcadaaaaacddbccabdcaddbcdadaadbccdbacbaadcaabacacabdaaaccadacabdcbaccddadaabdacccdcadbdbadadacaaccbbbbacbdadbbbcbbdcbdcccabdbccbbacabbbabcbdacbbdadbdaddbcbcbccbabadcaddddcaabdbdbcacddddacbdacdaacababdbddadabcbdaccadbbbbcdacdcabcccdababdadadcbcddbdccbbbabbdbccdddcabbaaabdcaaaacbacdaadabcbbacbccbdcccbacaabaabdcacabdaabdcdbdadddddbcdbdaaccbabcabbadaaccbaacaacbadccbabcbdadbaacadabcadddbddcbcdddcbdbdddaaacbcddccdadcbccbbadddbadcaddacacaabaaadadccbcadcabdababacccdbcddbdbadacbbcabadabaabcdbabbacadcdcadddbcdcbcaaabdcbcdcbbccacddcbbabdbcbcdcadbdcdddbacbdcbcacbdbbacdacbcbbdbabcdcdcbabdcaadbdbdaaacbccccbabadabaadcaccdbcdbdcacdcacdadbcbbabdacbdcdadbcdbdddcbccdaddbccaddbaddcbbcdbbbdccacaabdbdadcbdbabaababccbdccddaaaacdcaabcdddadaccbacbdcdbabcdcbbccadadbababbaddcccdcdadcddabacacaaadddabbcbddbccdddbdaaddadabdccaabbdcdcacccacacabcdcdcaadcbbbabdbdbacdacaddcbabbbcdddacbacddccabdadcbdaacccadcbdddacccacdbbbddbbcbccacbbbdadbbcdaccbcbbccbccdbaacdcddbdaabbdabacdcaacacbbbdcacbdbcbcdbabacabdaadabdbcdcbbaabddcacdbcdbcbbbbccabcdcbaadbaccdbbbcacccaacacddcaaadccbadbcdbaacbabbabdbccdadbcbcdcacaabdadccdabdddcdbdadcbbdadaddabddabdbcaccccbacbcabcdabcaababbcdadadcaaacbcaccbccccdcbaddcaabdcbbdbbbddcbbcadaabcccadbcdadacdbcdadcddabddcdbaddbcabddcdabbbdbbacadcddacbacdbcdcaaadcccbcaddcdbcdcbacdddccbbaccccaaaaabdbccbbcbcdcbbbccadbacbbaccabdcacdcccdcadabbbadbdaccdbdbbcbacdbcdccaacbddbacdcacccbabbdbaaaaaacbdbcddccbacbacbdbccadbbadabdcaadcccdddaacdccdddacdccaadbcaacacaaabbbdcdbbccaabbddaaabdcabadabdddcdcdcdbcbaccaddcdbaacdcbacadcabbbabaaccacdbbbcdabadaabacdacbdcbcacdabaabdbadacaacbadcbddbccdbcbcadcbbadbbdbacbbaaabddacbbdbcadbbdadadcbbccbcadbbdadcbbbaadbdbbbacbcadbdaadbbddbbdddabbacdbaccbbbcabbbbdbaadccbaccadddaccdaacaaccacdbadccabcdadaccdcccbdcbdcacdaddadddcddcddcbdcdcccbabcbaabbbdcacabccddadaabadbacdaaacbccdbccbaddaddcddbbbcdddabcadacbccaddbabaccbcdadacdcdbdcabaacdbcddaadaacbcbabdbddcadcaabbcdbdaadcdabadadaabbcdcdbdaccaddacaaccdcddacbbadcbadaacbaabcaadbddadaabcabcbdcabadcccabbabdcdbadbddbdcbddcdbcdddaadbbcccbbddcbcccdbacabbddcbbddcbdbabdaaccabadadcbccccbcadbcbbbddadccbaccdcadadbadabdbacadccbbbdccdabdbcacacdadaadbdbbcdacadaccdaaccacccbddbdbabcbaacbdbabacbdacccdddaacccacdddcdddcaadbddcbcdcbbbcdcbbdacacadabdacaaddbcddbbcacccbccccbcdcadcbdaccabbacaddbaacbabdabddbdabacadaabdbbcdbbcaaaadccdaaaabcabacabcbcbddbcabbbdabcdbdaaccbbbaacbcbcddbaacaacaabaabdabbcddabbccaaadcabaabbbbbdcaadcbbbcbcbdcdcaabcbcbdbdaaccacbbbdcacdccbdbdabadbccbccbadcacaccaaacaccdddddbbadddbadbbadacadbddadbcddaccdadaabdcbbcacbdadccaccbabddadbaaccbcbadcbcabdacdadbaccccbcbdacacdbddabbbacaaaddcbbdbdccbcaddcbaddcadbdccdabdcdbddcadccdacaabccbbabbdacddadcccabacbacdaaddbbddabdaaacdcbccdcbabcccbdaabdbbacbcbabbadbbaadbddccacddcdababcaabddcbbcbbbbdddccbadcdbdbbdabcddcbcbcbdabcadcbdbbcacddbdccacdcbbcaaaccdddbbddccbadbcddacaaabdbbdbdcddaaabdbdbdbcbbccccacbbcdbcdabcccdcdddcdddacaacddddacbbaccdcaabdadbbcababadddbabdadaabdbcbbddbdacabbbabddaaabcdabcbbdcccdaabaccdcbbdadbcdadadbccddacaccdacccdaddbddcabddaadcabdccccabbbcccccbabbaddddacdcdacbaddabcccacbbcdbbdbabbcbddacacabcacdccaaccbabdbdddadbadbccacdabdcbdcbadcdcdddbadcbcddddccddabddbddbabbabbbccbcbccdcdbcbdbbdbaccbcbddddccdccccbddbbccbdccddaabcccddcddccbddadaccaababdbcdddabbdbcaadabaaabbbabdcdabcbadaababadbbbbbcdbcdabbbdaabdccaabcbcdbaaacbabcacbdbdaaaaccadcdbcaacdbacabcdccdacccddcccbabacddbbbadcdaacdcdbbdcbbcdcbadacaccbaacccddddcdcbbacdcdcabcadacabdbbdbccdbbabaaaccadaacbbacbdccabbcdbcccdccbcbacdcdcdcaabbdbcbdcbadcdbadbcbacbdabcabbabcaaddabdcaabbbdbbabccbcacccbdcdcbacaabdbaabbacdcabbdcddcaccdbdcdccdaaaabbbcddddabcddbadcbdbdccbdabadaacaaddacaaacadaaccbdbccdddaadaababdabdadacbdacbcbbdabdbcbcbadbaddabcddddabdbcdacbbabaadbcddbbdccbadcdccdacdabddabdcbccbdbdadbbccdaacbbccccdaaadbaaddbadacacdcaabacdbbdbbbdaadabcddbcbcaaddcabdbccddaabccdcdadacdcaabcdacccabcbccdcaaddabdddaabdbdbacadaddbaddcccdbdbdcdcacdcaadcdccabbabddacddacdcbddaadcaabbcbcdddbddbadcadbdcccaadaaaadbbaadacbabcbcddbcaadbddbdddbcdbabcabbcdcdccdabcccadccbcabaddcdabdcabbbbbbcaabccddcbccdcdbdcdcdbadaddbadcbacbabdbcbcbabdacbabbbddabdacabdbddadacdacccbadbddbbadabadccadcabdddcbabdabaccbdaaaddaabddbbbadbbbbcddbcbdbdabdcbdcdbcddddcdcdbdbacdbdadbcccbbacdbcddcdbdbadaddbdacdcaddcababbdbccdaddcdddcacdcdddddbadbcaababcdbdcdadccaaabbcdcacdbaaccaacadaddcabbbaaacdbacabcccddcaabbbdbabbccacddbbbadaaccadbacbaddbadbacabdddbcddabcbaaaacbcdddcddadabaacdddadccdabababaddacabdacccacccababbdcbdcbcccbdcabccdadccabadbabcbbcbaacdcdcddcbccadaadddcaadcbacacaddddcaadbbdcbbadccccabacbcbdaaccdcdbcadcbbdacbcabdadddadbabcbacaabdbcddacdcbcacbbbadcdaabbdddbddcbdbbabbacbdbddcdbbbbbcbdaaabcaabcbabddcabddcaabdabddadcdcdbdbbcdccbddaccccadacdcabdccdaadadacdddcbacbcddccbbcddcccababadbbcbcbadcacaaaaaacbdcddbbbcccdcbadbacbdcabacbadbcdddbcaccdcacddcdbdbcacccdcdddacdbbadacdbaaabaaacbabbcacbbccbcaacddcddbccdadababcbdaddbbbacbaddbbacbccacbbdddaddccbacadddaaaddcccddbbcadcdabcabdbbcabaaabaaddcdaadcadcaddabacbdbddddbadcbcacaddabaadbbbabacbdabbbcaacdcadaabbbcbcabdadaccabbaaaabccbbbabcddbaaacdcabadbadcadcbbdabccadadadcabddbccbadcdbacadacdcabdbcddcabdbdcccaaadbacaaccddadbadbbccabddbdccccbadbcbbaccaaccdcbaddddcddbbcdddcbbddbaaabaddccdbabbdabbccdccddadbcddccabbdabcaadacddaadbabcccccdcaabcbbaaddccdbbdccdaacaaadbcddcaabdaccbccacbaadadacadbadabcdabccdcabcccadadbbdcdddbcddcddcdcacbbbcbabdcaacbbdabccacbabcdbacbaabadcbacbbcadccbddddccbbbbcbdccbbcabdbbaaddbcddbcaadddbcdccdccdbacdaddcbaaccddbcdaabaaabbdddacbbbbdbcaacdadbddbccacacccbcbdbdcbbcabdbccbdacaaaabdaddbbacaacaaabbcacccdddadabdcadbabadaaabbdddccacbddaadbbbbacadbdadbbdabccacabdacdcaccaadbadddbbaacbdcbccccdddccdadcaddadbaabaabbdbcadcccabbabaaacdabcadcaccacbcccbdacbbadbaabaddcdacdcdaaadbbbacbacbdbadaaabbcdbbadadbaccbadcbcaaccadaadcbbcbdaaddcbddbadbadbadadcbdaaaacbbacdadbddcbcaccbdddcbbcabbbbadabccaabacdbbcdbdcbbcbdbbbacbdadadccabdcacbddcacdbaccdddbdddaddcaacccdbbcbcadbaaccdcadadbbdbcbabcabdcdcbbddcbbbcbcababdadcbcdabddddabdcaacbbadcdccccdaabbbdcadbaccadcddacdbdbbddcbcdccbbdcdadbdadabbbdbbabaaadccbabbcadbaaaabddcddccabadcdbbacbbbcdcabccacbabcdabbccbaabdbdcabbbacadbacdbcdabdadcdbdccaabcdbdcdcdbabcbbdbdbcbabcadcbdcaccaccbacdcdddbcaabadacabddabbadacaadbcddddcbccbdcababadabdddddadccbbdbdbbcadccacbbbdcdacbdacbabcccabccdbbbdacabaccdcbdacdabbabddddacacdbccbdaadaddacbbbaaadaddcdadddbbacdcaacbccbdaaabacadccbbdccdccabcacabacbdadadbbdabcaccadccddbaddacaacaaddcbcaddbcadacaacbdabadcadccdcddbcdbdccbcbbdababbccaaadcdbbdaddccdaadbcdcdcabcaaaadcdacdcacbacbacdcbabbacddabaabccacaacababcaabcdcdcadbabbacacdadcaaadabbcbcabccbadaacbaabdaccdbdaadbdddcadbdddcacaacbdaacbaacbaccbcacdcacacaaddccbadcabacddcaddacabbbcbadbcbddcbbbdcbbaccadacaaabadaadcabdbabbbcccabacadbbdadddbcdcbaadbabcbabacbbbccdcbdcdcdccccccaddcbddbbbbadccdbaaacaadaabaddcbdcacdadaaddcbbcccccaacadbdaabddbacbdbdbbadacccbdbcdcbcaacbdbbbccdadbadbcbddaabdadbdcdcccdcbccbcabbacccbdacccaccdadaccabddabbcbcbadbdbdcadaccdbacbacabbdbabbcccccdbbdcaacbbbbabdbbacbabdcdcacccddcbbccddaadbbcdccddabbcbadcdddbccbbcccabaacbbacddacaabcbbadbccaacdbaacaddbdbddddbcbccacabdacdababadabaaaaddbdaaabdbdcbcdaacbddddabdccccabccbadabacbccabcdbcdcdadcddaabccacaabcdcccdcdcddbbdbcbcdbcacbbacbbccaddbdbdbacbccbdcbbccadcaaaabdbdbcadccadcbddaddccdcdaaabcadbacccddddaaacbcaabbdbabdaddbdddbcddcdaacdadbcdddbccbabcbbbbdddbcbbbaddabbdabbbcccccacbcdddabacdbcccbccbcbcabdaaccbabaadcdcaccdcdccdcdbccabdcdcdddcacbdaabaadcdabbaacdcbbcbcabbaacadbddaccadddaccaaacddaabcdabcdbcbdccacaacccacdcadcdbddacbdcdbbbaccbdacabcbadbabdcdbcaaaaacabbadadabadabcbaaddbabdccabbadcbaaabbcbbdcbdbcdacdbbbccaaacdcaccadcdabaaccbccccbcabaaadababaccadadacbdabcbbbcddcbdaccdbacccccdadddccacacddddacabbdcdbddcabaabbcdbbabdbccaccbbcddbcbcbcacaddcadccabdabbaadabccdbccdcacbdbdadddadbacbdbccddccaddbbbdddadabadacacdcbdccadaaaddaabbaacdcddcbcccadddaddbadcbddcccdacaaaadcabacbdcddacadbdbbddababbcbcabbbacbccddbbabacccddbacbaacdacadddcadccadbdacbaabcabbbcacaacbbadbabcdcabccbdccdddbcbdcbcaddddbcabababbabcdbdaadbdbcddccdbddcaabacbbbbabcdbcbbabdaabcabacaddccdaccbbbdacdbbbcabcdccacdddcbdcbdcddccabbcadbccccaaddacacbaaabccdcacbbccdddaabacbdcdbcacdaaddcdcacdbbaacdacbacabdaacdcdaaccabbadcbbacaaabaddbdacddacbaadcdcdccbabadadacbdaaaddabddbacadcabcbcacaccabcabdcdcaccdcacaccbdccbbccacdaadbdcabdacdcdbdabdccbbadbaabdbbdcdbaabccbbaabbaddbaacadbbbcaddcddcdadbcabbadbaaccdadbaccbdcdadbadddbccbbdbabadbaacdccccbdacdabdcdddacbcabdabbcdcdbbcdaacadcaabbdacbcadbdaadddddddbbaddccdadccccbccbdcdabadaacaaaccbcbbadcdccdcbaaaadaccbaadbbcdabbbabbccbdcbcbdbbabdbcacdccdbbddbababcddaadddcbdddabcdacdccaadadbcccaabcbcdabadbddcacacbbdbacddbbacbdabcdaabdcddabbaabdaabaaadddcbbcdbbbbacadcbabbbccabdbaccabbccaacaaaaacacdbdbaddcddbddadbacbcdbcdbcddaadbddaaaabcacbdacbbabcaadccbcdcddcdbbcdcdcdacdaccbdadcdbdbabdbcbbcbcacdaabaaddbdccbbdbbbccdcdacacdabdaacaaacacdadbcdacabcbccdbcdbddabccabadbacbbadbacdbdbcddcbdcaadacbaadadbccadabbbbaacacadbaabbdcaadabbcdacbbadddaddccabdbcbcdbaababbbbbddcbacbdadcbbcdadbcaadcaddbddabbdcbcabddadcabddbbbbaabcaddddcaabdabaabdbbaaabadbacaddadbdabcbcbcbabcaadbdaadbbcddcdaabcdbddaadaabbdabaacccbdbbdaacbaacdaccaddccdddbcccacbabdccabcdbdcacaaadcdcbcbdaacbbbaddddbdbcbacbcacbcccccdacbbcbbbbdbbadaabdaacdaacbdbbaccbbdddcdddddddabbbaccadaccdcbbdacbdadcabbbcaaccdddcbccdddbabaacadaaccaaadccbbbabaacbaaccadbcbaacccababcbbdaabdbcbaadabcaabbadacbbdbadbcaacdaabddbaadcdbbbbbdcddaaabadcdcdabcabcbddadcdbbaccdddbacaddaaaacbcbccdaaaaddbaabbaccdbbbdbdacbdcdcddccaababcaababccdadbddccbcddaaaabadadbbbabdbaccbdabccbcaaabaabcddcbdcaadabcbdcbcabcaccccbcbdbaaacadbdabccdbbbcaaabccbcccaabdcaaddcddccbcaadaaaadbccdcaddbaadddbabdacaccadbcabddbdbccbacccaacddbccbdbbaacacaaccbadadcabacdddcbddcbadbcabadbdaacdccdbdbbaabdbbdaabcccddcadabcbdacdbddcaaaaccdbadcbcaabbbdabdaddcdaddadcbdddbabaabaddbccacccdaacadaadcbcaddbccabddabccacacbdcbccbddbdddacbadccaabaacbcabaacdcacbdadcdbbabdadccadcdbbbdcbdbbaddbbababaabcdcdccaabbcbbdbdccdbddabbadadcdbacabcbbdbccbddbadcaddcacbcbbbabadcccdabcaddbaaaccbadddcabccbadaaaccbaacaacdccbdcaddcdbabdabacadbbdadabadaaabbbdcddadccadcdcdbbbddacaddacabcadbaccddbadacdddcdcaacdddbbdaaadbcbcddddadcacddbcabdbbdccdcaacdbcdcadbbcddadbabbacdacaacbabbcabcacdbccbdcacacdbdcaaaabacdaddaadcbcbdbdbcbdabdddcabadabccbcacdbacccbdbdbbbbcaccbbacacaaadcdbcdcaaacdbbbacadbddcbabdcbddccacddbabcdbdbbabbacdbcddccbddbdcadaaaabacdddcbccabcaccadddacdbcbdacccdcaabcdaaaabbccacbcccbddaadcdaaabbcaabbdbcdbcccacabaacaaacddaaddacbbcccbdcdcaacacbdbcdbbccddaabdbadcadccccabcabbcbddacdabddbdddbacdabaabccbaabdccbdcaaccdbbdbbdcdbccbdcbddbabbcacbddcadccacabbbbdadbdbddcaccaddacbddccbabbddcdbacbccddaadcccdbdcadcadbddddccdcbbcbabbaaccbbcdabccaadcbaababbaddcbabadabbbccbaaabcdccacdaadbadbbabbabdaddacccbadbbdbbdbdcdadccddcabdacdabbbddccdacabdbbaacaccbcbdaacaaddbbcbbababdbadccbddcbbcdabadcbcaddbdcbbaabcdbcdaababaabcdcbbbaddcccaabcaddcbcababaccdbaaacbbcdcabdbddcdaadbdccabdabccbdcbbacdaccddaaadbdadbadbcabadcacaddbdddcbbcbacbaccacaddbdacbbdbdbcacaddccdacaadaadabbacdccbacbdaabcbcdbcccdccbadbbabbabcbccdccbbdadbccdadbbcadcbaaacadadddccddccabdabbacdccccddcddabdacbccaabbadadacbabbcaacbcdaadcdcabbdcdbadcaabdcddddddddaabcdacdddcdbbabaadbdbccbddccbbcdbaacbabcccccbbddbccdbbabbaaaadbadacbccdccdaccbabdccdddacaacbbddaadbbcdbaccddcbabcccdcdbabcddaadcacdbaacaacbbdbcdadaaabcdbacabdbddcbaaaacaabcbabcdbaabdbcbdaccccdbbadbbaabbcccbaddccbddaacacccdcadccaaababcbccadacdcdcdbbcdadcdbacdbacdcbcdcbaddcbdddbbcdbbdbdaddcbacabcbabcbddadbdcdacdabccbbcbdccababaabbabbaadddddaadadacbdaadccabacaaaccadcddbadbbadaabbadddcbdabdacabcdccadbcbadbcadbaccabbaddacbdcbacccbbbdcbabaaddaacccdbdabcbbbaccbcdbbdacadcdcbddccabcabdcacbabcadbbdbccbdbccacacbbdbdcccdcabcdcddbcdccacaacdacbbbdcabaabddcdcaacdadadcdcdbccbaacbdaacdcdbccdbcdcabcbcacbaaaddadcabdddbadbddbcdbadacccaabcdcbbbcacabadbbabacddcbaabbbadbcccaaacdaccadcbdbccbadbbbdcbbccaabaccadbacccdbcccacdcdbcaddcbdababbbdccadcbcaccbaadabaacabcacccccdbcdbdbacdcaacabdacaddbaadcdbbadbccbcaacdcbaccdbabcacdbabbabaadcdacbccbaabbdcabcabacbdaccacdaabcbbadcccbcacbcbdaaccccdcbbabbacdcacdcabcadccddcdcaddbaacddccbadbcdaaadbdbbccbdbacadcabbacbacbbdbadaabdbbbbaaadbcddaabcdcbbddadbabcbcdcbaabccadbbacbadbabacccdccacdacbacdbaadbbabcdabdaadcbcabddacabcddaddcddaccccddbabbcaaabcdcadbacccbdcaaadaacbadaaddccbbaddabacccbdcbbacabcbdcbcbacdbdcadaddcadaaccbdcddbddbccdbcdcaaacdcadbababdaddaddabdcbddabacddddaccccaadcdcddabaabbdacdcababcbcbabcaadddabcdabbdacadabadadcdaaaabccacabdadbbcdacbbdbbacddabdadadabbadaddddabadbcccdbcbddbdcccbdabbacbcadcbbdadcbdaddabcdbcaaaacdccccbccdcbcdbaddadccaccdbbadaccbdaacccbdccbacacbacabcbcabaaaadacababcacacabccbcddacbdccbddcadacdcdbadabacdccbdabbccacbdaadbaabaabcaadaaaaabaababddacacadcdbacaddcbdbddabdcaadddabbdabaabdbdcdddcbbcddbbbabdcabbdcddcdccbbabacbdcdaccabccbacbacdaaddbaaaccadabaddaaacbbbcadbbabccadabbaddabdccbcacaacabdddaaacbdbbabbbcdaccabbacbcdcdbbacaddadadcbdbcbcbbdcdccbaabcdcadadbbaaacddbcababadcbdddccbbacdbbcdbdaddaabdbcaccababdacaabccbbadcdabdcccabacbcaaddaacdddabaaababbbddadcdddaddbbaddccbdabbbcadacabbdcbabbacaccdaaabdbcadaaddcdbccdbccbdccbccdccbddbdcdabcabdcddabdcdcaaacdcdaacacaddbcacbccbbcabcbbbaaabaadadbacbdbacdaacbcaccadcaccacadbdccdcabdbaddbdaacaddbabbbcbdbbacbbbbbadbccbdabcddaadbcdcddadaadaddcbacbacdaddbdcaaabbcddadbdcababdbbabbaadbddadadccbbdbbaccaacddbdabcddcddbbadbbdcaaacbcadccabcbacdababbbcbdccbdcccdabcaabcaabddcdbbcccbdbbbbadcabacadbadcacdaddbadaddcabdddcabadbbcccbabdcdddbacadaadcbdacbddbcbccaccacacaccbdbddaccddadddddabddaacccadaacadbcbdcaccbadbcaaccaacacaddbaaacbdcdadaacbdaadbdaaadccdbcbbbdcdcacacbbadabaccccdccbccbcccdccacdccbddbabcabbdaabddccdbcbcaacacadacdaabbadcbdaaaadcabdaacbccacacdcacaddcaadaddbbaadbabbcdaccbcaadacdccccbdcdbcbccdbacaaaabbadabcbaabcaacabbdbccdbacbbccababbbbacaaadaaabcdabdbcacbaadbadbbdabbabdddcbbdcdccccaaddaadcbdbbcbabddacccbdcdcbbdbadcccabdaacdbdcbabddcbcdbdddcdadcdcccdcddbacccaaacbbaadcdcbcdbdababcdcadabbaadcababacdbdcbbacacdcaadadcddabaacaaaacacaaadcccaadacaccbbdbdaadbbccbddadbdbabccaacbdbacadddadbacbcdcaddbbaccacacacdbcadbdcdaccaadabbbddbcbaddbabadbdbcccddacdcdcabadbccdadbbbcadacadbdddbbaccbcbbabbdcbccdcbcaadacaabdbbcbcbbccbbcabcccdcaaabcabaabccbcbaaddcbdabdacbacbcbbdcdacdcbccaaaccaccaabcdbbacbcccbaadacabacbcaccbadcdabcdcbaacdcdddadbcbcdcabbbbccdacaaaadacbcbbcbdbdcccdaabcbcdcbccbaadbbcbddccbddacdbaaaaababbcbccaabcddcbbcaaadbcabcacbbccbddbbadcbaaaaccccdccbbacdcacdadbbcacbaadcdbbdbdddbbdadadaaacdcabdaacabbdccddaccabbdbacadddaadaadacaaacbdbabbcacbcddaccababaabbdaabcbbdaacaacbdcacccdbbcbcbaababdbcdbacaaddcaccacdbcacdaadaadcacadbdbdaaddbabbbbddddabcababcddacbddddabcbddbbbddcbbdcdacbccacdabcbdddcbacdadacaaccbdbbadcadaadbcaacbcdaddddbddcbddccaccaaaaabadadabbdadbbdcddadbdbdacbacccbbaacbabadcacabdadaccacadadcddbbaaabcccccaddacbcdabaccbacdbccbddbaaacdbdcdbbcbcdbaddbbdcdcdaabbacdcaaacdacbccaacdbcdabbcaadcaabdbcdababbaaccacccddabcdbdbcdbccccbccadcaaddbccbbcacddacbbcbadaaadabcadbaacadacdcaabbddcbdcbadbdaaddaadbbaabbbbdbadacbabbbdbbdbdacbabbadcccdbbdacabdcaadbabdbddadababddbdcbddacbabbdcbbdabdccbcdbdaccabddcbccaaccadcacdaadbbddaabddbdbbdccbdbccbbccddcbcbbacabcccbccddbcccbcccdabbbbadcdbbbbabcbcabaacdbcdcdcdbcddbcbbcdcabaddddbadadadadbadadbbbddbcdbdabdccbbaabdbddbcdddaabbbaadcdcaabdbcccbaccbabdbabcddbcabdabccacadbcbaaabcaaabcdbddbbabccbdccbdacaadbbcdcbadbcdccadbbabdacbdcabaccaadacbddbbddaaccbbbcddadccbbcaddbdaadccccaaabacbacddddabddddbcdbccbcbdbbcaccbadabddcabaaaaaabcaadbbbccbaddaabacdbcabcacbddacaadcbbbcaabacdbdcbbcddccabbbbdabbdbdadbdccaacbbbbadcaccdddaaadaabddcabbdabccabdddddbbbbdddbdccbbbbdccdaaaabbccbbcbdcdaabbabaaaacdbbbaacbbdbaacbadbdcadaadcdacaababdaaccdbcbdbcbdddccacabbdcaccaddbdcbdbcddadbcbbbddacdbbdbcbaacccdabccdbdcacbccaccbccbdcbdbbbabacacbdabdaaacadcbdccdccdcabbabddccabccbcddaddbcbcacbaddbbdbddcdacbddabdcdddacccbdcdccbccdaababcdabaababdaadbabbaadcccbccdccdadaadabddcbbadcadbbdcbcdcaaabcabadbddbccdbdbabddcdbbcbadcdadaddccbdbccaccbdbbbbbaaadababcadbacddbbbddcdbdcddaaddaabcacbccadaabdbadcddaaaddbacccbdbcbdcadaadabdacbbcbdcaacccbcabcddbdbdbcdadacbdddcadbccbcadbdcabcddddbbdbaabccccdcabaabdacabcccbbaabbacbadbccdddcdccbaadadbbcddacccacbcbdacdbbacbccbbbbbccdccbcbaccbacddbcabbccdbcadcdbbcbdcdcdabcbbaaaaccbabaaacdccdcdabdccccbbbdbdbaacdcdcaacbdabbadccaccaadadcdccccbdcdaaccdddabcbacdadcbadcddbbdbcbcdacbbdabbdcaaddbaabccccadddbaacdcadaacdbdaadaadbbbadcdcacdcdbcadcccbdbabccccbdbabbcaaabacadbcacbbdcdbacbccbbccdacdbccdacdcabbacaddbcddaadbaaabdcbabaccdcbddaddbcdbbabadacbbddacdaacacacaccacbbbcdbdcdbcdbdddbddaabbcccadbdccaccdabbacbbbcbabdccbdbcbacbbbdbacdcacdcadaddacbbbdbaabdcddddaabbacaddbccdcdbabddcabdbababbcdbbdacabdcabbcdbbbcbcddcaccdbcaabcdbaccacacccddabbdaddbcddcbddcdbdcbdbcbacbbdbdaaccccccbdacdccbcddbcddccbabcbdadcacbccabbacdcccdaabbdcbcccccaabcbcabdcddddbdaaccbbddbcdabcbadbbaccbccbabbdaadbdbababadaaabcbcbccddccdbabcbcbabbcaddbbccbcccaccdbddcaccdbcadbbadcaaaacabcddabbacadabbdacbcaadcbbdcadbdbabbbccdacaabdbacddacddaaadabdbcbcabdcbabbbdcbcbbcbbcbdbabadbabbabdaabcaddaabbbcccbcddabdcccaaacadbccccbcabaddaaaccaacaadbddcbcbdbdaccbbaadddbbacbbbcbbcdadbdccadcbdacbbaacbacbbddbcdbbccbbddacacdcbcdbdcdacbdddaacbdbdcaacbbdadabdadadaadacccdabcaabbcabcbdbdbbadddbadacacccdccbbdacbaccbbddbdcdccaadcbabdaadbcdadababdccbcbadddadcccadcabddbcbcdababdacaaaabcbcdabdcabacadcdbccacdbdbcacbbaabaabddcbdbbadabcddcddbbacdacddcabacbbbacdccdbbcbbbaacccddddadabadcadcbcdadadaaaddbbbbcbacbcdbaccbbaabdadaadddbdcddbcdacdccdadbbabbbbcbaacdcbcdaddbcdabbacddddaaaabacaccaaddacbacdccacbcbbdcccccbbdddddcaccbdddcdadcdadbdccadbbbdbaccbbdcbdaccacacbacacdbaddcbddbdbbbddccabcbcaccacbcbddaaccddabddcbbbcdbbcddbccbccbdccbbbddbbbccdbcaccdcadcabaddccbbbaabaacabaacdbbbddddbbbacdddaaabadccdbcabbcbdddbcaadbdccadcccabdcacaacdcdccabaacdbccdbdcccbaaaddaaccdcadaddccdacdddaccdcddbadcaaacabcdaccbaddadbaddcdaccacbdbbdaadcbdaccbaaddaaaaddabaaadddcbaadbcabbdcacabaadabddbcaaacdbadcdbbacccacddcdaddcdbcbcdccdccababcbacddadadddcdcdccdaabacaaadcbbccadccccbdacabdcdacbdaadccacdbdbcabbaadabcdcbcadddabdbcaaaacacadbdacabdcbaadcdcbdddbdbabdcddccccaaacacaabcacddabacdbcdbccdaacdcaccbcddaabbbdbdcbbbdaacdbbaddbbacacdccbcaccbdbdadbdacdbadcdbadccbdddccddcbdbdcbcbdbbaabaccdaaddcccbbccbcddacadcdbcaacbcaacaaccadcabdacbccddccadddbdbddcaadddbaddcbdddadbadaacbcbbacadddcbbbdcaddacdaacdacabddaadbbbacdddaacccddbdaaacaabdbdaacdbcabdbdaddabcadccbccbaaaccadccdcbbabdacabbccbcadadccdcbadccbdbbbdddabcbaabdadadabadcccdcdaddabacdbabbcabddddcdaddcbbbacaaabaadbadababddcacdbaddcabccaabcbbdbcdaabddcadbbacbacaacdbcaacbbbbaaddbbadbbcdacbaabdbbccdddadccbbadcbacddbdcdbdcddadaaccaacbbbbcddcbdbdaabbbadcabcbcddbddadbadabbdadcadaccddadbaaddabdcadbbbcaabadadabbcbcabdadcbdbcbaaaacdddabcdddbcccbccbcdcaacadacaaabadabbbbbadbbbcbaddadacaccddcdbcdccbbdbcaaaaaacddbaccacdbccaaddbbcaabdabccccbbcaabdadccdbaacdcaaabcaadcddacaaccbcadbadbbbacdadcabbabbcadadccbcbdbddcbdbbadabdabbaabbcdcdddcdddadaadaadccddbcabddbccdbbabadcbddbbabccddadddaabdacbdcbbdadaacccdabbccabdbadcaacccadadadccababdaaadcddbdaabaaddcabcacbcaacaaaddaddadbbbddaaccaaaadbdadccabbbbbbdbadddbbdcbacbbddbadccaadccaaabcadddacadddcadadbdadddcdcabababbbcbddddaddcacbbddbbdadcadbbddddcbaddbdbdcadcaacccdbdacccdadbddaadacbabadacaccabcadddacabdcdadadaddabaddddddacddddbddacbadbbcadbbadbbdcdaaccdccbcbcbdbcccddacdabaccbdcdcdbcdadadacacdabbbbdcddbcbdcbbccaddcaaccbdbcaddabdccbabdcbbbbbbbddccabdbbbdaadacabbdcddaaabcbcbccbbbcadbaddddbdcabbbbacdcbccdacbabdcdadbcbbbcacbcacbcaabaabcdaccaaaacdcddcacdddcccddbbbcdddbbcdacdacdcbaabccbdadbdccddacdaadbdcbdcdbbbcaaaabbdcccccdacadbccbacadbdabdabdbaabccdbbaccbbaacbbbbabacddaadcccbccabccdcccabbbcadaabbbaaddbcacabccabadbacbbbcabbcdcaccaacdaaadaccdabcdbbbbdcbbaaaadadcbabcbdbddbbabaababdabaabbcddbbacaddabdaabdbddacbbcccddabbbbbdbdcdacadaabcbdbdbcaabaaddacddccccdaccddbdbdadcddbaaaccaadaacbccbbbcccbbadbdbdcabdcabbabbdbbccaaabccbdbbbacddddcdcaadbcbdccdbadaddbadbacbabcbacbbbddcbaacbcadddaacdababacdacbbdacababcccaaaddbabdbdaccacadaaadccdabadccdaabadbadbcacddddbdddcadbadaaadadcbaacbcbacaabbbdaaabbdcbdcabdadadcdcacdddabbbdbdcbaaaaaddacdaacababdbaadcacbddcabadcbabcabcdccaaacbbcaadcbcbdabdddcbaacdcbcdcbabcbbdabaaacaadbaacbbbbdcbabdacbbdcbbbccbabaddbaacdddbaaabdcdccadcbcbdaadccabccdbbbaabaddadadcbacbddabddccbdcdcbcdbdccdcccddddbdccaaadcbcddaacdbabacccabacccacabcbcdbccacdbaadddcccabaddacacdcabbccdaaaccaacadcdcccacbddcbddcbdabbccbaddcabccbacdcacbddcdaadabcdbbadccacbcacdbabdcbddaadcaacbbbbccddaaaabcddcbabacbcabddddbbbcacdacbaadbddddbbdabccbbccdcbdcdaacbcbccdbaadadcacbddbdbcbdbdcccbaddbccdbcdcbbdbcabacddcabdcdacdbdacadaaccdabbdcbdcabcaaddcacbbbcaabbddadcdbadabddcbacacadcacdaaaccdbcbdcdadbdcdbabcadbaddadaacccbadcbddcaababbddbcbadbcabaddbdacaaaadccadcbadcdbaadaaabcdcddadbbdadcddcccdbddbcadacddabccbddacdbdccddcbbdcdbbdaaacbcadbbdaacacadbbddcbcbbdaaadcaccdbdacaddadabcacdacadbacddccadaabddbabadbcdabdaabbbcbbcbbddadcabccdcacdcbadcdbadcccbcdcabbcdbbdbadacacabbcdbabadddcbccdbaabbdaacadcacccbabdadddcbdcdddbcacccdaabadadcdbadacdabcacbbcdcbdaaabdbdbbaabbbacbaddbdadacbbbcbbdabaccadbacdaccbaddbabddadbbdbccbabaddcaabcbbccbbbcccbcadccabbabaaddaacdabdcadbbaddabddcbccbacacacddbcadcddcadccabbcaaadbaaddacbddbdbadcbbbdbdddacdcdcbdcdcaacadbadbbdbcdcddacacdacddddccabcbadbaaccccadabbdbcbcdbdaacbbadaabbbcdcbccabbaddaabcbcdabacacacacbdbbcdcddcdddaaaabdcccbddddcbabcbdbdacbaddcdddcdcddcddabadcaccbcacaacaddbadddcbdadcbdddbaadbcbbccbdbdaaccccbabddabbacdbbbbcccddacccaabaaacbbcacdccadcbaacadadbbccdbabdcdcacccbbcbbbbbcdadbbdbcbcbbbaacadcddbbbccacbbbacadcbdbbcbabdbdddabbcdacbaadcdbaaddbabdccaaadabcccbcadacadcdaabcdcaaadbccdcacdddabddacccababbaddbcbdccadbccccadddbdaaadbaabdacbbabbdabdcabbacbbbcddbcdababaadacbcdbacbcbadcdcdccabdccaabcddbbdccdadadaabcaddbaaccdbacaabddcbccabcacdcbabcbdaabaababaabccdcccbcbbdacbadcbaabaacccccdaabbcaabddacaabbabcabaacddcccdddbdbabacbcccbbcbabbcacbccdbadccbaddcbcbdcadddacadbcbcacdbbabbbcbcaacbcabacaddcbbbcbbbcacbabddddbbaacabbbacbdbdacbbbbaabdbaccabdcbcbdbaadcdabcbccdbcccdaadbbdbbbccbabbcdaabaaccbaabbdbcbcbdbbacdbcccddbcbadbadcdcacacaacdabddddbaabdcdbdcccadbdbaadbdbbcbdccaccdbabaacdccdbadabaadaaddcdacccbddadbbcbcdabbbadabbccccacaaddcabbdcbcbbbaddbbabcbadabaddadcbcddbdadccbbacddadcccccbbbbcacccdabbddaaccbacbaababcbcdadccabdaadcdadbdabaaddcbabbbbcaddacccadcdcdbdbadacdcbcdcbacabbcbbacabbddaabdbaabcdbbccdccaaacababcababbdadccadcbcbcbddadcaadabbcabccaccddcbdcbdcdcccdadabcccdcbbbbbbbccaabdbdcaccaddadacaacbcddcccddadcddacbdcbdaccbccbcccdcdbbbacbaadbbadbaccbcbcadbacccbcbdddbcdaccaabbabdabaadbadccccbcdcdccacacbdbdcbbbaddbaccacbadaaabdbaaccdbcaccdcdabbbbaaddacbbadbcbadccbbaccdddbbcabdabbabbbccdddbbdcbaaadcccadddccdbccbdbcbbcaaadbaadaabadbaaccbababbdddacbcdddcdcbcbaabcacdacabddccdabddaccdcaabbccbcacdddcadccdbdcbbcaadbcabdabbbddbadaacdabcccccccdcbddaddbaaabdaacbcaadcbadbccbcadaddcbadbadbddcdabbbccaaddbcdcacddddbcaabbcabacdbcddaabbdddddaacacdcaadddabbbcacdccaadaacdbbbadccdaaadadbdbabdcbccdbadccdcdbaccabbbbdcaadbbcaaabbacadbccadcdddadcdcaabcccaccadcdcbddcdcbaacaaccbbabbaaaaacbdcaaabcbdaaddbddaaaababdccccdadbcbcdbddddbdccabadadaabcbdacdbcddbaaaaacacaadddcbadaacdacdbbcabacbabadccbacdddbcadbbcdbcbdacccbdaddcdadabadaadddaacbccbadbaccaccbadcbbbaacdaacbbddbbcbabccabcccbbddcddcccabdbdbacccabddcdacabdaddcbcdadcdcddacbaadccacadabdacbdbbbddddcdccddbcdaaabbacbcbdcdbadcdadcbdccdddacdabbcbdaaabbbbdbbabcbaabadacbddcbcadcdbacdaaddacbadccbcaaadbdbddbbaabaaccadacadccdbcacdadabbcddbcbccadcdbdacabacdcadabcbbddacbdcbadddddaabacbcbaaaccbccdddbbcbdbbbdbacccdaaabccaabacdabcadccadabbdccabcddbcddbdbdcdabbbcdaddbddcabdbbbdabadbaadcbcbccdbacbbabcccadaabddccbccdabdcacdadbcbcccccdddbbabcccbbbaaddadbcaaccbdccdabbbcbbbabacbdbcdddbbcdddcbddbaacaabdcaababadabcbbbdcdacabaaaccbcbbbbabccdcddcbcbdbaaabdabbbbbdcdccbababcaabbdcdddadccdcdcaacdddcddbbbacbdddabdbccddbcbddbcbccdcacddbbddacbaddaabcbdbcdbbbdcbcaaaccbaacbddacbdcdbaddbbbbcaaccbdbccaaaabcbcdcacbaacaccabacdbacabcddaaccabdddccbbbcccbacbacdbcbdcdbdacadabbadcdaababcbcabdbddddbaddccabdccbaacacacbadddddabdccaadbbddcccccbcbdababbabccbcacccbccdacacadcbbabdadbcbbddaaabbcaddacbbacddababcddabbdccbabbbcabdaaccadadcdddcbbbcbcddbdabdcacaabcdcdacbacbddadddaaddcadddddacccdcaadcbaadddbdcbaaacbdbabddabbdddbdacdcdaccadababacbcdaaddaccbbccabcdcbdaabdccadabacdcdbabbacabadcbcbcabaaccbddadbbdcbbdbcbcdadacacdcbbdadbcdabbbdcbbbdbdbcadacbcbcaadbbaadbdbcddbcdbdadcbbaddbabcbbcccddccabdaccacdbbbbbababcbdbcbbbbdadbcbdbcbacaccbbbcccdaacbaccadaacacdcdddbdcbdcdcaacbdadabbbdcbacdbadbbbbaabcabaddacaaabcddcdddbcbadbaccbcbbdcabbcddadcbbbaacccbabbccadbacadabdcdcaddbcbccddddbcabdabaacdccbcdcccccdcaabbbdddddacabdadaddacbabdabcdccaaaaabcbcbcddbccdccbcacabcbdcdcbbccdbabdaccdaacccdbadccdabdcdabdcbcacbccbadcbcacccbbbdbdbddbdbdbaddddaccbdbddcaacbbbbaacaaadccdcbdcadbbdcbbdccadbdadbbaabdcdccaccdddadcddbacddaabdcadbdadbdacaadaaacdabadccbdcddcddcbbbcaaabaabaaabddcadabcdaabbacbddadaabbdcacaaabbbdacccdacdbcabdacddacbccccddaacccbcdbabbbcabbadbdcbabdcbdabbccdcccddbdabcdcaacadcdaccaacaabdcbaaabbbddadcadbddbdbccbdbcadaccadaacdbcabcadddddaadabcdddbdcbabbadacdcddcccddabcdccbbcbbddadcadbacdaccaaaccbdacdacddbbbccbadaaaabdcdbdbdbccabcabadbaddcbdccaabccaadcacdadddacbaaadccdaadcdabcdcdbcabcacdabdbaaadbdcbcdadbdddccdbbacdddbcdaadbbbbcbaaadcccacabddbbcbaacacdcdbddbacbbcadbddadabddccbdbbcbaaaadaccdbcbdbbbddcdbaaaddbcdcbadbbbcbddbdbdbcaabcccddcbbabdccaccddcbbabcacdbbbdadcaabbdcdbcdaadadadbcdccacccdcdccdacbdddcbddbabacbdaddbacdaaabdcdacadcdaddddcccbdcadcadccccbadcbbdbbbcadcabdbbcbbabababbaaddbbbaacdccabcabccddbacaaaccbacbbbacdcbcdadadbddbccabdaaaacdbccadcdddbdbdbcbaddcdbcbdcabadccacccadddccbbabbabccdcbaccbbbbdcdddccaaadcabcdaadcbdbdacdaccaccbbbadbdcdabcbcbcdacdbbaadcbbbddccccaaccccbaccadadabdabaaadddaaadadbbaddcdbbaddcacbbdccacaaaccdccadaddcadbaaadcbdcbdcacdddccdbaaababbdabddddadbacbacccaccbddcbdacddadbbaccbcbbaabddaaabcbcbccaaccbbcdaddbdabddbacbbbbccdcddbcccddcdacaadadababcdbaaccdaacbaabcabdacddbabaabcacadbbcdcbaaddbccbaabccdbbccddadcccaaddbdaaacaadddbccbabcadcdbacdbcccabcdddcabbcbcbabcdcdbbbddbdcddbbaaacbdbdbcbcbbabdddcdbbdbbccaadaabaadabdccdaacdacbcbaacbcacaacadabbcddaccddcddabddccabbacbdcccbcdbdabaacdbcbacbbacdbbcdbccbddacbadcdbbcbdacbdbabcababdcaacdacdcbbbdbbbabcaaddbbcadddddddddaacbcbcbaaacabacdaacaacdcdcdaadbcbcbdbadccacdadbdcbcccbcaacdcbaaaacbcabaacbdbbadcbadacabaadacadcdddacdbccccadaadcadbbabdddacddaaddccabdbbabcabbddcddcddcddbabdcbddcdbaabaaaaabbccacbcbabcaaadcbbccdaacdbbabdbdbbbdbaabbacccaaaadbddabaaaaadcaaabdccdababcbbbbcdacddaaaddabbbcdbcadbaaadaabaabbbcaddbaabdbbcabcacabaacccbddadbbbcdbacbbaabacacbaadbcaadbcccacbdadacdaccadadbacaddddbdabccdcbdbaaacacdbbdacbabdcddadaacadbacaacbbbdbaaaabbdbbcdcbbdbcdbcabcadddbccdadcaaabcaabdabcbacbcdcbacbdcbddcdbbcbaaadaadbcdcbdabbbdbaadbcbcbcbcbcbadddbcbccbbbbcccdabaadacacbabbbbcddbcabdbbdbcbddbadbcdddbddacbdbcdcdcadcbdcbcaabacbabbcabdbbabaddbccdabbaacbcbdaabbbcbdacbbdabcaddbbcddabbdacccbccdadadaddcbbdcbbdcadaabadaaaacaaddbccbababcdccbbdaccdbccbbabdccbdccadadcaddddbaaabadcdcdcbddcbdddadddbdaadbbcbbcadacccacddccdbbbcdbadbdadbbddbcacdaccabbdacccdcddddcadcaaaccdddddbdbbbbacacacbcdbacbbbabaccdbcbbcaacdadbcbcdbcdbcdcaadadcbbcabadaadcbcacdadbcaddcdcccdabadbcdabdbacbaacaddcbcdacdccbabdcaadbbddbaddbcbadabadbcacdbcdcadddbcdcdaadbabdddbbbacbbaaaaacdcabddabbcbccbaccbdbcbbcdcaccaaaacdddbcaaaddcacababcdbbbbddcacccadcbbbcdcddddcadccadcdadcbcacbdcddddbdcbbcabddddadabbabcbbadcbcdaaadbbbdabbcdbcabaacccdabaccccbbcacdcbbbbcaddbddaaacbcbccccccaadbcbdcbdaacdbdadbcbcbcaaaddaadcdcbbcdddcdbbdcacabaadbdbadcaacadddddcccadbaaddaddcddaaacccbadbacabadaabacdbcabacbbdcbabdddbacaaacbddbcadcaadbababbcbaabdaaadcaacddbadbbbaabbcbddbcdbacacdbcbaaacbccacadcadcabbdddcbbaabdcbcaaabbacaadbbcddcddacbdadadbbaaaabdbbaabdadddcdccbbcbbbadbdadaaabcbdcbacbdbdcabcccdcbbdaabbbbddddadcabdddbdccbbcdcbdcbcdcadddbacbccccdcdaaccdbcdcaadddadccabdbddcacabacbcdbcababcbdbbcbbdcadacdccdbcbccdbbdbcaacabcabcdadbbcdbbdaccdddddcaabcbbadcbdadcbaddcacccddcdacbcaddbdccdcbadaabbcadbbdbcccccdbdabcadcabcbdbacaadbbdbbacaaaabdddcbadacbbcbccaadadbbadaaabadddabcdcdaaaadbbdbdbdbdbaacdcacbdabccddcdadbacbabdaabccabdcbdabcddccddddaadcbaccacdddcbbbcddccacbddbccaddcbcacadbdddcdaabbbaccdcdaaccbdcabdcbbbbbaadaddbabccdaaaabbabbdddbdaaacdbccbddbbddadddcaaaccabcbbaccadddcaaccbabcabdbddcdcddaadcdabbcbcaacadddbdcbbdcabcbaaabbcbdcdcbbcbdbaddccadbadbdbbddbbacddbcdcdccbcacdabcdcbcbddaababadcdaaabdbdccdcdbabbddcbaaddaaccbaadaaaaacddadbcaaadbdbbbcbcbdbdacaaaccdbcaacbdccdbddbdccbcbbddabacddcbcabbdcacbbbbdbcbbdadcbccdaccbacbbdadbbaaccaacaaacbcccdbcccccccaccbcbcdadacababddbdbddbbcbaacbaccbcaababcacbbdbdabbbdccdcdaccaccaccaddbbdacdcacacbaabcacabaadbcbdaacabcccbbaadbdcbaacdbbcdcdccbaadccacdabcddbdcadaacdcadcaacaadabcadabdadcccbdccbcdbcabaadaddacdbdcaccacbbbccaacacdacabdcbaaaaaadddbbbbccaaabcbbddcbbdbdbadccdbdbbbcacccdccaadcbdcbbacbcbbbdabbcadabaacacbabbbddbabbdbdbcdaacadcdccdccbdcbddcabddbaadcababccbabccccbccbbdcbacccddbdadaadcabddcbbddccaabdcabacbcaabcbbdccaabbcbcddcbcbbccadbdcabacbaccdababdbcabadcdcbacbadaaaacdabddcbdddabbabcbcbcabccadbcaacacabcdbacacbacacabdcbcaccbdccadddadaadbdddddadbdcbddabdaacddabacaaddbddcbddcddacdcbdabcadbadccdacdcbbbcaccaadbbdbdbbcddbabbdcbadacccdcbaadabbcacdbdbbbadadcadbbcdcddbaacdbccbdbadacadcccabbdacccddccbcbdaaddadbadabbbbabaccadabbccacdacbdccbcabcbbdcaaadddbdacbddcacdbbadbbccabcabbadcddbddaaabbcbcbbbabbdbdccddbbdbadcdadaabbadabbbbadbcccdabadcccbdabbccbadababcdaacdcddaaadcbddbdadcaaccacadcbdcbcbbdbbadccacbddcadabdacccdcdaacdcdccbdcadccacbaddbdbabbbaaabcbcdcbbccdccdcddbabcccddcaccacdcbaaaccadcabbbddcababdbbcbbcdabcbbacababcbdbbcbacbcabcaddaadacabdbcccbdcbacbabdbaabcdacbcddddcacacadabbdccaacbbaacdcccbdbcbadddcbadbabdddbacbaddadcdcaccbbbadcbacbdddccbdbbacdddbbabbabaddddbcaccabdcdcabbbddcadcbacdbbdbacdaaddbddbcdbbdcccabcaacdbdbaddcaabacaaacbbaccbbdadacabcacddacbbadbbadbaddbddccaaabcccbbdbaacbccbcdcbcddcaaabdaacbbdbabccabdcbdbcaaabcabaaaacccdbadcaaaddcdbbcadcccadddcbdbdbcacdaadddbdabdbcbbddacbadccbccccaddbdabbddcbcbbcabccddbddadbbcbcaabdbcacabdbaddababbbcddadddadcbbdcbdcbddccddacddacadaddcdacbacaacbaababddaacdabbbcbabadabdcaadbcdcdcbabbbacadabddcbdaddaaaabaddbcbdadbdacdadaacdddcbbcaaacbdbbcdababddbddbddcbdcdaadaccbddbdddcddaabbcaaadacbdbcdcbaaddadcdbddaaddcaaababdabbaddaddccbbbbadddccdbbacbcaadcacadbcccdbbdcbdddbadbcdbaaabbbababacacbdacacaccdcbabadbbcdccbcdbaadcddcdcbbdabbbbdbadaddabccccbdbcdbbcabcddcccdacbcbbccdbcadcbddcabaddcbdcbaadbaabccadddbddbbcbcdbcdccadaaabdaadacbddaddbcadbbdbbaaaadaaabbadbbacddcaabddcbbcbbadcbabadbadbbbbacbbcbccbbcdbdbcdaacccccacddbccbdbdbabadbddcbacaabdabbbaabbdbcdaddddddcbdadacbbabbadaacaaaadabddcdcdbabaacaccbdbbdaabbacbbbacdadddbaabcabccdbdbbcbadacbcabadbddbabbaaabdbbadcdbcbaadcacdbdcbbbbbbdcadbadcdbacbbbbbadccabbdacbcdcdcbdbaddbdccaaaaacdacaacaacadbbbaaaddadadbcacacdcccccdccabbdcddcaaadacdcdabcccacdacaacbcaaaccdcaaabcccadbacacddbcbaccbbbdcbcbcdccbadcdaaacddcbcacdccabbbcddcbacddbdddcacbccbdbabbabbcccbacdcabcadcbbbbccbbaccdbdaadddddabddbdacccddcdcbccbdcbdcdcdacbcccccdbccbacaccbccadcbbacbcaddbcdbddcbaabcdcbccdbbdcabdbbadbccaaadbaccdcaddaccdacdbcadbbdaddbcaabddcdaadbacbbaabccccdaabbccaabcabbcccacdcdcdbdccdbbdbaababaabbbbbadadcddddcbaccbcbaacabadcccccaaadcabcbbabbbcadabaaddabcbadbdabaacddbcbdadbcddcccdcabdcaacbbadaabccdbbcdcdcdaaddbcddabcdadadccabbdddcbacabbadccdacbbacdabcaadacbbbbdccdabccbabacdcaadbdcbddbadcadcccabbbcacddaacccdbabcdbcabdadacccdccdcbadcaddccbcabbbddabcbcdbacdccbddacaddacabbaabcbaaaddddbdbcadbcbcaadddcccdadcbadaadacbcadbaadbdbbaccaaacbcbdacbcabddaddcddccaadbdbcbadcacdccbcacbdabccccbbbdddbbadcbcccacddddbdaddcdbdcbcbdbcdbccccaacdaaacadcacaaddaaadbccbaaabcadddcbccdadabbbbbcbaacddbdbdccbdbacadbcabcbabdaadbbcaddaabadbcdacacadacbbbbcdbcbcaddacdadbdadbbcaddddaaacbbdaaaabbdaacabbacbdcbbdcdcdbdaacdbcaadcaacbccbaabbaddbccbcccbcaadbddcbcbbdbcbcccaadabacabbbdbdbdcadccbaccabcacbbdaabbbaddbacddcbcbbacdabdbcbcddcbacdaababacccbcdbaacbacdbbbdbdcbcbcdddacdbcadbcabbcdaadddcababaacadcddbbccccbbdbcacccadcdccbadadcdaacbddcadbcddaadcbdbdacdacbaaaaaaaabdacabdabbdaacbaddaaacabdcdbcadbbdbcbbbaacddcbcbaddccddcbcdbdccdaabaacadbbadbabbababcddcdbadccbbccacbdbdabbdacacabbdddcadbbabdaadbbdbdaacaccabbdabbbcacdcbbdbdabbccbbaaacdccababcdddabdabdacadbccbddcdbcccbabcbdbbddbcbbbbbdbadcdacabadbcbdbbaacbbcdbaccccbcacbabccdbdddadbdabbabcbbacaadddabbdcdaddbcdaacbdabaccacdbacdcaaccabbbdccbaabdcabadadacbbbbbaacdadabccbbbbadabdddbaadbbabaadacabcaaacddcababccdcbcdcbbcadbcdadbacdbabdaaacabdaadadbccadcccaadbdbbabbbdbcccbbdadacbcdaadabacbabbbcbbadadbabbdbbbbbdabcbbcaddbaacbabcbdbcabddddcdccddabcccaabcbabdacdadcccddaccbdabcbccbcbadbacdabaadbdbcdadabbcdccdcbcbcdcaadbbcbbcbbaabdbcadbbcadbdddcbbcadddadccbdaaccdbaabcbaadababdbbcadacabcaaaadabcdcdbcbdddacbbdadadabaadddaaacddabacdbadccaaacabbbbdbddadacdabcccdbadccdacbdbbdbcbacdabdddabcbdbdaadbabbcaccddadcccccdcacbbbadaabcdccdcddbbbcbbdbccdbabddcdabbabcadaaacadddaabaccdbbacaabbcdaacccadcccbacbbbaaaaabdccbabcbdaddbbadcbacaadadbbdcdadadbaabbbbcccaaddbcdbbbdbbcadcaadaddccbaabbcaabccacdbbcccadabaaabdddadbdbdcacdbcddbcdcbbbbbbdacbdddccdccbbccbdcbbbaaddbdaabaabcacdaaaccabdbcbbddabbdabaabddbdacaababaccbbbaaacabcbcacbaabdacbcaadccadadccdcddabddccbbbdcaadddacbdadadadcbcadcacbaacbcdbbbccccbaaabdbcbdbadbddbccbadcbacabadcbaacbcbbbcaacdcdcacbbcccdbabcbbaddbababbcaadcbdabdbcabdcaaaabaadaddacddbdcddaaadadccbcbdcdcbaadccdcdccbdcabdacddaabdccabdaaddccdcbabbdabacdbbcbcdaadddcbcabccddccdadacadbdaadcbbbbabbdbdcbdadabccdacaaaaaccaccbdcbcbccbdbcaccdbcbddcadcbdadadadacbbccacdbccaccbabbacccbddbbdbacbadbcdcdbddcbbaadaabbaaddccabbacaaccdbcadaababddcabcdcaaddaabccdabacbddcdaababcadbcdbdadadcbdbbddabaaddbcccdbbaadcbacbddddbcbcaabaabbcccdadcdccbbcdccbbcdbcabcabbaabcbbcaacadbcccdabccaccccacdcccbbbcdbaddcbccdcaccaadbdcacabacddddddddcbcbbbaacbbbdccaacbabddbdcbcddbdacaaaccbaadaadbacaccbdcddbbbbabdbbcdcabdabbbdacbaacaacaccbcabaccaccccddcdbdbbccddbdbbabbcbccdabdacdccddbddcbbdbabdcbdacbdcbaacbcdcbacdbaadbddcacabbaacbdcbbcadcccbcadbdcdcabbbacadadaddadccbadcbabcbbaddddbcadcacacbdbdcddbcdadccddcddbdadcddbdcadaaacabaccbaacccdaddadbdbcacaccddbbbcbcaccdbccadabdbdacabbbacccbaacbbdbbbcdbdbdbbdcaabccddbabbbdcaccdacaddbabdbcddabdbbcdccadbbdadbdddbbbccbcdbcdabcdcbdabddabbbcdccaaddcacbcbdccabbabbdcaaabbdaccadaddadbdbdbccbababdadddabbacbbccacbaaccdcbabdcaadbdcadddbcaaadaabcbddbbadadbcbddaccdbdacbcdabaadcababcbbabdcadacabaddbdcdbdbdccdaacabaababcabadbcbcadadacadccdbbddcbdcdcccdaaaabcbacdbcdbcddaccdabdadaacbbbadddabbaadbdbaadbbaabbacbdbabbbbabbdddcdccaaccbdaacbadcdccadbcbacbcacdddddbaadcbcdaabacaaacbbcbbaacbbaccaabcbaadcabdcaabcccacbcbabccbcbdbdbadbaadabbdadcbadbcbdbdcabaaadabdbcccdabdbccdbcadccdcadccdaacacbbadcbbabacdcbcdabbcabdbdcbaabadbabdbcdabcbaababcadcddbcabddbddacdbdddcbaabadbdddbadacdbbcdbcbdaacdddcccdccbcbdddaccbcbbbdbaabbdbdbabbadcbddccabbaddbcbddbaccadcdccddccacacbcdcabadbbcdbadcacabaaaccacbcaccddcadccdbcbbaaadccbbddcbddaadbaaccbdacdbaadbcbcdbdabbcababddadcbcacbcbcbbcaaccbdcbddcaccddaabdbbbadaaadbbcaccbcbacdcbddcbcbdccababdbcdcdbadcbddcbccadadabbcbccbcbbbbdccbbddcadacbcabacbcadbcdcaacaababcccbaaacacadcbccaaadcbbcdccdbdcbdcaadccdbdbccbcccddadbadbcacdbbdadadbcbcdbaaadbbcdacaaacabbdacccbaccacdacacbdddcdbcaccacddcbcddbbccdaabaaacaccbcdbacdaadadbcbdbbccbcbabbbadaacccdaadaaccdbddcbbdcdbdcccadcddacaddaddccbaadccdaadabdcbadadcdadbddaddbbdaddbdaddabddaabaabbadddbcbccdbbbccdcbdcadcbbcabbcbbdbbcacbdbdbaccbddaccdbbdbdccbbcdaccccbabbaaabadbbaddaabacddcbdbdaabaadacdccddbbdcabcaacabdcddcbccabadbdaabcbaabccdbbaccbdadacdcbcabbdcdacdbccdbcacbbcdcaddcacacdcbbccaabcbbcbbaadbaddabcccababacadaccbdaadbcccadbcbdcdcccacdadcbbcdcadbcddabcdbbabdbbbbdddddbaddcadadbaddcccccbdaabaaddacbbdabadcbdabdcbdaaacdcbbcbcbdcbaccdcbcbbaddbcacaaccaaadadaacdbbbdcaabddbbbbcadacabbdcabbbddabbababadcaaccbcdaddcbcacccbabacbbdbbcccdbbcbbdabbcababbcbcbacabaaddddddcccacacdadabaaaddaaadcaddbacbcdcadaadddbacdcbcdbdabacabcacddbdadbcabccbbcbcdcbddbbdacabcacdbdcacbccadbdcdcccaddbabcaccbacdbdacdaacacadcabbbcdbdadcaacaaaccccaadadccccbddacaddcddbabaabaacccdacaaacabcadbabbacacdbdadcabccddbdbcdaccccdddccabaabcdacbabdcddcaadabaabbabdcadcdcbbabcbbbadacacccbabaddcbadcdbadbbdcacdbabbacadcccabaddadacbdadabcdbdaddcbcdabbcabaacbbbaabcabdadcdabcbbccbbabdcaaacadbaaddcdbcbdbacbbddadadbacdbadbcacdcccccbcbbbbbbdaabbccccccccdbdacddcddbdcbdcdacbdaddbdadbdacbddbaddbbdbbdddbbababdaddbddcbdddccacddcbbcaccbddbcacacddbacbdbbabdacccbabcbdbddbaaddbdcdaaaabcaacdbacbbabdbcbdcbdcbaaaadcdcadbadcddbacaadddabbddcabaabcaddbadabdcccadccbdbdddbdddacaaaccbadbaddddcacbbcacaaccabcbdbbcacdcdacbdbbcbbddddcbcbcdcbcdccbaddaabcdccccaaaddbbbbcabdddcabdaabdbdddccbcbbcabdaccdadaccaaccaaabaaacddababcdcdaddabdadabbcaddabbcabdaccbabbcadccdcadaadadaccadbbadaddbabbadcdbdaddcbccdbadbaacccabdbddadabddcacdddccdcaddcabdadbacbcaacaccdbaadabdddbcddccbdcbbccabdbdabababcdcbdbcaabcdcababbaccabbddabdcabbacdbbcbccbcabcaabbcdbbbaaddabdcadacdccaadbbbbadbbadbcdbcaabbabddbcddcddbbcbacacccdaabdccabcacdbdadaddaccbbaddabdcbdddbddaccadccadbbcbbbcccbaddadbbbabdadddadbcccaabdcbadbbdacdcdbdcddabdaacacbcccdbbccdbbcabbdaaacbaababacadcbadddcdaddbababaddadcbcbacbcacbdddcacabbcccbdccadbbdadbdbdbbbacdacbccbcdbbbacdaddcaaacccabbbbaddcbdadbaadaadbdbaaccbdcdaaaddccabcabbcdabaaadbcbaaddcbadbaabbbbcdddcdabaacaacdcadcacccbababcbacacccabcbacdaccdcabcdcacbbbddcccaadcbdcaadabcaabbcbacaaadcbaaccadacdcbbdaacaacdcbaaddcddccdcdaccbddbcabdbccdbaaddcabadadbcadaaabcdacdbcdbcbdacbbcacdbdccbdcccccbccbdacbaaacdcccbbcbddddbdaccaacabaabcdbcdbdcaadcdbdaadbbcdabcdabbcadabdaaaccdbaabcadadadabddaccccbcdcbacaacabaccddcacabbccbaacbcdddadaddbdabdadbbdcdcddcaabcdbcdabdaccaabdbabbaabbccbaaabaadbbcadcdaaabddbbbcbbbcabbadbcddacbbbbaababacabdccddcaadadcacaaabbbcaaacddcaddccdaccbaaacdbacdaaabacacaabbdbdcbcbdcadaddbabbdcadbcbcdbddcaddbcaaaacbabcbbdcaadcccacaacddbcacdcacdddcbadcdaaddbcddaabbbaacbdacacdcbccdcbdbcdbdaaaddbcadaadddcadbdaacacacccbbadccbbcdbcbcccbddcccabddbcbcabbbadddabacababaaabbddabbdaddddacdbabbacacadadccbabaaacbdaadbbdddbdddbdaacbbcbddbaccbbbbdbadabbcbadbabbbdbadbbdbcadbcdbcbcdbcbaadabddcacadbaacdcacadcabcccaaabbacdadcbbbbbcaccdcdddcbbbabbccbdbddddccbcbbdadadaabdddbaabcccdbdaabccadadabbdbdaaaddaadadaabcadcddbaadbabcabbddcdccbcbcaabbaaccacacbcbadbddadaadadadadbacadbddcadcbbddaadcbcaddcddbabadaabcdaaadcabddaababadbdccdaadcaccacbdcaabbccdadddadddaddcdaabdddbdddaaaaabacacccbdbdbcbddaabaaccaabcdddcaacccbbadcbcdccadabdcdadaadcdccaabacabadaababdddcdbdbbcaadaacadcbadbcabcbaaaccbcbddbdccdbdcacdcadbdccabdabaabacbdaacdbbabccddacbcabbcaadcbbbdabbbcabaddcabddddaaaddabcacaabcbdcaccacbbbababdccaababbbbddcbabdbcacaacdbbcdcbdadcbabdbadcbdbdadccbcbadadbdacbacbbcdadcdadbdbbcdaccaaddbcaadcabdbcaabcabccadcbbcaaaadbdadcccdbcdcdaaccaccbdbbdbbbbbcdcccaacabddaabcaacacabdcbcaddacbadbbacacccbacdcbccdbdbdabdcabddcadbaadcbccabcabccddaaaddbbabccaababccdcbcdabdacbdabbaacbaccacaadcabaaaddcbaadcbacdaacddaaabbabcdddacbbddabdccaddacbdbccdcbdadacdabcbbdbaacbccddbccacdbacbcbbdcdbdbaccccacbdddbbcabdbdadbdbdbabdccbaddadbddbdcbcacbdadbabdaadbaadabcdcbcbdbacdbacdccababcdddbbadbcdaabbbabdcdcabdbbdbadaccccbadddccdaabbccdbaabcaaadacbcaaccdadbbaaabddbabcdbbbdddadbcddadbbbdaacdcdcbccabbddcbccaabbdacddaacdcacbdcbbcacabccdbcbdabdcbaadbacbacccddabdbcdcdbccdbaabbbdddcdbdacccbcbaaabbaaabbcdbbcbbcdcccbcabccccdbddaccaddaccdadadabcbddccdbcdcdcddbdacdcdadbddcdcbdabbadadaaaadcdbdddddbdbbcdcddcaabadcbdbccdcbdabaacdddabddbbdacadcabacbbdccababaaccbddadacdcbcdcacadadcabbaabbcdbdcdcdbdadaadbcbcddbdacdcababddcaaddcdddbdccdbdcbacddddcaccdbddbacdccbaaabdaabcaacdadabaddabdbddbdaadcccbaacaccaddadbdcbadcabcbaaaddcacabbcdddbaaabbbacaaccccddaacccbacbdbadcddcacbbabcbbdbacbacbdbbdcddbbbbdabbaaabadbcddcabaacdbbadbacababdaaabaccaabdbabddcbadcccdcddcddcacadbcabbbbbdbdbacccddbddaccacabdcadcccdbccabcbabdcdbcdcdbdcddbcbbbacadaaabdadbcabcddabbbcdaaddadbdcbacddbccdbccacdabccbdbbbcdbaccddaaddcdcabacbdcbbaaabadcdaabccaaddaacdadccacccdccbaabdcdcabadddbdbadcddcbabaaadcdbcdaaabcdbdcdaccbcacadcabcbaabddbddadddacbbddcccdbbcbbadddacbcbccdbbbcdbbabdbccdcaccabbbacddcaddbcbdbcbacaddbdbbcabbbccbdcdaadbbbbbbbcdddcccdacbddcdabbbdaaaaccbaccbaddbdbbbdbccaaddbbcbbdddacbabbdadadcdccccaabbdbcdddbacbbacbbccccadadbddacbaabbbccabadcdddddddbbdaccbaadbdccaacaacddabbddacaabdcaabbddbccbaadddcabddabbadcaaacdbdbbaccbabbdadddcaaccbdadadaadbcacacabccddacbaabbdbadbacbdbcbbbcaccaaacaccbbbcbbddddbaadbdccbaabbbdbaaaaacbbaabcabdbccddcaddbbbbcbbacabdcabdcbbacccbbdbacbdacbccddaccdbcdbadbddbccdbabbbdacbacdbacbcbbaaabdcdbababdcbdbbaccbadccdddaaddddbdaacccccbddbbccdbaadababdbcbbabcbccbbadbbbdbcacbabbcdbddaabcbcdbcdcbbabccadbccadbbacbdbcdaccddbabaabbbbdcadcabdbcbabdbacaaccacadadadbacbccddbacbddbdcdcacccdadbbdcdbdaaaacadaaacaddbbdabcaaaacaabacbaadcbccbbbabacbadcadbbdccbdaaabbcbaadcaacaddaaddcbadaaabcccdbbadddcbcdbabcdccdcdddbbdcbbbcbccbaadadbbacaddbdbdcaacdcaadaacbcaaabacbdbbbbddbbabbdcadacdaaccbdbbbdabbbcadbddaabcbaddcbccaddadccacdddacddcadbacdabdadcbbdcbdcabcdacccdadbdadabddddcbbadccccaccabcacacbdabbcbdcddaaccaaaaddabacbbbadddabadbdbbbbdcbbabccbdbcddadbbcdadcdcbddcdcbabddcbbadcdabdabdbccadcdbbbabdbadabaadaacddbccccccdddcccdbbccddcdbbaaacdadabdabccaadcdcdbcdbdadccdbcababbbbdbadcccbbaadcbacddbadbcccbcadccdabbcbccbaabdbbbacbaadaacdbaadbbbbaaabdddcbcdbcbdabccbccdadabcaabbdaaccaacdbdcbaacaddcdddcdbbabdadacadabcccdadacbadcbdbbabbbbbcddcadcccabbaccbcdddcdcbcccacbabacdbccbcbbcacbcbadbbdaccdabdacaabdcdcabbcccdcbbdcdbdbbcdadccabaabdbbbddbacdacdddccaadddbcddbbababcbcdacbdadbbccbcbccbabcddcbddbabdadcbddbabcbcabbcabcdaddccacddbbdbababcbabaabaaababddbccabbbbbcbadaabcdcdaddbbcadcbbaaddccbdcddcadccddbacdadbcdcbadcabdbcadcbccababcbacdbabaadacacadacbbbcbcabdacadbccbabcbaabadbcbdadcdccbccadbbacbacacdccbccccdcbabcbaadcccabbccbcacadbdcbccaabcccbaabccaddaddccdccabdacbbdddcaaadcadddccbbbdbbbbdbcdacaabbcccbabbcbcbacdccdaddcbacdccbdcbcccadadadadbaabddccadcaadbbaddccdabcacacdaabbaacbcaccdcaadaddadbbdcacbbadddbdadaacdcbadccccaacddbaadaaccccdcddababccccccabcdacdcccbabdaabbcbbcdacacaadaddddbdbcccccbdccaacabbbababdabdcabbdabacbbbcdbacaddccabdadcaabadcddcbccdccabdabadbdadbacaabbccacbbdadcbdbcabcdcaaacbcabccdaadaddbcccadddcbabaadabcdaaacbddbcccbbdaabbcbddcdcbccabcbbcbbabdddadbadabaaabbbbabbbbdaacbbbabbacaabdbbdccacaabcaabdbdccbabccadbbaaccdcabadabaccdabcbcbcdbcaabbcdcdddaacbbdadaacbdacddbdbdadcdcbcddbddaccabdddbcbaabbdbabbcddbbbdcaaaaacbbaccacabcbdcbadbbcbbbdabcdadcbccbcdabddbbcbdbcdcaacabdaccdccbddcacccbdbabcbaabadddbaccbbbdcadaaabcabadaaacdacaadccbcaabbbadcdcaaccdaacdbccabcaabdaddadadbabbbdadadcbcbddbaccdbaadbdbadccbddbccbbbdadcabccdaabdbbbdadbabdcdacdccdabdbddbdbdcacbdcacbcbdbccbaacddabaabdadbcbcaabdcaccbbabcaccacbaccacbaacacaadbbbcaacccaccdacccdcdbdbbaaacbdabcbbbcacdddaaaababacbccadddadddcadcbadcaaccaddbbcbacdbacbaabbbdcbcaadcabbdabbcdabbdacbdacccddbbdbdddbbadcdccaaadaddadabbccacdddcbbcabbaddadadcdbbcddacacabcbabdbdddbcbcdbbcdbacacabbabcbbaabdacababaacccdbcdcaaaacdaaddddadcccbbacbadcbaccacacadbcadadcabccbdccdcdbbbbbdaccdbddcacdcccbacccacccbcaaddbdabcccadaccddacddbbbdbccaacaacbaacbcbbacbccccaaccadcbcccbcdbaacbcaacbcbbcbbcacadacacababbbdddadcccbaadbcbbaacdabcddbaadbdcbbcdcdddbbdbdbbdcdbbcaadaacdbaaaadabdbdadcbacdbcacaaaabdbadaaddababbdbabcddcccdccddccbcabbdcdcbdccbcdbdaaccbadadbacacacbbdcdbcbaabdacccdcaaaddcdaddbccdaccbbcbacaddbddbddddbbcdbcacdabadaddddcbdadcabcadcbdcddcdaacdcbdbaccdaaaddcadaaddcbdddccccccddaccacabcdaacccadbdabdbdbcadbbbaddcbadaabbadacbdbcaaaabcdcbbbdcaaaccbaddbadacdcdcdddccbddcaababcaaacaccdaddaadbddaaabdccbcbcbcabbadbbdbddccbacddddaababbcdadddddcdcbbcdaacbbbcacccaacdcdddbcaadbdbcaccccadacbacbccaddbddccdaccddbacdbbcbbcbddccdbbcbcbcbddcdbcdccbdacaabcbbadaacbcadddcdbcddcddaddcccadacabdddacccdababbabaddaaaddacccdbdbaccdcbadbdbbaabbaddabbabbaacacacbbbbaaddbaabdddcddbbbabbcccdaaadbaacaabaccaccbabbaccdacdcbcababbdbbddcccdaacdddcdbbcbabbcaadbacdabababadaaddcabdbdbcbbcdcabacadccdccabaabdcbccaabdcdbcabdddbadaaccdbddadcbcccabbcaabdadbbcabbdaaabbbcadbdaaadcdbbbddaaaccccadaacdddcbaaacdaddcdaabcaaddbacacbabbdbaaaaabddbbcbdccbdbbadaadaabcbdbddddbadabcbacddccccdacbadcbcdcaddbbddddaaaadccbbbcabbbdccdacadacbddcdcabdaabbdaaaccbccdbaabccacadbdbbccbdbacbbadcabcaaabaadbadbacdacbbbcbcbbbcccbabbcddcdbddcbddbbcbabbcdcbadbacabaddaaaadcdbddbdadaacadcaaaababbcbadbadccbbdacdadabadadbbccdbdaddcaaabccadccdbcdccbdccddadbcdcbaabcbbabdaadacdadcbabacddbacbaccbdaaabadacadcccdbbaaccdbdaccadbbcaccccacbacbbaadcabccabadadbcdcdbdbbbccbabaddcaadadabddcbbdbbbbadabaaccbccccdbdcccbaddbbabbadccdbdccccbadcddbadabcbdbbbaadcdbbaaaabaccdaddbccccbbcbccbdaddcddababbdcccacabbcbdcdbdcacddaaababdbdaaccccddbcbbabbdcbaaadbcbbacdacbacacaddcbabacddacadbcbabcdcbaccaddbcdabbdaaacbbdbaacccaaccadccdddcaacabcbaccababaacdacdcccdcdbaaacaabbbacaddaacadaadbbddccbcbbcacadabcdabadddcabcbdbbbadaadddbcccbcabcaacabcccaaddbbbadcdccabdcbdabdbbaddbbaccddabbccbdcdabbbaadadabbbdcccadbacdbbddaacbababbdbbaacbbcbaddacbbaadddbbccbcacbacaccadbcdcdaacadaaacaaacadacdbbcacaaaaccdabbdaaabaadddbbadaacacbaacdcbdccbdaadccabaddbdacddbacbccadaccbcdddcadbbdbdbcbbbddbcabbbadadcdddbbaccddacaddbbbcbccdbcddbadccccbbbbdccadbcbbdcaabbbccbaaaccadccbabbaadcbdbcdcdcaddcadddcccabddcddaacbdabbadbdbbddbaadabacccadddbbaccbddddacbaadbaaddcdbacabddcdcbddccadcdcccaabdcbbbdddcddbdaddadcaacabccaadcbadbdbbdbbacacdacdbbcaacbbadbbbcbbcccabcbdadacabaadccaaadddcacbdabdccdadadbbddbdcbdbabaaabcbddccabaccdbacaadbababcddbacbaabbdbacaabcdcaccbcbcbaccbbddbadbbdcdadacccaaddbcdacbbbadabaadacaadacaadbdacacccadcbccccdbbdcaccbdaababcaababddcdbddccbccdacacccbabbbabbbdbcccbcdcdcdbbddddcadadaacccddcacccbccaabdcdcdddddbdbcabdcdcdddbaacbcbaacaabdbccadbdabbacccacadcaccabacbdadddabcdbbacddabdbdbdcbbaacdaacacaddaadbcdbccbbdddcacacabdaccdbcabdddabdcdbadbbdcdbadbbcaadabbdccbbcacaabadddbbdbddbcacbdadadbccbacbdcdbdaccbcdabacbaacacbcacdbdcdaddbbdaddcbabbbacdcddcbacabdccccdcbdbdcbcbbacdacbccdbbdcadcadcdbccddadbcdbdcbcadcaabcdbcdadbbaacbccaaacbdcdbcacccaaccdcdbbccaddcabccdcdabdcbcaaacddbdcbccdbcdcabacacdadbddacdbabddddcdcdbbcacdcabdacddccdaccdbcadbdacccdccbbcaaacabbbcadbabaacacabbacabbdddccabdbbbddacacdddaadddadabcdbcabcbaaadbbcadcbcbbaaddbadaadaabddaaddbbcdbbdabbccdcdbdbcaaacacaacbaaabadcbbcbcccdccbadadbbccabbdaacbaaacacdadbdddbdbdadbdbbcadcacdcddacdacacaacacaabbcdcbcbcbddacccbbdacdacabacbdbacdcdbbadcbbdaacaaacbacaaddacccdaddbadbadacadcbdbbcaccdcacbbababaabaabcddccbadbcccccdbabacadcabaddcddcadbcaadabacdbaabbdcddcaaaddbdccddaadcdbaacdbcaabaaabadbcbababbdacacadcddddadadcbbbddadccccbaadcaacccccbadddbdbabaacbbdcdaacbcdbcaacadcaadccbbaaabbcbcbacabacccdcbcdbcbcdabaabbcdcdcbacdaadcabdbbdabcabbbbdbbbbdbcddaadacabdbbbdbccdcaaabdaacaddddddabcaabcdaaabcdccdabcdaccabdccdbcbcbdadbbcbabbadbccdacacbbccadddabdadadadacaadadacbdbddaddddddaddcddaacbaddcccbcbcdccbbdcdddbddcdccbbdaadbbbdbacabccabbaaddcddbdcaadbdacdabcaddccaddaddbcbcdbadbdacdbaadccabdddddccabaaabbdbabbcaccdddabdbdadddbbddcabaddbbdbabdaabcadcbdacbaaddaabbbbcaaccdcbbbbbaabcbacdbaacadacacabaaaaaaacdadccadbddcccdcddbabddabbdbccddcababbdbbcbdabdbbcabcaaccacaacdcaaddbabbbacdbdcbddbcaabcdcddbbaadcbbbccbbdabadabdaacacaccdbacdbddbbbbbbdabaddddddaaadcdcaacdccccddbdbadacadbcabadcbbcdacbaabdcaacdbaddbdbdadcdbcccabdaabbbbcdcbccdcdadaaaadbaccbadddadccdadcaaccaaacacbccccdabbbbcbdcdccccdcacacddadccdbcaabaaddadcdaaaccdcdcbbccbdcdbaacdbcdadcbdccacabbdbdabbdcbcdcddabadaccabcdaacdddccaacdadabbbaacccdbddcbcbdaddbdccbdbbddacdabdbbcabbccccddddddadacdacbbcabaaacbbcaacababdabbbdbbcdaadabdcccacbbdcccaccdbbdcabcaadbabbbcbcbdaacdcadbbdbdabdbbdcccdccaacaddbacbaaacaaaccdaaccbcaddabaaacdcccadabcbdbcaccacdabdaaaabdbdcdacaabaabaaadaabcaabcaccccaacaddbbcbaccabdcdcbbabdabaaabddaccbdcabababdbacddddbbcbcccacbdabdddccbabcdddadcdbcabcdbdbcabcaabdbdbddbdbaacbacabbcadcabdbaccbdaabdbaccacbccccbcbabccbdaabbdababadcadcbcabcddcaacacbadadaaaabcbadccddcdccbdadbacaadadbcddbababdcddacabcccdddcbbdacaccaacbdbaabccbabadbbcbdbbbabadddbadcbdaddcacadcdadaadcaaccdaddcabcadddaccbbacadcacdabcdbdcccdaddcdcbbccbababbbaddcbddccddabaddbdcdcddcbacdcaaadcdabacbcbcbaccbcbbbcbdcaaacdabcacbbdcadcbcddccaccccadaadbabdbdabcdbcaadcdbdbccbabcababaacbadcabcbccbbbcbcbcabdcdcdaabbddabadbabaaaaacbddcabdaabaabddbcbabcbdcbddaddbacbaaddbacaaddadaddacdbcdbcbbbdbcbdcbaacdbcbcbaccbabacbcadccaadcbabbdabdbcaacbddabcdcadbaddbddadcbbddabdaaadbdbdbcaaacbcaaddaaaddbdaabadddadabcaddbaacddacccbacdadacdabcdacccdbdadacdcccadcccdaccbddabaabcccbaccdbacabaabbdbdacaabacaaabdcccbcdbdbbbcddbcddabcababccaddcadccdadaaabbdbadbddbadcdccbbbbdccddcdbcccdcbddcbacdcbddacbbabdbdabbdbdbdcbbbdcbaacbbdaabaccadccddcccbdbcdbbbbcbaccccbcbbacdbadbbcadbccbcdaabdcacbcbbbabccdcaabbbadbcdbbabdcbadcddbadaabdcbbcbadcddacaccdaddbccabaddadadcbbabaccabcdccabaadaaddbaabdcdcbbabbdabaabaabdadcbdddcbdcbcdbccadddbdabbbcccbdbaadaaabaaabbcddcdcaaddcacbaddbbcbcaadddccbbabcbaaacdbcacccdadbcdbcbbddbadadacddadacdabdddbcbbbbdcacddbccbbaadadaabcbbacbbbabaadbcccdccddbbddacbdabadbdcddadccbdabddbcdacabadbbabaabacbbdadabaaaaacbdcdbbbdbbcbbbaacdaaccacdbdabaabdbbccbddacaddddabcddbddadddcccddcaacdbcdbbcddcdcabaaadbcdbbabbadbcabcabddbbbabdaabadacdbbdbabbaaddadbdcbacccadbcdbdcdbdabacaabbbbdbcaabdacdabbaabbabcddddbbbdbdcbbbbbadcaaaabadbcbaacabdbbddcccaccdabcaadcddcdbccccddbcbbbbcbccccbabadcdcadabbadcccacdaddbbbddcbccbdcaabbbbabaadaaacbaacacaccabbbcbdadbdcbddcbdadcddcadbcdadadbacbdaacbacadacdabbacdddcdcbacddddadccbdadacababcadaccbbadcdcdbdbddcddcdbdacdcaacbbdcabdabbcdacdcccbbcbdaacbddcabcacaccccacddbcadaaacbcacdcaadbbdaabdcdbddbbcbdbcaacbcccdddcdaccacaaaaaaabcadacdbcdbdbdcddbaabcccadbdcbcbbaadacbbdcabcbccadccdbaadccbacbadadcacaabaadccabdabcacbaddbdbaabbcaddababcdbbdddbcdbbbdcdcccdcabdbdbaccdbdccdbcdaabccbcaacbbdaadddbdaacacbccdbcacaabbbaaacbdbaccababbcccbaacbddaccabbddabddbdbddcbcdaaccbdaadbbcccabbbbdacaadaccabaaaabaabdbbddbadbdcccbdbacbcdddabdbdadcdabdaabcaabaacdccccadbdabaadabddcdcdddccbbaddddbdddcbaddabccddabcabaddcabdacccbdadcddacbdadcdcbdabadbcabaddbcbddcbbabdcbadbabdbbabbbbcbdddacdbbaccddbadbbccdaddddbdabcdaccbacdcaccbcbdcbddddddcdbacdcbbadaddddcbbdacdcccbaabcdacdcbbacbacacdacdcacbbcdacdbcdadaddbbbdabcadbdbdcbdbacccdacdcbddbdcdacbddcaacdbabbccabdccbadcadbbdbcdabbacbacbbdaacbabaaaaabcbacbbbaaccbbbbaddacccdacdaacbaacabbabddcbbbbaaddaaacccddcaaacdbadadbbacccacbbdbdbacdbdbbddbacacdbacbcbbcccdbbdcabccbbabcdbbdcbdacbacacbdbcaaaabaabbcdcdbcbabdcddcbbaccacdcbdbbbacdacadabdbdbcdcbcbcaccacccbaccacbbcabadbddacaccadbbabdabaadbccaaabbccadacbcbaaadbccbbbaccacbbbbdadbdcbadccbccdddbbbccadbcdbaaabccabaaaacbaacacabbabdaabadadccccaaacaccdbdcaacbcdadaddabdcbdcdaacbcbddadcbacabccbbbdadbadbcdccaddacddadbbbbaabadcbcbddacbabacdabccbaaddcacadbabacddadbcbdbbdcbacaaccbcddbbcbdcababddcdcdadaadbddbbbadadbadbbacabbacdaabdbdbccbbbcbbacccacbabddddddddabadbdcbcccaadaabcdcaabbdcdcbbdcddbddbadbddccccddbbaccaacccababcbacbcddbbccdbacadabcbddcdcbdcabcdaabcbdaadabbdcabacacbdadaacbdaccacbdaabcccbbbdbdbbdbaacbbbaadadbcadcdcbcabbbccbbdaadcdbabadaaacbbabaaaccadbdbbbdcbcabdbabcbdbddbbcddaabadcbcbadbcbabadbbcdbbabaccbbadcccbaaccaddacddbcaacdbbaaaaddbddbaadbcabcbbdccadcbbdddcbbccbcdcaaabcaccacbbcabddaacaabcdaddcdcdbdddadcbbadadcbbdabccbacddadcadacbbbadacbcacbacbcbaccaacddabccbbbbcbdccdaddddbbacdaaabadabaacadadccccabdccdadbcacdcadbaabaadddcacdabbcabbdacdcdcdddcbbcbdaabbcbbccbbabbdccbdbadadcbcacbdbabdcddbcddadddadbdcbdbbcbbabdbdbcbbabddcbcddaccdcacbcbcbaddcbaacbdbaabdcbbbbbdabdbdccdccddcccdbbcdbdcbcbdabcbccabdadcdcddadaddddadddacbbdadbcbdbbacdcbdcaaacbddcaddabbaacccddcbdccadddccccbbbadbdccadabdbccdbcddacbbbaabaccdbbbabcbabdddcdbaaddabacbbbadbddbccbaacdcaadbdabadbdaadbdcbbaabcbbcadbccabdaadcaccabadddbcccbadacbccdddabcaaaddbabbacdbbabddcbbdccdbbacadcddcbbabcabcddadabdbbddadddcdacbccdbcdddcbdaccbaaacdcdcbaabdaabcbbcbbbbacddbdbcdbcddcaacacbdabddbadcdadbdbdacccdabcdbadcdbbadaadabdacaccbccbaabddcdccdbaacabbaadcdcabcacdccadbdbbbdbcbcccaacdcdaaaaddcdbadacacdcdabbcccbcbbbcabbadaaacaacccaabcbcdccccccacdbaccdbcdcadcdcdbccdaddaaadacbccbdaaddddccaabacabbcdddaabdaabaabcbbdaadcacdddadbcddcdbcbcbbababbdbbaaaaadabbbddbddabcccbdacdabdcdbadadaabcddaaadbbcdcdadcabbadcaccdbbadabcbcaabdadcaaabcaacadddcbaabbbacbdacacdbcdbbacdbdadcacbabcbadadddacdcacdddbadabadccbbbbbdbbbdabaddccbbcdcbbbacccbabbcaacddcccaabbcbbbdaabacdbdcbcddccabcbadbbccdbcddbacadacccaabdbbaabcbcacdadadadcbbbaabdbdbbdbdaadddacbacbdcbcbbadbdcbbdabccabcbadbbdddadddcccaabcdbdadbabccacacbdacccccaccdddadcbdbdbcbdddcdcdacdcabbcacdccbacdbdabdddcdbcabadbccadbccddadabcacacbbbddcbbccdddcdaccdccdbdabdaddcbddbaaacadbadcbbdaadbbcdaaacbbdccdcaabcabccccadbcabcbaacdaacddccddcdadabcccbbaaaaaddddcdcdaccaddaabccbcadcdaddaccababbdcbbcaacadbbabbddaacddbcddcaddbbbcccadadabbaacdacbaddbbbdcbcbabcbddbdbaddbdaacbdbcbbadccadcbbcbaaabcaabddbbadaaccacddcaaababbbbdadcddacbccbdcacbabaccadcbcaaddbcdaaadaabdbcbbdbdccdcbadcabdbcbabcbdcaaaabccbacbcbbacadddacbbbbbacbbaddcadddcbdcababbcccaabbbcccabbdbbbddbdabcacaacbbcbcdbbacaacdcacdddcbdcbdcbaadcbaadbccacbaccaccbcadddcddaadacbaddddaccdccacbbdaadabdbbabdccbccddbdbaadcdcbcddbdcbbcbabdaccdadaadaacccbdcbbaddcaabaaccbacaadacdbcaddddacdbabbaaacccadcdcabacbdaddcbdcaadadcdccbaddbdccdbcdbbdccaaacbbdbcacdbccabcbbaccdcbadbdbdcaacddbdbabbddacacaacabaccbddbccdddcdcbbddaccbacaabdbddbbaadbdcbaadadadbdaaccadddaacbcadddabbdbabcbdbcadcabcdacdcddcaaddbcdadcabcdddcabcddcacadacadbdccadaccacdbdbbadaaccbacacdcdbddcccbcccacbdacaddacbcdcddddcadbdbbdabcaaabbdcbddadadadbbdcdcbadaacdabdcdcabacddccadadcabacdadbabbbabdacbabbbdccccdddcdbaddacbbaadcdbbdaadacdaddaaaabaabdcdbaaddbcbdbbacdbcbbccdccaaaaddaadccccaacacadabdbcbabbbdbabcaaddccbadcabcacabbddcdcdcbdaacdacdbaadadadddbdacbccbadbddadccadddbdadbbddcbbdbadbbacbbddadbcdabcdddbbadacacddddcabcabcbdadadaabddaabdacccabacdaaaaacacbbddabbadcbaaabdbdcabbbabcdaacbcadaacaabbddabbaaaddaddddbacddbcdbdadcdbaabaaacbdddadccbdbdabcbcbdbdcdcacbbddbabbcabaddbcacddbcabdaadbaaddbdccccccdbcacccbbcabaaccadbabdbbccadaababaaabdcbadacacbbaaabcdbccbbbaacbcadcdcaccbdbbcdacddcccbbddbbdbdbababdacdccabadaadbddbbaabdccabcdacbbaddddbbbdabbbabbdabddabcadbbdccdcabbdbbdbbaacbcddcbbcadcacdaddcbabdbdaacbbacaaacadcccbaadccbcabdaadcbccbbbbbaaabcaabbabacdccdbbdbdbcdcdbcdbaabbbdaadadabbbcbacdcbbaaaabddbddaacaadcbdcaacadbddabdcbbacabcddabaacdddacccaacaccabbbdbaabcacaabadadbdcacdbabdababacdbbdcbddbbcdcdcbbcdbdbdcaaaacbcbdacbaddcadbadbadbbabbdadcdabbcddcdcbddcbadbccbbbadabcadbcdbadbaaccbdbccabaadbdbdbddbdadcbbbbdbdddaccaacadccaaaacaddbccaabacdacbabaaddbcbbcaccabaabcbcdbdadaadcaadcbabcbcccacabcdcaccccbdbbcabccccbbbdccabaadaddbcdadcbddabbcabadcdcbbadbdddaccbdbdbbcbbdcdbcbdaacdbcbacbdacdaccbcabacbcdabacdbdacdadccbcdccaacadcdbcbbbbcbadddcadcaaadcadbcadbdabbdbbabcbaaabbbcdcddbadddaaaadadaddccbbccdcdcadacdaaacbaaaabdcdddbdcccacadaaccbbddacbcdbaccacaaacbdcaadadadacdbbbaaaabacbdbccdacbcaacaccbabacdadbdccdddcbacbcaacadddaddbacbcdbadcbcdbaaddadccbbbcabdddbcddbabdbdadaddbdccaddddaacccaadacaacdcbdaaccababdcacbaddbaabbadacbbcaadcbbadddcbdaadccbdcaaabdcbcdccdadccbcacadbbcbbbabaabdbabbdbbbdbdbbbddbdddacdabaddaabccbddacaccaacaaabdbcdbcbdaacdbbdbbddaaccbddaccadcdccadbdaaaaccddddddbddcaaaacadcbcdcdbdcbbdcaaacccadbcbbddbabbbbabdacbdcaacbbcccdcccadbcbdddbacdaadaaacbabdbbdacdacbbbbadbbbcbaacabccbdabbddcabbbdcdbccadccaadaabcddacddaccbcdabdaaaadbddccabacbaabcdabcaccaddcddbcaaccdbcdbdcdbbdbcacadddbbcddadacaaabcbccbccdbbbcaaadabacadcbddcbbdabbdddaaacadcbbbadbacdabbadbdcadcbddbbaccdbabcacbbdcbddabccabbcdccbddccdbbcaacabdbdacbccbcbadacaccacbcdcabccbdbcbddabbdcddddbccddabbdacacdadcdcdadaccdcdcccaccbadcbaacdcbdbbaacdabaddabbdabbcbbacdadabdbaacbdcbcdbaaaababdcbbdcccadadddddcbddabcbbabcbccbdddbadaadbbababbbdddaddcbdbbabbaccbdcddcdbdaccaadaadabaddcbabdaaadbacdaadacdccdcccbacbcbcbdabcdccbcddabddadacdbdcbabddadcbbdccbcabbddabbbbbdadbbbccbaaabbbdcaabcadbbdbcbbcbacdacddacddcacbccabbbbdcbcabadbcbccaabacabdccbcddccddadcdcabaccddbbcbcabcbbcadbadadcbbbabcddcaadcacdbccaabbddddbbabcdbdddbddbcddcbdddbbbdabdaadbcdacaccbaadbbbaaadbdabcdcacdadcbcbaacbdcbdbdddccacaccdaabbbcdaadadaadacbdbbbacbbcdbacdddbaacbdcacdbadccbccbbbbbaddbcdaabcbbcbadaabaddaacbbdcadcbbaadcadacbccaccccadccbcdcbcabbbdbacaacdaadcbdaadaaaadaabcacacdabbdcdbaddabababdbcbbdcddbcdacbaaabdcccdacaaccaccbdcaacdcccbbabbabaadddaaabccbadacbcdcdcacdccacdbdcbbcbabcdbccdccbadbbccaaccbabcababaccbdddabbabddbcdcadaddabaaddaccbbbdadcbdacababcddacdababacbcdaabcdccbadcddaacddbadcdbddddbddbacdcbbdccacaabacaccdacdcdabaaaacddddbbadbcaadacddabadbcbaaadaddcaabdbbddccdcaabbacabdbdddbdbbbbddacdabadadbccbdddcdccbadbadcdcddacdccdabddcccbbadcaaccbddbabbaaabddbddaabacaadbbadaacdccdbabadabacccadccadacacabdbcaccbcdadaadbdacdadaccdcaabcccdcbdaaabcdcbcbddddbdacccddabdbdbadababbacabaaaababbbbaadccaabaaadcaacddccadcbbbdcabdbccdccbcbbbbaabddbabbdddcdbdabcdbbcdccdcbbabaabcacddbdcabdccbadaacaccbcdcbcddabbaabcabccbbbdcbcabcdcbccdcddbaacdcbaccaacadcccbbabdbbcacbbbdcccbabadcdacadcccaaabdcaaadbaadccadaacbbdacbaaccbacdddbddbbbabdbbadabddbacdcabddbacddcaabbdcadacccaddacbbabbcbccbbcddccdcacbdadbdbbbadabdcccbddbccbabdbadccdcccabdabcacbcbbbcdcdbadcbabcbcbcaccbdcbcdbddccabcadcacbbcabdcbdadcdcaadddbbdcdbdddcdcbdcacbcaabbaaaddbbddabbcbcbcbbbddcdbaaacbbaadbbbbabdaadcdcddcbaadaadcbccccbadbdccaabdacaccbabdcdccadabccbdbcbccabbcadababdbddacadcddddcbdacbcbdbbddcadddbaadcbacdbcabcbbbaabddcdbdcbcacacaaacddbddcbcadbaabbcdaaaccdbacdabbadcdccdaaabddcbbbdaddbcccaccdbcdaacabbccdcaabaaadccdbcdadcbabdddcdccbbcdadddbdbadadcccdbdbaadacadbdddbcbbdcddbbacabdaccdadcdbacadcbabcbdaaccccbcddbcbcdbdadbdababbbaaaaabadabdbcbbdcdbddbcccdbbcaccbaddcaccadadcdbdaddadaddaacababdccadaaccacdaadbbdbdcddbbdadadbbacccddabbbbaacbaadbcabcbdccccacaadacbdbcdccbaaaaabbaacdcacbcadcdadcddddccabdadbdbbbacbdcbaabcdbaaacbdaaaacdbabbcbaabcdcadcdbadbdddbbccdaabaaddbdabadddbdbadbababbcacacbbcadcdabcbbabdcccdcbcadbdadcbbccbbddaabbabbadcddccbbaabcbdadcbdbadabbcabcaddddbcbdcbdcddabbaccbacbbbabdaaaaadbabcddadabdbadbaddbbbadaabcccaabcddaaaccbdacdcbdddaadcbcdccbdadbaadbdaaadddbbbcdbdcaaadadadccabddaccabbcdddcdaabddabadbbadaacddbdaddbcccbbcdaacbddbcabcdbcdddaabcdbaccccbdcdcdaabadbaadaabbcaaccccabdbbacacddcacddbdbbcbbacdaadcdcbadddabbddbdbcbdbcaccbdbbadcaabbccdcbddcbdabbabaaddccdacaacdcddcdcaacbaaacddbcddcadcaabcaaabcdcdadcbbabccdbaddccbdaacdbbdbcbacacabaddcdcccbdbabacadaddaaccdddaddbcaabcbadcdbcbacbcaaabbadbddacddcdbaadabdbabccacbbcbcbcddcbabdcbcaacadaadcccbdacccaaddbdbacdcdabdadccbcbbdbaadccccaccddadbbbaaacabcdbaccbaccdaacbabcbaabdcaddabdbcadbaaadcbcdbcadcdbccaabbbcacddcbdcdbddcdccdbddbabcaababcccaaccacabbabcaabcbdaddacbcbbbdacabcdcbbabdbbbdbbdbaacdbbbbbddccdaccddccccdadbdcbdbdccdaacbdcdcbdcbcdadaadbdabcbdcadbdabadacbacdbcbcdadbbbcbdcaabdbcddbddadabbdcaaddacbbdaaacdabcbcdaadbaddccdbabddbdaaaabbaadabdcdbaabbadbdccbaabccbcdbbabddddbabbcabaaababbccbabbaaaaabcbbabdbdadbddabddabaabcaddbaacdaacddaccdcbacaaabbcbdadcadadcccccbcaaccddabcacaccddadacabcaaaccaaacabcacaddddacbaaacdaadbaccdbcccbbadcddcadabcbcbdacbaddbdcbcaadcadbcbbbdcbcdbdbbcdcbcbcdabcacdabdcdaadbbdaaaaaaccdbcbdaccbacbaadaabaaacadddbbcddbcacbdadbcdabcdbbcadabadcdaabdbabcbcdcbcdacbbabaabababbdabdadbbddadabcbcaababcaacdccccdbccdccbcdbadcddbabdcbdbcdaddccabccabacaadcaadcbbdabbaacbacadcdacddcbadbcbbcccbbdcddaccbcbacacadcaaaacacbdccbcbcbcabdcadbaaabdbdbadbacbbccbbaadbabbdbadbcaacccbdddccaabbaadcddbdcaabbdababddaaddccdddaabbdabdabaaddbcadadcbbbcbccbbdcbddbcdcbdddbbababadcccbadcbcdbaabccbbadccaadccacbccaabcdabdacdabaddcdbababdbcdccdbabccdcaaddbaaaddcdccddcbacbcbbcbcacbcaabcadbcbdaadbbdabcabcdaccaaacabdcabbbbaaacdbccdbdadccbabbaccddcccbcdaacacdbcaabcbacdabadaaabddacddbddcccdcccbacbbacddadbaaaccbdbabadcbacccbcdbdcccabcbcbbbbcbcbaacbbdadcdccaccbcbdddcdbaaacbaaaddcadddbacbbdbbaccbaccacddcaabcaaabcbbccccaaacdcaddcbdbdacbcadcacccdaadbbbabdccacbdacbbdaaaabacaaddddaabaddaacabdcddaccddacddabcadbacdbcbddbdcddccdadbacccabaadbbaccbccabacaadccbacbccadabcdcaabcaaaabcaddbcbacabccbdaddccccccbcddccdddbdbbdcacbbabcdcdbbcaadadaaccbbadcacdbacabccbdddacabbbbdbaabbacabbcbcbaccbcdcdacdbcbdbcddbdddabbdabcbaabbacbdbbaadddababdcbdccbacdddccddcbcacacbaacccaccbabbcbdacadbacacaccccaabcaaaddbdbdadcdabadcbbdadbbcbdabaaddbcdbccddadabacccbdaaccbcddcdcbbdcdbaddbddddababcbcdbbbccccadbddaacacccaabadcaadadcdbaacdbddaadabdccaddcbcccaccddcaaabcddcbadcacdbbaaccdccbadbdcaaccdbdbccbacbdbddbbdacabdadadcacbbcbbdbcdbabdbcbdcddaabbacbcbdbccdddbadacbcccbdcccbbbbababaccdacdabcdaddacbdbaddacddbbcbcadaddadccbadbcbdadbdabddbabaadcadbcccaacadbcdbdcbcacdaacbabacadcddcdccdaadacbcaccbbdddaddaccbdabbacdadbdbbaadddacbcbdddacbbdbbbbadcdbcccabcbccabddcbcbdbccadaccaaddccdbbacdbdbcbbbbbaaccddcadbcdaabaabbccdaaccdccbcbbdbacacbcdbbccdcbcbabdbbaabbccabbcdddcdbacdbadbdcabbcdbabccbbabbdadcdcdbbdbcbbdcacdacaacadddddacbacdaddcabddaaacddccdcabbdaaacbdaccdbcacdadbcbcacccddbaabcccaabaaacadbdcdbccadaabdaabdcdbacaabdbbbbabdaaddaddcaddadcaddcdcbbbdcacdadbaadcdbccbdabddbcaabdbddddbabadcdacbaacaaacbdbdadbdbbdbbbacbabbcaaacdddaddddbaccccaadcdbbacbcadbdcaaaddcddbbaadbabaacdaddbadcaaacbabcdcccddbdbcadccbbbcbcbcdbabddabbbdcbbdccbabbdddacabaacacbbbaddadbcccdabdcaadbbacdabdadacadbdccbbbccbbcdbabcbcddbcbdabcbdacacbaaccdbacbcddacaabcaddbadbdbdbbcdadddddddacabbdbddbaacdbdabaacadcabcaabccacbadddbbccdcbddadaccabacdddbbbbdbadccdcdcaaccdaabbdacbacaabbdbabbbacccadcadbcdadbbaabdadacbdbdcbabbaabacdbdbaacdccbaccadcddadcccaadacbdcdadcbccadacaabdccdcacdabdaadadcadacdcdbdcabddaddabcdabdddacbbcbdcddcbbacccbbadaccabacddcbcbbcdbdccddbbbdbaddabccddddbbcbbaccabddccbdabbdcbdcbcdbdccbdabcdcdbcbabaadcaddacaadcdababcbbdcbcccbbdacabbddddbaaccccdbdbbccbabccddbbbdcdccabacaccbbbbaddbcacaacbacbcdabdbdbbdaadaaccddadbbabaddccbcccabdcbdbaccabbcdacbdcacdbccadccaccadacadbcaaacdcbaccbadcbdadddabadcadbadbbdbbcaabbdbdabbdaacdacabcaccbcdddabcdabdabccbbddacccadbccabdadcacccdaccdccbccbdbddcaadbaaabbdddbabbbbbbaccbdcddbabcddbddcbacdbdacbdccaccacdcadbadbdabddccddcbbccccacaadddccbdbdabccaccbcaddddbaccadadbdadcdbaabddcbaddddcdbccbacccbabbcdcabcbababbcadccdaaddbbaabccbcbdaaadcdabcdccbbcbbacabbadbdadcadbbababaaadcdadabaaabcaccdcdbccdcbacbddaaabdcdccadcadadbcdcdacacbbaddcabccadbbbccaaccbaaacdabdabccdadbdcababbdaddbaacababbdccdccdbcacbcbaccdaabcbaabbbabdcccadddbdcabbacddbcacbccbacddddadbccddbabbbdbdbddcacadcbcccddadbccbbbdacdcbaddcacbdacccadcaccbaddbcbdbddaaccdbaaccddbbccdbaadabbabcccaaaacbbcaabcabccccbbcbddcbaacbcbbbddbcabdcaabaaaccbbbdcbcbbccbabcacccaccbbbabddbcbbcaccdcabbdbcbacdaddcdabcdadacbcabacccdabbcaccccbabbcbcbadbcccbabcadbbdcaccccbaacabcbbadbaaddaaaacdcdaaaddbcbabdccabcbddbaacbaadabcddbbbdcaddbcddadbbcdddccdadbdadcbadabdbbdbbdbaacaccadadbcddadcabacdccdcbdadddbdbaacdcabadabddaaabdbabdaaadcbadcdcdadbacaccccdcbbcadacdddcdcbbbcbadbbbbbcbbbccaccbaacbacbccccbbaadacabcdcaabaaacbbdaacbccddcccbaadcbddabbaccacdacaabccdaaacdacddbbacdbcddddbcbcdddacacabaddbcaadacacddbbbacaadccbdbcaacbbdacaaddcacaadcdddbcbdacdcadadcbbddcddccbdbdbaadccbbadabaccacababbabcdcbcdcccdaacbbabccddcdbaaabacddbcacbadcdaabacacadbbbcacdcdcababdcdbdcaacbbcdbddbacaaaaacccabcccdaccdcdcbdcaadabcdabacbbcdcbadcdcacabcbcbabdcdabdadbbacabbcdbabcdbcbadaaaccdaadbcbcaadcccdccbacdaaaabdcdaaacbbcdcdadabbbadcdbdbaacadaabdcbcbbddcbbcddbbbabcbacccdddbabddcdadbabcdadcdacbcbcddbaacaaaacbcbdcddddcaccdcdccddbddbcddbccddddbabacbcbabccdaddadcbbddbdcbbcbdadbbabccbacdbdccddadcacaacddacbaddbdbccbacddaacaaadadcbbcbacadcdadaabcacccaabdbabdbbaaadbcbadcacaddbcaadabccabadacabcdbcbcddabbdacabaacdcdabdacaabbcbabcdbbcacdbcadbccdaabccadacbbbbaaccaaacddabbcdaadabcbaaabdaacdcaccbcadcbaabbbdbbbcabdcabbccbbbdcccadacddcdccacbbcdcccdcaacdbaaddabddacbcdaadadabdddcdddccdabdbbbaddbcabcaddcbdbabaadbbdddadbcbbcdcbccddcaddacbacdacbadcdbcacbdaddddcbadcadbaaacccacdbcbababbbbdadbdbdbabbbccdbbbacaaadcddbddacbdbccbbddaaccbcababbbabbadccdddcbbdaaddabbaaccacdcdadccbdbbdaccacaacbdacabbcbadbadbbdaaccddccabbbdbddcabcccaaddcdbcddacdbaabcacbcbddcabdbcbcbbdaaacbddadbdcccdbaaadbccaacdcdcdbcbccbbdabbcaacaddacaaaccdbddabbdaadbdaadcacbbdcdbbacbbaadabbabaadaccdddacdccabdbbbdbbbdbcacdbddcbbacbcbccabbcaacaadcbbbbbdadbabdaacacbccaaaddccdaadbbcbcabababbdcdddcdbddbddbaaaccadcaddddacacccdabcbcbbaabcabbbdddcabacaabaaacddbdcaaacdbcddabcbdbbdddbdbcccbcbdcacbacccdbdabbbcdabaabacadbdcdadbbcdbddbdbabdadaaccbbdaaabdbdacccaccadcabdcababdcabdabdbbbdadccccbcdaaaabbaddcbddbaddcbacacaacacabbabaddbabccbcdcdbadcdcadddbccbccaccccacdbabbbabacdaccbacabbaabadbcdddaddcacdadcadddbbdcdddbcdccaabddaacccccaccdadcbcdcdbcbadadddcdccddaacbbdaabbdadddacbadbadbcadbbdadadabbadcabcabdbaadababbbcabcdacaddcadcadbddacddbcaabbaaccdcddcaaddbddcdcdbcadcdabccbdbdccddcdbccdcdcddbacdbcdaacddcddbbdbdabaabaccbaabdcbaccbdddcccbacdddbbbaddadaccdddacbdbbbccacaddadadbbcddddaccadccccbadcbadbddacdddaadbacaadaccdabddabaccbddbacbbcabbdcbbcaabbabbddaadbacbabddccabccbcacbbbbccdddaaccddbcdddcbccadbaabddcacacbbaddbdcabcaaaddcaddacdaccbdcaddddcdadcadcbdadadbcabaacccbcdabcaadcccccacadadddabcdabcdbbbcbbddabcadabdaabbacdbcdbbbbadbdacbcbbcdbcbddabdbcccbabdcbdadaaabbbbdccdadaaddbdccdababacddddddddbcdbcaccacaabcbbabcddaadccadbbbcaacbbaadabcdddcbdadcdabddabacddbbdcbabdabbadbcadcccabcbcaaaadbcbdadddddcabbccdbbbccaddabaddbbcbbbadddacdcccabcaccaadcabadbccbcabbbaadbcbadbabbbbbbcccccaadcaddabbccccbacdbddacccadaccbbabacbbcadbbcddcdccaadcbcbddcbcdadadbacabcaddddcdadddbdacbccbcabcbbabcabaabcbdabbdacdbdabdbbbbdaabcbdcbbabbcdcbaacbdacccccabdbbabacadbcdaaddccacdaaaacccddbccdacdddababcdcccbbaccccccdcaabadddbccdcddbdbdbbccabbddaadabbbdddbccbbbcadcbddadbaddccdabbcdadaadaddaccdbbabacaacbdbbdccbbccccbbacbbbcdbdbbbdbdbdcabcadaddbcbaacdabdacdcbcbbabdbabaddbbdbdccdaccdbccaddcabbdbdabbdcdcccbbaddacacdbdcbdbdabbdcacaaabbccbdcdcbbaadcacccccbccadddaacabdcacbdbaabaddcbcaabaccdcaaadadadabccbcaacdbddabbdbddcbbbccaddbbbdacabbacbbbadbaacbbcddbcaabaacddacdcaadbbaccdaaaadbdddbcdaacacaabaaccccbcbccddaabacbcdbbbddcdbccaddacacbcbcacababcbddadccccaacbcababadbcbccbddaacbadbacddccaadbbdcabdbdbdacadddbdabbdabcbcccccaaabcdbabddcacadddaadcdcbaaabbcdcdacbacdabaaacacdacccaddddbbbabcacdaaabccbdacaddcbacddbbcadcbcbcdaadacadddadacdaaddbbbadddbbdabcbacabbbcaaabbcbbabcaccabdbbccdcdabdabcaadabcadbbdbddabddcbabaabcdadcadbcdababdbcbabdcacdbddcbacdbcbaabadbdbbdbdcdabcabdacccadaaccbcaaabddabdbccaabbdaccddaaacabbabdaaaacadbdcdddaccadcdacabcabaaaccabbcdcdbbddcbddbcccddbaaccacacabadaaabccdaccdbaacaddacbaabccbabdcdccdabcbbdcaccbdccdbdaacdbccddcccbcbcbbdcddcdbcdbdddcacbbaadccaabbadccbcbdcbadaccddcdbbacdbbbbcdacadcdbaddcbadbaccbdadccbdcbbcbbaaabcaccdccbcaccdaabdbcdaadbadcccaaccdaccaddbdbdadcdbdcdcccbadbaddacdaacbcbbabcdbdabccaccdaaddaabbdabcaabcdbbdcadddbddabcacbdcabcbbdcabdbaccaaaabcdbdbdbbbacbcaaabbacbbdcdaadddbbddcbccacbcbbcadbccbdacacdccbdababaabdcbdacdcddcbbbdcaccccaaccababbbdaabcbbdaadccccacacabdadaadbbbbacaddaabbbbbbbcdbadddbdbcabaaddbcababdcbccdcabcabcabaacadaaccadbddacdcddbdabadcdbccbaababaadcadccdcbcabcbabadddaccddbcdabdcddacabaadacacccaadcbdbacdccacabccdcbbbaadcdcadabcacdbcadccaadadbacdaababadbbbcaabdccddacadcaaacdccbbbccaccbdddcdbaaacacddccdcacacdbadcbdcbabbcbcbacaddbadbabddcdbbcccbcacadadddccabaacabacbdcacdacbdababbadbacdcadbcaadadbbaabbaaadbadabbbdccbababcbccbbaabccbcbaacccadddcadbcacbacabbbcdadbbddbbadcbcbdabdbadbcaddacdadcddaabccbdcbbbaabacdbcbbaccadbbcacadabbbbdcadbadcbbddcbdcacdcbadcaadbddadabcacaabcbbbccabdbbdcbcadbbababbbdbaccbcddbccdbcaacccbacdbdadacdddcabdbccdbdcacbcbddaacbcbaacabbddddddbbbbddcddcdbbadabdcaddadbaaccdddbacacabdcaaccbabcabaacabbacddbbbaabadccdbdcccdcdddcbdcdbbdbdccaabcdbdbadabccbdddaddabbccbaccabcbcddaadcadaaadcaccadcdbcdbaddbbbcadddadbddaabacaababcabbabccbcbddacaadddbcdcdabdddcccdbbcabdbadbcdacdbcadaddbbbdccbaacccbcddcddccccccdbacddcbdbaabcacdacaccddaaacbaacadccaacbadaabdbdddbbcacbbccaccbddbcbadcddbbbadabddacadbdcbccaaaadabdbddbdcbdadbacdddbbccccadaccbdddcacdacacbcadbbdadbaaaabbccdddcdcbacabdabcccbbaacbdccaabbdbcdcadbaabbbcadadcddaacdcacaaccbdbbbcaacacdccbbaadccddcbdadbdaaaccaaabbbdcaabddccbdbadbdbdacadbbadaaabdaccbdbbbcdaddcaccadbcccbdddcccdbcdcbcaaccbaabaaabdaaddbacdcdbdddcdbcdcddbcadcabdccbccdbbacdbcbacbccbddcddddbcaddbbabcbacbcdddbbcabcccadccbbadcbbddbaacbddcbdbcbcabbbcadcbbbbddcaabdbdccaacbcbabdadadddbcbbabacdaddaabbcdbbaabaadcbaadddcbccbcddcabbadbdcaacbbcddadcdabdbbadabbbbbacbccacdccdabaabbdbcddacadbdabadacccdacdadbbbbabaabdcbccacbddddacdcaaddaddcaaabaccaddddccbdbbbdddbbcdbbacabcddabbddabcdbacdadbadcaaacbdaddccadcdadbbbccbcabbaabbaacbbcaabcbbdbcddcaaacbadababacbddbbbbcbaaadabacddddadddaaaddbadddcdcadaabbcaccaddbbcccddcdadbdadacdcaaabdabcaaddabbcbabadaaadddccddbdacbacbcbbdddaaddcacadbaabbcbdcaacccadaabdcccdcbabcaaabcaabcaddddadadddacccbabacdbdbabddaaaacdccadccbcdcdcbdadbdcbcadbbcbabcbccaccaadbdcbbacdaaddccadddccdbcccdaacdcbbdcbdbbdbcddaadabcbabbbcddbbddbbabaadabaadbdbdabadbadbabcbcbaacdcddcdbbbcbbabbbbddaabbacddbcdcadbacaaacdcbccccaccabaaacdbcbdcddbaacacaabaaadaddbadbcdcacdccacdaacddcabbddadcadbaddddaacacbdbbcdbbbacdbcdddadabbaadbcdcbcbbabaacaacacbcddbbbaabcacadcdbabbabbaababbadbccadbcdddadccbbcadabcdbbbadacdddabcddcbaabacbbbbbdbddcdbddadcacadbdbadcaddcdbbcbdbccbdbdbaccdadadaadacabbaaaddbabcadaacabdddcdaacddbaadcdbcabbcbcdbaaacdbcbabaccbaaacccaccddaaacadbbadbcabbacbbbdcadbdddcababbdccaddddbadcbcdaaddcbddddcbdcbdcdaacdaabbdccddacbdcabddcbdaacdaaddacbddaabaccbabcdaaabbbbdaaaabbacdbdbcdabaaadbacbccbddadccacdccbddcbdcaaaabaaccdaabcacacaddbdbdbaccadcbaababadbcabbbcaaaaddcccaacdcdaaaaddaacbbbddaaccccbbaaccdadbcddddabaaabcccaacaddabdaacdacadadabacdbcbcbbddddcdddcdcbdccaddabccaabdacadbcabadacdcddbddaaacbadbbbaaddcaaacaadacccadcacdcdcbaaddcaaabdadaaacacdaddcadbcdbbdcaaaacdbcbbbcbcaaabccbcbccdbcaabdddabcbacabbabacdccbddaabadbadaccbcdccbbadddbbcbaaabdaabdccaadcaabacccdbaabdcccabbacdcacddbcdcbadbdaaabacacbcddcacabbabdcdbbdcdcdcddacddaccadcdbbabcdcbcbcccaccbcaadacaccdbccabbcdcbbcaaabbdddcdcccbadcbaadbccbcbbaaacdacbbadccaaabaccdaacccaadcdbcbcbccbbadcaabccdbacccabaacbbddbabccdbadadbabcdacdcccadbcacbcbdbdbbbbdadbdbadbbdbcdcddaddcbcbcbbbbaaaacbdabbdccdccdbbcbdddcdacbacacdadcbacbdbabcdbdbacbcbabbcbdcccadacacdcabdaadbcadbbcddcbdccbbcdabdccadadbcabdadaacbacdcbbbccbccdabbcaccdaadacacbdadbadddadcaacddaaadaccdbbbbbddaabbbdbdaaabbcccdabaadbbbadbdbacccdcadcbabbdaaacadadbdacbacdcdcbbbbdacbddabdaaadaccaabdcaabcbcbcbcdbcbdcdcbdadcdabdcbabadbccbdbbacdddccdbdbdaaccbdaacaccdadcbdbddbdcdacbcdbbdcdbbabcccbdcaaabddaadbcccccccadbdbcbabcdcbcacdaaddcacacddaddacaabbcccdcbdadbccdacdddadaaaddccdbcdbcaaacddcaddbdcaacbaadbcdcdbcabdacadcddabbcbcbaaddabdbabcbcdabdcbdcbabdcabcabbddcdbaacbbdcdcaaabacdadddadacbdbcbaaddcbcbcccaaadabdbdcdcdbbddccccdababdccabdcbdddaabbcabbdcbcbbccbcccdccdbcaaacdadabbabbcadcddcccdaddcbbccaababccbcdccaadccbccdabbccadccacbbbccdbcabaddbdbcacaccccdabdcccbdbbccacccdcabddbabcaabbddbbcadcccbadbbcacaacabdabdaddbbacdcddabacbbbaaaaacdbbacaaaaababbdccbbaacababcddaddbdcccaccdbdabbaadbdacbadccddbdccbccddbbcbadccbabdbbdacccdaddaddabdbaadabccabaabcdccbddabcbabadaddaaadbdaaacadcbdcaababaacbccabacddbcdccaaaaadbbacaadbacadcbadbbdbadddaabccadabdbaaaccdabdccbddaaccaaddcadadddadbbdacbbaccdbdcaacdbdadccdcdaddbaccdddbddbbbbbddaacadadddbcdcaaabbaccdcdbdbacdacabcadddbcccacdadcbcadccbccdcbdbdadcbdcdbdccbbaacccdbaccdcdabdcddaabacadcccabcdacbcdabbacdbccbbbaddbddcbbbcabdaacaaccbddbcaaddcbccbdaabccbbbccccaccdccbdbdcdbbcccbdccadabcccdaacbcddbbcdcbccbbdbcdbdcaddaacdcbbacababddaacabbaadddddbcccbbbadcaaccabaaaacabbbacccbaccdbdbabbcdabdddadbcaaddacdabcaadaacabbbbaabbbaacabbdabdccbcadcdadbbdcbcbddcabaccbbdbdbccabbdacbdabccdacdabcadaaabacdbcdcdaadbdabababcaaabbcadbbbddbadaabccdccaaaacabdaacccbdcdcbcacacdadadacdaccabaddcaabcaadccbaaaccccbddcdcabddbdcabdcccdbcccacbcdcddbbdbdcdbabcdabcdabccddacdabbdadacbbaabddbdbbdacddadbdaabaddabcdddbdddcbbcbaaacbbdcdaaaddaadcabababdabbcadcdccdbdcacadbdacdbcdbccbbadacddbcabbbbbccbaddccdbddacdabcbcbaaacdbcabdcabadacdcdcdddadddbaddcddbdabcdbcabadaabdbadbcdbbddbbcbbcbccadcacacaacabcaacbdcacddbccdcbbaacccaccbcabadbacaaabbbbccadacbcaaaadabbddaaadabbbdbcaacbaadbcdbaabadcbbcdddacabbaaaccdcaddabaddbcaaadbbcbcabdbcbdabbdaacdaadcbdbacbddbbcaddccacdcdcadbccbdcadcaddacdaababcaaaccabdcacddbdbdbadbbdbabacaadaddbabbcbcdccbdcdcbbcacacbadcacdcadbabbcacbabbaacabdaccdccabddcaccadbabcdabbddadbbaaaabadcbbcddcbcbaccdbabcbcdacdacdbccbcdcacdacacddcdbbdadbdddabdaabbccbddcddccacdadbbacaaaabdbcbddadcbbababdccdbbdaaacbbbbdcabdacaddaccacccddcadaabaccaacacabdadbaabaabbccabcbddaccbdcabdabbadcddccaabddaccaddcbdccadbabbdbbbbdcbadcdbbbcccbbdabacacbddaaadbcddbacbdcabaabdcdadabaccdbdcacadbcdccbbccdbdbccbbcbdaadabdcdabddacbcddacaaddcddbdddcbdcaacbdcabdcbcaadadbdcdbdcbadccddacccabccbaadbbabdbccdacbcbcaabcbccbaccccbdbdcdabbcdadadcbadacacacdbccdccccdbabcaccddbccbcdbbaaacbcacdbcbcdbbcbcbdbaaacbdbcacbbadbcacbcdbaacadacaddacdabcccbbcabdbdccbccdbcbcdacddbaaddbacbbacaaaaddcccabaccddcaadbaaaadacaabbadbbadcacbccdacdbddcdacdcacabbcbcdcaddaacdaccbdccdaddaacacdcabadbabdbcddcbcbbbdddbaaaabcbbcbbdabbbacdcbbbcdbbbcaccdddcdbdcdadddbdabbddbaaddabbcadabcccbddddccaacadcbbcdcbdcdcbddacacbbadabdadaddbddaaacbddbcaccbbcdccdabaccdbdbcdaacacdbdaddbabbbdadcccbbdadcbbabcdaaaaaddacdacacdccbbcdcaaddccbcaacdccccbbaabdcdaacbccccccbddbdcadbcddbdcbcddbddaabcdbcababacabdcabdaaccbaaccbbbdcadcbababcaddcaabbddcdacdbdbabddacbcdabddbdacdccdadbabdacbcbcbacbbddacaabdbdbcdbdbcdbccaadacbccaaaaaabbddbbbbcdabcaccabddaccabcbddaaddddadacccdccaadcaaaccddbaaccdadbdbddaabddabcdcabdcdbccdbddacabadadabddbcbddcdcbaaacbbbddbddabdcbbdcddabdccdaddcbcabdcbddbbaacdadacbcbabcacddcaadcdadbcbccabcddddaddbbaccacbbbaaccdddcadbcdabbdaaaccccbababbaccccccaabccdcdddacabaaacbcdabacdbbbbbbaacbbdcdababdbacadadaaccaaabdadbcccddabdccdbdcacbacbbbbbcccacbcbadbdbcabccabbdcbadbabcabccbbdabcabdcddcbadbccaccaaccaaaccadcacadbbccdaadadccbbccdaadbbbbdbbccadbcccaabbcdbcdabdcaacbddcaadcaccacdcbcccbdcccdbcdbbdbcdadbaaabdbabcdbbbddbcdaadcbdbdcaccccdccddbbabdcdacaabdcbdcccbcdbbadcabcadcbaacbabaabaccbbcccdddbbcdbddaabcdacdbdcacacdccccddcadcabbaaabaacdadddbabbccabdbabddcdcddcabcaacbccdabbbcdacbadccccabcabacccbcdbbddbaabbcdbcbdbccbadddaddabaadccdadaacacccbacdaddcbaccdddccadbaabdacbdaccbacdcabdddbbdabcbbacdcbadbcaaccbdcdbdadadcaabdadadbdbcdbbdcbcaddbdccacababddcdadacdbbcbbcdbaacabaaaaaabdddacdcbbddbcaabaadaacaacabdabaaaadddacaaabadddccaacddbadabbaccccbccbddddccbbcbabcbcacdbcddbdbdcdabbbdabdccccbabddbccddbadbdccddabdbdbbababddaddddbbabdadcbcbbacaddacbaddbcdbabcdbccbdcbbdcbdadbaddccbcaddcccccdcbdaabbdbddcccaccdbcdbcdbaadabcdabcabbcdcccabbbdcbbddadabdabbbcacbdcdcbcabdbbbaabcbdaccdbabcabadabbddddacbdbbbaabcbcbbbbbcdacdbdcdbdcabbabdcaabdcccaaddcdbdbbddcbabdcbbacbaabdabdcdbaccdbcdbdbcacadcadbcbccbbddabcdaadaacbcccdcdacbdcaccbadbdbaccccccbbbcccabacbcacbcadaacadddabdadddddabadadbccbcccdddabaabbbaabaaddacddbbbbbdababdcdcdabddcdbbcbcabdacbcaacbadadbabbdbcacaaabcdabbcdcbabaabaabaabadadcddbdddcbddbbcacdcdcaaacadbcabbdddaabbccbbbbbbbccababdcdaabacbdadccdcacbadbadcdadabdcbdbaccddddabdccaabbaaaddcacdcbadbcdbaabccccdadbdacaaccddcbcdcacabcabccdccdbcbdbdbacdaccbadddbbbadbcacabcbbbbcdbcbbdbcaacdabdcacabaddbbadddbbdbabdbabcddcbcaacbcbccbcbcadcbccdadcaaccdbbabbcdcccbdbdbcbbcabbaaaadaacdbddcbacbdaddaddabadbcbadadadcabbbadbbadcbbdbcdacccddadaccdddbadabcccdbabdabbcbcdabaaddbdbacccbccdbdbbdadbcbaddaacbccaddbcabaadbccacdcacaabbbddbdabbddcddbccdcabacbbbadaacbbbccabaaddbcdcadadadbcdbcdbabcacacccbaabdadcbabaacbacbdadbcbddadadacacdcdcbadcacacdbaaabccdcccccdaccdacaacdbacaadabddacadcddbbdaabdacccccdcdddabdbbbddcdacaaabbddadaaccabadbacbddabdcdbcbabdacdcddddccbbbabdbdcdacddbddadddcdbacdcbbcbaabbdadbbabbcacabacaccddaacacbcddbbabcacddacbbacaaadcbadadcccadaccaadcdcddbccdadabcadbdaadcbcdbacddacddcbacabaadabcaddbbdaacbcdabaaddddadbcabaacdadbcacdbacbccdcbcbacbcabcdddaddaabbbcabacaaabbbadbbcaacbbadcdbccdddcbcbbdcadacbbabbccbdcbbbbadcacddbbcdbbacadabcbbdcadcbbcdbbadccbcababcacbbddbaaacbcdbddbdccacbdddacbcddcdcdaaaabaaaaddbbbcbadbadaabdabcdbbbcdadcadcdbbbcbcbaabaabaacccdcccadcbcdbabdbccdccaccddbdddbbaaddcbbaaccaddadcdbbcdbccabcaadccdbdadadbbbcbdcddbcacbacaacdddaacccdbbbcaacddaaddbaacabdacccdbdbcbaddbccccadbdabbdccdbcccccaaaabcccdcddccabbdddbabaabacbbdadaaacdbddadbadcdbadcdaacacadccdbdaacdbdcbcccaddddddcdaabdacacabdcadabdbdaaccacabbacadcacaddaabbaacbcaacdddaabcbdcacbabdbcaaadbcaacacdcdddabccacbbccddcbacbadbbbbcabddbcbdadbadbaddbcaacbacacacaabccbdcadbcdbbdaacaaabbaaabdddbaadcdaabbbcbdbabcaadddbabadcadbdaddaacabdaadbadddaadbbcdbbdbacdacbbbcbccdcccaacacdbbddcabbbdbdadbbcacccabaccbbddbbcccaddcdcddccdcdddcbaadcccbadcccdcdbbbbbcccabbbabaddbddbdaaacdccbcbbadbcbbaadadcbbdcacdcbcbddaacacbcdcadbaddcaadaccbcaaddbdacbdbdaaacbddcccaadcbbbcbdbadccdbdbabcbdadaddcccdcbcccbbbccdabaccaccbadbdbbaaabdbcddbdbdbddccbdbcaaabcdccbacacdbcdccacbdbaccabbdadbdbdabcadcaddadbccdcccbcbbbbdacabadbabbbadcbccdaacbcdaadabddddbadbacbdbadcadbacbcaabcacabadddcacddcdcaccacbbbdbadcbbaaaadbaabdadbcbbadbaabbbcddcdabbdcacbccaaabdacbbacccadbbdcbacbbabaabcbaabcdbaaddadaccbcdbbbacabdaacdbbbbdadaabcadababdcdcddaaabdcbcdaabbccbbacaadcdbcbcddbbabcbbbbabcbadccdddccdbcdaadaabaabaadcbbdcaacccaaacbddbabdbdaadbababacaabcacadbbabddcabcdbddacccaabddaddaacdddccadadbcccbdaaccbccadddbcbcddadcacadccaadaacacbabadadcdaacbabdcdadbdbdcbaaacdadbabbbacbaabdaacbacdbddcadaacccadbbaccadacbaccccaadbddaaadbdbadbddcbcbadcaaacaadbaadcbcadadcadbdbcdddbbdbbdacaabaadabddcbccbbdcaadabccdbcdaacaacdddcdacbcaccadcacadaacababaaacaacabdacbdbaaadddaddddabaaaddccaadacdcbbaaabbbbcdaddcadccbacbbadcccbbcbdcbdcbcbcbcadccadaacbcbddddadcbcbcdcbcccdaccbbacdddaaadbbadaaaabbcbbadaaaabbbdddcdbabcccdcdcbbbaadabdbabcdbddbabdccaddddabcbbbacdbcbaaadabdbaaccdbbbbddcbbdbacbcbacdbabddabacbbdbbadbcdbcacdaccadddcddbaccbcccddcbbcccdbdabccccdccdccdaadbabcdbadbabcacccbccddddcdaccdbccdbacccdaaaacccadabddbabddcbdaddccadcadcadbbadaccadbdbbaacadccbcaaadaabdbbdbdcbdcdaaabdabbaaabccaddbcabccbcadbdabdbadacdbbbadbbcbdbaccabcbacbbdcbddccabbdbaaadabcdcaacdcaabbbaabcadcbbbcabbbbdcbcdcdcddbbacdcdcdabccacccdbddbdcabacccbdcabbadcacddabdaaccabccbdbbabddcacadbabbaadddaabacdcdccabdaabdabbbbaccdcccbccaaabbdbcbdccadbaaadcdcacdadccbdbaddadaddcdbbccbdccbdbaccbdacbdaadbcbccbacccabcabbdbadddcbcdacbdddcbddccdbaaccdacdbbbbbaabadcabbcdacddacddbadcddbacdcadcbcbaaccddddaaacaabdbdcdccadbcaaaabdabbcbdabadccdabdcdadbbbcabacdbbabcbccbbcdadaacacaccacbdbdcadacacdacacabdbccbaadbcaacccabdddbabbaddacbbbbbdbacccabcabbbbdaaccdbcccacbdbcaccaabacadadacbaababaddbacaadbdccdbbadbdcbbbbcdacbdabcccbdbbacaabbdacddbbbaabcadddcbbbdddddabaadbbdaddbccccdcdcccbaaacbbcbabcadcbcbaaabcbbdacabbabcbbadcddcdaacbaaddaabdbabcabcdaaddaddaacdccbadbcadcbabcdbabdddacaaacddabccabacccabcddcdcdddcacadcbdaddcadadaaaadcdbcadabcbbbbaadbcdbddaaabcabcdacccbaaacdbdbaadaccccbcabdadcbcacabbbacbcdccbbbaabccddcccbdcadbacccabccbcdbdddbcbaadddbadbcacbbadddcdcddcaaadaddcaccccacdddaadcaadacbacdccdcaabdacbbcccdaddddcaccacbbaadbbcadbdcacdbdcdddaddcdccabababbbabccaaabcaabdbadabdbdcccdbaccdacabccacdcdbdbccbacdadcbdbadcdcccbcbabcdacacaaccaccaacdabcdccddbabacbdbdbbabbdcabcdbdddcdddbadabaacccabadddaacdbddacbbacacdbaabcdccbbbcccdcddadbdacbcabbabcaacadcbdbababcccdcbcbdcdddbdacbcbbaacbabbdcacadaddbacbdddcdbbdcbbcacdccdccbcbbdbcdaaddddadadbaabaadaccdbbbbbbbabbabbbbcdbaaaaabdbdaabcabdacccbdadaadaaddcbddcdbdbbabbbacccadcdcaacdaabcacdbcaabdbbcbdddccbcbdcadadbcbcacaccabadaacbaaadcbbcbcdbbaabbdccacbabcbddcddcddbccdcabdacbbdbbbcacdcadbaddcdbcdacbabbccdccddadaddcddabaaacadbaddcddaacacddcdacbbcabbbcaabdbbacbdbddbbdaaccbbdcacddbcdddacccbccddcbabdaabccdddcdbdacaaaddccbadacaccbdcbbcabbabadccbbcaaacbababcaddddadacbabadbcbdbddcacddddbdaccbdacddabcadcdabccdcacabaccabbdaacbcadcdaacdcddbdacabdbcadaddddcadddadababcbcbccbcaadcadcbdabbacaababadbcbcabcbacdabcacbcdddbcdcdbddddcdadcdcdabcadbcbbbdbcdddcbbdaccbdbababbcadbbbbdaaaadccddcadcbccbbabcacbcacdbcccccbddaddbccaaccbabbcdcaaddaccdadabadbdcacaabdbadbbbdbacbdbbcbacaccbdbcabdcaadbabacccbdcaccdcdadbcaddccbbccbacdcbbabcdccacddabcccbcaaaaccadaadcdcdddacccdacacbcadabdadbcbdacbaddcadcbdbdbdbaccbbdccccdcdbcabbbbbacccaacadacbdbdaabccbddbbbadccdcacdcccaabbdbdcaabdacdbabdcdadcbacbccdddbabcbccadadcabbbdcccbabbabdbadcdacbaaabcadbccdadbccccddacaadbcdcacbdcaaadcbbdcaacbacdbddacbccbbdcddbdbcacdccdaabdacbbcdcbadcbdccdccbdcacdbaacddcacdadcaabcdabbaabccacacacdbbdabdbbbdcdaccddbaacccdcaacbbaacdadbabaaadcbccdacbabbcadbadaadcbabaccdcbdddbddbdcdababbdcbbabacbdabadcbcddaccbbbacccabcabcdadbccddacbacbdbabcaaaacbcccddadaaabdbacaacadabddcddcbddcddacbdbbcaaadcdbdbcdcbcdbcddccabbcaadbcbdadcacdbdaaddacdddadaaabadbaacbbacbcccbdcacabadddbaaaabbcacdabadaddbddbddabcaacdcddcacabcbdcacbbadbccbbccdcaabcadbacbcbcbdcdbbaaccaddbaaacdaabbbabadaacdddccbbacddcdddadbddcbabcbdddacdbcbdbbabacccbbcdccbacbcbdbcaaaaacbcdadbcbddbcadabddcdbbbaaacdadbcbbcccadbccdbadcbacccabcddcbadbbdbbbdbdbcdbcacabbbaacbbbadbddddabbbddcbbddaadcabcdbbadbbddbdcbccbadbccaabcbdcacdbadbbbbbcbaabdacdcaababadacbccdacabdcbbcaacbcacadbbdbccbabcbbaabbbaadbdcbccdabaaacdbbcadcbcdabcaddddaaabdcbbbdcabbdcddbaddcbacccbddcccaddccabccdbdaaaabbddaabacdbabbccdacdaacabcabcccbccdbacaccdcaabccabddaaaccadbdcdbaabbabaddcbdddcdabcdbdddabbcdbdbdcccbdbbadbcccddbbcbddbcdddcddcdcdcdbcccabbbdabbdaabbdcdaabcaccbcdbbcacbccdcbbbacdcbccacdbccadbbcacbbcbdccaaacccdcbcbbdcdaaddbbabbabaaadbcdcdaadccdadbcabcdcabadcaccddacdabcbdddcacccacbccbcccdcddcabddabdacddadbaabcdcaacaddbcacdacdaadcacddcabbacdcdcbcaccddbaaccdbadccadbdadbccccdadcdccbdbcbbbbbdbdcbaccadddbdbbccdbccdacabcabcdcdccaabdccabbaddddddaaadccbcaccbabaabcddaddadcdddacbdccaadcddddabcaccdcbaaabdacacadabbdcdbaccaaaacacdcaabdcdddbccdabdddacaabadccdbbaaabcdbbbcaddabdbabcabbcdadbccdccabbdcbaaadaadabaacbbbcbccbcadcddcddbbdccbddabbacbcdddaadcbbabcbbcdbccdacababadddcddacdabcabaacbcddabbddbdbcabaabcdbdadadaccdddadbddccddbdbcbccdddababdcccbdcdbbcaacbcadbcacacbbaccddabcdcbbbdbdcbbbaddbdcdabbabbacadbbbbaabbcbababccdcbabdbcbcbadbdabbbcbcdbdcbadccaadbcdacdacbddbdaababdacabbaadcbdcdcbdadccacadacadaadbbbaacbadbdacbcadbbaaaadaddbacacabbcaadcddacabbacdadbacbccdcbbbaaacddbaacabdbdaaacabadbdcdddcbbbdabdccbdadcbcadadabdcbcacddbbbdbcbdaacacdbdcccdadbacbccadaabdcddcbaccdaacadbcadcbadaabcadcacdcadbcdcbbcbaadbabccdaadcacdaaaccddaddbabbbcbaabacbccaabdcddaadadacdbdbdcdbdabcdacddbabbaddadbcaabdbdbddcbbdccdbbbbddacbdbcbcabbbbcabbcdadccdbcaaddacbcdccdcdadcdadaabbcbdadaacaddcbccbabbaadcbaaaabcbbdcbcaddcacddaabdaaadacadacbacbbddabaaddccbdaadbbcabbaddadaadcbbccbcbaaabdcdcccacbaaaaacccdabdcacdcdcdddacbbddacabcccdaccabddccdddbabbbbadddadddcbabddccbcddcdbbcbbdcdccbadcbbdcccbcbcadabaccaddabdcbcabbadcabcdbdcccdbbabcdccbcddcccdccdbabdbccaabdcddbaacdbcabdadccabbacaacaccaddabddbccccdbddbcabaabccbaadabbaccccdbcbacdbdaaacabbdcdabcbbbacacccdabbcbcdacadbccbccabbcbbdbbadbdcadcbdbadcbcbbabdcadbcaaabddddacdcbcdbbbbdccbccadccacbddccdcbddddbcbdcbccaabdadbbccbbdddadbbadbcdadbbcddccdababcdbbbddbabadaccdbcbbbbbacacbbddcbcdbabaabdabadccbcbbddaddbabcccccaacbcabcabaaacbdbbddacddaadddbcddbdaacbbcabadcbacabcadbbcdaccaacadabbdbcccadbbccbacbadcabddbabacaacbcbaddddadbbababaddcdacddcbbaabaacccbbbddadacacbddbabddacaabcddadbdaddcccdbcbadddadacddddaacdbccdbbabbdbcacbabbccadbdacacacadbcadacacbdabacacadcdbccbcbacbdcbbbcaacccaddddbaaccddbcdccdcaddcddddcbdddcddcddcaadbaaccddbcaabadcccbcdddaaabaabccabdadddacdbabddbbdbbcbcdbacaadbdbbcaddacabbcbcadbabcbbcdbbaabcbacbbabbbaaaabaaaddabbbcacbbadcccdbadcdababbbdacadacbcdadcbdabbacaadcbcadbadccbbcabdbddadaddcdababdabddccdbabaacccbcbaaccbacbcabadddcbbbbcbbdcaabbcdccbbddacdadabaacdbccccdbacbcbabcddcbbdaadcddadcdadcbaababcdcabcddabcabdcbcccbbcbaaacbbbcdabacdcaabdccbcbbadbbbdabaadabccacacabccabddaabbcdbbbaaaabccbbaabccdccbbdcddaabaddbdbccbcadacbccdcbdbccdbadacdbcddbabcadcacabbaadadcabaabcdbabbdabaaadbccabcadbbaabaadbcddbbbccddaaaaaabdcbabddaddadadaddcabacbdcbbaadbdcdbadbabcddddabcbdaddddcdaaaccabbacabdcaaddbdddbcaabcddacadcdaaabcbddbcbccbdaadadbbbacccbacbacaacbdbadbcdbbabbaabddaacabcabdadaacddaddccadbcccbcbabacbcabbbdbddbacddcdbbbddccccbbdcabdaabbdbddaadddcbbadcdcbccbdcadcabaccccddacabbccadaaccdccbbdbabdaddcdbdddcbacadcbabdcdbbacbcbbdabcccbbdbbbcdcdaadbddcabdbbaaadabcddbbbbcbcdcdbdabbcacacadcaabbdacddddabababdacbcadacbacbaadbdcabbbaaccbacacbcabaddbcccdacdbdabdacbdbcdbadabbbdbadcdacbdadcabdddbcdbdbbdadacbaaacaaadbcadacbccdadccdadbdaaadcabdaddccbdbbdacccdcdcccabcadddbadaccddcaaabcacaccadbbabdbcaccaabcacbadadbadbacacddbacdcbbaccccdbadccadacbbacdadddbccabcbdbabbbbbcacdacbbabcbaccdababbacbccbbdbbacccbddbbaddbdcadccbababadbbacacbcdbbbdbbbacbcabccdbcbadbdcdbbdaaddcddadcccbdbdbccaabbcacacacdcabbbcbadcdabbadbccacabbbcdbbbbdbabccccabccaddccccbcabdadbdabbbccdabddcdbcccdadbcddbcdbcbbdbdadbabaaccdcdabaaadcdcbddcbbaaaddadbccdccabbdadbbdbbaadacddbabdaccdbcddaccdccacbcddbbccccdabdadaadbdddbcabbcadbbaacdadbdccacbabbbcdcaabbbdbdcaabaabdcaddacbbadabcdaccaabadbdacdabdacbdcbdcdbdacbadcadacccacaacabdcccdddbbadddccddabaaddcbdacacbadcbcaaaaaaaaddbadadccaaddbcddddccababbbaaddbadddabcacbbbacaabaacadaadababdbdccdacbacbbcdddbaabbddcccbaabacdacdacdbdacbaddacbaaaaddcddbdabdadacdbcadbddbcccbdbdddbadbcaccbadcbbbaadcbbbbcdbbabdbccdbcbbcacadcdcbbcadcadcdccbbcdcdcaadbccdcaccbbacdbaccdddaccddbdbdbcbbdbdababddccddabababbaaacacacdcadbaababdbcdcbabccdbbdaddaaaaddccdcdccadcccacbdcbddacacbcacccacadacdcbbcaabbddabdaaddddcdccabddbbdadaddddabbacbccabbcbcdcbbaabadcdbbacdadbbababaadabbcdabbcdadaabcbdbadcdbabcbccbaacadaadabccbadbdabddbddddccbdacbbabbbddbcdabdacbdcbdcacdaacacadbdadcdbaacdcacabadddcbacaaccdacabbbaadbcacabadcccbcacbdbadbcabababbdcbcbdcacbcddbcbddadcabdaacccaccdccbdbabbdabbcdbbcdcbcadabbcdbdbdbdadddccddacbbcbacdcaacabddcdbadaaccacabccabadaaaacadcbbacdbddddcaacbbcbaccbacabaaabdcdbaaaadbccbddaacabcadbdcdcacbdacccdcbdbddcadddacbbbcbbccddcdaddddaacddbdccaddbcdbaadddbddbccdcddadbbabdddacacbadcccdadcbbbacccdabdddcbbaacbacacdcdaabccdcbdaacbdadbbccacbdcdcbbbdaacbddcccccccbaddcdbdadcaadbaaabadaabaacbcabcbddacbcdabbadacdaacbccabdaacccadbbadaadbbdcccbacbcdccdcbabcaaacadcbbabcbdbbdaadcdabbcdcbabcdabbcbadccadbadcdddacccddbadbdcbdcbacdccaadbccdcbbcdaadababaddbbdcaacbaccdacaadbbdbcdcacaacababacadadcccacccccdadadccbcddddbbdccaddbccaaaacbdadacccaabcccbaabbcaaadaadcacbcdabdaaaabbacadbcbbaacdcdcbabbcbdccdccbbbaacacccbaccaaccacdadbccccabccbdaadddccdddcabbdbddcbcacdcabccdcbcbabbccbdbdacaccaadaabbbbcccbbcbdaddbcadcbbbbcddcbddcccdaadbcdacddadaabbccaadbaacbbbdcaadaccaabacdacbccbabbccbacccbbdacbaacbcadadbcbdaabdaccdbcaaabcaacdccadbdbcaadaadbbbdcbcbcdccbcadcaccabddabababcdacabacdccbcabcaacaaabdcabbddacabccaccdbbcaacbbbbccaaccdbddbcbddccbbaababbadaccdaaabbdbaaccacbbbaaacabacdaadddcacccbacbddbcddabbaadbdddbacaaabdcdadbcbddcddbadbacaccacaaadcbbabbcddccbcbbddbbbcdccabacacbabcaabaabbccabbbaaabbcdaabacbbdacdcacaddadaacabcbcadcdcacdbdaaaddaadcdcdacbbbdadabadcbbbbcbbbadcbbcacdbcdccdddbbbddccadcadcacdabdaacbbcdaacadbbaddaadbcdccdaadcbbcabddababbaddaadaccdcadbabcbadcacdacddddacacabdcdaabcbcbbbcbdcdbbadbaacddcbcaabcccddbabdddadaaddcbcdbdcbbcbddaabdcadcaaccdadcacccaadbdaaadbdbabcccbdddcdbddcbdcbadcdadbcabddcaacbadabadbddbbddddbcdabdbaacabdcabdaadabbbccbccbcdacccdcabbcbacccdcbbadbcbaaabdaacdbddabbbdbbadaabbcdaaaacacbaccddabdaabbcaacbabdccbdaaadaaaaadcabbbabdaabddcdabadbccdbcbbcacbacaddbbccacccaadadcddacbdccadacddcdcbbcdbcbabbaaadcaacabcddacccabbbbdcaadabbaddccbcccdcdcbaddaabaddddadabbccbdaabadcaadcabcccabdabdddaadbccccacbdcdaacdacddabccacababbbdbabdaaddbadcccaccbcaaaacccabbbdbdaadadababbbabbbaaddabbdadadccacdbbabbcdcaabacdccdddccdbcdadddcccbadbbaaadadaaddbcbbabbccaabcdbabbaaadbcddcaccaadbaaacdcddaadcaabbacddccddaaddcabcdbcabacadaccddddadbadcccbcaadaddbcbddbcbadbbdbbbcbbbaacbbbcaccaadcbcacccbacdcaacccddddaddbaadbdbccbdbdcbdaabadbabdcdbbcdcddcadbccabbcdbadacacdadaacbaabcadbdaccadbbbdbdcbccacdabaadbbbdcbcbcaabadcdbccdcdcdaddcabcdcdbdbbddbdcadadbaccccdbbdcabdbcdbbcdbabbccbadccdccccdadadaacabadaaacaaccccaababadbabdbdaddbbccaddccdccbadcbaddcbdaacabaccaabbbcbcacdbcccdbbbcdcadcdcddacabdddbbcadaddbcabccddbcbbcacbcddbdddabbcdddbcadabbaabbbcddaadaccddaddcabdcacdbbcbaacaadbccbadccdbacbbabcadbdddcdcabbabbdaacadcacdadbdaadaacabbacdbbbdabdbacbbdaacdddcadcdacabbbbdaabbbdadaaabbbbaccdacbcacdcddbdddccbbaabdabdabcbcabcccdaccbadcadbccbabcaabdbaabdcacbbaacbcdbbaacbddcdcdbabcbcdacbbbababadacaddbbdadadaadbcdabadbbabbbcbaaadddaccccccbdcaabdabdbadcacbbaddadadbadbddbccbaccbddcadaddcdadbddcdcacbcdaccadbcdacccdddacaaabcbdcdbacaaddddccaabaadcdabaabbbabdabacbabbbddddbdaccbaabcccaabdbdddbdcbddcacbcbcaacbadcbdcacbaccabcadddbacdcccdadacadabdacadcdcbbbbcbacbaddcacabcdbcdcdadbbbdddaaadacbcdcbacbcbbdcbaabcbbabcadccbbcaaacbabcdcdccdbadbabdcddbabdbacacbaaccddaddcbcdacaaccaddcccdcbbdbcaabcddcccddabccbacbabddcbbadbdccccbaadccacdaaddcacdcccbdcdbddaaccccbdccccaabaadbaadcabccccdcdbcabdcbcbbccbcbaabbdbccdcdbaddccbdbcbabbcbbdcaadcdbdbcbbcbabbaabbaccabaabcaaccbaddcbbdcaddcabdabadccbacbdbbaccaaadbcbabcadbacabbbcbccbcdadbbbdddcabdcdacdbcbccbcadcccbadbaaaadaccbdbaaabccaabdcaaabbdabcdaaadcdbcbdcbdadbdbdbddaaabddcbadcdaaaccbdcadbbcbdbbacadcbdbddbbcaaadddddbaaaadacadaadcdaacbccbdddacbbdabaacbdacabdddcacacbbbbcbcbcbadbbadbcadbcdcdcbcadbccddcddddcabcdccccabdddbadccabbdaacdacbbbbaadaddadbbcdacdadbbacccbcacbacaccbbacacaacaddcddbadccddacdbcadabcabbdbabadcbbaabcddcdadcdcbccaaadcbbcadbdacaabbbdcbcbadabddbdaabdabddcacbbdbbacacddadcddddaacbbddcbcadcbcddddcaddabaaabcaabcccbbacaddabdbdabaccdccbddacdbbadabcddcacdcddccbcaacccdaacdbaddacbbdbddbcacccaadaccadddddadbabdbcbdbdaaadaadbdbbcdbcbcddabbdbdcbdcbbbcdcccadbbdddaddaacdacabdbbacdaaddddbabadcccabcccbdaabaacabbdcdcdabdddbaccdaaccabdadcdcdcdcddacccbbacbbacdbacdadccdccbbabbccdaadddcaadadabacbbdcdbbbabcabbdaaaddcbaacccdcaddadbadcaaadadbbdbbcacaaadaadcabbddbabbbcacaaaccdcaabdbbaabadabdcbbdcdbcdbdbdaabdaaaaddcbdcdaccbacbcdcacdbadbdabcddbdbbbbdddcacbbcdaaaadbcdaccbdddacdbbcaaddbcbbabbbdcabbbccbdadcacabdccaaacaacababbbdabdbaaadcbcbcdbcbbabbcbcbdbbccdaabaadbaabdaabcaababacccdaddadbaddcadbbcdccdbccdbcbadccbdddcdbabbacdccbacbcbccadacdcbdabcababccbadaddddacbbcdbcdddddacacbabadbdbcccbbaaaabcaddbdbbaaaaabcccbbabadcbbccddcdbcdaaaaaddcaccbacdacbacabdacdbcbdacaddbabbbdaabdaccdbdccbbadaadbadacdbdccddabdadbdccdabdbdaddcdbcdabbdbdbcbcdbbdaacbcadaaaaadadcbbbbadccacdbccaaacabdbacbbcbbaadcbcadacabcbbddaadbaadacbdaaadaabddbdbbdbdacccdcdabbabbababcdcbdbbbdcbdcdbcdaacdddacadbdcaabadabddaadaadcdcdabadccdaabbacabbacbabccaacabccddadaabccdbcdbbddcbccbcdbadcaabcbadabbacaaabcaccdddcdddcdccbacdbcbabddbacbcbbdadaaacdcaddbbbbbbbabbabdbabbcdaddccaacdcdabcbdabcdcbabadcbadaaaaccbcbbdcdbbbddaddddacddaaccabadbaaddadbccbbabaaacdacdddbdcccaadcacbcdbdcbbacdaaaaaaaaaddcbcbabcaabcbbbdbbbdbdbabcacadcaccdaccbbdcdcccbccddaabaaacbcccbccaddabbbbbccccdcbdddcdddbadaccbdacabdddbbbaadcccddbaddacbdcbccdcddbaddccccdbcacddcbbcbcaddcddaaacddbdcaabacddacabcbcdbdcbdabcacbacbbdaacbbddbabdadaccdcbdddbdddcbdbcbbbbbcacdcaacdddccdcbdbbdccccdcbabbaddaabdbbccaaddacaddcdcadbbbcaccccdcbbdadcadacababbbaccbdaadabadaddacbcdccbcbdcdbcaababdbadccdbaadddcaadbaccacabddabcabaadacadbcdadacbdaaaabcadbbdbdbcbbdcdddcdbaaccbdbaabcaddddaabbdbaccbbcbacacbaccbdbbcacbbbbbbdbdacabdaacdbcdabaccababcddaccaacabcddacbccccdccdaddbddaaccaabbdbdcbdbdcbddccacacbbddcbdcaccdcabcaacacaababaacabbcacbdabbacdaadbbbccbacdcdbaadabaadbbadabbbcdacdadaccbdcddbdadcbbaacccddacdadbdcbacdbaadabdcbbddcbdbcaccabacdccccabbdcbdabadbcddbcaacdbadccdadcabadccaccbdcabdbbdbbbaadcddbbbdcaabcbcacdaaadcbdcdbcbaddbdddccbbbabcadcccdadbbccbbccbbccddbcababcbbdbccdaaccbdccaccddbbbbddbccadcdbbacacbabbbadaddabcaacaadbbdcadddaaddddaabcccdcdddcababadbaaababdcddabccdacbacdcdbdaddbdcaaabdcbddbbdcbdbabbacaaabadbbcccbcbdaabdbdadddadbbaadbaccadbcddaabcbcabbabccddddbaaadabdcdacaccaabcbbddccaccaaabbbaddcddbdcdcdcbdcdcdbddccdccabcccacabacaddddacdcaabcdacbaaaddcddbbbdacabcdccdacaddadbdbaddcabdbbdcbaadabdcddbbddddbddcaddaadabdadbddaacabadacadbcbdbaacadacccdbbccbbcadbbacaddcccbaccbbabaadbaddbcdcbdccddddabdbbdbbdaacccaabacdccacbbbbbccdcdbcdabcdccbaadadabbdbabbbcababacaacbdbdcabdaaabaccacccabdbacaddddadbabdbbdcaaaabbdbdcabcbbadcdbccbdacbaaadaacbdaccbdaddbddbcbbcaccbdbdbadabcbadbbdbcacbcdbcaadcbdcccdaacadaadccdbcaabbccaadabdbddbcabcdbddaaadbdbcdacbababbdcdaadbcbdcadaadbddadbcacdcbdbbabbddcaacbddaccccabcbddabdcaadbddbaacacbdadadddacbcdaaaccdaadddbcabdbdabccdaaadbdbdcaabcddadadacbcbdaaacadddbbabccbcbaaacadcacaabbbddcadccbdbabadbabbadabbbabbcdbdcaacdbbbbdacbacbdacbacbdccdcbacabddabcdcacddccdcdaccadcdcccbcbadcbbbbbdbcbadbadabbdabddcbadbdadcbbaabdcbddadabadaaddbccabddcccdbccbcbbdcabbaacacdbabbaddbbacaccaadbbccddbcddacadcabdbdabaaaddbcddadcbaaccdcadbbbacaaacdbcaaccabdadbbbcabbadbdcdbddacccbdcddaccbcddcabcabbdcbcabacddddadaadcbaddddbbddabcacdbabcbcccaccddbaaaaccacabacdcddbdbddcabcbddcbbbdbdaaacbbdacbcadbcadcaabacbccaacbddabbdbdacbabacbadcddbdddcbcdbbccdbbcaacadbcccdbdbaccaaadadbacccaabaccdaadbbbaccbdccadaacaddcabbacccdbbcccdddccbcbdcbbcbbdbdbdaaabbaabcbabbbaaddbbacbdbabbcabaccbbdcddadcabbdcbcbcbdbbccadaadcbbadcccbdabbcaaabbbcababdabacbbbbbccacdabddcaccdbdbbcaaccaaaabaadcbbdbabcdccabcbbbacadcdcbaabcbacbdaadbadccaabcabdbbbcaabccdcabcdbddccbdbcbcacdaddbadcdcababbacdadbdaadcabcdcdbcccbbadbccbbccadaaabaddacdcddaaabbbccacdbccadcadabababaacdbcacdccdbdcacbbacbaadccaddbabccacbdbabdddccbcdbdccdddcbcadcbdabdccbccacdccdcaacadbccdbadbddabcbaaaaabacdacccacdaadcdaabaaaabcbdcadbccbcaccbbbabaabccdaabddccbadaddccddabdacbaabddcdccdccaacbbdddabacccbccdcbbbcdadacaddcadabdadcbcccddbbddcbabddcbbccdabdcccbdabaacacbbaccddabbddbaacacabcbcaabdacbcaabaabccdbcaaabadcbacdbdbbdcccaacadbbacabccacddcdccbacacabadbbdcddbacbdcdbddcbbbbbaccbddaabbcadcdccdcdcbbdbacdddbdbccbadadacdcbdacbdcccbacdaaabccbdbcbccdbaccdaacdcbdbdbaddaadabcbacbdcbccdaacccdcdadaabdbcbabaccbdcdbaccbbaccbbaabccdbcabbcbdddbbcddabddbbacdccdbddcabbbadacdbabbdcdddcdccdbdbbdadddbdccdbbacadbcbacaaaccccabacbbadcbcaabaadbcbdbaadbcdbbdaaaddacddcabcdaadbdacbdbcdcdbcdcdabbddacccbddabcdbddabdbcccabaacbcddaaccbbaddaabbccbdbcbdacadcdddcaaaacddbdddacccaabbdaddcbccabccdcacbbbabababbddadaccbbcaacaaadcddbcbcacaadacacdbdccabbbadcaaabacccdaaadddbabacccaddbcbbaadccbaccccdccdaabddcbdbdddadadabddcbcacccadbdccaacaaaacddbbbbcdabdddbcdbcabcabaccbbacacccbdcbccadaaaadbccbdccabddcacaabcdaddbbabacdcabcdbabadaccabcddcbaaccacacbacbcbabbbcdcbbadabdabcbadacaacadacabdccdcddaaccccbbbdbcabcbcccacdacbdbddbdcacdccdbaababaabddbdcadaccdabbaccddbabdbacdabdadcbbccddbdcabdaaaacdbdadaadbbaadaaccbbcbbcdbbdaccbdbccbaabdcaadabcdabbdabdbdcbcbacacdcdbbbababbaaaaaabacdcadbcdacadadccddcdddccacaabdaabddbbdcabacbaddacbcaddcadaddcdabcaababdbdbccdccdbdddbabcdbaabbbdcddaccbbdcdbacddbcdddcbaaacddddcbbabaccdbccbcccdabbcacdbdcbdccddbbaddbcbcbdbabbcadcbcadcddddbaadabaaddddbcbbacccccdcdcabdcaacbdabaabaadbcccdbacbabdbcabcccaadddadacdbbaadcaabbbcabbbbaadcbdbcdadbbddcbbacbabdcbbabbbcadaaddbdaacbdacadadcbcadabadabccddddcbadcccccacacabdacccbbdcaddabcdacdddccacccdbcbcbddcbaacccbacbbccbcbccacbabacdabacdabcccadcabbcdbadbddbcbcdadbbabdbccdbcaccbcabadccdbcccbaaadacdbaccccbcdcdbbcaabccaaadcbdbdddbdcabddddbdccbbcadcdccddacbaacdcbacacaddcdcabddbdaabdcbdadcdbcbdddddddcdcbdabdbbcccdcbcaabababaaccabccddacddbabbcdbdcdcddddccaadccdacbbcadaacbcdcadbdaaccdadddaadddbaabdbdcdbbbccaacbbcbaaddbbcdaccdaabcddcdaccdbbcabdbdcbbdacbbddccbbdbdcaccbcbaabcabacdaaadbbbbadddbacddcacccdaabababbccbbbdaccccbcbbbccbbcdcaabccbcbbcaacddaccadccdcbaacbcaccaacbdcdbdddbbccbaabddbdcbcbccdbbbaddbadcdaacbddcaacbbaabbdcbdbcddbabcdddcbdaacddcddccdbbcaaddadcdacdbbbbbabdbadabcacbdcdcbcadddcdbabcdbbdabbbdcaabbddcbbacacdccddcbabaddbdaadaddcaddadbbdcbdbbbdbdbbaacabcadcaacbacdcdbbaaabbbababddaacdaadabdbacdccbcddcacaddbacbccdbdbccaacbbccadbbaaaaccbdbbdcbddccacbbbddbdacdaabbaaabbbcdbbaddbdbcdabbaabababbaacdbadaacacddddbcacdacacdacdcacdacaacabbdadcbcadbbcccdbccbdbbdaacdcdaabadbccadddcdcbdbabdbabbadbccccdaacaaaaddccbbbbcdbbcadcbbbcabcbbadadcdbdbdccdcdcdbbacbbcbadbbbbaadadbdbdaabbbaadadbbddbaadbccabacbcdabdadcdbaaacccbdcdacdccbadbddadbdaccacddabdccaabcdcdbbbbadabbddbbbaabaadbdacbaddbbcdddbbdcaadbcddcccacabbcdddbaaaccabbcbddbdcbadbaadbcadcaabbdccadcdcccddaacbbdaabcaccbdcdbddcbbabbcabbaccdbbdbdcabddacdaaddcdddcdbbbddaaabcdcbddbcacadbbddbcdbcdadaddacbcddaaaaadbdddcadcbaddbabaadcbaaddbbabcbdcddacbcdabdadddcccdbadcccaacbcaddccbccddbbddacbabacabcdcdbbadaacdbbadabcabbadcbacacdbcbdcbddbcdaddddbdccaabaabcdccadaddadaaaadbcdccdacaadccbacacaabcbabcadbddddccbdbaaaccaaadcdacadcccaabcdbcdadbcdbbcccccdabadccbdabcabbdcadacdcddccbdcdbccabadaadadbbdcdcbbddcbddbaadbacaacbdcdbbbddabdcbdadbbcddccdbacbcbadcccaaaacdbaccdbddbabadbacabbbcadaacbadcddadacbadaddbbccdacbdcdcbbcdaadcccbddaabcaddaaaacaaaabbdcccdabaadcdcddaadcbdcbcabaaacbbcbdbddddabbbabdcadadccadddbbdabcccbccadbbbbadcdadabcbcdbbcaaaacddccccaccaddcbadaccaccdccbdadcddbbaaccbddadccacddcaccbddabadbadbccacaabdabbbbdddaadcabddddcdaaccbaccaabdbddadbbaccabaacdabbcbdbdbbcbbbbcabaccaccbcadcccdaabbccadacacdbadcbcacbdaaaaabbaaacbbbabcababbaaabbbbadadaabbdccdcacdabdddbadbcdddbcadacbbbacbadcaabcbabcdabdadcddbabadcbdbaadbbdcdacaaadadbdbddbbcdccadaadcdccadbabdbccdcbbacbdababcaaaaaccacdacdbdccdddacbabaacccadabdaabadbdadadadbaccdadacdbaccaababccbbdbacdabcaaadabbccdbdbadccaadacadadcdcdcbdbcdadcbbcdccadbdcdcdabddbcddacdcdcadcdddccbdabacaacbbdcbacaaaaddababccabaaabddbcdccdcdcbcadcdcaabadababddbddcadbcddcdacbbaacbacbcdbacbcbcbcaaddbccabaacadaccccbacbaacdaaaabaabdbbacadcaaabacaaaabccaddcbcdbbaacacdddaaadaddccadaaadcbccccabdbccddccdacccbadccbcaacbaadadadcbadbdbdadcdbbbaddbcbaddcbbbaabdaaacddbcdddbbdddccdbaccaddaadcdbbcddcbcbbcbdabcadaacabccdabbcbbbcdbcccdaccddbadbcddaadbdbdcddbabadbcbabacadcbbcddbbdccdabddddadbddddbadbbcdccdcbdcdbbaabbcbbbbbaadcbdabacbcbdbdcddbcadccddddcbcbcddbdcbcdcddcaaddabbacbcddaccadccdddabcacdbacbbccacbdbdabbbaddcbabadadbcddbdadbbcbabcabbddbacccbbdcbddbcacdcdbcacacbacaccdcadbaccccccbababadadcdddbcacbcabbaabdcaabccadcabcdcccbcbbdbaaacaccabbdcccdbabdddcddaccdcbcbcbbcddaabaadbabcddddbddbcbcbddaccbbacbdcadaadacaccdabdbadcabaadbbccdcabbcacbdcbadcbcadccbacddcacaaaabcacdabccdadbcdbbccaadcdbbabacbddbbdcdbcabcdddbadbcdbacdbbadccbadababdbdbdaabdddaaadcdccdcbcabcabdbdacbddddcddcbadabbaddcddbbcacdabacaccbadcbabdaddddddbdbabbdddadacccadcbdbccdcdddbadadddaabaacadbbbaaaaabdcdbdbbbadbdbabbaabccaabdbcccbadabdabadbdcacabbdddcabacacadbabdaadddbccdbbbbaabdadddadbabacbcbccdaacddacddaccbbdadddabdadadcccabccbacccbdabadbccabcadaccadabcbaddccbbbbbdacaacdaccccdcbcacbbddddddacdabdbabcbdcbabaabaccdbbcccabbaccacbbbabbadcdaabccdabdbcccaabcbaabaaabbcbcdbdabddcbadbdaaaddddbddbccbbbbdcabcbabddcccccadaacdadaacdacdbbcabccbaacbdbacbddbcbacacabddccbcccddbdbaddbcccbdcdabbccddabaadbabdbacbabbbbbbddbddcdacaacacabccacccdcbbbdabcaacabadcddacabadbbdadbdacdcdcbdcaadcbbaabbdabdacbdbccdcdccbaabbdaaacabacbbdbccbbaddcbcccddbcbabababcdbcdccdcbadbccbbdaabadccaabcdcbdaaadaccccdcaadbbdacdacaccacacddbbabbcaabbdcdaddccbbbadcdbaadbcdbddbcabdabbdaddaabcbcbbaaddcaccbdcadabbbbcdacdacbdddcaaaddcdcdaccdcdbbcbcdbdcddcbadccdcabbdcbacbcacddbaaacbbdaaddbcbadacabcbcddddcdbdaaabcabdaabcbaaadcbbacdaabcabbdbababddadbadbabbcccaaacdadacbcadbbcdbcbacdbdbabadcabbabdbadacdbaabdcdacadccbcdadcadbdcadbdddddccacadcacccabdbbbbbbbcadcdbcabbcdddacacabbdcbbbdadababbbbcdbbdbaaacaacdcddddddcaaaddaaddbadcbbcdcdddaabacccacdadcbccbcbdcacdccbcbcddbbbcbcbadabbbbbdcdccacbcbbaaabbcdabbccbdcbbbbacbdcdbdbbcddacdcdddadacabacbaddcccabbadaadcadadcddbcdcabbdcaddaaadbbaaaaadbcccddccabbaccdcdbdbabbbabcdbddbdcdccdcbbcacbcbbabcdcabccddadcdcdbbbddaaaaddaacdaaccbdabcbdbcabcccbaadbdcdcbbbbcbddaccdcbbdcddcccdccbdacbcabaddaaacdcdaabbdabadaaccccdddbadcaccbaabdabcadbdddaddbaaccdaadddbdccbddbbabddbabcddadcadbbdcccbbaabcaadbbbacaadabcddcdbbbacbacaaaaabdaadbdcdbcabaccdbcdcaccbdaddcbcdacbcaccadaadbabcbcacddcdcddbaadbadacbaadabbadcbdcacdcdcadbcccbddadbbcccbbcbbaabddbdaadccbbadbbcabbbdcbbbacadcacadbabcbdadddabcacbdccaaaaaabccdaccbdadccbaccdbbdcbabacaabdaadbccdabdbcaaacaabdbbcccbcbcdadbbaaddbbdcdcaacdbdbcaccccdaaaabaacccbbbabbdaaaaadddbbcaddabcadbccccccadbddbaaadbdbdadbacbdaddacddccdcaabcabcabddbdbabbbddbbcddacdcadcccbacccaabcabccddadaabccaaccdddcdaababcccbabdcbbdccbcdccadddccbcdaaddacbbdadaddcbdaccbbccaacccdbdaabbbbcadaabbdaaaccccbaadddccbdcbbbbddcaacadabbaaadcdadacadacbbbabaddadbbcdbbdababdaccbacbbbbbcbbacabbbcdcaccccaccbcadabcbaddcabacaacadacbcdadcdaaccbdccbacaaabadaccbdaadcdbccacddcaccccacbbabbdabbdbcaddadbcbbcbcabacdbbcdabbcabbcbdbcbcccccbabcbbaddabdcbcabcacddbacaabbdccaddbadbaccabbbadbbbacabdbcbbccbcacddcdcaaccdbcdbddbbddadbbccbdccadcdcdcaccdacdacbbadcacbddcdbaabaacccadcbbdaddadadddababcddcdaaccdbbbdaaadccbaadcaddaadaabacddadaaccacacdabcdaddbaadbbbbbacaacbcacbaddccabcbaccaabdbaaadadadcbcdaabdddacbaddabddcdaaddabcccbbdbadcbcadcaabcbadbbacbdabcbdbdcbcbcacccabdccccccdaacabdadaaaccccaccccbdbaadcccdbaaaadacacddacaccabddcbbbdbdddbbbdcccdaadaadcccaacdabbcdcaaaaadacbdbdccddcacadccdbcabbbdaddbdbdccacdbbccbabbdabdbbbdcbaddcdcbcaabbdcacbdbdbadcaccabdccccdbcadabddddddbccbaddabbdcdacdadcdcbadcdacdabdbabcbbdaaabaaababbdbbddaaccabddabadddcbdacdabdbdbadbcdacaddbbbbabdbcaaaabdbbdcabccbabbaacbaddbbcdcbbadabbdcbbdcbdbadcddbaacdbacccbcddcdbacadddcbbdcdbbbadddcbbbacbccdabdacdacdcddaaccbaadbaabdcbcddbcbbcaddaacdaacabbaabdbabbbbcbbdcdbabddacdcacadcaccccaddcbdabccabdabcabbdacacbddccadaaadadaacbabccccdddadadacdacbcadbacacccbbccbccadcaaabbadbacbaabdaccbabcbbbccdaccbbcbbbbcbaddbbddcadddddccababbdbbacdbaaabcaaacddbddadcacabdcaaabdbbbcbbcaadddbddcadabbccdcbccdbddaddbbcbcbcbbcaadacbadadabdcdbdcbaabcdbcbbccddbdcdbabbcbbabccbcaddacddbcabdbdddacbcbdcdadaddabbcdadadbacabbddbdabcdabcbaadbccbbdccbabaabdaadabbbcadddcdabacbcadbcccbbdcdddadaccccacdddbcdbdcbadaddbdbcacddbdcacddabccccadabcdcaadbbcbdacddacaabddaccbbcbaddbdcaaabccdababcdbababbdddcddccacadacbcaadbddabdcdcddcacadcbadddabaaadbdccbabcaadcbdcacdcbdccabddddabbcadbaadabddabcaaacbcabadabdddbdadbdacdcbaaaacccbdbdcbcbabdccadaaccaaccadbbddccdbbabddbbbaaacbbaadaaadbddadacaccaaacbdcbcadaaadadbcaadaabbddcacbcddccbbacdddacdbbdcadcbabdbadbcadbabbdbaacbbabbcdcddddbddbcbaacbdbcbdddbcdbbaadcdbbaaadbaccacabbbcbdcbbdaaacbcdcaabdcaacbbaacdbabcdacacbbdbaaaaddabcbbaddcddcacadabdccbdbbadddbdacddbbaabaabdddbadbbcdcdacddbddabdadbbcdadcaaabbcdcdcaacdacddcdabadbccabbbcbbddcaabdddadaaadcbaadcbddbdcdbdcadaadbabbbcbabaababaadddcabcdbcadabdadcbaaacbabadcdbbcdabcbbcbdaadacddbcccbdcbdabbbcbdacacaaaaacbdddabbcdbbdcbcccacdacbbcddadcadbaabcaccaccbacacadacbbbbbdcccbdadbcdbdcaaccbbbccbbdbabbacdcacbdcdcaddabbbabbcdacaccdddacacadacbdacaaadabdacccccdacdbaadcbcbbccbbbcbbccdaaacbdacbdaaadaacdcdacbcaabcdaddbabaaaabaaadbcddccccbccdbadabaccbdcdaadacccbcabdbaddbdbdcbbadbdbaccddbccaacdadcbdcbcacdcbbbbdabbdacccbdaacbdcbbbacbcbccbcdaccacadacddcbabdacbbbcbcdcdbabcdbbacdbcaaddccdcbbbcccabaacacbcababadcddcdaccdabdddcadacdbbdcdcdaddbcdaacabccdcccbaddacadadbdbcaadcaacbbbdccccdccadcddcaccdcbaaabbcbcdcbcabdcbcbadbdbbdbbbccbdcccbaaabaaccbaacabaadabaabbdacddcbbcbabbaaaaccadabbdacddaccacbcbdbcabdbbccacdccccdadbcaacddacadacdbbdccddbdaddcbcbcacdccadbcaaddcabbcdbdbbcaddababcaddaccacabcbdbacddabaacdcdbbcbdaabdcbcaacdbbdadbdcaabcdbdabdbbbccddbdcdcdbcdddcbdcccacbcaddbadbcabcccdaaababcbbcaadbddcdcbbdbdccacbcddbdddbcadccdbbddbcbdccacacddcdaddbbacabcaabaadbbbaaabbadadabdccdaadaadccccabcabccabcccdccaadbbdacbdccbccbbabcdbaccbbccdddcbcbaadadabcdcddddbcbcdddcacacddcbcbbaddbbaaabbcdaaacbcbccdddbaadbbccbcacbaabaddadddacabdbcddbdbbcabcaaddbdcbadcaccdccdcaacadcabccbabcdcacbabbaaddbdaccbcbdcaaacabcccdccbadccbddbaacabdacaadbdccddaaaaabaccccdacaadccacbaabcbddcacdbbcaadbdcdbcacbbcacbddcbcbdcaabacaccabbbbaacbcddbcdbdccadddabcbcbdaacbbabbdcddcddcdbdccbdcbccdaddcdaccbbdcbacaacdaaabaabbbbcdacaccdddccabcdddcdbdcabbbbcaabdabdcacdaadbdadbbdddbdcabbbcacacbdcbaaccccbcadaddcdacccddcccbddbaddaaadddacacabcdadccdadbdacccadcbbacbaddbcacaabcabcbaddbdbaacccdbddcccdbbbcbdadcbbadadcabcbcbdcadcdcacaaaadabcbdddabccbdcaacdbdbaadddabbcdddbaadbabaaddaddaccccbabdcbbbabaadcaadaccdadcacabdddcaaccccddcadadabbbacdddbcddbbcbcbddbabbbbcdabcdadcabadccdabdbdacdbdaccbbcdddaddbddcbdcdcdaabbbdbccddcdbdaddddbadadccacccddbddbbaabacadcccaddacbacdabbbdabdacddcbccabddbabbbddadbbacacdbdcbddbbaadcadabaccbaadbdbcbabdaaccdadabcacbadcdcccdcbbcdbaddacdbbccccbbcaacabdaadacbacdbbbacadadbabaddabacddbcbcdcbdbcddbbbcbabaaadaacaaccabbdabcaadccdddaadcbddbdbcbadabbbcdbdbdaacbcbdbcdabccaaddbbddcdcaacacddadddabbdabbbcacdbdaddaddabccaddccccabbabababaccbccbbcabbabcbbdbdacbbbbbabdabdaabcddbbcaadbdcddcbbadabddaabbdcabdabcdacbccdcaaaccbadbdcbabbcabddbdbbdcadacbaacccbacdadbddacbdbdcccdacaacdbadcddddbcdbbcbadddacbbcaacadbdcaaacbcdacdddcdaddcbdaccbbbddcbdccbabadbcccaaabdabbccdbcdacbcdddbdcdccdbccbcaabbadcabacabcadaababcabaaddaddabcdbdabacbddcdddccdccaaabadccaacccadbbcddbdcadcbdbbaccaaccddcdcddadccbddcbbbcbccdabccbbbaabddaacdaccababcacccacacdbadbbbbbabccbccccadaddadabbbbbbcacbdbcabadddabacdddabbbaaacaadddbcabddbbacdaabbdbddbcbacaaddbaabccbbbccabdbaccaabbbbccdcdcdccbbadddcbbacddddbdabbcdbaaacbadacbbacddbccdcdcaccaabcddababccbacdbbbbacacbccdabbccccbacbdbadddcdaabcdcaabacabdababbbccaaaaddabbbbbbabbdbcbcaaabdccdbbaaadbcccdcddacdccaaababdadbdbdbabdccdccaababcaadcabdcdbbccbcbcacabaaccbbcbabcadcaaccdbcbcacdcaadbabcdcababdcccacbbdcaccdccadbdcabacbadbbabddccbcbdccdcabdbbccbdccbacbbaaabcbdabadccddacddbbdbdcbabacbbabdbcdccbabcdbacdcbbaacadddcadacbccabaaaabbcaaabcdadcbdddbadbccdddbcbcbdcddcabaddcccabcbaacbcccbabbadcadddddcbccbdccbaddcbbbabccbdabbbdbcbdcadacbbdacdaadaccbaadcadcccdbbbaabcbcdacadcacddcbbabdbdacbdcbcbbcaaadccbdccdddbaadccaabbccdbbbcbdddddaadbddcaacabdaababdcaabacacdbbdbbcbcdccccabcdccbdbcbcdaadccbddbcbcabcabcdcddacbcabcdbdaacbacdbbbaaacddbaabddbcbbbdaacddbdcccddbcabcccdadaddccbcaccacabaddbdbbbacbdbbccbcbbabccbcababbdcacbdabcbadbabcdaaabdbbcdabbbaadaadadbcdccbdaccaabcbbdbbcbccadaabbdbcdcbdddbdbdbbbaabaadaaacbbabadaaccbbbddcabaadccabbddadddcdbcbadaabaccdddaaaabadbdaabccdbadddadbdbcdadcdbbabcacbdacaacaabdbbcdaadbcadbaaabaddaadbbbbaacadadcabddadbaacbaacddbbbbbdbcbdbdbccdadaaaccccccdcbcbacbbbddadccaddabbbcddacbabaaadbcbddabddcbadbdddcabddddcccddcdcbacacbccdabdddbbdccbbaacbbcabddcbbcdcdcadbccabbbaaddacbcbadcddcabdbcdbacabdcbbdadbcbdbdcbdccaaddbcccdbdbddadddaacddcbacbbacccdcbdccacbaababcdadcaababcdddabadcbbbddbaabcdabdbdbccbddcccadabcabcdcbddabbddcdbabbcbdacbdcdcbbaaadbabdbadbcdcddbddcbdcaacddcaacbcdabcdaaabbcabbddadcccadbdcccadacdadcacaaacacbbcddbcbcdcadbdbccdbdaaacadccdadddaaaabaadcdababbbbdccddaacbdbacaacbbcaaacdbdcdcbcdadcaccbbbcbcadcbdaccaadbdddccbbdbccdaadbdabdcbacdcaccccccabdadbccdccdcadadabbabbbcacbbdbdadaacbcbbabcaabbdbbadbcccaabaaccbbcccdbbbdaadabcabcabccbcbbbbbbbbdcdddccdddcbdbcdcbdaaccccddcbcdcbaaddccadbbdbbdbbacbbdacddbccbbcccaccadddbcdabddabdbaccbdbdbcccbbacdcdbbbcccbcadddacdacddcadbbcbbdaabdbdabdaadadbcbcdccdcddadacaabacbcbccdccdaadccdcabadcaddbacbbadabcbacbddadddbbcdddddcbdcbbbbaacbcdcacbbdaabddcbbddcbbcccdbdccadccdacadbacddbaccbdbbbdbbcddbcbbbccccaccacadbbcaddbddcbdcaabddcacdbbddacbbcdbdacdabcccbacdccdcabadaadbabacccccabaccdcccabccdbaccbbbbaadabdabccaabccbcddbbaddbbbbcaacbddaaadcabccabaaccdcdadbbbdcddcacacdbcbaacbabbccbddcbdbbacdccabdcbbbcdcccacadcdaadcdbabadabcccabcbddbabdbdddccdabcdccbbbbccdcbbcbdcbdaadaccbccabbacbaabcaabacaddbddbdabdbcdacdddaaadbbbcabcdabddaacadabbacaacaabccadaabcacccacdddbddadbdccbcacdaadbcacccbdbcbddccadccaababdacabdbbdccaaaacbcccbccdbbaddbdbaacdcadacdabbcbabcaccddcdccbdaadaaccdadaabccadcacbdaddadcddbaadabaaccabdbcccdbaadbabbbdcaaadabacaabacadbaddacbcbbaddbccdaadababbbaadbdbdbbbbddbcdabcdcaadccadddabbcdaaddcbaabbcdabadcdaaacabbcbacbcddccdddcbbacdbcdbcdcdbacacccbbccccdcaabbbdddaaacabbdbcdaabbbccbacddbbcdcaacbddbbabdacbdbabcadbcbbdddcdbaaacccbcdcabdbdabbaccbabccabaabcddbabbdcddabcdcbbcdaddaacdcbaacaccdacdbbabdadacbabcccbdcaabdbaaddcddcacbcdaccbbcbaabddaccccbcbbddbcacacbdadabdabaaccacacdabbcaadcbcdabcbdcaddabddacbcacbaccdddddbbabcdbabadaadcbbbcbccadbcacddcbbccacbaabddcbdbbcaabaaabcdcacabccbcccccbaaccddbaddcaddbcdbadbbddbaadadcbaadacaaccbbbbdabdabbaddcdcadddbddbaadbdaddddbddaabccadbddcdccaccdaadacbdaddadbdbbddcdccacbbdaadadcaabadcdaadccadbbbddbcaabccdcddbbdbbcabdcdccddacbacbddacbdbddcbcacbbdddcbcacacbcbbdaabcdcdadbadccadbcacdadabcdccbaadaabccdcbcdbdabdbccdabcbacabbcacccdbbdddacbcaacbcbcaccadbddadadbaaabddccdddcaacacbdccbbabdbddacbbbbacdadcbaccdbdcbcadddacbcadadcbddabcdbaaccbadababaabdaadcdddacbdadddbbabccdaacccdadadacacccadbbbdddbcbacdcdcabbacccaaddcacbcdcdcddabcdccbcdaaaacdcccdadabcccdabcacdbadcdbddacaadcbbacaddbbacaddbbcadcaaabcacbdbdabcdcbcbdadcddddbaadcdcdcacdabdbcbdacddacdbbaccccbadbabdbddadbbdaddbdacaaabcdbbdadddbccdbcbbabccaadbacbdbdcabdcbacabdcabcdbabadabdacdbcbacbdcdcbdcddccbadbcbdaaacdbbcbadcaaadaadccbdbbddbacccaddcaaadcccbadcabcaabdbbbababcdadcdadbbcabccbbadcddddcacabbddabbabccaacdcdadddbaadabdbbbcbcbcdcbbbbadaaaabacbddaccdbadcadbccddadccabacdbcbcdaaddcaacdaaadccabcdadaadbaababcdbdbaacacdbdbabdbdadacabdccdccdccacbbacbcdcdcbccbdadadcccbbcddacdaadabdccddadbaadadbabbbdbabcdacbbbadaccccbaabacbadbbbbabcdbbaadbacdcaacadcaacacdaaadaadddddbddddadacdbdacdacaabccbcadadddcdccabbdddbbadcdaabcbabaddacdddccacabcacadacbccaccdaccbddccddcabaaaacbababadacabbdccccbdadbdaadbdcacaddddbdbbaabbbccccbadadbbcdbbbdbbbdccaccbcacdabbacddbbddbacbdbcbdaacbdabbaaadbcacddcdbbdccbdabdbdbbbdbcadcbdadcacacabbbdabadbbcbacabcbcbbcabdbbddacadcababdccadadbabcdbdbabddcbddbbccaaadacabcbddbcababddcdbacdbddcdbbcbbbcaaaddacddddcabddbabbbcbdbacdcccdbcdccddadcadcabbaddadbccbcaabdcdddbcaabbbababcdbacddddcbbccabbdbacddbddbdaaaaacadddbdabadaddabbcacdabcaadccdbdccadadbcabccbbbdcbcccdcdcacaaaabdbbbadcbbaaaacdabbcaadcddbcbadbdabdbbbacbcabbbacacbacdabcaabdabadadbbdccaacaabdbdbbdcabcabdaacdbbdbbbbaabccdddddacdbadaaadadcbacdcdcabccaddbdcdabbcbbcddbaddbcdabbadbdbbacacacbbcbccaabbbacccdcdbcdaddcdbcabbcdddbcbcaaddcdaaddddacabcdddcaaaacbbbdccaddcbacaccdccbbcbbdaaccdcbccbbbbacbccdcdddadabbddbadcaccbbbbdcbdcdbcaccaaabcbdcbbcbddaddbaadbadbbbcadadbcccaaabcbccabccacdbbcddacccdbcddddacbccdadddbdaacaaccdacdbabdadbcbaddbadaabcadacbaadbcbbaddaacccdcdbaddbaccadcbddadccccdaccabcbabdabacadccbadababbabccacdbaddccdbadcbaabbaccabdadcaadddbadabcbdbddadbbacaccbbabbdcadcacabbcbcdaddcdcacabdcaabdbadbdcabadacabacbcacaabbacadbdddcbbbbcbbdaacacbabcccdbdaacdbabccbaaaccddcbdaaddbcdaccabdccaadadbcbdcacbaddccacddbbacadcdccdbdbdaddccbdbbadacbacbbbcacbddbbdbccccbbcbcaddccbbaaddbccdbbbcdcdbdaccaddbdcbbbbabddbacdcbdbacabbcddbaddcbccabcadcbcccabbcbadbbbbadaadcdcaccdbcadaddddacbadbbadccbcddbaadaddabcdaacbbcadaacbcdabddcaaaaabaacbddadbbbcaadbccaabcabacdbcaacadacacaddbddabaacccdbddcadbbabbccbcccccaabacbaadadadcdddbdcaadbabccdaccbcdddadbadabbbdddcabdacdbddabcddabddccaddddbbbcabbcbacabbdccbdbddcabadaccccbdabadbdccdccbbcdbdddabbaacbbaaacdbddccbbdcbbadbccccacaaadccdbcccaaddabbacacaadacbbbccdbbcdabaaadcdbbbdbbdcaabadbdbadccabbabbbdacccacadbdddacadccbccdbcbaaacbdabdaacaaacdcadaacbaabdbadadbbdbbcbdcbbcccdbaddbbbbabbcaabbacbbadcddaddbdccaadbdbdcbabbacdbababbdbcacaacdcacdccccdaadadbddabacacdcdcacabcbabccabaabcaaccdbabdcdaccdcaaabadadbbaddbbcbccadaadbcdaaadccacddcdaaaadbbdaccdbbdbaccddcddccbdbadbbbbbbbbbdabdcadbcdacabddadababcdcdcaacbabacbdcdcccadbbaacbbbbcdbabbbbbbcabbabddcbcccdddccbbbaadddaccdaaaaabbcadcadcbaaabccdadabbaadbddddadadadadabcccaadabdaddadaaadbbddcdcabaadcbdacdadcbaccadbcacdcaaccdadabdaaaadbcdbaabccaccbbddbdaabccbbbbddcdbbaaadbacdacadaabdacdbadcaabbabcbcaddcddbadacccbbdabccbddcddddaaadcababacbdbabbdcaddacdcaababcabdadbbadccddcdcbcdbabaabbacacaccdbbabccccbcadbdadaccadcacdaaccaaccdddbdccbdcbadddabcbbccbdbabccdcddabaacdabcabaabbbdcddaaabdadbbaddacdcbbddbddccccddadaddcaddabdbdaccabbadccacaccdcdaabcddcbaddabdabccdaaacbcacacbcabcbaaadddcccdbdcabadbbbdaabdccaaaccadccdddbdddbbadccbddcaaacaacabcabbdaaabddacbcadbbbbbcbdaddaadabbdbbbdcdbacacacbaabdccbcbdaadcadcadaddacabccaabdcadcadbbaabdacbacbbdbcbdccadddcabcbabdbbbaabbacbcbdbcbcdcbdabdcaccdcdddcbcbccdaacdaadcabdcbcdaadbbbdccddddbcacbdbcbadaaacccbbdacbaaddbaabacbccdbbacdbbbcdabcbabddabacbbddacbcadbdcabdddddacdbccbacbbabaaabcdbdbddaabcbbddacaadbccacabacbcaaaadcbdbaddabbadcdabaabbaaddcabcadaacdcaaaccabbddbcccbacddccaabcddbccbdcadbacbbbadcdbcbabbdabbcadcbaaabacbcccbaddbddabacbcbbbcdbabadbaaacdccaaacbcacbacbbbbbbcccaaaacbabbaabaadaddcdbabaccaacaddbdcbccdcbbbbacaddadcdccdcbbbcabccacabcaaacdabadbbdabaddcccdccaaaddcddaacdccadaddacbdcbbadcdddbbcdbaddbaddbbabbddacddcdaddcacbddbcdadacbddabdbdcaccbbddcdcbcbabadbcbdbcdcadcdcaacabcabaaaaadbacbbaddbbdbcccdabacabbabbacacaabdbdcdacbbabaacbcdddcdaccaacdacdadcaddbabdadacdbbbdcabddacdaccbadcdadadabdaabbcacbcddccaabbabdcabadcacddcacbaaadbcddadddadbdddadbbcdcababcbddcbbdccdbcbdcbdaccbcabddabaccabadcbbaddccdccdbdcbbccabcbdbcbcadddadaaaabcdcdacadbaabdcbbaaccddbdccccdabdaccabbbabddadcbbcaaadbddcabbbccddabadaccdddacccabacddbbcdabbdbbdbcdddcadacdcbdadccbacadaaddccbbcabdbbacddcbdbdadbaacabbdbdcbbdcbcbaaaabaadacbdbdaadbcdbbaaacaacbbcabcabdcadbbddaaaababdaaadbdbdcaccabbdbabbbaacbccdcbdaadadbadaacdcadbbbaadcaacbdbbdcacadbaabbdbaaddcccabdcaabaddcacddbdbbaccdaabaacddbdadaadabdabbbbabdbddbbdcbcbcdaaadbbbbaacdaccbbbbcdccdbcbaccbacdcbdcdbdabacddbabadcdadaacacacdaaaccabcaaddddabdaabadadaaaccdbdcdaddacabcaaabccbbcaabbdcadddcccdcaddbbaabaacabdcdbcdaabadaddaabccccbccdaddbaccccddbcbbdaccccbbcacdcddcdadbbaddbccbdaaddacdcdbdbdcdcbcdaadacdaacdaadccbbdbbdadbdaaabbadbdcdcbbcdcadcdabacbdbdadddddcaccbbbabbbadacbcbadbacdacbcdabcadccdbcccabaddadbbccabbbbbbadcabaddbdccbcaabcccdbdcbaabcdddaccacabadadcdbaabdccadcddbbdabcbadbccadabdddabacddbabadccaadcacdcbbdaabbccdcabdcbddcdddcdbaaadacaddbbdcdcabdddacbbbbbbdbbaaabababddddabaddcacabcddbddccababcbccbacdcdbcbdbaadaaaaddbddcaccacbdcbacdddddbdbbacbbccacabccaadbcadddcdadcbcbcaadcadccaadabbccaccbddbbaddddabccbbdcdbbccadddbdabbbbaaddbcbddcccdaddbcdbcbddabcdccadbabbacaaabbadcacbbbcacdabbdacabdcddcabacdddbbdbadaaabbbaacbcabdbbbcdccbdaabbbbbccbdcadbcaaabdcaccbacdbacabcadacadaddbdbbccacaaccdcbcaaaaacaaaababbccdbcbbccdaaccbcbaabbabddadccbccbdabaaaaccccbbdbacdddcaabdabadcbbddcdaaabadcdbdbacaddbadcddddbacbcccbbcdcbbbbaabcabddcabbbacdccdaadcabdbabddcdbcbabababcbdbdcbadcacadddadcdadcbdadcabbacbdcbcdcababdcbcbadddbdcdbcadabaabbacdaddbdddbcddbccbadabdbaacacbbcddaabdadbdbdbbcccaaabcdbbbaccddddbacccabbbcdcccdccccbcadaababacabddccdcaacdacbabaadcdabacccccddbdbdbcbbcaabdacabaacacababbaacdadcbbbccdcbccdbdddaababcdcddadabbacdcbdbcaaabadacbbcbddcbacbdacaacabcaabbccaccdacbbaaaaaacddabcaddbddccbaccbacaadbabcaaadaabadccccaaaccdacbcdcadcbcdbdccaacacbaadaaacbbdbbdccbaccacbaaaccaddadcbbdbadbadcaabacaacabcabadbabcaaccabddcacbdcdbbcccdacaacbddccadadbdcbacbcbbccddbabcdccadcadbcaabddccdbadabcbaaaaabcdabadbadaccacaccadbdcbbbacdabccdaaddadacdddaacbcdabbaccdbdcddddbccabcacacadcbbdacababcabddddadcadbcccdcdcbbccbaacccdbcaaadaccdbcacccdbadcbbacdccaddddcaaddbdaacbcaabbaabcbcaddaabccdaccbddbdbbcdbcdaadcbbbadcaabdccdcadddbddaabadddcbababddaaabadcdaaccacddccdbaddabaccbdacdcdaddbaaaabbdadbadbcccdcadbdcadddbbdacbdcbacbccdbddddcbaabcbddaccdcacdbccbbaadaccbcacccabdbdabadbaadcbccbcbddadaaabdcaaacacccabadcabcacacbabacdaaddbcccadaaaadbdbddacacaccacdcdaaadacaccddacbcbdcdcbbacdaccabaaccbcddacaadacdbdacdadcbbcaaabbbbcacaabdccdcadcabbbdccbcdadcaddbbaabbccdccdbbdddaabaaacacccadaababbadabcadaacabbccbabababbbdaaccbaabccbbcabcddcccabddbbdbdaadaadbdccdadcdaabbccaadcabcaadbcadcbdcdcdabcddccdbcdbabbdbcaddcaddadcbbaaaddcadaadbdaadcaadcaaadccdbdcacabadbaddadaacdddbcbbacacccababbaadccbbcdbadcabcbcdadaaabaabddbcdbcdcddbbcbbbbdbbaaacabdacdadccddacbdbaddcadbacabcdcbaabaadadaaabcababccbabdbadbddadcdadcdabacadddacbcccacbcadaddabdcabcaacbdbaccdddbdbbaabcadabcdbdadbcdbcdbbbdcccacccaddddccdcccdbdcdbdcabddccdccacdbbbabacaacbadadcdcadcbabcddbbcbadaaaddbaaaacbdbdbbdaacaaadbaabbbddbccdacddbddbbcaabaabadadaaacbcdccacbbdbdadacacabdcdcaadadbccdaaadbbabaddddcbdddbbddababdbbddaadcbbbdbdcbbdbdbcacdbdbbbadccbcdbbdbcabcddcddbcbdddacadbddbdacbadbbccaaabcbbbdbcbccabdbabbdccdbbabcbdaccacdaacddacacbbdabddbcdabcbabdaddaddcbacccaaacabaacacdacddcbbcdbbbdaacccdbbddcdacbcbabdadadcdccabcdbbccbcbbcacbbdadcdcabdbabbbdbcdbcacdcadadcaacccaaadcbcbbbabbbbadcbbcdabddcbcacccccbcaadbcbbbdacaaddaaaacdaaacaddaddbdbcaddbdaaadbdbacbaabadcbaddddbcddbdbbaddbccabdacaacbcdcabcbcddcbbdababadddbabbddaacccccadbababcabdcacbdacbcdacbbbabdcaccccdcddbabaaaababdddcbdbacbbcdbaaaabddbcbdddaabdbbbbaabadddadbababbbdaaccadbcaabbccaacddbdddddacabccaabdcaddbbccdbcbdaabdacadbdbacdadcccaadacbddacdabbabdabcdbaacacaadddcacabdacddcbdbcddbccbbbacbbbdbabdccdabcccbcacaabbcbcacdbdaddcacdccaabaadabbbacbcadbdaaaddaabdbabbdcdcbacacadcadbccdcddaaadbdaabcacdcaadaadaaaaabadadccbbdbbcaadddadcbcdcadcdabbcbaaadadcabbbadbbbccddaadcbcdaddbdaddaabdbdaacbbabacdbdabadaddbbcaadcadaabdddbadcdccadcdbabbbacccabbddbdccbdcdbdcbbacdcbdaaaaaadcccdabcbdbadabbdaadddcbcbaacbbbcbaacabddaccccadaddbbabdaabababaaaadbcdddaddcdcdaacadcaddaabacdcdcbcabdcbcccdaacabdaccbcdabaabdbbbcbbcccdbdbbbadaaccdaaabbadddbccccddcaaabbbaabccaabbaddcacacabdabcddbdcbbbbdbbbacabdbcabadabcababccabbbdbcbdbcbbcbacdaacbcdbdbdbbcbdcdcbabadbcaabcabbabcccdcbcbcdacddcabbbdbcbabdcdbdccaddacdcbbcdcbcccabdadacaddabcdcdbbccbaaadbaababbcbdaaabbacabbacbaadddaabbbcbabdbacddcdcbaddcdadacbdcbddbcbadbaccaaacaddcdcbbabbbaddabcadadbcbbabccdbdadabdcacdbbbbdacabdddbcbddbcacabbddabaccdbcccbacccbadaabbcbbbbcdddcaabacbcaccbaababcadacdbabbcdaadddcacabdacccbdbdabaaaddaabacacacadbdcbccbbbdabcadabdadcbccccdbaabdbddcbcbddcddcacdcdbcdbbbabddbbcabdaaaadabcbcbdadddabbccaccacdbcaaccbaabbaadcdbdbbcddbcabaabdcabadccdbabacacdbaccddddaacdbbacabcccadbbcdacaaccdaaadabbbcdbbbbbbbaccacaaaaacaababadadcdaacbbbbcbbaccaacacbcbaacbaabaaaacbcbcabacbacbdbcbbacddcadabacbacdcdadacabaccccdcbdaacdbadcbabaddbbaadbacbbcddbbacbcaadadabacdbbccbbcccabdababddabbddddbbacbbdaccbbdbcaccbbabdcbadacdababaacbcaabddacbbdbbadccbdcacaacabcddddcdbaacaadadcbcddddccdcbaaddcaaadddddacaadddcbbcbdddabbdaadccabcbbaabdaddccadcbcbdcdbabadbcddccdaaabadbaabbddddcabdbaddaacdbadddcbacadbaaadcaaaaabaaacacccbbbddadccccdddbddaccdacdaaaccdbdddadbbabcbdbcdaabccbabddbdbaacababbaacdcaabbcadacdcdcabdcdabbcdcabdbdcabbbadcddbbaddaddbbcbcbddbadadbcaccdddcbbddbbbcaaddddabcabdaacbdddddabbcbcbdbcbbdcadacabdbcbadccbdddbcbbbccccaadccadcbdcaabcdbabdbacaaaabcbbaadcbbacbccdabcbbdbcaddcddbcabadddaaabbaccddcdbcdaadbddbddbdbaccddbdbdbccdbdadddaababdacddacddbcbbbacbabbcadddacadddcdccdabcbcacacaccaaaddcdbbabcdbcbbaaddbdcdcdadcddcbdaacabbbaccbbbabaaadddccacbacbccabacdcdcbdcbacbdabbbccaabadbabbbbccbbcccdabbadaacdbbbdcbdadbbcccbbbdbcbbbcbaddcddcadacaaababcbcdbbcccbbccacadcdccbbbdacabadbbbadddbddccdcbcccdaaccdcbbadacbbbcddcdcdcabdaabdcaaabcbdcbdccbcdbacbadbabddbbdccaacbbabbacabccddbacaddacbdcbdaabcdadaaaaddadabcccbcdacacccdaddcddbacccbadacaaabccbdbbabbaabacabbadaaccdbdccddacddbadbdacabbddcadcdddacdbbccacbaadcabbacccbdbddaccabdaccaccaadbcbbcdddaccccccbbbdabddddcbcabcdbbbacaddccddbcaccaacccdcacbbbcabbbdcabdccaabadddbddcdccbaadbdbbddaabcacdcbbacbaddcadcabcbcdadbdbcdcccacbdddaddbadabdaddcaacdcaacdbaccdcddbddaaacbcbddbcccdadaccddbdcddabdadcbcdaaacccbadaabcbcdbbbbbbabddaabccbcdcdcbcccdbbbadbdbddcbdcabbcccbbabdbbabbcdbdcdaacbdccadabbdcdbbbdbaddbabbcbbbbddaccccbdbcbacdbcabadccacdccdbdcbbbbacbaaacacbadaadcbdbabbddaccadddbdcbdbdadacacdccbdadcdaadddabddaaaddbcdccbdbbadadccaaabbcddbabdabddbbaabdabdbdcdbdcaaccaaaaadcbccbdacababacccaaadcdaabdcbdccbdbbacbcbadaaacdbcdadbddbddddcbbbbbcaddcbacadbcdbadaddccaadcbaccadcdadadcacccdddadaccdddbcaabbcdadabdbdacdcadbdbbacbbdbaccadbddccbcdcbcacbabdbcaddabdbaaddcbcbbddabdddcaccaabaaacbaddbabaccddabacdaadcacdbbbacabdbbaccddaddabacbabadcdbbbdbbddbcabbaaddbcadcdcbbddccbadaacabbccacccbddbbdbaabdbdbbbbdbaccbcbbbabbaccbacbcdbbcaaddaaabdabddddbddcaccbcbccadbbdabaddddabddadbacccbabcdcbcadbbddaabcaddbbcadabdacdabbadbbabbabadbbaaadaabababcbaddcdacbcbbcbbcbdccccabdaabaabaabcdaaabcddcbccbbccdbbacbaadcdaabcdddcaaccbcbdaaacdaabaacbbdbaddbcdacaadddabcdcbbaccdbcbbbdddaaddaddbcbadcaadbbcbaadaaabdcdbcacccdaabcacbddcdcbccccbcacaccbcbcddadacaadaaaccbdbbdbdbaaacbdcdccabcbcbbbccdccbbaddbdaaabcccbbddccbaaabbdbcbbbaaadccbbdbadddaddbaabbcabacaccbabcadbdddbbbcccbbbdddcbddacbdababbcacacabdcdcbbaabbbaacbcabbccbbcdbccccdbcbabcbabbbbdddacdabcdbbbbdcdcccddaaaabadccccbbcaacbdbbbbbadbcddbbddaadcdcccacddbdbbadbdccacadadbacddbaddcddbdbddbabdaccbcaaacdabdbbcdabadbacbccddcdcdcbcdbbaadaabcaadcaaabbdabbccdbcddbdbcbdccacccbcbbdadbddbccbbbaabbdbddbdadddcaadddaacaadaddcaadbbccccccdabbbbaabcbbaaaabbadbacbaddadbbaabaaddccbcbdbccccbdaaadbbaabbcbabbcacdaaadccbaddbcabdadacabbcdabbbbcabcdbcdcccaabddcccddaaaabaadcbdbbabcdabacdaadadbbadbcbaadcabbadbabbddcdbbcaacaabcccaabacabcdddaabdcccbdbababddcacdacbcdcaaaddcabadbdccabbacdabcadccdbbcbbccbbbdcbcadddbccbcdcdbcdacbdaadcbabbabccdadcbcaccababbdcacaacccabbbccdbdcbbabdaccbcbdbbaadcaaaacaddacdabdcdcddbddbbaaabdcaddddaaadbdbcdacbbccbaddaacbcbdacdbdabdbcdacdbbdbcabaccaadcbbbcbccabcddbcabbcddcdcbcadaaacdcacacddaabdbbbbaaabcdcabddbbacdcdcacaddacbcbdacccbbbdcddacbcbdcdbaabbddcaacddcdacbcbbdbadbbcccabddbcbaadacdaacaabacaacccadcdddaccccbadbbabacdcdbccdaacaababbadadabdbbccacdaadbccbbbabcacbbadadbdbcbccbbcbdbcacaccadadbaacdcbbccbdbadccdbbbbabdcaccdcbbbaaaadbaddbcbccdabaccaaacdccccbabaaaacddcbdbbdbcdcbdbcadbaaadaabadadbbabbaddbaabaabcdbaabbccddadddbcbaccdbddbbbdcadbaacdabbbdbbcbdbcacbcdcabbadadacccbccdadcacdaadccdcbdcacdbbccbcccabaaccbbbbbbcdacccbbdaaccdaabdccacbddcbcaacdabbbbcddbdbbabddabaddcdaccccbcaaacabbcaccbbaddbabddbcacbccbcbddaddcacccddcdcdadbbbaaabbbccaacabcdcbbcdaabdadcadbcdadbacdcccabbddcdcdacbcadacdcdbcbdbdabcddccadcbcbccabcddbdddccaddbbccabbccdacabaddcacdbcaadcbccdddacbbcdcdadcbaacdbaccdbcdadadcacaadadabdbdcbdbbcdadddddcbadcdddccbabacadddabdddadaadbdbdcbbabababadaabdacdcabdabaddabcbcccdcccbacaacadbbabbbcdbbaddddbdbaadbbbdbabaaccaccadcacdadccabccabcaaacddbddccaabacaacaacdddadcddacadababdabacddbcabaadcdcbabcaacadacbbdaccddbcabacbdccbaaddcabaabcbccdbaccacabdadaaadbbdcdbadbbadacabdccaddaaadabcacadbabbabbcabccacdcdcbbbbabbcdadbbbcdacacdbadccbabcdcabdbddbababbbbadaabdadccdadcadbbdaadbcdbcacdcdbdbcbbababcdacdbbbdadadbbdaaccabbcdabadcdcaccadbadcdbdaaccdaaaaaacabcdbabaddcbadbadaacaddbcabbddbddccdcbabbdbbccccccabaacdbcdcabbdcdabcdcbcaabcccdaabacddadbcbcddaaabcdddbddaacdbccacccadbdabdccdbbdcdaaadcaaacdccacdbccbbdadddbcdabdbdbabddccbabbccacdccbbddccddbacdaabdabccbddbcdadcdcdcbdabcdabdcccddabadbbabdbbdcadcdbaabbadbdbdcdbdaadbdcbbabcbdbdbcbadadcbcdcbaadaaadaaccbdbadbcbbbdcdbacdbcbcdbdbcddddcccdbdbbcdccabacdcabbbcadbbddddcbbccccabdaccdaccddbccbbbdabaaaddabcabdbaaddccbcdccacabbdcdcccdbdcbcaabdccabacbddcbccddddddbddbdadccddcabccbcacabccbcdddabccddaadbcccdbabccddccbbddbbabcbcdacaabccccdcbaccabbddcaddbabbdccadbcddcccacbbacaacccdddbabaccdbcabdccaacbdadbdcbaabcabaabcdacaacacadacdbcbdbbdccddddadbcdcdacddcccccddcccaadcaacbdbbbadcbbcbcdbdbccddccdbdaacbdcbcbbaaabcdbcaddbbabaacdabdacdcbcdabaadddbdaccadccaaaadcbcddcdbacdbcbcdcdbcdccadbbccabccacbcddbacaccbbbaccddbbccccadcaddccaadcacccbabdbcbacacbbbdadbdadacbaababcbcaaaaacacadabcbaabdacbccacadbacbddddcbabcccccdadacbadbbbbdcddbcbaacacaddbadbcaabcdbabcbccaddaaaddacadadabdabddbacbcabdccadaaaacabcbdccabcccabbacdbcacadcabddbdcdcbdbbbdcddbbadccaddbccddabbdcdcbcacccbabdadacbbbccbaaddcdbacbdabcddbaaaddcadacaabbbcadabcaddaaacdcdbdcdabcbbacdccadbdbdbccabcbbacbbccabdcdcbcbcdacbaadbcaabcadabcdccacddbcdcbbddddcccccdbbdcbcadddaabadcdcbbabbbadbabaaadaacbabcababababcccabdcbcdbddaadacddbdbddbabcdcacbacbabddbccddcbdbdddaabcbdbdacaadabdadbdbadbaddcdabddccabcadabdbdadbcaabdcacbbcaddadbacbbcadcbbbaabbdbaabddcacaddcaacbbaadcaccadcdbcacbcdacabcccdccababbdbbdcbacabbcdbbaadcacbbccacadddcbbcbadbbdadddabddbbbcdbddbadaabbaccddabbbadbdbcbcabbdabdcacacabaccbacabbacacaaadadbdacbbcbddcbabdcaaccdaabcabccbbbadbabddaadbbaabcbcbaddacaddcbdacdcaadbacdacacbadcbbdcbacbcccadcddddcbddaabbcdbddaaadaccdbbdcccadadbdbbcbddbbcadbbbabccaaabdddbadbdadbcacadaadababcaabcabddbdccaccaabcddbcbcaabdaababccbaabccacabdcdbdacaadacdbcdcbabdacbbccbcddbccbaddaadccabdadbbabbdbbcbdacdcbbcccaaccbcacbabbcadbaabacdaabbaadabdacbdcdcbdbcccbdcadacabbdddbdcbddcdbcdadaaddcaacdcdcccdcbbcbddaabdbabdcccbdbccddbdadadbcacddbbadadbbabbdadcdbababadbcdcdbabdbadcacadcbdddcacbdbbacccdbccacacdcaacbdbdccadbdbbcabbacbabdcddabdcbabdbccdabccdbaabacbcadccdaaacabcaadaccddcbcdbcbcabcacbacdbddcdcadaccbcbcccbcadccabdabdcadbcaabbbccaddacbdccaacbbcadbbbcccaabccbbdcdcccbbdcbbcdbbdcdbbbaabdcbccdcacaabaccaabcbdcabdbacadbaaadcdcbdcbadbcbaccbbccbbbadbbadadbaacdbaaacadddcabdbdccaacbacbddcdbcdaacdbcdacabacdbcccbadbaadbdbabaaddcbcbdaddbdcccdcacbcaaabbdbbbcabadbdbabcabddacddcbbaccdbdbbdddddaccbcbdcdbbbaacacabbcdccdccbacadccdaddddbabdabaabccdddbabcccaacbcdaabaaabcadddbdaabcccacaadadacdaaaccccccbcacabbabaaccabcaddcabbcbaccdddcddddcabbbcacadbacdbabbbdcaaabdadddaccabcbadaabcdddaaccacbcbccbbbccbdcbdbbbbadbbbabcadddccadabbdaaddccbacbadcdaadadaabdbdccaabcabcdabccdaddddaaddacddbdcbdbcbdcbbaadbbdcbbdaadadbbdabaacbbcabdacbbcacaaddaaddbbabaaacabdddcccbbdcdcddcdaaaaaccbdcccbdbaddbbbcbbcddaabddbadccdbbadbbbadaccbabbacabbaabdbacabcbcbaabbacbccaccbaabcaddbadcbbbaaccbcdbbadbbadbbbdcbddcabcdbcacdaacaddadaddbcbbdcaaaaacdcbabcabbbbbbcacccabdcccbaddcbdbabcdbbbbcdcdabccbaaccdbcadbbadaadcbbbaddcddcbabaabbbcbbdbbdbddaabcbcdbdaaccddccdaaaacbbcabdcdddddcaadddbbcacdacccdcadddddcaccacacccaddabddaaddcbccdbdaaadbcdbadadabcccbbcdcbadacdbcaabbbcdbbcbdbcbabcbdacdaddcbacadcabdbaaaabddacddbcccbbadcbaccaabbadaddbbababdbadcdbccdcdadbcaacdbdbcdbccbbccababdbcdbccacdaacaddbaaccccccbacbdaadbabaacaacaadcdacdbaacdacaacacbbaabaacdbdcdbbccacdbdcdcbdadacccaddbdadbdbababbadbcccacdaaadababbabbcddadddbcddbdabbcdcababcbbcccacbcabbbdaaadbabadbaccacbadcdaadbbadccbabacbcdbdcdcccaacbccccbacdcbcddabcdbccddbcbabddcdcbbdbbaddcadadbcbbaacdcabcdacbbddcddaadcbdddbbaabacbabdabaaacaaabaadaddaadaacaccccacaddababdbdbcbbaaadacabdacadbdddacaadbcdbbadccadbabdbaddcdaaadaadcbbcbabdcabdbabcdbdaadbaadacacdbdabcbcaaccccadccaadadbcdcaadbbdcbaccbbbcdacabddbcdacabbbccbacbadcdcaaacbbccaacacacddadcaacbbccdcbdbccbaccdcbcbbcbbcbbdbbabcacccdabaabbbbbbccadacdbbcadcacdbbabbccaaaaadacaacbddddaaaacbccabacbbcaabcabcadddaabbbddaccbcddcdabddcaaabadacaadbdbacbcbbcacdcdcbbcddbddcddbabbaddddabbdbcbdcabdabddcdaccdacbcdcbcaaddaccbdbaaddbdcbbbcabaacbdcdcadacccadcbddbbdbddbcddbddcccdbacabddcccacddacaccbbbdaabddcdbdabdcdbadbdaddcbcdcadcadbccaddaadbbcacbbaadacaadadddbacdddbacdcbcacbbcbaadbdabddbdccbaaacbabacbbdcdbacacdbbadcbdadabbbacdbbbcbdbadacaacaddbdabbbaabacbbbcbbdabcaddbcdbacacabcacbbcadccccacdddccbcabdacccdadabccaddcbddaabbdcdbbcbdcdbaababdcccabdccccccaadcabcbaadbdcbabccaabbbdadacaadbbcccbabccaaddbdbbbcadcadaddcbbcdbaadcdbaaacbcaccbdadcdabcaddddaaacabdbabbbcdabcbaaabdcdacddcccdacdadcbdbbbdcabcdcbbdaccbbcddadbabcaddbcababaaaadcadcbdacccabbccaacccbcdbaddcddaddadcccacddbbdbbdbaadcdbdcabcdcacadaadcdcbbddcdbcccccbbccccbdbdcbbcaccbccbdccadbabdbcaadbcbcadacdcbdbdbdbbdddcbdacacbbcaddcbbacaaabcddadbabaddbbccbdbaccaaccadbbbcbaacbdbadbcabcbccdbaabdbbcacbbadccddbbcbacaddcaaabacbbcaddbddbbcdbdddaacddaaaacdbcbaadcaadaccababacddcdaabdbdcdadcbaacbdbbbcaabadaadbacadcabdbadcbaabdbbbaadcbcdbacbdadadbadaaddcdbaaccabaacdcabbacdbaacccdcacaadcbaacaaddccdcddcdaaadcdadcddccdbaacbdcbbdcaaddbdadcdccbdbbcdccbdbdbbcccddcddcbcbcaddddaacbdbbadddacccccbddacddbdcdbcbbccbcccdcdccdaaabcccbcbbbccdadcdbcdccdccdadbdcacdaaccccbbbacbbcdcabbaaaacadcbdaccadacdbbbccdccdcbdbadccaabdadacadbaddadabcdbbdadbdbacccddbbbababddaacacbddccddaacbbcdcccadbabcacccddabdddcddbaddcbbcdacbddcabccbbcdadcaabacddccdcaaccbcbaadcabcdadaabacabbaaaddcaccdbdccbddccbaadaabddadbbbbadaccabdbbaabbddadcdaccbbdcdbbbbccdabdaabccaaddcccabdcdbabcbdbdcdbbdbccbbddadcddaccdacbacadaccddaabbadbcccabdadbcbdcacbbbddabbadcbdabaabddadacbacdddacacbacbcddacaadcabaadadacbcadbbcdddbcadbddddbcabdccbcbacbcacbddcbdccabbcdcbccbbbcaddbaaabbdcdaadaaddabbcbdccbabcbdbcdbbcdaccdcdacadcaddddddacaddbcadcabadacacbdbcbacabcadbcdbbbdcdadbdbdbdbbccbabccdadbccbbcacaabdababbbdccddddbdcbaacbcbbbdccdccdbbacdcddbbdcabbbacccdcbbbaacdaabaddacddabbdcdbbccccabdcdabacccadccdbcabbdbdbdaabdadbbddddabcbdaadddbaddcbbadcbcaaacdbbbbadbaddbbccaaddddaacaabdbdbaadbccdddabbdabcaabacdbaaacbcacacdadbddddbdbcadcadbadbaacddaabbdacbccdbdcbccddddabadcbbbcbadacbadbaaabaccadccddaadcbbdaccbadddbbacbdbcabdbabccddbcabcacaabddaacccbdbbcdcdcaccdabcbcdadccadabbaaabcadbabbdaccbddbcbaacacdbcacbcdadacdbbdaadbbdbccaadcccabcacdacaabbbbabbaccbdcddabcaddabbdbbccddaddababbdddcbdcbbddadaccdcbbdaaaadadabadaaababacaabaabdcbcccbccdaabdadcbdbddacdbdbbbcbbccbbaacbcdcadaccdbadbcaabbcacabadcadcbddabadabadadaadcdddddaccabcdbdcdadcdcddcbcbbdbcdccaddcbcdabbaadbaccbaadbcdcccccdbaddbcaddbabdcbbdcadabddbdaabcbadbddacdbcdacdbdbbdaaaabcdababaddacbadacddccdcdbaacdaacddbcddbddcbaddadacadabbbbaaaacdcdcbcaabcdacabdbdbaadaccdccbddbccacbcbcadddaccaacddacacadbcdbdbaabcdbbcbcccddbdadcaabadaaababacdabcaadaaabdbcbcbccabbcadacacbcdbbdaccdbbabbbccddbabcdaadcaccdbbcbbdcdbdddabccbdaccaadbdadabacbbbaaabacabbaccaddccbdabadaddababcccaccdbcacddaacaaaadcbbbdcbcacdaacaaddcbbdcabadbacdbdabdaaadbbbacbcaaacddbddbcbbbaabbbbbacacbdcacaadddbadcaaadadbbcbbccaaabdacdccaaadbbcddcbbbccdbdbdabbcaaadaadcbacbdbdbddaabaabbdabcbdcaabaabcaddbbcbbbaadddbcddcaadcdbbcacbcadabcdacdaaaacbbbccbbbccaadddbcbdbcbcadbdacbcbbdabdcdbdcabadbabbdcacbccdcdacaaadbaddcbccaadbbcbcbbcacabaabdbcdbdbcdcdabcacbcaacaabbbdbbaaacdcadbbbbbacdacaabbdaabcdbdaabaabadddbcdcabcbbccbcdabadbdbddbaadcbbcdaccdccaaacccdcdbbcbbddbbdbbbdbabccdabcaabcbdacbcbbccaadaabcbcabbbdbdcadcbcdbdbdccbbccdaabaacaabcbacdbbccdbdbcbaabbbabbbabadacdacccccbcaddddbcaadcccbdddbabdadbcbbaccdddddcabcaabcdadbaaacbdaabaaccbaaccacdcabcdbcdacddbcabacadbccabaadcdccbadadcaccaccaccdacddddadcdacdcdadcdcdbccddbccdadcadbcbccbdbbadbddcddaaadddbbaccbaadcaadcacabaddacdddabbddabccbcdcdcdbbbbdadabcdbbbcdbcccdcadbbbbccccbadccbdaccbccdcadcaddbbdacccbaddcaabacbdbddcadaacdbdcadbdbbcbdbbbcbbdacacdddcdcdbacdcabddccbcbbdccdbcdabcabbdcacbababaacdbcaadadbdaadbcaabddadaadaacccaddbbbdcddcccacdacdabbdabcadadabbbbdcdddcbacccdcdbaabbdcccbcccacacaccabdcacbadcdaacacacbdcbcdbbadbbbbdcaacccdbbcbadaccaaacdabdcbaabbacddacaaadbcdbdddcdbbadbbcacbcbccddbdadbcbaabbacbaaaadddaadcbaadccacdbcacdadbbaaddaabdcacbccabaddabcadcdbbacccadddacaccbbbcacbbcabaacdcbcbcbbaabcacdabbdbdaacdbdaadddbaacbbccdadcdccdacbddcbccaccaabbcbcbccdcccbdcbbdbddbdbcdbbccddbccdcbaacbddadbbdcbbbcadadbcdcacbbdadbcddacaabbbbccbcdccdddbdbdcddbddacdbadabcabddabdcaacbbadbbbbbccbbadadacdcaddacacaabacaabccacccddcdadabcdcbccbdaaddaabbdadbcddadabbabddcbbbcddaacadddcdbabcdcdbacacccadbcdccbbbcabacbddbadbbdcbddcbabbdcdbbbbcadbddbabddabdaadcabcabddbdcaaadbacbdccdabcccddaaddabddddabacacabcbcdabccbbdabcbbbbdcabcadabdccbcbbacdaccacdabbccdbbdbbcabddacdbbdabadbdcddaabacdaacacadabcadaabacdaddccbadabbabcacabaacdcaaacacddacaaadcdadcbccadbabbdcbabadcddabcbdccbbbbababaacadabddbacbacbccaaaaabcbccdaacabacbcbabdacbadccdbccbabcababdcccbaaadcbcbbaabcccabcbdabdabdcdbbcacadbadcbabcdababadddbadadbcdcabdccdacbbaababdddbdcdbcbbadcbdacdcabccbcabdacaadcacbaabdadabccbdadcbbdbddacabcabaaddbaacbbddbaccbabcaacbddddddacbaaddadccbabacadacbacdbdbcabacabbcdcdaacadcbacabbadbabacacdddbcacacdaacbddbbadccacdaadaddcdabadbcbaccbcbbdcacacbcddacbcaccacbacbaabadabddccdbdabbabcdddabdabaaacddaaacbdbadcbddbbdbdddbadcbcacaacacccacaacdbbcddbaccdddbdabccbaabbbcabadacabbbcbcbacdcbbdcbddbdcdbcddbcacbdcddabcddabdcdacdabddaacaadbcaabcddbbddbbbbadbbcdcbcdcaccbaaacbbabbbcddcdbbbbbdacbabbcaddbddbbcbacdcbdaaddddaaddcdccaadcabcadbaabccadacbadbdcaddcdbdccabccbbacabcabcddabcadbdccddbabdacabbbccbcdcbbcdabddcddbcbcbcadccacbababcdbadcccbbcbacbddcbbdacaaabbadbdcaddadaacddccbbdddbdcddaaddcbdacbaadbcadcaddcbbdcaaaadbbdabdcbdbcaaddbdbdabddccaccdccbadbddaddbacddbcdbddcdabbbbcacdcacacccbcadbaabddccacaabbcabbaaaabdcdaccdcdbdadbddaaadcccdabdcacbbdbddbcdabddcadcaccdbdccdbbccaadbbabcacccaadbaacadbbdaccbdbdccbbcbbdaccddbdbabddcadaadaccbccbcddacbbdbbbdaccbcbacacdddacddbbadbbcbbacadcaacbbcabbcadbcacdccacaaaaabdbcabadbcbaabaacdcddbcbbddcbabbdaaccacbbdbbbabcdaadcabcdcabcbdbbaabaaaaabbacbcdbbabaccbbbdccadcccbcbcaccaabcabadccbdccbaabaacccdbdbdaddcbcdabadcccbcbbddbcaaacccadccddcddcbaccacbbcdaccaaadbdbcacabdbbaddddddabadaacbbaadababdadbbaddaabaaacacbbaadbccdbcadcbbddbaaadabdadddbddadcbcbddcddbdaabccbacdccbaacdccdacbbacdccbdbacccdcccbcabbbacccbcbdcccdadcabaaacdacbcabdadddaabcddacbbaddbacdaadcaacacbacddaadaaaccdbacabcadccabdadcabdaccbdcdccbcddccadcdbbbadcbdaabdcdccddaaaabcbcadadcbddcadacaabcbcacddddbddabaaccdbaadaadadcabdbaabccbcccabbbcccbabdcdaaadbcbdcdcdcdbdbbdbdcccbbdadacdabacaabbacabaaababcdaadcdcadaccababbacddaabcdcabbaddcadbbbdbbdabbabbbccdadcacabccddacabbbddccbbdabaabcccbaddddbbbddcadcdbccacbacbaccbbaddddcabddbaacdbcaddabcbbaaddbbbdbdbdcccbbccabacabdddbbdbaddbbbbbddbdbcaabddaddcdbccdddbbdabdddddccdbdcdaacdddabaadaddcbcbdacdbbbcccddcacbddbadacbbcdadaaddcdccaabbbaabbbcddcccdcdaaaabdadaabbcbdabdabdcccbdacadadcdccdddbbdddcddcbaabbaadccacdddcaddacbbadacacabccbbdcdbbbaaadbcbadcddaacaaaaabdaaccbcbcdbcbdadcbdacbdbaacdabddaddccbbdbcdacacbddadcbcbacdcadcabaabaccdacbcadcbccbcbadbddddbababcbbbccbcbdadaccbadbbaacadbcbbbcadbadcdccddacbabbddadcbcddaaddcdcddcabdaabddbabbbacbddacbdabbbcdbcacabbabacdadacbaadaaaabaabbcdadadbbbdbcabacdcccadaccbacddbabbdcdcdbcccdcdbaddcadcbbacaabdabcbdacdcacbacadbbabddbddddcaabacddddabaccdddabdbaabbbdbdddcabaaaaccadcbccaabbccacccdbccaabdbacccdcbdccccaccacbbdaabbcbbaaaacddccddbadcbccbdbdcbdbaddbcaabcaccabbbaddabacbccacbdccabccbbdcbabaabdbbbbadaabbdbccdadcbcadacddddaccbddcbdaadabaddadabbdaacddccddacdbbdddbacacddcbddcbacbaacbacacccabbcddaadbdacadbbcacdbadbaaabdbdacbdbbbbdcadcaaadbbabcaabcdacbabdddddbcbaddcdddbbaddaacbdcbdbbbbcbbaaddbabbccccbcbbbcacaaadacaaaadcbdaaccccbcbbdcdcbcbadbcddadcbbdabadbcccabdaccdabdddbabddababbddabcbbbacbccbbccacbadddbcabaadacdcccbbacadcaacadabbbaaaacbcadcabaddacabcaaadbadcdcabdbdcdaabacdcadaaccbbabadaadccacacadaadcdbdccabbddcbbdcbcdbdaacabcbcccadbcddbbabdcadbdbbbbdacacacbdddacbbddadcddbcaddbcabdbabbdacbbadabcaaddddccddbcaadbccdabacdccbddabbbbadadaabbbdbcabbdaadcabdcddcaabaacbcbcacdabacbdadabccbbbbcdcacbbaaabccccadbbaabcbacbdddaacdabacbaabcdbbdbcdbdccbddddabbaabcacbdabbccbdcabacbcacbcdcbbddbcabbdcaacdacbcbbdaacaaaaacacaadccbcaadcbbbacbadccadddbbcdddaacacaacabccbbcbdcbbbdcccdcacacabccbaacabadaabcdadcaaccbacdaddbacbbddabdbbdcabaabacdaaccabddaccaadcdcdcddcdbcbcbacdcbcbbbddaddbadddabdaabbcdacaccacbabbacacbcaadcadacdbabaacaabcabdaddabcccdacbaacdccbdadacbaddddcbcdbcacccacdbdddbdbaadcbcbcbccbcddaaabddddbadacdccccdcbccadbdcdabacbcbabcccdbbaaccdbcabdbacdcaaaacbcadcbdbddabcdadbbcbdaddadbbcadcaccbaadccdbbdbccaabddcccbbdbccdddadcabbaacbcaacabcaddacbcdbaaabccbdaacccddbbbcaaddcbbabcdbacdcabbaccdcdddbacbaaaaabdabccdadcbcbdbdacaadcbbabbadcddcdabccbbcbcbdbdcdcbbcacddabdadacacdbabcbddbdcdddacdbdaabcdaabbccdabbbbbcdbcabadadcdbcaccbbbacbdcabbbbbdcbccbddbccacddaaddcabcaaabdcbabbcbddadbddacabdcdabdccbdababdcadaacdbddacdcdcaaacccabbbbbcdddbcbabacabcaacbcdcbbbbcdddadadcabdccabddcdabdabcaacbbcabbadbbbbcadbbbaddcdbbddacbadbdadacdbcddccbccabbcbdaccbcdcdbbcabbadabacdacbcbaacabcadbdbcbacdabdcccacdcabbccdbabbbccddbbdcdcbbddcdcbdadbdcbcdbcccbccbcdcadbcddadabbcddadcacbcabaaabcdcccabccccddbabcddcddcdcdbbacbabbcbacadbbbbcbabacdadbbdbdcdacddbbcbacbbccaddacdbbcdacdccdabbbccbacbdbddcdaaddacdddbabcaadacdbcadbcbddcacdbdadbbddcbacaaacbccdcbadacbabbacbabbcbcabbcbaadabbacdbdbdabdacddcabbdbaabdaddcdacdabddcacbbcbbcbcabdcabadcadcddbdbddabadbdabcdddaaacaacbdbbaddbbcdaabcdcabccabbcccbcbaaabbdccaccbacabadadccbddddccdcdcdcdcabbccaababbdbdbadbabbdbdbabcbdbdcdccacaadadbdabaacdacacaaccbdadcccbcaacdabcdaabdaabcadaadcaacadadababacbbacdbbabcccbddaaababcbbabacccbddcbdccbbbbcdbbabdaaadccaaddcadcacbbbcadadbacccddadbcaaddabaccbbaadbbdacbcbabacbddcacbbbbddcdddddcdaacaddaadadacacbbbabccdbdbdbdcabcbccadaadcbcacbdadbdbaacdbbccbbbcaaaddbbcbcddbbccbadcaadbbcdbcaaacdaccdcdddddabbcbbdcbcadbddadcbdbaddbcdabcbacabdadcbadbcddabadabbcdbcaabadcadbbadacaabcccdcbbcdacacacddaababdaaddaaabaadacccaccaacdaadacbddadcdaaabcadbdabacabdcdcadaaababbcdbdbbdcadabbaddbbcabaccbdbdbdcdabbbcbdcababdcabadbabcdaaddbbcbbbdbabbdcaadbaabaabbbbacbaddcbabbadbddcabddcccbaadcddcdbdaddbcdacddbbaddbacbbaaaddccbacaddaadbcaccbcbdddccdbacabadbbdcaababbdbbcdcadcbaccbbddcacdccccbacdbddacddbbbdacacbbdccabaabcdabdbccaabaadcaadccbdbcaaabdabcabdaaccbadadcbabbcabccbbdbbddcdcdbbadadcabadadadadbabbdddcaadccaddbcbcacabababbbdadcccbabddcddadbbbccdbdcbcbccabbbdaabacbdcdaadbadbadbcbdbdadcaccccababddaccdabacbdaaadbbaaaabcdbaddaddcbddbdcbaaaccaaccbadabcbdcabcbbcdabadcdcbdddabdcacabacdbdbabdcdddcdbadbcbdaabddaacaacbcbcbddabdcadacddabadacbbddbbcacdcccadbdcdcbbcdcdcdcababcacbbcaacacbbbdbcabbcaadbabdcaaadcdbcbaadbadcabccdbccbcaddbbdbcbaaaccbdddbcccbdcbaaaaadaaaacbbbdacdadaacdadabdbddbdbbdccdaaabaaaabcaaacdabdbbbbcbbbdaabdadbdcdbadabcdccccdabbdccdadbaaadacbaccdadbbbbdbaaadbdadddbacaaacbbaccbdbcbcdcbaddbbddbaaddcacdabdadcadcddbabdaccdbbaddbbbcbccdaddbcbadabadbcabccdbdbcacadadacdcaddbdaddacbaacbcdccacbadbbdbbccccbaacbacbcbaadcabbbbadbdbabbbccbcdbdadacacadbbbaaddbbcbadbaaccadadcbbacbbddddacadaacadcdabdaccdcbbaccdadaaacabbdcddcadbbdabdcaaaddabbbcbccabcadcdccbcbbccbacdddadaaddbddbcdcbadccaccbcdcaaaddcadbdadaadaacdbabaabaabaddbccaaabdbdabccadbcbabccbcdcadbadadcdbcaabbbbddacadccdaadccddccccaaadabbcdccabbdacabbcadabdaaadddddbaabbddccaccaabcbccacccdbbbdcacbdacbdddbbadaabcccddbbdddaccccabcddbcbadbdbdacbabcdcdbcdbbcdbbcadaccabaaabadcabaabcababdbbbddadacdaacabcaaddcdbcababbdabadbbbbacdcbaddabcdaaccadbdccacccacabbbcabddabdbaacdbcabdbbadcdbdddaadbacbcbcaccdaaaddaccacdbcacbbbbacbabcdaabaaadbbdbdbdbbdddacaadddbdbcbadcabcbaaddacadddcccbbcbccbdabccaacbaddbabbcbddaddcccddbcbbdbadcadacdcacdaccbaaaaddbabbcdbaccbcacbacbaabdadacababacadbccdcdbddbaaccbdaaccaddadcccbcddbacadbccbbcdcdcacddddcbcadadddbccdbabadaabaaabbbddcbcadbdbbadaaddcbcbbcdbbaaaaabcaddcaadbaaaaabcdabdabacddcddbbdbddaaababdcbdcaabbacbcbcccbbbadbaaabadcdcdcbbaddaccdccccdadbacccacabbddadbabdbccaaababdaccaccdbbdcdbcbdbdabbabdacbacbdaaddcdbcabcbbccbaabcbbbadaacdbbcdadcaaadddaadcdabbcabccdccddacccbcbccdaaccbcdbbdbbdcadcbaacadadaccaddcddbbadcbcacacbbaabadcadacdadcdccbbadbbddddcdddacaaaabaccbaaacdbbdbbbdddccdacdccbabdcccbaabdaaacacbdcbbacbababcabdaccbcbddaccdbbccabccbcadddaabcbdadddbbbabbbccdcbdbccdbabdccbaababbaacdcacabacacacadaaadbabccabadbdbadcacbbcddbaacaabaacdaccddcaabdcbcbbaadbbddcdddabaaadbddbbdbcbcadccdcadaddccbabbdadcabbbcbacdadbbcaddbbacccccacbabccaacacbbadbacbdbadcddcbbdbddcddaaacbdacdbdcdbadbaddbaacdddbbbbdcdcbbaacdaadaddddaaaadddbcaabdcdbbddaabddabaacdbbbcbbdbadabdbcdcbaadddadbabbabddcababbdadccadaacccaaccbdadbabcbaaabbcbaccbacccddadbdadcdcbadadbbdbabbdaaadddddbdcaacbcddabaabcaadbaddbddcabbbacaacbbaaaaadadaaabbacabcdaddacaaaadbadacddbbdbdcadcbdbabbbbbcddacdcbdddcddbccdccacccababcccbacdadcbbdbddbbabdcbcabdadcbdccaabccbdddcdccabbcddacdaadbbdbbddbcbabbdcbbababdddcdbadabdbdccaaacdcdccdaacabbdbacdaadcbdaaacdbdadaccbaadadcaaababdbadccdaadbbbcdcaddddbddcbdccdbaacddcbdbcabbcdcdbbdaacadadacbbdcddbdddbddcaacbcbabddddccdcabdaaacabbababdadddcbdbabdcbadbabdaaccdcccbbddabbacdbbdccdddbdcdcccddcbbbccbbcabaabdbbaadbaacaaaccacbadacadbaadaacacadbcaddbbdaccacbccbbdadabdcabdddabaacbdcadcdcbcdcaddacdbdccdbadbddbdacbdccddbacdccccdbbbcacddccdaddabcddcacdcddaadcdcbadaadaaaacadabddcaaaaabbacbbcabdacbcabbaddcbcdcdccddccacaacabdbbccacdbbbbbaacdcabaabcabcbbcdcbcbdcadbbcbcbbddccabdbcaacdbcdbcdccddaacaacdddcdbdabbbdbcbbdadbdcbaaabbdacddddbdcbcddaaabdabdddbcbddabbdcbbbbcbbbababcadbbabbaabcccdcbdbcadcabadbdbccccdbcacacccddbaaaacabccbbcdbbdccdbccabccaaacccdcbcababaaaaccccbaccaadcddcaadbcadbaddddbdddabaacdddddbaadcbbdbaabccacdbcdcdcadddaccbdbbacdbcdadcaacbbaccbbbcdbccdadbacbdbddddabcadacbbccbdaccdbaabccdcbcdabbaaaadababcbdacbbdabcaacccaccdbaadcaaddcdddcdccdbcccbbcbadbcabbabbcdddcdccaccbdaddccabbadddcbcadbcaaaaabdddbbcddbbabaddadaaacdbddbbdabddbccbcadbcacacaacccacddbadcdacacbaabcbccadcccddcccbbdbaabccbbdddcacbacaabcacadadccccbacdcdccaadadcdcdbdbdbabaaaccabdacccdaacacdcabddbcbababdabbcdbcbaacccdadcdcbdccddbddbbbccbaacacdcacabdccdcdbbabcdccdbacbabacaddcaabddcabbcbcddabdaaaacadcabcccddbabcbabacdacdadcbbabcdaadcbbdcacdbcddcbccabcdbabbccdacdcacacaddcbccbdabacaabbcbadcccccaaaccabacadaacdddacacbddbdacccdcddabdddbbaabbbbcdddcbbdccbcbdccdbbdadcdbacaddcbccaaaddbaacbbaccddbcadabcdbdbbdcbcadbadcdcbabacdbbacbaabdaddcdbcbddcaadacdadaccdbcdaadddacdaccddddbdcaddbbdddddcbacbccdbacbaaaacdcdcacdcbbddbaaadddcabcdcaaddcddabdbaccdaaddcddbbddcbbbbdcddcdddbaadcccccdbddbabbddcbabbadcbcaaaacbdddaddddbabbbbbcbcbdcacbddcacbddbcdccbddbadddaababbabbbdbbdccdaacbacacacdaaadcacdbccacadcbdacbcdcbdadaadcbcbcbcaaacacbdcdcddaccccdcccaabcdccbdbbdbcabbdbddcadddacacbbbacddbbcdbdabdcbdddbdcaaadabddacccbcddcaaacaabaabdcaadadbbaabdcaacdbaddcccccbaaaabbccdcabaacbaadaaadacdbadccbbadddbaaacabbacbadbabcadcabcdcbbaccdabdbbdddcaddbcccbbdaddcabacbadadbbdcbdbbcddcbadaacddcbbcbcdadbbdcddccbdbddbbbbddbdcdcabdacbacdbdcdddabbcbdcdbbaacccdcdcacabaaaabaadbddccccabaabadcbbdcbaddbccaababbcbcdbccccaabccbbadababaabdbcacbbabccbdcaadacccdbaddbaabdbbbabdbbaddbacadaacccbdcadcdbaccbcabbacadbadccbccaadacbadddcdabdcbbaabdbdaccccdaabcadacdaaaadbdbaacbdccdababbdaccbdddcabaaaccdccddabaddadadcdccabddacdcabbaacbadccbadcaaababbddccaadddbaddabbbdacacdbbbbddbcccccacacdcccdababccabdacbdccbdabadbcbcbdbcbdbcdabaaadbbdaaddacaadcaaddbaaaabccbbdababdddbcadbbbcbdcbdacddababcacabddddbdcadcdabdcbacaccdbddbabcddccbdbbcbccccccbbcccbaadccdcdccdcdddbcbadcdbdbdcabdbacdbacddbbabbddbdabcdacabbacaaacbdccbdccacabdcdbcbdbaacdccaaadbaadcbadddcdbaddacbbcacdccccaadbaacbddcbbbabcaadaadabcccdaccdddccdaddadbbdbcaaadcbddccbcdcbdadabdaccccccbcdbbaadccacbcbaadbbdaabacbbabcbdaabcbcbccadbddccdabdcaaaddddcddccbbccabdccadadbbabcbadcdacabdcabcdbacddcdcdddccccdbdcadabdcdbbbccddddbcadcdaaabdddaaaaabbbdbbbcdaddaadaacbabcdddbddbcdccbaacaacdbbbcadbbbddbcbbbddcabababcadcbdcacdbcacaccaaaaacaadbaabadcdbaccabcadbaaccbddabccbbcddddcbbcdbaaaadaababbddadbcbbacbdddbdbdadbdbbddacdaddaaddbdddaabaddaddabadabcbdbccbcacdccdbcbabacabbdcaddaddacbbccbdacbaacdbcadbdbcabadcbbaacbcadababcabdabbaaabaaabadadbddcddaddbdbccbdcdccaabddcaaaadddababcabcabaddbdadbbdabadcacbcabaccdabbbdcacacccdadccdbcacabacadccbbcaaaadadcaabdbdacbddcaacbaccdddacdaccbaabbabbabaaaccbddadbcabdccbccdbdacabbdbdbaacdcbcabdccaccdbbbdabddbbcbcadbcadabbccbbcaabbbdbbdcbcbdaaddacbbbdabddaabbbdcccbbacaaddbcbccdccdcdaccaabbbbdacbbdadcadbbcccabbaddbababcbcccddadddaabdbddbccadcccddbbbddbbcdbaadabdbcacdcaaacabbbbacacaabacadccdccccaddaabaaacdabcdcdcacaadaacaadbdcaddabcacdacbdadacacbcbcdcdcddcddabccccddbddcdaddddaaddbcccabcaddbcddacbbcbabaacdaabadddaaaadbbcadbabbaaadaabcbcdacadabcdcaabacdbacddcbbbbbcdacbdbacdacdbbdcacbdbdabbcddbcacdaaccccdadcbccdcbcacdddcbbdacabaccdaaaabbadddaccdbbcccbadcaacbbbacdcddcadcadccbadaaaccaccdaabdcccccdcadbbdbdaccddbbbcacbdddcddadbbcbdbabaccbbddddacdacdcdcdbaddcbcbcdaccacbdcaddcdbddcdcbaadaaccadcabddcbddbddaabccbcbbddcdcccbdcdbabbdbcadbbbbddadbadadabccdddbcaaaaabadcabcabdacabddbddadcbdbdcbddaddddbdccaadacccaccaabcaccadaccccbaccbaddadcddcddcacabbabaabddcaabdacaacdcdccbbabadacabbadcdcdbdddacdcaaddacbbbdadccabbbcccaabdabcbddbdbbcbddcadbcddacbbbdbacbcdabacbcbcabdadacbaacccdbddccaddcbbadacadbcdcccacddaddaabbddcbababbddbadccabcabacccdaaabbabbbbbbcbdddadcbaabbaabdadcdaccacacdadcabcbacbaccabbadbaadacbadbbadcdddaccadacccdcadadbabccadddbbbaabbacbacadadcddaaacbdadbdaaccddbcbcbcacaaaddccaaadcbbccbcadcabbabbdddcababdacbdaaaccbbbadbbacadddcbdbacbaadacbbdbbacadcaccbbabdacdbaacdbadcbadbdacdadbcdbbcbccdbacadadbabcdcabcbcbbcabdadbdbbcaddcbdbbbabbaccbcddbcacdabdddaabbddbdaacacabaddcaacdabbdcdaccdadcdbcddcddcadbdadabddbbddbacacaabaabdbcbbdcdbcadcacabbbcccdadabccabaccbdcadbaddbbbcabaccbcadaddddaabccdcccdabdadbbddcabbcbdabbbaacdcccbbdaddacbbbbcadbbdadcacabdacccbdacdcbcdcbabcbcdcddcadcccadccdaadbccadbccbcdaabcdcbddcbcbabcddcbdcdbcddbdcccbadbaabccccacddaaaabcbdbdbcdadaacbdbccdacabbcaacdcbcadcabaacaccaacccbcdabadcaddddcacadaadabcbdbdaadcaabddcbbbacbbbacbbbbcdabaadadadcadbcacdcbccbcabacacadcaaaacccababbadaddbabaccbababacbcdabddaadacaaadbbccbbccccbaabbcabaadbacdbccaccaacadbdcdbaacaabbdcacabcaaccdaddcbacabcbbacbadbdbbdcdaacaacabdddcbdcdaddaccacbcbdcadadadcbbbcacaaccbcddabcccbbabbbadbdbccbcbbbddccdcccbdaccacbcdaadccdbddcdbbadaadbdcabcdcdbdabaccccbcadcdbbaaabcaacbdccddcabbabccccbccaddaabcabacbbaccbaaadbbaddccadcbadbdccdaddbddcdcaacbbdaabaddbacccabacdcddddaacbbccaaacbccadacddbdddbcbadacccacbaddaccbaadbbdacabbdcaaccbdcbcbbddccaacdcbbccbbdcbadbcdbacdcbcbcdbbdbcbccaaddcddaaadccacaadbccaacacdbcbadcdaaddacacbabdbddacdbabadcdbdbcccbbcdccadbcadddadadbcabcababbaaaabdbbccadbbcddbbacbbccbdadbdbbcbdbbadbabdbabdbdbbdbbabcadcbcbaadddbacddbbbccddbaacabbdbacbdbacdccaaccaadbabbdbacdacdbbbbacadbbaabbbacbdcdcbcaccccdcccbabbbcadcbdabdbdbbcacbdbacddbdadacdbcccdbaacdadabddaaababcbbcdbdbbbaddcbbabdcacaacbcabadcdccdbbbcaadccccbbdddccbcacbcbabbddcbbcdbabbcddbacbaaddadacddacbcdddacdaccbbcabbcccbdbbbdcaadbddcbdadcadaabacbaddcadadbcadcadaccdcdcbdaacbbaacdbabacdcaaaccbccabacabddbabddacdabbdcccaddacbdcbadcbbbcccdcddbddbabbdcbccbbcdbbcdbacccadbaabcdcacaddadcadbbccaddddbabbbbdbdcdbcdccacbbddddaadacdaddadadddbdabcaddcccdcbddcaaabdbacddbbacbccaccbacabadaccabbbbbdadcadbccbcccddbadadcdaaaaddcdcaddababbcbccacbaaabdbcdacaacbdbabbccdaaabdbbacdaadccbaccaababbccdacabbacacababcabaddbccddabbdcaddbadcccadcaddddbcdaccbbdbbcdcadccddabccaabcdcdacbacadadbaaddddbdacdcbdacbaabdbddaabddaacbbdaccdcbbddacccadcddcaacbbaaddbbbbcdcbadcabacdbdbacdbbccbadaccaaaacbcbaabbacacccbcadadcacababaadbbbcacdbddddbbacaaaabbddbcaddbcccbadddccdcadbcadadddabacadcbddcaadcbaadcccdbdbcdacdcdaaddbacbabdbabaadcbababdddadaccdbbddacccaddbbbaaaccaaaadcbddabcabcdacccccdacdcdddbcddaddccdbabddbbdcdaccdcccddbacacddccdaccdaababdabdccdccbbbbdbaabbccbdddbbacdadbcdbababacabddaddcbbcbadabddbadddaaadaacaadacbcbcbacdbbbbdbbbcacdabcdabddabdbdbaacabbbbcbdcacdbccaadaddbbccdaddbbacdbdcbdcbcddbadcdcdacdbbcdbbaabbbbbcadaadacdccbbcddddaadddbbdaaccadbbcbddcddaaacbcadccadcbdadbacaabbcdccdadcabadcddbcdcaacabcddcaabaddacdbbbcdbdbddbbcdccdbbdacaacaabcbbbbdabbbbdaddcccadddaadccbcdcdcbaadacbaccdddababcbdbacbababdcddbadacabbddacadabaddcaadaadbabdcccaacccbadbcaaddccbdbbbccadddddbabcbbcbaaadbdaadabbbdcabcbaaacccbbcdcbcdddbbcadacccdaddabcababcadbacaabdcccdccabdbbcabcdbdabacbadaacdcdadccdccaacabacaaccaaccbbabbaddbcdaabbdcddaadadbcbcbdbbaacbacaccddcbadacdbdbbcbdcccbccabdacdcbbacabddccdbacbccbaabadabcbdaadccabdbcbdddcadcddabbbcaadcbcaabacbaadabaababdabdcbababbbbccdcbacdcdacdbabcacadcdbadabdabdacabaccaaccbdaaddabcbdaccdaadccccbcdcdabadcdcdabcbcdabadcdbaaccdcbbcdccbdabdcadccdbaaadbdcdddacadadcccddcccbbdbdbbcaaccdbcaddcaaaaadaadaacdbdacaccadaaccdcadacdcaccddababbdabcccaddbaaddbdbadaabcdcdddaabcddbbccbdbddbddcbbbcbdcbaaaabbaadaddddbdcdccbaaccbddababdbdcbdcddbbcacbccdadcdccbbcadacbbcaddbdbdcbddbacbcaaaaaabdcbddcbadacaaabdacabcacbddaababdadcbccaabddadcacbaacacacabdbccbdcadabccdcdadbadbbbcdbdbcdacadccacdcbcdbdbdbcdbbabccaacdadaaadbcbbbbadadadbbdacdacadacbbbcbbcadbddabcdbcdbdddcbbbdcabbdbddaccbcdbcdadbddacddaccdbdadcbcdcbaccabcbbcccccabdcbabbddacbbabadbabcddddbdacaaddaabacbababacbcccdbcbddadbcddcdbabdbbcdbcbacbbbdcaacdbcbbacdcddcbbabacbbaddcdccddbdaacddbcaccacbababaccdcdcbdddcdabddbbcbccbaacababbcbccabcbddbdccbabbcabbaadcaccdabdbbccacdcadbccddbdbabbddcadbbaacabdcccadcadcdcadcabbbbabccbdbaddbbbdcdabaabcbccdcbbcbbbbccdcdadccacdadaaadaddcdcccaabcbacbcdbadcbdadadbcdbaacabbcddddcdbbacaabbcbdaababbccdddcbadbadbdadabdbcbcdacbdbadddcccddadcaaccabccbbcddbbaadcbbbdacccbbbabacbcbbbdadbaacdbabaccbdaaadbdddcaccdabdbbcbbbccbdaaadbcbddacdddcadbbcaddaacacccbabcbdbbddbaacccaaccbbacbdcdbaaddccaabcdbbaccadcbbcacbbddbcbccadcdbacaddaddbdbabacaccdcddcacbbbbaacbcddbdbabddcabcbbcacdcacacabbbdcdadbbadbadbacadaabaacdcabacaabcbbdddcbbbbbdbaaacabbacbcdacdaaccdbcacdaabdbdcbacbdddcbcadcdcadaacadccaddcdbaddcdbacdaddbcdaababcaccdbbdacbbcbdddaadbdddbdbbabbbcacccdbdcacabddcbdaaccaacdbdabddbdcdabcdcbdaaabbbabbacbaaddcbaabbdbcdcaccbaccbcaababdbccbaaadcccddccbbaabdbadcbbabbcacacccdabadbbccbabddabdddadbbbbabbacacaaaddbcbddabdaacabdbacdadadaaacacdbabadddccdddbdccaaddaaabcbbacbbdaabcbcbdddaddcbbbacadccaccdbbbdabcdbacdbdbbdddbcbbcaacbddaaddddbcbccaacacaacbcbdddaaaaacbbacbcdbdaacadaccabacdcbbccbaadbaabdbcbbabdadbbcdaddbdddddbcabbddddaaaabadaaabcaacbdcddbcbbcaabdbdcaadcbbabbdcbddacbdaccbdbbcdddadddbcadcccbcccbddcadcdacdaadacaccdbacdaabdbddbbbbbcbbcaacbabccdaabbbcbbabcacaacbcacdcaadddbdbadadcabaaacacadbdddcaabadbbdacbabadbadbcdbadabcbddaaccddbdbddcddcdcaccaaabbbaabbabacdcaacadacccabdddcdcaabacdacaacbcbdaadbaccdcdbddbbbcbcddcdcdbcbbbcdcaadcbccdbaabdaabcaaaacdaaccabbcbdbbddcdccabbababdcbcdaddccbcdbacbbdcdcbdcdbdaaddbbacccadcbcbdbcbddaccddbadcacccbdbbcddccbbbdadabbcadcbcbdddcadcaaaacdcccacabcdbacdbabddcadbdbdcbbaddadabcacbcbdadcbcbbbdbdaaabddaabadddbaaacddabacbbbaaabcdbbadcddcbccccdbcacbaabacaabcddddddbcddadbbbabbddcdcacbbbaddadadacbacbdcaacdcdcdcabbcabccbdbbdabcdbcdbbacacbbbccbbcaadacccbdcbbbacdabaccbcadbdcbcbdbcdbddbbdbdabbaccadcbacacbcabacbbcdbbbdbabaccdbdacbcbccabcabccccbbaaababcadcbcbddbbbcdaaccbaddcdabdcccadbadbcadbccacaccaddbbadbcccdbcadcdaadccdababbdbcbbadabbbcaddbababbccaabdacccadcdadcacabbbbdddbaddcddcbacadabbadddbbcbacbbdadadccabdaddcdbdbabadcacdccbcadadadbcbdbcabacabadaacdbacacaadcbbdcaaaabcbaadaddaadbcbcddbdabadbcbdccddccdccdacaaadacbdaabcdaacccdaddbcccaddaddadcbaadccabbddadabddddabdbabbbaaccacbbdbaadddacddaacdddcddbcdbbbddcadacdcbbcdcacbdcaddcdbaacdcaccddbdaccdbbcdbacaabaadadaabacdddaacdbdacdadaddabcccccdbababdabbbaaacaccbdabbcbcbbaadaddddbadbababbadabcbbcbaadcccdddabbacdcddcdbdcdaacbbbadadaccdaaadadbbbcbbaaabdbdadaaadccadacdbabacdacccdacbbbdccaadaadcccbbadcbdccaabdbdcdcdbdddcccaaacbaabdcccadaccbbadcdccdadcbacadbacdccbabcbaacccacdbacacbcaddbcadacadadaadbcdccdbabdbddcdcabdaabbcbdccbcccdcdbababaccbddbaaadbbdaaccbcacdaacdcdddaccdadadbabaabdbdbacacbdbbdaccaaaaddbcbbbbdaccdbabcaddabcbcacbcdbdbbbcabaadaabbcddddadaabccbaabaadbcccdbacadcabadaccbabcadcbdbccaacabbbcdabdbacababcdddbcddbdcbbbabcacacbddcdcbbdabdaabbccadbbcccddcbcdcabddcdcabdabdacbbdcdcababbaabbcdcbdcacbdccdcaadcabbbaccabdadcbbacabddadabaabccbddbcdddabcadbbcbaabddbadbaacbcddddbadbbdbbccbdddaabdacddbccaccdddacdccabbacdddcbdccdbdcbabcbccdbbabadcbdadcaddddaddababdbaadaccbddadcbabcbaacbaccdccccbbbcbdbcbacdbdbcbbdbcbadcbddaaccccbbccbdbdabadbbbbcccdccddabbabcbccaadbaadcaddaabddcabbacadabbdddddabdaaabcbddbaacaccbbdadbddabdadabaacadbcbccdadbbbacbccdcccabcbcdbbbbccbddabdbdabdbbababbcbcbbbcaccadddcccacddcabbcbdaadabcacbcacabcdbabcdababccbbcbdbbdcababddacbcbdbbcabcdabbdaaccacacbdccccbcaaabbccbbbbcbdcbacacabadbadaacabcddcacdadbdaadcbbbbabaaaaccccbccdbbcacbbacbdcdbdbbaacaabbdddcaaadadcaaccccacdbbcbdaddaabddcbbccbbcdbcadcabdcbddcadaabcccbcabdddbbacadabbabccdcdadccbdacadbcbcbbcabbcbadadcacbabcaaadcdaabbcccbdcddccaaabbaddacdcdadbdcacadddcdbcdaccccdbaccacddbabdbddacbcbcbcddcbcabababbbbdbdaabdcbccabcdddabadcbacbadacbbbcadaadbdddbacadbbacdaabddddaaacbaadacabddacaadbcbacacdadccccbdccaddcaccacccbdcdccbdaacbcdbcdabbbadabdbbabcbbdcdbdcdcaaccacdcddaaddddaccacabcaacadbacacdacabbdbaabacabdabdddadbbdabcaccccbcabbacdbbaccddbaadcaacdccadbbacacacccaccdacdccdaaadadabccddcabcdcdcbdbdbdadcddbbacadbddabaddbbcacddbbadccbdadcddddcbcdcadaccbaabdbacadbccacadbbaacbaadcaddacadabacbcdbaddcddaadbaabadcdaddbdbdbcaabbdbabbccbcabacbbcdbbaabcabbdbaacdadddadbccbddadacbabddacdbdabbdccccbdbaadabacabcaacbdabdccbabbdaaddbbabbcddaadaabbadabdddcbaacbddacdadcbccdbbcddddaaaabaaddbddbbddacbacadbcbadaaccccabbccbbbdaaaddaddbcbadcaadcddccadadcdcddbdacacadbcabdcbdbdddbbbbcbdaaccdbbabcbdadbdacaaadabacbbacdbcadbbbabdcbdaaacccabbacbbaabbbbadbbccadcbbcabbdadabadbabbadaaadabdbcaccbacddacdacddbabbbacdbcdabcacdbcaaadbbcccaddbacadddacdbadcdcdcccdacdcbdbddcababbbcababbacdcdbbabbbcacaadbddbabddbaaccddcbbdbcaabbdacbddacbaccbdabbdadbdbcacaaaddcbdadaaacbccdcaaccdaddadcdbcdbbcaccbbbddaabbadbacdadadccdcdcdbcbabdcdcbcdbcbabbddcbdadaacddbccbacdbdccdcddddbcaadadddbcbddacbadcababcdbdabcbdacdbbcdccccbdaaadcbacdcadcbddcbccddabdcaacccbdccbcabbaccababadcaadbabadcbdaadbaadadbcbaadaccdcdcbdbabdadbbbbbcdbdbcacabadaacdbbbbacdadaaddaadcdacbbabcdaaabdbdcdcdaacbdcbbccbdacccacbbcdabbdddabbcababcadacbcbccadcadcdccdcbbbdbaaadbcdacdcdcddcbadbbacaccbcddbbcdbdbcacaacdbbbbcccdbdcdbcaddbdadadacbdddaaccbacdbaaaccadddbcbabbcdcadcbacbcdccbdccaddcccbbdccbbdadbbcbdccbcdbdbcaadccaaaabdbaadacbacadbadaacdccbbbadcaadacbcbcbbabccbddadabadddddacdccaddaadcababcdadbdaaaaccbcdbaaacaababbdaccaabbdadaaabcbcdbccbabcddcdcdddabbabaccdccbddcdbaacbbcaacadabdbcadcdcccacbcdbcbabbdcbdbccbdbcdabdbbcdacdaababbcccbbcacbacdbccadaacabcadbacacbbccaacabbcdbddadacbcadcccbbacaabacacaacbddbbbdddbcdcdbaacbcbbbabaabbdcdbbacbddacbddbbddddadbcbaabbbcbcaabcaccbcabccdbcacbcacbdacbbbdcdaccabcabaadbabbacdbdbbdbcadaaaaadcdbbbdddacbddbccacbaddccacdccbccaddacccbbaccdbccddbddaaccacdbadaabdbddcdaaccbbcdbcdcccbcbacbcaddaaadcccdabbddcaaadbcbcbccaabcbccdcdbbbbbaccdccdcbdccdaccddcabbaaaabcacacaddcabdbdbdbcbcbddcaccbbccdbabacbdbacbbdbbddddabacbbdacbdbddcbdbdbddbaadbabacabbcacacdabccbcccdbabacdadbbcacdddacadaabcadaaacddcbadcacbbbcbdddcccdadadcddccddcdacddcbddcbaadadbacdcbddcbbccdcccabcdaccbadcacababdbdacdcdbbcdbcccbcdbddabacbbacbbbdabdcbbdbaaaacadcdddbbbacabcacaabcbabcdccbdcccdacbbbaaddbccbacaaccdcacbaabacadaccabbadacccbdbadcbbccbccaaacbdaabdabbdacbbbbaaaaddcdbbcdabbaadbcbcbacababcdabcdcabdccbbcacdcadbdbdddccdaaddbbabacdaabbcdccabcbaabaaacaabcbbdabcaaadaddcccaadcbcccadbaccaddadcdcdccdcbabccaccbbaddabdabadabdcdacddaccaabcbbcacaabadccdaaadbcbbadabaabddcbbbaadcdccccaccddccaaabdbbccdcaaabacccddcddcaabbcacbbbcdadaddbaabddcaadbbabbbccbdaaabaadcbcdadbdcccdccbcaababdbcdadbabadbddcdacbcbdbaabddccaaabcadaddbcccadcdbabdccababbbbadcbcbdaadabacabbdcddbdbbadcbddcbdddaaccdadbdcaaadcccbacbdcdddadacacadaccbaacbddadbbbbbcbbbcaabacbdcdcdbaacadbdcadcdabbbcabdbbbacabbacbcacddcbaabdaadacbcdbdabdbddbcaabbacacabbcbcdbcdcddbdbabcdddbbdcccbdbdacbbadbadccbccbdbdbdcacddaaccabccaabdcdbccacacbddbdbcaaddbaccccadcdcdacbdccbbdadbbdcdaacbabadddddbadcacdaccadbacaacbbaccaaaabbaababdbcddacadbddcdcdcbdbbdbcdaaabdcadccadcdabbacdabdcddbdabbbddbcccdbbddbabbdcccaabddcacadbdbcdabcbdacccdabaabbacabbbbabacccadcdcadcdaaccaadbdbcbbcdabbbaabbaabdcabbaadabadbabbaddabdcabdbabbcaddbadabbddddbadbbaddbbbcccdbcbabadcaaaacadbcbcbcdaaabaadbbdbddacbcbbdbcbcdcdcbdaabdccbcccaddcabbdadbcadbaacddddababccbddbaddcbacadabacabcbbccccacdbcaabdabddbacadbbabcdbdbbacbbddbcbbcddddbcabdbbbcadbadcdccaaabccacdcbccbdcbdbdbddcadbcccbbbcababbaadcbccadcabaacdcaaaddacababcbbccddaabcaaccaadbbdbaaddbcbbdbcdbdacaaddadbbadddbccdcbddcabcbbbaccbbdadbbdaaddccaaadcdcaaabdcbcaabddcdddaccadbccacaddbbbcdbabbabdbddddadaabddbbbacbdbcdaaaaddacacaccddbaadacdabdbabccbcddddadabcabcacbdadbdacaddccdabddabbaccbadabbdbcaacabddcbadcdbbcbacacbcccbbcdccdababbaabbbcdadbcdcbdddcbbcbbabcabccaabdadaacaabadbcbbcbadbcdddccbbcbaddcaacbdccacbbdadbbdcddbaccdcaadacaaddbadbaaaacdcdbbaadbdbdcdaccbbbcbddddaaddccbdadabbadcdcaddbcdadabbbbabcbddbaddaacabcbdaccddaaabcccbddddcabcacbcddbccdddabcbbccaacbddbbbbdbbdacbdccacacbcdacccadacdddbadbdddaaddadabacbdbbccccabdadaabcdabdbadbcdbabcbdccbababacbaadadaaabcadcdbabcadabdacabbbabdbadddddcdabaccdbbddcdbacadbbdbbdcbbbbacabdaccaaaccbddadccacbaddddadccbcbcbadacabcaaddbabbaabbbbcdaacabdcbbbccccdcdcddabbaaaabcdacdaabdaddaadadcadbdabadbddbbbaadbdddbdcbcabcabadadcbbcabcdabccddccacddcdbbacdbbddcbadbdddcaddbbbccdbacacbbdbaadbacbbadbdabacbcddcadddabcbacbcdcddadcbadadcdddbccbaacabdccacababacabdcbcdaabcccacbcaaacbbadaabdccabbaaccaccbdbaadddcbbbbdbdbabddccdcacdbbadbcaccbbacbbbcacbdbcccdaadbbabcddabadcbadbcccdbadddddbbcaddaabcacbccadbaadcaaddddaabacdbbbbbdacabdabccbcbdbabbdbddddbbcdcbabbacaabbaddbaccdddaadccdbddbbdababadbbdcddccbacdbabcccddccdaadbdccdadabbccdacdbbbacaadccabcdcdcdcccadcabccadccacccabbdbddbaacbbdccabcababaabccccbdbaacaadcdcdabbbbabadabcbcaddaacdbbdbdaaabcdaabdaaaabcbdccdccbbaddddcdcddccdbbbcadcacacaddbcbdabcaccdcccacdcdaddcddddaddacdbcbbcabaaccddcdbdcbcdacbcbbbdbcaadcdbbbdcccbbcbcbaaddaccababdbdcccdacddadaaddacdcbbadadbdadbcdcdcbbbdccbddbcdbcbabdbbdbbcadaccbddbaabcbcaaacacbcaaccbcdbbcbbcaccadcbbbccbcadbdcbdacccaaddabbcadcbacdcabaaccbbcbbacddbcaccbdcadabbdcadadacddaabadcaadcccdbbaaadaadcaaccbbdaadbbdadaddbbabcdbcdacababbbadcdccacaacbccddcdddbccccbcacdbabadcaaacbcbcbcccdcccaabbccbcdabbcabbbdcacaadcccaadaccdbddcbbdbabbdddbdbbadabacdccdddddabbadaaddbbadbcddbbbdbdacadabbdacbaadddcbccabcbcabbbccbddbcdccadbaacddbdccaadabaadbabadbbbbccaddaddcbcbcbcccbcbccdbcddcbddabacaadcdbcdaabdbcdadaabbcadcccbcacdadbacdabbabdaaccbbdbabbccdcccdbbacbaadbdcdaabaabbabcdbaabcddccdcbacbcdccababbbadbbbcbbdabdbcaacdcbcddddcddcccbadabdacdddcdbbbaddbabddaaaddbcbccbdabcabbbacbcdaabcacaadbcbabcdbbdadcadabbbacccdbaadbacbdbbcbccbcabdaccdbcaabddbdcaabbbdadabdaabbbcaabcbcbcdccbacadccbdadbcbbbadbcbacaadbcabdcacaadcdacbbcbccbaabbcabccddabddacccadbdbcccaaaaadcddccddbdbdbbdabdcdbacdcbdbdccbaabcdabdadbaacdaaabacddaaacaddccaccaacbcccdacccbccdcbbbadabdaddbcdccaccddbcbadbbdcdadcbcdcddcbdccbadbccddbcdcdbbbbabaacbcaabcaabdbcaddbdbbacbdadabaaaddbbbcdbbdacbdcdcdbdddbbcbddacabbdbdaddbbacacaadcabbaadcdcaddcccddddacdddaaabacdbdcadbdbacdcbdbcbccabdcabaddcdcacbdbcbdcccccabcbcddabbcaaacaddbbdddbbaccabbabacbcccccbadbcacabcaddaccdccbaacabcbcdcdcbbddcdbccdccbbdabdcbaadacbbcbaaabccadcbadcdadbddbbbcbbbbbaacaacabdcdcdcbcbadccacdcaaacaddcaccbababcbcbcdcbabcbcabadbccaccbbaaaacbabbbdcaaddaacddcabbbdcdaddacdcbaadbbbbdaabcdbaccbabbbaaabcddbdaccbbabbadbcaabcabdaaddcdabbccdbdcbadbddadbbcabdccdbccccbccacdacccbacaacaccdaaddbbbdaacddadbacacddcddbaccbdbdabadaabaaadbcabdadbabdcdaccddadabaacddbaabcacccbdbbbabbdcbddacdabaabbdbabdccbbcddccbcdcadadadadabbaccdbdcbacadbdbabbcddbbadabadcababadcadadcadabdaadcbccdcbddacbcadbdacbddcaacbadbcbbccabbcdbadccccbccbdabddbbddbdbdadcabddaddbaddaccbdaccbaadabcdbbbdbcddacccdcccbdbaaacaddabcddaadddcbbdcbbcdcddbbcbcbddbbdaacddbdcccdaadcacadcdadbccddababdddbdadddadbbcacdddbdbdacaadaddcbaadadcadcccacddcbbdddacddcccdbcccdaaadbbcbbccddacbacdcadaacdcbbbccadaacadcaabcbbabaadbbbdcdcaddbcabacddbccdddcdcdbdddcddccaaaabdcdbbddadcabaadaabbdadbddbdccbcaabccdcbcaddacddabdcaaaabdbccbcdbcacabbdccccaacdbaccbbcaaadcccaddaadbcaddbbbdaadddadabdcaacadbcddbbcaababddbbabacbabddadbabbabcdbbbdccabccbabbdaaacadbaabbacbcbbdabbdbacbbbacbcdcdbbabccddddababccadbcbcddddbbcccaacbcaccbacccdacdcdbcacccaddbdbcbbaccabcbddaabcaddcccdddbdcbaccbcbdaddbaaaddaccbcdcaccbddaadcdbdbdbdccccacdbcbcccabbbcdbdcdcbccabacabaabdabaccbbcdbbacddbbabcdcbababdccadcccdbacdbddbaacdcdbacbccbdccddddddacdcdacadccbcbbcbabdccbcbdcaabbaadabcddddbbcacababcaacbbaacacbdcadcaadadbccacaabddaabadccbbbdaadadbaababbaabbcabcaacbbaabdaaacccabddaabbcdcbbaddacaaabdbacbccabccbcddcbadcbcaddcaabbddbdbaccddacdcbdbaaaddcdaacbbbadcadcaaaadadddbbabbabcbaaabcdabdabcdbacbbbdabbcddcabcbcadcbcddcbbdbadacddddaacdabdbbbbbccccdaddccccdbcccacbdbbacbcddbdaaadbdcbccbcdbbbbcaccaadacaadccccbddbdaabdbcdcabbcadabccabddccdddbcbdccdacccbdcadcbadaacaacbbabdbccbcdcdacacdbaaaacabccacbcaabcbdbbdbcaabcabcbabdabcddbcacadaddaacbabdabcbdddbccaadcbdcbbddaaadccccacbdabcaddbbccababdaccaacdbdbdccbdbacbdbaaccacdbdaccabbcddccbccdacdacdcdabaaaccbddbcbbbadddaccadbadbdaaddbbdacbaaacccdabbdadbdcccaabacaadcadaddbacbadbaacccabbcacdcaaaadacadbbaacdbbcdddbccdcabcbbcacabdcdbcdbcbccdddcbddbcbdccacdcbdabcabdaadcbabdccbabcbdbbbbbbadddaddbdabdbaabdcbdbcbdaddacddaabcdacdacaaabdbbabbcdccbbccdbcdacaaaacaabbcccddbdbcbbabaaabbcaababbbdcbcccaaddbadcbdcdcdbdadbbccccbbbadcadabdbdcddcaadccccaacadbbaababddadcdddbdddcccacbadcacadadcdadcbcbddddabbdbccdaadbaccaccaadaccbdbccbdccbdcaacbbabbcdacbdacacdadcdccacadabccbdcccadcdcdbdbcadabdddccbcdbcacabadbacaddbcbacabbdcddbcbdbbbaaccbcbaabddadbddbdadbcdadcccbbdbbdcbddaaacbaacccbdbadaddbddcddaabaaadcdabacbcacbaccdcacbbcdbdddbadbbdbdbcbdcbcaaddbdaadbdcaadbbdbbacbccdadcdacacbdcddbcbcccdcdddcbcbccbadaddaccbacabbadccaadaddcddcbccdbadddcaaaddacdddcadcdbbdcbcadccccdbdcddbcbddcdcaddadddacdddadcdbbacdccddabbbcccdcccaadccddcabaacaacbddabbddcdcbcacbcdbcaabdcdcdbdbcbcdacccbaaaadbcabcccdcccbcaaadbdccbcbbcacbdbdbcaabbcddbbaacabbadbcdbadcdbdadddaaaaadadacbabcaaaddcaabccbabccaadbabdccadacccddbbdbaadcdbddcadaadbabbccacdcabcddccdcbbbdbbabcabbdbdaddbdbdbcdcbbaccaabaadcdcaccdabbcbdbabccbabaabbdcadadabdacadacddacbabcbddabcddcbacbadcddaadbdcbccdabddacdadabcadacdcadcddabaadbdcdbcbbcdccaaaadcbcccdbcacdcaccbdbbbcccbccaaaacbddccabcabaccaadbbcddadbaddcdbaabdcbaabbdadbcdaaddbaaabcdaccbcbcbdadbcdccbcbcaaddccdcacdbacbabdcdacbcabadbcbcddbdbccbadcbcbcaaaacdadacdaadcbaccdcdbacdcacbabddcdacccadcaaddccdabbbcddadcaabadcaccbddbddccdacaaadadcccdcdbbbacdcabadbacaaaadadaabbbddacacbcbaacdbdacaabdaaadccdacbdbcdacbacbdbbbaccdcabbcbbbcccbbbddcdabcaabcbccbbaabbdabddcaadabbabdcaccccddadcdaddcccbddddabcaccdbcdddbaacccbcbbcddbaaccbcadaddddcbadbbbaadbcacaacadccabbddadbbdbddcccddcddcbdcdbcaabaabdadcbdcadccccadccdaabbdddaccdaddcdcdbdbbbdabbcaadbcabdcddbadbccabbbccdabdbddbccbdaccccdbadbcaccabcbbabbbbccbacadccaadbbadbcbcccbaccacbcabbbaabcbaaddcbccdccccbbbccbadcbaccccbbccadaaccddccdcbcaccdbdbbdadccbbaaccaaadadccddbcbdabbdbcaacbbadbdcacbbcadaccdaacbccbddabdcacdbbbbdabbdcbddbbbbdacbdccaaddcbabdbabacdcbacdbbdadbcacbdaababaadabcbbcdabcbcddbadbadcdaaacddacbbccccbacaababccdddddbcddcacccbdccbbcccaabcdcbddddbaadcaaaacabdaacddbbcaaccacadbadbdbbcbcaaaabdbaacbdddcaccbbdadabdddacadcaaadaaaaacdcbababdccabdbcadbaaadacabaaaaadaabddbbadacbcaccaabcccbdacdcacdcbdddbcdbadabbaabcaadabbbdadddddbaacadcbacbdbacccbcbbdbdcccdbabaaccdbdcdbabadabbdcbaaadcbdbddbbcacacacbacdddbddbdbdddababdacaacbdcabdacdcbadcccaacbaddcbdbdbbacadabcddabdbcdbcbaadaccadcbdaacaddbcadddacdccbdcdbcadcdcddcccccbbcddbdbbcdddccddabadbdddbdcdcdabbcbcdbadbcbdbdcdbbbadbcaddcdadbbcbccabbbabbdccaabaabdbccaddadbdcaacccadbaaacadbaacabdaabaabcdcdcdccbdccbdbbbdcadbadbccbdcabacccdbdabacabcdacdabdbccddaadddbabcabdaccbbdcdaccbddabdbabcccccbdbcbaccabcabbbacbcadbadbddddddbcabcaddaddcdcabcabccddbbacabaccbbbccbadaabadcbbadbcabccdadbcaccaccaccabaabacbaaababddcccbacbbbdbccccbaacbbcdbadbcbacbbdaccdbadabdcddcbbaabcbcadcaaaacbabcdcbabdcbaaddabacabbdbacbddcddaddabbaabbcadaadabdbbdccabcbabddbbcdabbbcbdbdbaabdacabaaadacdadadcdadbcbcacdcacbbbcbbadccdcdbcbdbdbbbabcabaaababdacadbccbabbddadbdbdccaccabdbbadbacaaaadcadcdcabdacbcbbabaaadbbabdbacddcdbccbbababbccacbdcccdddcbbbbadbddcdddbbcdacddbbdcbcccacaaaddcbbabcacadccaacbdadaaaabbdcababcdbadcdadbdacdacbccacdbabbddacacbadaabdacbcadacdbcadcddcbddabdcadbabcbacbabddacddadabbdcadbbccaccdbcabcbabbdcabadcaabdaacaaababacdcadabdbabbbcbbcadcbcabadadbbdcbcbabddbbabcaacccdbbdacdcbbaabccbcaccdccaadcbbbaccaaccadcbbbaacbadadbcdbabdbbaaaaadbabaaabbcddbccbbaadcabccddadcbdcdacddbdadbcaabccbaaacbbacbcdddcbcdddaddaddadcdbccddbcdddaaddcaddbdcdabaaaccbbacabaddbcdbcdccadccababbcdaccacbbbdcddcaabbbaabaccaacdcdcdacdbadbcbacbbaadadbacdcccddddcddbbcaabbdbabdaccbaddccdadabaadabbcddbbddacbacdbdcdacccdacdaabccbbcabccdbadcabdabbcbdbcdbdcacbacdadbdacbabdbcacdbbbdccdbadcaddaadababdcabaddcaccddcdbccbadbddadacbacacdabcabcdccbdacadbcdbdcaaacdcadccadbcbaccacaaabddbddcadbcdbcadabbbccabbbdddccabaaadbcdbaabbacdbdcabbddcdaacbbcccbbabcbcdabcbabdcbaacababbddcbbaabbaddccdbbcacdcaccbaccbcdacbbaaacddbcdadcadbbddcbccacadaabdaccadddbbddabaccbaabdcbddaaabdcdcbdcbcbcaacdbaaddbaababacbacdaadbcdaacaadddddbaabadacaaccdbadcaadccddbacddbbcccdcbbdddadcadcadbbbababcdaadbddbdadbdcccbdccddcccbbbabacdadbdabdaabadbbdaababbcdabcaaddaccdcdbccbbddaaddbccdcbdaccddadaabdccdaccdbbbcbcbcccacdbdabbaaaaddbbabacbcaacdccccaaccbddbdadcbadcabdaabdcdaccccaddaaaacdcaacaacbbacaadaddaddddcdcdcbcdccadccbccdbdccbddcadbcbbcddbbacddaadddbbbdaacacdcbabbbababdabbdabdddaaaadcabbabcbabddadbcdbabdbadcbabddcabdcccbbadddbbcadcddaccbaabbabcabadbcaabababdbadbbcddabadabbcdaccabadaadcdbccdddbadbcdbdaccadbbccdadbabcbaabdbcdddbbddaadadaacbdadbaccabdadbdbbabdcbcdacdcbdcbdcddaadbdcdccbbaadbbbdcacdccbcddacbdcdddacbbbacbcdbaccabbdbabbabdcadbdbddcddabcdaacbcbdaabccbdbdbacdcbcdabddbdcccacbcaccbaccaccabdcaadccbddabcbcbcaccbbdbbbbacbabdcbbcbbbddcbddbacbddadcccacdabacabcbbbadcdbdbcbbbabacbadddbbadbcdccacacaacdbabdcddbcaadaadcdbbadacabbcbadaddccbbbbadbabdcbbbacacdadccadaaaccbbdbddabcbcbbbbcabcaddadacabcddadbdadcbcdbcbbbcdabcccaaaacaccdadbcbabdcdadcabcacbaaddacdbaabcbddcddbcadddadbddbcdaacdbcccbacaddaddbacdabdddaddcdaacdcddadcacdcabcccbcbbbcabddcaaabadcdcabccaacbaddaddbcbcdbbacacbbdaccbdcacccbbdbbdbdaacdccaacacdddbcdacbbbcbbcbccdcabbdcdadcdaaacbbcadbbdbdadcdcddbddbbddadadadbdadcddadacdadaaccdababaadbcbaacaccddadddbbcadbdcdcbbbbddacdbdaadddabaccdbbccacbdbacdbcbcccdcbbaddbdbbbbdddccaacccacadccdbadaacbcdadcacddaadbccacacadcabcaadbddbbdadcbdcbbcbdaacdbcabcdbcdbcbadbbdbcdbcaccbaaccbddcdacaabdbaaddcdccbbddacbcbdbdaacdcaaabdbddcacabbcdcaaaccccbdbbaabbdcdadcbcaaaacadabaacdadaaddbbcacbaadbcbaacdaccccdbbdbdccddabbcaccacabbbcdaddbdaddccdcaaaddadccaacabaaadbbbcbacddadababcdddbbcbbdaccbddcabbadcccdddbcaccacdddbddbcbdbbcdcabccbcdbcdbddcddcbdcabbbbadaccddbdacaaacdddccbdcadacbabddcdbdcdbddbabcbaacbbdcdbdadbbbdccdacbbdbbdabccbaabbcdaccddbbbccbbadcdccbaddaaaddcbddbdcbcdacbbdadbcdbbcccaacbbabcadbabbdddddadbcdbacdabbccdddcdbdbddddaadccccbbcccddbcbcbdaaddcbbabdaddcdbddddaccaddcabdbacddacbbdcbadadbdbabcadddaabdbdbcaacbdcabbbdcbddacaddbcddddcccbbcabcaacabbcaadbaacbbaaaddaccbccbacdacdcbcddaddcaddabcdbbdbccdcbbabaaddadbabddabdacadcdcdbdccddbbabaadbdccabcddadabddbaddbcadcbacabacdabbccacdcdcadcdabaccbbaababacbcddbaacdaaacccdcadddaabccabcdbbbcdcbaaaddddbbcabcdaabbccddaaadcacbcbcbbdaacbcddadbbcccbbaacabcbacdadaccbbdbccdccaacaacadbdcdbddadbdccdbbbcdbadccababbcdbcbcdccdbadbccacabbbdadccdabdbccbddaadabdddbddacabbddbdbaabbcdcddabdacbcdbadadacdbacaaddaadbaadbbbdabdaabacddbbbdccccaaccddabddddbbdacbdcacddaddcdcddcbbdcadcaaaaccdaddaddbdaaadbcdddaadacabdadbbcabdcccbdcdcacaaadcdcccccaacaacdbadbcdabbaaccacbacdccadcdbadabaddcbddcbaacbdccaddadddaabdcbcaaadbbadbcadadcccbdbccccbbccbcbdbbcbbdbaccbcacaaacdbbccdcddabddacadddbcbcbadabadbcadcbadaaabcdcbaaaaacacbdadacddcbbdbccdbadccaccdaadabadacdadbaaabbacdaddabdddacccccdaddcadcadcbcabbaadbccbadbbbcdacbbddcccacdcdacacabdbdbdadccdcdadddbbadaaddbbccadbddbbdaddbbdaddabbdddddcdcbdccdacbcbcbbaaccbdbcbcbacbdaadcbcbcbdddccccccbaaacabdcbdbaadcadbddadcbbbcdbdbacabbadbabaadcababadaabddaadbbcdaddabacbdcccacdadacaaadcaaccccadbaacacbcdacbdadbddbbabdcddbdddcadcccbdbacdcabacacddcdbabbdbaaccdbcdbccdaddcbadcbddbdbbbcaabbcbcbaadcbdacbbcdbabcaddccaabcdbddadaccaacdacaaacbdbcddbaddccccdbdbdabcadccdadbadbaacaaadadbbdcdcccdcdcbdadbbbcdbdbdbddcdacdaaabaacaaddbdabbdadaacbabddcadababababacbbcddadaadabbdcccdbdbacdbabdcabdbaddaaaaccabbdabadccccbdddabcbaadddcbabbbaaacdabacaacbddacaaadbdaddabadccbaaccbacdabdadcccadacaddbacccacdbaabbddaabdbdcdadddcddcbaacdbbcabdcbabdcacaacbcaabcddbbbaababdcbdabdbbbaddddbbabcddcaddabacdadcacccccdadccdbbaabccaddabdcadcadddbdadaabdcacbddabbcaadbcadbbadaddbbaddcacabccbacbccadddadaaadcbcddcbdcabcdccdbcbdbdadbbbacbabccacdcbacddccbcbdbcababdddaccabccddbbdddccabbcbdabacacaadcdbbaacbacdaacaaddbddbddbadaddadbdcbabcccccabadbbbdbadcccabdaaadbcadbcbaadcabaaddaccaadcbabbbacbbbbaacccacadacbdddbbadcccbcdaccabadadadbdddcacabdbacbbbdcacbcbcdcbbccacaacbcbbbbbaaaaacbdbbdddacbaadbcdccaabdddbbbdbdcdcabcaccbdbdccbdacdbccaababaabbacccbbdadbacdcbdbbcccbdddadcccdaadabdcbdddbcdbdbaabcacbbbcddddaddabddacdbbbcaddcadcddbcbcccaccdbacabbcadaccddcdadcdddcdbdacbdcbbbdcbaaaacbaabdbadadccddcaacdccadddcddcddcdbaabcbdabbbcdaabcbdcdddabbddbcdaadcbccddcbdabcabacddcaaccaacadbcdccbdadbbcdccbcbcbcabbcdabdacdaabcdccbdbaabccaacdccdcacbcbbaccbaacddbacdccaacabbcbdbbddacbbabdbcccdcbccbcbacbbccdbabbdbbdccbbbccbadcddddbdbadcbbccbdbabdabbbcbbdcccddaadbcbcbaababbddcdabbdabbdaadacbdadbabbacbbdbccbadbabbcdadcbbbbccdcbcbabaacdbbdcbbbbbaabdbbcdabdaacadbcddbddadcbbbabdbdcacddcdbabcdcbccadcdadcbadbadaacabcbbbbbbbccdabbacbaacdccbdcaddbbcacadbadbdcccccaddbdbadcbabcaabcabcccadbaabaadddabaabcaabbababdacdabbccdbbddacbbcdccdbbbaccddcdadbdaacaaacacbbadddcabcacaacdbdbddbdddcabbdbacdaadccccbdbbaaabbdadbdbbdccacaadccddbaaaccdacdacbdcbcbcadaabdabbcbdbdccbbbdcdaaccacbbaabbbcdacbadbadbaccabaccdcacbdddcbaadcccbddcabdadddbacdbdaacaaabdbaadcabcbaaddbbcbbacabcaabdbbaabcbbbccacaacabcbbcbabcbcdadadadbacabdccccdaddcdabdccbaabdcbccdcbadbabbdbbccdaddabcbaadbccacbbdbdddccbadabbdbbdddcdbaaddcdcacdddbcbcaccdbabccaabcaddabcbcdcacdabbbadacacdcbdccdcadaacddaabacdaddacdacbdaaddabddabddaaaabccddcdababadcaadabadbcacbabcccdadcdcdccadbcdacacdaaaccacabbdcaacbddadcbaabaddbbdbabdbabbbdbcaccdadcacbbccbddababaddcdcbacaaddaaadadacbdbddcabdcdaabbabbbbbcabccbbdbccddbdcacdadcbccdcdadcbcbaadaaabaaddcdadcadcadacdcdcdccdbbbbbbddcdbdadadaadbcdaacccbaacdbbdbaabdbdccbddcadbcdccccabdbacadaabdcaaccbdabdadbadddaaacbcaabbbcddbdcadadddbbcbbbadcccddbbacbaddaacccaadbdbdabccabbdddbadbccabadabacbbbabdaddbdcdccdacdacdbaaaddacbcaacbbdbcdbcbccbbaadccddadcadddcbdbdcdbcabcbacaacbdbbdacbabcdcbcdbcddadbcdcbaacbbacaddbacbbcdddaaacdddbcdcbcdbbbabdaabbdabdcdbabdbadcbccdddcbbdbabbccccadcabbaacbabacbaddcbcbadababcadccdacdddcbcccdcbacabdccbaddcbddcdddbdadaadbcabddbbbcddcbaacacbcccdadbdacabacdccdddcadaddcdcabcddcbdcbdbbdcaadcdbbadabbdbbcbdcbaaabdcdcddbdcabdbcdbdddabdbcdaacdbabbcbaacdcdcbcdcdcaccbccabdbaddabdccddbcadaadadbbdbccadddbccaccabddaaccabdcbdcaabbcadacabaaaacdaacadcdcdabdcdbcdaddadbddbcdaddbacabccbbbabccccddbbbbdabbbdbbddababadbaabbbbadbdcbcababccbcacdcddcbdaabbdaccdcbabaadcbbcadccdaabcaaccaadcbdaacbabcdabdbbaaccbacbbbbaabcddbcacacdbbbddcadbdcbbbbcbbdbbbdbdccaaababacaababdcacdacadcdacdaccbddbdaaacdcbabaacaadcbcdadcdacdabcddcadbdcccadcaadbdcbbbdddaaabcaaddcabdaddaadbdaadaaaaddcccccbbcbcdacdbcccdbdcbcbdcdabdbcdaabcabcbdbbaccccbcdaaccbbdbacdcbadcddbdadcdbacbdadaaacddabbbcabcbcaaadbadbcaaccdcaaccbcadddbcaaabcdccdaacababbdbaaccbadaadcbcbbdcadbbacdcdabdcbcdbddbacbadbaacdaabcbcabadbacaaacaacdcbbcdadbcabaacbaabcccadcbacdddcbdadaacacddcdaaaadacddbcbcbabbdbdbcdbaabcdccdcaadcbcdcdbadaaabadcbdcbcaadbcbdadaaacaddbacadadcabbdbcabdcaabacddcbbcbddddcaddbbdccccbbbdacbbcacbbacccbabcacbabdacaaddbcddbaaaababadabcddbbccdbddaacbaddbccaaabbacbdcaabaacdbbddbddddbbacbbcacdacbbacdbcabaabcaabacddbabcadadddbaddabcaabbbcdccdbacbabcbccbccadcabddabbcbabcabcddbbacdadbdaabdbcadababbccbadbcdccadbcadcaadcaddcdccadcdcbcdaacbbdadbbcbcdaccbcaaadacaacaaddbcbdbbdbaddadbbdacdcbaccbcbbdbacacccacacdaccbacbbcbdddbcdaabbbdbdadcdaacdccdddabadbaddacdbccaabccaacabbddaccadbdccddbbbcbbdbabaccbbcaadabddbaabbdbbbcdbbbdbacdccdbbabaabbdaccbabccbaacbcaadbacbbbdbbacaadadddcdbbaddcbcaadacddaadbcabaddbaccbdacbdbcabbcaabddabcbaddcdcccacdbbcabccaacdbdabdaddcbbdaadcbcccabdddbaadaccaccdaacacabbbacbdababdccddabbcabddacadddaabdbbdbdddcdaaadcbdcbcbbdcccdbacbbcabcddbcbacccdccccadbcadcccdbcdaccddcbbcadbdbbabadabbddbdadcbbadaadbccaadcdacbbadadbbaabaabbccdadadbaccbadbdadcdcacdbdddbadcdabdbbcdcbbbcbadcadccdcabbbaabcccacbcacdcabcdcbbcaaacdabbcabdacbccabccdbdcadbcadabcadaadcababccdacaacadabaaddccdcbdbdbadadbaaaaddabddcbcbdcbbcdbccbababacbdbcacbaacccdabbcbdcbbacbacbcdabcadcbaddabbaccdadccbcadbbbcaacbadcddadcabbbcdabdadcbbcadcdbdabcbbccddcbddbcdacbabbbbdbacdabdbdcbbdaacbdcacdbddbcabbababdbcabcacdcbbbdadbddadbdbcbcdbbbcddaaadbdddbababcaddabacccabbbabbacbcddbcbbddbdaadcccacccaadbbadbcbbadbaaddcbbbdadacbccacaddaaadabaacbdcaacddbbdccadbbcdadbbcabadcddcabdccbbcdbcbcdccdabaacddcdadadaabdadcabdddccbbccdabadaccaccddaacdabddcdbadaddcbaacbbbacccabdaaadaadcbbccbddbcdcabccdacbaaaaccdcadbcccdcccacbaacadcbacdcdbacccbaccbdcabcdccbcccdbdcbcabcbbabdabcddbbdbccbbcadaccbdaaddaaaadbddacccdbdcabbbdcbbbbccdaabaddccdbaaacadaccccdbaccccacabbaaaadacdbdcdbbcddabdcadbbbdcaccbdadddbbbabaacdadaabbaacccbbcadddcabcdbdbccdbacbaccdccadaadbcdcacadddcbbbadcbcaddbdbbbbabbccccaacdbdcddaccacdaadcdcadaddddcbbaacccbadbadadbadddabcbcdbcbacbcbdacbcaadadbbcdacadacaccbbdbdadcdbbdabbcdddbcccddcaaddbcbbabdcccaacccbbcddddbabadddbabcbddddaaaacababbadbdbadccdccccddadcdcbdbdbaddbdcadbdaacddcdbaaacbbdccabbabcdadbdbbdcaacdddbdcdbabcbbacddcaadcabadaaabcdddcdbbbcaaadacddcacbbacbdbcccdddcaaaabdaddcbccbdbbacadccadbbbdbddcccdddabdabccaadcbcacbcbaccbbdbdcababdddbaacacccbbdadcdddbbdbbcdbdacdbbaaabbbddcbaabddadddadccbbddcccbacdcdabbccabccacbbdccaccabcbbbaabccbbdaaabcadcdccacbdccccddaabdbcbbccacdcbcdcdbbbaaddcdbabaaabacdddbddcbcbbdbcaddcaaddbcdcbcbbbbdccabcbadcdddaaacbdccbaccbddcadbbddcacddaddddacabababbdcbdaaabdadccbbcccdddadcabcbbcdbbacadcdaacabbdbbdccbcabababbbaabdabcbcdbcccdbccbadbcbbccddcadbaddbbacbabaddcbbdaddadaddbcbadabadadbddaccdabbaaccbdbaccacdcaadabddcaabdcdcbdcabbcbadbaccddbbbdaabadaadabbcadbbdbacbdcadcbaaaccaaabddabcbcccbbdcbccdbdcdcdbacdabcdccccabdaabadadadddbbdbdaaabdbbcdccdcabababbadbabdcabbadabdbabddbbbccdacdbcbbbccdabbbdcabbbcabbdcabaacdbaddbbcabdacddaacdcbbcdccacaacadddaaaacbaabbadadbabcbacdaaadbaabbbadbadbacdbbccdcddcdcaddcdcdbbbaabbcbbbbdbaacadbcaccdcdcdadbcbacdcdcdaabdacbdbbaabbbabdabdccbaccbaadbadaacccabacdbbadadcaaabcccaaccdbdcbbbbabbcbbdaabadabdbcccbdddababccaadbdbaaccddadacabbcbdacbbcaaddbabbadaaccdcdbcabcdcadbdbaabbdbadabadbadccdaaabcbbcdbcdcbdabaccadaaadacbcabbdbcadabcacadacaadaddacddcbacdabacdccdddacabdddddbacacdcadbabcbdcbcadccdaddbadbcbdbababbdccbdaccacdaacadaadccaccddbaaaddbdcaabbadabccdcabbaacbacacbcbabdaacbddddbbacacdbbdbbccdbdbacbacdbaaabcbddbddbbaacbdacadbbbdbdadaabdacbbddbabbcdbacddbccbcaacccbcaddbccdbbddbbaaacabcddccbaabbadabadccaccbdbcdccadacdddccddaacabbdabbddcddabcbcdbcdccdabcadbcadacdccddadadaaddaabcdcccabcdcabbdaaaabcaadacbaadaacbdbddcdaaccaabccabbddacdadcccdbcbcacccbdaddcaadbcbdccaabddbcdcdbaaaddaddbdabdcddaddacbdadcbdcddddbbbaacbdbbcaccadcdacbdaccdcaaabdabbcccadbcdcacdaadcaabaabccdbaabbccbdadbcbdcccacbdcdcbccbdbabddabbabbaaccabacacbabdbcadabbddbdacbbcaccbdcbcbdbbbbaacaadaabaccdabadcdbbbcadacbaabbcccddaaaccdabdaddddddbabccacdcddddddacccdcadcbdddbccddabbcacdacbddaabacaccbbbbcabacbdaaddbddadadddabbcccacacdbddbdbdaacaacddddaccacaaadadaadadbadcbcbdbccdacbbdcdcacdcdababdaddabbbaddbbbaabcacbdbbaaddddccaddcbdaabdaadbccadbabaaddbbaadcadaddcbabbbbacaadaabbcddcbbddcabaddcccbdaddcabaddbbcbadcdbcdcaadcdaadcaaabcaccbdaaaaaabaccaadbbaabdbcddcbdacadcbdbadbaccbcbccccbdacdaabdbddacdbabbbdcbcadcabdacbcbdacbccabbdacbbdbbbdcddcbdbacaadaabdaddcdbcaabaadbdadbdbdddbccccdaccbaabcbbaacaacdacbdddbcaaadbcdadadadacadacddbaadcdcdccadcaddcadbbbbaccdadbcbcacccacddbcbbccbadbddddaaadcabbcbbadccacdabbbdccbcaaabacabcbdadcdacacbbdcaacacbadadccbbbbaadbbcbaabadbdbcaadcbdaddaabbacadcbcdccdbadbbddaddbccccbcaaacaacacbabbccadabdcdacdbcdabdcacabababbbccacaccaabababddadadcbbcadacabbcbdbcdcaabbbdcdcccadbdacadbcccdabbcacbbcbabddccbdabdaddacbcdbccadddcabcadccbddcabadbbaacddccacdccddbbcbabdbcdadaadbdccbbdaacbdddcbbacaddbccbccaacbbccaccadcbabaabaddbaabbcbbdcaadbbbccbbdcbaddbbbbcdbabdcaabdadcbcdbdbbbddcbbabdadabbabbabcccaaacdcccadbabaacabddcaccadcbbadcacdadaabaacdccccbcdcdbbdbbabbdcbdbaccaaaacddadbbbcacaabcbbdccbddbbdacacdbaacabadacaaccbdddaccbbcadcbacddacaccdabccdbdccacddbdadbacabcdbbccaddcdbadddaadbdabbddabdcdccdabddcbacdadacbccbdabacabbcbdbcdabbccbaaaacbccbbcbabdbdacdbcbdbdbaadadcdcacbcacdbddbdbabbccbbacccdabadccbbcdabddabadddbbbbaadbaddbdcbbbdaaacacbddabdadbdaaadbcaccddacacdaabccbcdcacdddbbddacdcdcaabadddcddcdaacdcbbadccadccabadccaadcaaaddabaaadaaacaadbcdbaaadcabbdddabcadcdddcdccabbaadbcaacdaccaababaddbbbcaaaacaacbbaacadcbddddbabbdcacbdccadccbdaadbaccdbacdbabdacbcaabdabbdbcdbccbddcddcaccaadbddaacadcdbadabdacccccacadbdbabadbddcbbbdabcdcadcbcbcdcbbabbdabdbbdccabcbbbbccdcdbbbaabdcdbddbdbbbbdbcbabbbbdcdacddaacdccdabcdddcbbdddaacccbacaadddacbaccdccabdabdcdbcabadaaababcddcddddaccbccaabddbcbcdccbcabbcccbacbcdccadaaadaabaaababcbbcaddacbbadabbacbdccdadabababbdcdcbccadddccabadacbbbacaadccabddadddccbdaadcccdbdcdbdabacaddbcbdacaacddaadcdcbbbcdcbbaccdccbbadddccccbccbcabaabaaddbcadbaadabbccccbbcdbbcbdddcadacbdaaadbcaddaaddaaccdcdabadabaaadddddccbccadbbbbdaabdccadbbdaabaddbbaaaddbababbdcadbaaabbbbbccbabdadcdcdbcbdadbdcdcbaabaacdbaccbdababbabdcdcdddbabbdbdbbcddccacbccdcadbdcdabdadabbcdccaaabbbdbbbdddacbacdaabdabcadcccdcdbcddadabcbcacccadadcdbbcddddaadabcbabcaacbacbaaddacbcccdbabbcababdcbdcdaddcdddcdcdcbcababaacbaaadaccbcaaabbcbbadaabcaadcbbbbcbbaacaacacbdbdbacbacdccdbdcccccddacdabdaccadacccdaacdbccdbcdccdcdaacbcbddcbcaaabdbabbcdbabbdadcbcbccacccaaaadbbbadcdddbccbaacbcbcaaabdddaabdcaadbacddbbbbdddbdcababcdbadbacdbcdcaaddbbdacadbdbbaabcdbcdbbddbcabcabbccacaabcabdcdddcabccaccbdcbacddabaaadbddbaadbaabdabcaaabdabcabbacdbbdaddcbdbcccbddadaacdbbbbdbadadcdbbacbadddbbaabcbadacabbcababcabbddbcbdcbaddaabcbaabdabbbbbdabaabadaaacbdbbadabcaabbcdbddbaacadbababbcbdacabbdaacabcdacbcccbdbbaccbcaacbdaccddadaadaaaabbaacccddbcbdbccdaabdaadcddcadaaddddabbadbaabbbcddaaabacbddddacbcabdcbbadadaadbcabaabdccdbbbccaddcdbdaacbdddccdcbbaaadaadccbcddbcdccddcdadcdbababadcaaaabcbbadbadbdbbdccbbdbdcddbbdacbcbacaddacccbbcbacddaabddbbcbadcabbbbddcddbcbccbdaabbddccdbccaccdbabbbaccabcdcdcbcbccdbabcdcdadbdcdacdcdbdbacababdadbbdbdaaacdadcabcbabdabccbccadcbabccbbaadbdbbcdcccddaadacaddcdabbdaacdccbbbddcabbdaabdccabdddaddcdcdcdcddbcbdababccbddbddbbbbcbdbadbbabdbacacabbdddcbaddadccdbdbcabacacccbcdabdddddbdbbdbcaddcaabdcdcaccacacbdadccadcbdbcccddbadbacccddddcddbaacabaacccbabcacbcbadbaabaadaaacdcadcbdaddaabadbaaddcabdbcccdbbacbbdadddcccaadcacddacadcddadabbdaacdddcdcdbdbcabadbadaadadabaacccaccadbdccdabaacbabaabcaccababddbbdcbbdabadbadbddcabaccaaabdaadcdbbadbbbbbaabcacbdaccbdaaaacdcadcaccddaddcdaabdbdddaddaddcdcabddabdbbbcaabcbdcbaacacccdcacbabaddaaccccbbbbbbdcaacadaccdaababdaccaddadcdccdbcccaacbddbbbccbdddbdabaddacbaaccbdcccabbbacdabdccdacadbcbaaabcaaccdbdaddaccadaddcabccaacbadadbccaabadcadcadcbacabdcaccccbcbbccabbdaddabacccbcadcdacaccccaccbbadbacdccdacacbcdccdccbcbbadaaadcccdbbcdcaababbdbbcdbddaaacddbaaadaddccaddccabdcacbccddcbbdbacabcbddbabacaabaacdddabdacddddbdcdabcbccdaababdddccadcdcacaaadbdbbdbaaabbccbabcbdbdabdcabbaadcaddaabbddccbdbdbaadaddbcdccdbbdccdddcacbbdaaaabcccbdaadaaabacbddacdcbbdbacbcacbbdacdbbcacbacdddcbadbabbcddcaccbccbcadbdcacdaabbabcaaacdbcbdbabaaacdbccabbbcbbaaaaddddbadcbddbbadaaadacabcdcbdbbcdbbbccdbbcaabcdcbdcdabdacddaddadcbcbcccdbdbdacaabbddbadcbccbbbbddddccdacdcdaadcabdcbbaaddadaddccacbcaabccbacbcbabcdacadadadbbdbbcbcccddcabdbaaccacaddbabcabbdacabcbddddacdbddccddbbcaaabdadddcacdbdbadaaaddccbdbadcbbaabcaaadddbacaabccdcdddadabcaaadaccdcacbcdcbcaacabbcaaabaaadbaabadbadadabbdaacbbdacaacbdddcacbabbbcbadadbabcdcbdaddddacbcbabadaacbcbaccdbcdbbbaccabbcbbddcbbacbdbaadaaababccdacdbccccdddcadbabdabbbabdcaddbacaadcacaddaabdacdcdbcdccaddcdbaccccbbcdbabdccabbacccbbdccddbdbdbddadccbcccccadddbbdbaacacaaaadadaadabbbcaabbbbbdaddcacdbaddbacaccdcadadbbdacbabbdabbddcdadccbcdccaacdabacadcbdcccccbbcdaadbacbbcacbbaabadddadbbdbbaccdbdabadadabaacaddabcccbdadcbbccbbccbbbddbbbdbcaddbdcbabacccddacbbbdacadbcabaacbccdabbaaacadcacdcbbccbacdcbcbaacdcbbcdbdccbbccdcadbbbbbccbbabaddbadabccdaccccaaadbcdacaabddaacbbbbadacbcacdbacaaadabcbcbdbbcdcacabbcacbabbbcaddbdadadbcaddbbbabcbbbbdadadcaddacababadcbdabbadddbbaaaacbcccbbaabbbcdbcddddcabdddcadbbbbcabbacaaddddbcdaacabbcdabaccdcdbddbadcddcacadacdcbcbaddcadcbcddbadcccbaaadbaaadaabacdcabaddbacdadcbaacacddabcdacdcdcaadabbaacdbacacaacdccbcbbddcdbdcabbababbbddcdddddddbadddbcadddbcbcbadcabbdabbbccdcadbddbdcadcdbbcdbaabddcbbcbadadddbdaabcbbdcabadccdcccaabadcbadaabcbdbadbdcaddaccbdbadbbbbcbdabdddbdabaadddaddcdaabdaacbbccbdcdabdcbccbddaddcbcdcadcbdacbddccccbbbbcbbcaacdcbdbccbbcbaaadaaddbcdcadbadbdcabacaaccdbdadbddabbcdacbbbdcbcbcbcddcdabdcaddadddbddcbccdadcbaccbaadcbdbaacdccbcbbaaacdaabddbcccacaabcdcbacadabcbabdbabcbdcaacdbdbbacabadabbcdaccbcaddbacaddacbcdbbbadbbccabbbcdcaaddadaddcccadddaacbcddbdbbaadddbddbddaacccccdaccaacaabadbdbcaddbdadcadbaabcaabacdcbcbccbdcaabcdabdcbaadaaabbaacacdbddbcdadcdccadbdcdbbaaccdcccaabcabbadddbbdbdbbbdcadbcccdccddaacbbcaaabbbddbdaadadbbaaaccdddbaaabaaddbbcbaaaccbcaddbddadaadcdcccadaaacbdbaaccdbbcbbbacdbdcaadabcdddbbaddacddacbbadbcabbacaacaddddbcadaadccdbcbcdcccdacadabbadabccaacbcdcbdbbccddcbbdbbbdadadddacadabaccadacaddacbbcbccaadbdaaabdcdbbdcaddabddadaacddccaacbcbcbabbacaadaddcaabbdabdcccbacacbdababbcacacbddacdddcabdaaddacadbbacbbbcbdabbaacbabcdbbdbcbdbcaddaabcadbcdbabacabdadcabaaabbaabddcacabbdcbdabdcbdcabadcbcbcaaabddbdddbbbcddccaaddacbdcadbacbaadbdabcdbdaacacbabbabcabdcdcbbcbdaacdadcdccccbabdbcddddadcddadbbbcbadaadacadccbddbbadcaadacdabbdabcdaadcabccbbaaccccabaacbdbcbdccbcadcbdbbbbcddaaddbadddbdbaccbbbccccacaaacadacbcabccadbadbbcccaaacabdabdcddcaacdddbbadcacbcdbcbbdbacddaccdbaccaabdbcdbabbcddbbcabbacadacbdcadcbcdaaadcdaccaacbccdcbbdacddcadbbbacbbdcabaaddaaacaccbcbcbddccdaccdadbbadccdadacdaabccddbadccbcbdaadaccddccaddccacccacdcbbbdcdacaabcbbbbdbbcbbaaccbabbadbbcdadbbdadacacdcadaddcbbdbaacbaddddcdcaddccacdbcbbbdadacadcdabcbcbbacaccccacbbdaccdccabccbcacccadcdbcbdcbdabcaaacadbcdcaaadbcaabbddbccdbccadabdbccacdbacdcbabbbadbccaabbddadccadbacbcababbbbbdadcadacabaccdabcdcdbccbbbbbacddbcdbabcdaaccbacdbbcddcbdacdbacadcdcdcbdbcccbddaccbccdacddadcbbadbcdacacaccbbaadbccdadacaaddbadcaadadbcddbacbccbdcccdbbdaadccccdabcddacddcaacdbdcaddcbdadbcabddcbddbbaadcdcdaadacccdaadcccdcdbcabcddbcdcccabbdadbacddbbaacaabaabddbbbdbccdaaaacababbadbdbadccdadcdbabcabcdddbcddaaacdbbddbbaabcbcdbcacacddcbacdaabdddbdaccddaaacbbbadccbccbbcbcbddbacaaccdacadbccaaaddddccacdbacaddcdbbdddaccbccbccabdcdbdddacbdadaadabdbacccdcaadbadacbdcbabcbdcbabdccabcbaddbbcdbdaacadcdddcbcdaaaddacdbbdbdccdccabccccdadcadbddcbdbbdaddcacbaabcccbbdadadccccadbbddbccbbbacdaddbcdcdabddddaddabcdbbbdbdcaaccdccacddbacdddaddccbaacacabbaccdabcbaddabcacdadaaabbaaabbdccbdddbadcdccbcddcdcbcabdbdabdccbabbbcaaddabbddbadadacaacbbacbccbabbacbadddbaacdcbacabcaaacdcdbbadacacaacacbcbbaadbcaacbbaacacaadacccacaaacddccdadcbcddacbaabbddbbbacbdcabbcdbdadbcbadadbbbdcdcacbddacdccdbbdbbabacbacbaccaacdcbdccdabcdbbdaddaabbbaaaaaaddcccdacaacccdacccbbbbcadccbbbddcabdbdbcbaddcbadbccacbbddcccbadddbadbcccdbcbaaabcadcbdccabdbccbdbcaaaccdaacddbbaddbdbcaaddadcbbcbcdbdbcaadaddaccadbdabdadbacdadbdabcdacaadbabdbbcaabdccdbbdaaaacbccdcdbadbbaabdbdbdcbcadabcccdacacadddaadccabddbaacbdbcabbbaacdabbacbbbcabacddaabaaacdadbbaddddacdbbcccbcbcbcdabadbcaacadaaaaacdbcdbcddbdadbbdccbcccaddbaddaccbddcbcbaabbcbacdacbabaccbdacacaddccbcddcacdddbababbccbbbdddcbcaddaadaaddaccbbbccdaabbdbaababbcccccddbcbcacabaaabdacbbadaccaaddabdbaccdabcdddabbbcacacbbcbbaaaadddcbcabbcacbdbacabdcacdaaabbcbddabcdcabcaabacaacdbdadccbabcaaabdabcaabcbabacddcbaadaccaabdcdddddadaccaadcacdcbcdcbaadcbdbbcbadaddacbadcdbddbcadbccbabcdcabccbdaadbcccbcaaaacbcbcdcbcaccbcbbcacadabbbdcdcbacaaaaddbbbbbbbcaadaccbabbaaababaaddddbddadaaacacbcdccaadcbdbdaadbcbbcadacacaacbccbddabadaaccaabcdbabacccbcacbcdaabcddacbbaaadacacadaccabbbcadadaccccdadcacbadadaaadcbbdbaddabadbdacbdbdbdabcbdccdcdcabacdadddacbdabaacbaadccdbbbdcabccdcbbabbbbcdcaadbbbbabbcdaaaacddcdaddbcbbbaaaabadbaccbaddadddbdbbddcbadddccacbadcbdbdaadbabdddadcdbbaaabbadbdcabaacabbbcdabcccbdacbbabcabaccbdbaacabbcdbcddabbbadcdaaccbabccabbddbcdccbbddaddadbdddcdddbaddabcaadbcdcbacacbaddadbacadcaddaaaadacabcddcbbaacaaddcaacdaacabbdadcbbbbdcacacbcdbbccdaadcdacddddaacdabddabbddcadaabdacbcaacdcbbbcddccacbcacadcbccddbcaabbcbbddcbbcbddadcccdcdadabadbcccbbaacbbbbacbaddddcbdbadcabddabacdadcbbabcbdbbbaabdaddbddcddcdbbacccacdbcdabccdaadaaccbcccababdccbbcbdcaaaacbddadabbddcaabadbbbcbbdabababdaaaadbcaacadacdabaaddbcddcacaccdaadbdcdadcdbdcadadddbcadbcaddbdbbbbbcdbacdaadbcdbaddcbddbaaaccbdcbaacdcaabadcabbacccabcdcbcabcacbacbdadbdcbcdddacbdddbcdbbdbadcaaacbaacdaadcacadcabadbdcbcdcadddbcbdbacdcbcbddaabbdbbcbacbbbbacdaacbcabacbaadddcddaaaabcbccacabcbbbbbacbcabbabdadbdbddcddbdcbbdddaaacbadbdabbabdddaabaaaccaccbdcbbdaddddabdcdcdaadcbdbbdddacbcdaacbcacdaaddaccacaacabbbadbcdbddbbdababaccbdbbcbbaaaddbbacccbcdaadbccadbbacdbdcdbdccdbdcccdccddcbbbbcdcbddbbacabdcbdcdbbcdccbbbbdbbdaaaadddbabbcaaadbddcacbbbabcdabacadbabadacbcdacbbdbccaccdabadcbcadaccddabdbabdddadcaaaadbddcbddccbccddcabdccacabbdacdbdcdcabbbaddcdcabdcdbaccdadcbcbbdbbcaaabacaddcaabdbdcbdcdaadcbacdbaabddbbaacbabddccbdddaccbdbacdcabcacaaccacccdcbdbbcddbabdcbdccbddababbabddddadadcdbccdcaacdbaacccaabbcdaaccccaacbcabbccccddabaabcdcbbaddcadaddcbabdbbbcbdcdbcbbabcbccdaadacdccbabaccdbcaacdaadabdbabcbbabaccadadabaacbbadcdaddddadcdcdbdcababdcdcaccabacdbdbdbcbdccccacbbcaaccccccbccacdaddbcbdcccbbcacadcaccddbcdbbdcbcdcbddaadbddbdcdcadadbcbdabdbbbbcadacdcabcdcaadacbdbdccbadcdbbccaacccdadbbabbddbdcbccaaacabbaddacdcadbbdcdddcccbdbdcacbcadadbababdcabdaabdacdccccdacbccacbbbdbbadcaddaaacdcdabbcdaadabbaaaabdbaacdbabcbabbdbadacadcacdbaccbaddcbabdacbdcbcdabbacdcbbdbaddabacbbcbdaccddbaacdabcaddaaabcaddaacadbadbadabbdcdddacdddbdadbacbcdbcabbaaadacabbabadccacacbdbbbdaacdddcdbccbdcbbcbdccddcbdadabbacddccbcbaabaddbddbabaabbaaadcacdacabdbcabdaccbabacbcbdabdaabcbabdaddbcdbdcaaadcbdbadccaccadbcabccdaaacbddccddabdaabcacaadbcbbadcdacdcccbdabaaaaccbdacddacdaccdaaccdadacdddabbabcaabbbabbcadccdadacdbdadcbbdbccddadddacabbcadddabddbbabdccbdbcadbcabcccbdbccabaaadddcbdccdaadcadbadbbcabcaacbddbbdcccaadbcdadabdadbaccbabcbbddabbadbbabcdcbcaabbdcadddccddbdcabccacbdaddbbaaaccbdddcbacdbbcbbdbaabacdddcbdaababaadbccabcbcaccaddbdadaadcbcdddadaabadbcabbbcccbdccbbbacacccbbacaddcaacbadbbdaadabcaddadbddcbddcaaccabacaccabdaacacabdbbcbadacbbabbaaabddbbacccddcaddddbcddbbcddcbbcbacccdbaacbddbadaaacaacdbadddddbdbdddacdbdaadbbdaddcdcacdcdbcbbdddcdaddbbbadbcbbbdadbdcddcdabdbcdbaadbccacbaabccaacabdabbcbadacddabccdddadbcbaddbcdabdacdcaaacadbacaabaccaababaadbaaabcccbabacdabbabbabdcbaacdcbbdcbddbbbbdcddcddbacadadbdbcbbbdcdbdabbabdbcbcabbdbbbbabbbdadcacadbcdccaaddbbcccddbbdccdcbbdaabcbcadabcdccccaaadbbcaabacbdccdddcbddaabcbbadacdbaccdbcddccddbdcdcccabcbdcabcabbdbcbcccaaaccabdbdcabcbbbdadabdccbbddccdcccdbdcaccdadddcaddcbdbaadbbcaadddcadaaacbbdbacccbdbdabbdcbbdaacacdaddcbacbccdaddbdccbddacaaabcbcbcbadcadaddacadacdadcbacbabccbddccbcacacbabacbcbacbddcdbadacabdcdddcdbcbbabbccdbddacdadbcbdcddadbaacdadaddabdaadbacdbbadabcbccbbacdcadbdbdcdddddadcacdcbaaadbdbdbbcdaddacbdcbaacdaccadbdcbbadadcdcdbcaddcaabddbaccdbbaccdcacdcdcbadaddbcddccadacdabdccbddccaadddbddbbdcdbbbbcaddbdababbadbaabaadcbbadcdabbccacbdbddbadcaacacadcbacbcccadcacdbbcdacbddadbbbcdcadcbcabbbaabacbabccacbddbbbadcdcdcbdbaccddcdbadcdcaacdcbcbcccdaadabacacddccddbbacbadaabdacadabddadddbbdbbbabddbabbdcdbcbbaabdcabdacacacbdbabbacabbbbadbcadcccbbcabcbabacdcbcbddadbdcadaaacbabaaaabdcbcdbacccdcdaadbabcbdaaccdbbacdcbdaaabcaacbdbaaddddcbcadadaabbdcdbcaaccdcbdddaadbbcddabdacdbaddddcccccdbcaadbbdcbcabccaacbdddabdabbbbcdbcdccccdbcdbcbaaddadcbdbbcabadabcbbcdddbacddddcadcaaabadaccdaaaddadddcbdadddbdbbacdadccdcccdddcbbccbdbdabcaaaaaaababdabcbcabacaccddccacccbcccbadcacaaaabbbaaddcacadcdbabcbcccdddabccacdacacbadbbcdcdadadcbccabbabccddadaadcaddbacdcbcdabccadacdbbcdadabbdabdbcabdccbddbbadcbcdbcdadbcaadddcdbaaddbcdbdcbcdbbcbbcaadbdddaddcdbbadbbbbbbbaddbadabbdcdccabdcdbbbbbcddbbcbddbabcaccbbbadbbdaddcbbcccaccdddcdacccadbdacaaaddaaddabbcaacccadcabaabcccdcdacacacbbaadbccdabcdabbaabbcbcdcbbdcabadacbdadadacbcbaacbcbbdcabddbbadbbdabbbabbababccbcccdddddcacdadadbaadacaacadabbcdaddbacdcabdadcddabcdacdbdbcadbbdcaabbbdcdaabacccbcbadbbccaadcdabccacdababcdabbadcbcbacaddaadbbcbabcadbdacbddacccbaacabaaadcddbdcbbaabddbccabbabbccdccdbabadaddcbdbddaadaadbaacbaabbbbcbdcaacdcbcaadcbdcddabcaaadbbbdbbacaaddbabcababbdcbbabadccdbdadacddccbbabccbaccdaaaacbdabaacadcadcadcadbddaabcabacbacccdbabcdbbbcadacddcdacbbbdadbbdccbdbbbbcdcaadcddabbadbbdcabdadacbbaacbccddaacbadacdcdadabddccddbcacaaabccbcbadccbbcddbabcdddbdcbcacadcdaccbaaabcaabdbadbbccbddbcbcdaddaaaadbcdcbdccbabcbabcadaccddcddbbcabbccbbcadabccdabaabcccbbbcaacaacdbdaabdddbbcacbbccaaabdbcbbcaaddadbcdcdabdddadbdaabcabbdaaccacabdcbacbdacbacbaddacdcbbcdbaabcaabcdbbadabdbdbbcaaadabcccabccaacdadaacbcdccdccddbbacabdcabdbbcddcbadbbbddacdccadadccdcadcaabaacadcadbbbabdcbdbbadabdccddbdbddaaadbbabbdaabcdaacbcccddcaccabddabbcbbacbcbacdccbddcadbcabdaaacabbdaadbcacacbdbdccabcaaaddaabbcbcdacbddbcabdacbbbacbcadaacddccdbcdbbcadbadcbcbdbdbbadcbbabaaaacbbcdadaccbbcaabbacbddabdcbcabbadadaabaaddcbbaccadbdddbaaabcdabacdbbbdbbdaddbaccadabbbababadddabaaccabaaccadaacaccbbbacaadaacadacddaabdcbccddcccdcabcadacddbcddcacabbdddbbcccdaaddadabbdaccccdbbaaacddadbdbdbadbcccaaaccaddbddccbbadcbcbadbcccabcabbcdacbcddbbdaaccddacdbaddabdbbccaacadbbbadadbdbcccaccaaddcabcddbcbaddaccbabddbabbaabcaaaaaadbccbcbbcdcaadaddabbdabccbcaabcdddbacacbadbbabcbbdbabccdbbbbdabdaadcbbcdcbcccccbadaccabdccaabcababdbbbbccadcccdbbadcccdacabcccadddbcbadcbdabbbddcbcbdbbadcbbcabdbdcccbcdbdcacadcbdcadadbcbbdcaabaaaacbabcdacadcacddcadcabcbddcadadacdbdcddbabcccbbbddbcdaadadddcadadcbbcbacbcbcdcabcddbacbbccabdaaddbcadaadbadbddbcdddabbcdcdadaabbaadbbadddcbdabdabdadaadbacabcdadacaddbaacddacbbccdbdcbadbdbccddadaacdadcccccbadbcccbbcdaacbbddcbbddbadaddabdddadbdbdbdbdbaaddbdaddaaddabdbdbcbcdddadbddaacbbcbdbbcbbabbdcbcaababacaaacddaabdcccbbccadcadbdadadabccabcdbbadbaadaabdbbbaaabdacbcdbcaabdcacdacdddaadacbcbbcbadbabbbcbdaabbdadbacdccadaaddadcabdabadbaaaaabadacddcddccbbccccbcbdcdabdddcbcbbccdbbdacbbccbccacdbabdccbcbddcaaabdcccabacdddcdbbadaddcccbdbdbaadaabddbdabadddabcaddacbacddbccbaaaacdaaddcabcbcdcabcccaacbbbcbbabccddcbcccccadabbbcacadaabbccbbdcdbdcbcccdccccaccdabdcccddcacbccdcadbdddbccadbdbddadddbabcbcbadbbddbbdcdaabcaacabbdcadaddbaacabbddabbcbcbcbbabbbcbccdacabacdbacabacbbccdddcccdabbcdabdbbcccdccbcbaabbabcbbbcccababadcbcddbabbddbdbbdcacabdacbbbabdbdccbbaacccacabcdddacbbccaabcaaababaaaabcaadcdacacdcdccaadbdabcdaabccbcabbdcdadaccbabcadaacaabaadadcdddccbadcdadaccabdadacacdccabcacbdabbdccabacccdaabdbcdcdbadaacbbcdadcddcbcadddccaadcdabcaacdddacaacdaaaaacccbdddcacdadbaabaacdcabbccadcccccbdabbcadabaabbdbbccacddcacdcbbacbdbcbcaabbaddcdaacbbccddbbbbbdadcddccadbbbbccbdcdddddcbabbcabcdccccdaddadcbcbdbaabaaacabadbcdadcdcdddbddbcaccabcdcdccbabdbbbcacdcbbbdaaacabbbdaadbbaaadbaddccbadcdcaccbcbaaaacdbadacbbbccdcadcbaccabbbbddacadcabdbaaaddcababcdbabaacacdcdaaacdcaadabddacacbaaacadbadaccacaaaacddbaabbcaacaabcadabcdacbbcbacaadadcbcaccabaaccabaddcdddbadbaaddbbabdaacdacadaadcadaadaccaddcdcbbbacbdcddcacdcbbbaccaaaddaabdbbaccaddababbaadcccaacadaddccaaddabaabbadcaaacacddbcacdacbaadadaccbcbaabaadbbacaabdbdcbcdcacdbcacaabbabaadbdbdbdadcbaddcdacdadccdcbbbacadbaccaacaadcbdaddbcdddacaccbdcbcadaaccaacbadcbbdbbadcbbdbacddcddbdbadccbcaaacdccdbabcbcadcadcdadbbcbcdbbdaadadbccabcadabdabcbcbacaacccabcdcbcbaaddbbcacbccddacabdbacdabbcbbadbdbbbdcbbbddbacdcddbbdadbacaddbdaaabddccdccaadbbdacdabcbdbbadacabdbdcdcdbbcadbcabbbdccaccccbdcaadcbccccaacccbadcbcbacdbddbccabcabacbcccdcccddcabaacdbcbbaadadcabdcbacbbadbdcdbcbbcbaadcabbacacdbacbbaabdcbaadcbccdbcaaccdcdacaccbabdabccccbbacbcadabbddaabacadccbbdadabccbacaddacdbbdddbddacacaacaacadaccbabdddcbacbacabcabcdccccbbbdaaadddacdbcccabcdcccbcdbbdaddbabaacdaccbcddbadbdabcdcbaabbbddcbbdaddbdbabdcddccadccddcadcdabbbbadccdadcaaadbbbadbdcbcdcabcabbcbcadcddbddccbacddbbbcbbbbbbcbaacadbdcadcccabddbcdadbdbcbbacdcacaacaacabdbaacabaaccdaaacaabaddbabcadddbaacacbaabcbaccabbdcababcccddbbdbaccaabcdbbcbbabddacacbbdabaccbbcacbaaddddbadcacaaaddabacabdcccdbccabbbbddaddababaacdadaacaccdbcdbadbccadbddbdbababccbbcbadacbbbaabccdcdacacdcdabacbabccbdddddcbbcbbdddadbccaaabaaaddbabcabbadabcadabbbcadbbaaacbacaaaddcaaccaabdcbbcdbcbaadaabaddcdadbbbacbdccabbbbabaadacbddccbaacccbdbcacdcadddcbcbaadaddaabbbadcbdaacdbccaccdacdcccbddbacbbdbcbabdcddccccbcbddaccadbbcacabcdbddbbbddaadbbbdaabdaabcbbbcdbaababacddaabbccbcbccdbdbdabadcdacdbccccccdcabcabbdbadaadddcacdabbcdaadccbcbdbacadbbacacbadbbccaadbdcccabcbdacbaaddacacabcdbdadcdcccdcbabbdccbdcadbbdbddcabddcabcbaadbcdacaacbdbddcabddbdbdcacaaadacbcbcbdabaddcbadbccbcacccacbdacacacdbccabcddabcbaaaaadbabcbdacdccadccdadbdacdcccbbbdbddabcbacbadabcbbcbbadabaccbacacdabbbdbdbdaadbcbababbcdacdbaccadbbcbcbccadbddcdbaddbadaabcddaacacdabcbababccdccbbcbccdcdbdbbcbdccddbcdababcacdbadbbadadaadadbadaadcacbcdcddddaddbbababbdbdccbcadddadbbdcddbdabdaaadddabcbadcacacddabdddcdccddabcdcddbdaabcdadadcaccabcbabbbcbbcadbdddacabbccdcddaddadbbddabbdaddacbbdcbcbaaadbadccccbabdababbadadabdcadddaaccaaacadaaddacddddcdbbdcccacdbccddcccdbabaaacaddacbddccddbbaddbcbbdccadaabbcaccbcbbbdacdaabbdbaabdaaadddbdcbaacdaabccbccbaaacccdadbdcdbbacabbcbbdcbddbbddbaccdccbabcadabccbdcaadaabcddaddbdbacdacddbbcaaaccccdccddcabbdacacaaacbcbbcaadccbbdabcbadabdbcadbcbaababbadcdddccccaaadcddbacabcbbadccbcbbdabbccbcabdcbabbddabacbcbcacccdbdcaaddddddbcdabacbcaccaddbdccbdabbadddbbddaccacacbaabddccadabdacabcdabbdaadaadcbcaccbabdcbdaacdcbdadccbacccbbbdbcdcbadbcbcaaadddaaabbbddaaacdadbcabbdadabbabdbddccbacdcdabbcacbcabbdcddaaabababcbdbbbadabcadacbdbcbcadacbcbdbadbbdcbdaaacbdcbaddaacabccacaaacbaccacbcadddcbbbabdbdaadbdadddadadbbabaadcbcddddaacbccccdcbcbaadacbaabbbcbbaaabdbdaadbcabdddddadadbddbdbcdcdbaacbbdbbaacbadbdcbbdcbccbacbdabbacdabbdccccbddccadbdcdbdcdbbcacdccabaccccbbaadabcddcabcbcbbdbaaccddacdcadbaacabbacdacaddcddccbaadccbbbcccbacbbccadbcaddaccddabbccdaacdcacdcbdddcbddabbcdcaacccacbdbdcdccdbbabdbbaabcaabbaddacbdabbcdaccadcbcbcabbcadccbdccbdddbaacbaabdcaccbdbbadacaacbccccdabcccbbcbcbbabddcdbddcbdbaccacbadbcadcacdcdcdccbbbbbcdcbaaaddccccabcbccbcadaddbdabdadddccddbaabadacabaaabddcdaadbbdacbbdabbaacdcdabaddbcdddddcadaddbccbcbdddcbdbabaccbccdccbccabbabbbbbcdcbaddccccdcccbabbdcbbabaacdbcdadaadddcbadaadbdccaaaabcabadbcaddbbcdacabcdcbaacacbcaaadaaccbddadbacbabcadccbddbbdddcaabadaccbcaddcbccabcbbacbbadbaccdbabddcddaacadadbacbacdcbcbcbbadbdbbbacdbdabcaabdbaddddbacdcbdbacabcdcbaabababaaddcbccdcbdadaddbaddcbbddaddbaccaddbccabbcbbdadccddcbdaacaabcccbacdaccbbbbcdabbabdccbbbcdcdcabccccdbaaadabddccdaaabdcadcabadbaacadbbcbdcdbcdbccbdbdaadccbdbcabacccddabccacbccdbbbabcaacbcbaadaadbdacacddbbbcdddbddacbbcbdbcaacbdddccbcdddadbaadccbacbdacacababbabbabcbcbbcbacbaacaacabcbccccbbaddcbaabaabbbbcddccddbabbccccbadbccddbdcbdcaacbbadccdbccdbbddbcbccdbccaccadbdbcaadcbbbdbdccdbbbabcbbbbbcdadcdaccccbadcaababdcadcacddbadbadcdbcbcdcbdbaabccdcabaddbcaadbacaadbbadcbbadacdcacbadacdabbcbdaddccacdbcccccdddddaabddcdabdcbdabddbcaabdbaabcabdababbdccbbdadabbbabdbbbcbaadbacdbddaccddbcbcddbbccbdaccabcbdcadaadadbcccbbcaaadddbddbbcdcadccbccbdcabcdaabbcbabcdacbacbcdddbbcbdaadaadbccbadacbcabbcdbdcbacbdbbbbbdbaaababdaacaacaccdbabbbabdadbbcbcbcdaccdacccbcbdbcacddadbcbdabadcbcccbcdccbaaadbdddcabdadabdcaabaaaacdacdddbbdccbbcadaabcbbbccbbbddcddbbbcdccbddbabccccdccacbacdcdbbabaabacadddcacaabbaadadacddcbbcaaabddaddbbdcbaacbdacbbacddbccdbdbbbdcbadbbbccdbadcbacdccdcbbabcdacbdaabcdaccbcddbdbabacabbcdabcdabaadccadcabaadabaacbaaabccadbcaabdacdcacdacdbbabacadadcdddcadcdadbdaacabacdcacbdabacadaacbadabbbabcbbcdbddadabcbbbdbbcacccdaaabbacacdbadaaabbddbbbbaddbddbbdacbaaccccaddccadaadacbadddddadabcaaadcdcdccdababadaaadabbbcabcddcbdcbabdddbbcddbcacbadacbabaacbdcbcddccabbadadddcdcddcabadddbaddadcbdcbcccdcdcbdadcbcacbdcbcacbadcdbaaddadacbbcbcccbcbccacbdaaadcbabcbccdbabbdcdabbccaaadbaabaabaacabdacddddddacbadcdadabccdddddaadcdcbdcdcacacdcadcaacaaccaacbbdcdcdbbcabaddacabdbaabbbbcbcccbdabbaccdcdbdaaabaaadbcdcaadbbccbdcbdbcbdcdbbbbcadabddbbaabcdddaaccbbdddbbbddabdababbadcbbcaccbcccadcbcdcacbbddcaabcbbbcadbcbbdbcbdadbbabbbbbdcaccabdadabadcaadabcaccddccdadbabaddddcbcbcabababdbaddbcdbdcccbdcdabddcdaaccdbbdbabbdcdbcbdbbbbccccbbbcbccbdcadcddaccdaacbcccddccdbbddacabadaccdabdcddbbabaccdcadabcbdaacadcccdcbcacccadbdccabcbdbdcdcccabdcccdccdadcbcbbcacdbdcdbbdadddbacacdbccbcaccabbdacaaaacdcacaacbddabdcbbaabdbbbaadddaacdabdacbcddaaaaddbdbddbcbdccdbbbcdbdbabbcddcdccbbbaabcdccdcaaaaccacbacdcbccaccbbabcdcbaadcababcacadadcadbdcbbbdadadadaccabbcdcdabbbdcddcbdcdbabccadbbcbcbbbdcdaaadbabbddcdaacbacbdcadadcbdbacaaaadbdabbddaaaaddaddabcbdbddcbbcbcbbcadbdaacdbcbbaaddccccabaadddbbbbcccdadbabdbaddacaaacacdcbaccbadccbddbcacccaaabccaccdacbabaadcdbbcbccdbcbccacbabbcbbbbaadcaacabcdbdbaccbbbadcccbccdddccabcabbbcccbcbdcccddbaabaaddbbddddbabcaaddaacbbcbacdcacccccbaddddabddcbcabdcdcbdddbbdbaaabaabbdcbbdcbbbcbbbaabadbccbdbacabcaaccadcdaddaaaaccabbdababadbadbdbdbdcccadcdbacabcbbdadbbcdcbcdadddcaaacbdbabacdbdbaacaccaabccbcbbcbcddcadbcadbddbababadcccdadcddcadbbabdaabcacdbaaccacdabaaadbcbddbcbabbddbdacdabccbcabadbacbdadadbcdacadcdddbcadcdcaaccbdcbbaacddaadabdbbbdaaadbdcdabccbadbcbbacbdaadaadacddbaccdccadbaadadacbdaddaaacdcddbcbabaadcbcdcccbcbdabcbbcdddcddddcdbdccabccdbdaaadaccbabcbbdbccbcaaaabccdcacdbabdacbbddbabccdaaccdcaccadddbbabbababbdacadddabbabdbbbbdabbcdbaccbbaccbdddbccbccbddabababacbbabdacadbbcbbcbaadcbccdaacdbbbdcaaaaaadddcbdadaddaccbaacaabdcbdccadcdbabdcdabcdabbbcdcadbdbcdabcbbbdaabdbadadaaabbddadccbdbbcaabcccaabaddabdacdbbbaacddcbcdcadadddbaabbccacdabddbbcdcaaabbdaabacbcaacabaddddcaaaabdddabccbdacdcbbddbcbdbbacacddbdbbabbbdaccdbcdbdadacbdbaacdcddaccdbcbccbdbaaddacdbacccabcabdcccdaccdcddabdaddbdcddaadabcdccaabacbcbabdabaadcdbaaccbdbaaadcccbaaacacdcacdcaababbbbcdbdaadcaccddbbdccbdbbdababcdaaddacdbcadabdabdacccabcbdcccbbbaabbbbdbaacabccbbdbbbdaadcaaabaddcbcccccdcabdaabbcabdbddaabbdcaaacadddbbacacacdcbddbbccbbaaaccbdbbddbbacabcadaaccaabbbddcbdcddbbadddbcdbabdabcdadccbcaccaabdbddaccdcabdcccdbcdabbddacacdbdadddbccbdaddcacbacdbbccdcbcbcccbcbbaacbaadcdccacbccbaaadcaabaacbbaadadbadadccacdbbcccdbababaaccddcdbbbadacbcbdcabacccadacbdcababadddadabbbdbddbdaacbbdbdadccddbbbbbbdadbcddcdcddccbbaababbddcdcdcaddbdadddaadabdbbdaabcdcdbaaacabcdcdccddaadccbcabddcbccbdcbbabdcacbcccbccdcbabaabaccbbdcadcabcbdccaddbbcbdaacbadddbdaababccbcaaabcbdbbbaddadbccdcadacbabadcdddaaacdacabbbaacdaddbadcbcbbbadcbbabdadbbbaabdcadbcbacccaabcdacbccbcbccdadacaacbcdadcbdcaaabdcaadadcabcacbcaccacaaacbcbbacbbcbdaabbdadcbcdccabbdcbdabcababbbcbbdcdbaaadbbdccdbcdbabdcccbcadddbaaabcabdbdddaddcbcbabdbacadcbbdbdcbbbbbadabaabbdcabbbbcdddbdcabdcccbdccbdacaabbcbcdccddabddbaabddcdabccbdddbbdbbbacdddadcadacadcbacbcabaaabdacdaddadbcddcabbbacccaababdabaddbddcbdbadbdbddacbdcabbbddabadbcaddabbdadccadccdcadaaabacdbddbbddbdcbdcccbcacbbccabbdbddbacddccadbdccdbabbbcaabddddbcccbaadcaaabbcbccbbdddddbaadbcdcbababcadbbbababaadadcddacdaddbacdcbacaadddbcddbadaacaccbbaabcabccdbaaaacbdbbaaabccbbccacbcddcabdcbdbbcbdccaadcbccdadbacbabbdcadabcdacaccddabdcabcbaabaabccdbacabccdbcaadcdadbbddadbadcdcadbaddaacbddccbababccbadbadbbdbcabbbcbabdaddabcdcbbddddaddcbcadbaacdcbacbbbaaccbdcadaabdcdaaaabcddbdbbbccbdcadababcbbcdadacdbbadacaddbbababdcbcbbbbdccbbbcbacacadcbdbdaccbdbcbccabbbbcabbdabacccbbccbaadcbdbaadccbdacdbdaaccdcadbcbbaabbdacababbccabacbcdbccccccbabdcbadbbaccabacdbbdcdaddadaacbabdccacddcccbdadbdbbcdcbdddbbaccbcddcbaadccadabcaabdbcbababadcccbcabbcabbcacbdcccbaccbabddcaacbbabbcabaadccccbdabcddcbbdadaaddcdcdabdbcccaaccaaccbcbbdacaadadbdbdccaccdaaadccddbadddbcbbabcbcadadaacbdaacbcdacdaabdbdbbadadbabbcdcdbdcbdaaabdbabccbbcbcabbbdddacadaaccaaabdababdacbcabdbacadcdcadbbccbcbdacacbbbdbdccabccdaddacadbbcbaaccccbadbccacdaadddacacabbdcddaddbddbdaddbccbdabbdbcbadcbacddadddbddcabbbbadadaccacddacccdbcbccadcccabbbabccdccdcdbabbcddbbdcadcbbdbbdadcbcddcdaaddaababcccbddcccadbcdacdbcdcacbcbaaadabcacddadbacadcddcaaaddddabcbdabcbadbcddbabbadacadbcbcddbababddadbdaddbcaddbcabdccbdddcddbaaaabadaaaabcbbcababcbddadcdcabdcaaadaabdadcdcbbbdbddcbaadcdacdbacabdbbbccbbbadccacabbbcdabcdabdaabbaddbcdddababbacbccbacabbcccbbcacbaacbddbcddcbacdbcdbabdcbdabbddbddbabaccadbbcbdababbcdbbacbaabdaadcdbabcabacbccacbcbcbaccdacadbaaacacccadcaadbdbcacbbdacadccbbdaaaabaaacaabbacadbcdadbdaabbadadaabbdcccdabcdaabdacbadbcdddacdcadcdddddcacabbcbdacbdbadbcbbabcdbabbaddccadbdaaccdcbbadcdcabdabcdbdbccbcdbacbcbbdbbacadbdbadbdcbcaddbbdddcddcadcadaaaccaddaabadcdccdcadacabcddaacbabcdbaaadaadcdddbbadcbdcabbbdddcacdcbbcaccbcbcdcccabdbcbcbddbcdbbdcabbcadbbacbdbbbcbcabddbabbddbadbbabdcaabbaadccadcaacddccdcaabccbdccbcbdbbacbbccdcadcccaaacaaddcdbbaaddbcacdcadacbdbadaddbcbcbbaaadccabdadbcbadadbdbbcacabccbbbbbbdddcaaccabdbcabdccacddddcdaacbbcbcdadacdadbcacdcbbcbcadcbbdabbbdcadbcdbcbcbbbadbdbdbdddccdadcdbbadabdcbcbcaccdccabcddbdabaccddaadcbdabcbbbddbcdccbcadabcdaaadbbabdacbdddbccacbacabccdbccbadccbadddabbacdcdbacddbcabaddcdcaaccaacbdcabcccacbaaaadcacbbaabddadaabbddababbbbddcabaabdcdcbdbcacaccabbcddacddddbbcccddbadbadbacacdcdcbadcdaabbcbaaadcbbcbbbdcbaaacbbbabbaaabbabcabbbbbbbdbbbcababcbbcbbccadddbaabcdcabaccaccccbcacbaacbcbdbdbdbaaabbacaadaacdbddabddcccdadbaccdbbbbcaccacccbbcbdddacaacababdadbccdadcdbbcddacadbbcabacddaccddadacbdacbdbbccdddcadcbaddbdacbbccbccabcbbaabbbbaccdacabcdccabaddbcbcbdcaaccacdcdcdbcadaddbcaabcabbacdadddbbbcbccbbadddbbccbcacdcdaccdadbbdbccddabbacadcbccdbbdbcdcbbababadaacdaccdabcbdddbababdbcddcbbabccaabadddadabaaadcbcabcbcdbdbadcdbddcccdcbbbadcadbadadacadbaaaaacacaacaaccadcbdbbddcdacdbcbdacccbbbdbdbbbdddacddbdadbcdccdcccbbbddadadddadacbcdbcdabdcbadbadbdcccbaddccabbcdccbdcdbbbbbbbbacaddbaadccbaaddbcdddcbbdbccdbddcbbadaadccdbdccdcbabddaaccbadabbaabadaddbcbcdaadaaacdcbabcdbbcdabbcbdbbdccacddcabbaadbcdbcccccacdacddaaaadbcaaadbccccddcadcccbbbaadbdbbdacdabbcacdadabdbdbabbcddabdbabbccbbcaabbbdbcbacdbbccdabbcccbbcdbbbcaccaccccbcbbbccdbdbccadddcaddcdadcccdcdcbbdbdaabccdbcddacccddbccbbaaacabdbddcbdbaddddbdbcdbbdaabddabbdbdbccbbaadaaabdccadcacccabaaadbddcbccbcdabbcbcbdabdcbbcacabbccaccbaddaacbcdcabcddacbcbccacadbbbdbaacccaabcdacdaaccaadabaddbccdacbdacdadaddabbbbbcdaadddbccbbabcdbcacbcbadabaaacbcddcbcdcadbddcadbbdbcadccbcbabdddbdcaadcbbabddaccadbbbadaaddccbcdccaabcacccbbabaaacbcbbddddaaacdaccbccbccbcdaadcaabbddaccbcaabcabddbaccbabbadddbabdadcccdcaccadccdaaabaabdaddaccdaadcdacadbdabcbdbdacbadadaabcacddddbdaadaabaddccaccaacccdddaaccccdbdbbbdcddbcaccdadcbddbcbbcaadbdcacbdcdacccddbdcdbbbcdccacbbbcabcaabdabdccbcdacbcbabbbccdacbdbadcbbcdaacbbdaccbabdbbdccabcdddbbbabccccbbcbacdbadbdacabddbcaadcaabbbcaaabdcacabccbcaabacbababbbcabddaddcdcaadcabdbcddccbccbdbaaadaccabdcabccdbbddaacdacdbddccbaaacadbcdabcbcadbadabaccbdbdadbcdaccbaadacbcdcabcccbacbbbbaaacbdddabadcacbdbbaaabadbdbdcbdbccabdcbdcaaadaaacdaaabbadaaaaaabdbccdbdabdcdbacccbcacbcaddbddaadabcaccabdccbcdcdbcacbbbbdcabbaacccaccddcccdaacdabddaddabbbadacdccabddbcbccdabadccacbbbacdbcabcabdccaabcacdacccaccbdbdbdcdcccbddcdcabcbbdaabccbbcacababcbcddccdcadaccacadbbcacacacdacdbccbaadaabdaaaacdbabadddabdabbbbdbdbcbadcdbabbcbacddddadcbbbdbcbdaaccbcdaacdbaacddcbabbcdbdcacddbccccaabadadabdbcdbcbadcbdcbcaacabdddcabcddcbcbdddcddaabaccdbaadcaaccdcadaaddbdcdddcabbaacbdbabccbbcddaabbbdabddbbabddbcbddcdaddacaabcdbbcaaacdabdbadaadccbdabbacbbdcdbcadccdddabbbbdcddcbcabcbabcdbadbbaaddbaccadacaaacddcdbaacddddddacbdccaadaccdcbdacccdddddccababbbcaccdcabcbadddccacaabaaadacbccddcdaabadcaacadcdbddcadcacbbaadacdbbacbaccbbcadacbdadbbabacccbbbadaabdaccddabcbdabaabdccacaaddcabdddcbbccadbbbcaccddaaaccadcbadbbbbdaddabacdbabcbdcacadccaadbabbcabaadbdccdabbabddabaabdcdacccaaabdbcbcacaabcbbdbcadccacabacdadabadcccddbbdbbaaabdcacccbbccbbbdbbbdcbdaacadbaaccdccdbbddbbcabbbccadacdcbcacbcdbbccbcacdaaddcbbabbbcdbbdddbccdbaabcdddbbaaabdbbbccbddccdbdabbdccadcbcdadaddacbccddbbaacacbddaaabdcacacacbbacdcccbcddddcbbacbdbdacdbacaacbbbadacabadcdcbcbacadddddacbabcaccddcdcbcccadcbbaccbacbbbacdaadddaddcaddbacdcbcbbabcddcdddcadabccacbbabccddbbcadababdabcadccaadacaaaadbdbbddbbcacdaadabcdddccadcababacdadcaabbdcbccdbaabaaaacbcbbadcdbbaccabcbdabacccabcdbdaaaadcdbbccacbdbadaaccbaaacadcccbabacdbbdcbdcbbabdcbcdabacddbaacaaccbdbdbabacaabbaabccaccdbccaadccdbabcbabcbcadcaacdadcdaadccabcaddbbdacbcddcacbcccaabdacccbcdaacacabddbdabdadacaabdacaacdddbbdbddcadbcbddbaadbdddddabdbabbdddbaadbbccbccadccacccbcbcbbccbccccbbdbdbabadcbacbddaabdbacacbddadabcdccbdcbbcacbbaaacbdcbbbaabaacadcbccdcccdcababadabadbcacbddaccadbdbadcdcababdbbabdabadacdaddabdbaadddcdccbbbabcdbccdaccbabaadacccbcacbddbaccdcadbbacbddabbabbdbcbbaabdcddadbccacabddcaacacccaadbbcabacabcbdccabaadccdbcaabacdcadaabcdcddcbcabddbbdacdcddacbddaadbbbdbabaccbabcabcdbbcdabaccbacabbdcacaadabcbaaddcabbcdcbdbdccbabcdddddbcadddddaaccdbdadcbcbbbabbcabccadbdcddacdadcabbcccddcbaccaacadbbdbcdbcadcbbaaccbdbcbcccaaddbadccabacbbdcdabdbcbcabcbaacbdadbdbcbccdadbdaadcabcaadadddbdbdcacdacdaabdccaddadacacaabcaacdaaadcaadccdcbdadcbbbcabadbadcacdbbdbacaaddcadaaadccbdcdccbcaccbbddbccdbbbbabaacaabbddbdddbdbccbcddaadabbbaaabbbdbbcacacacdcdbabbaaaccdbdacbacacddccbadbcbdacaddbbabcaaabbabdadaabacdcaaccccdcddcabddaacdadcbbaababddcdcdabbdbbacbdddcccdcaacacdbdaccccccbbbbacbdacdbdacadaddadabcbdbccdcdacddabbbbcdcbcdcbdcacbbbacdaabcbbbbacaabddacadcdddadcbcdddcdabbadabcdadcbbcdcdacdddbbdccdabbcbcbbbccadcadcbcaacdbbcbdcaccccccaaacbddcaaddabcdaaabadbbabbcbcbcbacccbaccdaaddbaccccaabbdadadbcdcdccbcbadcbdabcbcdddbbacdbbbccdcbbacaabaaadbacdbdcbabddcbdadcbcdabbcabbdcbcdddcabccabacccbbdbcdcbcbdbdacacdaaddbcddccdddbbaaabacbbccdabaabbbccabbabbccbabddbdbccdccaccbadcddbabdddaccaccccdbbabbbbbbaddcdcabacbaacbccdabaadbcbbbcacadcbaaaacbddcbdbabdccbdabdbcadcbdcababcbdbaabadcdbbaadbbaaaddbccadcacbabbbaabbcdcacbbadaccacdcbaccbccbacacdadddbabbcbbbbcdadcbacbcabccccabccbaaadcadbcabacbddcaadcbabbccaacaadcaddbdabddacccacbbddbabdbdabaaadadaabcbabcabadcadbdddaaadcbaadaadbdababcbbcdbabdbcddbdabdbbbcdbaaacdbaaabcbbaaabcadcaddcbdbddbddbbdbabdacadcdbbbacaabacbadacbaacddcaadcdbdabdbddaaacacddbdcbcbaacddcbcdcbadbacbbadbdbccabbaaabdabdcadacdccbccbdcbaabbacbcbcdacdccbcccbcbdcccdbccbabcdbcadacccaabddbdcacbddbcbbbbadaddadddcdddcbbcbddddcbbdddcbbcbcbcababbabbcbcadcdaccbacdcaacddbacacacbbcacddcddaabbacdcdaddacbbbacccaaddbdadcacabbcdcacacdbacabcddccbadadaacdcabcbdadcccbcbbcacadadcadbacdcacabacbbcdaacbcbadbbbcbddddbaccaaaaacbdadadbbdcaabbaacbbabddbccadbcddcabdaabcaadbabcdccaaaabbdddacdacbdcabcbdbddaabdbdbcccbadadacddbababcbcbddccaacccbdccbaaadbbbbcdaddddbbdccbadbbaaadbddabaabcdcaddbcbbadabbcdbbdcabbbabacabcdbaaaacbccacdaabcdbcbdddbbdaddaabbbbdabcbcbaabdbddaadcadccdbcdccdbaadadccbcdabbccccabccbdcaaddcdbaacadcdbdddbbccbccdaddababdaaadaccacddcaadccabcacabcaccdaacdbbbbadcbdcbccabbbaadbaaddaabbbdacdaaaabccabdacbdbbbddbcabdbccaddbddbdcdaaababcdacbbbdcadbadbbacacccdbacbbccdccddcbddbdbbbcbbdabdadbdbbdddcccbadababcbdbddbdbdddaadcbccdcbccbadbccbdddcccdcdcddaacdcacbdacaacbdcaacacacccbbdcdadadccabddabddbbaadddddbbdaadcbabdbccbdbadbddbcbbbddabcccbcdcddbdbbcbbdcddcadacccbdcdbcabdbdaaabccdbaabdbdadacadbadbbaabaacaabbddadbdbadcacbaaadadcdbdbaabcdcadbbbcaddaaabadabdbacabdccdbbcaaccccdcbaacbacdcbbdaccaacbadcdcbbbadddbaccddaabbbddbbddbbbddccacccbcbbacacaacbadbbbccadbadcbabaacadcabdcaabddcbaccddbcdbaacbccbdbdcdcacaabccbacdcbccacaaaabdcadaadaddcbddcabbbbbadcdadadcddacdddcddabadddaadaabcaaaccddcdabdbdbcbbdbccddddbdccbbbddcdccbdacddcccdcdbdaaaacabcbddcdabdbbacccabdaaddcbcdabcbdbaddccdbcdcbacdaaabacbbbdcccbdabdbcccccbbbbaccdadbbcdabddcaaacbdcbbababacbcacacdbbcbaaacdcdbaadabbabcacdadcbaadbdbccdabbaccbcdbabddccadbccadcbdbaccbabddbabccdddbdaaadadbdbddcddbcadccaddabbcdbcbadaacccbcbccbadcdcbdbacabdccbaaccbddddacbcabaaabaddbcdacbdacccadcddbabdccacddbdccdcbbaacbccbadbdddcbbdacacdacadbcbabdbcdacccdcccbbbcacbaacddbaabaaddbdcdbbaacadbcaadcdcdccbadbacccbbcadbbccabdcddbcbccbadcdbacddcaacabcddaccccaddabbadbbdcdcbcababbabddbbcacbaacaadcbacbcbacbcbacdacdbbadcbcbaccbcaacaadddccdaccbaaabbcdccbacabbbbdcdccadddbccadbbccccdcbaaaddadbabddcdbcabdbbacbbadbbdbaaabbcdbabdcacccdcbcacdcbabbdadbaaccaadbadccbacabbaaaadaaccdbdbbdabaadcccbcbbadcdadabcbddbddbbdcbcbaabbdcdcdbbbcacdaacccbdcbcadbbdcdccadcdbacabddbddbbcccaaaacaadbcaacadbccdcdcdabdcdaccccdcbabcbccdbcaabaccaddcbcbadbcacdacabcdbdaaddbdccdcccdcbadacbbccbdadcadbcacdbbbcbbdaddadadaddbccdccbcabbcaaccccdbdbcadabaacbcacbcbdadaadcabddbadcacdbcbddaddddbccaaacbaccbccbdcdddcadbcbbbadababaadabadabbcbccaadbbdbacbccddaacbbcbdbdadacabdbdbadcccdadbdbaaabdcaaaddadddccdccacbdbdacadbdaccdabaadaddddaccbccbdabadcdabdbabcbddaaadbabccddcccdcdbadbddaadbcadaccadaaabbbcccadabcdcbcbdcbcdaabdaaddbbcdcbabdbddbcbbccbbdbdaadbbadcacddabccbdbcaacdcdcbbcbdbaadcdababbddccadcdbabaaddbdadcdcabacbbcbaadccacdbaadadaddddaccabbcddccabcaccaddbaacabbcdbddbaddadaacbcbbcdbcccdcdcdcbdcbdbddcbaacddbadddbccdccaabdcbdcdaacaaacaadabcdcadcccddcbdcdacdbdabbbccdcabaabdccacdddabaccccdacbbabcabbaabdcbbaacbadddcbbdddacdbcaabaadccddcddcabbdddcadabbcccccbcbbccbcbacbdcdabcdcccbbcadabdbbbcdacdccbbadcdcbdbacdcbdbbdadaaaddcbdadbbaadbacbbbdbabcbdbcbdabaabbcdabccdcbcbcbdaabcdbcddcbadccdaaddbaacdcaacddccacccbabcabaddaaaaacbcbaadbddbadabbdcabadcabbdabaaacdaaacbcbcacabddabbcadadaddbbcdbaacaaadaabdcdbaddbccadadbdbaddabbcdbdbdccddbbbacaaadbcadaddadbbbaabbbaccccacdaaaaaabdaabdcdbcaabbdcddbdadddbacacadbdaadbaacbaaacacaaacacdcbcdbdcccacbabadcaaabbccadaccaadaaabcdccbddaabcdaaaabadbbbcdadbbbcbabdaddadbcdbbadaacbdbdbadbdbacacdbabbbbdcaccbadbadbddaabcacbdbcabadbbdbdddaccaddbccaadaadacabdcabaabaccbdbbcdbabadcabbabbbabadbbaadcaabcbcaaacbacbabddababcadcdbddacbdcdbdcdcdadcbcbaddbccadadabcbbbcbbddadcabdccbadcdcbbababadcaaabcaaddcccbbbdcdaadadddbbcabbadcbddadababacbccbddaabcbdcadbaabdcabadbadcbadcbdcdacbaaaccdddbaccdccdacabcccaaaadadcbcabaddacabdbbbcbadacdccbacbacabbacbcbcbadcbbbacbabaabaadaaabaaabacacaadbdacadbdddcddcadcbcbcabccbacbbaddbcaccddccdadcababaaadcaabadacbaabbbccacdacbcbdaaabbbccbadbbbbcdadacccadddcddacaaaddacbaddcabcccdcabababddcccccbbdbdadcdcdcdbacbddabacbbbdbbccbccccdbbcddbdaacddbdacdcbbaacacdcccdbaaadcddcddbbccadbcabbacacdcdaaddddabdadadcaddcdbcbbdbdaccdcbbcbaaacaacadbabbbaabddaccbbbcbbabcbaabbbddbcdcdbadbaddaccccbddddabbdcabadacccabddccddbbbcccbbccdcdabdcbcbdcdbddbabddcdddbccccdacaacbababdcddacababcacdbddadbbccccccabcbadcdcbdddddaaacadbdddcbdccdacccccdaccabcbadbbbdaadccddbbdccbbdbccbacddccbccbcacaabadcdccacbdbdcbcbacddbdbabcbbddcccacbcaccdcddcdbbccccdacbaabadacdadbaddbcdaadbcbcccabcbccddcdcddabdaaabadcabaabbaadadcdddacddbdcacbdccabdadbcddaadcabaabbdaccbcbaabaabcabdacbcdbcdbaaabcccdcdcbcaadbcddcacabcaccbbacbbbaccbdbdabdbbacccaccdabaaacddaabadbdbcacaaadcbbcacacbbaacaddbbabcdccaacdccccaddddcabbacbaaddbabccaacbadddbdbcdbccbcdacbdddcdbbdaccbbcdcdcbaababcabababbdbbccbcccdcdbcddcbcdbcabdcbbadbabdbdbdcaadbbadcacbbbbbaadcccdabdcdacacbcadacdccbbdcccdabadccccacbbaacdbbcabdccaadaaddcadbbbccaaadcabbbcbcaaabcccadbbbdaccdccbaaaaadddcaddbabdaadbdcbbcdacccdadbdccadcaabbacbbcdbaaddbbbaacaaadacacccbbbbaadabbcddabaadabcdbabbabadaddbbabcdbccbdcdacaadcdbbcbddcbdcbbcaddddabcbbcccdcabdabdcdddbbdbddacabaabdccbccdcccabbcaddbaadbcaaabadbabbbbbcddaaaadbcabcdacddddbbdcccddabaacbcdbdcbcdcaabbbcbddbdcaccaaabdbbadbdaacabcddabacadadcbdbdccccbaddcbcaccbdbabacadbdadacdbdddddbdbbabcdbcdbccadcdaadabadcbbacbbccaabbcddddbcaabadbacddacbacddacdccbbbccbdccadaaacbccddccddcbadbbdddacabbabcbabcaabdccacbabcbbbdbaccbdcdddaddacddcabddcccbbbdddadcadcabcccadbaabcbaaccdcbdaabcbbbabdbbadcdddadcddbcbcacbaacacdbbbdcbccacbdcacbabccdbbacbcdbdadabbcbadcbdabadacbbbadbbbcadabbaabcabccadaaccdadbcbccadcbcbbcdbaadaacddabcbdbcacacaadbbbbddabccddccabaddabadaaadcaaacdacabdccbbcababdbbbbdaccacacdaaacccdbabcaaacdcababcabbddbbababbcdbccbbadacadddaaaddddddccbaacacbbbdccbccacaabdabdbcbcdcaddaaaadcadacccbddbcacadaabbcbccdaddbdbbbadcbabbacbdcadacbdaccdbddcdcddcdcdadbcacbdbadcbcaacacadabdccaaabcbcccdbacdcbddbddadbbddbcbaaacadadbdbddccabacacdbbbaccadbbcddacbdbbbaaccbaacbbddadbadaadabdbbaddabdabbaabadbbadacdcdcacddadcbabdbcbddadcababcbbddcbcbbacabbddbadabcbcdacbcbaccaadbccdbacaddddacbcbbcaaadcabadabdabdadbbdadbdabcbcdbdaccbcdccdbbbbcbbbaccbbbbbddddaccdcdcaabcbadbcacadddcdddaacadccbabdbbbbbacaabbddbdbcdcabcccdacbcadbbadbdadbbcbdccbdbacbdddddbacacbdbaddcdcccdcbcdcdcdddaabbadddccacabbcccccdbddbbddcdaabcdbcdaadbdacdcdbaadcabccdabcbadcbadbbbdccddbabdcaddcdccaaadaadbdbdacdaaacabcbbacdddaaaaaddcdacacabacbcbbcdadabbddbccbaacbbbdabdabdcaabbddaddaabababadbdbacbccadcadbcacdddacabdcbdabbaddcccbbccdabbadbcacbccacbaddbadbddabbccadbcaacbcdaabcbadddddcdadadbbddddbaabddadadaacadbaccaadcbaabddbaaabbabacddacbdadbadcbaabcbbbcbcbbbcdbbcbbcbaadddadaacaadbccaaccabdabacdcabcddacdccddaadcddcaadccdabcbcbcdadabdcbcddadddbdbbbaccccddbddbdacbddbbcdbcaacabdcbaccdcbaddccbcadcbdcaccddddcaacaaacdbcbcccbdbbaacdbbbabbbbdcddcaccddbcaadcbbdbadabaaacbbbabcddbaabaaaacbaaaadccccbdbbdcbcabacbccdddbdbaaccadcbcaccbdacacdccacacbaccaabaadcaadddcadadcdaccadcdcacadccccadddadddccbabbdbcdccbcbabdbddabbcddbcdbdbabbacaaacbdcbdacddbaacaadaaccacbbaababdccacbbadacdbbcabaaabdbbdacbddbddcdbdddacbbbcbdccdaabacdcccaccdcddddccadcadabacadcbbdbbdbbadaaadabcdcdddbadacccdccccdbbabcbddccdddaadbbacccdbdddadcaaabdabccabcaacdcdacdbcaabaddcbadabbdbbacabcabcbabcdacdaadbdccaadcbccbabacddbbbddbcaaadbabccdabadcaaaadcbdacabaadaacddacaccdcdbcbadbbaabadcdbdbabbddbbcaaabccdcaaadcddaccadabdddcddbacabbaabadaaabbadabcbcbbbdaabacccddadbcbccaadcccabcabdcdbbbadbbadcbddbabbcabadbbacbdbccbcdcaaaaabacdcccdbcddccbaadcdcadbcdcacbabacbbadddbdcbbaaaaabccaadbdacbcabbdcbcaaacdadbdcccbcacdaaaadcdbdadbabbacbadcadaaaacabdcadcabcccdbacddcccdcabdbacdadbbcbdcacdabacccabcdcdcdabbabbccdbcbdbaadcdbccdbbccbcdacbccacbdbcbccbdcbcdacabbcbbbababadbccdabddbaccdbaabbdccbabcadbbddaddabbcbaacdaaabaabbaccdaddabbbdbaaabccaabdcbbcdcddadaaaaaacaccddaaaadaccbaddccdcddacdcbccdaaacdcacdadcabaaccddaaccaddabaabbaabbdcbdccbccddbccdddcaadbddadcaadbdbadbbcbbdddccccabadbbbcbbdcddbcbaccbbcccbdbbdcddccbcddbacbbadaaddccbdcbbabdbbcaabaaabbcabcbcacbddcbdcbcaaccbaadbbbdcaaabccbdbcbccbcacbcadaddcbdbaabaacbbbcdbcdcbcccccccdadbbbbaccbccadbadbdcbdbddaddaccbdcaaaacdbcaaddccaabacdddbdadabccadbbddbcccacacdaadbbbadabdaddcddbabadacbbcaabbdcabaadbbccababaabcdcddaadcbdaccccacacaccddabcbabbdacccbadcddbdbbdadabdbdbaaababdbcadbbcdbbabdbccaaadcdaadcccdbcdacabdbccadbabbdbdbdaddbdabdabadcddbccccdacaacbbaccddddbbababbdddaccdacbcddccdabbcabcacccbcbbbbddaadddbcbaaccbdbaaaaacdbbcbcddaacbabdaaaccadbccabdadcaadccbbaccdcbbcbabbdddacbaccdbaadbccccddccbadbdcaabadabdcddbcdadbbcddbdbcaabcaaabdcbdbcdcadadcbcdbdcdbbbbddbddcdbaaacbcbccdbacccdbbdcbcacaacabdabacbdbdadcaadcdbbdddbdcdcbababdaadcababbdbdacddcdcbabaadcccdbbcccbbccacccbbcaadaadbbcacadddabcadbbaabbdcdcaddadbacadcbacdaaddacaacccdbddbaccdaabcbaabccbccdaaabcdcbbbdbdbddabdacaadccbbdacbbbaaddddcbaadadcbdcadbbbdcaddaaccdcacbaabaacdbaccccaadbadccbdacacaddcabcbadddddccdcdccacbabadcabcccbcdaaccabcbdccdacdacabbbadcdabbabbdbaabadbbdaddacddccacaddacaacaadbdbddacacdabcaacaabbaababddbcdcbbcbddbcbbbdbdbdabcbccaddbcdcdcdabaaaccaadcacabbabaabbbcaccdbcdabdadccccadbbcacabaccdababdcdbbbaaaddabbbcabccdccdbaaadadbdbabcdbacddccabdcdbcccdaccbadcabbaccbdcbcbbabcdcbbbccadcbdcccbcbbdccaddcdaaccbdadddddacbaadadcadbbcbacbcbcdbdbbcabbcdabdcbbadacdbddaacbddabadabbdccbababadcadabccdabaaddabadacabaddabbaadcdbcdaaaddadbdcdcaacddccbddddaaabdccabcaaabdccaacaadbdccacdbdaabdabcdcccdacadddccbcdadddacbcbcdadbaddadcdbaadbbcbbbcbadabbbdbcccaccdccccadaccccaadbbbbaabdcdadacabccbbdcbaadbdbccaccbadcadcabbbaabbddaaacdbbadcbabdacbaacadbcddbadddaacbddddbbbacbdcdaaddbcdbcddbacabcabdbadddccacbadcdbcdccccacbcbbbabababadaabaadbabdaaddbbcbaabbdcbcabbacccdcdcccdbddbdadccddcbadbbbacadddddcbabdacccabacddbcbbacabdacaccccddccabdaababdacacaabadadaaccaabbbccbdccdabcaaddbcdcabcaacddbabcbcabdacccbcacbcacdddbabdbbaacbaacdabddacbbcbbddadbbcdacdacbbdabbabbacbabcbbcadbdaccbccddcddacaadadadddbcdacdbcbdcddacbabcaddbaccdabaaadddbdacababdbbbdcbddddbdcdbcbbddcbdbddcbabacdbdddddbcbadcabacdddacbcbaacadddbcaabccddbdabdcccacdacdddbcadbacddcabadddcbbbadaacdccadbccdacdabbcacaddabacabbdadbbacbdccbdcdccacbadcdbcdcdbdcccbccdddacbbbccddbbbbbcccacdbcacaaaabbcabccdcdcdaaccdbcdbabccddcddddbcdbbbaaaccbcbdacdcbabcaadcbcbaacbcdcbcaddccdbabccabaccbdddadaabddbaccbbcaccbaadbaccacbcdaabdbcacdbdcaddcdadacaabcdcbadbbbbcabcbdcabacdbbdcbaadbadcabdddcddbdabdcdbcbacacadaaacddcacaabddcddacacabbccbbdcdddcbcdbbbdaacdbcccdcccbdbbdababdbbcbdadcbcaccccddadcdacdabbccccaadbccddabbbdbdcccacbbaabccdbbddababdbddccabbcaacbbbcdaadcacdbccbdcdacdbadddccbbdbbdacbbbacadccadbbadcdddadcabaddaacddcabcdccbdcdddbaaaadcbbdddcacdbbbcdbdbcccdcbcdcabbacddcaabccbdaccbbbbabcbdbaadccdcdbdbabcabadcbcdcccadbaaabacaddbabcaccdabcdadcbdbacbbcbdcdccacdadadbcacddabdbacccbaaccacaadcbbbcaaaaddbabdbacdcddbcdadbbaddabccdcdbcdbdbadcaddbbcabadcbdcccaccdbcccbbaadbcdddbbbaadacbadaabcbddaccaddabbaadaaacccadddcdcddadcaacadcabddcddabbaddabdbbcadccbadccadccdbbbbabdcaaddbadcddccabacbbdddadcbcaadcaadabbcdbaadaadcdccdaadadddcdbdbbdccdaadabaaacdaabdcdabddaaddbdbabdaddbbccacadbbbdaddabdabdcdadccaccdcdbcdbcbcbbaabccacaacddddcbbdbccacaddddaacbbcbbdbddabcaacaccdbadbadbabdcaccdbadcabbcbabaaccbbaaabbccdcbcbdadccdabdcbbcddbccbddcbbadcaacabdbdbbbacbcaabbbbcbdcacacdbccadaaacdbcdccdbabbcaabbabbcddcaaadabcccacbdbbdddcacddcbdccacbbbbcbcdcdabddcaabacdaddaccacdbcbacdcbbdccdcdbbcdbbbabacbbcbaabbbcaacccadbdbcccbcdabbdbcacacbbbcbcdbcacbccaccddccbabadaacacaaaaddcbccdcaadddabbddadcdaacbddbbcabaadacbdaabadcadbabaabcaaacaabbbdcbccadcbccdcbcacbcccdcabdcbdabaaadaccaadccbabdaadccaddccacdbcddccbddbbdccacbddcdbcbddbcdacbdcbcdddbacbbbbcdccccbdacdbdcabcdcdcbcabbdbddccabadadbaaadadadbcacbbdabacdcbdddbabcadbdccbbaddadbcccbbdbadaddbddcddabacbbdccaaccddbbadbadbcbbadacaaccdcacddbbdddbcdbcdabccadcdcaabacdbbccbdcacdacabcbddbbcdcdbbaabdbbdadadbddbbbbdcaccbbbbccaaddaacbcdcdddacadbadbacadabbaacabacabdaabdbbbaabaaacdbcadbdcbdbcdbbdccbddaaaddaaadcadadcbcbbaacbababcabdbcdbbccaabbdbbdbbabaabccdddcddcdbdadbddaadabbbdadbaadacbcdcdaadbdaddbbcbcbabdaddbdccaaaccccdaadaacdacbbbbbadacdccdbacacdbccdacaccccbaadbcaccbccdaddcdbdccacbcdaadbadbadbcbdbddaaadddabacddadaabcacabcabaadcbdcacbcacdcdaaaaaaaaddadddabacaaaddacbcdabbcbcabdcacbcdccaaadddcccbbaaacacacdbbbccbabcbcaddcdbcccbaaadacacadddddaacabbaddcabcdbccccbcddddabbbabdbabcaddacbcdddabccbdcabcabacddbabadabdccdadcadababbdcaccdbdbbacacacadaddcabcbbbaacaaacdacadaabbdacdcdcbadabdabdcacbcabccbaacbdcbcdbadbabadabcbbcbbdcbcbdacaaacdbabaccdbbccbbacbadcdcdaacbadaccadddddadccdccaabbaabacaccdcbadbdbaccbaaacaacdaaccbdddbcdcdaababcccbccbbaaaddadaddbcbbbcdadcccdddbbccbcaabadcbadaacdbbabcdcbbddaddacbaccbdaccabdcbbccdacdddbadaadaaccccabaabaccaaddcadabaabddabaabcaddddddbbaacacbabcbbdcbbaccaabddabacbbacaaaadcccadbcddbdaaccdababbbbbccbababdabcbdaccdbcbaaaaddaccadaaddabddcccdcbcbbcccacdabcbacccacacdbbcbcdaabbaaacddbaadcadaacbcbdadddbbccacdcbccbddddbbbbcacccbabaccadbcaaccbbdabdcdcbbbbdbcbcbdaddacadaabcbbcdabababaaadbbbadbcddccaaabdaddbdbcdabacdbdadbdabbadadcabcdcbacdccbadabbadcddacbcccadadabccddbbbccddaddcbddddcacaacadadabcabbdbdcdcbccdbadccbbccbbcbabcbadcaddcdabbdcdcdacdcbbccdaaadadabababdadcbabacdbdddbdcabacbddbbacbccaabdbcdaadadaddcabaacdbdcddaaacbcdcbabbbabcdcbbaadccbbbabbbbdcbdddababadcbdacdacdddccdbdcddabcdabcaccbdcddaabbcacbbcaadabababdcadadbcddbddbddcddbccabbddbabdadccbadcbcacadcddacadcdccbaaddccaadbdcdcbadbcadcadcbaccbddbabcccbcbaadccacddadbcdbaddbbbdcbaacccbbdbbabadbdccbdddddabbdcbbaaccbcbbdccbbaddbabcabdbbabadabbccadbadbdacbdcbacbcaccdbacadcddddbdababcdaabdacbbabdbcaaaacddcbbbdadbcdccdbcccbcbccccbaababdcacbbddccadcddbbaaccbcacadbcbbbbaccabdcadaddbdbbcdacacdbcdabaaacbcabbbdbdaabccadcddbdacddbaccddcbbccdadcaaabbcacdabbdcbdbbbaacdcabdcccddadbdaaccadcccbcbaccadbcbdccdbbbaadcaaddaaaaaaaadbcaaccdbaacddabccdbdacbbacdbbbdaabcbbdcdabaacaccbddcaaadddabacccaacbbcadddcbdcdabdbadaddbbdcbbddadbcaccdddbbaccdcbbdbdbbcdadbaacabaabacbdbcddbccbbcdbaaacddacbaccddadaaccbdcbdcbbaaddaccabadadacbaccccbaabcdbccbddadbabcbacdbcccacbbacdcaaddccabadbaadabbcbcbdcccbadabcbdcabdcdbddcbadbcccbacabaadbcccccddbaddbddabaadacdcdbadacabcbbaaaabcdddcabddabcaccbaadadcbdacbabbbabbaaaddccdbdbccbcaddbccacbabcacdbbcddacdccaaadbbbadcdcbcccbbccbccdbcbacdaacccdbdcaccdbdbdcdcdcaaabcddadaccddadcaabadccdadacbdaadadaccbaccddbcabadacacaadadddbaadbbbaabdcbddcaadaddddcdcbddbadbbababbdbabbabadccdbcbdcabdbcbcccaaadcdccbcaaccdcbcdddbdcdccccdcaabcdcaadaaddccdcbddbaddcaadaccbdcddbdddcdbbbdcbbccbcbacdcbcbabcadbacaaccddbaaababcaaaaaabccaddacdabadbcabccaabcabdcaaabddabcdcddccbabbaabcccbdcdacbbcdaadbddbaccdadbbddbcddaddbdbcaacbabcadcacdbadddbcccdcadacbbcacbdcadaacaadccaacbbabaaadbddaccccbbdadaddaadddddabbdcacbdaaacbadcbadbacbacbbbadcdacdddcccdabacaadbdaddcbcccbcdbdaacbdccacbbcdababaddbbcbdddcccbdaddabdbacddbbbcabcbddbcccabcbcdcacdbaaadbdbbbadccdadddccbadbbbacccadaadcdddccdbbcbdccaaccccbdbdbadcabacacdaccdcbcbddcddccbaacbcddadacdbdadddbbdbdcaaddddacaaadbbbdcbabbddcbcbcddaadbdabdbcbbdddaaaddbadbabdabddadadbcabbaaccaaaadacbbddcdccdcdbbadaabdddddcbcadccabcdcddbcbbddcbadcddcdbabdcddbaadbadaacdbdcdcbaccbacdbccccddcbbdddcbbdccadcaabdcdbbccccadddbdbdaccccbabdaddadaccdacaacabcadbacbddbccbbccabcabaddaacccbbdadcddcdacadbadbbdccbaddcbbcbbddccbabbdddcacddbccacdcdcbbbacdcdbaabacdcbbcccaabababcbbbcaadcbcbbacdabcbbaccaabccccbcdcccacdbdcabadbddbbcaccdbabbbdbbddbbcddbabccbbbabcaabbacbddcddaadccbcdbdbdcacdadbdbacaadaaabadbabbdddbaadcbddcbaadcacacbababadcbabcdadbabdaadddacbddbcbbddaccdbbdcabdbbddabcbbacabadbbcdaddccddaadaabaaacdbbadadababdcddbcacabbabccabdaaabcdddababcdacaadbdcdbbaddbddabdabdacdcdcccadbbbdbbdbbbcbcddbcdbcbacadddbacaadaacbbdbccbaabcdcaabbadaabbbbbcabbcbbcdddabbadbbcdcdacdccbbbaabcbaadbaccbbcbcbbbcbcbaaabcbcccadccdacadbdddcaccdbccccccbdadaaadbabbadaabaadcaaaabcbcdbdcdabdddddbbdcadacadbcbabbdddddbbdcbbdbbddadaacbbadddbacdddbadaadabdccaddbcabbaaaadabaaadbccbbddacabbbacbacabacdcbbbbaadcbdbbcbbcddcdadbddcbccbdabcbaaabcdcabdcaaabbdabcbcaddabbdbcacdaacdaaaaddbacabcacbbdcbbdbacacabbcaddbbcaabacaccadacbdaaabdcdccabadabbadabdcbcdbcabccabccbcaccbbdcbbadbabdbbadcdaccacdacbabbaadccbdbdbbadadcbacdbddccdadbcadbcccbdddacccdbbcddadbcacaccbbdccbcddbdcdbadddaacccbaccdacadcadbcbabcbcabddcdacbabccbcaddcbdccbacdbccbcdcabacadaacdcacaaadabbcdcaaccaddaccacddadabacccadcddaccbadbdbdcbdbbbcacbbcabdbccddcabdbddadcbccddadcdabaddbaaddcdacacbddacbcababadabcbbdadcadaccababdddabcaaccbdabcdbcaaadaddbcbbcdcccbbdbdcbbcccbabcbcbddaacacbdccacbdccabbccbadaddcdaacbbdbccdbdddcacdddadbddbbbbbabccabbcdbcaddacdbbdbcadcbabcadaababdddbbcacdcaddaccaadcdcadddcddcccdaddadcadabccdcdcdbcacdadbbadbbacaccbacdbcadbacbabbdcddcabccdcbccaccdddbbcbdbdadabcabbcaacddabdddababcbababbdaddcdbdaccacbccbcbbcdabdcbbbddddabcddcdcccddbdccdcbcadcbcacdacbbdcccabacdbdbccbbccbbacacbaabccabadbccccddcabbddbbbdcaadbddadcacbcbbbabddadddbcdbddbccccbcbdddcaadcdaacbbcdadbcacccdaccddbbdabcbaaccbcdccaaabbbcbbbdcbbcacacbdaacaadbadacadaadddbdbaaccadabaddabcdcadbaabdbabcbbdcbcbddaaaabdbacdbadcdadcbdccadabbabdaacbadbbcaaadddbbbaddacccbdaccaaddbcdadcccccdacbcaccbbbbddcdadaaadbdccdddcbcdaabdaaaadcacdcdacbddbcabcdaccbacbdbccadccbbdabbdcadbaccbadbdbadaacddadaabddacdcdcdbacadddcccaddacbcdadacbacacddbbdcdaccbabbaadacbcdcbbcdbaadbbcaadcbdbbccdbdddddcdabcbcddccaabcdabdbdcbcccbaacddababadcbddccacbcdcabdccabdcdccaccabaacaabccaddcabddbccbddccacabbcdcabdbbbcbcdbbaabcdcccdabcbaadbdbbdaccdabdadbccdbccbdbabcccbcbaacacaacbbabccaddcadbcdabddacccaccaccdadabdbcddccacbacddcbbcdaddbdccbbdbaabbadcacadbadaadccdcdaabdccbcbdbbaacacdbbbbbdbcbbcbabdcbabccacddaaacccdcaacddddbcbacdbddcacaccdcdaddbdaacaddadacdddccaddaabbbbbaccddbdabbccbaabbbdcacabdbcbcadaccaadaaaccdadbbbbdddcdcccdbabbaacbbdbdcbcbbbabadbdbddadcaaddcbcabbacbcdcdcbbabdbcbaaacacdbadaccbaacbdcadaabcdcdadcaddcddcadcaddbabbcabacccccdddbaacddabbadbcabccaddddcadaddcccacdcbbcdcdbcdbbbcddbacdbbddcabdcdbcbaaaaccdababbdbdcaddbacbcdccabbaadcbddcdcdabdadbdacabbabcccccdbbaaabbbcdcaadaaacdbcabbccbabbcccaddaccaaabdbbdabccdbcaccdccbdbbabbcddcccaddcbccaddaaccdaacdbddaadddcbbddddbcbdddadbcbcccbaccbddbbdddabcbbcbbacabdcdacdbaabdadbcadcaadadcdaabbaacdcabbaccdccacbbdccadcdabddcbdbcdbbcaddcacdddaabccbaaccdbabccbbbdcbdacbbdbaabccaabaddbaacdacbddaabcbaccbcacdacccadacdbdbdcadcbbcbacbcdadadbbbcddccbcbababcdbbadcbbbbdccdccccbaabdaabddaccdccbcabdbbdbdbbcacabbcdcdccccacbcaccaaadbcbabccacbbbdcbacbdcdddadabdcdcbccdacdbbcdbcbabacbcccdbacbcaccdadacadadbbacdbbadabcbccdccdcccdbabdcccaacdacbddcdaaaaddbddaaccaacdcacccbccabbbdbcdaabbabaccbaacdcbaacaacbcbccdaccdcbaaccabbbdabbcabccccdcbbcdcbdcadbabaccaadcaddbbdbbaaacaadbdcaaccbbbdbacabcbbcabadbbaaadbdbcbdacabdbbbbabaccbdaaabaacbcdbbadddbccabcadbbdccacddabcbbadbcabaddbcaacaadddadbcccdcddddbacdabacbbdcdbaaacdbbbadacacdccbdddaccdbaddbcbcbbabcdcccdbdadddacadacbdcddcdbcbacbcbdbbcbdbccdcdabadddbbaccaadbdcabccbacbaabddbddadadddcdbcdadcbabcbadddbadadcbbbbbaaadaccbdcddbacbddadcabcccdcdacbabbaccacaaacacbbcadddddbcddaacaaccbabadbdcaddbabccdbdaaadabaabcbdcdbdcdabbcaccaadaddadcaabaabbdaccdddcbbbcdadaaadccabadabcadaaaadacadbbadacbbdacddcbbadddadcccbdabbbabcbabbbacacadbcbacdadbdbcbbbacacbccdacbbdaccdabaaaddabbccddbcbbaaadadbaabbadccccddddccbcabbbadacabcabcdbdccbabdcadccbdcbcdcbbbabdcbbbdbcabbbddacdcbdccababaabaacddbabcbcdddbabdbbabdbcccdcbacacbbbbcbbccccaacbbdabaadddacababcdaacbddbdcdbddabbabdbcdbbbbcdabadcaaddacbcdcabcccadbccbbbdccadaabdddaccbabdddbbdbbbacbdbbcaaaabdbabbccdabdadbdbdbaacbdddcdbdbcccbaddbdbadbccabbcaabcadbdbcbabadbdcdaccadcbcccbbabdccccbcbdadaaaccdbacdbacbabdddadbcbacccaccdcadbdbbdddadcdccadacdcabcaadbbdcdddcddabbbbbbadbcacbcdbdbdadbbaddbbddababdcbbcddddbbdbabbbdadbbadabbdbacbcccaacbddbacdbbccddbbaccaccadbdcddabcaccdbdbdcaddbbbdcbddcbadadbbaccdbabcbdcdbaccdadcacbdddbccdaaabbabbdccccdbcdabdcbbbaaccbbcbccbcccbdadadadadaabacdbabbccaaadaccbcabdbdbcabccbdacbbcbdaccdbbbadababbbdaadccabbaacaacbbbbcadbccaadbcdadcbaaaabcbddcbacbacbabbcbadcabdbdcddbcbdbacdcdbbabdcaaddddaabcacabcdbddbaaccbdccbcbdaacdcdcdbaddcddcbdbbadbadbacaabdaacbbbcdacadaaccddbbbcbabddbbdbdccaaadbcbcdacbddbbaadcdcabdbbdcccdbddbbadbbbccaacdccbcbaccccccccbbcbdaabdaaacccadbaccbbadbbbcaccccdccbacdbaccdadccddddcdcbaaacdcbcaacadacddadddababccdbadcdbbcddbddccbaddbbddccdbbdcdbbccadcdaaabcbcadbcadadbcacadbdcbbcddaadddabdacdbcbcaabdbcadcabdaaadacccbabdddbdbaacdaabbbadaadccdddacbabcbaddbacacadccaadcdcbcddacccbdaaadcddcbbcbcadacbabbcdcdaacadddabccbaccbadaaacdbaaadddbbabacdcbbdadcbddacbdccbbaaddbacddbbaaadbcbcbccaccbcaddcacdbcdacdcabbbadcdbabbbbcadbdcdabdcabcdbbdccaddccbbdaacddddbddbdbcdabbababddabbdaadaaabcabdccbabdbbdabbcacbabcacabcbadcdccbdddddbcadbbbdddcbdaadcdacacbcbbddccbbcbbcbcddbadcbbababcddcadcbabbcccabbdcaddcdaabccccbcccdbcabbcddbbcadcaadcdcddbbdabccbaaccadcbdccccacaccbcdddbdbccaabcdaccacddaabbabbdcadaaadcbddcbdbdcaddbbcaacabbcbdacbaccaaacbdcddcabbacdbabbcdddcbacacbcbdaacdcbaccdcbcdbdaaccadbadccdbbacaddcacbaaaddaaddcdcbccbabddaddbbdbadbdcaabaacabdcaadadbddaacbaacdabddbcdbaacaaccbcbcddabbbcbabdbaacdcdbaacaaabcaaacddcbbacdcddbcadbbacdabdddcccbadacdaccbdbcdcbccdcbadbabbbcaddbabadaadcbdcdacbcadbababcabcacabbcbbdaacbcabaabdcddbccbccbaddacaaccbbaddbadbdaabdcacbcbbcccdadabcdaacbcdaddcddbacdbddadbbbbbdabaddcbdcdaabcbdcadbcabadaccadabbbcadbcbbabbcdbcddcddacdcbbabccdaacddcdcbbbcadaccbbdbbaabccbcbcdaddbaadcdbaabdddbbdbabacdbabccdcbadbdcbcdbcdabbddaddcabccdaaaddcdacadcbabdabdcaccccbcdddcdaccbcccadabdcbbbdcadcbddacbcdaaabdccddcadacbcccdcddabaadcccadaabccdcbaaadbdaaaacaaddbcbccbdbabccadbabccbadbdaccaacdcdcddadbbabcabaadbdbddbadbadacbbdcccccbabbdccaaddbdddcbbbcbacdcacdbcadccdbdccbdbaacacabacabbcaaacdddaaaadbcbbcaccbaddbccadabdacbaacbbdadcbbacdccbaababcacdccbbaababbdcbabdbcaaacdbccddadccbbbbbcbddcbcccadbcbdabdabccdaaaddbbaddcdadbaabdbcaabbaacbddaacaddabbccbbbdccdccdbbaaccdbdbbabbbabcaddcbbcabdbcacdabcbdacadbdbabbcbbaaddacaddcdbaacaacddcacaabdbcbbbcdddcbccbadccdadbcadbacdcaacacababdddaddcdbbabdabbcabbabcbdbaaddccbcdcacaaddabaabcdcddcdaddcdadbaadbaacbcdccdbdbcabdacddacbdbcaaddaaddbddbddbdcaddadddbbbabbcbdacdadaabaacdccddbcccbacbabdddbbdbdaadcdaaccbcdccdcbabbcddaadabdcaabdaccaacddbbacdaabbcbcccaccddcdbbcdcacaccdbacdbaccadcdabdaddddbbcddcccbcacaddaabbaabccbdadcbabdbbccbcbccabdaddcccddccbadbcbbdddadaccabdaaaddbcdbdcdcdbccdbdcdbcbcbbbdcdbdcdaddccdbcbbbabddccabdbcdcdddcacaacccbaadbacdbcdabadcaccdaabdacbddddcdccbaadcdacbccacbcbadabddddbaccbbaaddacabdcdccbbdcaaaabbdbcabaccaaaaadadabaabbdbdadbddabbddcadcacdccbcbcacdaabbbcdcbbcdcdaacdcabcbacdacaddabbabcadcdbbcadcccabdbbbadaadaadddacdabdbbadcabbcddcccdacaacabcbacbaaacbbdcbaacdddddacabddcbdbcaccddbaabadbdbcdadddbdccbadadbadbdbbbdadcdcbdbadabbaddddbcddaacdaabbbddcdadbadcddaaabaaaadcddbbdcdbdbbdccbdbbcdcaacadbabacbcabaababaaaaaabcdddbbbbbbadcadadbacdaaabacdcabcddcdbdbddbccdbcacdcddaaaaddcbbaaccbaabdddadbacddcaddabacacbbabaaddcaddadcbbaacbddabcdaabcbbcddddbddcbdcadddcadabccdadbadbdbbcdbacdcbacccbacbccdbddcccaccdbcbbdddcddcaadbdacddcbcaccbadcbaaaccbabadbbcdbcccccbbcabdcdcbbbcdabcaccddaaccbbadcdbbcbdcddbbaacdaaabbabbadbdbbccaddbcacacddaacbbadbbdaabaaabdacbbbcbbddbddabccbddccbcadcdbbadacaaabacabaabcbdaccdaabdacaacaaaddadacbaabbbaaccbcabbdacdacbcbabbcbcbdabacbbaacdbabaddcabaacbcddbdbbaccdbddcdbcccadcbcbddabaadbabbabcdcdaabddcabdcddadabaddbbdcddcbbcbcbaaccaadbabdcdbccdaccdbcbbacdadcabbcaadacbcbbccdbcbabddbcdbcddabcadadbccccdcdbcdcabaaadbdcaaccbdcbcdbbbbccdcabcbccdcdaddbcddacacaacccacbabccaadcbccdbcaadcbbabbccacbbadcbbcadccdbacbccadabddccddbbcdbacaddbdacbdbccdbcaccbaaabacddabcbddcdcbaadadccdcddbcccdaaabaacaccadcdcbacbabdabdbbcbbdacdaddcaddacacbaccaabdbadaacdadabbadcadccacddadcbacacadbbbcdcdcbbcbdbaadbdabbdbdacddcbccabcbdabbdcdcaabcadcabdcbabadaccccababcdcdddadabadbdbacacbdbbbbcdbdbbcabbbaddcadabcabacabcacacaccabadadddacdbcdadccadcbaddabddababadcbbbabcddcabbabcbccbcbabbbbbacbacbabbdacbbcccdbbbdbaadcacccaadacabadacdbdbbbddccdbdaadbcdcacacacabdcaccdddacaabddaaacacabdacabdadbdcbdcbadcacccadabbddcbcbcbdbcaaaadccdabcbaccccacaacacabbbcacbcabacbccddadbdbcdabcadcaabaabcccdcaddabdcdacadcbcbaccdcccdaadbabacdaadacdcaadbabcbcabccbdaaddbbabaccaaacababdcacdddcbcdcdaccbaadbbdaddcddccccdaddbdbaacdbcabbabdddcbbccadccddcdadcbbbcbcccdbacaddcdaacbcadcbddbbaadacdbbdccacccacabbcddccaacdbccddacdaaaaccaabbccbadddbccbcacbabcddcdcbcabdbbcbdccdccdcddabadddbcadcdacbdbcdcbdccbdbabbacdbdacdcadaadbcccadcacdaabdadabcbbdddacacddcbdbdabcaddbddbabbddcbdadbadcbabcbbabaacbcccbaccabcbabbbccddcbacdddcdbbddacadddbaddaacadcccbcbcdbacacbcacadabdcdadcacbccacadddbbbbdcdcbbddcacacaccbbccacbbbbbabdbcdcdbbddbdbcbcccbacbbccdbdcadcaadbdacbbabcccdcddbdaabccccdbaddaaabaabadbbaddcadaddcadcdacdbbcaaaadcdacbcacadddcddaccabcdabbacbabbdbbcccccbdccdbadadcdddbbaccdddccbdaacbcdcadcabadbbccddbaddbaddddcbcccbacabcbbacaccbadcabdbbdacbdbccacaacabbdcccccccccdccadbddadcdacdcacdbabcababacbccbaaddbaaadcdabbcdcbaabcdbddacbdddddabdbcbcccbbbcccbbcacbadccccacbcbcddcacbcdcbdbabcabbaccccddcdcadadcadbcbccdacdbaacddacccaacaadccddabdddbccddaacddbcbcccadcabbbdcabbdccdcbbbdbcdaaaacbbaaccdcbadbdbbddcacabdcdbccbababdaaccdddddddbcbadaabdcabcddcbaddbcdacaccccacccdcbaccbacbaadccaaabccbcbabddbabcdbacbcdcccabcdcdbcbbbdcbcbdddbacababdabcacacaaadcacdbabcadcddadabccadcacaabbdddccdbdadcdacbcaaaacbbaaddcccddabbccdadbabcaadbcbbabbdccdddcdaaddcdddadabcddadccdbadcacdbcdadadaadddccabbbdbaccdabadbdbaabcccaadbccccddaabddcdabaddccdcbaabcdbadbcabcbccdbacdddcaccbabcdbacdadcdcdcabbdbcbbaadbdcabbacbcbbcabcdabbabaddbdbadbdadbbcacbbcaccadbacacadacacbacdbdadcadcbddccbcbbcdbaacccacdaadbdbaadaadaacdbddcdabbbbacbbbbbaacbababcadcabdaddccbbcbdcdadcacbbdaacddccbcddbcbcbbdadbaadcbddaabbacdabcaaabcbbbaccdabaabaabdbaadcaccbcdcddddadabacaaddabcdadcaabbddaaabbbccbdbbcdaababadabdacbaddadbbbbaadabcbadccdbbadbaccccdacbccccbababbbbacdabdbcccbaacadcbdabadccdaacaacabcaabdadaaabacdbabdccadbbdcaccdabaabbcbaacbcdcdcddbdbcbaaaabccdbadaddaccadadddcacadabacbcbbbacbccabadcdacadbbccdbbccaaabdbbbcbaccbcdabbbcabbbadabcbbbbdaaaacbabadbababcdbcdbbdcdadbbbabcccbacadaaaacabdddbbdbabbacdbbddcaccdbabdcdabacbaabbbdbddbdbdacccccdcbcdbcddadbadbdbadcbabdcaabdadaacacbadbcaaadbdaddacabbadccbdbcadabcacabccbcdbcdbddbcababdabdcaddbbcbbddddaadcddddbcaabcabbbcddbdaddcadbdbdaabaaacaccbbacbabadcdcdacbadcdbabbbcccaadcdcddcbddbcdcdcdabcccababadbabaddddabddadaccaabadbbdbdacbdcddadcabbdacddadcadddddabbddddcdbcbddbadddcdbaadaadbcadabccddacacdaaaaddaaacacdbdbabcaccbdcccdbdcdabbadababbcbaabadbcacbdcdbaadabbdcccbacacbbabcadacbcbadaadacacdbdbddbdcdcbbcabdcccadabcadacdccddbcdcabcdaddbbddbdbccbbdacbddddcdbdbdbdbadaacaddbacacccacdbabccbbbbbdabdcdcdbacdaccbdccadaaacbbbbcbdbbadbabdbccccacbacdccbddaaacbabbcddcacddacbdbdbdddbaabbbdaddbdbbbbddccacaaacacabdcbcddddcccbdbdbbdabacadacbbbdacadcddbcddaaabdacccddddcdccaadaddbbbcbabdabdaccadbaabcabbdcbdbbbdcdabccdaadddadbabcddbcdbbbcbadcbdddcadcddbabbaccddbbaacbbbbbbbbacbccccaaacaacbcdddacddbddaccddcbaddddbbcdcbcdcacbbcbaaacabdacdadcbbbabbcbccddcbacaabcdaccdbadccdccddacaddbaadbaddbadcadbcbabacacbadccbbadaabbbdadaddaaadadbdccaaacaababcaabdcabacccadddcdbbbcbddbbcbdacdbbcdddbdabbacddcbabacadaacadcabddaadadacdcbadabbabcdccccdcabbdacbccddaabacdbcccabcbaaadbccadbacacaddddbadcddcacadccacadbdabacdbaabcbcacbbbcbbadcbcdcbcbadcdbddbabdaadcbcdacdacdcabdcacbdbccadbddbaddcccdadbbabcddbbbacdcdcbdbdcbcdabdbcbbcabddbdbacdacbbdabbbbaaacbabcdbdbddadaaccddbcadbcabadaccbdcacbdccabcbddacdadcacadaddacacbdcccbccbddcdadcdbcbcdacbbdabdcdbcdabdcacaaccdddbcccdcdbdcbdbaabddbadbdbadcdddbdbdcdaaabbbbccadbacdccbddabbaaaadadaddabdcdcbcddabdbababdabdacbabbbbacdbccdaaacdcbabbddaccdadbabddbaabadddddadbadccabaabdbacaabadbbdbdddaacbdaccbacdacaadaccdbacdbbabcacbbaadadbcbdccaadbacadadaadabbbccddcdddabbdcaadadbabddccddbaabbdbaaaacbbbcababacdbbbdbbacbcaaddbcdadbadaddcaaddbcdddacacabbccabcdbbdcaabcacdcacdacbaabccdddbbbcbdbaadccddbdabccacaacbdacadacaddadacddcdbdaddadcacbdaaacdbcdaaacacacdadbbdddbcabbccabcbcacdbcdbccaccbdcddadcdccddccbdcdcdccadacadcbdbdccddabbdbaddcdaaadbabbbcacccabdccdbcddbbaaabbadaddadcdbabbadbbcdcdbdbdbcbbabaccaabcdbbcbaccadabcbdaaaaaacabacabacbbcabccdddabbdbdbbbbcbbccbbbbabbccbdaddccccadbbcdbcacacbcccaadabaabaccdbccdbdbaddbbdcacdcaadcbaadcddbdddbcbdcdcbbdcbdacbacacabdbbbbcdaaccbdaabdcbacddddcabaadaccbbccdcadabdbbbbdbabaccacddccadadcddbddcadcbdbdadbdccccbdcccdcaaddcbbcbbbcbcaaacabadcbbbccdbbcdddbccaaabbadbacadcdccabbdabcddaddbcddddbabacaaacccbcbbdddaacaacdadacbabdbabaccdacdbdcbbaadaadbcdbddacdbbcbdbdbddcaccaccbaaadaaadcadadacdbcddccbdbbaadcadcdbabdabcdbbbcbccabbdacdaaddadaadabaccdcadbdcbcbbdcdcadcadaabdadbcacbaaadaadbdbacdabaaddcabdcdcaaddadabddaddcdabbabaaddccbacddbdbdaaabbabaccbdacbbdbdddbcddbbcbcbaaaddadabdbdbdbcadcdcadadbbccdaabacdbcdcbbccaacdbadbccaddddbcacdabcabdcbcababbbadbaddabccdadbbacbdcaaabcacdbabaadbbaddcbddaadddbdddccdaaabccdbccaadbdabbaabbdddcdcbccdacbaaacaaabccadabadbacabaaaaabcdcbcabbbacbdcacddbcabccddbacbdcababddbadacabacccadcdaadadddddcdddadbabbcdcbacbccccdacdbccdbcbdcadbbcdddaaddaaabddbbabbabbaacdababbabdcbcababddabbddcdbaccbdddabaabbacbbabbddaadcacbdcaaabcabaaddacbbdddbadaadabacbadaaddcdccdbadbadcbbabdcabcdbabcaaabcaddaabaddcaccbdadacbcadadddbdcdabacbbbadaadbbaadcaadcadadbcbbbbcdcbabccbccdaddbbbbcdbbabdbdabdaacbacadcadbabaddbaadcdbcabcbdbcccdacdbccbbdcccdadcadaadaaccbdcdabbacadcdbccbcbbcbdacddbdcbdabcdabbacbcaadbadcdbaabcacccdaddadddbabcdddbaaabaddcaabbddacdcaccaadccdabcdccadbaccabcacccaccbbdadbbddccccddcddddbbbaaacbdcdbaaabddbdbcdbacbadddbdbdbbddbcdaccddcadacdbdaddcbcbbcbbcaaaabbdabcaaddbbcbcaacdcdcbdbbcdcbbdbbacadddcccabbcccbcccdbccddbcdbadcabadcadcdaaaabbaccbbcaacabdaacaadddbcaadddacdcaacbbdbdabbcbbadcddbcaccccbacbaccbbacacbcdbbcdcbdcdbcabddcbdbabccdddcabbdaabaddccddccdcbcabbbabcdabbaabddcdbdabbcbaddcaddbabaaadbdbcadbddadddcdddccbcaadaaacddcbadcdcbabbdadbbddccdddaacabbbcbddcbcdadaaddcdcabcbbbccadabbcbbabdcbcbdaacbdaccdadbbcacacdbdadabdddacaadaddbddaabcacbddacddbaadcbddcdccaccbcbbdbabaacbbabadcccadabaacadbaddbbaccaccbbadcbdcbacdbdabcaadbacbaaadcdcbaaacbcabcccdbccdacccadccccadabbdcabdaadcddbacddbdacaaaabccdbcbadaccaccdabdbbdababbddddbacbdddbdbbcbcadccccbdcbddccbcbdcbcabdbcddcdcaccdaddcdbcdcbacccaddacbacccddabacbdabbbdddaabdbacadadbddccaabacaddbbbabbaadddcddcbccddadbcaacacbaabbdcbdccccacbbaaaccdacdbdbdbccaccbacbdabbadabbdcaccdaabddbcdbdcbddcdaacbdabccbadcabbddbbbbbaabddddcaacadadbcacacdddbaaccaaccdbbcbcdcbabadacabbdaadddaabdaabbdcabcbcabdcacbddbddabddcccabbbbcadbabdababbdaabcadadabdccdaacddccbdadbcbcbddbdaacdcaacbbbcbaddccccaccdacdddbdbabdddccadbadcccbabbcadcddaddabdabbbcaccddacacdaacacacadccaaabcdaaadddaccaddabbadddacdaadabbccdaacbbaabccaaaabbbbabdcdbadcbcabacadbdaabcadbbbabbdddcdbabcdaaacaccabddbdabcdbdcadadabdbbcbdcaadbddbabbcbcbdacdbbbdaacaccbddbadcdaadddbacdaaccbabdbbcddabcdcaaaacabaddcdbabcbddaddbdbcdcbadbbabdbbccbcdaddbbccbdaaddacadcdbbccddbabaddaddbcbadcccbcbababcbcdadcdbbadaabbbbddccbcdbaacddaccaacbbbacccdccadbaaccbbdadaccbdaacbbcacbadabcdcdbbccaadcbccbbbbcdbccaaabbbdddcbbcbaaacbdddbabbdbadbcccddbcbccddcdaacaaaabbabbdbcdcaaabbadacacdbabbabcabbdcdbbaddacabaddcbcbaddcbbcbcadbbbcddbdbcccbbcabbbaacabdddacbddbacadcaddcdbccabaabddcaabbadabdcddcadaddbdbbadcbcbcdadbabdccccccbccbdcacabacccadbaaacdacdacbcbaababbbaaadbacbcbcdbbdaddcddbabcaaccdacccbaccbadbadabccbbbdbddbccbbcabcacdbdaacabcdccdcdbbabcdddddddaaaaccadccbbcbbaaabcaaaccddcadddcbcbdcbcababcdabddbcbcccacbcbddadabbadbcbccaaacdbcccdcbaadddbccdaabdabccaccdaabadcbcdacdbbcbbddacddcdacdcdabbdcbadddcbddaadacbbdcbcacbddbdbccadacbbcadcdbcbacbbaddadcbdbaabcdcdabdbdbabadbbbadcabbdbccbddbacaabcdabadadabcacadbabcacaaabcdccbbbacccadaadcaabbcbcaabbddddcdacbddbcaaaacbdcdbacbdabcdaaabcdddcadccaacddbacbbbcababdacdcbdbccbdbcddbdcccbabcbbbadbaaaccddbaaabccaaabcdcddcaadadacadadbddbcdcadccbaadaabbbdbcddbbabaaaaaaaacbcbabdccadadddabbcdcadbaaccbccbcacbccbdcccbabdcdcabaccbbdcdcabbabaccbbddadcaadabbdccdabbdccdbcbbdbddabbcbbdbcacaccddbcbbcbaadabcddbaacaadbcdcdadaabcbcbabdacadbddcccaddddbbbdbaadbbdcbdddbbacbccdbacbaadadaccdcdbcbadaccdbccbcaaddddbbdacdcdcaaadadaccbbbbabcaabbcdaddddbcbdcccadccbbbbabadbbdacbcacdbdbaddddcdcbdcaccdaaddcbacdaaadbbdcdddabcbbbbdcdcaabbcbbcdbcaabadbbaccdabbdcadddbcdacaddaaadadadbddbdcbadaacccdaaabacdadabbdabbdccdbbdcacccdbdcdadcacabcdbcccaadbbadddcbacaccabbdaadcaabddbbaadbbcbcacdadabcbbbadcccbaadaaddcacaccbbbcabadcbdaaaaddadcaaddcaacbbabdbdcbdbcadcaddbdbbccccbbddaacaccdccdadbcbddabccdadbcccdcccbacacabaaaacdacdadaacadaccbbcbbdbcaacccbccccbbbdbbddbccdbdcddcccddaacbccbaadaabadbbdbcadcdccabcbdbaddabdbacadadddaacbcabadbbbbabdcabadcbabbcabbdbddbbbcacbccddbddaddcbbcdbbcdbcdadcaacdacbabaadcbddbcbbccdbaddddddadacdbacbaccccaabbcccaadddbdddadbbccdbbaaabcccdacdcdbbccbbabdcadaadccbabcbbbadcbbbbddbbcddbcccdaaccdabcaaddbabbadaaabbaaaacababcdddbbdbdbbcacddbabaaadbabdbcdadbcaabbbdcbbdacbdababbdbdcdbbbaddacbaaddddcaabdbbdcdcdbcdbbdbbacadbccdbcbbbacacdbddbbbadbaaadaadaabbcddbdcaabdcbbdcdadacbaddbabbbcccbddcadbccdcdabccddacadbacbbbbaadcdacccdacaaddabcddabbccacbdbbddcdabdcccaacccbbbacadddcadacdcdddaaaabbcdacaaadaacbcaacdaaaabdabbbddbbddbacacbdbcccddddbcacdbacbdcdabbbadabbaadacdadbacbcdbdddcdaccddcccabacdacacdbabadddcdbadcdacbdabbbdaacadcccccbbdaabcdbcabdaddbbdbcdabacdaabadbadbdcacabcbbbbaaacddabbdbdbadbbcbbcdaacddabdacadbdcaccabdbabdaccbdddacaabcbdbbbcbadcdbbadcbbbbdcbcdbaaacbadddbdcddcbccdbaadcacbcbcadddaabddbcbbcdaabdcddccdacbbadaaddcccccdbdcdadbabadaacbdacbdcbcaaaadcdcabdcaccdcbdacccdbcbdbcbaadcbbccdbdcbbdbdabdbdddccaddbadaddbbcdabbaabaccabbcdbadcbbdbcddababcaadbddccadbdcabdadaaadbdaabdadbbcbcbcadadcdcbcabcdccadddaccdcabaddacabcccbbdbbacdadcdacccadcdacccbcaaccddcdbacaaacadbadcbdddbbddaccdbadddbdbdcdddbdddbbcbccccbcaaccccaddbcdacbbcbbadbacccdbbbcabcdcdcbcbbbbadbadabccdcdbaacdcdcdacccacbdbcabaaaacabbacaacddabcaaabddababcbabdbaaccdabadbdadbacadcadacbaadabbcddbdacadaacdaaddbddaccabcaadcbccdccabcddbdbabbbdbaccadadcbdabdbcabcbbaababdcdbcbbbdcababaabdcaddabbcccbaaaadbddbadccdadadbddcdcbbaaabbbdbbdabddacdddadcdcbabcbadabcbdaabbccaddddcdcbaddcbaadccccdbabcdcdabbbdacdcbdbddbababcdbddccdddadccddddbdacddaccdddacabbbbdccaccadbcccbdbaacdcccdaaaacdbbadbcbdddccdabbccbdcaaccacaddbcddaaddbcccdabdacbbddccbbbabccccbccacccabacaadbadccbbdadabddbaddcdbcccbddbbbaddaddbbbcaccbddabdbadddbaaddcdadbcccdacaadcbaacdabdcbbbdbbbcbacbbccbbcbdaacbaaddbdcdacdbbccabcbacdcbcaddbdcacdabdcabaacbcdddacbddbdddcccaccbcbcabbccddcdbcdabacaddadbabcdacdbbbcddbbcdbcdcbcdcbdacddddbbdccbcbdadbaacbbbccbbddbabaadadabcdcacabaadbadcbabadddacadbbbbadabacabaabacdbcabaddcddbdbcbaacccdacbdcdacaaacdbacddddbccaabdadaabacaccabdccacccaccaaddbcbacddccdadbccccaacbbbcbbdcbcbddbddddbbabdcdcccbacccdacdcbabbaddbaadccdbbdabadabcddddacbddbcabdccbdbddcdabacbaccbdbcbccabddcbdbaddbbbbdccbdbbcaabdacdacaabbbcacbbdcaddabccdcdbdbccdadbdcddabcbacbabbbaabdbccccccdacbcdcbcaddddbdaacabccccccdbcaacaabcccccccbdbcaadabbcadccaabbbacdcdaabdadaaadddcacccccaadaaaaaccacdabbbbacadbacddccbdcccbcddbdcbbdbbadbdcdbcccabadcbbbabacbccadbabdcdddbbcbdaacadddaacabdcdccaabbddbadcbbaaabcddccddcdccbdcacbbbcadbdbcbabaaaacdaddcbabbddcdaabbbdaadbbcdbbdbabbddccbcbcabddbccbddccbcabdbbcccddddabbbdbcdcacdcabcdccdaaddcaddcabcdbdccddbcababacacbadbddddccdddddcadcaaddcaadcdabacbcbbabcbcdbcababcadcadacabadaaabbacacabaabccbdacabbabbbaddaaabbacdcbbcdbbbabacacbbbabdcaabcdccabacadbaccbdbcccacdadacacdcbbbabbdccdaaababbaabdccaadabbccadabdcdcbbccdaacdbdbdbdaacacaadbbdacacadbbdddddccaabcbacacbcadcdabbbabaaacbcdaadccdcbacdccdcabdddccdbddcdcdaaaddccdcacdaccbdcccdaddbdbdcadcccdaaaacdbcdcacbbcbddaadbdadccbacbdbaabdacbbdbcacabbabaaabcaadbccdddbbddabacdadabcaddaddcdcaaabbaddbbacbdabcbdcbbdddbbddbacccdabddabdddcdcdbaaabadcbcdcbdddbdccadbaccbbbcddacccadcdbbadbacbbcdbbbcbbdababaabccabcbdbbdbdacdcbaaaadadbddcdaabbaaacddbbdcccdddcbabcbcdcacbcbaddccdacdcacddbdcdbdcbabadcdbcdbaadccbbaacdbabcbbcdadabbacdabcadaccabacadcdccadabbdcadadcadccbdbcabcabdcacdcbdbdbdadcacdcacabcaccbaaaaccaccaaddbcabbdbdddcdabbdcacaddcaabccadadcbabadbbbdccbacccacbbcdbcbcabbcadcaccdbbdbabcaacdcabbcdabddaaccabdabbcdaacbdcbddbccabdacdadcacbcaacacdcbbdbcdcaacccbaaabbabbbbbbcaddabbdbbaddcdcbacadbdcbddbcaddddbcddaddbcdcadadacacddbcddacaaabccbbcbcbdcddacdbaaddcbcbcbdacdaabcaaddcdadabaababddbabcabcadbadddadccbabdabbbcdcadbcbccdaadbdabbbccddadcaababcbbdccccbbcdabdcccaddacccbcdbcabadadbddabdadcdabcbbddbccdadbdcdccdbabbacdacccccbabbadbaccbadbddcaacbddbdbdaddcddaaccbaadccdbbdadbbbcbbacbcaabddbcbbcbdcddbdcadbbbdaccacaadacccacddccaabacbbdacbdbcdabbccaccadacbbaaccaababadccbbbdcbbdbabcdbabacdcbcbdbccacccdbcbadadaccbacdacbcdaaaacdbabacbbcdcaabbbabadcddcbccaaddaaddacabcbacbcbcdbacaabcbdadbbbddadaccccabbabbbbadcdabbbcdadbadcccbbddbcbbabcdcabddcadbdbdbcddbbabbdcbaadcbaabcdcadcabaabccbaddbbacdccaacbabdcbdadadcdbadcddbacddbcdcccacbcaaddcdadcdddacaaccadcbaacbacdaaacaabbbccbadbdaaadaabbcdddcacaaddbabdbbdbaaabbacbbbbabaadbadbacaaacbddaacbdbaddaababbdacabbdccadaccbdbdabcbdabdacbbadcdbaababdbacdadbdadbadabdadcacbacbcadbdabccbabcbabbbdaaddadddcbacdbabbcbbdcbbabcbdbcbbdcbcaacdaadcbbbcdacbbcddbdcdbcdcbbbcbdbdbcdbaacddcccdabbbabdcddbccaadbbaacbccaaacbbcbbbbddaabbccabcacdacbbbacbddadcdaccddddbabcbbbbaddabccacbdaacabbcabadacabadddcbbbbbabdaabcdbdddacbacbccbcbcadcdbbaccaaadacbaaacadcbaacacaaabcaacdcadbaabbbabcbdcdbabdbddbabbbbcaaadaacaabbacacbcaabdcbbadbaaaddbdadcdcbcaccdddabadacabbdbbababccaaddaacadccbaabdacdacdccdbbbdbcabdcccccdccbdadbcacbbdbdcbadcadaccacdbddbdccdaabacabaccbbbdbcbcabaddcaaccacdcbabccdacaabbcabccbbbcaaddbbbdadcbcaacbdabddbcbddbcdccacbccdbdbdbaddabbdddabbaaabbddccbcbbabcdaabadaadbbdbdbbdacabacaadbbbcadcacbdbccadbabcbcbcadcdacdcdaddccdcaabbabdadacaacbdaadaddacdddbddaddacacdaabcadcbbdddbccabbbbacacadababcbacccdbdbbcdbabcaacaadcbbbccdcdbadcbabbadcadcdbbccacdaababdadbcabdababcbacaadadcdbdacaccbdddbdbadddcaadbbccadbdaccaacbbdccccaadddaddadbccbdcbbcccdccaccabbdcdccbbcabccbbdaabaaccdbabccaaacbaaaaaabdddbdaacdbbcacaabdbdbcbdcdddaaacabbdbacddacbbccadcbacccacaccacddabdaaacacbbdabaabacaacbdcbaaacadbbdbccbadddbacccdcdaabcddbccbadbdccddbdabdbbbacadaabcdaabcaaacbdcddacdabdccacbaddbcdbbbaacaaaaacbaccaaccbcdbdacdabccccadbabbdbdbbdddcddcdcbbddbacabccacbacddbdcbacbabdbdddddbbaadbdcccbcdacaabaabdaaadddabadccaaaccadccbdccaddabadbbabbdabaaababbdccbadcbaccdacbbdbcabdaaaccbacdcadcbbbbadaacbdaacbadbcbdbdbcbcbddcbccadaaccbaddbbdccaaddbdaabbaadbdaaabdddadbbacaaddbacabcdcbbccbdbabdddcdcdbccaadabadaabcdadaaccdbdababcddbcaadbdccbbcbaaaadddbcbabacdddcdacbbdadbadbadccbcaaacdcbabbacbadacabcaacdaaadcdcbcaadcaabbccddccbccddacbdbcbbdbbcbdcdcaacdabcabddcdabdcbdbbbabaccabdabbcaacbcbbadbaadbcbcaddbaacabaaddcabcdcbbdcbddddaadbabbcaccdacadcdaddccddbdabccdcacbddabdaaacdacdadbbcdabdddcdbcabccaccbdcdacbdbddacccbacbacaccababadccadbbcdddcbbadddddbcbaddcbbabdaddcbcdcdabaaacdbbaddbbbadaacacdbdabddacabaacbbddabdddbdbcdbbdabbcbbbaacdadccccacdddcbbddbbaccdccbcbadbabdaadbadaacdddacadabdbccaabccbbbaacbbbcbdbcdcacbccdababcbabdddabdcddbbdacaaaaacbdcbacccdaabacacadcabababcdbbcdcbcdcaaacabdbcabdaadcdbbbabbbdacbbbdcbcbadbbcabdcbaabddbdccccacacbddddcbadbcbcaadcdaddadbccdccbbcadcadadabdcdbbacaaccccadacadadabbbbbbbaccbbdbbabdbcaadaacbadccbabdbacbbcbddcdccbcbdcdcbbcadbdddadacaadadbcaaaabaaddcccbccabaddbabcddadacbdabbacccdabcbcbddcdbaaabdadcdaabcbdbacddcbabccacadcabaabbadccddbbdbddbcbdbbacadaadbbadcaabbbdcabcccbddcbcdadabcddadcbcbcaabadacdcabcbcacabcbdaddacdaabbddddadbbadbccdccbcacdccabbdbbaaddaddcadcbbbbaccadaacdbadbadbcdcddacdbbbdbdadddcbbcaaadaaddacdabcbcdabbbcbccdcdcaaabbdbbccdaadcbdbbdabacdbdbbcdbcddbbacdabacacdbadcaaddabcdadaaccbccbddcbcdbbaaaddcbbabbaacdbdbddcddbdaaadcabcbbbccbbcdbccabaabdabcdadadadccadbbabdbcbaabacbacbddbccbdcadbbbbadddaddcabaadddbccccacaababddaaaadddabccccdcaabcdadbdddacaaadbcdcbdbbdcdcdbaaccbcdbcadbababacdbadcbbaccaaabdccccdcacaadcaaaccbdbdccadabbcdbbaaabdcddcbadacabcbdcdcbdbdcabadcabbabbddadadacbbaadbacbaccadabcadbacbdabacadabacccabbdbcbbdcccbaddacaaaaddccbdbbbbbabddababcdbadcbbbacdbababddabacadaadbdadabadbaddabbaddbbacdabadaaccdbabdcbbcbccbabaabbdcdadcadbacdadcdbbdcabbdadadbbdcabbbcbdadccdcbbaadabdaadbcbbdcdbaccccddcdddbddcddabcdbacdababcabbbaddcccccbddcdbcbcbadbdadadbcdabdbcbaddbcccdabcddccadadbdbadbbddbbbbdccadddbcccbbcaacccadbacccdcacdbcbbcbbcbcbcdaddbcbbbccbbdacabdaabdadcccdadddbacacbabcdaddacccddbbadccdacdcbadbacaabbccddabaaaddbaaccdcdcdaccccbbcadcbbcdcbcddaacacccddaaababdaabbbbbdbcdcdbcadcdddbcabbaabbcbbcabccbcaacdabbdcccaababbbdbdbdcdbbaacdadbbadcddddabbabbcdbacacabadbcccdaaadcadcddbbdadabdddcbbdaacddcdadabbcdacadabbbbcbbadadcddadbbddcaccbddacbbbbdbaccaccacbbacdaabadcbbbcadccabbcdacdcbccaadcbbacacdcdabadadcbbbcadabacbcdcdabbabdcadbcddaadabacdbbdcdabbbdadaacbabbbcacbddaabcaaabbcbbdbbdcdcbaadbdddddbcadaaccbbdcacadbabcbcddbcdcbbdbcbcadcbbaccadbacbbddaddaddbcaaadbcdddabaadabbbbcccaabaddcbaaaaacbdadddbcdaacbdddcbbbaabddcabdbabcbdbcdccbdbcddbdbdcbbcbcbcddbaddabdcdadaabcbdcccccbdaaadbcacddcabccabcadcdbddabbcbdccadadacadddabcbbddddacbbcccbdadacbbcdaaabdddbdcaacbbadadcbddcadddbbdccdcbabcaadcbbcbdcbbccbbdaabdaacabaaadaaddbbabccaabaadbbcacdccdbaaccdcbdccbcbadbdacdcbbabbccddaacabbdbdddcadaabdbdcadadacbbdcbddccabcaaacbdcaaabaaabdbcdacaaadcccbabaccdbbaaddbcdacabdbadccdbacccadcbbaccddaaacdccdbacbacadcbabbbbbcbaaadcbbddcdadcaabcbaaaabacddcdbcbdcbbdcbcbbacbbdccddbcacababdbacdbacbdccdcaaacbabbbaadddbaadadabacacaadcdddcbdadccbcbcbdbbbacddcacddbdcaabcaccdcddbcadbbacdcbbddcaaacbaaacadaacacdbdaddaacdabcabaccaabccbdaddddcacacbcdcbcacaacbdbabacdadbbdbadaaddbdaaacaabddabadcbddadabbbdaacabbbadadbdaadaddacbdaddcadadddbdbaacccaacdbbccbcadcccababbdbabcbcdbdbbcccdbbdcabcbdcddcdcabcaabdbccdbbaccbacadcdbcddcbbadcbdbcdbccdcbdccbbdbacccccbbdddacbdaccbacdbaaddcbadcdcbadcddbbdbccccabadbbccdcaadbcdddccbdbcadaaddacdcbbadddcbaaddbabbdbcdbdbdbdacbddacddbaccbdddbabdbcbcbdacadccbabcacdcadadcacabbabaaccbacacadaccdbaadcccabababacbbbacbbdbcabbbacdabbbadcdccbdadadcaacbbbbbaaacadacbccdcacdbacadaaaacadbdcacaddbbddbabcacadbbbcbabcdadbdccdaacabadacddbabcbddadadccccdbbbbbaaddcabbdcbcdbaabcbbbdcbcddabbbabcddcbaccadbaaababcbbcddaadcbbcbbcdcbbacacbaddbdcbbbddccadadcbbcdaacaddddcaabcdacaddacadacccbdbaacdbccabccdbbdcddcabbdbbccbaabcdcbabbcbaaadabbbaddbdcabddbdbcbadcbaddaadaacbdcaabdcbdddadaccdbaddadbccbdcabadcacdccdccaddbbdbdbadbddcbaadabcdacadadabdbdcacdbbadddbcddcaaabcbaaacdcccaddcddbcbdabcdcddbcbadacbaaaacbddbdbbdbcbabcabdcccadbbdbadbdcaabcdbdddbbcdcaccbcccbabddbbbbacbaaddcacccccbdbcaccaaacbdbccadbddbbabcacbadcbccbdcbdcabcdcdacbaaaaabdadadcdcccdabcbabcbdbccdcacaccbcbbadcdcbcbdcadaaabccddbaacaadbbcbcddcadbacbcadaabdccbdcdddbcbbaadbacabaaaadadcbdbbabaddcbbcbbbdbcdaadbcccdbadaabadbbddbbbabcbaaaddabadccdccbbaccdaaaaccddcbabbbdbabbbdaacaacbacbcdbbbcaadcdabccddadbcdbccdadadbcdddadbaacadadcdcbbabdbbaccabdadbdcabdbdadabadadcabcacaabaacbdbaabddcccdababdbbdcbdbcddbcccdccdcadddcdcabccdabdabcaabcccbaadcbccbaadabcaaacccbbcabbbcbcdcadddbabcdbadabacadbdcabdcbabaabbdbddbddabacdbaabdbbdbadbabaddddcbbabdcbaacbdddcbcbccdcdcacadabadacbbbcadbbdacbabbcdaccddaadbdabcaacbdbaccaacdcaaabbcdbcbddabbaccdcacbacacbdbabcddbabcacdbdaacaacbbbcbbbdbabacbcdbcdaaccabacadcabbdbbbbccdadacdabccdcdccabcacacdbdbbbdbdddaabdddddbabdbbdcdbbbbdbacddbcdbdcabcbdddbcccbadadaacacabbbaddbaaacbdbdbcdaabbddddbcaabacddcabcabcdbcaaccbcbdabdbcbabbadccdbabcadbbcabcabdbdcbdcabccaadcbcbdacdbbbaaddbdadcadddcccbcacabdabdcbbadaaadbcabcbcdcadbbdbdcacccdbcbbabdddcdddabadddccdabbbcbcadbcdaaaabbbdbbcdaaadbbdacdbcaadacadcadacbaadacbbabccdadaddbbdbdbababdcaccccaddabcdcababcaaccdaccddbddcdadbdcccbcbdbdadbdacbbdcbcccccbbaaccccdabcaacbbcbbadbdcccccccabddbbdbacbcadacdddabccbcdadbbbacbbcdbbcccaddddadbbcaacdbdbbadbbdbadabcdabcdcbddcdbbddacbabdddbbadadcaacabdcddabccbccbdbabadcdcacdbabbcdadcbbbcadccdcaabdabadadbccdbcbbcbccaaaaaacababacacdbccbcbabacdbcccaddbccadbbbcadbabaacbadccbbadbaadbabaacbbcdccaddaccababcccdbcabcadddaadcbaaadcacaacdadccaababcccbbbbcbacbdabaaadcabdadabcbbbbcbcbcdcdcddaddbabcdbaacbbabddcdabbbbdcabcddadbdcacbcdbbccdacccddddabbaaadbdaabbaabcacbcadbdaaabbabdddbccabcdbdccbccacbdcdccabbcaadcdbdbacccbbbbcbbacccaaccdbdbbbccdbadbbdcccdbadcbdcbcabcdbacbcabbcdaacbccdbcdabdaacbabaccbccaacdbcbdbcaaccadbbcabbadabbdbdabbcddbbdccbcadccdcadbabbdcabcabcabaadabcdaccbaaabbbadcabcbbddcaddaddbcbabddadcadaabdcacbbbbadabcabdbbadcacdacddbaacbcdabcabcadacbddbddbcdccaacccaadbabbcdbccdcacaadcaccdabddaacbdddbbdadabbbcbcacdcaddddcbcdcaabdcbdcbbddbbaabdddaccddcbcaacbacabbbccbbacaacdacdbbdbaabcaaddcbcadddcbbbdacbddcbdabacaabccabaacccbbcbbcbbbddbdcbdbdbcadcbacdabcabcbbdbddccaabdbcdbbbacaddbbbbaacabacccabcbbdcdbdddbddbcddccdacdaadbacbccdcacccabccacbccddbaddcabcacddccabdccbabccadcdabbbdaacabdadbbdddcdacddbadddbbcccbdaacbcdccdbdacddcbcddaabadcdcdbcddccaacdccabddcadcababdaabcaabbdcadabcabccdbccaacccaccaaadccbdccadacaadddaababcabdbbacddabdbcccdddacacdbbbcdbabacdbbadddaccabbdacbabcccdacabdabcdbbadacccadaadccbabcbaadaadbbcbbdcbabbabddcadcccacbaabbccdccddcacacabddbdbdaababbadaaccddaabccdbcaddcdbdaabaccbccaaabcdbabaacbbcaccccaadbbacbdacacaddbcbbdcdbddccabcbaddadcdaabbcbbcdcadaabdbcacccaabdbccadcbccabaacdddaaadbbaaabcbcadddcbbbdaaaaaaadcdcbdccdaddaabbaabdabadaacadcbcbdadbbdccacaddabccbaadaddbcdaacccbccbbdabdcacaddbbaaacbddaccbdcadabaddcccbcacddbcbbabaddbacbdbbccbdbbccbbbababdbdaadbcbcbddccacddbdbccdbdccdabbdcadabbaaabaddcdacadbabdbccdbbdbabcabbcaabccbdcdcbacadcababbbcbaccdaccbddaddbbcaaabddddccacbbbabcddddcaddacbcbaabcbaabcccbddbcababddababbdabbbbddbbdacbdbacbbdbbadbbccdbbaccddccadaadaccdbabaabbdcaacaccbabcbcdbdcddaddcbbcbccdaacdcdbbcbcabdabaddcdadabcabacbacbaddbcacadcabbacdabbdbdcaabaabddddacadcdccbbbadccdbbdddbbcddabacdbcdcdbcabbaaadaabcbbcbbbcadcaacaadaabdcdcbadcacccdcdcbbabdbcbaccccbbdbaddbcdaddcdcdcaacddcadabbdcccadbbadaadcaddbbdadccacbbacdbbadcdbdbadcbcdcdbbacdbbdbddcbccbbcaddbbcaddcaacddbddcddcdcaacdabababdddaccadbbaadaddacadccbbdcbccdcbcdbdddddaaccabbcccbaaaccddcaadadadbcacdaabcdcdaabdadddaaabccbdddacabcbbbabdddcdcacbbbbbdcaacbaacbbdaaddacaddcdccccdadcdccbaacbcbabcbabacddcdacbbbdbcdcccabaccadbddcdabbdcacaadddbbacdbddabcdacccdabdbcbcaddacdadbccabdcbbdbaaabadddbcacbbcadaaacdaccccdbcdcbaccaabccbcddbbdadcccddadddcbdcbabdadacadcaadaaabdacaaaaabcbadaabbdbdbccacdbbbadddacbaaabdcabdcdbdababbdddbcbcbcdcaccbdddbdbcbbbdccdbcbdddacabacaaadddbbbcdabbcdbadbcbdabaacbbcacacbccdaaabdbdddbbaccabbcdabdbdbaacaabbdbddbcbcabdbbbacadddcabaadbbcdcccbaadcadbbaacbbcababbcdbbdadbcacaadbbdadaaababdaabddcbadcaacdabccdddcbabcdbbddddacdcacbddaabcaddcbcdadbbaadacaddbadaaccccaaccbabccbaaddacdcccddabdcbacdadaaaddabcdaaaadbbdcccaaddaadaacbbadabbbbdbbdbcaccdaabcbaadcbbbcadcabbaabdbdbadababadcabbbccccdcccdcdddabbdddabaaacdbddccbbadcbbccaacbdaccbcadcbabdbabdbdcbbcbbaaddbdcbbcacabdbadcdbacdbcdbbdbddbadcdadddcddccbcdabccdaabcaabbbbdbccdcbabdccabcabdbdbcddbcbdcadcdabababaabbdcacaadaacbcaabadcbaccabcbdccccccdbaaccdaccadcdbdabbabccbbcaddccdbdabaadadbbdbcdadcaacdcbabccaabbcdcddcdbbdddcdbcbaccbabbcdaaaccbcadaacdadcdddddbbadbbcdaababcbbcdaccbdbccadbddaabcbbcaccabbcbdacdcbccacbadcccabadcbbaaabaacbddaabbdddacbabddbadcdcbcdabcbbbaacdcddcadddccccabaabdcacaacdbddddabdbbbcbdacbbaabcbcbdbabbadbcbaabacbbcacbcdddccddaacbbcbaccdacbddabbccddaddcdcbdcbccdabdadaacabaabaccddcacbaddaddadaacbbddccddaddcbbdcdbcbadbcbababcabdccdbaadadabccaaaccaacabbbdadbabbcdbabcacacbaaabcbcbcacbdbabcbddbcddbddadcaababdcadcdccbdacddbcdccbcdccbdcdadbaabdbcaaddddacdcddbbcbcbcbbabdcadacaddcdbabacabcdddcbddaacacbabddcbdbbabbcdcaadcdaadbdabcaacbdacaacadddcbdbabacdabccadabaabaadadddbdcbbbaccccacbabadadccbacbbacaaddcdddcdacdcbdbcbbaaabbaaaababcccbcddbbaababbbdcadbbaadacbdddadabdbbabcaabcdccbaadbadbacdcbbcbcdbbcacabbcbdbabdcbacbccddbabdcbaccbaddaadbdbccadccacbdbddabdbdabadddccbdddadccadbacdacbbcdbdbbbdacdcddcbbbdbaacdadababacdaaabadabbbadcbbbadacbabaabcdcdadbdcadbadbcbadcaadcaccbdbdadbaadacbbbbbdcbdaacadaacaaddaccbacdbbbcabbdcabddbaddddbadacabdabdbcababbdbacacbbaacabacacacddbbabaccbaadbddbbbdbdcdcdadcbdccdcdbddbbcbbbbbabacbdbbddadadccdbdbbacddabccbbddcadddaabcdabddbbbaacaadaacdcdacdaacaccbdbabcdcdbdcadbcbbdbccacbacbabaabcccbdcbaccacbbbdddcbbcbdcdaabbddcbbbcadacacaaabaabbacadbdaadbdbdccbdbdadacdbababbcbcdadbcbccaaddcbbcacdaadbdacddddbdacbcbcddbccacbccaaabaadcabcbdbcdcaddcddbbabcbcddcbdacabbdbcbbacdccdbdcbcddadcaacbadbdbcaaccbccbcbcdcbbbbbaabacdadadddacccddcbbbdadaadabbaaabcbcbbbaaacdcbdbbbccddcdcccadacbcabdcbbbdcbaccccdcaadaccdcadcdabcabcdcdacadbcbcbbdadaddadaaccacaacdbdbcdaccbadbbadaadbddcbcdbbaadcbcacbcdddadcdbccadadaacdaacadcacdacbabdccbddcbbabcbabbadcddadbddcbbacacdcccdabbbdcabdcdbdacdddbcdcbaddcdcdababcadaccacacbbdddbabdadacccddbbdddbdbdccbbbdbdcbcbadbcdcacccaddbdabacaaabdbababbabddcaabccbddabddcacdacbcddcddaacdcacbbcdbaadabdaadddbdbbacddbbdbcccadddbacccbdddbdcaabbbccaccadcacbdbcaaaaadaabcbdbccdbddaaabaddbbbcdbbacbcddacacaacaccdcbccbddbdaaacbcacdaaacdabcdccabbbdabddbadcaaadaadbabdbcabacbcbcbabaabdcabddccaadbdbccdddcbbbbdbdacdacadbabbccdaccaacacddcbdbbcabcdcdccdabbcbaaacbdbdbdbbbdadcabcadccbddaddabbcabdcacabbdaaadddabacdbaadacbbccbbbabdaccdcdddcbabaccaaacadcdaaddabaadaddcdaaabadacacaabdbbddcabadddabccbacdbaabdddcbbbccbdabddcddbabbdbdbcdcacdaaabddbaaabbcaaabdbabccdaaadcdabbdddcacdabdcdbcbdcadacbdbddbccddbddacbbdcbcaababadbdbabcbcbbbbbaddbccbadadbbdbcdccdcaaccdaacbadcddcabbbcddcaaccbccbaadcabaabaaadcadbaaaccbdcbcdccabcddbbbddbddcbcacbabaddbbadbbbacdbcaabdbdaaadcabaddadbdcccacbdddbaddbadcbaaaabadbccbdccadccabbacbccbbbacddcdcbabbcdddcbddcacbdbcadcbbdbccdaccdbaadbadbbcbadbcaacaabbccadabdbcdaacbcacccababdaadacadbaddacacaaabdaacbbbabadcdbaddadbababaacdaacbddbabcbdaababccadddbddcabddbbcbadcdcbbdccddcddbbbcbdadbdbacbdccdcbddccdaabbaaabccbcbcbadcbcbcdadbdabcbbcabcaaabbcbcbcabbdbacbbbbabbbbcdbdcaaabcbaddabdbcababaadcdbbcdbdcddabbccbaaadccadbaacbacccaabcdaadcddabcdacabdadddcacbbdbbabadaccbdaabaccdbbdbadadcbaabdbaccbadcadbabbbdacaccbcccbadcddcadaddddcacbcddabaabbacabbcaabdcadadbdacddacaadaaadbabaddcaaabddadcbccacdccdccbadcbcdcacdcbbbbbaccacbbbbcbbdaacccacdbbabcadabccdbbcbcacaccabcacacbcdbdbbdbcbcddadbdabcbcadcacdadcbadacacadbbabacdbcdbddbcbadccdccbcabbbbdccaadcdbdccdadadacacaabcbdbcacadadcabbacdadcccbacbdbabccbacacbccacabaddbacdbbadbadcbbdaadbbdacbbdbbadddbcbddcccbbbbdaabadcddcaaababccdccbbbccddccdabcadbccbaabdccddcddcccbcabcbdcdcbabdacccabdacaabbcacddbdaadaabdbaddbccbbcdacdddacbaddadabcdcbdacdabaddaaabbbcaacbabbbdbcbcaddcadadcacadccaaadacaabacaacdddcbdddcbdbbaadbdaaaccaacbbdacdddddccbabdabbaacbbaacdccbbabaacabaacbacdaddddbaacbbdcbdaaabdaaabdaccbddacbcbcbdcadddbdcaccbaabbcdbdaddddddadadbababdcaacbcaccbdabcdcccbabcabdabcdbabaaccacacabbadcadbbbdcccddabadbbcbacadacadabaddaadabdccdaccdcaabbbadbdcbbbaadabbdabcdaacabddbaaaabccdcddbabcdccddbdcaadaacdbbcdbaacdaacbbbdbadcbdbaaabaaabdcacadaacabbabbadaaacbabadbaccaaaddabbcdadbcccbcdaabcccbaddbdabbaccadadbabcaacacddbcddccaabdaccccdaabcbbdadbbbacbdbadbcababdadbacadcdcbdbddadcbdcaaabdbbcbbbbcbdbcbabdbbdbbacdadbabbbddaccdbabbbccbbbaabbacdbdadadaacdaaccababdbbbabdbaccbbcabaabaaacddcadbadbdbdcbdbddccaaccbabdbdbdabbaacbcbabdadaadbccacbbbaadadbdcccdccbbdabcccdcaaccabbbaacbbdbaddbbabbacdccdadabddbdbcdcdabcbcdddadddadaababddddbadacccbbcccdccabccdcddbcababdcdbbcdaaaaaadcdcbccccbccdbbdbcbcdcbadaacdadbdbdaaabcacdabcbcccabcdadccddaacabdbcabacdbbaacdaccdbcaabaabbcadadaabdbbbbbcdbcaaacccbbcbcdabdbcbbddaaccaaaaaaaccaabddadddccbccbbbaddcccbaaacbcaacdddbbacdccccdddbcdadcacbcbcbbccacddcbddabdcacbababcaaabdcaccacccabcacacdaacdcdcdcdaccababadcdbcadabaaccabbdbbbbacdddcabbdbbacbbcacddcacbbbbdbcdbcadadacacdbdbbbcddbcaaacaaaddbcdabddbddaccccacaccccccadbbbbbaccbaadcdbbabdaddcdbccaabacbdccdcdadccdddbcddaaadcccdabbaccbadddccaaaacdabbadddcccdbcdccaaaaaccdcacdaadbddddcdbcbaacbacddccabdcdccacdacdbbbaddbbaacbdbabdddbabdaccbcabcbddcaaadddcccaadadbbbddacbbbdcddbabaadbacaaabcbcdaadaacadbbbddaaadaabdcdababdbcbdbbdadabcbdaddddababdddbbabacbcdcbcbcddbaabddacdaabcbdcaaacadababbadccbbaadbbbcdcabddcdcabaccccababbccbbdcadacdbaddacaaabdadcbcbabcaabbabdacccccdcaabbbabbdccabbacacdabaadddaaddcdcdbdaaccdcbcdabbbabadbbcbcdaddccaadadadcaabdbbaccdccccbadbdcdbbcccaddaddabdcddaababbadbcaaddbdbdcacaddbbbbcbdcdbdadbddabddbadbaccabbcbbddbcaacbacccdaadcbbdbabdbbcdaadaacdccccddacaabdcacdccddbdaccddcadbbbdabababcaccccaddddcdbaddbaccabdbcacacccabbdbdccbcabababaabdcbccdbcabdaadbadbbcddddaabadadddbbdacccbbdcbdacccaadbbdcabacdcabbadacbddbbbcbacdcaccbcbcddbdadcacdddadbdbbbaabcbccccacbcabcccddddccdddacbcaacccaabdbbdaacbbbbadaaadccdbcccacbdacadcabdddaddbdbcddababdabcabbcdccdaaacdaabdddacababacccdccbddcabaccdbaccaddabaadcabccbbdbcbadcdbbacbdcdccdacbacadcaddcaabbdcadbbbbdddaabddadcbcadcaabcccddadccdddaddcdbabbbcaddaacbcddbadbdaadadcabdcbcacacbaacacdaabaabbbcbacdcbdcddaabbbbbcbbddcdbbbddacbcbcdbacccdbbcbabbcacbcccbcdbbbddbbdddababddddacdbcbcdbdacbdcdaadcbdcacdcdcbbdddbaacccdccdbdbbbcdbdcbcadbaaddddbabdddccbacbaddcddcdabdddcddbdbcbdccbcdacbabdbbdaaaaabdccccaaaddbbaaccbcdbbbbbddcbccabdbadcdbcbdbcaabcdacbdaccacbdaccaaddcbbbaabccbbddbccbcdbdbcccbdbbbdabdaddadaccddadcadbddaaddcdbbbcbabddbdbcabcbadcadbbddccccbbbbadbddddbbcdaaddcaacaacbdccaddabbcbcdcccdbdcadbaacadaaddccbababdcadbbcdbccaddadbcadbbabdbbaaddcccadbaaaabdbbdadbcddddcccacdcdaadbdddaadbdbcacacdbdcdccbbcadbabbcacccddbbabacccaadbbabadbbdbadbbcccdaacacacccbadcadcddcabcdcbabddabcacccdaacdbdcbadabcbaccacaccabbbdcaadbdddbddbdddcdaacddbbaacdbadbbbcdbacaaaacbccabbdadabadbddddbcdcdcddbdcaccbbdcddbbdbadabaacaccbbacccbaacacbaabbabcdbdccacbddaacccabccdcadadbbdcbadaabdbbbbbbaadccaaaadaabadadaaacbcbadaadcccbdaadbabddddddcbacaaccabcddccbbadccbaacbdbbcbaacdbbaababaccacacdddccdcbdaadddbbcddddbabdabddaabdbdbcdaabcbadbcdcdaacddaccdcadcbcabddccccccbccbaababacababaacabcdaddbdbddbbccdddaadbdbcccacadadbaacccddadabbdbaddbbcccbaddacccdabdccbaccdcacbdcdacdadcadbbcbbcdddbcdbbbacdcdbdaabcccbcccabcccbdaccdbababcccbbacaabdaadacbadcbbbddbbbababddabbdddaaaddabdbacacaadddddbcabbddbaaaaacaabcbbdbbabdddcabcdbccaddabcbcaabbbcbaacccaddaabdacaddbdccbbbcddaaadddbcbaadbddcbcdbdccdacabacadaabcdaccbaccbbcccdbddcdcdacdaacbadadadcbaadcdbddaacdaaaaacccbbbbbadabddbaccddadabccaaacdccddacabcabccddabcadadbcababaccbbdcbaaaabbbcaddcdbcacbbdcaddacadbcdcbacacddcbabccdcbdbdbbbabddaacbbacbdaaabaabddaabcaabaddcdbadacaaacbcbddcdabbadaababccdbbbdaabcdbbcbbccccacaaadbacbabdcadcbadbaadbcbcaabdcbcbddbbbabbaacbccacbbcadbcbdabbdaabddabbbacbcbabaadcbbdacabdbbddbbcddadacacacdbcadcdddcdcbbddaacdcdabddccdcdbdbabaabdbdbccccdbbaaabcbcbcbbbaaddcbcdbaacbbdadbccbacccacdabdaadbdddabccabadbccaaccbbcdababdabaaadbaacbaacadcabcdbbbacdbbdcbcbbbacabbcbbddcaacbbbcbdaabdcdadbbaadccbaccaacbaaccbcbbccaccccbabdbbabbcbbdaadcadcbaabbaacabdddccbabcaadbdabbbdabbbcadaccbdddddbaaaadbadbddaaccbdadadbcbcccbcadbcddaaacdcdbbdbdbcaabddbcbbcadbbccbdcccbaaddcbcacdcdabccdacaaddddcaabcacddbcdbdadacdbadaddadadabbbadcbbdbbbdbacdadddbbcdbcabdddbccdcbbbddbadbbbcbadacdaabbabcacbdcbcacdcbbaddcccdcccdddcddccabbacacabadaaabacabdcccdddbaddadbadabddcccbcccacccbdcddcdbdaccbbcbacacddacbccddaacbbaadbadccdbcbbaddbcdbcbbcbdadadccbadcbdbccaccbacbbacdadcabaddaaadbabbdbbadbdabddbdabdaababcacbdadcbadddcaaabccdaaacddcbcdcdcbadbaccbbcbcdcdcdbadcdbccdcdcdbbadcabadcbcabbabcccddaacbbddaabbbaadbdccbbcbdabaabdbbbbbcdbaabbdbddabbbcbadabbddcabacaacdacbadbcbbddabddddabbdaadacdcacaadacdbbdabbccabacdbccacddbadaabcbdaacdcacaddbbcabbdcaaccbdabdadccabbbdcaacdbbdbbbcdacdbbdcdabbdcdadddcbbdacddccabacaabaabaddbabdadcdcdabadbdaddbbdaaccacdaccbdccdcabbdabbacabccddaddbddaaacdcbbcbbdcdcaddcabddcdcaacabcccdccabcdbadcdddabddadcbcbbaccdddadbcdccabacbaaacbddabdabbcacdcdaacbadaaadbbcbdacddadbbbdbccdabbdaadcdddbbcbbddbbbcdcbdcaacccdbbadcccbabbdbddcaaababccdddcddccdacbcbbcabddadcdcbaccbdbdaccdcbbdbdbcbabbbddadcdbacbccdcdbccbddbabbbabccdbcdddabaacababcccccdaabacdbaabdaaabcabbabaabbacdaabddccbcabbbcacbdbaaabbcbdbadbcadbabbacabdcaacddaaadaaddaaaadabbddbccbdbcbccaacadadadadadbbcbbacddddcddccbdacdcaadaabbababbbdbcabcadabdabbccbccbaaadbabdacacacabbdabcccbacabcdcddddddaabddbdcbdbdadabcdabddadbcdadaaaddaaabaccbdbdbbcbbbacdaacbbbbdbccbadcbdaaccbdabbcbaadbadddbbcddbaddaddbadadddbbaabdbbacbcbcdbccadccabcbccbbbcaddccbabdcbaabbaabaacabadcddbbaccddadcdcdcbcbdacccaabcbcaababddabbdbcdacabbacaadbcabbaadddcdcbaccdabbdcaacadccccdccdabbcbdacbcabadadcccacbdbacababdababcccccdbbbcaccdaddabddbbacddaadbabcadcdbaaaabddcbacacbcbabadacacccbaabcaccacacdbbadbbacbcaccabbddcacadaadcdccbbdababbbcadbcccbdabaccacdcaccacabdcacbcdddcdadaadbcbdbbaadcbabbacccbabcacccbddbdbcbaaccbddccdbabbbbddcbbccbdcaaacbddddccbbccaddcbaacbaadaadacbbbddcddadcdbdcccbcacadccddcaccadaaaccbdcdcabcaaccacaaacbadcdababcddabccbdcdcadaccccbcddbdbccdacbbbaadcaadbabcdcccadbccdaadacdcdcbdddacccbcdaccadbdacddacbcdbdddcadabcbdcbcbadadbbdabdcbdbaccbccbdcaaaaacbdadbbdacdccdcaddbdcdbcdddacaaababbbdaacdccbaddddbcbcbcccbcdcccdcbdcddccadcacbacbadaaadaadbdcbcbdbabaccddadcaddacbaccabbbcddacbcddbabbabcbabcdddaacdbabaabaadacaddbcbcbcbcabacbbdacdcdccdaddbbbcaddcadababbbccaccccaadabcdddadacaddbcbccdcacadadbdcacbbddccbccbbaaabdadccddbcbcbddbbbddddcbdaacdbbbbcdddaaacabaddbabccbaabbbcccccadcbcaacbbadcdcbdbcbcdcaabdadddcddcbdcccbcadcddbddbdabdaadbbbadcabaadbaadcaaddbcacddabbcbdaabcacdbddcacaccadcadabbdcdcccdcdadbbdddabbbacdbccbcdaaddbcaddacccbbbabbabccbaccddbaddabbcbcbabcadadaadcddcbdbccaadbcbcbaabcccabcbdbabdddbdacdcbdbccbcccbcbcbacabaaaababacddbcdddccbbdcacdcddcadcaccaabbbbbdadcadcadbbaadabbcaabdcdabbacbabdbcddbacdabaadccadbcabbbcbbdbaaaccabcdccdbcdccacbcbbacaccaaaddaccadbdcdbcbcdcbdbdaaccbaacdbdbbbcabadacabbaacbcaddbdcccdbbabacbcbaccdacbdccbaaaaccbbaccbcadbcabcdaaacabbbaccccdadbcbdaaaddcdcabaccbccdbbdcbdaccbacbcccaadacccbabdaccacbadbbbacccbaccbcadabcdbbdaccbadcdacbccccccdacbccddcaacabbaddbaccbadabcacccaabbccccbdddcadabccbcacdcbcdbabccbabcdddaabbabbcabdbcbacccdabcddcddccaccadddddcbcdccabccbcadaaddbdcbccdddcbadbcbabaaccdbdabcabddcacabbaadddbbbdcdadcacaadbacdaddcabcbaccadcabaadbacbaaabdbbbaddaccdbcbacbdabaaccdbcbdddbdddbbcbacdaddbcbbdadcdabbdaaaaddcdbaaaadaadbcabbbbadbdabcabbcdcabcbcadacbbdacabcacaccbdbdccbaddcbcbadaabdaccbbdabcbbcdadbaabcdcabaccaddaabdaddbdddaacdddcdbabbbacaaddbdbddbbdacddccadbaccaaabcabbbacbaabadbbbbbbbcacaaccaadcdaadacbbccabadabcabccddbacbdccccadddcdccbdcccddacaadcacbdbdcaddcbbbacadccaadcdbadcccbabdbdcacaaaddaaacbacacabdbdbdcbcaacddccdaabddbaacbadadbcbdbdacbaddbbccbabbccbccddcaccdddabcbdbcadddcbbbbddbbddccdcacbddcadbdcbbadcabbbdbcbbaabbacabccbadbccdacdcbbcccbaaabcbbbbcacbabcadbbdbcdbaccdacddadbbabcbccaddcdaddbbdbdcaddcdabcccbbdcacccaddaabbcbbacaccbcadccbabaadcdccbccbbcdadbcbacabbbdacddccbddddbdcddbdacacbbddddddbbbddbadabddbbacdccbbbdcddbbaacdaacaddacabaaadbdddbacbababdcbbbddaccabbcbdacdbcdcbbccdaccaacccdcaabaacababdbdccaacabbbbdddbbcdcdbbdbdaacbdacbbabddbbbddccbaacababcbbbcababaddcbabdbddadcaacccdcdddccddcdcdbacbcbdbdadababbdabcdcbdbdbcaddaabdcdabdacaccdbdbcdaaabbacbbbcadaadaddcbbcddcdbdddddabbbaadadacdaaccbaccbdcaacaadbbbcaadacddbbbddbabababaacbbdccccdaccbbdcdccdbdbaabbcacacbdbbcbabbbbcbacbbadcbaacaccdbacdaadbbadbdcbddadaddbbaaaadaadabcddbbaddcbdcdddbacbabdbcdbccaabbcbdbabddaddccbdccadacbdcbbddbcacbbdcaaabdbbddcacbadbadadcacadbdabcadbbabaacbbdccbddcdccacbcdbadabdabadadbdbcdaddcbcbaccbbcbccbabdcdadcbccccacbdbabbacbcbbacbbddbbdbbcacbadcdabaadbabcddccbddbacbbaccaccddbdbbadacabacadbaccccdcdaadcbbccbbddcdaabbbdbaaccdacdcacdbdacacccaaaaacdcbabddbbcaaabdcbbccaddbdddcdaadabbadddbdcdccbacddaccdbdbbadbabbaccaddbdacbaacccccdaaccdacadbdbdadcdccaddbccdcaabcacbacadbddaaaaaacaaadbadbaacacaabacdbdcbdaabdacdabccbddbcddacdbbdcaccacbdabcaacbbcdbcbbbccddaccaaddddbdcacbabbcaddbbabdaddbdccddcacdcacddcaacacadcbaabccaccabcadabaadbbbdbddcdcdcdacccabcbcbabdcccadaaacbcbdadadbbdbdbcadddbcccaaadbbdbdadadccadaacbdabcdcadcaadaddabaadcdcdadabbcbbbbababccbadcbacabccacbbaccbcdadcabbddacacacacadcacdaabbbcaaaacdcdbcdaaddddaaabadbddbcbdabdcbdccdbacadbaadbccbddacbadbdbdacddaaacddddaccdbdccaabcddcabaccbabcdbbbdacbddbdbbcbadadbdacaadcbbdcadabcbdabaababdbbccbbaaabaddbbbcccbbbdacaadadbaadcccaadbcdaadddbbcababbdcbbdbcdcbcadbbbccbacdabbcaaacdaadcbadbdcabcdbddbcdccdccbdcdbaadcdbbbabbabcbcadabcbbcdbbddbaacadddaabacdccacbabcaadaddbdbdbbcdcbdcaccdcddbccbabbadbacdadbdcccbdaacdddcdccccdcbdcbdbdddcdaaadaadadddcbbcaddcbbadcadbbabddcabdbaddddcadaddbcdbbcdbaacdaddcaabadacbdcddbabadbadccddddcbaabadcdcbcbaabccbccbaacadcabaabccbdbccccbadaaccddadcbdbaacadadcadccbcabcdbddbcdcdbbdbdbcdabbdcbdbbcacbcaccbaabdaabbcbbdbacbdcbbbcadcbcccddaaadbbdbbacbbdaadbddbbaabddaadaacdbcaaccaaddcccadbcbdbacddabadbbcddcdbcbccdacaadadccbdcadacbaccbcabddddbbcbccdccbccbcdbbbdcaabbddcbdbadcbbbbbcbdaaddbacabcadbdbadcbddcddacdabbdcbcacbdddcacdddabcbbcdbbdaadbcbddbcdaacbabaddabaaccaacbabdcabaabccdacaabbbcddcbaabcaccbddaacdaccdaadbababaadacbcdadddaaaacbdcdaddbacbacaadbddcabdbbbcabbdddbdccacacdbdddacdcadadcaaccbccdbdddabdddcbadadddbaccaabddacabccddbcdcadc
dacbdbbcbddccaaaabdabbbcaadbbbcdcdcbcbaacbdcdcacaaaadcabbcbadddddbdddacabbbbadbbaaadbbaaadabdbbbbdaabddacccdddbbccbbabddcdcdbccddcdabbaadacbbcaccabbadacdcbbabcdaabadaacbacaadccccadbaaaccbadaadcddcdbaccdbdcaabcaabdcddcbcabbcdcaacdaadbacbcbdabdcbcaabbcbaacbbacaadbbdcbbccdccbbcadddbdbdbaacabdcdcabbcabdcabcabcdddcdcadbddbbcaacdabbbbddcabaacbdbbbaadbcbbccabcaccddbddbddcddcddacddbccbbccdaccbaccdccbadcabddddcccacdaaacbbbaccccaabcbbccbccbdcdccabdcbcccaccacbbadcbadaadacbcabcaacdbdaaabcbdabcabdbbdddcddbbddacabccaddbbaacccacdbcaacccaccbacbcbadddbccaabbdbaddabdadcbbcbcdcdcccbcdddaaccabcddcbddbbdbcbbcadbdaacccddbadcbaaaccbddaccbadacdacdbacddadbbdcdcacbaccdaaabdaaadbdaaadacbcdcdabdcbadccaaddcaaaabcbccbcaaabbaacaabbdcbcccdadcaaddbbacdabcbdaabaaabdaaccacdbdbcbcbabaabddbbcacaaaabdbdccbaadadabcdcbaacbacacbacdcaaddccbdadccdacbccaacbadadaccadcbbaabddbdbcdcaadddadabbddbcdbbbacddbdaaccacddbbababbabccabcdabadaabcadddbdcdaccbcbdacabcaddbabcbaadbdadabbddaaacdadcddccddabcdadabbdbcaccadabbdccbadbaddaddddbdcbdccdbcbddbccaaacbdacadcbbacdadadaadaddaadaabcdcabdbcbdcadcdcdaddbcdacabcbaaadbadaadccaababadababadbbaabbcabcbccacbcdaddaacbbccbcddcbdccbdbdbbbbacbdbbddacbabbcdcbdadabbdbadacdadbdbadbdbbdbdabddabdddbbdabadccbbbdccccabbbcdaacabdcccaaabdbbddadaaaadcacdcbbdbcaabdabcdadccddcdddaacadccdbbaaccaabcccabcccccbbcdddbacddaadcadaacadbbcddaccdaaaabcddccbaccdcdbcdcbdddbbacccdccadacabaacbdbbcaddddccbbabaabccabddcacbccbbddacaababccdacabcccacaacddcddbadbacdcdbbdccdcbccabaaccdcabddddcdadcbcaddcdcadbdabbbacbcbccbbaacbcaddbdbbdadaccccbcccabcaaddabdccbadcdddbdabcdcbdbaddaaadcccadbdcbdcaddcdbabcdbbbaabbbccccccabadacbdcdbdadacaaddccdbcddcbbaaaddcabcabdbbacbbddcccabcbcbcdadddbccdbcaaddbdcabddadcbdacaabbccbdcddabbdddcbddddbbdbbacadccccadbcbbbbbabaaaadabcbaadbdcacdbbddcdaadaadbbbdbabdacbdddccddacbabbdaacbadddaadbadbacaabbdadcbccdbdadbbabbcabbbaaabcbaddbbcbabdccdcacabcaaccddcabbbbcdbddddaddacabddaaaaddccacccdacacdbcaaabacabbbcaccccdcdbbccccbaccababccadcbcbdadadcabbdddabdcdabcdbcbabbaddacbcbdbdbbabdaddcacccaacbbbabdcbcdccaaadabadcddbbbbdbcdccadaabdccababaccabbaacbdadbbccdacadaaaacbbcabbbbbbccaaadcbadbbbdbdcdcbdaaabbadcbdabaacaacdbaadabdccabaadabaabbccccdbdadababdbccacacdacdddbdccbabbadcbadbcdbabccbaadbabccdcddbabdabdcbcbacadaaabcdbddddcbcadcbcbacadbddabdcbccdababbcabbabcddccacbbaddcacbaccdadbdcbccddaddcccdbddabcdddbacddcdbddbcbaaaabddbcabaabaabcdccaacdbdbdcacabcbaacdbdaabdadddadadcadabbabbdbdccdccdbadccabcddadddbdadbdaddcddadaabadcbcabcaddccabcdbbdcbacaabadcdcadcdbccccdddbdadddabaadabcccbdddadddbabdaddbcbddacaaadcbaaacbddadcabbcbacbacbacbbccbadddddbdabacbcbdaacdabbaddcdabcccabccbaadcddcccbcccaabdcaaabbdaacaacabdbaddadabcaaabaabaaaaddcdcbcddacddcaadcdbcabcddacdcddaccccddcdcbabadacddbbcbdcdabddacabaaacbcccdccacadbbdcaaaadcadbacbbccbabaabddbaabaaaabddacbbbbcabbaccacbdccabccacadcabaddcaddaacacadacbadaaaaaaabaccdcccbbbcdacdacccddcacaaddddaadccababbbaccacdcbabbcccccdbbcacadabdddbdcadcbacccbdbcccbdcbcdbabbbdabcdbadbdacbdadadbcddcaddcccbdcadbdababbcdadcdabaccccbadaabcddbbacabddbabcdbdcdcccaddcdbddbdbacdaaddbbdbaacbdcdacddaadcacdbabddccabbcdbcdaadaccddcccabdcbcaadaccaabacdbaddbabcdacbdbdbbbbaadbaccccaaaddbbbdaabccabbcbccacdaccdbdddababacadababcdbdcbaddbaadaaadacbdddabdddcaccddbdcacacdcaadbacbbabcbccddcaccadaabcacaabdaccbcddabaabaaccdcadbcbcacadddaacaddbcadcadbabccbbacbadaadbccdacdbccaccdadcddbbcdcadddbddddcbbccbcacbbadbbbbabddabadcbdacdbaacbddabbddabbbbdcaaaaddbcaddcbbddbabdbdcbabcbbccabadbaabbcbbacaacccbdaaacbcddcacbaddcdacbdaccbdaacabacacddccdcaaaacbaabddcdbacdcddabdbcabcaabbcdabbaacbdcdadbaaaaacbdcccdcbaccdcbabdcbcaccbcacdcbabaccdbabbadcabcbdddcabbdcacacaadbdaaadcbbacadbacdddddcccbacbbcbdcdbddbcdddacdcababadcccbdbabaccdadaacadccccbadcddabbdccddccddcadaddabcaacbbaacddacddcbbcbacaacdddabdccdacdbababbacaaaaaabbbdddbbacdaadabababbcbdccabcbabbbdabaddadaddcdbaadadaccdcbdbcdcbdbbabdcabbabcaddcdcddacbccccdaaccbdadbbddadbdccbcdbabdcdccdccabcbbdbbadbdbbdbbdccacaabdcacbdbdacdcddbcbdbadadacccadbcdaddabdddbaddbcdcbdcacadacabcaddbdadaddddbcadaababcdbcabdddcaadccbbdcccddaadcccabccccabddccbcadcdddbdcbbcbcbccabcbbcacdccdbdabddaddddccababcbdabdabdaacbccadbdaccbcbaaaadcdccbdddcdbbbbcaccbbcccbaabccdccdcbcdbcacccabdbbcbabcaadcaabccccababaaadbccdbaaaaaadcdbadbabadbabddadccbddcdacbaaacaabcdcaacbadcbddcbcacbbbdcaabadccbccbdcabadddacbdcbdbbdaacccccaccccaabcbddadaaadbbbadacdcadcacdbbdbddcdacdddadcddaadddaddbabddabbcbdbcacaabbaacccadbbddcbabadbbdabddaacdcbdadacdcbbbcdddabbdbababbdaacbacdaadaddaacdbabbcdccaacaabacddbdddcbaddcbddcdadcbacdacbdbcddadcadbadadbadbcddcbacbbcbbacaccdbbacaccdbdcadcabaddaaccdccaddcbaacdabacddadbaabdcdacbdcdcddcdcbdbcdabaaaaccccdbaaddcaddacabbabcabaaadbcbadabbbcbbabcaccbbadcababbdaadaadaabbacbcaccaccadcadbaabccdadbdabbcccdbabdbadadabdadcdaadaabdaadbabcdacaabadaabbcbcdacbbbbdddccbdcbacdbcadcdaddacbadcaaddabdaaddcabacddaaccaabadadadddbacdcabcabccacddbacadccbddbabbdbbabcbaaacdbbddccaacacdcbcdccdbabacdcdacbdbcdcbcbadbcddabaadccabdcdbbabbdbbabbbbbbbbbddbbcaddccaccbabacbddbbaddddddcbcbbbcdbdaaabbcdcdcabdddbdacdbdabadcaaaadcacbbaadcbccbdddaaacacdacddacacdadacbccbabdccabdbcdaccdaabcbbccadbabbacdbaaabdddcabcdbaacbcaacabbcaddadcbcadadbcbdcbaacccbbddbacbbbaacbcdaadaabcbbdccdcbbbbccbaaacabcdccdaddcbbaccaabbaacbbbabcacdaaadcacdbdbccbdaddabdccbaccbacaadcaccbbbbbadaddccccabdcccbbcdadcdadbdabacabcbbacddaacbccabbbbbbadddbacdcccacbcbddadaabbbbaccddbacbbcbcbbabcdbbbbdbbcbddcacbcdbaabaddbcccaddbdabbccaacccbcdccbacadcdaabddcbdadcbbaddcbbaadabbdcacccbbdbdccdbcdcbbdabbaccdaddccbbbcccaaadbcccaaddbcdadbbabdadddbbabacbddaaadcddbadcddbccbbbcbcdbcacbabaddbccbadddcabaaaacbbabddbdadaadcbcbdcccbbbbabdbccbdcacabddbbaacddadbcdcacaadccdcccabdddadcbcbdadcbdcbddbdbabbbbcabbabadbdddbbdddabbaddcdcdddcabdcabbcaaabbaadccddbdbdcbaabdabbcbcdcadcbadbcbbbbbadbacdaaaabdcbabaddcdccabccaddccbcaacbdbbdccaadbddcaaccacaabddbabbcbbacacbcccabccaadadadbcdcbdbdccaacbcbadcabcadbcbdaccdbcbdbaddcdadacbbccbbcccdabbabbdbbdaddcacdccdbdcdababadadbcccbacabccbcdddbbaddcacbbddababaadcabcddcbcaabbdacdddaddccadbdcddabaadabcaddaabddadaaccaccbbacacaddbcbdacccbcdaaddcbacacbddcddabbaabbbbbadaabdcddccdbbdbbcddbbddbabbadcddbcccabacaacaabcaddccbcadccccbcbcbadbacddaaaabcacabddddcaadcbbaaaaadccdbcdabcbaacdcdcbaddadacadadbdddacabbcbcacdbccbdbbdcdcdabbdcacdddbccccacbccbcbdbbbadcdbaaadacdadccbbaabbacdddcdddbcddcbbdabacbcbcdcacdacaaaabadcababcccdabbbbbabbdddaddcddacbacdccacdddddbbbcaddddadbbddddcdadcaabdcbcacacbacbdccbdaabdabaddadbcdbbbbccbdcdadbcdcddccbdccddbbaabcccbdabadabbccacacacbdbdbccaabbbcbaabcdabdbcdacddccaabbdabacdcaaddcdacdacccdadcbaccaccadadccdabbdbadbadcabaabdccdbcbdacdcabbcbaabaccbbbbdbcbaaacccbaaacbbdaccbabcbbdacbbdbcbaddcddadabcbabbabcdbdcbbbdbcadbbbdacdaddbacbbcbbdbccadabccdaadddbccabcdadaabccbbbcabccdcbdcccacddaaaabcbbdbccbbbcdbbbadaabbacdaabcabbacadabbcdbbddbcdbcdcbaacaddcdbbccbbacaaddaabbdbdcadcaaabbaaaaadcabadbadcbcaccccbaadbcbacdabbbdcbddacbddcbabdadaacddcbccdddaadcacbccdbdcbdabdcddabbbbcbabbaccaadaadcbccdadddaacbbcacbbdaccbbdaacdabddabbdcdaacbcbaaddaddaccbcdbadabdbbcbcbaacdcbcabdbcbbdadcabaacabcbdcbcaccdccbbbdcacabddaadcdaccddadaaccbbbbcaabbccdccdccbbababdabbaccbccddaacbacabbddbabbdacbabacbdbdcdcbbaadbdaddbccaddabdbcdadacaacabccbbdbcadcbabddaaabadcabcccdddacabaaabbaaaccababacdcccabccdbdbccdaddbdacdddadcaaabddadccabdccacbdaadbcbadcbccbcbccdbbdaddabcbcdbbdbbcccbdcddaabadddadcccaccdbdabaaabcdcaaddbaabcbabaadbddcdacbaadadbdbdccdcdccdadbdcdaadbbcacccabaabdcacdaacdbcdccabbaccccbadbacabdcababcdbbcacacdbbdbdbcaccaccbabdbaacdadbdcaadacacababbbbdbdbbbcbbddbbbcbbabcbacacccdbbaaaaddaadbcbabaaacdbdbcaadbccdcabbdaabaaccadaddbcccdbbbcacaacdbaccdddaacaaaaddabddaadcdbadbdcbcdbaaabcaabadbaccccbaccdbdabbadabcadabdbacadbbdbcadcdacddcccddaddbcccdbddbbbbbacbbbabdbacdccbdacaaccddaabcdaababcdccbaabababdbcdcdabbccaddbcaabdadadaabdbabbbccdbdacabddaabdabaaddaacccdcdadbbdccccabaadbaacabaaaadbbdacbcdbabcacbdcccdadacaacdcadcacccccaabaccbbaaadbdbbaaacbdbdbadadbabaabdabddaadabcbadaccbabbcbddadddccabccbbaacbddbbcdbadbddbabccaddbdbbbdaddbcadcbdabccdbbdbcaacbaccababdbaddabddcacdcaabcdbadbccbbadbcadbdaacaabcbdaaddbdccadccccaddadaccbacbaacadbbdabbbadbbcccdddcabdbacbaddbbcddbdddcdcaadaaaccbaacddaacaacadcdccdaabbdccaabbadbdccaaadccdcdcdabbbbbcddcdadbbbdabddbdabbabbaddcdbccccacdbaabaadcddaddbccbbabdadbababbbbcdacdaabbbccccbcaadbadcabbdcabbbbcbbadddddcbcbbacadacccaadcbcbbcaccdbdbbcdabaadcacddccadcabcccdbbcbcaadbdccbaadbccdadbdacaacaddcaccaccbccddcbabcdcdbabdacacabdadabbcccacccdcdbbdcdcdbddacabababdbdbddbbcbdadacaaddabacbddcddbdddbaaaacdbcbbcbcbdccaadaaaabbddabbbbabaacccbbbccccbbdbccdcadbcdccccbcbccbdcbdddaccacbccacadacbccadbbabcddcaaacacaabcacbabaacabdbdbbbdadbcccbddadcbcabcdbbdcbbdcbbabadcdbcbabddaaccbccaacaccdcbbddbcabdcbbcdcdcddbaacccaddbdcadcabaccbccaadaacbdcadadacbdbcaccaadacdabbbbcdcddbddbcbdaabdbcdbccdabbdbcbdddbcdcaaccbabcbbbadbccddbaaacbbdaabbcdabdddaddadcbcdabaadcdbdadbdacddacabbabbbaacaacddbabdcaaaabcbaaabdddcabcdacbabbbcbdbdaddbddacbdbabcddcabcdbbcddbbbcbcdbbbaadabcbacdadbdbcddccdbaabaaccadcbccbcaccddbbadbcabdddbdddcddcaccaaaaddbcbbcaccabcdcccbddbaddbaaccadccbcdabacaabcdbdbadbbcbacbbadbdabdbdbdabbabbbccbcbbdbacdabddbbcdaadacaaabaaccaabcddacdcccabacdcddccdcdaabcddcaadcdbcaaaacbdcaacdcdcdaaaadababbdcbbdbdcbcbaadbabcabadccdbcdcbdcbaccbbbcdcadccacccaaadaabbacdbaabdbcabbbadabdbdcdadbdacbdbcaacdbcccabacdcaaaadbbcbbcadabdccdddbdcaabcadbdbddcddabcdbcaabbbaddddbbabaacdbdbcbcdcbcbccbddccbdcccdbbddddcccaabaaccdaccacaacdadacaabbcabbccbaacaaccabdccacbddaaaaddbabcaaacbaadcbadbabcdabcddababcdcbddbcbdbdcdddbccaabcbbdaccddcdaddbdcacdddabaccbbbbcabbadabbbddccacbcbaddaacabadddabbbcdbdbccabcdababbbcacaaabadadcddabccbbbdcabbdcdcacadcadaddddcbbaddbdaacdbabbccbdbababcdbadccbddccbadcdbbaddaabbcccdbccaacabbbabadabcdccaabaaccadabbadbcccdbbddaddddccaddaccdacaaacdacaccdbbbddcbaababddbdcacadadcacbbabbaddddcaaabcdcbbbcdcdddcaaaabaabdcbabccddcccbcacaabbdaadabadcdabaabdcccabadcbaccbcacbadcacddccdcbcacdaccabcdbbaaccbadbcddcbcbaabcdabaaccabddbabdcdaabdcddbacccbccccacbccdadccbbacabccddbbbdbbaddacadccacddacdcbbcddaccbaacdcbaadbacbccdbcdcbbdbbadaabacdcdbccbcdaaabaaccadbcdddbdcabacaadabcdcbcdbdacddbcabacbdcbbcbbccacbaddabcdccdbcbbccdcddcabaabcadbadcacdbbcbaacbacabbcccddbbddacadabdbacadabbbdddbacaadccdbdbcbcdccbddddcabbcbbbbadccbdbdbbbbbdcacbadabbbdbddcaaddccdccbdbbcdacddbacdbdbcbdbcaabbbcabdbcacbadaddadadadbdacdbcdabcccabdcbaccaabccccabbbbbcbacbbbcccdcabbbcadbbbcaadcccadccacbabbcddcddcbabccccacaddcbddcaadccadbacababaaadaabaaaaaaaaddbaccdabbbabacddbcabddabbdbcdbdcddcbdcccabcdaacdddabcbcbcadcbacabcdddbbcbbbbacaacacdddaddbabcbcacadbadabccacbadcccdbdcacadbabdcdcddaaaaddccaacddababcacacdcdcabcabbcaadcacddbdbaaabbcaabdbccacbdbcdbcdabcbcdcbbabcaccdbadccdcbabbdacdaaccdbddadadbbdcbbddcaddbdddbdcbadadcabcacdcccddbacaddcacbcdbbaaadcbacdaaaabcdbbccddcdacdcbbbdcdddbdababbaabdbbbddccdbbadbdabdbcbbbabababdabcddcdaacadbdcccdcbbacbaccdadddbcdaabdaabacbacaacbbcbabdccabddaadccdbdadcbacdbabdbbabcbcaabcbcdcacacaccaadacaaadacadabdacbcdbacdbabdbcbbccababdbbaacddbbcacaaaadccaadddccbbabbbcbadbaccbbabcaacccabdabcddcadbbdaaabbaadaaabdcdadbdbbbabcbbdbdcacbaaabdaddadbbadbadacdbbbdcbdcccbddabaddcabcbcbaadbcbbcabdbabdcbdaaacbacbdaddbdbbaaddbcdbccacbdbbcdddcbbabaaaabaddbabddacaacdcadcacbaabbddabdacbcabcdcbcdacbbadbccabdcdcadbbbdabcabbbaabbabaccddaabadbbbbbdcdcabcbaccbbcbacbacdbbccbdbaaddddcdabadbacbcbcddbbaacaddbdcaaacbdbdddadcdbaadadccdcdbbccbcbbaaabcdcbadaccdcccdabacccaabbabcbaaabacccbdddddaacbababcadaadcdbaaadcacaccacddaadbcdabddabadcbcbbdbdbdaaddaaaaccdadcaadabbaacaddcaabababadabbcbddbbbdcccdbbbaccbcacacbccddcbbddbbdddacacaaccacaaacaaadaccabddbccaccccbcbabbccccccbcbdbadaaabdbcabcccaaddcdbbbcdaabbcbccaacbcddddadcbcbbcabdbbacadabacccbdbbddbdabaadadbacddaccadaaadcbbcbddabcdacddaacadddcadbcaacbbaabaaadbbaaabadcaadcacbdcbdcbaddcccdbddcacbabdbdaacbdbccbcbdcdbaabbbdaccddbabcddbabddbccdcccdabcbcccabcbbbbbadacdbcacbddacdcdddcbaadccbbaddabbabadddaabaddabcabccbddadcbadabbcddccbabbccaccaadcbdabbbdbdcdabadaabddabacbaaacbadccdbbdbabddbcabdddbaccbdbbcaddddcacbadabdcbcccbdcaaabbbbccaccddcdabbdddcdbcdddbacadabdbacaddacdbdcbdcdbdadcdbdaaaacbbababacadddddbcdcdbcccaccaacadbacdabcbcaadcdccdccacadbacdcdbdbabdaadcdbacbabaaccdcbbccaabdcbaadaadccbacbbbbdcbdbdacbdbbcdacdcadcddabbcccbbcdcbcddddacbdacccbcbabaaadcbdaadcdcccabacdcabddaaadccadadabacbbcaabadaadabdcacabccbdcccaccababdabbccdbdbdcadcabbddaaabdcbdacbabdaaadabaadccdadadcadcacbaaadaddbcacbdbbbabbdddbabadbaaadbcbcabbabddddcdcacbccbaaabcbabbbbabacaddaaddcdbadcbbdcbabbddcadbdcabcbccdbdaddcadaacbabbaababdaacadacacdcadbabaccddbdadcbcaabababcccbadbcdcdbaacbddaaacbcbdcdbbabdbdcdcbabdcacabdbabdcabbcbaacabccdabdcbbddabcacacacabbcdcbcabacbbbcbccaadbcdbdcddbbcdbccbdbcdacabccccdddaddbbcaababaadcabbdbacdbbacdccbaacdabddaddbcdaacbcacacdabcdcadbbaadcbcbdaabaadbabadadacaadbadbbccdbbddabcacbccbbdbcdaadddaacaadcdccddcacddbacbcbdaddacaddbabbbabcdbcaddaaccbddabcdcdbabbdaddddaacadadbdddaaddcdabcabdaabbccbdbcbcbdccbddbacadccbadaadccdcdadacccbdbbdaadcddbacccdbdccdabacbdbcdddaabaacdaabdbcaadbbcccbabddabaccbcabdababacbdbacccbdcadbdaccbccdddabbdcdabaccccaadbbbccccdbdaaacbcbacccbcdcabccaddcdbacabdbdcccadbcacaacdbcdbbaaaadbabbadaccdbaabdbabaacbabbcbaccdaacadddbabccdddcabacaccabbdcccbabaabacbbcacacdcccbcacbccdbacbcdccadcdbacdcadbccadaabbcbbbddaabbddcbbdcbddcdaaacaacdacbddbabbabbcccbaadbbcddbdaddddcbcccbbccdadabdbaaacccabaaddaddaabddaaccabddcccdcbbdadbaccaccbabaabbaabcbcbbaccdddccbabddbaaddcccabadcbadcbcdbadccccdbdbccccccdddddacacbbcdcadcbcbcdbabdbbadadccccacaaabcddabcbdacaabbcadddaaacdbbbcbbdbadaadddcabbcbcdbccaacbbbcdcdcbcbadaabccdcdadcbabbcadaccacaabcaadbbaccacaccbadcabdcdbccccddbbaadcdccdbbdadadbbcbacacabcdbdcbccaccaaadddacdcdccbcdccbcdbbcbbdacaccacabadabdaddbbaccbbcdbbbddbddaacaddbaadddadbbbdadbddbbcadbbbdadccaccddddcabddacaacbdacdaabdddcbcbdabddbbccaaabaccddbdacbccbcdadaabdabccaccccdcbbddbccaaabcadcccddaadbbbbdbbdabbdcbadddabacbdcbabbcaacaddbdbdddcacdaccacbdbbaaaaabdddbbcdddacccdbcddbabcdacbbbdcbadadadacbddbacdbdbacddabbcaacbccbcccaadabaccabddcbdbbacadbddccdacabcdacdabcabbaccbdaddccabbdadadcccbabddbbdddbaaddcddcadbaaaddbdcbabbbddaccacdcdcaadaaadbbacbdddabdcdabbdddbbcccbdadaaabbdaaadcabbbaccaaddadcbbaababbacdccccaccbcbdbbacbabacadbabdacdaddadbbaacbdddaadddbbcbadacabdacaacdbdbbadcabccbadcdadbcabdbdabcddcdcdbaaadaccbcaabbdcdadbbdacbdbdbddbadbadabdccdcbaccacabcaabcccabcaaabbabbddbbdcadcccbcadbdabcacadbacbabbcdcbbadacaccccaabcbbbbdddaacccaadcabdbdabdddbabadcdbbcacacaccaabcaaacdccddaacacbcbccaccadaccbadccdccbddadaaccdbccccdabddbcbcdbaacadacbdbaddabdcdcaddbcacacdacabccaadddacaaacdcddadddddcdabcaadbdadabaadaaadcbdbababacacbccacabaddddccbdbaabdddcddccccdbcdbddbcbacdaddbbabccbcacccabcbcdbddddccdbdcbdbaaaacaddbbabaddabcdacbcabcabbcbdcdcdaccabcdadaaccddcadaadcbbadbbbcabcdbbcbadaaddcddcbddbbbaabdaddbdbcdcccddabcbbdbbaaaaabdacbaadaacadbaaccbbcccabbdddcccdadbccdbdbcabbdcbbcaaacdbccdabdbcdddacdaddaaddbadaaddbbdbabdbbdacaaadcacbdbadbcbbaadacabbbbbccdaadaccdcbbbdddacbbbbababcbcacbacccbcdaacaacaabccaacabdabdbbdaadaddadccbbddbcdaccdcbdadbbdbddbcadbcbcbddadbababbbdbccbbdcdcacaccccbccadadaadcccbaaaadcdcdcdadbbbdcacaaacadacddbdadadbcdabbbabcadddcdcadddbaddadcdaaabaddbdadbdbaddaaddbbadccaccbdbbdacdccadaddddcbdbbbdacabbcbadacacaaccbcdddbccbcdcdaabcbcbcdbbabbbbacababaadbaadbbabcbcdabccaadccdaccdddbbbdabddaccbcbacacbbdaaacbbccbdaaacddbcbaabbbbacabdacbbaaaddcacbdbdbbdacadcdbacbbcddaabaaddcdccdabaccddadccbabdabdbaacabdbbcacdadbcbdacdaaaaccaabcbadcabbbddabacdddadcabdbdcbdccdccbabdabaabcdbcdccbaabcbcdababcbabdbbaccbcdcdbddacbcadbdadbbdbabbbdaccccbdbbcacccaadbacdabcbddbbaadcdcdadbcbacdccaabcadcddadaaaabddbcbbcddbccbadaaabcacdadaabbdbdabdddbabbdabdcdcbbbddadcacbacccaddcccdddacdbbdcbdbcbcbccadcabdcbabdbcadcdbdcadaddddacbadcadccddcdcaddbbccdaacdbadbcbabcbdbacabbcabddaadaababddcdbdabccacacbcababbcabbaddbddbcadcacbabacbbadbbabbdbdabbdaddcdabccabbbcdcdcbdcbdbcaaccccbdddbbcdcbbbbcdbdabcaaccacbbcbaabbbdddaccccddcdccbdbbbdaaacaacaacbccaaabacadbdccbabdbbbaaacbdbcaddaccaadabcdcacccaacdabbbcbadbcaccbacbacdbaaacadababbcadcbbdbccbdbbdadccdbbdabbbdcbbcbbbcddddcbababbcddbbcccabcacaaadbbbdcaabcacacdabcababdbcacdddcacbbbadcbbddbbdbcacdbddbacabbbaadddcbbbdadbadabcadadaaaaddbbddcdbdddbbddbddcdaaaaaacccaddddcacddabdacbaabcaccbadbacbbadcdddcbbccbbabbddcbbdcabccaabdbdbcdaddbbaccbdcccdbcdcddcbdccbdcccccdbaacbbacbdcbddabddcbdbdbadadbdcbbbcadcdccddadbaddcbbbbabbccbdcbdaacaaaccbbbbadadadccaaadcdbbdbcdcacdbaadbdcabbccdbcbbcababbbdbadaccacacccdbddbabcadacabcabaabbbcbcbbdbdcddadbbcacdcbccbbcbdcaccdacddbdabdbdbaddcabdbbbbddadbacaaacbadabbcdddaaccadcdcbcdaccbcaaaaacdbadcddcbcdddcacccddacabbbbddbdbddaadcbccbbabcddccdbcbadbcadacbccbdddddcdbabacdabbcdcccddcdccadddacaddcdcccbadbcbbcaacbdcaddcdbcdaaddcabcabbdcabdabcabbcabdddbbacbdddddbbdbadbcacacadddccdbcabcaabcdcccacdaccbadcddbbccdccabccadbacaddbdadacbbdcdcbdcabacdccadacccdbdcadabaaacbbbbcbdbbababadaababaadbbabdbbaddadcdadcbbaacacbcbdacbddbadbcbdcacdcaacbdbbabdaacbdadcdacdcccddcbcacbcaadbadaaacdbcacbccbdabdbbbabababcddbdabdaccbdbabccbcbadbaadadacadaabdddaacbcbbadcadaaddcccccbbdbbcdacccccdabadabaddddcadcdcdcbabcdccddbacbccabdabadadddacccdadadadccadbbbaccdcbadaaacdacdaddbadaacbaccbacdacdcdacaccdacddcdadcdcbadbbdaccabaaadabdbdabacababdbdaaabbaaacccbdbddccdcaddbaabdadcbcccccdddcdcdcacdbacdbbcbaddabdbcabbdabdaaadccdbbddbbcabaadcddcddacbdaadbaccdacdcbacdbdcaacbbccdbbdbaddadcacdcbcbacababdaacdbcabbccdbcabbbcaaaabdacdcacdcdcdcbdadbdbacdaaddaadcbdacdbcdddbddcdbdaadaaacaccdbadacadccdaccaaabacabbacbaabdadcbccaccabdbcadcaabbddcadbababacbabdbbbcabcddcabacbabbccdbaaadddaaacbdabcdcbddccbcadddaadaddcacdbcdbbcbcacbcdcadaddcabcdcdabadaaadccacadadcabcbaacbccbabdcdabdbadaddabdbdcbdccdcbddcaddbccabdbcdaaaddaadbbcdcbcacbdbbadcbaabbddddabbcdacccbcaacdbacccaccddcddcdcdbdbaabbcbcddbccaaaddcccaaaccabbbdcaacbddacacdabcbddccbbbcbbcbbdbccdccbdadcadaccaddabadbdcdcaccdcabcaadcdbcdddcbbdcacabdabcbbabaccbdcaadadddcacccbabdcbdbdacdacdbabbbcbdcdbccbddbcabcdcbddabdcdcdcbcbcaababbbdbdbbaacbaacacbbcabbdbcbccdcccccddddddcbaddaccbabaabbadcaccbabddbcadcaaddadbdcbadbbbaabdbadbbbbdcdbabbbcababadabcbddddbbbbbabdcdbcadbacccaacabbbbadadcdcbcadcdabdbcbcadadcbcdaaabcdcabadcbbcbdccddadaabaddabddccbccdcdcaaabdcaabddbabdacdbaababcdbadcccdaadcbadaacbdbbbdaddcbcdbbcbbabaaddbdbcbcbdbcaccacdddccdadccbabadabacddbccadacdaccabdbdcabacdbcaadbbddabcbdaadadbbcacdcabbdacbcdadbcdbaabdcaaadddcddadadbcccbbabddcbddbdadadbbadccccbdcbaaccaddadcbbcaddacdddbbdbadcdccbcdadabbdccccdabacdbcbbbcdabdaddacccbadaabbcadaabccbbdadcacdbccaabdbbcabcacaabbdbccbcdcbcaadbdacaacaccbaabcadaaabcbacaccabbacdddddbdadbcccdbdbdbabdababccbbdbbaccadcdddcbcdcdaadbaacbababbdcadbbccbcdbdccadaaaaccbbcbcdbdbdabdadcacacbaadabdccacaccbadbdaacdbdbcdcbadcdadaadbdcbbadcdaadadcadacbbcbdaadbbdcdccddcadaaddcbddaabddacacdaccccbbabbaddbdbbdaccbcccbaabaabcbddbdabbbadcaddadccacddcbcddbbaabcbdacdddaabdcabcbcdadaccbcabcbcbadcdbacaabdbdbddbdcaaddacccbddbacbbabaccacbabbcbbdbadaccdcdaaacbdbadddadcdabbdaabaaadcabaddcadacbcdcabdacdcabcaabaacdbbcbbcabccbabbbacddcbcbbaddbaccbbaacbdcdbbdbbbdabdacbcacccdbacbcbacbaacadbbadabbcdaadababcaadcaadcbabcabdcbdbcbbdcdcaaadadbbbbddbbccddddbcbbaadddaadabdcccdddbbadbbbcadbbadaadddbcbcabccdbaaaadabcccaddcdabdcbccbcbbacbcaccaddacdcbbcaccababbddcacadbccaddabcdadbadbadbbbbbabcaadcbcdadbdabbcbcbddddbbcdcdbacaacbacbbdacdbcdbadacaccbbbbcddaaddbddbdbcbaabdbabdaaaacbabacabacbacbcccdccbdabaaadababbabcabdabbdddddaccdbbadbbbccbabadadcbdddadbaadcdddadcbdaaddbbcadbadaadaabcaaddaccacdabbaccaddbbcddcbccccbcbbbadacbccadbccbbaacdddaaacbdbaabaccbbccdcdbdabaaaaadbddcbbddadababdabcdcdcbaacdaabcacadbaddddcbdbbcdcbadbbcadccdcdcdabadbcccadccacacbbdaddbbdaccabcdcbccabdddbdddddcacbbbabcacacdddbcdccbcdaccadaacacbbacaaabdabadddaacbbcddcbbcdccbacadbbdbadbbcacccaabcacaabccbccadcaabdbbabcdbcdcddbbccbddcacacaddcadcdcdbadcacddcbcdbcbbabdcbdbccabccccdbdcbacadcabddababbababbdcbaaadcbddbccacbbbdcbbbcdcbacbbcdacddabbcacbacbbadcbadaaacdadcdddcccbcbabadcbdddccbcabacabbabadadbabdcbbdaaacadaaabddaadbdcbcdcbbacbdadbccddddacdbbdaabdadddbbccdbabcbdadcdcabcdbadaaaddccabcbcbccbaaddabbcbbccadbcdbcbaccdacbbabbdbddcacdbaddadabbabccdabbbddabbbccddcbdcbccadcddcdcbdbabacaacddbdbaaacddbbcddddbdaaacbddbcbdabcdbbbcdbbaccabdcabbcabaaadacbccacacaccdcbcadbabcabaccbaacdcccacdcdbddadcbccdaaccdbddbcbbddbddbdddbadabbdddbacdadbccacaccccdccdacddcdcccdcbbbcccaccbaaadbcccaccddbbcadacccbdaaacddcaccadaadaaaacdccaaddddacabcacbccacdccddcbabcaccbbdcadaadcbbdbaddcaaddbacaddccddacbdccdcaddacddabdbbdddcabcccbcdcaadcadadbdabdbbbddbdbacabdcadbdbbbacadcacabcabdbadcccaaaabdcbdacccdadccbddacaadadbabcbdabdbbbbcbcadacdcaccddabadddbabaccabdbbcacdaadabbcdbadadaaadccbdcbddbadccdaabadbadcbabcccbddccaaabcacbbddbcdbbaaccccbbbdddabbaaacbddacbcbaacaccddbdbadbcbadcddbdaaacbbdccddadaabcdddadabccccbbdacbcaddbdddbbacaccccbbcadbcbbddcdddacbaacadbbcabdbacdbdccdbccadbdbabbabcccbbbbacccdbbbaabdbcdacbdbcbcadaddacababbdbbabbccaaccdacaadbaddadbccaaadddaddcaadcccccbaabaaabacdaabacbbacbbbccbaabbbddcbcdddcacdcdadadccbddcdbccdddbbbadccabccadabddbcdcdaaababdcaaabcdccbadaccacbadbbbddbabaabdbbdaabdbcabbcddaccdcabdbcdadbcbcddbdbbcbdcdabccbbbdddaacdbabbdddbccdcacbbcdbbdcdcbbcadbdccccdcbaacacdabdcdcddacccbcbbbbabcbbcbbabcabcacdbacccdbcbcdadadbbadccabdabbcadacdccbdadbddcbcbabcdbacbbbddcbbcaaaacdbcaddababdbabdbaaadbdbcabdaabadaaacbcbcbcaccbadddbccaaadacdaacabcaccacdaaadcddbcdcaaacaadbdbbbdaabadcbbabdbbdbbbabacdbcabcdadbadcbcccbbabcadaabdbbcdbdcbaabbddcdddaadcdbbdbddabbdcaccbdcbcdbddddcaaaddbbadcdcaadcbadbadacdbdcddcdbacbccbdbcbcaaccdbbdcadcadabcdcddabccaaccdacdadbababdadaabbaccacdbbdcccccaaddbccbdabaaacdbdcaddddcbccbadcdcaacbaaadbddabdbabdccbabbacccabcacdadabaacbacbbcddccbacabadbcdcaacacddcabdcbacacbaacdbbcbcadccaadaccaddaaabadabbdccbadabaabdcdcbdcbacbaacabcbdbcbbaacbcdbdbdbcbacccdddaccaabcaaadccdbccbccbaaabadbbdbcbdbdbadaaacccbbcadbccadacdbddcdacbdcdadaddbbcdcabacdbaaaaaadccaabbbbadbccdcabdcbaadabcabaccadbabacabdaabbbbbdcaddbdabdcacbdccbbcbabacbccddcbdadbbccbabdbddbbcbdbcaddacdddbddbadcabbbcbbadabdbddbbcadaabacccbcabdddcadcdabdacadacaadcaabdbdcaabbdaabdabdcdcdbabcbaabaadbcbddcbbdcacccbbdaaddcbaddbccadccdbbcacabbdcbcbcccbdcbddcdddbcacaabdbacadacccbabdddcbacbacdbacbbccadbacbabbdbbcdadbbabbddbcdbccbaababbbbdcddbacaacdaadbddacbddaabacacdddccbccdddddbdcabbbadbbdbdbddbcabccbaacdbdbcdbccdcddabdcdcddcdddaadccbbbadbbdccbdaaabbcdcdcddaccdbbddccbcbddbaabcccddccaddbcdcdabbbdbdddccdbaaacbdbaccbaacaccbbcaabacbdabdbaabbdaadaccaaababccbbcdacacabaddcbdbbacdbaacdbccaaababacaadacabdbacbbbbddddacbacbcaddbaaccabbdccacadaccacddbcdcdacdbdaacdbdbbbcbbbcadddbabdcdcacdddcabaabcbdaccdbcddababccbbdbaabcbbddcbabbbdcdcdcbcdddbacadbcccabdccbadbadcabbcccbacbabdbbbbbaacdccdbacdbdbcbbacdccbabbacdabddccbcbaaabadaccccdcacadbcdbcbbcccdbdacccadddcdcadcddcbabbdabccbcdcabdadaabcbdcbdddaddbddabbaabdbdbbbbabcdbdbaaccbbddbbabcccbbdbabcdbcaabbcbaabdabdddbdddcbddbdcdcaccacdabddbdaddcddabaabcddabdbacbdabbcdcdcdadbccdcbbbacbadbccaaacacabbcaaddaadbbcadccadcdddcbbbcacbabdccdddddcabcacbaabcdcadcabcbbacabbbbaaddcddadcabbcdacbcbdbbcdcaacbadcaabdddaaaabccbdaddccdcdabbdacbbccadcdccbdddbddddabdcccbdaacbdbcacdbbcdbddbbdbabcadcdddbcdaddcdbaccdacdadbdcbdabcdcbbaaabaacdcdadccdddadccacccadaaadbbadccdcbaadcaabccddddbdcbcddbaabbbbdcbbdbcbbdcbaaabdcbcaadddacdbdcdddcbccacdcbbbdbdabbccdddbabcaddaaacbcbcbdcdbbdadaaacddcbabdabcaadabbbcdccbbddbcbdcadadaacccbaacddddbdbdbdbbcadbaccddbdbadcbaacaaaadcdbbddbbbddcaddadbabacddcddacaadbcdccbdccddbaacbddbbabadbbadabadcbdcdacdbcbdabaaaadabdcaacddaabddcbcacdcaabbabbadbabacbdcbcddcbadcccbdadcbabadbbcabdaaabadadbcddbbcdacabaaaccacbaddabddccbaaadaacadcaddbdabddcbabdaaadcbcddbbcddbddcdcadabcbdbaaccddabbaaabcdbbbacbbddccdbcbaacadbcbadbadcacdbbddcdbdbabcbaaadadacbbdcccbabccbdbddcbbdbdbcbdbabdbbabbaadaabdcdbddccbaddabcaddbbadbdbadbbcdcdbccbbbcabcdadacadcadcddbcbbbcacabbddcdccabaddbbbdcdbaaabdadaacaddabcbabdccdabaaabdaccaaccccabbbcdadbbbabbdbbbdabcdaaabccdadcdcbacdcdbdcbcbaccbaaabdcaabddadcaddcbddccccbacbbcaabaacabbcadacbddadcdccbbbbcdcdbbcccccdcbbbccddacabaabbbbccbbabdaadaababdabbccccbdddabacaabdccdcccaabdddadbbacdababdbdabbdbbccaababcdaaadcacdcadacbcbcacbbbdbbbcdccddcdbdaacacdccbdbabadbdccaacadacadccbababbccacdccaaacaddcbbcacdbccbddbbabccddabaaaddbdaadbdbcaabddbcaadbdababdbcbdcbabcdbcbcacbdaaabcbbaadbcdcdbbacacbbddabcadbadbcadadbcbbcdddddcbdcddaacaacbabadaaccabbcbbddcdcaadcaabccbbcdbbaadccbbcaccddddabdddbcadcabcdcbdbbdabcddcaacccbcaaadaadaccccccabdadcdcbadabddadbdcbbcdcbbbdddacacabadbddbccdbdbbdbcacadaccddddcbcbdbdaacdbbdaddadcdaccbdccadcabcbacaabddacabacabaaddccacdaabcaccdadbadbbcddcdadbdbadcbacadddcadbaadcdacaadcbdacdbcbacaacaddbdcadadadabcccbaaadacaacbcbbccdccdbadabcbbbdbbdabdbbbaaaadbabacacaaabccabccdaabcaddcddaadadcbddcacdcabaacdcaaacbdccaadccbcaccdbabdbbcdcbdbcbbddbbccbabdaabbbdcdcdbbcacbcdbdadccacbaaacacccddbbababdcabccbccddbaddaddbbddcddddbdacaabbcadaaaaaddbbaaabcabadadaaaabcdaacadacacbadcdcddbcdaccdbbcbdcdadacdaacabaabcacabcbacbbcccbdacadccdadcccbdaaaacbbcbbcbacaaacabbdcccccdadbaccbcbbcdbddacdcbcdbbcbbcaabddccbacbccacbaabdccdabdcccacdbbaaadcacdbbdabcdddaccacddcdbcbcaaddacdccbbcbcdcbdbdabbdaccccadcdbdbabdcbdcbcaccbbdbdbccbdacabdccadabbdbcacddbdcdbdcbcbdbacbcdccdacdccdbabddacadbaddadbbbcacdcbcbbdcadaccdaacdcdbcbbcabbdbaccbbaaabcadbbdabbdbddbdcdbcbaaadcacdadabcccbdacabdcddbbdddbacbdcbcbddcbbbabdddadbddcbadcbabccbddcbccaadabdaadadadbddaaabccaaadddbccdadabddaacacccdcabddbdcabcbdbbabaddddbcbccbdbdcbcaababbbaabaccbdaadaddbacdbbdacbabdacdbbbccabdabcdbcdcacbbadbadacbddabaaaaabbdbddcccbacdbcbbdadbbcdcdbaabaacdddadacbaaacccbdbcaacdabddcaaccbadabdaccdaadcbacbbbabdbdcdadacccbddabbadcabcadbdcadcdccbdaccbbddccacdabdabbadcdabcddbcddcdabcbccacbdbadcddaabdbdabdcdbbbccddcbbabcabaabdbadcdacbccbaabbcaadabacbcabaddcbbdbcadcdbdabababdaddaaacdaacbddcdbbbaaccaccbacbbcbdbdbccabbdcaddbdacbaaaabdaaccaaadcadcbacbadbaacbdccbcbabbddcdbcacbcddabaadadbbcadcbbabddcbacbcddcaaacadadcbacbcbadcddacddddadabcaadcdcccdbdbddaabccadaabcbbbcddddcbdcbbaabaabbaadabcbbcaaabacccabbccdccaaaabaaddbacbadaadaadbbadaacbbbbadacbdabdcbcadabdccdbaabcbcdddbbbadbddcaacadbbaddbcabdcacdadbbbcacbcadcbbdddaaccbbabbdbbaabcdccccbdbcbbbadcdcdbddcdaabdbacdcabdccbdabcaaaaacbaadbcbcaccbcaaacdcbacdabcdabacbacbdddbbdcdaddacadaabcacbdcbdabbddcdbbaccdcdabdaabcdbcccbbbaddddccacbcdcbbcdbcbdcdcadccdcddbabcdbcdccbdadcadccababaadcdaccbbddabcbbbcacdbcdcadccaddbbbdddcdcbcbcddbdcbdbbdabbcdabcbccabdbbdbbbbbdcacdbcadadddcbcdcbaabcbabdcbadaddcdadbbdabdcddcaddbdaadadcccccbdbcccaacbcaccaccaaadbcdcbcdbbcbbcbbacccbcccdcaaccaaaddaddabbccbabcdbaadabbbaadcaacdccddbdddadcadabbbdbdbbcdcdcdccadbdadddcadacaaacaaacaababdcacabcbcdcdbaacdbdbcdccabdcbbbbccacaabbcddbcbbdcabacadcababadcdbccadbdbccadccaccddaccaaadabdbabbabbaadcadbdacbcadcdcbdbcdaabccaaddbbaababcbcbdbcadbacabdcadacbbadbaadcdccdcacdddcdbbcbabdadaccdcdaccbabcbaddaaaaccdbacddbbdacbacadadcadacddcbcdcdddaabdcdbccdbccdbbbccaddaabccdbccdcabbccdbcbdbdaaaadcddcbdaccbdabcacccbcbccdbabadccabcbadaaaabdbbccadabdaddcabadcabdddccbdbccacadadbacaaccacacbccaadacdcbddbcdbadcabbbccbacacbadbaababbcbadcdacacadcddcbbbbdaaabbbbcdddabcddbbacbdcbdacacacadbcbbaddaddcbadcdabaabbbdcddbcadadaabcaaabbcbbcaccaccbdabcabddccaccdbbdbbbbdcabbadcdacbabbcdabbdbacdcabdbddbdbdaaaadbaadbbadddddcbbcacdadaacccdcddabdacacacaddacacbdddabdcbcaaacccbdccdddccddcacdcbcdbbaccdadbdaaabdacdabbaddabbcbdcdbacbbacaccdcdabbdbbbcddcbdcbabdadcdbcdbcdacdadbbaabdbbcdcdbddadaabddabcdddcadacdcccdcbcbadabdbdcbaaadabaaddcdbcacbcbcdacdddbbcaabaabdbdaddabcbbadddbadddbddcbaacdddbdabddaaabdcabaacccbaacdacdaadacadddbbddcbcaccbdcaddbcaaabbcbaaabcabdccdccbdacdabbdcdddcabdddabcbbdacdaccdbbdddcbbadbdddcacbbcbadaaccbdddbbbccaacadbbdaabdcbcbabdddacbcbaaccacbabbadadbddbdaabcdcaaacacadadabaadabbbddccdabcbcababcabccdacabbacdccacaddcaadccaacdbaacabcdbcbcaabdcbaaacaaaaabddcbcdbcadcdacabdcbaabbbbabcaccaddabbbdbacacdbcaddacdbdabcddcbcbabcbdbdddbccccccaccacbbbacaadacdbdccdaacbddacdddacbbbcbcdabcdadcaddcccdaccbcadacdbaabcccddbdbadddbabbcbdcddaabbabbbaddabbddccadabdbbdbbaccabcbdaabbdbccbbbddbdbbcabbcbadadacccbacbcddcbdbcdaacdbdbabadabdddaabdddacbbbacdbadababadacdcdacbddaddaaacadcdcbdadddbccadcbccbdbadbdbbbbaccdcbacbdadbacdbdcccdbbcdababdcabaadbcababbddabbcbbdbbbaaaacacabacbdbdbacaaacacdadadcdccdbcadacaadaaadcccbadacaacbabaccdbcacdbccbccbcacaddddcabbcdabbcacdbacbdddabbabdcaadabbdbccddadacbaadaacdcbddbcccdabbabcbdbbccadbcbcbcbcbaccbbbcabbaaddbdabaaabaaabcbaaacdddbaacbacaacabacaaaccbacdacbdaadbadbaccdcacbdabbdacdcdabdbadcdbbdbadadbcaabddddaddbbcaddaaaaaabbbdcbcccccaaddcabdcdaadcaababadccadacccccbcbaccacddabcdadacddbbcdbaacbdbdccacabaadbbcacddbbbbdadcaaccdabaabcdbdccbcdacbdcddcdbcdaaaddbdcdcabdacccbabcdbbbdacacadddbacacbbaddcdbcabdcbaddccdcbaddccbdbcbaccbabbcbdcabcabaabaabdcdcaacbcdccacbdbcdcaccabddcccdbadcaabaabcbdabcbbcbabbccbccccaabacacadaadddacbbabcdbdcaacbdcbaaacadbadcdabbbbcbdddadaabbddbdbbbadbddabcbdbadcbcddabbadcdcaccbaccbaadcbcbbabcdbbdaabcdbddbadaddcccdabcbbadcdaddbcccbabdcbbdccbbdcdabddbcddbaacbadbddaccbbdcdcdacbbbdbccdbcbcababadadbddaacdadacababdababaabbcdbcbdcbbcccbbccacabdbbdcaaadddabdccbdbdcbcdbcccdbcddadabacaaadbcaabbcdbdcacdbadabbabbaaaabadcdcdcdadbccdaaccacdaabaabbbacdacddaacadbcdacdbbcddabbdbdcdbadddaccbdcaaadbcbcbadacdaabddadadabccdcaddaccbcdaaccaadccbdbbbaabbbdcbcddcdacadbcdcdddaaacdddbdaaddbbbbadaabbddbbdddbabcacdcacccdabccdcdbbddcbbcccacddddadcccacbcdbacacbcabdbaccddaadcacbcbccdddbbccaddabacbaaddcbcaaddaaaacabadbbbcddabcadacabcabdccacdcbddddcddbaabddddabcbccdbdcccbadbbcdbacbdacccacddcdcadcbcadacbcbddbbbbddaacdabccbbbdcdddbdbbcdaabddbadddabacacdcbcbdaccadcaacbabbacbadadbbdacdcdaabacddccadcdadbbaacccacacabccdabddaadbccbbaaaadaccdcaddcaccccabacaccccababadbcccbabcbabdabbdcaaddbbcadcdaddddaddcaadddcacdbdbddcdbabcdccbabaabdadbcbdbdccadcaddaddccccdbabbacdbcadaababdbddbdabcaddbdcbabcbbaacaacddccdbdcabbcdacacddccbaabddaadddbaadbdddbbadddbbaacaaddbbbaadbddbdbbcbcdacabbccbddaaaacbaaddcacddcbdaccccbbccccccdddabcbddabbcaadcdaaaacdcaabbdbadabcdacaadaddabdccacccbdcacdbaacdabadcaabaaabccdcbccdbbdaddbbaaddccaaaddacddcdadadcbaabbabcabdcbadbbaabcbbcaaaabccabcdcbbabddbaabcdbcabcaabbbaaddcccdccbaabbadbbbbdbadcadaddaabadbbdabdacaaccdbddcccdddbddddbdbacdcadbcabbacdbcdadabbcbdaddabbbcaadacabbbcdaacacdcaaabadbdccdabcdbabacaaabddabdbbabcadbaadcdabadabddcddaacbbacbddbdbcbbccabacbbcacbcdabdacdcbcddadcbdabcaadbdcabbbcdcabbabaaaadabdbcbdddcbbadaabaaacacdacbdadbbccccacdddbaddddccabadbacacbcbcdaadddbabdaabbbdbbcabdbbbcacbcbabbcbbbacdbdbbdcbdcadabbacbbdabdcccadbadabadcbccddacabcdcbddadadbbddbcabcacadcbdcdadcddcdabcadcbabcdbccaaadbaabbdbaaaadbccadddcccdbbbbdddcabaddcdbbbcbaaabaadabdbdcdcccadcadaccdbaabcaaddabcdaaabdbbbcaacdcacbaddacdadcdbaabcddcbabbcbdaadbabcacbdcbbdcaaadcacbbdbbbccbbdddcaddddaabcddbcdbbbbcabccadcaaabadbaacbccaddbdcdcbbbddaacbdacbdcacccdcbabadacadcabbdbdcbadddaddbbccacbddacdddbcbbbaacdbbaaabccadacccaddaadccdacbdbccccdbaaabaabacaaabcbacaccdbbdbcbadcddabbdcdddcaccbcdcdbbbbadcbaaccaacbbcadcddcbdcdbbadddabcddccbdcdcaaddcadccabadaabcddbabaaccbbaaddbdabdbdaccadbcdadcdcbbbbacabacabbacbaaadaacdbcabbcdabdcabbaadbaabcbcddbcabccccbabcbddcadccaddbccccbdaccccbbabcbadbcbdbdadbdddacacacdcbacdbcadbdacaabcbbbdaaacababddaddbdadacbddacdbbcbddaccbcbccddcadacadccbcacbcacadaacdddbbaabacbababdbcdbbbcbaadcdbbdaaabbdcbcbadadadcbdadccdacacbccdadabacbbaadcbdccabccbbcdbccbbccddacabccabdbddcdaccacccababcbbdcbdcbdbddddccbaabaadddaaaccacbdbdddabdbadacdacbddbdccacbadadddcddcaadddbcacbcbbbddaaddccdcdddccacacdaddbdbcccdacccdddbbaadbbbbbacdcccacdbcccbaadaadbbcdcdadcdcdcaccdabdcbdabadcaaadbbddacacbbbbdcabbddccccdbccbbdcddbcbdbddcaacccdabcadbadbbabbabcabcbbdaacadbdbacdaddcadbdacaacbbdbdcdabcccbbbacdaaadccdabbadbbccadaacaadbbacbcaabbcdabdbaaacdadccdaabbadabcbdccbcbbcdbbddbdbcabdacbccbddcdadadacbcdbccabbdabbaadbdcdbdbbabcbaadbadbaddddcdabacbacccdddbbadccabaabbabcabaaaabccccaabadccddbdcbbcdbaadbacbbbcdcdcaadbcabbacaccbbdabdabddbcabcbbaaacbbabdbadaddbbdbddcccdcaaccdabdbcababdbbcabcaadbadaadccaabacbdaaaaaccabcbadcdabcbdcbdabbadabddcabdddcbcdcabbdacbabbccacbaaaccbbdaadadcdccbdcbbbdbaadccadcaabcbaaacadcabbbababcacadbbaadddacbacabcdcdddbcbdaadabaccbdbbbacccddaacadbacccaadaccddbaabcbaadadbccbdbabcbdcabbadbbaaccddbddbdcdbdbdcbacbddcbcbcdacccddddbddadbdbaabdacbbbcbaadbcbbacdccadadcbabbbbbdbbcdcdabbcaddcbbaddccabcdccccbcbdcabbbaacaababadacdcbcadddcdacbdcbacbabbcddcccccbbdaacbacdabdbbcaadaabadbabddbdcbdaacbadbdaacbdbdcbbdacdcadbbccdacabcdaddabbddabaddbbabdadcbddadcaadcadbbbcdbdbddbbbabddccccaaabddcdaabbadcdbddddbddbdbdbdbdbbaccdcdaadcbbbbbaaddadcacabddddcaaaabbbdbdacaadbbdabbabadbcaddddccbbcacdabdbcbbddccdbdcbcadbaadadacdaacdbdbadbadacbcbbbdddcbaacccdddacddcbaaacdbbabdabadabcdacabcbaabbcddacbcdbabccbdacdacddbcdbbdcadbcbaabcdcbacbdbadddccbcabdcdcbdadcbdaccddbcaddbbdacdcbaacbadabddacadcdcbccccacccbacdbbcdaccaabccbbcbbbbabdadbcddcccbdcdbaaccadddcdbbcaadbdabaccbbcbdaadacdcbdacbdcccadbaacabdddcabcddddccadbdbcaadacccaabdbbcabddccccdadcaccccacbbdabdaabdbbdccbbddbccabcbaccdcbbabbacbabaadcccdadcdabaabbdbcadbdbdddcdbdbaccdcaccbdbbccbcacddddbcbbcbbbacdabbadddbbcabdccccacdaccccdcaaacdddbcadcddbddbcaddadbdaacbcbbdccabdabbabdddbabdcddcbbadcaddaadcadcdbbbcbcabcabccbacbababbdaaddaababbccabdccdddccaddaadcbdccbdbcddccbdcabcdcaabbccbdddabddbcddaddaadaadddddcabaadccdbdbcdbcabdacdaccbadabbbbcdacdcdddacddcdabdbadaabaacbdacaaccacbdcadbddddbbbaacbcbddbacdadbbcdbabcccabddcbdaabbccccaabaddbaadcabaaaaccdbbdcbccabaaaadcadcaadbbdbbbccbccdcddbbccdcccadcadccaababcabccbabbdbbacbdcabacbbbbdcdccddcabbdabccababcbcaddcaabcdbcbccbddababacdcacbbdbbdbbcdbbbbcbabcabdaadbadbccbbddccacaabbcdbbccbdacdddacaadabacdacbdacbaadcdbccbdaaacababcbbacbaaddcdbbbdbdcabcdbbcbcbbadadddacbcdadcccaadcdaabaadccdabacccdbbacadcaacbcacacbbacbcdaaaddccdaddccbcadddaddabdaacabddccaacbadadccbbabddbdbaccbaaacbcdcdabdaccdbcbcacdacbccdbdbdbcbbbccdaaccaddcacaabdbbdcaabcaacbbcdbabbbdbcabaacccbbdaacaccbbccdccadadbbbddccbbabdababbacadccbcbbcbbbababdaacdccbaabbdcbabccacabaacabcabdbcdacabcadbdbbbbddccdaaaacadbbbbbabdcaaabdbddbabaccbbdcaccddacddbadaacbacbccddccdaaabdaddbddbbbcdabaabdcdbbdbadcbbbddcabaddbdccadcabcdadbaddcdacdbbbacbcaccbddcbdbcaaddabdcdabdbcdadbabddbdbabcaccdabbcbdcaddaabbaabcddadccddbcdbadacadbdbbcddabcdadadbcccbaadbcadbaddadcbadbccddbbcbbcbbddcadcadddbdabbcbbbccddabbdbcaccccabccccbaabcbdaddcababcdbaabcadcaadccddcdaabdcccccddcdbabcadccccbdacbbdbbdbabbbdbbbdcbbbadacdaaabdbccdcbcbdbddadbcbbbabcacacacbacaaccdacbdcacacadadadbbccdcbddddbdabacadbbdbbbccddcacaadbacaabaddcbcdbabacccbadbdcddbbdbbcdddbdcaacaaacdcacbacdbbacabbadddacccacdaabdbdaacddbbdaabddabadbddabbabdcccbaccdcbadcacbbdbabcaddadcbacbdbbaccbbbbbabbccbadabcbcbbcbadccbaddbbccadbcacbccacabdbdcadcbcdaddbaddaadcdbbbcbcdaddccdbaccbbacddbdcdaccadaddadaabdddcccacaccbbaadbacdcbcbdcbdcbccadccddabdcdbaadacaaaccbdccbbcdcaabcccdddcabaaacabaababcabadcddccababacbbcdbbcaaacdbbbccadddbbbcdbcdbbabaabbcddabadbbcaabcdccabdbbbdcacbacdbcacbdaccddbddcdcdccdccbabcdaddaadccdccdccadcacccabdbccbdabbcbabcbaadacadadacbdaacbdddbcadcacacaddabbadabbddaacadccddacdddabcbcbdbbdabdcdadbcdcaabbccddabaddddabcdadcbbdaaacdddcdbcbdcccdcacaadbdcabbbadabbdcccbbcaccdadbadcdcdbbdcabdccccdcadababacbcbbabbccdbbdbdbddcdbacccabaadbbcccdacdaaccabddbdadcabddbcdbdbcdcbadbccbabaacdaaaabaddcccdcbdabacccacbcadbbddaadccdaacdbacbabdbdbacdbbacadaacbbcbcacddcbdcdcadcacddbbbbbadabbdabbbbcbcbdacbbacadbacbccdcccadcbbcddbcadbcbcdcadcdbaadacbabcdbbdaacdccadabaddcdbabacbddaacaabbddcbccccdcadccdbdabdbdbdcadbbaacbcaaaadbaacdbcaadabbabacabcabdbdcccadbccccdcbcacddadacdcdadacdcddccbdcccacdbbdacabbabbdddaadbdbaabccbcadaddcbbdacaccaccbcadddbaabdbbcaadbbcdbccbbbbcdccaddaaaadabddbaaccddbaabdadbaddbccbdddccccdbacabbababadcdccabaccabdaadbcadaadadbbccbdddacddccbdbbcacdabddbcacbdabdbcdcccbadbcddcccadbadbaabcccdaccbcdcdbddcdbbdaddbccbcddccdbdddbddbbdbcaacdbbbbadbbbabbdaacbccdbabdaccaadcacaabbbddaaaaadbccabccadbaaaabdddcadadcdbaccaacdcdaabbdacdadaabcbbbbdaaddbdadacacabdddbaddaccaacbbbdbdcccdcabcaccbadabbbbdcbcbdbcddcacdbcdbaccaaacdadddcdcdacbcbcddbddabdcdcbcbcbccacdaadabbdccbdabaddcbcdabcabcadcacbbdbdabbdabcdcababcdbaccaddccbccdbccbdcacbbbcdccddddccdaaddadcbcdbdbddabdbddcdabdcbabaaacabcadadcbbbbccbabbadbcbdabacbaadbbacbbdbccbbabbdbbbadacbacbbdcdcdadccbabdcbddacddccdaacdcbbabccbcabbdaabadbcdcdaccaccddadbaacccacbddcdaaaacbabcbcbbaabadddabcccaabcbbbabadabcbbbcdabbaacaddbacdbcdbaaaadccbdbbadadddcacdbaaacdaccbaccbbaabcddbbbcccbabdcacbacdadcdcdcdacbdbaabccacbcbbcdbdcbbdcdcadadcdcccdacaaaddbacbaacadbbcaddcdabbadaccaacacacdccaccddacdddbbadaadcbdbdadcbdcdccddacaababbaacdcbbbaaabbcaacddabcabdbbaddbaadadbadcbbaaabcdadccbaddcbdbbabbdccbdbdacdadbdccbcdbccccdaadacddabaddabadcdddcbcaccdddbaacaacdbdbdbbaddaddcbcbadababcccbbcbddaaddcbbbdddccccdbddbaaadaadccaabbcaababcddacabbcbbaccabaadbdcbdbcacdcdbccbaabbaabacbddddbdcccadaabccbcdaabcaabcccaaaaabadcdccbbcccbbcabdadabbaaacaadddcaabacbcabbddcdcbcdbbcacbddccdcadcbbcbbdbdccdcdbdcbbacadaacbadcbdbadaacabbaccaccccabbddabadcbdddbbadccabdcbcabbddbaadbdaddadccbdccabcabddabcadcaaddbdbcbccdccdbdbaaaddaabbcbdadbadbbccaccbccbcbdcdcbaadcbccdadbaabdacdcbdaddcbcbaddacacdcadacdcabdaacaacdddbdabacbaaddbdabcddbcbcaddbacdbcbbccbabcdbbcdbbcbcdbacbcdabcdbcabacdbdbbbcbcdabdcadaccabdbaabcbcbbbcdcdbabbcacaddbbacdccbacaccaabcbccbabdbcccbaabaaabbdbdcacabdabcbddcdddcbdbbaacacbacccaddbadadabadaacddcbccdadbcbacdaddaabacaabddaccdddbbcbcbdcbabbcabbbccaabdcdbabcabbbaadcbbdabddbbdddacbbbcdacbdddadaccdcdabdadbbacdddbadbcdcccbbccccddccbbccdbadcaadcacbdddadddabddcbcdcdabaddcbccadadaabdbbddddbaccccddacdabbacddabaacacdaabbbbdbbdaadbbaadaadddbdadaddbadabbbcdadadcccdbadaaccbbabdacadbbacabdacabbbaaaaacaacaddaabaadccbdabdccdaaaaddbdbabbdcdbddacacbbbcbdacaaccdacccbccccadcddddcbbaabbdcbadbacccddccdaababdbbbdbccaccabbbdcbbcabacbaccabccbccababccbbadaadddcbdadacdcabdcbdcccddaabdcabddbddabbacaadaddbbcacabbbcadbcbbbdcccabddbcbbaadacbdbadccccddbbdccdbdcdbddbdbddacacbcadbabcbabccbdbdaddbdadcaabbcccaacabcacbabccbcbcbbcacaaadbbccaddcaaddbbcabdcddaabbbadbccddbdaccdbcaacbdcabdccdbcbdbdcadbcbbcdaccbdbabdaababaddbcaccbcababdcdbcadbaabddaccabaadbbdccabacabacdaadacdaddcbbdccaaaaadacdbbcccdbccdbcbcbaadbacbbdbbdacdaccbccacbcbdcbdadaacadccabacbbbbbacacacccddcabadadbdcabbcbddddbdacbcbcdbcbbacabdacddbcdbabcddadacdbdaacdddbbaaadcacaadbbcacbcbddcacacbddbccbbddabadacdbaccabbddaacadcbcdbccaabbabadadacabcdbbbcbbaccbccbbadbadcabdbdadcadabdcacabaccbbcbbddddcbaddbbdccdcaadacaccbddbbbdbddacbccdadbabcddacadacadaacccbcbbabbcbcadbaadcbdccbbdcdaacccdbbaaddbbbcadcbcbacaaaccddcdadbdbaadcabadddacbcacdaddbccdaaabbdbbdaaadccbbabbdaacbbaddbbdadaaabbaabbbcdbccbdddbdbdccdabaadccbcdddadadbabadbbcdaacdcdbdddacbcacbbacddbdbabdbcdacdbabcdbccacbacaabdcccaacaacbcccaaadaadbdddbdbbbdcccacdbaaadbcaaaabbdcdcdcdddbcdabacdbacabbbccbaadacacabdcaadccbbcbcaccacbbbdddcbcacdacacbdacadcccddadcacbbdcbdacbaaabdcdacbbddadaabcdbdbcccacacbadbaaaaadadcabbadcdaddbcccbaaaadcadacccbcadadbdcaaabbcacddbaaabbacdbaddbcbdcabcdaacdbbdddbcdbcbcddadbbdaddccbccccdadacbbbcdbbcdccaabdcacdcccddbcbbddcbabaccaacadbabccbcdcccabaaababdcccbcccbaccccaddacdbbcacdbbabcdbaaadcacabcbcaccdccadcabdbbdaadbcdccabcbcdaaaccbabcabdddbdadcbabccadbdcdbbcccbbdabccddbabbcbabaacbbabadbadcdccbbdcbdbbbbadddbaaccbadcaadaaadaacbaaccbddbadddccbaaadacaacadacacbbcdbacbaabccccddddbdaddddabddcaaabadcbadbcbcdcbacaacabdcbaccdadccabcdaccababbcbaabbcdacdaaccaddcbadbdbbacbcbacbaaacbacdabddaaccddbaabbccadccacadaddbabaaaadabbcccccabbcadabdaccaaccadbdddaadbdcbacabdcaddcdcaabacaadcddcaadddbcdabbbbdbbcddcaadcccaabcadcdaccbaabcbdabcbadbdcaabbadbbbcbacabcdbaaabdcbbcaabddbacaaacaccbcbcdbdbaacbcdcdababcbcddbdcaaabbaacddcbcdbaaddcdcaadcbcbdbcdccabdcbbcaddabddbacacdcbcccdbccdbdbdcdbaacbdabcbbcacdabbddaacbbdaabbbdcdbcdcaaadababacaabcbdcbcbacbbdbbccdbabacbdccacccdabbcddbadadddcbddbcaadaadacdcabbdddbdbaddacdddaccddbcdcabccbddbcbbabddbbdbaacdcabbddadaacaccacacccacdaaabbccbcbabcbadaccaddadbccbbbcbdbcdbcbcccdaacbbcdaddcbdaaaddaaaddccadbdbaadbdddcabacbacabbcbdccabacbaddbabbdaddaaaaabbcdbbdbccdbdcdbbbbaabcadccbcdadabaddaacddacbdccbdaaaacddaddcccacdcdbbabbaadddcbbccccadabdacdcdabbaaabcdadacdabadccaaccbcadbadbbcaadcadbbaabbbadbdbbbaadcaadcacaadbcaadbadbbcdbbdaddcbcaaadbcacaacbdbbdbacbdadbbdadababdabdcadcdaccbdbcaacbcbabcdabcdbdcabaadbacacddddabdbbacdcdcddaccbbddbacadabcdabaccddcabcdcabbaacddddddcaccdadbadbabccbadbdaaabbcaababbcbddcbbbaabcdaaaccdaabadbbbadcadbbbdcbdccdbbcccaaccaababcabdcdadbcbbdbaadbdbbadacbbbbbdddaadabcbdbcbdabdcbdcccbcdcbbdddbacbbaabacdbbadbddaabdddccbbaacabccaadacbbbcaddccbbcdccdaccbbaadabdcdddaaaabcbaabcddbbcbdddcadccdcdcccdbcbcaacacabbbdcbaddbcaddbaccbbcaccdcbaddbabcadcabacadbcaaabcaaccdcdbdbbbdcbaababcbdcaaaadcaddabbbaccdaacdcabdbacbcdbcdacddadabbbcbabcaccbcbacbdcabdcccacbcdcccccdaabcaaddbcddacbdcddbdccacbdcccacdddbbadbdbcdbccbbbcbcdbbbdcbccdddbbaaadccbdbbdcbcdbcdabdadacdacabccdbcdbbccdbdacbbddcccdddadbddbcadccabaaadcbacadbabbdacdbaaccacccdbadbbcaabcdddddabbcabddcacabccccabbccabbbbdbddccdccadbdaadbbdcbccccdddbbdaacccbddadbabcbdcdbdbcddddacbadabdccaaaabcddbbabcdaaddcdaabbabbacdadccbbcbaabccabddaadcdabbcabbbbdbcbdacbbccdadcbdbbdcdbadabcbabdacaadccadbddcbbadcadbdabcdcabdacdadccdbbdbccabadacacadaaadaacddacbccbdadddabcbdcbaaddbadddbdcbbbdccdacaabdcbbccdbdaaababbcaddddcdccdcacddcabbdacccdaaadbaabcccdbaabdddbbbdacacdbbbacbaaabdbacdbdbcacbdabbcddcdbdbddcdcbdcdccabcdcacbbdcbbacadcdaacaaaaaccbddabcbbdadbcdbccacbcadaddbbaabbdcdbacadacdcdaddcdbbadbdaabddcabdaaabccbabcbcdbdacadbcddaaacaaacbaddabbbdadbbabdadabbcdaadbaaccaccbcbbddbbdbcbabddbabdcabbbaacbdbdcbbaabacabcbcddcbacccababbddcddccdbacdabbdacdddbdaacbcccdbacbdddbbaaabddbbbdbaaddbccdcbbabbccacdddacadcbddddabddabdddadabdaabcccacabaaaabbbabbccdadccacddbdcdbaacacbbbadcdacddbdcdaddbcabbbabbadacbcdacaccbacccbcdaccbdccbddaabddadbdcbcaabdbddbcbdcdbcdcaaaabbaabccdcabcbdabccbbcbcbcacccdcadadccadbbbaaccdaadcdbbaabccdddacacacdaddbbdaabbadbcdabcbdcadababaadbcbbdcabacdbcdadabddbacbccaaabdbdbcddabbbcabbcdddcddcccdacdbdcdbcadabcaadacadcbcccbcacbbabcbcdabccbccdbbbbbabbdadcdaadcbadbddcddbddaabdbdacdbbbcdbadaabcdaccbbdacdabaaacadacbbbbbdabcdbccadabdabddcbbcabdadccdbbacabcbdbddabddccbbcdccdccbdbddaacadbcaabdcdbdcaccdbdacaaabccbcbddbcddabbdacbcdbccaaabcdcbcaacddddabbbbcbbbdabaabadcacdadaaddbcdcbbdadacccaccbdbaddbabbadbdaabbacaddcbddcdcbbdbaaaddbcadccbacccadbabbdabbbdbdacddadbdcbcccccaacbcabbdbaccdbaddabaddbdbbdbddbbabcbaaadcadccdcbbcbaddaacaddccccabbdcdbdaaddacbcbcdbaabdddacddbbbadcddcacbbaddaabbabdacbbbcbdacadbcdabaaccbbaccaadcaaabdcbddcaccdbdaacadbdaabccbaacddbccbcadbabbadbaaaaabcccbadbaadcdacbbdacbdcbccadbcdcbadddcaadcbbdacdbcbbbaabbbcbacbddacbcdaaaaaccdcbacbccbcaababdadbbcacdaaadacabdbabbbaddcdadcdadaaacdbabbaabdcbcdbdabacccdbadadabdbcdbccacbcdcdcbacbaacbdddaccdbccaaccbbaadabadccddcdaaaadbbbacdcaccaaadddaacaaccabcaccccbccbbabaaddabaaaccacbaabccdaadcddbdabaaddbccaabbbbcabcabaabbcaccdaaacbcbacbcbdcabdbcdbadcacbcdadabcacaabcbabccaddbabcadadabbdaacbcdadbaaabbaccacabaacbbcdbbadbdcacccdbdbaabdadbadbbbdcabdcdcbbbbbbabbcddcccadacccbcbcdbcbcaaadacadbaddcaddbdbdadbdbdddaacaaacddaabdaaacbcabbcdbadddaaddbbbadcccdcbdabdbdcabcaaddbabcddacbdbdcbaadddababaabbaabdcadbddadcdcdbadbdcdbcadbbbdcccdbccdbaaaadbdcdbbbdbacccacdadaaaabadddbdbadcdbddacaddccadbccadcddbdacaacabccbadcacbddddcbddbdbababddabcdcabdbaccbbbdbddddaaccbccbacdbdaaaaacabdcbdbcddcadabaaabcaaaacabddbcdaabdadacdbbbadaacbadaccbccaaababbdcabbadadbcdaddadcdcbaadacbadaaddbdccbbcadcacbbbccaabdcacddccacdbbbcdbcdbdbbacbdaadbbcbdaabdbcddacddaaddddddabbddcbcaacaabdcbadcdaccaabbbaaadbcdcbdbaaadbbcdbcbdaacaccbdadbdbcaaabcabdbabccbabcbdbdcbbcacadadddcacddaadcbdccabddcabaacbadcabbdccdbcdabadadcbcbbcaadaccacbcddcbdacdacddcdadaadbddbcadbadccbacdadbccacacaadcdcbdababaadbdbdbcdbcbbbcbabcbdcdbdccbdcdacdaabcdbdaaabdcdacacdabccbdaddcbabcddcaacdccabaabbbddcbdabdcdcdbadcbdcabbcdbbdabacdbcbcbabcdbaabacdabbdabaabbcbbabadddbabddcdbbbcdacbbabcdcbaccdbcabbbbbbbdbddabdbaadbbacbdcaaaadbacccdabcabbcbdaabdcbbacbacdcddcddcdcddbcacdbccdabcdbaacacdddcbbcadcbccddacbcddcdaabcdadbdcdaabcbbddddaccacdbadbdacdadccbcbdadaaaabdaabcdcdcdbbbaacccbacbcabbdcdadabccdbdbdddbdddcdaadcccbabdccbcbdbcbcbccccbdddbcabdbddacaddbbddbdbdcdabbddddbbaaacddabbcbdbdaacbbcbbadbacbdccddcabcacdadbaaddbdcabdabdcacdadabbccdccacaaabcadaacbbbcabcdcbcaacdbaadbbcbbbbdcbbdaacdbcbbbbbdccbabccacbdacabbcbaaaacdadabdbcabcbcaaaacccddbdcccdccdcbdadacbbacccdaaaacbbdddbdabcabacdbadadacbccddbbadbddddcdcdbaabbbabaddabcdadabcadaccdccacaccaabdbbadbdccdbdadbcbbdaddabddddbcdcacaaacdadccabccababbddbccbbbbcccbadddcdbbaaabccdccaccbadacdabbabdbdcabbdcdbccdaddbddddaaccbaabbdabaaddcaabadddcacaabbbdbcbacaddddbdbcacbddbaabdbbddcbbcadbcadaaaabbdabadcaaabacbddcddadccbbacccddddaabbdacaccddaabbbccadbcddcdbdcbddbcbdaccacacbaaaaacdbcdbdcccbbbbdccdbcacdaaccdbabcdbacccadbcdabadcbaabcbbdcacbdbddacacaddaddcbaaadbbbadaabaccbdbacaadbbcbbabdbcbaaacbaaddddcdbbdddbdccabaaddbdadccdbbabbccaccbcbbdcabacacbcacbbddadabddaacaaacbacdcbddabbdcbbadcdacbcadcabdaabdcadcdbcdaabdbabadcabcdbcbccabbbcdbcbbdaccccaabddcabdaddcabbdabbddbcbcccaccbdddcbbdcdcdbddddaaacbbbaadabbcbadbddaaacbcdbbcbacabbdacdccbbddacdcbdacbabbbbbdbcdcaacdaaabcccdcccdacddbccdddbaccbccabaccccddbcdabcbcbdcdcadbbcbbacbbbbbcdadbacaaddbdcccbbdbbdcbdccbbbbbcdbaccdcdbddacadabccdbacdbdabdbabdabdadaddaccbcadcbdcdcbbdbcaaccdcddcacbacdadbbabcadbbbcddcabacacdcbadcabbadcacddbccdcbccbcbcbadbabcdcbbdacdccdcacbbcdbbbccadbbdacbddaacccbdbaddbabcaaadcadccabcdcbcacadccddbdaccadbabbbbbbcdccdcaccaadcccbaaddadbbabdaadccdacbdaccabacbbddadccdbccbbdddadadacccdbddbddbaddbcacdcbbbabbdcadadacdaabcdcadcdacabadaaaaaaabcdaabdbbddcdadddbddabbcbbdadadadbcbbcdcbabdcbdaadddbccdabbcbaaaacdbbbaaadabcddcddcaccbbcbaccbddbbabdbdcbdbddabcbacbcaccaacbcaaacacccddaadbbaadadaabddcdcaadabbbdcccdcdccdbacbaaaddcaabaaddabdcdbadcbdacbcbacdcaaacdabcabbaaadcbabbdcbbddadccbcadddddbdbcdaacbdbcbbcbadcaccacbdcdbadbdbccbaacbddbccaaadcbdbcdcdacabccddcdadbbbadaddadabbadbcdbddbccacbacdbdadcabacbbbdddbbdaacdbdacbdaaacbbcaaabcdccaaacdddbdacdbaabacbcdbbbbddadbabdabcbaddadbdbaadcccdbccbddbabcaabbdccacdddabdcbdaacdbaaaaabcaabdbbbaccbaadaadccbabcdcaaaaacccbbbbbaccdbdcbdbbbbadbdbaadaaaddbabadcacdcdbadcdabdbdacabcbcbacbcdccaabdbadbccccadbacbbbbbdbadcadccdbdaaccadcddbdadcaccaddbdbadddaabbaddbcbdbdaabdacbccdbccbbcccbcbcdbcbbccdabdaabaccabbadaacdcbbaddcccdcabdcddccabddacbdaadcbaabaccacaddcbadcdbcdcddbaccdcadcbadcdabbaaddddddaabdcdcacccdaabcbadadbadbccabdcbbccaacaacdccddbbaccddadcdacddbdadccddbacdcdddccaabbdddbddcbccdbdadbaaabbcdddabcadcbcdbddddcacbdcadacababacbdbdbaadbbccbbacdbaabbccbdbcbbcaaaaccdaadccddcaadcaadaacabdcbbdbabaadcdbbcbdadacdaddcccacdadbcbcdbccadbbdbdcbccabdbaccbaaaaaabccccabccdbcadbbcacacadbaddaabbbaddbabaaabdaacdcadacdcbbdcdbcdabcadddacbdacbdddaccbdabcbdcdbcacacaaadcacbadaaabbddbdbbcccaaabacddbdacadbddddabcddacdbacacadacbaabbbcdccdabccdcdcbdcbadccddbcbbbbdddccacabdbbcddbbbbdacdbadaddcdbbabdacbbcaddaccbacbcdcbdccaaabaabadddcccadcaaacccbadadadbbadbbbcbbbddbbcacabacaccccadcabaccaabaddcabcadbaaacadcdddcbadccdcabbaabbadcadaabacadcabddcccabccddaddaddcbbaadbaaacbcaacadbcabcbdcccdccabcdddabacbadcacdabaaabbccbbbabaaccbbdabbbcbbbccbdaadcdbddbdcbcbbdcbcbabaacacbbbacadcdcbbddaccccdcdbbcbbbdcbadaabbaadccaadaccadabdbcabddddabcbbdcacdcadccadbdcdabcbaabcadcababadabbbcbaadddacbcbcaacacdbacabbaaaccdbacabbcddccccddcdcbbcacacbdadbccccbbcadabcccaccdcbbacdcbcadbadcbdabdbadcdcddbccccdbccbccbaabcdccaacdacabaccdacbcccdaadccbaddcbcaabacbaadbbbbdcacdddcaaccdcbddadddabaaddcbbdbbbdcbbdabcdadbdcccbbddccbddcdabaacadaccadbabbbcdccddadcaaccbcdbbbdcbcdbcccbcdcbcdacacdccddcdbccabacdaabcbcbcaabcdcdddacddcbbacbddaddcaaacdddbadababddbbdcccaacadbcdbadbdacdcacddbadcccddccacacaabddbadbbcdcdbabbabdaccaacaacbaddcdacabbabcadbcaaacddadabcacdbbaaadcdabaddccddcdbbcdcdcabbbbadacadccdacadcdcadaacbbabdbdccddcbdbbbdcadaacabdbaaddbaaaccabadbbdacbababdcbdbaacbbccdbdbcdcbbbbbbccbdadaacdcdccaaadabcacbbacbaaaabcbcaadabddacabbadbababdbcbacaabdacccabbaddddddbdcbcdaddcbdacbbbbdaacdaaacccbbbdadbbdccacbdacabbdaabddadddacacbbabbbadccbdadcddbadccbddcdaaddcbdadbaacdcdcaacbcacddcbacaaacbcddcbcbbaadacddadbdadbcacaabcbababdddacacadccbbbacaacbbddbaadddbcbdabbddbddbcaaacabcdbcccadacdcabbcdbdacccbcbbbdcadabbbacabcaaabccdbababddcdddbdcaacadbabbbcbbdccdddddbcbcaabdbdbcbccbcdcabacbacdcbbddcbdcdaabcbabcdbadccdcbbdcccdbbcdbcbcbbbdcdbdcdccdcdccbaaaccddaadcdcdcadbbcbdbddabbccacdabdbaccbbcbdbcbacacbdcdaacddbaccdcbaaddabbcabbbcbdaacbaddcadaaddacbadadbccadaddaabbddbbbbaacbddaaabcaaddbacccbaadbacccabadbdbccddbdccbbcabddbbbdccacacddddababacdbcbadcadbacacabaabddaddbabcbadcaccdcccccaaabcbbdcdabbcbbaccabbcdcbbdbaaccabbbdaccbcbbacdadabbbaadabbdbcdacbbcdcdbccbdddbacbddcadddccacccbbbbcadaabbddaaadcadbccdbbaabcbddcbccdbccababbaccddbbacdbbadadcdcdaaabdbdbdbaacddbcccdadaadacdbaacddcdbcbcbccabdcaadbabacabbccdddcdcabbbdcaaddacdadbacbaaabdccdbaabbacbacacdcadccaddabadcadbdbdddddbdaccaccdcbaccccddcdbccbddbbdadaccbaabcdcbadcabcdbddcbacbbcbbcacbcbdcdadcaadbdbbdcbcddbbbadaaaddabbcdaaddbcbdacdadbbacbdabcabdbdabbcddadddbbdaadcacdcaddadadbcdbdbabbbcdddcbdbadccdccdabbbdcccbdaabacaddacbdaddbdbcbdcaaadacdcdddcadbacdccdcdcddcbcdaacacaacacbbdcaadcbadbbbcacbdadcadcbbdbacadabaccaccabbdbdcbadacdccdcaaaaccaaaccbdcacbabadccbabacdcadbdcdddaaccaadbcccbacdcddacbdcdcacaababbddaaddaddccaddcaddccdacaddccbdbcdcacbadddaccbacadccabbbbcabdabdacdccdcaaadbbdcbbaaddbcabcadbcdcdcddbbcdcdcbcbadbacdbcababddbdddbacacbacbcdbbdcdbbdbccaccacdadccdbddaadcaccdccbbbcadacdddddaaadcabbdccbddbabddaaabdddacbbbacdabdbdddbacbccdacbddcbaadcaadabdaaddcbdcdcaacabcbacaabbcabbacbbacbdcdadbbdcaccdabdbcbbcaabbbbaacaacdcccaacbaabbdaccacdddcdacbacdaaccdcdadaddbbdbdaddacdacdcdcaacdcddccbaaabccabbaccbaacbabdddcdcbcdbdaaddaacbabdacbbbbcaccccccbbcadccbbdabdbabdbbdabdaddcdcacbadabaabbbbaadcbcbbbaccbbbadddcddabdadbcaccaaaadabccadacadabaabcdbdcdccdccbcaacaabdcacacaccbcddaabdccccadacbbdaabcdcacabccacaacbdbbccbbcaaabbacdaacddcdbbcdcbccbdccdabbbbdccdbadababcaccbbadbbbddcdcbdcdcacdbdbdabababdcbbdbdaadcdcddacbaabacacdacacadabdbbbbcccbccdbccacadabadabdadcdbddadbacadcaadadddbdbccccaabbddcbdbabcbbbacddccbbdcadcbddbacababdbdbcbdacbddbcdcdcccabcaaadaadadcddacdddcaccbaacbcbcdaccacbcaacadbcacccacbadacdccaccdcccdaccbdcbbabadbbdabcdbcdddcadcbbbbaaabacdaccdbbdccbdbbdaadadacaacdddcdcdbdcdaddadbdbaaccaaabdbddcadbcbbbcbabdaadbbbaaacddaaaadbabdcbaabdaaaabdacacdbaddbdbddabbadcbabbbdabdaccacabdaabaadddcadbbdacadcdadcbdadcbcaccccacaddccbbacdccbdddcdccbccdaccdacadcdcbbdbccacaabdbadbccaacaadaaacddddddccaabdddacaaabbdacccabaccaddcdbbbcbaccabbdccddcbdccbcbdadadacbdddcabddcacdbdcbcacababcccabaccbabaddcdacdbdddcbcacabaddabbccdabbddcadabbcbdcababddadadcacbdbdacdaccdbcacbcbcacacabcddadababdacacacabadbcbbdcacadabcabbddcccabaddcbdddacdabdbcbdbbdbaccbadcaaababdcbabdbaccadcbadcccacddbdbcbcabbdcbbababaadcdaacccabbdbadaccbbddaddddbabbcbabaadcdabadddbabbbccacdcdadbbacbccbbbbdbcaacbcaddaaadddcbccbcbbbbcbcbbaabaddccbcbcadcdbabbcacdcabdbacdabdbbddcddddbbdcbccbcacdcbbdbdccbadbdacabdbddaaacbbcbbbbaaccbdddbacacbbdadcaccbdacdbddbbbbabcacadcacaddbdbbcadcbaabaddddacabbcacccaabcdcacdbcaabbdabdcabcadacdcabcdbbcdccdaddacdccdbbddbcaacbdabdcadbbacdbcbaccadbdbbdbdaccdcaabbadadbabccabcdcaacaccccdbddadbdcdadbbcbdaabdbbddbcbadbcbababdcbabacbcdcbdcbccaccabdbcadbaddaaddbacabdbdbabcacbcacdcabdbcbcaccddccdbdcddbabacaadaccdcacccdcddabddddcabbabdacdbdddaccdadaacbabcbbadbaadbacaccbaadacbbdbbcdccdcdacccadbadcdbacabaaccdaacdbcaaaaaabdcbcbdccaccdbddbcabbcadcabcbcacdcdcdddbabccdcadaabdbacdccdabaddddbabbababdbbabddbcdbabcddcddddbbbaddcbdbcdbdddbbaacacdcabcbadbabdadbbdabcbcccbdbccddcbddbbdcaadaddcabbabccaadaddddcacaabddbcdbddbbbbabddccadcdbbadcbbcaccaaabdccbbcbdaabddabacdaababdaaaabcabaaaaadbbcadbdadccccbbdcdaadcbcddcdbccaadbacbdabcbbdddbccdbcbaacdbdcbcabdbcaabbdbbcdcaacabdabadcdaddbcbadbbabacaabadbdcddaddddadcccbcdadacaccbccdbaabbaddcaaddbbacaadabdbcbadbcbddccbccadccbdcbabccadabcaccabbbcacdcbddabcbdccbadacabcdccadcaabcccabccadccdcbdddccdcbdccabcddcccadabdbcbdcccccdcbdadacbadccdbadbbadbddadbbcdccddddabdcabcccdccccdbdabbacdababcddbdabcdbaaacbcdcdbacbcbbdbdbddaaddcdbdaccbabbababccddaababbbacdbddadacbcdaddbabddabacbadcbdccdbcdbcbaccddccbbbccdbdcbdaddaacadbbdbaacddcddacdabcacaaccaaddccdadcdcbacbbddbaddcdbbabbbbbcbbcabbdaabdcbabddbaddcdbcdcdbacbcaabbabbbcaacadbcdadccabbadcddadbdbadbccccbbdbacaaddbbabbdaddaadbadaadcddadccabacddbaadbddadaddcdbbccbcaccadadccbabbcbbbbabcccacbbbbdadbbadddcbcdcdaabcdadaaddddcdcacabaaabbbbcdbdbcdcacdabbacbbbbadadccabaccdbaccddbccbabddaabddbaadcabbbcccbbaaadbaadcbdaababacdadbcabacbbadabdcddcdacacdaccbbdcaddddacdacbbccadcacbadabadadccbbbbabddcbdaaccbdacaccdacabbcaccbbbadbdddadbbdabbbcccbdbdabbaaadaddddbdcbacabadbccdddadbddabcdaaaccdbbadddcabcbcdccabcadbcbbdddcbaccaacadcacdbbbdddcaadbdcabbbacbcccabcbbabbabddabdaddaabaabaaabbdcccdcdcdbccbdacccdacbaddbadcddcbacaadaddddaddcadcdababcabcbdccadcdccbdccbaccbccadbcdbdabbdacddadbaacbcdbdaaccbbadcaddcbdccbbbabaacaaabcbaaacbcabacabcbbcaadbbbcabbacccdbbadcdbdcdadaaabbdaabcdbcaddcbccdacbcbbaddcbbdcacdccdbaaaababaccabaaadbccadbbbddaadcabbbbbdaddbaabacdbdaddbbaccddaacbbbddcaaadabdabbabbbcacbcbdcadadbdbadcdbbaacdabbdbddcdcadcbadcdccdabcbddabbbddddaccdbcadcbbcacaadaaaadbcbdbbcacbdacddbbacacaacaddadbacbdbaddcddaaccbdaddadbdbdbbbddbacaadbadaaadcaddbbcabdbadcddddcbccbaaddbcdbcaabadaddbcbdbaaaccabdcdcbccbcaabbbccdacbcbadccacdbbdacdadacbdccaacdddabddbcbddabcbadabbaabddaaddccdddbbbacbddabbcbdadbadddbcbdabadccddbddbbbddacccbbcbdbbababadbdbcdcadaccbbaadcbccacdccbccbacbbabbcbbdcbdddcddcbdddcddadccdcbddcaccabddacbbadddccccdcdaaabcdaabcacaddacbbcbcbcbcbbbcdccacbcdaddcbbbccadcbaddddddadbbcdbccdbdccbbdbcacadaaaaaddcadcbcaabbaddabdaaacdababdabadbcdadbdacaddcbbabbdcbaabaddbdaaaacdadaaaacbdbbcbcbaccaabaaddacbbabcdadbcbbbdddadbaccaaabddcacddaaccbcbabdaccdddbadbcbddadaabbacacabddcadddbabccddbadcaadccccdcadcaaddaadbbcddcccbbcaacddabcbbacdbacacbbaddadbbadbcdadbbcbdadcabcbbccaddbcadcdbbbbadcbccdcacaabcbddcdbabdbccbbdaacddaccbbaaadbaaddacbdcabadbdcccccabcaaabbacabacccabdabcbcbbcddaabbcbccacadcabccdbcbbbcadddbccdabaaaccdacbdddbdcccaacbdbaadabaadadccaccdbaacbdcabcbacbacaabdabcaaccbdacadcdbbaccadcabccacccbaacadcaabbdcdccdbdbbdddcaaadcccadcbcbadbdaddabacbdcdbdadcddbbbacccbcccdaccdacacbcddbdaacdadbaadcdaaaaadbcbccdbbcabdccdcdbdbabcdadccadbaccdccaccdcaabababcbbacbadbcdbcdddcbabacbdabdcbbadacbadbdcababdabdaabaadbacccccccadbcabaacbbaabbdbcacadcbcacdacacddbbcccdddddbcaddbccadddbdacbddaacbbabdbaddadcbcbcacddcadbabcdbccadcbaabdacaddcccdadbbbdbadbbaababccbadabdbdcdabdddbbbdadbcdbcdbaccccaacaabcacaddccbadcabdbbadcabbbbccdaccbbbbadcdddcdabcababbadbccadabbcccbaacabbcbdbbadbdabaaacbdaabdccddbaaacbadabacbaccabdccabcccbcdaacdbcbbcbddbacbdbadbacacdcdcdadcddbcaaadaddcacaaaccccbddbbcbbdbcacbccadbadadcbbcbbcbccabdcacdababddbcacaadcbcddbdcbcdcaccbdcdbdbdcbccbcbbacdcacdaacdaacdaacdbcbbacadcaccddabbaadbbcaadaddaddddbdaadcdbdccacaaabdaadddbcbabbbbabaabcbcccadadcdcccdcdbcaaaadddccbdbdddcabbacabcacdcbdacbccabbcbacdaddadbdddabdaccdadacbccbddbcaccdaccaacdbacdaaacaaacccaccdcbdaabdcacabdddbdcacbdddddcacabadddbacbddadbaaaaccadbcdabcbdbaddcdadbccbaaaccdadbddbbcdbdbdccaccdbcdbdddadcbbbbdcdddbbacbcbcacbacbcbcbbcbbcbbbcbdcaadabaddbbacdbbadccbdcadccbcdaccccbcabdccddbbdbaabdbdcccbcaaabaacdacbddbbadacdbbbccbcdbbbacacccadcbbbcdaadaaccbbadcbcbadacadbacaadddbdadbabdabadadbddcddcdbadbdaaaabbabbabcbbdcdddcbbabdbaddcdccabdccbbacdbdddccbbcabaacddabccdbabbbabdbaccdbcbbdbdacbacddcbcccadbabcdddadcbbcbbcbbdbbccbdddcbaabbacddaccacabbcbacccaddacaacddadcacddabdcbaacbccadbbdcddadddcddaccbccdadbcbdddcdacbddadcccaddadadcbddccdcbbcdcabacddbbcaadccccdcdbdbadabccbbbdcccaacdccdadddbcbadaadbddadaaccadbbdcccdacadcaddcbcdcabdaaddbababdbcbaddbacccccdaccbccaccacaabdcddaddbddbcccbbaabcaaaabaacaaabaccbcbabddcddcadccabadbddbdabcbcdcbdacdbccbccdcbacbaadbabdaaaacbbaaaaacabbbabbdbdbdbddddbbdbddaddbcccddcabacacbbcabcddadbccdbdaacaaabdbcddcdbbbabbabbcdaacbbdaabdbbddddccbdddbcdcaaddddddcddbddbbddacdddacabbdcddabddbcdaabacdcabaadacdddcadcddcbcadabcabdbbdacccccbaacdbcbdabdcbbcbbabcaadabbdbaaddbbcdbcdbdcdaacbcbdababcbdcbabcaacacbaddcdbbccdcacadaddabccdbbbcaaccbdabadaaccccdcbdbbdcabccbbcdddcbcadccddbbdaaccbaaacacbcabcbadbccaddbcadcaddbdbcbdcbadddddbabbdbbabbbcdcaddabdbbbadcdbddbddaadacbdddacabbcbacbcbcccabccdbcadadacabbabaadacbbcdadddcdcbaadaccddacbbadcaaabbbbaccabcacdabcadcbcdcabcbddddadaabababaadbddbdcbbcddbdabbdddcdaddaabbdcaadcdabddcbddaabaccadccbbadbaaddbacdcbaacdcaadccbdbdadbbaccdaabcaabdcdbdbddbddabacddddcabccccdbadabadbbadacbadbdcabadcacabbccbcccbaacadacdcacdbabacddbababdacdccbadacbaccccddacbbadcdcdabbcdaaabbdaddbcaabadcdaaabcdcdbbbaacccbcddbaaaabcdbabcdcdbcaacdbddbbddbabbbbdaabdaaccdaacccaacacaaaacccccacabcacadcadbbccbcbaddaaabdacbcdaccbbdbdaadacbadabadccabaccaccaacaaacbadaaaabdbaabdbcbdcdbbdbbbacbbcdbdcbabbbddcbdbacdcbabdbbbcabddaaabccddbdabccadbcbabdccadaacbbdbdcdccadbdadabaacbcaaccbaddbbcaadcbbcdddcaabbcdbdbdcdccacbdcdabddacdacbddcccccddabcacbbabcdccbbaadbdaabdbcbdabbcacabcdaadbddaddaddacccadccadccdbbabbbabdddcbdacaaadabdbabadaadcdadabbccacbbccadcdcbddacdaaadbacaaccbacbdcdbdcbdadddaaaabcdbaabcdabbddcabdaaccdbdcbbbbdaddbdadbdaacddcccbcbbbdcbcabddbcaddcdadabcccaadccadccacbdbadcbccaaadabccabbaccbddcdbddbbbbcaddddcadacbdaacdbaccbdccacdccccbddcbaadbabbccbaaacdbcdcddadddaccabaabbdddcbdcaabbdbaaccabdababbcaadaaaacacadaccadbdbddcacbccaaadaabcdcbbddacddbcaddcacdbabcbbcdcadbccbbcadbbcadddabcbbbccbdbdbdcdbcaddadbbcaddacabdbccbaacabcbcbbccdbaaccbcacdabbbbbcccdacadcadadddcabddabbcdaaddcbdbddbdbbbccdcacbdcccbaaacbcccaddcddaadadbddddbddacacabddccacbadddacaadbdbdcdabcdbdaccdaddcacaabdbbcacbcddaaacabbdbccbdcabbabbacdccadaaccabaacaadcccbcacbcdbdbddcdbcddbbdbaaccbaddcdcbadbcbbaababcbaacbccdccbabdbcbbbdbdacbabdabcbaddaaccbddccddbaccbcbbbcadbddbbaabdadccdbabcaabadabaaddbabcadacaaaddadbbbaddcccbcbcbdbdddbbdaadbbdbccbddddcddccaaaddbaaacaccadacbdaaacbbdbcabbcdcdbaddccaabbdcdcaccbcccaccabccbbabdddaccbcabaccbabbccbaaccbccdbdddbaacaabcdcbccabbbacbbcdbcacbaccbdbbdabbbccbbdbadcdbaacadadcacadbadccbadcdabacbbaacdbcaadbacbdaaaaadbbcdbcdccddbadccdbabadbdaadbaabccbaccdbabddbddbdcdabbcacaccddbbbbbabababbbabdbcbadcbcdccdcbcacddcdbbbadddccdaaaacbcccabcbdbdabcbbcabbcbccadbaacdddadcabaccabbbdadcdddbbdbabbadbdaddccdaabbaadaabbbadbadbbdbcbdccbabdbddabaccaddbccaacbbcbbadddabbdcddbaaadcddcababcddcdddbddccbcaaccbddadcbccdccbccadaaacabdbacabbacdadbddadbcdadacdadbcccabacbbccddaababaddbccddaddccdcacaaadabaabcdaabbcdddaabcdcbcccccbcbbabdbbabbbbdbddbddbbabbadbaabcaabcacaccccdaddcbdbabacadcbdabbbcadadcabaaacbbdbbcadadcacadbcaaddcabdabcaddcbcdccdacccbbbbdcadbacdbddcddcbbabadcaadcadbadddbacdbcbdcbaadacddbaaacdaabbbcddcadaadcaabbcadcdbdbaacbddcabdddabdabccadbabdcbdabaaabadbcabcccdaabdbccddcddcacddcdcaccdbdbabcbbabcdddaccccacadcadacccbdbcdabbabddbcdabddcabcadadbdcbaacbaaaabaabadacacacbcaadccccbddcaaabaaaabacabdccccccbcadacbbacddcccbbcbbbcdcccdbbcabdcaacaabcdbacaddcdcbdaaadacabbccddcdbdcadbaaccdabcbbbddabcabadbbdadccadabbdbcaccadbccccbbbcbbaddcbabbababccbbacabdaaacbacdaabbdcaccacdadbdabcdadabdcaaccbbbbaccbdbcbaaacddabaabccbbdaacbdacdacbcdcbcdccddccbbbddbaabbdbbcbbaabbbdacdbdadcbdaccadcdacadabdbbdbabaabccdacadcabbacccbcdbabdcbcbabbddabcabaabccbacddcbdbddbdbcadcacbdcdadddbdcabdddbbcadacdbdbcbccdbbbcbddacacdccbbbacccbccacbbcdcdbcdbbdabbdbbdbcaabbdadbbabcacadbabddcdacbcabdbcbdcabacadbbadcacdbabbbbbbccaaacbadcadaabcccccacbdcacbcccdddaaaaacbdbcdabacbaddaabcdcbabadcacaabccccbaadccbbbcbadaaddadadaddaadccaacaabddaaddabccccaaabdcbccddcdcbcbacdcacdbabaddddbddbbabdcbabacbbacabcdaadcaccbdccacbaabdcadacbdbdcabcdacdcabacbadddacdbbcdbbdaacaacdddbbcdacbbdcacaadbcdaadccdaababacbcdbcaabcacccbdabdabcdcbbbcccdddddcbdadaadadcbccbbaadcbdcadaddbdcabdaddcbcbddbdadbaaccbcabbdaaddbbacbdbdddbaccbdcadccbadcdcaacaaccbccddaccbaadbbaaacabdbdddcbadadacbacabadddddbaaaadadbcabcdaabadbdaddabcbccccaccccbccbacbdaddcddcaaaacccabdddcabbdccabdddbbabcddbbdbabcdadbbbdbbaccbbaddacbdcdccdccccdaadbdbbadbaadbddcbccbddbadcabacdabbcbaddcaddccbadddbbadcbacdadadddcbdcabccddbbbcacaccbaaacbabcdcbcbcbcccadbbddaaacbaabcddbcbdbddbadbbcdddcbcbbaacbdbcabacabcadbadcbdbcaacadcabbbaabbdacaddcaddddbcdcdbddbbaaddbaaaddbbccbbcadbdaaccbbcdbdbdcaaacabbbcdccbabddbabbbacccddcddddbbbabbcbbacbccaacadabbbdccbbadabaddddddadcbdbddaadbcbcacaabcdabcacbcadabaccdcddcbabcccdacbdcadcdcbbbbccdcccbccbdbbbbdbbccdbdbdadacadcbdcaccbdddddadbdbbdabbddabcdbadcbadabcabcbcadadaccdcdcbcdcddbbcdaccbbbccbccddcadcdbacabbaddadbcbbdbbdcdcbdbacdcdacaaaacccbcacccbbbbddaabdbaacabbccbbbadabcdadcddbbdabacadcccdcaddcdccbcacbdbadddbccdadacccbabccdcbcdcdaabddbaadaccccbcccccacdaabbcbacbdbcdbcdcdcdbdcadacdbccbdddacdabccbddcaadabbbadcbbdccbcaacdcccdcbbbcdaadcddddbccbaacbccbcacaacacdbdcaadbadbbcdcccaccdbbabbcbdddbbacddabbaabdcbacccadbbabbdbbbaddcbcdaaaadbcabcccdbaaddbdcbcacaccdcbaaadbbcadccabaddcdadcbaacbbbcdbacabbcacbcccdcddbcdbdbaaadcbcdbacddcadadbbadabbcadcaadbbccdaccddbacbbacdaacdbdcadabbbaccaccaacdcbdcdcadcdcadacccccadabcaccdaaddbbcdcbbcabbadacdaadcaccacadcbbccdbcbbbabcadbdbacdccbbadbddbaacdaaccaccbbabdcccdcacdbadababdbacdabbacccbdcbcadcbccaababbccddaaabadaadadbbaacdacdadaacdbaaacbabaacadbaacaddbdadbabcadcddbaacddcacbbccddaacdbbdaaabdabcaacdbacdddabcddcccbdcbcaaaabbbdcdbabcbdadbddcbcbbadabaaacddbbdcadbcaadadacdcdaaaddddbacaddcbcabbbcbdbddcaabaddaacdaabacaadbbaacadbacdbcbbaddbcddcabbdacabcbbbbbcadcdddcbaacccaddcadcaaddbabaabbbccdbcdaabbdddbbbcbbccbccdbcdcbaacbadabbbabbaaadaabddcaadcadbdddcacbdbaccbdbadbcdbddddabacbcaabdbcbcbbcadcbdbacdcdbadaccbdcadbccccbadaacccdacabdbdbabbbacabacbcdcdacbdabcdcaadcdcaabadaadaacacbababdbbbbabaccdbbacdcbaddbddddccdcbadaabcbdddabacadbcbdccbaacacdccaaaabcccccdbcacadbccddadbcadcbaccdbabdadccdcdcccdddbdcdbccadadddddacbddccadabbdacddabcaccdbaccabacddbdabcddbacccddbcbbbbabdbcddbbcacadadcbdbdddbbdbacacddcaddaabbbabcdccbabdbdbadcacdabdbbcccbcdacddddccbddbacacdddbdbccbbcccdcbccdaccdddabaadbdbaaabdaaabdbbdcdcaabdaadcbdcbddddbcbdadcddcbaacddddabdabdcccaacdbcbdabcdcaccdabaabcccbdadaaadcdacadcaaddbcbbbacbaccdaadcdcacddcbdddabbbdacabcbbcbabccdddaccbbabdcabccadacbdbaabbdcababbbbcaadbabacddcdbaababcaccddacccabddabdacdacdacdadaccabdccbbccaacccadacadbcadabacabaacbdbbcdcdbddadaaabbcbbcbdacbbdacabadaddacddbaccabccabbaabccacdcccabdbddaaadcaacdaabcdbdbbbadcbbaacacbbcbdddcaccacdcdaadcaccdbddabcaddcddcabddcadbcbbdcdbcccacccdacdbcacabbccdbabaacbbcddaadbdcaacdabadbaacaccadbdcaaadbdddbaaabbbdabdcccdacdbaacdccdacacabbabaaccdcbaddbaccdaacadaccdbddcdcbdccbcddbbcddadabdcdbcbccaacaddcbbcaccadcdabbcbabdbaaacbaaadcbccadaddbddabbbddbcdccacbcacddabbdddaaccddbdbdaabdabddbccbbddbcbbbcbdcaabddacbbacbabcbcdaddcccbddbbdccdabcacdabdbbbadadaabbabccccdcdbaccbbcdccbbdddaccbbdbbbdacbbbaacabcbbabbdcdacadbcbbacdccacdabcaccabdcacbbbdbdccccadccbddcadbaadbcaddbbaccabcccbbabbccbbddbcdacccaaccacacbcddbbabacaaadcaccdcdadaabccdabacbabbaddcadcdbcdddabcddbaabccdbcadcbbccadbcadcdbaadbdccbbcccdcdadadaccccacadaaadddcbcdabcdaddabdaadbcbccddbabcaddabaabcbbccadaabbbdabcddaabbdcbbdabdaadabdbcbbcdcdccddacaaadacacacbbdacbcdcdcddacaaabdcdadcdcdcbacdbabccbddcaabcacdbbbbccabacdbacaccabbaccbccabdccbccabbbbbdddbaacdcabdabaadcababbabdcbadcaaddaabcacaabbaaadacdcdbbcaaaaccbaababdcccbaaccdddbcabccdcaaaabaadabbdbcabbcdadaaadbdcadccaaadadbaadacabadcddbaaabaabcabcdaaaccddadcaabbcabbcaacdcbbbbccadacabddbbcddcddbacbcadbdcabbdccddcacacbcbadddabddbddcbcdcdcdabccaabdcacaccdcbccaacdadacdbbbbbdacdbbacaaaddcabcbaaccbbabcdbccbcbccabdccacbdaaddcabdbdddcadbbbadbacbdacdccadcbadbbadccdddbabcadcacdddbbddcccdabbaccbbdbabdcdcccbcdbbcbcaccdcabbddbdbabaadcbbddbbbbdbbbdacacccaddadaddcabacacdcccbcbbadbcaccdbcacacdbdcdcacaaccbcbdacddbaaaadbabcdcbcbcacbdcbadcdaaaacdcccdcadaabaabbccddcacadcadcdacccbbbdadbaddcacbadcbcdbaddddcdbbacaabdccdccabccccdcdacdcaaacbaccacbcdabcbddcdadbcbabccdabcbdbbabacbadaaadbdbdddbcbcbbbacdbdabbcdbccdadcabdccadabcadddcdbacbadcabcdddcccbccddadbacacddcbdabdcadccbcadacaaabbddabacbbbcbcbacadbcacdbacdaaacddccdccbbdbdbdcabaccdbccbdcdbccbcbbaaccbaaaccbdcbaadbabbbadbcadbddacddcaacabbacdcaaacbaacbadccbcabbadccbbbddabadaacdcbabbddbdddbcdbcaccbbbadbbaaaacacaabbcdabbbdccdadcbddaabbacbabadacadabdccdacbbdcdbcadddadbddadbbdbdcaacaccaadcaddbaacabddabbcddcdbbaacadabcbaccdbccbadbdccdddcadacddadacdaacbbbdbbaacbcdcacccacacaabbdddddacdaabcddacadadbccdcabbbccaacddcaddacdcacbbdabdbddbabbdbaaacbdcbdbddadabcdadccdbccabcccbaddcddcabdddbbcddcccbbdcdddaacaccadbcdccdacdbbbbacbacadaaaadbabdacadcdacbcbddcdcccbabccccbaddadcccddacbddbdbcbdcbcbdbbcabdaadbdbbdddbdbbaddbddaadcbbbcaabdabcacaacdcaaadddbbdcabcadaacadbcddacccbadcddcdbcabaaaccbddbdcdabaccdcdcbccdabccabbbabbdadbaccbdddbbaabcacdbbabbccbccdcbbcbddccabbbdadaaaadcadaadbbdaaaddbbcacbddcdccbdabcaadbabaccbcdccdbbdbcbabdbbaacdbdddcdcdbdddbbadabdacdcbdddcdacabcbddddccadaacbdcbadcdcbdcadcdabbdabaabcddbdcbdcdcaabaaaabbcacdbcabddacaadaccdbbbcaacccccadcbadabccbdaadcacdbcbdaabbaadccbacddcacbbdddddcdadbcaadaabcbacaacdabbccacabcbbbbccdbcaadbcbaacabacddadacdabccdbabbdcacccdbcdacbbdadaabdccccaabdccbadbaddccdaacddadadbdaaaabbbdababcabadaaddcccbdccadcbacabccdbdacdadcbdcbdadadcddcdabcabaadacddbbbddabadababaadccabadabdabddccaaaddddbdadbaabcdcbbadaccdbacbcddacddbbbbbcddccabbaadbdaabddcdaabcdadaccdbcbcababaacddcdcbcdabaadcdccbbcacabcbbdccadbababacbbcdcbadaaddaababaabccacccdddccddabbdbcabadacacaacbbbdccbabcbdbbdbddabcabbbdcabdacddddaddacbcabcdcaacaadadacbdabadbbdddacabcbbcaddbbaccbbabdcdbcdcbcdbbacabdaddcdaaccdcdacbbcadcaacbcccdaacddbacddbbacdccaccbaabdabbbcdbadddacbadcaccbddbcdcbaccdcbbbddcbbdabaddcddbdcadaaabaddbbadabbdaacbddcbcbdacdabcdcdddaababccabbabacbbaddbbdcddcacaaddccddaadbccdbcccbbddbcccbdcdbddaacaaccddddddabddddbbadadbacbdcbcbbcdaddddcddbaadccbcbbadadbadcaacdccacdcadcbdccddddcbbdcddbaabacbbbdbbabcbdbcaddbdacdbacdbddbdaaaacabcbcdcbcccadbdaabdbdabcbdbadaccbbbadbacdcabbddaabadbabddcdaaaabbdcccdcaabcbdaadbbbddccbdbcdbaaacaabdcdcbbbdbbdabadbbabacdbbbdaddccbdcaacacdcbaadcbaadcddcbdcaadbacbbdccccabdbdacdadacaacdcdcbdcbaadcdadcbdabddadaaaacbadbcbdbadccccbcdacadcdadaddbdacccaabccbbadbbaabaacaababccacdccacaabdddbbcdababaacaccbcdcadacdaadbcdcdbbdabddbcaabcabcbdddcaccbdacdacdbaccbcaddabcaabcbbaaaaacbddcdccadacbdaaaaababdadadccaccaadcadbbbcbdadccadabcaaadaaadcaddacbdcbacdbacbabbbbcdddbbdcadabadcabdbcddbdcbadbcbbdadabdbccbdcdbddbbccdacdddbabbbccdcdbdabbdddadcbcabaabccabadbaabcbaddcccdabdcbadcaacbcddcadddbdbaccaadccababdbacbbadbcbabdabadbcbcbcabaabbcbbaaacabdccbdacddccaccbaddccaacabccbabaacbadcabbabaddcbcabccaacabdbbddccaabacbdcdaaaddabdddcddbaabcdbbcdcbbbbbccbadaadbbdccaacbadcacdbcadcacddaacbbdbdacbdaccdbdbabdbcdbababdabdcbddcdcdbbbcbcadbccbbcadaaccbbacdddbcdcdacadbbdbbbdcbdbdbcbccabbadbbcbadadaabcccdccdccaadabcccbaabdbbbaadabccdabcdacdbdbabbdbcbbcddacaacacbdbbcbaababacbdbcbcadbcbdaddacbcbbccaccbaddcbddacabadadbccbdcbaacabdacccdacdaacdcbabdaccbdddacaaacbdadbccaacccabccabaadbcddcddabdbbccacadcbdcdadbbdadcbcacdcdcccbaabdbccdccaabbbdadabbdbaaaaccccdcaccdccbabbbbcacaadadbbcdbaaadcbaadbcdcdacaddcbbdbdcbabbaddacdcdabbcdbcabdbaaabdbbbdbbcaaadcacaaccacdccaddbdaccccbbabdbbdcdcddadbacdadbcbbccadadbcadaacddddcbbbccccdbddbdcbbadccbabccacacbcdabdcbcacadccccbbbbddbbbadcbbaddbcdadcabadcbdddacbcddadabadbbddabacacbabdccbbbabccccacbbaccadddbcabacdcabcbbcbadabbdbadacbcdadaddcdaabdbccdbdbaccdabbabdacbbcddcadacaadadaabbbcbacbcdaacbaacdbcdaccccadccdaaadcccbdcaddbcacbcddbcdcadacbabbdccbbacddddaacbddcacbdddccbadccdbccacabdcdbacdbbabddabccdaaccdbcdcdcbaabbbcadabdadcbadbdbbbbaadddddcaaabaacadccdccaadbababaadbdbdadbddbdacacbcabcbacbcbcabbabdbdcaaacaabbdadccaddaadadacbcdbaaaabcddcaadbbcdacabddaabaaccdbcccdaacdbbcacbcdcbcdcadadbdcaabcdbacddaacddabccccbaaddcdbcbacdabaaacccaddcbcdaabbbdabccbabcbcbacadbcacabbdbbcdbacbdddacbbbcdadbdadabcbcbcabccbccabcacabadaccdddbcabdaccbbadbaaddacbacbccaabbabdabbaccdcccddcdadaababababdbacdabacddadcaddbdaadaabbbbdacddaccddbaabcaccdbdaddacccaabdcaddcbcbbcbccdccacccccbbcbddaddddccabccdaccbdadddbacbcdcdcaaacbbcddcaadabbccabdabdbbaacbcbdbabdcddcdbbbcbdccbadbabdcbbcdbaaccbaabccddcdcaaacccbabadaacaaccccbcdadcbacbdaaddabddcbaadbcbdabccdbbacaaaadccdbadadcdabbddcaaddbdccddddddaaccdadbddcbbbaabacaabccccadbbacaddcadccadbbcbddcdcbdcacbcadccabdccdcbddbaaadbcbcbcdcaabdaaacbabaddcdbcbccbbdddacdbcacccbabddbbcccbccaccdcbdadbacbbccdcbcadabbcbabdabacccbcdbccccbcbdccbaaaaabdcdacabbdcbabcbbcddabaccabacbbdadbbbdabddadddbaabdaddbcbdcadbdaccacbdcdbaaacaccbbbcadabdadcabdcadacbaacbdcaacddbbdaddabdccbdbddbdacbbbadcbcbdbbdbcbccdabcccbddbbaaccabacaabbcdccbcdbcdbbabbaaadabcbddbbcdabdaaadbdbddcccbddadccbdbcbcacbadcbbbbbbaacbadccddaaddaabbdabddbbdadcaddcadbacdabbbdacccdabdbbdaabaddbadaddbbcccbdadccdccbbcbcaddbcacdbcdcdacabcabbbccaaaaadaaddbcbdadccdbdcdbcdbbacbbbbcccdbbbacbdaaccddbcacbdadadbbaacabddacdbbcaabcbacdaadacaccdcdbcdddcbccaddbcbccadacaaadcbdbdbbaadacdccacdcdcacbbacaddbbbbbdcbbabadadbdddadbbabcabdccadacbdccdacccbdcccbcdaabccdcbccbccbbcbacaccadbacdacbcbdbcbdcaaabcdcaddadccbdbbacaacabadbcaaaadbddbdacbbdddccaacaaddacbcaabcacbdadcbcbdbcbddcadcacdbdcbddccaaabccdbaabddabbadabadbadadbacbddcbbbabbabddabdadaaabdbacaddadbdbababdcaabbbbabbbcccbdaacacdbadccbddddadcdccbbbccadacadacdbadddccdcdcccbbddacbcdcddacaadaabcdcbcadcbabaadbddabaacdcadcabacacbadddbccadacccaadcaaccabdadcbbcbbadbbaaccbdaacdcdacdaadcbbadbdabcbabdcaccdbdaadcbdadadadacdcddaacdcbdbdccdacaddcadaacaddbaaaccdccbaaadcadbaabdbbabcabaadbbdcbcbbdcadcadaddaaaadaadaabddbbcbbcdcdaaabdccbbbcacacddcdbbabcdcccdaddbaabbcabdacbacbdacbcdccbcdadacddadbcbdabadcbcabcaddbdcdaacbdbabcadaacbccdbccbdbadabddadcccdabaacbdbcadadabbcdbdcccddabbcccdcdadaccadacacaaaaadbbaabccacbcabcbcdddddbcbbababcdcccadbbddadbaddadacdccaccdbacaadadaacbaccdcbbbdbcccaabcbacaaababcdcdbabadcadcacdabbdcdcbddcdbbddcdacdcbcacdcbdbcdcabcbcaaabbdaabcccbbcabacdbaabaacbdccbbcabbdaaadbbbcddadbddadbcacbdcacbabdabcadbaaacddbdaacbcdadccbcdcadbbacbbabbdabccbdccacabdaddabbdccccbadbdcdcadabcbbdddcdabbcddacacaabbbcbabadaacbcbdcddacaaddccbaacabdcdbbabaabcaabcbacaadbbacbaaaccddabccaacdbaddabccbdbbbbcaaaacdbdbbacbcacbdcbaadddbddccccdbcdbbdaddcbcdccddabadbbacbadbdaadacadbaaaddbddccaaabddbabbcadcabcacadddaaacccbbcaabdbcadbbbacdccacadddccbdccddddbcdccbaabcbcaddbdddccadcadbbcadcdcadbbcaabbcacddadbbbaabdbbbdcbdcbbbbacddccaaababaababcdaddddbdcdddccaccccadacbcbcbbbadadcddccdccddcdbbbbdbaaadbadddbcdddabbbcabddadadccbaadabdbaccdaaddbbacadcbcbadddbbdcabacbaccaadabcbbbdcbdacabccbdddbacacbccddadaadccbdbcbdbadbdbdaaccbdcbabcaabdbbcbdbcbbbbbaadbbdadbadaddcacabcdbabbdccbcbcdcdbcbbadddbcaccbbcddadaabaaabdabbabcccdcdbcdabadacdabdacbacddadcacdcbddbaaacacbbadbddadaaabbadacadaadbcaadbcbdbaddccdbccdbdaabbbbdadcaabcdcbcadcdcccccbcbaaddcabbbabadbdaaaabcadaacddbcbbbdcabbbbdcbabbbadbadbcbcaccbacbcccaaabcaabcbaacdbddccbccbdadaacccbbdabbbcdbbbaacbaaacdacdaaadcccbdccdbbddacacaabadbcbbaccdcbcddacaabdbdddbcaadbbdcadccacbaccbdbcbcdacbdcdabbdacabaacdcabdbadbdbbcacdbbdcccdcdbdbaabaabaabcaadbbbacdcdaaacddabcbdccadaabbbccdcadcccacabcdbadcbbcaadbdcdadbaaccadaabdabaabdddcdcaaabadabdcabdacbaabdcbacddacababcbcaabcaddccdcaaadbdddbccbccbacbbbddbabbaabbbdbaccdcdbccbdbcbadddccdabdccdcabdbbdbcabcdaacdbddcdcdbaabdddaccadccbccbcdbdaadacbadcadbcccdaacabcadbbacbacacabcbbcadcbbaddaaaacccbcbccbacccdccdacddbcadcbdbcdbddcccbdadddcddcddbdccacbbdbbbcdaaabdabbaccccacabccacabdcadccacaccddadbccdbcbccbadbadbcacaccddcaccaddbcbbbccccbacdcaadacacabdcdbdcdcdbacbacbadacbbcbbbadbbaddccdaadddcdccabbdcbdaaaaddddbbbddcbacadddcbbbddabbdbcadcbabbbdddaaccdcabbbcddbbbabdacccdadbcaabdccdadbaababbaacadbccbccdcdbdcddcbcbbcbbcdbdcddcbdbcdcccdcdbaadbcbdbadbbbbcacbacbababbcbaacbcddbcaccdaacaabbbbbccdacacacacabbcbcbbbdccabaadddbacacdacaddcbcacdddbdcddabccbdbdcaadbcabbdcdaaacddbabccdbdbbdacbcbddcabadbbbacdccbaabdbbbadcacadabcdcaaddacacccbadbdcadddcabcbdacdbaddcdbbdcbbdcbbbbbddabaccddcdabccbddadabaaabcbcaacabcbcadbaacacbadcbbdbacdcdacdacabbcbcbadddabacdbcbacadbbdcabdddcbddbbcccbaabdcdacaccabcdbdccdaadbcbcddddddbbdbcccababdccdaaacdccdbdbabaaadbcdbbdcddadcbbabcbcbcbbdabdaabcbbcbbbcdcbcbdbadbdcdbbbadadbbdababcabbaacabdadcbcdcacbbbbbabddcabcbbdbbdacbadddcabcdbbcddcdaccaadadcdacbdbccbcbadabcccdacccdcbabdcaccdbcbcdcacacaabbacbdccbcbaaaaacdaccbcaaddbadaababcbabaaddaaddbbcbccbcbbcacbbbdcccdbbabddbdcadadcddbbbdaabdbadcdabaacaadbcbcbdccaabadabdcaaaddaadbcabbdabdcbdaddcdddaabcbbbdcdcbaddaccacdadaabaaddcbddcbabbdbbdbacbcbddbaacdababddccadbaaaadbacadcadbbcbddccbdbdbddbbccddcccaabccdbdbbddacdcabdaaadbcdcddabcccacdcbabadbcbaabdcccdbcbdbdabbddbdcbdcadbdbacdcdbacaddabbaaabcbbdbbcbcddabcddbadaacccaaabbbbdbabddbcaaabbddbacdbdadcaccbcdcaccddddbccbbadadbbdbbaacccbdaccdaaacbbbdcadbdcbacdacaacbddaacadaabdabaacccabbbbccacbdcbdabaaabdbdbaccdacabacccbdcaccbbbdbadbabdccbbdbcdddcbaaddbdadddadbdccaabadccbcdbadbdbccbbcacdaabdcbcbcbcacdcdadbbabccabdcbbcdcbccdddcdaaadadacacbdacdbcbbdccadbccabadbccbabccccacbaddbcdaacdbdabbadbdbccdcdadccadadadabbcddbbbdbbcdcbcaacdcccaaacaccacaaabdddacbdadacbacbadbccbbaaabcddbbcbbacdcabcacdddbcabbdcaaababdcdcbcaccbdbcbcdaacacbdbcacbccabdaabbadbbaadddbadabaddadabcdbbdbbcdacdaabcbddbbaccddabbabcbdbdddccdcbbbcacaddcdcdaaabbcdccabaccacdbbaacccaabddbcdbddaccccaadcdbbacdabdbbabadbdddddcbaaccacbdcdbbbabaccacccbddcbcbdabcaaacaacabadcaacdddaaaccdbacddacbbcadadcacbdcadabcdcdcbadcbdcbaaccacabdaadddaaacbdcabdcccbcadaccbabadddbddadccdcadaacbcaabdddbabcccdacacbccadcdaddadcdcccadabbaccbababcaabbcbbacbaddcbddcddbdaddadabbdcadddbccdbabbbdadabdbdcbcdaacdaacbdaacdbabdddacddadcaaadbacbcdacdbdddbdddccabacdaadcaabcbddaacbdabbcabcaddbbbcdcdddaabdabacabcbabdcbcaadacbcdaabacddcdcbbbccbaabacbbabaabddabcacddaccacccababddcbbcbbabbbbddaaaababdabbcccdcccbbbcbabbbcdddbdbcadbcbdcdcbddadabcdccbccacbdcdbbdaddabaabacbddaababacdcaacabbbcbbbdabacbdbbaaddbddbdaaccacacacbbaddacbccccdcdaaadbadcbcababbaadbdaaabdbddcaddadccbdbcbaacadcbacddaabdaacdbbbbcbcbcdcdddbadbabbddcccdbbaddccbcdaaacbbadbbdadcccdddacabcabdbbdcaaacbacdcdcccbdbccbcbccacaabcbaaabcdcacccbbcacdadadbcddbacacbaabbbbccdbdbcbcdbbaadbbacbcacacccabaddacaaacdcccacdacabadaadcdbbdddbbcaabadcbbbcddcbbdcaadbbaddcbcbacbcbacadbbbcbdacbdbbdbacbdadaddcddcbcdaccaacadcbdcbaccbdccdddbcbadddaccbabcadacdbadbbccaacacacdbabadaacacdcacacbcadacaaaccbcbcdbabbddddabcaaddbccbddbddddbcabcdcdbaadadbcbddadcadcdacddbbbdcccacbbbbcdddaddcbbdcbdbbbddbcbbdbdaaddacccbcacbbbabaadbcdbdbdcbcdbacdcaabddaabababdacdadaabbaaabdcbbbbcacabbddbccbacdbabcabbaaccdcdacbacababdadacdcdcbbdbabdabbccdbccdcddbadbcbaadbaadbccbbbdbaacdcadcadbbadabcaacdcadacabbcbcddacaacdbaabcbddabbdbddacadcbdccbcbdadacdccacbacdcdaccbaddaddcddcacccaadaabdcbcdbcbdbdabcbbdabcddbacddbdcacdadbacaccaadddddbddcbccccadcbdcaccbcddccdcdcdccdadbdacbdaddabbdaadaccddbaabbaccdcddddcbcbaddaaabaacadaabcdcdcddadacabbaacbbbabddbdbabaaaddbcdddcacdcadcaaaaabcbcacacddddcadcccdbacbdadbcbbdbacabcaaddbbbddccbccbcbbacdabbbaadaabbddaaacaacacabaaccababccbcddddbbdbccaddccddacddacdbccdcabcdddacdcbbaaaaddabcccddaacdcdddabddabaacaccababbbcbdbdccbbcbbddacacbbdbddddddaabbcddcdddcbcadcddadcdadcdccbbdccacabbaadbdadaccccbddacacabcdccbcbccccddcbcadddcadbccadddbbaaacbdccccaacaaccaccbbcbdcdbaacbbcbdccccaacbcabccacdbccbccabdbbacabbbcbbaadcdaabbbbacababccdbbcaadbacabbcbaadcdcbacbcdddbadadddbcabcbabcababdaddbcdadaddbdbccadbbacdaaddaacdabaabcaddabdaccdaababddcdabccccacacadadacdbcadbccaadcbbcbbabbcdbdbdbcddccdacbdcbaacbdacbdbabdbddbdbdccbbdaaabbadacbcabcbacbccadacbcacdabccbcbdaabcccacdcadacbbdaddbdcccdbabdacacddacbaacdabccabbbaaddcdabcdcdbcdadbaaaadbcaddaacdddcabacbddbcbddabcdbbdabdccbdcccdcdbabadcdbbdcbbcbdbcacabddcbcaddbdccabdacaddbbbdabcdadcbaababbabccbbbaddbacacbccdcdcaadddbdddcababbacbabcabaadddabcbadbacdbcacdbbadcacababcbabaabdbbacacdadacaaddbdcdccccaadbcbcdadadaddacdccdacccccbdddbbcbbbaacabbbabdcbdacccdbbaddcbbbbabbaabdcaabccdacaacabaddabdbdbdcbccdcabdadddaaadbabaabbddacabccbcbaacccbdbacbdabbacdcaaadabdcbcccbbadbdcdddccdabbbcbcccbaaccaaaabdcbaadabbaccdaccbabdbdddabcbabcacdabcaddacabacbaaaabddbbcddccdbcaadabadbdbbaaddabdacccaabccdcbcacdabbbdaabcbcdaacacccdaacccacaaacbdcbdaacdadbbcdccbbcddcdcaabcbcdbcaaccacbddbbdadcabdbdabdcdbddaadcdddbabddabccadadadacabaacacabdcadccdaacddccaadaacbcbadbccbdadcbcbdcaacdddabcabadcdcddbbacbdadbcbbadabaadbbcdcacbaadcdbcbbbaadabbacbbddddbaccbdddcbadbcbcbcbbcaccadbcabadbabbcdccccccbcbcdcdadbbcdaaadabcabcbdbaaababcddbaddaddacbbbcccdbccbdcacbbbbdabaddadcacbdacdcbbbbdbabdbbbccdadccabacbdaabdaacbbbbbdaccbbabaddbdbbadcbacacdcacbaacaaaccacdccbadccaabcddadbadcaadaddaccdbcabcaccadacbbdabbcccacdbbdbadabccddcbadcbcbdbdabcbbbaddbcbcbadacacdcdbacdddaaacbbccdaaadbbdaaddadaddbcbccbcdbaadcddacccadbcbadcaddcddaccdabbcdccacdbbabcccbbcacadcbcddadacadaaaadddcaddccddacbbdbdcaabddaadbcdbcabdbbcbbbcdbcbbdbcbabdbbbdbccacbccccbaddcbacabbdacacabcabdccadadccacdcaacbabcacbdddcdcdabbcadddcdababddccadaccbbdcaccdaddcbaccacabbddcacbbbdbcacdccccbddbbbccbbaccddccadaabddddaacbdbaaddcaabcbcbcabcaaadbbaddaaddddaccbdadbcaaccdbcdddbbcbdcdccdddcbaddabbbaaddcbbbcababaaadaadccbddcbcaacacdcaddbbbaacaadbdcddaaaddbdaaaaacbddddbabbabbadcadacdbbacadccacdaccbbacbbddbbacdbcadacbbabbacdbccdccbdcbbabaabaacadddcdacbaabbbcbbcabdabcdbbaabdccadbdbcabaddacccccbddbcaddacdabdacadabdbaaaabdcdaccdcaccdccadccbccdbcbacbdbacccacacdcddaddabadcadbcbbdadcdbbccacabbbcccadbcdbcadabddaacbacabccbaabcacbcbdbcabccdbdcddbbcbbbaabbbbcdbbabccaadaccdbddaadbddbacbccdbabdcccbbaacdcadcbbaccdbacbdabbacbdbbdbacabdcddaabaccbccccbaabcbbbdaacccdbcbbaaddbadaccdadbdaddbabdcadbcbacdccdaddcbbbbcbdddbadddbdccaabacdabacdabcdbcadcaccabcaabaaddcdabbbbdccbcbcbbbdbdbabadcacccabdcacaaadddbbcaadcbdbcbbcdbacabcbdbccdadcbdcaadbddaaacaacbcdcdbbbdbbdaabdaddaacadccbcaccbbacadbcacabbaabbbcaddbcadbcadacacbdcabcbbbbdacaacaddacdaaacbdcbdcdadabcbdaaccacabdabaccadadabadadcdbdbadddaabadddababcbadcacdbcbababacbcdabacdbacdbbdccbcddcdaaccdcddbcacdbcccdcbbdbadbcdcccdcaabbddbacbccddabdbadaaadcdbcabccdadacbcaabdacbaccbcbbccdcdaadadddcdbbbbaddaddaabbcbbdcaacabdabaccbbacdabcaaaadcbaaabadacaadccbdbabcaabadddbabdbbdbdbdaccdabcbadddcadbabadddcbdbbbccaaaababdcdbacbabdbbbbaadaacbdbccccadacdcbcdaababacacdadddddabdabcbbbccaacbaccdaabacadcbccdbcacabccbccccaccadcdcdaabbadbbabcdbaaabcccbbbdacadcabbdcdccaddbcccbbacacbbdabdacdbcbdbaaababbdbdbdcadabadccccaabddbdaadbcbbccabbaadccadacadabddcacaabcaccdadcabbccbdcdddabacadabadbdacaadbabcdadccbaccaddacbbbdaaacadadbcdaadcabbddbaadadaccaadacccbccdaabdbabbadcadbadabaabcbbbbaddddcaddadcccaacdccaccaddcddccdaaadabacccccdcadbadbcddcccbddadcdccbabdcabbdbabdddbbccbabbbbbaaccbcbccadddbabdcadccdccdbdcdaacbabdcabbdadbadcddbcadabaadbbccbcdacabdcbdddadbabcdbdcdcbcdcaabbbccadacadaccadccbbaccdabadaccabdcbbdcdbabbdcaaccaaccabdddadbbbccabacccaabcacdcaaddcdabcacacbdcdadbcddbaabbbbbccbdbbdacdbbbcdbcbdcbcadabbbbbccddbcbbddcbccadcdbdbadbabddcbdcdbaacaaabccacdbcbcccbaccadbdabcaddbabaacccdccdcabcabacabccbbcdddbbbdbdbbdddcdddabdcbbcbbbcccacddbcaabbababadabbcadbaacadbbbbacdbacaaaabbddbcdbbdcabbabcabdacdaadabaabaadaabdbacaababcbddababbcdccadabdacccaabbbaabbabdcbbbbdaabcdadbbdcdcabbadddacdbdbddabaacbdcaadddcdbdbbadbaadbbdacddaacdbcdabbbcbdbadaadadbcdcdbacabbbaababaadacccbccbdcbcdcadcaccadcbdaabdabaacbcccbcdccddcacccabdccbaaabbcdacacdbcbabdbaabacbbbacdbbdcbbcdcccbcaacbbccdbbccaddccaadbbdbaacccbdabadbbaadadaacccacbaadcdcadbdaaacabdaddcccccbadbdbacccccbabbbabdccdbbccdbbbbaabbdadabcaadbaacdadbbcbbaadabdaddddbabbdababbbcdcccdbbbacbaddddabddbcaaccdbbbdbcddacababbaadaddabcdaaabcdccabbcadccaddabcbccbadcdddcbdaabbcbdddbdbbdbcabbcbabcbacaadbdccbbddccddaacddbccbcdcabbdcddabbbccadcdccabccbbaabbbcbcbcddaaabbabacdabddadadcbbbbbcdabbccadcacbbcaabbdaaadcdabddbaadcbdbddcbcbcaddacabaaabaabcdacdbcbbabacdaadabbbccaadcabdadadbbdadaccddadbcabcbdabddabbacabdabaccddcdacbcacabaabbadcbbdbcaddadaabdababbabcbcdddbbbbaaabadbbbcbcaddcdadbbabdcbccddddddbbbbdbbccdbdbdbadbbadbbabdaabbcbdacaacbdabcdabcbdcdbbcdabaaabaacbdaaadaccabbbcadcdbbdadadbaddacdbdcbacccdabacbadbaddaaabdcabdcdbbdbcbbcaababbabddbcadadcdccddabdaadaacccdbbcabadcbbcbdbabcadcaccadcbbbbbcbbaacbbdcddadacdddaacaabbccaaaddaccbaadcdcacbabbbbbcdaabddccccdcbcbdcadaaddbadcddcaaddbdbcabdddabbddbbbdaccacdccccbadacdcbcdcdbcddccccabbbcdbadbcdcdbbaccaadaaaabccadbdcbbcdbaddcbdaaccbaaacdcbddbbadacdbdbddacaaddbbdcabdcbdbcdcdacabddbcddbcaadbbcaabbcccaabbbddabbdbaabaacacaccbbabcdcbcadcadddadacddbcbaabdaaccbcbdbbcaabacbcdacccdddbbdacabcaaadbadbaabcccdcadabdaaadbadcdcbacddccdacadcbddccdcccccdbadabcccbcacbbcccddbdbccaabddcabacdaadbcaaaadccacbddbbbbabbdacbddaccabdbacdddcdcbbccddacacbacdadccddbdbcabcadcdcbcddbaacdcdcacaaadcddddabddaabcbaacacdbbdacaaaadbdaccdbcbbcacccddaaadcabcbabbdcccbdbacddddacdcdacdccbdabbabaabcbbbbadbbbdbdbaddcabbcdddbabbabcbaaaddbcccddcdbddddbacbabaacdaabcbddcdbccaadcbbaabcacbdacccddabbdaadcccccdabdcddddadcaaddabbbadcbddcbbbddaddaacdbbabdadaddbaddbccddaccbaccccbcdadadbbbbbbcabbcddccdadddcacdacabddbcccbdbbcacdbaaaadbdbabacbcdababbddaabcccbcddabbbcaabaaccbdaabbdabacabddbdaaaacdaaaabbcbcacbaddcdccdadbbdcaaabccddddccdbabdbccadadbdacaabddabadbcdcabaabbbbbbbccccbcabbcbacddaadaaccbdddaccabbddababdbccabdbccbddbbcddaaadadaabdbabdadaddcdddbdcdaccaacbbdbcdbbabbbaacabbddddddcdbbbaaadabaaccdddbdcabccdaacbcacbacadaacdabddadbcabbbcbcdcaacbabbbccdbbcdcbcadddbdbabbdcaaadbbcaaabbbdbdaaabcacdabcacbdbaabcbccabbabdaaccdbbdabdabbcababbaddbbccccdcaabcbbbbabcaadbbdaddcdccabaacaccacdbddbadbcaaadaabdccdaaaabccbdaadadccbdcbadacbbbbccaccaaaacbdabacdcadbbbcacbadcbcbdcddbbddccdcacadbaacabdabccdcabaadcabdcbcbabbdccadadbdaacbdadacaaddadabbbddadcacbcaaddbddadacdcabdccabcaabbccabcabbbbdddabdddbcbaacaaaabbdccabbadcdbbadcdadcaaaddbddadbcbacaddbabadabcbdabcdbabcacdddbbbdbdccaccdcacdadbbdabadbbbabccdddadbcaabddbdbabaacbbdcaabbaacdcbbddcabadcbcbdbdcadcabacbaccddddbadbcdccadacbaddcbccdbdcaccaaccbcbcdbdbdddcccdadabcabcdcdcdcdadcbcbbbcbaabcaccccbadcbcbacdaddabbdddaccdbcbbbbcbaccdbcccbdcbcbdaabccacbdbbcdaddbbdabbddddcaabccaddaacaddadadadacccbdabaaccddcaadcbbdabbcadcbaabacddcdbddddcadacadbddcddcbcccabaccdcadccbbbcbdbdcacdbaadaaccbcdabccdacaccabaaccdbcbccbcdbdabbdacacdaaacaabddbadcbbcbccaccaccbbadbccdddcdcababdacdcbbaaababdcacbcdbcadbaddcccbacbddddbccbcabdccbdbdcdbdbacccccdabbcbcbdccdbbddbbddbadcbbccbdcacdaaaacbcddaacacabaccbbdbacdcbdcaabcbdcacacdddacacbcbbbaabbddacddcabdcdbdcddbbbadaaababadacbdbbccbacccdadcbabddbcbbdadbacabdbdabacbdadabcddbdbaaddbdbbcbaacdbcdabdcccbcbddabdbdacdbbcbccbbcdacadbbabcacbaddcabddcabcacadbdaddbbdadddccdaadaaabdcdbcdbccadadbbcacbdbddbaddccababaacdccaacaddddbbadcabbaaddacbabaddbdbdbdddbadccadbcaadbdaaccdcbcdbcccccacbadbacaabcbacdbbdacdadccaadddbbdbccdcbbbdbbbadaabbcdbabdaadaddacbdccaababddddbcddcdbcacadadabcaacaddcbacbdddcabadbddadcbddaccbdacbccacaadaccddacadaaadaaddcabdcaaddacdcbddacccddababcbdddababcabbcbabcbabbdbccababacdbdccbdacbccacddcbcccababbabdcbdddcdbbabcadacdcccaabdbddbadddacbbdcccddbbabdacadbdacccdacabbadbddbdbbbadccbaccddcdadbadaabbdbdcbcababbacbdacbacbbaccbbbbbcacdbacbccbdaacbbdcddacdadcabdbaccababbbacdbcbcdbcbdcadacacbddcaddbdcbaabcddccdbdddaacdadcbdcbccddbbabdaaaacaabcccabdddcadbbccbddabbabbbaddbbbcaccbaccbddcbbbadbdbbaaaaacbcdacbbbbdbbbacbdddbbccadbcadcddddcabadacaccbcddabdcbaadadacadbccabcddddccbbcaadbcbabbdbcaddacddbdccbdcdccccbcbacdccabddacbbbcdbbacddcbabdccdcddcaddddcdbaddcabdbbcaacbcaabddbabbabaaacccabccbbdaadadabbdcaabdddadbabcccddabdbbdaccdabbccddacbabddbbcacbacbdcccdddbdcdabcdbbddbdbaccddadbacdbbdabcdbbbccaadcdcccbccddbadabddbacaacdbcccabaacbababbbcdcbbbdabdcacaddcdbabababaadaccdbcbbabaabdbdaacaddbcaadcbdcbddadcdcbdcbddaaaacdaadbbdcabcbcabaaddbabcdabddcaadbabdbdbaabccbcabbdbbacbababccdaabadaccdbbdbaabacbdbcaaaddacbbabbdcdbdcbdabdabdbaacdadddcdbccddababbccababdabddddbdcddaadcddabdcbdacaacbcdbbcdaaacddcdabdabcabccbdbdbdbbcdcdcdcaadacdcbcddcbacbcddbbbdbddbdcaaaacdddadacddaadbabcdbddcbdbccddcddbcbadcabcaabdbaabaaaddacdacdadacbabbacdddbcacdadccdccaaaaaddaaabcabaadcbacccbcadbbadcaadabcccdacbcbaabcdbccdacdabdbcdddbdccdacbbdddbaddacacbcadbabbcdbbcccaabbdccdcabdaccaccdbbacdbacadbdacdcacbbabbcbaabbbddbcbbccdbbcdbdbaddaabcddcacaaabaadcacdbcbacadadccbcaaaacbcadcccadcbdcdccbcbbcbcddadcccbdaaddbccbddaabccdbbacbdcbcbcccbbbccaadbaabddbacbbbacaacbabddbccadcdbacccabaccdaccbcdcacbaadddbdbbacddbddcadadaacadbdbdacdcdaacbbcaddbbbdbdcacdcddccacacbdccdbbdccbbaaccadbcaddbbddaaabccdaccdcaabdbbcbcccdcbbdcbddcaacacdacdadbddbbdcccdbbaaabcbcaabdbbdabbaddddbabaabbbabadbadbcadbbbccbcdbbabcadadcacdabdcdbabbbcdccbdccadbbdbdbcbccadcababdddbcccdcdcbcdababdacbbdbcaadacddcbdbaadbcaabbbbccdbabbddcddddbdabdddcadabbbacddcadbcababcabbbdacccadbdcacbdcabdccdbcdbbbbacbdddbaadcdbdcabdcadacbddccdadddbabcdbadbbbbdccbcadadcdddbbdabbcabddddbcdbbdaacaabbaccbdadbddbccbccadddbbdcdbdabdbadabadabbdcdbaacaadcbaddbaadadbabbbcccddbccdddaaacddbcccdbcadcdbacbdbdadcaddbddcacbbddcdbccdcbaddaabdaaaddbdbdbadbdcbdbdbdbbcddacdadbaccabddcbcacaacbcdadbbcdaaabcdbbdadbcbdaddcbaaabdacaaaaabccabcdddaddcccbcaabddbdcadbaabbcdaadbaddbabcabcaacccdaacaddacccddaddcccbadbbdcabcdbdbbdbbccbdaccbbcbbdcdbdbcacacbacacdcbdbcbaadabddbabaddcbcbbadbbbdacbdacadcbbbdadacddddadccabbaadbdaaabbdccadcdbbcccdccbdcbcaaaacdbddbbbdddacdabdaabcadaddabbcaddadaabccabcbbcadbabaaacbadaddbcadadbcbdbccbbbaccdcbabaaadcbbbaabbccbaccacaacacccabccdbcddacacbaadabddddbaddcdccbcccabdcdbaababddbbdccbccdcdcdbcacdadadbdaacdaacbcbcacbbabbdbbbdbbccbacaadadadadaacdaaaacdcaaaaacddaddcabcadccbabcbbaaabacbcccdccaddbccaaddcbbbdaacdccdbbbadabbdcbdcddbcbbbbbabdddbcdaccadbddcdddcdbaccadcaddbcadcdcabddbcaacccacdaccbcadcababdddddcbddbbbdacdacbccbddacdccdbbcbdbbbdccacdbcaaacaabbdadacbcdbaacabbbcabaaccdcbccabdcddbaccbbcadaddcccddddaccccdcaadaccdaadcdccbcbababcbaccbaddbbbccabdcabdccbadbacddddccbcdbdbcdcbcdddabaaacddbdbdbbcbdbbbcbdabadbdadbcabccbddcbcacbcaaabcccbcdabcaddaaddcaaaabcacbbadcccaccdddabcdbccccbbaddcaabbbadcabacbbccbbddbbcadcadbcdcbcddaaaddcdcacdaacdaaddaaadccacacbdbdabcdabbbacdcabcaaadadddbbcdccdbbcdadbbadbbdcabadaccddadacaadbccddbcbaddaaabaaabdbcbaaacddbbaccbbddbccbbadcccbabacbcacdadcacbbacbcbbabbacdadaddaacaaabcadbcddcdaaaabdcbcddacbdaaaabcdcabddbacacaadbccbdbadacdbccaabbdcdaadbddabaadbbbdbbacaddadbdbacdaaabdcacacacdbddbcbabdbabbbdadaccdccacdaccabbdddcbbddcdabcaacdddbabdbacbccbadccdbbcaabbaabdcdacdbddccbaabbaccbabbbcabccacddcacbdaddbabddccabcdcaabaadbdcabdbcddaaacacccddacbddbabbacdcacdbbbbcaabddaadadaabdbcabccaacaacabbacaababbbcbbacaddcaadcacdcbaadaabaabdddbdabcbacaabbccbbabcdcbbbddcbcadaacccadcaaabadbdcdbccdddabcdddcbbadbbaaacccacbcdbbcbdcbbacbaabbbdcbabcdbcaaddbdaadcbcddcdabcacaccdabcdccbbbcbcbcdcbbaacdcbcbbddcabbdadbddaacdcbcacbaccdaabdbbcbbccbcdaaaacdbbbcbbbdbbbcbbdccccbcbbabdbcbabbbdcbacabaaccddcadcdcdabcccdddcdddabcbbcadadaccdddcbbbadbaaabadcbabcadcccacbdabdbbdccdbaadcddabbbdcbddcacccadabcaaaadcdbbdcdaccabcdbbcbbbaaacbddbddbdabdbbdaadcbccbcdaaaababcdccdcacdbbbbaaaccaddbccdcaacdcacabbdbadadbbcbababcacaabbbbcdbddaddbbbacccbdbdbbcacdbcdbaaccddddcababbaacaccdbbcddccaadadbabbccaabdaacbbbcaaacbcacdacddabaccddacaaadddacabddcbdbbadccbcdadaacdbabbcbddadcdaacaddddbdaaccacaccbbaadbacacdccdabbbadbccaadcaddddcdbacaddbddbadbabccdacbabccdadabbcbddadacbbabbddddbadddcaacccdadabdbdbaacbadbdcbbadbdccbdbdaaccbddcaaadaddcccdcdcccacbcacdaddadbcbccadaccbdbbbaaababdbdbdcadcdabdbbcdadccbddacbbacaaccbcdbbbcaddbadcbbcadbaddbbcabcddcbbcdccccadabdacdbbcacbaddcaadababdadcbbacacdbdbcbacadacabcdcbcdcdbcccacadcbacacacabddccdcbccddcaccaaacdabcdcababdacacabbbbaacbbbcbcbbadcbbbcdacddadcccdadccaabbabadcbddcbaaddabdacddcbbcbccbddccbbbbbabaaabadddbbbdaabbddddaadbcdcdbbcbbbadbcadbcadccbbdadabddabcbddcbbcaaddccbcccddbcccbcdbdbdcbbbbcbbcdbdccddbcdbadaaccdadbdabdddbcadbbbddbccddacadccbccdcbbcadccccccbadccccddcdbdaaccbccadddaabcdcbddbddabababbdabddcaddcccadccdacaddbcabadcaacaacbbbdabbdbbbbbaaaccbdaccdbcdbbaccdabccccbbbccaccdcdbaadadabcddcaddbbaaabcdbdbdbadbbadcdcbdddcaaddcbbbbbbbdbbccbcdbadbddcdadaccadccbabdbaacdbbdbdcddadddbdbaabcabdbaadbabdccabacbcdddaadacbaabbddaabaddacbdadcacabcdcccbddacbbdccbdbcbbdadbcbdcdacabadcadbbdcabddddbbcbbdbcadbaaaadbabdcbccbdbbddacbbcbcadbbbbadadcacdbcabcbdcacadabbcbddbdabbbbabddcbaccccbcabbccbbacdcbccbdbdcdabccddbdccbbbcaabdbcabbcdadbddcbabbdaddacbbbdbdcbddbcabdadbddacadaddddcdaddacbcccddabcdaccaaddccabbadcdadcdadaccaccbbcdaabacdcdcddcdddcdddcddaacccdcdbddaaabbdbacacaacaddcccaccacbaaabdbdccabccabaccadcdacbbadcbcdbaacbaddacddbdcbccaaadcabccabaccbacdaabbddaaacdaaadbaabdbaccbdccdcccbcdbdadcccbccbdbbbaaddbacccbccbbdccadaabcbcaddabbaadadcababbddcbadddbaaaddbadcdddcbacdccdbbcbacbcbccacbbbcaddabaccacccbcbbacdabdbcdadabbbbcabccbddaabdadadacdbccccabbbaacbddbabaddaaadacacbbdbccababaaadaddddbcdcbcbbccdaddcadcddcabbbbbcaacbbabcadadbabdbabdcdaabbadbdccabadcdacdabdcbbddbbdbdacdbcbabbbabcbdcdadbabbbbbbbbacdadcdbdddaaaacaadacdcbcaacbdbdcdcddcaaaabdaabbbccddbcbddabbddacaaddbcbbbadddcbcabadadaccddadbbbacadddbbaddddaaccbcadaaabcccccabaadaacddaaadadaabacdabbbcdcdaaaddadaddcbcbbabdadaacacdaadbbccabccbbcaabccbbdbdcdcadabcaccbbaadbbaadbcaaccabcccdbcdbbabccdcddbdaddaaccabdcacbcabacabbdddacadbcdcacdcbdbdcaabbaabcaababaadccdbcbcbbaddccaadbddaadcdbadbcdbbcbcababbcbccddaacabaaadbadcdbadaabcbcadcdbddcbdcccddcadcaaacacaacaabcbccccbdccadadbcbdaddcaaadbcccdacbdbacadaccccdadddbaabdbcacabcaaccaccacbbbaaddcddbbdcbccbddbcbadcabbbbcbdcccccccbadacdcaabccddccbacbdcacabcbccdbdadcadbaccbccdcddcddcaadcbacbacdcbdbbcaaddbccbcdcbbddbabdbcbadcdbadbcccdcdacdcadbbbaadccacabadcccbadcaccdaacdbaddaddbcbdabaacbbabbdbccbcacabdabadbdaaccbcaadccaaccbdaabccacacbccdabdaabbcdcddaadabdbacdcaadbcbcbbccbaccbbaacabdacabacacdaadbadbccdaaadbdbaccdcdbdadbaababcdadabdddbabbccaaacbbbaadddbccbbcdaacbbcccacdbcaccbcaddddbabacbabababcaabadcbadbbaaabaabdaabadaaddadbbbabdcbaaddadbddbbdbabbdadbcbadddadacaccadabbaacdbdaaddbdcbddbbbdbbaabbcbbaccdabaddbbbcdbacbcabdddcacaaaadaabbbbacbaadcdbabcaabacbadbadacbcacdabcdbddcbbadcabaacadcacdcdaadbabdcdcbaccabaddcadcbcbddacbdcbddaaacbdadabaacaccacbcababbbbcdbcdaabbabaaababdcccdacdddbdbaddbdbdcabbddccaaacddcdcdbaccbdcdbacddaabcdacbdcbcccbacdddacbbdadbcccdcbcdabbadcddccdacbdccbcdccdbbdbacdadddbadacbbdddbcadadaccdacacddcbbdaacadacdddaaacdbaacccaccdaacbacbcbcbadcbddbcdbccdcadaacaaccdcdbaaacccbbcaaadcaaddcdcdcdaababaaccaddacbadcbbcdddabdddddcbdcbacaaaacddbadabbacdbabcadbdcbbacdacdcccdbcaaddcbdabaacdcdbcdbdbacadcaadcbcbabddacdbadccacddbdbadabbddaabcbbbccddcbcadcbaccaaabbcddddbcdabbccbdaccccdadaaccbccbdacdbdcccdaabacaddccbddcbbbdccddcbacdddacbbbadaccccccddccdacaaabaadccdbbaabbcbccacaabbddacbdcacdabadddcabdcacdbbbbabbbbdcadadbdcbabddbdbbacbbddddadbdbcdcabdbcbadbaabddabdbadccaacbaaaabdacbbccadaccddbcabadcddacacbbcbcccabadbddbcbbdcacddcbcccdbccaacdcddcaadbadbacbbacdbcdbdabdaadccdbbddddbadddabbbabcbbabacdcddaddabacacbbbcddaccdadddcdacaaadcbabbbddabdadbdccaabadddbcbdabbbddcbdcadcccabdbcdcbbddbcbdbdbbdacbcaddbaacdacbaabbbbcdbbabbaacccdbbddbcaaddbdcdcbdbdbcacacbcbbdbbabbdccabcaaadacaccbabddacbbbcbdcbbcaccaaddbbacdbadbbdaadcadccbbccbdacccabababccaabababdaddbbacaaaaacdcacacbcacddbcdddacbaacbaaabddacdcaccacbdddacdabaaadddcbcabbbccddadbdbdcadaaaaaaacacdcabcdcdbbbaaaacbaaddbbbadddbddcdbbccdbaccabaaaddaaccdcdbacddccaabdcbdacacacddcdaacbcdbadadadbaaddbbdbdaaabdcaaadbadccdddaaccddaccaaccddadaadddaccacccdccabbadcdacaabbddcbdcdacacdcbbdbcbcaddbdcddabaccdaaacaddbaccabcdcbcaaaadbdbbbdcccdadbcdcdddbcdabcbbbccbbbdcbddbbcadbdcadbcddcddadcbdadbabdaacaaabadddadcbabbdbdbdcccaaacdbcadbcccbccdabcccacccaddadcdbcbcdbbbccbdbcdabdbbbcadcbabbbdbcdbaaaabdddbccbabacbcdbcbbdccabcbaabadaacbddabddccdacbadbbddddcbbddbbcbabcdacdaadbdbacbdcbdccabbadbbbdaccacddbcdbddcccdbadadbdabbdbcccacbbcbbdabbaacddacaabdcbbbbcabaacbdcddbaccbdbcbdcdaddcbaddcbbabaabbcdcbbddaaacacbbacaccccbbcadbdddacdccdaadcddcaaaaabdcdcccdcdaaacddabcbacddcdccdcbcdbbdbcdabdccacbcdcaaadccbccbdbbbcbcaccbdbabcbdaabacacbaacddaaccdacbbdaabaccbadbaabddabacabbcbdbbbbcdbcaddacddcaaddbccbdbcaabcacabbcdacabccbdcddbdacbadbdccdcdbccadbabdbddccddddadddabddddaabbbcddabccabbabbbbdcbccadcdbadaadabbcdabdcadbaabbcdcbbddbabdbbbccadacdcadaadcddbbcbaccdcadbdbbbacccbadaddbcbdaccbbcddacbdbabbbcbacacabcdbddbbcbbbadaabdbdbacdbabcbdcdbdabbaadaadddacaadcdccbadbcdbbccbcabddadabddbccdaccdacbcdbcbaabadbabdabddaaddbbcddbbcacacabbabaddbaadcdaadadaccbdddabababdadadaacdaaabaccbaccbddcadcddadbbabbbbddcdcadaacabbcdcabcabdcbcbcbacbbcbaddbccbaabbcbdabdbcabdbdccdddcdaabcaccccabdaabcabcccbbbbdabdcdadabdcbadacacaabacbcadbcbacddccdccdabacabbcbdbddbbbdcdbddcabbacdabccdcbcbcdccddbabcbdcbdacbabbabcbacdaccbbcadddacaabcbddddadbddacbabcddabcdabbdcccdcacbdaadbadcdddbbcbacccabbdddadabddbcbcabadbbcccacbbccaaccdbadbcabbdbdcccadadbcaaacdcdddabccabacdddaccadbbccbbdbdcccadbbbbccabadccdcadcaabcbdcccaabcccbdbdccdbbdbacacadaddbadbadbdabbcadbabbdcdbdbcbddccdcaacbdccabddccccdccbbdcdcaaaaacddcdacbccaadbcdbccdbadbcdacbbbcaadcccbcdccbccdcadbdcccabcacadcbcaadcbdcccdbbcaccbdabcbadddcdaddbacbabaabdaabadbdbacbbadacdcaabaddcdcdcbbacdbacdccadcccdbdcabcbbdabbcacdaadbcbaadbaadccbabcdbcccbddacadcbcaadcabaccbaaadababaaacccddddbadadbcbbbdddadbcbcbdbbbbdadbabcdaacbccbabcbccccbcaacbbdbdacbccdcddadccdcaabdcaadcbacdccdacddbbccaadcabcdadcaaabcabdcbdcacdddbcccdababdcbbcccaaadbbcabaddaacdacbbdbcddcddbbdbbdbbbdbaddddcaabcbabcbccabaaddbbdbdbacbbdacaccdaadbbdbaacdbcbbdbacdcacdbdcdbadbadccabaaabcbdcccacdddcbbdadbcabddbadabddadacadbbabdbbdbdbbaccbaddabccaaabccacaadbdaadababbabadaddcaddadbadddbdacbaaadbbaabdcbacbbcaccacaadaaadccbddcdcbbbbbcccdbaacdcabcccbcbadacadaabcacdacacddcbcaddcbaccaccccaaddacabbaaaacbbdcababddbbbabdacccaaaaaabbccbcaababbaabdddbbcddadcbbddaacbbdbdbbbdcabddbacbaabaddaddaddbcdcdbdccadbcbcbccbddbbaacabcccaadbccccabdcdacbaccbcaadadbcaabacdaabbbddacbdcacbcccdcabccaadbbddbadbcabccbabdaadaaddddddcdcdcbdbacdbabadaacaaaddddcabdcccdadbabdddbbcdadadcdbcbabddabbcdddbcdddcadabaccaabadcaaaabbbdcccdbabadccbacbccdabbaccccdaaadcbdcddacdbbaccccaaaacccdbcadadaccdbdbdbccbddacbbccbcddbdddabdaccaadadbbacdaddddccdabdabcadcdddbdaddbcddcbdcbadcaadcbcdcdbdbcdadbcbdacdbcadbaaacadbaacbccadbdadbcaddadbbbaddcbadccacbaccacbbccadcbaddaadbdbcdadabdbbacbccbcacbdcdbabbbabaddabbbbabaaacddbbccabdbcbbcbaccdacbbdbaccaacdbadccdacacadcdcbdbbababcabbadbddbcabbbcbcdabaacbdbabdbabaaacaaadbdddacccacdaadaabaabcbdbdadcbcdabcdacbbdacbbaccbbcbcdcabdaabadbaccccbcbabdcbaccaccbdabbdcddbcbcadbcddbabadcabbaddbcbbaacdaaccbababacdcbdcdbaaacbcdddddccbddabaacacdbadbacbdadbcdabadccaabdddbccbbaaabdadaacaaccaabdddbcaaaddddddacbcdbdadbcabdadaccacbacbbadadbdacdabbdcdacacabbabaacbcdbcaacbadcbcadcbbdadabcbcdcacbdcbaccdbaadaccdcbdbdabddabbccdccaaacbcabdbbcaaaaaaacabbaabaccdcacaadccbbacabdcbbddcbacaadcbbaaabcaabcdccbabcdcbdddbacbbcaadccdcdddddbbddabcbaccddbaddaabccddadbcbadcabbdabdccccccdbcabacaaadbdaabbbcddcccdcaadababddcaacddabadcabcbdbbbccdccadabcbdadaccadccccddaccdbccdcdbabdacbabdbbacdddbccadcabbbbdadcbadbddcdbddaddaccdbcccadbbddabbddcaabddbbbcbbacbdcdcccdcaabdcadddadadacdaabbadbadcabccaadbcabcdbaacddddacbaddccacbcddaccabadbcdbbcbdbdadaddbccdacbabaddcabbdacdacabbbbcddbbccbbcdbbaacdbdcdcbaadcacccddbcaaadbbbbbaacbaadacaabdbdadbccbcbdbcadacbbcdaacdccdcbdddcabbcaababcbabcbbbdddaacbbbbcabccbcbaadcccbacbbdddbdcccacbdbcabbaacabbadddacdadbcbabdbacacdbdbcdcabacaccdbacbcdbabbccdadbccbcdcbcdabddcdbcaadcababbbdccddcdbbcaddbbcddaabbcdbadcbadcaabcccddbaabaaabacacbbbdcdcbaddcdccdaaabbbbccbbabdbcbdcaacdacaccacbbcbcadcdaaabbacadcbacbbabdacddddddbdcbabcccadccbbbddccdbbdddcbcaaacdddbdbabaacbcbddcaacddbacaaaadabaaaddcadcbcabddcdcaadaabdbdcbadabdabdabddbabdadbdcdcdcdcccaababdbadabaaacdacdbaacbccdbdcbdcddaabccccabbddcdadccabbdbccbabbccbbbbdbcbbbcaababddacaadcacaacdbaadddbacadbcdabdcacbccacdabbcbcacacbabdaabcbaacadddacabacabbdbadddacdddbacdbabcabcacbdcdacbbccaccbaacbababcabbdbbdbddbbbbbabcaccbabacaabcddbbcccadcbdbadccbacabdcbabaddaabaacacabbcddaddabaacbddabbbbcbbbbacdabdccaaaacadccdaaacccddbaaabdcaadccabdcabbdccabdadcdbdbdbabdcbbcdabaacaadaabbcbbcdcbacaccadbcccababdcddbdbccbaabbbddccdcadcdcbccdadbdbbaacadbbdbdbdaabbbaadacacbcbbdcbddadcdadadbcbbbbdccaadbbcbdbddabddaccbbacacacaabacbbdccbdcabadcadbbaddabbcccddbbcacdbaabddbaadbbbdadbccbbdbaacdadccabbaaaccdbbddaddccacacdddcbadadcbbaacaabbddccbcbdcdbbcdaababcdabcaadbacbdcbbcccdddaacddabccbaadcdbddcddbaaddacbbccaaccabcbdbdaaddaccbdaaadbcccbdacbbbbabddabdadcddadacbabaadadbbaabaccbacdaadadaddbbbadbcbdbabacaadcaacbcabadccccacdcdaccaddbddccabdaddadacdcddcaddcbcadcacdddbcadcdabddaacacbcdbcbccaacbabccdcbbccbdcacacccabcbbdbaabdcbbcabccaabbbcdcbaacdcdcbdaabcaddcaabcdcdabcdbcaabacadbaabcbdaacdabadadaabcccacdcccdccaccccdcdcaadacbdbaaaadcbbdddbaaadddbddaadccbdaccddacdbcdbaaaccacdcbaccddbacacdbaadbdcdccbccbbccccbbddadadcdcdabababcddcddbcadaaaccbacbacbbbabdcabbdddaadbcacadaccddaaabacddbaadbbbdcbaccdddcdcaadcdbdcddacdbbcdcddcdaddaccdbddbabdadbbdaadcadcdabdbcdaaabbcccbcddadabbabbcbcacabdbaaacbbcdcdddcacdadabccddabdadaddbddcddaaaaccabadcacabcdbddbacbaabadbaccadacacbaaacabaabbdddaccbbacaabdcbbadcaadabbdbbbaabbdacdaacaaadcccbccdabcbbddbacdbbbddbbcdabaabaddbaccabccddbbdadbbaabbcbabbcbddbdadbaaaaabdacdcaaddabbadcaaadcacbbdcaaadcabccdbdcdadddbbcaadaaabdabacabdcbadbddcbdadcccbadcddaccaaadbaacdcdbdcbababadcdaabdcccbddbccaacaaadcacbcccdacabcaacadbbdcbbbaadaabaadbbcbaaabdbbabacbacaabacbccabbcbcdbbbadcadaacdaacabadbccdbdccaacadcacadaabcbdbcabbbbbcdbdcddddaacdbbccbbcadadaaccdddccbabadddbcabadbacadbcdccdbbbbaaadaddbcadcdbbadbcbbccbaadbdcadbcccadcdaccaccdacbbcbbdadcdbdddbcdaaccacacccddbdabdbaaddacabcacaadcdadddadbccabccbdabbadcbaccdcbdddcaaadabaacdcdcabcddcabaaabbcabcadadbcbabdaaabcddcdcdacccacabacbbadddaabbcadbddbdccadcddcabadbacbccbcdaabadbbdbadccbcdbbdbbbcacdddcadbcccabcadbbdabaddabaaaccccbcaabacbcddadbabaadccdbbcacbbbdaadadabcdddbccabaacacbcadbdcbcacdcdbbbddababdcbabdddcbadaaccbacbdbbadbadcaaaaddbadcdcbacbbbabcdbaaddcacaddcbbcaaaccdccdbdacadaadcdcbdbacadcddabacbbbaadaacdbcaacabcdabdbdbdbbbaccbbadbbaadabcbbacaddacdacbcaadbdbddaccadadcbacbaccbbdbaaabbbdbabbdbbbdcaddbcbccabbabadacccdadbabaddcbcadcdacbdacadabaabbdaccaabdcaabadcbadcccaaddbcdacbbabcaddbcadcbabbcbbbcdcbdccbdcdacdbdabbcbbdaaccbabaadabbbacccbccaaacbabcacbadbacdabddddbaacbacaabcccacaadbdbaabbacacdbdbddcccabccccacacbaccadabbaabcaabcdaacdbaddadcbbccaaadacbaddacbdacbcdbbadacddacbddbbcaabbcbcdabdaabccddbcbaacbdbbabadcbbddbbabddbdbbaccbdadbaadcbbccadbacdadaddcdddddbbbccdbcbbbccdaadadadbbbacccaddbaacdbadcacdbcbdcadaaacaabcaabdaaaaadaaddcbbadcadaccbbaddaccdbbbaddbdbabbdcadcccdcbabcdbababadbaabbcdcdbbbbbdbbcccdadaadcadcaccbbbbdaadbcdcadcbaddcabdbbcdcdadbcdadbabdabddcacaaddcdccbadacbbbabbacdccbabddadbbbbdbbbdbabccaabcbdcbcdccbabddacabbbcdddccadbbabcbabbbdddddabaddcbdbaaddacccdcadbaaddaabaaddcabbcbcbdcdaadbdabacdbadadcaacbabbcbbddcaaccbbdcbdbcbabddccbaacbdccbcbbccdccaaddbdacaadacdcddddbacaccddabbddadccbdbcdbbcbacabadbaccddaccdcdadbbcdaccccdbcacdbdbddbcbaddbbaababbdbcccabcdaaccaadddacacaaddccccbdcdcbababdacaadadcbbbacbccdbdbddccaaadacabbcdcabddaddcdabdbabaddaaddcacadbbbabbcbbddbdbbdddccdcabbccddadcbadcdcddcabaacccdbcadbcdcbabdbbddbddddcdacdcbcddbccdccdcaabbbcaaaaadccadacbddbacbacdadcbdaabccbbbdaaabaabadbcbcbacacbcbcbaddcbcaccbdcadaaaddabdbdcccaddbababadbdbbbcdaadaaccaacbdcbcdaabbcdabccdbddabbaaccdadbdadcdbbcaaddbadcacadaccbbcbcbadcbbbdabcdcbbbdbacbcdacabbbcaaacbbcdbdadbcdabddcbabadbadbccadddabbdcdbcccddaadcdabbcabcaabbdbdcbaccdbcdbccdabbbacbcdabddbaccbdddbcacadbbcdadaaddcacbbadbccddbcbcdcdabcacabaacadbbbacdbddcbbabdbbdccbdcbacadbabcadcdcdababdaaacbccddbbbbadbdbdbcadcdbacdabbdbcccdadbdcdcdcacccbccddbdaacaabddabcbccaacccbcaaacdacacdbccabaccadadcaadbbdaabdddcdddabbdddcacacbcdcbccccbaddcbacdddbabcaddbdbcacadcabacbcaadcdcbbbcdccbccddbcbdadbdddabddbcbcbbbcccbdddcbabdcbdddcdacdccdabdaabbdadbaacdddcabbabababbcdcabdbcbcdaabcbbacccbccdcdcbdbcadaddaadcddcccbaacbbcbacdccadaacbababbddccccccdadaacdcdbbbabacddbcbccaaaadbdccddaabbdaacaadadcccaddaabaadcbadabacccdacdcbdabbbbadbbcdddcadabbabbadbbbbacdaacbadccbacdaabdcddacbdcccddbdbbbccbddacbbdacdbaababcaabbdcddbcaabcbbcbccbacbadbbdcbdcdaadaccbcdddccdcadabcaaadbbbaccadabcbdaabcdbcbaadbaacabbaadcbcbddcaaccbbbadbdacccabacdcabccbadaabcdcacdacbadaaddbaacadbcdacadbaabcaadcdbaabcbbbcabcaacdadacadcbaddaccbabcaabbacaadbccacdddddadaddbccbdaacccadbacdddaacdbbdbbbdbaaacdabbbdcdccadbadadcacdabdddcacaaccabcbaabbaacbababdbdbdddabacddbcccbdddadccabbccdcacbacbadacccdbdacddadbcbdadbaabbbbacaddabcdddabacddbbabdaaabccdadcabcacbccdcdaabdbccaabacdbbccdadaddbaccabadcabcbbbbacabcbcaacbbbacbbbcbadcbbbbadbdbcaabbbcdacccdccbaaababdbabdcdddccccbaabdcabbbaddcccbadbacddcbadaaaaadadadaccdccddbddaadbccbcaaccddcbaccdbcdabdabdadbddccdcbcaaaddcdbaddcacdcccdcbddbbdbacbbcddcbdbdddaddbaaaabacbcbabdadadcacaccccbacccccdbbaabdacbdbabccbbbbacdbbddcdcadbacbbddabacacadacdcbaaaadbbdcbbabdcbdcddacbacccdaadabadaacabdbacbdcdabaaadbcbacbaccaacdaddacbabcbdadddbabacdaadddbaacabccdcccacbbacdacccdddcabaccbbcabadcdacabababaacdcbabddbacaccdbcbbacbddaddcddcbbabddaddaddddcddcdccabbabcacddaddacbbdcabddaacbdccbdbdaacacbbbbddcabcdbdcccdbdddaacbbabdddcbcabbdddccdaddacaabbcdbbdcadddacbcbababacaddaacdadaaddcdadddccaadccdcadadddddabddccbbccbaacbdaccbdbccccbdadacccabcdccbddababbaaabcddccaacabbbabcbaabadbccadacdaadddccbddbcbcccaaccdddaabbddabaaccdacbdbddbaddacbbaaccdbbbaabacaddaaaddbdcbcbcacaaaacbddbdaabcadbdbdbcaddaabcbbbabacbdbaadccdcabaaccbcbbddbaadacdcbbcbcdabdddcaccdababccccadbdcdcbbbbddbcdddddddbbbabdbcdccacdbacaaaabaabaacbcbcdccdddadaacbdcbaabddbaccbdaddbdaaadadddabcaadabddacdbdbddbadaaabdbdbbcbbdddcdccabaabcdddbdbbadcaccaaccacbcbbabdadcdcbbccadbaccaaaadcadcbaccddbdbacbcabcccbbcbabbcdccdbadcdabcdadcbdbbcbdbdbcdcbbccaaaadcbccaaaabdbdcaaaabadacacdcdcadbbdcdaabcbbaacdaadccbccdccbbdbcadbdccabdbdbddcbddccbacabcaadcdddddadbadcddbccdbbccbcdaabcccdccbcaaaacddcaccaaabaabdbdbdbbddbdadcccdbadbdcdaaabdbbdacabdcacbbadadaccbadcbabbabcacbdbcacbccdaabcddabcdcbacddbcadababcadaddabaaacbdcdaabbdabbdabcbabcdccdbddbcabbbaccdaababcacabdccadabadbccddbcaaaaacdbddbbdcddbccddbdcccaddddabadacccdbbbcabdabcabcdcacbdcdabbbdacaabadadadbcdcdabaabbcccdbdddaaacdbcbabcdcbdcddddadbdcaaddcaaadccabcdccbbdbbdcdbddbcbbddcabdabbbadbadbbaadadbbcbccacaccdcacdabddbcdddccaaabacbcbadbcacdccbdbbaadcaabddbbcdcbbbbacdbbcbbadbccadccdadcdcbacdbbbcabdacbbddabcbbdbbdbabcaabdccdcaadaadcddcaacacbcddbaaababbacdbcaccadacadbaaccddddadaaadadbbccbcccbcdcbbbaddadcccabdcacaddbcbaddbbaccbcdbadcddadddddaaaaaccdcddcacaaacbdbbabadcdacbcbbababccbdcacbcbdaddcddbbbaabccbaadbccdcdaabdddbddbcaabcdcdccccbcaabdacdbbacdaaabadbdbdcdcbbdbbaaccadcabbabcadbcdacadcdcacabbddcbcbcabdbbcdcbbdbdccbdbbbcaaddaadbbdadacdcaaabdacbadaccdadabacacddbaccacaacbccdccacddcccccdcccdbbaacaabbcdccddbddcbcdbdaccdcaddaddbdacdabcdbdbaaabdbaccdccaadadcbadabccdccbbdcbaccbddbcccadbabcbbccbcbdddccbdddcccaaaabbddabddaabddbcbcdddccbcabcacdaacdaaaabadaadcdbccbacadbbbbbadbbcbbacdadbaabddabbccccccaadbadcadbbabdbbacdabcadcdddbaaddbbaddadddddbcbdaabacdbbcdcdbcadcbcabdcbcbddadaaacabaaccbdddcdbadadcddcdbcbdcacbddccddddbcbaaadadcabcbbadadcbcabaabaaccadaabdaabadbdbcdcdcdcaabacacbadbdddbcdadaccdddbbddababdcbdaadddbbdbcabbcaccbdcabaadcbbcabdcdbaaacbcddaddcbbadbacabccbcbadddcdbcdcdaabbbcaddcabccdbacacabddcaadbabdaddbbccccbccdbdbdcbcddadbcadacabcdccabadcdcadadaddbcdabbcdbcdadaccddacddbdcdaabcaadcdbdddacddccbbdbdabbaabdcbdacdadcaddbdabbdaacddcdadbaccdadddcaadccadcdbabbbdbbbdcdcacaaabcaddcddabddadcbbaaacaabcaddbacbdbadcacbbbbbbdabcdddcbccdabadbdabdcaaabaacbbdadbbccdbbcabccabdbcccccbbcaabaddcaacccbdadccccbbbbbdbcccdcbbcdcacbcdacaddbbbddbdbdbbbcdcaabdcacabddbbdbbaaababccbdacaddacddbcbbaabcadaccabccbaddcdcdaadacadadbcadbcbdbdbadbbcccacbabcbabdabbddccddaabccaccaacdbccdccdcccdbcccccaacccaacdddcddbbbdabdcbcdcdcdbdcacaaaaabcddbbcdcaaddacdabbdcdddcbbdccbcbcbbdcdaabbdabaaadddddcddcbccaadddbacaabcadbbabadbbdbbbdabcbddcacddadbbbdcbdbbacabddcccadabdccdcddcdddbbaccacbbdbbcbdaabddbbabbadcbcdcdcbdbdcdbaabcacdabdcccdbdbaaadbaccdaddcdbabaddcacadbbbccdcbcbbbbacacbccacadcdaccdbaccadddcadcaacbbdabaaaaacabdbcaababaaaacddbcdabbbbdbddcbaccdacbcbbadabcbaadabbdbadaaacbdbabdaaddadcdbdaacabaabcaaabcdcbbaadaccccccccdbbddabdbcabdaadcbcdaadbcbbadbbddcabbbaddaabcbddcabcdbdcccdddbdbdcabbddbbccadbbdabcdddbccbdadabccdabcabadabcbdacdbbdbcdbadddccbddcdabdbcaacbbabcacdacabbbccadddcbdcdaacddbbdcccbabdaadbcabcbbadacbbccddccdaaadccaddbddccbadaadcadacdccabcbaabcbacdcbbbcdddbdabbcdcabdacbdacbcdddababdbbadcddbaabccdbaaabacadaababbaaadbddbdadbacbacbbaaddaaccdbdabbadacbcadbcdbbcccaabbcccadacdcdcacadabaacddabddacadabdbcadcaaaacbacdbdddddcbaabcccdcaacbacbadabbbcdbaaaaddbadbcaacbacacdacbdbcabccdcddbddadadaddcdcaabadccdbdacccddbdacdbcdabbdcdccdddcadddbacbadbbbadbbcdbabaabbcbaacbddbdcaabbdbdcbdddbcbacdddabdbbcdaddccdcdccaadbbabbcbdbaddccbbabdbccdcddabcccabccbaccbdabacabcbabdbaaabbababbabbaddbbaaddddaccaadcaabcaaddbbadaccddbbaacbcaacacbcbcaaadbbcaacdaacdddcdbbdcdcddcadacbbdaadcaddaacabbcccaddcadcccbbdbcbdabcdcacdccadabcadbcbbddbadbdbadcabaacdcdacacdddbbababbdccbcdbbbbaddbabdbdbccaacdabdaacabcadadbdbaddaadccccdcdacbacddbbdaccabcdbcdabccdbcaaaadcbabbbcbabbdbcdabdcbadcbddddadcdcadbcacdabdbcdadbcbcccabacdddaabaadaabaadaabacbcbccbddcbbcacacdccccacdbcccdddcbddabbaaddcbcdddcdbddabadcbadcbdabbaacacdcbdaccbdbdcbaccabaddabadcccbaccddddbccabdcaabcbcdaaccabbdcabbcbbdbddacbdcddbdabdcdccdcccabbaccbaddbddcbcdcddadacadcbccddbddcbddadabddcdabdcdabdddcbbaddadcbbddcabbbbdbcaccadaaaaddbdadaaadbdccbdacbbaccddddbdbcaddcaabbcdccadadaccadabddaaacacccaacbadcadaaacbbccdcbaacdcbbaddcddbddbddaaacdbcbdbdacdbdadadbbccbcbdccdcaaddcbcbcbbbbacbbcabcabdcbcddbbaababaacddcabcbcdcbbcbdddadcbcacaabadbddbaccbbaaddbdadaabbdaccbbddaabbbbdaacaaccbddbdbaddcdddcddbbcbbacbcaabcbcdbadbaddcbccbdbcbacbcbdccbddabcbbdaaadcbdbbabacbbadcbdbaddaddbddbbdcdbbabcddabcdadbcccacbdbaadddbdcccbacddcccdcadcdacddbcaadcddbbcdaaaacbdbacdaacadadcddbbbacbdbddabdacaccdcbcdcdcacabbdacbdcccbbcbaacdbcacbadbccddbbddbcbbdccdcdcbbbdaacdcddddbdaddbbcbbcdacbaacaabcbabaacdaacbdbbbbdabdcabaccccadcccbdadbaddbbccacbadaadbbddbcbaddbbdddccdadacdbaccadbadbdaabbbbbcbaadacbdcaaaddcaddbabcadbddcdccdacaabdbbcaaadaaccccdababaccdabdddcdacabadbbbddccddacbbbcbcbcabbcaabbacbacbdddcbdbccdbdbabaaccdccdddbdcddcccaadcabacdccbbaadabbaddbdbaacaccbcbdbcabbbcacaabbbcacbcacbdccdbcbccdacdbcbcccabdcbcabdacbcbcabadccbccccdcaaadacbabdbcdadbabdadcdadccccccbdadbdbaccdcbbabcacbabdccdbacdabbdacdcdbcdabcbbdbdabbcccbbcbabcbaabbcadddabbcbacaccbadabbdcdadcbdbcbddacabdbbacbdddacddacccbabacbabadbcbbdddcccabcacabcaddccbccacdaaabcccabadaabacadcadbdbacdaccbbcacdadabcbacdaacbcccbcdcdcaabbcdadccabcacbcadcadabdcccaacaddbadaabdababcdabdadcaacdbcaadbcaaddadbaabbcdddcdcbcccbcbaaaaccddcabbbdbbbbaabdbbbdbbdccadcbcbdcbabdcdccabaaababdaccbaacacadcdccaacacbaaaabdbbdabbcccbddbadabdbadbbacddaaddcbcacdddbdcabccccdcdbcdcdaaacbcdbccdbbdccadbdabdabacccaaaacdacbbccddbbccdbacbaaabcdcbccabcddcbbaccabaccdddaccbddbadbacbaabbababcddbbaababaacacdbaccbbbbcadcbcaddcaccabbdccbcbcbbbddcacacadaabcdbbddbadbcddcbcacbbbabaadcaaabcdacdbaddcadcabbbbccbbddadcaacccaabaccbddcbbabbcdcbabdaacabccbaccbaddabadbaddcabacadcdbdaadadaabcaacbadbdaaddbbcbbdbbaadccbdabbacbbacdadcbacccaddbcccccbabbaababbbbababcbbbcadbccacaacbddacdaccdcbcddbacacdacaabaaacbccbadbcbdacdccdbbabcdcbcaccaccbbdbbacaddcdcacaaacddabcdacaacdacaaddcadacbcbadccdbcacabaddddbdddcacbbaccadbabdaaacbdcabdabbaccacaaaacdbbbbdaacddbbccaadaabddcdcdadcdbcdbcdbdbbaabdbabccccccadadbaaadcabaccababcadbbccababcdddbcadccacccdabdddaccbaabbcddcbbdabadbabccdaabcccadccabdccdaacaccccddddadcdccbddbccdbabdcccbddabdccddbacbbbcdaabdacabbcbcbbdcabaadcbbbaaabdcabdcdbaabdaaddcacbdbbabaccccacdcdcbcdcaaabccddbbbbacaacaabdcdccaabcadccdacadcabacbcdadcaaaabbaccdadddabddcdcbbbaabbccbbabacdacccccdbcacbbababdcabdcabdaabaddcadcdcdddabcacbaacbbdcdacaaccacaaddbbbddadbccddbadccdddacdbcdadbbbbacdbcbcadcacccbdadaaabacdbccadbdadbdbdbadccabddabbbcccbbbdbddccabcccabbdcdbaabcabdcccbadbdcbbdddadcadcbdbcabccdcdccbdccdccdddcabdabddbbdaaacddbadcdcdccccdabccbdaaccdaccdaccdcbdbdcdccaabbbcbbbbddcdcdabbdadbcdacabccbdcdadccbabadbdacaacacadadacacbdacadcdbbdcaddadbdcccaccabbccddacccdbddcdadaaaaacdbacdbcdcadcdcdcddabddccadcbdbaadccadbcbddcbbddcdcdadacccbaadcbccacdbccbdbbcaabcdaacaddbbabdabdcccdaadaadbdcacbbcbbabcadccdbccbbccbbaccdabddbcbacabddccaaacaadbdabdbcdddcbbcbcdbdbccbadcdabbdadcbbbcccdbcbbbdbdadbabddcccbdddacdbabaaadadcacdddbcababbbacddacbcacadbabadcabcbaacdaddcdcadcdcccaccabbdbabaccdbbdccbddcccddababdccadcbbcbaacbcbdaacabaddabaadaacdddcabaabbdcbdcbacbbbabdaaddaddddcddbaacdbcacbaadcdddcdbaaabbabaabcbcdccabdbacacddacaccdccaddcdccbbacdccdddccbcdcdcbaaccdcdbcbcdcabcaaababcbabdacbbaabcacbdcbdbbdabccaddbaadddacaddbabadadbcacaadcaddacbbaddcbaaadaaccbacdddaddccccdadbdadbbbcdaccadcaadddbcbcccbcaccaadcdcdcdcbcaddacdbcacbcdcabcdddddcacaadbbdcdccccabdaaabbbcabaaaabbcddcdbbdcbbbccacdddbbcbbbcccccabaadddcbaaccdaaddbdadcacbbacdbbcbdbbbabdcbaddcddacbdcbdddbbbccbacbbcadbddadacacabcadabbdcbbaadcccacbbdcdaccbbacaddbababaaccadccaaaabcbdaabbabbddcbbdaabbabcabaacddaccdadaabccbacbbdacdbcbccdcbcbcaaadaccdbcdbcdbdcbbaaadcbddccdbaabddccdaaabaacbdbbabbcdbbdcccdaaaddbdaccccbacacaaabcdcdbdaabdcbbbacaddadabdcaaccacdcdccdcbcbdbdaadbaddcbdddaadcbaccadddbbcacddcdacdcacdcadadccccbdbabcddabcbabcacabbabddbaacaddcabbacbdcdccdbbabcbbaccbabcadbdbacdcabbaadcadddbbdacbbcaddcccdacdcbbbacdacbccbccccbddcdcdbdbdbbbdccdbdccadbddbbcdbbabcbdbcaccbaabbacabdcbdbcdcaabadaabddbddbadbbcbaaaaaccccabdcddcbdbdddbdadcdbaabbabdacbaaacbbcbcacddbbaddbdabbadddbccbbbdadcdbcaabcbbbaaababcabacdabbdbabdcbdbccdaaaadaddcbbbdddacbbaaabbaadacbbacdabbbcaababcbcbbadbaacbcabacaababaddccbccbbbcccbdbccddabacbacdbaccbdcbaddddbcbcadbabbadaadbcbbabadbcabdcbadbcaacdccdbbcbabbbbadddacacaaccadacdadcadbabbcddcdbdbbcaaaccacdbdcadccddccdabcbbdcbaacabbacacdbcacbdcaddddabdcaabdaaaabdbadcbacbcbabdbcabbbbbcbcabbacddddddaccdbddabaaaccccaacccddddbccccabbababddbdcbaabcabadbcccbbbddbabbcdbbdbddcabdcbbbbdbcbbcbbccdcaabbbabadbabbbababadbddcdadababdccaccaadcbabdacacbaaddbabdacaaabdbadbaccbcdaabdccbbacddcabcdbcbbdddbdcbabddbcccdadaddbbcbabccacbbbdddcaacdcacbbddadadbcabddadbbcbbbbcadbdccbabbbacccdadbcdbdddbdbaacdacbaddbbbdcbaacabbcaadcddbbadabddacaddbbbddcddbdcbcbdcdcadcbcacadddcaabaacdbdadaadcacacdbdbbbaccbaabacdbadcbddcccdcbadcaddbbbaacacabdcdcbbdbdbabcbdbcddcadbcaccaacdcdcdabbdcbbbcbabadcdacdbaddacbdaababcbdbcbadcadbacbbbbdddadacdacaabdcdaacacabbcdabdcbcccbcddcbadadbcacccdcdddbcaaddbbcabbccdcbbaccbccbaddcdaadbaaddddaccdacbcdaadabbdabadaddbdcbcdbabdbcaaddcddcbccbcaccdaacdcbdaabbddcdcbcccadcdcbdcabaabddddbdcbcbaaaadcdddacbdaaadcaaddddbbaadbbcaddbdbadaabcccdbbbabccdaaddbacaabaccdabaaddbdbbdbbdaabadcdcdbadbddbdbdbcabdcacbbbddaabdbcbdaacbaccdcddbdacddbbbaabddadcbbddacadacbdaacbdaabcbddbbacdadcbcacccccdadbcdcacddbadcbaddcbadcddacadaadddabbcbdaddcdcabddbaaadbaaacdbbbdcaccdadbababacadacbbadcacbcbaabdabcddbcbcbccacbcbccadbabcbdcacadcdadbdbaabdccddacbbabcbdcdcbcdcaaccddcdbdbddacbacdcbadddaadadadbabdcbccadabaaddbccbbdddacabbbabcbaccddcccbbdbaaccbbccbaabdccbcaccdadccddaddabcdcbdcbacdcadadccabcbbdabcabdabacbaaddbacdbcddbdaabdabbbcaddaddddbcaddcccbacddaddaccacdbbbbcdddababccabcabccbddadccbdbadabaacbbaaabcbaaaaaadaacbcacbbcbababadabbaacbbaddbdabacbcaabcaccdbbccadabacacaadbcdbabdabddcacadbcccdacaddacabbbabccbdddcbdcdcbdbbbbbcaaadcdaaccddaabdcaaaadbcdbdcddcdbccadcbbaadcacdcbbbcacabddbcbacabacbdcaabdabdbabacbaaccdbdccbaabcdbbaabadbdadcbadcbbacacabaabacadbbacadbbdcaddddccacdcadccdcadacbabdbcdddbbacadacdaabccbbcabaccddccdaadccadabdcaccababbdbdbbbacbacababbcbaddbdadcadddcadcdccbcabbacadbcbababcaacdbcabbdccadcaacccacbbcbaadaaadbadddadbcdbbacbcbaaadcbcdacdcbdadddcbbbdbdddaaacadddaddacdadddabdccdbabbcdaddabddaacdacbacdaccddbacaadaddcabadcbcadbbdabcdcdcccbdbbdaacbcacdbcdaacdcddcbaccadcdcbacacacbbaadcdabaaccaadaacaabcadacabdaaabccacddcacbdbddcbcdabbcdccacdacaadcdcacccbcacddbacaaddaccaacdccaddabddabadbadacbadddccbccbccacacccbbbbccbdaddbccdddbbdaacbcddabbcaadaaaddbdbdbcbdcbaddbdabacabbcabaccbcbdcdcdcabdcaaacdddcdacacbcabcbbcccdbbbaadccaaacbcddbabdddaaacbbcaddabaabbabbccacdcdcbbaddaddbadbaabdbbcacdbadcddcdcbcdcbdcccaadcabbaacbbbbacbacdbcaacbccbcaacdbdcbdbddbabbdccaaccdcdccbbdacbccbbcddbcddabadcbdcabdccdcbabdbddbdddcbdbadadbcbbaabbbcdcbdcbabccdadcbaccabccaadaddaaacadcaaccdcdaadbbdbaacdbbaaabdadabbdacacaacdaadbdbadcaddbdacdaddbcaaccbaaababacacddbbcbbddabdbddacbcdbaaadadcbddcbdbaacbbddcddbcbacccadbacdaacddbabccdcabcbcabacddbcdbadccdaabccccbbdbdcccacaddaacdaabccacbabcaddbcadbcddbdcbcabcdaadbdccacdbacddaadcdccaabdddbdcdbcbabacbcaabbaabccabdccbcccabcbcabcbcacbddcbcdcaabcccdcacaadadbbcbabcaacccbacbacdabbbbadcccacaaccabbbbcaabccbcdbdcbcbccadbdccddbdddbcdbbbdcdbbaaaaabcaccdabdcbdacaadddabaccdadcbdaccccdbdbbdadabbbadcdcccbcbaddcccdbcbdadbaaadbddcdadbddcabcadbabbccdacbdacabdbcaabcdbcdcdccdaadddbacbabbbccdcacacbbbdbbccabcdcdaaabbbdaccddcadbabdadacbcbbaccaadbdcdcabcbacbcbdabbacdcaddcddadccacdaacbdbcddbdcbbcadabbacbaddabdddbbaadadadacdcddddbdaabbabbdbaabcdacbdccbcacdbbcdcddcbabdaacdbcdbcccabccdadccbabdaacbddbaaabcccccccdcbabcddddabccbbccccbdbdbdcddbaadadbadbaaacbccdcdccbcabcbcccaddbbbbdcaccddddadcdccbddbbadabcddaabaabdbbaadaaacdaddbdcccadbacddbbcbaabdacbdadadcbccccaaddabbccccaaccdbdaaadabcccabcdadcbddbcbcbcadbaaccdcacbabaccbbdababbacdabcbacbddabdaaabdadcbcccacdddcbbbdcabadaaadaacdbdbccdbddbacabcdaadbabcacaaacdcbbbabaccdcadabbbaaccacabaaccbaddddcdaaccdbbbadbbacdacdbddadbbabdbddccccadbaaacddacbbcacabddcbdbbdacbdcdddacacddbadaabcbacabccbcccacdaacdaababcdcabdacdaaaaabcbbbcbaacbddcdbcbabadbaccbdbcbacdcdabddcabdcdcccbdbbabdddaadacbdcadccdaaddadaddcadcadcacbaccbdbabbbbdcdbadbdcbbdabbdbcacdccbcaabbcbcdcaacabbbbacbabddadbaaccadbaddabcabaadaaaacadbccdcaadcdcbababbccabdbdccabcdcabaaaaddadcbddabbbbbddcadaabaddbdbdddaaacadbdbccabaabdcabbddddccdabaadbdabbcbbacbababdcdaddadabadcccbbbbdbbdaabcdbcaaddaddbcdcacdbddacaacdcbacdadcddcbbbaadcbbbdaccbccccdcccbbaddaadbdadcdcdabdbddabbbdbdbdaccbcddbadbadaaacabcacbdaccdbdaadbbcbcaccbdadacdbbcbddddadbaabbadbacaabccbcadbcdcdcadccbddbccabbdaccccbddbabdadccaaccdadddababdbccbdadabbcdbcbcbdbadadaccacdbcabbaddcbbdddbadddcdaadabbacdcdbaddbaabccdaaabdaabdbddcdbaadaadcdbdbababccabadcadddabcacaddbcdcccbbdabcabccaaaadcbdaaabcdaacacccccdabbabbbacdcaddcadbabcacadbbabdddbadbdbdbbcdddcccccbdbacbacddbdaadbaabbbbcbbadabcdaaacacbbccadabbbaadcccbcdbdabddcadaaadcacdbcccbabbbbaaccbdabacbabbcbdbdcbaaadcccbabcbacdcdbccdacbabbbccdbbcccddadbbdababddcabacccddcbbccdaddbdbdbdddbdabadcbcdabcaabbdcaaaccacbbbaccacbbacbadbddbbcbabaaccabbacaccabccababbbdaaabdcccdcabadaacbbbcdbabacdbdabaabacbdaabdcdbcdcbdadacbbdaadbbcccbcacbccbbbcadadddcdbcabdaddbcbcadcaaabbdbcdaaccdcddbbcdaaccdcbbabcbbdaccacdaadabddbacbbcddaaabaddcacdabddbcddabbbccaacaccddbdacdbccabcbcbcabcaddadacdccdbaccdbbbdaaabdacbdabaacbacdbaccaddddcdcadbdcacdcaadadadbbbdddaadaddabbcbcbaacabaacdaddcaccbcaccbdcdaabbcbbaacccdaadccccacdddbdddddabbacbccbdabdabacadacccdaccbbadbbcdbccbccacadaddbcacdaaccabcdaaaabdacccdbbdbccaacaacbcdbdacdaadbdadbacadbcddbccaabcbabcdabbbbbcaaacbdbcabbcdbabaadcdcbdbabacabbdbdddabcadabbdcbcbbabdbbdaccddaadddabbbdabaaacdbabcbcbbbdcdabdbabcacccabaddbddaccabdaaccddaaabbbaddaccdaacdccdbbcbcdbbdcdabddbbaddabccbaccddadbcbdbcdabcbdbcdadccacdcbbabccbcbbbaadbcbdbcadcadccbcdccacbccaaadcbddaccddbdacaaddabcabdbddbcbdcdcccccadabaacccaabcbdcbcaabcadbbcbdbbbaaacccdacddbccddcbaabbcdabaccbacdcdabaccabcdddddbacccdcbabdadddbbbdddaaaabcdaaadddbbbdbbabcadbbdcbbbbddbbcbaacccdbcdbdbcdcbbbbbbdcababbdccdbaadcdadcbacabcaddbbcabcadbaaacdbcdbbcaaaabcbccdaddacbdbcadbabbcbbacdddbccbbcadccbbadcbbdbddbabdbaadbbbddcadbcccacbcccddbddbcbdcdcbbacdbcaccbdccdacabaaddccccdcabddcbbbccbaacadcacbdcbacbbcccbdbaacddcbdcdabddbcbbcdbcdcbadacaccacbbccdcbabddbcddbbcdbcddbdbbadbaadadcdacdaadbbddbbddacabaccdbadcbcacabcdaccaddadcdbbddbbbacaadccdbdcabdcaaaaadabdadadaababbcbdadaaccccacbadcbbbcbcaccccbadbadacbbdcddbddcdbdbadadbcababaaacabacabdcdaacaddacaabccdaabdddcbdbdaaddbdbcaaadabbadacdaddbadccaccdcdaadbbaadbcacabbccdacabacdaaccabcaddbcdaabcbbdbabdcdadbcddbddacdbddaaaddacbcbaadccbcdbbbabddbdbbcdbadaaadcddbadadaabcbcbcddcabadbbcabdccaabdaaccddbabdddbcbbdacdcbbdddabcbbbcbbdbbaadbbacbdcacacadcccbcbaaadcabdccbbddcbbbbbccdacdddcdcbabacdcdcaabcdbdcaccbbaaaabdbcbcaccbbadcacbdbdaccbcabcabcabcbacdbdcbcdcddcabccadadbbacccdaaadcccbaddabccbcccbddccdbccacacaacabcaaadbbbaabddbcaccacddccbdacaaabcdadbdaccccacadadbbdacdbbcbcaadaddddccdaaddadbbacbbaabcaddbacaaabdbddabadbcbdbbbdcbddcaaadccbbccbdccacbbdaacdaccbdbbbabbaacabccbdbbaacddbaccdacdbbcbccdccbdcaaacccddbbcaadadacadcdbdcaabcddbbacacabbbdccbbcadcccdcbdddaabddbccacdbdabddcbbbabbaaadcdbdaacbbdbbaddbaddabbbadbbcdcdbacdbbbcbddcabdccbbddbabdbbbccbabcbbdacadcdabcdaccdbdcabdacaaabbdcddbaaaadbabbbdbdacbddcdaaaacacdaabdcaacddabcadaadddabcdbabccdacdaccaabdcabdaacabdacdcaddcccccbcccdbddaddbbadbadbaaadacdccdbccaabdbcadadcbcacccababcdcccccdabbbacdccdbbbddadbdcabcadbbbbbaabcccabcdcdaacaadbcdbccaaabbbddbccdcccabacdbaaacabcccaacdcccabbacdbbdcacacdbadccbbdaaabbaccdddabccbbacddaabbcccbaaacbbcbcbbbbcdcbdcbccddaadccbbdabcbacdccdbacacdcaadcbbcbdaabbcdcbcdbaadbbdcbabcacbdcacdabdbabccaccbcbbbddbcbcdadcabdddadddbddccaccdacadacdcbddaaabaccaadcddcdcbbacaacdcdaabacbabbabbbcccdcccbaadcbacbabbaddabbdabaadabadcddabbacdcddbbccdaabbccaacbdcddaaddcadaadccbccaaddbcbccdcacdbbcbcbabcbbadbcbbaabcaabbbbacbdbbdcdbdcdacabcbadabbccbdadcdccdcdddacbccbcddcadcdacbadbabdbbadcaabbcbccbdacaabaddaaababcbbcbcdaaddaadcbaaaaadcaccbbddbcccababdbdcddbabbbaadcbaaddacdbaccbcbdcaddccacdccbdcacacccbcabddcabdccacbabbacabbcddbadaaabccabaaadbaabdcbccdadccbbaaccdcbbdccabbdcadabcacacaaddaaababbdccccbcbacbcdaaddbdbbbcadbcacdcabbcbbacccaaddcdcaccbccaadacacbadbbddddcdbcbbcabacccdbabdabadbcccaabbbcbbcabbbdbbaccaaddabbdcbccaaccbaccabbcaadadacbbcabcabadcbabdcdabdddbaabaabccadcdcdadcccbcabdadacacdaccdccccbacdaacacdcccdcbaadabbacdabcadababbdaacadcdcababadcabbbcbdbadcaaaaccbbcbaadabdabbcacdacaaddddbabbbadbdddddcddbccdbabbbaabddacbcdbacbabdadbcdbbcbbddaabdcabaabbcdbadcbababbbaacdbdcbacdcddacbcbbbabdbdbabbddbccddadcbbbddbaabbcbbbadcbdabddaccabdabaaaaadcacabbaddbacbadcabdaddddbadbdbcbaadcdabdccbcdbdcbbabdacbbaaabccdadbadbdaddbabaaadccccccdbbbbcbdaacbddbaacabdcadaddcdbcdcbdbaabcddbbcabccacdbcdddbdabbbdcbabaccccddbababdadadcaabbcacdcbbcdaaaaabbbabacdbadbccbbaaadcdcacdbccdaacacacbbbbabdadbaccaabacbcbdbbaccdaacbdbbdbdaadcbbdbcdcaaadadabddcbbababbdaacbcdabbacaabdddbccacbabaccabddadbbccbdbccadbdbbbcddbddbabcbcbcbbacdbccbbcdbdabcdbdaabcacdbddddbabcabbaddaacbbbcabacbbddbbbdbbacaaadcdabaccadaababacacdcdbbbabdbbccbdddacbddcdadbadacdbdadaddbdcaacbbacbbddcdaddcadbdcddbabcbcdddacbcdbacbaddadcbadadccbccaaacbacbadaababbdaabcdbdabbbbddccdaadbdcadacbbbacbabacbdacaccccbddcccadccdabcacdaadcadaaacbbbdaadadbabacddbdacdddbabdcdbdcccaddcbadabcaddcaaadadcadcdaadadadcadcdabacbbdccbbadadabaddddddbdddaccbadbaabccadbbbdbbdacbcabccadbcadadbccdbbdbdcaabcddcddbbadbabcdcacacdcabbdcdabcabaccddbbcbacabccabdcabccaaaddcbcaacadbcdbdcacddbbcbcccadcbbccdbcacdbdaccaabdbcdbddadcbacbdbdbdbacaaccbaaddadbcadaadbbbccdddcbdbcdddcbcabbabadaabddcacacdbdccdddbbccaadacabaddcacbcddcaacbbbadbcdabdbdabbdbbdddabbccdaddcbbcdacaabcbcbaddbadbadbbdabcabddcacbbddadbdadccddadbdcdcdcdddcdccddaababaccdbcdbdcddacccabcdcbbbaaadbbcaaabbbbdcaccbbabadbbabbbabcaabdbbabdbccdadcacbacccbbacaddcadccdbcbabcbccdcadcbddbdabccddbdcacbcabbdabccaccadcacababacbbaccbbdbddaccdaccdcdcaaaacaadccbcbdabdbadbcddbccabdddbacaacdcccdaacdcacadbbacabacadadadacdcacbcbdcccdbcdbbdbbddbadddbcbbacbaaacbcaccdcccadbbccdbbdcdacabddbbabcdbdbbcdcabcbabdbdcdacccadbabcddbbbbabbabadcacaabdcdabaddabcccaaaadcdccbcbabbdabbdbcdacadcaacaccdabdcabcdacbccddcdcaccabbbccbadbbcdcacbbbdbdbbdadbaddaccbcabdddcbcbcbdbdbdcbdaaddcbbbbcadadbabbacdabdcdaccacbcacdddaaccbcdbddbdbdbaabcdbdbbdcadbbbaadaaccdcbdcacccdaabbbbbbabbdadcccabdccaaccccdbabbcbbadbcbdcbbbadbbbaccadacbabdddaacabcbbabdaaddcbdadaddbdddbcaabaabacbbaadaabdcbcaaabdbbccdcbabdbccaabbdaabccbddddbcbcccbabccdcabbbbdbbcdcbadbaccdaabcaaaaacaddaddbaadddbabcbbadabbdbdabacbacddddabddabcabcbabbadbcdadbadbbcacdbdadaccbbabbaccadcacddcadcabacbaccabcdacbcdccadaadabbdddbdbbadbcdbaadadcccbddacacbbccccbaacbddbcaddadcbcabccdabcbcdbdaacabddbadbaaacdbadbaacbdddaddabcdabbccbbdcdabdaabbbcaaadacdcccbdddaddaccdcdaccaabacccaabddabccdaccadcdbbcadcdbdadadabccabdaabbbbcaddaabbbbabbacbbdcaadbaddbcbccadbdccdcaccbaadbdabbcabaaddbdabacbccaddadcaadcbbdcadaddbdcdcadcdccdbbdddaddaadcddbddbcabdccbddcbaccbddcaabcdabdcbbcdcbbacadcbcacaaddbadcacacdbdbdaaaaacdaddcbabccdabbddcbddccbbbbddbaddcaaddbcbbbcccaddbbbdcbdbdccbcbbcbdbcddaddbddccddadbdbaabadcbcbbbdaddddcbcbbdbbcaabaccbbdacdacabbdccacddcadaadcbdaaddbdaddabbdaabbdbcdbcbdbdddadcacbbadadaabcbadcacbdbdcadbaaacbcbddaccbbbcdbbaaabdaaaacdbabdbccadacdaaccdccaddcbbcddbbdbbabddcbddadabbabdabdacbbbbddaaadbdcbbbdcdcadcaccdbbadbadcadcbabcdddbbdcacbaacaaaaabaabdbcaaadddaccddcbbcdcaaaccddbaadbcaaaabacbbcdcbabcadcaadcbbccaabaaabcdadccdbcbdcadbcdaabddacaadcdbcbcdbacadbbcadabcbdccabbcdcdcacacddbbbaacadadaaacbbaaddbdccdabcbbcccddcbcccdddbdcdaccdccddcbccbbacdbddacadaddcabdddbbddaaddcbccdaccaaaddaabadadacdbdcabbddbcddcdbbcbcbccaabaccaabbddcdddadcccbbcdcadcaabaddbadcabcbbbdabddbcaddbbabbddccdbacadaddbabcaccdcbdbcbccbcadacdcbbbcbdcdadbbabaadddbdcdbcbbaddbccbaabbddacbaabbdbdaaccabdcbccacabddddcaaccbcabdcabcabaacdbbbaaccbbcbadcdbcddddcabaadadcbadcacccacccbabcadbacbdaacdabbbadbcacaabbabdddbbbdbabbacdbbcbbcdcadcdcdcaddbadbdcdccbbdbcbadcbddcdddadaadcdcabdddcbaddcdcccacbccbdacadbccadbaddbccbaccbbccdcacdadbdcabbcbcaaadcddbbbdddcddbddcaddcaddbbdbcccddaddbbbaacabbcddaaccdbbabdaaabcbbcbcdbcaaadacdbdddddddbcbaaabdabadbcbbcbabcadaabcabaabdadbdcaadddddbdcadbbbccaabbcabddccbdcdbcdccadbcdbbcbdbccbbadbaadbadbadcdcacacdbbcdbbabbcddbdddbcdbbaaabcdcbabaabddddcbbbbadccabbabbbcabddacddcacbadcbcbaabdcdacbcdbdbdadbdcbdcbddcccddaaabbccacbcbabaabdcabaabaaaabbcadaadcdadcaddcbadbddaccbcbadcbbbdbbdddacabcdbdbddbccbdbccaadccccdabcdadccadbbcccaddbaabcaaabcdaccadbabadbcdddadadbcbbddaddacbdabdcccdadcddadcabdbbadddccbbacbdccbbcbcdaacdadbdccacacddddcccdaaccaaccddcbabbaddadddbbbdbabbabaddbacbbcaaaaddbacdbbcccdddababdbccbdababbbbacacdbaddabccadcddbabccccaabccaabcbcbdcccccdbbabdbbaacbacbbdccdbcbadbaaaccaaabbdaaaddadaadaddacadaabbbbbccddcadccbadcbbbadadabddbadcddabdcddadddaabacbaaaddbbccaacddaddbadcbcbbacadbddccdbcabdbcbdbbdbbacbdadddbbaaaddadabcaabbdabcabbddddadbdcbacdaabbdbdbdabbccdccbddadccccbaaaddcaccbabbdbadbbcbdaaabdcdbbddbcddbbbaccbdacaadcaaaddaddccddbaccbbbbcbcccaccbcbaadacaaaabcacbdaadcabbdbbbdccdbbccbbcdbbbdadcbcdadddcbdddbcdbdccbcabcdbbdacacddcababdbddcbadbbdcbbabadabccbccdbcacdcdaadbbaadadbdcbcadbccddaaccdcaaaccbdddabbddadcdabaadacbccbcadcabcbbcbdcbbbdbabbbaabbccbcacacacbdbdbaaccbdcddabddbaaaabacdadbddbcabcbccbacaaadccbaadbdbabcbacbbacbbbccbcdccddbcaabbdaabbaddabccaaacaaabcabbdccabbddaadcdbaabccccabacbcccbccbacadaaabbadccddacacddbddcdbabdcccccbabcababcdaadbdbddbacbdcbadacbcaabbbddadacbcaacccabdcbaadbcdabbadbabbcdbcabdcbcbdccaaccbabacdbabbcadabdccdbacaaacaacabcdabacddcccabcccdaaaaabdddaccdccaccabcdcaccccabbddacadadcbadccadcadbababaabbadaaabccaacddbcdbbaccacabbcdddacbcaccdabbadcccabbdcaddbccacbbbcabdbbbadbbbabdaabcdbbbcbddabaadbabcdaadaccddcadcbcdcdbdbabbdcdbcdbbabdcddbbbbccbdadaddbcddabdcaccabbcacdccbdcadcbcadaaddaddddbdabcccdbdcbcadcdbacddcadaaddacddbadaaadacbcdcdbbcaacacddaaccdadadaccddaaddabbcabbcbdabbacdadaaacbbbddbbaacacdcaccccbdacbcbddbcacabcacbababcacbdbcdbbdaacddcacbdcbbadbbaadaacdabccdbcbabbccabcaddaccccadbbdadbbcbbddddcbadabdbbbabacbcaabcdabdcdcbdadccbadcddbcacbcacabbcabbcdbaaacaddabddbbbcdcacbdbadcbabaabbcbbdcbbddbcdbdbdacadadabbcbdcbdaccacbdadcbcbbadccdabdadddacbdddabcbdaacaacbacbabcacaadaddcdcdbcbbaaaabbabaabddacdcddcabadccdbddadddcbaadddbdbcbccdcccbbabdaddbbbabbccadaacdddacdaadcddbbcbbdcbbbccdaacaccccccbdbdcbdacbacbdcbdadcdccbabccdcbabbadbacdbbaaacddcaccacabbcdcaabacdaadacdcdbacaabddbcdaccdadacdbdbaaabbcbcabdbdbcccbacaadbdacdcbdccccadabacabcdabcbadcaadacdacaacddcaaadbbccdcdbddbcabadbacaabbdcdbbaccaabdcbddddccacbdddbcbadbbcadbbcaaddddbdcbdbcbcbadbbccdaddaddccbdbbbdadcadbddcbbdcccacbdcddcbbbbbbbadabdcbcadccdadbbadcdcbabddbddcacdaadbacdacbadabaddaaadababaaddadbcddaccaccacadbbaddadbbcbbadddbadabdccbaacaabdccbdbcadcccbdabadbdaccccbacaabccdcabcbcdcaabccaddddbbddbccabacccbabddcdccaddcbcbdadbaaccbbbacbbbacbbcaaaddbdbdaaaaccabbbbdddbcbcaaccaacccbacbdcacbbddcabbadcbbcdaabdbbababaaabbbacbbaddbdacbdbdbbdbacadcacacddbdcbcbdadadcbdcddcdabbbbcccadcbabdcddcaaadddbdbdadadacddbbccabbdbabbbbbbdabdbaccadcabacbbadcddcaacabaddcabbcdbcabdacbdbabcdbaddbbdcaddcaaadadadaabbccabbcbacccddccdcbdabccabccbbaacaaadddbdacdcdbaccbcdbacbabbddcbdcbcbccbbbdacbcdcacbdbabbcdcddbcaddcdccdcacadccacbacddbccaaadaccddbddbacddbbcbaabacadbdadbbadbcadabbddabcabadbdbdddbadacdaaccddacddbabdbadacbddbdbaadaaddbcacbdacbaaccbbbbabadaaddbcbbabbcaacbcdcbdccbadcabdbdaaddacbbbbbcacaadabddabdbdcbcabdcaaabbacdbdcbbdcacddaacaddcdcdbcadbbcddbaadcabacdbaacbaccddbdabddaabbbabadbadcccaccbbbacbbacddcdadadccbaddbbaabacdcbdcdcbdcaccbdbdaabbccbaddabadcabacaacadabcddbacabdadccbddcdcdbccbadacddbbcabcbddcccdcabcabbbccaadddcdbbbcabddbcbababbdadabaabadbbcccaccdddaddbcccaabbbcadacdbacddabbadadcccbbcbdcabdbdddddbcacbcdabbdccbbdccdccbaadaabdaaadcbbadcdcacabbdbdaabcccdbcaadcbcdddbcdbbaabcdaadbbbccdaabaddaacbcacbaaabaacbbcccdcaccacadbdddbbccababbacdabcdbabdbbdadababbbdabddcadaaacdbdaadccdcdbbdbdbaccacdcaccbcaaabbdadababcabacaadbccdcaaaadaabdaccdbbbcbbcbcbadabacaaccbacacdadcadabddaacbcacdcacdbcadddbcdbdababbbbccbddbaaddcacbaaabbdcddadcdadbaddddcadadbbabbabbccaaaaccabbdbcbcadbdbcaccddabbdabdaacbadaaccbccbadadcbbacdccdcdbadbdddddbcbdcccdbdccadaabbaccbcbcbccdddbdadcdddbdadabccbdaabcdbccbbdbddaccacccaabbbabaccbcdaadbadccbdcdcadccbbbbaabbddadccbdacccacbaaacbaaccacbadacabbaacbaaccadaacacdbdbdaacddabcdcdbbdcccbabddcdbbddcbaadabadaaaccddbdbccbacdbcdbcacacbbabddbcacaaadbdcdbbabacdbacaaaacbdabdddbbacbdcaaaaadbccddcbbadbbadadabaddacdaabbddcaabccbbcdaacdbccbccbdbbdcbbaacbbdadaaabacddbadadcbdcbdbaccddddbbaabaddbcbabdbbadacbbbddbdacbcaacadbabadababaddabbdcbbddcccdcabadcaabcdaaccdaacdbdcacabbdbcaaabcdaadcdcabaaddbcbbccbbbbcaacadddcacccabcccdbbbdaabcdbddbacdcddccaaaabcccaacbacdbcbaabbdcdcbdcdaaccbbbbbdaccacdbdadabbdcbadacccdaccadacdbbcbaabacdbaaddaadbcadacbadacdaaadddddbbbbcdbdcbadddaccdaacbadbcbacabaaddbcbcaacacabbbcbbdccbadcacacaadbacabaacbdaabdcbdcbcacabcbcbdbbbbdaabaadbadbadacabacaddbadccabdaaaaabadcdbbadbacadbadabdbddcdabbddbbcabcccbcbdadcdcdbaccdddbaacaacbcbaabbddaccdadcbababdcbcddbdcbcbccacaabbccdbdccacadbdcccccddbcaaaaacbdbbcabcabdabcbdabdaddcbbdcdddabbddbbdadaddabcaccbccabcbbcdaadcbbdadacdbddcbdddadacccacccbdbdabdcbdbbabddddacabadcbbbdbccdabcaabdddadbaabbdcbcdabaadbdbadbcabdaabadbddabbdcbbbcbacdabdbdddcddcdbccbabaaaadbdacdbccbadadccdbacdcdbdcccbbddabadbcaabaddacbabbacbccabdabcdbccadacbdcacccacadccddccdaacdaabbaacbdcaadcdcccabbdaacbbabdaacdbbcdaaabbdcdbcbbbbccaccbccccddacbaacaabccacccbcbdbbdacbdbbdcdcdcdbdabcdadddadabdbdcacbbaacadbcdcaaacdbddabdcdabccabddbbdccbcbaaadbddacccddadbbbcdaadbcbacbbdbbcaadcdaabdbccdbddbcbaaaabbbaccdbcadcbdcdddaadcdbbbabdcbddbdcabcccdadbabbdcddcadcacccdacccbbaccdbdcabddabbbaabddbdccabddacdbdbbbabacdacacbcacabaadacbaaabbdddcbcdbbbadcdcdcbbbdbbaaaddcdaaacbaaadbdbdaaadbdcaaaccaaaddbbacdcdadbddbccdabcacdccbdacdcbabbaadbddbcacccaabbacbbddddcbbcabbdbaddacaacddbdcccbdccdaacaccacaabacbabaccbcabbadbbbaadcacccbadbaadadaaabdbdcbdaccabddadcaddbddcbbdbadcaccdbabdabaabdcdbbaaabdaddacdbcddddbaaacababcdcbdadbbdddddcacababcacabdbaccddcbdaadaaabcbbbdabdaccddaacdcaacaadccaaadccaddbaaababbdcdccbcaddcaaaaddbdbccabaaaadbbbbbadabddaadaadcbcdaaadcdbacccabcbbdaaaaccdbcbcbbbddbbdcdbabbddcddaccddcbccdacaaccddaabccddbacddabdbbaaabaacadcccdabadcbdcbdcbcbbccbabadbdcdbbddabbcbcbcbcccdcbccbbccbbbdbcdcabadbbcdcdabccdbddccdcdaadacaccbddbbbbadaddcdbdcdabaddbacbcdcbacbdcccdaccbdbabdaaddacabacbbbbdddacabdbadadbddadcbbbaadddaadbbddacbdbbdaadbddbcaabddaacbbbcbbdabccbbcdcabcadcabcaacadbdbbabadcacbcbcdbdabadbddccacdccddadbabbabdccddcdddcadacdccbcacaaadadcacbddbabbabcbbadccdcccdcacbdcdcbccbcddadacbcacadcdcdaabbcccddccdaadbcaccbbbcbccbbcddcdcacdaaddbdddcbbabcbabdabcbbacbcccbcabdcacbddadabdccbbcdbdacaadbcdaadcbbabcdbbbdacabbdbabbddaaabbcdcdbdcdbbbcbccdcadcbcccdbbbccccddaaabaadabdcdcbdccacbdbcbbdabcddbcccbccdaaacddcabcccacdbabbbcaadadadacddaddbcccacbcccdcbacddbabcabcdcdbdbdddddaaaacbacdbaacdbaccbbcdaddadddcccccbdcdccbbdacadccacdbcbabbcaaccbabdcdccaabacccbaabbbaadaddddbdcdbddcddaddacbcacacbccccaaaadbbccdabcaacdababdddccdcbcbbddcdcacaaaabdbabaccdadaddcdddcbabbaacaaacacbaacbaaadaabdbdbbbbcbddcddddcbbccccadacdcabcbddabbabcbaddacccbcbaacaacdacabbadaabcbdcbddcbaddbbaacbaadcaaaccddcdabbbcccddcbdcabdabddbdaababdbdcaacdadccddacbcaaddcdccbcaaadcaddadccdddcaacdabbcbaaabbdccbdabdacdabcbacbabadabdcacabadbbbcdbabbddaddaadabbbcbdcababbdcbadbcabdaadaadbaadddaaadccaaaabccdbcdaabcbaadabbabbcdbbbcadcabbbaabaccabccddbddcbcbbadccbdbaabbdababdddddbbddcbbaadadcbbbbacabadddbcacacbccaaadcabbacbccdabdacadcbbacadcdabcccabbdcabcdcdbdbdbbcabaabcabdacddabbacaabcadddabcaaabddcddbbbdacaccababdbacdbbbddcbbcbbcaadacabcbabadacacaddbdbaacdccbddddcbbaaabccccaaaacaccacbccbadcbcadbcbacadbabdbcaccbcbbbbdaccaacadcdbcbdddbcdcbadddcdbbbaacdaaacbdacabdababdcddabdadbccadcdaadbbacbcdaaaccaaadcababaadbddbcdabdbabcbdbbdbaccaaaabddaaddadabcdcbdacccccabaaacdbacbcddcdaaddcbbdaccdddabcacaaaccccdccccbdbcdbcbdcacacacdacacdbdaaddadbbdccbbdaddadbdbccdbdbcbdcadadaaacbabadcdbaacaadbabccbadcdddbbdcdacdcbaaabaccaccadabdcabdbccaabbaadbbbddcbcdccbcacdabadccbdcadddadcabdaccccbbdcdcbccdbdccbccdbcdbbdcbccbddaaacbaacdbaacbcdbccdccaddbabadbccaccbcbbabddcbcbcbddccdcaaabbacadcdbbdbdcacbbcbaacaadbccbadcababbcdadbdbabccbdcadaaabdbabacdcadcdabcdcccbbdacdbbbcdddbbadddadbbadbdaaaccdcccbdadaaccbdcbbabcddcadadbcccbdacddbcacdbcdacddbbdadbbdccbbaaddcacdaacaaaddbadbbcabccdbdbadbbaadaaacaaabdbbbaccacaabaacbcbabdadbaaddacbcbabdababdadadadbdbdcddacaabdadacabdddabcdcabbaaabdabccbbdcacdbcbbdaabaaddcdadabcddabddcbdadcbcbadcdbdcddacbbcabaacdbbadbaaddcbabbaccaaaacbccddbdcaddadccbcdbcbdabbdbbbacababbddbdbbaccdbdbbddbcbabdcacbbacdbcabcacacbcabbaddabdcadbddbdccccaacbbbdabcdacadaccbcdaaaaabadbbdbbcbddabcdbddcdddadcccccaccdcbacccccdddbdacaacaccbcabaacdadacdbddabaaaadcdbcddbabcabbcbacbaaddbbdbabbdbdadbdddbdbaabadbaabaaadcadacbacabbbbcdcaacbbdacddabadcbabcdcbcaabcacdacabcdbccbdaadbcccaacdddbbdcaabcbdbcaaaddadacccbabbbdadcdcdaadabcdbddbaaaacccadcabbdcadaadbbddcccacabaccddabdbacacabbcdacacdadabaaddcadddbcdccbdbdcccbdabbaaccadccaacbabbabdacdcacddcaabaddabadccabcccbcdaccaddcbacdcabbddaaaaddaabacddaabdacadddcccaabaddaaddaddccabaaabdcacbdcacddadbccdaaabdddacbbdddaacabbdadccbcdacaacdacddcdcdaddbaddaccdbcaadaaaabdbcddbcaacaccaacbbaddbbadbbbaccdabbbbdbcbcbdcacbccbacbcadcabbddbbdcabcabbddaaccbcccdadadcdcbabcbbdaaddbbdbbcdadccbbcddaacbadaadbccadccbdabdbdadbdbabbbaacdcdcbbbdcdaabbadcaadcccabbdbccbddcdcadbacacbcdddcaacaacbbdadabaacddabccbcdadaccbaccadcbddcbccbdacaaadaadcdbaaccbcbcbbddabaccbaadcddadabcaadbdcabcbacbbdacccadadbbbcbddcaaccaadcacdbadbdacbcaaadcbbddbdacdadaabcbcdbbaacadcbdbababdcddcccdabcbaddddcbcbacacdabbabadddaabdabdabbaccbcbdbccccadaaaccdbbddcddcbadcabadbcccabdbddcdddccdadbbbdaaccdddbcaabbcdbbcccbadcdbdbdbcdcadcabdbaacbacbcdacbcbccabdcbcbcadadddadaadaddababdabbadaadbdaadaadbabaabdcddaddbdcaabadcdbccdbbbbddddccdcdcdadccadcadbadddcacbbbdcabbbddbdbdaabcbdacdbbbcdacbdbbbadacacccacacbdcbcdacdcbacadbbcdcaccdacdbbabaacccbbaadcabdcdbadcbcaaacacaadddcccdabadabdcbcaddadbbdbdbadddccbdcdbabcaacbbabdbdcbadbddcbcaaabacdaabaacababcccbbbacacdaabbbddcccdddcbbdddcbdbaacdbcacbcccadcbbccbbcdddddacdacdacaabdabacbaadccccdcbdbdcdbadabcadbcddacbabdcdababbccaaccabdbacaadaddddddbaddcbbbddbcdbacbcbcdcadcacdcbbcadbbdabcaaaddbdbddcacbacdadbcdbaadbdadbcbddaccabdbbacbbacacbadaabaadcbbadddbadaccadadbdbaaadbabadcdaacaadcdcacbcccbaddbbdcbaaabcacbadabbcdbdddaaaaacbbaadacbcbbacaabaadbbdbdcddbcbbbbccbdddbccdbddadbbdbcccdcddbababbadbacdbacaaacdaacaabbacbaaccdacabccacdbdbaabcdcaccbcbccabdbcabccdbbacbbbbbbddadaacbadacbdccaaaacaacaddbdcaddbccacdaccdbbbdbccbdbdcbdddcbacddbadcabcaabdaddaaddbbaccdbabaaaddcccdcaddcdcdddcdabdaacbcbadcbaacbabdddbabddadcbcdbacbbcdbcbdbccdcdbbbcddbddbdcadbcdddcccbbdabddcdbbdbbbcaddccabbcccbdacbbcccadbbccaabaccbbadbaaabacbadacbdacacdcabdbddcdbdddcbbdcccdbabadbaaddaaaacadbdaddbdbcdacbdcbbdcbaabcaacaaaacabaacbbabbaaddbccdacbaacdaccdbbbccbacadbbbabbcadddcdbaccbaddbabdaaadacccacacaccaddddbaabbcdddcadcabaadabaabcabacbddbabcadddadaaadbdcddadcabadbbacbcadbdabdbdcccabcaccdadbdbbbcaabadadacbbdbddcacbcacdcbbadbdaccbdaccaadbccdabbaaabacacabbbaadaccbaaabacadcabbadbcbdbdbaaabaddccdacdaccdbdcccdaccbcdcdacccabccddbdaaadadbbbdcbaadadbacaacabaddcbcddbcadcbcbddacacbacaddbdccaccdbddbdacaddadccaccbccabaabdbdbdaadcdabbacccccdcddcabdabcdaacbccbcacaaccdaddcadacabcdbbcaabdabbddaccccdbacdbdacacccddadadaaddddcdaabcaaddabcabddcdabbabdaabddbcdcdbbdcccbaddaaabdcddabaccbcaabcdcacbabddcbbbabcacdaacdbadadcbccbdccccdbcabdabdbdbabdcdbdcacabbdcbaddddcbaccdbdaccdbbccdadadaabacaaacddcddddacabbbcbcbcabbdcaaadccdbcccddcdbdaaccdcaaddbbbaccabcddbcdcaaddacdacddaddbdbaaadbbcbbaaccccacbbccccbcbdbdbccdbcbbbcadcabaddcabcbdaaacaccabbcadcaccdabadadcbbccadabdacadbddbadddccbcbcabbbaababcdbbbccbcaabaccaccddbbbddbcadabbdbadbdbdccaddaacbcdbbadddcdbdbcabccbacadbabaabacdacacbcbbabccadadabdbdbbacadbaadcddcaddddbadbbcbdadbdaabdcbcacdcabaaddcdaaaabcadbbdbbbddddbdcbcbccbddcdddbdbadaccbbddcacaaccdcaacbbddacdcadcbcbcaaccaadccbbdabdabadddbccabacddcbbdadbcbcdddbaadabbbcbabadaaacacddcbbbdcaaaadabdadbbdcbbbdadacbbcddcbcacbaddbdbbadbcdddbbdabbaddbbcdabaaaddcbbccbaacbdbabadbcccbbaddddaddbbabcbbbcacbdddbadcbadbacbacaabcdbbcbcadbadadacdaacbdcbdababbacdabcaabbacbaccadbddbbdabadbbdabdcccdbacbacaadacdbaacbbdbadcddddaddbbdddccabccacaacbdddabccdabcdbdacddaabddabcadadbaaddadccabcacdbddcdcbbcadabccbcbbdacddcddbbbcacaddddaaccbabdccbbacdcabaabcbcdbcbacdbabccadbaacbccdcadabccdacabaadcdbaaacbadaddadcccdcbabdacbacbacbadabdcbdbdadabadbababacdabcbdbddacbaddcbabccccabadcdabcddadccdaabaacdbccbbdadddbcbcdcabdcbdacbbddcdbddaaabdccabdbbcaddadbcadccaaadbccbaadbcccbdbbddbadacdaaddcbacdaadccbcabaacabcbdcaacaadcadabcadcdbbbabbadbbcacdabdcadadacbaddddabdcbccbddbabdccccdbbcdabbbacacbbabddcacadcdbadaaddcdbdbbacddabcadccbabcbdcccdaaacddadbaadccbccacacaacdddccaadbacbacadbadacdcdcaacdbcbbbdccbcacbbccdadbdacccbacdbcdadbbccccdbabcbdbbddacabacddddcabbbdbcaabccbcdccbdabbdbbaaaddcbbaaadcaaccadcddccdddddbcaabbccaccdaccbbcdadcadadccdabbabcaadcbaacabaddcdabdbddaddbdbbbcddddcbbcadbbddabbbdadbbbbdadbabbcdbddbdccbabbabacacdabdcddabbacabbbbdacbbdbacbaacbadbcbdacdccabcdcaadcbbbacdbbdaccabdbdabdccbbbadcbbaddacadbcacbccbbcbddadbbcdcadccadababddaabbddbababdbacdcccbdabcccbccaacbaacabbbcdbcdcbdadbcadddbdabbacadabaccbabbbdacaabdbdcccdbbbccacbabdcddccbdcbbcacdabacbbcdbbbcacbcbadadddbdddbbdbbdadbbacbdaacbdbabdddccaaadcddddccdcbbbdcbbdbabcbbcabcdbbdbcacdabbbcdaddabbdcacabddadabcadbabadbccdcdcaccddacdcabdbaadaacabaaadaacabdcdddbddcbbdddbbdddadddcabddddbacddcacbbcdcbcbcacbadabbabcdbadaacdabcdddadcaadabdacddaccababdbaddbdddadacddcdcabcbaadacaaddbddbcddbdacadabbadcabcdddadbcdcdcddcaccdaaaabcbbbcbddccaacabbcdbcabbadabcabcdcbbdcdbbbddadabcbcddadbbcddbbcdacbccdaccdcaddbdacacddadacacdbababcabcbcddcdbcadcadcbccaabddcababbcbdbbbaaacccdddbacaabccbdddccadbddcacdbcdadbbbbcadbcdbcdbddbcdbabdababacccddaadbaadcdbdbccdcbbbdddaddbadbcccaccaababbdbcdbcdcdcdbdbabcaccaccadbaabbbaabbdbcadbabcdcbdadbbdcbacbacdacbacaddaadadbaabcbcbbacbbbcbcdcabdcdabdcccbabbbadbcbaacabaacdaaccbddccdaadcccccaddbbbddbbdcaacddaccbbbabaadbdacacdcacbaadbacacdccacbcacbcbdabacdcbacbdcbcdccdbddbdcdcddbbacadacbbabaacadcbdadacaaabccacadbbdcccadddcaddcbbdaddcbaccbdacbcdcddaadadcbbbcacbaaaddbddbbdacacbadbaddbacacbadaaabbacddbccdbdabaacddbbdbbabbbacbbbbadcccbabdbddbaccbbbbbbcbccaadcdcaacadaddcbdbdabdbaabcdbbbbabbcbcbdaddcdbadbaabdccddacddabacdbbacbbcabdbaddadacddbabcbcdcabddbcbacaadbdddccddbacacacdacbdabcadabaccaddddaacababaabcdcdccbdcacddbbcdabbbaacddacdbcbbacdbcdbbcaadbaacadadbbaacbdbaddbcccbdbccacdaabbdbacbcbacdccbdbabcbccadcdabcddaccdaadacacbdadbcdacdccbbdbddadacdbdcbddaccababdcdbccbabccbbddbaababdcdbcdbaccdccacabcdaddbdbbdacacbbaabbcababcdaadbbbddbcadbcddaabadaddacabbadbbdbcbacbaaddcdaaadabcbbddbabcaaddbddbadddabacdcabdcadaccdddbdacabcdadacdabbdcacdcbbbbabdbbbccbadddabdacdacbbbcadcbbbddaaabcdbddcbdadababdbbccccbadabddbcdddaadbadcabaabbdcdddaadccbcdccdcaadbbdaaacdddcbcababbcabcaabbbcadbdcadbdaabacddcddaaabddadaaabdbaaaadaaaababbbdacbdcadbbdcccdaddccbdccacccdaadccdbcbadcbbdaccbdbbbdaacbcbacadcdbababbdcbdcccacaabdbbccaccaaaabcaabadcbcbdbadbadbdbaaaabbbacdbdabcbbabdacbcdadddadddaaadadaddbcabccadbbcdddacbbcbcbadcacbdcacbdadbabadccbdbdbcbcdbbdcacbdaaccbbbbdbbbcbbccdbccbbbbbadbcbdddddcadbbcabddccbbabcdadabadccadccbbaccaadddacbddcdccabaadbbaccabbdaabdcddbdabddaaacdddabcbdadacbbdacddbadbbddbdcdbdabbaddbccabdbddabbdccbcccddadaacdcdccadbbbddbcddadddccbaddadacabcddcdccddaaaabacdcdacbabcbababaaccddacddbabdadcdcdbccaaccacddadbdadaacdbaddacbddbacaddcbaadbdadcbccdacacdbcacadbaaabbcabddaaabbadcdaacabadadbbbcabacdabbacbdcbaddabdbabccaabccbdabbbcbcbabdcddcbdcadddaaacbdcaacadccbbabcdbadacdacacaaacdacabdbacdbcdabbcdaddbbbddadcdccbabcddbaccadcadcdcbcbabbdbbbbdaadbdccddaacacabacbacaddccbdbbadcbbbcdbbaabacdbacdbcbcddabbdcdabdcadbaabcaaabadaabbddcaadccbabddcdadabcadaadcdaddbdacdacdcaacaddbabbbcccabacaacbcabaabbbcabdbbdaacaaaaabacdadaddcbbcdddcdccccbbdabbcadddccaacadcdabacaadbcaccdaddadcbdabacccbdbdcaaadddbbadadacdabaabbbbbcdcbcaddcadcaabdcacadcaabcbcbcadbccacbbbabdaccbbbccdcabbccddbcadacccbdcbcabdbbccbbccaabbdcdddaacccbaadbbbdacadcdbcadbdadcacadbbbbbbcdbdabbcdadababcabdccaabaabbdcdaacccdcdcdbdaaabccbcbacbbdadbbcadadbbcabbadbaabaccbdbdcdacaabcabadbccdadaaabaabdcadbaccbaccabcdcadaabcaacdcdcddacdbbacdabacdbadadcdbbdadbdacdabcbdbbadccabddcdddccbadcdbbbdabbdccbaacccdcccabdaabcdbabbaadbcaddacaabcbbccdbccdabddbccbababcddadababababaadacbadbabccbbbddabbdccbdbcdbbbccdabcaaabcccababdabcdabbccccccdddadddcacacadbddaccbcabdaddbbcbcabbdcabcdbaabaacbbaddbbdbdbbddbcdccbdaadddadadadbcbabaacddbddadcadbcadbbccbdccdcdcaabaadbdcacccbadddcbdbcaaacacabbcacdbcbddbcdbbdddbdbddddcdcdcccbacabbadaadadddbdabadbcbbdbbccddaddbcddbabcbaacbdabddbdbcbaacbaabdcbabaabcaaabaacbcbdddcccdaacdbcabcaaccadbdaadaaacbccdaaadcaadcbdbcbddabadcaadcbaaaacacbbdbcadcbbacdbacdadbadbdbccdbdddcbcccdbcdbbaaacabcaaadddcbcbdcdbdbaabcdaacbcacddaccdbaabadcacabcbadccbbcacbddbccbaacbdbbbcaacbabbbaacdabdacbbdbdadbacdacabdbabaabcccbbcdbdcacdacdbcabdccdbdabbdccbaabdaaaaabcadddaccccbdacccccadacbdaaaabddacbcbbaaadbacbdccbaaabcacaadabdbdbbbddbbcdbdbdacadbbbdabcbcabddcdbdabbbcdaaadbaaaaacaaccacaccababcadaccdbcabcddbaaaddadbcbbabcbbdbadccccccddbbcdccaabaabdadcdbdcdddbccadbbcdddbaadbbacdddcccbdccaadcdcaaabcabddbcabdabbcccccabddddbabcbacdacabbbcaabbcacbdcdbdabcdddcacabaaaaadddcdbcaccdcdadbbadcbdbaccdcacdadabbcadaccbdcccdabbdabbacccbacdabbbcbbdcbcbbbdbabbaabadabcbacdadbcbbcddbbaacdbacbadbbbccabbbdabccabdadcbdbdccadcacabdabaccdaacabcbbadbcbbcacacacbcacbbbcabcdcccaacbacbadadcbaccbdcddbbdadbadaaccabdcbcacbcabdbbdbaadcbcddacadaddccbacdcbcccaadcddcdbaaabdcbcbdbdcdcccaddcccabdcadbcccdbaabdddcaddaaddcabddadcccacbdccbbccddbdcdcbbdabbdcdbcdbbdccaacdcdcbaddbacbabcacbadadcdadcdbabbadccdddbcddbdcddcdadabbabacabddabacdabdcacddcbdadcadcabcaccadcbddbabccbdddcdbbbabccaaddddadccadcacdaacddbaabacaccbdbaccbdbaddbacdcaccdbbdacbaadbdbcabcddcdbcdbbadcacdddccbbacaabaaccabbbdaaccbdaddaacbdababadabdbacbccbdaabcabaaccaccbabbcdcbacabbdaacbdccbdacdbccabbcdbdcbaacabccdcdabccacdacddcaccaadababdbabdbcadbccdadddacabccdddadcdbcdcdddddcaadcaadaccbdccdbbbccddccdcabdbccbbdcdbbdccbdacbcccbaccacbdccdbcabccbccabdccbddacdcbcadddbbbadadcdadbabbcbdaaccdacacbbbbbdacaacdaadccccaaadbcbcaadabdcbbbbcabcdddaddbdaabbbdaddbcccabbaaacaacacccbdcacaacccccabcacddbaccbdacdadbbccbaabbdccbaccccbdabadbcabcbaaccadbdbdacddaccddabaabcdbcadbcbdbbadbddabccbbcdccbbbdbbbcdddacaabbabdadadbbdbdbdbcbbdcbdcdccbdddbbaaccdacbbadbabdbcbaccbdaacaabcadbbcbbcddcdcdbcacddbacacdbbcccadbbddddcabcabbcccbccadbbbcaddccbcbcdcdbccbadaadbabcdbbbaadcdcbcdcdadaadbbdcddacbcbbcabbdcdccbbccbdadbcbaaaabddddbacabdcbdbccabbddabaaaababdddadaabdcdcbcdcbabccddabbdcacacdadcbaabcdacadccdbdddaccbcacadadadacadbbaacbaaddccdadcbbaacdddbdacdcadcbabcbcabddddbcaacdcaacbcacdaacadadadcbabbcbdadccbbdacbbabdbbacadabbbcbbccdbadbaabbaadbaabacdadaadbacbcaddadabbbaaadababddaadbddadbbaaadccdccbcaccddabbbbbcddaadabbccdcaaccadcbadbddbaaadaaaadcbbacabddcbaadadaaaaaddbbdbdccdabcbaccbdabdadccacdabdbdaabcddbdcadbacdacdbabccaddbddbaabbcadddbcccadbcabcdcbbacccbbcdacdcbbaaddccdaabbdcabccdacbbaabdbcaacaacaadabacbbbbccdcadbcccbdbdadacdcddcdddddbdddaaddbcbcdadddbabadbdbacdbbdadacacccdbdbabdcbbcabbaaadbcadadacadcbaabcbccadcbcaabacaabdcabcadcbcadddbadadcdddababbbaccaadabdacbabbaddccbcbacbccdbbdadbaaabbaadbadddacdbaccabddababdaaadbcadaadbcdcacabddaccbccabdddaacdaadaaabaadbcbbddbcdbdbdcaddadbbdddddbabcccabcacbbdaabbaabdbddcbadacdddbdcbccdbdccccbcbbcdccccbddaaaccccdcaddaadacabcabcabbccacdccdbadbdaccdcaabaccbbddabdbbbaddbcadbaacaabdcdaabbaaadbdcbbddadabacdacabccccbadcacacbcbcbaabcccbbccbdcdcccbbadcbcbdccaccbbcddcbcccbadddabdbbabdbadccdbdbabdbadaabdccaacaacbacadcbbcbaabbadacaaddaccbaccbacacdcaddcacdcaaaacbbbccbabdcdcdbaabbdbacacaaacdcbbcddcbbbaddcbcaddacaccbbaacacaaaabdcadbbaadcabbbabadcadbdabbddbdcdcbadabbdabbcddccbacadcbdddacbcbabdcdaccccccacdaccbbdbadbadcabaadabccabbcbbdbaaaadddccbaabbabccacdddbdaabbaabbbdcdaaabbdabcbbbcbcaaacdaddcacddbacdcccbaabcaacaaaddcadbccaaaaadbccabaaadcccdccaadbdbacdcdbabbddacdcadadbcbcbddcbccabbcbccbaaaaaaacdcdadaaacadbcbbbcdabbdddadbbbbcbcccbadbaaadcdbbaccdbcccdadaacdaddacdcdcaacababccacbabcdbdbcabbdbacbbcbbbcdcdbbcbcbdccadcbcbbaadbdadadadabbaccbcbdadbaccbdaacdbcdddcbdaccacdacacdacbdbcddacaabbadbdbcacdbcadbdadadccbbabaacadbdbaccbbdddcaddbdadcaabdccddcababbcabdccccdabbcadcabacccaaccadbbcaadcbaaaabdcccbcbadcacdacdaddbcdacccaddaccaccbcadbdbcadcaddaacacabbccbdbbbdcdacdcdcbbaadbcbdaacacbdcccdcaccddaacccbbcabdbcdbadbaadbcacaddadbcaacdccdbacdddbbbadbaadacbbdbbbdadacccabbbabdbccbdcdbdcbaabdbccadadcacbdcddddcccccbcbadaccadddbddcbadacbbcbbdcdbbabbcccbaadadabacdabbcbcbcaaaaaaabdaacddabddcdbbbacbdddcaabcbabdacdadccdbccacbcabcdaabdddacadccdbcdadbabbddcdcbababbbcbdbccdbcdacbdccabbbaccdcadbdbacadaabcdabddacacdadaccdcaadaccdcbaabdddbbdcbdccbbcbdacaabdbbacdacdcbdbddcbcbabbaccccccadaddaaaacbbccacabcbddbbbddcdaaccbaddaaadabcdadaddabccadacccccadbaccadcbabcbdaadbddaabddbdaddbdbacadcabaccadbcbdabdbdbcdbbbcbaddadaddaaadccacbaccdaaaddddcdddcddcdcaaccaadbdbaaadabdcaccbcbacccbcbbaaabcbbcccdabdabdcbcbcacbacdbbdcddabdbcdadabcaaccbcbcbcbbdbbcddaccddcdabccbdadaabccccabcacccaabdcbaaadcbcbabdadbaccdadbbcbadccaabadbcbccbddcaadacdabaabbacdbdcdbcabababdddcbbabcadadddddddccdccbdbdaccdbdbbaccdacaaabacbabddbdacdcdacdcddaaddaaccbacbabcdbbddcacbdaacbbcaabcdcddcbcdcbddcdbbdaacbbcbbabcbdbbbdbcbdaddcbccbdabddcdbdbcddaccddcacaababadddcbadbdcabcabdddcdaaacaaacacccdbcbabacccbbadbcdbbdacbbadaddbcbdadbccacdcdcddccadbdcabcccadadddaadcacdccbbdbcbbcbacbdcdacacbaddabadadddbaacbdabbdabcdcddbcdabdbccbdbcdabcabadddbcbdcaaadbbbdcaacdbbdbbcdbcbacccddbaabdacbdbadbabcbcbaadbcbdcbabbbcdadbdaaabdbcbcbabbabaadcbbbbadcaaaadcadbcababdbbddcaccddaabbbbcdbdccabacddabbacccbbaccbbddcacbbdcaadbdadbbdcbdbabbaadacaddccbdbdcacaabdcabbdcbaddcddbacdccabdddddbdabdabccdadacbbaddbcccaabbacccbababdbabccccadaacdacbcbacccbccdbabbadbbcaaaaadcabcabcbacdaddbdabaadadcaddadcbdabdbabcdbabccdbddcdcccdcccbcacacbbcccbadccddbcacdccdcdccbdbccddbaccdacbcdcacbdabbaaaacdadbdbaddccdcadcbabcbbadbbadacaabcabbbbdacccdacacccbdbaacadbdcbadbdbdbcbdbaaddabaccdabcaabdabbcbbdadddcbaadbbabbbccdccbbcbcdbccaaabbaccbccccbcadcdcadbdaddbcabbdbaddadbccccdbdcadddabbdacabbbcbabdcdbacdbdddbbdcabaabaadadbacddbbcadccbacccbacaabadbabadacccdabcdadcdcddabdddcbccccaabaadcbbbaaadbacabcacdcbbcabcbdbddcddcdcdcdddacdacbcaadaadcacaddabaddaababbbccbbacddbadcaaaccdddddcdacccacbdcbbdaacadcddbbdcbdababbcccddcadbbbdcccacbbbcbaaccbacadcdbabaacadcadaabbaaabcdcbbaacababdccbcabacbadccccbbaaacadacbcdacdadcbcadaacdcadbcaabccaaaababbcabcbdaaccddcbabdacbbcddbaaddbabacdbaabcddcaadcbcbbaddacbdbdcdaabcabaadacdaadaaccabdddddabaaaccbbcbaabdcbcabdabadccdcbcbccbdacbdcacdddbadadcccccbcaaaabdcadcccabcaabddcccababacaacbaaadbccadaabbcbbccadadbbcbadbacddcdbaacccaabadbaabbcddcadbaaacccacdbdaccccdaccabbbcaabbacdddcdcbcabbaaccccdaddbbaacdcbbbaacdccdccdacbbddcddcdbcabaadabbcbbdbacbccacbcdaaaaccdcdabddcbbdcabcbbbabaabbbaccbdabbcbdbbbacdacccbadddbccaacbbccbaddbcbbcbcddabccadbaabbbbbcacdbbacabbdccbbabbcbaaabdbbacbaadcccbdccbbdadbdacddadcdcdbccbbbbadbdacdadaaadcadadbddbbdcabbbdbcdbdcdddcddccbbdabccbdbbaacacddbdddcccddcdcdbaadbbaaaadbccbaddcbababdabcddbcbbcddaabccdcabacddacbaadacabdcccdcccadadadcdbbbcdacabacbbdcdadcddabdcadabdacabccaccdccbdbdcaaaaaadcbbbbbdbcdcdcbaadcadbdccabcbaacbcccadbdbbcbdbbbacbccbaddbbbcbbcaccdddbbbcdbdcbdcbdccabadbadcddbcdcbdcddbcdaaacccbddccccdbabcbbccadcbdacdcbbdbdbcabdbcdddddcacbcbcdcbcdbbccdbabadacadcacbbdbaaaaacccaaadbbcacbacdbcbdbbddbcccbabbbcbaacadacacadabdbabadaccbdcbcdcabdadcbbcaadcbadcabbcdaadabbadbddddbcdccccabdabbbaccdbdaccabbccdbbacccbbaddaccaabacabdccbbcdaaddddcabcabacbdacbcabacccccaaaacccbcaaddbaaaacddcdbdbaddcddccccabbbbcbbaddcdbcacdcdbdbbccacddccdccbdadcbcadabdababcadccdbbccbcadcdbbdacccbcacbabdbcbbabaccacdcbccccaccadadcbaccdbcdcbbbdbdccadbccbacbaabdddaabbbbdbcababbdcdcaccdaacacdddccabbaaddcdcbdaacdccccddccdbaaaddcdbabcbcccbbacabdabacddabadbacaacdddadcbdabbdcbbaaddadcdaaaaddbdbdabdbdacaadcaaddbaaccdbdcabbcddbdbbcdadabcdddabacabdabddbccdadbddbcbbbdcdcdcbdbbdbcdaabacabadcadcaaaaaaadaabdabbdcbbabbaccaacbaaddbbcdbdddadcdadbdaacaddccabcbaaddbcccadadcccacdaaddbadacddadbcdbbdcdbabcabbabcabcaaddacbbbaaaddacccbdcddcadbabbbadcacabacdddacdbbcbabcccbcbabaabccabcdababbdaadaabbbbcbabdcddbacbcbdbdabbddccdbaacabbcbacbdacadbcbaabcbccdaabdcddbdccdabbbabcbccdadadbcdbcdcbaccaaacdacacccbcbdddcddcdcdcbaaaabaaddaadadcadccdcbdbcccacbaabddacabcbaccaddbcabacaabbaccddcacbabaadbdcacaabddadaddcbdbcadcdacccdbbbbbbdabcccabacbdcbbadadccccbadabccadcdabccabdacabaacdcdbaabbcbdbbdddcdbadacbdddcabdcbdcadccccdcdbabdbaacbacdcbadbccadcbbcaacccabdaaaddbcaadccbbcabcbcccdcbbcdaddadcdbaddbdcdccbdddbcddcbcbbbbddbbadcadbbbcbacbccbcddbccddbaddccbaacadadaaccccadadcdaaccacbcdabbddbbabdbbcaccdbdbadabbccccbadcddddbdabbacccdbaabcddbbacdaacdbddcdcdccbabcdabcdddcacbaccbdbbbbdcdaabbadbcbddbbbabcabbdddaaabbcadcdccdbdaabbdcbadabadaaddaaaadaacbdddccccbdcddcbbbbcbbcaddcbbacacabcdbdaacdcddaaabccdcbabcacbbaccaaccbcbdcadadcbcadcabccaadbbdbddcadcbacddccdcabaddcabdbbddcdddacbccbaabcacbbadacdcbaddbaccbbacddabbddddadaadccdbbbbdacdaccbbddbadcddcdbacbdcaaddabbcccdaccddbdddbdabacccaaadaccadcaadabcbacdccddccdaaacdadcbcdaccddbbadbcadbcccbccdaaddcdacccdabdaccabbacccbaabdcdabcdadcbadacdcaadbddcbbcadbcacbddcadcdcccdbcdacbbcacccdbddbdaaccdccabbcadaacddaabccaadccddbcbbadaaacabcdbdcdabadcccdcdbaacbabcdccabaddcbbbdccaadaacccdcddadcdbbbbcbcabddbcddbcabcbaacdcbdbbabcdcabdbcbabcdacbadbbabccdcdadabdacbbdacbbddbaacdcbbacbabbcdbaadbbcaabacabdadbccabbabadcdcbbdcbdbcacdbbaccadaadaadaadcdcdabaaddacdadbbaabdbbcdacaabadcbccbcbacaabbacbcdbdabdbdcaacaaaabaabdacadbcdaddaadcccbddccdcdadddbdbbbcbabaabccadcbcaccbbcabdaaadbbaddcaabdbacdaccbcbbabbbdcaabdadcadbcbadadddbbaabbccadcbadbbcaaaaaccbbbadcccabbacdbcdaddcdaccddacacdbdcadbbaccdcbcbabddccabaccdcaadabdcdadcaabbcbbdaadcdbcaaabcbbdbaacdbaaabbdaddddacbaccddbacabbacbcabdbbddaddbbcbbdbbbddbadccdbbbbccbbbcdbadcabbbdaadcdbdbcccbcbbaaddddbcbcacdccccdadadbddccddcbddbcacacbaaabccabaabcadbbbaabacccabbbbdbadcdddaddacbacbdcaccbbbabddaddacaaadcdbadbacdcdadcbdacbadccdcdacdaccaddcddabdadddaddcdadccacdaaabccaadddacccbbdacbdbbcdddadaabdcbbcdccbccbcbdbacadacddadababbddaccdbaddaaaadbdbabddbbadcbcbcdacdaabdcaadcdbadcaacdcabcdbcaccdbbabacabadbdbddbabdddabbccdbbcdcbbdcdabcdcacdabdbcdcbdbddbdadbbbdaabadaaddbaddbbccbdcbacbcabbbdbbadbdadbaccbabbadcdaacbdddccabcbabdcbaddbbccaddddddacadddbddddabaabdcdbacabdcbccacdbadabaddcdadbaabcaacdcdabdaacdbaccdbacdacacdadbaccbaacddcdacbdaadabadcbbbbdbddbccbaacbbadbaacdaacadbcbabccbcdbdbdcabaadaacddabcdaabbcdbddcdcacaaabdbdbcddddacacccaddbadaccbbbcaadbdaaaabaabbdbbcbcbbccacbbaddccdaadcdbcabbdabdcaccdbbbbacdddbadacddddbcaacacbaacddbddddbadadcbdaabacabccbbdddddabcdacddcacdbababddacabdcbbcbbabdadcabbdcdbdbbaabbabbaddcbddcbdcbbcabdbcccbaabbcbdabdabacdabdbcbdcbbcdaacdadddaccbabcbadbbcacbdcabcbcddcbcabaddcbcdaaccdabcbacdbbccbbdadcaaaaacddbdccbabdcbcdcbdcddaaadccdaabdaccccacddacadcbdcacadcadbcdadcbabdaaacdaabddabddcaaaadcbcababdbdbbacbcccaadccadbccadddcadddddddbdabcbcdacdaacccabbbdadccdaddcdcadabcdccbbcabbbdaadcdbdbbaddacccdccbcaadbbbabdacccaadbaadaadadabbacdabddbabcdababccaccbcbbdabddcddccbccddaddbbdbbbccbcabccbabcbcbabadaddbabbbbaccaabbbbabdbdadddcdcaabddcadbbaddacbcdbbadaadcbbabbcddacdbbcccdcbbabcccbccbabbbdbdccdbacddaddaccbdbbdbacbdcdcaccaacbbdbcbdcbbcdaabcbbcaadbdacccadaacdacacadcbbcdccbcaadcabcdcdcbccbcadbaabbdcadabbaddbcdccaabbccccdaaaabbcddaabbbcbbaddccccddaddbddaccbbbaabbdbcdccbcccaabdcadacbccaddabadbdccbdbdbdadbbdbcacadadaccabaccacdbbddbbaabddaabbcbbddbadabbdcaacbddbdbaaadabcdabbdcacbabcdbcbabaaabcdddcbdadabbacdacbbdcabacbbbbacdccbababdcddbabcbbddbdaacacccbaabbbaadbabcccaddbdacaacdbcabcbacddadcbbcbcacaccaacdbacdbaadddcbdbcabcccdcbadbbdabaccccbdccdbddbadcacabbcbbabdaddadddddacddcbccbcddbadccabcbddbbbcdcdadaaccaadaacbabdccbddcacacbbccabacccdcccdadbadcbadaddaadbcabcacbdcadbdcbabcbcababdbbbbdbdbbcbcabbbcdbbcbdaacbdccbdddbdaddcabbacbabdbdcdcabaccdbaacbcbbddbbbdbabcdcbbcbaddcbccbcccbbadccbccacdcdcacbacddacdadadcdccddccbcccaadcaacccaacabbadacbaccdacaacaddccdbdabcddabdcadaddccabaacababacaadddaacccdccdbcbbdabbcaaddbccdbaccdacdbcbaadbbbaaabdbdbcdcdacdcdacacbddccbdcaacadbccbbddacdadadddadccdadcaabcaccacbdccccbdbcdababbdbcabcadcbbddbccdbcadaddaacacaabbbbddcbcadcdcdcbaddbdcddabdbbdaadccabcdccdcabcbbbcdcbcaaadaaaaadccdaddacbccaabdddcababdaabbaaaadabbdbcddbccbbaddaabacabacacddadbaadaaccdacbabdaddcaddadcbacdbdbaaabadccbbdbdadcddcbcbdaccdcbcdadaddadcbabbbdbdadcdabddbddbdaaabdbdcbbbbbdcabddbbacdbaacacbcaddccbaabdbddccadbbcbadacbcdcdbaadaaddddcbcdbcbacbbabdabaadaabbabcdacbcbbddbaccccdaaddcabcdaaacbdbcccbaccddabdaacbbbcddbcabddccdcccabcdcaccdcccddddcbaaabdddacaaabdbbccadabdbbacaacacbddbdbbbbdabbdddaaacabbbcdbcadadbdacadacabbaacccdaaaadaacaaddaddcaacdadadbacdcabdbabbaacdadcdcdddadcccaadaaaabbdbbbbcaaccadcaaabbccadcbcbaabacbbbdabddccbadcadaaadabbcacbcbbbcdbabdbbaddbdabdaadbddacadbcbacbbcaadaccaabacacabdbcacabbbaadcdacacabbcbaacaddacadcabcbcdaaadbdccadabccdcbbdbccacabbdcacdcaacccbacadcadcadadbccaddccbadddadddabacbdbcbdbbbbbadccacddddcdddccbbddacdbdacaaabcdddbcacadbaacbaabbcdbdabacdcabbcdbdbaabacccbbadcbcdcdabbaadcbcccddabacccdacdbabababaabddcabbccccbcbccdabcddacdcdddbcdbdaabbabbbbdcbdcbbbccabcdbdaabbdbaacaddcabbbbdacaaddcabccdadaddaaaaadabbcccbabcbbcbdcaaadccbcadabcdcbbcddcdbbdddddbbdddbadbbdacdbcacbccbbdabcbdababcdcadbbcddbabcadcdcbbadbbcddbcdbbdacddbdddcdabdcdacbccaccdcbbbaddbbaadaaaabaadbdbbddbdaccbacbddccacccbccdccadabccaacdbddddacadabacbddaccabcdcccabdbcbacabdbbdadbbdaabbbcdbadcdddbcadadcbbaacdcababcbaaacccbbdbcacacabcccdcdacbabbaabdabccbabcddddacdbcbddacdbcacccbcdcaddcbcdcadcbccbbdadcababaabdabddbbcacaadbbbbcbaaccdcabccbcdbcbcbbccadacbadbdddbdbababadacccadccbbaabacabccbdbbcaddadbddddaddbabdddbaccbcdbcacabddadcdccbbabdaaabddcdacbdcdcaadcaacbbabbaadaaadddbadaaddbbadbdbacdabbdddbdbcdcaadbdaadbdddbbcbdbabddcbbddcbcaabacdbaadcbcaaccbddabbbcaabdcdcbdbbcbabbcbdddabbdacdadbabcacdcbbddcbccbcbccdbccacbbdbcdbbbdadbbcdccdcbddcaddbbcaacabaacdcaadaabacccdddbdbaaacaaabccbbbcacdddadadddabdbbddcacbaccaacbdcbdabdadadcacaabcadbbcccdcbbabbcadcaaddbabdcabadbadabaadcddaabddbcdcacaddbccbabddbdabaacadbadbdacadaddcabdcbadbadadcdcabadbbbbdbaacbdbadccbacbcbcbadbadbdcadadcbddaccdabcbdcacbcbdaabcbdacaddcacdbbcdaddddadbcabbbadcbacbdbbdccdbaabddcadcacabbcabccbbbbbdcccdabdbaabccdacddbccccdcbbdcddbcbacadddbcbddabbdccadbddbdbcdccdabdddaccacaccddcaaabaddadbddbdabcdcabddacbcaacdbdddbddcaaaddbbaddadacabbdcbcabbdbbdacaddbbdbacbbdaadbaaddcaadcbabccccbcacccbcbadaccdbbcdbabadaddcdcaaccddabbdbaabaabacadddcdaacccccbaacadddbcaabcabbbbacdcbadccccaabdbbdcabbaaadccbacdbacccaaabababaadcddacacbdcdacdcaddcbcaabcabcbacdcdabbbbbacbdbdcbddddaabcbacdcadbaaccaaadcacdbbdccbbacabcdbdaddccabacccadbdbabdbbdadaaaacaabbadddddcdbbaaacccdcbcdcacbdccdccacdacbacbbcabdcbcdaabdbaabddacadadccbabcbaadcadaabcdaacdcdcccbcacbcdccaddaadacaadadbdcccdcbcadbdbdabbdcdcbdbdbcdaaabcbacdacabaacbaaaddcaadadaacdccacaadbccdbcadcdacddabbadbcddacdbccdaccdbbcabbddadccaabcdaadcbaacbdbdcddcacdbdacbbcbccbdacbbbdcacccbbbcdbbdbcbddcadcaccacabbbddaaacbdcdadcddcbbdbacbcdbacdcaadcabdbbdbaaadacadbadbbdcaadabacbbabbdacacbabcbdabacaadabbdbdcbdaadcadaccacdcacabbdddadbbabdbcaacccbcbcbacadbdcabbbadbccbcdacaabaccdbabbccdddbabbcbcbbcdbabddcabbdddacacabddaababddbbbaaaadbaadcbbaadabdcbcbbadaddbbdacbbdabbccacdacaccdccdbcdbcbddbdadbabaabbccbbccacdcdddddacadadddaadcbdbcdaadbaaabbccabacddddabbdaacbcabbcdddbbbaacddaaccadabddaccdbcbcbadbcdcdadbbdddcccbddabcdbbdccadacaccaabbcacadbcddcbbaacbbbcaccbdbcdabbbdcbaabcddccbddaaabbadbdccabaccbaccacdcdbbdaacbccacbcaadbbadbcdbbcaccabdabdcbdbbbccaabdbdbaadbdbcddddddccabdacaabbccbdadcbcbbbcadabcdadcdcaaaabbdcddacbbddacccdacccbdcdddcaccbcdaacaabdcbbbcabbcaddbbbadbbddacdddcbcaadbbbbdddbbbddcbacbaccdcadaaadcddadabddacdbabdadbccabbbaabbbcaabdccbdddabcdbdbcbbdcddabaaababbdbdbaaaaccddcccbcbdabccabbcbbbdaddbaadddaddbbadadbbadccbdcdaaaaccdcaacabccbbcacbcbaaaabbdcdbadbadbbaacaacaadbbdccbcbbdccbdacabaaacddccccdbdcbbbdabadacccdabaccddabcadcadacadddaacadbbdbcdacdddbbabcdcdbdaadadbccdcdabbdbcabacdbccabcaabbbdbddabccadacacbcdccbdadabccaddabdbdcbcdbbcbbcbcbacbddaadabdcccbbabbbdacdbdabadddddcbbcdbddbccbdbabababaccddcdcdbaaaaaddbdacdbcdddbbcbbdadbdbaacadbbacaabacdaaacdacbccacbbbdbcabaacacacbcbddbbadcaaacbabacbcdbcbcbdabcabbbbcdbbccbccacbdaaaabbccabacadcbbbcabbacaacabbabddabcabdccabdbaacbdcbbbbbbdcadbbbdbbadbcbbcdcccaacaccabaaadcdddbdaaaacbcaddadbdaabbdcbabcdcbbccbdadcccbbbadddcbcddadacdacdddbdcacdbdaddbdaabdbddaaddccacdccdddcccddcdaddcbaabddccaaabadbaddbdcdbdcbccdccbdabbabadcbccdaaccddadacdcdddcadcddcaddccabbddcbccaccbcccacbdaadaddaddbbaacaabcbcbdaacddadccabacacabdadbaabddaabcbbabbcdbbbbcbbabcaabcbadccbabcacaabcacddabcacbcbdbdcaddcbcbcaacbdacbdbabbabdcbccaaacdaabdcbcbdbdaddabbbcabdcdbabdbaaabadabbbaaadccaddccabcbbabdbcacccacdbcacccaccadbcaabcadddbcabdbccbbbaddcbcaacaacbdbbbdbdddbdbbdcadddcdcaadcbcbadacbcdbdcadabccbddbacdaaacbaabcbdacaddadccacbcbccdaadaabbcdcddcadbbabdcdddddaabbddbbcbadcdddacacbbddbacbadcccddcbdbabbbcdaccbbacdabacacacadddabdccbacdaacdddcccddbdaccaaccacaacbccdbaabbcbbccbcbdccdadbcdacaaddbddbccddaccddcccadbadbdaddaadcdadacabacabacdbadccaabbbddcacbbcdbcaccdadaaaddbbccbaccdddcaaadbcaabbadcdcdaacdbcbcabccaaaaacacbcdadabbbacabbcccbcbabadccadaabbcabdabdccbcdccbaccacbcbdbdccaaababbbbcdccbdbbdabdbcadcccbbcaccddbaadaaadaadbdcdcaaacbadbdadcdacdbdbdbadaacbddbcbbdddcccdcbdacadacbbdadabdaaadbccccbadbaccdcddabcabadddbcbadcbbabdcbabbbccbabbbccdacdbddabcadbdcdccdcccadcdaddadbdbbacdddaabbbadccacbcbaadaaddcbdccbacbccdbdbdccacbadcaccdbddcaabddbdbadcdaabcdaadcccbdcdadaddcbcbadbccdbaddbdbadbdcaddbccdadabbaaaadddcbdbbbdbdaabddccadacdddbccdddcdbcadcaaacabaddccddcabbccdcdbcadbaccbdcbaadaaccdbdacbabdddcbbabbdcbbbcdcdabcdadacbcdadbbdcbccabbdcccaacbcddbdbdbbdbbaabddcaaddcbcbaadbbbdddcdbbadacaadbcdadcaccadccacbbbdcdcbbcddadabbcdcddccbddaaccddcadaacccdcddadbcbcdccacdcdcabcdabbbdaabcbcdcbabaaccdcddabbccadbbccdbbccbbcbcbaddbabbbdaabcbcbbdabdcbacbbbcbbacccbdabdbccbadcadbadddabadababccdbbbcacccbdaaacdbadabcbaaadbacccbbbcacbbdcbddcacbdcdbccbbcadcccaacdcccddcadacbddbbdcddbccbcaccdcabccdbdadccabcacddddbaaababbabcabddaaaabbcaddcddbbabcccdbbadcaabdacdacbabbccdaaaaaaabbcabdbababbcddaadbabadcadbbbbadaadbbdaaaabdabccdcbcdcddacbcbcddbbbbaccabbbdcdaddbacbcaadbccddccdcdcbbbaccadddcadbaccccdadbcbcbdcabccbcdcbadcdccbcdbcddcbcadaddbdacaccbadcdacdbdacbcccacacdabccbdcdccddacacdcccdabcdcbdcdddaaccdcddbabcdccddbcbdcaaaddccbaacaccccbdadcdbddcbcbcdcdddaabcaadcabbbcacbaddcdbcbcacccdaaadbdbadcbdaabbcccbdbbcbadadcaaacaabcaadbaacdcdbbbccbddabcbdbbacdbbccbcbdbdcacdababbadbbdaccabbbcbccbbcdabadddcddaddbdbdacaabcaabcaacabcdcbadadaadcbacbacdbccdcaaddadbabbbcdaaddcaabacbaacaddabbacdddbaddcddccabbcbdadbdabdcbdabdaaccadccdcdcdbdbcdabdaaabcadcddddacdbcbaddcaaadbcdacaacdcdaabcdbccbcacbacaccdbaacdabdaddcbcaaaabcdcaaadaacacabbbdacadaadbbcaacdcaabbaacbabdcaacacacdcacdadddaabdcbcddbbadddabcaabcdcbabacabaccbaddcadcacdbbbcadaadcddbabdaabbacadccbbcbdcdabaccabddadbacccbbddaabddccaabaadbbbbbdbcaaddcbbddddbcbdbbddbaadbcdaacccabcbccdccdadaccbaacaaabcabcbaabbdaaacadbbacbddbbdbbbbdcadbadcbdcdaddcbbbcbacabccbaaaccdccadadddbabbdaaadbbcbbcdcdcacbcddccbbdbacbbccdccddadbacbbdaaddbcdddddddcdccdadcddcaacbdccdbcacdccdbbbbdcadccacbbccccadbbbaccbadbcaddcccdbaadccbdbcadbcbbadabddbacbcacbcabaabddcadbbbcdaabddacabbddbaabaddccbbadcbcaaacdcabbbccdcbdcdbdbacacacdadcabbabadcdabcacadcabbcdcbbabbbdccbcbaadddcbbcdcbdcdaccabbccaaddcdadbcdbbcddcdadaacdcbbdcacabdacccccbaacbbaadbdbdccadadcbdcadbaacbbadcbcdbcdabacdddcccbccadcccdacbcbbbbadaabccabbabdbccabccabdcdbdaaabdcbcdbdcdaddaccaaddacaacbbbcdaaddadddbadddcaaacbaabdadaadbabddbbaadbcbbabcacbbdbcdaacccdbcddbbbaadcdcaddadaadccdbcaccdcdaacdbccbcadbbcbcbcbabbaaaabdaaccccabaadacbcdbdabdbabcdacdcacbbcbddaadddcdabbabdaabbaadabbdabccacdcbdbbabaaccbdbccabcccddddcacdccccbdbdcddabcaadaadddabcbccdbacaddcadcdbaccbdcdaddcbaacacbcdbbabdbcbdcccdacbdcbdcdaccadaaccddaaacccacdcdcbbacdcbcdabbacdddcbbdadbcbbdbbbacacbdcabababbcaddcdcbdbdbdaadcbcabddddcaacbabaadbbbbdcccccabcaacccdbddbdabcbadabacddbdaadacaabccdcdbccacbbbbabcbcacbdbaababdcacacdcaabbbbbbbbbbddbdccbdbcabbbabbcbcaadcabdddccdcccddcbcaacacadcaaaaccacdbdabbbdaacbaaacbcaaccddcaccbbbdcdadbdbddbcdbbadbaaaaddadddbbdacdabbbcaadbbdccaadbabbacbbdacdcabbcabdccdacdcbddbbabbacdadcdacaacddccabcdcdcbdbddddaccaddcbbbacdabadcbadcbacccbbccabaddcadbaaaccaacacddcdacccdbdccccccdddbdacabddcdcbbacbcdccacccabccdaaacbbcbcabbacccbbdccdddcabbdcaacaadbdaacdccddbbdbcdbbcaadaacdaaddbabbccccbacbabadccadcacdcbcccbcbdabcccdadbcbaabbadbdbaacdaccaabcdbabadddbaadccaaccddbadbcacdcbbcbdabdcddbaddccabbdcbbccdbbcdddabdccaadbbaadadbddaacbbcbcddcdbbbdababbddcdbadbddcdaaaabbdacbbccbddbcaabcddaddacbaccddbbbbabddbadadbdabbadbbaddaccbdaababaddadbdadbcddbadaddcbbcdbaaadddaddacbcaaabcbbaaccdaabacaaacdadccdbcbdadbddbabccbaabbaccdadbcddcddcddddadaabcbdcbcddacacadcdddcbdaadacddacdbdbabcbbcaadacdaccacabcabbadddadcabccbbdcabaabcdadbdbdbcabcababdcbdaacbcdbcbcadabcbcaaadcacabaaaadccdbbcdbcdcaacacbcacdadcccbbcdcbdabbcabbadcdcbddacbcbcccccbabcbdadbdaadbdbdabcabdcccbaadbabadcaabbbaaddcddbcdcdcadbabdcdbbadbbbabccadbcaaccbccbababbadcaadbccbdbcbbaacccbccdcdadcdcdcbbaccaadcbbbacbaacdbcdbdacaaddcddcacaaadbcaadacccddbcaaaddacadbdbadbabaddadabaaddbcbdbccdabdcbbdcdbabbbdcdaadcaccdaadddaccaddbccccbacdcddaccacbddbcdbdbcbdbaacccbaabbdacabacbccbdcbbbcaadcacccadccccbcacabcbbdacdbdcbbbddaccbddcddbcdaadbbdadccdbdcbacbcabbcbccbcdcddcdcddaabccbdccccccdbaccbdcacdbbdbcddacbbbcadbccdbbbdaacbdbccbdbdccabddccaddccacdaabcbbbcdcdcbdbbcdbcbcbcacbbdddcaabccadcbabdbdbbcdddbadddcdbcdbdcccdccacadcddcbcbaabbdbccadcaddabaacdbdcdbacabcbadbacaddddabaccadbcbadcbadacccabbadaacadbdadbcbaccdcaadaabccdbacacdcadadbbbcccacdaddbcddbaddbbccddbbbccdcbddbddadaabcbcbccbbccbbdbcbbbddaddaadddbaabdddababdaaabbdbbaccbdaabddcbbccaaddbbadacdddcacbdadacccdccadcadcadaddacbdcdbdacacdbacbcdcaabbbccbbccacbbaaacdabcbcacaaadccabdaccdddcccacdcadbacabcbdcbacdbdccbdcbcbbabcccaabaccadcbdbdadacdddbddddaccddbbbababcdbddbcbbcaaccddddaacdaccabaccbbdabdbbdcbdbadbcdccdbcabcdbaadacacdccacbdacbabccdcbdcdbdccbdbbccdbbadcbabdbdbdaddddadcdcbdbdabddadbcadbaccaadddbabcbdababddddbdabaaacbcbcccdabbdcbacccaccadaddcbacddabadbccdbdbdcddbbabacabcccdbcacaadadcdbcbcddbbaccccdadddcbbbaaddaaaccccdabbbddcbcbbddcacacccdddbccadcacaddcabcdddcdcbbaaaaaddcccacdacacaddbddbadccdcabcdddaccbdbccccddaabbcdddbbccadbcbbbbbdcdcbabaaaddadcbadbdbbaaacdcbddadbccaacbbacaabcbbbcbaaaaaaacdcbabddddbabaccdaaababcbbbccccccbcdcccdaacbacabaaadbcabbacbdacabadccdcdcadabdaadbaacbdabbaadcaadaacdabcbdcbdabdcccddbcbadacddadacdbdacadacbdaaacaaddbbbcadacaddcabcdddbaaddadbcabdcdcbabccacbdcddacbdcaaacacbbbaabaadcaacdddbcdabcbbcdcacaadbcacccabcbbdcbcadddaccbbbbaabcbacaaddcdaddbcdbaabbbcaabdacacbdabadddcddcdcdbcbdababacbcdaaddbaabadabcabddabcbdacaacaccabbaaaabcdabdbaaacaabddacdcbacabcacdbadbbabbdcdabbabcdbbcdcabddcabbadabcacadccdbaaddbacdcccbcbcdbdcabddabdaabaaaaaacbcbbacbaaacbdcbabbbcacbbbdcbccdcaaadaddcbbbbabccadabcccacabaacaabcaaadbbdcabccbadcdccdbacccabbabbccacaaabdbaadadbabbabbdddaaccdbdabaaddbbbbcccabcdddcbbbbccbbadcbdcbacadbcbdaabcccaaaddcacaacbbaddbcddcbccdbddabcbcdabddccbddcaabbcbbbbabdcaaccdbadbadcccacbcdbacdcadbbdabbacdadadabaaadadbcbdbbbcaaacbbbadddcaabbabbaadcddddbbaabddaddcabdcbccabddacdcbdbabdcaccbddbbbaddbadbabcdcbacbadbccbadcdbbbadcbcdaaabbadbdcbccbdcdacaacdbdadaacdbabcddbbbddbbcbadbbbcacccabdaddcacabbbacacbccbdaadcbabddddabadbaabbccddaccbbdbadddbacbabccdabcbaddabbdbdbbbabddcadadadccacbdcdddcdcaccbbcaabdcacbcbccdbbaabdcbbaabbdadcbdcabbbaaaaccdadbccdaccdbbdccacbadbcbbbdbccccabbbbbdcbbcbdadaaaccddcccbdbcddcadadcdbbadcccabbcddbbadabbaaacbdaccdccacaabcdbcbacccccccacddaaaaddccbdddbbccadbcccdbaacaacbbddaddbbbbbcadcbadbadadbadbcbcabcbbcdcddadaacdacaaccadbbddbcbdcbcaccdbababadaadcaababdaacbbbcdcbbcddabcbacdbadbbcdadbccdbcdaacadccbbdbbbbdbdacadcbbacbcacbaaabdbabcbbbcacddaddadbbddddcccdbdaabcbbcaaadddcbdabadabccbcccadccadbbccbaccbcbbaabadbbabdbbcacdbbcccdccacdacddbbdbcabdccbbaacdaadccbbdbbaaddabcacacbdbbcbdbaddcccacabbacbbabacbacabdbaaabbabbdcaadcdcdcdcccbbcacadaabdbacccadcadcdbcbcbcbdaaadaaddaadbcdaadddcbcdbdbdccbadddacaadccbccaacccbcadaadccdcdaaadbaacbbabbccdbbadaaabcdcbabdcadccbcadcacccbacaaadadbbacadbbcacadcccaadcdadaaabddbdcbddacdccdcacdcacdbdabbadbcacbcaadbbcbdbcaaacbdcbccdcbcbcdcdcdabaabcbbdbcccdcabaacccbdbccdddddcdbdadbcbcaaaacabbaccbbbddcadabcbccddbaabaadbbcbbadbcccdbacbacaaabdbcbddbcccccaabbccccdbbaddaabcdcbbcacbaacddbdcbacccccbabcbaccaddcdaaccbaccaccdaddbaaabdcdcccbcdadaccbcccdadcbbaaacabcdbdbbbcadbcccabbacdbcbcbcdaaaccaabaddddacccbdcbacdbdccaccbdaacadbbaddddadaddbdacbbadddacdcaacaaacbbdbadabaaacdcdaacadbccdbcccdcadbacbabbdcaabcddadcbbabaabdcdbcbabaabccaaccaabbcdbadadcbaabdcadccbccdabcdadccccaabbdaaadadbbaaaacccacacacdbddaadcaaddccdaaddbabcdbbddacccbbbcdddcbdbbbccccadaabdaddcbcbcccbddbabaddbcbccadcbcabdcdcaddacbabcbaaabcaacacacddbabbcccbaaccbcccdccbdcacbbbbdbbdcbddbaadbccccdbdbcbdadcbaadbadaacbdbbdabcccdabcbccdadadcbacccbaacbaccbcbbaaacdbbacbbadcdbdbcbdaddacdddaadabbbdddadaddaacdbcdcbdaaccddcdbaccaacbbccddaddaddbabbaababcccbbbdcacaadbbdabbddacbcdbbadcccaddccdcaabcbdddabadddcdcdcbccbbababccbabccbbdbadddbbadabcbabcbaaaadbaddaaddccaccddcbdaccabddcdbbbaabdabcabbbcbcbcbabacadbdcacccaaccacbadbbbabddaddaababdccbacbcbcbbddaccdccddbbdacdcdccbaaadacccadacccabddcbdccdcabcacabcbbdbcdbacabccadddbaacadcbccabbbcbadddacbbddddbaaaccbbabcdaacdddccdcbcdbdcbabbbbadabacccbdcadbddbdcbbcaaaaacaadcadbadddbdabcadadddccdbddaadcbdaadbabadcdbabcccbcdabacdcbcacbbdbbaaabcddbdcaaddbdcacbbbacbdcdcbddcddacbcbbdadadbddbbcbaddbacbbccacbcdadacdbbbcdaabdcdbdcbaadcdcddbaadacbdadbabccadbbbdccdcacdccbabbadadacadabdccacdccbbddddadcadbbabcdbcbcdabaaccdcadacbadacbdacbcdabacaddbbdcaadabdabcbabcddcaaabdbbdaacbdcdcddcababbbadccaaacdcdaaacdbcacccdbbadbbacbcbdbcdbcdbbaadabbccbcbcddbdbcdcdcaaabddcbaabadccbdabdadbaacbbcbbacaccabdcbacaabbcbcdabbdbcdadbdcbadbaacbdccacddababadcaaadacbbbdabdddabdcbcbbccbabdadcbbdcddcdadadabbccddcbbccbbcbdabcadcbaddacbadaaabdcdadccbcdcdcdbbdacdcaaddabbcbdccdaabcbbaadbbcacaabdbcdccddadcadababcbadbadbddbcbcadbdccbbdbbddaaddcdaccacacbbbccdbccbcddaaaaccbcadcdbacbbdbdccdbddbaaaadddbccbdcbcbcabdababbbdadbbbbacbbcdabaabaadadccddbddcdcbbcaaaabaadbbcacaacadacdbabcbcaaaaaacabbbdabcccddbcacacddccadbaddbadbaaaadabdadabdababacabccbddbcccbabcbbbccadbcaabbabbddcbbadbbdbdcadcdbccacdbbdadcdddcdadbabacdcbbbbcccacccdabadaaddabbbcdbdbdbbacbddbcdbbabbdadaaaabcaccccccdccdcadaaccbdbdbdddbbcbabaadccadccbdbddbbdbbbaadbabadccdcbbbbaacaaaddbabbdacabdaaaabbcbadddaadcadbcdadcdddaacbaccacbccbdcbaddacbadcbaadacddbdbcccdcaadddbdbbaccdacaccdcbddbdacbabacdbaadcdaaaaddabbabcbdccaccaccabadddcabbaccdcaaaddcdcaccbcbccbdbdaddbdbdbdbbdabcdddcabcadccabbdaddbdbcadcbabccbbdbcdaddbbdabcdaabacdbacaaddacbabcaacdccdbabdbadbadbbbdaabbadcbbcdbdcddddbccacddadbaaccdbbaabbcbccacbcabcbbccccbccbbcddbdaabdadbbaaabcadbdcbbabbbbabcaabdaaacdddbabccbbdbcbcabbaadbcdbacabcdbadbbadadcccccdcbababacdaaacccbdccacccdabdbacabcddccacddaadddbcdaacbdacadbdbcdacbbccabdddabbcbadbdccacadadccdcbcbdbacacccaccdadbcddcaaadabcbdaccaaddaababadacbbdabccbcdcdaadccbcdccbccbcdadadcbadccbcdcddabcdcbdcbcbabaaadcdddbcdabdbbdaadaaccdaaabcdabaddbdbdaccbdabdddcbdbdaadcbbbbbacdbacacbddbcabcabdaadbbabdcabdbacbcbaccdcaddbcdadcbbbbcbcbbdcbdcaabdbcdadacbbdbdacddbbcabdabdcdacdcbdcddcddbdbcabacccbaacddcadaacccccbcbacdcbaaabadbbdcabbaadcabaccbabadddadddacdaddcbbcbbddabaacdaddbaacbbbbadbacabacbcadcbbdcaccccbcadbbbcacabdbbabbdacccdaaccaabaccdcabbdacabdbccbbacccbbaccadccdabaccbadcabddcababdbcadbddcdcbbcaccabaacaadcdcdbcadbcccdcbabccdadcabcdadccdccccbdbaddbcbaddddbdacddbdbcddbbdabbbdcbcdcaddcbdbbacdabacbbccdbbadbbcabbbbbdaadabadbbcdccbbddddccbaabcbcbdadbbdbabcbcabbdcacaacdadabaabcbaddbbbcbbbaccbbdbbcbbcbccaadcdadbcacaabcbacbbcaadbdacaabcdbbdddbccbddcbaddccadaccbdacadbdadcadccdcadcbcacdccbdcbccdaacbccabcabdcaddcabbdaccccdbcccadcdcdcadbccadacbcdbbddcaccbdcdaabbcbaabaccbbdabcdcdbddddbbcddadbbaabbbabadbbcdcdcbabacdaccbccbdaabddbdcdcabaabbabccdaddbbddbacbcbcccadadbddaaaadcbbbdccbaabdabbdaaaaabbbbacaacacdbddcdabbbbcdaaddaddaadbddacaddbaadabdbbbdaadacbbbabadaababccddacdbdaddbccabdabaabdaacbcbdbabddcbdbbadbadbbaccdacabcbccadadbcbaccadbcacddbdcacddccddccbddbdbabdcabcadadcabcbadcbdbccacdbcabdcbdacdbcacddbcdaaaacddbccbadccbbdaabababcbdbdbbdacdaaddbdddadaacdcaccccadcbccbabcbbcccdbdbabdabcadccdbaadcccdccdabbcbdbbbacaccaccaddabdcdacabacdbdbcadcbcdddcbabdaabbaddcaababdcadbdabdccdcbabaccacbcbaabdababbabdcbaaabccacbbaabcdaababddaabdcadaabaccdacdccdbdddacadbcaacddacabdccdbaabcdcbbcdbcdccaccdcbbccdaddccbbcdacdcadacccddddbdabcccacadcdbdddbbdccaaaadbbbadbbabacabbdcdbaabdcbcbcbbdadcbdaadadadacccdccabbadcdcbdddabbcdcbddadcbdbdcaaacdbcbccbccdcaadbcdddbdcbbcabacacccacbddcdcdbaadcdbbdcdabadcdbcbdcadacbaaabccadabbadabdbbacaaadbaaddccaddcbbdcbbdcdbccccdccababbabaadbcdcaccdbcccdbccccdddbdcdcbaadbcbcdbacbdbaadaaddabadcdbcdaacbabcbcbbaccdcbadadbbdcbcdabbcddccababdbbbcadcbbadadaaadabcbdcabacbbcacaadddbacbabaacbddabadbdacacccbbabacabaccdbadaadcbcabdaaacabcddccccdcdcdcdaabbaaacabcadaacacbbacdbadcbcdaaacdcbdcbbdcdaadddbadccdbaacdbbcabddaddbbacdbcbbadcaddcbccadadbacddbaddcbbdcbbaddabbcdcacbbdadcadbaabaaddcdcbdbbacbbdcccabbcdadcdaabddddadccccccbcdbbadaacdcaaddaabcddcdcbabdcbbdaaacacaabdaabdbaddbadbccdbabbdcaabcdadddbdbdadabdddcacdccdabaaaacdabbdbccbdaaadbcccbcadbababdcdbbdcabcbcdbdbadbdcdccacbcdabbbcdaacdaacddaccacababccccccdddbabbcacacbdcbacbcdddbacbcdccccdbadbaabcccdbbaaacddbdbabbbbcdacccbacdddddbdbbbdadaccdaabbaabbddbbadadcdadcdaaddacaabacdacbcbbadddbdbcccaaadbccdcadddcadbbdbbacccbcbcacdbdbdcddcaddacdaacbabddacabcddbacdadcadadabbcccdbccbadddaddabaccddbabbbcdcdbcbbbdabbabcbdbadbcdbcdbbddddcbddadbdcccadbbcacadbcbdabcbbcabbcacbadbbadaaabbbddadbadbbccbbcbccabaababadcadbaccdacdcccaaabbbcdbbddcadcdaabbacccdbabccddccbdadababdacadbdddbabadddaadadbabddbadbdccdcabcdbadbaabadbbadabddbdcdcbdbabccccdabbabaaadcbabddddccacbcdcacaaaaaadbbbdbbdacdbdcbbbdbccdbacdabccbadcdabdddaccaaccbdddccaaacbdabdadaaccdddccdacaabcdccccbbbadbaaddbacbdcccabacbcbbcabdbcdadccdcbbdbcdbcacbbabdcddabcbccbacabadbcbdababdacadddadbdcdcbbdadaadddcdbbdbbcbccbbbcadacdcdbaabbccbcbabcdabddccaaddcddbcaacabdcdaccccbadaaadbabdaccaaadaaacdccdadccaaacbbcbbcaddccdaccbbaaabdabcdaaddaacbbdacabcbcabccbaacdcdadddcdabccbaacdcaaddaccdcbbadcbabdcadcbdcdcdcaaddccaaaaacdadadbbbddcbacbaacddaaadbaacccccadcaaadaccdddcdcccbcaadaacdabdbabbdbbbabbddbaccdcbacdacaabddaabbdacdbcdaccbdacacddbdcbacabacbcacdaaababaddadcbbdddcabdcadabcbadaddaccaabbadababacdbcdaaaccbabddbbbbbcbadcaadbddcaadbcbaadbccbbdabdcbdddbbbcdddacaaccdcadaacbdabbdaddcdcbdddcbbcdbbbaabaadcbadaabcaabcddaaacbbdaacbaddbbcacbaacccbbbbbddcbccbacbbabbbcdaaddaccabbdbcbbdcdbccabbdccccdcdccbbbdccdacacaaccbcbaadddcbacdbdcbbcdcdccbdcddaadcbccdccaaddacbcdcbdbdcacdbbaadabacbdaacbbcbabacbbcdaababadaabddbbbaddbdadcccadddcbbdbdccddaaccdbdcbabcacdddcaddccacaadbaabbcbddbcddcddcbabcbdbbdacdaabcbbcbdbbcdacadcbddcaddcbbabaaadcaccddacaadadabadcdadbdcbcdbadcdddcbaaadcbdadcbddacabaadacadcacccbdbcccabccabaaabadbcbcabadbcaadaccaacbddcababaacccddacaacdabaacdcdcdaddbdbbaaabacbacbbdcbdbbabaaddcbaaadddcbabdbcabbcdaadbbabcaacadcbcadcdcbaccadcccadbacddcbabbadbaabbaddabadcabadcdbddbdcaaadccdcadcbabdccaabbabaaabbccbbbbdaddbdbaabbabcabacbbdcdabdddcaabcdaadbbcbababdadcabcbbdddcddbddacbaddaaabbcaddddacdbcdbddaccdcaacbdcdbbbddbcbbcadacbacadddcbbccacaacbcdcacdaadbdacbbbabadcaddacdbcdcbabadcdacdcccdddccbaabaddbddddadcbaccacdbcddabccbbaacdcaabbcbdccacdbdacacbddddaacadadcabbdacabaaddbbbdbddcadaccccbcbcddaaacbcadbaaccacabdccbaaadbccaadbcdcaccbaddbddddbbacccabbcdccbbdbadadcbbbcacaddccbdcdbbaaccbccbddcabdbaacbdbcbaabbbbcacdaddbdcacdbcdadaddcbccbbbdadcbcdcdadadaaadacbbacbaddbdbabbbbacbdcabcbccdcdaaddccdaacaabdddddbbbbbcaadbaddcbaaabcadccbabadaddccbcbdccdbdadadbdbbbdacbbbcbdabcadaccccaaaaabbadbabacaabcaadaccacbabbdaddaccbaadbcaccccbcacdcddcbacbabbdbbaadcdddabdabbdabaaadbbabbadaadbcbaabbbbbadcadaaababbbcaadcaabbbddcdacbbbacbbaddbcbbaddbcddccbbadbbddcdcaabbcbdacbbbbbdbdbbaabbbbbadccbdccbddaccdbccbbbababcbadbbcaaaadbcbabddbcdbdabbbbcaaadaccdaabadacdbaacdbababababdbdabbadcdbdbaadbcabacbbdcccdccacdcbcddbcabccbdcbcadcbbbbcddbbbbdbcabbddacbcbbdcbaccbccbbdbbbcbbcccdbccdccacbbdccbcdcbbbdbcababdbcdccaacaabdabbbaddbbbaaadcccddccabaabdbabaddcbbadcbacdcaaacddbacaaadacdabbcacaddadbcdddccddaadbdcaabcacbcadcbddabaacdacbcbacbccaddbcdcadcabcdaacbdbdcddaaababbcdaabdddaadabbabbcbbbdbbabacabbddcddadcccbddbbcdbaabbbdadcadcadbbadcaddcadaadbcbcbccbaacdcacdaaaacaadddbdadcabbcbabcccbbacacdaaaaacadddbcddbacdbabddbdcddbddacdcdcacbcdcadcacabbbdcdcbbababccdcddcadacdacbbdbcbbccaabacaacdbaadbbdcabdadbbdadcbdbaabbcbbadbddbaccaacbdcadcaabdddbcbbdbbdaabacbbddcdbaddcbacbbacaaaaaaccbdccabdaabaddbdbaacaabbbdacabccdaadadaacbbcabcaacdacacaacbdbacbcbbbcadaacbcaaccdbdcabbcabddddcdccdaadadddcaccddbabccdaadaccbbccaaccdacacbcdccbdabaacaddacadccdcbcdbbabadaadddcdcaaddaabddcadcbacaaabdaabaacaababccabbcabaabcddccacbccdaacaddcbddcbcbdcbccbcbaacbbddaddacddaabdabcabcabddacdcdcdcbbbdcbaacabacbbbbbcccdccacadcdbadadcaddaaaddbcaddcdddcddbbddaacbcddabccccbcdbdaccdbaaddddaabcdcdaabbcacbbcaadaadbbdabadbaccadaaabcccccddbcdddacddacaddbdbacdabbdbccddcbcabbacadbaacdadcadadcbbcdbcacbcdabdddaadcaaccbbddbbcdbcbdddadcddbdbaacabadbbdaabadcdaaadbdaddbddbcbbaadcccddacdcaccccbbaadbbadadcdbbbdaacadacaababbcbcddbdaabdadcbcaccaabcdcccbbcbddbcabcdabaababbddbcbaaacabababcbabacdccbcbcbacbbbdbdbaadbdccddcdcdabbbcbbddadccbcadcddabdbdcddbcbaacdcacdbdbcbacbdccdbcacabbaadddcddaaddabdbdaadcacbbcbbacaabdccdbaabbcbdabacdcddadbcdabdcbbacdaabbccadddaaadbacadabcbaabdcccccbcabcdccdcbcadbbdcdadacbacadccbbbacbbdbdcbcbdbadaacaccacdccadddcbcddcdcabbadcdbadbcdababcdaddbdbcbbccdbadbbbcddaabbdccabcaaccdbcbbdccdbadcabdcaaddbcdddcadcbabbccacdaccacbbdcdaaddacddcacbdcbaacabdcbbbcdbddaabaaccdaccddabccacdbcbcccdbdaaabdbccdbbbdabcdcdcdacbdccbdacdacbdbaccaaaabcaddabadcabadddcaaaacaddcbcbdcddacacaaabcbbaaddcabdcccbbbabcccbabcbdabbcacabcbaabddaacddaacacdabdbdaaddbcbcaccdcdadbdacacbadabddaaabbabcabbdbbccbabdaddbbccbbaddccbacadadbdbbaddbadbcdbdcdadcdbcccdbbadbbadacbbbaaaaaccdbdabbcdaacbbadbaddbcddabbdbabdddadcbadbacdccbbbddbbcbabbadcdadbdcdacbbadddbccadddccaddcdbbbbadcccaaccbddacabcdaadabadbdcaadddbcbdabbbaacdabdddcadcaadcaaaabbdbaadadcdccacbadaabcccbcabbccababbdddaccdaaacacdccdaabbbacaadcacddbcacbabdcbcdacabadbcdcabcdacdacddacbbabcbaabacaabaaabaacccdccdacaaddcdccaacabcdccabdbabcddccddbcbcdcbdcacabbcadccdddcbdadcbcdcadabdaaadccbbddbdabbadddcbaabcbdbcbdbaddbcdcadcbcaabdbbbdbccaacddcaabbabbcbcdcddabbcbadcccbaaccbbcddbaadbcacdaccdddddbcccdcaaaaaabadbddbcaaddabdcdcadcaccdbbaddababdcbbcbdccccbcddbaaaddddcbcabbcdddbdaddcbbbccdbbddaacbdbbcdcdcabdbcbbacbacaadbcaddbcbccaacbacadcdcadcaadadcaacbbcbacdcababcbbadaacbbbbcbdcaacbabdcadbdbdbacaccadacbdccadcaaddddddcbaaacacaccaddddcaacadacaacdcacbdadddcbcaaaabbdacdbaadddcaacacabaddcbacbacddacdddbcdcbaddccccbadaaabdbcaaacabaadabcdbdccccadaabccbdaddbacbbcbdcaccadbdbbbcacdaccaadcbdbdbadaacaacbdadbaabaddcadadbddacaacaaaddadbccddbabaccbbbddcabbdcbcaabbccadbbbbabddbdbcdadcbddcddabacacadddcddbbbbbdbdbabccdddbbacdcababbbdabcaacccccddabbcacbdbddddadaddadbaabdbdbabdbbcdbbbacadabaabcccbbdacbcdcdcacdabddabcdaccaacdbaaacbcbcadccadcccddcbadadcbaadddbbdacdcabdddcdcdaabddacbdbccabbdbcbabdbaabcbbdbaccdcbdbdddddaaacaacadcdbcbbbbdcccdddcddddddccccdacbbbbaaaddbcddccbddccacdcccccccdadadbccdcbacbcbdbaaacdccddbcaddbbabccbbbdccccbacaaabacaacdcdbddcbaccbcddbdbacddadddbaabbaccdbcbcadccdcbdbcbdbcdaaccaccbacdcacacdccbcaccacddbbbdaddacdaabcbbdabbbbaccdabdbaacdacabdcdbbddcdacbbbcbbbccdabcdabbbbaddacbdaabaccdacacabadadaaacaddcabbbcbbdacdbbaabacabcadaccbcdcbbcccccadcbcbcacbabbcadacabcccaabbacadacdadcacddaaaabbddbcddabbbacbabcbbddaccbabbccccaaadddbadcbbbbbcacdddbdabdabdcaadaccacaccdadabccdadbbccacbbdddcadaccacbbbcdcacdadcdaccadbaabaaadcbadbccbcbcacbcdcacbcddbcdbcaacaadbbdcadcdbacacdbbcdddcadacddaddbbccdbcabdcbdbdabdcbaabdccdccbbcaddbaddbccbbbcaadccaabdbacccdccaababdacdacbabbcbdbdcabddddcdcbcdbcaabcaabaccbdacdbdadcabbbacdaabbbdbcccdadaabcbbccaacaaaaccacadcbccbaccddccabbcabacaaccdccdcaaccddcbcaaacccddaabaacddaacaadcccbacadadcbbbacccdbcddbcbcdaacadcbcaadcabbbbdddbcacabbdcbdbdbcbbcbcbcdccaaacddadbaadccaaccccbaddcadcdaaaaddabdabbcbdadabbbaddbbbcbdcdaacdcdabdbbaccccabaadcbbcababdabbadcabccbbcccdacbccacdddbcacbcbdddccbbdcbbdccadbadbdaadbacdadaaddcaadddcbcbbdbadabacbadbccbbdccdcccddbcbdacdbdbbdaacddcdaacabadcdaaaccbccdcdccddcbccbaaadbdacadbbbccbbacbcadabdbdcdacbccddcdacbadbbbacacabbcbdadbbdaccabaccbdcaccbbdbdbadccdcdabdccadddddadbbcccdddddcddccaabacbacdbcddadbacbccadacdaaddbadcddbcdccaaaabdabddaaacacddacbdcbadcbacdacddcaaabcabcabddcaddcdcadabbbcbccabbdadbccddbcbdaabababdccbccaacbbccbbdcdadbbccacbcbccadcabcbadaadccdcddbcadcadcadcadbccabbdabdbdaabcbcadcbcbcccbabcdbaabaacdcbabadadddcbcbadcbbcccabadccdbbbddcdcabccbabdbaccbbcbdbddcccbaddabacdbdbaccddadbbcccdddaccacadaacddbbccdcdbdbddbdbadabbbddbcaaddbbdccbbbaadbcdadcdbbdbddadbbbccbddaccabcdaadcccdcadbbabbdacabbcdbccbddabcbbdcdabbdbaadcdccdbdcdaccdadadcccaadbcaadadaccbcbcdcabaccbccddbbaddcdcbddbcacadbbbdaaacacbadbabaaccdbdbcbccccccbbccbacadbabdddaacddcbaabaaaabccacaadccbcdccddadabcaccdacddccdadddadcbbbcddcdacaddaaddcadcdcdbddbbcccabccdddbccdbcbcaccbddbdcbcbdbcadcdbdccaabdcabacdddddacccddcbadcccdcacdddccbadbadbaadadcbbdbddacdbabccaaaabdaaabcdcbcdababadbcdccdacdbcccbbccaaabaadcdaabbbabcacabddcbbcbddababcabdbadbcddabccdccccaaccaacadadbbbbcbdcccdbddbcabcabbdbddabdbdbdacbabccadbcddcbddcddddcdcadaabbdcaaaabbbadacdbabbdcdcaccbbcdbbcbabaaaadcdcdaddbbaaabdccbbdddcabcbcdbbccbbbdaccabbbcccdacaadaacbcacbbabddacdcbbbdbdadccbccadcdbaddcacddabbdaacdcbdccbcdccdadadcdadaadadcdcccdbdabddccdadcacbdbacacbccadddbcbbdcddcababdbaadcabddcbcaacacddccdcdddbdcdacbcabbadcbaddadcabdbddcdbcddccccddbdcaddabaaaddccadaabddbbbbadabdbccbcaddbdbdccacbdbdcaddabdaadacdccdccadccabbdcacdbaaddbcababbccababbadaabdbbbcddcacaabcbbcdbaabaacbaccaadacdddddacdddadacdbbcbcbcdabddadcddcdbcdcadccaadddbbbddadcdcbacbcaaadaadccdaabdcbdbabddccbacadaadaaccaadbdcdddccacdbbbbbdcbcddcadcabcacdddccdcbdbaacccadbbbbaccdbadabacaccaddcaabbccbdbacddcdadbbcacbacabddbcbbcabdacacdabacdddbddbcbabcaacbbdabcdcdaacdaabbadacdabcccbcbabddbddaaaccccccdbbbacbbcadcdddadaccbddccdcccbccdcdcbcbddacbcbbdcccbcbdddcbabcaaccbadcacacdabddaaadbadcdcacaddacccbdacadbddcdacccabdbbcbdcbcdaccddccbaacdbcabdcadcccdaaabdadadccbabdaaaadbbbbddbaaacbcabbcabbdadcabdddcbdbaccacbbbddcacddbcbacabbdddabcbcbabdacaacacaacbcaaadabadadcdbbdbdbcdbaddbbacaadcabbcdbaccdddbbbbaccbbacdacadcbdcdadbddcdcacbaccbddaacbbadcbaababadcdbccdccbdbbddaaabadddabadcdccbdaddbbacdabadbcccbcccccccdacaabbabddabbdacccccbcaabbdcbcbdddddccccbcabcddabaaadaadacbacaadcdabdabcaacacddbdbaddbabbdddaacdaaddddcccaccddacabdcaddddacbbacbcdbcbbbcdbbbbabbabbdbbdcccabbddbbdcdaddbdbdcabccadbbbadcbddbdbbacdbadbcdabbcdcdcbdddcbbcdabbaaabaabbaadbbbbaddcdccacccccdddaadbdaacaddbbbbadacabaddbbbbddbdcdbbcadaadabdbbcabddaabacddbadccbdacbbcdaacdccccacdccaccbacdcbdadbbcdcaadacbdaabcbaacabbdbabcbadbacabcadddaccbcaabdabcdbccdcbbabcdbaccccdcdaaadcdbdbcbbbdbcbbdabbdabdacadadabbadacdbcaddbbbbcdaabcbabbccacaaccdadbbcdddbacbccdbddbcdcadcdcbddcbbdccdbcdadcacddcbcccbbabadbdaccbcadbcccdcdaadbbccadadccaaadddbdccdbbdabbdabababbcbcdccaadcccbcdabacaaddcadcbdaddccbaddbdacaccbabcabbacadcbcdabaddddacabbbaccdbdbccbddbcbddbdcacbbcacacbcbbaacbbdadbcacdacddbbcddabababacddccaadbdddbbcabcbdddcdabccbdaccbdabaadacdabadaaabcccbbbddcadcadaabdabbbadabdcccdcdadaccbabcddbadbaaccabbcaccacddcbdbbddaddbbaabbccadbbdbccacbbadabdccbbbbaabbcdbccbaabcbdbcabdccccbbaadcdbababbaadddaaabaddbaadabbcccdddaacaadccdcbabcddcbcdccbccdaaadbddaabadcbbbcaddcddabadbbbbddaadacaacacbacaacabacbaaacdabdccddbbdacccabacacbcaabbaddabdadaccdabcdbdaccddcdcdaacdcbddbdccabddbbdbadabaddadcbdaadbddddcccbccddaaccbbaddabddcabdbabadadbdadcacccdccdccaababccbcacbabbbaacbcbcadcabcaabbaadbaababbbbaaacccbacaddddaaccbbbcbcabababbcbadaaaacdcccbadccbcdbdbccadbaabaaadaaacabadcccdbadaacbcaabadcdabbcadabcbabcddaacbbcdadbdaaabbcdcbaacaaadcccbabaacacbdccdbccccadabbabbdabcaadbbcacadddabcdddbccbdaaabcadaadcacacdcdddadaaddaababdbdcabaabcdbbdacbababdabdbcbcabdcbaaacacdabcbdcacabdcbadadbdcbaadacccdcacbcaabcaacccbaddddaaaaaccaabcaadacbaaabdddcddddaccbdccbddcacbccabdbccbabdbbdbdbbdadccadaaadddabcbbccccdabacaaaaddcbddbcdccdddacaadaddcababdaacdbcaadbdddaadaaddddccdcbbbddbdabddbacddbbdbcdbcdbcbdabdabadaabcdddcbccbabadbbbcbabddcbcadbcaccdbccabbabbcbdbddccbacccbcbccaababcdaabbabbbbaccbdbadbbccddabcbdacbdbdaaddbadbcdbddcbadccdbabbcacdcdbbbaaaadcbdbbbcdccabbdbbbaabccbaccaabaddaadabcbadcdabadacbcdcddcdadbdbcdddcacdccabbddcdbcabababdcaccdcadcadcdddccddccbbddbbcdbcdddcaadbbaacdddaacbcdabadccbaabdcabddbacdcddddcbbabbbcbccaacaddadbddccaddcdabacbdddddbcbaaccaacdacadaacbbadaccdbadccbbcbcbcaaadbdaddcdaaabcdbcdcbcdbbbcdbbdbabcabbbdcaaaaddcbccbcbaccddbaababaccdadbcbcdcbdaaabbcdddabdcaaaccacdbbbdaaaadcdcbdbddabcbdbbacbbadcbdbdccaacdaaaaddccadccbccdabbbdcbddacbcdbbbdbddbacbdbccddabbdcccadbcdaaacdbadabbabbddbabbbcbdaaabbccabcdabbdbbbdacabdbadcbbbbbcabbbdacaadabdacacadcbdaacbcaabbbabacadbdbbbccbadbabdaabddcbddadcbadcbacdcccadacdabbdbcbbdcadccaaaddaaabdcbabccbdbdcadcdbadbdccdbbbdacdbbbcbabdddbcbadadbcbdcdddccabadaaddcbbcdadbbabcabadaabaccbbaadabcbdccbbcabadbcbcbdddcddaaccbcdcbbbbddadabccbcbbdcdccbcacdbcabaddacadacbabddbadabbddcddabdcacdccdcbcadcadbcbaacabacaadddadaccabadaabaaaaacdabddcdadaadabcdddbddddbbcbddbaaadcabdaadcdcbccdcbadaddddcacbcccdcccaacdccbdcabccbbcbcdcdbcdcbcadbadaacaddbbbdadcacdcbddadbcdbaaaacccdbbcaaccdaabbcccccdabbccabbbabadaabaacbcbddaadabbcbcdabccbabaccccccbdbcbcdaacddcaaddccbcbdabcccbadabbccddbcbdcccacaaaddaacadabcccddadccacacaabcacdccdaccbcbbdbdbcbdcacbcaaacbddabdbbcbadbcbdddabaacccadcdddbabcadcadbcbbcbbbdabccdbadadcadacacbcaacaccbcbbddabcabdccbcbadbabbadcadadbaabdbabbbbbcaabaacbaccdccbdcccccbdbadacaccbabcdadaaddddcacaadbddbcdabcabccacdacaacacbbdbaabcddcbddcbbdaaacdaaccbdcadbbadcbabcdadaadcabdcddacdcdadbacadddcdbacbddcabcbbadcbbdbcbbccbdbadabdbbabbdbaaacbbbccbadbcdabaababbbaaacbabcccddcccbaaaadaddccadcbacdadbddabadcdcddcccadddccadacdccbcbbaadcdacabaccccbccccbaadabcbcaabccaabbdbcdbccbacacbabbbbddbbadabcacacdcabbbcccbbbdabaccddabbbabcaadcdbdbcbcbaaddbdbbbbcbcabccadabbbddacdadbbaaccccccbcaacaccbcdcdacccdccbcbabadaabbcabbbdcdadcdadddddddbbacccccddbbdcacacdbcdbbcbadaaabdccddbddbcddcbcccbbacdbcaaaddbadbbacbbbdacdaaddaaabbbdbcbbccdccddabcccaccdaccbcbbabadcbbacbcacdbccadcadaadbabcbccacdadbdcdddaabcddbbacbbabddbdabbddcdcabddbdcaccadacddddddbbaababcdcabcbdbaddccdddcddddabbdacdbacaabacaabadabddadbcabdbacbbdaaaabcaddabbacaccbaaaacdccbbbaadacccbacbabdcbdbdbbdcadbbdcccdddbbddbbbcaabccbccbbddaaadcabcadbdabbbccbbdbcaacadcbbbdddcbcabdaaccdaaacccbccbabbbdabcbcbcdbdaaddbbcdcddadddcadabbdaadbadbadadbaaaaabbbddadaabbdcdbaacbdbbcbbbdcaabdaaacadcdbdbbaadacbcddbacabcabccdbbabaaadcaacdcaddbcdccbbddccaaaadaccaccacbabccbcdaacdbcbdbabccbbcbabdddbbdacabbdaaababccbacdaabddccadcbbbacdbbabacbbcdcbccbbabbcbdcbbddbacccccdccbdadaaacdcdabbbbaddddaacdcbbcbcbdaabaaaabaddcdbaaccbbcbacbabbaacaddbdbbacbbcddcdbcadcccabbbdcbaacbcdacaccdbcaaddccbdccdcaccbcdbdbdddbbbdacbadddbddbaccdcbaacdccacdddbbbccddbdddbdaaacaadacdabcabbbacbccdcbdcdabdaaccddcdcbbbbcadbcbccdadcabcddaabcbabdbbdcaaccabaccacddddccaddaddbccdbbbbdacbdcbccacdbacdaacbbaabbaaaabbaddadccddcabdaaacdcadbaaaaaadcadbabbbbcbaacaccccbcddbdcaabbdabbbabdddbdacbddacabdbdccddaccbbcaacaababacbbcdbaccacddabbbccdcdadaccdcbbbbbcbcdabbccdbaabacddbdbbcacbaddccbbcadccbdcbdcdacdbcdbbaccdbbbbccabbcbdaddcddcbbbcabdaccaaacbcadcacddabbdcddadcacbcaababcbababaadbbacbdbcbddcdddbccbaadacaaadbbdbdbbabddcabadbcdcccccabdacbadbcabbadcadcbdaadcaadbcbbdbccdbdbdacaaadabddcdbabbdadcddcbadaaabdcaacaacbdaacbbbbdcadaabbabaaadabaadcddadbbdaabccbbbdcbabddcdbcbabcddbccdbdcdaddcddddccadcabcbcdcabbdbadcbcadbdcaaabadadcccacbbccdabbadcacabbddadababbadcbadbabdccbadbbdddabcbdadbcbacbdccbbacaddbdacbcadccbcacaaaabcaabddabbcdcccbbbaddbcccacdbdbcbccbbabcdbbbacdbbaccdbcaabcddaddabbacacdcacccbacddccdacaccacbbbaabdcbaabddcaaabadaacbbcdabbcabdabbdbdaaaadaabdbdbcabbabdbbdaaacadbacaaabbdcdbcbabcdbddbcccadddbccbdbddccdddcbbcbbcacdaccdcccbdabcbaddbbabdabababaabddbacdbcaabcbdbdbccbbbbbbcbddaddadbabaabbdbccadbbacbbacacdaddbdbbcaaacbdbdccbabaddacbacacadbbaacdbccdcccdadcabddaabbdddddbdbbbcadbbcacbacbadbdabbcdbaddcbcaabcadcbdaacababcabdcddccccbcabcabdbbcddcaccdbbbcbaacabbcbdbbaddcccbaaaabacabaacacbdcacaaadddabcdbbcabcdbbaacbbcbaccbcdbdbdccdaabdcacbabdaaabcbbbcbcdabcbdbdbccbabcaccbddcdbdaaaacbaaccbaabcdbdbaccbacdbabbdadcadacaaacacdbdcbdccbcdcaaadacdcddadccdccbdbccbdaccaddacdaacaccdbbcbdabcbddbdcbdddddbbdbcbdcabdcddaccbcdddcabacbcbdbaccabaaadaddaadcbbdcccbabadcdaddddabbbacbdcbccabdbdaadcdbdadaacbaacaacccbdcbcbdacdbddaababcbcccdacaadacaadaabdaadbccdabdaaabdcdbaddcdaaabacdadcbadacaabbcabdbbcaccdabdccbdcbdbdaaaabbaacdadcdcbaddbccccccacaabcabadbcdccbacbcaadbbcaacaacbaabdcccbbaaaacbadcdbdadbddddcabcacbbdccbbdaaacabcdadcdbdcbddaaaddccbabcaccbbbadbabdcadddbacbdaacdcadbdccadddbddacbdaddcbadddadccacabbdadbbcababdaccdcdcaadcadbaabcbdcbdabccabdcdbbdcdcbdaccabcaadacacddbcbbcdccacaabbadcdbbaaadbbcbbcddcbccccbaaadcbdbdcbcdaaadbcabdcbccbaddddbbabdadbaaccdacdabbacaadbdcbcbbcbccdddcadcdacdbbabaabacdacbcabcbdccddddbccabbdabbadbaadbaacdcccdbcbacbddcbacabdccdbabaacbadbcddccaddabbabcdcbcbcabaadcbabbddbddbdbdccdcaddbadacdbdbacabccaabbdbcbbcdabcccbdbdbcccdcdcbabacccdacbbdcdcbdacbdbacadaaaddbbbcacdbdddacdabdbddddcacbccbcaaddbddbacaacaadcacdcacdaccbacaabbcbabccaacdcadcbaddcaaaacaccabaacabbbadadbacadbaacadaaadbdabbaabdcdcccacaaccaadadbbbadaccacbddacdcdaaadbcaaddcdcaadbcbcdbdbbadccccdabdacdccadccaaccacccbbccaccabddbbaaaccaaadbcdcccdabcddbacacaaccdbdabbaababcbdcdbbdbcacddcbdcdadabcdbacbccabbacbadcddbccdccaccbdbdacdbabcbcbbddddcdbdccbddbccacbdcacdcaadbcaaccaddddadcaabdadcbdddcbcdcccbddadcadacbcbcccbdcddddcbcbcccdcacdaabaddbcbbadcccacabbcacabdbacaacadcaddcaadcccacbdddccacaaaadbcabccddbccaacaddaccaabbdcbbbcdddbccaacbabcdbdbcccdadbdbdabcaccddaaaddcaccbdaacaccdcaabcdbbbadadacdccdbbbcbacadadaadccabaddadabbdbbbbacbdbcbaccaaadbdabbdbbadcbaaaaadabdddadabadcdbbcbcacaabddbbadabaddddbcbcbccbbabdaaddbadacadbbaaccbbadcadddcccccccdbbcbcccdcbabdbadaccaddcbddbdbaccadaaddcadacdbbacaaadddbabadcdcbacddabbbdcbccaabadbccacbabcbdabcbbdbcabddbadddaabdbbbaadbdbdbbcccdddaaadbdddaddaddcaddbbbdabaadbdaccdccbbcbdcddcacccdbcbacdabccccccdcbcdaccdadacddadcbbcaabccbbdaadcdddbcbbdaacbcddbadbcbdadbdcbdcbbdbbcabbbbbdbccdaddacdccccdcaabbccbdbdbaabbdaddbacbbbdccddbbcdbccadbdcbaddaacbdaabdbacaaddddbbdbbadaaabdccacdbbdbabbdaadddcddbabccbabaacdcbbabdadbcbbdcacbdddcdadbcaccddbdcbacdbbccbaacbdbbadacaacdabbdccbcaccbbdcdcacdcbdddbacbdddbbbddbbabaacadcbcdabbabadbcbabcacbcdbabdccdabdccbadbccbbccbcbaaacaacbbdcccddaabaaaddbcdcdbcbadacaadaabcadaadcbbabbdcbcabcaccacbdbdcdddcbcbddbccbcbacaacdddccbdccaabccdbdaacabacadacadacbdbccbbadbcaabbbcaaaccabdaacabaacbdccacbadcadcdcbcbddcdbdabaabbbaabcabddccabaacaccddbcdcddddcaadcbcadcacdadbabdbdbcddbbcdcdbbacccdababdaabdcbadbdddcacbacdadbadbbcacaacdadcbcdcabcbccadaaaadccacbadaabbabdbcdbadbcabaddabdcaccccbddccdacdbaaadbdcabcbcddaaabdcbcaaccaadaddaadadbccbbdcaaabddcabcadbbdabbcacbaacdccccaacdcbbbddadbddcbdbddddbccacbadbddbadbbdaaabbdabaaabdddaacaccdbccadcdbcbdacbbbcbccaaabdddadadacacbdbddaaccccaddbabbdaadbddabbdbbdddbdbcdccdccdaadcabaadcbcbcabcdadcbcbdaabddbaddbcabbaaabbabaaacdbabbbcaaacabadccaaabcddaacadbbbaacadddaadbabaaadcabbbcdaacbbdbdbdadcddaadddadcbadadabddcadddabaddcacbbdaabadbcbdcbdbcabcadddbcdcbbcbaacccdbccacdbdcbaacbbacdddabbdccdbbacdbbdcbbacbbcbbacadddccddcdbbbacbbbabaddaacbddccdbdcbdbdadaacdbaacccdbdbacadccdbdacabdbbbcdaccbdcaabcbbbccdacbdcdbadbdddcddcbbccaccbdbccadbabddabbbbbdccdbdaaadddcabccdcccdbdcdccaaaccbbdcaaaabcdbbccaaccdaccccddaaaabbbacaaadcabcaacbacdcabcdbdcdbcccdbdbccabcabbadccdccacbcaaadbaddbbbcbbabaabddcbabbbbacdbbacabbcdabdbdcccbdacddddddcbdcbbaaacbdbdadadaddaddcbccbddcbbcdaacbddbaadbcbbbcadadbcbbcbacbcbaddabccbdbadcdacdccaacbaaaaccdbcdabbdacdbddacabdbccadcbbcbcccdbbccaababaabcabcccadbbdcaaacdacbaacdaacbdabaaddcdcbcbbbcaacbccbbdbcbbcbcabccbbccabbdabcadcbccddcaccaabaabdadccabddcdbbabcbdccaddaabadbbbbcccaacadaadccddcbbcbbacbbdbbabcacdbacbacabaaaabcbccabdbdacaccdbcdaabcacbabcbaacccbdbaabababddddabbaaabbcdccddabcacbaddbdcabbabaabaaccbcbcaaabdddddaacdaddcaabcbcabddbbddaaaaadbabaadccdbddcbaddcbccaccdbbaaabdcccadbaaadddacdbabdcdadbbddbdabbbabbbaadbccbcbabbaabcabccbbcdaabbbabadbbadcadbccdcacdddbbbbaddbadbcccbdbddcddbdabdcabddbcbdcbdbdbdcccdbbabbddbaddbdacacdccabadccbddcdbbacdbdaddabbbbccdcacdaadcadabbcadabdcdbdaaabdadadacddbaaddcacbadcabdbbaaaabdbccdbacbccdadbcccbdcacbcccbabdccdccdcbcdcdbadaacbcdaccabadbcdcccaaacdccdbbabadbaaaaaddadbbbbabddbdabadccdbaaabbdaabcadbbccaaccabaccaadccddadbacacbdbacdcabaabbdcccbbcdaabdacdcdabaddbdccdadadccabbcaabbcbddbddaabdbacddabbbaabcbdcacbdbabddbdbadddddbacdaacaaaabacbaabaddbacdcadabbacbacabcbbdabadcabdacadbabbbdabdccaccbaccaacdddcaaaaccbabbcacbacaaaabddaaadbbcccaaadadbddbbbcabcbaabbbddcbcbbaacbcddbbdbadabaacabcbbcdaababbbbdbbabdadddbadcbdbcdadabdacacbcadddcddccbcbdcdaabacbccabaadbaabdbcadddcbcbcacbddbbacdbcbbadbcdbdbbddacbcccdaabbdaddaddabdcddbbbaabcdcddbdbddacdccacbcdacbbcabdccdcdbcbdbaddccaaaccbadbacdbaabadbadcacacbdbabacbdacbaccdddccabdabadbdccbabccaacaabdbacabadacddbdacdadbdbabbcccaabaabacbbbdbcacaddbdddaabbdaccdadaddccdbcdaccacacdacdaccdacbcddaccaacacacdabbbadcabdbbbabbabdbdbcdccaccadadaacbcacdcbcdcaaabbdccddbbdddbcabdbdcacbbcdcadcadaddbabaacabacbcbbadbdcabadbaacddcdcdcdacadaadcaadcbccbadcccacddabcdbbdabababdbbddbcacbdcbadbdbabdadacddbbbcbbdbcbdcccdbbddadadbbaccdabddadcbaaddbccaabbabbacbcadddaabdacddcbccddbdacadacadcddabdabccddaddaddaadadcddccbdbaccbcdaabdbcababbcbaacadbacdcbbdcadddbdbbcbddaabbabdabdddbcabdcccaacaaddbcbaaddcaddacddcdacbabaddccddcdddbcdcbddacbacadcbcbbdcdbaaddacabdcccababbddddbaadcdbdaaccddabbcadaacbdcdcabccbddaacddcdbbaccdbddbdaacabbaacdaddcbdaccdaaacdcbadabcccbabccdbcddbbddaaccadbbcaaccaababadcbbbcaadbbabbbbbbaccdbdaabadabdcdaadcccbdbbadbcaccacaadcccbbccbbddcabccdaadacabdcaddaaabddcdddcaaabdaadababbddaddbcccdabcbabbacdadabacaabdadbbbbaacbbadbaadbbbccabcaacbbbbadbcddbddaabadacbdbdbacaabaaaabdcbbbadbcdddcabccdcbcacadcadabbdbcdabaadbbdabacddbccbdbdcaaaadddbbcbaadcaacccccbbbdbbcadbbcadaacdaacccbcaddcbacccdccbdbccdddbbdcbcbccddddcbccaddacbbbacacbcaccabcccaabbacdbbdbacabcbbddbbdadcbbcadabaabbdbadddccddbdcbadbdacbccdbdcadcbbbaaaababacacabdcaacbcaadccbdccacdadacbcadcdbcbbaabacdacabddcbcaccddadbdcadccaddbdccbcbddbcbadaadcdbddcddcbbccddbabbcbbdbbacdcaddccddddbbdabbcccbaacdbcdcddccbbaccdbcbbdaaaccdcbbaddabbcddacbcbbbbdbbacbbcbdcccbcbcaaabaacadaadcabbdaadabbdddcdddbacbdadcacabbcdcdaccdbdcdadbabbccadcdcbaabadaccbdbaaccbdbdaccdbaaabdadccccdbabcdbbabbbbdbdcabdacdbdbdcbcdbdacacbbbdcabcbaaabbcdccaabcacbbcdbcbdababdcabbbddcccccbdacbdbdacbadcabbbbbabccdcababcabbcadabccadaaaddbccaadabcbaaadacdbbbdaacacdadbcaabcdcddddaacbccbdcacbcaaddbcacaccaccbccdbdaaddcdcadcabbdbaccbccdbcadababbdaccdcdcdbbaacbccddccbdcddbccdbcaacacdbbdcbbcacbaccbdbdabaccaadabdbabcccdabbdabdacdccbdabcaccaabdccadcddbdcdbcacbbaaadbbbcdacbbdcbdbcddbddbbaaddbbcbdbbbdcdbdaaddacadcdddccabbbcacabcccdabdbccadcbbccbbdaaabbccdddbbaabbbcbdbcccdacaacddcbdcdbaadbcbbaacbbdbcadbdacdacdbcaccadaabbcacdbdcaddbccbabadbacdacdddbabdbabdaabbdbddcdcaabbaacdacdbbadbaabbbdcbddbabcdadabbacabcdddacdbababdbadbdbababdcddbbccddabbabcbadbacdbdaaabaccadcdbaaddcdadbabcdaaacbdcaacbdddddcbcadacaabddacadcddacdcdacbdcadadccdcaabccdaaccabdccbbaccacbacccbdbbdcabcddbdbdddbbdacdaabbbbcbddadbcacdddddbadcdacbbdbdacddaccccabdbcddbaddcbdcbdcadbbadbaaddcdbcabbbabdbbaacddacbddddcbabbddbdcaaccbaaacbabbccccdbbdcabcbaaccadaddcdaccdabdaccdcbdbdddabacaadccbcccddcbccbdcacbabdaabdcddaccdcaadcbcadbdabcbdcdbaadcddbdccccddbcddbadbcaaddaadbcccdaadcbbbbddcccbacabadcccdadccdabbadcaccccadacbbdbbdbdccadbccbabddabddaddbbbbacddbdbbbddbcaabbacacbabdcacacaacbccaaccbaadadccaccbdcbabbdaaaaabdbdbccacbaaaaadbdacddacdbbaaacdcbabaccadbcddddddbcbbadacdbcacadbbddcbccacacabbdbcabdbaaccbacabdcccbcddbdddcaabcbadacdadaacacddcbdaacdadbdcadcacddabdacdbccabbaacbdacdcabcbbdbccbbddcbccbcbaddbcdddcbcbbddbdabdacdcbdacdababaabbbcadbcacadadacaccababbdbdbcdccdddddbacdcbcdbaabdbcacabcddaadbacdabaacdcbccbdcaabdddccddaacaaddbaccddabbdcdbddadaccdbacaddbbacabddbcccbcddadcbcdaacadcdddcacbbabadbccbaabbcdcdbbdcbacacbaabdaadcbccbacdcdbcabddaacbabdcadcaaacccbcabdbccbbaaccbadcdcdacbaaabdadddbcaabacddabcbaadadbabdaddbdbdaacbaadbcbcabaacdcdbcbacccccdcabcdacdbcccbdbcccbabcabaaddabbbccbbbbdbbdbdddadabcdacadbccabadcadbaaaaacabcddcaacccaabcdcdcdadcaaaabccbacddaabccbaccdbccabdddbcbcddcbabdddcbcddbccbdcdbbbadbbbadbccccbcadacdddbaddacbadacccbcabdabcbbbadbacdacacaabacadcdaccabbbdcdbccdcdadccdbbbabaadcacdddbadaaacbbddacaaddbcacdcdcdbaacdddcccaacbaacbbbabacddaaccabbddbadabdcdcdccbaddbdaadccdcbddabcadadbbaaaddcdaadccbacbdabbccabacbbabaabcaadbaccdccdbdbacaadadcaaacaadadadadaadcabdbdccaaccaddbbdabcbcaaacacabbbdccbdcacbabaddcadcdcddcccaadbdbbcccadbbbcabbaddcabddababdabcbadcaccadaacbaabbdcbbcbacdbccbdaadaaadbcbcddbdddbcdacdacccdcadcadbaccdcbbdcdbcdabccadbcbacdabdcbaccbdbacddbadcaadbdacabdcddbcaddabccaacbaadcaaccdcacadbdcdccbaddbdbddcdbdbdadadcdcdcaddadaadbdaabcbddadaacbdababbcbdabccddbddaccadbaadccdbaabbaaddddbbdaadcaadccababbdabddacdbccdbaabddabbadacdadbaacdbacdbbdddacadccacaacdcdbabccbbdaacbbaabddadbcdbdccaabdaacaaccdcdbdabdcdaaabcbdddbbabcbbabdcdbdbabbcbdabccdcadddbabcbcdddddaddacddddacdbcabbbbbbbaddaaddbdbabdacdcbddddcddccbadaccaadacdaaaccabbabadddbcacdbacbbbcdbabcddccbdbccdacddaaacadcdacaadbabdcdbdcddadcbddcbadcbbcaabacdacadbdbdddbadbabddbaccbcacdcbaddbaddcadcccdcadaaacabcadcbccaccaaababddcbdbbbbacababadccdbbaaaccbaabaaabdbbcdbcccbddacabbacababccaacabbbdaaabaaaddadcddccbbcddddcaaaddbdadcbacbbccbdcaaaacaabaddaacadbdbcadbcdacdaaacabcabbaacccdddcbdcdcccccacdadabcdcdccaccbdabbdadcddddacbbdbcaabbddacaaddcbdcabdbdbccaabcccddbdbdacaadbaadadaacdbaadacdabdcbdbacbcdccadadddbbccaaaccabacddbcacbbaaddbaacdccadaaadadaacadcccacdcaccbdccbddaddbadabcbcccbcacbcdcddcbdcbaccbccaccddabcadacaadbacdaccddabacbacdbdcacacdaacacadbddadbbddbabbaacaddacdcccccdabccaaaadccbbbaacbccabdadadbaccacacbcddbbbcbcbbdbccdadbbcddaadcddaaadcaaaccccdcbbccabcaacddadccccbacccddcbdddbdaadacabdaacdaabbaccadadaaabdbccaabaddccaaddcacaaddcccbccbabbbcbadccabbcdcbbbdbababddddaccbdcaabddbcbcdacbbcdbaacabaadacabacbdcdaaacbcbabcaddaabaaaabddabcdadbadcdaacccbcddadcdcadbbdaadcadcacbcaddacabbbcddcbbaddcbabdbbaabdcdcccdbbabcabbbadacbdbbbcadaadacbdcaccbbabacbdddccbbbddcadcaccadbcadcdabbbdaaacdacabcdcdbbbcdbaacaaabadccbaccaccbbccbdddaaabdbbcabaacbcbdaddcccacbadddbdccbbcdbdddacbbcddccbcdcadadccabbcdccaaacccaccacccbaddddaadcdbcdacdabbabaacdabddbddcaabaddcbcbacadbccdabcadcdcbdcbbbbcacdbdddaaddbddbcacdcdcdaddbcaacbdbccbccbbadacadccbbbbcaccdadccbbcddaacdacacbaccadacbdcdabbbdbbcdaadcdbddababbadcdccaabcdccacdbabbcdabddcaabbbabcbaacbbaaccbcbbdcaaadccdddbacbdbdcbbadcdbcdadccccbaacadacacaacddccbcdacadacacbbadacdddabccaacbabbbcccdadccdbcdbbdbcddcbbdacddabbccadbaabaaabcbaaccdbcdabbadbdcccccdcdacabbadbacacadddacdbbbbdbcacadcccbcdddbccacbbbdcacccaddbdcacabdbdabaacacababcabbcaadbaacbabadbaaabccbbcddadddaaaddcbcbccddddbcaadccbcdadbbcddcdadbdcbdcabbbcbadcdcbddbbcdbbddcbcdbbddadabbbccadcacbbbbdadbacbabbcaacaaabbacdcadbdbabccabbddcdcadbbccabcbbbbbcadcacddabdaacaabacddaaabdbdbbcbaaaadaddaacacbdaddbacacdabbbdcddcadddbcbaabcaabbdccdaadbbaacaaacaacacaccbbaaddddabdaadadacdcbbaadccabcdcbbcaabccdbcaddabdbcbbddcddcddcbcababbccbaddaccbadcabbadbdaaaddddaaadaadccdbcbacccdccdaaacabbbdccbdccdadcaccddabccaccaabbcdaacbaacdaaabadabcdadbdbcdcbdbcadcabdacddacbaaccbdbdbbcdabbdbababababdadbcbbdbddddcabacbadbaccdcbdcbbddcaabbbcdaacddacbadaaddcbbdcbdbbbbccbdcabbacaaddccdbcbbacdbdbbcdaccbaaaadacabadcccadbbcbadabbbadbcabadbcdbddbaddadddcdbacddcabdddbaadcdccacbcddcbcbacabbbbbddadbbcbaadcabcdacbbdacaaccddbabdacdaaadcbdcbaabdcadabaaaaabacabdcdabcbdcdcccaaabbadcacddbcddcbdbccbbdacbaadcdcacddbbccdaccdbaddacdaaadabdbcbddbbbaccddbbaacddaabcbadbcdabcacbabdbbccddacaaacdabadacbdbadddbaacbabcccbaaadaabcabbbdcbdbaaacdbcabdabdcbbabbdcaaacbbcabdccddababddbbcbccddabbdaabdbdcabacdbbcbabddbdcbaacbbbcccbbbcbbccaccdcaccbbacadcddacacadbcdaaadcacbcdaccabccacbbdabbabbddbaababbadadaccaaadcdbbbdbbadcccdbaddcaddcdccdbbbabaabccdaaddbcbbddcbdccbbabccbcbcdaabbbaaaacdbaaabdddabdaadcddcadbcacdabcbaaccacbbbdbacdccdbbbbabbccbbdddbddbabbcdcdacddabdbacbcbadccdccbcadacbabbaaadbbbbacbabaadbaaddcccbbdcbbbbaadcdaacddbabcbdabbababbdabacbdbbbbbdcdbbcdbbaacaaacddcbcbdbcabdcabbdbddcbabcddcdbddcacdcdcabadbbaabbcbcabcbcaabaadbdddadccdabdcdcbddabbcbcdccccaababcbadabcbdbddacadacdbbdadcdacdbbacdbadcacbbcbaaacaacaaaddbbbbbdaaacdbaddaddbcdbaccdacbbbacacdaddaadbccddcbbadabcbaaccabdbbcbccbbddcccdaccacacbdcdbdddcadccccdaaccdddaddaadbcbbcbabbbbbdbadcddabababacdaacddcccdadbdcdcbaadcdadcccccccaccdbbdaccddbbcdacddccdddbaaabcccdcdaadccadcadacdbdacbdddbcadcabcddbaadaacccdccaccbadcabdddcadbabdccdaabcadaaacabaccddcaabcbdbabbbababbcdddadcacbbbccbbabddccadbbaacadbabdaadabacdbbbdacdbbbadacaaacddccadbacdbdaabaddbcaaaadbadadbcbabbcbcdddbdbaadbdaaacbdacddaadbaadabddddaabadbbdddddddaccaddbcbbbbccdcccdbdcdbddbcdabdcdbcbcaccbaabdccdbcbacbbdaacddcbddcaadabadaddcaaddbacbddbdbdbcacaadadcbbbcdbdbcadaccadbcbbcbdcdaabdbccabdbcdabacdaccabaddcbddbdbcdacaaaaadbdbcacaaaabaaacacbcabaaacbacbdbcccaacaacdadcacaaabcaaddcbbbabdcdbacadcadbcdbbbcdddddaabcababacdddbcdbbddbddacdbadbacbcaacdaddbbbdabdbcadbdbdbadbccdddbcadaabcdbbccbcbbdcabacaabbbdccdcbddbddcccbdbaaacdcdababcbdcdcdadabccdabbacaaaabdddbdddbcddabcdacdddcbabcbabcdccdacdaccddbbbacbbbcbcdcdbabaaccacbbadccbbbabdaababdbdbcbbddcddccbadbdbaaaacbdcacabcaabadabcdaadcabbddbcdcdddbbcdccbcbaadaaddaddcbbcdddabaabdacaacdbdcddacadccbbbbacdacddcccdcbbacdcbabdcbdbdadcccdcccadcacdddadaabcaacddaddbbacdbcdcacbbbdbcadcbbddddacbbabacadcadaabaaadaabdbcaadcbcaadcbdbcbcdadcadbbcccdbacdcbdbcccdbdcdcdabdadccdabbdadccbbdababaddaddddaddbcbdacdbacbbddaadbcdddddcbdbabbccdbadbbcaaddacabbbabdcbbbdcccbadcddccbddcddbadcbacbadbabcbcdbdabbaccbcabccdacdaddcababaabaabcbaddbcccccccbabcbdabacadabdcaabddccacbdadbabccabcbbdbbabaadbcccacabbadaadbdbabdaacaaaadccddbcabadbaaacbabbdadcbaaccbbbbbcdccdcbbadaabbaabdccbccccadbaabbcaacdbbbcaabccbddbdacdbccacbdcaacbbadbabccbcacbbacbcbccdababacdbcaacbdcbcbccddcbccacccdadbbdcdbcabcbabbbddaddbbdbcbdbacbaaababdcacabddadddddbbbcacacdbacacababaddccbccbdbcbacbbbcbcbdcaaacdbaabbcbbbaaaddddccdbbcbbdcbdaabdcabbbdacaaccdbbbccdadaabcbdabbcdadacbcaadbaccdadcdcccbbdaabbabbbbdbbadbddcaacdacbabaacbdabadbdcdcbabdcdacdaacdacbbaaccdabdbabbdccabadabadbacbabdabbbaadcbddaadbaadbabdddaabadacdabadadbadabadbadddaabacabcbabdbdcdcadadbabbcbccbdbaccdaacdbadcdbdaaccbbbccbcbaaadddbbcbadcabbbdaadddadabcdbcabdabcbcdcbccdacccaadbacddbdaabdbacbaacadadbbaaabdaddacbaddcbadcddccdabdcddcbdddadaddadcbdbcdddacdadbacdbbbdcadcdbdbcddcddacbaddbaabdabbabbdbbbacadaaaacddbdadabcdadacbabcbabccdbacabccbacccddbbbdcadbcabdddcbaaadadbadcabcdcdaadbacdbabbbbddabababcabddacabdbabcaacbbbddaddccbbccdccdbdadbcddccccbacbcdddabbdcbaacdddbbbadcdcdcbddcabbabbdddcdbddddbdaadcbacaabbaadbcaaccaacbddacbadddbbdddcdcddbcbacabbbadcbcbaaadbcddbbbddacdddbddaadbaddddadddcdbbbbabcdaabadbcbccdccbdaddcaccbccbcabcacdddacabcccaccddbdbcbbbdbacddbabcdddcadacbbcdccadbcadbcdbdadabbbbcbbbddabbbdbdabdbaabadbacbababdaadadcacacbbbdbaaabadaacacbadacbdbbcddaddacbaabddbcacdddaaabaaadaacababbabdbcbaadbdbdbccbddabaddcbabbcadbaccdddaacaaaddbddbdabdabcacabcdbbbcdcbdcdaccccadcbcdacbcbbbcadbbbaabbbabaddbbbcbcacbcbdaddbcbaacbbbddccbcdbcabdadacddbbbdbabdcdaadcdbbbcbbbcaccadccbcddadcbcabccdcdabccbacddcadddcbdacbddbdcadacddccccddaadbbaddbddcacdaddabbcabbabcadbdbaddcbadacdcacccadccacccacabbacbdaababbcdbbabccaddabaccbbccddababbdacdcbdbabdbcabbddbadcaabaccacdaacbbddbbddbabadddbadbddcbbbcabbacccaaddbcbadabbbcabcabbdaddccaabadccbacacddcacadcbacdbcddabadacaadbabdadbcabaaadddcacccadbacdaabdaacdbbbcdddaccccabbacacaabccccacbdacccacccadadcbadaccdacdbdacaadbbadbdacdccccdbbccdbccabbddcabcacddbbbbbbaabbaabcadddbbcacccaccaababbacabcdaddbbdccadaabdaaadababbaabddaacbddaabdbccdcbdacddbadbadabcadabadcaaddbbbdcdaacabddccbcccabdccbaadaacbccbbbdacccddbcbcdcadbbcccadaaaddcacdbaadbbcbadbadadcbbccbdbabdbcbbbdbabcbbaaaddbdbddadacbbabdcaaabcacaabbbdbccabddbbbaababbdcacbdaabbbcdbcddcaabaccbbdbaacddcbccaaabbdbcadacdbbbccccaccdddbdcaccadbadbaaabdabacbdabbddbbcddabbbbcbbddcababaabddaccdbcbcdbdbacbaaacdacabcddbcccaccbbcbbaabbaaacdccbbddbcacddcddcabcaccaaaccbdbdadddbabbdadaccacabcdbcdbadddcabddcbddbabbaadddaacabcadaccaabbacddbdccaddccdcdcbcadadcbddadabaabbbcddbbaddccdacddbbaaabcbbccaaaaabcdcabdacabbbaccaabbbabcbcbaccdcdcdcbabbdbbabcbcbbcacaccddbccccbaaddcadabcbbbddadcdbcacaddddbcbabcccacbdbcbdcaaacbbddaddbdaacacdbdbbbcdacabbaaabadbabdababbbcacbdbcdddddabddcbbbdbcdabaabdbddccdcdadcacdaadbcddaacdabdabacdddcbdadaddbbbaccbccacccdadaaacddbcdcdccbacadbcbcbcdacadcacbabacccbcadadccbdabcbdbadbabdddadbcddbabcadbabbabbcdbabadbabcacacdccbaccadcabccdddcbbabbccacccabaacacddcbaddacddbaddbadadbcbbbaacbbadddbdcbcbaabacdcccaaabcdccaccdbbcbbbdbaaabbacbccdbbbbbadbaacaccbcbcbdbdbccdcaabdcdaaacaadbdbacaabbbbbaabbcdaabbdbdacbaaababddaccccadadadddbbccccdbdaddbadbcabcadababddabdcdcccabdabccabcaadadbdaacaddcadbbaabcdbcadaadbdbabbbaadccbccdddcdcbdcaddbcdbaacbbabcbababdccdbccbdcadbbddadabaadaabcbdadcbcddddbcddbbdcccdddcabbbaabdcaccacdcdabacccabbddcdabdcdcdaaddcbdaddddddaadcadabbacadcadddadddbcacccdcccbacbaccabbabdaddbbcdcaaaccddbdacaadababdabbdabadbaabbcacbacaacaccadbdaddaccdadbbddbbcbaabadcaddccaacaddadaccbcccbcdcbddcdadcbccbabddcbaaadcadccdaaabcabbbddacacddaaaacdaabbccbbacdccdacacbdbbdddabdcdbdbbcdcdabddabdabdbbaccaddaabdadaccdcadcbadbbdbcddbbdbdacdbdcbaadaadddcdccddbbaddcdaccdabaccacbaacabbdabbbcaadabdaadbcbbaadccacadccacccbaabbbcdbccbcacacbbbccadabcdccdbdadbabddabdcdccbbdabbbcacbbbbdbdcbdbdacacdbcccbccadbbaabaddcdcadcbcccacdccdacacccabdaddcdaaadaaaadacadddbaacbbadcbaccdcccbdabdadbddbadbbbdbabadcdcacddbbbadddbdbacbbdbacdcbaababdccbdcbbbbbccaddbbaccccaaddacbabccdbaabbddccbdcaaccccbcbdccdbbbbdcaccbbabacabbbdddcbdbacdbabcdaacbcdddabcccacacbddcdbdcdacaabcddaccbdddcccaccddbccaaccabdddbcdddabdadbdaccccdcddaccdcbaddadcbacbadbdadcbdadcbcbaabaaacadcdbcbbdabcadadbddadcbccdbbccdaccdabbdaabcdabacabccdababcaabbcbdaccdabddbccaaacabbadcbbcdbddaccadbbaaaacddcddcbcaadacdbdcaccdddbabacabccbbdcabbabdddbcbdbbacadadbbbcdbaccbbaadbadcbbacdbcaabccdbddaabdacdbdadadaabdccddbdccbadacaabdcdbddddcbdaacbcacbcccaddcbdcdadbabcbcddbbbaadadbbdcabdcbdbaabcdaabcddbcacabbccbccdacddbbacbdcaaddbdbbcaabdaacbbbacabbcadbacbcadbaadbcdaacbcbbcacacddcdcacbababccccadbddbababdbdbbcbacdcdaacaaaccbadcddadbddbcddddccbbddcdcdccbcdbdabacbcaaacdaabcacaaabadaddadbbadaacbcdaccdbabbaacacababbbdaabbcdcdcbcddbdbbdbdacdacddabddcbbbbbbdcdbdaabddbbcddbabbaaabcbdbcdccdbbabdbcbaccaacbbddccaaaaacddaddcdddabacddabdaaccabaddccdcaddbbdabdacbbbcacccdcbbddabbabdaadcbcaddbadbababaddddaaddbdaccdccdbabdbcbdacabadababdaabbaabcacbababadcdaddcbbcddcdadbcddaddbdccaacbcabacdcdabbdababbbdccaabadcbbaccdabbccabccbddcccadacbbacccdbdccaadcbcabbbacdbbdcbcccaadabbbbcbadcbcdbcdccbdaadacccbddabcdacadbaadabdaaaabadbdacbadbbbcaabaabcaaabaabcdbcdabbaaaccbdaababcdcccdbdbaadcddcaacbabacabbcbadacdddbbdcbbacdaaadccacbbccbdaadbcaddabcbddddbbbcdcddddbbbcdddabcccccdbddbdcbcdbdbbdaaddcccbdadacdcbccadddabbddcdbbcabdcdaddbccadccddbadabccbbdbbcaadbacddccbdcbccdbbbaaabadadadccdbcbbccccbbabbaadcababbbadaadacbbccacdddcabcbcbacaacbdcdcdcadadbdadaabbabcabbcdddbdadcbbdbcddbdddbadcbdbbbddcbacacaacbacadadbbcccdbbcbbbbbddcdcdddabbccadddbbbcbccbaadcdbdccacdcababdcdcbbdccdadbabcddccacadbbdbcaccbacaaabbdbbaacccbcbdcbcdcbbcbacaabaadadaacdcccdbacaccddddccabdccbadabbbabddbcbaccbcbabddaababacabcaabccbdbcbabcacccbccbccddacadbacadadaababbcdaacaddabcdaacabaaacbcbdbacbbdcbdbbcbadcacaaaacbcbdcdadbbadbddacdccbadbadababccbddcdccbaacbccaaabdcbddbbcbbdacdcbbdcbacaadbabdbabbacacbbcdbdaacbbdccbbbacbbbacacbabcddbdaddcdcdccdaaddbccbdccbcbcddcabcacdcabcdaacacddbdaccbdddcccacdbddbcbcdbabcacaccddbddddbbdbaadbbdbcadbdbcbdacccdcaddbcbcbddcababdbddaddbdbcbbcccaccaabdcaaddadcdcaccdbccbdbdbadbcbaaddbbcadcdbadaadaaddcbbbcbdcbadcaccbdcabccccbcccbbbbddabaadbabcaacddbdcccdbabacbadddbddcdddccbbcccbacccccbabdaabbccbdabbdabbadaaadbaddadacacadcacadcdababddbcaccabadbbdadcddcabaacbbcccdabacdabaadbacdcdbcdbbaaaaaabdcadaabbdcdababadccadcbbbbaddbddadbccacbdadcbabbabccdabadcbcaaccadccadadaacbbdbdaaadbcdcbdddabcdadcccaadacbddbdcbbbddabababcabddcbabaaccacddcddabcacabacacbaabcdbcdddddacdddcdbcacacccacadccbaddacccaacdccadbcccdcabdcdbdbcbdadcdcadcbbddacccaadbbdaddaabbccbdcddccaaaddabbccaaadbcacaccdaaccacabdacaaaacdcaddcabdbabdaacbabddbbcdcacaddaabbcbdcbaaaacbdbbaacdabbcbccddbdcaadbbdbdbabaccdcabacbcdbdcdcbdcdcccadacabbcacccbcadbacaabddcbdbbbbbcdbaddcabdcccccbcdaabcaaacadacaabcccddcacdbcbbbcabadbddacbadcddabaacbddaabaddbcaccdccdadcadaacacbcbcbaadaadaaabddadbbdbdacbcbcdcacdbdcdbabcbbabaccccaabcdadacacacbdbbcadaacbdbccaccdcccdabdbbbcddbcbdcaaabddbbdaabaccdbbabdbdcadbacadcbcbbabccddcacbbbbdddaabcbacbaddacdbcadcddbcdcacacbbbbaacaabadddacdccbaddbadbacbbabdbdbcbcacdabacaaaaddcdadbabadcbcadcccbcbbaaadddcbdccdbddcccacaadbddaabbcdbccdcbacdbccacbdbadadaadbcbaaababaacaaadbdbbadcadbbbcbacbcabdbdadbbddacabbcbaaabbcccbbbaadadcbabbcbbdbcaabdcddbcddccbdbbbcbaaaddabdbadbcabbcadbadadccdbcbabacdbddabdaccbccdddaddcadbadcdbcbdbabcccabaddadbbaaabddadacabcbdabdbdcdcddbabcdabcaaddcdbcdbbbcdabcaccccababbdddbdaccbabcaaadcbbdddabbbcdccacdbdabadbbcaacbbbabccdcaabcaddddccbdbadaddbbcabdcccdddcbcddaabcbbcbcdcadabcaabdcadbbdcbdcccdcdbacdddbcdbdcbacaaadcbddbdbadbbddaaabadbccacaadcccdddadaddccbdbcbccddcaabbadbbcbbcbadcdbacdabaddaacacccccbcdccbcaccbaddcdcaaccbdcccadcacdccaaddbaaaccacdbbbabaaabacabacdadacbdacccbcbbacabcaddbdbdbaabddbaabacbbbdcabbcaaadddccadabbbacdcbddbcabcdacbcbaadaabbcdbddbcbcbabdcaabcaccbdddadcadbbcbcabaadcacdcaaccdacdacccdacbacdbdcdbccdcdbcdbcbcbcabdcddddacdaaaddcaababcdacdabbbcddbabcbbaabaddcdcdcdacaacbdddccbdabbcdadbbadaccdcccbccbcdccccdbcdaaacaadbaaaabadaacbacbcaccdbaabccadbdcdaccabbbccaddacabbdacabdaacababacbddbaaacbcddbccdacddaddbcbadcaccdaddbabacdbadadbcacabdadddcabacbdcbccbbadcddacdbcbbcddababbabbaaabbddcdacdacbdbadbaabdaabcabddccacdcbbddbabbacdcadbabdbdacabadadbbcdadbacdadaaacababdcabbbdaaddcacbacdccbddccbacccbbdaddbaabddccccdbacbacadbdddcbabbaccaadaccabcbbadaddbcaddaaddddacbbbcaadcacbaadadbcdbbbaabddcbccbccabcdbabbccbdcbdacdcbabdbdcccaccdddbcaaccaabddababaadbcabababaccabdcbdabbccccbccacbabaacbcabbbdbdccbbbacdbcddbadcabbbaddcabdabacbadcbbbbbcddccbabcdaacbcbadbbbdcadabcbadbdadacdccacbbdaadbbacdbaaabdabcbbabcccbdaddcabcabdbdadcdcbcacdabaddbcbbcaccdbddbcdbddcdacaccaaacdccbdaccbbdcdaaacdbcbacadaddcbaacababdcdcdbbbcabdaacdabdabdcaacdbbdaabdbdcaadabdddcbbaadddcbddadcbabbdccaccdabbdacdccbccbdabbabbddadbbbcccbacacbadbaaadcdcacadbddcdccbbcabaacdaabdcadcdcbdacdccabbacdccaaccdabcbdadcabcadbbbcabdbacbbabcccdaabddcdacabddadcbdddaadcbdbdddbbaddbcbdcbccadbbabbdbbbcbcabadcaddadaacbbcabbdadddcddccabbcbdbddddacbacabcdaccccdacdbdaababcbdabadbbbdababbbcaacbbaabbddbcbacbdaadacdbcbdabbcdabcdbbdbdbbbaabacbbabbccaacccccdcaacaaadbdccadabbccddacdaccabacccadaaacabbdabcaddababadcdccabbacbbababccbcdbacbaaadbabbbcbdcadadbaaaaccbacabbadcdabdcabcacbcdccccddbacabadbadbcccdaadcbdacbacbdcddccdbaccdacddabaabcbadcbcbadbdadabddbddcbababbbcacdadaacbdcbdacabcbbcbcbacdddcaadbcdbdbcdbbcaddddcdbdbabbdacddbcadbdaaaadcbcbccabcbccbdcbbcdcabaadbcdbdcbddcbaddabbababbdbaccdccccdaaccbadaabbbddcbbbadcacacbccaabaadbacacdadcaccdabccbabbcdcdbdbcaacabcbdacbbbdbaccbbdbcabdadcdbddadbababbcbcddcaaccccbaabcdcabdcdbdccacabbdbcdabcdadbbacbdcdadbbbddbccbaaccbacacabcbbadadcbadbdddbbddddcbadaacdacddbdccccaccccbbcdcdcaddcdcdbddadbbbaacbdbbbacaacaadabbdaacdbadcdcdcaacdabcaccbaadacdcdaabddbdbbccbacdcdacdcdacbbcddcbdabccbbccdacddabddabddcddbddccdcdbddcdddccabbaaaddbadddccdcdcbdabbabbcacdbccbdaadddcbdcdabcbbcdcaabbbccccbababccbbccaabcaadcbcacaabdadddbcdccbbcacdbcddcdcdddaddbacdcdadbcdcccdbcdbdbabaddadbabdacaacabbcbacddcddcbaddbdacdbdabbcdbabdcbcacdcabdbbababcbdaddbdcdbbdbbbbbacdbadcdbaaabcccbadbaaccdcaddabbaabacaddabaacabdcbbbcbbbbaaddbcadcccdccaacabdbbcbccabcbadaabcaababbbdddacdacbcccdcabdddadbbbbddcacbcacbbcdcdacccbdadbdcddbccbaaccaadabbdcdbcddbbaddaaadaaccccacdddabdbaaadcdcacdaaacadcdbbacdacabaaddabcabadabbbbabdabcccbccaabdbbaccbccabadccabaacbabcdaaccdcadddbbbdccbbbccbdccabaddabdbbddbacacadcbcdcdcdbddccadccbdbdaddccaddccabaccbdcbcdaabdbdbcdddadbabbbdbaccccdcbaabdbbddcbcabcabaaacbccbacccbbdccbddddbacabbdccaaccddbbacccadcaacaadbdbbbdcaacacacaacdcadccdbdbbdaabbabbbadaddbcaddcadddcdaadcbabdddbacbddddaddabdaacadabacdacbadaadcbddacdbabacdbcdbdcdbbbcdabacaccdbbacdbdaabdcadaaaadccbcccadbadaacbbcdcddabbbcdbcbddbcdbdbccccdccdddbcbbbdacdbdcdadbaabdcccabdadbdbcbbcddadccbbbadbdccbbcabbbddddddbabbcacddabadabbbacacaacbbdcddddadbabbbdddcbccaadacbdccddbbcbddbbddbdbcddcadcadcccbddbabddccdadbdbdcdcccdcdcaadcadaabdbcdcbcbbccbbacccacadadbadbbcddbabcadbcbddcacdccdccbdddabcaaacdadccddcaaadaadcacacddaaaaccdabbdaabcbccccbdddbaacbaddaddbcdccbbaabaddbbdcddddbcccaadbabacbaccaaadaaddadbdbaacadcbdbdbccdabbcbbddcdacdbbacdabbccbaaddbcbbddbcaacdaaccccacbccbdcbccdcdcabcbbcdabbdccbbddaadccaabdcccbbddbaadbcadbadcddcbadddbcadacaadaabdabbccdcccdcacabaaacddccbcaccdcdccbbaacdbacaddddadcdcbdbaacdadaabdbacbdadbcdadadccabdbbadacdcabbdcbdcbdcaaacccbcdbaabadbbbdbdddababcbacbcdcdabdacbbdddabcccacaaacbcdccaacdcabdccdcabadacdccbcdddcadcabbcbcacadaaabbddbbbbbccdcccaabcbccbdbbaccccabcdccbbcddcacdacbddbcacbcccdaccccdccabbbbbaabcccdaddbdccadbacbaadbcaaabcdcddaaabbbbdbcbbcdcabdccabcabdbbadcbabacdbcddbbcaadcbdcbdaaddaabddabbdccadbbdabbcaaccacabbbbbdbbcacaaadbdbdccaadaabbdbdbdadccdbbdbcbdcbacddbadbaadcbbdddaadacaaaaadbddbabdabbdaddacbcadbaaadbcabdcbcdadadcbbdbdcbddadddbbbdbdbadacbdcddabbcbcccadbadddadaddddcdcccbacbdacacaaccbddcdbdcadcdcdcbacbcbcccbccaccabddaddaacccccdcadadcdbcadbdacadcaaddbbdbdbbbbacbaddcadcacbcbdaddaabcdcbdcbcbbcaddddbbcabbbcaadacbdcaccaabadcbadbcdbabdcbdddabadcbbaaddcdbaadcaabbdcaddadbbabcaadddcccdddcbdbddcbdcbddcbdcbdbbbbadbcbabaadcacbddadbabcabaaddcaddbdcbcdbabdbadbccdaadbbbbdbbdbdcdbaadcacacbadcccaacaadabdabbdaccbacaddccabbddbbdddcaddbdcacbbbccbcaccaccdbbccbbbaaacdabcadbccaaaacbcbadbdcbccaadcdacccbdabaacbbdcbdcbbacdabaddaddbabbbbcbbcbabcbcbdcaccccababccbdaddcbabbcbcaabaddcbddccbaccccbbacddcddabbbbdaabbbccccbbbdbdbadbabdaccadbdbbdcddbdccbdadaadcabdbabdacabccaaacadaaabccaabdbbcdbabaddbbbbcabbcabdcbaacbdadbdbaaadadaaabcbdcdbddbbbdbbaacadcbdddacbbcaabbbddbcaccabbacdcaabcdadacadacbbcbcaadaabdbbcbaabdddabbcdbadbcabbcbccdbbdadbacabacdcddccccbbcdbadbdcbdadbbadccdaaadaccbaccdacacbdcbcdbccbbdacadabcdabaabccdabbddaddcaaacdbcbdaabdcdabacbbbbabaaabcdddbbabccdcbacccbbdcdaacacbcacccaabcdccbcaacbaaddbdabbdbcabccbdabdaaadacacbadcadabaaabbcaabdbabdbababcadddcaaddcacaabbaabdcccaaddadbdbaadcbabbbcdbaabbbccadbccbcaaddacdccabcbcbdcddccddcabaabadababbbbbcaabbdbcdcadacdcdadaadadccacbaadbaaabdcdbaaabcdbadadddcbbadadbacccdcbabbcdcbdabbadcdaaabbcbaaaddcdcbbbbabacbbcacdbdabcccbdcccbabddaccdcbdddcabcbcccccbccbcbadcccbddcbcdbddcdcaddadccdbdddcdbddccbadbabcbbddcaddcbccddccadbbbccabbabcadbcddcaaccabbbcddbdbabbacbbbaccdadcccddabccabaacbdbdbcdabdacdddcdcadcddaaadbabbbbaadadcbdcddacbccacbbbadcbccacdaccabadcdadcabdabdbdbacdbabccdbbddacdacbadaaccbaccabcacacdbabbbcaaadcdddadbddbcbdcaadcdabbccbabddcabdbcabdccbcbdacdbcaadadbacccdacdadbbcadaadaabacdbacbbacbbacbcabaaccacbcdaacbdbabadacbbbcddaccddcdbbddcaababdbcdabccdcbcaccdcbcbdbadbcdaaadaaacccddbbcdbbcabdbbaccdbdadbbadccccbcaddbccdbdbcccbcbaccdbbacbdbdbaaabbbadddcdbdbadcaacdacdcaddbbbaabdcbcbcbbcaddbcddbaacbcccbbdbbbdabadddbacdabbaadabbdbbcbaabdaabcdcabcdbcbdabbcdaaacaaacacbabbadcbcbcacaacaabbddaccbbbcabddddacaacaadaaccadbadbdcddabcacbacdbbbbcacabadbbcbcdabbdabaddabadbabaccbdbdabcdbaadacbacdaaddbdbabbbbabdbabbdcdcdbabddbbccbbacbdddcddacdbacddaacdcdddcbbcbcbcabbabbabdadadabbbcbcacdbdcbbbdabaaacdbcccdcdbdcaaadacbbbabccaadadcdddbdcbddccadaabbcbabbbbdcdbdccdbcccacbaadcaddbbabcbdcbbbbdbcbdcbbddbdcdabbbdccacdacbdbbbdbdbdaabdddbacadddaddcbaddacbabadbcddcccbdbdacabaaaacaaaabbbbbbddbdadbdaaadcdcbbadbabdbbdbcbdadaddadcacbaadbbdbccbbdddcadccacdcacadabbadbadbbadacbdaadcabdbacdccbbbccbddccdbbdccbcaaabcacdaadcbbcccdddbdbdacaccbbaccaabdabbabbbbcccbbccacacdbdccdddcbadbccdacdcbdccdbdcaacbdabacacdbdccdabdbdbbcccbadcdbdbcdcddadccacbbccbbdabdcbddbcabbdcbdaddbdaadbabdadadcbbccbdbdabbcbbbccdbbbcbccbacdabcbbadbdacbbadcacbccddcbdbdccbbcddcabbdadbccaaadcbabccaabcbadcdcbbdbbbbccabddbcddcabbcbbcaacbabcbdabdbdbadcabcdccbdccbcbcccacdcdbdcacacacbdcabcbcdbdcacabbbcdaadcdccccdcbaccdadddbddcdbaaadcacbadcbbdbddabaacbdadddbdbcbbaaacacbdbacdcbdaacdaddbdcddbcddaaccbdccddaaabdddabddabdaadbcdbacdbabbdaccacdabcbcbdbdcddacddcbbccbabcdbabbbbcdbccddadaabbbcbadcdbaabadbcbbcddadddabdadabbacbdbcbdcacbdbccaadadaccbbbabacaddcbaaabbdcbbbdcbbdccabcdbbdcccabcaddcbcadcacaabaabcbbaaddbcacbbcbdbbaacbdbdaacccbabbcdcbbdabbaaaadcadacacdbacacbbcdcbbbdaadccdadbcdaadccbcbcadddabbccdbdcdaaaacccccaccadcbddddabdcdbcbbdcddccabcbdbcababdbcdbbcacbdacdcabcbadbcacdacbbbbbdcdabacdcaadabadabbaaddbacbabadcaccdadcdaddbcaabadacaadbdbdcadacbbdaadadcabdaaccdacdcbbcdadbdcdbcadcccccdabbbcdbcccccdabdaacbdacababdacbccbcbbadbdccbabcaacccdbdbbbdbddbadcadbdcacbdaadabdbccbbcbcddabcdcccadcbddacdbdaacabdbcabbabdadbbdadcbbadcabacdadbabddbdabccddbccbcbdccaccccdcccdbdccddccaabcbcdccdcdcbadadaacdbacacaacdbddaacdcacbabbdaacbdcbddabcdadaabcddcdddbddcdaadaddbcbddcdaadddbcabcabbadcdaacdaccbbadccacddbadbcccdaadbdcddadabbadbcbddcccdbabbdcbbbbabadbacbdbddadcddbbdbcabbccbcaabbadbabaccdbbbdbcccacddbadccbbbaaaadbdbaccadbcbacbccbcccacbdcaacbdbdcccacaabbdcdabaccaccbaababcbadadacddaaabacddbcaaabacddabaabdaabbdbcdbcbdabcbbbbabadacddaacbacdabaabaadcccddbdbabbddcdbaabaaccdabaccdadabdabccbbdbdadcbdbbdbbdbaadacdbccabdadcaccbacccdbabbdabdcacdbaaddccbbdaccbadbacbccaddaccbbddccdcadccabbacacdcdbdabbdbbddacadabbabbdcaaddbcbbbcbacabadacbcabdbcbccbbabbbbbabcaddaaabdabdbdcdabcccbaabacdbdbacdbccacacdaabbaacbccaabdcbccabbbddbbdccaacabacadddabbaccddddcdadabdbaabcabaccdbcacbadddccacddabdcdccbbddacccbbdcdcbdccadaabdcbacdacddbaabaaabdaddadaddbdabadbcdcbdbdccabbadcdaacaabacdbbaadcaddbbdccdacaacdacacaabddbbaadcabbadbadcbabacbaaddabccbcbdaccdcdcdccbcacbbacaaddaaaccdddaacbbdacacdbdbdbaababaabadadabacbddcdabccdccacabccdcbadaccadbdcaadbaacbacbcabccccaaaaaaabbdacdcadaabcbcdcddbbccdcbacacbcbcdcadcbbabbdcadbddacdaccdcaaacddaacbbcdabaddaacdcdcadddacaadcccdadcdccccdacaabcccccadadcabddacdddbcccadbdadcabbbddbdbcabcabaaddcbccabdddbcbdcabbddcbcbaabaddbcadddcbbccacbacdcdbbcbaddacbcdbbbabbdccbcaadaaaacbbacabcacbdaddddddcdaddaabaddcacacdabadcbbbdabdcdaccbaaaabcadbcddacdadbbdbacdcadbdbdabccccdbcccabcdaadbbadcdbbcdaadbbababbdaabdaaadaaaaddacaadddadbccadbacbbbbaddcdbdccdaabdcbacddccdcbcddabcbbdbbdddbcbcadccccabacccaacdaadbadcdbcababadcadaabbadcacaaddabacacbaacacdbcdbbdbdbdbcdbcadbbcabccbcbcdccaabdcadccbdbccbbccadaddadadccdbaccdcdbbbbcdbccabcbbbbdbbdabccdcdddbbaabddcbddcdabcaaddbbdcaaaddaddddcabdcabdbabacdcabcdddaccdabbcadabcddcadbaddbddcbbadacaccdbdbddcbcdddacbbabaaaadadcaddcdadbddcbdbbadbbcdddacbddaaccabdadbbbaccadcccbbacccacbbaaccbccdacababbbbbcbccabccdbcddbcbabbaaaddacbcacddacbabdaacbdbdbddcaadcbacdcadcdbbacaaabbdbcbbadddbccddaacbdabccaccbcaddbbccddadbaacccacabaadbdcbdbacbbdbcbddbaaadcbbdccaacaaabacdbbaabdcbaababbcccdddabababadbbcaddcddadccccbdbdcccbbdcbabdbbdadbbabbcbaccbaadaaddbaaacbcadadcddadadcbdaaccbddabababbbcabbddcacbddccdccbbccaddbdabcdcaabdbdaaadbdadddbddaabbbbbcacdaddaacccacdcccdbdddccdbdbddddbabcbabcbbdadcaadbadcdcccdacabbaaddcbabbcacddcbbcbaccacddadababdbbcbddddabaaaaacabbddbaabdcaddbdbcdadccdaadbbccbcaababbbdccacdcdbddbacddcaaddadcabbdbccccaabdbaacdcbbdbdcddacbcbaaaddbbbbcdbdabcbdccacdbaaddcbdaddcbddacaacbbdddcbabcbdbacabbabcbcaaacbbaaabbadcbccbdcdadbdbaccdadbddbbcdaddddcddbcabbdbbadbbbaaddacdcdbdcbaadabadbbdabdbddacabbcbbdacdddbaaacbabbbbdbccddccdcbabaabdabccbbdacbadcabadacaabccdbcdbaabbbbbcacaabacddccddbbdbdbbdcabbabbdaddbaabbadbccaacdcbadaccbdadacdaadbcdaddbdbadabbdddddbbddaacbbbcbdaadcaacabbbacddbcdcbcbcbbdcbdacdaddddddbacbdcaccacaadaabbddbbbccabaddbbabcbaacdcccbddaabbaaadbbbacddcadabbcaabcbdabbcddcbbbcddacacaabbdddbacbcacddccdabcbbdddacdacbbdadcadbbdbdacdbbccccbccabcbddccadadaccccaababaaccbddabbabaaccbdbabdbadcdcabbcdabbdaaacccbaadcdccdcacaadbdbcacaabaacabcadcbdcdddbaababddbbbcddbabbccadccdddacdaabcdcdbccccabddbccccdbaacddcccaaacddcaadbdadadbcaccbddcbaadaaaccdabbcaaabbdaccbdddcddbabbbcbabcdbdcdbcbdcdcdcddcdbbdcdbaddaababdbdbbaababbaabcacbbbcacdabbdbcddbbcddacaabdacccbabdcaadcabddbbcdccbdbdacbcbcaacdbdacbbcbdcdbdcdabbcbdbabbbdcbdadddbacdddaccbbcdabbbcdbdabccabcdcaddbccdddddbbdbababaadccbbddbcbddacddbbdcadadbadacdbdddbcbccbadadabcbddadbbddbddcdddbcdacbabccccbaccabbcbddcdbcbadabaaabcbabacbdbccadccbdadadcabdadadabcccdadaccbcbbdccacdbbbabcccaabbddacbadbdcddaacbaacacadaccccdaddabbadbcddaccdccbbbcadbcddacaccabcdacabdcddcdacacbaabccbbbbbdbbbbbcabdbdcaaaacbdbdcddcbaacdaddadccbccddbdadcadbbdcbadbcadccadcdabdbacbddcbcabdbcddadbdbcdbaacabaadaaadbdccdacbdcdbbbacdcdbababcacacbcbcacbccbccaccdaadaabcbbaccddbaacddabcaacdbbdbdddaaacddaaadabacacdabcbdbcccddbcbdadcbdcdabbdacbbcacacaacacbcdaccaaacadaddbdbaddddcaacdccdacdaadbbccdadcdcacddcaadcccdababadabacdcdabbaabbacdabdcbddddcbcabacaadaacbacaacacddacdbaadabdcbaacabcddcccdadabaccacccccbaccbcbdcbcabbbabbbacabbddaabaddbcabbacabbccddbadabadaabcacbbaadbdadcabbbcacbcacdcacdbcccdbacddaabccbadadadbcaabadbaaabcbcdbbcaccaadcbdbbbbbccbcddcbaabdabaccddcacccbcaabbcdddacdccbdbcaaadabcbacabcbaaabdcbbddadcbaabcbcccdddadcbdbdcbbbdbbdbadbcadadadddcdaccccddccacaaabababcaabbcbcaabbdaddbcdbdacbdddbcbbdcbbbbabbbcdbcdaccccaabbdabdaadbdaabdabacacabdadadcdcaddcdddcadcdcccddaaccdadbadbbaaccaacabbbcdaddaddabcdbcdcccadabdccccdbacbabaaaababbacbcdbdbdadacabccdabdddcaddbbdadadbadbdabaadaabbdccaaccbccbbbdadbbccacbdbcdcdadcdcabcbcddcdaacddbcddddcacdbdaaaccbacbccbaacddcdcbbddcbdcddacdddcdbaccacddacaccddcdaccaacaabaacbaaadacdadcbbcdcddcaddabbcdbacaddbadbaccdbddcbbaaaaaaddcacdddbcabdbbcbbbddccdabdabbccbdadcdaaacdbdbbbdcbdbdcadbccdaaddbaadcccccbbdacaacccdbcdaadcdabddadaddbddacccacbdcdcdbcabcaadaadaadbacddababdaaddbcaddbabbacbbdcdcddcabaccbcaaacacdcdcadddaccdbddbadabdddcddadaacddcbddbaabdbccdcdcaabadbddccbacbabbdbddadabcbccdbabcdcaacacbdcdacbacddbdcbbaddbabdccddbbdcbcabbabbbaaaaacdabadcddcabaacaccabbdcaabddbcadbaddadbdccabcccacbdbcddcacacddccabbaacdbdabbabcccbbbabdcdacdcaacacccbdbcdaaaaddbcabbdcdcaddbcdbaabdaadbdabbcadbadcacddcbccbdbaaadbdddcabdccbcbadcccdadcacdcddbadbbcdaabbbdddbaadbbbbbdcdbddabbadacaadabdddccbdbbaaaccaabcbbdababcbaaabcbbcbbabbbcdddadddaabadacccabcddbaddcbaccadcacccdaadbdcabdacbcbcbbaabbdbdadcabcdccacdcadbdbcacdaabacbbacacdabbdcdbacddaccaabbdbdabdbddbcbabaacbaadbabbbddbadbaddaacadadbabcaddacdcdabcbddddbbddddddccacacbdbbcccccbbdbdadbadbadabacbaadbbdadbbccbabdbbaddbacdcccaabbaddadddacbbdcbaadbbaabaddabbacdbabadadcbcdadaabbcbbddaaaabbaddcdbcacdacbbdaabccabaaabaccbcacbdcabbcaacdcbdaddbacdbdccbdddbbcaccbccadbbdbdaccdabcccbdccabdacdbdbdddccbddcacccdababdccaadabcdabdddbccbcdddccccbdccabbaabaacaaabcdadbbdcdaaccdccacbaaccbabdccbccaadbcbaadbdbdcccbdbadcdaddbddabccadcdcadacdaccbcabbcaccbdaadadaadadbbdabaadcbacccaacacdadbaddcbbbadbabddaadcdaaabbdbbbbbccdddabcadbddacbcccaadbdcccdcdadcdcccacbbdcabacababcdcbdcdccacddbabadbabdddbcdadacdccdacaddacdcddcdcdbaccbcadabdadddcccabcccdcccddbdacdbdacbabbabacbacbaccddaadbbdacadaaabcbcbdabaccdbadbdcbbaadddddcddcadcbdccdacaadaabcacdddddcacabcddbadaadadadacdaccbdaddcccdcadcadbccddbdccbbccddcbaaaabccdcdbcdddbdcbaadbabcccddadbacaacdbcbabadabacdcbbcdbbbacddcdcdbaaccabbddccbdddbcbbdcccccaaaadbdddbdcdacdadabcabbadadcdcbcbdbbabcdccbcbdddabdababdcaccadbabaacbbdbbcdbdcdabababdabddadaabdddbdabaddbbadbadabbcddacacbabcbabdbbccdcaadbaddacacddbabcbacdacbbbcaaaacaaaaadcabbbbcdabccdcaacaaacacdbdbccbcadaccabadddaaaabacadbcbdbcdcaaddbaddacabdddabbdbbcdbccadbbaaacbbdccddbcacdaccabcaadbadaabbbababaaccbabcbbbbbbcddbbbcbcabcbabadbacabbcdcabcddcbbaddcadacccadabbabcacaadacdcbdbdadccbadbdaabacbcdcdbbbbacaadaadcabbadabcbdbaddcbbbbcaaacbcacbcdcdbcdbdccccaabdadccbdddcaadbacdcaabcbaccccbbcbbcddbadcabbababcbabccddbdbdcbbdabadddabbccaaacbddddbdcaaddabbcbaddbcabcbcbaacabbccbdacaadbcbdadacabcbdccbcacaaadcccdcccbbbdaadacbbdbcdbdcaadbdadcabacdcbcdbdbdbdddabbbcdbddccdcabbdddccbdcadbcbdbaacaccabadbcabccaaaddabcbbcacdabcdbabbbbdcbacccadabbccbcbababddbccbdbaabbdcddbdacabbbcbcabbcddbccdcabcdaaabcdccadddcaadaacdbbbbbdcbcbcdcabdadbddacdadccbadbbcbccccaccddcbaccaacbbabbddbacdbbdddddcdabbbbddddadbbbbddbbaaacbccdbddadcaddbdcaadaadadbdbbbcbcabbbdcdaabbaaabaacbaacdccabdccbdcdccacdbbbacadbbbddcdbaccbdcbbadcbabbddaccdaddabccdcaacbccabcacccabcbadcadbbabbcddbdbdabbcccdcdaaccbbbcacbbddaacadabdbbdcacdbdadbbccbbcddcdcabbbabcacdabbdbdcacaaaaabccacaacbbbdaabdcbbaccacbdbdbcccabdbccccccdbdcdbdbadaddcabcbbbacbbdccabaadbcdccaaaacbacadbaacabdbdacaaadbbddcaadabbdbbbbbcbbbbccacdcbdcbdcccbabcbdccbdacccbabccdcbcdcabdacaabcbddcadbccbcddacaacbdaadacaacdabbbcbcaccdaacbccdadaccaadabcdabadadddaccdcacbddacdaccdcddbacbabcbdbddcdbacabbabcacbcaaccbbbaddcbcdcadcdddbacdacacbddbadbddcabcbcddbabcccadacbabdcbbbcacabdccbabdacbccaadddddacdbdcbcabdacbabcbbbcdbbccacbccccddcaaddbadabaacaccdabddbadbabdcdcbaabddcccaaaaddcabddacdcbaccaaddccabcdacbaaacdbadbcdcabdbcdcadcdbcadbdbabdbaabbbdcbbdccbaadddcbbdadbcdbaabccdbcaacbcacdacacdabbacabdacaacdbccadbccdacadaddabbddbbdbaccadcbadcacdbabacdcddccaabdbccccdabdcdaacbacdbdaaaabcbbdbbdcdcacdaaacacaaaddbdacbaacaadcddcaddcaababccdcaadcdaaaaccbddbcddbbdadcdaddccdabdaacabdbcccbcdacddabcccdaccbbddcabaccabacbddccbaacabbbcdacaaaadcbabcacacdacaccbcbdbddbadcacbddddaaababaabbdaadaadcababababcacbdcbcccbbbddddaccbdacbadbcbdccaabbcbddbddabccbdadcdcbabdccbcabccbadaccaacccbcdcabbbaacbcaacdbacacbddcaddddabbabdcadabdabdbbabbcaababdadaadcdbcdccdaccaccdddbdbdbbbcddccdabadbcbbaccccccdcbbdddadadbdabadacdddabbbbdccbbcbacdadbcbdabcabccdbbdcacacbbbccbabbcccbbbbbadcbbdcdbdacdccbddcbabbdcccabbcddcdcdbbacdbcbcdadcbddcddbcbdacadbaaaddbbbcddbddcbdbcddadaadcdadccabddbddcadabbcdbdccdacdbbadcbccbaabbaaadaaabcdacacbcddbabbcaadabcddacaadcbadaaccbaccdccbdccaaadbbabcbaacbbcdddaacaabbccbdbbbabdaaaacdcddccacbccacdbdaccbaddbdaacabcdbbabcbbdbadccacadadabdbdccbadacaabdbdacbdcdbcacbcdaacbdababaaabaacabbaacbabddbabbdcbadbbbcbadcaaaddbddbabcdbabbbdadcadcdbdbabcdcdacdcccbbbccadcdccdaabdddbacaadbadcbbacdababccaaabdcdcabaddbcacbdaadadaaadcaddbddbbdcabaabbdacbdcccaabdbabcdbdadbcccbcddbccaddddbbbcaabbabcdadbabaabacdaccbcaaaddddbdaccbcdbccbcabddaaacbcdabdbbbacbabdadbcabccaaadaababdacdacccaccabbbcabdaacabbdcaaccadccaccbbbbaacddababbaadaacadcbbabcbcaacbadbccaacacadcaaabcbadabcadbdcdacdcdbbbdcdddbdcabbcbbacbcbabddbacdadcdaaabbbbdcdcadadbaababdcccbbdbccddcdccacbdadadddbaabacdcdbacccacaaadaaacdcaccbcdbdaabbabbbbcbbddbdcabbbbcbdccdaddcabbaacbdddaabacbaaabbaabdaaddaddaabaaacdccbdccbdcdbacbadabbcacbbcdcdacddcdcbcabadcdcbbdbdbaaccabcbccaccbcbdadaacbabadcddcaadcbaadcccbcccbcbdbcddcbbbdcccbbbccbacadaacbcddabdacddaadbbbdcacabddcdbdcbbcdaadbbccaadbbcaddadddbbbddbdadaaacaccdcadbddaabdaaccdddddddaabdbabdaaabdabccbaaacbabdbbcadbbdcabadcdadaaddbdcdaddbaccbcbcbdbbaccbabaabcbcdbcaaadccaabdacadcadadbadadbaaadaadccbdbbadccdbaabbcacbddadaaadccddccdbbdcacadcbddadbbcbdddcdbbdaabcdbcbbcbdcdbabaaacacacbdccccddcabdccbbaaddcdcdccabbdbdcddbbdabbbbaaaadabaadccdcddabdaaaadabddcbdcccdddbdabcbbcdcbaacdbdaacddabaacccbacdaaddabccadcbcccbbdbadaabcbacaddabcccccdaccacbbbaddbddbcadccacbbddcbbabacbdcadbdbdacacdcaacbbcaabccaddadadadcaccdabcddaadccadccdbacaabcbbccdddccacacabdacbdadabcbcdbbdbdabddbabcaddacccddaddcadbcabdabacacaccbcbbcdbdacbbbcddcaacbaddcaddbcacdcaddbabcacaaabaaabcbcdabddbaddcaaacabbaacaaddccacbcccbacadaacbdbbcdcdacdcaaaddacaadcddcbbbbdcaadbcacccccacdbcaadabdabdcaccccdccccdabbcccadbbbcbadddddccabbdcbdbccccbddbadccabbccbadabdabcbddcbbbbbdbbcbbcdbcbabbadaabacccabbcaaacddccdaccccccbdaccaaabdbbcbabccddcabbdcdcbadbbadbdabbcaccbaacbcaacccddddbddcaacbacbbbbdccbcbdbddbbabadacabcdcacdbccdaaabbbdccbcddaaacddbbcabbabdbcddddcbdbccbaaaaaadacaadaadccbcacbddcccbccbaccbdbadbccbcaababdcbacddbcabaaaddacdababaddbcdcbdbcadaadcddbdaaabdbbadabbaaaddabaddadacacadabcdaaccadddbbabaaccdcbabadccbbdbcadbddbddcbbdddaddbdbcbcbadcbdcaaacaaabdbbabcabcddcdacadacdabaaaacbdccababbcbcaccdaadbdcdccadabaaddbdbacabcdbbcacdbdcbacdddddacabadcaaadacddacdacbbddcccdacacccdddbdbbbcaadcaabbdbbddcdadccddcaacbdabaddbaaccaabcbcddbddadcddaabcdcaabdbaaccbddbabcbdbbbdaacabacaddaabcbcddcbaccaabdcdaddcbccccabccbabaaabaaabccccbdaddaaccbbdbadcdcdbabacaabbbcbcbacaddccccdcbcbcdddcdcbccabbbbaabdadccddbddcadacacdbcabdcdbcbbabdbdcbbbbdbcccabcbadddaddbabadbdaabdcdbcadaaddabdbadabddacabddcddadddbbbddaaccbabdcadccbbbdcaaabacdccacbdbdbdcbaddddcabcbbabcaaaabbcdbddbccadbabdabdbaabadbadbaacbddbaccbaccdbdacadcddaabadbbbadbbdcbcacdaadccdbabaacbaaabacddcccbacdbbaadbadcbcdabaadbbccbccbcbadbdbdaacadbabcdcaabdcabadddbbadbadcbadcaabbddccdbcacdccaabbbbcddcbbabcabdddcbccbcccacdabbdabccabccbaddddaabdaaacdcdbcbbbaaaabddadcacbadcadaacdadbbdcacadaaccbaadadcbdcdbddbbdbabddabcacadddcaabcdacdaaaddadbdddbabbddbddbaabddddcababbdabbacbbadcdcdadabcbcbdbbaabbdbcdbbadaacdcadabccadcbacbcdacacbdaacabbcddbbccbdcaddddcbddbacacbaabcababcddbcdadddaddcbbdccdbbbabbdbbaadbdddbcdaddacaabcdbccdcdcadddbcbbbaccddbdaaaacdaaccccdacdccadddbadadcbbababbdbdddaccbcbabbbbdcbbaadccdbccabbccbcddcdcbdaccbabadbdbbcbbbbdddbbdacccbdddcbbcabadbaaccbdcdbbdaadbadcaacccbdccaadcacbbcaddabddccdcbcbdbcbbdbbbabacdbbbabdacbadbabbcdcaaccccabdcadaddcbdbbdcabddcababadbacbadacabbbccbbbdbcbdbccadadbadbbccdcdadbddaabbcacccbbccbdbbbcccacdbbdbdcbaabcddcabdbbaababbadaccddcbbadcacbccadaacbbbaaacabbcdacaddbddcdaadcdcacadabbdaddabdaacbbdbabccddcddaabdbddddaabbacccdabbadcacacabbbdabacdddabcdbcdcaaabcadabdddabacbbcbddddcbbbdadddbdbabbcdccdcadcccbcbcadabbdcbbbabccbcaacaaaaabdbbdcbbacdddccccdcdbdcadcddadbcdbdbadccadcbddcdcacaaacabddccbdaacaadbcbdbadccabcdadadbacbcacdcddccccdcabbbacaaddcaccaddadbbdbdccbdcddbbbdbcabdbcadadadbaccddaadbbddabacaddcddadaddddccbacbacaadcacbaabbccbdacdcdddabcdaadcbdbbcbdbddabccbadcbdbdadbddbcbabcbabcbcdaaadcaacdabcbabdbcccadbaadcddacbcbaddbcbbdbbbcacaabdababddacadcabababdaddcaddaabbdcdcacbbabdccaddabdcabbbacbdbabcdadbccdbddabaadddacaaccbcbcdbaababbaadadbcdaabbdcdbaddabbbdccaacabcbaacccdcbcacbbbbdbabcbacabbaabcbdbdaabcbdcdabbcbbdcbccdcdcddbdcbdabcacbddbadaaccdadddaadcbdcbbabddabadbaaadbdbbacdcbaccaabdabcabcccbadccabcdccdcdbdbcbbacddcadbaaacbbdbcbbbaddcbccccadabcababcbccddddacdaddadbdacabbdbcabcadcccbaadddabbadcccdbccdadbaabbaccbbdacaacddccbbcaaabaccddbacbdcccadcbdcdabddcbabbccaaadabcddaddccbadcdadbccaccadbaacdacabacbaadcaadbacaabccabadbddcadaadadaaadcaaadaacaddcdcccbdbbcaabcbddabcbabbcbdcabdcbaddaaaadccadccabadadcbdccdbabdababbadbbcbbbacdcbabbbcccdacccbccccccacbadabbbcdccabdcadacaaacacbbcccabdbcbbaccdcbcaacdbcbcbcbbabcbcaadcbcbabbbabbcbddccabaabcbabcaabcbbabbdbddadaccdabababddadabbdbbdaaabbdddbccaaadccdbbacdbccaddabacaaaccdddbdacbdcbdbadadcaddcabdaacbdcadcbbcdaabacbaacddbcdaddadcdbacdccacddbdcabbabbcddbdcccadbcbbaadccaadcccaaccbdddacdadbadabaacacbccdbbddcdcccabdbdaacdddbcaabddaddcadcbbaddbddaadccdbacccadcacabcbdadcabaddacbdccaccdaadcbdbdccbcdcdcabadcdcdddbcaddccddadacdddcddbaaddbdabaaaabbbabbcaddcbbcdadaaacdabbbacbbbbabadbcdbdbaabcdddbdcccadaddbcdabaccbaaccadcbdadcadcabbadcdcbdaccddccbadadcabbcdaacbcacdcbbdadacadddbdccaddacbbdbabdcdadbabdbbacaacbcdbcdbddadbccbababddcbcaadbaababababbbdddaccadcaaadacbdbcbcdccbaaaccdaccbcabdbbabcadbccabcddaaacabdcadbcadddbbddcdddbabaacccabdbacabaadcbdbcdcbabaaaaadacacaaabbbcccaaacdbddaaddaaabbdccaadbadcbcdbddcaadbaaabdbccbdaddbccadcaddcddadabdbdbacaabdaccaddaddaccaabbbdddbdacbdbabcabcddacdcbccccdccadaaccbdbacdbdaddcdaacadbdbbcccdabdacdbdddacdcbdadbadacbcdbcaadbddcddbbababcbaadcbadccaacbdcabbbdcddcacddcaacacdaadadacdbcbabddaacbbbbbccbbcaaddacdadabbccbcdabddcadbcbabcabddcadbddcabbccacddbdabbbaacdbcbdbcadacddccbcbccadaaccbddbacddddbaabbcbcbdabbdabcdacabdacddcabdabacddabcbbcdacacbdbcbabaccdadbcadbddbdacdcbcccaaababbbaadbccdcbabadddacaddcbddddcdcbbcccadcacdbcdbadbbbbbcccdaabcdcaccadadcabddbccacdccacacbdcbbcccbccabbbacccadacacaddbcaadcbcaccddcdcccaadacaabdbcddddadcdadabcbbacbabbdcabdcbddcdddbbbabcdacbdacabcccddcddccdbabdadcddcdbcdcbaaabbddadccbbccabaccdbccdaadbababdccadbbdcbcdbdbaaccdbddacddbbabdadccbdbdcdbaadcabcbbdddcdadddbdccbcbdbacacaadbacbacadcbbaacdcdcccabddccbacdadbdbbdcadabbddddaaccdbacbbdabbdddacdaabbdbdbdcdaabbbcaaabbbbcacccbbcccddcaabccacbdcbaddcbddbdcccbabdaacaddcbadbadacddcddcadcaaccaaddccacabcddbcbadcaccaaaaaabdcabbacbaaacadcbbdaccabbbbbaacacdcadacbddcbabdacbacbccbdcaddabdadadaccbacbbcbbcbbaccddadabcccbcbbcaacbadbaabaddaaccbcacdcabdbdaabaabdbcdababcdcbcbcabbbcacbbcacbcabcbbaccacbcbbbcadcadbdbabacadacdbbbbdcdbbadbdabbcbadabcbbdacabddabcdccdcabacacbdbadcaccbbbdddadaaadbbcabcbccbcdcddddbdaccdddabcdadaaadcbdcaaabcbaacbcddbdacacabbccbcdadabbbacbaadbdbdabbdabdaccccaadacadcabadcaaacdddcccadbcbcabddcbbcbbacaddcbcbacbcbbaabacaaabddbdddccadddadaddddcbdcbcacbadaddbabacaddabaaadcdbdbddbdbdbdaaabbacbaabcdddbacdaaaabcdaabaabadacbacdcbccbbaddbcbbcadaadbccadbdcbcccbcabaadddbcacdbdcdbdccbccabbdbcdaabdcbbbdaaadddcbddcddbbbbbadcdbcdddccaabddbdddbdabbbbbbbbdbbabadcdaddacaccabcdbcaabaabdabbacaccabdbaddbdccabccacbcbddadbcddbabcbbbcbacbdbcddbaaddbababcdbdcbdbbbadcbaccdcdddbdacbccadddbdccbcdcccdcaadddbbcbbabacbbbbadacddbcbdccdaaaacbbcadacaabbccbdbbabaaccdabdbbdaaacabbddcccbdcacdbcccbcbddbcadaaadbadcbcacabbcaccdbdaabbbbddbdaccddbcdddcdacccabdabbcbbaaccacaaaababbacaadbdacddaadbccdcdbabdbaabdccbcaccdbbcaabbbcddbdcddcbbddbccbaccbabbcbaaccbacaadbcbccbbdbbbccdbbcdccabaddccbadaabccaccaddcccbababbbcaacdcbcadbabccdbbccdaabcbcbcbcabbbbbcbdbbdccbdbbacacdbdbdcaaccbbbdcadaccaaddcaabadabacacdbbbddaabadcacbdbdaddddbcbacccddbbdbbbcaacdcccacbbadbbddcdaacddcabbdbcccadccadcbaddaddbbdbadddadbdbdccbbbaaddccbdcbbdccacadadaadbdabdcabaacbbadbacbdadbcbbcdcbbabccdbbabdcdbcccbcdbccaccbdabdabbacbbdcaadaddaacaddbcbaddacdcaabcbacdcccaccadccbbbdcbdcbcbaadadccabbcdadccdcadbcabccccbccbbcadbaabacaccacbcbdabbabbdcabaacbbbcacbaacdddbcadbbdbbcbcbdbdaabacabcabccadcabbaaaddddbdcacdbbddbddbdadaadadbbaacbcbabbaadabbbbdabdaabddccaabaabccbcacbabadaddbdaadaadcccbdbbcdbaacbcbcadbadadccbdabbdacabcbdacdadbbbcdbdcabddabcaadbabbdbccbcaaddccbadbbbaaacabcbbcddbbaacddcbdcbdcbacdabadbbdadadaadcaacacababdacabcdbcddbbaacabdbbdbdcabbbcaacaacadcdaabbdbacaacabaaddaaabbbbddcbdcbbbbcdacacbbcbabcbbabddbabdcccadbcbdddcbcccbbcbacaadbbdddbdadcdbcddbbadaddcaddddaabaaacaaabccdabadaaccdbbdcccddaadabccbbcabaaccbbdbbdddbbbcacddddadcdbbdcaaabdaaaaabccadccbbdccbcbddcbabddcbacccbcadbabddbdcdcaacbbbaacbcbcdcbaccabadaacabccbccccbbdddbabdccdacccbbdaadcdcddaabbadbabcdaacbcbbcdacccdcdabcbcadcdbdacbdbaacbcddaccbbbadcccdbabcbbbbabcaddcbddbbbdbadcbcaacacddabdddcadbdadcdadbabababdccadbcbdbdaabddaabbcacbacbcdcbcdacdaadbaccbcddcadcabaadbcbaadabcdcbaddccbababcbadcaaacbcccadccababaabcbcbdaccaddacdaddbabdbdbacabbbdcddbbabaadbddccdbcbbacabacbdbbabbaaadcddbdaadacbdccacbadddbdaacacdabbcbcacbddcbdbddccddadbbdabdbbdbdcbbbacabbbaabdcbadadabdbcbbbccddabccbbcddacbdbbaadaddabdacbacadbbddbaccabdcabdcbaaaabdccabdccbbbdcbdccbcaadbdcacadaadadcaabddcdbdbcaabccbacbbadcbcccadbbddcaacdcbcabadabbdaccbadbcccabdaacbbbdbacabbccadbdaaababacdddcbdbcabbbcaaccbdccbdddcccbbcbcacaaaadabbbbbaacabbaacbbbdacabddabaabcdadbddccbaaabbccdcbdcabbadaddabcadddddddabadcbbccdbccbacbbcbdabbacdabdacbbdaaaadbcccacadbdbdbaaacadadbcdcbcdbcbbabadaddcbcbdabdbbccbddacaaabbaadccddacdababaddcaabacdacbbcbddbabdcaacccdbaadbabaabcdccdcbaddccddbccdcddbaddcbcbcdcdddbdbdddabbbdbabadcdbddddcabbcccadadacaacadbdcacaaddcaccdbaaaccbddacccbabdacadbcbcbbdcaadcbaaddacdadadbacaaddcacdadbdddbcbaaadcbacdadddcadabbcacdcabddbdcddaadacdaaacdbdaaccdddbadbdcccdacbdcbdacccddccbaccccddddcddaccbcbabbcddbdbbccbccccddadcaabbdddcddbdcadacddbcbacdaaadcadcabdbdaadbbaabcabbadaccababbbdcbacacaadcabdaaadccdabcdcadbdbcdadcccdcadddcbbbccdcdcdbddbcbccacbccadcabcdcdaddadccbbbadacbbbbdaaaacbbbdbbcbcdadccdbbabbdbcaccbaadddcbadbbcbbdcabadbacdacccddbbabdccadccbbadbabcacbcbdabdacabacbdcaaadacabddbdaccdcbdcdcbdbcbbbaadcdbdcadcdadccbcddccabbbccbdabaacdcdbaabcdddcbabbccdabbdacbbdababadacdbbdccdaabbbaddbabbdbbacbaabddadcabbdcbdbbadcabdadcaacccccbaabcbcaaddbcccaacbabdadaabbbdbbbbddbabddadadbdaabbdacdbdbdabcbdbdddbadacdbaaadbdddcacacddbaddddaadbdabaccccadbcdbbaadaabbacbdcaacddabbbdabdccabcbabbdccccdbdccdabcddaaadbbdcdbddbadababbdbdacabcbababbdacdaadadbaacbcdcaadbddcdbacacdbdcbdbdddcbcaadbcabbcbbcdcacaaacabbbddcadcddcbdbddabadcdddabdbadbdaccdacccdaaaddbbdaadadbaccabbacadbcbbcdbbbbcdacddacbcdabaabdaadadabaabdccdcacbbdccabcdaccddacadadbccadbbbaaccabcccaababcabcdbbdbcaadcaccbabbcccccadbddabcbccaabbccbcbbcbaaaabccacacadaaadbbcbcdbacdaaaccaabddbcacdabcbcacabcbacdbddaddbccacbbdcbcbdabdbcbdbbcadbaddcbabdaacccbcacaccbcdbacdccccbdababbcccbdadcabacdacbdacabdccdcaadccccdabbcaccdccadcadbcbbcbbcdcacbbdbbdcadcdcbdcbbbddbdddcbdbcabbbadbcbacaabbadcacdccbaadbbdadadcbccbdcaccbcaacadcdcbacdaabcbccbdccdacacadcaccbcbddccdcaabbcaadcddbacacabddcdaaddabbddbdcddadbbacacdacdabdbddbdcddcdbaadaaacbdcbbbadbbbaaccddbaccdadcdbbbddacabdabaccccddccdcabbdcbcadaadadaadbccaccccdbcbbbbbddbcccdbbdaadbcadadaadcdbbdccdbcdbddbbacabacddbbcaccadcadadbbdcbbabdbaaabdcdacdbddbbbababacaddbbdbacabbbaddcaccaacbbdcbbdadcbbcbbbbaccaccdbadabccbccbdaddbbcbbdbabdddbbdbccddcbcbccdccdabccabacccdcddcabdcadaacddbbccccbcbbdbdcabdbacaddadabcdaacdaababbcdcbcbcbcbdccdaadcdcdbdcaabbaadaaaccdaacdccddbbaabaaddbcccdbddadcbbaccbbcdcadbcdabcabcccadddcadcaabcdaacabbbcacccabddcbdcdbbcabbcdbdbcbabbdccbccabbaaadbdacddcdcabaccdabccccacadddcacaacddcbaadabcbacbdbbaacbdddccbdcdacaaabdbacddbcabacadabbbdbacadcddddacadccacddaaacbdaddaddcdbaddcdadddacdababcbadbdbcabaababcbcbcdaaabbdcddacdaccacdacadaadabababdacbaaacdbabbcbcbcbbcbaccdadbccbbcdadabcbdbaadbcddaccdabacccadcaacdacaddabbbcbcdaaacadaabcdcabaaaadbdbbadcbcaabcbdbcacdcdccadbdabcabacdaccbabdacbaababbacbbddbcdadcbdabbcdccdcccbbbdadabaccaaddbbaacabdbdbbabbabcdbdcbadbccbdcddddcbbdbbcbabdaabdcacaacbadbabdaacabbbcddddcbdcdcdbcabddcdddabcdcccdddcaadbbadccddbccaacccbcadacbabaccdddcaabdcadbdacdadcadccadbbcbbaddcdadaabcbacaccbdcadbacbbbaaccdbcbacabbbbbccdddaadadacaadaddddcbcddadbdddcdbaddbcadbaaddccbadadacadbcdbddccbcdccabddaaabdccbadcaadcabbcdabadddcdcbddcddcbacccbcbdabbabdcdcacaccaabbbcccbadcdbccbccbacadbdccccadcbcabacdaabcbddabbdbbbdbbbbabacacbdbbdabdadcdacdcdcbddbcdcaddbabddaabccdadadbdaabcdcdccadcaadcbaddaacacbbadcbcdddbabaadadcdabccbbdbbabbbdadabbcdcacdcddcddcbccabbcdbccbbaabaabacbbabdbbbabcdaddddccbbacabaabbcdacccccddabcaaaacaddcabcddcadcacbdacdbadbacbbcbddbbdadcbcbdcadabcdbaaccaabbbabaaadcdadabaaaaaccaadaadacdbcdacdbaccaadabdaddadcbbdaccdadbccdbaccccdccadaccbabcbbcdccbcabdbacdcdbdaadcbdaacabdcacacdabcbdbddaadbcbdcaccbddcabdcbaabdcbabddaccbdbbccadaddbbbbbcabdcaaacdabdcddbdcdbaaabdabaaaacaadbcacdddccbbcdcbbcbbbdaabbbabcaadaddcdbdcdddccddbdcaacacacacdbcdccbbadbcabcabaabbabcadbdabbdaaaabcdcbbadbacbddbdadcbcbabbdabaddcdacaddacdbacbbbacaabaadcccbddddbdabaaadcdbccbbbaddcbccdcccdacabbdcdcaacdbaadbbdaacccbaadccadaabaacdcabacbccbdcaccbdbbababccacaaaccbdbcdcbbabcbaaabbacbcadadcdbcdaaaadbacddccbbdaaacccdbbbabccdadcbbcacbabdbdbcdadcabdbbddaaaddaaadbcadbdacddabdbabbccaddbcccbdbbbabcdbcabbdacabaacadcccbdddadbbadddbadbaaddacacddaccdabadaacaaacacdccaabaddabcaaaaacaabbdabaadaacbbcacdabcabcbaccbcdcabdacdadbbdbdddbbaabadcadcdddddbabcaacccccbacdcdbdcbdbaddcaababadcbbccacbcddbddbdbddcbcbdadbccccbacadabdabcbbadcaaccbcbbdbaddbadbaabacbcbcadddbacaacaabadbacccbadcbccadddcddccaaaadbcaccccacaddaddcaadabdccbdcaccbaaaadbdbabcaabbcbcbcbcccbacbbbcabacbcbbccdacacdacdbcddadddbdabbadadaabdddbdbaaadacdbbccadcbcacabbbcadbdcccdbaaaaddbddcbdacacbdcaadcacdabaccbdbabdbddbbaadbdbbbaaabdbdbdacabddbaabdbddddaaaddbbcaccabacaabcabbabaadcbbaaacbbbcaacbbdbacbbbaccaddcdbaddadaabddcddbcdbadddabbaadadbdccabdddcdbdaabdcdcdabbcacbcaaccddbcbbaaacbddccabbcdccccacbbaaddcdbcdadacacaaabccbdbdddabcbbabcabbcdabddacbaaabcdddbdacdaccbabbccdbbdcaadacaaabadccccbbccdbdacadaacdacdcddbdaaadacbbdabdbcabacddadbbadbcccadbddacabbaabccbacdaddabdddabbccdaabbdcbaacbaccabddcaacdbdddbdcccadcbdabdcaacdadbcddccccdcbadbbdadcbdcabbddccbababcbacddbbdaabddcbabdaaacbaaccaccdbbbabcadbccbbccdadbbdddcccccddbbbcbbddccbacbdaadabdadcdacacabddacdaccbbccbccdcbdcdcdbaabbacaddbadcaddbabbcbadcadccdcddbaadcbadccdcdbbbdccddbbdabcacccdbcbabddddcacdadcbacccbabcdbcdbddcbaacadddbddccdcdacaabaabadccbcabacbaddccbcbbdccbacbcacabdacddbdaaadccabcadcdddbccdbaacabcddabababbbdcdbddabaadbcbcbdadcdccdbddcbaaabdcaaddcdaadccbbbadbcbbacdbbacbacbbdcccdddbcbbadbaccbadccacbbccababcbddaacaadccadbccccbccacdabbbccddbcdaabcabdbadacbdbcbdcccaaadbbdadbddadcbcadbcbbcdbbbbdbdccabdbbbbbcdbbacccbcddaaadcacdcddcaadadaadbcbdcbcbbcbdcccabaddddadcbcadbaccdadccabddbbdbdddaabbddaccbcbabdbcdbacbbcdaabbbbbbdadaccbdcdbbcccadcbddbcdabaabddccdcdcacbbdbdaaabcdbacccdbabbddbbbbcddabbddcabcbacacdddcdbaaacbcbcdadcdbbdbdacdcadcadbdcbddbabdadcaaabadbacbcacccbbacadbdaadacbadaadbdaaddaadbbbacdbbcbcdbbcdcbbddabcabcaddccdbdabadadabcabbabcabdcbaabaadadbacbcababddadadaabbcdbccdbccdbaddabdaabaabdcbcbdbaccdcddaaabdacbacacbbddccbcdaaabbaaacdacddbadcddcdddbdcddbbcbcdcadcbadddccabcbadaacbcddabcbdcbbcccaaacadbddbacadbaddabadbcabbcacbdcbaabbabbbacacdbddcbadadabccddbdddbccbdaabcbbcaaabdabbddcbabadcdddacdbdcabacbccaaaadadacdcbadacddbadbabdabbacdabddabaabddcbbdcdcaddacddbdbabbcdddaccaacddbabbdaaabddbbcccdcdcddcbcbddbbcbccbbddddaaacbcdcacbbcadbbddcdddaacdadabbbbaabdbdbccaaabababbcbabddcacabdcdabbaccbacdadcbbcdadacaaccadadaaabacbaddacbdbdbdaccdbbaddbdcdbccbbacbcaabaacbdacadbabdacaddddbccbdabdcbcddaadacaaadaadcdcddcaaacddddbdbdcccdcbacdbadbbbcabdcbbaaccccbddccabcbdcbbbaacacddabbdcddbadabcccdbcabcbdadbcccddacaadababcaccbdadbdcbddbbcbadcbadccdacbbcdaaabaddcbabbaabbaabcababdcaacdcccabbcacdaadadcdbaddbcddbdbadcabbccdbbadddccdddcabbaaaabbacaccaddbacdadccdadcbcdcaadbabccbbbccabcddababcaadadababddacdadbcaaccaabbaaadbcbaabcbacdabcccdcbcbcdabcadddcbcdadbadcdcbdbaacdbdbbaabcabaaabcdabbdaddcabaabcdccacdcabdbbaabadbdabbcbdddddddabbcdbdacdbdddddbbaadcbcabaadcadbddcaadbcacaaacdadcbbdaddcadcadbdddadadabbadcdbbcbcddadabcbbbcdcbabbacdcdcaabcacddccadccdacadbdaababaadaccaccacccccaaabacaaccbcccbbadcbacaaddcdadcbdcdabddbacbdcbdcbdbdbadbcbbccaabbbddbcdcdbbbdbdbacdbcadaabdbcbddccacabcadbdbabaabdcacdacbaddbcdbddaabdbccdcaccdcbacabbbdcabccabadbacaaaaddaddbbacbccaacdcadaaddaacddbdcbaadadbcadccbbbadbabcdabadcbccdbdcaccdabbdcdacdcbbabcbccaadbdacbdddcbcdbaadddadcdccadadccddbddcbabddbccdcdbddbabdbcbaaddccadbacccabdaacdcaadbabbdddacddabbbbcbbcbcddababdadddadaddabbbaddacbcacdababcaadbcaadbcdbcadccadbbbdacaaaccddaadcbaaababaaacadaadcccabbcabdbddabadadadccaaacddaddaccdddbaadccdcadaccbcbacccadadcdcdacaccbaaabcdacdcdaaacbcbddbbadadbbddccdbbdcacddbaadacacccaacabbcacdbcdcdcaaadaaabdcbbdacccbbaadddadbaabcdbcbabccaccbbdabdbccbdadbccabcddccdcddcbabbddaccddbcdcdabdacbccdabccbdaddccbbbbcbabdcbabdddaadddabacdaaaabddcdbabbbbcddbcacaaaccdbdcdcddcaabadcbbccbbaddccddcddbbabcccbbbbbddcccbcadabbdddddcadccdaadcbcbaaddcadbcacdcadcccddbbbcadabdabcdcdbdbdcbaddbccacadddcacbbabdcbdccbacccbcaabadcdbdbbabbddbaacabccccabdccadacbcbcbbabdbaaddbbcaabbcababdccaabbbacacadcbbdbdaadcbdbdcaccbacbccbbbddabaaadbdabbaabddacccabbcbbadcdadabdcbddbbbcbaddacdbbcbdcaddddabdadadddbbdbccaaccddcdbccdaccaaababbcdccdddbdbabaccdcdcdbcbdcacbcbdbadbddccbcaabcbdbaaabdcbcaddbbbbbacddabddbbaccaacaaadabdbaaadbacccadcdcbadaaacdbacaaddabaabcccbadbdadcbbcbacbcbcdbcbbabcaaddacdbdddcdaaaabcccddbdbcdddacddcaaadaabdbabdaacbddccdccccaddbcdacaacdbbcaccaddbcbccdbccaaaadacaadccdcacbacccddbabaccdddcbadabcadcabdbbaabaadccaacbadccaabaaacccccadadbcdadcccacbcabdacdadaaaacdbbbcacacbdcaccdbaccccdcbbcdaaaddddcbbccabadaccaaabbdaacdbbaaddcccabbdccbdbdacaacaddadaddbdbacacbbbabbdbdaadcbcdcacddcbdcacbbdaaababcbcdbbcaacbdbcabcbccdcccdccadbaacaccddcaacdddabdabacaaddcaacabaadcadcbdcccaaccaddccabcadcbadcabccbbadacdabbddcccbaaccacbddbbcbabbadbcbcbdbbbbadddacdbcccbdbabadbacccbbbcbcadccdacbcdcacbddcbaadcacababcdccdbcbcabacaadadcbabddbadbbaacbadbadbaaaababdbabbdcabccdddabbadbcbcccbbcdabcacdacabbcdcacccdadbdcacacabdcdabbbddaacddbbdcccaadcdaacaddbaccaacbbcbbcaaaaacaaabacdbcbbdacccdcdbcbbddbdbacbbacbcdabccadbcddbdacadbddbbaacdcccbdcbabcacddaadcbdccddbbbbacaccdddabbbcdcdbbaddcadbbdccbdccdbddbcdcbdcbdcacddbbcccccbaabacdadbabadaabddcdbbddbadcbbbbbdaddaccacaddbdaadabbdadabadbbdbcacaddabbddcabbacccbbccbcdbccddddabbcdbdcbcdddacbbbbccbbdbacbdcbbdcabadbdaddbbbccabccbaaaacbababadbccdbbcddbcbbbcbadbbdccaaaacabbaaddcdadcbbadaaabbacbddcabdbccddadacababacbdcaaddaadbadabbbdabdbbcdcbacddaacbbbbbbbdbbcbabbddcbcddabbcdcbaadbdddaaabbcbbadcbacbcdabadcdbbaccddcddddaddcacbbcdddcdadcdcaacccdddbdbcacddcdabbbcbdcdaaabcdabbcadbacbaabdabcbcbcbdcdbabcbdbdcbdddaaaccacadaabcabddcaabcadbbabcdcaacddbccbccdabaaacdaacabcbbccccaadbbdbddacdacabbcabaccdbaaddacaddbdccdbbddcbdcbddcbacdcdaadcacaaadaabbddbcabccaddcccaaddbcccacccdacadccaaccdabcbbaaacbcbabccccbbcbcbcbbbcacdadadcacbddaddddbacadbdabdbbcccdcbdaabbacbcabccdcbbddbcdddcaaacbaadcdcaadbcccaaaacadbbccbdbaabcdbccbdadcccdbcbaaccdaadaadccdccddcacbbbcbcadcbbaddbdbdddbcccbcdbbbaacbdadbbcdaaadaccdcadcaaababdbddadccdbabcccbabacccababccdabbddcaddbaaacaabdbcbaaabdcccddbbdabcbcdbddccdddcdaaadbcdaaadcabdabdddcbddabdabcbcbddcccaddcdadbccaccabbbbbbbadacdcacdccdaacccdaabdbdbcdbbbbbccbdbdccbcdaabcbabdcbdaadbacbbbcadabcbcaaddaabababbddddbaabbdbabcbdadddadddccbabaccddbbacccaaddcacdcbdbdbdbcdbbadaacbbccdbacdcaadccbcbcbacdccbaddadddacdcaadaccdcdbdbbdacabbcdbdbacbdcbbacacbcacbaadcdbbdbbbabbcabbbaadcacddcbbbdaabaccbaccbbcccdbbcaddcdaddddccbddabbcbcbacadbdcbdabdacbdcaaabbccbaadbcabbdcccbbddabbaaadaabddbdbcdcdbcdbcadcaddcadcccaadbddadabdcacdccbdcbdcddcaadbbaacaccdacdcddaadaadabdabbabbabbdcaddacbaababcbbccbdbcdbbadbdacaddbdbbbaaaaadcbadbcddacccabbcdadccdcadcaabacbdcdbaaaaaadccbdcabcddcccadabdaacbcbddabcbaababdcccadddbabdbcdbcadbcadbbbdaacbcbbaabdcbcbbbcdddbddbdbaddcbabbadbcbaccddddaccaacdcbddbcdbdddbcdaacbdddbcacddbaaccaddcbcdbbcbcbcdcabccbdabdcdaaddcbddadcbdaabccbbbdcadcdbcdbddaabbadacaadbbadacbcacbadbcbdcaacddadbacbdcccdabcdbbbbaacabbcbdccbbaadbcdaaadbcdcabcadcaaababdcadccdbddacaccccacbabcacadbaaabbadbabbacbcdbbcacdddabdccbacacdcbadacdcbacbbadacdbddacdbddacabcbbcdbdcdbbdcaaccdcaddcbdacbcdbacaddabdcaaaddacabcbdcacaddbccbbddaabdbaabcdcacdbdbbbcccdbdabdbabadcccbdaccdddbadcaaaaddbdbacdcdcbabcaccdaccdcdbbaacbcdbcdddacdbabdcaaddadccbbdcbcadbdbbbacccaaabdcdadbbcacaaadbcabaacbdddbbdbabdcbacbdbdadbbdbabcdcdadcdcbabddccbaaabdabbddabdbdcbcbcdcdddbbbcdaabddbdcabdbccaabcddaccbabacaababaaaababdbbcbacdacabbcdcacbabdacddcdadbaadbadabaaddccbbabddbcbbddcabacddacbcbcdccdbbcdbdacbcaccaddaabdbddcaacdccadccbbdbcbacbaccacaabaadddcacbbacbaabbbdddbcbdcccddacbbbcbdbcdbbccaabbabbddddbcdbbbbcacdbccabdacbbcdbabbbcdcbacdacbdddccbdddbdbbacdccbcbaacbbadbabacabdddcadcacdabbadccaaddaddcbcadabadddaccacdbaabbcbadddbcdcddbabbacdaacaddcaaabcadbadacabdccbccadbcbdbacbbaaddadbaaccaacaaaaddbcccacbdcaccbbdbbbdaacabcddbacdcbcaaabdabaaacabccccbcbaadaabbcadcbcbbcdccacaadcaddacdaccdcdacaadcddbcdbadaaccadacaaadbcdcabaadbcdccccdcdccaacbdddccdbcacbacccdbddacbcacabdabbacdbaaaabaaabadccdacbacccaadbdabcabcacadacabbabbabcccdaacdacababaadbabdacbaabccacbbddbbdadcccdbcddcdcbdababacbbacddcddaabadddabbdbabcdcbacaabbdcddbbccbcadbdddadadccbcdcadcdbaabbdcbcdabcaaccbbcddcabddaadbcbcbddadbbcadbcddddbbdbcacbdcdaccdaaaaccdbcdddaddadcbdbbabbdcaacdbcdadbcbabbccbbdccaadadadadbdadbddaccbaccdabcbdadcacdaddbaababacbcabdabadabdabcaacbbabddbbdbbcdabadaaacacbddabbbbadaadabdcbbaaccbccdaaccbbadadaccdbcddcadaadddcacddcabcdcbbbdccbcacbacdbcbbbdabbdbdabdabddbcaaccdbddcccccddbbbbbcdcdcabccbdaacbacacabbcddaaccdbddbacbbbcabbbdcdaacbabccdbdaccadcbabdabdbdabccbcdbbccabadbdbbdacccdcdddacdbbbcdadbdaaccabcbdbadcdaadbbdcacadcabbccadaaddbcdadccddcdadbbdbddbbcdaccccaadcdcaaacbcbbccdcadcbddddbdbaadcaabababbcdbaddddbddbcacbadaacbbbcbcbddabbdacbbdccbbcbdcadadbcbddbbcabbccaacbbbccaccdacadcdbaaacaaaddcccbdbbbacccaddbdcdbadcbadddcaaaaaabbaacadabbbbcbacdaadcdccbbdcbbadaacdcdccdbccdcbcbcaaddcbdcbbdbcaddbabcaddabdaccbaadbbacbbdbcddcdadacaacccadcdacbacbadbcbccbbbccbbdaabacaacccadbccaadcaacdabbacbdbdcdddccaadaacddbaccaadddcdabadcacddababbbcbdddbdddcdccdaddcbabdbcacdbdaabbabbababbbdccdcdabdcadbdaddddabcacdddadccbbccadadbbbcadacaaabbaacbbbcbdacddaacaacaddbaaddbacbccdaaabaaadbcaadaaabdbdcdbadadcacacdacdccccbbcdcbaddaccbaaddcbccaabcabdaddbacbccabbcbccdddbadaddccbdbcaaabbcdbdddadadbbacccadcaadaaabadabaddacabcabaabcabcdaacaccccbdbcbbacaadcddccccacacdccbcbbcdbdcbaaadadcaacacabcbccdbcdabcbaddcddbacbabddadacabbabdaccacbadcadaaddcadabdbdbccdbacbbdaccbbcdbcccbbcdccbcacdcaaabdddaccababdbdbcbccbbdbbabcbaadddabcccaacdbddccbbdbbacdaacbdacbcbbbddaccaadaacbaadbabdddacbcccbcdcbbdabbcbcbbbdcabbcbdccabacaacdcaadaddacdababdacbdadddabdcdcdbdddbdaadabccadbbccdcbddcadccbdbcbdcadbadcbdacbbbacbaccbaaddcacdbbabdcdadccaacadbcdcdabcaacddbddbdaadddcddbcbdddbcbbbdccdadddbbccaabccbacabbddbddacadbdccaddddaadcdcdbdabccbdbcbcdcdcbaaabcaacdabbadcbdbdbdbddaacccbabdbcccabcbcaccbcbbcbcbadbbcabaacddbdcbddabcccdacdbdcdddccdadbdababccdacbaabdadababbbbadcacacadcbdbadccaacdccbcbbaacaaacacddcaacabbdbccbabbaadbccaabbbcbbdbdbbbcbabddbddbdccbaaaaacbbdddcbddacdcadbccdbdbccdcbbacacadcbadcdadccbdacaaacdabadbcbccaabddacbcabccadacbddcadaaabacaadcacbbdabdbcabbadadacbcbadbddacccbbdadabcbdabacdbbbbbbbaddcbdbdadcbdcccaaabdbcadccadbbbcbbcabaccddbdabbbdabdaababccabbbdcaaddaabdcccddbddaabbabdcbacabadbbdadabcccdbcbaddbdcdaabadbdbdbbdcdadddccddabccacadddaabaccabacacdabddbadddbbdbdaacddabcaaddbdbadbdaaadacaddddbabbcddbdddcaddadbdcdcaabcbcbcbdcbcbccbdddbababacccaccbcbcdbcbcddbcdccdbdcdbabcabbacbbddbababdbdcbaaabcbbadaadcaaadacbbdacdcccadacadcdcbdbbbdbbbbdabcdcbcdbdaddddcaabbbdabadcaddaaacbddbabbcbadcbaadddacbccdbddbbaddaacdbbdbbbbbdccdaaaddccccadbaaadbaabccbbcdadcddbcdacbbcdcabbbcdbbdbbbddaccabcabcadacbacadabcaadccbbaacddbaabdadbcdccbcdaaabaabdadbcdbbdaaddbdcadbddcdabbabdbccadcbbcdbdccdbdcaadddacbcbdaaabbadadccbbdbcbddabbccdcbcbcacaddbbabbacccabdcdddaaacbdcddaadbddcacabdcadcbcdbddbbcabacbbdcbabcccdbabbaddbaaaddbbdcbbadabdbdadcdadacababcdaccbaacbaaaadbccaabbbcabdaddcabddcbbbaacddacdcbababbdcbacadacbdbcdaabdbadbcdccddaadaacbbcaaaadcdaacdcbccccdddcaacacccbacdadaaddbbbcbaddcdccbdbacdbcdacccddadbcbacaadbcccaacbbcdaadabbdcddcdaddacbbabdbcccbaccadadbdbabbbcbdaccbbcabbbaacaaabdccdadddcdbaaabacddcbacaadbcdddaaccdabbccaaabdacccaaacbbddbbbaabcddcccadacbabacdcdcbbaadabacdbcacbbccdcabcccbdbdabddcbbbddabcbbbadcbaabcdadaaabdcdabcaabdcdcdcbadddbdbabbaadbbccabcdbbdcddbadcdcbcbadcbddbbdbbbbcaccaaaadcdddadbbbbbbcbaadddcadcdcbbabcbabddbcaabadbabcacdbabacbcdaccbbbbbddcbacdabccabbdbbccaabddacbbbddbdbbdcadcdddbdccabdcacaacdccccbaddcacbcccbdbadababdabbddbccdbddddccaaccaabcbaadcbcadbacadabbdabbdbbcdcbdbcdcbcdbddccdddcbdbbbacacadacbadadacadbbaaadcbddadbbbdcbddaadccbadcdccbdcccaaacaabcbcadddccbbdcdcbadcdbdbcdcacdbadbbbadbdcbcbbdbbcababcbbddadcddadcadadccbadcbbdbbccddbdcbcbbadcadcddbdadddddaddacbadabcdbdccacacdaccdccdcbbadaabcdcbcdadcabdcccddcabccbdaaccbbcdcddddbcdddbdcbbbcabbccbcccbcddbcdaadbaacbccdcccbbbccdccababaddcbabcbcaacaaacddadcbaddbaccacababcadacbccaadcbbacbcbbbddcdbadadbbdcddccacabdcbccccccadccabbcdcadccabbddcdcddbabaacaabacbaaaaddccdcbbcbddbaaaaacaacacbcdcadabcabaabbbcbabddabbcaccadcdcdabddccabcccabdbccbcacaccbcabdbcdcababbaaddddcaabadbdbbccdbcbdbbacabadcdcacccdbbcbbcbdbabacbcbbdabbbcaaadddabadcbbcdcbdabcabadacbbbbcdddaabcabcbbbcaacdccadcbcacdbcbdaababbddcdaadaaaccccabdccbcabdbdcacdbabcaaccadaddbacbddbcaabdadbcbccbacbcadadcacbbddbbdbadbcdbcdacddaadbcbabbbadddcbabbadbdccababdcdccbdddddaaaacdcdbdbbacdcdbcacbadacadbcabacddabcdbbbabdbddacaaaadacdcdddbdbccbaddacacaadcabccbbccaccbdbcbcaddaacadbccadbbdaccdbbdbaaabcccabcaddacbdabdbbdbbddcabdcdcadabbdddaddddcacbbddacbbcccaaccdddbccaaccdaaddcbdadbacbbaadbcaabbcccbabadcdddbbbdbacdacaaabcbacbccabdcdcdcbcabdacbdcdbcaccabdabaddbadaccddaadbcaaabacaabacddcbaaddaaabcaabaabaddcbbcaddbaccabdabdadccbdbcdbcbbdbdbdbabcaabdcadcbdcadbcaddbdaadabbccbaaaacccccabdbacaccacbdaabadcadbbacbdbacdcbabaabbbddcbbbccadabbabcbdaabddbdddbacaadaabbccbbbbdbbdaaccbdcbbaadcaccaadccaccbadcbcddddaddbaccccdbbdaccdabdddbcaaabbbccccaadcbdbdbddaaaccabcdbddccacdcaacabcbcdccbaaabbaddcdabdbbcdacccdcabcbbdbbdaacbbdaccbaabdacbabbcbadaaccdabbdcadabdbddcaaabcddccdcdcaaacbcadbcbabdabdbccdbdadacbbbdabbaaacbbabcacbcadaacadaadabacbbaaccaabdbcdccbdbabdaadaaacccabcbcadddacdbccacbbdadbababcbddbcabbddcacabbddccbbcabbcdbbbdbaacbadadbcdcbaabbdaadbabdabacdcbbaccadddcacdbdbccabdbcabccbddacabacddcbacdbabdadababaccccaddcbdabdcccaccaabdcabccbdacacbdddabcbcdaaaaacdcadcabababadccccdabbbdaccadaddcabbcccacbcdcabcbbddbbcaadadbccabccdccbbcbacabaccdaddddcdabababbcdbcbaacbccbccddcdcbdddaacbaccbcbddddbbcacdddbccccbdabdaccbbadabdacccacccabbcbcdcbdcabaaabcdcaadacdacabbddabaaabcacacdbddbcccccbdcabcbadabddcbbdaddbacbccdddbcbabbbdcdbcdcdbbbbcabbbacdcdabdadcbdaadadbcccbdabbbbbbbadabdcadbbdcabbdcadaddcccdbdadcacddcbddbcabbdcabcabdcbdcbabcdbddadccdbcccabacddcbadbbccadbdcdcacbbadcacdaccbdcbacccdbbdbacadbdbbddadaaccbddadddbdaaddcccdccbabdbcacccdbcadcaadadcdcbadacbdaabbbdadbacaddbadccbbabdbbacadbabbdcbbdbaabbbddacbdacbdbdbbaabbbcbbadcdccbdcdcaddbcbddacdcbddbdcbdccdbacaaacdddaaccdadabcdbdcdbdbddaacddcdcadbbbcccbbbdbbcadcdcccdbdbbbbdbbdddadccbdacdcacbdaabdcdbbabccccbaababdccbaabdbaadacbbcbabdbddcddacaddadadbcaadaaadddbdaaaaddddcbdaadcccbccccabacbadabbdcaadcdaccdbbccbbbaabadbbadcabacbddabcbdcbadadbdcbabcccabaaacbcaddacddcbdacdcdababbdabbbbdbbbbaaccdabdabdabaadadbcabadaacaacabdccbdbddcaadbacaabccadbcabdcaadcbcabbaaabacadbadbddabcadcdbccaabddacdaaaccbbdacacbdcdbaacbcdddcdbcaddcbbdabbadbaacabcdcabdddddbdddbadbaaaadbdddbcabcbaaccbcadcccdddbaaddaaddccbdbababadaaabbcdbaadbddaaabbcccbcbdbccacbdcddccbaddaadcbcbbcadacbbaddccbddbdaaaccbacadbcabddcbaadccdaccadaccdcdcdbabddbdccdcaddaaabbdcbaccdbdcdddadadacbbcabbdbbabaabdcbbaadabcbbbabcacdbbcccbbdbdbacbcbddbccbddbdbdadcdccdcaaadaabbbccdcdcbcadbbcadcdacbddbaabcbbbaacabbdadcadbddcdbababdccbdcacdbbaddadcadccaadaabcbabaccccbccdcbaadadcbcbdddccbbacbdcdcdbacdcdbcdddbddbcadbdbcbacabaddbcdbbaacdbabdcddbadddbbdbcdbdcddabaabaccbbccadadbddaacabbbdaababadadacacadabaccdcabbddcddaaabbabcdadcacbdaabbdbddcdbdabdddcccabbabadaaabdcdbcdbaaadbbabdabaccbcadcccdcbdbbacbdadcabbaddaddcaaddbdbbdbcbcbabcccbabdbcabbadacbcabccdadbcbbacbccaddabbcccbbcbabadbbaccddbdaabccabacaadacbcbcaccadccdcadabddbcdcddbcdaacabaabbabdbccdadddadcdcdcdacdbaddcbbdaabddcbbbccacababbbbbdabdaddbabbbbbdaddabdcdbccbccdbadcabcdcacdbbbcdadbbbbdbdacbbbaabbbdcacbdbdccaaabbaccaaccdbbdbdadaddaaadbcbddcbbdbaccaadaaddcbcddcaadadadcbdcdcabadbcbdabbaacaacbabdbbcacacccbcccabaccbbcbdaddbcdcaccdddcaddcdbdbbbddcdcaacbaacabbdbcabdabcccccadaabcddddabbacabdbdbbbcbdbdbddcdcdddbcddacbbacdadabddbacaabbdcdadcdbbdaddacccdccbabcacbbdbaabaaabccdabcdbcdbadacccababacbddadcacdddbdabacaaabaacdbadadcdbbbbabdbdcbbbbcabaabcbbcbcdabacdaacbdbabbdaccdbcdbacbbbdbacbdacddcdadabcbbbaaaadbabcdbbdddbacccabbbdcddcdddaccbcbbaaabdcbcacadbddacbaacaadbbdbdcdbbccdacadcaccababbbdaaccbcabdabbcdcadccacccacacdddcdcbaaabbddabbddbabbdabbcdaccdacddacadccdccdaaaacdbccadcacabcaacdacbaadbaadabcddbbcadbbcdbdcdabdaccdbabdabbacaddbbccccccbdbaabbcaaccaaaccbacacdcbdddaaabaddcbbadbbcadbabbbbccbbcdacaddcddacdbcbdababbbaadaabbcbdddaddcbbaabcbdbabcabaccabccdadbcacdcbbcdcdcddcaccaabdabdbbcaadcabcababdbbacdcddbbcbdbaacdcbdcabccbdcbadcbbaadaabadabbdcacdaacbacbbaacabbaccdccacbcaadccdbabbdcdcdccdcbadddbabcacbadbaadbdcacbcacabcdabbbdccbbbcccadbabbacabcabdbbdbdacaaccacdbccbcdababcddadbdacccdaadcacdddbcbbacdcdaacdaabacbcddcdadabbdabcdcdbadadacbccabcaaacabbaddccbbbcaacccadbabcddabdaddcdcabccbcaabbdbadbcdcddccacddacbbabaababacbbddccaaacaadbccbddbbccdcddcacacbbbbbcbcbbddaccadddccdaadddaacadcdaccaaaaccbabcdaacbdcdabbddbadccbdddcaacdacadcbcadadbdbdaabcdbdbadbcbcdddcdbbacaccbcacadbccabaaacaccccccdacccacbadccbbabcbdcdbbacdaacbdbddcbacdcacdcbbbbddaaabcaccdbbcbcdddccbababbcaadddcbccadadaccdaacadcdccaaabaadabaabcccbdaaccbdbdcdaccadcdddbbbddcabccbadcddbcdbadddabbcaddcaaccaabadbdddcadababcaccbcaabcdabacbdbdbcaddbbacadbbbcdbbdbdcadddbcabdbcadaccabdcdabdbbbacbabbbdbdacbdddabdaadabbaaccdaabbacbbcaaaddcddaccdbdbcbabacadbcabdcdaabaddddabcabbbccddbddccadcbaabadddcddaadabcbbdbcbacadaaabbdaaabdbccaccadacbdababccbdbacadbacbaabacbccacbbdbdaacdbccdaaddbccbdcaadaddbbaddbcccccdcbdbdbcadbaaacddabbbddbadcccaddbddbcccbccdccadbadccaadbbadccdcdbdcbbaaacacccdddcccccaaccadacaddabbdaadbcbabbbdcabdaaddcbdbbaadcbcadcdaadbaadbaadaacdadaadadcdacbbcabccddbadabcaabddaccdadcddabadabccbccadbdbcadbdbdcccbaccbbaabbcaabcddcbcadbbcddbabdcabcbdacdcdbbdbdcdbaacacacbcbdacddbabbabbcaaacbddacaadbaccbbadcbddcbdbbbbacbddbbdbdbbacdbdabdcaacacdbadadccbdbbbcacbbadccaccdcbdcbcdacdacbabadbccdbdaadaacaddadaaadcddcccadbcdcbabccaacccccaccccabacdcacdabdbaacdccadbdcbaaaccddadacbdbbaacbaadddcbaddcdbaabacbccdbccadccbbdabacaaabcbbdddcddacabbaacabdcccaacadadbdddbbabbadadcdacbacaabbcdcbacdcdbabdddcadcadaabbacbcadcdaaccadbcacabaaaacacbacadadacddcdbdbbdcababbdbbbadaadcaccabbcdaddadabccacdccdbcabcadddbbdcbadcccdadaadabdaaaacbcdccbbbdadcacabbadcabccacdbababdaabcabdbabbcbcaaaadbadbaaddbadadcacccdccbbcbdcccbabbabbbdccbbdbadbcaacaabdadcaaacaccccaaddacacabdbdcabbdccabcdaabcbdccddbcadabdadccabddbcababdcbbbbaaaddaabbadcdbbccbbadbaabcabdddcdcaadbbbddaabdcccdbbcbcbdcdbbddbbbcababddccdcbbbaabacaddccccdbdacdbcbabadbabdcbcdabbabaccacbabcbccbccbaabbdbcadbcdaabcdabaabbcdcbccdabddbbbccddabcbdadbbccadbaabcbaccdddacccacbcdbcacacbaaabdaddadbbddcaccbcacacbbbccaabbaaaadbcdbbbbcbccabbbdaacacccaccddcabbddcdaabbdcacdabdacaadbacacbcbbadbbdacdaabbdbabdbbcabdccddccacacadbacbcccbcaadcdaacbddabddaabbdacdabdcadacadbcadbdabbadcdccbbdbacbdacbbcdbaabcbbbcccccdacdabbaabbbbaadabdcbbddcbabccbdadcadabdabbdcdbbdaddcdbaabdccaaccbbdbbbabddabddaadcadcabdaddddbbacaabcaabbaddbbcbcdaccbcadacdbbdccacccdbabdcbccacabacadbabaaabdddcccbacbbbccccadbabcaddbadaabdacbacdbaabdbbaaacdddcbbabbccdbccdbdcdccadacdadcbbdcbdcacabcadbdacbdcdbbacacdcabcdccadbbcdcaddcdadbbbacbcbdabacccbcbcddcbcbadbbbbccbbcccabcabcbcabddccbaabcdccabbabcabaddbbabadbaaddcdcadddaaacdddcdcbdbadccacbadcccaacbdbbdabcdbdaabdaadaabccbadbcccdcbccdacbdbaadcbbacdddccaadddbabbaacaccdcbcabdcdbbadaaadbaaacdbbccdcaaccaacccaaddddcbbaacaababdddacddbcaabbcccadaccacaaccdacadccababbdacadbcacdddcbabaabbbbdbbcbdcbabccdcdabbabbaddacdcccbcdbacaaaacacdddaaccdbddabadcdabdbaddabddddabccaacaddbdcabcdaddbdadacadadcdccbabccadcdacbbaacdababccbbbabaaadddccbbddcdcdcabcabbddadbdccabbbacaaddacadcccadcaddcadadcbcacadabdaabdddadaaabaaabdcdadaaabdbdcdbbcaabbababccdaadbbccbbcbccacabdadbadacbaabbcaaaadbaddcdbbdbbccbbacddbdacacbbbdcbdaccbacadabbcddaabdddcccbcdcadaddcddddcbaaaaabaccdcaaacbbbcaaaaddaabbcdcdaacccbbdaadbaabccabccbadabdccbbdccdcddbcbaacdadcadaabdabbddcddbdbbaccdbdbababcbccbadbacaccbdbbadddababbcbbcdbaccdddbcbaddacbacdbabbdacbdbbcacbcbacbbcabddadbcacbdddbacbbacbcdcbbbdadaadbbcbbcadbaccddbdabbdcdbaadcacdbacaccdcaacaabbbddacbadcccbdacadbacaacdabcdcaccdddacbaabdacdbacdcaabdbacccdcbdcdaaacddcddacbcdbcadddcabdcccaaaadbcbaaacacacccddcdddabdacacbadcdbdcdcccdcadccadbbadcdccabadbccdbacdddbbaabaabababcdbdadbdbcdddcddcadabadcccbdbbaacdbbdbdbdddaccbcaabacccddabbdcccccabdcbddbaabdaadcadddbcacbacaccabcdcbcbcdbadabccbcadaabbccacbacbbbdbacccbdaaccbbababcadadaccdcccddbbaadbacbdaaddccbabccacbabccdccbabcaaacabdbbcdddabdabcdabccbccbcccabdcdacaddabcaabacbabbdbaadacddccaddbabdabccabadbcbbabcbaacbaccbdabbddbbdbaadcccbcbdbbcdacdccdaccdcbbadbcdbdbcacddabbdccaadacacabacaadccaadddbcaaadccabbddaaddcaacbbccdcabbbbdddadcbdbabaddacaacbcdddbdbbabcdabdabdadcacdbaccbdcbadacabadcccabcbbabdbbbdaadccadcbdadbddbbcadaddcdaaacbadbcaadcbdbccdbaccbabcdcacbcaccdbcadcdabcdaccbdbdcbabcadbdbdaddcdccbbadaacccbaaacbacadcdabacdbaaacabbaccaaddaadcacabcbababddcdbabcccbdcacdcadddcdddcddcbcadbacaaaabcbbbabcbcacbddadcbabcdbdcbcdddaaddacccdddcdbbcdbbbdddcdacdadbdbbcabadacbcdaadcaaaadbccabbdddacbabdcbdbcbccccccbccdaaabcbbddabcdcdbbdcdcbbdaadcbcadcccbbbcbdcbdbdbccaaaadbbbacaccbdbaaadcddccdcdcdddadbbbcdbcaaaabcbbddcdacacdabdcababacabccacacabdadbcadbbcacdbcdaadbabddaddbccdacddbcaacdbdccbdaacaaacaddabadadcaadabdacacbababdbaaaaaaadcddddcbabdbabccdacdccaaabdbabbbbddacabddcbccbccaaccdbabacdacddcccabcddcddbacdaacdccccbdcbaabbbadddbbbcabdacbcabadcbbccabcdaaabdabaabbbcadddcddaacbbbbbbddcaacdcbbcbadadabdabacdbaabdadacdaaaaacadbdcbdaabcdababaccbbabaaccbcdbaabbbcadcabccadcaccddabacacddbcdbdbcababaadcabdabcbcdabcdbdbcaabbbdaabdaddddaaacccbdabcdabbabddcdddbbbaaaccbddbdbddabadcbdabbbadacadcbacabcbcdddaabcbadcacbcbacddacbabbbbbbabccbbbdbbcadadcdcdbacbbbabbdccbaddaccbbddcccdcadaaaabcaadbbdadddaacbbbcbbdddbadadacadcadcabdaacabbaaccbbbcadaabddaacdcbbadbbabcdacdccccdbddbbbcbdacbbdccbbcaaadcccadccaddaaaacbabcbabbcdbbcadadddbdbadcbddbcaaccabbaccbcadbabbdbbdadabbbabcaacdccbccabdbbaabcddadabbbabbbbcccbcaaccadcadcdddcbcdaaadddabbbbacbdcbcaccbacaadcadcdcabbbcbbcdaacdcbbcacbdbaabaabcbaacacdcccdbbadbccbcccbdacaaddcdaaacbddbaddbcabdcadacadbabacaddacadbcdcaaaacdabaccddaddcadacdabacacaddbbcbdcccddbacddbdcabababcddddbbcbdbdaacacbcdcbbabaaabdaabacadcdadaaccdcbccababccabdbbaabbdbadadaccabddbbcbbbabcbcddbbdcadbacddadcbdbddaabcbcdacbdabdbababcacbadacdcbcdcacccbdaaacddadadcccbcbbaaccaadcccbcccabaddcbdabaddabadbadbcdbdacbddbbcbcbadcbabacdabdaccbdadccbabcbbcdbabdcdbcdccaccdccdadddcbbabcabbabccaddbdcbcddaccbcbacaddabbbaccbdccaabaddadcdaacbdaaabdddaacdabbddbbaaddbccadccbccdaabbcaadcbbcbacabbbcbacacbacaabccbccbdadababdcaccdadccabbabaabcdabddbaacbabdbdbacbdacbcdbbccabbccaadcdaadddbcdcaacdaaccacadabaaacbdcaccaabdbbddaccaaaacabbaccdcdbdaacabdccdacaadbaccccdbbcaacdccdabcaaadaadabcccccaabdadcdaddacdcdcadbaabddbdaaabccaacaaaabbddadadbbbdabddbcdbadbcdccccaacabbbbccdaccbbbbacbccdbdbbcdbabadccdaaaacdbacbdaddcdbacbbaacacadddacbcdbcaabbcbcaabcaaabbbccaddaaabbcaabbdbdaaaccabccdbbcccbdaccacdadcabcaacdbccadaaacadcdcbacbcccdaddcadddccccaabcadabccaaacacdcdbabdbdcbabababccdacacaaaababaddadbbacccacaddaacccbcadccddbaacbcadbbcddcabacbccbdadabbdacbacbbaaadccbbdacdabccdcbaaacabcabcadcdcdbdcadbcbbbdcadbabcbcccaadcccacaadaadbddbacbacbcbbaadaddadbcccbcbdddbacbbbcbdabcdcbaabcbbaaaccacadaabccbadbadbabbacbdadbaaaaabdadbbaacbdbbcbcadddbbbcccadcdddabbdcbccddbccbdbbababadcaccbddaddaccabbbadcacddadbabadccbbcddbddbbadbacdabcdccbdbdcbcddacabcdcdaaabbbddbbacacbacbcdcadcdcdbbaadacbccdacadbdadababccbccaccdddddadddbabcbcccdcababdbcacddacdadadddcbabdacdbddbaddcbddcbaddcdbbaccaddaabdcbdcbcdaacacddccaadccdbbbdcbbdcdacdcbdbcabbddcbdcbbaaccabdadacbacddbcddccbdccbdbbdcdaaaadaddaccaccadcabaadccdddcbabdaacddbcdbbcbacadcabbadadbdabcbcacdcdabdadcbababbccbdbcccbdcbbcccaddaacdbcaaadddccbddcacadadaabcaddacbcdcaddbdcdcdcbbcbbddddabbdacbcdacbcdbddadbaddbcdddaaadccdcdcbaddcbaacccbccdcbbcbaccbcadcaabbacaccacddccaccdbacbbcacdadacaaaacaadbbdcbcccabbdcabdacbbbbdbbdacbabcdaaabdbcdabbcaddbbdbcacbdaccccabbacbdbaadadaddcbabcaaaaabcaaadaccccddbbccdcdacabdbbdbdaacdcacdddddaadacbadbcdabbbcddcdccadcdcdadadccaaadcbcadbcbcaacacdddabdbcbbcbbbcdcbacdaadabbdbdcdbbdcdcbacbccadcaabdbddcddbcdadcacccbcbcbcbabcbbabadccababadbabccdccbbcbaaaacbbcdcbdccbaccbaccdacdddabdccbcdccddbaccdcdabaacacaaabbbcccacacdaacacacbadbbacdabcdbaabccacaccacadcbbadbdbcacbacaabdddcdcababbcabbbacbbaababdcbbadbabaabdddadbcddcdbaadbcabcbabbdbcbdbdbcddabcadaaddaccbcdccacbddcbadcacbdbddbaababdbdadadadabaddddbbaabddcddccbdbabbdababbddbbbdbaacacabacdaadcbbbdcaddababcadccabddacbabbbbaadbbdbcadcdbcdabdbcaaddbbdaabddbcaadacbbccaaabdadabaabaccdcadbadccdcddbbbcdcbdbbbdacdcdcbabbbdbadcdabbcabcdcbbcdbaababbccbcddcaccbddaaacacbacacbbbadbababdbacbcccdaaccddccadccccdcbcdacbdabcaccbbbdcdddbdccdbdbbadbddcdaddddabdbaaabaacbadbaadbaccacabbccdcdbacdcaadbcadbacaaacbdaaaacaaaccacdcaaacdddadabdcacccbdbddddbaabcbbdadddaddbcbcccccbabaabacbacbddbabacbabacccddbdbcabbbdbbbcaddaddabaababdcaadbbdcbbdcadcdbaccddcbadbddadbabcadadabcbddbdcbccadbdcdcddadbcddcadbbacbddadbbdbdccaccbabccadcdcdcadacdbbddcadbddababcdddcccbbbdddaadbddabaacdadcbdcacdaadbbbdabdaadabcdaabbddacdcabdaddbaadcbbacbbcdbaadbababaaaccddadddabbdcbcddbbcddccabcadcbcabbdbbadbacabbbdbaabdcadacadabbacdbdaaabadcccabccdbbdabbbbaadabccdcabdbcaaadcbadbdacbdbcbcbacbcabcdbbbdbdddcaccbcdaabadcbdbbbacddbdaabbacbabaabcbaadabdadcdbcdacbdddddddbbcaaabccdcaddcadaaaccbcddddcacdaddacddccdcabadacbbbbdddcbcabddbdcaadbaacaacaccbcaadccaadababdbcaddbbacdadccdbccdaaccdabcbccdbccdcdcabddcacdacbdbbababdaabaacdcdbccdbddbdccbbbdcabdbcbaccbbdccdddacadcdbdbdaddbcdcccdbcabcbbdbdbabadcdacacdaccbabbccdddacdcadaacacbaabaddbccadddaddacdbbcbddddadddddadbadabadbbbccaccdbdddaacdbabdcbdcbadcdbabaadcccabdbabcdbcbcacccacacbdcababbcccdbaccbbcddcddabcdcdadcdadbbdcccbcccddabaadbdccddbcbdbaddadcacbbabccbbabbcdbaccbbbbdaddaadddbdbcccbdcbdadbcaaabbcdddcdabcabbcbbcddabbadaaaddccbaccadacddcccccbcbaaddadcdddaadaadaaacacbccaabbccdcdccbdabbacabdcbcbacccccbacaddacadadddbbadcddacbbcbbbdacaadbbbadaadbccdbbacabbdacacddbbbdccdaaadbcbadcbbdabdcadbcdcbccbbaddccdacacccdadabbaccbddadadcddadccdaaccadbbdacddbdcacbcbddaabdabbaddbbacbcdcbcccccbcbabccdbbbcdbbadbdbdadaabbacaadbabaddcbbdabbadabbcdbcaaaccdcbabbaaacbbacbbcabbbbddabacdbcadabcdbdbabadcbdbbbdabcbcccbcbbadddbaaaaacabdccacdccbcdddddbacacddaddabbbbcbbdddbcaddcdbddbcbdcbdcbddbadccacabaddaacbcbcbdacaccddbdbcdaabadbbbbbcddbdbbdbdcadbaddddcdddaacdaaaaddccdcbcccaaaddcdcbdbbbbbadcdacbadadbabcbcabaddcaaadadcdaccdbdbdacdbcabccdbbbdbbdbddbbcdbbaaaadcdababaaabdaacaacbadcddacbbbdcdcdcadccdababbdccbbbdabdabcbaaaaddadddabacddcccbdaaaaacbdcbaabdaabdbdcbdbddbbaddbbadabbdaccddbcdccccadaabcbcbdaadccaccbadccdaadaddaaadccbcbabcdddaaacdcabbbdbdbdcabcbcdbdcabbdcdabcdbaabbdbadbddccbdbadcadcbcabbacddddcacacacacacbacdcbabbbdcccbacdcdcbddcdaadcaccadcadbbaacdaccacddacadcaacdbbcabdddcbbbbbbadbcacbbbdbdbdbddacaabbaccccaadcbdbbbccdabddacdccccdacbbdacdcbacacbdddbabdacbcdbbdcaadbabbbbbdadbacbacbdbaaaaaccccdcbaddddbbdbadbcacdbaadabacbdcaddaadcbadacaadbbccbccabcdaddadabddccbcaddcddbdbadcdddaaabdbacaacbababcbdaccdacdcbadaccbaabaacaadcbdaabccaccdcbddbabbbaddbbccddcbdccdbbbddddcaddccaaddbdaddbdaacccccaaddccdaacabdaddddabdddbcadbccbabccdbabaddbdcacbbaccbddbcbaaccbdbcdaaabcdccabbccaccbcdcabbadadadbbbdbcbbbabbcadacaadbbccbcaabcadcbbbbacbaacdbbabddcacabdcdbdcdacccbabcbbdbbacacbcbabaaabbdadcbaccdbbacabbbabbbbbabbccdaccccacdabaddaddadaacabddbdaacbcccbbcccdcbdbcaddadadbaccdbdcdddacbdbbbdddccadadadbabbdcabcbcadacdaaddcbccdadabdbddccccaaabcbbcbcaccbdabbbbdddcbabcccaddcdccbdacddabbdaddcdaaabaabdcdbbbbabaadadbdacddadabaadacabdabaabababcdacbcdababccadcacdaadcabcdcccaacdcbcaccbdbccdabdbaaddaaacbabdaddcbacabaaacaaaadacdbbcdcdadcbbdddbcddcdcddabddcdbacbcbaabadbdbdabdbdbbbcdbaddbcbadbdbaabaaccdbbcdddccbbddaabddbbccdbaddcdcadaddabdacccdcbadbdcbdaddcdcaaadadbadcddcaccdadcdabbdccddadadbbacbacbbaabadbcacdbdbbacdadbccabbdaaaaacccdcbcdbbaabbdbdddadadcbddccadbdaacdccaadcaadbaccaccbababdbbaaacabdddccadcdaccdbbdcadbddcdbbdbdddabacdaadbbbbddaaaacdddacaccacdacbddadbacbcacbcccabadaaadbddcaadabbabddbaacabaadcbcbbddacbbaacdcacdbdabdaadbddcabcdaccadcadccbaabcaabbcbcabacbacdabcddaaacdccadadadbdcbdcadcacabcacdcabcdbdbbadaacdbcacdcaabdaddadbbcacaccbabbcbccbbdbcdbbaaadcbadbdaaadbbacdbacbddcbddbbccabdbdaccdadbbaaaccdbbdaabcbbacdbccbcdcbadbdbacddcabdadacbcdddddacadbbdccbadbbcadaababbbcaaacbbdbdabcddbabbbacacbbabaccccaaccaaaadabbacdabbadcbbadbdcdbcdbaacadacadcaacbdadbaddcbbdddcbddcabaddacbdcdbcabbbaaadbbbcccddbdaabbacaabdcbbddbdcbccaaabdbdadccdbbbcdddbbacdcbdccccdbbcddccababbcdcdbdabcaaabbabaabcacacbbbdccdadbbdbccccbdbaabcadcbbcbcdbbccdacbabadbddacbbaaccddcccbbbaabddcdaddbdccddadddcdbdabbdbbaddcaddacccadbccaddadccabbdadcbdddadabbccdbacbccbbbbadbcbabaadddcdccabbcbcbaddacccbdddddccbcacbdccdcaabdbcaddcdcdadadabbacbabdddddcbbbdccbcdccbabadacaccbcbacdadbbaadbadcbdbbaaaaacbdbbadabdddddbddcdcdccccdacaccbccbdbabdadccbabccabaaacdbccaabbcdcbdbbcbcdbbdbabdddbabdccccbaccdacdccababadbddcccbadbbcbaacaccdbaabcdbacdacbbbbadbbcbbbadcdbaddcddddacdacdcacbaaddcddabcccddcbcdcbdbdbadbdddaddabcbabccbbbacbaabdabcccacaacaccacdbdccadbabbddbcdbdccacbdddcdcbdaacaadbdaddabcbabbdcaaaddbbdcaccbdcbdbbdaaddbbaaaadabddbdaabcbddddadbacaabbddadababbabbbaddcddbcddcabbbcccbcbbaddcaadacacdaadacbdddccababcabddaaacdcdcddbcbdbcccacabcbabdacbcadbcbadbdbbacdbbacddaabddaaaacdbdddbabaacbbcadcacdaccbabbdbddadaccdccccaddacdbcabadaddcccbcadccdbababbabdbcdcaddbbcbbacbadbdcddccabddbbccbabdbbddaacbbadadcaccdbbbbccacbbaadacdcdaccdbbcbcddaccbbcadbdaaaabdcdabddbcdcabdacaccabdbbddbdaabbdbabadcabcaccdcbbcddbabdaaaabbccabcdbccdacdcaddcabacdbcbdadacacdaaaddddcadcbdcadbabbacbbbaabddadacbadaabccdbcaccccbdccbbdabdcabacbcbdabbdacabdbcbbbcaadbbdbdbbbdadabacdbbabbdaadabcdaccabcdabcdacbabacabdcacbbabbabccdaccddbcabcddddddbabcdababccddadbcacccccbcddccdbabbcbbdddadaddbdaccdbdcdcddadcdbbccacdccadbcacbdabaabddaccddcadbcaadccaacdbacdaccdaaccdbabbbaadadaadbabbbbcacabbdcaddcbaacdaaacdbdcbddbbcdddabcbbbdddaaadbbaacbccdadababbabbbdddadcdccdddcbbdddbbcbbdddbabcdcbddcacabadbaddbccadccccccadbddbdbbbdcacbbadbcdbbdbaabdbdcacccacbaababdbcaabadacbabbccbbaddbaddbbbbbbabbacbbdabadcccacabddcccccddddacdcbddcdcadabcacabbacdbdbdaaacbcaacccbbcaaddabcddacadddcdcbcaccaaabacbddabccbdaabcbccabbadbbcddbcdbaddbbbcdcaadbcbcbaccdaadccdcacbdadacddcabbbbbbadcaddcbbbabddddbcbcabdabdabcdbaacccdcaaaadadcaccbbbaadcaacabdbccdbbdcbbabacacbadacdddadcdbbcabdbaacabcccadbacaacabbcaacbbaaadbbcabaaccdccccaaddddcdbcabbadadbaacccddcaddcdabdddccbccdaddcccdbcabdcdcabdadccbacdbdadaadcdcababaddbadcbbbbddcaabababccbdabdbcccddacadadbababcbbdbdadccdbcbaaaaaacdbbbccbcbbbbccbadccadcbbacdccadbddcadadcbcccbbbcdacdaaddcaddbacbbdbadccabaaaddbdaaadccdadacacdbbabcbdaabdabdaadcddbdbbabbadbbbbacbaccaabacccbaaacdabcddbbdabdcaadaabadbdbbccbacdaddbbdcccacdbcdcbdbdbddacdbcbaaacccdcdbadbacdcdcccbabbbdbccbcbcabbdccddddcbbbccdbcccdcaddbcababbbbcddaacbccabdcadadbbdbaabbabcccaadcbaadddbbcbcdbcbaabcacaabdbaabcbcccdcdbdcbbcccbbdbcaaabbbadaccccdabcddbccabbbddbbadcdddddaccbbdbdbbdbbacbcaabbcacbaddcdababcddbbbdccddccbacdadaadcccbbdabaabcadcdaabdbcdcbcccadcaaacdbccbabdacdbdcbddadccdadcabbbcdaadddcccddcdacdccbbdaccaccdabbbdaabcdcadcddccaacadbabbdbcbcdadcccbbbccdccdcaabbdbbdcbccaaababbaaaacdabcbdaaacccdcabdccbcbadbbbabdbbdcabcdaacdcbcbbaccbdcbdabadcbaacddabbccbaabbaabcddacbcadcdcabcccdcdacdcbcbbbacdddbbbbacbaddacddaadbbdccacdddabacacdbddadaccbbabbadacccccbcbbbbbaccdbadbbdabbcbddabbdcbbbaacdcabdcddbbdddbbdadaddababbbbcabbcadcacdbcbcabddcdcbbaaccdddbacacacbdcdccadcdcdcccabaaadadbdadbacdacbcbbdccdccacbadcabdcadcabaaadbcdccadadccdbbdcabdddadaadcbaadbbcbbbacaccbcbdcaddcdcbcbbaacccdcaacdcbdacbbaadccaadaabccbcdbbcbbdaadbaadcdbbbddaabcabddcbaacadccbbbccbdaacacadbcaacbabadcadcbcbacbdbbdaadaadbdabbabcadddbaccccddaddaaddabcbcbccabdbbbaadcbbbcacbbcbccaaccadbacdbbccabdcabcbccdaabdbcaaadbacaadbdacdccaaabdcbdcdaccbbbbbbaabbdabcabdaaabcaddcbcdbabdabbcaacbaccaacbdbacbbcbbcdaabbbcaadbaccadacadbcbddacabadddaacaabdadacdabdbcbbcbacdcccabdbacbbaaaddbcabadabdccdbdadbdbcbbbdbbaccbbcacdbbcabadcbbdbacabbbaabbcaadcbccdadcccaacdcaccdacddacadccacdddbbaddbdacdadaaabadacbaadacbabbbbdcccbadadadaddbcadbcabacbbbddacdddcdaacdddacdbddacbccdaaaddccbdaacbcbaddaabbbdacddbcdbcaadcbccdabccdbcddabbbacadcdcacdaccaccddabbbdadaccabbbdbbdccadddcdacccadddcbadcddddcaabbccadbdacabbadbdaadccacaacaaadaadaadcaacbdacbaddaddbbdcccddbcaddcccdbdcbcabcaadabbcdabbadccdbdbbdaacaacdcdadacddcddacdcdabdaacbdaddaddbbbddcadddabaaadacdabaddbbaababbccdddbabccccddcaacaaabdcbdabddaccdbbddbaabbcbccbcaaacddbdaadcbcacdbbbbddbbdbdaccccaaaaabcdadacdbdaaacccbabcbdcccbbbdacabdddaaabdbbbaaddacacaabbbbaddcacbaacabacccbddadcadbddddccaddbacccadccdccddbcdccacabccdcacdcccaddbdaddadbdcdccbccdadbdaddacbaaddacbcddbccaadaaacbbbcdadabcdaddadccabaacbbbbacdcdabbbadaaaacaabccbbabccabddcbdcdcccabcbabcdabacdccaacbabbcdcaaabbbbabbccaaabaadbcaacdccabcddcabcdcdaddabcccabaabdabacccdacdbacbddbcacdddadcbacccacadabbccdacadabbcacabbbaadbdbccdcabbddbbbcbcadcbbcdccaabddcaaabcadaaadacccacdbcadbabbbbdbdbbacbcbbcabcbcacdbdddaccbdacbcacbbdbdaacdddcdbdcbbccbadbaaddcccabaadaaaccbcbabdcdaacbbbdcacbdbbddacaaadddcabdbaaaacdbabdadadddbdbbbdbadbbcaaaabaddccbddbccdcdddaadaaaabaadbbddacdddcabcbbdcadccbcbdcdaacdcdadbddabdbbadabdbbccdbbdcdabcddcdccccacbccbbcddcddcddbddddcdaddccbbcccacdcacddaccdcdbacbbdaddbcccccbaaccbbbcabaacbabcabddbbbbbcccabbddbcdcbcdbbabdcdaccccdccdbbcccbdcbdcbdbdbcddcdaadbddadcdbdcaaadbcddbadabbccbdbdcabccbccbddcddbccabbcccacbdcccadbbabbcdbacbcdabcddaabacccaaabbccdadbdcddabaadbcabbacdbadcbacddbbdbdacacaabcbccddaababddbcaccddbabdccbbcbbdcbdbddddcadcddadcacadacbabaaccacdddacdbaadacccbabacacabbdbbaababbccbaadccbdddbcddcdaccaddacbabcdaddddddbcacccadcccdcaadbdabacaaabdbadcacdbbddadaccbcbcbcababdadcbbddbcccabaddbcacbcbcbdcccdbdccdbabddaabdbccbcbbdcbbdaabdcaabbddbdadbadacddadbbdcbddcbdbccaadcadcddcdbddabdbacdccdbbbadbacacddbbaddbbacaabadcdcddaadcbbddcbacdaaadcdcdacdacbbacddbbbaaadaccbaadbdbcbbabcdabbacbdcccbbcbbcabcdcaaccdcadaacadccbcccdbbaacadadaacddcbbabadcabacbabbaccaccbbdcdaccacccdbababdcccbababddcdbabdacbadcbbadccdcadcaaacdabcaaaacbccddcadbbdabdcaccdbcaadccbdadbcaabdcdaccbcaaaaaddbdabcdaaddbccddbbbdbddbcddddddddbdddbcadadbbcbdbccadcbbbdbacacdcddcadcaacbabaadbbcbaccccddbdbdbdadbccaacbdaabccabdabdcdbadaaacccbdcbccaacddbdcacbcdcdcbbbaabdcbcaaabdbcdaccdcaaddbacaccdccbcbddbbadddbddadacaaabbaccccadbacbacbbabaaabccadbdcdddcdacdabacdabbdbbbacddadcacccbdaabcadacacdabcdadabccacabaaabacdcddbcbdcacdabbbbbcccadabcaaadabbdadbacbbbaaaabccdbcccbbcdacbdadcbabaadcbbadddbadaddcbbdbbddaaaabdbbbcccacaacdaddccdbcdbcacdaaacadcaddcdbbccdbadcbdcbdbcadacdbdcbaccabbbdccaadacacbcabbdddccdababdbdaabbbcabbdadbcbdcbcccbdbdbbcaacbcdbbbdaddadbbbabcdbdcdbcdaaaddaddbbacbcbadcdbadddcaaabcadccbddcdaadcadbbdbbbdadaadbbcdbbdaabdbccdacaaacccbccbbcbddabdcbdabcabaabdcccaaaadcbaacbdcbaabbbcccadcbabccadaabdadcddbaaadbcdabbbbdadadabdcdbdcbddbbcbcbcdaaadbddddbcdaaadbcbcbcbcbbaccbcbbddabbbbbbddcaabcaccabcdbcbbacbdddccaddabdbcabccdababcadbbbddaaadabbbbabccdbbcabdbcabbccdaaccdbdadcaccdacabdaacbdadabdcdcdccbdcbacbdbdcdaaccccbaacbbbcaccbccacdadbcadbbacdccdbdddccaacbacdcccccccacadabcbbbdccddaaccabdbacddbdbdcadabbbadcaccadbbccbbdabaadacddbcbbacbaabbddbdddcddaaccdccbabbdabbaaaaabddbcddcdbcbddabaccdbbcdcdcddadcbaacdbdbccaabbbbadcdaddcaddbdcbbcdcddadbdbdcddcdbcabadbbcdccaaaccbdaaaaccadddaaacdddacabcdabbaacbcadcacdadcbbadccadbbcacabcbddcaacacdaaacadbbdccbdbbbcacbcddbcbccdcabcdacbaaaadcabcaccbcabddcdbcaadaadadababaadbdabbacbabcbdccbbcbacaccdbdcaadbdcadcbdbbddcddbaaaddbacacdaddaaddbbdaabccbcdddbcddbdbaddbcbdbadccdbcaadadcbabadacccddbdaaabdbcccabacbbbdaacddddbdbbdcdbcdcbbaaccddadbbdcbbdbddbdaabdaccdbdabdcdacaadacddaddbdbbabccdacbaddcabbccbcdcacabadddbbcadcaacadbaccdbdabdabaccaadcdcdabadbdbddddbcccbabccadbaaaccbbbcdbdaaccdbabbaddcaddbbcadadaddbdbbddddcddcacaaaabdabdbbccadabcbbbabbdcddcddcabcddbdbbaaccacccccbcbddadcadbdabbbcdbbcbcdabcbddbbbcbccdbcaccdabbaabbbbaccdacdcadabbbddbbaaccdbbacadacdddacabaabaacabccddbcdcdbcdddbacbcbbdbbcdaaaaddbbcdbabbbdadbaababcddbdccbdbaacacbdacbacccbdaacadbacbddbabcadadcdadcdddcdbccaddddbccccababcbddaabadaadccdaccaccdbdbbbcaddbdbbdcadcbbbacbccbbaddadacacdbbccabacbdbcdbbbabdbcbaddccdbbbacaddacdbabdbacccacabbdbdcadccbacadaadcccbddccbcdbbdbadcbdcdbbbdadbbbddccbdbacbdabbabcbbaaabbaaabaaabaddabbbcbdddacababbcdaddccdbbabbdbbaabcaadabbcacbadaccadbbdacdabacadcadcddccbddccbcdcacddccbccbaddcbcaaacbacbadacbcddabdbcddcdcbabaddcbbddabcbbcabdaabacbaccadccbcaaaaabadddbcaccdbccacabacbbbbdbddbccbdcddacbddbcbbddadcbcbbbbcdccadccabdadcccabdbdcdcbbbababaaaadbbabacabaaadcbdabaacdcdbcaabcbabbaababbdacccccdbdacacabaacdcabcadbdbbbcdcabddaacbdddbcabacdcdabcacccdddbbdcbabaaacaabcbdbdbccbbcbdbacdcdacaddadcbdcbcadbbcbcacbbabcbaabadbbaabdacdbdbddababcdbacdbcccddcdccdbcddacdbdabaccacdcccaabbadcbdadbaddaddabdbcadccbdbbcadbacdbdaacccdaaccddccbaaddcacbcbadcccdcbddccbdbdcbbdaabdabbdddbbdddccbbdcbccacbbbcdabadddabbdadadbcaddbddcaabbbdaccacbadaacbdbaaabbcadabccbabbbabcbabdccacacccabdddaaccbcbddcbbbcbbacccdaaabbddddbdcdbccaacbbdadaaddcbbccaddaacdaabcaabddccabacbaccabcccccbdbddadacddbaabbaadabccddcacaccccddbadaaadadbdddcbcaabcadbcdbcddcdaddcbcbbddbcacacbdbbbacdcccdcdcddbccddabbadbbaccbcacbdaccadcdbaabdccacddbdddaaaaabbcbcadbabddabbcbdabbadddabbdbcccdacbbadabddcbacbbccbdcaaaaacadbccbabbcdaadbddabadbaccaddcdcaaccaddabbaacbacabbabaddcdadbacbcdbcdbdbcaddcbdbddbadbabdcbcbcdbddddadcbbcaccabdccbaacbdadbbbddccbacadabdddbbdbaddddcddbcbadbadccdbcddbbdadabaddddcacadbdabcdbabdadccdddcddcbabadbbbacbadacdbcbadccdbdabccacccacbcadaadacadcdaccabbdbbabcbdbbaadbcbcabaabdbdbcddaaccbbddcabdacbcbadcabdaddaabdcacccdaabdacaaacddaabcdcbddbaadbbcddacdbcddcbbcddbdbddbdcabbcbabadaabccdccbabdbbcaddbbbccdbadaaccbdbdcdaadcbcbabcabaccccbdcacbaaaadbcbbbaaaccacacabbbaaabbcbcaadcaabbcacadccddccacccdabcacabbcdbaaddcadccddbbbabbcdbaddccccbcccbdccdbdcaddadddcccdcddcabcddcbbccaaaccbbababbbabaccdbacccbccbdbacbcbcdbbadadbaadbcdabcbcdccadddccbcbdcbbcdbdacaacbcbabbbbdcdccddcbabaddcbbcaccdabdcccbdcdcbbdcdbaddaddacdddacabcbbbdaaccccdaabbbdbccabbcdbaddadacacbdcbabdabddcdbdcdcdabcccadcbdbcaaabbdadbcbbdcccadcdbcddbbbabbacacdadcbcaadcdbbbbaccbabcacbbbbcddbadadadadaacabccccaabbbcadddbcddddcadbcbbcbbddcabbdbdadccccdddcbcddddabbddadcaccbdcadaaadcacadcadcaacbdbabcaadbbadddcbaabaabcaabcdbaccdcbccaaacbaadbcaacbbbdccbcaabccbabbccdcbcbbacbbcccdddcccaaadadbdcaacabbccbacdbbccbbcdcdadbaaababcccaccbdcaaccbccccddcdbbbbbccaadaacbbbbdaabacaaddbabbbdcdcdbbddcbaddbadcaccaaadbacccddbcabcbbdbbacadccdbbdaabacbccabbbadbdabdbddaabbddbadccacddbbddbababacdbcdbbcddbadababbbcbdcdcbcacadbacdbdaccdbaaadadaaadabdaaabbcabdaabaddcbddccbdcbabccdbbaaddccbacbddacbabbcdcbbcabbdddbbbabbaaaddabbdabcaddababcadacbccbccdacbdbccbacabccababadbdabcbbddbdbaddbadabddbbabbcaddabaabcaaabddaccacabbaabddbbabbcbdaccccdbbcbddccdccccccbddbaadbaadcddcbbdbabaccddcaadccacbcbbbcddbabcdcabcdcddccbcbccccaccbcabdaddaaacdbadabdbbacbdbcbaadabadcaabcaadccddacabacbaabccdccdadaaaacbbcbcbcbdbbcaacbbcadbdacbabccaddcddcadcacacdadccbcbddbacacccbacbdcdcacbdbcaabcbdddddcaacdaabbccbdccdcabcbaacadbbababaccdadaaddbdadbcccccbccbacbccdadccacaacaccdbdbcccdbdddaddcdadaadaccaaacdbbcdaddcacccbccdbbcbbddbbbacaccdbcbcabaaaccaabbdcdababbdadabcadbcccbaadababacbaababdcadcadcdcbabaaabbabbbbbdaacbcbcacabddaacbaaabcaabddacabacabccdbdcdbcdadbbcadbdbbdcbadbbccbdcabababcbbadcbcbbadbbdaadbbbdbbdabadadaccccdaabaacccaacdabcbdcaadacbacdaddcbbbdbbddacdddabdbddbbbdcbbccdaccbadaccdbbddcabbcaddaadcbaacdcbbbbccdcddcaacdcdcacccbcbdcbabcbbdbdabacddcbdabcdcacccadaccbcacdcabdaacadbcdbdbbdaccabdcbabcddbcbadbabbacdbadbbbabdbcbcbccadabbdcacaadcbaacdcccbbbaabaadabdbdadadccbdcaadaaccbbcbbdaccbbbaddbbdcccbcccccdbbdabbacabbcadadadbccbabbcadcadbdacbdbabbabcddcdcbdbcdcabaaaacbdccacaddabdcacddaddbcddadbabdbccbdccaacabcbcddcacbbcbcacadddcccdadcccadcccababbdaddabaabbbadaacdcbbacdddbcbddbbbbacdcbbdccddbbcbabcacdbaacacdbabadacabaaccbccaadaccdbaccbbdcacdacbcbadaaacbccdaadbcbcddabbaaaacbcbabdaaddccddbcddbbdcdaabddcbbdcdbadadbdbdabbcbdcdaabaacdcdadabdbacaabbbdacbbdbcacadbaabcbccacbdbbbacdbbabdcbdbabacdcbbbdcdcacacabddbbbccbbabadacdbdbcaaabacbadaadcdaacddcdccacdbdacbbaabbdabdbbcbbaddbcbbacacbdbbbdddadbbbcddadaddbbacbcadbdbaaaaacdbaacdabdddadbcadcacaccdadcbddcdbadcadbccbabacddcbbcddbbadaccadccddddcacbaaabcdacacacdcabbddbdbcadabddcbbdbbdbbdcdcacbdbbcdcdddccbbcabdddccdbdaadabddbbdacababaaccccbdaadbcbadccacbdaaddcbcbabbaaacbdcdcaabbbabddbdaddbcaaadcddcaabdcbdcddcdbbbbdcadcdbaadaabcdccccbaccddbacbcdaadaddcbdbbbdadddaddcbdcbabddcabbccabbacccbbcdacbabbdbaddcabaabddababdcbccccdcadcbccabddadbddcbaabcbacdcbadaddbcddabadbdbaddabddbaaabccbdbcadacabdbcccaadabbabccdcdcabddcccdcddcbcbdcdcdccbdacbdddaddbbdccacbadacbdbcadcdbbadbbccbadbbddddaaaabcaadadabcddddcddbadbadccdcdaadacbdabbcbdcacccadabccddcaccaacdadabddcabdbdadddabbadadbccdcacdaaddcccdcabadddabcbbabbabaabcbddbbddbdcddacccdbbbcacbdacdcabdcaddddcbcdcddbabbddbcaacddabbaadacdddbadaacdccbbbcdaddadaddbdbbaabdadbddcadbdacdacacdccabbcdbbcdcbcabbddadbddcccacdaabaccccbdabcaccabbbbcdddccccabbddaaaaccdadbdddddbbabbaddccddbbadabadaddbbdbaabcbabccddccbdcdcdcaadbcddcadcbbadcccbcabbdccdccbcabdcbcbadccbccbdadabbccacdbccbbcddccccadadabbababdabbbbbdcdddacdbcbccabacdbdccccbddcdddccaacdbbabacabcdcbcadacddcdcdccabbbbabaacdcccdcbacdbdaccadbcdbbcbbccddabcaadacdabdddbbdaaacacadcbbcabcaccbbadaccdbbccadaddaddaababbaaadadadcbcbdacdcaddcdcadaddaadacdadbcbcccccbacabbddaaaacdbbbbcbdcaadaccdcbddcddaaddcadbabbadcdbabdacdadcdacbddcaaddbdddcdcacbbabccccdcbadcbdddaacccadcdbaaaadadabdcdabbababacdbdaabcbcccabccbcbadcdcabababcdbddaadaabddbbddddadbcbacdddbaddbacddacbaddcdbcaccdbdccaaabadccadabaaabcdbabccbcacdcbacacdacdcddbbcbacbbddacddccabcbddacdbddbdacdcdabbbdcacccbcbdaccddbdaaddcacdbabcdbdadabddbddcdbdcaadabbcbbabddbdbddacdccdbcccdddddcbadabcbcddbdacddcdaccddddaddcdacbddbbaacadcdaacbaabbaabcabaabbcabdadbdacbdbcaabbcccbcabbbbadcaaccbabcccbdcdacbaacbccdbaaaadbbbaccabbacccdcdadcbccbaaddaaacccbabbccdcdadabbacbdddccccbbcddbcbbddaddabcddbabbacbcadabcabbccdbadabcdadbcaaccdcdacdbbcdacdabcaccbccbbabdcbabadabbbdccbbbcbadcdbaaabddacdccaaaaabdaddbcdcccbcaaddcdbaadccadadcdbabdbbacbccabbcacabddcccdbbabdddabdcabbaacbdabacabddacacadcbddaddadcaadcdcadbbcccbddcccbddaabdbdaccbcbcbcacdaacbccbdaabbadabcadbdabbdaadcdcccccaccdcbcdbbbddabbbbcdaadcdbcadbdaacacbbbbcbbcdbaadabdabacbddccbdaadcbadbbbcdacbbaccdbadbaccccabbbcdddbbccbcdadaaadcacbdccbdcdaaaabccdccddcbbaddcbdaacbcbcddccabddbabcbadbadcdabadbbabcbcbbbcacdaabcdadcdcadacddccbdbbcdcdaccaddabbacdccababcddaddcdcdccaacdbdcaccaaddaaddddcbbaccadcdcababddabdddbddcbdcdabbabbdcbdaadccdabdadcbaaccdcbdaabcabcdcdddaccacccbdccdabcacdaadcbdbdbdcccbdadcdaadbcbcbdaccacaaabdbbbbcdbdccaaadccdccddcccaacccabbbaaaccdddcdcadbbabcbbbdbbdadaaddccacadbcbbcacbdbbaaaaddbbdcddaabcdbcdbabdcacabccdbbbacacbabbdcdbbbcacdadbacababbaabdacbdcdccdcdcadbabaacbbbbbbadcabccdddadadbcbddcbbabdcccdaccbdbddbcacabccdaadbdbbbbddccadaddcdcaddaadacbdcadbdacadbdbdccbadbbbdbacdcadbbabcaddbdabbccbaabbbdddaabbaccababdddadcacadaddbdbaabdcbadacacbcdcdbdddacdaabadddabdadadcabcababcacadbbdbbccdbbddccbdbccbdaacaabcdbbdcccacacabccacbccdcbadcdccdadacbbcdbccddcdbabbdcbbcddcaaaaaddbccdddcccacdadabaadabcadcabdcdbaccbcbdbbaaccddcbcbccccdcabcabaabcbaadccaabcaaddbadccccddccccacbdccbbbadddcbcbbdcbdacabcbaadccaacdcbdbdadabdbbabadccccbdacbddddddbcbcbccddddbcadbdbdccbcaaaaacccbacddbdbddbddcbadadaabbbbbbbabbdabbacaccccdcccccaadabaccbdddccbcabbacacacccdbdaddbccddcdabddadddacabbadbbcaabdddbacacbbbcbcdabdadddbdabcbdddaaddadcdaaacccddbddbadccdadbabdadddcbddabdbdddccbdabcacdcdcdcbcdaddacbdadbdcaaccbcdacabaccddbddbcaaaaacbacdcaabacbadcbccdbadcaddcddcccaaabccbabadcccdbdbbcacbcaabddddccaaacbcacacdabaddcbcdcdadadddbcabccdbaaadbbbdbcaabcdabdbdabbcdbaddadddcdbcbdaabcbbbabbacbadcababbbcbbbcadcbcbbbdacccbcddbbdcadbbabddcdbdbabadcccbbaccccdcaddddbcacddcdcbbaddabcdcacabbcaccabbdcdddbacaabacadbbaabaddadddbabccbaaccdbbcdcaddaddcaccddccabadcbbcdbaaccbdbdadadbdcbddabaababdcabbccbacbdacccaadbabaadcbbabbdacccdacbbabdbdcdabcbcbdabacabddccbaadbddacccdabddbbcddddbdcacbdddbbacdcbdabdbcbabcabadbbbccdcbadcbabdbadbdddcaaaadcdddabdabdbaddbcbbaddadccbccacbbbabcbdccaddcaccbbbdabadbdaabcaadbacadbadcacdbadddabcccaaddbdddddbbccdcacbdddcbbbadcdbdddbaaacbabacccbbdabdcddbdcabcdacacacdaabaabadcbdccdacbcaadacaaabacbbccdcacccbcddabcbcbcddddabcbdbdaadbdcacacacddbbadbbacbdccbddddaacaaadddbacbbcbbabacdbaababddbcccdabcbbbcacdddaaadbdbbacdaccabbaabccbdadabdbabdbcddcaaacbacbdbdddaaadcbdbccbaaaaadaaaadcdbddabdabdadbcdacbbddaddadcddddccdaabcdcdbdbaabdaaccbcaaabcabcdabbbbbaabddcacdcaaadaacccaacadcbddccdcacacddaaabbdbaabbabdddaddbdabdbccacacdcdabbdcbdddadcadbdcadcdcbcbbbadaadcbdcacdcadadbcabcbdccbaccbcbdbbaaaabaaabdcabbbdadcbbdcdababbbadcdcaaccabdacbadbadbcccddbccbaadbabaadcadcaaaadcccadbaddacdbcdcacaaddcadccadcaacadcdcdaabbbadcabbaddcdcbcbbaaaaccbadcaabcacdbacdbdcdadacbdddaabadbbbbdcdabccdbcddcdbabdabbcccdbdcacaddddcaacbbbaaabdabddcbabbcbabcbdadcbcbcabdaaccaccbddcbcbdbabdcaacccbadccccadddadabdbddbcbbccaccdcbacbadabcccbbcadbddcabcccadcbbadbdabdcdbcbaacadacbadcdadbbcbdbcabaadacbcbabcddbbabbadcbabbacdaaccabbbcdcbcdaadbdacbcabdabdcccaccbdadbbcdbdcbbaddacdcbbdcbcddbbcddabadcdddbadadacddabbbcbdcdbcccccdcbabbbcbdddbdccacabcbcdccbdcdbdcddbabcccbbaabccacdadabcaadcaabacbaaddabbbbaaacbdcddbccaccdcbccaadbdcbcaacddabbbdbbbabaadabadaccabdcabdccdacccbadacabbaddcaadcadbccdbdaaabbaabcbddaacbcaaacbcdbabbddabdadaccdabcbddcaaaacacbabbdabdcbabbcdbacaabdaaabbdbdcabaaabcbdbadbccacddacaabacdcbbcbddcbcdcaadcddbabbbdbabcdadbdbcdcaaddadaadaaccabaddaadccbbdacdcbbaadcacacbcbdadbbdcbaababadddccacaabaddabdbdabdcddddadcbdadbddabdbdbacbcccdddbdcbadddaddcddabbbcdcdadaabdcadadaacbbdbadacbadbbcdabadabddaabdadabdbccabbbaadaacccbacacbcdaabbabcddbaabcccbcbddbabaabcacdbddbdbccacbacabcadaacccacccddccbdcbcccddccabacddcbcddcccbaddadacdcaccccbabbddbbdcabbccbacadacdbbbbabaabaadadccacdabdbbdacccdcbdcbdbddccdbaccddbaaadbbdbadccacccbdcbabdccabdacacdabbacdacabdabbccbacdddadaddccbbdadcddabddaaacaccbbcbcbcadaadbbabbcbbadcacdabadcabddbadcdacdddbbbcbcaccaadbdccacddddacdcbaadbbccbbbadddadbbbdbcbadccaaadacccbccbaaabbbdaccdcabcbaccdbbbbdcccdacdadcbbdabdaabdacabcdaccaddcbcdabdbdacbabdcddbaccbcdddaaddbcabcccdbbdccabcacbccdbcbdcccbbdcdabcadcabaddbabdbcbdcccdbcbcadcddbcdcbacaccadabbabadbaacbbdacbaddabbacccaabadabbbbbdbcdbcbadddcbbaccaaaccdcabccdadaacbdccabcddbbaccaacbdccbdcbbddabccabcbadcbaddcbccaadbacccaccadbcccbbbbbcadcaddddcadabaadaacbdcdaccaaaacaaacadbbbbcdaadaabbdcabccddbbabbbcdadcbddbbcccdaaddacdabdaadadccaabbacbcbbbacdabbcdddbdacbadcdcbbbdcdbcdcdadadbdababcdbaacddddaaadadcbaadaacabccbdddbcdadaacdccdbdaddbdbcbadadcbaadccbcddbdcacbdbdddbdaccadabacdbcdccbbbaadaaabdcdadcdbdabaabacdcbcddccccbbccadddbaccddcbbdcbbbdabadbcbcbbdaacdbbddadadddbcaabbbcbcdddadbdbadbaadcadbbbdaccaddbababdabccbccbbbdbbcbacdbbdcbcabbccababcadbcbbddabbdbccdcdccadacbabcacbabadadbadbbaaaadbdacbcaadaccabaacbbdccdccccdbcccccababcdbdabaacddabadbabdabccabcccadadbbcbcbbdaacdddbdbdadabbdcaaaaaabcacccdcbabadadbdbbcbbacdbbdbacacbdddabbcdcbcbbcccabbdcadbcaddbdcbcccdcccabcdbbbcddbddcddadadcccbbdbdcbcbddccdcabaabaaabcabcbcabdddcaaadbcaabcdbabaddaabbbbbdcbdbdcdacbbacdbdddbbdadcbaccbbabbcbbcbddaaccadbddaccbcacbaddbaccbcdbbcabbbdbbdcacdbcbcbbadbacddbcdcbdbadacbaaaabdbccddcbdbcabdddaadacbbdccbbddaabbdbdadaacaddbbdcdcdbdddbaddcdbacdccaabdcbabbcbcbacacddadcaabaabcabccdabdabbcdcacaccbbcdccdcaadddbacdadbdabdcbcbadcccaccdcdbaacbadcdadcdbaccdbdacbabcdabdbaadbbbbcdccdbdbdbbdbcddabbcdbaddababacadbacaabcbddadabdddbcddabbbdacabcabadcdcbddbcbcaacddacaaadacdcdcacddcbbacdbdddacbcbcdbccdbcbdddcddcadbdbdaadddacadbbbaacdbbdadcaddaaddbdbbccbcddacdbcdbaddbcbcbadacccbaacccbbadbdccbdbbaaabbdddacbbbbadcaabcaccdcdabbbabaccbbbcbacdaadbcbacdbadbbccbbacabdacbbdcaaacddaabcaadabdccaddbbddacbdcbcdaccdcddccabcbbbdbcbabadbaccabaacbccdaacddacacdcbdbbbadcacdbabadccdddbdccdbbdbaccacbabcadbacdcbdccdbaaaacabbdbddcdddbccabdddbabcadabcadcdddacbcbabddddbccaaccddacadbdbdabcabcdbbbacbdcdaadccbddbdacddddbcaccddcdadbadaadcdcaadabcdaacbacdcdacbaabdbdcbadcaaacacadddcbbcbababcbddacdaddadccdcddbacadbaababcbdabadcabdaadbcbbbaaacbabdbaddcacdadbcddbaccbacdbdadcaaacabcccdcdcaacccccaacdabadccbdccccccddbdbbdcccdbdadbcdacdcdabcaabdbdbdaddccdcaaddadaaacacbcdacdbaaccbadddccbabadcbcaddbacddbbcdcaadccabdbdbcdbbbaadbcbcbbdabacbdcdccaadaabbcbabdcaabddabcdbdcaaddddbadbcadcaabcbcbbcddabaadacadaadcabccddcdcababdaadbdcadaaccdbbcdccbadabcdadaaddabbdaccdaddbacacddcdabdcabdabbcdcbcbddddacabaaccccadcbdcacbbababddaadbbabbdcbbadabbbabbaadcdcbbbbacdbbdcdadccabbcdbddbcdcabccacdcbcbadbdbdbbbbccbcacdbbdabaccacccbcbdbabcbaadabcbadcbdcddaaaaadbabaddaddaabbabaabcbccddcdcaaaaacdddbbadbbbbdbaccacdacabbaddcadccbcdcdcbdbadaacdcdadaaacbaadbdbbdaaadcbdacbaacccbbbcabbcbbcbddcbacadcbdbdbcdabddbcaaabbacacdcccabbcbcdadbbdbaaabababdaddbabdddcbadacaccdcdbccaadbcddcddcdddaacbccccbddddccbcabdacdabdcdcbbadadbbdaabbcacdccabcbcbbbcccbbcbdaabdacccbabdcbbccbdbcbdcaadaccbbcaadbaddcaaddaacaababcbacbcaabcbcdddcdbabbabaacacbadaddacdabdcdacbbcabbcacddccaaadaabcabadcbabdacabaacbdabadbadbbacdadaabcbcacabcbccdcaddabaddbdabdbcaaaaaadcadcddaacabdcdacbcadacddbbbdddbdbcdadcccdcaaacdccacbdcbadbcccddbcdbbbbcbbadbbcdbdaaddcbcbacdcddbcdaccccacbccacdcdbccbccbdddbaadccabbaaabbcbcbbbbaaaabacbbadcdddcdccdaaaacbcbbccaacbbadaadcbddabcbacabacbdcdddbbcbabddabdcccbdcacbaabccbbbabcbcccaaddcaacccaaabdbcdbccccbbaabbcbadbdcadabcbccabcdcbcbaacabddbaaadabaccddcdddacabdabddaaababdadcdddabdbdaccdabacabbacaacbcabaadadacccbabcbbbbadabcbbacbadaacdbaabcdacbccbccdbbacbcdbaacacccbbbddbcadbdaaaacccbdbbdbbdcbcdcbccacdbcdcccdbdcadcccbabdbaacbdcabadddcbaacacdabdbbcbcdabcbbabbddadddbbdaddbabcccbbdaccbccaddbadaaddddcbbcacdcabddcacbcbbabdccabbaccbbbbbadccaddccbdabcabcdaacdbbccbccbcdbcbddabddabbcbbccababbaddaddaacbdacaddabacbbbbacdcdbdacddaacbcbcaaccdbabdabccbbadccaacbabdabaabacdbbaadccdbdadaddddbbacbdbaddadbdbcacbadddbcdddaddbcacccdbabbcddcdcbdbdbbdcabccddbbcdbabcaabdadacdccbcadbcccdccdcdabadcbbdcacacdcdcbcacdadadbccbcabadbbaadbadadccadddbcacacaddcccdbbadadaadcacbdcdacaaabdbccadccbabdcddbddcddabdaadaadcabadcbdaddabaabacdcacccddaaadbbbbadbdaacbdbbcbadbdabcacdbcdaadcdacbdaababbddcacccaddaadbbcdbdbbcdaadbbcdcdcdacadcbdadabdacabcaaccdcbbdcccbccabdcdaacbddadacbcccbaacadcbaddcbddacdcdaddcbbdaddabcbcccacaccddacccaaddbbacccbccdbdcbbababddcdddddcdadbcdaadcccadaaabcacaccbcadaaabdbdcacaadddcdddcbadbcbbddbabcbdcdbbaaddcbbabbacadbcccabcbbddaadddcbabbbddcaccabbaccacbdabcaccbdddacdcbadabadcbcbdcccadddbcaaadbdccdddddbdacccadadcacbaabdabbbabddabcdccdaaadcbbcbabaabddccbacbdcabacbdddaccadcabccbcbbaabbbaaacbbabddbdcddcdababdbababbbaaacadadaabccccdacbddabadbbadbbcacaccdacaccadcddbdbacbbbcadbadbbddbdabdbcabcabdacbabaddcdddaaabcbdbcabbddcbaddabccbbcccbbabdccbcdcacbcddddabddddcaacbdbdcccadcbadddbdcaabdbcbcbcddccdccabbaccccdacdcddcadbaabcccabdacdbaaabddcbcacabdccddccaaacbbccdabdcdcabaaccaabddbcadbabbcaadbaacbcacdaccacddcacbcaabcbcbcaabadcadbdbbdacdcdcaacaabbcdabaaadbcabbcccdbcaccacbddddcbbdcccbbadcadaddabbddacdadbadcbacdbadbbdbcacbbccbdcdacabdbdbbbbdcdcbadccbcbacabcaaaacbbdbbccabcccdadcdaaadbbcabcbcbadadaadcaaacbcccdcacabcdcddabaccabddbdbabbadcbbdacbdccacdbcbaadadadccbdacbadacaadcaadcbacbbadddbacbccbbbbdaadbbdcddaddadcaadccacadaadcbaddbbddcbbdddcabddbbabcdbdbbcddacbdbbcccbdbabdbdbddaacbabaaabadbdbdddbaabaacadcddbddcdbaccaadaabadcdbbcababbcbcacbbdcdcbdcdbddbbcdaaddddadabcbabcddabcddccdadbdbaaadadcdccdbdadcadcddaccabbdbaddbdbdbbaacabcddaccaccdababcbcbcdabdadddaccbbdadddadbddbcaacadccabaaddcdbdaaccdcbccacddccbdbcddddccaddbacbcaabaaabcaaaaaadadcddadcddcabdcddbcbbbbbacacadccacbcaccbccdddcddaaaadbbdaacbdbbbdabadbabaddbabbacddbbcbbabbaaacbaccdacabbdcacacaacacbaccccbacbdbbcabbdbdddababbdacacdbbaadadcaaacbbbdccdbadccdbcdbdbbdaacdacacbccdbdbacaccdabbacdadaabdbcddacbcccabcaccabcacccdbdccaccbcaaccdacccaccaaabdcddcbdabdaadcbdcbccaccaacadcabdbadbdcbcdcdcdbcabcacabaacbbdcaacbadcadcdbbabbaabbcccadbccadaaccbdadadbdbaccbadaacbdbaaccabaaabababacbdbdccdaadbabacbbccddbadbbdccacbbdcbddcbaabaadabadabcbdaddaaaddcdddbdccadbdbbdbadcbbabbbbbcabcdcbbacbcacccadabcdcaabbabddccacbccacadcbbcdcacabccabacbdccbcbbacdbdcbdbacdcadddddbbdbdabcbadcbccbadbccbdadcbbdbaaaaaaacbcbcdacdbcabccdbcacdbcdbaaadabcbcbdddaaddcccadbdbbbabbbddbdcdcdaaacccabacdaaadcaadbbcaddddabcaccdcabaadacdcbbbacabdcbcadbabbbdbbbdcaddaacbccaabbbadbdabbbcabbaccbacaadaaddaadccbaccbcbacdbdbabdbbaabccbaacbcbcbadbabccaabbbcdbcababccacadbdbadbdcbaacdcabdcaadcbdcbabbbbbabccbdbbdaadbbbbcaccdcbbcccccaababcadcbcacabdbbbaccabcadcdabaaababcccaaacabbcaddabdbddcbdccaaacdbddbbcbdcdabcbdadacabcbaaaddbaadbdcdbbbccbddcaadadaacaadabdadaccaaacabbddcbccccbaabbdaaacddcadadcaaaccabbadadbbcdddbbcacdbdccddacdcaaaacbaabacbbccbbdabdbbdcdacbbccbaacccbabccbaadacadcdbbdaaacacccdbcbcabdbdaddbadaaabdadcbbaabbaddadaadbcddbbdbbacaabcaabcdadcdbcdaddbbdadabcddddaccddcbcbaddcbaddaadcaddcbbbdcbbdbcbcbaacbacadddcdadbbddabcbabbdcabdacbdcabadddbdadcbbcabdacacbaccccaaaaaabbcaaccbddbcbbaabbbacababddcabcaccccaababadbaaaabbacbdabcbcaabdabbcdbcdbacaccdcdbdacacddbdddbbcdddccdbbbacacbadbbbcbbaabdcbbcaaddccabdabaabdacadacddcdaadaaacaddbdcdcabacaabcccdbccadbdcadddddbddcbdadcccbbbcaacccaddbacdcdaddbddbadadccacdcdbbccaabaddbacabdadbdddcdaaadbcdcaabccdaadccdaccbdddbcdaaaaacaaabadbbdbbbdbccdbabacbdbadcdcbdbdbbcccbddcbadbdabcdabaddabbbdcddbcadccbaabcddccabacabdbcaaadbcabcadbbdccbbccaadabdddaabbbbacacaaadabbccdbbbcadbcccadadbdaacbbadcdbadddaddcdbdcddcaccbccaacbbbbcadaacacbabbcbacdacdbddcbacdabbaddabadcdbaccdaabdcccabcddddbbbaccbdcbdbcccbcbbbbbdaabcbddabccaccccdbadddddbbccbadbaaddacbadadccbdaacdbbbcbdddbdbccadbdbbaadcacbcaabaadbbbacdbcbadbabdaacdaabcdcccbccccdcdbaabaabcdaccbdcaacccbbbacbcadcacdadbadbaadaddccabadccccdcaaaacadbdcabbcbabcdccacbdacaadcdacabcbbccdcbdabbcbcbdbcddccdcadcbdbcbcbadaaacdcdbcbbdabbcdccbcacacabbcbadaaddbacccadbcacacdaadcbcacccbbcbdbadcccbdddaaaacdabcbdbbddddddbcacdacbadbcacacabcdddcdbaadaccadccadccabbdcbaddbdbccadcbccaaaacccddbdbcdbdcaddbbbddbcacaddccbddbbbbcacdcbdacbbaacbcaabdddbaacbabcadaccadacbccabacbaadbbbabbccdbbadccbabdbaaaabdacdadaabdaadcdcccdaadaacacbabacccddacaadccadcadbbbbcdaacdcacddddadbccbaddaaddbacddbaadaadbdaadbcadbbbbcadabddccddbbdadaacacdababbdcadbcbbdaddaacacaadaabdabaadaacadacbcbbabbabcbbcdcadbabcaadddcacbcccadbbaadcbdcadccabbcdcaacbbcbcccbdcacbadbcbdaddcdcacbbcbaacbbdcadaaddcacadcbadbdcbbbadaddbcbbbcdcdabcbadaabaccabadbbcbcdddacbcabaccdacdababaccabcbaddbccccbdaccbddadbccbbcbcadbaabbadbdcdcdcdbbadbaddabbdbdcdbaacaaadbbdbaabcdddcdabccadcaddababbabacbdbdabcacccbdcabadbdddddadbbdacbbdcdabbadbabccbdadbbbdcbaccaccbbbabcccadcdabbdcddddcbddbadacbdaacacacaaccaaccadabddcadadbabacbccabccbdbcdcdcdccbdbcabdcbdabcddddaccdccbdddbcccacbcbccaadbabdacdbbcbdbaaacacadacbacdccbbabccbdcdadcaccdbbabbabdcacdaabdaacaccbccddbbcadcdbbdaadbbdbdabbadcdbbcadaccdbadddbcbbbaacbbacababcddcabacdbcaabcbdcdcaadcdbacccadacaaacbbcdabdbacdcacabbcddbdaaddccccbcccbcaacaacccdbdaababcccddbcdcbacccddddcaccadcabcccbcabccdaaddcadaaacbcabdccaccdcbababccddaacacdacbdbcadcbabbaddaddbbaadddbcabdaabdbcadbdbbabdcbacabccabdbabcbbaacbabbccabddcacbbbdccdcccacaabacccbacaccccabcacddaabdbdddacadddbbcabdddcdaccddddbdacbccabaccbdaaacadcbdcaadbaaaacbddbbbbbabccabbdadbdccdbbdcbbbabdbbaddbccaadccdcccacdccaadcbdcdaccbdcaddddadbbcaddaccbadcdbadccccbaaaabadadaddbadccdcddcbddbcbadcbbcbcacabbdabaabbacdcaadcbdaccadbddcadacaaaddbacbcbbbddcbcdbbdbddddbcccacabdbcbadadcccbcabacadddaaacbdcdcbbcdcdbbaaccacdadddbddccccabacaaaadacdcdbcbadbbcbadddbcaacadaadaddcadbaadcbdacbbadadacdacbdbdbbcbbddadaaccdacbaababdacbbaccadaabcbcddbcaaabbdcbbaacccdcacccbccdacabbcbbbabbbbdbdadbbdabacdcbddadcbddbcbbaddbaacbbbbabadbcdcaaacddcabddccadbbccbbacdbbdcdbcbbbdcacbababdabaadbbaccbddcaccabbcbacaacaaadbbcbabbdcaabdbcdabdcddcbabcdcddcddccabaabbcbcadbdddbdacaaadcbcdcdbbbcccaddababcdcdcbbabaadcccdbdacabdccddcbadcaaacbdbddabbabdbcdcbdddbbdbdcdbacdbcdcabbdcbbadddcbccaabbdddaadbddcdbbdcccdadbccdabadbcdacdbbbdaaccdcdcaadacbcdddadddabbadabaacdadcbabdccbddcbaccdddbabcbddddbacaaddcccdbdcbcdacbccaabdcdbbcacacadbbbabcadcdbdcdbaccacbdadbddadbcccbbacadaccdcaacdcbcaddaabcbacdaddcbcdaacabbcadcadacaaaaabbcbddaadaabacdcbdabccacddbabdcaddcbcbadadcbacaccccdccdcdaacbadbcbccddabbaacbacaabdccbbdbcadbabcbbaccdddabcdccacaabdaacabdcddcdbddacdabdbdaaccdadbdccbdbdbcabaddbbdaddbacaaccadbbaaadbdcacabadbdbddddbdbabbaabacddbdbdcbbddcbcbdddcacabcabdcaaccbdbdcbccbbdcdbbadaadbbddaadccacadadbabdddcccbdbbbddbadaacbbbacddaaacbbcbccbdadbaddadbcaaadbbbaccddbbabbbcbbbccdadabaaadccdabcacdcacbdbdaabcbcbaabaadbddbadccbaadbacdcacdccaadaaccddadccbbcabdddddacaccdaacacdacbbabccddcdacccabcbadbbbdbcaadabcbdcdabbdcbcacaccbacddbcabcccdcbacddcaabcbbcccdddbdacddddccaacbbbddbcbcdccacccbacacbcadadcacbadcdacdcdbacabaccaacddaacbaccabdbdddbadbdbbdcdacdbaaccbddbaaacbdcabbdaddadaadddacbaaddcbdcabdcbcbccbbdadbbcbdddbbcabaadcdcdccbbccabcdbadcaccaddbbaccddacaccacdababdbdaabcbddbbbddcbbdacdddbaddcadabcdddbccdcccdaccdcabacbccdabcacdbacabdbdbdadbdaabbdddbcdaacbdacdababbaacdcadcaacdcaadcbaabbdccbcbdbdbbdadbdcacabaacaccaaacdcaadddacbdaddacdabcacababaabbbdddbcdacbccacbccadddadaadcdccabdabcddddadbbbbcaabbbbbcaaddcccabdcbababbaabddbdbdbcacbcccabdadbdcdccdbccbccabbdcdacdabcabdaabcbdacabddccacddcdacdcdcaaaacccbadbcadcdbabacccbdcdaacabddcbccbbbbacccdbbddbaacbbdbcbabadaccadbabbcaadadcaccbacbabcadbdadbbcddcbadaaccbdbbdddccaddcbcdbaaabbbccdbdcccbbadcdddaddcbbcadacaccdbabddcaddcaabbccbccbbcbabbcdaddaadadbcbdbabdadcbcacddcdadddbcdddddaddadacbccccddaabddddbaddbacbdcbcdbddbaabbbcdcbcacaabcbbdbcdddbcbbbcaddcbdbcdcdbdbbdbdcaaabccaaacbdaaaddbcbccacddbbddbcaacbacdbaccbaddabadacbbddcaddbdadcdbdcbbbdbabbbdcbccbcabdcbabacbcadbddadbdbaaccdcabbbcbdacddbacbbdaaddabacbcabcacaabddcaadcdcacccbdabacdaadacadbdcccdcaadabacaacbdcacdcdbcdacccdcccbddbabaddbbbbdcdaabbbdabbcabdaacdadaccddabcdbabcdcadabbcdcbddacbbcaaaadacaaadcddbbdabbbacacccacdabbcadccacccbdbdbddaddbbaabadbbbbaddcbdadcaabcccbcccccaacccaaaadcbbdcdcaacadddaddddbdcdaadcadaccbdaddddbbdcbacdbabacdccadcbdbbcbcbdccbdbcabbdaddddadcabdbbbbdbbbcadaaaddbcacdbcdbbcdcacddcbccabbcabbbddbbbabddbcdbcacdddcadbccdbcbcadbccacdbcadcadbdbbbdbdaaadadcbbdadabbdcbdcaacadbcbddbddacbbdbadaaaccddcbaaacddbbdbdccddbcccdbbbdcdaacbbbdabdacdcabbbccbbacddaaaadcadbacacaabbbacdcdcccdbbdcdbdcbcbbacbbbbdbadabdabdccababcbcbbdcddddbbbdaacacbaaccabacdddaaacdabdcdccdbcccdaaddabdddcdaccddbabdcabacbcadddbaccdbadbacbadaddbcdcdddadcdbcaacaaabbaccbbbddaacbdddababdcabdacadcbacbcccdacbadadacabaadabcbdbadcabcdbbabdcbcdccabbacbaacacdbadcccccbcddbddbcbdadaacadcbdcbadbabadacbbaaadbcacdbddacadcdcdaccabbabcbdddbadbccbdcdbadcbaaabdbddbdacbbddacdcbaaccacaacccdaabbabcaddcddcdbbabbbddabacaabddbabadddcdbbbaacdcdbdcaacdcccdcbbaabcaccabbccbdcabdddaddbaacdbccabdddadcaabcbacddbcddadabddadbdcbddaabaaaaadbcdcadaaacdcbdaacdcabddbacbcacdadddabadccdbdaaadacdbdbbdbbacbccaabbbaddcbaaadcacaacaabdccacacdbddcccaaacccdcddbbbdbabaccaacccbdcacccbcdaaacadcdddbdacdbccbdcdacbaddbbdcdadbbdadbcdbaccaacbdacdbaccaadbccbbdbcbdabdbdadbabbbacbacddacadbcdbcdabccacdbdbdbddadccbddaaccbbbabbddbbacadbdacaaaabdabadbdddacdaccbaacccdadbcabccdddacabdadcdcaaaabbabcccbbcbdbacdddacaabacbaadbddaddddcdbdcdcaddbaadabaacccbcaabbbbcccdaaabcbcdbdcbccbadcbbddbcbcccdbaadcbbdcbdbdacbdaadbaadcbdccdaddbaadcccdaddabdbbdabbccbaaabaddddcacddaddccaddadabcaabbddadcdbcddbacacadadcdddbbbaaddbcbbcccbbddacbacaaddcdbcaccccbabbdacaccbaabdccbcabacdbdbdddbaacdacbabcdddaaabccbaaadacbddccbdbacdabaccbbbaacbbaadbacbdabbaadaccdbbabddabaddcababbacdbcacadabbbadcbacbcddbbcdaabccadacaccdbacbbadadabbdccdcdaccdbbbccdddcdccaacbbadcbdaccbcaacbbacabababacdabadbcbacdccdaabbaadddbacbddbccdbaccabcadaababaaacbddaababccabdabaccbddabadcbdabababbdccbdddadcccaabaacddbccbbbaabddacabacacdaccabdcbacdaccabddcccccaddddbdacacddcbdabcbcbdbaacadbaadabaaccccadacaadbdacabaabbdcdbbaaacabadbabbdddccdccdaaadcccabcadaadcbdcacdaacbdbddbabbcbabdbbdaabcaabaadbadbcacccdbabaadcccaccdacadccdbcabbcacdabaaddbcbcadbcbadacabcaccdbddcabdadcaabbdadbabdcadcbbdbacbdaacaaadbdadabbbcbcacaacbdccadbacdaabcabccaaddddcbccbaacbdadabbccbdbdadcadabbdddbdbaddddbccbccaaaacacdacabccdaadbcddbcbcadcdbbdacbcbbadbbaaaddcdcccaadaddcbcacacaddddaddbacacaaababdacaaabcadcbdadddbccadbbdbaaadacacdbabbbabbbdbcbaaadbbdaabadcbaccbcdcdbcaadccbdacabdbcaccdbccacaddacdadbbbddcdcbbcacddbbabddbbbcaadcbcddbcdddcbcbdddaacbbcbcdddcbdabdccbaaaadddbadadacdadbaabbadcbbcadcaaabaabbcdcaccbcddbdcbcacacacdddabcdbbbcbccdbcdaaccbbdaccaacacbdcdabbdcbdbdbabcabddbdbdcdaaccacdaabddccdcdadcccaccbaaaadbcccacbadacddcaacbaabacaddccadacbdabccddcbdbdbbcaaadccaddadccdbaddcdcdbabacccaccddcacbbbccbbabbbaddbcdcdbbcddacdcadccbcddadccdbdddaddddbdbcccdadcdcabbacaacabcbbbaddadcaabbddabbcbbadbbaddbdccadabcdadbcbcdcbdcdabacbdcacabbbbddbcdcdddaadaabcccbdbdaaabcabddccbdcdcddbdcabdadaabccbaccabadbcaccacdbcdbcccaacbcbcbbcacdddbdabcbaccadddaaddccdbdcbbcbcbdcaadaacccadbbbccbcdcbbddccccadcbaababaaacddacadbdaacaccdbbcbbdbdbaabccbbdabcbccaccdcbbaadaccdcccdacccbcaadbdbaadcbaccbcbccccddcddcbacccbcdbabacabcdddbabdbabddbccbddaabaaabcdadbbaaaddcaabcdcbcbbdcbcdcabbaddbbacbbdaadabaadcabccaaccdcbcdabadadbccdcddcabbbacaabcaacaacabdbcbcbccbadcdaabdbbcbdbaaabbaaacbbbbbddcbaccddccbcdbcadbabbbdabdcbcdcacccbadbbdaabbcbbcaadddcdbddcdaacdcccbcaaaaadbbccdadccdcacdabcddacacddadadbdabbdbabaaabddbddacdcdbadacbdcdaddaacbadbdbcacccbdacacdacbcdcbccaaacccccbcbcdcdaccaadcaddcdbaddadbacadbdaddaabccddbaacbccbcdbdaacbbbbddbcbbabdbdbdbacaadabaccadcaddcaabaccacacdadddbabddcccdadbccddbbbdbdcdbaaaaccacbcaaacdabddbaadaacdbabbdbabbdacbacddcdadccadccdbbaadcdbdabacbbadcdcdabdcdaaabaadcccdbddaaccddadaabccbdddbbdadbdbcbcaddabadccbbacdbccacbbabaccdccadcaabbbcdccbdcaaadbbccddbcddabbdaacdbbaddbbadaacaadbbdacccdcabacbbdcdbdcaaadbcacabdacacacdabccdcaddcdaaaccadadadcbadcccabddcdbbbbdabbbddcddaabdacbccadaadbaccacdbdaddbadaacddaccdabdacdcacaaababbcacbbcaadcbcadddaabdcadbddacbbbdbcdbcdbbdcabdcdacdbcbcbdddbccbbadbbcabbcbdcaddbdabbabcbabbcbcdccadddcdabcacbabdcdaabcdcaabccbdcbdbbdadaacbdbccadadabddccbdcccdbacccacaadddabbcaadbcadbdcadacdaacadccbcbccdadbdbdbacbaaadacdbbccddcddcabcadbbdddbcbaaddddabcaaddbacbaacbbdbdddbddcbcadbdcacaddaadccdcadddbbabaadcddcbddbcabaddadaabbaabbbbcbbdbccccbccbbbabaaccacbdcdddabcccbbbccabacdbcdcdacabdcbbdbccdbcdbadbcaaaddcddccaccbcbdddabacbcdcbbddcadccbcccdbcaaddacbdbccdadcbdcbcaadcdbdaabaacbbbbacbdcbbabbbacbccbbbbaaaacddbdaddcdddccbcadbabcbadcdcacbbbbcccdddcdaaabccbccaddabbdbccaaaacadbadabbcccccaabbdadaaaabccdcbaadcadcabcdbcccaccdcbcdbddbaacadcdbdababaddaadcbcacababcbcdbbaabdcddccabbbcbcdcaaacddcbcbaadbacccabdbcdacdabababbadddbadddbdcdccabbcbdaabdddddbaaccabddbddbccacabdaabaccbadbcacacbccadadbbcbddabbcdddbcdaadbccdababadbaadaadcacddbabdbdcacccbdbaabadaaccbccbddcbddbbcbcbdbadddaaccdabaaaaccacbdcdcccbbdcbbbaacdadcbaabbbbbddbcccbdabaacbdbbcbbcaadabbacbccdddccdacdaaabbcbdabaddcdbdddabcadddcdbbcdbccdadadacbbaadccaacbcbdbbcdccccdacbcdbcbdcdccaccacbcdaacccbcccdabaaabdcbcccdaddcdbcdaadcabbabdbaddcdccbcdaadbabdadababdadbcaacdbadacdddbbcbacbbdabaccbadbccddabcbccadddacaccbcdbbbccaadcbdadbcdbdccacbbcdbbdcbbcddbdbaddabadbbdccacdbbcbabccbaddbddbbacacbbbacabbbbacbadbadadbddbcacacdbbccaacaddabacccbaccacaddaaadabddaddccddcdabbbdcbcbbcbabdcddabbabddbbbccbacbcbcccbdcdbbcbdadccdddacadbcabcccbaaaddabadccbadbcbdccccdcbabbbbbbbababcaabbadadccdcccbaccbdbccdbaddacbacbcdaabadcabccbbadbcadcabcdccadabcacbddcddadacccdcdbaabdcaabcaadbbdbacbabdbadbbcbbaabddaabcbdcaadcbbcbcbbbbdaacadcbddbaadbbaaadbbacadcabbccbbbccaabdcbaddadabcddacdbbdbcbbbbacbccbddcbbdaddadabdbbabaabdddabbdbcbcdccdacbaadbdbaacdcdbdabdddcdacaddddbdadabccbdbdcccccccdcddadbdabdaabcabaddcbbdcccbcbabbbcacddcbdddbacdbccdcddcbadcdbbabdaabbdcaddbadbcadddddddcdbcadbabdadddaaacdcbdbccacacadbdacbdbbddddccbdbdbdbdbcaadbadcccbbcdbdaccbabcabaadaacadcbcccadcccccbdababaccdadabcbbbacbcbcbaacadccaaabccccbaacbbbbbadabcaddddbbdcbcadabddddbdbacaddbbdbcbbcabbbcdddccbdabbbaacdcdcadadabcccaaccbbbabdacdbdccaddcbbdcdbacdbccccdbbaaaadbcdcdbccacaababdcabaadcbcbacabacbbbacbadccbaabbdbbbccbaaccbbcbbdbccdacacbcaadbaaadadcdbcbdcacdcabbadcaaddcaadaabcabaadaabaadadbbbbdccabcabdddadcddcadadabdccadcdbdbdbbcababaaabcddbcbdbdddaadcdbbcdbbcaccddbbbacbbacadaadbdbddabcbbdaadcabbbbdcbbdbbbdcaccabcabcdcadcdacddbaaaddaababbccdcdaccbdcbccabcbcccdcbccbaacbbcabcddabbdccadbbdccbdaccacbabacadabbcabdacacddaaddadbdcabbcdadbcabcaddbcdbbbcbcdbdadabdbbadaadcdbbdacabdbcbdbadacbcddcacdbaabdaabababcdcdcbbdabcccbaabcdadbccccaabcdbbbcbccadcacbcbdcadcadcbabbbbbdcaacbdbaabbbbadcbbadddbdcacaddbddbdabccdbaaddababbadcccccdcbaacdccbccacdaddcaacddbabdcbbcdadbdaacdccaadabacaddacdacdddaacadaccdbbdddcabddbbbdcdddbaabdaabbdccaaaacccabcddcdcbbdcabbbcdbcbcccdacbadddaaacbbbdbbabbcbdabbcddcdbdcbbaddcaabddaddcadbacccbdbccadccacccdbdcaabcdaacccaaaccbddddccbadbaabaacaaabdbbbbaacacccbccdcadaccbadaadbaabadbbcbdcddbadbcbdbcacdbdbaddcccddbcbcbbdcabddcaacacacadbdbcacbcccbdbdabbbcccdbbbdbdbbadcdbdabbdbcdbdbdcdddddbaaccbacdcbadbdbdbcbdcaacccbdabbbcadbccdcdcdacaaaaaabcdcaddaadcdadacdbccbadccbbdbbdcbbaddacddabbbdbdbdbdacbcdbcabaccadcdcdccbdcabaaccacbddbcddcbccabbdbabcaadcbaaadaaabdacadaddaaadaddcaadddaabcbdbbbcadabccababbaaccdcbbbdbbbdbdbcbaabbbddaddccaaaacaddaddaddddccbcaddcbcddbbaaadabcbcbacbdbdadaaccacdbdbbdbbbccadacbdaabccdbadbbcaabdbdabbabdbadcdadadabaacddcaccccddbbbabcdaccbdaccbdabbaaacddabaaccaadaccbdbcdabacacbdccdbdddcbbaadbdaccccbcaddacaccadbbadbcabcacbbbccabbcacabdadccacaadabbcabbacbcbcbadbbdccadbbbcdccaddccdccdbaddccdadbcabccbaaaaabadaabbcccbcddabcdcbddaaabbdcccbabbcacabadbbdacaabdccbaddbbddadadbaadcddaaddbcddacaccaccdbdbcddcbabdcaabbacbabbcdaccacbdbdbabacdbabbacdbbbaadcbcddcbaacabcbbcbbcbdaddcbcdbbabbcdcadaababbcbbadccddbacbdcbadadcbbdbcdbbdaabacdacbdcabdccacdbcdadcddccaacaaadabcadabadcdbabcddbbcabccabbcadaaaaaadadaaacacddaacdbdbdccdbdbcddadacababcadbbadaccbacbbacdbdaccdcccaddaadbaadbccdbabbccbcaaaabacdbadacaddbcabcadbbcadbcdbbbbbcbbdadbcddacaacbadcdccddaadbdddbccdccbbdbdbaccdaadaacabaddddbdbabaccaaadacacdabdbcbbddacbdacdabdcaaacdbadbbabbbdddbbadbbdcdddbbdacdbdbccababbcdbddbadbbadbacbddcbdccbabddcdbdaadcbdcddadbdacddaddacddadbddadbaaababddbdaadaabcbdaccccaacabdbbabddaddbbcdcbccaddadbbdcccddcbadaccaaadccacaddaddccabbaabbdbdcadddcdadabbadcbcacaccadabbbdbaacddcaabdaddbccdcbbdcbcaddcaabddaaabadaabbbcdbdaabdddccdbbbbacddaaaddcbdacbcddbbcbbdcbbcbbccbadaaacddddccbddbabbdcaabddcaadabdabddabdbbcacadddbacdddcdadbbacbdbaabcdddbddabcbbacaacbcabdcabdbcbcacaddabbbacaacdacbbccbbabaabacbcabcadcdbccdaaccdbdbaabbccadcbddbcbaadbdaccaccddadcccdaadbcdababadbdabadacdbccdddaabcdabcdbccabbbcbcddacaadccabcaabadadabdbdaddacacadbdababbbcccdadbacaddbbcccdabcabacbaadcaaadaccbcbadddcdacdbaccbdbbbcccccbcadcabbdddbdcdccdacdbabcbbabdaddcbabcaccbdbddcacabaacdbdabcadcabababcaaacdcddaaccdabcccdddacaabdaaaabddcdcbbcdaabadacadadccbcdbabadaadababdbabdcbddbbacbcadbdabcbbacccadccaacddcbbbdbdbaabbbccdddaacdccacaadbacbdacbcacaacbacadaabcdbcbddcabbcdbbaadcbdaacacbdcdcbdcbabbcbbcaadaadadbadadaccaccaabccccdbccdccbaccbccacdaddccdbabdcbdbcaacabbddbcadccddadadcababcccaaddcdaadaaacadadddaccddbdddaadadbcaacabadbdaabdabdadbbddaacbabbdaaaaddbbacccbbbcdbacbbcacbaccabcddccccbccdaadbcdbbdbbaacbcbbcccacdbadacaaacdbbbdabccbcacadabbccaadcbadaddbbdadbabdbcadcaadcaaccbccdacdabadccbcbaadadbbdabbdaccdccdaddbdaabbaacbbdbcbcaacadbdacabcacadccdccadcacbadddadbdabcddacbbadddaddbcbdccccccbcdcdbccbadcaabbdbcadbdadcdcdcdabccbcdddaccdbbdbabacbccaaadbbccaddaddddcbaacabdcdbddbbcbddddcbdadcacbcbaacddcabbacbbbdcaaacbadbbddacccddcabaddabbbadcabdccdbaccbabcbbdcdabacaadbddaabdacdabdbbbbdbacdadddacdcdaccadaadaaadddcabadacbbcdcbdcdcdaaacabcdcbdcbcacbdbbdcbadbbaacbcaabbdbcdbdadcbdadcddadabbcacbcdcddddbcaacaabcaabaaabdaadacaacadcdaccccdadcdadcbcadcbbdddccddbdbbbccadddcbddccdacacaadbcbaabbddaaaaadcacabcaaacdbdcbaaccdcbdbbbdccbdbccdcdbbbcbbaaabbabadaddbacbababddaadccdcaaaacbdcbabcbacabacddacbccaccdcabbbbdddaddcbababdbdddcccbabbaabcababbcaadccacbacabcddbabccccaddcadaacadcadbbcacdaddddbcbabdcccbcaacdcbdaddcacbadbdcdadabcbcbcdbbadcadbbacbbaaaacbbcacabbbdcdabdaabadaddcbadddcdccdbdcbbbcccccbddcbdcdabcdcacbcaccdbdadacdbdadccdbabbbdbbabcacbbbcddbdcccdbdbcdccaccbbbabcacbcccbbadacccbaddddbbdccccbcddbaadcdadcbccdbdcbccabbbbdcabccbccdddbcccabaaccdbcaabcacdbdaccacaaabbcaadaadacadbbccbaaaabcddcdbbdaddbcdadadcacbadcddbadcbbadbbdabcdcadbbabccbabadacdbcddaddcbccaadbababdddbdacdaadbaacaaadbccacbabbcddabbaddbdaccdccbdaccdadadbddacdcaabccbccbcccdcaaddccbcdbababbabdcdabbadbcabbacbabbbcacdcaadbbdbdaaaabcaacccabcdadbacddbbdaabdbcdbabdccbbababbddcccabcbdcddacaaccbbacadbbbcbcbaacbccabdbcddcdaaaacdcabcccbadddddcddbabacadaaabbabbbbddacaacbccddcadcccbbddcdacbdbcddcbdddbadadbacbcbcdcbbacdddbbacbcccbdbcbaccabbdaabadbacbbdddbdbdcabbcdcdabbdabdadddccacbbddacdaccacbadcbabadcccaccbdcdbbbdabaaaddcbcdacabdcdcabcaddcbbbcadccbbddcbbaadddadacbbabaaccdabcadadacbdbdcddbddccdbdccdcdacdabbaddcadaddccbcccdacddbabaddbadddacaaccdbdcdcadbbcddabbdacbdcddddcddbbabaccbbaaadaadbcbdbdcdabcbdbdbaadacbabbbcadbabbddabbaadcaccdcaadcaadcbddabdbbddddcddaddabbbacccbabdbdadacbabacddabcbbdabdbdccabcbddcdccbacddcbbbcdbadcccbaabdaaadccdabadadbacbddaccabdabcadbcabccdcabcccdacddddddddbbbccddccbdbbdddcdbcaaabdadcdbaaacbdaccdadcadabbccaccdbdcbdddbbdaabacdbddcbaddbddddbbbcabcccadccaccbdbddddacabbddadcaaadcadbdacaaddbaccacbbcbababbacaadcabccdcddbcbaaabdcccadccccdaaccbacccbcdcaccdbdbcabbdbabaccdddcbbdbabbbccddbbcbdbdcbdbaaccacdbabbddcbddbdbbcdacbcdbdbbcbbaccdbcdcbcdcacbbcbdddcbbcccdbadadacaccaccadccaccbcddbaaaccdaaacbcacdbcabdbaabcddcbddcdcdbcdcdcbbaadaddbdcdcdbadbdbabdbcbccbaabccababcbcabcaaadacabcabcbcbcbdabdacabbccaccbacdccacadcadaccaaadbcacbccddacaacabccacddcccadbbbacabccbdabcddccdacdbbccababcbaddacbcabdbdcadccbccaccaabbcbbbccdabdbbbcdbbddcdacbacccbbbaabaacdbbbaaabbdbabbadcddaabbacbacacacbddbbbbdddaaadbaaaadcaaaaccdbddaddcbddcababcaccdaabdabcdbabcddcbbaccacbadcdacccadbcadaaacbbdbddacabdbdbdcacdbaacccddbdbcddddbdabacdaadbbdbbddaaccbaaccdbabdbdcbabacdcbdcbdddcdaacdaddbbbdacdaabadbaccbaaaacadadbabdbdcbcdddcbadbabccaabdbbcacdcdbacacdbdcbbbacbaaddbcddbddaddccabdcdcaaacacbbddbdbaaadcabcabcdcdbdcdcbbcdabccdbacbdddbaadacccdcbdcbddabbdcdacacaabacdcaaddcccadabababbdcdccbbdbadaccaabdbdbbcaddbdbcabaadacdcccdbcbaaacdddcbdbbdcaabcdcbbcabcaabbdcccbbdccbdbcddbbaaddacdacacbadadbbabaacccabcacccadccdbcbcdddcdcdbdddbbbcacdaccddaaadcaddccabdaadbcdaccdaabdbacbcddbdbbcdbbbadadbdbbdadcdcaddacadbaadcdbcdaabcbadbcbcdbdbdddadbaabababccbdbcadbdbacbdaaddbbaddacaddadbacdbbccadcabbddcbcaccadcabacdacbcabcdddaaabdcdcbaabbbababaccaccdabbacabdaacdbccaaaabcbacabaaabcbadccadcbdbbadcdbaddabaababcbbdbcabaaabacaabadaaabdacdbcaadccdbabcabaddbabdddddaaddddadaaddbddbccdaccdbacdacccbaabacdcbaacddcccbdbacaadccaddcbdaddcdbbdcdbadbccbcabcdbdcbcaaaacbadabdcdcadbaabcbcbdaaabcaabcdabadddabcbacddacabbbbccdddcdaacccadcaccddaccbacdaaccbcabdccdaacaabaacadadcbcddcccaacacddacaabdcaacbabaadabcaacdddaaabaddacaaddcdbdcccbbdacdbabdbccdbdccabdccbadbabcdbdcacbcbbbdccdccdcdbaadaaadcadadacddbabbbcaadbaadbbcddabadbbbcbadbdbacaccdbadcaddbadadadcbcdacadabaacddabdabacbccadbaaabaaddacdcbcbcbababccddaaadbaabcbaabcadacccddabcaadbdadbadacaabbccabaaacbcdabddbcbcbbabadbbcdcbbadcaadabbdbcdaadcbbabdcccacdbcbaaccbacddacbddbccadcdaadbbadacacabcabdbdcabbbadbbbbaadcccbbddbacbddbdcbdbdcdcaddabdcbacbcbcdccbdbcbbaadcaddbccbcacaccdbbabbcadaccdababbbabcccadbcbbaacddddcdbabadbcdcbdbddbbdcdbadadddccacddddaacacacbadaacbdcabdbcccccdbdccaabadbbdcadbdabcbaabccbdabcbbabcdbdccddabaaabdadddddcaaaabacbbabcbdbacabdabccbcbcddadaddbacabddaadadddaccbabdbbcbdcbdababbabddccdacbaccbbbabbcdccaababcbcaddbabaadbdabcbabbddadbbadbccccdddaacddaaadbdbcadababcddaacabcadbbcacbadadbbadbcbccdcbdccccabccdbcadbcbadbbbdbbddbbabbbbbbbababddbcdabcccbadaaabdaaaaacadccdaaddcdaaaadbcdbdaacacadbdcccdbacddacadabacdabbccacbccdcdddcdaaddbdcdadbbacdadababdacbdbbddabdabccaabbbccdbddbddcacadcabbdbadbcbcbacccddbdbadaadcddbdddbdaabbcddccadcdadccbdbcbbaadbccdadddbdaddacabcabcabbaddadaccdcabccabbadcbccdbddbadbdabcccdbbcdbcbbcccbdacccbdcddbddcdbcbbdacacbdababdbddddcacbdacbcdabdbcabaccacadcabbacadddabaaabbbcbdadbaadddbdbcabcaabcabbbbbdbddddddabbcdaadbaadadaacabdabcadcbdadadbbbdaddbabddcabcddbccbdcadcbdddbbdbddbcabbbbabbccadacccbdcbcabdcdbcbcadacdacccadbcbacabcaddbccaabdccbcacdbaddbdbabdcdcccbadddbccabacbaaadccaaacbccbdabbcaddcdbbadcabbaabaddbbabbaddcaccabaabcadddccacdcaccbbbdadbdccbcbaaccbadbdbddbadccbadcdddaddaddacccdbcbdabdccaacdacbbbdcccddadbadcbbbcccccbcaadaadcaddcacbaccabaaccddcdadcbbbcacaacccbbbaaccbaaaddacadbbaaabaaaacbbdddcdcbadcaadadabddcaadabacadbbcadbaccdccacaacccbadbaabcdaccddabaaccabcadababdabcdabbcddcdabdbccbccbdcbcbaaacadcdabdadaabcdacdccbacabbdcadbddbdccadccccbaabbdccaadbcaacacccdcaacdcadbdddddaadbbcbcccbadcbcacbbddabaccbcabbcbdcdabcacaddabbcbbabcccdadaacabbbdacacbbcbadaabcdbbbbabdcdadddcbdacbbdabaaabcdbbbdaaadabbabadaccddddbdaddbdccabdadcadadabddabcbcbcdbabdcaabdcddcbbaaddbdbddcbcabbdbbaadcbcbdbdcbdbdabdabbbdcbbccddaaccacbdbbcbcdabaabcadadcbbdabadaddcaccddbaaaddabbdbbcacababcbccaacdbcbdbdcdacaddbdadcbcddcadbbadcaacaddbcbbcbdcabaacdaddbdadcbcabccbbcabdbabdaabbdcacddbcbcdccdddbaabcccdabbdcdbdcabcadcbdaccdbcccbbdadabdbbcdbcdacbcbbbcacadcddddadadbbacbcdcbbdcdcbccabacbddacabacdaccaddcbdcccbcdabdcaacdcbadabbadbadbcdbacaccdabbbacbdbabccdcbaddbcccacddbbcddbbbbdbdababcddabbdbddbbdbacdadbddbdaddabcaadadccdbaccadbadbbdddcbadabbbabadbcaadbbdbcdccccddbcbdadcaabacbcbbacdbbbdbcaadaaaabcaaddaaadcbacdaadcbdacdadddabaddacaddbbcdbcccdaaabdcabdadbbcddacbdbddbbcaaabadabaadbcabccabdbdcbbbdbaabcbdbddbddbbdabccccdcbadacaccbacaddcbcccdbddadbbbcaadcdaacddabcdaddcdcacccddaacbccdcccdacaadcaddaacbaacbabddbdddcddcdccbcacabbdbbaadcaadcbababbbcabdbbcadadbdadaaaadbddbcbbcacaddbcdaccaabbacadbbcdcaaadadacadccaaddaddacadbdacdbcdbccaaadcaabbadcbcbdcbbddddcdccddbbdcdbddaccbcbccccacaaacbabcadacadabaaaccbdbabddbbcbbbdaddbcddabbdbbcdddcaabbbcbbacdbabdcabbdbbcaabcbacacabaddddcdabdbbcadbaaabcdbabccbadbcabaadcbbacaddcddbacdddcaacadbdbbbccdddbabdcddcdbacdadabdbdbdabacdadccddcbddbcdddcdcbcadaaadbcbbcbacaadcddbbccbbcadaabdadbcbababcdcbdbbadbcabdbbaabaaddadcaccdacdcdacbbcdadbdacdbabdcdbacdcccaccccccbaabccbacccbdddbbccadbcdacababdbdbaaccdaadabbaddcdbabbdbdbcccaadccdcdcbdbadbdcacdadbacdddcbabadaaadccdaaaabbcdcbbcbabdddaddcbbddaaaccbdcccbcbaaddbddbabbdaaacacddbadbadbacdadaddbdcbcaabaaaddacbdbddbcdbababccdddbabbadccbdcaabdbdbaabddbbaabadabcccddacccbaddbcccdbccbcbdadccddccdabddbcadbcacdacddccdddaacabddbcdabdbbbdaadbbdacbdcbdbddbcbbadddccbaaccdddbcddabbddcddcccbdcabbbcdcaabbbbbdaababdddbcdccdabcacbddaddbbdddcabdcdacaacaaaabbcadbbbccddccacbbabacdaaabbcacbbcbcbabadbdcddaccdbcbbdcbdaabacdbcaadbbcdabcdcdaabaaadacadcdbadcdababbccbbccddcdbcbccbcabbddbcdabcddadadccdccaabbccbbccbaadbbaccdbbbbdcadbdddbacccdaaaaacbdbcddccacdccaddadaddadcdbcaabdabacddacaabdcdcbabdabdcdbdbbaaccacbdbabdaddccaaabadcbabdccbddcacdaabcbddddacddddaaddbbbddcdaadbdddcccddadadcadcacdcbcdbbbdcabdbdabbaddaddbbbddbacabcaacabddcddbaccccdbacbbbdcabccaabbbbaadccadcbdacdcbbdbdaddbaddbcccccacbbaacddaabccaacdccbccabbbacdddbcacabcdcaabdcabcdcdcbcbadabbaccaabdbacabdbbabcbaabaaddcdadaacdbcabdadbbacccbbdbcccabbcbbbbadacdaabcbcddbbbcdabacabacaacaccbbcaadaddcddabcbccddccbadaddccbbabddbabbdbddabdbdcbbcbdacababdbcadbaddaccdbcabccdcbdadbabadcacbacaccccaddddccccdbaaabacbbddacabacbddaadccdadbaaaacccdccbababbbbdccacbacbaaccddddddabbcbacadabbdaacadccbbcaddcddbcbacbbccbccccccdacaabddaaadbcbdcaddaddaacdcdbbbccadbcacadbabddbaccacdaababbcadcadababaabbacdcadccadabbabbdbccabcacbdbadcccaccbcccbdcadccdcbaaabbccdbcdbcbbbdcadddacdcadcbaccdddccdadbccdaabcdcacbbdcbdcdabbcaadbdaaccccdabcdadcdaacaddabbaacddabacccbaccbaaaaacbcacdcccbdbcacbbadcddcaadcbdccbbcbcdbaadbaacdadbabdadcddbbadadbccdddbddcccbbbcabddcdadbccdbbadccaccddacbdbbadbdbdcaabdabdcbbbdbbdcbbacdddabaddcdbacbddadcadccaacdabadbdbdaaaaabcccdbdcddbbaadbdaaacbdcaacdaabddaacccbbbadabaddcbaaaccdaacbdbaccddbbdcdbbadcdbadbccaacbaabddbacbaddbdbdddcdbbdcbcbcaadacdcbabcabbdbabcbddcacdcacdaacbdccaaccccdaaaabbacbbbdbcddbdbcacbaaaabcdccacdadadaccadcdbbccdabddbabbdcbddaccadadcbbdcdcabccadabcbacbacacaccaadabcddcaacddaacabbdcbcbdacadcabcbbaabbbaddbbcaabcbcbdaddcccdbdbcacadaacababaaacbccadbaccadbdadbcabbbadcaadbadabcbcacadaacddadbcbacdcbaaccbdccdcbcddaacccddcbbaddbdbcbbbacdbdbcbbcadadabaaccdcadbddacdddddbbccbbbaddddcdaccdbbacccbbabbbdabdbbdcdccddccacbaadcdbbdddcbdbdcaaadbaccdaacdabcdadccbdcddbabadaaacadddabadacaabadaadadbbcdccccbaaacacadabcaabadcdcdbadcacddbdbcaabcbbdbaddadcbbcdcacaaabddbacbadaaccabbabdacaccacccbadccbbadddcadcbbabaaacccaadbddcadcddbdcbbdbdbdbbbabcccbdadbaccdbcbaacddbbcccabbbabbbbadcdaaabcdcbaacbdaccbbbdaccabbcdaaaabbadaadbabcbaaacdbdddcacdadaabbdcccaaabaadbbbbcbdcaabacdabdadbddcddaccbabacdaaccbcdaabdbdddadbccbcbdcccddcdbadacccdcbaccbbaaccbcadaadbdddcaddacccbcdcbcdcadbaaacbaadbcadcccbdbbcbbbbadbddacadadcadbbdbdadaadbcbabaadcaaabaacadccacadddbabccdbdbdcabbaabdaaadabdaaccdcadcaacbacbdaccdaacbcdcdcdaabddcdabbbacaaaddcbccbbcbcccadbcaabdadcdcdacaddddabaacaaccbacdacaddababcdcaacbadacaaadbcbabbdcccaccbcdcdcaccacdddaddbdbbcabddcacbddccccbdaabcdcaaacdacddccdadbdbbbbcaaddcdbbddcabddbdbdacbcdaaabbbdbbccddccbbaccddaadbbccdcdcbaccbbdcbadaadcdabdbddbcbddbddabdadbbcabdabdaabbdccacaccaabdacaaacbcbdbcaddcbdcddcbcdbdbddacbababbacacaacddcbcbdbaacbbabaadbccddccdcbbcbbdbdddccbbbdccacbaacacdacdaacacccbddccbbadcbcdbadddcdbcdcdccdbdadabbdccbcbacbcdaaacccdbcccddadcbbcdbdbdaacbcbbbdaddbbccaddacbabdbababacdabbcccdbbdacbdcdabdaacdddccaadadcdbddbddabbbddabcaacbadbbbbcbdcdcdccadddadcdddbddbadaabddcaaabcdbcdddcbdcdaddbcbdbcdcdcccdbcbaabbacaddcbabcddadddcdbbacddbadcacdbabbacbcddbcdadddccacdcbdcdcdcdccddbdabbcacddaddccdabbccbddbdabbddbbbccbdbcdbaaccbcaabbcadcadcccccbaaccccbcadbccbdddbccddcddadbccdacaaabddbcbdbccadbcbaacadcbbaddddacddbadadcbcccbddccbaddaacaabcacddcbcabadacbbdbdbdbcadbadcbbcacdbbacbdadbaabddacbbdddcddcaddccbdccacbaccbaadbbdaddabadacdbccdcaacdabacbaaadcbdaaadcadaddccadbcbbbabdcdbaacaadadcdbdabcacdcddbadaabdcbaadbdbbdbcbabccbbdbbbdcbdaadacbabbcddadcdcccaabccbbdacbbcbacdcaddbcccdaccdacdadcddcadbabbdacccaabaaccccaadddcacdbbbbbdcaabbdccbbbcccddaaaddabbdadacdcbcdbbbccbdbbbcdacbbacbccadcdcddcdbbacdbcddbcbbaddaacbbbdbcbacccccacabdccaadcabcbdccacabbbcabdaacbdabcdadddbaddddbabcdaccbbbabcdacaabbbbbbbbdcadccddcbbbabcbcbadabbbcbacbbdbabdabcdbdacaddbdccdddbabbcacadacdbcbdbadacaadcbddbdbadaacdbbbabbadcdbbbdcccdabbbdcacadcbbcbbaacbdbacdcbabccbbaddcbdddcdccbbcdbddcccadccbabcacadbabdacabcacccacacbadadbdddbbaacccbcbdaddbadaadbddddbbccccdabaadbcbccccdbbbcdacacbbbbaaabdadcbdbdbbcadadbbdccaadcdadadacabbcccccabdaadbddcbcddbaabadaccabcdabbdbcddbcaddcccdcbdbbaacaddbbbbbabdcccdbcddaaabcacbbbbdbdcabaadcaddaccaababdaccaccdbdadacdbdbbcdcacadcbbbbbccbdadaadddcbaaabaccdccbbcaabdbdaddcccabbdcabddbbacbdddcaccbcbaadaaacbbadbcdacbacddcdcbaadacbccddcdbdbaddaccccbabbcddbaacacadabbddcbbbdddbaaccdabccbddccacddcbdbcaacbabcbdabdbcaacacbbdaabdaadbbccdcaaadcacaadbcdabccaadbcbcdbcdcdabbdcaacaddbddbbcdbdccaaddcadadddbbddadadbddcbbcdcacaaadabbccadcabcbaabdbdabcabaaccdacdabdabaaaddaaabadabbcbcbbadbbbbdacaabcacacadcbcaccaccddabdbbbacbbacbbccdaadadcdccabcaadaaabcaabadaaadcbccacabbcbdabcddcbbdaabbbabbaabddadbccbdbdbdbdccadadacbdbbcbddabdcadbccdbaaaacdddaccddabbbddbddadddbdccbbbcaadbcbcbaadbcabccdcdabbcccbccbbabbbbadcccaddbbaaadccabaddbaadaacdcadcaacdbccbbddcabdabbdccbbbcdbddabaadacccadabcdcbcccdbdacbbacaacbacbbbaddbdabcadbbdcddcabadbcacbbbaacbadbbccaacbbbbbbbbdcaabacabbcbaabcdbcacaaccbacdbddddcacdaacacdcdabadcdcbdadaaaccdcbdddcdbcdccbcdcbbdaabacabcdcdabbdddcdaadcbaabaaaadddddccbccddcdcaddcccbbaaabacbbdbbcbcabcdbabadccacccbabcaccbacdcbcaccbbdcbccacbcadccbcdcabacbcdcabadddaaacaacccccdcabdccdccbccbbcdcabbacabbdbbdcbcccdbcaddbbbaccbdadbdbcccbbabdadcabbababbaadaaabaaacaacbcaadbdddbbadbcacdbddaabcacbddbbabbcabbddbddbbbadccaddcdbabdbadabadbacdaadadabcdcdddadbdcbcdbbdaddadcbaacdbdabacddcdddcccbbcabbabdddaddcdbdccabbdbbaccadadcbabbbcbddccbcbabdddacccaabcbbdcacdbabdbaccbbadbdbbdaaddbccdadbdaadaadbcdaadbaddacacdbbdbcccbbcdaddacdbcddbabadbbaadbdcbaddbaabbadddbddbacadcbbbbbaacbabbccbbdccdbbaddcbddbaccbabcaacabccdbbbcdbacbcbddcdbadbcdabbacadbabddadcddcadbbcacbcbdccabdcacdcabbcccabaaaccaaaaccbdbdbbdabaacacabbddbdcddbabddbcacbbadbdcaddbbcadcbcccddadcdbcabdbbbbdbcddaaaaccdabbcdcdcdbcbcadbdcadbdbadddddaacbcbcabbccbcadbbccdbcacddbcbcaaaddbdbacdacdaabbaccddadbcdddadddacacbcacbcabcbdbdccabadddacbdaacadcdbbbdaccbbbcdddadadbbabbdddccdccdaaadcbcabcbccddaccbacdbdabacadcadcbaadadddddcdbcbbaaaccabbbcdddbdcaccbbabadbacccabcddcbacaadbdcadccadbdbccccdaaccccabaaadddabcdcabcadbdaccccdcbdccadadddaccdbccbcdadbbddccdaabcccccdcbadcacacccbabbacdccdcbcddcddbadaccbbbdddacbabdcabcdcaabacbbcbdababbbaabdbcdcdbcdbadabdaaccbddbdbbcaabacddacaadcbcbaabcaacabdbadddcdbacddcccaabdbcadbdcbbdcadbdbcdbbadccbaaadcabccbdddaaccdddbbccddbdaddaacabaccbacaddbdbdccbbabdbaadaaabdcbbabdcdcddcdbddabcaacbbbacccddcabcbdacdbdacabdbbcaacaabaccbdbbcbcddbcdbcaaaaccdbccbaababcabdadababddaccabcdcbcaacddddccdaabacaabcdccddcdccbcacddcabcccdbbdabaadcacbbdacaadcadabdccbdbccdacbdbbbccaacddaddabdababadbcdaccdcbcdddcdbccababbcababbcdbdcbabaadcadcacdddddacaadcbbacdcbbaacaacbbbdcdbcbbbabbabbacbdbcdaadccddbaaadaaaddacabcbbbddacddcdbaaddbbbdcbbaacdbdacbbbaddbdcddbdbabcbbbcbcdacdabacaabdadbdbacccccadcbbabcbaaccbbdaaaabbbbbadccbacdddcbaddabddcbdddadbdbcbcdcdbcdddccabadccdcdacdbcdadaaddcbbdbbddcddbbbcbdcdcdabdcdbddbdddcbdcbabbabccbbcadabcccacbabdbccbdbcdcabcabbcdacdadabdcddadbaddaacabcccdddadcabbdcbbcbcdcbabdbaabaccbcacbcdcbdbaadabbdcbdbdbcacdcbabbdbbbcaccacbacbdacbcacbbcadcaababdcbbdbabcbadddabcaddbcbdbaaacbdcbbbcbcbcadaccdaddacdbbcacdbbddaddccaabcbcbcabcbcaccbccaacdacbbabcddbdacbcabbcbbddbadcdabcdcaadaccbcdccbccddaabbadbabbdddccabcaacbcbacaddcbdcaddccbcdbdbdabbbabdcbccdabcddcddddaacdcdcdaccacbdacddcdcadbadaabdacdacbdddcdcbacbdacabadcacadbabccdbddaddcbacaddabbbacabbbabacccdbdcbbddbbcbdccabcacabbdabdaacccdbcacadbbadbadbcdabbaabdbbabbadbaabdaabdcbbacdabacdcddbddcbcccabbbbbabadcbbdddcdbcdacdabccddaacddccbadaaaacbcabdcabbdddbbdcdcbcbddbbabbbbcddcbdddbbbbacadcdabccadcadaadcabcdbcbccacadddbbcdbbdcdccaadcadcbbadcbdbcabdcaaabdcdbadcadabacdbabbbdcbcadccacddacaacbcdddbbddcbbacbcddbcacccdcaaccbbacacdbbbaaacaddcdabbaaaddaacdbbbccaacccbdddbabcbdcdacbbddbabbaccbbddcabbbcacacddcbcccaacaddaacacadcabaaadacadcacbdddaabbcbddadbcdcacbacaadabbbabbdbbaddbbaddccdabccaaacddbacbaddbccbaccdabdabdadcbddaaddcabcadbcbcaacdccacbbcdbbbdccbacdcdbbcccadadbdddcddcaacbbccaddbaaacdbcdaadbdbbddabbaddacdaaabccdbcdbbacbbdbddbbbbacabddcbbdacababdbcbaaacbddcdadaaddbbccdcccdbbacabdacbdcdacacdddbcaaabcdaaddadaacaacccbdcdaccaabcbcaaaccccbdcddaadcaccbccbaaccbaddadaacaddaabcabaccacdbbcddbcacaadababadaddbdadddccacbbcaabcadacadbbddbdcdccaaacccadacbccdccaaadddaadacdcbdcbcadbabbcddbadccacaccdddbbddbccabbcdbddabcdbaabbbdbcaabbaccddacbccdbbbdccdaccabbacaddaccdccbacbcbdddbadcccadcbacddabdcacdbbabcbccdbcbcddaacadbcadddbadcaccacbddbaaacdccdcaddacbdabcddbbcbdbbddaaacccaabaaadcaabacdcabbaaddacadadddbbcccdccddbccbaddadabdbdbdcabaacddbdcadbcdcddaaddabccdabdbccabcdcbbdbbdbdacdddddccabdbabccbcacbbbddaabddaddcacaacbdccbbbcdbacbcddabdabcaaaadacadccadacaddbbbbabaaacbddddcaddddccadbbccdcdbbcaacacdbbcabbcbdcdbddbcddcbdadbbcbacdcacdddadbcdbbdcdbdababdbbcacbccbadccbcccdbdbdbadcdcdacbadbabdddcdcadacbcabcdbbbcabcdbaaadbdcdcbcbcbcacdadadadadcdadcbdbdbddbbbdbabacbcccdbdacbcaabbccacadbaadbbadbdaddbacdaabcdabbcadbcdcccbabbcbbdbbdbadbcbcdbdcacabadddadacbbddccabccdbcabbbcdacbbacacdbbadaaaabcaacadcaabcdabddcacabcbadcccdccdcddacbcacbaabcccbbaabbabbccabdcdabbaadccbdcdadaaacdcdccabadadddbdddbdccabdbdbccabadcabaacacadbbcccacaacdccaacbaacacbdbbdcdabadccccbacaaaacdadacdddcbbdddcabdbacacddbcdcbbbaacdaaacdcadddcbdcaaaadaaabcbdbccbbccadddadbaccbadacaddddbdcdcbbcdccabaabcdbdadbbbadcaadcabbbccdadcccaadddbddcabbddacacccbcdcaadabacdadadccacdadbabbadcbbbddaccddacadaabcdcacacacabdddbbcbcaccbbababcdbccdbaaaabcdccbdaddadcbcabbdaaaabdcdbbcddbbcacacaddbaddaddacdabbadaaabdcacaddadccbbdbcdbbababdbdbbcbcbaddcbbccdbbabaadbbbcadaacbdaadaaabddcbbacbdacddaadcaadabdaabcaccbbbdacccdacaadccdcccbcccdacacccdacdaaddbcdabdabcaddacacdadabbcaddcabbcbaaccccbaddcccbabadadddcababcdbdadbadabaacdacaaccdbbdadbbdccaddaaddbbacdccadadcddadccccccabdbcbbadbcabacbbbccaccaadcbacaadcbaabaabbcaabcabdabdbcddbbcabaacbddabcdbcdadcadaddbbbbdaaccbdaabddbbdbabbbbcabacacccbcbbdcdbbaacaabcaabbbabacddcbcccccbbbabadbabcaacadbddbbadccdbbbdbdbababdddbdccaccddbcbadccddcdcddcdbdbbbcdcdbdbbbaaccbcbdacbccdbddbdacacadaadabcabbaccabcdabbababcadcaabcdbbbabccbcaadcbcddcdbadbbbcdbbcacaadbbbcacddacbaabddccbbdaababbcdcddbbddacccbdaadacaccaddcccdbbbbbcddbcdbaddbcdbcdacddacaccccabcccaadacaaadbcdcbcacccadbadbadbccaacdbbdcacdabbbabdcbbbdddccccbacaaddacbabdbdbaccdbcccbddadcddcbbbcadaacddbaabddbcdccddbcbbabdbddbbdbdacabdadbddccbbdacbadddcacacabcdcaaccdabadbbaddccdaababaabcdcbccbdacaadddcbadbdaadbddabdccaadadcacabddadcabdababbabacadacbcdbcddcbbdaddbaccdccabcadcbcdbaacdbdbdccbccccbbabdcbbabbbacabdaddddabcbccccdaaadccaababddabbcaacdadabdabbaccabdbacbddbbbdccacbcdccdcbdcbbddbbdccaabaccdbdbdbbcbbccdabacbacacabbcaabbdcbdacabdabdbacbcaadbacccadbbbdccddcbcbbbccaaadbcbdcbdcadbcbbcaddcddadbaccbcdccdddcdcaacacabcccccdabcacaacabddbdcdcdbaadadadbccdabbbdbdababcdbaabbcabaccabcaaadcadadbcadcadbbbdcadbbbdadbbcadddccbdbdbdaabcabddddddcdaddbaccccdabcacbddcbacbdbbbadbcbadaaddcadabddadcaacadcbccbbcbbbdaabbababdcddaddbdbbacaacdaccadcddbacadabdcabcabccacbdbaccdccbaaaadcdbddbcaabbccdaabcbcccacaacbacdccbccacbcaadbbcbaaccaccbbdabbccaabaaadbadbadcbdcdababddabbcacdccddccdbaccbcdcdcaadcabcabbacabadbdbaddbbbdbadbddbcbaadbccabbccbdbbcbdcbabdcbabacaccacbdccadbddcbacadbabbdbbbbddaddcdddddbabadcbbccbddacbaabbdbbaabbbdcddccdaccbbabcbacaaacddccdcdcdacbadccddcbadabddbbbddbdbacaadcbbbbbbdabbcbaadcbaabbcbadadabbdcdccadbbabcbcdddcaabdddacacdabcddcdaaadadbcabacabddadbabbbbacdbcbcbdbbcaacbddcabcddbdbcbbbcbadaddbbddabaccaaddbdcbbdbaabcadcbcdcadaabbadddbdaddadccbaaaabacacbbddaddbabaccccbcccbbbcbadcbbbbccbcaddcddacbddddacbcbbcdacbcdaadaaaadbbbbadcdbcbacbcbdbccadbdbcadaddaacabcdbccdaddacabacdcaacbadcdaababddadadbddbaabcbcbdbdcaacabdcbabdbddbbbbacbdacaddcbabcdbdaddbccbcbddacdcccdcabadbbdabddabcccaabdcacbccbdcaaaadcabccdbcdddcaaddccbadbcdaccabdbdcbdbcbdddbbdcbacdbddacdcabbbacbdbadbcbbccdcdcddbdabdccdcccddbdabbdbacbbdcbbbbdcbcdcbbbbcaccbacbacdabcbdccbbbcacbbdbbccdabacbbabdcbbdbcbabdbcacdccabcbcccaacbbccabdccaabacdbddddccdcccabdcbcbbaadcaaacaddabbdcbbdbbcddabbbaccddcdbcccddcbdcadcbcbbaabcacabacbcbccccaccdbdabbcdcbabcbadabaabdaccddaabcdbbacdaaddbbdccacbabadcbabcdcbddcbdacdcbdcddbbbdccbbbacdbbbacabbcaaccabcccbccbbcadabacdcbaaadbcbdbcdbdbcccdcdbdbabdbcdacaaabcaaadabbbabaaddbdbbddadbddcabddcaacababccbcacccaaaaaaadcacbdbbacccaacdcdacbacbacadcaaccbaaaaabccadddcdcbdabbababbdbacdaddacccccbaaabcdbdbaacaccdcbdccacbccccbdcadacddcbabdcbcbccdbbbaaadaacddbbbdaddabababcdbbbdcaddccbadccbbbabddcbbcdcaabddcbddccacddadbacddcaaadabddddbcabdacdccbbdddcdcddbddcddaaadcacdacbddabcbddbbadabadaadabdabbdbdaaabaddabccdbdabaadcabcbacacacdbacddacbdcdddadccbacbdccccdbcdccacccccabbabddaadaddaabbadadcdcbdcaaadcaadabcacacdbddbdaaaaaacbbabcbbdaabcbabaaccabbaaddddbacadbdadabcccabccacddcbbbbbcdccdcbbdabdadaacaaddadcbbacdbbcccbbacacdbdbbadbbbdcbabbadbabcdcdadcadacacbddbbdacaadbbbdaddddcbdcabcabbccccdbbcbdcbbbbddccaddaccbcbcbdbbbabaccddcbdbaacbddccdadddcadadcaacaaabccbadadbaaddaaacccdcdaaadbcdcddabcaacdaddabcdddcddbbccbdccbbbbacdaaaabbaaadbabbbddbbadadbbbcaaccccbbdbdcaacddabcababcacdccdcddcabcdcdaadacdccbcadadbdddbcacaccbdcbdccbcbdcbbaddabcdcacaabadadddbcbdbcaccccdbcbacdaaaccdcccbbbabaddaabdbadbcbbdcbcbdbdcacaadabcdbdcdabcbbdaaaabbbbcbcadbcdbdbbccbcabaaabdaabdcdacbaccddddbccdbacbbcccdcdbbbdacadaddcdddccddcddcddcddcbbcabbacbbaaadcdccdbcbcdbbdabaaddbcccbbbcdcbaccacdbadaccaccaabcdabcbaddcddbbbcbbbbddbcccaabcacbcdcadabaacbbbaabbcbddcbddcbadacabbaaacccdbbabcccccccabcbccccadcccdabdcbbcabdbbbadddaaddccdbabbbbacdcbbbbdaddadadbcdcbcccdcabacdabaaccbbdcabacbdadbcbaacbacddcaabbbcbadcaddbacaaddbcadadaaaabaaddcdcdbcdccbdbdbccadbdbdbacccabcbbcaabcacabcdabbbbdccdddbbaaacdaacddbcddbdccccdbaadbacbacadbacabaabdbcbddbccbcdbcddabacbbbccadddcddbabbcabaccbbbdbcbccadbabcdacbcacadcdcdbbaabdcdaabacabddbdcaadcbaadabbabbcaaaabbadcdaadbdabcbcdbdbddccaadbcdcabcdcccabcdcadddbdadbdccaddcababcbdddcbbaaadcdddbbbbadcdcdadbadaabddacbccdcaccbbcddcdcdcdddcdbbdadbcacadaadcbccadcabcdbcadcbcadbcdbbddbbbacdcbcaacdbadbcadbcaadcccabbadbbbbbadbdbccbadcbddadbcbcdbcbbddacbdcaaccbbbbaaaabaddbacdbaababcadbccddbccacccbdccdddcadcddbadbcdadcddbcbbaccbccaabddcddddbaadcdbbddbadcdbabcdcbbcabbadadbcdabbcdccbcbdbbdbdabdcdacddabccadcbdddbabbdbbaabcbacbdababaaadccabbbdbacdcbbcdcaccbdcccabddacaccbcbdbdabdcddadccbddadbbaadadbaccddbabcaddbcbabcadbadccacbbacabaadbbddbabdacabaadddbdabcbdbbcaadcddbcddbcbcbbbaabccdbbccdbcccdabcaccbdbaddddbbccdccbccdccdcbdbdadbdbbdcaaabccbbacdccbdddbcdddbcabdddabbcdcddacaacdbccbbcdbbcaacbdadaaccccbcddcdcddacdccadadcbbbcbcabbdbdddadbdcbdaaddbcddbcacdacbddaadbdacbcbdcbbcadbcaabaddbdbaadbddaadaabcddcccadddddacdcacbbcdacbcabcbdbbcdcbcbcccbccddaaddcdddccaabbdccacdcddbaacbbcabcdcacccbcaaaadbcaccaadaaccadbdbdcdccdaccdbbcdddadaabdcaabccbabaaccdccbacddaadadccaddbacddadaccbcbdbbbbbbbcabdbacdbcaaaadadaaadcaaddaaabadddcbaddadadaadbccaccadcadacbbabdcdccabdbdccadcdcacaacdcccbdbdabcbdcababcbabcdbaddccaabbaccccdbcbdcbcacabdcdbaadaddbbcadabaabaabacacbaacabdacbbaacaddbacaaabacbacaadccdccaacbdcdaccacbaaccbbdbbcadcdaadcdaabbbbadcabcaddcdabdcbdadcdadadddcbabcabbbccddbacdbcbcacbadaaacbbcbddadbdddabadbbaabcbacbdabcbdababbdabdcbbbddaccdaabbadbbadbcdcdccbdcbdcdadcdcbdabbdbbcbaaaccdadbdadbaccccdcabcdbdbdcbacdccbaccbbabbcdcbdcbccaacadbbabbaadbaaaacccddddbddcabcdbdcabadcdacdddadbaacddddbdbcdadcbccaddbcbcabbdcddcdbacacddddbdcddddbcccacacaabaadbacbbdaddaddbccdcbdccbdadadabddacddbcbdbabccdacaddbadbcbdddaabacacbcdcdaadadbcdabbddbabdcbccbcddbcdbababcaccaaadcbddaadcccdcdbadddaddadadacbcadcacdbcaddbbadcaabbaccaaabbadddadddabdbababbdaaaabaacbbbadbcdcaaabcccabbdbdcadbadddccdccccababccdcbaacdadcdaacddbdbbbdccdbbacdbcbcaccdadcbacdcdadcabaccaacbdabadbbccddbadcbddadddbabbadbcdccdcaddacbdcaddccabbddbadaacdcbdbcbbddcbccccbdcdadacdadddcdcbbdbcacabbbbacbcbcdccabacccccbbbbcbabbbabcbdadaabaddbabcbdbadbaddcddccabccbbababccdacbdabcdddbaccabaabbaddbbddaabcdabdccdbcadabdbcadcdcaacdbbcdcbcdcadacbbcdbacadccaadbccdaddcbaddababcabcacdbddbadababbddaccbacbbacbdbbaadcadddcdaaaccdabbbacddddddabdcddacdcabacdcbbcadddacdccbdaaacdadbccbaabdbbcadccabbabadcbacbcbcdbcdcdbbbadbcbcbbabbdcadddadccbbdcbbbdadbaaadadbbdbcacbcbcdabbadaddbdaabbdbbcabdbacadabdcadadcbccbbabdcdcdacdcadcdcbdaaabcbcdbdaacaadabccbbdadcbaabccacdaabbbaabcadcadbbdddbdccbcdcadacdcddabddccbdaaddabacbcdbdcdbbacddcadcabddcccbbcccaadbadbcdcdccadaaddaabdadcacbcbdacaddaabcaabdacbabcbcbdcdbccbbddcdaabcadbccaacddcbbcdccbacadabddcaacccaddbdcadadadcbadddbadbdbbaacddddddabaddaaabccdcbbbbbdacaddaabadaaababdbadcdcbbcaabcbdacbbbbabcccbdbccbcbabdbbbacabaabaadccabcacbdbddcbddbbaccabbddccccdccbdbadddbaabcaddbabacabbaadcbbcadcadadbdbbddbbbaccddbbcacbacbbdbcaddabaacbcdacbadcdabcbabcbcabbbacadcdadccaaddbdcbccdcdbaaccdbabaaddcbdcbabbdbbadbcbdccddaaccddcbbddcabbccbaaabbabdacbdcdcdccbacabadacdbadaaddbadadacaacccbaddadcbabcdadbccbbbbbbdcbccaabaabcdbdcdaccdcaacaccacbbbacabbdccbdbcccdacaaaaabbcaaabbbabdcbbbbbdbdacadbccbbdadbaddddcbababaadcacbbbadcbaccddbdbbbbbcacdbccdacbbbdbcdaccabdcbbdbcadddbdbcadcdddbaaaabbadaabdbccaabcdddbbacbbdbdbabbbbbbbbbdccddcdddbddcbcabccdbbccdbadddbcdcddcdbaadcbbcbdcdcdcdacdbdcddbbcdcbbcaddbdbcdaddabbdbadaaacbddcbbabdcadaabbbbcbbaadbbadabcacbbdacaaccdddadcadcacdcddbaccccbdbcdadcbabdcadabbcdadbbccaaabdbcdcaadabaddaacacdcdaababdddcddbcabcaabbaddabbacddacbbacddcaddbacabcaadacaddbccabbdadbabdcdaadddbdbaadabdadbaccaabbbabdbabbbacccdcbcbcadbbbcaddcdcaadaacddcdabbaccdabcbcdbbaddabbabcbdbdaccabbbbddcdcabbdbddcbcdcadbbcbbcdbdcbdbdabbbaaaaadaadbaaccccbcbbdddddbbcaabadaabdcbadbcbdcaccdadbdcaadaabdbbdacbccbdbcbcacaccbdadbbbbdccccaadbabcabcaacabdaabcbbbddbcccadcdaacddaabbdcadbbbccdcabddaaaadcbadbdcbdabddacababbabbddaccccacbacbdabcbdaddaaadcdbbcabcacdbcdccaccadcaabcaccadaaaddbccaacbdcacddbadbcbbabaabaacadcaddabbdaadabcdacbbadbdabcbdccbaacdbcaddcaabbdacabdbbcbabbbbbaddbadccacdcbacbcdccacdcdbcdbbaaadbaabdbcbdabbccabdbadcdbacdbdacaaddbddcddbbabbbbcabbcbacdcccaabddddcacddaddccdacaabdbccabdcbcaaabbabcdabcaabadaaababcabaccdacdcacbcbadbbbdbcaddbabddbcbbbdcbcacaaabadcdbcccddaacabacbcbcddcdaccabcddddbdacaabcdbcdbbcadabcabdbabddbbddabbdbbcdadcdacbcbaddbbcaccbdbadcbcccaddddbbbdbddccabddddacccacdbccacaabadddccbabdadcbcacadbaccdabdcbbccdabbccbacdadddaacaacccbdcddadaccababbdbcddacacbbccacbaabbabdccdacabdaabbdbaccbdabcabbbbaacbbcbcbddcabadcabbdbcbbbbdababbacadcddbbbacadabbaddcdbdabdcddabdbcbcddcccbbaaccccdaacacabdbabddbdcaabaacacdcadcddbadacdcabadacbbacadbbbaccccbabcacbcdbaabbbdbabbaacbddabdaccabcbccbbcdbbbdbcbdccbbbbcbaddacdacbbdccadbdccbbbabbcbddadbdbacabacbadcdbddbcdbadabababbbbaacccaddbdccdbaaaacdbdbcabdadcdccddbddacacaaaaacaadcdcbdbaababccbbcdbabcabbabaadcaaadddddcbdaabdadadccddacbacdbddcddaaaabaabdcdcabaaddbbbaabcdcadcdaadddbdcddbdacabbcaacdadaaacabccbdbcadbbcddabcbacabacddabdacdcbcdabccbcddcdbdbcbcddbcccaabdadccbcddddcdcabcdddccdbcabaabbbdbbbbabcabcacdbaaddcbbdccbbddbdbcaadadcbbcbbacbdbcaacbcbdaacdcbcbadcacdbddadaaabbbaabcbdabdddadbaddbcbdddbacadcbbdddcbadcbbdcdbacbccbcbaccbbaddbaabbadabbccabaaacbaccabdcdcdbbdadbbcacabcdabdaaaacacdcdcdadddcccadcadadacacdbcaadbabddaccbcdcdaabadacbbdbddddccbdcaddbcdcdbadbcdaddbdbdabddacdbaccdadabacdadddacacbcbdcbddadddbdacaabbadcccddacacccbcbcdddabbdcdbbcaacbcabccbbaaadbcdacdadaaacbbbbbacaddadabbbaaacaddcadbaadcaaabadbaccabacbaccbbbbaccabccdadbddcdcbcddccdadccdcddcdccdacabbadbabaacaabcbdadcaacabaadbdccdccdcaddccdbadacaabdaacdaadacadaccdaaaadcbaddbadddaadacdaabaadabdccadadacadbccdcadccddbabdabcaadcdccaadcbbbdbabadcbadbadbccdadccabbacabaddcabccacccdacbabccdcbdccddacabdaabbbaccbccbabaaddaddddcbaddddabdbaacddaaabccbccccdbacdcbabdbddbbbdabadbbddddcaddccdcaabbdadaaccbaccadadbabdbacdbaccbadadcaadbadcbaacdcaddbabadabcaccbccdaadadbbaddcdbacaddccbddcdbaadaadaddcbcabcdadbbbcdbbdbacdbaaccabaaaccdbadabcbbadddcabdaacccccbacdbcdbcacbdcdbacdacdbddbddacdaaacacdcaccbbbababdccabacabcbcdabcabacaddbbcacccdccbcababcabacdccdbbcbabdbbcdcbbccdcdccdaacaccdacdcbcaddabbbcbcddabdccdbdaddbdbbaaddadcaaaadcabbadabbcaaddbabbcabbbccbaddaaaccdbccbcdcbdddaddcddddcadcabcbadcdaadddccdaacdbcbbbadddadbcdbbddaaabddcdacaddcabbcabddcccbdcdccbdacbcccbbdbdcdbaccbabaacbdddbbddbdbddddddacdbacbcadbcabdbdddadbdbaccdacdabacacbcddbbddacbcabcdccddbaaabbccccccaddbadaccbcabdbdcaaccaccbddaaadcaabdccddddbbdddabaddbdaaddbcdbcdcbaacbbadcaabdabccdcdababacdcdcbdcbacdabbbaddaaddccaaccdbcccabaddcdadadcadcaccbcdabcbcdacbbccdbcddababcadccddcbcadbdbccdcbadddabbbccdddcbcacacacdaacccbbbacddbbabdbdcadbaccacddcadaaaacccdaadcdadbaaabcbcbdccaddbdddbcdbcdcaccaddaacdadadaabbccbbacacabacbbacbababbcaabbddddaddbdbacdbdbbccbcccababdabccdacccccdcdadbaaddabcabcdabcabcaacbaacbbbadabacddcaaaaaaddcdbacdcbddddddcccccdcbaacadadaccadaddccbaddadccbcbacbbcbacbdbcabdbcdaddbadbbcbbbbcacbadcbcddbbdaddbaddacdcadbcbccadcbbdccadacacbdaaacacccabbacaaadabcacdcdadbcbdccacdcacdccdbabcbdbadbcadcaaabaaabcdbcddadbcbacacbaccadddadabdbbadbacdddddcbdddbbcbaabbcbcdcbbcbadbbadccaddcaabcabdcddcdcbdbcdaabcabbbcbcabddbdbddcddababcdadcdabdcbbdbcbbdbdccdadcaabcbaaabaddaccacabacabadbccaddaabcaacadbbcabdcdbbccacabcacdddccbccadbbbdabacdacaccdcabdaddbacdabccddcdaddadbcaccdaacaccbacbdbbadbabcbabcacbbdbaddccbbaabdddddbdabaddcdcadbdbcaddabdacaadcccddbccbdddaacdcabbaddaacaadbbaccacdbbcbddcacbaaccaacbbcacbbcdaccadaacdcddaabcdcbadaabdacdcadabddbcdadbaacbdbddcacadadddadddccaadccdcddbcdbbbacdabbabccabdbcdabbcdbdaadbacdccdbccdddaacdacacbabacbccacbdcacbddbdcababccdbadbddccaaaacdadcacdabdabdabdaadaabdbbdbcbdabaababdbdabdbcacaabbbbdcaadbccddaaacdcdbbacbddbadcbbacadbcdaccaacdbdddaccabcccbaabccaaabdcaadbbabadcadaccccdaadbbbaaaabdcacdbadbbabccdcdbcbdbaddbaadbbcadabacdccaddbccccaabcbcacdcabcacccadccabccbcbcacdbbaabdaddcccbbdcdbcaccbbaabacdccdaababbcaabaaaddcdddbcddbbacadddabdccbdaddbcbbcaddcababdabbacdaccccdcaaadbacdbddadabbccdcdaddcbdbcdadddabdbbbacaadcbdaadaadaadcbacddaacdadccdabcddbccdcdccdddccccccbacaabaaccbcabadbbcaacbabcdcabaadabcddbdaaddaaccadbcbcaacabcbcbbcbdcbabcbccbbdbdccdccdadddabbbdabddadaccbbbcaaaacdbaadcbadddbcabadcccacccababcbcdaacadddacadabaacdacabbbabcdbadcaacaaccccaaabdaccdbdbdadcbcbabaccddbaabacbaddacdbdaddddbadabbbbbadabdbabdbddbccbdacbccbdcdddbdadabcdbacdaddccbccaabbdbaccdaacccabcccddbcddbddbdccdbddccadbbcaaacadcbccdacaccdccdadbbccadbbcbdcddacdaabcbbccabcdabbcccbbaabbaacdacbacbaadaacdaabdcdbcbbdcdbcccaddbcacaccadcadbbcacdacdcccacbbaacdcdacaacbbbbcdcccbddabdabbbdcbdcabdabcaddaadcadcbcdcacacdddbbaaacaadcabdcbddadbbcacbdbddcccccaccbddbbbcadddbabbdcdacdbcbbdcbdbadcababdaaacbacacadadadbdbadaacdaabcaaabdbaddcacdbbabbadcadacaabadccdbdccbcacadbbcaaccbaabababbcccaaabdbaddcbbaabaccabddbabbbbdcccdcadddbcdabbcbdaccccbadcddbbdbababcabbbcaddddadcacbcdbbabcbcddababbbaaabcbbaadaadcaccbbdabddcccdcacdaadabdddccbcbabcacddadbbbcdbbadbdcbccbacccbbadbbaadacbdbbabaabdababdadbdbabacdabdbdbccdbcdcbbcaaadbdadcbdadaddbdbddcaaacbcabbbbdcbcabcbdabcacbdabbcdcddcbcddcccacbbdacbcdabcccdbcabaacdaaacdbbbcbcbbcadcadadcadacbdccbccadaacdacdcadacdabadcbacabaacaabdacdcbcaddaacbadccdcddcbdabbcdbcbbcbacbbdcddcacbabaabcaaddcbacdcccaddcabdcbdbdddaacaccaaabacaadcdacccbdabcaabacdadbaaccbbdcaadbbdddacbbdbbabcaadcaccbaadadbdbdbadcbaaabcdbbaaabaadbdccbbdadcabddacadccbdadbdacbadcadcdadbcaacdcbaadccadcbbdabbbbbdcabaabdbbdcacdccbbbccbdddabcacdbadacaaacddaabacaccbdacacddaaacddccbbcaaacdbcdccdaacbcacdbdcdbdbdadbdababbaacbaadcabcbaccaababbbcccdcdabadbbbdaccbcddaddacbbbcbcbbbbdcacdbccddccdbcbaadccabdacccbbbcbadaccadbcdabdbccccdbddcbdaaaacaabbbddcdcadddaabdbaababacadacabddaddcabcbbccdcbddabbbadcbabaddcaaccadcbadbacbaccadadacccdddbdacacaaddbbaccbabcdabaacddbbccdbcadabcbbcbbbddbcdbdbdaccbccbabbdababcbccabaabcbcdbdcdcdabdadbbcbdabdadcbdbcabdbcacbbdcadcccdacdcdcccbbdbcdadcaaacdabcaadcabaddbcbabaacdacaadbbdacbddbdbbcadaaacbbccbababacccddbadddbadbcaacbbdcaabddccadbacbcbccbbcbadcbcdabbcabdbdacbbabacaccdddcdaccacaabddddabdaddbcaccdabdcdbdbcaabdaabaccbcbcbdbcbdaabbdaaccdadcddddbacabbcdbbadabcbdbbbddbcacdbbbabcabdbdacdbddaabdddddbbabacbacbdadddbddbdcdbdcacadbaaaaadccaacddbdbcdaabddcccadbcccadadabdbddccbbbcccdbcbbaadbacddaadcbbadcbaddcccccdccbccabdccccdcdddbcadcdacbdcbababdbbddbddaccbcacaabbcacbbcaacadacbbacdadcddcdaadcadacbdddbdbbcbaacaccdcdccdccbcdbdbcdacbddbabcaaaaadacaacdccddadbbadbbbdcbbdbbddcbccdccbaaadbaccbdadccdabbaddbbbbddbdcdbddbaccadadbcacdbdacdbbadcddcdbdccaaaacbdbbabdadaddddabcbcdabccccdbbdbadddccbdacdddabccaacdbcaaabcadddbbdadddcccdbaabbabccbddcabccacbcaaabbbcbbcdcdccadcbacddccaabcbbaadbbdbadabbcabbbcaaaddbcdbdcaddbcbbbddadcdaccbdabcbddcbcaaaaabbccbdcdacdbcdadcddddaaaadaabaacaabbaddbaadaccbdbaccddcdcadcbbcdadbbddacdbdccacaccadbcabbcacdcaadcacbbdcbddccacdbdacacbbcdccabbcdbadabbbbbcaccaadbdcadadcdaddcbbdbcaacbabcdaccdaaccdcdacaddacbdaccaabddacdbdbbccbcbacdbcdbbacadccdcbcccdaddbbbdbddccddabbbbcbbddcbbcdcacbbcbdcadabbbdccdababaaaacddcbbdcdaccdcbacccdcbabbdbcdddbcdcdaaadcbacadaccdaccabdaccdbbbaddddccbacbbabcbbcbddadacabbabaddcbcdcbcacdcbbaaacaaabcbdbbbadccacbdaacddccbabdbaadaaacaadbddcbaccbcaadaaaaddaabdadacddbddccddaabccbcaadbdbcbbaaccbadddcdccdbabacddbcddbbdaadadcdbbdacacddcdcdadabacaabdaaadaadbbacbbcaadcdabaadbbcbadbcbcacbabdddadcbabbabdcbcadbadadbbacbcaccabbbdbdcacdaadabddddcadaccadddddcdcdbabacababcababddbadadabacdddabaddccacdadcaccbddbcccdbaaaacdaccdbcadaabadaddddbabbbcbadbbadcbaaacadcbdbcaaccbdbbdbbbddccdacaaacabbddbcdacdbcbdbdbbcbcddbcdbdddabdaddbcbdabbbaddbbccdcbabadabacacacdabbbdcbaabdbcdcaaccabdbdcbbabcbcababcadaadabcabaabcccbaabcabdadacdcadcdbbadbcaabcacaacaadaddcbabaaaccaadbbcadadcdbbbdbababcaddadcbacabaadbcddbdaabccdabdbcbcddbcdbbcdabbcadacadaddbacaabaaabadabbababbbcbaccacacabaddddbaaaddcbccababddccdadcdbbdbccacdcacccdadabaccaccbaddcdadcadcddcdccdcccbbbaaacbccadbacaccbbcadcacaabadcdbbcdcbbddccdaabdbdacbdddcdabdacaddccaaccdaababdababbaddccbaddbbbdddcddbbacbdbabbdaabdbbccdcbcaccbaabdbaccbbcdddcccaddcbacdabadbdccaccadbacdbccccabdccdadcbbbacaacbaccbcdbacadcbadbbbddbaddaccaaddaaddbacabcdbadaddbaabbabbabbbcbdaddbddbdcbbcacddaadcabdababcacaaaccbbcdaccbaacbadadcbcddbcbdbabbaabdcbbcbddabbbaaaacadbacdbadcddaabdabbabaacaabababccbbcccdcdcbbcbdbcaadaadbccabadbccdbbcbcbbccdcdcabdbadcdabcccddccbbccdcddcbaaaddccdcccaccbdbccbaaadcacccadbbaaabdbdbddcbcbddbdadbdaaaccdaaadbacbbaaabbbbbbdcccccdbadcdabbabbdaccdbddabddcdcbcdaddbcbbaaacacbdcdcbadcccbdadcdadcdddcbcabcaabadccdbbbdcabcacbacbcabcbabbcbccdcdacadbcbdbadaccdbaadacadbccdbbbbbbdcdcbdacdccddacacbbbdaabdbcbcacdabbdbddaabcbbbcddaaacaadaacdcbddddbcadbbaacbbbcacdbdacbcbccaaaacacbcbdccbadbcbcacacddcaaadaaaacbdaaadbabcbaabccdbcadccdaaaadccccaacabbacadaaaaccdddccdaaaacbbcbcbaccbdbcabbcacaacadcdaccccbbbaabcdcadcbaabadccdbadbcdbdcdccbbcabcababbccdacdcadadaaacbbaabbaaaabaaddcadacbddadadcbbadacbaddbbabdbbbaabbadcbdbadccadbbadaabdbbdaabcccaadbdcbdacaadbdacbcbcccaabccbaadbbbcbdbbcbadbdcbdcdbacbbaccddbdabacddbaaacccaabcdbaacdbcadcdddbbdccdddcaaabbcadcaabbbdccabdbbacbdacaadcbabdbdcbcddaddacabddadacacbccbbdabddbaadbbdbadbcbbbbaacadcabdccdaccdacadcdccdccbabbcdcacabadccdabdccddddacbddbbbbcabdcbbddbbacabdaadccccbcdbccccdbbbaccbbcaddccdbdadbbcbadccccaccbcbabccacabacbdccccdbdacccbcbbdabbaaabddbdccbbbcaadbacaabacdabcdcdbabadabcbabadbdcacdbbacdadcbbdbbbadcbadbdaadcacabcbcaaaabbcdcbcdbcaaadadcaabbdccbacbbbcadabdbbadbaccbdbddcbaacaccccbbddadacaadccaaacadacabcacbbadcdbabdaddaccbacadadcccbcddacdbadaacbacabaadccbbaabbbccddcadacbaddbbadddadaacabdabdbcdbbccaaccacabddcbdbdaadbdcddbdabdbbcdccaacbdbdaadabccbdcabcccbaadbaabcaabbaccddddaaacaadbabaaaacadcdddbadabcdbcabcaadccadcadabcaabcaddbdaabdcbcdbaadccbaaabbdcaccdacbcaadadddbaccdabccdacdbbcdaaaabbacdcdcddabaccaabdbaacacbdaabdbbbbdacdaccdddacdabdaaabbcdacaadcbbcdccabdacbdbbaddbbaccdbcddccdcbbdcdcbabccdacbadbbaaaacacbadcbacccdacdacaaadadaddacdcdcddacdabdbbadcdcacdcadcaddccaacbaccbababbcccbbacbbdacaccbbbddcbacbccbbabbdbbcbabdcbbccbcccdcdccbdaacdbdccbbbaccbccdbadcacbbaacaddacbbbadcabaabdaacbcdcdbbabddcabcdaabdadcbacaacbbaabdaadaddcacabdadbbdaadcdcbadbabdcacbacddcdccdddaaabaddaaddcabddabbbadaabbccaadbcaaccbbdcbbccbbabdcccacbbbdabacaccdacbccdbbbcaddadcdbcccdcccddbababbabacabadbccbaabdcdbcacbcbdabdaaaadddcaabdcadaaacaccdacbccbcacabdabbbdababbdcacdbdaccdaccdabdaacbcbcbcabdabbdcadcdcabacdddbbaadcddadadaacbacaaadabdacbbdcabbaccdddcacacadcdbbcdaabcdabbcbcdbbccbabaacaadbcacdaddbdaaaacacbcbcbabbbdcaacbcdddbbddcbbcddcbacacbacaacbbdcaddaddadcdbadbaabbbdbdbacdadacdcaacbccdcdaadcabacdcbbdaabdadacdcbdbddbadadacdaaacaaddddddaacbbdbbccccccbaccadccdabddcacbdcddacabcaccadbcdccacabbaadbcbbccddbdbabbdcaaaacadcabbdcadbcabdadababccabcbabccacadadbdcbacacdacdbdcbaadcaadbcdababdccdcbbcadaddcdaaacaaaccccbddbbcdadaadbdbabcbadaacbaddcabdccacdccaabadabccccdbaababdbdcddbddccdbdcdabbcdbdbccddadbccccadabdbddbbacbbbadaabccdabbbcdccacdbcbbdbaadbbbccbcadacbdbaaadabbddbdcbcddbbdcddabadadcbbacbbbdddddbdbabcabaacbdaabcbccdbddbabcbbbaabccaaacdbcadcbbccabcdaadddccbbcdbdabcccddacabdcababcbcbdbdbddcdccbbccccbdddbccddabbacbcbadcaacdbdbcbaddabcdbcddddddddbbdadcaccccabdaabcdcdcdcdbcdaadadbccbcdaacbccccbacbcadcccbbbdabaccacaacadaddcaddabdbddbcacaabcdcdbdaccccbdcdbdcccccaaaddbbadcbdbbcaaabcddbcccdaaccabcaccadcdbaaddbcbbaccbccbaadcdbcdbcbbbddcaddbaadbbdcadcaacdacbbdbdadddbdbddccdccacbddbbccdddcbdccdbcabacdabcccaacdcbbcaacadacddacdcdcbccbabaccccdacbbddacadcbacababccbbcbbcdacaaccbadbddcbbbbbbbabbcbcabbacccbcbdacaccdbacabcaacbbadadddcacccdbcbddacaaabaacddbdcddbbaaccacadcccdadccdbccbbcdbccaaacdaacbaabdcaaddcadbcaabddcacdbabaabdbdbcaddbaacdabaadccccadbabdaaddabaabcaacbbdddcbdbcccccdcabdccbaabbacaabbbdcadbccadaacacabcbbabcaaddbcbbdadddaaaddabcbadcdcabdcabadbcccbdbbcaadccbdbdcbddbdcaacccbdaccdbdaadbdbdcacccbddadaaacabddbaadbbddbdabbdcddbdbddadcdadbacccabdcdacabaaadcbccdbadcbdbbbcaabcddbadaaabbcaadcbcbadbbcbcddddabccabdadccdacdaabacdccadcaabdbaadaddcdadbaaabbcadcbaaccccdccddaaddaadababbbcadcbabdccccdbdbacbdcdcabacbcccddaacddaddaddcdabadbabaaaaacbcdabcabdbbaabcadcdcabbdbbdbaaacccaadcbbdcbdbcbddddcddcacbcbabbdcdabaacabdcbcdcdbdacbaaccadbdabdadbacdadcaacaadadabbaabadcaddbcdddcbdccccbababacddaddccabdbcdcabdbbcdbaddaccbadcacbcaccdbbbbbabcbcdcbaaccaacaadbcadcadcddcaccdddadabcacbccbabbbbcabcadcbaabbbacdcddddcabdddacabbbcabacbbccccbdabdcbcabbcaadadbcdbdbcbadccbcbdcaabdbbbacccabdabcbadcdcbacbbcddccdcdabaccacccbdadabaccbcddbabdaaadccadcbabdcddbbbdbcbbbcdbbdccacaacdbcbcaaccccaadabccddcbcbbddacdccabadaabcbadccabadbdcbaacccbaaaaccbbccdacbbdaadcbdaaabaaccacbdcddccadccbaabcbdcccadcbacbcdbbbdbdabcadadddcadbcdcacbdaabdabdcddcbcabdacabdbbaacacdabdadcbbdcdbcdbcbcbbdbbcddabbbbabcdabaaddabdbbbbbccabbacbbbbdbacdcaaccbbbbaaacbabcdcbdbdbacdcdadbbacbcdddccddbabacadadcdaddbbdddacbccdcdbaabaccbadcdcbbcbbacdcdabbadcdbcadbaaaddbbcabaabcbbdbabcdaabadcbaccaabccabaccaabadadccaaabbccaadabcbbaacbadadccddaacabdcadcdcdcbabbbddaccdaabbcdabbdbaacddddbaacdcdadcdacabdbccccaccbbddaaaabdbcdabccccaacbbbdddadbaacbcbdccccabbacadacdabbbccbaccacccadddabdbbdccabbbabdbbddcdadadbadbbbabddaacacdabddccadacbacabdcdbbbcacbdaaccabdbddcadddbcabcbbbaddcdabadcbcdcccdaaaadaaccdccbdcbccbaddababcbdbcabccdccdadccdadaadcaabdbabcccaaabcbaadaddbdbbbcbcabdbbaddddaadddbdbbdbdcaaddaaccbbaacbdbcaadcdbbdcdbbcbaddbcdbddaaaabcdccbddddbdbabbcadabcccbbcbcabdadcacdabbdbdaaabddbdbdcacdacabadbcddadbccaacbcbabccadbaabadadccbdadddcbbadacccbbccabcdddbdbaadbbccadccddcccdcadabadbcaadcdccbaadddbcddbbaaccaabdcdbadadddacacbaaccdadcbdcbddabdbdabbabdabbdcdcccdbdcbbbaadabdddbbbbcaaabcabbaabccbddcdbbddbcabaadbddacdaacbadbabaacbcacaaadbbcbddaddadcccdcacdddbcdbdbaadadadcaddbdcccccacbaccaabbcdacabccacabcabcbcbbbaabbdbbbbdbbabddabcddbbccdbbaccdabbcbbddcdaccbcccacbbcdbdadcabcdbcabaadddcdbcccabdbdbdbbacdbbcdbdbdbbabacdbcacddaadaddbaddaaccbabacaaadcbacbababccacbdcdbabacaaccababcbbaaaadacbdccbbbddddddbbcabdccbbbaaabaccaacacdddbbbcadbacbbadabaccdbdbababcbbbcaadcbbdbddabdcabdabacbabcacbaacadbdccadbbbcddadbccacdbcdaabdcccadcaaccbcabaacbdaaaadacabdcdcddbcccddcdbbbcbcbadbccaddccbbcbadadcddacddcbbbdcbbccbdaddddbdbddaaadbabccdccdbbabcdccccaabdadccbabccdaababbbcbabdcbcacbbdddbddbdaddbcdacabddadacabaabcaaaabaabddcbbbbdccccdcbcdaddccbaaababdbcbaddacdcdabcabcdddcdcbacabdbccaddcbbaaaddbdbaadcabcadbadbdbdbdbdacdadcdacbaaccdaccaccbabcdbcdcababadadbdbdbddaaaacdbddbbdbaddabcababdbbbdbbbccdbddaccbacbbdaabacacabcddcacaddddaabbbabcdbaabaacdaaccbacbabcddbdadaccbabdadbdcdbcbabcdacdadccadbcdcbaaabcadacbcdcbabdcdbcbdcdbadbbbadbdcddcacbbccaacaddcadcaadbdaccbdbccdcddbaddbcddacadacbcadcbabbdacdcdbdabbcccabdbbcddcbcddcaadddcaabbbbacacadacdbdddbaabaaccccaddaaacabbcbaadacdadcaaaacaaaababaaddacacddddaabccaacbcbddabccddbdcbcacaacbddadbccbbcbdabdbadbdbcacbdbdcdabdadbcdbcdcacabaaacddbbadbdaabcddccbccadcacacaddcdcdbcbbdbcdbddcdadadcabaddcdaabbccdcabccbbcbdcddaabbbddbaacbadacddacacddbaccddcbadddccbdcddbbbcbbdddacaacbbddbcacbbdaacbbccacccdbadbcacbaaccbddbdaddaacbadcbadabdbaccabddaccaccadbadacdaccdcbcdcbcccddadddcacdbdaadaadbacccccbdcbcadcddabddccbcdbbadbcccccacddbbcdcaabadddcbbbaccbbcdaddbdcbcdabdcbbccbaadbaddcccccddacbcadcdaaddccdabbacbbbccbaabbadccccaabbbcbacddcabbccadacbcccccaacaabdadcddcadcdbcbaccbadcbdadacaaacbaacaddcbdbbdaaadbbbaacdadccdcddbccbbddaadaadbcbadbaddcddbbddcbcaadaadcdcadbddccbabdcdaacaddadccdaccdaaacbadcaaabdccddbcbdcbddcbbbcbaadabaccdbcdccaabdbaabdaccdbcbabcabcbbcbcbcaaaccbcdcdaadcbaccaddccdabcddcddcbbcbcaaaaaadbcaaccacaaaadbdcbbadbbbcdcbacbbbbddcdacddcdddcbddbbbccbabbdcabccbbddbbadacdcbbbadadccbaabcbbbabdcbdbabaccaaccabcbddacacdbbdaacbcbdccaacbbbcabaadcdccbdddaabcabdbcbabbbbcdaccccddcbdcacbbbbacbbbdcaaacdacdbcbacacaddcbdbbcbbdccbabadddddccbddbdddaaaabbaadbcdbdacbaaabaddadadababcdcdcabbccddbbdacbdaccbaabcbadacbdcaacbacdddaddbdcadaabcbabaabcccccddcdcccacaabbdccaddacbbaaabdddcdbcabbcdbaccadadcabaaabbbadbbbaacadbccaccbbcacdcccdaadadaacbbdccbbdddbabadbdbaccbcabcacbcccadbbacddbcdaccacdadbdbcddcccbbcdacdbbadbbdaabbadbcacaabbcbaadcaadcbcbdbbcadacccbbaacbbcacdacadbadaaabcddcaddcbbaaddcdddbcbbbacadbcdbcaccbabadcaacdcacdacbcdcccaacbccacaddccdcacdcabcbadbdabbacbbbcbacdbadacdacdbadcdaaccdabbcabcadcccaadcbdbdaaccbabbccaaadadacabbaddbbdcbadbddccaddabababbacacddaddaacbdcbadcbdcdcacdbdbddabcbadbdbcbcaacadaccdcdbcdcabacbcbbccbadabddcdaacadddbbdbbabadacdbbbbadcdcabddbbdbacdaacdbabadcbbacadbbdddaaddabacabbbcbcccbadabdaadccccbbabadccacdaaacccbdababcdbbcabaddbcddaabdbaaacbabbaadcadcbaddbaabccadbdabdcacddbbbcccdacbcdccabacdabdabbdcabccddabadbacbacccbaabbdbdccdcbbdbccccabbcbabcdddacdbcbcbcdaaaccaccddbbcdbbbbaacbdadbdbadacbcacbbdadcdcdccdabbdaabbcbabbcbadddbdddbccacdddcdabacbadabdbdcadbbbacdbbcadbaccccbacbcbcadaabbcdbabbaddabbdcdbdaacdbddbacddcaaddcbbabbbbadbccbcacdbabdbcacbbcacdaacbadaadaddddaacbcbddacaaacbdcaaacdaadaadbdcbbbbabbcabadccdcbdbaccacccdcbcdaccdbacbadbacdbaacbbbcdcdabacacbbacdaadaacddcaacbddbdcabccccaababaaacdacdadbcacbaacbbdddcddaabaccbcbdadddbbaaacdabcbdaabcbbaddcddacdcdccaadadbdbbcbdacdcbdcccdcaccacdaadaddacacbabccadccbdabcbbdadcaabccbcdadadabdacddcddcaacccaadbdbdaadbbbcddacbdbbdabdccbabdddbabccdcdadbcbaddadacbddccbaabbccacacacbbaddbbadbccbddbccbdaabcbabcbdbdaadcdccbdccbbdcaaddcbbabbdbabbbcbdcdcbcbcbaaaddbbacbcaabdcdddccaabbadcacacaadaadddadabacabbbcbcdbdddaaaaadadaaacaaddcddaababbadadacbbbcbaccbcaddaccbcbacacabadaddccbabbababbbdacbaacbadabdacbdabddadbddccabbbcdddbacbabcaccbabcaaabbccbbaccbbcaaddabdabbbacccbdddbcdddcaaaadbdcbbbdbbaddcdbabcabbabaaabbaadabaaacdcdadcdbbcddbcddcabcdbbcacdadcdcbcbcacabbbbbccbdddabcaacadbccdabdbbcbcaccabcabbaadbbacdbdcdabbdbdaabdabbbdbccdaccbdcdacbddbbcdabacdccbacdcacaabaacaacbbadaabdaddcbabcaadadbdcbacbccabaddaabdaaadbccbdcaababdadacabacddccbcacdccabcbdadaaacdaadbcbcccdcbabbabaccdcaadccddbbbcddaddcdbcddcacdcacdadcdacbbdbdaacdbadcbdbcaabaccdbbccbccdacabcacccbccadbadbdcacbbdbdddbacbdaabddddcdcbbdbadbdcbcacddddcddaacadbabbcaacbccddbdaacabbdcacdacddbbccacccdccdcdcdacbbacdccabcbbacadccdcdcabacbdadcbacdadcdcadcbcaadbbcdadbacadbbbbcbcdcccdaddddccccbabaaaacaabdccaabdadddcacacdddbabbbacacdbbdcabadaaaaadbbaccabcabcbcccdbddaddadbdddcdbabccbddcbbababcdaaccddcdddcacacdbbadacbcacccacbcbbbdaabdacdccaabbadaccbcdbbdddabacdcacaaccadacbdcadbaaadccbbbcccacdbadabaccdaadcccbcdacdbbcdccbcdadacbcdbacbdabcccbccacbabdadcabbcadcdbcdaddacbbbdaabdccadddabaddacddbdacdabcccccbdcaadbcaabddcadbcacabdbbabacabaaadcdabcabdcaccbbdcbcbcbcbbacddcabbdadacdabcabbcdcacacabdacbbcabdabbaccddaacdbbcccddabcdcdaddbccbbaaadbcdbcadcddbbdcdbcbccccaacaacacbadacaddbababdbbabccbbbdabbdcdcddbadddadbccccdbbccabaabbcadabcabbbabaacdcdbbcccbaacaaabcccdbcbbabbbdacbccbcabcccaadcbdbbbcdbcbdcddaccdaccbcbdaabbadbabccdcdaadcadbdbdacbaacacaadaddaccdabaaddddcbbbcbdbcdcccacdddddcdbcabbbcdbbdcdbcddbddabccadcadbabdbaadbbcaabbdccbcaadbcdcbababbdabccabcbdacaaccacacdabbbdbcaccdaddccbaabcbbcccacbcbcbabdbabcdadbbcaacccbccbdcadaddabbbdcadabbaccadbccddabaccdbabdabdaabaddacaddadaadadbbadbcadcbbcbbddcacadccdabdaabadabaaababaaacdbcacabaacdaaadaacaadabadcaacbcddaacbbcbacdaccabdabadddcbcadbcbddbbddaadccacbabbbcbbadbbabcbbcdadaaddaabadddbdbbabcbcdadbccadacacbdcbcadbaddcaaacdcabbdbadacababcaaabdabcdbabcaddbdbdbbcbacbabbaccaaacdcdcccbcbbddacaddbaccbabcbbdbcdcdcbcbdbbbdccadadccccaacaddbcacdbbdcdcdabbbadbccbdcaabbcbcacddaccacddadbcbddaaaaadbcbbdaddabdbdaacbbbaabcabbacbdacacadaacbcbaccadadcdbdbbcaabdaacccdcccbcdadbaacddcbdcaaadbcdbaacdabaabcbdcbbcabcdcbdddacdabcbbcbabbaabcadbabadabcddcaaaadbdbacacdaaacccbbaadbdcabaaaaabdccdddbcdabdcdcbbcaaccdacbcbccdbacdaabcdddcaddccadbbaaabcacbdabaccadcacddabbbddcbcdadcdcbadbdcbdcdcbccacdbbcbbdbbbbbddccacbdddbcabdbdabdbbbbaaacdcacbcdbbacdddadbcadbddadbcabaaaaccbacdcdcbbddacdabccbddbbdaddcbbaacdcbcccccbcccbacbbcbcbbbbcddddaacacabddaaadcdacbadabbabccaaadcbcdcdabcbccaadcccdccababbbccbcbbdaabbccabaabbababcababbdbcddaddbddadabcbadaacbbacdaccbaadccddaacbcbdcddabbbddbccbabddcbacddabbddabcccbdadbdcbdbacbbbaabaddadaddddbbbacbdddbaadcdbaacbbbdbdacacacadabadbbccabdcabdaadadddbdcbabadcccadbacdcabbabdacacabbdbbdbdcbbadbbcacdbbccbbacacabbabdbdbaaaaadddbcdbccdaabcaaaccdcdbdbcddabaccadcdacdcdcbddabbcabaadaacdcaaabaddccdadadbdacbaacdacaaabddcbdbdbbacacbbccabdbadddacadcdbbcabccbcdaabddcbabdabddadbbabdacbbdaaaadcdadbaacdbbcbcadccaabaddccacaadbadacddddacdbcdcdbaaadbbacbdccdcbdcbdaacabdacbcbbcadcaaabacbabdacbabcdcbcaaaabbdadacbdacddacddabcdbacadbdccbacbbcbdcbbbabdcbdbcddbaaaadbbaaaddabbbaddcdbcbdbacbbcdccdabacbcbacccaabdbccbdbbabcbcbcbcdbdabcacbacdcccbccbdaababcbbcddacccacdaccdccbbddbaabbccbbcbcbbcaaddaacbbbcadcbbacdbacdcabdbdccdcbdadabbbbabcacdabcaccadcdbdbbdaabcdcacbcaacacdbddddccaaaacdbdcabaccadddadbabbdcbaccaccddddaadbcbaaaabcbbbcabccabdcdbbbabbddabbbaaaadcccaddaccdbbdcbaddbcdbcdcbbbdcdbabaddddbccadbbddbccccaabbbcdadcbbdbbccccadcbaccacabcdcccdadbcabdcbabaaacbbbdacaacdddadcbdbadbcccdaabdbacdcabdabaaacbadcccbdadadbdbccbdbadcbdcbdabacabbbbaadaadbbccdcacdadaacbbbccddbaacccbbbabadbbbcaacadbcdacdddadcadcbdbacabdccbdadabaadbcbaadadddddcadcaacababbacdbcbdabccabbbcbdbabbbbccdcccaddaabbcbcadbababadbccdcbdaabdabadbaaddacadcbadbcadcbaccbccbbdcbcaabdbdccacbdddcbadadadcbbaaabcaabddadaacdadbddaaddbacbabdccdbadabbcadbdadbadddaddbbcdcdaaabaaacbdbadbccabdbaddaaaaaadabdcbcabcbddbddaaadbcacdcaabcdddcacbcccccdadbabbabbaddacbdbbacadacbdcccabbabcaaaddcbcdcadacbbaaddbbddbcdcbadaaadaadbcaabcbaadaabcbabbddabdadddddcbbcbbcaddbcddacddaddcaabadcddbbabbdacbcdadadddadbabdcdbdddabadbdbdccbabdcadbcaaddcdabdccdbccaadccabbbddaacddccddcaaacabcdbcadabbbccdccbaddadcbabaaaaacbabacacbcbcbcdbbddddcbacacaabacccaddddcccbcaacccbcabaddbababbcbaabcdbacadaacbcdcdccdcbccddcacddababbdbcaddcaacaacbbbdbdccccdcbcadbcbcddadcccdadaacbccacacbddadaccbbdaababaddccadddadbbbbdaaaacbbdcadaddbbbcabbcdabbdbbcacaaacabdabbadacaacdbababbabdabdcbdbaaaddbaadbdccdbabbbdabbbbbddcccbccacbadabdbaabaadddddcdddcbdbdcbbaadcbadcabccbbcbadcaaadcbcadccdddbbbcbadbdbcbabdbadbbcbacacbbbddbbdadbccacabdadcdbcbcddcacacdbcbbabbbaaadadcdcabadddcadbdaccbcccbdbbccdbbdbcadccbdaadcbccccdcdabcacbbcccdcacabdbaaacacccadbbdddadabdcdadbdcbdcdbbccdcbdbacdbabbcddabcabacdbaadccbcdaaddccccdababcdcadcbaadabdabbbdacaacadbaadcadaadddabacddccaccdaaaabdacbddcdadabdbaccbdaddacdcaabcbabaddcdbbcbbadbacadccdcbdcdbbdcaaabbbdcccabdababadddbdccbcdbdddbddababadaaacdacabbdcaaaacadcccacbdcabcbcabbbdaccbbcacddabbccaadbcbcbbcabdaadccababbaaccdcacbbacbcadbabababcdbccbabbaddccabaacbbcaddccbadbacdaaabbaccbbcbabdacacabadbdadbbbccdacdcabdbbaccacbbbddcbdbacbadcbbbbdbcdcbcbbbcbdbbccdcaccbbcbaccddacabcdbcddcacdaaadbbacabbcabadbababbcdadaacabbcddaaaabdcbcacabbcadcbbdcbddbcdcbaddcadbbabaabacbddcbdaaccbaddcbbbcbaadcdbbaabddddbdaddcbaaccaabaddcbbdcdbdcdacbdcddaaabbdbdddddbdddddabaadddcccbdbbcdccccccacabbadacdaabacdadaabcadaaaabbcccddbcbcadddcabbdbccaccbbbdcadccabacdbddaacbdcccacbddcdcaaaaccdacabcabccaccddbdcdddcdcaacaccaaabacbdcdcababbdcabddbddcbbcddbcbdcbdcbbddbadcaabdaaddcaabbdaacdccbccbaabbabccbbaccbbcadbaadbadabdadcdccbacaacdcbbbaabddaccbbbcdcbcddbbcdaddccabbdbacbabbabdbcbacaababadccdabcdacddbdabdaaaaddaddbddabbbcccaaddaccaddbbabddcaadcabaabdddddaccdacaaabddadbccbadccddccacacaababcabcccdbdadbdbccddabacabccbcaadcbdccacddbdcaddbbbccdbacacdaaccdbccabddaaadabbdadacbcaacddccdcbcbbbccbaddabdcbcddbcbbddcbbadbadcaddadcbadcbccbabacdccdcdbdccdcaddcbaabaabadbdbcaabcdddcbacaacaacccdddcdcbcadcddbbbcdcaabaabcbcdabdbccbccaaabdadcaadbaaababdbaddbaadadcacacdcddcdbdcbddccdbdaadbbdbcdcbcdaacacddcbdadbbbbaccddbcbcbadbdbddaccaaccbcbbbbdcdbacdbccadddcadabdaabdbdcdddacdadabcbccadadcccaccddbdcadccbacadbbdaabbacdabdbaddaaccdccddbaabbcaadbcddadbbcabbddaadaaabdbabccbddcaacbabdaadbcbdcdbaabbbbaabdbcddabacaabbabbdddacadcaaccbaaaabbdacdcacabcaacabdadddbcacdcacbcdbaabaadbbdbdbdcdcacacccdddbdddcbbadbccaabbcacdcabccaadabacdcdbacadabbcbccacccdbcbcdaccadbbdbaccccabbbcacdacccdbbcadacababbccbaaddadbcdabcabbbbdbaabbddcdbdddcacbbabbcbaaadcccabbadbdcccbcdacddbcbdacdbcdbacadccacdaaacdaadbccacabbbbbccdaacabcadcaddaacbcdbdccbdbcdacddaacbcddcabcbdcdaddddbaaaadddabaccdbaacaddccbbbaaabdbdcacdcdccbbaaadadacddcbcddaacbbaadcdabdddbcadaaccadddaaaacadddbcababdcddaddcbcbabbbdbabbabacaabdacddabcbcdcbabadbcadcccdabcbaddacaadcbdaacaadaabcacdbbbdbbddcdaabaddbcbdabacaaccdcccbbddbcddabcdbcbbbccbcdacacddcdbccacdacccbdbbdbcadabadcdcdacacabbddadcdbddaabcdcbacbdbdbacacbbbcdcdcdcadcdaccbaadabadbdddabcdbddcccbdcbacccbdbadbccbbcababaadaddbdbdadbaccdccbacbadaaddbdcdacaaabacbcdbdbddbaccbcaacacdbdcbbcbdadcdcdaccdddabacbcdbbbbbdbdbbbcbabbdbcbdbaaabbbbaadcddabcccddadcbbabcbccaadbdcdbcbacbdcdccdbdaaaabbbabdbddcdbdadbacadcdcdaabdaadacdbddcdbabdcbccbcdbdbdcddcbbbcadccbabddddcbdbacdbcdbcdbdbcbaabcaacccbcaaacbdbdbddacbddabdcabcdccdbdcbdbabaaaddcccdbcdcdbcdcdadabbaabcdbddaccdabcdadcaddcacacbadcbbbdaddacbaccbbcabbdadcaaacacbabbbdbccdbbdccbbdbacdbdbcadadccbcaaccbbbdbbaddbbacadccdabbddbcacadcbbcaabdbbbbaacadcdaacadbcbccdbcacdabadccabcaabdcddcaddcbadbbaaabbcabcabcbcbabcadddcacbbbaaaadacddadbcdabcaabbacaddcbcbaabbaacdbdbbabcabdccbccddbcaccbabbdbcddbaddadbbddcdabadcdcaaddccaaadcbaccbdacdccdaacbcabbbbcddbaacbadbbcdbbbddbbcdaadadaccbabadccaaacbccbdbbbaacacbcdbbccdcaaccadbddaacbdabcdabcaabcaabadcabdbbcdbdaabddccbcabdadaadcdbcacdabaabcdddaaadddddabbdadbcabcaadacdadccadacbacbadbaabdcacaddbddaddddbcbacdbcadbbcadcabcccaabbcbcdacddaddaadabdcadbbbdcdbddbcaaacbcdbcaacacdbbbbacdbcabcaccbbcccbadabbacbcbdbcdddbdcbaacadccadaabcdbddccacdaadcaacddcccbbbbdbdcabbcbcabdabccbdbbcbadccdaabababadacdacdadbdbaadbdccdaaadcbbacddbdbbbaaabaaaacbdbbcddbaaaadcababbdcdaaabddcabdcbccbcbbcbcacbbdcdcbbaabbdbabadbcabccbbbdddcddccddbbadcdbddbbccccdcdcdcbbdcaaaaabadaacbbabcababadbaddabbadaaabbccdaadadcdccbbbdacdbbcdcdcbbabcdbddcbbbdcbdbacabbaddcadaccbabdcdcbbbaddaacbbdcccabcabadbdbaaaadddadcdbcbcaaaadadbcbabbbbaabdbaaccbddbaababcbdcacabbaccccaaaaccdaddbcdadacadddcdcccaacadcaaacadaabdacbbadcbcaabdacbdddacbbdababbcadbcdcadabdbdcdaabbdbbddadadccdcaaddabcddadbdbbacaacbcddbaaabcbbabdbddcacaabadacdcdcdaccdababcccddabddbdbccabbbdccbbccbdcabbddbbbbcbacbbaccdcbbabadbcdbbccadcadcccdcaccaaadbbccccddadabaddbbdaddcadddbbcabcabbcbcadaacaaaccdccbcaaaccbaadadabcbdbcaccdbabcdbadcaddadabbcadbbdcaabbbbacdcbbabccccbddadcbdbdcaaabcabadddbbbbbaabdbbbccbcbbbaabccaadcdbaacdbcdbbdbdadccbdacdcbdbdddcbdccacbabaacdbdcbccbadadabccdbbbbcaccddbbaacdcaabddadbdbdbdbacddaccdabcdacdcbdcdcdcbaabbcdddaadacaaadaccaaabcbcdcdccbcbbbacdcacacaaccdbcaacabaacdcabacdbbddbbcbcadbbccaaadacbdacccdabbadcaccadccdcbbbbaddbccdabacadacacdddbdcdaabbdddaabaabcddcccacadbabadbadbddadcbcacbdcccccacacdbaaddccaccadbcabbababbccdaaabdabcadbdbaabbbcddcacadaabcdbdcdcabbdbdcacabdaccadbacacdcbadbcadccccabcadcbcacdadbcadaccabddbadacaddbcabbcddbdaddbadcadcdabcbacbcbdabacdcccdbcdacbabadbaccaccccdbbddbcddaabdabaccabcddcbcbdcccbccbaacacadcbccadcacdacbbbcbaddbcaaadaaaaabdbbbbbcbadcbcababccbdcdaaaccbabaadbccacdcdcacaddadcccdbddaadcdadbdcbcbcaadaccbbacdaaabdbcaddadabcdccdbcbabdacdcbadadbccdbcddddcbdcacaaaccdadbbbccbaabcccccdcddddcbacaacadbbbcbbdbabacadbdabadbaadcddabcbbacccbbbacdaddcaaddbdaaacddaabccacbbdbaabddcdaccdabcbccbddcaabcdbdbdcdcbadbdcbbbcddbdbccbaaddabacaddaadcbdcdbccbdabbbcaacacddbcbadbbabcccadbbddcdabdccccbbcadbbbbaccacbdbbbcccabacadddbadcdaccdaadbdcbadcbaadacadacdaacbdacccacadcccdbccdacacaddaaaabccaaaccccbaababcdbdbbccaabdccbbbadaabbcddccabcdacddcbbbdcdcbaddddaadaadddaddacbbabdcddddbbaaddcabcbbcdddcaccacaaddcdabacdcbadcbdcccbaccdcccbdddbacdcaabcaadccaddacacacaacccccdbaacdccdbbcbdbbdbdaaadcaaaacaabadbdaddbbaaaddaddcbbadabdbabdacadddaccdbbaadbdbbdaabdcdbcbbbdaadadcdcbcddddaaccdaaacccdddcbcadacdbcbbcddaadcadbadbadbddadbcbaadcadddacdcccdcbcdcdbcbcddacbacadadaabaacbcacaccbcbcaadddcbabcdaabbddaccaadadaadababbbabbcbbbacddddddbcbacbadbabcaccbbbdcdadcbcbcbddbacabddcdcbbacbddcdadcddadbbdbddaabcccbddbdccbcbcdbcdadcdcaabbdbddaadabddddbbadcabcadcaaddbadaacccdbacbcdcdacddbddddbaaadbcdabdaddbdababbdbbcacbdbcaacacbbabcccdadcbdcdddbaadbabcdbbcdcabacbdcbbadbcdcbdcbdbaddcbabdadaaadbacbbbacdbbcadcbdcbbcbdddcdddabbaaadababddabddabddaaabbcbddbdadddabcddcdcbdcccacdccdcadaddacaaacabacacadbdbbaacabbcabbacacaabcdcaaccdabbabaaadbdbadcacbcabbdbdbbdccbcdccbabcacdcabdcadccbbadbadabdacdcdbdcbbdcaddddbbaaaabccddbabbdadadbcaaaaaccddcdabdbbabbaacaaaacdbdcdacdabaabdcbbababdbbbbcccdcbdbbcddadddbabbbadcbbcbcabcacabdccbccbcdabbdcbdbcaaacdbbaddcdaadabccadaaccaabaabbdccdbadbabbbcabbaccabdbcabdddcbdddbbdbdbcbccbcbadcdacbaabcdcaaacdcbcabcaadddcacaadcbcdabaabadcdcbdddabaacacdcadcbbdcdcccccbadccaacbaacdacacacddccaacacaabccaadbbacddcaababcdbbabcbccbbdccadbdaddbdaaaaccbbbbbcbbcaacdaddbbcabaabdbccaacdcadaddadcdbddabdcaccabcadccbaddcadbccabccbddcbdaaccbcccdadcdabcbcddabadbcccaadbccacddadaddabcdbabcbcdbdbabacbadbcccdddcbcdabadcbdbdccddbbcabbaabcacbcbbbacbbcbdccbbbdbdbcbacbddbbcaacacdaaccccbacaaadbcaaccdccadacddadcbaccccbbbadbaaaaacaccddbccbdbdccadcdbdadaccabdcaaabdaddcddabcbacbbdbdadabbbcbbcbbabacadbcadacdbdcaadadaaabccadabbbaadbcdddcadbbbabdbcdabbbaddbcdcadcddbaabbddbccacaabbbbcdadaddbabbcdaadbbdbddaabadacbcbcdbcccbcaacacbabbabcbcdccabbcbbddaacaaacdcbadaaadcacdadcccdbacbdcadcbdbadcacbdbaadcdaadddddccdbccabadaddcbcbcdbcbbbbdbdcddbccaddddaacadccaaadbbabccdcbbbbdbdabbdcaabdbccdcdcabaddacadbdcacaabcbbcddbdcbbbccabdacdbbacddbadcccbdddcddddcacbcbbaadabcadbaddaadbaddbcdbbdaabbacdbababdabcdcbddbdadddabbdabcbaabcabbbbcddacdaaacdbcdabbbbdbbddcdccaaddcdbacdbdbbdcccdcadacbaddbdbcaacbbcbabcbabacbdababacddccddadabdbadbadacccabacbabaacaabadddbabdaabdccbacdcbdabbbdaadcbadabcaaaccadddbdaabcbcdccabbbbabcadcdcadbdcccccdacaaacddaaabccacccbcbcacbbbcbaadaddacddcaacccccddccddcabddbcbcacabddbcdbbabaacacbcbbbadbbbccdcbaaaddaccccdcaccbddaababcbbcdacacabddbbcbaadddbdcbaaabaddbaddaaabdccddbcabbcdcdddcaabcccdcbdccdacbaacabaddacaddcbcdcddddcdcdabaccdbdddcbdbbabbccdabddbcbbbbaddbcadcdcdaadacacddcbcaccdaacdccdcdcdbdcddbbabacdccbdbcabbaadcbadacbdbbcbaaadbdaacbaccaabddbacaadcbbbdddaacbdadaacbacbaaaabaabddcbbdbadcbabcdbbcbdaddcbbdbbadcacdbcddbcabadbaddcbcddcccbdcdbaaaadaadcbcbcaabccdcaaaadccbdadcadaccbacabacdcdcbbbbcabacadcccabdbcaaaadadddcccaccaabbcdbdbcdaabcbddadbacdadcdadacaddcaacacdabcbacdbacaccbccdbbbccdddbbbdaaddabaccbcddddbdaddcddccdcabbcadbdcdacbdabdbacbbacccabbcabbdcdbdcbcadcdcaddbbdcdddbbdadaacddbcbbbccadbaaddcdabcbcbbdbddddbcbccccbdaacbddcdcbadabcadcabcdcaddacadddacadcdbacdcaddadacddccbcacddcadbcdabbbccacbabccabdccdbadcbddccbaaacbdbbcbdabddaaddbaacdcbcbcccabbbdbbacddadaddabdcbabcabcacabdbddbcadbbdbbdaccddcbbcccbcadaadbddccaaacadbcdaaadadbacbdabacdcdddabdabcaddcdacbbdcadacacdbcdadbcdadcbcddccbacabdcabcccddcccabcbbdddccdbcdcdbadadbdaacaaaddadbbaccaabbcadacbccabdddcacaccabdadbcadccddaccaacbcbbddabdbadacabdaddccbdacacddbacabccdddcccdadbcbcbabbdbbcbcdcbaddccbaddcacccaababddacdadadaabcaaddcdababddbdbbdcdbbdcaccbdbbbdbdddccdbadbcadbbbbdbabdabacbccdbccbacdabaababacacdabdbabdccbcaaaacbdcabaadddcaddbcabbbcaadbbcbaacbbccabcabbcdbadcabdddbdbbcdbbdcdacccbabcdaadaacadcbbccaccaabdbdccbdcccdcccabcbabbbbcababcadbdccdccaaabacbbababcddadbdccdcabbcababcdacadbbccbccbbaabbbcaccadbccdddbbaabcbdcabaabcdcbaaadcdbccbacdabdaccaccccbdadbdcdbbdcbcabaadcdaaaaaaddacdacabdbcdbdbcdabcbabcdaaddaabbdaccdcdcdcaaacccbbcbccaabcccaadcadcbbdacdbdabadcaddcdddcbcacccdbcdddaaababddccabcdbabdcbadcdadcdddacaabaabdcacadcadabbdabdccccaabacdcbcdcabaccbbcbdaacdaaaacddbcaaabbbdbbbabacadccdaacabbdccddcadcbcadcbacdadcabcdcaaabbcdcdacdddaadbaabbcaabaccbababdcacacadcdadcacdbbaadccdcdabadbccccbdcdccdbacbacbcccbdabdbccdcddcdabdbdbbacdcddaabccccccbcdadcdbbbcabcbbdcbbbbcdbbdcdbbcdaaabcdddddddbcdaadcdddbcbcbdcababbbbbbcaadbccccacdabddbdbbabddabaaaaadbbbccabbabdbadbadcdbcbccaaadcbacabcbbcddcccdcaabcabdacccabbccbcddaaddbbcdadcaabcbacdaacaaacaddddcabbaccccbbdcbbabcccdbdcbcdaadcbaaacbaaccbdacbdcccaabdbccaacabbabbbdbcdcdddbcccdccbcbcdadbbdbacdaaacdccdbdbaccbddcccbdcbdadadbddcdbcbaaddccdcdbcbadcadcdbcddacadbacbcacbabbabccdbabcadbbdadaaabbadacaadbcaadddabaccadbcdbccabaadaccdbbadcdaadbcbcbaaadcaaaabacbccccbcdcaacdcbdddbaabaacacdcabaacbdaacdcdbaaccdbbabadadbbaaaaadaabcadddcdabcdcacdbcccbadbddbcbccaadcbdadcddabbcdcabccaccbcadcbbababcbabbbaccdabcaccbcdddbdcaaabddcbacbbdccabcccbacdbcacdacdcccccaddbcaabdbadcaacadcbbccaabdddccbccdcbbcbccccbbdccbccabbcdaccbcdbdaadbdddabbcdadbacbcddcbcacdbaaadccabacdbbbcdbcadabcbcbcdbbbacdabadadacadcdbbbbcccaaadcdcddbcdbbdbdcbdabbddabcabdbbbdbcbaccaccbcdbabcdcdbcbcadbcdcdacaabaadacdbaadddcdbaacadadadcddbabbbcdacdbdcbcaccdccbdddababacddacaabacabaadaadcdbabbcdadcbcdacacbadcadcccdaabdaccacbbdaddbdcbccdcccaaadbdabbccdbdbbdbaccccbcdcabcabbcabcdcbbdccbbcaadadaacddabbbabcdadbbcdccbdadbbdbdaacdaabdbdadadcabcccccdcbcaaadbcbbcbcdbbaacdcdddabaaacadccdbcbccccdbdaddabbbdcdacccddcbaaacccbdbbcadaccbaccddddddcabbdaadccddbdcbcdaddbbbadcabdacccbdadacddacbbbdddaccadcdbaaccdddaacbdccacadbaacbadddaabbbbaadbcdcbacadacaabbbdababbabccdddbbbadacdbbcdddcabaacbcacabbaaddddbbbcbdcaabccabdcacdcbadbdacbcdcdbddcabcdbbdbbcacbaccabcaaaabcbbacccddccaabbaacbaaabdcdbdbacaddaadbccaabbaabdcbaaaacadcacaaddbdaabdbbccaacdbdcdbdbbadbcdcbaddbaabadcbadabbcaaadadddccbbbddadaddabdcdccbcabdadbdacddaacdccbbacadbdacacaddccaabbcddaaadbababbaabccbbacdadccabbbbddbadabcbdaacbcabdadddcbdcbbcabdbddbddbacccdbdcbdbacdabdbbaaddaabadacdcdabcadcbcaadaaabbbdacadadacbaabddbdbbdbababcabbdbdbcbacbbabdbbcddaadbcadcddbddbaaccdaddcdaaccbacaabbccccbbcaacdabacdbacacdddddabbabbcbdabadbcdabdcabbddcdddbdadcadcdbaddbdbbadbcbcacaaccaabbbabbbdacbcbbdbacaadccdcdddabbcbcdadadbaaacaababbaddadbbbcdbdaccadddbccbdcdbbcadcdccccdaacacbbcdbbdbdadbbadcccdbcacddcddaccbcdbabbacaccddcacadcacaccabbdadcbbbcababdddccbaaaabdbcadbddbccdcdaabadcaadaacddccdcaacbacbcbaccacbbdbbdcdbaadbccdaddbbbabbbbbbddbaaaccacdbddcdbccdbcdaabdacdbbddccabadacaacbaddcdadacacaabdbabbaddcccabcbbacdcdbdccbbbacbcdcbcdabbccdcbcadaaaaddbccdbabdbaccabcaabbdbacddbcdabaabddcacdadcaabdadacbcdccccbacbccbaaacdcbcdbcabcccbccadbbbcdadadaaccddcbdcccbddbcabadcdcadcddbdbbcbdccdcdcdbccabddddaccdcaabcccbbabcbadddbcddadadddacbddaadcacadddbbdbcddacbcbbcaacacaabaacdacdabacaccbbcbcdabaadddadacbccaacabcbdbddabbadcdcbabbbcdbbaababccbbaabadbbdbbcacadcacdadbacabaadbaacadcadcdcacbcadbdacaabbbccdccbcddcaadbcbdacbcbccacbbbcbbbdbdcdcacabbacccdabaccbdabdbdbadbcbabccbdcbbacbcccaccdaaaddddbbddbabbcacabcadbddcadaddbccdcbabddaddbdbacabbabdcdabcdddddcdbbdbcdcaacadccbdaaabbdbabdacbaadcbdabcbabbbacdabbabcbccdadadbddaacaaccbdadbcaadacdaaccadadcaaddddadbdadacadbababaccaabbcaddcbabdbdadaacdbadcdcdbccbbcdaaaaddddcacccacdcacbcadddabddaccababaabcbddbcadccbabbcabbabcbccbdbaddbbcbdaddbabcacabaacaaddbcaadaddbaaccbaaaddddbcccccdabbbdabcadcbaddaabccdacdcadddcddbcacddaddcdcddaabcccbbacccaabdacdadbbbdcdadbcdacdcbbdddcaadadccbbadccbacdbbcadbcabbacbcbaaaccccabbacbbbdadcbdddadaccdabcabdbcbbcdbdabacbbbcbbbddccbbbaccaddcacbbaadcdcbbcdadabbdcbdaccdbdcdaabcdaabddaadcdccbdbaccdcbadcacdbaaaabcbadacbcdccbcdacddbbbaadcbabcaaddbcaaccacbcbcdaacadabccabcddacbdbbbdbbddaccbaadaccbcddbadcbbaaabddbacbaaccaccdbdccaadbcacbabcbbadbcdcdddbccaaaddabbddddddbbbadcdbabcdcacddccadbacbabcbdcdbabcbdcdadbaadccdacbcadcacabbccdabadadabacccddcddcdbdaddbabadacaccbddbddabadcadaadcdbcbbdcbcbdbaadcddbcdacdabddabdbdbbabddcbdcadbbdaaaccacbdcaccadbaabddcbdddcbaadbddadcaacbcccdcdbaabbadaacbabcdbcdbcadcdacdaaabaacddadbbddcdcddcbcacacabbacdddbbccbccbbbbaddcdaaabcbbbcccbbdbaabadbbaacabbadcdbcabbdcabdcbdacdaabbcccadbdacaaaddccabdaccdcddbbaacccdccbccbcbbccdabcaddbcdccdaaacbddbcdadacbaaccaaddaadbdddbdabbbcbaacadaddaddaacddbbdabaaacadcaaabbddcbcdbacdccddaacbadbccaaccbbdcdccaacdadbcbbdcccadaabcbddaaaddcbaaadcdbdbaccdbccacaaacbbadcbcaabcacddaccccacddbdacdcbbcccaacdbcdbadaccacbdccdadbcdcaccdbcdcabdcdbbccbdbccdacaccabbbcacdddddaaadbbbbdcabbadbcadbbccaddbbabcddddbbbddbcddabdaaadaadcdbaadcbdcbbdcdbcdabbddbcbaacaccbaabbcbbaabadcdcadcbbabccdcacbcbcdbaabaabadcbcbcdabdadbccbcaccbccdadcbadaabcbbadaabccabacbbddcbcbdcaacbdadcbabdaabdacbaabdadccbbabacccbcbcdcbdadcbaadcacadcdaacbbbddabadddbcacddbbbbbcdadaabdcdbadcbbddcaddcdbbadbcbddcdaaddbbccacbddbabddbddbbcaadcbcacdddbbdaacdbcbbbaddcbcdddccbadaacddacabacbcbcdbdddcbcddddacdcbcccadbaccbaacadddcbcaabdabcbbdbbbcdacaaccdadcadaadccbdbcbdbdacccbccbabdbccabcdabdddbcdaadccdddbdabccaacbaaddbdacdacbcaaccbbdabbddbacbcadbdacacacdccabaaaadbbabdabbdddbadddbddbccddbdbacbaaaaacdaccbcacccaaadbbcdaabbbdadbaacddbbccaacabcabcbdadcabacbacdbadcadadbcdccabbcbadacbcbabbaaabaadbdccdaaaaaabacccbabbdcabddaaccbdbccaaacbddbbcdddaccdcdadcaaabdbdcacbcbcabcbcbdcccccdbccabbbabdaaadbbcdabcdcdbaccadadaaccdcdcacaadadadddbbcabbabddaaddcdaddbbdabcccaaacaccbbadcbdbbbabbccaababdbcbaaccabaadcbbccdadcaacaddbddabbbacdaacaadbbcdabacdcabdbabcbadadcdbcdcaadbaaabdcbcddacdacccccabddabadddccabcabbcdcccddaddcacabbbcabcdcaaadbcdbbaccdabddbddbdbdcdcacaacaacdddbaddbcaddbccadcaadcbbdbabdccbaabddcacdcdcbaccddadcaacaabdccbabdccabaddaadcacacbabadcbdccdacabbdbbadccbababdbaccacccadbcdbbbaabbbccbdcbddbcacacbcaaabcccccacddcbdddbabdcadadcddaddacaccabccddbcadbbabbbdbcdadacbdabcacaaddbbcdabcdddccdcbaabadbbcbbcccdababcdcdadddcdcbaccacbacacadbccddccbacddcdddbdacaaddacbccccadbccaabcdadccacbbccccbcaccbcdcddbdbcbdbccaacdbbbddbcdddbdddabcabcdbdbdbcdccddcacdcbabaaaccabcdaacbcdbbacabcdbaaadabbabdabbbdcabbbdbcddcbaacccabbcacbcdaaabbcdadcdcabbbcddcdcbaddacbcddbddbcaabacadbababacadccdbccabcdacccbdddcadbddbdcdcaddbabbdcaacdbaadcddabdcbbcbbdabacdcabbcbabccaadcbbdadbbaacccdbdadcbbabddaccaccbdaaccaddddbbcbabccabbdbacdbadbacbbaddbbbcdbadddcacacddbcadbbbdcbcbdabadcaacccdabdacabdbbdaccabbacabbcbcaabcdccdcbbbcaaccddbacacabcaccbabbbcaabbbdcabadccdbbbcbaabbcabbacdbdcacbdabbcadcbaddabdcbbaaccadbdccacaaaccdadcbbcbdbcabababbcadcdaaadbbbccacadcccddccbdbddbbddcdddcbdbadacddabbddabbadadddccbbcbcdcdbddabdabdccdacdbacadaabdccdabdbbdccbbdcdaaddbcbabbdbdbcdbaaacabdabbabbbbcddbdccbcaabbababcbbdcccadcddbcdcbcbdabbacdbdcabbabcddcccdcbadcabdbdbccdcddbbabcddaacdaddbdaabbbadbbabcbdbbbacbaadaaabbbddaacabdaabbccbbadadbaaddaccabadddbbbabcbbaaabcabcaddcacadacdccdabccacbbdbbdacaaaabcccaaabccccdddbaddbccabcadcbdbcdcdaabdbcbbcbaacbaacbbbacaaabcdabdbaabbbabcdbadcdcdcadddcadaabcaacbcdabaccbdccddcdbdabbbccaaabdcabadbccbcccdccdddcdadacdbaacbaaaccacbbcdaadcccbdbdabbadccbdadcbccddccbdadaabbacddabdabadbccdacaadbabcdabcacdbcacdbabbccabababcdbacbdddbabbbcacababbdcddcccadcbdbbacbbbbacdbddbdbbdabcacdacabcbbdbadcdbabbdbbddbddbcccccaaabadaadddbbddbbaadccccdcacabdaabddbdcddcbaddcdccdaabbabdbbdadbbaacbaacbabcacaadbcdccbcddadcbdbacbddcabcbcdcbacdbbbbaaaacbdcbbabadabdbdbacabbabacdadbddacdabbbccbacbcbaacbdaabcccbacdaddccbcaacadcacdacadcccaddadbacdbcdcbbadabbcdcbbabdddcccabcabdcaccacabbddcabbcbaaadcaabbbaccddbcaadbcadcbbbadbaddccaaacdbaabaccdbdbaccaaacbccbacdaabdcadbccbbcbcbdbbaacbadacbaacbddccdbbdbbaddadbabdcdddadaddaacddbbddabccabaaaabdddbcdbcbcaccdbbcaaabcdcdcbcbdddbddcbbbccccadaabccabdcbdabdcadbaddbcdbccabdcdacadaabacbacbbddaabaaccacccbcbcaddacacabddabcdcbddadcadcbdbbccadccbbbacdbccbccbaadcbabacabaaddbaaaaabcddaabdcbccaacbdddacdacccdcbdbbddbcdcbdacabbccdacdcadcacdcdbdadcacdaaabacdabcbbcbcdaccacbdbadabcabdccadabdddcadbbdccddaccaaaddacdccbadbbccbacaabadacccdacddbdbcdbcaadbcbdddcccbbddaabbcbcaccacbbccadabcabadacacbcbbdabbbacaaadacdacccacdcadaaadbbcbaddcadaccdccadcbcdaacadbccacaaaabdcbabbddbdababaabdbcacdcaddddbabddbbdadaaacbbdbaccabcabbcadaaacbcbdcdbdbccbbdccadbcbcacdcaadbacbbbcddccaadabbcccdcaadaddbaabdaacadcdcbbdcaddaacbbadcddcabaabccdaaccdcabbacbbadaccbbdbadaacdcdcabbaacacdcdaccccdcdbbdbdcbdbddbacbaacdddacdcdccbcccbddcaaaadbbbcbbaaabdcdcdabdacdbcaadbdbdcbcbaabaaaddbacccdbccbddacdbdbdcdaaabccbddbcacddaadabbcacbcccbcbdbcbaaacbaababcccbabccaababdddabbcddcbdcacbbdabaabcdababcdbadcbbcddddcabddbcbcadabdaaddaacbbcaabdcbbdbbccdcacbbabbdcadcbbccbcbdbcbbacccadbacdadadbaacddddcbacbaabbdaabbbabdaaddddbdadbcbccbacbbbadcddabcdadaaccbdbcdccbacbcdcdbcddcdbabbdcdababadbcbdcdccdcaaaadbcababcbaabbcdbdbddbbcaaccbabadcbacdccddcabccabdabbdbdaaabadbcdbaccaacbbdbddbbcacbcbdadbdcadcdacaabddbabddbdadbbdddcbabadcdbabdcaaaacdbdcbaddaabcbaadbbbccbdbbdadccbaabbcaddcabadcacddbdbaababdadcdbdbcabcacdbabdbdacabbbcbcbbcaccbacaccbbaacdcaacdadbbddacadadbbcacdadcaaaacdcadddccbaaaadcdadcabadbdbbcabdccdbadabaacdddcaddcacdacdaaabbdcbacbaddcbbbaaccddccbcaabadaaaccacdadbaadccbcacbdbdcbcadddabcdcccaadabaabbacddbcbdbdcacbddaaccbddabcabadaadbaacbbdbaabaaccbccbcbbaaadabdadacdbddbcccddcbdbcaaddddabcacbbbacbcbdcddddbcbdccaabbbadaacaabccadbacbccabbbbbcbcbcadcccddadbccdabcadaadbabdcbddcaaccdbbbbcdbbbdabbdcdcdbaddbcbcdbaddacddddcdaccddbabbbcbccdcacbdddbbdbcaacdaccbaadbbcabccacdbbbdaadbbbdbabbdcdacdccbdadbbabbaccaccabcdddbdcbccccaabcdbbbadcabbcadabbabcbcaabbbcdbdccadcccbcdadaacadccddddbbbabbadccbcdddcabacadddadcbdccbbcabacbabbabbadacccacdcdcdaacaaddcbdddbccdabaddbacdbbcbaabddaaccbaddaccadaaadabadbcbbaabdaadbdbdddddbcdbadcbcddadcdccddcbdadddabacbadbdaddbddccdbccbdaddabaadcdaddcbdcccdcbbcadcabbdddabadcaadddadbcacbdbccddcbbbdccdbababbcbbdaabdcbbdadbacadacabdbccbbcbdcccbbbdcdababccaaddadbbaacaddbdaccdddbbadadbaddddcbbdabadbddaddbbaadbbbbbacccdabdddadbcddaddaabbcbaddcabcaadbcbacaabbdbbbdbcddbcadcdaddbdadbcaaaddddddbccbbcdababaaadbbcbcaadcabbdadbdaaddbcacdadadbbbdbbdadbcdccacddbaabdccccccddcdabcacabbbccaacdbbccdaacbdbbbccbdabadbcccdacadddbbddaacdcbbdaabaabdddddaadcdadadbbdbcdaddddcbbdcbbdacaaadacabbcaaadddadcaadcaaaadacbbadacddbcddcdbdddacaddbbdbbbacdbabccbadbababaacdccabcccaabccbdaaddaddbbbadcccdaabbbddddbaacaccbbdaabdabcdaacdbcdbdbdabdddccddccbabbadcacbabbddcacdccaacddacdcdbbddacbddbaadaddbbaacbcddabcaaddddcaaaacacadcddbddcdacababdcbbadaccabdbcbddccbcaacdccdabaaaaaacdcbaaccadbbdcadbadbdddbcdcbbabbabbdbdccbaacbdbccbdcdcbaaacdbbabdcddddcaaaddbaaacadadccddcccaddbcbaddccdcdcadadcbabdaacddbcbbdcbdcddbcdddcbccddbacddccdaabbbdcbccbabcabcaaddbbadbcaddbdababdcbbccacddadcbbbddbcddaabdccbacbdbacbddcabaccdcaabdbcaababccadbbbadbdbcaaacaccbbacdbdcacacbbcdacabcbccccbbdddddbbadbbadbbbccdbbbdcccabddbdbcdbbaddcadbbccabacbaddaabbbdabddccbdcaaabdbbccbdcbddbbababcbdadbcdaadcbddabcbccadcdacdadbababbadbcddabaabddcbadcbcdbddabccacbbdbbdbbddcbacccaadbabddaadddbcbcbaadddcdbbcadacbbdacddcbddaabdbcdbbcbdcbdbcbbbbaccdccbdbbadbcadabaacdaadcbcdbcbdcbdaaabcaccdcbaaacadabadbacddcaacbbaaaaaaaaccdbccaddccacccbacbbdcbcddcabddcbcddccddaacdddcbcdbacccbdbcaddabcdbacdbcbababadacbaccbabbaadbadacaabadabbbbbdaabbdccdabcabcbabdcaadaaabccbccaacaacabaacdbcbacdddbcdacbacdbdacdbbbdddddddbddbcbbcccaaaccddcdadcbaabbddaabbdabaddbcabcdacadacdbdcacddbbaaadbdbaccdbbabcddbbbcabdcbcdabadbdacacaccbdbdaccdadbcbaccddadacbbaddabbadcddbcaabbcabbddcbdadaaacabadcdbaddbbcdaaaaabbccbbbadccdbaaccacdcbcacbbbacacbcbcacddbdcbdccabacbbddbcacabdabbbbbabbdcdbadbbdcccdbbccbbdccaacabdcdcddcbbbccdbddbdcbbadbcbcaacdbbbbbcbaabcccabdddcaacdcaddacddabbbdcbcdcbabaaddbdbbbddabdacacccdbdcacbcaccbaacbdbddbbddcdbadbdacbdadbcdcadadbacbbccccbaccbdacccdcdaddcabddcdadabddabbacddabbbdaabaaddcaacccbbdbabadbccacbaddcabacdacaadadadcddaabddcdbdaadbbbabcbcdaadabcbdbacdddcbbaadadccbcddcdbddcbacaacbcdcbaaabcacadcbbcabbddbdabbbcbccacbadbbcdcccacbabbcacacdcbbbabdcdcabcbdddbdaacbacbcaaccdcacbcbcdcccdaddabccadccacdbddbbabaacccdacdababcacbdccbcacbadadaccddadbdabddcdaccadabccacbbcdbdbbbaaacaaadcdcccddbcbcadcdbbcdbccccdcbcacbdbbdbbbcdccbacbaabdbdcadcaccbcabdbacdcadddabddcddcaacacdaddcccccaabaccdbcccdbdbbbbaacbbcdaadacdccccadcccababaabbdbcaddaabbcdcbcbbccccbcdcbadaabbcccbbbabdbbdddcdbcdbbcbbcddddbadaccccbdcbaababbcabdddbcccbcbacccadddcbbbadcacacdcadddcdacaaaabcdaabbdbcbbcadcdbddcbcbccbcccdbdaabbccddbbbaddcaaaccdbaaadacabddbcddcddbdbbbdddcabbadcdcdabbaadccdaadbacbdcacbcdbddccaadbccacdbadbacdaacdccbddbaabcacabaddcdbaadabdcccaadbcabacbadaccbcbbadbddbcddaaadccdcabccaadccbbdaadaaabdbcbcdabdcbddcbdcdabdbbdbcccadaddcddbabbcadbcbaabdaddcbbdbacccadbccadbdaddbabdbbadbbbbacddddbdaaabdcdaddccbccbcabbccccdddcacdbbdcdacdaadaaaddaaddadbadbbbdcadcddbacdacabdadbbbcbbbbccdabbcccdbdcdbbdababbbbbacadcadaddaccbbbcccdbaabbbacdbcababdcdddacbbdbbacbcaaaacacbbdddbabbcbacaccbcaddbcacacabdadaacbacbcacbdbdadccddacbbadbdbcbccccacdbbbaaaaaddbbabdcbcdbcddbcaaaaddaacbbbbbcacadcdccbcbdacdaacadaaabddadcbbbaacdddcbbdacbbdbcaabdabcabcaccdbcbabadbbddabcadcccbacdacdbabcaaacadccbcdcaccdbddabcddacddbdcbbccbcacccdcabacbcdccbccdbbdcdbddbbcdddcbcdcccccdbdbddacddcaacdcbbcaadaaabccdacabbcbcbbadbaaadabadbcaacaabdbdabbbadcdbdbddbbacbbdcbaddababaaabcbdbabbacdcdccbbabbdcddaacbaacbcbdbacbccaabccbdadbcaaccbddbdabbdbabbdabbaaababaaadaccddcaacdcabccccdcaacaabaaddbaadbbbbacabdbdadddcadababbdcabadddcaaaaabdcbcacbdabcbdcbdccbdddabdcadbdcbaddcdaaacdcdcbdabdacadbcddbcdbcbaadadcdbaccbaadacbbcddcabbaccdbbddddaadddbabbbadbbabdacacdaccbbadaccdbacbdaccddaadcacdabcdbabbdcdaccdcccbcadccbbddddadcadccabacccdccbadbbbaaaaadaddccaddaacbaddcbbccadccadbbcadbccbcdbdadbccaacccddcadcccdbaadbdcdbbbbcdadbdacabaaadcbabaaccdaaaacaadabbbabdbcddcccccaddacbddabcddcacdbbbdababbcbbddabccdbdacbcccaaccaadacaadbadbccdcbdacdddddcdacbdcacdbcdabdabadcccdddbbcaaacccbddcdccbbaadcbadbbbdacbccbbbcdaacadbbaccddbdbddbdaacbcacbcbdabddacdaccdbcaacaacdcbbcbbdcbadacccacbbcddaaabddbadacdabbddcbcbccddadbcabcadbbbbaadadcbdabdaaccaaaddaacccaabcdbaadbababddacbcdcacccbbdacbdccdddbaccabdbadadcbaacbbcbcdbcdbcbaacddbacadaccbdacadabbcdcbbaaaaccdddcacbcbaacbcddaabdbacdadcaadbacabbdbbbbdbdcbadbadddcdaadaccadbcbbcbcaabbadabdbcadbbdaabcaacccadbaacbaabcbdbbcbcbcabdbcdccadcdacdcabaccaadbdabbdabdcccdbcdcddbddddbddcdbbabcdcaacbbcadaccdaadaadbbbbbcdcaadbabccacababacadcddbccbaadadbacdccaacddbaadddbccdcadabbddabccbdadcbaaccbacdbbacddcdbbcbaddbddbaabccdcbaabadaccaacccacaccdcdadadcddccacbddcbabdcdccbbbdcbabadadbbaabddddacaabbaccdaccbccddbcdbacccdcdaaddbacddbdbaaaadddcbddbdddbccdbbdbbdaacbdbddbaabcddadbcdcaccabbacbaabaccaaacdbadabdbbddabdbacbabccadbacdddacbccbaadcdadaacdbabaddbdadbbaccccccabcbcdbaadcbdcacdbcdcddbabbabbaaaacadcacdbadcdcacdabddadbcdabbacababababaadccaaadbbcbcddbdadddbbdadbdcdabccddcdcddcabdbddaabbcddabdcbcbdbcbcbdcdbcaadccbabddddcaaabccdabbabbcbbcbaaaddcaddccacdcacabadcabaccccaaaadcbdbdaccddccdbcadbcadcbbbcdacbdbdcdbbaadbbcabcabbdbabbbacbacdbcacabdcaacdaabbbccdcbcadaacbbbccdbcbbdaaaababdcabaacaddbaacdaacccbdaddbabcbcdbbaadcaaadbaaccdaddddddcddbdbadbddcadbcdcabcabccbcadbddddbcdbaabbddddbcdbccdbbddabcdabcdaaccababcaaccadcbbabbbdcbbacdbbbabbbdbaccbcaababdcccaadcdbbdacbbbadcaabbdadccadcbdbabbabdcdccbacbbbbadccbcbdacacabddbcdddbbbaadbdcbdbbddaccabdabdacadabadbdababdaccdccddbddabcbaacabdcbbbbabbdddcddbdbbaaaacababdacaccbababadcbacdacdacbacbbaccaaacabcbddaabacdbcaadccdbcdddbcdccbbbaabbbabdcdcdbddabccdddcdaacadcbcabbbbbcbbcbddddcbbacabcadbaabbabcccddbddcaadcaadbbbacdcdbccbadbcddbabdcbdcbbbcbbaadcaabcdabacadbacdbbabcadadbdcabbbdbcbbbaaddbbbcddddddcadcaabdadadacaaccdbdbbababadccbabacabdacbcaabdacaaacaabdbbbacbaadabadbcaabcbdcccbacdabbabcbdaaadbaddadbaadbdaacccacbadbccbbdadbcaacdadacaaabddaccdabcbbcbbdddcbbdbdcdbbdcacaddbccbddccacdadbabdcccbbdbccacdccdccdcaddddcbaaaacdbadbdcaadcdbcadcbcadbcacdbbadcabdbbcdaadccbbaddccccaabbbccdbbbbdbdadbabbcdabddddaccabddcbcadaaaddaabbdadcaaddbaacbcdaaadcadcbcbcdccaddbadacdbcddadabbdcaabdbcbadbbdcdcaabdcabadaaddcdbbbccaacabaddbadcabaabcaccdbabdbcddcadbdcbdcdbdadadacdcddbccdaabccddbbbdcaccabcbdadadbbccdbcdbdaaadabaddbaccdadccacddcbcdadccdaaacbccabaaabddaabadcbdaadabcbcabdabcdacbacbbddbaababbbbaadddcabccccabdaccdcbdadccaddadcdacccbaacacaadcdddbaccabdbbdabadbdaccbdaacccacdcacbaacdbacbdbddaccbabadacdadcddbccddaadadadadddaddbdacabbccbbcdbbabbdcdacccabaacdccdacaaaabdbcbdbabcdccbacdaadcdadddddbcbaadcadadddcbdaadadbddaaabcababbbcdbabdabbccdccaadaabbdcaacadcdcddbddaaadcabdabddcdddabaacbcbacdbacbdacadbbdacbbbcdcbcbcdadbdacdccdcbdbcabdbaabacccabdddddbbbccbdaaadbdbbadcdcbacddabcdaadbbacccacababadabcbbcbccdaabccacaabdbadddacbaaadadacbbbccacdbdbdbddcabdddbddbddcbbcbbaabadbdbcbbaddbcbdbadcddcdccabbbbaddadbddcdcdbaddaccacadddccdabdbdadbbccacdccbabadabbaacadaadbaddacaadadcdbacbdcddbcaccbcbbbacaccdbcbbabacdabbcdabcbdcccacbbcbaccdbddcdccddcbdadbbbcbcabccabcdcaadbababdaaabcdabbddabbcccdaddadbcadcaacdbcadbcabdbccaacdacbaaabacabbdabddddbbdcaddbdbcccacdbddabcccdaacacdcbcacdadbbcdccccabbbbadbcbcabccaaccabbadacbdcccacdcdaddaccadbccdcaddcccdacddddabddcddcdcabbdcacabccabdabccadcbdadabababbdabaddbbdaccbdbaadbddccaabcacbdcacccdadcadbddcabdcdbdcdccaadadadbdbadcaadbbbddcdabdcacabddcadcccccbaacdaaabdacaccacbdcdcccbadbcacccadbccdbabaadcdacccaddacddbbdbbdbbddcdadbdcbbbdccacdcacbcdcdbbddaadacccbadbabdcbcaddaabaadbacdadadacddcaaabdcbabdcddbdaacbdcddbacddccdcadccaadccdbababddcbcdbaabcbdcbbbaabcbbbddbabadaccdabcbbddccccbbabcabacdcdbddaacccabbacccbabdadabbcaaaaadaccaccadccaaddcabbaabcbdcbabdddcdadbdabcddadacdcdcacadcdadbaacaaacbcdddacacbdcdabacccbabcacacddcaaabbccacdcadbaccccbaaadaccbabadcddcabaccaadbaacddabdcadcccacdbacdabcaaddabddccccbdabcdddbddaadadbabbbacbabdabdaaabbdadcbdbccdddaddabdcacabaccbdadaabadbbdccccccaabbacdacccdacaabcdbdbbccccadccccbdbacaacaadccbbdaabbbbbdbabccadaadbdbbbbccacbdaacdaaacabdcdabcbbddcacadadccbbccaacccacacbcbadccadbbabadadaabcbaadbcaddcbbdbcdbddbcbaddaacdcaaadbbdacccaacdcccbdabdcaddbdacdbbdadcdbdbccdbbcdbbdacdcdcaccacbccaaddbccdacbdbaabbdadbcadcbccbbaadccadbabacdbcbbacbdadbabacddabcacbadbcbbcacbbbcacbcbabbbcbcdaccbbbddcddbcbcdbbbbadbaccacbddabcbaddbdbdddbaddaddcbbadbaabdcbcddcdbcbadacddbacadbaacbbcdccaccbabdabccbabcbcbabddbbcadcdcadbaadccdddaccbddcdcccabcbaaaacdbccdccddbcbbdbaaabbabddadcdabadbacacbcbabdbabbdddbcaabddadbacdacdddddadacddbbddcaaacccddbdccdababacaaadbccccadcaccbabccacdadbbaccbabccabcabcadbcbaccbcdbbcddbabdccdabaddcdaaaccaacabacadbbddbbbdaccdcdcbacaacabdccbccbbddaaccbaccdbcbaacaaccddbbdbbadcdcbbacbbabdcaabbdcdabccabacccaadacddbddbabacbcdaaccabbbcdbcaddbcdaaaabbbcbdbddbbcbddcddadddccbadddacaccbabdbcdcaacadcadabdcdcbcabbcacbdaddadcbbcdccacaacbcaddbaacacdabdbddddddcccdbaaadadcbabbadbbcabcababcbbcdcbbbddbdddcbdbbdccdcabaaddaabcbddbbbbcbadbcbdcbacccbcbddccddaaadccccdacdbcdabdccacbdcdbaccdbbccadbacacbbdadbccbaaacdbaacbcadcbdaacaddddcdcdcdaacdbddabdcddcbacdcdccadacddccaabdaddbdacbddcadbbcadcdaaadcabddaccbababbcddcbdbcdbbbdbcbdaadaccdabadaabdbcabbbadcdcbbcbaaadcccdccacccdccabdaddbcabbabccabcdcddcdccddcbbcbabbaaddbddddbacbbbbcabbbbbabbcabacddbcacabccdccaadaadbbdcadcbabaccbaadaaacbdadaadbabbcacbabbbcbccbaacbbccbdcbdcdcdadbcaadcdbccbcbbaccdbabccbccbbdbcbcbccabcbbccadccbdcabddaccaaaaaaddddcabddaddbddadaadbddddbcdbccabadcbcdcabcaaacbcbbcadbccaaacccbddabdcbbabdcdccabaddcbbbbdbacbddbbdbbdddbbabdccddbbcbbcbbdbdacbaccdddbabcdbbaddcccbacbbaabdbcbdababcdabadabaacabaaabdbadcadbbcaabddcccbcadabdbcccccbcddccccbdaabdabaccdcaddabdbbaaddddadbbbcbdbdaadddabdabcadbbccacdcabaaddccaddcdcaccadbccacababbacdccccbcbadbbdddaaadcbbdbabdcdcaaadbbacddbbbaddcbbdddbaaddaaabbabbdaccbbadbdaacaacabbdcaadddbabacdcdabbddabcabadccadaaacbddccdbccdbaabacddcdadcddbcdabcbcaabdcdddaabcbbcbadadbadbcaadbadaddccacbdbbcbdcabdbbcabaccddcadbabacaabdcdbaadadacbccdbddcccdcdcaadaaaabcacccbababccddbccabcabadccdcddadbbddcddcbdadcadbdcaddabaccaccbcccbdbbbabacdaaccabcbabaccccdbdccdadabcbbcdbacbcbcdaddaabccccccccdaacdadcdacbabadcacbcacbccccddcaacadcddcddbbcadcacaaccccccaabdccddbbbbbccaadbbadcbacbdcbcbaabbadadcaaacbbdcbacbcdcdabccbdccbbccaadadacabcacdcbcdcbbaacabbdbccdbdbacdaabdbdaacaddcdbbbadadaccbdcbcbbcadbddbdbccccbabaabbbbbacdcadacacbdbbcabdccbccabcacadbbbccadbaabcabacbdaabdadddbcdbbaadccaacbdbcbdabbbdcbdcaabcccaaacabcacbbccccdccbdadbbbadccabaabadddccccbaaccbcaccdbccadaccbdbabcbbcbbaadcadbaddaabbbdbabcdddbdaaaabdbabbaaacbcabbccccbaccdacbdacabddcaabcbddbbcbcddbdbbabbbddabbdccdbacaacccadacdaacbbbdabacacbaddbabcbdcbdcbbbccdaaabbcdadbcdcacbaacadaaaababdadbbadcdcabacdabbaadbdbcbdaadbbcddccacabdddabbdcbcadcdbdcbabdcacbdadaccacaccabaaadddaaaccdaccadaddacccbccaccdcbcaccccaddbaaadbdacbacaddaababbadcccccbddaaccbcdcabbabaccaacabdbbbabdcbaadaddacccadcdbcadcacbdbdabdbddcbbcdbdccddcbbcddccbdcbccdbcbbbcdcbabdccdbbcdddbcdbacadaaaabaddacbabbdbabdddadacccaddbaaaabbaabdacdccbccdbbcbcbcdcdadaccaccaddacabcaccdbddcbcbadccbccababbcaddbcdcaaaaaddcccdddccacbbdabcdadaaaddcdabbabbbbbaacddcbcbbdbccaaaabbbbadbaabacbbcdcaabcbadcaacbcdabcaaaaacdcaddbccaaabdbacacbbbaccbdbdadccccdcaaaccbbdbcabaaaaccbdbbbcbabdbbccaababdccbbabdabadbbbbbbddaabbdbacccadabcbbbbdbcdbdbddacbdaacacadadcccddbccdbdacaaadcaccdcaaabbbdaacbcddabaccddcbacbddbcddbacacabaacadbdadccbaccbcbbcaaabbdbbddcdcabaccdbcdccaadcbdabbcdcdabcbddcbbdcbdadbbababbabbabbdacdaadbdccbbacaaacabbbababdcbdcdcdbabacbababbdcaaacadcaccccaadddbbbabbadbdbcdadaddddbaadabbadbadcdadddcaccdbaabbccbaddbacdcbacdbbdcccacbaaaccacbddcbacbcdbacbdabaaaabdcabdcaabacccdaccdbcaabddbdcbcdacddcbccdcbdacbddbccbdcdaadaaaacddddacacaddadabdccbaddabbdddcbacccbaaadcddadabccbbababbcabbbccccbacbdaccaadbdccbbbabbcbdcccdabbadadadadcbbcdbddccddcbabadaabcddddbbddabcadbdadbcaddcbcbcbbbbbcbcbbbccccaadcbdbbbbbacdabbadcdabddaababbddbbcbbcccadadddcbcaabbcaacdbdcbabddcabdbdbcaccabdabccdbaaccbdbaabdadbcbbbbbbdadaccbcbadcccadbbaccddcddcbaaababdbdcbacaccaccbdcddcddaaadbcdadaacbbaccaaacdcabdbababbdbddbcbcaabadbbddccbddcccbdbdabcbbbcdadadcbcbdbadccdacabddbccbaddbaddbabacdbddacdabdcbbaababdbbccbaacadbdbddacabcdddababbbdbbbcaabcddaaabcdbddbbcbaabcbcbdddcdacdbdacddbcdbcddbbbbaabbaadbcbdbbccdcdacbdcdcbddbbccacbcbcbbdbbcbbdbdcbbccdaaccbddadacdacbdccbacbcaacabbaaabadcdcccadaccadacbcadcacdbcbadabdaaabbbdcabbddaaabaddcaccdcacbbddaaadbbcaaabacaadbbdbbcddcaadcbdcabbacacbcbbddacacaadcbdddbbbcdbaabdaadcbadbccbbbccbbdabcabbbcbccdcbbddabddadcccccacbdcadcbdbbcbcdacdbbbaacdcbdacdadbaccbacdcddcccbcbddbddcdcaacadbddcdbdacddcdadccbcdcbbbadcdcbcadbbbbddaadabdbaacabcbdacacdadbadcdbbbdddcbadcdbadddddbaccaabbbaabdbacdbaacaddbcccbcaadcddbdaaabaacbbdbcaabbaabdacccbbbbcbbcaaabbdcbbaabddccaddabcddcbacbadcdcbcbbadaabacadacabaabccddddccdbababacdccaccadbabcdabcabaccbdbbadacdcdcbbcdbbcdbaccccccdbabbcacdbdcacdaaaaacbadcdaccaadcddcbcabbabddcddbdcdacdadcccbaacadbacbacbdbaabaabaaaadcbcbbdaccdadabdabdddcacacacddaaabccdcbdbdcbcdddcadcaddcaadcabbbbaddbbcbabddbcaadbdbcccaadbbadadbdcccdbccabdddcabbcdabbdbddaddddcddbbdbbdbbaccaccabaddcaaabddbaacacccdaabcaaddadccbbaabbadcdcdcbaaaabdbacdcdbccdcabbcadcacccbbccdbadcdbbaaddbbbabcbcdbbcbbcadccbddabadcbaaddcccaacdaacbbbcbbadbcabacccdcbbaabccbabcdcaadbdadbbaacdaccbccddbdcbbaccbccddcccdbddbbcccadaaddadccbcadddbaabbabacdcacdccccadacabadbdabcbadbcbbdbbbbcabddabaaccdbbbdbdabbacabcbaccccaadbaabcdbadabcbabddcabaaabacadbcadbbbdddaacaddabcaddcacdcaabbadccabdcdabcddbbdabaddbbcacbbccdaabcbcaddbbbcccbdaaadbbbcbdcdcbdccadddcccbdcabbbbcaadaababcccdcbabbcbdcdcdbbdaaccaaddaadddcdbdcadddbadcaacdbdbcaabcabbbabbdccbbabbaaccbaccabccaacdaaaddbdcbadadcbcdabcabbddcbdacdcaaccdabaabcbdddabaacbbbbbbbccbabadacbababaabbbaaaabdcdaaddaaaacccddcadbbcadacbbddbabdddcacdcdadbcdaadbbcabbdaaddacdcdbacaadaabbddbccdcbabcaabdcbaaccccdcbadcbbcbdccbbbadbbdcbbdbaadbacacccdbbcbaddbdbaabcacdcbcbababcaddcbacbacbadadddaabbcadddcdccdccdcaaccacacbadcdbdddadbbbdbbadbcccabcdccdaababddadabcabdcbbabcbdaddabdaadacaacdadcdaaabcadbbbdbacdaddaacbdbddcddababadbdbdabcacbbcdabdcadabbaccbccaacacaacbabdcbdcddaccadcdaaccbadabdcaadadaaadbcdcdaadaabaaacdbacbcbacbcbbcdcaddccdbbccbadbdbabbddadcbcddaccccdbbbdbdddadaabdabaaccaacaccbabcacacdbcadbabddcabbcacbcccbaacadbcdacbacabaaaaadbcacacbbcaaccdddbaadadabbdadbcdbcbaccbbabbcbbdacdbdccdbadddcaacbcbcdbdccddaddbcdccdccdcbadcbbadcbbbacabbacdbbadaccaccbbddcbbacdbdbbbcbdbbaddacbcddabcaddcacaaadddbcccdbaaacaadadbaddccdaadadcbcaddbdbcacbbccdcadaddacbcbdadaccdccaddbaccdcacdcddccbcdbbadcaadcdccabbcacadcaacbcadacbdcadbcadbbcadbbddcababddaddbbcbacdbaaadcbcddacbcdaaaaacbddbcaacaaccbcbaaabcaaabbccadabbcbbcbdabbdddcbbaabbbaaccbabacddddbdbbbbabdcbdaabccacdbacadccbaddabcbbabdbdcbabaddccabaabcccdabdbcacccacaadddbbcaaaabddbacaccabbdbcdbdbbccbaccabbbdcbdddbcacbcccddaaccadacacbcbcbccccabbbbbbaccaccbbbcacbbcbcdbcbbddbcabbddddadbdbbddccaadaddaddcbdbddbbdddbcbaabcdacccdadbddbccbadcacaaabaddccaddbbdabdaddbdaaabddbaccdbbccbaccbbaadcabaabcbcbbbddcbaadcdbdbddcdadbbcabbddccbbbcbbbbcaadcdcdadbdddbcbddadcbdcaddbaddbcacdbbabbaaaadbabbcddbcdbaacbbbdbccdcccdcaaddbdcababdacaadcabaddbcbbabcbabbbaaccbcaccabddbdddabcabcddbcdaabacbdcdddaaaabbcbcdbabbaadabcbdcdbdddbdbbbababdadcbddbcacbcadcbabbbbdcddbddcbcbccaabacddabccdacacddaabbcaddbabccacabcbdacbcdccabbbbdbccdbbcddddcabbbcdddaabbddcacdcaddbaabccacbbcbcbaabadabccabbcdababcbdcdcdcabcaabcaabdcbcadcbdcaddccabcdcdaddddbbadcaaacccacabdbadacababadcdcdaabccdabbbbaaadcbdcbacbdabdcccbadbddcddccdcbcaacadcdbcbcadccaaccadccacababacdbdddaabcabaadaadbadccaccbbaadcbccbdadbdbadbdbddcdadaaddddcaccbadcbbdaadbaccbdbbaabdaddcdadabaaccadbddaabbddbbbaacadbbcabbcbccbbbcdabbaccbbcdbbbbddbdccccdbaadddbbbbddacddbdcdbbaacdcacdabbacbbbdbbcbcbadcaccbcbacdadabccaacdaacdbcdcbbbcadbabddcccbadccdabbaccdcaadcddbdbbcacabbcadccbcdcbbababcaacacabcaccacdadbcbbdaaddcaddadbcaacbcabbdcdabccbcaadcacaaddbdcaccdbbbaaddacdccdbbabacbcaccbdccdbbabadcabacdcddbcabbbddcbdccaababaadaacccccddaccddaaaddbaacbadbaddcbddbccbadaabacccdacbcbdadddbbcdccccbcadcaadacdcbacbdbdddadaccdadccabbbbadbcdbcabcccbaaddcacccabbccabbdbbddddbdaddbcadadcdcacaabddcacbbddbbbbaaadbbabdadabbcbcabdddcdcbdadabadacaccacbbccbdccdacccbcdbcdacadbbaacdbababccadcccaadccbbabdacbddacccbdbdacaabdbcadacaadaaddbbcdbadcbccaddbcbdcbaccddcaddcbcdbdcabaddbdcdbacdbcacdbddbdbbabcddaabdcdccdddbdddbbbcdbdaddadabbbacbadaaccccddabdbbbbaccbbcadddbacbacbbcbbacbdbbcdcbdcdaccccdbacddbbccbcdbcddacabdbdcbbbbbaaaaccabdbcddddbacdcbbcdabbbdabbddccabbadcaccbacbdbbdcadbaaacdaaddacaabacdacbabbcadbbccddccddbaaacaddcbbadbababaaaadadbbacdcccacaadaadbbbaacadcccccbdabbacbdbdcbbaacbbcabcabaaddaabdbabbcdcdacbbdbdadbcdddbadadabdbddaaaabcabddcdabbbbcaccccbacbddcbadbbcababaacdcbddbbbbbccddcbcbaaacbdbbbcadddaaccdcbabbcccbdbbcababbaaddcdabadbdbdbbdbdbdabababcddabcddbcacdddddadacaadbdadbdcddacdbccbbbbdbcddcbcacbaddabaccdaadbabdddcdaaadabbcbaabbdbdbcbabccddbbdcaadacdbcbddcadcbadbdbdcacbcccccbcbababbaaacabcadabacddbbcacacdbacdbadddacbbaccccbabcdbdcbbcabcbdbbdaadbbabbcdcacbabccdcadbbccbacccddbbcaddabcbdbdacdbdaabdcaadcadbbdbbadbbdccbdbdacbacabdcaacdbaadccadaadbcacbbbaadabccdccabbcbcadabadaccbcddcddcbccbcaddcbdbbbdaccbbaddacccbdbdaccdabdcaababdcbcdbadcdadabcacbadcdcdcaaaaacbcaaaabadaccaddcdcbcbbdadbbbdcdaccadbabaddcabcbddccaabadadcaabddcadddbbdbcdaabccdaadaabbcabaabbaaacdbabdcbaccdcccadacdcdcadacbddabdcbcdadaddabcbbdcbcbcdacdbcdcadbdaddcadacbdadaccdbdbadddbbccbdbcbbdbabacbcdbbdaadbccbccdbddddbbaaaabcdddbdbddbccbbcdcabcdccadcdccacccbacbcaacbcbacbcdabccdbdcadabcbdcdaddbccbbdacccaacdbdaabdcaaccdaccddcbccacabdddaddacabbbcbcbcbbcbdbaaaccdbbcbdccddabbbacacdcdaacddadaccbaabadddaccbdaaacdaaaddacbabbcdbaccaaaccadacccdbbabadbadbbcaaccddccbacacdbadbbacdbaadaacadbdbbabbcdcbaabdaaacddbcccbadbaaaadcdbbcadaccdbcbbbccdbdddcddcdadcccddbacbbcdabbbbcadcaadabbdcbdbdbadbcdbdbdaacdbdcddbababbbcdcdaccbcbbaaaaacccabdbbbbcacdbadabcacbcdaaccbcbbddbbbdbdddcdbaacacacdbacbdaabcddccccbabdabcbbddcacdabdbbbbbbacaabbbbcbbbbcabbddccdabccabcdbddcdccccbcadbddabcdcdccddbbdcdcbbabbcdccadadbddadaccdcaaabcbdaaccbacbccababcabccbbbcdcccccccaccaacbcacdabccadbaccdaccbbdcddcabdbcbaadaaacdbcdcccbdcbdcdabcaddbaaccbbddcaccaacaabddcbdcddababadbdadcddcdbdccbbbdddddbccdcbdabbdbbcdbdabcbaacbddbcabdbdddcdcabdbdcdccdacbcaadadacddccbdcdbbdddaccbbcbadbaabcaadbdacabacacccbbcdcdcbcdccbccdadbacdcacabddcbadababbcadabaaccbcacbccdcaccaddacdcdccdadcbbbbdccddbadaccacbcdaddcbddadabcaaaaaabaaabacbaccabababddcaaabaddbcbacabddddaacabdcacccbbdbaacdddbdcabacddaaaccdacabbccdbccbcdabbabdcbbadacaaaaacdcbbbdcbddbdcabadbbccbacdcbcdadcddcddcdaacabadabddccbbcbaadaadabdbccdccccbaddcbbbcdadccbcdabbdbdcbaababdbcaacdaadaadbaabdaabdbdbbdcbdccadddddaacbdacaadaacdadaabbabdacbbcbaabcbadbcacadbdbadaabbdcdddcbacaacbccabdadccdadddddaacdbddaccccddacaacbdcddcbbabdbabdbabaccacabdbdbccbddbcdcbacbddcdddbcccacbbadabadddaacdbbabababdbddbbddaaabcccdadaaccdbdaccdcacabbadabadbdcbabbcabacdaaadabcdaabaaadacdabbcdbddcacbbaddadabdbcdccacaacbcbabccabccadbdcaaadaaabdabbdababdcddcbddaabadadcdbdacbdbadbdcbccaccdddcccaaaccbddbccacbbbadbbdcdcdadddcacdcaaabacbccdcbaacdcabcbdddddacddcadcaadabccaddbccacbcdbbbbabcaacdddadadccaacaabbbbacadaadccdddbcaacccddacaabdbcdabcbdddcacbcbdabdbddcdadaacddcaacbcaadabbdcacddddaccbdcaccccbaaccccccdadcdaddbccaacaabcacbccabbadaaaabdddcccdbbbcdbdccababddcbdbcbdabaddbcdadddabaadcdababbbbaddddbbbbacaacbbadcadcabdccabccabbaaaccacacbcaabbbbcbbbcdcddaababacccbccdccbcdabcdbaadabdddcbabacdaddcadadccadabadbbabacddcadcaabbababaacdbabddbbdcdccabdddccdabbdcdcbcbabcaaabcdccaabdcdaddbbbacdbbdcdcddabaacbcbcdabcddcbadcbdcbccccdddaccdabccbccaababadbcaccccdbbbaaacbdcaaccbbdcaaddabbdbbdbacbbbcddcdadccabccbadacccdbdaaadbcdcbccaddcccdddddaccabcbbbbbccdcdcdccdadaadcccabcdbabaddbbbabacddacdbcbdbcccaaccdbbaddadcdabddabadcdbaabcdcccaaadcddbdaaaadcdcbbbbababbcadcdabbdbabddbbdacaabcdddbccabadaadcaccbdaaaacacdbdbbcaccdaabdddbcadbdbacddbbbcacaadbdabbabcdbbdcbabcaabddaabbabaacabbdbddcdbcbdcbbddaacaacbbccbbdabccddabbbccbaabaaabcaacabdbccaddbacbdacccdadcabccacadddadcbcdcabcacaababbdadaddbdaabaabaccdcadcbbabadacacaabcdaccadaaabbadaadcccdbaccaaaabadbbadcbdddddbbdcdbddabadaddbacacddacaccdbacbcdbddaadaadbcabbbbbdaddcdbbadcbcbdacccdabbabdacccbcccaacccbacdaabacbdbdddbaddababaabccbcaaccdddccdabdcacaabdcbcdbcdacbacabdadbdbbcdaddbacabccdabbbacbccdbacddbcdccdcbbaaacabcdaddbbaadaddcdabaabdbbcbdbccccdcbdddcadadddddcbababddcdbbdaacaabacdaabacbddbbddcbcbabcbaabbcccbdccbdbdbcccbdcadcbbbadcabcbcbadcdacdccccccaccadbccabbbcabadadcaacccdcaddbbaccbcdbbaddcccaaabdcbadcddccacbaddddccdabbdbddcacbdabadddbddbbdcacaaadbccaacddbabcdbaacdaccddccddbacdccaabbaddacdbacabbdaaaddccbcbaabdbbbdcbabddaabbcbbadabbdbdabcbcdcbbdcbddabadbdccdaadcccccdadaddbbddacbcabdbbaaccdcdddbadabbbadddaddacdcdccbdacadbbdcaddacdbacadbdcbcbccbdabbbdbbbcdddaabaddbdddddbccbcdacdcddcaabaabadcddccdadaadcddcccdbcabadbcdbdabdcbdabccddbabdaabaddaddbddadddbcdcadaaadcdabaddcdcadcaddbdbadadbcdcbaddcbddaaaababccbadacbaaaaddbacadaadbaabacbddccdcabdccdaaccacacdcaddbcbaddacdcdbaaabbdabcdcbccadcabbbddbbdadbbddbdbcbaacbbcdccbdadbbaaacddcaacdadaaddbaddaadacbbababddcdabbbadbaccdaacdaacdcddddcacbacbbdbcaadabdbbbdadabdbbccbdbdabdbdbabbcdacbbaacacdcdaadcaadddbdbacddbbdccabcddaacaadddabadcbbcaccddbbbcdbcdacddabdcdbddcdcabdcacdccaaabcbcbcadbbbbbccacdcdddcbbaddadaccddbddacdacccaabaccaaddddcaabdbadbdcdddbcbbaacabcdbdcddcabbddcaddddcdabcccabbaabaabccccbdaddbbbdbbadcadbdabcccabcbddddbdacabcbccddaaadcdcdccbbadcbbdbdbdacdadabcaabadbacdbbcdcdcaaddbbbcbabbbcdcbbbacddcccbabaacbbddcbcddadaaadacaaadcddddbbcbacaacacbacdbdbdbbbbddaacdacadaaadbacbababcbccccbdddcddabddddcadbdcbbdaabddabcdaacccdbdaaabbdbbddcbdcacdbdddbdabdbcabacdabcbdbaadccabacdacaabacbdccbbdcdccdabbbdbcccbabbdccdbbbbcbccddccdbbaccdcbbacdddbaaaddacdcdabcaadcbbacdaacaddadabcaabddadddbbdaacabdcabadbdadaddcdabdaccccdbaaadbabbdcccbababdccbdcabaabddbabdccaddbccbbabcbadcadcddbbbabdbaabddbbcaadbdbdbcbbbdbbcbdcaaaadbabbbaddacabababdbbabcbdadcbcbabbbabbaccdcaddbbaadbbbcbbdbdcbdcadaabbdaadcabbcddccddbcbaabaabcccabababbbdcabcbccadbdaaadaddbadbaccbaaacbdddcdadacbaacccddcadacbdaddcdddadcdabcdbdbbbbbbddbdaaaaaaacbaacbcacacabddccddbcdcdcddddabcddabacdcccdbcbddcaaabaaacbdbaacbdddcbbddcabacccadbdbcabdcbadabdbabdccbdacadcbbbaccacabddddbdcadcacbdacdbcbcdbacaadabaadcbadcdababbccbbcbccaccccaccccaacbdbbdcaccdddbaaabbacbbcabdcbdabdddccbaacddbcdcbcaaccbaaccdbcdbcbcddaccdcbdabbccdbadbadbcdbcaadaccbadbcdbacdbcdacaddbcabdbbaaaccdbddddaaacacbabbddddbdabdccbbabbaabbcabadabbcccbbdaaccaddbbcbcccabdbcacbbaadaadcbbadabccccdbbbdadcbadababbddaabcaaadbbbacbabbaaacddaacabdbbcabdccbbdbcbbacaaacbadaadbbccdaddcadcacddbdbadbbbddabbacadbccccbbcbacdaaacadbcbbcacdddaacaaacadabbcdccabbbbbcabbaabcccdaadccddabbbdccbbbaabbddaabdabdcdbbadbbcdcbdbcdaccbdbbcbcdabbbbaacdccbadccbbdbbbbaaddccbabaaabcdabdcabcbadbaddabdcdabcacbccdbddbcaccdbdcddacccaddacaccccaddacadbbadadcaccaaadbaabdccbcadabccdbaccdbdcadccdbdcadcddaabcacaaadbdbacdcaadcccbcadbbbbbcaddcddcbdddbadbddcbdcbcdbbcddcdbcacddddbabbbdabaabbdbcbdbdcccaccdcacddccddcdbdbcbdadbbdbdbddbaaadcadbaddbacbcaaaadadcccacacbbbcdcdaadbbcddbbbdabbdbccadddcdcbddacbbcaabcccdcaaccabacacbcdcbabdbbbcccbbdaacabcbaaaaaacbcdbcdababcdadbcccccacbdcddddbbcbdbdadabdadbacabcabbdddddbdcddadcababdacddcdbdddbdabdcbbdbbbbdabadacbdbcdaaaadccacaabbdaadbbcacaaccadcdbbaaaabcdcaccadbdadaddcbbcacdbdcbdccbbadcbaabbbdcbcabbaaacaacbcdabacccbaaabbaaddcddabadabbacdaadddbcabcbacdabccbacaacdbadcaccdcdabdcbaddbbcbdacbccbccaadddbcdcdbcaaccdcdcabbadcdbdcdccccccccdcdbcbccdbdbccccbcabcbbccabccbbacbdcbbadccbdbbdcdcbbbaacccbddaaddaabddbbddbcadcbabbdccdacddbabbabacaddcbcadcbcbcbdbdadadbcdbaddababdaacacabdaacdcaaddcaaabcadabbdbbccdabbccdbcdbcbccbcdbddcbabbbcddacadbcccccacdcbbcaadacadcdbcaccbabdbacbbbaddcaadbcccbbdddaddbacbacbabadadcacaabddccdcdddaaccabababdaddccbabbbcdbccdbdccbccdccaccabacdbacbbdaccabcdcdcbaacccbcbbcaabcabdaccbacacbbbbbdadcaabbdaacabdcddadbbacadcbccdadddaddaaabaccbdddbadbddacbcbaccbddccbbadbccdccabacbaabbacdbccaccbabadbbdcccacdbadaadaaaadcbbddcaadababdbccccaabdbdbccdaddcbdadcabacddbccabaaccaacdcaaccabdbdcabddbcadcccaaddacabadbcadcdbabccabccdcaadccadbddddddcdcaabbbacacdbabdcaadbabcadcbcbbdbabbacbbcbbaaddadbbdccbaacdccdccbccdddcaddddbcbadadbddababcadcccdbbbcccddbcbdcddcaaacbccadadaaacacacbbbabacacabbdaccacaddcaccdbdddcbddadcacbcdbaacdcadcdadaadbbcbabaabdbaadbabcbbbddabacadccbbbcbbcbccbabacacbcbdabbdacabcbadbabdaacbdcddabbccbaabddccacbdcdcbdbaccbbcdabdddbcbabbbcccaddddcaacbacbdddbbdccabbdabccbdaccadaaabbdcabbaabdcbaccbccaabbbaacbacdacacdadcadcdacbcbdbcbadacdcdacbbcabbddaabdccdadbddaaaabaaddbbaccbbabdaabcbdbdbacddabcdabdabaddbccdbcdbacdaabadacacccaddbbaadbdcdcaccbbcbcacbcacbcbdbcbbdcaddabababacbbbdbbbcdcdabdbdcdddacbcddabccabdadabbbcacadddddccdaddaabcccccbaacdbbacabbbbbdcaaadbbcadabdccaabcbccbcdbbcdbabcddaaacabcbbddcdbcabacbadaacbadaadbcbbccbddbdddcabdcdbddccbaddcadacccdaabdaaadcddbdbcbccacdabdcbcaacbabbaaabddabcbadcdcabcbacbaadadaabbddbabbcddbdbddaddacbdacadacccabcdccbdadcacccabddaccdcddbadbbbacaabdcacabccdacdbaccbddddadacbddadbdadadbcbdddccbabbddcbdabdccbcbabccaacbbbdbbbacbbdbcdcaadbcacaabaabaacbccabcaccaacdbacdbdbdadbdbddbdbdcdccbdccddccbddabdbbbabbaaadacbbdbccbbddddcccabbdcdbcdcbabbcabacbbcdaddcbbaadadbdbcadcbdcdacacaccddbbaacddddbdbbddbdadbaacbbdcbadadaacaabcacadcdccaaddbdbddbdbacddccabaddbcaccdadbcacdbbbaacccadcbcdbbcbbddacdcaccadbacbcddddcaddabcababddcadcdcddccadcdadbddbbdbcaddaaccdbccdbaddcbccccdcacbdccbddaccbadbdbbcbacbadcbdaacaddcddcadaacdddcbdadaaccdccacdbbaccddabccabadbdadbbbdcabdccddddbcdddbbaaccadddcdadacbabaddbabcccdcbabbaacbcddcacbcdddcaaaabcdbddbaccbacadccbdcbbadbacbcddbacabbaaccbcadcadbbdbcdcaadacdaabdcdbcaadabdbbaccadbabccddbcdabaccdbcbadcabddaaccddbcabaadacabbacdcddadabdaaddabddbccabbdbcacdbcddbbcaadbdbdbcdbcabccbcdcbccbdbdcdaaabddbdabbbcaabbcacdccccdadabbbbccddcddbdbbacdacdaabcaadbdbcaccaadbbdacacccdccdddacddcbaaadcbcdccabaccbbdbcdcaabdbdbcccadcbcaaadcdcbbdbbdcddbdcababcdacaccbccaccbdbbcdbbbbddadbdbdccddbaaacdcaaddcbcdadcbcaddddadbbabdbaddcaacccbaccabdbcdacabaaadacaadddbabdabdbcbaadaacdabdacbdacdcdcddcbabdbacbdcacdaddbdbbcdabbcbccddabdbcacaaadcbbccaacbbcadcbcdcdaddbddcabbbbbcdccbcadcbbbccccdbbccaaacaabdcdbbddbdbabcdbbabbabbcadcdbadccacacbadbdcbacdaddbababdbdccadcabcaabbadcdbabdcdbbaaaacbcdcababacaaadcadbdbcbaaddbcdacddcaabbdcabcaddbcbbccacababcddaacababbbcbcbbdabdbacdacbbadbcbbdacddcdddcbbbcbddbccabaddbdbdbdabdaabcddacdbcddbcadcdadbbabcdccdccbacadababccbbdaaaabaadbbadbccbcaaddaacadbbcbcdcccdbadcadbbdaaaddaabcbcdbdcdbbbddaadcbcdacaabdcbcdbacccbbbbcacccdacdcbdabdccbdcbbddddabdadacabaabbbadbdbcaadccccabaabdbacdadcadbbcbccdcbbbaccaddaddcaccabcdcaadadcbdadbcdacdaaccdbdddadaababbccbccabbddcddccbbdbaddadacdbcdcbbabbdbacbbaccabbaccaaccacdaccdcdcbacbaadbbdbddbcaaddcdbddbdaccabadbaaccccacbccadcbbcabbbdbbadcbbcbcdccacbbdcbbadddbcbacdbacbabbaddabdacdacaaadbaacdccaadaddddbadcadabbadcaabdabcbcaabcdbbbadbbddcaddbaacbbcbcddaddadbbcabacccdcbdbadcdacdbacddaccbbacaaabadbcdbcdcddbbacdaccccbcbdbbbdcaccbabccdbbcabdacbcbcdaaaaddadbcbbdbddddbaacbbbcabdacccbadbbbbddddcbccddabdcacadacbcdaadbadddbccbdcbbcaabbacbaaaacdaacbbdbacdcbbbcbaacbdbaaccabaabdabadccdbcdcdacbabbbcdccbdbbdaacaabdcacacbbdccccddcbbcdabdacccaddcbccaaaccacccdcacbbcbacbacdcddcadbcaacbaacbddddcbdddbcbacbcabbcabbbbcacdddbdacbacbbcadaaccdccdccbdabdbccddcbaadcddcdbbadbcdadaddabbacbdbdacaadcdcccdccddbbdabbccbaaaddababbdbdcabdcbbbcdbaddbbcdbabbaabcabdaadcdaaddbbcabaaadcdbdacbcddadbcdaccbcaacadcbadbaddcbabbcddcbccccbcddacaabddcbcbcacdcdabaccbbbbbbaabaadacaaadcbcacaccdcacbadcadddcabadaabadcbddabdccccbbbcdaadbabdcdbadabcbdccbaaaabbaddbbdabbdccccbcdccbbaccdddcbbabddddcdbacaacacabcadacabddaadccbcdacadbacbdddcdabcdbddaacbbdabbbcbaababacbcdbaddbbcccccddaddcacdaddaccdddabaccbaaaadaaadbbadcabdaadddbcbacaaadaccbbbdccacaabadabbaccddacadaadbcddbababcdcbadcadbcdbbbcbbaadcaabaabbbdccbdcdccbcabadabcdbdaabcaacbdabccbadadadcabdbdbcddcaabadcaddbaabdbbddabbdadcadbdbacabbbbbccbabcdbaaacacabdacacaadbdcacccddbcbdcddadcbbdaccddcdbbbadcdccdbacaadacdcccdcaadadbaddbddaabaaaabaadbdbabacadbcbdadcadacbbbabccbbccbddacdbacccbabbdbddabbadaddacbabcbacbdacadcaddcbbdcbacaaadcbbbacdbbdacdbdbbbadaadacddadbaabbcadcbadabaadbaddbaaaaaacbadbbacdabccbcbcdadccbdbbabddaabcddccabdcdbddcabaaaaadadabacbccabcacbddbbbcbddddcdbacdccbddbdcdacadbdaddcadbacbaacabdddcadbdddcbbcabcbacbaaaccddccabbbbcccdcaabbdbbcabcdddbcbcbbdcddbccdcbaadadcaabccbbacddaadacbdaadabadbccacdbdbaaacdabbaaaacabaaacbcadaacacddccccccdbccdbbdbbcbbdcaaccdbadbcccdcdbdabbddaacdccccaddbdacdbccdcbcadadcddddccddaaaacabaacbdbabdacadcddacbcabacabdbbadacccadbabbabacabbbcacadacaadaddbddccdcaabbdccbadadddddcddaabdbacbaabcddcadccbabacadaadabadbcbbbdabbabdacbacacabaabdbdacabddadcaabbbaacdcabbdbdbacbdacbcbacccadccdcbbdaccdaabaccacbbdcdccdcdccdbcbdcbadcccabdaccdddadbbadcccadaadbbdacabcdbddcdaababdbabaccbbbdbbcdadddcacabbddaabdcccbaacbacadadabcadddccbcacabbdbdccbabcbadbacbdabbdaacaadaaadcdccbbbbdacccaaadcbdcbddacccddccacaccdcbbbbdbacbaacdddaabccccdddddbdaabbbacadbabaddcbdcdcbdbbdcbbababbacdcbdcccdabadbddbcdbcdacdbccdcccddbabbadccaddddbdbcaadcdaaccccaccdcaabbbaddcdcadcbbcaccaddbcdbdaccdddaaabdddcbdbbddadadbdcccadacddcaaccccacbacadbababbdbcaabaccdaccbbbbdcabbacaddbbdccbcaddbcbcbaccaabadbbbcdcddbdcbcddcaddaacaabccdbabbabdaaabbddbbddaabbdcaccaaccaabbadbddccacbabcabbdcadbdcaabcacccadddcdadaabadbadbdaaabddabbddcaabcabdaabbddddbdcbadaaaaddacacacccabbabacdadbbbadadbddcccabbaaacdccbcdacbdcbcadccbcadcccccdacdbbaccadbcdcbdcaaadaacbcccbdaadadbdcbdbabacdbdbbbcdbdddbccaaacdbbcbabdaababadbcbabdadacbbbaadcbcbcaccabdbaddcdbbaaaccabbaddbdaaaacbbdaadbddbdcababcaddabcdaddadabacaadcdbcbcaacaabdcddcbaaddbcdacddccabdcaacdaabacadbbdabdddbdcbadbdcacdabdacbdacabcccabbbdcdbdacbaacddadddbbdadabadddcaaacabdbbababddaabddaccbacabbdcdadbdcacdaddcbddbddabdbaaaabdbcabbabdcdabbcbbdaaabcbcdbccccdbccbdababbcdcccaddaadbabbacccbacadcadbaddadabdbbddcacabdcabcddcccdccaadddcadcacbbcdcaccaaddccbdabcdaacaaacacabadccaadbbaaadbcacdcdadbcdbaabacaabdcabadbccbbadabaddbaccbcbcbdadaabbdacbccacccccaddccbccdbaddbddcdbccaabbccacccaadadbaddccddadbdbbbccbdcabacbadaadbabcaadaacdddaabcdadbdcccccccdbcbdaccbdcbdacaaadbbbbcbaccbabbacbbcaababacbddcabbaddbddcadbbdadabdaaacbabadabbcdccadabdcaadcabdbababcbcbabcdabccdabbcbbdcdbabcacdcabcadbdcbaddbccadaadddabbaadaaacccbccbdcdcdccaddcdccbcdbadbbadaaaabaddddbbddaacbacdcdbbdddbdcdadddbcacbdaacaabcadbdabddcccbbdcadbdddbcbbbbcdcadadbaaacabcadadacdcdddabcccbcacacdddbbdccbaaabbaccabaccaabccddbbbabcadbdbbcdddacddcaccddbaabadccdcddbabdcddaccddcbdaaabddbabcbbcbbdbcadabccdbabcccccaabdbcdbdbcaaabcdabcbcddbcbcaaddddabdaadccdcbbbcdccaaacacbdbdcacbabbdaabaabdcdbcbcacdccbbbabbddddcdbbddbbccdcbccddccdcabcaccabadbdbccbaabdbbaabbaacccccbcdaddbdaacbcbbcccdddcbaadabdadbbbcccaadaabcabbbccdcaadbcacdabbcdcbaddddcddbdcaabbabcdbaaccdbdbcdbcccbaadadbbddabbabccbbbdabadbbcdababcccddcaaccaabddcdabdaacbdcbcadcadbcadadbbacdbdabacdcdaabacdbbdccabaaccddacbbacdcddacbaddbcdaabdbadcacacadbbcbdacbbadabdccbcbdbabacacaccbababdddccbbdbdcbdaabcbaccccbbcadddbbcdbacaabbbcaacdcaadadaaaabdccdddbccdbadcacdadaccddadbbdcabbbabcdcddaddacbacbadcacbccbdacdaaacabdcbdabaabdaabcdbdcabababcbadacaadddcbcdbadcbdcaabcddcbcabcadbbcaccadabdddcddcaccadbcdbacaabbadccacbadbcacaacbcbbaaccadaadcacabdadccacaaaaaabdadcadcddabbadcdacabacbccdccaadbccadcbcbcdacaabcbdacabddbcdcbdbbddacbcdbcdbdadbbddcabdddccccbdcaaabbcdbcabadbabbadcdbbaadddcacaabadccdaddcddcbbdaccaabadacdccddcdbadddbbccadbdddbcbdbbccccbdadbadddbcadbaadbbdadcacbccccbacdadbcdcaadbabddcdbdbdbcddaadccddcabaabaaadaacacdddbcabdbcbdbccdddbdcdaaadbddcaadacabbbcbabdabccbcdbbcdcacadabdacacdaadcdbbaccacbaacdbdcbcbbcdbbcabcabbbaabbadcadcdabccaddadcdbabdaabddbdabdadcbdaacdacbddddbbbdcdccdcdbcbccccbcaacaabcbaccacadddaabcadbcbbdbbbcdadbcbbcbccbddabdbabcaddcbbabcbdbbbabbccdcdaaadacbcdbbbbddcbacdbdbcbccaabdcabdbbcddabbaabacacacdaadacbdbccabbdacbcddbcbcabdadbbbbcdadadcbdacaaaccdcbdcccdcccccbdaabaacbbcbcddbdadcddddbaabcddcdaaddddcbcaaadcbbdbabbdabbcdcbadcbddbaddacddccdcaadacadaaadbdccbbccabcccbdcaddbcaacbadcdbcaaaacadadaddccbcbacccbbbbdddbdcbbaccaadbacadbbcccdcaadbcbaddaddbadbaddbccaabbddcdacdaabbddcdbacbdddcbccaabddaacabddddaccbbabcdaabaaadbcbbccaaddadbcdcbddabddaacccabadbccbbbaadbbbbbadacdccdbcadbbcaddaddbdbcbbcdddabcabacddbdadabcbcbbdadcdaaaaaddabaaabbccabdbcddcabcabbaddcaaaaabbcdabaaacbccddbadcbaacabbcdddaaabaddcabaddadcaddccadacddccdcadaacbababaaccabbadabbadcaddbaacbccbacbaddacbdbacbcbbdcddacbacdcaddaccdbababacddcbdbdbacaccaacbccdcdacdcbddaddaddbabbdccbbdbddbcadaddacadbbbcadbbdcbdbcdbacddbccdccadbdbcbabbcacdccabbbcddaddaaccbcacadbcabdbdaaccddcbbdbcadccadaacbcccaddcbacddbadabcdbccbbacbddccddccbddbbbdcabdddcabacabbcbcaddbbccbbccbddabadbccccbaacddcdcddddbbcbcbaacdcbaadcdddddcabacbbacabaabbcdcbdddabdbdacadcdacccadbadddadadbdcaccabacdccaabcdadcdcabcbabcccdadccbbccddddddbabddcccaaccbdbddaccdaaabcdcadcadddabcabdadabaabdbaccdacddbcaabddcacabdbbaabcaaabbabbbccbccbddcdcdcadadbdcbbdacbcbadacbadddbbdbbdacbcdbccccbabbcbdbcdaabcbdacdbbcacbdcabbcccdaacadddcdcadcdaadddccbcbdbbacdcccbdcabbbdaccddddcbddaadabdcaabadccdabbabcbaddbcdbcabdbdacacacbcbabccbbbaabbbcddadabbbdcbcccbdadbacacaabadaccacbbcaabbccdaaaccdcccabbaabbddbbdcbadbcbacdacabaccabaccaadbcdbcbbccabbcbbdaabacabbbcaddaabbadabdddabdadacbdbcbccdcdacdccdbdabdcbbdbdadbaccbabccdaadcaadcbdbadcdcadcabdcacdaaccaababbcbaacccdcdbabcadababddaaaccaacddabbdbddccbbcaaadacdcaddabbdcaaaddbaccbbacbadacdccbbbcaddbbacdbcbabbdbaacacbddcdbaccddabdaddcdbccdadcdcbbccbbccdbdbaabcbacacbdbcabbadcbaccbbdddddbcabdadcdadbcdbbbbacbaabdadddaadcddcadbccbaaaccadccdabbcbdddcacdacabdccabcddcababbcdbaacbabcadabbcbcaabdabbcccbacabcacdbdbbabbdbcddcdcbddccbbbdabaddbbaabdadcdaadaabbdacbadbaabcacdddaddcddcbdbabbbdaaabdacadcabbadbbababaddcaaabbbdddcdbcccabcdbdbaccbdcadadcdcddbcaadcacabdadbababbaabcbacdbabcadcdbabdbbcaaadcadbdabababccabcdcadddcdddbbbddaadcdbcaadbbcadacccddaabdbcaadbcacacacdacdbccccdabcbbdabcbaccddddbbbabcbdbdadddadccddaaddbdbccbcacacaabcbbbabcadbbabbcddcaacaadabcabcadcdbdaaaacaadddacbbdcdbbcabcbdbdbbcdcbaadabddacdcabdcdadbbbdaacdcaadbcadcacbbbbcddccbbdcadbaaadaccacadddcaadabbcdbaaabdbdacbbabaaabacdbddacbdcdbbaaaaaacddbddbccadcaadcdcabcdcdaddbcbabccdbadaaaccbbddbaacdadcadbbaddababcddabcbaaadcabbbdbdbcdacbdbddaddbbcacbddbcdcbbddcccbcdbbbbdaaacdcdbdccbdcbbcbaacdcdcbbadbddcadcbaccdabbacdcccbbcccaccdbddbdabcdbdcadccbadccbbbcaabbcaddcdcdcccbccababbdccbcaaabdcddbdddcbadbaccbaaabaabddbdcaaacdcadddabdccbcbbdbdcabcbdcbddccbdabdbcbacbbacabcbdccbacbbadabdddaabddcbabcccbcbbaccdbaaaccaabcbdcacaaabbcaabaccacadacdcbacabccddadcccabdcdcdbbacbaacacabcaabaabadcbadcadcdbdccbbcabcdccadaacbcdcaacbacdacddddcadcdbbbbcacddccbdcdbbaacdaaaacbcdaaacbcabccccabcdabddcbcadabacdadbdcadaabbcbbcbacbacdbacdcabbccdcbdaadbcdbbaacaacdadaacdddbacbdbaabbbdcbbcaabddcaadccacbbacbdcdacacddcadabadbdacaccdbbdcaacaaabbcaccadccadaacdbcaadcdacbbbccbbbcbcdaadabbddcaddbadcbdaacdcbabacdcbabcccadcaaaaddbcdabaadbdaddcdaabbcaaaddcbddbdcabcdbadbadacdcccacbaaaaccbcaaadabbddbcdadbcabbcdbcdaacbdaadaaaacdddcccdddddccddcddcbdbdcbdbabcdbaacbdbaacbdbcddbaacdbabadaddbacdadcccadbddcbbdddacbadcaaacdadaabccbdaacdcabcddadbccbddcdabadbcddabadadddcaabddbaacaaacaaccbcdbbbdbbcadcadbccbbcadbbdcdddcacdaaabcbdcdbddaadcbcbccbccbcccddcaadbcbaaccdaaacadcdbdabccdccddbcdccbdaccdddccadccbdababcdbcbaaccbbcdaddcaddabcccadabbbddbbbcccdbbbcbcccabaccdbbbbdadbcddabcbcbddcbabbaacaadddcbcaddbccabcaacabcadccccabddbbbccdcddddddcdcabacdabccdadacdbcacabdaaddbccbcaabbbaabcdadccbacbdabbadbaaacdacdaababbbdbaacbdddbdbccddabbacadbaacbaabbcaddddadccbacdaaacbcddabbcbabcaddcdcbcaaaadabadbdbacabbcbddcbaddbaaabcdacdbbbadddcbaccdbdbdbcacdabadddadacaaddbbcbcbccdabbacbcabaccbadcdacbdcacccacacabdbabbdadcababcdccabacdaddaacadcbbcbacaabcdabbdbdddcabdabcccbcbccdacacbcbabcaadbbdbdbcaddbdccacdacaaddcbdbdbdaccbbcccdcdbcddcaddcddbdccdabcdacabdcccdabaccdcccaaccbccbadabdadcccdaccaadbcbdbcdbdcbbabdbbbccddabacdcaaccbbaaaadcddddccaddccccdaccbbdaccdbaddccbcadcbdbccdaaacabbddcbdaacacbacadccacbbabacaccabcaaaabcdddaddacccdadccbadbbcadddcdabdcbdaacacacbbdbabbbbdbbaccbbaaacbdbbdbcadcdcbbdaccdbcaccbbbcdaadccddbcdccdbcabdababcdabacacdabacdcbcddbaccbacdaabbdbbabbcbddcaadaaabbbbccbadcbccbaabdcddbbabcccbdacaabddcdbdbbabcbbacbbacbdaaacdabaaacbbbcdcadccaaccddaaabccacbbbaaccbdaadacdabccdadbbabddaacbacddddbdaadddccbaadccbdabcbcbbbabdbbddbacbdbbabdbbddccdccacbddadabddbbcaadaaabcddbcadbbbacbdbdbbbcdbcdacbcaacdcacdbaacabaadacabcdaaddaadacadcdddabbabababaacacacccbacdbdcbbdccaadbddbbdddbcbaacbbcbadbdadcaddcccbacdbababdabbdbaddabbdbdadccdbcbcaaddabaacbdbabbcdaaaabaadbddbccdcaacccacdbccdcdbbbaaaabddbbdbdbcddaaddccdddbaccdcadbadaacdbdbcccaaaddbccdccddaddaabadbcdcbdbccadddcbdccabcaddcbcbacbbababcccdabacdbabcbcaadbbdccdbcdaaddcccbcbbdbaacbdcdbacbaaabdddbbbddbbbbabcbdadcaadadaadccabcaadcbccdadcbababdbddbddcadbbbccdcbababdbdabbcacabaadbadaddbadadcbcbdacabaddcabdbcdababbcdaddcdacdbadcbbdccddccbacbdbbdccdcdabbdcbadcadbadddbabdccddcdbabcddbbadcbcdaaadcacbbacdcdbaaadcbbdadabdbcacabbbacbcdacadcbdabcbdbcaddbaaadcbcbbdabcbcdababdacdaaaabaaaaddbcadbdbbcbaabbdcbcaddbdbcbbdddddaacdbbcabbcbbbbccbadcccadcbbddccbabbadbcabbababdbdbdcdcdbabaabdacbbbccacabcadacddcdcacaabacbbdddabbaaacacddbaadaccbddaddbcabdabbbbacbccacdcbdccadbbcbacbaaaacbbdbbdbaccdadcbbddcaaacdadabcdbbccbabbcdbdadbddcbbccabacdccadbbcdbdcdcddbbdccaccbaadbcdabaaaadbcddcbbcaaaccbccbcddcbcdbacacccababdbbcbaadabdbaabcabadbacbcdaccadaaaabbbcbacdcccdaccddabcaacbcbdcaacbdcbbdaabaccbbadbbacabcbbcbcbccaabbaccaabdbcabdbbbbddcdcbccdcabddbdcabacadddaaccdbcadbccdadbbbcddcbdacccbbbadccacabbdabbaaccccddbdcddaaadcaacdaccbbbacadbdacbdabdaacbbacccdacdadabbcddddccaacabcccbbdaddbcbabdbdbdcdcaaaaaddcdccbadacdcccdacccdbacccbbcbccdbcbcadbdbbccaacaadabbddaccaddabbcbabbbddcdccdabddaacbdbcccadabdcdbcbbcaadbdbdcaabcbaddaccacaacbddbbbaadadbbacbcdcbbbdcccababbddcdbbcbdaadcaabccddaddaccdbcdbbdbbcbcbbbaaacdbbaccddcadccadccdadcddadbbdbaabddbcabadbcbcabbcbcccbccabddccabbbadcdbcbdadccaaadaddbdbbcdccaacbadccacccadaaddacbaabaaaacbdcbcbbadabadbaaabccaabadacddcbddccdaccbcbcbcbadaabccbbadddbdabcbdcaacdcdabbcaaddbbdcbbbcaabddbabbccaaabcbdcaddcdadcbaddcabcdccbacdbbacbccacbbcbccdaabbccadbcbddcbccccacabcabcddacbadcbbdbcaabaaadcddbadacbabbadddbdcbdaabdadbdbbabcccacbcdbcbccaccdacbbadddcdaddabcdaaccbbaddadccdbcbacabbcbadabacccddadcadbccbbaabacddcadbccdcbdadccaaddbadabbcabacacabbaabdbdadbdddabbcdabacdbdbabdbcbaaacadcccdcdaddcabbbdaabacadacbcdccdbabddabddbacdbccdcbaabbdacbbcdcddbdcdabbcbbaadcdaccadabcaddcaddbadabccddcabdaddcdcbbdcdbabbbaccadadabcdabddcdbcbcacadabbdadabcbcaccadaccaddadbcaaababcccabbabcadccbccbcbaadabbddbbdbaadbdacbabbbbbcbababcdadddbacbacacaaddbccdcccbdaacababdcbbdabdaccbddbaadaadbcaabdcbbbbdabaabbadbbbbdababbddbacbbbdcdaccdabcbbabddadadbdccbccabadcdaadbadcaacdabdddddabaabbdbccddaaacdcdadcbcbbbcbbbcbacabbbbccbadabbadddcacbbdcbcdacbdaacbabddabbcdabddadabaadacbbcbadbcabbcadcdadabcbbdbddaaabdbddadcccaaabdcccbdbcdabbdddadcaaabaababbbddcadcdbddabbdcbdccdbddbbdbddcddbacabbcbdbbdbccdbbbacccbdbbdbcbcbdbbccbbbcdadbacdbbbcdbacabccdcdbbbcadcbbabccbbbcabacdbccdacaddaabcddcadacadbdddbcbacbbccbbcbbbccccaaccbdcbbccacadcdabcbbbbbcacdadcadbdababacaadacabddadbdddaaacbbbaabddacbdccdcabdcddacaccbbdaddaaadcbcbadabcdacacdcadadcadbcacccacaadbccdddddaccbdcbbadbaaaddacdbcbaddaaddbadbccbbcadcaabcbbdadacdcabcbcddcdbaaaaccaaaaaccaddccdacbcbaccddaadddadcbdbcccdabbaddaadacacdacacbacabbdaddabbbdacacbcadccddbccccaddacccdacccbbcbbbacbabbccaabdcbbdbbaabbdaaacdcdcdbcddbcadbcdcdcdbbbdcadbbcbcdcadbcadabccdcaacacdcbcbabacdbbcaabbdaabccbccbbccdaaccdacabbbcacbadacbbbbacddababacddaccadddccacddcaaddbcacdddcdaabdcbcdadcccbcabcdabdadacbddaabbaddbccadbdaadbbbbdaadcdcdcbccddbbddadddadaabbabaadabdabacdbdaacbddacbdccbdbababcddaacbbbbddbadcdabccabcdccbcdcbcbbbbdcdcadcddbbaabcbadbaaadcbdccddacabbcdbcbcabbadcdcbbbabddbacbcbcbbcbddacddccccdcbbdbdcabdccaddcddcccdbdacabbdbaacbabcbdddabdcccbbbbccdccaccaddbadaccbbbdadabbbdcbdadabbcbccabbbbddbabdaadacbbaaadbbddbccdcabddcdccbaaabddcbdccaddabdcbbbccddbddcddadcabcbcbccabcdacdbbadbdcaccadbaaccbcaacbabcabbcbadbdadaacccbbdcbdccddcdcbabdaaddcdbdbbdbbabbcacbabcacadcbcbdbaaabaaccbdbabbbbbcdbccaddbbdbbbbbdbbbddbbacccccbaacbbccbddddcdbdaadddccccbcbcdaccccabadbbbbbdaccdbcbacdddaabdddddbdbdaaccbbccaccddbdcaddbbacaacdddbddaacabcbcccaaddbdccacbdaadcbadbaaacdacdbabcaddcbcbccabbbdbadacdabccbbcdbdbabbdbdadccbdbcbacbadacabaaddcadbbcddddcbcbcbbcdbbabacdacdbbaaaabcbbadaabddacabaaddddcddbddbbcdabdcaddbabcdcccbaddabbaddcbbbbccabdadcccacababdbaaccbcabcbbbcddddabdbabaadbbcbacacdcdbbdcdabcabcdadabbdaaabadbddacbdccddbcabacacadbdcbaabbbdcbcadacdaadccadcabaddbdcbaaaabddbddbbbbdcabcbaadcccbcdadaccccaccbcccdaccbabdacadabcadaadcdadbbcbcbdbbbcbdcbbdcabcccbccdaddddaaddddcdcdaccdccdcbcdacddbbbddccdadbcdaddbcddbbbdadbbdaddbabbcbabbcbcdabadbbacaddaaadddddbacbbadacbddaaababdabcccdbabdcbdccddbbacacabdcaccbadbacaddabdcaabddcdbaccdcabadbaabaacdbdbddabcbabddcdbcbdcacdacdcdacbcabddbcacbababbbddcdadcbbdbbacadaccbddbdbacaadbdbdacaddaacddabcdcbaaadccaadddddcbdaaacbcddcdbabaccacbbacadddabbdbbaaadcdddaccbadcadaacbdaabdacbbdbbaacdbcbcaadddabbbbaddbdcadcbbcccabaddcbdbadcaaabbdcbbaaabacbadaddabdddcbcbccbadcbdbdaabcccbdddaccadbabbccccaabdadccacaacbcdbdadaadcaabcdaabbcadcdcbdbacbdacdbdcaaaddacbbccaddccbdabdccbbdccdbcdbbcddddaacbcaccbaacadddcdadadcdcdcccccaabacabaadbbaddacbccbcbdcbbaabdbdcdbacdabddabbadcdbbdabcdaabdccdcaadbbddaadbbacdcccdadadbdcccbbacbcadadddbdaadcbabddaddaaabacbaaacacbadcadcaaddcabaccdaaaaacccacdbcdbabaacdbbcadaacbbbbbbcadddabbbddcbbcbbdadccacbddcbdcddbbdadcdcbbdabacddbddadaacaacbacbbbdcbdcaaaaadbdbbdcbabadaaccadaabbddbcdbaddbcbcabccdcbacbaacddbdacdaaabbbabbabdadddcdbabaaacccbcabbaaaddcdcacadcaaabcaacddbdcdddaaadadcddcbdbadbaaabdbccbacbaddcbbccabccbbbaaaabdcacdddabbaaabbdbdcdddcabdadbacccccbcabbcdddadbbcddbcaaccddacbbababdcadacdccbbbaaaddcdbdbccbdbbbdcacccbbccbcdcdabcbccdbabaacddacbcbdcbcaddccadbdabaaacaabbbbcacdcabbcbaccacdacddddcdcaacbaccabbcbabcbbbaacdacdddadcdaddbdadbdbbcdcccdbacdacaacabddbddcddaddbddcdabbaacacadcbddbbabadbabdbbbddbbacabbdcdbdbcbcbbdbaddaaadcdabcbcccacddcadaaaabaccdacbabbbacbabdaadabadcaadddabbcbcbacccdbaadcabcbbbbaaadaaddbcbbdaabacbadbbbdcaddbdbdcddcbdadbbcadcddbcdbccbabacddbbdcbaccdddbddccabddcadadbabcbdbdadcdacacaabddacdddbaaaaadabdbccdbdaaddcbbbdbbdbddcdbcbaacadabcddaaadcbacbcdbacdabbbaccbcccdbbcccdddbabaabdaddbbcbccddddbccadbacddabaddaacccdbbddcaabccadcdadbabcbaacbacdacabdddcdcddbbcaaabdabbcaccabdbcccadccbbbcabcacdcaacbcbcbabacbbabaadbbbaadbaabcdacacddcddacabccbcdabbabcdcdcdbcdcdbacadcdaaddbcbaccaacccaaddcadcdbcdabaaddccadbddaaacbcddaddddbadbcbdcccdaccbaddbdcccdaabdddddcacabdcadccababdbaabbddabccacbaacbdbadbbabcdcddaaacbcadcdddaabbdbdacbddadabdacbaabbaacccdcccaaccccaadbddcbaaaddbacabbaccbdcdabddaacbdcbdadaacaacbbaaacbbcadbaaadbbddadabacaaaabcbadbdbdcbaabdccdadcdadcbbdadcccabbdcbbdbaabccdabdadaadadcaccbdcbbadbcbadabbbcdabbcdadddccbacccbbacbdbacabbbacdabcdcbccaccbacadaccbbdabbbdbbabbdddaabbbcaaabddababaddccadabacdababacaaacbdccabacbccdaddbcdaadbcdacacdcabadddbbcdcbbddbcbcadbcdccaccbbcbdbddcdacbccaabcacbdadbacdadbabcdaabcbbbadcabdaadcdadbbbcdabddcbaadcbbbadaacbbacccaaddccbabbaacddbbcdccbcbcbaaacccbdcaaacbacdddcaabbabcaabbaaaaddcadddbdaabdddabadcddddabcbbbaddcbbbacddabbddcacbdcdcabadcdacdaaccaaadddcbdddbbbcabcdcdaababdbaddabaccdaaadadaacbccdbdcbacadcbcdacddbadccacddadacbaabacddbbbcdcaddcdadbcacccddbddbacaabcbacbcacadbbdccbddbccbdccbcdddccbdabdcdccbcddacdabbdbaccabdaaaabcacdcabdbddbacbdabbbdcacdcddabadadaaabdcdcbaaaabccddbbaccddabdaccbdcacdddbadacaddbdbccaadbbcbdabcadadaaabbcaadbdddbbbdbdcdcbcbabbbcacbaaabcadbcdacaddbaddcddcaaaabbdbcaaaccddabcbacaabbacaaadacbbccbdcdbdcdbbaadbddcbabccacdddaddadaaabddcdcdacdcdcdbdbcadadccdbabbbacdaabbbadabdddaadcacdbcdabdcbccadadbcdaabdbacddbabcbddacbcaacbdccdcbaaadbdbbccbcbadacdacccdcbdaadaacdddaacddadbbcddadbcdcbadcccccbacdccaddaccbdddbaddadbaabdadcbdabddbcbbddabdccaaccbbdaccdddadbbcadbcbbaddbcbdbbcbdadcdbadacbdaabcbabdaadaddcdbcdddcbccaccaaacaaadbbbccbcdcdbcaabccbdaadcaabdccabbccbacadadcaaaabddbadadcdacaacdacbbbdcdbdadcabbbbdcaaaaccacabcabbdbbcaacaacbdaddcdacbbacacbcacdcccdacdccdabbaabcbacbbcdccdcaccbbacdaadcccddccbbdaccabaaaaaccbdcccaacbddbccbdbccdabdadbaabddacbcabdccacadbdccbbacadbaacdacacadddcdadcccbddcadbcdbdaaacdacabbcdacbabcbdbbccbcbbbbabcbbbaddabaadbadbbdbadcaddaaccdcdadabdabccaadbcbaabdbbdacccdabcadcaaaaccbbddacdacaddaadcacacddacbdacddabcbbddabbdacbbacadccdccbaddcaaaabdaaadbdaaabcbbccccabdacaaccdbdcbcdabddaaaabbaadcbdadacacabababbcdddacbdadaacddaddbbdaccbbdcccdbacccbacbddbabacdacdcabbababcbcdbcaddacadabdccabaccaadbabbdabbbdcdbacdcbaabdbbdddbdbadaadccdbcadabbababaadbcccaacacaabcaadcbbabdadcaabbbcacdbbbadcccdacbdccacadaaddbccdadbbbcadcabdbbcacdaddddbadbbdaabbcccabcbbdccbbdadccaacaabbdcdbbcaacaaaddcabaabcdbccdbbadddbcbabcabcbcdddcddbbbbdaddacbbbadabcaacacbcaddbabacdaccdddabbdddabbdaccccbbdaacddbcaaacdaadaadbcabdbdbadddbcabadcbbdbcabacacabcaadaddabdddcdacacbddbabdcbdabdbaaaadacbdcabaccbbcdbbbbaccbcabacaadbdcdcddbdaddaadcadccabccaccbaabdbaccaaabbccabbccaddbbabddcdbabbbaadaadbdabdcdcbdbaddbadbdbddbcdcbdccbbdbaccbccdbddccdcbbbbaadcdaadcadacadadcbccaccbabbaccdcaabadacbcdbcdbccdcddbbbcbdadbcaaddacbdabadabccadabcbababdbcdbbacbcccdbdabbdddbdbaabcbccaabbddadbbdbbddcaabababacbaccdaaaccdacabbddcbdaadcdbdcbadddaabadccabbbccadbcbddcaaabdabadaadbcbadbabcbbbdbcbdbdddcbcbcbbaabbbacdcaadbbdaccadbaaddadcbacdccddcbcaccdddbbadbdddddcbcdbaacadbdacddaddbcadccacadaabcabaaacbbddaadcbbcbbdabdaadbadaaacaddccbbababdbdcddbcddcbdccbcadadcdabcaacbbcbdcbdbcdbdcdaddadbcbcbadcadcadbacbbaacdccdcbdacdcbddbdadacadcadcadbbadacbdacabbabbccaccabbbbcbcabcbabbabdddccbccdcbbcbdcdaacaabaadadbabdbdabadccabddcbbbcdaddbdbbbacbcdcbbdbabbabbcadbacbdbbbdbccbabcdcdbdccdbcbdbbbcdabcdaabcbcdcbcccadbbdabbbcadcbdacacccddccaadddddaaadcadcadbbccdcacadcabddccaabbabacbbdcbabadbbdabcaaacbddddaadcabdcdbbaacbdcbbcddbacbabacaacccccdabbcddacccbdadddccddcddcaddcbdbcddabcdabbddcadcbbbbbbcbddbbbcacdbcbcaabbdbccbdabddaddcdabacdcabcdcccdabbdacacbbcdbcbaaccabcaaccdcbbbdadbcaacdaaaddaddcbaacaabacdaaaacddabccbcccbabaadcbbdcbcdcbaacbcbddcdccdbaddbabacaadbcabbccbccccaaaadbabdbdabbcbbacdccdccaddcbaabdadbbcabcabbccbccbbccbdabdaacbadcdcadbddadbbbdabbcaacbbacbddbbcadbdbddacbabdcddbccccbbdbbaaccaacabcbcbccdbbcbadddadcdbdddcabccaabccccdbbdbacacbbccdadcdaaaaabdaacdbbbaacdbdcadcbddbabbbaaccaaccbaaaaacbadcbdcbdacacadccbabcadacdbbcdaaacbaabddccbaabdaacbbccdacddbcbcdadbccbcccbbcbaccbdbcdadcdbcbcccbbacdadcbbbdadacaabacbccacdacabcdbbadbdbddaabbbdddbbdaabbdbabcdcbaacdddaabcadacccdbdbbabbaaaaacdbaaccdccbdadaacbbadccacdbbaabbccddbbcaccaadcacbacdcaaccacdbaaaabaabbbbccbcddaddcacaddadaddabbcbbdacccaaddadacabcdbadcbbbbdbbbbabbaabacdcdaccccbddcbdbcbbcadadabbcababddacbdbdcbcbaabdbcbbbbababbbbbdcdcabaabbccdacdabadaabcabccddbbcaaccbdbabbbbbcdaaacbcbcddbbabbdaacaccaaddadbbbcbacdccdabdacbbcacbaaabcbbbccdacbdacccbdbdbaaaabcaaddcbcccbddaddcbddcacdbcdbcdbdbbdadabacbcabdbcdccbdcdbddababccdddcbabccabcdbddadacccccbdacdcaaacbddcaddcaccbabdabdddaccbbcbaaaaabcaadbacdaddcbbbcccdcbaabcabadbbbabdacadcadcbcabacaddacbddcdddbdbadbbbcccadddcdddccdccddbddbccaabacbdaccbaccaddbbababddcddabbbacbccbcbbccdcdaddddcdaddcccdcccacdbacabdcdbcccbcacdaabdcdaaacbbacdbaddcbccdccbbabdcacbcbadadbcadbaabdbcadddbbdaaaddcbdacadbcccbbbddadabcbdbcaacbbbdcdbbcdaccdcdbdcbbbddcccbcbacbacadbbacddcacaadababcbadbddcacdccbcccdabccabbadbcabbddcacadcccbcdbdcbcdcbaccaaddaacdcdadacddcdaaccadddacbcbddccabaacbdbdbcadbccbddccdddaadddbcddaaccccdcdccadbacadbcaaadcdbabdabccdccbbbacacddcaaccddcbacdbacdbbacddcbadcdaabbcbcbcccbcdbccacaddccbcabddacababdbbddaaacbbbdbcabacaabbddcdaadbabdcbcccbaaadddcdbbcbccbcbacabcbbadaadcccdacbccadabbabadbaccdbaadbdabbbdccdcdcacbbabdbcadddacbccacabdcaaaaacdbaaacbdbdcccadcccbcabcabdccccbaddddabbdaccbcdcdaddaddaaccdabccaaccadcddcacdcaadaccabddbdccabbabddabcbbbdaacdacbaabaccdcbdbcccaccabccbadddcdbbacbddaadabdabbccdcbdabdaacaacaddcabbccdcdbbaccabccbcabcddcadbbddcaaaacdcababbadcdabadbcdbbacdabdcadaadcccccddcdaddbbacadbcbdabdadbbcabbbcdaaaadbcddcbadbdabbbccbaabcddbbaacaacbddcaaaaacaabcddbcacaaddacbcbaccabbcabdaaccbcbbabacdcccadccbcbbcccbaccaacccaddbabbabcaababddbaadbbadcdbcbaababdacdbbabdacbbcddbcdaabcadcacbabdbabdbadadacababbccdddddccddaccbbcbdcbdbdcadadbcbdaaabccaacbcdaadbcabbbacadddcabdddbabbaadbcbcadaadccacdadadccdbbdbbaccaacdbaacddadadbddadacacccaddccddabcaabadcadcdabacdcaabaabbaacabbacaadcaacacadabcccdbbbcdcdadadbcdcbaccdcdbbdbcbaaaccabcdbdccdcdddadbddcddcadbaaaccddabdacddacbdadaaaccaddbadabcabccadadbbcbbdcbaccbcbbdddaaabbbcbdddcbbaccbadbbbadbbabbcbcddcbbddcccbacdbddbbbabdabdadbadbdddbaaddddbbdbdcdcbdaacddacbdccddadcbcccccabbcdbadcbccdcdccbdaaaddcbddbbcaddbcaadaccbbccdbbcbddcaabadaaacbacdadbaacdcbbadbdaabcbabcdadcabaacdcddcdaadcadccdaaaaaddcadbcadabadadbcabaadadabcddcacaddbdbacdacbadcccadcdcddcbdcdcbddbdbccbcccccddadabdbddaaaddddbaccbddaccbcaccbcdcdddbccbcaddcbdcbdbbcbdaaccbcabddbddbcbacabaacbadcbcdbccbbaadbabdabcccbadcacadacccdabdcaabbdaadccacdcbbcacdcbddbcdbaacabdbcaacabadcaaabccdbbdcabadcdbabbcdddddbdbcbabadabdadccccbcdddbbaacbbdadbabccccdbadbcabdcaaaabbdabdbcdaacbadabbcbababbbbabbabdcdaaaaabcacaaacababdcacccccdcdddabddadcabbbccbaabcabbadcbdaadaddcdcaaabbbccbaddbacadcacbbaddcacbdccaaadbdadcaacacdccbdacdaacdadcdaaccbddaadcddadcdcbabadbcbdbdaaacacdacaccbdaaabbcdcbbadcdcbaacabacddbbbccddccbacacdbddadaccbabccdacadcbbcbadaaaaccbaccdbbdaaacdbccdabbaccabddaadbcbbbdcdaaaaadcdaaabaacadaddcbcddcbdbaddabdaaabcbbadddbcdddbdccbabdcbddcddbcbbabdbcbaddccacddbacbccddbccddabadccddbcddccddadcacddcbcbddadaabcbcacccbbdcddabdbdcdadbaddbbddbabcacdbdccbadababaababcbaacdabcbddbadbbbaadcdaadaabbcdaddbccddaccbddbddccdacdadabccdccabadcbdabaccbaadcddbbdcccdbabadddcbadccbdbaaccbdcccabbacaaabbacbabdbbbdbccabdaddcdabccccaccbcdaacabbbadbbcbadcbadadbbacdcbcbdcbacbadcacacdabbcccbbdacacdadbaaaccbbaaadcabaddddbaddbabadbbccdaddbacbaddabbadabcbcddcbdbbbcbcccbcaddadbbbbbddacbcbbcaaccbcbaabcbdddbdddbbdadcbbbdbabdddaddadaacbcabacdacddcdcacbccbcbabbaddaabbbcadbdcacacbaaadbcbdaccccbacdbdcbacbbddabaacbaacacdcdbbacacdaaaaccadddbdbddbcbcaddcddacdcbacbcaaadbdddbddbabccdccaaabaababacbaaddcccbdbabbbcbbbbcabdddbccbadcdcdadbaacbbbdbdadbcdacaaccabbbcaabccbadbdbdbbabacdcbdddacbbbbadbcabbadbbcddbbccddccccbaccacbcadccdbdacdbbbcaacaabdaabcccaabaaccdadcbbbddbbbdcadbabbcbcabdddbcdddbdacddcbcadbbbcaaaadacddbadddaddbabadcdbbcadcaaaccbcacabadbdcbaadbadbbaaacbccdccbbaadbddcdbddbddbccccdcddbdddaabdcdbccdabababaabcdcddccbcadcbbcbcbacccdccabdcabababacadaadbccadcbdbbcdcccbbdaddbabbdccccccdbdbcdccdcbbccbaabadadddbccbccaaaabadcbbdaaccabdbbdcdcddaabaddadacabccbccbbbdbdbadbbabaddacacbdbbabacdabdcccccacbdbddaccdbcdddabbcbcacdbadcadcbdbadbaabcdadabcbcdbbbadccdaacdaccbbcbadccbbaccdbcdbddabbbdbacaddbdbabdabddacdcaaccdcadaabdaadbbbcacacbabdaadbbacacdcadcdbabbcbcddaabacbabcaadacdbbbbbdaabaadadcaaabbbdcacaccbbacabdcbcdccbdabdcbcdcddcccabcccdaaaddacdcabccdcdbbaaaccaaacdbddccdddccaadcababbaaaabbabacccccaddbddbdbddcdbdacdabbadbccacbcbbabbccbbaddbcacbdcbcdcbbcacaadaccbdbbddddbadacadabdaddbaddaddaddcbbddcdbcdbbddcbbcbdabdcbcdaacccdbaacadbbbddaccdadaccbcdcacbdabccddddbdbcbbddabbcbddbcdaaaacdacdbcdcadacadbdddbbbcccbbdcadcddbdbcbdddbcddbdacdbdcbacdaaaabdcadabdbabbccccaaadadbabbccdbaacdbaabaaabcacddbdccaaaaababcacbadaddbaabacddaccbbcabdcaadbbcabdcabadabdcddbccacdbcabcababbbcbdcabdabccacdabdbadddbabbbdbcdddbbabcabcabcccbcabbddabbddbbcadbdadccbbadbdaccacddbadbbdbbbcbdacbcacdbaabdacabadaabaadbadcdadacbbadacbdbcadddacbbbcacbdabacdddcddaacadadcdbabbdccccabaccdbdccdcbaccbbcabababbdbaabdbbacbcdcaaacacabdabdcbababcddabadacddcaadadcbbddcccacacadcbcaaccdbdacdadddacdbdbbadcabdaabbdbdaacbdadcccdcccccddadbbaabacdbdabcccdaccaabacadbbbbccadbababaccbbaadabdddcadabccbdddbdbbbbaddbbacdcdbaddbbbbbdcbbcacbdbabcaaaccdbdbbacbcabaacbacccbddbcdbcbcbcbbbdcdbddddddabcacdddbbcacbccbcdcdbbaabcaaddbcbaccbaabccbdbdcadcbdbbaabcbbbadccbacaadcaacabcbdcdbcbbcccbdaccabadbadddbadaabbbbcbdbabccaddcaabcbbdbdcdbdcbbddbadbbddbbdaccbbddababadcbaadcdaacabaaccbccdcadbcadbddbbbbadddacaaabdbbcddabaddccbdbabaccddcbaacdabbabbcadadcacbccdaccddadbbaabdcddacbbcadabddbcadcbcdcdaddcdddcbdcbaadddcaaadbdcbbcadccacabbacaaaaddcbababbdbdddccdbbdbaacddacaccdcdbddbcaddacacadadadcaddddbbdcacacdaabadadbcabbdccdabdaaacdbbabddaddddabaaaacbbcdabdcbbbabcabdbaccaccacaaccccddcaacdbdddacbdadadbbdbdcdccddacadddcadabbacbbacdababbdadbcdbcccdbbbcccbadbdbddbddcdbcddaaccaabdaadacdacdddddcabadbcbbadbcacbdcddcdaddcccccbcbcaddcaccacccdabbcdaacdbababbabdaadbaadabadadbdcdcadaaaccdbcdcacbbdddccddbcbdcdbccdadbbaabaddcbdaccdcbacdcbdcadbdacbccddcaccaacaacbbdaabcddbaacccaaccaacbcdaaacaacdacdcccaabaddccdcdabbabdbacacdcbadcdccbbbadcbabcaccaacbdddcacacdabacabcddaabcbdcaccaacbcacdcadcadcdacbaadacdabccbcbcaabbdbaabbcabaccaadcccabbbcacbccacaaadcdddbaadaadddcbabadcaccbcadcccaaaaccbcdcbcccccadacaabdadbdaaabcaddaccdccbbbcaccdbabadcdccabcbdcbbdbddcdcdcdcadbdadacadcdcbaadcdaacadadbabcdccdcdabbaaddbdddadcdbbdaddbbacadabcdbdbddaaacdcdddcdaddcbbbaacdacbdbcdbdadacdadcddcacbabcdbcbcbddcdccdcddbacaddbacbddcbbcaacdbdacbbcdddccdabbbacacabacaacaabbacabdddcdcdbbdacabccccabbbdbcbababbabaddbdcbacabcadbbabbcdbabcacdaccadddadddadbabacdbdbddbddddcddacddbcdaabccaddcdcadbbacbdbbaabddddcbbdbdbdbddcdaacbbdcdcdbbacacaddccbadbbacdcadabcabaacdcdbdbcccbdaccaddacbccadddcbcddabbdbbaaddacddcbcccaddccbdbbcdaaadbdaadbdacaababcadccbccdaabadcdbdccbbccbcacabcadccaaaacccdaccddcabaacabaacbbadcccbbccddabdaabacbcbbdbdaaccdaadaadbdddddcdcddabddadacaadabbbbccacacdaacbdacaaddadacbcbddababcaabaaccddbcbbdcbabdbdcdcddcaadabcdaabcdcdadbbbcaaaabaabcabcbbcdacbbbccabdcdbdbcdbbcbddcccdbdbccadadaaccadbdcddbdaddbacacccdcccdddbcbacbccbdacbcacddaddcbcabaabbbabccbcabbcbbdcacbaccbbacabcaabbccdbaaabbcaadbbbdbdbacccbbdadddcaddcacdbdcbaadcbdbbdacaacbabcdacdabadabaadbbabbabbdcbbadcccdbdcabbacddbcbdbcbbadacaadbbaaccddcdcaadcccdacaacdbdbbacaddcbaacbabccbdddcadcacdcdddbcdbcdbcaccccdbbadaddcabbdccadddbdaaddcbcdcbadaaddadbbccdaaacaddcdacaadadbdbcababbdbbadcbaacbcdbddbdcdcbaabbdacaaaababbdaaaccdcbbdadcddddccacacbcbdadddacbddcadcdaaaccaacabbcadacbdddacdbdcdbbbcbddaddcdcdbabcdccdbbbaacaccdadbbbabbabadabbaadbadaacccbcdbcdbaddacdcbbdbbcdcbcccccadbdbbadcbaadabdcbbdccdbabbaacadcbbdcbccdaabbdccdaacbbbcbabdadcbbcbccbcdccbddccaaabadcaaaaadbacccbcccadbcdaaccbcdcbcbbdabbaabbbccdcdccbdbcdddddacbaccdddbbcaacadaabbdbdcdbacbbabccbccadcadabcabcbcdabaadddadcdccabcdccbcdaaaacddbdcabacdbcabcdaaaaaaddddaaabdacbdcadcaabdcdacbcccdbabbcbddcdcabbbdaddcbdbddaccbadddaaccccbaabbbdddadabdacbdcbddcddabcaadcbadabbccabaddbabbaccbdbdaaccacaadbacabdbabcdaadbcccccaacddbdaacacaaacacabcaddcbdadbbcdbbbbdaadcadbaccccaaccdacadbbabdaccbabbabacadacbbcbacaaacaabacddbcbadcdcbdddcaadbbbdcadaaadbcadcbdbbdaaabcdaaabbbabbaccbcaccaccabbbadcacdddbabdcddcdcbaaddababcccadabdbbabbcdadadaccbccbdbccbdacdbcbbbcdcbdcbabcdabcbcbddbccdacddccbdacdadbccbcacbddcaaaabdcdacdbbcadadbdacbbabacdbacadbcbbbdddaaabdbacdbdbccdcaadbdbcdadccdcbaaadbacaadbbabddbcabbcccbabdcdddbbccdbbababacddcdaddabaaabbbadcbbdddcbcbdaddcacbbdadaaabdcccbdcbddcbbdabddcccbaccaadabdddabcbaccadbacdbcacaabccadddbccdccbbdbadccacbcdaccbcddbcbcacacbddbcbccbcbacdddbbccdaccbacddcacccabadcdcdbcadaaacaabbddddbbdacbdacdbdabcbcbacabacaccdddaddbcbddcacdaabbbabaaaddacadadabaacadabcaadabcbcdbcdadcaabbbccdddbaadcbadcddbdcbcbbdddcabccbcddbdaaaaadacddbbbbacdbacaccdbacdcdbdcadddcbbdbabcdadadcaadcadcacccbcadbdaddbdcaccadbadabcbcdabdacabadbadbbadbdddadacccbaaaabdddccdcaadccccadaaadddacdcabddbbacbccaaabdaccbdababcbabcaacacbbcacccaabacddcbbcdbcbcaacbacacabbcacacdbdaabbabdabcdbabcdccddabcadbadcabccdccbbcdbdbaccbabbdadaccbaabcbcdcbbbcddbddadcddbbaaadbaccbcbaabbdacdccddbbbaacbbabbacaadaaaabdcdbddbacdcbbdabccadadacaaadcdadcbaaaccacbacabdcddadaaacbbbbcaaabbbbdbbbabdbdcbbabddabaccadabcaaccdacdbaccdccadbdcdcbbcdcadbdbbaaddcdaddcaabcbdddcaaaacddacbdabbcbdccdacdcbcbbacbbcdcaaaabdbcbaabadcbcdbdcbacbdddbaabdadbabadacbdcbaacbddccdaacccaacaabcbbadddcbdbabcaabdacbcdccdcdbddbdccabbabaddddbadcbbacdaacccabacccaadababdddbaacbbcadcaacddadcabadcbdacaacbdaacadcbdddacaaabbbbaaaaaaccbcbdaabacaddccccdbbdaaddddabbbcabcbcdbdccaadabbcdbacabbbbccbbdddabbdabaddbaaddbcdadccacddcaddabaddddcccababcdbcccbbcdbcbbdbadacaaadbdccddcacdbddcacadbbbaadcbcaccacccdaddbacbdadbaabbddbbdcbadbddbdbbacaaabdbdcbdbcddacacdacbdbcabaacbadbddcaabddcdbabbdababbabbbddcaccbacabadbbbcdbbdbacbbabcbccabcdbdabddddbdcbadbcadbaabbcddcbdadcabddbadddaaacaacddbaaabdccdcdcdaccccdbdbbaabccaabcdcccabbcdbdbbacbcabbabbacddabcbdacabbbcbacbaacaabbaabaaccddbcdcaccbcacbaadcbbbdcaacdcddbadbcadcbcaacdadbcdaddbcddbcbbdcbcccadbcbdccdddcdaaadcdcbcbbccdcbcdacdadcaabcdbbacdcbdcbdbddcdbddcbbbbcdabbaabaaacbacdadacddddbcdbcdbaadabdaabccaccbaabcacacdabdaccbddbccabdcdabbddadacdcacadddaadddbabbcbdadaccddacabcadabcbcbaccbbcdaacddaaadadadbcdddabcbacccbccbbbbbbcdaacbbdacaabbaadcdadcaabdacdbabbcaabbadbbbcaaadaabbccaaccadcadbbdcbcdbccabdadaddaabcbcddaabbbdcdbacddacddacbaccdabbddabbdcdaaacdbdcbddbdbacadddabbbdaacbcbdacbabccbdcacddddabcacaabdbbdabcdbdbbbdbcdbdcdabdaacbdbcddcbabcddadcdaacbcdddbbcbadbabbdbdbcccccddadabcbcaaadbcadbddaadaddbbdbbbabbbbcadaccbbabcdbaabcabbbdccccdadbbddbdacbdadbadbbaddacadaacaadddcdddaaccbbbabcacccbcaadbdbabdacdbacabaabcdabacbaccabcccaadcdbcacbabaababbbbbddbdaacbbdbccbddcdcbccdaacadbcbbadadcaaccccaabddbbbdcadddbbaaaababbccaccbbbabddaaddcabbbcabddbaddabcbbbdbbaddacdbbaadddbcacccbdbdbbdcadabaacddcbbcbaacbdadcdcdddcadcccadbaaaccdaabaccdcdbbdbdbddbcbaabdadbdccaddabdbbcacababadbdbcabbdadcbadaddcbabacdddbbababcdccbaacabbcddddddbbbbdbbcadccbbbadccabbccdaabaaccbcdabaadbdcddddadadcaabbdabdcbabbcbddbdcaccccbcbacdcddbdcbcbbbcbdcdcddcbbdaddbccabababaacbacdcccddbaddddbcaddcaaacbbcbabdbbbacadaddacbbdcaaadddaaabbbcaabacaaacbadccbcacbdddadbabbbdbccdbaddbbdcccbbcadbbccbaabbacacbcddababcadcdbbbccdbbadabbacdcbdbcacbdcaaccdbbdcaacbdabaacdbddacddbcadcabdacabbcbcbbbdcbcccabbcccdbdbbdcaacdcdabccdaaadbbaaaacdbdbbbabbdabadddccbaddbbdbcabaaabbaddcaadbbaccbcacbacbabccddcbdcacadbbbbbbdccbacabaaadaaabdacbbbacbbadccccabbaadcdcbcdaacadadccddbaccdacdbddbcbcaaaabccadddabbaaaccdacdbaabdacacdbabdcbddbabcdcdaaaccadbbaabdcbadaabdbccbbccdccaabcbbbcdcdcbdadaddaabadaadcabbcbcbacddddccbdaaabaadcbbbdbcccddbcbbadcbcbbdbbddadbbcddabdbcacdddcbabbcdccbcbabcbaaacbabcadbdbababdbdccddddbcaaadcbdcccbbdacdcabbdbcbdadbadbcdbcacbbdcaddbcabdaabacccacaaadcabbccddaaaaaccccbdacabccacaddbdccdcdadcacddcabdabaaadbcbddcbcbcdabdaccdbadddbcabbcabbdbaddcacdaaacbcdcadbaccaabbdabadccbdbaaacabcadadabbdababdbbbdadbdaabddbcbbbdbcadbabaccaadabdddadbdcdbccbbdccdccbdaaadbadcacacaabbdbddcbdadcdbcabccbaabcabbdbacddbbccabccbdaadabbcdabbaabdcabbdadacccdacacaabdccccabdccbacdddaabcadadacdbddccccbbabaccdadcdbaabcdcdcaaccadcdddbdbaccdbddbdadddadadbadcbbdbaaabddabdcddadcbcbbbbdcbcabdbcdbbaccbabbbdabcbbbdcbdcbcdbdddbdcdcdabddcbdbdaccddacadbcbadbcdaddbdaadddbbbababdccacacbcdbbcaacddacbbcdaaaccaddbadbaddcddbbadbbdbcdccdadbcbcdcbaabbddcdcbacdbcdbccacaacdcdaaabcdcadaacaddbdddbbabbadbadddaadcaadcdcacdacacabdabaadbccaaacdddbbccddabcbdaabbdabdbdcdabbddcbdddadcaddbdcbbabccbdccbdaccadccdcacdacbcaacdcbcddbaabbcaaddbcaaacaaddadcadacabbbbabdcdbccabacdbddcacbccbdbababadaadacaaaaddadaccdadcccbdccdcdaaddbcbacadbbbcdbbbbcddaaccdabbababaccbaddccddabdccbdcddcccaabaacdddadadcdddbdccdccbbaccababaaadddbadaaccdbbcccdcbabbbddddaaddbbaaacccdabdbcdbcaccaacaaacdcddcaddacbdbbabbaddacdddaadbdbaacaacdbbcdbdbcbabaabaabbbacdcddddaddcdbdaabaaacddddbdabadbcadbadbbadbcbccacbcdddbbbbabbdddadbdadabdccdcdcddbccdadcdddbbacbdbbacaccccbddabaaddbdadabbbaccdbbaadbbdabaabdabcbadcacabdabdbcddcdaabaaacbaddcbcaadcbbcbdbacbdbbadbdababacbcbaadccbbbadbcdcdcbacaaacbdbbdbcbcaadbbcaccbaaddbdaadbbbbdcaaaabbdbbdbcaadbcbdbcdbabcacbcacbdaabdbddabccbbacbabcdbbcbbccbbacbcdcaaabaabbdbbdaccccdbcadcdbbaaccccdbcbccabdacaadcbddddcaabbdbababcbdadadcbcadcddadcccbcdccdbbabcadccaaaaaccacbbabcddadddcbdbccbccbddaadaaccbdddcbabcdbbbabaaadbbbbcddabbabdbddbadddcadadcddcbabcbaacccaadbbbdaddaaacbcddacabadcbbaaacbbcbcbccdcddbcdacccdacddabaccdbdaaabcdabadcdaccdbbcaccabacbdacdddbbadaacbaadccdbdcccbbcabbccbbbcabbdbbdabbddbddaccdbdaabdcabdcbdddaabaaccabccadadccabbbcadcabcccdbaccbbcdcadadbcccbdadbacdcadddbababacbbcaaabdbcdaaabcadcccdbcddabacbdcabaaddccbdcbcaaaaacdabdbbdcbdabcbbbddccbbccadcdcdddccacbcdcdabadbbbdcdbdabdcaaddcaaccacccdcdbddabcbdaadaccabacadbdabbccbaddcbaabbbabcacbbdabcbaddbcbbbccdbdccadccbbbcabbdbdaadcacdcabcddbddacdaaddcabddadcdaaddaaaaadcabbdbbbdcbcbcddccbbaddcddadabdbbcabdbbdddbcbdabcdbcabbacbdacabbbccdaaabccddcdacbcbcdbdacdcbaabdbcbdaaddddcbadbabdbcabacbccabdbbddbcbcdcccadcddccdaacddddcbbccbbcccbdadaddcbbbbacacdbabdbccdccbdcbcbcdcdddaacccdbbacaccabbbbacbdbcccbcacbbcaacdabacbdacccacbacadaaadbaaadadbacbabbabdcbbdcdddccbadddbdacbdadaadcbbbccdbacdcccaaaccdccdcbccbccdcdbadacbcadddbdbccdadacdacaabcbbccabababccaddcdbcccccbabaacbbdbdbcabbbdacaadaabaaccbdccdcbcaccbcbabdccdacbaaddaaddcabbddbadcabcdaddcddbccccccddbaadccbddbdadddaaadcdcddaccdcdddbadcabaacaadacaadcccacdbdbdbddadacadaabbdbdbdabcbadcbcddbaaacaaaaddaaccacccdbcacbadbbdbacbddcbcbddacdccdadadccadbdaabdcaacdacdaadabccadabbccadcbccbdbacdabcabcacdddcadcddccbcccccbaaaaddbcdaaaabbdcacbbbcddbdbcddbbabbddbaddcabadbddccdabcbddaadabbaccabddbbdbbdbcacaadcaabcadddccadccaadbadbbbdccdddbdbccddddabbabcddccdcbbccadaaccacacddcacddbadbabdccdaaccbcbaccdabbddabddcdcaddcccacdbacddbbdbcadacdcdcccdbcaadabbaadbdbdbbccdbbdadacbdccaaaaababbcacbcdbabdabcaaadddadbbbddcdcaacdcdcccabdcaacacddcbbcadaaadccbcdbddcccddddbacccbcdcaabcdbbcadcbdaacadabccbdcacaabacacdddccbcaaaaaddcaddbbdadadabddabbbdcddcbbdaacabdcaadacacbbcabbdcdbaaabdbadadadddcbcdaaaabbbbadacdadcabaabdcaaadccacacaaababbdabaddaacddbabbaadbccadaabcadcabdcbaccaabdcddddaadcbcaccdbbadccdaaacadccaacbcdcadcdbcbcdbadabacadbcddddbadbbaccbcaacccdcacbdadbabddccacdbbbdcbdadbccacadaabddbcbdabcacbbbbccacdcdcccccacbcbbdbccacadcaabbbaddbcadccdcdaaaabcdacddcdcacbabdcaadabddbbccbcccdaacabdcacbacbacccdddacacdcdbabbbacdbadbdaaccbbddaccbbbcccadcbcdcdaaabbdccccddcbddaadcabdccbbcccbadabcdcdbcccaccadadbbbcbbbcbaabadcbbdbaaabababcbcdccdbdadadadacdabdcdcccbbdababcaacddabbbdabbaacccbabacadcddbcbddbdaababccdaddabacdabdcabbbddcdbcaacbbddbcdcbbababbdccbbddadddcddadadaadddcccdbadbbbcdaadbbaabdbcccddddacacbaaaaccdadcaccdbaddbbdcbaacaacbbdcabdbbbbbcdbacbacaacabdcabddbcaabacbbbcdaacddbaaccaacaacadcbcdaabcccccdbdacbddcbbcdcccbaacadccadbcacabbdbaaddadcdaddbbccacbccbbdadbdbabdbcdacabdcabcbaaaaccdccbacdccddaddbdbdccacbbbcdabccccaddcacbadccaabbaaddccbcdbbadadbbabacaacdcababbbbbaabcdcaaabadbbdddbcdcdaddcdcbbbdcacadcccccaabddbabdcbbbadadcaabbacacbbddabcdcadabaabaaaadcdbacdcbaccdccbcbaabaaabdbaddbabbbbacbacabbccbccccaabadbdcdcdabbccdbdbabadaabcdbadbdddaadbbaabbddbdadaaabcabcbaddbaabbaabdbcccadbacbabadaababbddcccbbbabccdabdadccdcbbabdbcadabdadddcbbacccbbcdbcddabbbacacaacbacbdccbadddcdddbdaabacaaadadbabcccdacadaddcacdcbacabcbbbdbacbcdbcbadbcdddadabcadacbbcacddabbaccbcabbcaabbcdabbbbadacacbcdcbbdbadcbbabaaabacbcbaadaabadabccdabdabdbadcccbabcbaccbbcccbaabcdddbcabccdabcaabacacadcdcccbbabdddbdcdbcadaacdcabadacaabcaadbdacddbcbdaaddacbdccbbabacbadcabdabcddbccddccabbdcaadadccaccbcadbaaacdbdadddbaccaacccdbbacdccdabbbadabcddabdcaccccbbdddacdbdcbcdcddbdbdcaaabdbccabadcaaaacbbabdcabcadaddbcdcdbbbaaabcdacbdcbbdbcbdbcbaabdaaabadcccddbbbabbbdcccabdcddabcacbdcdabaacdcabcdaabdaabcbbdbdccddbcabadcbbdbddcdabcccbbdddcadadcdddbdcadcccdaaddbdbbabadabbcdabaccbcdabadaddbdccbabcacddadbaadbdaabacbacdcdbcaaadcaadaccbcacabcbbcdddbacdaaadabddbbbacaabbbbdcbdbbdbbabcbadddcabbaadcdaddccddabddaddaaaadcdccccaadbbadaadadddbaccaaabdaccbbdcbdabdcaadcabcdaadcdbbadbcabbabcdcbdadabdcaccdddbdaaabcdabdabaabdadcdcdbdbaacccbadacbcbadabbddbdccabdcadaacdbdddcbbcccbbbadabbacbddadddadccbaabbcbcdcaddacaaaacabbdcddacaabcbabdadabcaaccdcdacabcdacbdacdacdabdbacbcadcabcaaaaddababdccaabadbddddccddcaabcddddbbddbbcbbbcdcaadbddadbbdddaddddcdaadabbddbbacbacbbdaacccaaabbdccbacbcaddabcbdbdbddacbdcadabccacbcccbdbdcdcbbbcdbdacbadbbcaadacacaadbaabccaabcdaadbaaabbbacdbbbdbdcbabddaaddcdbadabcadabaaddbdccacdabbbcabbaacbddbdadbadacdccdccdddaaacadacbadccacddbcbcbadbcababcaacabadbbbaabbadddcdadcbccbaaaccabddcbcabacdabaccdbccbaadbbadddddcabacddabbacacdabcdacddadaccdaccbdaaccbacadcacbbbcbbadbbddcabadabbbdbcbbbcaabccbbccbdcdbdbdccaacddbcbbddcacbacbabdbacbadacdadcadcddaaaddbabacbdcababcdacadabacccaabddcaadbaddaddcdcaaddcdccaccaaccdcddccdbbbabbdcbcabdbbbcdddadaaaccaadbcdddbbdbdbddaacccdbdbdababcdaaccabbbabccabaccccccbbccdcbbacbbadddcbacabbcbbccadadbddbbabcaadbcdaaaadaabaaacdadbbcddaadbcdccacbdbdadabdaaaadcadbaccddcdccdcbcbaaaabbbbcbdcbbcbbcaddddacbdccacdabcabbccacabdccabddbaacaddddadacbcadccdabdbabdcaacdacbdcddbddbbbabbabcbabcabccaaaccaaabdaabccaaaaabcbabccadcaaaaccdcccdbbadcabcbdcacccdcbdadadabcdbbbccdaadcdbbcbaadaabdddbacbdccadccbbabadbbbababcdccabbcdbdbbacddaccbbbaabccdbbadadddbbbbddaaccabdaacccbbcacbcdcdcbaadbdabaadccaddacabdbaddcaccbdbadddacacdcbbcdbbdcadcacbdadaabdcdcbcdcdacccdabdcabbdadbbbcacadbaacbaccacdcaaabbcdcadbadacabbaacabcbccdacdbaababddcddacddccccacdaaacaabdbcbbacabaccbacdcaabdaaaddbbabcdcdaabdddbbdadcadbbcacadbabdcbbccdadabdabacbdcadbdaaaaddccbaddbcaabdcbdcbaccbbccabcdcbccbcbdadddcbbbddadcbcbbcbccdbdaccbbbdbbabccdbaaadcddbaacaddbaccbccbacbacdbdddbabcdbadcaacdcdbccdaddddccbdcbcbbabaacbcddcaccccbbabadcbadaaaddbabaacadbaadabdcdbdbdddaabadbddcbcaabbaabcdbdbcdcadadbcacbddaaddaacbddbadaccabcccccdbbdcdcadadcbdbcbaabacadababdcdabbddcccacbaacacbadddcbddbbaccabacbdaccabdacabccabddccddadcbaadccbcdabccddcddcdcbadbcabbcdaabccbdbabbbbcbcdbbbbbccbbbdaadaadacbdbbccdcadcaddccddabaacbacbabacccaabcacdadbabdbddbccadcdbdabdccdbdbbabbbcbaaacbccbabbaddcabcbddbccadbdddddbacadccbdccbcabcccadddaabcdbdddccbacccbabbbcdcabdcbadbbbcabbddbcaaadcbcdccaaaaabdbcbdbcbbbcbababadadabbdcbddbbaddddbbcbdbdcccbddcdaabbdcadddbbaaaaadcddbbadbbbababacabdaacdcacacccadacacaacddadcbdbacbbbabcadccbabbaadabdcbcbacdddcdbbdaaabacabdbdbdbacaaddabbcbadabcabdcbbbccadcadacdbbabbbbacacbacdcdcacbbcaaaddbbbcdaababcdbbbddddbbcbdaaabcddcadacabdcacbaddaaddcdcbdccbcaadbabdbbacbddadcdcdadabbccababbdddcadaccbdcabbbabdbddcbcbdaacccddddadcdbbabcaabbbabbdcaacabcbbacadcaccbcbbddcccdbbabacccbbccddcbacdcbcaccddaabcbbbddcacabcdddbabddadbdabbbddadbdcabaddabddbdaabbddbabadddbdbdadababacdadaacbbcadabbcaadddcdcddcdadcdadbcbacccbabbbcdddcacbcdbdbdcdbcccaccbcddcdaaabdbaacbdbbaccacbababacbddadcacddcdcacdacbccadbcbaaabcaccdcdaabbddbbbdbdbdabadccacbddabddbdbdabdabaabdcddcaaaadddadddaacabcbacdaadcadcaccbbbcdabbdcbacabbadccbccaccbcccaabbbcabdcbbcccbcbddcacbdcbbdaacabacccaaaacaaadbdaacbccadacdcbaaadadbacaddcdaabdbcdacbbcbccbccdbbadabbbbcdaccbbdacddcbaadaaabaacbdbdbabacbbbaccbaddbbbbdbbbdddbbbddddbddccdabbbbbbdadcddabcdcabaaddcdababddabcaabbadbcbbacacccddbadcadcabbcabddabdcaccbaadcdddbbaaacabcdaabdddbadbdacabdabacbcbcabacaccaccdaabbaaddcbcacaabccbdaddcdcccbcddbdddddccddbadbdabbbddcbaaddacbdcbbbdcbcddcabdaddabbbbbbcacadcbdcbbadaaadbbabaacccbaccdbdacdbcbadcbddddbabbacdacaaaadcbddbccdbacbdaaabbbaccbdabacaaacdcaabcacdaddcdbadcdadcbccddaabbbaacccbdccccdbdababddaddbdddcadaaabdbadcdbaadabbbdddbdaccadddcabcadddbdaabbdcabcdabccdcdbdddddabbababddcdbbadbabbdcdccbdaabcbdbbbbbabacbdaaddcaaaacbcacaaddcdccdbdadaabdaadbaadaabbcdaabbdcddcabbcdbbdddddbbadddbccbadbcdbdaabadbadcbcacbbcdbdcaaddcbbddcddbcbabbaaddbbbcdcbddbcdbbaabacbddbbbdcdcadabaabddacdadacbadadbdbddccdccccbdcacbbabbacabaddcadbaddcacdabbddaacaaccdabdcacbdcdddadaccdcdbdadcbdbdabbcddbbbaaabcbdbdcbbacacbcccddbbbdccaacaccdbddaadbacdbacbaabdcdabbcbacbbcbdbdabdabcabdbabbcdbabbbbbccbabcbbbbdcddcccddcdbadacaddcbccbbcccaadaccabcbccdcaaaddcaaaabcbdbbacbdcbbdaacdadcbabadadbcdaaacdbcbdbdaaacdbbbacabdbbdabaaddbcacbbacdaaddbbccacaaccabacdcbdccbabccabbbdaadaccaddcbdcddadacbacdddbbbaddbcabbdccabdddbdcbabbaddcabccccacaaadbdbcaadddddbabcccaadcccaaaccccdcddaacdcacacbdcbbddabbbbdcaddbbadaadbabcdbdaabbbcadadccacdacbacddbcbcbccaacdbcadaabbddbddbbbcadbcacababcbbabdaaadccbdadddcbbbaaaabbbcdabdbdbacacdbbadacbcbabbdbabddcaddbaddaabbbbcccdbabbbcdacdbdbabbbcdbaadcdadddacddddcabcaaaabcabbaddaddbaabdbadbcabaadbdbcaabdcddddcccadadddbcbbbaabadbbbcdddbaacaacbcadcbcccbbbddbcdacddcdbaddcabacdbadabbbdbabcbacdaaccaadaccccacabbabcacacccdaddbccdacbbdadcacccbaadcabbcabdaddbbddcdddbbdbacbbbccdcbaaddcabaddadbaaccabacadacbddddbbacdcbcbaacdccbbdccadcbbcabbaaddcbbacddacdacbdcbadaddddcadcbccdbcaaaabbcaccdddccacabbdbcdadbdcabdbbaacdabbadbcccdaacaabbcbbcdcbddcbacacbcabdacbdbbabaccabacabdbdadcddbacbbaacdcdacabadbdddddaabbaddbadcdaadbabbddcdddcddbdaacadcacabbaccddcbaaddabcbcccbadcdabcccdbcabcabacabbbbadadbdddbdcdadabbcadabcdcbbbcacbaacdbaabdbcdbcdddadaaccbcbacbdcaacddaaabdddbcbcbdacacdbbbabcaaccbbcbabbaadbdcbcbddccbdbbcdacdcdbbadcbabbccbcacaccdacbbbcdcbbcdcadbcacccaaccaacabbccbcddcbcccddcbdacdababacaaadbaaacaacdcbcccdadcdaabccdadcbabcbbccdbbccbabbdbbccdddaadbaaddbabaccdbdbdabdcdadcacadacaccbaabadabacbbddbbadbaddddbdbaabadcdbcdadccddabbaabcbdadbbddaacdadcbdbdccbbcbbadbacbbbcbdcadbdccbacddbbadddcdadcbbdddabbbabbdbbbcbbdcbaacccdbdcaddcacbbcababbbcbcacdabaacbadbcddcaaccdabcbcdddadacaabdddcbdadddadcbdabacabdcdbccccabdddbdcbadacacdaabaddabdbbdccbbdcdbcdadadabdcbcdbddbbdbccadbbbbdbcbdccababbbccbadddccbdccdddcbccbcdacccbaddccdbdbdacbcdabdadcdccdaadbdbdcacbacccacaddcadaccadbbcbaabddcccdcdbdadcbacbcdaabdaaabbcaacabacbcddaabcdbdddbabccccaacbccbbdbacbbadddcccbcadabadaadbcbdbdbdcdbadddbcdcccabcaadcddacddddacddbdcaacdbacadcaadabbacbbbdddbbbccaabdacdcbcbdcaccbcadbddacdbabbadbbaabcbaaaddcbdbadaadcadbccccbbcbcbcaaaaacabbbccbbbbabdccdcccdaacadaccacadadbddcdabacaacbaacbdaaddacccbaaacccdadbddbccbddacabcdbbccbdbddabdacabacacacacbbcdbcbcacaadadddbbbdaccbacccbcadacddbacacdbbcbdaacaaaaaccadaaaddcdcdbbacbcddbabdaccdcccaadcbbccaadddbdabbacabaaccaaacbddbcbaccbbbdaadcbdddacacbbaacaaadacabbbbcddaacbddcdbadabbdaddabbcdacdadcbbdbdbbbadaabbcdacdccddbcdddaddaadcbaacaabaccaccabaddadabdbacabadbcaddabcdcdbdcbacadddcabaacacddbbcbcccadaddbbbccbbcdcccacbbbbbacbabcccddccdbccbdbadaadadaaabcccabadccaabbbbbdcadddbaaabbbacdacbacbaccdcdbcccccacadbadddbbabdbcdabdbaacbbbddbcbdbddcbbabadbaddacbbdabcacbaddcccdbddbdcabbcbcdaaaabcabcbabcdcadddbcbaadcbbbddadbdcdadacdddccadddbaaaababcbaaddacacadccdadccdbcbbadcdddcbddbcabcdcbbaccbadabcdddbabccbdbabcadaadabadbbcdbbbabacbaabccdcbcabaaacccbdbbacabbcbdadcdadbdaddccbdcbcbddcbdcbcddbccbccccacdcbbdcbcbdbcbdbddccadadabddccbcaadcccddacaabacbddababcacdbbbccdbcdbdcaacdaaddabdbdaccacddcbaddcccccbddddbcbadbcdcddacdcaabdcdcbabdbadabaccddbcaacbabcbccadabcdadddbaccbabcabdbcbcacccbcdccbbaacccbadcdacdadaddcbdccdacdabccadacaddbbadddbbccbababbbdddacdacbaadccbbddccdbacabbabbabbddcdcabdaddacbbbdbdcbddacbadbdaccacddcaccbddadaaddcabbdbcccccccabccbdadadbbbabccbdbacaacbdcacaabaadbdabadbbbaadcaccadcacbbababbcdbdbbdcdbdbbabacbddaaadccaadddbcaadcdddccddbabcddacdabddbccdcddbcbccddbccaacdadcccbbcbdcccbcccdababcabbbaddccdcbcdbbcdbcaacbbcdcbddbbdaadbbbbbacabcdbcabadacccccacadddadbdbccbddaccbdaabbacdadadbbcbbccbcdaddbaabcaabbdabbaabdddcbbbcabcbbdaabcdccbdaadcadbdcdaaacabbbbabbcbccbabaadadbdbdcdbcbcaabdcdaddbcbaaacdbaccdccacbdddbcdbdaccaaaddbbdabaacccbdbcacddccddcbcccdcdcdbacacdabbcbbabccbbbadadcadcbdcbcaccddbcdacaaadcabbbcabaccdbdbcdcbdccdbabbdabccdbdbbcdacbbcdbbdaacabaaacddbbcddddccbbcadadabcddcababbcbcdababdaccbaaaaaacdcddccadacdabbaaddcacdcbcbabcaaacdbbbdcccdcacababbbbdabbbadbaaacdddcdcacdccbcccbbbcaacdbadabcdbbcbacacbaccdbbcabdccdaacdbadbadabcdcdbadadbdbdbbdcbababbbacdababcbaabbcbbdbcbabadaacbcdbdbacdbdddacbdddadbabbccbaadcadbdddbdabbbabbadddbbaadcdcccadacccdddabdddcdcdcabdbbbcadbccbaadacabadccabbdbdccbadababddbadacdccbdbcddadbcaadcabdadadcaacabbbaadacabadccbadbbccaddbcbdbccadaacdacacbbacbcabdcbacbcdbbabbbcacacbdddcaabacdcdabcbcdabbccaddbadbbadddbcbbdcdbacbcaddadbdddacdbadcaabdbacdcaacccbbdbacacdcadadbabdaacacccbbdabcabdbdbbccdcbbbabcdbacadbcbbbbbaabccbcbccbaaaadadabdcacaddddaadccadbdaccdaccabaadcbcbdabbcbccaadcacdcdaddbcbbcdccbaddcdddadcabccdbddaabccbcdacabaacbcdcddaddabddacaaccdbbccbbabdaaababaaadcdacbcbcacdaccddcbcbbadbabbdaabcbabbcbcacadbbbbaccaddcdacccbaacdbaacacddacdcbdbabbbccdabdbdccbbdbaccbbcdadddccdcaccccbcdddbdaacccccaaccbbccbbddbbbabbdaaacaadadccbdadabcddbaabdcacabccbbadacadddabcbcdddaadadcdbccaadccaadcddddabbcaddaacabaccacbadddcadababccadcdbadbbdddacddacbadbbabdaacacabcbddcdbbddcccbccbbcdacdddacbdbbcbbbbaaacadacdaaddbabbbcddacadbddbabaabddcbabcdcaacbacdbccbddcbaacdbaccabcbbdccbacacbacdadcddaddcdbbabacbbcccabdaaaaddabcbcacdbdacdadadddbacddbbdccbcaccddcbbcdacdbdcdadcbcdcbaccbddccccabbacaabacaacacbbadacdddbdacbbbbabcaabadbdddcdddcbcccadccbbcdcbaabcbbddaadcadbadbcbaaadcadaccaacdabdddbacbddbacdbbbdcbdaacccbadddabcaaadaabdbbdacdcbadcddabaacadbbbdccdcabacdccaaabaddadddaadbdbabdabccaaddcccdacbcabdccdcacdcddbbdcaabcdacbbabddccccacdcaaacbcaabdbacadaabdaaaddbabbcbbadcabacabddaaacbaaaacdccabccbbacccadadcbbdbdddbdbbbaaaacddbdcdacdbcdddaddbabccacdadddcddacbdbcaacdbadaabbbcbbcdcddabcacabbbacbbcbababcbbccabdbccccacbaccbbbdcbbcacacdadaddabddaddacacaaaadbadcabbbbbbcbcdbdadcdbdccabcccbddcbabddacddbacbbdddddcddcacbabbadaddcdabdaaabddcddabdcababbdbbadcddbbbdadabdbbddccccaabdcccbcccaabaadccadddddaabcdcbabbadcbddcdcadbaccadacaaccdbbdbaadddcbbbcbcdabbdbaddcbdcdddcdcbbadaaddcdacbdacabdbccdabaccccbadcdadabbaabdbbabaabaddacbacbcdadddbdddbaacdabcaccccbaabcacbadcacadabcaaacadcdddbddaabdcbadcbddacdbcbdaaddaddcbdabbaabdaccaadaacdacddbabcdbcacccdaabbaddabddabcabcabaadccdabdbbcaccccbcbbcbdaacccbbccaadcdccacdabbcaabcdaacdabddcaadababcddaabddaacbdbbbcdcadcddccabdddcccddcdcbbbdbaddbaacaddadbabdaacdabbacacdbaabcddcddadbdacdcbdcbbbadaaaabdcddddbdaaaaadaadcacccaacdacacbdbbdbacddbdcbbdddcbdddcaacbbbdccddabadcbdbdcdbbbaabacbaddacaabdddaccdbbdadabbdaddbdcaddbdabcaddaacaabadbbbdacbaccdacbadbbbacaaaadacaabaacadbddaccabbbaacdcabcdaacadcccbdbcaacabbacccdcdddcbaaabdddcdcdabbcccdaadacbdcccacabbcaccccdcdaadbdbddcddbcbabdccacaabddcdccbccddbccabdbccabadccccbbbdbbcccacddcaddccadbccaccdbdccccddcbcaacdcacbbacacbcdcddabbccbcdbbddacdcdbbdcdabbadcaadbbadcbbbddbbbcbabaabaaadbcadaccababdacdcdadccbdbacbbcbadcddcbacdddcccccbaacadaddccababbaadcdbcdbcaacaaddababbbbbbbdaaabcbddcbabbccdbadcdacbacaddcbcaddbbccccdcdadbaccaaccdabcdabddcdabcacbaadabcdbdacbacddabaaccabbcdcdaaacbdadcdaaaacbdbcacabaccdaccdbbbadcbacbcbbbaacacaddbdbcdacadbcacbabadacdccbbacabcdcaaddacbaabbcdddccccabcabaacabaadbddbdcccbadaddadacaaabadaadbadadabcbcdddcadcbdbdadddbaaadadcbdcdbcbdaacbabcdbbadddabbdabbadccbdbccacdaacabcdbadbcdbddbdccabdbacaaaddaccdbadcdbadddcbccaadaaadddcccbbaadccdcbbaadacbbadacadcbaacbdccdcccccbbababcdccbdbbddcbbaaacadbaaacbdbbdcddbcdbcaadaadcdcbccbbcddbccdcdbabcbdbcbbccdbababdccddacbdbdcdcadddabaaacccdacabbdbddcabacbcbdbabcddbacdacbcbbacbbdddddcaaabcacdcdaccbdadcbcdcddcbccbcdcbadbdcaaddbcabcddabbcdaccbbccabbabccdcacdadbdbbbbcccccdcbbccaacacbccaacaabcdabaccaabbbbaddddaddcbdccdbbbddcaacddcdcabaaacccaadbacbcabacabcdcdaaaaccbabdcddbcbbdbbbccbdabadaaadcbbbabcaaaaadabadccaaaddbdddadaddacdcccabcdcdaccabdddcaabcddddbddcabbbabbddacdacbddbacccabdcdcabcabddbbcabcddcbdbacdacbdcbaacaccaddcacccabcbaccacbccabbbdabcbbabbadcabcbbbdaadccdccadcccbbabdcabcabdaabcbbbdaacdbbabbadbadbcabdbbdcddbbdcdbbbaadbcbdcdcacdbcacdcdcdbcacadcbddbdccbbacbaddccadaadbbbbbadbccaaddccbabccdbcdbddcbcacbbcdcbddbdcbccbacacbbaacdccbdbbabacaadcdbdbdddaaadabddccdcaddcbbabbacdbdddcdccbcbabaacdcaccbbcbcabbbbdadcadcadacdcdabacdaabdadbbdcccbbabacaaadcdbacbcddacdddccabbbcbbaabdbcacdbdabcbbdbcbbcabdacdcbababaaadadaacdbbbbddaadddcdbaabcbdabccabdcbaaaabbcdccbddaaccacaaacbabcabbacdcdbdddcacdcaaaaaddbcbcdadabbcdccdacddbdbccdbadcdbddcdcacadabbcbddbbbbbaddaddcaacaaddabcbabdbdacabacddccaacbdacaacdcdcbcddaaaabdaddacadbaaccdacbdaabbaaddcbcbaaccdbdbbbcabaadabdacaadcdbccdcccabdbddadbcbbbdccdaccdcdaacacbcbaacdcacccccbcaaddbaacbcdbacccdbbddbacbdcabcdbabbccdbaababbbbdcadaacbcbdbdcabaaddcbdbacdabcddacabacbcdccacbbabaaddbdbdbcdcaccdbabdcbcccadadddbabacbbbdcacbbbadccdccdbcbbbaddcacaaacbbcaaccdcaddbaaacacbddcadcddabbbbdcbbdaccadcbbbadaddbacdddcdcabadacdcdcbaaabccbbcbbbaccabbbdbadccddaacbbdbbdaadacdabacdddcacbdbadbdcbbbddcdabcccdddaacabbbacddddcbdcbddccbcccbaccadabacdaaabcabcbdabdbaacddbcaababaaddaacbccadcbbbbaaccabbbdccbadabdadcbddbbccddcdcbbcdcaabbdacbcbabccabadaaddabcbbababdabdbbabbcddcdadaaadaabdadaddcdbabddadadaadacabbbcaaadabdbdbabcdbcddbbbbbadacacbabdabacbddaadccdbaadccabdbadacbbaacaabdddaddadbaadddcaaccbccaabadbcbccdccdddacccacbabadcbbcadbaabbbadbdcccdabbcbbdccdddcdcbccacdaacaaccacaacabcbbdaacadacdaddddaabbbaaaadaacbbbacdcaaacbbcbcbdabacddddcbabaababccdccbcaddcbbabddbabddddcbaacacdcacadcbdabcacaacbbbbdbbcabbadccaabcdccbcdcbaddcbcbaacdbbadbccaabdcabddbcdbdacaacdcbbbbbdadaabadabaabacbbabbdccccbaadabaadbdcdadadcdcabdddbbadbbdacccbbbccdbdddcbbcaddcaaaadbbccbcbcbdbcbaccbdbcccdccaaadaabbbabcbabbcaabbccaacacdcccadaaaabdbadcccbcabbccdadabbdbcccaaddababdcdacdbabbcccdbdcbbcdbdaadbcacddcaccadaabdaabcdacacadcbcbaaadddcadbccccadcbcbdbbbdadbbbccbbddbabbbabdcdabddacccabcbdcacadddababbabaaabdbacdbcbdabcacbbaabadcaccddadadbbdacddababadbddbcdbddccbabacbcbcacbcddbdbcbccaccadbdadbdcabaaacbdccbdbabbbbcccbbbccdadacabdbbbabdddcdbbaccdcbcbaccddabcaadbacddcbdddaaccbadbcbdadcbdccccddbdabdbbabdabcbabcccbcbabcdbbbcdcdbbadcaabcbadbcbacaddccccadbdadccdcdcdcacdcdcacdabddbdddabdadacbbcdaacddabbbdddaadcdbbcbdbcbcadddaacabdcbdabadccddacacdbcdcadccddcdccdccabaababcacccbcbcacadcacadacbdacbbdcccadbdcbacdbdddbbcddbcaadabcbccadddabdabcddbabdabccbdcdbcbdaabbdcbacbbacabcacbadbddcbbacdcbbacbdacbcbbddaddcadcbcacddbbcdcdacbcbaabdcdbccaadbbacbcaaabdcddddbadbcbbadccbcbbdbdbdddbcbadcaaddaccaabcbccacaacddabcbccaabadcaddabbbcbbabdacdacdcdcacdaabbbcbcdbdbdadccdcddbccccbadbbcaddaacacaddccccabaccddbbbdbaccdaabbdccdccacadcccacbcdccdaabaaccbcaacaaddbacccadaccaddcaadbacbaaabaadddbccaccababbacdccddaaccabccaddcdacbaddcddcbacdcccddbacaacdbaddccccbbdaababddbcacacbcbdbccbbbdcaddddbcabcabdbddcbcadbccacdbbdbabacdaaacaccccdbbbabddbbabaacbddbacdaadbddbbbddcdbdddddccaabccacdacadaccdcbbbbadaaacddcadbccaaaaabbcbabbdaacbbabdbcacccadcbbdadcadabcbddcbdbdaacaccbcccbdbadaabbcdabaccdbbbbdaaacadacbbdcbacddabdbcaaadbbaccdbcaadccccbddacdabcabaabaabddddadbdbbcadbbdddccbdbdbcddccdccdcbdabddabacdadcbdddcacaaaaaaccacdacdbadccdaadbbcdbddcabbddbabbdccacbaabccbcddbddadbdcbbcdbcbaaccabacdcbcbacadbaabcccabcccbdcaadcbdcadcadcdbbccdadbcbcaccabdcbbacaaddddaacccadcdabcadadddabcaabdacbadddbabcadacaacbcacbdbdcdbadcabacbccadddbddbdcbbdcdabacbddbbaccdddbaacddaddadacbaaaddcdaacacbbdbbdbabacaabacabbbabdbcccaabacbbdbdcdbdcadcadbbbacadbcadaacbdbacddbdbabaabdcdddbdbbdddccccaabbcadccaaadbcdcddacbbbcacbbaacaabcdddcdcbddbccdaacabacdbbcbabcbcbccaabacaaaddcddbabdaaacbbbacaddcbadbdccadbccabbbacbbbabdbabdadcbdadbbacaaadddadadcdcccbdadcadbbcdddcbacbdabcadacaaacdcadacbaddccadbadacddaddbcbbdccacaacccdcabccadbdabcbdaaccdaccaaaacbccabaadcdbbbaadcbdddababacaccacadcdddccdcaabcabbbabbacacbdaabbabccddddabdacdbcddadcbacacbabdacacddcabdacdaaccadbcabddddbcbdaacabacdcbdcaaaccccacabdaadbdcccdbaacbdcdabaabadaccbcbcdddccdcaabcaaadacabaddbcabdccdbcbbdbcdccbdbbcacdbcbcbcabdccbddcbddaacddbccbbbbcaacaddccccccdbaccaaaccdbbbdacbaaaaabaccbaadbbabbdaabdddddbabdbcabcbaaaacdcccbcdcdadcacadddaddbcadbbabdcddbbbadabdccccdccbddadaaddddccbdbddbaadaaabdccbbcaabadbcacbccdcdacbacbabbcbadbbbbdadcccdbcabbccccddacacaadcdacbbbaccbacddbcdccddbdbcdadabddadddbbdbacabdcaccccdabcadabdbcdaabbacacbccbababbaddccbdbacbdcbdadcbcbbbdaddccbbcadcbaccbbdbdadbcdabadbbcadaacabbbabcdaccbbdbdadbcbdabdbadbdbdcadddbadacddacbddccacbacaabbcbdbccbbcbbdddccdacddacbaaddabaaddabbbcdbbadcbccdcdbadbadcbcdbadbacdccddcdcabbbaacaddbabbcbdcaaadabdbcadcabbdcbabccacbadaacaabdcbcaabbbbbcdcbacbaaaccabdadcdcbaccbabdbbdaababbaacadbbddcadababcdabadbbadcdddbdbdbdabcacdcdcaccabbccbcbbdaddbdabdbadbdabbaccdcccadaccdbccdbccbcbdbadbcbadbbbcdadcdccaddccddcdabcbdcadcbcccdadadddaaadcbdabcacbddbcabdacdcbacabcdbdaaacadacdddaabdcdaadbdcdacabdcbbadcddbbcacdadadcdbdaaadcddcaadadaacadcbddbbacccaacbadabaccbdbbaadcbcddabdbbaaabcaacbbddcbdaddabbbacdcbcdabbababdbcbacddbccadcdccacdcacadaaaadddadbbbaccaaccbdddcadcccbaddbcddbaddcabacacacddcccbaacabcbdadacdcdadbdabbbbcbacadcbbddbdbbacaccaccddadbcdbdabbadbbabbcdcccbbbccabcbbbcccdbcdadbcbaccacccaaccbcbbddddddacadbaabaacbcdcdadcbcddddbcbadbbcdabdacbadcaddcdadacdbbabaaddacadccbbddacbbcdaacbccababadccdddcaaddcdbbdbcddacdbccadbadaaddacdddabcaccaacbdaaaaaccabcacccbdcdbdaadadaaadddcbdbbbccacddcdbbcacadadaddbbcddbacadcbadabbbbdadbcdabdbcdaaababadbddabcacdbdbcbbdadacdbcdabddacbaaabbcbbbacaacccbdbccadcddccbbacdbddbdbcdacaacddbbcbacddddcabcdcdcbadaacadaccdbacbbcbcccbbdacaaccccdadaadbdcadcabadadbbbccaabdbcaacdacbbdbbaaadadbcbdcbdcadcdadcdbbacdbbccdbddcbdccbdcaccdbbcbaddbcababcbbabadbbbaaaabbccdcaddbdbcaccadcccaccbcbbbcabbbacdbacacdaacacdcadaddbcaddaadbccadbdcbcdddbacdadbdbaccdaaddcbbdbddbacccaddcadacccbcbcdbddddabdddcacbcdbbdccaabadcaabbcddacccaccbcddcadccaaddadccdbaadaabcccddbcadadbdabdcacdadaaabacbcaaccbdacacdbaaddcbaabacbcdcaacdddabcbabbbdbddbcdaaaabbdbadaaaabaabbbdaabcaababccbbddcabbbdcbccaacbcdbcccdccdadbdcaacaacaddaaaabcdcaddadbbdbdabdbdbbaadcabdaacaddddabbdbdabdcaacbbbbdbcdddcccdbbcddaadaabcaccaadbabdcbdcaacacddcbdaccbbaaadccbbbbacbacabacabbddbadbccdbabbbacaaaadbdbacdbcccabbcbdcaaaccdcdbbcdbbaabadbcccbacccaabdcdabddbbdaddbbabaacbcdcbcbbdbdbcbdbcacbdcbadbcdbabdacdbabcaddabddaadbbdadcdaaacbdacccbaddaacabcdbbcbcaabbdbdccdadadcbcaabacbcbcbbcabacbddbddbdacdcabcabdbbcacddbdbabcbbdcdbddcdadbdacbccbbddabbcbadadcdcccdacaabaaaabdbdacadabaaaddddaadbababbbdcdacdbadaabdacccaadaddbadddaddadccbdaccabbadccdbbaaacddabcbdcdddabbaaaadaaabaacaccbdbcbcbabaddbdbbbddaacacdddabcbdabcddbcddbcbbcdccababcdaacddcdccbdbcaccdcbbcabdcacccbaddccdaaaaaabcbcababdbcddbddabbddcccacaccbddbdcaddbbcadcbdbabbadaabcadddccadccdaaabdcbbcdcbacbddabdcbccbcbcccccbabbccdaacbdbbdaccadccdbbabadacdaaddaddaddacacdbacbbccaaddbcbccbdcaabadababbacdabcdcdcdccacdbddcbacbdabaadbcbddabdbbadddaccdbcbddbdbdcaddbbdaadcdcddccddbaaacaccabcadbacdadddcbccacdcbccbbbdaaabacbdabcabaabcadcddccdaccddaabcadcbacdabababcddcbdacdcacbccbbbbacadbcaacabcbbacbcbacabccbabddbaabbabcbdbabdcbcaacaacaacbdbdcadcdbaaccdaadaddcabacccaaacabcdbaabdcdabccccdbbddbaacdcdacdaabdaabcbadccbcabbacacbcaaabdadadbadabdabcaadddcccadbbadcdcbaaadbbdaccdbcacdcadcccadbdccadddcdabbccdabaababbdbcabcbdcddcbbaaccbbdbcbabccbbbaadacbddcdcaabbbcacbbcbdaddabdcbcbbdddccdddddbdbacdaaaabbcdaadbadbbddadbcacbbaccdaacbdaddabccaacdacdcbcdbcddbbccadbbcacddbbbdccabcbabacbaacccaaccabcabdabcbddddbdddbccbbbadadbcbcdabbcaaaadbbdbbdaacccbacbddbbbbbdaccaadddcbdcbccbddcbabdccabdacbaaadcdabcacacaccdcdcdddbacdcdbbcbdcbcbdccdabbdacccaddbaaadbcadbcaddcbbcbabcbddbccaaaabdcddababbcccbabacbbadcabdcbdaacdbabbccacdbadabdbbaccccdacbbcbccbdbcaadddcbbcddbacccdabacbbacdcbacccddbcadbbdaadcdbcaddaabaabcdabcdcadddcdaccadccbcadbbabbbaadabadacadaddbdacabcbdbdaaddaaaacdccbbacbcbbacddbdabcdabdbddbaaacadadcbbaabddadbbcabacabadbcaacacccbdaabdaccbabbbddaccbbdbaccdbbabddbcadddacbdcdccdcacdccadabaadbdacbccbbacadcbdcdaccaadcadbbdbdaadaabbbacabbcacaccdcccadbddabdbbccabcbddddbadabdaadacbcaaccabadbcccdbbdcbabbdaadbcccbdadacaccddbcbbbbbcbbdbcabbdbadcddbbcacbcddcaddcabacaaddbacdbadababadccdbdbacbddcddbdbbcbddbcccdadcdabcddaabccccbddbdaacdabdbdaccbbdaddcaabcdcdcdcbbddcbbbcccdbcdbaaabddabaacacbbbaaadadabdaabdcdbbaaabbadddccdccbabdcddddaddbcbdcbbcdcddadaaddbbababaddddbbddaaadbaaaadbddaacdcdbccbddadbbabbadacdcdbdbddccbbbbbbaaccaddccdbccdadcaccacbbcdcacddcbcbdcdbabdabbdacadcacbbcbddcbabbadcbcdcaaaaaaacbbddabccaaabdcadacccddacccadbcbccbddbccaabdbdbcdbacabccccdaadaacddcadbddbaacdaccabcbccbabbdaaccbadbcddabbabccdacbcbadbccdbccccabdbdcabdbadccbbcbbdcbaadcdabcaccccbccacbdccbdccaadaacdbaaabadbcacbcdcbbcabdbbbbdbdbaccbcbaccbbaadcbdcbbcaabcdbcacddcbacbbacabaacbabdaacdcdbcbdbaccbbcaccacdcbdcaaaadcdadacdbcddaaaabdccaaadbbbdbbabbabbcdbdacbaacbbddcbadcacdcbbcdcaaacaadabcbdddaadcccdbccbacdcdaaacacaaababbcaabcdcbcaaaaabadaabbccbcdaadbdbadccdacdabcccbcdcbdaabdbbacbcdddaaabbbcbbcdcadddaadbdcbbaaacabdbddaacaddcbabcbbacbaddadadbcbadbaccccbbadccacdcaacbbbaddadacddbaaddccabbddbadaaaaccbdacabbcadbdadccaaadaaaaaabaaabbcacccaaabacdbadcaddacdcbcdcacbaabbbbacbddcbaaabbacccbccddbbddbbcacaccacdabbbcbdddbbbbdaacbcbadaccabcbdabcabdadcbabdbbcbdbcdabcbcdcaccdcadbbabdadbdbdaddadccccbdadbcdabbbddcddccacbbabdccabdadcbbdbaabcdddcccdbaacdbbcdcadbbbcbcadbadabbbaadcccbdcbccdadcdabadcdbbccdbdaddbdadccccbcaabbacbaadbadbcbabcabccbaadcdaaaabcbaccbbabbadcacbcdbdcbdbcdbdaabddbcbabacdabcbabbcdaabcbccddaacbacccccdbcbbbcdadbadbbcdbcacacadcdbdacdabbdccbcbdabbdaddcdacbdcbcdcacbbaacaccaccdacaabdcdbacacdabdcadcabccbcccbdbbacdcacdacccadaacbbcbddaabdabababbdcbcbccdbbdbbcbbbddbdddbadabbdbddbacaaccdacbdbbdadabbcabbcabacabbcaadcbcbcabbdaaaddcdcbdabdcbbdaabbaacadcccdaacabbcbbbbcabcdbdbbaccbccbacbbaadccbcabdaccbcbdaadddbbcdadadcabcbcdbabbadbdabbddbbaaacbdddcbbcdcdbdbdbbbdacabcdabaccdcddacaccdabaacdccadabaaaabdadcccaaadbadacabddcbdadadddadaaddbbabbbcbacddadbabadbcbdbadcbabdcbcbaddcdccbdacbdaadacccadbbbbcabccadddbbcdbddbddacabbbcddcbdabccbcddbddcabdbccbaddacbbacbadabbcdbaaacdbcbbcdadaabcdbcacdbcadabdbdbaddbaaccddcdcbcadbdbbbbacbbccccdcbdadcdbdbbbbdbaddbdaddddbbdbbddccadadcbbccacbcbbbcbbcaabccddbcbdaaccbddcbccccbcabcaaacbadabbcaaaaddaacdcabcbbbccbddbcdaaddbbbbcdddadabddcbdbccdccdaaccacaacbadacadccdcbbacdcddcdbbaaabcaddcaccacbaabaaabddbbbbbddacbaddaadbaacdcbacadbbbaaacdcbdaaaadbbbdcdcdaabbdbcccaabbcbbabdacbdacdadcdbcccabaccbbcdaacbcdaabdccadbbdcbccaacbabccddcbcdcddbdcbcdabbcbbdcdaccddacadddccccaaabcacbddccdacbddabdbabcbbabcdccbacdaacacbbdddadccbcbddccdadacdcdaacbdcdcddcaaccbcabcabdccabccbacbdcdcbbcccaddbaabaaccaddcabcbcdacbdbadcaddabcabacbdabbdbdaadccacbdcadccbdbcbcaaddccbadcaadaccacddbbcdcbdcdcbabdaabcddbabaaaaddadabcdbbcbabccdcadccdddddcdbdcacaabcdbbaaaccadbbdcabacdacaadddcdbcaabbadbdadccacdcbcdcabbbadcaccabaacbbcbdabadddddabcaacdddcbbaabdcaacbacdcdbccccccbdbaacabbddccabddbbdcabcacdacbcbdcddddacccaacdabbabbbcdbcddddabbccabdbadddcbddcacbadbbbacbbcabcdbcdaaabbdaaddcdabadaacaabdbacdcbbdddbccddbbdadbacbcaaabadabbcdcacaddbcccaaabbbcbcabcbbbcdaacaddcbcacdddabdabdaabbddacddcddbaccadddbabccadaaadddacbdcabdddabdbdbdbabadabcccddcbdbbbcdbccdccaddabbadbdadbbcccdbaccaddadbabaabbdddcabbbcbbdadcdddaacabacadbdadcdbacdbabcabbdbcacbcdcccdcbacabdbacbadabcddcbabadcccbcbbccbbacddcddcddcaaddaacbbbccaccbacbcdadbbdcccbcbadaccbbabadcbbdddbddcbacdadbcbdbcdcdccadcbaadbaccbdbdcbdaaddbddadcdbacdaaaabddccbccdaacaacaccbabddbdabcabacdddbbadbbdbbcacaaccacbccdacbacddbbdabadbdddbbbbbaacdabadadbbdbbdbdcadcdacbadaccaaabadbdadbaaacbddbadaaaaacbccaadbadccdabccddbbddabdccaaadbdcdbabdccbbacbaaddacbddbabcaddaccabcbbbdbccbaccdcbbbabadbabbaacbcaababababdcccbacbccaddacaadadaacadacbcbabcaddbddacbbacbadadcaabaadddddadcbbdcdcddadccddcdcbadcccddbaabadcdcbccbbabdacddabbcdcacabaabcaaaacccdcadadabbddbbaaccbddacaacbdabdddcadabbdbabccbcbdbdddbdaaadccbbdbcbcadacbcacdadaabaacadcacdbcbbccaaaccdbcdbdadabdcadcaadaddcdbbdaadbbbacddabaaadabbcababcacabadaaccabddcadadbdabbdbdbadddacdcaabcbaccdabddcbbcdcdcbbdccddacacdcbddabdcccacddcbcdadaadacaabcbdabbadcbaadbbccbdbdadacacabdabcaaadcbbdbabcdbdcdccdcadcbbcccbddcabdaaddbdabbaabddbbcaaccbcadadaacbaadcbcdbabbabbddacadbbccaccdaaccbdadbaaacaabbaaacbcdaacaadbcdadacbccdccbbbbabdacdcabdcdaadbaadaabaaadddaaddbacadbabcdbaaacbdccadbbacbadacbabacababdadbcadddaabbaccacadcadacbcabbcdbccadccaccabcbdcacbdbddbddccdbcbbcdabcbcadbcbcdcaacacbaccbcbdbbddcddbbdcbacbacaabdadbbacadccccdbbdcadacabcdddcaccbddaadbbdbbbbababaaddaccdabacbdcbdcdacacddbccbcdbccbbddaccdbcccacbcbbcccdcabaacdcccadcabbacbdbaddacbadcabccaabcddcdbbabbadaddabcabbacadacdabdaccdddaaaadcdcbadcbccbabcbaacacbaabcadbdcbbbbddbaaddabbbdddaacbcdbbbddaccdbbbdacdbdccadcbddcabbcbbddcbbaabbabbcbabccbadabacbbbcddcbaacbbacbdddbbdbbcbdbbdabdabaaddcabdbddcbdcdbdcdacbaccccdddbcddddaadabbdcdaaddcaaaddbdcbcabcaacbbacaacadddccdadddacbbbadbbaccbcdbdcadacacddacbddacacbcdacbbbccaadcbacacabbbdbbdacbcabcdabbddbbccaddabdccdbdbdbcaaccbccbbcbcccccacdccccddbabcadbccbbdacdcabdcdbbaaaabdddadbcbbcbadbcaccbbacbbdccbaadadbbbadbaabbcbbcababbdbbcdbbaabcdacacbdabdcdcddcadabbaddaccaaddcbbaaccadcaaaddcadcbcdbcbabdcbbbddcbddcccacccddadacdbbdccdcbaadcdbcbadbdbddabdacbbaaccdacdbaadbdacdadadaaabbcdddddcbbdbcacdabbdcdadddbdddbbacddadabcabdbbccdbcbbddacccdabdddbcbbccbbbbbaabbcdacdbacaacbdbdbbaddbacbcdcacccaacdacbbbdaaadbbddcdadabbcaddcacbaaacadacadddbdbaddbccccbacabbdddbcdcdbbcabccbddbbaaddaabbddaadbcaccdacbbaacacadacbabcddbbddbadaacabdacddbddaabcbabccbaabdadcacadcdbdaabcccadbaccbaaadaddaaadccabbaabacbbdcadcaddbaabdbcabbcbbabbcbbbdabbdaddbdbdddbbbaddacaadcbcdccccbcccdbbddacdbbccbacdbacbcdacacabaccaddaddcacaacdabcbdbbbddcbbcddbaabcbccbccdadddadbacaacdacaaabdabdabacaacbaaabbcaddabaabdcbbacadaacccabbcdaddcbbdacbbbdacdbabbccdaaadcdaabdaaabaabacacaddacacabbbccbdbdccbbdddddaddbcbdbacddadbaaaccbbdcdcbdadaddbabbadcaccdbbbdcbcdccdcbbcabbbccdbdaaabdbccccbdcabbdcddcbcadacddcacacacccdabcadabdaaccbcbaccaaadcabdccdbcdcacbbacacaaadacabadaccddcdbdbacccbcaabbddccdbdcdbdccbbcdaabdaabcbcdaccadcdadccddabababcabbccdccdcbdddaacabdbaadadaabacdbdbadbdacdbdacbabaaadcdcabbaaabccadaddbddbbacbadaaddbdcaccabbaaadaabaddaadcbcbddbdcbacbcbcdadccaddabcdcdbcabbbacbbaaaddbcdcdabaaccddddaccadaacbaaccadbcccccacbcddadccbacacdcabcacdababbabcccdbcbaccddcbcbbbcbaabdcbbcadaadcbddcabcccddcdaaaddbcdbbdcbdbcaabaaaabbddacbcbcbddaadbcbddaabbcadccbbbacbabbcdbcabbbddaadbaabccbdbcddccbacdbacaacbcbbbaadccddcbbbcbaddabdaabaacbcdaccdbdaadccbdbacbacbdaabcaaddbbcdbcbabaaccaaabbdcaddacbddaacdbcccabdcadadcacbadcbbdadbabdbaadabbaaccbbadbcbbcdacbaadabadaabdababdbcdcaabaddbacadabcbcbdadbddbdcbbaddabadabcabdddbcaabcaaccdcdcbdadbbbccaddbdabdcbdaadaaaadbddacbdbadadadbcbdcaaaaaccdbbbbcaaddbbdbddadbcaddcaddadddabddaadcbddccdbbbbadcbdbdbaabcdababccbadbaadbabbdacadababdabacaabbbcbddccdabacdacacbccdbaadadabcdbbbccbbcdcdbdccadadcdadbacdbadcacaaaddadcbddbcdaacbcdcdccbbccacaaaacbacabdabdabacaaccabaabadbcddacbaddbbdcacaaadccbbaabdbddddaaadbbaacbdddcdbbcadadcdcbcbcdaaabdaacddbabaacadbcdcdcddbdaadddaccbcbccbacccbbddadbaacbbcbaaddaadddabcdbddacbcdddabdacdabdddcabbdacacbcdcbcdbabddabbdbcddcddbdacbcacbcbdabaddcccdcddaddcbdacbdcbcddaacdbadbcccddcdcdaadddbaaadbbbdbcabddbaccabbaababddbdcbddbcaabbcdbabbacbdadddcddbddaabbcadacccdccbcdccdbacadcbcacadabacbcaabdacdabcbbabdbacbacbcaabdccdcaaabccbdbcbccddbbaaadbcaaadbbcddadaadbcbabcabaabadbaaaadddcdabcacbcdabcdbabdaabcbdcccccbccbabdcacababbcdadbbbcababcdbabadaaaacdddaadcbbddcddabaadbdaaddbcdaabddcdbaaabbccdbdddbddaadddbabdaadacdbcdddcdccacdcabaacaadadadabdaddacdadaccdbcadabdbabccaacbbdcdcaacaacabbcddacbadbddbcbddaddaadbcacbbcabdbdbcbcaccdcaadaadaaccbabdaabdbcdadcdcaccadbbabbbdbcccdbacddbcbbcacabcdbbbcdcacaabacaabddbddddbbcccddadabbbbadaaaaadcccaddbccbdadabaddbcdcabbcccabcbabbaddadbadbbacbccacdaaacdccbcddddcdbbcabadaccabcdaccddaccbdbabbababacdbacddaddacdccccadbdacbcbadbdbdbbcaadddaacbbcbcabbccdbbdcbdababcdacbddccdcbcabccabadbbcdacbdaccdbbbddbabadadacbdcbcaabdbcbadddaacdaaabcbcdcadaabdbddadbcdddcbdadaacbabddcaacacbaaacddbacbabcbcddcbadddaaabdcccaddcdbaddadaccbbcbbcdddcdbabcabdaadbcdcdaccbaabbaddcbdbdaddcbbaaddbbcdbbbdddcbddabacaadbababbaaabcbddcddacbdacbccadabdbddbccadbcbaadbdacabaccbcbbbadbdbcadabcbaaadbdcbcaaaacacdbdcbccbdccccdbdaabddccdcccbcdaacaacbbdcccbaabdbbdbbbadaacdadbaccdadbaccaddcbcdcacdcaacaabacbdaaabdcddcaabaabcddccacbacacdcbccddddcdabdbdbdabcdbbabadaaaabddbadcdaaccbbadcdcdaadddabdacbababdbdbadddbaacbdcdbaaaacadbaababcadcaaabcabccbaddaddddadcacdccddcaaddacaadcccbdcbccccbacccdcdddccadadaaaccdaadddaddacdaddbcdbaadbbdbbcdaacbaababdcdabddabaddaabddabdbcabdccdaaddccaadddcabbaacaabdcabdccabdbccbbbbaadadbcaaababadcdcacadacbdcbdaddccdbbadaabbcdbbbdaacbccbbbccccccdcadaaabaacdabbcdbbbcaacaababdccdadcaacacaacdcddbbddddbbbcdcdaaccdadcadddcccbbddbbbcdabaaadcaacdbaaaacdaadbcbacaaabbdacddbdcddcdddacbacadaaabdbdcaccdabadcdaacdbdbbcabdcccadcbdccdcbcabbbadadacddbdddabdbbcbacbaaccdacdcbbdcdbcaabbbdacbdaaadccadcacabaaccbbbcbbadaccabaabcdaccbbbcddbdcdbdccddbdacbbbaabdbcbbababbdaadaaabcdaacabccdccaacccddddcdcbaabddddbcaacdababbcdbbadbccaddbaadddabacadbadbdbcbcdbbdacabccccdbcbdbbcaccbabdaddbdbcddaacbcbccdbacdbcbdadaadacabbcbbacbdcbaaabcaabddcaaabadaadbbdcbdddcbadddcddabaabddddcacacbcbdbdabacaaaddbabbaaddadcdbdbdcccbbdcbddbccbbcbbdccdcddaabcbdaddcccbccacbbbdddaccadbdbdcadcabbacaddbcaacbcdbdbaaacdccdaddbcbaaacbbcaabacdabdcdbcbbcbdbccddaabbbccadacadaacbcddbbcbcdbddbacaababaddabddabbabcbaadddddcbaabdddcadcdddaabbdbaaddaacccccadcbdbbcddcbbacdcadddcbbdcadadddbcaccabbacbddcbdccaadbbbcaaddaaaadaccdbdacccbbdabcdcdaddaabcdbbcacbcacaccabddbcddddbcbdddadbacdcaabcdbbcadbbbdaaaaccdaacccadcbdcdbccabcdbdcbdadcdcacccccabcdccbaccdccacdcbabbdbdcdaddddacbacbbcbabbaabdcbdbaabacacbbbaabcddbcbbbcbbdbaaabaabbcddbdaddcbadccdcdbabbdddcabaddadaacbadbccabcbcbbbabbdcddbcaccadbadddacbabbcbddbcddbbcbbddbdbadbacbcbabcdaaaabdbcbddcdababcddbdcabccccdbbabbcddadaacddadcababcbbdbdbaacccaacdcccbcbcbdabaccbabdcadbabbbbbadbcdbdacacddabdcacdbacbcabbdacbdccddbabcbcdacdcbbadcaaadcadbcdbabadbcbdcaabaccdbcabcaacbbaacdabcabddcaabccaadcaacabdabbcddcbaabcdcbcdaabbddaddcbbdcbbcdcddaaddbccbddbcccabbcadaabbabdbcddabaabcccabddcbaaacaacccaaabdcbdbbbbbddacdcbabccaaccbaaaabdcbdcbabaaaaaaddcabdbcdbbaabbdacdacabbbbdbbbdccdaddcdbaacdaddcbbadcbdaaadbadbdbdcaddbcdbaaaaaacddabbbbbdcdddcbacddbdabdabbcaadbddadcddccadacadcdbcdbdcbccbddcacbbbccdcbacddbddcaabcbcacabaccaddcbabaddcacacdaadaaabbdcdbbdabbcbbabaccaacadabadddababbbbdccabbccacbbbcbcbbccdacaadbdcbaccdbdbdbdddcbabacbbdaacabcdadddcbaabbadbddcaaabcbdaccaaabcaaccdcbdcdbbaaccabbadddaccccccbcaadcadcdcacdbaaccdacbccaacadcaaacaddbddaddcabdcddaaacddadcdbbbbdddbbddbdacdabdcdadadababdcabcaccbbdbacadcaddcdcaabacdcdbcabdbabcbddbacdbdbcdcccacdaababcbbbabbdbcdbccccdabdadbbaaacdbdadbaacbababbddbcbacbcbdcacdacdcacacbcacccdcabddadabdcaabbbcabbaabbadbcabbbdadacbcdccaacbdadacddadbcacabbdbbbdaaabbaddbadacabdabbcddaacdcdbbaadddbdbbcdcadabccaaabdaddcdaccadcaabcbdddbcbdcbabacbcbdcacadbcbcabcbdcbcbbbadcabdaacaccadddbbdacbabadbacccbdbcddcaddcbabcbbacadcaacbcbaadccaccadbcddbcbdbadbccdddbacacbaabadbbccbabacdddacbccbadbdabbdbaddabdabddbaaaddcbdacacbaabcdabbadaacbddaadbdadccbaadbdacbbdacbacbbcadcdbaaccbbdcdbadaadbdbccadcbdbbcaadccadbcbdbaddbbbbbcddbbbbcacbcdccadbcdcbbbcdadbddcacccacadbccbabdbcbdabadcbcadcaacdbaacdbcacacbbddbddcacbadacbcabbaddbdccbaacabadaccacbbdabacabadccbccbcbbabccabbccccbccdabbdadcdcdbdbddbdcbbbcccdbdcbacbacabdcdddaaccddbaaabcccaabbcadbddbaccaddddbcdbccadaabcdcaacbbddabcbbccbdadacdccbdadbadbbdbaccaddcbaabdcadbbbadcaaccbcbcdbaccadcadccbddaddccccdddabadcbabbdcccaadaddacbacdcadaaaadcadddccbcdbcaccaacdbabcacbcdbcbdcccacdcabbbcdbddcacdbacbbdabdbdbddcabdadadacabdbaabdcdaaacaaccacdbbddbbacaababcaaddcbacabddcdbabbdaabadaaccabcbbccbbdacbbccbccdcccdabdbdbbcbdabdacaacdcddabddacbdddcabdbbadcdadbaccbddbddcbcacdccbcadbddcdabdcaacdabdbdccacdadaacccdbdaccbbadacdcaacbbbcdadcaacbabccccaaadabbccdcdccdccdcabaaabbbddabaacaadaccbdbcdbcbccbcdddcadbacaddbdbababbccccadcacdbccadccdadddddbadadcddabaadddcbdbbcccddbddadbcdaadddadbaddabdbcddbacbcdcaabbbbbdcbadcadddbddbcbbcabbbddaccddacccccddcbcdbdcbdcaabbcdcadbbdddcccabcdbccccabcadbbdacccddcaababbddbcbcbaaaacbbabacbbbdccdcdbbbaccbbddcdacbdccaaaddcaabccdbacbabdcbccabcddbbaabbcbddddbbbccbaddcbdbbdadbcadddacddcbacccddbbbbcccacccbaabbcacdcacacadcaaadbdaacadacbcbbcadcabdaacaddbabdcbabdbdcbbaacaabadacadddaacabbcdcabdcdbbaabdabaddadaacddbaddaacbbbbdcdbaaaaaaabddbbcccdddcabbddcdabccbadbbabbcabaccdacddbaaadbaccbcbbadaabaadcbbcdadcdbdabccbcbabbbdcdbcabbdcbddddbccdaccccccaadaabdacbadbccbccacbccccbdaddcdddccdbddcaaabdbdabdbdacbddabcbadbdbbcaacadbbdacbddcdbadddcdaccbbbcbaadbbbabdaaccbaadabbcdaadcbdddbbabcdcdcbacdaccabbdabcddcdaaaccbdbcdbaadbaaaaaabdbbcacacadbaaadcdbbdabccacccdcbdbdbacddaaadbdaaccacbadacdacadcddddcbdacadaaaccaadabcdcaabaaabcccbcbcdacbcbcbcbbadcdadddadccacddbcdbcdbcadcdbccaacdacacbcaaaacdcccaabdadbbcabbdbbacadacbdddddcbcdddcabcadaaabcacdbbddabbdaadbbbadcadbabbcabcdbbcaaacbccbacdcdccaaddababbbcbaaaabaabbdabaadabccdcabdabacddaaabcdcabbcaddcbbdbbbcadccdaddddcdacbbdbabcaddcdcaccbdccadddcbcaaadbabcbccdcbaabacdddcbbcdaaacaaacdcadbdacbacdbdaabbacbcbdadccdbcaadabadcadacddbcdcacdadaddcdbdbcbbcabcaabcaccbcacabacbdddaacccbbbccbabbbdccdadccaaccdaccbbdbbadabaccdcdddcccbbcdbdaabaaccbabbdbdcbddbdbabccaaabbcaaabcdbabbaccabbcbcaabaadabbdaadbcddddbcdacbcbcbabaacbdcbddcabddddccbbababcddcdababaabaabbddaacdcbbccccddcadcbadacbddbdabbaacdcabbcaabcbabbadabcadbdabcabcacbcabcbadaddcbdbabccbbaacbbcbddadbbaabbcaabccdacabcacdbcddbdabadcaaadaccaabdaccdbcacbdadbaccdcbddaaccbbbcaadcabddabdacbdbadacbabacdbbaacddbaaacbbbacdaadbaaddbbdaababdddaabcadbccdcabdddcacdbaacaaacdadcbbddcaccbdabdcaaabbdcaadabdabcdacadadccbabdbdaacaabdaaadaadbbbbcaabbcbbbdddbadaddbaaaaadbaacbaddbbadbacdcdaddbabaddaacabbdbcbccbbdbcbdaacdaddacdacdbcabcabdbccbbbbdbcaabbbbdbdaabbcbdabbdccbaddcabdcddadbbadadbacdbabdcdaccccdcbdddcbcbcdcbbacbbaabbbbdcbcbdbaadccaabbccabcdbcbacdaacadbbbaabdbddadaccdbbcddcaccababbbabbcccabaaccaaaacbddacdbacacacadbaadbaaaaaacacbcdacacdbaaadcbadbcaaaaacdaacadcddcddaacdccdaacaaacbbadbabadbdabdddbdacdcbcccabaddcdcadcaaadcdabdcbaadabbcdbbccbbbdabaadabaaacabbadccbacdadbcdaaabbbbbcbbbaddacabccbdbccadbcbdcabababddcacdbbcdaccacdddabddcbddacbaddbbdcccdcadcddbcbdcbacabadccbdaadcdaccaabbbccbbddcbdaaaccbbcddbbbacbabdcccacbccbcdacaddabadcdbcbdaccdbbdbdcacadbacababcbcadacccabbababbbdccdabcddabdacdacbdabdcdbdccbdcdbcbdaabadcbcdcddbabbdbdcdcdddcdbbcdbbadacacacbbdbdcacbbbbabaacdddddacccddadcddabbddcbacdbacbaddbacacccddcbbcabbbbbaccbdbbddcacbdddbdddadcacabcbddbcabbdabdacddbaccacaadaaddddaaadaadbdaabcabddcacadddbabcbcacccaacbcaccaddcaaadaccadcbdbdddbbdddbdbcbcdbadbdddbcacccdcdbddcbbacbaadcdddbdabbbbbaccdbdbaddaaabdbabaaccbbaddcabbaddaadabbbbdcddacccbcbbddaccbbdccadcdcacdaccddadbbddbddaddcbacaccdccabcbdcdaadbdaabcdbbddaaadddccbaabacaacbddacadbbcbdadcddadabcbcbddaacaaaccacdbcbbcbcaabddcbaccdcbdccbddaacabbaadbdadbcbcaaabbaaacaaaacdbabadababadddccdaddccdcbcdbbaaccdcbbbbcdcabacddbdadcacaadbbbdcadccbbdcdcdababbdaadadcdbcccbbadcadadbdbbabaabbbcabdabdcdcbcabbabdbacaccbaabcdcdaaabbacabccacccbaacacaabccbbbacacdbabbdddcadccabbccdacbdddadaccaaadcbabbcccbdcabadbabcdbacacbbaadbcddcdbcaaddaaccbdaaddbbdcdccdbcbddccdbaaabdbbaaaabcababbaadccbadbadacbcbdabccaddbbbccadabdbacbaddcbbdbdaabaddbdddccdadbabbdbabadbabdccdbcaabaaadaccaacbddbbcdabcdcbdcbabdbacacbdcdabdbcddbdaacadaddbacbabcdaaccaacabacadcbbcdacbbdbdddcaabbcbddccddaddbccbddadbdcacadacdacbbcbbdbbcdbbcadcaddcbdcabcbbacdbcbbacdaccdccddbdbccadbadccdabcbbcdadacababbcbbbbbcabaadabacdcaccdacaacdcacddbdabddaacadcbccdbdcdccbadcbcccaaadbcacaddbccbacccadccaabddddccddbadbbcabaadbcdbcacccdadabcaacccaacbaaaababbcacddddbbdbcacccacacaddcabbaabdbcbdacadccdaaadccabaacccbaadbcdbcabbcbccdccbbaadaadacddcdcacbdccbdaacddaaadcddbbddadadddcaaaaadaabcdacbbdbdacbccddbdbddbaadbaacddbdaabcaddbdbdcdcbadacacaacddcaaabaaddbdccdddcabbbdbadaacacbbaacadababcbbbbcbcbcdacdaabacdbcbaddcbcaabcbcccabbddbacbadadbbddbbcbdaddabbaccbddadbbcacbcbaddabcaabdabdcdcbcdbcdabaaccaacdddadddcdbadccbcadbdddacaabcdbadbdcadcddcccbcdccdadcdbdabbabdcbccaaabcbabddadabbbcddadabbbbbadacdabbbbcaaadadcaccabddddcbabdbdcacbbddbacaadacdbbabcdcccbdcbadbdbcdbdadbdacccdadbcbabbcabddaaddcbbcccbaaacbbcaccaccbbbdcbccdcaaabbaddcbddaaaabdbcadaddaaddcaccbdadddccbbccbbbbbddaacdcabbadbabbbaabdadacdbddbbbbcbabcbdcadbcadabdbccdabacabbabadabcbbbbbdbbadaadcabdbcaaddbddabbbcbbdbaacabaddbdcaabbcadcdabdaddbcdcdacaccdaaacdddadabadcaadcacaccacaddacdbbabccaabdabdbcccbadcaddabcccbadbcbbaabdbdbdcddbcdaaabbbdbabdbabbbbdcddbbdcbadbdcaacaccbbdbcdbcdbcacdacbdadbddcdbadbcadcdbbccdaacdccacbbcdaccaacbbacbcdbabadbbbdcdabcdcdcaabadbdbddbddbcccdabaadadcddddddacddcaccdabaccbbdabbbddadacdbaddcdacacccccddbbaabdddbccbadcddcabacaabbddabddaadaaccadabddbadcdcacaccbdbbbdabadddbcbacabcddbcaacabcbaddddcbccbbabbcbaacaacbcaddacddbccaaababcddccaacdccbbdacbcbcbaddcababaaaadcdcabcbdddcbdddbdaaccacbddcbbcacdccbbbccaaccadadcbaddcadcdcdcdccbcabacdccadaababcacdbdddcadbadcbaabccdcccdbacaaccabccabdaaacaaaabcacdacdbbbbacbbcacadcbcadbcaccddadbcdccbaacdacaccdcababccaadcdadcbbadaaaddbacbbcdcababcabcabbccaddbbcadacacbaddbcddcdbdacccbdabbddddbaccaacadaddbadacdbdacdcddabcacbbabdcdccadacabaaacabacadbbbcbbdabaccdcddbacbaaaaadbbdbbacdccabcdbbcaabbbcbaadadbccccabcdadcbccbccccdacbbacadaaadacccbadabcddadbcdbbaaaccadbcacbcbcbddaccbcbbdcaabaadddaccddbbdbbcadbaddbbbddabaabadbbcadbdddccdcbdacdcbcababddcaccbddacbcdbadacdabbbadabcdccccccdbdadcbaadbcdccddaaddaaabadcacdacbcacdcbddadabddbcacdbbabcccabddccdbcddcbbdcacaadcdcbdcdabacccdacccadbdadacaaacaccdbadadabbccbcadddcdcacadacaccabcacabbbcdabddbcdcaaccadaabdacbbdbbdbdaacddcdccbbbdbbaccccdcccdddadbbdacabbdadbddbcbdccbbbdacdbccbcaabbaacadabdccacbcadcddbcdabbcbababdbcabdbdabddbdaabcdacbdcdcaaccdbadccbdddcdddbaacdddddcdaddcacbcbacdcdcddbccadbababbdaddabbbacdbadabcbcaaaaddccdbbdabacdaabbadcbabccbabbdaadcdabbacbdbbaaabbadccbcdbdbddacddbadcdcbacbaaaacdcbbaadcabadcbdbcbbdabaccbbbcbddcaccbcdaabccaddcccccbbcccbaccaacadabaabdcbccaabccccbcbbacaadbdbadadcbccddbdbcaccadabdcabaacaabbabacdbdacadaacdddadbdddaaaaccbaccccabdbcdabacccabbcbabbccaccbaaacdcdabcaddaadabcadcdbbdaadbccbadbdacabbcdcabaadabadbaddacaaaabdcccaabbbdcbbcccaaccccababbbbccacbbaccbbdadccacadacbddbcdcbaadcabadcacdcacccbccbacdbbdadacdbcdabdbdadddbcabdccccbaabbdaddbacbacadccbccdcdcdcacdcaaccbbaccbaabbccdbbddaacccbaaabadadabaacabbdbdbabdacaddaabddbbddddaddaacdabddddbdadcaabcabcbdbdbdccccabddcaabcbddddcdcdcccddbdbacaddbdaadbbdcaaaddbbabadccdadadbcaaababddaccdbcccdbdbabcbaaaddacadcbababacddbdbaaacadcbbdbdbcabcaddccccadcadcaadbdcadaaaabcbbdaaacaacdacacddcdcabbadbdbdbabcbbbadcbbbcbbcaadbcaaddcbdcddccadacabcdbaacbcbbacbcdaacbdcabaadcbdbbdbacaddabbdcdddcccaccabbacdababdbaddadbdaaaacbcdcccdcbdaacaadbddbcccbdccdbababadcddaaabacdcadbcdcbaddaccadcbacbbddcdabaccbadcddcadbacacdbdadcbddbacbddddcdbdadaaabaccdcbaacdccbbcdcabaddbddcdcacbcaddbbccdcaccadcabcdddbcbdcdaccacbaccccabddacbcaacdaddacaacbbccabcadcbbadabaaacbabacadbbbbddadabddbbdbbdbbcabbadaddbdabccacdbbddcadcbbaaacaddddbdcdaaaabaddcbaabbddcaaadbdcdbbddbbbcbabbaaaadababbbcdddbadcdabdccabacbadbdddaaacddabddaacaaadccbdabbcbddcaaccdabbcacabdbcaadacbaddbaadbdbccccacacccccdbdccbcccbcaabbbcbacddadcdacaaabcdddbddcdacdacacaddadcbabbcadcddddcabdabacddaadcaadccdabdaaadcaaadccbcaaabcbadbbacdaaacabacdababdadcdbacbccbdbabbbcdbdcaacdaabdddddaadbdadbdddbdaacbbbadbbbbccabcbbbcadcddacbacacddabdcdadbaabddcccacaacccbbacbaacdcccbdbadadbcdbcaddabcccababaadacbdbddaaddbadcdaddcbbbddddccbdcbdabaabdabdbbacbdbbbbaaabbacbbddadbabbcdaaabbbadcbadccdcbacabbddacaaaccccdcbbbdadcbdcdbcadbdccaababcaabddcbdcadddbbddacaccbddbaaaccdaaaddcadbddbcbdabcbcbdcacdbdcaddbaccdabddaccaacddbcbdadbccccccdcaabcbbccacbabbbbabbcacbccdabaabccacbabdbbbbacdcdadbbabbbcdcabbdbaccbccacabdcdbdbcbdbbccdddbdaacabddbcabbbbbaacbcddbacadbaadcbdccbaabaadcddddabbdcababcbdabccdcbcccacaaadcdbcddadddacdbcdcacbbcdcbcdadddddbacadcbcbccbbcddbabbaaacabbdddcaaaaabdaaddcaabadbaabcbacccdcaddaccabbadcdcbbdbbcabdbbdaabadbdabdcddadabbaddccaabdbdadaabbdaabdddbaaadbccccbccabadbadaadbacbdbbbbcddddbddaccdcbacdbccbbaacdbccbbbdcdaccdabdbacadcacbaacbcdddbbbbbdaadacadcbdcbbacbaabbababbbabdaccabdacdcccadababbdbbaccbdbdadacdacccbdddcbcdbadadadacdcccacaccbbdcabdadabbccdadcccaabdaaacdbadcbbbcbdaccbbbbbaadbccabdcccacdaaccabccdbbddbaaacddcbcbdaacbbdccbdadbccbdcaabbaaaabdcabdddddcbbbbabbcbacbcacddccbddddcdabcabdbcbadacaccaccbbdbbccadaabbacacbcdddcabcddabddabdbcccddcbcdcbcbbadbcdaaaccdabbdaccacbadabaaadababaabbccaaabaabbacaddddbdadcccbdbddbdbacddbdaddcdcdbdccbcccdaabcdbdaacdacdcdcbccbadcbcbcccddbbacbabcbdcdbaaaacaadaacbdbbcccaccacdcdcacbbabdccbcdcbbcabadaababdacbdcbcdccdbdacddaccadccdcdcbdaacbcdacbbbdccdbcccadbdacabbdcadbabacaabcdcaaabacaadbaccbbdbcaaccbbbbabaabbdccaddaddaabdddbcdcccbdddcabcadccbcadcbbcabacbbbbadbdddddadacdacdbdacdabbaaabaccaaadddadcacdcdadcbdbaaccdbcbdabaccbdbbbadccbbdbbaabbdcaadcbaacabddaaccbcdddaadbbcbbccdaacbaadcbbddccbcddaccbbccbdddcddabbbcbdbbdacbcacbcabadbdacbcaddbacdddaacaacacdaacaaadbddccbcaaccdabaadddaaabccdddcbdbdddbcdbcddaadcdabbdaddaccdabaacacbcbbdcbcaacbdadcbadabbbdbdcbdabdadddadadbddadccaccabbadaabddaacacadcbcdbcdbccaccdcabdadbdabadaadaddddbabadccdcddaacddcbbccbccbcaadaabcabddaadbabacddabaaaababbaddaacbbabcdccaccaabadaabcdacaabaddbbcadbdacbbcddbccbaaccabbbcbcbabadbbdabbbbcdccacdacbdcaacdcbcdaadcbadbccbdbddcbbcaabacaaaadacbbdccdabbbdbbbdaacdabbcaddaabccaadcbbccbcacdddbdddaaadcacdcdbcbbddaacacabaadadbcbbadaabccccccbbcbcdabcdbbcbabdcaaccbbadabcaadcbddbcdbcadadbcbcddbaadbaacdcccabaabacdddccdcaaaacbcacaccddaadbcccbadcdaadcdcaadadbdccbbbdbcddccdacabdabababcbdccddcdcdcbbcdcacabbaaadaacaadbcbacacddccdcdcddcabcddababbadbbcdabdbcaddcddacaaccbdbcbacacddcddbaabadcacbbcbaadcbbbdbbbadaaacbadcacaacdcdaacaaadaabdabdcbbaacbabcbacbabbcccdbddccbdcaacdabbcdacbcbdddcbadaaadaddbbccdcdccacbadcbbbbcdbdccdbcabbcacaccbcbddaccbbbbccdcbddccabaaacbcddbaadccbbbbddcdcadbbabdddbcacddcdccabbbdadcaadbcacbbbbbdbadcdaadbbcddbaacadcdcbdaaaccdbccaaacbaccdbadadcbbabbdcccaddbaccbacaadbdbbdbdccaabbbcdacbcbdbdabdbdccbaccddadbbdadaccbadaabcbbbdccbbcbdacdbbcacccabaabbaacbabdabcbabaadaccadadcddbdbddadbadaddbacabcbdaabcabcbcbadaabbdcbadbadcaaddccbbccadcabdbcdacabacbdccdddbbbbbdcbbacbbadbddcddbccdadbcdbcbbbbabdddadbaaddcbacdbacbacacccdddccadcbcaccbbbadaddcdddababcccccddaabcadbcaabaacbcaccabadbcabdccaddaabdaaddadbccdbbaaccdbccddddbcdbabacbbcdccdbdabddcdacbdcbdcdabcdbbdaadbaabcbbadaababcdabcdcbadbddcbddacccddabccbdccdcaddcaabbabdddabbacdddcaabcdbcacdbcdcbadaabacaabdcadaccdbcbdbaabaaaadbbbbbdadaccadbddbdccdcdcbbccacbdbaccdbddabcbdaaaabacdabdcacddddcbbcaacdadbaddababddbdcbbccbbbbcdaccddcbbbabdbbbbadbabcbdccbabacabcdbcdbbdaddccbdadcadaabcdbacabacacdbdacccccbdcaddadaadadcadaddacbcdadabcdcaccdddccbabbbadadadaabadbcbbbddabcbbabcabbabccaccbbcacbbddbbbdadbbaaaddbdcbcaccaabcbbdddabcdcdcabdbbcdddbcbdadcadbcdababadbacaddaaaaabddadcbdcbdbbcacdcbacacadacacabadbbdaacdbadcadcbcabdcadbcdbdaaccdcabccdcaacbcdcdbadccddbcaccdacddbccadacbbcdcccabdadccbacdbcaadcdddbbadcdddbbcccdcbcaacadccaadccaaabbcddcbbdcaaadcacadbadacbbddcadcbaadddaababacbbaddcdccbbbddabadcdadccaacbdddccaabcbcbbbacacdbcaaaadabdadcbdaabdabacccddbaaadabcbcbbcdbdbcdcacadbbccbdaabcababdaabacdbcaabdccbbcdaccdaabdaabbbabbaacabbcdbcbbadaccbabdbbaaabddbccbaabcaadcdbbacacabbbaacdbdbbabbcdabddbbcccbccdacdbdaaaabcacabdabadddabbcadadbaaacadababcacbdadbcabbcbcccaabcdddbcdbaaadccdabbabcbbbdacdcabcabbdababccdcabdabccaaabacbdcabacddddabbcccaaadbbaaaacdcbdbcacdcdddddccbdbcaadcacccbdaadddcdddaabcabdaabbcadddbbdbbbccbbadaccddbacbcaaaacdbdabdacabbbddcacaacccbbbcccbabbbaaabbbdbdcaacabcaabcaccabbddcdbcbcabdbddcbadadabdadcadbabdcbbbbbddbbbbbdabbccdacbcacaabbcababcacccacacbdabbcbbaacadabadabbbacadaccbdabbabcdacadbddbbadbcadbaaaaddacdcccabbadbdbcadccabaddbdacacdbadddcdbbcdadabdabdacabcadbababdaadddcaaadcbbaacaacaacbbbcdccabaccacbcababbcbcdcddcdddbcbbdacadbdabbccbadabdbbacdabdddadbaabddcdcabdbdcdbbbddcdacdcbabbbbbbdcbcaccbccaaadaaddbdaaadadbaaabaaaaddbddcbcdacdccbabbadaabcacabcbacbccacdcbcbdcaacdbbbbdbaadcbcdcbbdcdaccdbbcbabcadadcbcdaaaadbdbcabaaddbbdbddbbdaacaabdbacaccacbdacccacbbbddccbbddcdbcababaacbdbdcccccdabbacacadbbdbbdadbdacacadddccbdbbadaabdaaaccababaaacbcbdddbcaccdbdbbbcacdbdddabdaacdaaccddbddccbddbdccdabbadabaadbbbbccdcddaadbdadcdcadcdcdbacdadabddcddbcaddddccdccacdcbbddbaabaadabbcdbcaadaddbdabdbcbacadbbdccdabbbadcbbcdbccbcdacbdcdddbdaadbbddabcdccccbbdcccccacddccabaabacbdabbaaddabdbacadcaccbdaddddaaadcbcbdadbbcbbdaabcaccdabbddaaddbcdbadaadcadabbbadacdadacbaccacdbcdaddbabcbdddccbcbcaacdabaabcbcbbdcbcbddcabcacabbcababbbddcadabdacaaaadbcadbcbcaaababdadadacbcacabcabcacadcacabcbcaaaccdcbdcccadbccdaabcdbddcabbbcaacabbbcbaccadbbddccdbacccdbcddaacaacdcddbddcaadbcbbbaddadbcdcbbbbbcaaaaaabbddcdaacbadddaacdcadddadabbaacaacbdcabcacacabddabccdbbbaadccacdbcbddbcbbacaccddbcdbdcbaaabbbcaaadddbcacdaacdbdcacbcdddbddbabdbdcadaccabcdcdabdbdcdbdabdccdbaadaacbbbdbbbddbcbbbccdaddbbcdccccdccddbdbbdbdaaaaacbdaacaacbaccacbcacaacbbdaacddadcdbcbccccabdccccdbdbdadbccdbdbaaabadccacbcbcaaabacacbddbdaaadbaaacdbcabdaabddcabbabbdbcdcddbaccdadcacaaabcbccddcdcdcadabbccbbddddabcbabdaabacbaaddccdbaaaddacdcddbdcdccdbbbdbbaccbabaaadbcdabdaddaccaccbdcacccbbbdadacbcadaacccccbbcdabbccaabdbcabbbaadcacabdcbdccdcacbabccbcdcbdadaaacbdbadbacabacdbbaabacaacbabadcdcbdaadbadddccbddadaadadbddacdccdbdaacacddcbcdcbcddcdbbdcbbdddbcacbdddaddacadcbcccaddbbdbbbcccccbbcbcbcdddabbbddcaacabddbbdbadaddcaabcbbbdccdcdbdbdbdcbadbdddacaddbcabcbabbdccdccaddcbcadbcbbcaacbdabbbcacbacbccbdbdadbbaccaddcddccaacbcaddcacddcdbbcdbbccddaccbadccccbbbabdbbdacacabdaccabcdaaabbdbcddaddbbdababbcadadcbdcaaccdcbcbaadcacbdbadcbdbccbccddbdcbbcdddcacaccdcddcdcbddcdcdcbdcbbabacacbaadbbdbccbabcdabcbcaadacbbdcdaddacadaadbaddacbbdabaabccbadcbbdbcbbccbbaacbccaddaddcccabaababcabdacdaacbacdaccabcadcbdacdcbbbcdadbccdcaacbdaadbbcdbacacadbdaddbbcddcccbaadabadacbadcbcaabcdddbbbaddbdadccadccddcdcabdcdacdddababcbdddbdcadcdcabacccaadbdbcdcdbcdabcddbcbdaddbbcdadbbbdadcaccaadccbddccbbdbbcabadcababcdaaaacacdadadcadbaadbdcaabdacaaacdbcdcbbaccbbbddcbccbcadaabcdbcabdababdbdaacacaddadccacbacbabdaabcbbbcdcbdcdaddbbaaddbcddacabcabdddbabbcbdacbaddcccaadbbcdbabdcabccbdbaaddcdccbaacadadcbbbdbccacbdcbaadbbbaddbccadaddcdbdbdddacccccdaaabbbcdaadcaadbccbdbdaadcbdcacccbabadcabaacabdbabacbddccaaccbabadaababccbacbddacbcddbcbabaacabaaccbabaaadabcddccdabbaaccccccbbaddbccbaaaddccdadccaababdacaadcabddaadbddddbdbbaaddbcacaaadcaccaabaddbcbadccddbcadcbdddcadddcdccbbbbcdbcbadaabdcddccacacddcbcccabadbdcabbbcbacaadcdabbccabcbaacccccbabbacccadaccdcbdbdacddccbcbaabaacbcbacaccaacbbdaaccdddcbbabcdaabccbbcacbcaccbdadccbbcbbcbbaababcdccccbbabdaaabaaddaaddcbdaddcadcaaccabdcbabbacbabbdccbdadcdcacacddabbbdcbbdcbccdbdbcbbddbbbdbcbdcbadccbcbddaadacbabacaacbabadabbdcdcadcbcbaddcacdcdbbaadcbaadbdbbbcbddccadccacbbadbcddbacdacaccaaccdcddabbcbbbdbdcdcdddbdaadbbcdaacadbcaaaabbcdbbcbbaddacaadbabbacaabcadbcbbbadadbcadcbabacdbbbdcddcdccbbcaabcccbbdaadaacdbcbcddbababcdcaacaddcabcbcccbbcacdcbaddbdbcccdbdbcbbacdcaaaacabdaaccbcdacdbacdacdaaaadbdbabdaaacbdbcdcbacbddacaaaaabcddbbabadcccdbaadcddadccaabaddaccbaadbbccaacacddcbdccaaccadbccabbcaccacbcbacadabcabcaacdbdbacacaacbbbacbadabcdbdacbbdcccacddccdaddccccdbcbcadabbadddccbddbbbdddacbacddadbdabcbbdadaacddbcddcacabbcbdadcdcdbaabcdbbdbabddcccaacbdabbcabdadccdbddcdcabaaacbbaddbddacacacbabdbadbcccacdadaaccababadabdbddcabcbabcbccbdcadcacaadaacbcdbddbaabddadacadccbcdcacdcbdbadaabbacacbadadaabadbdcbabaacbbaaaccbabdcdcaaccbbdbcbbdcbaabdcdabcbcbbbabbbddbbabddcddadcbcacabdcddabbadbaadbbdbddadbdcbbccbbbcbabddadcdbabbbbbcdbdacdbaaaacccacacaddadbabccadcaadbbdbcabcabdadaadbcbdbaccccbcbdabbdcdcdccddbbadbbcaccbbcacdcbccaabcacccbdbadaccabbaddcadbcbdabdacbcdbddadbbdccbbbddbcdcaaabccddcadbbcacdcdbaddccbcbcbdaaaccdbcbbddcbbbbdcabcbcadbbccbbadbcbacdaaabdcccdbacadabaabccbdabddbbdcdccacacdcbdbbbdabbdcdcccdacdadcbaacccbccddbcbbbdcbccdaaadacccaaacdcbabcbbbbddcacabcaaccdbdbbdbbcdaaaadaacbbacadccbcacdcddddcaabbcbabacbbacdbcabaccddacccccbbdddadacccddaaadbdccdaadbbddadbcacdbbdaabcabbaadabcddbddccbbdcbbbcdabaaaadcbdbcbdbadcdcdadcbabdcdbdaaddccdcbdcccacdbaaddcbadcacaddbbcbdaacaccaccacdbabadcbdbaaaaacbabadcdbdccaaccbcbdccbabaadccbdacadcaaabaadaacabdcdcbbcdbdbdbbcbaccaccbadacadaadbcbdcbcdccdaadbbacadbcddbbccbbdcacabdbaacdddcbaadabadbbcbabcabaddcdcdcbdccaddadadbdbbbcccdcccacdaaaccbaddbbcbbbabdbcaccbbbcddbccbccadaadbaacdbaabadbacbabcbbcaabbcdcbadcbbdcdabbabddabcccabccacaabbdadcaabbdbdbdbaadabacdabcdbccdacbaddbccccaabdbadadbccdcddabcbbbadbbacddbbbabbaddabdbdabbdbbcaddbbcbaabbdabcdbcdddaccdacdbacbcdaacccaabbbccabbdbcacbacbdbcaddbcdbcdbcbdcdaccdadacdcdbbadaadccbcbaccdabbdbbbbdbdbaddcccaadcbcadcdddaadccbdddaacadbaddddbadddbddbbbaadabaccdbaacaaaabacdadababbadbdabcccdddabdbcbabadccabbdaddadaaacbccaccbccdadcdacadddbbbcccbbcaabbcbdccbaaaababcbcabaddbbdbdcbbacdadbdaadbcbbaacddbccbdbcacddbdabbbaddbdabcaaddcdabaaddbcbcbadbddccddccacdbbdbaabdddcadabcddbdaadcdaaacaadbdaadaaccabcbcddacbccabaaabacacacacdcbaddbcaaaccddccbbbbcadcccdbcaabdcaddacddadccadabadaddaccaacbacdbadbdaccbdacdddacacdbccdccadaaadbbdcaddbacdcdbacccaaadcdbdadacccdbccbdbbbadcdddbbadcdbbaacacacbdddacbddbbbaadccbccbaacacbccdbabdccbbadcddadbdbacbbdddddaaaaacbcdcccbabbabaadddacaacaddbbcdddcddabbcaadadddccaabbbadddbbdbabdddadadbddcbbaadbdbbcdbaadcadddcdcaabddbbdbcbcbccacdbacddddcbdaaddadcacbaddaacdcddabaccaccbdddaddbaaddbaacccddaaaacddcbaacaabdcbdbabccbbbadcdacdccabdcacaabababcddbabbadddabcbbddaddcbbbaacdccdcabcaccdadaacbacdddadbcdaccdbbbbddbddbbaccdacbdcccdbddbdbbabdccbbbabbdacacdddcbbdddbcabdbdcdaabcbbdccadcdbddbbccbbddcbabcbabaaadcbdcdbbabaabbadacbdbddcbddcadbbbddccddbbbabccddbbcaabdaabadcbcdbaddcbbddcddabdcddccdcbacbddacdabdabdbbdbadcbacbadddbdbdabdaabdaadbaacbcccbabdccddaaacbaaacdbcabbbbcbdadccdbbddcbdcbcbcbabacaadaaacaacaababdbbabbccbbbcdcbbbcaddcacaaccbbaadacbdaabdcddadcadadbcabbabcdabbcabadaacddbdbcaacdbbadddbbdabcacbbadcaabdbabdcccdddcbcdccdccadaabcbbbdbddabaddacdabbcaadaccacbbdbaddccddacdaaccbdbdaaadbcbbcccadcadcbcdacabaaaadbbdadbadcadbbcccbbacbabdbdcbbccccccacddbcdbccddabbbcdbcaacbdabaacdadadccddcdddccaaddccbcdcaaddccaccbccccdcdbdadcacbdaccdadbdccbcadbbdbdcdccadaacaddbaacaaddbcbbaadacacaccccdddcbadcbdadabddccadbcdadddddadbcaaabcadccaaccbbbacadcccbbbbacbcbcbaabdaaaacabadcbdcdadabddaabcddababddcadddcbdadbdcbdcdddcadbcdbaacbdcdcbaadbcdaacdcabdbdcbbccbcbaabcabcabbcddbacddcbaccdbdbdacbbbbcbcdccbbcadddcdcccbddbdcbddbcbcbcacbcdbdacaccbbadddccbaccccdadcbbbbbcbbbbaddddabdddcdaabbaaaadabaacbccddccddbabbcbbbabcccdaccbbbadcdabdaabdcabdcdaddbbcbcbbdaddddbdcbcbdacbdbdabcdcbbbdbdccacdbcaaacdbcbadccbcabcdddddcadbcababaddaaadddccacbabcbaccadcdcaabcabadbaddaaccdbdaccadbdcaccdbcdbcddbdaaddbdcdabbdcaaacadbccbbdbcbacbbaacadcccacbababacbcbbbababcadaadcaaacacabdcaaacccbbadcbcaccbabaacacabaaadbdccbdccabacccdacadbacaddbbcbddcccddacdcacdcadaddabdddaadcdaaacccdcbccccaccaacbddcaacbdbbdddabbbdddaaccbbbaabbadccbadcacddccdbbbcbadbbbdacbbcacadcabccddbadbacccbccccdddbdbabdababbadbcbbbccdbadbccdcbdcccccbcabddbbdbdcdcbabdbdbabdadbbcacbcabdbbaddcdcdacdcccaddccadbdccaacdcabcdaabddbbbaddccababaacaacdbcddadadbcdbadaccbdcbddbbbbdcbcdcbcaaabcbdacdaabbdcddbbcadcbcdddbdbaddaccaabaaaaacadadbbcbbdddcadcdaccabccdccabbadbcabbadddabbddcaccaddcbcaaccccadacacadacbaaccbdbaacddbcbbaddddbdadbdabbdcaadaddbbdacccdacbdcccdcaacabacbbccbaacdddddbcddacaababccadabbbaabdbcabbcdabbcadbabcbcaadcaaacdabccadbdadbdadcbadcdddcadababcabaabccaacaaaacddadbcadabbcdddbbddddcbcbcddbdcadddccbadadcbbbbadbddaadcbadcacaccacbbddcbbaccdabbbabddbcbbdcbbcaccaacbcadcabdbadbabcbacccbddddbaccbdabbdbcdbcdbdbcbcbaacbbacdcdbcaaabdddbcccacababaacabaaacdbcbadcdcddbdaacdbddabbabdbacabbbbcbacbadbdbcacadbbcccabacaaaadbddbcdbdbaaddbcababababadbbccabaabdaabddadabbcacaabddcbcaaccdddcccbbbcccbaaadabdbabbadbbbbcabdbccdadbbcaddabbbbcadadcccacbaaaacdbdaadbbbbccbdcdcbbdaadcdacbcbddbdcdbcdaaacdbabbbdaabbcdabbabaacbcabaacaaadaccabbddbbaaadbabddbdccacccdabddacdddabcbbcaaddcacccaccacdccbbdabbdccaabaddcddbcdabcadcbcdbaddadbbbcabadddaaaacaddaadbbdcccbcbaabcdaaccdcaccbbaaabaabcabcacadcddadcbcabdadcaccddbbddcaccccccdbcdcccddddddbaacacdbbbdcbacabbbbaacbbcdbbdddcbaacaddccccccabacbaadcaddbadbddddbabacbcdaadbcbccaabdaabbddbcbbcccbadcaddcbdbaaacadcbdcbcdadcddbbddcaccdadddbbabbbcdaccabaabcdcdbcdababccbcdddbcdbbadaaabcaabbcdbaadddaacaadaadbcbdadacadbdcbbdbdbbdcbabdcccddccdbacacbcdbdccdccbdabbabbbacdbdabcdddbbccbccddbbacabcadcacbabbbacbbcdaababbcbbcacdadbcadcabcbabbaadcbcdcdccaccbdbddbdccabadbdacacccddaccadbbabacdbdacddadaddcabadaadbdaacdaacaabadbcbbcdcccaccacaabcaacbbaaccdacbbbbaccacbacdbdddbbbbadaaccacabdcddadcacabaadacdddaddbcbbaabcdabadcaaabbbdcaddbdbbadcbcacdddcccacdbdddcacbbdbabdbdcaccacdbcbabaabbbdbbddcbddbaababbddbaabbdbcddcacadbabddccacbcaabbdbadabaaddbbccadbdbbdddaccccddabccbcbadbcaacccccaccddcbcaaccbadcaadbbcdbdcccdbabacdbbddcbcdcdcdddbbbcacaccbacacbcacaaabbbcbabaccbadbbabadbadaccddccbdbbbcddbdacabdbcabbdbccdbcdaababbcacbacaabdabbbdbcbdbabcaaccbcadddbccbbcacaddaaacaadddbaadddbaccdbbadccacdcababacbdabcccbadbcbccddcacaacdcddabadbdbbabbbaacddccbaaabdaacadaccdacbacaabdabccddabadaabdabbcacbddccddaaaabcdabbbcabbdcacbdcdbddcacaaaaababaaabbaaadabccabacbacacddcdadabaccaccacaabcaabccbdadbbdbdbcbbccdbcdcaadcdcbabaaacbacbbcadaabcddbdababdadbbcabbbdcddcbbccabdddbbadbcbdaabdccdbadcbdadadbaaadbdacbacddacbdcbaccadcabbcacddcaaddbaacbaacdbabadcabddabababbcbaccadbcddcccabdbacccccbdabdbcbcbbbbaacbdcbadabbcadbadacbbabacdbbdaaccdbbdbcaabbdcacaacaabddbdbadbabdddcbcbdcbacbabcaddabcbbbbccaaabcababbbcdaaccaaddcabadaabccbaadcaadaddadbaadbdadbbcbbdbdbbbddddddadbdbcbbcbdabdbbbbbcdbcabdbbbdcadbdbbbdcadaabbacbdbcbacacccaddcadccadbacbbacdbcccaaddcbbaadbbbcbccbadaacbabadcdaaacadddcbcbbbdadaaddcbadbcacadbdbdbddcdaacbabadbdddabdbcbccdbbdbdbdcccbaddbddbaaadddaaddbbcbcccbccdcacadbccacabacabbcdabbaddcbacabcbdbcadcbddcdcdcbcdbdbaadbdbdccaadadcccdabbaaabdaadcdbddccaaccccadcbabcccaaacadccdbcdcdcdcbcbbccddcdaabccadbabddbbdacaaddcdcaaacbbbabaacaadbccdcbccabbdddbbadbbdadcaaccbbaacdddaabaacbcccbddccddccbbaccaacbbacaacbcbdabbacdcdbcdcbccdaaaaacddccbacbbdccddbacddaacddabacbbdabdcdcbdbcadccdabdabdcacadcdaabcacbacdcbcbbcaaacccdbcdaddadaabbaadacbbccccbadabcbababaccadcadaababdccbaddbccccaaadadacabccabcdabcdcabcacdbadddcbdbbbbbddbaccdabaaaccdbacadbaabdcaccbbbbcabdcccbdbbabdadbcbdacdaadbcccbdcdcaacddaccdcdcbaccbdabaacacabacababddbabddccbaadadbacbccdbccabdacdcdaacbaabbdbddcaccaaacbcddaddaaddbccaccdcbbdaabacdbacdcbbbadbacabaccaccababcacbcdcbbcccabcbaddbbbcbbabddadaccdccdcdadbcadbbababdcbdbbcdccdbdddbdaaabccdccbbaddcabdadbcdbdacccbdadcddabbbdbbdbbbccbacbdbbbbcadabaddbbadaacbcdbcccdbbccdbccabddadbbbaabacccbaabccadcbbcadbbaabdbcdcbcbbadcadaddadadbacdacbbdbbaaddadccbaacdcddbacbbcbaacacdcbbbcacdcdcadabacbbbadcdbbcbbaacdcbbcabbdcadcdbabccbbbbdbbcbdabcdcaccccaaddbcadcdcadbdbcdbbbcbccdddcdadcaddcdcdababcbdbdbbbbabaabccdcbccbdbaaddcddbdbccbaaccaddbdcacacacdacbadcabaddbacbcbdbbabaddabbccccddbbcaacbcbccacbbdddcdabbdbdbdaaccbaaadbadacdbcbdadacbbbacabddbdaaaacddbdbbdbaddaaddddbababbabcddcaacaacdcbbacadabbddaddccacacacccbbdbadbbcbbbaabdcdaddbabadcbabcbccacccabdddaadbcabadbcccabdacaabaacabccbbbdabaaaabdcdaaadcbbdddcacbabcddadadcadaaddbcabcbbadaabaddcabdbabddabcddccadcacabddbbcccddabdbcacccabccacbaccdddcdcdabababccbbaaadcbbbcadcdcbdbdadbccdbabcdcccdccacccccccacbbbbcbbdbccaabadadccbcbabbbddadacbbabaddacdaddbddbcdadabbbbdaaadccdbbbddcaaacadcdadcbcccadcddbaacacaaddbcbacddddcadcddbddbdcbdbddbadbdbdcbabdbbcaaabbacddabdbcbdacbcbacbcadbbddbdabcdddbcddbddbbdabacdaccacbabcabdbdccaddabdccddaabdcaaadcdddaacbbcccccbdacbabbcabbbdabaadbacbcbacccdbcdacccacaacdbdadbbdbcacdddcccdddddadcadcacaacbddddcbbadabaadbacaaacdaddacdbaaacccdabdbccccadcdccbccdbbcbdbcbbccdacbadddbababaadcacadcbabaabbacabcbddbdbacdbbbdbcdbdbcdccdaaacadcabddbccdbdccdcabababcaabaadaddabbacacbbcdcdacbddcacbbbabcddaccaddacbcccbadacbaddbdcdccdbbbaadbbbdababdacddcdaddcaaddbcccbdcdabcdddccbdddbaccccadccddabbddcdaacabaccbcabdabacccabcaddaabbdbccbbadbdaaadcaccddacdbadacdadbbbaadcababbcacadcccdbdbabcadabdbcaaabccccdbabbcbdcacddcabccadabcbcaabcbadbbcadbadbdbdbdbdaadbdadadbadcddbacddadbbcdbababcdacddbbadbaabadbcbccadcdcdbbaadbacdbbbaaccdbaababcccdbabbacbacacacacacdabdaabcdddddccbacdddcddbabdcabcabcacbaabbabdccdcbcdcabbbddbddddacdbbbccccddaabacbaddcbddabbdbcbcaaccbbccaabaaddbcccbaddcaabddddaaabbbadbbbdaddadcbcdadbcdacbbddbabccadcdcdcbcbbbaadacddbbaacacabcdddbaabbdaadbbdbdcbacadccddccbcbdcacdccbccaaccbcacbadaacdbccddbbcaabddaccbadbcaabbbdaabaacacccbcaaaaacbbcacdaacaadadcccbcaddaccbddcbddccaaabdcbddcbaaaadaddccaccdbccacdabbadcdddadbacdcdcbbbdcbcbbbbabbbbcdbddbdbbabcccabbbacbccdbaadbccacbccbdadcbcbacbbabccabaaccaacdcddbbbcdbdccaadbdccdddbbdcbbdccabbdadabcabdddccbdcbccdabdbabcdaacccbbdabddadcbdbadbcabdcadbbcadbdbbbaadbababccaaadbaaadbacabddbaacddacbbcdcdbbbdcddadccbddcbabbacbbdaacadcbbcdaaaaadaababcccadabbbcbddcbaabddcddbcabbcacdcbacdacdbadadbaabcaadabbcddccbcddcbbbdcbdbbcaadacbbabdbaadcaddbdacbcccdccbadcddbcaadbbaabdbcbbadbbccaabdcdddaadaadcbbdcaddadaacbbabadadaddcdcbcaddccbcdacbdbcadcdabdbbbadabdddaabbdbaacddadbddcaccaccaddcadcccdcaaaccddddcbcdccdcbacdcacdbbbbdddbcbddabaabbdabcadaaacbbdddacabdcbcdaadacbccbbaaaabcadbabadabcdbddaabbadbdacabaadbcdbcadcaccccccbabaddaacacdadcbaddcbabbdcababaadbabadddbcabbaacadbbaacdacbbaabbacbbcabaacbccbbbbbbdbcbaadddaddbcdccdbbbaaccbdacccabbddccdacdbbbbbbddcabbcbdddaaadcddacbbbabbaabccdcbcbbaccbcbbbbbbddcabadcaadcacdbadcbbabbadbdbbdccacdddaacbdbabdbaacbdcbdacccdbdcbdacdddbddcacccaddccabdabbcabcadcacaddcbbcacdbdadaaacaacbcdbcacccdbadbddacbbcaabbcccbaabbaddaabcaddcdcccbadddbddbbccbcaaccdbabdcdacdbbdbbcabcaadadbbdbdbcabbdccbabdcbdbdddadacbbbbaaccbcdadbadbbaabdcaccbdbdcccccbaacbcbbbddaccdcbcbccbbdcdbbdddcbaccbabbababcdcccbbdcbbbbddbcdccccccaacdabcadbcdddbabbabcddcbcddcdddcadbdcddaddcaadcbbbdccacbbdbbdddcabadbddbcaaccacaadabddcabcddbdaaddbabcacdabbdaababdbccccdcbcdacadbdcaddabccacbdbaabadabcaabdaaccbdccadcbaabbabdccaabbdddcabcdaddcbbdbddccbcdcacacdbaddcadcbccddabbdcacddaadcbaccbbcadcbccbcbdadbdcaacbcbbbdbaddbdabdcccdccbbcbcbaadcccddbdcadcdabcdccdacdbbbbccacbaacbbcacbadabdcccadccbcadbbabbaccbdccdababacaadbabccbbdcbccccdbcdacbaddabbdadcddaccdbbcbbadadaacbdddcddbcaaddbbdddcacdccabadabdbbcadccbdbccbabbdacbcdccbacbabbdadbcbbdabcdcbcacaadcddacbdbdaabbccbbcdccacdcbdacccddaccdcabcababddcdbcbdadccacbcaccbbbdbdacdcbaddcbbbabbdabcacbcaddababacabadcccadddccadddcdcbadadcdbbcaacdcaccdbbccccddaccbbdbdcdbabaddaabadadababdaabadcdaabadaabcadcdcbbdbaaddacabdcacbcabbdcadbadacdcdacdbadabdccabdcacbddcbdbbaabacbcbdccdbdccbbcdbbccbbccdbccaacdbdbccbaadacacadbcbdcbbbcccdcbdcccdadcddbddabddbadabcbbbaabdcdbccbadabcccddabccadcacabbdaabdbccccacbdabbbdccabcccdbcdcbbcbbbccbaabdbcddabbbdaccdcbcddbdcdaacaabadbdcbadaccdbbacadbbdcbacccbcddddbddaaddaadadcdcdbaabdbcacdbddbabcacdcdcadacbbacabaddadabadcaabcabadcbbddbccbbbdbcaacddbbdcbcdcdbcabacadbbbbaadddadcbdbbcadcbbaccaadccdbddbbbbdcdadbbdcdbbcbdbcdddbaaacadabadbcacadcdbbbbaacadaabbdacddcbadbbccbdaddbbbcdcaccdacdbabbbdadadaabddaabbcbcdaaaaaacdadbdbacaaddbccaabddbabbcabcbdbabccddbdaadaadbcddcdadcbaaababdccbccabccbbbbbaacabcabacdcbcadcbbadbaadaadcaabbdaccaccacdbabdcddcbacbbabcdacaabaccbbbbbbdabacccaabcbbaaaadcdccdcaccdbbdcaddbaabbaaaabbaabccdbaaddcdbbacbcbcaadacddddbabcaabbacddddaccdabddcaaaddbadbdbdcbdbcbabaaaaccababddbabcaacbbddbddbbdddbcabacbcbdbdbccadcdcbcaabcbbbcddbccdaaabacbbbbcbcadbabcdccaadddcccadddabbcbbabcdacbaadbcdbadbdbbbabcacdacbadaacdbbdabababccdcaacdcccccabdbcbcbdccdbbbcddbcdcbdbdabaacbdbbacacbdbbdbdbcccdcadbcbdccddbbbdcadbbccbaadcdcdbbcccacaabbdadbdddabdcacbccbbabadbbbddccbabbbddddcdddcaddbcddadcbcaabadbcdbdbabbbbdcdacdacdadbddaabcbdcbacabadbcdddcdbabdccbabbbccacadbabdacaccbddabdcaacdacadacdaadadacdadcaddabdaaccbdcbadabbddabbbbabdcaaabcacddccbdcbabaacdbaddacabcdaabdbaacdbbcacdacdbcdcbddccdadaddcdbcdbcdbbbcaaaacdbdabadbccccaacbacabcdcccadcbcaddbbabcaccbdabdbdccdcccccacdddccbbcbaaaaacccdabbcbcadcbacdbcabbcccaacabcaccbddcabbadbbdbacdaccbcbcaacaabdadcdcaabdcbacbaddaaccacabbacdadcddadbbdddbbcadbcaacccabdcaadbbcbacdbdbccdadcbacccccbaacdbcbaaddbcdbddddaadbbadaacbabadcdcbcddbadbdcbbbbddbabbcccbbcddcaacbaddacabbbcbdabacaaabdadcdbababddbcbdcdbcabbcdcbdbadbdcdcdcaadcdadaacbcacdcacbbddbcdaccdcbcaabaaadbcbaaadcabadbddbdbcabbdbcacdbcdcacaabadabcddadaaddadbbcbcddbdaabbaaabacdbcadaacdcbbcdbcdabddccacaacbacaacaadcadcabbcdddbccadabdbdbcccbcaccbddabdbccdbaccdbbdadccacbcbbbaaddddbddbdbbbbcdcdccbdcaccddbacccaacacbbcadbaabbcbdcadaaaccdddcdddccbdcbacabbdabcdabaaddbdbacbabdbbbcbcdcddadbdddaccadaabaddbdbabcdcbdcdcddddbadbdbdbdbdddcbcdbcbbdaabbbcdcbbbdddddabadbbdaddbcadbcaaccdacabcddbdddbdabacaaacacacdbacaaadbbdbadcabaabcbcadacbcadacdaabddcadbcaadbddbdcddbcabadbbbabcbbbdbadacdabdbcadcbabdbaacbccdccdccddddaabdcbbbacadcbddbdadcbddcabaaddadacaadacdadcbaccdbcaaddbdddbcdccaccccdcaaadbbbcbcbdcbdbdccbcbadabaabadbbcadbbcdcbdaabbcbbbabccbccaaaadcacbcbabcaaabadcadadcadddadacaacccdddddcbdaabcdcdccadbdccaaacbadcdabbabcdabdabdabbadbccdbaadbcadcbcdccadccaadaabaacabadabbbaadbbdbdddddacccabcaccadbccdabcaacccacacbccccbcabdaadcbadcbcaabcacbaaadcccbcddddaabdddaabbadadbbdaacbcccddacdcabcdaaabdbdaacddcbaabcabbcddcbbcbdcddacbbcaccbcddbaddabdacbbbabdaadccbdcbacababaababccccddbbdbbdacbdbddabdaabacccdbabcdcaaacadaadbcaddbbcbacbbcaadcabbcdcdadbbcaddcabcdacddcbcbbddacadcddbbcdbddacdbbbcdbcadacbccbcbcdadbdaddaccaccbdccddbdbbdaddbcbddbbadacbdacabbbddbabacacbbcabbdccbccababbbdddbbbcaadbdbcbcdcdaccaacacddababdbbcbdacabdccbbaacacdaadaacaadbacdaaaaabdacccbbcdbdddccdbdcbaadbacdccacdacdcaabdabddabbabacacdbaacbacdacdbbaacaaddbacabddcbcaaddaabdddbcdcbcbdbcdababbcadbbddbdacbdddbdbcadadbabdbdbbdddaddccabbadbbadaccabcdbcdcbdaccbddbbcbcaadbbdcbbbaabadadaaddbbacadcbbddbdbbdccddacbadcbacddabbcbdbbdacbcadbdaacbcbdccaccbbcbddbbdcbdcddcdddcbaaababaaabdbdbcdcbcbaaaacbabccbdbdbacbaaadbcbabaacbbbacdcdbbbbcbaabcbdcaaccbddcabbabababccccdabdadaacdbaacbdcdadbaadcacdccadaddddbbbcbcababdaddccacdcccbbdacdacccdabaddaaddaadabccaaccbdcccacacacaadacadaabaacaddddacacaabbdcabbddccadbbabacbadaddcaacacdaaddcdaccccddbddbadcdbdcdbabbacddaabdddddadddcbdcbabbcbadcbdcbbcbaccdbcacdcabacbbdcccccdcaadabdbbccaddbddbbcdabdadccbbdaccbaadcdacacdbbadbddddabbdbdabbdbabbbabcddabcdbddabbabacdacaddacbacdcbcbcadccddacddadacddccbbacaababaaabcadabdcbdbdbcbbbcdcabdabddbaaabdddcbcabbdcbbcdcccaaababbcbcbbbaaacacddccbcccdaadddddddabadccbbcdcbacbddbbdbadacdbaccaacbacbccddbadccbcbdbbbaacadcabbccadddbccbccbbcabbdccbabdacabaadcddaadaccddbbdbdacccbccdbddacaaacdacddabacaadddccbaaabcaacdababddabbccbdddbdcbcaccdbadcadabccdddbbaaaacbcaacacaacacdbcbcbcaaadcbdbaadaddbccaddbcaaacbadbddbbdacbcbacccdaaadadadbbabcdcacdcbbbbadcdccbaddccddcdcaaacdcaabaabbaddcbdaaddbccbdcaabadbdaabcdabcabadabdbcbcaacbbcbbdbccbbbcaaacdddccabdcdbcbacadcdaddcdbadcbbbdaabccdbdacdccdcdacdadbbaacbabbaabddccdabacdacdabbdaaaccbbbdccabadbbccbbcdcbcbbcbacbbccddcaabdabcdacbabaacacbccadcdbbcbacbcdadcaadddbbacadbcdcccdcacdcaaaccbacacabcabbbbacbbadcccbdcccacbdadbabdaaabcbcbaaacbaaacddaccbbdcbaddadbcbdabcbdcbcbcdaccdbbbadbdbcbcabbbadadbadabcadcadaddddaabddcacacbbbbadddccbacaddabcbbcaadccbdbadaddcddaccbdcdbdadaabcacacacbadbbabdcadcdaadcccbccdddbabadcacabcdcabcacbcbcadaacaadbbdccdbbbaacadcddbadadadabbddbbdccdddbbcaadadabbbcacbbdcdcdbaddadccbccbdcabaadadcabbddccadaaadcbbdabdabacbabdacadddbaacaadddabdbdbabdadbbcbbcaabbbbcccabdaddacbbabcbcaddccaabccabbadcbdbdbcddcbddcadbbabdacadbbbdbbcabbbbbdbbcbaaddbcddbabdacdcdbccdcddabdaaaadadcbcbcdcccdccaadcbbdcadccddccadabbadbadcdabddcddadddcdcacdccbbcabccccddbdcacacccadddbcacbcaaaacbbccaaaccadbccabacbababcbbbadacacaabaababddacabacadbbbbdbccbdcabacbccddbbbabaddcdccacadacaabddddacddaaddcadcabdccabdcdbccaaabcccbdbbdbacddddaadbbaccacbaabbadbabadcaddbddbdccdbabadadcbcbbcdccbbacdbdbcaddcacbddcbbccccbdbdbdcdddcdbddddbbdbbadcacbcccacdbcdbccaabbdaadadddcabadacbaccabbcdbdaaccadddbdbadaaddbdddaddabcabdadddaacbcdccabababbbcdabbbbdbbaccdcbdaadcdaaacbddccaaaddacbabcdbcdcdaddcbabbcbaaabbadddbcdddbbccabddabcbcbadaddcbdddaaacbaadcbdcaacbccbdbbbbddadaadbbdcbdbccbcaacbbcbadadadaaabbbdacabadcadccabccccaadcbacabccdbcdcddbbadbadbddbcaaddccbdabbadbaddacbbdbaacaccbbccaccdcacddabbbaccaacbdccccbbddaaddcabcacaadabcacaabadaccdcdccbaadbcadddaaccabbdbdbdacccdadbbcabdcbdbcadcbbbcadbcddbbcccddcbbcbcadcdbcbabdbacdcaccaaaadddcbcdadbcccacaacbdbacbaabbcdddbabaabadaddbbdcacaaaacccbdcdabaaaabadccabcbabbccbabddbcaccdccdcbcccbdadcbabacbdbddbaabaadcacabacaabcabbbcccbaaaaaaacacbccaacaaaccbbbdbaacadaacbcccbbaddadcadbbdcbdbcddaddcaacabbccbbcadbcccaabaccdccbbbcbadddbcbabaccddabdddcbdabccaccdddccbbbbddcacabddabaaacdababdddcbcabcaccacdddcdacbcabadddaabaaccadaddbccadaddabbbbcaccacdbbbcdccdabdbddbdabacabddadbacdcdcbacbccadbdcbbaccddabbadcdadcccddadcbcaddcddcadbdbabdabcdaccbddbcddadbdccddabacdcbdabdbaabbdbabbddcbccdddacbcaaacbbbdbcadbdacdbaacdbbddaaadbdcbaabdadadcdbcacbadddaaddbadbacabacbcabbcabacbdadddcaddcabdbabadccdcacacaaddbabaccdbaabbcbabddaacaaaccbbdbbadbacbcbcbacdcadcadbbaccbbacacdbadadcdbacdbdddcdbcbdcdaacbdbbcbbacaccabdbddbacdabcacbdddbaabccdddacbdbdbbddcbcbbacaabcadcdcaaaacacdadaddbbcbaacadcbabadbaaaddaddbacdccacaddcdabcddbacdcdaabcccbabdcddbacbddcacadbcadacccdbbdbbcbbbdaccbcbcdbabcaacbdaaadbddbccdabddcadddbccdbcbdbabcadabdddbaaccaddbbabacdcccdddbcbacdbabcddacccbdbabdddcdbdddadcabdcdbcbabbcccaababcbdbbbcdcadacabbbaababcddadacddbbddbaaabaadcadbaddbaadbdccabbbbdaadacabcaccdcadbbcacbbabcdbadcbdabaaaadbabdddbdcbdccabccbabcbabacacdaabdacdadbbcacddbbacbababbccadccadddcbadaabdbdacabdcacbcdcbadcaabccdbccdbbdaddbbbdccaacdcbacbdcdcbddcbbcbbbadcdddcbddaadbadcdbddbbadadabaaacbddcccbbacddddcbabdabbddbdccadbdcdbaaaabaaddbaddacbccdadbccadabbacacbbcdabbcdacaccbcddaacabddccbadaccbbabacddccabacbbbdddaccbbcddcbacccadccddcbcbbccdddabbcccadcbdaaddccbcbabacbaadaabcbbddbbdcdcbbdcccddccbdcdaacaddbaaccdcdbadadbdbadabbccacdadbbaaabcbabaddccdcdccacabbcdacabcaaaaabdddaadccbdbdacccbcdbdbbadccaabbbbcbabcbbcbaabacaaccdbdbdbcacbadcabaccccbdaaddaabddcbabadacadaaccacbcacaccbdaadbddbabbbadcccdcdccdcbcdadbdaddddadaadacdcdaaaabcbddbcaabacccdcaaadcbcdccacddccdcadccabacaabcdbabcacbabaababaaabbcbbbacbbdddbcdbbbabbaacdbacaacbddcabaaddcdbababacacaaadbcbbaaaaadbbcabacbbbcbddaddbbdacacbdbccbccccaabadbcadacaadaccccacdbdacacabcacdbbcdaadcbacdbdccbbcbacbcababbbadaaadddbbabccadbbdccdddddbbaddadbbdabcdadbbcabccbcadbcbcddcdcadbbdddccabbbbcbdbdabcccdcbbadccbcbdabbbbcabdccdaaaabbbdadbccaabbcbaacadadacbcdacdcdacdaacdbabccabcddaaaabaccadbbccbcdcacdcbdcddaccaaccdbbbadcdbcdbbcbccddbcdcdcabcbadcdbadaccbccababbbdbbddbccccccdbcdbbbdbadcdacddbdbcbcccdadcabddabdaddbcabcccbcacbccddcbcddbcaccdaaccccdaddddbbdbbbacbcbacbaccbcdddcbddcdbcdcdabbbbbcabaacccdadbabcdcbacbbcdcabbbdcaddddbddcacddcddaacbadbcbdcbddaccbcbcdcaabbdbdcbcaabcbbbabdccacacdccbddcadacbccbbabbccbcccccaddabbbacaabcbbadcadabaadcbdcccddadbdbbcbcabcadbbddbdddaabacccbdcdabcabacadacdcbdbcababbabbadababbccacaccadabdddcdbbbaddcdabbbccdadbcabcbabdbcacacdbdcdbcbbdcbcaaccdcdabcbbbbabaadcaaaccbbbcabbccddbcbbddabcbbabadccccbaacdcccadcacbcdcadbbcbbbbcbacbcabbbdccaaadddddacbbaabaccadbccadbabdccabdabdcdaccaccaccbaddaacbcbccdcabcbdababcaadaddbcaacaabcabcddacbdcadacccbdbdbaadbcdbaccacbdaccccbaddacddbdadcadabacbcbcbdabcaabcaabdbacdadcbaabdbacadaaadbacabdbcccdbbdcbadccaabacdbdccbbbadddcbadcbcdcbadaadbaddaccddddccbccccbddaabcdaaacdddacbcaaccccbdcccccaadcdcdaaaabbaaddbcacbccbcbccabdabbccabcacacbaacabdbbbbbaabccbbabdadacbacbabcdccacdadadbdadbbdacadbcdbcccdacbadccaacdcdbdcddddccaabdbbdcacdcaabbcacaccacadbdadaababdbdbdacbaadadabdaabbcbdacccacabdacdddadbdcdcddbbcdcbcccbcccbdbcbdbddcadcbbbddbbddaccacbcbdcccabccacbddbbbabbdcddadacdddbacdabacdcaaacbcddcccbdbcbdbcbbbcbccabbbdadacabdbdbdadbbbddadbabbcddadcaabbdababacacccacaabacdbdbaaabcdcadadaadcadaacdaaabbaaadcacabbaccdcccacacacddbbbcdcbbaccdbcacdbbcabddadbacacbbccdaaadbaaadddaacbcdabbbcbdccbdcdbadbcacdddbdbbaaaaabbccaadcacdccddaabcdcddaabddaaddbacbbddddaabcdcdbcddcbaacaaccadcddbddaaaadbaacdcbccbbddacdacaaccabbbbaccdbbabacbaacdacbcdbababccacddbabcbbcdadbbbccacabcdbadaaacadaccacbcbaaacbccbcdbadddcddbdadacdcbbcccdbcaabdadaccdbcdcdbbdddcacbaabcdddadcacdbbaabcdabcbcccabbdddbbaccccabcbbbdcabddcbdaccababdbaccbaabdddcbabaddbccaacdacaacdcabdcaccbcdaccacdaccdcccaabcbababaddccdabcacbdccabacbacbdbdcaadaabdabddbdbbdccdbdccdbadaacadbabacdbbabbadcddbcbbabdcbddcbbaadccabdaddbbcdacaabdccdcbadccaacacbbbbbcdcdcddabbcbdddaabcdcabadacbcbbaccdaddbcabbacbbadaabcdbaddcbdabbaaacbbddbaadcdccdaacadaccacadaaabbccaddcdbcccdadadcaccdadbaaaabbaadbbdaccdcdcdaddcccdbdcdacbbdcddcacacbcaaddabcdbcbcbbaaaddabcaccddddddcdccdcacbacaacdabccdcdacdbcdbadddabcdbbcbcbaddcdbcdbcdaddcaaadcbadaddddaabdddbbaaabbcdadcdaaacbacbdcccbdabbcaccacadbdcdcdadbabccddddadadabcbbacccdcbdcbccbbbabadccbbdacdabbccbcbcbabbacbdabbccbcabbdbbaabdaccadbdbabdcbbbabbadbccbdbdbcdccbdaacacdbcacaddabbdaabbdacdbbbbcbdabdbbbaddccbabccbababdcddbbcbbccdbbdddadbcdbcdbaadcdcbcdcaacaddaaacddbbcaaadcdddbcdaaadbddaddcacdbaaadcbbabdadaacabaccdddccaacdcbdadbddddbdbbbdacbbcccbbcbbbcddbccacbacbcadbabcdcadccbbccdbccbbaddabbdcbbddabcabcaccadabcdaabaccbcbacdadbbbbcdaddabddccccdddbcacbcacbcadababbdccddccbdbdddadddacbdbddbbcdabcddacdadacbcbddcccadaddbdbbacdddaaccbabbabbdcaabbdbbadaacccabddabcdcacbcddccacdddaadabcdcaddacdbcccaaacbdbdaaccadaadbdbbdabddccbbadacdbcddbdcadccddbdadcddcabcdbbacdbadcdddcabcacbbbcaddbcbabdadcbcbbabadbabcbcabcbcddddacdbacaadcbbccbdbacddacddcacbadabbdaddcbbaaccbdcaacbdbbbdaaadcbbbbabcaabbbdabdacbcbcacaddaaabadccbbacccbdaddaddcaccbbbbbbccdddbccbbddbccbadbcccbcbdbaadacddcdaccdbbbcabcdcbdaabbdddcaadcddcbdbdabddbabcdcadcdbabddaccababdcadbaaabacababcacdbddcdbddbaccbddababadcabdddaadddadabbbbaccaabdcbdccabbdddbbcabacacbcaaccdaaabbdcdbdcbacbcbcdabddcaacbcbdacbaabcbcbdcadbddbcdacbdabdddcdbdddccabadacabcadbccddbbaccbbcadddaaacdaadcaddcdcdcaddcadbacbdcadbcbdabbbbccdaddadbbccdcccddbdabacdacabbcdccdabdbbcdccbbbcdabcadadacbddddacadbcddaabcccdbadbacaabdcdacabdddbbbdddadccbbbdbcaddbcdcabbcbadbdcbabdabbabcaadbdbddbddacbdabdccdccbababdcadcbcbbababdcdabbdcadaddccdaacdadccbcacacaaabaabbdbcaadacdabaababdccabcdbabbbbdcbdbbcbaabcadccabdcdcccaabbadbcbdbdccbbdcbaacdcbdbabbbaabcddddbaaaddbaccdbcadcabaccdcccbccbcccbccdcbddaacbddadcabbcbabdacdccdbaacddaaabbabcbdaaddbcbaccddadddaddcdcbcacdbbdabbdcacacabdacbadbbdcdabcbbbaddaabccdcbaabbbbadaccdaabdabaacaabbbdcaccbabbdddcacbbbbaaacdabaccccadaabddacbcbddcbabbcdbcddcaccaccabcabcdacbaccdbbbbdadaaacbadbaadbddcbbbaadbcdabbbaaaadabacbacbbdbcacabddabcdbccdbaadcdcccbccddbbaadcbdbcbbdcaabdbddadcbddaadbbdccccccabcbddaaaacacbdacccccbccadaccaacadbacabcbaddbbcdcbdcdbcdabccabbbcddbdcdbabccccbcccaabdcddbcbacadccdbcaaddabdabadccaddcbcadadcbbcbccbdacdbcccdcacdccacbabdcdbcdcccdaddabddcaabacbadbacdbbbaabadbbaccbbbadbbcbbacadccccdaaaabaaaaacdadbcadbbdbddabdddacbdaabaccbbabcaadcababdcbcabdacacadcdcbbccdacddabdbaababbcbbbadcacdbddcacacaddbadddcbddcbaaacbcdbadcaacbdcbdcdddacdbacbbbcabbabbdcbcaadbaaadaabcacbdadadbbbcdddabbbbadddbccdacabddbaaaadbacddcabadddaadcccbbadccbaccbcccbdcadccbaacdbddbbdaadbcbacacbacbdacaddaaacadcccbbbacabcdddaddddcbdbadabddcabcabccdaadcbaddbadbcaacdbaacddabacdbaadcaacaaabdcaccbdbddbdadadcabcbbdaacdbcdccbdcdbccdcbdbcbbaacaadcacbdadababbbdcdaaaababbbbdaabcdcbcdcdcdacbcccbbbaacdbbabadacaadbaaadbcacadccbacaaacdaabadbabbcbccacabbabdabdcddcdbdcdadbcdcbbdbbbabdcddabaddbcabaaaddbbadddaacdcdcbbadcdcbbacddcccbdbbcddaccbcbccaabccccbdcaddadbabcdcdccbcbcdddcbdbcccbddbbdbacabcbacddbabbbbdbadddddbcdccdadbacaabdbbbcbdccabccdaddbdcdbdbbccabcaddbdaacccdaababbabdbccbcbbdabdaaccbacbaaaacadcddbccdddadbadcdcddadbbbbcbbbdbadccccbcdcabdcaaccacaddccbabbabacbddaababccbdaaadcacccbdcabbdbbacdaaaaaabcbdbbdcbdbdddbbbdccbbadbbcaccacdbbbdbabddddbdbbcacadbbdcbabbcdaaacbccabdcababbbadcacdacabcdabdcbbdacdabdbbbabbcbbacdbcbaacccdacdbbdccabbcbbbbdbccdbcbabbdbbddcbaabcdbdccacddbaddadbaaacddcbbcdddbdbdcbaccdcdcddbdadddcbbcbdbdddbadbccbbccadcbbcbbcccdccabbcdacbdbadabbdddbdaaccddcccbbcccaabbbbbdcdbacdbccddaabddaabcaddcbbacdbdddbccaaadbaaabadbaaaadabdbdbbcdbaddaaadddcdaacdbbccdbccdcdbdabdbbdbdbadcacccacaabdbcbdaccdccaacbbdbdcabcabcbbccdbbddbdbddbaabadbcdbdbdbdaadabcaabccddbabbbdbbabaaabcdcbcbcdbacbdbdcadccaaacdcccbdbabcbadabbaadaabbdacdcabbacddabcdddcdaccdbcdadabddabddaadbdcdaacaadccbadacdbbacccbccadbabaccdaabacaacdcabbcaaababadbadaabbdccdbbbdbbdabdcdcdbdcdcaccaaaccaaaabbbaccacdbbddcabcbdadbabbbcbdacabccddccbdacbdddacdcadbdbaaabdabaabcddcbcbdacbbdcdbacdbbcaaaaadbcdbabacaadddcadbacdbccddcadbbdddcdbdcccbacdacbdaccbcaaddbbbcdaaabcdabbadcbdcadcdcadbddbbccbabbdaaaddadacdadcbcabcbbaacbbbacaabdcbabbabbddcbcccabbddacacaaacacaaacdddbadbabcbbacdccdbcbaaddccbaacdbababbabccdccdaacbdacddadbbaddccccbcabcbccbbabcdaabacadaabcacacacdbcadacaddcaadddcbddcdcbdbbaabccdcbcbdabdadacbcccddcbdcadadbbcadacaaabddcbaadcdbadadabbdadcbdacbbdddacbaaacdaabadbacbdacadadbdadbdccddbdaaccdbacbcbdbbbcbdbbdcbbcbaaabbbdcddbcbcadbcbcdcdabccccccacdddabccbaddcababddbcdcdbabbadcaccaddabddcdaddadacadbcbaddccbadcdcabbcbdacbabcbaaccdabdddbbbdcbccbcadbaacdccdbcacbcbdabcdacccbbcadccdadacdddddcccbbbcbabbbabcbdaacaabadaabbdccdddcdbcbdbaaadcadccacdbcbadbcaddacadcabddbdcdbadcdabcccaddbbccbcbaaacadbbdabaadcddbddccbcabcaccdbaababbdbbbaacadbcaacbcadcacdaaccaaddcabacdacdbccdbdcaabcdbdacbbadcaccccbdbbbcbaaddaaabdbaaccdcddadabccbcbdbddbaaccdbabbddbbdaddcababcabcdcdbadacbddcaadacaabcddbbaaaacdaaaaaadcccadcadccadadcbcdbccdccccbacddcaddbcaaadbdcadadccdbaddccddbacbcdcbdaaacccbbbcdcaacbadbccbcddacbbbddcaddcbadbdadbcbccdaaddcbabcdbddabaaccdbdbcaddbbbbcaddcdccbcacdbcbbcbbdbacadcbdcbcbbcaacddbabcaabaabddddbbabcbbdccdddbddacaabaddcdadddaabaccdbaddaddbccbdbdabdbdabbccccadcdabbaabdbacbaddaaccabdcdcdddbbcacdddadccbbaccdbbcdccadcbbcadabbbddbddabaddaacdbcabdbcaacadcdddbcdabdcbdadadadadadbcaaccbbcacbdaabdbcabbcadbbbdbcdadbbbcdcaadbcbccdbabbdbcdcbbcdbddaacbddcccdcdabadbabbdbdbccbcdabcacccdddabcabbcdbbdaaadbbadbcbbabcabaacbccdbabcddbbcddccaccacdbbdbccbaacbcabacacdbacdbacabcdbaddbabddadcacdcdbaccbaccbadbbcaadddcccaddbbbdccbbadbbdabddbbaddccbabdbdabdaddbccdadbacaabcbcbdcbaaddcdacabbabdccaaabcaabcdcbadcbbbbbdcbdaccadbdacaaadcaabaddbabdacdbdbddcadaaabcadbddbccddbcacdddadaddddacddccbddcacbbabcbaaabacbbdbacbaccbbdadddbdddbbacccbcdbaaaaadcdcdbbdabdcadbcaacbadbcdcadacbdbbcbbbadddddadadbaddcdbbbcdddbcbcbaabbccdbdcdcdacdbabdddbcadabcddacdccbabbbbcaadadbdbdbdacadddcadababdcccabbabdadcaabaccaaadabdacbccaabaddddadaaaddccccbaacdbdddcaaddcdcabdaacdddcdcadbbcdadbbbabdbcbcbcabcabdbdbbcbbadaaaddddbbaaddababbccbbaaddbadbabbdbadbdbadbadcdcccdaaaabdacabcdbcbbbaabdcdddbbdbacbaaabdadcdbcdacaaccaddbdddcabbddbcaccabacdcdbbdadbbdbccdbdbcddddaabdbbabddaabbabdbbcbbcdabdcacbccaadacbccbcbcacdabdccbcdccbdbabcaacbcdabcdddbadbdabadadcbcdaaabddcddccaabaccdacdcdcaacccacbbbcbaacccaabddaaaadbadbaacaaabbbabbbaacdcbdbccbcadabccadbdabbdbbdabbbddbbddccbbcbccbcdcddbbcbabcbacbdabcbdcdacdadababaddbcdbaddacabdcacdbacccdacbcdbaabccacdbacdbaadcadabbcbaaabbdacacddddcccbddababaacaadbbddccbdcccbbbbaacbbdccabdccbaabbdbdbacdabaddcbdadcdabcabddaccccdaddccadbcdadbbabaadcdaccdaabcadbcbdbdadadddcabadbcdbaadcaddaaccbaacacacdabbdcdbcdbcacacbacdbdbdacddcdbcccaadbdbcdbbcddadababdbdbcdbddbaddbcadbbbaadabbddcddbacbbcdaddadbbaadbabaaabaabdaaadbccdbdddbddaccdacabdbadddbdddabcccdcbcdacdcdddbabbdbdddcaaaccbababbdcbcadabcdbdaaaaaaaaadcdddcaacadacabcbcbacaccaacdcadacabbcdcacbacddaacdbdaabababbdcbbbcddcbaccddacbddadbbabbcadddbbcbadbaabccbdabdbaccdccdcdabbcaaaaadbbddabbddcdcdcdbcaddcbcabdbaadbcadbddbcaabaaccadcddbbcbbbbccdacdcabdcdbaddbdaabcbccaaabaaaacacdbcbbbaddaccddbccacacbaabccbaadabdbaacdabbadcbabbcbbacddccddadcacbbdcddbcddababbcddbacbbccbbbbbaacbdcbabacbaacadccbdcabbbdcadccdacaaadcacbcbcccdcbabaabadadaaacdbcddddacbabcbabcabcbcdbdbcbadadbaadcccdaccaccdbdacaccaacdaabcdbaadcdadadccaaadcdcbbcbdacaddcccdbdadacacccdddbcdadacdbabbddaaabdcccbaababcddbccdbcbbabbccdaadddccbbcbdacdbbacdbcdbabdbddccacababcccadcccbbaddcccbddabbaacbcbcccadccbdacdbaababbadcadbaaddbbcbbbdadbabdbcbbcddacaabacbdcadbcdccdccbdaccccbdaaacadbadccaadbbbbbdcbaaabbdaccacacacbcdcccaababcbddbbaddbbccccdaabbdbbbabcbcbcaadcdcbabbcaaadddbdcddddabdcaddcaaddaaabbacbbddbdbdadbddcdcddccdcccbabcdabddcdbdaacbccdcdbdbbacaaaabdabacddacabadbcbabcaabaadacaaacaadacbcbbbdaaddccbdabbdaddcccdababcdbbaaddcbbdbbdaaabcbbaccababdcccdddbbadabbccdbbcbbdcbbdccccdcdaaccbbaacbbdddabcaadbcabdbdbdacbbbbbaadbcabbcabacaddbbdacbcababcaacaaccbaabccdbabccbccabcccbbdccdbcbcacccccadcbbcdaadbbdbbdbaabbccdccddacacdadccdbabaccabcdcdcdacbbdbdcadcdbbbdddbdcddadddcadcbadcacbdabbdabaabcdacddddcbddcbccacddbadbbdaacddcaadbdabddacdcabdaaabbddbccaaabadbddcdcadadbdccbdcacacaabddaddbdcddadbbdbcacdddddccbbcdddadbdccabdacbbdbbadacaabcdbcbbbbdbabccddaddacaccdbdabcabdabbadbabacbabddabccccddadabccdbacabcaaaaabdbbacdbdcbdcdaadbdcbcabaabbbbaccaadcdbcabbacbddadcbbadaabbdbdbbcdaadbbadbcdcdabdcdcddbdcccbddddbbaadabdbcbdabadddbacbdcddcbcadbcadacddbabadbcdccaaaacdccdcadaacdbbbdddcbaddaababbdaabdaaaabbbccdcbcbdddaccbcdabcaaadcbadbbbbbacdadcaacacbbaaaaccabdddaaaaadcbdbabcbacdbdacacdccbcccccdbbaacbdaadaadbacbaaadbcabaddbdddadccaacbdcbddacdcadaaddadcbdcccddabdaaccdaaadbadaddaccbbadcddabcbdbdadbdcdcbcddcadaccbbbbdcdcabcdbacbcdbcddddaddacaaccdcbaaaacdaabdbdcbadabaacbbbdcabddbccccacbbdbaadabbacabbbaadaacbdddaccadcbbccdaddadbacabdacbdbcacaddabaccbabcaacbbacddbcdbcdacdcacbbcabdaddbacabacbccbcadadbccccdcdccbcdaabddcddcbbacdacbbbabbcbacbddddbacbabbcbccbdaabadddcbabbabcddbcabcccbdddabcaccabbcccbabbbbaddcaccdbcadbcbbbdacabacdccadbdabaddbbbdcbddadccdcdcacbdcbabbdbddccbccbbbddabaccdadccdbaddacbdcacdabcdcadbdcabdbcbddcaabcbbccadcabbccdccccdabcadabbcbaaabaadccbaaadbcbbcdddbcdbdbdaacbcbcbadddccccdcaabdbabbbdbdbaaccccabacdcbabcacbcaddcaddccacdacbcaccabcdbabdccbcdccdcdcccbcddbddbcbddbdadabaabcacbdaaadaaadaaadacbdaddcddaccdadabcdacacbcbcddcabcaacbcabddcbdadbabcdddcaadddcccccbdcbdbbcdcbadbcbcabdbabbdddcbcaacdbabaaadbddbbadadbbcbacdbccaababbdddacdbcbdccabddabbdccbbdaadcddcdbdbccadabddbdcbaccdcabddddddcabdcdaadbdccacccbdaddbcbaccdcbbabdbbdaaccbbbcaaddddccacbdababacccaaddcdbadacababbddcdcbcbbdcdbdabbdcbacadaccdbdcdccccabcdadaadcaccdabcbaddabbacbdbbccaddbcabdabbadcbbcaacccddcaaccbcdcdbbbcbaabbacdccbbcdcadbcabadddcddacacdbdbdacbbacdddddadcaacacddddabdcbaddbddcbbacbbbdbcaacccadccccddddcdbdddaabcbbdacccadbbdcabdadcaabbaaccbaacabdcdbdcbacaaddccbbdcdabdddcbdbbaccbcddbcdcadcbbbcbcdacdcdabcdaadbcacbadccdadcbabdbbbabcbddcabddcbdbddcacbbdaacbcaabddcdccbaccdbacdadcdadcdddcddacccdbbddabcbbccccbabcadaaccadcadaddccabacabcadbcbcdabcbccdddabbdbdacabccdcaadbcacadbdccabaadccdcdaddccaacbadaadcabdcdadbcdbbdbdbaddbaadaddbbbabdccbdbdbbdababcdbaddaacabddabddabaddcacabdbdbccbdddadbccbabcccdddbbdbbadbdbdaabbbabcacbdbaaaadbcddbacddbcacdddcabcdbcbbabdbcccaccddacdbbdacadaaccdacbbaddcadddaabadacddcabcdaddaabbcccdccddcdaacbaacdbcabadabdbdbbddbdddacbdbbbcbdcddcdccddcaddacdcbaccddbdabadacbaaaadaadcbdaaaaccacdccabbcbbdbbdadbbdddbcbcbcbddbcbbccccbcdddcbaabdcdaaaccdbcbbbaabbbcbbbdbcbdddcbccbcdbdaaadacdadccbbcdbcbdbddcdbdabbbbdcdadaadbbbdadaacccccabbbabbccccdcbddbcabbcaabcbacddaccabbcbcaadbdccddccdabacbdbacabcccadacdcabdcdbaaaddcdcbdacadaacbabaabdddcadbabdcadabbbadcdcaaaacbdbaabcacdddbdbbdcaccbbadcabddbcdbcbdbdadaacddcadcaabdacbbccaddbbcddacbacbbdbbabbadcdaddbbbcdcddbdbacdcdadccaadcadbcbcabacadccdcbcdcdddddcbddbabbbbcbdbbcaaaacdadacdaabcdbcadccbcaccaabbcdadddbcccbababddbabacdbbdcddddbacccdabaabbabcdccbabcdadbaabdbcbcbcdbdcaacdccdacdccadbdccaacdadacacbddcbcccdddcacdacaaabbbbabccdbbcdcddbcadbadbadddcadabacbbddcccccbcccabbaabccaaaaabdbbbbadbcdabbaadbcddcaabaadcdbbdbbcccabaababaacdddbbccabbcdddbadcbadbdadbddcdacdababbaacbdacdcacacbaadbcdacbcbadaaadddadcbaadaadbdcbbdacaaddbbbabaacababadacaddaadaacadadadbaacadcadbcbdbdbddcaaddadacadbaacadcadbbcaacabbdbaaadcacbdaccbcdacdcaddcbadcbbcacacbcaddddcdbbdacdabddbacbcaddadbabacdaacadcdccdbbcdcaccdbdcdbbcbddbcddacbbbcbbbbbbaabdadcabdaddbadadbbbdadbbaaabbcccccaabcdaabacdbadcdbbcabdcdccbcadcdacbdbbcbbccdccddcbbbbddbdcbbcdaababbcddacddabccbbdddcbbbbccabddabcccabadabbbadbcbcabddbbccbdddbdcaaccdaccdccbbdbddbaabbccdbbadbccabbccdbdcbbccaaaaadbcabaccaaaaacccbbbcbcbccdbcbcaddcdbabaaabdbacaccaacacbdddcbdabdbdbccabbdbdccdcacabcacaaddbccabcdaadbbcbbdbcaadbcbdddadddabdcacdaccbacdddbadbccadbabdbcdcddacadacdadbbdadddadbdbdaaabbbcbbcacbbadbdaaaddaddcdddbadabcadcdbabdcdadbbdbbacdaaaccdacacbbbaddadcddaabdccbdadcabaaaccbdbdcbddcbcacccbcbabbdcadbdbbabdbcdbbdbdabadabdcacbdbbbdcbacddbacdbbdabdaabadccacbdaaacccabdaaadcbdbdcadddbbdddddbbdadbaacbbccdbdbdbadbdcadccdbcbdabddcdaabdcaccadcbddacbbacbabdcdbbaacccdbbcbcbbbdcccdccacccacbdabccbaadbbbaaacdaddbbddacdbaaadbdddddbaddccbacbcacbcbccdadbcddbbcbaccbabbbcadbbcabadcbbccdaaaccbcdabccdbdddacaccdbdabcbabbdcabbdaaccacaccbcacbdcbaabccdddddcdbbbbbddbaccbcacdacaddbbacaddbcddcdbcabcdacaacbbdbdccacbbcddadacbcbaadbbdcaadbaacaacaaccbcbcaadabbbacaadccdcdadbbcacbdbdabdabdcddacbbdaadcdcddbbaaabddcabcdadccbcbdbcacaadbadbcdcdbacdabbaddbccddbadbdcbddbdcdddddcddbbddbddcacacacaddbddddcdbbbbbaaabbbbcbacbdadcdcdcbaaacacacbbbaccbccdbcddccddaababcacaddcbbbbacabcdccdbdbadddbbaabcdcacbacbaaccccdcadbbccbdcddbbcabddbdcdcbcdbcaabccabacaababadcccbbaabbcaddbdaaccacabaabacccadcaccdcdccdaaddbaddaddabbcaddbcddcccbcacaccbcbacbcaabcbcdbabcdddcadaacbbbdbadcadcbabbbcddabaaadcaabacbddcbacbcddbaddcacccdaaacbdacbcadcdacdddcbdbbaaccbbbdcbaccddbbcdbdadacbdacbccdcadbddbcdbbcadaadbaaddccccacaacbacbbaccbcbdaadddcbaaddbbbcbdabaccdbbabacdddcddcaadabaabbcadbabbdcdbdcccaddabdaaaaaabbccccccbcaabdbbbcbbdbbbbcbbdbdbcaaccadccacabbaabbabdcaabcdbbcadadcdabdccddbdccbdcbcdcabacbadcdddcdaaccabcadbabbbcbaddacccabbacabddbacddccabdbaabdcaaadbcdbabababcdccacdcaaccdbbcbcbdadcccabcabccabaccabccbbadcbabccdabdabcbddcbacbbcdcdbbcdddadcddaaabbdbaaabbadadbdaaccdcccbacbaddccbaacbadccbababcbcbcabcadbabbbcacdacabcbbdbbbbacdacbdcdadccddadbdadbbadddbcdcdacdacdcaabdddbdcccbddcdacbaddcadcdbacadaccacbcddddbabacbdccddcbadabbbadbacdddabbdcccdccabdadaabaccbbbcaaccdcbadaaddccbbcbaaccabbbadbcabcabcddcacddaacbcddaddbcdacbddcdaaadcacbdaadccaddacacdbdcadcdbdadccdbabccdbbbcdadcaddcbbaacbdbdcdaababcacacbdbbbddaaddddcbcaaddbadbbbbbdbaccdddcaabbccdbdbdbaadcabbaaabcdabbbdccbdcdddcbbcdcdababcbdcbcbcdbabcbadbdabdbaccbddcacdacbbbddbcbccadbbcbddaabdcbdbcddbadcabdacbaabdbdbdabdabcaacbbdcbdacdadbbbacdbadabbdbbcaabbbddaaddbcabddadbbcdadbaaacabccddaadccbdcabdbabdabdbcaabbbadcaaddaddbdabddbdabcdbbbdaaacdbcdcaaabcbaabaccddbcacabbdbaddbdbaacaccadabdbcaacccbddcccbcdcbadbcaabbcdcbcdddddacddabccbbcbbacdbcadccdabdcccaccbddbcbbacdcdddbdbccadccccdaacacbcbcadaabbadacaddddccdcdbadcaabadccdaadadbcbdbabaaaadadbadcbcccdcdacacdcacbbdbbadaaddadddbbacdcadddaadaaddddcddccbabbbdabbbcbdcbbbdbdcadabbddccbbaaabccddccddbacddbdccbbbcdbdcaadaaddcdbbddcbadccbdddacaabcaabcabccabdbccdacbccdcddaccddaacbdbacccdabdacbaaccbbaacdabbadddadccaabbdcddbabdcacdbdbdbabcaaddbddbdcaddccddcbbacbdadaacdaadddabccbababdcdbaddcbbdcabddcadcbdadccdbccbacaddcdaabbcadadabccacbcaadcbdabcaadcaccbdcbcdccbbcdbdbccbbcbdccacdcccbdcbccabacbabcadabaabbbacbacbdcdaddcbcdbbcbabdadacddaccacdacccaaccdaccabdbbabaadcdbcaaddadbacccbadbbbcabbbcdccdbabcdbacbacccbababddbaccbdbaaddaabbdcdbcdbcdbbbacdbabbdadbcaabbbdabcbcacabcdabadbdadbdcddbbccdcacdbdcaadbbcaaacdcabbbdbddbbbadcaadbaddabdaabdcadabaadccddcdbbadcdddacdaddbdbbcdcacbbcdaacaacbcbdbbaadbddcccaaabbcaadaccbbacbdacaccacdaadbacaaadddcddabadbbaaadadcabdbcbdbdaccdccbcdabcadabdbaacdaddaaadabccbbbaccbacbcdadbabbaccbcddaadaccbacbbdabaadbbdbadabdcdaccadabcbbaadbbcabbcbbadababcbcbabccaacbabbbbcbcbbcdcdadbbadbdbbbbbbabddbcdbadadcdcaaddadbddbbdbddcacaccaddcbbddbbdbaddcacddbcdabcdaadbaadadcadaaaddabbdddccdadbdbdaaaaddcddacaadadcccdcadabbacbadaddacacacdacdcbddcbaacbbcaacdbbbbdbaacdcbadcacdbdaccdcbaabcadcccabcddabccbacbcabbddccdcdabbbcbabddacaaabcddaabbdbdadadbabacacddabcccabcadbaddbabdabbdbbadacddbbbdadbaccddbcaccbbaaaccccbddddabbadddbbadccdbccdccadcdacdddacddabdbdcccdccadbcbbaddbdddbbddbdddcaaaabbbbcbbaacdacdacaddcccbabbccbacbadbacadadbadbdcaadadadbbdabddbccbbbacacaaabaccbadadababcccaaaaadbadbadcbabcaabcdacacdcdbdcabccbcbdbdcbabacabadbaddadbbdadbbdbcdcccddadcaabcaabcadccccacabbccbdcacdcbcbbcdabccccbbcdcbcbcbdcdabacdbbbabbdbddbcabccbdbcccddadddcdcdcdcbccbdccbcabbbcddccbbbabaadbaaaaaadacaacbccdacdabaabcabaabccacbdcddccccdbdadaccaacdcdcdbbadccbbbccdabdbccbdbcdaddaacdacacacdbcbdbdbbbaabbbddddbbaabdabdacbcdcbdbdcbbccacbbaacdccdadcddbaacbbaabbccabbbdcabbaccbcabccbacbcadddcdabcaadbbbbcababccddbabdabdcbdaddcbddcadbdcbbdbdbcadaabcaabdcdbcccadbdcbacabdcdcbbbcdbcbbcbdbaadaaacbccadccabbbbabbaabccddbddcadbddadbcbbababaacdbaddaccbcbbcbddcbdcabadacbddadcdcacbadbdadcbcdbaadddcadbcabaaabccacaaccdbaddbbbbbdabccbccbdcdaaabdddcbccdccccabcadbcbdcbdcbabcbbcbcddaadbbaddbbbbccbdaacabcdbcdabaadcddcddadaccbacdbdcbcabddccdbacabadccabbccabbccbaabdadbadbaaaaabddcaddcddcddacbdddadddadcdaaddbdabadaabbaaccadcdaaaaaabdcdbbbadbaabcccbbdbcabaabcbabddbccddaaabbbadaccacddddbbdacbdccbabdacdaaaacddddcbbadaacdbbcadcdddddbacaadcabccdbabaaaacbaabbbbbacbcddccdcddaacbcbbbabaaacaadbcdbdaddabcbacdbabccbbacacdbabddadadabbdddaaacddbaaddadadbdbdbcccdbcacababacbdbcbdadbaadcbbdadccdcadbbdacdcbdbcbddaaababccababcaddbdbadabbadadbccabcaaccaccaacdcabbbdaaadbdadadcadabdbdadddddbddbdaddcbcaccadcacacadabaaccaadbaababcdcadbacddabbcdbbddacadaabdacbadddcdbdacdaadbdaabadccdbcbabaccdabdbccddcbbacacaadccbabbabbbcdaddcaddccbcccaabdbccdbadaabcbdcabcabdbbcdacdcdabadbadcbdbababcdacbbcdcadcdcabbcdddbbdcacdbcaaadcbdbacccacacbadaccabddaadacccacbbabdcdbabaabcbdaaaabbaccadcbdcbbbcbacdabbbcacbdbaabcdaabbacbcddcdaacabccddbadcaccdbddbdcabaccbbdabbadadabdabdbbabdadcbdacbcccadcdbdabacaadcddadaacccabacbcddabbacddbdabbadacbddbbacaddddcbddccbdcbcabbdadacbcabdabaabcacbdacdadddacababaccaadcaddaccadabcdcdbbbdbdcbbbbcbbdabdaabdddacdbcbddddcadcabbbcbcccadbbcaaacacccbadcabcadadaacabdbbcbbadacbcbabadbbcdbcccdcdcaaccadabaabaababdabdbacdddcadccddccdcbdbaabbddddbbbcddbbbccbcacbccbdcdacccdcbcccaccccbcccdbacacdcbcdaabbadddabddadbbcccccdaababdcacacbdbdbcccdbbcbacbcdabccdbbcdcabcacbbddaddadabbaccaadaacdbaadcbaccabacbcccccddabaadaadcbdbbcaadbdcbcbcdbadddbdcbcdabdacdccbcdbdcaacdcabcacabbaabbcbdddddddadbcddacccbbcbcbabaadacaccddacbabcacdaccdaccddbcdabaaacacddcacbabadbbddbbcdcdaddbbdbdddacdabadbbcdccbadadaccbcdbbabbbbdddbdbaddbbbaddabdddcbdbdbaddbbdaccdcbdcaadadbbdcddcbaaacbdddbbddcddaccbaacbcadccdbabbcccbccadccdcadadcacccccbdcbbdddadbbbccbaacadddbaccbdcccacbacacdadddbbbbdbacbcadbaadcbddbbdbccadbabbadacadbbbadbacdcdbaabbcccaaadbaaaaddbbccbbaabadcccbccdbbcdbbbcdabcaaaddcdabdbcdcbabcbbadbbcbbbacabaddaccbbacdddbabaadcaadacdcbccdcbdaadaddaabddcbdacbacadacbcccddbcacdbbbdaddbdabbaddcdccacaccddbcaaddcbcacabbbcaaaabdabdccacbbddadacdacbbababdcabcccacaadcbacbbaccddabdbcdcddbccbbabaacddbddadcdbdbbdccbbcbdcacbcaabaddaabcdbbdbdccbbabbdabdddaaabdabccbcbacacdcccacadadcbcbabcdaaddabcddadabdcbdddcacbdacbcacbababaaacdabdbcbcbdcaabdcaabbbddccaaabbaabacadbcacbbccacddadcbbcbbadaddcdadcaaccbcabbbcbabacbddddbbddcadbaabbccbbabdcacbcdbdabbdcdabbcaddddaccbbccbdddbcadaadbbccacddabdbcdcaaddddcbaadbabcbbbdcccabccabdcbcabaaccbdddadcdcaaaabdddbbcbdbbcabbcdacacaadabbbdddabbacbabbabcddadbcdbbabdcaacbcdadddcdbadbcdacbbaadddbcdbbbabcdbbcbaabbaccbaccacaacdadabaccccccdacddcabddbadcbcbcbdcbaabbbaacdbabbddbbdbbababcdaabaaaddbacdcabdbadbbdbaadcbdcbcbacdbacadbaacdbbaadadabccbcbabaddddcaacdbdcbdbcdddacdaddabdbdcadbbccbdcdbdccddcccdaddabccacaaaaddacdcabdcdcbbabbbdadaacddaccbccbbdabbabbcbcdbdbcadbdadccdaadbbdacacbadccabcaaacdacaaccbabdbbaadbcadbcaadcdbdcbbdbdbccbcbadadbbdabcdbdcdbccdacbdcdbcbbccdbdbacbabbdcdcaabcdcddadbdacbbcdccdaccdadddabaacbabddccaacaabcdaccaccacbdbabdcbabaccbdabcdaaadddcbdddccbdbcbaacddccadababaadadadacaacbdaadddbabacccbddaadbadcbbaaccdbbcbaddddbabaccdadcbcbbbbbaddcbdcccdccacddcbccbddcbcbadaddbbdddbaababbdacaddaaccbbcaacabbaadcbccdcdcadacdcbbcdabacbdbdcbbcbacbdbaccbaaabcadcdcdbdcdbbcbdbdbcadadbaaaabbcbcbdadcbdbaaddbddacdcbdbacdaadbcccccbaabbbccbbadabcaacdcaabddaabbdaadcdcdccdddbbcadccbabaaaaabdcdbbdbbabcbdcddaacddbcacabcdbadcdcbbabbcddbbccdacbcdacabdbdadbbdddbddabcbcddcadddaaadcbdbbcadbaabbcddcbbdcbbddcddcacccdaacacabaaabbaababadcbcdccdbbdabdaabdddacbbdcacbcababbdacaaccbdacbdaacadccddbcaaaccbabbabbddbababcbadddaddacaddacaacbdabbdddacdbcadacabbdcacaddaccbcdaabacbbdddcbdbccdbbddbaadcddbadabacbabddccadabccdbbbcccdcdaadcbcadcadbdccdcccddbacccabbcaadbabadabaccdabbddddadabaaaaabbaccbcccacdabcaabaacbddddbabbddbdbaddddbbcaaababdacbccbaacaddacdcabcbcdddaadadabaaccacbacbcbcbcbbdcccccacdaddbcacdaaaaabdcacbadaccbbaabadadaacbdbbabadbabbdbbccbbcbcacababaddbbbdcbbccbccddbcbbbcccbcdadbacbdbaaccaabdbabbbbbcbcccbdcbdabcdadbbbadcccccacadbcddadcdcbddcabbccddcdabbabcadadbaaabacbdcccbbacddcbcbbdbbdbccdbbddbbcbbdbcaacdbcdaadbddadccdaaabbbacdbdcbdccaddcdcbbcbcdcdabcbbbcaabdbadcbccaccdabdacabcdcdbcbabadbcccaccbdbcdadccbbdadaccaddabdddcbacbabccccbddbaaabdbddcdcbcaadacddbaddabbbcdadddaacbdaacdccaabdacbccbadacacbccccdddcbcddbcbbadabbbcbdcdcadbdcbdbadabdbccbbaddadabdacbacabadcdcddbcdacccbdcadbddccbccccdcdadcbccbdbcbccbdbcadccddbcbdbacdaadabbcaababaaabddcdbadaadbbcacbcbbbdadbdabacbcdbbbdadadbdacbabccbbbdbcbbccdbbcaabbaaaaddcabdaccaabacccdbaccadabddaacddabbcccbbdbabadadcdbddababddbdacbdccbacaddacbcbbddcacbadcbbdaacacdcdbdaadcacacddbdabacbcbbbddcbbdaaddbddabcbcdacbbdcddccdadbacccdcaddcbcccacacabccadcbcbbddbdbddaadcaddacdcbcbbbdaaccaacdaabdcaabbccbabbbaadcacdcaaddcbccadbcaabcbcbbadcbccaccdddcccdcdaccbccaabaabbbdbabbbddbddcbddbdbbacbbdaddcdcaabdabcdaacabcacaddcddbaccdbbacbacbbdbabdbccdcdadcbcccdddbaabcccbaaddccdbaaccbdacadbcbbbddbbbbdcaddabdabbabcbddabcdaabccbadcbdbaaaacccabcbcadaddaddaacaacbcccccaddccacbbddaadabcabddacbdbaddbacbadbcaacbadbcccdddcddabaaaabdaacdcdbabbbcddddccbbbcabccaccaddcadcbbbdccbadbccadcbbdabaddbacbddbbcbdbcddbdaacbabdcddcdbcaadcadbacccccdaabdacdabbadbcabcdbdccdccbddcdcacadbbbacacaadcadbacbcbbdcdcbddcdacdbadaddcddcbadccdbbabbcacdbbccdcdacaabdcdbdcdcdabaddbbcdbddaadcaaaccacaacdbcbabaaacbdcdcdbaaacccbcbbcbcdacaadbabccccdadbbdddcbddcdabdcdbdcadaacdbdccdcadbdcbccbbddcaddaacacdadbccdaabddcbaacbdbbcabccdbbbacbddbcccbbcccacddbcacdbcadadbbaddcbaaadcbbdbaddcbadbacdabbbabbdabbcdcaaadbbddbdaababaaacaccbacbbdabbaabddaabbbaabcdcabbaccdccbcbcadbadbdababadacbacaacdbbccbddbdbddacdcbcdccbdaddcdcdccaccadaaaaacabbdcacdaadcaabbaaccadcaddbdcdbddabbcdcadbcabadaadadaccbdbaaabccddcbdadbdcaddccddcaaaccdbacaacaccbccaabccddacddaacacabbabcaccdbbddbccadcbbcdbdacbbccddcbbaadbdaddbbbdaabccbccccaabcdcaadacbadbbddacdbacdabdbaaddabcbcaccaadaabbcbdddbcacdbbbdbabcdbbdccdaacdadcdddbbcdaadbddbdadcdbadbcbbbdbaccdabcbcdabbddacaaaccbbcdacaabdbddbddbcddaccadcbbaabbacdbcbdbbadadcaaacbbdbbcdabcaabacadacddaccaacdcacbbadddacbcdcbcdcaaddccaddacaacdabcdbcbaddbabbbdcabdddcdcdcccaccddccbdabcdbaaacbdcbccddaaabcddbadccdbbdaaaddbcaccdcbbbaccccbdcaabacaadcdccdccaacdaabadcdddaccbdccdddbbdbcabcbaacaaadbbdbdbacdcbdcbddcbbcaadaacabbcbbdccabcdbabbaddddccbcabcccadbdacacabcaccabcddabaacddddcdbdadcaccaccccccadcaabcaabaacbcbccdcacaccaacdbbbddcccdcabbcdbbcbacacccaacdbaccbbbdaadbaadcbcadbaacbbbbcbbbaccbbdddcbdddcbadaccbbbabdadccbabaaacaacbddabcbbdcaddabbdddabbaccdbbdaaacbadabbddcabccdccadabaabccdcbdbdbcabdbcaabdaccaabaaadcadbbcaaddababddcadbbacabadacccdaaacabbbcdbccbdbaadabcbaabbabbcabdcbddcaccbabddacddbcccdbbcaacaddababcddddddacdcaaaddcacbababdaadddcbbacbabbbdadcccadbbdcbdbadbcaacbdaabcbcabddaadaabbadbbbdbdcdbcddcbbaabcbaccbdcacabbaabdcddcbabbcacbddbdabcdbdcdbddcaaaacaddddaacbcaabdcbbcbccddbaaccdbbdbdccbbcdacdaadbacbcbdacdddabcabbcddacadaadcaacacbabcddccbbacbdbbcdbaaabccbbcbcbaabadccddaddccbddcbbabcbadaddabbbcacbcadbdccbaaabddbabbddabbddbbdadbadccadcadaddccdbbbcccabdaabbabccdbdbcbcdbabadbadcadadcdbcabbdccadbccaacbaacdacdcbdbbabbcbbddbbdcaabcadddaddbbdbccabadbbbdcdbccbbbbbcdccadbcddadbcbdcdcabbcadacdbdcbddbbaacccaadcccdcccaadcddadbcdddbacaaadaccdccddacbccaccaabacacbdcdaaabdcddabcbaaaddcbcdaacccacbabaddcdbcaddcdbadacbaabcaddddaaabbacdbbdcbabcbabddaadbdcbbdcacbbbdbdbdaabacbdcbaabadaabaddcacbcdcaabadadddbcddaaabcbcbcdccaadabcdcacbbacdaadcbdaccaccbddbacdacdcdcabbaaacbcadaabbbcdbdcddbdcaaacdabcaccddabdcddacbbccdaadacdddddbcccbbddcacdbcddcbcdbcaddbcadddaccbabccbddbabacdddabababdbaadaaccbdbcbaadbdbbadaaaabbdabdbbdaadbddbcaacaadbddbdbabddabbbbadaadccddbcbbcdbdbccbcabacddcdabbdabaaadbdddbbbbabbcbaabadbaaaddbbdbabcdabdcddddbcdabbdbacadcddcddbcdcbcbabdaddaddcbbabaddcbcbaababccabaacabcbdabaaadbabccabddbcbadcacadacbabadabbacbdbdabddaaacdddcdccbbadcdbacdabcabadbcdddcdcccddcbddadaccabcdccbcadadbdaadcacbbcddcdacbcbcaaccdcdabbdccbbcdbccbbcdddccdccdbbbadababbbabaadaadccbaabdbaacdcadaadbdabcdbabbcadbddaccbaddcbdaccdbcddbddacbcaadccdcccaaccbbcdcdbcbbbbbbccdbbddcbccccdbaabcabdabcdcdcadcddbbcaadbbababbabacbcbdddbbccadbcccbabcbadabcbcdbaadadddababadbdbaaadcbbdabdccaabcaaadbdcbbdbcdadccdaaaccaccbabbbdbabdcbcdbabbdaaccdaadabcbabbddddadbdcbccddbbbadaaadbcddadaaacddbbbabbaacadccabacbcdbbcbabbbbaabadcccdaacabbbbaccccbbbdabdcbabdbdcdcdababdbbddacadcdddadcbbccdabadccdcbcacdbadbddaabacdadabbbdadbcaacbbcaaccdbbbcdcddbaccbcdbdbbccbacabddadbdccdcdbbbbcaaccbddacbabbcaccaccbabbbcabcabdcddbbdccbcbdbcaaacbcbdcdcabdddcddbcdbcbbbabacaddccdbcacaccbcabcbddbcdaabcdcabcdcddbcbbcddbcdcbcbacccdaddccbacdcabdcaaadccadddbaacbbdcccbbadbbcaddbaacbddbccaabcaaaaaacbabdbbadddcbdacdaaabcbbdbbcdacabadbdccdacaacadadcaadbdaccccaadccadaccdcccabdadbdbcbdadbccbacbdbabdcdddbcaddbadddaabbddabaabcabdadbbcbbadbdbaddccdcdaaccccbbadaccbbbccadcdbdadabbaacdccacbadacaaabadddcabcbddaababbaccacbcdbcbacabcccccdabccbccacdacaabababaadabdbacddaddddadaaabbabdadcdababddcabdacddacbaadabaddabcdadcbccdcbaccadbdccadadcbcbdcaacabbccbbdabccbdabdaabdddbdbccaabdadcacbaacadbddabacdccdaadaabcacdcbadbadbabbbbbbdaacbdcccccbabadbabbcddbcddcbbadcdcdddaddabacaabaddabddadadbdacdccaabdaadaacdbbdadadaddcbadabdcdcdcccdababadbddcabbdbbacabddaccccadacdcbcbadbcdabcbdbadbadcdacccdcccdbcadadacaddddbbbbbdacdbddabaccbbaadcbcdddbccbacbaadbdbbadabcdcbdcbbcccbbcbabcdbacbdccdbcbaccaadacbbddcbdbaccdcabcbdadabcacaccdacbacdcaabdaddaabdcabdbcbddbdcbdbadbbddbcbdbabbbccddccabcbcccdaabbaccabcddadbbabcbadcdccccdbbaacdadcbcdadcbddaabaccaddadacdbcacccddcdadcacbbbaabbcaabbccbccbdcaacaabcdabcdccacbccdcdaaaabbdbdadcdabaccbcdbbacbbcbacdabadaadabdccddaabdaabccdbbdcddaaaccccacccdcadcddccbcbddcdacdbbdaddbbcaabdadcdaacadcacadbbcacbadadcaaaddcdccbadcaaadcbdccccadabbacdbdddbdccacacbdcacdccdbcdbdbdabbdccaabcdbdacccaaccdbcdcbaabdbaadbccababdcacbabddbbcabcccddccccddbcbcdccddbccaabddbbbbbcaabaddbdacacdbacdcddccbacddbddbcbddcbddccababbddbbbcbcaaccdddcaacabbddddacabadacbdabcaccccacdbadbadbdaacbdaddcccddbaaadccbcbadabdddddbbdbacbaaabbabdadaddbadbdcbccaaabcadbbdaabcdbbaacdddddccbaaabbbdbbdabccbbdbbbcadcaccbabbddbabcdcbbbcbdbcbcbaadaabcbacbbacddddcadccddbaccddbcabddcbbcdaaccbbdbdacabadaabbcdadbbccbaccdcacdbabdcbaddbbbcdddadbabdccbdabbaddbabcdbcccacaabcbdcabaaadcdcaacccbbcbccbccbacbcbbaacabaaacaadbacbbacdbdbadbdbdbadaacaacccdbddbcddaadbaaaacbbadaccccbadaaadccaddcbdcbdaadbbdddbddddbbccabccbabbaabdadddcaccbdcdbcabdbdadbcdbccaadccbdcdccdcdadadadabacccbcbcdccbdbacccbdcaaaaddcdadaacadabdddbacacccabdddcbbcccddacadccacbcdadcccdcdbabddbbbaadaaacbcbdccadabaadadbdcadbabdabdbbcabdccadcdbbbbdddbbbddcaddaccaabcbdddbdacaaabbacacbacadaaababcbddcabbdaaadadacbaddbdbccabdaaccabdbacccadaabdaacaaadcbdabacbccdcbbbcccaacdabcdcbbdadaaddccddccbaaabcdbbaacdbbaddbbbbcadddcdabcaddabbaabaacadccabbbabbddcdabbbccdabccbccadccabaadbaacabcccccdadccdcadddbcdabdacdbacdbdccdcaaaaaccaadddccccabaacabababcddbcbbcabdbdacaababdacaddbabdacdcbbaacbacaabcbbcacabcddbcbcaaadaaabccbbcacbccbaaadcbbbcaacabdabbccbdabdbdddaacbcccddbaadbddddabcbcdcbccdddcbcbdbcdacccabbabcbddaaaabbbdabdcdddcacbbddbbcbdbcaabbdbabbadabddaaccdaaddcbaadccccbabbabccdbdddaccaaadbacabccdcabcdbdbcdbdccccaccccccabcdaddbdbaccabbadadaababcbcccdaccddbacbacbcabadccbbdccaddadcbacbcbcacdcabaacaadbdabaccddabbbbcccbdddcbbaaccbccdabdacaaaabdbdaabcdcdbbdaacadbbcccdbaaadbccbddbddbdbadaabaabdbcaaacaadcddbdbdadacbacacbdcbcbbbbabdaccabdbadbccdcabdabbcdbaddcddcaabcaccadddabbdadddcadcccbdddcbacdaccbcaddabdaabcbccddcdcbabbadcdcacddcacdbbbbbdaabbddcdbccbbadcbbbacdbcdbaddbcccbcddaababacaddddbabacbbdbddddcbacdcabaadcbdabdcbcaccdbdbcadbccccccdacbadcacbddbcbaccbcbcdccdbdbacabbadaacddbcddcbdbcdbaabbdaadbaacbdcdcaaaddddbaddcdcbddcaabdbabcdddbcbdbadcbadbcaacbdcacdcbdcacdbbdcccacbcaccaaadcbddaddddaadadcaddabaaabcdcdaadabcabbdabbdacdaaadaacabdadbaadbddadbdbadbcbccacbacbababaadabdcbcbdbabdbcababbcbadacbbccdcbacbadcdadbbacacaccdcddccdddccddaddbbbcbcbadbddbabccaaadddddabddcdaadbccabdbadcacbcacadddcccaadbadcdcabbcacbdcdccccaacbadbbddcaddbdadbcabcccddddbbdbaccadddcdaabcdbbadbabdacbdadadaddaadbaadcacadbaddddcccbcdacdcbcdcadadcaaaddddcadadcaadbcdbbababcdadbdccddcacaaacccadbdacaadbdadacddadddbcddbbddbdddcccdabcbcdaabbbbaaacdcbbdddcbaacdabdadbbcddcbcdacbbddaaddaabcacbcbcaacacddbbaadbbccbbadcbaaaabddbbcccdbbdccdbdbacdabcacabdbbdbabbabbcabcdccdaddaaaccbcccabacbdcbbccdbbbccbcabbccdccaaacbabccacbddaababcdababcacbcaadacaaddadaccabadbcbadabaaaadbcdcdcbddccdbabaccabddddbdacddcacbdadadcddcdadacbbacacbccdacbbbcaddaaaddadcaadcbccabcdbddcbadddacbccdacbbdabbcaacadabaddaabdbacdcdcddcddcadcaababcbcbcadddabdcacbdcddcdbdbdcacacbaccdabaabdcdddadcccacdcdacdbcdcdbabbbdcdbbdaddcaaadbbbaaadbcaadcdcacbabbbbaabdacbcbcdddacbbaddadadddbddabbadacabbcccdbdacddbbbdababaddaddcaadabbbdcdddcadbbabcacadabacccabadccdaadcdaaabcdcddbdbdaccacbbbaccbcaacdabdccbcccaccbddadcdcadccdbcbddadbdbbddaacdacaddcbaaacacaabdabacaaddbcdadbcbddadccbacacdcbdaaaacccbcbdbbdddbbabcccabcaacdabccdcdaacbcddcdccbccadcdaabddddccdcdacdcadccbdbdadbabcababcbdbdbacadddcadddcbcccccababbddadadddcacddadabcdacbadabcbddaacbdcbadcacbabdbaddbdddbccdbbdcadcdbcacbdaaabbbddacbbdadbdbcbdbdbdaabcadddbaacddcdbbccacaccacaaccacdbcccaccadabacbccaaccdcacbcccbaccdacbcaabddddbdddcacadaddcdadadbaaddadacabacbacdddcadcabbdadcaaadaccbbccbbdcbdbadccbbddbbabddccadbccabaaaddaaddadaaacbdcaaddcdcbdcddccbcdcaadbbdcabcdbbbabaccabcbdbcaaabadbdcbacdcdadababdadcacadaacbdaabdcddcabbcadcadcbcccdddbaddcccbbaddcadcadbbcacbbdccdcacbacbbcccdabcadaadcbddadbbbcadbabdddcaadcbdbccaaaadaaacddcadddbdbcbdbccbccbcbbbddacacaacdbccdbcaadcdcdbdbddaaddddbcaaadbdcdaabaaabbbddbbddbdaacbacccbbbccccbabbabbbbacdcaddddadadbacbaabacddaadccbacabdcdcdbaadccadadcddcbddcdacdbbddaaabbdccaaacacbbbaabbbcccccbcacbbaabcbddbcaddcadcdaddbacabdbcaaccaacddcdbbaaadaddccdcbabcbdbddbaaadcddcdcabdcbccbaacdabcacaabcadccbcbaddbddccdccbaabacadcddadbdabbccbcbbdbcabdaddbcbbcbbabddbdbabaccccbcabcdcbabcdcacaabbabdcbaaabcdcdbdaabadcaabadddbdadbddcacaabccacaddccccbacbdacbbbbbccbbbdaccaadcbdcdbddcddccbcaabdabacbabcdcdacddbcccdddabdddcddbadcdbacdcbcbbcdaabcbbaadbcdcddbcbdbaabbdccbbdacccdadaadbbdbadbddcccdbbcdaccccadbabadcabbdbbacddccdbdbddcbbcbdcbaabbdbccddadbadbbbbaddaaccaaacaabcdbabbdcadbdabcabcbcbbcdacbbaadbcbbdccbdbbabdccadabccadbbaadaabbcaacacacdcbabbcdcddaabaacadcbbdcbbdcabdcccdddddbaddddabadabbcbdadddcbaadbdcbddcdaaccddcccdccdccbaadcbcdddccdbacaabbdddacddcdbcbabbaacabcadddbcdbcbdcbcdcdcbcdcdcdabcccadabdbcbbcacbacaaaabcdadccacacbacbdbaabbcdccdabaabcacaabbdbbacbaaabaabdccbaaddaddaabbcabdbbcbcbbccbbdbdaadddaacccddccdcbdbbddcabadcbddbdccdddadaaaccadcbcbcddddabadcbbbdabaabadcccaaabdbdaaabaddabddbdcbabdbabababcbcdaaccddabdbcdcbddbaaddbbdbdaababacbddcacabdaadcbddbbdcdbcdcdaccaacdcacbdcbcaaacacbaaabdbddadaacabbdbbacdabacacdaaadaaccbcacadbddadcabbcdbadbaaabaaadddcddadbbcdbcdaadcabbcbaabadaccdbaaaadcadbcddbcbdbaababbbdaddcdcbcaadccabcabccdbacccddbbddcbcbaddcadcaccdcacccbdddadbdbbabbbbbcbbbcadbddbdbdadabdadcdaababdccbaacbdacaacaaabbdadddccbddadbcaabaaacbacaacdccbccddccddcadddcacbdddaccbbbadbbdccbcbdacdabbcbdbdbdababbdbccddadcdcadadbcdacddacbdcbcddbbbbcdccbabcadbbbbbdbbbdbccabbdbadadadcabbadcdcbacccccacbcbcddcddbcaacbbbccacbdabdbdaacacdcadbcbaaccadcbabddaddaabdacddabdbadacbbbaaaacbcccddccbdbdabadddddbccacadcdabcaaaadccccabacaabbabcbdcacacbcaccdcaabaaaacdadacdcdddaabacdaacacbbbbbbcdcbaadccacddbcdddadbabaccaadbbbbaaacbdbbbbcadbbbbcbaaaaadcbbdcddbcaaaaadccacccbbcdbbbbbdcbdddbcacbcabbdabbacabaadbbaddababbdddabaabcdbcddbcbabbabdabdaacdddaaabadddbbacddcadbcdcbbcccdbcccbcbdbccbccccaddaabdabddadccabdbadcbaaabdabcbdbacbcdcacaadaddadcacacccdbacdacaddcdbcbaccabcddbddabccadcdbaddaacadddbcbbabcababdabccdaacddcbcdbacddbcbdcaaaadbdadccadbabbcdbaddccdabbbcddbdbbcacbbddcadbcdcadbdbacbccbdbdbaaaabbabccaadbcbcdcadaaacdabbbbaacdcacccbacddbabadacbccccababcdcadabbbaacbcdbbdbdacbbacabababcbadcbabddbacdcbacccaaadddddcdaaadddbbaaacdacbdcbbadcdccdcadbaaaadcbdcbbcdaabdccdcdabbadabbcccacacbdbdbdbbabddbcdbdcbbcbbcdcaadabcaccdbccccdbabbcaccaaaaccdadcdbacabcbbabadbdbcbdbccbbabadcaddacbcdadbbadddabdbccdadcbcbccdbccbacdcbabcdacbbbaabbdaddabdcacdddadbbddaddccaddaabbbabcbdbbaacabacbcdbdccdaaddacbbbbbaddacbcacabdbdadcccdbabadbcbdaadcdccbccbbacccbdabddbcdaaaccacddbbcbbbccbcadaacbcababbbbbbdcbbbbdadbdaacccadabdcbdcaccdacdbbacdadbddcbbabddbddbaaccbadcccdacaadabdabbbdadbbabacabdcaabddcaadcbdbacabddababaadadadcdacbcdcdaabbaacaadaaaddbddcbcabbbbcbaabcccddbdbdbcbcdabbbddcbaddbabbbcbdcbdccaadaddbccdbdbbabadbbdcaccaababacdbbbbabadbbaaabccacabcdcddaabbabcdddcdcabdddababdcbbabcdcccdbbabbcbaadacbbbdcbddbbdacaacdbdababdcbbabddbbcccbcddabcbddbdaddbcdaabbaaaccccbacdddabdbcbbbdbdddbdbbaddbbbacadcdcdabbdadbcdddacbacdbaadbbcbbcaaccabbbbdbddbcadacbadddcadcbdacbdabcdddcadbbbdacbacbccbadbadcbbbacbdcccccadabcddabdcdbadcccabaabcccadccdcbbbdbbddbbaadddbcaadccbcdaacabbbabbcbabbbbabcddbadccbcaddcabcdcbabccdbcacacbcaabbdadaddbddbccaabdcaabcbbacbcabbbbacdccacacdbddbcdccaddccbddbccdaaaaabcbccdaaaccddbbaacdccdaaaabbbdcdaaccdcddbadbacbdcacdaadbddbdaaddddaabaddadaddaaaadaabacbacdcdadbdbbddbcaccaddcacabdaadacbdddadcbcbaddbccccaaabbacddcbdaaccdabbccdbcbabaccabcbaddbdbdbbddcababddbcbbdbbcdadbacdccbcbcdacdccbdaddbcbdcbccbcbabdcbcadddaabacacdcdccbaacaaddadcdbcddcdbadbabcabacdbdddbdbdbcacdbaaadbcbdcdcabcddacadbddabadcdddabcdbdbbbaaaabbdbcaabaadababdacddabdccacdcdbbdbdccddccdbbadccbdadacabddbdbbccbbacccdacddadccabdadacabaaacaaccbbcbacdddacaddbcbabdbbaddaccbcdbacaddadcdcacabdbadabaadabadbabbcadbddbdcdcbdccabbbbbabdddbabdcddcbdbdbcbbbdadaaccaaccdaacbdcaacdccdcdcdadcdabbdbabdbadaddabaacdadbaadadadcadcacadadbbaccaddabcddababbdddcbccdabcbadcddddcadcabbdabacdccccacdbbbcaddbbadddacaaadabcabadccccbdabbabbdccadcbaacbbdbaacabdbddddbcddacaccdabbcdcdbcbcddaaacdcdacacabcccddbcaadabccbdacdcdbbabbdbbbcbbcaabddabcabdcdbddccdcaaaadbcdbcbdaccccadcaabdcabdabcabbccdacdcbbaabdacdbbcaadbbadbaaabbcbabbbabbddbbcbcabccddbcbcaacacdcddbacdcbcaababdbdaccbcdacbbaaadcdddbddbccaddcdaabdcacddadadcbcdaccdbddbadcddcdcbcbcdddbcadcbacbbdbcbaaddbbbcacbbbddadcddcddddccacbbabcacdadcbcdacabadacacaadcaabcabdabacbaadabcacdaaddddccbdddabadbdcbacdbbabacbaabddbdddcccaacdcbbdbcbcccbddbcaacaadbadbbbacaabbdcabacdaabdbadadbddabaccdbadadbbbcdbadcaaaabdacadcdbbaddcdbcaabcabbdcaccaddbacadaaccdcaabbddacccdbbabccdcadcabbaacdadabdbdbbaddabbcadcdabadcdadbccbaccbcdcdbbbabccccadabdddcbbbcbcdbdadddbadbdcdbcbacdaaabbaccccacabdadccbacbdbacaacbdbaadcabbbbbacabacdcbbadadcbdababcbccababccdcabcabcddbbaadacdcbbacdcdddcacdbdccadcdbccdcdcaaabaacaaccdacacdcddacabcbdcadbddddacdaccaaabdadacbbdaabacbcababbcddbabcacacbcbddbacdcadaabdddddacaaaccaadbcddbadcaacacdbdcabdcdbcdbbccabacbddaacbbddbbaadbcbabbadbdcaabaabbdbbbcbcbbbabcbcdbcadcbcddbcccbcaacddbcbcbdccdabcbcacccbabcacbcccbcccaddccccbbaabdcdbaadbacbbdaaaccbcdaaddbbcdcabbcdbcdcadaccabbdbccdcddbdcdabdbdcabcddacbaaacdcabdaddbdddacbadbdbaadcbabaadcbbccbaabccacababdadadcdbdcddccbcabdaddbdaccacaaccbbbacabcbdbddbdbacbaccdbbaccbabadadaaccdaaabcddacdddccbacdbbcccdccacacabdbbaabdccadbbbcdbacbcbbbdbddcbdabacadcdcdcdbbbdcbadbcadabbbabaadbdbacbdccaabdbbcabcbdacdcbabcddbbccdccdbadabbbbacbcdbdbadbccabbdcbabcbaaccbdbbdcaaaddbdbadcbacacdcbdcbcabdcbbacccdbcdcadaadaacccbabcbbaddcbddbacccdbccbdcadbddaddbacabddbacccccdcababddaaacbbbbbbbbdccdbdbccdbaddaccabadcbcabdacabcdccdacccacadbacbaddbacbbddcdbaddcbbbccbdcadbcccaccdbbbaacdadaddcbccaacbbadcdbaddaadddadcbacadbdbbcbaadcbaabaddddadccbbbbbccbadabbbbdbcdaacdbaaaccdbbbccbdddbbbaaaaacbbdaaddbcacbcadbdaaaadccbabbdbacacacbcdcdaaadcdbdbbcaadaacdbabcaadadccbaacdcadabbcddacaccadacddaabdadcdbdaadbdccddbcbabdbbacdadcbcaabdddbacbadcdcbaccdadaacbdadaadcbadddcbabccababdbcdbdabbaddccadccaaababbbdacbcccbbdbccabbcaadccdabdcccdcbbcbcbaaababdbcdddcadcbbbcbabcdaddbacbdcabadbaacbdcabcaaccdcbdacbdcabacadddacbbbcabdadccdaabcdabdddddbabddbacbacabccdabbccacaaacccadbdcacdcbbababacacdabaadbbabdaabbbdacbbcbddddaadbdcbcddbcbbdcdaccadbdbabbacbacaccbbabacacacdaaaacaadadaadddbdcbaacacabbcccadbddbddddaacbdccaccbcbbdcbccabdacdabbacaadbacacdbdbddddcccbabadadccaddbbacccbaccbddbadabbccddcaacbcdcbdabadbacadcabacabbaaddbbcdabaddccdcbaaabdbdbcdabcbacccaaabdbccaadbbcbbabdcbdccadccbcdcccbacbdaaadabacaabaddddadabbdcadcdddadbcdbbddcabadddbccbacdaabdcaaacdbbdcbbcabcdbadcdabbdccdbcccccbddbbacccccbabbcdddcaaadabbddbbaacddcdaccdcbcdcbbbccdaabaddcaacbaabbaaabbbbadcbccbadaaddbbdadbdddadbddcbacdcdabacbcdbcaababaaaaadbccabdcbcccdbddaddbabdccacbaddabdabadbbddcccccdaadabdadadcbaabcdbaadcdbcdaccddbbaaabaaacdccbaacdabdabbadadddadadccbbddddacabcabbbdcbaacccdaacacbacbabcabdcccabddabcbccadadbdaabdacbbacccadbbdabaaadabdbbaabdacbdddcdaaaaacdadbbcadbdcdddaccbdbbddadaddcaddbbacbddbacdcbbbbcababcbdddbdbbaddcbddadcddbabdcacacdabbcccabdabbdcacdaacbbacadddaddbaccddadaccdabdddccdbcaadcdccdbbcacabcbddacadddcdcbcbaddaccbacbbacdcccbdabcbcbdbbcbccadbddccabcddcaabdabbdddbbcbacbcadbddbdaccbadaacaadacbabbbcddcacbbdcdcdddcaccbbadadaabcddbccdcbdbabddabdabbdaddbdbabaaacbdcccaaddccddbbddcbbcddacaaacdcdbaccbdbadccccdadccbddbaccaabbdadacaacaacbcdacbddaaaccacadbcbbddaabbaccccccccdbcdcccbaddbcacbcabccdbbbddbdddbcadacbdcbdcdccdcadbddcdccddbdbcbccaddbdcdcccbacadcbdabdaacbdcdadcabacabdcadcdaacaacdbcdbcbbcbddbccadabdbddcacbcadbcdbcddbbbcaaabbabdadabbbadcbcaacdacadbaddcddaccdabdcddcbacdcccadbcbcbdaaddadcccbdaacacbbbabbabacdbdaacaadbddaccbcadbadccadcbdcdcbdddddccbbddcbdadaccdbaaddbcbabdabdbdcabacbacacdcacadadcbdcadcbcdacddbdbdbdddccaccabdcddbdcdbddcdccaaddaddcacdbacaadcbcbcccdacacdaddbabbdddadabcaccadccdadbddcdcbaaaddaccaddbdcbcccababaaaacbbbccccdbbbccddcccabcacaaabaddddaccbdaabacadbccbacdbddddacbccbadcababaadbddcacddcabbbcbcaaabcacacbadbcaabcbcdbacadcdbdddaadcadddcdbaacdbdaaddcbdcaadbcccdccbccaababcbbdbcdbadaaaddccbddabbcaddccccaccacdadacddcdacaddccbdddbbbaabbdacccdcdabbbcddddddbccadbbcacadbbdadcdabcbaccbacbddbddddabbbcdcbabddabaadadcbcaadcaacbbbbbdbdbbadccaddaabdcddbbcbdcabbbaacbdcbccbbacabbcaaacbccddbcbdabcadbabacacbcccdcbcabdbacddccbbdacddbcaacbdbabcbabaddbcaadcacbcbcbbaadadbdbbaddccbaddbccadcbcdcdbaacddcdddaacbadbabadbdcdddaddbabbadbccaddadbabdbcdcabcabcddcbccbaccbcccacadddbadccbbccbdddadaccdccccaaabbbadadabddadbaadaacabcbacaadacababbadbaaaacacdaccabbaacabcdadbacabcdbabdddabdbbdabbdcbaadbbbcdcdcdbbaabcdbdaddcbbbdbdacdbddabcacabdacdabbdbccbcdbbadbbacadbaccbabcbaccdabbabcccdbbaaabddadcdababcddaabdbbbcddaaabdbacbabbbdaaaacabbacbcadcbdbcbdadddaacbdaabddbbacadaccccbddaccdbaccddbcbcbcbbbbcadbddbacdadaddabdadcbbabcaabadbcdabadcacbaaddcbcadabadbaabdbbbccbcadccdcdbddbcaddbcdacddcddaacdaacaccccdcaaaaccacbbabaccbabdcccddbcddaccccbaabdadaabbbccabababddbbcbbbabbcbbcaccbbabbabacbdbccdcdcccccaacbbdadacdbabababdaaaaccadddabcddabbcbbbcacbbddbaadddaabcaabcbcdcdaacbcbbcacdbcaaacbccaaacaccabbdbcaadcbbbcaaddcaccaacbdaabdaabbaccadcccbcbaccbbbcacdbacbadadaccacdbbddbabddbadddcbbbbbabccddadacbaaabdababcabbdddbdbaccbbacabbdabcdddabdaaacdbadddbbbccdbcccabbaabadcdcdcabbbabccddddbdbdbacbdcddcbddadaacccaddbcbccacaaadbbdddcaadddbacbddddbbadcbbacbaddcadcabbcdbaadbaacccaaabddadacdaacdadacdabdcbddcdacabdacbcbccdbdabdaaacabacdcbdcbdabcbccdcaaccaaadabcccdcdcadaacadacadccdcbbbcbaadabdabcbaccacdbaddaccddaccdcbbcabdabdccddbdbccaacbcddcbaabdcaacabccbaabdcdaccdaddcbbdcdacabbbaaaacdcdbccacbcaaabbdaaacdaddaaabbddbddacaddaccccaabcbabbbccbdbcdccbdbdddcdadccdaabcbdaccbcdcdddddbbdbabdbcbcdcdbdcacdddbadbdabaabacdbabdcaccbcdabccdbcbaaaacdbacdcaaaaacccaaccadcdacbddbdcdabccabdaacbaadaccbaddccdbddcbbcacabdbdcbaadadabcbbadacaacbbdcadaccdbbcbadabbcdbcaacadabddaabdcadcbccaacbbdcbacbcaacbddacaadbacbcdcccbadbbcbadaadbacbbcabcbdccbaadcbdacdadbccacbcbbdbcbabdcbabcdabaaacaaccadcbcdddddcaccaaaddaacdbbdbbdcdaddbabcdcccaddbbbbaddabcddaabcacbdbabbcaabaddbdaaddadbdcbbabbcadccdddacddbadbcadabbdccccdaabcbcbabadbdaddacacacdbbadacdcddaabbbdbcbdbbadcbaabcbcadabdaacdddadaaaadcbbccbccbbabddbabccabcadcabbccdbbdbdadcdcbbcdcaacbabcaabcdccaaccaddabdbbabbbabccccbdaacbcddccbbbcbdaaaabbdccadcddcaaadabacacadbdcbbcabdbcabbcdbabdaaccacddaddacccbbbcbbdadbdbadacdddccbcbbbcabbbccbbcbccccdbcccacdaadaccadbdaadccaacdcdadbadbcdbbbbcaaaddccabbbbcbbbbcddbcbcbabcadbcdabbbdbdbcaaddcaabaacccccaabababcbaabbdbcddbadaddccbdaccbcabddcacaccbdadbddbbbabdbdcdcbddadbcddddcacdacdbabdbdcabbccbacddbbcbabdacbcddaabbdcdddbbcdbaabcbaddcccabcaccddcbbbbcaadaadaacbdadabdabbdadadcddacdaddcccacdcdcdbacabaadacdadabcbddaddcdbdbcbdabddcbbdcacaadbddadcbbbdbcdbdddcccacdaacbdcbcccbccaadaaccbcbaccdddbcddcccdacaababbcbbdcacaadcbbadbbdbccadbabacadcbbabbbbcadddddddbbacadadbcdbbaabccbddacaccdbabdbbdbdbcaadaaacccababbaccabbbdabddbbbcacacbddccdcbbaadddbadbbbbaddacadacdbbaaddcbbacabbcdcdbacadddbddddddadbddacadcadbcaccacdaadbbacdbcccdbbddbaaddadbbbcbadbcbbdabcbabcbbabacbcbaaddbdbaddbdbbcacdbccdcabcdacbdcdbcccbbdcddcadcbabcdbccabaaaacdacddababadbcdabbcbdaababcdcacabbabbabbcccadbccbddacbdbabacbbadbdaccdccaacccddbbdabcbcaccbcdbadbdbddbddccccddaaccacbadcdcdaadbccbddabbbcabdbdadaaddbcdacabcccaccbdabaacccdbcdbbbbddbdcabbdacaacdcacbdabcbcbdaabbaacdddbbcadcbabbdbabdadbdbdabcabadbbbbbadbbcbddbbcbadcbcbdaabcdbadbcabdccdbabddbbccacdacbdaaddbcaacbcbbaabcdcbaacddbabbbdabbadbbccbbccddbabadccdcdabcaddbbbcdcabbbbbdcdbdaddabcdbbbbabdabcdacbdbadabdccdbcccdcacddbabacabbbaaadacdcddacdcdaaaddcbbabadcaacbaadbbbadadbdbdbcaaabdbccbacababaabdcddbdcdcbaacdbccbacaacbbdcbabdbbcaaadcccaadcbaababcddaadddadbabdbcabdcbdcdbadabadaadcbdbbabcdcdaacdaddacaddcdabdcabcddacbabaccbbbdabbcbcacddbbaddbbbddbadbacbbbccbadddbdaaacddadddbcabdddbdbbdcbacddbdcbdbbcdaadbaabacbadddcddcbccbbcccbdbcddbcabbacbadcddbcdacaccdacbbaadcddbccccadbacddadcccccddacadabbacbccccdbadcbadbddccaddacaabccdbbcdccddccbbdbbaaadabcacaccbdbacbdcbdddddcdcbaccbcbcaacadcbbadcdadbcbcbdbddddcdcabcccadabbbcbdaabbdcbcaaddcdbdcdcacdadadaabdbccddcdbadcdadbbaaccaccbbcdaaccadcddadcbababcbaaddccbdabdcbdacbcdcbdddabddaadacbbdbddcdcbdabcbcbcbbbdaaadbbdcaababbdbcbbbcccbccbbaccacbccbccabddcbdbabdcdddcdcadaaacaccdbaccabbcdacbddcbddcddaadbdddbadbbddadcabacbaccbdbaadcdbccdbadcdbdaadddcaacdabaadadcdbaacabccdadbbbdaadadcbabbbbbddcbddbccccbbcaabdacbababdcacaacdacbaaddccaacdcdcdbacccdddcdaaadabbadadaddbdbdaaacdcdbdcdcdaddaccdaacdccdacbadbacadbbdcdcadacadbbbaaccaaacdbcccddddcdcabbbdbcaacbbaddacababbaccbbcbbbaabbcbbabbbccccbcdbbddccaadaaabdbabdbdcbdabbccdcdacabbabbaabdddcbdccdcabcbcdddbdddddacdacccaaccdacdababddbdcccdbbdbbabbbbccbcccbcbdbbcabcbabddbdcaaddbdbcadbcadddbdbdcdcccbadbbaccbbcdcbccdadcdccdcbddcdbcdcbcccdcabbbaabcabcdbacaddddddabacaaacdaaadaccdbbbbcaaddbbacccddccdabcadbacddacddcadcdaccaddddacdacbabacbbdaaabacccacbcddbbcccdaccbdddbbbbddcddcbaabcbbbcacbbddbacbacadadcaabdddddddbcdacbcccaacbabcbbbaaabaccaccadbadcbdbdbbcccaaccbbadaadaccadbcdadbaadadacbcbbbdccdbdbbaadbabacccacabcadbbbbdcbabbdbbbdadabbcdbaaddcaadccdbcdacbbcaabcdcbccaadcddbbdaaadbcccddccbbcabacbcdaacbdbdcbadddabacdaddcccbacdbdcdbdbdacddbbdcaacddacbdaadacddbbcaacdcdaabbdcdadaaacbcbaaaadabbbaabcbaddacbbbcdaaaadabacbdddccdccbddcdcbdddbbcadbccbacbcdccddbaccccddaccabcababbcbbbbaadadcccaabbcdbdabdddabcdddcadbbbbbdbabcbbbcbaabdcdbdccacccdcdbadacdbdbaccaabbdbbdbadcdddaadaaddabdadadcdbbcadacbbdcdbadbccdaabacbcbaaadbdacdacbcdaabdbbacdbdacdabdbbbcadccddcabcccbbdabcbcbabbcadcbacccaccddbadabbaccacdbacbcddbbdaacbabacddaaadbcdacacbbcbbadcadcccdcbadbdacbacabdcbcdbbdabbcdacdaddcaaadcacabdbccdabdbcbbbdbbbacabbcbdabcdabcbbdaadaadcdddbdbddacaaadbacdbddbbdaacbdcbcccaddbbcccaddccbaaacbaaacaaddcacabdbabadbdacbacabdbdcccbcbcbaabcabcabcdacdccbcbabcabbdccccaaabddacbdccdbbbddbcccbbdbbababcbbbdbbdcbcadaadabbcadccbbbcccacdcdbacacccdbdbcdbbcccdabdaccbdadabddcbadddcdbdbadbbccbdbddadcdaadccaacaddcabdaabbbbcabdbdcbccbacdddbabadbbbababdbcdaacbaddbccaadbdbaccbacbdacacddccdcbaaabdbcbccdbcddcdccdabaacbcdaddddbbdcdacdcbdcddbcccddbddccbaacbccdbbdaccabacaadbccacdcddbbdccbcdbcaacddadcddacbbacabbbabadcbaabcadbddcacacdbcadbccacabcbcbabcbabcbdaddbcaddddacbddbcacbbbbadbdddbaaccacbccadacacadbddddaadcccacdbbabadacbaccdcbdccddbdddcddcbdbbcdcaaaadacdcdcdccccccdbbaacbcaadbddadadabadabbbcaacddbccabbbddcccbcbbddbbdacdcbcccdbcccdbcaabcacccadcacbccacbcbbdcbdbbbdacacacbcccacdbacbcaaadddddadacbbcadabaabdaccbacbcabdccadadcbadbbdccddbaddcccabadbdbdacbcaabaaaaadadacacaddcdccbabcccccdddbacdaaaacbdccddcbcdabbcbddaccaadbcdccbbabdcacadbccdcdcdcaddbdccbcbddaddbcacbcdcdcadabacadbbcaaabcbaabcdbacbbbdbadbdbaacacdddbbaaaaacdddabaddbcdbbccdbbadacadbcdcdbbcacbcdbcbcdabacbcdcdbaadacacdadbddcadbabbbbdcdcddddbcaadaadddbcadbaacbaacbacbaddbaacaabbdbdbdbdbccabaabddbbbdbadcadadcdcddbbbddbcacabdccdcddcacacdddaadaaabadabadaacbbaadccaaaddadbaacaaccadbdcbcabbbcdbbbacbddddcbbaccddabcbdabcbabdaaadccdbbdbbbccbbdadbddabacccaaacbbcadbaddadaddaaadaabcdbaddcadaddbbddccdacddbccdacbdbdcddcaaabadccaaaacdbabacacdbbbadbabbdacbbdbadcacccbbdbbdbdbcddccaccbbaddddcbbccbccdadcdaabbccdcacbcbdcabaabdccaaabdcabaaaccccaddbddddcbccaabbacbdcbcbdcdaabdbaacbdccdbcabcbcbabddadccbdadbccccaccdcdddbdaacbbcdbddcbcbbccbabacddadadcddbbbaadaaaaccdddddccaabcaccaadabadacddacbbdcacaababbcbdadcdbcbddacbcddaaaadadbdadabdbdbcbabdacdccacadabcababcdbadbbddccdaaddadccacaadddacbcaddbcbdbddbcbaaccdcbacccdbcaccbacabaabdabccddcaacabdabcdbcbaacaaccdcaadcdcbaaaadaccbdabbcdbaccdddcaddbbccbbddadcdbcdaddcbdabacdbcbbddaccabdbbbddcdcadbadcadccbbbabddcacdababdaadcddabbbabbbaccdcadcbabbaadcbccacacddabacdbdbdddcdbcabaadcdccbadacccdcddccddaaaabbdcdbbdbaaacabcacacdabdddcaabaabbbcadbddacddcbadadddcacbccabcbddddbacacadadddcbaccdababbbbccaaaacbbbcababaacdaddbddccbccbcacdbcbdaacdcbbcdcbcdabdacdcbdaabbdcaaababadaaccbdabaddacaadbbddccdcddbddbbbcccdabbacccaddbbcabdbcbdacdabacdcadadbcbdabdacddcabdadaadaaddabcacbdcdaadccacbdbbabcdbadbcdcbccdbadcbddcacbccbbdddbbbdcdcbcdcddccabdbdbdcbabbdbcdddccdcadbabaadcbdcbbabcbcddacddcbdbdbadbcdadacadabbbcaddbdbaccbdbdbcaddddbabcdacddcbdababacbdcaaadbbdcdddbbbcdbdadbbbcbaadabdbaaacaccbabbbadaaabaddbcabdbddccbddaadbccdaccadabcaabcdddbcddadabdcaacbcbaddcaadbbbacacadcdacccccbdccdadabdddcbcbbbacdbdbcdcddbbcdcbcbaaaccaabcdadbbcadbbdcadbadaaadcccdbabcdcddcaaabddccbccbadabdaabdaacaaccbadcccbcdabdccbcbacbdacdabccdccbbdbbdacadbbaaddcdbaadcbacddbbcabcdaaaacacdbbcdbacbacdcabaadaacdadbabcacbcbcbadbadabcabdddbbccbadcdbbddddccddacaabdbdbbcaadcbadcdddaadaaabdacdcacbbabadcdadcacbccdadcdaadabbbdbbbcddadabdddabdcdcbbccdadacccaddaccadbdcbbdcadcbbdccbadccdbcdababbdcbbbcdcabdabbbcccdadaaadadcddbccddcddadbacdaabbbdbbbddddcaadbcbdbccabdbbdcdbabcadaccaccbcdadcbbdddbcddcaaacdbbdddacaddbacdcdbddcaacbbaadabbcbabaacdcbabcadcdbdcaccbcacdddcdbdcaacaddcddbbbcbdcdabdccdbbabcabbbcdcdadacdbbbcbdbcaababdbcdacbbdcdbddcbbcacadaddababadadacbacbaadadcabccdababaacaaadbabddccacbdacababbdabaacbbcdcdcbdccaaddcaacadbbdddddcaabacddbadccbbacbabacacacadbbacabcccccbbaccdabdadddaaaddbcadcbcbcacabbacdaaaabaadbdcddbbcadaacbcdcabccbdbbdbbabdcbdacacbccbacbaaaaccbbaaccbccdbadadadddabcddbcdddbaadcbcccababdacaabbabaaddbccacbdcdacaadbcaccbcbabcbbaaabbddbaabbcbbaabcddaadbbddabbcaabaabbacacadcaadddabacbbcdcbddcababaadacdacdabbaacccabbcaaddbcaddbbadadadcbbdddccadbadbccacdddcbacacabacbcdcbddadabcbdbcddcbcbbcbcbacabdccacbcbbcbacdabdaadbabdaaababbdbccccbacaabadbadbaadacccccdcdccdaddacbbccccddacabbcdacccbcdcbbcaacbabddadaccddcddcbccaccadcdcdabbbdbdcbaaacadcddbbcddbdcabbcdccbccaaacabbcdcaccdbabacbbcbbdaaaccdccddbcdbdcbdbdccbaaaaadaccaadccadbbccccbddcacbababcabccaacdddddabcababdbbbabcdabcadacbbccdcadbadbbcabaccaabaccadabacacbdcddcbaaabaccdcbcbdabaddaaccbdbdcadcaddbddcaadacdddcbbbddcadbdcbbbddaccadacdbcddbabbbddbcbaacdacbcaccdcbbbabdadabcbabaddaaccdbcaadbdccaacabbacbacaaddcdbacbcbddaaccabcdbcbbddddaacdbbbcdacdabdadcccdadcdaddbddabccabcdbdcbdcddacbcdcdbcdddbdbcaccabaadbdbadcabccbbdccadaaabaacdcddcddcbdbbadcaaacadccccccccdddcacbbbbdacbacbcccbdaaaacacbddddbababcdabadacbbdbdddcadadbddcddaddcaddbbabbcbaabbcaadaadbbbdcbabbdbcacdcabdabcbbacdabccbadaddddaacdddbddbbaabddcabdadcddbaacadbbdcbdcbcdcacadacdacddbabbcdaadbabdcdbdaadabadcbababcddbbacaccabacacbbccbaadcaccbcdadbdcdcdcbadbaaacacbbdbaaaabbdddaababadcbbcbaaacbbccadcddbdcbbddcabacdcccbcccccdcdbddcabadacaabccaccacdadbbaddbcdcdccaaabccdacbdcdccabbdaadcacaddccacbccabaacbadacababccacacbabdacdddcacbdadaccdccdbabbddacccdcaacdcdadcbabdcaabcbcdddadccddbdbbdaabcccdabdcbacacdcdbaacaccdcaacdaaabbcadbbcaaacdcdaacaddacbbddccabacdaaaacccdadcdbcdadaccbcbddcbabdcbddbadccdbdabcaccadaccdbddbbbcaabbacdcbbaadbcdadcaaadadbbacdaddaaadbcdaaacaaccacabdacccdbcaddbcddbbdcabaaddcadccacadbbbdbbdaaacdcaabbbbddaddcdbbdbcbcddcabcbabbcaabdbbbbcacbbcbcabbcbadadcdcaccdadddcbbaadcbcadbdabaddbaaaccacbcbdaabbbaaddaaddcdbbcaccdcdddddbbcdacdcdcddbdcbdaabdbcdbdcbddcdcbcdaccaaaabadcddddcccddbbbbddababcaaaadaccaaabbcdcabdcadaddaaacadbabbccaccaadbbadbcadcbdbaccdbddbabddabddcdddbcbbabcdaabacdacbdbadaadaccacabddabacdcccbabddabbabdaabcbaabbaaaaddddbabcadcadbcdddcdcacdbdccdbadacaacccbbabbaabddbbcdabaadacccaccabdcdabcbcabdbacdbdbbbddddcacacdcdcdaddcbcdaaabddbdbdcacbcdbcadbcbbcbcdcbcbbbaabbaabbbaabaadcccacdbabccbbccabbddacbbdabaabaaddacaacaccdaaabbcabddbbcabbbbcacbbcddbbccdbcbacbcdbbaacdbdbacadadbcbccbaaacacabddaadadbbdaabdacadabdabbaabcbaaddaccbcbaaabdaacacbbcdcbdbaddcbbbabaddcbbbdbdbabaaadacccaccbdbabbbbdbbdaabaabdbccbdddddbcbabaccbaaccdbcabaababdbccddbacbbcdccbbbdaaacbdcbbdabcdccabcccacbabcaddabcbcccbacabdcdbaabaabbaaaddcbcabadcbbddabcbaabbadcdcdccbcdaadbcacaccabdacaadcddbdccaacdcdaacbddddddadbbdbbdaccddbcdbacbaabadddcdcdadacacadccacaddbcdccadbddcdddcbddbbaddcbbccbbccbccaaccaaccbbabcbbbdabccaacdcabbdabacddccabdbdcccbcddabadbccccabaaccdaabbcaadadbdcabadbdbdbcdaccaaabcbcdbabdddddccdbbccbaadccabaccdbbbdcabbccddccbcbaddaccbbccadbdcdabaddcdcbacabcbdadbdbbadcdaadaaccbbabbdadbadcaddbbcbdbdbcccdabaacbcbcabbddbbbcaaccddaabccacddcabacbcddbcabbaccbbccbbdcbcabcdabdbccbdabbdababdaccdbcbccbbcbdbbddcaabadcdaaaccbcdaacbdcdbbcaadaacbddbcbcbcacbdbccdacdbadcbbdbdcadddbabbabacbdbaabcaadddbdccaaaccadcddaddddcbaaaddabddaadbadbbdcbabaddbccdaaadcddbbcdbdabbdaadccbaaabdcbbaacaadbabaabaccdddcdaddbdaccadabbdcdccbdbbabbbdcbbaabbcddcaddddcdbdcddcbddbbabcaaaabdbcddcccbcddbcdaaaccdbbbdcaacccacacdccdbabddcdbbdccdbbbbadcccddbcbbccdbbdcabdabadbadbbbcdcabaddcccaaaabbaddbbccdbcaabaabbdcbdddbabdacabbbccadddabbacabacacbddaddbddbcbcabcbdbbdcdacddadcacbaccbbdaccaacccbdbbabdbcbbacbccbdcbbcbadabcbbdabbcbdcccaaadabbcbddcbbacbcabdadbaaaaaabdbacdcbcacbbabaaabaccdbddccadbbabadaddabdbaccbaaadaaacabccbdcddacbabbaaacdbacbcbbbbddbbccaacdadbcbcadccabbadcdcddcdabaddbccacbabcdadcabbaabcaaaabcdbdbdbabddbabbdccbabbbbabbdaabbaaddadbacaadddbdcbdcbadddaadccbabdcbddaadddbbddbaadbcadddaababddacadbccacabcdababccabbacbadbbdcacbcbddcbdadcddcbddddcbdaabacbcccabbcbdabcbbddabadaadcbaabdaacadcabcccacbcaaddabdacbadbbcaabbaabcaccacaccbbdadcaccdaaadcdcadbcbdadbcdaaabbabbcbabbcbccbabcdbdaacbadccbcbbaaddcbcacacaacadddacbdccbdbbdbaccadbadcaaacdbadddbddccaadabacabddbaabdabbddbadddcbccbbcddcbdabdbcaaadcdacadadacbdaaddbdccacbadbdacbdaaadcababcdaadcbcbdaabaccaaddbacacbbbddadddaacdadabdccdbcbabbdaccddccdccdaaccaabbdbbdccddcaddacccdacddbcdcacddbdbbcdcbddadbddbcbbbdddcdacaaaaddddbcbaaccadbaacdbcaaddaccbddacacbccbbadabaabbaacdcaaaddacaaacdbdcaddddcbabacddcccddbaabcdcdbaaabaddbdbabdbbbabdbcddbcdddabbbddbabaaccdbbdaabcadcdaacccbabcbdcacbcadcdbcbbcddcddcbbaddabcddbbdcddccaccdabbaacbbcbcccddaabdcbcbabcbdddcabdbbbdaccabcccccbcbadcbcdddccdbbbbcccdbbcdcabdcdcdadbcaccccadcadccdddcbdcadacbdcbdbdbdcabdddcaccbddbdaaccbabdccbccbbdbdaacbcbdcdbdaaacbcddcbbdddbdbcdbcccbdbcbbaccbaacaddadcacbdcabccacdaadcbdbbcabdbdddcbabbcdabdadcdabaaaaccdacbcacccdbcbdbdbabbccdadddadbbcbdcbcbbcccdcabbddadcbccdccccadbcbaddbbaacabaccbcbabddbcbbcbaacbdbdddcadccccbacbcbaddbbdaadccccbdaabababcbabdbaaccccadcaaaaaccabdabbdccaaabbadabdcccdcddbdbaaddddcabbcaadbbbcbadddaaaacacdcccbbbddabcdcabaadaaabbdbbdcbcbdadaddbdbcdbadccaddcbdcbacbaaaaaadabbbdcbabbabcdbbcdcabcaaddaacddacbdcdbdcabccbacccbabdccccddcbacbbcbaabbcdbbcbbadcdbacdcaadccabcabbbdcdabacacbbadabdaacbaacddcabbcdbbaabcaabbdacdbbcccbdddadbbdadaddbbddabcbcdddacabcacbcbcacbabdccbbbccabdcbcbbdddbcabccbdcddaaccdcdbbdbccdaaadcacbabccbabbbcacbaacbbddabdaacbbcdbbdaadcbcbabbbdaaccbccabbdbdaaabbbacadabcbcadbbdddaabbdadbbbbbaaadaaddbbabacdddaabaaddbbaacdbadbbadadcbcaccdbdcaabaadccbbcddabaabaabbabadcadbacbadadbacddcbcdddbacabdbbacbbcbbdcbdadbabadcadaadacbcacccddaadbacddccbddbcddbdcadadaccaabbabbabbaddccbabddbbababcaaabbadbcaddcbaacaabdaccaacbbaaaaacabacdbacbccacddaadaccabcdaacaddccdacdcbcdbcacadbacbcbddccbabddcdaacddcccacbdcdadbbcdbccdddacbcadddaccaccadbddbaaacacddbdabbbbacddbdaaaacccddccabaacbccdcdacadbabaaacbcccaadbcabdcaddccaacbcccbbdcddcacdcbbdddcbcabbbadaadacdabbddbcbdadadbdbdcdacbcbdcddadccdbbdbdadcacbabaacabbacadadddddaacacddcdabbacabcbabbddcdbbcdbcacaddcdddbabdccccddcaaddbbcabbadcbbcdcadcddacbcbbccddcdddcbabaadcadacdacdccdcdabdcccbaddbbddcdacdddddddddbdddaaddaccbdbdbbcdbaddbcbdbccabbcbccbcccbadbdabbcbaaddcdbaababddcbaabccabdbdcdccaabbadaccbcdabdacbcddcccddacdaacabaadbdbbdcccaccdddcdcabcabcbbbcbbdacddaabbbaacbddacacbbcbcbddcadabadcdcdccbdbbabaacadaddbdbbddccbaadcdbcadaaaaabdcbbcabbaddbbbbcacccccdcaacaaadcdcdcdaaacaaadcccdbaabcbbcdbaaaabcdabadcdbbddcabdaaaacaaabdaaabccaabbccdddacbcadccadbaadcbabddcdacdbaaccdabcbbcadacabbcbcbbcaadddadacccbcbdbdcdaadccddccabccacccbcadacbdcdaaacacbbdbcccdcbaaacabbcbabbcabbadcbadaaacddbaabbbdcbcdbcbdbdbcdbbdcabbdcbccaacacabaaddbadcdcdcbdabbaaaabaadadbcdaccbbaabcbadadaacdacaacacaaacbacccbccadcbdbcdcbaddcbbacbadddabadbcccadbbcccbadbabbaccacbbdcaabbbdadaadbabdddaadcbcbbbddcbbcbdaddacbcbadbdbdbaacbacccaadacdddaaacdcacacabdbaaccccbcbcbabcbacdcddbdbabababbcbadbaaacdaacdddbadcbbdcaadddcaaccdddbccbccddadcbabacbbbdcdaddbddcbabddddcdcbcbcbbadacdaaaccbcddabbcbdbabdcbbaacdacbbaccabdababbbcbdccddacdacabcacbadbbbdcdbdaccaabdbaaccadaabccbcdaadbaacbdcadbdccabadccbadbcdbccacdcdabaabbcdbbccaacdbddbdabadadcbaabadcaaccadcbdabcccabacdcbcabababcadbbdcbdbcdababbcbccbddcaabcddcadbbdbdacaabadbbaadacabdbadcddcbcabbacbabdaadaaddbdbbbacbadbdabbdbaadabacaccaadcacbccbdcbabadbcbdabbadbdcacbadbdddcaadddbbbcbabdbaadbbcdddacbcccdcdaddacdcacdcbbabddaaadcddaddbccdcaadbddadbddbcbadaaaccdadbdbdcdccabcccbcadcccacdadabaaddabcaccdaacdbcbdabbddadbcccabcdddcdcbddbdadaddddacdaddbcddbababcabadabdcbcabcbabdcdbdbcdcdddbbabacbadacaaabccdbbbddcbaabcaaddacdcacaccbbbcadababbaddbbdacaacaabbbaddbbbdbdcccbddbccccdddcdddabdcadbaccadbddadcbaacbdddacbdaddccaadaccacdbbadbabcaabdccdcadaabdbbcdbccccdbdaacbbddbbcadaabddabdccbbcaadacdbbaadccbdccabaabbbcaadaadaabdacdaadcbadddbddbcabcdcdbbdabcccbcabcdbabbdaacccbbbdbaaadcbccdaababaddadcbadbbdbbbbaaacaabacbcadbaaadabccbdbcbddadcdaccbbccdcccacacdccdcadbbcbcbddaacdaacdabaaaacbbaaaccbaabcbddcacbabdbbcacdadabaaabacbadcbccddcbcbdadcbbcbdbabbcdcbdbabbbdabccdbccbccbadccbabcaabacadacacabaddccdbacabdbbabcbcbbcaddacdabbbdcabacbcdacbbdcadccdcbddbcdcdcbbdbdcbbadcdbbbddddccddadbabadbcabcdbbcabddcbcdabcaddccacdbbddcbbcaadaccdadcccdbcaadabccaabbdcdccabacaabaacacdcccccdccabdcaacdccbdbcdbccaabdbcdccdcaddcccbdbabbbcbccaddcbbdadccdaaccabcadabccdbabbabababcaacccbcccaaccbcadadbabadabaaabbdbccbdcbdcadadabdccbddababcadbccdadcaccbbcbdacadadadcaadaaacbbaaddabbcadcbdbccdabdbacdcbaabdcbdabbaadbdccacdccddcdcabacbbbababaabccdacabbcccbadaacdabaddaaacdbacbacbbdabbcdbcdbacddabbdbccddcadddacbbdacbbccdccdabcbcdbdadddaccdbaccddbdbccbbdcddacccacbbbcccdbdddbbcdabccaadddcddabdbcaccdcadcacdbcabbabacdbdabdacdbadbddcdadcddbcdccccdaccdbcccdbbaacddbbdccdbdcdbadccddacbcacdbaaccadaddbdccccbdcadbbdcabacaabbcbcdbdbcaababbcaadccccadcaddccdcccdabdacbccacccdbabcddaaabcabcbbccccdaabdbdadaadaaacadcdcccdbcadbcbabbbddddcabaadadabcbdccdacbcdbbbcabbcabccbaddbdcbbcbcdbcdcacbccdbbddcccbbddabdcbacdbaaddbbbabccababbdaabadaadbddaaaaccccbccdaccbbdbcddabcccdcbcadbacdcccddbbabddadbaabbccbcbddcbababdcaadadcacacbbbbcbaacaabadacaabdbbdddbccbcdbbdcccacabaccbccbaddddcbddadcbcbcbcbbddaddacabbdddaacbcdbabdcddadbbbcdadcdbbaaaadbcdcbcdbcccdaabcaaabdbcbdcaddaacacbabcdacaddddcabddbaabbdcdbbcbdbcabaabdbadcdcabdacdcbcddcbdccdacbbcabaacacaddbbbacddbcdadbbaacaccdadcdcbcaaddbbbccbcaadddaccbabddbcccbbaaccdcccdabdcabadcdcabbbcaccbbabcaaabbcaabdcbbacadcaccbdcacbddaabdcbdbcacddcacaabacccdbcbaadaddacdbcbbdadddabdddaaaabaacccacdbbcaccabddacdcbdaaabddbabbbdcdaabddccdcbdaabdadabacaabdddadabaabddaadbdcbdaddcbcadcdaacbadbacacadddddcacbdbabdcabdcdcddcdabbbaabcdababbbadaaccabcddaaacbabbbcabcadddddcdcbbabbbadcddabacdadbdbcdbacbdaddcacacdacdcbbabaaaddbcbddbcbddcaadbbbadbaaacccbabcabcbcacddabadddbcccccdbdbbcdcaacaabdbaddcdcdddacabaddcdcbccdcdbbccabdacdcbbddbddbdacbadddccaccaabaacbddccaabcdcabdadcdcadadacacdbdabcbcbcdabdcaaabddcddcaadcbaacccbccdcadbcacadcaacbacaddddabddccbbdcadaaaaccdbaccabacbdaccdccbbdabaabaababadccabbcaaacabbbbddabdcbdbccbddadcbddacacadadcdcabbdbbbddbcabcbadccdadabacdddbdcabacadcccadaaaadacacdcdcaadadcccdaaababcbbabccaccdcdcaadcacdacdaddcabbadbbabcbbbcdbadcbcccacbabaabcbacaababaabacdbadadbccdcaabcbdbcdbbcdacbcbabccacdddbbcdbabbbbacddaadbdcdcbbcbbcdcdcdddaacababadacaccabcdbaadbadabbaaddadbccccdbbbacbbbdcbcadcbbdddacbbdcdaacadcbcacdaababbbccbbabbdbacbdabdccdbbcabdaddcadababbbacaaadbaabbbccbddcddcdcaacaaaddacdaadcbcaadccdddddbdddbddcbdabcbbbacdddbbdacbaaaadadacbdcbcaadcaacbabddbcdabaadaacadcbcddbaaaaaccacabcdbabababcacccdadccdbccdcaaccacaddccbbbadcdbbddccdcbacaaaccaadbbcbadacbccdcdababadadadbbdabbbbccbaccccbbbdaccdccdabdbdadcabccbdababaabacdccbacccccbacccdadcbcaadabbabcaacaddbabcbcaccdcbbbaaaccacdbcbcbdbbacbbdaddbcbbcbccabbdbcdbccdadbbdbbddcdcddccbaaadcbabadbabcbadbddddcabaddcbadbccaacdacadbaaaccbccdabaddaccdddbcdbccbbbccaaadcdcabcadaccbbdcacdcdccaabdcbcbddcacdaacadddaccaccbbdadccabddaadabbbddcdcdddacdbbcbbdbdddddadaabdbdcbaabbbdbcaaccbcdbccbbabbcbbbcbabaabbddbdcbacbabaacaacdcdacbcbdbbcdbcbcadcdbcbdcaadbcdacbccdbcbcdacdaaccacabacbbdbbddcbdbbbabaadbbaababccbbddaccacadbbabcccadbaabcdcdcbdcbbdcbaadadcadbabbcbbadbbccbbabddddcabcccacdadacbdbbaadacbbbcdcdcccbcdabcaadaaabbdacacadbabccbccbabccaccbabcdcaadbcdbbcdadbcacaddabaabbbdbabcaaaaacdbccdcbddacaacbbbdbbddccdacacddbaddaabdaaabdddbcdcdcbbbbcdccadcacbcadbcbcbcbcadadcadbabdbdaacdbbccdcbacbbdccddadbabacddcaacdddcbcbabcaabbcdbacbdcddabddddadaccbbabbdababdbdbbdccbddbaaaadcaadccdaabbdccadabaabdbdacabdccacccacaddadbbccaacacddacadcadddcdacddabbdadcdbccddbbdcbaccccbacdaaaaacadcbddcdcddcadddddbdbacaaacbbdcadadcacbadbdadcbccaadabaabacabdbddacbdbdacbccbabdbcbcdbdccdcabdbcaddddabbbbabccbbcaacdbbbbabcdbbadbbcacdaaacacbbcabaadabadcdbadbdbabaaacaddaaddbaddccdbabdabccdccacccdbbbabdabdacaddbcbbabbacddababdcdbbaccdbacbdcabcabaaadcadabccbcbdaabababcbdbbcbdcdbaaaadadacdbcacbccccddadcbaccbacdabbabccdbccbdcdaadacbdbbaaabaaddacccbaaccbbbaadcdadbbdddbababccacdacccbbdcbaaaddcabbccbbdadabacabbbcbbaabcabdbbdacdacbdddbadcabdadbbbbacabadabbbbdccdadcbdacbbcabcbcaacdccbccdcadcddcaacdacbdaadacadadcccdcccddcdadabdbcabbcaadabbadbbddccabbcccbacdcddbccbacaabcbaccdcbccbdadbaddccbdcbdaabbdcbcbadcabbadaaaccaddaccdddccaadaacdcbdacdccabaabcdbacabdbdadcaaabbdccbdbcabdccabcadccdbdbbdbdccaacbcacdcadabdabddcdccdddbccdbdccaddcdbcbcdaaaabdddcbbccacdabdbcbbccbdcdcbbdbdbbbcbccdbddadcdbacacbcbbdcabcbbacdadcdacdbaddaacadbaacdabcdbdcbcbdccbdbbddbdcacbbbcdbbcdaadcbdddcbdcdcdaaccdccccdbdacdacdddacaaacbaacdcbabcbadaacdccccbbaabaabbacdddaccabbabcaccabadcdcbabdbdcadcacaabbdcbabbcdddbcbbdabdadaaababcbbaaccadbddbaadbcdbcdbddcbccdbcdaccdabbcbadacaccaccaadcbadbaccadcdbbdbcbbbddaccdabbaaabddcbcbdbdcbdacadabddadcbcacacaacabdccdacbbccadacddbdcdabcddabbcbdabcdccaaaadccbdcbbdabcacaddadaccbabdabdbabdadacbcdbabdaccdbacccdbbbacbbccbabddcdcdbdaacadcadaacdaaccbdcacacbbabdaccccbddcababdcaabcddbdcdbbbbaaddcdddddcbaacbbdacdbcaacccbbacbadcaabdbdcadaacddddbdaabbdcdbdaabdcbcdabbcbaaccccacdbbcabcacabaacdbcabacccccddbcbdbdabbadbdcbdabcbcccccaccdbdbdadbbabcacdacdccddaadbcbddbbbbdddcdcbbdcbdbaddbcbdbabbcbabcacdadbdddcdcccacbccdcdbbdbccbbacadbdbcacabdbcaaabdbcbacabcbadbadcaddddaadbbadccdaabbabbbdaaaabbcbddabbabacddacacbdcbbaccbaddacddcddddcbcddcaddaadadbddcbaddcdabccacccbaabbdbbdcdaaccbaadcccbadbabdadabacddbbbcdaadaddacbacabbcdcdbbcdaddaacddcdcadbdbddbcababbdbbbdaaabaaadcadbbdddaccdcbacaadcccabcbdaadadadbbccacbbbbcbbbacaabdbddcbccbcdbbcbdbbbcaababdabaacbcaacdaaccacbacbddddbdbcaaaacacddcddacbdaddadacdbdadddacccbdcaccabadccccbacdddcdbdcbadbcdadcababbbadaacddbcbadccadbbcdaabccbdbbbcdbdaaabababdcbcdadbdbbdaacbdddcbadccbcdadcbdcbbdbcbacdabcaaddcbdcccabcabdadcbacaababcdccbcacdacbdaacacabdbddabbdcabaaacbabdbcadcbcabacbccadadcbbccbabababdaacddacaacabcddadbddacbdaaacaadacbbbccbcbaccdbadaaddbbccaccdbdadbaccbdadbdaaddccbbbaccbabddcdabdbbddcaaaddccdbabbabbaddbdcadadbbacacadcaabcaabaabbbadadbbddccbbbbdddcdccccdcbbccccdcdddaadddddcdacbadaaacdcddbbaddacccddbdcddabdcbcadcbdccbdaacbaddddcbdbccbcdacaacddadbdbadbdccbdcbabaaadacbbabdadadddddbdddabbddcaaaadabadcadcaacaccabcdacbaacacbabacdcaacbabbabdacbdaccdbaccaacbbadbabbdccccdbacdccdabddbddcccbcccaaacabdcacbdadaddabcdccabdbddcabddbdadaacdbbccbbbcacdabcaacadbcbbadbacdaddddbacddbccdbccccadbccdababacccbdccdadcdaddccccddcabdcccdacacaabbacacbdbaacdaabcddcbdabcdaaabbddadacaabdaabbacadaaaacdababbbcbdcdccbcbcbabbbaaddaaddbcbbacbcacdbcddccddbdaabaaaaabaaaacdddbccadbcdccdbbcdbaaacdbabcaadccccbcdadcbaddbbcdddcbddbbcadbbdadddababbcbccdbccadacddcadaccacbbbddcaaaaaadddddbacaddcbccadcaddcbccbdcbadcacbcbcbabaddabcbddddcbacbdbdcddcdabccbcaddcbadcbddccdadcacbddcdddaaacbbdaddadcdbdabcdabdaaaadbcbacbcabddacadbcbacbcabacacacaaddbdadadadbbaddbacccadbdccdbbbbbcabdbddcdabadddcadcccdddcccbdadbdabcbbdbbadcbcbabacdcacabcbccbacabacabaaccbbbbccacdbcbdbcdddcdaabbdcdadbbcdacacaaddccccdcaddbbccdbaaaaadddcbadadcdddbaacbcbababdbacbddcdbaddadabacdadcbabacdacadaddbaabacbdaacdbcdcdccdbcbcadcbdbaabcacbcabbccadcddddcbadcdbabbbccbaddbbbaabdbddccababdcacdcaccdbdbcaccddcddbabcdbcabadccdcadabbbbaacaaaaaaddcbbbcdbbcbccbabadbacbcbdbcacbbbdadbdadbdadccbaabacdcbabaacbcacaadcdcdcadbadbabcabadbbdbcbcddcaddccaccccacbdbbdbccdaaabbdccbabaabcddddacdabcddcbdbadccccccdbdcdacabcaccbababccadbadaddaabddcabaaaaccacdacbcbddcbccddbaccbcbcadabbcbdddacabbdbccbaacdadabddddcadccabacddcbcccbacaaacdcbccbaaabacbcabaacdcaacabdbdaaccbbcbbdadcaccbddabbcbdcccdcbccdcdccbaaccaabbaadbbdcbcadadcaaacbbcdbbcbadcacadacaccdddcdaadaaaacbaacbaacdbbbbdcdaaddbbdbbbadcbdbdbccdcbbbacdbdcadcdbacdccdadccccaacccdbcdaadbccbbdabddbdcbdcbcdcccdcccddaabddaaacbddbdadbabbdcdacbbabbcccbdccabddddbcdcdbcaabadadddbbbbabbccbbaadadddbdbddaaccadaadccddddbbbabaddaccabddacdabdddcdbddcbbdababdaabbbbddcaacbbcddaabccabadabbadbbcaadcdccdacdbacadbdbccddbdadbacdadaadbdccbacabdbdabbadcddbdbbbddaddbdcacdabdabdaadcddcaadcacaaaadaacbababaadbbdbccdaabbaacddddbbaccbdbdaddabbccabccabadaadccdcaaadbbaddcdabacdcabdabaccccaccdbccbabdccaadbdbacbccbcdcbddddbcbbbccbdaabbccbabacaddadddabcbbdcbcabdadcbdaabbadccacadcdcdaabdaddcbbcbbadcbbbcaadbcccaaddbdcdcadbcaaccdbbadbbcdbbacabbbacdcbaadcdabcbcdcbcaacbabddbddaaccdbcddbadcdddbdcccaaccbbacaddbccdbbadbdbcabddccccadaaaaccdbadccdadddbcdcabacaaccdcbdccbaabbbaabaabdcdcdcbbaaabdbbbdaccabaadacbbccbddbbbabccadaaaadadccccbdababbcdbdabdbdddcacdcabbaccdddaaadaadacabdbcababbacdbdbbcadcdbbdcdcddcdcdabbccdbbbdcadadbdcbacbadddabccbaddacadaacbbcbbaadcddbbadbacddaaddccabbccbaadaabddbcccccddcbdbadacbcaacbacccddbdacccbcbbccabcaadbcddbccbcabaaabbbaabcdddcaddcdabcddbcaadbcaddcddccabbbddcadcabdcaabdbcbaaabcabbdbaaabdcadcddcdabdddabacbdabccaacdbdbbccacbbcbdcacccccdddacabbbaddccabdbddcbaacdbdacdcdadadbccccbdacadbbdacbcadabbdccadaddcbdabdcabbccbcbbbbaaddbdadadcbcacdadbddbadbbcbcbbccbdbddbbacddcdaaccdcdbdccabadbcadbbdddaabdabcdbcaababcdddccbdcbacaccbdddbdadbdbbdaccadbdbccacdbacddbcdbcdccdbdbadcbdbddcacbbdbdcbcabcccaadabccccabdbcbbbdbadcbbdacbccabbbbbcbbccbdcdddddaadabcbddbcbacccbbcbbcbdbabbcabcddddaabbdaccacbadbccbabbbacdddcdbcbdbcdacbcbbdadbadaabdcbdbabdaaddbcaaabbbbbbccbabbcdcaaabbcbcdcbdadaabcadbaddcdcccdaccacccbbcbacdbcdcbbcbbacadcdbbdadbbbcabbdcbdaacacbdacdcadaccdbdbacabbcbdaabccccbaaabdbddaaabdbbccdaadcddbdbcdbdddcaccaadddccabaccdbbcbdbdaacbdaaadbbddaaccdbbaacacdabcdadbdccdaacddbadadddacbbcdbddcdadccadcccaaadcbbdadaaadcdaadcddadaabdcabdaccaddddabdcdacddaddbadadddcbbdbacbaabddddcbcbdbcdcddddcccdaaabaaaccbbacdcccbbaaaccdbbbaaabacbaacadaabaabcaccdddbbdcaccbadadcbddbbdddbbdadcadcbabdbccacdaddcbdabaaaacabbadcccacdaacacbcdaacbcdddddcabcccdbcbdcbcdccacbcadadacdaaabbacabdbbbbdadcddbdacacbbaaacdbdadcbbcbcdbcbdcabccbbdcbcbacdccaaccbcdbcabbbbbdaadbcdadbbbabdcdadbbcaadbdbdcdbbacdcbbaacdcabaddacdaadadcacdcadabccaddadaaabcdaacbaaddbdcabddaacdcbcdbccccbbccccacacbcbccdcdddbacdcbdacbaddddbdbdbcdbcbaadcdacbbdccdddcaaacaabadbacbbdbababadacaacbbcbdddcdbbcabdcdccdbaaddcabcdababbaaddbdbacabacddcddbbcadbcbdaabbcbddbbdbcbdaaacdbdcabcacdcdbaddcbddaabcacccdccbcdddbdbbbabadacaacacacabdddbdacddccbdcabadcdcdaccdabdcdaddcbdabcbbbcadbcdcddbddabdcdadabccabadcdbcbcabdaacddcacadadacdadbcbcdadccacbcdbdcddbbbbbcdddccbdaadbabccbdcaccbdaddddaddbddccccdadacbaaddaaabacdaaccadcbbbcaaccdcdbcbdaabcadcccdccbdbbbaccaacbbdbbaadacbddaadadcbcddacdccadbcdadccdcaadccaacaddadccdcbcacaabddabbbccdaadbcacdabaabcadcdbdaaaabdbdbbddadccbbccbcbbbcbacaadccdbdacacbdaabacbcbbadccadbcadbdaccdabadcbdadadadbcadcaccccbcbccbbacdcdcdccdbdbbccdcccdabbbaadcdcdccbcaacaacabbddbacdcacddccdabdcbcbdaadddbdbdcccbaaadccadbcddadcdaccbbdbacdcdccaccbdacdcacadcdbadabdacbddbdbabbdacddddcaccbccccaccabbcbbadddbcccadbbdabadadccbaaacccdabbccccdbaaacbbccbddcbcdcabadadadcdbcdbddbcbdabbcbacbaacabdbdbccdaaabccadbabbaabccdcabccddddbcbaaaccddaacccadcabaddbdbbadaccabcdccbdbdbaadcbacdddbbbcbdbadcdbddbbcaacdabdbabcdcbacaadcdadddbbadadadbbabbcccbbdaadcdbccabcdbdbddacacadcabadbbaccadcddabbbcaccccdcacdabbccddabdbccdbabccacbaacdcbbdcaccaaababadbaccbccadbbabadadaccdacbdbbbbbcccccbbbaabadcccddbaabcdccdaabcadacbaddaabbaccdacbcbcccadcbccdddababbaadbddacdccdbacbcadcbbccabbacbbccdcdbdaadaccdcaaccbaaadbaaacadaaabcdddabdbbbdcdbbabccaadcbdbbbdabbaabadbaabdbbcccccacadcacabdacdacddbdbbcccaadbdbccdbbcabdbbaddcaadaddbccbcbdbdccbbbbbcabbaabdcbcaddcbbbbbbadacbcacccabbcdbacbbcacadabddacbccdcacbbcccddbdaabdccdbaabdcbdbcccddbbbcbdddddbbcdccdbdcaadcbbbbaddcaaaaaaddcbdccbbaddbdbcdcddabdaccbabadadcaabaabdabdbdbdddbacbabddabbaacdbbacacbdddbdddbdbccdbddcaccccddbabcbdbdbccddbaccbcabbdcbacacccddcdabdaadbcadccdcbaddcabcdaacdddabdcbcaadcbadcccadbacdddabcbcdcaadcccbcbcdacaababacdbbdcbdadddcdbbacdcbdcbdbcaccdcadbdaadadcdabdaaccdbcccacbcaabadbcabccbadbbdaddadbccdbadaacdadabccaaadbabcddbdbcccbbacdbbddbccccaabbcbdddaccdbaabaddbcaaacacddbadbaacbdabadbdabdaadadcadacabddcddcbaacdbbcdcbabccbaabbbcdcacdcabbccbdabdbbabbabdacdabdcddbcbdaabcdccdbbddddaddddcbddbdaaaadcdacbccbbaacddccdcbbcdbdbdcadcadcddadacbdaaaddadccbbaaccbcddbbadccabaaccabacaaccccdccbddbcacbcadcaaccabcabaaacddacddaaddbcddccabdcdccabdcdabbdccdcccbcabdbbbcccddbcccddbcbaababcadcbbcaccbadcccbddabbadbbcadbabbaadaabacadaaaabcbbadccccabdccbaadacbbcddbaabdcbababacadbdabcdcdbcbcdbaabbdacbbdcdadcbcdcaddcbdacbbacaaccadaadcbacacacbccbccadabdcadaddcaddcadcaadbabaaadcaccdbbdcaabaaddbbdabdbdddcbcdabcabdcaaccdddbaaaacdcccabbbcbabbdcddbbbccaadacddadbbadadcdaaddbbccdbdccaabcbcbbabdadaadabcaadddbabdcbacdbbcbcccacacdcaacddbbcccbcaabdbcccaabccdabdaacdbcccdddbabbcabacdcdcabbacccaaabcdadcabcacbaddacdbddcbbacdcbdbacccbcccaccbbbaaddbabcaaabadbaddcabdbbbdaabbcbcbadcabbcddddaabdaabcccbcaadaadbbdddaccacbaadbbcccaababaddcbccbddddcbcadbcaadbccbdcdccdddbbbccddcbccaccdbddacaadbbcbcbdddddbdadbabccbdadbdbaabbbdaacddcaccdcbbdbcbbaaddcdbcdadcdbbddabddaabdddaabdbddabbbcdcddaacaaabcdddaddbcddbabbbccacbadbcddcdadadbcbbdcabdaacabcdabcbcaaddaadabcaccdbbadcdcdcbccbabbabbadcaaddcbacbdadbdbcaccbaaadaabdcbcabddadddbaaacaabdaacdbcabdcbccabcabdaaccbcabddbcaaabbbcabdadbbabcdacdcacbbcacadaaaabcbddaadacdacbddcbcaccddcabbddabbdabbdacbbcbdccacbdcdcdabcaacabaacacabaabdbbbdaaadbdadabcaacdaacccbcddabdabccbdacbabcbcbcacbcdabccaabadabbdccdacaddddbaaaaaaabbdbcaaccdbdddcccbacaacbdcddbaadbdadbadadccbddddcabaaddaaaaddabdbddacbcbcbbbdcdaabccbcbbcbdabadabbccbbbbadbdcbbdadabdccbbcddccbccdbcddbadbbdcbbadbcadabacdcadbbdabbbaacdcaaddabacddabdcdcaabcacbaabcbdccdaaaadccaddadabbcbbbcacccbcddbddaacdbadbdcacbaddddbcbaccbaacdabbbbaccccbdddcbdcbdbbcbcabccbaaacadaadcabcbabaabcbbacaccabbbcbcbaacbcccdbbddacadbacbbdbcccccabbbadcadadbdabbddaacdcaddbaadbbddacaaabbdccccbddbdbcabdabdacbcabdadcaadabdcdabbbbccaddaccaddaadacdccdacdaaddbcbadabcadacddcdaaaaaccbadcdbdacbcdddccabbbcdababacdbccbdadcabbdbbbbacdbaaacbdababcbaddddbdabbcabdcbadadcbababbcaabbcbbddcadcdbaaadbbdaaaddccaadacddaacccdacbacdbdbacdbadaabbcbabbcaadacbadabadbbabdddcbdbcaacdacabddbbdcadbcbcabdcabbbbcaddbbacaaadbccddcddcdcbbbcdbcbbcbaacccabcabaabcdbaacdabadcbdaaadbcddcdbcddaacbbabdbbdccccdccacbccbabdbabacaccacdccdacdaadadbcddcabdcccabcababdaddbabaaabcabccacdabcaccccdabaabcacbcbdcbbbaadaaabcabddddcacacddacaadadabbbbacdbddccaacdbbbbabccdaddbbcbbcdcbcccbccabcbcdcabccdbddacdcababdaadcabcdbcdadccbccddddacdbaaaabdccdcaddbbbbcadbcbadccadaadacabaaaaaabccadbdbdcacdddbabddacbacdbbddcacaccbadaadbccbcddabacabdacbdcacdccddadacaadccbddabbdbdcdddcadadadbdbbacbdacbdcbbbadccacaabdadbcacdddaaddccbadddbbabdaadcccbbcddbacbddbabaabbddcdcddcddbbabbbdcaadaabdccdbadcdbbdcddabacddaaadadcdcbdabadaabbcacadabbbdbaabdcdcdbdbcbadcaaddbabdccaaabdaacacadbacacdaddbaddcccccdccbdcddaaaabbccacbacbaccbaadbbaaabbaacdcdcddbdbdbbdbdcbadaaaaadcdbdaaaadabddbcdadcbccbbccabbacaddddbcdbdadcbddabdaaaaacacbcbbdadcddbcabdacdbdbbcdcbbbccbabadddadcddcddddcccdcbadbacbaccbdbdbbbcbdcaadbdacabcddadaaabcdcdbdddccbcdcaacbbccacaaccadcddcacddbcdddacbcbaaabdbbcdaacdabcdacbcddbadcccccbabdcccddddacbddddbdccabdbdbaccadbaacadadbcabaccbbdcbacccabccbcbdaacbdabccbdccccbbaabccccdabaaacadccdccdccaadabdadcdccdaabdcddbdbcacdacdbddabdbbbcbddbcddcbadabaadaabdbbabdabddbadcbbaabdddaacadbadddccccdcdccbdaaddcbbaaddaacdccaddbaacbbddbdcccdadacdcabdcbbbadddbccddbddacadcaccdcbbdcbbaacaacccdbddcaacadacccdbdcdcbddbdaabbccdabcbdbabdadcbddcddbacacddbdcbbcacabcbbbddaaccbccbbabadabdacbadccdbbdacccdcabaadcdcdabcadbadaabcbcacadccdcbacbdadddbddcdaaccbaaadbbcaabadcddbbacbbddbbcbacbdbbcaaacdacadbcccddabaabaaadcdbcacdbaccaddcaddabaaadacbbacdcddccbbccdabdccdaabbbdbabdddbdbbcbbacdccabaaadddddaacacdacacdbdcbdaaccbddcbdbddacbddbbbcbbddaccacdbccbadaddabacacaddccccabaccdddacaabbdcbcdcbbadcdccddcddcbaabccaaaadbaabddabbbcdccacccabcccccdbbddcdadaadcbbabdcabbacbbccddbdcdabdcccbacacccdadbdcdacdaabbcdcbdbacdcdcbcacbcaaddabbacdbcbadbdcbcdbcbbabacddcddcbacbbabadbddababacaadaaacaabaabcabddabbacdbdbabbbadabbbbcddbdbbdcdbbcbbacdadcabdddbdbbddcbabcabadaddababdaababaabdbdbacdddccccacdcbdaccdbdcddabdcddadaabcdabcdbdadcadbaddacacbaaaabbdcdddbbbcadbaaaaddbabacdcbbcbbdbdadcbaababcbacdbcddaddbdabddcdacaaccbdbaccbaabdbaddcbabbcccabdcddaadcbccbbbdcbadbcadabcbbadbabadbaccabdabcbdacaabbbcbdbbaccddcabacabaadbcdbcbcabdbcdcdbbdacbbbbbacdbbadaddddaccadcadbccccaaabbcaadaadcbbcaaaabcabbdcabacbbdbaabcaaddbcabacbdadcbdbccdddadbbacdcacbbbaadababdcbabaddbcdbddacdcccdbbdccbadadcddbbddbbcbabdaddbaccdbacabadabaaadadbbadcdaccbccddcbadddddaccbbaabdbdbddbdcccdcabdaddcddbbaccbcddaaacccbaddcbcadbddbbbbcbcacbbccdcccddbdabdbbaadbdbbdbbcbacbabccadccabaadbbbaccadacdacacdbbabacdcdddacccaadcbababcddccbacacccdcdbabbcdbbdcbdabaadbbbbcabbbcdcbadbcdbdaabdbbcddcadbbcdadaadacaccbbbcabbddbbbcaabbbaccbbdccadabdcdaddbabaabbabbcacbbaaaccabcbbaaccbbbcbaadaaccccdaabaccbddabcdddacccbdabbacccdbccabcdaacccbbadacbdbbdddaabaccaabcdddbddabdbcbbdcdddbddaddcdcaccdbbdddbcbaacabdacacdabaccdcaadacdcddddbdcadcdcacccdccdcacdabdcddaadaaacddcccdcadacaaadabbbbaadbbaabcddbdcddbbcdbacaaaabbdcbacbcdaaabaddcaaddaabdcadadbddbcbacabadbabdccabababbdbabccbcdccddcacdacbcbcdddbdbdabdbdbdbbbaccabcbcbcdbdcabdabcdbccababbcdbddcbccccacdadddacacbdaadcabbcabdcbcbbcacbabaccdbdbdbdbbaabbaaadccdcbdcdcccccbcacadddacbcdcdcdacbacbbcdbacdbabcdddaacdcccabdddbdcaabbddbdcdcccdabaccbbbdcbadbbadccbacabbccccbdbcbbdbaaabcdaaabaabdbadadcaadcdbcbacddadccbcbbabcabbccdadbaacbacbcdacadbddacacabaacbaccabadaccbaccadddcdcddadbbbdadabbabcaabaacdccabcbdcdaccdbcdbaabdbdcdaaabcbadabacabdbaabdbbbcdaaaccabacbdcabcbaaccbbaccdaddabdcbadbbdccccbbcddaaccadabdcbdccdaacbdddbddccdaccdbccdccaccbcbbddddaddddddbbacacadcdbcadcdbcbdacbdcbdddccddcabcaaadbbcbdabccdaabadddcbdccbcdcdbdaccadcbcddcccdcccdaaacbacccacbcdccabacdaddcbaacaaadadabbbaaadcaddacbbbadbdbbddbdcacccacddcacadcaadbbdcacbddbaccdbbcdbdadddbddccbadccbcabbaaacaabbcbcbadadbaabbbbcccdadacccdabbaaaaddcabbacdbdaddbabaccacdcbdbabcccccdbbccdbcdbbadddbbaadacdccabdabddcbabbbccccdcabdacaacbccdbdabadbacbccabbadbbaadddcdacabdcddcdcdbcaabaaaccacabcbdabbacddacabadcabcbadbcbdaadabcbacbccdbdbbacccaccadbacaaabdadcabadccddcbdabbbcbccbbbdbcaaddcbbadbcbdcaacacadddaaccdabcdcdcdbdddcadbdbabacbbabaabddbcbbabbaaddabbcadbabbdcaababcbdcbcadcbdbbdbddddacbcabaaccccbbcdbadadccaaccadcdddacccababbdbabdcbdaabbdcacbbbadaabcaaabcdabdddbdadcacddcdacacabdbbbcaccaaadadcbccacaacbdbbcbcbbcdaddacaaadaadacdaaabbbbcdbdbbbaddddbcadddadbbcdadbbdddddaadacbacddccbcbcabcbbadbcbacbccdaacdabcbbdadbdabdbadbdadaaaadacbccaaaaababdbbdbabccabcaaabacdacccdacaacacbaabbccdababdcccbddddaccccadcdbaaadadabcbaacbabdbccbdbbdbcddcacacaacdbcabbacbacdccdbbdbcbbcabdcbcaddbadcddbdbdaacdaadadcacdaabbaadabdcddcdcbcaadcbbaadadcdddddcaddcdbdabbcabbaacdbbacabbacbbccabbdbdcacabaaaabadbdbbaaddbdcadddccdadadaacbaddcbbbbbdcdcbcbcbdadbbabaadaacdadcaabcbbcdabdddcddbccbdbcabcddbabdabddbbabacbbbcbdaabdcccddbbdabddbcdaadbbddbdacbcbbdcacadabcadcadaddbbdadcbbadbadcbccdbbcddbaccaadbabbadddbadcdaacbcdcaabdaabaabcbddcbbacccdababcadbadccddddcdbacddadadcaaddbdbbdcdadcacadacbabbcbbbaddcabaccabaaaddadbddcdaccccdbabacbaacccddcbaacddadbbbbbdcbbbcbddaadcacacddcdabddaccdcbbbbcaccdcbcabcbacdddbdbccbaddccacccdcdbacaabbdcabdaacbcdddabcbababcdbccdccddaadcacddadbdadcbbcbddabcddcbcbdabbbcabaaacacdabccbbadbbcacdbbcdcbcccddcdcacabbabdddcdbaadbcbdcdadbccbacabdbbcdcdbdbbaacccccdddddacaacbbddcdbccdddbccbcadbbcacadacadadddcdabddcdbbcdbcbcadbcbdadcbdddaadaacdaaadbadaaccbdbbddddcbacababbadacccacdbddcabcabaadabdaadadbccabbadddadcbaabbcacccdbacbcbadbcddcdbdcbcdbcabbddbdacccddcccdccaadcadaabbabdbdcaabacadabdbcabddabcddcccbdadbcaacbcbaaaabadcdadbbcbaaadaaaccbaaddabaddcccccaabbbcccadcabcbcdbaaaadcbdbadbddcdaaaadbadcacbbbabaadbbacaacccadddbccacbcbddcbabdaccdaccdbbbcdaabcccbdbdbdbbbacdadbdadbadabaadababcccddaacccccadbbbdaadabcabaacaadbddacbddbbbbdaccdacaadacbbddcccbbcdbcadddcabdacdaacbcacdcbabdccbbabbadbccddbbabaccabadcabcdadddbcabbccadcccbcbddbabdcbacbdbacbcadacaabcdcaddaacddcacabbcdbadcccadccacdacdcaccccbcadbcbcadcbbcbcbdddcadaaacdcaadccabbbaaaccdbdcbaaadcbabcababbbaabddbdbddbadbbaabcdbacabdcadaabaaabdbbaaaadbbbaababdaaabcaccddddaacbcdcacacacdabcdbbcbbcbdbcdabadaabdcddabdacddaddbadadacbaaddbcbbdaacbabdcccbcabdacbdbaacaddbacbdbbadcddbaacddbabbdbdcddadaabccbbaaabcccdbccbcaccbcadacadcccdbabdccddcddadbdcaaacbaabcadbaabccbaabbdbaabdabadbdabbbaccaaddbabbaaacdaadcabaaacadcbadadcadadbcccdbcadadaabbdccbbbadacddabbcddcabbdcabadcadbbadabbcaccbdcdacddaaaaadbcbcbaddcaaccadbdadacccdddbdbdbcaaccbddadabbcbcbdbcaddcccadbbaacaaddabcccddacbdacaabcdbbbabacdcdbcbbddaadbcdccadbdaacabccbadadaabacdbdbacaccaadaddbaddbbbaaadcdbbcdabdabdccbbdccbbbbdbdccacababbacbaddbcdbaaaddabdbdbdaaaaadacaaabbdabdabcdcaabacdcddbaccbddaddbacddbdbccabbdbbcccaaddbabcacaaabacdcccdcbccbbcbabccbacbdcbdabbdccaaddaabbdbcbdcadcbadcdbbddcdcbdaacaaccaabccdcdcadabaaabcdcccbdbcbcbcbdadbadcabbaddbcaddbbdbcdbbbbccabcacccaabbbbdbcacbdadcccbdbacadbbccbdbbbdcdccadbcacbaddddabdccbcdaaddcadcbbcbaccdbdaaaadbdaabdadadabddbddabbbbdbdaccdbcddbaaddccdddbbcccadadbbaacccdbdcbbbacbadaabaccdcadddcccdbbbbcabbcacbbddabdabcbacbbdadbcdaaabbbcadaabbaccabbbccaabcbbdbaadaddabcddddcababdaabdcaaaadacbdabddcbabacdbaaaabddaccdacabcddddcdcbccbadbbbcccbcdcbbbabccabdacabbcccbbadbdbccbbbaaacaacadddbacacaadcabdcdccbaddacdaacdddaabbcddaaadbbdbdbbcbcbddbdaaccdacacbaacbbccdcdbccdbbaacdddbdadacdbcaddbdacbadbdbdbbcddcdaabcbdcccbcccbaaaccdbcabdbcbacccabdbaabbccdbddddaadddaccaacccbcddbdbabcdbbcbacbabaccbbdcbcaacbabdadbcbbcacadacbabdacddbcdcbdadbabbaaabacdadcdbbabbbbbbbcaddaababbbddcdbbbddbddcbbdbbbddbadacbacaccbbbdbbdabcbaddcaccbbcbbadcbbbbbabbcdbbbcbddcaabdbcddcddaccabadbcbcbcdcbdbbdcadaabcbddacbacacdadaaaabbbddcabdcabbcabcadabddacdaaaacbadbadbdddadcccccbabbbbaacdcddacdccdcaaaacbcabdaddddbbcdbbabdbddddadccbdcccbccbaaccdbdacbccabaaadbcabdbbaccdcbdaacbcacabdaabcdadcdcbcdbcdadbdabddaddbbadabdcacdbccdbacacadcbabcdacacaaddbdcacbdbacbcabdaacacbdcbbcdbbdacbccdbacdababacddbbdacdadbbbcdccacaabaabacbadcbdaccdabbbabdcdcadaccdbabbbbdbdabacaadcdccaabbbddaccdbdbaadaadcddcadaaabcdabbaadbdbcdcccdccaadaabddcbaddbabacacdacbcccaccbcbaadaadcccdcaacddbcdabdbcbdbccccdadcadbbdaaaccccddcbdbbcabcabcdcdbdbbdaabbcdbaaccabddcbaadcadbabdbdbdabcddccdbadbbdcaccbbbcbbacaacbacabdbacddbcdcaadbbaddddcacadcadbadacacacbcdaadaaaccaddccadccbdcbdcbdbbddbcdacbabbdbbcabbdabbddaaaddabacbbcbdbadcddacbbddcbabcdbababbcaadacddbcacdcddccacbdabcbaaddabdcdccbaccdcbdaabcdbdbcddbcbbcabaadddabdbcddbaaacacdcabdcbdacbbcdcccdaddbcaabdddbacabacbacdcaadcbadaacacbbbbbaacbaaccbaadaacdabcaabbcdadcadbadbcaccabadbcaaabacbdacadbdbdabdcbbdcdcbbdcddadbdbacdadababaadccddbacbddbcadccacaabcabddbcaadadbbddcabbddbadcbcaacbacacaddcaadcacbcaaabbbadddaabccdadddcaccddbaacdbbbaccabccbcbdcdbdaabccdabdbdacccccbadadaacbdddbbaddcccdacbabcbabdadccbabbaaabdacaacdbddbaddbdbbccaddbacdbddbbdbbcbdddaadcbaabccccdcacbccddbcbccadacdbccdcbddcbadcccdcbabbdabaaccdbadaddabaccccacaaabddddbcbbbacadadddbadcabdadcccbdccddcccadadbabcdbdcbaacadcaabcadcbbaabaccbbbcddddaaddbddccbbccbbbbdabcacbccdccdccbcccdcbddadbbbcadabbbdbababcddaacddbacdbbadaaccccddbbcabcadcdcbdcbadabddaacdddddbacdddabcacbccaacbdccacdcabaacdacbdcdbcaccbbaacddaccdbdddcacdadcdacdcddacbdbbacdcbbddcdbbcdddcbbbbacdcdddbbbbbadbcbbccacadabdcaadbdadadddcdcbdaaadabbcbdbbadbaabbccbcdaabbaaabaadbdbcaaabdbcdaabbdbcddadcbaabadccddbaacbdddcdbbbbddbccdcadddddddbdbcbcddcdccbaabddbbdddcdcabcbacadbabbdbdddccdcdaacbddabcdadbbbcabcacbacbcbbbcdbdadbdaaadacccabbccbcbacdadaccbaddcdbccabccdddcdbdcbababbccbadbdaacccdcddcbcccbcaacbddcbdbbbaabbcaacdacaaabaadbbbbdacdacacaadacdccccbccbcdaddbadaadccccccdbbcbaaaabadaaaadddddbadcddbdcbdddccbdbccadadcbbbcabbadbcddcaddcbddccadadddadadcdbcdcbcbadbdaaabaacbdbddabbbdddacaccddcacddcdcaaacdadbadbccacacbaddcdaadadbaaabdcdbdaacbbddbdbdabcdabbacbaabcbcacbddcdadcbaaddcabbbcddabbbdaaddcaacaadddcabdabbdbbbabddbcccaaadbbbbbbdcdbdbbbabcadbbcaadcccccccdcdcdadddbcaabbababdbdbccbadabadddadccaaaddddbaaacaabbbaabdaacaddcbcccacdcabddabcaaabbcbadacbabbbcadabcdcaccdcbadbaaadaacdbbbaacddcbdabdcbdcdcddbbaccbcdcbaddbabddcbcdabcacaccabcbcdcddbccbcbdacaabbaddaaaaacdbdccbbbbccabccdcaabcdadaabcbaaacdccdbbaddacdcbdaacaaddcccbdbcdaaabbbbdacdcdabdabdbccdadddccdabdddbadccadddabcacbcdadaacadcbdbaccbcdaaccdcdbcdbbccbcabddccacbacbcbbcabdcabcadbaccdbbaaccadababdccdcbcbcbadbdcbaadcacdcacacabbcbcbcabddccaabcddcabddadbbacbbcabbccbbbbddcbacacbcadadbcdacbbadaaccbbccddcccdbcbacdabbabdccddaaadcbacbdbdbdccbdaaacccbdccacdbacbdcbcdccdaaacaccdaadccbddaccdbaadddcabddadbdacabcacabcaaadbcdbcdadcbaccccbdcbabbdabbabdbbddaaadaccbbdbdabaaadadcaccccadbdcabbabbbbabbadabcaaccacbdbcbaadaadcbbdcaaaccaccacacdcccbcaaadabcacdccdaddbbbdbbacccabaddacbaadcabbaabaddddaacccbadcaddcabbabcdaaddcddabadcbaaddadbddbcbbcabcddbacddaadcacdbbadddabbbbadbcbccddcdbbcabbbabcbbbcdbaccbdbdacacdbaccbdbaabbababddcacaabcaddacbcdcdcdcdcacabbacdcadbdadadaddccdbdbbdddcaaacbacbaadabbcdabbbdaaadbbbdabdcbbdaccddddbadbabbdadadcccabcdddcaacaccdbadabaaacbbbaaabbddcdbdaccbbabdcaadacbdddadddaaddabacdbacddbccaccadabcccdcbbbabcccbbdddaccbccccbccacacbacbdbdaaccbbbdadbccacbbbdabadbccdaccbaddbabcdcadbabbabcbcacdabdcbcaaaabdcbcdadddbbcddaccdacdbaacababaaaadbdbbcacacbccccbbcdbdadbadbddaadddabcccdacaacccbcaacbddabdcabbdbaabcdcabbbdaadcdcabcddadccdddbbbdadabdadcbbcabdcbdcaacccbaacbaaadddccddbbadababacadbdaaabdbcbacbdcbccbcdcadcdccbdabbbdbccbbaccbbcbacabdabcdbabcddcbcddbcddaacaabaccacbddcccacddabdccccaacbbabdbdddbdabcccaccbdaddaaadddcbbdadcddbacddbdabcdabcbabddbabdbbcbacabcaadcbcdccddcadcbacbddcadcaabdabacabbadbcabaddbabbacbdcdcbdcbcccaabbcacdbaadacbadbabccbbcaaddbcacbbaaaacadcdbcccbbacbaddccccdbddcddbbdbbdcbbbdcddcdabcbbdadcadddacbcbbbbddaababbdacccddacdcbbbccddbadacdcbbaccdbbadcccadbabcbccdabdcacdcbacdbddabdbacddbdbdcdbccddddcbdabbaadbddcaddadbbaababdabababccbcddbdaddbaaaccbdaccbdbbcccddbbdbabdaddcaaacacdddaacacbaacccbacaaaabcaccdbaccdcdcdaaaccdbcddbcaacdacbadbbbbccaccabbcbaaccabbddbdccaadcdcdbcbddbabaddaabdbdcdccaccacdcacacaabdccdcdacabdbdcaadbccbbaadbdcaccabdbaacadbcbccbbcbcdcccddcbdcaaadabcadaabbabcbcbcdbbdadbaabccbadcbacaddcdcbabbbdccbaddabccacbdddddcaccddcdbddbbcaddcabbadbbacaacacdacabcccdbaaaababcdcdacadbdbbacbccdbccbdbadcabddbadcdbbbbcdcbdabbbcbcabbabdcdabaabaccddbdadaaccdddbacdacccdbbdcacbcbdcbbdabdddbdbdcacccdadbbcaabbbbacabbbcdadaaaadabcdbcdbabcabaaacccdcbdbdbbddababdbcadddcbbcabcadaababbaabaadbcabddbcdabcaaacbcadaadadabaacbadaabddabacbbcdcbacbddcbcbdcbbbbdbbcbbcdcbbbddabcadaaddccabaddbddcbaccdbdddbccdaadababbccacddccdccbabcccabdbcccaccdadbadbddaacbcaacabcbabddccdcdabaadbcbddccddabddcdbcdaabddbdcddcabdbbdbdababbcaccccbdaaaadcbcacdddacdbbaddbccacaadbbdbcbcacccaaaabcdbccacbadbdbbdcbcacbbaacbcddacdadabaccdbddcdaabbabcaaaaabaaddbbddadaabccbabdabcaccccdbcbcdbdddaababdbdbdabcaccbbcacbdcaccdabdcbdccbccdacbbdbdbadcbadcbdbbccacbdbaccadcbcdcaaddbdacdcaaabaaacabcbdaccaabddaddcaadaabbadcdabcaabcaaddcabdaacaadaccdcdacbbcbcbbbbbbccabdddbdaacbcdadddabbdacdccadadbaddccbdbbcabccdadcdcdacdccbacacccdbbabcdaaabbacadbababdbaddadbdcbbccadcdbbcccbddaacaabbbababcdbdbdbcdacbaccdacacbcdbbbaacdbadbccacbccabdadcdbbbbdcbcddbcbaddcabacadcddbbdbacbadbdacbcacaadbddddcbcdcdbccdddcbbbaaaaadcacbadbbbdbbcaabbbcbacaadcbadacadbccbacdbbcaadbccabaaddbdbcbccbabdcddcabbaaacabadbacccdcaacabbcbcbbabadcddbcdadaacddcdbbbbaadacbcacbababdbdbacbaabccbabaacdaabcadaabaaabbbcbddccaadaccbbdabacbcccadccdbbcccbaabdccaaddabddddcbddacaddcadbdaadadadbacdbcbacacdbccdcdccbcbcaddbbdabbacbdabccacdacdcdcdaddaccdcbdccacdabbcaccaddabcddabcdbbcbcadaccbdabcbcdcabadabaccabccadddddccbcabdbdbdadccddcbcddbabcadbacacbbcdcbaadacacbccaaabdbbcaaacdcdcdcabdacbaabababadcdbabdacbbabbbcdcdbaabdabbcdaddadccccbccacdbdbadcbdaababbccacdcaacccdbcbcdacabcbbbadbaccbccdbaddccaacbdbaacabddbddbcddcabddbccdabdbbcacccdbbdbdabdbcdcacbdaacabcdaacddbbbbcdcacdbbbdabcabdadcbcaaaddadddbddadabbbbdcccdadbaabbdacdabbaabcbacbcabddaababaacbbdcdcadaabbdadabacbcddcddcdadbaddbdccaddaaacababdcbdcdaddabddcaacbbcbaabcadadcdbbdaadbbaddabccdbcbbadaaddccddbcadaddadaadaadadaacddcdddaddaadadbbaadddabbacbbcaabacabbacdbcbbdcabbabcdbdcddcdbdaaccbdbabddcbbdacbdbdaaccacabccdbccacccdcdcddaccbbadbcbbcdadaadabddccdaacaacaabaadabcbbdcbccdcdcbddcbaaddbdbcbdbaadbbdddaaddddcbbbbadbdaaadcadccdcaaaadbdadaccabdcaaaddbdcdaabddaadadccaacbdcbdcccbabaaccaacbacaabccdbbadccadbabddcbbbcdddbdaaacdcaaabcbacbcacbcbbddcacbcaccaccdabaabcbadadcdaddacdcdccabacadaaacadacabdabddcbdacbaddddccacbabdadaccdabcacbabadbcddadaaddbcbcabcdccbdaddadcdcbadccbdabdcaddcadbcabbbcabccccaacccbdcddaccccdabbbdabbccdbdadddcaabdabbadcbdccdaacabbcaaccbaccadacdbdaccaddbbaabccdcaccbdcdbdaacddaadcbddaadcbabcccccabaccdbccadcabbcdbacbaccdacbacbcbdbaaaabbccddcdcadadcdaddaccbbcdadcdbbacdddcacabacadbdbbcbbbbadabcbdbadbbdacadbdbaddbbaabcdaddbbbcccdbbcacdbabbcacdabdbcbcbabbccaaacacacabbabcdabbabaaaddbabbcbcbbbdcdacdaacaacdcccbcbcaaccdddcccdccaabcccbcbbcabaacdaabbcacadcdacdcddcdadbcccbaccdabbbacbdacabcbbddabdacbabdbcdbaadacddbcdbdabccccbaadcddcadddddbdbaaabbbdbdcbccabbcbdbcbbdcdabddabadbcdcbbdddaaccbccddacbbbcbadcbbaaacbcbacadccacabccdadbbabaabdabdbdddcadaddccbcbbaacaccdcdcbabdabdccacbbddbbccaccbaddabbccbcdabdaadbbaadaacadbcbcadcbdbdabbddddcdccdbcddbbccaddbadbabaacadacabbcacddcdcbcaadcbcadcadddacabbacadbcbbabadbabdbcdddabdacddcdcdabcaddbcbdcdcabacbbacbccbdbcabddabcbcbddccaabacbbbabaabccdbdcddabddccdbccaacdbbaabcaacacdcbbbcabddddbbdacbacbdbabaccbbbbdbaaccbdacbcbabaddcabdbaacdccbccaccbdbabbbdbccdacddacdcdcadcadcbadddadcaabcbcddbcccbacdcaccbabddccadbabddbabccabdcbbdddbdcdcadabcacadcddcdcddadcdddcaadcaacccbabcbdbdacbdddcbccacabccbbbbaacdcacbcccacbddbcdadbdadaccadccbcdcbbddbaddadbdbcaadbdbbccbbdbaaaadbbadbbabbcabaccaadcacddcbbdacdbadbbdddcbdaaddcbdbbcbcccdbaccccbcccadcdadcdbcbacaccdabaddabdabdabacddbcbdcccbbacacbacaabddbdbdabcaaabccdbadcbcbbaaaadabbcdddbaccdcdacbbaadbcbcacbaabaabdcbdabadccaccdabdcabbdabdabddacdaddcdddccbcadaabbcabddcabbacbdaadacccdddabcacbccbccddbcbbcbddacdaaacddcbbbbdcdcacabdbbacccdbaddddbbdcbddcdabdbbaaccddabdcdccbaabadabbcdbdadabbdcaddabbcbcbadbcbdcaadbdcdccbabbbddacddaabdbadbccabcccbbccccbdaacdadbbcacaacdcabbadcccbadcddbbacacaccaabbcbcddbddbacabbddacaaaadcdcadcdaccabcbbcaacaaccaddbbadcadaddadcbbcbddccadcacbbddbcbcdbbbbabcaaaaadaadabadcbbababbababbcbcdccabccbdbbaaacaabcdcabbbaaccccbadbcbcdddcaabdddddaaacbdccdddacadabcbdbaaacbabdcddbdbdddcdabbbabbdcacadbdaaacabcaaadcabbbdcccdadabaadbbcdaabdcaddcccbdabaadcdaddaacaabdcacadabcdcccdabbcacbabcdbcdaaaabaadddccdbdbcbbaaddbdcdbbabbcabaccddaddbcbcdaadaadadadabbcdcaadcbcbacacbddaabdbbddbbddadacddddacabbdcbadcdddbadacbbdacbdcadabbbddbdbcbdaabcacbbacbcbbbdaadcaccbdbadbbdadacbbcdbbbaddacadbcddddbaddabdccdcadcdbaddcbdabccadadcaddcddbdcbbdcadbdabacbbbbaabadadacdbcbdadabbaddbddccdacdbabbdaadbbdaabddbabdbacbbacabaaccabadddddbdcadaabdadddabdbacbbacabcdbcdddbdddaabccccabcbdacaaccbcacadabbcaadcbddcdaddabbbccdaaaacbcdbbacbacdbbaadaadddbadddadcbbdcbcbdcaadccdacdbaacddccbabccabcaadadbcadcbbcaccadbbaccaaaaaddaaadccbccadcbcddcabdcddaadadbccaababacccabdcdbabdddcacabbbbabbabbcaccdbdabadcbccdcdccbcdcabcdabdddcaddacbaacabdaaadccadcbbdcbdadcaabbaaadcdbbdccccdbaddaacdadaadadbcbaadbcbadabcbabdadaaaadcbbcbdddacddbaccabaacbadadddcbbbbdcaddddcaadbbdbcbbbacddaddcabbbacabababcbbbcbdcddcaacacaccabcdbadbdcbacbcdabbacbadbdbdadadbbadabacddabcabaddbccdbadabccadabcccdddbbdabdddaabcabacdbadcbadcdabccadaaaacbbbadcabbdadacdbbacdcbacadaaacbddbdbcaddbbcccbabacbdcdcabdbbacdbabcdccbadccdaacbcaccaaaacdbabdbddcdcdcabcadccabcaaaadccaadbabcccbdabdaacdbabdccddcdbcbacddacdacdacadbccdcbbaacbdbcdaabaddcdbcdbbcdccaddccdcdabdbbddddabbbdbbdddbbccdacbcdbbbddadbccddcdbabadbdbdbcadabbaddbcaaccadcadcdddcdabbacbaabdabcdadaacdcaacccdcdbcbbddccbcbacbaadbdcbabdbaadcacbdbcdcaddcdadaccadaccbadccddccccaaabdbaaadbcbdbabbddaabaddcabcacdcadabdadcdbbabccbbacabdacbdadddddbacaddacbbaacccbdbbaababcbaccbbbacdbdbbaddacdbacaccaddaccdcdbdaacdccdbcabcbadcdddaadcdddaaaaddcbbddadacdaccccadbadbacbbadabacddaaccadddccaadaaccbcbdcacbaaacbaadddbbdaaaccabbbbbdcdabcccddaddaacaabdccbabccabbcacabaadcbaabacaaaccccddcabcbacbbdcbaddbdaccbcaddbbbacabddcbddbdabcaccbcabdccccccdaacbcdabdadadcaaddbcccaccbbdabaaababbbbccdacbcddbababddcbdaddabbdcbcaaaaabacdddaddacbddaddacbcaacacadcdaaabccaaccaadcadadbcbccbcccbabaacabbdbcaccabddbaaadbccbcccabbacdabbadccccdadabacddbdccbaabcbdadbadcadcadddbbdbcbbcbcbcaadabacbbdccbcbabaddadcbbdcccacaddbcadbccccccacddcbccbcbabccbddbababdddaaaddadbcbcaacdbadbbcadaccdccbccdbbcabdcdcbaabbcccdcccdcbcdcdaacacabcdcdbadbcbcbadbdbdbaddbcdcdcbbbcdabcbbcdbacadddbdcacbadddcbdcdbcccbabcabcbaaacbbdaccbabadbddbcadbabacadcbcbbadacdcdcaccdabdacacbcdcdcdaaaadbbdcbdddacdccbbcadaadcbbcdbddabdbcbcaaccdccadcdddbbdbaacbabcdacdabdbcbbbbcbbadadadaccabbbdbaadbbbaabdbabdadbdadaaadbaacddbbbaadbbbbaadcdabacabaaabbdacdcdabbaaacbcaadacddbddacaabadcabcbcaddccaacbadabccbbdaccdbdabadabbcbdaabbdbdcabcaadabacaacaadcacbcbdabbddcaaccacabdcadcdabaadaaacbbccbaaddbddcccadbbcadcdcacacccaabadddaaabacdbbcbabdadcbcbabddabcdcadacacbbbabcdbacabdddbbbbcaacdccdbdbcdbdbddaacccddcdaccdaabdcabcdbdddcaadacbccaacaacbccbbabbbccbcccdbadabaaaadadacbacbbacdaabbbacdaaaddcdcdbbdcaabbdaabbbbcaddddacdcdbdabcdbbdcbbcabcbcbabdcdaccccdbbbdabdbdacddabacacadddcadaccadaaaadcdadcbccddaacdacbccdaabbaadcbcddbccddcdaccbabdcbadbccddcdbcbaabdbcbdcdbaabdddbcbcaaabacdbaddcbacdabddaabcddcdbdcdabacddcbcdbacaaaddbaaccddccadddbacacacddbddccaddaddacacccadcddcaddcdaccbdcabaddcdbbdbbcccbbdadbbabcbdccdbaabccacddacdddacaddaacdcdbcdcdacddbcaccabaababcbccdacbdaacababdadcadbadcdbbaabddcacdacdcbaadcdcbabacdcddaccabcbdbcbddddbbdacbcacaaaddaccbdcadaddaddbccbcaabacaddbbbdddacddcabadbbdbcdddbbcbbdbacdabdabbdacbdddadaccbaadddcbbbbdadcdbcbccabbbcccadcdacdabaccbbadacbdbdbcccbcbabcdcdbbbcaaaaaadcadacccddbbacbbacdcdbccabadcbccaacbdcbcbdbbdcadbdbaccbabacbcaacdbcdacbcbaacdcacacdabcacabccdbcccadadbacddaaaacdadadadbbbdabddabdcbbcdddbdcddddbdabdcbbdbccbbddacbdacdbdadbcadbccbdababdcacbabddcddcbaccdddcccdabcbcddcdccacdccbcdbddbadbcbdbbcacdbcdaddaaacaadbdddcabdbcbddcddbbdbbccbaaabddbcccdccddccabbacacbcbacacddbacdcbdbbdabbabcaadbbabdcbacbbcbabacbabadabadccaccdbddbddcbcbcbcabcddcbaabbabbbacbdaccdbdbbddbddcbddbcaaadcdcdccbaccaddbacabaabcbdbdaddadbccccabaccdcdbabbdcdadadadaadabbadbacaabcdcaabcbbaabccdaadbbcdaccbadbabcccacdbadbcadbbcdcabadbcdbbcabcbcbbacaddbdbbccadbddcbcabccabdcccdacbaaddcccadcaaccadbcacbddbcccdbbcbbcadaddccccdcbbbcabcbaaabcddaabdbbadbadbbaddabcdacbaccadddcdabacdbcbbbcddaadddbcbcbdaaccbdcaddacaabbdddbadaccdabcaadccdcddbadbbaacadbbadacccccdadabbcddacbcaaabbcbabbdccbdababadddccaacbdbcaadbadabacdcccadabcadccadacdaccbadddbcdbbcaabccbcaaacdaddccbddbbcbccdaaadbcadcdcccddbdacdbcbbcdbcbacacdbbadccdcdbbbcadbdaadbbccadadccbcabbabacccaaadbccccbaddadcdbdccddbbcbcdbbcabdaddadacdbddbbabadacdbdaaacbbdcaabacdcddaddbbcbdddcbcbdcbaadddaaadbaccdcbadcbbcbacadbcaaabbdacbacbdccdcaaddcbbcddaabddbadbbbbbbacbcdbcdcbcdccaababcbbcabdadbbdccdabbcddddbabcdabdacaabbbcaddddddadcacddbccbddbbbbbbdbbcdcadccddbdccacbcbddccdbaddbacacdabbcdadabcdaadccdbbabbadccdcddabbabaabdacbddadcdbdbdddabacddaadaaadbaddadcacabacdcbdaabcccbddbabdcbbaaadbcdcaadccacabbcdcbdacdcdacadddaabdabadcbcabaaaababaacddcacbddcbdcbcadbadcdbcdddadccdadbdabdbaaaccbbdaadbdddcbbcbadbacbbddcaaaddbcabddcbadbbabddcccdbdbadcaaaccbcbbcbccbcdaccbcadcdbcacddbadbacababbbcaacabdabdabacdbacbdbcabcaddcabaabccaccbadcddbadddccbbaadabbbdabdadaddabaacacabdacbdacdddcaabddcabddbdbdcaddadabdcadcaacdcccadbdabcdbabccbbcddbdbdacaacdcaccdcbcdbbdcbcdaadbcbdaaadbcadcbbdddbbabbadaccdcadabcdcdaaacbaadacbccddadaacaabbcddddddbdabdbbadbccdaacdbabadacadcbcadcbcbcdadbdddcbbacadccabdbcbcabacacadbddcdadccdcbcbddbbcdbbcaddcbabacacdcacabbbdcacacadacbcbdbadbababacbdacaabbdddbcbbdccabcdabbbdcbdcaddccabdbbdcadbacacdbaabbadbcdcdbbdaaaccdcabcdbaacbddbbcadddbbdaadadaababdcbbcccacbbdaaabadacadacbcbacaddbcccdadbcdcdbdadadabbaaaddcbababaacdabbabdbdbdbabdadbaddcbddbbddcddadbcbbabbcbabcabbcdbbdaacccdddbbbdddcbbcbcdddadacbacbaccbddacbbcbccdabccddacbbcaddbbacddabacdaadbaababdabbbccaadababcccabadbacdcbcccdbacccacabadacbacaddcabcbcaddaaaabadbaaaaacbdbacbaacdccaddbbdcbbacdbacccadbdaccccaaadcacddacbcdcbdcbbbddddddcbbbbbcddacddcabdddcabbdcddbdcabadadbdadbbadccacddcddccbdacabdbcbdadbbabacdadcccbbcdbbbaabdbcdbbaadcaccdcbbacbbcadaacccbabbdddbbcddbcaccdacbcabdcdabdbcbabbdcabdcabdbcdddbbddcdcccaaabdacacdaabdbddcaddbdbaddabdcadacdbacaacccddacaaadcbddaaaddadcaabcbcabcdccbbbcaaddcbddbacbccddbdddcdaddccccbcbaccbcbbbbdcbcadcbdbdbbcbbdbcdbbaadbcbddaabbadcabaddccbabdccacddcacacdbcacbbcdaddbaacbcbbadbcbbcddaabcabdbadcbcdbcddcbccdabcbccccbaadccdcbcabbcabcacdcccabbdaccabbddcabddadbacadcdbbdcccdcdbbbadadcbbdacdadbbdbabcccbacccdbbaccbbddaabadcccadddaabcbbadccadcdcccccdcdaaccdbbcccbacbabdaaccbbbdaabdcdadcbddbadadabdcacabaacdcdbcddcbccbdcddbadbddbdbcbdbaaccdcddbcbcacbadbcaabcdabaacddabddccadbaddbcccabbcbccbdadaaddabbacdbbcadaadccbccaacdbcbacdcdcabaacbdbbcacbcababcccccdcacdaccabdacaacdaaccdadcdabdcabbdaababbbbbcdcabbcccbaacacacadaddcabaacbbcabcdadbcccddcacacacbbcdbbdcabaccccdddbcaaaaaaaccdbaacaccbbaddadbcbbddbdccacdbacabbcacddadabacbcbbbdccdddbacdabcbcccdbcabcdbbaccaadabbbbdcbccbbabcaaccadacbbaadbacbbdbaaaabcccccdcabcacadadbaabbcadbdabbcdbaaadbcbbcdababaabcdcbadababaaccbaaabccacbdabbbbcdcbcdabddbacabcdaccbadddcdcdaadcccbbbddabbdacdacaccddbcbbbabcdcaaaabcccbaacaaaaadaaaabacadbcbbbbabdbcdccdabdcdbbdddcaabbddaacbdaaadcccadaadbaaaabadbccbbcdadcacbbcaabbabcdccbcdcaccabdaabcaabbcadcaaacccbcbcdcdbbacaccadaddcccddbcddabbdbbaabcdbbcdcdaabbddcbadadabbacadbdccaaaccbaadacaccdbacdbbbcdbcdbdbabadbdcabcbabadcbcbcddbbcddbaccbddccdccdbdddcbcccdacbbcaadbacdcabbbbbdcaacabaadcddcbddaccabadaadbcbdcbcdabbdabababaacbbacbcbabdacabdadcdbbdcbbddddcacaaddabcdcadccbbcacdadbcbddddcccaaaabacbcccaaabbbbbbccbadccacdbacbcdccaabdbbddccaaadcbdcadaccaaaaacdcbacbdbababcccdabaabbccbdcadbaddababcbcabadadbdddadcaddcbccbabdccbbdccbaabddaabbccbaadacccbddcdcadbacaabbbdbbaabbcdccccbbbdbbbbdadcbaccacdaacdcaddcdadaadbcbacbbabadcabdbcccdadbabdbcabaadacacbbdddadcacccadacbdaddbdaaaaaaabdcbaadcccacaabaddadacbbdccdaccdddcbabbdccbcaabbabaadaadabaaddcaccbdcbbbccbaccdbcabbacdbdccccbbddbdaaabddbabaddcaaccddbcaacbadddadbbcdaacbaaddbddabcbbcbdbdcaaabcacaaadaccbcadcaddddcabbaabacbcabddddddcadbabbdcccbbddcaabcbdacdcdcdbdbdcbcbcacdbbdbcbddbccddcdcaddbcbcaccadccccacbdaaddaabcacbdddabbddcadadaaaababcacabbacbddbbbccbabdbcdccdbbbcbbcccbabcbcaddcdbcacbaadbaacbadadbacacbbacbcbaaabacdcaadaaabdbcdabdbaddcbdaddaccdddaddddbbdbcddabbcaddaccbadcadadbdcddadbcdbacadddabbcbddcbdbcaccbbdddcabadddaaadbbcdbadbaacbbabaacadcacacadacdbbadaacbacbbcabbacaccddcbcddbdabbbbadcbabddcdadadbcdcbbbbbbcbccabcddbcbbddaadddadcdbacdddbdbadbdbcdcddbdbbcaccddbbbcbcbabbabbdabbacbbccaacbcdbbdcaaacbdaaadcabadbbbbccaabdadbddaacdbabbaabbadbabcbdabcbdbdddddbbacdddbdbccddddbcabbdbcbcbcdbdadadadbbcadabbbdcaacabbdcddcaadddbdbdcadcbabadcadcbccbacddadcdcacdabccaacacbdadaccbdaaadacccdaabcdaacdcaabcadcaccccbbcdbdadcddcbbdcbcbdabdcdabaaccddccdcccaccdaccadacbbdabcbdccdcdbaddbcdccabaadcccaabcccdbdaccacdbbbcacdccaaddaacaabbbaadcaaccbbaabddcddacdccaabbaddacaaadabbdadbdacbdaddcabcaccbbddcdbcdccabdaaccdbdcabdcdacdaadbbccbbabbdcbadcdcbdababbcbbcbbbaaccbaddbdcdddcdccdcdcbcadddbaaccaccbbadbbccdccdbdbacacccdcdbdabdbaddbbdadbdaadabcdaddbdadacbdbdbddcabddddbabaadbbaaaacbaaddaddadacbbbabbbcccbdcdadccbaacaaddbddbcdaaaddcbabacbbaddbbcabbdaddbbddabcbbddbccbaacbcbbdddbdbcaabbdcdbdacabdcccbbacdcbddaacdccbcbaddbbaddaaaacdabdbcbddbcadcddacbaaccbaaabdccddabcaadcdbabdbabddabcadaacbdbcabcadcabaabddcbcbaddabdbbbdbccabcdabcbdadbcadabaaadbcadbacdbbbccccccabdabdbcacddadcdadbccacbddbbdadbdabcbcbbbdbadbdbcbdbadadbdcaddadadbbacdbcdccabccaccdccdbbbadcdccadbbdadbaaaccaadbbabbaacbccccbcdaabdbacbcbcbcaadbbdbacdbbaacdcdadaddbbbdbcbabcaacaabdccadcbacbaadcdcbddddbcdacdcacadabdccbadcbbdababbdaabcabddaadaccdadaaccdcbcbcbabcaacbbbbbacaccddacaabcbcbddbdcbccabcbabcbcacbacadcaaccdcdbdcbcabdcdbbacdcacccdcadbccbcbccaadbddbbbcacaddaabbdcccbcadcccdbbabddacacbabcaabcbcccaabcabdddbaaccbdbabbabdbccbbacdadaacbdaadaaabddcbbddaacbaabaadbcccaccdcddaaaaaadddcbcbccbabdbbccbacddbdbbacbccabaaccaaabadbaabacddbacbdbbcacccdaaaccddacabbbdaacccadbdddacaacabdaddabbcccbcadcabdacacaccbdbdcbcacbaabaacdbacdccdaabdcdbabacbcddcbddaaacaacbbadddbaaadbabbbbcdbbcddcdcdbbdbdcbddbabaaabdbcdabcadaadbbcadaddcacacbaadbcbcbcbaacdbdacbbdacdbdbdddadcaddbcdaddbbcadcaaadbdadcacdabadccbababadcbbdccbabbacdaaaaadabbcadadcadddbbdcadbaccadacbccbbdbacaacbbcaddabbdbbbdcdaacbcaabbbaccbcaadbdbbbadddaaddacdcddcadbbacbdaacddbdbaaabcbbcdcaacdcddbadcacbcaadbcbabadaadacaaaadadcbbbcddadbdbcadbdbbacaababdbcbdcadbbcaacbcacbbbaaddadabcdccbbaabdaaaabbdbadbacbabbadaaabdbdbcbdaddccacbbdccbabacdbdbbadcbddadccbddbadacdabccbcbbdbdcaddaadcbbdbdccdaadcbcbcabacbcddcacaccdbbdcacddccaddaacdbcadbddccccccbdcaacaadcdacbadbbdcdbaabaaaaccadddccaccbdcdbdadcdaadcabbdabdcbdcbcadacbdadbbacaccbacdccbcbadddcddddcdbbaacdaccabcbadcacdbddddcdcddbdaccabcaadcbcbbbbbddbbcabadcbaabdcadcdbcbddabaacbdcacaacadaaccbcadccdddbdbbcaccbdcbcabdcadddaadaadcdbdadccdbccbbcbacdaccabdaccaccddddabdcdccbdbddbabbdddcccadadabccdbacccaccddaacaadbacadcbbbbdbccdacccbbabccddbdcbaacadabacddbdcaddaacdaadaddbccbdbaaacbbaddbcaaabbdddbcacbababdcdcbcbcbbdcdcdcccbbcaccbdaaacddbcdacdbccabcbdccabbbacdcabccacbcbcddaccbdbcbcdabbccaccbccdcbcbacbcadadcdcacbccdbdcdbdddbbabddbbaccacaacacdcadabacddacdbcabdcccddcbcbaadccddcdadbdbbdbcdbcbdacdcdbbabbabcacadccacabcbbdbcabbdbcbddaccdcbdcabcbacaaacdccccbbddbbadaddaaacdcbdbbccddaaadabcdaacbbaabbcdccbbabdddccabdaccbcddcdacddddbccddacbaaaccdbbabbccaacadababadbaddadccaadbdabcadaccbdddbddbaaccabadcacbadaacadddddcacaccadabcabccccccaaacbbaaddcacccddbcbcaaabcdcdcdbccbbdcddbdcbccabcbcddbaacbdcbabccbcddcbbccbdbcbbdcdadccbbbbaddacddadbbcbddadcaccbdbdcadabbcccabdbddbccababacabbacbbcaadaddddaddadcaaaccbaccdddbddaaddccccabcbcbcabbbbccadcadcabcccdacbbbcbaacabdcbcdbbdcdcbadcbbdaadbbababcbabbdadddadccdccdcacccdcccbcaadcadbadccdacbdbabccaacbacccadcdabaccccaacdcdaadbcbccadccaaaadbdcdaacdcbccddbcccadbccdadaabddaabcabcacababcbbcadbcccacdbcacccddacbbbdbccbdddaadddbaddacccabbbdcdaabcbdbbacaddbbbaaddacdabcbcbbccbbdcdccaacbaacadbaadbbaacaadddadddbcbcdacdacbcccdbdabdabbbcabdcaaacaccccadbddbabaaacaadcaaccbaadcbcadacdacbddacaabbcdcdccdbacadbacbddaccdcddcdbbcaaadababcccccddbbbacdbadabbcbdaadccccdbbaaabdccaaddacdaccbcadcbabbaaadbbdabdbccccbbccbcbaabaacddcdbaddbcacaddadbccdcadaaddbccddbbbbdbcbdadabcccdbadcccccdadcbabcdddddcbacdccabbdaabbdbdacdddcadaadacbdacbddcdbadbaadbbabdcdbccdaaadaaabbcdcbdaacacaccbcaababcaccbdcdadddcddbcacacbcdbcacabbaadbccaacbcadcdccbcdccddbbbaadbabcddcbcbbbdcccccaaccbabacaadcdbadccbbbcbdcacdcacadddbddccaaaacdacdbcddadbaaabaaabadbaddadacdbbaddbdbaacbdcbabcdbbacadadddadcbcccdcccbdacacaabcddbcccdabcbcdaccbbaddddbbabbcdbdbcccccabcbdbadbaccdabcbcadcddbaddcbbabdcbdbddabdbddbcadcdddbbbcaacaacdbbbdaacacabaccddbbcdbdabbabaacbbbacddddbccaabdabcbbcacdddabcdaacbcacaadaacbbccabbcbbabcaddccbccaadbcbdaaababdabcabdbcdadcadbdaacddddbbddadadcaabdbbbdcbbbbacccbccdcaabccccaccccdaadbccbcabdcbdddcbdacccaacababcdacaadddddddcddbbbcabbdcdddbcbdccacaaacbbaaccbbbcabdddbadabababdacacbabccddcdcbbdaccbdcaabcbbbaadcdabbbabbacaadcdcbcbdbaadbcdddaaccdacdaabbdbbbbddcdaaabdbdabdcbbdabadcaacbdddcbbccbdcccbdaaacdccacabbbcabbdadabbbccccaccbddadcbaaabbddadddcdbaadadcbbcabbdcbdabacacabcaaaaacabccdccaccaaabcdadcdbcbadbddbabbcbacabdaaccbacadbdcccdacbbcbdbcaccacdabbaaaabbadbdbbabbcdcaadaaaacacccdbbcacddabbaddcccdcddccadaaadbbccabddcddbbdccbdabaccdbdadaaabbcacdadadddbcddbbabcbabcbdbcbdcddbadaabdbddcddbcabcacabbdaaaabcadbdcdcdabdadbcbddbabdbacabcdbccbcddbdbdcdbadcddacdcddabaabacccbababdbddcdcbbcadbbcababdbccadbdbbdbcdcabdbaccdaabcbbbccaaddcaabadbacdacabdbbdacdaaaadccadbcdcadbababcdabdbccdccabcaccccbddbabaacaddbdacbddcccbcadcccaddbdaadbdcdbadadbabbaccbdabadacbadccbaccbcbbacdcddbbadbbaaccdbddcdddacaabcabcbcdbaaabbdbaaadcdddcbbddacabbdbdbdaddabaaadbaacbcaaadacbbbcdbbcaabcbacaababaaaabcccbbcddbccddabbcababccabbbabaccbbddacddaddbdabcbcdbcdaddbabddbabaacbcccbadbaaaddacdcbdcccddccbbdcbdacbcbadbabaacbcbcaacdbabdacbbbbcadabaaaabdaddacbcbdaacacbcdbcababcbdbbadbadabaacaaaccbdbccaccdbcaddaaaaabaabdaadcddbbaddddcdbaaacdacbcadabdaddadabadaabcbaccadabacbccddaaacabcaaacbcdcabdcdaabdcbadbdbccaabccddacbadbbcdbdbadbbdcdcacacbbbdbcbbddcccbbbcdddacbcacbcdabbbbabdbcddaccddbaddcadbdbaaadbbbaaccdaabaabacbacbdddbbdcbcbcdcbdbccdadcabbddaabcabdcaaaddacbacabaaacbabaabdabaaaabdcdcabaaabccbcbbcaacbaabdddadbccbbccddabdaabbddcdacabbdabdbcdaaccdbbcbcacbddabbbcdddadcadbacbdaacadbabdbbbbdddcabddbdabacbbddbcccbaaaadbcbadccdcbdbabdaddcdabbadcaacdabcbddbbbcccdbdbcdaabacdbdbcadabbccddbbbcddbbbaccaacbadddbccddcddadbcaddbadddbddcbcaabadbbdaaacbdadcccdbaaadaccddbaabbcdcbacbcbcbdcdcdadabccabcabbbbbbccddbcbddcadcdbabddcbaadcbbdaadddcbacbbddddcaccbdcdcdcdaabddbcdbbbdcdbaddaacccdabbaadbdabbabbacdcccbdbcdadcacbbdbcbdaaaccdaaaacaacbcdccddddadcabadabddbddcadabcaadabdbdacadaddadbbcadbdbbabaadaacdaabaacccbcabaadbddadbacbdbdccdacabbaaccbbadabccccabdbbaddabadaaabdabcbabbcbccbbdacdbdaaddbbadbdcbaaabbdbbddbcdccbbddcbdcdbdbdcbcccddabccbdcbacccbabbdcdbbbabdbdcaddbbbbcaaadaacabaadbdaccbdbacacabdccaaaadddbbaddbdaabacabcbcabdbdbadcaccbcbadaabaabdcbbdcdcddbbcdbbbbccbbdadbdcdcabdcaddbccbcabddcaacadabdcbcbbacdbdacdaaaccddbbcbbabdcacccaaaadcacdaccbccbbbbcdbccaacadbbdcacbddbcdabdadadaccddadbcabaddccdcabcadccaacabbbabccbdbdacdddaadbdddbaadddddbcacdaaadbddabcdcbaadcbddadbdadacddadacdadcabbcbcaddbbaacbcccbcdabacddddbaacccdcbbacdbccacbdbbabbbadcbbccdbacadccabcbbccaccbcaacccbcaaccbacbaadddddddabbbaaacadcccabbdddcbbdddbbacbcdbcccbacdccabcbdcbdbdacbbabdbacbddcdcbadacbdccabdaababaccccacacaaccbabbbabcdbbcaadcdbdcadcdbabcddaaddcbcbbddacabbcbcaddacaccbaccaabacadadabdcccbcbcddbddbaccadcdbdaabbccdaadabbbcbcaaabbcadbcaddcdddcaabbbcabcccdbcddcdaabbccdcbdcacbcbbaadddcacdaadaacbbabaaaabacbddbbbcbcaabcaaadacddbdbaccdcabaaacacaaacdbadcaaabccbdcddbbcaabccdadaccdbccbaacdbbdccacccdacbbdbcbdcccdbdcadadadadcccadbbccaacadbcbadbcdcbacbcbcaadaaaccccbadaabbaddadaddbabdaabddacddaabddcaaadccabdddbbcdabacaaaddabbcbaccdacbdaaabadbccdbbaacccdbbccdbcacbaabcddaccbabbdaacbaacbcddddacddcdddacaacdbccdccabcbcbccabcbdcaadbbcaabdddacbbacbbdacacbbcbbbacacbadaabbacbacaacccbacabdcccbbbccbcbbacdbbcdbabcbcdcdbdaddaadccdaadbbdadacbbbbaadbdccaaaabbbdaaddacdcadccccbbdcbdbbddbbadcddccaaddcdddbbaddcbdaaabdcccccdbccccaaddcbcaccacbcdbccdbcdaaadbcaddabccacacdbadcbbacabcdbadaddcbdcacdcadbbbbadbaccddbbcdbcdacabbadadcdccccdadcddbdbaddcabcacddbddadbadbdbdccaadabaabcbcddcddaadaaccdcddacccaabcaddccbcadbdddcabbcabdababccadbdbcbbddccbcbcaaccdababbbdadccbdbacddddaababcbcbcbcccbbcdadbabccaacdbaabbbdbbccadacaababadbccbadaacadcbcdccabcdcddaddcdbacbddccabacdddbbbdcadcdddcccbbbadabcbbbccdbdddaadcaadabacadaaddcbcbadacadbcdacdbbcaaabbacabbdabcadabababbccddcccddadccaccadddcddccbcdbacbaaadccdcaccadabbaaadbabdcccdaabdcbbdbcbabbcbcdadccdcdcdcabbdcdcdbacdcddbaccbaccbaacdbacabacbadbadbdcbbdacadbbaadbdddcdbbabdccadcdbbddccbdacbabadbacbccbbbccacbacadbbdacaacdaabbccccdadddcbaddccaccaaacdccacaaaccbddbccaadaaacbcddbaacacbcdabdacacdbbabbcadddababbcadbdaacdcccaadddaabdbbbbabbcbdcbababddabcaabbbccbadbdadacdcadaaadcdbbaabacadcacdadadbdbbddaddbaccdcbccdbacbaaaccbccbccbccddcacccbbbdbcaabbcdbcadbdcacacbacccdaabdaaabadccddccadccadddbdacdcbddadcabcbddccddadacbdcbabcbdaabacaacbbbbddaababdcadbabdaaccaacddbcddcbcaaccdcaadbcaddbadcdcdbbabbdacdadbcddcdadabbdacbddabdccddbdaddddacdaddabaabdcbdbbaabddcbbababdcaddadcbcdcccccabdbaaabcadcddcaacadccbcbdcccdddabbadadbcdaaadacbcbbbbaccccbdaabcbbacdcbacbadbadcbbcbddbcadddddccadbbdcabbaacabaacccdccaadacabbaddddddccdccbaabddbdcbacbbadbcbcabdcbbdddcdcbddbdadabbcbdadadccbdbcbcacabcacbdabbcbcbcbcadbaccdbbdaadcabdbbadbcacbddabdcadadcacccdbabbdbcbabbbbbdcbacbbbabadcadccdcbbccdabbadccddbadabddcabbddabddcbcabbcabbbdbadabacaccadcabbdcbbaacdbdccbabccbadcdacbadadcbaacdccbcdbdbaccdbddcddadadcccabbcbbaaddcaabcadacabbbddccbddbccddaddccaaccbcabcdbaaaacbbcabbdcdcbccbbcbdbbbabbdcaacaaadddbaadabbaaadccaadcbdddbadbabcadbdaddbcbcdcdacaabcbbcaabaaaacdddcdbacbdcacababdbaddabcdcdbdccadbcadbaddcddaacddbbdbccbaabdcabadbdbbacdbdcaaacadaccbdbdacaadcccaadbdddbdaabcaadbdddddadadccadacdcdddccddcabbbdabadacabddcdbbddcbabddabcaadaddbaaccbccaccbbbdaddaddbcdbcadcddabcbcbacccccaadbabddbcbcdcdcbccddcdaccabacabadbcbdcaccaadddcbdacbabcdbcabcbaaaacbadcdabbaccbddcddcdbaabbbcacbbbbbcdcbdbcbcdabbbdcdccdbcccdddbdcdbbccadbadcbabaaacaacbaacacbbacddaaaaccccccdadcbddddcadcbccdbccdcaaddddbdcdcdbadbadbbbcaadacbaddadbbbddccbdbababdcaadcbcacdcbcdbbcdcbabaadacaacbcababaccaacddcaaacacddcbbaddbabddcaabadaaccdaabdcacbddcdabbaaccddaddbcbdcdbdcbdbdcdbddaadcddcbccdcccccdadbdccaabcabbbabdadaddabcbdbbddddbbcacbdcbdaacbbaabcdabaaacbbacdaababbdabbbcabcddbbbccccabcdcbdbdbaddcbbcacaabbddcbaacddaabcdaadababcbaabcadcccbbbbcdddddbaadcdbbbbcadaacbbaadcccdbccddabdbadadcaaaddcddbaddbbccaccbdabbcacbaccbbaddbcaddbbacaaadaadcadbbacdaaabaacbbccbbbaaabcdbddbdaaccaccdabcdabbcbadddbdddcbbacbbbdbdcbdcbcbccdbadaaaadaddcdacaadaabddbcbadacbaabccbbbccaaddbdbcdbabdabbbdbbcdbabdcdcdccadbadacdacbccbcccadacdcddcadabaccacdbaabbbdbbcbccbdbbcbabbcdadcbcccaabccddbdaaaaddabbacdabcccaaaddbccdcbcbdacabdcccbaccaccbbcacabcadbcbcbcacadbbadcdabcbbaaabbcdddddcbbddcbcddacaccbdcdcbabaacadbadacbdadcddadbccaddaacbaacdbbadacdccbbdddcaabccddaacadbbaaabcabaadbdbcbababaccbacadbdacdcbbddacbaadbcdabcbaaadbcdddbcdccbccaabcdbdaadcaabbdccdddcdacadddbcaadbbadcdcdabdabaabbbdbdacbcbccbcbabcbbaadcbbdbcadcdbdbccbacabbbcadbddabacabdcbcbacccbbdabdddcdbbbbdcccaddcbcabbddcdbacadcbdbdcaadacaacaccbbcbcabdbbadadbdabaababdbcbdcbbcbabacacabcaadcbabcbbadddcabdbabddcbccbcddaaccdbcbcbbadacdcbbcaaddcbbaaaccbaabbabcddbabdaaacdbdabcabbbbbaddcbbdcddccaabcaddcbaababcbddabbbbababddabdbccbdcbbbbbdbcabbcadaacbcacaacdcbdbbaadcbcdbabcbbaaacbbccddabddacbdadaadaabddadcdbddbbdbbcabdbccbdccaabbcdcdbaadadcbabdcbcdcdaadcdddcbacdadcdaaccbdbdabdababcbcdcacbdbdaacbadbbdacccaaaccbdaacaacaabdcdcacabbcadadbcbbdacadabdcddcdcbdcccbdbdbbcaadcbbbaacdbadccbbadddbdbdbccdcdcbcbadadbbdadcbabbcddcbcbbaaadcdacacadabcaccadcbcbdbabbbadcddaaaadcacccdccacddbcbaacbddabcccbabbcdbbcbcdbacbadcddbacbadccbdbaccbbaacddaaacddbddadacbdbbacbdaabcbbcccacdadbababbabccbcadddbadddcbcaacdddbaaadbbbdaacabbbcddaaabdacbbcbdcbabbcaabcddcabbcccbccdaaacdddcdbdcccbbcaccababdbaabdaddbdbbbaabcbabcbccacbdcddccabaddcdadbbcadbcaadaaddbadbaacdaabccddbcbcbccbdccbcbbcdbcadbbdcdcbcdbbdabdabddbdbcaacaacdccadbdddccaaaababbdcdadcaabaabcbccdbacbdcaadbdbbbbaadbaadcbbacbcdbdbbabccdbacddbdcaabaaaacadadcadbacddcccbacbdcccbddddccddcddcccccdabdbabcdabcbbbdbbadbaabcdcdbdddbabcadcdbbdcaaabcdabbcdabbddaaccbbcbacadaacaabcadccacacbdacaccaaddbbbcbcddcbcccbbcbdcdcbddbcdcabaccbccbacaddbadacddcdababbbbbcbbacabbdadbababddacdbddadacddbcdbccbabdaabaccbcdcdaadbadcbbcbcacababccdadcdcacdbdcaabbcccbaaccabcadcdcbabcbbdaccddadcccdbbdbbbdaccacdabdaacadcdbcadbcbbcadccdadccacdddadcddaddcccddcdbcbbbdaccbcbaaadaabdadbcccadadcaaccadbbbdddaaaadaccabdadcaaaacbcbdcaddcbdacbdddabddbdbcbcbdabdcbcccddddaaaddbccbbcbbbdabaabadbccbdbdccdbcbbdaabaaccadaaabdcccabbdccaacdaabbdacdacccaadddcaabadaabbcbabddaacbaabcadabbbcbcdcacadddddbabacbdacdcacdbdcaddbdcddcacaacadabaacbbdbabbaabdaadaddbbbbbdbbccbcacdcccabbabdcaacddbdbbbcbaccdbdccaaacadadbacccdadbdaadadcdabbdbcaddcddabacddccdbadcacbbddadcbbabbacddcaaabdcccbcababbdcddadaaddcadcadbbaaaddcbdcdcdcdbabcdbccaadadbadabadbacdbabacbdcddbcccacdcabaaccaabbdbbabbcdbddaabbacccadbbcdccbbcdbbbdccccaadcddddcdddccbdacabcbbdbdacaccbdaabadddccccaaaabadaccbcbbaaddabccacacaabcacdcaacddcacbaaacbdaabcdddddbbdbcacdbbbbbbacacabaabcabcdbdbacbdcbdcbacaccdbcdcdcbadbcadacaccacaddbbaddbbdbcddbdccabbbacbbacdcbcdcadbdbaccbcaacbdbbbcabdaadadbcacddabbaaacbaacbaccdaacdbadcdaddbcabcbdbdbacbbdbaacccbaaadbaadbacbadadcaccacbabcbcdddaaacdbccbaabcacddaabdaadbdccbcababbaabaabdbbaaacacccdcddaccbabcdacddddabbabccaaccbdcaccdaaabdadcaacaaddacadbdddcacdbaddaacabccacbbadacacdbcccababaccaaccbbacabbdbadddbbadbadbbbacacbdcdbcbbbadccabddccacbccbdaadbaaddaabddadcbacaadaacaadbbcdaaabdaabadadddacdaaddbbddaabbcbbaaaaddbddabbbdbdcdaacaadbaadccbbccbcdbcdccadaaacbbdbacddabbbacbbbaadadabcbaadccaadaaaaadcdaaadcabaaabaaabacbbdabccaaccbbaccdbcbcbaaddabacccddccaabbaacbdaccddbadbbadcbdddccaaddbcacdacaddbaddadaacbdcadbbabbbdcdcabbbbbdbddcdccdccdbbcacbdcdbcabcbdcbccdcdcacdaaccdabcabccabbadddbdccabddacbdbbcaccbbcbabaababbbbbcdaacbdbcdaddbcadbddcbbbcbbbcdbbddacacbadbcddaaddaccdcbcacabbccbabbacadabbcaddabdbcbbddbbcdbdccccbabbddbcaaaccdbccdacddccbdbcccdaddcdabccacdbccddadddbcacbacdcadccadcdbcddbcdbcbcaccaabccdbbabcacdbcdbcccbabaabaaadabbcbaaccbcdabdbaabdbacccbaccdbdabcabbbadadccaccbacbdccabaaacadbbabdbdcdacdbbbddcadabaddbbbbdccdcdbdbadbbdcbbdcddbabaaacdbadadbddccccabdcdddbbddbbcaaaadbbbbbadacbdcbbdbbbcddabadddaabaaccdaaccbadbacbcabdbddccacddcbcddbacadacbbbaadccbaababcacaacddbdbdbbbcbdbaddcbdbcccbcabcdbacbdcacadabdbdddbbbbbbbaaadcddcbddcbccbbcaadcbadbbdddcdcadaacdacbbddbccbccbccabaccbbbcddabacaaccabccdbdddbdbdbaddccdbcaadddbabbbdccaccdbdaccabccbbddaaadacbaaadcdccbcccbddbddadcdcacacbbbdbbcadbcbbacdbbbbdddcbadccddccaaaddbbbaacccaaddcbcbdaaabbdadbcabdabcaabbacabdccbbdaacbcbacadcdabaadaaacbddcbdbdacabbdcaccdbbddaddaabdbdaaaabadbbcdabcacdbcbaaddcaaaadbddabcddacaaacccadacccddbcdaaabbdaccdcaaadacdaccdbbcdbbcacdcdcdcaacdbcddabbbdccdcbdbdacbaababaabbcadbdbdbdcbbbacdadbcbdcaacacaddbabdccacdcacdccdaaabaadbbcaadbcbbadbcdcdcaddaaabcaaacbbdcabbdcdabadadddbddcaacbbdbcdadaccabcabbcccbcbdaadacbabaaaccdccadacbcdcbabcadbbbcdbdbaaddbabacdacbabadcddcbaadaadddcacdaabdccbccadbacbdaccaaccacaccabdcabbcdcddccdcbdbcadabbddbbacccacdaddcbcbaabdcdacdbcabbccdccbccbaabbaaccddbcbbbbbdacadadbdbdacbbadabccbbdcbccbbabdaacaadddbaadbcbbacbbdbbbccacbccdbdcbcdbccbddadabacbadcddbddbddbccccbabccdddacdccaabdadcdadababdbdacaaabcabcdcdcdaacbbbbbbabcddcbacdbbaabcdbcbcddacbbdadbbbdabddbdbbaabbbddbaaddbdaabcaddbcaadccbccbcbccdbbacdbbddbcabccbadbaccaacabbdacdbcaaddaadbddbddcdddbbdcdccdcaaaadcdcbccdddadccdacccbcddddcbabbadacddabcdbbbcdbdaccccabdcaabcacbbddbbbddaddbadbddaddbacdcacddaaaadbcddcbdcabddabbdbcccddcabdbbbcaabdccabcadaacbddbdcbcdacdbcbaddabddbdcdbaabaddbcddbcdccdaabaddadbdddddadcbcddacddbcddaadcacbbcbccbacacadcdbcbbbaddbabadbbbdcbdaaaabdbccdbbdcdbadbbccaddbdacbabcdbdacacababdccbccacbdcbaaaacdbacbddaccbaadaccdbddcccbadddbddabccdbbabbddcbdbdbbaaaacdcdcdcacaacdddcccabcdabacaaddbabddcabcdaabcadbdbddcacddaabdbcdaccbaccbbaccccdaaaacabbaabdbaaabcaaaaadabdabccccbacdaadccdbabcbaacddacdabbcdbbaaacadabadbacadacdcddcaddbbcacbcccadbdbadbccdabcbacdaddddcbdccaaadddbdaabdbadccdddbdaaadddcccbdbdaadadbddbbcdbbaababdcdddabccbcbdcbcbccaccdbcbabcaaddbbaacbcccbbcaadbcacdcbdabbccbabcdbaaacdccdaacbbbddbccbbcadcadadbbdcacbccacdaccbbcbddcabdbccdaabaabbadccbdcdcdddabcadcaadbdbcbacdaadcdadcccadcbbaaacddbcbdbbaddabdddaccadbcdabcdddacabbdcccccccdbcdbcaababbadcddcabcdabcddacabcadcaccbcbadccbdddbccbacbddcbbdcbcaacbdadbcddbcacacddacdccbcabbdabbbcaaadddbbdcbaaacacdadadddddcdbcadaaacaadddacdcacacbacdbbaccadadacddbddbddbccbdabccbcbcdbcdcbddabcadabbdbacacaccdacaaaacbdacdddbbbabbadbbcdbabdbcbdcdbdddacbadaadbdbcdaacbcdcabaadaaacaaabacdbabdccabbadadabccddaaadccdadcdbadbcccbadccbbdabcaaaddcddcdacbdcddacabcdadddbaaccdcadacdaabbaaaacdacaccbdbcddbdbabbdddbcdbdadbdbaccdbccdabcccbabbbcbbabcddadbacbaadbabcbdaabdccbddaaacdcadbbdcdddccadabaacabccacdcdaabaaddaabdcdcaacccccdbcbddcacbdbadacdbdddacdaccddccabbaadcabdadddadcbdadbbdbcbccddbbcdcdbadaccabbaaaacdacbdacdddbddcbaadbaacdaacabdbacbdbbbdbabbdbccacdcbaddcdbbdcddddddccaccbaacbdbdbcdbacadbbbaacdccbcdabaabaadbcaabbacaaddcaccacdaacaadbbdccdaaccadbacbcdbbcabdcccacacaccdbdbaacdabcaacbacccaacdcdddbaabbbbacdbaaddbacabdbbcbacdbbdcbbbadbacdbaacaabcacadcbccdbbaabddaadddcadbbadbbaacccdadcaddddcdcbdcddccbaabcccccddabadddbbdddcdcabcdaccbdbbbaacddbaacacadaabdabbaabcbdddabaaaacdadcabccdddcbbbbabdbbdaacdbacddacbbcaacbcdddabddbdadccdbbcdabddaacdbddadbbcbdbadacbabbbbadcddddbbbcbaddababdbcadccadbdcddcbbdaddcbdbbbcbbabdaccdccdbddbcadddcccacbdaaaaccdacbddbaddbcadcbdbcccacdaccccdadbdabccbadbdaaccbacabdaccdbccdbabbbcabdcbadabcbbbbbdcccdbbbddbaccabbdaacdcdacdaaabbdcdbbbadcccdaadcaabdbbabcbdadabbdcdbdabbdbacbbcdacdbbbaaddaabdadcbabdabacdbababaadddcdbdcbbcdcbccabdabdbdcbcdbcccdcababddcaabdccccaaccabdcaddbdabdbdacbacbcbaddccdddcdbddaddbbadadabcbbddbcccbdabacbdccdcbacbcbadbbaabcabaadbbccccbaaddbbdaccacdbdbabcdbdddbbabccacbbdbabacdccddcbccbccacbdacbaacbabcdaccdbaaaccacacccacdadcbcdaaddcacdadacbbbacacdadaaacdccddcacdadcbcacaaabcbbdcdccaccdcadbccbcbcdbcadcadacdaaaacdcbbbcddadddddabddadbbbccdbcaacbabbdbabbcddcbddadcadbbcaabadadddacdbaccccbacbadadcaabacdccccdcdcabdaaaccdacbabadabddaabcbcbaccdbdbbabaddbadbddaaaacabdcdbcbbaababbbccaacdbaabcabaabacaaddcbcadddaaadcccbcbabcabccabbcbbbbbdcadbacbcbcbdcabbdccdaacccdcdddaabcacadbbdadabdddadbcbbbaacdbaadccdadcddcabaadcdadacbddacaccabbdbbacddbbdcdbcbccaccdcddbccbbabaadababcdcbdbacddabbcbdbadbcbadbcaabdbdbaabbadbbacaccaaacadbbdaabdacbdbbcaccdcbaabbdbbaaccbbdcacddddaaddacdabddbcdcdbcbdcccccdccdbcccdabcbabbcbbbcaccddbcadacabccbcaadcdaadcaabccadcccbdbddbacbdbbbdccccabbacbcabdcccbcbcddccddbbabbddbccddabaabcacbacbaddbadaabcbdbbaaadbacbcbccaadcdcccaacabbabdbaaccdbaadcdacccbcddacacaabcadaaccdbdadccaccacaccdddcadabbcbaccbcdbbbbacdadcbaccddadaacdcdacdbbbacbbdbaacccaddaaccbbcbbccbdadbdaadccdcabcddacbcdbbdaaadbdbbdacddabdabccdaadbabccddaaadcadbdcdddccadabcbbcacccabddbacabcdcbdbaccabcaabdabdaacbdbdcabbbdcdbddaabbbacdaaababbcbbdcdcaadabcbbabcbdcadaaadccbabbddcacbadabcdcdcbaaaadaabdcccacbdbadabdbacaabaddccdddacbbdacdacacdaccacbabaddddcbbbdbacdaccdbcbbaadabbacdabbbdbabcaaccddaddcaaaacbacbcabbbbcdccdccccaaacbacaccabdbcdaacdbcbaddbddcbcccdccbbacbaaadbdcdcbcdadccaaacbdbddabbdbddccccdaacadbcdacbabdaddbbbcddddbccbbdacaccaabcbcdbbbbdbbbccdbaabdcbbadddcbbbabdbdbabbcaabcddccdbaadacbcbcaddbccdbdadbddbcccccbdabcbbddbaacdcdabdadaaabbbccabacbdcaacaddcadadcccaaadacccadddbcdbcddddccacbaaaabdbdcdbcbcaacbcbbbcabaadcbcdccdabaddbbacabbacacadddabbbabbcabcbdbdbddbccdcbcbbcbcbbbadcccddccadacadacbacaabbcbcdadabddaacadaddacbdacaaabccbcaccabbabbcddcbcdabacaabbbcbcdbabcbadccaadcddadcadbbdcdddcbdccdcabadacbddbccddccdbbbadcacdcddcdabbccdbabaabdcdbbbdcaaaadcbadaacbcdccacabcaccdcdadbabaabbccbdabacabdaacddbaadcaaabcacbbdddddcbbcddaacbbdacaadabadccbbcdcbadadbccacdcacabadabcaabdbdddbbcbddbdbcabcdcbbcbaaadbababacaaaaaadcdcddcacabdcbabbbcdbdbcbcacbddccbddbbdcccabdcababcabbbbbbababcdacdddbdbcbbbbbaabcbbcdbdacbcadcabbcbccdccccdddadbddcadaacbdacabcdcadddaaadabcbcbbdcbabcdbababddbccacacbbbabcdddddcbcaabcbdbabaaadcbdddbbabbdcdddadacdbdbadacacdbbddaddbcccdbdacbcbccdcdacddabcbbccbbaabbbacbcbabcdccbdbbddbbbdacaabaacabddcacadddbcaacbcbbdacacbcbdcaabcadbddbaccbccdcbdbbaccdcbcbaddbbdcacddbaaadbabaaadacaadcbadadabaaabadbbdcbcbbcbacddbabbacbcbacaacbaaaadabddcdccdbcbaddbcaabaadacaaaccbadbcacadcabdaddaacdbccbaaaaccdabcbacaaabbdccdddcbbbcaccbcadcadbacbdabdcbacdaacdbdacbcacbcabdbcdccbcccbacadabcbcddccdbdcdaadaadbbcabdcccddadccbdbabcaddbaabcccdaabcddddbaaabdccbcddcddddaacbcdabbcdddbcdbbddacdbdbddbacadaddabbaddacdabacbddbcbccdbcacccbbbcacbadaaccbacaccdadbcccddbabddbcaaddcbbadcabadaabbcaddacbbabdbcdcddbcccaddbaabaabcbadaabdcccdbdaadcdaddabaacaadabddabdddacbbbbccdccaccbbaabdbaaaaacdabcddaadaadaabdccdccdcbdccbbcddcddccbbddbaadabccadabdcacbbcbbabcaadbdaccddcabaccbabcaaacdddcdbdcbbdbdcacaddddacaaaaddabdcacbdadcbadaabcabbbccbaaadbacddbabcacbababdccbacaaababadcadacbaadcbaaaadabcaadbabdaadbddbbcbcbdcacbdabaadbadbccccabbdccdcdabadbadbbdbcbccbcbbbabaccbcaddbdbddddaddbcabcacddcaccaaabdcdabcaddcbaaaccdccdbdcdacacabcdabbdcadbdbbdddbddbdaacccbdbbadaadaacbadabbdccabcaabadaadcdacccddbaadacbcdabcccabcbadddbddddddabadddccbabdabbcaabcbaadaaccdbddcbabcdbabdcdbabcdcbcdababdbbcbbbadcaaddacabbdababacdbabbdcbdddcccbdcbbcdcbbbdbddacccdaadbabbcccabbdddacbbcadcddabcabdbbcdaddadbccdcdcbbcbdaaacdaacdadcdadacbbbcbabaabacbdcbddddacddbcdbccbdacaadbdbcdcbccbacdacaabdcdcdcdabbcdbcabcddacbdbdcbbaadaacacaacdbbcbbbbdbdcbccbaadbbadcacdddadbbdabbbadddacdaabaccacbcabbdcacdbbcacccdacdcaabaadbadaaccadcdddacccabbddaddabcdbadaabcdccbaddcbaaddabbbadcadbbbccbadabbdadcdbaaabdadddccccccadbdbcccacccdbacaaadacdaabbaddbbaacdcadbbacdcdcbbdbbccccaddbdbbbcddadcbadbdbbaddcbbcbbcbababbcabdbbccdaacdbbcacdaabaccdbcbddcadacadbcadbcdbababaabdaaccaaaacddbacdbbabaacdddbaabddcbaadbacccbdbaaccbaddaacaaaccbcaaddbbbcabacacaaabbbdaaabcdadbdddcdbaaaaccbaaaacbbdbaabddcbbddcdcdcacbccabcbcdbddbbabcadcbcdbbccbdaabacbdbccbcdcddcdbccbcbadaaaacccddbdcababdddbcadcbccdaacbbddaabbdccadcdbbbdaaaabcabbcccbcdcbbabaccaabdaddddaababdaaabacdaacbdcbbdccdcbdbbbcabdbdbaadcddbbadaaddabbcbbabcacbcacdcadccbaccdcabcdadaabdbabcaabaddccbbdabbcacccbcbbbdbabcdbdbdcdaddacbdbadabddddaacadbbddcdbbdcdaabcccaacbacbbdbabbdadabbaabcdbabacdbbabadacdccadbaddddabccaddccbbaadabaaddacbcaabcdbdabbaabbaaabddabddbbbaddadaccacddabccddccdabddcababcbabcbbccacaddccabdbbbbbbddabdccdadaddabdadabbccdbdabcabaacdabdbaccbcaadaadbdbbaacdbaabaaabcdabbcaabcdadddbdacbbbabbdbddaddcacbcadcacaaaddbbacdacdabdcddabdacdcacbabdaccddbcbbcadbbbddcdbbabcbbdcbabbbcadcbadbacadbcbadbabadcbbccdbadddcbaabddbaddccdacbdbbbadabcaccbadddcabddbdccbadbbddcdcdbacdadaacbcdbbbdddbdcabaabaadadacddbcddaacddcdbdbbddcabbcccbaacbabccbbadbaddcbacbadabddcdbdbaddbdbbabcdabaacaddcbbacdcddcaaaccccdcbdbdadbcbbadaabdacccbdabcddaacbbbacbcbcbaacacdbccddddadacaccadadcdccbbddbadacddbaaccadddbbaabbbbbbcbbaccbabaadcdadadbabbcadacbcaadcdcacbbaabaddbabaaadcbcacaadccabdbaacababcdccabbcabcdcbdddcababbbbccdbcdbcbcdbdcacccbaccabbdbadacdbbccbdadaabbbcddbcbcbbcbdcadbaaaaccddabddcaddaabcadbabcddabdacbdbdacddaccbacddbaddbaabaddddabccddcadbabdccccababcdaddcaabddadbcaaaccacacbbdbdcdcddabccadddcdcdadcdcddbbaddabbbdbbabdabcadbdbcabcdcbccdbbbaabcadacbbbdcdccaacaddcdbaccaadbaccdaccdbaccaddacbaacbbadaaadddaccdbabbcbcbaadcadacbdaccaaddcdcdddbbdaccbdddbacdbacbcdcbacdccaadcddcdccdddccbadddabcdadaacccddddcdcaaaadbaddccaaaacabaccbcbcadbaacbcdcccdbaabcddddababdabdddbdbcdcbaacbdcdcddbccbbdaacdccdcccddcccbabbdcaacccccdaadcaabcccddcdabdcdaadabaadadbadbbaadbcdccaabaabbacacadcdadbbbaacbaacbaaadccdabaacbcdbaaddcbbdacdbcdddbbabbcabacadaacbadabcddccbdbdababbcbacddcdadadacdacbaabbaaabdacbbaccccaabbdddaaccbdcabaaaccadcdcbccaacdbabcabbabddadbaacacbddcccdbcbadabcaddaacbdabcdbccdacabcccbadccabdbcabdcabddccdbbcbaacacdaacbbbdcdcadcbacabbcbccaadddbabcdabcdaadabbbabcddbaaddcdcaaccbdaccddbbaaacbcbadbadddcadbaddcddadcccacbadadabdbdaddcbbbbabdacdbcdabaaabbccadcccabdacdcbcdcbdacaabcdcccdaaabdacadabdbccabcbcacdbdacacadabacdaddcdbadbbcaacdaacccdaaabdcbcdcbddddcbbdacccdbabaacaacdcdcccabbacadbbadcacbdadbdcdadcdccdabadccabbdaddcabdabcdaddbcddccbcadbcdaccbaddddacddabddbabcddacacbaacaadcccdaaaabddcddaccbbaaccddbbbccabbdbcbbcbaabcddcbdcbacccaadbdbcabaddabadbdacaccddbbdadbdbbbadaddaccacddcdabbddcabadcdbbbbbbcbcadaaddcccadbbddbbddaadabcddcadbddacbadabbdacbbcacaaaabcbacabddccbdddddbbcaacbacbabdddcbdacbabadabdddbbaadaacbdacbbdaccdbdbbbdaddbbcabdbddabdadcabbaaaaabbaabdcadccadcacaccbcbdbbcddbcbaadcbcbcddddddbcbcdcdbdcacdcbbbabadddbaddadabbbadacccbbbacdbabdcddccddbbacdcadbbddbabdacadabcbdccdadcaaadbccbbddcdabadbcdbcdacdbcabcabdcaaaaaaaabbcdcbbbcbadcbaabdcdddbbcdbbbbdacaacdddbdbbcdccbcbaccadccddbadaaccbbdacabdcaccacadabccdcccdbbbadadabddacacbadcaabbcaacabbbabdacabbdccabccacddcabccdcacbadcacdbcdddbccabdbddabcccdcdaaadccadabcaadaacbcdcdddaacaaadcbabdbadcaadccbaccdacdaabcbcdacaadcaabbcaccbaabbccbdddaaadcbdbaabcbdcbdcacdbcddcbbadadbacdcacadccbbacaccdbdadccdabbddbcbbdcbcadccccabbcdbdbbbadacdaddcaaacabbdbbbabacaaadabcadadcdcacbcaaccadabddcdbbbacdcdccadadbccaabddddbddddaaaacbadbbaabbcbdddddbcbdadadbbacaccddddaaadbaaacdacbabbabbbbdddadbccbcdddddabadbcaddabacddbdaabcabadbdbccbaccaacabcddcbbdaacdacadcbcabbcdacdadadbccaacacbbdaddcbabbddbcbbdbdddabdcacddbaddadbaccbcbbcdadccdbacbbbaacacccdbdbbbbaaaaabbbcdcaadbbbdccbdaaddddadbcabdaaccbcaadcaaddabbddaaacdbbabcccbaaccbadcdaabaaaddbccabbcdcbcbcbdcdabcbddbccaacacdaaccbcdaadcbcccccadaccdbdcbddacdbabcdadbadbddcdbccaabdcbcaddbbabcacbbbdadbbcadabaabdcdbdabbdaadbbdaadbcbcbdbbdcbdddbaadbdbadcabcdcdbcbbdcdacdddbbbcadcadcdadababdacddcbddcaabaabaccdcaacbbbbbbdadddbddcbbddccddcdacbddbdccdddcdaaabcdbaacbabbdcdabbaccabdbcbaccddddbcacbaccbbddcccbbccbdcdbaabcbbcaddaadabadcabbcdbccabbabcdcbabaccabbdadbabddddbdadddcabcbabadbbcdadbdcbcdbadadadaaabcaaabddbbdcbbdabdcccbcdaaadaaddccddaaabadabccacdcaadbababcdcbbdbcabcabdbcdaadbacabcbaddbbddabcadccdbdcdbbbddccddacdbcbddcbcdccbadddbabaadadcbddcbbdbcaddcbbdabcbadbdcaddadcccacbcabcadadbbbbdccaabcbaaacacacadccabbbaabaccbdacccdcbacddabddbddbaddcddcaddadcdccdbcadaacbbbbbaaacaacdbbbadabdacccaacdabddacbbccbaaabdcdddabcaaaaacacddbaccdccacbaadcaabadbcdaadbdcbcdccdabbddbdccbdbacbbbcbbdabdcbccddbcdaccbcabadacddcccbcbddbccbbaaacdaabdcddbadcacacbdccbbbaacdcddbacdcdacadbdabccaabdcadbbcabaaaaacbabdbddabcadcbbdcdbdadaabadcadbadbbdabddadbbbcdcaabaabaabdddccdaabbbaabddabaacbcddacdabaacbccdacdaccbdbcbcabbbaddbcaaaaccbabddabddbabbaaacaacbbbcdbbccacaaacddcbcdbaacdabadcdbcabcbbbbadcaddcbcaaabbcadbbddddabbabacbbdababbbdddddaacccdadcdcbbacdbbccdacbdbbbbcbaabbdcbdbdcaddcbcbcaacbdbabbbcaaccdcbcccababdaccaaaacaacdacadbadbcbdddcbdaacdccbbadccaacbaadcdbdcccdddabbbaaaccbddcabdcbdcadaacbaacdbcbbadcdcaacbcbdabaaadccabdaaacdddacccabbabdaabcbcddacdbdbbdcdddacacccbdddabbcbddbbadcaaacabddbbbabcdaaacadabbbbdabcdbaacaddbcbbbbcccabdcbabdabbddbcbdcdbdaadcbcddbcdaaaabacdcdcdabbcccdadcacbacaabbcbcaadbcccbadcadadcbccaabadddcbbbcdaacdcddcadbdbbaccbaabdbabddcbbbbaccdabcdacbdcacbacabcadcdcabbdbccadcbcbddcaabaccbdbcdcdbdadaccbaccdacbcabddbaadccddbaabbbabaacaadacdccaadcaddbdcacbdabdacbcbccccdbccdbcaddbabbcadbbadddbbdbbbdaccdbccdcbccddabaaabccbbacbabbddbabdbabcbabcbacbdbaaaadccdaccbadcdbaddccbcdccccccbbcadcaaaddcbbbcabcdcbcaaaddccabdccbbcdccddccbbaadcbdcacbcdcdddcadcabbbaaabaaccdbacdabcddddaccddcbbaccdacaaadcacbdacbadacbbdcaddcdcdcdabcdcbccdbcbddaaaabdbdabaabbdbdbbaacabaadbbcbdadddaabbabcbccadcbbdbcdbbccbdcbbabdadabcabbcdcadbddcbcaddbcbcabcbaccdacdaccadddcbddcbdaccacccbbbcbacccabcabcaccddcccaaabdcdccdaccddccbbdcdbcacdcbcacbbbbbbbcaccddcabdbdbdbadabaababcaddcdcdddadcdcbcddbcaaaddabcdbacababdbdccadbbaaaadaabcdcbabbadbacbdaacdccbcdcaaaccadbabdbabcbbddddcacadddbbcbdbacbbaaabcbdadccdcbcddcaacbadbcccdacadaacabadcdacdacaabaaddbaabdbaaabddbcdddbcdacdabdababbddddcbdbabcbccbdccaabdccbdcddcaadbaaacbbacbcbcdbbdabbaccdacccbdadbcdabcaabdacdbdcdbccbbddcabbdddcabbdabbabadacbdccadcddbbbacdddcbbacaadbccccccaadadcccbccdacabbdacdcdbccbabdacbbdaccbadadabacbbacabdccdbddaaaaddddbdadcabddcdaacbcdcdbddddabadaadbadacdcbcbaacbcccddbcacccadacbdbddbcbbaabbcbbcdbdbaacdadacbbbddaccdcdbddbdcddadbcbcdccdcaadadabbcbcdbddaccacbcdcbadbcbccbbaaacdbddcbabcadddcbcbaccabdaadaabbaddbbdcdbcddbaaddcadbbdcaccacbdcacaaadbcaaaadcdcbcdadbcbbddbbdbabddbcbacbdcbbcdcddabacaabdbabbdcbacbacbabbbcdabddcbdbcdaaaadbdaabaccbbbaccccbabdccacbbcdccdabbcadddcdcdbbdbcaacbdacbdabbaddabaabcdbdacabdddbcbabbcbaddaddcccdcdacacbacadccbddbbdcbbcdacdacbaabccdbddbabdccbbcdcdcbccbcaabacbadaaabaacccbdabbacdacabcddddcbbbabcbdabdaadaadbaadaabdadbaaaccdaacdbbadcdcbdcddcccbbccdaabcbcbbaabaccdaaabacdacbddcdcbddaccadddcccadbdcacadcdcbddbadcbdbbcdbbaababbcdbbccdabcaabbddcabbbbccccbdaddcbdbddccdcdddbcacaccabaabaacdaddcdacaadbbdbcacabadcbbdccaddbccdddccabcaaccbdcabdbabcbabdbacbcabaddaaacbdbdcdacdbddbdbbcdcabdbaccbbdbbdcdddbadbbbadbbcddcbdccbcdbccbbccdbbabcdddadddabdbbdddcdbdcbaaddcaadabbbabbdcacdabccbcdaacacddbddbbddaddddcbbbdabdadcbddccbbcdbaadadcacbcdadaacdbdcbbabacadadbabddccbaccccddaadccddbbaccdccbdcdcdadcabaadbbcbcbdbdbacbdabcccccddbadccdbdcaacddcbacddadbcbbbdcbcccdabadbccbabaaadddaacccddadadacbdabcacbdddbacdccaacbabaabadbcdacdcdbcbdcbcaaaddcbdbabbcadacdcacbacbdaacdcdcbdbdabdabadbccacaacabaabbcbcdacbdbaacbddbbbcdbccaabdcaaabdbabcacccbcaccddbdcbbabddbabdbbdcccdaadacaaadadadcdbcabdcccadaadbcdadbdabdabcadacbcabdaaaccdadabbbdcbdcadbaabcdcbcdddaababdcbbaacbdcadaaabbddddbbbcadabacbacaaadcaadcadcbbaaabbdcacdcbbacaadabdcccabdbbabcbbabbbbcddabaabcdbddcabcaccbcaabbadddaacaaabddbccaccbadcbadcdddcaccbbccdccdcbdbcdbaabdbcdbbcbaccdcacbaddaababcddbcdcabaabbdaaabcdaabacbbbacdbdabcdacccadbbbccadcddddcdcbcaaacaabbbacbbbdcbbaaadcddcccabbacbcdbbbbcabdabddaaabbabbcababdacacbccbcbcbabcbdbaaadcbadcbbbbcbccdddacddababdcabcaabcbddcadccbcbddaccdcabadaaccccbbdcdaababcbbaaaabccccddccdadbcdcdddbdaaccdabadbddbdbdabbbdbddbaccbddacdbdcacacbbccbcdccdaccbbbaaaabcdbabdabdbadcccdaddcadbaadbbbbcbcabbacbcabaabbadbcdbdbbacdcabaadbadbcbdacbaacaaddcddbbcdddadbddddccccbbabdcbdaaccbaccbacdcadcabcccacdbcaaddcdacccbaccdcadcdcdbccbcbbdccbbbbdddbdbbbdbcabbcdadcdcdaaabcaacdcadbabdbcbcdbbaadadddcabaccaababaccdbabdccabacdcdcbbcbdddadbbcbbdbdbddbcccaccbadccbbcbcdabcabbbccccbacbcabcdddcbabcbcacbcabbaccaccbdaaadccccccdbbabcbbaacabbcbcdadccdcdbbcabacadbaadcdaabcacaaacdabadbcbbbbdccdbbbcdcdddbcccabbccbaacdadddddaabbcbbbbdadbbcbaddabdadbadbcbcdcabdcccadcadddacdadbdbbcddcbdbacdbdcabbdaaabcaccaaadadbbacccaaccabcadcdaaabbadabdbaaccdbaaadbdbcdcbcaccdbaaabddbddcbcabbacadaccbcdbadcaadaddbbbdbbbdbdabcdbbdbcdddabdabdbcbababbababdaadcdddabdbbbdaccccbdccaaacccddadcbcbcaccbbacacbdbbddbcaaabbcccaacbaacccabbcccadbcbcdaddddcbccabaadbbacccdaaadaddbccadbdcbcddddadbcabbbcbcabdcadcbdccccdbbbbccdbabbbacdadacacacbcdacaabdcadcabcacdcbddcdbcbabbcaaacaacdaaacdcbcbbccaaaabaccdbcaacdacadbacacdcaaacaabdcacadbadcacdadacbbdababadbdaaadabcdcbcdabacabdbbdddddbcdaabbadddcbdccabdbdcdcbbacbcbbbbbbbcdbbdadbcabbdcdbadbcbdacdccddabcbcccdbaadcbcbacddcbcbbdcaccbbdccdcbbbdddcdadadbdbababaddcaaadbcadbadbdbbbbcdaaabbabddbdadbcdcdbddddddaadbbcdcbdbcdddcbdcccdbdcbcbcbcadbccbdaaaabdbddbdcddbacdadabaaadacadbaadbacccbbbcadbdbdccacbbccdccbabbddbadaabdbdbcbaabcdddbdcdcbaccdabdaadccccbabcbbcadcabcccddbcbaacccabbabcbbccadbccddcccbaaaccaacbcbdbbadcaacbbdabadbcbbdddadaaadcabcddbbddddaaaddbbdadcdbacdcbadbadaacacacddccddcdcbbbcadcbadadcadccadcdbbcaaaddbdcbcaacdbaababcccabbabcdacccacbcabbccdbacdaddbbcadbbccccadcbbcccdbdabdcbabacabbdddbcdbcccacaacdabddabdacdacddcabbadddaddddcbcbbbacbdddcdbbbdcbcdbcbdadbaaccaacadbdcaaabbbdbcbcbcbcdcadddcbacaddbacadabdccbcbaababaadcabaacacacbbcaaddadbcbaccadacadaaacdbddbbbccbabdadcdbdcaddcbcaccabbabccbcdcaddacbcaddaddcbbccdcbbbbabadbbabccacacdddabcddbcdacadbdacdcabbcddabddabbaddbadbcacadbcdddbbcdbbbbdabbcdaaccbcacacdabcbacaaacabdbcdaccacbcbddabacaddbdbdcdccbcdbabadbdbdbcbdaabbcaacccdbabbbdbccaadcacdaabadacdabacddbbcdbdabcabdadbaaccdadbacbaadddbbcbdbdacbcdccaacbacddcdaaadcbdbccddcdbdbbdaacacaaddccbacbbbadadaaabdacbbaddacdaadcbaaaccaaaddbdbbbabacdbcbcbcdcdbaaddabaccabdabdccaadbaadbbabbdccbcddbcbcacbccacadcaadcacaadbaddbbbabbabcbdddbaccdacbdcbbcdddddbddabbdbccbabbdacdddbbbdbabcbdbddbaaabaadbdabccccbacdadabcbaabadbadaacadbccbdbadccbddabacdacacdaccddcababccddbdcaaccdbcbbabbbacddddbbcbcbacccadbadaabcccaaabcbcccabaccdbdcabcbddddabdddabdddccdcbbaaadaadaadbdbdbdabdadacdbcdcadacadbdbbbcabbcddcaddddddadbbadcccccdabadbbadccdcbbbdabbdddcacacbbadcdcdbdacabcbaadbbaacabbaaabdcccababdcdacccabadddbcaacdbcacbbcbbadbcddbdbbdbabadaabdbabccdcbccbbbbcdcadadaababcadbdaddcbdaadbbbddbaccdcbbbbcbabcabccbcbcbadcbabadabbaaccabadddbacccbadabcdaddbdbbddcbbaaaaaadabababbcaacaddcbbcacbaccdcddacdabbadddacbdcaadddbdcaaaaadbddcabcaabbbdcacabbbacdabbaaabbadbaaaadccccacadabbaaaaddadbdabcadaabbabcbddbcccccacaacabbabddbbababbcbbabaacbcbdabddbcadabaabbbaccbcdbacbcbdcdacdccabadcdbdadccdddcadddbcadcabdcdaadcdacbdccdaadabdacdbddbdcbbaaacdacacddbbbcacbadaababacbdbdccaaadcddccaadbcbdbdaaabadcdbdabdbbdbbdabdaccadcccaadadacaaaccaaabddbacccdbaddacbdadabdbaaddcaabbdaacdbbddbdddaaddddddabcdaabbaabdcacbacabccacaacbddbadbdcdacddbccbabcbabcabcaadcbccbbdbadaccaabcddbaabbccbbadabdadbbdcbcbdaadaacbacccaccbabcaccddcbbcbdbddcddbcbbccbbdddcbadabbbddbaddccbbbcbdbabbdabbbcbdbcbdabbcbbaadaccddbdaabcbddcbdddbcdadababddcdacabdcbcdbaacccbdaddaaccdbbcdbdddccacbccbacaaabcbcdbaaccabacbbbdbcbbcacbccdddddccadcbcbbadcdacabacdabdadbdacadcbcbccbbcdddbcddcbdddadabbaacacdadacbdcadcdbdbabaabdadbbcabbacdbacbbdccaabbcabaadddbcabcdbcbdbbacccddbcddcdcacbdbaccddbabdccdbdabdaaaccdcbacbbcadbadbbababcdbabbbdbbacccadaccdbddbcddcbddabdbaddaddaddbcccbdcbdaaaddaacbbbaaadadaacdcabbcccaaddbdcbcbacdcaccdbcdbbdcacabacaccbdbababaababbcaaddcaabcdddccabaabdcdbbbdbdaabdddbbdbdddacbcaacbacdddcacbacdcacbdaccdcdbccaaccddaddaddcaacaabcbcccbacadcddaddddadbccbccabbabbdadbaddbcaacdbdbbdccbdabdaccbcaccdadaadbabcdabcddadacdbbaddaabadcccacdbaaddaccbbaabbbdbaabbacdcadbadddadcccaacddabaacdddaadcbbdbabadcabbbcbacaaccbcbdcadbdadccdccbdccaabadaccbddbacabbbcbdbdbbaabadcadadcdadcccbcdddabbccbdcbbcaaabcdabbdbcdcbdbcbaddbaccaabaacddcbbbcdddbddbbccbbabbbccbaccbddcddababbdddabcccdcccdabadcdcbbdaaaddddabaddbbddbbbdacbaacdbbbcaccbdccabbadcbccdadabdbacddbdaddadbbcdddabddcaaaadbccabdbcbaddbdbcdcacabbbaaabadcddcacbbdbdaaaccccdccdcabccccdddccbaaddbabcdaacacbbbcddaabdabcbadcbcccadabbcdbcdaabcbccbdcbaabdbcdcacdddcdcababadcdadcbaaadbdadcabbbcbddabdcacadcacccaddaabacdaadddbacacdbccddabdaacdbbbdbdbdcbccdacbabbaacadbaabbddabddabdcdabcbcbddaacadbddcaabaccbadcdaadbcdbaaccadccdaadcdadbbacacbbbccbbaaccdabccaacdadabaaabadcbabcaacdcdcbbbaaabdbababcababaddabdcdbddbaaadbcbaabaadcabaacabacdbabdaccabcccbbcdacbccabbccbbabdacdbbdaddccdbacadaaaaccacabddbcdbbaacadcdadbacacdaccabccadbdacdbbcaadacccddacaddadcbbadaaadddddbbdacaaaaabcdacadbadddaacabccbbacccacdcaaaacaadcccdadcaaccdbcbcbdbaaaadabbddabbacbdbdbddbacdabdacdacaddbccccbacddccbdbaddbaacbadccdbdaccbadacbbadddcdadabdaccdabbabaaacdaacccacbaacabbcabdadadbabadbdabcddadbccdadbdddcabdbacbbdaddaccdbaccacddccccbbbadbbcdbcadddaccddbdbabddcaaaaccbdbabcbbccdbbdcbcccaddcbbbbbcdbccbcbdadcadacacbaabddcaacdcaaccdbcbaadccbdaaccbdcdacdbdaddaacbaabaccbcdcdccaadaacbbdcddcdccdddbddccadddadccccacdddacacabcabbdcccacbbadcbbccddbabdbcdddccaddccaddcdccabdaaaabcbbddcadcdaccdacdcddaacaacdaadbadbbbbaddacabccaddadabbaaddaabdcbbdbdccacbcbdbcbbddbddcdadcdbdbadcdbcadcccadbcacabbadcbbdccdaacbacbcdabccbadacbccbcadbbcacccabbadabcababcdccadcccccccbcadcbacadddbacbcdacbcabdacbdbdbddadacddabddddaaddbdacabdbbdcdadbdcdaaadabaacbcbcbcabdaacdbadccacbddbbabddccdacacbbcdbdbdabbcaccdaacabcbcdadbcdadadaaadaabccaabbdbabcbcbdddbbcdaabbaabccacdcaddbcbdbbdabdacaacabbcacbbbcbbccbbabddbbaddbdbccdccdbcdbdacbcdbcccdcaacbacabcccdabccbdbaacdcddbbdacccbbaaaacbadadcacbcbbadbccbcaccbccabaabcccacccaadbbadddadaccdcdbcdabcdcdacacabbbccccccbbddadcdbaacccaacabadcabcbcdbcbaadaaddaadbdaabccacaccadcbaabbcadbaaddcdcabacabaddccdcacacbbbaadcdadccbbcdbbdcbacaacaacacbcadbbabbddaddbddadbcbdbacadadcdbacdcbdcccbbddddddbcdabcacccaccacdbddcabbabaaacabdcddccbbdccadddcaaccbcabdcddadddbaadaadabbadbddbacacdcabaacabdcbbbcdbaddaadbdaaaddaadbccacbdbdbbacbdcadbccbcababcdbcdadcbddcdcdaacdcadcdbbadddbabcdabcdabccbbabcddbccdacdcbbcaaddbbabdbdcdbbcbabadccacaabbbbccbddcdaccbdbbdbdabdbabaacccbdcbdbdaaddccdddddcbcaabdcbbbcccaaaaabdbcbadccddbcdaddddcaaaadbadcbddaabdbcdabcbdcbbccbabdbbbadcdaabddcbcddbbbabcbbdbcbdbddacaacdcbacbcabbcbadcdbdcbbabacaacccbcaacdcdbbdaddddacddadabbbbbabddcccbbabcbccacbcbbaadbcdbccaacacdccdbaacacbdcdbcddbaccbdbdccabdadbbbabdabacbaaacdbcbbbdaaaddbaadaacdbaadaadcabbaabdddcbabbdbdbddbbbdbcddbbabbabcbdbccbaaaddcbacbccccbdcbcbcaadabbabcbaaaacdbbaadddcaabaddcdbabccacaaadbbbacbdddaccababaddccbbbbadbcaaaddccdbcddbddacdabcbdcaaaacaacadcddbcdacbdbbaabddaaaaacbaacdcdabcdcabcbadcadacdbcaadbadbaaacaadacaacdcddbcacbbbcaaaadbcbcadabdddcdbabadbcabcacadacacabcdbacdaaddbccbaccbbdcbbabadbdccdacccabacbdddbdbdccacbcadccccdccacacbddbabcadccdcbbaacbbbaaabdcadaddbbcdcdaccbcdbdccbddccacdbabadbadcaddcababaadcadcdcaaadabacdaddbdaabdaddcdbaadacaadbcabcdbdabbddadaaacbabbdaddcdbbcbbcadcbbdddcdbcbabdaacacabbcadcdababccbbddaaabadbcdbdddbaaaabbddbbaabbadcacdabcbadadbacdaaccdacaaacdcaaccdcabbcbccbdbabbbcdabcbcbdbcbbcddcbdbaaaccdacbadccadbabaaddadacddbdcbaddbcbbaaadcdbcbacdcddacccbccbabdcdbcddadbccbbccacbbbcbaabaabbbadcbddcdadcabbdbadcbcaabddbacdcbaacabdbcbdcbdcbabbaccdbdaaadaacacaddcdababbdcddccabbcdadacbbaaacbaadddacaaddacbdbdaacccbaacaaaabdcbabcbbbcdcaadccaaacabbddbbcadcddbcccdcdbaaddcccabbbbdbdabdbcdbdbbbddaacaddbaacdddaadbbabaacdcbddddcacdbdccaadcbbacbdbacdadcdbcdbaadaccdacadadabdacadacddabadbdcdcccbabcdcdddadbbbcdcdcadadbcabbdabbddbdbcabcdadbdacacccacaccadcaccadadccbddccdcccdbbaccbabcadadaccadccddcdacbdbacbbcadccabbcdacadcdadadddddbddbbacccbcaabbacdcbdbbddadcaacdbbccaddbabcbdabdbdbcddbcaacaabddbaadcadadbbadaaccaddadbbababdabbaddcbcdbaddbbcbbabadabcdacddcbaccccabddbdccdaadbbcaaddaaccddcbbdcdabbbccddccccabdbcbbabcddcddddccacddbabbbaaddadddbadabcccadaddddbaadcddabbadccaadccccdcaaccabdbcbdcadacbcaddcaaaacccdccaadabacacbccbdccdbadcdcdabcccacbabdaabacccbcdddccbdcdbbcaddddabcabccddbbdcdbcddcbdcbcabbddcadacabdbbbcbdcdabcdbccdbbdcccddbbdcbbbabdcbcacadbbaccdcdaabcbcaccbddcdbbddccbcaddcdddaacccbacdabdcccdadccdddbccdabddcdacbdcaabcbddbbdbbcbbdbbdadddbbddbbabbbbddcccccbabdbcadbcabadcaccdaaadddbacbaacdcbbcaabbcbdddbaccbaabdadacaaccdbccacdbdbbadcdcadaabcdbaabbddbbdcdaacaabbbadbaabcadacabbbbadabdbcadddddccbdddbbbcbdcacbcadddbcdbcbbdcabcbdcccbbadbbbdbccaacaacbcabbacadabddacbccbaddbdccbdcdbadbcddaaccadaacbdadccaabcccbdaabaddbccacadadddabdabdcaccbaaababbdaabbdcbddcacdccacabbcdbabacdbcbbcdbbdbcacbcbaabddadacdbbaaadbccdccbcadccadcbadcccbabbaaacbcdccbaaddcdcdabddadadccaacccdaaabaaaaadcbdaabbaabcdbabbcacabdbbcbacacdbaabddcbdcbcdadcbddbcacabbcccadcaadcccccadcadbaadcdcdcbdbcbcadacbbaaadbdcccacbddaaacacaabdbddcdbdccdaacdabcccbbacbdaabbcbdbabdddbddbccbaccaddaabddccbaccaddddabbdbdcdcdadadbadcdadcbbdaaccadbbaadcaabdbabbacacabdcaaadacdcbcaddcdcaaaacacacdacbcbacaabdaccabdccbacbdbadddadacaabdbcbbdbaacddadbbbdcdabdabdccdcbcbcdaccacdcbddaadcbabbbcadbdbaaacaddcdcbcbbdbbbbcaccdcbddcaccbabaddcacddbaccbbcbbbcbbbdbbddabddbabcccabdbcccabdbaababdaddcaddcabbdaddacdddcbacacdabbaddaddabcbcddacaddbaadbacdabdbdacdabadddbaaabdabdacadacdacaaaaabdbcbabdabbbdbcacbccaaaccacacbaacbbacbddcacadadccddbbbdbadbaaabbbdbaccdcaccdabdacddadcdcbbcabccbaaccacbcacbadbaaaccbacacdbddcbcdadcadbddadaabccbcdaabdbcaacbbaaacbbcdacbcbaacdbaddadabbaddcaabaddccacabaccaaccacdadbacdacdbcdcccabccbbacccbacabcbabaddddaddaadddbcaadaadadaddaadbcbbadcababcbbddcdddcbbbabbacadacbcabdadbcbccabcdadcaacbcdccbdcddcbccacdbaaddbbacaaacabacbaaddacdcbbbacccacaacbddbcbdbbacabadbbdccabdbccbbdddcdacbcbcdbdcabbcbddcbaabcabbcabddbdccdcccbadcdaaaaaaabcbcccbcdddddbdabdbcaaabcbbcbacadbcbddaabdcabdaaddccccdbadbcbaabbadbdaabdddbbabaadcabbdbadbadcdbdcdbdabadcdaadabcbbbcadbcacabbccacbbcadadbabbabadbdaacabadabbbdcdcdacabaacabaabaadcddddcabcdcccbacbcaddbccaabdbbbdababcdbcadaabdabddbabababbdbddacccddadadccdcbdaaccdbccbddabbcacdbcbccdbdccadaddaddbdabdbabdccacabaadcbddcabbbdababbbddaaadcbaacdabddcacaacdcaabacccccdcaacddacabbccbabbbdabcbbddabbaccaadbdbababddbcaaacbbabaddcbbddaaccbdcdbcbacaaaaadbacadcadadaccbbcbbccddcadbddbdbdccdaacbbbddbcbadababdbddcdbbacdccadcbbbbccccdbdccabcabbcbdbdabaccadddccbdcdcbdcdbbddccdacaaabdbacacbdddcbdaadbcdadcdbbdbdbdcaabdacaaaaabbdbbadcbbccacdbcacbdbcbcbbaaaabcaabccadbadcccbdbbbccbbddacdcbcacdabbbcbabbbcbcccdbdcdbbbdddadcdabcbacaaabaabbbdbadaacddbabbcbbcadbbadabacabbadddbbadbcabbdcadacabadaaaaddbacdadaaadcccaacbddbaadcdcbbdaadabcabbdbabdcbbdbdbcacbcacddcddaccccabaddbabcdddbacaabcacaadccbbdddbacbadaddacbccbcaabddadbabbdcdcccabbacbddbbcdabdacbbbcacadbadaabacaababbdddadabdcbacbccddddccbbcababaddcacaccadaccabbdbddabaaccababddbdacaaddabdbbdacbacdcbbbcccababaadcbadcccccddddbcbcacdbdcbbdadadbdcbcddaddacdbdbbadbabadbbdcdbccccabdbbbaaccdbbcadacbabdbabcdcbcaacacaacbbdaabbabacbaccabcbbcaccddbbbddccdcdbdaaadbbbbcdadabccaadcbbdaaccacadaddabdbbdbabccbbdbaacaaccbcdcdccbacdcccdaaabbccbdbbccaaccabbacddadbbcccbbdbdccddcdccccdadbbdcdcbaabdacdcbdbbcbbaddcbcbdbbbcbcddacbcbcbaddaaaabbdccaaacddbacaddbdcdcbadbabcdbcbcbbddccbbcdabcbabcbadbcbbddcabdcbadcccbbcccbbadaacdaddbcaadabbdcdcabcabcacccbdcddccacadacdbcacbdccbbdabcabbcbbacccbcbaccdcbbdbacccadabdbbcddadccbcbaddabbcdcacacabaacbabccbddddcbdbcacadababbdcdbcbdbabbccdcbcbddccccadaaadbccaddbaddbdcaaaccdbaadcbabdbddbdacbcdcbbbacdbacabacddbacbcacbdadcbcbccdabcabcbadabcbabdcaddbdbbbddabcdcaaaacaacddaadabddbdbcabddabbbaaacdbaccabbaacdabcbbdcbaddbbbbcabacadacbddddcbbccdbaacadaddcbacccaadadadcbabdcdacbabdbaaabcdaadcccababcdbbdbcddddbcabcdbcbaacbbdccacabaaccddbbaaaadadbdccabdbdcbdaddabcdddcadccabbbaadbcdddabcdcabacdbbadaaaaadccadbcadbdaadabbbcbcabbacdcaddbdbcbcdacbdddcdbadcddacbacbbadabaaadaabbddddcccbbaadbaaaadaadaabbbacddadcdcdcccacddaadabbbbdabcdcdabcddabcbbdabcbddabcbaddcdcdabdcdacabcadddaaadcbccadcabbcacbabacabaadbbdbadbbdcadcdbdccccdaddaccdddbaaccbdbbdaccdacccccbddddabbcbacdbacaacaacdcccccdbacabdddbcaadadbadcbabaaddabaabbdbbcacaabbadccbadadbcdbbbaacabaabcbaaadbdbdbcacbadbdbbdaccadacacabcdcbdabcdddcbacdccdbdadcdaaaddbcbadadccbbaadbbbadcaccbdadabbcabbdbaaddcaadbdbddcaccbbadbcddbaadbacdbcdacbabadbaadbadbcdcdadadbbccbacacaddcadbdacdadbbaacccbabcadbcaccaccadababaccaddbacaabdddabbdbaadaabadbaacdcdbccdbddddcdaaadcbdaabaccbacbabdadbddddddcdacbcabdbaccbcabdaadacaadbcbdbbcddbadcbdadacbddccacbddcbbdbaabbccdabacdcaccbdbbbcaabbabcccbadddddbdcbbddaaaddbbcbdbbbddaaacddbcdbdaabdbccbabccabcdacdbdacdddcabadbaaabcbcbccdbbccdcaadcdadaacddaadcdacbbaadbacddcdccadadbcabaaaaccbbbdbcbadccaaabbcdcadbdacdbbbdcdaabcdaadcbdccabdddaacbcdaddcbdabaccddabccacaadaddbbabadbacbacdcbddacdbbddcdbccdbbaadbaadadaacdbdbcdcabbaabbddbdcbdabbcaaabbddcdacadabcbcbbcadccabdbbcbccbadadbaccdcacadddcddcaacadcdbdcbdcbbcbbcadaaddcbddcacbbdccbdccccdbdcadbaacdbbbbddadaabbbadaddadcbbaaaaddbcdbadabbdbdbbadcacccacbaaaaabdbdcdbbdaaabcdcabccdcdbcdabcaaaaaabdbdacabbabacddadaabcccabdcacaacbaaaabaabdbdaacadbbccbadabcccbcdbadbadccbcdcddadadbbacbbcbccdbbdbbbccbadcacaddcacccddbbcbacadcccbcabbdacdabadcdcadccaabdbccdcabbcacaabbdadbabbcbcbabcbaabbacdbdabcbbcacadddcbdbbadbdcbccacabdddbdabaaacdaaacaddddbbabbaaddbacbbabcccbacdadcddbdabbacbaccdacaabcaccabbddbbcabdcbdcdabdddacccacddbcaabacddcdcbccdcdddcddccdabbaccdacbadcdaadbabddccadcbbbbcabbcdcdabadbdaacccacdddaacdddaccdbcdbadacaccbcbadcdcddccdddacbaccaacdaccbcaabcbaabbcbbbadcddcbbdbdacaadabcabdcaacadaacbccdbbcadcccbccccabcdcdcaddccbabdbdcaaabbbcadaabaaadcdcacbcaaadaddcaaadbccbbaddaccaccacbdcdbcbbbcbdccacdcdbdddbcdcabbaacbcdddbbbcbccacbccaabaddaaaadabcbadcdbaaddaabcbcadcdaddcbdabbacbaaaddbdcaaaabaabdcdcbacaabbacaaacadbcccbabbcaaddadcbbcaadcdaacadbbaabddacddaacdbbacacccdbdaacbaccdbaddbdcbbbdadddbacdbbadcdbadadddcccacbdcadddaadddadcdccaddaacdaadaddacaaaddbcddbacadaabbbddadcdddacaacabbcadccadaaaccbbddbccbcaaccddbbabacacdcbbcaababaabdbdacbabdbcbcaabcabbdbbbcbdbbcaddaaacddabcbbbbdbadadbdabdccbdbdddacccdccabddbaaddbcddcaaddccdcaaccbddcbdbcdbadacababadddacacaccdccbdbddaddbddababaadcbbdddbdccdcddadacbbdbadadccbdadcadaadcbcbabbdadbadbbbddbbddabbbbcaaabacdaacabbdadababababcadbbaaddbbaacdaaccccccbaddcdccaccbcabcbdcbabcbbbabdddcbbadbddcbbddaacdcadbaddbcabccccbadbbdbdbccdabbdbdabbadaadbcadbadbdcddabaccbdbaaabadcdbbdcabbbbcacbcbbabdaabbdacdcbdcdddaccdcdddbcacdcacbcdaabbbbaaadaadbcdbaacdcacbbbdcdabddcababdbabaccaadcbabcadbbccbdbddbcaabadcbdabbcacbdccabcadddddccdbabcbaabcacbbccbcccaabccddaadbcabddacaaccdccbacdbdbabbdaddbdacbabcbadddbdaadcadbacdbccbadbaccaabbdaccdcabdddbccddaacbdbcbdbaabbcbcbbbcdccbabdcaaccbcdaaddaabbbdacacaccdaacdbbbadcdbbbcbdbbcacabdccaddcbabdbbddddacabcaadaddaabacddcdbacccdbcadbccbabbadacdbaadbdaadcdadacabccbaacbbcaddbdbdddbadacdcbacbacdcacbbabcbbdacdbaaaaaaccbaaacbbacabddbdbcaccbddbcaccdccbcddbcadcaccdcbcdbdbdbcbcabacddaccccdbbdadcbaabbaabcbabdbabbddcbdbcaacabdaccbdddbdbdddaacbabdbdbcadbbccbcbaabbabbcddbcddbaddbbdbddcaaadbbbadbdcadcdadcccccadcdcbccdbcacbccacaabdbdbcbcabdcbcbabdbcbbabdaabdacbbbcaacdbbbcccdbbcdcadcaddddbcaacdbdadcbaacbbbdadccaabaddadbdaadccbaccaadacbdcacdbbcbbcdbbcccbcbdccbacaaddccabbdccacdccdbabcbbaccdacabdaabcddcbbbcabdabcabcdcccdcbbcbdcbaaaddacbdacadbdbbccdacacdbdaacddabaaccbababbccbaaacbdabbdbcddadcabbcadcaabcccddacacdbdbacaadaccdcbdbadaadddccbdcacdbbcbbcadadcabdcccadbbacabcbaacabbadbdcadbcbbacdcbbdccdcadcccdadaadadcddadbdcaaaababbbccbdacabcbdacdccbbabcacdcaadacdcadcbdcbcbdbccdbdbbacccaaadabdbbdacaaabaddbdadcadabbcdcdcababcdbddcabdaddccaddccadacccccccacdadbcccbcdbdcabbbbcadcbdbadddccacaccbbcccccbcdcdbabbdccbabbadcadcacdcdabcbdddacbbcbcdccdabdcaccdcadccbabbdabcbaddacdaddcabdcadbddbabcbdbdbdccddbadbdbcddbbacacccdbdadcbbdadbaaccbdabbccddbbaaaabaaddaddccccabcbccbaacdadbdcbadadccdcbdbaccdcdbaaccbcdccacacddbabacccdbddbccbcddbbabcbdcdcaacadbcdbbdcdbacbadbdcdcbaddacbddabadaddaaacbaddbbbbcbabbaccccabacbacaaccabbcccbbdbcccadabbcccbddabdabbaadaabdcacbbbbcabcdbcbacbcdcdbdadccddddccaaaadbcdcaccbcbdbbcbbbaddccabdabbaadccabaaabcdbaabcabbdacbddcabbaaabdadcdbdcbacddbcbadabbabccabccdcdcabbddcaacdbadacacdbcbababcdabccbadddbccbabddcdcdababcaabbdbdcddbbbaaccbaadcbbbaaaaddadcacdcdbbccbadcabdbacdaabdddcaadccbddbdddcdbdacdbcacccdbdacbbcbdccaadbbaacdbacdccbbaaadabbcdbdbddddbdbddcbdabaadbdabaaaabcdadadbbbdababdbcbccabaaaaaaddddabddbbdaacbddccdbadbdaddddcdcdbccdcbabdbddbbccdcdccaddabccddaabadaaacdbbddacbadccbdadcccabcdabbbbccdbbadbaaaccbdabdbcddcaabcacaccbcdccaaddacaccddabdccacacccdaaddbdcbbaadcbbcdcdabcadbdbabacdccdabcbacadaaaddbbabaacaccbdaaabbbabcbdbcbbbdabbbaaabcccdacdbbcbdabadcdaddccbbcbdbcbbdaabcacbddddacbacbacdbdbcccaaadcbdabbcbdabccdcbadcdcdbcbabccbacbabcbbacccabdadbccacdabdcbbbcbbdacbadccccaaddcbadcdacbddddabdcbbdbdcdcacccccbccdabbabccdbadadbbdabdaccdccacddacdcbcbcabbccbbcbbdcbcccdadbcdbcacabadadadbbbcbbbdbbbbdbdbaccadbdbcacbdabbaabacdbddddabbddcaaaaabdcbacdaabbdababccbcabbbaaaabdcaccadbcacabdbdadcadcdcbcacdcbdccaddcdbbadbadbccacaacdcaabbabcabcdcccaabcbaacdbbaddabcbbbccbdbcbdbdbcbcccbbdbbccccbacaaddabcbcdbcadcccccbdddcbcdbdacdcaacaabcccacadcaadcaccacdaadbaadacadbcabadcaabacbddaaaddbbadccdadcabccddacddacaaaabbddcaabbbcdbbcdbcaaddccabaabbdaddcdbcabbaabbccbcdcadaddcdcacbbababbccacacaccabdcacdbccdddadddcccdbdcdbbcccdabcbadcbdccccacbbacabdbdacbbbacccbbbcdbdaaacbbccbbcabbcadcbdadbbacdbcbbdbbcdcaabbccdddbbaccbbbbdddbdacbddacddacccabccddbdcacbdccaacabdcbbdcdcaddababcccaaaabcbdcabacbdadaddbacbbdabacdbcdcaabdbcbbbcccdadcccadcbdcdbbdccbcacaccbadcbdcacabdabadbdadabdaaacddaabcdddbdadaddcbdddcabbbbdbcadacbadbbbbdaaccadbdbabacabdaabcbcdccdccddaddabccbdcbacdaaccabaddcdacbaacdcbacabbacacdcbdcdbdbbaadcbbadcdcbbddacaccbbaacdbcbbccaddadadcacadddcdabacabdbdcdcacdccdbcdcdddbabbccccddcabaadaaaaacbcdcadadccdccdadbdccdcbbbcababcadcdcbaacaadbbbdbbbacacdabccbdccddddcccbdabddcddadccdbcdaaccacccbabaaaacdbbdcadadcdbabbaccccccddcbcdccbddbcabcbccdcbbadbacdacbaacadacbdcaacaadaccababbcacddcdacaaaccbadacaddcdbdccaccdccdbcaddbabcddbcbcdbaccdbbdccbbaaabbdcaddbcadccdabdddcabadccdddaaadccbdbbdbccacdbcacbbdbaccaadadbbddacccaddabcbcacccbbbabdbbdabaabcddcdccccaabbaabdccddbabcccaacbbbdbcadcbadbcdadbccdbbdbcaacbdaabcaaabbdcadacdbbccbdabcbcbbbaddcacbdabdaccbdabddaacabcbddaabadcbdbdacdcacaadddcdacdccddbccdddcbdacdbddbdbccbcaddbcaddabbdcbbbdacbdaabcabcdcccbacbabcadddacacbcdcdcdaddcbbddadcaabbdbabdbdcabcbacaacbacbcdccabccbcdcddbbcddabcbbcdccbbcdcbacbbaccbaabdbbaccddaaddacbadaabbbdaabbabbccadaaddbaadcdaacabbcaadaadbbbccbbdccaabccabddadbcacddadbaadbbcbadaddadcacabcaaabacdbbaabddadddbabdccabbcbdabccacbdaabdacdaddacdaddbdadccdbbaadbdbbadcbadbaddcdbbadcbbadcaddcaabacabdbddadcddbddacbcbcbbbcaacddbaabdbbbbccbdbacddadbadcdadaadadccbdddcaaddcadacdabacddbdcbccaccbbacdcbdcaaacbaadcadcacdccdbbabdccdcbaccbbdccdbcbabaaadcaacccbcadcadddcbcbaabcabddaabdbbaacccbaaaabbdaabadadbccaacddccdbcdaddbbbbcbaccabaddcabaddbdbcdadacbbdcabaddbbabdbbbbdadbcbbdbdbcacbcbcccabdccdacdbcdacdddabcdcabaddccbaacacabadacaadbcaabddaabbbbaddbdcdbcbadcacacdcbbabdbccdccddbdadddabbbabccddaacadadbccdddacbbadacacbdcdddaacaabcaccacabbaaacddcaaaddaaccaccdbddbcacaabaabcbadcadacaaccddbbbddabcbaccbadcacdbdcbbdccdabadcccdcadbbcbcdbaabaabcdccaacddcacccbbabdcdccccacdccdbabcbcdbbccdaabdadaabcadadddcdbabccbcbbbddddddadccbcdbaacadcadabbcccacbacaacadacdbdbcdcdbcaaaccccdaacdddcdccdcacbabbaaaabcaabdccddadadadcdadcbbbabacbcaaadbaddaaabacdabcdcbcaddabababddadcdaacbbababdcabbcbbabdcaacdbabbbbacabdabdacdaaaacdbdabbcbddcccaacdbbcdbbdcbcbcdbcaacbdbcbbadbcdababbcacacacbbccbadbcdbcbacaaccabbaaddadcddabbbaabddbcbccbacabdbcaacaabdbdbbabccabcdbdccacddaccbcadbbabcdddadcaabaacccabcbabdbaaccbbdddabbddaadbbaadbccdbadcbbddcbdabdcbccaaadabcdbbbababccccbbcaddcdbcdcbccdcdbccddcbabdbbacdadbccbbbcbddcdcccaddcadcdbcdcbabbccbccdbacacadbcbbbaaccbdbbabccdbaddbbddacddbbcbcddbdbbdcdbdbbaaddbddcdbabcdaaccccdcbbaddbaccdadbccdadadcaddcdbdadbcbcccacbdbbdcbadaaddaaabababcbbdbddbccaaaccdbbacbbabadbabbabbccccddabddddcdbddabcacbcaadbdcaddbadaccbbdaabbdcdacdadcacbabddccadcccddadadcdcdbacadaabaaaadcdadcccbcbbddbbbddbccbbddddbbcddbddaddcddbcbbccadccccdcaacbaddcacbdabddaacaaadcacacacdcbabcddacdbabdccadcdbcaccbdddadcccabdcaaadcdddcbddbacabcbbacdcccbcddccbadcdaadbcbcdcdabdbbaddddabbabbcbabacbdbccddbdcaabddbacbaaacdbbbcbbadbdbdaabddaddadccdaacbbcdcaccccbdbcddcbbcbbbcaabcbdbcccccbadadcdcccbbdccddcdbadbdccdcbbdacbdddcdaacdbadaaacdbccaaddbccbaaccdbbadcbddcdaadadaccbdccddbbcdbdbbbbbcbbbbdbbbaacadbaaaddacabbdcbaadbbabacabcbaccdaabccadbbbdccacbcaaccabbccdbdaacddaccdaddbccdcaaadbbcdbbbddbaccdcbcbcbcababababddcadccadbadadccddbacabadcacbcabbbcbdacaadbaaacbadabcbdcadbbcdbccaabbdadcccaccbcddddadbcaaddbabccdbcbcbdacccbbadbabdbccbdcdbbabdcaaaddbbabdbdaccccbdabbcdcdbdddbcddbdbaadbbcbdaddddddbbbcacdbbbdcdadcbcbabdbadadccadcadbaddabcaaccbdcaddabccbabbdaacbaabdbbbbcaabbacacdaaababdccacdadddccbdbcabaabcdcbdaaadabbaabbadcbdabcdbbdcaaadbbaabbdbcdddbccbcdbaadcdccadaddadcaccaacadbdbbadbdbbabdcdddcdddcccbacbaadbbcbaaadcdbddcbdbcbabcabcddaabaccaccacabcccdcaabdddabacaacbbcccdbcddcdcdcdbdabdcbcabbccabcbcdbabcabadabbcbdcdabadaaaadbadbaaccbabdcbbddcabcaacbabadaacaabdbaaccdadaaadcbcbbccddbddbbbaccacaccbcddcccbdbbbcdadaccbbddacaaaadbbdadccabaabbbccaacdcabbbaddcbabcccbabaddbdccdacaabcbcccccdbcbcdcbcddabcaddcbcaaabcbbababbaddadabaccdbadbacbdbdacdccaadadaaccbdcabdaaacccbdadadcacbacaaadccdddbcdcdbacbcdcbbbbacdacbdcaccdcbbdacbdbdaabbccdddabcdcbaadcbaaaabdcdbdcdacabacdddbdcbabddbbbbbcddbbabdcaaccbbdbdabbcaaaaacbdcccabcbdaddbbaaaadbbddcaacbbcdccbbaabdbcdbabadaccabaccbabdbaaabcbcabcaadbcddbdccaaabbddabbccbbbccabacbcadbccdabbdbaaacaacabcaabdbaacbbdabdcbaddacbabdcdddadacacbcbcaaacaaaddabcaacbbadbbbbdacdcdbbbbbbcbdcdcacaadaaddacadcbbadcdbaabadaadbbcbaabcccacdabaacabdbaaddadbcabbbacabbabddbadcbbacdccdcabcbccbdbccbaaadddbbcddccddccaadddabccddbddbbccaabdcabbdcacbdcdcaabccddcbbaddcbcbadbddcbaaacacbddabadbddcacacbadddcccbabcabccadcbbcbbaaacabcadbdababbaabadcdaaaccaddaaaddcbacbbdadaabdbdcbbcddbaacaaabdcdddaaadddbababdcacbccbcbcdaabadccaddcaaabccdbbadbaaadadbcacbddcdbbacbdddbbddbdddbbadcdbabadbbccdbddbbacaaabcbbcdccbacdadcbbabcbcbcaadadccbabacdaccddbbddaabcdacaddadbdcabdbbbaccbbabdddaccbbcccccadbcaacdcabbbdaaaaacdbacacbdbbadaaddabcacaabaabdbdaadbbddbabaacbcbaaaddadaaabababbbacbbcaaabdcbdbbabbbdcadddbcdcbbabddaacdbabbdbcbdbaabcbacdbbaddcdbccadcdbbbadcdcdadbbbcdbadabcdbdadadcacbbbabbacddcacbbcaabaddbcbbaaacddddbcbaaccdbdabababaabbdadabcbdbdccbdbbcaaaadddbdadcccccaabacadbdcabbcbcbcdaccbbddcdcdbcbcbadcbcdcdaabadaadcbabacbbdccaadbdabadaaadbcdcbadacbbcdcbdaadbdddccdaaaadbdbaabbabbcbbddaddacbcaaabbdccabdaaddcacbabcbbaddadbdacdccbdacadbdcabdcacccadcdbdbcbcddbdbdbbadbbcbbcddcbacaacdcdbcaadddadacbcdbdbaccdccdddaaaddbdbdaadacaabcdacdaaaccaddaaddadaccbcdcdcbbcbaaacdaacabbabacacabccadccadcdbaabaccbaccacbddadbcbabddccbdaaadcabdabdacbdadcddaacccabaabadcdadaddbdbabdcbcadcdcadaddcbbcacccdccbaccdaccbddddbaabdaabddcccaccaabdaadcdabbaaaddcbbcabacdbdbadcabdcacdcabcbaacddbcaadddcddabcaccaadbdadcdabbdabaabcbcdddbcabaabdccacbaabdababcbdddddbabaacccbdabdbdbddcdbbccdaaaabcdadcaccaacbccbdccbbdcacacaabdbbadcaabbcaaaababccbbccbcacccdacbaccddcbacbccbddbabdcddcaacddadcabcbdacadbbbdcbbcbadacaabcabacddbadacbdcddcdddbabbcaaaaadadaadbdbdcdacaabbbabcaaabababaaddbbbdbddbdddababbacdaddccbbabadbdabaacdacdcdcbdcbcbccbbaadbcbadddbabbccdcdabddbabbadcbbddcdabcccaaadabadbcbacbbdbcaccdabdbccaddadaadddacdaaccdccdcccdbabddbdababcbcdddaaabdbaccddcdaabdcbbaadcbdcaccabcdcaadaabccccaddabdbccbdcabcbddddabdaaadddbcaaabdcbcbccbcdbbbabbbcdddaccbdabaccbddcacdddbababcccbbbdbcacbdabdbbacdcbccbdacdaabbbcadcbccddbbdadcabacbbcdbddaddcdcaaaadcaccacadcddbccbcbdccddadaaadbdbcbbcbbadcbacdbddcbcbbaaacaaadcabaddadabddbbbbdbcadaaddcdbabbcdccbcccbdcbaaacbbbcabbabdaaaccbcacddddcdaabcddddcdabddadddbcdddaadbbaadcdacbaacddcaacbbdcaaaaaabccbbabcdbdbdcccbabacddacbbdabcabaaddbcbdaaaccabaccccdbacacbdddacadacdbcacdabcdddcacccdaaabbdcadbbbccbbdacbcacbacaacbbbbddbacbdcdcccadcccdbdcbbcbbbdbcadcbdcbdcdcdcbadcdcadbcbccbcddcbccbabcdccbadcbcddcdcdccdaaccdcbddaddcaddbbdcacddbdbaccbbdddbdaacdabccbdbaaadddcccbcbcacbacccdddbcddccababcbbbcbdaaddcdbdcbbcbaacbacccdbabadadaaaddadcaaaaabbdcdccccddbcadbbdabdaabbccdadaddabcbccbcbccaccabdbbdbddbcbcbdabdaddcbdacbbbbacaacadaaccdbddcdbacbadbacabddddcccbbbbbbbcbaddddabcacdbcdacdcccbbcbddadbaabddaccddbdaaccbdadddddbaccdccadccadadbdabcabddbddcdcbcabcaddbdadaabbcacadbadaccccdcbdcdcddcbadccccdaacabdcabdbbcccaabdcadccaaaaccccdbabccaddbcbbcbbbcadcdabdddadaaccbcdccabcccbcaabcbacccdddcadcabddabacabbadaabdcbacbcbacbaacdbbdbbabbabaaabbaaabccccadacabddccbbcbbcbbbabbcacbaaaaaccdabadbadcbacddccdbdabcbcdbaacabaddabbccaccdacdbadacbcddabcadacdccbbddabdacdcdcccbcdddbcddcbadaaabdccadcdbabccababdcaccabdbadbbcadbcddbdabaabdccccadaaadbbcdcddcabaddcdacaddbdbcdbddaaabadcaabbbcddaadbabcdbdaacbbcbddcabcacacdcaaccabcadbacacbadcdcacaaaaabcddcdbaadacbbaadbbdcabcddbbcdcbdbaccbddaacaaccddbcabcbaccddddacbbdabdbcaddbdbaaadbcabdbabbbabcdccacaccbacacddcaacacdcdcadbdbcbdababaccaabcabdcaadbccbcdbdddbbdcadcabbcddcaacabadccaaaddabaaabdabbcccccbbcdaddadacdacdaacdbbbdbbccbdddbdbdadbdbabbcdabccdcccaadbbdbdcbcbcdbabdcabbdcddcbcdcacacacdcbbdbabcaabdcdcbbbaabaddddabcadbcdaaadccdaacacacadcdbbbccadbbbdaccccaaabdcdbcadbdabdbbbccbcbcbccdabdbdabadabcdddbcabdaaabddcccbcbaadcabacbdcbabadbbaccccbddacababaccaccbdcbcbabbbbdccdaabcdcdddaaaccddaddbcacdbcacaccdcbcbcdadbccbcaddccbcddabbdadabacccaaaadabdbabaabaabcbabacaacbdbaddbbbbdcbadcbcaabdbbdaaabaaacdadbbabbcdcdcdbcaccbabddcaabadccdccbcddbcdaadbadcaccaadbcbbcbddcddaabcaaaaabcdabdacdcabcabbaaaaaacccaddcbbacdbbdbaaddbcbacbbdcacbcbadbdccacbbdccadacdaddadabbcaaacabdddccdbdcbaadbbbacdcabcdadacacccbcdcbadacabaaabbcbaddacabacdadbbbadbacabcdaaccdaabacbaccaccbaccabdbabbaccbadcdadbcdbddaacbbbacacadddcbdacccabcbaccddbccabbcacdbadabadbdaaaabbbddcaaabaaadccbdddbadcabbdbbbaaccdaaddcdbddddcbbadcbcaddbabcdcabdddccaaaaacddaabdaccbaacbbcdbdcbcbabbaccadcdabddddabddcbbccbcaadaabaaddaadccdccddbadaacdabacccddcbdcabbddacaccccccadcaababaaddabdabbbbaccababbcaccbaccbbacadbaadbbbccdabcaabbabbddbbbcdababcdccbcbdbcbcacbaccdbccadcccdbdcdcdbdabdcaacdbabaddcdaaaaccbccddabcbbddbaadaadcaccaadbcaabddddadbcadcbbbbccbdabcdcdcbadcabbccabdccabcbbcacdaadbcbbccdddbaccbbabacabbcbabdcdcaadccaacdabaacaddcbacaacddbccbddbaddcdacdadbbdbccdddbbaacaaabbabddcabaabdcabbbdbaaaddbabcbdcbaadbccddbdaadacccdaddaaaaddaaaccabbbbdcdcabcbacdbdbdbabbdbbbbaddcbadcbddacacdbbaabaadcddbaabaaacacddaabdbbbacadcdcbddcbbabbccbabaabddccbdbccacdbdbabccbdacabbcadcddcdbbbaaaadbcabbdccddcaadaccaadacacdbbbbcbdccabcadbdbcbddcccabbbbccbccabcbdcbabcacaddbbbbcaadabccccdabcbcdbbdcddcaacbbdcabbdacdbcadcdcddaacdbcbaadacbbbccddcddcdcbbcbbbcbababcdaabdaccbdbadacdcdbdbddabdcbaaccdacadaacaabdcbadcbaacdccbccbddcaaabaacaddaacccdcacbdbbbbbdbdbaddaacbcdabcbcaacdacaaddcabcbdaabbaaabacacbbbcccccdcccdadcbcabbdacddaaabbbcacddbddbcadcbdddabcaabaabcdccddaababdaabadccdacadcccdcabadbadcbbdaccaaabccccbbcdabbabdbacdbdbacbddacadaabdcddddadacadbbdcaaddbadbaacbaacbbcbddddcbacabcdbbabddaacbdabbdbbbacbbdbddabdbbadaacdabaacbbbbbbcdcbccdddcdadbdacabbdabbabccaacddbcabdcbbadaabcadcacdabaaadbdabbaacbaccbbaaccdcbcacaaddcadabccaaadddcdaacaddaabbcbadcdbcabdcbdcacdbbaadbcbdcbabbcdabadcbdadbbbdaadbacaaabaaadbccdaacdcdbbacadddadcababbdbdbdddabbcdaaacccdcaaddacccaaacbcacbbbaccbababaaadbacccaadccbacdddbbbcbadaabaadbcbbdcddcadbcdcdcbabbdccbdcdaccdabbccccbabacbcbddccacdadbbdddcccbacbbdbaadabaabcbababdcbcbcbadbaacbadddaabaddbdadaddbbadbabcaabbcddddddaaacdbbbdbadbabcdcabaadbbbaddbacaacbabddbcabccbbdcdbdadcacbccccdbbbcbabcacabbdbabbbbddcbcdcdacbaddcdcdcbbdbaadadbabdacdbadadbdcbcbaaaadaacddddcbbadcddcdccabbabaadadcabccdaadaacbdbddbcaacbabadcbcaaacdadaadacddcddcaccacaacbbbdbcbaaadbdaaabacbddbbbdbbdcaacacddbdbacadbdbdcccacbbacaadadabbbdbcccdddaccacacccabdddbcbdbadacddcbbbabcbccaddbadccbcaaccbabaabadacbccbccbacdabcccabbddbadabaaaadadcadaadabddbacbacbbacaaacddabdcdadbaadccbaabbddadbddcddadaabaadabdadbacbbaaacaadbbccdaabbcbbcaccdbddcbccaaccbbaddbcbbcbcbcdadabcadbdbcbcccacbdbacddcdaaaaabbcbcbcabcaacaddbcbdadcbbdbdacdacabaadabbdadbcdbbdddbaddcbbcaadccaabbacbcbdddadccbbdbdccbbbcdcacbadbabbbdbadaaccabbbaccbccbbadabddabdccaabbccbdcdaadabcdadcbbddabbbabdaaadabdbccbccacdbccbdbbcdbdadbbbccabddbabcaddcbcbcbccbadbacaddbbacbdcccbcbabdccdbaddabdcbdabdcaccaccbbccddababccdcbdcccabbbacaabcacbcdbbadbaadcaccbbabcdcaaacacdddabccbccdddacbacabcbcddbbacbabcacccdaaaddabaccaadcbcadddcbbcaadcaddccacbcbbaabddcbadddcaadadbccdcacdccbcdacccbdabbccbbbddadadbbaaadbdbdabdcbcdccaabbbdcbdcadbaccbaccbbcabbcaccaccccadcccbaabdbcdbbbbbcbcddcbcbbaccabdaddbbbddddddacdbcdbdddcdbabbcbaccbbbaabdccbcbbaddbbcdcdbcbccbcdbddcdbbcbbcdaacadcbdcdabbddccbdaccbbacbabbbcbcabdaaaaaccbcacbaacdbcabbdabbdacbcaacccbcccbbcbcbbcaaadbccdabccacbbdababbcbbacbcdacbbcccdcdabaadcdbacbaddacbccdcbdadcababcdbdcdccabccdddaabdadcbbdbcdbddbcccccdbcaddcdbcadbdbdcdabdccbcacddcdcacdbcbaadcbaabdbacaabddabdccccdbbbcbddbccbbbcdddaaccbadbabbadbcbbbadcccdadabdccabaaccdbcaccaccdbbbdddbacaccaadbcadcbdcaabbbaddcacbcacaacdcbdaacdbcbcdddadbccbdcdadcbadacabbbadccbbacdaddbadcbabdadaddcaccbaaacccbdbbdcccabbdaaaabddbbcbdcdbaccdbbcadbacdaddbacbbbabbcbdacbcccaaacaaacccddcddbbacadaadbcbcdbabbdaaabadcbcdacddadcbdcdbbbddbaaabacabaadbabcbcacabadcddaccaabdcccbcadbcbdcbbddaabcbaadcdbddcccdcabacbdbbbacbdbcadaabcbbdbcdabadcccccdccadbabbabbccabccccdaaabdcddcacccadbaaddddbdcddcdbaacdcbddbacdcdcbadbddbdccdadabbbdabcaaaccbcbdbdcababdcbbdbdcbcaccbbccbdbbddddddabdacbadbdcdcbbcaabcdcccabdaadacbadaaaabcdcdbdcdbadacabcadcdcaaabbcdccabccbaacbcdabcababababaccaabcaaaddcdbabdadadcddcdddccacccaaadddacbbcbacadcbbadadaadcbbbcccdabbccdbcddddbccdacabacabadcdbdccacbdbdabbcbdccaadabcbdadabaddbdcdaccabcbbacdacccbcdccdcbaccbcaadcabcacdabdacdddbcbcccdadddbdbccdadaabcbbadddbccadcdadbdcaccaacdadcdcbcbbccdcbcacacbbbcbccddcdaaacbdaadaccbbddcaacdcdcdcddccdccbcacdabbccbdacbdadbdbdcdabadaaccdcabacdbcabbbcbcdadbdabbddcbddaccabbbdacbbaaacdadccadbcabaccababbcbdddaacbdbdbcacdccddddbaacbddbbdbccabaacbabcbbabadacdcdaaacccaaaadadcbaacabaccdbddacddcdddacaaaababcbcabbbbacdbbaadbcddddbddadbaddaccdbcdbcadbacbbbaababcdabcdabdcbacbaacccdaaabcbbbbbdabadbbaaacabddddcdabbcdbdabccbddaaadabbcacccdccaddbcbabbdddcddcbbbacbddbadbabcbaabacbccbabbadcadbdbccdcdaacacabbcbdaaacaccbaccdbcacbbbabcddabdaaddacddbbddbbdacdcbbdcdddcbbadcdaacadbbccacbabacadbcdcccbacbabbcadbacaaddabccbacdddcbadcdabcdcdabbbaaabcdacddaacadddabcdbccdbcbcbdcddadaaadccbcbcbabcccdcacddddacdacdaaccdccaaccbcbddbaddcaababdabbdcddcdacaaddaabbbabccacbabcdaabacadbaaabdbdbadddcbdaadcccadcbdadcaaabdadacbabcbbdcbabddacbddbdccbdaccadacaaccddddccddcabdbaaccddcddbcdbbdcdbdcbacadccacdbdacbbaadbbdccbaadbbddadbddbbbbabbadadbbdddccccdcabdddacaacddcdbccdccaaaddbddbaadcdabaacddbcddbdddbbababaabcadccdddbbcdabddbadbccbbaccdbcbadddaadabbdcabaddbcdbcadbccaaaadcddabaddcdadbcbcbbccdaadbadacbacdbcbbddbbabbddbaadadabacdadbcadaddcadddcddcbdbdcaaababbaccbcbcabbddaaaccdddcccbdccaabaacbcddddbccaccdbbacbcdabadbadaddaabdbdadbdabbadcbddaddadcaadabbcbaacabacbcdabdbbcdabbbbadbcdbacdaaabccabbacbaaacbdbddbbcaccbbdacaaabbcbacdbdaccbaaaadddaaacdccbbaadadddccaccbcdddddbaadcbbdbaacabcabccacbacaaddaabccaaaabbaddacacdbaaabbababbdddcbdacadabdccccacbacbcbbbcbcdcbabdcbdacdbdbdcaabccccbcddabbdbcaddbdaabdbdddbbdbaabdbbacaaddaaababdaddbcbdabbabcacbdacdbdabdadddacdcacbbcaacacadbaaadcbbabaddcbbadcdddcbbcaaccbacbdbbdaccbcabdccbaaacbbbaacadbbdbddcccbabbccdcbbbcbacccdccbaadadcacbacaabddbbcaabaadbbadaadcdaadccccdddbcdbabcddbdbcaccdbbccbdbaddacdccbbaabaabcbadadacaddbaaabcdcbadadccabcaaabdaabbddcddabcabadbdccdacbdaccbaadcbcacbadabcddacbadababcdaababbdabaadacabcbdabdabbaabcdccdbcbddbbdabaacdabdcbacbbbdaabbcbbcaaaabdcaacadaabbbcaababcaccaabcdccacccccbacbdcdddcacbdbbddcbcbadccbbadabaabbdcdadadcdacadacaadacccccadddbdbabcdbbabacbdbabbacccdcdabbaaabcbcdcbdcdccabdadbaddcbadcdbbabdbbbaaacddaabcbddbbbbadadaadcddbbccadabdccccabdaddacbcbbdacabbcdaaabbbbbcbcdbaaaccbdbcabdaaacbbdacbdabacaaaabaddacaadccbcbaadbaacccccadabcccacaaabcacaccbbadbdbcdcbacdadcdbaccccbabcdacaacacccbbacabddabdcbccaccaaabbddababdaddabcdbadbdbbcacadbbacadddaabaddabcaadaababcbccbaaabcbddaabbcadccbccdbddadddbadabcbcdccbcdaacbbdcbaabbcdbacddaacbbdbbacaadbdcddddcbcbbabbdabdbacabdcbbbcadabcccdbdaddcdacabdbabbdbbcdbaddcbbcbddcdbddbaaacbcaaddcdbcccbcbdabdbcdccdabdabbaccabadccbddddaadbcbbbabcacdccbdbdccbadbccbbabccbaddabbdadbdbbbbadbbbbbaadcddbdbbdbbbaaacccbdbdbcaabccaaacacbdcabcadbcdddbaaccbbcdddabcccddbbddbdddcabadbccacbaaaccddadcaddbbdcbbdddaabdaddacaaacdbababdaddbbcdbbddbabbacbdbddabdbbcdcabcddbccadadcbcacbddddbdbbccaccaabcbdbbdbdaddaadccccdacaabdddcbbcdddaddadbcdcdaabbbbcaddccccacacbbadaaacacabaddbddcadddcddacdcbbdcabbccdbcdcdcabaddbabcdbadbabdadcbbcaabbccdcaabbccdcabbdbabcacccbcdbccbabbdbabbdabbcdaddcbccdaccbbddaabbbbcdbddbaacdabcadcdacaaccbcaaacbbaacbcbaacaacbbadbbcddcadbbbddbabcabdacabddddbaaaaaccbaddbcbccabcbabbadacdbacbdcdddcbacdddbadcbbcaaaccdddcbbccaadbbdadaadaabcdadadbdadbbacdabbbaccabdbcadaadccadbaaccbccbdcbdabccabccbbcbbbcdbacdabddccdcaccdcbaddccdbcabddcccddabcbcadbcdbbcbccbaabbddadcaaddacadcdaccbbabccddcdbabbbdabdacabcabacbdabbabcbbcbbdadcbdbdbdccccccbccdbdbdbbccaaabbdcadadbddbcaadcdbbdadbbbdcacbdadbdabaaccabdbcabbccacbabddcaacdbbcdaccadcccacccdcccadacbbccbddacbdddbccbdddacbdcabcdcbaacabbdddbbcbbadbcaadbccadbabbbdcacababcdbacabaaababddbbbbaabbcbbcdccddbdcddacbcdccddccccaadcdacadbdacddacabddccdabaabbcbaadcccbcddbcacdcadcadbddccbabaadccbababbaabcdadcbcaaddcaaacbbdcaadbacbbaddacddcbadddbabbcaabddbcdbbbddacbcaadbcabcddbdcdabaccdcaddbbaacbdacabcbdddbacaaacccdadcdabdbccbacadaabcaaabbddaccdddbbdcaaccbbcacadababccaddcabdadaabdcaaaaccabaaabcabaadddcbaddaccdbacbabbbcbbbadadddcacdcbbcbdabadadacccaabdcaabbdbddadaddbcbbbccddacadccddcccbdacdcaccbbdcababbcdabcacdddbccabaadaaababcabdddcdaacbbddcdacabccbababddacaddbcbdacaadcbccaacccabcccbdddcdbdccbbacbbabdcadabdcacabdadcbddcaddacbcadacacadaadbdbcbbbcadcaaacbadacbdbbadbbbbbadaadaaccddbcbcdcddacbbaaaaacbbddcbbabbdcbabcbbbcbadbadacabccddcbacacbaaaaccbddddaaababbaacdcbcaccdbbddddacdccadbdbbaacdbcccdacddcbabcdccccaadbcdababbadccdbdbdbcabdccaaacacadabbabdbdabcadccacbaabacdacdbacabcbadbbadcddacdcbddbcadaccdcbaccccbccabbcadbbdbddbbcaabbadabdbabcbbcaaccdacabdcabddbabbbacbbbcbabbdbcacaacddbcaaacbacbadabdadddcbadcaadcadccdddaacdcdcaabdbcdaaaadbdbbdcaccbaabcdcabaaddadbadacaabaabaddddddddcdccbbddaadaaaadabcddbadacdddacbacaaadddccdbcdbccddaadbaabbcddbcddabcbadbdaadbccdbbdbbbdbbdabbcabaaaadabdadcabdacaabbbdccbbbaadddcbbdccdbdcadcabbdddccabadadbcababbcabaacbdbbddbdcbdcdbacccbacdaadbddadacdbaacbcabdabadbbbadbdacdaaadaacdcdabdcabddccaadaabacacaabcdbbdabacbdcacbbbdcbdabacdabdadccabdbbbaaaabdbdcccaddbbbbbaacababddbabaabbbcdcbaadbcaadcbcbdcdcdbcbdbbcdbcacbdcddddcdaababaddacddccbbacddaaccddbabacbaccbccaccbdbbdbddbcabbbabbcaaabaddbbbbddcaabdbcdadbabbdaacaadabddddddccbbdaabddacddbbaabccadacacdacccbcbadcdacababadcdbbaabcddabdabaabadbcadddadddcbcbacdcdbbdbcbbbddbdacbcadacadccbdcbbaccaaaddcbdadcaccbbaabcabdaadcbbaabbbdccbbcddccbcdbcdbdcccbaaaaacaddddcbcabddacacdccdabcabacdbcaadacddbcaacbbbbdbdcdaadbaccbbbadcbcbbacbabcbaadbdcbcbcdbbabbdbbbcaacddbbddcbdbbadaacadbaaabdbcdbcacaaacaaadaadbcbcdabbaacadbdbbbbcddcaabbabcbaabbbabcbbbabaadbbdabdbabdadacbadbcdaacbccdaddabdcbbccbaddcbbdcbabbdcdabcabcdaccdaacabcaaacbbabacaaadaadabadbabcbcdccdbcaadcbadccddacdabcdbbadbdcccdbbabcaadccbbbaadcccbcababbaadbacccbccadcbbdcbdbbababcbcadacddcddddccdccbaddcdccdccaaddddbdbcdaabdcbddbacabccccbabccbcadabaacdbddadaabccaacdaabcdddbaadcddbbadaabbccaadcdadbbdbccdadcbadacbaabcccdddddcdabdcddacbbbdbbdcbbaacababbbacacbcabbbcaacadabbbddddbcdacacadcbdcacdbbabbbcdaadcabbddaabccacbbdaddcbabbacaadccdcdcadbbcdbdcddcaabbaacdbbadddaddccdcabdaaadaaddbbdaccaccbabcaadccaabbaaaaacacaaacbacdcbdbdbbadbbdcaaccdabccbcaaaacccccbcbcdbdcdccacdcdabdcbaabbadccbdccbaababaccbccccaddadcadadbcccbdabaccbbaaacbdaaaddbcabcbacdbabcbaadddabdbdcddcbcbcacbcbabcdaccbcddbcabaabcbbbbcddbaacbbccccacbdbaabcbbddadbbdbdddabaadcdcabaadbaacdcabacabacadddbabcbaacccddaddbdddcbbaacddbdabddbdaccbadabbbaabaadbbdbdddcccdcbcadccbaadbdbbddbdcacaaaaadbaabcbacacacadcccdcacbdcadadbcabbbbcabccdbdcabbdccddcdaadbdbbacdddaaabdccaabacdbddbabdcabbbadbacdaabbdabdabbccabbacdacbbabdcadcdabbbcdcadcbdadcdbdcaadccdadbddddababcdaabccabbccadbcaaabdbcdaacadaadcddadacacbbdbdddacbbdcacabbadddcaccbcaccbbcaabdcdbdadbaabaabbaabcddabccdcbbbdcddbccccdaabadaddbdaacdbbddababadddcbbaccccdbbdaaaddabcdaccbabcaabacabbabbaabddadcdcdaabddbbabdbddbdbcacdcdacbdcaddbbdbbbdccaddadabbacaadcddddabdcdcacaabbcaacbcdcdacadcdaabdadcbbdcdbddbcdaaabbdbdcdddadcdcdbacbabdbacaadcbbcbaadddbcdbabadbabbadadcbdbadbbadaaddbaccaaddcbdaadcbdacabccadbaadbadcbacccdabbcacaacadddbcacbabacbdcbadcadcdcbdbbddcdddcddabcccbdaaabdddbbabbabbabbbbdbadcdbdbcdbcbcbddcbabdcddbacadadbddddcabcacccbcdababcccbcdbdbbbdbbbcbdcaabbaacbdcaaabadcaddabbdbacbacdaaaadadbadacbbddccbddbacadbbbababbcadddbbacbcbadbaccbdaaadadbbbbbbcdabdbdbcdbacbcadaabdddbaccdbdcbcdbbcbdccccbbaacddcadbddbcbbcacabbaccddbcdbdcddcdccabbbcadacbabddaabdaadcadbcdccdbabadcbacbbadbcabbcddbbdbbccaaccaaaddacdbcbcbdadcadcbccdcbcacacbcccbcabaaabbddddbcdbdddcddddbdcddbbcdccdaaadcdacaccbddcacddaabccddbadabddcaccdbcabddaddaadbacdadbdbcacacacbaadcabcdcbacccacaccdcbdaabdddbadcddcddadbbcbadcbdaabbaacaabbbcccabbdbbdbcbbcaccbbadccdcadcbccacdbadabccaacdcdababdcccdaaadcadccccdcccdaaaaabbccdcaacaaaddaddcaacbdaabdaabbbdbdccaadaaabaaaabddabdddadacdcacdbcdadaccbbbddabdbacdbccaabadbdbcaadcabbaaababcccabbadcbdcdabbcdddbdbabbbacacbdacddcddbcbbdacddaacbcbaabbccadbaccdabddadbbcaacbbbbbcbbabcdbcccabbddabbdadaacadbadcddaacbcdddbdabdacbdaddbcdddacaadbcbcbacbadbbdbabcbdbabadacdbcbdbccbbabddcbbbcdbabdbdabbbdccabaccdabcbbacdadbbddbbbacdcddabbacbdcabaaaddbaabacaaabdbddabddaacdbccccbbaaabdaaadaaadcccbdacddcacabdbbbddcddcdcddbccddcabcdbcbabcacbccbdaaaacbccbaadcdcaccbbdbadaddcbaabadcdadabbbbaddccaacdaaadbdbdcddbdbddcdadcbcbccaadccccbaaddbcccbbcdcdbadcddbcbbcbbcddddddbcbabcadbacbdcbbdbaaaabddadcdbcbcbcdbcaddcccbbbbbdbaccaabcbdabbbddbcaabbaaddcaabcbbdbdcbabdbbdccaaadcbddbccddabccaddcdcaaadaddbabddadaaddabcbcaaccbabccadaccddccdaccbaadbbbcdbbadbbcddcabdbcaadbabdbdaaccdccdcaabcadbddbddbacbdaddbacaddabdbbdccccbdbbccaacaacaddaccddaccacbacdcccbacdbcddddaddbaccaacbbcaadcdabbddbcaaabddcbdcabbbddacaabdbbdbdddaabcacabcdbbdbcdcdacbddacbccdddbcbbbbabacbcacdbadadcabcacbbbbdcbbcdbacbdacdcbbdbbddccaadcdcbbbabcdccdcaabdcddabaacaaccadcaaacccbdabcbabadabadbcdddcdabddabcddaacbbdabaaadcbbdababdbddbaaacbddcbbcbbcdbabaaacdcbddcbaaabcdccbccbdbdcacabddccbbdbbaaaaccbdadcbccddddcadcbbabccdcdbcbccbcbddcccddaddbbdbddabbcdbbaddcacccbcaacadabacbcaaacdcdccddcbcbabddacaddcddbbcbbbddcbdaaabacbdcbcdbabaabdacaabddaaabcaaaabbabdadacdcddbadadadcccadbbaddccacadcadacbdbbccaacbbcbbdaccabadbdbdbdcdabdacadbadddbddaccddbdcdabdbaccbdcaddcddacbddacaadcbacbdcbacbacbccccccaacdbabcbcdbadbcdccdcbacdbcbcbcbabaddcdccbccaabbaacbcbadaadadaaddaacdaaaaacadcccaddacbdbcddcdccadadacadbcdabcbbadadaccbbaabdccabdaadadddaddcbcaacdacbddababdadbdcadaadaaabddcbbaddcabdcdbabbdcbbccdcbdccbcdacccbadcbcbddacbacaccbdcaaacbadbdaccbdaabddaddccacbddaaccbbacadcbbbbacdaabbabddbccaddcbccbddacbcacbacbadbcbadbdcadadccbcacaaabcddccbaaaadcbdaaacdaccccaaadcbcacadcadabdadbcbccadcbdaccdbcadbbbbcadacccdacdbadbcacbacaadaccaacaddcbccacbdbbaadbbadcacbbacbacbcaddcacbacbdabdccdaccdbbcdddbccaaacbcabbddbabbbbacaacbbdbbbaccaddacdbcbaccccdaacddbbdaaddaddcaddccabacdadccddbcababdbdbbbaaaadaadaaabdddccdcacbbaadacbdbbdbcdccadbdcbbccdacbaadabdaddadaccbdabbcabbbaadcccccabdccdcadaddadccbaddccbdbbbbdaacdcabdcbaaacbcabddbcaddcdcdaabcdbacdcaacbdbadcdbcaabbbbddcbabdaabbcbdabcbaacbdadabbdadabcdbbdccdadcbbcdabacdaddbcaccdacdcaaaacddccadddbacacacbbddabddbbcdaddcabbbdabbdacbcbbdccabbdcdadcbcccbdaadcdcdabdaaaaacdbbacaadbbadcbadcbdabbbacbdddcdcbbdbccadbbaacdacacadbcccacccabbacbbbdadbdacdbcdaabdcddcbbbbccbbacaadccaabdddaaacdcadbdbacabdaaadddbacdbcdacabccdbaaacbccccdddbbdbcbdcdabccacddcdaaddabdaadadbcbbdbcbbbaddcccdabdbbacddcabbcbcaaacbdaccadbabadaccbbdaabcbddbbabdaddbbdadaccabbacaabadcbabdcabdbdcbbaddcdabadacadccbbbbbcbbacbbcadacccbdbbacdbcaddacdabaacddacbcbcacbcdaddcddcdbdbaabccdbdcdaccccbdcabddadadccaacbbdcadddbbaadadbabbddbddaaaaabddabdddbacabbabccdbbddbbdbbbdabacadccbbdccaaacaacbadacbabadcddaccaabbcdacabbbdacbadababddacbcccacadaabcbdcaabadacbacdabacbdbcbcbaaaddcccbadbcacbcbcacadcdadabbbcdccbacdaddcbbacabcadbaabdaaaadcbdcccaadcaabdcaababcdbdbdddcdcaadddcaddacdbdaccddabacdbdcbdbcacaadbbcddcadcbccacdacbacabdcbdbdadbaddaddcabcadcccaddcdbcddacbccbdcbcacdbdcbadddaabbbddabbddcabbbcadaaccabcaccbacbbbadccbbcdabaccbbcababbdbaddacdabaacddcdadbaaacddbbccbcaacbcacaadcabcdbaaddadadaaddcbdcbcadbabbbcadacbadcdabadacbadbabaaaabbdbcbbbacbccacaccdcbbdacacdbbbdadabbcccabdcdddcddcbdbcaaddbbaabbddcaaaaabadcabbabcaccbbbaaacbcbdacddddadbabbbbacdcabdbbbcabdadcdbadcdbbbcccdbbcbcbbcadbdcadaabbbabbaabdcabaadbbbaacddccbdbadbcdcdaccaccadbbabbdccaccadcdbbdddcbacbdcadccdddbacbbabbaccbddbbbcddcdadcabadaabbdabaccdcdddcbdddcbbdbacacaadddacbbcbdbdccccadddcddbbacbacacdccbddacacdbbcccadcddccadcbcbabcaddbbcaaacddcdcbbbdcdacadcbaaaadabccbbcdcbcadaadbdacbdcabcbcbddaaadddcdcabcddabbbcadbdcbbbcbaacdacddddbbabdcbbbbacabbdbaabacbdbbaacbccddaadbbcbbbbcdccddacdcaddadcaaabaacbacbabcdabadbacaadccbbdcabacdccddcbaaacdbbbccdddbcabcdddcdbcbdbabadbddcdaabccddacdcbcbbacbddcbdaabdabcdcbbadbccccdddbbaaddabccaabadabcadaddabcdaccadcbbbaaabbccacbddbcdddadbbddaadadccadcccddbabcaccabdcdadadbdaccdbadcddccbabaddadbaadcddabacbcdddabdbdabcabcbdadbdadbbddccaccbabaaaabcaccbdddbcdccacbaccabbadabbbbcadcbbdcdacbcdaaaacadacdbbcdcdaabaaacddbdadbdbdacdcaabaaaabaacddbcacdccaccacddbbcdcdbccbcdcccbbadcdabaccdaacdabbbbdbbaaacaadccbccbadddabbbbdbdbabdbddbcadabddabadbadacbddcbcbcbcbcbacacdbbddcdbaadbdbbaadddbcabcdbbcadbdcadccdbcccdcbabbdbacbddaabddddabcdddbbacdcdcadbdaacbdabddacbdcbdbabcaabadbcacbcababbdbccbaabbbdccbccacadcbacddcbdcdcabdcacdccbadadbaacdcbcdabdabcacadbdaadabaaacbbdddcbdaaadaabcccdabaaddcdadcddcabcddbdbaaddcbabdcadcdcaadaaabbbcddcadbaaabadadbbabbdccabcddcccadaacaabcaaadbadabadabadadaaadbaacbbcdccddbbadcbdbbbdadcdccdcaadbcacbbbabcadcbadddcabbadcdacbddbcacdcbcacbdadbabdbcaaacbbcddbadaadbccbbbdbdbabaabcbaddcccdcccdacdacaacdadadabaabbccbabdaccdcadaabaaabbcadaacdbacddcddccdaaddbacaccadbdaccbdbddccaddcbaaccdcdddbcccabddcdbddcdbbbccabbcaaaaddccaaacaddccdbabcdbcadaddaacbdaddcddacbdabbdbdcadbdbbcabaabdccbccdccadddcbbbbaaabaabdccdcadacdcbdcdbababaccacddbacaddadbcbcacadabdbcbdbccabcbaabdcddacbcbbacdcacddccadddbccdcdbcbddbbccdabacbaadacacddbbcabbddddabcdbcbbdadaabaacbbadacbbbaacbbdbcaccabcddacdaabdccabbdcbbabdaacaaacbacdbacababbcbdbbabbbaabddbaacacabacadaaddddcbbcabbacbccaccdddaaadbbbaaaccdacbcddbbacdccbdbbbcaacaddccdaccdbbbaaacabdbcbdcabbaadaabadcacbcccabddbadccdbddccbcbacbdcbdbababccaacabdddadbadabcbadaaaaacadacdaaadbacaacbaadbbddcbddadadbaaddccadadbbcadccdacbdbdbadcddbaddbcadadadbcddbdcaddcccbbcdbcbdadbcabaabcaabbdbcbacddabbccabdbbccbdbaccaabbddbdddadabadbccbddbbbbccbcbbccdbccbbcdbaacbddcaabbbaaaaabadbbdaaacdccdccdccacbdcbaaddddcbbadcdadccabddbabbabaddaaaacdbcdcdbbadddbcbaaccdcdccabbdddaadabcbadacbbbbbcddbcbaacbdbbbbcabbcbccbbcbacddcaababbcaabccbcabadcbcabccdcbaaadccdadccdbcddbbccacbcabcbadaabccdacddbadabcaddccabbcdcabaccddcbccdabcaabdbcddaabcbbdcbaabaaaccdcadcacbdbdbaacdbbacdabbdcaabacbcddcdbbdaddaacdadbcadccacdcaccabddadcbbbcabacdacbdacdcdbccadacdbaddddaaaccdadbccacdcadadcbdcaccadbbbbcacdcbaaaccaaaacddccbccbdcbcabcaddadcdbbbcbaadccddbccadddbccdddccddbabddaacaccdddbdcdccbaddaddabcdcddcdcdccabacdcdddadbcbbdbcacddbcbcdadddcabbbccdbddccaaddaabcdaddaddcaccdcdccdddaabbaccadababbbcbaddcabadbcccaccdcaabbbdcaaccdddcbdbaadbbcbcbddcdddadcdcdabadbbadbbcdaabbbcdbbcbcccbabdaabbcbcdbabbbdacbdacaaccaddccbccbddddaadadcddbbdddadbdbcddcaddadccbcdbbcacbdbcdcabcccbadcbacbbbcaaaccdbcdbdccbbbdbcaddaabbdabbbdcbbabddcaaaaaacacddabcbbaddcdddbcbbbcbccbabcbccaccabdacabbdbbbaabbacabdbbccabbcddcacdaadbbadccccacbccdbacdbbbccbbabddaabaccbbcadbaabdbdbabbcabcdbbaccdddacaaabcbccabadadaabddacdccdddbcdbbdbcbccbcdbdacdaabdcddcdbbdcbbbbaacaacabcdcdaaacbaadccdbadadddbddabbcaabaadcabaacdddaabbbabcadddccbbcbcccaccaaabcdccdbacdcbaabccbaaabbbdddaacbdddcddadadacabdabbdccaaadacdadbccbdddbaddabbbadccaaacaccbaadbbccddbbbaabbabbacbbdddacadddadcbcbbcabcddacdaaaabbccccacdacccdaabbcacbababdddaacadaddbacaaaddbdbbcadcdccccccbbbdbbbbcadadddabbddbadaccbcbacaadbbdccabcababcaddcbadbbcacabddcdcdbcabddbcdbbaddbdadbadddbdccaccbbbdcbddccdcdacbcdcbaccabacddacacdbdadcbdbaacbdadccdbbcbaaabaddbaccbccccdbbcbccaacaadddaabaaaccddddbddcbccccbcbddaacadabacdbdbbdbdcdddcbaaddacbbaabcddadbbacacdbbdcbdbddbdcbacdbabcdabcaacbdcbccdcabbbdabddadacdadaaadbddbcaddbabacddbdbddbcdcdbccdddccdaccbccbbbacabbcbdadbbadbbddadcccababbdacbdacbccdbcabdcdadadcbbdabdbcaaabcdcbadcaaaddcbbbaaacddbabccacaccbcbbcadacacbbcbbdbaccababbbbdbccacbbbddaaccbbcbbccaccbdcbcccbbbbbbbcbcaadacbcccabbbbadcdaccdddbdcbacbbadbadcbccbccdbbaadcadcccadcadbccabcdbbccbdacdcaabdcbbdaddcbcbbbdcdaaacaadabbaadbbbdaddcabcbddbccbdcbdacbdcccacabaadddbcdacbccddabadacbdcbabcdbcadbbbadadbcccbcccaaddcbbaacccccbabbcbdadddabbdabbdcbcaadacdbaadcdbdddddadbbccdabcabdaddccdaccbccddcaaadbcdaaccabdcddacbdbdbacddcdacbccabdacacbbddcadbaccbabbbbdcdcdbdccabbbcddadcddabbbbcdabbabadddaddbacdaaaddccccbbbddaaacbccddbdcdbbcddbdcbbddaccbdcdbbabcabaaccdbbaaadcdabdcbccbdbdacacbcabbcaadbdcabbbcbaaddcccbbabacaacdadbdbddddbdbbdcddcaacbbadddaccacdccaabdaabbcbaddacbbdacbdbdacdcadaccbbcacadcbccbcdccdadcacbcccacdbbdaaddbcbbbacdccaaadddacbaccbddadbdaaaccbdcdbcdbcbcccdaabcadababdbbaacdcbdddddbdcccadcccacbbadbacadcbbbddcaaacadaabdddccadccaaadbaaccdcdbbadbccbbcdadcadbdacbdbacdbcbcbdcddadcbacbdbaaccdcbbacbbddbdbabaacddcaadcdcbbdccbcbabbabacdcbaadddbcacbcbdbcadbcaacbaaccbdacbaaabdcccbabdcddaddaaacaabcdbddacadbcdcdbdaabcabbccacdccbcdddaadbaaabbccbcaaddacbaabbacabbddcaadcdcaaccbaadbbcccccbdacdaaacdcdbdbaccddddaababbcbddcbbabbdccbccacaadbddcbabbdbbccdadaadacbbdcdbdcbdddbdacaacbbadddbbccbdadbacacccbccadacdccddadadcbdcbccbacccbcbbabbbcaacdaaddbbaaabcacacbcadddbbcdddbcbcadcbdbbcddcdabacdbcbbbbacaccdccbdccdcabcbdcaaadddbcadddaadbacdbccccbdcbaabddabcbcdccbdadcddcadaabdcaaabbccaccabcdbabdcbbccdbcaadddcbbddccbccbabbcadbdcabccbbddbddccadbacddcdcbcdccccbcbbcacbbddcbdababaadbccdbabcacacdbcabdadbabdcbaabccddcbbdbdcbacacdabbabcbcaacdbbdcabacbdcbcaadbadacdbcdabddcbabababbcccdbacdbddbacdabbadcacbbdcbabaddbacbbbbcbdaddabcbbbbddcacbaadccdbcbdadbaabaacabbaccdbddaccdddbbbcbadccbabcabbabbabbddcaddcdddbbdddbbcacdcacbdbcbcdcdabacdcdbdbbbddbddddacabdacbccbccdacdddbdbcbdacacddaaababcbdababcbcaabcccadcddccbccdabaabdcdbaadbdcadddbddcccbadbdcbdaacadadbbdbcdcdaabbdadacccbdddbdbcdbdbccdcbdaabcbadacabacabbddcadbabadccbcbdcbdaacabdadcdbbbabadbabcbbbcbddbbadbcbdccadcbccdbddaabccbdcacabcbbcaacbcbadcbdababaaadbbcbbdacbbaacdabdaaadcbdacadcacbddbaacacdbbdacdcdabbccddcbaddcdacadacbcddcddacaaddddaccdcbcbbcabdcbdddadbadcbdbadcaaacdbcddbabddbbaacdbbbabcbbdccaabdcadbaadccbccbdcccabdcddddacbcbaabadbacadadbdacbbcdccbacdacabcdcadbacbadcabbabddadbcbadcbddabbccabccacdbbcbccddabadaadabbcbbbadbcbbdcdaddabcabcbbabddadbabbbbcaabddabccbbccbdadaaccbaabdaacaabcaddaababadcaabacccbcddaabbdabcbaccbbdabdcbaaaabdacccbdaddccdbabdacdacddcddaaddcacbcbadabbabdacddcbabbaccccaddbaccadbcacdbdabaccadddcbadbadbdbbccbcddaaabbadbbdddadbcdcdbadadacaacacabbcbdaacbacddbaaaccaddabcdbdccbdacbddcbbcccdaaadbbdcadbbcdcababaaacaaddcdcbccdddaddbcbdbadaadcdccbbdabbdcacbacdaaddabcdaddbcbbcdbcbdaaddaabaddaaabdbcddbdabcadddacabbabccbaccabccbcdacabbdacddddbbcdcacdbcaaabdacbddcacabcaabddcacdaabbddacaadccbcaabccdacbbcbdcdcdbccdccbbaadbdbbdbdbdbcbabaabdccadcdcabdabcbaacabbadacbbdaacaabddbcbaccabccaaadbbdabaabdcccddaccccabbbdcbddbccabdabcbaabaccccbccbcccaaabaacbbbbadddcdabbdabbcdccaaacacdbcacdaacdababcaaddcaddcdcbacdddaacdbdadddccacbabdbbcadddadcdabbdcdaabcaaddbddbaabddbbabdcacddbdaabbcaaadbcaaaabcddcbaadcbaabccbcdaadaddbdbcaabdddabdcccbaacbcadbdaadabacdaadadbdbbadbcbabcbcadccdccaddbccacbbdddccabacdaddbdbbabdcbaabadacbcdaababcbcaabaadddbdbadbabbcbddddadabbcbdacdcbcdbadcaccbadaaddbbaadcabccabcccdacbabcbbadcbccccdbdabcddcaadddbcacbbabbaabacbbbccdddaaabaadccbddcbddbbddbbababdbadbdccbcdcdabaabddbcdcadadbcaacbacaacbdaabcacdadcdaccddcccaaccdadcbacaaaaaaaacbaddbaabbcccaabdbbcbdcaacddaadadbabcadbbbaddbcbadbdaaacbddaacadaccacacbbbcacdbcadcdaacbbaaadbbbcabcdbadbdaaadbcccaccaadbdaadccdabdacbabcdabddbdcdccacbbdcdcbbacbcdbadcddaabcacdbbacdadcdabcbcccbcbcbdcccbccbaadbacddcbbabdadddcbdacbbddcbdbcaddbadacbddcbdadddaaacbdccbcaacadacdbcdadcbacdbcbcacacbccabbdccbdadaabbcadddabadccccdcbaadabdaaaacdaacacacbdbcdadacaaddacbddaabacdbbddcdbdddddcdbbadabadccadbcbdcccddaccabdbcccaaccaabaddaacddddcddbabdcbdcbabbdcdcdbbcddbaccbdaccacdcacddbdcacbbdadabbbacacaaddbcbcdcaadcacacddbacabdaccbcabadcabcccddabcadabbdaabddabdbcbdbccababaadccbccaacbccdddacdabbabcbadcdaabbdaabbddccddddadbacbddcccaabddaddbacbcdccbdacdccdbdaddbabbaaaaaadbddbbbbacdaabadbdcdcbaadaddaccddbdcabbcadccdbcadbacccdbadaacabdcbbcbbcdbaddacdaacabdbbdabaababbacbbbbabdcaacabaddccdbdddbdbcdccccdcabacadababaabdaaabccbadacbdbccdccdcacdabddacdaabdaccaddcacbccbabddbbcdcdbbcaabcccccacbaadcbdaacdbdddadcbdabcadbbbdacabcddbbaadbccccbcabbbbabdbbbcbcdbcabababbacabacbddbacddaacdcdcacbdbbbbaaddbbcdddaaaddcddbbcdddcdccbbbabbadaaacdccbabccabbbabcdcddbdaabbbbcdccacbbddbdacaabacacbddccbcdbddbadcadbababbcbaccbcabbabddbdddcdbccbdbabbcbbcaacaadbccddccabdbdddcbcccacacbaadabbdbbdcbabdaabcccbdbdcdbcbccdbdcdbcbcacbcccbcbacdbbbcccdcdbbdbabdbcbdbdaabccacbccdabddaaabbacdadbdbcadbccaabcadcbaabbcbcbbbabcddadbcbadaccbaacadbdaabcdccadccadddbbaacdbcabcccdcbccddaddbcbaccdcdbbdbabcbbccabbabadcdadcddcadabcbbbabcbdadbbbabcbbdaccbccdbdbcabadabdcacddccdaccdaccdbabaccbaccbdbabcbdadabbbbccccccbcdbbbcbdaddabbabdacbdbcadabdcbcdbcbadababbbcdcdccbbbacbdcbdbdbbaabdcbdddddcbababbcbccadcbabaaadadcadddadabdbccbbbdaaabadcbaadcdbcadcdcdcbabccbaddddcdddcbaabbaacbcacdbcbdaaabccccadccdccdbdbacbbcdabdaabadbbbbaaccadddcdabcbbccbdbcbbadbaadaacdacbcccadcdbddddbbacbacdadbdcdccbbdabdabcccadcdcdacaddacacdcabddbdabbdcdadbcccccabcdacddadbbaacbbcdcaaddabcbddccabdaaacccdbbbcdaccadaccaccacbdbbdabcccdcdbdbcbadccdcacbddbcbdcbaaaababababdabcdbabdcdbabadaadcacddcbdbddacadccabcdbbadbcbadcddabcccdbddccdbadaccbbcbdbacdcbbbbcddcabadcabcbacccbacccacdbacabaccbaabcbdbacabdbacadbdbbcaabdadddcddcadbaccbdbcbbaddaabdcbbaaadcabaadabcdbbccbdaabccabcddcbdabdccdcacccbcdacabdcdbcbdbbcdddcbbbcacbcbcadbbabaacbbcaddbccacbbccdccbbcdccacdbdcbcdcdcaddaabcbbaaabbabbcbacddabaabccdbdbbabcadbdddccdbccacaaabdcaccccabbacabdcbdddbaccacbcaabbddccacdbdcbacacaddbcdabdcbadbdddcccacdcbbaadcaccbcbdaaaddbcbbbbcccdadabddacddabddbadddcabbbaaddbcdccdcadcabcabdbcdaadbdacaaadddcabacddaddadadcbcaadbdbbbcdcdccdbaccbdbbaccdcdadaccbacaacdcbaddbaadaccddbcdcadadcabacbdbadcaacaacbdabbddbdccacadabcbcddcdbbacaddacabddccacddaabbaadbdcbdcabadacddbbbadcdbddaaaacbaccacaaccaacddcbabacabaadcbcddabdbdbdcabbcaabdcabcddbaccdcdcbccbbccabcccccadaddbabdadacdaadaacccbddbbdbacdddbdabaccabdccbcddcbabcaddbadaaddbaadaabbbdbcabdaadadaaadacaaaccbbcbccdddaabdcabcbbabcdadcccbaabaddbccdbabcbbcadababdbdcdaacccccbdabacbcbaccbcaccacdbdacacabcabcaababcdacbbbcdddcacacabbcaacacdbcbcabaddcadbbcdcddbaadbacdccddcdcdaacabccaaaabaabddbbdbbbacbdaacddadaacbcbcdcbdbbccadcacbdccccccaaabbdabdddacabbabdbdabacacccaddbbbddbcccddadaaacdadccdcdcdbcabdcdddbbdaddbdabbdccbdbacbabdbadbabddccabaaaccbdcaddacadbdbbbccabbaacdabbbdcdddadcdcdbcabbdbaabbabaaddbbabccddddbddadbcddabaadcbabbdacbadcbccaaadbddcdddbdbcaadbdccdadaccbbbacabbacbabadddaaaddbcdbabdaabcdaababdccbdcdaacabadbacbcdcbbddddbadbcdbdadbbaaaccbbcaccccbacdcdcadbcccddadaabdbbdddccabcaccbbaabbddbcdcdadbdcbcbcddaacaddabacbccdddbaabacbcbcabdabacdabdadcabacaababdbadbaabacadcdabddaabcbdabdbccccaababccacdbccdaaccdddccabbcaacadbcbaddcdbbacadbbbacabbccbacbbaddbbbbaddbcaddbcbacbccbcdccdabbbcaddddacdabcadadcbaacbbbdadcdbcbbbdadbccbbaaaabaaadcbdbddbabccacdcbabbabaaaadddcaadcccacabdcdbdbabbccbbccbaadadacbdcababdbcdcaaccbccaababaccbaadbdaccdbdadddbbddddccbbcbcabccabaaabbbddccccdbbabcaccacabdbbcbacbddbddabadabbddcbddccaadddccacddcccaaccccccddabaacbaadbaaacdcbccacbcbbacbbabcddcccccddabadcbddbaddbaabcadddcdbdbbbadadacbabcbbbcabcabbacbcdcbdadaacccacbbdbcdaacbcdcccbcaccdbadbdbdcbcdbcacaabadadddbabbcaccbbbbdcbddcbbddbdadddbaccbadbbbcdbaccccacabcabcccadaddabdacdbacaccdbaacabaacacdacdccbacbcbdcdbccbdcabcaacacadcaacdccdcbabccdcdaddabdaddcdcddbccdddddcbadabcbdddcdaaddcdddcabdbdcbbbdbdacddbbcaacdbccbdaaabdcabdbdaaccadbddacdbbbcccddcdbbdbccbdbadababaccdcdbbdbbdababcaaaacbcabaadbdaacbacbdbbcdcaadaccaabbbdddbcaacdbaccbbaddccacabdbdadcaabdbacadbcbbabcaddcdaccdbdbcbbbcbbadbbcccabddddbdccdbaccacaadcbddbcbdbaddcbcabadbacaccacdddadabdcbcadddddddbacaacacccaaccddbcabcccacaacabbabcdaadadacdcbdddbdabdabadcbcabcbcbadabcadbcbdcabdacdbdcddaadacadabbcbacbbdaccdcababaaaddcdcdccdddaabaacacdbbdbbbacdcdccaaabddbcbccabcddcaabbccbbadadabbbcbdaadcdabbccbcabadacbacdadabdaccbbbcddcbacacdadbaaacacccababbcbabbaacbcbcadcbbcbdabbcacacbcdbbaabcacacbadbcdcadbdbddaadaddbbcbdaabddabcccdabccdbdbbbbcaaadaccbabbaadacadddcdccddabdaadcaddddbdbdbaddcdaddabdcbaaadbbddbbddddaacacbcaaacaaacaabbcabbdcdadddaccddccbbbdbcdbbadcdbbdbcdcacccdccbdddbbcbbccadbbbdababbbdaaaaaacbcbccbbdabdbdabcdbdabbabcddbcbdaaccadaccddbcaababdbaaadcadcbbdabcdcdbadaddccbaadddbcaccbacbdcbdcaacabcbcacacabbbcbccbaadcacabbbddbdcddddcacaabcbcddcddbabbbbcdbadcacacdccddddbddcccdbabadcdddcccdddbbdabbbcdabbdcabdcdbccddadbbddbdcddaaccadaccbddadbabbdccbbdabbcbcdadcabbcdbddbaabaddaabddacbadadaddcccdbccccacbadaaccadbadbcabccbdaaaddabcabdcdbbbabcbdabbbaabdacacbbcbdddbddccdadddbccadccbcacacbdccabbcdbcccbbcbcbddcbccccddcacabbcbaaccbaaacdbadadbaabdabbaadcbbbccdbcdbdbaddbcbdbbcdbbbcaacadbdddcbaaadbcadccdcbdbadccbcdaadcadbdaadababbbdbdccabdabbcbbdabbabcdacabbbdaccbcdabbdcbbcabdadbcaccadcbbcbcbdaddbbbdcbcdcbcbccdbbbbbbdabcacccccaaabcabcdacadaccbbcdacdcbbadaaadaccabdaaabbcaccddcccacbbbdcabcbbccdcdbadaddcddacbcdddcddabacddcadcaaadddbcdcdbbbddaddbccdabcacbcaabcbbabaaaaaaabbccabdbaccccdcbdbadcaacccabbbbccdddcccdccbddbddbbcccabdaddadcdbdaddbcccbababdacbbaaddccdcdcbdddbbbabbaddacaaaaaccdbaaacdccbccbbabacdaacaaabbbbccacdbaccbbdbdcaadbbddbdccddbaabbdbccaadbaddbbbcdabcbdbbbbddbccdbcdbbdacbbdadcabbcbabbdcbaadbadcbcccbacdcdaccbabcbbcbdaaaabdadcacababaacdcdbcdbbcccacdcbadabaaacadcbbbabdcdaacbddcbaaccdbbdccadacdcbcdbadccdbacaaacaccbcacdcbababaabdddaabcaaacbaacaacccdabadbbabddabcbbbacadadcccdccddacacbcbabcbdcdacdddabdcddbcacbdaacbccccbdcbbacbdaacdaacbcbdaabbcabdcadbbaadccdddccdabbcccaacccbaadabbbbaccddbadcbcaccbcdaacccdddcbcdaabddabacccbbabcbcdcddcccacacbcbbcbdbcdccddaaccbdbccbcdbddbbbbbabdcaaddcaaddddbacbdbabbbbcdbdcdbbaadbcbcdcccdcbadccddbddcdcccabaadadcabbdcdbadbdaadaddcdbcccdbdcbbdacaadcbcabbdbdbcacacbdcdbdcdccdccddaddaacddbddcbbbbbdacaddaaabccabbbbcbabcdcddcdddaccaabbcdcccbaadbbbbccadadcacbadadbbbdddcbdcadbabccacbdabdaadacacadcdddabdabdddddbbadbdcbcacbbbaacadcdaabadadacdcccacccbbddabdddbdaccccbddbabddaacacbcbbaddcbbbcbabdcaaaccbbcacbddadacaddcccacdccbbccabbacdacbadaacbbdbddcadaabdabdcaadbaaccbdcbbadddcddbddabccddcbabbdabdbbdcbbabaaabbbcbbaacbddabadaacdccddabaabaabbddacdaadaabddaaacdbdadcbccdbbaccdbaadbbadbdbaddadbbacddadbdcddbddaacdabadcdbcdaaacacbdddaabbcbaadbdccdccbbdabbaadabbbdbaabdcbbccbadcdcabbbbbacaacabbacdaccdddbacbacabdbbacbbcdcddabbcababbbcababcaaccadddccccdbbdaaadabbdaacbababbbbdadbaacbcbbcddadbadddcdbcadbcbcdbadcdccaabadcdacccacdcadcbccdabcabbbadcababaaacdcbaaddacbacbcabaabacccbdddbddbacdadcdccbdaaadaadabbababddaaabbabadcbcdcaabbcabbddaccdcbbdccdababacabaaddbbbdddcdddbbdccabdaccddbabadcccbcdbdcdddacdadcdddddcbcbbcadaddbdcbcbcaccdbdadadabdddbbdcacacbadcddcbbcbbaccdddaccdbcbcacdcaacadbbaacbabccdccaacabcbddadddcbbbbbbccaaddddacdbaabaaaccacaddcbabadddccdaadcddaadcbbbcbbaadbcdddccdaaabbaabcdcaadbbbccaaaaacbadcdbbdbbdbccbabaababaabbcbdababbdcbacadaabaccccaabcdddcccbacbaaabddaacdadcabadbabcaabcbbbabdcddcccdacababadabadddbdcdddadaccbccdbdbdbaccbcdcccabddcbabcdbdabccdddcababcbcdaddcabcdabdcbbcbbadddbdbaaaddacdcdbaccccdbbcdddbaddcbbadbaaacddcabbccaddbbdddaacaaacccadbccaccdcbacdccacabddcbadcacddcccbbbddadadcdadcbdbcdabbccabaacabcadadcbbdabbdcdbadbabbabcddcdabdcdadbdddcddbccdbdbdabbbcbdccccaaacbcdaabcdacccdaaddcbaabdabdbccccdbbcbadbddaacaccdbbdcdacdcdddbadbdbdaaaaabbbdbbbbcdbabbbbaaaaaddacbaaacdaaacbabbdacdbdadacccdcbdaddcabdcbcbbbabdbddbbaabbdcadaabbccbbdcdbbdddddcbadbacccbddbaaccaaadacbababdbaabcacdddadbadacaacdaadccbdbdcdadbacdbcdccbbcbccabcbcbccdabaccdaabcddabcbccbbabdbdbbbadbadbbcaaabcabdaccdadadcdbabbabcdcdcaacdaaacdacdbbcdbbcdbaddaabcbabadccadbcaadacbdaddcbbbdddcadabdbcbcabddbbcbbddbbadcadadbdadbbcdadcabbccacdbaadbcadbdccdcccbcdddccabddbbcbbadcacadaaddbaadaddcbcbbbbdcdacddcbddbddbccabbacccdadbaddadbcdcaddddcbccdaaabcaabbdddbcabdbcacdbcbbbcabbcadbcdbaccabbaabccccdddbdbcaaccdabaacbdbabadcacddaabcaabbcaaccdbaccbddcbbacbddbcdbcadbadbdbdcdbaadabbddaadddbbcbbdcbbdccdbcdccdaacaadbaadddbacccaddadabbbaccddddcdaddadaccadaaacacadbdccadbaccadcdadbcbccbdcacbcdbabdacaccccccdcacddbcdcddabbddadadbcbbabaababbbdbabbacbddddbdddbdbbcddaabcdcacdcdbabbbadccacbdbccbacaddcabcdbccaddcadcbccddcdadaadacbccdbaacbbbbabbcdcabdbdbcababbbaaabaddbdacacdbadccbbcccaacdccccddaabcaddabaaddcddcbcdddbbcaaddcddbbccabdadbbcbbbaabcbcdcacdacdcdcacababddcbccbccccabddbdcdaaacaccccbbbababcdaddabacbcbcacadbaccacdadaccbbcabdadacaadcbbaadaabcccbdbddcaaccabbdccaadddbdbcbaaabdadcbcacccdbaaddcacadaaaabacbadadddddbcbcddababcdcaadbacdbbddacabcdaaddbcbdbcbcdadbdcacabbccacaaacccbaabdbcdbcdbbccdccbcabaccdbdacaacaccacccabababadcdacaadbccdabdacaaabbdcadabadbccbcdcacdaddacccbddbbbaaddcaddccacccacdaddccbcbdadddbccbbbadcbccbbddabadbaacabcdcdaaccdcdccbbbbbdcacbcdbbbacbcaabaccdcdacacdacbdddcbbabddbcbbccacabbdadadcadadcacabcaabdbaddbbdccdcaacaacccadbddadbbbcddaacbbabadbccabdabbacbdabcdccdbcdbdbcbcdaadcaddbcccddadcdbdbabddbcdbdaaccbaadcdacabbdadbbcdabacdadccbbadbdabadcababdddbbcbcdbcaabbdcbccabbdddacccacbdcacbabdcbaabcadbbbcdcabccbbcbcbbbadabccbaaadcdbcacabacdbccbacbacdbcbdcdbcacbcbabababbacddbdaabcdacbbddbdbcdccadddcdccacbacdadbbdbccdaaadcaddcababcadddbadadccacadddacabbbadcdbdcbcccddaabababdccbdcaaacdcaaaabcacbdaaddcaabcbdbbccbbaddabbaadabbaaabcaadcacbbdacadabaacdbbddbbaabaababcaddaacdacadddcaaaddbcdaaaccacbacabdbbdcbadccccbbbbbadddcbbbaaccabcddcabaaabcbbadababaabccacdddbadcadcdbbacbccaccaabbabdacbaaaaccdaabcdcbcccaddcaccdacccbbaacdbdbaaccadabbcdacdaabdccdbdcdadbcaaaaabbddcbddcdcdddaadcbddaccbdacbccaccacabcdadbdcbbbcdaccbbacddacacabcabaccacbbdddbbacdbcbcaccdcacabbcbdaddcbcbddbcdaccdbbbcdbccdcadbadbdddbccdadabddcbaddbbdaaddacacccbdbdcdbdbccbaaaaaacdaabadbadbbbcbddcdcbcaabadaddbcacadbaababbdbdcadbddbddaadbacdccaabdabcaabbabbcacabccdacbbddabaacdbbbbdbabcdacbcabdbbbadbcabbccaacabbdbcdddacaabdcdacbbddbaabbdcabcadcbaacdcbddaaabbacbcdaacddcddddbdcddacbdbacbcabbdbaccadcbddbadacdbccacabdcccaccacdcaabaabadaccaddbaadcdcdaabcccbaadadacbbdbcbbcbbacaddcddcabaddacaabcabccaabbcddaccccbdacdcbccabadbcbbdcbddacbcacdcdcbdddadbbaabdacdccabcadabbaabacbacdbcadddaabddcbcddabddcabdabaaddabdbcbdbcccdcbdcccdaabcbcaaadcdbabcdbaaaaacacbbddcacbdbcaaccdaddaddcaacabccdadddbbbddccababccaddaabcdcaccabbcbdbacdbdabbadbabbcadaacbddacabadacabcaabaccadbbcadcddbdbcabcabddabdbadbcdcaabdabbcdadcaabdaddbcbbcbdabdbacddacbdccadbddbacadcacdcaddbddbbddcabbcdaddcdacccaadccdddcbabbdbbcccadabbcdbbbcacacbaacdadbddbbbbabacabadbdcbbbcbcbdbbdcaabaabddddcddadcabcbdadbadbbcaadbdabdbabcdbabcddbabcbdaaaabdbbdcbdbdacacddcbbcaddbacddbbbcadadcdcbacdbdacdccdcdaaacaabcdcbbbadaacbaadaaadabcbcbbcbacccaccabdacbbabbaccccadadaccccdcddbaaabddbbcacadaddadbccacdacabccdbdbcdadcabdbcbddadbacadccbdcbcbdddbaccbcdcabadcaabccbaaccdaadcbdbdcabcbdaaaaadcacdbdaaadcacadbcdabdcdacbacbbdbddbcdbacbcbcbcadbddaccddcbddccbccadadbcbcdcdaddaddadcabdadccaadbdaacaddbbbbddaddcbdacbdbcccdababacccaabdabccbbbcdddcaaaccbbaccabdcabddccdbccdaaddbaaddadaaccbdcadcdbddbaadbaacacdcaccdaaaaabddaaacccbdacbdbbbdccdbbdbbcadbcdaabdccbabcadaddcdadcdddbcaabcaddbbaaccacdadcbdddbcdbdaaaaabcbbbbbddabbcdbaabbaaccabbdddcacaccdcccbadbadabcbbbbcaaaacddbacdccabcdccacdaacbccdbdbaaaacddbcabacabbccbccaabdacccbdaadbacaabbabdcdcbddcdddcaaacdaaddbacbdbddcbacdddbddbcdcbcccdbcdaaddbcccdabcabaaacacdcdbaaddabdccabbbabbadaabcdcbbbcbcdddaabcbbdbbdbcacbbdddcbdbcdddcddababddabdacacddcacaacaabababccabbaacbcabdbbccccddabdabbbaaccadbccdbbdcbbbbbccabcbadacbdcbaacdcbdaccabcadacbacabbbdbadcbabdabaddddddaddddbadacacadbbdabcaacbabccabccbaddcaaacadacaccdbbdddaadadcbddbdcccccbadcbbdaaacddbcadbdddcdbbdbdcccbdabddaabcccacababacbaccabcddbdcabdcdaabcdbbcaccdabbbbaababcaddaaacdacddabcbdcbdcbabbaaadbaccbcdcddbadbddbdacdbbaacacaccbcadbacbadbacdaddacdddadcadcaaaaabbbdcacaaccacdcadabbdccbcaadcabcacdbcaabdaaaadddcbccdadacbdbbcaacbdabdbbadbcacddbadbdcabdabccccdcbbabcbbdbabadbbcdbbcdcbdadadcdddccbddabaabdddaadbdbcacddbaddcdccbcadaddbcdcbadcbbddbddacdaaabbadddbdbabccabacdddccdbadcbbbddbdddbbdbadadcdbdcacacaddcaccdacccccabdbbbdcdabaccdcdcdcdccdaacaadabbacadccbcabdadbdcbdadacabbbcbcbabbcbbdbacdcacbdddcdacbdadcbbaacdcacbacbbdcacccdbaccdadccccdcbbaadcbddaabbaaccddbdadacacaabdbccaaaacbcdcbbddbadaaabddcababdbbababdcccdbdabcdccddbddbaaabddddacbbdacbdcbddaaaabccabbaaadabdbbaccddbcdaacdcdddbdbbcdaabdccbdabcaaacaaaabbbddbaccccbbccbdaaddadbdcdbcbadcbbbccbadcbadcaddbadadccbbbbbdacbccabcadaddcddacabbdbacacddccdadacdbacbaadbdadbbbbbcadcacbbcadcaadbaaabcdbdabbacacaadbcbabbdbbdcdadbaaabdcdbcbcdcaadcdddadbdbbcdaaddcbbabaccdcacddcdddaabbbcdaadcbdabdcadbbcacadbccdbbbacdbdbacbddbaddbddcdcbdbdadbdbdaccccadacbbdcaddbccabbcdccadbdbaddddabbbdccdadbdccabcdcbdabdaabdabaaabdddadbabbdcdbbbcdbadbcbbaaddbddbacadbadbbacbacbbdbdddbdcaababbccbdbcadaaaddbbcdcacadbabcbacacddcbacbddadccdddaddcbabddbcddbbacaaabdcabdcddddbcaccbbdabbcccbbddabacaadabdabcadbcacdadadcbdcdddacbadbbcbcababccaabbabaddaadabdcbbbdcdcccabbddbbaccccabadbcdadcaddcbddabbdbddabbddbdbddcacabbabbbdcbabdaaccdacadbbddddbcaccacbaacccbcaadbcabbdbccacabddaddabcbccdcdddcdacacdbcbcccccdbccbabbabcccbadddadabaabdcbdaddccbdbcacadbbdbbbaadcdbdadddadddddabddaaadbaaddbccbadcbaaacdbdcdbbbaabacdbbbadaccdbdcdbabcbccaadabdcccddaacbacabcddbaabdcbdccddbaacdbccbbaacddadccdcabddabdbbccaccdcddccccbbcaccaccdbadddabddacdbbacacaacadabdbcabdbbbbcaddacacbbdacdcaddbcbddbcdcaaacbdaabbbdcabccdbdccbbcbcbacbddcdabdbdabbccdbcddcdccbcddccacacaadbacdbabacdcbcbaaaabcccbcccddcbcbaccdccbddddaccaccbabdbccadadddbcbdbcadbdababbdaadaacbbcddbcabdaddbdaadcadcbcbacbccacdbccccabcacbabcbccbdaadbdaddabcbddbaabadbbbbcabbbaddaabaddccbbccadaabcbbcccbccdbbadccddcdcacaddbabaacbddcabaacbcbdddbccaaadbcdacbdddccaabcaabccadcddcdacbcababcacdbbbddadcddabbdcdadcccbaaacbcdccadccacaababacdccabddbacbcbcdbddcccbdcdcdbdccaddcbddddaddbcdbbabbbdddcacdcccdbbdabddadcbcdadacaabbabbcdcbdddabcadccdcbbaacccdabaabadcccbccdcbdcbdabadcabbbabbbbbbcbdabaabacbcabcabdaccabccbcdadbbcdbacadabdddccccddbbbdddcabbbbabcccdbacabcadbdcdbdbccbbbdbbcdadadcdbdcbcdbbaaacababdabbdddddbdddadddadcdaaaaadccccddbaaabdcacaadacddddaaababdddccdacbddbdcaaababbabaaadbbabcabcbbabbbbdccbdaccdcccbcdbcccbdccdabccabbdcadadaccdbbadadaacdcbabddcccbddcdbdcdbdbdaaaaadcabdbacdddcddcbcadcadcaccdacbbdadabdabdbdccdadbbcbbabcddddbadaacdccaaaacdababaadaaaabcddababdddaaababaababddbacbbcdacaadbbbcddabdbbcdaabddbaaddcadacaadbcabcdcaccbbcddcdcaaaaaadbdadadabbcbabbabcabaccbaabcadbabccbcaadbacbaaccbddbbdaacbcbadbdcdaacbbbbddadcbbdadbacaabdacbbbcaddbbaacbdaaabcacbdddddcbbaacaabbdcdbdbdccdcadbdcbcddbbbdbccdabbcdcacbbbdaadbbaacdbaaaccccbbcccaaacbbaacdacddbadbccddcdcdabbcdcbadabcddaabbaaabbccbcbcaaddbcabbdaaddacdbdacbbbacccbaccbaabbbbcaddddcbccbacbcbdbababbdaabbdaddddcdcaaabdaabbbbddaabacbdbbacbddcbcbabbabcdcdaabadbbbdddbadcdacbaadccbabbaccdccaacccaaaccbacacadbdccdddbadbdbcadccabdbbbcacdcdacbbbdacaccdbaabaddcbcdbbbcabccadaddddccddadccdacdcaaacdbcbdddadccdaaababadcdadcbbabaccdcbcbaddcdccbaabdaadbdacdabddbdddddbdabacbcacbdbacccabbdcdacdbacbaacadbdacdcddbbdcadccccddcbcdaadcddcbcaabbacdbacddbcacbbaaaddabdcaacbcacdaccabaadcdadaaddcdcbacacdbaaccccbbadcacaaabbadcaccadcbcdbcddcddbccdbacadaddbdbcddaaccabaabccbcadacaccabaabbbcabddbaccccddadcacabcbcdccbaddaadccdcbaacabcbdcdcccdaabcdabaabcaaccaadcabcdcbbbabcacccdcbcbccdbddccdccdcccabddaaaaadabbadbbcccabddcdcacaddddacbbdbbbdbbacddbbdacdaadadcbbdadabbdacaccbddaacdbdccdadcbddadbcbcdcacaabdabaabbacdabacbcadaccdaacaaccacadcccacdcddcbaadccdcbabbdbccacabcbbadbcccaaaabbcbabbaacdcacbcdbbacacdcdbabccdddabdadbdddcdcabbdcbcbbbdaddbcdbbdbdbbdbcdaacaacbcdbabcccbdccabaadcdbcbaacbadcaacbccccccdbbbcbdadbaaabbdbbccbabbbddaacadcdadabbacacdbabcabdddcdabacaaacacbadcddbbbddcbbccbacabdbddcaadcbdbcbaababacddaadcbccbccbbdadcbcbaddbbaaabcbdadacbbdbabcdbbdcdccaabdcaabcdcdacdbbabddbcaadccdcbadbaacdbadcbabcbaddadbacdaadbabbdcdcbbdccddaddabdbcccdddacddacadadadabccdcdabdcdaabadbdaadbbdacbbbcaabccadcbadaadcdbccbaddaddacdbaabdccdbdccdbbdadbbbccabccbcccbbdacbbaabccadaddcdcaccbaaaaabddabdadbadaaabadadcbdccdbcacddacbdbbabcaacdaababcccacacdcdbadabdddabacdacabcaddaccdabbddcbacabdcbcbdacadccbcddcdabcbbdcbbdadacaccbdcbcbcbcacccccacdaabdcadcccbbcbbddbbddccaabacbdcdcbcbbabdbcabbcdabadaacdcdadadabccdacdadbddabdbcdccdcadaccdadbddcdaadabdccacaadbacadbbbcabdccddbdcdbaddaabbbbacabdddaacaaacbdacbbbccbbaaccaabcbcbadbcaddabaabcdadbdacbdddcbdaaadbaabadbacbabdbdaccbbdcccbbacacdcbbbadddcdaacaabddbcbccadcadbaaadddaddddbbbdaadbacabaddcdddcaccccbaaddabdbcdcdbababddbddddcbaadcbdaccbcbbcbbaaccaadccbbcaccdccabbcccbbbadddbcdcaaadadaacabbabccaccbacccddcddbcdddbbddccacaaccbdacddcbaaaadbcbbbccaabababbbbabdddabbcdaccbccacdcbadbccdaddaababadddadbacdddacbaaaabdaadcbcdcbbdddccccdaadabadbdabbbbaaccbbadbdaddbdbdabbbdbbbdcdaadbbcaddbabbabbaabcabccaabcddacababacddaadcdbdcdbabbaacabdbddacdcdbacabccbaaccbabadddccbddadacabccbcaabadddabdbadccdbdbbbcbabcddcadadbbcdbbcbdcbcccdacdcadabdccdbaadbbdbbdcabbbabddcaadcdbaabbbdabaabbacaaadbabbdabadbddbacabbbddcaabcabccbacdcddbcdbdcdddccacaadbdbacbadabcdaabdddabccbaabbbcdcbdadbdbdbababbdbdbdadccbdbdbcdcddbaaacdcdbaccbddbbddacdabbadcaaababacbcddbccbbbddbcbbcdbdbdbcddbddabdbdadbdcaacbabacbbaccbccdaacbccbcbaacbcbaabbbdddbbbddabcacdacbaccddbcadcbabaacccacbddaaaccbabaaabbadcdbdcabaddaddacdaddbadccbcddbcbadbcdddccdaddbbcccbbdbbdcdacadbaaaaaabadbbabcddacabddbbaabcbadccccccabccddbaabbccbdaadabcccbcadbdddbbcaacacabddcbadcdbddabbacdcccaacdbbcdbaddaacddbabbaadcbabacabbbbaddadbcbccdaddbcbbaabcdddabbacaddcbacdcbbdababaacabddadabddcdcbccabdbdabacbaddcbcbdcbdbadcadaaadbdaabbbcbbabddcacdcacbcacaaddbbacddcabbddaddccabbdacdccbcbccdaddacadbacababddadbdaaabcbaadbbaccbccbdcabbaaadccbcbcbccadcbcdddaddccaababbdaababcccbdaddaaacaacaccacbbcbadcdadabadcddaccadcdcbbadccccdddacaaddacadaabccaadbaddbcdbaadddadabcabcbaaacabccbcdcbbbbaaaaacddbcdbdcdaaabcdcacbdadbdabcadaddcdcbccdddcbddbcdadcabdacdacbcabadbbcaabccdaadaddadadbcaddccdbdaccbabcaabdbdaccddcabdcdacabacaaaacbbcadccabacbbccbbcccaaddbdbadaadaabbcabdcddddcccacdddbacdaabccbbaadbabcdcacbbcaabdcbabbaddbbbbccdddadaabcadcbaabbddcacaabdbcdbbadbadbbbaabaabdbaccbaadbacbaccadccbabbccbabbbadbacadabdacaacabbbcbdaababcdabbdaaabcddababcdcbccbabbcbccbbddcdcaaaabbabcadaacbababadcacccccbcaddbdacbabcbaaabccbaabdbcaccbbabccaacbbabbadddcadbadbacbdbbbccdbdbadcdbbdabaacdaacbccbbdacdbbdcdbbdccddddbaadbbdcbbcccddcdcdbbcabdaabcdcbacdaccdbcdcdbbbcccbabbcdabcbbdcbbadddcccdbdaadcbcdcbdcaadcaabcbabddddbbdabbbdadbcdbdaddcdabcccacaccbcaabaabcbadcdbabacadbcbbdcbabbddaaabdcdbbaacccababdbcabaabbdadbacacaabccacbbdaaddbdacbdaabddbcbbcbcaacddcbdcaaabccbbabdbcaaaddacdddacaadabdadaadacadaccbcddbbbcabaaacccdaccdccbbaacdccbadaacdcbbbdcbcdbddbaaadbaadddbbbcbccbaaddcbabbcdccaadccdacbcdcccddcadbaaccdbbcadddcdcabaadbbbbbdacadcabbddddbccddaacdcddcbacabddbbdccacacadaabdcacacdcbadcbadcdcabbaddadcaddaadcabbabadbdbdabdcccadbabbdbadaadcddbbaccacabbadcacadbccddccbdadcabddcbdbbbbddaadadbddacdabacaaacddbcabbcadcacaacccacdbcabaccbbccabacdbdbbaaaadccbaccdbbddddccbbcbcabababccdbdbddbadcdabcdaacbbaabaccdcbccbcbadccbacbbbacadcbccbdacdadacbabbbcabaddcaddcbcabadddcabcbabbdaadcadadddcdacdaaabcaaaadbcccdccbbcddbdbcacccbbddaaacadbcbdcaccdccaddccdcabdababadccacddbababadccacdcadcddbbdbddddadcddadcabcbcccadaddbdbaaacdbdccdbddcddbcdcabacdadadbdbcbbdacbdbcacbadbaaccdcacabcaabccadcbaccddaacbccaabccdbdcccabcabddddcbadccbcadcadcbaadabcbbcddcbdacdaadcdbbbddccddacbcacbdbbdbbbdacadbadaadccabcdbadcabaaccbbcdadcdcaadcbbccdadababcccbdcbabbdbadacaabccccbadadddabbbdbcaacdbcadccccacbcacadbdbbcadbbccdcbdbdddcdadcaddddcdddaacacbcdbacddcaadabccadbddddaaaababacdaddbbccbcaaaabacadabcbaddcddcddddaaccbddbcdbccdbdaaaacacbcccabbcdbbcddaadabcdcabacbabddcacaacbdbacbbbadadcadabdbbbacacdbadbbbdbddcacbbdbcbbdbcbaccdabbbcbbbbaccbdabadbdaaddbcdddddaddaadcbbcddadbaacccddadacdbcabcdbbdbdcadbcdacacdadaddadbbcabdbcccbbabdaadbcbdbbbcdbcbbbcdcddbcadabbcddaaabcbdaddcabccddcbbdcadbdcbabccbbbcdbaacddaacddcaabdadbbdcababdbbcbcadddacacaacbacbdabcbdbcbdaacbacbabadcdababddbabbdbccbaacbdddcabcaadddbbcabcbaddababbbbaaadbbddcababdaabcabbaccbccbdbcbcbcadbcabcbcbddaccdcdddacabcbdaaddcddcbadcacdcddbcddaacbdaccccbbcabaccabbaadddaabbbbdbdbadacaacbcbbcbbaaacadbabadaccadbcbadcddcbabaaabccabcdcdcbdbabdbcaaacacbdbadbcbbcadadbcacaccbdbbbcddbbcaacddbbdccdabbdbbccbcddadbdaccbbaaacababbdbdcbaadbdadaaccdcabbddcccabcddaaaaacaaadccabaadbadcbacbcababbbaccadcacdacbcaddbdbbbbcdbcabbbccbcbacadbddccdbbabddabbcdcaaacbcadddbbbdabbabbaabdacbaadbdbcbbaccaaadbacbabcbadaabccbdcbabcddbdddcaddbbcbcccaddacccdcddcabcdacaaaabdbcdbdbcdcacdbadcdbdddbdaacbdbdcbddaddacadaddcbbbdadcababcbacbaabcdcadcadbbdaacddccdabcccdaacccbcbdbdbabbdcababcbdbbdcbbaadbdbbbbcdccaadcbddaccbccbcacacabdbcccdddcadcdbbddbccabaddacadabacaccbdbddadaccddbcccaacaddbadaccdadddbcbbbdbaddcbbbddcdddbdacbbdbbabadabcdbcbcbdacccbbaabdcabcaddbcdadcbcbaaddacaccbddcccadccadabacbacccadcbaaccaccbdcdbdadacbaacbbccdcbdaddaccbbdbbcacadbdbdaaaaacddcacbadabababbaccccdddaabacdacbbbdaacbbcbaaccddbbaddaadccddaddccddbdadaaacbcdbbacaaaddaacacbdcdcaaadddadddcbccacabbcbcbbabbaabdbccddcbbbbaddbcbbcbabcbbcbcbcbaaaccdbddaaabaacccccadcdcdbadbaacbdddbcbcdabcbaaaddcdabacdbccdccdacbbdccadbcdadadabdcbbbbbcaaacbbcbccacddbbbccabdccadddbdddbabddbbabbbadbadcbaabbaadadcddabdbcacdcacabdaadcdbcabadcacacbaddbdabcaaccaaaaccddcddcbbdbcbdbbacaccdaccadadadcadadccdbbcadcccadccbaccbaddacdcacacbabdcaabdbcddaccbadaadbbbcacacbabadababacadabacbcdcabacdadcadbacbbabcdbaabdcdbaababababcccdbdcddbabdccadcaabcbcdcccdcbabaacadbdccaadaddbbddbcdaaadaccabcdabdcbcaaaccabcaadcccacbcabbdccbabdcaddcbddacdcbccbdbaadcadbcbacbcbcbabbcdcdbdacbbdadbaabbddbcacadabcbaadbcbcdcbacacbbbccbbcddaddabdbbcbadddccccbbbcbdbcaaddcaddacaadcbadaccaaabcadbadadaaaabcbbadbccdcacabcccbdaaaddcaaadabadcdbddbacacbbcdbadcadabbabaddbbabccacdabddccbcbcdcadbacbcdacadbbddbaabdccdabadaccbbddabcaabdccbcdacaaacdbccddbdbbdbbccbdcaddaddaddbabddbbdcdacddaabaaabdccdbacaaaabcdabdcdcadaddddbccccddbcdddccabcdcdccccddacdacbdacbccaacdddacacbaccabaadcaacccaaabddccdbcabaadadbacbcddaadaaddcabbaddcbcdbabbbacbcbccbbdabdbdbadcdcbdadcbcbacacaccddabcaaacdaadacacbaadcabccbababacaacdaacaddaddcdbcdadadbaabcbddcccaabbddacdadbccbddcddddccdbaadcdabdcbaaadcdccacacaabddddabccaaaabcbabddcacbdcaddbcbcbcabbcddddbbdbdccbdbcdcddaccbdddbdbcccdcbccbabdacbcaddcddaaacbbaaccbccdacdbbaccaaddacdbcbbbbdbcadaadaddaadabbddadadcbdaabbdcabbcbccdcbaddaadcbdaccbcadccdadcddaaacbdaddddddabcbabddcadadacbdcbadddbddaaadbaccccacbbbacddbdadaacbaddaacdacdabddcacdabacacdcabaadddccacaabaaadaaaadbddacaabaccccdaddbdddadbccdcadcbdaabacddacdababacdadaccbabbcdaccbddccadcbddadcbcdcacadacdbbdabaccbbbdbcbabbdbdbaddaabaddcbdbcabbcadcadcacdddcbcbbbdbadddabcdbcdbdcdbacaacacabdbacdabcbccdbabddbbaabcddcacaabdaccbdcadabbdaccacaadcbacacbacbaaaacbacbaddbbcabbadaccadadbdaaacdddadddcbbaadbacbdbdcdcbcdaaccbbbcddbbcaaddaaddbabdcacddccbccbdadbbacbdcbaaccabcacbcacaacdcccbaacddcdbddcbbaacdadbddcdcccccddbddbaaacaabbcccbcaaabbbcbccccacbabdaadaabdabbcdcdcaabbbbacaccadacdcabdbadaccbacdcaddccbcddadcdcbcdbabcccddbcdbdcacaccdadbbcaccbccbabdabdcacccdadaadcbcdabdcbdbbcccbddadcaabbdbbcdbaaccbadadababccdcccaadddbdacaabbcdaddaaaaabbacacbbbcccdbdbbdabdbadbcdcbbccbabbdadadaacbbbcddbdcaaaabcbbdcdcdbccbccabcadadaabdcdbdbbddcaaddabaabdabadabaaacdcdcbacbbddcddcacbabadcdcacdcdbacbacabbdbabacbbbcadababdcdbcdddcbdccdcdbcdabdcbcccdbdccadcbaacdbdadddabdbdcbdadcdbcccdccbaacdbcbaccacdbaacacbcdcdbdadacdccbdaadabacaacabdababadacdbcbcacddbdddcbadaacbddccbbabcddddddbbdbdabacadcdaaadabddaabddbcbbdcabdadaddbdabbadbdbaccaddcaaddbdddadccdcabcabbdcaddaadbccacdadacdcacbcadccaacdadddbcddcbaccbccccaababdcbcadccccadcabdbbbacbbbccbdcaadccccbbbbdbdcdcddcdabbdbcabacbcbcbacbdccdcababbbdbbaaabcdccabcdbbabdddaaaccdadcacbacdbdbdbacbacccdabadaddccbabcaaabcbbadccbcbaaccdbcdbdcabdbbbbaadcdbcbaaccbbdccbddbbbbcaddbccadabbcbdcbcbcddcacaaadbadcddddbbabcbcbcbaddcbadcbcddcbbccdaadadcdbdaddddaaccdcdbacddcacaddabaadcbacdbabbcbdadcbcccadabaabdabbadabbaacdadbcbbcdbcaabbaaaccdcabacabbaaacddcdbccacbbdcdabaacdaddcbbbddddabcccbadbdcdcdaacbdbbaaacdbdacbdbddddcabdabdddacbabaddbdcabadccddaddbcddddbdcdbbbadbcdddbdbaadcbadadcaadcdbccddcaadcccdcaccaadbbadbccbddbabbabbdbcddbadddbdaadbbacccbaabcdaccbccdcdccbbabcbccbccabddcaacdabbbacadaddbbdcacbcbddaaccacbadabccdbacdddaaccaccacaacbaacacbbbbacbaacdcadccabcabcbddbdabdbbdaabcbbadcacdcadbbccbaacbcdabbdccccadacbddddccacbdcbdbdbbdcabbcaaaaabdccbadaddcbbcaaadaadabcdbaddbbddbabbaccddddbcdbaaccbbaaaabbccbdcdddadcbdaabbcadcbbabbadabdbdabbbdadbbcacadbaaacdccddabbbaacdcccdddabaadcbadbdacadaadaabdbaccbaabcaacabccaddabcccbdcbabdddacbdccdcaababddcdbaadddddcaaccaccddcbaaaaabdbddddbbaaccbdbbddcbabaaabccccacabdbdddcbaadacbbbdccbbbdcbccaaddcadddabaddcbccccddcbbbbbaccdadcbbbbadbdcbdbccbddbbdcbbcadbcbabacdcadbadcdcacacccbccbbcaadddcadbdbbacaccaadaadccbdddbdcdacbcbdbaddddacdcacddbdabdbdddcddaadbbbbbbbabdbcaddddacbadaacabbbcbbbabcaacadbdaccabccbbbccadcadddbaddbbbcacdbdacbaacdbcabccccdddaadaddddcacbdbdadbddadaadabbbdadadbbddcaddadabbaaababaaddcdabacdbccbbdacdbaadbadccdcadddcdaaabddabdddcbcabcdabaadabcabacabcdadcadaabaccdaaadcbaaccadddaaccdaadbcaaaacccbbbdadabdadddccccaadbcabbddddcdcdacadbcdaabddcbabbbcabcdcccdcabcacbcadbbadabddcbabcdabcbcccccccccbcdcccbccccadbcaacaabdacabdbdbbbaadadcaabcdacbbddcbcdbcdcccdaccabdcbcaaacbddccabbbdabbcaccbcadccbbadadcabdaacbcccdaacabbcdbbdcadaccdccbbaccdbbdcdbbcbbacbccaaddccddbbcbddbacabacbbdcbabacacacadbadbdbacabdaddbddbdadcbacddaaacbdccbbbcadacbdadcabccdcdccaabcaaadbadacabbdabcbcdaadababaabdaabddbdbacbcabbdaaabcadcaaddacacadbbbcabbcabddbaaadbbababcdaaabacaaaacbadccbbaabadbdabadcaaacacabdcaacdbbdacdbabdddcabaddccbccbddabcccdaaacabdaadddadcdcdddbacdbcacaaadbcadbddabcccccbcddbddccbcbcbaaddabcdbddbacaacacdadabbbabcabadddcdcccacbcadaabdabbacabcbcdbdcbddbadbdbccaaccbcbbccabbbaddddcbcdbdcbacdacaaaadcdabcddbcbbcbdabacaabdaaccdcdcdaccbdbbbbbdaccddbacdbabdcaadacbbcaddbadbbacddbaadaabccbacddbdccaabaaccdabacdcbbabccbadaddcdcabbbbaabbcabdbbdbbbaddabbcabbcdcdcbddaabaccadabddcdccadcccbbbcddbdccbacdbdbcdbcbabadcbbbdcdadaaddbbdacbcdbbcdaababbadddcacdbbcabbdabaacadaadbbccbcacaaadbcacdcdbdcacddcbacacdbabccccdadcbaabbdbddcbbababadbaaacacacbbbbdbbdabbbbbcbacaccbcaabadccabadbcbabbbbadddccdabaaacddbbbcdaaadbdaabccabdcdbbdabbdbccbccadbdbbbdccaccaabacbdbdbdccbacabcdadaaddaacacadadabdadbdbaadcdbccdaccacacbccbccadcaaabcabdababdcadaadbaccaccaacbcdbbdcdabbcdbccbdbcbbbdbababbdcadacdbbdcbabbaaaabcdbaaddbacbdcaaaadbaddccccdbddbaabdccdbadabdcbcadcbddaaadadddddbddccabccabaaaaccbaddbdbbcdbcbacccbbbaccbcdbbabbccdcbaacbcdcacbcbaabbdabbbaaacbbdbcadbababaccbbadbdcdbdddadcaacddabbbbbcadadccdbdbacacbbccaacbbcdbaccbcdabcdccdabcdcacadadacbaddacdacbacbcaabcabaccdaddaaabdcbacbadbaacadddadcbdacbdbaabddbcdcbdcadbcadcdcacddcaaaaadcaaaaaaaddadabdcccaacbcaaabbaaaacaacaadbbcbcaadbdcdbcadcbbaaddabbcacbbadcabcdcadcdcaabbdbbaddcbaaccabbcbbcbdbcadadbadacdbdcdcbacbbaacbaabddbcdaaacabddadccabcacbcabaaaddcdcddbabbcacbdcdcbbaaaadcadbcaabbcbcabdbdbdacddbcbacddbbcccccabcbacdbccddbcddccacbaddddaabdccadaacddcdbdacdabcbcdbbcbccbccddbbaacdcaccabbcbbaabbacabbcdbcdccbcdccaccdbccbcbabbdaabccbacabbaddadaaccbcbbaabaacaaddbcccccccccadabbddddddbcddccccbcdcbaaddcbadabbaaccbbbbddcbbabbbcbcaabdbddcdbbabbdccdccbcdaabbbdacbbabcbdaabbccddcbcaddccadccadbbbbbbaadccabddacccbdacbadbcbcdbdccccdadbaabaabcccbbcbbbbcddbcbbacdadccacaadaabbcadbaabbdaadacbadadcaaddadaaabbbaabcbddaaacadbabbbaabdbccadccbbdababdccbdbcdadcdbdaccbaaadcddaabcabdcaacabaadcbadcaccdbddadcccdaabdbbbdadcaacbadaacbbadacdbbdadcbdccaabbccbcaaabcdddccddbdccabdcadccbdabdabcdacbddabddcccbabdabaccddcbaddcddddcaccacabcdaccdbbdddbdaabcdabadacbcdcddcbdcdbbdaacacbdccbbccaadbbacccbbdccaaddaacbcddbbacdcbddacdbbcbbacababcabdcabaaccbdabbdccbbaacdabbbdabcbdaccdacdbbbdbbcbcdddadacdccccdbddbbcadddbcdcdcdadadbcdcbcaacacdccdbccabadaaadccbadaabdcabbbadcacbdbaacbcacdacaadbdcdbdabaccdccdabccaadbacbbddbbcdcababcbbbacaabdbdcdccbccdbaabdddddcabbdcdddcaadcccaaacccccdacaadbbbcdbcdddddabacaccdbccbadcaaaaddcdbcbbdbddbaddcadccddbacbcdbbacbbabbccdbaaaccbadaababadbbbbaabddcdababadbcbdbdabdcbccbdccadddcdbdcbadbcaabcddcdcdcbbbddadbaacadbccdbbddadbdabccabbccbcbbccdcaddaddcabbccacdbacbbddadcbcdddaadddbdddcddadbdbcbccdadddbcaccdbbacbdabaacddccabccbdbdaaccbadcddcbadccbddddabddcaddccbcbbdbdcadaccbdacabacdcdacdacccabcaababdaaadccbdcdcdccbccbdbadadadaaadcbcdbcbcdccdccdbbbbddacdbaccadaddadcbdbcacbbaaadbddcdaaddabcbbdabccacbacbdcddcacadcdcbaccbcbddacdaabcadabbcdbacccdbcacbaaadaaddadbccbdbbbdcddcdacabcdcccdbdadaacadabbcddcaabdddadddcbbbdcbccaddaabdbcccaaacdaadbaaabcacbcddbbcaddbccbcdccdacaaacaabcaaddabaacdcbcdaacccbbaaccdbcdbcadcdcdbccacacbcbddabdccdcddbbacccaaccddddacacbadbabcabbcaabcdbbdababddcaadbacbaadaadaabdcbaddccddcbabbdaddbbccbbbbabbaaadcaadbbbdcdbdcdbdccddddcadcaabddaccdcdacdddacbdcabbcddaaaabbcdcabdaacccaacdacddbcadcbdbcdaadbcdcadbccbdaddbadccaadcacadbdbdcddaadbcbbbbaccaccdaccacacccabbccaddbaaaaacaababbbccdcaacaddcdacacbaaadcdbbaadaacddadbdbacabbaaaddbaccacbabdabdcadaddcacdabccbcdaacbdadaaaaddacbdaccacdaadcacdcaaaaabbcbaccdbdacaaaaadccdccddbdbddcbbdcbbabcaacaddadccbcdcadbacccdbabbaccbbcccaccbddccdccdcdbacddacbdcaabacbbbcccabdbbbbcaacdaccbacbdacbddcadbcaddbdccabdbbdaddcaaabccacbbabbddcadddcddaabcbadadaacbabcccabbddbbaabcabccbccccdcbdddcabaabacacdcadcdcaadacbbbbabcbaccacdbdadbaabababaddbbdbdbdbaaacbbccaabdcbbbbdcabdacccabbdcadaaccabbcbdadabbcbabbcddbbaaadbbdaacbcbcbbcbccdbcdadabbddbdcdbdbdcdcdcacbcbddbaaadcacacdbaabbacdcadbbadcbdcaccacadaccacdaaaaadcccbcdadcbaccbcacdcdbbdadccbccbbcaacccddddbaabcadddbdaddcaabbddcbcabadacadacbbcbabdddccacbacbacddbbcbbddbbcabacdddadcaaacabbaabbdcacdcaddacabbcbaadabadbadddcbdaaaaddbccbbddabaaaacbddddbcbdbbabdacbcaadcccccbbaabbdcddcadcbdbaacbdbcbadbcdabcbddacbbaadabbbcddcdabdccdbbdbacbcddccdaabaaaabcccadbabaccaccdbdaaccddcbabddbdcaabbaccbbbcdacdabbbaadcbcbdccddaccaaaacccaadcbdcbadbddddbadccababdadcdbabccdaaacbcacdaacbdabacdddccabdbcbcacbaabbdddaabbabacdddacdbdbbccadcbcbbadbbabccadaccdbccadacbbcbcabcdcbadcabbacaccdaccadbcdccaabbbdaacdddbacdaadcbdabbbdddcacbcabadcaadcbcdcbabddacabadcbcbbcbacdbdbbbaddcbcbcbccacbcbaddcabcbcbacacdbbcddbbadcccbddaddacbcddcdaadcbdbbbbaabdcdcaabbaadabbaadcbdadbdbbadcbabcdcbbdddddccdacaabdbcaababacbbadbdacadcdccacbadccbcbbccacdaacabccabdcdaddbaaaabcadbdcbccbcadcdbacdbcdacacddbcbbddbadbbdcdccaaaccacdbcabdbbcbdacdababbabbccbcdcddcdacbdbbbbbccbbcddbcbabadbbdabdbdcddabcabcbabaaaccdaaaddabadcbabbdabcdbcacdadbcbadbdddacacddcdcdccccbcdaadcacbbabddcbaddadbccaabadbdcbabadbbbadbddbacaddddbdbaacddcdacacaddadaaccccccacdcaacdddaadcccbbcaaaddbbcababbabdaccbddddccabcdbcadbcccadcbaabbbdcbddddbbbdcabdacbbccbdaacccddcacbbdabcccabccbababccccacbabccdadcaabcdadccbdcdddcdcbacddcddaccdcacacdcbddcccbabbbadbadddadcabdacaaccbaacbddacdabcbaaaadbbbdcbddacacacbcadbdcdabcddccbaabcdddcdcaacbddbdbcbcbbcbddababdbbacadcddddcdbadbbdabacbdcaadbabddddccddddaacdbabccadaabccbdabbaccabcbabbdaabcddacdcabddbbcddaddcadbaaddbcbdccadcddaccbcacbaccaaadcdbdccadbacadcdccddbdabdddcbbacdacddadbcddbdbbdbacdccdcdcbdadadbaaacdbddcdcaabdccbadbbddbcdabccdccddbbcbbcdacbbacaabbcbabdadaaddcbbdadcbdcdbdbcdbbadadbdabddcdacdcbcabddadcbccdabdaccddbdcdccdaadbbaccdaabcccdddbbcacdcccabbbbdbcadabbccdbdcabcbacabbdddadcabadccdaabcbddbbabddbcbdddbbdbcbdbcababdbdbddbaacbcccaadaadbaacdddaccbcacadddcaacdabdccbdddcddbdaaabadcacaabbaccdaabdcdbcdbbccbdcdbcbaccdaacaaadaadcadccbbaaccdbacabacdbdddbdbdcadcadadcbbdddacabcbbaccaccbbbdbdacbbddbaadccbcdadbadabdbcdabadacccddbcbaadcdadadcabcaadcbdddccacbadbbcaabbddbcbaaaaacddbdaacacaaaabbcdcdcbcaaadccdbcdbbbbbdabdbaccdadacdabcbbbccaabccdbaacbdcbdbaabcccbdcacaabbbbadbacddcccacbbccbbcacbcadbabadabdaddcacaadcbbccdddbcbcbbbdccbddbadacbabdcbdbcabdaccbdacdbdbdcabcadcbacbbaaddcdaddbadbbabacddbccabacdbbaacabdadaaddbaabddacdacdcdccbaacdcbaccabdbbdbbcbcdbaadcccdddcbddccccaabdabaaabaddcbbaaacdacbcdaccbbdabcddcbcdcbabaddccababddddaaadabdbacacbabddaddbbdcaddbcadbbcabdbcccdcbabbcaabcbaddcbdccbbdaabaababadcaadbaaadadcdbaacbdcccdcdbabcbabbdbbacdcabdaddaacbdbacdbabbcdcbbaadaddacbacdbbbcbdababbdabdbcbdcbaaabdcdccaabbabadacbcddcacacbdcdadddbcdaccabcbccdacadacbccabcbddbbdaaadaddcaaddcbadbddbadcdabbbbccbadadcadcbdbbbddbbcbbbbcdbdaadabacabddbbcbbcbacdbdddaccbcccadccaabdadabbbddbaaddbabdadddddbcbccacabbbaaabcbdcacbadcccbaaaccacdcaabdbcdacccbbbabaddacacbcacbdbbbadcdcbbbacadbddaacdcdbaabacbaabcbbcdacabddcabacdadcdddbabbacccddccdbdadddacaadddaddddccccabdabcbbcabaccacabcdddcccacccbbbacdbcdaddaabcabdaacaddbcdbbdcaacbbcccaaacadbacccbbaaaccabccdbcadcccaabaabbbacadbaababbdbdcbdabcdacbabddaacbbddbabcbddaabddbcbaadacccbbccaacbcbcabcdaaddcdddaabacbbabbbabbccdbdababacabdaddabaddacccdadcbcaacdbacdadaccacaccbcbaabbbbdbdabccdaadbdbccbdadbaaddcbdccabaacddcddaabcdddddcdbbdcddcbdaacddbdccaaabdbabbcabbccbababaacdcaabcdaaabbbcabdbbacbadddbbbadcbbaaddcaabddaccccbcdccacdbbcddaaacabbaccacdddcaacddddadcdbcdbdacdabaabbccccadbcbacadabcbdbbabadbcaaddbdcdbcadbbaaabdadbbabcdbaacdcacddbadcacbcbaccabcdccbccbbdddaaaccbbddbdbaadadcccddcbbccbdadbdcabdbbddbcbacdcaadadcdabbabaacbcbcaaaccdcaccabcabcdcaaaaadcacddbadbbbbcabbacddaabacdcbbaacababacbdaacdbacddbdacbdcaaadcdbaadaadabcdbdcdbbabddcccaabcdadccdbaadaadccaaccdcdbbaaaddbbcddbccaabdcbdcdabdcdbcdbcaadbbcccacadbbadbbbddacbdcaabacbdccadbddcddbcacaccbdaccabdbdbddbccaaabdaadbdbccdbcbacddccaadbbadbcbcabddcbbdbbbdaaaaadacbbccaaddcaddabaadabddaaccdbcadddaadacbbdbacbccbaaabdbdaaabdaddacbabadaabcdbdbabacccdcddcaaacaddbdccddccaacacbbcbdccabdbbcaabcbdbcbdaddcddbcbcbccaddacdcbcbbddcbdacbbddcaaaacbdcbbaaddbaabdadbdbcabbbbabddabbcdcddacbdcadababdaabaabccdbdcadcbadcdadddbdacdcdccacbadcacbddacdbabbbccdbacaadcaaaaadcaaaccacbbaccadcbbddbbbcdabccccabbbcdcbbddaacadbadddcbddabbabbdbaacdcdcdbaabaaababdadacbaaaabbdcbcdcaaabacadadaaaabccacbdaabaaacdaddbadddddcdcaaabbdbcadcdabadcbdcbdaddcdcbddaaabdcacabdbdadcbddccbacdbcddbbacabcaadabdcdadddadadccbbdddbcdadddcddccacbcaccdacccabaadcabdccbbacbcddadacbdadacbcbbccbdaadbdaaccccdaccbddabdbddccbdcacbabbcdbaaadcdbdcacbbdbbcaccbcccadbabdacbcaabddcdddcbdcbbaababddaabcddbbbdddddabbdddddaadacacccaddcccacacabdaaddacbcacbdcadbbadcbbbbcadadbacbdaddaccdcabbaccadcbbabddbdacabaacabcdbbbbadabadcbdcdbacadcdcbcabdacabcdbcbbaccdcbacdccaccccaaaddbbabdcbdbddccbcbcbbaacbdbabaadbcacaacacaddbccbddaddccbcaaabacccadbbbaacaadbbbbddbbbdbdcaabdbccaacdadcabbddbccbcdbbacabbaaaaacbdadbdaacdbbcddbcbcaadccaacdbbbaadbadccacabdacadbbbbbcadbcadcbcbdcacbccaaaadddadcabbbdaacaabacdcabaabdcdcdaccbbbcadcaabccdbacaabadcadbbdbccbdaaccddddadbcabcbbcadaaaaacacdbaddbbccbdcddadddbcaadadcdaccdcbdacbdddcbdbcdbbadbbcddcadaaacabaaaababbbbcbabbabaabaadbabcbabdabcadadcbadaacdacccbdbbcbaadbbdabddddbbddcabbacbdccbdadcaccbcacdcaaccabcdacdadaaaaccacbdbcdddbbddcabcbbbbadddabbacabccbbddadbcacacccbcadcaddbdddcbdbcbcddacacddaaaadadccabcbdaabcadaacbdcbcbdacaaccdadccbbbbbbddacadbbcaaabaadbadccabaaddaabdcdbaaaccbacbccddabababadcacaddbdcddcbabaadaccdadcbabdcbcbcbbacaddccabadccbbdaaabdbadbacacadadcaaaccdbdaadbdabcabcbdaddccbcabbddbcccdacaabacaabacdacdabcdccdbcbbdabbdabbdcaaabaccaccdccadccdabcbcabcdbbbcabbbaaababbbbcccbddcdbdbacadbacccdbacaabbddcaabaaddaaddabdbbabadbcadaabcdcdccbccdaaccbbcbbcbdcccacababadcabcbaccdaaccadbbbbdccaccbdcababdbdbdcdadddcdaadacddbcadbbdcbabcabdbadbaaaabcbcbaccddcaabadddabaabdbcbcdaacdbdcacddacdccdcdadaababdcbddbabdadcdbbabadccdabcdbbabcdadadcacddcbcabbcabcccacddadcbddcadaababbbbbcadcadcaddccadbbbabbddbbcbcbcbaaaabbdcdaabbbbdbbadacbbcbadbbacdbdddaccdcdddcbddbadaccbcdddadadcccdadaadcdabbdababaccccbcdacaaccdbdaaabbcaddddadddbabdadbbbdaacbcacabdddcaaacdccdabcdabaaaccddcddccdcbababdbcaccbcbbddcabadcabacabbaacbcdcdccccdcdabbbddbcccbacbadacbcaaaaaacabccdcbbcabbdacacdaadbdacdaddddabcaacbcddbaaabbcabccdbaadddadbddabdddaaddbcdddcabbbddbbbaaacddaaabdbdcbadbcadbadacbcbccddbbbbbbccabcbbbcdabdadcbcbbdccdaccdcbcbbbcabbcdcbcacaaddbbcdbcbaabbdcdabadbddbabccacdbbdadaacdccdbbcadacbcdcabccdaacccdcdcbdbdbaacddcdaaacabcadcbcbcdcbccdcbbcbabcaaddccbababcbaccbbaaaacadadabbcbdbbadabcbbcdcdbbabcccdbddacacaaacabdbcdccbadbbdbdbaacbbcaddabbabbbbcdbdbcccacbbcddcbcdbcadcbccaacadcdddbccbbabcddccbcacccdbdbaddabddbbdbccbdbbbbbcabdacddbdddcaadbdadabaacbbdacdbacabcbcadccabdbcdaabcadabbbcaacaddaaacdcdbabddbccbbaacaaaaacaaddcbadbcbccddcdabccbbbcadddcdcadcbbaddddccadcdaacbdabdcbbadcabcdbddcdcaddaacdbbdcabcabbddddcbcaacdaaacddbadddcddadaadddcbabaddbaccacacdddabbbbabbadadcababcaccadaabdabccccdbbbdbaadbcdcbdadbcccbcacdcacdbcbcabdadccddabbdccbdacdbaabdddcbadcdcdcdccdbaddcabccacbbddccaabccaabbcabdbbbdcdaccdbccbdcccccdacbacddbbbdcbccadaaddbdbdabcababcaacbcababaddbbacbddaaaddbaabadaaccadbdbbccaaacdbbdcbdbcbbbbdbbcbbdddabddaadbadabdccddcccbababbddaddccbadcaccabbddbaacacdbdbabcbbbcacacdabddddbcccabcbbaabbaacbdcbaabaabccccadcdcccdabadacddacbadacbdbaabbdabdbcaabbabbbcbacccaabccadbccbdadcddacdadccdbcbcabccbbccdcdbadbccbcbcddcbadaccdbcaacaabcddddacdcabcadadcacdbdcddcaabcaababbbdbadadababbabaabbdbaabbddcdcaabdbaddbcabdaddcddbdddbbabdaddabbbbacbabddcdabdbdccadbaccccbadbdabbdadbbaddaadccbdabdcacccdbdcabbdccccbcdaaabdccabadddcbcabdacbaadcbcdbdbacbddcaaddcbbadcaddbcadccddcbcccabbdcbaaaadaabadabbaadcbaabbcdcdcbdbddbdbadabbacdaaadbacbdbdddabdbabcbdbdddabbdbbabaccbdbddcbcbcbcccddbbbccabccdcdccbdadcacdccaabcbaaadbcdaaadddcbdccbacbdaccaccbcdcdcddbcdabbcbcdbaacbacbdcadabcbcbbdcbdaaadcbcbdaaadaabdaaacabbcbbddbacadbcbbaaaddbacbdaddccadcdacbbbbdabadaaabddbbdcabdbdabddcabddbcbcbdbcdddcadbbadabbdcddadaaaadaacdcdcaaccdbaaacdcbcaaacdbbccbbdcccabdaabdccbacababbacddcadbbcabaadddcbbdbbddcdbbdbdbccddadcbadcabcddcbddacabcbabcdcbcbbbcaadddbdcbbdadcbccbcccaaaaacabcdcbbcccdcbcadbddbcbccdcbadddbbaabadcabdbcddccdbbacabbdbbbdbbbbcdcbbbbadcdccabcdaacddbbaccadcabadabcdbadccddabdabbadddbdbbdddcadacddabaaabacdcbdadbbcccaadaadccbcbdcbbacbbbddabbaabbbdcdaaabbabbabbcdacccabaabbcddbbcadcbbdabaacabbaccabacadbddccdcbabcacabccdabccbdadddbacadcbbddaaddddbbbaccbcbcdabaacadaaddbcaccbcddcadacacdcdccabdbdddcbbdcabbadbbccadbdbbdbbabdcaaddbbaaabbaadddaaaccdcbaccbcadadadbddbccacaddccbbcabacbbdacbccdabbdadcbcabababbaddbadbcbbaddaabbbabcacadbcdbcbccdadcdaabbbaccbcddadccdbcbacdabccdddcbddccdcadcbbbcadccbbcabccbbcbbbcccaddabdadaaddcbdbadabbcbabcbcdabacaccacdcdbcabcdabbdbcdbacbcdbbcdbadcacabaaabaadccdaaadbcdccccbddbbabbabbbaadddbaccaacbabcdaddbaaacdbaabccddbbbbccbaacabadabbdcbccdbcabaadcddacabcbcacbbaddccaaddcdcbbbcaacabbcdbaccdcaccccbaaccccdbdbbdbdbccacdcaaccdcbbdaababdcdbacbdcbdbdccaabcacabbdadabdacbdcbbbddcbcdcccbabddcbbcaabcdccbacabdbbabaacbcaaddcbbdbadcccddbcacbbbbbcdacddacdbcdddcbddcbabbacacbdbbbddbdbcbdbadcadabbcadcbaaaccabbbdaaabbdcabadbdcabacbcccadabbababcaaaddcdacccacdbaddbdabccacabbbcdbdbcccadadcdabdcabcbbcbaabadccdcadadbddadcdcccccbabacbaccbdcabbbaabbbdcbcabbcdcbabbbadcacbdaccddacaccabdbdbbddaacdaccdaddddcdabbdccdadddaaccbcdbacaccacccdddcadbaaccddccbdbcccbcadabbacdadcbcbaaadbbabbbbdcbabbcaabccadcbcadcdaddddbabbbbabbcbacbbdcdcdbdbdcacdcdcdabadcbbdcdcaaacbdbccacbdabaadcdadbdddbbacccbcddbadaaacbdbbabdcabbbabbaaddbcbbbbccaadbdcacccbadcdaaddbccddbdbdccdbdddbcaacdcabadbcdaabbcabccacdbbaaaddadcbaddbbbdcbbbbbabbddcdabbcccadadddbdabdbacdcbacadccdcbbdbabddbcbcaababbcbcbbbbadcabdbdadddabdbcbacacbadcdbabcdcaaacadacdcbdbaadddadcacbdbacbadcaadccabcabddacaacbcbdcbcdbacdcccabddcccadcaddbaadbbaaabbbdaccdcdaadadaadbabaddbbabaaadbcadcccdbacbcabbddcbbccdcdbbbccccadccaddddcddacbcacdbdababbddbbacddcabddbbddadaccdcadcaaacaabadbdcadbbbbccdbabbadadddbcccbcdbadabcaddcdcddcccbbcdbcdcddbaabdccbacabacacbbadaadbccaabcccdcadabadbabbbabbdcbdbababcbcdccdacbbadddadcadcbdaabbaddcabdcdbcaccdabddadaababcdcccdcdbbbbaccdbcababaabaccddadcbddccbcdadabcbdddbdddadacbdccbadccabacdadabbcabcaabcbbbdbbabdbdcacbdabcdbbdacddbbaadbcbccadadacccdaadadacdaabaadbdddbdcdabdcdcbcddddbddaaddcacaacdbbbbbccdcbabbddcdbabadbbbaacacbacdcccddccddddbaabdbbddbbbcbdaaddcdddbbdbadccddbddbbadabcabdcdbbcbacbddbdddcaaadcabbdbaaddcabdaddbcacccbddcdcccaaadadddddadbdccacdabdabbbbbccbddaaccaacabccbdabdabbaaacbcccdabcaaddbadbdabaaaaaacbbddccacbabbcacbbabcabdbbbbbbbdddbcabcdababdbbdcdabcbaaaadcbcddcacaacddcaabcbcdcdbccaccccbcacacddcadcacbabacdadbdcbcaaccabbbccbdcccacabcaddabcddbaabacaccdddbcddbccaacbbdadbaacbadbacdaabbbaabdbbcbddddaadccadaddabbbbcdbddbbdabcaacdcdaacaccddacccabcbcbacdabaadacaaadaaaddaaccbcabaccadddddcbdbaccacdcbcbbdcbbcaddbdbbcbcadbcbdbdbadcbdaccbcabcbdabadcbcaaddbddddcdbdcabbcabbcddbcbdcadacdabdaaabaccddacdcdabccdddbdddbaccbcbbdbabcddcbdcaddcadabddccabddcbabbcadcadddccacbddccaccdcdcaaacacadbadccacddbccbdccacacbbdbaacdcabbabdbabddcbdcdcbcbdabadaddbaddbddadbadbdbcabbdcdaabcaaabdcddabbbcaaaabdadbdaaadccbcbbbabdbcacdcbcbbcdadaacbcdbacaddddbccaacbbabbaccdaabaadbdddabbdaaadddddbdacbadcdccbddcbbadcaaabbddbaadbacaaaaaadaacbbbdabcdbaacbabdadcaaadbbdbbbabaaabdcbadaccbbdcccdbcacdbacbcaccddbbbabbabddcaaddcabadcdcdacdddccdcacaccaccabddbabbcdaddbcabdcacccabbaddccccabbbbadabbcadaabdbbdbddccdbdcddbdcdababcababaaacacaccddababababbbcdbbcdcdbcabbbbdddbbcbbdcddaacdbabddabbdbdacbdbbbdacdbdbaabacdaccbaddcddcbcbacccacbccdbabcdbdbccddbccbcccaadaaadddccdbcabaabacdcadbaaadadccbccabaacdabadddbcccacdcdbcbddacdaabbbcabadccbcdabdaabccababbddcccadabdbccbbddcaddbabcbccdabccbbcbbcdcaadbdddbaababacaccbbdbbadcbbcbcccaddcdbdbdccbdcddcccdadddbdbccdaaaaacbaccdbaacbbdbcacbaadbadbbddaaababdcbcccdcbbbdacdbdbdbbdadcbcdbdddcbaadbaabddbccdbcdcabcdabadbdbdadcbccdacaabacaddcbabbbdbbdabcdbddbaabcacaabddbbbccbdacacacbccbaccadadcbcbdcbadbacddddccdbcdacbaccbabaababbdabbcadddcbccddcabccbddbadccdbdaaabbcccdbdadcdcbbccdabdbcaaabaccddbccdadbbcadaadbadcccddbcdacbbdbdbbdddbdacbcaadcbaaddccdcddbcbbdddcabacdaabcbaaddcadabbdbddbbaabacbabbacdaddbaaccdbbbcaddbadacdddabacdcdbbdcccbddbccacdbdadcaddcbbcbbdcdacaccccaadcadbaaacdbddabdaabdccadaadaacbcaabbbbbcdccdbbabcbaaccaadbbddbddbaacbdaacbdcdbbaaaabcbacdbadbabcbbadaaadddddcbabdcdacbcdcaddcbabbbbabdbbabdabaacbbbdacabdadcdccbccaaaccbccbabdacabadddbbbdbcbbbdbdddabadabdddbbbaadbccddcbcbabbbddbaacbabacbcddcadccabaabaccdcdadbbdadcbaccdabababacddcdcbbcbadcdcdcddaddcbdbdabbadddaacadcccbcabacbdadccaddadacaadbacabcdccacbcdadbbbdbcaaabbabaaaccdbacabccdccdabadacbcabbbabcacacaccabddaadccbaabbbdacbadcdacdacaddbcadcbbdacadbccadcaadddaaaccacbaaabaadadacadadaabbdadcacbbaaadacbbaaadbdadcdacaabbbabcbbacadbadbbbcdadbdbdcabccbaddbbadacbccccccadbaddbacbbcabdccccababdaaabaadbaaababbcdabcccddaddbabcacaaacaccbccdcbddddcacdbbcadbccbabaccddcabadbddbcadcbbbcdaccbddabadccabbbcadbabbcabadabdcccaabbadbcddbdccccbaabbbabdaadcdccaadbabddbdcaaaabadadcddbbaabbaacabddbccaddadccdddcbddcadccaaccbbcdbdbbbbbbbacdaaacdbcccadbddabdcdbdddddcdaacaadaaddbaabbadbdcddabacdbddbbcaabcacacddcbdbbbbcaaddccdadaabbacbccdadddaccdbacbdaadaddcdddcddcadbbdadcbcbbbadaabcdcabbcaaaacadcbdbcadccaabdcccbbdbdadadccabdbbddbdbdbbdddaccabaabcadbabccbccdacbacadcdabbbcbadbddacdddbbcdcbddabdaddaabdccbbadcbcbadcdcdabdbbbaddbadaadacadcbcbaddcdddabcddccccbcbdadabdbaaaabddcacdabccabddbcdbdbdbdcbcdacbcddbacaabadcdbbbcdadbbbaccbcbadadaabbdcdcacdaccbdbbdbcabddbacaaddcccbcddccaadbabdcadbdaabcbbacbabdbcddbcddadccbcacbabdababdbbacbacaadbbcccdcacbbadcbddbccabcaacacabcdcadcbbbabcccabbbaddbcadddcdcdabbbdbbbacdcdbbbbadbcaaabdcbccabababbaabdaacbaaccdaadccacdbdcadddddcdadcbaccccddddcadadabdcadbcccbbbbadabcccaccdbbacdaaddbadcbaacbbbccccbdcdcdaabbaddcbcacbacbacccbaacdcddacbbdbacbcbdbccbbbddadbdacabdcbccacaaccbadbccbdbbacabbccdcdddcdabdddabcabbdccabdcaabcccaacddcccadcdcadcaddaabbddacbbbacaddddcdccaaccdcacdbadaaaccbacbdadbacddcacccbadcbccddbaabcadadbbbccdddaadaaacabacaaadbcbdcdacbdcaaddabbaadbaddbbcaaadbbbdabddcaccbadaadbaaaacbdbcbdcbadbdccacaabcadaabacadbdbbacbadcabdbaacbdddbbacccddbbdacdddbbacbcdacddabbaddacbcdddbacabccdbabdcdbbdabcdbadabccababaddbbdbbbbdbbdadbcabdaabdbcabbcccdbcdaadacaddcaddcbacbcaaaacddacdbdcbacacabcdbdbcbcadacbabacbddadadbcadcabaadaabcbccdabcadddcdbddbccabaaccabbbabdddaaadcacdaabadbcbccddcdbdaaabaadcacbbcacadcccdbbabcbdbdaaccbcdabcdaddadcaacbacbdbadddccdddcdcaacccbbaadaccacdabbabcabbcccbcdacadacdcdbcdadadbdaaaaaabcdcbbdacbcbcadadbaaaadcdcdbcaccacbacaabaacacdcacdcddacdcdbabbdcbddcbadadcbdacaabdcbbdbdcbacddcabadbaabcadbdcacaaccccccdcbdabbaccababddbaddddbaadbbaabaccbcdcbadadbdbddabbcdaaabadcbdccbcbacdabccbbdbacabadadbcccddabbcacdabacaccababdddddaadbbabdadcbababadcabaadbabaabbbaabccbababdbabaaabaaacbaaaccccbddcccbabcdccbaccdbcbbcaacaddddcdcddcaccddbaacadadbcdccabdacaaccabcaaddcacbcacccbdaabacadddcadaadddaccabbbdbcbcacadbdaacacbcacaacacccadcdbbaddccbdbbcdbcdacacacdcbbccddcbdddddddbaabbdbccbdbabdadbadaadddcbbacbacbcccdbbdabbbcaccbbdbbabdbdbbcccdbdacddbdabbbadccbdcbaabbbccabdddcccddddcaabadbddadcccacaabcbcdbcaadabbddacacbcdabdbcbbbccaabbbcaddcacabccbdbadbdbbcddccbbcbdaccdaaaaadbacaabacbbccbbdaaacacabacbabcadcdcdbdcdbbcbdcdacddacbbcdacbcdcbdcacbdaabbacadbcbabbcdcbdcccaacccbcaacaccbbcabacaaacdaababbbdadddcacaacaacbcbdcdaacdcccbdbaabbacccaabccbbddbddbddcccabcbbacadaacbaabdbbcbcbbcdcdccabdadcccadbacabbabadbdabbbcccaaabbdcbcadcbbcaabbcccbaaadcbcdcbdcbacaaabdaccbccaccbdbcaabdcbddadbddadaddadadcbcdcadbdccbbaabcdacbcbcaddbccdccbcdcbbbdbabbbbbdcdbccbcacdcbddddacadaaccdcacbbadcbaabccbcadbdddbbadbdbccdaadcabbadacacccbbadabccbbabadddddadcaacddacddaacdbadcaaaadabcadbdddabcacdadddacbcaddbccbcbbbbddddcbbbadacbbabbdbbaccbcaddcdacbccdcaddcdaadadaadbccadccbccdcbbcddaacbaacbddccbcdacddbcdbcdabdbdbadddcbbbccdaddbcacddccdddcccdcbcaddcabdbadcdabdaaccbdcbdabbdbccdcadadbbbccaadacbcdbbdbdbabcddaddddcddcdababbdcbabdbbbbbdadacacaabbabdbdbbabcaabbbaccadddddacdaaddcccbabcddacadaadcbccbdcacdaabcacbacdcdacbddaaaacbccbaccbacaadcdbcddaabdbbbccbbbddbcacbdbcbdcbddbcbddacdadaabcaddcbadcdacacbadcbccdbdcaccacaddadaadcdddbbccdadcbbadabcaccdbddbaccaccbcacdbbbabdbcdcdbacaabddccaacddadbccaadbbcbdbddcbccababacadaccadabbbbabdccdbabcdddabcadaadcacaccdcdbddcdcdcddcdaadaaabbaaaacbdbcbccacbddcbcbddbbdcbdaaacbdddbdabdbbdcacabbbaddbccaaddcbbcacbbbdccbbcdadddcaacdaabddcccdabddccadbbcdaadaadbadddacbdccaaadccbdbcdbabdaaabcdccdcbbacbdaabacbdcdddcdcabacbdaadabcdcdaabcabaddbcdcdaabbaddcbddbbacabcadadadbddcddadabaadccabddacbdccbcaadcdcbbcacaaccaabddacbdccbdcacdcbacdbacddaabdabdadddacdcccaabdbaaaadbdccbcabcccabaaaccadbccdbccbcabbccbdacbdcacdcabcddaadcaddadccaabcdcbdccbcdadccdacbacccabbdabcbcccbacbcacaacdabbcaaddbaaaddcaaaabbaddbabbacadcddbdcaaacaacbbadcbcddddacaccdacadddccaaddcbcbacbbdcbbbdcdabacbaccacdcabdcaabbcddaaaaddddcbcacabcadcdaadbdaaabcddabcdbdaaabcaabcdaaabdacdbcacabbaaddcdbaabdbdbadccabcabddcbabababbbdaddbbbbacddcdddddacddbcdbaaaabcdaccbbbbbadbacdbcccdabcbddbbabbcdaabaccdcaacaddbdabbabdcaabbbadaacabcdadbcacbdaadadccbdaccadacddbbcabdbacbaaacdcccdadacdbbbacbdabccadacddadbcbcbdcdccadcaccdaaccdbddddbdaabaccadddaddbccaacaadaadacdcbdcccdaacbddcaadaadacbdbcbadddddbacdbaaddbbcdabdbbdcdbcacbcababbdbcdddcacabbbbbddddbcabdcaaddacaddbaaccabdaabadcaacbcbabacdacadbdcbaddccbcbabbdbbbaaddcdcddbbcddddcbaadacdabbbdbcaabaccdddbdbaddaaddcaaddbbddaccdacbbacdcaccbcbbdcbabdcbbadaabddbcdadacaabaaddcacaccccbcdaadccacbcacdbdadcbbacadcdaddadbbadcbdbadbddbbcbadcbbadababdaccccdcabbbbaadadbccdadacabdccdacdaadaababaabbcbdacdbcbdbbdaddacacdadbbcdbaccadbbbbcadacdabaaccdbccdacabcdbacddcbdadaccbaccdaaabbddbddcbabbabdbddaadcbacaddabbbacabdaabcdbdcaabbaccbcbdbcabbcdaacddcbdbcdcaddbcdaabdccabccbaabccbbacaaadbcbcaabaddaccddcccaaccbcbddbcaddaadabbccbdbabaddcababdabccabbdcbdbddcddcbdcbdabadbddabbccdbbcbbdbcbcbabbbaadcbadbdcdbacbaddbbbabdbaccacdcddcbadbbbbcaacddcbcaaaabadbcdcbaddacabbdcbbaabccbcdbbdcdcbcccbbadaabcbbddbbcacddcddbaddcccddddcbabbaadbabbabbacaadaaabadbccababbccbabadbdcadddcdcccdcdcacdadbabababccdbaccaddcbadacdcbabacbbdbdbadddddcdddccccacbacaacdbbbbabccabaccbdcbdbcdbcaadbbbbdcbbbdcadbabcdccbbcaaaabababccacbacabbabcdaddabcdbcabdbbbaccdbacdcaccdbcdaabdbcdcbdcaacbcdbadccabdabbaadbbcbaddbcbcbaddabbcacbbbccadbcbbcabbbdacbddcbaadddbaadacabbadbddbccdbcdababbcadacbdacaacdbbbbcddccadcccbaaddbaddbddbbbbacbcbbacadcdbcbcbdddbdcdadcbbbbbbaccabcbadcabbadddbcabaaddbbcabaadccacaabcccbacaddaaadbbbabaacabaadbabcbabbdacdbcbcddccdaccdbdbcdadbbdbbaadbccdbcdcddccccbdadacacadbcdacdabdccdaabccccbadbaddbacabcaaccbbcbbacdbbbdacaaaaddddbcabdadbdbbdcbddcbcdbdadcadcddcbdabbcabdbdaadcaadbdbccddbcaabbccaadaadbbbababcdbbbccdcdbcdbaddcdccddcbdadccdaddcacdbcacadcabddadbcadcdacccdbdcdbcabcacbadcbbbdbddbcdcadcccbcabbcabbabcdbddaacdddabbabdabdadcabbbccccdaccdaabbbadbdcccdaccaccdccbabbaaccaddcbaaabbdadbabbbbacaaddbabbbcddcbbddadabcaabcccabcdbbdadccbacdbdaadbacdcbcabcabdcccbacdbdabaccdabbcbbccddbacaabaabdbbdbcadadccaccbbbdcbcbdcbdbbbabaaccdbabbdbdcacccbdbdbcabbdabbddcccddbdbbdadddadccccadacadbdcccacccdbbcbabccddbcbcbbbdaabddcadabbbcadabcbccbdcccdbdbdaaabcadabcadabaadddcacdcbababbadbbadcadccdbbbadbcdccacdcbcaccddbdacacddbbdcccdccddacdaaddbddbdddcbcdacacdabadaccbaaababbddbccbcacddadbbcdbccbabccabcdacbbcbaadcddbdadabdaabacdabddbacaabbaabbdddaccdccaacdcdbcaccbcabbbabdbbbaadcbcbbdbadcccabbabccddddccaccdddccacdcbccbacbbdcdcdaacdacadccbadaadbddbdcddbbbabdcbcacdadccaccdaabadddccbccdacadbbddbaccccddcbbaccddaabbaabacaaadaacbbcbcddcbbcdcbcdddaabbccdbdaaccadcdabbbbcbdccccaddbccbbddabbbccdddcdacccddaccccdbdcbcbdbdbbccbdabcacdbaccbaadddcbddcbaaccddcacbdbbdccbccabddacabccdcdabccbccababdcdbbabcaccbadbcbcabbabaaddbcabdacbdccbdbdacddbdcdcdcbccacacbcacabbdcbbbadccbbbbccadabacdbccdcdaadcccddccacabbadaabadcccacdaabdbcacbaddbadaddadbababdbdacbbbacbadadcddbccdbdbbbbccdddcaadccbbddbbcdbaaaacbdcbddabbaabcbacbdcdccaddcdaccbcbaddbcaaacabdbbdbbacaabcbbaaacdbdbadbbcbbddacdbbbcabdddbdcadcbbddcbcdcbbdbabdabacbdbdabcaddaabdabbdddababdbbbcdcaddadbcbacdcabaaaaacabbdcdaacbabccaccbcabcabcadbdadaddbacdaadbbccbdccbaacbbaabddaadccdbcccbdcdacaddbdaaacccaddbdbabccaacccbbadadaddbdccccacaaccdddbcaccddaaabdacaaacbaacbdccaaccccabdbcbcacadbbdbccdcbbbdcddddcbbdbaabaccbbdacbbdcbadbcaabbbdadcdaccdadbcaaadbacddadbdadbcaacbcccbcaccacbaccccbcddcadaacabcaacbcbdbdbaabaaccbcdcacadbaacaacccabccacbadcbbbdccbbbddabacbadbabcabadbddbabccbacbadcbadcabbabbddcaccbdccaddbdcdbadbbcdaaabddbdddccbaaacaddccabdbbdaccbcccdcadbadccacacabcccaaaaaccdcbbbcaaabbddccddddbdbbdddbababdaccacbdcbdacbaccadaccbcdadabcccccccbddbdccbccadaababddbdbbcbabaadbabccacdcbdddcdbcbdbaaaabacaacbdabdcacaaaadaaccdddacdacbcbbbdbcacbdccabcbcbbabbaabbcdaaababaabbacbdabbabdcbabbaabdcbaccdbcbdacbbdababddbcababacadbbbadbddadbbbabacdcdadddcddabdcdadcdadcbbdacaabcacdccacdbbbbacbadbbbddbababababdcbbcbdbbdbdabbccacccbccccacacbaaddbdbaccbcdccaddccacccdcdcccbadbcbddbaaadacabdabaccccdccaddbdbcbdaddabcaddacddabbadabadbddbbcbccbbaddaadcbdcbadaccdabcddadcccdddacdaabddbaadaddbdaabcbbbacbadabcddaaaaddccadaacbcabadccaccabdcccbacbbdabddccbdccddadbdbbdbddcacbadaaabaadcdddbbccddbcbadbbaabcbaadcbcadddcdadaaacdbcbdadadbcabccdcabacbcddcabbbadccdbbbacbcccdbcdbbcddbbcbdbccdcaadbaaaccaaaaadbdadcdcbbcbcaaaadddccbcabccddbbbabcbdcddcdcacabbddaccdabadaccdaacaaadccdcabcbdabbcaacdddaabbbdcacdacabbcaddaadccbbcdbdcccaacbadcbcccdaabdbbbdaddccaaabbddddcccabbcbddcbbdcbdbcddbbaccbacabdaaabdababccacccdbdcdaaccbbbbcbbcaddabbbbccbadccbdbdccdababaacccbcdacbbbacdcdcaadcbbcdcbbababbaacacabdcddccddacacbdcacbdbbcbcdabdbbcdbbdcbdbcabbaadcdbdabbbaadddcabdacccdacbbdadccdcacaccddaadbaabdaddabccdbacdbdadbccababcdbadcbcddcabdbbadbaccbbbcdaadcddabbdadbbcddddacbdbbbcbbcdddbdacaddddddcbbaccbacdbbaccdcbbcbdaacaadacdaacdacaaaccccdddbadcdacadbadbaaabbcbbabaacabcbaadbbaadadadcdcbacddadadcdadaddadbbbdaacbcabbdabcdcddbdbabadbbccbccadbadadddaabddacbcacdbcaabaaabdcccacbbbaacbcaccdababbcddcdbcbadddabbadccaaccdcccdaabbcabdddbbaaacdbabcccdbaddbbaadcbdaccaabcacaabcaccbacbdadacbabbcdaaacdcbcabdcddcdccdacdcbcadcacbbcdbdcaaadaccadbadddbdbcbdcddabcaaddbadbacdcaddddaabacdccbcadabcacbccdbcbabbbbbdddddbbbadcccacbcaadcaabbbddcbabbbacddddcaadacbcbcbdabdcacdacdcddacbaaccadcccccccaadbaccccbcadcaacbcbcdbddacacdadadddabdcabadadabdbccbdacdcacccaaadabbacdaabbcdabdbddbdbaadccddbcbadaccbddcdadbdbdbcdbadbaadbbdccabdcccddabdadadcdabadbdcdaadcdbddcbbacaabaaccbbddbdbaddaadbdabbaadddaaadcadbcbdddcacacdadbdbacabbaccbccbcbbbddbddbdcbcabbabacacadcddbabbdbdddcdadbaaddabbabdacacadbabaabdabbbcaaabccbadccacbabdadbdabdbbdacbaacddadbbaabccbcbdcdcccbabacddccdbcbbabbdcacbacadaababbabaabdabcbcbdbdadbdcabdcbcdbcabbacbccbadbbabcbdcaabddcccacacdccdabacddacbcddadcdbcdbcbcabdcabaadcbccdccddcbddddaadccdbbaccacabbabcdababdcaabbbdcacdaabcdcbadadbabddabcbcaccaadcbaccbdcdccadccdcadbdbcaadaaadccbbbcddbdbddacbcabbbcaddacabcbadaacdacdccaaccaacccaaccacbccabdbcacaccabbaddccadaabdbcaabaadbacddbaabcdbacaabdabaddddaccddaddbddaddaabcbbbaadabbbdcbcbbabddcdddbaccbaabcacbaadbbbaddbddccccdcaacbbbbbadacaabcdcdaabaaabdddcdbdbcbcbcccdacadcaacddaacbcbdbbacbaacbbdabcccdcdacbdbdbadaabdaaabbbaccabbbcbdaabdbdacdaacdcdaabdbccabadbcdccdacbcdcadabddaccbbbadbdbcbabcabbabdaddaddddcdcdcdbbcabadbdccbbbbdcadddcdadabbcdcbdabdccdddbcacddcbbdccaacabdcaaccbdcbdbdaddbcbcabccdaabadbcadbcbadbcacdbccdbadabdadbacddabccbccdacadacacaabcabddabcdcdaadbccbdacdbdacadcbdadacabcdddcccaaaaccacdbcdbbcdadccbddddadacbcabbaddddbddbcbbacaadcbbcbbcabdbbadaabaccccadabacabdbccacabaabbaacabcdbdabaababdbabacbbdcacbcabdaabaccbcbabaddacddcdbcabdbdbdbcdaaacbaacddddadddcbaabacdbdcdacddcaacdabccbabaccdbabdabaacbddbbabccaddbadbdbacdccbaabcdaadbbabbcdccabdcbddbdddcacbccbcdcdadccbcddbbdbcaaabcaaaccccacadbdbacacaacdbacbdcccadcadabdabdcacbcabbdabdacbcbcadcabccbcdbacbbddccacdbabbabdcaaadcbbdbbbcbaabdadadbdadccacbcabdbabaccadcdbaccadbaaccbaccbbacbdadcabcbdcdbbbdbdbcdabccacbdcaddccdbcbbbddcccdaccbbbabdaaabbbdadddadcbbdadadacbccdcddddabbcdbdadabadbabdbcdacddaccadbcbacbaaddccbbbdbbdadbaccddcdcccaaabdccababddcdadabaabaccaaddbaadacdbdddcdbdddddbbcdbadcdbbcdbbabcabbdbacdbbbdcdcbacbbbcaadccdccdbadbcddacdacbdaababbacddacdbbabdbcacdaaaddbacdcabbddaababbbdcadbbdadbbdcadccccaacbbabbdcbbcbbdbadacbdcddbaabdccdadbccdcdddabddcccbcbcaaacccbdbcdbbdcbccacdddbabdddaadadbbbbadcacdbaccbcacadbaacadbccdddccccacdcbcdccdcadcbdccdcdccdcaddabcbdabadccacdbcdadcdaabdacdcbccddccacdbdaadcbacbccacbcdcdddddcbdccddcdbcddcaababaaddccbcbcadaadcbbdbaabadbddaddbdacccdaaccdcccdbcbbbccadbdaacdadbdadbabbadbddbdcaadabcbdadcbababaddcabadddddbbabacddccdaadcdbccacabdccaccbbabdccddacbaadbbcadcabcbcdbbcddadacbbbcdadadcbbabbabacabddbaacdcdbdbccabddbaaddcdcadcacdaadadbaaacbbcbacabbdcbdbacdcdaccaaadcdcaadadbbdbbccdbacbbbddabdbaccdccbcaaaccccddbaccdccbdcdbabcdcdcdbdddabbabbcdddaacddccadcbacbacccaadccacaaaddaabbbbbdaacdcdaacdaabdacdbabddaadbbacbbcdaaadababbabccddacaabddadbccbadbccbacdcdaacaccbddbdabcccbcdbbdacaabaacaccbbacdcababcadbcddbaadacaccbadaccccacbaddcdddbaaacbbccaaaddadcabdcbdcbaaabaabcdbccaddcdbcdcbabdcdcdbaadbbdcbaadbaaaacbabaacacddccacbdbadbbdcdacccaaaaccbcddababddacadadadacdabccddbdbbbadbccddbdcdaddddaabccddbdccccaabacacddabbcbcdcbcbdbbcddadabaaacaabaadbaaccaaabccdcacbbccdcddccdddabccacabdddcccdbadaaaaacdbaabbcdddcaaccbbadbdbdccdaabaadaaadcdaddabadbdbdadadadaabdcdbcddbadacdccdbbdcababdbddcacddacacbabcbdbcbcccbadcacaadcabacccabacabcdddbcaddabbbdccddbbdcdadccdcabcdbcdcdaccdaadaadbacccdbbbcadcbaabdbcbddcddbaaadcdccbbbddcdccbbcabbbaacaaababddbaaaadbabaddcbbbacadbbcaabaddabaabcccabaacbdcdbbbbadaaaabdaaadbbcbddcbddddcdacdacbbbadcdcaaadbabbbbabdbcccabcabccdabcbdddbdbbbbbcacddcbcaaccabcdaadabcbaddddcbadbddbcccddbdbdacdbaacabdbabbbdacbcbdcbadbddbdcdacacccababccdcddadaddabaabacbcacbaadcbaaabbbabccaaaacccaccabaadcccdccbaacaccdddadaccabccdabadbaabcdbabbbbdcacdaabccbbcbbaaabacaddbcdaddbabbdaaabbabdaabbdacadcabdacaaaacccddaadcbdbcbccdbcbdaadadabbbcdccbdccbbcdbcdddbbacacccbacbddaaadcaaaacaaccdcaaddaadcabbddacbbbcaabdcccacddabdcdcdcbacccaacaacdbcbbadaaddcdaccdcbdbbccdcbacdaccbccdbbbcbdcaccdcbdabaddcbdaaaddababadaddccacbabcddddbdbbbdccdacbbdbadcacabdbbcbcacbacdabbacbdbdccabdacdacaabadbdacabdaabbcbdabacaacdabcaacababbadbcddcbdbcbdddcdaadcbcdabdbacbdbbbacbcbbbaccdddbbbbabacccdcadddabdcbbbdcdccbabaaddbbbbdacdadbaaacdddccaabdcbacdabcbaddacccbcadbbaadcdddbcddabaababbbccadcadcacadaaaadbcdabcdcdcdbddabacbcccddbcacadcbdccbbcdbcbdddabcbacdaabdcccadcbcddabaadadcbdcacaadbdbacccbbdcacddbcbacbabaaaacbdacdcdbbaccdbbbcdbcdbbccaacbbdbdaadccabcbbabcbabdbbbbbabadcacbccabbdbaaaddccdadaaabdcabdabdacbcdbcddcbabaddbadbbaddcaabdcdbbabbcddadbdaccbdddddacbccabacaabbaddccbdadbaccabcbcdccbbccbbdcabbcbdadccbacabaadaaaabbdbcdbdcbbadbaabccbacdacaabadbaacaccdbddaddbdddccbadacdccdbbdabaaadddbcadbdbddabbaabdcccbdabbdbdabbdbcdacdcaabcbcdbcdabccbbddbbddacacdaccbcdcaacabbbdbbcddabdbdaabbcaddbbaacdcadcbcabbaaabcdcdcbaaaabccbdcdbabdaaadbaaadcacaabcbaddbbacbbdabaadbdddbbabdccbaababaddcbabdaadccdadabbccdabacbabbbbadcccbdcabbdaabcacabdccabdadddbadbaabadabcdcdabdccdddbdacacdccabccdcbabcbacabcbaaacbbbacbcddccbdcdcdadcdbcbcdbabcaddaddcccccacbabdaacbcdacaaabbbabddadcbdbddbcbacdbbabbcdbddcabcdbdbadacabddaccccbacccaabacabbdddbccdccbccabadadaaabddbcdbcddbacdcbadacaadacbaaaccdaaaadabddadaddbbababadbcabdbadddddbbdbadaddccacdcdaccdcadbacbbaaadcbddbabbabaaccbccaabddbaaabdccbaaaabbdadaccdbbbabdcaadbabaadcbdacdaadcababcdbdbbccadadaadabbccdcdbaabaabbaddadcabbacccadccdbabbadacabbddcacdccaacccaddacbbbcaccbabbdaaaaabdbdbcbadcdacbacccdacdcadbacaadbccbadbdddadddccdaccacddbddcdcaabadaadacadbccaaddbbbddbcdcbbdddbcbbcacccadddacddbccbdcddbbbbabccdcddacacbcaadbadbacdbabddccaccbacbdbadbbcbbdbbaadadddacbbbccaaaccaddacabaaabdddbdbdaabccbdadabdbbabddababdbddccaaabdacadbacbdbcddbdcacdaddabcbcaaabbdccdbdccadbacdadddbabbbccdcbcacbbcdbaaacadbcbcbcbcbbacbbbdcdbcbabcddbbbbbcdcbabdddcdaadbaacacaaadcdcdbccbdbbacbadbacdacdbdcbbbaabbddcaadcbbcbadaddcbcccdddcabcaabbaaabbabdcdbcacaadbbaccacbcdcaddbccddbabddddadcaaddbdcbcccddbdaadbdcddddcdaacdcbcbdbbdabcbddadacdcadabdbbddadccaadbacddcaabcdcaadadaadcddddbcbcbadadcbaabcbcbabdcddcccbdacaccddbccdadcdabcdaaacbddbbbbcccddbdcbddaaaacbaaccadcdcaaccdcbddacbacddcaddbcbccaaadccbaaacbdbdbaacbdbaaacabdaacdcbcddcbacdddbcacbbbdddaadabcdaacaaccbbaababbddbdccbbddaadbdabcbacacccbbcabadccdadddddbacbacaadcaddabaccacdbacbdadccbaaddacdccacdbcdaabadccbdbadabaddccbbbbcdacbaaacabcccaddbbbacdbbcaaaaddaaaaaadaaadcdbbccbcccacaaaabcddcdbabadacccbbacabbcdbcdaabddadbabaaacbcddddddcbcbaaaabdbdbdccbbcbaabcdacddbcccdbabbcabadbccbcdabacbdcbdbbddcdcbbcccbdbdaacabddbdbdbccacdccdbbcaddcbadcbabbbaacdbacccabcdaddcabcdaacdccdaadaaaddacddaacbcdbbadddabccbccaaaccccdacbcbcdbadbdccacdbccadbcdaadcacdccddcbbdbadcccaacbccbddadaacbbdbadaccddbcdbadcbbdcdabccbbabdaaaddcdcadbbaabdcdbdcbdbabdbdcdabaadccacaadcdabcdabbddbabcaabcacbacddadabbbabcadcdbacabddcabdaabcacdaacaaddcacbbbbaccabbdddacbabcdcddbcbcbbdbcdddababdbabcbabbbdcacbddcbddcaccacabbbadbcccadcbddbaabcdcdbacacadabccbdcdabdacdacacdbddabbdbcddbacdddcbdabdccdbabdcbcbbcddcdcdcacddacdbddccdabcddddabbcddbbacbdbccbccabaadbadcdbcdbcadcbbdadbdbdddbbdbbbaaaacddacbccacbacbbaadacbdabddccbdaccbabaaadbcddddddabbcddadabcdcbabadaddadababdcbababbdadcaddaabaccacdadccdaddcaddabdcaacaacaccdcacababadbaaabcddbaabdccdcbabbdcccbbddabdbaccddacbbbcbaaddabbbcdcbdacaaabbbcdabbbbabbcccacbdcdcdcdabcbadcbbddbdcdddccbcdbbbdddbcaacadaababdcbdcbbddbdadbacdbcbdbababcbacadaccaaddadaddadddacdddadbcbccacaadbbcaaddcdcdccadacdcacbbdcccaababdbbcaddddacaadddcbaabaabdaabccaadccacbabccdacdcacaccccccabaadaadbdbcaacaacacdabbdadcdbbdcabbddccddaadddcdbbdbaabacaaacadbcdaacdacbddacdccbdadcaabbdbaacddabadaacdddddbbdbbacbcdbdcccacaccbcabbacacabaabbccddcbdbdccddabddddbbbbbdccdacdbbbbdbadccadcabdbdaccbabcbaacacccacdbacbdaddacbcdbdcaaacaddbbbaddcacadabadcdbcdccbbddbcdbaababbcbdbccaadcdcbabbcaccdaabaadabbbdbcbddbcdaadbabbbdcdacaddccdbacddccabdbbdcbaabccacbdbdbdddabcaacdccbdcaddcdadaabbddadccdbbabdadbcdcddabdcbcbbddbdaacdbacabdbcbddddadbdacdcabdcbcbaadbbcdcdcdbbdcabbcbaabdaddcccadbdbbaabdadbbaddccadbbbcbcdabcdabdccadcabacbbbaacacddcacbbdacbcdcabcacacadcddbbccdcaddcaabcbddbbadcdacbbcaaddaaabddbcaaaaddbcaaddadacddbbabcdbbbcbbaacbccdcccbabdabdcdcddaccaadadcadadabcccabccccbbdacacaabaaddcddabdaccadbccbcadcacbabccaacbcdaddbbcbabcbabcaabcaadbcbbbcdbbbcddabbcaaadcabaaadbbdbbacbaabdddbbcbcbdbadcbaccdccdbbcadabddcacaadbcaaccccddcaccbcdbbcaaaacaddbdcdaabbacdbcbdbdcddbabbdbababbbbbcddabcbdadcddcacccdccacacabbbbddddacbddcdbaddabbdbdbdabddbbbabdabcaadabbbacbbabbabcdaabbaaadcbabbccacddabdcbcdccadaacdbdbaddadccbdcccbdbdbadbcbbaddbbddcacdbbdaccbdbdaabbdddddbacbacaddbacbdacabadcadccccdaacbdbbaaadbacddbdaabbacbaadcaadababbbacbbdaaaabdbdcaccadaaccaabaaccbcabaccbbcccddaabaaacabdcdbbcababaaacaacccbacadabaaadccaacccdaabcdcbadcbbbcaaabdcacabbaacdddacacddacdadcccacaaabcbbdcacdabbcdacccbacbbacdcbbbacaadcabbadabaccbbdbdccddaacacdddddaaaccaacddbbabcdaacccdaabacabaccccacabcdbbabbcbcbcacccdacadcdbcddabaadbccdbddcbcabadcaabcaaadbdbabacacdcddccdcadcbcbaadacadcbbadbbbbaaaaccaddaaaabcdbccababddadbbbadbacbacabbccdcacadadaacbddadadbdbcdccdaadabaabaacccbabbaadabcbbcacaaabaabddbcabadbbcdbadbcdcabccaddcddbbdccdcbbccdbcbcbbcadcccdbdaccabdabbddababdbaabcdcdcbbadccdcddbaccccbdcadacdbdccbabcacabbdacbbdcccaabacaaccaaaaccbbbdddbbadcdacbaacbdcadbddddcbcdaddaaaaaadcaadcdaddabdaaacdcababababacccbacadcabdcbaddacaacacaaabaadadbccbddbadabcdcddabadcaddddccbcdbaddaaacbbccdcbaccbabbbababadaabcddbadcdabadddbdaaddbdcbaddacbdabababdbcaaaaccbabdbadccaadbdbbdabcbadadddbcbbccacdcdabacadbaaaccabdbacdcbdacaacccbcaadadcaacbdbdddcbaaabbcaabbddabcccdbbaabcacdbdabdbacdbccccabdcdcdddccdaacbaccdacbcaaaabaacacccdabbcacccddcddcadaabacdacddababdcadbacddadabaabadcbaacaacabbadabbacdbacbdbbbdbdcadabaddadbabdddcdcdababcabdccabaaaabdbadddbcdbabbabaadccaadddcbcbdbaaabbdaaaabbdbcabadaaccbdcadbcddccadabbdcdbbdbaacbdcdadacaccccbabbadccbdabddbabdcbcbbdbdbcbdabbdddcdbabbdcabcbacdcaaaaadbdaadccdaddadaccdddbdbbbadcdacaabcaddacdbcaddddaabdcaabcbdcdadccbabbcadbaabadcdbbbdbaaaabdbacdaabcaadacdabdcbbcdaabbbabcdcacdbdcdccdaadbbdcbbaddddbcaabcaaddaccaadbdadbabdacadbbdddabcbbcaccdbccdabddabdbcdbccacbdbacbddcbaabbbdddbcdadbbbcaddadcbadddddcbbaadaadaadbcbdadabddbaacdbccaddbddbaccddbbdbbcdbdabadddddacbbccabbbddddacabcbbadccacbcdcadcdaddabdadbccadddabddbccddbcbcdaaddabadccabaccccbbbcabbdddbcabaccadcbddcadbacdddbbcaaccdbacdabcabbbabdcbbaccdadbcbcbcdbdbacbadaadddcadababcacbcdaadbcccddddcdbbaaaaadbdcadccdbcdddbccdbbbbccdaddacbdaadcdcacdbbbcaaddabdbdbccababdbcbbabbbcdccabcbababbcdbcbdcdcacdddcdabaabbbaaaacdbacbabbbdadcdaacbcacabdbbdbcbaaabdacbdbdcbcdadcadccbdbbdacadbaccddacaacacacdcccdaddcdcabccbaccabbabbbaabbbaaacdbcdccadacaaccdccacbbbdcdadababcbaabcadcdaadccdbcadccbccdaabcdbdddbdacddadbdcddcbbdabaaabadbcdcdcbbccdadbdcccccbadcbabacdaddbbcdbbbdcacaadbbbdababdbbccaabaaabbaabadbcdabdccbadbcacadcabdbacbabcdccdadcaabbbddabccdababcbacdbaaaadaadcadcaadbcddaadcdaacdacbabcadacbdaadbdabdbbaabbabdabdbaaccadcababddddacaababddccdccbaccabadcbdabdcaccddaaddbacabdcadcbbdcaddaabcddaadaccddadababbbddadaabbcacdccbabdaccdcabcbccaababbacbbbcabccdcadbcacbbbcdbccaadaddcbcccdbddbaabadabcbdcdadbbccbaaaacaaaccabccbdaaddbcddadcacbddccacaddbbbbacbacaaacaaaabaaacacbdccdacbabbcbcbdbadcdbabcbcdabdcbbaccdacadcbdbadbdccbacbcaacacbbcddababddbaddbdbbbdcdaaddddbcdadabbcaaccbcacadcccadbcaddcdbcbcacbaadabddacbdccdabcbcdbbbbbbcbacacbadccbbaaacacdccddcabcbdaaddcbccbcadbbadacdbacbadbcabbcaaddaadbabababcadcdbdbcbcdbcdbdacbcbccdadbbdddaabdbcacabbacccdadbcbcbcbcdbddccacbcadaadacddcccaddbbdacbbccbaddaaabddbdabcdbbadaadaaddadcdabbbcdcadbcdbbddabccbdadcdacaabaacabbacdacaccdaacaacdbdccbdaabdaaddbdadbccaaacddadcaabcaadcacbcddddbbddaacccbcabcbadaaaaddbcabcacddddccaababdcababdbadaabbdabcaaaacadbcbadabddaccbcbbacbcdddddbadbddccccdccabddbaaddaaacdabccaaaadbddddbdadbdccbcabccbdbabdbdadbacabaababacdabbacbadcaadbcdababdbcabbbadaaadbddcbcdccaadbbccdcbdbdccbccaabcaddbdabcaccdcbbdcaadcdabcdaaccadadaadccbabcdcbdbbdbaacbccdbddbdcdacdaadcbbbcbcaccdabdadbacdccbbdacdbddaabaadcdccbcccdaddabbdbaadadbbddcddbccaccbddbdcdbcdacbcaabbdaabcbcabccbccddacdcaccdaaaaddcbcddaddcadacbbcaccadbdbacdbacdbcdcdadbcacddbacaabccdabababcdbcddcdcdaaabadbcabbdccbbadaabdddcabdabcdbcddadccdbccaaddbccbadcdcdddadadacaadbdacaccdcbbddacdcbbbabdababaabadadbbabaacaccdccacabcbbcdddccbadcabaadbccabbbdcbdacddaacdcaccbadcccddcbcabcaabbdadbabaddbdbbddcbdcaadcddccdcdbdbababcdbdaaacaacbdbbbadbacddbcccccccadcbaaccdbbdbbdcbcbdaacbbbdcbcacbbdaaacbdcbdccaabcabbcbbcbbacbbddccbdcacabbddadadbaadacbcacccccbdbacbbcbaccadcadbdaadcbddbadccacdbdbdbcddccdbbbccddbcbbaaababccdccbcdabccccbccbcaddcdcbbbcccadcbbcaacbababbaddadddbbaadbbaacdbdbcccbccadcbbadaaacbccddaccbdabacadacdabbaddcabacaaaacdbadcdacbdbdcbdbdcacccbbdccdcdcdddbccbbdbacdadcabdcbabcbdacbccbbcbccabbadccaacaadcbbccadcbaacbdcdbacdbaadcdabdaccdadabdcbbaaaacabbddccccdabacbcbbbdbbdaaccbccbcddabbcbbdaaddcacbabcbbcbcdaacaccdbcaddcabbabccdcaacabdbcbdaadaaccdabbdaadacccddbbabdbbbdcbcabaddbcacaaadcbadbdcadccbcddcdbbccbcaacaabdbbcbdcbcaaacdddbbaadcbaddcacdbbabdadbbdaacbbcaadbcdddcccaccbddcdccdcabcadcccbbcacbddcdacadaccbcaaaaddcaababdbadbadddbcbcdadabaabcabaaaaccabccaaabcdadbaadbaccbbadccbdbabbbbdbdbccdbccaadcddbcdacadcbcdbddccbcdcddbccaaabbaaddbadcdbdcbadcddcbbdbaabadcaabccdddacccbacddddaacadcdbaccdbbacdcdcadcadbcbdcaabcdcadadbdcbccacbaabcaadcbdbbddaccddcaadccdcccdbabbadcbccbcbadcdccdbbcbbcabdaacbddcadddadbdcbcbbdabdbcaaadadbdbbbcdacdccabdaadcaadbcabcbadaadaaddcdadacbbddacabcaabbbcccdddcbbaacaadddbadbabcaaaadcbadbaaadcbccdcacddbbbabbcabacdabbdbaccdbcdbddcddbadacdabbcccbdacaacadbabcaccdcbcadaaadacabaaaccdbbcababaadbacadaacacbbcdbcbccbccadbdabbdbbdcbdbdcbcbcabdbdcdaccddcdaccabcacacbdcabbaaacbdaabcbdccabbdaddabcbbbcbcdbbaccbdabdbdbcdbabcbcbddcbbaddbbabbdccaccbbcdcccdddcbdaadaddadcdbdbcdbcdcbcdaabcdccbabacccddbadddadaabacbbdaaaadbddcbcdabaddccbcbcacbbaccdaabbcadadbdbabcaadcdbddbccacdddddcddcbdaabddcabdacdcacdcbddaabbbbcccdbbadbdbcbccaadabbbaaacdaaccabdddacdbdabccaccccbcaaaadbabddcabdddaabddbdbbcbcdbbbdcdcdddabaacbcdcdaaabdbcaacdacbcbadbccaaccabcccbbdddbcdbcabddcbbcccbbaacaacbbbabbdbbbcdddacdacbcddababaadacdbdccdbbbddbdbbcdaabacbcacabaaaadcbbbccdaabddacbdabaabbdacdadcaccacbbaddadabdbdddbdbbcdddbcbdaabbacdbccddddadaddbdccdaadccbcbaabcaacbbddcadcccccabddbacbcbbddbbbbcababcdbacabaaddaddcdbbcccbabcdacadbacbaddacaaddbcbabcdcbdaacadbbbcbbaddbabccdaacdcdabbccdbddbcabdcdcccabcddaabbacdacdcadaaddabbcdacbacdbcababcaaddddacdbadaacddbbdacacbbbbbdcadaabacbbcacdcadddaadcdabcddbccbaccadccacbccabccdadabcdcccaccddddcadcdbdadcccbbddbdbaadaddacbcacbdddaabccdbcbcddcaabdbdabdacacaddaabcbacacbbbccbacbdcbcabacadaaddacccdccaddcbcadccaabcbaabadcaabcdaddabccbbacbbbaddccaadcbbddacbcaabadccdacabdadbbbcdaabadbcbababdcddbabdccadaaabbabccbbdcbddaacccbdcccccabcbabdbbbbbacddadcabbabadbcdadcbbdbcacdcaadbbccabbdcbabdcdadbbcaacccbcdbcabccdabbbdabababbbcdccadaadccbacacacbacccadcaddacbaccbaadcdbacccaacbbbdbcababcdabbadccbddacdcacbadbbbcabbdccabcddddadcbddcbadcdaaccbadcadbbbbdcacabacbbabbddccdaccbdcccbdcbcccbbccdcddcacbabccbdccaabbaaccbbccdbccdbcabdacbbbcccdbcbaabadbbbacccbbabdabdbcdcdbabdabddaadadddcaaadcbdbcbdabadaabcdbcacdbcccdbbaabcdadabbaddacbbaccccacddbbbbcbabcbdddaacdadbbccadabacacbaaccabdcacbbcbcddccbabdaaacadcabbcacdbbcacaccaaaaaabacdacdcbcdcddbacdaccccbbbcbaadadbcdabcabadadaadcdabaaccddadbcdaabdbdcdadbcbacaabbcddbbdbccbaaabdcbbdabdcaaacaccadaccbdaccabdcddbdcbabdaadbacaaabccbbbdbcdaabadbcacdacbadadbddbaacabcbbcbbbbdcadaabddbcdcccaacabdaadcdcaadddaaacbaaacacbbcbbdbadcddbbbddccacdcccaddcadccdabdaacbbddadcaabbcbbdbcbaadddbabbbbcdccdcbbabcdacadddadbabcaabdaacbbbbcdacddbbaddbdccdccbaaabaadabbbdcdaddbddcaacdadccabcadbbcdddcdbccadbddbcbdbcbcadaacdabccdddbccdccccdcbcbcddbcddccdaacadaddcbacbcdacbcbaabdbacbaaabcacbbbdddbaacdcccaaabdacbcadbabadaaccbddccacaaadbddcbcdccdbdbdadddbbbcdddbbacdacbbabaacabdbdcacadabddababcadbbdbaccacdbaaacbbcacaadbcccbdacbcbbababdaabbddbdbcdabdbacccbbbdcbcacaddbacabdccaaadbbbddddbacdbdcbdaddcadabaadcbadbdcdacbcbbbaadbadddabddddbdacdbbcacbacbdbabbdacbdbaddbcbbdaadbdcbdddbaababbcdabcdabddbdadbbaacccdbccbddabdaacdbccbdcbbbdccbdbccccbacbaddaddaadaacddddacaacbacdbcbddbdcdbadaabbdcbddcbccbccaaabbccccaccbdcacdccbdbdbbbbbaadcbaabdddcabadbabbadbabaddaaddaaaaabbddbcdaadcdbacccdcacdacaddbdaabddcabccacbdaabbaadaadddbcdcabdbdccdacadbdddabbbbbbcbacbacaaccbaccdcccccdbdcbcbabbaaadbcaddbbcbadacdacaccbbaddbabaabcdcaabcccdababcbabbdaddcdbaccdccbabacccdaddbcdaacdcadbddabcadccbcbbadcdcaadddcbadbaaacdacddcbabdbdaabbbacaddbcaccccaacdddbacabcaabcacaddbabdbbcddcdccbcdadddcacabadadddaccadddaddcaabccddabbaccddbcdbddbddbcbbdadcbcbcccacbbdcadbcccdbbdadcabcdcbabaabdcbdbcbcccddacaaadadbabbcaaccacdddddcaaaadbacdaabbdcadabbbcbcababdcdbcadbbcaddcccabcbdbdaaccaccbabaddccccacdbcbdaaabdcababcdabbcabdbbaabadbabdbcdaabcaabccaaddbdccbcddbbbaabccddddcddddcddcbbdbdcaadcdaabdbdddbadcaabaaddadbbabdddcdaacdacacbbbddcbccccaccdaddabdbbbdabddadabcabbdbababbaddbdcaaaabbbaabbaadabaabbcdaabdaadaadccddddbdbbabdcbcaadbbdccbaadddbddabcbcdacabcddbdcbadcbcacabcaaaadadcbbacaababbabbbbaadaabacdaaadcaacbccdcdcaccaacbdcaddcbccdbaaddacaddccdccbcdaccbabacddadbadacaccbdaadadaabddcaabcdbaabcbbbadbbababbacbddbbbbbcacdcabaaabdbbdbaccdabaadcbcacaadbdabcbaccdbadddcdacddccadcabadddabbddabdacacddddbcaccaddcdaccdcccbbaddbdcacaaaacdddddcadccdccacbabadddcbdacdcaaaccbaaadadccababadddcacdbcaacbcadddabbbdaddcacddbbbbdddaadabbdcdbacdabcbdcaccacbbaacdcdaaaccabbcdabddbbbdcdcccacccddaddbaaabbacdacdccabaaddccaadbadbdcbaaccbaacbcaaccbbcabbdbabbcdcdaaabdabbaaaaccccddbdadacacabadbccccbdbbabdcaabbbdcbcddddabdadcadbddccbaddddddcdbbbdacabdcbcdcccaccbbdabcbbbcdbdbdbcadacbbbcdbdbcbddccbcaccaddbadccabbaddaadcbacacbcdadbdcdcabbbbddacacaddbababccbabdaabdbcadaccbbbabdacccacbdacddddccdbcaddbbdddaababbbbdcbcbcdcabccbadddcaaddbcaabbcabdccacaccdacbbcccbcaaddddabbcbcacbccddbcdadbabcbcbbccddcbbbddabcdccbaaddcdaabccbdbacdcacabdbdcdcaadcbdbddabccdcdbbaaddbcdcbcbbbaabdbcddabaacababbcdbbcabcdaadcbbbccddabbdbbddcdccccabccbadabcdddbbccdabccbcbbcaabdabbddbdcddbdbcacadbcbbbdbcdbabcacbdaddaacbaabbbbabcaacddabaccdcdbcdababaddcababcdbbdaccdbdbbdcdbbadabdadbabdcbaacbbacccdcbdbcaddccbbabcbabdaadcbcdbcbacaacddbbbcdaddcdcabbadbdbdcadbcdddbaaacdaddccdddcacacabdcacacadbcacaddcaadaadbdcabbaaaadabdaacbbdadcbcccdbbcccabbaccbaadaaacdbbcdbaddaacbabbccbdabcdcbadaccbbbdcbbacdaddddacabdcbadcabaabbbcbadcdcdbcaabacccbdabbbdaabacacbacbcddccdbcdadaccddddabacabacbcaccbdcccaadcaaabdadbcbddcdbccdcddbcbcaccadcccacacbabaacababdbbbbdcadbdbccaacadaaacadbabcdaddbbbbbaddcbabcdddcbbccadbbadcaabdadbcaaaccdabcdbbabcddbbaacabbdcbaaddbbccacdcbacbdbddddbaabcdcaadbcaadadbbdaadaacbdadacdaadadddadabaacbdcaccdcacbdaabdaaddddbccabbbbdddddcdccbbdddbcabbccdcdcacbbcaacccaccadbbcbdcdbcabdccacabacacbbbacbaabbddbcaaaaddccabddcabdbdddaaabbbdacbaccbcccacbccccbdccbdbadccdddbadbdcbabaacabcaadcbbabbdabbbaaabbcadcbaacababdbccbaaabccaacacbbbcccddcacbccddabbcddcccadbcccdbcabddbababbaabaaaaacdadbaddbabccadddcbcdcadbcbddbbadbcabbbdacbdacddcabdddcadabacadcdaccbbcbddcccacdbdaadabdbaaaacbcbddabdbcbcddddaacacbbbbadccaddcbacbcaabcddcbacbcdcacacbddcacbabccbbaccdbbaacdaabddadadccbacbdcacacbcabcbbbdccacbcddacaadacbacaabdbadadbdcabdbbacaacdddbbabcbbadadccdbbaadcbaadadaaccddcbcaadaccddcacbcdacddcabbbbddabacabaccdadddaddccabbdbaaaabaabcdccccabacccdaabbbaacdabbbbccccadaddaaaadabcbcdabcbdcaadbaabcabdbddcaaddddcbcabaaacacccccbcdaaacdddacacdccdaabbcaaadcccabccaadacacbccacbaaccabcdbacabbddbdbabcbdcbbdccddabadddabacabaaccddacddabbdcbbdadcddabcaaaccdabbacbcdcaaacbcaacdcaabbbbbacbcccaccadaddadacbdabcccdcdccacccbddabcaabddabdbbcdabccdbcbcccaabbdabbdadcdaaaacadcdacdbbbabcbcdbaaadacababdcbddacdcaddcabacbddcbddacbadaccccadabccbbcaacdccabdabccbdaadbcbaccdbaadbbcdbbadddaabdacbabbbaccbbcaaadacccaaddddccaacdcadaaddbcadadbadacccbbdbddcaacacacddbbcaaddaabadbddcbbacccadbadabdcdcddbadbcccaabcdccbddbbdbcabdaabbccdddcbbbabacabbacbbccacacbbcdbbbadcbccacaadcadadbaddcbacdbbaccabbccdadabaddcccaabaabbadcdbcdbaaddbbabddacabaadbccdcbacacbcabddbdaaccbddcacadabacdbbaabbbcbaabccdccbaacdbbbcdaaabbbbabcbddabddabddcdcddbbbbcbddabdaacadbaddbaadbaddbccbaadcccbdcdaaabacabbddcbdcbbdccccbbaacdbdcdacbcabddcadbbdccaabbbcbdbdddcbcaddcadbddbaacbbdcdcbbddcdbadbaabdcdccacbbaaacddbaabdcadcabaacbdbddcdcaadcbaabcadbbbacabcaccccbcdddaccadaddddbbdbadacdcdbdbbcdddddadbcdabcacbdddbbcabaddccdcdacdbbcbabddcaaaadcbdacbacbbcbcdadcdabadddbdbacbcabcdcadabdbbdbabbcabbdabdaacacddddddbbcbcdbbbdbddcdcdaddbcbdcdadbdbcbdcaaddbbaaabdbdccbbaadccdaaaacbcbdbddbdcdbcbaacbabcdbddbcbcbcddbddbcdadacdccccadacbcdcbdababdbcccbcacdcbaacaacbcacddcababbadcabbadbccbaacaddccacccbbcadcadaccdcdaccacaacaabdacddacadaddbbbbbddadbadbddaaabbcdadaaacbdaaccdbdbaddacabcaadcbabbbdbdcdabcadabadacabdadabacacdacdadbbbaaacaddcddbbaaabbcdbdbbbdcbadaddccddcdcdddabadaacacacdbbcadcdbcdbbaacaaaddbddaaccaddbbbbcddcddbdccccbaacadbcacbcaacdaaddabbacbaaddcaaacbbdcbbbcddbdaaaaadddabaabdabacddbdddacaddacbdcbbcdccddbbddbaadaacdcabcbdccbabcaabddbcdacacacdabcaaaacdadcdabddcdbdcacdbacabadccbaccbdbbacbdcabbbcbbcadddacbbcbcdbcdbcddcbabbccdacacbbddbddcabcadbadcddbcaccddadcbaaabbaddcdbdacbbbaabbcdbdbbaddbdbcaaabcacdaaabcaacacaddcbadbacbabbacadcbabccdbcdbbbbaacbdbbabddacabcbcbdbabdbcdbbdcadddbdcacadacdaccbbbbcbaadabaccddcccdadcdbbdbacaccccdcbcbbbddbacbcbdbbbadacbacaadccccdaccccbcacdccbadcacdcbbbaabcdddbdaddbcccdbdbdacaabdcaabcccaacbbdbacdbadddddadcabcacadbdcdcccacbddadabcaabbdccbdabdbadcadcacbbdcacccaacccbdaabacbddddbccdcaaacaddabbbdaddbdcadabbaddcacbcbbbdbabcdbbddccdaccddadbdaaabaacadadaacccdddbadaababbdccbababdbcabdbdcabacbbcdaacbababaabacbdadbcbddcaaabacddccdddaaaacdaabdacaaacbacaaadabdacaccaabdbacbcdadabacacdccbadabcaddbadababbdacadccbcbabbdabbcacbbddddcabadabbbbcdbadaddcadccacbdcdaddccdadcbaddcbcccddcccbcccbadbdbcadbcdbcacdbccbbcdbdcdaaaccaadbadcabdadbacdbdcdbddadbbcbaddaabcddacdadaaabcbcbbdcaccbabbbbacdcccadcbbcaccdaccaacdbaddbadadaddcaacacbbbdbdcabccbbdcdcdccdbddbdadccdcdacabdaaabbbbadbddddcbbcadadbacddcacbaddcbbdbadbcbccaacdabcbccacbbcdbcccdcccddadcdaabdabccccccaaacacbdbddcadbcdccdcdaadccaaadbabdbdaabbacacaaabbbbcacbadcdabbdbacabcbddadcbdcdaabccdaaccadadcdbcbcbabaccabdbdaacbdacccaadaadcaabbadccabbbcabdddccccdbccddbbacdcdbdcbbcddcddcdadadbadbadcbaacdcacbbdcbdbbdbcbbabccdcdbaacbbccdaabacdddaadabccbbcbcdaacabcacadbcddadbbcdacdbbddadabbbacccddccdbacccbaaabbacddcbbaaacaacabdddcdabccddaddcbaccccdabcdabbacabadabdcabbddccdbacdcbbadadcbcadacadddcbcaccdabcdbcbcadaaddccbaaadaabadbaadabcbaaacbbcdaaaccadbddbddcadbcdacaccbbbaabbbbcacdccbbbaacdbdbcbbaacbbdbdcdaabddbaaccccdaadddaadcdaddddddbcbbbcddbddcdaacaccbaddbbadbddbdabacbdcadbcdddbabcbaadcaaccddddaccacdbccbcbcadbaaddadaadbcdcdbcccbbadabadbdabcdcbcacdadacabbabaadcacddbbcadaaabccddcbcbbabccaadabdbccdabadacbaabddcadaccaddabcdccdabccccbacddcabbbdbabdbbaabbcadbcaabadadbdccdbbbbddbdbcdacdcadbcdcabddabdccaaccbaacbcbbbbbcbccbabaadbcbababbdbbcaaacacadadadbbbdcdaaccddccdcadaaaabdbbacdbcacbdbcabcdaccdccccaabccbccdcadcbbbdbaccdcaadaaababcbbdbabdcdabccddcbcdadaaddababcccbcccabcacadcbbbbccabcdccdddacadcdcccadcdcdadacbcadbbcbbbddadcbaaddccbddacdcddcbdabadcbbbddcdcbdbdabbcdaacbbbcdccdabdbdacccbbccbdbdcdbbbaccaacdddcbabbccbaacbbaaadcabbaacadacdbcbbcbaddddddddbdbabacbbaacdbbcacccacacbaaadbcabbbbcddabccbabddaccacbdaccdadcabdadcdaabaadcdcacdddacaaaacddadcdadbabdddadcdcdbcabbabcbdcbcdcddbccccbccadcdccabadcdbcbdbbbccbaabdbacaacabcbbbacaaddcdadddacabdccacdbccbdaaccadabdbaabacaaabacabdaadaccadaccacadbabdbacccdcdcddbcbacbcaaacbcccccaabdabcbbdabbcbdbdabbadadccbbcdbabcacbaacbcaaadadbacbdadddcdaddbbbccdcacbaaabcddababbcbcadcdccadcbcaddcbbdbdddccbbacbddabacddbbddbbacacbadababbcbcdddcdacadadddaacbcaabacdcabddaadaddbcddbaacacdbaaaacdddabbbdbdacacadcdcbbaadaaabdcbccddcddcabbbccbcdcbcdccaacccaadcacababcddccddadaabcdbbcdbcaddbaabbdcdbcdbbbadaccabdbbcacdcbdadbdacccbadccbdaaacdbdacbabcdccccbcaabdbadacaabaabdccadcdccbcbddaddcddaabaccbcdaabbdaddadcadbccbabcbbbdabcccdcdbaddbbddbbbadacadabdcbbddbbdbdddbcdaaadcbbdbabdcbbaacadadaadbaadbbddaacabacccacbababdbacbccdccddbadadcaacaabcbdbbaaadbabcabdcbcbbcbdcccdbbaddcabcddbcdcbabcbdbcbbbbbaaabbcadacbdbadddbabdbcccaaacabcaccddacdcdbbbacbcbdaacdadbbbacdbdbcbadabacbaabadabcadbbaadadaaacddadcccabdabdccadcdacdbddcdadcabbcadcaaabbcdacaaadbdbdcaaaaacdaabcadadcbdacbbccadaaababbbbcadbdcdbddbcccbbadcbccbabaccbdbbcdccdcddacabaadbdccdabdbcddcababcdcddddadaaadaabccadcbccddddbbbaccadabbcddbdaadadbbccbdaaabdaabbbaacadabacbcddddcdcccaabdbcbabdbcadadbbaadbadbadcaaacdbabbadbacbabadaacaddcaaacbbabbcadcaccbdbcbdcbdcadbdcaddacdbcaadcbcbbdcaadbcdcdadcbccbdaaaadadbbadbbcdccdbcbabddbcdddbabdccbcbbbbbcacbccabbbbccaaabcbcbbbadddbacdacbccbacbcaddbbdabbacadddabcbbabcaacaaddabacaaacaaccdaccddccaabdabdddddccbccabbdbbaccbcccdadaaabbddbbadcdcbbaddcacbaadccabadbddabadccddadabddadbacadcccbaabbacbaaaaccadcaacbcabbbcdcbadbcabcdacbbccacdaadaccaddabcabccabbbdccabbabbcccbdcccbccdbccacdaccbacbbbadccccbadddaacaacbcbdbdbadbdabdddbabadbdbadccbbddcdcaacaadadbdbaacbcdababadccbbbbdcbbaaacdddbcbbbccbaccdbabcdbdbbbdbdcbbacbdbacbdbcbbdbabdbbdbccadcadaaaddbdacdaaddcdcaaadaadbababcbcddadcbdadabbbadcccaaacdbcadabadbbddbbdbadbaddcaacbaddddadabacaccccabcbbccbbabbacadacbdbbbcbadabacaddbaaaabadcaadcacabadcbadacbbddcccbadacacbcdccbdbbacbdbaaaccccabdbcdddddabcbaddbabcdaddcccddcbccbcacabaaabccabdbbccacdbbcabdababbdacaabadaacdddccbbbacbbbadbddcbbacdcbaabbccbdbadbaaaabcbbaccbcbbbaacbcbddaadcdbbbbbbaabcddacddbdacbdaacbadbddcdbaaaaacbbbcbaaddaabdddddabbcccaaadadabbcadbcbbaaabcbdbcbddcbcddbbcbcaaadbdacdbadcbbbddcddbbbcccbacdbacbdabbbbaacdbcdcbbbbddcdcdccacddbccadbcbbabddbbcbbddabacdbbcacadbababcbdacaccabbbcbdbddcdcacbddacaccdacdcbbbaabdcbaabccbccdcbadcaddaaaadcdcbdbabababbcaaabbadccbaadadbdccbcbdbdadcacbacdbcdabaaccdacbadcbcbdcadbcaaccbabdccccdddacacabbacbabbbaddbccdcbbabdcbddabddabbcbcaaacdbcbccacdcbbcaddaadacddbccccdababadcddacdccacbcdadcbbcaacdbbacbdccccdcbbbabbabbadbdabbcbcabadbcddbaddddbbccdaaacaccacaddcabcccbbbccccdacccbcdbcddcabccacbddadcbaadabdbcccbcbaccacccdadaacbddddaadabbbacadbdcddaacabacdabdaadaccaabdabbabcdcbbbbdbadabddcbbacccaaaabbcadddccbccaaaccbdcdccbcbcbbcdadabadcacaabcbbcacdadccbcbadcdcbddbdbabbbbccccaaabaabccbddbdaddccadbcdcabdbaabadbbddcdadcbcbcdcaadcddcbacbdcbdbdacaddbadbbcbbcbaadcdbaaacbaacbdababaccbccccdabaabcddcbdbbaaccbacacacccaccbddbcbbbbaaccdabbaaccdbdcabcddadddaddbcbdcaccdaaadbbbddcbbabbcbcabddbcaccabacdcbcbcbbaaaacbdbbcdadcccdccaadacbbacdaadccddadbcdacacdbaaaccabbdbaccddaccddcbadabcaacbbbbadbabcadaaabacabccddddabccbdcaadbdcdbccccbbdccdcadaabcaddcadabaddbdcdccabaddcdcacbcbabbbbabaabdcccbddcbcadabadaaaacbadbbdccdabdadcbcaadbccdacbcbbbcdadaaacaddcdcddcbdbccadcbccabaabdacdccbbaaddbaacbcbccdccabdabbaccdddbbdbadaccbdccacbdabcbcdcccdabccdaccddacdadccddcbdadacdacdbddcccacbadcbbbdadbbabaadcbcdabcdbbdcdbbddadcbaabbabbcdccddadbbcdddacdcdabddcacadcababdabcabcbcaaaacdcbdaacccaadccdadbcbcddcddaddbcdbcdcacddcabdbbdadbdcadbdddcaccbbacaabdbaacbbbbbdabcababbdcaadccaaadabcaddcbacadddcabcaadaccbacbcddbbbabacbbdaabaccacabbdcdcbdddcdccbaccabcacbaccdabdbddccadcaadddddabddabbdbdddccadcbbdaabbbddcacbcacbbbccabaacdcdbcbdbadaabdaacaacaacdabcbbaacbcdbdcdcdacaaadcacbbabdccaabdababdcaadcdcadaaccbacaccbbbcdaabcbcadbaaddacbccdcacbbdddcbacaccddcdcacccddbaaddbacbbddbbdddddccddbdcadcccdcaabdaaaabddabaddbdacbcadabbdcaddcdaabbcbbcbacabcabadccdaddbddddacdacbaccdbababaabdbbdcccacaccacbddcccbcadcddadcabaddccaadbdcdcaccdaaacdddaacdbbccdcacaddbdbbdbaaadcbcbaadddcbcccccddbbdddbdbbccddadbaacdcddcbbacbbbcbcddcabbcabddacabcaccbddacacbccbcbbcbbddcabbaadadaadaacbbcacdabdbccdcbdbabcddaacbbcababdcccdbccbaacbabddcddcdcdbbcbaddbbbdabadbddccdbdcdbcaaccbbacccdadcacaaddaaacacaddababcdbdbabddbbacbddacdaadbcbdbbdadaacdbbdaaaacccbaccbdcddabdcaabddbaaabaaaadcabdaadcbbbdccbbaacdccbcbacdaabbcdbbcbadcbbbbccadaabcadbaddcccbbcbddcbaccbbacdadadbadcddbaadcdadbdbaaadacbcadbaacdcaccbddacabaabacbbabcbbccbaacbccdaaaabcbccadaadbaabbddabdabdbbcaaacabbadbcccaababbadaabcaabbbdcbcddbbcbabcbcddcccbaacdadcccbdcbbbabaaabddaababcaccccbddddccccbaabcaacdcdbaaccdacdbacabbdabdbcabcccbdcdacacbbcdbcaaadbbccdbcdadacdbadccaacddacdcaacbabbaddccdaabdabdaccdbcbaccdbddbcdaacdddbcaccdacdbbcaadaaabbcbcddcaadbdaacbcbdbbcaddaadaaaccddbbdacaacdaddaabcadcddacdddbadbcdcbbcadaaddbacaacbbbadbcadaaccbddabccdbcbbdbccabcbaadccaddaddcccdcbabcaacbddcbccabdbddddcdadacbbdbdabccbacadacccddaaacdbabbcabccadbbadadcdbcaddabcbcbabdabdcbcacccdabdabdcbcabacadadcdcccbcbacbdbccabccdbcdddaacccdbcbacdbdddbaaddadbbbbaaabbacabcadbaabaddaccbdcccdacaccdbbadaccaacaaabbdadcccbdccabbddacacbcaadddccabdadadaaaddddcabaddaabbcdababbbcabbcbdbdaaccbcadaddcddabacbacdcaabaaaddaaabccbdbabacabacadbdbabacccabbadbaabddddcbcdabdabacbacadadbdacbdaddcbdcacaababcbcddcdcdcddaacdcdbdbbcbccbdbdbabbdbbcdbbcabcbcbcbaccbcaadbcbaacabaaccdbaaddaccdbcdcdbddbddcacbcddbadccadcdcbbadcccdddacaabbbdccdaabdcacaddacabbbbacbcccdbcdccababbaaccacbadadbbdaaccbcacdddcbccbdcaaaadcdbaddbcaacccddaadcbacdaacbccdcaacacbdcbbcbddbddaccdcbbdbacacbacadaadaacabbdadcdcbadddcdbcdaabdcddcadabdddabadccbbccabbcbcdcdccaacadabdadbbdddccabcdbabaddddababacdabccadcdcccddaaadcddccdabaccbaacabbbabcbcbaadbbddcacbbbacccacaaddabadddadabcdbcdbbcdccbacbaddaaacbccabdbdbcacbcabbbabcadbdbbaccaacddcdddacadabaadaaccddbddacacadcabdbbacabcbdbcadaaabdbdcccacbbabdbddbddadbbccacaddbbcdcbccbcadaaacdcacaaccdbbbdcbbabcacaccbbabbabbaccdaaaddbbccaccacccbccdabcbccabdbccababdccadccdbadaadcdacadbbcacadddadcabdadcbcddcbdbbdacbccdbaacbccdadadccbdadbbdcdaddaadaccddcacdacacccdbcdaadcdbdacddabcabccbaccdadcbbcaabcadbcaadadcbbacaadaccbacabdcdaadcddaccccdabcadaadbacdbcbdabdadbaddbabdadcaaabbbabdcaaddadabaddbcadbabbabbbddcbbdbabcccdbdcbddcadaccababbcdbdacabdddbcccccbbadcaadcdabadbddcadabbbcaaaadabcacdcccbbbbbabadddaacbabdaadddbcdbbabdababcabbbbcbabcddaddbbcbcaabadaadcabaacdcaaadbbdcbacdbdaaccacbdccdbdaadcbbdacbdbaacaacccacaadaccbcaadccbdbcddadbaacababcbabadacddaaccbdacddadadcbabcbcdababdcadbdadbddbcdbdccdbbadcdccabdcaacbdddcdcabdacdadddaacabaabdaadbdcbaaaadccbaaabddcdcccdccbcbddbadabdbdacccddcdcddacabacaabcddaccbbcccbcbcdbdbbaabcdcacabcdaacdbbbdbacacdaadadacccbaabdabcbdbacacbbabcdbdccabaddbdbacddaddcaadadbbadaaaaccdbacdbaccaccbddbbdaabbcdabdcdabbdbdadcaddddcbbbcbcdadacccdababbcdadacaabcaabdabbbcdbabdcdaddbcbdbadadbaaabadabbabcaabbddaccccaabdabcabadbcbddadbadbbcadbdbbbcaaccadbcabaddccbcdbbdabddcacbdcdabcabbbbcbacadabacccbbaabaabbdbbcacbddcacbbcaaddcbccbccdacbbaaaccaadcacacabdccbbdccdbcaabbddacbaabbbdcdcacabdabdcdbcaaaddaccdbccdccbcdddddabbcbadcccbbdddabdcccabcddbabacbbaabcbbdccaababcadcaaadaabdcadabbabbaaacacbcabacbabbbacddaccdcaddabdbcacdbddcdbdcdcaaccdbdbaddbdabbccdacbaaddbcbaacabcddbdbbbaaccbdcdbbddbaccdbdadbaadadbacbcbdadadccadcddccbdbddaddbcddbcabbddcddcbacbbcadccbaaddbcccbaaaaddcdbbdbadccccbbcbcbcacddabcabdbcbcacabbdacaddadabcccddcbccbddccaacababcbabdddddbbcccabadcccbcbdadadcacdbbdabadbcaddbadbdbadbcbabbccddcadacbbbbaccbbaadcdbaaaccbbcbddbcbbdadccdbdbbdbbaaaacdbcababbcaabcdbcccdccbaacbbbcaddbcacbcaabaccbdddccdacccadcdcbdadccaccadbcabacbbdcadcacbcbacdaaddcadaacdcdcbbcccadcdadaadccdcabdabdbdaadbaaaccdacdbdabcdadccbcddacbdbaddcbccddbdbccacbdcdbddbbdbdcccdabaccbcdddccabaaacdabababcbcbcabcddcdcadbcabcbdbdddbbbcadcbcdadbddacdbcabbcbcdcabccbdcdbabbdabcacbcbccbaadbaacddcdadbbbbcadcacacacaacbbaabaddbaaccccbdaccbcbdcacacabbbcdadabdcccbbbcbaaccdabdddcdccabadddcddbcbbabaabcabbdabbaabccbccdddcababbcbbccbdabdccccdbccbcabdbbacddabcadcbbbaaadcbdbbcdaccabcbbcacacaabbabccabadbbccdddaccdcbdbbbccdabcacdacdcdabbadbaabccbcbdacbcabbbdbdaadbdbabcadbbbcaacdccccbbcdaaaabadccdcddcbbbacccaddcdbccbbacdcbcddcabbbdcbdddbddacdccbabcdbbadacdbdbbdadcdbbbcdaadccaddcabbbcdacaaccaabccbddadcaaabdbaaccbbddbaacddabbdcbacadbbaaccdadcbacaaccbbbaccbcbddcacabdabaabadadbdddbbdbbbdbcccbbccbcaccbdcadbddbdbbaddbcbbbcaabdcdddaccddbdbabaaaccacbbaadaddaddddbccbbbcddcbadadbcbddbaabdbbadbcaabbcbbccdccbbdbbbcddbddacccbdbacdaaacdcbbaccbcbddaacbacccddacabddddcdbbbbddbdbdbacddbdabbadcdbaaadbacdbcdbdcccacbabbdbacaacdddacdacdbbaacdcbccbadacddadbbabadcccdcbabddcccccdabdbccabdabccaabbaddadbdbcaacaddcdabdddbadbbaacabdbacadcbabaccabddbadcaddbddbababbbadaacdbdbbcacdcdccdadabcbabbddccbaabbdcabadcacbbaccacddadcadddcdcdcdbbcabdccdcdaabdcaccccadacabaabacdaaaddbaadaacbdacbacdcbbccccbabdabbbaddcbddaddddddacaaaaacccbbddbdaacbcabacbdddbccbdaabddbcbccbbdcbcacddcccadacddacbacddbccdaaccdcbbadbcdbacdcadccbabbadbbbcaacbdcabdbcacaabadadaabdcdcacccdabcbcbcbaadddbdaaddbadcabdbbbdbcdbaacbbdaddababddcadacdbbdbbaddcccbccadadddbabaacbbbdaacdccddccdcacbdbbadabbbbacdabccadcacbdcbbdcbbccaadcbbcaabddacbcbdadbadbabdcccbdbddacaadddcdcaacdbbcdbdcaacdbdbdbadbddababcabdadbcbdcbcbabcdbacaabddabaaaadccabddcbccdbdcaadcddccdbadabaaababaacccbaabdabdbdcbadbacdabdccbddbcaaacbdbacbbbbacacbababbaaadcdbbcdbcccbddbccbddcbdcaccccacbaaaaabdcddcdcdbccbcbaccabadadcbaadcbdadaccdadcbccaadbdcddbaddddcaadabbadccbbdaadddbcddabacdcdbbdbadadcaadbbdbdabcbbdbcaadbddabcbccdaaddccaccbbbadcbabccbabbbbbbdbaabdcccdaccbbbbaaaacbbcadaacaabcdaabbbadbacddddddcdabdddacbacadadbbabbbccdcbcaadadbccdbbadccbacacbaccdbddaccbddddcccdbadbddbbadbadccdaabaabdbcccbcdcbdccbbdcabbcccbaadbabdabccbbadccdcdbaacaadcabadcbadcbccbbcbcbdbadcbaccdddcacacbabbbbdcbbbbdadaacaacadacbbdaabdbdbccdddcdaddcdaaddcccbbdbbbbbcbadcabadadcacdbcdcdccadbaccbdaccdacdccccbbaacadcbaaaaaaaabacbcaccbcabadcbcbcdbbbccbabcdabacabbdabbabccbddbcbaccddcdbcacadbbabcabaaaaddaadbdccbdcbdcdcdbdcbbccadcbddcaddbabdbaadcbcbdcdbbcbdaacaaaaadaccaccdcccccbacbbbdaacdcdccbcbbaacdcbbdbbcbbbdaabcdbbdcbbabcbbdbaccdabbadaadbdabdccdcadbdacccbdbdbddcccdabbabaacddcadcdddbcdcdbcbbbbccddcbdbdbaaabbaadbdaabaccbcddcabdaabbddcacaccbdabdabbaaadadbccdacdcdbaabddbcdddcaaccaadcddbcddccbcabbcbabbbbcbabbbcbbbcdbdbdcdadbbbdabbcaccbdbcbccbcdddbabadcdddaddcdbdbccbbbcbdbacbbbabcddcdcacddacdaaadcbaabacadacaddaabccabdbcbcaabcdadbcacbdbacdcdbcdbdcddacdddcdbddaadbacbddbddcccddcbabdaaababdbddadcbcbdbdbdcabcaddaadddcabbbccadcbcaabcadcdcabaacaacccaacaadbabdbccdbcaddbdbcacdbbbddbaacccbddaabdcddcdbdbccdddbaacabbdbcdbccabdbccbddbddaabdabdaabbcbcddccadcbadddacdaabddacaccaabbdbaacacbaaabcbdcaacbddbaaccdccbdbaabccdbbbbacacadbaadabdbdbcbcccdcadbcbadbaacccbadddccccdbbdadbdbdbcdcdbcbbbbcbbccbdbaccadbaadaccabaccbdaaaccdcdbcabbababcabccdcdbddbdcacacbdbbabcaaacbabdddbddbbbbaabcccdbcbcdcbdaddacacaddddababcbdadadabdaccdbdcabbdbacabbbdbdadbbaaacbcadcbadcdcdccdabbdabaacbbaddabaaacababcdbcbabaacbabaabdbbcabcbaccbcddaddadbaccbcbddadabcdadabaccdbccdddabbcdabbadddaaddcbdabdaabddbdcadabcacccccabbbadbdadbcabccdcbcbccbddbcccccaddbbddcbabcaccbdcabcdabdbbcaacacbdbacdabddaaccdadaccbababbccbbaaabbbbdcbaacddbdacccbdccccddacdbbdbdcacaabddadcbacdbdcbadacadabbddcbbacdcccbdcdaabbdcdcaabadcbccbcbcbdcaacccccbbbbddabccdaaacccdcddcdbdbcacccdcabbdcdbbabadbcbddcababbccbbcccdacdabccdaaacbadcdcaddcbbdaacaabadcaaccadbbdccbabbcccccbabddbcddadccdaaabbcdacabcbbdcacabbdaaacdacbcdadcabccdcddcaddaaababacadcadbadaccadbaddadcbcbbaabbdadaccbcdcdccabccacbaabdbcdbccdcacbaadacaaccbadaacdbcaababdddaccbabbcdbbcddabccbbdbbaddaacddacdbccbbdaaadcdbbabcbbccabddadabcabcdccccccdbbcddcaabbcadadbbaaacacdbcbbbacccdcbccccdbcacdcbbbcadbdcddddadcaabbcaaaacabddcaaccccbaacdabaacabdcabaccdaaccdddaadcbbcbacbcaadcbbdcbbccbbccbdbaadabadcabdcdcaddbacbdcadadccdbdacdacacabbaddcaadbcbdadabbcbcdabbbabaccabcdbaababcdaaccbaddddaabbdabaadbdabbbcaddadcbbbacdbababcdccddddcaaaaddddabadacdacaccaddbacdbcbbccdcabaacdbdddddbbbdbdcaacacdaaccbcdbdbbbcadddadccbbdacdaaaaabdacddccbacaccddbcbdababaccddbadbadaaddcdbcbcdaaabababcdcacacbaddccbcbdccbabcccbcdccbbcacdadcbcabbdcadbcccabaccdcacddcbaadddbbabcacadbddaddadcbaaddacbcbdcdcbabcadddcadcbcbadabbbaacdbcdbccddcddccadccdbbabbaccddbaccbcddcbabbbdcadcccadbadbbcdbdcbddbbccbbddcabbaddcdababccdcaccbddcdccacdddcbabbaaaacdbaddcbdbccdbccaaacbcbaddcbabbddaaaadbdadcbdcbadbdcdacdacdbadadcdddaaaadaddbcaaccdcbdcaadaaacbbbabcbacdcbabaaadbdaaddabdbbaabcadbddbcaddcaaabbdcbccbdccaacdcdaadbdcbbdbcddbbcdaccacdacddddadbdbcdcaacdccadcbaccdcaaaccccacdabaacaddabdcccccbbcddabcaddcaacbcaabadcacabacbcbadcbdacbadaccdccadbbcccabbcadacbccaacdcddbbacbaccadbdcaaadaadbacacaabdbccbccbababaaaccbcdabadddccaaacaacccbcdadacaacbabcdcbcdbcccbcaadbcccdbbcbadcbcddabacdcbccbcccdaaaacbaacbbdbacabbdaccadcaccdbabdaccadbabdadddcadaaaadcdabdbddddaabaadadaaccadaddabccaccaaddabbdccbdacacdcadcbadcdcadcccdbaaaaddcddaaddcdaaddcdccaaddcccacbbaccaacbdbdcdcbbbcacbcabddcddaaddbdaaccdbbbcadaddcddddacdbdbdbaabbbbcdadccbabdddaabdabddcaaacbddccaaccadabaadccbdacbbddadbccdcadcdcadcbbbbbcbbbbbbcdbbdbdadaaacbaaabbcadbdbabddabbdbdbbdbbaacbddabdcbbaacdddabaadabacdcbaccbccdcbbabbaccdbacacccacacbddcbacdabdaacdbdadacbdaddabccdbacbbdababcabbaddbbdbccdcaccdddcbdadbadaaabdacdabcccaadcddcadbbcdbcbbdbbbddddcdcdddacabdacaddddcdbbaabccbdadddbcbcadccbacbdbdcaabcbcddacbcbaddabddccbbbccddcbacccaddcdabcccbacbddcbcdbcdbdbbdbaabddcddcabcddcbccccdbadccdccacdddabadbaadbccbbdbbbaadcabcdccaaaddacddbdcadbaabaaabdacdbbbcdcbaccccadbbddcabcddbabdcbbcbacdcddbacbdbdccbdbcabdcbcadddacdcaaccbdabbdbaaaddcbdbbdacbaabdbadadcaacbadaabcdbbadddacacdacaaabdcbadbccccacabcbadbdbddccabcdaddbdcdbaccadabbaaccdddcabcccbbcbabdccadcbddcbabdadcaacbcdacbbdabccacadcdcaadabbcbcabddacdcdababbaaaddccdcbdadcbbabbccccadcdbdababcabacdadacddbabcabaddaabcadacabddaabbcbadbccdaddaddaccccabcbcddbcdaccddaacbdcddbcbdbbbccccabbbaabaabcccaacdaadaacbcaacdaabaaddbaaaadcddbbdcbcaaccbdbcdabadddccbbaabdabdbdaaabccaacbccabdbaaabbcaadbdcadcccdadbaaabdbccaacddddbdadbdacdcacbaacbbabddbaddaacddaaacacadaabaaacacbaacdaccbbbbdbccaccbcadbdaddccaaaacabbbcbccabbcdccbaacdcaabdaaccadcaccdadcbdcaadcdbbbbdddbdbaccabbdacdadacdbcbccbadcdadccbdaadcbadaaacbccccacaccadbadcdcbcaabbadacabddacddbbdcddaabadbbdbdbbcbccbabccddddabbcdabbdcbdacaccdbadbccadbccbbacbbccbdcccdaddcaabcbdddbccdccddbcaadcdbaadddacbbaccbdadbccbdababdbabbcacadabcbbbddccadaadccacddddcabdcbbdaccdcdaaabcbcbabadbcaddadcaabadaaacdabcacbbcaddabcacdabccbacabbabdbbddaabaadacaccdadcabcaacbacdbcdbbaabdcbaddbcdbaddadbccabaaacbacaddabcaddbbacabcddcadcadaabddbacdbaacbabbbddcaabbaaddacdcbaccaacabdabcdbacdcbcdcbdadcdccaaacddddbcbbbcbcbacabdcaacdbaaaddabdbbbdcdbdabddcaaaaaddddaaaddadcdbbbbcaccaabaddcccadacddaacaccdbbadbcacdaabdbadcdcddbdadbabcbcbacacabcabacabbadcacaddbadaaabcdcabbabccdcdccacbaaddccbdcaddbcbacddcabdcbcacdaaadacbacbbaabbaddaadacbaabbacbbddccbbaadbbdbacdaabdddbcddaaccbbcbdccbababbbcbcababddadccddccacbcadaaadddccdcbbcdbabbcadabbcccdabbabbdbbddcddbbbcdabbdcccbdacdcaaaddaabcbbacccddbaaaddabacabcbdbdccaaddaddddcdaddabcccdacbbcccbbdbdbccabadbdcddabcdcadbbcaacdaacacbbaaddacbccadbddbdbaababccbcdbcaddbdbabcababdbdccbcdcdbcdabcbdcdaabddacbacaccdcdbdcbbcdccbdadccdcaccadcaababccdaaaaaccbadadbcbcadcddabdadcabaccccadbcadbdcacdacbabbdbcbbbbdcaacdbbdadbdadadcabadcddccbabaaabcbccacdbdcadaacadcabdabbcaaabccdbabbcdbdadababbcbdbcbaddacadaadadbabacdccddadcaddacbccccbbccadcaaaaaadddbcbbadcdabdadabcbcbbacbdaaddaacacbbbcbbbbaaadbababcaaaadbadacacccdacbdacabcdcddcaabacddddddcabbbdababdcbcddbdacdcbcadbbaabcdaccadbbdcbaadbbdcccdccbdacbcabddbdcddcababdbddcacbacadbcacbbdbdacabbcbbadccaacddabaaccabbbddddbcbbddbcabccaccbdadbddbdcdaababdcbabddddcbbbcaacaaccdcbabdacadbbdcabcaddddbbaddbbaaadbbdacdccacccacbdabadccbbbbdcbdbdbcccddaaccddacdadacccaacacbabcabcababcadabcdddcccbccabacacaccdcdbcadaadbdaabacdcabbbcaccddaccdacbbddbaacdaccdbbbbabdcddcbdbcadbaadddadddcbabcaccddaacbdaacdaacadcdcbbcbbaaddddaadcccdbdbabacdacdddcadcbbaaaaaddbccbbcdacdcddbcbdadbcdacdaaacbdadccdddcacdbdbcabcdacbbcbbabbcbadbbaaddaccacccdaadcdcccabddbcdaddbdbbbdcccabbcddccaccdbcbcabaddaacadacbdcdbabaaccabbcbdaabdbacdbccbccaabcacaabddacdcbacdbdbdaaabcbdccdbaaddcacccabbaaabccbdcdacdacbbdcabbcbdcccdcddcadacaccdaccbabbdaacbdcacbacacbaccbdacbaabddbbdacbccbbaadacabbabdcbddccbcabcccddbdbdaccdbccbaadaacbadcbababbacdcbdabdadcadcadbbaaaaaddcbaddbbbcdaabdabcdaadcacadcbddcdadabacadaaddadbcbbddcababaddaabcdccadccbccbdbbabaababcabdcadacaacbdbbdaadbcdddbacabbacdccbdbbdbdadcadadacaddabdcdcaabbaddddaaabdcbdbbdbdadcdcacacbddccbadbcaabdcbabadbdbaaccdddbbddaacdabdcacdbaacdcbadddbddbbdabcbcdbcacbddaccacbbcaaababbaacbaabadcaadaabbbbbdacdcdbcdabcacbdabadacaccabdbcbabcdacaddcbaaabbcdbbcacccdabcaacdcaaabadcccbaaadaadddbbadbdbccbaaddbadabcbdadcdcdbdaddcabbacabdcdbdcdabccbcbccddcaaabbcaaddcaccbbddabbdabdaccbbacacbccbcbbcabcbdddcdbdacaabadaaaacdbddababbabdaaccbdcccbcbdadaaadbbdbcabbacbadbcacacabadddccbddbcdacddbbdbabadacccdcbbabddacdddccacaadacacadcddaaadabccdddadabcaadbabdaadcbddbadbcbaddcbaabdadabbaaabdddbacdaaccdbaabcacdbdacdabaaabdadabccdbacababbcdcaccbadbaccdbcddddbcaabbaabbbbcdacdabbcdddadacabdcabcbbddbcaabdcadcaacaccddcabbbdccaadcdaacacccbacadadddaccdcdbcacadbdbbacbbadaacaaaadbcaccbbcccdcbccbcbdacddaadcbddcaddbabdadaaacbadbbdddabadbdbcdddcbbddcbbcacaccaabccacdaddbcabdabdaadadddbdadccadcccddaacbdbcabdaaabdbcabccbbabcbdbdadbbbdcaddacddbddcdddbbcdaddcbdccbbadddbaaacadbbaddbddbccaaadcaadcdcbbdaaabbdcdddbbdaccbaddcdaccabcacdadaccbdcdcadadddbabddccaababdddccaadaadaacacaddcdacbaabcbbbdaddbbcdcacaadabbbddaadadcacaddbbdbdcaacaaacdaddcbabdacccdbaccddbbbbdacdbbbcabadddcccdaadaaaabdccbdccbaabcadbdbaaccddbadcbbcbcddabbccacbcbbcbbcdabbbacaddcddcddaababdcbbcbcdbcdcacabbaaddaddadacbbaabbacaabacbcaaaadcbadddbaacbbdaaddccbdcacbadadaaacacddaaaadbcbcacadbdadbacaccbbaaacdbbaabdccdabadabcdbdbadaaaacdbbdcdacbcaaccbccbcbcddbcccadadbbdbacbbadbdbdaacacababdcacbbdaabdaddaacbddaccbcadadaadddddcaacabcbadbacadbdcbaadadbabddccccbccbdcdbbbdbcccdbaadcaadbbddbbabaabdcccdbbbaaabddcdcccaaaaadcbabcaadcbabbbaadabdbbcaccddacccbadacdbcabaacabcbabbccdcdcaadcdcabbdbbccacbcaababdddcadcadabadaddcdabbaadaadadbadbdcadcadccdbbcbddbadbadcbcbdacadbaaaaaacccdcdddbdcbddcdcbadbcacabaddabadcacaddbcaaddaddacabdcdaaaccabcdbaaacbaadbcdccccccdcbddddaadacdccbaaabcbdbadcbbbbcdccaccaaccabdabbbcbccacaddabdbabcdacacabbdcccbdacdaacadbcbaaacdadcdaacaacbaaadaacbadadaacabbbcbdccadaccbcdbdacdacbcaccacddadbbabcdcbbdabdcbdcdcaabbdbcadbdaccbacccbcccacdbabdbacccaacababcbbdcbcacaabcbbdaabcbcbddbddbdbaaabcbabcdadabbddcddbaabbcabbbababbdbcbdbcbcddccacabddadcaddadbcaabbbcbbccccdccdaadddcccadbcdbaddccdaabccbacdcdbabccddcaddbdddccacbcbbcbbcdcbbadaaabbadbcadbdccdbdabadacbcabdbcdccdbdaaaaabbcbbaaabdcbdcccadbdcbcabcddacabccaabbbbabbadccddabcbacdbcdaaaadddacabbdddbbbcccdcacaabbddadcdbabcbddbdcacaabbabbaaaccdbbabdcbbacbbadcbbbabbcabbdaddacaccababbccdbaccabcacccdbbdbcbddadbbdbacbacdbbcddbbbdcabcbdccddbabbdbcdcdddaacbcdaaacbccccbaaccddabbccdadaadadcaabcaaabddabaaaaacbbacbdddcbbbcdbbbccabaddabadbbadaacadaccadbddcaacbdbabaababcccadbddaddbacadbaaaadaadcdbcdacbacdbacdcabbcacaddcacdbdcababcbcadcaccdbaadaccbdaddcbdadcbadcbbbbdbabdbccddbcbaaaabbdddacbbabaddbbcaccbcbbbaababdbaaacaaadaccabbbdcbabaabdaddbabcddcbacacbcccdcccdaabcadaddbdacaddbbaabccbbccacacabcbadbbbdbcadbabcaddbcddbbdbbabcdaaaadbaacadadddddcbbacbacbbadcdbcddabacbbdaddcaabbbcbbbaabbbabddbbbbdaadddcbbcbdaacdaadcdbadbacdadbbbadcdccbbdcdccaadbcbdbbdcbdabcddbadadadbccdccaacaccabdbabccccdabcaabcdbcbacdbacaaacbcbbddbcadadabacccddcbdbbcbcdadbbcddabbbaadadaaacccaccdbcdccccabcbcbcdadbcdbdbdbbabacabddaadbcdaacbbdcbaadacbabbbbddbaacdbcdddcbdbbddbdacaadbabcccabcdadbcaadddbcdaddcabbccbcdbcadbbdcbccabacbdacccacbaccbbbbdbbacadbddaaaabdccccbbdbabbabbaacddcddadaacdddcbcbaaacdbdbdcbdddccadbacacdddcccbcabcabdcbcbbbadbcddccdbbcbcaacdabdbdccdaaccddaaabdddadbbabaabbdaaaacbbbbccadddbacaacbbdbbbabcbccabbbacaadadaabaabdababdaabdbaccbcdbccdcdadcbdaccdcdadaccdaabbaababbcdaadaadabcbdabacdcaaaddaddbcbacdaddbcacbcbcbddadabbbcdbbbaccabdacbaadcaadcabdddaddcbbbccaddacdbdcdccdcacdbdadcbdaccaabdbabccbaabdccddbdddacdbadbaabaabaddcaacdbacdccccadbacddbdcdcabacbcbdddcabbccadbbadcdddcbdcdbadabddabbbbdadcbabaacacaddcdddaadadcaabdacadccdccbbcccbcbbbdaadcccbdcacdddabdcbcbcbadddccbabccadbccdbdbbdabcbcadcdbbbcbdbbccdcaacdbacdbbddbadaccabaddadbccacaaabcbbbdccadbccbcaaaaabadbbbdbadadbdaccadbdbcaabccbcdbaaadddbbdcdacdbcddcbbaadbcbdcdbbbacbccbcababbddadadbccabccabdabddccbdcbdacbadbbdbdaadcdcccaacbacdccdddddddacccbbcaaadbbbcddadcbacdabbcdcbddaccbbbaaadbddaababbbdcdcccdbaacaadcbccadbbddbacbdbdcbcdcacccbdcddacdabbddbdccbaacbcdddcdccacdcdbdacadaabaadcdddacaaaababddccdddbccccbabbdaddaacdbacbdcdcdbbddaccaddbbcaadadaabacbdcbbbbabadadcbabbdabadbacddcadadcdcbdcabddaddddcbabacdacdbdcacaadcbdcbacbcdabdcacbcbddbbdbdbcccaaaadacbbdbbcaabdcdbaadaddcbbccdabbbdaddcaaabddddbcbacddddcaabcbacaacadabacbdbddbbdbdacbdbaaaccdbbcbccdcccaadabcdbddaabcaadbbbbaacbcddcadcdccbcbabbbbabbacabaababdaddaadbcdccacdbbdcdaccadbcdabadaabcdbabddccdcbaaabbddaadcdbdabbcbdccdabbbabdbabacccaabddbabacbabdcadaadddabbccbadadcdcccbdddcccbcddccbccaaacabccccaaaaabcbcddacaddbbabaccbdbccbddacadbbdaacadcddcccddadabbdbddacbbdaaddcbdbdabbbacaddacbcbdcccdcaadcaacdadddacbabbdaacabdaadddccbacdcbcdabdbbadbccdbdadccccaaddddaddbcadacacdadaabbdaabcbccaadadbcccdcdaabababaaaadcaccadcbcddcdcbaabddbbdccadcccaaabacacdcdcbaddaccabcdadadbcbdcacabababcdaaddbcccadaccaaacccbccccccccdbabdcadbbddccbbbddbabcbcacbccababadcabdadaacbcacabbbdbabbbcacaddabbbcbdbbdbdbdadadcccdbdabbadbbadabaaddbabccacbdaccadabcaddcbbadcbddaccabbccdddaacdcbdbdbcabcccacdbacdddbddccaadabadacbacddabbbdcbbcdccadccdbdacaddabdbcaccccdbbcbbacbdadadcacbbcabdbcdcccdacdcdbadacbacddccdcccbaccacabcabbccadadbbdbcabbcbadccadaccabbadbacbddbacddbcbadbbcaccddaadbbcadaabdcccacabaccddadababacddacddbabcbbccdbbaadbabcccbaaacbdbbcaddaacbbbbccdcccaabcbcaaadbdbabcbddbababbddbbccbbbcacabccdbcbcbadcddaaadaacbdcbdbbccccdaacbcacddccaadccaddbbcbbbcccacdaabcbabccbdaaacbaccaabdcbbaadcaccdcddcabbbcddabcbaadaddaddbdcbcddacbdccaddddcbcdbcacddacbcdadbddbbbaddaadadbbdcbbdcaadacbabdcabcbcabbdbadaacbbabddddcdbbadcabacdbacabdbccdabbcaabaacccddbcbdcbddddccdbbabdbdbadcacbbdbcddbbdbbddbacdcdaaaabdbdccaddbccdbbbadabbdcccddacbdbaccacdbdacaaabbcacacadabcddacabdbaadbdbdcbcdcaaabcadcdbbbacdbbccaabbaaddaaabccabdabdabbcacacbabcadcdabcdcdbbcdcbabaabbbcdadcdbcacdcdccbcaadddbaaadbdbbbbcaadadbcdaacaabadddbadccccdcabbbdcbbdcbdacbaddbcbaaaabbcbbdccbadaadadcbabdbdbacdacbaaaaaacacddadabccdbdcdabcbdacbcdccbdbddaaacbadbcbbabdccbcacadcdaabcaacdcddabdacadacacdabdbbbdccccadcadadcabdaabbddcbabdcdbbbdbcacbbdacbadbabcacdaadbdaabadaaabbaccdbabddbabaccbacbcdcdcbadadacdaddbabdabccdcacacacdcadcdbdadcccadddabcdacccdddacbbbdbcdccbddabdaaddddadbbaabdcdacaddcbbadabcbbcbdacddcddadcaaaabcdddaaababbcccdaabddbdbccbcdcbaacdcbbcacbdbbbccbccdbaccbcadaadbbdcbdbddbcaacbacaabcddbacdaddbdacbaabcbbbcbdbbababccbbcbbbdcbbdccbcbabcbdbacbadcdccaabacaaddbbbbddcbaaddadbbddbccaccabdcbacaadddbccaddbbcbaacbbaaabaadcaadacbdbdadbccdddbbcbbcaabcbcbdcdcadabacadcdabdbaacbaccaabbbbcbddccdddadbaabdddbbddbbdbcabcbbdbbadcaccacddcaccacdcccccbbcddadaacbdabaadcdbccdaaabbcabcbadabbddddcacbcbdacdaccdcaaadccbabccbbdcaaadccbccbddbcdbbbbcdccadadaabbabcdcbaadaddccdcaddccddddcabdcbddbacaddcabaacadccbbcdbcddacbbbdbccadcaaabdaddbdcdcabccbdbaaaccbdddadaadbbcaaddbbdbacaaaddbdddbbbddcdcbbbcabdcdddcbaaaabccbaacbbadcbdadabbcddaccabdcdbabadabcbccbcdcabddbbdccadcddadcdbbadbcddbdbbaccdaabdddbbddccdcbbabbdcababdbbccaaddccbdacdbcabdcddbbdbbaabbddbaacadbbbabbdbbdcadcacccbacaaaabcdabddadbcbdbbadabbccbbacbdbbcadddcadcbdbaddccdabbcdbdcabbdbabcbcdcacabcdaacdabcaccbdccbcacccadcbbbdaccbdaadbbaaadaabdcbcdbbaccddddcbadddbbbbdcadbbccaadcaacdaccddabdddcbccdbaadcaacdcbababbcdaccabacdddcabbadbbcabacbacdddcccddababbacbdcdabdbaacabaaddddabccaaddbdbcccadbabbccdccaabdacbacaccadaddbbcadcaaaabcddadbacccdcdbcbdbcbcdabccdadaabccbddadccccdbbabcbdbbcbdcbbabdabdccddacddbdbbcdbbcbaaaabdacacdddbcabcbcdadbdacbcddcacdaaaabccccdaacbcdadcbdcbbaadbdcbcccbcacbabdcdbccdcabcabbbacbcddcbacbcccbacccadccadbbcdbcabaddbbaacadbadaadcddbaddcdbcccddbbadbabbdcbbacbdadaccbabdddacdbcbaabcaadddbccccdbdbdbaaacabaaddbbbbcadccaacdacaaddbbaadcadcdcabacbbacbddddadbdadcaaaadaaabbdbdbdbadaabdaabccbacbcaacdcaacabbdbcbdbddcabcdadcbdaaaccbbcadaaddacaabddbbacacdabddbcacacbabcbddccdaacbcdcdadbabdbbccadddcadcbabbdccbbbdbbaabbcbcdabdacbdccbcadbabdccbacdddbaabbdcabcdbabdabdbaacbacdbcbabbabddcacabcdacbadaccbccdbddacbadddcddaaabcbdaabbdccbbdbcaacabaccadaddadccdcbcbaaaaabacadacbbbcdaaadcbaacbdbcacabcacccdaccbbacdaaccccacdaaabdbcbdabacbabababadcdacacbacccbdbcbcacccbbdbaabcccdcacacbaadbacaabbabdbaaccbcbbdadbcdadbcdcdbadcdcabbbdacadcbbdddbadaadacdcadcadccdbcbcdbcacadbcaddbbcddacbdbdbccaababacaababbbabcbdccabcdabccbbccbddbaddcbcddcdabddaadbddaddbdaacacacdabbcaddbadbaacdcdbdbdbaadbbdacbabadcbcadcdddbbbddaabdcaadabdcaaaacdcccaaabbdacbdabbacadbacddacbdddadcccbddcddcabcccddbccbcbadcadbcbcadbcbbdcabcbcccddccbdcbcdccddcaadbbcaccbcbbcbcbadcabddbccdbacdcbaccaaabcdbbbbdaccbabcbbbdbcbdcacacbcddbcaccdabbdddaccdbdbadaabbbcadabacbdcbcbbccaaabacdbcccabdccabcdacaaccbbaaacaaccdcbddabdbbadcbcbcdcdbcabaccacbbbbdccababacddcadadcbdddcdcdcdcaccbdccadabbcccccadbcdaddaacdaccddbdbddabbbdadabddcaaacdacbcaddaccdcdadacbbcdbccccdbcadbdacbabbdbcadbccbbabcdaabbdadbacddbbdcdcbabddaababcbcabcbdbddadadbaaacdadbcdbcaaddbbadcdabddddaabbddbbbbaacaacbcbdabccdcaaccdbbcdacdcdbadaabbcdbaadccccbadaccbcdbcdaaaadbbadadcbcacadcbabdaccccdbbdccccbaccbbdaaaddddcbbcbcbcbdccbadbbabcbbadbdddaadcabacaabcddbcdcacadcbcdbdbccdbcbdcbbbdccccdbbbbdaaddbccadabcacdbdbbcbddbcadccdccbcdbcabdddcdcaabbbcdabccacabbbdcadbaabdcacaaabcbcdadbdbcccaadaccbbbbbdbadcbbcdabadbacdbdaaabdaadbdaccaadbddccdddcbccdcabcdbbcabbddacdcdbbbadcbcbdcacdabbcabbaabacccccbdcdacbadaabcdbaadcbbdbabcaaddcdcabaadadcddcddbcddbbbbdbcdbbadaaacbccdaadaabcdacbbdcaadacbaadbdcbccadacbaacdbbcbcdccadddcccdcbdcdcaadcbccdabbbbbbacccddccdccabccccbdddbcbabadbbbaddddbcccadbdcabbdccdaaddbdacccccabcacccbdcdccabaabadcbbddcdacddcadbdcaaaacdddbccddaadaddbdcbcccbacabdbcdbacbabcacccadbdabcbdbdadcabaacdcccababbaaabcbbbdccabcacaccbddaddabadcbccabbbcdaddadbbbbabacdbaaccddcaccbddabdcacadbaaabdadcbdbbaabbdaddcbcddaaacdaacbcbbdadccabbbbacdcbdcaaabdcabdaccccccbdcdbbbccbddbbccdaabadbdcabbbdcdccbdadaddcdcddbabdbcabacabcabdcadcdbcdabcadddadabaaadbbaacdadbbccdbccddaaacdaabaaabccacabdbadcacaacddaddacaaacacacdcccdcabbcabcabcdddbcdacdcdbccacbdbdbcabdabbbadcadacccbacacbadcbabcaadcbcbdadbabcbcccaaddbaacaaabbdcdbcccacdacaacaccbaaccbddcabacccabaabcabadadaaaadbbddacddcdbaadabccdcdcabadddcccdcbacbadbbdcadccacacbbbccaddddbbdbbaabcbbdbdbddadddbccabbcdbadbbababddbcaadaccdbccaccccaadbaadababdbabacddcdcdbcdcdcdccabcbbaaabbdcbcdacccdbdcacddbabccbddcadcbacdbddcdaabdcdbcdabcdbcaccdbbacaddbccadcbcabdadaadaabbacbdbcbaccbdbbdbccdaacdaadacdcaccabcdbacbbcdddbdbdaabababaaabddbddaabacdbcbbddacbbaaacdcdbbbdcddbadaaaddddbcdbcbbccbaccadadbccabcdcadcabccbddbbbbabdcddcdddaadadacbcbdabcdddbcaddbacaabacadcdbdddcdadcdabadbbadbddbbdccdccaadbcbbabccdcbaadbdbabcaabbadbdbdacddcbcdddddbdbdddcdcccbadbcbbbbcabbdadabaccdddbbdacbcbaadbbabcdaadddacdddcdbdccdbbacbcdaaabbbdaabdabcacccaadaacbabcacbdbbbdbadccdaaddbbdcbdddbbaaaaddcddddbddbdacbdaaaddcacacadabbabdcadcdaaccbdccdcabddcdcdddbadacbaaddbbaddbbaddccadbbaddbbadcdbddbbdadbbdcbbcbdadcdacabcbcacaddaaccdaaacbccdadcdcbcaadbabbcacccbbddadacdcadbbccacbbccbcaabccacacabccbcbabbcadbccddcdaaaaddcdcaaaaababbaabddbbbdabcabddcdaadacbddadbabdadbbbabddacacadbaadbbbdabacbbaddccacddccadcabbbdcbcbcdbbabbbdcadcddbcdccdddaccdacbbcddcbcbbbcaaabcddbcdbbbdacdabbcdaadbddabbcbbacddbbbacabbdcdacbabbbdccaacccdacaacbddcdcbacdacccadbbcdcbcbdadddccdccbbccbaaddbddaabccccacdaabbccdadbddacdcbdadcbaddbbbcadcbddbdadcadcdbaabcbddacddabacdaabbbabcdcbabcacdcdbaabdcbbbaababacdccdcdbbcbcbdcdbdcbdcdddcaacdcabbbdbbaabcbcccbacbdbdddacaddaaaabadddabbabbaaaddaadcddbdbbcdaadabdaacdbcacadabcaddcaadcdaddaccdddabcddabacbabcbddcbaadbdbdadaccbbcbcddbabacbcbcbbababcbaddbcdaaddbcdacaccdcdbcbbadccddaacdcbdabbdcabbdbdccbddcddbaddabccbbcadaaaccdbbbabdcdbdddbdbbdcbabbabccdbbbdcacdbdcddababbcaabdcddccbcbbacddcdcdbabbddaacacdcddccbbcbdaacdaabbbcabadacdaabcbaccbdbacaadaabaacdcccabccdbcabddcbbcbdadbadccdbcdbbdccbdddbcdacdcabacbddccdccabcacbdcbcccbabcadccadaabbdaaaccbbcccabcbcadbaabdcddcdddaaaadcdbbbcbaaabdbaaabbdabddcdcbcbabbabaaacdbdbbaaccaccaaccbaccddcadbdaaabbdcbcbbbdddbacacabcbdccaabdaddcbddddabcddbacddcdaccacdabdcdadbbcaaadadcddbdbbdabdbccdbaacadadcdcbcbdcbacddbcbabcdacbadbdbdddbdccccdabcadcbdbbaacdadaccbcdbcdcaccacdccacdcabdcacbdccdcbaccbccbdbdaaacccbcacddabacbcdacbabdbcacbddccdcddbbaccbddcacbdbdcddbddcdbcacccadbabddacaababdadaddbbbbadccadddbccbcadcdaabbacacbcccbacabdcabcdbabcaabdacdadbcbabdddacdbdcaccbddacaddcdbcababddddcadbccdcdcbddbccadabcaccccdaccacababbbcbccbcabdaccdbacddcadccdbadcbdaabcacadbcbadcaacdbddadabcddadddcadddcddbcbdbccadbbcbbbabdbdbcdbaccdabdbdaabcacdacaaddacbdacddddbdcbbccbbbbaadddddcdbdacbacdaabbbddbcbcbddabaadcbdabbacdadcdbbcaccdbaadaabcdadbcdddcaccdddddacbabbabadacdcdcbdbcdabccacaadcccbcbcaccccdabcacdbaccbbcbadbdbabaaadbddcadccdcbddbdddddcaccddddcabcddbccbbdcdcbcacdcbbcbbcabadbcaacdcdabdcadabbacdaaddbacbcacabbcacbcdccbbdcaddcbbcdcdacbdddacdddbbcbdabbbcdcbcabbdacdcddcdddbddbbabcdacacddddbcdcaadcbcbdcbaabcbcbbcaadcddcadacdadbdaaaddbcdddbcbcdddbacdabbcabbcccdbddbababbddcabacccbaadbcbbcaaadcccddbdacbdcbdbaaabdbbddcbabdacadbacbcbbcccdcadccbdbcbbdadcdacbdbcaccbcaacbabdddcaaaabaabcccbbaaaddabadadcbadbbbdcbdcdcaabcacadbdbdadddacbcbdadacddbdacdbcabdaccbabdaaaadaaadbbacbcddcddabddaaadbadacbbcdbbdadbbbcdbcccbaccadcddabbabcdbacdcccacdabaadbddcaadaaacaacbcbcabdabdaadcbaccdbbcabaabccaddbcccdcdccadcaddcabbcbacacbdacdaabcccbdacabbabccbbdcabddbbdcdcdacaddcbdbdccddadcdcdacbbdbddcacababdbdcaaacdcaadcaccbabacbdacddcddacbbddcbabcabacaacbacdbbdcdaabccccaacdbccdcabdbdddacdbcacadbadcaaacacadcdddabccdcaacdbbbccbcbdbbabbdddaaadabbaabbacabdcadcdaacdbcdababbbbddaacacbcabacabbdacbcdcbcadcbaaacbbbaddacbcccabdddbcabddaddcadabcadabdcababdabaadbdccbacdbdcddcaccbdbbabbccbbcdcabaadaadcbacadbbbdaacaabcbbcddabdcbdabadbdbbdcacbacbcbaabbcadcabddccddadacbdcdabcbddbbcaddbbddcdaadbddabbbcbcbcadaabdbdadacacbccabcdaddbadbabadbcdabadadcdcbccdaabdccddcdcacbddabdbbbacdadacbcacdcbacdaccdccdaababbbdddbbcaddacacdcbcadcdcacbaabcdbadcdddcbddcdacabbdbdccacccdcbaccadaadcbcbcdacadaadcbdccdddbaaacbccbaaaadbbdacbcabcddcacbbcadbbbabaccadcabdadbdbdcabbaadbbcdadbbaaaacdcddbbcaacbabdbaadabbbadcaadcdababcdcabbadabbcdbaddbbbdbcdbbbbbbcdbaabcbdbbadcbcdcabddccdccbdcbbdbcbcaabbddaddbbccdacddabadbccaacccabccababbbcbabcddbcaaabaabcadacabbcabbbcbadbcdaadbccadaccacdcccbdcadbcbbdcdcbdbccdadaabbdaccaaabbbabddbdcbcbabcccbdbcdaccdaadcdcbdcaaccddddbadbdcdddcbdbcaabdddaaaccbcbdbdadbdbcadcbaaaaadccdacbbcbcadbddadddcaabbbcacacbcadabbdcbbadabccadaadbaaacabbdcbdcaadbdcbdaaacbbbbcaccbccdbacbcadcbacdaadadbabaacdbdbdadbbbcbbdadccacdcdbbcbadbcdcbacbcccbcadddaadadddcdddbadbccdcbbdccabacbcddcdaaaadcadcadcbacdbcdcbacdccdcdbdbbdbcddadcbdbbaabddadbbdcbaaccaccbbdcabcccbcdbdbddcdabddbcdbacddbbabcbabbadcadabdccaddcacdbabbaaabddcbbacadbabbdbadaaddabadaabcabcdddbbdbddddbcaccbbaadabcbbaddabacdcbbccddddcabaddbaadacbcbbbcadcdcbabddbddcbabadaaddaabbddabdcaadbcabbdbbcabdadbacdacacbdcabbdcbccaaaacbdcbdbbbbccbdaccbbcbadbadbaaaddabadcacdcaabdaccdabcacbddccbcabdbdadadaaacccdcaacddbaacdddbdcbbdaccbdcbbaaacbdacaccabbbddabcaaaddbbbdadbbacdacdacdabdcccbdaccdddbbcbadadbaadbbacaacdbdddacbcdcccbbdcccdaddccbcabaabdacbccdadbaddbdadaadbddcdbcabdcabdbbadbdcabbaaacaddcabddabccabdcaaabdcdcbdabbadabdddcaddacaaccbbccddaccabbcdacadbbcbcabccbbcbbbaccbccdbbbcababcbdabdcdacdbbdadccddddcdcaddccbdccbaccbdbacdaaabdddacbcbdbbccabaabcdadcbccdcdbbbacdbbddcddbcbccbbaadbbccbbcbddaabacdcbdcadadcdbbaaadcacabcbacbbdccbcaddbdddadaddbbccdaccbbbddbdabaadaabbbddaabddbdacbdbabcbdadddddbbccdbcaadddddddbddbddbbccbdbaccbbbaacbacaddbbbdbbdadacbcaaaacbbdddacccccbaddadcdcaaccddcaaaacaaaccadcdaacabddaccabccbcccbdccbaacabacaabdbcacccabdcababbbdcbcdcdadbbcaadadbabddddaddabdbbbcbcbadcbbdcadcbcbbcbbcbabcdbbdbdabccbddacadcbabcbadcbbabccbdabbbacbdadbadaacacadccbdacbabcbdcaaabcccadabbbdbdbacbbaabdaabccdbabbabbccbbbccbabbbdbbdcbbbabddaccbacabbaaadbdbdddddcddabcabcdcbdcbddaabcdbaadbaaaabdccbcccccbbbcabdcaddbadcaacdaadbcdccbdcbbcbbdadaaddbbdbbbbbbdadccdcdccdcbbdcaddbbcdadcaddadbdbadacdbbaddbddcbdbddbadbcaccbcdbcbadabbdcbbbacbddbbbcacdcacdcabbcaadabbadbabcbcadbdadcbabadbbddbcadadcabddadcddcbddddddaccbbdadcbdbbacbadcbcbbbdabbcdabdbabaacccbcdadabbccddaacbbcbdcdbbdadbdddcadbabaabdaacadadabdccaacbccddbddaadcccbcdabdcbacacbdacaabcbcbbbcbdcabaccbadcbbdcddcbdaaccbdcabdacbabbbcdbcadbacbccadabbddcabddcabaaccdababadaaadbadbddacdacdddabccdaaccbcadbbbcbbbabbbddbdbacbbabccaaaacdccadadadacdbcdbbaaadaaabcaabcdcbacdbcdbbdaccdcbcdbcbbdccbccdaddacbbccaddaaccbdcbcdcdaccabccdcbaaaaaadbbcbdaacbdbcacdddaadcdcdaddadcdcdadbdcaccdbddbbdddcccaadbbaddccaddabbabcbdabdacabbbcdabbcccacaabcaacbbbcddbacabadcdabdacbcbdcaadcccdcbaaddcdcbdcbcbdcaaabdbccdccccdccccaadbdbbdddbdcbdabdddacdbcaacbadcacccaabbbbbddcbcccdcbaabbdbbddabdbddbccabdacccddcabbccdaabcaacbcadaadadabacacbdcdddbbcdcbbcaccbbbbadccdaaacdcbaabccddcbdbaaccddccacdcadcbbddaddabdbbdbbcababbbdbbbcadddbddcdbdabaabacbdbaccbdbbcbbdcadacddbbaacababbccdbdacdbbccabccaabaaadaabbbaadddbcdccdcdddccbbcadbdbbbabdbdbadcbbaabacadccbacdadcbbadcbdbddbbcabddbbdccaadabbbadddcbabbdcbabdbbdbaddbdddbabdcadaabcbbccacccdcbbbcdbcdcbccccadaabbadbadbacaacbbadabcdacdbcdbabbbcaadbcadbbbcaadcabbacadadcbdbadaabcababdbacadbddccdadddaaadbccddcaaccdcbbbbcbcdbcabcbdbdccbadaadbbddaabaadabaadcabbcbbacaaabddadbdacdaaccdcdbbccbdcbcacadcbcdbbabdbbadbaabccdaaaabbdbcbadcacdccdadaabdbbadabdcbaaaacacbdaaaddbacabcbabdbbaaaabcbbabccdcdaddcbdddabababddcbbdbdcdddcbdddabaccdadacadddddaaccdddabbcdbbbcbccaacaccdbcacadbdddaadcbadbddcdbcdccdabaadabbbadbcaccdbdcccdbdcddadadbddcacaacbbdcaacabaccdaadbbbddaaacbccbbddbadcaaacaaabadaabacaacbdccdccdcabddbccbcacbccccbacbacabdcaccbccbaaadcaddbdcbdabaabcacbbaadaadccaabcacccaddabcbaddadadccdbadbaaaabbccadacbcdcbacadacbbcdbdcdbaadaaaccdabdbababdbaabbbccadacbacacbbaddbdbcddcaacacddbadbbcabcbacbbdbdaadccaaccddbabbccaacdbdcddabdbaccdcbabadacbdbadcddcccbcbadcbadadcdcdccdcbbcddbaddbcccbabaaaadbaaabcacddaabdddabdacacbbddcdacbccbcbbcaccacadaabdddddddaaababbcdaaabbdadcdabacdcabbbbdabcdcbbddcadbdbcaacbdaaccdcddcbccccbccaddddacbacbbbaacbaccbbdddcbbadbaabbabcbcbaadcdcacccacabcacbabdcbcccadcccdcbadbbdcbdcdbdaabadabdcdaddcdcacccbdabacdaabcdbddadbdcaaabbdadaacdcbbbccdabacaccdacbadadadccdcbbdacdcccbcbbddbaababdbcbaabdadadbabcaaccdcccdaacadcbbbccbcdbcacdcdcdcadabadbccbccadbdcbadbcdcdbdcdcabadadbdaabacacbdcaacdacaaaabddbdddcbbadcddcadaddadcbbbcdcdcdabdddccadacaaaadbccacbababbaadbbdbbdbcadcddcccacaaddbbaadbdbcccccdabacacadadcdcbaaacdbcacaaccbcbbabdcdcbbacdaaacacbddcabbccbcddbbbcccdbcbbaadcdbbdbbcdabacbadcadbbbbbcaabbbabcbcbbdbcadccaaccdbcbdaaddcacbbcabcdacacdabbcbbadabddabbddcaccbcbabdacaacabaabbaadccabdabacabcabdabcaabdbaaadcdcdacabcbcccaccaabccbdcdaddaabbcbdccabaddbaaccbacbacbccaaaddcdbbccdaadbdbdbadbadbddaddaaadddbbcaadaabcaaacbadacaacacadbcabaabadaaadcbcddbababbdaacdaabaaabddccaddcdccbcadabbbbcbddaacbadcccaddcaacbaddcacbdccadbbcbcaddbabaacccddaacabddcdcdbaabddbcddaddbabdcaaadccabdbaabbcacddcdcabdaddaccabddbbabdadcaacdadaddbbddaccbcbbbcccaadababbcbdadcdbbcbccdbdddbdacbcdbbcdacdbabdddcccaaaabcaabcdcccbaaacdabbaccaddbdbdddbbabbaabdcdacbccabcaddbbabadbbadcbdddadccddbdcdcbacaddadcaacdbbbddbbaccbdbbbabccadbbbbaddbdbbdcaccbbdcdabbccaabddaaabbabcdcacdcbbbdaabadbcabccbdaacdbacddbccabcdacbcbdacbabcbbdbdadacccbadcccddaaddaaabccdcaaaddbbbadcbdbdcccadbbadbbbbaddcdbcabcdbacbacbcabaccbabdcadccadcddbabbcdacdcbbbbcbadcbadaddacdacaabcdcbdbaccbadaadabcacaccccbbdbccabcacbdadcbdddacaabcbcaabcdcbacadcbdbcdddccddbcacaaddbcdaabbdbccadccdaddccdbccbcabbccacabdcbdaacddcddcadcabbadbbaaabcdccadcbddcdacddbdcaddcdcadbdcacdbaabcaabdadccbacaabaabdddbcccdaacbccbabcabdbabdbdddcabcaddabdcddcdbdbdbddcaadabbbbcaadacbcbaacaadbbdcbbabacdbcdccddbbdadacdbdbcdbdaabcbbbcdabcbdacdaccabdacbcddbaabdaccdccdaabdccbbdbbcccbdacdcacbbddddbaddaaacabdcabbadaddcaaccabccadabbaccbabcabacdcadcdadbabacddabbbbadabadccddabababbdcdaddadddcaccccbccbadababacabbcdaacadbcccbbbdbbaadaaddbbbbddbbcbdbccacbabcbdbbcaccacccbcbaacdabadcaccaacccbaabdbdacbdbccddaaadbaadbbcbabbcbddddcacacadbdddddbbdabababadacabcadaccbddbbddaabccddcdcccdaaddddabbbbabaaccdcaaabaabdbcbdababbbadccbadcaccadacdcabbaccddcacccbcbaacaccacacbcaabcacadcabaccccbddbbbcacabdcccabadbdcabaacbddacdccddcacddacadcddcbcccddaaccccaddcbbaadbdadcbdccbaccbacbddabdaddadabadccdddbbddbacabadbdccadbdbbcdbaabbbccaabcdbacdbccccaabbbabccacbaddcdaccbdbbdacacbccdadddccbcdaddadcaabbbcadbbbaacdacbadbbcdbacccdaabbabdacdbbccddcdbdbadaddabdddcbcccdbdccdbbaaaacbdccdddddccbacdaabaccbbabbcacaadccbbadccdbddacbcdabadcacbddbdddabdacaaddbacadcabaadcccbdacbbadabadabbadbccdaabddbadbcbacabcaacaacacdcbabdbaadbaabcdaaccdcbacccaadbbdbccadcbdabbdbdcbcabaccbbbabcbddcdcabadabbcbcabcbbcacacaccabbbcdbccdbbbbbbbcbbddcdbcaabbaadcdbcabdddcbaccbdbbdbdbabaabdadcdbaccabdadbbcbbbacdbddcacbacdbddcbbccbabddcddddabdbabaccddcdccaaabbabcaddcdcdaadcaccdaddbbaacdbcdcabaccadaaddaacdcdbdbbbdcbddbaadbdbccaabdaadbbbacccdddcdaacdadaaccdaadbbbddadabccddccdbddcaaacdbdbccbbdaaabcdcddaadacbabdadacadccbbbcbddbcbacbbcbcdaccdbadcdbdbaabbaadacacbbabbcaacacbcacddbdbdcbaccaaccaccbdbdbbaddbcbadaabbbccaccccbaadadbacbcabaacdadaaaadabcbdcdbdcbbddacdcddccabaacabcdababacbcbcdcbdcabacdaddaadaabbcbcddddbcdcacdbacaacbcdaadabdcbbabbbabcadbdbadcbdcdcbdaccbdbacaabaadbcddccbbbdabbadcadbccaacbccbcabcadddbadcddaaaccccadaccbbbdbcddddcbadccadbbacdadbaccaaadbcdbcbaddbbbcdbdccbbdbbbdcacdadabcccbbdbcaacbabbcdddaaddcdbcddbbbbdbbadbccacdcaccbddbbadbadbcdabccbbbabbacacaabdcadddaccbabcbdbbbbaddcdcbbbaacdadabbdabaacbaaadccbdaacbacdbdcbdadddaadbcdcccacabbcaacaabdaadcdcdbddcabadcadcbabbcdababdaddbbaccaaabddacadcaaccdcadaddaacaddabdcabdacdacbcacbdcaaacccababbcabbdadcbddbaaadacdbaacbdcccdaccaaacdcababbddabddaaaadccadddcbbcbcddcadccbacaddbbdcaabddaabdacbcbadccbcbbccdbabdabdcabddddacccdbbabcdaddcabdccdbcdaabccadbcdcadadcbdabcabdddbdabbcddabcddbdcdacbaabbcbbbccacccaddddcbcacabaaacbdbabdcacdbcbaaabcabaacdbccddacbbdcdcabbbcaddcccacaabbddbbaddacdbbacdaddddcadccbabcabdbcaadabaddddbcbdddccadacbaadcdaaabaaacbcacdcbbbbdaabccbdcabcadabcabccbacaacbbcacacbccdabbadbdaddaaddbababbdbbccdaacbcabcbadcbaabbcdccacbdcdbbdccdcdbccdabcdacdabddcaddbdbbddcccdbbaccdacaacdbdaaabcdcacaaacbdaadcadccbacccddabbaacaccabdcbbddcbdccbdbacdbbcdacdbadacdccdcccccdcccddccdcacdacdbccdbbbacbddaccadddcacdaabdcdcccadcbbdcbbaddbcadbcadbbbcdaacbcbcacadbcaadccaabdcabcbabcabcdadbdcddcacbcbdddadcadcbcbdadcaabcdcabcaccaacabdddabbbbcbaddcbbdaadddbcdadbbcadcbbbdbddddacabbcacaadadbdbbdaccdcbdaccaabdbacbcaadcdabbdaccbdbcbcabdbcdbccdbddbdabacbabcaccbabcddbaadcddbbdcbacdaabdddbbbbabbbdcdbadaabddcaccdaccbabbbddcdbbaccdaaabcbbdadaaccddbabccdcbbdadbbbddbbdaabcdacbcaadbbcdbacbbddacccaadacaaadaabadabbacdcacbadaacbbdbddaadaccbaccacaaadbcbdccccabbccadbbbdaacbcaaacbbaaccdbabbcdcabaacaaccacccddbbbdabaadacdcbccbcbcdbcdbdbdddcdcdbabbdcbacacbcaaccddcadaadcdaaacaabcbccbacacdccdbbacbbcaadadabcccbadcbdccabaadbdccadcccbcbabbbcccdcccdcbccbdcbcccbbabcadbadddcdcacdcadbccdddcdbccbccbbbccbbcbcacdbcddbbaacdbbbbbbcabbacaddcbbddabdabcdabbcbcbbcdcddbdbcabcddacddcbcabddabccabcdddabcadbbbddcdaaaadcaacbccbadbbbddcdaadaabacdaadacccaaccadcdbbdbaccadabadccbbbddcbbbccbbcbdadbcddcdacbadbccbadadadbabcbcbdddccbbcbbdbbddaaccabacaabaddcdacbabdaabdccbcbcdabcddacbcbadbabcbbddacaaacbdbbacadbcccdaabddbdbacbabbaabacabdbabbdcccddbbabdabacbbacaddaacbcdcbbcccddbddccccbcacdcdbbbbabdcbaacbddddbdbccbadcccadbdbdbdacbbdcdaabbccbabccddaabdbdddaacabacbaccbbbadbbddddbcbbbcadbccaadcbaddbabaaacdddccdbdccdadbbccacabdbadbaddbdbcaabaddcbacaddbccacccabcbcbdbcddabbbababbdbabbddccacccadcadbbaccabcaabcaddcdbbbdcddadacaaaabacbdcbcdaabdacabbddabaabcbdcacdcbddbbadbbcacdddcccbbadbcdcddddadaadccdcddabccacbbcdcbbaccdddaaccbaddbacddbabdcadaccddbbbaddaccdacbdddadbadaddbbdababbcdbcababccdadbcdacdcaacabddbdaadbbcabdcdacabcbdabdadbbbdcdaddbcdbbbcacccbcbcdcdbacddcbadabdabaabbadbdcccdcacdbacbadabcaabadadbabbddaddccaabcdddaddadcacbbdbaadababbdabdcdadbcbdccdbbbbbbadcdbcddbccacccddbbcacbadddcbcbddbadacabbadbcdbdadccacadbacbcadcbaccacdcbcdadbcadaacbacaacaccbbcacbcacccaacccbabccdbbadabccddbdcbdcabbbbbbaaccaaadcdccabbbcbababaababcadcccddcabbbaaabdcbabbcccdadccdcbccdadddcacdabdbbcabccabddbadcbcadcbadcaaabcadddbcbcbcabdccddabccdabbbdcdcbcbaadbbddabbaaaacaccadcddaaccdabddcbcdbbbbcddcccadadbabcdccadaaadbbbbdaccddbbdcdccaabbdbaadcbcacaccdaddabbdcbdcbcbaaacccbbabcdbacbddadddddbbddacdcbbbcccdadadbbacddcddbbcdddcaaabdbabadadacdbdadbcabababbdaaacbaabddacdbacbccabaaadbdabaddcdbbdcbcaadaadccccacaacdcddadabbdbddacbdaabacbbdbabcaabdbcadbdccbacdbaaabbddbddcbaacdaaabbccababaabaccddddcbbccdadcdccbdadbdddcaacbaabcabbcbacdcacaddadacadcdbadbccbdadbccabdbddcaacbdababdacccccbbccdcaccbabccdcadbaaaccbbdacdbadddddabbcaadacdddddbdbbbcccdccacaabcdcbddabccbbadaabcbdadabbdacacbdabaddabdcccccbdaaaabacbbdacbccbccacddcdaccaabbdbadcdbcbbaabdbbdcbbaaabacdbdbccdaadaccaacdadabacdcaabbddbbbdaaddabcbdcacdadaadbaaacdbdccabcccbdbbdcbaadddcdacdddbdbbcacbccdbcdcddacbddbdbcccdbccbdbdbaaccdbaabdbcddbbdcbcadabdcacdbadbdbdbdbcddababcabdcbdbabcabadcaabacccadddacabadbddaaaadacddadbdabdddabccbccbbaabadddbddddcaacdbbdbcbacaddacbbddbcaadadbccddcaabbabbbccbdbbabdbabdbcbcdabdabdaabbdaabcbbdaaaabdccabaccbaabdcbdccaaddbddabcadbdbddbbabbabcaddcdcababbdbacbccdcadadadabaddbcdacdccbbdddaccadcadbadccdbdddcdacaacbcdcbcdcdaaddaacbddcdccbdcaccccbdbcbdacdcacaddddbcbdadddcddaabbadbcccadaccbdabdbaadacacdcacccacbaddabbbcbdccbacabbcbacbbcadbabbbacdbbbaadabcacaadbdbadcccabacabbdcbbcbddddadbccacaacdcdcbcaadbdcaaadccdbdabdaabccbcacbabddddacdadcbbddaaacaacbcdcdcccadccbbcdcddacdcbacbbbdcbbabdaccbacddaadabaadadcbabbbaadadacbdaababbcdbcdabccdcaabddadacabadbdabdcadcabbcdadcacbaacddacabdcdacccccaabdadbdabbddbaccbdacbcbbcbccdbdbbccbdcadaddabbccbccdacdbcbaadaddbdbcbbbdbdcbddbaccbabddaccdaadbbabcbcacaabdddbddbbaadcaabdbcbaabbadacdbddabcbddcbaaadcacacdadcacbdcdaaabddccccdbbbcaaaabccabbcabadcdcdacccdbdbddcdacdcccdcaadddbadbacbdccccbbbdcaaacbbdadddbadaadcbdccabcccabcdcadadabbcdcbabdbdacaacdbacbcdcdcbdcddddaccbcddcabadabcdcbacbacbadcacabdbdababdaadcabbcbddbcbacccbbacaddbcbcbdababacddcbbcabcaccdbabdddcbcdbbaccbaaccccddadbcccdaabbdcdacaacdcbdbcbdaadbcbcbddbdcddacddcabcbcdbdcaadbdccabbcabbacaabcbcbaaaaccacbaabbccbdacbdddaabddccabdcddaadcbadbddbadccaacdddcabccbdadcccbacbcdababccacdbddcdccbcbdbabdddacdddbcaacbcddbddcccdcddadbddbcaacdcdcbcddbbbadacbddaddcccaaabaacdbadcacbcdcbaacbbddadcaccbaddabaaaaccadaaddddcbdbbbbcddbdbdabaddddddabdadcdacbdcbadbcdacdccabaabcdcddbcbcbabcdbaacbcbabaacbbbdadbcadbbdbacdbbdcdaadcdaabaadbcaccabdcdaadadcadacccbcdadcccaccbcbacaabdadbdaadcccacabccdbcbddcbbddcadabcbbcbbbcdbdadbbbbcbcdacddcaabcadcaaaaddbabdacabbdbdbaddbcdbbacdadbcdaddcdddcccbadcdbadddccadccdabaadacdcddaacbdbbdaddacddbaacacbacaddbcaaadcbddbaddabbacbbdbaabcdadcdbacdadcdcababcaddadcaddbadcaccdbbddacdacbdadacbcbcdcdbbdbdaaabcdcbabdbbcbbaadbdacadabbcaadbcdcbddbaadbdabacdddddccdbddcbdcbaccbcbbbacbadcdbbbbcadbabbbdbdddacdaaadadccbbacdaccaddcbbdbbbaadbcaaddbdcacaaabcdbdbbdaccdabccabbdccaabbbcdcccbddcdbaadabbcadaabcbabdcacbaccddbacacccbabbdabdcdacdddcbaccdbdacccbccacbbbbaccbdbccccbbbaabbdacabdaddbcacdccbaaabbbdbdccbdcbcdbbbcccbdbcaaadcdabaddbddddcaaacdadbdacabaaccbcbdcbdbddbcabacadacacdbbccdbcbdaddbbdbdabbabaabacbacccbdacaaddbbbbaccaabccabccddcacbdddcdccacacdccadcbddacdbcacbddababbcbbabdcdcbacaabaaaabaacadbdbbdbbcddddcbbddbdabcacbddabacdadbaccccaacaddccdddcbcbaacdcbccbdbbbccdbccabdcacdadabbdcbcbacbdddbcdabcdbcbadcaddadaaddbdcdccbcddccddcbbabdcabdcccbbbbbadbdccaabadccacadaddcdcccddbcbbabdabcbdbadccddadcbbdbbacdcddcabcbbbcacaccaaacccaacbcccbacdcabdacadaaddcbabbbcbbadbcddbacbbbbadbacabdbccacadacccaabdccddddabcbbbcabdaccbdaabadccbcaaabadccdbdabdddbcacabccbbacacbdabdbbdbadcbcddbabdbbbdbbcdbcddaddcbddacdbabaadabdccbdaaacacddaddbddcbdbccbbacabcbcbcadbdcdcdcadcacbaaacccabaaddcaaddcccbadabadbadabadcbccdcadadaadcdcdcdbddcbaddcaddaacaacabdaccbaadcddbbbdbaabbaabadaaabadcbdaaddbbbbccbdbccdbcbaacdabcddacaadbcbadbdaacbcaccaaaaaaadbadadcdbaacabaabbbbbaabbadbabaddddadcccbcacbbbdbbbcbdbdabcdaadaaaacdbaabccbbddcbaadaaccbbcddaacdcdbddcdddbacccbccdcabbbadacdbdbbdaaadaccaaccacadacacbabddcbdacddddccabbaadaccabbbcacccdddddcddabdcacabacdbccaaadcaabbaddacacdabadcaacdadddadcbbbbbabbbddbcabcbcddbbacbcdaaddccbbcbbccbacadcaacccdabdbcbddddadccbaaadbdcbdcdccacacabbbcdcdcdadababccddbcdabdcbcaadbccaccdbacaaddacabcabacdbcbadacbcaccadacddbbcbaddccdcdddbdbddbbbbaabdbdddddcabadcabdbadbacdbbbbdbcbbccddccdadbbdddbcbbbdbdcaaacdbbaaaddccadbcbdbdbcabacacbacdbcaddcbcaacdcaabcdccddabbbcddbddadcdaddcdccaadbccddaadacdddcbbbdbdaddadccbcacadacbacbacabcbbaddabcadabbbaaddbabcaddcabbddacccdadaacadcdbbbdcbbdbdddaabcbbbddcccaacdddaacaacadbadaddccddcacbbaabacddaccdacabdaaddbcbdbcacbbcbabdbbdabbaddcaabbcabcacdcbaaacadabaabbaacccbabcaababbcabdadaadaaaddacbbcdcccbabcadbbdcddbbddcdcabdabbadbabdcdacbccaddbacbdbdaccbcbdcdbcbacdbadabbacdccacabbdadcbdddcaabdacacbcbbddbbaadaacddcacddbdcbbbddcdddadaadabdaddabcbadacaaacabcacdcbdcdcdadcdbccbaacdbaccbbdaacbaccaaaaaabaccaccbbcadbbcbcbabccbccbbadbdaacdcabbddbcddcacccccdcadbdaacdaddcadbddaaaddbddbdbbabadcababdadbccaacacbbacbaccbbdbbcccbbbcaccbcddddccbbccdcbbdabcdbbadcaacdbabdacaddbbdcbdaabbabbdcbdcbbcacbcadcdbdaaabbcdddccbbbaddbddccaccbccdcaaabbcabdcbdabcbabaddaaadcbcbabbcaaacccaaacddbdcabaddcadccdaccbbcccbbabccbcccbadcbbcbcaacccaadcadadcbdcaaccdadddaabcdbcbcbaccdddcadaadabbabbddadadccdadadbadcaabdabbddadbbabcddccddccdaadccccabcdcdbbdccbbddccabbccccdcbadabdddcbcbccbdcddddcbabcadddadbdddcadbccbadacdadcadbbadcadaddacdbdbbcdddddccbcaccaadaacdabadaddddbabcdbddcbadbbaaddbaaaddaabdaccbbbcccbcddbacdabbabacababdbcccababccbadadcabaacbcdcddacdaabbcadddabcdcbcbadabdcbdcaacbdabacdcadbbadbaababdcabdbdbcdbabdbcdbcbdacaaadbddacabcbdbbaadbbcddccdbbbabcbdaacccaabdccdddbadcdcbddbabddbaddaabcaaadaaacbbddcbacabccdbbaccadcbddbcdcdccddccdbcdbccbcccadabbbcadccdcbdadbdbcaddbbdadcaaaabccbdcdbbcccdccaccbbcaccbbccccadbdccdabdbddabbbababcdddabbbbaccabcddddbbbaadadcaaccabcddabcdacaaaabbbdabccccbacdaadcbcddcddcddcbbabcabcabddbadbaccbddbaaabcdbabaacbbdbcbdbbadbbabacbdbcadadccadcbcabdabcacdbcdcdaabcdacccddcbdadcccdcaaccdaddbcdbabaaabdcabcbbbbbdbbbbdabbcbcbacbadaddcdbcadcdddadaaccabbbdaabbbccbdaddcadbcadbdbaaabbccaacbaaabcdddccbaabbabdaccabdaddcdddccbcccbabcadcccccbabbaaddbabadcccccacbdababbdccdcbbcbccdabcbacddaacdbaabccaaacccabcbabbabdbbcbaaddaadbcdaabdacabcbcbbcdcdbddabbbdbcabadacbcdbaddbbcddacdaddbdaacbacdccdbdadacdadbdaadadbdaaabcbacdcabdcdbabbbcaacacdabccbaadbbbdccbabacabaacdadddcabbddadccdadccdcabdbdbbacddbdcddacbdcccadbdcccabaacdbcdbbbadabcdaddabbadcbbadcccabcdcbcdbdddbbcdaabbadbacaaddadacccaccaaccabcbdbcbcbdcbaccbacbcddbdaacaacaccccdcdcabdccadddacdbbbddcccdbdcaccdadacdbacbdccdaaabdbcdcbaadbaddbcddaddccdddcbbbabbadccdbbcbaccbaaabadacaadbcdabbaaacdbdadbcadddbddcbaddbdbbdbcdcdcdcabadacdbbabdcdbccbdadbaddbacbabbdbccddaadddbdabcddacbdbadbcacabbaaabccdcdaccdbadaadacaacdddbacabacabcaacbcbbdcdadbcdcacabbbdbacbbbcbdccacadcddcaacaadabbadabbdcdacbadcbcbadadcbcadbcadbcccdaaacbadbcacbaaacbbcdadbdbdaddcacbbadacddddccaacbadddcaabbaabababddddddabcabdcdbadacabbcdbdcddcaaadddcdcdacbbbcbdbcacacacdcbdacdacdaabacbbbbbaddbbbdcabddcdbacccdadadbdabcccccbbdabacdccdbbcabddbaddbcbdaccdaacdccdbbcccadccadddacdbabadbdaccdbacdddbcddadcbddbcdabbbccabdacbaadbdccadcacabccccacdbacacbdadbbcbadbababbddaddadbcaacbdadbadaccbdbbccbccbdadddcdbbbdbbadbcdadcaaaabbbaaabbaaddccdababaadababaaabbabbadbcabcbcbbcacccbddcbcabcbbbbdcbcbabbdbbcadcadcdabcbdaabadbaddcdacbdadabbbbdccdbadaaabccabddbadcdccadccacaaddcbbbabccabdabdcadbbcabacabaaaacdaacdabaacbbcbdaccabadcdcbcbacacabdbbbcbacacdccddccbbccccbddbdccbbcacbcadabbadcbccabdabacbccadddcbaaacbaaddaddcddbcbcabbbdbdbbbdadcaacdbdadadaadabaacbdbccbccbbcddcabaccbdabaccbcccaddbbacccabbaabbaabbcbcbbaaacdddccdaaacbcacdcbdbdcccccabadbacdbabbbbaacbddbcdbaadadabcbcbabbaaddacccbcdbcacacbbddaaccaaabcaaddbdddddbcabaaccbcccbdbbdddccadaabdacdbaaaaacabcdadcddbdadcddbcaccdcadcbaccaadbcdabdcbbdacaabbabaaadccaaaacbadcbcbbbdddccabdadadaadbbbbacbcaddaccdddbccdaabdbdbaabadcdadabccbacdcdcaabaddbdadbdaccdabcdcdcdcddccbcdadbabcbcbbcacbccabbbadcdddacaddacbadbcdccacdbdbaaacdacbdababcadaaabddcadccdcadddbaabbadbdaaccbbdbccaacbcdaddbdcdbcadccaadbccdbcabdbacdcaacaacdabcdcbabacacadaabcabadddabccbdbcdadabbaadddcbcdacbaabdadbccdcacdcacacddccdabddaddadcaaabdadcbcddbcdccadcbcaacdccdaadaaacdbbdcdacdcddbdcadcabcdabddcaacacabccabbddddadcdbccbacacdcdcbdddbdaaadaaacaddbcaddbcbccacddbdbdcbccddbbbdabddccdbdcddbdaccacbbbdbabbabbaddbbdbcaaadccdaaadabbdbcadddcadcadcdcddaabddcbaacdcccdadcddbcddaaccbcbbcacccabacbbbcccbcdbacbbcabccdddddacabddbddcccdacadcddcaacaaacaababbacdddabdcbbcdbbabbbbabacbdadbdaddbcddbcddbcacdbcccddccbbcbadcadabcaddcdaacdaddbdddaadaccdcbdbadddaaabbccabddaabddddbbdbabcdbbabdbdcacdaadacbacabdbddccbbacbaaabbcdcbcbcdbabbddbbbabddcbdaaadadbaadcdaccbbadcdcdaacacdbdbbccabacaccbbbdaabaabdabccdbdadbbbddcbdbcabaabadbdcbbcbacbadddaadcabbaadabddbbdcddadbaccabbbbbcaccaadaddbcadcdcaaacbcdaaddcabddbaaabdbccaacadaaaddcdbdccadcdcacbbdaaddcdbccddddbbddcaaabbabccbcbacdbbcdbdccddcbccddccdddaadcadaacbbbabadcbddaadcbccbdcacdabdbbcbddaababdaddbcdbdbbbabbaacdbccccccbcadbcbcbbaddddbddadbdcbacdbbdabbabbdaabdbccccabdbbbcaaacbddccdabcddbbcbcbabcacababcabadbccbbcaabccbdbdabaadabcbabacbbaccabdaddbccabbcaccbcdddaaacabacdccccacbcdbaccbbbaadabdaabaabddbbcabbaaacdadaadabddbbccdbabcaadbabcdcbadabcacddbbaabbdbcdddbcdcdcdddbdaccbddabdbadddddabacdcdbacbdcacdcddabacdacddcacccdabddbbbbdccddddcacccaaaabdaaabaaccaadcdcadaaadacdbbacaadadbbcdbbdddabadacbbbbcdcbaccaaadbbdbbdcababadaaaaddacccaddaaaacbbbbcacadbdddbbbaaabdabaaaabddddabadadabddacaacaacbdbdddbadaddaaacacadadbcbcdcadaaabcbdcabaadbcdadbaacbcaaacbabdcaacaadbbcacadadbaccbccccdcabaddbdcbbbcaaabacadbcadadadcbcaccdababbdcbadcbddaabcacdcddacbaaabbcddaaacadacdabcaaadcddadbbcddaddacdabcabdbbddcccbbbcbdabcddabdddacddcdadbbadcdacddddbcdaacaaabbadacbbcdcdacbadcdbbdaadcdcccbcddcdabdbbdabcadadbdbaaccaacbccbccccabdbacaaaabcdcbbdcdadbccbadbcababaadbadbddbadcaabdabdccdbbcbbbaddcabbacbacddabcaaadacccacbcdcdccacbdcaadcbdccdbbdddcddbbadabcdadbbadcbdbaabbabccdcbbcaadbbdaddaabcbadbdcadcbdbdbaadbabcbdbcccacdcdaccbadcdbccdcadcdccccbadddcaaddaadcdcddcbccbbdbbcbbcccaddcdcbddbcbddccdbcaacdaaabccdaacbdbdbdcddabdbcacabcbdbcdccdaddadddbcaddccdbdcdacbbcdccacadacacbadcdcadbabbabbccdcdcadddccdbbbbbcdacacbbcaaabbbdbbacddbbcdacacdcdaaadcaaacadcbcbcddabbadbcbdacacbadddaaaddbbcddcabacababdadbdcbbbabadcbccabaabccdccbabbdbbdddcabdadcbddabbcaddaaadbbbcadbabccccdbbcbbaaccddaacdcdcbaddacadddabacadaddddbcacccccccbdbabddcbdacbbbdddcdcccaddadbcdbbbcadbadabdbdabaddcdbadabdbcadbacbdccdbbcadacaacabbccadbdcdbddcdcaacbbdbbdcadbcdabdbadcdabaccddacddcadbdabadbbdbddbcaacbcbcdcbadbbcbcddadddadaabdadcdaaabaacabccbaaadaccdbcbaabccacccbaadaddbcaccaabbaddbdccccdaacbcbabbcadacbdaabadddadcadcdbabaaadddcccadababacadcadcadbcbadccbcddbccadadddcddadcbdbbccabdddaabdbdabbaaaadcbdcddaaacdaaaabbcbddccaaaaddddabdaaacbaadbbabbadbcddccabccdcddadaaabdcabbcdcaaccdaacccbbccacbadabccacbbadacbbbdcdbddbcddcacdabdbbcbaddabbbdcddacdbdddbacdbbdabadbacabddababaacdcccddccabbacdbcbccaddccaadccddacdcaabdcbcababaadabcabadcbcdbadddabcaaacdcadcdcaacccacddaaddbdcdcbcaddccbdbdabbdaadadddcbcdcacabbbdbcddaabdccbadcdacdcbcdbacbcbdaadcdabcaaacdadcabcbacbcadbccbdbccdbdbbabdcbdbbacbddcdadcddbbadabcdccbdaadabcbbadbcdbbcdaddbbccddbabbdacbadcaccdabdddaddadbdcbabbacadadadbbabdababacacaadccdcabccccabdbdadcabcdccbdbabcabbbacbcbdbaccacdbcddbcdbdddaabbacbcaccdcbaacadcadccddaadbbddbadaddabadddadcdbcadccacbdcabbdbaccdcbdbbccdddcbddddccdbacadbcadbdcabcbabdbdbdcddccaaadacacbbbadcbdabdaddddbddabcbbdcddadcbbadaabaddabddcbcadcdbabadcbaabccaccdccadcaaadbddcaabcddbdbcaacadbbbdaacaabddaddbbbabdbcaabdcdacacdbbdcabccababbdbccdaadddabadbabddcdbdcdcaaacaabbbdaccdcabcbbdbaaadbbcbbddadaddbadcaabbacbcbccabdbdcaabbbaaadddcbdccccacdccdaaadcaccaaabcaaabcdbadcddbbdbdbdcdcbbadbbdbadaaddbcddcadbaccadaddddddcadddddcdbadadcbdbbccacabbbddcdbcbcddddbdbaacaabadacadbdddcadacacaaadaddccacaccccbdbdbbcacccbacdcdacdbadbcdcbcacdabcbaabdcdabacdbbbadaddcadabdbccddbbbdbcdbdcbabdbdccdccaaccadbadaabaadaacccacbcaaddbcbcaadbbabbdbcbbcabbdcdcadcdcadcccdccdabaadcdcabdadacacccccaacbcabbcaccdadbadcbccdaaabcbaabbcaccccaddcbcabacdbbabacacdcbadabadaaadadcdacbacddbabcbddcadcbbdcdcccdcabcddacbadbdccdabbabadbdbcaddcbddddddaababaaadcaccbadcdabaabbabbcbaadabcdddabcccdccdabaacbdcbcacbbcddbdbddccbbaacddbdcaccdbcbcadccbddcbdddabddaaadcbcdabaaacdbacdbcdabbcbcdbbccabcbdcabbbdadbdcadbabbbbacbbbdbbdbbaaadaaccdcaccbbaddacbbbbbcbabddabcbcbaccbaddcbadacddcbbbdbcdaddddabcaaabcabbbcdcdaacdcdaaccaddcbabccbcbddbaacacdaccdcdabbbcdddabbcccaadbdaaaabbbbadbacddccbcbbbbcaabacddbdcddbbacccaacabdddacacbcbcdaadadccadbdcabbcaacbdccbaaaddcbaaddbdaaacabdbaabdcadaacddddbabcbcbbcdacbbacdabcbbdacdcdcdadbcbdabbbaaadbcbaadcabababddacacbabcbddcbadabcbccadabbcdcaacadbcbbbabdccabbdaacbaaacddbcabdcbadcbacbddbadddcbcccdadbbccdcbcbdbdabdcadbccabaacbdbcabaadbdbaaddadbcdcccdbaaacddbddbdacabcdbaadacccdcddababaacccbdaabcdaadcdcbaaabbcdaaccccaadbbcabbbbddbcbcaacdcaddbbbcbdcddbcdacdbababcacbacdddaadbcabaccccdbbabbbbadccdcdcbbccddbdcaadbbdcadddacbbdabadbdaacdddcbbbdbbadcabdabcdcddcdccbddbdcbdddaabaababaaddcdbacaadaccccbcbbbcddddabdcbbbcdcacabadadbaddbabaccaacdbddcbaaccdbcaaaadbdcdccdacbdddbabbcacabdacacaabbbadaccadbbacaaadcdbbadcaaadbdabdaaaadbccdbdbcbccbadbaccacdccdaadbabcdcaadbcdbabdbbbddaaaaabdcbcbcddbdadcadddbcbddabcbacccadbcababcddadadbdcbaabdcaadacbcdaacccacdaadabddaadcbcdabaaaddbaccbcddaacbbcacbaddccadabaaccbcbcbbdcbaaabbcdbadadbbdbbbdccaddaddcdddccccbbadcadbadabcabcddbacabccbcccdabbbbdaacababadbbbadbbbcadbacbbdccdccddacdbbbbacbabbddacbcabdbddaadcdcccdbbcbaaadbabddaadddbbccccbdacbdccccabdddbcacccabcaadaccaabbdcababdadabbaaccaccccdddcbccccbdbdbbcaadabcbbddabbaadabdbdadaaaadbcdccbbdbcdbbbdccbccadaddccbaacbabacbadcaadddabcabbcaacbcabddccdbacdbcdcdbdbbdbdbcadcadddadacddbadbadaadbcbaacaabcadaaaddcbcdcacabcaccaaddcbdcddbaccacaccdcdbcaddaabbcbdbdacabcdbaacbbbdddadababcacbaabbcccadbddcbdbccadcbcabdcddcaadccdacdabbaacdbcbabccaabdbaddccdbcdbbddbaaacaadccdcbdaaccbbbbaabddccbddbadacabdddbddccaabaccddaacddacacccdddadbcbdaabdaccbbddabacaaccabaaddcddbbabaaadcdccacdbbbddbcdcbdbabbaadcdaaaddcbcdcdaabdddbacadcdccbdadbbbdccbcbcdbacbdbaddacbcbaaccbbcadcadcbbdacbdbbadcbabcadabdcabacbcbbaaaaadaddcacddbccaacbabbcdadcaddcdbabdbabddaaadbcbaabdbadcacbacbabcdabdbdbaccdcccbdcdccdadbbccbddbcccacbdcaadabbcbaabacacabaacaabddaadaabccddaadbbcbbdaacdddbabbddaccaacccaaabbcabbdcbcbabcabcdadacabdcbcbcccdddacacbacddaccacdccdccadcdcddccbbddbbbcccadddddabdbdddaacdcbcabbacdbabdbdbcdadbbcdcddbadbcdacdaadcdddadaccbdcacdadccdbaabdccabccaaddaabaddbccbcbdbcbaaaccdcacdbdddaabdccbbcacdcdcbdbdcaabccccddccdbcadccbbbaccabbdbbbdbdcabcbbbadddbbcaaaaabbdcbaccddbadacdccacadcdbbabdbcaccabddddaadbaadaacbbcbbbdddcaadbbbbbbddbbbaaaacdbddadbcaddbacdbcbabcbdcddaacbdccbdddcacaddbdcbbbcbbbcdcdaaadbdbabdbbbbbcaccbbcccccdbddbbcbaacbdcdbbcacabcddccdbcbaadbcbcababadbcccccbcaadcbbbcdcbdacaacbababacabdcbcacdaabbcdaacddbbcbbdbbcbadabbabbcdcabccacdccbadbdbdbababccdacbccdabbbbbddacbdbadbacbbddaaacccdcdddbaadaccbbbabacaadccbccacdddacccdabdcbacabdbcbdcddcdbcacabaaddbdcabbcbccaadaaddaddbabaccbaddccdcabbcddcbdacabbdaaccdddbcaaaacdcabcbbdaabcaaacdcaacabcaccaababdcaaccccabbabbaabcbcbdababddbdaaaabadcbacaacddddddbcbddbbadbacadbacbcbddaacacbadcdcdbbcdabbbcbaadbcadcacacdbdccdbababccccaacdddabdddbbdddadcbbacdadbccbacabbadcaddbbabacbcabdcbdcdcdbdcbacbccabbadabbbccacababbcaaacccccdccadabbbabcbbabddbbcdabdcaaabbccaabaacbdaabbabbbabdaabaaaadddabdbbadcabbbccdccbdddbbbadccddcccaccbaccbacdbcbdccdacdcdcdacdaadbacddbabcbdcdaaacbdcadbabadbcbcbbcbbcdbbacdcdccbddbdccabadcdbaadadbbdcadadbbbcdbacabadccaacccbccabcabbadaaabbabbcbcaaadbcdccabdbdbddabcccacbdadcdabdcadcabbdcabccdcacaccbcddadcbbdcccdcbdcdbabadbccdcabdbbdabdcccbbbaccddbadddacadbaabdbdaabbdddbcaddccdbccacacacaacadbbbbdaaccdccdcbcdcabbbbcdccabdabcbbdabbcbcdcdbdbbcabcadcabbdddcaadcbcccbbacccdabbcbaabcbcdacaaddbbabdbadcababddbdbbcbcabcddbdbacdcbbadabadccbabcdcbdbadbdbdbbdbcadcbaaacdcccaacadcbbbcaabacbbddbcabbbccddbbccdbabdcadbadaabbaaadbcbaddcdbbbbbadadabcbccabbdddddcaabddbbadaddddcaadadacccbcaaccbcdadbdddcbcbdcababdaadbbddbdbbcdbbdacbdaccbbdbadbabbccdccddbcabbcbcdbabbaacdbddacdacabdcaadabadbbbccbaadabcdddbadaabddddabbccdbdbcbcdabbcddadcbabcbbcbdaaabadbdcddbcacdddabdddbabbccdddbbacaacbcaacacacabdbbbacabcbcabdbddbabbbadccbdbaaadadccadaadbdadadadcdbcdabddccccbddcaaaaadcbdadbacbbbcdbbabbdcacaabdbcddcbdcbadbacbbdddcdcbdacbdabcdcaadaacadddcdbbdaabbbdddaadaacdabddcdadcccbaabcdabadadcabccbacadbdccbabbbcdccdcadbaccaddcccdbbccadacacbacccdbccdbacbdcbadadbbabcdaddbcacadcbbabbaaacbccaddcdacbbdcbdcbbddbbcaddcabddbababddbadbdaabdabbbcbdbcbbbcbbdcccdbadabcddbcddaadbcabdccdbddabcaaacddacdbbddadddcacadcaabddccbbbbabbcdbcacbdcbcbddaaaabdaacbbbbabacbccadacdcadcababbaaaacccddaacacdaddcccabbdbccbcddcaddadaaacdbcbadabdadbaabadcaddbaabcdbabacdcbdbdbcdcccaacbbdbdccbdbdbacbabccadacdbbbcbcaddbdabbbbccccdbbaabdbacabadaddbbdaabcacbadbdbcdbbaadbaaaabccdbaacbcaadddbcdcaccdbbacabcddbadcaadabcaacacacdadcbabcbcdbabdbccacdcdccaacbddbbddcaaacdadccbcbadddcbddabadaccdbdaacccccccbaddbbddadbccbbccdcdccabbddcaccbdcaccddaddbdbcacdbbccdaaddcccddcbdbadbdcbcbbcbbaaacbabbddcdddacdbdbbacccddcbcdadaddbabdcddcdbdcaaccdaccbbcbabddadccdcdabcbacbddbacaacdcabaadcabdddaacbddcbadabaadadcbcbbaabbdcdacdcdbcbdccbdbcdccbcbabdcbbadaccdabababbbbcdadaddbadaccbccbcadddbcbdcacdbbbaaaaabbbdcadabcdcabadacaddaadccddabcbabcbacdababaccdccbbcaccacaaddccccbcaddcddcdcbadbcbcbcbacabbaacbdcadddcacbbadaabbdacdcdacddabaaddcbddbddaababbaabbabddccadbbbadabbabacbbabadbdbbdbcaaccbcaaccccccacacaabaabbbddbacabddcdacccbdddbcdaabcdcacacacdbbdabaccbcdcbcaadaaaaacaaaddbcbdaabbbcbbadcbdabcbcacbbbadaabddaddcbbbadccbcccdcddacabcacbadcdcccdaccbdddbddbcddbdadaaaababbbacadbcdbcbadbbabdcdbabdbcabdcadacbcdadcbbbdcdcabbadbcabdbddcdcabccdabdbcbadcadccadbddddaacddddabcadadaaabdabdacacaadacacbadbbbcaccdcabbbdbdcbbddabbcdabacdbdbacaabcdabdbdadacaccaadbbccdaabdadbdbbbdbdddccadcccdbbaaabacbbbcadadacaabcaaccbabbdbacabbbdabddcbcadaacdbacbbccdaaccacdcabdbddabadddbbcabbcbdddddcadddcdbcdabdcddabddcdbdbcabadcdcacdcdaccaaabcacacbaddacdcaabaabbcaccbbbcccadccabaacabdbdadcccdbdccadbcadaabbbcccadacbacccacabadaddcaacbababcdaccbccbdbcdbdaaacdabaabcbdadbcdabdcbabadccbdbdccacbbcdcaccbccaddcbbabcbcdbbcccacdcaaabbbcdabaaabbbadcababadbdcccbdacdaaddddccaabbabdddbbbdacadaaaccacbaacbcdcbbbccdbadbccbbadccadbbaacaddccababadcccddbdacbcccdadbabbbaacbbddddcddbacdabcbbdaabacaaabbdabbbcccbbccbadabbddacccbbbccaddccdabbcccdaaaacbdbaabdcabaccbdbdcdbaddbccdbaccdabcabaaadcdcdadadcdcaccadacbcddbacaaaacbdbdbcdaccdbdadabaacdabdacccdadabbccdcddcdbdabbcaccabaabbbcdacccabacbcadcadaabdbaccabadcccdbccdbdacdacdadccbbccbabdacaaaacbcacbccacdadccddbbccacbbdcadbdbcdbbbbdbdababbdbbccdbdabaccdcddcdbabbadbabbdabbbcbcdccdabbcdcddabacadddaacabdddcdbddabacdbabbddbccbaacbbddcbdbcabadbbadbdadbbcaccaabdccccdadbaccdbabddacdaacbaddbdbbbadabdacacbadadacdcccabbcbbcbbbdbcaaccdaccdaddacbdbbdcdacddacbdcbdbadbcabdccaccaddbbabdbaaccbbaddcaaacccdbbcbbcdacdddabbdaabcbbdcaddaaacdadcbddcdaabccaaddacddddcaacabacdcaabaddaccbcacabcdcbabaacbbddcddadcdcaddabaaccbddcacddddbdbcbadaabaadcccbababcdccdacacbdbbccaadbddacccdcbbddcabcbbdcbcdaacaabcaaadcabbcbccacbddadcdacadbcccbbabaacbdbcaadbdcbcabbcbdbaaacaddabacacdbdcddddbdddbccabccdacdbaacabdabadbdadaccdcbdccacddbbaadbbdaaaaadddcadbaddddbcadacdbdbaaacddbcddbcabaddcadaddcbdbcddaadcccdacbbcdddcbdcccdcdbcaaabdaaddaccadddabddbdbaddaacacdddccdbdddddccdbadadbdabdaacddbdccddbbbbcbbadccdddbcccdbdabbaacdaaaacdaaadacddddacdbacbaacacbcadadddadaaccbcadabdadcdabbdbcabddbcadbabdcdbbbbabbdbbacccdacccbbaaabdddcbcddbcddabaabdaccbdbcbdaccccdbaabdadadaddbddbbadcbcabcbadaddaddbbccaaccbdaadaaabbaaabdacbabaabdacdcaabbdccbbbdbdddbacadcbbdabccccddacdabdddbbbaccbdabbadbdbcacdcadcdabcbacccbadcbdabbacbbbbaabbabbadadaaabbbacaccacdbacdacabdbabbdddcbcaccaacaccaccccbbbcbdabdbabdbdbdacbcaadbaadcbcacdbcabbdadcacdaccacbbadcdbdcbadadccddbbcbacdbadbdadcdadadacbcdbcbbbdadabaadcabadddbbbadbdabdbbbbbbbaaabadcaaddcabdadadbbbcbbddaccaacacddbabcdabaddbbbdadacbcadcccdcddbdcbddbdbdbbdcbaaabaddccdadaabaccdcabcacdabaadaddcadbbaacbaccdbdbaaaaabadccbddbaabbcbbcaaadbdcbbacddbbbdbddcadabacdbddaabdaabcdcbcdadcacdcabdddbdbbcaadbcbcababcbacbddcdaabadbbadbbbbddbcddbcdbdcdcbdaddcdabbccbaaabbccdbdccaaaaadabadcadcdccbaaabccacaabddadcaadbdacbadddbcbacacccbccacddccdcccddadacdadacccbcbcdbaaddbbccdbbaccbdabbcbdbccbbccadcbbbbbcbabcbcbdaaaadacddabcccbaddcdbdabbcbdcdadcbcbcadbbcddbdcdaadadabcbaaabcadaacdccbacaacdcdcacadaadbdadacdadabcacddbccdaadbcdcadaccbbddbacabaadddabcadccadbababcacaddbbadabcabadcbdbddcbabcbddcbaddbadacbcacaaadcaaabddacabbadbdadabdabcadcbcdaddbcaadabdaccbabdbdbcaaaddbadbccbabbaadbddddcbaaccaaacadccdacaaddbcbadcbdabdacabbadccbdbccacddabddbcbdaaabbbcbbcddacbacdcddcdbaadcdbaadcadacdcbbcaacbccbacaadcddaabddaccaddaadcbbbcdbcdccdbcdcbaacdddddcdadcccadddbddcbadbbccabaccabbddcdaaabbdccabadcdbbdcbccabcaacdbbdaccbbbacdaaacadbbaacacdabbdcaadcdaddaaddaadcdbcacdbaaddbaabbddbbbabbcddaacabacbbcabdccacaadcccbbcaacbdcabccdcbdadbbdbbdddcaaccbddcbbdddbacadbbbaabaacabdcadbacccacadccacdccabdadcbbcadabacadbddcbbbdbdaabbdcccbcdbacdddabddaaaccacbbbcadcadaacabbaccccdcbccbbcadccdabbddbacaccdddccbcccaccdacbcdbdadabacadcbbdbbdbbacaaabbabccbccacadacbdbcbdacdcdddaaadbddcbdabdcdccdbaaddaddbcddabbddbbdaacddbbdabaaacdddddbbdaddacacaddadcccbaabbaddcaaaabcccbdbccdcadddcdbbbbcdcbbacdcaddbcbddbcbdbcdaaaabbabadabbacbdcaacbbbadaadcbbacbbddbcaaadbcdbabdbdadddbdaddbcdbcdbbdccbbdccdcbcdcbacddadbdacdcdadbddcdaaabcbbaabbbdbbddccaaddccdcdabbbbbddcdcddcdadacaccdabcbdccabdbdcbadbbdadaaddacacdcaaabbbdcbcadcccdccadbdbccabbbbabbbbbbcdddcdddbbabdcdccadadadadddacbaabcdabdcadabcddbaadddcdabcabbbacbdbdbaabdbcaadbdaabdabdbabadbdcccbbbcdbaaccdaadadbbabbabadaadacbacaaaccdddaaccadbadadaacdbabacbabbbddcbbabbbcbdcdbddbcdbddcdccccbbcaadcbdcccabbdcdcadabccdacddbbabcdadcbbddbdaddcadcdacabbaaabaacdaabbdbcdcbbcadbccccabcbcaaaacdacbbacabacccdddaccbccadbddacdddccbdbbcabaabcbcabddcddcbdddbbdacacbcaddbbcbbcacdaaadbdccdaacbcdbddbbbcdabadadcacbbbabdcdacaccbbbbaaadaaadbbabdaaadabbbabcacbdcbdbdacdcbaacbbaccccbcaabadbbabbdcaddcaaaadbcdaddccccdcacccbcdbdadacdbcccadcbddccadcddbcbcbcadddabcadcbbdddaddcddacaaddddcbbadaaddaaddbbbdbbabadabdcbcbcaaddbbddbdcaaaaaddaaaddbbddbdaccbabdadbbbacccbccdbcadbccabcabbadbbcbaabdacadbcdaabbaadaaadcdaddaacaacdababbcacbcbdaacaddbdbbacdbaabbcbbbcbaaabaaaadcbbbbddaccdcddcbbddacccdbdadcddddcbaccccdabbbbddcbdbbadcddbadcbcdbadabdabdbcadaacdcdaddcbdcdbcadabdbdacdacadcddcbbbccbcbabdaccbdabbcbcbaacbcbdaabcadcdbaacdcbccdaadaaacbcdbcbababbcacbbbbaadaccccaacaaabbbcccbdaaacaabadaabacbbbcdaacbcdaabdbadababcaccdbbcddccbbcdddccdbaabcbdaacbaaabacbaaddbacdddacdbccaabadcdbacbbddaaacabaddaaddcdadbbbacabacbbaadcccbaddbbddbbbacccbcbadcaacbaddbcadccdcaaabcaacddbabddbadbcdbcdcbdabcdabdddcdcdbccacacdccaddcaacbdacdcaacabccabddbbbaabddbaccdabdbaacbabbcaabcaccddbbcddcabcbdbdbaacccadabdaddcdaadbdcabbbcbddddcaacbcdaaacaabbccbaacccaacdbcaaccdcbaaacbbdbccacbacbcadcbbbabcdbadacabddcdadbbaaccdbbacbbdaabcdcdacdacaaacbbdcccddcbbddcdadacacbdbbcabdccddddcbadabdabadaddadcaacaaaccdbbabbaddcababbabaaaabaaddabcabaaddaadabacadadaaabdbbbbbdcaaddacaabdcbdbcdcadbccbcbcccbddbadbdaaaadbaacadaacaacaaacdaabccddbcbdccbadabaddbaabadacdabbacdddadbabaacbadddddacdbdccacbabbbccaccbcbcdaaaacdccbcdacdabcbcabcacdaadaddbcddcaabcdaabbdcddbcaabddcbcdcbbbbbbaddbdbaacaabadcdcdbbaddcccdabcdabbacbcdcccbaabdabdcbcdadcddcdbdddcaaadddaaadbbabbabcbbcdbdbccddaaddbcbaaddbbcdddcccaccaacdbbbaddddbdbcdabcdbcdddcdbadcddccccbdadcdbabadbaaddcdddcdcbcbabdacacdcbdddcddccacccadaddaaabdadaadbdcccbdaadcbadddcbdcadabbabaabcadaaaaacabbcbcbccbcdbbccbbdabcccaccbcddccdcdcabdabcacbacdbadbdddddcbbacccacaaaddcccdcabaabcbdbbcdaccadabcdbacadaadbbccaaadcddadbabbdadacdabcbdadaaaabddcacadcaadcddbbcadbdddcabccaadcaabadadccabcadacdcddbcabcbadbaaccdccababbbdbddcadaccbbdaddbdcdbacdbbbbbbaabbcbaabcdccadcacbcddddddccdcaadaccccbacdbcbcdcadcddacddcccadccbbccccaaabdccbadaadcadbdbcbdadadbdcdcbdccccbaddbacccacaaabbcbbabdbddbbcbddacadcbbddbbcabdddcbddbabbacabaabaacacacbaddbddbdcbacbdcddcbccccbcaaabaaddaacbacbbcacbdbbccaddaabbdcbdbcabadcbadcbbcccdddcdbacbdacdcdadcaadabccdabcbcbdcdbababcccaababdccabcdabcbaddbdabdabbbdbababbdbbdbcdabcaabcdadcaabcabdddbdcdbbabddbcdcddaddaccadbacddababddcdbbadadcdbdacaabaaabaaabdadcdcccbabdbddcaacbbacadbdacabdcaaddcdbdabbbbbbdcaabcaaacddbddbabccccddcacccccdaddddbadbdadaaddbcdaadccbddadbacbddbacdabdbcbcbcccbdcadbccddbbdabaaddbacbdcabdcaaaaaccbbbadbcdcadccccdbcaaddcbcacddbdbcbbcbaadccccdbbcadabbbabcbbddacdadabaaadcbdbdbdbbbdadddbabdacacabcbdadaccdddbbddabbaabbdabacddabddcaacdbcbbadbbaddaabbacccdcacdbdbacadbcccbbbacccbacdccbacbdcbbbccbbcdcabbbbbccabbdabbadbcbaabbcdbcdbabadbaadcbcddaccccacaaaaabbaaddabdbdcaabddbdcbacdacdbaddabacadbcccdcccaacbddddbdcbcbcaddbdcabadddbcacddcdacbbbddbabbaadaccddbccaddbbcdbccdbabbacbbddbbdbadbaabbbbacdbbddccbabdabbbdacaacdcdbbbbadbcbccccbccbdadbadccaaacdcddcadacadadcdaddbaccbddcddddadddabbbbdbcaadbadaadbaaaadbaacaddaccaacacadacccacacbbbcbcccdcbdaababbbbaaacabdabbcbadbbcbdbbcbadbdcdbadcaacdcbdaacdaaaadabaadcbacdbcccddcdabbcacdcadbcdbdaaccdcccacaaabcaaccacacbccdcdcbcdcdbcaacaacbadcacabcbbbbdabccdcbcdbdacccbdacaccdcabadacbcdaccdcacbbabddabcbddaddcdddbababcabcbbbdacbcabcdcbcdabbbccbbddbaacdbbacdabbcccbbadacabccccdbbacccaacddcbdccaabadcbaccddadabccacbcacbdacaacddcabaaabaccdccccdbbacccadcbabbaabcbdcbccddabbacddcccbbadaacbbbbddcacbbdccbaabddcdcacacdbccbdbcdaacbaacbbcaaacdbaabcbbacabbacdcadbbadcbaddbcdbabddbcabdaabcccdabbdccbdadbabccddabdacbccdcdbcdddacbadbabcdaaaaaaadcacddcddaaabbcaabcddacdcdddaabdddbcbbdcdacccccaacabcaabcdcbbaaaddccdadacaadccabccddadcbccdababdaabcbcbcdcabbcddcdbbccddbadabcbcbbbabdcaddddaccccdcdddccdddbbbdbcdcbdccbaaabbcccccdddabdcdbccbbcbdccaadcdcabccdcabcdaccabcaacbbcddcbabcabacabaabcdabdabbcccaacaadaabcbcdcacdbdbaddddddcbbbabadbddcadababcadaccbcacdaadadcabcccaaaaddabacabaacbbbbdacbadacbddbcbcabcbabbdcaaccbdadabdaccbdcaaadbabbaababbbdbbcaabbcdbbabbcddccdaddabbdccbcabbbbabacbadabaabcadabcbbccdccdcaddccaddadaabdbbcbdbbababcccdabadaabbbcdacbcdacaacbbbccccbaaabdddacddcaaadbdcbbadbadabbacbdbbbdccacddabcaaacdddcbbcdccabdadcacabcacabbadccabcdacacdaabdaabaddcccdabcdcccabcddbddbacaaaccddadabadabccdddcaacabccbadabaccdaabcbbddddddbcbdddcccdbcdabaaacbdbcdaddadabbbbbacdddbabbcaacbcdbdcdbdcdddcbcdaadbcabacddccbbddacbcdacbddcdaaacdaccbcbadbcbcbbdadcbadabacacccccddddaabdccdbdddaaddcaacacbbbabccadbacaaabbcdaddcadbabdadccaabcdddacadcdbdcadbdcddbadbaddddcaadcbaaddcbabbdcbdccadadaacabbdaaaddddbadbccbabaabaacdbbbdddbdcadddbbbcdcbbccbbcdbbbddbaaabdbbcccbbadbadbdcddcbddadcabdadadddabcbcadcdadbccacccdcaadcaddcaccdcccdbabdcdaacaabbabbadcadddbadbdcaacaaacdaacdbbacbadabcbbccacaddbabdccbdaabbcababcadaccdcbaadbbacddcdabbdabdcbcddbabcadcbaaabbcdbacabccdbacdcabcadacddbbdaadddbccbdaddddbbaddcababbcaaccdbbabdbdabdabdabbcabdcdbddbbbbaadcdddabdacdcdcccacdcdbdbdbaadbbaaacadaacaadcbbcbabddccdccdaaaddcadbdcabaaabcacdcbadbabadddccacdbabacbddabdbbddcacabdcdcdabddaacabaaacbcdadbbadaabdbcaacdbbbdacbddabcadadbccdccddadcdabcddccbabaaabddccabcbcabcbcddbbccdcacbbbadabbcabdbccdadcaabdadcacdcddbbadcdcbabcacdadaabbbacaadbacdabaacbcbcadcabddbddccccadbacabcdbbdaaacccbbadbcbbbbdcdadabcdadadaacbbdbdcdbadbaabbabaabddcddbcbadaadddabadcaddddaaadcbcadaaaadbacdcbbbcaccaadaddccbabcacbbbbdbbcdaaabbbbaaccccccbaadacdbbacbcabcdaadcacdbadbbdbddcddcadaaaacacbabdbdddacadcacdadcabddababbcadadaaddcdcddbccbbbbacabcabaaacdaddbbbadccbddaabacabadabdaccdacbcbabbaabbdbcaccabdadabdcccdcbacabdccddcdcbaabcabcaacabcabaabdcbbdbcbbdbbdbaddbaaaabdbbabddcacdddcaadbadcdcddccbcadacaaccbacdbdbbccdabadadcdabbbddaacccddabdcdcddccddbbabaaaccbacbcbdcabddcdcddbbcbabdbbdbbaadcbbdacdddccaacdcaddddaadddcbaadaaabbabbddbbadaccdcacacbddadbadacadcaaabcbbccddcbdbadcccadcbbcdbbbadddaccddabbbcadbdcdbcbbcbdccdccabcbadcdcdbccacacabbdacdaddbacabbaabbdbdccbbbddadccdcadbacabcbadbbacabbdbadadaabcbdacbaaabddadcbbaabcbaacbadcaaccccbddddccbbbbdbcabbdccbcacccbbdcadacdbdcdbabaacadcaddcdbabddbcabbbdadcdaaddaaacaaccddbcacabadaabddbdcdcbcbcacbdadcddcbdddcadddcabadbdababbddcddcdbbbadaccccdbcbbdcabacccaccdaacbaaacdbcbcacaaabcdbccacccbddabadabacbabbccbddadcbaaadaadaddbdbbaaaddadacbbaaddcdddccddcdacbbaadccbabcacadbcbacdaccdbbdadacabcccbabcbaccacdcacabcbabbddacbaddddccbdddddcaaacacbcaaacdaddddaacbdadacbdccbbddbdddaccaabcdddbaccdabadcaadbbcccaddbddabaadccdcacadadaccbcccdcacdadcbcbadccddcbdbcbaccbbccbcdacbdcddaccbbcddacccbdcabdcacdcdacaaaddcbbbabbabdbccbaddaaddbdaabdacdcbdbbbcadcbbdbcddbabbcaacddcddabbdcdabcbcccdddcdbadcadbcccdadaabadcbaadbcbacbdbddbcabacbcbdcbcccbdbcbdddbccdccadccdcdddbdaccdbcacbbccbbadbddbabddababbcacdddcdabbabddaddccbcdcbacaabdcdacadbabcbddcdababccbbccdacacbdacacbddcacadcdcccdddaccabaddddcbbbcdcabdbabbaacdbbacacdadaabaacdccaabdbdcaddbdabdbcabddddacaaaacacaacacbccccdddacaacdcbaabcdbbdcdaddcdbabacbacdbbaccdddcabaacacccbaadaabddbdaacdbaabdbdcdbacbacbaccccdbbcdbbabdddaddbadcccdababbabadbbaccbcccddbabcadcdbcdaddcbaabaddcdbaadcdaadacadccbccdcbabbbbcbbcbdacacabdccbabadcccdcaacdbadcbdbaacddccababdaaabccbbbacdbccdcbbcdbabdcaddbadaabdaccaaacdbadabdbacddcaacaacbabccdacbaddaadcadcbcbdaddaaaabcbaaabdccbdcbdcccdadbdbdccaccacdbbadcadcadcbbaaddcdbdadacbabbaccadbdbaabcabdacaaadcccaaacccbabbbccaaacacaadabcdcbbdbaacdcabcdbbdddaadbabdbdbbbaacaccdaadbccaadccccbcacadbccdacbcddddddbadcdcaccbcdcacdcacabacadadcaaddbbaabcabcadccadbaaacabdccbdbbabdbccdbbccbccdddbdadadcaababbacacadccdbddcbabaacaabcabacbadabaadadacdaccaacbdbaaacbccadcacabdcbaddbaabcdaccdbcbdacbdabccddaaadacccbdabdadccacabdadadcddbdbadccdcdadaabcbdbdabbbcbbdbcbaddabddabbddcacaabaacaabbbadcbddccddccbabbcdbdbcccdacaabcdccbdbdbdabaaadcaddbbabcbdbdbdabbccabddcbdcbacddaadcddbbcbbbbccaddcbacbddbdbcbcaddbdbbaccadbabbbbcdaabbadbbabaabaabbbddadbcbdbbbcbaaaddbdbcccccccccaadacdcdcbdcacbbadddaacdacdabcbabdabcbdcbdbbddabdddaadacaacaadccacaabdadaaadadbacdcdbbaacdcaacaacbdaccaccdadcaccacbddabbbcbccbbadabdadbabcdbdaacbdabdcabdbacddbbdaabbdbbddccbbdddacdaacbaccdcbdaccbadccbcdbcdbcbccdddcdbdbabccadbbadbaccdbdbdbccbbdbbdcdbdcacbadbdcbacabdabacacaaabcabbcdadccabdadcadcbccbbdabbaddadcccabacdaaabdddaaccddbabacabddccdabbcdbacbdcbaacdcdcdcbcddddccdccabbbbdcabddaadcbdacdaddacbbacccccadbdbcbaaccabdbadddccdbccacbdbdcabccbbbcabdacbcddddcdabaddcaddababbaacdaaadadabdcadaadbabbcdaabdbbcdabccddcdcddcdaaabccdbadccbcaacdbccaddcdaacbdcdaacdbacdcbccbdcbdbcbaadccadbbcdbabababccccacdccdddbcdbdcaadbbbcadcddcbdbcdbbaadcccbcdcabacbbdbbbbddacdcababdbccbbdcbbcadcbaadcddddbcbdbaaaccdaadcaabbbacbccbccabccdaacbbdbaabbdbcdccabdabaabddbabbddcccdcdadccdcbaaadcaacddcbdbabccaccddbdcbacdbddbdadadadaaacbcbababcdbdaccbdbcbddacdbddddbabccdcdacbcbadadadcdddcbbaabbacbcdbbbcdbaccccdcbaccaccddbbaacdabcdddcbbaaddbccbbaacdbcbddacddbccbddcbacccdbdbdadbbbaadadbcbccddbdacdbabddbcdabbdddaadcaadcddcaaabdacaaccbdbbaaddabbbdacbcbdbdadbbdbdcdbaabdbdcdcdddcaddcbaddccbdcbabdcaccdbdabbcdaadcabcdaaaddaddadbdcacbdccbccadaacadacbbadbcdbdadadcbbbacddddaacaaccbadbcdaabaaccabaaaaaddccacdcdbcadabadcabbacdacbaddcdadbcaacbaabaacbbaccddcdcdddbccdddbcddbdbddaaacdcbbcaabddcccbbabcaccdccadbcddccccdccddcbccbabbaaaddadccbbacaabaddcdbccbbabbdacacbccdcaadaadddabdbaccbabbaddaaaabaddacdcbccaddddcdadccddbcdadcabdddddccdabdddbbdaccdcccadaabaddabbbbadaddcbbcdcdcbdcdddcbcddadababddabdacddacccbbdcbdccdaabbddaaccaabacdbddbbbacdddbdcdbddacbbacdbadbaabcacabbaaccbbbabdbcddcddddbcbdcddcbcadbbbacdddccbbabacadcdbdbbaccadcacddbdcacbdbbaaabcadabaabadbdccbcbbcbbbcdcadcaacbccabadbbbccaadacaacbccbbadbbdaadcabcdddbcbdabcadcbadcddacbdbcbbcbdadcbbbdacaaacbcbcdddcaccabadacdbbddabdddbababbccdbbbcdcbdddbdaabcadbacdbabbacbdbcabcabbabadddbbdcddaaacdbabdacccabaaccbbddabdadbbcdaacdccdaadcdccdadcaaaacadddbaaccaaabcabdddabdbcadbdcdabdacaacaadcbbcbdcaadacbddcdcdddbbaaadadbccdccdaccdbbbdbccbababacaabccdacdacddaacddbdcaddcddcaddbccdbcdcbaacaddbdddbdcdcaacddbcbdabaabccabdacbddbdcabcbddddcadadddbccbcdbbdabcddccdbbcddbccaaadabdddaddbaaacdabccbddbbaadcddcaadacbbddbdbcdbadabaaddbacdbacbddbaaaddbbaddddbdaaabaababbdcccadcadbabbcdcdaaabcbabbcdddabdaabddbdbacbcdaabbddbbacbacdabdbcacbdddcddaaabbcaddaacbbacddaddbaccddaaddbbcdaacccaadcbbcbcdbbdcddcaaaaadccdcdcdbbababdbdabddaaacbbddbccbdadddddbcdbdbdcacbccaaaacacddcbbcabbabcacdadbccccbbcddcdadcdcbdbdcdaabdbdbcdbadadcadbdcbcbdadbaaacbcbdcbccbacdbdabdddcccbbbdcbbcdabacdcddbbdacbccdababcacaabcadacbcdabdbdbadcdccabcbabbbbcbddaadaadaadadbabacacbbdaaddddcddcdbacddbbcacabcbddabadcdacabdcabaaddabcacccacddacabbbbabbbddbddbdadccaabbdcdccaccbaacdacadbbccdddccaddbabaccdbccabbcdbadccaccbbbccbadcddcbbdddaddaacbcdcdbabcabccbdbdccadcddadddabcaaaacbcacbaacbcdbbacbbccababbcddadacababddccccaaddcccbaaccadccaabacdbcdccaaaddbbbdacaacbdaaccddcdddccacbdddccccccdbcbabddbbdcbacbaccbcdbbddcbdadbacbaaaadccbcbaadadbacaadaabacdbbbdaaabcaadacddddaccaccaaadaacbdbaddbaccddcbdbbcaccdbdaacdbcdaabbdbccdcccdcbcccdddaacabbddadbcbdabddbaabcdddbbbaaaadcacadadbbacbadabdcbdddaaddcabaacaabadcdbdbcddacabcaadaddcbdcbdbbddaaccbdbacaadaadddcabdaaaccbbcbbcbddabdacadbadbacdacdadbdbbdadcdaccbcacbdbabacbabbacdacccdcbbbcccdbbdbbacbbbccdcdbcabdcccddbaacadcbaddabadadbabbbbcacbdccaadddabdbddccdccabaaabcbcddabacbcabbdbcbccacccdbadaabcbcdacddabcdbdccddacabcadccabcadcababdccacdbaaccdacccacdaddcdabdadcaddabcaacabddaadbbcdbbdcbbdaacddcdbcacdcccddccabaccbcdbccddbcabdcdbdbbddacabcabcdbdbbdcddcbbadcacbdcbdcacddbcabbddcabdcdbcbbccbddccccbadaabcdbadcbaddabbcabaadcaddcaabcbcccbbcbcadbcccbacdbdccacbcbdccdcbdbddaaabdaaaaccacdbbccabbabdbbbcbdadbcabbaddbababcadcddbbabcaacadcdbaacadcabddabcbbadcbddabdddaacddbbaadbdbadbbbbbadcbcabcddbdccdadadbcdcbddbcbdbbacbdcdcccdabdaabbcbddcabdcbacbbadbbbdacbdaabdcabbacbdcccccbbddcaabaccacdbaadaadcdbaabbabadadadddcbdddccadaabacccabdddddbacbaccacccccbbaadcbbcddaddccbdbdbdbabcbdacbbcddbadacdadbbdcabbbaaddaddbbdcdbaabcaaccdabcdbbaadbabdcbcaccbbcbdabaacccbdadbcddcdcbbbacababdcdbdaabddcccddacbaabcdaadaadddaddcccdccbcabdabaadbacccdbdcddbabcdadaccbabddacbbabbddaacbcdcbcdabaabacbcbdaaddbdbbdddbcdbdcdbddcdcdababacaadaacccacdaccadaabccadaddabcddbddaccaaddcdbcadcabdaabcccbacbcaccdaaadddbbbadcacacbdbbcbcdabbcaaadbcddaabbcbabccbcdbaaadabcbbddccabaddcdadbbcdcddacdbdacdadbdddccbbcabdbcabbbadcbdacdbbddabacdbbcbdaabcbbcbdcdaaccacbcdadcbddcbcadbddbcdbcdcbbccbabacbdabbacdcadcdcbadddddaaaaabbdcdcacbcbabaabcdcadccacbbcddaddbccbcdabdbbddbbddaaccacdaadaaadbcadaacdbbdacdcdbabbcdbdbdaddddddbbcdbadcaddadcccbbbacbdbccacabdacababbcbcbcdaccabddbbaadccdadcbbdababccbbacbdbdddacaccdadacddbdbdbddbbaacaacbdcdddbbdaccadcaabaccbbaaacdcacabdbaaccaccbdbdcbabdcdccdccbddbcaacdadaaccbdaadbbabaadddadbddaacdacabcbbdbbbaadcdcadbbcbdbacaadadadadddccacccbdacdcadddaddcdcadadacbbaacbcbcaccbabccbdcdcabdccdacbdcadddbbdabbaaddbccaadcaacdcbadddadddabbdbddacbbdbcbdcbdabdcdaaaddbbaddabbbacbcbcbbdcdbcacdccaacbdbcaacacbdddaccdbbbdbbaccddaabdbacacdbadcabcddbaabbdadddadaabaaaccbaabaaddaacadccabddaacdccbcadbadbcdacdbbdccabbddbddbbdcaabdaccccdadbbbccdaccdcaacdddcbcddbdbabbcaaabcdbdbaacddbbbbadaddbaccbacaabbccacadcdcbbcddadabcaacbbacaddaacbdddddcadcccabadcccdbccacccdadcddaadcaccdcdbcbbabdabcaaadcccabdccdddaaabdcbaccbbbadbccccbbdbbdddbdcdaabddbbcdbbddccdcdcabaccacbcbccbbbdbbacbccbbdcdabbcbaccbacbaddadbabcdbcdbdcbbadddbcdcbcccccabcabdadacbdddccdadbdcabaaacacdacacbccdbacbcdbdbadaddcddabababaacbdadbdaacccdddbacdacbabadcccabbcaddacabbdcababcdbbcddacdbbcbbddbddcabbdadadddcacdbbcbbddcccbabbddbbdcbbabacdcaabbdacdddbccaddcddadaccbdbdcaaaaccaacaadddabacdcbacaddcdccbaababbcbdbadacaadadbbadddabddaabbdbcadcdaabdcabadcbccccabdddcaaccbdccadcdbbadbcabdccbcdbabcdaacdabdbbadadbbdbacbcaaabcdadcddcbbaddbbcdbccdadbcaaaaddbdbcabbbdddbcabdddcddbaddcbdaacdbbcbcbbdcdbccbcddccdcbbcbdbbaacbbddddaccdbddcdbcdcbdcdadbaccbccbababdbcaaabaaaddcddcddcbacbddcbdacdbddccbccdbbbdcabcdbcbcdddabddcadbddcabcdddadadcbacbdadbcacddcacabddadddddacdbbcdbbbbdbbcdccbddcdacccadbcaadccbaacdbdddbbcdbbbcadbbbaddbcbbabbdcabccbbadcbadcaccabcadcaddbabddbcadbdccaddcdacdcdddcdaaaacddaabaaabaaddbccbbbdcdbbdccbcaccddbabdddbbabdaaaabbacbaadcddadcbbdcaaadabbcdbcadaacbacadddbcbcdcadadaddcdabdccdccdddddabaaabbaaacaabbdcddbcdadadaabccadbccdbdccdaaccaaadaaddcabccaabbdcadabaadbccdaadbdadcbdadccaccbcacdccaabcababdadaaadbaccaababdbadbcbaaaabacdcccbcccacadadccaaddadcbdabbdacabddbbdbcaabcccbabadcaacddbcdcccbcabdccdddbabddbcacccbbdbbcdcdadbadaddacdcdddbbdcbdacdcbcdddbadaabddbbbdcbaabcaabcddbbdacacadbcabddbcacaacaacadcdbbcbabcccbdbbabbbaacccacccaabcbaaddabbadcddcbadaccbaddaccbbcabbadbbcdbcdccccabbdcbbcabcdddccadcadbbdddbcacaadadabdabbcdcacbaccddaddbcbbbbdddaaaadcbbccbaccbcaaaacbabbbcbacadbcdccaabbcdcdabcadbcadbdadbdabcaabadbacddcccbbbccabddcaadcaabcddaccbccbdcdbcacdabdcadbdcccbdabccbabcbbaadacacdacbdbdbdabddcbaabacbdaabbcdaacddbaaabddcadbcbbbdaccbdbcddaabaddabdccbcbcccaddaacabbabadbcaaabaddccbaabadcacbabbcdbadbacabadcabdaabdaabbabadbaadddbaaadddbccabaccbbaacddaddbcadabbcccccdccbcdaabcddddcaccbcaaacbadacdbbadbbadbabdcccdaaccbabdaacdabbcadbbaddabdbbbdbdabacddbabdbdaacadabdaccabbbcbabdabbbbcacacccbddcadababbccbbbbabaaddcadccdabaaaccbddcbdacacaddacddacbdddcbddbcbdaaaacbacdcbbcddcaddbcaaccaaabacdddcababbdcdacbdccddbddcadbdadabddacbadbbadaabdddcacacaaabacddddcbaabbbdbdbcbcbacbbdacdcbacbccbadbdbbbbdacabbddadcdcaccdacdaddbdcaadbabcbddbabbaadaaccbbcccabdcabddcdabdadccbcbbcbbdbdcbdadcabbadbccbbbbcccabcbccdbaadbcadbbabdbcdaacdcccdccbcbcccaaaadcabadbbcadcddbccdaddcbdbbcdcaaaadadbcdcdcdbcbdaddacdccdccbddababccbdbbccbdcbdcbddccdbaababaadaaccabaaacdacadcbaaaddbbcbcdabdaababcbbbadbabbabcadaacdbbbabacbcabbcdbccddbbdbcbadccacddcadaaabcbddbbcdddcccddcaaaccbbddabdadacccadaccaaddabbbcdacadbbbbbdddccccbcbaaadcbdccacbdaacabdbdaabcabcdbdcdbacaddaccbadcccaacccddcbbaaccdbadaddcbcbaccbbbbabaadbbbdbbdcbdadbababdacbccaaabcabbdabacadbbbababacbaccaadbccdaaadcbccdcdabbaaacbcadaadcadbadddcaabdcabddddaadbcdbbdddcbdbbaabbdccabcbdcdaacaccbaddddcacbbbacaccdaccbbdcbdaccccdaadacadcaccabbcdabaadbccaddabccbccdcdcccccccaabdbdcdccbddacdcbaaadaccbccdaaacdcbaaddcbcbacbcddbaaaadccadbcbbabcacaacaddbbdcaddbdbdabbbdaabdbdaccbdaabcdbddddaabaaacaacbdcdabcbdbcdbbbdcddcacacaccbddbaabccaabbddbdbcddadbdcdccdbbbbbbbcbdbcddcdacdbbcadbddbbabaabaaadabccbccbbadaccaacadaacbbadadbddcbaacdddacdcccccaddbddbbdbcbaabbbcdabddcddcadddcabaccdddbbbbcdadbcbadbabadcdaadbdacbbbbcddaaacdaaacbbabadcdddaabdadcdbbacbdbaabbddcbaacaaadabddcbabccdadaccadbbaabbbadccababdabdddcddabaaabadadabbcabdaddaadbcabcdabbcaacbbcaddcacababbcbbcbccabcdcdbcbdaadacabddadaccaccdbccdaaababcadbacbbaccbcdbbacaaaabadcdaabcabcccbddadccdbdacbcabbdcaaaaabcadcbddcbcccccadbdabdcdacbbadcadddacadddadbcbcbbbaadbaddcbabbdbabccdcbcdcacbddadbadaacadaabcbcdbcccdbbbdadbbaaaaabbbaabcdddabbdaaabddbbcbbccacadcacdcbbbadacbddbbddcbcbdbdbdcabccbacdbadbcdaabdaddccbbdabcbdbcbcbdcddddddacaabbdccbcbacaadbccacbbdcccacdabcbbbddadaccbcbcbaaacdbcbacdacccababbcbdcbbaddbbabdccdadddcaaadaddcaacdcababcdbbaddabdabcabcdddcbbabbabbbaacbbccddcdababacdbdabccdbabccdacacbdcdbbdbdbdaadbbccbbbbacdacddcabcadaccbadacbbacdaccaabbbbabddcacccbcaabbbddbcdbaacdacaccdbaddcabdcbcdcaacaadacbaabbbdccbabadbdbdcacddaadbbdddcacbbcdcdbaaabdcbcbbbbbcdbbcbdadbaaaaddbccdccacaaacdcdacccbcbbdbccbdbddabdadadadbadaacbcabdaccccabbbaccbaadabdadabaccdbabbddadcdbbdaddbdcacbbbaacbbcabbaaacddaadddbddbbcccabcddcdaadaadddbcbccdcacadccdbabcacdcbbbadbbdacdadbdbaacabaabddbcacaaaabdccbcbabdbababcacdcdcdcabbcdcadaacdbbcdbccadadddbcddbdadbabdcddbddadaaccacdabbadadcbacbcadadcaabbbcbacbacacbcbbabadbbddbcdbbdbbdbbacabddbaaadccdbabaccbaabcbcdbadbddbabadbcabdcbccbdcacbdcbccacdddbbadcbbbdcddcabbacbcccbbabadabdcbdcbcccadcaaabddacadadcdbdacaaddcddccdbcababccaaadcbbbacacbabbdcaddbaddbdababdbdcdaadbbdddcbbccddcdcbbbcbbbabbdcadcbdcdaadabcbdcadaaacbacdbbaaaadccdaccbabbdaadabbbacdccaaadcadbcbacdcdacccaacaaabaaddddcdadbaadddbcbddbadbaccacbcbbbadacadacccdadabcccdddcdddccddcabdacacbbabbdbcbdbdbbbdbdcdcccbabcdcacccacbccacbdcbcccccdddbbdacadaabacbbabbacbccaacdbbcbbcbdbcddacbbcacdcaccadddccbcdcbdadabbddddbcabbadacbaddccdabdcdcadbcbbdbddbcdbadddbcaadbcbdcbcabaccbdbdacbaacddadaaddbdacaaacccabcbbdcabdcaacbbabbbcdccadcaadaacdccadcdaaabadbcbabaddddacddbbcaaccccdcbdadbaddccccbbdcdacbadcdcbdcdcaccababdacabdbbabdcaddadbdacbdbdddcccbbbdadbabaaddbcddcccddcaccddabaaabbbbbadaccbbcbcbaccbbbcdcccaacbddadddabcdbdaddaadcdcdbddcabbccbdddddbbacdbdccabcaaadcdabbdaadcaadcbdcadadbdccddddbadacdbbbdbbbbddbdabbbbdaabadacaccbcddaaddbbbbcadcdcdcdbbcacdabcbbacbdbbbddbccdbadccacddcdbccbcddacbaaddcadadabddbbbcdaabadcacccddcdaaabbaaaabbbdbacbcddabcccbdbaacbbcadbcdabdccbbccabcdccdadccbbdbcbadacdbcddaddacddacdcbbcdbbcdadadadcdadbcbbacdadcdbccabdabdbbdaaaaccaacaaaddcddbbcbbbdaabbdbaacbadcbbbdcabbaaccccccbdbcdbbcbdbcabbbcabacdbccdbadbdaaabcdbddbbccdbaacabaccbbaadbabdbdbdaddbcddababdddaadaacddaccdbcdbdbdbbdabdadacaaaaababbbccbaabdbaadadbaddbddabbabbdcabddcbdbbaccdbabcbaacddbcadbabbbaaaabcccdacccdddadbcdcaacbdbbbaadcadabbcbcdbbccbbaccdadbdcbdbbdaaddccccccadbcaaacddaabccaddbcdcbaaccdcbcbbcadbdaacdcbddbbdcacdcdadabbdbcbcadcaababadcbbcabdcbcabcabacccbaddaacbdbddbcdbaabcbadacbdacddddacbddabbaccbdadbcaddacabcacbacbaccbccbbbbdddcdbccbadabadbbddddbdacbdbbaaabbaddbddaacccbbababcddcbabdcadababddbdbabacbacbabccdacaabcccbbcbabcbddcaccbbbabaddbdcabbcbddaaccbcabcaaaaacdbcbbcbbbacbbdacbbdddaaacacddbbcddbbabbbbcbcddddcacccdddccdcdbaccbbbacbaaabaccdbdabbccacdddccaaddcbdbcccacccadbddbaccbdbccaddabcbaabcadadadcdbadabdddbcabbbabddbcababacabdbabaaddadcdcbdaccdddcdcbddbaabaccacbbcbcaadbbaddbadbacbcccadccbbddbbbabbacddcbdcdabacdcadabccaddbccddccbdddcaaccccdcacaaabccadbcaddabadbdaacddadacadcbabacbaddacbccdbccacdccaadcbacbabcaaddadcdcdadbbdaaadcbaadbcadaadaaacabaccdcbbdbbbbacaddcccadacbbcdbdcabdbabcdbabadcaaabacacccbbddbdcdddcbacccdbdcdaadddaccbdddddacdbaaacccacdcaddcdaabbcabcdcddaddbbdcbcadbdbadbabacdbacdbdbadcbdbccbbaddaadacbcdcadcbcababdbacdcddccdddcadbdccdbbdadabccdbccaddccbbbdcbacdbdaccabdddcacdabccbddbdaccaacaaddddbdacbcabaacdacccbdbcacbcdbadccabbddbbbdcdaddbbbbbcccdddbabdccbcacbdbdcbbdcbcddbdbdadaaabddacbdabcbaabbcdcadabbacbabadbabdbaddccbcbcadddcabacbdccdcdaadacdadcabddbdbaddbbbdddbcdabdabacacbccabbbabdacadcbbdaaaaacadababccdddacbddabcdaababdaaaadbadabcddcacbcabcbaabaabbbabcdbcdcbdccacaabdaadbdcbabdadcdacabbdbcdbccaddcddcbabaccabbccaddbabbdadcaacbbaccdaddacdbddcacabdbbbcccaddcacbbdcdaadabcbdcacdabadadbdbcaddbdbdabddcbaacbcdacddddbcabbbcbcabbdcabccccbbcbdbdadbcbbdadccaddcbbadddbbbddbdbcbbcbcbabbdbdaabdcdadcaaaabcdbabaddbbaadacccadcaadadcbcacdacacccbbdbacacaabbdbbcccbbdddabbabdcdbbdcaddcdabbacaddaacdbcddaccbacbcdcbabacadbdbcccdbdcbcbacddcacdbbdadbdaacbcdccadbadcadadacbdccaabcaaaccbadbdabbdbcadddbdccbadacdaacdacbddabcbacdabaaaadadbabaadbccababdcdabcadaabbcbbbabdaabaadbbaaddcdbcccbcdbbbbbdddbcadcdbadddcabacdccbaababacabdbaaaacccabdbaddbccaadbdaccccbcdbcaadcbbcbcbdaabdccdbccabddcabdcdcacdbcddbccabdcaaabccbdcbcccbccdbabaaacaaccddddcdbdcbaddbcbbbbcbacbbdbadcbbcbbdaaadcbdacdbbcbbddddacdacccdcccabbaadbacccdacdadacbabdbdacccccdbcbcdbdbcbbabdaaabbdaddbadbbccccaabccbcadbbccdacdcdcbadddbbcaddcbaadcdaaabdcdbbbcdbabadcbcacddadacddaabdcadcacdabadaccaabdcabaabdcbbcbabbccdcbaccbcadaadbddccbccdcaadaddbbacccbcdadbddacccddaacbccdacacccbacabcbcdabaabcabacdbcbabdacacacbdabbdcbcaaaaacdbccabaacbbbcbaababcccbdddabcdaadcabcdaaadaaaccbaabbcddccabaaabcdbabcddddabbccbcbaadddcadccbddbcacaabdbadddbdccbddccacaacacabbadadccaabddcbdcabdacbabbdabbccdcbacbdcddbacdbababaaaadbbbbacbddbcaacbddcddcbdadaacabcbdcdbadcaddbdccdcaaddabadacaccaacdcbdaaccddbababaddcccddbaabccacccbcabcdbaccdcdccacdcdabbcddbccbbcaddbdabdbaadadbcbdadbabddbaabcabaccbacaddaadddbdaaddcbbccabdacbdbdcbaacddbcabbddaaabddccaadcbdaddbdbbadbcadcbcbdbaabacaababbdbbbcbbcccccccdadcdbdbacbcbaabcaddbbabadccdddbcdadacdcabcccbaccdcabadbcbbacaadbcccadbbddcbbabcbbcccbbcacabadcdadcbabaaacaaccacbcdbdbacdbdcadaacaadaaacdabbcdadbddacdddcaccacacbaddacbdcbaabdcdaddcacdbadcbcdaabcddadcccbbacbacccdbbdcadacdbdaabdddcccdadabcbdaabdbcbaadbaccddadbcbabadcbbaacacccadcdbbcaddcbadbdaccbadccbbabaaddccdcdbdbcaaddbdbddcdbdddbdddaabacccbaacaaacabdccddcaddbbbccbaababacacacccadbdbaaccbdccaadcaadabbaaabaacbcdaacdccdbbadbaadbddcacadccdadbbccbcdbcaadaadccddccbacdccdccdacdaadadababadcacdddbcadccdadbcaacbabbcadadccdcbcddbdcdaacadacddbdbacbadacdbbbacccddcaaadacdacddaabdabbdaccdddbcaaacdcaadbaacaaccababccabacddbabadbadcddacbcbbdcabdbdbbbdaaccddaacbbdccdabbabbddaabcabbcadadbaaadaabaddaddcddaddaabbbbbaababcadaccaadbcdadbbbacdaaddbcbabbadbdbccbacccaadaadccbbadcdaadcadbabcbabddabcabacccadccbcabdbcacbcdaddadddcbaababcdadcccaadccdcbcbbddabddcaddbdbdcdabdbaabdbbcbaddddddcbbccdcdabcbbabadcacccadcaccdcbcbacacaacccdccdabbdaacbdcbbcdddaaaaaccbbcadccbabacbbabcdcccddbbccddbabacdaaaaacaccbacccdbbcdbdcbcbcddbbdbacadabccccabcbcaadddbdbadcccbaaddacbdbddbbcadbabddacbbddcbaddbbdbbdbdaaaadbbcacbccaddbabbcacbbaacababbaadddccbccdabaabdbbbaaaaddbbabbddbdadbaadbcbcbaddccdcddbdcaaddcbcdddbdbbbadaacdaddddaaddccccadaaacdcbbaddcbbdcddaacdccbacbaacdddadacdaadaaadddddbcdcabdcccdbbcaaacddadaacdbcccdddbaacdcddadbbcdaadadccadddcaacdcbcacdcbbcabdbdabcbdddadbcabbdbdcadabbbcddaadbadcdcacacdddddbbddbdccdccbdbaaacabbdcdbdbabccbbbababcdccaddcdbddbdbbcdaccbdcdaabcbaacdabcbbdacccabadcdddabdcdcdddcabdbadadcccdbcddccabdbbbdbbcbbabcacbaaaadabdddadcdaaacddccaccabcdbbddacaccadaacbdbcbabbacddbdaadaaacadadaaacddcccbadbdaadcaacaadbcdccbddccbbbbcdccaccdbbddaccbaabcaaccdbaaddbbabddcababcccddccabbacdbdbbcbddcaabddaacadbbcadbdbacdbadbdbbcccbbbbcdbcccccabbcabdcadbddbbddccacaccabacaddbccbcadbdcbbbbcdabcbbdbbcadccbabccadadabdbacabccddacababbabdcddbdacacbaaddcdbdabbcbdacddaacabacacbdcaacabccacdacddcdbbdbcbaaccdcccdabcdddaaddbcacdaaddbdbaabcbbddcdcbadacabbaaaabbddaadababbddadbcdcabbdaaccdcbbcaaccbdbdaccbbacaacdddccbaccdbbbbbcbdcadaacbabdacbcdccabdcadcdbcdddcacdadbcccabcadaacbbabbcddbccaabaacabcbbdaccdcbbbcbcbaabbdbabaabaaddabdccabcdadcbcdddbddbabcacaadddadaacbadcbaaccdddddbadccdacdcccbcbcbdcabbddcddbbbbdaabaabbbbcdaabdbcabcacdbcbcbaacbbcabacaadbdacbdabdddabbccdddcbcddcaccabcbacdacbbbccbcacdadcbbbaaadbbbdbadbabcabacdddbabddacdaaaddbabacacabacbcdcabaccadaadddabdacbcccbaccaabadbcbdbabbcbdcdaaccbbaabcadbdbacccbdbdbadcabdadadbddbccbccaddacddadaddacdaadabbddbdabbcacaadddcadcacadbbcadaccdacdaadadccdadaddcdaabbbababbbabaadddadcdacacbadbcbddaabcccbacbbdcacdbbccddbcacdcdccbbcccdcdabaaacdcbddcbcbcaccbdadacababbbaacacbcbbbdbbcbdbacdbbcbdbdbaacbccccabbabbaabacaadbcabbbdbcddbdcbabbdbbdcbdbacbcbbdaccadacdbdbadccbddcadbcddbdbdbacbacdbbbdabcccbbcbaccdcddacdbccbacddabccaadbdaadbdcbaddcddbcaabbbdbcbaccdbdcaabdccbbacccaaccbdcdcdcdcdcaaacdbdbbdbcbbadddbdaccdcdacaddaddcabbcaddddadabddadaacaaacbabcddbabcbddaabbabbdbadaabbbccabbbcacbdddabbdddcaccbcdcabcbdacabcdadbadabcbcaaadaabbdbbbcdadbadbdbabccdddcacdadbcbcddccbcabbbaaacbbddabbcddacdcaddacdcdbaacbdcabcbadbdbadaabdbadabdcdbbdddbabccbacacadadbdaabaababdbbbcccdabcdcdcbbccbcdcacbaadccbadcbbdccbabccbabdcccaacbdacdbadcbcdbdddbbccdbbbdbbcbacacbcdacdddbbadacbcdcadbbcdcccaddbddabbcddadcadcdcabaadddbcabddaccbadaacdaccdaabcdddddabbbdcddadddaacadbbcdbcabddbdbddddbddddacbdcddacaabdddcdcdaccabbaaccbdabbcdacaccdddabdcbcbccaadddbdcbddbadbcadbcabadcaaccbacbbdcbbbdaabbddccbccddcdaccdbbbdccbdcdcaacdcdaacbcdcbcbabaacdbcccaaccdcbabbaddbbdaabbbcdbabcdcdbbdbccaabaccbbbddcbcbbaadabbabaaacddccddadbaabdbccbdcaabcdcbbbadabbcdaadbadadacdaabdbbaaabacdadcccabccacdddddcaadacbcdbbdadcadbccabcbbcbcbcbaddbdaddaaabbdcaccadcaccadcccaaadacbcbbbdbbadcaadbbbbcdcbbbabbccbdddcaddabdaddcaaacadccbcabadbbbbadbbabacacacbbabbacbcadbcaadcdddddccddddaabcbcbacbccbcbbbbbbcdbabadbbbabddbacbcbbacdbcdacdddccabddcddbdbbddcdacdbcdaaacabadcbbaddaacaadaabbcddbcddbcadcdbaadcadaabacccdabdcadddcbaaccccbdccdbccdbcdbcbccdcbcddcabadcbccbaaaaaccacbddcaddadccccaaacabadcacadabcccddcdcadbbccbacaddbbdcaddbabbccdcbabbccdaacdabddbbdcbababbdbdcaaabcbdcacadcadacaacdcbddcbaadddabcaccabaacccbbdcbbcdcbddcdddbdbddbcaaccbacabcbdadbdacbdabbdcbbadcdcabcbdccddcbcdbbcabdadcccbdacccbcadccbddccdcbbabcdcdbbdacbadcdcdbabaabbadcbabbbdaabdbbddbbabccdabbdcbdddcabaccacbdcabccbaacacccbdcbcdaccaadcaaccadccdcadabdbabcdbcdccacdaabdabdcbbdccdaddcdbdacbdcacbbabbcbadbaaabdababbaaaadbdcabcddcdbdbcdbcbbadcdadcadbcbdccbaabdcdaccaaadbdacccbddcbabaaaaacaadbddbcadbaaadcdcabbcdccacbccbacdbaabcadccaadcabbcdbcdbaacdbdbccbbcbbacbabcccdbcacccdaaccbbacacbbcacbcaacaaababbddcdaaabddbcbccdcabbbbcdddaaadacadddccbbcacdabdadabadacbbbbbaddccdacbccacdbdadcaaabcadcbdbdcaacdbbdaabcbcaabcbbbccbabacbacbddbdccbacabcccdacdbbadccabcbadbacbcdccabaadbdccacaaadabacdbbabbddcadaacdcccdaadcbadbcdbdbccdcbdcdccabcbbacdcaddbddbcabdbbcdbaabdbbcbbbdcdccbdddcadbacdddbbadbddcddabdadbdddbcdbbbdbbcccdbaccdacdbbccbaccccbaccbdadcadcbcabbcbcabccbcbbdccbaaadbccabdcccdadabcbabdcdcdbcdddcdcadcacacdcdcbaddbcbccbccaccadcdcccacdddcacbaacdddbadcdcbcbcccaddabcdadbacdaaaddaaacdcdcaaadcdbdccbdaacccdabbdbbdaadcbacaadaaaaddcbbaababbdbadbdcacbdbdaddcbadcccbcbcccbccbcbbabcaabbdcadbacdabaabdbccdabdcdabdcbcdcaccbbdabdabccddcadbbddaacbdbbbaaccaabcacdbbbdbcbdcccbdbcacabdcdbdccbbdddcbbdddadbdcccadbdaddcdcdacbbbcdaabaadcdcaccbcadbddddddaaacddbadcabcdccbccabdcaabcdbbcbaabdccddddbaadbdcddbbbddbcdcababacadbadddbdbdcaaabdaccbadabccccbaccacaadddbbdabbaddcdcbabadbcdabcbcacbcbdbcbabadaabdddadadcbcbcabcbbbdacddbdadcadadcccbdcadcdadbbdadacacccacdcadaaadacadbbdabddbdbacbbcdccbdbbccabccddaadaddabbbdbcbaccbbdbcacbbdbdbaddbdcaddcbdbabbcccbbdcccaacbdcdbbddabcbdbadcbbadcabcbccdcbccaaadadbdcddcabbcdbbbbbbabcdbccadbcbbbcaabdbadaaabbcdcccadcadadbadbbbcdbdadddbbbcabadcccdacdbcdabbdaacdcbbbcabcbcddcaacbdbcdaaaddcdcacbbaaabbcaabdddbaccdabcbdccdaccadbcbcddaaddbddccdadcbbdbcaadcababbbcddddcbccaacabcbabcdcaabbcddddbcabcbdbccdadaaddccabbccdaacabddaddccdbaaabaaabdadabbcbcaccbbabbbabcccabccadbbdcbdcccdbbccbaaccdbdbdcbbacdccbcbdacbdcdacbdabcddcbddbbbacbacaadadddbddccbaaadaaaabcbdcbadcaddddacabbdadaddccaadabdddbcabbbdadccccadccbbacbabaadaabdbadccddbbdadaccdcdbaddcdcacdbcbadcbbadabdbabacdbcdbddddcbdcaaacbccdcccaaadcbbaadabdddbdcabbcbcacaccdbddcbacacbcadcdcdabdabadbacbdbcdbaaabcccbbbabdabccabaabdcdbabbaddacdabcbcbdabdcbdcbdbccddbaadbdbabbccabddadabcddabcacabacccacddccdbddbadcdacdccaddaddadacbbdddbcbbabadbaabbaadbdbbccbcdbdccbdbcdbddadcacbdbcdbdcbcbaabdacdccbdcacbdcbccbddbdbdccadadbabdcdbdbdcdccbbdacccbcbaaccabdcbbaddccbbbcbccaddabccdcdcdbdaadbdcaaddaadcdabbdccbbabdadaadaccbaaadbdcbabadbacccdacdaadbdaaaabcabccccadbddaadacadccdbadbdadcbdbbcddcadadbdadbcacbaabcccdcccbccbdcddadcbccbabcdcdacddabdadbcabdcabdccaadbdcdcaacabbadaabdddacacdaabadbdcababacdccdcaddbdbadddcacbbdddcdbdddcdbdabcaaaadcccabcdcdacdccbdddddadcaaaabbbacbbddabbaadbcdbddadcbcbcadadcbbbcabdbadbcadaacbabbabdbaaaaaaccaacbcbcacdadaaddbdbdcbcbabdaabbacccbcaaaabdabbacadabcadacdbcddbddbbbbabcabadcaababdcccccdbabcbbccbbdccddcbbcdacccbdbccbddaaabcbcdbdbdbdabbbabdcbadaaaabdcccbdabdcbccdcbbacddcbcbacbbcdabbdbabacddbcccbaacdabbbbaaacbbabdcccbdbbcbcbbccbbdcdabdabbcdbaacddbaadddbcbdaacbcbcabbabcababccadbacadddbdaacddacadcdadbdcdcbadbccbbdcababcbabacbbabdccaaabbbbdaacddacdcabccccbbaaadbabccaacaccbbbbcdbaaddabcaddcaaaaabccbcaccdbbdbbccaadcaadbbccbdcadbbcbdcdabccbaddacabccdabdbaaacccaddaabdcabacaadbbccdbdbaddcbdacabddcccbcaccddbdbcdcabbabcaabababdaaddcbdddbdacccdccddcaddcdbcabbdaacbdddbdbcbdcdcbaaadbcdaadbccacdbbdcbdbbbbaaadcbdccbdbcdabdaddddadccbaaacacaaabbbbadaddabacadcbdcbabdbcbddccbbbdcababdacbdbcddbbaacabbddbccddaaadbcabbcccbbccbcadcdcdadacbddcbccaadcbdaacccaadbcbbbdbbdacbcdbcbddadbcadbddbddcabbabcacbbccbcbdbadacdacbcbcbdddbcdbaaacbbbdbabdccadcabcbcbcaadbbaaabccdabaddbcbbddadbcbdcbdabdcbddacadbacdbcbacacbadacbcbabbacababcadcaadbdcdaababbaccdacdacccdbdccbbddabcdacdcaaaabccdcdbcbaaacddaadaabdbadcddddadbacbbddcaadbadbbbaaabdcdacdbbbdcddcbddbabcdcbaccaadbabddcddbacddbaccbbdbdbcaaccdacddcdaacdbcbaaacbcdcacddbacccddabbcabbcbbdbbdcacdddbccdcadacaabbddabdadaacbcbacbcdcabcbddbacadabacdbdcbacbddccbcacdbdcaabcabdcacbbddbbbcbdacbdccbabcbabacbdababacabaddbbbaabccddddadbdbbbdbbbbddbddcdccabbbddbdcacddbdbbbbbccdcdcacbcccdaddadddcbdcdabcaacdcadcabbabadacadcdbbdabaadcdaccdaabccccddadcdcabbdcdcbadccbbbdaaccdcdcdaccccaccabcaaccdcaccbbadbbbdcdcbdbbcccdaadbdbaaaadaccbcbcdaddabddccbdbcbdddaadcbaaacccaacaaacaccccdaddbddadcbacbbcccbbcaabacccaacdddcdcbdbcdcddcccdacabbcdbaababcbbcadcbdaaaacbbddadbaaccbbdccdadcbabbbbaadabddbacdddddcccacdccadccdddababbbbdbbdbaacddaddaddadcccdbddbdbbaabbddadcadcdbdbcbacccbcbdcdbbbdacaaadbabccacdbadabaabcbdabbcbbbbcbcacdabbacbabaabbccbdaaadbbaabdbaaaccbcababacbccbcabcabbcbbaaabdabdacaaabcbcacabadcaaccaadadacbddbabddbabaccacccbddabacacadcaadbdadcbcdcddbcadbabbcdaccbddbdbdbcaccdcddbaaddbcbdbcdddbdccacbbcdbbadddccacccbbacabbadbabdabaadbadbdcabacdacbbcadbdcccbabcaaacdcabcdabbccdbababcabbdabaabaccacbbaddacbabaacabadaababdcdcccbcddbcacdaaaabdcadcbbbadcbcccbcbabacdabcdadcdbbaaacaaddcbccddabbbbadcdaaaadacdcdcdadcaaaccbcbdcbacdacbdbcaddbccabbbdbbcadbbadadcadbcdbdcabaddcdadbbbbdbdcdbbdbdadbcdbcddbdbabddaacbbccaddbbdcccaabdacddadbaddbadacbbbaddabcabcccdbaabbacbdadcdbaccbbabdcbbbcabdbcaadacbadccdcaddcdaddbddcdcbbcbddadbaddbddbbcdbabbccbaabdccaccccaccbbaacdabadccaadcbdccbdacccadbdacadbbbdbbdabdcbbdbdbbdccbcdbbbadcccaacbdcbacdbdccdcbdacbabdbcdcdaacaabdcdabdcbacdcbcdcddbbdcaabddcbaadbcbadadaddbdaacbbbbddddadbbdbbbcdadadacbbbddacbacbaaadbcbcabcdabbcdbbadacaaacacacccdbbcccbacdaccccdcacdccdcaddcaaacbadbacddabdbcdbbbaacbccbdaacccdcddbdadaccbdccaddcbddcadbacdcdbdddccddaccdbbadadabaabadabcadcccdabacaaacdddacdabdbcccccaccdaaaadbdbaaadadcdadccbdcbdabddcbdcdaadabdbdabbadabbdcabdccdddbcacdbadadaababdbcbdbdbcaccacdbccaaadccdabacaacadcdaaccdcaabddccbbcdcaadbdaccdbabcaddcdadabbaabdbdacabcbabdcaabcdcbcacacabcbcbadacbccdccaccaabbdbaccbadbdcdacaadcadcbcccbdacdcadabcbcbacddcabadbdabbdcaddcbadccaabaccbcbdbcadadbddbdaccacbcdaccdcacbcadacaadacabdbdabbabbcdbbccdbdbbbacbdccabdcddcbdaadbcddadddabdaccaccddaaccdccbcaacdbcbbbdababbaadaacddcabcbcddadacdbaccdacbdadbbdacbcbcdcdbcdbcdbcddbacdadcadbbabcaadadabbadbddaaabcdabaabbcddabcdcbdbadacbccadaacccbddaabddcacbbddbbcbbdbccdbdcdddbcbabcdaacdcdcacbccbbcbccdacbdcdabcdbdabcdabdcbbacbabdbadbaaaddbcdbcdacabdadcddcacadabaadbdbcbcbacacccabbdbbaadcdcbbbaadccbbaaabcbaddadcbadaaddccddbadcaaddcdcccdcaccadacccdcaacbdbdbacddacdbdadcddbdbdaadcdabbddabdcdbaccbbddcdaccbbbcdbccadacaacdcbdbbccbddddabddaacbdbdbacdcbdabdaabdcadadcdbabcbbaacdbbbbdadcddadcacababdbcaadcabdddaaabdabccdcacdabddcddcaddbacabbcabbccaddacbbdccddaccabcddadaacbccacbadbaaddbbbcaddcdbcbaddcabbccbaabcbadacdcdcaacacccdcbadddcdaadcabdddcadcdbcdaadccdbbcabbdbacbcbcacbacbdccbbadaccdccaccadcaaaacdcbababadaccabbccbbdbabcabdcbddddcddccdccdaabdddcccdbbbabddbdadaddaadbddcccbacddaaadaabacabcaabdababadbdadaabdcaccdabacdacbdbddbacbaacbbadccbdcdaadaaabdacdadcabdacdbbbacaacabcdccaacacadbabbdaccaadacbbdbbbbcbbadbcdbcccaabbdcdcacbabbcbbacadddbbbcbcbbadcccaabdaaaddabddabbaabbcaaccddacbcbbbddabdbdddaddbccaddbcabcdaacadacaaabddbdccdbbadbccbdcdbdacccabcbcbbbdcbccabacdbaaccaddbcdccadaabddcaacdccabddbbadacbbcabbbaaadabaccbcdcabdcbabbbddbcbacbcdccdcbacdbadaacaabaacdcaadddcdaadddadbddcacdbdbdbaadbbbaabcabbbdcaaddcdbddadcabbaacbbbabcacdddcabbcbcbdadcbbdddcbdccdacccacdcadacadabcbadacadddddbabbdbaccacbaccdcbbbdacbddaaabbdaadbdacdadcbdddadcacccdabbaaaadacdccadcdbbddbddbdbbcacadabcccdbaddabcaaabbadcbdadabacdacbbdcaadccdadadbdcaaababbdccccddddcddbdbadccbbcaaaadcbbdaddabbadcaccbbdcccccbaabaddcabbcdaabdaaacbabbacaadbcbddcabdbcddbccacbbdacdbaddccbbbcbbbacabcbcdbbacbbbcbcaacabccdbbaaacaccdaaaacacbbcadaddddacbaabaccadaabdcadcaaccaddaaacdbbbaabdbbbbadbcbabbdabadcabdccdbccbabcacaaddbbdbacaabbaacadabcacaabbcabddddcdabccababbddabbbbccadabbbdcdddcbbabacbcdcddcddbbadcacadadbdddbdaaddccaddcbbaacddbbbacacccacbbddcddbcdddbcadbddaacbdaddbaaaadcabcbacdbdccddadddbabcddaccdcdbabcdbcabccbcbbcdacacbbcaaaadddcccbbcbcadaaadacbcdaccbaacadccdcaabbadcdccddccbdcdcdabbbabdaccccdbbbdbdabccbbadbbaabddcaadcbadaddbdbdbcdabaccdcbaddadbcddaaabbacddcadbacbdbdbdcacadabaddaddadbdbbcdbcdaabddaacdaacbbddababcccdccaaacbbcdadaacabdbacbddadddacdddbabbabbcdccbbcdaaadadaaabddbbbabaddddbcdcbdcbbbbbcdbbcaadadbcdaabdbabcacaddcadcbacdddabbdabdacdddcaaccbbadcccabddadccdddcababcbcabcbddddcbbbbcaabcdbaccddcddbdbbaddccaccbacaddbdbadccadccdaabdacaadbbdcdadcadccbdbdbdabbadbbabadabbcacacacddabaacbacdbccdbbdccddcccbabbacabbadbdcbdddcadadbdaddddacbddaabacabcddacbaabdabdadcaabdcaaadadccacbccdabbdbadaddabbdbcddaaadacbcbabcacdbbcbdbcdbcdacddcbacbbabddabbccddbbddcadddbcbdbbbadbcbdcccdaadbbdcbaddbdbbbbddbccbbbddbdbaccdbddbabacbdbdbbdbbbcacacbcdccddbcbbcabacbbdabbbbcbbbbabaddbdadbbadcacbcdaaabcacbbcaddcddbcdcabdabbdabdcbdbddcaaabbcbaddbbbbcabcddacdaadbabccadccdaabbcdbbdcddadbdddccadcacbabbddbbbdcdddbadbdddadadcccbdcaacabbbabcdbaacacdbdcccabdbbddccbddabcccccbddadbbbbdddbdbccdcdadcabdabcbbbbddcaddddbcbdcbdaabbbcaadbaaacdabbbbcbaadcddbaacadabbbacddddcaccbdccbabbacdbbacdbdbacdcbcbcacdacdcdbdaccbabbddcaccdccaabaddbcbdbcddbaaadadbcadddbacbabcacccbbaadbcbbbcbbcaaccbbbcdcccbbaaaaaccdbbcbbdabccdbdacacbdbddcabacdcaccccabadcbabdcccbdbccacccbbdcdaaacdabadccdbcdddadbadbbbdbbabbdccbbccabdbdcbdaccbadccbabaddabaddbcccacacacadddbaacacabbbcabbdacbabaddddcdaadcccaabcdacbcbcbbaadddcbcddbcaacaadbbdcdadabbbddcbaabcbadcbabaccadccddacccacabbdcccabacaaabaaadadddddaccbdbacacbbaaacabacdacdacaabdacacdcabccbbaddcaccdbaabddaacbdccbaaaaabdacababbaadaacbaabdabacabbdcbbdcbdddbdbbadccabadcbddcbdabcbccabddccacdddbbdbcbcccacacdaabccdcaababcacacdccaaccccaaaaccddcdbcdbbdaaddcaccaccabaaacbdcbbacddccccdcabbaabbddccdbaccdccbccbabcbabbabcbdaddddcdddcbdcabdcbababaacbccdabcccdddaccbdaaaddcdbcddbccbcdaacbcbdadbcdbabacaccbacbbabdcdbcbdaaaccaacaccacabcdbacccccdcaabbbbbdabbcacbbadbcabadabcddbabaaaadabacdbcccacdbadcaaabababccccbcbcbcaaabccbbbadbabcbadddccdcccdbabadddbbccbdcbcbbdbdbaadccbacccddabbddaadcdbddaddabdccbcbdcbdbdbabdacbccdcccbccbbbbdbaacdacabccdcddacacaabbbaacdcaacccbdcbccaabdcdddcdcbcbcbbdabdbdcbbaabdbadcbdacbbddaccaaddacdddddcbdbccdbddddbaccdaddaabcdccbabaabdbbdcdacbbccacccaaacdbabdbdcccbbababbbdacdbdbddaadddbacdcbddabdcbddcaababbcbadccbacbdcadbadaabdbdaabdbbcccabaddaacabaadbccdaabcddaabccdadbcdcaaabbdcbdbbbdcdabcbbdaccdccabaadaccdbacdadacccbddcabbbacbcabddcacaaaabdadbcbbacbbccdbaadaabbacdccacaacbbabbccdaddccdacbccdacaaabccadbccdddbcaabacddadcbbcbcaacbadaababadcddccbabdabddcccdbdcccaaaabcdcccdbabdccdbcbbdbdaccbddaaccdbdcdddbdccadcdcbabddabdcdbdaddbadcccdbddcacbdcddbbdbdbdbcdcdabdbcabcbcbbaaabcadcdaabaaaccdcababccabccabdcbaacccabcbcaccdaccaacbdcaacbdcbccacabdaacddadaccaddcdbcbdbbbdbdddcaabacbdaaccabaddcaccaaabdbbdaaccbbadccddbcaccacaddcdcacbdbddaddbdcbabbcacccacbcbcbbacaddabddccbacdbbacacbdadccbccaadccdcdababadadbcccddcdbbdabbdbbabcbbdcbcacadadcabadaddccadaabcbbabbabbadadacccdbdcababdccabcacdbacabccdddadaaccbbbaccdcacbccacacdbbccdbbabacbabbcdbcdddcbdcbaccddadccabdbdddbdaddcbabdaaacaadcbcbcbdcbdbdbadcccbdcdacbbadbadacbcbabbbddacbadabddcabdcaccbddabccabadcababdadbcacddcabbaaabbdbcdadadbbdabbcdadbdadccdddbcdacbabadcdaccbbaddaddbabbadcaccdbcdaddaddccadcdcacbacbcddaaabbdaaddcdabbdcbabaaccabacbcdbcbdccccbaabcbbbaabbbbdacbaaacbbdabdbbbaaadddccccddaacbacabddcabacdcbdcbcaacdcdbbdbbdccddaacadcdbbbcdabdcbbcbccabacddadcacbaabcdbacdabcddddddaaccaaabbbbbbcacdbcdaadccbbdbdacbbbdacdabdccabaaababbbbbacddbbbdbbcddcbaaccaccdcbbadabcbdbaaddddaccdbacbddbdbdabddabaaaaabbdcddcacadccddbabcbccdccdcbabcbbcbabbacdbccdbacbbcccbcaabcdbbdbccbaabddbacaadacbcdaaacddbcadcdccabcaaabaaaddccadacbadccbbaacbbddccacbacdddccacdcbaddabacbaabbbabbdabcbdbbccdabbbcbcbbadcdbcaadccdbcbbcabaabcadbaabcbaabbcabdccdacadbaacdbabcbddddabbdaaddccababdccbcbbbbdbdabcaddddcbacacacababcbdcdcadbabaddccbcdcdacddabaccdbdbbccacacbadbdbadadbddccbcabbccbaddccaaaabdaddadcdbbacdaaabaaacaabbcbdcabbbcdadbdcdcbcddddaabdddacadbddbcacdddbdbddbcdcdcdabaacbbdaadcdcbccabdaaabbcacbaabcabcdadadabaccdbcabdacbcabbcdddbacbdcdaccbdacaabadadacdacbcbcbdbaaabbbbbccdabcccacbbaccabaabadaddaadaddcacbbaaaacdcbdacdcbacacadbcadbdcdbabbcccadacabcbdcccacbcbacdcababcacabdccdbadbcdacbdcbabdcdbaadbccadcccabcddcbbddbbcadbacdadbcdcdccdbbddacccdddcaacadbcbcbdaabbbabdcbacbbccccddbcdadadbbcadcaadcccbabccaadabddddbbcccbcbddcadcbbdadcdcccaaddbccbdbadbacbbadcadaddbcbcaabcbdbcacdccaccbbcbbacadaaabcdcccbbdabdaaddaddbdaccccdaadccacbcddabdddbccddbcacbacadddacbdaaababbddccbbcdadddddbbacbccbccdaccccbaabddbcabaccbcaadcadbddcbcabcdcdbacccdbbdaadadcbbdbbcbbbdbbdbddddcbcbddbccadcabbbdbcbcccaddcdbbcabadcbcbdabacbcbaddbddacabdbdcbabadcdbacbcadabacacbddcdaabbbdccbacdcddbdcdaabdaaaaaaaccccdbaadbbbabdaaadcaccaaaccdacbbdbbdbcbcbcaabdaaccadcdbaddadacdaaddbbcadaddbcdbddbddaaababbcccccbbcccdcdbbcbdacccaaabbbadacaaadccdcccacbdcaacbdddbaadabacabbcadccdbcdcddacdccdabacacbbbabcabcbddbdcddbbdcaaddccbcbbbadcddcbaaabcbadcbccbcbddcdaacdadcaaddccccdddddabcbacabdccdacaddccadbbdcaadbaccccdabbacccbbcabadbccddcadaccdbbcbbdddadbdbabadbabcbadcacdaabccaabbdcdbbaddbdbcdcacbadddaababbbcddccabcbcabaddbacddcaaacacacdbadabcadaccbadaaaccccbdbcabccdcbbdcbcdcadadbdabcdbcbcaacccdadbdbaabdccaccccadbbdacdacabcbdacaaadcaacacbadcddcacabaabcdbbaadccabdbacbccaadaaaabacbadccdccdcccacabcdacaabcbcababacdbccacdacddaddcabbccdcccddadbcaacadbbabdbbbdaadbaaddcbbcbcdcadccdddcadaccababcbcccaaaccbbcbaaacbbdcdbcbddbbddcdcbaccbaaaadbdcdbdadadbbccaaacbddcbcdddadddaadbadbaaacdacbbddbcdcabadabccadbcaaddaaacabbdaabadccabcbabbcaabdadcadacadbddbbacabddadcdbdbdbadcadccdacbbbdcccbacbdaacccaccdacdddacbaaadcacbcdadaaadaaccaacbcadaacabdaabdbbdcdcbbadcbbbbbdaadcbdcaccdcbcabcbbbbccacdbcccdacdabccabdcbddbdbbdcabbabddbdbdbaacbaaccbcacdacabbccabddaadbaccccabdbacabddabbcacacbbaaccaccdcbaaaabcacbbbbcddbdcadcdccaabdcbcbaccaaabababbbadccccacadbbdcdccacdacbddddddbbccbcaacddcaddcadbdbcbdcdcdcbacdbbdddccdbbdbcbbddaccbaadcdabcdcdabcabbaacabbcbcbaadabbbbdabccdbcdbdacdcccddddbbdccdbbccaccababdddbddddacccbbdbbdbbaddcaabcaaccadccabaabdabdaababaabcbcbbbbcdadccbcbbadcddbdcddbdabddcadacbcaadddcabcdbddaababcbcaaadccacbbcdbcdddddacddcdcddbdccddcadadbababbaacabcccddcdbbdcdcaabccadbdccaabbcbcddcaadbbdbbcddaaabcdbddcddcadbadbbddacbaaaaaaacacadadaacaccbacddaadabbddbdadcadcadbdaccbcadcdbdaaaacbdabcdbaddbabcadbcdaaadbcddadbdaadadadddcdaabcdddbadbbdccddaadabdacddbcaaaacbaaaabcdbdaccbbcdbdaccacbbdaddabbccbdbbadcbaadbccabccdadaaabcacdacbbbaaacadddacabbaccdadaaddcdbddccbbaccacaadbbcbcbdabdaacccaddcacdacdbacadbbacacdbcbddcccacdcacbccdabbaacaabccccaadcadabababbbdbbbaddaaddbddccbabadcacbabcacdddbdcbbcbcacbdbabacdacdcaaabdbdcdcbdccdcdbacacdbbcbbacbbaabadbdcacacacaacbbbbaadcbdaddddbbabaccbccabcbddcdcbdbdcbbbcacbacddcdbcddadbaaddcabaabdddadbacdadcacbabadbbaabddabcccabacbacdcdccdddaacbcbcbbccabaabdadddbaacadddbaacabbdddbddadaaadbdddabdcdbcdbacabccbcaabbbaccbddabdaaacbcbabbbcdcbcdbdbcccbcaccadcdccbdaccdbbadadbaaddcbadaacdadcddcaaaacdcadccbddaacccacbdadbaacbcbacbbddaccbdabbdaadcddbdcbbcabdbbaababacdaabadbcddccdaddcdcabbbcabdaacddcbdcbaddcdbabccbbaccbddaabcdbdadacddabaababaaaaccbbdbdcddbdddbcacbabadadcdabdbbacdcbcddbbdcbdbacababdccabadadabbcdbbacabaddadabbaacbccbadddccbcccacbbdbabdcbadccbbbaccdcadbdabaddbcbacbcacbacacadbddaacdbbabcddaacabcddaddddacdbaaccbcdbddccadabcdcaddbaacdcccdacbdbacddaaaaadcabbdddbbadacacdbaadbbaaccddadddadcdcdbddbbcabbcbbbbdabadddabbdaaabddcacaddbbbbaccaadacddcbdbbbacdabdbadbadacaabbbbcbdccdbdabaabaadbbddbddbcccaddccbddcabbbbdaacbbccabcddacaddcbcdabadbcddcbdbbdbacbcaabcbaaddcaaabdcadaaacaaddbaaabdbbbcabdbbdcbccbccbddabdbcbabacadadbcbbdbacbbbcdbccaddddababddadbcccccddaaacbbacdbabcadbaddcaabbdcaadbbbbbbbbdbbacabacdaddaddbcbdddaabaacadaadbaaaaabbaccaaaabbbaabcacaccacabbbaacacacdbaadacccdcdbcbcccbcdacbddcacdbbbbdcccccaaadcabdbbbcaadababbcababbacbcdcddcdcdabacccabdcdcdbdcdddcddcbdddddcbbddcddacbabbbadcbcababbdaadbabbbbbadbaccdbbaadcbcbbbabdabcdbddccccccdaadcaddccbbcdaccadbcbabacbbdcbaadbaadaaabdbbcddabbdaaccdddbbabdbaaccdbbbdcdacdbdbcdcbdbaacabbbdbccbcddaabddddbdaabbcbccdbddbacbbbccbacbacaaadcaddabbdaccabadabaabbcbdaadbddbccbbabbdcacddccdadcbcabbbcbaadaadcbdbabaadacbdbbddaadacbacccdcdcacdcadcbdbcaccdcccbababacbdbdbcdbbbacdccaacbdaadbdababddbbccaabccbbababdbdcccdcacbccccdacbdbdcacbcbdbaaccbccbacadccdacadbaccdbddcdcdcdbaabcbbcacbcbacddbccbddcbaacbdbbbbaadadddacddbadbcbadcdcbcccbcbcdbbcdaddcccbababcabccabdcaaaaaadcdbbdcddbdbbccbcaddaddcbdaaddbcbccdbddcccbbcabcbdbaddbdbaabcbbdccdcccbadddaaccacadccdcbdccccbbabdacbdccddcdaadccdaadcbcdbdbaddcabbddddacadbcabbdabbadccdcabbcdcbbaaaadbdaadcbaaacabbdbbbdccbaacdbdacdddbdabcbddaddccaacaccdadaaddbcabdddabddcbccddccbdacddccaacdccaadccddbaaaaacbdbcccbdbdcdaabbcdabacdccddcdbcdbcbaccbabdbbcabaabcbbdcdabcdacbdabacdaadcdbbdbcabbdaddddcaccccabdaadacaaacbbabccdcdcddddaacacdabbadddaccbabbcaddbdaadbabacccddbbbdbbaccdbbcbaadccacddcadccbdbabdbcadcbbbcdbbdabbbbcadcbbdcaaaaacddcdccaccbdaaaddaaaaaccdbaadcbdaddcabdaaacbaacdbbcdabcbaaddccbaacdcbddbbdaacbcadadccddabddcdbddcdacbbbaaabcddbcaabcbdcdbbccdadbbddaabbbddcbaacbcdccadbabddddadcbaaacdddaacbcacaccdaaaacdadcadacacadddbbcbaababdabbabbccbbbdcddaaaddbabcdcdbbdaabcdbcbbbdaabdabcdccccdbabbaabadcdabacbabcaacdcaabcdabbcdcacaccdadbdbadcbbbdbcadccbadbcddaaadbddaabddddccbadabdaacdadaacaddcbabcdbaddbbaccdddcbccbdbccdbdddaaacddcabaccdbcccbacacaddaaccaabcabbcdddaabaacabbabadabdbaadadcdbbbadcbccddbbaaacdbcbabddddabbabbadbdbbcabccdaacacdacdaabaadbcdabdcdbcaccaabdccdbdabdcdccabcbcbcbbccccbcabacbdbdadaacdccbcdaaaadbaddccdccdadcdacabdbdaacabbbbddbbbcbdbacdcbacadcadadbddccaaadadbcbbabdbbdcbbdbdcbccbccaaddbadddaabdbaccccadccdbdbacbbddbdbcbccaccabdabacbbbcacbdabddbdabcaacbbdaacccabdbbddccaaccbdabdbcabaabaddcadbcadcbcbccaaddbdbbdcdccadbbdcadddbabbcbbdccbaddbdbbabdbbdaaaacdaddbbacabcdddbadcadacbcdadaadbbcbccbdbdadcaccbddacbccdacaddaabcddcbbddcdcdadacddcccbdddcdadacddadabbddbadcddcddacadddddacadbcbcbcbdcaddbcccaddbadaccabaddbccaabaaccdccacbbaccbdbdabccccadbcbcbdbabbbbbdabccabacbccabbddbabdcdaacdbbcbdbaaddbabdcbdadabbcabdbcbaddcdccdbbdabcaadabaccdddddcaadccddddddbbdadbacdadbccdadcbcccbcbabaabcadcddacdbabcdcdbbbbbcadaddadbdcbbcbcbdbbadabaccbbbbbababcdadcdacaacbaaaacbcdaccabdbdbaddbacbccdddabcbcbaddcbbabdacaaddbcbdabcbbddcdcddcacbdabbacdcadbbddbbbcaabcdddadddbdddccbdcadbbcdbaacacdabccdbabdbadcccbdcddbadbbdcbbdbdcaabcbdbadbacbdadbdcacdccadcbbbcaadbdaaaacbbbadbcaacbbccdcacdcccddcccacbbaaabddbacabdccbcaabccadadbcbbbccacbdcbbaddcccbcdaadbcdabcadccdaadadddbdcaccbbcacdadbcbdbabbbdaaccbdcdcdddbdbbcabcbbdcbcbdbbbcddbdcdbabbbbdababadaccbcdccaccdbabddadaacaacacbbdcdadcbdacdbddbaadcbdcdcbbdaddacaabadddcdbcddddabbcadbbbbbdbacddcaddccaaddcddaaaccbcbaacaccdbaccabbcdcbdbcabcdccdabaddadaddacdadbcbdbcccddcdddbccacbaddbbbabcaadabbccdbdadbcaddbabadbaadbccacbadcbcabddbbabbcbacbbaadacbacaaaaaccdbbccdaaaacccdcbcddacdccaabddbbabadbdabbdcdbdbcbbdabacadacaabdbbcdbcdddddcbbcdcabdcabcccdbadacbdddbcbbcdbcdacaaaaaadccdcdabdcacadaddcadbddabdbdbcbdcabbcaacdcdcbcbaaacbdccddbbaababadcdacabddbbbbbbddacaaddbcacdcabcaadcadcccbccbcbdabacbddbcabdacbaddbbdabdabbbaaabbabbbcbcddcccadaacacbcbccaddbddbccabbcbaccabadcaddccbcdcdacbcbcdabdbdaabacbbaabbbdabcddcbcadaccaadabccaaadbddabaccdbdabdaddbbdbccbaddbbbcadccaadcdbacbaaddbacbbddacbacaccbaabbabaacdcaaaccddcccdcddadcdaacddbaacbacbcbcadddbdcbdbbabcacdacdddbbbbabdbcbdbacdadabbbbddbbbdabaaacdcbddbdbdadccaaadcdcabbaacdccaaacaadabbdddbcdbcaadbbcabadbaacdcacabcddabdcdbbbadadabbdccaadcbbccbdadbdccddccbbaadabcbacdacadbcdbcacccbdacbddbcbbdbccdacbbcbbdabbdaddadbddcbbacccabcdcbbcbdacdddcdcdacdbddacddabacdbcbaaccbabbddadaadcdabdcbbacbdaabaacaaaacccacddcaaccabdbbdaadbdadcbaabcbcabacababbddbcdccbadbcbabacdddbcbaddcaacbcadbdacdcbbdacbcacddbabbcabbccbaabcddcbbadddbdadabccadbcdcbdaadcbbaacdcaababcddabcabcddddcabccbaacdcaaaabadbaddddcdadcbdbadbaddcbabadaaccbbadbcaaddaaabdaaadbadcadddcaaaababcbadbabccccbdbcbbacbaacdddbacdcbbbdacdacbbadbbbabccacbccbdcacbbacdbddbccdddddababcacddbcaaccaacddbcccbcccadbaccdcbcaddbbadbbbbbabacacaabddabaaacdccbcbddacabbabcabacdadcbacdddcbdbcbbcbbbcdaabbdaadabcdbcddabbabaaadbdbaaccaddbdaaabbaddcacaacdbccddbacacddbadbaadbdadadbacbdbcdbbdbcacdbaaacccabdaccababaccadcbcdcccadadbdacbbbbbacacdabdbcdbaaacbdcddbdccaaaabaaabadcadcbacabbccdccdcbccaccdaadacbbaccbdadadcadcbadbcbdbdbdabcdbabbccdadacdbdbacaadabadadaabbddaaaaccdacabcbcdbcadcadadcbbddbbcaabddbbdbdabdbadbdddcccbbadbbadccbdbccadcbadcbcacabababbbaddbcdddcbbddbaccabbdcabccacbddaabbdadcdcaababdbbddcbcbdccabbaadabcbaddbcdbcbbbbdcdccaadddbaaadccdbdbcdadcdcaabdbccdbbadadabbacbddccabdddbcbacbdaacdbbaacbbdddaaccdbacdcacbddddbcdcdbbbcaaacdbacdabbcadcdccbcccdcdddbbbcdbdcbaacccaadddcacadaccbdcdcbadbdcdbaabcaddbbaaaddbdcbdcabaabccbcbabaddaabacbaacadacdadacdadbdacaacbdadbccdabbbcccadddcbabbcabccbdccbddbcbaababaadcabccaadadaacbcdccdbbbaccccacbadccacdccdcdaaaadbdadcbddaabbdadddddddcaaabcbabdaacddabccbcbbdddaaadbddadbdaaccbddcdccbaacccdaaabbbcbccdcdddadabcabbabcbadcdbbdaacdaddcaaadbdcdbcacacdbcccccbbabacddacbacdaaaddbcaccddcaccddabbbabbbbacabacbbccccacaadacdddadbbacabaccbbadaaadbbacacbdadcdbbacdadccccdbbbadbcadadbaabacbccdabaaddaaddccdcadcacadcbdabcbbdadacadcaabdaacabbadccbababcdababdbccddcdcabddbcccccbaccbbbcccbdbccdbcdcbaabaccdcadabcdaccdbacdccbdaabcbdaadccababdcbcbadbbbcbcabadaaadcabcbaadaacdcabcbcbbbacadacdbcbcacadddbcbbddcddbbbbaabadddcbaaddabdaacccbbcaabdccacbbdcbadabbabbcababdccdccbabccdbdbadcadbdbdabadbdccbbbdcabcdcdcbcbdcccaabbdbbcaababcdbbbdbbddbcabbdabdbbabdccadbdbccadbbdaaddbbcacadcbcaadbbdabdcbbdcbccaaddabddabaddcaccdcadbabccbadccaccdbcdbbaabbccaaadbccaaadcadbccadaacbddcbdcbbbacaabadbcdaabcaadddacdbbdadaddcdbcacddbcdcacbbddbbcadccbdccdaaaccdbaaadbadcbbadbdacdcaaccdacbddcaddbabcdababcadcbbdddddcdcbdbacbbbabcabdddbdbbbccdababaacbbdabacbabcdaaaabbdbbdaddbcbbdaabccaccccbbdbcacdbcccaadcdaccbbcbbbdbbadbddbdddabcabcccddddaacbbcdbddcdabdaabdabbcaddaaabccadacdcbcdddcabcadaccacadddbdbccabdabcdcadabacababbaaabdcacacccddacdccadbcdabbcbdcddcaddaccbcdacbcddcdbdadbaacdaabadbdccbbacacacdaacccddaacadbcaacbcbbddbbcbccadbbcbcabcaaddccbbccccbcdacbbddbbdacadbabccaaaaddcdabcdacccbdacbcadbdcdcbbdcacccdacddbcbadbcbbdbdadddbabbdcaddbacaacabbcabadcadcdbddcbcccaccddadabcabcadacacbdbccacabbcaaaadcdadcbacaccadacbbdaaabdabccbaadaddbaaadcbadbdaaccadadcaaacccbdcbbbadbabcccadddacdacacbcbdaddbbabbacabddccbddcdcacdcdbcccbbaccbbdbbbdbdcdbdddbcbaabcbbcabccabadcababbadadabdaabccdcadcddbdadacabbacdcbabccddcbbdcdbcbbbcabbdddbdcdbabbcdcdaaadbbccbbadbabccadbdcaacaccbdcabcbcbaabccaaabbcacacabbababccccadddcacbaaaacdcadabdbbbdacddddbcbcdcdaadcbdcabdbdaadbabbadbababcdcbddddcdcabcddcbbaaaaabdabcdabddcdcdbddabbababacdcdcabaacdcabbcaaacacdacbcdccaccacbaabcadadcdccadbdddcdcbdcdddaddccdcabbcaccabbcccbdcaccacdbabacacacdbbdccdcabccdcababaccbdaadccabacadccaabaddaadcbcbcbccbdacbacdbdacddddddabdcbdcdcaabbacdddbbdadadbbdaaadaddbddacbbcaccacbadcbdcbdabdcdaddabcadccaccbdcbdbdcddaabbccdcdccdcdbacbcbacaacbbcbbdbcccabacaacaaacaaccadadabbaccdaccdacacdacccabaadbadabbbaddccabaaddbdccdbaaacbcaabcdbcbdbbbdbbbbddccbaadaccdadacdbcaaaccbadcdbbabccbcbdbdcbabcdcdcadccadcbcbdddbabdcbacaddcdacdacacdccdbcacabdbddbcdcabbcbbdcdddabdbdbacdccdbacdcaadbabaabcbabaaacdcbdcccaadaaabaacdcbdbbbddcaabcbaddbbbbcdabcdaacbcabcdcddddddcccbbaabbadbdadbdadbdbaadbdadbcdbddabdbaddbabdbbcadccdacdacdddccdaacdbbadbabacdcaddaacbbcccdacbacbaaddaadabbdddaccccbbbdadaccacbdbabccdcddbdddcbcaaacccababdbccaccacbbbacadcdcaddbababbdacccbacdcbdabacadadabcaababddcbddcbdcaabacbbcdacdabadcaadadbabdaddabbcdcbbdabddacddccabcdcaacdaddabccababdbbdcabbbadbbdddabbdacbdcadaacaabbbbcacdbadaaddddccdababddbdcdcbbabcdbabaddcdadddaacadbddcdabddbbccccdcbbabaddbcdabbdadabaccdacaabbacbcbabbaabddabcddcaadcbaacbbccbadccadcbacbcbcdcbbbcbdcacbbcdbbadacbcadabcbabdadbcdaabcbbbbbacccdbcdbccdaadbcadbadcdbaaaadbcbbacaacaaaabddcbbbabadcbabaddccdbdcadbbbcdacbcddaaddacaaccbabacccaaddcdbcbacdcaacdcdbddcccaaccbbdddadbacccdaccbdbbdacacdacbdcddbbdbcabcddcbdbdacccabbdcdcddadcccadbdbccdbbcddbacabdbbcdbddbcccccbcaadabccdcbcabccccbcabaaaabadcadcdadacdbdabdabcdcdbddcdbbcdbaddcdddbccacccbbbdcdaddcbacaadadcbcbbacdccddcdadabdbadabbdadacacdcdacadbccddacbdddadacccdcbdbdbbadacabdcadabbddadddadcaaaaabbdcaabaaabcccdbdcddbdbdbdaddcdbbbcaacacdbacbaacdabbbdacabaacdbdddcadababbcbddbddbbbdaaacdbbcdbdcabbddddcaadcbcdbdbbadddccddabccbabdacccdaacdabbbbdadabadcbaaaabaabcbccacbabbbdccabdacdabaacbaabbcbcbcdcbbabdcccbbaadabdcbaddccddacdabcdcbadcbaccdacddbabbcdaddcdacdabdddaddcacdcdcdccbaddcadacacbadaddbcbbabcddcbdccadcacbcbbcabdabadcdddadadacdddcbdabcbcdacabaddabbcaccabcdaababcadbabcbabbccdbabbdcabbbdbacdcacbcdcbabcdaadcbcddbaadccccabcadaacbbdadacadcaaaacdbcaaabcddbbaaacbcaccabdabbbdaaabbbdcbcaabdabdbdacccddcdcdabaabdbabaabbaabccbcabbadabdbbbabcaacaddcacddddbdabacbcddbdbbcdcccadddcaabcbaaddbcddacdbcbbddbbabccdabdcaaaaacccbabdacbbbcdbbbdcabbaddabdcbcbaccccddbaccbccbabdcdccdcbaccccdbbadcdcacbcdcabdbacbdacadddddcccccbdcdacaaacdabbaddaaccbdcacccccaaddacdababcacbdcaaacbabbcddbadbcacabadbccabdddaadaddabbcbabdbdcbdacbcbdabdbccadbdbbaaddadbdbcdbdcbadbcccbcdcbdacccdbbcbdcdbadbadcdaaccbdbadcacdaadaacbaacabaaaaccacbaabacaadcbcbacbcbcddaddbabcabcaaddabcaaaabccccddcacddaccbabbabcbdcbddcadaccabcadbbaccbabcbabcacccccaabcddcbbabddbaaccabdcdcaaddcadadbabdbdabacdacaabdcacbbcbdccbbacbdcabbbadbddcdbcddabccccdcbbcccccbdbdbdaacdbcddabadabbacdadccbddccaacbbdbadbdabbabacaaabaaabcdaacdcabcacaddccbddcaabcadcdaabcabaababbaadacbcabadccacbdaabcaaccbdcbcdbdaabbaaaaccbaddbadbcdddcddbabcbddcbccaacbdabdbcdadadbdccdbcbacacadcaabacabcdcadddddabdabdbcabcdcbcaacaacbbabaabcdbaabacdbdaacbaadadcbbdcbacddadbbdbdccbacbdacadacbadcaacdcabccaacbbadaccaacdaaccbbdacdaadaadbdbbbbbccbdcdcbddbcbabcddaaabcadcbabddbaaadcbcdabdaddddabdacdbdcdcccdbaccadddbcdbbdcbbdaaddddbcdddbdcdcbdacbaabababcaacacadaccdbdcbbbbccccbbcdbcccdbcabdcdadaddbdcbddddabadabccdcacbbccdccbcdaadbbbbaddbbcbcddbdcbadbbcddabcbcccdddddccccdaccbcdccaacbccbdadbdcddaadccbccbccdcabddabcddcacdbbacdcabcbcdcacabdacacdaadbaadbcdbddbbdcbbbacdbaaddcccabdbcdcacbbbbbdccaddabdabaddbadcccababadaaccdadbabdadbdcbcbacaaacdaabcaaddbaacdcabccbdacccddcadaccabdbdbbddabaccdbcdcaaacbabbbddaacadddbcaaacddaabbbcbddcdcabaabcdbdccabbcbbdcccbaaabaabbaccbdbadbdaadbabcabccddccaddaaaacacadbdbaabbadaddbbbacddabdbdacaaabcbbcacdbcdaaadcabddcddcacccbdbaacbcbadabdcdccaacddbcddbddbcbccdbccbcbdcbacbdbacbcadaccdaaccaabdabbdabdaddcbabdcaddddbddccddcccdcadcbccadabbdccdccaaaddbbaccabddbdbdddddddcacccdddbbcadcadadacdaaadbcbadaaccacbcccaddccbdcdaadadbbbdaadddcdbaadaccbdbcaacdccddcaadccbacdbcddcdbbdbcdaccbbadbadcdaaaaaadacbdcacbdcddbccdcabacbdacddbcaccddadacaaaaddddbcccabcaacbabdbccacbdcacaacccdbdacadadaaccbdcaadbbcaacdddbccdcddbbcaacccdaacaabbdacdddaddbcddadcdcdccacddababaadbadbdaccbadabbdadbdbdccadccbbacdcbccbacbcbdbbdcadcadcabdbaddbbccdcddbccccbddadddabdadabddacadcbaaaddbbdcdaaccccddccbbdbdaacabbacaadacbadabccbddcabcdccacdabddcccccdabcddacbadbcabcaacabccdbbbdadaccadacbddcabbddaadbabdadacbddbbbdcbbbbbcdacbccacbbadcdabbdaccccdabbccaaababddcabcccddbcaabadbaabbdbbacbbcccbdbdaaccdcdabcbdbbddbdbdbcbdadadcaaabdddccabcbdcbaaadadabadbddcbccddbbadbcdbabdadddbbdcaddababbadbacccabaddcdbcacbbaadbabbcbaaacbdddadaaccdcbaddcdcdaddadcabadbaccbdbbdddadbbdacdadacbdcdaadcdbcaacabbddbccabccaacdadbabcccaaabccddcdacbcbdbbdabdddabbacdbdcbacdbddabccbddccbddcabcadbbbbdddccbacccaddcdbbbcdddaaacbdcbbcadcaabccdadcbdbccbadddcdbccaacdbcddcbcddbbbaccdabaaccccbabbadcacddccadcdbdacaadccddcdbccabcabbbbcddbbbddcbbabaabdbadbcdacbcbbccbabdacbdcddcbdaaadcaadbbdacacadcbbcadbcabdaaabdacdaabdbacbcaddadccbcbcbabadbdddcbdaddbaccdccbcbddbbaaacdabdcdcaaabbcbbbacccbcddcbdcccbdbabbaddbdcddaccabbbadcacadcdccbccaccddcbbbccbccabbbddcdcbccabbbdbddbdbcdcbbaddbdddbbdbacacbddddcaaadcdcabbcccdcddaddcdcbcabababacbbdddccbdbbbcacbcadbbacdcadccacaabbbbbacaaccddcadbcadddddbdcaabaccbcbcaaacbaabcbaaaadabbacddadcacaadbddccabcdcdbbccccbabacccbaadcdbadbdcadcadcaadadabddbadbaddaacdbbbadbbbbdababdbadaaacdbbcbddbbbaabccabbdaacadacacddcadcdbcdacadbabcdacdbcbcccbbcabcbdabbdaddddabaddaddadacbccaaabdbbbabdadbbbacbcddcbcacbdaccbddadccdcbbaadcccaadddbbaccddcccbadddabbdbbdacddcbcbddbbaadbaaacbdaddcdbbabbbcbbbcddbdaadddbbcbadcbbabaadbdcabbaccbdbbbdcddcdcacbdccdcbcbaaddaabbdddabaabbbacacdaccacdbbacaabdaccccddcdcbadcbcaaaadbddabbdaababbcbdddcccbbaccdbcbadcdcbcbbbaccaaccaaadbcdccdbacaaaabddddaadbbccbddaccadddbacccacdbcdaddbaaadccdadccaadbbabbaadaddbdddaddaaabcbcabcaaacbabadcdcbddccbdcbbcaaabdacbadacaadcadbccbdcabbbdaababdbdabdabcdbddbdbccbcadbdabdacaabdaabbdbadddbddcccccbbcbcdddcdbbadccddcccdabddaaddccacbdccadcdcbcaadbbababaaccddbdabcdbccdadbdddcbaaaaadcaabccbcdbddbccacdccacdacdddbddccaddacdaadbabdcbdadbdddacbaccdcbbddccadddbbcccbabdddccddcadadacacdcbabcdccaddaaadbcbbcdcbadaacdbdbcddbccaccdcbbacacadcdbbddbcbcbaaaaaacabaadcdcddcadcbbddadaaacdddcaabbcccdadbcdadcdadcbcbaadcbdadcdbbbcabccdcadbadbacbaccbcdcccbbbddbcbdacddddaaabacbccabaacaabdacddcbaaadbbdaacacbbadcbbdbcaadbadaccdadaacacdacdbbcbdcccdcdbbdaabbaabadaddcabccdcdabaaadaaabdacaabbbcbcaacdbcbbdaabcdcdacbcadadcabccaddaaaadbcaaccaaaaccddacacaddaabacdbcbccbcddbacdbacaadbbdbcdacdbbcdcdbdcbbaaddcdbaaccbdabdbddacabacdabbdcbaccccbdadcccabbadabacddbcbbcbbdbacccabcbaddaadabbaaccdbdcbdcbddbcbcdbbccbddddbcacbbabcbbacacadadcdbabccdbbccbaaabadcabbcaaabdcdabdcabaddaabcccbbbbabacaadbdacbdadabcbaaddabbbacddadbbbcccdadbaababdbdccbadabbcddacadabbacdabdbaacccdadcbcbcbccbaacddaaacaaddbadbdbcadbbdcdaadacbcabbacdcccdccbcadbddcddbdccccbcbbaabaadabddadbbabdcdadccaccbbacaddbcddcacbdbcccddccdbadaacbacaacddbdccacaddabddaccbdbbcacdbacdccaabbbdcbbbcdcdadcbbaccaaddaacbcaddbadbccddccaddbcbbabbccabcdddabbccbadcbacabbbaddccdabaccdbcaacabbccdbaaadccabddbcdcdcbccccddabbcaabacbadadcdcabdbdacbccdaaaaabaddcabaccadbaccddcdcbabcaaccacdcbdbaccbdccbddcbabcbddabdccdbbdbbbcccddccbdadabadacbcbcabcbdacdabcacdcdbbcaccbadbcabbdcaccabadabdcacaabaacbdacddcddbacbadacbcadaacdbdadbcacbcabacaacccbaddddababbddaddcbdcbbbadcbcacbbbaabccaabcbdcdbccbadbbcbaabadcbccabacdccccddbcdccddbcdcccbcccdbdabdbcacadabbddaccaaaadacbbacbbbaacaddacadabaaccdbaadbacabcbbbcccbccadacdbcdcbccdcabbddbacaccdddcaddaacabbaaacabccbbbacbddcadabbcadcddddadbacaccdbdabccdcddbdbbdcddabdbbdacacbbbdcadaaaacbabbaacacbadcbbabbccdcbdcbcabddcdddcddccbdbbdadbbadabbdbdacadaabdbabdccbbcbaddbccbdbbcddbaaabacacccbbbbdcbbdabdcacbcdbdcddcacbacdbadbabdadcaaabbbabaddababcadcadbddbcabacabbcbbbbddddabdcbdadaabaccbcacdbaaacdcbcdbdacaaccdadaabccbabbdaadbdcdddbadcdbcccdbbcbdcddddbdbacdcacdcabdaacaaddcbdcacccdbcbabbbcddbaccdabccaaadcdccbddcaccdacdbbddadbabdadacaccccccaaddadacbddcccbcbbaadbcbccddadbaaccbabcbbcbdbdccdbcbdbcadccbccadadbadddcccaddbabbdbddabcaaabdcdbadbbccbaddcccaddabcbadacdcbcbcdcadbaaddbdbddbbabbbdbdbccbdcadbdcaabdacdcaacacbcadcddcbcaaacadaabadaacddddbaacdbcbbdaddacbcbcaacbbcdccdbdddbcdaddaacddcababcadabaccbabdcdabbaabbcbacadcbbaadbabbddddaaccabadddddbbbabbcacdbbdccbadacbdabbcbaadcbabcccacbbabaaccaabcacabcabcbdcccccabdadbdbdbaacbdddacacbbadcdcccabcaacccbdcbccdbabacadbbbcdddbbaadbbbcaddcbddaccadbdbcddbaababaddcadbbccdbadbaaccbccaaabdadcddbcccccbdcdccacbcccaaccacdbbccdcacbacdccdddacbcdadddbbaadbcdaaddbccabcaadcaaabcccddcacdaabcbcacbabdacbbaccdcacacabccbdcbbcdabacdcdbbbcdbadacbdccaddcddbdabaaddbcaabcbaadbcadbaadcbbcaacbcbabbccbbbadabdcbaacdbccbadccabacdbadbcbbdcaaacacbaacabcabdabccdbcbaaacbdaadaaacdbabbbaadccdcadccdbcadcccdbcdcbaaddccbddcbacacdbbbbabbcacdbcdddbbbbabacdcddaaaadaadcbbcbabbbdbbbbccadadabaaddbbddaaddcbacbaaacbacdbcaddcaadbabcdbccaacbacadaddbbcababccbcabbbdaacbadcbbdabbbccaadadccabadcdbdacdbbdabdadcacbbccddcdbaaababbcbbbccadaddacdddcacddabbabdcdaaddbbabdabbbdaaaddbbbcdddcbacddbadcddaacbbdddcbdbbdaddaabbbcbbcdababddcbdcacadcdadbddcdbabccacdddcdbbddbbcaadcddccbdbdccddccbdbdbadbdbbcccbaabdadccaccabccdbadbaaddadcdbcbcddcbdabcacbcbcdcabbcdccabaccdcacbbdddbdbbdcddddcdaddabcdcbcddabbadbcaabdaaddacbddbcaadddcacccabccaacbabdacaadadbcbcdaabbaddddddcaabbbbacacabababacbbaddadbabdadcdbacaadbaaddacccdacdcccbbbdccbadbabaabcbdaaacccdccddaadbdcbaacddcdbcbadcddccadddcdcbdccabaabbbbdcdcddadbcacbbcdddaccccbddbdaadcdccccacaaaabdbdacadaccdbaaccbbddadbbaddcaacdabbacdbdbdbabcabaccdacdcbdddbadcdaaccdcaabbaacbaaddbbaaacdccbaabccdbbddcddcabdcdbcbdaddbacdbaccdcbcabdbdcddbcbbdacccbbdcbbbddcaccbbabaaccbcaadacdaddbdbdadbbccaccdaccbabccacdccdbbccdadbcbdcaaccacddbbabdbbccadbcbadbccdbbbbcbcbbddbccaacbbdbbbdcbdacccbadaaacbbdadacabdbdbbdacacccaddadbcaabaddccadacabdaabddbdbadadddcacbcadccbabbaaccdcbabcacdccbabaaabacbbdcccbbbdcdbdcbdbbbacacccaabacaadabaadabababaacacbcababcccbbcaadbddbbabbddabdcabcbccdadbdbddabdcccbddcbcbddabbbdcaadcabdadacaccbaaccddaacabbbcaaabdbacbcbcacabaccbccdbbdabccaacdaddcaabbbbabaacbabaabadcbcdbaaabbccabdddcdcdbdadabacddccdacacaccddacacccccaabaddacbdabaaabacdbdbdbabbbccaacbabcaacbcddcaacbbaddaaddcbbbccaabcbdadbaacaccccbdcbdacbbaacbddcdbdaabbcbabbccabcaadbcdadbabbdbcabbcbaadddbadbdbbcddbbcdbcacdcbbbacbbbdbacadaadbdddbddaacddbbaaadacdbdadacaabdcadbbcacacdcbbddababaaabaaadababdbdbdabcdbdccbcaddcacaadcdbbabcacccabaacccccbdbbbacbdcabcbdcbdccadddbcabdddaccddbcbdbdddbbcaaaabaaaaddbdbabdddcbcaabddbdcbabcaaacaabddbbdcddabbbacccaacdcdbaaddcbcbccbdbccccddaabbcdabccacbbbdcabadcddbcdbdaabcdccbaadadbdadcacccacadaabdcbcbaacdabcddcbbcbdccdcaddbbdaacdaadaabcdbbcabcdbbcbbbadbbdddccadaabdbcbbdccbbddbabacddcbaacaacacddccadccdcaadbacbabddddadcaadadddabcaabcdccacbbbaaddcbaabacddadababaacaacdbaaaadbccacacdbcdabdccabdcacbadbdcaabbcdaacccccaaadbcbaacdcddcaaccadaadacdcbbadbbdbbadccbadcbbaaccabddcbbdadcbdbdddcabccdbdddcbdadadcaababaabbbadbcbdadcacdbbccdcbcccccacdcbcbdbbddadcbababcdbbcaaabcdcbccdabcdaacabaadaaddccbadcddcaaabaaacadaddbaaaaaccddcabcabaccddbdbcdadbaacddbcdcabddadccdbbbacaddaccbcbabadcdcdbcccbcccbdadabdadabbaddcdacacddcbbddbcbddacadaabcaddaabadbcbdbacbbabbbbbaabddaaabdadcdbbaadcdadbbbdbbcbdbdabdaadddccacacadadcdacdddbcacaccdcdbacbbadbdbbdcbabbdcadaacbcdbbbdbdddaaaabbadcdcadadcbbdabcccccadccbdcaabaddaacdcadaaabacadbabadccdbddcadccadacdbbdaabcaaacbbdcbcbaadddbddbbccdaccaaabaaaadaccabdccbcadbcbddcbcbbbdaacabcbccbbdacddddbddabcbaaccbbacccdbccdbacbccbabaaaccacabbccdcbbadadadbaaaababaaadcddcbbbbaabcdbbbdcbaabaccadadddadcbddddcbbdcdbcdacccbaaabcdadcadbccaabdbddbcacdddcbdcacbacdbaccdacbdcdadddbadaccabacbbcbdbaaabcbddbdaaaabbcddcabacaccddabdadabddbdabcdbddbdddabccccbdcbdaacabcababdbbccdcbbccdbcaddbdddcadabbdcddbbdddcbbcacbadcccdacbcbccabaaaaaacadcbadadbdbbbaabbabaabddaacabaaacabbcbcabcaacabcadbadbdaaadcbacdbcacdadbaabadaddabcccabdacacdadbcbbddabbaaadbbadcabdadaccadabaaaadccbbdbcbaccaccbbdacddbcdbbdcadcaacdabdbdcbdcdbadcdccdadccccdbbcbbdddbcdaadabbddbccbbbbdcdbbabdbbacdbdcbbababbccddcbdadadcabadbabadbccbbcbdccbdbbbcabbbadadbdbcdbcccaddcbbdbbdacaacadccdbadbbbcbbdbcdacdbcdacbdadbabababadadcaabccbcbdcdaddcbbddddbdbbcdcababcbdbbbdbdbdbaacddbccaabacddbddabbaacbdcddaabcdaacbbbbbacbbabcacaaacbdabdbbdbdbdcbddbdbccacdbcbbaadddcaaadaccdbaabdabbacacdbcadabcacdcbacdbdddbbadbbbacdbcacdbcacacabdbcdbbdddadbaacaabbadcbccadcbbcbbcdadaabcbbccaaabaaccaaabbbbbdaacaadcdbacdcdcabaacabaacbaacdcbbdacdaadbaabddaddaadadbccabccbcabdbbdbccabdacbabdaabcbcbdddabccbadddbcccaaaddbabbbbabaccaabddcbbabbacadbaadcabddccacacdadbcacccddabdddaddcbcbdcbdbbacacbcdbddbbdaaadcdaabdabdabbbbabdbbabcaadbabdbaccbcccccbabcbbabadbcadcacdcbdaddcabdbbdbcbbbabaacdcddcbcadcbdadadaaadbbcccccccbbbdcccbccdbdddbcccbacdbdbadbbdbcdaadbdddaaccaadccaddcbddccabcdbadbabcaddcbaadbdbcbabbbcdbcddabcddcaaacbdddccadbdcacbcabbcbbddadcdbcabdbbadbdadaadcbcbbacbbaaaaccbaddaabadbacdcadabaccbcdacbdbbdddddabdbccbdbacbaadcbbbbdbcccdbdcdbacdcdcdacadbdadabaddccbaadcddcacabdbbbaacbbdddbddbaddadbbdcbabaccdbcdacaabadadabdcbabbccdbdaccbcbdcaccbcbdcacadbcaadcaacbcabaacdabbaccbdabadcbababcabcabddbccacdaabbabdacbaababdbaaddcdcaaddbabddbbcaabbabacdcdbaccdaaabdcdbdccaabcbbadbbbadcdacbdcdccbcbccdbdbdbaddabccdccbbcdadabdadbccaccadcbacdaabbccdcbccdabbababdaaadadddadcccababaadcdbdcadacbacabcccbbabbcbdcbaddacbdddaaabdcacbabbdbcadacacaaabcbacabdddacadccbcdcbadcadaacdcbdcddcdaaccdcbacdcbbacbbdcaddbacdddcabcdbbbbadcbdbccdacaaacbbbbddbaaaacdacccbdaabbcdadbdbcdaaccbabbdcbaabaadbcadabdcbaaccadabbcdcdcaddbdbcdcaddcdbddbdabbaaddcaaaacccbadbdcdbccdccdadadbdadacbdcacbcdcaddbbcdabcadcabdccababaccbabaaadcbbccabdbbddabbddcabaaccaababbcbdcbdbdcabababdadcbbddbbdadcdaccbcdabcbdacdcadbadbbbcdddabdbabaacacdcbcacccbdccacdbddcbaddcdaddbdbbdcabdbcabccbcabaadbaacdbaaababdddcacaaddcacbdacbbabacabcadcccbaaddabacdcabadbdcabcdcdbabcbdbdbdaacaccbdddddbbcbcbdabaaaabcabdadcbbdcdbdaaabbaddabcdbdcddaccdabaaaccacbacbcabcdacdddccdaabadacddadbdcaacdcbbdaabdbdbccdababadcaabbbddcacbbbcbbcbaddddbbcbadaaaddbbaabaccdacccbcdbbaababacbbaccccdddabcddcadacdccbbadbdddbcdcddbbdddaabbcbdbacbdadcaadcdadcbbaaadcadcddacbdccdbacdaddcbaacadcbbdbcdabaaccbdbbdaacadabaaadccbdabccccddbbbdbacccddccdacbddddccadabdddbacabddabacbcbadaadbadcadbabaacabdabdcdabcccbdcabccddbacdbcdaabbbcddacbbacbacdcdccbbbbadbabdddbdbbcdddacbaccbabcbdcdbacccdcbaccbcbcdbbddcaabcccdadaadadadbcdadbbcdbddddcdbcabddaabdcabadabcbdadabcdcbaabbcaddbdcddcbdaccacdabdbddadccbacdadbbbdbaddaabbadbdcdbabbccaadacaaddaccaabcabbccadbdaddaaadbcbccadbccccddccbdbadcdcddbbbccadddacabbbabbcadbddbdacbabbcacbadaccdaddcbcdcbaccaccddbbdadcbabcbadbaaddcaccdbdccaacbacaccbbbccbdddcdbbcaabdacabacabcabdaccaddbbdcdaabaadbacbbdbdaacaaddbdccdabbccddacbbbaddabdbbbcabccacbabacbacbacdadaabacababacaaddadbcaccdcbcdcbbabccbddbacbaaabaccdbadcbcdbccacdbbddbacddccaaaddbbcbccabddadabcacdbcbccadbdddccbabbdbccdabbadadbdadbabccdabddddcacaadddaabddccadadbcaaabccbbddbbacbcacdcabddcddbcdcddbdbcadccbacacbbbddcaadbddbaabddccddaccdcdaabcdddabcdaabacdcaccdacbddabdabcdddbbacbccbabbadddbbbbdcdcadaacbbabacbacbcabddccbcdcbdcdbbbabcdbcbadabdaabadbdaddbbcbadaabaccbdbbaacbbdbacbcacddbbdcddddcbccababcbdbbabbbcaacabdbbcddcaacbdaabaccaadcacabdabacbadbcaadbccbddddbccdddccdcbbaadbcdccacbbaddaaddaadcbdadabaaccbcabaccdbcbdcdbabaabcdddaacdaaabbbdbddbbcadadcddbddbbcccabaddbabbdbddacaddaacbbaccbcaaadadadbddccbbaddbddccbaacbadbacbcaabcdcdaccaaacaabcbcdbcdbdababaacabbaabddcbcddabbaadddadcaccccdcbbabbabdadabaaabdadcbababcddababcdacadbbacdcacbdbcbacbdcadddcccacaacbbbcccadaabcdcbadacadadaadabcacbccdbccbacdbcdabababbccaabccdaacaaddbcbdbbcbccdccacaaadbcdcaccabadbcdacdbaccbbdccbaabdbabdcdddaadaabcbabddccdddabacbccabcccdbdcbbaaacbacabbacadbdcabbdcdbdcaaddcadaccdacccbdcbbacbaabbabccaddbbddcbdadcdcbabdbaaabcbcbbcdacdacbccdaccbbcbdccabbaabbadbaaacbbdbbcdcdbaddbaadcbadbdaaacbccbcdcdccaaddababbdcaccacaddacbbccbbdbdcaddbddabcdaacabdadbbbbdcacdcdccaabbdcaaccbccabbbdddacdcdddabcdaadacaadbadcdbcaaadbdcadabbddbdcaaccbdbdababbbbcdbdababbcacdbccadcdbbbcdbabbddbcbacdaabbaddcbbadcbbbababddaadbddabcccbddbdbaaacadbcdaacdcbdbbdbbddcdcacbabaccbcacdbddddddbbdcbcaadcbaadaadbddaddccbadadadcbccadbdcdbdbdbdbcbccacbcccdbdcbacbacaaaadaaaaacbcbccabaabdccdbadcbdbddacaabaacbaadabbbbddaaacdbcabccaaabcdadcbcdbdbbcaacccccdbccccbbbccbaddaaadbbdabadabccbdacbdacaadccbdabdadbbaddbaddadddccdacdcbbbbddbcbacadccbacaddbbaabadaadccbbcdbcabddcacdbabaccbcddbdbbbdaadadacbcbaacaccbacbaabbdaccbcddddbdcbddadcaddcdcbdbbabdaadccabadacdbccadbccaccbadbbabacaacbcdaaaabbbdacdccaaacdbcdddddbbacadbbaddcbadbbddbabcdcbcabbcbadcdbcdbaadbadabcabcaadbdccdaaaaabbcbaccadcbbadbbbdccdabbdcdaacccbbdbaadbccbbbbabccaadaccaaddcdddaadbbdcadaacabcccdabcdbdabdcdcbcaabdbbbddadcdbcdcaccaabcacccacaddbaccadbacddaacbbcdcbbabcbbddacbccababbcbdcccbcdbcbddcdacdbcbcbdbcadcccbadbbddaaaddcbddcdcbccccaccbdacdcaaadbbcbbdbaacdadcccacbaadaaddaaadbbdddddadcbadcdbdbadcdabadaaaaaccdbcddcbcddbcccbdaddccdbddccabadaacaacbbaadabbdaaddaccbacbbcbaccacacdbcdddbadbddcbccbacddaaaaadbddccacdabcbaaccaaaaccdcbddbbdcdbcbbdcdaddadacdbabcbccdacbcacdcbddaddddaccbbcaaacabbbcddcbcbadbccabcaabbdaabdadbbcdbcdddcbdbadbddccbbbbbcbbdbdababdcdcbadaccabdaabdacdbdcabacbdcddadaccaaabdacccbbdabdcddccbbbcbadcaacaadcaadbdaddcbcaacabbbcdaccdccaacacaaabcadaccadcaacdaabcbdbbdcacbcadbaccdaaabdacbadddccccacbbdbadcbaaddadccbdadcdabdcdcadbddbabcccdcacbbcabccbdccbbaadcbbcbdbaccdadccaaabcdcdbabbcbbdcdaaadbcdabdbcbbabdadaabdcdcdcccabaaaadbaddcbcacdbbacdcbacbdbababccdacdcabdaaacbcadddbcdadaadabbadcbbcabcadbabcbabdcdaabdbbbbcabbddcbacbbdbdddbdadaaacbdaddaaababcbdcccacdaaccacbcdaadbdbaabdcccbabcaccdcbdabdbdbbadacbcccaadddadbcdcdadcacbadacddaacbdbacacabdcdbcacabbbabdcdcadbcaaaaabacbccabdcbdaccabcdaddabdbdcdabdaaddabbdadbcddbbccdcdbcdbbadbddcbbbabadaabdabaccddcaadcacdacaaddaabddcbbabadbddbdcdbcabbadabddcdbaaccdcbbbdaddadcbabacbadcdaabbbdcadbdddaaacaacccbddbdabadabbbadbaadadcddddccbccbcdacbdbccaaacbaaabcdddbdabbcbddbcbaabcbcbaabccdcbccdcaadcbaadccddcaacadadddccadacccdbbdadabaddbbdbddbdcdaacbaabddbaaabcdbbbcaaacaaacdadddacbcbcdcbbaabadaaadacbacdbbcbdaabdbbdaacddadabdcddcadbcbcdbcaaddcabddbccbacddddbccdabbddaadacdabadaccbddaaccabdbdacbabbbdacddaaddbaabbccabdbabdddbcdaacbdaadccbadddbabbaaccaaacaaccddacddcabbbbacdbbcadddbbddabdaccbcdcbdbdccbabcabcdacdbadabccdabbbbccbaccadcdaadaaabbcbbcbddcbddbaacccccdbbddabccbacddacddbbaadbdbbdcdbbacddccbacdbcabddcaaadabacdabcacbcabddaddcaddcdcabacdbcabbdabbcbcbdddbdbacbdbddbcbcbabcdccdaaaadaaabaaabbdabccbdcddaccadcacdacdacdcbdbbcdbaabbadbdcbbbccaddcdacddacacdbabbdccbcdacaacbdddddbbddcbbabaccaddbbdbadccdcdbacdadbbdbcdbabddbaacabcabdbcbabcaaaacadacdbadacccbacccdcbcaaabbdccdcaabbddbcdbacdccbcbaadaddaaadbdccddbddaaabcddcabcbcadababaddaccbdaccbddbacdacabacaddbdbacabdcaaacbbcdcdbacdddbdcdcccdaadbdcabccbdddaddbbcdbbcdbcacdacdcacddcadbabbbcbbdcdddbdbaabdcabbcacadbaaabaddabdbbaddbdaaaddadccbaadbcddabcdccabdbddcdbbdadcacbcbbddbcbcbaaadaacbbacbadbaaacabbaabdacabdbbbdaabdabccddcbccdcccaddcaacdddacbdbbadabbcddcddcabaaccdbccbacbbabbcabdddbbadaacadccaccccbdaadaaaabdacabbcdcbccadbccccdacbabdacdbccbbaddbbbabcbcbacadbacadaddbbdabaacbbabbadbbbccbddaaaacbbaabacdcbbbadadbcacadbdabdaccdddcabacabbadabacbddbabaccdcdbbadbdcbbddcddacbdcddbdacddcbdddcdccadccdabbdaaabcbbacdacdbaabbabcccabcaaddadacaabbbdbdcbdcacdcccaababccbccdbbacdadcdcdccccbbadcddbddadadbccaabdddbacbcabcdbacbccacaabacdacbdcaadcbdbdcaacbbabdddaacdbbaaabdbccddaccccaccdaacbcdcbaacadccbbadbcdccaccdddadbdacccbdddcdcccdaabdcdcbdaccabdbaacccdbbdcdaaccdaabccddaabdabcaabdbaaabbbcccdacaadacaccbdbbdcbdaccdbacbbccbcbabaababddbdaaadddacbabacdaaacabbdcaabaabbabcaccbaadaccdcacbdacaababcdcacbccccacccbbccaadccbcacdbabdcaacbabacdbddaaccbaaddbcaadccbbabdbcbdadbcbbccbcbbcddbdccacbbcbbccacccabbadabaadbdcacbdadcccadadbacadddcbccadacbbbdcadbdbbdabacbbdcabdbaacdbabbbccbbcaadcbbcccbcbbcabaadacabcddcbdadcbdaccccadbbadcacccdccbadcbaddadcbacccabaaadbbadccabcdaacaababaccdadcdabdbbbcccbacbbdadacaabdacbcbcadcbadbbbcbbccadabccbcbdbbbabaddcbbacaacbabbaadddabcadccddbbacdcddaddadcacdcddaaccabaabdccccabdbbccadbccacabbbbbdaacbbcdacabbdababddbdbacdddcccbadddaaaccbaabcbbddbccdcdcdadbaaacaabbbddcbdacbdbaadadcacdacbdbdaacbbaaaacabccbbcbdcbddcbddccaccdbbbcbbbdddccbcadbccbccaacddcadbdbbbdccaacbdddcadcbbbccabbdcdaaddbdcaddbbaaaacbbadaaacdcdbaaabbddbcabbccacdadcbdcaddcadadacaaabdcdbbbbddbaaadccbcadbdaacdadccacbabdbcdaddaabdccacdddbcccdbbdbbbbabbcdaccabbdcbaababddacbabcbdcacdcbbcadabdacddddadccdadcaabbcbbbcbdcbabacacddccddbbbadbbdacddcadcbbadccacdcadcbcddabadadcdcadacdbbcaacacbadcbbccbdcbccbbbbacccdbcaadbdddabbcdababcadbacabbdbcddbdaaabcbbcbcdbcdadaaccdbcdaaabacbbdbcdcdbabdabddbbbacdcddbadcabbabcadaddbcbbdbacbbcdbbbadbcaabcaadcbcdbcabdcdaacabdabaadabcdccddaabcdbcdcbdcbddccccbaaabbbcbabdabbcbdaabadcddcbccccbbdddbadbaabbabaaccccabddabcdcbdbaccaadcccabcabbabcddbacacaccdcadcadacdbdcaccaadaaddbdabdaadccccaadcdcbbdccacababcdadabbcdccdbbaccbacdcdddbabcdbcdcbbdbddbbcaccbccdddabadddbabbcbcacaccabcddaccdcbcbbaaaaddaaaadacdddbaabdbabbcdddcdcaaddcbbadadaaadbaabccacdabbacdabbadbcaddabdbcddcbdccbbcadcbadcaaadaabddababccacbcacbadcdbabccbdcdacbcadacbbbaddddcaacbbbbacabcbcadcaadcdbcbcdaddaabaabdadcaaccccdcbddbdbcbddbaaccadbaccadaadabbbbcdaccbaabaaaababdadababcbcddbddccccccdacdcccadbcdcaccadadbdbcccddaadbbababcaabadbdbdbcdbbbabccbbbcbddbbddddacddaccabcccbddbaaacdaddababddabdacccbacbcdccbbbcbadbacbabdcaacddacacabbdaabbbccaaaabbdcdaaddabdcbccbddabdaddccccacbcbcdcccabccdadabdcdaabbaaacddbddbacdbcddabbbbaccdbdbdcabccbbabbbadcbadddabcccbccdcdddbacbdabbcbddbcabdbabacddcaccbaadbcccaddcbbaabcbabdaccdababbcadacddacdaabaddabacbbcdcdbbdcdddbdaaccaadadddcbbdaaddbaabcadcbbdaaccaabacdbaacabdbbadbcabbbddcccdacdbdacdcababbaccccdddcdbdadbbdcbcbcdcbdcdaacabdcdcddadbcaadacaababbacdabbabaccbabacdbbbaadacdbbdddbbacbabbbbadabccdbacdcadcbdbccbaababcccdacadaddabbddabcdccdccdbdbcbbdabadacdcadadaabcdccbadabcabaadabdacbaacaccacdadacaacbaaabdcbbaaadcbcbbbcacbabcdadccacbaaaababdacdbdaabadcdccdbcbccbbccbdaaaabbcaccdabbcadacabdacdbbccabbdacbbbccdabcccdbbbadcaddccdbbaddbcddcbdcbaadaddddcdbabacbadcdaadccbcdbcdccddabccdcdbbcadacdbbadabbaaabbcdcdbddadbdabbabccaacaaadbcabdbdcccdcdccbdaabcdcbbbcbdddddcbccdbacbdcaaddddbacdbbcbdcdbccbadbcbcbcbcccdbabbbadacbbbadbdcabccdbaadacbcdccbdaabbbbcdbbbdbcccdbbcdbdadbdddadddaddccaabdcbdacbdabaddcbadcbbddcabadccaaacddbdbbdbbccdbadcccdbcdabbaacadccaccacbdacacaccccbadbcababdbadaababccdacbdddbbddcdcaaccddddaaabcdcaaabdcbbddbdaacbbbdcdddadacaccdacbdabbaacbdabacacabcbbbdbdbdcddbccbabaaaccaccbdbbbcbadcaddddabcdccdaabddadbbccbdcddbcddccabbabacbdcabcbbcccbbddbcbaaabaddcdcdadcbdacaaabacddcbbabdacbbacaabcabbccbbbadaaaaaaddadbcbcdcdacdaddbcbcdbbcabcdcbcaddaccabdcadadbbaadbadaabbdacbcdbbabbdadaccbdbcddbbdbbccdcaabcacadcdadabaaddccdbabdadcdbdacadcbdcbddbddcaddddbbbaaabaabacccacacdaacacbdbadadbbaaccdadcdbccabcdadddadbbbcdcdaacbdddcddcdbbdbbabdcaddbbaadbbadbabaabdbbdbbcacaabbcddbbdabdbaccbadccacacaadaadadaaaccddcddccdadcbccadbdbbbddcabcadccdacbcbabcacaabdbacbbccabbdbdcbbbcdccbbcbddadbaadaabdbaacadbbddcddccbcdbabdabababaddaabadcddadaccbddcbabbdaddbdaccabcccbadacaaddbbbcbacccdcaaacccdccababbdaabaacdbdcadbadbbabbddbbbdaddcaddbccadbdacbbabddcacacccaabccdddcdacdabcddaccabccaacbbcdcbabccdbbadadddbdbaaaddbccaaaabbaddcabcabbbabcdbdacbccccdcddaadbcddbbcbbadbbbaddbdccdbdddddddcdcdaccccadaacdacabcbdcaacadccddabcbcaabacccbddbbddddccbadddbdacccbdaabbbdccacdccddacccddccaddacbccaaadbcdbbcddccbbaaccdcbddaaadabadbaadccaadccbabbddbbcbadbbdddbdddcbbbbabbcbcaadacaacdbdbcbbdbccaccaddbdaabaacddbddddaadaaadabdcacddddcbbbbaccddbbbadacccacbbcaddcaabbdbddbaacddbbbcbcbcbaacddddbaabaabbcdabacabacccadbcbaaaddbbdbdacaaddaaccaaccdadcddacaaccdccbbaabaaaabcaccdccaabcabbddabbdddbcccdbbddcdccacbdbdacaaadcbbdccdadbabdddabcbcadbabdabaacdacddadaccacccccddcbccdddccbbbdddcabdaaccddbbcbdaadbcaccacbcadaaabaccaaccbcbdcabbcbaacaadbbdabcbaaddadbdccabdbbcdccabcdbaabdddabcdacacdbbacabbcddadbdacacadcdbdadbcbadaadacbbacbdabddccbdcaacbacdcbbaaccbccdabacdbdbaabdabdcddbccccbccacaddbbcbaccacbaabcbaadcccbcaccacbcabcdcdbaabdbaabccabdaddabbdbbdddcbabcdccbddbcccabbdcadccccdaabbadaaaaddcaabccaaaabbacbcaabadaccabcbdcbbcabaaadaaddccaddadbabdbadabdcaddaadcbdabdbbbbccbcaabcdaadbbaaadbdcabbcdadcacdbbadaaaabdbcaacdcccbbadccacacaadbdbdcacacabddaaadddbacbacbabdadacbbaccadccacbacadacdbcabbbbadacadcdcbbcbdadacaddddcabbaadddbcbadacabdbdcbbadcacabcbaccabddbbabccdbbbccbbdbdbbacccabbcacaaadbaccaabdcaaddbdbcdacbbdbbcaaddadaddacccdbddbcdbdabbaadcacbbaacccddbacbccbaacbdaaacbdcaaacdddbadaaacdbaacabbacdcbabdaaddccacbccadbbdbaccccaadacdcacaacdacbccdccaacccaaadddbcbbdaadbabadbdcabdcddaabdcdbdddccaccabcdbbabbcdcabccbdddcdadbcdddcccaddaaacdcbacaaaccdddadcdabcabdcbdaabcdccdcbdcbcbdccbbbaddcabdcaadcbaaccaccbdbdccdacccdacdcabbacbdcdadadaadbadabdbdadcbdbdbcbdbdcbbaddaddbddaabbcdbddaccabdbbbdccaabcdcdabcacdcacdcabccddcdaddbadcaacddbabdcbdccacabbbbccbbdcaccbdaadddaddaccacacdddbddabbaccdcabbabdacbbacdcccdbbccbcdccbdacdddacaccbcadaaabbbadcaadbdbaababdbcdbdbddbbaaabdbacdaccdbbddbabddbacccadbaadbdcbdadbccbbbdcdcbadbccbdbddaccabbbadaccdaacdccbcbdbbaddabdabbadbacbbbdaadcbbcbcacbacaabaddcdbddbbadabacbcaabbbcccbcdccdbdddbbdabbdcabadddcdaccbadbbaccbaddaacbaaabcaaadcddbddadbdadbaadbacdbacccbaaadcbbabdcbcdccbaacaadbadbddddbdccbcadccdaddadcacdaadbaadcadadbcdabcbbbdbbaabbbdbbcaaddbbbaadbcaaddcddadbdcbacbaacbbdcbbcbcdabcccdaaadcddccbbaccdadacacddccdaddccbadcaabacddabcdbababdabdddcaccadcaadbbdbbabcadbcdbaddccdaccaddbdabdddccdcbdcbabbcbdcbcbbadacdcdacddbbbddacdadcdaabcddbabbaabdcddbbcccabaaadbadabacabdbdaabacbbccddacabcacacbdacdbacbacacdacdccdcddcdbbbdddbbbbbcdabcdcaabaacdadddcabbcdbccbabdbbadcaccbdcbcddcaadbcadccacdaabddbbcaabbcbbbbcdbdbbacabddaaaccdbaddcadabaddacdabbcdaddcbacbacabddcacadbadcddbdcaacddbadbadcacbcabdbdcbadbaddcbccdbbdcdabcbadbbacbccaadbcdcdccbbbcddcbadacadabbbaadbacadbbabaacbcbbacaadbcccacdddccdacaacadadcacdaaccdbbbccadcabbabcdcabadbadbbaacbacddacdbabcbbdbabcabaabcabccbcdbadcccabdcbbacbdacbacacdaddbdabbabacababcbddaacabbbbccbbdaabaadcacadbdaaddcadabddbcdcbcbaaabcbadababcabdcbbdcacdacbabdcaddabbaabbbdbbdcbacaddbcdabacddadadcdcadacbdcaddcbbcdbddbdbbcaabaddcbccccdadcdadddabbcaadcdacbddacdadcbabbcabcdbcddaccaacaadacbbabdcdcbccdbbaccbbbbccbbadbbbcdaddcdbdaccddbbabbcbdcdaadaaddcddccbdbdaddadbcadadcccbaccdddcabdaaacbddbdcdabddccabcaacadbaadadadccabddbcabcaabdcbcabaacbdadbcbadacdacdcaabcaccccddccccddbbdacacbbdbbcaaacdbdadcdcdbabdbdacbddbbdbcbaadabbdcaaacdcdcdcbdddbaacccbccaccaacbdcdbcaacdbccdcbaccbbbcbddaaddcbacdccccdcdccadddaabadcccdbdbdccccbccdcbadddbbdacacddbbdaadabcbadcdcbddbaabcacadddadaabcbadbdbdcadbdabbabdbccacdcbcabcbbacaabdbbacbcccacaabcabaabbcccadadbbbdadacccdcaddddbdbddbcadabbccaabbacccacadcdadacdaadbcdabdbbcbabcabbbaacccbbcadcddaacddcaccdbbcbccabcbccbadabadcbdbdbbcccbdcacdbaabccddabaccbaaccbbbaaacdcadbbbbcdbbcbbbbcdbbcaacbabbcaaccbacabbcacaacbcaaddbcddadabdddaccdddbcdabcaadadbcdabbdabdcabdbbcdddbddbbccbbdbcdcdcaccadbdcbaadbbdbccdbdcabcdbbcbcdbadcdadabbacdcdcbacabcdcdaabddddbbcaddaadcbadadbbbcaaccabaaabddadbadbabdbbdabacaaaddabbccbddcaaaccacacdcadabcdbbbcadbbcabaccdbddcababcdbcdababdacdbabbdccbadcadbbbccababaacbbbaacacbabacababbdcdacbacbbbbbdbbcbddccdcccbccdddabacccdbadcbdcabdcacabdccbcdaddcadabbaabddddcadddaadbaabdcabbaadbcddbcaabbccbbadbdccbddcbbbabaaaaccadcaccbdbcdbcbabcacddcbbaaadaaabaacdcabddbbcadcdccacbcdbadaddbadacababdbdbdcccdbacadaaacccabdbcccbcababdcbbdbcbabbbacdacdabcadacacbbcdbddadbcdbbdabbdabdccddddbbcbcdddcacdcbbdbaabbbcadcdbdaabaabddbcbdaddcccbbdaabcdcddabaadadcdccbddcacbbabadcdddcdaacbbbcdaccdacaccaacdcccabcadacccccbdbdbcccadacdaaddcbbdaaddaadacdbbdbadbdbacaacdcccadabcaaccbbccdbdbcacbcadcdbaaacbaaddddaabccbcbcacadaaaabaaaaacabcdbdbbcdaadcbabaccbccbbadbadcbacbcbdcaadcaacabbabacbbdababcddcbcabbddbbdbbdcccbcbaabcdabdacbbccdabbcbdddbcbdaaaaaaabbdbccdaabdcdabccaabdcadccccccaccabaaadddabadddbcbccadcaadbdcabbbcadbbdcdaacadaabacbcccccabbacbbccdbbabdabccabdababcdbbbddbccbdbabcccdcacbdbcaadcdaccadaadbdadccdbacccacacbaadabbabcabdccbbdbaddacaababddbcaccdadbabddacbcabdadbddacbcdcaadbcdbadbdaaaccddbdbbdcdbcacdadbbabdccbdccadbbbdaaacdcbadcbdaabadcbdaccdaaccabdacaaaacbabcddabacdacbbcbdaaabaabbccdbccbcdcccccbadddadbcbabccababddbdabdacbdadccbbcbadcbacccabaacbbbdbbbdbabaadcddacddaddaddaabcbbaadbbdddddaacadbbbcbadadbcabcdddacbbbdccbadbcbbcbdbdcabcdcdbdcdcaaaacbccaabdaaddaaddbaaddcaccdabbddbdccdcacddaacbccacacdcaacdcdbdabbabbaadcabcacddabbcbdbbaaaaddccbccdaccdcccdbdbaabcdabddcacadaaadddbcbaaccdbdbdbabddccabbbbaaadbdbccccdcdbdccaccbaccadbbcccaaaaccbcacadcdacbbccbadcabcdbdcdcabdcccbcdcaaaccacdababbddddcbdbcbaabbbddddabadbccbbbadcabcbdacccacdbadbaadadabcbaccaadddbadcccbaccdcbddaaadbadbcccdcbadbadacbdadbcabbcdbdccccacccdbcdbccdcdcddbbcaddbbbcddaadcbdccdaddbacbbabbcbaaaadbacacadcdadbaadbbcdccdaacbdcbdcddcbdbaaddcbdbdbbdcbcdbcaacacabdadabdbcdcdadaaaaabacabbaabdcccddaddacaabdccdbdabacbcbbabdacdacbdbdbdccdabcbccbbbaabbdadabcbddddbacdaabddaabcaabbdaccacccabbdabcdabaaddcbbbdcdadaaabcdcdacabbbdabdcabddccccababbddbccbbcbcbdaadcacdabdbdbbddadddabbddbcadcdaadaaaadabbbadbbdabacbcdadccaacaaaccacbcacacadbcacbcbcbadcaacbadccdbcbaaaddbbacbcddabdbbddbdcbcaacbdbdbbcccadcdbbadbcaaacbbabdcbcbcdbccabcdccdbcacdcbbaaaabdddabcdcacbabacabbbcdcaccaacccccaaaabdbabcaaabaddcbcaaacabcadacdbdcabbbaabaadbbdadabbcbbdddcacdcbdcbdcdbcacbadccacbbadbaabdcddbdbdabbaabcbcaccbdcdbbabddbdabcdbadbaabdadacdaacaddaaddadcbaaaaaddbbdaacdcddcaadacdcbdcbdcababccdaadbcbbcacaadbdccaaddbbaaabcdadccbaddbcbdabdbbbcbdcdcdccbbbaddadccdcdcbbcbabbacddbcccbadcaddbccbddbddcbccbbbdbdbdabbddadbdcdcdaacccaaccaccabccadccddcaddbdbcacdbbdbccacccbcdbccaabaccdcdcadddbacddbdddcbbcdadacbbcbbabcdbbcbcbcacdcbacabbcaaccddcdccdbdbabcbdacacbdabdbbaabbdcacddbbddabcccdacdadacadbcdcccbcbabadaadabcdcccaaadbcbbabbadddcddbdcdbbccbabbcdcbddcadbaccccadacabdbbbaaaabaadabcdbaddbdccbdbdcacbcddbbcccdbcabbacddacbadbcccdadcaaddcbbabbbbcabbdbddccbdaddbadabcbbdcdbddbddbdabbacbcbaaddaccaadaaadbadccdcdacbddbcbadbdcbddbbddacbbdbccdaababcbcdbccddbabaacbddbdaddacaddccdbdcbaaadcdddbcdbccbcabacbcccaddcdcbadaaaabbcddabcbbbbbbcbadbdadbdccdcbbccdaadadbccddaadacbddcbacbbddbabdddaddddabcbbcdabaddbcddcabadbbaabcbbcdabadcbdaddbbaaabcbdabdcbdcdccdcbadaabaaadcbbccdadcabcbacadbddcbadcdddacdaaaccabbabbaaadccdbcaaaaaccbbdbbcccdcbbddbbcdbddccabdcbbaacaadadabcdcacdbdccccadcbbbadabaacdcbcddbddcaabcdcccdbcddcdccdbcddbdacacdcababdbabcdbadddbdddbacabbddadcdabbddbbabbcddcddaabadcbdadcabbbcbddbcdbabbdddddbbcdddbbdbcdabcadbddbacdbadcccaabaabcbabcbbbdaabbddbdbbbdaddbadddbabbdccacabadbbacdadbccdabcdadabddcccbcaaaabdcbdcdacbdccaadcbdcacaaddbaadcdcacdaacbdcdaddccdcaabcabddccddcbddbbbcccabbbabbababdbadccadbdbcacdcdaaadbdcdddbacbabbadbcaacddadaccccdbbbbabaaacbabdddbdbabacabbbcacdcbbdaaccbdabcdadddddccaccbbbcacaabdccdbdbaabdcbdddcaaccbcadcdccaccbacbdbbdacdcbcccddcdadbddcdcbcccdbdcbdcabbbbdcaabdacadcdbaadbccccacbdadaacabbddbdbcacddccbaacadccbbbcabdcdddaccbcbdabacdddbddaddadbaabcbabbccccdcabcaadabcbacbccacddcacacdbbabadbacccdcccccbbbacddadabadcbbdddabcbacdaccbccabbcadcdbbbacccdcbbbaccbccccbdaaddbacccbdabdacadadadacdaaadcbccadcbbcabbbdbccbdacbcabadccdbbcbdaccdadadaaacdbccbcbaddddcabcbbaccaadbbadccadccdbccaabcdcdcdbdbcccbcddcddbccdbddcaabacadcccbcbbcadaabbddbdccacbccdcabccabdbbddaaacdbdabbbaabbcbadbccdacdbdcdcddbcaaadbcabdbbdbabbcdabdddbadcbbbadadcdcbadbcabdccdbcacaacadccaabacaccbdcbbadcbacbcddbbbbbcdbcabbbcddccbdbccdbccaadcbbccbdbabacbbcdabdcabbcbabdbdbdcbcbdacadbdbdbcadabbbabaabaaaddacbddbbadcdcbabaadaacdcacdabcbacadabbddbcdaadcbcabdbddcaacbabdbdbbdbdddbaaaadabacbbcbdaaaaccadcacbcbcdbccbabdbbdbacbbdabdccaccabaccadcbadddbbabacadcabdcabdcacccdcbcbbcdabadcadacdbbabcbcaaadcdcbcaacabaddcbaadbbdadbcdccaabcadcadadaabdccccbacaacaccdabcdcabddbaaadcccdadcdddcabadacbacdccdbdbbddbaacbdcabacdaacacdacbbacccdcadcccadbbaaccabbdaabdbdadcccabcdcacabadccbcaaabdbbaddbcdddcdbbcbdcabbbbcaacaccaccdacbbbcddcdcaccabbaddccbabbbadcbabdbdadbaddcaacbbaaacddabadcabdcdbaaacdaaccdbaaddbaddbccdcbbbdaadddaadabbbccdaaacbcdacbddaccbaabbcbabbdcccaabaaadcabcbdacdcdbccdccacdcaabbcdababcdbbacadcbdcdcbbacaaacacdcbbbcdabdcbddddbdbdbbbdddbbccccbdcdbcddacaccdabaaacacbbdaabbdcbabcbadacbcdaadabaccddcbddddaadacddbacbbdcaacdababcdcbbdcccbddbdcaadbbacbbbbacdbdcccbdcbbdbcdccbbbdddbbdcdcaacadddbcacbacdbdcbcbdcccdccbababccabddaddadabdaaabdbcaddabdbdcacdabdbbddaccbbcbaaabcaacbbcccacddabbcccccdbccdacdabacdadaacabbddacdddaccaaaabcacadaaddbbcccbddacbacdabdbcddaabdcabbbadcdbcaaccdbccacbddbdacaacbdbbccabdddcbcacccdbbdbdadbdadcadddcdadacabaccccddbdcadbcdbdbbacdbbddddccbcdcbcdbaccabdbcabdccbbaabdbcadbdadddccbcabdcdbcdacddadbcbcdddbadcadcbbaadbadacdcdbadbcabbaaddaadaaaddabdcaacaccbcdcdddacccdcbbacdddbadcccbabacababcbbcddabbbdccbadbacaadbbbbcadcdcddddcbbabaddbdaadbccdcdbcccbaabccadbcdcdddcaddcaccddddabadddddacadcadabdcbbdbbadbbbdaddcdcddaadbaddbacabcccdcbbacbcaaccccbabbdbadbdaddccbacbdbabcabbacbdcaadbacaaababddbaccbbbcddcbabbcbcbcadbabcbbbadddadbacaadbdacbabdccbdaddbcaacaadbcadadbaddbbccadcdcdcbbbcddcdaddbacdbadbdddcadbbbccbacbddbcabbbdcbdbaccbcdcbbddbcbaadbabbcdbcdbaabdddcadbcddbdcacbcdcaaccddacbcaddbdcbbcbaabbdbabddbddbcbcdcbaaccadbdccbbbbccbabcdddadbadcaabababcaaccaaacabbdbabbaadadadcdaccbcbacbadccacdccbcdcbcdbbbbdabacbbaaaaacdabdbaacacbbccdcaaadababbcadacbccbdcadbacabdcbcbcbdbccdabcbbdbdabaaaacaaaabbbbabbdcbbdbbbbbadbbaabdadbbabcadcdbdcbcdccbbcaddcdbddddacbbaaadadbbcbcdabbbccdaadbadabacadbcbacacbcabccbcdadacbacbdccdcccbaaaaaacddbbadaccadddcddbdacabdbdddcadbcaccbcbcdbddbdbcbacbcddadbcabdbdbbbbbababaabbccacddcdbbaabaabacbccaaabdcacabdccdbdbdadbcabaaddddbaabbddbcdbadcaabaabbcddbaccabccbabbaacbbabadaacaabcdcbbcabbddcbbbbcdaaddccaadcdabbabaabbdadbbadcdacaadcbcdcbcbcdcccdbabcdccbaadbabacbdbcaabbbbabaabdddbbcdabdddbddbccdacdbcbcdcdcabdbdaddabcbcbaaacaabdcbcdacdbccdaadbbcacdcddabddbacdaabbcadccaaaddbcddcdbbcadbccdbdbcabaadddaabcaddabaddddcbbabbcaabacddaaabcdccadbdacdaccddddcaabdbbcdcbaadbcbcbdbcdbbcabbbdcabdccdcdaaaadcacaddccbabbaabcabbbdadbabbaddcdcbbdddbcbbdaadabbbdcdabbcdcddacadbadaaddadbdcacacacbbcaccadcadccbbbaabbccaabadddcadacaacbdaddbadbcbbcdaddaaacaddbbcdaabbdcbddaadcccdabcbdcdcdcbbdccdbdbbacbbdacacbbbabacdacbabbdcbbcdaabbaddbbacddadccbabbbbdabbacbbcdaadbaccddbaadadccbbdcaadcbbdbabacbcdcdacbaabccbadadadaacdbcccabddbbdcaadaadbdaaccbaadabadabccbbaadadadbaaacdcbbcdbbcccbbdabadbcaacbbdcaaaadbcaabbabdacbadadbcbbacadabbacbbddccdcdbdadddcabbcdacbddaaccabadcbbcbbcddbbddacdbcdabdadbcdaccdbdddabbcbbdcadbdbdbbbaabdbccdbcdcdddddbadbdbbaddddbdcddbbddabbaabbabbaabbbdddbddcdcdbcdacdadabcccdcacabcacbabcbdbabbaccadcdcdbdbbbcadccabcaaccbcccddbccbddadaddbabcdbadbcabcabaadccbdbadcbcacdbcccbcdccddbbcbaabcbaaabbccbcbcaaaadbbaaaadaacbdddabcdacabddbdccdadddbacacacaddbcacddcdccbaadcabcddadaadcbaccddacdbdbbabdbdcbbddadcdaddccddbbcdadbaadacacbacbbacbcdacbdcdbaadbbabddcdababcddaccbdabaacdbaadbcbdadadaddaaccbcaadcdbbcccdadbcacaadbbccdaabaaacdbdbacdcbdbbbbadacdabdddacbcbdadabbbacadddcddcadaddcadbbadabccabcaaddbbbcadddabcbbabdcbcddaddabcdcdbbcdbaadaabdbabcaabdaaaaaddbdabaaccabdcbdabbabbccdcdbdcbacccacdddbbbbbaaaddacddaaaacdaddbcadabdcabcbbadccaaaacdcdbbddaacbadadcbdacdcbddaaaddbabbacddbbddbdbcdcaccbbbcaacbcbacaaadadcabdbbcddaacbccaaadbcaabadbdccbdbbbbcaaddbbbdadacabbddbaccadddadddbcbdcaabacbaaadcddcbabdabcbbcaadbdadbadbcbbbdccbcacaadcdabaaacbbddbcaadaabdbdbadabccdacacbcaabadddbbbbccdabdadddbabbdbacdddbadcddccbacdcbacdddaaddbadaddaabaaaabadaacadcbabbdcbcadbccbcaacabbdddccdcccadbbaccaaccbbdcacbdbccdccabdcdcdaacbbaabdcdcabaababddbcbccbdbddabbacbabcbaadcbcbbbbaadcbbddbccaddacacbccbddaaccbbbdcbcbaabdaaabacabbadcdcbacaacaaaaaadbcbdcbcacababbcdbdbabdcbcddcbdddcdadcbabbdcbbbccdacdcddacabbcbccaacbcabcadacddbabaaddbcdadaaccddbddcccbacbbdcdadddddccddbbabcccdcbcbcccdddcaddcdcbbabccaacdccccabbccdaabbaabaaabcdaadadaccbcdaabdcbbacdabdbdabcaccaccaabbbccaaaaaadadbdbaabbadababdbdbacbadddabcbcdcbdbabdcbcbbddaaccbbbdbaaadcdaabcddabcbccbbdcdcbdbbdbaabcccacbabbccabbcaddbaccccccaadbdcccbbaabddccbcbacdbdbacdbaaddbddadcddccbdabdaaabdcddcdcbcbdddacdadabbdbdbabcbdbbbdbbbdabadaacaabcbdbadccdbababddbcdbabbcaadaabdaadbabddbdaadbabcbcdbaacbaacbbdcccdccbadcabaaabadbdbabcabbdaadacccbadcddcabacdbbbbadbcdcdaabdabdadddcdcdcabcadcdbcaaddabbbacabadbcdbddcdcaacbcaabaadaabbbcacdaadaccaccdbccabcadaacbbacdbbbddacccdacdbcbaadcddbdbdbdcdcddcadadcabcdbabcacbbaaadccddcbadabdcadbbaabbcbcaddabbccbcbaacacbadbcaabdbbacbbdcadddababbbdabdacabdbddccbbacabaaabdabacbcddbcddbbdacadcdcbdccacdbaaaccccccbadabdbbcacdbbddccacdacdaabaadcbbdcbcbaabbbbadbcacdbcccbdddcdbcddacddbdcdbcdaddddbacbdbdcaccaaddbabbaabddbddadbacbdaacdacdcabdbbdcdcdbbababcaacbbcaccbbdbbcaaccdccabaddbdcbabcaaddacddddcacaacdbbbddaaacdcabddcdadcbccaacaaaadcbacddbcbdbdcccbcdbbaadadaabdaacaddadddcbdabababcbbbacddaacdbcacbdcdcdccbbcacccccbccbdbbabaccbacddcbdbdbdbcaadabbbbbbccdabbacaaaadaadcccbabdcabbdddacbccdddaaabccaccacbabdabcdbaabdddadabcbaddaacdcbddbabccbcbcdadbabdabdccbbbabdcbabbdcdccaddccccbacacddcdbabaabbbcdddccbbccdaaddddddadcacadacdabcbccbbacbbcaaadbdabdbabccabbbcdccdcacbcdddcdabdbdcadcbbbcbadccbbbdcdccaabaaacabadddbbaadaadbbbbcbcaaaacbacbadcddccadccdbbdaacaddcdcbcadddbdacdaacaaaabacccbcadcabcccabcaaabbccbadaaabaadddccabacccacccdacaabbccadaadcdbabdacabdcaabbcdcaacdcaadaccabbdccdbddcdcaddcbadaddddbbdbccbbacddccccbacbccdccbbbadcddbbabcbbdacbabccaadadcdabadbabadbbaddbbcccabaddbdbdabbccabbbcacbbddbcddabbabcdccbdcccbbaadcacbddadbbdcbaddbdcacacbcaccabbbadadadcbaadcbcbdbdcccbdabbbccdcdccccdddbbdccaaccccabbcdcabdbbbacbdcabbbcacbbdbbaabadababccacadbabcbccabcdcddcabaaadacccdcdaccacbddcacacbbbccadddbbbabbbbaadaabcdabdbdabcbbddabbadcbcdaacabbbdcacaaacddabddccbcbbaddbdbddaddcdbcbcaddadbdccacacddabcabbbdccbacabadadddddbcadcccddadcccbcdbdacbddcdbdccbbdcdacdcbaddbbcdabaacdbcabbbdddabbabacbbacbcdaadbcacddcddcaacacccaaaccabdbbbaccbcaaccbabbbdacccdcddbabbadbbddbaccbacaaacbbcbdbcdbcdcaabbddcdadcaaabbacbbdccaadcdbacdacbdabadabdaccbabddddcdaacbcdcaabbacddaadcdbdcbbcaddcbadcbacdadbccbddacbcddbcaddacbaabaabdddbcadabdbaabdaccccbcbbbcabaadabdabaddaabcaaabbaadcdcbbdcacdaaabdbccabbaabccabcccddbdddddbcaaacdcbbdcbcaababadbaccccdadadbbddbbdccababbadaacbdccccaadacaababbababacaadaaccdaabdcdbddcbbdabbcbdcdddbadcbcbcdadddabcdacdabadcccbdaddcabcbccadcacadaccbcbdbdbcbbadabddddddccbaddcccacaccacddbbcbcadacbbcdacbbdcabcadadcbaacdaaabbbcdaabddaddcbacccbcbcbaaabadadcdbddbacdacbcbccabdccdbdaacdaadadbaddadcbdcbbbdbcdccaccbdbdbcacacdadcaddadbdabadddbaabdbaccbbcadbdbabdcacdaaacdaaaaddaccbcadddaababbadbbbbdcaccbacddcacccaddbaddccbcdacdcaaccdaadddbbddbccbdadddbcdaddcccaccabcbcdacdbcdcdaadbbaddbcacbcadcabdbccbaaddbdaaabdccddacaabbcdcdabcdbcaadbdaabbcacabcbbdbcacbdabddddacdadadbcaabcdddabdbaccbcbabcaddbdbcdacbaccdcddddddabccbbbabdcdcdbacddacdbcbbcabddacabdbdadbbdbacaaaaacaaabdcaabccbdadbababbabdadadcdbcbdccdcccabbcbcdbbcbcbcdbdabcdddcdbcadcbddbccacaabdabcacabdbbbccaddadadabdabdddbcabccdddddbdbadaabdcccccdcccccacacaabbdcdcacacbccdbaaddabccadcaacbabbabaddcdaabbcaccdcadadbabcadcadcababcaccbbaadaaadbaaddabdaaaadaaadadcbdaaaabdacccdbdcdaabdcbcbccdabdddacadabbbbcbdcababcdacdbddcaacabdccdccbdadcdcdddcddaddabbadcacbdadadbdadadbadaaadbcccabcaccabddbaaacadcaccdccbdcdddbbcddddabbbdbbaaacaabdaadcabbcdabbaacdcaddbadcbcdcdcdacdbbcbadcdacbcabaadcadabdaddcacdcccaabcabacaccdadccbcaddbdcbcbdbccdbbaccaccdacbbcbacdccbdabadcbdbbadacaccbbbaacbdaddccdadcabdababdcbaccbcbcbbaadcdacccababdbcdaaacabbababcdbcdcddcaccdbbabccddbdccaddbcddcccaaabcaccdbcdabcabadbbbbcbdcaabddaccbbaddadadaaabacbbaacdccbbbcddcacddadadadbdcaddbadddccaaadcdbccbabdcbdbadaaaabcacdbcacdbddcacdbabaccccdcbdcadbabddddbabdbccaacadabdaadddcababbcbdabcadcaadabddadbabbdcccabcbdacdbcbcaaacbaabaacbabbaccadcabcbacbaacaddaaccdbdcaabadbbbdcbadacdddaadcabcaabdbcdaacbdddacabbdccdcdddacdacdbcacbdbccddabdbdabbaaabcadcbcaadababbbadcacddbbcdcadbcabbcbcdadcdcaccdacdabcbdaccccbcddcacbbddadbcdacadadcbdacbddbbbdabbddbccacbbdabccdbdbcbdadbbbbdcdcbccdacdabacabbbbcaaadbaccbaccaaacccdaccbcdacccbddcbaabdbcaaaccddcdaccabbdcacccdbdbadacddddacccaabcabccbacbbdcbdaaabbaadcadadabccaaddabaacdacdcbdacacacdaadbbccdaaadccbdcbdcabdadcabbbabccbcccbdabadacbcccdbadbcbbbabddabcccbbbdccdcbcbabbcacbddadaadadccbbabddcbdacddaccbdacbccaccdabbadaddaaaccddcbccddbacadcbabdcdaaccaabdbbdbdaddbdaddbaddbbcbbdbcdbabcaabbddcbcdacaddabddacdacbbbddbaddcabccadbbcbdaccbbcdcbaccdaacdbdccdabdccadcacbccabdbbbcdabcddabcdaacbacacdbbbddadcdddabadadcdcadcbdbcaaacdcaadacaccccdbbbadcbadaaadcccdbcbdcdbaaadaddbccaaaddacbcdacdddbbbcdaacabcacbcaccadaacaabbdbdddbadacadadcaadddcccbdbccbddccdbccbaaacdbcacdccaccaabccbabdcdabaccddbdccaacbcaabcabcbdcadaddadbdabbbacddbbcabdddbcdcaaadabcdbacdaadcbddacdadaacbbdadbccbcbcbcacbbcaabbddadaddadbccbaacbbcabaaaaaabddbcbacabadbdddcbabadbdadaaadbaacbbbacdbabcadccaabdbdbbbdaaadabdbabdbbdcbbaadaabddbbadbcbdbccddbadbdddcbddacbaddbbbdddabbbcdccccacbabadddbabdbabdbbdbcbdbbbdbcadddbccdbdadbddcddcccaddbddabccdcbdcdadcabdaaaddcdbabdadcdcacdcabcdabdcbbdcaaabddaacbdddccbbdcaabaccacabbcbadabaabcccdccaaddadaccacaadacbcbddbbbccaabdbdaabbadddbddcabaadaacaddaacbdbcabdacbcdadcddadddbbaccabdabbdbbdcabadbbaaccabcdaabacdaddacdbbcccacbabcabdaddddcaacdaadbabcbdcbdbbcacdaccbaaabbbcabcbbadbaacbaaabbdbcdbcbcddbacbacacbdabacbbabdddcdcbdccbadbcbccaaaaadabacbdddaaddcaaabadbcbcbbdcdaabbcbccadbbcbaddcbcdcdbddcacdbdccabbabbaaccddcabadabdcdcabbaacdbdcaaabdababbbbbdcdcaaadcbdccdbbacbcbadcdcccddaadcadaacbbbbdbabbccbccbcdbdaccdadddcababaaacacdcadaabcabcdcadbcccdbabcbacbacdcbbbcdcacaabdcaaccbacabbdacbdabdcbcbabddcddcdbcadcdabddabcdacbdaadbcdbcbacabaaababcdbddcbdccdbdbdcacdbcaaaabdcdbdcbcadcaacdbddddcaaaaabaabccadaccbbcdbbcbdcbcdcacaabcabbcbacdcdaccaabdccbbccdccabccdacbababdcbbccaabdbaaabaacbdcdbdacbbadccbacddadbcaaccaadcdaaaddacbdbabdadcaddbabbdcadbccabbcbccccacacdddcccddbccbaacaaaddbcbabcdddcaaaccadbdbccaacadbbddcabcbdaadabbccbdbbbbaccddccbabbaccdabbbcaacdddbdbbacdbabcbdbbacccbdabbcaccdcdccbdaaabccbadbcddbdadbcbaabcaaacbcccdaccaccdaacacbbccbbdbaccdcbbacbacbbccadbddbcbbaaaddbabaddbcabcbbbddbdadbdbdcdbcbdaacdbdaabcadcbaadbcabacbbaacbdbcdabdadbccabbababcbcdbcdabcddaabdbdcadadbbaacbadcccbbcbcdccdbddbccadacabdddacabbdcdcccbacaaddcddaccbddbaabcccdddcbacbdbddbadbdddadbdabbbacccddcbbacbdcdcdbaccdbcdabaacbcdccddbcdccddbbbddaaddcdddcbcdcbbacdbacdcbbdaaaddbccbbccadadaaccdbdaaccdcbabaadbddaadcbbcbccabccabaabbbdcbcaccdadbbdacbdcaccdcbccdcdadaaccbbadccbacbcdabaddaddcccbddacadacaabaabaddabcbccdadacbcabdcbdabccdcbaddccdcdccbccdbcdbbbabacdbadbdcaaadbddcbabcaaacddbdabcbdabcaadabbbbcdacbcdacdbdaaddaabdbbbddbdcdddccadacadbaacbdcabbdaddcbccdddcaadddbcdadcadcbdcabbbbbdbbbcdaddacababdaaccdccabcaaccbcbdbcdccdcbbddadcbdadaddbacadbcccbaaaaabbcccdcddcdcddddccabacddabcadcdaabadcdbdcacbdabdadabcdccaaacdccdbacbdcdcbdadcbdcabadbdabbdbcdcbaabdccaaadaadcabacdadbaddaacdbccdaadbbadbdacaccdbcadcdadadabacacacbaddbcaddcdcccbbaddcbadbccbadcabacbdaabbbacccbdcbaccddccaadaccdcdcbdbdbcaabcbcacacadcabcccccbabdbdcbdadddaaacdccdcdbddcdcdbababdbadcbdddacadbdbdccaadcdaacdadbadcaddbdbbcadaacbaabdaaaaaccddacdabaddaaacaacddcbcabbaabcababbbbdaaaacbcacbabdadadcacacbdacdbbdaadacadbaaadbdaacddbcbadcabaaadcadcddccbcaadddaddacdaadccabdaddabbcadabcccacbdaacdadbcdadbcdcbacadbddcdcccbadcdcaaccddcacccbbccabaddbbbacacdaabdccdacddbbaddddbaabdcddcadbdacbdbadddcbddbcdabadcccbbcdacbbaabbdabcdddaadabbbadbcbbcacccbaacbcadcbabddccccaabdddacddacdbddcdbbcaddbcccbdbdaccdbdcadccacbdcdbcbbbcdadcadacdcbcdcdddbdddcddbaaabbbbabbdddcccbabacdbabcacbcacddcdaaddadbaccbbbbbbadddbadaadbcaacdacdcbdddcccdbcdccaccbbddbdabdccbaacaaddbbbdbdbdbbacdcdbdadcdbaddccaccbbbbcdccdadddabcababbacdaacbcaaddababdccbcdbcadbdccaabbdabaddacbaabaccaacddacadcacdcbadcccaaacbbaaaacabddaacddabaccabddaccadcbaabbacbabcdadccccbbbaacbcccdcbcadcccdcdbdcbaabbddcdaacaccdaadccdddbbddaabddcbcdccbbaacdabacddddcadababccddaabbcbbaaddbdcabcaacddcccddccacbddbbddbdcbaacdbcddccddabbdaaadbadaacaadbdacbcdadccddabdbddcccacaababbbacbcddccabaddcaadaddabaccdddadbbcbbdcacbaadcaaadcabccacbbcdaacacddaaadbdabcbadaabdccbddddbbbcdbdadddbbdcdbabbabadcdcddcabbdcdacadcbdcdddcddabdbdabbbadcacdcdcabbcacacbadccbcaadababdcdcdcbcbcbbaaabaccddbdbbbabccdaddbccaadabaddbdacbdcacadabadcdabcccacabadbcccbbdacbddacdcdccbbccddcbdbbdbabdbacacabcbbcbddadcccacbaccbcdcbccacaacabbcbbcadcaadadadaaddcaaddcaabddddabddadcbabcbdbddabcadaabbdcbadcaabacacadbbdbddabdccbcaccbddabcabcbaccccadbbddacdcacadbdbcbdbabcddaaabddaaadbadadabccdcacabdbbacbdbccabbcbabadcccbdbadbdaacdccddccbbcaaaabacdbdbdbdbbdaddddbcbbbdcbdcddadcabcabbccdacbddddcadccbcddccdddbddbcbcbccddacdadccacbccdcadcbdaabdcccdccdabbdcadadadcbccadcacdcbddbdadcaccdddddbaacdcabcddbaadccbdccbccacddcbbcbddadabddbbddbbcdaddcdccaadbbdabcbbabbcbdabdbaddcdadbabdcdbcbdcddcdacbdaacbcacbddaccbdcbbbabcaaaadbaaabaaccbbddddabccbabdcbdbbbcdacbdcccccddddcbbbdbabdcbaabacdbbbbcdbbdccdacadbacadcadbdcbcbaabcaacaaaabdaaabbbccabddbdadbcbadaaacdabbbcadacacdddcbaccadbddccdbdcabccbbadddacabdaccdcabbabdcbaaaaaccbdadaddabaddcbdbcaccbbbcdccdcabddcdbaccddbcdbdcbdabccabdcdcdbddccdacaabcadcbcbbbbddcabccdcbddaabcaacaaccdccbcdddbacacbbcbcbcdaabcbddabadabcbdadabcaddaaaaabdcdcaabbabaaaabddbabdbdddabddcadddcddabcadacaaabaacabbcdcddabadadcacdacbcabbcbabdcacdcaaaabdadcabbbabcdcbbbbbccbacbdabbdcabbaaacdcbcdaadbbccddcbbcdacabddabcbabccbbdbdbcacbadccbaacabacddccddcabbadddbbcbddabcbbadcbcbbabbbaaccdbdcabcbdddbdabdccacbcbdcacacbbbcabdccdccccacbdabaacccaaadccbbbabccacbabaacdbdbcbacddbddaacbcbdbbbcabcaadbbcbabcbcbacadbbbbbccbdacaabaaacbadacaacaadccccbccaccbbddadcdaadcdacdddbcbcacbcbdabaacacbbbdccaadbccccaddbcdbdadbddcbadacddcbadadabccddadcdacbabdcbabcddacbddbddaaaccaccbbdbaadbcaadadbababdbccadbbabaacbacdaabddadaadbbdacaacbaccacabaccabbccdbcccadcaacbbbbcadbbdcdbcdcbbbdabdcbddaddaadbdbaabbdbcdbbcadcdbbadbaacbadacccbdbbdaadbdcccbabbbabddbcdbcdbcbbadbaccabdddbabcdaabcdbaddcbccbbadbdaaabcbbbdabdcaacacdccaabaabbcddcdddbccbccacdddbabbbdcbddccaadbaacadbdabaabaabdcccddbcbbcaabbcdbabddacdbadccadacdaadbcadbaadbbbcbcacddddddbbcbaaabdaccadcccaabcbaabacababcadacbddabbcabcbcbcabcaacbabdaaccbabbbccddcdcbacdabaadddbcbabbddbbdccacbdbaaaabdaddbcbababaabdcdcdccadbccdddbadbddbadabdbcbcadbadbaacdbbbdcaadcddacadaccaadaccdacbccbcabbdadccbadaaacdadccabbaaccbaadbbcbaabdaadbcacadcccdbaabbddbdbbccdcbdabcbadacdcdbbdcaabbcadccccdbbddcadbccacdbaddabbbccdbacccadaadccbbdddabccbbadaddcaacabbcdaadabaddbbbaddbbbacbbbddaccabbaddcdbadddcccacbcacbaaaddcbaacadbbbdbaccacbbacadccdacdddcdbbaaaabbadadcbbdbddbddaadcacdadcaacadaabdbabadcddcabaddaadacadbbcbbcdabbdcadaddaddcdbccccbbacaaadcccacdccdcacbbcbacddcdbcadbdbbbbcddbbcacdcdbcacbdbaadabbdabacdcbdaacabdadadabddbbcddabcbbaacacdcacdbcbcddbcbcabcccdabbbaaaadddccccbcdaabdcbadadabcbbcaddcddaacabccacdbdabcddaccdaadbccadbdbbbbbbbaccddccdbaddadcdabcbaaacacbacdcbaacadcddddcbadbdbaccabaccadbabcccacdbcacdbddccdacabdccacaacbdccabdacbadbbbacaaadbcbabddddccbcbdacbcbbbccadabdcdccabcaddbbabcbcbcbccadaabbadcaaadbdbaabcdbbabacbccadddbacbaabaaaccdccbdcdcccbdccabcaaaabbcbdadbbbcbdacbbaaaaddaaccabbdccdcbcbbbacdbbaaadcbdbddddabddbcbdaaaadabaadddbbbadadbaaaacdbbbadcbbdbcddccadddddcbdbbadbabbbddaababdddbddcddacccddaddaadcaacaddbdaabbdcbdcdcbbadacbbbbcaddddadadddbdcacbcbacdabcbcadcabaddbbdbbddbbadbabbcccdacddbbbaadabaaadccccdcddbbcdcbcccdacddccbdccdabcdbdbbcdbcaabcbcacadbdaabbdaacdccbdcbdccbaabbcdcdcbdadbadbdbbddbbcbdaccaaabbbaaaddacbdcdbdbcbcdcccbcbbbdadcadabcadcacccdbaabacbaccacbabbddbcdbadababbaacbaabbcccbdcabbccbdadabbdacaccaacdbdaaadacbbdccabcbddcacdcadcacdbaacccddcadbccbdbabccacdbdbbaaadcbbbcbabdcdcacdabcabdacaaacadcbcdabbabdadbbbacadaaaccbdcbdcbccccbddadcbbdcaabaccabdaabcdaadbcbdaabccaadbabdcbdcbcdbbdbcdcddbcbbabbddbbaadbdacadabccdaddbcbbcaacbbccbbdaccabddccabcdccdbcbbbdcbcbbacdaadacabbcbaccaadbdcdbcaacbacddacdddabbcbccbcbbddbdaaacbdbbbdcbdabaadbababdabacaccbacbdbdbcdbaddadcadaaabddcdabcaddacadbbdbabcadddadaccccbbcaadacbdbbcbbabbdcadbacbcccbccbcddbcbbcabcabcccdcbdacdbacdcacdaddcabbdacccacacaddabdbabbbdbaadacabbddacabaadbdcbdddcdbadcacdacdbabbbccbcddbbacdbbcdccbabdacadcbbccbcaabbbadcbdddaabadcbadcdbaaacaaabcddabcacaccbcadaddcdddcddadcdadaddcddabccaadddacbddaddcadabdcdbdccadbaccbbcabaaabbbbbdcacaaadaaaaaabdcccdcdbacaacaadadadaaabbdbdbcbabcbddcbabbabcabbcbbbbdcaadbabdbdbcbcdabddbbccabaccbbadbaccddbaddbbccdcabdccacdbccbcddcccacbdbbccdaabbcbababbdbcdcbcacadcacabaccaabbbbcabacdcbbdabcadccddaaabbdacddacdcaaabadabbaadccccbaaacddabadaccccdbbdcabdcdddcaddadcacbdabcbcbbbdaabdcbcdbcacbbbdccddadddaaddcbdcbdbbbbddcdacbdadabccdcccadcdccdcbbbaddbddcccacacaadaabdbbdacbdddaaddadaacacaaaaabdacdcaaddadcaacabdacaabdaadbdbcabbbacbcbbcccbbdcaabbaccdcdccbcbdadcbdbaddddcadbcdbbbadccbacbdbddcbabcddcdaaaacdccbcdddbabdacaadbbdcccaccadcdcadbaacdabbaacbddabcabcbcdabbcdddcbcbcdbacaacdcbdaabbdddcdcccacbaaadbbacddadbccacabcdcbccadbbbcbdddcbaaaaadadbbdbabccdadacddbdbdbadcdbdbaabcadbbadbbbaccbddaddcdbacdadaacbcbbcddbbddddbcbadbdbabbdbdcbdcabcdcbaddbbacdcccdccabdbdbbadbadcabcdaaaaccbddcbbabcaaccaabadbcbacabbadbbddbccbacdbcdcdcddddccbbcbabbbacdccbcdcbdcbcbcccadadacbaaacbcbbabdcbbcccbdbcadbbbcdddacbcaccdbaabddbdabacddcbadcaddccbccccdddcbcdcbdacccbccdcddbdddbaccbbabddddbdacbdabdcbcadcacddadcccabdaaccccdaadcbcccbcacdaadbbdacaacacdbcdadcaabcdacccdbdbcddcadadbacbccabaaabcbcdcbcddbcdbdbbdaaddbbacbcbacbdbbdcacbbaabccbadaddacddbccbaccccdaadbacdbcdaadacccbaacaacaacadbbcbdddbccdbdcdbadacbaadcdbdccdbaddbbcbcdddadddbcaddaddcaddadabababdabaacdaaaacbadbcaacdddabbaddcbacbabbdcaadadabbadbaadadcbaadbbbcadaadbaddddbccadadbdaaadaaadaccdaacddccbcaabaacdaadaaabcbdbcddabdddadbbdcccabddbacbcbcccabcddbcadaabbbbaacbbdcccdbbcbaadbbadbbbcbcbaaddddcdaabacadaadccdbbacbacadcbacdcabbdbbcbdcdccacacbbbdcbaccbbcaadbcdbcdaabbaddabaacdaabaabdaccbacbcdcdccdccdabdbbcbdacabbddbbabdbdaddbcabcbddbdbbabbacbdbaaccabcdbabbdaaccaabbddccccccdccbcacaacdbbcbbddaacacdabdcbaabbbdbccbaadaaaaccbbdacabaacadddabdbbbacbacbbbcaabcccbcddbaacdcddbdadcdaacabadadcdbbbbddabdadadadcadcbdababcbbbbdbaddcaaabdaddbdacbbdbbadbabbadaadcddabcabcdaabbccacdadccacbdcabdacbcbdbdabdcbaabdbabbadabbacadcbbdbdbdadadabaabccabcddbbdbcbbdbadbcdbbdbddddabbbabcaccacbbdaabccccadaaacdaddcdacdcdacbddacbccbdcaaadcbdacbdaccbbaaabdadbbcdbcdaaadadaabdcbbbadacdddababdbdaadadbaddbccbcdbadcdbddcdbbbbbccddabadbadcdaccabdbcbaaabcadabcbaacabdadcabaacadbbcadaacaadabbdbddbcadcaabbaaaabacadcabbccccdcdcabcadccabccabbdbaabbadbcabaccbcacadcabcdcabcbacabcccccccaaddccbbadaddadaccabcbbdbdadadaabcddbdddaccaccdccdcbdcccdacbbbcccadabdaaadacaacddadcabcbdbcaacacbbccacdcdddcbaaaacabbcacbcbabcbcbacdbdcdbccbddbbcdcbcdcdaabcbdadadcadcdbacdbaccbdadadabcaccbbdcdcccdadbcacccbcaccdaddddbbaadabaaabbabccbcdaacbabbbddcacadcccaacdadddbcdbbccccbdcadaadacabbcdaaabdcbccbbcbaabbaccdaadbbcbcaddadbcddddccdcccbcaddbadccacadcdddccbccacdbabbddbdbcccbbacccdbdabbabcacbbbcdadddbbcbdbccacddacadbbdbdabbdacacccdaaadadbcbdbbbbabacbdbaadbbddadbdacaaccaacdaccdbdaddbccabdadaddcdbbdbbcdcdcdbcdddbccdbcacadadaaabddacccacbbdcacaabcdcbbcdadddcbcbcdabbcaaacbcdabcbcacbdddaacabcbacaabccbbdcdcccdcccbbdabcaabbccacccabdbbddaddddacbbadcbdccbabaaddccbddcbcadcbcddccaadddbdbbcdddacabbbcbdabcdddddddadcdabbbdabcbbabaabbbadbddacaabbdadbcbdcadbcdbbbbcbcdcbdabbaabcaacdccaccadaabcdbabbdbccaccaddbacabbbacbacdbbdddbccbaacabbccddbbaababddacdcbdcacadbbadaaaaddccbcddbcbddcbaaccddccbccacddcdddbbdabdcccabdcbbccaadccaaacdcadccadcbddcbbdccdcbccbddadccabbaadadabcdccddbbccadcaccbdddcadbccbacbcacabdcdcbaaadbbbdbcbdcdbacabbbabcabcbdbabdababddcabddcbbdbbaccdbabbdbbbbbcaacccdcaabaccacdaacbcbdddbabbabdddbbbbaabaadcdcdabcbdbaabcdbaaaccabcabbcaadccababababddccdcdccbcdbcdaccdaadaaadbcbbdbdbcdcdcbcaccdbbdbcbdabacccddcbddaabcacacabbacacbcddbabcdadbaaacbbacdbcdddababaacaaccbcdbdcdbccddbdbbbcccbdccbaaccddadbadabadcaccbccbaabbdcbbcddcabbbcadacacddcbcbadbbadcdcbaabcddcacaabcbcbabbcadbadcccacabbddcdccaacacadcbbaacbcabbbddcdadcdacddaddbacdaacccbccadaabdcacacadcbbdbaddaddbbabdabbbaabccdbcddbcabbccddbaddbdbdadbbabbbcccbcbabadcdadcbddcdcbddcaaccbcbbdacddcbbcadbaadabbaaadbaacabbacccaacddadddaababbaccbdadbcaccdddcddacbabcbbbaadcbadacaccabccdddaccadddadbadbcdcbdbadcccdcccdabdacadddcbabaaaacdccccdcdaddababccadcdbbaaabacdccddbabaacbaaccacddbbadcaacacdbadbdbbdbdabdaccacdccabcaadcdddbccdaaccdbddbbabadddcacdbadcadbcdaabbbacaabbacbddcdbdaabdccacaabddbadbdbcbbcdbadcbddbdabdacddadbbbccbdabddabbcccadabdbdbaaccadacdacdcbbbcdcccabdddbbbcddbaabacdbacbacbdacdabadbbddaadaaadaabaabbcccbababbcacaaccdaccbadbdaabdbbcdadbdccababbbabaccdbcbdacaabdbbcdcbcadcddabdcbadbcdbcddaadbabcddaaccdddadbacdbbbccdbdbabcddccdabccaacdacacbcabbbaacbdddaddbadcadacdbabcbbacdddbbbcadbaabaccadbbdddcabaaaccabbaadbbadbababbbadbabacdccabadcdbcaaccdabbdabddaddcbcdccacddbbbcbbcddbaadccbcaadabbdbcdcddbbadcdaadbdbdaccadbaccaabbdaacddbdcabacccbababacddcaacadcbcbbdbbbadcbddcbcbbcacadaaadcadabbccbddaaddddabbcbcdbdcddabccbdabbcddbbaccbaacaccdadbbabddacbcbccbcbcdaddbbdaaccbdbddddbabccdcbcabccacaabdaaabacabccbaaabdcbcbadbaaabbacdaccddbbbcbabdcacccdcadccadacdbcbdadddcadcdddccdbacadacccbccdbccdddbcbdcbdbbacbcbabddaadcdcddbbbbbdcbdacabcdabcdccacbdccacbaaadbbaaadccbcdcdcbcbdcdcdbdbabbccccdbdcdaccccbbaddddccadacababbdccdabdaaaaaacaacbbbbdbaccdcadccbddcaabbaddcabcacadadcdabaadcbbadcbcadcdbdbdcbdabacbabadddacaacdddbbbcabdbcbadbcaadcabdacdbadacadcbcdbccaacbacdddcddccaacaddcbabdaabdcbdabdabdbdcddbdcaddbdacabdcdadcdbdbaadcbadadabcdcadabbbbccbbaacbaaaacabdcdddddbdbbccccccacbdbdcdabdddabdadaabbccdcdaabdbcdcdcabdbaaaabdcdcbadbacaccbccdbcbcacaabcabdddcbcbbaaccaccababcadcaaaaddcbcdcacdbdbabbadcdddacaacbabbcbcdbcdccddddbdbbadccddaaadccdadaadacabccdaddccaacabcaaccacdabbaabaacadcdddbcaababddbcabdcdccadccacbbabcdadbccddbaddbadabcbbbdbcbdcaacbbbaaaabbbbbdbddbaccbcdacdabbcaaddcdcaccbcddbbadbbddadbbacdbbbcccbdddcababcadbbcbbcbccacbddaacdcbacaddadabaccccddbccdcdbbcccbbaccdaddccacbdacabaaaabdbbdaadaaccbcbadbdcbcbdbdbdcbabaacbaaddccdddbbddcdbddbaccbdadaabdddbcacacddbdddacbddabbdccdacccbacddbbcabbaaaaddacdabcdcadbccdaddcccabccbaccdbdcacbaacdcdbcdbdcbcacccbdbadcaddbbcdcbddadadcdaaaddbbaabbabbdbdaccbdbaccaddadbbcbdbbbcbdcbabadcdcbadbbbbddbdadddcabcbccbaabbdacaaaddadcbacdbdcadbccccadbabcacabddccdcdaccadcdcadcaccadbcbcbbdccaababddbdccabdcdcaccdabacbabbdcacacbccccccbdcccdbcacbbbbbddadbdbcdccbddbcaacabbadcadacbdddbcadccdacaaacccccbcdabcddcbababacdcdbbdcbaddaabccdcdcccbcacadccbdbdccddcbdaaccdaabdcadcdcadddbcdbacacaccbdddaaccccdbcacabcadacadabaadcdcbddbdabcadaddddbadbdddacbccaccaadaadcdacaabcacaddababbdcadcdacaabadcbbbabcdacabadcdcbbdbaacbdbaccaddbcbaccdbccbdddcbbbcdddccdababdcddabbdbcdbddadadcbdabaddcaadbaadabdcabdaacbdddcdcbacbcbddabcadddacbcacbacbdbaadcbbbdcccbbadccccccdcaacbcdaaadabaadabccbbccdddbbacabaddaaababadcdacdaaccbdbacdcdbcadddccdddcbbaadcacbcaabbcccabbcadaabaadccdcdccabbaccaadbdbdbcbbddcdddaacdcbdcccdabbbdcbbdabddccccdacaaddabddddaaaddaaabcaaadcabbbaccaadacbacadbacbaadacbbbdaababdbbbcacccddbaddaacaddcabdacaabcdbdcababaccabccbacdcdbcdbacababdcdcbdbbdcbcbbddcddacaddccaadddabdccabaaccadaacabdcccdcdbabddcbbcddcbbcaacaadcdaabdadbddbbcaabbaddcabbdccadbbabcbcdbcbcbadcddddddacbadacabcdcddcadaacaaabadabcddddacadcddadddaadcdcbaacdbdbaaccccddccdddcdaddbdbaabbaabcdabaabcaaadabadcbdcddaaababcbabaaadbdbacbcaacbcbbdccabaaaaccbabbcddabbadbbdbcbbbcdabcacadbadabdabacabdcbbbaacaaacdbdadabcbcabbbadacbadbabaddcdcacbcacdbdcaacadabcaabadddcdacabbcaaddacabacdadaabdadbdccacabddacccbdddccbabaccddbbcccdccbbccabddaaabbdcbdbabacadabcbdabdaabcddccadaccbabbaccdcdbcacbbaccbccdadacdaddcadddcbccabacabbbbcbdcddcabddbcdbacccbbbbbababbcabcbddacddacabcaadddcbabddbbbbbcaabaacaacdcaadadcdabcddcaabacccbaacacbdabbccbabbbaadbdadbbddaadaadddddaccddcbdbbdcbaaaabcacdccbcaaacbcaacbacacaadacdacadaaddadbbaddbbcdcaabddabbcbcadcbdabdddcbcaddddccdaaadcadbdacccdbcdacccbddbaddadaacbacadbcdbdacadaddcadadbcbbdbddbaddaaddcabbddcdddcbcdabcbcbadadbddcbacbacddbcddbcdbddbacdbaaaccaccbcccbdddadddddabbadcbdbddddcbddcaaaaaacdbaadddcbccabbdcdcdcbcabcdcdcbaacccbbacbbbbbdddbdbdddacccccdcbbbbdaddaabdabbabbaddcdddbbddddaaddbaadabbbcccbbaadbdabaacaaaaccdbadddcaacaabcaaabbcbcabcbbcdaadddccbdacaadddbcaabddadcbcdbababbbcbdaacacdbcddddadbbdcdcabcadcacabaadcaacbadbcdbdbaddbdbaabaccdbddbaccdaddbbddababcbcadbbbbacdbddbcdabcdcdabbcbaddbddcbcdcdcbadccadacbddcacaddcaadaacacdbddacaacdbaaddbcdbababcaadbdddccbcbdbcaddbbbddaaccabcccbdbdbccacdbdaaaacabddcadddadccabdccddbdacbaaacaabcacbabdbdaabddbdcacdadcdddbcaabbcddcacacbdbaddaaccdbaabddbdadcaccbcbaccccdbacadddccabdabdccacabbacdbbdbccdbbdbbbaabcddddabbadbdbbacbbaacdbadbabdbccaaabcdbcdcbcdacbaabcbddacdbbabddbcdbababbbbccdcdcdaddcddabccddcbddbdbdbcdbdbbdbcadbabaaccadcccaacadcbccadcdababcbcbbdbabaadcababbdadcbcbcbbddcbbbaadacbccacbdbcdccdadcacabdcdbacbcdbadbbddcdcdaaadddcbcddbdbaabccabdadaaabdbbcbdbbadaccddbccbddbccbdadcabbacbaadbbadcbdaabbcbddbcacdbbabacacaccdaccbacabcdcdbacaacaacdcacacdbbbdabbabbdbbbdbddccbcdadbbcacdbdbbabddbccaccccabbdddaddadaabdaaccbdadacaaddabcbadabcacdacbbabcbdaaddabaccaaadbbabdadcccaabaacbadcbdcdbbbaadcdacdbdbcacaccaddaacabacbbcabcadaadbbaddbcdbacbbaddcacdbcbbadcdcbdbbdbccbdcaadbabcbacdadabaaadadaccdcdaccddacbbbbdcbdcbddcccdaccdacbcadadbbdbcccaacdaadbbdacdcadbdcdbddacdbcdabbbcaacabbadcbcadbbabacddbacdabaddadddcbaaacdaadccdbbbaccbddabdcdddadccbcabbdcadaccaacbbddaabacaddcaaacccaadcdaabdadcddbcdbbdbccbadcccacbacdaaadcbdbbaaaaddadddabbabbaccabccbdcacdcbccacbcaaaddaabbcddbbacdddcbbdbcbadddacbccccaabbbbccdadbbcabbddaacbcdcbbaddabcbbdacaaaacbdccacabddcbbdbdcaabdbdddabdcaabdaabdaadccdaabcadbccbcddaaccaaaadbbbbbaddacbabbadcdaadacbbbbdcacadabbbacbcbdacbadcaaadcaababcdabcbaccadbdadccdaddaabbabbbcddbbbabbabacaccccddcbbbcacbaacdbbcabcadabdbddbbabccacaaddaacdcaccacdbcacdbdbabbadabaddcaabdcdbbcaccbdbccbcddacbcabdbbdbcbccdabcdaaccacbbcaaaaaabbbcacacadbadbcaddbdcaccdccdcdbcbbbbadcbbacaadcdbdcbcacadcddbadddacbddbcbadcacddcadcdadbdaccaaccaadcbbcacadbdccaacacabadcdddbabaabadaabddaadddbaabdbccbbcaddcbddcddaddabaadcbaaacdaaccbaaabdcbcbddcabcddabcddbdbbddbdccbbaccadccbbcdaaadbaabaadcbbbababcabdacdccaaccacbaabbdabdadaabdcddabadadcaacaccacacaabbbddadccbddcadbdbacaaddcdaccddccbdabdabbababcdcbaababcbbddaadadabaaabaaccbdcabdbadacaabcdddbdacacaadcdaaadadadbdacbddbaccbcdabbcbbabadaabccdcadbbcaabbcabaacbbaaabcacddabacbcacdbcdbacbbbcadbabacbdccdccabccdababbcdaaaacbccbcbbbbcdddcdcabcdbbadbddccdaacabcabccaacacdcdddbcbcbbbcadbdbdcbccababdaaacaabbdbabccadacbabdbcaaacdbbabdcddababaaaaaaadacbcbddcdaccaaccadddbaabcaddacdcddcccacdcabaabdbbccaabdcbcabdbbcabbddbbaddaaddabdcbacbcbccbbbbbddbdacacaabcbcdbcbdbbaadadbdcadbcdcbbdbdaabbdcdccbddbbbcbdabbdbbacaddababdccdbadbdadcdbbbbdcddcccbddccccdaacbdcadccddcdbccdcaaabaadbacacabcdcabaadcacdccdbccaadaaccaadaaabdbdbcbcddbaaacbdbdbacbcddbbdcaccbccabcaabcddbcaccdcadcbcbbdcadcdccbbabcabcdabaadabbcabbdcbdcbbbccccbccccdbbdbccaadddcdbabbcbcbadbbbabddbcadbdcccbacdacdcbbdaddcdacdbdbdcdbdbcbbbbdadbcdaddcdabcaabccadaadddcdaccacdbaccabccdaacdbdbbbbbcbccbcbccbdcabccbaacbcbaaabacaabbabdcaabaaacdadcbccaabdaabcddcbcaaabbabbdbdabbccbcaccbbdcbccabbcbabaccdbaddbdcadaabaccddcbbdbccdabdbacadbcccbdcbbbbbcddabdcaddadccacccabbccdccdaabcbcbcdcbcadabdcbacacdbbabbcddcccbaddbccbdaadaddaddabcabbddaccadbacbadbccdacbbccabbdddcadabdbadaaabbdbbacdabdbdaaadadcdbccadccaccbacdbadcbddbcdcbdadcccaaaadadcccdacdbabbcadcdcbcbaabacbcaaccdacdaabcdbddcccadbbbbcadacacbbdcdcaccbbbaadcdddbddbbdadcddddbcbcadacbaddddcbacbbbbdcbddaadadccadaccdbcabbbbbbcbbacbacdabbdcabcbadadcaacdaddbaddcdadadacabbacdcbcbdbadadbbccacddbabcdddccdbbaddadaccccbcbddbcadcdcabadcaacbacdddcccaccabbdacdcabacbdcdaacdccdbbaccacadabdacdadacbdcdcbcbcdaadcaccccbadabcbaaaaaabdbabbcabadadccbacdadacbabdbdbcacdbabadcbadbbccbcbaddcacdcdbbcbcbcbdbadadcddcacabcdccbccccdababcaababbbdcaadcdacbcbcabdcacabbaaddbdbcdabdcbbbbdaaaabaaadccbbdddbdcbcbcccbcdddbabccbbdcadadbadacbcbaabdadbbdcdaacabbadcacdbbbdcbbadcaabbadadddadacccdbbbcadadcbcdbddaddbadbadacaabcbadcabcadbdbabdadbaadbcccbadcbabaadbaddaaccdbacbadadccaacadcbaadbdbbbabcdddcddcdaaddbdadcbbbcabcdadcaacadcaacdababdccadbcaccdadddacaadbdaabcacaaacbddbcdddbdadaddccbdacbccaabcddacbcdccadbcadbccbabacacdaccacaaacbdcdcbbbddacaadcdadaddacadadcabdcbcbdbcbacdadbcadbcbcacadccbbddadddcaabdbcbbccdabdbaddcbbbcdabacabddacabbcccbdccccccddbaccacbadcddbabbdcccccaabbdbddadacdabbacdaaabababadbdcbddaddccabacdccbcdaabccaaccdadbcbadababccbbccbaccdbbddaacaacccbcbabbdcabddaababcddccababcbaccacaadbbaabdaaddbccbdddacaddaabddddbcaddddcdabbaaadbbdbbabdccdaddccddaaacdbbdaaadcadcbccbbbbbcbadcbbdcbbadcaabcdddbabacaadddaaaabbaadccbdccacdabbbddacadadcdcddcccbbbdccbabbbbbdbadcdbbacdbaddddddbddbacdbaadcbbbaddcdaabcaacadcdcaadcdbadbbcdcbbdbdccbdbacbcadbdbdcaccabdbbabdacaccbbcbdacdddbaadcdaadbadcbcbdcdabccdaadcabcdcbcabbadcbdbbcccccbdaaabcabdbbdadbacacbdddabcdbbddcabdbbacdbcdcacdddaadbadcdbdccacdbaadbbacdccbaabadaaacacbdbdcdaaaabbacbcdbdddadbaaaabdddcabdabcddadcdcacdcdddacbcbbbdbdbdcdbbacdcdcbaadcacabbbdbdbabbabacbabbabdcbddaabbabcbcacdabbbbdabbadadbcdbacbbdaaababccaddcbacacacbddcbaabbcbbdaadbddddcbcadaaabcdcdbddbaabaccddaaddaacbababadaacdbcadadddbaccbadbacbabbdbdbbbcbcbabbcdcaaabbbbbabdaacbddababcacaccaabcddabadbcbcadcbbdbaaacdaccbdbcaabbaccdabaabdcdcadbccacbacabacdcdbdcadbbcabcadbccbccdbcabdbaadaabcdcbcdbcdcabacccabdddabcbaccbacddcdcbdadcbccbcbbaddcabaddddbccdddadacabbdaaaddbbccdbddbbadbdcbbbabadbacddbbdcbdabbcadacbdcbbdabcbccababbccdaadadadbbaaacabbddcccbcaacadabbacddddadccbacdacaccccdddbccbcaacaddaaccaabadbcbdddcaacbcbccacadbdabbccbcbaaddbacbddddcbdabdaaacadabbadbabacddcaadcdbaaadadbccdaccdbbdabdbbbaddbdcdbdbbbdcaddbbddbaadbabdcbcccdbaddcadacdcbdbcbabdbccaaadbbbdadbbcdddcbacabaabccaddbbccbbcccaadaabacdcbdddacdabdbabccadbdadadcdacdbaccdcbaccdadabcbbbbcacbacabccadccacadbdacdcbcdcbdcbaacabbbdaaaddacdacacbdacbdcbdadbbdaaaaaccadcddaaddbcdbaadbaadccaabdababbcbbdabbbadcabaaaaaccccddaaaccdaadbcbbcbcbbbdbbddbacdccaabbaccbbadbaaaadaddcdbbcaddcaaabcddaabcbadadbdaabdcadadbcbbdccddddbaddddaacbcbabbbcaabbdbbbbbadcadcaadcddcbcabbbbaabacbbaabbaadaccdbccbbcddacdadcacbdbbbcbbbbdddbccdbadccacadbddbdadddadcdbbcdaadbbddcbbdaccddabcdacdbcbaddcadcdaddabccdcaacbdadbadcbdccccbcdcadbbaaddbdcbcabbccdacbacdddddabacabccbcadddcddcabcbbbcdcdcadacacccdddcdbdadccbddddaabaacddddabcdbdbcbddadbbdabbcccdbadbbbdbbdadbcdbccacdadbcbbdcbaadacaddbaabbddbbadcaaababacbdcadbcbcddcdaaabbdcbbcbdbbacaadccbabdcbcdbabadbdcddbaaadddacccadccaaaddaadccbdabddcbbcdccdbcadcabacdaddadbabbdadbbddadcacadabbadcccdcaabbdabcbbaaddbddadcddddbcadbbbaddbddccbaaabababdabaabcddaabdcdcddbccdabacabcdddadadcccccaabbadacaccccbcbadccadcbdcbbbbccdddbdcbadccbbdccaaccabaaccdbccbaadbcadcddadcddacddcadbaaddbacdacbabaaabbddbbcddbbcdbcddabbbcdabddccbacdbdaacadacddcadcdaaaadbdbacbbdbacbdacdbccbddacbdcdccbbdacabaccbdbbbcdccdcccdddbadbadbddbdbadccaccbaccaddbbabbaccabdddbaabdaabcabbbabdbababbacaddcccbbcaadabababadbbadbbbadaccbbaacadcbabcdcadcbaacdccccbbaaabbdaabcddbaddacaccacbdcacbdabcddbbacaadaccdbbdcbdaabbccdcbdadbddbbdbbccbdddbcbbadacaabddcdadabbbadccdbcdacadabcaadacbbbdcdabbdadabadadaccbacbcdcaabdaadabbbbcbcdaaddadccdababadddbbdcdcbcadadacadbdacacbddccbcaccdaccbbcacabbbbbaabcccaabacdaddaccdcbbcdddddbccdadcabbaadaddddbdabbabdabccdcdbcdbbddabbccabcaaacbacbdacbbdacdcdabcabcbaaadbcbccabbccbcaccaccbaaddbdbbaacbcbbdbcbaacddaaadaaccbaaabddacaaccdabcddddbdcaacddbbaccadbcbbbbbcaaaddaaacbbccbaaddadaaadccddacabdbacdaaddcccbcaddcabbddcdaddaabbbdabbdbcccdbdabcbaaaacbdacdbdbacdcbccdabacbaabdaacacaabbacccccaadcbddddcdcbbcbabdacbabbcbdaaabdbdaabbcbacacdbcbcbacddaaaabbcddaddbccdccccabbacbbdcacbdcadbddddbacaacaccadbabcdbbbcbabcddaddacaddcdbccdcbaabcdbdcacacbccdacaddbdbbcbbacbcbabacdbdbdcdcbaadbadcbcadcccacbbbacdadcdddacdcdbbcdabdbaddababaaadcacbcbbbadacddadcdbacdccacbdbabadbaacddcacaddbadcdbddcddcbdcbbbaabdadbabacddcbcacdabbdbadaaabbbadbbdcbbdcdccdcacacbdcccacbcbbbababdcabacadcadbdbcabdccbdcbcccbdddbdaccbbbcbbcdcddaddacbbcdaccdcbdaddccbcdcadbbaddaaadccdbadabdbbacbcabcddcbddddadbbbacabddbcbddbbcbccbddbacbddcdbdbdaaacbbdcccaccbbdadcaacbcdabbbdbcdaabcdaabdcabbaaddacaabaddaaabdbccadabcaadbbaaacaadcbbcbaddcbaccdcdbbaccccbaccdaababaddacababdbdbbcabccaacbaaaaaccdcacacdadabcdcaabbacdbabaddcdccabdcdacccccbabcbcddaadccdbdabdccbababcacdccaabdbcbcacccddaacbdaccacdbccbadcacddaccccaabccddbcdccbbcacacbdddaabaccacbaccbadccdcdbdbcdabcabcbdccbdabcdcadcddcddaaaddccccccabbcbbccacccbcdaadcddccaacdbaaacaabbdacaccbaaaadbdcdcabbbbababdcbdcaccdcbcdcdacccbcadcdadccabbcbdcabddaaaadbcaadabbdacdccbddaaacadcccdbbbbdcababcacdacadaaabbbccaadabcabdbddddddcaddaabbaccbccbccbddbbabcbaddbdacaabacaabdbaddcacaacabadddaaccaccadbcddbaadbbcdbdcabbbdcdcbcdbccadcbdddbbbacabcdbaabbcdbbadddcddbdddadcccacadcbacbdbaddaabbccdbcccaabbadddaabbabcbcdacbdccbcaaaaaaababbbdcbccbcaabdccddbdbdadbbcaabdaacbaddadaaacbcaacdabdbaaddccdaadadadbbdadbdcddbbbcdcacdacddbaabadcacccacccaaabcbcdbbdcbccdabadbcacdbcdadbadbccccabcbbbdcdbccbadcaadbbbacabdccababadadabadcbdcdcbbdcdbcddaabadcdcbbcdcacccdbdcdbaaacaacddbdcbadbccabbdcdcbbbbbcbacdabacdabacccdcccbdabddcadbddcdbacdacbbdaaaddbbaddcbbacacdddadcdcbaddbcdbaadbddddddcbddcbdcacbaaabccdbcaaaddcbcdcbbbbdbadaacbccdbdcacdcbdbbccacaccdabdccacbadcccacdddcaadcbcbcddabdccbddadbaaacbddbcabbaabddbbcdbcabbccabdaacbcdcdbcccdbbdbcabdddddbdbcddcccdcdcbacbdccdcdaacadbbadaddcbcabddbabccbaccaacbadabaadcabbbccdcbcdddccdaddcdcabbcdbcabcdbbacaabbbdadbcabccabacadcababababddbcadbbabcdcadacadbdabdadcbcddaccdbdcdaccbaadcdbddadcabbbcbddacccbbcaccdacccabbdcddbccbbbcdcbabbbacdacbcbaabacbbbdcdacacdcdabbaacaacacddaaabbdbcbbcadddbbbcdadcadccdcdacbccadcacacbcdbdcabadbaaacacdaddbbbcdcddcabbdbbbcabadcdaabcdbbbbbddbcaccabccccbaadbdadbacabdabdabdcaddcdaddacaadcaccbdadbdabacccbaccdaaccaadcabaadbbcdcdbaaaabacbbcbadbaacbdbdacccbadcdcbcdaabcdadddcccacccbadacdcacaccabdabbcdabbaacbadbdddbacdccbdbbadbbcaadccaccaaadacccddadabadcbadabbddcccadbbadbdddacadccbadcdacdacbbdbddabbabddddaaadcbdaccaacacbcbcbbacacdbddbcddbbbcabdcaccdcdccbcadaabbdbdaadaddacadcadacaccbbddaccaadcccbccacbadcadbacbbbabccbbaabbbcdadbbcbbbbdaadabbcbcbbbccdccbbcdcabbbdaaabbddaacbbddcacbdccbaddacaccddabdddcadcbbcbcaacacdddcbbdbbcdcccccacbddbacbaaadddbbacbacccbaddcaadcdccbccdcaabcaddbbdbabbacbdbcdcbaadddcaaaadacccbccccdbbaadccbddcbbcbcabdcabbcbabdcbaabadcacadaadadbbabdddcdbabcbabacabdacdbdcbaacacabdddcbbabadbcccbbcbcbdaaacbdcbddbabacdbddcbabcaacdddaabaaaccbbdcdcdcddcbbdabcaaadbcbaddabdaccbbdabcbacdacaadbdbadddbaaadcaddacdccddbdcbcacacdcdacabdababcadddabadacddcadababdcddcccddadabbbdbabaccbacacccccaabbdbbcbcadddbdbdcaabbdbcbbaadccbbddbcaddbbcbcddbbddaabbcbacbdbbcbadbdadbccbdcabcadbcbacadaaaccacbddabdaacdadacacaccacccabbdcddccbcbbadbccaacdcccddadbbbccbcbcdbdddaaabcbbabcaabadadcacdccbbbbdacaacccbabddbacadccdadaadcdccaadbcadbcdcaaaacaabbbcddbcdddbcbcbbdddbccacdcadaabdbdadcacadabbdabaadbadacdbdbacbcdcaddbaccbbcaaccdabcdbbdcabdcbabdacaabcbbcadabbdccccbbcabccdcadabccbcccabcbbdcaaaaababdabcdadaddbaabadccbaacddbbcddcdaaacabdbdbdbcccbddacbbadaacbcabdbdccacbcabcdcacabaabddcbcaccccdadbcbccbabcabbbcaccccdaaadadbacdaabcdcaaddcddadcacaadbccaccadcddccbcacdddbcbdcabdbdcaddcccaddbcdcacacccddcddcbaccaddcaabaddbaabdcdcccbcdbddbdcdccaaaaccdbdbcacaadbcabdaacddddcbaacdaddddaddbacaabccbbadbadcccbabdccdcbbacababbbaaacbbccbadcdcbddbddbbbddbcdcdccadaaaacdbccccabacdabbdcaaabddbccdccdcbabcaccbddabcbbcccabbcccadadddcdcccabcaaccadbaadccbdbbaaabbcbbaabbacacdcbdaadcbdcacdaabadadcbaaaacccdaadcdcddccccbdcabcdbaddccbbdbbbccdcaadcbcbdccbbcadadbccdadbccbcbbdaaacbcddccdcdadbbbaabacddbcbbbddbabcbdbcbaccddacdacacdbcdacbacbaabbaddbdccbbbacdcdddadadaacaadacabaabccdbccaadbdcddcbbdbbbcbcdbaabbabdadbbdbcdccbdaaabbbdacbddbddadadadbcadcccbccdcbcbcbaccbcaccdbddcaabbddccbbbbcccacbabdbcbaccddbaabccaccbdbcbccaabbbcabbaacbddcddddaacbdccdbbdabbadddbbcdddbabddcaddbbcdddacabdabdbaaccabdcaabacdcbadaacbdcbadcabbccadbbcbddcdacacabcbbbdddcadbbbbabcbdbcaddcabdabbcccacacbbdaccddddadadcdadadcdcaccddacabbcaacbdbaabadabddacbbabdbcdccdbddcadbdbddbbddddbbdacccacdbbdabcbccabdabaddaaacaabcdddbbcacdadbbacaabcaaaacdcacabcbcbdbabdacadbcadbcacacabcdaadacabdcbaaddbbbddaacaddcbacbdabdcabaccabdbbcaaacacbbbdaadbcdcabddbdcbacaababcdadbbdbaaddcababadddcacdcabdabcbcdbabccaabcddcbbabdbbddcbcbacaacdcdbcaaacbbcbccbbdabbadcdaaddcdaaddddbdcbcdbbabbcdcdccacadadabbcacabdddaabcbcdbabcaaabdccdccbbccbbcccbadbdcbcdacabdcbaddbcdadaaddcabbcdabdacaadbcdccabdacaddbadabcdabccdaacababbdabcabbcbaccbcddadaddbccdcbccdaddacdcbcbbbbcdcdccadcbcbdabadaadbacccaadccacbaacacdaacdacdcccaadabcdcaadbbdbbbddbdabdcdbbdbdacdbcdcaadcdadabbacdbbbadadbaccbcdbccccbcaaacbbbbcbccbacccabadbaaccdbbbcaabdccdcaccbdbdabcacbdcaabcddcccaaddbcadbdccbcddccabacadbacdcaabbdadbcdacbaabcbcabacbcbbdadcadacbcbdbdbbdadadaadbbcbdbadbbddddccdccacccdcaadcbaccccdbaaacdcddbdcacdbdcbbbaddbccadaccddabdacdaccaabdabcaaadddadabcaababdacacbcdaddbadadbdcacabaadccccaabcccbadddcdadcabdbabbdcdbcbcbabcbacccdbcbabaadabbbccbdbbccbbcadcccabdababcbabcbcaccbacdaaadbbadaabadcacbbcbbbbbdbdadaddbbbdbbaddccaabadcdbccaccdadddadddbbddbdaabcaadddcacccdbdbacdccdcacdcacdadbbddaacccbcbbbbadcddacdccdababbcdcbddbababcbcdabcccabbcacbadbddadcbaacbabcbadcabcdacbcabbacbbdaaaadadcadaccdccccbadaccacaacabddbddababadbdcadbbaaaccccaabdaabddccddaccbacdcdcacbcabbdadaacbbabbabcbdbbcbabbabdbbddbbdacabddbccdbbadcdddddddabcbbdadbdacbdddbdbadccdcbddbcdbcbaabbacbdcbdacdadbabacbcaacdbadcccdbbbbbcaabddabccbdcdcbbbdaadcadadbccbcabdccbbbbbbbdcbbcdbdcbaacccbaabbbccdcbddadbdbaabcccbababaaabbdbbbdbcdbbbbdbadcbcdabddbbcadabdbaddbbdcdcacccdbababbdbbcddbaaddadcdcacdbbdadbcddbcaccacacbacbaacdbadcdbacbdcbcabdadacddadaadbcababcdcddababcdbddacdbbcacbbdaddbabdcbccadbbbccdbcddcbdccdabccbdbacccbdcddaabcddacdcddcdaabbdbdbaadbccbbbdccdbdddacaacaddcdbbdbbdaaabdbdccbbaabbbaccbdbabcdcabaabcaddcdacccccaaabdabaddacbaadcbddcdddcaabaccccadbdadaaddcccabaabdbdbdcbaacccddcbcccbbcadaddccbdabdcdcdbbbababbbdccccaabdaacdbdadcbddcbcccaddbcaacbdcccbbcbcacbacdccabaccbcadbbaaabbdbbdccccabbbdcdaabbbdbcbddccddcbdbcdcbadbcbcadbdbadbcdaaadcadbbaacccbbdbadadbaccbdabacdcbcabdddbbbaabaabbbcbdddabccbcdbaddbddadbababdbcdbaabbbbcaddbdabccdabcdaabbdacbbcaacccbdcdadbcaccdaaccdacddbaadabbdacacccadabbabcbdbdbbabdabcbadccadccbcaddcbdccccbdacddddbaddbaabdbddccdaaacacdaaadadadcabaaacaddabdababcbbabaaabbacbdabcdaddcaadbadcbbbbbadcbcccbadbaadaacccbacbdcbccbaccdbcacdbcbdbddabbaaabcbdadaaadbbaadbbddbbbdbcbaaacadbaadcabdcbaccbcddbddcabddabbbcbabbdccddcbbccdcdbcbdaaddddbbacbacbabdacdbdbadadcddbdaadcadddaddbbbdccdcdaaadcadadaadadcdbbaccdccbdbdabadadbbbaabbaaacbbddaaaacbbabadbcddbcaddbabcabdaccbabdccabaaacaccbaccccbcdbbcdbabcadbabbcbaaacbdacdabbaddbcdbadccbbadccdbaadccddcdcdccaddabdbbdcdccadabbdbcaddbcaabbdabcaccadaabcbacdcccdbdacdacadacbcadddbdbabccaadcdbbadbadabcabadccaaddcdccaddcaacdbcbddbdcbacaaadbdccaacbabbcbaabcddbcbdbccaddadadcdbbdccbdccccaccbaddbcabdcacaabddbdaabdcdaaccdbcddbbcacaccaccbcacdcbcdcdcacaabbbaaabacaabdcadcacdbcadbbaccdacabacdbcacadadbdbbcdbbadbdccdabbdcddddabcbdbdadbdbababbcaaabddcbcdcdcdabbabbcdbdcacdacdcdbbabaaaaddbdcbaabcccadbcbabdccbbdbacbdabbcccdbdadabdcccbbbccddcadabaadbbbaaacadcdcddadcdadbacdcabdaaabcbddbaaccadaccbadaddbaadcbccccbaabbbbadcdcccacbbababcacdacbabcccdbccdcbcacbdbbcccbdadbbbccaabbbdbadadbaaddddabaabccaadcbbdabadbdacddccbdbcdacbcbbbdbbbdacbbcacaadabbdcacabddabccbbadbbccabbcccacadacbbbbaccdcbbbcbddcbaadbabbadbdcbbddccdbddacaccccbacbcddbcbacdcbdadbdaaddaabdacacaacdbbbadbcbacdbdbcbabdbcbaccacbaabdcacabbbbadddcddcdcabcbdccadbccacdcccbdabddcaddcadbabbbadbcbdbddbdddaabbaacbdcaaccbacabbdbccdddccabadcbdddcabacddabacbdbadcaaaaaaacbdcbcbcdddaabdabccbdbcaddccbddcdcddbbdbdbbdbcbbcabaddbbadccccdbbddcbabbcccbcacdacbcbddadbbacddaddbbcdcccdadccbbdbdcccddcaccacbcabbdaddacbdccbaadbcbbadbdbbcccdaddcadbadaabdadabacacccddcbcacadcbbcabbbadccdccbcaabdaddacbcccaabcddcbcacbbabcdaaabaabadcdadaacaaccdccaadcabdabdabddbccbabcdacabddcbcbbdaccacdabdadaaabadadabbaddbbcaccbbabbaadabaaccccbabaaabbcbcbdabbdbcbbccdaabbadbbbaabacccbdddbacdaaaabcabbccbdbbbcdddbaacdbdccddcbadbccdccddaaaabbbddbbbcbabdbbcaaacddabbcbbddbbdcabdbadcaadbacadcdcbcabddddcbbbadbbbcdcbbadbaabccabbdbcadddcddbcbabcccdadddddcaadacacacdbadddaabdbabcbcacdcdadccbadaacbabaddcaadaabaabaaacdbcaacbdaacacbadabdacddaabdadbbbbdbdacdabcdddbabcdbdccdcccbcbdcaadcccabaabaabcbbdbacabcdacaacacccaabdaabbccbcdcdacbdbcadddaadacccaacccbcdbbbaddbddbddaaadabcdbbcbabacdcbaaccabdbbadcccacbadbaabdcdadbdcdbaccbaabcdbbbbcbcbdccbdacbdcccddbdcabdadddaddadacdcccdbddcbcdccdaccbbbaccbcacbdcadacacccabadcdcadcaddddadaddcbcabddaccbbcabdbaccacbcbaacadddccdbdddabbaccabcadcbcbddbccaacbddacbacdcbbddbcabbcabcdaaaaccacadcaadbddabbdabddcaccaabbabcbabaabbdbacddaaccbbcacadcaccabbdaabcccacbaccbcdabdbcabdcdaaadaaaabddddccadcbaddbadbdcddbdbadacacdaacdacccaccddddbabbadbdacabdbbcbddbbdcbbcddbadbcacdadacdbbcccbbaabdacacdbababdcaddcdccacdbdacccaaaacbcacdbaaabaaddadcadabbadccdbadcccaadbacdaabacdaabadccdbaacbacccbbbcadbbbcabdccbbabcacbcbcdcbbccabdddbcbcbcaccbcdbacbcadcddcabbaaaddbbaabdabbaddccdaccabcbccdcdcaccdbaaacddbcacaadababacbdddabacccacacaabbcadabdbdccadbbbcbdcaabbdbbbadccbccddccaaddbdbbcbcacccacadbcdbcadddccbabccddaaabbbbabbdcabcdaabbadcccdadcabcaddccaaacccaabcaaaadcaccbbdbcdabdbcabddabcdccbacaabaabacdcbaacacaaabcbdacbdaddabcdbbcacdbcdaadcabbadcaccbadcaddaadccbbccdbadcddbddccdcaccbabcbccdacdcacbcbbdbaccdcaccdcaadbaaaadabdccbadaddbacdcdbaccbaabdcdcbcdbcadcccbccbaabbcdabcaaccdadacbbdcbcdccbdccaabbcbaddadaaadcbadacacaadbbdbbacbcabdcabbadaabddccabcddacacdcbbcabdaadcbbdbaaadabcdbbdcdcbaddbbabcdcbacadbccbacdcdaabcaacabdcacdacabbbacadaaddbaddcccabbdbabdcbcadddccdadbadabbabaadbaacccdbacdbadccbdccbbdbdadcbbcdbadccdadcbdcbadaaabdbccddbcadabadaadbcbddcabcaddaddcdbabadbccdcdddbcbcccdcbccdacbdbcccbbadacccdbdaaddaaadaadacdccdbdcbcccdddcdcbdddaaadaaabdbbdbabaaabccaadbbadbdaddccbccdadcbacaadbcbdcbbdcacccbdcdcadddbbcbccacbbaaddbdadbdadacbbcdadddbcdcaacdcbdbcbcbccdabdabcddcabaddbbabacaacadbcaadaaaadcbdcdababbaacdbbcadaacabbdabdbcbcacdacacbaadbbbbcdccacbdccdcabdadcdcdcddacbbdbbaddcddddcbcbddcdcaccaadacaccaaacbccbabbdadddcdcadbbbbbcddbadbbbbbbcccababdcdddbcacccbbcacdbbdccbcdaccaddbcaddbbdcabbbbbdcdbdccbccadacbdddadabdacdcbccccdcccccdbaaacccbddccdbbcdabbbccdcbaacdbbaaabbaadabdcaccdacccbdaabaccaabcdbbbcdbdbcddacbcddccaaabbcbbbcacbbdbbaddbcbddaaaaacdabadbdabddccacbccdbcbaadccccadbbbbacddddcdcaccacaadbcccccbabbcbdccddcbbdaacbbdcdadccacbacdbbcacdddaabdbbaaaabdbcdcdbcadbcadbadbacbaaaabcdcbbbabcaadabbbbcddaacabccdcbbcbacabbbbacbbacacddadbdbcccddaaaaacacbcddcbdcdabdaaaddcacaacdcddbcbbcbdaabdabcadbbaddaaadcadabbdacababbbdcccddcbdddbdccdadcabcabdccaccdbccadbbddcbcabbbadaddaadddadbbbbcddcabbbbcacdccbbdacdccacbbadbdbadbcccaaccaadcdbcbdadbcbdacddcdcbacbacbaabdacababcbcdcdcacbdbcabcababbcaadabdaacdbaacdccadccadcadacdcbbdacccddcdaadccbcacdaccddcbdcdacaddcccdbbbcbdbabddbbadddddabcbabadbbaadcbadcabdcaddacdcbcbcbdcbdaddaacbbaaacdbdacdbcbcdbbbdbcccbcabcdcabdcdcabbbabcbbaabccdaccdbdcabccdcbbddcccacdbcdadaaabbbabaaacbabbcccdbccbaabbbcbabcbabcbbccdddbcbadbbcddddbdccccccbacaabdadabdcbaddabdbcaadddcbcdababcdbdbadaacbcadbabcabaaaacdabdbbcbbcbcdaaddacccdbbabadbaabcdacaabaabbaabdaaddcaabccccaaadcccaccbbaadddddccabcabccbacacacdcbadcdbcddabddcdbcdadbdaaadcbdcdcbbcbdcdacbbbdcddabadaddcabcaabadbcddcdaaadbcbaaadccabcbddadcbbbadbacdcaddaaadbdccccbdcbaddcadcbbdcaacaccbacccbdabddaaababbabadabadbcbbabcaddacaababcdacbdbaaaaaddccdcdddaacdaccdacbcdbcdccbcccddbabcadadaadccdbabbbabacdabbdadbcaaabdbccacadadcbaadcdaaccaaabdbccccbbdcdcbddddabadcbcdbbbdaccdbcabdacccbbcdcdadddaabbaacadcbcdbacbacdccdaacdbaacadbccaaaadababcccbacaadbcbbdccddaddbccbbdcbaadaaddddcabbdbbdacacaddacacdccaadbbccdacaaabacaadbcaccaababdcbadbdabbdabbcdbadddbacddccccabccaadabcabdbbacbbaaadcadaababaacddcabbacdadcaabdababaabbadbbaaadbccbcabcadaaadacdbdcdacacaddbdbbbcabcbcadddcccacbdabdaacadbaabcddaacbdcabdcadddcdadaadddababccadbadadddadadbccabdaabaccbcbbbdcbcbbcbdddbacacababbaadcddddccbadbdcbcdcbabcdbaabbbaaacbdccdbdccaaaacadbabdbbaacdbabcdcbcacccbdabccabbcbdabdddbccbbddababcbbcdccccdbaacaabaabccdcaabbbcdcaadbbdbcccddcaadbbcadaddaacbbdcdaccdcaabcacbabddbdacbacdbcadbaadabdddaddcdadacbabaadcdcaddccabbdcdacdcdbbdddbacbcbdaabbbcbabbcadbdcddadbaadccabdaddbdbaddcdaaacbdccacacdbddbbbcbddbdbbababcdbacadbabcbbcadbbbbcbcdcccbdcddbabdddaddcbdcabadcbdccaddadcdbbdababccbabadadcdbcbadccbbdacddbddcdbbddbbcccbdbdaadbaabbbcadcbacdadbcccddadaadcccabdbdcdabdabdaaccdccbbdabcbdcdaabaadacaddbaadcdbaccabbaaacbbdbbdcdcacbccaccbcdcbbcdacadadccdababdddcdcbdbdcbaabbbccadcccbbcaddaadcbcbcbcaccaabbdcdbbacbdcdccacdddcbdaababbbaadcaddcdadcccddcddabbcaaadddbcaacdbcbaccbcdacbdccccccbdbbababbbcdaaaabacdcdacabccdbadcaabdbadccbaacadcbbadbdcccadddbcacddcbdacacdcbccddbabbabdbcababdcabbddaabaaacddccbddbaaddbbcdcbcdcaccdbaaaaccbacbcbbbbdcdbcbabbdbadacbadcccadaadadccdccacdcbcddbccabcbbdddbbbacbbbacaabaabddcddabbdbbcdabbbdbcabbbcdbdbbdaaaddcccadddadadddccdcbcccdadbbdccdbddbdbdddbaaaabbdaddabcdbabadbdddaacdadaddddcaacdcadcddcabcadcdcaddacdbabaadabacdbdabcdabbbcadbdaabccddadbcabababbabaccacbbdadddcabcbcdcdccaadbacdadccbbadadbdbbbadbadbacdddbbdcaccbdcacaadddbdcbaccdbcbaccdbbdcabbbbcdcabdabbcbbbddbabcacbbaabbaccbcaddadcabbbdacdcbcacdcbdddabdaacaddcadccbbccdcbbacbaacbdcbaacddadddaaccabcddadacabacbacbacccdddbbacabbcacaddaadcdabccdcdaaadbbbacdbcbdddabcbcbccbabadddcadccbacdcadcccbcccccccabddcdcbadcabcdddaccddccdbabcaababbcbdccdbdbadbcdabbbdccbadccdcaabcccbdccbbbacbbdbbdabcdadcdaacdcbbccdadbaacdbbcabaaddbacbbdcdacdbccadaacaddabcaaaccdccbbcdbbdcdcabaacdabbccdadaadbcadcdaaaacdcaadbbdbdbcabbabdbdbcabdbaccddccabbdbccbbccdddacbbcacddccddbbdbbccbaccbaddcbbadaadddddbbabddcbcaaddbdcdcddcdcbabdabbbbadbacdddaadbdabdbcbdabcbcbddddadabbbcbbbadacbbdadbabdaddcbcbccaddcdbcdbaacdbbbdddcdadddddcdbcddccbdddbbadcbdadaacaccaccacdccdaddddbbbcbbbaaddacbcddacddbcdbddcaacaadccbbdaacccbdbddcabcbabdccdcbddabcacddddccacadbdcbccaccbcadadcddabdadccbbcaabcaabbdbcacbbbcdcbcbabbacdacdaccbdcbabdcbccccdbcccbaacbaaacbddaccddaaddddbdddadbadaddaaccccdbcabcbbaabccacabcccddabcbabddcdcdaabccadbdabaacacddadabdcbaabbaadbbbdcdcccdcdcdacbddcbdddcddadbaaabcbbbdcaaaaaddbddadaabdbdbdbddacbabbabbabcbaadcbbcadddbcaaacbcbbbdddadabaababbdababcbdcdcacdddddbccdbbcbacabcaadbcbaddccbbcbcbdadbabdbdcadadcaacbbccadbaaddbcbcddaaadaabdbbbaabdbbcadbbbcbbaddbcadbaddcacaabbabbcbbcddbcbadaaccabbcaabadcabaaabcaabbbacaacdbdcbbadaaccdccbcdacbbbbbbaacdbadabbbccbbbaacaaabbacdbbbbcabcadaddbdbcbaccbcacadbdadadcccadbaddbacabccabdbacdddcbacabdcbdcdbbbddcbabcdbaaadabdccbaadddccbddccddbdbdaccbaccbbbbdadccaaadbdbcaabacacccdcdcdacccbbcddccaddcbbcbaadbadbbbdccbabbaddccaadbacaddcdcddabbbbddbbcabdcdcbaaddaddbacbcbcdcbcbaddadbacbbbbbdccccddadbbacdcbcdabbabaacdbbdcddbbaddaccaabaabbdbbbccdabdcdadaddcdabbccdaccabdbddbacbcadacbabcaddcabacdbbcdcddbaadaacdacdcdcacdabbacdcdaaccdcddacbabcabddcbbadadaabcdccabcbbcabccadddacccabdbaacadbdcddddaadbccbbcddddddccbbacbdacdcbababddbdcabadcbddbcbddaadcacccadaabcdaccbdaabcbbbdadbcabcbcccbcaaccadcbdcdccbbbaaaaadddddbcdddddccbcdaadcaccccabccbabbabcbbdaadddccdadbbccaaaddbbadbabbcacdabdabdacdcbbccbbbaddddcccdbdaabadacadbdacacddbccadcbbccadcdcdcccacaabddbbcdcacadbdaaddcaddccabbcaabbbaadbadcbbabcabdbcdaddccbabadaacadcacbadbaccdbbcbaacbdbbbbbcdbccabaddcdaacdcbdbbdbcabddadaaddccabbbbdcadbcbaabadabacbcbcabdbbbbbbbddcadcbabbdccdcaadacaddacaaccddbbbdbbcacaddbacbcdcccabccdaabddcbacdabbcbbdbddcbccdaaadbdaacbbdcbdbcdbbcabcaabdaacdbdcaabbdabbbdcaadcdbbbbccbcdcabaaaddbcbabbbccabbdbcbcbaacadcabbcdbabbadaacadbacdcddcbbbadbccdabdabdccaddacadbaddaaacbbcbdacbbddadcadcdcbdaccacbdabbacddbbcbacddbccdcddbbcacddabcbbacbbaabaaaaabacabdccbcdbcdaacbcaacbdcbdbcbaccbbaaaabcacadacabbadbabaddbdadaabbdbaabacdcbcadbccdacacbaccbdccbabbcbacdaacababadadcadccacabbdcdccddccaadadabcbddabbddbaacdadabdcdccdaaadabbdcddbbcccdaccabaacdbdaddddaadaddddaabdcbbdbaccbdccaaaccbbbaaadcdcababcbaabdcaccaddcbdcbdbbcbabdabddbbadcdbdabdadbccbcdccddcabbaacbcacbbaaacbbadababcacbbccacacbcadcdaadbcbcbbdcaacccbbcbadcdcdbabddcdcbacdcbddccacabdbadccccbcabcdadaaacdadacabadbcbdbcdbdccabdcaadddaddcddbcbcadcbcadbadcbaaddacdcadddbabcddcbdbbabcaadaaaddcbadccdbbbbddbbcacdadadaadadacbbadcdadccddddabaadaddaaabcdcabbadbbcaaccdbbdaddadddddddacbcabacdadbcdbadcabcabacdcaabbbbbadbcbddbdaadadabbaddcdcaccbdadaadbacabcbbbdadabbabaccbccdbaacddcbddbaacbdcccaaaaabacabbaaaadbbdccdababccabaadbbbaaacccbabdadddbacbcaabadbadbaadadcbbdadbbbadabacbbbabcdbdccacaadcddcaaacddbbaadbbbdabbcbaababbacdcdcddbcbddacdcccddaaabdabccdcccaddabbccbcbaacbdbcdadbdddbcddaccdabcbbdcbcaddccaabadbaabcbdadaadbcddbdbcabddaacbbbbdcdbbddacaadbcddacbcbaaddcabddddcbbbccbaabdbddddcddacacabcbbdabadccbacdbaacacaaabbcbcaaccacabccccbdcbbabcaabbdcaddccbcaacacbbdbccbadcbabbcccabbcbaddcdabadcaccccbccbccdcbcdcbaadabacdbcbaaccdbdbdcddbadcaadabddbbcacbcbccabbccacbcbcdacddcbabcbcaccbbadcdcaacabaccccdbabbadbbdcdaabbaddcbcbabdbddcababddcaccdccbcadbbbbdcdcbbdbcbbbdbadcdaacaabdadbcbbadcaacbbccacadacaabbcbccbdadaddacbaccdcbabdcbacbdabacabbabcdcbbdccdaddbccdbdabdbccbbacddbddadbaddccbcbbcaccccdbcacccccbbcbddcabbadbaddcabcaabdcdddddbccccbcdcacbabadacaccbccaacaddbadcacaaadabdacaabdcaaccadabaadcccddbcbbbdadbadbdbaababbdbdbdbdadabbbadcabadcadccdbcaaabccdaadcdaddabddbcdddadddcbacdbbcaabcddacbbadbcdcdcaabddbcdacacacbabaabccbdcdcdddabdccdaccaabbbabdabbbcbcaacbddacadcdabddaddabcdabccaccabaddadbdacacbbacadbadacdcccddbcabbddbcabbdbbcbcbdcbdcbdbdddbdccabdbcbcccbbcdcdbbccccaacabacaddcddacdbbcddadacacadbabadcacababadcdaadcdbbabcdcdccabcacadaddddbcdadbadbcbaccaaaabbdcbcbbcccbcbbbacddbacbccccdbcacdadcbadadcdcdadacbadabbababdbbccdaddaddcdbcbdbabdcabdbacbacabdddaccdcadadcaadabbabbcacbcabbbdabccacbbcaadddadbaabdcdcbadddcaadccbaadcbabcccdbdbadadddbaccbbbbadcadccbcccbdcddadbdbddbcabddcbcdabacdbbbcabbdcbbdaacadbcccccddabadcdaccadbcabcddaadbccabcdddccbdbcbcbaccabcaccbabadaaabadcdcdcddbdcaadaacbbcdbabdddbbacccdddcabcdcdaddbbacbcdcdddcdcddbcdcbdaaddbcadaddcdbbcababdbdadaccdabaddcadcacaadcbaadbcbaccdcdcbdddbcdcbbbbcdbaaabcaaaadaccaddbcdbccdbcdcacbbccacdbcaabdaccbbbbddbaddaccadcdbdcaddaddcddabccacacaaccbdabbbcaaaaacadaccddbabdbccddadcdcdaadbabccdadbcbccdbcbaaadcbdbaaacbbaacabaacbaacbdbadcdacdcaabddbbabbdadcdcdabaadcaddcdbdccddaddacbaddcbbbbacccbdbbbaacdcaadabbdbaabccbccaddbcabdddabadbcabbaaabbcddaacdbdcdcbbabbaddbdaddbbdbabdcbdacabaabadcbcbabdaddacadbadbbbdaaccdbcbbacaddccdaabcdaacbdcaaacadadacbabbdaacbdaadadcabaaaccadbdbacaacadbbccdbdbaddccdadaaddcacaabccbbcbdbabcdaadcbbadadcddcddbddbbdcaabbacaaadcdbabaababbdaacaadbbabbbbbdacddccbddcadbccbbabaccdccabbdaabcacdccaabbcaacdbabadabddccbdbcdccccccbdaacbbdaccdbacdaaadbdbbcababdbabbdaaabbbdbdaaabdaabcbdbdbcbcdcbdddddaadabbbabbcaaadadacacdbacbddacaadcababcbdcdbbbdcdabdbacdacbbbcbdabcdcbacbcdbabcbaddbadccddbbaddaacacdbbaacabbdbdacdbcbdbcdadadcddcccccababbabdcdcbddcdadcccdcacbbdcbccacbbababbbbbcbbdddabdabdcaabbdaacbdacccacaddabaacaccadbbbaaccdddaabbdccdccdcbaadccdaddcbacbddbaccbabbbacbaabbdabbccbdbddddadcbbbccbabbdabbaddcaabdaadbcddbbacbaabbcdacdcabcbbadbacbdbdadcbcdacaababcaddbddadadacbaacadbdaacbbbbddbababdbabbcadbdcacbdcaaddbddcadaadbdcaacccadddbadcddabbdcaddbdddabbccddddbdacbcbbdcabbcbbbcccddcbddbbcdcabbacacdbcadbadcbccbbbdbdbcaccdacaadcabbbdadaadbcbcadcacabdbbddccbbcbabdbbbaabaaadddcabddaccdbabcdacbbaadabaacdcaaabdbcbaadbccdcacccdbacdcdadbadadbdadadddaaacbccdabdcdaabaccaccccbaaadaadcabaacdddcbaadbbdacbdbbcadccbbbdcdcaccbbcbabadbbddcbbabcdcacdaccdabdddbccbcdccbabadabddcbddcbbbabdcccabdaadacbabacadcbdccdbacdcbacdabcbccccbbcbadacbcdccbbcacbcbcbcbcdddadcddaaddbcbcbcdadbbddbcdacbbdbdbbadbbdcacddbdbbcbabaaccdacaacaadcdcbbcbcbdbdacabdacbcbaacdaccdbbbacdccdcabcaacacdabbcccbdaacccdaddccccbccbcbbaabdcacabbbcddbdaaabcabcdcdccbddaddccbbacaadbcadccadababababababacdabbbbbbdccbcdcbaddacccbacbcddccbabbdbdcaaabdaababdbaadcabaaadcdaddabdcaabdcbbdbaccabbcdadbaabdcdccddaaadbbacacdddaadbacdbadcdbbbcdaddccadcdccbdbbdbddccddacccbaccbddacbbabacaddacabccdabdddddcdcacdcdccccddadaadcdccbadabbabbbbcabdcacbcabcacababaaadaccccbcbbadcbaaddcadaacadaabbabbcbadcbdacbaacbdbcddadcdcccdabdacacbaccababdbbdccbaabbbdabacadbddbadbacaadabbddccacabbaddacdcbcdcdbadaaacabccacacadaacbcdcbacaccdbabbacbdcaaadcbddbaacaccacbddccabccabcbdbabaddcdbbcadccdcaabcbbcbbbbcbcccccaddacbbdacdacdccccaddbcdabbbccabbbbcdbdababcbccdabaabcccabddbdadddbddbdabaaabcbbabdbaabdcbbbaacacddabacdbcdcdcabbddbcdcadcbcbbdaccabcbcbdddadcacccdbcdadbacccacaadbdcdcdacccbcdcdbdbddcdbdbbbdcdaadbbddcbdbbcbabbaddbaaddaabbbdaddaacdcabbdaaacacbdbbcaddbbaabcdabbdddccbacbdcbbbababdccbcabccbbbacbbdabcaddbcbdcbcdcccddbbaadcdadcdadccacdccbbacdcddbaccbaabddbcbacddbbdccbbbacaaaaadcaaaabbbcadccdacaddabbbbbbbacdcacbababcbbcbaacdbacbacadbdbdbaacdacddacdabdbacaccdaabdcbdcbbdbbccdbdcbcacabdcbbbacbbadbabcdcaabcacbbcabdadcdbbcdbaababbacccddaccdcdcdbadadabbdaacaaacacabccdcaacabaacaddcbdcabbbdcaddcccbaacbdabdcadaaaabddacaaabdcbcdadbddabcdcccaabbcaacdadbbcbaddbacabbccaddcdaaacddacaddbcbcdadcbbddddddbdbaabbccadacabacabaadbabbacdbdcacaaabbcdacdacaadacdbaabbccccaabdacacddcabacbabdbbdbcdaacdcacddabbadbddccbcddcadadabccaaddacbccbcbcdacbacddbaacbaabdcdddcbcdadcdabbdcbbdbadbbddbbaabdccbccaaadbaadcbcccdccdadddbcdddbbdbaddcdacbdbbcacadacacbabacdaabbbcaaddbdcaaaadbbcdacdbdcdaaddcdaadbcddddcdaccaacddcbbbbcacdcabaaabddcdabaadaadbabdaccccacaccbdcaabaddbbadadbccaddaadcccdddddabdadacadccbddadcacbbacacccabadbabbdcaabbdbcbbbcabddddcaddccbdddccbbbcacddaacdccccadadbddacbabddcdbacabaadbdbabbdddddcbaccbddccaccadadaadaddacddbacacabdacaadaaccbdcabddabdbdabcabcccbbddaadbccaddcaabcccdadbabbbdbdacdcaccdcadaaabcdadabcaaabbdadcdaccabcbaacdcdcaabdcccccbbdbccbdccdcaacaddbddacdabdcdbaaacbcabadcdbacbaabbdbcddcbbcbbbcbcbaddccabcdaddacbbbaddabcbabacbbaacbaddddbbcdcdadaccadccadbbdcacaccdacdacddbabdabbddcddcbaddabaacaabbadcdcddbbdcaaacbaabdbbdabaaabdbabbadcccbaddbbcacadaabdccdbbcccbadbdbbabcbbccccbacdbbaacbdcddbddacaccbadadaadadabacbcbbacdaacdbcaacbcbadacdccaabcbdbddbaddddddcbcbbbdaadbcdcbaacccbdddaabcaccbbcadbbadbdbaadaddbacaacdcbaaddcccdccacddddbabbddcabcacdcaccadbddadcccbabcddcabcdacbcdaccacacbcdbaaccbbaabdccdccccaadbccbabdbdaaccadccbccaacdccaababaabacdacdcbbaabdcbcabdddcdadbcbadddadbbdaacaadbdbdcdbcdcadcabbaadccacccacddcbabcddcdcbadaacddcaddcbbcbcdbaddbcdbdbdbdabbdcdbddadabcdcbaabcccabbbdbcdbcabbabaabcccbabcccbcbcbccdadaaabccaacdcdbbacccdbadbaaccbbccaabbccbabcabadcabaccacbcbbaacacdacdabcabdcaccbbbccdabcacdcabbdbdccacdaaddaddacddcaadcdcadddbcaacccdcdcacdacbabbbadcbdaaadcbbdacdbabcdbaacdabdbbcdadaccadbaadacbaccacdcabdacbdaabdcbdadcbaccccbcadcdddbbcddcadaddcdbaaadacacabbbacbbdbdaadccccdbddbcdcbdadadcbababaacbaddadddccdbcbcdcbbadabaadbcdbcaadbdabcbacccabcabaabcacacdcbdabdaacdbabaaaabbddddbdbaaaadbdabbdbddddbbdcddaabbcbcbdabcbbabccdddadadbccaddbaaacaadadbaaabddbaadabcddaaddbcdbcbcccdacbbcaaabcccbbbcabcbbbcacbdccadbbbbdacdaccdabcccaabadbadcdddcbaddbdbcabadaddacdadddcabddbacdcaaaacdaaaacddacdbdbabaadcababaabdaacdcbddadcdacbbdbcbaaabbbbbacacdbabaacddbdabdaaaaabbdcccbacdcbbbccdcbacadaadddaadbcabddcdddacddcdbbdbbbaacaaabbbcdccbdaabadcbdcbdaaccaadcddadcbdcbbcdddcbababbcbadbdbaaabbdcacaabdacacacacabccadacddbcbcccacbcdbdacacddbcbddbcbcbbbdbbcbdcacbbdadaacabcccbadcacdabcccdbbdccaadddcddabdcbdadcbbddbbcdadacbcdcdcadcbababdbbbdcacdddcaadbbbcdbbabdacccaacdbdccccdddcacacbccacbaaaadddcdddabcdaadccdbdbdccbabcdddbdbbccdbdccbbbcabaaaaaacddcdaaabbdbabbdcaaccbabcbccadbadbccbdbabbbacbdcbbbbbcadcadaacabbabbcbdddccdbccabcdccbbcdbccbddadacdacdaaaaabdbdabcddddccbdccddbdbcbcbcdbdabbcccaacadadabdcdbabcabdbbbbdddabcccdabddacdabdaddcdbccaaccacacaaaaaadcbbdbbccddcdacdacaababbcaddbddabacbaaacbdccadbdadadcbcdccaaccbcaabbccbdadacaacbcabbbbcabdbdaddcdabcbdaccdbacaadabbcabaaccbacdbabacbabddbbcbcdddbabdcaddbacbacccaaaaacbbdbbcbadaccdbcbabcddcbddbccddcbadbdcacbcbcbdcaadcabcbabbaadcdacbbbbddccbcbdcbbaadcddddcbdccbdcdbcbcadaacbbcbddbddcaddadcbdabcaddaddbdcbdcadbbcaabbabddcdcdbddaabddbdabaadbcbdcadaddcbcdabcbbccabccdabbacddbbaadadacddddabccddcadaaadbacbbccadccabbdbdddadddbcbcadbdabddbccdbcbbdacadcabbcdbdbdacaacacacbaaddacbabcbcbdadacadaaabdcdcccbadddaadaacacccacdcdacbcbbaacaddbcaadcccdaddaddbbbcadbbdabdbbdddadddbcadadaaabcbdcddbabdcdadaabaacbbbddacddbbbabaacbdccddddcbddddcbbbacdabdabdbcbddabccbabcdcbabbbbbacddabbcbdcadbccacdbdcbdabcabcbabadcdaaabbccbdaaabcccdccbdbabbbbdcbaacbdddbcaabcdabcdbddbadbababdabcdcdccbdbbccdbbadcaddcacddcabddbcbbdbbcbaddbbbcbabdbcdcbabbddbcacaabbddacaacadaabdadcdccadacdcddaacdbcabdaabacababddbdbbadbcaddabdccaaddaadddbaddcdbcbacaddddccacbacdbcdabdacadbddcbdbaadcdccdadccbccabddadacbcdcddadbacbbccbdbabbbddccacbcabcddabaaaadbddaadbacdabdacdacadbacacaccbdbcdadadcbbdddbcaabaabdadbbdbacaadbcdccbcbbdabadacdccabdccdcbcbdcccadbbbcdcaabbdbbcdbbcccbaabddddaabbbccddbddbaaabbddbcddaacaddddacbcbcaccaaaabcdbbabbbadbccadaccdcaabdcbacbccaccdcdabcccaaaacdbdbaaabbbaccaaabcbabbdadbbacacaaadddbddadcbbcdadabbbcddbdccbbccaaccbcdaabdbccbabadcacdabcdcdaaabddbdbcbbbbadcacdbcadbacdcabadaddddcdacdabdcdbbadcddaddbcdaadabdbdbaabcaadcabbcacdbddadbdbacccdccbabbdadbbdcabdbabdcbaacbddbcdbbcbabadbddbbbcdbdcaccbdcabaacdccbabcbbaadbbacbcacccaabdbdbbaadbcbcbccbadddbbdbbcadccbbabbcdcdddabaabbdbccbdccaccccabaacadcccccdcbcaddbaabdcdcdcbdcdaacadacccbddaccdbdcbaddbcacddaadcbcdaaabccabcbdddcbcbbdddbdcdddcbccdddbabdbacdadcddddabcbadcaabdadcbabbcbbdbdbbabcbadddddbbabdbaccdbacabcbddcbaadaabacacbdaaabdaddacdccbdbabcbbbdbbbbbaaacdaddaabcabbbbdaabdbdadbccddbdbcdabdccbabcbbacdbbbddabdbcbbdddcabdabdaadcbabccbbdbccaababdbaababaabdbaacdacdadbdbcddddacbdbccacbbadadabcdaddbcaaddbcccaadaaddcacbbabbaadbbdcdabcdcdababaacbcacccccbdcbbaadbcaccddcadddaddbdddcaccabddacbbdaaababdcdcbcbddaccbbcacacabbbdcbccbbcbbabcddcbdabcbdadbaabadbacdcbcbaabbbbdccbbbaabbdaaabbadccbacddbbddcdadbccccbbdbadaadcadbbacadddcdacbcdadcaaaacbaabbcbdddaacabaabbbacbcdacddadbddbdcccdddaaddbdccabaaadbaabaadcbadcccdbbccbbdbabacbbbdadccacbacddcaaaccbacacdbcbdbcabdccbacdcdadccdbcacadbbbcccdaddbacccaddddabbbdbdaddccdccdcbcbdaababcbddadabcacccbaadcadccadcdbdadccacbccadbbacadccbccadcbcbdcbaabcbbcbbaaababcdbaadbdbdacdabaadbbaccacbababcacbdaaaacbdbadbcdcccaabcbbdaddadabdabaabacadadabaadaabbcacbcbbdcddbcabadaadbacccaacbbabadbddcbccbcbbababbbddcaccdcdddbcbbdcadbbbdcadacdcaadacabaabcddcccdadaabaddaacaddacdaaddcacaacbdadcacbabacadbadbbcdcaacabbdcbccadcacccadadbcbabdadcdcacacabaccdcdddcbbcdcdabdcadabcddbcabdadadcbbabcadddbdababdbbbacabcabaacdadcccbbbbacadddcddbabcacbcccbaaaddaddcdbbcbdaccbcddabcabcbdabdbcdaaabbbddbbcaadbddadacadbddbcdcbadbdacacaabbbcddcccbbdcccacbbadbdcabaacbbdcadacacbcbcdcbccdbacaaddacbcaacccccabccdbdccbbcddacacdacbbccbdacabaaaaabcabcadbcbcbdadcdcbcaaddbbbcbacbdaaabcaccacbadbadaadccabbddcaadacdcbdcbbbccbbaaccbcaacbdadddbcdaadcbbddabdaddcdabadabddadbdcaacbaabdddcdbcdbcdcadbcddbcadabbbcbcdacccbddaacbcbcbdabcbcbaddbbaddcdaadcabccdcbbbcbbcbbdccbbccbddabbdbdbbaaacadcbcbaacbdbbadadbbcabdcddbbdbadcadaddcccdcaddbacbbadbdbcaadaadadcdabadaaadbcadbbbdccdcbddabdaaacbbdddcadabacaaabcbabbdbbdcbcbbdabcdcbaabbbbacacaabbdaadccaaaabdcbdcaddbbcbadbbcbdddabdddbaadadcdbabacababbdabdbccaacbbcbdbdadbbaccbaaddaacbcddcdbacdcbadacdabaddabcdcbcadbcdddbbdacbcadbbbacdcbcdbabbcaadbaacddadbbcdbdaabdddacbdbdaddaacbadadcadbdddaddacdccccaabbdbbcadbbdbbdbdbadabdabdababaaddadcaddccadabcbbaabbbdbbbdabddadbadcabdbaaccabacbbaccbdcdcbadadbcacbababddaaddcdbaabbcdcddbcddddbdddddadadbbdacbdabdcbdacbdacabbdcddcbcddabaabcccaccbaccbcccdcbcbcbcdcdbbaccbdcdcbacadaddcbbadcbacdbdcbcdbabacaacbaaaabbcadbbbabcadbacaadcaabbcabdcaabccbbaccdacdbddccdacbbbdaadccbacbcacdddadbdbcadacdbbaacaaaccabdadbbcbcbdcbacbdadababdbadcbcacbabaccbaddbabbcdadadcbdaddbdbddaadcdaabacdddcdbaabaadadbaddddcbdddacdcaaddaaaaadadcddacbdacdbabdbbbdbcddcbacdaaaadabbbabdddbababbaadbbcdbcacadcbbaddcbdaaddddbcdcaaaccaadcaddbdadbbcdbbcdaddcadaadbccadddabcacaaaccbdbbdabbdddcdcccccbabbcddccdcabdacabbbcabdadddbbbcbbdcbadbbcacdbddbbdcccbcddbbaaacaadcadbbcbdcccbabddbbaaacccbcabbbabadbdcacbbbdabccdaccbcbdbbcdcbbdacddabadcacabacacabbcdbdbacdadcdbdbbbadbbabccbcdccaadabacacbbbcbadbbddcbcdacccacadababcbbcbaadcdbbbbdcbcdadadcaacbbdaacddbbbacbcbcdbabaaaaaacdacdcaabacabccccdacddbdbddaddadcadacacbddbaadaacbcbcaaaaacaabadaacddccababdccdaacaccadbbbacdbcaaacbdcbbbbcacaaadbcdcdbcddbbdaccbcccadcdbbbdbddcacbcddbcdbdaacdcadcbcbcbbcbcbbbcaddcacbcdacacbbcdcbaaccababaabbaacddbcccddbcccdababbadaddaabddbbadccacbccaadabdaadbabaccbdbaaababbacbbdcdbdbdccaaaacaaabbbdbddcccbddbbddabaddacdddaacbbadccdbaabbaadbccabbbabcdbacabbcabddaddbcbcbbdacdcadabcadcbbdbdadbadddbadaacacbbacdbdababcdadbcddaabdcadcbbaacbddbacdbbcadddddaaacddbadbbbbbdabbcbdbbccccabbcbcabbadacccdbbbdacbbabcddacddcabaccaaccddcadbaddcacdbdcdbadacccbaabcbbadcadcdbaacdadadcdbdaccadcbacaaaabcbaaadddcbdabdaabbcadbaddbdddadaaccdcdcabcbbddcacdcbdbcbabdcbbbbcdbdbadbadbadacdaadacdcbdacacbbaacabdccdbadadbcbadadddbbbcbdaaccdadcbdddcbbdacabddcdaddbddcadcaddaaadacccdbcdbacbcacbcabcdacccbbdcacabdcdabaaabcdaaccdadacdccdbccbacaddcadbdbbbcccddbdbdbcbaadbadabaadcddcaaacaddbccdcacabacbbbbabbccccbadbadcccabbaabadbabddcbbdcddbaadbdabdccabbaadabdbbdcbbccdadbbbccdbcdcdddadbaaacadabcbdbacabcbccbcbddbccdacdbbadcaacbdcccbbccdccdabadacbabbcadddaaabccccacbadbcacddabadabcccadddbcdcccdadacddbdddabdbabcacadbddccdabbccbdacacbadcbbbdddcbcbbcaacadbcabdbcacbadddbdbdbadabdbcdbdbbbbaadbbdaaddcadaaccbdcadacddcadcdbdbccaddadbcaabadbdbaadaccacacdbabdbcbccacccbdbdbdbbabdadacdcddbbbdddccadcabccddcbaadadbbadaadaacabbcacddbdbccdbcdbadaadbccccdbdadaaaddcddbcbadacbaadabbdcdaaabacdbbdabadcabbabbcbbccdabddddadabdccdbbadbdaabdbdaddbbcbabcabbdbdbacaabadbcdbccaaadccbdbdaaddaacbabbbadadabdcaccabdddcccdacbdcbbcaaaaccbccabbcdcdddcbccdadcbdadbbbcbacbdbdabaddccdaddccccdcddacbcdaddbdcbbadddbadcdabdacdccadacabacbddaabbaaacdbcbacdddaadacdbdabdbddbbbcaddbacbadbdabcaddcbdddabdcacadbdcddadadadcddcddcbcbbbcbadaadaddbddacbccdaadaccdaadacbadcaccadddbadaccddcaccbbdabdcdcadbbabcabdcaadbbcbcaabcacaaadbdabcaddadddddcacdddcbccdddcbaabaddbbbdcdadabacadbccccdbccbabbcdcbbdadbaccbbcaddddddcbcbbcdaccaddbaacabccddcddbbabacdbdddddabccdaaabdbdbcbcdcbbdadabaadcaddbccbaaaacadddbdbaadddabbcbdaabdaddcacbdddadcbcadbbaaacbbbcddcadbbcababdddabdbcdbaaacdddccaabcddbcacbbabdaabdddccbbbdbbadabcbaddbadabcccbccddbcbabbcdcddccccdaddcbabcdcadbabdccaccdbacbbcbaccadbaabcaddcacababaadddbbbcadcbccaadbdabaabadacaacaaccabcbbbaddcbdcbadbcbadcaaddccbbcbbcbacdbaddacdcbcddacdaccdabcdbaabcbaadcaacdacddccabdbaacbabdaadbcccacdbcbbbdacaddbdccabbdcacbbdcadcddcdccdacbabcbcacccdacddaacdabbccaccaabdbabcdbdbdbabaabdacdcdcacabbddabddbdcbadddcaabbbcbdbdbdcbabbccaddccbcdadcacadbdccbadbabdbdbcaaacbaadacacabaccdbbbabccbbbbccadcabbcdaabddbcdbcbdddaccabddbdddcbdbdcaadcbbacbdddabadbdbaabdcacabdcbdabdabddcdabcccddcacbddcbccbcdcddbbdbbdbcdbaccbdbacaddaabcbbdcdadaadaaccdbaddbbcdacdaaddaaabdabcdabcaadaabccccacbabaaadaadcabcdccadcbdccbdcabbdadabacddcbbdbcbdacacbdcddabacaaaadbbbdaadbdacdccccdcbdcbaadbabaabadbbadaacbbcacddadbbbacacbbccadadbcccdabbbbcbcbdcccbcaadbcabdddaabcccbabdbcaabcaddcaaadcdacdabdbcdccabbdbcdddaadcdaabdbbadaddaabadcadabcbacdbacddcabdbdaaccbbbdcbbcbdbbdcabacbdabbbabbabbabbacaadcaacbbddbccdcaabcdbcbadbabaaaabcdddacdcddccbdccbbcacdbbaddaaacbcaddcbadddddbcccddcadacbbdcaacabadaddddbbdbdcabdbbdddabaabcadbabdbababdaabdaaccbbcadbddcadcbbbabbcbcbbbdbbcacaaaabbcdbabaccbcbddabccdadcbccaddcaabbccdabccdabbdddcdcacccaadcacbaaddbacaddbbadbddcadaddbdcadcbbabbdadcadaacacbddbabbdbdbaacabdaabbcaaaaacbdaaaddddcabbbacccdbbacbdaacbdbcbccabdadbdbbccadabaccbdbbadbdcbddbbabbabbdcdccadccacabdcccabcabdbaddabdacdbbdbdacbdbdbdbddcccddacbbbabdadbddcadcaddbbadcbacaccabbbcbabbdbddddccbcddadbacacdccccaddccacbcdbbbaacacaadcadabacddaabbabcdcbcccddbbacbcbccdbbbcdcabacbadcabdcbdbdaadcccbdccbbcbaadbbcbdcddabbadbdbdabaabdbabdcdbacbaddbacadcccbbcacababadbabbddacbbdacabbbdcdcaabbbacbdbcccbbddbacadaccbaddcadaaccbacbbabccddaadaddabccabbdddccbdcccdbddbcbdddaaaadaaccbbbbdaadbdcdadadabdbbbdbabbbdbcabdacaaadcbdbdcabbdaccccddadbbaaaabcdacbbcdbadbadacaabdacdcaabacaccdacacdcbdaadbcdcaacbcdcaaabbdbcaaacdccaabcabadbddaabbcbbdbadbdbcbbbbdacdbbbabacdacbdacbadddadccddadbddcbdacdcdcbdaaddcdcbdbccabdbaaacaddacccccadaccacabaddbbcbcdacccbccbdaadccbbadcbbbaacbcddaaaccccadcdadaddacbadccdbbccdacccbabccbadbddbbdbacaababdbdddcdacabdabbbcbacdcdcabcbabbbccbabbdbacaaabdaddbdcdacccdcddcdcaadcdbcdaddcdcbdbdaadacadcababbcbdadbdccbcdbcbadcbdacacacbaccdadaaccbdbdbbdbdbbabadbcccbacabbccacabcabdcdaaadcccdacadcacbbadadbdabbddcbddcaaadbbcadbcaccbdaaadcadaddcbabbbaddcbdbcadbddbcdcbcccbbabbabdaddcddcaabdccccacddcadaadadccaadbccadcbdbdabbcccccdcbcabbdcdadadacadbdadbcbaababdbaaaaddddddacccdcdcacbdbadcabadbcabcddddbdcbcacaabbbcbcaadadbcabcbbcbbccbccbabbadaaaddcdadadccbdbcbdadcadbdabccccdacbccdabcbbcdbdcccccdcbdaadabbdabdcaabaacbdbbdcadccccdcaddcbccbbadabbcdcacaadccbdddcbbcbaabbbdaccdbbdbabbacbbaaacbcbdccdaccccbcabaaaddbabcddbddddccabacacbbcaaadcccadcbdcdbddddccbaababcbbddcbcdcaccdccccdaddaaddcbbcacddadacdabcbbadabadacaddcbdbbacccadabbcbdccbaaacccbdddccdcbcbcabdccbbacbdcbcddcbdcaacdbacdcabddaaddbcabdadbbddbdbcdcabddacdbbcabbbbbbbdaaccabddbdcbbcaccbabcacaddbbbacacddbcccabcbaabbbbcacbddaaabccaccdbccaccccdbdabccdaadacadabacdadaccbcdcbbcaabccbbddabaadbdbccdbbcdcadbccbcddacdddaadcbcbcacbcadaaacbddabacaacccbbdaacbbabbadbbbbabaaaabcbccabacddacddddaabaacdaccaccbbabdacbcbbcaaacbccbccaacbdadddcbbdbacacccbbaaabcddbadbcbacdcbadddaacbddcbacbdcdcaaabcbaadbbcdbdadaccabaadadbadaabcadcbdaddddbbbccadcaaaabcadcaccdbaddbcdcddddbabadaadcabdbddcdacdbaddcbbabbdbbccccacbbdcdbcaabdcaddddcadabbdcaadcdaacadbdbbbcddccabaacddddbaadbdacabdbabdbcaabbddbcaaacaaadbdddcdcdacbdbbbcbbaabbcdabbdbcabcbadbacccbbbbdcbbaadbbcdbadcccadcdbbcadcbbdbacccabcdacddaabbdbcbabcababcdacacbdadcbcaaacbcbbaadbddcaddbaaabddcbcdbcddcaddccadcdbabbaabdbacbacdcdaccccadaccbdacaabcadbacbcaddbbdcbbbabdbacdabccadccadaacdccbbabdccdaaaadcabcadaaababddbbdccccabaacddbaabadcaddadadccacbddbdcbdbabcddbcbabcadbaaabacbaaccaaadddaacacacabacdbcabbdddbcdcaaabbcacaabccaabbdaccbabaabbbddcbbabcdddcbcaabddcbdcdbbadcdbccaddbddadbbabdbcacbdddbbcbaccbbbcddaaadbddccacbabaadccbaadaaaacbabbdcbbccccbadbdbbdaacaddccabdccadcadabbbbdbcbbdbadcbadabbdabbdccccdbacbababccbbabccdacbbadadbadbddaadabbcbbccbacadacaddaaaccbaadcabadbbdccddbcbababcbcadbdcbcdacbbdadaaacadbddccbddbabcbdbddadaacadbaaaabadbcabacccadbcbacadddbacddcbccbcdccddbacbdddaaacbcaaadcbdcbbdbdcaabcbcccdaabbccdcbaacaddbbcdbbbdcbcdbcbdacadaadcacadabddbbaacaaacdbacdccdbcdcdacbbaddcbcadbcdaadbbdcaaccdaaddcdacccaddcdaddcadaacadabaabbadababcbbbbbcabdcbcdbdccdabdcbdbbdbacaccdbbadbbdcbaaabbaadacbabadcacdcbbaadcdbbacadcccacdbacbcdaadcbccbaaabdbbaaabbccabbcdabddaadbdcbacccaaaaacabaccddaddaadabddbabacddadabaacbadbddbdcacbddcaddabcbacbaaabddcbbdbcadacacaababdabadbcbbdbbabdcbcdadbcbbadccacaadaabacbcdbabcbccdcccdacdddbcacbcdaacabdcbacbabdadbabcccddbadcdccbccbdaabacbadcdabccdddccbbaddcabcbacaabbadddbacdccbdadadaccdaaccccddaabbcababdabccccaaaddbabaabbbbdbcbdcbbdcabdccdbddaababdbbbccadbdadacdaaabcabdadacdaacccbaddbdddbccaddbdacbcaacdaacbabcccdacadcccdccbdbbcbaaaacdcdaddacacadacabbabaacabbbddddaddacadcbdabdcabddcddcadcadaccdadccbbdabbddadbadbcbabacbcacacbaaccadaccdbabbcadaddbabcbcababdbadbddbbdaccaabddcabacdcaacabdccacdbcbbdbbddcaabadcababdcdcdbbaacaadbddbacddcaabccbbacccdbabcbcaabbcdbcabdddbdaaaddddcddadbacacbdbdddacabaddccbbbbabbdcadddbadbdccbdbbbcdbabcaadcdcdbbdaacaaaaaccbccdadbcaacadbddbdcbdcadabadbcbaccdbbddbbccbdbabababacacadacdbabdccbacaadacbaddcadacdbbcabdbdbdacbdbdccbddaabaddcdbcadbbccbaccaaaccdcdccbbcbabdaadbbabbdabbcaddbdacccbccbcbababcabbdcbbabaccacdacadbdccabdaaddbcdaacadadcbabbddccbbccdabbabbadbbaadccbcddadcbabbcdaccdcbcccbdddccccbdddbdbddcabaacabababcdbcaabacbcbbaadaccdacbadbadcdcccaaabddadadbaaadcbabcbbddcabccbdddddbccdbaacbcbdcdaacacbdacdddadabaadabbadacbbabaaaaacbbcdabdadbddaccacabcddabacdccadadcabdddbbdabdaddccbacbbadcbdddadccdbdcdcdccbacdccbabaddbdadbabadccadbccdddaadbcdbccaaccccabdabaaababcdacccdacdaccbaadbddaabbccddcbcdacbbdcdcadcacacccbdabacbbdaabbaaadaaacbcbacadabcabcccbcbdcbadaadaaaccbbcabcadadccddbcabdcdccacccbbdcbacdabcccadabbabcccbaaddaccddacacbcadccbaaddadddccbdccaabaddaacdbbadabaabcabddcdbbbbaddddcdbdabaacadddcbdbacbabbcaddcbacaacbdabccbabadbcdabcaadcadbdcccddcbdabdddadbaacbbbbddabddaaabcdadaaddabccbabbacbbaaabaababaadbcdbabbcbaaabdbdcdadbdcacbdacdbdccacabdcbcacdbbdddadddcadcdcadbbdcbbcddccdcdbdbdbcbddccadccdadaccbbdabadadcaddddcbabdcccadcaabcdaacbbdbdcaadbdaabcdacdadadabdaccacaadbdcdaadbcddbcbbaaabbaadabdabdbaacdcdabbddbdbaabdbaaababcdabaabdccbadbddaccaaddcddaccdbdadbcaaddaabcabaadababdbaddbaadacbbaddcbacbbaaaaddbcacaddaabbddcacbbbaaddddacbcbdabdccdabbcaabbddbbccacddcaccaadccbaaddcaaddbdcbabacdcccdadabbcccdbdbbdabccbbdaacbacbadcaabddabccabacbdbadacbbdbcbcdbcccbdddddbdcdbcaddacccdacbccdddbcccdbdbdaacacbbacadadcbddbaadcbdacaabcadbdabcbccbbcbddcdabdbbbbbadadcbdcdcadaaccbdaacdccaddcdcbcbaccaccbbbddaabbcaaaaaababdbcacbdacbabddcaacbcacadacbcacaabaabbdddbdcaddabcbadddbbdacabddbacacccadbbacbaabdcadcbdacabbdaccdcdddcacabdbbdcdcddcadcbaadcdcacbadacaadacddacbbaacbddbccabacddbcccadbcabbdaaabdccbdbacbbcbbccdcaabbaccacbddabcbdcbadcbcaabaabaacdbaccaadbbdcbaacbddddadacbbbcbadabcbbabcbddbadcdadddcbddbbdbaacccccbadababcadadadbdabcadabddbdcdddaccddbcddaaddcacbdbaabbcaaadcdddcadbdbcbbdbaaaadbdadbcddcddadaccdccbaabaacbbcdbadbdaabdacadbadbbdbcddacdadbaabbbaddddcbcadbbbcadadbdddbdcdbcddcdbacddacdabccdbaacadaadaabdacadccbdccdabbcdbabbcaccbbdbcaadcccddddbbdbbcdcccbabaabbdbcbbbcdbbdaddcdbdcbabcdbcdcdbcbccabdccdcabccbacbbdccbbcaccdcbcbadbaacabaabdadcdbbcabbdabccbbccdbdccdbacaaddadabbbdabdabccccabaabdbacdbdcccabcddcdddcdccbaaadabbcddbacccbcabacbbdbdbabccabcbdbbadacdbdbbbdabdbbbacbacccadcacdcadacbdabddaabdbddcbdbbcdbcddbaabacddacbbbbcbbccbbacbbacacbccababaaaccdccaaccdbdbdcccccdbbbacaccadbcddaabcbacdcdcbbcdddacacddbadbacbcbdcabdcddccbcdabcacaddcadbaaabbddcdbccbdcbcbdbaccadddccccdbaabcacbcddacbdcdbbdabbadbbaccadcdbcaacabaadabcbccaacbdcdbaadbacabadbcadcbdccdccbbddbbabadbaccbccaccaaadabaacbaacdcddccadcdbdcddbbabadaadcabcadacacdabbdcddbbbabcdacdabcabadbdbadaacdacadabdccdddbcdbadbabcadcbcdabbdaaadddccbdbabdcbabbdbbbccddaaaaabbcbdbcadabdbdbaaaddbcabadacabddcdbbacdcbdcadaddaabcccaddbbccddabcbaadcbadabdbcaacbdcbaaabbbbccdddbadaddadbcdbdcddabbaddddccdaabdcacabcabaddbadcadbbdcaddabbcaccdddbbcccadaabcdbbadddbbddcdadddcaadcbbcdcaaabcaaccabcaadacacacacbbadadbdddaddbbdaddcccaccbcbccbdccccadcccaaddbcacaabccbadcdcccbcbbcdbadacdababcdbbaccbadaadcbdabacbaacdcbbbbccddbcaabacddddbcaadcbbdaccdcadacdbbdbbcdbdaddbabbcbbacacbbcccdbcbdddddbccdcbdbddbccacbaabbbbabbcdbdaaababcdbcccbabbccabcbabcddadadaacbbdcbcdacccdcdbdaadcbcbdcbaddcdcdbbdcdbdbbdbdaabbcddbddcbbcbccabbaaabbbbdbbdabccddabcdbbdbddccddbddabcacdddacaabbdbcabdddabadabbbcbaccbabaaaacaddaaddcccdbccabcdccdbdacbdcdabbbaddcaabaccbbddccaddcdaaccacabbbbdbabdbadbcadababbccabbaaaababcbdbacaccdaacaabbcaadcddbacbcacdbbdcccdcaaaddbbbcbcddbdbacbcddbabcaddcccbbddccaadcaacbcbbdaaadacdbddaadabcabdbbabccbacacaaaadcccbacbbdacdbcbaadbbdbbacabdddaadcbbbcdbcbbbccaadccbbdcbaddbcdbaabadaadadcddbabddbadcbaabcbdcabdbcccacbdabcaacbdbcababcabdddcdaddbbacabacdbbbacdddccacdabbbdbbdcbdcbcacdbaaccddbabdbdbcbcadabdaddaacaadcabaacabbbbbdcdbdccdddaccabdadbcbcacbcbcadcacdabaabaaddbdaaaacbdbdacbaacababdadbbddaabbbcabcddbbddaabddacbadccbcbacbacdadbcabbcccccdabdcadbacbadbcbbdabcabbadbcadadbcdbdaaaccbabbbabbcbdaadaabcbabbdcccbcddabddcdbdcbdcaddbcdcabdccbcbbccbcbbcdddbccbdbbccacadabdaacddadacbdadcdacbcbaadaaadabdddbdbbacacdbdccbaaadccbcdbdbcbddbbaaccbdcbbaacddadccdddcabcbbbbccadaccccddbdaaaaacbbcbdabcddccdbccadddcbbcccdccbdabcbcbbabcaababbbddbabcbbcaabdbdaacdbacdacbcbacacddabbaaccdddabacaadcdccbbbbadcdbdbdbbabdcbdabbdcaacdbdcccdbbddccbaddadcccadacdcddbacaccaaaccbcabdccdddcadccdabbdcaabcdddcbacccbabddaddddbadadaccaaacbddbccccdabbcadabaaaacccdcccbdcccacccbccaddccabacccabdbdbdddabcadcdcaddacaaaccdccddcdabdbbabbccbaacabbdaacaacacbdacacabaaabcbddbbbabcadababdadcbacbbabbbcbbbcbccdcddcbadabbadcdaadddcdbbdddcdccdcdcacbdadccbbcddbadbadcabaaaccddbacacdcdcaabadbabbcdbdcddcbcadbdcabbacbaddbdcddababcbbdabbbcdaabdabbdcaabadcacdcbcdddabbbddaccbddcbcbacaaacdadabdbbcbdaccabbdddbddccdadbaadcadddbacbbbbcdbbabaadbcaadcabbabdabacddccdcccbaacbbccdbcbdbacbadbdcdacaadaabbbddcdbacacdaaddbccbacbdacbcabbcabbdcbdbdaacaabbbaabbabcaccbadadacadcdddbbdababbcbbdaddabdadccdbdddabcbddcadabcccadadadbcbbcdbaabbbdddcbcbbbcadbddaacbdccccacaabdccaddacdbaacccccbddbbacddacaaaabaabaccacccaacbcababddcbcdadbcacbcccdbcbaaadadaabaadadbbacadacbcbccddbdacdcadbabddaacdaaaadcbcaabbcbabcdbddcadccbdaabaaaccadbbcbacbacdadbaadadacdacbdbcadbcdcbabaddcdcdaabdacadaabdadbbacbcbcababaaabdcdabddbaababcbdacbacccabdbbdaaacccbbcadcbcbccadcdaaabbcacbccdcccbbacaddcbcbddcbbbbbcdabbcbcdbbabbbcbbabacacabdbaddcbadacbdbddcbcacadccacabbddbaabaddddacacdddbacbaccbacabaccadacbddccccaacaabbacbccaaacdabbbabddbaaabadaddbccbdcbdaacbdaaaaaaacacaadcbacadbbbdcbcccbbddacdcbcacacbbacabbccacadcccabaabcccbabaaaaccdbbbaddcbcbabdcdbdbdbddbcbacacbdcababadadaacdccacaccaadbcdbdadadbabdddacbcaadcadcabcbdbbcbacdaabcabbccaacaccdadbdcbbacbdbadcbcdabddcdabbcdbdcbbcbcccaabdbdaddadbddbacbdddabaaadcacbacdacadcabcdbbabbbccbdbcacabaaddddcaabcbdbcbbdabcadbcdbdcadaaaccbcdddbbaabdccccacdcabdaaaacbdcbdbbababdcaabcdbadcdcabcaaacddbaccccdabadabdcaccbcacbabdbbcdbdabababccadbcbcaccdababaadabbcadbcccbbdbcdbdcdbacddaddaaadacdbacbaabacdadccadcadabbdacbabbbbabdbdbaabaddbcdbcabdcccdcbadadabbdacbdcdbdbddabbdddaccbabcccaccddabdaccccabdcbaabbcabaacbbbcbcadcdcacccbdcdbcdbcacbaaccadadbcdacbbabaadaaaabdbddabddabaaaacacdcacbbcdaaaccbcabbdadaaccabccbaacdcbdbbcbdcdddccadddddbddccdcdcbcccdccbabbdcdbbdacbcbdbbaccacacaddcabaabdddbcdbabcbcacbcaaadccdcbbbacabcddcbbcbcdbabdabdcdddcacbcaddbdcadaaddbbbcdccccaccccabaabcdccabbbbdccdbbdcdcbcdaabbcddbdacdacaacccabcccdbdacaaacdbbbabbccdadbabadbcaccccacaabacadcccdbddcbdadcbacdabccddacaddcbabcdacacbbacddddcddaccccdadcdddadccbcabbbbabbaadbbddddbbbccaacdbdbbabacaabdbdabcccbbcbdacbbcadbccddbcbdbdaacadcccdddcdadacbadbdcdcbdcbdbdbadccbaacdbadbaaacabddccacbddcabddbcdbabbddaabdaddaccadaaadddbbbaabcdacbbacbdcccccabbcadcacccadadbcdbabcdcbcddddcaddcacddddadcbbbadccabacbdbbbdcdaabcccddcdbcbddddbbddbdaacdaabcbaaaccaabaccaababbdddbbbbbccdbddbacbcbccccbbbacabbddcbdbdacddbddddbacdabdbddbbaababbdcdbaababaabaddbdaadabcadddbacdcbcbddddaabcbccbdddbddbdacccaabacddcabccbadccaccbccbbcccbcadbacdcbaaaaddadbdbccbdadcdddabadcbcbbacbdbdbcadbacbacdacddddbacdbddabbaccacdcdbdacaccccbbcccbaacddaaaccacaddcaddbbccbccddbdbdacaccaabcdaabccdcccddcbacdddccadcddddadcccabcbcddcdbacacdcbcbaaabadddbbcabaaddbbcbddbcabcccadaddadbcbccacdbacccbbdbcbddbdcaaacacadbabbaccaacaccabddccdbdbabcdbcdcdadaabddddaabddacddbaddaabbabccbcbcdaaccdadaaacddbbacccccaaacdbdddbabbbdbadacbabdabdacbccdbcaddaccdcaccbbabdbabccaccdaccdcdcbabacbbccbbbaccadcbbbdadcabdadcdbdbbaccaabcbdacbbdbbdcabbcabbacdbbcadcadaabbcddabdbcbadcdbcddbacaabbbdbdacaadadbabcadddcdccbcbbbccbadcdcadcdddaaccdccdccadddbabaddccbadbbaacdaddbacadcabbbbbacdccabbdbcadbdbbcdacabcabcadcbaacbdadcbdababbacabbcadbacabbadcdacdabcbdddacdccbbdbcbccdbbabbbaadacbaaaacaabdbacdcccaadbacadccccabdccacbdcdddaddbdcdccbbbcacdddddbbcaaadccbdbbccdbddabddaaddaccbbabcdbbcbcdcddbdcacccdcdccadcdcaadaccaacccbaababbbcdcadbaccbbdcddcdcbcdadbcbbdaccccadbacbcadccbcdbcbaacbbbdabcaaddcabccbcdddbaaccaacdadacdacbacaadcbaccdddaacdacadcbdbbacabdbcabdacccbacbadaabbbbcabadcdcbdddddbcdccabcaaddacbadbcdcaabccddbdcacbbbacdbccdbacbcccabbabbabdcbabdaadaaaabaadbdadcdddcdbcabdcccbcabcbcbcbbaccdbcbdabcdcadbdbbadcdbadacbccdbaaadbbdddbccdaaccddbdcbaabadbabdadadabcbdaaabbbbccdacccabccccaddadabcacddabaabcdcdbadcbccccccababbdddcadbccabaadddbbbabddbdbbccdaadcdbccbcbcbdddcacaccbbbaccccbddbdbbddadbacabcbadbacbaaaacdaaccacddddacaccccbdcbdbadcabddbddbbcabdacadabaaabccacbadddbadabdbcdbdacabacbcbacddabacaaccdccdbaaadbcaacadbcacccddacdddabdddcdcdaccccdbaaddcdbbdbbbcccbbadabdbcccdbacdbabbcadccadbdcaaaaccdbacbbbdcdbbadbcaccdcbadddbcaaaacdcbdabdbccabcdbdcbcdaabdbdabddaaddabddacdccdacdacbcaddcdacdadccbadcaaacacadabbadccaddbbdbaacacdbbcbbaddabcccacccaaabccdacbccbabcacaadbdbacbdbcdcdbbdabcdabddbbdcbdbddbcaaaacdadabbcccbaaabdcbddadccdcdcbcaacbdcbcdacdcbbddbdcadbcacbbbddabdbccbdaaadbbbdddddddbaddcdddadcaaaaaabccdabbccaccdbadccddacccbcdabadcacabacdbcbaacaaaccabbdadbaccdcdbcbababbabbbdcdabccccccbccacbacccbbbcdbbbcdbaaaaacbcbabbddcaccadacbbdbbddcbcbbcacacbbacbcaacabbaadbcabcdabccbabdbddcdcbbbbccbdbbbdbabcdacacabbdadbbcadacdacabdbabdbdbaaaaccddaaddbcdadadbddcbdccbbbbdbdcbbbcaaabbdbbaccacbddadaacdccbacdcbabdabbbaaacdcbcadacbaacbbdbccbadaabbbcabcbccbbacadbdddddcadccaccdcacabbcadaadbdcddcdaacdcdabdaabccbbaddcadbdcbccccdbcadbcdabdbdadddbdccdabcdbcdcabbbccbdabccccdcbaaccdbcdccacacacbadbdabbacbbbbcbdabcacaadadcdaaddddaabdacbddbccabdaadcccbdbddbcbcdddaccadcdabbdbdbbddcdbbdadcaddbcaadbbaabdbbdcbdbabcbdcdbbbdcdcdbdbbaccdbadbbaddbbcdccdabababdcbabccccdaddcccccddbadaabaabccbcadaaccaaabaddacadaacccbdaaabdcbcabaacaccbbcabdcdbcdcbccddadadcccccdadcaddbcbccabcddbacaababddcdbdcbbbacccbdbadadbccbbbadcadabcccdbbbddaacdbadbaddccabccadddddaaddcdcdbacddadbcaadbaddacbdabdccacdddbaddccccccabbcdbcaaaacccacaacccacccdacbaddcdacddcdadcaddabccdccbdacdadacbdaabdbddabdabcdaccdbdcbbdadbbdbcbaddccaabccdbdddddcadaabdddaabdbbacbbbaacdabccaddbbaaaccbddbbcdadadacabcdcadcdbcdcbcaadcaabbdcdbadcddcddccdbbdcadacbccddbbcdaccbbcbdbccddbabaacbddbddaabddcccadbbdbdcadbdcdbaadbdacbabaadabdaadbadbbaddcadcbddccabdaabdccbdbadbadbccadcddbddadacaadaababcbcbbbcadacadcacabcadccaabdcdccabcccbacdacbdcbcdbcabdbcdbdcbdddbcaaaabaadbccbcddacaaaabcbdadbbcacdccbacccacddbbccdddddaaaddbbdcdabbdbbdcdcbacaabaacbdbbcabbccaddaccddacbacbdabbdbcddbcbdacbabdacacaabbdcbdaaaadaddcbbabaacdbcabbbaabdddcbbcbacdababcccbdccadbcdabcaaaddabbdcdadcdbdbdddaddbccddcbbcbbaccacadbdcdababbbcdcdcbcbcbcacbcbdacdabdadbcabbcaadcaaccddbcddaaccdcdacdcdadcaaaaabadbaccdddbbbbdbacabaababadccdaaacdcdacabbcdacbdddbbcdbbcabdccabacaacbdacdbadbbcddaddcccddbbccbcbbabdbcddbbbcdddccccaccbaababddbbdabdbcbcddadbcabacdcdaabbbbaaddaaacbcbcbbdbaaadbadbaabccdcaabbaaadddabcbdcbbadccbbdbcdccbcdbdbdacbbdbcdcabbbbcbabbccbaddbababbbdbdabcddbbdddcdbdbbcbdbdbdabccbbbddacababbcabccdbadabadacacbcdabcbbcbcbbcacbbccbaacaaaabaabcabcbabdababcbadcaccadaddbbcaaaaaadcaadacdadacdaabcdbdacbdaadbaddbaccadccbadccbdaaabacadcaacdcddaaadbcabaacabbabdbcaabbbdbacdcdbcdcbbcadbacddaccddbcdcdaaccbbaaddabbbbcccccbcbacacccaabdddbbcbdcbbcdbdaabaacadacbaccacbacaddbdcdbdaacbbbdbdddbbcccbcbacbdbbbbdacaaccdadbacbbdccbdadcabdabcaccaddbcadaaadbcabaacaacabcccbbddaaaadbcdadbcccdbcdaddddadccdcbcadadcdddabccbcadcdbabbbaccccbabcbabbcbbbcacddbdbbcdbaddcddaaabddbbdadaacacabbbadabdbdadbaccccdbbaccbdccadcdcadcccdddbbdbcbcabcdcbcbbcadcdabddbdacbcabdadabdaacadbaddbbccbddddbddbbaddcccdabdbaadabcadbaddcdadcbcddacbddbdbddddbcacbcaadadcbdcbabddaaadabddcddccadbaadbccddbccdabdabddcdadcaadcababddbcabdbcaacddcddacbcdaadabdbbadccbbdbadbccaaadcdcacaabbdccddacdcbdcdbaaadcacadaccaacdcdbabcbcaabcccacacdccdadccacaddadcbcabdabacccabbaddcbdbbbcbbcbdbababacddbbbbacbcdddbaadcccaddacadaabadbbdacdbbddbbdbcaddddcdcadcbbbcaadccadaadbdaccbbbccccbddacddadbacbbbabacbcbbcaadcdcbabadbdaddddbddabdcdadaaadcbadbacdacdabbdddbbdadaddaddbdccccbdbbbccdccdbcccbdbacdbbaacbbbdadddabacbbbabbcccacdcbaaabdddbacabbbbcbbdaadbdddaddacacacccabdadacadadaadcaaaadbadaccddbcadddbadcdbaabaddcaacaccddacdccbbacccacbbcbcadbcadcbabccadcdbbcaadabdabdbccbbcbdbcddccacddcddccbadaabbbbdddccacdbcdcabbcbccbaccddbbbbacbacadbdaddcbbdbbcccabbccddcabdbccddbabdaacbcaabddbddaacbcccabdddbbabcdadabbadbabbcadabbcdbadcaabcbbadddcbddcabdabbcdadbdbdbbadcbabadbbcadadaaaaccddbcdbdcaccdbbaadabbbcccdadcabbbadcadadbccacbddddccadcddaacbdabbbacdcddbcbabcacbdacacabadcddccdccdaddabaddbaadbbdcadcdbddcdcbdadbbacdacbbcbbdadbbbbcbabbccaabbcccabbacabbbcdcaaadccdbccccddcdcddaaacdacbcadaccbaaabbaadbccacbbaabbccbdadcdbbcaaaaaaacbcbbababdaacccadcbacadcabaabcbaadcdbabdbcabdccbbacdabaaaaabcaabddcbccbbbdacdccbcdcbdccddbabbbcbbbcbbbbbdacadcabaaabbbdaadbbbbdcccaadbbdaddbbcbcddbbabacbbddbbccccbadccdcabadbbabccbacdadcbaabbbbcadcabaacaccccdbbabdaccdbacccbddbabacacddacdccadbbaadbcbddbdaacbddbababddadadaadcddbdcccacaccdcbaaaaaaabbccaaaaacbbaaadccbbdcdbddbdabdaabadccdcbccbdccabbbbabddcabbacacadcbcdaacacabdacadbabacccdbdbabbbbdccdccccccccbabcccbbcbcdbbddacbdbccacaddaacbcbdcacaadbbbddbaaaaacbbcadacccbaabccbdddadaaadabaabcdbbaacaccddaadabdcbabcadacdbddadbaacbacbdacbcabdabaddaccbbbddccccaddcdbcbbbccdccadbbaabaaacbbdcddbcdddabdbadcabadbbdbccdabcdddadaabbbcbcbadcabcdcdaddbabadabbbabcbdbadccbdddbaabaacbaadbcdbadabbadbdaadaaadddbbaaccaccaabcabdbabdccdcbcdacdbdadabbdcaabdbdcdbcdbacddbdbbaadcacaccaaacaadcbadcaddcbbbdcdcabddbcccdcaccbcccdccacddbcdbaccbabbdcaddcacbaccbcbdccdadccdbcdbcbcdbdccabdadcaaacbcadadccacddcbbbcabccbaccbcaacbaabacbdbadcbdbadbabaccbbabaaacddadcbdcadaddaddcbbabcbdcddbccacaaaacbdaadbadaacbbcbbbcbcbacbcdadbabbbbccccccdcdacdaccacdbadddabbacbdbcbabbaabcbbbbdbbddacdcccaddaadccbdaadabbcccadbcdbbddccbddabbbbbdbdacabcbccaddbaadbdbabbacdadcbabacabadcdcccddbdddbddabbbaddbdbcdcbadabcdcadcbbacdaabcdabacbcaadadcaabbdbadaccdccaadcaabcdacdadbcbdbcbcbccaabadbbacbcddcddccaacbcdabdaaaacccdcacbaabbcccddaacadcbdbcdbadbadaaccddddbcaacdcccddbcacaddccbddbccadbbabacdcddbdcbddaaaaccabcdbcadabdcbcbaabbabdcdcbdcbddbacbccbabdbababadacbbcadcdadbdaadadbbdbbccbdccbbbadcbacbcaccaddacaacacacbabbdcaddacabbacaabadcccbbaadcdbdddccddddcbcdaadaccdbdbacaabddabaadbaaadbdbbbbddbddcaaaadccaccbabcaccbbbaacaabbcdbcadacdacbcacaaacaccbcdcaccadcdaaaabaaacaacacadaaaddabaccbdcddcbbbdcbcaadcbcdabbcadcbbbacabdcbacabdbbddcbcddcabcaddddccaaccaadbabdadddacaacabdcdcadcbbdbbdabaacbacbcaababcddccbbcabbcdccaddbcbddbbcbabbbaaddcbcbcabdddccdcdabcdcbdabaabcacddbcdbccccdbbcdddbbaaccaabbbbcddadbacccbdbdddbaacddbbadabbcbbdcabaaabaabdabbaaadadcbcbcbaabbddddcbdacbcbadccdabcaacbaabcbcacddbabaabcdcdbcabcdcbdcdbaddcabddbdbadccddcaccbdcdabdaabcdccdbdbaadbbdacbdcacbbacdbbcdaccdaacabacacaddccbabdddccaccddaddaddcabdcadababdadabacbddbcabaaacbacdbdbbbadabdbbcababcdccbbdabacbbbbddbaccccbcddddcdacacbcabadbaabdacbabcbdcaacccaacadaabadaabddccbdcbdbbccdaaccacabacbadaadabcbbbbaacabdadcabacdaaababdbbadbbbcdccbabbbdadcdcdcacadbabdbaccbdcaccadadcdbaabaddcacbbadadabbabbabccdcddabbccbbccbababbcadabbdddcbbaadcbbadaadcccaaaadbaadbbdbabacddbcadbcaccaacdbbdadbaacacadaaccbcccbadacbbdacacdcccccdbbabcbadddaddcabcadbaddcbaabcbcddcabddbcbbdbaabbabdbdbadbbdddbcbbbcdccdbabcabbdcdaccdccbccbdbcdcabdacadcdadcbacabcdcadaddbaabdabcaadbdccbdaddabbcabcccbbcccadcbacdbbabbcbadcddbdbbbbbcacaaddbbabddacdcbdbadadcbadddcdccbdcdaaaabbabdbaddbadbbcdbcbaccabacbdcccacaddcadabacdbcabccdacbdadbdcdbcbadbcddaabdcdbbcbcdcbbaadaccdcacaccddcbacabbdadcacbbcbbaccabbbaaddcaacdaacadbaddbdccdcabccdcdcccdcabdacbaacdcaacddaaabddbaadabccbbdabccccbaaadcbbbdbcdcdcadcddcabababbcadcbbcbcadbacbcdbcbadddbbddacaaccddcbcddbcdaaccabcbdbdacababdabccbacacbdaaaadacbdadccbbdcdacddbaaaabababbdaabcabbdadcbaccbbaadcccaacbcabaadbbcabddcdabaaadabdbbbbdcacdcacaacbddbbccddbccbaadcbcbacddbbccddaccbbadccccdadccdbcdccbcadbdaadcdaababcbacadcacbbbccaabccbdbdadbbccabcbdccaddcdccbaadbbdccbbdbbbcbbcadcaabcbbcaccacbaaaaacbabdbadacdbbacacadbadcaccbcccbcbddbdbaaababaaddddddbbbdbbcccdddbbacaabcdcaddaacdbaaaaacbbaacbccacbddccbbbddbbdccbcadbcbbaabddbccdcdbccdbcbcadacbddcbdbcadacbaccaaacdaaccddacbabcbdabbdbcddaccddbddbbcacbdbccddbbdbccaddaaaccbdbaaaccbabdbacbbdbbbbadbaccbbcadccaccaabddabccdaabdbbcbaacbddcdcaacaadddabcbaaabbaaabddbdddaabccdcbbadcbccdcbcaadbccaaccadbbcccccbbbbcbbcdabbacdcadcccbbaacdcbcbbdddbdcdcaccabdabaadcbaabbadacbbbaadbdddadccaccbcbacacdddcadddddbbdadcdcdabddadbbabdbadcaaabcadcdbcabcdcbcccccadaaacaadabadcabcccadadbdbaacddccdbccddcbabaaccacccaabccccabbacaaacdbabccadccacaababaddadcacccbddbddadbaaadcabbaaaddadabcccdddbababadacaaddaaabcdaaaabbccdcdbbccdcacabddddbdabadddacadddbcbadccacdaabbbcbacdbaccbbdbabddabbaaabddbbacbccacadcbbdbbbddbaccababbbcbccabadaadbaabcbaacdddacacdbdacdbbcdbdabdcdcaacdbbdacbadabaabcbcaccbdcbbbccdcbbdccadccbabbbbbbabcdcbcbdbcdcbbbabdbbdbcbcdaddacbbbbbacacbcabbcbaddbaacbdbacaadaddcdcdbaacdcbbdbcdcddacddbddddacccdcbdbcbcddddddaccabcbadcaaccacddabaaaacbbcddabacddcbccbbaaacabdadaaddbacabbadbabadaddaddbddddbacbdccbaacdbbaadbadcdbbbcbbbdabbbbbccdccddddacdbcaccabaabccbacbcaabacacabbaacaaaaccabdaddaaabbbbdccabdbcdcddbdaccadddcadacddbdbccdacdbbbaacdcdcdbabcabbdacccbdbcbdabbaccbbadcbabaddbadabdaddcdbcabaadbaaabbbbdcbdccddbbaddacddaabacabbbbbdaadbbbabdadcadaacdccdabcdcdadaadaabcdbbdbaddcdbcdbaddcaccddcaabddddddddbaabdcbabcbdbcaaddcaddbdcbddbdcccacaaabcacdcdbbabcbdacbcdaabbdbbbacdcdddbcdaadcaacbdaccbcccaabdbbaddbdddbcabccdcbbadddabacdccbdadddcbcadabaacdcbaacbdbdaaadbbcbcbadadaaabdabcbbdaabaacaaadcacddcbcdccddaddcdcdcdcadbacbdddaacacbdbdadccaaaddacaaabacdababbccdbbcbdabbabdaadcaaadcbabbcccacddadadddaddbdaacbcdcbcdbcbccddcddcabdbdbbdbaabbcdbbbcadccadaacccbbacaaddcaadabdaacacbcbadddabbdbaabdcbcdbacaabbadccadadccdcdccacbdbcdaccbaccdabbcccdbcbccdbcababbbbbcccacccbacdbcdaaabdabddbbccbabacbbcacbdddbcadcabbaaadcabcccacadcbbdccaabddbdccdaacdacbbddbadacabbdbdabadabddddcbcaccbdcacaadaacddadaccdcdcccabbccddcdbcbddcbadccdccdaddcdacaadcbddccadaddbdbadbacaadddcdcdababbbccadbcbdacbbcaabdbcbacbdddcbdabccbaadabadadcccaabdcaabaabdcaaaaaccacdabcbddccdbaabbcdbbcbcacacdbababdcbddddcdbcccbcabaccdaaabbbbbadaadabbcbdbcaadaacddaaaaacacbcddabbdbccdbccdaccccaadbcbcdaadbbacbdabdaaabcbdccaabdbcbdddadbdacbdbdbaddabadcbcbacdccdacabcdbbcdaccacabdacacbdbbcacdcbbcbccdcbaddbdaccddaadcdcbabdddbacdabdbacabcaaaacacacadddccccdabbccbcbcdabcdabcadddbbdabdbcadddddddbdbbbadbccbdbdbdddcaadcbdcdbabcaabbdddbcbccdccbbcabadbbacbaddbbaaccdadaabbccddadacbabbbdaacadaadadcddcdddbbdbdababddbcdbabdabbdcabbadbbcbddbdbbadbacbcdbddbabbcdbacabacdacdcadbbcacaddaaaacddbbdbdaabccbcbadbcabaadbdbddadcaadbddddadacccddddadadaacadcaabbcdbbbbaccbbddcbaadaccbaabddddbaaadacabcdcaaacccabccdabbbadcadcbbbccaabbbaaacbadbddadbbbcdacbdadccbbaddadbbdcdbbdbddcdaddacacdddaadccdaddabdbbbcbcabaaabccbcabbddbadbdbbddbccdcccbaadbaacbbbddcdacaddaadcbbacddabcbaabdddcbbaddccbdabdddbbaccddddbcbbcbdacdadababbbcbbbbbcbaabacbdddcadbadcccaaccacbbdcadbbbaaabcadccccbcdbcabdddcadbcabdabcbbdacbdcdcbbbddddbbcccccadddadcdbadbbccaaaadbccdabadabdabcdcaadddddaddaadcacdbccabdaadcadbcadbadbcbcdcbacdbbcacaddcbcdbdabdbcddcacdaacdbccabbaabdddaddddcbdbadbaccdbcbaaaccbddbcdadbabcacaddacbababaccdcccadadbdacacddbdbcccbabcdaddbcaccacbcbabccdbaccccddadbbccbdaccbbbaaabcaaaccbdddaccdcbadbcabacddcadabbdccadcabcadacdbbbabdacdbdbccababbccbadbbaadddbbbabbbcaacdbcdcccadaadcacdbabdcddcbbddcddcccaadaaddddaaddcabacddcbcaadddbdbcbacbabddaaadadcdaccdcbbccdaccdcacdcccaacabaddcdacadcbccaadababdadacdaccacbcbddacccbdbdacbddaacabbbcdaddcacacccddcbbcccadaabdabbbdacdbdadbdaccddcbcbcbbcadadacbdcbcbaadcabadbbacdccbcaddcbccdcaadaaddcadacdddcdacbaabadabcaaddaccbdcaddbbbbabdacaabdabbcaaddadaacbddadccbadddabdaadbacddcacabaacadcbbccbcbcbdcbddcdbddcdcbbcddbdbdddbdccbdbdcabcccbdaccbdccbaddcbdbbddbbbddacaddbcdbaddbcccaaaaababadccdcdabdbdcabbaaacdbadbcddbdadccdabbbbdcdabbddaaabddaccdacdcdaccddcddcbbacaabbdbaccabcaabccaddbadcaccbbababcdababcacabbdcdbaabdbcdcddadbcbccacaaacbdbcbcdcdbcabadaddacbcdbbaddadbddddbbcabdcbbadcccdcaaacbabdabdabbbcadddccacbdcbaaadbbcddcbbbadddbdcdabcabdddbddaabddccdacdbdacacabbaadcbadacbabdddbaaadadcdbcdddadabadcadbdacbbccdadcbbbcdbddbbcaaaabbcddbbbbcdbbdddbabbdbaaadbacdbbbcadbdcabdcdbcadbbdbcbdacbbdaaddbbcaababcadddadbaadddabdcbccadcdbdddccbaacdbacbcdddabbacaacddaabadbdacbccbdababddadccddadbcabacbcabadcdacacccbcdaddbbabccccabdaadbcababcdacddacdadadcbaabbbaabadbbbccdadcdabddcbadaabadbcdadcdcabdbabdadddbbbbbbbdbcdacdbddaabbbabcaadccdaacbdbabdabbdcbdadacbdccdacddcdbbddadcabbbcddaacddbddbcabbaadadacbcdbdcabcccbccadddddbabcdcbcdbbdbbcbdbdccddaadbccbcdadbcbaccbacbccaabaddbddabbdbabcacadcbdcaaccdcadbdddabdcacadcdaddbbdccbadadababbbbadaabbbaacbcdabddddacadcbabacadccbddddcbaadcabaccabcbcdacaaccbaabdccbabdcdcddadccacdcccdbdaaaddccbcddadcbabbaaddbbcaaddaabcadddbabdbadcacacdcadbdddaccdccbabdaccdcbcdbcdacdbdabadccacacbbbbcaaddbdacccbabcbccabacdcddabdadcbaadbccdcadbccbddccacdabddabbbbccdccddddbabbbcaacaadcdabdcbaccbdcddcdcabcbdaacdcbcabccbadcbddddabdadbcbcccabccbaaccbddbabbbadadadaaacacdaabccbcdaccddddbaaaaadadccadbbbbdcdcaaababcdaaccadbccbbdcdddbcdcaccacbbcabbacdadcaadbadcadbaabbddccadabdbbaacbddabdccbdccdbbcadbdbcacbdadadadaacbcabaddbaaadaddaccaabbdbcacdadcdaaacdabcdadadccbaaaacbbaacdabdcbcabddcddccabacaaccbdacbcbdbaabbccccbbbdbbccdaaaadbcbaabcadcaabbaadacdbbabadbcadbcbabcbddacabacbdacbdacbcddcddcabaaacbcccbbdbdaddddcbdccdbddddbbbbcdccdcbcaababacacaacdccddccbabaccbdccddcbccdbbbdbbbddbdadabcadbbbbcacddbcdaccbcdacddbbabdbaabaccccaccccdaabbacbabcadabcbbaaaadacaaadcdbbadbaacdaadcdaabdcddcdccbbdbbaddbdcdbcdddabddbadbddbdcbdbaaccbbbaadbadddabababbbcdddadabdcaadbadccdcbcbbdaccabccdadccbcaacbabbacdcddaacadbaadbadbdcaaaaaccbaccbdbcabccdcabbabdcadadbbbdcdacbbcdacaabdbddbcddbadbacccbdbaabcbcaccabcbbbdadacbadbcdcdaddbdcdddbaabdccbbbcbdadbccacadbaccccabbabdbbabcbbccdcbcbaadbccbacdccbaacdcaabacaabadaadccbcdaabdbddbccabcabcbaadcadaadadbaddbbacdcbcbddbabdddbbacbaacbbabacddbbaacabacdcbadcacaccdcccbaaaabbcbbccdddccdcacccdaddcdcdcaadabbdbdcdacccaabcdcbcddcdcdddbcdddcdccdcdbaccabababcdbccaabacbabddddbcbabaddcdbadcabbccbbdddbcddaaaabaadadadaabcbcadbabaabbbccbbddbacadbcbdbddaaadbdadddadbdbbaaabbccccbcdcdaccccddbdcadabacdcbbcbcdccacbbcdccacaaadddbcdbcbddbdabdcabaadcdcbdccbbdcbdcadbcaccadcaaacccaabcadcbdcbbcddcabaadacabaddcbdbdacdbacabccabcbabbcdcbdbbcdaccacababdddccbcdbcaccacaacabccdbcdbcdbadabbbaaadaaaaddccccddbabbbaaabadbbcbbbaddddbdbabbaddaddbbcdbbacacbaddbbdbbddcdadbaddacadccadccdabbcacbdcaababadbacaacdbbabdadbaaababadbddbbbabbadcdacbcadbbbddccdbdcbcccabdaabccacadcbdbabdaacabcdbcbaacabdbcbadbccaabcadabaadacadccbbcdabcbdbacaddaddbacdaacacbabdcccbccdcbbcbbcbaaaccabbaccdbbcbabacdacbdcabaaddaddcdddcddaccdbabdacdaaabaadaccdccacddabbccbccbcabaaaccccdbcdabadaccbdaabadbdbbbacccaccacbdcdddcacbbabdabdddcccccbdddddcdbbabaadddbddbabcdcccaaacbaabcbdbaabaccdacdcbbcbbdcdbadcddbacbdbbdaadbccccaaacdcbdcacbdbdbddacdadadadbbbcbaccbddcdbcbadddadbdabbcadcadaaaaabcdddbbcbacaacdbaccacbdcacddcabbccabccadaadcccdddcabbcdabadcabdbbadabbacbcdbdacbddcaacdbdbdabbcbdbccbdacaaaaacadddbaabbadcbabbcddaabbcbcddcbdbaabbccbcbbbbdddbabcaacbbddabaddabaacabdccbadaabbcaddbddddccddcacddcbbcddbbdbcdaadadbcbbacdaabcdbbccbaddbabdacaabcdbcdabcdcacbcbcdaadabaadbaadcccdbbdabccbbcacdcbdbadacadcccdcaddaddccbccacdababdbabbdcaaaaccaddadbcbabdcadaccaddcdcccbccbbbaaadbdbdbbbbdbacbcccbdcaacbaadbbadadaddbddcbacdccdcacbaadcbbccdddaaccdbcbcbdcaabcabbcbacddaddbbbddbbbbaabbbbaadadccdbddbbbdacacaddcabcaacccacbbcbcdaaccdbcadabbcbacaabbdbcdadbaabbdadcdbbcabbbbcaaddcadcadbbddbabdbbbddaaaddbbbdccabcaddcbabadcccbadccbbcdabdacdacdcbdbaaaaadbadcdaadbacabdcdacabacabcbdbadcadcbdbdbcdcdcabacdddbacdcbcdbcacdaabdbbcacbcccacacdaaabdadcccbbbabdcdcbdaddcbdcbdaaaaccaaacbcdaacddbaaabcbabdcddbaddaaaadbababaccabdbaacbcdbbacbcbccaacaabbcbbdbabdbdcbbbaccbcbbccdcddcddaacdbdaadcddbbcacccacddcccadabbcbbaddcbbbbbdcdbacbcdcadaaccbddaacaabddccadbddabaaddaddbcacccbccaabacadbcddcbddddbbcabbcdcbaacabbacbdadaddcbabaaaddcdabcdacabdcdbdadaacdaaaccabdacdacccdacbcaaacdbbcbacdcbabadbbbaaabbcabccabcbddcdcccdbabaacaddcdabbbdadddddcbababacdbabcbccbdccadcbdaabdbcabcdcdcddcccccdbcbacdcdbbbabbacdbacddcadbdaadacdbcdcbbbcccbdddddadbdbaadbdaaacbaccddacdacadddbcdbddbcdaaabaaaaadbcdddbbaadbddaddcbadaadbcccacbcccbcabcbdbaacbadaaabcdaccacbbbdcbcddcdbccccbdccdbacdddcdadbaabdbccdbcdbbcbdbdcbbdbbcabaddccaaadacbaadddbccdababddbbaccadddcbdcdbacacdbadadcadcdabdcacaabbcbbcddbdbbbbccabbacddaabcacbdcbcbdbbdbbaddccbdcadcbcdacbadcbdcccdacabdacdacacdabadacabdccdbadbdddcadacaddcccbbcdadaaabcadbadcacbacdaccbbbcddbcdcadccadbdcbdbcbcaccbbbdbdcccadcbbcaadcaadadbcadbcaacbdcdacdcaacddcccdbbcaababcbccaabacacbbbabcbabdbdabaddcbcbabaddbdcccccadcdacbbdddddaadcdbacbcdbaabdbcccdadacbadddccaccbdaaabbdbabacdadaacbabcaaddacdcdbccababcddbdccbccbdadabdbaddbdbdbdbbdbaaadadaddabbbdbbbcddadccdcddbbdcadbdaaaadbabdadbacccbdbdbaabcaccabdacbccaccddaccadbbcbcccabdbbcacdbcdaaaacbadabbcdcaabdaabcdbcaddddcbcbcbadbbdaadddccabdbbbcbdbbdcbdadcacdcddcadbaaadcadbccabdcaddadabcabcbdbbdbddbabdcdabaabdbdaabcbacaaddabdbdcabcacddaaaccadbacbabbcdcddddddacbbbcddbbbaabdaaabbcbdcdcbdddadccdbcdbbccdcadcbabbbadccbbdcaacbbcbddcadbdcdbbccccabacacdcccdcadcbdccbdacaccabddddbcbbcdbdcacbcabbdaddbddcacbaaaddcbcdabaaccddccacddcbadcadbcbcbccaabcdbaadbbaaaabdbbdadbacbccaaccdcababdbcccadccabadcaabacbdcacbccbcccaadbdabaadadccbaddacdabdbbaabbccbcaaaadcbadbacaddababcabacaccdcbcccddacaddddbcbdcdbbbacbadbcddacadbbdcdddccdccbabbcbdcbcbaaacdadcbabcdadaaccdaadadbaddbcbaccbadcdbabaccaabbbbaddcccdbaccdcabbaadccbadcabdcdcbdbbaddaaacdcbbcbadbddcaddcdaacdccdacacacdcdccccadabcadaddccdbbcabcdadbcdccdbdbdadcaaacccabcbdbaaabcbaaddcccadadddddcdccdbbbabddacbcdcddacddacddcbaabcdadabcdbcddbbabacacdcdddcdacbbcaccddabdabaacbbbabbcdadbcaabbacbbccbdabdbbcdcacbdacaabcdabaacdaadaccacabdadadbcadaccadbccddbbbabbdcccbcbbbbbaadabdbabbccbdccdadddaacddcdddccccaaacdbcabbccdbadadaaccdbbcbabdabdbdbdacdaccabbcdaabbdaaccdddccbbbcdbdbdbdcadbabcddaabbbccdcbaccdbbcbbabbdbacbbaddddaabdddadadcdabccaacdcbadddbcddadaabdcbabbabccdcabadbddadbbbaadbbccddbdbbcbcaaacbaababdcaacbdcccadbbbacbcccdcabcabbbbdbaababddddcbacbcaddcddccbadccdccabaccacddbbdcdbabccdbbdadadadaaccdbadbbaadbdbdcddbaabcdaaaaaccbdddaacbbbaabadcdbaacbbddcbcbcaddcbaabbbbccbcbccdabcdbddcbdadbddaadcbcbabdadcaaaaabdddaacdbacdacbbbadaacbcdbbccadadcdacaadaadbdcabbcaaccdbcdcdccbcbcbbaaaaddadaabcadbdaadadcacbcdbbddadcdbddddcaadaccacaaaabababaaccdbdcaddcdcdcbcbcbdccbaacbaadcbdaddbacbdbadcdcbaabdbdcbabcadcadbccadbcdcabbacccbcccdbdbdcbabdbcdddccaaccddcbbdaabbdbbbbcdaddcbdcbbddabababdccbccabdcdaabdbadadbccaaabcbbbbbdbbbdbabdaddaadbddbabddaddaadcbadcdbadaddcababdcdaccadbdddabaaddbacdadcdbcbdcadcaabdddaabdcacdcacccabddbdadadcbadddbdbadbdadadaacacabcdddbbcacaaabcbbacdbabcaabbcaaadbbcdcadacbcbccadabdaccdacdaadabaaddaaadccdcbacccdcaaabcaabaacbbccbaacccacdbcdbcbbbdcbdccddbccdccbdbcacbadcdcbaddcbdcdadbadbcdbadadbadaacbcadcdcbdcbcccdaadacdcadcdabcbabdcbcabccaccabbddbddcccbccccadbacbabdbcbbbbcdcdaaccacaadbbdccabbaacdbdbbcdcddcccbbadddcdbaacbcdbdaadcddacdabcdcdcdaccacaddcbabadcdbbcaccbaacaacaacbbcaccdadbacbbbacbbaccabbdccadaadacaadbbbdaaacccbcdacbaabdcdbadbbbadababbcdcabbccddbcdcacbabcaabddadccadcabdcacabbaaddccbcddcababcbddddcbacacabacdbadbddcacaadcccaccddcdccadccbacaacdbbabdcbdbadaaaaabaaabbbcacacdacaacacbdacbdbaadcabaaaabbadcacacaadccdcccaacacbbbbbcacacbdacdccabdbbadadddddcdcbaaabbcdbbaccaadaabcbcdbcdccaaadcdababacbbbaccbabcabcacddacadaaddbabdbababddbcaaadabcdddbcbbaddaddacddacbadcbabcdcdbbdddaccdbabbadcdadcbdabacddbaddbabaaadcabcddcccbbddbbbdacdbadadbbacdbcacccacadaccbcdcdaabcdbadcacbcccdcbabdacccadacadcacbadbaddcabbcbdbadbaddbbbadcacbdcdbdcaabdcbadbbdadcacaccaccccddcbcdaccddcbcdaabbaddddbbaabccdcaadadbcabaabaadbabccbaccddcbabacbdbdddbdcccababbbbbacdcaddaacbcdbdacaacbaacbacdabbcbacbaabcdaddcdcdaccacacdbacabcbcdbbaadaacdbdcbadbadbbdbdcbbdcbcbdcdddbdddcabaadcdbbaadabdaaabbbddcaabdbacababdcdaaccacabddbdddbbddbccaadacacacacbdddaaacbbdcbacbdddaadddabbdbdbbcdcdcaadbadabaaaadabdccabdcbbbdcadadcabbacaadbdbdacbddcdcbccbabcccdcabaccaccdbcdbdccbddcadccbdcccbcbbdccdcaacdbbddbadbccbcaaddbabdbaddcbcccdadabbdcdbcbabbcddbbdcddccaacdbbbdcdbbdddcdcaabbbcacccbcdccbdadbbdcdaabddcdadcbddadabdacdacdabbbadbdccbdbbdcdaacdddcccaabdddadbcadcdadccdcdbdaabddabbbdcddbadaaaadbdacbbccdbddbaadaddaaabdcdddbcaaabdabdbadccdcbbadbbaddcbbbccdcadbdaadaaadcacccaaabdcadcbbbccaccdbdcabccacbbbbbcdbbccaaacadddadcbbdadbcbbbbcaadabacabaaabdbacbbdbabbacacbadcdbadcaaddcbcbadcbdbcabdccbdbdacbbddbabccadbbdcbcbccdbcddbddcdaabcaacbccddbccdcabaddbcccadbcadbddcddbdddcabcdcddaaaccdbacccaaccbbbabcabbadcdbabcbbbbdabdccbbbbbbbbcdcacadddbadcacddaabdcaddcdacbdbacdacbbccdddbcabbcacbaccdcdcabdbacddababdccdcccdadbbdacbbdabbcacccbcbababddcbbddabaccdcabdbadaadbdcbbbaadccddadbaaacbbbdabcadccbcdcccbdacdaacabcdacadaaccacdbbcdbccdacdbdbdacacbcbbdbbcbacbccccabbabddaaccbcccdddbabcbdccdaaabcdccdcbbbccccdddacbdadcbdcdacadbbaddbaabccdcaaddacdcabcabcccdcadcdddcaddbdaddccabccadadadacddcdabdadbbdaaadcbbcbbbbbdcadadccdbaccccdddadbbdcbcdbcabaaacbadbddbdcddcdbacbdbdcdbcbaccabcaddaabbacbdcabbddadbddcdcacacdabbacdbdcabdbdcacdddcdacadacaaaacbdcadcdcbdcbabadddacbbdbdabdcdcdcadacdcdaccdbccabcabaacdcbcdacdbdcbdabddadbaadbdbcbbdabbaccdddbbcdbdcacbcbabccdbccacbaccbdbdbabbbcdabababccaaccababaacacbbdaaabaccbdcbdbdacabdaaccbbacdadbdbacbdbbbcabcaabccaacdbdcaddbdcccdccccccdacabbdcdcdaddcadcbbdbdbdcbcbdcbcdbbccaaccccccaadacbdccccbaddcbbabbabcbaddabdcdbdabcacdddabcbaaaadddadbbabbcacbbaccbdcbcbccaddccdaadacacddcdbaaaccabadbcddcdacaaaaabddbadaabacdbabcbabbadaaddaccbcabaddcdaddbbaaabdacbddaccabccdcbaadadbabcbdcbaacdbaddbdcddbddacdcdadddbdccbcddcaacabcdcddddbcbccabdbdaabddbbadacdcaccbabbcbdacddbaabadbacbbaaabbaacbdcdbddbdcdbdbcccdabacacbdaaadbccaabcbcaabbacdacbacaccbcdccdcddddddcaacacbabcbdabddbaddcadacacaccacdbdbcdadccdbccbbaadcccdcccbbbaadabbcacabbbbbdaadaabcccacbaabacdbdbdbdbdabccbaaddbadaaddddadcbdacadcccabbbbbdddbcabacbdbccbcabdcabdcbbaddadbcbaaadadabbabcdddbaccacbdcccccabaabbbbcbdddcccaacacaaaddaadbcaadccacdbabaccdccdcbcadadddcdabcbdacaddbbcdbadbdabbccdcdbcbbaccbccbacaaccaabadbdbabbaacdabacacaabbdababacabaabbcddbaaabcccabcbadcbbdabaccbaadbcdbbadcacacdbdaadabbcabddcadcdbdddaaabbacdcaccdbbdacdbdaabdabdaaddcdbbdbcaadddbabddccdbcccccadbdaabdcabbbccabdddbbadbdcdbadbddcbcdbbdaddcabacdbcbcbadcabddadaadccaccabbabcdbbcdbcdacbacacdaaaddcccddadbddbaabccbcaddabbaabbdcaacdbcdcddbdbbbbaadcdbbdacaacddabbcdbbabcadcbdddadaaddccbcbccaccabdaaaaccabdcbababcababbddaaddadbabddcabbacddcbaacbccdbadacaddaaddaacadbbcabccacbacbcdabbabddbcdaadbdddaaddcbdadcdccccbcdcbbbacbcabcaddbdaddbabdbcbaaaaacdbbbacbdabddadcdbcbddcbaaadcdbdaabbddbcaccdadbadddaaccbbadabbbbccbcbbccccaddbabbccdbbbcbcaccbbbacbdabaacadabdabbbadddcabaabddacbacdccccccacabbbbdacabdcdcbbadddcdcdcbcbcabcbacadbadbbbdaabdbabcdbdbccacbdbacbbadadcbbdcdcabbcaaddbacdcdbcbbdaacacbcdadbcdaabacdbbdbdbbabbcddaacadbcacbdadadccadbccbddcdbcaaddbbabdbccbbabaacdbbccbbabdacdbbadcbbaccbcbdbaaadcddabbbdaccdbdacbbbbdbcdcddadbcaacdbbbadbacaadcbababbdcdcabdcacaaaaccbcabdacbdcdcabaccdabadbcbcbddcdcaaaccdcccacbccaadddbadbdbdabadadabadaabcdbdbdcacdacaccaabddbadbbcadcbaabcdaabbcdabcdaccccbaccdccaddddccbcbaddabbdaaacbaccaabbaabddddcabdddcadacaabddbbcbcbccacaddbbacacaacdddaabadcaddbcddabaaaaaacddbcaaaaacdbbbcaacdabadcabbccdcacbcaaddcadbacccdcbaabcccadcdddbabdccbdddaaabdcaacddabccdcabdcbbacddaaddcddcdaabbcbdcdddbbcbcabcacabaacccaddacabacdadddcdbddcabbdcbdabcbbcbaacabcabdcaccccadadbacbdbcbdaccdccbaabacdbbaaccbbcaddbdbbbdacdaccbccabbdacabdcbdbbdccadcdcdbdaaacbbbaaaaadadbbbacddcdcccacddbdbdbbdbbadccbbbcbddaabccadbcdbbabbaabbacbaadadacbdbaacdbccbbaacdadbdbcbbacbbaaadaadabbdccaccdabcdbadbacbdcadacbdbaacaabddcacaadaccbaddcbcbaaddcaaddcbbbcaddadddccbdaaacadadadcaccabcbcbdbdddccdaccabbcccdaccdbbbaabccaabbacdcbabbcabccbccccacdaabcbcaaacbdbddcbcbdbdabddcbbaddcdaabdabcabbdadadabdcadadaccdabababcbbcaddbcbbcdbcabbaadcacdbdaccdddaddbabacbaacabbacacdddcadbbbaababdccadbccdccdddbbddbacaccdbbacdbaadadaabcbdabbdacbadcbaadadbacbaacbccbababdddcbbdbbdcbcbdcdcddbcdcdddadccaabdaabbcabaaddbaccbbabdddbcadbaabaccabdacaaaddbcccacaacaabdaabaaacabccddaaababdcbbaccbbaacadcbcaaabbbbccababbbbcbbdbcbbadbdabadccacacbccbabbcbadddcbadaddcdcabacbbacaaaacdccdacababddabbdbccbcbcbabaaccabbccadcabcdaacdabdbdbbcdddcdcccbbadbbdddbdabaddbdbbbcabcadbbbdadbcdabbbdabbbdadccdbcccbcdcaccbddcbdbdacdddddabcadcdacccdcbaabdcacadacacbbbddcbcdcdadadadaacaabaadbabcddbacbcabcbdbadbcbbcdbdbbbbcddbdbabbdabbcddbbbabdabccdbcaabdbaabccbdbbdcbbdabacabaaacdbbcdccddccdddddcccbabaabdbbdcccdcabcaacabbcacdbccccaadacacbbddbbabbbbdaacbddbdcdabbccbbccdacdbdcbbdbaabdacbdbbdaccbbcadbdaaadbbcddbbdaddadcbddbbccabdcbcaabbabbadabdcbdcadbdcaadacdddccbdbbcddcccdaddabbbdbcbbbcbbacbbbbaaccdcccddbbdbcdadcaabaabdabdcddbcccdbdcacbccbadcbccbadaacdabdadcccbcbbcbbdccdacababbadcdbdcdbcaacadadacbbcddaabcdbababadabdcbcbaaaaccaacbbabbcadbdacbcdbdbadadbdacbddbdaabaaaacacadacdbcdcdaaacabcdcdbcdccacbaaaccddaadbcdaacabccacbbbcdcaadcbbdcdcaaddabdbcddadbabbbbdadacadadadddbbcccccbdbcbbdddbadcbbacbdbdbacaadabdabbcbabdabdacbddcdaadcbbacaaaaacbbddcadcdabcccbbbbacbaccadcdcbcdcacccdaaddbbcdbaadabadcccdbcabbaabacdcdadccccdbbddadcdbbadbaacbcbbabacddbbdbcbbaadccdccadcdbcccaaccdbcabaacdbbbcaaaaacdacbdacaddbcabcaadbcddcbbccaaaddbcbcaadbacabaaadddcddcbadaddbcdabdcaacbdbcaabdaccdbbbdaabdababdddcbccbccabacbbccbcdacdaddccbbdccbbccbdbbbdabcabbddddcdbcdbcddcabcbbdcccdbaadcbdbbdcdcbadabbadbbbaadadcdbacbbcbdcacbabbbaccddddaaabbdcaddadccdacadaaadabacbbdadadbbdcbcdadbccdacbcdddcdbcddccdabbdccdbccadcbdabcddcabbdccdbbbabababacbaabadccdcdcabdcbdbdbdaabddcacaddbadbcadcddcccadccadcbccddaddbdcbaadbcbbcbcbcbadcaaddcaccdbbdacdaabaccbcdabbdccdacbadbbddbdddabcdacadcbaacabbdccabdbcdadacbdacabccddbcbcdadbdabdcacdbbbcbdcbbdadbaadcbaaadadaadcccdbdabdcdbdccacaddbcbdaaabcbdbaaabddabcddaabbcabddbbcaacadbcaacbbdcaddcabcddcdadcbbbccbddccbaaacbbbabdacccddacdcbdcabcdacbcccbabcbcabaaaadccadaddbccbcadaababcacacccbdbdbbbacdbcbcbccbbbbaacccbbbadaccddbcbaddcdacdcbdbdaaadbbdadbcadcbcbacaaddadaabddcdddbaacbbbdadbbbddbabdaaabdcccdbbcdbadcbdabaaddabcdbabdbdbbbccdbccbddadbcbdaaacabaaddddccbcddbcdbbcacddcdddbcdaaddcccaddcbbbaabcccdbaddadbabbdbabccdbcaacddcccacdcccbdddcdbcaacadddbbccdcdbbbbccadaabcccaabccdabacbdadadbcbdacdccadacbdbcaddcdaaadcccaacbaaabacdbbabbcacdaaadbcdaacbaaddbbdbcacdbaddadbbccbbbbbcdbccabadbaabbbcddabbcbdabacaacaccdbdcdccdaabbdbcabdadacbacbddbbadccdcbbbcbacccccabaccacdbcbdacbdaacdacbcacdcacdbcbadbabccdabadaaabaacbdadaaacbacbcbaddbdabbcdbabbbcdcbdccabbdccdabacbddccdbbcadadacddacddacdaccacbacdbdaacdbbdbbaadabadbbbacbcdbbcbabcdccaabdbcadcbddcbabccaaaabbbaaccddbbadcacaaacccbbbbaddababcdabdacddbbbdccaabdadcbcdacccaccddbccdddcabddcccbbacacabdddcbabbaddcbdbbacddbddcbdaaaccadbbadbabccaccbdccdacacdadacbbbbbcbaadbddabacccdbbdbabcbdadacbacccddabacbdccccbabdbbcdbbdaccadddcbabaaadcabdbabaccaabcbbbdccddcbacbbddbaddbcacaadaabdaaadabdbacbbadaacbdbadcdddcddabadabdccbdadaaddbcabbabcbbabbdaddcbbbcaabababbdbbdddbacabadbdabdcdaaaadbbddcdaaccadacaabbbadabaacdcaddcddbdaaabddadcaabddddbacdbaacdbdbaadabcabccbaaabdadccbcdcbccbddaadbcdadbcdbaaaabcdadbdabbbcbdcbaaddbdbdbcacdccdabcaabbcacbdbdacbbdcdcabbbdcbabbddcdbbbddcbccbaacbbbbdadbddccdcdababcadaabadaaabcbbbdabddcbbbacbcccdcbcbccadadbdbddaaabaacbbabcabcadddbbadcdacbbdcaddcddbaccadcacdabcaabababddccacccaadcabaabadaabdcabacdaabdcbdacdccaccbbadcacabdacccdbbdaabcdcbcbaaccddddabadabdadbabdbcbbdaaacdaadcbbadacdcabddabcbadabacccdcaabcdcdbdbdcbcbdcbccbdcbdcccdbbaaaaadbbbdcdcddcbcaccabcadbbdbddacdabcbbaccadccdbccabcccbaabaddacacbbdbbddccdcdcccbaadbdaacacbbcdddbcabcbdbdbbdcaddbcacdadbadccdbdadccccbacacabdcaadcccadabadbddbbaccdcdaadcbabdbabbbcbbddcbbbaaacddadaadbbdabbaabcddaabacbdabacddcccbdddcbabdabbdabcdcabbcdcdccbdacaacccbdaabcaabcccbcababbbbddcbbbaacdabdadcbcaaacbbacdddddcaccaabbcdacddadbcccddbdcbbdccabdbcddabcdabbcaaccddbacabadccbbadacccdcabbacdbacaddcbacccabaaabcaabcacbbbbadacbbcacbadcdccbcadacdddcbccdbacabccbcbcaaaaccabdbdabdccddddbcdcddcbdadcaabbaabccabdacddacacbbdabbbdcccdabaabdcdcacbcaccddcbbddababbcccbddbdddabbbcdbcbbcabacccbdcdaaddddbcbacdccadbabbcbcacbdbadcacbbababbddacdbaacbbdadbcacbbccdaacabbdcddbcaabcaacbcdabccdabbdadddcbbadaddcbdcdcdcbbbdcbdcbdcacbbcadadadbbcbbddacbcacacccbbaaacdadacdcdadcbabbabbdacdbaaabaabdbdccdcbdccdbccacdbcbaaaaadcbcabababdaadcdbbcbddabbbacbbccdddaacacdaaaaddbcaaadddadbddcbbbadcdaccbccdacdcbbadbcdabcdbdcaabcbcdbbddacadbcbadadddbbcadabaaccccbcabadacdacbabbdabaccabbccbbcacacbdcbbbdcbcbbbccaadacdadbdbcdabaacdadccdadabcbaacddaccddadbbbdabcbaacbadacdbcacacabdcaaaaacccdaacbcddcadacccacbaaaddccabacabcbacbadcbdadabcccaacdbadbbcddcaaabbbddcdbddaabdbcdcbcaadddacbcaaccdacacacbbbcdcacccbccadbdbcbdddccbdacccbccabacdadbaabdaccbbddacccbdddadbcaccdcaababababaacccadadcdccbcdddcbcbcbcadcdacabdccaaadbbddbbcbdadbabadbababcbabbdaacdcadbacdcccabbcacadabcccbdbaadbcacbadcadadccabbcaaddbcdabcbacbaccbdaaaddadbdacabcabbaaadcacbacdbddccddcaaaadbbdbabdadbdcccbadaddccdabbcdacacacdadddcdccccccbcabcbacdbaabbcdbdaabbbcdcdcbdbababbbdcbabbbdcddccbdadbdbdccbdaccccddcacabdbbaacacbbdbccccddaccdcdddaababadcdbccdddccdbdcabacbdaccadadbcacabdbcdcadccdadccabdbaabbdaadabbdacacbbadaddbadcadaaabcaccdaccdcccdadbacadbbbcaaabbbdbbacdbcacadcdcacdbcccdbdcbcbdccdbdbabadcbcdbbccccbacbacaaaddbbcdbaadabaadccddcdddddaadbaccbbdabadddabdcbddbabdcbddbbbbbadcbcdcabcddcbccacccabdaadacbaccbbcdddcababccdcdcbdadcaccdadacabcbacabacbbcadddcddcabccccaaccbdbbaddddcddacacbdbdacaabbdadaabcaabadabdabdccbbacddcdddbbdbccdaaccadcdddbaadbcdcbcadbacdcdadaacacbbdababcbdcccdcccacbaddbccdbbcaabababbbadbbbabccbbabbaaccbdcacccdaaccdcddbaabbcdadbbdcababcdbcbbccdcadbacdabddbbdacbaadcbbbcadcdccadadcbbabaadccaccabdbcbccdbadaaabdaccdabadddabcdaddbdcdcacdaccdccabcdbbddbdcbbaddcdbbbbdcbabdacaddacdddbdcbdbccccaddbcdbbdcbcbdcabacbcbabccdcdaddadcbcdadbaadcdabcdddbdcadbccacabbdacadccaaacaacbdadbcdddadbadaddcdbbcaabaaadbdcadcacaabbbabdbbabdbcbacacbaccacbddaaccddcadbcbadaabcdbcdbddbbdabdbdbbbdacbdbdbcbbaaddddcbbddccccaddddccccabadacdadcabddcaaddaacdaaadadadcdccbacacbbcccacaccbdccacbbbdbacdaabccaddddadaaacccddddccbccdadabddbadbbdacbaaacacabbcbcbadaaccdddcaabadcaddacddcdaccccaddbdcccbcbdcdbdbccacbcdbababacccbbabcabadbccdcdbbddacdbbcabbcdaaaadbaabbcaaadccdbcacccbabbadabccddaadbcbadabbcdaadbdaadacabbcccdababacccabababbbdaaadacdababbacaaaaddcababbadbbddbcbabdbbabaabbcacbdccaddbcdbdaabcbbdcaaabadadbaabbcddcdadabdacbddddacdadccbbdbddbadaddcbdaabaacadacabbacdbdbdaacdacadacbadbbcbccdddbbcaaccccbacaadcccbdcbbbddacadbbdcccddbbcdbbbacdbbabadadccdcadcdccbcaaacbababbdbdcdbbbbcdacdacbccaddaccabccacccccdabbabdcbcbdbcabcbbbabacbcaccadddbbdadddcbdcadccbddababcddacdadaccbbddcadadabdabbadcbbdacccabacabbabacbbacbddbcddadadbddbbbccbcaadabbddccbaababcbdbdbacababdcddaaacdabacdcadcbadacbdbbabbddcdbacacbddbcdddbadbdcbaaddcbbdaadcdddbbccabbddbddcacabdbadbbdcbbdbdcaadcccdcbbdbdbabccbbbcabccddaccbacddbacdbdbbdcbdaaacacbacdaaaddcdcddbdcaaddaabbaaacacdbcdbaadaccbdadbcabbdbcbabcbbabaddcaacacddbbaccccbcadbdbacdcbcccbdaadbabdbdcaabdbbddacabdbcccacbaaccbaaaacccbccaadabcbaabadbbbacabdcacbacbbcdbbabcaadacbdaaaabdbacbaacddbcccdbdacbcccabbbdbcbaadcdbcbddccddbaaccbdcabddcdbcacabdadbdccdaaccdacdcbcccbbbccdbacbacaaaccddbacdacbabdabccbdcadbabacbbbaadbdaabbbdcadbadcdbaaddacacabdbcabccabcbadbdadaddabcdacdbdbcbdbdbdbbcbcbbabbacaaaddaadbbdabdbcaaccbabaabbbcbacbcbbdaabdbcadacbabbabadadccabbabbbcacabcbacdcddbbdbaccacdcacdcdbdcddbaacbbbaddbcacdcadcbcbcbdcadbacbcaabbaadabbcadcaddcacabbabadddcbbdddadadbbaacccbdbcadbcdcdbadcacbddbbdcbbabcdbccdabbadadbddcccabacaabdcadbccbdaabacdbccacbbbdbcdbaabdaddbdacdcddbdaadadcccbbadcbcdbcaaccabbcabadcbdcdadbddbbccbbcadacbdcabcddcabdadbdcdadccabacbcbbdcaacdbdbdcdbbbbdccabcbdddabdabbbdbacaacabbdbbcbccacdacacccbdcccbbbbbcacbaaadbcabadbbdbbccdcdadaaacaacacaaacaccdacdcadbdcdaacbcadbccddcacdadcddaababcaddcdadccdbadcccdccbdabaacbdcacdabbcaacbcaacdaabddaaaacbaaccccacacbbaaddddcabcdcbddcddacaabaccbcabaccccbdddabdcacdddbcbadcbdbccabbaaddbcdbcbbcbdbadccdcddcdbbdacbabdbcbbaabbbcdbccadabcaacbbcabcaadccdcaddaccadacdadbabbbdaccdcbdbdadaadaccddccabccbabadbadcacbacbbccdccbaacccbcdcdccbdccaabbbdcaadcabcbaacabbbbcdbcbccccddcbaddddcdcacaccbccacbbcacdcddaadbbadbaddadbaadabcabdcaabdbadbbdbddcaaddcccdabbdbbbbaacababbadddcbabdbbdbbbcbccaccbabbddaacaabcdddcadcdbbcacddbabbcadbadbbbacaccadbabbadbabadaabacbbcbcdcbdddbbccbbbabcdcdcddcdbbbbcadaadabdadccbbccacddbbacaabbadccbaababbbabbdacbababdbabbccbddcabdbdacbcadbcccaadbcbcbcccbbbbdabcccacbbbbacbababccbdaabcacbaddbdcaabaadcddaaccbadcbdcccdddbbdbcabbcaabbdbabadcdaccbdccabcbcdcacabcdcacbddcdbcaaadbccbdacbccbbbbaaaacaacbbadaccdaababddabcbacbbbadcaccddcaccbabcddcdcaadcaacabcddcbaacdcdcdabbabdaadbddccacbcbbccaabbadaadcbbacdadabddacadaddcbaacadbbbdcdcabbdaacbdacbabaabaccabadadadaccbacdddddccbbbbbaddccdacdddddccadddaddaabdacdbababbbdbddcbbdddddbadbbadaccbccdadbccaabacaadcdcadbcadabccbacdabdaccbaadbcdabdcaacdaddcdcdbdcbdcdaacbdddbcbaadbaccbabcdaaabdbcaccabadacbbcbdacaccabcbbcbcccbabddcabaaccacbacdcabbbbbabdbdbacacbbcccdadaabccacbabadcdabcdbddbdbcdabcbaacdadcabccdcbaaaddbabcaadcbbbbabbacbdbbcdbbcddbbdcbdbaddbbdbabacacdacbbcbbdacbcdbbbccabbdcbacdadaddccadabcbdabbbbbbadbbccddddcdbaaaaaacdcdbddbabdbbcaaaddaccdbcaddcbacacadccacadccdaadcadbcbabadabadacdaddddacbdbdabbbabcdbbdbbddbdddadcaccbcdacbbbddadbccdabcddcabaccaadccaaabacabcbbdbddbdccbbdcadcbbdcaabcddbdcbabcacabcccacdcbbbacbbbdddbbccccaabbcdcaabcddbacbcaaccdaadddcccbcdccdcbacaaaaaabccbabbdccdacdccaccdcdadddccbbccacccbcddbadcbaabaadcaaccddaadabdadbacddbddbaaacdcbaaabcccaaacbcaddbbbdbaacdcababbbbcdcacbacadacddabdbdddcdddbcbddabcbabdabdbbabccbccbdddddccacdcbdaaabccddacccabcacdaadccdbdcabaddbccdcdaaaacdacdddcbbdbdcbcdaaccdabbdadcadcbddcdacdcddccdacaabbdbbbabacbaddaadaccbbcddabaadbbbacddcdbcacdcbbccdabcaadccbcaabccdbbdbdbbbdbaddbcacbdbcabcccacbabdcdadaddadbddabbdadadcdccbabadcdcdbbdaddbcdacdbddacaccadbdbacbcadbababaadbdaabbbbddcdadcbbdddbddcaddccdbadbbbabbbccdcdddcccdabaaabdcabdccaccbaadcbcccdddcaabccdacdadacdbacacadbcabacbadbaacbccdacdbcbbdbaaacbdbcaaacddadabbdcbbbadcccbaaddaacbadccdbcdaddabddbbcbdadacacdbccbdaaadadccbbbabbdbcbaddcacbbbcccbcbabccbddaaaadddcacbaabaddddddbcccdcdbdacaaadabaacdbcccdddbcacbccaaddcdbdbdbababdacbadcdaadaaaacdaacbadbcddacaaaacbddacacdddaadbdbbabaaccbaddbcbcdddaadacadacbabbabdadadbbadbddccbcacbddbcbbbadabccbbaaabadbbcdbdaadbaacdcddbacbbdbdacdcbcdccddddbdbdabdcacdbacbddbcdbdaadbbcaddbabbcacbdadaabddacccbddcdddbbcbaadcccddcdddabdaaacbcbbdcccbbcaccccacdbaadcabbabdacddcacdadacddddacddcbdbbbcdadcbdbdaaddbadbcbcccbbaadbccccaacbdddbcdcdcddbcbadbcbacbcdaadcdbaccdacacbabcbcabcdabdcdbcaacdccccdadbbdbbadadbccdcdcbadcacbdbdccddabcaaccbbdbdbcddaabacbaadababbbdabaabcdaacbbddbdcdccbcbdbdbddddcbabcabbcbbcdbdacadcccdddbccacbbcddaacacddaddcacabcccbbddbdaacbdcabbbabcaacbbbccddcbdcbbdbacabbcdabccddcabadbcacbddcbabcacdacadbccabbdbdabcaaabddbbcdbbabdacdcdbbcabcccbaddaddadaadabbdbdcbccaaaadbdaaaadddadcbcbcccdccbaccaabbdddabcdabddddaacddbabddccdcacbaddcbccbacccadddddaaddbbdadacbbadbacdccbddcbbbdbaacdadabbabbbcbaccdbbcddddaabcccdbcbcabbacbcbcdaadddbbacdbabacdcbdbcabaccbbbccbbbbbaacccaaabaacdaacdbccdbacaccdabcaaaaacbadccaccaadaababdadbabdaaadcabacadcccdddbdabcccdbdadaacabbddbacdbdbaabbacdababbaaaccccdacaddcdddacbcacaacacdacddacadbbdababdacdabcdcaacdcbdbbababcaabaadadbadbbbcdbdaddadcccaacbcdbadcacadbbdbbdabccbbaaddcacbbbbdcdcaadbcdbcdcadbbcdbababbbdbaddcaacadacddbcabcccdaddcbbaaacbcacaaabdcdcdbdbbbccdabacbbcdcdcdcacaadcbabcabdcdcbadcccbbbaacaaacbbaaccccdbdbaaadacdabbccacbbadabacbdabbbababddcbddaddcadcaabdaacddaacbddadcccdacccbdaabdaacadcccbbbbaaabcddaadabaadbccbabccbcaacacaaadbddaacaacbbddbacaacaaaabaddbbcaabcccadaadadabbccdcbdabcbdbbdbcaddbddbdbaabccbcccbbadbcdccdcaaddcbcdbaadadcadacdbaabaaddbbcbccbddaddbcbbdcadcbcdbccbaadaccbababcacbdcbccccdbabacacdbbbabaacdbcabcccdbaccdcbbddcbbbbbcccbbdaaabccdabaadbdbdabdcaacaabbcadbbcadbcbddbccbccbdabaddacdcdcbcddbbbdbcddbbdbcdddddcccdaadbbbcbdcbbdacbbccccbaadcabaacdbacaadbdbdccbabbccadcdccabadabbadbacdabdcbccaaaacbaaccaadbacaadacbabdacdcddcbdbabbadbbababdbabcaddccbbdadbdcbbacacccaaacacdadcdcdaacccacaaadbacbcdcabbbdacaadabcaaacbcbaaaacdcbbcadcccdbcdadaddbcadbdcaacadccbcaaddbaddcbaabcacbcbbcccdadcccdbbdcaaaadacddccaacaccddbdcbabdacbdbccbaaadaacdcbccbdabdccabdcbcabbabddbcaaadbacdbcaddcdadcbdacbdddadaabaccbbddadddcbcbcabddbcdcbadabbbacbdcbbdadcdbddbccdbcccadcbbccdbadcbaaabdbacabcddaccdbaaccddaacdcdadbcaacdddabaaabdcdbbcbbcbaadbabcabbcdcccddcabcbdbbdaccdbdbbcabdabbcdbbdbcdadcacbddcdbdbabacbdbcdbbccadddabdbbcbcdcdbacbbccbaccadbbbddadcbddcdacbddcaabdccbbdbabdcdccbadccaacbadcadcccbdabbbadcaadcabbaacabbbdbabbacdbbdccbbacacbaacdcbbbbbcccddbbbcacaaabadaaddacaaadbdaccbbadbacaadbaccbaaccaacbaacbdbdbbacdaacbaccccbcadcdbdbbcdabcaacaaccccdccdddcbcdccdacbbbdcdddbbcaacbdacadbcdbbacadcccaaaddddaaaccabbbaadabccaadcbdbcbccaaacddcbbccdaccbbccdbcacadabbabbbcacadddccaacaaacdbabdcdadbddbbddabbcdbcdcabaddacaccaadbccbccbadbacbadacdbdabacccddcacdadadddaacdccddbcdcdabbabadacdcaadadcbbbbaaccdbaccaaabcddcbacacbddccbccacddccdacbdcbdcdabbcbbaaddadbbdcabdcbbbaababadbaabcabccaccbbcaccbcaabaabbcddaaacacccbbabbcddcccbbdaddccbbddcdddbbcbdcbbaaacbacdabcdbcbddcaaaccaacbacaaddcccbddbccbdaacbdbcccdcdbaaaaabdbbacdbaadcbccbbcaadabbcaaacbbbadbbdabdddbdcbbdccadbbcbcbcdcbadbbabccccaacaabcaddbcbcacdaabaaccaabdbbcabdcdbbdadbdbdadcdddcbbaaddabbbbbdaabdaaadabccaabbbcbaabccdccdcddbccddcaabbaddcbcdcadddbcdbdcbbabbabacdadccabaaaacbbcabaaabdcdbbadccbbabbccddacbaddcdcdbcbcacaacaadddccbabcbcaacdacbbbdabdddbabbddbcbbbcabbdaaabcaaadcbadaccbbaccccdacdbccccdbadcbccbacccacdcddbdbddbdbcaadbbdddbcddbaaadacbadaacacbcbdcbabbadbbdbddbaccbdcadcdbbcbdabcacdccbabdbdcdadadcbdbbbcbaabbbdccdcbbdbcacababcdcbddbcbbdccbaadbbabcacccdacdaaaabcadaddccaccbdccdbadababddabdbbacccdbdcdadccabdbadbbbccbabbddcaadcabadbaacadbdabbdbddddbbadbadcbdacdbadbbbabbdcbdbaacaddacdbbdaaacdcdccdbbbcaabddcccccbcccbaaddacaccccdbccbadccadcdccddabbddcbbababccbabbcaadbccbdcddccbdbaacbccadaccadaaacdbcbbdccaddbdabddaccbaadaacbdadbadcadccbcbaddabbabccbbabdcadcdababccbdccaacbacaccbcacdcdadbccdbacacbdaccbdccdbccaabacdbccacdbacbbbabbcabadbddabbddaadbcbabbadcdacaccccadbadcdacdcbaaacabadccddcbddbbdbcbbaabcdcaaadbdddbbdacccaaabdabdcacbdcacdcdabbdaccdbacdbcbbbdcbaccaaaccdbbcabbdaacdaccacbaabdcaacddcacbbbccbdbabcddaccbddbbacaaddcbcbccddbcaddcabbdbcaabaddabcbbbcabbdbabccbbbdaccbbbadbbccaaaacdddbabddcaadacacadaccbbbadcdcbaadaacdabccbcacdadbbabacbbccbdddabdccbbaabdcadddbaaddcdababcacbdcdacccdbdbdcccddadbaaccdcbabababdccaabcddaccbcddccbadddbbadaaccadcbabbbaaddbaddaadbbbbbbbaaaaadcaccddbabccbcbbcddbbbcacbcabbaabdbabcbcbdcaccadabdcbaddbcdabddccbbccbccbbacdccacabdcaaacbdababbcbbacbbcdbccbcbdbccababdbbbaadababbbcdabadadabcdddbacbbbbdbdaaacbabaccbdbccdccabddacbcabccbdbbcdcaaaabadddaadbbaadcdbaaaddadabdbcdbbdadbbacbcdaabdbcddaaaacdcddcbaaaaaadcbcaaabacdcdbccbbbaacacdadcbacdcadaacdaaacbbdadccdbadbabcbbddbdcccabcbadbccaadcccbbdcabdbcdabaaadbdbddcababdcbcadbdaadbdcdaadccaccdbcddcbdadbdcacadccadcacddabbcdcaadaacdbaadbdcaccbcdbcbcbaacdcdbbdaacbbbcbacdcadbadacccadaadccdddbbbcdbcccdccbcabccdbcdcbbbadbadcbddbdcddbcaccdbbacdaaacdcdaacddabbbdbcddbcabcdbbccdccaadacabbbbacbacaacbdabadabaabababadddccdcbdcddababdcaacbcbcabaccdacadcdaccacdacbbabcababdaaabacddddcadadadbcdacbadcbbbcccdadbabcddbbcabbbcdcbcadaaccabcacccabccadddbbbbacbdbbacadcccbcddabacaaccbabcdbddbdccddaadadcaaadacabdbcbbbdcbaccdacbbcabcccaadacabadbccbbdbbabacacbcbadabaaddccdcacbbdacbadcdaadbabdaaaadcbdcbaacacbccaaaacddccabdacbbcddbdbdabaddcbddbabbccdbcbbddbbcaabaccaddcacacdddbcdbcbddbaacaadcdbbdcccbadcbccbccdcbcabadcbdacacbdadcbcadcaaadddaddddbabaacbcaaacbccbadddaaaabbcbadadcbabcdabcccdcaccdcbdabccdbdacdbdcccaccbbdcbcadcbbdadbaacacdbcddcadacdabcbaabcaddaccddacdabadbdbbcbbbbdbcdcbcddbdbdccddbbbcdbcccbacdbacabcbdbbaccbcdbaaccbbccabdddcbcaccccdcaccadcbccccbdcddabbbccadcbcddbbbbbbcbbacbdbbdbadccacbdacbccabbdbdbabbbcaadbdbdcbcacdacbbacdadabcbddaaacbadacccdcabccaccdbbcabdabcccadbbdbcddaadadabbaacaccacdbcccaaaacdabadcdcccbccccdcbccacaddaaddbcdbacbbbcccabbbbdacdbcbbcbacbaabbcabddbcbaddbdcdddadddbddbcadacbbdbcbddccbbcadbaabcdcbcddcddcdaacabaadaacdbbbcccddbcdbaacaaaaadbaccaabbcaacdbaddbcadcdaacdcabaaadbccbdbddccddddaabdadbbaaccdabcacaddbaadadcabddddccdabbaccdadcbbdaddcccabacadcbdccbccabcacabbcaababdbacdbcddccabdddaabddadcbddaaccdcbbbcbbdcbdabdacdcbcaabbcacbbdbaadcdbaddcbaadbcbcacaaaacddbbbcadadbaaccdcaabddcabbbbaabbdbbaccbcdacdccdaaddbbccadadddcccadbbaababbbdaaaaabbabdcccadabbbaddbcbcbaadcdacbcdbcabccaadcbaabbdcbcababdddbaadbacacddbbdacccddacdbddddbaaccadbdbcddaccccdddcddaacdcdbccaaccdabaababccdbacbcacdaddabaabadbbadaabcccdccaddaadacbcbbaabdcaadbcdacdcccbbcdabbaaaaabaabaacabdbbcccabbacdbbbdacccdbddcdbddbbacdacacaddabddddbaddcbcababadabcbadcdbccbaacdbabacacaabbcccabbbdbbdcccddabadaaccbbdcaaabbaaacbabdbcbadbcadbbbcbdbddddbdbdcacdddbbcadabbcdbdbccdbbabbbbcbccabdbaacbacddbbaacabcdabaabbddabdbdbdcddcbaabbdbadccddaacadbccbbadddcadaaaabcacbadcaaccbbbaddcbdadbcacabacccbacbddbbbdcdabbacddccbbcdadbbcccbcbaabcaabbbaccaabdaccdadbbccacbddbbdadbbadbccbdccbbbadcabcacdbcccbbaccdcdcdcdddbbcacbbddaabbdcacbadaadbabdcaaccacadacddbaabdbacacbdbdcdaaadbbbdcbccbacadcabacdbadbdacaadadcdadccacdbbddccbacabdadbbdadccacbbdbaabbdbabbccabddbbcabaaabccbbcbcdabbabbaccddbdcbdcbbbcabccdbbacdaacabaccbcbbbbdcdbacddaaaaccabacaacbdcabadbdabdacadabdabcababbbbdcdcabacdbbdcbdbbbadccddcdacaddaaaacccccdbbdbcdbccacbadbccdcbccccdacaabbaccaddcdadbcdddadcbacbbdccbdbdbcbaaacccddddacabcdddabbbdaabdbabaccabdaaacabacadadcdbcbcdddddcdcdaaabdcccabdabdcbdadbadaccbabcddcaadbbccacbdcbacbdaccdcbbdaadcdaaadcbccdcaabdaaddabbbcdacbbcabbdbcbadaccbbdddcabccbcddbbccdaabddddcabaddbbcdccdbcdcaaaacbbddbbcdbabbdccbdcdcdbcdaccbbcdadcdbdcdbdaaacdcdbbacddbaccadaddddbccadbaddddbbadbaccbcbdbdaabaadabdcdbbdcdcaddcbcccacdcdbdddaddcdcdcbbdbdbacbdacbbcccccbcaacbccadcbbdadcdddacabcddababcdddcddcdbacccbccbbdaacdaddcddddbaaccbbdaabdabcbbcabccbcabaabacabdbaccabaadcaabccadbccdabdabddbacbaddadcdcdddadabcbddbdaabcabaaabaadccaccadbddabaacddddbbccbddbbabdcdabbabdbcccbdaadcccaabddbdcdbdabaacccbcddbcbdacabcadabbcaabbcccccbbcdcabaddcdbcccdadbbdabddbcccacdacdadaabacbababbadabaddcdbcdbbbbdbdacacbbdbdaddababaadcabbddcbcbadcbbdddaccabaaabdaaadaadbccaaccbcbdacbdbbccdaaccdbcbbbdcabdacdabadcbcddbcacdcaabdadabaacddccddcbcacdbaddcdcbdbcabbbabacbdabacdbcabdacdacbdbcdabdcbadddbabddbbdcddcdaddbdcabaddbacccdcbadaaabbcbdcdccacbbdacddcdbadcdddabcccadddbdcbdbdbbbacccababbbcddcdacadbddbcdddbcbadbbdacaabddcacbcacdcbcaddccacccacbcdbabdcacddddbaaaacccababbdcbaacdacbdcbbdbbdbbcccaaabadbbaacdccddaddbadddadcbcdaaaccbddddcbdaccbbbdccccabacccbaadadacbcdcbbbccaddaddccbcdccbaadababdcddcaabddacddbbcbdbcbdcbbabdcdcdcdddbaabbbdcabbacbbdabadadcdaddaacbabdbcbbdcccbaadcabcccabbcdbaaddcadadbdcaaaaaababbdbabbaccbcacbbbcccababbadccdabacadcbbddbdbbbbbbbdadbddbadbbbbbcdddbacccadcccdddcacbabcdabccdcccdacbabcccccaabacdabadabddaaabddddaccdbabbbcadadbbdaabacbcbdbccdbbacaaadbcbbcddcbccadabdbbccdbdbccdbccacaadbccccadbbccddccdddccdcdcadbadcdbbabdabbaabdabddcbaacbcdbcddacccbaaaccbbabadbdcadcbbbbbdadabdaaacccdaabcdcbbdaabacbaacbbdbdddcbbabccaabbbdddccddabaaabbdacdcacccbdadbbbdbddadbbbacbdbcbdacaccbbddddaadbdaacaaccccaccbbabcdcaccbdcbaadaabacbbbddadcdcadabcdbcabacaaacdabdacbddbcdacbadbbbcbcabbadadbcdabaabaccdbcacbbbbababddddcaadcdabdacbcdaadbaabdccdadbdcdcbbcbacadbabddaabcabbbbccdcddababcccabbdbacccadacbcacbdadcbbdadccccbcacbcbaaadbcdaccaccbadbaaabcdddcacabbbcaabcddadcaaadbbdacabcdaadddcbdbadcbddddbbccccacacdabdddddbcbadacdbbddaacbbdbbcaccddddabaacbbbadaddaaaddadccdaadcdcdcdddbdbdddbccbdddbcabbccdbabbcaacdbcbbaacbcaaaadcdcccdcddcaddddbcbcbbbababdaacbaabbbbbbcacddaccaaaddbadadcabbbdccaaaacadcbacccccaaaaddbcbacdbacabbdcdabcdddbccbdbdcddbbddccdabaacdbdbadddcccccbbbcaadcbbcaadcbbccdcaabddddbcbdbbaddbcadccdbbbbdacaaabccbdabadccdccacdacbbbadbbdabccddbbaccaaaadabdacbacabccdadcaddadcddcdaaaccbcdcadcdcdcbccdbdbbccacadbbcacdcacaddadccccdbccbbccddccddcdbcbbcdbcbadbbaabacbdcaaabdcabadabbdacccdbddbabcdccdacdbbaddadadcccbaaacaabcbcddaaccaabccbccbcdccdbadcbbccbadaacdcabadbdbcbacbccaccbaaadbabddabcbcbdaaabcabdaaacdbaacdccbadbbcbddadbccaadbcdccdacbbabcabdbabbacdaccddbacaaabcdccadadbacbdcbdbdbacadbccbcbadcdbbddaaacbbaacddacdbcadcbbcbabcacbaadadbccaacacadaaacbadacadbcbcaabbcadccdbcbdcaadbdaaccbadcabbaaabaadabdcdbddaabacdccbdbcbacbbbdcddccbbddadddbdcbbacdaacbcdcddcddccdccacdbbccaccdbcaacdbdccccdbacdccbadabdbddcbbdaaabcddbdddccdcdacabbdadcacdcddddababbadcacabaccdccdcdacbdcababacabadcddabbddabdcaadddaaacbabaddccddddaddabbccaabbadcadcabcbdccccddbcabcbbbcccbcddbdcbcbabcaacdcbcbabbadbabaaacdbcacbaacaaabdabbbacdadcabbdadabbbcbdaddadabadddacdccdbabbaaacaddbcccddbdabcadadaadddcadbbdcabddccaddabbdabbbddadbaacdcbcccddbbcacbbbbbbdcccdcdaacaaabccacaadaaaaccdbdadddbaccacbcaddccbccdbdadaacdbccbbdbaddadcdbcdbacdaadaccbcdddadcbbcaacdbdcdbcbccdcbccbdccadccaadadddacadbcdcacbcccbcacbabbabcacdacacdcaadbacccdaaaaabbcdbbbcadabcaadadbccbacabdddcddbddaabdacabdabaccaaaaddddcddccccacaccbbdaddddcbccbdbdbbcbcccaddbcbbabbbbccabdacabdcbbaacbdbcbdacabbccbbaababdbbaabacadbddacadddadabadccbacabdbcadcbcbcbcadacccccbdbdbcbcdabbccabcbdbbcadabcdcbcababadbbdbadaddacbcbdddaaadabbacdbabaaccdddbcbabddadcdaddabdabcbbdcdaddccbbabbcccdcacadabbcaacaadadbabadccdcbcadbcddcbaccdadadddabaacabbababdbbbaacabcacdbadcaacababcdccbdcabbbbdabaaadbbbdcdddbdccdacccaacdabdacdddcddacdbcbaacbaaaaddbbccbaadaabaaadcabcbcbbbbdcbdbacacacdcdbbdcccaabdabababdcbdbadacaadcbbbbddbccbbccadcbbdbabbbdabcdbaabddbaaddbaacabadbbbdbadcbaccccacbbcabddbbddcaadbcadacdccbbadbdccbcaabccacddbbdacdbcbdbdbabcdacdaccbdaccbcdaddccacbcccadcbbdcdddbcdadcaccdcaabcbddcbbcdcacacadbcbaadcdcabadbdddcccdadaacadacbdadcdbbdcaccbdcbaddcabbcbccbbcadccbcadcabdcccbdcbcdadbcbabdbcbccdbabaddcdbdcccdcddbabcacbdcbabbadabdbccdcccdddcbbdcdaadcbbdadbddaadadacddadcaddbbacbdaddbdbbbdcbadbcbaacdaabbabbdbbacdcccddbacdbccbdbadabccdabcdcccbdabbaddddcacadaadacbbcddbddddadadacbbdabbdbdacccbbdcdadabadbdadbdadbcbbdacdcbddadddaacacabdaaacbbdacaddcccdabccccbaaadaacdbacdccddddcbdbccdbaacccbaaddbddbaaaaccdacddaccbdbacaaabbbccdaacdacbaabcaacaddccddbbaadbbadbadbbabdbccbadbcbdbbbabddbbbabdbbccdaabacaccaacaabbaabdcabcdbbdacbbbdcadbdbadaccdaacbccbbdbbdbbbccabdccdbdacbaadcadaacbcdabbadcacdddccccacdddabbacdaddbcddadbddabccddcacbbcdabcaddbadcbcbdabccccdbdaacaadbdacaaadccbbcbdacccddbcdaadcdaabdddadbcbdaabaadadbadbaddcdacdadcbcabbacaabacbbcdaccacbdcdbcadcdbbcbdccbcddbaddaacddcdaacdaabaddaaabddcbbdddbccbabdcaddbacacdddbaadacaabbadbbacabccbbaaadccbcbaaababcdcdbdbcdbcbadcbcacddabaccccaaaddbbcabbdcabaacbbbcdacabaaadbcbdbbddbcbdcbaabcbbbbcbacadbacabadadcbaaaccbddbaaacbbabcdbcccccacccabbbbbaaddcbdddbcdaaccadddbadbdbccbbbbcdacdddadaadacdbddbaaccaddbadaaccbcacabcbcbcbddddaacbbbcccadbdccdbadadcadcbbccddbaddcabccabacbdcddbdccbdbbbbbacadbaadabdabadacacbbbbccccdcadacbbbdccbdadbbdcccaababdbcdbccccddddadccacabadabadcbabdaddabdbccbcadacabacbbaccdbdaacdcaccabbbabdddaddbcbbbddaccdddbdbdcabbdcddbdccbcbbadadbabbddbbbaddccbadadacbbcbdababdacadbbdccacbbbaadacbccbcdddcbcbabdbbbaabbbbabbaaccabddabbcbbcdadbdbdaaaacbcabcccccbddababccbbcaccbbbbdacbbadadbadbabdbcaadbbcadcadcbcddbcdccaabbdbbcadddaacaccbbcadcdbadcdbddbcbbcaccbaacbddacdacccbcdbbdcddaacadccbdbaaacdaaacdbcdbdbcaaaaaaccaccacdacbccbcacbaabdddcbdbbadabbcddbdcdbbbdbadbdbbcdabddacbaaddaabaddbdddbccbddadbccccbcddadabbbbbcadadbdcaddbacdbdcabaaaaacccdccbddaabbbbbccbbdbdcaacbddacaacdddbbcdddbdadadbcaaabdbadadddcabaddcdcadddabcbadbbccbccbbbcaddbcdaacadaadbcbdcacbbbdcdcdbbddbdcabadcaaddcadadadabbbcadbcbddbcbabbcaadbabaadaaadcddcdcbdbcacddcdabcbacdddcbbaaacadacdcaacbdaaadbdbadbddaaddadbbbbaddbdbcbbaadaabdbcdcdbddcabbbdabcaddbcbbbcddddacaccddaabccddccddbccddccabddabdcdabdaaabdbddcbadacdadbadbadabddabbdcbdaacccababccdadbdaacdcabcbdcbabdabadbadbdacccdcabcdaaabccadacbabddcdadccdcaabdbbbacdbaabddabbaaccbaaadacaccccbdbdbaccbdddacadbbdccdcdbdbcacbbabadbbbababbbbccccdacdacdbabcbacbcaaaddbcacabababacabdacbabdcababcbccdddabdabaddaaaaaadbaaccaadabcccdcaccdaacbbccadabcbcbadbbcddbbccdcabddcbbaabaacbdaccdcbdbbbdcabdcbaaccabbcddbbabbdcbcbbdbaabcbcdddbdcddcaadabdabdabbcddcdbccddbcadacbdccbbdbbdcdcabddcadccdcabcbacaacbcdadcdaabcbdcadcdbaabbdacbadbcbccabaaaccaabbcdcdaacadacccaaccaadddbdddbbcabdddbccbacadacdabbaadcabcaaadaddccdbabacccaccccccdbbdacccabdcbcdbddadadcbdbbbdbdccadadacccadbaccaaccdccaddbbacababcbccbcbbbdddabcddbccccccbcabbbbdccaaaaabaccbacadcabccdcdbaaaaddcadccaadaddbcadabccbdcadabadaddabaabcdcacaddabaabcdcabaccbccdbbbbcbaacdbcbcabcacaddacbdcabcdcccabdcdbbdcaabcbccdcbccbdddbcacccaaccdbddabaaacadadbbaadcbdaacabccaacdbcaadccacbadcbbdabdababcadbcdbacbbcbaabadadadbabadbbadabdacddaaddddbabbcbadcbbaddcdabcccdbbbbadbaacaccaddbcbacabbcaadadcaccccaabddcccdbabdaacbabbdbabdbdaddbcdaabdaaddbbacbcbbdbbacbaaabcabbbadaaaccddccdbdcddcabbcaaaacaddcbcaabcccaccadbcbcbbbbacbbaddbacddcadddbdccccaaaabbacdddcddaccbacaadccddacbdaadaacabcabddbbbbacbcdbdabdaddbcacbcbcadacbacddacdadcddcadabbdddccaaadacbadbcdaccbcacbadabccabdbacadcbdbdbbdbcaabacadaccaabacbbdaddcbdadcadddbaadadaabdabcbcadddcaddcddbbdbdcadcabaaddadcabbabbdabdbadabdabdbabbdaabcbabaddcccdddbcbdccbbccacaaabcaadadaabbdbddbbaacbdcadabbbcaabdcbabacbccbcbacaaabbcbadddaadcbdbacdddbaddbbccccbbabdcbbdaabbcdbcccdbcbaccdadbbbdabbabdcdbcddbaddaddbcdbcbcbcdcdadcababcdbccacbcdcbcaadcbdaddcccbcadbdacaddbacbccacdbdbacaaccdcaacacbaccabdbacaaaaaacbcabcccccbcacdaadabacadcabdcabaddacbcadababbbcbbbabbcbccdaabacbaccaaaccadbaccbcabbaddbccddcabbcdabadbacbabdddabcadddbddbaccbdbcabccbbccacdadbadacbaadaaddbaddabccdcaacccbdcddcbbadccccdccbcadbdbbaaccbaaaaaabbdccdabcaccbcbaabbaaacaccaadbbbabaacddccbcddabddbbaabddacdbccacaabbbdccdbbaabcbaddaacaabccdbcabdbcbcadacdbdcbbcdabddbdbbccddccadbabbacbdbddaddcbdbdcacbababccaaadbbbaccaadbdbcbdadabbcccdbdcabcbcdaccbbbabbbabaabdbbbadbacdcdbabbccddcadaacbabadbcdacccaddadaadbcabccaaccbcccbcbdabdbddbdbdaacacccaacaacddadccabacdaaacbbdbdacddbdcbcacdcddcccdccadbcabaccdaacdadbaacccbbccadcbbdabbacbbcbcabbdcbabbdcbccbcbabbacacdddabadaaaaabaadcbcacdccdcbbbcbccabcaabbabaabaccdccdbcaacbbadcbadbaabbaccddabbbdadadddbccbbcabacbbbcdcddddaabdbbddbaaacdcabdcbbcabbdccacbdbadcacaadddbbdaaabbadcdbbdbbcbaccdbdacccaaccaaaccddcbbbaabacadbddacadbadacaadcaacddacbccadbccdcaaacdacdadbaaabaccbbddddabbbccbbbacdabbabbdddcadddbccbbccaabdbddccababbbaaccddbdbaccdbbbbbdcdadcaacadacbdaaddcaacabdadbcaadcbdabcbdbdbbdaddddbbadbbababdddaabaccabbacadddabcbaddcdcadadaccbdabaaaddcccacbbcdbadddbccbabadaaabbdcbcaacacddacddaadbccadbcbddbbcdccaaddbbabcbcdccadbadcabbdbcacadcbcaadccdcdbdcdaacdbacbdbdbdacacdacaadaadaaddbdbbdaacdddcccbcbdccacdbccdadbbbcdbcdcbaaacbacdaaaadcabcccdacbbaaccddbadbadabbbdcdbaabadbbcbabdcbaacdcaabdbdddbccbbdcdcdbdcddbdaccddddcabadcdbdcbcdddbbbdadbbbdabbbadabcccbcdbbbdbaadbcabbcbacdbccdbdacacdbcbcadbcdcdababacabbcacbbddbaaadaaadadbaddbadbbcdcccabbdddbaabaddcaddccbbbccbababcaccdaabacbbabadbcbddcddbadcccbabcacadddaaaaacacccaabaaaabdbdbcaaaccbbcaaababdcaabdcbcbdadadbcddbdabcdcacccbadbabdaccaaddddaacbacbcdacddacadbdbabdabdbcaacabaaddbcbdcaabadbadabcdbbcbacddcabdcbcccbdaddaadbdadadcdbbbbdabaccacabdcabcdcdbdccbbbcdcabcbbbcbadabdcabcdcacbaddbaabbbcddaabaccccdacdcabbbadbcadadcbbbbcabcbbabbdcbadaccbaadcbcbdaddababbbdbbabcdadacaacdddabbcbbbababbdbbadaaaaaccabadcccdddcacdcdabbcaccaabdddccdcbbddcbdbacacccbcacbcccbdccdaccdaabadbbccbabdacbbccccdacdbccaddaaddbbadbaccdddbcdabdcaaabacaddacccabcdcdbddabbaadacbabbbbaaaddcbbcbcaaabaddadbdcccbdabdadccaadcbadbdbabcbdabcbcacbbbdcabaacabaddabccadabacdbddaaabddbdbdaacacabacbdcccbdccaabcdcddacdddcdbbdadbadcaaadaaabbdbcbdaadacadbaddbacbbddcdbdcbcbacacbcaddbdbcbdcaabdadbcdccadddbcdbdacdabaacdbbadbccccbabdadbddaaadadddaadbddacbaadddaccbdddadbcdcdbaacdcacbbdbcdcbbdaaabcabaccbdbbaadbacbbbacbbcadaccadccbabcdcabdbaadaabbcdadbadcaaabdcbcdbcadabbadbcdcddabdadaabbaaddddccdbaddacddbbcabcabbbaaddbcddcaaabdcdcdbccbaaaabdcacaaccbbbcaabdabbabadcaabadabaadddabcacdbddbcaacabcabbabccdadcddbbcdaddcbcbccabcbaacbcabcccbaaacadacadbbbddccbadbacbccdadbbacbcbbdbdadcadbdcddcdccaaadadbcbdcaabdbdabdcbacdcbdcddcbbbdcdccadadbccdbbbbdbdbbdaccbbabcbbbbdddcdbadbadcbbdbabbadcaadcdaabbdddccaabaadbacccdabbddacbacdbddabaadaaabbcbabacbaccbdaccabaadddbccdbdccddddddadcabcbaabccaadbbbcdabadcabbccaabbabdbbccdcbabcaababbbbacababbaaabacddaabbdbbabdcbcdcbadcacbcdabdbbaccaaabbaabaababccbcacbbbdcabbacddaacbbaabadadbcddbadcaaadcaddadcabbbbdbddcdadcababbacbbdabcbaddbaaaddccabcaccdababdbbbdccbdbacbabbbaaaacbbcdbbcaddbabdaddddcbabaacacbdadbadcaddbbabbdbdcccababcbccbadacdadacccdcddbdbdbdcdabcddcaccaaaadcbdaaacbbabadccbbaadbdbcbaadcdbaaacbcaccbbdbcbaabbcdacddadccdadacabcbcadddbcbdadbdabbdadadaadcabababdcacdbccdbbacddaadcadbabacaaddbdcdababdcdbaabcddaadababcaaddcddcdcadcdbbdcaccdababaadbccdcacaaaadccaaabbbcbaddddcdbccabccdcabbcbcbaddccbacbacacdababaadbaabdcaaacdbccbdbaddaadaaabacdcccbbaaccbdcdcbdbccbdacbdbcdbdacbacaadbcdddabcdddbcacbdadddcadacbcccaaadadaabbcdcabbcadacbddcbbaaadcaccbdacadbbdadbadddbcdacadbcbaaccdccdabccdacacaddbbcdccabadacdbbaaabbdababbcabcaaccaddddabcddbdcbddabbbdaccdacdaccdcaccabdccadbbaacccaadbdddcccaaaabdacabacacdacabccbddbcbacadacddccdcddacbabdccdcbcddacadddaccabcbcacaccbdbaaddbcbbcdabbcdbabbcbbcabcdccbbaacccadbcacdaccdddcbbccacbacabcbaaccbdbacabaddabaadcacdacaabbabadbabdddcadaabdbbdbdbdbdcabaccbabacccabbbdddcacaccaaabaccddadcdccabbbddcaadcdbbdcbabdcdddadddcccacbabbadcbdaabcacddababaccbbbdbdadbcbabcbdabbdadbdcdccbbccdacabbdbaaacbcbacccdababbddabdbbcaaaabadbadccbbdbbcacbdadcbadddccabdbdcbacbcacdbaddacccaaadbccaaacdcdabdbaabdbdddbbcbadccdacadabdbcdccbdbaadddbcbcbadacaccddddcaabdaddbcccdccadcadcbcabadcabaadbdbcaddabadbdbcddabbdddbaccbadbcaacadbccdacccaaaadaacaaadccbccbcacdadcaaadaccdcbddcdbbaacaaabadbadadbacacabbdddcaaaccdaaabaabdbcdacbbdcdbccdbddacbcdbcacababbdcbbbdccadabccaaddbadaacabbccdaacccabcabccdbaccaccaadadbaaddcccacddddaabbdbddbdcadabcdbbacbddbadccdbcbadbabddbdadadcbdacabcdacdbaaadacaacbdbbcccdcbbaacabcbcacddcbdcbcdcbcdcbdcaccbbcbdbcdaabaadbbdaabaccccdddadabdbadbcbbabbcadcaabbddbbcbddbbbaaaccbccaddabdcddcbdabbddbbadcccabbadcdcbbacabbcacdddbbdadacdcdbcacaccdaddccccccacaacabdacdbaacabbdabbbdcaabdadccdbccaaccabaacbdaabdcacccbcdbdbddbbadbcdcdbbddcdabdccaadabbbdbccbbcaabddbadacbbcdbabcacdaadbaddbdbcddaaacabaccadadbabccbcccadaabbbbbadcacabccbdbbcdcbbdccbdaadbcccdcdbadcddcdbdacacdabcbbcdacdacccccbdbddcdadbaaccaacabdadcddcacbdbccbbcbbbccbaabbcbdbdbacdccbcdccbbadbdadabadbabccbbbadaaaadaabddabbbadcaaccaadacbdcbbadbbdddbaddacbbddbdbdbabdacaadbbbbdadbccadddadbcbbdbbaccbbdacaadbacaccadcaadbdbcbdadabcaaadabbadbbaabacacccbbccaddadcbbabcacabdcdabccccaddabdcdddcdddcadaabbaaddadacaacabcddcaadccadaacabbccccdcdcaccdaddbdcbdbcdbbcbcccbbacccabbbabaabcadacacdccbddabddcdbcbacabdbadcddccdcacdadcdbaddcaabdadbddbdabaaacbbccdabccccadddbacbacdbacbcdabdabdbbcccaabcbabbababcadaaddcaabbcbabddababbbaccbcddadbacabdadacddbdbcbccacbbcaadbadcbbaaaccdacbdcddacbbddbcdadbccbcbbbbbabcbacbaaddbabdbdacadabdbdacaccaddbcabbabdbbaabaadbbaaadadbdddbddacaacadcadbbdcaadbbbdadccdcdbacaaadbdcacdcbbbcadcacddcddbaaddccdcdccdbbbbbbabcdcadbdcaddddacdbdbcccddadcadacccdaabadcddaddacdcbacaccccbdcbdbddbaccaccaccccdacbaacbacadbbcccbaabdadcaacdbddbcaaaabbbadbdbdbbabbbbcdddbdcbadbdddaaacbaadaabbadcdcadccbdbbbbdacbcadbccccdcddaadcddaadabadbcbbcaacbaacbccdcdddbcdddadbccdaabcaabadbaadddbcdddbbabbbcddacbaaacbcbacbabdcadbbdddcbabdbdbbbdbadcdabbccdbbbdddaabddabbadcaadbccdbdcabbacaddacbdcccabdcdbcbdcaadcbaadcacdccddbaaddbbbacbdcabacbbbddaccabaabbabbcbbbacccabdadcaaccbdabcccdacddbbbdcaaadcdaaddaaabcbbbdadadcdbdadadbacbabbabbcdcddcddbdcadacdbdabcbbcadcddbdbccaccddcdacadcaababdbdabcbdaabdaadcdcbabcdbccaacacdaadbacbdcabbdccbaadbdadaaccbbdaccbbbcacaccbbdbdcdbddbcdbbccdaddccdbaacccbbdbaabccdaccabcbaacdcbccbdcbcdcaabccbbaacacaaabcddcbcccdaabbaddbabddaadbbbddaaacadabcbcbbacdcccbddabcabdcaadabaaccaacddbabdacabcddadabcacbcbabacccdacabcbadbccccddccacdbdbccdbcdcbaaddadcbadabbcdbacaabcccdbacbcbbaaacdccbababcaaddaadcdaccdddbaacacccccbdabcdbabbbcdacabdbbbabdcbcdaabbdbbbdaddccbacdbdbbadcbaadabbabaddcbccdbcdbdacdadddbccabccccdcabaabdbbbddcacaccbcadccacabbbdcabcbcbddccaacadbadddadbcbdbbaacbcbacbbcbbdbbaacbabcdbddabadcaddbdadaabaabbccaaabccbbcddbcdbaabbabdaadabddacbadbcabbacbbbaabcbcdacabddbbcdbddbbdbadaadccadcbcbdbcdacbabcbcccacbbdbbcbcaadbcbdbdabdbdaccccbabccbddcdccbbadbdacdacbcdbdccdccadaccadaacdaccdbddaabacadcadaddabddbabdccaadaadaaacdacaddbcccddadadabbbbcbcccccadbacaacddbabcccabdabbcabccdbbdcddccacbaccabcacdbacdcabddbdacdcbdcabcccbddaaacbcdabaacbdbbbadbbcbcdbdbccdbaccabcbbbcbbadcbbcccacddbbbacbdcbbacdacbbcddacdaddddbddcdaababdbbdacdddcbaabadddbccbbccddbbcadbbccdacbdcbcbbcdccacbdddddbdbdaaadddccbbabbbadadcbbaababadaabdababdcccbdacddbbaccccbbddacdacabddacbdabccbaaacadadbadcdaccdcaddcdaacaabccbaddcaaabbcbadbbbccabcddddbbabcdbbdbabdbbdcaddbcdaacccdadaccacbdadbbccdcdbbddddbabdbadbadbdbdccbbdbabbabcdcbcdacabadabdbddccdbcddddadbbcaddadbcaacbaaccdabccbddcdadabcbddaacabbccacbcacbdbdccccacacbcdadabcdcccdccbccaaddcaaabaabaccbcbccbadacbbcbadccaccbcddbcdbdabdcadddaaccacbcadbadddcadbdcdddbaccabadbcadbbaacdddabbaaadcdcdaacaddadaddbccbdcdcdccacdbbbbdabcbcdcadbddacccdcacbcdcdadbbcdbdaacaaabacbdcdcaadbdbadacbbddaadcadbcdcbadbacadbdcccbdaaddaddcacbacccaadddcbbdbcddaabacccabaddbbbdbacbcabaddcbcacbdcccabcdccdbdcaccccbbccbbbacbdcbcadbdbacaddddbcacbadacadcdacaadcddabccacacddbabaaaacadadbbaabcdbaabdcabdcbbbdacbbcaabacdabcbacadbcbddacddbccdcbdbdabbbdddadddabcdbaabadcbdacbabbdadaccbaadcaddbccacadddccacdbabadcbccbccacaaababcbabbcdaccdccbadabcbacdcbaabaaabccbaadaabcbaabcdadaddbdcdccaddcabdbccababcdaccbbaccbcdbcadadcdcadbdbcabcdacbdbbcbbdbabbccaddabadddadaccbdcadcdcbbdaabbbdbbcdaaabaabadbabdabadadcbbababbbdcddcdbdcbdccadbbbbabdbaabbccbbddadccabacdccacbcdabdbdcaabccdcadcaddbbddcdddbacddbaabadabbbcddbcdcaccbcbcabdccddbcaacddcadabaadadbdbdcdbdcbccddcacbbcbccbbbdddbddccaaabdbccccdddddcadcabbbbcccdbdcacbcabdbdddbaadbbcadccacdbacdccacccdbabcaacdaacdbaabddcbabccababcdbcabccabcdbacbbbdaababbcdacdccaadbdbbabaadddcbddccdcadcbacbabbbdccacdbbddaaddcbbaacdabbccabdccdaaacbadadbaaabcabcbacbbaacdbcbcadbcdbbdbdaccadbabbcabaacababcbaadcaaddcbaaddababacabdaadbabccababacdcadbcaaacbadbbdccccdcbdacbadcddacadbcbbdcbcddbabbaccbbddddabdcdadadadbabcdcbacbaddcadbdddacabbaddbdbbadbdbbbdaabcdaddcdbbbcdadbbaccaacbadbdbdcbacaabdadabcccdaccbabacaaaaccacbacdaaddaacccdcdcbabbbabcabcabaddbacdccababcbdcbcaaddbaaddbdccdbbcbdabcdcddadcdbcaabcbbaccaadaaddcaacdacbacbcccdaabcaccccdbaadbadbaaaadacdabdcacdccaadccbdabbbadbcccdddaccbdcabaacabaacacccbadcdbdbabcbbbbbcbdcdabbabcdbddbacbababbdcadddbaacbccbddcaadbdcadcdabdbdbcbcbdaacadcaacbdddabbadcbbaccdaaddbcbbbdaaadddaaddcbbdadbcdccdbcdcdbccccbcccbdbbabcadbccccddcdbcbadacdaabdcdbabcbacacbccaaddbbbcacbaabcabbcaaaabcdabadbbcdbcdcabdbadbcbccbdaddacabdcbcdacdabddacabaccbbdcadbcaaddbbccadcaccbcaacbadcabcacdbcbadddaaaccabbddbddbaccbdbccbcaccbbadacccdbdaadbadbcacdcaabcbddcddbccaccdacbbbdbcdbcdbdcdccbcbdbdccbacaadbbbabdbccdbbdcbadacadadbaadadaccacdcdccdccbdabcdbcadabbdccbabadcbbcabdbdbbbbdaabcdddbaaaaddddbacbcbcddcdcadbaaccabbbbcdaccdccadbbccbbcaabbbcaaabddcaddccaadbcacacbcadababccdbbdcaddbbbcdbcbcddcaababddcadbcdabccdbadccacdcbbbadbcbacbddcdbbbcdaacaabbccadccbabdbdabbdbabcacacccddbacbccdabaadddcbaddaaaaacbbadbbbbcccdcddacbaddbdddcdccaddbdddddaacdbdbbbcaccacbccaaabcdacabcccaaaddbcaabacabcdabdacdabadbccbbcacabdcbcbaccdbabaabbbcdaadbdbdacbadcadccacaccdbaabdbcdcbdddbadccabbcddbcdabcacdddccadacbcdbbdabdadbcdaccdbadadcdaadcbcadadcabccbdbcacdbccbaaccccbcccdcaacbcbdcbcadacdcbdacbdcabdcbcdaaadacdbbcabdaddabcddbbcbdbccbacadbbbddbdaaccacbacacaabcdbbcabaddbccddcaddabbcddbccddbcbbbacbcdcdccddadcdacbcdbcbdcabdaabcabdddcbaaadabbdbcccddcbbcdbbcacbcdcaaddcabdbcddddcdddddbbcbbbacacaaadccababcacdabdabbbbbbdbdcdbcbbbbccbddaaabddddcbacaacbadacacbcbbddddbbbdaccdcdadacadacdabbbbcaabcdcabcbdcbcbababdbdacdcbbcacbbbdcdbcacbdcdbbbdcacdacbbacbbbbacdabbcddbbddabadadbbaccccaadcbcbdddaacbadaacabdacadaacddbdccdaabddaabbbcddbdcbdbbcdacddccdddbcaaccadbbabcbcdcdddaaadcdabdadcbbdaabacabcdacdcaabaacdccbbdbbdbaadddbdcbadbcbcbcdccbcabcbaadcdcdbaaacbdcdcbbaabbcabbcabdbbdacaabcbbcabaccaccccadbbbacbabbaacccbbcbccccddccabbdccbccbabadcdcaddacaacddcacddaabddabaaacacdbbacabddaadaaadcacdabcabdcbaabdacaabddbddbdbccadddbadcbddcccaaccbdbadbbbdcbbbdbbdadccbbcaabcccdcbbaadaacaabdddbccccbdabccccabcbbcccddcdbbaccdadcdddcdbdbbdacbccacaaadbdbadbbcabcdaaaaadaaabbbddaaaadbcdccadcdddcbcbbcbcbcdbddbaddbbadbbbdcbddaabcddbbadcaddbcadbcddbbdadcdcbaabbdbadddcdddbbdccdbddacddbdccdbacdabbbccdcaacccbbbadadbdbbccabdadbacbacaacdaaaaddadbdbcaabaacadbacbaaddcdcaacaddbbaccaddbdabbbabccaadcaabadadcabcabbabcdddabdadbbdbdbaddadacccdbbbacbdbabbaddccaabcbbdacaacacbcdcdddabdbcacddaabbcbdcacccdcdabdadacaadabbcbdbccaabacbaabaaabadddcbbacbaddacbabdcbdcbcddabcabbbadccabdbdbdcbdbdbcabcabdcbcbcadacbcbbacaccdbdddbddbddbadcbccccabbddababbbcbaabbbcadcbccbadcacacbbddcddbcddbdcabdcccdacddaacacdcdcdaaabababaabdbcaccbdacddbaccbadadaadcccccbdbbbbbcaabaccccbcbcabaaaababaddbbbddddbbcabbcbdabbadcdaacaddaccadadcdacbddbbcacccbcccdcaddcbdcddbbbaabcaababaddbdcabbaacaabbdbdbabbcbbabbbcdcbbddabbaccabaaddbcbadaaccbcbaccbacbbdbdbcbcadcbddcbbcdbbaccabbaaacbbbbccdddcbacaacccabccddcaaddacddccccbcaaccdababadaaaacdcabaadcddccccccacddadbbbcbdcdabddbbadabcdcacdadbdbcdcababbabdabbdcadcdbddcdcababdddbadaacbacaadcacbbccdbbcdcdcbcaadbadcaaddaabaadccaadccbdbdcaadbddadacaacbdbabcbacdbcabadccabaddcbaaccbcacdbcdbabdabadadbbcbcddcccbcdcddacdddbcaccddcbabddcdaacbddcdccdcaddbbabbddcabacbdcbdbddaadacbbdcbaabacdbcdcbdccccadcddabbdbabdbdcccdbbddcdddbbacadbcbbacaccdbbaaaddbddabdaaccddddddbbacaaccccddcaadcbbddbadccbbacaddcdcbdcbbcadabbccbcacbbadbcbcabcbdbabdbabbbabcdacbdcddddccbdcadbccbbcadcccbbccdadadabcbbdccabdcddbcabcdcacdcdddbdcbacbacaadcaadccdbcbcabddccbbddcabbbbdbaabdaddbbbcaadddbccaadcaacdbacccaacccabdccbbbcbabadbbdaccbbbadbbcacccdcbbabcaadadadacdcdcaacbcdcbcaabdddadbdadbccbdbcbdcdbabbbbbcdcacdddababbdbaadddbbddbcbcaadbcadcaddabbbabddddcacaadbbcabcdddabcbbaddaabdaaaddadadbbdabacdbbcaaadbabacdaacddcbcdbabbabdbdaaaacadbcadbcbddbcaddabccccbcbcbcdacddadcddbddabadddabcdcdadaadadacdadbcaadcccbacadccbacbddbddcccbacbcabcccacabddbbaddbaccdbbcaabdbdddbcbddccbcccddcbadcbdbabdcccacbcbababdabbcbddadcdbcbaccddadadcbbbbcadaabbcacbdbddaddddaccbccbdcabdacbbaaacddcacadcbcbaadbaaccbdbdacbdbdcaaccdbcdbdbacaaadacbcacadcbbadacadadacaadadbddabbadaabcbadddbcbbcdbacdbccddbacdbdacdcaccdddbbabbbcbbdccabaaccbbdacdcbdcbdddaacdaccbbdbbaadadcdbcbdccdcbbdcbacdbcbbadcdcddaacdadbdabadaddacddadccbadbdbdbcdbaaadaacdacaccbdaadcdcacaabdcbdbadddcbadcddbccdccbcccbbccddbbacdaaacccbadadccabdcacaabcdcbbccacacdcbadddacccaacbbbadcbccdcdcdccbcacbbbbcccabaaaabccbccdccbbbbccaccacacdababadddaddbbdaaaccadadddababbddabcbbdabaccadadcabbbbacacbcddadadabcaabbcbddcbcbddcccacddccddcacccabbbcaaccbbabacbcaaabaababcbdbbbddacdbcadddccbddddabccbabcaacdcdbcccacbcacbbabbbdbdcbabdcccbbaddccabddcccabbdacaccacacaaabbaacccadadbaccbdbcbaadbcdabdcbbddabcbdcadccddaccaacabbcccacdaaddbdabaabaaccbaaaddabbaaaaadabbdbdddbcabdadbbcccaaabbabacbcadabdbbdababddaddaaacdbbdbaadabbaddcbabcbaccbbcdadcbcbdcccddaadbdbaccdcacacbddbdcccadcdccaadcdbcaabbabcbbabaaadbcdcaddcabddcaababcabbbcbbabaabddacbdacadcbbabcaabcdbacbccbcadcabaadbcddcadacabcbcadcaaadbbccdbcbbbdbaadacacbacdaabaabcadbddcaabdadbbccddacbddadaadabadaabcdbbdcdbdadadbabddabcdadacaabddbbcbabbbadbccbaacdbcbbcabdabbbdcbbdacdbcddbbaadbacccaaabdaabcbabdcccbdccddcccdadadddaaccbbaaaacdbcdcdccdddbabccbbbddddaababbdbdbabbabadabdaabddcbaacbccbabaacbcdabcacdbdacdcdacbbacabcdcdbbdcaaacdadbabdbacdababbadccdaccbdbdccdacacacacabbacccabcddcaddccbccbbdccdaaadbabbdccdaccbcbbbccddcbbdcababadadabdbdcaacdcbaaaadabbbddaabdcdbbcadabbbabacabaaacabccbcaadbabbccddbacdabdddddccabdddcdaaaabbbdacdbccddabbdddcbccaddddbcbdccdadccbacddbbabbbddccdbdaadddadadcbcadbdcddbcbacdcabddbdadbbcbabddbaccbdcdbdccdbadaaddbccdddccbbbbbddadcdcdbadaaabbdbbccbadddbdcbbbbdbcdbdccababaacbcacabbbbdccccabadcccbcddccbbdddbccbaadccacdcababacbddccbcbacaaccadadacdadbbcddaddaccaacbdcabaabdddbbbacaddabaadbacbccaabadccdcaaaababdcddadcabababbcaaaaabaabacdbbcbdbcbacaacaccbabcabcdbdbbacacbbbabbacdaadadcbdbcaaabcccddcdbaaacaaccacdadccddabccbbdbcdbcddcddadcadaaabcaddacddcbddcbaccadcdbbabcccbbbadacdaabcaacddbdacacbbddbaaabbcbbbcbdadbdaadcdcdbbcdbbbbccddaacbdcdacbdccbacacaacdcccccbcbddbdbbacabddbdcacbcdbaccaddcdbbabccabbacdbbdabbbdabcaacbaadabbcbdbbddbaababbabbbcbcdcccdaabbcabbddddadccaddabbcaccacdcbbbdabdbcbabdbaaabbdcbcccaaaabacbadabbacddadbcbdbbccccccabcbbddcbbbbcbcaccbbcdcddbdcacdcabbcdccbcabcdbacabbaaccbaccdaddabdcbcadbddbcbabbdadbdabbdbdcabadbcbadadbcbddacdacadbdabdcaadadccccaddacbcdaadddaacaabbccabcdaddacccddaddacadbdbdcbcccabcbaaddbbcbccadbddbbbddccdaabdaccacbbddbbcacbbbbaaccbbdabcccdccaccadbabcadbbcdaabcdbaabadbaccdcbbcaddbbcaadabbbaaacaaacbccbbbaccabbddccacaddccddaabaaccccbacddbdaaacdcddbbdabbbcaccccdcaacddbbbaacabbcdbdadcddbbabacaacbacdbdaabbcaaabacadcbbadacbacdaaacbbbabcbdaabbccdccdadbcbddccaaccbcdabddcadcdddccbbdacbcaccddbacdbbadcabccdbbcbadabbcbaacadaddddccdcddcddcbbabcbabbcdaaadcadccaacaddbcccdbabacbccdddaccbabdacdcbbccbcccbaaadcddadcccbadddacdaddbdcddabddbcdddccbdcaadddabcddddadabadddbaadcbbadccbbacdbcacbcdddabcbadadcddababcadcbbccdabdbbbdbdbacacccabdaadacabbbcbbcaacbbccadadcacdbadccdadbcdcdbbacbccbcbacadbcdcabaddacbdbacddbcbdadcaddaaddbadaddcacccdbbbacccbddacdbabdbaccddbcbbcaabccbaaccbbbbccacdcddbdbcddbbacbcbadbbacccaaccbbadccadccbddbcadbbbddcadaccbbbabaccbbcacabdccdddbaacaddaabdbdcadadbdbdddaaccdabaabdbabdcbbdcdbcacbabdacbcacdbdbcabdcbbddabdcabdacbaccdcbacdccccadddbcdbdccdcbbddacaddabcdbdcdcabcaabbbababdababcdbccdddabadabcbdcbbbbacaabaddbddbdbdcbcabadbaadddbcbbdcddbdcddbbaaaaacddcbdacddabcdcdcdbadcacaadbdbcabbbccdadbdaddcdcdaccaadcbdbbaccabbcccdddbbdacbdbdaacdadcabbabbbbdcadaccdaabbcbabbcdbbcbdbbaaddaacaaddbaababcbbbbaccddadcccbcaacadbabbdaaadcaaaccbbaacdacbcdcbdcbbcddcbdcaddbcbdcbdcaadadcbcbaddaabbcacbabdcbcdaabbdbdbbcaaacbbbcdaaadbdacabcdaccbbdccbadcccaabdcbcdcbdccdadbacbbacdacbaaadcacdcdbbcaccbbbbcacbcbbbaddbccadbddddbacbbaacdbcdddbddaadccacdcacdaacbbcddcadcbaacdbadbbcacabcccbbdcacbcbdabdacaadacccccbadaccdbccccdbcccbdcddcccadccaddbacccbdcdccccadcbdaaaadcbccbadcdabdccbdcabcdcdbcaadcdddbbdcccacacdbdbccbcbdaabbaacdacdbaadcbabbdbcdddcbdacddaaddbdcdaabdacddcbaaacbcccddddbdbdbcabccccbcaabdddcaaacaabdaabcaddccdddcbcbadaacacbacaaccacbbcaccaaccbdcabdabdbbbdbcacdaddcabddadabbbcdbddddbdbabddcdcbddddadacdadcdcbbcacdddaccdbbbaccbbdbdccaccacabaddddcacbddadaadaacacaccccbacdabccadadccdcdbdaadbbaadadadbccdcbdaddcddcdddadadacdadbcbbabccdacabdcbdadaabdcbdcabbdbcaadaaabcabdcacbaaabbcdaddabdbddaabacadccaaaadbdadaddbccaadcbdcdaaaddadddddccddbddaccabccdaabbcdcdaacbabdcdadabcdbcbdacabaabccaacdbdcabdddbbccadcaaadadbbbccbbadcddddcadcbdaaaddbabdbaacbadacccbcdbcccbdbbbbdbbdcbadacbddbdbbbcddcadaacbbdabcaacacaaadbcdaabcccadddbdcaaadcadcadbabdacbccbdcdbbabddbdaacdbdddcadaaaacddcbcccbcdabcaaadbabcccbaccbabdddacbdccdbcbdbadcdcddbdadccdbaacbacdcccbbadacbadadcadcabddaccabbcaadbcacccabccaacddddddbdddcdaccdddcdbabcaabaddaddcbcdbaccdbddcccabaadadbbcaadbbdddacdbcacdacbdbacdabaddbacdcacacabababbabacdccacdbdcbdbccdbababbbadcbdbcacabbcdaabdbbdadbddaabacbddaadabbcdcdadaacbdddacbcbcbddbbaabddcccaacaadcaaddbdabcabcacbbcadbabdbcdccbabacbcdbbbbbddbdbddddcbcdddcbdabcbdcabcdabdabddcbadcdcacadaacaaabdcaacaadcacbbcbcbadbdcdcdcadccccabbcdbdcddcdccabbbabdbbbabbdccdbdaababcaabcacababacbcbadacdacbbcccadbdbcabcbcbadbbdadcccabbdcacdadcacacddcacacbcaacdaaaacacdacaaddcbacaacdadccbcccbaaacbbdbdcddbbdaacbacbacdcccdccdddbabacdcacabccdbdbbdcbadbabddccbcbcdadcdadbaabbdbbabbbdccabbdbcdccddaccdacdaaaacadbdabcacdddbcabcbadcccdcddbaacdacaddbcaddaaabdacabaddababbbcbacacabacbdcaccbdaaacbbdcbaabccabacbdcdacdcbbadcccadaddabacccacabdcccbbabcddbcdbbcbbaacdacaddaaadcbadbacadbbccadcccadbdbddaacbacaddadbdbbabdddcbaccdccaccdabbaababcbddcdcbbaacddabcbcadcccdccdddadbccbddccdbcdabbbdbbcacadcbbaddadbdbcabbabbaaaadacdcbccbdbdbbaabdcdcadacaccbdcbcdadbcaaddbacdddbccbddbbcddcdadcaacaaccbbccdbaaababbbbbbdacacbccacdcdddbaabbdcdcddabaaacdabcbcddbdbbadcacbdddcaadcdcbcacbbddaacaddadcadcbcdaaadabadabdbaabaacbbabdddcdacdadbcdcacdbadbdbdabdabdbcbdcdadbddbcbbcddbaacbaaccdacbcbcaabdabbabcccddbadbccadaaababdcccbddbdbcddcddbaaaaaacaccdcdadccccdacadabcccadbaccdababacadbcdadcabcaccbcbbcacdcdbcbdabcdbaaccccbdcaadddccaadcaddbbbdaccbaabacbbccbaccdcddbbcacacdcadbccbbcbcbddcbabcbdddadbccccdabaccbdbabccdacabddabbaabcacbabaccccaaaddadacdaccdbcdaaacadadaababcacacaadcbdbdbdddbbcbdbabbacdcdddddbaabbcabaaddacddbcdccaaddabdcdbaacdcbcaaddbbdacdcdcdcbcacbadcaaaacdaacbbbccacdaadcaacbabdccbbaaaabacadddcdabdacdddbacaabcbdddaddccabdcacaacccbababcbcddacdaacacddbdccabaaaabbbdcacdacccbbacaabaaccabacbabcdcdaaaacadcbbacddcbcddcabdbccbcdbabacdbbaabadbddacbcacbdaadcadadddabddddcdcbabadbdbbaaaaaaccdcccdbabbccccbddbabdcdbbddcabadcaddaacbcaaddcccbbadacadaaadccbbbadcadcccabccdbacddbadbcdbcbbabacdcdbcdbbdddadbcacabcaadbaddaddabdababbddacdccaccadccacbbaadbdddaabcaccbdadcabcddcbdadabaaadcbaaaaadbbabbaadbadbadadabdabaacbbacbdcbddaaccaccdabbcbaaaccdcccbcbcbdcddbaddcdcbcadbddabcabcccabcadbbabacdbacabbcaadcccabccdadbcbaadabacbddabbcbacbbddbcddbbcbcbdadadccaccdcaddaddcababbcdbddcadadbbbbadadbaadcabdbdbbdadbddcadabcbbbbdaddacadbbdabdcbcddcbdbbdcabdcdcbbccadaabcccbdbaaccacdbbabccbcbaacbbbbcaddbaccaabbdcbbdddcaaabdabdbcadadabcaccdcbdbbbcbcbdbddcadcbacccdacbdbcccabbabaacacadadddbcaabdbcabbaabddddcccbcacddcdcdbaaccdcbcaababcbaccdbcbbcddadacdcdaccacaaddbdacdccdcacaadbcbdbbcccdcaaaacdaaaacdddbaaabcacddaababddccbcccddbadcccbbcbcbbbdadadabbdabdaacdabcdcaacadaadddccbddbacbacdbdcdaccdbcbdbabaddbbcdbccdacadcdcbccdabdcbdbaddbabcbbabdaddaadadaaadaadddcdaccdacdadacdabbddaddacdbddabaadacccbcdbdcbdbaadcdcbabbaaddbddbadcccdabddcaddbdaacbbacdcacdacbabbddaabbaccdbccbbdaacccbabadcdccbcbaccddcdbccadbccddbcccbcbbcaadbbdbacdbcaaaacbdadababbcacabacabbaaabcdbcccbdbbbdcadbdddcdadaaddcadddcacbbbbabccadcbacaabaacbcacadabbabbbacdcbbaccdddcabccddcaaccabcbbcccdbdcacdbbccbbcbbbaacdddacccddababacccdaddbcabbdabbdddcabcbabdabdbddcabadbdaccdbbcbccabdbacbcabcbccbdbddcadcacdddccbdbcadbccadcaaaddddbabccadbdddaadbcabaccabcdabcdccbcababccbbdaabacdbabbbdcacdccabdcbcddddcbcdcdccddcbdadabbcaabdadddbaacbddbddadcbbbdccdccaccddcbaacdabbbabbbcacbabdadadbcbbaaacdcadcbdbadcdccacbacabbcadadaccdacdcccacaacbdbaaccdacbcbdaaadccdbdbaabcaadadacdccddcdbcbbcacdabaccbbadbbaccdcdabcdddabccdcbcdcdabbdabbbcdcaaadacbcdcaddccdbdcbddccabaddbaccabaddbbbabbdccbdbbbdaacdabacdbdbdcddacaabccdadccaccbcbccbabbcddbadbdaaccadcadbbdcddbbcacabdccaccdcddacdadacdadbdacbcbcccacbccdbcaccdcadbcdabbbaaccaddbadacdcbccccacddcbdcdcccdbacbdbbcddddbdaadccbdbccbcdbaabbcccbbadcbdaccabdddcabbcbbaadcbaadccbcaaababcbadddccadacaaadbaaaccdbccccdcddbbdcdbcacabadacbbdaabbbdbadaddadaabcddcbaacbcabbdaacbabdadcbdcaabadccaaadabaaddbbddbaaaacbbdcabccbcdcbacacdaaaabddbbcbdaadbcbdbdacbdcccddbbbdabbdbabbabbdccacababbdbadcbdbbbacadabacbabdbbcdcdddabdbdbbddaadbabbbabcabaaadababadbdbdbccbbcdcdccddbdacbacdcaacbabbbbaaccadddccbddbabacbdbcdbdabccbadabaddbccdcbabbdaddbcaddbababcdcacbcbccabdbbadbccbbdcabaabdacdcadaabcddbbdddcdadbbddddcbababbbadadddbdacabdccabcdccadacbdcadbcddcbabbdccdacabcbdcbdcdbbaabcccbaaabbdadbbcbacbadaccdbddddddcabccbcbbbdacccdbdbbabbbdcccdbacbabbaabbcaccabdbacccdcabcabbccbcdbbbbabcabcbadddbdbdbdbacdabcddccdddccabcaacccccbbaadddcdbbccadaaabdaccadabddbcaacaacbbacacbaabaddddbabdacabcabbdabcddbbdbcbaacccaaccacbcbbabddacccccbbaaddbdacaccdbbcddddcbddbddcaddbaadaaadaacabcaccbdabcbbbbaccddabcacabddbcbbdcbddbdbbdcacabbdcbacdacaabaddbdbbaadbaddabcadcbbdaccaddacddbabddadbdbbbbabbcccabddbbabcdadcccdcbcacaccbbbbcbadadcddddcbabccdaacdccaddcadadaddbabdbbbabcbdbbdaaddbabbcdcbabbdcdbacbbcabbaaaaddcbcdbdbacaccabadabbbcdddaadbbdbdcaacddbcddcbdaddadaaadbaaaccaddbcdbcdaaccccdbbdcaaaadadacaccddccdacbbddbbdbccabdddadaddccaaccaadcbcaaccbbabdadaacaaabcdcaccdabdbabdacdcbdbdaacaccdbbacbabcaddcacddccbabbdcbaddaadcccdddcccaddaddabdbacddcaaddbaabdabdaabdcdaccddcbaabacacccbcbaaadacbbdcaacadaaaccaacdddbdabcbdbdcccabbdcbacdcddcaacbcbccccdbaddacbbcdcabdcadddabdacbbbabdacbacbacbcbddadaacccdabcdacbbbaaadcdcbbcaddbcbabadadcaabadbcccbaaadbddcbacbcbaabdaaacbbdadaacbcdbbaabdaddccdcaabcaabacbbccbbccddccbbccdaacddcccabacddcdbbbddbdaacbabaadddcabcabcdacbccbbdadcdadcaabaddbddabadcbbabbadbbcbddbddabdcdacdacccbcdcdbcabbbccbacaccabacadcbdcaddbdcacdcabbcaacddcbbccabbbbadddcaabdcccaaadbdbbbabdbdaabcdbddaababbaadaabaababdbcaccddbdaaddcaabcbdbdaabdabbaddddcadaaaaabbbbdcccdaddcbcbaadcbcbbdbbdbcaddcdcaaaddbcadddbcddbdbacdccdabacbbddaacbbdbddadaadcbdccababddcacccbcbdbcaccabaccaacbddddccadadcbadcbbddaccbdababdbbbdbacbdabbdbddaacdaaaabaadaddcdccbbdcbcbddbaccbaadaaacaddaaccabcccabbadadcbcbcdcdaccadddadbcdaaaaaacadaabbcadbbbbcccaabcaadabbbadcaaaddabacddacbccbddaaacccbbdacabbccbcbdcccadaddacabdcbdbabbddcbbcbcbabcaadbcdcbdadaaddcacccabaddccaaccdbadabdcdbbcaddadaacadcaaabbbadddddacaaacabddcaccbabadabbcdadcabdbcbcadadbbbdabadabcddacdbdbcadbaaaacbcadcbdbdcbbbcaddabaacdadbaadbcdddbdadcbbdbabdcaadbdabcbadbcacbdadbbbbbabbabbbccbaacbddbcccdaabdacadbdcddccdbbcdaaddbdccbdbdcdadaccdbcaddaccbabbacdcaaadbdcdbbdbbddbbaadcbcbabdaacabcdcbdacabdcdddaaadbaacadbbdcbbcdbbbbbbcbddbbcddccacacaaddaacbccbbaddcbcdbcdaaccdabbbcaaaacdcabcdabdcbcaabdbadbdccdccdcbbbdbbbbdbcabccdddaddcbbcddcaadabddabacabbaddccdddaabcdcadacacbdabadcabddcadcacccabbcadbbcbbbabcadabaadbcddbdddacdbbdcdacdbcccaaacdaaaacaddcbccbddbcacbccdbcabadbcdadcdbaadccbbcaddbaabdaabbccbcddddcabcbcdacdbbdddccdccacaabbdcbcbbcaabbdacdcadaadadabcbcbabbaaabadabadcccbdacaaadddddbbadbdbcdadacdddabdbbcdcdbdcccdbbacadbcdbacacdbbadbbbbaccbbaaadccdccdaadbdcdddbdbabdbcbadcaacacbbdbdbccccadabdaccdddaabccaabccbcadabbcaadcbbbaaccbaadcbdcabcadacacddbcbcabcdbcabbcbaaababcadbcddbabaddbcbbdaacbdacbadcacaccccbbabacbdbaadbaacbcbdaacbbcbdadbbdbaacdacdadddadaadabbcddbababbdaccaccaccdccabbdbbcabdadddbacbaabcacabcadbdbbddadcbdddbabbaababaabdbdddacdccbccdbcabbcdbdcbdcbbcbcccdccabcdbbacacbaabddadaddcddcbbdbdcbadabcaabbbcccccbbdddacbcaddcccbaaddcdadbadbcadcbcacabaccababbcddacaaaacddaaabdabbbbacbcddbddbaddcaaaddcbdaacadccbbbaaabadbddbadbccdadcaadcdbdccbdddaaddaaabbdccbdcbadcbbaabddccbdabcdcbdabadbbdbaadcaccccabdbbdcacdcdcbddbbdddaaccddbbbcdadcdadcdbabddcaabcaaaadcbdcdbccdabbbbdabdbaabcccccaabcccabbbcadaddcccbaddcdbadddabaaabcdcadcdaabddcaadabdbcdaccbddcdcccababadcaccabddcacbcdacbbccddaccbabaaccadaadccbcabbabdabadaccabdbcbdbcbacbaabaacdcdbcbbabaaabddaacdcdcaacabaccbbdcadaddccabdbbcdcbdcbbcaadcbbccdbbcddabdabbcbbdcbcaadcdbbbdbddabbcdbbccaccbccbdabdbabbbcccacadbdccbbdddddbdbbbcddacaaaacdadccddabadbcbbcbaabbbdccabbacdbabcacbdcbadcdbcdaddcaccbbabaababcbdaacabbabbaccaccbbdabbddddacdddcdcaaabccbbbbbacbbbbccccbabadbaddbbdccaacddbadcdbbccaadccdddbbddcdbbadbddccdcbbcdddcbabccdaadadcdccbcbacbadcdbdddccbdcadaacbdaddcbbaccbdcabccbbcbddaadcdccdbbdbadcdabcbcaabdacbacccbdddcacddaaddabbbadcbbbcadcbcddacbbadbabcabcbabcddbbcdbaadbcdbdbccdbcdbbcabcacdddcdcbaccddbadbbcaaadcbbbdadcbadbcbcbcbcaaddbdabdbcbdaabcdcdcbaddadacccbdbbdacbcddbbaddcccadbbdddbddbabddadaccbcdccbadcaababcbacbdcaccdbbdccadbdbdabbddaaacbbacaddcbcacadbcadcdcbcbcaacdbaacacadcdcabababadacbdbaadddacdbccdbacbdcaacabdcddaabaddacaacdcaaccabdbabbcadcbdaabbabcdabbccbdabcbcbadbcbcadbabcdaccbdcabccccbbdddbdabbddcdddadaaadbabdddbcabadbbcababdcacabaaacbbdacbadbddbdbcabdacacbbddaacabdcbabbbdadadcacacadbdabacdaddcddccdacabcacadadacdbddccbbdbcacbddaaaaccdbcdaaaaaabcbdbddcaabccccdcabaddbdabdcddcabccdbcdcdcabbbabaabdccbdccdbbdcccbccbccbdadbaacabcadcdbdbbcbadabddbddccdbabdbbddddcddbadbabcbdbdcacbddcdbbcdcdccabbdcdcbadacabcbcabbccdacccddbccbbdcdcdcddccddabcdccabdcbdbcdddadbabaaabcddcbaaabadacccdcbbccadccdcbdacacabcaaccbbbdbbdacaddcabaabccabbcaababbdbccdcdcadadcdbbaccacadabbcdcdcdcbdacacabababdbdcdbddccccbbcbaabaaabaadccbddccdaaaccdbbbabadcaccadbacabbcdcbbbddddaabadbcbdcbcdaabbbdaddcaddbadabaccbdbcddacbababddabcbcbddbcbbcabdcbbcaddabbbccccadcbacddcabaadaaadccaadaccccdccbcaabadaabbbccccaacdadcabbbdabbdabbccccccaaddcbddbbcbdadbddaabcdccdbbbbabadbbabdbabbccacadaaaddacdbcbddbcdabdbdccbddbaabcacdbcbabbbcdaccdbacdbbcbcdbccdaadddadadacadbabbaadabaccaaddcdbcbdccdaaabadcbabababaadcadbabdadabdbbadbaaaccacdbadacbdabdaddbcdccddcabbcaadacbcdbcdcbdabbddbddacabdddcacdabcbbadbcbccabdacbacdadabcdddaacdddaccdadcdbddccaaabbbdcdadcabdabaacadcbbbccdcdddbaaadcdcddcddbabaccdddabdbcaacdaadabadcadadbdccabccabaddaadbaadbcaddcddbcadaadbbdbddbbcdcdadbcbcacdddbbabbddbbcadddbadbdcbcdcbcbdadbacddaabdbbbbdcbaaadababaaaabdabadcbdcaadcccaddadcbaadbdcccbdcddabaccacbacabcdbbdacadaddacbacbadadbaaccaacacbdbdccacdbbdcbadaccbbbbaadaccccbcadbbdbbaadcddcdcccabacabbcdabbcdccabbcbcdddddcaccaabcadddadadcdbabdacddacdcdabdbccddbcbbddbadcaddadccbdadccddddaaddcccaddcdccddabcdaaccbaaccdccccbcccaddcdadbbaabadadbabcdbdacbadbadcabdddddcadcdadadaddcdccdbdbddddaccabbdadbdaccdabdabaddddbddddababcddcbdbadadccbcdaacdccdacabababdddccdaaccbbadcccdbaacdccddbcbdbbcaaadacbdcbbccdcadadbbcadabbccddcddccabbcbbaccaaccaccdadaccdcddacbaaddbcdcbcdbdcbaabbbabccccdbdaddcdaabddcbcbadacbbdbddadcaddabdddabcabaabacbacabcccaacccdadbcccccdacbbcdccadcddbaaaddacbccaaaabcdbbadcbdbdacddbcdcbcbabbcccdcaabaabadcdbbacbddbdddacaddacdcdacbadcdccbabdabaacccabbddadddcdacccddbbdcccdbabdaaaaabcccacacaacbcabdacbbdbdbddabbabbdddcbdcdabdcbcadbcadacabbdabcbcbccdabcccddbcabcbbddadddcdddadcbccdbdcccadbbbdbdacccbbbcbcbdcdaaadadbabadabadaaaabdcdbbbabcbcaadadbbaaccbcdacbcbbabcdabadaacacaacadacbdcbbcbbaadaaabacaabbadcbcccddcdaadabcadbcbccadaadbbaabbabdcbacdbdcadaacddaaacaaacbabddaddcbbbccbcacdbcbbcadbdcaadbadddbbbaadaaaabaaccdbcabadbcdbacdadcbdbdcdadcbaacbcaaadbbaadacdbbcdcaacadcddcccdbcbacbcdccaaccdcccbdbbbabbcaabbaccadbbcaaabcbcdcbddcabdcadbaaadaabaaaadbdcbcbcaadccddbbbbadddbcaadaadbadbdadbbcbdcdbcbcbacbcbcaaadcdddaacccabcacccdbbccbcdacdadcaadbddcbaabbabbacbccaddcdbdcdbbbadbabcdcabbddabcdaaddacccccbbccdbcabcdaaaabdadccdbdbbcacccadbcdcbbbbacabcadbabaabdccbdccdaabdabddaadddcbbacabbdddbbacddbccbdcbbcdacbccccdbdaaabcbddcaacbbbaccacbdaaaacdcaacbcccddbacbbacbddbbdaaadbbbddbdaacbabdccdacbbdbcdddabbddaabdbbabdaababacbccddbdbcababccdcadcabbcadcbacdacacaaaddbaacbbaabbccdbadaaabacdaccbacdadccdcdadadabdabdddcabbbccbbcdcbbbdcdbddaabbddbcdacbccaadbaaaccddabcdabbbccdbaaacaabdddabdabcbbabadcaddbbbbadccbabacabbbdbbdbadccdbccdaadaadadbdcdadaaddbbddcdbbddccbcacaaadbdbbaacbaddddabaadddccbabaddcacdcacdbdbacbddaabbcbbbcddbdaaadbbbbdccdaccccbdcddcabbbcacdabaababcbaabaddaacbdbcbcbbcababcdacaacacdabdbdbcdaabcaaaaccadbcdadcbcabbcccaadabdaabcdcbddadbddaccddccadcdaacbdddbaaaaadcabadacdccbdaddabababbbccbbddddacddadadcdcbbdbccbccbaccddcdbcccbbcabcbcaacccbabdbdacbcbbdbccbdabccbbadcdadbbddccdaadccadaaccbcdccabdcbddbcaabdbdbcbcbabcdbcbdddabcbdaabbcaccbdaddbbcabccdaddacdddbddabbbbadddccdbdcbdddbabcbcacbdcabacaadbcbddbcbdbcbbcbbaaabdaabbcdacabcabccacbcacadccacaadbcdbaabcabaadbbbbabcdaadcdaacddcccbbbbccaadcdaccbdcccabbadccdcbacddbcaacabadccbacbabdadbcdbacbcabddcbdadbdccbdcbabbbdaadbdcacccaaccaddadccabdccbbdddcdcdababbaddddcbbccdbbabcdcbcacddddcdccbcaabcbdbbdcbbdaabbcdddbdbdabaadbccacdbdddcaaaabbbadacaabcdbcddddbaddcaabdbccdaadcacadbadcaadcbaccdcacdbdcbacccdcbaacacccdccadbdbbccbccbcdadbbcacabcaabbcabdaddbcbadbddbbabccbdabaacbdccdabdbacbcddddccccdbcdadaddbdbbbcbbbadaadcbccbbccdacaccbdabcbbdaadccbcabbabbbacbcbacbcbcaadbcbbaccccbddbbddacbdacbacabdbabbcddcbadcaaabacbccbdcdbaadbdcdcbabbabbdaacdddcdcbaabaccdbabdbdbbadcdcdcabadbcacadcdacdbcabcbdbbbdaccccaaddaaabcabdbbbddacdcdabbbdbbcaaccbdcaaadcaddabcaccddcddcddcdccccdaacabbdcbcabaccacacacbbdbdcababbdcabccdbdbcdcbdbcdddabbbacaccddbdabbbddbccccbddbbaacdadabcacacbcbccbcbaabbdbcaddaccdcdcacbbccaccacadddcddcbcaadccdacdadddbcaaccdcadccbdcabbadcbbdbcbbcacaaccbccabddbabbbccbcbcacacdbcbacbacdbadcddbbcacaccabcdaddadcbcccbcdabbbcbacbbadcbbabdadbbaadbbdbbccadbbaabbbddbabddcbaadcadbdacddbbdbcabccccdbddddbaccadcacddaabdbabadcdbcabccddccacddabbadddcbbaadccbbbbacdccccbacaaadccaacaacaadaaddcdbbddccbadadaddbddbcacacdcaabcccacdabcaccccadaabcdcaadcdacacdadddcbdbddcbdadadddcabbbabbaacdaacacaddccccaddabaabaccbdabcbdcbdaaababadacbcaaccbddbadacaccdaadbabbccbbcdadaadaaccdbcabddcdacddcbbbbcabbabcadcabddcdacccabbdadaaaddbbaaadcbbbaacdacbbababcdabdcbcbbdadccbbbcccbcdcbacdaddcdaaaddddaadcccdbdccbddaacbadcaccbddababbcdbadccacdbadaddccbbddbacadaabcaaaadbbdaadbaacbdaacdcaacccaadabaaacbcccabdbdacaaddcddcabdddacddbaacbccaabbdcabcbdacdbdccaadbababcabccbdaaadddbccdbbbadbaaadbdaacaaabccbadabaadbbbdacacbcabacabcbbbbbdaaacbaddacacadbdaaacabcbbdbcabadddcddbacaaabaccbdbbbcadaadacbbaccdabcccdabdbccacbbbdbbcddccdbdbadccaddcdaaaccbbacacabbccdababdbdcacacbdbdcdbababbbddbcaccadbabbaabcdadbbdbccdcadbdddaddddbcccdaabaabdccddabacaaccdcaccacabbddaaabcbcbbddacacbbadcbdcaaadccdaabccaadbbdbdaabaaadcbabbaabcdacdacdccbddabaddccddbdacadaccdaddbbcacddbdddcbacbcbabdbddbabdcabccddaacdbbdacacadbbdabcddbdaacacdadbadabbaadadbcaaccaacbcbbaacabdbbdadcbcdaddacdbcdabdcbbcdbcbabdacbcdaddcdabbdabababbdcadbadcacccaabbbbdccdbadbabaaacdbabcabaddadcbadcabcccaadacbddabdbbacacbbbccdacdacdbdcddcbdccaaaacacccbcabcddbbbacbbaacabdaddddccaabddbacbcbbbdbbcbaabccbbcbccbdadcdddbbcacbccabadaccbcdbdcccacaaccaddddadbcacdccbdbdadadbacababadaccbabababbbccbccdaaacbdbcbccbdddadbabbaddbddcaabbdcdadbadcacbdacabdbcaacdbdacddcccadcdcacaccabbbadcabccaddadcccabbdddbbbadddacdddcbcaadadbbdabbaddaacccbdddaccbddddadcbdabbbdcbaddaaabddccddcbcdabddbbdbbabbaacdcdacdcccdbddcabdccaabbcddcabdbaaacdbcabcbaacbabbddbcbdcbcbcabdbaaabdacaadcddccdaabdcdcbadbccdacdabadddbdbbbdcdaabbbcccdabdddddacdbdaccabcadcbcdacaadbcacccdbdddbaadabdaacbdcabcbacbaadacaadccabacdaaaabcdaddadacaaccbcaadcbccacaaddcdbbacbabbaacadaaabbbcddaabcaacbccbbdcdcacddccaaaaadbcaabacabbaadbdcbbdbbadadaaaaaadababdddcccdbbabdacbbcbbdcaadbbabacbccdaaababbabbccdcaaaaabbdabdabbaadbcbdccdbcbabdadbcabaaccdaadccbccdadbadbcbbdbdbadbbabaaabacadbbcdaadaacccdaabaaacabcaaddcdcbbabdaabbbabdbccbcbcbbddacbdbabdbccdbdadcbcddadbaccdcbdaadbaddbcdaaaccadbccadcabddbaadbbabbccccdadbbdadaaababddbdacbaacbaacbbdbdacbccdadbcbacbbadbcabaddcadaccbdaabbcdcadcacdadddaabddadaacdcddbdcaadabbbbddcdacbbbbdbdcbabcccdbbddbdccbcbbbdbdaabdadbabdaaaaadbbbadacdcdaacbadbddaccdddcdababdddbaccddbaaadcbabbdbdcbcbacbcabcaaccdcbbdbdbbccccabcbbdcaaaddaaadabcdcbccccaacadddcaccdaabcdaaabdbbadcbaddacddcadacaacbdaadbcabacdbddcbbbdcacacdbddabdccacacaabdacdbbbbadbddbbcadabaacccaaddbacdcbdbcbdadaaddadccabacadbbdbdbdacacadbaccadbbbcbcccbccacdacdbabbccbdabbcbacdcbdbdcbcdabaaababaaaadacbababbaaabadcbabdcbabbbcbdbdcaccabccbbdaccdbbdacdacbbdbcbbccddcccbdbbbdcdadabbdadadadadaccadccbbdbabbbbbadadaccdaacdbdcbbcdcdabbbbbdbdcabcabdbcdadbabdabddcdbcdbccabdaaddaddcbdaadadccaaabddcbabcacdadaabadaccdadadabdcbcddaacbbbaaaabcbcdbacddbbbbcbdaaabdcaaddacadccdcddaabaccbaaaddccbcbdbbcbbdcbcdbaabacadbcdcbbdcbcccbbacaaccbaaabacbddaaaadbcbbcaaaabacbabaacdbaabcdccbdadbddadcbadccdbbdacaddabcaadcdcbcccadbdaabaaaabdacccbcbbbaaabdcaadaabdaaadcdadbcdccaadabbadbdcdcccacdaccdccaabcaabacbbaddcdccdadbcdaadbdbbacbbaadbbccacbdbcbbcbdabbbacddadaddcaaacdbcddaabacadabbbdbaabbccbcdcbaabbbbcaabaabdcbabaaddbccdbddcbdaaacacdddaddddcbcddddcbdbddbbbbcaddcdbdccacbaaadbadbbcdcbcacabcadbdbbbdbaaaddaabbcdbdcacdddbadabacdabacacbabdcababbcbbadcadcdaddcdcdddcbccbddadcaaaadbcacbcbdddabcdbdbabacaabbbcdcdddadadaddbabccdacadcabcbcdccddcdbdacbadcbacaaccddccbdcdcbddcbdcaaadddcdcbabcddcdbadaddabcbaccddbbbdcabbcddacadadbdcbddbbdacadaacbcacbdcdbbcbababcddbdddbbcaababdabcddaddcbbdabccacccadbcdcdadcccabcdbbbdcabdcacacbcadbadcaadbabcaabbccaaccabdcdcabcabbdcadaaccacccbddbcabcccbdaccabdcccadcdddacbcbdcdbdadbbbcababcdcccccbdbbaccdaddadbccacaacbbdbadacbcbdabacdddbcaacdcadddaadcaddbbdbadcccdaddbdccbddbdbaaacabbaacddcacadaadabbdbcadddbcbdadcdcacbbdbccddcbadcccdabaaaaadcbdbadbaaaaacdbccadcbaddacdddaabdddbcaddccacdcaabdbccabdaadcaddbbcabbcbdadadaddcbbadcacadaaccddbbdbababbcdddcccdcdcbcdadccbcdadbcdabbacbcddcbbdacdbcaddadcdabbabbccdddcbbcccabdcbcabbaaabbcacbaadbbbcddcdcdcccadbdcbbabbaabdbacbddcadbbabbbaabbcdcdccbbcddcbbbdbbcbabbdabadcbdccbbccabcbbbbbdcdcddcadaacdadddcbccdaaddccaabdaadaacbadccccbcadacacbbcbcccccdcbbdcdaadacdbdcaccdbaabbdbacddcdddabdccacacbbabddbcabacdcdcbdbbabbddcbaababbddccbbacdacddbbaccdabaabcdbaccbacbbbadbbbcaaaacdcdbacddaacbcdddcdbccaccbdbdacacbccadabddbbaaaacdbaddaccbaadaccadabbdcddadcaacdcdbccabaaccdcbdabdaccaddabadcbcdbaddbddcabcbadcdbdcddbbbbcacbadcbabcbcdbbaaadccbcbdbacbddbdaadbcbacbcbbcbbaaccdbcbbcdabacabccdbcdcddacdbdbddcdaaaddadaadddddaabacccdbdaabdaadcbbddadadbdddacadadacdddaccabadbabbacbbbacacbbadccadbcdbcbcdcdcabbacdbbbaccabadbadcdaadcdbcbdadccaccdcccbdcadaadacaaccdcdabaddabadcdcdbbbddaddacabbbddbcadddcaabbbbbacbcaacbdadccaabcbddacbcdaadcacbcbcbaabbdaacbbdaabaaacabbcccddcaabadcbcaaaacccacbccabbbdbcddcaccddaccacdcccdbcacaddcadbbccbbacbdbbcacddcabdbbcabaccacbdbccaaadbabdccaaabbaacacbbbccccaddaadbaccbddccdbacccabdaadbbcababbbdadbddbdaccbdbdbdacdaaddaabadcadbbabdaaadabbdaababadccdcaabbdaadbbdabbccacdcbdabdcdddddbbcccaacabaaacbcdddacbddcdabaddbadddcabdaacabdabaddbcbaaaaaacbcbbbccbbccddcbaabacbbbabacccddbcdcbacddbadbbbabdbadbccbbddabaacdbaaddaddadccccaaddcdcdbddadbaaabdbdccbcacbbbbcabccbddbabccdbbbbabaacbdacaccbcddaccbcbbacddbabcbadbaddbbdbbdacadacadabccbacabacacadacddcdbbbcddacaccddaadabadcdddaabdbcaababacccdcccdbaacbcaadccbabaabbcbccbccbabbbaabbcbaaccbcdaccbbacbdbcdcabbbbbaddbaabbddbdcdddbbdbcdabaabdacababdcccabcbdcdabacccadbbcacbdcabdaaabacaacdbdbbdaaabacbccdbabccadabcabdaadcbdacccbabacddbacbdacccdacdbcdaacdcbbbaabcdadddccaccccdabdadadcbbdcaababaaadcdcdcccbddaaabdbcccadaccddbcbcccbcbacdcdccabddcdcbcbaaaabdacbcbddcabbaaddabcbbcbbabdcdcbbbcdcdadadbadcddcbbbaadacaadcacbabbacbccbacabcccdcacadddcccaadbbcaacdbdbacaaacadaaaadcccdadddcdcccdacccdcabdcbcacabddddabaaadacddddcbcbbcdbdbbdbdacbbabdabddddccbbdcbacdadddacddddabaaaaacbccbdabdabcbacbaaabccdcbbbddccadcababbbcdaccbcdadaaabbccccdadbbabdaadbadcbdbdcbbbdcabaadacbbadadcddabdacdbddcbbcbadbcdbbcbbccabaacdacbbadabdaabbcabbcbadbcabdaddadcbcdaddcbcdbcadbdcabdbddbadaddacddbaabcdcabccabccdadcaaabdbddaadaddddccaaadadaddcaabdcabdcdabcdaabbababbbbbaabbdabacdcacbccaddcdcbaabcdaadddddbbabcacccdcddcadabacbdbdbcdcdacaabadddbdadcbbaccdcdcddaaaddbdaddcbcabdccabaacbcadbbaacbdaabaaacccbccadbcbaabbccdddadcdaccaaacaacbadcdbabdaabbbaabcbccaccddacbadbabcbdbaddbddabcbadbbcddcbbabcdbccaabdbcbbdcaddaaabcaacabdadbbbbadcbadbdddadabdcbabbbadcaccadbcaccbaaaadbddbaabdcbacbbbbababbdbdbbcaabcdaaaacbdadddbbacbbdbaadddccaadbbbdcdcbdadacbaddcdacdaccdcbdcbdabbbbabcbadaaccdcbbababadbcbabcbbbdacbbacbbdadacacabdcaddbdbdcccdcbaabdbcbbcbbdcabdbaacdacacadccaddabbbdadbcaadcacdaadcdcadbcbcabbccbbccbabbbcccdbadadaccadddbabaacaccdcdccddbcbdaaabdcbddcbdcacaccacadbcddccdbabcdcbbcbbbaacaddcddcaaacbdbcdcbdaaabbbababcddbddaadadbcaccdabcaddaccaccaddbdcbdddaaacbaaaabbabcccaccdbbbcadbdbccddbbcbcbcdcaaccdacbdaaddcacadabbdbababcccdbaaddcbdacabcddacabdadccbacbbbbcddbcaaacabbbaaadbdadacabdbddaaddaaddaadddaababcbcbcaaaccdacddcbcaacaadaabbdbacadaaadacbdacdcccdcadbcbddbacbbaaccdbbbdaacacabbdbbabbaacbddcbcbdcddcbbacdbdacbbcaadbdadcaaacabcbdabcadadaaacdccbbdccdadaddddddbccddbcdaadbdddcaabbadcdbcbddcacbacdabbaaccdbdbbbcdacbccdbdcbbdbccbadaaddabbabddaccddcddbaadaadbcbccbcabcdbbccdaadcacbdcaabdbdcbbcbabcbcacaaaacbbcddaabcacaabadaabcbdacabadbbacaadcbbcbbaadcacadbdcdbcabcacbdddbaaddbbbcdbaabdbcbacdcccbdbbbdcbbabacbbbbcdbadabdcdddabcdaccbadcbdcccadcccbadbcacccadcbbabaddcbcdddacabbdbabbccababcbdcacaadccdbabdabccccddbabbdcadcdbdabbadaddcdcbbaddccbadacbaadbbaadcbabbcbbbdddccddcdbdabccdddbaddbddcbbbaaaddbdadddadacbaacbddaddccaababcabaccddcdbdbacccdbcbadaadbbcadaabdcdabddddbacdcaacdadacabbcddccdccbdccdcccbccdabcabccacbaddbdcaccdaddadbaccbdacababacdbccaabdaacddabaaabdcaacdbccdbcccaccbccdbdcdcdccacabbabddbcdbdcccbbbcdaddaccadacdacadbccbbbdbdbabadaccbccbcbcbabbcdcbdcddaaccacabccacbdcdcddbbcacaddcdabdbcdadbbdccaccacbbdaabcadcbbbacbacbbcababcacadcdabcbddcdcaabcbbdcbbcdaaadacaddabbbdbbddadaacccbadaddbbcbaadadabddaabcabcccdbddbbadbbabbaabcbacdcaabcbbabdadbddacbddbacbcabcbcddbaadcbaadddbcddcacbbbdddddcbcbcddadddbabbcbacbbdbdaabbddccabdadbbabbdbbbadbbadcabcaabccccbbbcbaaadbbabcacdcaaddcdabcbadadcbacaadcbcabbdaaabcccbaadbadccdbdacdaabdbbcbadabbaabcadbdcacbadbaabdbcabbdcdcbaadcadccbccddcbaabbadbabacaccbbdbdcadbbdcdaadacbaabddbaacacdcdabdddbddcdcddcdbdccdacbcbcadadcbdcabdcaaacddbdabbcabcbdaacdcbadcdaaabaabcdbdcaadbbabdaaccbcaccdbccabbcbdbddbabdccbbdacbcabdcbaaadaaaabadabdddbbacccccbcbdcbadadadabbdccabbccaccbcacbabccaabacdccacdcbabbdcabcabdbdcdddcdbabbcacaabdbadcdcaaacdbcddaaaaaddddbddccdcbabbadddcddddacccaccabbdadcddddbdabddbacdbcadbdbddcacaddbccbbadcbcbbbbdbcddddacdabbdbdbbaddbccdacadcbacbbadbacbdcadccbccaacbdbaabcaaabdbacabdabcdabcabadbbdcccadacaacaaaaddbbaacccccdcbdcdaaccbdbcddcacabcbcbabdaddabbdaabcadadadabbadcadaccdbdacacdbbbabababbabcddcdcddddddbddccdbbccbacddcccbddddcbdcdaaadbcdbbabadcdcaaadcbcabbbabddcbcaabcdbbabcbbbaadadcbdbdcabacbcbaaccbcbcacddbccabbcccccccadbcccaaccabcbabccddaadbbadcbabadbccabbadbabbddcaacacbbdbdbbbbbddbcadaacccbdaddbbdbabdacabbcdcbcbbddbacbcacccaacdddadcbadacacaabdbcdcacadbcdccbcddbddddadadddcdacdbdcdbbdaaabddccbddacabadadbdaadabcaaacadcccaabbdccdbcdbbaadbcacacbacaaabdcacdabbadcadcddccbbadddccdacdacdabdcbcadaaccbadbcbcacdbcaccccbbbddddaabacbbdcdcaadbbbaccadaabacbaacdababbbcccddacacccbbbbcacabccdabcbcdbccaabbbdddbdddbdbaadcccddcacdbbbdcbacdcbcbddaaababaacccbbbbdcdacaddbcababbbcdbdcccbcdbdcadcaddacdccdbaaadbdcdabadadddaacbabdcbbcbccabaadbbbbcabbdbabdadacaabcbcdaacbaababcbdaacbddcaabdbbccacdddbacddaababbadaaadcaaacccdacaabbadbaabdbabddddbbdaabbbbacacbabbdbddbcdbbdadacdcbadbddbdaddcbbbbbccbcbacacccccdddabadbaccabdabbcdadccdcbadadccacbdabcaddaadcbacbdccccbdcbdcdcaacabbadcaccabcadabdbdaddbccbdcacacbaaadadcdcdcccdbaaaabaaddbbbbccddcacccbcdbcdddaaddbdbadaddbbacccbdbdbadabaddcabcccdbbbdccbbbcdadbabdbacacbccaadabcaddcaabacabaccdbdcdddbbacaabbcaaabdbdaddbbcdddaacacabbcbbcbddccaddbbbbddadaadcdcbbbdbdaaddaaacdacbaccbcaaadabcccddabcacbdddcccccabddacdbdaabacadacaacabbdabacdbaabadbdcacaccbcadacdbbccdcbbdadadcdadcacadabddacbaabaddbbccadbddbadcacbcbacdaaabcbbacbbbdaabdadcbdbbaaddbbadccadabcdccadbabbcdaaddbbabcadabdbbabcbabaaabdbdccbcddbdcdcdacdaabacddcdbcccadacdbdbccabcdccdbacaacbcbadabbdcadbcdbbbcddaddcadcdacbadbdcddacdcabbbacbbddbaadacdddaadcdccbbbccbcacbaddcdbdcbdcbbcccccdcbdabcabcccbbddbbbdabbacdbcdddbaccddaabdaccacacbdadcaaddccbbbddbbdcadcaaabcccaacadcbdaabcbcabbbcdcbabdcaddbbbddbcacacdbddacabcbdbbadcbdddcaaddaaaaccbdddaacbcdbccccbaadbaaccbccbbccacadcddbcbabddcaaaacdadbcdccbbdabdcbbddcbacbcaabddabdababababdbddcbacdddbbdacccddadcddcbdaacccabbdabaccbacabccaccabacddaccaccbdcbaabcbccbbbddbbadcbdbbaddabacaaccdcadddcdddbddbbbbcbcbacdcdcbdddbaddbcacacbddcdababccabcbdbbabbbbbcccaacaabcbddaabddbddabdbbaacbabaddcaadcabacababbbddbbadbcadcccccdbddabddccaddccbdcaaadcbbcdbabaacaddcacadbabdadddbdaddbbbccaaadadaabbaaabcdabadacabddbabcdbacbcbbabadccdbaaabbcdbdacbbddbcbabcccddaabccbcbdcbddabcbbdbbbdbddbdaccdadaaadacbbccdbbccdcdcddcabbdddcbadaccccdabaccdacaadcacdcacbbaacadabbcbaaacdacdcbadcdccabbbddaacdbcbbcbacbddabbcbacdabbadabccadbbccabcaacdadadadcacaaaabccdacbdddbbcbacbcdabbddadbddbbccbcbaabcaaadcddbaaaacbbccdaaaaabcdbabbdbdbcddddddddbddbacdcccddabbdcbcdbbbbdccdcaaaddacdadbacbdbccddbcccccadaddbdacbddbcbadddccccddababbcababababbdcacadadabcbcadcadbadcdcacaacadcaacdddaccbaababaabdccdabcadcbdacdbbaadcadbddcddacaadbabdcbcaddcbbccadddaaaaabccaacadbacdddcabcdbacaacacdcbdacbccddddcaaccaaccdcdacdbbcbcabccbacabadcadabbccaabddbccdabcdcbcdcadbdbccbaaabdccbaacbcbbbbcacccbadbacacccdbbdbacbcaddabaccacaacdcbbcdbdabccacabaccdacadccaadbadabcacccbdcacaacccdaabbbbabdbcddaacacbccbbdaaaabdcbaaaabbdadabcdccdbcddbbcdbbcdcadddcdaccbacbabacbdcbacdadbcbdabcccadcabacababdddbdadcaababbccadaabdbdababbbbccbcdcbcbdcaababccbababcdababcababcdcadbabaabdbcbdacbddbcdbdbbddcdddbccddcdbaaacbacddbaadacbcdaaacbbdccdcdcaddcadbbacbcaabcdabcaabcdacaaabbcddaddddbbaccacaadcbdbcabcbbbcccaabbabcbbdbcdbbdabbddacacaabbbddbdacccbdbccddcbbbcccbdcbadcccbaaabccbcbadcbaabcaadabbbddddadababbaccdcbccdadcbbaddadccbdbabccabccaaddbdcbcbcbaabdcbdcbbaabbacdaacabcabadcbddcccaadadbbbbaccddcaaabbbbdcadcaabddaaadadabbbcbaccabbdaabcddcdcaacaadccdbadcdacbcccbcdbcacddabcacccbdcdcdabccbbbdbdbdcbabcbadcaabdaddbbabcbaddacdacdacbdcdaaaccbbabcabacaacdcdbcdcdddbacbcbcbdcbbabacbbcdbcbbbcacbacdbbbdccaddacbddddabbadbcacadaaddbaaadabababddbcbbdcdddabcbabbacabdcacbabaccddbdbddbabbddccbbcdbbccbccadadacbaaccbbabcbcaabbcbdaddadddbbbaadcbcaddcbbbcdcdbaddadcbacabbdacadbccccaadbdacbabcabdaaaadbbdcddbcbabcddabccadbadccacadaabcabadacbadaacdbbdbcdbdcbcdacdaacbbdcbbdaacbcccbaccdbcaccaaaabcbcabddbadbdbccbbdccbcbdcabdbabbcababdabacabdbbabcacccbbaadcbddadddddcdacabcccdcdccdcdbdbccddaddbcabddabdbcbabdaadcbccdabdbcbcaabbabbccddccbcbbcddbbcccdcacbadbdadddcdbcaabdcabcacacbddcadcaababdcadabaddbadddcbbcdbbddbaaadadbbbacbabaaddbcccabccccbbbbadbcbabddddabaacaaabbbbdbdcaadacbccbdcbbcdcacdadcadbacccdcbdcadabdbbadcdbbdccbabbacccaadacaabaacaabbabababcdbcabcabdbadaccadadcbbccacacabdddddcdccbbdabbbacacaaddcaaddcbddabbcbcadabdbdbcccbdcaadccdbbbbccaabadddcbaadcddaabaddaadacbadadcabaabddbdddacaccabdbdcbccdccbbdabdccdcaabbdaddcacdbddcbbdbcbbdccdabcdcaccbbabcbdbcccadbdcacdbbbdcccabbacdbbbaccccddbadaabdddadddaaddaddcbbbbcdcdbcdaccbddbdbaacaacaabaaccbaacacabbbabbbbdaddcaadcaabbaaaaabacaadaababbaaabbccbbdcbaaadadcbcabcddcddcaabdaaacdddcddacbabdcdbdcaaabcdacbdcacabaacadacaabcddbdbabbaddadbbacdddacccddaaaabbdcbbcabdbddddacdcccbdcddadacdddccdcacdbccbbbababbccbcbadbddbccbbdcadaadcadcacccaddacbdabbbacdbcbdbaccaaddbbcbbbdcbbbdcadccaabcdadbdcbcabbcdaabdcddbdaabbdcdaadcaabbbdcaadcbdbcdccacadcbbddcaacbbdacdadadcdcbadcaaacabcddaacbadcbaadcbccdcaacaddcdabcccdbdccbcbbddabddccbdbcacbdcadbbdccddcdcdbaccbbdcdcccccdabacabaaababcdaccbcabdcacaabbccdadcaabbabadbaabccdbcabcaaddadadabcdabacbdbabaacadacbacdbbabaccdbdcbdddbaabbdbcbcbcabdcddadbcdbcbaacbdbbdcbddaccbacbcadbddcddbbacabbaccbaabbacdccccbaddbcaabcbbaabbaccccacbabadcdccdcaacbdbbacaddabbdabdcaddadcbbaccddccabbdccdcacabdcaabadddcaaaabcabcaadacdbcccbdccdccdbbaadabddcccbcbcbaacbaddcdcacddadddbcaddbaabadabdabcbcdcbdacacacabcccbabddccbdccbbacdcccdaddacabdddbdcccabcccdbbaccacbabccdbabbbadbdccbbccbadcbcdadcacbbbdbadababcbacaadabdbbadcadbaaaccbdddbcaaccbadbbbaacbbbcddccabcdbdaddacadbbbbbbcccbbdbcaaabacabdccbcdddabbcacdbdbbaadddacdddbbaaaabcbcaabbbadaddcbcddbaaabcacbacbdbdcadabaddaadadcaabccdccdccadbcaccdcccabadccacdacdddcbbbbabbbcdccaaadccbaabbdddadbdcaaccadbddcddabacababcdbccdbbcdbbdcaccbdcbabcddbaddbcacbbaacadacdbaccdbaacccbbbccaddddcbbccdcdbacccaadbddabdacccbcdabbcadabcdbbbbbadcdddbdcdaaddddbbacdcaccaaadbdacadddddabddbacbadaccbbdbdbbcadccdabcbdabcbcaccabcbaaabddadccdcabdbdaccdcdccaccbcacbdddacbaacdbddacdbbabbaddcddabbbadaaccacacaabacadbaabcbbbaddbcdccadcbabaacddbbbbabbdccdaabadbddcbdbbbacccabaacabbddbbacabdbdcdddbddddaaccdbcdcaabacaabccaddbddadcddcddccaddbcbbdcdcdcbaddbadbbaaaaaabddaacdddaabaccadccddddccabbcbadbdacbddaadbaacacdbbdbbbbdbacdaaccdbddaaddddcacbadcaddadcdbccbaccddbbdacadbcbcdbdcbdddcadcccaacacdddacbcaaddaddaddaddbaccbaccdadcdcbcbaadacdbdacbaddddabaccadaabdbcccaddbddccdaaaadddcddaccaadaadabbaacdbadabccdbcdbbabbbabccadababadddbddcacaadacccbdaaaabababdabbacdbbcdbaabdbcdcddacadaabdadaadcdcacdbbabacabdcbacccbdbcadcbbdacdcbcbabaddabdbddbaddbadabccbaddaabbdbdaddaaadcddcbcbdbacadbdbbadbadccbcbdaabdcaadaddddaabbddacbbccbaabaabbbdddaddddabbccccdcadbacbaaddbdcbabbddabbcadcbddcbacdaabbcbcdddaabbbbdcbbdbadacbabddcabacdbdbaaadccccccbcdadcddbcddbdcbcdcbacdabaaddcdabddaddaccacaacadcbcaccaabdbadacacdabadacadacdcdadaccdcabdbccaddaaabdbdccbccaccadcbcabbcacaacabcbdbcbcddddcbabcbcbbcbacdcbaccaacadababdacbdaaddccdddcbcdaacccbbcbcbbbddadbdaacaadabddabccbbdddbdaadbbaacaaabbdadcdacbdcdddadacddcbaabdbdcbcaacbadabbbcaacdcbccddcadcdcccbcbcbcabdacdacaaaaccbcdadadbbccbbcddcddbabbdbdddabdadabdcabddddccccddacabdcbaaadbddcdcbddaccdadcccdabbbacabcbcabdcdaddbdbbcdcaccbddbacbbaddbbdbcabccddccadaddbcbacbbddcaccbaaaabcdcaadbccddbcacadabaccddcdbabaadadaabddbbbacacdaaadabbadbbccbbccacccababdadabaadcabccdbccacccdaaaddccabddaccadaddbabaaccdddcadccbddacacaccccbddbcaccdabbbabbddbdccbbadaadbaaabdcaacdddbacacabdbcbadadcccadbdccccdbcbdbbbdccadcbdcbbbacddaacccaddacacbcccdddcabcccdcaabcaaaaaabccccdbbdabcacaccdcaadbdcbadabdcbbbaadcdccdbddbabdbdcbbcdddbddabcbdddaabdccdbbccabacadadbbdcbcbcbacdddbbdbdccdccaaaaabaadcccbcaadbaadadccbbaacadadcdbaaacdbcadddbacbddbddcddaccabaddbdacccbccbbadcbadaaaadddacbaabddbdadabbbcdbdadadcaaabcabaaccbbcdbbabcbbbdccbcddbadbcdddbdabadaadbabccdbdbcaddbbbdbdddbbaccdcdcaccddcaaccbaaaacabacadcbabaadcddacbacdcdddcddbadddbbacddbccbddabbbbcdacbbcadbcabddabcbddaaccaaabacbddccdbccadadabdcccadbaabbaddddcdbddbdbccdacdcbacdcdddccdbcbdbddbcddabdbaacbbacadbccccbaadcdacddddbadcddcaaabbacdcdccdacbdbaabbbcdaabbdaacacdaacdcadcacdcabdbadcdbdadbddbbbcbaddbddcbbbcdaadaabbbabcbaddcacddabbbacdbcdddacacabdbbddbddabaadcabcbbbabadbaccdcadbabdcadccadcaaccbdacbaccbbdbcddacaccdabcdbcdabdaccadddcbccdbababdbbadabdcddcdaaadddddcbacbaaabadcdddbddbdaccabddabdbbbcacadccbdacabcbcddbddbcaadadddadabbacdcaddddcdddaaccccadadacaadacadbcaddccccccbdacababbacabdbcadbadccdcbdbaacacacbbdcdabcdccddcdcddbabadcdaacdbbbbdcacdbcddcadbcccadbcccccabcddccabbdacddbabdcacdbbbccbadaabdaadbacdabdbabcdbabcdbbcaacdbbddabcbdadbcbbacdadcdadcacabbcaaabbddcaababdaccadcadcbabbbbbbadaccaadaacdbacacadcbccaccacdbbccbaadbbbbbaddaaaaadbabbdbbbacbaaadaacaadaabbddbdabbacbbdbcccdacbccbabdbaabbcdbbbcddccbccacbbadcaabdbababcbdbbbbbbaddbbbcbacaaabaacddbdddaabcdbbbaddcdbcacadaaadcccadbcaadcccdcdbcbdcacadccacddacccbabbbbdcaccccaacaccaaadbdbcdbaacbcbdcdadccbbcbccddbcaccdadcbcdbbdaacabdaddacddadbbbcdacadddabdacdbdbdbdddbbdabdcaddcabcbaabbddcdcbbcdddbabacabaddaabbbccbcbdccbbcacabaaaaabddaadcddacbbcdaacbcacabbcdacdcbdbbbccddabcddaadcdcabcccbcabcadbcdcabcdccdbcddcdddbdbcadacbdcdcdcbbdbdaabbbadadadaacacccdbbabadcacbcbdcbdcabccadadddbdbcbacaadbaddacaddabbdccbcdcbaadcddaadbdbcccdadccabadadcccbbddaaaaddcddabcdbadaccdbcbdbbcbdbcdddbbcccbcaaacdddcdcbbbdddbcccccabcdbadbcaccdbdabbcbcaccdabaacdadddacbbbdadcbdaaacdbdacbcdddaaadbabaccaccdbbbdcdaabcbcdacdcbddacdccdbccadbccbbcdbadabacbddbacbbdcbcbacbcbaabcbdbcdaddababaacacacbcdabcbaacdcabcdbbbcbbcddcaacacabcbdaabbdabacabccbbabcaddbacbcbcbcaddbadacddcabbcaadacbaddbcadcbddcccbbaabdcbddbddddbabbaccaadbccbbcdbbabadbddaaabbaacadcdabdcacdabccaaddbcdadabdbccdcaddaaaccadaddbdbbabbbdacaddbbdcbaccbaccbaadcbacbabcabdbbbcdbdadbbcdbbcbbdbcdcccccdccbdabbacbdbbcdcdcccbadcbadaaabbccbdccdabbccbacbdbccaccdabcaccccdbddaccbcbbcdadaadbadccccbbcbbdbbabbacabdccbbaabcacccaaacddcaaaccacacacdbbcdbdcacabdccbdddbcccaddaadcacbcbcaababbdabcdcdbddaddddcbbbabdaacddaaabaaaabddbbdcdddccbdddddcbcddddaacbdabbddaabaabbdbbaabcdabbadaccbaaabcdbbabddbbadaaddcbbbaddcdbdcddaccbadbcabcbdbbcbcbcbccccadbccbcccccaaaadbccccaabddbbbddaacbcaaabcbbdcdabdbcadbdaacbcddbabcdccbbdcacabbbccaabbdacdccbabdabdcacabadddacbababcccabbcbbcaabddcbcdabcacdadbbdbcbbbbcbbacadcadcdadccabccdbdaccabbdbbaddabdabacabdcbbdacabaaabdccbaacaccccbccdacdcadbaadabbcadbdcbaaddbcdabadcabbdbabbaadbcabbccaddddcdacbacbdcdcbabbdbdcbabaadcaacdaccabbcaaacdbddcbabaddaadadcbabaadaaadcbcdddacaadaadcbacacaabdcccacabbcbdacbbbcbbaaaccacbdbababbcbaacccbdcbadacbbcbcdabacbaadcccaacbdddcdcabcbcadaccdccadaadbdcbaaccaaccabbdadacbbbacdccadbdabbaacaddbdbccdababcadbbccdaaccdcccdddbcccbadddbbbdcbadcbbaabbccccbddaadadcdacdbaadcdbbbadaabbbaccabdaccdaaaadaabbcbbdbbabdcdadccacabbcacacbabbdcabdacdcdbdaaddabdaadbacdccabbdbabbdcacbacaaacadbcabdbaabddbdadadcbbcbbbccbdbaaacbabcdcadcbbbdcacbdddaccddaccccabbaacdbadbddcacddaaaaabadacabbbcaccccdcaabbbdaccacbbacacdaaadcdddaacacaadabbcccabccdacbdacbcbaddacdddbddcaaabadccddaadcdbacdcccbaaddbcabbdabbbbccbbdbbbbcaddacaaaacaddccbbabbddbcabcabbdbdaabbaaabababbbbaddadcacbbcdcabbaddccaadbadcdbcdbbdaaddacddcdbcabaabadcadbaabbbbdacbddcdaaadbccaaaacddbddcdadadbadbddbbbaaaacbcabbdcbcbbddadadcacbcbbdaddbddacaacddadcdddaaabaacaacdbbccbdadadadbcadabaadcdbcccddcdccabccabccaacbccdcccddbcccdcbcaadabcbddccbbdcadaccbbadccaddddbdcacddbccdbbcadddcdadddcbbaccdbbcddbacbcdbaaaacbabacbdbddddacbdabbdbdddbbdcdadcddbddaacaaabbdbcabadbcdbcdabaadbacddaaadcabbddcdccadcadcddbdcaaccbbdadcabcdbdbbdaaaabcaabdabbcbbdbcdbbddcbabbbcaaccabbbacdbdbacbbadbcddbccbccabdcdcacbabbcbbcbdbaaacbcccdaadcaacbabaccacccccabcdcabddcddbdddcdbcddbddbbaccadadaaaadcdacccdbcdacaaddbcddbdbdbbdccdcdacddadaaaccaaccdddbdadbacdbdcdddbacacacdbabbcabcbdacbbaccbcdaddbdccbccbabcbdcaddbdbabcacaabbacbbddcaadddbacabdababcabcbacbbbdacbcddddcabccdbbddbccadadcadbdbcddcdcacddaaaaadccccaaccccbdccaaccddaacdcdacdadabccdbddbbbacbddaadbdadddcbadccddacabcbdcddcadadcbbabdacddabcdadacbccaacdbcaddbbbabbbadbdbbdcbcabdbddbadcccdcaababdabbaadacdcdaaaabdbdbacdbccbbdbbddadabbdadbcccbbccaabaababbbabddbcbdcddbacbbbadcdcddadbddabadcdadbbdadadbcbcbdabcdadacbccaadcaaccbbadcdbbaaabdbbdaccdccaabdbcaccddcbbccdcaacbbaddcccacdcbcbabcdcbadbcbcdccddbdbbcdbadaabaadabcddcbcdabadbcdcccbaaaaccadbbdcdbabadcdcdbdcacbacdaaabcbcbbccdccadbabbabdacdbdbbbddbcbbddcaddbdbbabcddccadbabcaabbacacbcbadadaabadbdddddcababccccbbaadaabadccaabbadacadacdcbcdcdabaabbcdababdcddcdcbbbbcdcaddccdcbadcdcadabccbcbdaccbacabdbcbaddcbdbababbdddbaaadaddccaacbdbabdddbbadbdcdadcaadcbdabbdbdaabacabcaaadabbdccadacdbacbccbadadabddbbbbabdbdbadbabcbacdbcbbacdbbcbcabddbdabcaacdcbbcddbbcdcdadbbccccdbbabacaadbcccbdbbccdbcabcaccbbcbcaacdbbcbbcdddbdaddbdcaccaddbacddcbaabaadbadcdcbbccabcbdacaabccabbcdccabcddcbcaaccbcccaaadcbdddabcaabbadadacdcaccdccbdaadddaaaadcdccadbdbccaaaaccbdbccbdccbdbbddaddbacaccbdadacaaabccaaacdbcccddacbbbcbdcabdcaadacaddccccabadadddcaccbdbbccbbcbccbcacabbcbdacacdabcddbdbabdbddbacbabbcadbaacddddcaabcacdbccddaadadacaadddbabbcdbcdacdacaaccabbaadbdbdbbdaaaadcdcddbaabddbbbaccdabcdcbbddcccbbacbbccbcabcbdbbbddbccdabdccbcbacdadcbacbbcbabbccacdaddbacbbdbaccddacaadcbbbacbaabbddadbccbbcbbdbaddacbcbcaddcabcabdcdacdbdcddddbaacdccabdbddddcabbccadcacacdabdcdadcccdcdccddaaadbcdbadcdcbaaaadbbbbcdddcdbcdbbddbcdbadbcabbbbdccdccabccdacaacddadaaccabbaaddbcadaaaddcbdbdddbaddcdbbbcddbdadbbdbaaaddbbddddbccbacdaadbcadaccbacddadaccacbcacdacdcdaccacbcacabdbadcdbdbcbaaadbdbcdabdadcabddaaccaacacdbdaadcbcaadacdbadcbdaaadcdbcdbddddcdadadcbbdacbcabddddbdccdadcbdbcadabcacbcbbcccaadbcbccaacaaabaaaaabaddacdacdbaccabdcabcdbdacdabddccdbcbcbbdcccabdcbcddddadbaadcdabcbdccacabcbcabbbdbaabacabbdbbabacbcdbabbbbbbdbdaaacdcabcbddbdaccdbccaacacbaddcbdcaaacbcacadadbcdabbbabbaddcaadddccbcddabdacbdaadbdbbdcccbaccdcacdbdababcaaccabbbabbcdbabbbbdadabcdbaadadcacaddaccdcdbacbdabaacbccdacbccdcddbbdadcabcccdccbdcddbbcdbcbadddacddcacadacdabbddbdbcdcaabbacaccbabadaccdbdcadadcdbacbbddccabbdbabcadcdcdbabbabacdaaabcbbcbbadccabdbddcbdcbadbaadbdccbadacaccddaddcadddcbbdbaaadbabdabccdcabcbbcdadabbccbaddadbbbabdacdbcbaacacddbbbbdccbcddbaacbdadcababcbddccaddbacbdccdabcdddaaddddbbcaabadabddddacdaacbacacbbdccabcddaabacabbcbdcdadbcaadaadddcbababcbababbdababcacadcdabdbacaaaccacbaccabdcadbdaabbdaddabbbcbcabcbccbdbdbbbcdcaaaaddcbbcabdcbbbbbacddcacadcaabdbbdbaccaadddcbaacaddcdbcbacbbddcdacdbdaddcbdbbacddcbaaadbbcbacbdaaaaacbcbdbdacbdccbcaddacaaccaadaacddbadaaddcdbaabadccbddcabdcbcdabbacaccdabdbcbcdabddabaaadbcaaccbdbadcbaadaacddaadabcbdaaacddadcccbdbddbcccccddadbcbcdcabbdbbccaaddcbddbdbccbdcbddaababdddaaababacdadcbdbdaccadcadbadcccbcddddbabbcbcdcdbcccaadcaaccbcddabbcacbadbcbadcdbdcbaaadaabdabcacdcadcdbbddadadaadbdcbacdaddbaaaaadabcbdddcbabcadcbccdbbdcccacdacbdbddddbdaacabbdcbbcdcabadbbaaaaababcccbcacaccbabcbbbabdaddcbcadacccaccdcbcdbaccdaabbbbbcdbbbdabcdadcdadcdcbaccabdabcadcdbcaaadacccdccbdaddacccbcbabcadadbcdacacabbabcccbddadcbbdcccccbcbbdbaacccdcadbaccaddacdccbbcbbcabdabbdcadacadcaaadccbdcdaacbdcadbbbaddbdcacbccbacabcbbbbacbccacddbdbadbbdaccaaacdddaacdaddabacbdcaaaccaddaacbdccbdcacbdddccddcaccbadbdadcaadcddbbdacbdaabdccabdbcdacccbcadaacababdadccbdcbddabacadcaacaccbcccccadcdbadabaabbcacaddadabdaccdacdcddcabccadbbaddbacaacdaddcddcccaadcdabbddcdadbddcacbabaaabccddbbabccbbabcddadbabdacdaccbbdcdbcdcbdabacadbaaadbcdcdcadbdcadadcdacadccbbadaadadaabbbbdbccbbaacbdbaccddaabbcbaddccaabdbbaaabcaddcadabbdbbbdabcdabdabdcaadbbadcccbacaaadcdddcdbabdcbcadadabaacbcccccbccbabcdaacbadbcacadaaadcdcacdabdaadcbcdabbaccadbdaaccaadbcdddbccbdccddadadcdbdaacabdcbdcaaacbbbcaccdccabaaddbcdcaabdaaacdcbadddccadddbcdcddacbddcddbbcabcaddbccccddbcbdbadadcabdcddcaaabbbababaddaccdcdcdabbabaadacaaaddcbdacaaacccbcabcdcdaabdbbdbbdbdccddcadaacbabcacccdcdddbababacbbaabbbadcdabdaacddbcdbcabdaccdabccdaaaabbbbdbdaaadcbbbadbcbcdadadacaaaaacbbcbbacbaadaabdcccdcbdbddccbddcbdacdbaacacbbbabdadcdaadddcaddbdcddbbbdcacabccdcaadaccbddcacdccbbacdabdaaddddacadabaccdccbcabacaadddbbccadcadbcbdccbaddcdbbcdcddddcacdacaccdabcdbdaaccbbddbbbccdddaabbddbccabdbdaddabbdbbbcddabaddddaccdcdcccaaaccadcadbbacbbcaccdbadadbbbcaddddcdbddcacbbdcbabccddaacddbaddaacacbaaaacdcdbbabbcddbacccdcbadcabdbaadabdabcdcbccbabbcbadccdbcbcbcbbdbaacdcbdabccddbbdaadaccbacbcdbbbdddcbdaddacddbddaccdbcbddcaacbcdcbacaadbbbcacddacdbdacabbcbdadbccbaacbbbaaabaddcadbdcabaabcaadddbbababbcadcddacbdbdbbcaccacbcadcbabcbbadbadcccabbabbdabdbdcaddabdadcbdbbbbacdcacddacacbdcbdbbdbbdcbadcccaaddaadbaacabcdbdaadabaccbcbdacdcbbaddbacdbcbbcddacdcccbbcdbdaaabcccaabcacbcbcdabcbcbdcadacacdbbbcdbcbbbdbadbdacbcaddcdadddccbadccbbcbddbdaaccbbcccbdaccccbbdaccabbcbacdcbabcccbdacaacdbdacbdbbaccbcdcacccbccadaabbabdcbcbbadcbcbdaacbaccabdadcbcbbabcadbcacbcabbcbdaabcbabaccaacadabbacbcacbcbbddbbabcdcdacdbcacdddabcbbcbbacbcbccdccccbaaddaccbcbcaacacccbdaccacaddcacbcdcdbbcadbadbddbcbacbcccadbacbccacabdbcababadadaabbcaacadbacaaaaacdadadcddddaaddccadcabdcacbbbccdbccdbadaddbbcdcbaabacccadcbaccdcbddadabaadbdaaddbbccbdbccbdcbbbadbaabaddacacbabbccbabdddcbddaaddcddbdacdbaacbaabddcdacbbacbdbdcadbacbaacdbbcdddcbabdadaadabbbdadcbdcdbabccdabbbdabcadbdbbabccbdadcadcadacbbcbaaadddaaddbdabbabcaaacabcabadcdabcaaddcaaabcaddbcccbdcbbbccacdaaddadaacadbdbdadbaacaacddccbdcbabbbdddcdaddabaaabdbdccbddcbcaaaadcbaccaadbadcdcaddbabbabbcbadbcddddacaabcdaadccddcbbbbbcddcccaacbcdbaabbdadbbbbcdbcaddbdadddbcdaabcccdbabcbdcdbaadcadacdabbdccbdabbbabcaccddddccbaaaccdddbcaccdadababbbbcccaadddcbdcbbcabcacacbcbdbbcbbcbbccdabbcdcddcdabdcabdbacacbcddadcbbbbddbaccadbdccacdcdbccadbbcdacaaadbbcbbacbdbacdbbdbadbbdccbdbcadcadcbbadaaadbccbbaccbbabacbdccacdcddadcdbdbadcbdcddbacbbabaaccadcdcdccbdbadbcbddbaacdabaccaadbacbbcdcabcdababacadcdbadbdbabadaadcaadcdadcadcdcaddcdcddadddbddcccbdcaabddcdbcaddbacdccbaabbaacbcbbaaabdaaadabacbdbbccccaadbaccbcbadbddcdcccbddccbbadbaabbbccbbccacbaccddbbadddadabdbddcccddbbaacbdcccdcbacabdbcacadcaacdccbaabbddabbbbaccbbdcccabdbabbcadbcbcabdabbbadabbdaabcabdbbacacadaddddabddacbaabddcdabaaaacdabccabbadbdbccbcabdbcccbaacabbabccdbbaabcddbddddcdbbddbadaababdccdbacddaccddcdbbcaddccbdaaccdbbdbcabdbddbcccabdacbacdbcbbdbccbddcaaadbbcdbabbdbbaaacacaaacccbbaacbbbddbaddacbdabadddcacaccddcbdaadaccdcabdcdbaaaacabcddbbabdddccaacdbbaccbdccdaccdbccbbaacddcbdadcdaabbbaccbcaababddcddaddabccdcdadcbcabbcccbbaacbabddbacddcdddaddbadaadbadacacdcddcdccbaabadadacccacadadbcdcddcabccaabcadaccdccbacdcbcbbbabbbbbbaaabababdbbaabaaaadcccacadadbbabaaadadbbbdadbdccdddaaabbcbcdadbddadcdbbbcadddddbddacdbcbcccdabdcbabaccccdadbdacbdcdbcaadccbaadddaaaadadcccbaadcccbaccdabddccabbbbcdabadbbaabcdbbcbbbaacbdacdadadccbbacdcdbccadbababadccccaaababbbbcbcdbbcabcbcdbccdbbbbdbcaccbaddcdccbdaccbabaaddbbdccaaaddaaababcabcdcddadcbbbaaabcabadaabacccbbbbcbdcbabdbdaacadddbdddbdcadaaddcdbcdccaccbbbcbabdababdcaddcadabbcaabbbaadabbdcadcbcaccacddddbdaacdbcccaccaabbaaaabcabcdbdcbdbcadcbcdaaaacbcacdcbbabbccbbdbbcabcbdbbbaaabbbbdaaabbbdcccbdccdcabdcaacdccdcbbcbcbdabbabcdcdcdcababbdddabddbcadcadbabdbbccdbaadcdadcacadcaabbdccaaadbbbcaadbabcabbacddbbbcbadcdcdabdaddabbbcdbabcccbbcabadcdddadbacbddbdcabbbdccbbcdcbbbabcccadcbadaabdaaaabddbbaaddaccbbaabcdcacabdcdcddbccdccccacbddbbabcbdbbaaaabadddcaaacdbacdbdbbaadcbcddacbaaacbdaccabcabdcabbdadcaccabbbbacbcacdcdaabacabcbdbdcccbbddbbaabdaccbdbdbbbacabbbcdacabcdadadaadccadaaddddddaccccabcabdbdbcdcaacbbabcbdbbdaacbbabdccdcdccbddadcdbbdbacdbadcbdccadcbdabbdddbbcacccdbcaccabbcdabdbabbbdacbdadbccbdaaddbbadadbbbcbcbacbddcabbbadbccbdbdbcabccdadbcbddbdacdadcaccadcbbddddbdaaaaaccdacdcaabddddacaadbcbdabaccccdaaddacaadaacbadadabbbacbbccdaabbdcbddccdbdbbaacdbbddbcabcabbbdbaacacaaadaacbbbbabbdcabbabcbbaddabcadbcbcacddcdbdcbacbbcdbbbbbabcacaccabaadabbacaaddacbacdabbbadcabdacbabbdbcaacacdcbabacdbdcacddddabbdacadcabbbbbdcadadaccbdacbcbbbabaaaacbdccbdcbddccccbabababbcabbabacbbbadaabbdbacaaccabcdcbcbccdacbbadbddcdacbacabdcbddaddbbacabbcbcdddadcbcdbbdabacbcdacdbbcddbbdcacbdbcddacdbcddacacacadaabbbbccccbbcadcbbbdbcddcbbbcabcadcdcccdbbcbaaaacccadacabadacbadcdcdcbdccacdaddcbddcaddacbacdcdddbbacadbadddaacdcddbdbbbabdbbbdcddcddabdaaacbbdcaacdabbcbcdbaadcadbdcbcbdbaacabbbcabcaaabaccdccabcabdbbbbdddadabbdbbcbbcbdbcaaadcbdccacbbdccbdaadbbdadbdbabdcaacbaacabaabcaacaddbacaabdaacbbacdaddabcbbcdcdbbbddccccdbbbcbdcbcaacaaadaaadbabdccdabadbcdcbbadadcdaacbaddcbcbbdbdabbacacdadccbbcaaaacddbbcaaddbcdbbadbdccbbcbbcabccbbaccdbadadcbbbdccdcbaabcbaaabcaaadbddaddaabbaccbccaabccccabaadbdabddccbbcdacaacbcbaaadcabaaaddbacaadbbadbbabadacbcdaccdbcdabbddbdcaaccabcabacdcbdabcbdacdcacacaadbcdcdaadddbaadbbabdaabbdbaddcaddcbcbababadbdcabbaacdbbabbcdacbabaaabaddadcadadcdbdddccddacaccabbcbcdabdaccabcccdccbdbcbacbddabdbdbaaccbdbbcccdcaccbdbcdbddaddbdcccaccccbcbdcdbcadaaabaabdbbddacabacabacabddaccaabaadaacccaddccadbcaadcaaccccacacdbdcccaacddbacbadcbdabbcdbacdbcbcaabbaaaabbdcbcbbdbcbbbaacabadcacadbdccbbcaacadcdacabbcccabddddabbaaddddbdddaabdcddddadcccdbadbabbdaddabbcdabcddddcdddbbbcbacddbcacaddbddabcadabdccabcbdabbcaabcdaccbcabcbdbcacbbccbdbbdabababdbacbbbddbcacddbbdabcacadaddcbcadbcbbabdaaddabddaccbabccaabdaabbdbbddbdcdaaacdbbaddcbaacbdddcbadadadbbcabdcdbbbdbcbbcbcdcdbbacbbbabcbbbccbbacbbbbdbacdbdbcbabaabbaaaaaadcbdaaccdcbcccddbdbcddadcbbccdaaabcbbcabbbbccdbbaaacdcbbbcbbabdbcdbbbccdbbaccaadcddbcbdddbdccbbabbbaaaadadacddccccdaaacbbdabddbadcdbccadcbbaaccdcdbcbbcdaacbdabdddbdccaddccabbbcdddcccdbbdbdddcaaaabdcbdbddadcbbcbbaacbdcbbabaaddcdbacddcbadccaabcadccbdcbcadacacdbbcdbccabbbaddbacdabbddbbabcadcaadcbadbaccdaaddaccaddcadcacaaabbbbabbddadcdcbcdbbdcacadbcdbddbdcdbaddbbaadcadbdbacbbcbacdabbbcbbacdaacadbbaacdbdaaadbddabaaabddddbbbcddcdbddcdddccadbcccccabbcaaaccabbdbacadbaaaaacaaddabdbdaacbaabdcadbbaabdddacbdcaccbbbabdadbcbbabccddbddaaababadababcddbddcdbabbaabbbaacdccaccbbccabdcbcdbbddcbdadbccddbbdaaddacbbadadbbdbbdccabaabbabdbbccccaddbbcacbdcaccbcbbcaaddccddddbacacbdbaabcdcccdbdbcacdacccaadaccaaadabdccaddcaacadaaababcaaacacbbcbbdbbdcbdccbbaaccadadddbddabaadcadddbdcdbcbaabdccdbdabdadbdbabcdbcdbccccbcdbadbdbbbbddbbbadcabadbacccadcdcacbabcaddbadbbadcdccddbacaadbadcbdbacaadddcbcbadabcaccdcadbbabbdddacbdbbbddaadcabaabbbbacbbdcdaabbdadabddcdcbcabadcddcdcddccdcacabacdaabacbcadbacabcbcadbdcadbbbbcaaaaabcdcdccbcacdbddabacbaaabbbdaddccbadbababccdadddccccbaddbaacdcaaadadbdccdddbddcdccccddddacaadcddcadddbdaddaabcabaaadbdaccddcaccabdcdddddbdcbbdadcdcdadccbadcabdaccbcddadadbddcadbbaadaacacbccdcaccdddddadadaaaccbadccdaadcdcacddabdccacdbdbdcbdabaddddbbadabbadacadcadcacdbcbbcbddcbdaddccaddcadbbbbabbbdacaacbcacbdaadbbacbcbabbbadbcdbbbcbdbbabcccaddcdccdcdaadcacddbbdcbbccaddabdadbaccacdacbadcccdaaabdacacbddddabbbacbdccdddbbddcbdabcaacacaaaaacadbdbbacccaddcbbadcaadabdbcddbabdcadcbdcacaaadbbacbcdbcbddcdcdccdabdbbadaaccbcadaccbdbdbdcadbcadbcbaccbbcbddcbbaccdccacddcadadccddaabcbadcbaccadcaddbdaacddccdccdacdcabdcdcaadddcaadddbaadbabbdcbdccbbbddccabcadaaadbaccbcbccdbcaccccccccbabbbcbcaabcdccddbbdcdbaccccbacdccccabbadcdadcdcdacbcadaaacbdcddcbdcdabdcddbabaaabdddddaaababacccaadbcbdcdcbccdadccbbcbdaadacbbbccadbbddaacacdbabcaacbbacdadbbdaddcccacabbabaabaccccbdccdcbcccbbcbbaabdaddccbadadabbccadcadbbcbdddaccbddaadccabbacbdbddcbbabccdbccaaacdccababccdacaacacdbaaaacdcddabbaaabcddacbcabcdcbccadadbaddababcaabbacdbcaadcbcdcdadcabacdacacaccccacbdbbbcdcddadccdbbcdcdaaadbbcddcdaabbdbcccadbabbdcbcacdbcccadcbcddcaabdbcabacadddbbcbabddaabadcdbbabcaacdccbbabbbcadaccdcacbddabdcdabcdcacbbccabbbcabddaaaacabcbddbddbacabdcaabddacddaadbbccdacbdacabbbabcacdccddbbccaabbddabcbdbcbdacabcbacadcbdddcaccdcaabacdadadbdbaddaabdcdbadccbcbdaadaadbadaadadbbaccdcdbbcbbadaabbcabdabcbadabbdbaccacbdbcdbdadcddadcccbaabbdabadabbacadbccdbacdabdcbadacbcbadbdccccabacddcbbbbbaccaabbdddcadbadcbbababcadaacaddacabbcbacbbaccccadacadaadbdcbaccbddcabaaccccdacaacbabcdbbdcbacaccdacadbaccdddcdaabcdadaaadccdbadbbbddacdabccdbbddcdbbdcabcbadcadacbbacbaabccacbdcbaadbbcdddaadddbcdbbcdbcbcaabcdcaaaabdcdaccddabcccacbbbcdbcddadbdbcbccbcbdcdacbdbbaccadcdcdcadbaaaddcbaadddbdacacbdbcadabaacdbabccaccacbaccabdccbdaaadbaacadccbbdadcadbdbcaadcddcbdbbadbbcaabcdacacabacddcbcdbabbbdababacdbccbbbdaaccacbbdbdcbcacaddbbbdcdaaabdadbcbcadbddbcdbcddcddabaacbaacacbbccdcbacdbcccbbcccacbcbddbacdbbabcddbbbacdccbbddcbbdbbbbccddcadaadbbaadabadaaadbdcaadcdccdbddccdacbddaacabbaacdcaaabcbbbbbbdcddadbcdbcbcddcaabbdbbdcdbccbddcbbcdccbdcdaccabbcbbbbbccaaaaaaadcacdbddabddbcbaddbcddcbdccbacbcbcddaacbccbdacbbdabdbbdababcaabdbdcbaaccbbacaadaabbdddbaabdbdacdacbbcbddcddcacbaaabdbcdbcabcaadcdaadbcddbbabcddcbcddacbabdcbddabdacddaddcaadbccababadcbadcccdabdbddccbdacbbaaabbddbbdbadbdbabbdacaaabdbbddccadcddcdbcabdadcccacbbbaabbaccaddabaabcbbdbdcdccdcaccdaabbaacabbdcddaabadbbcbadbcbaadbabdabbacadbacbbcbabdbacadddcbcadcdccadccdaaddaadcaaccdbbbbcaadcacbbddabccacccadbbbabaccadbdcdacbbcbcaaaacdadacbdcdbaccdbdbcccacdabdadadccaadcbddabdccdccacdadddbcabdbbadccacbacdbcbabbadbadaddcaadcdbadcdadacacbabbdbdcbdccdcdccaacaadcddcdaccaaaacbcdcabddbaababbcddcdcbcacadadadbbabcccabbbcaabbddcabaccacadbcbacdddabbdadbaadbbaabdbadaaabcbadccbdbdacbaddabaccacddcdaccacaaabcdabcbdaadcdcdddddbcdbbcaddcbcabdcddbbacddaaccabddbaabacbdbadbcccccabaccdacbdcddccdcabbbaddddbaddabbbdddddcaadabbaabbbbbcddbacabaddbbbbabdcbbbdbaadbdaacabbdddddaacddadadadacaccabacbdcadaaccbccadbccdcabbccdabaadddadddacadcdbdaacabbbcbcdcadccadcbcbacbdbbaaabdcacacaaccccddcbddbdbccabdaddabacddadacddaddbccbaaaacbcbbdddacbadcadaccbcdacdcbadbbbabccacaaadccbbadcaabaddcabbcdadaccaabbbbdcbacbdcacbcabaccdbacdcacdacaacbbdddbacacacacbdbdbccdcbbccdbcbcaadddabbbcdbdbcdbdbbaaadadbdbbcabbcbcddbbbbabcbacdcdbdddcaabdccbcdaddcccaaacacadddaccdccccbdddcdccdcdaddcbaccadcbcbbdacbdbbdadbacdbbadcdcadaadaccaacaaadaaddbcaaddcdbadacbbacaaabcdbdbcddadcabcabdbaadabadbdabdcaddddccddbbdbcbdabacdccccccadacaacdccadccdaaaadbcbddcaabdbdbdbdacddcadbbbacbbcadaadddcbabdcbaddadcdccbbdabadcababadcacaccbcccaadbdbaacdbbacbaccaccabdabcaacbdadadbccbbadacddadcacdbbcbabcddaabadcaadbdaccbdcdacaacbdaaabcddccdbcadcaadccbbbacabbaacbdddbcbdcbdabaaacadccacbaacacdcccdcccaabbdbdabacddcdbabbddcdaabbbaadbadabbbacbdbbbacabbcabdbbbcaccdbaaadadbaaddabaacbcdbddccaabddabdaccbcabbabcdcccacddcccddaaccaacddbaabdcdaacdddbdcddbcbcabdbcabacbccadbcbbacbcddcdcbacaadaadacbbcbccadaacaabccccdadcbbbcbddcccbcbcadcbbccdaacaabddccadadcdddcabdbaadaaaabdbabdccbbddcdadcbdadacdadbbcbbdaaddbbadabbdcdaaacbabbdbcbdacbdadbddccaccddcbabdabbdcbcaaccaaaadadacccadbacacdacabdbdabbcbcdbdacbcbbaaabcabadccddababadddcdddccadccdbcbaaacaaabdccbdbbbdbccadccacbdaacbaaadabbaccbbbacaacdbbdbcddcbabdbdaacdcdabaaadbcacbdadbbcbbbaddacaaadbdacdcdbbadccccadbbcaddababbbcdbcaddcaacdddcdacacabddcaddcbbddadccdacaabaddddaaabdccddcbbccbdccccaaabaacadbaddabddabcaddbabdcddbddbbddbccdcabdbcacbbcdcdcddbbccabbcbccbbbbaaddccadaddbaaccaddbacccdacdddabaabcccaccaaaabcdaccdcbcaaccaacbbcbbcbdacdaabdbaabcdccbcddddccabbbbbddccadacaabadcadddbadacbcbccacbcbcbaaaddbbddbbbadbddbabcababcadaabbdddbadbccdabddbbbdddbdbbccacaaabbccddcacdaaaaaadcadbabbadbdabdddcaccbaacccabcbbcabbbdabadabdccdabacabdddbdabccaacdbadaaaacdacadaaabcaabcdbdbccdacabdbcabcbbcdcadbdaacdcadcbaccbbddbadaddcabcdabdddacbbdabcdcbcabaabadbbcddcdadbbbadaadacabbbcdacabacddaabacadcbabddcddbaacabaaabdbddbccbaabadcbabdbacdbdadcbbadadcaccaddcacdcdcdabddacdbccdcdcbcabdaddcdbddbbbdacbcadbaddabacbcdabbcbbcdbbdaacadaccbccacbdbdaaabbcccdcabaacbabbacbbbadadbccdcddccbcdbcbcbcabacbdaadcbdbdbabdccaacdbacadddbaddbaacabcdddbdaccadcdaacabaaddcbbdaaccdddccbbcccbaacbbbbbbdbbddadcbdddaacdacbacaccadbacaadcddcbdadacaccbddbcaabbbcaadcdaccacbcabcadadabbacbbcadcbadaddbcaaadcacadbcbabcacdabadaaacbbdbcbdcbaaabdcdadbcdbacadbbdadadaadabcdadccbaaddbdcbabbbabcdacbdddcbdbbcdcaabbddbbabccbadcdacaaadcaadcdcababdaadddadaadbdbbbcddadacbdddcbbcbcbbdcabbcbbdcccbabadbcddcdabbcbabcccdcaaacbabcdadbaacacaabdabaccdbbccbdabdacadabdddadaaacaadccbaacaababcccbcdccccdbdbbbbaadaccdacdddcdddacbaabcddccadbdbdcdccbcccdababddcdbcbcadaccdcdcdabcacbbcadcdbcbcabcbcdccbdcaadbdabdbabdccabcbbabcabaccddadbdcaabaadbaaccabbadaaacbddaadccaaddacddcbddccacbaadbbcdacadacdbaaacdcbbccacdabcddabcabdbcaaccdadbcadccddbdddbcdbcbdaaaccaadddbbdbcadaccbaabdbadbddbcaddacbcbbbaddbbbaabdaacccabcbcabbaddbadbdcddacabcbbacbaadbaaabdbcaddcccddabddacdcbaadcadbccbacddbadabbaadbbdabccbcabdbbbdccbddccddacbcddbcbcaabbdcbdbbbccbdadacbcdcadcbbcadabdbdbbdcaddbbcddacacaacabbaccaaaaaaabaababcdbdccbdcbbcccddcbdbacccbbabcacbdaabaabcdbadcaabcdcccbbadccabaddbcdacbcdcacddbabcaddcabbaddcdbdaccdbbaacbbadcabcaddcabbdadaddddabdabacdbdccaacbadccdbccdbadccbcdcabcdcaccbcaaaaacbdabddcbdcbdcaadbcdbdccabcbbdbbbddacaddabacdbbdaaadaabbcaaddcbccdbbabcaddacdccdddbddcacbdcbcaadabbacabbdcaddddccbcabbcdcacbccbabaaaabacdaddbddcddbbadcaaccdadaaacabbbbcbbbbbbadbdccaaccdbcdcbbacddcbcbbcdabbadbbcdcccabadabcddccdcbbbaadcaadbbddbcbaabcccdbcdcdcdaccdcccaaacbccaccdcdbbdcdaddcbdadbbaabbbabadbabcdadcddbbdaabdabcaaacdcdbdbbbddbcacdbcbaacdbdbbabdbbdcccbdcdadcdbaabcadcddaaadbdaccbbcaadbdbbdccbbadbababbdaaccdacccbcbddaaacdcadcdbdddcccdcbccadbcbdbcbbcadcbdcbbbccdbbddaccccbbdacbdcbadbadccadaacaacaacabbbbbadbccacaddabbccbcacabdbaadcdbacaaccbdadcdcdcbaaccaadcdbdcccdadcbcacddacdbcccdabbcdbabadcabbbdbadbaabdcbcbcbbdcdaaacbcdcdabacbddccbbcccdddacdbcdbcdcdbdbbdacabcdbbbbddacbbbcbaabdbaddabdcbaccddabcddaacaabcabbdccbcacccdcaccaaabbadbaababdcdabababdcadacbadcbdbdadbbabdaccbddabddcddcdddbdddaabbccbabdcbbddbdaaadddbcddcbdbdacddbcacadbacbabbadbdbbdcacbaabdbbcdddbbcadbdabaddccdbcacaacdbdbcccbadbddcbadcadbdbdcbdddbbcababccadabccdbbcaaaabcacccacdacabdbbdbcbaabadccdbcacbddcdbdadcddbcaaaabcdacbabbbdaccdcaabdbcdddabbdbababdcbbcbdddbdabacbaacdccbbdcbacdbacabcdaabdbacbdcbadabdbdadcccaacaacdcbabadccdbdddacdcbaabdacaaadaacdadbcacccbaacdadbcdccdcaaadccdaadacbdadcdbccddcaaaccdbbaccbdcaddddbabaadacdbbaaacddccdacabaadccaacbaaacdbbddaccdcbdabcdcbcddabacbbddbcdcadccddcbccbbcddbbacadddddbcdbcbdcdaadbbdabddaddbcddddccdabcdbdddaaacbcaadcdddacddbcddaaadabdaadadbadbbcdbbcaddbcbbcabbadabdccdcacaccaddcabacaacbbbaaddccbcbcbbcbcbabdddaaabdcbdcdccaabbaacdcacaadadcadaddbdccacaccdacdccddaaabaaccaccccbddabbadadaabdcdbaddacbcacadadbcccacddacdbddadaccbadcbacdacdabdccaacdcbaadcaadcddbcccbdacdcdcadccacadbaccdccaaabccaaadddbaaabacddcdbcaddaddddacacbadcbddcbcdbcbccabadaaadacbacbbdddadabbcbcbacdbbadbbabacbabdbbcdbbbddabcbdabcadddaddbacbdbacbabcaaccbdacaabcbccaaadcbdabdcbabdabcabaaddaaaaadadaccddabcbbcdcbccdbcdccabcdabaacdbbcacbdbbaaccbcabddaaacdacdcddccaaadcccbabccaccdcabbdbcdccbaccaadddcbbbbcdaacabbcbacadaddcdacabdbccadcbcacbbadaacdabbdadbbbccddbcdddcabcadcaaaaccadccdadaadbdaadbbcdadccdabcdcdadccdadcbdbcbbcdbddabaaadcdbcaacabdbabcacbdbccdbddacdbacbabdbccadccdaaadcdcdcbacdadcacdccbadcacdaabcaabaaddcabdbadbdbcdbcaaadbbbdcdcaaddbcabbadccdacabddcbdaaddaacddbaccbcdcbdbcabccaabadbbaaccdbdddbaadbbcbbbbaaabddcbdcbbaabbaaccdcaddcbbacacdaccdcbcddccbaadadabcbdcacbcbdacccbcddadadaccdbbbaaccacabddacdbdbbaccdabdbcacbcbcdaaddcacabadbbbcdccdcbabdbcdcacadcbbdabbdbdacbcbbacdbcddbcbddcbdadcdababbcdbacabbbacaadbbdadacaaadddcbaaddbcbaddaacdcbccabcbacbcccbccdccddddddcddbcbbcddbadcdccdcaabdbccaabaadbbcabddacacbabbbddaadbdcdcddadddbbaabaaddccbbbcaadcadbbddddccddccdcdacccdabccaaabaadadadaadaddcbccbabbaccbbcaaabaddabcabacbdbdbbdbdddadcddababddcadcbccaadbbcadaddcabbdabbaaccccdcdddabadbbabadbabbdadbdabdccabbcbdbddadaaabdccbdcbbcdabcadacabdbacdbdabdcdbadccccacbddcdaccacaaaadaddcbaacdadabddbccbcccbbbbccbcaaaacbacbcbcadcaccccbbdadabdbcbbbbcacbbbaaacdacabadbbccdabcdcdddbcbcbcdcbccbbbbbaacdcdddaacbbabbddadaacbacbcdbbaabcbdddcccabddbacccdccaaccaacababababaccbbccdacbbbbaccdcaabdbcddbaaadbabccdacdcdbccbddbcaaabcbcbbccdcadccadcddacdcabdadabacccbabcdcacacbacbbabddbbbcdbdbadabccccacdbdacbcadbadbdbcdcdbaccadbbbcccdadcabcacbccdabadbbacdbcbdddaddaacbaaababadbacbdcdddbcdddadbbbcbbabbdccdccdccabccabdcccdaabaadcdabaddccbbdbbdcbbaababaaccacbdaabdcddbdaabccbaacadcddabcdbdcaccaccddcdbbbbbbdcbbbacaccacbbaabccddccccaacaaaabaabcaaadcbabaacdcdcabcacbdccadaaabdadbdcabaabacaaadaaddcdadcccdcccbbddbadbaabddbabdbdcbccddacdccadcaccddcbdadadcccdaccbaabbabcccacddacdbbabacbdacdbcbcadbaddcdccacdaadaccaaadcbcdaabbccccccddccbcbabcbacaabccddcdaaaccdcccbcdbdbcaaaddcabbbbdbddbbcdcaabbdabbccadbcbcaaccabacddabbdabddccabbcbdbbbaaacbacdabadacccaabdaaadbdbcdbdcbdbcbdbcdccddabbbaacdaaaacaddaccddcaabbabdbaccdbcdbcbaacbcadbadcbacabbcbbcbcbcbcccadddcaabbbdcdbcdaabdcdcaacdaacdcdabccbbbcbbbbabaccadadbadabcbdadbcabaadbddcccdadaadbcaabcddcbbbacacbcbccdabaddbbdbbacdcccadacabcbddabbadcbacbaadbadabaabbdbdcdadacddadbdacacbacadaaccddcbacbdbcccbcdadbccbddcadbacaaaccdbdadbaccdbbbccdabaabdbbbdbaaddaddbaccbbadcdabddcdaadadbbddbcbddcdbdabcaabcaccbddabdcadcacabdcaddbaaabbbddadbabdbbacabadaddacadbccacbbdcdbbbaddbaddbcabbcbdcaaaadcbcccdbdbaacdaaacaacdcbcacdbcaddcabbddbbdbcbcdabbbaddcbaccabacdccddcacababbbccaaccbaaacabbbccdaabccacdddcdacacacbccadacbdbaaccddbadccbdaaabbabcdabccaacdcacdacacbcdddbbbcacccbcbadccbdbaaabaacacaabababaddadbdbdbddccccdddbdbdbdcddbccacbcddaddbabbddccaddbdaddbadbcdbdbbbccacdabddbaccababbbdaacdcacdbcababcbaacdddbabdaaabdcbaababacbbadccbcdccaabadcbdcbbddbaadcdabbdbadcacdbaadbdcdcdcaaacacddcddcabbcdcaacddbddaababdcddbdddcaccadcdcdccddabcabadadacadcdbdcdbbdbaacabdcdbdccdbdabbbcbdcbdbaacaabccddbccdbddcbbccbcaccdcacbcccabaabacbdbabdadbdcccdbcabaadcadadbdbcddbdbdcabaabddcdbcdaaaacadacbdbdacddbacdaaaaabdcbdbcccddcaaccadaddcccbcdbbccdcdbabadbacbbcbcdbacdbaccdcaacadcdbccacbaaaaccdacadcddcbbccbddcdcbabcadbabddcbaccdcddabadcccadddabacabaadacaacbbabcbaabdcdbaddccbcdbaaccbcddbbccbbbddadcbacddbcddddadacdccbbccddaabaccbccbbbbcadacbbcdcdcaaccbbdbaadcbdacadababcbdabbddbddabbacbdbdbdcdabdaaabcaaacdadcacaccababadbbbcdabbdaadcadbcdcdacbcdcccdbccacabbcbaccbbadbddbadbdababbcdddbbacaadaacdbbbccbdcdcddcaccbaabbdcacdddbbbaddabcbbacbbdbbcddcdacbcdddabcbddcbdaddbcacddaadaaacdbbdadccbdaaddbcabddccddbcccbcbddadabbdbabbccccbdcbbbcbccbacaaccbcabcbbbcadacacdaddcbcaddcacdccbbbcadaabcbddabccddbadbbadbabcbbbcddaddbdddcabbcaacaddccacadbabdbaaacbcbabdccbadbccaddbaddcdcdaaadbbaddbcbadabbadcbaccbdacbbdacdadbacadddbbcaccdaadbadbbcadbaddcdcaddcdcdaacaaccbbacadbdabadbabcdcddccbcdbdcaababcdbdcbacbabaadcbcbcdccaabdadacdcaaabdbbcaccadabbcbdbaadbbbdacbadbddbdccbadcaacacdccbcbcbddbbbddcbadbcdcbdccddcddccbdbbccacddbacadcbaccdaadaabaaabccbccabbdacccdddcdbacbdbcdddcbdbbaabcdabbccbbcbadccbbdabacccddcdbbaaaaadcbcbaaabcbbbbbdbabdadccbbacddcabddddccabdbdbccdcbbabdcdbadbbacabdddcadacbbbcabdcccbbddbccbdbbbcacaddacbdabadcbdabacaadaacdddabcbdbccbcddacabbcaaddbbbddbaddababbbccaabcbbaabccdcaaaccaddcccccdbdabcaaddbaaddcdadcbcadaaacbaaadccabccdbcbcaadcdbbacbdbcdcabbadbadaaadcabdccadbdaacccbaaabdadaccbaacddcbcdabadbadadbdadacadabccdaddccdcbcdbbdddccbbbadccadbbacaaacdacabcdabbbccccacbddbdddcbdbcbcbabdadccacdbdaccabbbababbccbdababbdcddbdcbdcdacbddcdccbbcdcbcabdabdcbdbbdcaccbacacbadbbccdcabdadcadbcadadaaddcccccdbbbdbdddaddbccbcddccbdcdbddddddcddbdcddbcaacaacbddcbdacbbcccaadadadbcbaccaccddbaaddddaacddcadbdcccabddbcbddcbcbdcadbaabdaabdaadbbddadbacadddbcacbdaadadccdcdcdcdadacaabacacdcbcdacaaaccdddadbdcbbcabccabdcacaccdbdaabbbcdaccdaabdbdbbaadbdcbdddcdabbdbcabadcaacdcbcbbbdaccdbddaabbbcdcdbcddbccbcdacbbbabcdaaccbbcdcbdcaccadbaadbcccacaabbcbcbbbcaaccbbdcadbbacddccbaccbbdcbbdbbbdccdcbaacdaccadcbccaadcbacddcbddbbcccabcabacddcbdbbbdbbdaddcbbaacaaddcbdadcbcacbadcdcbbdbbacccbbbbcdddddcddabaadacdcdacbdbbadabbadacaaccadcbbbacbcadaacbbbbdccbbadadbdbbdcbcabbcdbadabaccabddadbcccbcbccbadccccbdcbcbbdccccccdaaabbdaaababccaaadbcdbbbcddaccddcdbabadcdadbbcccbccadaabcabaddbbcbadcbcdcdcadcdadcabbbcdccccadabdcbbbdcdcccbccadcbdbacbdbbabaccdbcbbcbcdbcbbcccbdcdbcdaacaaacbaaccddddbbddcdcabbbdbabdccccbdbdcdbaaacabcccbbccbdbcacdadbcbcaaaddbbbdaadadcdcbbddbbbbabaaddbcacdccaadcaccbcbaabccadbcbcbcddbdbabacbcbbbcccdcbaadbdaadcbcdaddbadadccacdbdbacdbaccaddadbcadbcbbaccbcdabbdbccbadcbaccbccaadbcdaabaacdcdcabaddbacbabbcbdbacacabbdcabcacacbdadbbaccddbddcabcbdabbaaaaaabadcdbaaddbcdcacbcdadbabcadbbbbadbcabbcacacdcacaacdcbdbaaddaabbdbdadccbabbbcaddcdadccadbcbcddaccabdbddaadacdadbaababcbcccbdbdaadcbbcaababddcdcadbddcbcdadbccbcdccbbddaababccbcdbbbbdcadbcaacaababacdbcbddbbdbccbcdcabbcbbaaaacacccbacadccbbccdccbacabccacaccadbdcdacabbbcdabbadbabbbadcbbdbccabaccddadcdcdadaddddadcabadbcbacbcdbbbaddabdbbbbdbbbccdbdacaddddccacbbbaabbdbbdcdaabadbacbaabccaaddbbbcbbcdccaacadcdbccbbacacacadbaabddccdddcdbbcdddaacbcbdddcccbbbcdadddcdcaddbbbcbccdacdddbdadccbdcddbdcacdbcbdcbcaabaddadadbcabdbbbabddcdbadccdcccdcccaccaaddadbadccbdbaaaacacdcbaabacaaaabdcdbaaadbbacbddabdabbddcabdccdbaadabcbccacdaabadcdaabdbccbcdbcabdbaccbabbbbcaaadadaacdaacdccbdbbdbbbabaccbbaaadbcbbbddabddddbabcddbbcaacadbaaddbadcbbcbadcbdccbabbbbdadbabdbbacccbacdcbdaccccbbbbaaacadddbcdacccbccccdbabadbbabadacaaddabcbdddcdbcbccabbbadabdbacbdcccadcddcbbbbbadacccbabcaccdcbcadaaccbdbabcddbdacbdbdcaaacadcaadbabbcbaddcdcbbcdcdbcddbccdcdbcccddaadbcbddaaccadbdcdbadbccbaddccaacabdcbbbdacdcbcaacdccddadacdaaddcacabdababaccaaabcdabaccaaaadabdcaddaabdaacacbbcacbbdcdcbdaabdacadddcbdbcdbbdabaabaacdbbaacabbaaaccaaddbbcdacacbdcbadaacbdccdccbdabacbadccdbbdbaabbcdbccbabbddcddbccddbccdbbbabdabbaadcabbabacbdbdbadadbaadcdcaaadadcdbbdccdacccdcdabacbddcdddcccaabccabbcadddaddadddacdddaaadabcdcbbddbbbaaadcacbbacbcaddacdabbcddabcbccddcadaaabcccbcadbcddcabcdadddbbbddcacaabbabdbcaadababaaccadbcbddccdbddaabadabbddaabbbcdcdabdcdbabcdcbbdcbddaaadcbbaccbbbbcbbdbdaadaaddabaadccdbcbbaaddadbaacbbbadadcaddbddadcdccbcbdadccdaacddcacaccbaddccdaddcdbaadbccdacaddccbddadccdcdacdbbbcdccdcaccbdbbdbbdcdbcadcaabdcbbbbccddbcbaacdaddaabdaaaccadcddcadcbcbdaadadddbdbcdccdbaddadbaacdaccdccabcdadcdccbcaadccdaccdcbcbccdccaccdbcddadabcccabbcababbbbbdcbddaacacaddcdabdbabbaddaaadcbadbcacbdacacadcacbccbdbcacbccdaaadbbbccccbadaaccacbccbbcdbbcabdbabdccadabcdbabbdacbcdbadddbaabbbcdddbaaaababbdbcdbabadaccacacabbbadbcabddababdaddbadaacdcaaabbdcdddadaabbdbcbacacacbdadbccaadbcbcaddcdcbacbcdbdddabcdcbccdadddcacdcbadabadadbadabdbcbdababdaddbadaaddcbcacccadaccdacbcbdcddcddbcacbbbdcccacccdaaaacacbaccaaadcdccaccddbdcacccadbacdbadabcdaabbcbadcdbddccbacbdcdaabdbabdbaddbdadddbadbcaadcbdabbdcbcddabadabddadbbbadbbddcdddbcadaabbccbcacacbddbcdbbdaacdacbdbaccccbddddddbabbadcacbdbdbcabdbcdcddddcbcacdbcdadacccaccbbddacaaccbcaacadddbddbbdbbdbcdabdbabaaadcacdccbcdddbdbccbddacbcddbbdadddddbdbcbaabdbdcabdcbdabddabddacccbccdbdbabdddadcabcdababccdadcaddabddabddabdccabaaacdadacdadacdddcadbcaadbbacccacbbcacadddcbadccdcddacbddaacdbbcdccbdbacdcaacbdcacdcbcccbbaacbabbdccabdaabddddbcbbddddcbdddabcbbddcacaaccddabadbdcaadaaccbacdccdcaaadcabcccbbadcdcbaacabdacdcabdbbccacbbbddcdcdbcdaaacacbcacddbcbbbbdccbbbccdadbbcdbccdcbadcbcaccdaacbabcbaadbcbddcccaabbbababbdadddcbadacdbaccbaacccdacdcabbdddaacaaabdbdcbacaaadbcdcdcdadacdccbdbababdbdadbddbbcbdddbbbbdcadcccdbbcbcccdccdbdacacacaddabaabaabbddccadabcabcaacbcdacabdbacbabccdcacdabbbacbbbbbadacbaaccdcdcccccaddbadcaabccbccdbbdbbaacaadadacacbcdcbdcadbabbddbcbcdddbaacddcabaaaacbdaacbccdccdcdddccbdddcccbbcdbbababcaadbbcbbccccdbbabbdbaddcabccdcddbabcaaabcabdbacbdcbbdbcccbcbadbcadbadbbcdacbccbdaccbcbaddddcaabdadadcbbbbdddabcbcbbdbabdbddaaccddbaaacdaccaccbcddbcbaccaddddddacdacddccdacabaadaaccddcbdcabdadbcbcaacdaadcadddcbdbacabddccddabddbcacddbacddccdacabdccbaaddacbdcdcbadddcacabcdbdbddbcadbbcbadddacddabaddadabccaccdbbdabadadcabddcddbcbdcaabdbdbabbcbadbdcdadbbadaaacbbbacbadbbbabbdbaccadaaabaababdcbacacdcacacbddcacadccacccbdcacdbcaabadcccccbdbcbdcddddabdaacdcbcadddcdcbdcadcabbcbcbbcdbbacacbdabacdabdcaadddaddddddbdacddabaadabdadddcbdaacccbddbbaaccdbaabaabddacdadcacbdcccacaabbabbaabbbddcbdcccaabcdddacaabddbbacbacccaabdcdaddbadcaddcbcacacadacddadcacbddbdbaacdcabbbdcadacadddabcccbdbbacbcacadcddcdddbbaaadccbaabadadaaccccdbacdcdacdbbdbdcaacbbddbdddbdaabdbcdcddaddccdcbbacbaadcadbbbcdabdadcdbacdabccdabbdddddababcaadcbaddbabbbaccdccacbbababccbccadaacbccbcabddcaccdbbcdccbbbbdcbdbcdbbacddbbaacacaadaaaababdddddcddabcdbbdbbccbdcbcbcbbbbdaaadbccbbcaacdaabbcdcaddacccadaaddcabdcbcbabaddbdbbaabcabddcadaccacaaaabccdccacdaabaadccdbadaacaabbccbdaaddcbaabcacbbadcbdccaacbacacabddaccbdbdccbdbbdddccbabbcadcdbaddddbadbdccddadcbdadbacdbaddabcbcbcccacabcddbaaadbccabacaadbdddacbbbcdcbbbdbabdcbdbbcacadcaadcadddacabaaacdbccbcabbbbaccddccdcdbdddcddcddddcbccaddcacdadddabbcbdadbccdcbcbcbbadacacadaaccabbdcbcdddcbdabddbbbdddbbcccababddbcdaddacacbcddbccabbcbcabbbcaadcadabbcbdddbccaabddabcccdddcbabcbadddccbbadcacccbadddabddbbdbacdccaabcaadcbaabdbbbbadbddcdcdcaabddcdaacddccbdaacbabbaaccbddacaacacbacccbbcbcbdbccbdbabadabcabacbdcacabbdcddddcdcabbabccdaacaadcabcdcacaacbabdcaddbcdbddacbabaccbbccdacacbccadbacbdbdacbbaccbccdcbbdaaaabadacdaacbbaddccaacdbacaaaddbabcadabdddddbdcabccbdcccabdbdbbbdaaacbdacbcbdbdbdaccddcbdabcddccdabaabcbbadbaaadabcababccdbbadadabbcbaabddadcbbbcaccdcbbabbbccbdbdaacaaacabbcabadadacdccdabcbabddddbcababbcddacdbcaccdadaabcdbddccdaadabbdabddbbbabbcacabdadcddbacadcbbdadbabbcbcabdbadcddcbdadbbbdbcbaddacdbacacdcaccadcdcaadddabaccbaddadaabdbdddbbcbbbbcaaadbcabbdacdbbcaddcadbbcdddcdadaaddabddccbabddbcbabaaabccacacbdddacaddadbdcacbaabcababdbbaccaadbaadacaccabcaababddaabccbdbcdaaddaabbacbbbcacddadccbbcccaaaccaaadabdccbccddbbaadadccbabcdadbdcbadadcbcaadabadddddddcdacdadcbbbcacabbcabbcdcdbdcdcddcddccacadaadaadaddbcbcccabcdcbcdbdccccbadddacbdddabddcdadbddcdaadcadbcbabadccbbdbdcacbadacdcaabdddcddbbaddbcbdbaacbcdddddddadbbccbbbcdccadccccaacadbcbadcbcdcbdabcdcdabdddddddabbdcabbabbcaabcddbbcbabddbddcccbabdddaabcbcbadadbcabdbaadcdacdcdabddaacdcbcacdddcdbabbcbaacdadadccddcbdcddbadacbbdaadccacadbaddaababbbbdbacacbddaadcadbacadccbddacbcbcbcbcdcbaacdaaacabcbbdcbabcabdadaabbbacabdacbaacadbcbdaccdbadaaaccbbbbdccddadcdaddbaccdaaddabbbbcadaacccaabaccacbabdbbdaadaaabcaacbcbdbacdbcadbcdcdbadacbdbbdbccadadbacacdbcdaaddbacbabadcbaadacdbcaddbddaddbbbcbdcdccbdcdddbdcacabbabbdbddaabbcbdaaabdcbacaababbcabbccaddcaadbdaddddbdbaaabcbacabdbdcccaacaadbaccbdcacccaaaddddcdaacbcdcbcaabcbcdacdcacacaacccdbdcacaabaccdadcbcaacaacdccbcbbdbabbcdacbccddbccdadcadaacbbbbaccbbcddabdadddacddbbbbddbdbcdaabdbcbbaaccabdbaaddcdbccaddbadcbdaabcdcbcddaabbbdbccbadcbbbcddaabbcdbacadcabdbdddcaddaaccbadbcaccddbbbaabbadccccbccaacdbadbcdcbbadaadccbcdccbacabbdabdcbcaacddadbabccdcdbdbdbccbdbbacdbcbbabccbcabacccbadcaadbccccdadbacacdcaabdbccbdddaadddccddddbbaacbdcdccaaddcadcaccabdccbdadddcbccadaccdadacaaaadbaaacbbdbcbcdbdcaabccddaccbaadaacadbdaadbbbdacaddabdcbbcddbabaccaacaacdcbdbcbabcbbdabdaabddcdcdabcadbccbddabcdcdaaddbdcdccbacaccdbabcdadcccabadadbdddadacdaabddddabdaaaaaabbcaddcbbbaabbcbadbbaccbddbaabcbacbbabaaabdbddcabacadacabdccddcddbabdbbcacdcabdbadbbbccccbbcdacbccbddddaadbacadbbaabaaabcbbacdacbbccdaccbabdbcccabaacbbbdbbbaccbdbcbcbdbdaaaacaacabcbddadaddcccdbdcbdcbacadadbbdacbddbdcbccaddaaadcdcbaadaddcbdabbbabacccaddcddaabbbbdddbadbadddbadcdabdabdcacbbddcccdaacacbcbbcaddabdccdcddddcdbcacdacccacbbcbbcdbbbccaababadbbdbcbcdbbdbddbddcbcaaddddcdabccadadbbdbdddbbcaddcbcbacdcaabdbcadaadadccbbaadcddbcbcccadcaacbacacbdabaadddbdbaadabcbadacdcdddbbcdadbbacbcddbbdbdbbdcadcbaacdbdcbbcdacccdccaccbbbccdaadabcaacddbdbdbaacddbabaaaaabccddaabaabdbbdaccdaacdbbbabcaabaaccdcdcbbcdcbaccdbacaddcaaaabaaccaddaaaaccbdcaddbaadbccbbddbcbcdbddaddbacccbbbacaaaaaacacabcbddcaaaadbddcdacadbabadbdbbbdcddbdadacaabbddddbadcbdbdbabcbcaaacccccaddaabcbcbbaacacccccdbdddbdcdaccaaababccaacbcabdadbbdaaadabdcdaacaccdacaccbcabddbaaddcaaabbdcbcadabdccbcbdaabcdbacabbddaddcbbadbaccacacdbcccbadbabbdddaccacaadcbbbddcbddbbacddccdddaadcaabbdcaadaddbacabddbddcdcbdbdadbbdaababbddbbbbddcadbbbdaababcdccbddbccbadabccbaaddddcacccccabbcbdcaacacadbddbcadacadaacdddbabcdbdcadabdcddbaaaaaadaccbdcbdbcbcbabdcccbbacbabdcdabcbcbbbadbbdcbdadbcabbacaaccdcacbbcbdcdbccaddcacdcdddacabbabbdccdadabdabaccbdacdbacdcbccccdbcbaccabdcacdbaaddaacbddcdbdaccdaccbcacdcadbbdddccddbcbdbbdccdacabddabacaadcccdadbbbcbadddcbbcdadbaabbdbdbbbbcacdcdccbdddaaacdacdaadcbdaddaccdbccddddbacacdcbbbacddbadacbbcaacdcabcaaacadbbabcdbbbddbaadbaaaaddcbadadbabbadcccacdcccbdbaddacadbababdbbabdcadccbadcdcbdbdbdaadbdabbacbbcabbbdcdcbddbdbdaabacbbbbdadccbbadbbdcdcaaababccbdbbdbdddacdcabcdddcabccbdbbbcbabdbcdccdbbaccadbcdbdcbadcbbdcdbcbbaccbdaacdcdccbdddddcdbcdabccbcabacdcdbadcdbbbbacaabdddadccadaaaaccaababbbcabcaccbccdbcbdabccadddbddaacaaaabbacccdbaadcaccbaddddbaddbadaabdccddbdbdcbddbcadacddbaacdacadddccbabcbbbcabababdcdcdccbacadaccaddddaacaadbcccbbadbcdadbdbdabdccacdcddcbdcbdcaabdabdacdbbdcdabacddacccbdddabbcabdacccbabbabddbdaccbbcacabccccdcbabddbcdabcbddbbddabbaabdcbacccadadcacbdbdcaaddcbacdbdacdadcbdccccbdcbcabbaabbbcbbcbdcccddaddabdbbcbdcdbaccccbdbcdcbabbcdddacabacccabacbbabbbbabcdacdacccbadaccccacdbddadbdbccaaabaadabbbaacbbaacdacccbdbaaacccabadabacacdadabdabbdcdcacabdadbcdbcddccddcaddcdbdbdbdabbbbabbcbadbbbddccbcadbcaabcbdbabcabdaaccaabbcdcbccacdccccbbbabcbbddccbbacbbddccbdbdaaabddadacabadaddadddddaabbadddbdaabdacccddbdddcdaacaadacbbabdaacaacdaadbadddddbbabbbbccdbbdcdabbcbcccbabcbbcdcdcabdaddbcadbdcabdabaacdcdadaaaaddbaddddbbbbbcdcdaacdbcdaabccbcccdcdabdcabbdddbcbaadddaddccccdccbcdaaadcdacadacaacbaadcbadcacccaddccdbacacacdcbcabacaabdcddbdabcbcbddbcddbbadcabdaabbaadcdbbdaccabcaacdccdadcadacadddcddacbaaadabddbdbbddaabaccbccdbcbdacabbcdadcbcadbacbacbcbcdccdddaaabbccccabbbdddccadaddbadbdcdbdaacabcccaccaccdcbbcdbadacdadbdabcccddccbdaccadbbdcbcbabdabccabdcdabbaacadabbdadcbcadaacaadcabdadbcdcdaaadacbacbabcacabbdabbdcdabadcccbbadbbbdbadddcdbcacbbacdcdcdbddbdcdbcbaaccbbdcaadbbbdabddddaaabcccbdabbcadddbcdcdaccbacacdbaabcaccdbaddacbabdcbdbbcaadaadadcbacdbdacaacbbcdcaaccbcabdcdbababddccccdacbdbccaaaabdacdcadadcbaddabacabcadccbbccdcdcddacbcbdbcdadcababdbcbbbcbcbbaddcaaacbaaadabbbcddcadbacbacabbddadcdabcdbcdcadaaccbabacbaddabacdbbdadacabccacaccdadaaacbbaacbbdbddadbcbbddacaabdcbaacbcaacdabdcdbbdbabbadaccbdaabaaccdbabdbadccbbcccdbcadccdaccaddbbdddcbccbdbdaacdabdabcbdbdaacccdbdcacccbccbccdcccabccbbadabcaabcddacbadbcdbcdaaadbccdadddbaacabccdbccadabcdadbbadaabacbbbaadadcbbdaddbdbdbadbaadcbacbbbabcdcadbadbbdddddcbbbddbcadadcadddbccaddbdadccabbdbcadbdabbdccabcccccdbcaadbdadabccbabbdccddbcaabbcdddbdccdccdddadbbcbccbddbcdaaddcabacadddadbdadbdccddbadccddabcacabccccbdcbaadbcbcdddaacbccbddcdbbccbadccdbaacaadddaabdacbadcccbdbabacdabcbccbbacadaddddcbcabbcaabaccacbddcccbbbbccddbcaddbadcbcbdbabaaaabdbabcbaadccdbbabcbccbdcbdaadbdccdcdaaabdbaaadacdadaabbbccbbadadadbcbddcabcbadcddabcabadacacbabaabcadbcdcbbddddadccbddadabbdaaccaadacbbaacbddcddcacbdcbacccbacadaaadcdabbcdbcddbccabcddadacbcabacadaadadcabbbdbabcabaadaadabcbbdabaccaccabbccdbcbdccbbddcddcabcbdadbbcbdddcabddabbdadacbbcbcbcbaababdbcbcbbcacbacacacdbadbdabbcabcccabcdacbaddcdabcaccaccacaddcbadabaadadcbadcaabcbabaccddababcbdcdbdabbabaccbaaccdcadaddaccccbbaacbbcbabaddacdabaddcbaadcaadacccdcbdabcbddcaabcacbcddcbbaabccbbccdaadbcbcccdddacbbdadbdbddabdbacaabccdacccbaacabdbacdcbdcdbdbbccdadabcbcbacdddaabdcaacaabbbbccdabbbadbcdaccaababdbdacddacabdccdccdddaadbadaadbacdcdbddaaadabbddddbacdcbdccdcbcddbaaaacbadaaccbdcbacadcccccbcabcdcadaccdabaaabddbbdadbbbbbdaddcaabbddbcabbabbacbbccbaddbbcbbaadadbdbbcbabcacdaccdcdaccabbaacbcaacacacdbdbcdccdbcbaccbcaacaaadaddcbddadbbcadabaacbbcabdaaacddbbaacadaddcaabadabadcacdcbdbaddacdcbacbacbcdaaccbddbdadabccadcdbabdbaadabaaacbadbdbaaabadbbddacdcbcadbcabbbcadadaadaadbbddaaabbabcdbbdbbaaddcdaabaabbacccdbdaabacdcacbcaccdbabacaaccacbcbcaabbdbddccccadcccbabaaabcdcbbcabcbbdbdcbabdbdaaaabddcabbbcdaaadcabdcbabacbbabdadcbadcadbdabbcdcbcabcdbdaaabaacdbbdaaadbdaadaddcabdcaabccdadcbdaadcdbdcaabadcaaadbbdacbbdacbdcddccacbcdccdddccaacbbbbbdbcaddbcaccbdccacaddbcacacbdcabdcadccbbcacdacddcababadcadcdadaadacadcaadbbccbabdaccabdccbbbabadbbcdcacdaaddddbacbabdcdbbaacabbcccdccaabadbababddccbcadadbcbdbacddacadbdabbaaaddbdccaacacdabbbbcbbbbbddcbaccbdaccdcbdabaadabcaccadaaaddbacdcdccacaadbdcaaabbdbadbaababcbddaadcdbabbcbaabcaccdadacbcbaccaacabadccccbbadadacbaacaacdbacaaadaddbadaacdadadcadbbabcaadbbcabcdaddbacaaabbddbcbbdddcccccddacababbdabadacbccaadcacbccaccdbdcccadbaddaaaccabbcdacabbbcdbbcabbdaaadddcacbdccaacadacacdcbdcbccadbdddacbdbdabcbadaadbabcaccaaabccadbddbbaacbdabbbbaababdccbddababcbcacbdcbcbaccdbadbdccbcbcbbcbccbcdbddabcbdbccdcccbcadbcacdcbbbadaacabdadbcbdbacaadcdbccdbcdcaccdcadddadbdbddccccacdbdabbbcccadddbcbdbbbaadcddcdbadcaadbadbacbcaabdacbabccabaccdcbcbcddbbbbabaddaaaddaabbbdbaaaabaadddcbadaabcbbacbdccccadacbacacbcdcacdbadbbcacccaaacbddcbdcbcbdadbaccbbcabbdcdddbdbacabacaccbdbabbccdccadaabdbbcdbddcdcacbbaabcabdacacbbbdcadabdabaabbcaaaddbabbbdbcbbbcbcdabaaabbaadcdcbcdbbbdcdbacdddddacadcbcadbcccbabcdcbacbcbaaddacccaabaabcdbccbbdabacaaaaaaadccdbcaddbadbbdacdbbccbaacccdbabdbaddabadadcdbcccdabccddcadddbbbaccaccccdbbbbbabbbcdcddbbadabbabddabcdcccccbabadcbcbbccbdbbdcbaddadabbbbdcacbbabccddcddccabdccbaadddcdbcbadadbbccacbbccbacdadcdbbacadddbabdacccbbaaacadccdcabbcaddaccabcbadbcdcddcbdbacddbcdababadbbccaaacdbcdbaadcacaccaaccdddcbbdadadccdabcadaacbccdcdbcdbaaadcbadcccbadacccdbbbbacacabacdbddbcdcdcbacccdbdabbbadbbbdaadadbcacbdbcabcaccdcbaadaabccbcddcdcdacabdcccdbdbaadabdabcaadbdaaadaacacbbbbaaadcdcabdcbbadacdcbacbddccbdadabdaaddbbbbaccddccbddbadccdcabaacbdddaaacbabacccadbcccabcdbdaabdbdbacaadadcbdabadadacdbdbbaadddcdddabdbbabbcbacbaddcabdbdccadcbcacbbbcccbbdadcaadadcccbcbbbdaabdccbbcdadcddbccdaaacdabddacdccdaabbdacbccdbbbcbbcbadcbcdadcdaddbddbdbbadbaaccdaabaddcddcabbddcababbaddbcbdbdcacbcbaadcdcbbacbccaaabbbcabdcabdbacabacdddacccbaacbcdabacdcaaadbbbcbcbbacbddabdaaddaacabbbcbbaabddbcacacaccbadccdddbacdbdbcaacbcddacdacadacabbdccbdaccaccbddbcbdacadabcdccbccdcddabacacdbacbcbacabbaaacddbacddcddcbcaccabccdacddabdcbddcbadbcdcbddbcbdddddcadbabbaadddbdaccadddbdadbcacddcbadccabccddaabdcbbbbaddbbdccbbccacabcbabcbacbdccacbbcadcaabdaacabbabcdaddabbdbdbcdccdbbcdbacbaacabccbdbbcbdbddcabcdadacdcdaaacdaddabbcddddcadaacacbddbcdbbdcaabbabbdcddacacbbabbddbcacbccbbddccaaaabdababccbddacadadcdcadaabbacabdbdabbaaabbbacccadcdccbacacbdbbbcdbcdbcccddccadbccbcccadbcdcbdcbbadabdaabbadcaacaadcabaaccdcdcbcaddadcdbdbdbdbbcbbdbbcadaadbbddbadcdabcccbdccbaccdbcbababcabbddabccddbadbcccdbaddcbdaddbadbaddbbcbdcbaddcabbdcdadcdbbacbcbbccdabaccadacbcdaaadabaccbabcbbbbdbdaddabaadbcbdbadcdaabbdbadddccbdbaccbddcbbadccabdbabccbbabddbdaddcacabbbaabdbdadbdcaabdabbacaccbabdbdcaddbadccbbcabbdacbaaadddcdcccdbcdbaddcdaaccccbdcadcccdabdbbddcadbdaddababcacdbdbdcbcbbabcddbbdacbccadcdbbaaaddcdbddcbaabbbbdacaaaddcaabcadcabdbdadaccaadccabdbaaacaddabbbbccacbdcadabaabddaabdbccaabdcabbccdbbbababcdcadabcbadccabbcacdadaacdbbddbcccbccdcaadadccadbdcaacbbaddadcadcbddbccbdbbabbdcbcddccabbababcbbbccbdabcbdccccacddbdaaccdacacdbcdbcbaaddbdacaadacbccdaabdcdadcdabdbcccbbcdcbdbaabdbadbcbcbbbabaababcbcbdcddddcdadbaababdbccdbbdcaacbccaacbcdcbadcddcaccbdcdabbcbbbcabbbbdcbcaaabddccabdcadbcbcdacabccbbbabcabcbccaccdadbacddbccbbcbdaddacbabdacaddaadabaacabbacabcbdcbcbaaabccddcccadbbcdadbaacbbaaadcddbacbcccccdbdbbabddbdabbdacadddcdaddaacccbcbbbbcccdcabdadddbdbddcdcdbbacaaadaabadbbabbbbcadbbadbabdbcadcaabbcddadabbbddaddbadcabccccddabbdddabcdccadcaaaadababaccdbddcaadcbbcbdcdadccbdbcdcdadaacccaadbaaccabadacaacabdaacbddbcbcdbcdccbbbbabdcbcacababaccabbcbadbaabccadcaadbdddcbdddaabcbcddacbbbbbcdddcbcdbdabcabccabbdaacbacbbccdcbddbbabcadabcdcbccdcbdbcccaadadbcbadaabcdbcbbcacdcdabcbadcdbbbcaccbdbdbdccbdbbbcaacbcbcabbabdddaacdbcccbcccccbabcbcddadbcaabbdacaccbdccbaacacccdcdddbbabcddbbcddcdbcacbadddbddcadadabadbcdacabcccbcaaacabcdbbbaadadcdddbbdabcbcacbcdcbdbaaccbbcbdbddddcdadadcaadbcbaccdaaddadabdcababbcdaacdbcabaabdcaaabadbdbdcdbbdcbcacabacbdacbadaaaddaacaabbdacdcdacacbdbaacacabcadacbdacacdbccdbccddaadddabbddbbccabdacabdabdaccbcadaddddadcbcdcbbaabdcbbbabcdccaddddbacdbcccbbabdaacdbbaababcbcddacddadaaddcaadbbdcdacbcacddaccaadabacdcabbdcdabdccccbddadccabdaadcbbbadbbdbbbcdddddbbddcaacccacacbbaadacbcbdcaaddaddbbbcddcaddaddaadbadadddbbaaccabbabdbaabacbbdcccadaacdcdaaccaddaabadbdbabccbacdabadbdadcdcadcbbbcdcbcbdbbdbadabdaadaaabcadaacbbcabadcadbbdbdcaccdcbbcbcccddaabdbbcacaacdbdcbdadbccddbabcbaadbabacbccddabadbbbacdbcdbccbdcddbcdbbadadadbaaccbbdddbbcbbcaaabbcdabdcabbdcadaacdbcdcaddddbabdacbddcdcbbadcdbdadbbcdbcadadbdaccdbdbaadcbdcaacbacbcbddaddbcdabdddcccabcddbdcdababcdbbadcddaaaddbdbdaaccadbbbdacaccbacdddbaaaaddaaaccacddbdaddbbaaaabbadbdbacdcdaaccaadbcabccdbbccdcbdaaabcccadcdaacbdcbdbdabbcadaacddbaacbadcbdcbacbcaacbdbacbbbaacccdabbbaacacdbbddaacbcacabcbabbcacacadaddbbbabccaddcbdacacccaccddaabcbadcacdbddabacbcaacdaacdaabdcdbadccdbbbdcabdbdcaacaabccbabdadaadcdcbaccacacddabdbbdbdbbddaccadcbaacadbcbadcbbddbbbdbbacacbabbddabaccccbddcccadbbccbbdcbacbaabbdbcbbdcadbbadaaacdbdaadbbddadcbabdbbbacbabadbbdcbbaaddccddcdbddcbadacdddcbacddcdaaacbbdcbdabaadabdbbddaaddbbcababbadbbdaaddaaaaacaabadbccaabacdacdccccbcabaabcbccaddabadbaccdabdcbbdcbcccbdaaccdbdddaaacacaccbcaaadcbddbdddadbcabbcbbdbbabbdacaaccbdcadbcabacdcdadacdaaaabccaadbcdcacbbaddcabcccdcbaabbdcccbcbcacddbbacbcbcbcbbccbcccdcbccadaccaccbcdbadabaadcaabcacbdccababbcbdcbcbcbadadbccabcbaaabdbddaadcaddbddcbaacacbdadaacabadbddaccbaabccbbbcacbaabbdbaabbcccccdddcbbdbcbcdcdcaabbdabdccaddcdccddadababadcacdaacbcacbdcdccbbcbaaaabbabdadbbbcbccdddaddddcbbbddbcaacbbaaccddbbcdacbbabaaccccabadccabddcaaacbccabaadddbadbacadaabbbbbdcadbcbccaabdbbbccabaadaccabbbdabacbdaddcabbdbaadacbbdadbbaaabcbcbddabacbcbaabdbdbaaabdcdcaacaabcabaabbbbacbdcbcadcadbabaacbaacdcbbdbcaaabbcbabdcaaccbcdabcaadcaaabaacabacbcaacaaabdbddabdcdbbadddcbaaaaaaaddcdabcabddccacbcbdbaabccbbdacbddddadbaaababbddbddbbdddcbadbacabdcccbcddcdcacdccdaddbcdccababdbcaabddadbdcadaaabaaaadbcabcdcdadadddddbccbcbbbaccccacadaddadabdddaabcddcbbbbdaccaddbadacaadbdaacadbdadcdcdbdbcdbbadbcaccbbbdddaadcdccdbcdcbacabdddcbccabbbabcbbadbabcddcdacbddabaabcdbcddaaabadccdacbabdccbadccbddbabcaabadbcbcaccbdaaadadddccbbcbcadabbddaaccdbacdbbddacbaacaacabdccaadaddabcdbcdbccbadcabacbcbbcdddbbabbdddbcbdbcbadccddddacccccacdbacbbccdcccdaadcdbbadbbbbbcbabdbbdadccddbaaadbccbbcacaacccbaabbbbcacbbddbcaabbccdcadddbdacdccacabacbcddaadccccbbddddddbdbddbdaccccddaccbdcdcbdbddbbbaaacacddabccdbdbdcbaabccbadcddabbdadcbcbdcdabcabadaddcdadcaaadbcbccdaddbcdbbcabdddcdccadaddcbbbadcccdbcbbcbdbacacaccdbadbbbabaabdbdcdcdcbacadbdccbcbcbdaddbaabddcdcbdcabadbbdcdbcbadcdabbabdcbdcdaaaddabcadbabcababaccadcaadacbdddadddbdcabcdddacdbbbcaddbcdcaadcbdbcddddcacabcddabccdbddadabacbadcadcddabdcaccccaddccdcbdaddadbbcabcbdbdacddbadacddcaaccadabdcbbbdabdacadbcaaabadbdaabbbcaabcabddcabadcdacbddbacddbaabdabcabbcadcacbdbbdaabcccdbccbdbdcbaabbaaaabadcbaaadbacabbacaacbabcabaaaabbdabdbbcddbcdcbbbcddcdbdbcbbabcdabcdacbcadacabdbdddbbbcddbdbacccabaddacdddbaaabaaaddddabbcadbaccbdabdcbabcbdabdddbbdacacabadcbacddbbcbbacdaadcdacbdcdacabbcaccbccababdddcaaccdabaaddbadbbaabbacacabcdadccbacabccabbcdbdbbbddccdbccbabacdcbcbdcabcdcbcdaadadbacdcbbbacadabbadcabbaabacaacdbdcccbcdbdbcbabaacabbbadcbddbcacccbaabbdadbccbacacaaddcbbdadbbbaacaaaaaaadbbccddadbccacddabaccdaddbdadccaacbdbaacdccaddddbaabcddbbcccbbdadcacbccdddbadddaccaaabddbaadbcbcddbdcacbdacadabcabbbabcaddaccadcccdacadcabaadadbcdddcdaaabacaaadbabbacdadabdcacacadbacadddacddbbbabccbccdabcbbbbcbcadbacbbccaabbcdddbdbaccdcadaaabdccdadbaacbbbaadddaccddbdbabbbadbbcdcdadacbcdbbbccacddcdbbcbdcaabdbdaddcadccaacbdbccacdcbadadcbbacaccbdbcaddbaabaadbdccaaacbaccccdcdcccccabcdadcacccbdacdabcdbdcaccacbcdcbacdccccbdbacddddacababccaccadbdaddddadbabbcbacdcaadcccabccadacccacbcaddccddcbbbabcdabcbdbbbdacdcadbcadababcccbcaabdacccacadbdaacbabddaccaddccabaadcadbbacbddcbbcdabbbbaacbcdbccaaabacaadaaaabcbcaacabcdccacbdabddacdaadacdddccaacbaccdabddcaacdadaaaacbdccbbbccbbaadaacbacccbabcacaccaccbacaccdcdbadcaaacccbbaccccdadaddddacabddddccbabcdcbddbdadcbddcbdcbbabbbdddbbadcdadacbbcaacdbbcbacddbdacacbaccbccbcbcdddcddddabbababbdccccccdacacdabcbbacabbddcacaaabdbaccabacabdabddaadbbadbbdababccdcdbadcbcabcabdcbabddadbaadccbadbbcacdcddbdddddacdadababddddbcabcbcaadacbabbabcbbabbaabcbbbdccdbaabdbdbbacbbbcdbccdadbccdaaccbdbaabbbbddbbcbbcbddddbddcadcbddbaaddacbdcacacaaaadbcacbacdbdaadbdcbccaadccbadaadbbbacaadcabadbcbacaabcbbaddccdbdbdacbccbbbbcdddabbbcadddcbdbabacdbdcbaaacbcdcbababadadbbabcadcabbbdbaddbbdabbbaadcbbccadddabcbcbbadcddbacccadcacaddbbbbbbaadcbacdbdcaaccaacbcabddbadaccadcbccdcddabcbdcdaabadadddcbdcabbdbdcabacdccacccbadbccbacacabdbbaabddbcbadabcaaddcdbcccdbdcadcddbacbabdcbbadbaababcbbcdbbdaaccaaccacdaddabaabcdcdbbdacbcccaadbacabbbbbaaccdcdcaaadaccddcddbabbbdcddaccbdaccbbdcddbcabdabbcbabdccbdbcbacdbbdbadcdccbddadadcacacaadbcaadbcdadaddbbdaddddddbccbbdaabaaccabadddddbcdbaabdbacccbcbabcabcdccbcdacbbacdbcaccbcbdcdacbcadbbbcadccdcbddbdccabaadbddbabbdbcbbaaccdcbdcbcbddadcaccddabdbccaccdbabbcddabaabccdccbdccadddcdccbbcadaacdbddcbabacaddddbacccbcbddcaacbdccdbdadabbacddacdadbdcaadbbbcbbdaddaccbcadcabdadccdbaadaadaaadbacacbadcdddddcbdaadabcbcdbdacadabcccaacccdbbadcdbcaaaaabdbaacaaddcdccacddabbdcbcdbaacabbbcadabdabdbcaabbdbcdbabdbddbacdaabaaacaadbcabdcbdcdbbdabbcacdaaccdbabdcdcaddadaddcdddbcdccbddabdccbbdbdcddbadcbcddaccdbdbaacbbbbaacbdbabccccbdddcbdabbabdaaaddbdccdcccccbbaabbcbbcccdacabbabbccabacbaddacccbdcccaabbbabacbcbddcccbcdabdccbcaaddbabdddbbdbbdcbaaabbcdcdbbaaadbdabcccdabaccbbbcbddccbacaddbaccacdbcacbcdacaabbacbadaaddcbcdccaccbaadbadcbaabaadbdccdaddddaaddcaaaadcdcdccabbcdbdbaddadcbbacddaaacabacdabadbbdaadcbadccabadaacbaaccccdccdbadbcbbdaaabaabbbbbbcccddaaddbabbcabbadaddadbddccbbaacbadbdcccabdddbddcdddbbcccccdbddcdbcdbbcadbcdcaddccabdadccbcdaabaabcddbcabdddabcccbbdbbddcaaadadbbacdaababbbdaadcacbbaccacccbcadaaadccaadbdbcabacccdacdcdcbdcaabbdcaabadbcbcbdddbdbaabadcbabcbbabadccbcbbcbabaccdbaccacaaabcdabbbcbbcdadccacccbcdaccddcdacdbccdaaddcaabbaadbdbddccadbbbdbbcbaabccacabbddbddbcbdccaadcddaaddaacdbbdcadbbbccabadbdadacbdbaadbababbbbaccdcbacdbabbabbbacbdbccaddadaacbcacbcdbdbdacadaccbcdcabbbbbcbacabccdcccabbddacaaadbbaabaccdcadccacccdcabcaacccdccdacbdccdacbadcacadcdbbbcdabdadbdadcabbdacdacacbdcbaababacdabddcdcbcdbbdcccabdbacaaabacbaaadbccddcacaadaacaaaccaaadbcccacdabcabcbacbbbbcbaccbdadbbccbbabdcbbcadbcdcccdaabcdcadbbbdddbdbdcaddbddccabdaaddcaabbccbdccddabcddbcdcaabadabcddacccdddddcabddddbcdaddccdacaabdbcbcbbdbddbdbdcdddbcaaaaabcbadccdabcaccbaddbbddbaacbbcbcdabadcdcacdadcdbdcdbdadabbbdcbadbaaddacbbcbacabdaaacbaacdcaaabccaaddaacdabcbdcdbacdbcdddbbcdbddbcddbdcbaacccbccadabdbadacbdbdaadcdabaabadbcbbaabdabcdcadcacadbacabbcbbdbbcbcbbdaddabcabdaddbcbcdacdacabccdadadaddcababbcacdddadacddbacbacccbdcdbcbbbccbbaccabbaaddcaddacbdaddbabdadcaabdaaccbcadacdbbbbbcdbbbcdbccabadbbadbbcdbbdcabaaddacbdacdcadddbbddcabdbddbacdddcbaaabdbbacaaddcaddabcddbcadcdabcbdcbabcabcbaacadcbabdcbdcddbdcacaddcabcccdcadddbcdcbcdadaccdadcccadbdaaddaadccadcbaadbccdbcaacacbdbdaaaacadbcaaacaadcdccadadbacdcaddcdcdbbacaadbaaacaabbaddabdadddcdbaaacadadddbccbcdadddbddadcdbdcdadddaacdadbbabcabdcabcccaacddbadaaddbbaacdcdcbcbbbbbbbdcabcbbccdbcdacdacaabcbadabcaadcdbbaaccddbbbaabacddbaddbadaadaacacddaabdadcbbabddaaaaacdddbdcacabdddaabadabcbaaadbbbbdadbccadbbbdacddaccadacabdadaabcbdacadacbadbdabadabcbbcdddadbaaacddcbbddaabdbbcacdaccacdcaddcbbcddcdccabcadabadddbcbabcdcbddccacabadadaadbbccddacdcbadaaddbdbdcdacbddacbdcdabaccbacdadabdbabaadaabbbdcaddcbccdbdcdbcacdccababacbcabccdadcabcbddabddddcdadccdbabbddbdcbcdbaaadaabdbdacadddbccbcdabbacadadadabddbbacdadbbabcabbdddbdcdaccddaaadcaadaaccccaacdaccdacaaabbcbacaacadcdcdabaaddcdcddccdcdbcccadcdaaabdcbbaadddccabcadcacccdcbbbdcbcccdbcbddccbaabdabdbcaaadbdabaacbbccaccaababbbcbabcbbaadcdbadbcaaabacccacbcccacadccdddbccdcacbadacdcaccbaaabbabaadcccaaadddbcacdaccbaaacbccbbaddcbbdadabccbbabcccbdacaddacaaabdcbbdadcdbcadddaabdaabbbbaaabaadbadcaacacdcdccdcbacdaccaaaddcddacbdbdadcddcdccddaabbdabbdaaacdbcadcbdddbacaaaacdccaadaccbabcbaacabcdcccdbdaabcaabaadcccdabbaacbdbbccdcaddcdabaddbdabadcbaacadbabbbcadacbccccaacbbacadabadabdcdaadcbccdaccbacdbcbcacaddadddbcbbcdcdaaddaabadccbcadaddcabaddcbbdcaababaacccaccababbddbaccbdddbdcbbcaddbdcddacbbbccccbdcaacadadcaadccdbdbbcbcddadbbbddaddbabbcbacbdbabdacacccadbdbddaddccbcacccaabcabadadbacbaabbdbcdabdcdbccdbccabcdcdbbcbddbadccaccbddbccdcaabdadadaddaaaaaddbccdcbdcddccbcbbdcbcdabbaacccdacddbdaccdcdabacccccbbaaaccadcbdabdadaacaabdcdadcbbcccdacbbbbbbbccacdddacaabacaddbbdababacddccacbbcadcccabdacbbdabcaababbaaadbdbdbcbabcbaabdcacaaccdcbcaaaacdddacadbacabbcdadadcdabcdadbabbabdadccaccdadbacabadccabbccbabcaacadbadcbadacdbcbbdcdadbabdbaaaacadbbddaabbbbadcbcacaabaccddccabdcadccadaabacbbdbaaaabaaaddadadbaacccdccbaccbdbcdacadddaadcaadddcdadadaabdadabccddbcccabdadaabdaabbaacdbbaddadaddbcbcabcacbacbcdddacdadcaaaabbaaabdaabadbdbaaaaaacabacabdcadbbbcdbcaadaddbcabcaddddaadaccabcababbaddacaccdcbcbdaccabaadcdddacdabadacbbdbbbabcbccbadccbcaddddabaacdaddadccbbdddbadccabbdabccddacaabdccbbbaddddaaaaabcaadcacdcdabcabddcccdddacdacbccadaacbbbbdcdaaaddcddbccbbdcadbcbbcbcadccababbabaccbdbcbcdacdabacadbacddbcbaabcdccbdbcdcbddcdddbcdaaaaaaaccabbabbaaaabbdddbdbbbadbcacaaadbabacadaddaabbaacbabdadcbdbaabaadbbabcaabdcdddcbdcaabbbacaadcbabcaaaabacccccabaabbbbcbbdaaabbdbbccaaadabddcdddcbddcabcccccbcbabdcddcccccbdcaddaaadccbacaccdcabbbbadbcadbacbdbbababbbbadbdabaddcddacdbbdaaadbcaadcadcacbacdbadbadbbcaaddcdbabdbadcaccabdaababcddccaccbaadbcacacaddbacdcbaadccbdbbddccdabdcacddabadddacaadcadcaaabdbdbcdadccdbcbdaccabbbcbcbbcccaabccdbbcaacdbcddbaddbaabcbbdacdabadbddcdbbabdbcaaddaadccaccaacadacaaacddcccbdadbdcbbabcccbabdccbdaaacdbbaabdcbcacacabdabacddaccccbaaccadadbadbcbbabddbdabbaadababdbbdbbcbacdbdadbdabbddabcabcdccdbabddbadddddadadadacadabdcddaacababcccdbdabccaadadbaacbaaacddbacabaabdbddccababccacaadbbdcdacabbccbdbbdacaabacdcdcdccdddcccdbddbadcadbcdabbcccdaaaaaacabbadacacaccaccdccbcbcaaccbbacdcadddbccccaabcbcbbdbccbbddbdcaacbadabaacbdbddbcdabdadcddadbacbdddacccbbdcdcadbadacbdbabbabcbabdbdabbcddaabccbbbbdcbcbdcbcbdbaadabbddbaaccacbbadaadcaacccdcdcdadcdababddcbdcaccabbccbacadbdabbcbbcadbdcababddcdabccbdbabbcababdbcbadbabdcabcbdcdadbcdabbddccabaacdcccabcabcddaabdccdaabddadadbcadbacddcabcdbbabbaaadbaacbbabbbbcacbdddbdaabccaadbbdcbdcacdcddddabccdcdaacaabadcccdcacbbabbdacbaaabadbacaccdccacbacabbcaddbbaacccabdcbbbcbbcbdadbdccdabaadcdcaadbabdbcdaccbcaaadabbadbddcddadabddabddaadcdddabdabbbcbddababacdadbaccdabdaaddbcddddcadabbcbcbcaaddacdabdacadadbcddcbbcabbacbdcacddadbcbadcbcdbbdcdcbdcadcdbaabccbadcdbacdbbaadbcddaabaacacdabcaaacccbbabdbbaacadacacacdabddcacaaadbbdabaabbdcbccbacbbdbdbddabdacadabcdadabaccccdcdddddcacdabddddaadaccbcbbdbcdabbbabddcddaabbdabbdacbccdcccabbdacbccccbaadabbaccdaaddcbcbadaacdabcccdbdadddacddabcbdddcbbcddccbaadcbaccccbadaadcccbacbdcbddcbadaacdbcaaababbbcddacccdbdaaaddabababbbabdcddddadaacadbbdbccadaaabacbacadaadacaddbdcdcacadbcbcddddbccbcccddcbbddacdadbacaaacaaddbbddcdbbdbbdadbbcbdacddadbacbaccdbadaadadcabacccdcbbaabccddaacdaaaadacbccbcaddbddacbdaabbdddccbdcdbdcaaddadacabdbdcdcbcbabdacbadaddcabcbdbabcabbbcdccaabccaddacacbcccabcadcbdddccadcbbbacbccbdcabbbdababbbdbdddccdcabccbdabadccbdaacadccadcacbcbbcdbbaadabdadddcaabcbdacdbacbccddabbdaadadccbcbdaaaccadcbadabcbccadddbcbddccbbabdcccdbbdbbbdcbbdbccbabdaacacdcacaddbbbdaabcadbabcbdaabbaaacddddbccbbcabacbaaaccdcaaccdbbbadbcdccdabdbcbbbdcbadccbbccaadbcdbcccabbcccccddcdcabcacaccdaddcabcbddadccdddbbbaaadacbacbdcbbccbddccdcaaabbabdbbbabbabdadacbacbaacacdbdadbbaaacbccaccbacacddbcdabbaadacccccabcacabcacdacdcdbbacabbacccabccaadccbbdddacdabdbccbcbaaadbbccadbdaaaacbdccaabbcaccaaacdacddabdccdddcccabbbacacabbbcdccdcbabbaacabaadadbccdbcbbcaabbaaaabdcdbabaadcdcaabccdcbdaabddbcabaabcadcdadabcbaccdbdcbaadccccbabbabbcbbbcbcbdcddcaccaccacccbcbadbcaacadbacdcaadcaaacdcacdabaabadbbbaaaddcbadbccbbbaababccbbccaaabbddacbaabbcbbadaaaddcdbcbddbccdbddabdacdaaadbacbbbbdabbbccadcdbdddcbaaccdbbcdcacaaaaaabbcabcbbdddbbacabbdaababddcbdcaddbabbbbdadadabdaccbabdbaadbbcdabdaddaddcaadabacdccbabdacccbabcccacbaddbdadbacaaddaacdddbadcdbdccaacbaacddabcaccbcbbbcbdcbbdaaacaabddcdcbbcaadcabddacbbacbcaadbcacbaccddcdababcccadabcbdbdbabcadcccabadddcababdcadbdcdaaddcdaddcbbcadccdcbacccdababcaaacccabdbccdccbacdbabdccbcdbbdbdaaaaabcbbbaaccacaadbbdacaddbdbbcdcdabbadcadbadacdbadcdabbcaacadbdbdabcdadacdcbdddccbaabbcbdbcbaccdbaabcbcdcdbbbdacdbaddbabacadadabdbbbacdcbbaabbcbddddaabcdadcdcbacbadcacadcbacddcbbcdbcdcaccadaddcbcbdccdbadcdadbbabaacbadaccadacaaddddbdddcadabaadabbdcbbdddacddcbcdabbacadbccabaddaadaccbccdadbbaccbadcacbbddbdbbddabacadcaccbccdabcbbbdddddcadbcdbaaadbacabaabccacdcccdacdbaabadbddababccabcadcdaddccabddabbdadbcaacabaddddcaacdcbbdabddccdaaaadcccdccaaadcdcdbbdbbbaabcabcdbdaaadabacaadabdadbbbcadaaabdbcaaadaabbdaaaccadbbdabcaccaabbdabbaaacbbcadcacabcccbcdcdadaabcbbbdcabbcdadcdaaabbacaddddcdaabcdbcbbaadacdcccabcabbabbbbccacccdadcdccdbdcccbccacddddaabccaababddbaabbcbdddbbbaabcdcdcacbcdabcbcabbddaadbcadcacadddcccdcdbadbccbddbbdbbdadacaaaacbdbcacbadcccccadcbbccbbbabdddccddacaadbbdbdabacaccacdbddbdabcccbdbbdabdcadcacbbdbaccaacadbcdbcdbdaaadbbbdaccdbcdaccdcbdbaaabcdddbdbabcbbcdabadcbaccccddbbdbaccbadcacaddabcccbdbdbabddcbaabaababdbcbdbddcbaabbdaadccbadbbcadaacbdcacadaccacdaddcdacbaddacadaadddbaddcbdadcacabccbccbbcbdadacabbddcdbdcbcadabdaaabdbccbadcccbbcccadaddaccacddcdcccbdccbbbcddcacdabbbbabcbadbcbddcacbacadcdcdacaabccabbcdcaaabddabddddadbbdaadbddadabaccdcacabcdcabcbbbccdabadadbabacbbbdbdddccdacdbdbcddcbbadaaccdcadadbbcddbbabcabdcdbbddccacabababbcdabbcbacacabbaaacbaadbbdbbbcacbabcaaadabaadcacbcabdbaadccbdabacdcaddbdbbcdddaaddacbbbddcdbbbdbbcdabaadabdbdaaadccabaabbdccadabbdcacccabaadbddabdbbdbcbadcdbcabaddbcabadacbadcabbdacadddadddadbcbdadadacdcbadddcaccaadbccbdcbabcdccdbcdacaddcddcbacabcbdcdbbccaccacbcdaaccabdacaaaadccbcdabbdaabbbcdbadbdcbbdcaacabbcadcdbbcdadabdcdcadbadabbabadaddccabacbacababcbabaddcddabadcbcccacddbdcbabbdbccdadaccaaacbacbacdcaaabbbbbddcbcaabababbddbbaabcdddbbbbddbabddbbbabdcddbadacbdaacbbacaaadaaddcaabbbbbcaadadbddcccbbacdbabcabdacddbcccdccbadddbcbdcdcddababdabddcdcbaacbbdbadabaacaccdbaccbbaacbaaaaabacadaadacaadbcbdbdbcdcbcabbacbbbdcaadaddbadccdabbdbcaabaddcaccddcdcdcaaaacbbcdacdaaacdabaaaadcabbdbcbdbdcbbddaccbdcadccaddddbbaaddaaddbcacaabacabbddcdcccdbbbbcddbbabacbbaacccccbabcabdbdcbcadbdbbdaababddacacbdbcaaacaabdacaccabcacdbccbbbdaadcadcadbdcabaccbaabdccdbdaaadacbaacaccdcbdadbddaadddcacdcdccdbcbababbccaacaaacababbdbddcbbddbdbccdbcaadbccccbbbcacadcacbcddbcadabbddbacdbbaabbbaccbdddddabdaacaacbdddbdddccadadacddababdddcbbabbcdcaaabcaddbcbbdaadccdcddacbcbddbbcbccbdcacdcbacadaccaddbccdbcdddddaadcccdcbcbdadadaababbddddccaddcdcbccbbcaaabcbdaacacaddbcabccaabadccddbacddbaaacddddbdbacbabdacbbdbbadabacacabdcdacdddaccdacbbdcbbadddbcdbdacddccdbbdaaaddcdcacaaacbcbdcaabcabdacdccbccddbdacdadbcbadbabacdccbbbabddabdcaaacccaccbbbddacbbbbadaaaabddbaadbbbacccdbccbbbbdbdccbbadadadbcddabdbcadbbacbdcabcdcdcbbbdddbbdcccbcadadcadaacadbbdbcbaaddcabbdbabbadabdacadcaaccdcdbbbcacaaddbcccbbbbacdaacbcddcdbbddbbacbdbacaacddcdcddaacabccccbccaabbbbdbcbcddcbcdabbbabcabbaccccdacbdbbbbcadccccabdcacacdacbbdaacadabbdcdddabdacabcdabddbdccadadcaccbaaacbadabddacdaabccdcacbdbbbdbbcaacddbabcabdddbcbbcaddaabbacabdcbcddcbccdaacbccaccaccacdbdcdccacdcccbbbccaacacadcabcdbcbddbbdbcdddcaadadaaaabccbbddacaaadccbaabdadacbcbdbcccaabbcddabbdacddbbcaadccbcdcdcdbdadaaadaccaaaccbadccdcacbcbbbdacabcaddcbaacaddcbacddcccabadbccaddddaaabcccdcaaabdbcadbcdaadbadbddbcddddddbbcccadaaccacddabaccabcabadbacbbadddabdcadcdbbccdbccddbdbcbbbcdcaddacbddcbadcabdbbcdcbbbcaacdbabdacbbddaadadbbbdbdadddbdcbbddcacbdacdbbadaabdddcbacaabbcbdcdcbbaabcadacadccbcacbcdbabcddccbdbabddadbaabcbbdaacddddcdabaacabcdbdcacacccabadbdddcbdbcaaaddbaaadabdababdccbabbddbabdacacacaadbbaabbdcbddaacdabdccbbddbdcdabcaadacbbadccccbccbaadaadbbcbabcccbbabbdbaaccbcabbdcabbaabdcaadddadaccbbbbcabbbbcccbbcadbdababcaabddcdbcbdacccbbbbbcdaaddacacbcbacdaaddbbabbabacdadbbdbdabcdcddacbdaabcddddcbcbabcbabadbccdaabdbbdcbcccbabadbcacbbbaddbdcbaabbbabcaabadbadabddbdbcbbdbabbbbcbbcdbbadbadbcddbcbaaabbadabadaccbbddcdbcacdcabddbcaaddbdbacadbacaddbbdcadbdddabdddacbcbdccbaacacdccacdaccddbcdaaaabcaadacdabcaabbadddbcdcdacbbdcadcadaaaabcaabcdcdcabcbadbabcbaabcadabbbbdaadbdbccbadadacddadacdcbacdadadbdccccabcdcdddbcbabdaabcaabcdadbcaacabcabddacbbdbadbddadadcadaccccaccbabdccbdadccbdaacdacdccdaccacabbdacabcabccbdcbdabddaddadbbabdccabdccaaabdddacbbcdbddabcbadcdbbdcabdcadcbcccccdaadbbddabddbccbbcdbcccddddaadaaddcddadcbdbccabcaccdaccdcacbabdcbddbcdccbaaddcdddcaaacaabcbbbdbabcbddcbdabddaaabcdacbbbacaabaacbabadcbbcccbcbcdadadbaacbccaddcdacbbccccddbcdcdadcdbbdadacdbbbdbbdbadbbbbdcabbaaaddcaacdbbccdbcddaccbcbbadcacaccdacabcdbbbbabdaadacdcdddcbdddccddbccacdcbacacdcadadaccbcdabddaccabaadbbaddabadbaaacabbdaacbcbbacdbbaaaaacddcaaacdcaaaabcbbbcdbddbddcbbaccbccdaaabbcbccccbbbcacabbdababaddbdbddbccacbcbcacbdacbbdbddaadacbddcbcaccdabbdbaacacbddabcaccbabaaaaadcbdacaddabccccddbdcdadcdbccbbddbbccbdbacdbdcadcacccdbcccacdbaddddbacdcccbbacbbdbaadcbabdddbbcadacadccccdbbdbacabccdbcccabbddbbaddbbcdacbbdbbcdbbacaaacdddcbacbbaabcaddbdbccdadaddddcacddabadccddddaadadabbabbbbccccbddabcdbaccdcbddcaadbcdadababbbdbbbacbcbadccabcbbdabcccaaadbabdbdcacbdbaddabcbdbdcbdcdcbbdabbacacccbaccdadbdadbcbdcaadacacaacbbcbcdbbaacdcdddbddcdccacbdddbaddbdbadcdbcdbcaabadcdaddacbdadcccaddcbacadadbcbcdbabbcdcccddcadaadaaccaaabbacabcbacadcdabcbbdbcaaaaaccdcbacdaddcddbbddcabddbbabddcdbdddcabbababbabdcddcbbcdddbbcccaacbdcbddcacaaadacacdbcbcdbaacddaadcbdbcabdbbdcadccaabdbdcbaccbccddcdaadddbaddbdbbdbabdbbbabddadbdcccdabcadcddcaaaabcddbccaccadaadccdccddaacbdccacddbbdcdddbdaaabdcddbbabdcaacabdabdddcccababaddbbbbadaccbcacdcbabbcaadadbabddcddabbadddbacccbcccbabaddccbddabcacdadbdccbdccbacdcddababdaabbaaccddccccdabcbadbdccaacadcddadaddcbadacabdadddbdacddabcbbdddacccabbdcbdbdadbacaacbdbbabcddacbabadbcadbdcadbdcaabbcabacabcddcddcaacaabddcabbaaadddabaabcacabddabdbaaacbddbacdbbacdbdbbbdadabbbaaddbdcbadcaadbbacaddcccacabcbacdccabdcdacacaddddcbbcaabcacddbaaddaddbaaddcdadbbbccadbabcacccbdcbccbacbbcdcadaadabaaccbcabdbabaaadddabdcbaadcabdadccdbddbddbbaaacdabacbccdcaabdcaaadccbbdccaadabacccddabddddcbbaababaabbcbdccacbddbadacddbacdaabaacdbbadcabcaadaaaacdbaccbdaaaddaaaacacbbacaadcdacabdbaaaaaacaccdcdddcacdbabcbadaabddbcccadbaaadbaabbcddbccaddcadccbccbcccdccbbabbbaccdababdccabbdaddcbbacaaccbbbbaacaacbcdaccdaadbccacacdbdacdbabddbbbaabcdccabbdbadadcdddbbcabdbabddcbaaacdadabcaaccbbdccdcaaabcabbccacbdabababcabbcdcacbcbbcbcbdbaadbabcacacadbbcabbcabaddcbdaaaaacbdacdaaaddccbdaacdaaabaadbcddcdabcccbdccbadbdbdcaaadbdabcddcabaddadcaabdaccdccaddddcadaadcbadaddccdacbacbabbaacbbdcaddcddddbbdcacdccbaabaadbabacbaadabdaabadddbccabaadcdaabacbccacacbbcbbddcbdbcdcbddbbdaaaccdaacbbabacadadccbdabbdbabdbdbdbbddcadbdbbbdcbcaddaaadbdadbaacddacbdccabbcbbcbdddbbdabddddacdaaaccadaaabdcadbcdbbddcbbbaadbadbdabdacacacbcbdcccaadadabcbcdccaabcbabaabaddbddbdbccadcbbacaaccbbcddbbbddccdabbbbbadcacddddbcbaacccdbddcdcbccbdcdcadccddbabbdaabbcbbbaddddcabdcdadbbabcaddccdbcdbcbbbabadcacbacccdcdaabbbdaadcccdddddacaaadbadacddaaabdadcbdbdacacbccccdbbaabcadccbcbcdadcbbbdddcdcbdacacddbdcabbdcddaaacdbcadbcbcbbcbcbdcccbcabbaccdbcdbbadbaabdbcccdaccabcbbdcccdddaadcbabbbdccadcdbcdbcdcdddddddadcbabbbdbaddcccbdcddadbccdacbcdbbcbcbcccaadabbcaaadbdcaaddadcccdccbacbbadccadddabddbbbcddbddbcdddccaddbdbcdcbaddcaaaddddbcabccbabaabbdbaacdbcdbccccbaddbacddabcdcbdcbddccbbdacbcdbdcbcadddbccbccbbbbabcbabdadccbadaaccbcdbaacdddaaaabcccabcacdacacdccbccdacabdacbacaddabdacbbdcbcaacdcaabcbbaccdadcddabbdbaddabacbacaacacdaadaacbaabbdcbacbbbdaaaadbadbaacccabcababbadabdbbccdbcbaaddadabacbddcbdaddcacdccbbcaaccbcbdbdcacdadbbdbdbbdacdacadbdcbdbccbacacdbdaddadcaabbddcbdcccadadbaadccdcdddadbababdbaddddcbddddaacdcbddddbcddacacbadcdacadbdacbadccdabbadbbbcaaccccccccbadccaacaabacccbccbbdcbddaacdadbbadbaaddadaacdcaddaacdbddcccbababdbbacbbdaaccdaadaacaccdbbcacccbabccbbaaadaadccdccadcdcdbccccdcbcadddbbcdadbdbabdddbacbcaddabadcccaacbabcccdacddddcddcdacbbbadadcbcbabdbdabdacbdabbbcabbcdabdbdacacaaddaaacbbdadabcbccbbdabdcddcaaabdaddcbbccccbcbdddbaadcdcdabacdbabcabacdcdbbcccccdcbccdcaaadabbdaabcbcbdbddbadcadddcdbcbbbcdbdbbcbabbadbcacbdcdcbacbbbbbaacdaacdddbbdbbabcaaaabdbbddccbdbacaaadccaddddcadcdcaddabcdababbbbbdacaccaacccdadbadabccbccdcbacbdbcacdbaadcaadbbdcdcbdbbdbaddaaaabccacdcbaadccdbdbacbbdabcabdccabccdabdcccbdbacdbddcdacdcdcccccdcaaccabbbdddcdaabdbccbdacdddbadaabcbccbdadbdaaabaaddccdccdcadcbcbacabadcaaadccdabcdcaddbddaacdaacadbccacdaadbcbbbdbcaacbdcbdbdaccbdcbddabddcbdabbccaabbabbadaaaccaaabbcbacddddbcbccddbcbbbcadbddbcbadadcdddbacbbcddbddaccddcbbcbdccababdbbbcbbdcdcabbccccbdcbcdcbbdddaacdcdddbbadbacbbcaacdabbaabbdaaabddbdcdcddddaddbcdbaadddcadcabcadbbbddadcbacbdaccbadbabdbdcacbcdbdaaadccccdadadcddabdabdccdcbccbaaacdbabcccaccbbdcbaaaacacbadabbaacbbbadcbdaddcaacdcbbcadaabbbcdadbcbabdccddcabbacaaadabadbabadbadcdcabdadbadccbdcaabdaddbcbdbdbadbaccabdbdacbaabdcdcbdbbdaddcbcbabcaddacdccacccbbadcccccaaddbbabaacaaaaddadcbacaccaccdcbacacadcbabababdcbcdadcbdacabbddcdddcaccbdbcdbabcaaddaadbccaccacbcbcddbcabcbcdcbccabbaacabbacbababcdcbbaabcdbadcbaabbccacdcadabdbcadcdbbcacaaabacabbbddadadababcbdbdaabdaaacddbbdbcbbbbddaacdcbacbaccdcabbbbbddaaaaacdcacaccacacbacbddaccbdbdcaccdcacdacaaccaacdccdccbdbdcabdcbcddaccdccbcccaadabbdabbdacaabadaabdbddbdabdbcbdcdbabdcdcaccccddaddccbdaccdabadcdadaaaadabdcbbcbdcbccaccbbcbbccdddbbcbcababcbabacaccadccbbcbbbadbccbadabccbcdcaccaacdbdaadbbccabcdcdbbcbadbbbacdaadabccacdddadaaabbcdadbcacbcbdbabdabadadcdbdcdddadcccdddcaacccbcdaadbbbbbbcacabcaddacabbabcbcaaadbbaacacbabcdcaaccddabcdabbbcbaabbadbadacccbcddbdbbbcaabcbbacbcccadccbdcddcddabbaddbdbbdcbccdacbcdcdbaaadadaaaaabbddcbaabaccaddbaacdbdbbcadaabcaabbaabbcbbcdbaaabadbbaadcbdcdabcbdbdcdabadacdbdddabaabbaacdccbdcaccbacdddbbcacacdcbbaccddaaddaccdccdcacdaaccbbbbacacccddcbbbcaaccadccdbabccbddbcbcabdcddadadcdccdabddcdcbaabadbbcdbbbcaaadddddcdadabaaacacbaaabccdbadabdaacadcbddbacbabbbcabacddbbbcccbdccdabaddcdcabcbdabccbbaaadcdbdabdbacbcdacbabcaaddadcbabcbbaacbcaabdabccadbdbbbcabdaacabcbacdbcbaaaddcaddbabdaadccbccabcbdcdaaadccdcadcbbcdbcababdbaaddaadcbadbdccdadccbccbccabacccbdadcdbdbcaccccdbbaddddbadcddddaaaaacacbbcddccccbbcdcbbbdccbcbbcdadacbdacadbcacdccaaaccacccbbcacbbbccbddbbbdccbdbddabcbaccbcbdabdbcaddaaacddddbdddbbbccdcdcaaacadcbdaabbdbdbbdcabcdbddabdcaacbacbabcdcbbabcadcadddbabbddabddbcbcdbadaaaddbdbabbabdbabbcaadacdcacbaadccbbbcacaacbabaabddcdcbacbbdadbdbbcacbbccdcbdbaccbccbcbdadadadabdaacddbddaccadcdcbbbdcabbdbddbcbdacbaccbbcabdabdaccadcadbccdcdabadcbdbcbdddabbcddcdabcdbbbabccadcaddababdacbaaacacdbabbcabcbddbddaabbbdcbdcddaddabccbdbcbdccacacaddcbcddbcadbaadaccbdbbdddcdadadaadbabbdbcdcadddcbbbdbadccccabcddabdaabcdcadcabdacaacacdcdcabcbdbbddbbccabbaadcabddcdbdacbacccbbddaddcacadbaabacbbdaabddabbaddcacdadaccbcdacdcbdaabbddaadcacaaabdadcbbccaddbabdabcdababcbbaaabcccdcaacdbaccdcdbbcbcbdacdacdddbaabccbbacbabdcdccabcdddcdcbdabbacbdcdccdabcbabbadaaccacccbacdbaabdbabdccbbbadccdacdbcaddabaddabdbdaadcabadadccbbdbdddacdaaadbcadbdacaadcddabadbdbdbbbccccdabaaccaaabcddcadaccdbbddbadbcdcdccaccbaacdbbdcdbbadacccbaabddaacbddbacdcdbabbcadbcbcaddbdcbcaabbacdaddcabbdcacbddcdbaabaaccbccbddabcadacdbdbddbdcdaddbaacbbcacabbbbadddbcdbabbbdaacaaccdbbddbacbdbbbdaddddccdcabbadabcbddaacbdbcacbdddcddbddaccabdbcccccadcdadbbbacdddcbcccdddcadbbcbacccbacbcdcbdbababaabddcdcdbbcbbddbdabacbbdbdcdabcaaacdbacacacaabdbcbdacdaacddbdbdbadacabddbadaadaddddbddcdbdaddddaddcaaaabaacaddcddccccaacaccacdcbdbcbdbaabcbcadcaaaadbcdbdbdacadabbadccabbdacbbacbbaaaaaacadadcaabcadcbaabadaadaccabacdccdababbadbcbccbcabcacdcadcdcabdccdbdadddcaacacbcadaadbbcbadbcdddabcbcadaddacdcbccddcbcbbabadabacdaccbadaddccbaddabdacbbadbaadcddcccccddcccdaabdbacaadaaddddddcbabaccdadcdcacacbccdaabdadaacaabdbcacdadbbbbadbcccaccaadcadcacbbadcdcaabcdadbaabddbaacbccaadabbcbbcdddabbbdbdaacddccddabdcacacacbabdbadddbbcaaddcdbccdbacdacdccdcaddabbbbcbcabcddaabdccdccbcdbbddcccabcbbcdcbbabbaadaaddccbbdaccddbbcdcadbaacaaaadaaaabbaadadcacacccbadccdbdbbcbbcbaccbadbcccbdcacdcddadddbacccdaacdacbbcadcbadccdabcaddcabbdddcaccbabcbbdabccdbdbdabdabddcbdacbbabcaaacacacdcdbabbcbcbdbdbadabcdddbacdcbdcddbbaabadadabbddbaaaaaccacccbddccdddccbdadbdabcaacacbccacbddaccdcbccdccdbcdacaccdccaacbddababbadbcabcababbbcbaddccaddaabbabbbcaacbddaadcaddabcdddbccadccabbbdbdaccacccbabbcbdcaadcdadadbabbaaaabccdababcaababcbccdadadccadcadbaddadddadadaddbadcccdccbddbdabbaacbdcdbcdcbaccbbabccdbadbdadddadbabcabadabcddbacdbccdbaabbdcbadabbbadcdbcddbadaadcdabbdaacbbbacdddbdbbddccbdaddaaadabcabbbdbbbacdadbdcddbacaccdcbabcdabadccacdcaabccdaddbdabcdccbadaacdccbadbcdcbcbcdacaaabcbccaadcbaacadcdcbadcaddcabbdacccccabdcddadbcbcdcbbabccdbcbddaaadbbbaacdddcadacbbbdbbdbbabacddcaccdacaaacadbbaabcbaabcbcadddbbadbaaadadaabdabcbabdbdbcdddbdacbccacbabbcdcaddcacabbcbbabaddabbbadcbddabdcaadadcdccacbcabcacaabbabccacddcdbcbdddaaadcdddcaacacbabddaadcbcacbaacdbbaaacdbaadacbdcddbdddcddbcadabbcaaabbdcaaddbacdbabdcaccdbbbbbcbadacacaaddaadadcbabcbbddbcaddbddaabbccacdddbabdcdcdacbadccbbadaaaacbdbacabbdbcbbcaccabcbdcacbbdcaccacdadabaaaacaccbddbbbbcaddabadccaccdbdbcaaccacaaaddccadcccabbdcadbabbadadbcadbcadcaccddcbbaaccabacdccbacadabdbbdaddabbacbdbccdbaabdaacaddddccdcbbdbbaaadaaadadbdaaaddcdddabcaadcdbadcabaccbddddddbdccddccacccbdbbdbbcababcabdcdacdbcadbdadaabcdabbabdababddcacbcaaaacdbdbabaadabdbdcbdcabacdcccaadcabcadbaaccdaabaacbadabbabbcdbdcdbdbcbddcbdbddacdcaaddaabdcdddaccadbbbadbcdadacbbdcdddcaadadddddcbcccdbaddaaabcacbdbdddacaaabbadcaaadabdadaccdbcbcbdccbdbbbbcdcbbbbdacbabbcdbccabaacbccaaadbbdaabaacbcbabbbcdcbabbdcddcccbcbbabbdacabddbdadcbcabcacdbbadadaadbdddccdbcacadbccbcdaccacdbaddcbdbdacacbdbcbaabbddccaadccdccdddbdddcbbbacaaadbcdbababadaccbaaabcaaaddbdcbadbbaabbaddaacbbacbcdabcbbadabbbcdcadccbdbacbadbadcddcdbacbadcabccaacdcbdaadbcdcccbdccdabadacccbcdbabdbbbdcbddcdbbbcdabdcababaabcdddcdabddcabdcbdccdcdbdabdddbddaccbbbadaadcaababcbbbabdababbdaacaadaadcdcbaadcadbdbbdaadaabcbbabdbbdccdcbcabbdbaabbbabdaaddabdaaabadbbcbdbdbbccdaacadadaadabdbaddddcddbcbbdbdaccdcbdccccadacabaccccaadccddcccdddadbbdcdbdcadbddbddacddbbbaddccddddcadcdcdaacacdadcbcdbdaababccaaaccabdbccabbbcabbaccabbabbbaabcdbbdadccdbcdddbcdddadadccdaddacdcdcdabdaababbbdbbddbacaaabbabbdbacadbdccadccbcbdacaacadababdcdcdabbdadddcacaabcaadbbdccdbcbcaacdbdbaaaaaadadddccaaaccbbcbacaccdbcaabaabacabdbccdcddcbbdaabbcbabbbcaaacdacbbabdbabddddaaaaaccacddddcaaccccdbaacbbdabdbabaccaddcbbacbadaccaddbbccbcaacbddcdcdadbccbbcbaddacdabadbdaaadaccdbccaababbccddbdcccdbdbdddcdcadaddbbdbdadabdcbaddccbcccddadcdaadbbdccddacaaacbacdddbbdbcacbcbcdbaaababdcbccbbbddadbddddbbdbcbdacbdbbcdcddbcabacaacabcacaccacddbadbddcddbbbcbbadbabdabaadbddccdacdcabdaccbbcacddcdbbadaacdbbcdccdcaacdcdcbcdacbcdaabacbdbcaabbccbcdacadaabcaddcaaaabacdcabaadbaaadbaaaaabbdadcdddddbdadbbbccbdaccaadbbaccadccdaadcdbaabddddddcdaaacabcbacbdbbdcdbbdbcddccaccabddcdcaacaccdbdddccdaaccadcaacacdccccbabbcbadcaabaacccabdadbdababcadabcdbabaadbcdabbdbdccbbcbacdbadbdacdadbdbaccdcbdbbaabbbdccacbaccabdabdcbcacdccdacbccbccbbccababbdaddcdcbaacaabbcddccdabcbbaaccadccbaccdbccdddabcccaaadddbaadcdacccbdbaadcaabadabbbdadcacabcbadbabbcbbbaddbcbacadbbcaacdabdadcbacbacbcdadadbdbcbdacdcdabcbcabadbdaadcbdcddddaaacbdbdabacaaacccbadacbdaabbdbbdaabdbabbbdaabdbbbcacaadcdddacbbdaacdccdcccdbdbaabadadbabadccbbbbdddcccbbbacbdccdaaddddbdbcbdcbbcccaacddabdcccdbcbddbaccbdadddccbbaccdccbdcdbdadadabcbabbaaacadbcdbbaddadccacbbdcbddaddccbadaaaaababdcbbdcacdaabcdaaacdcadcdacbcbcbcaabbddcdbacdaddccbbbcdabbccccaacbacdbacbdbcbbcbbbdacdcdccbbddbcddaadcabacadbdcbaaaccbaacaddaadcbdacdbabdcaaadbaacccbcdcaabaaabcbaddbaaddcaadddbadababbaccddcbcaacadaadcaadaddbbabacddbdadbdbddbccdcbcabbcdbdcccddbaadcbdacbcababccdcbcccaaddbacaadabbabbaddaacbbdaabccababdacaacbcbddaaaadabaaabbadbcbbddbcbadacdadcdcadcaaccdbaacdbabdbdccdacdadacaddcbababdbabbadddcdbcabbdccacbbaaadacbcabbbabddbcdadcabdaddcbadccccccddddaadabbbaccddccbcadaaabccbdadacdcbdaddbbdbdbdcaaadccbdcaabbdbddddbcdacaddacdaabdacbaadacbdccddacabccabddcccadbcbdaddcaccaacccdbcdccabaaddbddbbcbcaacdcbacadbbaacaccddbbaabbdaaddabccbdddcbdcacaadcbaddcaacbbcbdddabaccacbaadccddababdbcdbadcadbdcbacdaddddbadbdbbcdbbcaababdcadaabbdddbcbaabaaabdabcdddcadcbccbbcbdaccabbdbabcccccdcacdcababbcabdbdacbccddcccaaadadabacbdacccbddccbcbaabadbcaddddbdaacdbacdcaddcdddcaddbdabdcdacbcdccddddcddcabddbdcadbbaadbddbccdbaddddaabcaacbcbdcdababdabcacaacbabcadddcabdbcdabcadbdcbbcadccaaddbdcaccaccbddadacdbbccaadcdadacdcadbbcbdcbcaccdcbcdcdbbbdadccbbdbbccaaacddbaccbbcdcdbdccbbcbccccccdcbacbcbadbddaccbcddddbdcabdbcabbccbbaabccbcbabcbdccbcdcbcbcccaadaaabbaabbadbdccbbadcbabaccbdbcaadacabadbdccdbddbddbabbccdbdaaaabadaddbcaababddacbbbbccdaaacdbcadaacbbdabbaacaacbddaaccdbacdabdcdbbccdaacdbcaaabdcbbcacaaaacbdbcbadbcacadcdaaaacacdbaddaacccbbcbbbabacaccdadaddbdddcadcacddccabddadadabacdadcadaaddcdaabbbacabcccabbbddddbdcbdbbaccdcbdadccadcccacccbbbabaabcbbabcdababacdbddcbbabdcbcacacddddccbddbcdcaacccadaccadccadddabbbacbabadcbacccbcbbacabdcbdbddaabbccbaccccdadddddabadbbcaccdcacbaddcbcccaacddcddbacdbccadbcdaabbdbadddccabcddbdbcddcbaccbdcadcbabdbcdcdcaabbbddabbdacdaaabadbdacacbaaadaabaaababbbabcabcddaacbabaaabaabaaccabddcbcaabcabdbcaaccacbdacaddcbddcaddcbabbbacadabbcadcbbbadbdcaabbabdbadabcacabddcabacbdddbcadcaabacdbaabdadacddcdadcbbbcdbabacbdbcdcaaddbbaabadddadcabddbdddaaccaadcddcdabdbbccbacdbdccaaaabdcacdacaadcdcacccccdacaddaaadcadbddcccabcbcaabadacdbcabbbabbdaaccdbcbdbbaabddcdddacccbdccbcbddabcaaabbcadddadbaadcddddaccdcdabbbbaaaababadbdcacbcacdaacabdcbcbdcdcbadcdaacbddadddabccaabcdcbbbcdacaccaaabbadaddddacddbcbdcabbccdbccdddbaadcbcbbdbccadbdddaadbaadcdcbaaddacdadcbdcdadacbacdbbdcbabcbacadcadacbadadccdcccaabaacaccaaadadbcadcbdbcdcdcdabacdbccbdbdaccdddcbbdcdbbddddacbdcbccbabcddacdbadbdabccbcaddddccdcaccabaaabdaccdbabccdbcccbdadcccdbadcdaccbbccdcccbadbbdccbbabbbabacbdbbaccbdccbbdcaddadbdcbbcadabdbbdaadcbdcaaadbcbdcacbaddcdcdaaacdadaaaddaaabacdabadaaddcacddbaacbcdbdbcddbcdaabdcccbbbdcdaddabdcdddabcabbaccdbbcdbdccabbcdbbddcddbdbadacaccdbbcbaacadddbaccbbbbdcdbaccdadccbbdaaaccbcbacdcccaaddccdbaabacbabcbdccbbcdadcbcccddbcbaabbddbcbdaddbdcaddcccbdabdbcaabcdabddcbddcbbcbbabcaddcadcbcadadacaabcbbadaadcadddbbcdbdddabdabdaccbcababdbaabaacbcabaacbdbbccbcbbcbadabcdababdaccabdcacaadbcdcababbacababbccdbcbbcbdabbabaddadcaccdccdadcccbdcdabbbaabcbbcbbccdbabcaadbcaadbcacbdcbdbbccbbbcaccdcddddacbabadaacbbacacdcbcacccbddbbdacacadabdcbbdaabadcccbacbbcbbaddcdbdcbcdcbdccaccdcacbcacbcaaddaabacbadcdcbbcbcdaaacdbbcdcdccaabddccbcddbbbacbccdaaccbbccdbccbdcadcaacdccccdbabadabdcbdcbbabcacdbcaccaabbbcdadddbdabacdbadabadbbccbcdaaadccdaccddcdacccadccdaabddabdccccbbddadadcaddadbdbabbbadbcbadabdabbbdcdaadadacaddbaccbacddcccabdababbdbbbcbdccadbcdcdcdadababbbcdcacdaabbbbdcddbabcbbbdbcabcbdbddadaabcaaabcabccbcdacadcbbddaaccaadabbcdcbadaabccdddabdcbcdddcaaccbccccacddbddcbcdacaddaacccbdacbcbcacacdadaaaadcbabddcabbadbbcbddccdabdcabcdaabdbbbcdcaabccbabcdcdacbdcbdccadabacdadbddbbbdcacaccaaadacabdcabcdcbcccddbcacbdcbccdbdbcdbbccababdcadccbbcabbbcadddcdacabbadcbaabcddbbccbdddcbddbddbcdcacddadbdacacccbdcabbacacaaccadbdabdadcccdaadbdbcccdbccccbddbdacdbddcaddcddddaadbadddbdbacddcdbdddacbcdbaaadcdbdccdcaaadcdbaacddbbcadddadadcabbbaccdbaadbcbddcbdaaacccdbabaaabbabbbbaadbcdbdcbdbdcdacaddacdabdbadacdbcddbccbaccccbabbaaccadddccaacddabdbbcaccbbddccaaaabcccddbcaaddbcdadaacdadaddcdddababdccbddbccaddccabddbdddbadcdaadcabcbabdbbccbbdccbaacacadddddabcdccbddaabdabbcdcdbdbaacbaaadadbbbbaaccdbcabcacbacadbbddacdbdcbacbbabcaadbcacabbcddccacabdbabbbadadacdaaddadcddcdccdaabaccdadcaacadcabcabdcaadacdaccdacbcdacdabdcbaacccbdbaaabaddccaccdcbdcbdcbdababbbbdcbcacccdaccbdcdbabacbaabcaababbddabcdbcdadbcbcabccbdbaddcdcadcbdabccdddddababdaadbbdaddccccadcdcaaddccbaaddbbdbaccaccbcacbcbcdcbcdadadabbbbdcdbacdcacbcbaacacdbabaddaacbcbcbcbccbbadcdbddbccddacacdacdbbcadcdbcdcdbacacbcdaaaccccbcdbcabaccabbdabcaaccaddabaddcdbacaaaacccacadccacabacdbbbdcccdcccabbbababbdaacddaaadccacbcbccbddadbdaaadcdbacabbaaaaacbccdaaaadcbdaacdddaabbacbbcadabdbdcabddbbcaaddcacccababaabdcdbccbddaccbcbaddbabdcddccdbdbcabbbbbadacbbbdddddadbadaaacadccbdbcccddbdccdacabaadddadbdbbbaadacccadacbadbbbdacdbabddaddacdbbcdbacabcadcaabcdabacbdaadbdddbbbbdddacabdbbdcdbbdaadabadbadcbccacadaadcaccbdcccdaabcccccbaacdbaacdcbbbcacddbabdbadabcbdbabdbbbbdadcdcabdaacccaddccbddaaadadccbcbdacbbcdbbcacaabbadbdaddbbadbcdacdabdabdcadaddccdcadcacdcddaabdbddcaaccdcdccacdadcabcabbbcbdbddbbbacacabacbcbcabbcabadddcbccacaadcccbcbcdabacbadaabdcdcbcaccdcbdbcdcadabcabdbdabbbbdadcadcbabaddcbccddadcdcbbcadbddbdaacaacaacaaaddaddcdcbbdbdddaadbdadadddccbacaccabadcbdcddbbdcdcabbdbdaabacacdbadcdddddabdaabbbbdcabacbddbadabbadcaaaacdbcabcdadbdbdbbacadcdddacdbacabcbacaadcacdccbcbbadcdccdcadacdddacabacabadbdcadadccbadcbaabadaddccbcbcbbaacdaabbbcacbcbbdbdabdcacbadcadabdcddcbbbabccdbbacbaddcddcddaadabdcbaccdbddcddadacababdacabccacbdbcabddaaaddbabdbbbbadbbdacababcdbcbbbbdaddbbacacddccddbbdaddadaccabddcbbddcdaacdcbcadaaabdaacacaaacbdbabdccdbbabbbcaaadbbdcaabdbcbbdadddacacdbacabadbaacdcacbbdcaccaaccbbcaddccbbcbbdbdbbcccadddcbddbbabbbadcddabddabaacabbdcbbdbbbcddbcbbdcbddbbbbbdbbbacbadcabccadaadaccbcccadddbadcbbdadcaacccdddccdcabcccaadbddcacbdcddcabcadabbdacbaacacbcdbdbccabdcbaadccccabadcdcdcddbdaabaadbdadbbdddcaadcbbdcbbcdcdbbadabacbbcbddbabacbcbbcdcdcadcdaddababcdbabcbdbacacdcdcacddabcabcbccddcdbcbcadcaadcdcaaaddadbacaabaadadcdcaacddcdadcaaacbaccdacadbcbddbccdaaadccbbbcadbbdcbdbccccaddacdddacaadcabbdbcbcbdccdcbacbdcbbcccbcbaadcaddadaabccabbaacbcdccbbabcbadddcacdadbdaaddaaabaacdbabccaddbdcabdacbdcbbacaacdbdbbbddcbacbbdcacabdcccaaabcddadbbacbbacdcdbaacbabcadddbbadacbbccacccadcabbdaadbcdcdabbbcaacbbabdacadbbccbcccbddbadddabdcabbcbdcabbbacabcdbacbbcccacccbadbadcdadbaabbdbbaccdbabdadcddbbcccaddbacadcbdddddbdacddabadaaccbbcbaacdcbacbdbabaccabadcbbdcababbdbcdbaabadadcaaacbdcbdcdabbccacbadabcabbddcacaabcdbacdccdabccbdcbdabbdcddbbcbadcddaddddcdbcdabcdcbadadcbcbabcabdcaacdaaccddcccdbabccbabbdbaddbccaabbdbcdbccaabbddbbabadcbaacababbbbadcbbddbaaadbcaadbdbabbdcbacbbabdcabcbdbbdbcbdbbacdddcdadcabbdcdaaaccbdccbbccdacddcacccbcadaaabccbcabadbddadddaadacbccbdbddddadbacbddaacdbbdcdaadbcbdbcbbacaccbccacbabdbdcddddabbbdcbcdcdcdabbccabbbbabcbcbccabddcccddacccddbaabdaaacbccaddbbdaccbadabbcaabdaaccdbbbbccdbcddbbcddadcbcccbdabdcbdccabddadbadbaccbcccddbdbaddbadccabbbddcaaabacaaddadcbaccaddcbbbbcdbdbadcaadbaddcacddcdcddbbbccbababcaabbccaabccbbadbadcdccbbdcbcbcbcadaadcaacbdddbbbbdcddcbaacadbcddcdbaababacacbbabaddadbdddcabdddaacbcadbaacbddadcdcdbadbbdabcbcabdabbbcddbabbbccccabadccdcbadabcadadbbacdddbbdbdddabdcbcdacbdadccbacaacadaabddccddbccbbdcdabcdadbddccabddaddcbbdcbcbdbbbcacdbabdaccaaacaabdbbdbadabdaabadccbacbcccaddcaaacbadcabadcdcbdcccbbbacabaadcccddcaaacabbadcccbbabbabbbcdadddccdacbdccbbbbabbbbcadaabcdccadbabcadaddbcadaadddcdcadddacdbdbcbbcdaaccbabbcdccdadbcdaccddbcbaacdbcadbbdcaacccabaddbbddcaccbdbabcbbbababbbdddcabaaddabcbaaddabcbcccbbcaaabbabdbdbbadadbdbbddacbaaacdccbbbaabbcbbacabbacaaaaadcccbbaacbcbcbbaacbcbaabcbdcddcdbcaccdbbcabcaaaaacdcacbabcddbbdadadababdbadcbabdadabddbcdaccbaddcadbaadddbddbbbaccabaabaacaaaadbacdbbdcaccbbbaddcdbdddadcbdcbbcbdaabdccdabdcbacdacadddbcdabbbcbbcdcdccbbacabdddcdbcabbbaaacabddbdcdaadbaadcacadddbaabbcabbcaccababcabcadbbadcbabacabbbaaaccadbdcaaacacdaacccdbbdcdbbaabcacdcdcaabcacbdbaddcabdbadacdcbdccabdcbccdbbdbaaaadcacbbdadcddbccbdabcbbbacbbbbaabaccbacbbddbbccaddcadcacdcaaaddccabbcdbddccabbdbdbcbcbdcdaccdabadabaabdbdadaaacbdacbbbcacacdacaadbaaacbaadcbbddabdaaccbcabdaccddacadcbbbbadbdadcddcccbabccbdabdcdcdadccbdddcbaacbacbaccbcbadccdaabcaccadbdbddaabcadbaaadccdddbdadaaaadaaadccdcdaaddbbbbacaddacbbcbacbdadcbdccaddbbccccbdcdaaabccadacbdbbccbddbaaccddabdcdccdadbdadcbddcaaacdbbbdabcabdddabcdabcccbccbaccdacaaadbadddbaadaaddadcaaddcddbcbcbdcacacbcbadbabccbabdbbabcabccaabacbcbdbadbcbcdcacbadcadcdccbbdadbcdbcacddbabaacbdbacbcdabdbcddbcaddcdbddbdabbdacbbddbbccdbdbabddabdcaaaabdbbbacbbbbbdbddbbdcdadcbcaacdbacbbdbdaadaccacabddcdbbadccaacabaddcaccabbaaaddbddcbddbcbabcbdbcdcbabaabacadddcbdcdcddbdccdbaddcdbbabddadabbdaccdabddbdbcaccadddbcdbacabdbbabdcabdcbadacaccabbcbaaccbaccddbacdcdbbcccbbbcbddbdbacdccabbdaadbbaddadcdaacdcdccccacbdcdbacaaccababbadbdcccabababbcbaabddbcbcdddacccddcacabaabdbacadadbdbcdcacabddbbddbdadaabdaacccddaadcdbbdbbcbcbacbadcdbcabacabdcdddbcddacabbacdadcbabbdcbdbdbcaacdcbbdbdaabccbbaaacbcccabdaaaaaaddadaaaabadadcccaabcdbdbcaaaddaaacbbcdaaccbccdccbcabccdaddcbdaadbabbadcadbccbbaddbaacdcccbddcccbddcbccaadcbccbcaddcaadbaddcaaacbbdaaccccdccbcddbdbacdbabdadacccddcbbbdbcbdaababccaaaaaacaccbbbcddabacbccacdcddaabbcbaccadbcbddadbabbbcadbbcbaabdaccbabdccaabdacbdcabacdcddacaaccabbbabdcbaadcaacaabaabbcbbcbccdacaaaccbdbcaacaaadbbadaaaddcdcddcacacdbdbbcccbbdbccaabacabddbdbccabbddcbbdcadabcdbccbadabaabcadbcadcadbbdbccdabddcdcdbdabdcbbbbbbbabaaabdaadbcdcbbbbbdddadcbdacbcbbadaabdaaadbbcaadcbbaddbcddcbdbdcbddaddaabdddbddabdacddcdabcacdbadbddaadbcdbbdbdaddbaaabccbcdcbdcbaaccbccabdcabadaacacccacdddababdccadbdcbdddcbadabbbcacaccccbcbcdbbacbcdaadaabddcabadccbdacdabddbdcdabbbdaaabdaadbcbcddbcdbbdabdddaaddbacabcacdbcadabccbadaabbbcdddaabcaccbabcbbabbaabdbcbccadbcdbbcadccbccbdadcddaadbbddcddccbcbcaaaacbacdcbdbcacadbcdcdcdabdabbcbaddcccdaddbdcdaccbccaddbadcbcccdccdddacddbbadccbacbdabcbcadcaddcbacdcadddbbdabbbacbcbababcbabdcdbbdddabdacbcbddaacabcadadcdaabddabcdabdddacadcbaabccbaddabcaccbbabdbcadbdbbcabcbdcccdcbaacacdccbbdabdcdcaabdbbcdbdacddccbbbbadabcbbcccbbddccabbdabaccdbabadccccabadcaacbaaaccabadbcdbddaaacbbbdbdadcabbbcddcbcdabbcbdaacdcccddaccbbdcbbbdcaccbaaccbcdabaccbbdcdddcaccdbbabccabdacdabbcaacaaacbabddbccbbabdbdaabaadcadbccbcbacbbcbacbbcacdbaadbbdbbdcddbdbcdccdaacdabddbaabadadbdddbdccddcbaaacddabddcacbabadbaaaadadabbcccdbbcaddcadcdabdddababddbbcadbbdaabdcaccaaaaadacabbcaccddacbdbdcdbbdaaacdadbacdcdbdccbaccddaddaaaddddabbdababbbbadbddcaabcdbbbcbcadacacccabacbaddabaaddabcccbddacaaacbcdccaccbbbaabcbabdddbccbcdbabbcaaddcbcdddaddbbdbcbddcaabaaacdadcadbabbcccaadbaacaadbacdccbaacbbbdccbbcddcbdbaaccbcbbabbacdcbbadddbaaadbadababbacbddccabbabdbbdabacbdcdaadcbacbddcabbbdcbadbddcaacadcadccdabcacbababbbcacdbcdcbacbbddccbdbbccacbdacddabcdaccdadbacbcbabbdcdbbcaccbcbbabdadbaacadcddaababbbcaacbcdacbbdaadabbabbbcacbaaddbadbbbaabbbcadabbabcadbbbcacbbadaacbadcbabbacbcaabcdccabcacadabdcaabdbadaaacabdccddcbccbbbabdbadabddaaadabbbcaccdcdcaccbaadbbadabbabddcacaaacbaccbacbcdadabcaaaacbcdbbdabadacdbbacaaacacdabdbbaabadcdbbacbccacbcacdcbbabadccbddbccccabbcbcddcdddbacabcdcbabcddcbbdadcbcbddbcbcbcabcaacbbcacaadbbdadbbadddcdcaccddacbdbcdaaadcdcaadaadbdcdccabdadccdbdccbccdbcacdacdabbdaabaabcaaadbadddcdbdcdaddbddbbccabcbbbcdaaccccadbcabcdcaabdbcbaadbbccbdabddadddabbdcdcdbcdbbbaacddcdccabbcabaabcbcddaababaccccdbcbcbdabaccaabbbcdabcbbbabccdbbdbacaccadcdcabaadadbddbdddbcacdcadbabbacdcbadbccdbbbbccbabdcdbcdcbcbdbdddacacbcbadcbdbbbddaddcbdddcdbdabacdaaacbdacdbccbcdacdcdbdbbbbacbcaaaccacdaabaabddabaabcdddcaaaccaddcaaccbaadcbbdcabdcbacccbbadcacccaccdcacbcbbbcdbcdcdcddbadbacaabbbaabaabbacbbccbddcdcacadbababddabbddcdccdabacdbaacddadbcbaacabbdcbcbbcabadababaacdaadacacaacbcdabbddaabadaabbcabcbbcabdbddbcdcbaabcabcdcaddbbacbbdacadcccaaaddcddadddaacdaabbccdcbbabadabbbdddddbabbcbbadcbcbaabaacadbabbbabbbbddcaaabbaabcdbddbcddccdbdbaaabbdbdddbbdbdaacdcdcdcdcdcdbbadadcacdabaaabadccaaacddcbddccbcbbdcdbcccaabcadcbbbccddbabdbccdddacddaacacdabbaabbacabdbcbdddbdcbbbadcdcacabcbcaacbbccadccdcadabbbbcaddddddcddcddcadaabaddacacddaaaccbddbbcabaacdcdcdcbcdbbccddbbdddcdcbbcadcdbdaaddbcabbdabdcdbdcccbdcddbdbbdabaaabaadbaaaaaacdaaacdbdbdabaaacccbababbacaabdcabcabaccdcdbbcccaaadadcaabaaabdddbccbbbbbdbdcaadcacbcdabadbdadddadbadadadadbdaadcdddccabcbbbbbcbcbdccacaaddcddbcbbbcbdbcdcbbacbaabbbbaddcdadabcabbbdcabacccddcdccddaddabdabcddababbdaaccabaabbaadbcdadcbdabdbbddbcbbbaabdabcadbcbaadddddbcbbabcaacaccbabcabdcadccdddadabcadcacbcdddccdababbdbcabbbabdadacbcbcbcccdddabcaabcdccacccccbaadaacdaccabcacdacaaadddccaddcddabcdddcbabbcdabaacdaaccbbcdddbdacbacbacacdbcaacadcaacdaacabdbccbaacdcbaacadbbddbdbdccccdbaabcddccaacabdcbabdbadbacabccdaaddacdbbabbabcbdadbcadcbcaccdcdcdbabaaabcacbacddadccccbdbcacaacaccdcbcdcbdbcbccaaabdcdcdadbdbadddbcccadacbadcabdadbbddbbaccbaaabdbabcdccbbacbbcdccdabbcdaabccbbaabacdbaaddadabbacbcdacadcdaaddbabcbadaadccbcbdaabbaccbbbcbaabbcdddbbdddddaacddcdadcabadaccdbbbabdbbbcdccbadcdcaccbbaaacddccacabacccddddbcaddaddadcabacbdacbdddbcaddbdccbbcabddaacdbddacaddbbcdccbdddddccdbcccbadadacacadddbcdacadbadbbbcacbabcbccbababddaaaabddcbdabccabddccbdaaaccabdcaaacdbadadbcccdaaaadbcbcbabbbcadbdcadccacdbcaacbdccacbabdcaccaccdcccabcabcdbbcaabacdacdcacccbbccbdbbdbdcadccbaccaaadcaadddbcdadccabbbcdbdbaccbdcbcababdccdaddcdddaccbacabdccadaaabaaaadbaaaacdbadddcdabcabddcccaccbddddddbdbdcccaccbcbbbcdccbbbdacdbcbacaccdbaacbdddacbcadcddcaaacbacaadbbdbacbdbdbbdabcbacabacbcadadccacacdaaddacadacbbdaccabbadabdaacaadddddaaaddacadbcdbaabbadabccabccbdacaabddbaddbdbacadbcadaabbbbabccadccbdcbdbcbabaabacadaaadacabdcdcbcdbbdcbcdbbabcdbcbdadbabbadbdaabdbabbdacbcbdadbdbbddaccbadbacdbdacacaacbcacdaddcdcdaddadbadcabacdbddcbacccaabcbabcacabbaacabdcbdabdcbcadbdbadcddddccddaaaabcddcbbdddddabbdcbdbadcadcdadbbcbcddcaacabadaaabdcdbdbbbbbddaaacbcbcacadcbbdcbabbcccddaaddacacadbabadbacccdbcadaccadcbaddbccbdbdaabcdaadacbccdbabcddddbcbcdcdcaadcbcbaccdcacbdadddaaabbaddabbabbcaaddbcbbccaadaddbabbdaacabbaacdcdadcbbcccccaddcaadccdcbaacaabcacbdabbcdcadabdacdaaabcdddbaabdcabaddbaabdddbbdbabdbdccccaaddacdabcdaccddbaccddbbadccbddacccdababddabddadcdbaadcbababccdacaacabbbacdaaddccbbbdabdbbaacdadbbabdbcbacdddbabacbabbadddcadbaddaaccddcdcdbbccddbadcdbbdbaaddbabacadbabcbcaacbbddbbbacabcdbdbabaccbbddabbaabadbaccbbbababcaadbbddbcabccbcdcdbdcacdbcccdadadccdabcaabddcdbadddbcdccbccacdccacbaaaaddddcccdbacbbdaadbaddbddbbababddbabcbadaadddddaaabddaacdbcccddaddadadabcbbdabcbacbbccdcbbcdacdbbacbacabdabbaabdcbadbdcccbcbbcabbaaadbdcaccbddcbaaacabcbcbadcbddcabdbaacbaccbbcaccaacdbbbaaccddaaaabcbdddbbabcdabdccacacdbadccccdabbabbccccdadadaacbdbbdabcaadcdbabbbdddbbdbcbadbddacbcddbacddacbdabaacbadcdbcaddbccbdcadadcddccabdaddcdbcbbacadbdbcbcbdbbbcdbcbaacbbcacdbabcddcccbaabadcacbbdbcbadaddbcccabbcccbccbbcbbdacccddbacbbbdbdacbcbdcdcccbcdbcdadaadccdcbbdccdbdbbcdbbcacacabdacbbbdbdacddccaadcccddaabcbcddcaababadccbdbdadabbdbcbdbbdcabaccbcdaadacbadddcadbdacccbccaacbadbdbaabaccabccddbdcacddcccbccbbcaddcbaaddbccdabbadaccdcaacbbacccbdbbabacdcdcccabcbcacacccddcbccdaabcbdacdaaabbbaccabdbccdaaacdcaaadababcbaadacccccccbcdbbbaadcbaddabacdcbacdddbcbcbabbcabaccbcbbbddddaaddcbabadadbdbcbadabdcdbabbbddaaabddcdbbcdabacabcadccacbbcabadddccddbbddcddbcccdacdbbddbabbbadacdbbccaadcaddbbcbaabcccdcbbbccdccbbbbcabbacbddadbdaadaccabcaaaabaabdbcdccbbaccbdbabbcdbdabbbadcdccdcdbacdbcbbcaabaaacbcdabddbbddabcadaccddcddcccddabdadcbddbdccbdadbabdbbabadadbccbababbcbbcbdbdbabbcaaddcdbadacbcabcadbcdaadcbaacbbcbcdddaabdaacadbbccaadaadcdaccbbabbabcbacbcadcddacddadcaababdabcadbbccdcaddaacddddccbacdddddaaacbccbcbadbbcaadadccbdaddbacbadbbdcdbcbacdbdbcdbaaaadbbbaabdbabddcbbdbbdbddcabadcadcbbdddaadcbbbdcdbbdaacadabaddbccacccccadddcadbcabbabbbdbcbcddcabbdcbddaaadaacabaaabdcabccbcdbbbbddccdabcaddcadbddaadadaaacaddabccbbbbdaccdadaccaccccaccbccadcdddaddaddcddccababdbccbdaddbcbbbabbcacdbaccccdabbdacbaadcaaacbcdbbdbcbdcbcdcbddcadadbccbcdcbcadcdacdbaddbaacccadcdbbdacbcbabbabadcdaddcdddddcdabbbadadbcaccdddcdcdcbdbabdcbbbcddadddaccaaaaabdccbcabacddaaaadbbdabbdbccbbabacccccddcbbdaacdabadbdbcdcdabbacaaaabbddddcacacacbbbdbdacccdaaaddccabbcdabdcdabccbccbbbaadcadacbdbabdcbacbddacdabdaabdcbaccdabcaadcbaadbddbbdacdcaadbccdcadacabddccdcdddadaddcacddbcbaabacdbbbdcdcbbdbcbcbddbaabccacbdcaadaadcdabddcdbdbaacdddbcadddddaaabbabdddaaddcdbddbcabbacbcbdbddabdaddbbcaaaadacacacbdabadaabdcbcdbdddbdbaabbcadbbcabccdbbbdaadcaacaddbdbddadddcbcbbbdddbacddcdbcbddacdbacdcdcbbcabaaacbddddcddcdcdbdddabbacbaacbdabbababcbadadbbcaabcccadcadacaadcdcadadccdcbcadcacabcbcccaabadcabacabaaabbcbadacaabbcaabacacdcacdacdcccdbbbdcdaccaaaaadbbbadddbaacbacaabcbcbcdccbcdbcdabccabcabcdcbacacccbcdcaddaccbabacddaaddbdcdbabacdacaadabbabdbdbacdcdbaabcadbabacdabdaadbbbdaccabadbbddddcadadaadbcbdcbadbabdbdbbbdabdcdbabcbdbddcabdbaadddadbabadabbbadcabbabcbdbabaddbaccbbabbabcccacbdaabdbdbcaaaacdbbcaababbdbdcdadcbbdbbdccdcbbacdcbbcbbbcbcabbcdbbadaacccdcccccbdcacdbcccdbcdcdbbbdcabaadcdadabcdcacccbaaaacdbcdcaabbdaabddbaccdbadababaccabaabcdbbdcbcaaabacdccbbdabcaaddbccbbbcbacbcaabdddcdbbbaaabadccdaacddcbdaaaaabcbdabdcabccdbdbcacbabaaababcdabcdccdaacaddbdddabdcbacdadabadcaccdbdaccdddcdadadcbbdcbacaadbcbbdbdacbcdcacdcddbacccabcdaadccaaadcbbdacaacdbaacccabbdaaadcdcbbadcdddcddbcaadacbbadcdacdbbdbdbcdabcdbcccadbdbbabcabbbccabdaaccbaadccdddddbaddadaadbaddddadcacabdbbabddaccccbdcbbbadcabddbdbbddbbccdcdddaabdacdbacacdcbccaddbbcdcbacdbabbabacdddddbcbcdcbcddaaabcdacaaabcddcbcbbbaddccabbdcaacabdddbcdacddaadccadccbbbdccbacbdabbbdadcaaaaacababacaddaddcccbbcbbbaddbcacdbccbcbdaaaadcbdadcbcabddcaadcdbddcbacddcbdababbcadbdabdcbdabcacabbabdbdcddaababdadadbbcbaabcdbcbcdaccbbdbacdbdbccbacbcccbdddbacbbbdbcdacacbccabcbddcdacacaaddccdddaaadcabcabbbcbdbbcccaaaabdbcbadbdacbacabddbbbdabddddadbbcdcaaadddcadcaaacdbcaacbcccaaacbbcdbdbddacacdbbcbccabbccdbdcacbbbcbdcdbaaaacddbaddbabbbcbbabcadcacbcbdbcdbaaccbacaacacbcacdaabbadacacccdcdaccdddcdabdcdcdddcacbcacbdbdddcbaccaccacabaadbccbacddcbcacdddbacdccbdaadacddbabcdcccbcadaaadcdccbddcbdaabdacddacbcddcbacadbddaadbbcddcbacacabadccdbaaddddcdacbdddbbbbaabbdccbabababacacaabaadbaddaaadbbcbabacbdbbcabcbdaadbdadabaccbbbaadcbcbccbacabddadddbbcbbcaadcacccdaaccdaacbbccaadacbdacabaabcbdadbcacacbddabdbadcabdcddcdadabbddcdaabcdddbdcbddaababbbbacdbadccdbdadcabacaabcbccbdbdcbcaaaccabdacdccdacdcacaacdaadbababbacbcacadcbabcddbadaaddcbbcacaadaaddbaaaaacabbcbdddccdbcadabcacaaccdcadcbddddccadcacbdbcddbacbbadcdcddbaddccabdabaadddccadddccbbdbaacdddabadcacacbccddbcccababbadadddccaacdadaadbdccddbcabcdcbaadbbacbcbbaadcbcdcacbadacdbcadabdbccadddcaddddddccbcaaddcbccdbabcdddbacbbbdbbcacbcdccbcaacacacaabadabacaccbcaaacdaadcdccbcdaabcbcdbaacaabadacaddcdbdabcbacbcacbaccaadcacaccbcadcabbabcacdaadaadbccabcdbdcddccdcadbcacabcaadbcdaadacddbdddbcdcdaccdaabbdacdccccacaccaddcdadcaadddccdbcacaccaadabbdabacdcbbdadadbbccbcacbcabcabbdadaadbbccbbbaadcbcbddcbcbacbccbbaabddcaddbacdbbbbacccccbdbbddcbcbbdacbdbdadccdcccdbcabbdabbabcabbcdacdaddacabccbabdaaacbbbdadcabdbbbbcadccdbccabbbcbdbcbbacdcddbdbcadbaabaccdbabaacadaccadcadacabbbddadbdbadbcaadacaadcaaadadadabbadbcdacadabaadddaadacdcaabccdbbccdcabcbcdbcbadacacbdababdaddcadaddabcbcacbcaaaabcbabcaddbccdbbabadadabdcaaccccadacdbdbdcaabcccdacddbcccccbdddaacccddacbcdabdcddbcacccdabbbdbaccbacabaadcaabbadbdbbddcdabdbcccadadcddacacadcdcadbacdcaccdcdbaacbacaacbbcbabbaadacaadccdcdbbbbcddbadbadbbcccdbaabcaabbbcadabaaababddbaaabacddbbbabaaaccbcababadcdacaacccabdadbbcaccabbbbcdcbbabddaadabcdbcdcbcbdabbacbcadccbbdbdababbadabaaccdadbddbccbdccaddddbbbbddbdccdbddcbbbdacdaccddbbddacbcdaaadbdcbdbbccacbdcbdacccbcbdaabcaddabdddadaacbabdcacbbaccccbcccddbbddabadbaddaddddbbcdcdbadabcadcccadabbacadaaabaadbbadcaccddbddbdccaaaaadacccaacbbbddbdccdccbadddbacdcccbcbacdcdcdcccbbbbaddaaadadbabdbdcdcccbabbdbdccacbacbabdcdaabbbbcddbadbbccddacdbabdabdddcadccccaaacbadaabdaadcdbcaddcaadbbbaddacacbdcbcaaccbacdcabdbbdcbbbacabacccbabbccaddcaddaccdbddcadabddbdadcaacacbbbbcaadcadcaaacadddcbbadaaadabdabbbbabcadadcadacdcbbdabbdadcacababbcabdccdccdccbddadaacdacbabadcccdadcbdaadabdbcbcacacbdccdbbccdbcadabaadbabbbbbddcccddddcabdddbdbccbccdcbcbcacdbdcaaccabacbddccbadacaddabdadcabdcaabbcacbacaccccbbddaabacbaacccbcbaabccdccadddaaccddabdcddddddbbbcdabbdbcdbdaaabddcdcbacdaabdbbdaccccacdddaadabadacacaacabccaaacacbdcbbcdadbababccdbdabccacbaacbdddabdbbddacbcaddcdbaadaaabdbabccbcbcabcbabbbcbaabbadabbddbaabcbdbacccabbdcbdcccaccaddaccbacdacbdccbadbdabdaadcabcabbcddddccddaabaaccadbcbaadaccbcacabbdbcddccabcbaddbbccdadadabaaddaaaaadbccdccbdabbaadbddbdcbbabddccbcccdbbaaababccbdbbbaacbbbcbacdabcbdddcbdcdbddcccbcdbcbbbadccdbbbacdbacdaabacaccdbbaabdcaaabbdaacdbbdabbcccddadcbaababcdddadcaaadbadcbbcdccacbdabbccabbaadcdabbaacbccacbbccbacadbdddbaacbbbcabbccdabbddcacacccadccbdadaabaddccbadbcbabadcccbadacacbbaaddcdcabdbbdacacdccddadadbaaadadabbaadddacdadcdbcdacadcdababbccbbdabcdaccabaaaabbdabbdcbaaaccaaaadcacbddbacbbadacabbdabccaddcdccbcccbddddbaaacadddcaacdbaaccadcabbddabbabcabacbdaabbdbdbcbdacaaacbabcaababdaccacccddbaadcbbcddcdcccdabadadacacbbcbbdaacdacbaacdbcbbdaacaacbbbddbaadaaabbdacabcaacdccccbbbcaccdcbdbdbcbbccabdddbabcddbcbacbbbdbdacdabdbbcadcbddbbdddddbdbcabbbcacbabdaabbdaaadaaaccbcbbcdddcddcdaccbdcccbcacbdccddacacbcbccaacaadbbcbadcdbaabbdacbacddabddbaaaddaddbdaaabdbaccccaacdabdacaadaccabacbacbadacadddddcaadadaacbdadbbdcacdbaaabccaaadbacdaaddbaaacabbcccbababacbddabcdabadcaabbdbaccddbbadaadbdcdcbdcbdacaabacdbccdcccabdbcbdbccdbaaadbcbbdcbabccdcccddddaadbadddcdbcbccddcacddddcccdddadaddcddddcaddaccaacaabaccbcbabbabdbcbddaadadcaabdababaccbcdcabaabccbcbdcabaccbbdbddcdbddaaaaccabcadcadaaabacccadbaaccdcbaabcbbbdddbcdacdbccdbadcababdcbccaacacdcccccccacabacaaabbcdaaabcdbaccbbdbcccdbbadadabdbccaddccaaaacbdacdaaaaadcdaacaccddaacabcdddcddaacacddacaacbdbbabacadcaacaacbcddcbcadcdaaaabdbddbadadbdccaaccaddaddacdadcddccbdaabaabdadadacbbdababcbbadccabacabacdcdbcbadcbdadbcbbacacaacbacadcbbaccacbacdacadbdcabbdccbdcadbbbacdcbddcbcbdbbaddcbaaaccccadaaadacddbcbadaacdacbacbdbdcdcbbcaababaaddacdbbacdcdbaccccdcddaccdddadacdabbdabcdaadaccbdbaacddadaccababdacccacddcddbdcdaadcdcabadaaccddaacdcccbbbcddababcdddcabcdcbcdcacbbbdadddcddaabccbbbabcaacbbbddadccadcbabccdddaccacdbabdbccadbbddcacabcbccdbcbcdbddcccaaccdabcaaddabbbadbcbdccdbaadcabbbdcdabbddddcbaabadbcddcbcbbadccbabdaacaabdbbbadbadbbdaadcacaabaccbdcabcbaadadcbddbbcaacadbaabdccdadaaabababbaccdbbdcbbcbbababbabdccbbdadbdabbdccddacadcdadbdaddbdabacbcadabaccbaabddadcabaacabdaaaadddabbacbcddcdccdddaddaaabbaabbdcaabdbccbdcdddcbdcdcbdadbdbcccbdaacbbdbbbaccbdadbbdbacbaaacbcaccbbddbdcbadbbbbbbcbaabacababcdbdaddcabcaadccdabacddbcbabcdacdbccbdbdccaddcbcbbabddadddcccabaabdbacdaabacbaddcbcacaabadbbdbccddadadbbcbcddacdcdadabddacddadbbbcccdcaaaccdcbbbcbabbbdaccacccbcabdbddddcddadcddcbbacdbdddbbaaddadcbdcadadcbdacbbcabacddcacdcacacacaddcdabdbacaadbbcabbcaadcbdaaccbbbadbabdcadcdaadccbcbdacbcdcbcaacbcdcdacdacdaabbbaadcabdbcdcbadbaccacdddabdabbcadbbcbcdbbcdbcdaabcbacadbdaacdcbbccdaadbccdcbcbdbadcddcaddcccdadaadbcddcbbadccdacdaaadcddbcabbbdabdbdbcdcddadcbcbbbcddcaadaadaacddddbbcbacdcadcccdbcbbadccabbabdcacdcacabccdacacaabdcdbdcdbadccbaaabbcdddcdbacdcabbcdacbbddaddaaabadddbdddbbbacaccacddaccdddbcdabbcaaabdcbaacbdcaabbdabccacdadcacbdbdbcbccbcdbacddcdabbacabaababaadabccabadaabcadbdacccdcdbbccbaddbaabdbbcacacaabcbbdccaddcddbbdcaaacaacaacbcbcdacacaabaddcbccbcccaadbbcbcaaaababddccdccdddadbbadbcaccbaccdaccdbaabdddadcbbdbdaadaccdccdccabcbdccaaacacaaaadddbcacbcdabcdbbcadccbabbadccdacbdbcbbadcbdcccabbdbccaddaccaaabbbadadacbabbdbcdcdcdbcbdadbadbcbbddadabdcdcbbaddbabaaadcabddccdbbddbacdaadcdbadbcdbaabcadddcbcbbbacdcdadaadadcabacccdbcbcbddccdacdbcbaccabccbccbbcdaddccdbabdcbcaaacbaaabbccdaabddbadbdadcdcbdabacadcccabbddbbaddccdbbddcbbabacacbdcdbcbcabaaadacdcbabbcdbacdadbadddbdcbdccdccbdbbadabdaddaadaabddddccbcadbbacdcccbaadcdcadacbddbbccabadcddabccdcadcaadadbcbbbcacdaaaccaddcddcbccbacabdccccbbaccbbcdaaabcccddcdbaccdadddbdbdaabccddccbdababababdcddaccabdbdccccabbcdaccccbadadadccaddcbcdaabccdddbbdaddbcbcbdaadcbdbddabdaccbcbccadbcbcbcdbddccdaddbbcbbbdbababbbbbbaccbaccbbcacbdbbbdbaabacccdbdbadbddcbdccbbcdcdadddaadabccccddbbbbbcddaadcddbcdadaacdcbbddcdcdcdcdbdbadadcadabadcbbdbcacddabccadbcacaacdadbcbbdcbbaacddbabbdaccbbcaddaabbdaacddcaacdddbabdacaabdccaabdcddbdbcbdddabcccabddaddbddaddabcaacccaccdadabdbbcbddaaccaddddcddabaaadadcadcbccbaddcdbacadcddddbacabdbddbaadbacbbdbddbdddbadbdbbaabaddcbcaabcbbabbdbbabccbbdaaaadcddcbccabcbabddacbbadbbaccbadadbddcbdbdddccccdacbcbdddaacbcaaadcdccdcdaacadbcddcddbdccddbdabcddbccbaabcacadbcbbcadabacdcabccccacaabaccacacabacaacacdddbdcdabddbdddbbcdbcdbaaadaddbbaaddaabdadadcbaadccacdacbbbcccaabbbacadddddbcccccdccddcbabdaacbaaadbccbbadbbbaacdabdddbaaddccdcaaabbdbacdbdcacadbbcccddbbdcacbbaaabccbdcdcbbcbcdcddcbbdbaddddcdcbcbcbdbccdcdbbdcabbcbdaacaadcbdbcaaaacbaaacbaaddaabdbacbcaadacdcbbdbbacccacbbcdbbbdbcabaaabbdcccabbdaaaaaabcacbbbcbbaddcdaccbdbcdacbcccbaaddbcbccbdcbccdbccbacdacbcaddbacbaacdcbcadbdbdccccbbdaadcccbadbcaaaddddabcdadddcbadcbcabcdbdcaddadbaaacacbacdaacabbcbbaddcacabdadabadaadcdaddacaaccbaacbaaddcbabadcbaccadbabbdbbdbbcabadbcabcbdacbcaabcaddbcadbadddacdbbcbbacabacdcddbbacdbbaacaacbdbdacdabcabaddddacaccdaadccbdabcbadbcbbbacabccdbcacddddbccdbbabbaabaaccbabaaabbdadabaadbcadacdcdadabbbcacccbcacbabbbacacadcbaccbbdbcacbbbaaaabddddcaaddddaadaaabccdabbadcaabbbcbbcadcdbcdbaccdccccddcbddcccdbcadccaddcabdbcdaacdbabdbdacaaaadcbdcbcadcabdbacdddbdabaacdbdaccbcbcbccaabdaabbbacabacdcccccccdadcddcddbbbbbbdbadbabdacdadcdcbbbababdcdddbbcdbbdbadcbaacdcbaacbbbbadabbbcdadcbadaaddcbacbacaabccdababacbadddabadaaccbcdabdddcadbcdadbddcaaabbbbacbdcddabdaadbdaaadccbcddcbdbbadbdcbadccdabcabcbcacbbacdadaabbdbdcabdddccabaaddbcbcbadacbbbcaddbcbccbadccccabbbaacbdbdbbcabbddcdccbaacdddbbdddcaabdbcacbdaabbdbcbaccdbaaabbabbacaabdbddcddaddccacdacdbbacdccbcdaabcbbcddbbbbbdadcdbbcbddabcbcdaccaaaadabddbadbbcbbacdddbadbaabcbbdbadbbbbcdcbbdbacccacacacbacdddbbbcbcabdaddaacbddaacccccbccabcdcbbdaacbbddcabccbdbdddbcdabacbabaaaacabccaaadbbacbaabcdadcaaacadbdacbadaacddacdadccabaacabcbdcbbcabcdddcadadbadccbbcdddababbdbbbbbadddccadaabcbabacddacccaabdacbbdcabaddcbaabaaadacbdccdcabdabbabdcbaabcabdccadbbcaaacbdbacacdabcbdbabbbadabaddccdbdadccddbbdadbcaaccbdcdaaaacbbaddacabacbacccddcacdadadbbacacabaabbabaaadbcccbcbdbabbacdaaaadbdccaccbababbbdaabddbacbaadacdccbcbacbcbccccacacbccabcaacbdacabbdabbaabacacbdddbdcbadaadaacbabdcbdabbcbdcdcdccdcdadbcddcaadadbcbcdccadcacdbadbdaddabccacbcdcaabaacdcaccddadbddabacccabdabcadcdacddbcdaaadcbdcddabadddcaacaadbcbacacbacbacadbdacbccddbbaaacddcccdcbcbbbabcdbdcdaabacdcbbabdabccddaabddbabcbddabaadbcbdabacdcbcccbbdacbbadabcadaaacccdaaddcacbdcbddbddcabaadbdacdadbacdbddaababbaabcddacdbbabcdbadadaaaaccacccdabccadacddaaacdaaabcbcaabccadaabbddddcdacdacabbbdcdcdabccbccdbabaccabcbadcdcdacdaccbabcabbdaadcbbadbbbabadbbaaccabdcdcabbbcadaabdbdbacbbbadbacbaaddddcadddbdbbadbddaadccadaddbdcaabcaaabbbbaccdacdddaddabdbcddadcaccbdbacbbcdbddcbaacbdaadaccdcdbcccbbddcbdbacbddcbabcdccdadbbcacabbdccbbcdcbbdcccaababcdcbabcabbccacdbabaadacdddcdabaadbdacbcdbacbabcbbbcacabdddcabdacdcbadddcacacdcdcbdcaccabbcabddddcaadabddcadbacadbaabcbdbdcacacddddcabdaabcdadacbabdacabcdbdaddacbcabcadcadcabaacdddbbbaadadbbaabccdbdcbddadddcbbbaabaaaddabdbbabdbddcccabddadccabbaabadbcbdddbdadbabcacaaacbaddbaaacddddabccddcbaaadabdabaccdaacbadaaaacadadcdaaccaaaabdbbadacabcbcddcbadbdcdbcabdcdaccbcbbadbbbdcdabcadcdacbcaacdddcdabcbbbdacadbaacddcbbbdbdacccdbddaadbdbbbdabcbbddbbdddbbcdbddbbdabbcbdcccbcaaabadaacabaaabcccabcaabddadcacbbbcdccadbdaddbcaabbccdabaabadcbaccddcdbddbbdababdcdaacacabddcbcccdaccbbadccbdadaccbdcdccccddaddccbaaabaabacaacbbbcbabacdacbbababbaadabcbdaccadacadabddddababcbaccdbbbcdaaabcbcacbddbcbdcddabbbbddabbabcacdcaaaadadaadcbbbbaabdddbbadbccbabcaadbaaddcacdcaababccddcbbcdbbadcddaccabaadbabccbdddbcccddacdcddcccbbcacadcdbdacaccccddabbabacbabadaacaabdddcdcaccadbcadbdbbdcbcbbdddcabaacaccaaaadbaddaddbddcddcbddabacdbbababbcbcddcdddabcabbdcacdbcaadaadaadabdcbacdacbcbdbcaaddcadbcbadabbcbdccccdcccdbaacbbbaacaddaaaddcbadadddcdaddddbddbccbabdbbadaaadcbbcadddbdbbcabaccbaacbddcddcadbacbabaadbdbaddcbbaccdabbdababbdbaaddcaccbdbbbaddabcdbdbcccccbbdccdabdaacabaaccacccdaabadbacdbbbcbdcacacdadddbcbdaabdacdbbbbbcbcbbdcacdbccdbdccdcbaadadcddcbddcacabbbbadbddabcbcbddaddcadadcdbbcaacaacaccbcadabacbadacdcddbabddcdbdcbddbddbaacbadbdcccccbbcaadbcbdadacbdbaaacdbabcccadabbbaadccacdabadddaaabbddacadbcaaabbdddaddacbbddccbdbbbddacbacbadaccdacbacbbbabdbddbcbccbacbcacdadbaabccdbaddbaaccbdbacadbcaaacacbbadbdbdcbabcccbadbcdabaaabbdaadaaabdbdacaabbccbacdbabdbcdadaaabdccdcababddbaacacabbcaabbdaadcdbadbbdacdbacaaadacbbcddababaddcdaddbdccddbddacdbdadabcacdbcddacccbacdbdadaccdbdaccbddcacdcbcabbbaabccdcbcdddadaccddbdbbcdccddccdbbcbaadadbbbdadbdcdbbcbddadadacccbaabbacdccbbccccabcdbcaadbdcaddbccdcdbaacddacbcdbbcccdcdacabcdcbbacdbadbcbaadcacbddcbbcddddddbabddcbaadcdccabaaaabdbaccccacdcdadcadaccacbadbccbdcaabbaaacabbdcadabbcdbaadbdcaccdaccbcacaccadaabaadbbdbddacdacabcccbcdcadbaaaabacaababcbdcbbcbcdcdbdccdaaacbbbaaddbcdbbadaaaadbcdaabacbdbcdbcaaaaadbcadccbaaaabbcccbaabdacbacbbdbcbaccdacbdbcddcdcdddaabbaddababaadaababdabddcdcdaabbddbbddbccdbddcdbdbaabdcdaabcdcacdddadcaddbcaacdcdbdbaacbbcbdbddbabddcbdcddaacdbbdcdcaddddcacabbaaccdcccbbdacdddcddddadabbcababbbdcbbaabaccccadbccbccdadbadaaacabccdbacbbdcbdbccaaadcabbaccadbacdcbacccabdbcdbccadddbdadcabbcadbcacadbcabacaaddcbabcacdbcbdaadddcdbcdccdaabdacaacbcabdccddbdbdcacbdbaccaaabdcdcbdcbabcaacccabdcbdbbcabbddcaaccbabddbcaaaddbbdadaccccbacdbdbdbdcdbdaaccacbdccdacabdaabacacbbbaadddccbadaacbddbbacadcbacbabacdddddcbaddcbbbbddbbbcbbddababcdbbcbdbcdabdccbddccddadbdabddbcbaaccabccaadabcdbbcadbccccaddddddbbdcbbddaaadcbcbadccaabadbacccdbbdcaddbdcadcbaadaabdadbbababcddaabbcddbbaadcdddcabdccbbcdaccddaddbcaaababbddcbcbddbccdbcddaabbcccddaddbcbaaabdcbccadcbadaccdabaccbdccbcadddbbaabbbdcbabcbaacccaaddddddcbdcdbbbacdccdabbccaddbbabcccdcacadcdbbaaaccadbcaaabccdcaadadacbbbccacdbcddadcbcbcddcbbabcaddbacaaadaccdacabcdabaabaaaaacdbbbabcacadaacbaacabaabbacdaadadcaccbbddaddcbbbdcaacccdcabdbdcaabddcbabadbbabbbacccccabcaaadccbbdcdccaaabcadaccaccccdabdadddbaccdcbbaddacbdcdadcbdbbbadbbdaaaabbbbddcbcdddabbadadabababddcdbcdbbdccaccbaccbbbbcbbdccbdcbacadbbaacbdaaaabbdaaccadbdbdaacbaacbaaaaddcdddbaabadcbcbaaccccbadabdcbdbbdabaaadbaddadaadbbaacddbcbdaaccdbdbccdacddbabbbaaaaaaaadabbcddaddbbdaadcaabbdcdbaccabcbbbdabbacdaaabdaadcbbacdbaaaddcbdcaadbbabcbaadbabdddcdacadbbacccbccbcccbbabddbcbccdbcccdddbddabaacdaddababbbdddbaacdcccdcbadcacdcbdcababacdbcbcabcbcddccbdcacaadaabadbabdacaccdcdcabbbabbdacbdabdacbbcabccdbdbaccdcdcbbbbbbdaddacaadadacabdbaadadaacaddcccadcbcdccaaaabacddadcdbcadcdabcacbabdcbabbbdbbbcddacadcdacddcaaacbbacddabddcaddbcbabcbadddaccbcdcbacdbdabcababbddcabcbbddcbcaccdccadacbcddaabadcadddabccdabbbbdccbaaacddabbcccddbaaadbcacbcdcdcbdddbadbadcbacccdcabccdbbcbadaacbbbcbcccaadacbcccdcdcbacbdbcaaddabcaabdcdacccaaaababcaacabcbbaddcbdaacdcadcbaccdadddadcbabbccaaaccdcdaaacccdddadbbcabccbdaababbcadbcbbaadbbbcccabbcaccbaaaabbdccadcaadadaccbcbacbabdaabcccbcbdddddaccacaaaacdaaddbaabdbdbccbabbaccbcadabbaaddddddcadabbdbcddcaabdccabaabbdcbacccdaaaddccbcaabccbdadddbdcbabaaadbdddbbbbabcddcacddbaabdcbcddacbaacdabddaadcbbbbddaddaaaacddbdabbdcaccbcdbaabddbadccbdbaacaacddcccbcbdbadaabddddbbaadaccadbcdadddbccdcbccbacaddabdbdabadbdcddaacaabdbbccaaacaddabaddabdbadaaadcacbdaaccdbbcdcadacdddbcddccbcbdacdcaabdbccadbdcdadddcadbbcaabbccccdccdcadddcaddcdadcaaccdbdbadabdbacacccbcbbaaabddabcacbcccddbaddaaabacddbcdbabdbdadbdddadddbbabbbcddccacadddbcadbdaaccabcacabcaaccbcadaaacdcdbcccdddbcdddcbbbabbaccabaaadbdcdccabacbcccabdcacabcbbacababccbbdccddbdcdacbcdaadddacccddbbddbadacbbdcbbbccbdadcbaddccddbccbdacdaccddadddbadabdcaaaddbbbbabbabbdadaaaccaacadcbcaacddcbdbdcccabacadbdabcdaacacdccbbdbcdccbabbadccbdbabaacacadabdbadbaccdadaccadcadbadccadabbcaaacbbadcadccccccbbddcabaccbcddadcbaadbabaaccdcccadbabaddddaabdccddbbdaabbacbabbbacacdddbdcbbbbbbabbbbaaddcdddccddbadacbbcabdddbcadaabbccaaadbabbacadddacddacbbdacbdcdbddcadaaddbdbabcbabadbdddbbddabaadccdaaacbcacabbcabbbadbabcbdcaadaddcbdcdcaacbbdbacbbcacbabcdabbbddbdaabcbadcadcabcbbcabcbdacccdabaaddddacdccbbadabddcddbbadcbdbbadadbdccacdbdbaddadbcbdcacbdbbbbdcdaacdbadbbccccddddbdbbcbcabbbabdabcddddccccbabccadcdbbabcaddbaadabdcabadbadbbaabdbdcacaaacadbcaabdddcdcdddadbbbccaabdcbbacacaddcbaabbdaaadadabbdabdcdadbbdacaccdbbbaabcbdcbbaadcdbbbdaabcabbadccdccccbdbbdbcdbaadadaacdcdcbdbcacadddbccdccacccabdbdccbdababacbabacadabcaddbccbcbbdbdaadaacbddccbaabcdddddcdbbbbbdddacdacbaccbddccadbbbcbbabadbddacabcbabcbbccabbcbdadcddaddadbcdddbcdbbadbaaadcabddddabccbbcaabbdccdcbddcdbbbbbdadbdcaabcacccbdcddccdaabcdcaadddbdcbcaaabbadcbaabcbaccbabbbbdcbbabbacdbdaaddbadbbdaccbcdccddbadbbcdcaddbdcbdcacdbcaaadaaadaadbabcbbdccbdccbccbdbddbddbbbcbbddaadabdddcbdadbdcbcaaccbdbbbccaaabcacbdbddcdacdccdbddccbcbdbbadabdcdcddccadbbcadbaababbaabaacdadbacabcdaaddccccbcadaccdcdcaadbababcbdaabbddcbbacddabddaabaadadcbbcdadadaacdaaccabccbabdabdacbcabbcddaabaabacbcaabadacdacaabbdbbdddbcadcbddababcabcbadcbdccdccbabbaabbadaabdcdddacbacddbbbbaacdddbddacbaabcaaccdcdcbaccdcdbdadcacdbaddcaadaabbbdcbcadcbcaccdbdbcdccbcbcbabadbabbcbbcddbccdcbdbcdacadcaaccddcacbdbccbcdbcbbccdbadbccaaadbdcdbbccccccaadcabdbbcadcadcddbcdbacadabcbcaabdddbdaacadddcdcbcdacdcaadbddddacacadbbdaadaabbcabbdbacddabccccabbcbdcdbdbabdbcdccdaaaddcbadcbaaaaabddacaadaccdaddaccbcccbcbccdbcdbadabccbadacaddaccdbbbcbaccaaccdcbbadaaabddccdabbbbbdaacabaabbcccdaadddadbbdcddabaadbbaacacabacdbabdbacdbcdcccdddadcbcdcbcddadaddbcaaccbbaddbadddcbbbdddbbccccbdddbbbdddabbcddadaccdbbadacccddaacabdbdaabbdcbcdbbdcaabcabdccdacbbddbdadbabaadcddddbdcaaadaccbcbbadddbbdbbcacaddaddcddadacbbcdaacbadcabcdbaddbcdddbaabbbcadaccbacaadcabdadaadabacbccdcaabbbdabdababacbddccaadddcbbbbcbacbdccbdabadcbabcbaccdcbdcaaadcdbadbdacddccdabdcaacddaadbdbadbbbcbadcacbdcaccaacddabdbdbbbddddbabacbddbabdaacbbaddcbdbabcbcdccbddaccddcdacbbcdbccadbaaccccaadcddacddadcaaaccddbabaabdabaaddcaddcddaddddaccadbabaddaddcacaccbacbdbbdddadcacacaadadbbcbacdadabdcadadbbddbdbcdbaccaccbbbbcddbbabadabadbdcabcbdcdbabcdaaaadccaacbdcbcdadbbbbbdacbcbbcbabadcadbddddbadadbccddddccdcdaaccdacabccacdadaacdcdcaddaddcdcbdbdabacbcccabadcdbbadcaadabddbccacbcaddcbaddcaaddaadbdacabdadbcbaacbbdcbccbaacbabcbbcaacdbadccbccddcdbbcbbbaadddbdbbaacabbdaccaabddacdcbddabdbcabaacbaccccdddacdadcdccbdcabdcccacacdcacabbabbcdcbbcacbdcbccaadbcbbaacbccadaaabadddbcccddbbdacacddaaacabcdbccdaacccbdadcdaaacdaacaddacdcadaaccbdddaabacccacadabdbbaccbcdbdadccaccbbcbdabcdbbcbccdccccbcaadccadccdbadcaadcccccbacbdadbbaaabcbcbcddcdacdbadabbabaccadcabcadddabbddaccbdbcbbbbabcbdabaadcaabbdcacbbcadbdddadbccbdbddddaadddccabcbaaccaababbdbaacddccdbacadacddbdbaabddccaccbadbdabccadbcaacaaacaccbdcbacadddcbbccddadabbdcbdcbabaadccbbccdababdcadbbbacabbccadbdcadbccccbbcbbadcabcbbbbcdcdbbbddbcdccadbbcdbcdbaaaabdbbdcdaacabdccddadacbddadabcccadcdaddbabdbddddbcdcaccbcbbacdddbcbcdaccacbaaaacbbacccccbbcdacdbabbbddabcaaaaabbbdcacabbdaadbdbccdadacaddabadcdbcdabbabcacdcbcddccbdcbbaadbbacabaacbdbcdcccdcaccbababbdbccdabdbcddcabdbaabbaabbbbdbcdcddbadbbbdcdbdacbbbcbcdcbbbbddaaabababcadbaaadbddabbbcaaabaddabdccdccaccbabadcdcaacbacdadccbadbaccadadddadcbadccddadcaaaadaddabbcdcdbdacdcabdbbacbbabcaadbdcbbccaadacbbbabdaaddacdbacdcbccaaaacacdbdcccdcbdcdcdadbcbccaaacdbdcdcdacabdacdcdbbbbdcababbdcbabbdadcdcdbdbcdbbbbdadbbcdbbdbccbaaaacdbadaaaabbdacdbdaddcccdaadcadcbabbadabddcdaccccaaaccdccdcbadbacabdcdcbacacacadabacacdabdadcdddacddbddcdcbacacdcaddcaccbdbdcccabbdaddccbbbaccbbaccacbbabbbddaadbdadabcdcbddaaaabacaadddadbdaddbbdbaccdddadacdabbdabbdababcbdcbcdcabbccbbaacdddcaddcdcbacdbaddcddaccadccddcbabdaacdcbabddabdaadbdbddcdcddcbdadccabaccdbabcadccabadbdbaddccdaccdcddbcaddcdbbadccdccccbacaaadabaddbacbbadbbacabcddbdaddbabacdadccbddcacabbdaadbdaccdbbcadbbabbbbdadbabbbdaaddbbcbdcbaaabacaabbdadadaaaadabbaadacbbdcdcbdbaabbcdabbbcdbccbaddbacabacabbaacbbaddccdbabcdcabdccabccabdaaccaaacdddbccbcacbbcdaabdbdbbbcdccdcdbdcadcdbbdbadcadaadbdbaaccadacadcbddbaadddaabbcbcdacbcadacdbbcadddbadbaacbcaccbcccabbabdacacdbbbbccdabcaaabacabbaccabbcbdbcbcbdacacdbccaadbabddccacdabbcbacabbaadbbdcbdacdadbbbacbbdddadacacbaccacddbdcacbcdcdccbacacccdcaadabcaabddcadaacbacabacacccaadbbddbdcdcaccabddbbaaadbbdcdbabddbbbadadbadcddddcddcababaaaacdbcdaddbddbcbbaacdaabbccaabacdccdcacddbbdcbacbbbbdcabcbcccbaaccdacbcbaacdcdbabbadccbabaababbacddabcaaccccbbaadddbbdacabddadadcabadadbbdadbcccdbaaaaddbcadaaddaababdadaccbcccbcabdaaadaddccaddbadbbbddbdbbcbcbdbbbcddcbbcabadcadbaccadacabdbcbcccacabadcbbdaaacccdbaaddcdbdbbaacccbbbabacbdccccdadcbcabbcbccdabcaabdbadccabddbdbcaadaaccbacccbbbbbdcaabacaabcaadcbccbbdcccdccbbbdbdcbdcddabcdadcaacdcdcaacdbbdaaddcdcbbbaaccbbdccbdabbbddacdbaccabaadaccbcbaaadbadadcabdadccbddcdbdaabadbbcbcdbbcbabccabddbdcbccccbdcbaaadadbcabbbcacccacdacbbbdcaacbacbddacddcdcaccdccabbddbccabdcbbcaabcdaddbdbcbcddcaabdbbbaacdcaacabdbadbacdccbaaccadabcabadbbabbbdabbdcdabadbdcdbabdadcdbcccbbcdcacbacbbdddcccaaaadbacadbacbacbcacccbdcccbbcbdbaabbbbaabacbbbbcdabbacaabbbabccddacacacadcaabbbacbbddcbaddddddbbdbabcabbcbddbbcdacbcbccadbabbcbacccacaadcbacaddaadbbbdcdcbbdcbcaadcdbcbcabbdcdaaddaaabcdbcdccddaaccabccadabbbbccbcdabaaabcadcdddcdbddbdabdccadddaaaacdcddadaabdcbcdbdbbdbbabdbcbaacdddcdcacccddadaaadabcaccddbdbbdddadabccaabadddbddccbaaabdcdacdbccbaaccbaddddcdadbcbaaddddadaabdcdbabcbcddccaaccdbadaacdcdcdddccdcdcadbabbdbaabccacbcdccabddaccaaadccbcbdbdcaabdcabbdbcdbabddcdaabaacaacbbaaccbddbbaccbaddadcadabdbddbdadbabaadaabbadbcacababcbcccadbccbdabccdbdbcdcbddaabcbbabadbddbdbdaaaccdaadabddacacbadabcaacdcbcdbdbdbcdbacbcbbddaccdaacdcadacaabcbcccaaabdcddbbacdccbbdbbdabdbbcabbcddbdcdbbbaacacabcabcbdbadabbbbdbcacbaacbdadcccdddcbadaaccbacccccabccbbccadacacadacccccbbaacadaccbbdadbddadabdbbbdddccadccabccdccddaaadcbcdaabdbcaaaababcaacccbdbccaabbbbdcbbbababaacadddaabacdacddcbabdbdbbacdaccbddadbbacbbacaddacdddcacaddbdbbcbbabbdaddcabbdadcaabadbcabbadbdccbcdbdaddaabcacbaaabbdacdadccccaabbcadbbcaabacabbdaccdbcbadcdcdccbdacbddaaaaaadccdcccaadbaadbdacbcdbbbdbdcacdbddbabcacbabdcadbabcbcdbdbcbcaadcdbcaddabbbbaaddcabbcaccbbbbcbaaadbbcbbbaccabddcccdcbdddcdaaaacbcdbdabcbdccbadbbaddbadbbcbbbcccacdbbacaacdbddbcccdabadcadabbbbdaaddabadbccbcabbbbcbadabcbaaccaddbdddadacadbdcababdddbadcddabbdbdbddbaddbaaadccdbdddabaabbcdbdadcaabacaacdccaddbbbdbadadcbbdabaccaddddacdabbbacdcdcaddcddcddcccddcbbcdcabdbdcdcbcdbadcccdabaddcccadaccddbcdbdabbdabdcbcacccababdccdabadccddabbbcaccccbdbbcaccabbddddbdcddcaddbccabbdcdaabddcdddddcdbbcbabcdaddbabbcddbbdabccabbbdabccdbbadccacaccaaacbaacbcdabbbbabdaabbacddbdbbdbddaccbcbdbabccbdadbdccdccaabbacddaacabdccababcbcdbcbdddabaabccccdcbadcdbbcbdcdaadbcddddbdbbbcbdacacaaacaaaaabadcbddddcdbacbdcdcbabcadadaabcdbddddcdaadbdabaddbccabaacabdcaadadbaccbcaabddddaacbacbcaddcaaddbdcdcbaaaadabaccabbddabcacdcacddabdaccabadbcbbdabccaabccbdbbddcdddbcaccababbbcaaadacaadcacbcdbbaaacbadbacbbaccaabdabcdcaabaccbabccadcadccbadbdaadddaccbdabbacdcbcdcdcdaadacbdcbddbacdccbdbcaaacdacdbdcbdadbcacbcbbadcabdbcddcccbadaaaaabcadcbcddcadcacadbcbacaadacaabccabdaadcbacdccbadcaccadbbbabdaaacdaaccbdadacabbabbbdaddbccbcacdbcbcabddbddbacddadddcdaacbcdbadacbbcbabcdbdacbadaabbbabddcdacccaaabbcadcabdcadbcabaabbaccbacbcbbaaadaabaaddccacabddbaddddbccaaaadacdcdaddddabaccacdcbabcbdccadbbccaadabbcdcccadaabdabcacbdadcaaccdbaabbcabbdbbbbabadbddbdbabddadddbdcadaabadcadcccabcaccabcddaabadabcbdbaaddbcbabcbdccbadacbbdaacbbdababcddddddaccacdddbdcddcaaabbcbbcbcabdabccdddcddaaadbddabcddbadaacaabbdcbacbbcbbddccdbcdbacbaacacbacbccbaaadaddbadcdbdcdcdadaddbcbbddbbaabcdbbbcacadccbdbbcbbdcadccdaacccccacdddcbccbdadbbdaaadbdcbbdacdcaabdabacbbbcbcbabcdddbbaabdadddddacacbacddbabbaabadbadcbcccdacacdacccbbdccadabcaccbbdadababbcbcbadcaadcdaabcdcbbdaacacabdbabbadcabadbadbadbddcbdddadcdadcabaaaaacdbdbbbcdaaacddbbaddbabddddaccccaaabcdcbbaadbadaadcdbccadccbcabbcadcdcdadccbacddaadaccccdbbdadddabdbdcdaadbbbdabbccbabaddabddccbbcccbbddacbbcaddaaddaadcbcdddcdccaaaddcabcbcabcbbdcdbaaaacccacdddcabbbdabdaadcddbcabbbabcbbacbccbbccadcabcabdccdcbdbcdbabaacdccbbbddcccdaccdbbccdcddcddacababbdddacdaacbbdbaaadbcaddddacdcdbadcbcbbbabdbbdadaadacbabacdcdbabcdcccddbcbbbddabcacbccaddcccaabcddccbcccccbbbbddddddbadbccdcabbaacccbcdcadabdbbcddbaaaacadaccdcdcbbabdbbacdbacbcbcddcdbdabbddbbcabaaddccaccacccbdddbddcaacbbcddacdaccacddbcbabacbcbabcdbbcbaabddcabdcddaccacaacdbbcbccbdcccdddbdbbabdadcaaccddddddbcdcccbadbdbbcbdbcabaccbbcbaccbadcdcabaddddcdadcdcaadccdabdbdaddcccbddaaccbaaababddddbbdadbbcacbbbcccccdddbdccbbddabcacdbbadbadbdbcaccaddcdbdabdaaddcbbaabcabcaccbcbdcacdcbadbbbabdccbdddbabbbdbabdcdadadddcacaddbdbbcaabbbbdadcbcacacbbadadabbbbadadacadbcdabbcadabdccdbdddabaadcaccbcccaabcbabdbaabaddcbadbacadaddcabadcdccccadbdbcaacddaabaccacbbdbbcadadbcacabbddacaccdcacbcbadbbbdcaabbcaddaaacbdbbadaadabadbdbacbababbbbdbdccddabbbbadcbaccaaabadbbcadabcbbbabcbcaccbdbdaabadbdddadadababcbcdabadbddcbdcbabdcbdbccaacadcdbcaccdcccbaacadbbbcacdccaabccadcbbbdacababccdcadbbdddbbdaccadcdbbdccbbddcdabcaadbacddbcbaabcbabddbcbcaabccccacbbcdabbdacbadcbccabddbbbbabbdcccabaaccaaaaadabacbcdcaacaaabadcbdacbcdaaabccacbbacadcbdbbabbdcccbbabcdacbbdbbdccdcbddcbbdcdbdbbbabcabdbcbbcccaadbabbdccdbbdcbdbcabcddcaccabdcbccbdadbbbcaccddaabaacbcbaabcaccbaaacdcbccbcdadbaadccdcadbcabcaaaddcddcacdddddccdbabdbddaaccdcaaabbaacbadabcdbccbaccbaabcbcdadddccaaddcadadcdcbacdccdaddbbbdcddcdacadaadcbbdcbdcbbbcadddbdbdaadbddbcdcbaacbbadccbbbdbcbccdcbaccacaaccaccdddadcabdcdcbbbcddcdcdcbdaccaacdabcbabaddbddbcaadbcbccbcaaaacbbdcbadcbdcabbccdbcbabddbdccaddaaacdbadcdcdbabcbacabbcaabcacabcacccacbcaccacabcdbbcccdaddaddaadcbdacbaabcabdbababbabdbadabaabdcabcbdacadcdacdcccdcdadbabdacbdbccacddbacaddbaaaacddcdbcdacbcaddcbbbacdbbadbadadacbdcccaadaddacacacdacdbccbddcdabdbcabaaadcbbcacdbccbbdbbbdacdbdabacdbcbcbacacaddacddabccaccccbabbabdbccabdcbaccababbbdbcdbbdbdcbcbaaacaabdbbdbbcdcabcbadcbbacabddaddbaccdaddcaacabbddaabadbaddcbbdcdcbbcdbccaadabdcccdbddaaadbcaccdadaadbaaabacbbabbcdadcddcaabcbaaacbbbcacabcabcddcabcccccddadabbcbbbabbbbcaddabbdcaddcccdbbacadabadbcabcbadbcbaabddadbaaabcdbdddaabdddcbcaacdccaaccdccabbdadbddddbabddcdabcdcbacacdabdbaadadbbddcbbadbadcbacbcabdbaddbbbbdcccbaccdbcdbcddcacabcbbddacaddbbadbcdcadcddaddccadcabdcadbadabcbadbbdacdcbdddabbbcbababdccdbddaaaadcdcabacbbdcddddaacaaabacacdaaadcdbaaddddbdbdbcaacccbcdabbacbababcdcabbaadbdbcdaccababbabcabddbdbadbcccbdcddcbacdaacadacdabbaadbddcbabdbdbbcbaabbccdbbcccabbabbccdddacbcbcadbbcbdbdcdcbdcbdddbddabacabccacacbccacdbaabcacddcbcbcaddcdadbbdccbabdbbdcbbacdcdbbbacdccacbcaccdbabbcddcbdbbacadbbbccbbcabbbbbaaaabbabdaadbcadacdbabdaaadabacdcbcdbccdadbadcaaabcddccacacacdbacddcaaacbbcbcbccbccdcaaabcbbbcdabbbbbbbacbdbcadcdacccbcaadbabbbaaaacccabccbbcbaccaadccacadabdaabbdbdccaddbbbacbaacbadcddaacaabaddcbdaaccabacacaaacbbcaaccdbaacddcdbaccccadacbcdbcabdcccdcdaaadcbbdddcdacdcdcaabcccaccccacacbaabdcadbdcacdccabccdddcdbabdbcbcbbbdddacadcacbacacbddbcaddbbacdbdbdaabccddadbbdaaacddaabddbbdddaacdcbadcbbadcababaccbbcdcbccbccabcdacbaabcdcaccbbcadbaababcdacacadcddaadacdbaaabddcdaacbdcdaacacbaacacbbaddbacbcdddcdababaadabcbdbcabcbddcacacbbbcddbabaacdbcacbbdabdadddcbcbdaccdbacaaaabcabdcaaaaaddcdbabadaabdbcdcccbdcbbdabbadadaaacaccdaddccbaccbdcdbcabacacacdbdcaaabdcbdbaddbdabbacccbccccbcaadbacdaaccbbadddcadddbbdabcdacaccababadccbbddaddcadcdbaabbcabbbcddaadcdbaccdbaadaababadddddbcccbbaabccabdabcbccbcaadacbaadcdcddaddbcaacadaabddadddcaddcccadacbcdbcaaacddaaabccddaaddaabddddddaabcaabdcddbdbbdbbcabbdcbdbdadacbabcccabcaadcbcccacdbbaadcccbdccdabacaadaacacbbbacdddccbabbdcddaacaabdcccbccdabadbdbbaccaadcabadabccbdbadcacbbadccbbbbcdcabadabbbcdccdbdabdcbaccbadddabccbdcaadcddddbccdbacacdcabcabdbabadacbdddadabdabaabccdddcddddcbadcbabcdadabaddadcdaaaddbdbacbaacdadacdaabccdabbdbcadbaccabcacdbbbdacacadabbcaddbbdcbabdaadacdaabacdabbbcaadbadaadddbbbadbdbcdaabdbdaccadcdddabbdcccabdcdddaccbbddbdbddccdabdcaaabbbbbdbbdabbdabbbdbbdcdbcbdbdcbbbcbdacbcdcccbdcadbbcbdabcdadcdbcbbdaacbbabcadbbbacbacccadcdbaacdadddbacaadcdbbbcaddbaaccbbcccacbabccbadcadbcaddcbacdcbbcdcbdbcddbcaaddbadabcaddbcddbdcddbccbbaabbcdaabdacddadcddbbdbdabaccdacbbabbccbddbdddaddaaccdaacdadcaaddcaadddadbbacbaabdbdadbddcaaacbdccdaccaddccbcccbdcdcbddadabdcbcdbdabcadddadadadcdacbcaaddbbbcdabcabbccaccbcdabbcadaadccdadccccbcdbcdacdcbbcabcbccdbddacadabaadbddaaadddcdddbcbcccbdcabcababccdbbbabacdcadbbaddabcccbcabbdcbccbdcaccdabaaacccbcdbcbdbbdaababccdcbaacabdcbdaacdcdbdddaddaadadcccbabcaacccbdaadaabccbddacabadaabcccdcbbbdabbaabbaacacadbcbcdcbdddaabcabdcabcbcbddbacabbdabbdbcdcbccaaadcbaaccbbdbcdadbcddcacadcaddcbaababdaccdbacabcbdabcdcdccbadcabcbbcdbbdbddbabbaacdaaccdccbbddaadbbdabcaaddabcaadadabaccadadadcdcbcbbbacbbababbacddcabdabaabcadcabdabcccadbbccdcbbdbdcacabcdabaccdbcaadaabaabbdcbcdbdcaddddabdcadabcbbccdbddbcabbbbdbabbacbcaabdddaababbacabaacbadddccdcbcdcaccabcccdbdbcbbdbadbcacbcbadbbcccdaccadcbaddbcbcdcdacbddbdbaabcbdbbbbddbbcaacdabbcdaacccbaddbbdddddabcbaababbabacdbbaadbabdcdaabbdccdddddadcdabcaddddaccbddacbbcbddbcadbbbaacbbabbcccaccbddcbacbabbabddcabccbadddaaaddadddcbadddccacabdaabdbdabbccadbbcadbdcabdbccddadbdbacdbadcbcbbbadaabcbcdcaacccacdaaacdaccdaccdbbbcadabcdddcbabdcaccdaccabcadbcbcdbbbacabcaaaccddaccbddccbcbaaababcdcaddbacbcdbbabbdacbdacacbcaabadbabdbcdbacccbcadbcdddbccddabbbcbadaadabdcddbcbdcdbadabacddbddcbbacbbaadccbbdbaacaadaccbbbaacacacdbaacddcabacbbcdcdabdaaabdcadcccdadabbaadcccdbccdaabdcadddccaaacabbcdaadadbddcadabbbbdbdbcabaccdacdbdbcaabbaabdccbbdcccadbacbcccaaadabcddaaaaccddbbbaabbccccacadbcbcacdaadbbcdddcaddaccbcbbcabbaadbdccdddbabbbcdaaccaabbdaacdcddccdcadbcbdacdacaacccdbadadacdacbbccdadbabccabdabccbbabcbbacacdcdcadbaacdddccdcddccdcddcbdbccbacbddbababbcbcddbcbaaddbbcdabbbbbacddcaaacddddadcadcdcaddababdcccbcdcaddcbbadddbadadbddabdcdcaadbadadabcacdbdddaaabddcaaadbcdaaabbbbcccabbacacdbdccdcbdbabbddabdadcdcdadbdbbcaccaccaacbbdcacdcaacddadabcdbcddbacdabdadcbbcdcbaccabcccbbcdbdcddddacbadcdacbcbcaabaacdacadaabaabbcddcdbdbabbdcaabbccdddbcdabbbbbbdcaadadabccccacdbcdcddcaacaccdbbadadcddaaadbdcdabdbdccaadacabdacbccbbcbaaaadcacdaadbcdaacadaacdabdccdaaccdadccdacbddddabdadbadcbcabdabbbbdbdddacbcddabbbbdcccddcddaabdbcdbdccdddadcdcdcdcbbcdbaabaaacdacdcaddcbbcdacbbdddbdcbbbadbccdbcabacbcacbadbcadcdaadbdaabdadccaccbcacdbccccdaddbabccaddacabdbddaaaabdbababcabdbababcacdadacbddaccdcdabccdacabdcbddaaddbddbdacbbabbacabadaaccbcbcabdcbcacbccddbbbacbadabccacdcabaacdbbbbbbccabadcdbacdddcbcbcdadcdccdbadaddbdaacbcbbdaadbbccdcdcdbcaccdadaacdbdabcdaaacbcdababdccdaccbdccabacbacdabdabadaaddcddcbbcddaccccbbcbdcbddbabccbbdbabdbacadddabdacdaccdacdcacdacbdbcddcbdddccabacabbacbdcacdaccbdcababacbacabaccbcabbcacababcdbbdcddbacadbcbbdcbcbcacdbdbbdbcccbdcdbbdaddaddcddbacddbaabdbcbabcdcacbcdabaaabbdabcdbbdcaaaabcaaaaddbaaabcbadcdbdccbacbccabdadacbbbbcbdbddccccbbabdcbadcdbdaadadbccddadccccdacadccaddcbdadcadabcbbcadbacabdddbcdddaaabdadbbabaadcddcdbccbdccbacacbbbdacbbbdbabbcbacadddaaccaccbbcabdcbadabbbbbabdabccabcaacccbadabaadbcbabccbbddbccccbacbdbbdbbaccacabacccddcaabbdbcaaddbdcbcaaaaddccbacaadbabccccacacccdbbacbdaacbccaccaaabbabbacbabdcbbccdddddacbdbdbaadacbdacbabdbdcdbcadcdadaddababdcbbdabbdbabcabaadabcdbcbaabcbcaadabddcbddacbcccccbacacabacacabcaddcccdaddddcaabadacdccbadadbbacdabdcdbbbcbbdabacbaadbadbdbdbdbddabdbccccacddbcdaabdacadcbdccaabcbbccacadaaccaadacababdadcdbdccccdbcccddbaababdbccbabdababbbbbbdcbdabddbdaddbacdddbcdddbdcaaaadcacbbddbbacdcbdaddccaccddacdaabadddacbacdadddbcdcccaacdccadbdcbadcccadddadaaacaccbaacbdaadbbdaabdadbcadadcbdcddbdcbdbbdacdbbbacdddbdcbbdccabdcacddcbcbbdcdbbaacdddbacccaadadaadcccbaacabccbcdaaabddccdacaccdcddaaaccbccdbddcdbdbdacbbddbcdaddcacdbacbcdbddaabcdabbbcdacbbcdcbdcbdcdaaadabbcbcaaacacbbcacbaccdbbbcacdbaccbdcddbbaabccbbdaadcbababadadabacbcacabddabbbbabcbcbdacabddccdbbdbcadaadbdbdcdbaacbdababbbddccadcbacbccaabbaabcdaddacbaabdddaaccaddcacbdcdcaadbbcbabbcdbadcaadcabcdcbbddacdddbaacaaaaacbddcacbdbdcdaccaacaadcaacbcbddccddcdcaababadcbbbaacadcaababcbdbbdccddcbdbbccdbdcddbdababacccdddcdbbacadddbcbcdbbddaaccbddcbbccaaadadadaaccadccacdadbbaccdacdbbaabdbaabdadddcbacbdbbccdbbbbbcdbaddaaaccbdbcbcbadbdbadcdcbcdabbddbcddabbbadadbabdcaccadadddccccaabcabdadddcbbcaabdabcacdcddcdddbbbadacbbdcdbacbcbcaadacccccadabcacbddbbcbadcbbbacbaacbabdadaabdabdccabdadcbddaddcbddacbcdaaddbddbcbacbcdcbbbdaabdacddaacbabbbadbddccaababdcacaabccdbdcbbdccbcaadcdadcddacbbcaddacdabaadbcadbbaccdbcbbadadbcacdcaadbaacacdbadcbccdcbbcdbabdbadadaadaacaaacaddbcacdbabaabaaacddabaabcdadbcdabacddcdaccabbbbcccddddabddaadcdcdbbbbbbbdbbcdbbcdcdacdbdaadcbbddbbcbdddaaccacabccadaddcdcaaaccccbcaabcddbbacbbcccbddacdcccdbdaccdadcabadcabcbcacacbcaccbdcaabbabcacdabadbadbdbccacbcdabcccbcdcdcbbdaadccdbcdbababddbcccbddbcabbbadbacaddaccbbadbabbabaaaddbbaacddaabdcdadbacbcabcdbcdabbdabbbaabccaadbadabbcbadddbdabbcbcbabdabacabbcadbdbcdccbabccbdcddacbbabcddcdddadadaaddcbbccaabcaacacbdcdabdabdccdabddcbbaadadaabdaddcadddcbdabbbcabddbbdabddbcadabaadbbbabbcadadabdddabbbcaaacadcbcdbccaccabdcddaddcbaacbadbdbababdcbcdcdaccdbcaabbbdaddbbcbcdabbdacdacddadccadaccdabdacbbcdacbcdabccbbabcdbbacaccadddddddaddacbcbddbadccdabbcbbaccdbccbdbcbdbcbdbaacabbabdbbbdcccadababaacbabccacabcadbadbcbbdaccabdcbbaacbacaadbbbcaccadccbcadbadadccbcdbdacccbbbadccbdddbaddabccaadcacbccdadcbcddbabbabbdbbdcdccbabacbdccbbcbaddccdcdbbcdadadbddcdbddcbdadddadccadccccacaadbabdcbcdcbcbabacccbadcadcdbcbacbaadadaddcdbbaddbbdacbbdabbabcddaadbcbadbdcbbdaaabbacccdcddbacdbabaddbdcccdabbbbddcaabcacadbcdaadbbcbbddabbdbbbadabbccddbbbbdcbaccbacccbdaadbccaabbdbdadabaaaccacbcbbcdcdcbbdaacadcddaacaddaaaabddaddabdabdabacbbbabbdccddabcccacbdbbdbbcbcadccacbbadcbadbcbbddcbbbbaabbadcbbbcddbbdaacabaabbbdaddaabaadabbbcdadbdcdaacababcbddcdbddbbdcdbcaddcbddaadcbddbaadbcbbdbdacbcacddccaccaddbbadacdaabdbdccdcabcbcbcadbcabdabbdababacccdcabcadbbbdbaaddcccbcacacdddcabadcabdcbaacacdaaacbdbaccdabcdbdaabddbbdbbaabcaddbacccddddaaadbccbdbabcdcacaadbabaabbccadcccabbcbbacdbdbbbbdccdbdaccdacaacacbcdbbbbacaabcadaabacaaaccddcbaabbdcddcaacdcbbdaaabcabddbccbbdbcbacaadcabdccabbcccadcbabdaadaacdcccbcbbadddaaddcdddbdbcdcabbdaaabbcbbdcbcccccacaccbcabacbaacbabbcdcdbdcacabaaadddcadabcbbaaddadacbbaaccadacbdaaddcdcadbcabaabcbbbacadbadabbdbdadacddcddaaaaddccbacbdbcddbdbcdcddacdadbbccadbcddddbbcdbcdddbddbcbcdcaadddaadbcbbdcdcaddcaadcaabddcbdddccbbcdacdcccddcbddbcdcbddaabbaacddacadacdabbaddccbcabbabdabbddcddaabdcdadadbbbbddabccadaabaaaabdbabadbbbddcaaadadbccbdbacbadddbbcdcabcbbbacaccbcddccbaabacddbacbaaccdbdbbddaccbddccadaadaaaccbdacbcbacacbadcddccdbbbdbadbbadbbadbccdddaabaaadacaaacdacbaaaaacdbbbdaccbcadbcddcdabbacdccdabdbccdcabcbdbdbddbcbacbadddabcdabbbbdaaaddbbcbcaaccbbacbbdddbabbcbdabbaadabcabdacccccadccbbdcccbdddbcbadcbcacbddaababcdddadcbddbcccbacbcddbdddbbcbbbcccaaacacaadbcdbaaabcdbadabaacadbbaabddaabddcbabacbabbbabbaccadaaaabccbdbbdcdaadaacddccacaabcdccddadcdbdacaaccaadcbabbcabbbaacacabcabcabbcadcabbcdcdbacbdacbdbcbacddcdcdabaabcccadabbadadbdbabbcbaaadbdaaddcaaacdddccccaaabbdcbbaabdcdcadadadcdacaacddaabcbdacbcccbcbdbcaacbbdccdacaccdbdcccadbbccbaccbcabbdcbdcccddcacbdcaababddbbdcccccbddcabbdaddcdbddbabbddbccbdababbbdcddbacbbddbaaabdcbdcddabdddabdbdddcacadddcdcddbbbccaddaaddadbccdbabcddbbdaacbadacccbacabbdcacccdacbabacbddbaccbbacccabbccdbbabcbdadbbdcabdbabababdcacbccbaccadcccadabcbbadcdcccddaacabaabdcabbcaababbdbaddbbabcdccabbbbadbaadbbcbccadbabbdcdbaaadadabbbcbdccadbcdaaddcdaaddbabbadbacbbcacbbadbbdbbbccbbaacddbcaadbdadbbaddbaaddbbaddadababaabccaadddccaabddaddaadbddcbcaadcdcdcadbddbccbccdbcbaaddcbbdabdcaccadbabaabcaacbaadcdacacacbbdabaacdbccbccbacccabaccdaddcdabddbcaacbbdbaaccccabcabdbbaaacbaadcacacbcbdaacbbbbcdbdbbbcaabbdcbdcadbdbbcdccbadbdccaadccadccbddcdadaccddcabdacdbcddbbcaccbcaabcbcdcbbbacbaaaadbdcddddbbadaabbdbaaadcdcadbbabbbdcbcddbacbadcccdccbcccabddcbacbbbabcaabdbbbbbabdbcbbacbdbadaaaaccabbbdbacddadcabdddadaccbbbabaaadcabdadbbbbccadacbadaccccdacbacacdcdcbbacbbbcccbcbacbccbaaacabbdbddcdcdcdbcbcbddcdcacbaddaadabcaabbabcbaddbccdcdaaaabcbacbcaaadaccccaabcbbddadbacbbbacccbccdbcdbcabbbcacbbbaaadadcdbdbcdabaaabaccabbaccdacacbabdcbadbabbbdcababcbaadbadacccbcbccddbdbcdbdddbaddacdcaccacddabaabdababcadcbbcbcacdccbccdcacaadbdcacdbaaabadbbaabccadddcaddbdaabdbccacdcccabddbcccdaadadbbccbcddbcbbdcabcccaddcdbccbdabbdcacdbdcddccaaacdccbbbdbdadddccbcdbcbbacdabdaabacdddabccdababdbdddaaaaabccdacabbbbabddadcbadabadbbadbbadacbcdadaadbaacaaaacbabbacdcbabcbaaabaccaadbadabdddbbdaacbabbdcdbddccdbcadadadaacacacacddacdacdbbadbcddbbccdaadcbbaddbbbdabcccccdbaccaabddababaadcabbcaacbcbccabbdadabbbdbdccdcadacbbcbbcbddcbdccabbdcabcdcaddabddcbdbbbcbdddaacdddaaaaadabaaddbbcccdbccbdababcdccdbbbbaaacaadbcbaaaaabbddbbbdcddabdaacabccbcacabbcaadbbdbaaabbdadccacaacbbabcdccbdcdcabbadcaaccbdcacaccaabbaacaddccdccacbbdabbdcdcbdbcbabddccaacabbcaaadabcacabcacaddbbdddaccbcdbcccdaaababcadddcbddbbbaabcbddbdaacbdccdcaadcacaababbadbadbadbcabaadbaccabadacdbbcacbbabaccccbbcbcbabacaaaaaabbcabbcdbbccddaccabdccbdbadacabababdddcbaddbbbacdcadadadadcddbbbcbcaadcaaabaccbaaaccddadcbdddcbabbbdacadaaddadddbdcbadccdbabdcccddaaaacdddacbadcadddcacbbdbabdcbadbbcbdacdaacbddbddccccadbbdbcbacbcadadaccbddbcdacdccdacbbabadddcbabbdcdbcaccdbccdcbbcddbbbadcacdbacdadbaadbbcddabccdcabbbaddabdcdadccdaaddbabdbdccdbdaaacdcdcadcadbcbaaabbdabaccccdbabdadadbddcdddbbababcddbbcddabbdcabbccbdaddaacbadcbbddaadccaaabcdbccadbdbdcaaabaaacdcbaadabddbaabdaacbbdaaaabcadddcabaccbddcbbcbdccabbcbcabaabbbcbdadcadcddcacdaabaacbabddbadcddabcbdbdaadaddbacaababcdaccdbbbddbdccaccdbacbbdbcbdacabacabbcaddcdbadcddcababbbaabccbbcbddabdcbadbaccdccdcdcdacaadacbabbcbadaaadcdccdbdacccacdcdbabbbbcbcabbabdabaccdaadadbabdacbacacababbdcbbbccaacacdcabdccccbbdcdccbaabacbacbbcccccdbddcabaaabaacbcbdadbccbccadbaabcbadadaadbdcbbdcaabbadabdcaabaddcadbbdbcddbdccabaccacdacbabbadcddcccccbdcbbacbcccadccbaddcaadacbadaadaddaadaabbabdbdbbcacadadaaabcabddabddacbddadadbbccdabcdcacbbadbacbcaddcbbabdbbcabcdbcbbadccbdcaabdcacaabccdcbcccbcaabbcabcbaaacbbccbccbcdaabdcdbbdaabacbacaabaacabbddcddbbbabbaabbdddbdcacbcacbddbddccbddacacccdbbaccaddddaccabbcdcbdcbbbccbdbcacbdbddcaccaadbdacddccbbcdbcadabdbbaaddccdddcbcdabdcaabccccaaaddabbdbcdcbcddddbccddbcbdabdaacadcbdaddbcdcdbcbacacddbbdacaddaadabadbcadabacadcadcbaaddbdbacbbabccccbcbccbcbbccdadbaaaddbccaadbacccccacccbdbaaadbdbacadbbdcadbaaaaacbdcddcbdcccabbdbcadbdacdcbacacdabdbbbccacbccaacacbbddbbcaaaabaaadbdbabaacaabcdaddbddabcddaddabdccaacdbaabacadbddddbbdcacbabbcabdddddcdabddacbccabbbdcdadbcdbcdcddbbbbccbabcabbcbddcdcbccdbaabaddcaaadcaabccbdcdababcccacaccdaadadcaadcbbbcdbbcbbbdbbdbbcdddbaaaaacbbcdcaccaaaccabcdbcacbbdbbbcdababcdacccaadbbaadbcaadaacbaaccdccdaaaacaddcbddabbabbbbbcbaddbdddbaadaaadbabbacdddaacaabdccaadaddcbcaabdccabacbcccccbdccbddbcdbbbdabbbcbdadbdcbaabcaadbcbcadbabcbbabcaacabcaccdbacadcaabccccbababcddbadbacacbbcbaadccccbaacdcbbbcbaabdcdbabaabacccccdbcacddacdcbccadabcabcaacdadbcaabaaddbbcabbbadccdacaacbabadadaaadcbdbabadbaadcbbcdbbcadaccbbabbddbbbcccbdadacdbddddbacdcbbadddcbbbccadaccacadbadccdcddaacadcdabbabccbdddaccccdcbbdddacdbcccabbbdbddbbcbcadabaaacabaabccbdbabdbddcdbaabadcacbadbacbcccbbbcbbbacbbdcbabdddbddddadccdbcadbabadcabbddcccdcbbadaaacccbaaddddbcbdabdaaabdbcacbdbcaccdbabbbdaadaaccdbabdcbcbaabbdcdddadaacaabbcddabddbbcadadbccadcdccadcccdaaabdacdbccbadbdcdabdddbbabaacdbbbcbaddbcdaccacdccabbbdcbadbcbcacdcabbdcbacdcacaabababdbccbbcbbcaadccdbbdddaddbddcacabaabbcbddcacdbbbbadadbbddabdbbcdcccabbdddaaccaacacbbdccbaabdabcacbcabcdaabadbcbddbdaadccaccdaaadabaccccbaddaabaacabbabcadabcbbcacdccddccbbaacbdaccdaacbaccddabaccdaadbabcabcdbcdabbddcbaaaadcbacbddcdbccbddadadbbdbabdbdcbabadaaacabcdabcccbdbcbaaabcdcaaadadbaaccbcdadadbdbabcabdbbacbcdacaacaddacabcbbccbdadcbdabdbabadccbadcbbaadcbdcdbabdabdacaddbabccbaacdcbcdccbddddbdddbcccbadccacbcdcccadcdccadddcdaaaddcbdcdcddabdaaddcbcbadcdabccbabacabbbbacccbdaddaccadadabdcdaddacbdabaddadacadabbdacdbcdbdaabadadadcbcdcacabdadbdabacacbcbbabaaacbdcddcacdacbcbccccdaddadddabccabcccdcdcdbdccdadbadaabacbdcaababccddddcbabdbbbaacabbddadadcbabcbbdbadcadaddbaccdaddbcaccccabbbbadaadddbadacbbacbbcdcaacddbdacbdcaabbcccdcabdaabbaaabdcddddbdddbcddacaacbcdaabcdccadbabbabadacbbdadacdbaddcdddcaccdbddbccacbbabdaabaaaddbcbbbbdbcdcddccddcaddcadcdacbcacbbdbbdabdccbdccdadacddcabdcacbccbadaaccbdbaddddbbdcacdcbdbbcccbbaadcdcadabbcddccaadcbacacddccbbcbdddbdbabcbacbaabddaadcdcdcdcddabcdcbbcdcabacdacdddddabddbaadbcadcbcdbbbbcccdbcdabcabadaaaaacdcbaacdbaabaacbbbdadabcdadaadacaaaabcdbbccdbdadddaaabadcddcccdbcbbbdbdcdbbcacbabcbadddcdddbcdccbaabdbbbbddacbcddcbccabcbccabbcadacacbbbaadaddabbacadacaccdbaadddabbadddadbdccadaddbccacbddcabdbbaaccacddbdbdbacdbccdbaacdddccdbcddbdbacdadcdcdbbcdcabcddbcbcccbadabcaccbadcbadacbddbbbbddadbdcaaccddabaacbcacacbdbcaadbbbcccccbddcadbadbcbcdbdadbaacbacadcddbabababbbbaabcaacabddcbbaccdacbdbcdadacadcbacaabaddbdacdaaadbbdbacdccdccacaaccccadbbcdcbbabdadcacabbcdbdcacdbacbbcdddcccbaccabcabbdccbdbccddbdbcbaadcdabadbccabdccbbaacdcbaccddcbddaadcbcdcaccbcdcdddbadcbbbcbccddbdbbdcbdbbcaabaacbacddaadacbdbcaabdabdacacbaababbdcbdbcbcdbabbccdabbaacbbbaccccbcbbcaadbcaddabcdbdcdcbddadbdccccbacbcabbcbadaddbaadbdacacbbddcdbdcabbadbcbadcdbaacbdaaddbabbcaaddadcaacabbcadddbbaddbaaaaccdbcdbdccbddcadbcddbaaaadcbcdccbbcabbddbcbbccbddaccbccbdacabccdacbddacdaaacdddbababccbcccdbaaadacbabcbaacaaadabcbcdcddcbdacbcacbaabbabddbbadabdccbaddaaadabacbccbacddccdddbdcbdbddacabccddcadcccadddddcbcbacbbbcbddaaddbcdcbdadcbbddcbcacbaaadadcabbdcdaaabacbccadbdaacddccdbddbdbbdaacaabbadaaccccaddabbaacabdcaababbabadbccbbbbcbdacacdaacccdbadcdbddcdadcbaabaacdbbaadcdcbdcbdccdabcbcbdbcaddbabbcdbbbabbddbbcaccbbcaccabbddabcdabaaadbbbbdcddababacbcaaddbdbaabbbcadbdcbdbddaccbbadbccbbdaddabbbaccbbacbcbbbbcbdbccdaadcbcbcdcbdaaaacadaacbcbbbdbbdadacbacddaaccabdccabbcbcdabadaacccbbdaccbaacbbadcbcacacccdddbcdbabbacbdcbdcbbcaadcbadabbacbaccacabccdaccbbccdaacdaddabababacabbaccddababccaddacaacccbbdbbabaadbaddacbaccddbcacccaadabdbddcaacbccccddcabcdcdccadadaacdacbccdacaaacabdbadabcdbbbcabaaddbccdaccdabdadabbbbccdddaadbdcaadbbbdadacaabcdbdccdabbcbaccdadcbdbacbdddcbdddcbdcbbaadbadbccaddcdcacdbcadcdbdddccaaabadcacddddcaaddccccbaacdcddcbdcddacdabdddcabaadaabbbbccabbccbddddbbadbbdacadcdababadcbccbaccdcdbbabbacdcdddabcbdbbccddbdcadddbcddbbdcdadddabccabdabddcccabbaaacbadaadcabacbdcdadaaddabbabaaabbacabbacbdbbbadbcadbbcbdbbbbcaacddaaacdcbcdddaacddacacacaadbbbdcbdabbdacdbbabbbcbccccbccdbcdbadcbddcdcaaadccbddbabadccbbbabcaddccddcccdabdbccdcaadbbcaaabcddcaaaacbacdaababcbabcbbaaaddadacadcbccbcdbbccdbaadbdcbdccbadcbccdabbadbcddcbbabadacaccacdaddaccbbcdacddbddcddcbaddccbbbadcbccacaacdcadcacadcbbacaccdbaadddbdbcbbdbbbbcdbbddcbccdcbbcdddddcabccdabccccaaaabcccddbbbbcadabaccabbaacaacdabdcdbbcddccabbabbddbbbcabcbcabacbabdddcdcbdddaddcdacbbabbddbaddcadcbacbbababdccbdaaaacaabcdabddbadbabdadacbccaacbaadbadbcaabbbdbcbbbacabdaccacdadbbacdbcbbcccdacbadcabdbbaadbbacdacbbbbabacadabaabccbcbddbccaccddcadccacdbbdcaacbbdccdabccbbdaadbbcdaabdaabadddabdadddabdcacabdddadbadbdcaaadaadabbdcacbadacbbabcbdbcadbbccabbbabccdbbddbccaaabbacccbcaabbdcddaccdbdcdccadbcbacddbadbcbdaabadabcbadbdcdbbcbabaaabdadbddcbdcbddacabbbcdcaaadbbbbbdabccbacdddbabbcadcacdbcbbadbcddaaddbbacadbaccdbaccabaccbbcdbbcadbdcccddbccdcbaadbadcdbdddadabcbcdccabbbbdaadaadbaacccdcbbbbbbaadbddcadcdccdbdadadbdbcbcbadcadbcddbadbbbcbbdcdaaadcbcdbcdbcaacccdbbbcbbbdaaadaacbdaadcbdabcdcabdccccabccccadcacccdadadaccbcbddadbcacacdaabccbddacacbcdababcdccddbcacdabcbadcacaaabdccacdacaccccbabdccdacaccccbddabbcbcadadddcadaaaabcbcbddabcadcbcddbbdcacdbcbcddbdcccaabaaabcdcdbcbaabcbacbdbdcdadbcbcaaacdddccbdabcbcdbdbddaabaadccdccdadacdccccbbdcdcdcdccbdccdaddcbcbdaabcbbddcbcddddabdbdbadbdbbdccbaadbdabdcbcdbadddddaacaaadabdbabdbcaadddbaacacdcccaccabddccdbacaaddbddaaadbdabdcacdaccccdcaabacadaddcdbbddddddbaaaaccbdccdddcccadaabbacdabbcdabbaddacbdbcabbcddcbdcdccbdbccacaabbaadcbcbbbdacddbdabcdaabbccbdcccdaabccbbaddaacccbadbddcbdbbccddcabdbdccaccaddacacccadbccbddbaacbdbcabddbdacbbacbbadaaccbcacbcacbdacbcccbaccadccbbddddacdcdddababdccccbaacaadbccaccbadbcadadadabacddbccbbcbaccbbcbcaaadbcaacbbadbdabaacabcbaddaaaccdaacccadcaccadbcddcbbcaacddbdbcbbccdbbbaadaccdbbdadbbbcbbaacaabacdaaabbdacbddcabadbbdacabbccbccaaabcbccaabcdcdbcadbbadabdcacccdabbbbadbcdabbdabdbadbdbbacdcbababcddbbadacbadabacbdcdbcbdcbaacbcdbcabcddbacbdccabacdacbbcbbaaabaddbadcbbcaddddddbababacabbccbccbdaaaabbcbbccadbbaccbdbaadbaaccacbaadccbadbabdccacaabbdaccadadbccadcdbccbbcadcdbbacbcdccacbdcdcaadadccabdbabbdbdcadcbbbbadbacdabbddabcacdadccccddaccdacbdbbdcacdcddaadddcabbacbaadbbbdbaaacddcaccdacddaaaadbcbcccaabbaaaabbdbcbcaddaabdcbabaaccdddcdaabbaccdbcbbdacdbadadcccddababacabdbaaaddaaabdccddccbdcbabdbcacddccdbadddaaacbcdadabbacbaccbbccdcccbbcbbacbaabbcbbbbbbdbcdabdddcbaccccaacbbcaadbaacdcbbddabbaabbbadadcbbdbaccacbabdcbdaccadccbbabacaacaddddadbdaabdbbacccddccbadbaabaccbabdcccaaddcdcdbddbbaacdbbcccbcbbdabcdccabadabdaabadbdcaabaddacaabdcacacccacdbcadacccbadcaaabbbcbcdadcbdaddaccdacbabdaddaaaacbbcacdabbbbababbbcaabcddcbccdcbdbabadbccbbadadcacabdcaaccadbdbbcbbcaadcbddccdcddddbcacacaaccdadadbdadcbccaddcdbaddcbccccabbcdacddbbddccdaddbbcdccadccbabdccadadcdcdacddbbaacaddddadbcbdabdcaaadbcaaadbdbdaabaadcdbadacdbdccccbcbbbabdbadadddccbcccddacbdbcaacbcdbdcbccacbdbdccbdcbaababaaddbcababcbcbcdabdabbaaddacdadccdaaaccbbacbbbbbcbdbabdddcaabaaacbbcddbcccdadcccacdadaddaaacdbcddaaacacadbabdbbdbacbccdcbababbcbcbdaccbdcabcabbcbbcdccccddddadbdbabbcacdcdcddadcaadddaadbcdccadbadcbacbdccbadcdacbbccdcbcdcccddcdacabbabaaaaaababbcaacddbacbbccdabacbccddcadcaccccdccaabbbacdbbaaabdcdcdcbcbbadcdcaddddcacddcbddbdabadadacbbcaddbbbddbdbdbcadacadbadaaadddaabaddbbdbcdccdcaacabcccbabababbabadcaaccaccaccabcaddacdbdddcdbbbaaabdcabddcacdcbaaddabbcdbabdccdcbbddddbbbbacbccbbddacaddacacadbbacbbcdccddbbdbbcccacdbcadbdcacbabbabcccababacccdbaddcccdcdaacadaadaabcccdcccabdcdbbdbcdabaabbccababbbdddcbaaccbcaabaaccdbdddabccdaaabcbbcbbddbabaabdcccdccaccaacdcdaccdacabcbbcdccadbbdacbcbccabccdbcaabcccaaadcbbccbacacbaacaabdcddbbaccbabddbbdbaaabccabddcbddbbcdbbbbbadabbbadaddacdaaadbbabdbcdddaabbaddbbacaccbbddabaaabacdcdacabdacbdcbaacaadcdbaadadbbddaabaddbabbccdddadccabddccdbaabbacbcbcacdbccbdbbbadcbdcbbdbdddcdabcddbabcbddbaaaaccadbcbbaccbadadbdcddadcadccbddabdcbcbabbbccdaccbbdabbabccadccdbbbadbdacbdcdbbadaddbbbbbcddadcacbbaccdcbdbbaababcbdacadcabacdcdccadaccaaadcbcdaabcdbadabbbbcbdbaacdccbadbaabcbcdcdcaabcbcacbbbabdcccacbbbbdacadbbccadabaabaaadaccdcacadadddcabddcbcbcbbbcccccbddadbcdddccadccadcbbbaaadcdcdaadaaddcadadabddbdbdbcbcdddadadbdcbabbcdccabbbcdddcbcdadbdbcadaccbbcababcbcaaaadddddbaaccabcacdcbcbddbbbccdcbcbcabadddbbaabbbbddaadcabccbdbaddcdcbdaadccaadcbbcccdccacaccbbaaabaaabbcbccbdbcbabbdadabbaacbdcabcacdbcbabaadbaacbbcabaaacbabadccbcdddabcabccccddaddcdbccbcdddddbbcdccacdccabadcddaaabccabcdccdaadbbcbcdabdbcbbdaaccbdaaadcdbaabbdcbccddbdbbdabaadaabccaddacdcbadbcbaccadadcdcabcccddcaacaadcbddaccddacdaadabcdbacdbdbcabccbccabdcdcbabbacddbcccbbcdbdbccbddbcbcaccabbbdbbacccadaaacdcacacabcadbdbdaaccbabcabaabdadaaabcdaaaadabdcaccaacccadabacaddcdbdabbbaacccaabbcdcbaacbaaddcaacccdcacbcabbbdcbbabbaccbbdddddcbabddcaadacacbdbdbadacbacaadbcdcadbabbcdcbbdacdbcdccccbbdbbddaadaadbccbcdaacbbcbbdbcbdcdcbbbbdabbaabdccbdbdbbadbbacbddbcaaccaabcddabaabcabcbddacdcacabacddbabbcabccaccadbccbcbbcbdcdbdbdddbdcbcacabaaddbacccaacacddadbabdbccbacdadbbbabbddadbbbdacbccbabbddadcdacbacaadcbbaaacdcdcdcdacbcccccdaacdbcbbbccabacccbaccabcbcaddabbdcdcbadaccdddacdacdbcbcdcbbdacadbcaaadccdadabaaadbdabbaccdadbbbadcaccbccbbcdcabdadcaadabccccccabcbdaabdcacbdcdabdbacaaddddaaccbcbccdaaaddccaaaabbaabbcbccaaabddcbccdaabbddcbadbdbcdcaccacaccbdbbaabcddadbdacbaaacaacdcaaaacbdbdbbcbbbabddbbabaacbbbbdadbdcbbdccccacdddabcddadabcccbddacdbdaacaaddbcddacdaadbaabccbdcdbdbaabcaaaadbddbdbacdddcdbbabaabbcaccadabbbbbcbbadcbdcdbdadbbbdabaacdcdbcbcdcaacaddbacdbacadcdabbdbccbcddbcaababdbdbadacaabaddbaacaccccdcdccdabadcaddbdcbdbabbacdbbdadddcccccdbddbdddbbaccccbaccaacabdacddbabbbcdcbbcdacdadcccaaddabbacdadabcabdbcbccbadbdddcabcaaaadacccccabccabdbabddbbcabcdccadbaaabbbddcdbacbbabbdcdaccdcaaadcdcbdaacababcbbddabddacadbddacccbbaacddbdbcdcdacbcadddadcbdadbbcadbcddbddcaaaadadabcdcaaadddaaadcbddddbbcdaabacbdddaabacbccbabddaabaaadddbbbabbcccadddabdcabdadadadaabcacbacdbdccdcccccaabbcacadadbaadcdbabaabbabbbcdbcddbacddcadbbadacddcdaddbabbccdcbcadbbaaddadbdbcdbcddccdbababacbcabdcdaaaacbcaacbddcdaaaacbbddcabdcbabacaccaccbddbbaccdabccaaacbdcbacbcccccbdaaabcbbddcdccbdbbaadddbbaaddacdcaacdabcbacbcacdcbabdcddbabcbaaaaccccbccccbbabddbaaccadadcabddcbaaaccdbbcddcdacbcdacabacbcabbadadcccbccadacddcadadbdbbcbacbbabdcaaccdaacbcbbdccdbcacdcccaacbabaddaccacbaadcbbacaadaaacbaaabbabaccbabbabdbcbdbacbbbbcaaacabbacdbcbbdbaccacaddaccacdddabccbdbbaabaaabdabcccadabcabdabdbdbadcdadbdacacaddacddcbcdddddbbcdddabdcddcacdddadabababaadaaadcddcdcbcdbccabaccbddaacacabcccabcbcaddbbcaaccbabdbbdcbddaaaadabcadcaccdbdccbcdaadbadbdbcadcdcbbabcdacccacdbccdccdacccdaadbcaccbcddadbaaddbdcbbdcbbbacccdacdbdcabbcccbaaccacccbacdbdabccadaaacdcbdaaccbdabddadcaadbbddccbccdcacbcbdcacabacaacdacabdcabbdbabaadabababbccadbcabacaadbccccabadbcbcabbccaabbcbddcaacbbcddcbdcccbbcddcabcadbdbdabdabcbcdcbdbdabdbcdddddcabbbcadacadbcbabddacbbdabcabcbbaaddbbcbcccbabaccadacdbdccdbcdcddbddbacbadbbbcbcbacbcbaabcbdcbbdadbcaaacbcdddcbcdbbcaacddcdccdccaadcbbbccadbdbbcabacabdbcbcadcdadacddbddadbdadbbcdcbbdccccdcaaddcbbcbbddcadbbddbcbdbaaabbbdbabcddadaaacdccdbaddadacacbadcddccadadabcbccbbdbcabcadaaadcbbddccbabddacbdadacdddcddadbcbbbddccdababbabddbdcabaabacdbdbabbccdcadccaacccddadddaabcdacabcdcbbabcbcabbcbddabcdddaabdbbacccddccaabbabadbddacabdbaadcdddaaacaccbabcaacdcbdbabbccbbdbcdcadbdaaaadbcaadcbaddccbddbdcddddbbacbbdbdccccbcddbdaadaacbadcaacdccbddccabcdcbcaadadcaadcaacccdabacdbbacaaaacbaddddabdadcdacbcbbcdaabddbdbbdaddadadcddbdacabbcbaaaccdaabbdbdbcabadddcddbdddbbbcadddccdbcaaaabcbadcddddddacadcbcbddccabbbcddbdabacadcddbaddbddcacdcccbdacbacdaadbbbbabdabdaaaddaccabbdcadababccaadabddbadbbbdbdcadddbaaabcbcbdababbccddbcababcabbbbaaabddabddbdabbaaccdcaddbbdbbbbaaabddabddbbbabddadadbcbdaaddcdaadddbcbbbcdcbcadbbcadcddaccbdddabcccaaababaadcbcabcadddcbdbcdccacacbccbbadacabdabbbdcbdcddbccaddcbbacbbbbbdcdadaacdbacccaabbcbaabadabddcdcabacdadacdcdbcaaccbabacaccdacccbabaabcacdcddacdbbdbcbddbaaaabdabbbacbbaccbdcdacdddacadcdccbddbbdcdccdbbacbbccccccdadbbbddaacdccbaadadbdbddcdadbaaccdcdcabdcbdbadadbbcccccddbbbdbbcaaddacadaadccabbacdadcddadbddcbabbdcbbcdcaaaaacbbdadbdabcbdabcacbaaddcbbbaacbaabacbdabbbcdadabaadcacbddabccccdacbbdadbaadccdbadcbbbacdcccaaabbbdcbcccbcbdccabbdbbdcbaadcacdbdbbbbacdcbcabdbdbabccdacbcbbdccaadddddbcdbdbaabdccaccdbbbcdbdccaadbdbdaaaabbadcadbcdbabcdacddabcaadabddadadbdbadbcbdadcbacbddcbabccbacabcaababccdabaaadbddcbbbcacaddbbcdbbdbbcccacccbacdbbbaaabcaaccbdbdabddadbdbddaabcdacbdbababaacbdccdcdaccbabdbbddbcabdabcbaacdbaacbdcbcbbcdabbddddcbccadccadbadabddddbdbddacddcbcbadccaaabbbbcaaabbdbaabadaacbcaccbaacbbacddcddacaabbcdbdbacccbbcacddcacdbbdabadadcdcccbdcdbdbababccacbdcdacdcacaaaaccdaccacdadadbadcbcccbdaadabdaccdddbcbdbbdbcacbabcadbaaadcabbbddccbacdcbaccbacbbbddbccdaccabddadbbbbaadaacaddaadbacccdbddbbadcadcbbacbaabbaacdcadaabaadacdccbbaaadbbbaadbacadcbdbbbcddbacbcabbadddaaacccdabdbcbbcdaaaaaadccabaddbadbadccdbcbaabbddbccdaadbadcaababbccaddabbbdabaadbcabbcccbdaadbacbbddbdadbcdbbccabacdaaccacadaabcdbacbadadccdacaccdddbdababcadcabbadbaadbbbdcbdacccbbbadbdcdacbbcbbdcdaddcbcdaaaabdbcacbaaadabdddddbddcbabdacacadbdddabbcbcbddbbbcaacacadcbbaacabbacacdcaaddcbcbbdbcacdadddaccacdbbdaadbcbcdddbdcbccccadacabaddacdbabddbabadccdababacdacdbbcbaaabcbbddaddbbbddcdacadbbbcabcccabcbaacdcdcbdcbbcbabaacaadccbbbacdcadacbdabcddabbccbbccadacbcbcdacccdccddddbacabbcadabaccdacbacacbabbcbdbdabccbdbbdaaadccaccaadbbbdcbccddadbcaccddcdcccdbbccbdccbbbbacdaddbbdbabbacdcddaadcdadddcababacabdcadcaaabccbaabcdcdcdcbcdbbadcacdacdbcacacacacccdabcccbcabacaccaacdddccdbbadbbccdcdbcbbbacaaaabacdbdbddbbcbccccbcaacdcbcdadbdbaaababdbbbacdcaaccacdbabbbdaacabdddadcbcaccacdcaccddccaadaddbbbcbaccbbbbdccbbcaadaaaaadccbbddbcdaacbbdcadbaaaccdbdbbbdccaaaabdacbdcabcdbcccddabddabbdccbcacacdbbdcbcadabccbdababbdbaaabdabbdcbaccdddbacabadbbbabccaabdcaaccadaccaabbddbdacdbbbcadadadaadbcacbbbbadbadaddaabaaddbcdabdcdacbbcabaadddbacdbbbbbdcadcdbcaddbdaaabdccbcdccccbbbcccbbadbaaddbbdacdabcbbbdadacaddcabaadaabbcdaaddcccdbdddbbcadabdabacacacbabbbbdacbaababdbdcbdcadadadcddabcbacbbbdcbbbaacacacaccdabdcccdcbbabcadcabaabaddcdcadddcddbdaadccddaaccbababcbddacddabcdccaccccaacdacaccacdbbacdcabbadcbacaacdcbddddaacdcaddcdbcbadacdcdcdddbaaabbbdcdccccacbbcdcacdaabaacaccdacddacdaacdbcccbdcbaccbccdaddbdbbdbcdacdbaaaddbacbdcaddbbbdcaadbcaaadbdcbdaccddddbcadcdccadacccbcbbdadcddcbadbbcaddacaccaabdadaacdbccdcadbaabdaadbddbcacadddadacbbddcbdaacdbacaddabbdbcabbabcaacaabcbaaaccdcacbbaccdacddaddaaddabcbbaaabbbcbdbdaabddcbbaabbdccbbddbccddbdcbaadcbdadacccacbcdddbcdcabdbaaccccbdcdccacbbacddadbdaadcbbbadcbacaadbcbabcbadbaaaccaacbbccdbcbdcddadccddddcabadaadcddbaacdcbabcbddadbacadbdbcdacaacaaddcabbaddbcbccdbbbddacaadaadacddcbdbdccdacbaddadcbbdddcacbddabacbbcbabddbbcacdcaadbdaababccccbdbccbcadddddaababbabcdacdcbbcccabccbacbdcddccaacbbdbbacbbadaaddadbdbdaaabbbbcdcdabacabbbdcbaacccacbbbbabacccdbcdccacccdcdbcbcabbabaddbabdabbdcdddddddbcabdaddbbdaddbcaccbbadacbaadcbaacdbbcacadacbbaadaabdaaacccbaddbbdbcbbcdabbadbccdddccdbcccbbcdadbaadccdbbbdabbadcbdccacbbcbbaddcaacadcbbadbbbbcbbdbcbaadaaddcbbbadbaaabcadbdddadaccccbccaacabcadadbdabddbbcdaaabbbcbabadcacaccdbacdaadcdcacccdbacaadcbaabcbbbdbbdacddbdabcdaaccbccbdcbbacaddaaaaadacaadabbdbdcbcdbdabbcaddbcbbdbddabddaccdabaaaadbbcccaadcbadcbdddcddbacdcabdddacadcdddbcdbbbadbcbaadcdbdcbcbabcabbadaadcabddbacdaaaacbaadcdbddcbbaaacaccbddacacdabbbbaddccdbdacbccabbabcddbdcbdbbdcacababdddcddaddaacbcbdcbdcacaabdcccadbcdaddaadaddaaaaccbdcbacccadacddadaadddbacccadbdacdcdcbdacadadbbbbbadbaaaaddcdcadacababcdcaddcdcdbcacabbbbaadddbbcccaabbdddbcbbabbccccddaccaddaabbbcdbdccbbabccdcaddcacacaaadabbacdbaccbaaaacdcbccacdccabbdabaaaabdcbbaadcbcbaddbcabbcadbdbccadabaabdcabaadbdbbbbdabaddbcdbcbccdcadbcbddcbbbbbbdcbcdacabcacaaabccbbaccccabdbbcbbabbbdabccbcdadcbcdbdbbacaddbaabadadadcbcddbdaadbcddccbddddbabacddbbdbbccccccbbdaadbbbcbdbdaaabacdcacddddcddccaaadcdacdbdccdcddccccbbacabddaddcdbacbcdcadabcadbcbdbdcdcdabddadcdbcdcdbccdbdccbccdbcdbdcdbccdabbccbabaabcdbdcaaacccddaacadcccccdaadacdbcaccacacbcbadbdcdabcbddbdbcdbaccccadcaabddbcdadcdcabcbcdabbbccbbaaacaadbcabbaddcdabdcbcabdcdadacbdbdadabddcbbacccacaabdcdddabbbcccbdbaddddddbadbcdacaacddbdacbacabcbdabccdccbbbaadcccccbaaacabcabacddddabacbcaccbdcdcaabbbcbcdaaacddcadaddbddcaddbcaacbdcabbabbdddddbbcbbbbaacbaddcbddcbdccddbbddacbbddaaacdcdbcadbbcabcabcadcaabaaaccdacbaacccaaaacddabbcaadbdabdacccbadbbcbdabdabbbdbcdcbbccdabbcbadccdbbaddddbbaaaddaaadacbbdbbcdbadbaabcbccabcccaaddcadabbcdababbabddadbccadcabddacdacbbdbabcdaacdcdaaaacddadaddcaddacdcbaccccaabcccdcdababbbabcdbbcbaabdddadbaaacdbdbabcababaaabaccdddcaababdbdcddaabdcdcbcadccbacbaabaadcdbbdbbdaacdcaadbdbcbcadbdcbcbcccbbacdabcdcabcddcdccadcbabdcadccdadcdbcbbacdbaabdcbaaccbddbdddadabcaabbcbaaaaadddcabcddbadbcbbcbdcadcccabdaddaacacbccaabbdcadbadddddbcdcdbdbaddaccaacabaabbaaaddbccdbabdbaaaabcdbddacacbdbbcddbcaddcbdabcbcacaaddacabdacdabcdadcbaabbaaabdabcbccdbcdddadbbaaccacaabacccbbccacdbdcdcdbccabcddccccbaccbcddcdaacaabcdaadaaddabacdbddaababccdacdaaabcbbbbdddacbccdbbdabbddcbaccaacbcadbbdddbaadaaddcaccbdbddabdddbcbddbdadddccaddbabcadbbbdbabbdaaccccbcadbbbdccbcdbdddddbabaaabccbadacbbbcdcbabdddcddbcbcadbcdddbcbdaddcaaccddbacacbbccdbacbdbbbdabccaccabdbccbdcdabdbdacddabcdbacbbddbdcaaadabdcdcaabccaacaabaacdaadadadccbcacadccbcdcdcacaaadcaccbcbccaaaacccbcccbacbdbdcccdbdbabbadbadddbdcbabbdcccdaabbcaaccaadbabbcadaabcbccdcbaaddcadddacbcdbcddadbdaadccbdbaacdcccdaaadacbacdbacbbbbaadbccbbcbabdddaacadbadbbccbaccadacdcccdcbcbbbacbdccaddcddbbbddddddcbcbbdabdbacaddccaadbadaddbdaccaabaabcccacdaaddccdccadbddcdacdcdcbadaddbbdbabbddaaacabdbbccddccdbdadaddddbcadaabdbcbbcbabbcadaabbdcbddacccbaadcabdddddddcdbadaacdbbacbdcaadbcdcabaabbddbdbdcacaaadadddacbdabaddababcdaaaabababdadabcacabdbcacddcccaddbdbcabdbcbadcbdcbaddabcaaabccabbdcabacadaabaccaddadbcbabddcbadacbdcdacabcaacbdcaadcdbdcbcddadbbaacbacbbdbadcbbaaabbbdaabdbbcaaddbdcbacccddcbbddcdacaaabcdbdacabaddbbbdcccdaabadabaddacadccdcdccbbadbacbbbddabadabaacadddbdbdbcdbdacbdacaddaabacbccdcbaacaabcadddccaabbadcaabbdbcdaaddccaaacbdcbabccbdbabddcadacabaabdadbcbabdaccabadbcddddcdcdcaaacbcdddaaabddcddcdcbbadcaababadbcbdabddbdbccbbdabbdcacabdbadadcadbadddccbbdbacdcdadcbacbabacadbcdcbbcaddddcdbabcaccdcdaaaddcdaccadddccbccadcacbcbdbcbacbccaaaabcabcadcccaddccdcacbcdcaccccbcbbdccdbacbbccacbccbbcdbdabcbabdbaddcbaddcccbbcddabddbdacdccbaaacbcbdbaacaacccdbcdbbaaabddccaacdbaacdbbcbbadccbbacadddcbdccadabbacabddbdaacccabadbcacbcbdabadadaaabacaacbbacbdbbcdbcdadaacaabbdcdbbabdcdbacdabcadadbaccacbccccaaacbaaabbabcccabccddbbbcaaaabbddabcddcdbdabddbcddaddacdbdacdcaddbcccdaabcddacdcdccaabdacbcbdcadabaabaddbcdaaadbbcdbaaaddbdadbdacdddbabdabbbccbdcccbcbcabbdccdaccddbddacadbcccdadcccdaabcbccdbcbdadadbdcdaabbaaddbcdddbbdcaccadabcadabdddadcccdaddbaabbdacbaddbdcaaddaaccabbcdbccbddbabbabcdcdabdcbaabaabbacaadddbbddddcdabbbaacbbacddacbdaaabbabdccbbaddbcccccdcdabcdcbddcacacbbddbcbddbdcbcdcdddacddbbcbdacbcaabaabdddcaacdcdccdbdcabcbbddbacdcadabcadacaacddccabdbcdddcaabacadbbcbbdaadddcbcabddbcbdccdbbbbddbbbaacbbaaacbbcccbadadcdbabdccdcaacccccbbbcbabaccbcdcdbcacddbdbccadccdbdadcbaaaccbcbacacbadcbbdcdbcaaacaadcacabaaacaccdbbacdbbcacbcbcbcdabbdcadacdbcabacadaccdcccbdabcddddacccdcbbbcbadadacdbddabcadccbdaacdbbbcdcdaacdccbcabcadcdadacacccadadbccdcbccaddcaddddcccbabcddddbcacdcbbbacadbbbbcbdbbcdccbcadbbdddbabbcdabdacaddcaadaddacbdbdaddabacbbaaaddacbaddccbdabbadaabcddcdbcbdabbdbcdcbdbdbdbaddcbacdddbaabcaddabacccacbdaccbccbcccdadbbabaddcacdabcbdbcadadcaacdddcdabcccddcddadccbdbcdaaaaccdadcacadbcadcccbcdabdcdaaacabbbbbdaacaaabddadddabbcbbadaaaaadbbadcdbababbbdabdcbacdbcbcdbadcbbbaccdddadbdcbdbcbaabdcdddabacdaabadaadcdccbaadadabccaadacbcaadcaaddbcaadbdccbbabddddbadcabcdbcdccaadcbadcbbabbdaabadccbcadcdadccadacdbdbccacdadacdbcbbcdcdddbccacbddcacdcbabcdababbcaccbbbdcbccbdddcbabaccbbacacbabbcbbaccdddcadbdcbccbdbbcbcadaaaabbbbcadcccbaaacccbdbbccbbcbabcbbdcadbbbcbbcabbdcadddcaabbaabdcdddaaacdcbcaddbdacabbaaacabaaadddbaabdacadddcdacdcdbdcaccaaccbccccddadddaabdddaddcbcccaadbbbdadacbbcacdbbbbccbdadacacaddabbabcbdbdbbaabbbaadaaccadcbaccbabbcbcadbacaadabacdbcbaadbbdddbbacbaaddddddaadbbbbabbdcdbcbdcaacabdbcadcadbdbacddadacaadacbbadacdbdccddaabcdcdcaabcdbabbacabacdbccbcdacacaaddccdcdbdccbbccadbacdbaacaadabadbbccbccdacbdccbdcababcaddbbccbdadbaaacdcabdcabaddbaaadaaabbdabdcaddadadddcbdabcadabcdaccdbbddacbacbacdbcabdcddbabccabdcacbdcdbaccbabccdbcbcbdaadbdabdbabaacdadbaadbcbcdbaacadacdabcaddbbabcabaaddaadcdcacdcdaadadabbaaadabcdaacbbcbdbcaddaadbcdacdddaaacaaaaccaabddaadbcbacbdadcbbaaaaddddccadccadcabcccdccccaadccbbabacadaadbcdbacaacdbbdacabdaacbbabdbddddcadbadbdacbaadbcbcbddddaccbbdcabcaacadabbcbbbaadcadbcacccaabdabaaadaddbdabbdbcdbbccdbcdaaaddcbbdacdcdccacbbabaacabddbbcbaadabababababbadccaddaadddbdbaaccbddadcbabdcccbdccabcdbbbdcadcbadabbbbacabcadbabaaaddcadaabadbdabcabdbdbaacadbaabcbbdbcacccbbccacdbcdbccababacaddaabacabaadacbaacadccacccaababdbcdbaaddacdbbacccabcccaaddccbddaaadcabdaabcaccdddcaaddacaaacbaadddddcadacccadcbccaddbadadcbcbabbabcccbdbddbdccccbcaccbbdbacbbcacacdbddbbcdbcbdaabaaaabcbccbccdabdbbdcdcbbbacabbcabdcddadabacddacbbaaddaacdcdbccbbabcdccccbbccdbccbbccccabbdcabdaddcbdaabcadadabddddddadaacdcaddabdbddcadbabcdabcdcdbbdbdcdaccccccacabdbabcbcddbcbaddbddbabcaccdbacbabcaaddaaaadcdbaaadccbbdbbbacbbaacacddbdcdbbbcacbcadddadabdacaaabcdccddadbabadcddbababccbbdbbaacacbcbbadaaccddddbcdddcccbaaaddacadacbdcdcdbabbcacbabbdccadacdcddbcddbacbcacdabacacadddccbdcbddcbcbbaabdcdddcbadcadccbcbbbdadcdbaacadbacbdcdccdbdbddbdabaaaabbbcbddadaadddcbbadbacadcabababcdccdcbbcbcbcbcbbdbacaadaaabcddcbdacddddccdaaccbdabadcccbbcdadbcbababadcbcdddaccdcadddccbcdddabbcbdadcdddccaadbdabaabdbdbbddbaccbddddaccbdbdaaabacccabadbbddcbddcabddababcadcabacbabdccaadbcbcabbdaabddcdcadddbcadbdcddbbdabbbcbbaccddbbdbdddbbbaaccbbdcaaadddaabaacaacbcdbbacacbababadcddaaabccdacdbcbdcdcbcbdbccbbccdbadbadacadbccddccaccaaaaababbddacacdbbcbdcccabcbcdbabddadbabdccadbabdccbdadadbaabadabbaccaabbadaddcacabaabadcadcabdacabaabbaddaacacdbabdccaddbbdbabcbbdbbbdccbcabdcbbcacaacacaacdcdabcacaccadbabccbddacdbdaaabaddcbcdbbaccbbacabbaddcccbdaacacaabbbcddbddadcdbddbaccabccbbdbcbdbacaabcdcbcdaabaddadbabccaabbabbdadacddbdabadcdbbbcdaccccacbaaadcacdcdbabbddbbccababbabbbcbdcbcaadbcdccbacaacdbcccdddacabddacbbcbdabcdccdbbddcbdccdabdbcbbddbadbabddcaaddddabbcdbdcacabbbccdcbbbbcbccbabdccbcdbcbdabaaccacbabadccdbabcbbccdddbcbadabbdabcacbdabbddbabacdddabdddbbdbadccccdccddbbacdabacccacbbdcdababaddccbcddcbdbabdcddbddcbdddabcddbbddbdadcbabbdbdbccbcbaabbcdcaadddcdddadbbadabbddbaacdbaacabdbdbddbadbddaacbcdaddabbddccdbadbbcbaaabddadadcabbcdbbbabadabdcacddabaadcbdcabddcbcbdccaabdadbcacdaadbbbaaabadcdaababdcacbdbcacadcdcbaacdbabdaadbaadccbdaaadcdaacacdbdbddacbcbaacdcadacbdabcdccbcbbbcbaddaadcaccdbdcdabababddcbaccccdadaadadcabbdabdabcbcadbccdddbadcdbaabbdddbcbdcbbbaccbcbddabaabbccccbbdacbacdcaadaadcabaaadabdbaddaabaabbcacdbabcdbbbaacdcbbbcabcdadadbbdbaadbaccbabadbbacddbabcacdccdcaaaddbbdccbaccdcbadcabdbcbaaaadcbaccdcbcbcbcadbcacdbacbbacccadbbccbdbdddbcbcacdacbacbdcbddbddabbdccccdcbadbcddddbdcbcabcbbbdbdababbbacddddcdbdbaabdccbaaccacbacbadccaabdcccddaadcdcbdadaddaacbddcbcabbcdabbbbdbdaccaaaaddaabaddcbbbbbbdcbbdddcbbdabcbcbcccdddbcadacbdbdbcbacabdbdacbcbdbbcadaacbcadadbabbaaccddbdaacbbcadbbabcabbcabdaacdccadccadcbdbcccbadaaacbddbaabbdcdabbdcabacbcdbadccadaddadcbcccadbdabaacbddbadbcaccbdcdcccbdcadcbbccdcdacbdabbaadcdcdabddadccbbdccdddacdbbcdaadcabcadcdabcdacadddabbbacccdccccbdbdccaacaaabbbdcbbadcbaadbaabdacbacbcbcbacbbcbdbabbcaabacbbadcacbddbdbccadbbbcdaadcadcccabbaacaabdaaddcbbcbddabbccddbadabdbacadcccdbbadabdbbdcbcdacdcdcbaddbccccabdabdbbbbbddabcdccccbbcdcdacbccdbdcaaddacbddccdbdcbadcaddaacdccdabcccacaaabcbaaadaddcdababdbddbdaccacdcdccbadacadcaddabdbdcddccbbbacaabcaddaabbccadacacaaaaabdbaccdcacbcdbdccaadddcdadcaccdabbbcacddbbbdabbabdbbbddccdbccadadacbdbcbacddccaddcdccabacadcdaacaabdbbbdaabcdcbbcbbbbdabdcbaddcabaadacbdabcbbdbcbdbdddcbacbccdcacbdaaaaaacddcdacdbcabbddccbbbbbaabbaaaaaabacbccbdadcdcdbcacccdbdaadbddacbdbcadccdddbddbbddcdccbccddabbccaadbaccbbacdaadbcbcadcabcdbbaaddcbdbdaaaaaaaabacadcdbdaabcbdaadadaadacabacccbadaccacabcaaddabdbcccdbcdaccbaabddccdcaabcbcbcaadddabcbacbdcabdcaccccccbbadbbcdddbbcbdccbdbaaabddcdcbbcabacadadcdddbdabddbaccabcaaabacbdcdcabdcacacbcadbcddbdbbabbabddccacbcbcabaccabcbccacbacccdcdaaddcbccbdacbbcbcdbdaddacacbbccaccdacaddaacbcacaacabbadabadcaaddddabaddbdadccaabadbbcbadccaaccbddbcabdcbbcccadcdadcbbbcdabbdcadaabccaadcbbbbcbcdcccbcbdbdadbccdabadccdaaabdadacbdbcbddbbdcbbadddaabdbdabdabbbbdddadbbacadbdbdaadcdbbbabcdaacbdcbdbbadcdbaddddbddaabacbdbbcdddddbbacdaddaaaddcdccbcbddbaccbabadcacddcccdadbcddcbaaabacbcbdcbbddbdbcbbcccadcbacdcdccaccaabccadcdabdadddcbbbcbcdddacdcbdabbcaabaccabcbadbbacdcaacbcabadabbcaabddcddbdbbcdabbaccabdaabadadccabcaddbaaabbbbbdbcacaaaccdcdbdcbacdcaaadbdcadcabbcdabdaccaabbdbadacbabbaddbddcddbdccbddacbaacccbaddabaababbbcdaaacbcdaadddbdcbcaaabbcdcacdabddcdabbdccccaabbbccccddcbcbbaadacacaccbddbddabbabddcbdbdbcdaddbbccaddbddbbccaabbbbacdbdbbbdaabbabddadcbabadadbdccbddadcacbbadcabdacbabcadbabccabdbaddbdcbbcbaccbadacabcdadbacddccdccbddcaadbbbaacddddccbdadabadbabaaccaccdbbaacdcbccadccacbccadabdbbdcdcbaabcaaccbbdbdddadccaabbbdcaadbccabadabbddabbbbacbdbcccaacaabdcdbbaaddbdcbbbbaaacccadccbdabbdccadcadacaaccaddbadaccbbbcdaaccdcdddaccaccabbcbabbbacdccccccdadaacdcbacdabccdbcaaabdbcbaabadbcdcacdcdbbcccbbaadbadcddbdcbcdadabbdddaabdaddddbacbadbaddcdaabdccbcccdaddcbbcaaaccbcaaccbcbcccdadbcdddabcbbadaaddddaaacabcccacbbacbdddddadaabadcddabadbbadbddaaddabcbbacddacaddddcababdbadaabbaacbbaaacccbdbbaabbabacdadacbcbdccacddcdbacdcccbabaccbcdadddccbdcdddacaddcaddcdbdcadaaaddbadbcdaacdbadaddacabbbcacaabacabbbdacbdbbdccdabbccadbabcdbabacabbbdbdcabcdcccadccacddacaccdacccabcbdababdbcabcbcdabadcabaacbbcabcdadccabccbabcdcbdbdbcadadcadadccccabccadddcaccacdbdadaaaaabaaaadcabccdaadcdccaddbcaddacbbcdcbadadbcacbaabbdbaaddacabcccdddbadcdaabacaacbdaacdaaaaadbdadcadbbbbccdcbddaaccddacddbbcbcbcdababbbcbcbccbdcbdaacadbdbcccabdaabddbbcaabadbccddbbcddbdadabcadddcbcdaddbbddbdbaaddabacbbaacacbbdcdaccadaaddbccabaccbbaabbccbbaacccadbabdaabdbbbdcbadbcbaabbcbacdaaaadbbdabacacdddccdaddbbaddaadaaaddbccdccdcadcadbbdddcbaadbabcddabbaaccabdccaabbbddadbaabcaadcdcbacbbcabbabdaaaddcabcdabccacdbccaabdadbbcdbcdbaabbadacdbacbddaacdaabddbbadbaacacdcabdacbbccabbaadadbddcadccccaaaaaddcddbadddadbababbdaadcbdcbcadabcaaddaabdbdcdadbbdcdbadbbbbddaaddddcaadcbaadbcbccddadcbcbbbcddccdadabddaabdaabbdaaaccdbdddaaabdacdbabcbaadccbbdacacbbbdbcdaccbccaaaacddbaaabcabbcaccdccbbdabbaddadbdacdcccbaacbdacbbdaadbaaaddbaccdadcbaabdadadcaaacdabaabdaddcccdccdbccaddadcbababcccbcdcccacccadcddacccaccbcadddcbbcdacccccbcbdcdcbdaaabccaaabdbddccdabbabcbadacdbddabacccdcadbabbbdcbaddacbacdaddcddbdadbcdbabccacaaacdddaacaaadadbccbcbcdcddbdaabcddaaddbbbddaacdcbaaaddcbaacdabcacdbadccbdbbcacaaabdccddbacccdbbacdccaddccabbcbabbbdaaccddacdcbabdaabaaddbddbadaabcaacabbbaabcdbdcabbbcbdccacaacbabbcbcdcaaadcbabdcadbabcdbcbcacbbcbbcddbdbbccadbcaacddabdaadcaaccccbacbabbdabbbccabdcaddcabcdccaadadbcddccabadabbbabdaccbdcbadabdaccbcdbbbbbcdadcbcbbcccdaacaddaabcdcdccababaabcacacbbbdcacacadbcdbabdadcdacccaddbddbcdadbaabcbadccdaaacdadadaababacddabbbacddcbbabcccccacaaaddbbdbddcadbaccbcdbcdcdcbdbccaaabccdccbbdbabcadcbaddbccdcdadaabbadcccbcccdcdaaddbaccdadaacdbaadddccbbcbaaabacdaddbbcaababababdadcbddaaaddddcababcbccbbbdcacabacccbbccdbdbbcbbbbaaddaaccdbadadbbcabdbcccdddccabadccdcbbddbbdcbcddadadcbdacaddccaabdbbbcdaaddbdcbccadcddacadaacbacbbddbbbdaacaaadbcbdbbdccdbddbccbbdabacacdcdcccbbcdccbadbdbdaadbcadcaacabbbccdccdbaabbcdaccacdaccdcaccbacaaaddddbdbcacccbcddaadadcbbaccddbdbbcabccbbabadbcccbcbadcddabcaabaccadababdbabbbaaccdddbdcdcacaddcbbddcacbadabacdabcadcbcdaadcadcdbddbaddbddcbabccdaddcabdbdaadadbadbaabddabccccabbcabdbbdccccabdcacbacadaaccccadddddacabdddabcacacaddcbdbccbddaaccaaaccbbdddaabbabccbcbbcaaabcabbddaadbbdbdbddbcbccdaaccbccdccddabbabcbbaadaaaaccccdcacacacbdaaacabccccdbddadbaccdbdcccacabaacbcaaacaaadcdacdccddababbbbabbaabdbaadcabdacabaaccccdcaaccbdcdaccdaddbccabbbbdaaccbaddddaaaaccadabadacaaabdccbbbcbdacccaddadccbdcabaaabdcbbdbadbddbdadadcbacbbaddbaddccaddbdacabacadbbcdadbccbaccdccbdbaddadcbdbbbabdddbcddaccddbadaacdabababbdbadcbdbdacaaadbcddcbdabcbaccabbdcacaddcbbcaabcabbabbdbccdcbbdaadddaaddcbcdcbdcbdccbcabadcacadccbddacbadbdaabadbbdbbdbabbacdabdbcadaaddcdbaaddaccadbddcddddbadbdcbcddbbccbbcacbacdbcaaacdcadadadbdabacbabcabaaccddadbbcdbbddadbdbccaaddcabbadabcadddcdddbcdcabaabadbbbcdccdccaadbbdaabbbaadbddbcababcacddddcbbdccacdccdbadcbdcdaddabaaddcccdaddacbbdbcddbdbcadbdbddcdacddcdbdaddbdcbcccdcaaaccddacadcacaadcbcdadbadcdacbcbcdacacdadcbbcbaccddbdccacaadcbdcdadabcbcacacadaaadbcddaacdcadcbcdbcddddacaaccbbcadcdacaccbcbbddbaabbacddbbaadacadbadbdbbdaabaadbbcbacadcbbcbcabbadaaaadcdcdddcdbaadadcacbcdcaabbbaddbdcbaacdbbaababbabddbcbaccaccccdcacbcbaababcacbdababcbdbbdabdbdabdaccacadcdbccbdbcacadbcdcbcccabcbbacbbcdaddcddccadacddcaaabadacabdcccbdcdbaadacdacaccdaccadddcbacaadcbaddcabddacdbaadcdcbcaabcdacdabdbadccccadadcaabbccabbcabcadbabddaddbcdadabaabdcccbbbabbcaaadcbaacabccabddbdcaaacdcbbcdcdabdcdbacccdbaccacaddcdddadbabbbbcaccacabdcccabcadbcadcaababaaddadddccaabbcabacbbaadcabbcadcbbdcdbacddcbdbccbdcabacccdbaacdbbddacbacdbbcdbabaccaaccadcbdaabccbdcaccccdcbaacccdacacdcccaabdddcabaccaccbbcbdbdadcabadddcabccdcdaadccaaacddccdbdddccbcdbbcddbaabcbaadcbdaacbcaabdddbbadccccbdcddadaaaaacaabbccabdcadbdabcdbcdbbbccadcbbcdcdddcdaadbbdccdaaaaabbbbbddcccadababccbdaacddaabbbcddbdacbbbdddbddacccaddaaadbcbcbdccdabdcbdbbccbbcbbccccbbbaaacdccdcdbbbbbbcdcdcaabddbddcddcbddbdacaacbaddccddbccdabaccdadcbaaaddaabdbcabbdabaddbccabcaaadadacdbaaacdabdbaabbdabcadcbaabcdcbdbaaddaabddcdbbddcaaabaccabcbaadadcbbcccbcaddddacbaaadadddaddbdbdbabdbadcbabbbbddcdcbabdbdccacdabbdbaadcbddcdaaaabbacaaaabbddcaddddbbddcbcbcbcadaccdabccaccbaadbdddbaddaadaccdacadaadcccdddcbadccadabaccacbadbadbacadbbbcdcdabcdaaabcabaccdababbdbcbcbcaaaaaacbddbcbbcaddadbaccacdcddbdaaaacaccdcddcdbbbddbbadbbabbadacdcbdabddddbdddbdacbcccbbdbbcbacbdccaaaddbabbcdbddacbcccabadbbaaaadcdbddadbabdcdacadabbbabcdcacccadadccccdaacadcbaccbadaaaadcbdbdcbcdbcddccaadccdaddaadabdcbdcdbcbbbacbabcacdbdcddccbaccaabacbdbcdbbacbbbcadcdadbbbaaadbbcbdcddadbdaaacdacdbdbcbdcbbcaabddabbdabdaabdbccdacbbbcbcaccaabcbcaabbbbccabdbbbbbcdacadbbaaaabbbdabdcbbddbcbbbbbbdacccccbaccdccdbdaaaaaddaddcacbdbdcccaabccdaacbccadaabadbcbcaacaacccacadbaddbbbbaaccbdbdacdcdccbbabacdcdacdbcbbcacaadadbadddbdbccdbccdddbdddcbabaacabaadbbbcacccbcbbccddddcadbabdacbdbcbccdddbbddadaccdcdccabcdcbddabcddcdbcbccbacdbccdcacadabdcaabdcddabaabbdbbdacaccdbdbbcbbaacabcdaaddbbaddaddddadbcccddccddbcaccdacbddddccdbddbbabcaccbdcdaabcbbdabcdcabacdacaacbaddadddbbcbbdbbaaaacddbacbdcbcdcadccccddddddcadcaaacbbbadcdabbcdabbcdcbacabdccdacbbdbcadbcaaabcaaacadcbbbacdbdbdabdaccabdcaadbdacabbaddddcddcddccabaddcbaddbcdddbbbdadcbdaddaabdadbdcbacdbddbadacabaaaacaddacccadbdbcaddcddbbcdabbcdaaaabbbcabddbbdcaacabbbcbbbdabcadbddbaabdbacdadaacbdcdccdacdaacaacdbccbccddacbcbdcccbbadddcaccaaddacbcbbdbcdbdbddccacdaabdbcaaabaaadbbbbbbbbbcbabbaaadbbacccdabcbddcbbcbcddadadaabadacacadcdccbdccadbdadcbcbbabaaddbdbccbcccdcbdcbbbbccaabcaabaabdacdbbdcabcddcbbabddabbccbbabcbbbcbcadabcbdcbcdbcbddbaababdcaabcabcabddbcbddcbbbbababcbbdbccabbddddddbaabdadcbdadccdbccaacacbbdccdbbcacdabcaabcdaddbdcacbdbdbaadcacadcbdbbcbcaacadaadccbdaccdbbcccdbaaadadabbabccadcbddbbdcbcadbbddddaddccccbbccddaadbaddbddcbadacbcbbbdadcbcdcdcaadbdabdabddccdaabcddcdabaadabacacbadccbdccadcddacadcaabccdabbcaccabddaadacadbbacababadbbaadbababbbbacaddbbcddddabbdabcdbdbbbbcccdccbadbbabccdcccaaadbcbddcdbaacddcabbdacaabccabdbabacbbadcdcacababbbcadcaacbadbaacbbcaadadbaddcacaddacdababcaaadcadbabdaaacadacbadcadabbbadaccddabcdbddbbdcdcaadddcabbcdbaccddccdbdbcbadcdababbaccbbcdbcddcadabbdbdaabaabacbadaadabbbadcdaabacaabbbdbadbddadcddaddbccdadacbbbaaacbcaaadcccbaccacbdbaabdacbdbdaabccbcdbaddabacaaccbdadccdccacacaaaaddcbccdbcacddbadbcbdbdabbcaabbccabcdcababdbcbadbddbdbddbabcacbbbdddcbbddccdbdbdccbaabcaccddacbcacadbdddbaaaaadcaadcddadcccbcdbcdcbcccacbdcbbdbbccababcccbdadcbccdbcddaadccdacdacdadbcabcdcdcdabcdccdacdaacdcaaccbcbccbabaadaabcccaacadacdaadaabbdcddacadadbdbdbcdabaadabbaddbbacabcaccdbccbbabdabcdcddbacadbbadcbdaaabcabcccbccbabcbacaaadcddbcbcdaacbaaaddadaddacdacddccadcdabcdbdddcdcabacbadbcbbcaccccbdabccbdaadddbddcccdbcdddadcccaabddaccbcaaddcdadcbadbcdcabddabcacccbbaaaabbccbaadabbaacbdcabcacdadddaabaaabdaaaababdddbcdcadcdcbdabdacdbbbcddacaaadaaaacdcacdbabdacbacdbddaadcbbadcddaadabbbbcdbcddcacadadbdaccbbbddadbbdbadadacaaddadcbbdcccacacddcddabbbabbcaabbcabacaddabdabdbcadabddadbccbadbcacbadbdddadbbbbbabddddddbccdbbaddbadacabcadadababdddddddcddadaacccbcccacaaccdcdbcbdcaaadbcabdbdbacacbadbaadddadcbcbdcdbccccddcacabaccacdddbadadbdbbdaadbcbcbbccbaacddadaccbcabcddccbaaaaaadaabcbcbdbddadbdaccdaccccdcbaacddccdcbcccbacdcbdcbbadbdaaaaddaabddccdacbcdacdbdbdcbbcadcdacabaaadbdcadcacbbdabdddbcabbcacabbabbddccccbdadbbbcabcaacbddbaaddbbdbaadacbaaadddbddcbccaddbacddcaacdabccbbadbddcccddbaccdbbdbcdccaaabcbaadaaddabcbccbbadacaaaddbaabbaaaaadbaaaacdbbabdcdabbaadcccdbadababccbbcadcddcbadaaaadbddbcddabdbdcacbddddddbcadcbdaadbcbbacdbaadddcbdcaccbabdddccdabbccaccdbabbaddcaccadbbcbcabcaccbabdbcabdbdccadaabbabaadadacaacaaddddcbdcadbbacdbdbbdbadacdcaaabbddaadbbabdabccdbbddddabaddabbcbbabbbbcddbbacccabdabababdcbbccaadbaaaddbcabbaabcdadbacabdaabdbadcdacccccaabdddcdbbbbdbcbadbabddabcabccdbdbbdbcbddbdaddcdbcdbcbcdabbcbdcaddcbaadaaaadcacbddcaaadddbbccaabaccddaabbbaadbbdbbdaabccbadabadbacbaddbacbcaccaaacdbddabddbacdaddccacccbdbccdbbdddcadcababbbcadabaccbbadaadaadbbacaddacdaddacacaaadadbcccbcdaccdabcbbccddbcdccdbdcabdbacacbdddbbbdbabdbccdcabdddacabbdcdcaabbcbbadbcaadbbccbcddccdcddccddcbddaccccbbcdccbcdcdcbbddcddbbaadbddadabbdcaacbcbabbdbaaadbcdccbabbbdccdacdcabdabcdbddbabccdaadcabbcbddbcabdbdabbdaddacdaadbddbdccddcacbaacbbdadaaabddbdcabacacdddadaddbaccacbddacdaccdbcabdddbcaccdcabdaaccddababbbacbbccaabbcacddcccccbcaabaacccdbcbcaddbbbaaacadcbadaadbdbaaacbbababaaadbbdaddcacdddcdbcaccadbbbdcdcdacaacbcccdcbcdddcacaaabdcbcabbbacbccddbabbbdaadcbabbcbddccbbadacbbcacbabacbcbadcbacadbaccabbdddbbabdcabacacbccacdcccdbdaddbdbcdbaccbdcccadcccddacbdbccdddcccacabcadbcabaaddbccdddbccbacaacaaaccadbdcdbdddcbddcbacdbadccbbccbaacdcbadcdbddbdbcaaadcabdaabdccbaadadbcbdddcdbdaacbdccdcaaaabcdbadcbadbdbcbdcabddbabbdddabdcbddbabcddcacbbbbcdabbbddaacbaacdaccbbcdccddcaaddbcbdacbbaccacddcbadcdbdcbbcaacaacacacdbcbdbadbabbbdadcadcdaaaaaaabccccdcbcdddcdadbbacadcaabdcabdadbcdcbdcbaaaccbcbcccbadcddccdcddcacabbacbbbbbcbbdbdcadbddcccbddcbacadddaddbbbdabdbcddbadbdbaccbddbbbbdcbbcdbcbbbadcbbabddddacdabbdcdadcabcdacbabbcbaabcdadddcbdabcbdccadbbaccddaaadbdabccccccccabdcaaacddbdadbdaabbacaabdccbacbbbcbbcadaadadacbcdabbcaabbabbaaabaaacbcdaccbcbaaaaddacaaccaccdbbdabcdccbbbbbdbdbadbbdabaaabacaaccbdcbbdaccabccbbcbbdbcacacbcddccccccabbacbadbabdccdbadcacccdacbdacdbddaddcacddbdacbbbcddccdcadcabcbcbcbdbcddbdadcdcddbdabcbadddcdcbdbbcdccdcccaacdaccddddaddabcaaaaddabcbbadcddcadbbadadbdaabccbcadbaaabcacdbdaabaddbbaabbaddaadbdbbbabcacaabcdadbbdbcdaddadcdbdadcbbadbaddddbdcaadacacbaccabaacbbbcbacadcacadddddcddbbacbbbdbacbbdaaacadcabcbacaaaadbbcdcdcbaadbbddbaadddacdddadcadbccbacbacacdbbdcabbddbcbadbbcdccdddbdadddcaacabbadbcbddbddccbadbbdcbadcddadadddadaabddcbddabddacbcbccdaacbccdaacadbbccadcccaadbccbacacbaddbadbbbcbddddddabdbcdbcbcabdcdabdbbcdbabcbbcbdaadcbababccacdcaadacbaacadacadaabacdaadacacbcacdcabdcaadcdcddbbdccdabbaccaadbaabcddbabdacababbaaabadcdbcbaacccbdcddcdbdbdbcaccaaabdbccdddaadbadcaadccbddccadabcbcabddcdddbdadbacbdbbdaaacddcaccabdaabbcbcbdddcaaaadbbcaaaccbddcbccbccabacdcdccabdccabbcbaaaacaadcbbcbdcbcbbdddadadcaabacacbaaaadbbddabdacdbcdadbdacdaaaccaacacdabbdadcbbcbbadbadaddcaabcbaacdbbcabcadaaccabcddabdcadacdbcabccadbcddcbaabdbdacbbbcdcabdbbcacbaaddcadadbccdccddbdcaacdabdbccbcdbbbbcdbcbabccdaabdddccadbcbacacaabddaaddbaaaacaadadcbdbcbdddcabadabddcdbabaabdadbccddacccdbabdcacbaadcabddaaaadddbcddbbbdbcaddccabacaacaddccaccddcacbaaaacbcdcdbabbcacbcbcbbabcabcdbaaddbddcadbdadbdcccaccabbacdadbbdbddbbcdacacbccccacdcddbbbaddcbbdcddaaabcccdcbdcbdacccbdcbdccbcabdbdaacbabbbcddcadabbacbbdbddabaaccbbaaddcddcccdaccdbabaccacacabbadacccacacdddadbdcaacccacdcccbbdcacaaaddcabcaabbbbacbcbddadcacabccacaccccadabadcaaabccbaacbddbddddcdddcbcbabbbbbcadcddaaacdaadbdbbcacadabcacbdbacbccddacccbcbabbcccbbbbddababcbdcbabbdaabcddaccddbacdddaaadbddadaacacbcdccacaadaaacdbdcbcbbccddadacadadcccadbaaaacdbadaacbbbaaccdcabdbbddbcabbbacdddaccbcdaaddaaacdcbcbbbcabddcaaaddcacabdcdbabdbcbdabbdbcdabbadbadcdcadcadbbbaabaadddbcbbdbdbcadacaddbacdccacccdacdccbcaddddacbbadababbcabcccbabcadadbcadbadcaaacbdbbdcdcdaababaaadddcabdcdcabcdbcdcbcdbcbcdbcccbcaabddccbccbcaadbadcacdbbabccddabbaabcdaaabdbdaddacbbdbabacbdcccadbbabaacbcddabccacacaddddcbddbacbddccbdcbbbdbbbadacacbdabcaccbacaaacccababdcdadcabccbbcaacddacbbbbababbccbbdaccbbddadbdcccdbadbabcdadcbcdcaacbbddcdcbadabccccbbacbbcbbabaacdabbbbcacbcbccbcbcadcbbbbbaacccbcbdddccbbcbacaccdbbcadadcdbbaadbdcdddaccdbdcddcacdbcdcabdbaadcadbdbbdacddabbcdacdacbdddbbdabcdaccdcdacdcddbacddaccdcdbadcababccddbcdddccaabcdbcaadbbcadabbcdaabdabbbccbabddacaaadbbdcadccccbdbabcbbaaacddccbcbdbdbbadcaaccabbabddabdaaccbdaacbdcbddcddcbaaaacbdacaabdcdadbabcbdbcbbdbdcaabdcbadddcaadaacabbddcaaacadbadabaabababbdadccccddbcccadcbddbcbbabcbbacaabaacbbbcdbdadcbdddbacbabbabdacadbccaaaaababdaacdcdbdaddccdccdcbadcbdaaaacdabcdbdcdabcccddbdddddcdbbadbcacbcdbacabaccccacabaaccacdcbcbdbadbbcadbbcdcdbcbbacbddbbccbbcbbcbaccdaddbbbcabcbdcacdcdaaaadccdcbabdcacbaadadbabbbbabaaaadcadddcdbcccacccbbdcdcdbbdcddbcaadcbcbbccaaddadadabadbbadcdabddbcbbbbaadbbdcbacdadbdbcacbbbbadcdcbaaaccacbccddbcaaabbbaaccddbcbddadcdddbdcbdadbdabbdacbabdcabaaacacabadbdbcddaabdadcdbcdaabbbbdbbadaaddacdbcaacdccacabbdabaccbcbdcccddcddcadcaabdddcdbcadaacbccdacadbbabcbabacccbacabbcddcbaacbddcdabadcaadbbdacadbccdacddadbacddbaddaaadccbcbdcbdccaaddddcccbaddbddcdddadbcccadcdcdbdbdbbddbbcabcaacbdbcbdddbaacbaacbdbdbadbbbccdccccdaacbddccbbaddbcdadbaddbadcbcbcdcbdcaabcadaadbbddbdcabdaddaccbadcdaaacdbdcddcbdbdbccddbddbadbadadaccacdcdabcaacdacdbbdbbcaaaacaaacbbbabdcdbbbbaababcabdbbcccbddbabbcaccadbdcbaadccabcdbbbdbabdbadbcabdcdacdbacbdcccdcbdacaabcabcbdcdaabbddacdcdbdacacbabccbcdcacbcddbcbbaaddcabdabbdacdbbdccdcadabdcbcacdadccbbcdaacccbacbdbabddadcddbabbdddcaadaadabbacaaaddbdbacdaadbabcababaddaaddabdcbbbadbbcbababbccdbaadbadabaacdabcdccadbbddcddabccabbaaadadcdddbaddadbcdaddaacccdababbabdbcbcbbdcbbbbddcaaadcbcdcdacaaccacccdcbbdbcbadbaddacdabdcaccccbaccaccddbbcabbbadbacccadbcabacdbacbadaaabbddcabdcabddccbcaddcdaaabaadbcbcbbabddccccbdcddabbdbccaddcaaacaabdadaccababcabbbaccdbaadcdbabbbcaaddbdacdbabddadcbdbdbacaacadbcbcdcbbcdaaacacaccbcdcddcbbaacadddbadcbbdcbdadccbdcbadbdcdbadbbbbdcbdaddabcaaabddcdddabcadbdddbaaddacbcdccabaccbcdbdcacbbcababbdadcbdddaacddbadbaaaaadadabccbabbacddcdaddacdcbcdadabbbdcddcbddbabadddcacccaddaadabcccacaaadddccbaddacdcdbbaadbbdbbaabbddbcbacbabcccbcdaddaacadbaadcbdccdbddbadbbdaaabdbbabadcabcccddccbcdddacccbdabbbcdccdbbdaabbdddbbadadbabcdcdccccbabacdabdaaaadcabbccbcaacbaacdadddbdacdbcbdbcabaacbcbbdababbcbbbccbdbcaccbddccdbbdcdcaacbcabbddcddaadbbdbbbcddcbaddbaccdadcdbcaddaaadcaaddcdabddbbbcadaacbaddacccabababbdacdadcdcaaccbccbbdccdbaaabbbaaadadaaacacbdaaacddabbdbaddabddbbccdbdcbabaabaccbcbbdcdcadddadbbabdabdaddadccdcbacddcbccdbbdbaaacbabcaaddadabdcacdadcbdbabbdacadbbcaddaabadaabcabaddbddccaacaacbdabadddabbdcacbabccbacdbaaadbbbcdbcadbdacabcdddbcacadcabacbcbbbacdbbdccaacddbcdabdabcdcaaccccdadcbddcadcbbdcbdcbbcbbabcbcbabcaacaabdaabbccccdcccabaacdccbaabbaabbdcaccdcdddcccbdccadbabcbdcaaabbaaadcaadcdbacbdadadbbbdcabcdbadcdcaddcbacabdcbbbddacbadacdabbcdbcccabbcdbbdacabcdcbaadcdacdaaadbbcadacaadccdddbccbbadcacbcbdaaadcbbcabbccdbcbcccddabadaccdaaabdaddbcdaabbaaccaabbcddccddbaccbadabcdddabddccbbcacabdbcddcaadaababbcacccbbdcdbdcddddcccdbccbaaaaaaacbadcbaddabaddcbcbcaacacbadabbcaaacadcbbaaabdddadabacdabababbbaaadbacbddabdcbdccaacaaccaaccbcccbcbbdcdcbaaaadadadbcbdaddcababddadccbadbbbcbacbdccdcddddccbdbbabccacabcaccdcbcdcbdacbdacddabacadccddbaadbabcaabbcccdccdccbcbcbbcacbaabbbaaabdccdddbcdabccacabbbbddbababdbdbcbbaccbbcccdaccacbcddbbbdbdbbddacabdabcacacdcaccaddbacdbabdcbdcbabadccadbbdcdbbaabaabbcaaabbabdcacbcccabdabcadcdbbbbcbaadadbbabdabcbcaadcbdccbcabdcacacdaadbacdcccdbddddadcaaabdcdacdadbbddabaadddcbadadbddcdabcbdbbdcddddcaaabdcdadddabdacccabdbdabbbdddbdbdbabbbacdacccaccadabaaacdbabcacbdddbadcdcadbdcccccadddaaddbcacbcaccccacddbbadacbcaacaddbcccbabcbbdabcdaabaacbdbaddcdadbabcacbaadcabdddadbddaacbcbbabcbbcbaabadcccaaabcbaddacddbbbcbcabcdccbdcbcdabbdcccbabbacbdbacadddcddddadccbaaccacccdcbbbaaddbaaadcbdddcabccadcbaabddbbbcbcabdddddbcddcdcbbdacdbccbccabcbbbcddbddbccdddacdacaddadbaacaaaaacdccddaaccdbbcbacbbbcdaacccdbdcbacaacbdcbdbddabaccdadbaaabbadbadddacaacbacbabcbdccdbcddacbcadbcccbdcbadcccddadcbcddaabccabbcccccbdacdbddddcdaaaccdadddcdcadcdadbaaddbcaddddadbbcaaadabcddacddcacacaadaadadbddbbcaadcdbabdacddcadbcbcaabbddcadadccaaccdcbbadadacdcbbbccdaacacdbdaadbccddcadabcccaaaabaadcabbadcbaadaaacadbcbbbabdcdababdcaabddaacbcbdadacbbabaccdbbcbcbdcbddbccccdcdabcacdbbacbbacadaccbacdcbcccdbcbddccacaddaacdcbbcbaccddccbddabacdbacbcbbaabdbbaaccdcdccbbdccaddbdbcdcbbccacaaabdabcbbcdcaccaaadbccddaabaacaabbbbadbcbdbdccaccbdcbccddbdbcbbadcbadddbdbcdababdadbbdbcaabbcaaddabaaddbaccabbcbbcacbbaccdabdddacccacdcbdabdbdcacaadbccbacbaaccdcbaadadadabbbdbbddcdcdacdacbbaccabccdaccbaccddaddddcbccbbbdddccaacdccbccbcdcaaccdaabacadccdadbadcbccdaababbddadbcccbdbaadabbacbdbaddaacbdcddabdbbcccaccdacdccabcacaddccccdcbbaabdbcdcbdbbbcbabbabaaadcbacbabccabcdcabdbbdccddadddcbcdddbddacacaabcbcdadbcacbbacbbdcdaccddbcddbdabbccdbdcbcdbccbabbacccaaddacdabddcdddbabbcbacbbcbcccbccbaabccdcaacbacbbbbcbbbadbbacabbacabbbbcdbaabbbaacaddbbbddcdcbbacbcbbdabddacbdaaacdbabbcdadabaaadbadcdccbcdbadacbbcdcabdabdcacadbddcaabadbbcdbcbdacbbdabbdcddbbdccabdcbacdaabaadcbbcdddddcaabcadabdacdbdaaacccbbaacbbbbbadddbbadcacaadabbadacdcacadbaadabccdbabcbddbadbbbdbcacdcccaabacdaaddbaaadccdccaacddbcacbadabcdddbcdcadadbbccddddbcabacaccdcbbacddabbcaaddabaccdcaabdcbcbddaacdbccbadcbcdbbdbbcbcdaccaacbaddbccbaaacaccaababaccbdaaacbcacadbbdbdcdbcdcaccbaaabbcaabbacbccbcdadaaaaacadaccddbdcbbabacbdcbaabdddddddabdbddbadccbaacadcbcbcdaaddcadcabdabbbdaccacacadbbcbdbcdbbadaddbaccababaacbdcabbccbdaccaddcaccdcababbbdadcbccbadabcdccddbdcdacbcccbdaccbdacddcdabdccbcaabdabadcddabdcadacbcaaadbdbdbacdcbdaacbdcaddbcccddcadbbadaadacbcbabdcabdbcddddbacbabdbbbabbababdacaacdcdcbabbccaaddacabbaabddccadcdaadbccccadcbaaaabbbcacabacdcacbccdaddaacadaacccdcbadcaaabcdbbcccbccabdcbdbbbcdacdbadacdaabdccdbbabadbccdaddbaadbbaadbccdaabdcaccccdcccdddaccadabbdcaabaadbdbcdbdcdabdbacdcdbbbdcbdbacabcaaddadddcbdccbababbabbbacbdcbccbaddabdbdcaaddbbaabacbabdddbaaddcdcdbcdcbbdbcaacbdaacadabbdcccbddacacdcaaaadccddadadddcdccccbbbdbdcabdbcccaabdbcdcccbdaaddbddadabcbbacaaccbcbdccaabcbcbbdcaacadbacbbbcdddbbbcbacbbaabcddbacdccddddadcdcacbabdabbadbacdbdbaabbcacdadadaabdabddbacdcaddddadabbdcdcbdccadbdccddacdacbabbdadbcdcdcabdbddcadbabdbcbdadaaabdcdcbbbdccaccaaddcbbadccbbdabccbaabcbdadbbaccbcccabcbdcaaddbcddbcabcdcbcadddaabbacaadcacdbcccdbcdddcbbcadcadabaabacdabdbacaaabbcbbabbcdbbbcccdadcacbcabccbaaabdaccaadbdddcbcddcbdbcbcbbacdbacccbbdbbccbbbcdbbcbbcaccccbbbccacaddbabcabaccaabcbddbdabacddbcbccbcbdabddbddbabacabbddcddcddddccccddcbaadcaaabdcabdddbabaddbbbdacabbacdbccdcdcbaadbcccaddbbcbdcbddcacaddaccdabddbabccbbcaacbccabbcbbccdbccbccccadbabacbcccababbccbbadacbaadbacabcabaccacdaacbbcacbcccabacaaaaadabadcbaccabccaaccdcbabbadaaaaccadcacbcaacdcdadbbdadaaabaddaddadaaaadccadbcbaacaaaadcabadacdcbcdcdbdddbdccdcacdbaccdbdcdbbbabbabcddadbaacdadbddadcdbddaacaacbaaddacdacaccdcdaccccacaabdcbdbcbbacdbbccabcaccaaaddccdaacadadcdcaccccdcaacddcabcbbacbddadcbaabbbcbaabaabcabacbbccbaadaacadaadaacabdbdcacbaacadacddcbadaadbccacbabbcbddcdcccdaaaaccddaabbdabbbbaccdddccbddaaacadbdabddbbcbadcbacacacdbbdbabcaadadcadcadabadaacccaddcdcccbaccdabaddaacdcbdddccadaabbbdaabbbdcadaacdadbdbcbadcddbbaddadaacbbbcbcbabcadbdbaabdcadccdccdbcaddacdbbbcaabddabcbdcabbccacbbdaabccababbaddbcaacbcdbabdbcdcbcbabdbbcdbdbbbadbdbadbabcdaadbdaaadcadcbcabacbcacddbbcabbcadaadaabbcaaccccddddcadabadbbabbcdaadbcdaadbdddcdbadcadbaaaacadaaadbddacadbaaacbbdddcbccbaddbbbdbcddcdbbbbdbccccaadbadadaddbcadaadbdbaaddaaccbacdacabdbbcdcdcbbdcbbaddcdddddaccaadccccccbcdcabdbdbdbccdabccdbcdaaadccccabccbaacaadbacdbaaababdbbdaabdcbabddcabbcaaababdcbabaabbcbccaccbbacccbaaddbbabcacdabaccacacddbaddbacbddccabccacdbacdacadbacdbcdbadababdbaabaccbcdbbaadbcbddaccdabcdbaadbcdbbbadaccccaddcbabadcaabbdbababaddcbbbbccddcccccaddcbadadadbadbdccabccbbdccacbdbdbcadaddbdddddaacbbccbdacdbccaccaacbdaddaaccaadcadaadcabbdabcaacbbbbdcadcabacababcdadbbbbcdbbdbdbbcdcbdcdcdacbbdbcdaddabbbcbccacacacddabcacbcbbbdacaaabcaccdbccacaaadbdccdbccbbccadbdcdcccdbbdbdbcabddcaacddacdcadabddbdbcdcbdcaddacdbadbbddbbccdaabacccacdaacbbabddcdadbdabbaadddddaacbdcdcdaaaadadbdacdcddbcccbcadbdabaaaaccadddacabcccdbabccdacbccdcdcdbcdccdccadaaabdabccaaaadacdaaabbcbbdbacabbdcbcabdcbaccaabbcdaddccccadcccdcacabddadcacadbcccbadadaddddcababbacabdddcacddcaacacabaddccabcdcbaaaddabacabdddbdacadccabaadcdadbcbdadbcbbcbacbbcdcabcbcaaddacdbcdbcadadbcadbcabbbcccbabccbddabbabaabdbcccddabaabcbdccddbdcdccbccbcabdcdbdaddacadadabccadbaacbdbcdaadcbdaacccabdcaaaddcdadcccbdabcdbbcaacdcddbbcbdaabbbcabccabbcbbddacacdbabdaaddaddbadbbcdabdbcdcdcdbdaadbbdbccadccdbbbabbcbacdcabcbdacbbbbcadcdcdaaddbaabddcdbbcccdbccadcacaaccaacdbdccbdaaacdbdbbbcabdbcdbadccbcccbdcbadbcabcadddabbdbdddcbbabbabacaacacacdcbaadcaccadcabaaababcbdabdbdaaadacacacdaddadaddaadbdbdcccbdacddcabaccdabcabdaaccbbcdcaadcddbacddddbaacadddacbabdbdddabacbaabcabaacccadcbbbadbddabbddcadaabdaababddaaaaacddadbdcdccccdcdbcbdccbdadbdaddcaabddabdcaabadcdbacacbdbdadbadcabdaadbcdbadbccccbddbdcdabcbdaaabccadbbabcdddbdcdabdbdcaccabadbdcbadbaabccdacbddadddbdbdbbacaabdaddaaabdcaaddcaaacadbbdacbbddcbadaacbddbcabaacaddbbaabadbbcccdacadcadacabdbaadbcaddddbbbccacdcbadaccdaaccadcbacdbcdaadbbabdcbbbaccddcabcadbbcbdbddbbcbdadbdbdbddadbccaddbabcdaadbcaaabbdbdbbabccaccbabbcccddbabbdacbbabdaddbcdadbdacbdddacacacdbcadadbbabcadcbdbacbcababdadbacbcaacabadcadcddbbbaccccddbbdaaacbacddaabbdcbcbaddbccabdccbbddcbdbdbcbabddbcaadabbdbcacbbaccddccccacbbddbcdbbbaaaacbbdbaccdaaddabcabcccabbadbbaaaddabccbabbabbadaccdbbbcdcacaacdccbcbabdaabbabbabbddbacadbacccdcdacaaaccaddaaaacbbcdbaabbdabaabacccadacaadcddaaadcabdbdbbdcbbaadcabbdbaadcbddcdcdadcdacbadbdcaaddbcabaaadacacdddabdadadbbcccbbcdbbccddddadbbbadbaabbcaddaaacbdccdcdbcbbacbdaacbbcbbdcdbadddbbdccabcbbaabcddabbdabcbdabbdcdbdcccbdddadacbaaacbacddccacbcadbbbccabacbdcdcdcacacccbabababccaacbcaccddcababdccbbdbbcccdddcbcbdbdccccddddbccacbbaabcaaacabcdccacdbccacabcbccddcbacaddddddcacccccbbbaaadcdcccadbaccccdbdbaaccbaadaaddbbcdbcddbddcbccabccaddcabcdcbccaddcccbbbdddaadcddcbabacddabcdbdddddccbddadacdbbbadaccbbbdcaabcdccbbadbcbbaadcacdbbaabaccbcbbdcadcacddbccbaacbddcdbcaccdacccbcdbdcbaaadcccabadbbbddabdabadaabadabcacdddddacbcdcbccbddcaacbdacbabcddcddabcddabccacbccccccdadbcaabbaadabacadccaccaddaabdacabbcababddbcdbccaabdabaaabdcdbbabcabddbaabaaacddcbadaaadaccbabdbaadbdccbaaaabcaddcdccdabbbcdbcadccdbaacadbbabbabaccbbaacadacdabddcdababaabdacbdbcacbcaccbcdbbcababdbaaabacaabbbcabaacdaccdbcaabcaacdcaacbccadbadadcbcdbbbcbdccccacbbaddcbbaacccbdabbdcaddbbdbcaabdddabacabbcbdbcdbdbdbcbaccdabccdcacacabdbddadcddbbdcbdcaddcdbbabcbdbaccdbabddbdccbabbabcbdcdcadccbdaadabdbdacabaddbdbdbbccaaccacadcabbdacabaccbaadabcdbcccadbccbcdddacaabbacbddaadacccbdcbcdabdbcacbacaadbcdaaaadbdbdabcbcdaadbabddcaddbdcbbcacddcdabbccacbbabaabdbaacdadaabdaabddaaddcbacdcdbbbbbcdaaacacdbaabaccdbbcabbccbdcdaadbccdcaaaabbadbabbabdabdaabdbddbacbacbbcaaccdabcdbadbdcbaccacadbdcbdccadbaddacdcccabddddbaadbccacbdcbadcccabcadaccbbccdacbbbbddbdbccbdabbcdaabbadccbbccaadabddcaacdddddcbdadabcddabcdaadcbdaaddadacbaccabaacaacdaadbbaddabadacbaccaaabaddcabdcbbcccddcddabdccddadbddabccddaabdcccbbdddccbcdccbcccacbcabaaadcdccabacddacbabacbcbadbcbcbbbdcacdcabaaacbdbbbdbacacccbbaacbbdbdccaddcbccbbdaddadaccaabdadababddbbaadbabbddddaacbcadcabbccacddbdbdaaddbaaadcaabdcbbdabbcbcdaadacabacabcbacbccaddbbbaddbbcbdbadacababacadaaabdaadbdacccadabbbadbdccbbcddccbbadcbacaabbbcabadaadaaabbbbccccdbbcdcdbccdbcdbddccccacaacbadacabbdbccadcbbcbcddccaddadddacddacbbbdcddcadcbdbcbbbbbadbbaddbbcbcbacaccccadcbaadcdbcddcaabdacdacdbdcbaaacbcdbcbddccddbddbbcdcdbadaacddaabdcdbabbaacdddddddcbccdcaacadbcdbaacabbccbbdcdadcdbacacdddacabbbdbbaaddcdacabbccadbddcddadbcbbcabdadabdccadcbdcdccabdbbcdbdddddbbdcdcaadcdbaccbcbabaaadcdbbdcbbdacadbccbdbbcdabbccbadccbccacccbcbacbdaadaccddddddbabccbdbaadabdbabddbbacccbaabddcbababbacddcbcbcccabccdaabbbbcbaccdbddcdcaddadadabaacaaababdcdccabcbbcbbabdbdbbbaaccdacdccadcbdbbcbbbddcdbbcadaacaccbdcabbcccbccbaacbaddbaacdbcbbdbdddcdbaddcdabcadcddabbaadddbdaccdbbccacccdaccdadddacabbbdcccdacccacbdacccacbbbaaacddccdbccbdbaddcababdaccbbbcabbccbbabbbabbacadbdacabdbdcabbbdbabacdcbbaacdbbdcbabcbaadcadcdcbbadadbcbbbccabbbdccbdcbadcabbccddaababbacdabddbabbdababbaddcaacbbbdbbadddaaadcccacacdacbcaccdbbdbcbadddacdadcdaccbdaddcabddbbdbbabcabbacaccbbcbabdcbbacaabbcccabacdbccdbbbccaaccdccacdbddbdcdabcddacddbcccdcacacbabdacbdabcdddababcaadbcccadbccdbdbdbbdaacbdbccbdbbdcdabcabacbaddaadccccdbdbbbddcddddbcbdccbcbbdabdabddabdcdacdaacbacacccddcdaaddccabadcaadcbdacdddcbccccdbccbbbcabadbdbcbbaccabdddbdcdadccddcabcababccadadccbcdcbbcbbdaacadbbcdcacbbddcabbbbaadbbabbbaccbccacccbdaaacbbacccdbaddcacccabdcccbabcabcabbabcadadcbaabadddbccbdcddaaabcbdcdacaaaacbdbdabccbdcbcdcdacdcbdbcddddccdcbcaccbaccaacbbcddabccddbbbbaddacbddacbcdddbdbbdcabadccacdcdabbacccbdaaddbadddaabdcbaadaaaccccdcccaccaddadacdccacccabdddcccbbacaccccbbbabccbdddcabdcadcbddcbdcccccbdbcdddaccbbbabdbdcdbbbbcaadadcabaddacbdbadcbddcabdbbdbababcdaaabddcbbdabaddbaacdabbabcbcccadcabddadcaccadcbbaadbabababacdadadacbbbbbccbdaaddadccdcddcddbddbddbcaadbbdcdcdcbbbbdcbccddcbbccbbadcccdddbccabdddaddaacdcdddadaaddabcbbcddbbdaccddbacbbadabcdacccbcbaaabacaabbadbdababbcaaaaabadcdbacdbaacaaaacbdabccddcddccdcdcbcdcbbaabbadacdbaadaadbaddadaccaadcbadbdbcbaabdabcdacacacddbbadabdcaddabbadbaaadbccbcacacbdbacdadabacdababbcacaddccbccbacdbbdcbbbdcdbcdbccdbdcbdbcdccdcbdcdbaddbcddbdabbcdaaadddacddacdadbbbadddddddbdadcccbabbdbcabcadddcabbbaaccadaadaccadabdaccdcdabcdcbddbcaadaccdbdcbabbcacbcbaabdbbbabadcbbbbbcbdaabdadcddaddbbccdbbbcddbdbaabbaacbcbdbcbdbcdcaabbaccbbccababbcddbbbbabacbaaacbadcabdbcddcdaaabaddaddadcdabbbbbcacddadbdaccdadbacacdcbddcbcaaddbddcdcabcddaabdadadccabdabacdccadcbddbcdcacdbadbbdaadbdbcbdbbabcbaadaccabcdbddbbbaacdadaaaacabacbdcdbdbaabccddbadaabdabcddbcbbdbccacbcddbdabdbbacbbbacbacbadcbacbbcdbdddacdccbdccaadabddbdaadcdcdbcaaaacbacaccbabcaddbdcaabcbccbadbcabaaccdaabdcdbaaddbbaacdcdcdcddaddbdccdcacccbcdbadcbcdcaccababbdbdbacddbcbaabdaacbdcabcdbccccdddbbadaaabdccbdccbdbabbacaabbbccddccbcdcdaccdbbbbcbbbcdababbcdbcacdcadbdadbaddabcdbcddadcadadbbcddccacaccbdacdacdbdcabdaaddabaadcabaabacadcbbdabcabbcbadacbbbddbddddbbaccbabccbaacdbbdcbcadcbadbabbcbdcdaaadbdddcacdbabbabcbdbdbcdcbdcadcdaaaaccbccdbcbbbbddcbcddadcdcdcbacadbacabbcaabcaccdadcddbdcbdbcbcdbaddbaacdaddcddcdbdbdaaacabbadcdbaddacdbbacbbbbbdabbcbadacdccdcddacbbbcacaccaaadcbdcaddccaadcbdaddadcbdbbddabddabcdbbbdbdbcbcbccbbccddddaadabdcbbbacaabbdcaaabaabbccddcadabcaabadabdcabdaccdcacdacbdcdcddbdcaccbcbdbccadacacaabdcaddcccccadabbcabaadaccbcacbacdaaacaacbaadccaadccbabaaabbbabcdccadaabcdcdddbbbbddaaccbcaabbcacdbaddddbaddcbaddcbcbbddcccddabbbbbacccccabbcaccdaabdcdbbaddbdabababadcbdccbcaddaacdcbdbdaacabcdadcbbcdcbabbacdcdaaddabbbbdbaadcbaacbcdaabdabadcacbbcdddcddabacbdabddabcdababbbbdcdaadabaddbcdbbcbcdababdbbdcabbbccdbbbbaaacabbacbadabadabccbcdbbbcacbcdbbadaaababccacaddbcaabbccdadaabdabccbbabbccddcccdacaccdcacccbdcbdabddbabdcabadbaddddccdcadbadcdcdcabcdcbdddcabbbcbbdbaaabbadaacdcbdbcdaabcdabdccbcdddabaacbaccdbbbadddccdcddaaacbbcdbdaacdbbcbbcbccdccddddbcdbdbacaadacdccacdbaaaaccdbbcabbdddddacbacbbcbdcbacdccabacacabdcccacbbabcdcdddddcadbbbbbacbcccbcbadacbdcccabadccccbdaddcbddabacbdbadbacccdddbdddbbadabcbaadcabccccbbcbdcadbcaaacccdbbdaadbcdcbabbcadabdcbdadbcabbaddbaabaccbaaccdcbacbdadbccaabdbcddddddaadbbcbcabbdbdabbdaacaaaadaacadbccdcbdadaabcbcbdabdaccddddacbababdabbadcbcdccacbcbcdcdcdbcbdcbaacaadbbcbccadabbbabbadcddbdddabbcbcacbdabbbbcbdbbbcbdbbabdcdbcbccdbaadabaacbbdcacaabbabdbbccbdbdbcbaaddaadabaadbccabcdddaacccdbcdcadacadbbbcbdbcdcaabadabcdccadbddddabdcccadcacddcdadbadaaccdddcdaabaccbdcbddbcbdcaadcdcbcdbcdaccbacaabbaaacadbbbacccddcddcdaccddaaaddadbbdbadbadcdcaadaccdbccacdacbaaaddabcacccdbcdacabacccbdbdbcbdbbbccddbbaccdbdbbdcabaddccbbbbbacadcbadcbcabbbdabbbbadaabaabcccbacbcbdddcacbbadcddabdabddacaaababdbcbacccdbdbdaaadcacdadbabacbdadccacdaabdaabadabccaccabaccdbababcbbdccccacbddbabbacddabdcdcddbcbbaaddbddabdcabddbcdccddaabacaaccdcdabdacbcababcaddaaccbbcdbddddbaaccdbabadbaccbbccacccbcdabdbdbadcdacbadaabaccdbdcdcacadbcbaabdaccaacbdaccabdbbdabcacabcaaadadddabbcbcbdbaadcdacbdaddcdccadabddbadddabaadcdbdbbddcbcdcacbacdcbbccccddacdcdbaacadcabcddbcbcbdbcccdcbccacacbbcabcbcbdacbaddadccdcbbdcbcdbabdcdaacddbadbbbcbcddccadbbabdabbdbabaaddaabbdbdcccdaabaacdabdccdbaadddbaaadabdbddadccdaddbdddbcdacdbdacbababcaadadbdacbacdccbabcadcdbbcabcdccadbaaacbcddbcbbabcddaacbddbbabcacccdcaabbadaabbcbbadacdaccdabccacdcadcdbaadacdaaccbcdabdbdcaadadabbbcdcacabbdcbabadabbaaccaddbacbbcbaabaabdcaacbdabdabbddcbcdbccadcdbcaaaaaacaaabdcccdadacadacaadaccdcbdbdbcbdacbcdaacacbbaaabdcbccdadddcdbdcdbbbdddcbdbcabddbacdbaccbcddcabcabddcbdcccdddbdbaaaadddabdbdbabbaccabadcbbdcccdbbcccbcdbcdbbadddadcdcdbacbcaccabbaddaccdbbcdbcccbcddbbadbccaccdbddcbaabcabdabdccaddbddabbacdabdbabaddacbadcdadbdbbdbcccdacacbbbccdadacabdaabbabdbaabdbabdbbbaacdbbbaacbaadaabadaaccbbcabccaaadcdddbabcdbcbaccbbbccbdcdabddadcabdbddcbdcdddcdddbaddbacbbcabcaddadddcbadacabaaadcdcddddadcbbabacbbacccddccababcbacacccbaabdcdabcadbacbababdbcddccbddadbcdcadadcddadbababbbcbbabbbadacaacacdadbbaaadddacdbcacddbabddddabacaababdacdbaaccdbabaacacddadccaadaabaddacbabcdbcbcdcbbaccacacbadadcaabdcaaaabddaacadcaaabcddbadadddddacaccabccaacccdddbdadacaacabacaddcadaddccadadcaabaacacacdaccddcdaabcbacdbacbcddccaacddcbdcabaacbdddcabbbaadabcddbdbdbacbbbacdaadcbbaabcadadacbbcbdacadccabccdcdcbadbcaacacbdcdbdabdbabbbaabccaacaabbccdccddbdbbcbabdbaccaacbabcdacadaadcbcbadccbdddaccabaacbabdacaaadcadabacdbdcdccccbdadcbabdcadddccacacaddddbadbddcbbdadbcadbdcbdadcacbbdadabadaaacbbcbbabdbbbaacdacccdbdbdbdadabdbdbaadabbbddadbadaabacdcbbddbcacdcbcdddddcdddccabccabdbdaaddabbcabddbbbbbacadbacaddbacdcdacbbcbbacdcbcabaccdcdddbabdadbaccacccddaaacaacccdadabadbdbccdbbaadbbcbacdccbcabdbddabbcdbaabdddccaccdcbbccdabbdcbcacadddacbdcdbabbccaccabddbcdcccbbbaaaddbbccdbaaabbcccabdbddccdddbdaabaccddcabbdabcdcdbdcddadccadcdacabbddabcdaaccbccbdbadbbbabaacbcbbbbcaccbbcacdbabdbbabacdbdcaabdaadbccdcbccddbdaacaccadbacbbabbadcacacdcbccbbcbabbcccabaabcacbdadcdadbbbdbcbcbdcbdcdaaacabccabcbbaddccbdaadbbbabababcaddddbbbabaaadcacbcaacbbdcbcddacbcdbaadabdccdddcddbbbdaddccbdcacdbaaddacdbbacdcadcacaccdaaaccbddcacbbbacbddabcccdcbbdadcbbcdbaccacaccdbdbbbadadbdbabdadcacbbdcabaabbdabacccacbdacbdcddcdabaabccccbadddbbcdaabbbaacdaabaaacccadabacddcacdcadbbcddbaaacbadaabaaaccbacaacbddbcdacabacbdcadadbdbdcdbcccccdddbcbcdddcddbaaacbdcbdccdaaadbaababbccdddbccbadcababbdccbdbcabdcddbcbacbaabdbbdccaacdbabbbbadaccadcbacbadbcabdacbbaddaadccbbdbbccccdccabdddbdaddbbadbdbdaaccabbadbaaaddcdacaddadcaccbabadccbcadcadbbdabdbcadabcdabdbadbdbbccdacdbbddadcdcaadaccdccbdcbcaaacdbcabbdcacdabddbcbabacbabdbccbaadbdacabcbbadbbbcacdadcaacadaabaacacabbdcaaccdadbbccbbadcacaabadaaadbacddbcacdbdcbddcbcdcdaacdaaadaddaaabddabcbadaadbcadbdcaabddccdadabacbcddcbaabbabbdddabdccdcbccbbcadcaaccacdaacbbddbdaadacccddbbccdddbaaaddbdbacbacddbcbdddbcbdcabbbcabcacdbccbaacdbadcdcbcaacaaaacbccbcdbbadabcbbadddbbcdacabaadabaadababdcabbcaaacdbdcdbdccabcbadaabdcccbbcababdbdbaddcbaadcadccdbcbadcbdcaacdabddaccdabacbcbccaddddacadbdbdadcbacdbabdcdddacdaaddbbbddbbabacbccdadddcddbaddbbacaaddcbbacacdaacbbbccbbbcbbdcaccabdbccabaaccccbabccddddadbdcbcacccbcdddabbcaabdbbdcccddccabdbddaacbbcaaccdbbdcdacbbcdabadbddabccbddabccdbbdbdaacdabaabacbcaaacbbbccadbaddabcbbadbbadcbacdbcbcbaddaaaccdabcbdbbadbaacbbcaadbcadbdcbbdadcaaaccbbcddbdcadcaadadddcbdcbddbadadccdcccaddacbaddbadabcccdbaccccaaacbcdccaabaddcdacbdaddcacabcaabbdbadbbcaccadbdbdabbdabcbbdcdabacadcdcdacadacdbbcaabbcdddccddadcdddcbaadcdbadabddaaddacacdadccccacddcbadaabbcadbbaaaddbbdacabdaacccbbacbdaabcdaccdbbcadbadcbdcdacaaacbcbbcdacaddbadbdcbabbcbacccabcabdcdbabcacadabadbcbadcaacdaddcbcdaaaabaadbdbacdddbaacdcabdbdabcaacdcacaddccbbaddbcadddbddadabccbccbaaacdbdbabcbaacadcbccaaccddabbabbddaacabbcacbcbbbcaacbbccaacbdcbdbdcadcbcadacdabcadadbabbacdaabacacccdabcdbcdcdcabbbbccbcddbddcbabdccbbccdbddccddbdabbbababbbcacddbbbddbcdbcddadcddcbbcbccacaddddbccddcbcdcbbaadcbacababdcbbdacaddcdccbccaacdacaaacbadbccbcddacabcacabcabbabadaddddaadbaabbdcacabbbbcdbaaabadbabaaaccdcbcacddcbbccbcbcccadbcadaacbadaabcaadcadbabdcabbdbbabcbdcbabaaaccbdcbccbcbddabbdbacdabcbcacbcacabcdddcdadacbcddcdbdbdcccdbcdbbcaabaddcccbddaababdcacaaabdcdaddbccacdacdacacaaaaadacdaaddbcaacaaabcbaacaddbdbddcabbbcbacccabbccdddcadcbaadacbabddcaccbabdbdcaabbaaabcdabadccadabbaacadcacdabaaacdadccabdcbadcdbbbcaacdcacbaabadcdcdaaaddcdcacbcccdbacddddabdddadbdbbdadbbcbccbbbddcabcdbbddcbcaadcddbcabdcdadbaaacbadaddaaabdaddcbccacdbacabccadcadbaabcadbcacddacabbbdcabccdcacdcdbdbbbcccabaaddddaaadcbdaaabdacaadacbcadacdabbdcccacdbccadabaaadcdbbadacdbabdaadbaadccbccaddccaadbacbdaadbdcddcdcabbdabbbbcbabdbcdbaaaabbbacdbdcbadcbdaadbbdbabdbccbcdcccbcaaacddbbdbacabadbdcdadbccbacbbddcdccdbaabbcbdcbcdbdcbbbcdcccbacddabbddabbcbccdccddbdbcdcdbbcddacadbccdaaabcbbbbbdaaaabbddcacdcaccbcddccbdabccdcbcaccbdaddacdcadcbbabacbcbbbbbddbcccdadbbdbaaddbbcbddcbadabacbbdbcacdbaddbbcddcadabadcbaacabaaaabcbdacabbcbdbacbbdcdacbadbaacccdadcbcabbccbbbcaddabaaccaccabddbdacbbbbccbcabdaadaaacdaccaabcddbddbbcbbadacaddacdcababcdabbbacaaaadcdbaddbcadcbcaacaabdcadbddddcdadddbcdcbbbaacacacdaabcaacdddddcddddcbdddcaabcdcabdbabdaaaaaddadacbddaabccadbdacacdccddbaddbaadbbcdbacdcabcabadcdcbcbaadddddbdadaddcbbdacaabacdbaaaccbdadcdcdcdabddbbbddaabdabaccbcddddbdddadabababcbcddaacbdadbdcdcbadcbcacddadadcadbaddcccbbadddbdccbccabcababbaaababacddaddabbacadaaabbadabcacdadbbbdbabdbacdddcddbccbbbaadbabdbcdcbdacaccacdaaabdacbabdbabbbddbadabddabccacbdcdaaccdbddadbdadacaabbcdbbdbaadaaadddddcbcbcacdcabcadbcbddbdaccbbbaababbbbacacdaadbbbcaddcbdacccdadadbaddbbbdcacdcaaddbdabcccbdbcaacaddcccbaadacaccadddddababddbbbabbdcbbdbabdaddacaabcbcadbcdacdadddbbabcbbbbcbccbdadbbacbabbcaccbdacdcdcabdadbdabdaacbabaadddcbcbacbacaccccaccdabdccdccdadcacbcdcabcbdcadbbdbbdabacdcacdbaddabbadacbcadaabbbdbdddbaaccbbbbbbddbccbcdadcdcadbdcaaacdcbbccdcdabdbcbcdbdaaccdbcaddcbbadbbdabaccadaccdddacaacddabdcdcaddbbcaabdabaaccacddaadcbcdcbaccbdaadbabdcdaadccccbdacaabdabacbbccbacbdcadacabaaacadaaaacbdacbbcbacabdbabbcddccbbdccdcbbdccbdcabdbbdcdcacdcdcccdabaadabdbbaacdcbcbcaacdcdcddbcbacdacbccbcdabacadddbdccddbbdcacbabbcacddbbddacbabadadaabdbadcbbcaabbdacbacabadbbcabdaccdcdcaddcbdbbbaddbaccbbcddaabdbbbabdaabaaacccaddbcdacacbbadcaaaaabbbbdabadbcabcadadadddbbccabddabaddbaddadbbacbadadcbadccabbcddddaaabbdcaddcbcaabdacbaccadcacdcdacaaccddddaabbdcdbaaacdcbadccdcaabaaacbcacbcbddccccacdbcbddbddccacbabdbaabddbacdbdccbdabcdccddcaccbcbcbbcdacdaccbaddcdcabcdcabacbadcbbbbdbbbadacddababbbcaadadcbcdbdcdacadadbabdcbccabbccbaacacdbdcccadbdacaadcaadcabddcbbacbbbbbdbbabccbcacaddbdddbadddaadddcaabaadaacdccdaddbdabbadbcaddacccddcaabbbdadadabaadabbdacbcbbbcbbcadbdaccacadadadabaabbabaacbcaddbbcaabddddaaaacdacababaabaadccabacddcaccbabcabdccdacbcbcbcccaccbbdcaddcabadccdcbaaabbdabadcbdcbcbcbcdbadcaccbbddacadadabacacbcbadaaddddbbcbdddacaddadcabdbdbdabcbadabcbdddcdacdbccbdbccdddcdaadaaadcbadacacabcdbdbddabcabdcdcacbbbdabdababbaddcaaaadccdcdcbccccaabbccbbddacabdbbadaadacdcbadcbcdddaadaacdacabaddbdcbbcbdadcaacabbcdbbacdabbbbdadcbdacddddbcabbccccccbabddacabbbcdbccbbbadbdbddacacbbbbabaccbbaddcbbacdcabbadccbddaddacdcdbabddcabcbbcbcaabccdbaccaddabdadacadbadddabdcbcdcccbacabacdcaaabaccdbcbaccdaaccadacbcacccddcadddbcaddbdbcccbddcdcdcdaaddabdddadcbacbaacbccbdbbaccdbdbdcbacdaadabddbbaddabbdbbbdcbdbcdbaccdbddbaddbdadabccbabaabddaacaabcdccdbcdcabcdbbabccdbbccaadbdbdbbcbccbbbacacacdbaddcaddbdccbdabadadabaccdddbdccacdbbbdadabccacbdcccbadabddbcbbadbaabdabcabbcabcabaadcdaaacdaaddcdccdddccddcdaadbbaddbacabcadaacdddbddbaaaddccbabbccacdaaccdbdbdbbbbbbbabcaacbadbcbcddbbaaccbddccadacacddbacdacdcdbdaccacccabacbdbcbbdaacaadbbbddcaaaaccadaddaddaabaaddaadcddcdcdadcdbacdccaccbcdcabcaacdbbaabcbdaaacbdcabbdbdabacdaabbcacabbabadaadadbbbbbaabcbdcdbcdaacbdabbbcdbbccdddccdbbbdacdacbdcbbacbdacccccccbccbdacbdbbbbaccccbdabcbaacadacccdaaacbdbbbaaccbcaadcdaadacdaacdcddabdbdddbababcdacddabcaadcbbcadaacadabdbbccbacccbbdcacddcdcbaabbbddcbbdbbbbaacbcdddbbdaddbbbddcbcbcbddbaabdcbdadcbabdacbbbacaccbacbbaacacbaabdcdbbbdcaacddcdbdccdccbdbbaacbcbcdcabdabadaaaabdabcbdbdcbabdddbcbbbbadaabababbaddddaaccbbbdaacdcccdbdabdadbaacddcbcabcadbbcbdbdcdcbacdbacccaacbccbaadddbacbabaacbccbbdbdbdcdbdadbcbdcbadbdcddaabccbababaacabbcdbabacbcbcdddddaadaccabdcbcdddbcdccdccabbdacbdabcbccdddbcdabcdabdddddadadbaadddccdadabbbddabcdacaaaaccdcdcbdbdbcbdddabdacddbaddccaacbcbccdbcbcaaabbcddbadcdbaaacddccbcccbbdcbbdaadaacadbddaadabbdbccaadbbcbcccabaccdbccabaaabcbababcdabcccdcdbabbdbddbaacacbdccbbbdacddbcbbbbbbaddbbdcccdcaddbabccbaacddbbddccddcdaccbddbcdbccabcacdaabddcaccabbcbccdccdbbbaaaaccddddacadacabdabbcccbcbdcbcdababdaaabcdaadacaaccabcbdbddddaabbcccdadcaabbdadacbaaacccaacabbaabdbbbcbacdbdbadcdcacdcbaccbdbdbaabdcbacbabbaacaaddbbaaacbcaccacadabbacabbacaaddabbccdaddbcdcddbaccadacaccdcdaabbddcacadcdccbdbcadadabcaabcaaadcbdcdbcccacaabcbbccdacdcdcacbccbddabdcdcbbacddcbbbdcadbacaaaddbabacdcbbdaccabbcaaddabddcddbddabddadadbdbdcbbdddccbdaccaddccbdcbcadadacbcdcadcadbddcdabcadbacacddbcccdcbbcbdaaddcaaaaddbcaabaccaccadaabadbbddcadcbaaaddbcbcccaacdbdcdbdcddaaddbddcbbdcccbbdbdaadddcababdacccddbcbdaadaccccbbbcdacdabdbbbddcaaabaadacbcbbcacbaaddadcadcbabbcddacaaaaacbcddccccabbabcdddcbbabadcbcaccbbdcbcccbcabaaaabbcbabbcdbaadabbcaaacbacaddbdcabcabaaabadcbbdcddcddabdccbbabdcdabbdbaddbcadddcacbbbbaadacddccdaacdcbaccdcccdcaaabbccbcdababbbacaabdbacbbaadcbcbbbadddbdadddadaccdbcbccdcccccdcdacbcacaaccacdaadcbdababdddbcdcddabdaddbbddccdaaacdacdcdbcbbadbccacbbabcbdccadbbacdccbaadbcababdbcacacdcbdacaabdbccbaacdbacdaaddcaacbdaacbdccbcbadddaadaadabbbdcadbcbbaabcbbbdddacccbaacbdabaacdcbbcbadccaacaadcbbbacbbdacccbaaaddcdcaadbdacdcaaddbbccddbacbdcadbadcdcdcabcabdccabaccbacbcddadbbdcddcaacaddbbabbcdbadaccbddcbcadbcdabdababdcccacdbaacbdacdcaadaadbbdadabbbcddddaaabadcaccdacbccbbbacadadbdcaadddacabbcbacbcbbabacaabbabccdadbaddaaddbccbcbaddccdabcbbbcbdbbacbabadbaaadcacddccaaaabcaacbadaacadcbadbccaaaaacabcabbadaddadaacdbccbaddbbbdcbbddabccdddaacabcacccbbbbbdcdaccdbaabaabdddacbdbbcacaaccdbcdcddbbbcbdabbddacbbbcbcaddacdcaacbddabddabbbdcddddbdccbaaacdccdcadaadabbaacddbcaaadcdcbbaddacbdbbdaccbcdbdcaadbbacbdccaddbadbdccddacbaddabdaaadadcbbdccaabababdcacdccbbabddbdbcbbbaadabbbcadadaabcbacababcbbadabccdccbcccddaabddadbdddbddcbbcabcdbabbacbbdacddcdcaacacacadbaadadaccbacccdcbcadcadabcaccbabbbddcdbdaaadccccbbbadbacdaddaccabdcdcbdbcccddaaaaaacdaccdccacdadadaaaddbcccadcbdcacbbdbcdacaabddbcacbabacbbbbcbcabaaacacdddacbcbabcaacbcaaaabcbaacbdcbdbaadaacabdbabcbdbcdcbbcbacaaaacbdddacacbcacbaaabdaacdbbcbaadcbbabdabbabaccdbcbccaadcaccbbcaaacbacabddddcdadbaacbbccddbdddaadddcdaacdcdcdcacbcdcdbaddabdacbbaddbadadadcddcdddbcbccaacbcacddbccabdddbacdadabdaacdbabdbdcbcdbcdbbdcbaaccbabbcbbcccdbddbadcbbddbccbbcaabbadbdaaccaabbdbccbbaddbbabcbcdaddbdccbcdadaaaaddcadcdcdaccabcdcadadbcbdabbdcabcccdbaaccbccdaacbdabcdacdbdbbcabdaccddaddabaddaccdddccbdcabdcbdcabbabccadcdcbcccbdcdbcdcddbbacddcacabbcabadddcbcbcdcbbaabccdaabbaadaaaddcddbcaabcdabbdbdaaddaaabdbadabddcdababdaccccbcccaaadddbcccddcabadbcbbacdacadcdcacbdaccdbabcabcbdcccdabbadddbbdccbcbaabccccbccacacadcbbbdcbcbcbdbbccbbdabccbcdbcdbddaaadaccbbababbaacbaaabbbbadcabdbbbddcaaadcaabbbadbaadbbacdcaacbcdccaaacbbbbcaaaaabadbacadacddbcabbaabcaadbccabdabbccacbbadcdbddcbbbbdbbaccccaddaccabdbbbdddadcbcabdbbadaddbddadbadbcadabcaaabaddcdddabcdcaaadcdcdbcdabbcbbdcdcdaadcdabbbabdabdccabaccaddabdaacabccbcdaabbddaaddccdaabbabdbcccbbdddacbaccadccacacdbcbbaacadcbacdbabbcadbccbdcddbbbcbcaacbdccbccaabbacadabcdaaaadbbdcccbdcbbbbaaaacdbbcbaaddacadddcadadacdacaddcccbddaccbacbbddcccacbcbdbaadccdcccbcbbabbbcaccadabdaccbcdabdacbcabacccacbdcbbdaddabbabbabbdacbabaaadaadbacdddddccccddcbcabbdaaddbdbdddddbacddabdacdccadadddbdbbadacbadabcadbabcdcddbabadbbaaaacdaddaacdbacacdcbbcccddccbdabdddaaaabdadacbadbbbadcadaabaddaaddababaccbcddbdbaacaacaabdbdccbdbdabcddabcadcdddbcddddacacbaabbccccabdadaccbcbaabadabdbadcdcdcccbbbdcddbbcbccbccdddbcbcdbbddbccabcacbddccbdacbaddcbdcacabdbdcbdbdcbbaaaaccdadcdccaaacaaccaaaabdbbaaabdddadcabdaccbcbdcbacbddaacddaadcbbbbacacbbadbadcabaccccbabddaddbdbdacccbdcacccbcbacddcbacbccbbcbcbcbcbabbcddaaadcaabcaccddaddddbdcbbbbdacaccbabadabcacabbcdaaacbaddcbaddbcdadbbacdadadabdbbcccddbbaddacdbacbabccbcdadbbbaadcdaabdcdbdcacbccbdccdbabcabaacbaacbcdaadbcbbdabcbbdbaaccbaddcadacaabdabcababacbcdbdabbbabbcaadcabbdabbbabbbdacddbcdcaabccdacbbbcadcccddcbddccbcdabcadacdabdcddcddadaaccaacaccddabdcababaadadacccacadbcdbbccbdaabbcadcadabccddacdbcdbdbbaabaccdcaacddcaddabcaccbbdadcddacababcddddbbddbcdcdadcbdacaabcdcabdaaccbddccbdcbdaababaacbbaabaadbaacdbbdabcbbacaccdabbaccccdacdabbdbbdbbcbacabcacdabccbaadabaacbbddbcddcaaaabbdcadcdabbbacbdcdbaaaccbbabcabadbabdccbccbbcdacbcdbdabadddbaadcacadabbdaccadbbdccbdabaadcdabadbbabdabcaacbbdaabccccadacdddbbabbddcabbacdcdccdbcbddaccbcadbcdabaddacbacddddcdbcaadbdabdcbcaabcdccadbcaacddccddadbadbcccadcdabbaadaabcdabbdadcacbddbddbabbcdbddbdbbdaaacccbcadbabcdbbcdbacdabadbbbdcdbccaadbdbadbbdadcaddcbbdadaacdcacbcddbbcbccbdcdbdcabacdaccadbdcdccdcbabdaccccaacdaaababdbadaccbcbacabbabadcdbdddcdacbcaaaadbdcbbcbcaacbcaccbaadbacbbddbcccddcccadcbdcaaabadaabdcdcdcbabbddbcddcbdccbcadaccbbbdccbcabbadacbabcbcccccccbbbddaddabcbdaacdaddccbdccaabaadbdbbabbdccdddcacddcaddbcdadadcdddadbdaaaabbbabbccabcdaddbccabbbbdccccabcdabbaccbbdccabbddadcbcdccaacbcaacabccccadbcabaaacbdbbddbcbabbabadabcbbbbcaabddaccaabbbaddaccddccbdbaaccdaacbaaddcbbaabcadcaccccddbbdddabdddbbdadcadbabaadabacdcccdbdbababbacacacdbcadaabdcdbabbacdadacbacdadaccbccddbabccbabbddbacacdbbcdbdbabaabbcbddcacbccbacdcdacbcaccbcabdddddcbbdaccdcdcdacdadcbdbccbcdaadcaacbbcccabbccdababdabdbdaadbaccddaaccabcbacaacaacddaccdadcbaadacbadcdbbccabbdbabcdcaacccbaddadddbdcdcbadbcabcbaadcccbdcacabcbbccddccbcbbabadcdabaaddccbbacadacccdbbcaaaccdbcbabacbdacaddabcbcacdaacdbcadcbcbcdabbabdacacbdadacbddacdbadcbdaabdcddadcbadaabbdcbcabddccaadaacbbdbbdadcbdbbbbacaadcaacaabdbbbbbacacdacddbdaddabaacbbadccacadcdddcddddbcdaddcbacccbadbabcbabcccbdcddbadccdabbcbaacdcccdbcddbcdbaccdcddbddadcbcccdbdbbbbcbcdaccbadacacbbbacdbcdcdcccbddbcbacddcabbcbcabccababaccadcabcdbcdadcbcbbbadddaaabdcacdbbcbccaaccbdcbdcdbadadbdbdbcbccadcacdccbbbccaabcabbdaacdbcbdbbdabcaacdabcadaaabbcddbccbcddbdabcbdddacccaaddacbbdddadaddacdaabdbcbbaababbddabdddcbacdaaacabddbdbddaadddbbbcdccccbccdcbcddbaadcacbaaadadcddbbbdaccadaabcddcdbadbababacbdacadadbbcddbaddbcdabbcdcbadacadabbdcdbbabdbcbadabbcbadcaccaaabdacaccabcbbbacdcaaddcabacdcdaccdbacbdabacabdaaaccbabcbabaacaddacddabdaabcbbdcacabaccabcdababddbdacccccadcbdbadbadddadcbbdbabdcdbadcbbbdbcaacacbcbddbdbbadadcbdddbadaabdcdcaaccadcdccbcdacccadcaadcbdacacbcacccbbcabccaccaadabacddbbadabcadbccadabbaadbcacbbdcdacddcaabdbbabaddaacaddbcbbcbabdaddbcbaadaacdccccababbacbcbbdbbcadbcacddadabbadddcbaacdabcdabccaddbccadcbbbbbbaacdcdadcbacbcbbdddabbabbccddbccbbbbbcaddadaabcaabacbadddbaacadadbadcccbdbadbdbcbdccdaaaaadcdbdcdbbdcbababddadabddccbcdbbbaddcaacacdacacbcaccbcbacdccddaddcdcdacaaacadaddccdcdaabaccbaacdaabdaadccabcccdbcadabdccbdccbaddbbaadcbbbddabdaccabaacabbaacdcbbccbbabacabcadacbbcdccdaccdddddaadcadcdaaacbdcacadcabdbbdcbaadcbcdadbbacaccbcbabaadbdacbdcccadcddccbacbaaaacbcbaadcacacbccdcacbbabdbacbcadbbabdcbcdabbbdcbbbbacccdcccbcaccacacbbaabdcbddcddcdbcbdcbbcdaccaccbbbadaccdcdccbddacabcddbcddaadaacbbcdcbbaddcadccbdddaaaaabdbacabcdbaaaadbcaddcdcdbcaabcbcaadcaaacbacbdaccbcdabbbcbdbcacccbabcddbdbbcdcbbddbabaadcbabdcdaadacdbccdbcbaccabcbaddcacbbabaaabdaabccabbcbdaadaddbcbadadaddcacddcadaadbbddbacdcdbabacdaccbcdbbccabcadcbcccaabaaacbabcacbadaddcaaadccdcbccdccddbcdcdaccdcdcaaadaadaddcdddacabdababbdadcadbcccdaccdcbdddbaddbdcacdbadacccccababcccbcccbabcbbbaaccbdbdabdcaccdaadcabcddadbaddcaddcbccdabdbcdbcaadddcbacbccadacccbddbcbddcccdbcadcdabbcbdccbdccddcaabbddadaabdbbccacbabcaddbccbacccbdcdacddccacbacabcadabbbbbdbccbbadcbddccadcbcbdcbbadcdbacbdbaadcadddddbcabcabccdbadcaccabcbdcacaddcdacadbbabdcdcadadcddddcbdcccdcaddacdcbabdbbbcaddccdaaaaaddadabdaddddbdcbdabdcdcacdcdadaccdcadbcdbbaabcaccacadabcadabaddcbaabccdbcbacbccdbdcccabdbccdacdacabdddcddaadbadaadcddbbdcddbdcbccdbaacdbddcccbdbbcdbacaabbcaabaccdabdbdcbaccdbbcbdaaaaddbdbadaacdcdcdabacdbabbcaccbdaaaaaabacbdcabcbadbdccbdbcaabbaddcdbdaddccaccbdadccbcdbbcacbbcabdbacdbdbbdcbcacddaacdccbbddccdbcbbcadbacaaaaaabdcbbbaabadacddcdcdcddadaaaabbcabaaabdbcdbdaabdcdccdbbacadbcddbddbaabbccbcddacabcaadbbdbdaacbbdacaabbacdcbacdbbcabbdcbbdabcbdccbdadbadcdccdcddbbaadbdddcdbcbccbddbcabadadcdaadcacacaadadadaabcdacaccaaccccbddcadaaacdcadacbcbbaadaaaaacbbbadddaadccbaaccdbcdcadacabcddcabddaccababdcdccdddbbccbbbbbbcabbddcdcaabdcacaadacbdbcadcbbdabdbabbbddbadacababbdcdadaccdbddcbaaccbacacdbbddddaaddbbacacdcbcadbccbadddcdbccbcbcccddbcaccdcccadcddccabcacabbdbbdbccabaabadbabaacbdbdddccbacbabcbaabbbcccdadcbadadbacbbcbdabcbabadbbdaaabbbcbcddacddbaabaccacbbcbcdbaacaadadacbbacbcadadbbcbcdabddbccadddcddccccdcabbadccdcabccbbcbbcacdbaabbabaaaaacccccddbaddaaadacddbccbddadabbacbbbdbaaababaabcbdacaacbbadcaaaddcccadcdbdacdaccbcbdbcccdacabcbdbbdabadcabddbbaddcbbdcbddcccdddbbbacadbbbbabbdbddcadddacbaaadcdbdcaacdabaadacaaabbbdbbcaddadcddaaccbaadbdacbcdabcbcbbabdaaccbcabdacbbdaccacaadccdbccdbddbbabaabcbabbaaddcaddddbcdbbdcadddddbaddbcaaabddcaadbcddcccbaabdacaacadbbadabbaaadddbccdcccdabbaaabdbabccdddacaccdcbbacdcadbdccacdbddcdcbdcbcadaacbbdbbaddabcacaccbbacddddaadacbdcdaccaabcbabbbbbbcbbabdcddacdcabbcbaaddccbbaaacdabccbabacbdbbadaddcdcddadcaadadcbbaccbdcdabbabaccabddcdcaccdbcdcbadcacadaababbdcaacbaadcdccbacadaadbdaaaddacdbdcacdbcccbccdbadbdcddadbbbabaaaccdabacacdbcddaabcdbabdcacaabacbcbdbdbdcdbdadbcdaddcbaacdbdddbbdcbdbbdacaabacdbbbbccdcadddabcdccdaadcccaccdddadadbddabcdccaaddcdbadcababadbdabbacadacddabacbaccdcdcaccdbccdcabcccabacbcdbabaadbadacbdcdabbddacacadbbddcadbabbcddccdbcdbbdcccbdbddadaccbcacacaabababccdcdddcccdaaccdcddcaadacbacccbadcabddadbbcccaddddddcbdcabdbcdcadccdcaaddaadcdbbdaaadbbdcababdddcdabddbccdbbadacbbcccacbddbbbbcccabdbaccbccccdcacddadadcdcdacdbddacabaaaaadbbbbcbdddbcccadaddbbdcdccadddaadbbabdbbcabbabcbdbdcbdddadcdddbcbbdbbacbcadbccccbaadbbdaccbabadbbcbccbadbcddaddaabddcbbcccbcbdaccdbdcaddbbdcbbbcadaababaaacaadcbdadbdbabccabcdbdcbadbdcddadacdabcaabaabadbaabdbbadadaccadbadadddaaccadaaacdacabdbbadcdbddddbacbdbdaadbcbccdcbbdcaadaaddccbbdbdddddddcabacbcbbabacbbacbbacdadcbaddcabcbbdcbbbbcdcabbadaddbdbbdacbdbccbdaddaddbcbbbbacdbdbcacbbabcadabdcdddbbdccbdbdccdadaaccbbccdccbcabbddcaccccddcbdccddacabcaabccabbbddcacccdbadcddcdddcaaddcabaaabadadaaaabbbdbbaaabcbbcdcbacbcbbdbbabbbcdddcaaccbbbccdccdbabccddcadadcbddbcabccbcccbbacbabdcbcddadababbbbaacacacdccdbaadaadbbcbccaacdacabacadcacdddcbbacbdcccbbccacdcdcbcddabddbaaaabbdbdbcadbdabbcacaaddaccccdaacdbdbddbabddbbbdccacbbbbbdcddbadbacbdacdcdbbdcddacaadabbacbbabbbdaddacaabcdacdbaddbcdbcaadabdddadbbcabbcaaabcbbacbdcbbbdcdabbdabccdcdbdadabbdaaaaabbccdbacbdaddcaaccbbadadbccbbacdbbbbbcabdcbcddadbbdddddcaabdbccbabbbadcbcdbbadbaadaacacaabbbbdbabdcdacdacbbcdccbccdbcadcdcccbdababbcbdaabaacacdbcdabbcdbbabbadddddccbdbbcacbaadaddcdcacdcdcdbbcaabbbaaaddcdaadcddcabdcacdadcaaaccdcdbbdcbbacddcdbbcdcdbabccbbacbcdcaabbabcacdcbdccacaabbdbacddabdcbbdaaccaddddcddcdcbcddaadbccabaadccbcabcccddcdabdbcbabaadacbdacbcaacbddbcdbabddabacdcdabadabcddbbababbabbaacbccccdbdaccdbaadabbbccbbcddcccaadcbbababcbcaacbcdacbadabbddacdcaacddacbbcccbbdbbdadbcbdcaacddabacdbbccbaabacbdbaccddccdccdbbbdaaccddacdadcddaaddadabcabaabcddccacdcadcdacbacabddcabdacdcbddccbdbbcbaabdcdaacadcbdaacbcdbbbdcccbcbbdbcdbbbdababbdcbbdaddcccacbcdcccacbbccccdabacbcccdabbcbbdddcbadcbbcdcbcdcadaacbabbcbdbbdcbddddbcabbdaabbcbacbcbccabcccaacaddabbcbccdbaddadbdcbbcadabcaaccbdbccddbbdaaaadcbdcdcbccaaacacaacbbdcdbadacdadbabacadbdaaacacdcdbacbdadcddcdccbadcdcbbddbdbdcabddadabcdacdcabddcdcdddaadbbccbdcdbdbbbbacaaadcabcbddbbadddbbdabbddcaacbcbcbcbabddbbabbbaccccbcaddbbdcbdddaaadbabbacbabcbcbdbdcadcdddddacadbccacbadbbbcaadbacbbaadacacadacbddacacdabacdbacdacaadbabcbcadabbcaacacbdaacbddbbbdabbacbabdaaddccdbbbaccddbbdacbacdbbdbaaccccdbdbcbdaacccbdbdcccccabbdaaaaddbbdabadaaabaababcacadbbddbdbcbcaacbbaaaddbcbcdccadabbdbbadaacdadabbbaacbccdcccdcdbbbddadacbddcccaacbbbaabcbbabbbddcaddbdadcbbbacbbadabddcbcadbabdcbaacadacaccdbbdaddcdadccadabadcdabccbabcbaacbbcddcbdabbdadbcabcbdadbbbcaabbbcdbbbdddbcbbdcaabbccbccaabccbaacdcadabcdabdcbabdabcacabaabbabbcbcaacdcdccbdcdadbbdaadcbccbcdccbadcaacabcaabaddadddcbdadcbbbbacbcddaabddddcdabccabbdbcabcacaadbadccdccbccbbacbbabbcbcccdcaddcbdcabdcbaadabacbcdbbdbadccccacabbcbacabbcacadaadaabbbbdacbbbdbacbcacacccaddbbbdabcdbdcdbddbdbdddbacbcabdbdbbdbccacdabdddcabadcabcaabcacdadaabadcdbadbddadcbdcabbadadcccccbcbaabbdddcddaaadddddbcbdaaddddddcaabbdabdbcccbaaaaabdcacdacddacaaaccadcccaddbdbcddddbbacdaadbcabdcbcbadcacadbaaadacaaabcddaadbbddaaabdbcacadbccccadbadcbdcadcabcdaaccdbbdbdaddbabdcdcdbddbabdccdbdbbccaaddbdbcbbdadacdacdcacaadabaacccdcaadabdacaaddccbcbcdddcbdacbacaabdcbdccdcaaacbcbcabcbbddadbbbadccbdcacccdbcbadaddcacdcadbbaccacaaabccdddaabadcdddbaababccccbaabddddcadbadadadcbdbdcaacadaabaaddddadbdbabbdbadabdbbdcabcaaabacaaacddaadcbabbdaaabadcbbdcacacdcdacacddadacdcbaaacaaacbdadcddddabbddbcaadaaccaddabdddaccddbabbaaabdbabadbdbacdccdddaddcacccbdcadcabadbccadacbabaadadbcccdcdaabcbdcacbbbacbdccdcaadaacbaadcbbcbbbcbabddababdcabdadabdcabbdabddacaddbacbabaadbbbcddaccbcbadbccaaadaabaccacbcbabadabadbdcdcddcdaacbbcbabbaaacbbdbcabbbacadcabdcbbccdbacbcabcbccdbbdadacccbdacddcadbadabdbacbabbdcabbdcdbbccadadccbcbcdaabdddacacddabddabdddbdddddcdcdbadcbbdaccdbbacdaabdbcccbcccaacdaddabbbdaacbbcaccabdcbdabcdcaabbcadadbdddadcadcadabdcabbdcbbadaacdcdcaabbcbcccbbddcbccacadaabdbbaacccabaaabbbbddcbdcdaaacabdacdcbaacdabddcbbdcbdbbadccbcadbbaaacadacdbbdcadacbcdbbaaccaddddddbbdcdcabaccabaaadaadbbadaadbdcdddaacdcbdccadbddbaaacccddacacdcbbbabcbccbbbadcdacdbcabcdacacaacabacadadddabacdaddbabcddcccadccdcbbcdddcacbbdbbaadacdbabbdacacdcddcbcbcdbbacdabbbddcdddaacacbadcabcacbdbcacacbacbaacabdddddbccddabdbaacaabacccaadbccdbacacdcbddaccacacacbdddcadbaaddaddbdddaadbbadbadbdcbbbbabacdcbadddddbadcadaadbcaccabacddbbbcdbcccaadcbabbcdcadddddcabdbddcdacccbbcaacdccdbcaddacdddbdccdcabcdacaabaabdaccdddcdabddbacbdbabccdbcaccadaabdcaadbcbddbdcdddddbadcbbddacdbabcddbcbcdadadabdcbcdbbdaadabbadbcddcacbbadddbbcacccbdcbbbacdcdacbbaccbdbabdbdbccccbbacaddddbbdbaaabbccccabcbabcccbcbbbbddabcacbaddabbbbddcabdcdcaccccadcbbcaabcddcdcadaccccadadcbbdadcbbccbdbbcadaaddadddbaabbdadbcaddacaadccbabccaaddcaaabcbaaaaaadbabbaaabaadbadcabbccccdcdcabdbbdddcddaabadbbccbdbbbcbccdcccddaadcbcacaadacdcadcdccabdddbaacadacbcbbcabadbabadcbdcaabbcddcadcbabdabbcdcdcdcdcdbbbadbdbcdbdcdbcabbbcaddbcbdbbdadacaaadccbdccaaccdacabcddcdddbdbcdccdddddbadadcdabdaadadabcbcddaacbcdcacadbbbababbccdadbbbadddababaccabbddbdddcbcdddabbaddacacdacabbaaabcaaddabdababbabbcbbbbabadaacdcadccbcaacabbbbaaccadacbbabbdacbaadacbaadcccdaadbaaacccdacbbddbbacbcbcadcdabaccaabbcddcbaccbdaacdabcaaddabbaaccdbbcbdabbcbccaccbdcadcabcdcabbdbcbbaaacbadbcbacdbbddbabadabcbacadccbcadaccdcacabcccabdbaccbaddbdbadaaacbbdbbcbdbabaabdbbbaacddcbbccbbbabababcbddbcdacdaccdddcbddadcbdabdacadbdddabcccddcdbcdbacadccaccdbdadaadadaacddaddbdcddcddaadbbcbdddbdadccbbbaadbccbbcdabbdacbcbbdbabadacbdbcaacdbbdbaabcabcbacbacdcdcbbaddcdaddccdcbaaacabcabdbccdcbdddcdbdcaaaaabdacbdaabbadbcdadaaaaddddddaadccadaaadbdaabbbdadbadadcbcdddddadbcaacabddbcbccbcbbcccaaaabdadcdbcbcbdbdcadabcbdaddccbbcbbdbbdcccdbabdbdccbbdbdcaaaccbadcbbcababcabdabaaacbbadacbacacabdadccabbdaaddbbdaacbccbbdacbaacaddacccadababbdabbccbbabadcacbaabaccddadcaaadbbdcbdbbacdbccabaddacbacdccdddddbcaabcbbcdabccbccaddbdbdadbccbbcbbcdabccadcbacddabbcbddddaccacaddbcdcabbccccaacbbbddabbbaaabddddcbdabbccdadcdaadbcbcbcdacdbccbdbbbddbccdccaababdbaaaddbdbcccdcddccbcabadacacbbaaccbdccbdbbcabdcaadcdacacdbaadccbdbdbbdccabaacbdcdcabacbabdbcabcdbcbbbbdaaddaaddcccaacbbcbaaacdbdacbdbbcdacccdcbdcbabacacbcbaadcccdbdcadbdbcaaadddbadcdcddbdccabcaadcbccddbdcabdabbacbdadcdaacabdabcddddcaadabadbaaccbbccbcbddcbdccacbaaaaaabbbbcbdacadbadbdbabdaadcbbbabcbadbcdbdddbabdbbaccabcabbbaacbabcbabacdccbbbaddabddcaddabcdaaacbdadcabdbbdadbccdcddbdbadaccaacacdbcddbddcbbdcdbdaaccbadcaadbcddcadddaccdcaddbbdccbbbbaccacaccbdbcdbbcccadababdcccbbbadadbcdccdcdabdcdabbccbcdabcbdddcdbcadabdbbbcddabcdaaacadacadaaaabdbaacbcdccaadbccdbcbbbdadbacbcdcccabbccacdbaacbdbdbacbabcbababddbdaadbaaacdaaaabcddbbbacabbaddbbbababccccdabacacdadddaadccbbabddbacbddccacadacbdcabadadaadccbdddaaddcdddbdabdbdbddbbddbbbbdcbacdbbddddcaddabbbadaadbdbbcabaccdaabcadcdcbadddcdcddbcbbcbcadbbbcbccbccddadbcdcacbabcdbabcbdccbddcbbaabddccbdbacdbdbacadcaddcaddaacaadabbacbadbdcccaadddcddccabcdccddcbbadccbdcbdcbcccbbdacacacbdddbcdccbcbccdaddbbdcbcaccabccccddaadbacbcddccdbaabcdbdddacdbcbadcdbdadacadadbcabbccbbddaacdbabbddbbdaaccbaabbadaacaabaaadbccdbabbddbcabbacccdcdcaccacccddbbdcdadacbdbddbaadabdbcdddacabccbcccbbdbcbcbdbccbcbababddbbccaabcadcbdcdacdabbdbbaadddaccdcaabbbccddabdaabccbacdadacccbcadacaabaaddcbbaccdbbbacbccddcbdbabaadbcbbdabbdbbcadabacccaabbbcacbacbcdaadcbcbdccbcbdadcadaadbaacdadbcdbdcdabcdaadbdadbacddcddaadaacdcaadddbbcccbdcaccabdabdadcadbccdacacccbdcaaaaabbbbbbcaadcaaddcbcddcadbdaacbabcaccbabdabdaccaadbdbdbdacabbdddadcbaaaaddcdbdbbbaaddbcbabcbdcabbbbdccbbbdabbacadbbccbdcaacbaacbccbabdacddcddcabdcbcadbdacbaccaaccbdcddbcabbcabacaadcddbbcaacbcbaaabbacaadbaacabcacccdabdacdbcbbdacbddcdcdbcdbbdadbacbcdacabbbbadcadcbbadddacdcabaaacbdcbcaccbdccdcbcacdbdaacdbcbbaaabaabaabcdaadadcadbdbbdaccbccccccdadadbdaddbabcaaaadaacdcbabddddddacdcddaadcbddbdbdcddcaddabacdabccadbbbabacbacbadaacccaadccadaddddcabcdcbbcdadccacddcbbbacbdcdcccaaacdacdacbaddbbcacdccbbddcbbbbcbbcacababbbbbabbaadbbcacdddaccdaabdaadaccbcbacabadccacbabdbaaadadbadadabddcaadcadcabccacadcaadadccbaadcabbdaddccdabaabbcdbcdcccdbbcadbcacaaaccbbddbdbadbbbdadcbdddbdccccabaaddccadabdccbbcbbdccbdbacdbcdbadcbdacccdbbdcbdcdbdbbbdcdbdddacbacacdcaaaadadabadddddcdbadcdcbcddbbbcdbdcbcbaaabadbadacbababdbbcccdbabacaaabbdbbabbdadbcddccccacbaabbdacdcbbbdabcadcaaaacdadbabddacaabdddccddbdbcbcdaabcacccabcccadddbbbbddadbbcbadacddbaabaaabbaaaabbdddddaadcbdbadacabccaabdbadcccadbbacbddccabdabddabbdddddabdbccbcbdaabccddbabcbbbcbabcbcdbadddaacbbccdcccbcccbdcbbcdcaccbadbaaaddcadcabbacabadcabdacdbbadcaadcdccabbadbbbcaaddddbadadcddddcbaccaacabaaddcbaadbddadbcaaababdabcdbcdbaabcccadcdbdbdbcbdbabaabdbbacdabcabcbaabdcbbabbbccaadcaaadbbcccaacbacbadbddccdaacabdbddcaccbaaccbbddaadcaacaadaddbcdddcabaccacbbcabbbadacadcdabcbcbacbababacababdcbbadaaacccdbcdcccaadbdcbdabddcccdbdabaacbdddcdbabcddbadbdcbdcbcbbcabbaadaacadbcbcabbddaacdccdabbdddaabdcbabbdacaabcaaaacaaaaadcccaddadabdaddadddadbcadbacbacdddacbdbabcbbaddbbdabddbcdbdccddcccccdcabacccadddbabbdaadaadcdbabaadabbdbccadaadddccdcbbaaacbaccdccbbcdccbabdbcabbcddddbbcaddabdcbdadabdcbdaadacabdbccbaabcbabacacbcacddddbbbbadbcbcdabddbcababcbbdbbbccacdbbcdbbaaabccddbadcccaccbddabccadcbccbddbdbbcbbaaaadcbbbaacddaddaaddacdaacbbdaacddccdccababaabacddcdcdcccbdddcddaadaacadacbcdbdddbdccbbaacbcbcddcbadcdbabbaccbdadcdbbdddbadcdbdbbcdcddddccbaaaabdcdcacaacbadbdccbcadcadabacabcccbcdaabbcddcbccbbbcbccdddbbbbdbcddabadddcccbcbbbdaabcaccdbabbbaacdcbdbdcddbbbacdbacccbccbdbccbbabdbcacbcacddaccddaadbdcaddbbcbddcbbddaaccddadbaaabaddcbbbbaccbacacabcdcadcdbbcacbabbdbadbbabababbadbbdbbcaccccacbdccddabbddccbacdcbacaadddabbabcdadcbabdbadaddacbadadbcdcbddcccabbdadacbdbcacdcaadabcabbcddccdbacacdaaddcaadaacbabaadbaabcdaaccbbdacbccccaaaaabbbabbbbbabcdcbcbcdddbbcaacccaadbababbdadccddbdacadbdadbbdbdabaccbabdcddacacdbcbdaccbdbdaaabcabdacaddcadbacdcddbdddbbcacddbaaacbacaddcbcdbbcdccddbcdcabdbaaaadcdaabacdcadadadbaccddcbadaacccaabcbbbdadaadabcdccaccbcccccaadacdbcbdcccdddbcbaacdbbacdaccbbbbcccccdadddbaadbbdaaccbadabcacadabbbcddaadcacddcbcccadaddadcbcdaaaaccdabacadcbbbabcdcdaaccccccaabcbbccadbddaccddbcdddbcbabaaaccbadbcabbcdbcaadabcacabadcdddddbdaabadddbdcbaacabcaabcdbcccabbccaacdbccabccdbabdcdaaaacddddbdbccadbbbbddddbcbbdabacdbabcabdaccadcdadddabdacdcdbacabcddbbaacdcacbaadcdcacbccbdcbccdddababbdbbbcbabbabadaadaaccccdadbbbcccbacbcdacdbaccaacaaadbdbaacadaaddcabdbabbaacddaaddcadadaccbccbbcdabaacbdacbddddbabcdbbbcaaabdacddabaccabbacdcaabacaddaacaacaccaabadcddbbbabcaaacabddbbadbacdabbbcadcabddcbacbadcababdcccddcabcdcdcdcccabbbcaaadcbaddacddcbbcadbbdbbddacaadbdbccbddddbdbbbcbbdadabababcdacbcddccaddbbbddabadbdaccdcacbdaacbadacddbacdacaadaabaabbbbbbdabadaababbcddabbbbaccdbcdadabadcdbbdaaabbdbbccdbccdbcacccdcaddcabbdcdddbdbbdbdacdcdcaccaabddbcbbbabdbbacbdabcddcccbdddadcbacbcacbdbbddddbbaccaacbcaaadbaabacaacabbaddbccdbabbbcdacccdacbccccbbbdbbddacaabccdabcaddcccacbaaadccbccbaaaddddadabacdaaddcacadbabcccdcbbaccdbacbabdbbbdadbadbbbaacbbbcdadcacaddddaabcbbaaacdcbccccbccadaacbbaccbbdbaababcdccdaadbdcdbbdabccabbcdaddadabcacdbacadddabbcaddadadcaccbbbdcabbcbccabadcbcdadcacabddabbadcadabadbcdbddccacbdbadcacdadddbddcbdcacdabaddcbabddcaababadacddaacbcdcddbcddbcdadcbcdaabdcdcabaaaabccdabbcadcabaadbdbadcbdcbaacbcdaacbdadbabbcdabacdabddbbcbbddaaacadaabdbdacdbbadbbdbaccbdadddbcabcccddbcabcdcabbabbdccccaaadcddbcbadccdddadcaddcbcbabddcdcacddaaddaddcccadaddacadcdcdacbbbccbcbabcdbcddaadbcddaaddadacbbaddbcddacbdaddaadbacbdcaacacacdadacaddddcabdcccadcddbcddbacbcbdacaaccbcccbaacabcccdbdbcacdddadcddaadcbbdabbccdcabbadbabbadadccacaadbddbdcadaaaabdabdaaabcbccacabdaacbbcbbcacbbddbcccabdadcaccbccccaaabbcabddcabbcbdbbaadcabaaddcbdcaadcbadccbbabcadaccdbdcaaccadbddbbbaaccadacdbccddadacdbacdbaadbdccadcbbadabdabbcabacabcbaddddadabdbcabbbddbcaabcdbddbbadddcbbbcadcdacbcdbdbaaadccbdbcbbbccdddcadcdcacdacacdbbbbaddacdabcdacdccacdcddaadcdccabcdabaccdcacbdccbacdacabccbcddcbcdaadcadbdccabbbaccabcdcbcabcaadcaaddddcdbbbcdcdcdccdbbcacbabcacadcdaccabdcdbbcacbcbabdaababbbddccdcbcdbdddcddaabddcdcddcacaddbbaacbcbadcaababdcacddccabbacbddababbddbdbdbdcddbdcacdbcbbdcddcbdbbddddcccbcacabbcacaaadccdadaacdadddbbcdaccadcccaccaabdbbabaccbcbcadddacbddaaababdaabdcdbddbadbcaaaababdbcabbdcabaabcbdbababdddbbdaabcbcdcaabddddbbaabaaabbdcddacccbacbbcbdaddacaddddababdcaaadbaaaaaadacabdadddbcdbabcccaccbbbbbcacddbdabbcabddbbaabbaddbaabaabdcbcbcdccbaabcabacdbdaacdbcccbaacaddcbdccacadadcdacacabacccacdcbcbbbaccdaaaccaddbdcdbaccacdcbcdccadcadbddcdbaaabdaddbddcaadacddbabadcadcadabddddddbcdcbacdcadbdabcbbdbbadbddddcdcbacddddcabbbadbbcabddcdbcdcabdbccbddadababcaadcacddcbacbdbdcccddbacbdcbcaccdacadcadaddacaaccdddcbcabbdcdacbdcbccbccbaacaaacdbaabdddbcbacbaccdcbabbbbcdbddcabcaccbcbdadabdcddbccbbdcdcadbbdaabbbccbbbbdbacaccbabbbdcdcbbaddddcaddbbaacdadbabdcaaadadccccacacccaaabcbbcbbababcbcabbadcbdabcccbbabdcdabacdbccbbdccacbdddcbdcacbcaaabdcccbababbbdbcbadcacbdcdabcbaabdccdaaccbdaadacccbbaccbadbcabadcbbdbaacbaabdcccbdccbababbdcccadbdbacdbbadcccbccddcaaadccccbacbcaaaacdddbdcaaddbabdccacccdbaaacbadddaacbdddacdddacbdaddcddbdacdbcdadcabdbdaccbcdbdabbcdbcabcdcdcadcadabdbbdbabbadddcabaadcababacacbbdcaacdacdaaabbccaaccabccabcbccdaaaadaaaddadbdcababaabdabababdbcdbbdcbbbbbbaaccacaccabbcabaabcbbcdccccacbdbdcabbcbbdbdddaacdcbdadccbddccabcbcababcbadcbccacbcdaddbabaabdbbbcccbbddbdabdccabaabadddcaabccabbdbbacdacdcbbddbdaacacbbacaddbcadcacdadbdabbdbcadcddbccbabcbcabadbaddadbacababdbcbbdbacbbcdccabbcbbadcccbbbaaaccccabaaacbbddcaaacadaaaabbbcdccdcdbcabccabbaabdaaadccadcbdabcdbdcdcdbadcbdcbcacbcbcccbbbdbbbabcbddacabbbdacaabbdabacadabccbbcabdbdbbabdbbabdacbabdaddacddbcacddbdddcdabcaadaabbdddadcdbbddadcacadaabcdcbaadaaddcadcbdcbbbbdcdbcbdddbcaccbabdcbbdbbddbabdcabbdabadabaacdbcdbddadaaacbdbbbccabcbdaaabcbbcddcdbdaabacadddaaddbbccdbdabbadaddbcabbcbbdaadbbdbcabcdbdbbadcdacdacbbdadbaaacbdcabcacbabbcccdcbaacbacccacacbacdabbcbccbdaabbaaaaccaadcbcadcaabbacadabacabbcccdccbddbcccbbdcddddbdbcacdbdabcaacaccaaadbadbccaaacdaccacadcddbddaccbdcadadadbdcbbcabbcccdadabbdaadcdbcdbbacbabdaddbbacbdaccccbcbbbcdadcbcacaccbaaadcacccbdbcacbbcdabadacdbcddbaaacacbdbcaaddaddaccbbcbbcadbbbcdcbabaadcccadcadccbbcacabdabcdcabddbdbdddcdcdbdbdccaabddcbddadadaaccbbdacadaddbddbdbccbaccbdccbcccdcaddacadacdbdcdcabdddaccccbacddbbbbccaaadddcdbccdaaddabbcacabcaaccacbdcddabdabbbbbdcdbadcdbdbdadabbcdcddbdcbbcaadddcccbbcdbdcddcabcacadadcadaadbbdcdddbaabccadbaaacaababccdcdbbcbcddbbdabacddadbbaccabcbacdadabcaacbdcccabdddbbbcabddcbdccbcbbaccbbacdbcdaabbdcacdbddddcaaaaaabaacccaabbbddbadcddacbaadbcdcabbaadaadcadbacdbbadccadbdbadaddbbbdbdadddbbcbdccddddabcaddcbbcdaddddcddbadaacadcaaaaacacbbacdadcbaadacabaaababbcbdbccdacccadddbabcbdaccaabbdaadaacddbdadcbcdbdcadcdccbacccccddcbbdcacaaacbbdabbadcbaccdcbcaddccdacacdadabdadccdddbbbcbabadadbadddacdadcadddddcadacbbcbcdabcddccaababbaaaadccaabbbbadabbcadacbaccabdcacdbaacabacbcabdcbabadabdbddcddabdabadcbcadcdcbccdbcddaccdbccadaccbdbddccbbbadcdcdadddcbcdbcacccccccdadacddacbdabdbbacdaaabacccdcadbaabaacabbcacadbacabdbbdabccaacdabdddbcabdbadbbdabdddddcaadabcdadbbabcdbbbbbbcccbdbdcdcdacbacabbadbacbcacbcccbbcdbbccadaaaabbcdbcabacdabcaabacdbccddcbabcddbcaaadbbdddaabaabbcdcccbbadadbdbabbacbbcbcdbbcbddccbaaaaccbddccdcaddaacbdbcddbaaaaaccbabbccddbabcbcbadbadccddcdbccababbaacbdcdccbcdaddbaddcddabddadbddbbbccdcabccabbbbabadbcbdcaadddabaddcdcdcadddcddacacbbdabbabbadbbbbcacbcbbbccdaaadacccbccbcbbddcbbbdadddadddbabccaaaacdbaaadbadcabcacbadddcbccadbdaddccdaccacdcadcbdbddbbbdacbaadcaacbdccbdcdbabcacbdbdcccaddccdbddbdbdaacddbcacdacaccbbdcabcddacbdcbdbdabdabcadbabdddcbdaccdcddcadbbdaaadbbcacadabddaaacbcbdddcacadacbddcadbaabbbabcbaacbbdabcaddaddbcadacacabdcdcadcdcdddddddaabbdbbddbaacacbbabdabccbaadacbdaadbdcbdcccdbabbcaaabcdcbbaadacbbdbdaacbbbaddbddbcddcbadacabaabbdabccdacabddaabcacbdcabaadcbdbcadbadaaccdabaddabbbadcdadbbcdbdbddadadadcdcdcabcddbcaaddcdabcacbbbcbdbaacbacddddacddbbacccccaabdccabcdcadbbcadacdddccdadbacbbcdbadccbabdbbdbccbabdaaaacbdccbccbabaabbddbbcdacaaaaaaabbbaadcbadaacaaadbccaadcabadbdadbdbbcdbdbccdbdcbabbdbcdbdcbdacdbcbaaacdcdadaddadccddcdcaaddddcbbaadccbcaabbbaacbccadaaabbbccdcddbaddbccbbadccdcddbabbdcdbaccccdabbacdcddbbccccadcabdcbbccbbccdadadcaddacdabdbcdbabcbcbdaabbbbcdcdacdacbbcdacdbabdccdbaaddcddacddbddacdaaddaccdcbcaaabadbcabddbcbccadbdddadacbdacabdbadbccacababbaabbbbbaddbbbdccbdbbbdbbcaaaadcddccacbbdabaccdabbbdbcabacbabccddbaabaadadcdadbbdabacdaaaaaabadddabdabbdadabbcccdbcabcbcbadccabccbbdbcabbddadbababcbdcacbdbccaacacddbcbddcdacdbadacbbccadabbdcbcdbddaaacadaccdadbaacdbcbddcccdbbbcbacccbadabdaadccbbbbdcbdbdcccbabdbdbdbbcbbcadacbbbbcbcaaddcdaaaabacacaacbdddcbcbadaacbdaabadcbbadaccbacbdabddbaaaacbbcbacccaabdabdcbcdacacdbabcbaddbcbdddccaccbadcbcdcbdbbbdcdadbbdabdbcddadbdaccdaabcdcaabdddcbdccdddaabdaccdcaccddacdbcddbdadbdcdbbcdabacdacabaaacacdaadbabaacbcabaacdddababacbccdaccddacabdabdccaacadbabcccdcbaaaacaddcbaccacbdaccdccbabcaacdbbadaabbdaacdadcddcaddbbdcdbdaacadccbbcddacdbcabcddabcabdbbdabdbdcdbdbabadbbdcabcbdbdcbbcdababaddaabcdcacdadbdddccbdbaabbdaaccadcddcababdcadabcdccabddccabadddbccccaccccbbddbaacaabaadcbdcccbacbbbdcdbbbcdcabaabccabadcacdcdbaadbadadabdccccccbababdccccaaddacadcbaaabbbbcbcdabadaaaaabddbacbdabbaccccbcaccccaccbbdccabdbacadccdbcdbbbbbbdacbbccddadaddccdabccacddcacadabdabcdbcccdbbcabbbddbaaaadadbcdaaaabcccabdbdccbabaadbbcdabdaaccaacdabddbcdaddabdcbaaabcdcbdbcbadcabaaabaadadbbdbdabdbdbccbdbcdabaacbdadbdaabaccadccddbdbdbdacdbacdbcaabcccbdbbbaaccdcbdddaaddbcbcdaaabbcdbcbcaabbcccccadaadcbdccbadccdacddddbccdccbadacdddbadccbaabdddacddbcaaddbcdcdaadacacddadaaccbadddadadabcabbcbbaaaadcabdaabaddabcbbdccdddbdcbbddbcbbccbcbdcdcadaccdcddbbdabacbdacacdadddbdbaaacbaadcbabdbbbacabaddaacdbdadababbcbccdaadadcddddcabcbabbbadcdcaacccdddbadacababadadadcacaaadbbbbdbcbaabbaadddabdbcccbcdbbdbadcaaabbabaaccddacbbdabcdbabaadcccabbdababcaccbcbbbdcdbdcbabcbaacadccadadbbadbdcdbaabcbdacadbccabbcadcdaaaacdadddaacbcaababcabbdcccdbbacacdaabdccabdcdccdaadcdbbbbbdcaaaadcdbddbdbbdaaabcddaadaddbbdcdadacabcdadbdcdadddbabcbbbdaadcdacbcaadbddbbabaccdcadcbdcbccddadbcbabcddadddaabbbbcbcddadcdbdcbacdbaddcacddddadbaacadbcaadcaacaacdaadacaddaccddcabbbdbdccddbdcdbbcccacadcadadaabcbaabdcbadacccccabadbdacaaccbabdacbabbbaacdaacddcdaacccabbcdcaddabaaacaaababbadcadbaaaccbccaadbacbbccbacccddcacadaaacbabbbdaddaccddabddccbddbccbadcbbbbcdbcbdbddbbcabbdbbdcacacccdcaacdccadcbbabdddaddbdcdcdaddbcbbdacbdbbabddbdbccadabddbcacbdbcccbcdbcdadcbcbdcaadadaaaadccbdacacaacbadcdcbdccdbadddacbbbddcacbcaccbabbadbddaacaacdbdadbdbacaaabbddadbcdbacbadbcabdcabadadbcaacaabdadababaadbaacacadccdbcbcbcdcacaacadadcbbbbdcbabcbcddaabcbadaddadcdccdbdacdadaddaadabbccaccadababbddaacdaababccddbdbcbcbacdcacdbcbccadabdcdcbcaddadbdabbdabdccadbdabdbabdabbdbbcabbbaadccccdacaddddbacccdbbabcdcccaacdaccbadddbabdbcccdcccddadcbcbdabacaababdaabcbbdacccdabdbddaabcbbaddcdadddbcbaaadcbdaabdbdaaaadbcacabdcdddbaccadbbbacbbaabcbdabacbdabdadabdaadadcdccacdaacabdacbcbcaddbdcaadaaabcaabbadbcadcbbbbacbcbacacbbbdbdddbdbdadbbddccaccdddbccadcbddcabcaadbccdadbadccbcbaccddccddbdbcdaccacabacbdcaddaacbdcccbcaccddaccbbccacacdbaadabadbccdaddabbdaadacadbddddcdcbbbdcbdaddbacdbababaccbdbaabccacaabbdccdbcccabaddcaccdadbdacacadbadcbdbbcbdabdbdbaabddbabcdbbddbabbdabbabcccbbabbcdabadbdacbdcabaacdadbaabbdddccadcabdccbbacaccdaddacbdaabdcccaddcccbaddacbbbdaababccccccabdddcbabccdbdbccccadccacbabaabccbbbcdabaccbbbadaaccbbdabaaccbccabccaccadaccaaaacadcacbbdbdddbdbdccaccabaabadddbcdcacdcdccbcdcbcadddccdacbcbccdddccbcbdbccdcbcdcddcbcbdcbaccbacddbabbabddcbbdcbaaadcdbbcbdadcabbddbcbddbadccbabdacccdaaaaacadcbaaccdabcdabddddbcbdacddaabbaadbdbcdababdccdbaacbdbdabbacbcabacdcabcdcdbbbdacbacddaccbddbdaccbbcdcadbcaaaddaacdaabdddcaccaddaccbcdcaaabcaddddddccacaccdccdabacbdddbaabcdbdddcbddbcdcaddcaadcaabadbcddbddbabbbccdbcdacadbcdbbbacabaadaacaadbcbcdcbaddbdcaabaabdacbbbadbaaddcccdacbbcbcdbddbaaaaacbbcdcadbbaaaacddcacddcabbaaadababcdaabbdadbcbbacbddbcacbcccbbaabdddbadabaaccacaabccabcdcbbddbdbabdbccbcaccddbcaadacadbbdbbcdbdbdbcbbaaaabdccaababbbdbdccdaccbcaadbbaaacdadbabbdcdababacbbddbddbaadaccbbdddbccccadcddbdcccdadabcccbadacaadabbbcddaddcbcacbdacbcbdcacbdbadbdbdbccaacdabbaaddccbdbcbacdabcbacdcaacadbacbbcdcabbbbccdddcddaddccdcdcbbcbdcddadcdbcdaabadaadbadbddcdcaddaacacccbccbcbddbdbddbaaddcccbacdadacbcbddddadadcabaaadddbbcbdadadaaacbbcccbbbccdacccbabcddaaadaaabdbbbbccdcdaadabdbdadbcbcababacddbbdaccbcdcabacccccdaadadddaaadacdcdddccbbdabbcadbbdcaacabdddaadbbdabaadbbdddbddcddcdabbcaabbbccaddbbccadacddbadaaadcdcacabaaccabadddaccacbbbdbcccdaadaaccddaaaabbdddccbbccccdbddcddacdacbcdbadacabaacabddcdaddcadabcacdabccaccdbdbdaacbcdddddabdbabddddadadbbbacbcaccacadbaaaaacacaccacdaddaadbbbcbaaadddbabcbccaacddcdadbacaccdaabbcbcdadbbdabbcbabcaadcaddddbcdaddcccdcacabcacbabadbcccdcbaadddcddbcacaabbdbdcadcabcdbcddabbbacdaacbddbcdddcdccabcbcacaabcbbcdcadbdcbaaccccadddbaadbcbaacabdadabdacbccbcccdbacddaabdccddacabccbbaabdddbbdcbdbdcbacbdcaabaaccadbdadcaadccddbcddbdcbbabcbddabcdaaabbccacdcadcadadacbdcacccaadcddcccadbccbdbcbabddccaaaddbacddaabaaababbbbaaaadabdbcbbcccdaccbbbddbbcaadbddadadcaaaaccacadbdacddadcacdbdbdbaaacdccddacdbdbaabadaaaaaaaaaaabcacdaaaadddcacaddcdaacabbbabcadacbbabdbaaabdaaddbaabadaacadbbccddbadaddadabacaaccdddbbdadaddbdcdccbabdaabcbcdcbadbaccdcabaaadbcadaadabdbdacacdbabcddacbacdcdadaccbdbdabbbbbdcaacaabdabcbabacdcddddbddbbddaccccbccbcdaadbbdcbdbbacbbabdcbadddcdaadadaadbcbdcabadaaccabdbbdadabbcbbaabcdcdcadddcaacacbdbaaababaddadcaaddbadaddaabccbbdbdbaccdcdaacadbcbaaacbabdacbdaaabccbbbcdbbdabcbabcdccadbcaadbccbbaacdbadcadddabadcdcdccddbcbcabaacbdcabdabaabacbdcbbddaccccbaccaddbaaabdbbbddcaacadcbbcddacdcabdbccdcbabcbabcadcacacdadabdddcbcddbcdcadbddcacddbbbbabadbdabcbdaaababcdbcdbbcbcabcdbaacaccdaacbdaabacbcdaadabdbaaddadcadcabaaacdccaadbdddacbaacbcdcaacdaaaadbdabcabbbcbbcacaccddabcbcddcdbbbdbccaaabbcbdcacabacddbdcbdadadbdaaabdbddabaadbabaacdcbcbaacbddaabbaadabcdcbcabccbaacacdaccdcbdaccbcbbaacccbbbddcbcdbbbcccaabbacbadcbcacaacbbaaabbbbbbccbbdbdcdbccddcbddbacaccbcbbaaaabcdabbadbcbaabcddcbcbcadddcbbaadbbbddbbbcaaacddddadcdcaddbcdcabbbcdcdbccccbabaabdddacbdbaaacddcadcdbdbcacbabaaacacddddbbbacbdaaabdcccabccbaadddcabbdacadaabdcabaaadccacddcaaadddbcdcbdaababbbabdccbccaacccbcccbaaadacaaabababcacaacbcababcbbdcddbcdaccadcbadadcddcccdcaaaaacaaadaadcbdacadbbbcaaabcddbacdddbdabdddaaaaacdbdaccbaabbdbdddcdcacbbbaddddacdcbbacbdabcbcabbacddccbcbccdcaadbabccbcdadcadcccbcbabdccbbdaacadccabdcdbbcaadaadccddacacddcbdaaacaccadaccbacddcbbdbcbdacdaabccdcaaccdcacaacaadddbdaaaddbcbbcabdaccdbabbcdcdbbcddcbdbaaccaddccdacaabbadaccbbdbbddabaabaabccccadbdcdddcbddadcbdabdaddacccbabbbcdcabadcbbcaccbcabcbaadcacccbadbcddaacadabbcbbbdabcaccaccbabccdacbacbcadaaacbbcdcccbcacacbbcbaabdadaaaabbcdcbcdbdaaccccbaddabccdccbdcabdacddbcaacdddcbadcaccdcccbaacabbcddaacdaadbcbaacaadddbbdbcaadcbadccccadccccddccbcdbbcdddbaacabbcabbacdcdacadddddddddbdaccbbadbcbbcbacbaacdaccdbdbdbdcbdadddaccdbaabdbabdcdcaaacbcddccbaabadccccdabcbcbbdccbddddbdcbbddaabadbaadcdccaccacdcadbbdabddddbadacddcdbdbbccdbabdaabadccdbdbccbdaccadbaaacbaddddddbbcbbacabdacbadabbbbbbdaadcbcdbbabaadaaadbadbcadbdaddbdbddbbbbcbbcbabcbacddccdbbaaadccccbdcccbabcacbbbbabcdccacccbdbdbbbaaccadadbbcdabccaaabacbdaacbbbdadaaabcccdbbabbbdaacdbdbcaddbbbccbdcacdbccccbbbcbbdbbddccabacbaaabdacddbabaacabdbbdadcbbcdcbacdbbabcdacdacaaacccdcdcbbadddcddaccabdddbaaadccbccdababcccdcbbbaadcbdcaadcaddacdbdbacaddbddcadadccdcaadadbbdbabdcacbababddcdbdbaacadbaaabbaacbbaabdddbbdbaccbdcbabddbdcccaadcbacbcbccbbbdbdccbcbbddacbbaacbcaabccdbdaddccbadcabadadcadccbabddcacdadacbabaaadabcaacabdaaabbaabacdbbaccbbddcacdbcbadbcaaacbdbadbbcaaddddadacdcdcadbcabdadadccadbdcaaabdcddbadadcdbdccaddccdbdcaabdacccdccacdbbadacaaaaababcdcccdbbdcabbbaadbabdbbbcbdcdccdcabbbacccdcacbcbbbccbbadbccacbddbcabdcddccadcbadabbbddbbdcbdddacdcdbabcbcacddacbdcdcaddccdbcaccadabcbadabcbdadbabcdadcdbbcdccbbbccdadcdacabbcabbdacbcbbdbccacdaddbbabbdddcdbbabaaadbccbcdabacdcdddbacbbadacdbbbadbdccbdadbcdadcbcbacccbaacdcdcaacbcdabdbadcdcbaddbcddbbadbdbbcadcbaccbdbcccccccbaacbccdccdbccadabbcbdaacbacdcbdadbddbcdddcdcdadaddaadacbdbdcacbadaaacdbcacbadacaacccbcaaadbcadcbccbaababdadcbbcabdddddbcacbbaccbdbdbdcbcabacbbcaadcbcdbbbcdcbbcccbabadcdcdbacbbaaaaadbaadadbacabadabaddaabbbbaabcabccdcadcbcaabdcaaadcdabdcadbbdddcbcbdcbcaacbdbabadddbbcacdacccaacbcdacdabddbaddcdcbcdabbdacabdbbdbadbddbabbccccbccbbabbcddbddbcbbabccccbdadbcddbdcaddbcdccaccdccccddbbdaadddbabdbcbabbdcbaabbaccbadaddcdacabaabccaddbdbcdadcaacdabbdcbcdbdbdcdbddbaaabddcdbdbdaccabaccdccccbcaddbaaadcdabccacdccbdacccdcdbbdcdcccacabaacdcdbdbbcccccbdbdcdccdbaabbbaabdcbacddddbdcddddbdcccacabadadcbdadaacbbbbadaddbbbbddbbaacbdaccdbbacbdccbdbbcbdcbcabbdddbcabdadccdadbbddaadcdbbcbbbdccccbcdddabbcaabbbddadabbdbaabdccbcdbdccbbdbbdcbbdbbcdbcbbdbddddcabbaacddcbdbaddabcacacddbcabbcabddbcdbdbbadddbdddcaadbbcdbddbaaddacacdacbcdddcdcdbdbcabdcdabdabcabbcaadadcddbbadabcbdcccdacdcdaccbcaadadaaddacacadbdaddabddadbabcaaacbdbbdabbaabbdaacbbabcddddbdbadbddcbcabbbacccddadbaddddbaabcbbddddccadbaabdbdbddacadaaaacdadbddcdddccbbdbabcadcdcbbbcadbddabcabbdcdbabbbdcdbcabcadcabbcaacccbaccaabdabadcdbdabdbbaaddcdaacabcacdcdbbacdbabbbddaadbddbdcbaccacdacccddddcabbddcdcbbbabbbcaadbddabcbcddaacaaacabdabcbacbaaabadadadaaadaaccccacabbacacaaadcbcaaacddcbccbacbbadddabcbddbbccdbccabacaabbcabdddbbbbcdaacabbdcdbdadcbdaccddacbbcacbdaadddcbdccdacdcdcadbcbbdcbabaccabddbaadcaabbdababcccababbabdadbcacbcccbbdcaabbccddadbddabddcdbacddcccdacaabcdcdbabbccaacbddbdbbacbaadccbbadccdddaababcaacaabbcbbdbcdadabbcabcbadabadcbdbdcddadcbccbcadadcacbbababdcbdaaacdddcdcaabaaacbdcddabcdddbacbcdccbdcaaacdaddabcacbdacabdacdcdbaaaaddddbabacdccabaacbabaddabddacbcbcccabcadadbbccccbabbdbbcdaaccadacadbbddddbcaccaabacabaaacabcaabcaccbbdadcdccacbacabbddbbabdcbabcbdacdacbdabbcdbacdcbaabdbcbbaddcddbcbbbbdbcccadcddbbccbbabaacdadaadbccbdcbaacdbbbcdccbbabbadccacccbdcaccccbcddcbabbccbadddbcbcbcadaddcadbdaccdcaaabcdbdcbccdbcabcbdbcbbddbbcabdbcacaadcbbdaddccabbacccacdddaacccccdcbbbadbccdccbadacdcaccdacdbdddabaaadddcabddbacacdacdabcbacaabbbbdaabacbdddddbbadbccdccdabaadccbcdcadcdcdccbdddadcdaacdadddbdbaaadcdcdbacadaadcdcbcdbbdcccccccdcdbcabdaccbdabadbabcacadbaaccadcddacabcbddacbdbbacdaccabdcdbbcabdcbddbcaaccbbbcbabcaaddbbaadaadacacbbccabddbaaaabddcddcdccaacdcdabdaccbdcccdbcdccdbdcbbaacbccabbbbbcacacabaabbdbaccadcbbcaccbdbbcdbccbbdbbbdbbabbababbcabdddcdbaaabcdaddbdaddabbcbbccabaaaccdabaadbcdddcaaaacbdbbdbadccbcdddbacbdddbcbdddcdbccdddaccccbcbadccccbabcdddbbcdcbbbcbcadaaabbdcddcddbcddaadabbcbcdbcbbdbbaabadcbcbbbcbcbcadcaadbadbdcacdaadcdcabaaadabdbbbaaabbaddadbdcccdbadacddaabaddcbcdbbaccbbacacbabcbbdabddbdaaacddccbadaadcacacccdbdcadcdbbaabccaadbcadbcbcabccdcbdabdabdabdabccadddbcabbcdcbdccaaadaaacacadbadcddddacbbccadcbdcbddaaaaacbdddadadcdcabbcdbadcdacacddadcaacbcddabdadaabbccdcdaabdaacdddabccbbadcdbbbdbcbbcbcddaacadbcdbbbdbbaccbddadbbddabdcdcdadadadccdbbbbccacdbabdabaadccdbaaabdbdabccdbbaaacaaacccabcdbcddccacbcaddbaabdadaaddabaadcacabcbadcdacbdbccdabcadadbcacdcdcbcbaadabcccaacdbcacacdddbdabacbaacbbadbadabadcadddccacaaadcddbcdaaabccaaadcbcbdcadcdbaccddbccbadddbbdccdcacbddbcadabdbcbbbacdabdaddbbacbdcacbadbacbaabaddabdacacbaadaadbdabcdaccbabbbadbaadabaddcadcbdbdaccacaadbddbacadbcaddcbaabaaaccbbaaabcaadddcbddbdcbbbbbcddbbddbbbdaccabacacdcccadaadbbaddcadbdcaccbbbdadccbdbbabaabaaabadbcbcaaddbadcddcdcdddadcaddbcabadccdbaaabaadbdaaadcdaacbbbbdacdcaaccccbbbddbbcdabdabcbabbcdaccadcabacddcbadbacdbddadccaaabcbdaadcddbcabbccbbcdbbbbbcccabddbcbdbbbdabdadbccddbdddadaabdcbdcaccdbbabadddbcbdbacacccbdacdbcdabaaaabadbcbcdcbdbaacbdadcbcadbacbdcacabbddaddccacacaccdbacdddadddacdccbddcaddadccbcabbdcbcdcccabaccbbcaaacdddacdabdbcadacabbcaadcabcbbacaccaabdddbaaccaaacdbcaabcdccababadabdccbadbbdadaabbaadbbabdccaadbdbacbdbaacaddabccadbbadddabddbdcddddbaddccabcaadddbdbabccbdcdbbdcbbddddccdcbaccbabcccdbabbaacdcdddcbcbbaabcaccdcaabcddbdabbaacccddcbcbcddcddabbdaabcabccddcbadabccbccddaccdbdbcabcbbaacbbacbabbbcdcacdbdcbdcdcddcaadcbbdaccbbadabbadadcbbbbdccbdabaababdbdcddcbdaadcaabccdacabadddbdacdcdbbdbbdbcdbabacdbdbddabababcbaaaadcdbcddcbccbcdbbdcdcaccaacbbbdbbaadaddadbbbdddcccadabbaacbdbdcdaddcdaaddbcbbbdcabdccccccabcacdbabcababdbddccadbdcadbcccbabddadbddcbaadccacdbbbcdbddcbccccdadccbcabdccddbbbbaccbccbbdbcccbadaadcbaadbcaddbdbbbcbdcccadcdbccadccdadbdabacbbadddabbddbbcadbbdaababcaaaadacabbbbcdddacadabdaabdbdcbbbcdbcddcbcbadaddcbacaaaaadbbddbcadcdccabdabcdaabaaccaacbcacccbdbbabcdbbbbaccbbbbdcbcaadcdbbbbaacbbaadbbadaccaadaacacbbcdbcaabdcddbdaddbbddccddbddddadcbcdbadaaacdabdbcdddabddcbaddbbbcccbaaddcadcbdbcccdadbcdbadbbdbdcacbadadacdcdcbbbadcbbcbbbdbddadababcbdadcababacdddcbaddbcacaddabcabacabdabdcbcabbbaaddbabdcbadcdbbdcacabdddadddbacbbccbacbaacbbcaadddbbdaadccddaabddcdcddddabdabccdbdbcbbbbbabccbdbcddacccbdabdaccababaaacbdcdaaabaadaddbbdbdcbacdbcbcccdadcbcddcdaadccbcbdbbbacbbbdadcccabacbbbadcadaabddaadcbcbdbcadabaaccaacadbbadcacaccdbcaadcddaadacbaccddbadabaaddbbcabaaabacdcbadabadbdccddbabbcbcaaddcdacdaadbdccdadbcbdadabcbdbdbbbabbcbadabdbacdadcabbcbacbbabddccabbdcdcbbdaaccccbcacacdcabaabacbcdbdabadcdadadcaadadbabddabacbcbadaccccdcadbbacbbdacccbbabccaacaabbaabadbaabaaaabcccddcacabadaaddbcccaddabdcbbcbcabdababbbdbdbaaadbbbdbbcdccdccccbddacdbdaaabdbadbabbbdbcdcacdaddccddaddaabdadaaaccdbadcdaddccbaaaddbbbcccbccdbaddabacbaabbccabddabbcbadbddcbccdcbdbaaccdacacbbdcddcacaabacaddcabdcbaabcbddacdaccccaabcddddbcbbccdbaddaaacaabdccaaabbcccbbabccaadcadddcabbcbbbbabdcddccbcddabaabddcbadbdccdbdabcddaabbcabcbbcabdcacaadacddbcadcdacccbbdcccdaaddaadcbddcbdbbdbbaababdcabbacccdddabdcddbdcccdadccaacdcdbdabbbcdaadbcddbabcdbbacabdcdaabacbbbacdabacbccacdcaaabbdbcddacbdbccdbdccabadbabbdccbdcbbcbcbcdddaacdcaddccadbdadababccbdbbbdccbaaadcddcadbccdacaddbcacdddcabdbdbcdbabccdccdddcdcddbdaccaaacbbdacbdbcdbcaaddccbbadcbbcabbadbbdddddcdbcadbcdadabbcdbbbcbdbbacdccdbdaadccdcbabbcbccaacabbbacdbacbdadaaadaadccabacdddacdcaaccbcddcdcdccacadadadadbacddcbdbcdccadbaddbabbddbbbbdcdbcaadbdaccdbccabaabaabbabbddccaabdcddbabddbcbcbbbabbccddcbacaaadccadaacdddcbcacdabaddaaaccdaacdbcbbadadbdbddbddcddaaacbacabcccadcabcabccaacbdaadbbdaddddcdbdcaddcdadcdcdbdcbbdacbcadbaddcdbbdcccbaccbdbbbddabbadbcdccdbbacddaddddcbcacacddaabdbcaccbadababdaaadccdcccbdaaacccdbbaccbadbccbcbdbcaabaadcddddbaccbbadcbddadadbdacacdadbbddaccbdabcdcbbacadddbcaddcddacacccabdbaccbcbaaddccadbaaababbbdbacbcbdccbdaccbddacccbccbadbbaaabcbccbabbcddcbcbacbdaadaccabaabbadcacabcaccacbdbccbbcdbadbcccdcdcbbcabdbadaabccbbbccbaccaaadabacddbddcaddabcadcddddbbccabdbcdddabacacddbabcacaabbababcbdddccdcddbbaccabacddadcdcbbbaacaabcdcccbbcdaaccccbbadbbaacddcacadbadcacbaccaacccbbbaabdcdabbabddbcabccaacbaadaacddbcaddcbcddcbdcbbbabddadadcadacbccbbdaabadaaadbaaaadcbcddbdacbbabcccbcdbabbcdbdabbbbbdbccddadcadaabdbabdbccabadbdddabddabdacacdbadbbcdcbdcbadcababbcacddcabbddbadaabacbcbaaddcdacaadadbdcabddbacddbbcababdbcdacabadacbdddabbabdbbcadcdaacdcdbbdacdbccdccaaabdddabcddbcdccabbdbabdcaabbbcdbdcbaaacbbdbcdaabccdccdadbdbacbaddcacacabcddccaacdddcdabbdcbdaddcdbbddbccdbddbbcaaacabcbccadadddcccabdabaabadddcccdbdcddcbcbdaaaabcddcccbdbcaabbdabbcbcbccbbadbacaaababaaadadcbabbadaadabaadcbccaadcacdaadddccacdacadbccdadddcdddcabdcbabcabcccbbbcdadadddabaadbcbaddabcccdcbdbdacbacdbcbccdcaaaabbdcabcbaacdcacddbaddcdbcadcbacaaddabadaadcbcacbaddcccbbdbaddcddcccdbabcdbdbbbaabbbbddddbabadaaadbabbcbabcaadbdbdaacdccadccccddabdbdbccdddaccbadcdadcaccabddadcdccbabbcaacdadbbbdbaabdddbacaacabdbcbbbcacbbaabccdcdaaaabbcabcadbcacbbcabbddbdbacbbbcddccddddddaaddababdcadadbcbdcccaadabcdcdacccdabdcdddbdcbdcadbbdbcbcdccddccccacabdacadcbbcdbaabaabacccbaccdcdddbdcddcadbbabaaaaadbbbadccbcaaddbadcccbadbdcdadbbaadbaabbdbcbaddcdcadabcbcbbdccaacacaaadbbabbcbbbccaddaccabcdcbbdbdadbdabdbdcadcdbbdbaacbddababaaacacdadacdcccdabaadbdbbdddbcccacddacddccbbbaabacbddadcdbaaabdcdbbdbcaccbccdcdbcaabadbdcbabbbcccbddabdbdadbabbdaacabbaacbdadcdddbcaabadcdccddbbcabccdcaccbdaacbcbbbcaddbabbbcdaaabbabcccdabdacaabdadaadcbaacdbabcdddbbacacdabbdaadbabbdbcbdabadbdcdccdaddbbcdbcbccaacccabbbcbddabdababbadbccacdccbacdaccabcddbbbacaddadcabcacaabaaabdadcabadbbdaadddbdcaaaabbaaacadccdcabcccabddbddbadcabacdbcbbbbbaacbbbadcaadbadadccabbcabddabacbcaddbaaadacbdbdabdddcdbbcdcbbcdbcdadccdcbabddcacbddcdadbadaabbccddaccacabdddcbbcdccbaddddccacddacccddcaddddbccccadacabacbbacddbbcbaddbcbcdbaddabdccbdddadcdbcdcbbbccabbabbadcddaadddbbccbbbddbbacccbccddbdbcbaacadccbbcaaddbbdcabdbbcdbaadcdaabacabacbbbaddacdbadcdbaadccabadbbbddacbdabbbbcbbcabadbcaacdadcaaadaababbdbcabacbcddbdbbdbdbcdbccdbdadabcaddbbaddaaccaacccabbcaccaabaadbbbacbcddbbbdadacabbbadbcdbbbcddbddcbbcbabdcdbbbabaccdadaacbdcdcccdbabcadababcacabbababccbbacccbcdcbdacaddccbcccdddcacacddabbdbdbddbaaaabdabddccbbbbadbbdcadbbcbdadcbadabdabbbcaaabbbaddbbcccbaabdbcdabcdcbccdcddacddaddcddabdbaccdbcdddbaaddbbbdabaccbadcddddbbacaaadbdabaddcabdacdcccabddabdcbbddadccbcccdcadddababcdbdabaabbdaaccbaabbcccbbbacbbbccaccadaadbddcddabdabacdacbddbcaddbbadbaaaadacdcacdaaaacccdabdcbccbcaaababddcccddccbdbcbadcddcdbcbbdbaadcacabdacddabacbdbccacdababbadacbabdbdbadbbadbdbbadaabcadddcacdabbdbdbadbcabdbbdabdbabaddbbcabcaddbbdbcdbbbbbdcbaccdadaaddacabddbadbbcdbbbbbbdddcdddbbdccaabcaacbdbbccadcaaccbacbdcdcaaabcaaddccbadccddbbccaabcdbdbbabadbdcbcaacabdbddcdcacdbcdcbccbabacbacbabaddcabbdadaacaaacadadacaaadaacccabaabcddbdcaccbccbcdccacccadacdaddbcbabdaddacbbaabccdabaadcdcccacbdbdbcaccbcdcdbdbacacdbabbbbcaccdbadadbacabdcbdcbbacacadbabacdabbcdddbaaaadccccccabdcaadddcbaddddcccbdcdbcacdbcaddadacabdadbddbacdcacddabacbaddbacabddcbcdbaabadcbbcbcddabcbacbadadcabcacdcabdccdcaabcdbcbdbddabaacbbcbbdbddcbacccadaacdaaadcbdcaabdcbaaadabdbaccadaaaaadbcbaccdcddabdddadcdbaabdadccacadcbcabcbbbcccccadddabcdbdcdabadccbccaabddbcabbdaacbcddbcaddcadcbbdaddddadbbccbaddadababbacbababcbdaacaadaaadcddbcdbcbbabbbbabdcbccadccbddbdcdcbddccdccddbbdacdcccbcdcdbdbdbdddaddcbbadbbbbacccacddaccdcbdbcdabcdbdbcccbdcaadbcbdadadbcbbcdbddbcaacadbdcccacbdaababcccbbadccdaccbbadabacbaccdacdcacadcbadbddbdddbdbdccbabbdbcaadabcdcccabbaaabdadccadacbddcacbcddddbcdbcaddabbbcddccabbcdaccdaaabdcacdbaddbccbbacdbbccabcbcacdadbabbccaacacbaaddcbcadbcbadcdabbcbabcbbbdaacbdacbdbbddbacdbaaccbccddbbdbbdcabbaaddacaaaddcdabcddccaabdccbcbdbadbdccdcdacccbdacdccdcdccabbabaababaaddbcaadabddadbaababcdbdbaadcdbaadcbaaddcaaadcadbccacaadacadcabdadcadcbccbbccbcbadbaababbdbabdcbbdacdacadcbdabdcbccdbaabdcdccbabadabcacdcaadaabbbdbcacdccbbbcadcacbbcbbdbdaaddcdbcbdbdabbcccdbddbbdbcacbbacbbdcadcdbccbabdccadcabdaabacdcbdbbddbdacbbcdbccbbbadaaddccdcdcacabcdbadabaaaccdacdbdcacddaabaccdbcacbadbadbbabdbdccdbcadbbcacaabcacbdbdacbcbbcbcdbccccacbbacdaadacbcbbbddbcbddbadbdbbbabbcabccbbcbbbbbadadbadbddaabcdbaabaddadbcacddcabdccdadbacacbcadbddbbbcbbcdccdcbddbcbdcddbbdadbaadbbcababcdabcccbdcbdcbbbbccbcddaabbcccaadabddbddbbaaddcdbacbdcabdcbbcaabcbdaacbbdbadbdacdcbbdcccddadaccdacccadcbcccaadddbabbbccacddbcbabaabcbbabcdbdabbcabbdbacbadbcaacbcabacbbdcabaaccccbcabbddabbbcadbdaabadccbadccdbdccdbcbabbcccadacbdbdddaabdababddcdcccddcacdbddbaacddbccaabdccabccabbbabcbcbbddbaaaacbbabcccdbdddbdbdbdddbbdbbdcbabacbbdddcdbbaadabbbbdabdccaaaacccccdcdddbddbcbcbbcadcacacdcacbaddaaadbadbaabaccaabdbdcdabcbcaadadbdacacdbbbddbbbcaccdadcdcdbbbccdcbbcacbcddbdcdcdbadcbbacaccaadadcaaaaabddbacbaccadaddaccdaabdcacadacbbdadaaaacbccbccabacbcdcbdabcbccdbbcabdaadbdbcacddcbbbbacbaccbcccacacadadacadcacdaaacdaabadabbabbabcbccdcddbbacadbdaaaccacccbdcbdadddacbccadddcddbadbbbddbcdbaaaccbdbcdbcbbacddbbdbbcbabaacddacabdcaccadabbcbddcdddaaaaccdbcdcadaddcacadcbcbbcdcdcabaddbdbdabccbabcbddcacddbaadbabaadcbcbcddbaadacdaadadaacdbdaaacdbabdbbadcdbacbadaccacdbcbccacccacdcdbabcabccdcbaadcabddcbcabaccccadddabccbacbccdcdbadadcacaabaadaddaccbdbadacccbcdbcddcacbaccadaddcbccbdabbcdacbddadddbbdbaccbacbccddcaaaddabdabccbddcdddddcaabbcccacaccaddddcdcabcbbcbabaadcdadcbdbcdaaabbcdabadabbcbaaccdddcbdbbdcaccbdbddddcabdbacdcadbdcdcaddcdbdcdbbcaabdddadbaadbccdbadaaadacadaddbabdcadddaadcdcadccbccaddccbbbaadaaddddcdabcdbccaabcccbddadadddcdccbbcdabaadbdbcabdbdccdadcddcdabddbdcdbaabcbcccaddadabaadddcccbddaaacdaacbaaddddcaaaaabbdacadbaccabaadbaadabacdabaccaaaccdaacccbdacccbbccdbacdcbdbcdadcaabdcddddcacabdddcabdababcacbcbcacbbbaddacadcdacdaacbbadbbadacbcdadddbbaccabbaddccddadbacbdbcaaddbcbbbdcabbdabdbdddbdabdbbccaddadbdbbbadcbcabbcaabbaacaddbbdacbbdcaabddbdacdcbddbbccbaddbbcbbdbadbabcaaaabbaacacacabaadcaddaabbbcbcadbacdcacbccaccdcddacbbbddbddbdbabbbdccbcbaabcacccddadccbaaacbdcdccbbaccbaddcadaaaababcacabdabacbdbddbbddbdbabcdaabbccddbadbbbaacbbcdcaacadbacbcdaaadcbacaadcbdcbcadcaaaabcbaabcaabcbadaddbadccbabcccdcbccccadbdbcbdcbacaadcbbaccaccbbcacacabdcdacbddccaadaaddaaaabdddcbdaadabdccdbdcaabcccaccdcbdabdbcccccbaadcdcaddbacababbcdacddcdabdbaccbcadcaabbbdababdcdccaccacadccbcbaadccbcbcbcacacdbbcdddabadcacdbbccdbcbcbacaccdcabddcacdcbbccabdbaaaabcbdddbaabcdcabdbddabbdcddcbccccbddaaacdaddbddbccadcbccdbcbbcbcaaaaadcbbadcabadacdcdcabaabcabddacaccdadcbbbbcccdacddbddabbabadbbadaabcdaddddcabcdcdcacadbbdcaadbcabacacadddcbbadbacadacaaadaabbccabadbbabacbddaababbacbcbdcccdacacbddbabbcbbbbbdcddbbbdcdaabdcacbdcadbdabcabbdadabaabbaccbaddbcdbcbbcbcabbdbbacccddbadcabacdbdbcbddacacdcbadcbaabddaaabcbdbcacccdcdabdbabbdbbcabbadadcdbddadadadabbabcdcadabdbaadbddabdcaddbccadbccaaaddcadbacbdcdcdbbcdcabcbdbabcaaccdcbdbadddbcaadabaabbbbbababaddabaaddbddbbacaadacddadaacdaaabdcbaddcaabcdaccbbbdcbdadcbbacbabcadaaadddbddacddbcddabccdddcaccbaabbadbcbcabcabbaacabdccdacdbbadcacbccacabdaddbcdcdcbdaadbaaacaadcbdbcacdbbacbcaaaadaddccbbabaacaabddaacdabdacbcadbadcacbcccddbdabdacacccdbacbacaaddcbcadddadacababdbcbcacccdbdaabcadaacdbabbccbcabbaddccbdbbcdacaabdcbcacadcdcdccdabcdadddbdadaacaddacaccbacdacbcccbadbcbccbabcddbbddbacabcbaaaabdabdbdcbcbdcbbddacccdcaddbcaacacbacdbdabadbbaccadbddbaaabcabbcacddadacadacbbdddddbaddccaadcacccadbbabdcdacabbacddabdbdbdbbabddbccacdbbcaccccdaccccabdadaabdabddcdbdbacccbdacdabadbdabbabdbddaaabbaaadbcbabcbaadccaabbbccadaccbaddbcabcacaaccdbdbaccbdcbbbabbbccccdccabadbddacbabdcacacdcbadacbbcbdccacdcddacacacdddbcaabaccdaabccacdaccaddbabaaadcacccdacdddabaccdabcdcbccbbcbbabbccdcacabbcaaadcacbaacbdbacbddcabacccadccddababbaadaaddabadcddbbcdbccccbcadbcdbcdcbdbdbcbcddbbdbdbadcabcdddbbcadacdabbbbbccdcbccdbcdcccabccdddabccdccdcccacbaadbcaaabaadbdbaabbbacdcdaaddaaababaabaddcddbbacddacabddcdcaadcddabdbaacaabbcaadabacccbdbbdddbbabccaaddabbabcbccdaaabccdddadddbbdbbdbbaacbadaacbcdcbaaaddbccddcdabcaddadcaadbabccaadbbaaaaacbdcbadaacdadabccddbcbcdcbcddbbcccabcadaadaddbdaaaacdcadaccddbbdbadcbabccdbbbdcacbdcdbbcccdcacbdbcbbdccaddaccadacbadcaadccddccbdcaaaccdcbbcdbdcbaaaaabcaadcccadadcdbacabbaccabcbcbababadbcddaabadbaddabdbadbadadadaaccacbcbdaccacbaaccdbaacbbaabbacbcabbaabcdabbbabdcaaaabcdbdaacbcbdbabbdacbaddbadcdbadbddadacdcbcadaabdaabaacadcbacbdbccaaaccbccddadbdcdabcdbcbaccacadacaadadcadaaabacddadccddcdbabbadcdddcccadbaacddbcadcdcdbbbadadbcbcacbbbacbacccdacbbddcccabdbadbccddbdccaaadabdccadaadcdccbbabdacdbaacabaacccbcbdbdcdabbabcabcbdcacbbcacadcdbdacbadaccdccacdcdcababbbdbabdaabbdcacdcabcabccbcabdaacababaccdbcdabdbadddbacbcabaabbbcdcabbdddbdcbcdcdcaddcccabaadbcdadccccdaddaccaddaaddcdababcdaadccabdaaadbaabcabdabddcaccadccdcccadcbdacaddbdddadccbcbcaccccdbdcdbcabcdbdaaaadcccdaaadcabbabdaccdbdadabbdcdcbaacbbcabcbdaddabacbababddacacabacaaaadbbbaaccdbdaddcdaacdaaacdccddddbbadbdadcdbbcdbacbbabbcdacdaacbaacccbbddcbacdcaaadcdbcdcabbaabdddcdacbdcacccdcacdbdbcbadbdaacbbcdaaaddccdbabababccadbcaddacbdccdaddcddbacbcbbdcbdccdbcbabdadabddbacbcccdcbbadbcbbaaccddaacacdddbbabddaacbadadbaddbcdcddbcbdabcaddcbbdccbacddcbaaaaadadcaabaddadcdbcbcbbddbadddaabdcaddbabdacacacacaabcbcaaccdcbdbcbadcbbaabcbdaaaaadcdcbbdcbabbacdbcddbacdadbdbbabccdbdbbcbabcabacbdbcabaaccccbabadcbdddcabaddcdadbbdacbbdaabcddbadadcdddccdaddcbdbcbdbaabcdaccbcaaccbcadabdcddaccccddaaadacdadbbdbcacaabdddbbbabbcaddcdddbdcbcccbdccbacbdcbcdbbbbdadadbdadcbbdbdbdabdbdcbbbaaddccccddcdbdabcacdbcdaddacddcbaaccabdaacdbcbbdddbbaabcaabcadadbbdcbbddadbcbbcdadbacdabbcbdbbcbdcddddccbccaadddbaabaddcdaababcccccdabbabaacacdaabdcdcbdacadbadcbadaadaccdcbcddbcbadbbdbababcabbacccccbdadadcddaccadcaaccdacdcddbcaabdcdaccbdbaaababbccdacbacbabddadddaaacdccbdbbaadadcddbbababdabcccbddbdaadcacdaacaaadabdcdbbbdabbaadbccadccbbdcabbdcabbaccdbbbaacaaccdaadbcaacdacdaadbdcddcdbbabbdccbbdaaaddcdcbcdadbbbcaababcbabcdacbcadadbadadcaadcbcaaccdbddcbbadbaacadabaabdbaddbaccdbdcacacabbaabaabaddbdadbcccdbcabbcbbdccdbadcdbcddcababadcdbddbdaacaccabbdbddbbbbcbacabbcdcddcadacaadaccacadddabbddcbdddcacddbaadbdacbbbddbbddccbbdddbdddcbbbaacaadacdbbcacaccddcbbbdaddacbcabdbddbcbbbddbdbdadabdaaddaacdbbaacadbbbadbbbacbcaddcbbdbbbcbabdbabbdcbaccbbdadbddbbdcadcacccbccbbdddcbbbbbaabbbbbdbcacdabaaacacdabccddaacddccaabdbadddbccacdabdbdacbddbadaaaacbabbbddbbdbabddccabccdaabbdbadcacabdcaaabcdbdbacbaddabddaacabbbabbdcbaaabbbacaabcaadcddcabaccbacccacbccbcbdabbcbabbbbbcbcddcdcdcbbcbabadabdabcbacbaaccbcabbcacccccbbcadbdbcddccaababcbdbcbbbababcccbadacaccadbbbccbdbcdcacacbadaddddcbabcaabbadabbcbcddddaaacdcaccadacccbbabbaadabcdcbdabcbabaddcbaacbbadbbabddacbccbbbdcbbaddcdcadabdddbcbaadcbcccabaadcbadcdaccababdddccadddcdddbbbdadcbaabccabddcadbaacdcbdbdcaddabadaddaacbdbddaddcdacaacbacadbadcdcbbadabbbcadddbcbbaaadddcdddcbabcbdbdacddacdadbaadadaabccaaacdcacaadbccdcbbbcccbdcacbacbdaaacbdbcadcabdccccdadabbabacddbaabbddbcdacabcbabbacbbbbcccddcdbdbbcbacbbadcabcbcacccdccabaacacadbaccdcbcbdcaaadadbbdcdcbdcacddbcaabdbbbccacaccddaabaacbdbcdadddbdbdbcdabadacdddbdbbadaccadbaaacbdbdadadcaddcbbaaabbbacdbdcdaacdcabbcadabaaacbbaccacdbdbccadcdcdcabccaacdadbbcadcbcdddcaaadabcdbcaaccdcdabccccbdaabaacddbcccaabbbbdaabdadcbdadccdbabcbaccadabddcccbdddbccbaadbbbcdcadcacbacbcabcdccabbdaabdcccdaccbdaccccdbaacbdabdadcbaaabaaabcdaaadbcdcbbdacbbcbbdabcbaadaadacacadbccbabcaaadaddabaadbdccadcabdbcdcaabddccaddbaacadcbbbccdddbcacccddcdbdcbccaddbbcdcaaccdccbacdcdcbcdacdbbbbacadcbbcdacdcccacbcbdcabacbcacccdadcbbddbbcabbadcdabaccacdcaaabcbbbbcabaacccbdcbbaaaddbadadbbdabcdbccbbdcadbbdadcbbcaddbbddcbadaccadbbcbcbaccdaccaaaabcbabbbccdbbadcbdddcddcdbbbddaadcdcbabacbdbacbabdbadaabdbdadbacddacacaccdadaaababccaacadccaacbaaaadacaacbdbbdaadbcbdaabccacbadcbaddcaccabaacdccbaddcbdcbaadbabdabbbcdacdbaddcdcaccbaabbdabbdadabacacbcdbbcbdbbcacbaaaaadcaacbaabdbbdcbbbcaadcbcccdddabadaccbbddbccadcacaccbcdddbbbccdbbabbccdccbbdbcaabaaababcbcbcacabdaccbddaccadadccccadcadbbcbaddbccadaccddcbcaaabaaccbcbdbdcaabdbddbbbbaadcadbabadadaacccccdbcacbbaddcdabbaabbcdbdbbbdcacddcdcadabbaddbddbbcdaddddaadcdaacbcaacbcabbcabbbccbacbacbbcdbcbccdbcdcbcacdacbbdcdacabbdcbdcdbadaadddadaabababaddddaaccbadbcadaacbcadcdcdaaddcacaabadbadaddcadcadaacbcdacdbaacbbcbabbbdabbdbdddaadcbddacacccbadacdbadcbacbabcbbbadbdcadcdbbbdbcccdbacadbbcccdbacbcbabddacbcacbcacccbbdcbacbbdcbaddacbabdddbbaabacaaadcacbddbacbdbbababdacdacbbbacacbdadddbabdacdbadbcbbccaaddbdccccaaacccccadbdcdabaaaccbbbdbbcdacccacacaabdbcbaabbbbabdbcabccdcbacdcdabbdccaacdaddccddaabcdacdacbababbbbcaccbccabcdddcccbcddacaaddbcccdcdcdacbccbbbbdbdbcbbbcbddcddcbddcdbbdcabaccbbbdaccaaccbcddcbbcdbccccbababdcbdaacdbbbdbddabbddaccccaddabdbcdbdccbaabccabcdbaadaacddbddaaabaabdacdbdbbdddcbcdababaacabbadbbdcacbbccdadcdbcddcdcaccbbacbabcbcbccccacddadcabbacdadacaacaaccbaaadbadbbbdbccaaaabdccbbbddccdacbbbcbcbbbcadcdaaddccbcacabdbdddaccbdcdbbdcdcbbcabacbacbdbaaaabdacdbabcbdbaddbbbddcadddcbbbcbbaddcadcaccaaabbcaacacbbccbddbcadbbacccbbccbccbabacabcccabcccdddbbdaaccbbbdcddccccdbdbaddcddcddbcbdbdacdcaaacbcacdbbddccbaccddbaaaabddcbcbcaaccbdacabdacaddcbaabdcaddbdccbbcaaabacaabccdbabdddbcbdacbcadbbbcbadaacbbaacdcdacdbcddcccaddccaacbcbbdcdcbaccaccdbbddcdcbaabcbaccaacaadcaccaacbabbbddbbaadcdaabbbccddcbbbacbccdcdcaabdadabcccaabcaabadbbaaacabdccacdcccbcaaaccabbdccbcdcbcdaddaabdbccaabbacbdcdaddaccadadddadcabccddccbcadbcbcabccccaddaddaaacaccccbaccccdbcaddbbcacddbabbddcaccdabacdbdacabaadcaccbcbdcabcaaaababadadbcdbaacaacacbbcbdcaabacaadbbbcdbdccdcdadaddaadabaabaabdbcdbccaddddacadcabaaccccbdadcbdcaabbcbddaacdacabdbdaaccaabaadcaaadbdbdbbbbdacbdccdaacbbccbdadbbccdbcabdaabcccdbdbbabaabdbdbdccbcccaccbacdcdbcbcaccdaabbcdcbdcabdaabdadbadaccbaddbcabbbcabaacbbbaaaacdacacadccdbbacaacdabacbbddabadbdbcccadcdbababbbcbdddbddadbcccbccdcbdbbcdaddbcacdcabbdaadabccdbadddcbbcaaabcccbbcdcaddaabddbcbabdbacbbdbacacddbcccdbdabbadbbadadaacaddcbbadcdbcacdddadbacddcaadcbabdddbbcddbcbcabcdccaacbddbaccbbddcacadbdbaabaaddaacbadacccbbbaddbbacccaabcbaadcbacbaaacccdbbaabbbddbbbabcdcadcabdccbdaaccdbabacaabbcacbbaacdcdadaccdcbccaaaccaadadcbacdcaabcaaddbabdcdcabddbddbaaaabbacadadaaacbadbbcaaacdcbcbaccdbcdbaadcdabadcaadddcabccbabacacdbcabcaaadbcddacadccaaddbcadcddccbbcacbaaddcaadccbdaacbbcaabdcbbadddbbbcccccbaadbdcdabccabaaddccdabadbacbacddbbcbbdadadabbcbbdaabbbbadbdbcdabdddcacacaacdbccbdabdddccbaabdbdbbabdabdddaaacabaaadbdadcacbcaaaaaccbababdabbdccbacdaadccabbbcbaabcccacdabbdcaababacaaadaacdabdabbabadbcccaddabcdadccacccdddbbbacccbcaccadaabcdcbacbacdbcdbdcaadcaccaaadbcddcdbcabaaabbdbaddacadcddbcdbbdbcaccaacccacdccdabbaccacdaddbaddccdacdabbdcbacdcbbdbbdbbcccadbbaaccddcddcbbbbcacbcaaccaccccdabdacdddbbacbbcadbdadcdacabbccddbaadaacbdbabbcccccbbccdcdddacadcdbbbbdadaacbbcdbaadcccabbcaaabcabdbdbbccdaadabbccdcddcdbdbccbbaadaaaadbaaddbdbbbbbdbddcbbcabaddddccdadaaabbbadccdddabbbcbcbbaaccdbcacdbabccdbccbcabbcadadbcdbdbbdaddddcdbdacdbdabdddcccacbbbddacddcaadcddcaabadcaadccbbabbaaacbbcbccaaccabdacbccdcdabcdaccccdcaccacaadbbcadcabdcbdcbbbbcdbdcadaccbddbbbcddababbadcbddbadcddcaacbabdbdababbcdbaadaadabbccccacbccdacbbdaddccdaabbbccddbdcbaccaaaccabdbbdadddddddbdcccbaaadbdcbabbadccbcbbbddcbcdbbcbcdbbbbbdbadabcadccddbaadabdcabdaacbcbcbbbbacdcbaddaadabbdbdbcbcdcbdaddbcaddbbcadadcdbdbbdddcbcdbaaaaccadabcbaaabcdcbddcbcabcaaaddaaddbdabacabbdbabcadcbaacbaadddbaabbbcdcbbbdaaaaaadbddbccdcdbdabaccbadbdbdbadbcddbbddddbbbbacbdbbbbcbaddabdcddcadadbaaaadaccdccdadbcdbbbcdcadbdabbbaaccbaabacdbabbdadacbbcbaccdcddabbdddcacabccabcbabaaccdddcacbabccccdcacbbcbbcaabadaaadcadbcabbcbacddbaccbcaadbaccacbadbccacabadcadabdbddcacdaccabacabbacbcadbacdcddcddcadbccaaaaccbccddabaadbdcdccdccabccadbdcaadcbdabcababdaacddbacdbcccbddbaadcabbcabddcadadbbbbbdddaaacccbaacbdaacaddbccbacdccaacdcbbabbdddaadbbaddcdcdbdddbcdbccbdbababaccccbddaadbdbccbaaddaddbccdcbaccdbaacaaaabacaacdaccbabddbbcabbbadcadabbbabbdbcdaacdbdabbacabddddcadacbdcacaaaaaddabacdbabbdcacadcbdcbadbdcbcbabbdccbbdcabcddacbccaccacddcbbdcabaaabbadaaabcadaabadbbabccccadbddccaaddbdabdbabbdadabaaadaccaacdcdabacdbcdbbacbaabccbcbbbaaabbddabcdbdadacabcaabcbddbdaabcdacdcacbcdcadbccadbbdbccbcaaabacdbcbabbacdbdcadcbabdcdcabacadccadbbccdaddcbbacccccabcccadcdacddbbcabdabacbddadabdddbcddcadcdaaadcabcbaccaaddadbbbcabbdaadbaccaddbcacacabbdaabdbbdabcabaacdadbcdaccccacbbcbacccbbdcbdbacacacacbcdcdbbdbbadabcbdbcccbbacbddaaadadbdbcbbcadccdacdbbaacdcccbbccaadaccbbaaaccabbddcdcbddbbcaaaabdbcaccdacadbbdadacdaddabdbabaccbcdbcadcbcbbadabbcddadbcadbdbdbccdacdbcaabbddadcbcabddacabdcccbbacccaaccabbbabddcadddacaacaaadbabdbccbcbdbdbdbbbdbdababbccacbdbcdbbaaabdbdccccbabbadabacbcdacdbcbacddacacdccdbdcbcdbaacdaaadcabdabdbcddccdacbadaadbadcadabddcdabdccddabbcddcacaddbadcbddbdcabbddddaacdbaaabcabdddbabaacccccdbbdaacadccbdcaaddbdbcabaabaacbacacccadcadbbbddabbbbcbcadbddccabcbddddacabbbadbadcdbbdabdbbbdabbabccdadaddddbdbccadcbbcbabdcabcacbabbddbacdcdddabbdbaabadbadabbdbcdcbdadccdadadcbbcdbbdbbabacdcacdabaaacabbbcdaddbbacbdbbbbdcbdbdbccacdbdbdacdbdabcabccbcadcaddaaccdcabadccababdbccaabadaddbacdabccbcbddabdababaaaaaaadbacadabdccabadcdaadaaaccbabbdbbcacadccbbadbbdcdbcdcdaadcbcabadaacbdcaaacacdabdbabccbcbcbdadaabdaddaccbbcccccbabaadcbdbbbdbaaacbaddcacdbabbabcccbccbbadaccbccbbcbbbbdbacbbabbbadbcdccbacdcbdadcdcadadbcbdccbaadcadbdaadabaccdacdbcadaaadcbccbacddabcacabddbacabcaadbddbdbdbcaddacbadcbdddbccdccaacbdacbabdbdcbcdaddbdabcdabbcaaacadaacbdbaacdccdcaccbdddbaadbcccdbdacbccdadcbaccdabcbccaabdcbccdcabcaababcdbcddababaabbcaacacbbddacddcbbbcbaaacdbcccdbcdccabacbdddcdcacabdacbcdcddcbccdbbdbbacabcabdaaabdabaaaacdbaaabacbddddcbcabdbddcbcadcabcbcaacbabcbdbacbbccaaadcbdbddcddacaaabdacbadbadadadaddbbddcbdcdccbaacacadcccbbdaaabaadabcacacbbaadabbaacdcccbdadcdbdcbbddabdadcdddadcabdadbadbaddacccbdbabdcddcddcdacabcdcbbaccbacacbdbdaadabcdadabdccdbbcdaacdaaccdacadbabdbbcdcbdcbbbdabbaabbccbddaddccadbdbbbcabdaacdcdabcbdacbaabccdddbddcdcabdcaaddbddabbaababdaabdbbdccdbccdbaabccadcddadbdcdaaaabcbdacdbdaacdbdbddcccddbcddcacbbabdacabacabcadcadcacadbddababadccaabcbbaaddbcabcadcaabdcdaaacbaddabcaacadaddcabbabdddcabbcdcaaacbacbdccdabcacdabbddbddbcbbdaaaaabdadbcabadaacbacaadbcaaadabaabbdbddcdbbbcabcacbdbcacbacaabbabddcbbacbbcddbdbacdbcdaacbdbabdbbdcdaabdccadcabaaccddddcaabadabacccbcbbacdddcccaaaabdcacadcddccdbaacabacdabdaaaddcccbdcbbadcabccacacbaadbdadbabdcaaccbaabdbdcabbbccbcbdcbcbaaadcbaadabaddbdcdbbddcccbaadbbbbdbbcbdbbccbcacabbdacbbcaccbcaccaabcddacdbbddabacccbaaabcbdbbaccdcaabdcddcdabbbddcdccaaacabacbdbdbacabadbdbadbbcdcbccddababbaacbddcbdbcdcddddadbbcacbaaadacadacacabbaddbbcbdaddcdcaacbdadaabadbdbcbbabccaadacdadcccacccbbacdbadadaacacbccadaddcbaaabdacbcabdaacbcbdabacbcbbaddbdcdbcaaccabcbacdabbbcabcbccadbbccbcdccdccababbcbaddddddccbccbcabbadccbcaacccdddacbacaadcccccdbdadddcccadbacbbbabcbcadbdacadbbacbacaadcddbdcbccaccacdcababacdbccdddcaacacdcdbaddddacbdcbdddbaacacaadcadbbddbadccababdabbcdaaccbbbadacababcddbcdbccacacaadcccbbbbddbadbaabcbdacbbcbdbdcbabbcbcccbbccabbcddadbdabbdbddddabdbbdbacbcdcdabadcdcabaacbbbccdabdaaccbcbdaabdaddaabbacddadcbbbbccbccdaadbddabdbccbdacabdbadcdaadccbbbaabdcbddbcdadcdcddbcdacbbbcaacadcddbcabaddddbcabacabdcacacadbabbcbdcbbdcaccddccaccbdbcbdcccdbaaabcabdbacbadbddaacbdbadadbbbbddabdadbdbcabacdccaacaddbabadcaaabcaadabaacbdcaddacacabcdcabdbbdadabcaaadacadddcccbcbbacbacacaabcadcdcbdcadbcbaadcbaddbcccdbcbccdcadcdcadcdaacdbbdbbcddcdbaaaacaadbbbabccbddbdcbcccbabcbcccaadddcacbdabbbadacdbdccaccacccdbbbbbbcbcdadccbbaccabbcdadaabcbbbcdbddbcbacbdcbdbcabacdabdbacccdcadaadbbabcdbddbdacdaabcccdadbbbdbbcbbadadcccbbabcbabccbbacddccdadabbaccadadaadcbaccaaabbcccdcaadcaacdacbbacbdbbbddccababbdcbdadcaddaabacaabdccdcaddcdaddabcbbacacabaddaddcbbadcccbccbdabcbccdcdaaacdcdccaaacaaacababcacaaaccbddcbbdccbabdadddcdddddcbdddcccdadacdbbaadcdccbadddcdddcbabcbbbddabbdcbdbbbcacabbcdccaabcdbbdacabcbaddbabcbdadcdcdbcbaacddcadcdddabcccdababddbddabdaadacbcbbdddccbdccdadadbcdbcaddacdccacbaaabbdcacabbccdcdcabdaaaabdbcbdacabdcdcdbbddbdcbadbcbdbbadabcccababbbcbccccadabaabaadccdbadaaaddbbbbcabdababdadbdbbdbcbbbbdadcbbdbdacaadcdbbdccddadadbcdddcbcbaaaaccabbbccddbacbbdabbccbcababbcbbcddaabdbbcdccbdbbcaaaacadbcdcdbbccbcddbaacadbaddadbcbbcdbbbbdbddcddbbcbaaddddbaccacbbbacbddcdbaaacaadcdccbddcdaddcaabbddbdadbadbbcbbbccdcdcbaadbcbcbacaabbcbdcacbaaacccbabbddacbadccdbacaaabcbdbdaacbadddcadadcbccdcaabddabcbdcbcbdababdabbcccbccbbccadcaadcddddbaadccccdcdddabcaabacdddbccdabaaaaddcabdcbddbaccdbdacabbcddcacbacabaaacacbdccdbadbdcbbcacaddacaaaaababdcaaacbacacadddbaacaacbbddbacdddadcddaadbaacabccaaabadccbccaccbbdacabaabdddbcabbabbcadbbdbbccbbababaccbccbcdccbdacddadcbbcbacadcbaaaaaaabdabbbbccadacdcdbacdabaadcdbadabbababaaaaabbbcdbabcbcdcaabdccccdbbbddaacccdbbacbbbbabadcababccbcccbdaaaaacdabbccabbabaaaaddaaaacaccddbaaabdaadbbcbbdccccbcbbbbdcacabdcadbadddcadbcbbdadcbcbbabdcbcddadcbabddccccbdababddbbcdacadcdcacadaaccdacabbdbddbbcdabcccbbddcdbdddcccccbaaccacbbcbcbbdacbbbabdcacadbbabccbaccbdacccaccbadbcdbccaabcdbbaacabcdabdaddacdccbcbdddaadccabbabbbcaabdbbbddbcdccbbabcbaaadbaadcacdbbbcbddbbadcbbaabbdbbcbdcbcadcaaaaadababdaacddacccaaccdddbadaaccabdcbabadbcbdcadbadcbaadacdddbcbdcabbbdcacccbadabadacacdbdcacabddcddccbbcbddcaadcabcadbcabdabcccccdcddcadddbcdcadaaaaddddcabacbcbabddbbdbbabaaadbdaaaacbaaddacbacdccddddcdddbddaabcbadacdbdccdbacbadcdddadcbadbdbdadcddcddbccbccdacacacdbadabbddaabdcbabdbdcdcadadbdadccbdabbbcdbaabbabbbdaaabdaddccdacdadcdddcbbbddbcdaaacbacdacdaaaccacbabbddddabbcabcdabadcccdbdaddaabbabadbbcdbdbaabcdaabacadadbcdccaccbcaaccbcbaccbadbaddbbdcbbddddbbdacddcdacacdcabaddcbbdcdbdbdbdcdaddaabaacaddadddacdcaabdcdcadacddacbbcacdcdcccadbdacbadabbabcabbacbcdaabccaddddaddacbbcdccbcaacbbddbbdbdcddcaabddbbbbdcddabddccccdaccaddcdddccbacadbccaabddbdccccabbacddabcbcdaacdaabcbaccddbbaddcccaccaaaaaccdbdbcdccadadbdbdcccbdaddbadbbacacddaccdcabbcaadcdcaabcbccabbddabacdbdcdaadacdccbccdcadadbadcdbacabbcdcbaadcdccaabcdadabaabcacbbdbdcddaaabbbdadcabaacdcdadbabacbcccdaacddacabbadbaabbbbbaabcaaabbadcacbbdaaaddabddacaddbdadccbcaaccdaddcacdbaaaccabbadabdccdccaadbaddcaccbadbadbbdbbdaccaadccddcacdabdcdabaaccbacabdbadcdaddccbdcbcabcccccacccdddcaddacbdaadbbabccbccacabbabacabbdbababcaddbcbccdcdccbababddccabbdbbbdbaadbcccdadacaadcacbcabcbdbdabcdccbadcbdbbabddcddbaadadbdaaabaadccaababcddcbdcbcaddcabbacbadccadcacddddbbcddddccaacbbbbdcddccdcacdcbdbddbcdbcbcbcacaddcdabbbcadabbacacbadcabdacbcbbaacdccdcadccaacbbaacbccaabdbdccdbbdaddadccdaabaaabcddabcdbdabaaaaabdddabbdcabccdaabcbdcdccdaaadcabacccaabcabaadacbaaccbdabacdbccdcacacabdacbdadcdacabdbdaabaccbcacadacbbacbbbacabacccddababbaccacbbdadabcdaccbbddbbaacbcbcaaaaababacddbadddbdabadcabadbbddbdddccddaccbccdbccbdcbbbdadbdcbdabdcadbcadabaddabcaacbccabbdcdaaddccccbcbcdcabdbaadaadbdcdadddabadbaccadbaddccdddacaadabcdcaddcdddcbdbadccdadacdcddbacdcaadcbcdadaddadbcdbacacddcabcdbcccaccddbbabdbbbccddabdbbbcccaaaccdcabadbdbcabdbcacdcabaccbaadbcccbcbdbabcaaaddcaaadcaabbdaaaddcdbcdccbabcadaacbdacdaadcbcdaadacaccbaccabdaabcdbccddaadbababaddadcccdbbcdadaabccddcdccdbcddbddaddcdaacdcdadaccbddacbacdcdbdbaadcdacadcacbadadccbaaaacabcaaabcbdaaccabacbadcdcbacdabcbdaabbcddabbdaaacadacacaadbbbbaddcbddaaccbbcdcdcddcdbcacdccbbaaabacbbabbdadddaabcdacadccdccdccddcbdbbddaabcdacccaccbbbabadddabaadaacddbbddaabcbbaddbcbaabaddcadccdcbbbacbaadabaddbbcabbcdcbbbccaccdadbccabcbcbaddaaacadcbbdadcdaacccabdbcddbdbcbdcbabddbdbdbbadbcdacdbbdadcacadadbdabcbddbdcadcbcdaaaadbbacccaddbddabdccdaadcdddabadaaaddbabcabcddbdbddaacdacadcdbaadcddddbadcddcddcccbbdabbdbccdabdaabbdbdddbabaaacbcbbaddccddaadcdcdbaacadcbbdabdacdcbddbbcccbcccacabaccbdddbbbadbcaacacadbddcbbdbccbdbddbbdbababdaccdcdadcdbdbdbacbcabacbcdddadbbaacdddcbcbccbcddddbcddabdaaadadaabcacabbdabcbaabbcadcadaabaddcaaadabdbdddbadbaabbddcdcaaaddbddddccbbdaccaacaaaccdcdacadbdccccbcaaddccdabccdbbdbcdbccbadcdbadcbdaabdbadbcacabacdccdcbbbdcdbbdbbaccacddbacbdbaacaabbdcbccdbabdbbdabdbcbdcbdccdbadbaaacbadcbdaddcccaababdccbccdcaadacccadcbdcacaaacbdcccaddbbbccaccabbbddabcdaadcdddbccdcddbcdbabbdabaaddaacbacddbbdadcbbabbdcbdaabbddabcbbbbcacdbbbbbbdadcdaadbddacccbcdcbcabaaadacaaaaddcbaabbcdadcdbacdcbdddbabaadcbaddbbddbbdbdcdbbcbcbdcccadababacaacbbaddabbdcaaacdcdacbccdbbabdbccdbdbaccaaccdbacdbcaccaccdbdccacdcaadaacdbbddaaaacbddcaabdbacbacaaddaaddadcccacbcbbbaccbcabbccaddacbbbddcbcbdcccdcaaddccbdaacbbdacacadabaccadcdbdcaadbbdacbbbadccdcacbdbbdddbaabadaaaccdbdcbbbbaaacccdcbbaabddbdcdabcddbdadbbccabbdbcbadccdcbccaccbbaccabdbabbdacdcdbddbabcaaaaacdbacaabcbbcaaadbbccabcadcbddabbacabdbdcacdacdbdadbaacdddadcdcdcddcbdcaadddbabbabadbbcdcaccdbdbcbddcbbbcbbbbabbdbdccbdbddadbaaacbadaccbdaaccaabadaccbacdbbabddbacabccdaccaaadbbacddccbadacddbdadbdcbbacdddddaaddcddcadbbbbbbbadbccbdbabcdcddadbaabdadddbccabcbcaabcdacddbbbadaadaadcccbaadcbcbbdbabbcdadaacadaccaacaaadcdbabbbccdbcccbadaccaaabdbcccbbbdddbddbbabadddabddadbcdbdddabaacdaaadcdaabcbacacdadbcbdddbbbccbdbdabbbbcdabdbadcdcabddbcbbbbcbbcacaaaadddbaccdcbdbcccbaddcaadbcccdabaaddbcdaadddbaacdcbdcbcddabcdcbbcbdcccacadacbdacddcabdbadacaacdccdbacbdbadaaabadbdcbdcabbbacbcababdbdcadddcbbdccabbddcbdcbbacadabcadbcbaadcdadaabbddcbacbcdbacbcbbcdcabdabdaabbcaccaccacacbaabbbdaacdbccbbcddccabbadacccdabdcbdbdbadccaacdbaddacaabdccadddcdbbcadbdddabcdacccdaddcbaaaccdbddddadcbddacdcdcbcadbbbbcaaccccaaabdbcddabadabaddcbacdcdcbdadcbbdaabcbadaaabcadcadcccdaaaabbbdddcdabddaacadcaccdabdccaaddcdadbddcdccbaadcbcbbcbcbdaadaddbdaccadaddcdaddaccddbcaacdbccbddaaaabbcbcaabbddbcbabdcddbdddcbdbabacdabccbbbbddbabcbbdaddbbacdccaabdacacbcdddddbadacddaabcbcabbddddaacbabdcaadaaacbbcbcabadbdacddbdabbcadcacabbadbcaadbbdbbddbdacdbdcbdbcaccaaddabcdcacbcdcbdcdbcbbbdcdbcbccbbabaccdcbcbabbdaaaabddacdabddcbbbbddccdcdaccccdacccccbcdbadccacdddaddccdaacacbdbccbbbacacdccaccdccbcbbbdadbacdddcbdbdddbbdbaacbaabadbddcacbdaaaccbccddcddddabbdabddaddcdbabdcddbacacccdbabddadddcdacdbbcacbbccbadbbaddabdcccaacaacadacbcadadaccdbaadababbcbdbccccaaadabdcccadccdbddbbcadcdddbbcbabdacbcaaddcccbaabdcdddaccddbcabbbdcdbdcddcadbaaacdacacdbbbcbcdbaacbcaaaddbadbdddcbaadcdcdaddccbbbdabdbbbbdccbbbadacdaabbabadabacdacacbbbabbabccdaccddbadaaadbcbabcacddcdbabdabcdccccbcdccdcdbccddcbdcdbdacdcacdbdadbbabcaabbddaaaadadcbbcdacbdacdabddccbabbdcddbddcbbdbaacaaacdccdccccddcccaacabbcddadabddbbadbadbabbabdaddadcbdbbbbaacadabcddcbbbbbddadaccddbcaaddccbcdabaadddcbdddbaccbddbacdcdbcaabaacabbdcabbddbdbdcabcdadaabbdbbcbabdacccabaddcbdbddabdbcdcdcadcdababbbbbaccbcbbccbacddcdaaaaacaacdacaacdabcdbcababdcdbbaaadaadacdcabdcbbdbacacbccaabbdbbcdaccbbabcbabcaaaadcbaabdabaccdadbbaadbbaadcbbadbcdbbadbacbbbdbcdcdbddcaaaaccaadbdcccbbcaaaadadacbabbdaacaabadcbbaacdbacccbbbcbdacacbaccdacbaccccdbddccbdddbcbadddacaaabcadcadbdbdbdcaacbdbdcddaacabbbabacbdbccabaaddccbdddcdaababadaadacdccbbcbdcdabaadcaaaddbbabcdccdacadbaacbcdaadcaaaadccadcdcaacbbbcbadacdccddcbcabaccaacbdababbccbadcdcacdbdaacdbbdadbdbcabbabbdddbaabbdbacaccbcacaadccddbdddbddcadbbddcbbcabbbabaabbaccdbcbddbbbdacbadbdacbcccddcabcbcbbdcabcabcddbddbccacabacbbbcbcbbcabbabcbadabdacbbdbbcdadcdbbdaadcbacaabcadacddcbababdbaadadacadaccccaadbcaacabbdbcdccadcbdacccbbdadbdccbbbddccaccaccccbaddcdcbcdbcbbcacbbbabdcbddaacddccadadaacabcbaccbdbdccddbabdbbbbddacacdbdbadbbaccaabbbbccbdaaaaaaccacbadbdcdaacaaaccdddbbadddcddabadcbadccbdcdbdddccdccbbbacabdcadbadaddbdbccaaadbabccabdcbbabcacdbdaabccaabdcabbaadbbadddbbccddddaadbbaadbbacaaccbdaadadabcdbaccaaadcdbcbdababadaabaaccabacadddddddababcdcabbbdababaadacadabaaabadbacbcadabaadbccbddaacdcaabbadcbbdaacbcbdccacccaabcdacbddbbcddaadadccccadcdcacddbcdbdddcaadadabbaadadcccbcbaddccddcacabacdbdacdaccddcdcabacdbabaddbadadabacadccdbdcbcbddccddabdcacbdcdcdddddcccddcabcadddbdacdabbdccdbcbbcadacaadaabcbabbdacadcddadddabbadbdaacbaadbdcbdababdcbbdbdabcdabbababcaaccdbaddcbbbddcccdbaddacbcdddacbdccbccbcdacadddcbbbaaabdbddbdcbbdcbadabbaaddddababadcaaaaacddbcbbaacdadccadbaccbcdabcccbddacaaacaaacbcbcaaadbddabadaacacbbcadbcabaaccbdabdbbabdbabbabbdcddbdaacccbddccacddbbaccbdaadabdabacdabbdabaddaddbdbaabaaabcbdcbacbacdcaddcddcbacdcadbcaacadacdcddcbcbdbcddbbcddcaabbabdcdcdaabdcbbccbacaadddabcbcacbaaaabbdaabdadccdacbaddcbcbdbbbcacccbbcacaabcdbbaadaaddbcddbdbaccacabadcaaacdbddacacaccbdcacddbdbdabdbdccbddbccdbcbadaabbadcaddcbccdbcdacdaadadddcadacdbccaaaabcddaddbccaccbdabcacdadbaacbaadbacadbdaacccaaadcddaacbbababbaabbbcbadbdddcaaaadadddccdadbcbaddbdcaaddbbcdcbccccdcbbcabdabcdabbaddcbdadcadacdabdadaddccccdcaccbaabbdacbbbcbdcdcdbabdbaacbdbadbaadacacccbcddbcbbdcbadcabbadbcacbadcddbcbdcabccccbbdadadccbddbdaabaaabbbcaadcddabdbcbdabcbcbcacaccccabcabdcccdbabdcadddccbbaadbdcabadaaccbbccbdcacacabacbddddbabbabbadcacaaacdbbcacadacbcaabadcdbadbbccdacabaccabccaddcbaabacdbdccdcacabcbcdbdbccdbdcbbabbbaccdbdcdaabcaadaaadbcacdddadabadcbbdaacaddcaccccbbdacccaaacbacbdcbacabbcadbbaccbdbcbdbccbddaddbddbacdbbcbacbdadcbabaccabdbbdbcaddcaacdcdcbcaccbbabcabbbdadbbddbaddddcdbbaddcdddcdddbccabccadccdcbbbcbabddbbbcdadadbcbcdadccbdcdddaacaccabaacdbaacaabaadcdbdadabdabdcbbbabdaaaaaddaccbdbcacaacdcdbbcabdaadcaccabbaadbdaddcddcddbbbbacdbcdccbabdcddbcdbbacbddaddbadcdabccaabdcaacaaacbacdadaccdccbaccdabdaccacbaabcbcbadcdddabdacbccbbcddcadcddcbbcddacbaaadaccdcbacadadcdacccbcddcdaddaaaabdaccbddaddcbdcabcaddababaddbddaddcccdbddaccbbabacdabaaabbacccadaccddcacaacaadbdbcbdbcdccacbdbccacbcacaababdcdcdbbccdaabcdbbabaadcddcabaaacbcbdbdbaaabbdaacbacbcdccbaacdcaabddbbcaadcdbdcdcdbbcbcddcacaacacdaabcbaddbbccabacddacddadbdadbbaaddbdbcacbbbdccabcbaaaddadbadacdcbcbdcacccdcdcbdbbbacbdcdabadbccdadabdacbcdbdbcadbacacabddbbcbbbddcddcdbabbccaadabcadcbbadcabbbcabdacdaccccdbcbaaacadccaddcbbdaacadacdaabddacddacdccabcbcbccadcacabbbaabbaacdaddbdacbbabdacddbccdacdaccdbbacbadcaacbccbddaadabdacdcbaaaddbbcdcbabdaabcababcccacbdabdcbabddcccccdbdaabbcbcbbabcdaabbbbcdbbcadcacbbdbaacdcbdcadccbacddcbdcdddacdbacabcaccbaddbdbbbdbdabbbbbcccddaddbaaaaddcddbbbaaaacddcaaabcdbdbaabdaadbdddcddcdcbaccccbddaadcddccdbaadaaccccbbccbbadbdccdbbcadcbdbdbaacccdbbbdacccbadaacdbbccbabdcbbaaaabbcdadacaaacdbbcddcdddddddbdbbdadbccabbaaaaaacdacacdbdaabdccbbcabbddacabdabadccdbbdddccbcabcbcbdccbbdcdbcbbabbbccdbbccdabcccadaaacbcddbbcabbabbbbbcadbdbaddadcbcaccdccddbddabccaacbdcbcabddadcdcdadbbcababbbddbdcbdbccaabbdbaddbcdbbbcccddadabdadcbacaabcabccddcbddbbccdccabdacabddcdcdadbdadddbdbdbddbbcbaacdaddabbbadbcaabcddccadcbcacddddbadcddcddaacacadcbbacacacadccccdcdacdaabccbacacbdcacdbccbbdcbbcdccccccbbadaabccbdddcacacbbdcdddacdbbcbcabadacdccbdddbbcbcdbcbdabccbbaaabbaadbdcddbacbabbbcaabacbcbadcbbcbbbdcdcaabbaacddcccbdcbbcbaddccdcbdccddacbbaaabbabcdddbbabaaadaaddddadddcdbaaabbacaaddbbbdbbdcdbbaaabaadadddaddcbcdacccccaabaacbbbbddbabcabcccdbdacdddaaacdabbacaabcaddbbabdaccaccadbbbaaccbaccdadbaccddcbccddabbbcacccbcddacdbbbabbdacaababbadddaaddcabdcacdbaabdcbcdbcbcacbddacbcaaaacdabbababbadbbacacaaccabccbaacddcabcabadacdbdabacbcddcbadbbcccbdbdaabbabdabcaddbcbdacadddbaabbcaccdadddbbbbddcdccbbccdbdabbdaccbddcbbbdbbaaaccbabbbcacdbcaddcdcdccdccbbcababaccdbddbbbccdcbcdcddabccadbbcddacbadadbdcccabbdcaddcbbccddcaabcdbbacacbcabdaaaaccdacbbbdcbddabdadbaabdbcdcadabbbcaddbdacdadabbabbdcacddaaccbddbcbcbdacabcbddccdccbaabddbccabdbbccccbabaddcdaabdbcabdccabbbdbdcbabddddcccbdcccabcccdacaccabbcabbaadacddccabcdcaadadaddbdcdcbbabacbaabbbabcbccbdccddacddbcdbccdadcababcbabcbbdabadcbdaaabaabccaddbdacdcddadcadadaacddbbdbddcdaadcacccacbcacadabcbbabbbacbbcccaaabacbacacbbbbaddcdaaaadbdabccdabbbcccdbdaacbccaabdddbbbbbcbcbdbaccacaabcbdcdbbabcaccddcaaccacccbdbadadaccccabccaaadacbaccaccdadacadbcbbbbaadbccadddddcbccccabbcbcccccaaaacbabacdddbccbddcbadcdcbaaaabdccddccaadabcadbdbaaaacdcdabacaadbabccbcbcbaadcbdbdbbbddbdabacdabacaaddaaccabcbabbbbabaabcabcdabbaaaaabdbabbddbdddabadbabdbbddaabbacadcabccccdbcdacdcdaacabdbbcbdcdabbccbaacbadcaadcacddaaacabbbcbbcbdabbcdcdbcababddbaadaddcdccdacadbadcdadddbbadccabcdccddbaabcdbaaabbacadbbcdbbcdbaadbdddadaabbababdaccccdbbbbdadabdddabaabcdaadcdaabcbbbbcdbacbadadadcacbcadadaaaaadbcbdcbcbcacbbbccdbdaddacccaccccdbdccacdcabccdabcadcdaadbccbaadccdaaccabcadbddcacccaddacbdcbbcaddcbdcccdbbcbaadadbbcbbadbdbbbacddaacdbbcbcccdaacccaadacbcddaaccbcdbacdbdcdbcdcbabbadcbcbcbbddddbbadadbddbddcbbcaddcbdddacbbdaaacdabcdbbcabbbabacdcbdbababdbdcddbbccdbacbabdcabcadcabaabdccdaddbcaabaaadcbdabbbbbacbaababddbacbcbdbdaddacbccbbbbabcdaacbadbccdccbdbaddacbbacacdacadbacdbbbcdadaaaddbcbbaabacabccdcbcadddbadabcaacdcbbbddcaaabdcabdbacaccbcbbaabbcaddcaacbddbaabbddddddbdbbbccadddabbaacbbbabbbdbabadbbabcacdacbddabdaaacccbababaccaadbadaccabaaabdcbbaddaccbdaddcdabbbcabbaacaccdacdacacccacacbbcaacbccbcbbcdabcdaaabadaabadcaaddaabdddcbcbdabcadcccabbadbcadaccacbbdabbdabcabcdccdcdcadabaaaaacdbaddbbabadcdbaddcbbccccbbdccaabaadbdbbccaaccbccadabbdaabddbabcccdacdbbacbdcdbbcabbcacdaaaccadbbcacbabbcdddddcbaaccbbcdaddaabaacddcaaaccdabcbbdccadcbdacbacbcdcdcdabccbcddcdcbdababadabadcbcbcdddcbabadddaacccdababbcdcdcccdaccdbadbcdbddbdaddbbdadabdaaadbccbabddddadaddcbccbbdaaaaacbbdccaacaabacacbddddabdbccaadbaaabacdabbadadadabcdcacdcbbdbaaababcccbcdacddccbbacdcdbbdbacdadacbccbaddaacdbabaccbdbacdbbdadcaabccbbccbadcdccdddbbcacdbbddcdccabcabccbdcdbcdaccddbacccddaabdbaccadaacbdbadcdcacdcadbbacdbcadbbabcababccbaddcabdaddcacaccdaacaaddbaaccacabbdbcccbcdbdbbcadbbbabbbbdbbadddaacdcbccdababdcadcaababacbabadccacdadbbbcabcadccabaacdbddbdbaababdabdbcadddbbdbbcbdcbaabdaacacaccdbcbddadaaacacbabbdddcdabaddbcbdcbdcbcbbacddadbbdccadcccddaaaaccabbbbbcbccbbccdcccabdadcaddcbdbacdbddbbdcddccdaabcbabcaacadcddaadacbbcbcbbacdcdadadcccdadcabbacbcbbbdddacaabaaccdccbdcdbbdbcdbaabcbdbccbbdbaaaddbbacacaddbcddaddcadcbcdccbaddaccbcabdaacddabcacabccbaaaaddccddddaadddbaabdddbdbabddbdaababadbcbcbcccdacdbcdcddadbdacabdaadddcdcddbdcabdaddbcdbbcaccdbccacbdaccdccddcbdaacabcdcdadcbdcacccbcbaccbabbcccbbcdbccaadaccabdddcbcddaacddddaabadaababbcdcdcabacbdbdddccbddbbdddbabacaadcbdbccaccddabdadaacbdccdcddabdabacbacadbddadcbdaaaddabbadcbbbcabdbabdaaaacadccdbaacbadbcbddacdcdabcccdacbdddbdcdcbbcbdccbbcdadbabcdcbaabbcbccddbccbabdaacadacccacdcbcccdacaccbcdcbdbdcbddabbabcabbaaaabaabbddbdcdcddccabbcbabbdcadddbadcadbabcdadcbabdcaccadadccdadcacbbacbaaccbddbaccddbbcbbbccbcbacbbcabcdcbdaddcdbabcbcccdcbccddadababcddbdcdbacbdbbcdcdbccbcbdaaadcdabdbbdacbadddabbdbaccacddddacacdaccdbcadbaaaabababacadbbacdaaadcccccbacdcbaddadcddcbcabdcbbdbcbdbaadbdacacdcbaddcaadbdccdbbbddaccbcbabadddbacadadbddddadbacbbdcbcdaacbdadddcaddaddddbaadcaddabcbdcbaccbccddacadbddbdbacbadaccddccbdccbbcabbdaddcacdabccdaababbbdbaccbcadacdcacbbcdcadaacaabacdadbdaabdcccdbdabadddabdaaddabdadbadcabdaaaaaacaccbdaaaadcabdccbacbdcadaacdcdccbcdcacadcdbaadcbcadacdcaccadabcdcadaccadaddabcaaaacaaacbdaacacabdaccbcddccadcbbcbcbbabcadacaadbbaddacadccbbadaddcdbbbbccdaaaccdabbcbccbdcdcbccdbdcadabbacdbccdabbbbacaaccdcbbcccccacacacdcdaacadcccdcbccdcadccdababcadcdcbddcaadddacbcaadaacaaccbdabddcbcdaddccbcbbddbaacaacbddcbaddadddbbdaacbbdbbcdbbbaadbdaadbcaadcbabbcdddcdbdabbcacbbabbaccddacbbdbccdbacddadbacddcbcbbcbbbacbcdddcdacdcdbaddcaddabaabbcadbdddcabbdcbbcbddbababbabbdccabacabbddcbcbaaaadbbabdadbadbaadcddbdbbbbdabcbadaadbcbaabacccddbbddacdddcdcacaadbdaabcadccabdbdbdbdaccabcccdcabcabddabbccabbcbdacdacabcabbccabcabcbdbbcbdbadaaadccdbcdaddabbacaaddbabcdacdacdacdccdaccacbcadddbcacdbdaccadbdacaabdcddabbabadcbbaaccaabbccabadcdccdddcdcbbbbdbaabbdbcbaacbddddaadcbccbbbaabccbcaabdddbdaaaadaabaddcbbcaaabcdcbbabcbbddacdcabaacbcbdcdacbbbacaabdcaccabbacababaaaaabacbbabaaaaabcbdabbddddbcaacadbcdabcdbaacaadbaddbaacbbaabbddbbbcddcdbadcaadbddbacbababcbacbbbbdacbcbcbdadbdbcbdcdcadbabddacbadabbcdbdbbccbcddcdccbcccdccdbcaadaccaaacdaabdbacccadcbcbabdcdbdddbaaaccacdbbdacbbddabdddadadaabdadabcbbabadbdaabbddbaabbcdbdcccbddbcaabadacdbdcabcdcdcbabababcbacadbbabdabbaccdbabbccdddcdbabbdadabcaadbaabcbcdcacaaaccccdccacbaccbbdbacbbbdadacbacdabbbdbbbccdbdddcbaadaaabddcbadccbacddadcbbcdaddcacdcdadaaddbcdbdbbdaabcdbdadabccdbcddbdbcbbdaacdadcaadbbccdabaddcdbcdbccdbccbdaccbcdabcbddbdadcbadcaabacbddacadbdccccabdabddaddbacdddababdbdaccabadcddccbbcdcddbdcbdcddbddbcdaacbdddbcaddacabdcbaabaddcdddabcabdcabcccbbcdaadbabcbdbabadaadadccdccbccaabdaccbaccbacbbdbddccbcaacddbabdbaccbdbccabbdbccabccdbadbacaccdacabcabcbbabdbbddaabddaaabccaddcaccddabaaaddacbccdccdbadbdcdbdcddbbdacccdbdbdbadbdddabccadddaaacdbddbdcaacbbccabbdaccaabddddaacacacbdcbdbcbdadcccddbadcbaacdbaabdcaaabdbcaaddcdddbccaadadadabdabddbcbdaabcacdddcaccbcdccbcadcdcdacacccdddddbbbbcabcacaddcabbcdcbacabbcadacabaccbbabdddddadccbacdadbbadccdcbadbccabddbcbdbabaaaccdcbbcaaacdcdddbccbacdbabdacdcacaacadbaaaaccadabdadadaccddcaaacbbbabaabacadddcbbaabbddbbbbbabcbddbcacbdbacbabbccdddddaaadddccbbbddcababbbcbadcabbcbccddbbbcdcbabacdabacdbaaaabddcbbcddcbaccbbbbcbccdbdcbbcadcadcccbcbdbdccbdbdbbdacacbbbcbbadbcbaaaabbcabdbccadaadaaabcdddaacddcbbdcadddbdcaaaabacddaccadbcddadbdbddcdabadcadddbbddccdbbdaddbbbbdacdbdcaccddcdbdcbaacadbdabaddccacbdbdabdddacacbdddbabcabadacdabacaaabacaacbbdbcdddcadbdbbbcdaaadbccdaaddadbcaadcbbbdbbaabdbbbddbacaabdacbbdbadadbcbbbbbbbcabbacbacdcbcdbdcaddddcbdcbdaddcabdabbddabdbbbabbaaddaabdaabacdacbdaaddacbddddbaadbcaaccdcaaccadaccbadadbdcacccdabaaacacaddccaaaaaacbdbdabaadacdcccaaccbadddaabbbdccdabaadadabbbcddacbaccdcdaacaddccbbabbdaaaadddddbbacbcbbdadabbbddcbadabdbcbbbaaabaaadddaacccbcccbbaccaaaaacbaabccbbadcddaabccbdbcaacdccbcabcaddbaddbadcadadadbbdacaababdcdacbcccdcababddcddcbbdaddcaacdddddcbdddccbdadcddaabcbdcbccacdaabdbdcdababdddabbadbcddddcadcabbddacdbcacbcaccdccaccbdcbacababaddbccdccacccbcabbdcdadccbacdccccbdabcbadaccdcbbcacabbabababadaaabcaaacccbabaadddabdbcadcbcaacbacabadcabbccbcaabcadacbccdaabbadbcadcbddbdbcbbaaadbabadccbdaacbdbadcabcdbdddcacddcccbdbddddaddaccbddbcbdbdadbbdadccddadadbdacadacaabbbabcbdbbbccbadcbbacdacbbdacdcadcbbdacdbdbcdcadbbdbbabbbdcdbabdbdbacacdbccdadababbdbcaccbcadcadbbdadacbbbbaadcbbabcbdccacbabdabccccbcccdbcdacbdacddbcbccadcccddaadbcbccabcdacbdddbbccdcbacacdcbdcccddccacacbdaddcacdbcacbccdcdcbbbcccbadaacdbacccbbcdbdcadacaccdaadcbccabdcdacddabdbddccacabcdbacccaaacdbadadcdbbaadcbddbdcacbdbbaccdccabddaddcacacaadcccaaabdbddbddccbbdcacdcccbcdbcbbcbcbaadcddbddacbcccacbcccacbbaadbbaacdcbbdbcabdcddbcdccacdaaddbaacbcdcbbbbbcddbccacbbaadbbdacbacbabbacccddabbbcabcbcacbdaacbdabccaccabcccbcacdbdbdadddacbaacadabcbcbccdbcbdddbaaccdbdaaddbdababddccabcdbdbbadadccdabbdaacdbbcbaaaaabbaaacacccbcbdbcdadaaaadadbadaadcdadbaaaacaaccacdddddcbcbcdbdadbadcbdcadccbccbaddaddcdadabdbadaacabccddcbaccadcccadaaaccbacaadcaccbcdbcccbdcdbaadcbdbdddbcbaacaccadaaadcbbbcdcaadbdbcbcddabccddcaaddccbbababdaacaaddbcdbcbdaababbababadabaccaabdabdaaadccbaabbbbaddbaaadbbbdcadabdbaaacbadbbcbcabcbacbaabacddccaccbbcacaaacabddbcdadddabcccdcdacccddbadbacbdbabacadddbbdacbbbbabddaabbdadcddcddbcacbcbababacdbcbcbacdbabddaacdacbbdbbdccbbbcdabdbbcccbaabbdacacaabddaabcdaaaacbbbbdadbdcaadcdaddcbcdccbcdbdacdcbcdaccccccbbdbcdabdacbdacbbccdaaddcadcdbdabbbbdadbbaaddddcadbdcabccddbcadcccbbcbbbdabdabdcbadabaabbdbbbdccdddbcbbdbbbaaabbcdbabacdbdabdcbdddaadabbabbadbadaaaaaaddcacacbbdbdababbddbacdccbdacbbbadbacdacbabbdadbcdaadacccbbcbacbdddcbcbadcbdcacbdadbabaaaccadbdcaaacddbacdacadacdaaaacbddcccbadddbbccbadacacbadaacabbbdaddbdaccdabdadaddbbaadadbdbcbacbadbabdbcaaaadcddcdcccacdaddcddbcbabdabdbcccdbdbccccbcbbddcbbdcbacbcabcaadcadccbdddaddbbaaaaabcddacbacabdcbdbadabdacaaaaddcdcdcaadabcbabbbcbbcdbadbbaadcdcdbaacdbabcddbdaadccddcdcccbdacbbcbcbccbbcabbcccadaaccbccdddadbdbaccaddbadbcccbcccaccdcdcdddbdcbabcbaaabadbcacbddacabacbcabbccacacdbaabccdcddccdcccdbcbcadcbcaabcdcaabcddbadccddcbccaababbbabbbccaccbdbbccbbbbbcacaacaadddddcddacddcabbadbbbbadbacbbcbccbacdababbdaacdccdcbcbcbdccbbbbdaabccdcabbabcabdcccdbdcacdccdbdbaddcbccabacbcbadaabcabdcaddcbbcbabacaaacdbababddcbaccdbdbddcabbadbabdcdabbccacbdbabcbcdbccdddbadbdccdcddcbcdbcccddcbbcdaacbddabdcbddddadcccdbdadcacbdcbdabdccdadbacaaaadbdcdcbddcbcadcabaabbabcabccdcbcadbabccbbadddcacacabaccbbacacccaadabbadabbbcabbcaacaacdcbbccbbcaddacdddbcdbcbbdcaccabadddaabaddacdcdccbbbadbbaacbcaabbdacbdcaaabdbcccbabdcbccacbbabaccddacdbadadbdbccbbdbdabdbcdcdbcaddbaccbcdbbdbaadcdacccadabdbdbdbaccabaabdaabaadccaaacaddbabcdcdcbcbbdcbcddcdcdaacaaadcadaadbaacaabcaaccbccdcbccccbcbaaaaddbddabcbabbaadbbcabdabddabaadaadacbcbcadbcbdbcccadaadbacdabcabcbdcbbdadcacbadadcabacadcbbbbcaccccaadbcdaadcdbbbaabcbaacccaadbdccdcbaaaabcdbccdcabdbccacbadadbbcdbbaabadcdcacbbaabcabbadcdbbddbccddccddcbdbdaabcbabdabbdddddbdbbdbcddccbbdbddbcbdaabbdabdbccddddccbcbaabbdbbbddcdbdccacbaacabdbddbabaacbcacbdadddddabcadadaacaddabbbbbacdabcdadacbaabdadcdbbbddcddcdadcacbbdbadbbdcaaddbdababbccabdbddbacdddbbcacbbdccdbabbdcccdaaddcabcbcdcccaaddbcacacaddaabaabbbaddcaacdddbadaddbcbabbbadbbdddddbcbdbbddadabaccaacddcbbdcbdbbbadbabdbbcbabadbdcdacdaabbddcddccbdbbcbadbdadaccdabacddcaacbddbaddcdbcdcbbacadbbbabaadbcbcbcdbbbcccdcddddddbacdaaacdbbbabddababcbacbbdcdaadadcbacdabcdbdbbacdcdbbaabdacdacbadcadbcabacbdcbdddcabcddbcbdcadcadccaacbbddcbbcbbcabcbddddcdccddcccabddbddbaaabbbadbbadcbabacadbccacccbbdcbbaadcdacbabaaadaaccadcbddddacdbbdcdbcacdccdcacdcddcbddaccaddcaadddccbaaacccdcacbacdacddadbaddbccdbbabdbbcadcaaccaadcabbacbbdddddbcadcbacaadbcacbccddcadcccadacdbbcacaaaaaacadbdbdddbadcbabbbadbcbddaacbcbbcbdcabbadcdcbdbbacdaaacbcddbbaadbadcbdcccdaccabcbbcbaaaccabbdabbccbcaaccdbbcacaccbdddcdcabcabdddbdbabcbdcdcddccccbcaadccadababcdbcbadaccddacdccccddbabdcbbbacadbbbddcbbcaccdaaaabbccaabacccbbcdddbbccabdcbddcbbddbbaccdabbadaddbbbcbdabadbcdabbcdcbccbcdabcdddbdbaaadacacdcbabbccbbcddcbccbbdcadabacbacabbadbbdbbabcaccadcabcbddddccbcddcacaadbdadcabdaddaacdddbabacddcdcadaadaadccbcacbadcdcbdcaababdaddbcadcaaabadcaacaabcdcbabdddbaaabcaccbbddccbadaadbbddcdccaabbbddabaddbdcadddbdbaabbcacadbdabadabbccaacdabbbadbdaddbdcbbabaccacdbabdcacdbdabbddbdadddbdccbcadbcbbcbdaacadcbaadcbddbdadcdaddbdcbadccdbbcadabcadccaddaddbaaaaabbdbacacccacbabaccddccccbcbcbbcdcaacabbbcddbbddbcddabbcbadababacbccbbcaababccacbabbccbaaacbdcaacaacccabdcbdadaaacbdbcdcbdcdcddadccabbacaaddacadbaacabcbcccdaccbacbadcaddcabdbaccdbaaabbdccbbdccacbccaadbbcbaadbbcdbadbdacbcdcdccaadabdacadadccdbddaddcabddbcaadcbbcccbaabddbaaddbcadbdabddbcacadcdcdabddabccbadcaacddcdccddbabadcbdbbccdcddcacbbcadcdcabbcbadcddccbbbacbabbcdacabbdcddcbdabdbaababaddbddbcbdcbbddcbbbaccbdacddadcaaaabbbaacaacbbbddcdacbbbacddbccbaccbccadababdbddacaccdccdacacdbaaababbacdcacdbadcadbccbcbaacddaacdcaabbdacccabbdddcdbdcaacbbbdcadabbbbabcdabcabddcddbbcddcdbbbbccaaadbcaaabadcabddadabacdaddbddbdacdaaccdddddacabbdabbbaddddddcdbcaaacbbdacddabadabbcdadaddcbdcacaccaabadabbccdcbdaddbaddcaadadadbcbbdbdccbcaccbbdcccbdcacdddabcbbadbdaabcbcaccbddacbbcbadbcaccccaccaacaddcbccddadbdbcbbbdbdacbdcabcdaadabbcaabccdadcbbdbdcbcbdbbbdabbbacdcdbbbdddacdbdaddcbbbddaccbdccdcdcccdcadcaaaccdaddbabdbcdabcdbcaabdcaaabcababaadaddbcddcbabacaaaddcadabdcddbdbababbbaacdacbdbabbddbaccabccacdbdbcdccbabdbdabbacdbbdddcdabaabddbacbdbaabadcaaadabdbdcdabdddcbdccdcbabdccbbabccaacddaadabbbadccabdcbcccabdcddaaadddcacddabcaaacabbbdcbcbcdbbacbadaacbdadcdbdccbadcbdcbdcdcddbabbcbbccdbcaababcddaadbcdabdddcbbaadddddddcbbbcccbcdabdacabbcabbbbbcbdccdacbbabcaaddacaaacccbccccdbaaadaabcbaccbdabdbabbdadacaccdadcbbacbdbbdcaaabcaccaaacabcbbdcddbdbaabdabdbcbbdcacdadbbaacbbdbbdbaaccdacdcbdaacbabaacaabbcacdbdabaabcacbcababbcbbaadbbbaccbbbdadcaadaacbcdbdadbabdabdccbdbadbbcabbaacccbcccaabdddacbcbbcacbddddbccacdddbddbcddaccbcdbdddbacdcddaabbdaabddbacbdabbddbacacaccbadbbbacdcbddadaccbbbbbcddbcccbddcdbbcbdbbdbabdccabacbabdcaccbabccadbaccadbcccdccaccbcababcacaccdacdbbdbadcadabdbacbbccbdbadbdaaddbdadadcdaddbcaadadcacadbaddadbdccabbdaabcdcbabacccdcaadacbadbadbabcdcbaabbbaabccbbcbbdbcbdaaccdcdbacdcbdaaaaaacbdccaaaabacbdddbdabbdccdcacbccbabdaddcabbddadbbbbcbdccbcadabdbaaabdcabacaddcbadddbdddaabbabbabbaadcdacbcaddcbabccccbaaaaadcdcccbcdcadcdadcaddbbcacdacbcddcdbcaabbcadbcbdcdaddadbddcbbdbbcaaaddaddbdcdccbcaddbbccdadddbbaadbcbcddcbcdabdbacdaabaccdababcbaabdbbddacaabcddbaabbcaaaaaaaccdabbdabbbadbdcdcbabaadddbcbacdbddcdcbbcadcabccccddbddbdbdabcbcaadacbabaaabcbabcaccacdaddcddddbacdbaddbddbadbdcaccdcbbcababcdaabbcbddcabbbbcddaccddbbdababbbbbdadccbbaddbdbbaddddaddabbbababaccadccaacbdbacccddddddcaadbcdcdddcaadddbdcbbacdccdbbdbcaadbccbdbbbdaddadabbdacddbdacdbdaddadaaddcddcbdcacdbbcabcbbbccadcadcdbcbcaddbaaabdbadbdbbabbbdcbdbcccbdcdcaaadacdbdccccababadacacadcbaddcdadacbbbdcbcbdabdccccadbbcdcacadcdcccabccdddaacdadbaaacbdcdcaabdbbcbaaadadcbacabcbdbbaccbbbbddadccadbbcdaabaabdadaaabadadadbcaaadadcaaccdaadbabaabddacdccbbcacbabbdacdcdbdabcaabccdbbbddcddcacdacdaaabbdbdddababdccbdaaabcababdbadbbdcdbadcccbcbabadbdcbddbacdbcbdbacdcdcccaaccdaacadaaabacccbcddcaabdccdcaddccbcccacdadcacbbdadcadbcacdaabcacdcdcabcaacabbddacdacbcbaccaddbdacbcdbbbbabccccdaabaddcbbbcdddbccdacdaccbaabcaaacddddcbccbbcabdcdcabbcbdcacdbcbcbdaaabbacdbacaadcabcadaaccabbaddacddcdcbacbdbcdddaabbaaddcbdabadcadcccbbcabcdcdbcabccddbcddddcaadbbdbdabcbbdadbabbaaaaabbccdddcbdcdcccbdcbddccbccbcbdaccaaccadbcbdcbacbbddcbbcacdccacaaadccbdcdbcdbdcaadaabcccacdabcacacdcccdcaddabdbcaadbdbccccccddbccacdbaccdacdbcbdadaddbbcdadcbadaadcdacabcacaccbccbddbaaddcbadbdaaacdbdddadaadccccdcabbaccaccdacbaabacdaacaaabadadabadbdddddcbbcddbbdbcddcdbccbaabbccaaacabdbbbabdbbbaaabdbcbbdbcdccdbcdabbbcdddbbaccadaabccccdbacdcabcbcbbdcaadaacbbcabbddddddbaddbdacbdddadaaabbbaabccaadcbaaddabcddccccdadcdabcbcbcdaabadabadcbacacbcccdaabcdaadccdbcbdaacccdcddcabdcdbbbcbccacbcbacddcbdcdbdbcbaccbbddcaddccbcdabcaacdcacdbdaaaddaddcbadaacacaacccbaccdbcabaddddcbadbccbabacabcbaaabaccbddcabcbaadcddbcdbcacdacccbccdbddadbcbacddacdaababcbbabaddadbccdcbdabdddcbcadaccabdbdbabaabcaddddbdbcdbddbabbdbbaaddcdccbdadaddcaadddbcacbcccaacdaccabdacbddddcdbbabccaddccbddaaccddbcaacdbbdbcbccabbaaaddbccacbaadccdcdbddbdadbdcddddddabdbadddbbabdabcdadbcddddddaaabbccbabcbabbcbdabcdbbddcdbcdcacdadcbabaacabdbbbdccaaaadbdbdcaadacdacbbcabaccdabbcaabbbddacbdaddddbcbddbacadbbcccbabdacacbbacccadbcababadbabaabccacbdbcdbbdbdbdcbdddadcbcbcdacdcdbadabbccbcddbdbabcdbbdbaccabbabdbdbddbdcbddacaddbcaccdbcacdbcacccaddbddcdadaaaadbabcdddbdaabaccabcadcadababaaddbddbcdcbbcbbccadbabcccbdbcaacacbcccddcddcbdbabbbabbbdaaabadbadadccdbbabaaaacbddbcabaaabaddbdabdabbdcccacddacdadbbabacadcdbddbbadadbcbaaccdcacacbabbadadadacdadbbbcdaabacabcdbcbdcdcacccabbbcacdcccabdabbdaddacbbcabadbcccaaacbadacdabdacbbcbdaabacdbcbdaccbbbdcaacdaaaabadbaddcdbcbcadabccacabbcabccaaaccdaadbcdabdadbdabdcdccdaaaacbdacdabdaccdcabbbcbacdcabdacbdabcbbbbadbddccdabdbdaabcbaababbbcbbbadbcbbbacaaadcadaacbccbdacbbdccabbbbcadbddbdbabdabcacddbababdbbbcbdcabaabadddbddabbaaddcbbbbdcddaabcbabccabbdbdcbdabdccabaadcaaaccddcbcbccbddbaccacdcbdaaadacbdadadcbbcdbbaaccbdabcacbbaaccabbddcdadbcdbbddccabadcbaaddbcacbcadbddcbcdcdddacdcbbbbddbdbcabcdacdcacdadaadcccbadddacbaddbadcbaabcbdaabcbacbbcccbdcddcaabbccdabddcabcacdbbbdcdcacbaacaaabbaadacdabccddadddddcbdcdcbaacbdbcadcbaabcdddaacacbdbdbdbcabaaacaadbaabbcadaaadbacadbdcdbadddcddadddadaacbaacabdbcdcdcbdcabdccbbcbadaddccccccccbabddbbccccbaacdccbccbacdadbcbdacccacababcabbcdcbcdddbbcbaaacbaaaabcabdbaccdbcacbabcdbaababdaaadbbdbbddcdabbddadcddbcdcdbdacacbcdaaddbabbacaacaadbccabbcccdcadcccabdbbcaaaacacaaaadcbdbdbaccbabcbdaddacbadccdaddbccaddcdccabcccabbdaadaacccdddcccadbdabbbdccaaadcdcccdcaaaadbccddadabbdacbddccaabdddccddadadbbdabbabadbcbdbabccbbacccaabdaaacaacdcddcccddcaccdcaadbdbaabcdadbdcbbacbdcbacbacadacdbcbbbccdaccaadcabbabdcbccbdbcbbbcdbcdbcdaddbcdcdbbdcccadccacababbcbcabcadcaccacbcbddadcbdaadcbdacbdbcaddddcdadbdadcaadcbacaacbbdadbbdacabbbdadddbadcbbabddbddcbdbddccaaadacccccbabadccdacbbcddbadddbabddbcbaaccbddccdbcbdbbcaaabacddbdbaddcbaabcbbcbcacacadcbbccbccdbbbacabbbcaddcaddbbcdbaccbccaccacacbcbcbadbadcbabcabccacdbaccbaaaacbacdcbabdddbdbddabbbabdccbbddaaaccbaababbaaabcadddcaaaabaabddccccacbacbbbdddbcdaadcbdcddddbbbdcdadcacddbdccdccaddacaabccaabbbdbdaadadabbccdabcbaaabacbbdbdcbdcaddcaddaacbdadccddcacdcbacbdcddbbdadaddaabcbcadbcabcdbdccaaccdaabbbbaacacbcddbcadabdccaaacaaacccccadddabcadbcbcbcacabddacaddadcabcdcddabcdbdcbdbbccacabbcbcdddaccadacbdbbcaacdabddcdcbaabcadddbadabbcdabbdadcaabadbacaaacadddcccbbdccdbacabddbabbddddacddddbabccbdccddcadbddacadbcdcaaacdddbdadbbbbcbccadbbbccaabaacaababdadcadddadcdcadabbcabccbbddbbccbadaddbddaadaacaabaaccdccdbdbacccaccacaababdbabdbdcaddcdcadbbaddaadbbabdacddaaacbcbcabaccabcccccbacbdcacadadabcddbdcddadbabcdbabdcbbcdccbdaadabacdbbcaccdbdacbcdcbdcaaaadacdadccddbadcccdbacbaccaabbdbabbbdaaddaaadcdadabdacbdcdbcccbdacacaabdbcdcaaadaaabbbdbcaaddbbbdbdcbdbbbbdacacdbacacccadbbcdbacddabbbccdccacabdbdabbadabdbcdddcbbdaacadccdcaaaacccccabcdadacbbaaaddadabacbadcdddccacbdbbcabddbdcbccaadcbaddadadcccacbaabddbdadcddddacabaccdddacbbddccabaadcabcdadbabadcdccaadbbbccdabcaadddbadccdcdadbcaaacabcdaddacbcdcdcadaabccbabddaddbbadaddcaacdcadbcaaabacdbcbcbcdbdcbdbcdddddcdddcdcdbdcbdccaaaacadcbaaacdbacdadcdcdcbbcccaacbcdccbaaaccacadbaccbadcdaddabddabdabbdbcaacabadbcdababccbcaaabdcdacbabdaabacaaacbbaddcabdbaacbcbacadccabdddcadcabadcadcbbaabdcdabdcdbcbcabdbaddcbdacccacabbccbabcbbadbcbcdaadbcdabdcaabbccdacbcccdbbaacdbbdaabacadcddbdababbbabdbcddaabadbbdcbdbccddddcadbaccdadbbbddadcabddbccaccaabaaabaddaddcddddcbccabcbcadbaaddbbcbdbbccbabdcadbcccaacbadacdcabcdcaacbddcdbbbbaadaaabddcbaacccacacbacbddcdcbbccaadccdbcdbcacdaddabacdadbcdbcdcddbacccacdadaabbbcadbacbdadaaacdacacaabdaddbaaabaaadbaccabaaacdbbcbcabdcdbdccbdcddddabddddbbbabccdddbcadbddcdcdbbdcbabdbcabacbdcdbcdcbdbddbdbbbdbbabadddadcddabbdcacddcdcbddaabcabcddbcaaddabbcabddcddbadccbbdbaccbadbcadcdbaacdcdabadddacbddabddaccdacdabdbbdcabcbbabbaddbabcabadccadcddbccdcddacaacdcbdadddaacdcabbaabccbdcabdacaadcbaaccddcadcaacdbbadadbadadadccbcdbacbbdacdccadbcbaddcdcdbdddaddbbadcaccacdaacdcbdcbbdccbcdaadadadcadabddcbdbaddacadabbdcacbdbadacdcdccbcbadbcbbddcdacacadaabdddcaccaacabccddbabbdccaadbcbacaaaaaadbacbccbdbddbabdcdbaaabdbaacbbddadcddacbcadaadcbabcdccddccabbbbbaabcbcdbcaaaccaccbbaccddbdcdbccccdddaadbdcbabadaccdbbcaddaccdabccabbcbcadabadabcdaacdbbbabcbdcbddbdbcbdbaabcaccccbabdbdddcbbbaaccdcbbbdadcbaabdccbcababbadadaaadcbbbbbbcdcadaddcbcdaddddbcdbddabcdccadcdbcacbbcdccdbaadbcbabcdcabdcdaaaabdbaaddbadaccbbccaabdccabbabbbbbaaddddcaadabcaacacbcccaacddabbdaaaababcdbdbdddcaaddacdcdddaaccdddacabddccbcbadadbdbaacaababcbcabdaaaadbddbdbbcadddaddcdcdcabacabbccbaddbdbccdabdbdaddbcdaddbccbdbaccdcadddcabccccccdcbcdccbccbbaccaaaccbacbbaadbaddadadbdaccbccbdbbadcbbcbdcdaaabbcabcbcdcccabdddbbadcdcdadaddcbbbcdcbcbaccbadccdbadbbddbcaaadcdbdaaccdcabcbbacaccdcaaacccaaaddabaddaaaabcdbbacbccdadabababdddadbbbbddaadccdaabdaabadddadabaddcdacbabdbddaacdbcbdbacacaabbcaadbdcbcacbcbadbbdcadbbdcbcddaadddcbdabccdcdaacdaabccabbacaccbcbdcddaaddbabdcacdcddcccbcbbcdcddabcaaddbbbaadbdadcaabacacddcbdacccbdcbbdcbcdcbddddaaddacbbbbccbccbcacccbccaccdbaccabbcaacdcdbcbaadbcdbbcacbccacabdadacbdacddcdcdccbdcbadbccaaabadbcacabbbabaadbbcccabadcadcaddcdbcabdcaabbbcacbbadaaaddbbdbcdbabdcccbcdabdcdaddacdaddccadbabbbdcadbcaddbbbccaadccbabacbdabacacddbddbdddddbbaddacdaaacacbdabbcbbddaabdabbddccdadcddadbbbdbbcccadbadbdabababdabacabbadbadbddccdbdbccdcddaaabcccbadaaabdcaccdabdcdcbdcaabacbccddaadadcdbbcabadabddcddbcbbdabdadacdadbdcadaddabcabdddbdadcbbddbbbbbdcbacdabaacadbbcbdadabbdbdaadcaabaadbcddbadaccaccbbccbccccaadddddcbabaadcacadcccbdcbdabbddacddacbaddbdbaabccaaadabbdbdcaaadaaccdbcbdddadadcbaaaabadddacaddadacadcabcadccbbadcbbbbcaddaaacabbaabbabddbcbcababcbbdbdcbcbbaabbbbdcaddbcbdbcdaaabddadacddacbcdaacdcbcbbdaaaaaaaabcaaddcbaaacccbdcabdadacabacacaddccccdbbbadcdcdcbbbdcadcbcccdcabaabdaacbdabaababcbbddbabaccbccbaacbcbdacbbbdcbddabddadcdcdcccacaaabccdbdaacbbcacbadadbdaabbcbbddbbbccccbbdcaaabcbaaaddbbdccccaabcacbadbaabdbcadbbcbaabdcbcddcadcbcacdccdbaddbbababcdbcbbbccbdbdccddaabbdbdcaccadbbdbbcbbbbddadaddbcaccabcccbdacccabccdcabcdccaaacaaacbdbbacccdacacaabdbacacaaacbaadbabbccdbadaaccbabbccabdacacadcccadaaabdaaaccadbcaabadccbccdbcdccdadbaaabacbdccbcdccdbadaddcadacaaabdabddabcabaabcabccacbccdcbbcabaaacadaabaabddaabcbdabcdbdcccdbadbbbcdabbcdccdbccaabccacbdadbbaddadddcaadcadbcdcbdbbaadcbccbdacbabdbbacbdacadbbbbcaabbabdccdcbbbdbabddbdabacaabbaccaabbccdacdaacabbaaadbaadabbaabadcdddbabddbdadadcddaccdbcbabddaccbdcbbddcdbdadcaadccdcccddabacbcddabaaaabcbbcddccbacdbccabdaacbbacabdcacbbabddaadcacaacabaccddcbbcdbbacadbbdabdadddaddbcddaccbbcbccdbdadbdbcdccbdbbabcaddbcdadcbbbcacddaddbbcbacddcaddddaacdaaddcbabdabacacdccbccbcadbbcdcaccccddbbabdcbadccbbbacddccbddbcdbccababddcdccacacdddaaddcbbbaccbcbabdbbcccdcbaccabbaabbdcbaabbbaabdadcbdadcdcaaccbbacbccbdbbdbdabbbcacbdccdcbaccabbabadacbdbbbbcabdaaabaddcbbacaddcdabdcdbcdcaccdcbcbdaabbdcdbccddbddbcbdccdcccbbabacbdadbadaacbddacaaccdaacabbbacccabaabddccdbdccdcbbbcddbbdccacccabdacbbbddcaccabadacbddadbbcaacdccbdbbdbccbbaabdcadcdddccbcbbbbdbdddacbdaddbbdddcaabdccabaabaaacadadacdbdcbdccadcbdaccbbcbbaacaacbabbdcaabadabbacacbbddacdcdbdcbcacbddadddcdcccdacbbcdbccdcccbbddadcdcdaaaabadddbdbaaaaddabbdbdbccccbdadddadaabcdaddadbbbdcaacdcdcabbcccbabbbdaabbdcaadbadcbddddcabdcddcddacbaadccbdccbddabcdabcbacbabbcabdadabbcbbbdcdcabadcbccbbddcadaabbbbababbcdbdcadbcbbdaacddabcabcaadacacddddcbccbdcabbdcdaabdcccbccbbddbaddddccbdbddcacdaadabdaaabbdbcaccdcdccdcbabaaccdcaccbbaadbccdbabcdccdcacbcdabdbbbbddacbbbcabacaccdadcdccbaaabcdaadcbbcbdbbdbcdbacabddabbadabacdabbcbdbbdcccbabdcbbbcbddadacabdadabcbcacadadadcbddcdadaababbbdbbdadcbddcbcaddaddaababcbacbaddbbcbbaabddbddbcbdbddddbdbbccbdcbbcdbdccdcadbbbcbdaacdcabaacddadcadbdadcddadaadbbaadaaddbcadabcdaadcacabdcdaaddcabcadcacbcddccddaccbcccbdadbccbdcadbdaadcacaaccbdbbddabccadaddbcdcddbacbdbadadddabacbdcabdbcbdbdbdccbcbdadddadaccdccbcdcccdadcbcbcabccabdccadbabadbadbdacdadadddbbcaaadaacacddbbdddddaccabadacdcbacdbcbbdacbcddcdbacadabdddcccdabbbcbcbdccdadadbdcbddccdbbabaccbadcacbaabacdaaccbbcaaddcadacbdbaaaccdcabcdaabadadbaaadbbcacdbbdaaabbddacacbbbaddabdcdcccaabaacbddaabddcbabcbdcbdacbccabdbacabbdacadccdddaddabbcbccabddaaaacdcbbbdabcdacbcaacabbcadcbdbacdddbdadaabbcbdddabaabdabdabaccdcddcbaddabbaacbdddacbbddcbdbaabadbaabaaaadcdabdbdcdccbbdddacadaabaaadadbcaccaabcacaaaadabddabcabdadadcbdbdbdcdadccaaadabdcccdadbcdbdabdaddccbdcdbdcadddacdacadddccaadbbbaccbcaadcaccbdbbaccaaabbadaaabbadcaacadbbbdcdaccabcbddcabbbbbabbcdcaadbbabccbbaacadabcbbdbacacbdaabcbdaddcdcbbcbccbccbaacaadcdbcccabadcdccbddccbdccdbacbbbbddacdaacbaadadacddcdccdddbaaadcdbcacdccdbaabadaddbaacccbccdadbdaaaddddcddbabadccacbcddcdcccabbbadaccacaaaddddaadbcddcddccccbdbcacaaddadcacdbcccddaddccbcdddbdddccadbdaadcbccbdabbbbcbdaaabbddcbbddcdbcbadabbcbbccbcbadddbbddcadcaadabcbcbadddaacccabcbcdaacaabdddababcdbbddbbdabbbbcbcbdabdbcccddddbcdbadbaabcaabccbcbbccbdcadcdbcdadbdcdbadcdcddcbcbacacacdccbbdcbabaddbcbabcbdcbcbcdcacdbcddccaacacdcaacbacabaddabcbbbaacdddbbbadcdacbaabbdcadaacdcbaadddaadaaaccaacccbdadbdcadcbddbcadbdaadbdaacdbdcdbdcccabddccbccaacbbdaccabaabbcabbcabacbcbabadbdcbdabcabddbdcbcabbdbccadcdbacbabcabdccccaacccdbdbbdcdadcdbdcaddbdcbbcabccababacabdddcacabbbbbdadbbaaaddbcccdaaacdbcbcaabcdccbabccbaccabbbdcaacacacbdbdcdabacabadbbabccdabbbbccdbdaaabcdcdddcddcddaaadbbdbcbbadacadcbdadacbbacbcadbdaaadbccdaaddaadbbaacbcacbddadcdacabbaddbccabbacdccdcadcbdbcadbdadbacccdcdbdcbcddacbcbabddbdaadbbaabddcbbaabbacccacadcbabdcbdabbacdcdaaabcbccabacbddadbcccacbbacbdcdcdcbdcdbaddabbcddbaccdcdaadccccadddacdbcdbcbdabacdbaabadbcddccbbbbacaadcbbbadadcbdaadbdbcabadacabcaccddbadcabdacbbdabcbcccddadbdbdcbcabbabddbcbcaabbaaaccccabadaccbbacccbadbcabcdaaddddcdddacbcbcadbaaacacadabddcdbaaacacbddddccdddadbacbcbccbbdddacabababbbdcdbdacbccbadcdaadbcaadccbacbbcbaddadbddaddaccdbadccdaaacbabbccdbadcaadccadcabdbdcadadbdcbdbddccddabbddcaacdaadddddbdcacaacbbdcbcdbccbddcaadabbddaabaacbccaacdcbccabdbdcbbdccdaabcdaabcbbdcdbbdbaaaaccddcbbbaaababacbabcdadbbcbddcbbabdbabddacdddcbcdaccbbaadbdcaaaacaaddbccadcbbacdbabacabbcdbbadddbbadddbddddacbdabcaddbbbdbbaccbdcbaaaabcababacbdaabcdcbcddbdbdabbbdbbdbdaaabbaababcbccdaddbbabadaccddabbcbbabbddaaddcddcdacabcdcadaadbcddadaacdaadabacdccaaacbbddabdbcadbdaadcdcbbdbaaacdbadddabbaabaabcaabacacabbbccccdddabdbdcddddacdbbbcdbdcdbdcdcddbccbaccabbadabcbbaccbaddadacadbddbcbcbadbacbadadbabdbbdcadcbaaddcabdbaddaacbddbdadbcdabcbdcacacacdbdaaabccdaacacdabcdcbdbaacddcdbdbacbdadadaaabbcdadcbaacbddadccccccddbdbcaabddabaadabbbbaaaaccadacdbcaabcccbcbdbdcccabccddbddcaaacbddabbcadacdabdcacabdabddbadbdbaddbcabbababbaddbbbbbbaabdacdddbdabcaccdbbacaddccbacccbdaabcbaaadabccdcadbbabaadacbdccbdaaabacdbaacaddaccabadacccccdbbbcdbabcdddadbdbbddaabbbbbccadaabbddabbcaaccdacccdabddaaadcddadcccccccddcdbcdaaabbbbddcdcaacccbbdccbcaaacadadccdcccbabdaaabbbbabbdacaaacccdcaddbabdbddacdaaababcaddddbbcbacbbbddacdacbcabbadcbccbdcdaabddbdcdddcbacbdccdabadcbddcddbaacbadcccacdacdacbbcbabcdbbdbddcbbbaabaacabdbabacacbdcadcabccabdadbbcacacdddbabdcdadcbaddddcccdcdcbdaadbaccdbcbccdccbdbaaaacbaddabcdacccbcadbbddbabacbcadcdddccdcdcdbcbaaacbdbbcdadaadbcbadcddbddbcdbdcadaadcacbbdbabcdaaccdadbaadbbadabcdbdbbbdcbccdcdabdabdcabaaacbbcbcbbcdadaddaabacdaaaadbacdacabaadcdbdabbaaddddcaccdabdcdbdbcbbcdabbaaadbacddbdbcaaddbcadbbdbababcacddbcaddbccbbbbddadaabbdcadbcbdddcbacbddbacdcabcadaacabaaacadabacaababaabcbbbaaacccaabcbcbbcaccbcbbcbdcccadbaaacbdbadbadaccdcddcbcadcaaabbabcbaaaaaccccbddbddbacacbcaccddcadccdbaabcbcadadbdbabcacdcacbbdbaaacadcbbbabadcdddcbbabdabddbbbacadadcbacdbcbcbbddccddbadbaacdcaabcadcddaacaadacacbbdacddabaaddbadacddbaadbaddababababdccbacabdbdbcdbdccccdaddaddbdbacdaacabddaaacbaabaaadddcacddbcbbbdbbbbdbbcddcabbddccbbddbabaabcdcbbbadbbabdbcadbdccddabbaadbbdacbcbbddadcdabdcbdcacccabdaababcbacdbaacabdaacbaadccdbbbccccdbcacaacaadacdabdbaacabadaabcadcbcccbabcdbbcddbababbacbaabbcdabcadadbadbddadccdacbcbddadcbadcdacacacdcaaccaacabcdadcabcabbcbbbdbccdbbddccbbbabbdcacacaddaaacdaadaaddcbaaacccbbccaaaabddacbadaaaddcaaadabacbdddbdcadcacbcbccacbbbbdacaacdbdbdcdaadcadbbdbacbddcbbddbccbdcaacdcbaabbbabdaababbaabdaddbccaaacbccaaadccbcbcaaddaddccdcababaddacdccbbbaacbdaccdddbddbadccdabbddbacdccbbdaabcdcbacbadcbddbcadbdbbabcaaadddaaadabbacbbcaaaaaaadccbaabbbbdccbbddcaaabbbbccadbbbcabccadaaabdacdccbacaadbbcdddaccdcacaacbbdaadcabaaaadcacdcbaadaccbcbabdbbdacaadbcbbbcabcccbbddcdbcadbadcdccbadbcdbdbbabbcccccdbcbdcdbbababcccadaddaaadddcbbbaddccbdcdbadcaacbbabdadbacadcbaadcabaabccaacbdcacdccbcbcbbbdbdbcbadbadcaaadddbcaacadcccccbccccdadacabcadcdadaaaaacbccddabaddbcaadaacddddbdadaabdbbcbbadcaaaabdcddbdcbdcaaabbcbacbaadccbaabdcacbbbcabbccaaaaaaabbbdaccccbaaabdabccbadccdcdaccbdbbbdacbbacacdaacddaccbddaabbdaaaccdadddadaccabcdbbdddcbcbcaadcdabcdcdadcbabdddcbcbddcbdccbacbaadcdaddcababbbbbbdacdccbbadbadbcaaabacadaccddcdaadadbcaaabcbacadccaaaabbbdcaadabaaabcacccdbddcbbbcbdbdacdccccacaaddabddbdcabdddddccabcbdccaabbdbdabbacbdbbdadabbddabaacbababaaadbbbabadbbcdbcacdaabcadabdcbaccddcccddaacacbdabbdddabbacabbdabbccbcaabcddbdbcdbbddcbaaaadcbadcaaadbabcdcbabcabddcbdadaccaabcccacccbaacabbacaacdbacdbcadcdddddadacdbaadaadbbddaadcdaaabdcbbddcadacdbadbcbddbdacbdbbccdbcabacddbbbcbadbaabccdcaaabacddcbcacddddcdccaababccdbadbacbbabaccabddaaddbaacdbcbddbdacccacacbcdcacbabacacdccccbbcbabcdadabbcacbccdaacbacbbdabdddcbbbbdcbdaaabcbcddbaabdacbccdcdacbbbcbbabddaacdaabcdaaccdaadacaccababadbcbabacdccdcdcbdbacadadabacbacddadddcacabcbadadacabccbcbbbcbbdbacbcdddacabdaacbbabbaaacbaddacdcccbdadccdddbababbddaabbacdacabdbacaabdbaccdddcdabbabdccacabbcbddcdcadabbabbcadbcdacdbbdcdbadaaccdaccbadabcddccacbdcbdcaccaacccdccbbbaddcbdadabcadbbabbabdbddaaaddcabcddbababdaccabbbcbcdcadcbdaccddadcadabbddbadcadbaabdbadcdaaddaccacdcaabacdaaabaacabcccbbabddaadcdccbccbabbdbabacdaabdadbbadddbadcbacabbcbddcaccabadbdcdbcdbccaabbacbbdbbcbdddcacddccbccdadbdccdcadacdadcaccacabbdbcddacaddcdbadbcabdbacdacacdacbacddcbdcdadbdcacbbacccddccabdaadaddbcbbcaabcbcdaabbccdaacabddabcdddccbaddadabcbbdacbadbdbbdcacdaaccacacbdbdcdabbddcbcbbaddbdddcdabcaaaaccddaaadcaaacabadcbdaaddaddacdbcddbdabacdabbdbccbccababccbaccdbdadccddcdadddacbbbaddcbbadbdcbdabbbacacccdbbaadbcaaacdbbbacbccdabaadabddaccaddbdbcacdbcbacacccbddddbddbdbacbcacacaccbdcccdcbadcababcdadaabbcbabbddadcacbabcddaaadddbccdbaacccbabbdcdbadbabdaabdcbbbcbadaaabacbadacaadcabacdccadaacbddabbbdabdaabcbacbbcaddcbbccacbcddcacbcbbcbccddcacaacdadcdbadbcadcdbbacadbddddcbddbbacddcdbbddbbabaddcbddabadaccddcdcaaabccbdbcbbcddcdcddbcdbcabdcdaabbadabccddbdbaaaccccdcdbbbbaacbabbcccbddacaccbdadbdaaadacbadcbcbbabaadbbbbbbaccabcbcaaadadbabbbcadcdbbddaaabaabcdabbccdcdcdbdadcabbcbcccaddbaccadbcabadcbccaabbccaabcbacaadababbddabcbddcacdbaadaaabaaacccbdadbcdcdccbacccdbcabcbccacbbcacbcabacbaabbcaaadcaddbbbcbcdadabcbcbbbcddcadcabddaadccaddacbaabccdabaadaddcbaaabbaaabbcccbbddacddcbbcdcababbdcddaabcbccbbcbbadcbdcbaabcaabcdccbbdbccababdbcaacccdbcabcbabccbcaccabbdadcbbdcaddbbccccbacdcaaaaadbdddcbdccccacaccdcadabdcdbccaadcaacadcdaacbacccdccbabaabcbdbadddbbcdcbccabdcbccbdcadbdbaccdabdbadccdddcabdabdbaddcadabaadabadcddccbdbdcdadababbdadabccbcbaabbdbccabdacadbddbaacbbbdbbaccbabcaacbcdcbbbaadadabaacbdcaacaaaacaacccbccccbaabdacbddddbdbbbdabacccabaaabcccbcacdbdadabdbcdbdcbbcdbdadacdbdbcccbcbacadabacadcadcbaddbddddddcbadbcbbbbcdbdbbcdcbbaaadbcadbddbcbaaaddbabaaddbadbbddcbbddddadabbadaabdadbbbaccbddbbdadddbbcbcdbabbaacbccacbdcbcccbbbcbaadccddaddacdcbbdcaccadcadccbcdaaaacbbdcadcdcbadacbbccdcdcacadcbdcabbdbabcabdbcbbdadcdcabbddbdbbbaccabbcbddadddccacacddcdcddcaaddcdbbacdcccbbdcdcabaddadbaddcaabcbdbdadcaccdbbadaddaabcacbadabdbbcdbabdbbcdcbdadaacdcdbcbbdacccadcddccadccdadcdbddcaddccaaaacaacdabbdccddccacaccabcbdcbbbccacdcaababbcbadabbdcacbadcccbacaadcdcddbbddccbddcbddabacabaccddbabcbaddbacccbcaddcdbcaaaadcabbdaabaadadbbbdabbcaabaaaaabddacacbbaddbbbcbbdadbcaacbadbdcdcadbaadadbbdbacdadccabbdbcddacabbddcddbabbddbaaccdaabacdbaddbbdbacdddbabddccbabacacabbbcdcabdbddaaaaabadadabadbdacbbbccbddcbdddbacbbbcadabdcdcabcadbbbaddcbccacdbcababcdbbcddbbdcddcabccabcbdccdddcaadcbcadbbcbbdbdddbdddddadabcaaaadcaacabadabcbadcdadccdcbadccaadcacadbdcdbdccbabadaadaadccaabbcdccacddccadcbabdbdcaadbabcdcbcacaccdbdcbacdbcccdddcbaaddaabaabdccccdaddbcdadacdacacdbabdbbccbcacdcaacacadaabbdacdbaccbdcabddabacbacbababbaacacbbadadcdaddcbdcdbbdbcdbcaacaadbcbdbaaaccdbbdabbabdaddcbbbcccdddbdadcadabaaacddcadbaabdacbbdaabdcdadadabcdbadcbccbbdbcabdcacbbcbcccbbbadbcbcddcdadbabdacbdbbbcbbabbcaabbacaddaadcdadddadbaacaabbbcabaaabaaabbddabdaacadbddbbdaadbaddbacdadcccccacaadbbdccaccdaccddbadbcaabdcdacccbbbbddaddbdbaabbdadcbbbdadaaacbcddcbddbcacccaaabbaddadbccbbabdddaabadcbddbacbadbccacacbcdcbcabdcabddcdcbbbaaaddabacacdcbacaddaabaaacbddbbddbdbcacdbbadacadbbaaaaccabdbacbdadbdddbacdcbbcbdcaaadcdddbadcbabddcabbabdcaacdbbcbaadbcdbddacbbadccababcadddddcacbaaabccaddbababadcbcbcbcbdbccdaccacbdbbdbbaaddcdcbbcbddbcbdaaccbcacbcbaabbbbbaadcddcccacdddaadabcccbdacaaadcbdbcdcabddbaddbdddadbcadbccccdaaccacbccdcbbcbbcdaddcbacadbcadcaaadbcaacdacdcadcaadbbcbadcbdaaddbabbbcdacaadbdddcbbbdcabdbbdaadaddccaacabacccdbcddbdccaacbdcdbbbdbabbcaacbadbccabccddbcacbbadaddacdadadbcabcdbcacbddddbcdadbdacdadcdcdbaaddcacddcabccaabcccabcacadadccbbadababdaddcbbdbabbbcabaccacdcaacabbdbbddbdbdbdcdaacadacccadbdcabbcbbbcdbbabcddddcccababadaabddaadcccbccccabbdcaccacbccbabdcddbdcbaaddbbaaccccadadacdcacbdddccdacdccaaddbdcbcbbdbacdddbdcdccdcdaacaaabababcaaddbdacaaadbbbbabbdaadcddacababccccaadabcbcdabaccbdbaaacdacbddabdaacddbcddddbbcdbaacbcbcbbdcdcadbcddbabaaabbaddacadcacbaccabdadcabcacdcaddaccdbacccbaddddabccaabadbbcdddcaccbcbcdbbccdbcaadabbdabdaaabbabbbddcaadbbcbccabddacadcccbccbbcbaabdcdabdcbabadddadbacdbbdbdbcbcbdbdcabcddcadabadcdbabcabcaccadacbddccadaccadabcdcaccdaaaaaddabdabaacccaabddcbadbadbdaaacdbbababadbddbcbadcbaaabbbaabddcbccacaaacbbacacbabbbbcbbbbadbcbbdcbbcccbccbcbcbbadbabbbcadbaabcdcbadadddadbaaddcddcccaabcbdadbbcbbbcbbadbdcbddaaabcddacddccdbcdabdcbbdcabcadcdcadbccdcdaaaaadbccbadcdcdaddbbdcdacbdccdbadcbdbdabbbdddddaacadccdaadcbbbdbacabbabdacddcdacbdacadabcdcdcadbdcadadbbabddddcddaaabdadccdcdaabaacabdbcdcabdbcbdddbdddcdbbabadacbdbdbaccbdcacaccccdddadbdbcccadddacdacacbbcdbbcdcdcacbdcdddbaddacbbccbbcbcdddaaaccaccadbcccabadcccccddcbadacbdcaadabcccdcdbbcdbbdbcabcaddddbabdccbdacaccbbbcacbcadbccbdaababcbbcccababbabbadabcacbdddddbcbcbadacdaaabdcabbacaaccdcbacdbabcdbbbddbcbcddbbabcbbbdaadccabcdbbbacdbcacccaaddcacadaddbddccdababdaabcaacbdbbbdadcbaccaabdccbcccacbdcdcdaabcbdbacbddbdddaacbccacbcbdbdabbcdadbadacdaadaaccabbdaabccdcbddbdbacacacbbddadacbbcbccbdbbbbcdacaabacbdcddbdccabcaadddcacbaccdccababaddacdcdbdbcbacacbcabbddbddbbbaddbbacbadbdacdaccabbabbdccdddaacbbadcdccacddacdacadcbbadcacdccadabacdddacdabadbacaaacbcbbcacbcadaccbacdcbccbcbcbabadbaadbdbdbcaddcdccbbdabdcabaaaababdddbccccbbccddbadcccaaccdaabbadcbdbdaddbbabbbaadaaaadccaaaddbbbcdbaadacdcabadacaabacbbaddcacdcaacdcdadbdbddaadcdcddccadaddbcaabcaccdaddccbcabccadbbadabdddcbcbdbdcdcdccaddaabcacccdadbcbcdbbdbdcdcaccadaabbdabdacdbbccccdaddccbcaacdbdcccaaadccbaabdbadadabcaadbbdbcdcabbbcaaaaabdbddacaaccbdbbcbcccbdcaadabddaddaabaccbabddadbaccdbcccacbabcccddcadcdbadcdadbdbdcbaacbdacddcdcababaacccaccbdbadddcdbbbdbbbadbcdbbdcbdacbdcdbbdbbccdcbabadcddddccacbbcaadbabbdcbcdbcbbaacdddcbbcadcddcdcbddbbcdaabadadaacadadcdabcacccaacbdaddacaaadcadcbcaccddddadbaacbabccacdaaccdddabbacbbcbcbaacadcddccaaaabccbdccbbddbdccaabacaaddcabbdacbdcdcbcacbcbaaabddabcadabcbbababcbaaaabadcbbdbbdccaccdabbaaddbdcdbbccdcdcbbbdbaddababbabdcaccdcddbbdcbadcbacdcbdabddbbcabadaabadcbbabbcaabaadacaabaddabdacabacaaccbaabcdbbcbdadabcadaabbdabdabcbcdbdbaccbcdaacbcdccbccccbabaddcaacdbabdccacdbcdbdaadaacdbccddcacbaabcdabaacdacddacbbcdacccbdbdbccdacadcddadddbaaadbdcbaabcddcadbcabcbbdaaccbdbadaaabbddadacbdbcaadddbcbcadbcddbbdcabbcbdadcdddcdcbcbaddcabcdbcdadaccddbdcdcdaabaacbbdbdbdabddbdcbaabddbbabaaaabbdabccdaccddbbbcdadbcabbcbbcbcdbbbbccabdddaddadcaaabbcbacbddbccacaaacdbcabddddaccdababdaabccdaacbabadcbdcddabcccbcacabdaddacaccdbaabdbbccdaaacbaacdbadddbadabdaaddaabacccddabaaadaccbcbbccbdccdbaadbaccccbcbccdcdaadbacacaaccabdcbcabbcaccaaddadaabccbcddcaacbcacacaddbadbbdacaaadcdaacbccdcabdcbcccbccdcdcbcbbcbbcaacbddcbaabdbbbddbdbcddadabddabdcdcccaaaaddbcdadbdbcbbcdcccbcdadcaabaabcddadaccaaabbabcacdacadbdacadbccbbdadddcddccccbdbbccdcccbbacbcdbadaabbccabbaccacdddbabbbcbdbcdbbaadcadcdddcbbaaccdbcadbacaaabadcdbacbabacbdbdaadbcbbbddadbddcdbaabbddbabbcbacbbddbdbdcacbbbbbbcbcbbaccdccbcddcdbddddcbcccdcbbabadbdabcadbbcaacacbabaaaadcabdcccacadbaacadacdbacbccccdddbbbaccbbaadbabdcaacbccdcadbbbdbdddbbadadbdbccbddcaccbcccbbdbadbabbcadaddbdacabacadaacbdcdabaacdaddbaaabdcdcabbbdcabddccbadbbbccdccbaaadacbaadabcbbabbdcdbbdddcdbdbcdadcdcdcdadaaadbdcdbbabdadcacddddcadbddcabddbcccbcbdddbbdadbddbdbdbbbdababcdadabbdcacdcddbbbaabbacdacbbaaabbcdccbbbbacbbdacbddbdadaacadabcdcdcacdcabaaaaabbccdbbddaabcbddcaddbbbabdbaccdbadabcdccbabaaabadadbcbdacbacacddddacdcbcbbabcddbcacddacbcdcbabcddabbdacdcabbbbbccbdddbacbdddacbcabbccdcaacacdcadccacabbcdbdacacdbcabadcadadbaddbbdcddaadbccbbdacaddbacbdaacaabbcdbababcaccdadcdcbcabcddbbdaadcddbdaddabbbbcdbddbbaccadcbdbcbcdccbdcbacddcbbabadcbacaddabaddddcdabdaabcbabbaabbaacacbddcdadcddabcccbaaccbdcaacdcddcccdabdaaddadbcbddacbbddadcadcabddbababcdbdaacdccbbabcbadbdbbccabcdbcbdababbcabacbcbdcadbdbadcadcbccdcbadcbccbadbdddbcbbdaabbadadcadadccbabcdbbbdddbcdbdacccadbbaabacddadcdaaddaadaaacdbccdadbccdddadcabbabbcbadbbcaddcddbddbbcdacabbbcadbcdaacbacccbcdaaccbdbadddbdbbdbaaadbbddcaadabaaccccabbbabbcbaacaddbddcdccdcdbcdababcdbaadcdcdcbddcaddcdcbdbdaaacbdbdcaddcdddbcaabcbccdbddcdccabddbcbbddbaddcccdbabbdbcccccbcccaaaadacddcbabdbdbadacbaaddabbccbdabbcaccbdaddcdbadaaaaccdbbcdbbcccdbcabacaabdcbdabadbaabccbcadbaddadcddccaaaccbdcdabacddbccdcdcccdadccccbaabcabadcaddcabbccababddcdbabddcddacaacbdbaddbcccabdbbddadddcccaadabadbabacabcaacdbbbccbdbbbdaadaacadcabcaacbacbaacbbabbdbaabcaaccbbacbbadcbabaddaacbadaccbdbdcdcdccacaacdcadaccbdbbcddbbddbabacdbdddadbcbadadcddbadababbbaccbcadcdadaacdbbbdacacdcbbabddcbdbbbadbcdbcbcccaddabdcddbabbddbbddbbccddadbdccccbadbccaaddaddbbdbbacadbcabdbabaadaabadadddbdbccdbdbbccbccdcddbadbdddacabacbdadcccaddbcbababadbaacccdcbdabbdcacaabdcbbabbdbdaddbddadbacdddccabccbdadbbcabbacdbdabcbbdcbbdbcbbdcdbdddcabcacbabdaabdbbabcacccdbadbdbcbbdaabadbaabddababbadabbdababcdbdccaddbddbaabdabcacdacddcbabadbdbaccbccdbbcdddaddcaacadcddcdcacdadccbdccacabdccacbaaadbccadddcdcbcbcdcbbcbcbcbcbdadcbaaabbbdaaaaaabddaaabcdcaaabbabcddcbdaacacabdacdbabdcdcaddaacabcbabbadcadccdcccdcdccabbdbdbdbabbdcadcdabdcbadadbcdabdaadccbdbccbbdbbdcdcbaddaaadbbcacdcbcccdcddaaddcddcccdcabddbbccddabcbddcdacdddddbaaccababdaabbcdacbbcacacddbdcaadcbdcdccacaccdbdcdccbbbdcddcaaabbdbabbdcddaaddccdbcbdbcdccddddcbddcdbbacbcbabacccbabbbcbbbabcadabadcacabbbbbdbdccadddacbdcdbacacccdcdacadabbcdcbbaccaaabbabbadcabccccbcabcddcaddabddddaadbacddbacddabcdcdbbbadaccdccbddcadabadaadadcdbabccaaacbdcdaabccdcdbaaccdcabbaaccdddaddaadbdacbddacbbaabcbdcdbbcaabcdccbdaabddcabbbdabbaaababdcadaccbacaaacdcadccddcacbbcacdccabbddcbdaabcacbaaccbcadcbcbdcabacbabacadacaacddbbdbbaacdaaddbccdbdaaddbcbbacdbcdbddcdcbbaacddbaacacccdbbabaddbdccccbadbcbdbdbabbbcaaaadbcaccacdbaccbbddabdbadddcdccbdccbbcdcacacdbacdcbbdacdbabdabacbcbcababadcdbbabaccbddcbccdcaccbbddcbaaacccdbcbbccbaaaccbdcdccddcddadbdbbbabcbaabcddabcaccdcdbcbcaaaccbdbcddaddadcbaaabbdcdbdcbdbbbbabbcbdbabaddbcbbddcdcabcddaaddabbcdaacbaaadcbcabdacdbdcbbbdbcbbaaaddaddbdbbacaaaacdacacccbadadbabdababdbcacdbaddddbaddbddbabdddbaccddaacdcbccdacdccbabdccdacdcbdcbaabadbabaaadcbaaacdbcadbdddddbbabbaddaddbdaddbabaadadddaacabdacbcbdbcabcababbacacbcadbbbcacbaaccdbbbaaddddbaadbccabaaabadacdddadccbababddbbabbaacaaadabccaacbcdcdbbbaddbbdadbcadbdccbdabbcabcadccabddcbdcdbabcbbcbcabdadbabbaadbbbdbdbdddbdacdaabaacadcadcdaaaccabbbcddccabbdbadabcacbababbcdbacbccaaabdbddccbaccdcbdddacdbbbbacdabaaadcaccdabaababddbcbdadcaddcddcbcabaabcbdcdcbaddbdccaddadaadababddaccbcdddcbdacababcdacbdaddddbbddacababbbcadcdabdabaaababccadbcbddcdcdbcbaccdabbdcbcdacbdacdabdbddddcdcaccaccaadcacbbadabacadcdcaaadddaabcaacdbdbbaddbbacacbabababddbbbabbbadccdbcdcbbddbdcbadabdbbbbdccdababadacaaccadcacbdcccaabbdcbdacdbabbdbddbabcaacbaadccaaaadbabcdacacdacacadbdcabdaabcaadcbaadaacdadcaaaadadacbddadbccdbbcdcbaddbbbbaaaccbbcadcbaabaaadcadabadbbbdbdacacaacaaddbaabbbbaadcaddcbddbacbccaadbbbabcdcbadddccbcbcacbccaacddcbbccbbaccaadbcdcdbbdccaacdbbababbccdbacbdacaccbdaacbccadacddcabbccacabdaccbadabbacaacbcbadcbbaabadacabcbaddbddabcabaadbbabbcbcadcbdbbcacaadbddaddabcbbdddddaaacadbccccdaccacdbdabbacbdbdcadabaaabdccdbcacabcccaadabadcbcddadadabbccbabcbdabcbddbbadbcdbcbcbbaaacdcaccadaaccababacbcbcabdcdcdcbabbbbcbdabacdcbbaacdcadcaabdadaaaadcabcabaddacbacddbbddbdcbabcdcbacbcbadabcadccdbdcbcddcbcacccbadaddcadbbdabccdbacbdbaadbdccabacdddadacaccbbbbdcaadbaabadbdadddacbdbcadadaabdcddabddccccdadbcccdcccacacbabbacddbdcaaabcbadabdcdabcadcddcbddadbdcbbbcbaaadaaccbcdbdbadbbaabdcdddbdaabbcbcbbbbcdbcacbdbdacaddccdcaacdbadadabbdbcacdddaadacddbdbacacddcaccbdbcccbbaadccbabadaaccbbcaccabcaccdbaacbcaddaadacdcaadddcbdcdcdaaadaccbdaadbaaacaddcadbcccaacbacbbaddbddbdcdbbcccdbdcacdccacddaaabcdaccbacaabcbabdddaadaaddacdbbddbdbdcccaccdaaddabcacbbabcadbabddccbaccacabddddacdbdacddaabbadabcdacddadccdcaadddbdaddccbabdbbdbacdcdbdbbaccddaaddcdccdcbaddcabdcccbbdddcdcccaaddadbdbadcccbabbbbcdcbcddacccacddbbaaddacadcbbdbaabcbcacadaaaadadbdacdcadbdccacaddbcbabcdddaaacdaaadccaacbacccbbcbbcbbbbaadbbadadbddbbbaddadcaddbbbdaabaadcdccbcaadbaccbccdaddabcdbdcddbabcddadcabcdaabcacdbabcbccbbcabcacadbccbcbddbbccaccdbbaddbcdcbdbbbcdbdbddaabacaccbdadbcbbacbaccdadbabbccccbabcdbadbcbbadcdadcadbcddcacaadddadcaaacdabbcdabcdddcddbcacbddcabbcdcadccabaaddbbbadacbddccddaabaccbcdbcaadcdaccbccbdabbddddcadacdaadbcacccabcccaadcaaabdacddcaccdbbabacaccacabaddcbaaaccbbcadcddcbaabccdcadcbbabcabdcaabcccaabacbdcbdccdbdadcdbbbdccdacaddcddbabcdbbabacbdbacbcacccaaabcbbcaddbbbaccdbbacdaaaaaadcbcabadcabdcbabcddcaadbbbbbccccddbbcacadbdacacddcabcbccaaaaabcbacdbdbabbabcbcbcaccacbbcddbaccbbbdcbacaaacaaacabbccadddaaccbbbdcdddbaadadabdacdbabcddabdadbdcabcddbacbadbacbdccbdbcbcbdabdbcbdbaddabcbbdccacbadddbbbbdccdaaabcabdcadcaddacacabdcdbcacaaccdaacdbcbcddddddaacabcdcacababdaccdadbcbbdaddcdcbcaccccbddadbdcaadbbbdaaadddbdbbadacbddaaabadbdaacdcdcbccdcbcabdbcadbaddbbbbabbadcabaddbadccdacdbcaabbbcccdbccdddbabdaadaacdadcbcacdadccccaaacbddcbcdadbbbcccccdcbcbaacabbdbaaaccacdcabaadccdaaacccdddcdbdddadccdaacaccbcdaaabcdbabbdaddbcdbcaabbdaaccaadabddbddbdaaccdcaccababcdddaccddbcdbbbacabddcdacbcdcbacddcadddbccbacdbadcbcdadcdbadccbcbbcdabcdcddcddcccbcdbddbddddbbdccabdcdbdbcdddddabbcddaadbdaaacadcdddccaddbdcbbbdadbcdbcdddbdbddbaabbbdcbdaaccbacdcabdacbcccdccbdbdbdacabcabcbbadcaadacbbabbabcdaddadbdddabcabbcbcbdbdbddadadbbbcdddcccbccdbccbacaabcacccbabdabadbbddabbddbdcadccaaaabcddddadaaddbacbcdcccdcdcdbcabacbbcacacdbdcdbbbadabcbdccddbddadbdbbddcdaacbbbdaadbacadddacdbbcbcabaacbccdbdabaccbccbdbabbbcadcdccaabdadaddaabcbaccdbaabadbabdcbcdaaaddacbabcacadaccdadbdaccaacbaabaacccaddcaaaccbcdcaacdcacddabdbbbdaabcdacdabcbaacacdbaaaccacdcbcdbcadcdbcdbbdddadbcacccadccbdddbdccbddbdbadabbcdddabcdcddcbdbbbdddcbbacdccbccbdddbdaaadaacbdcacdcabdbdacdabbcbddbcadbaddcadbaabdccabbbddcaadaacbabbbbcdcabdcbaaccabaaacbccbdbbbdbcbcbdadcbbbabdddccaaacbcbcdcbbaacabbcadbdbcbadabbaadbabbbaccccadbcccadbccdcbbdcaaadabbbcacbccbccdabdcacbddbddabccadcddccdcdbbddccdbcdaddabcccdcddcdaddacaaacdcdbbcdcbbaadadcabdcbabdcabbcdbbbcdbcdacccdcdbbaccadadaacaabbacbcaabcbccbacbacccdcaadbcdddacdcbabbbbcbbccabbbdbcacadcadacbdaabbddcacaccbdcdacdbdadadacaaabdcaabdbdcaadcacddabbdbbcccdbdbaabcbcbcdadbdcbbbacaabbadbbdadaabdacabbbcdbcbaadccdacabbaddbbbccaaacbbbcddbcddbdddbcdbcbabbcccbadcdcbbaddcdcabcbaadbdabaccdcbcbcdabcdacdcbdacbdccdcccbbcabdbbdcbcbaddaccdcdadcabddbaccdcbcdbdbdcadabccbaaccadcaacbbdacaacaababcbbaaaacdbbcdbaadcaabbbcabdcabdcdcbdbcabadacdcccaadccaadbaddccdcdaacacaacbaababaadadbaadcbbddbbabadadaaacbdbddccdabbbbcabaacadadbcaabcbdaaccbadcccdccccccadabbdacacbabacbaabaaccbbcababadaaccdbbacabadbbccdbabbdbaadbadbbdcacccdbcaccbdadbbcdadadadcacabadcacbadacdaaaaaabbbcccabbbbbbcdbacbcdddbdccaddcbcabdaabbdacbdcacabcccacadcccbbbbcccaaabdaddbdcdbadbdabdcbaabbdabccababdabbdbccdcacdcbacdbaaccacabccccdbddacdddcddabaabcaccadabcccbccdcacbbcddbcdbdabbddbcbcdcbbabadbabcabcbdccdaacddbddbddbbacdbaccadabbdaacddbbaccbdcddabcccacbccaaaccabbaddcabbbddadaabaabababcdacdbcdbaabaddbcdbbacdaaadabdbddadcbccaadcbaddccbddabbaabbccbccdbdbdbbcabbcadbabaabaadadbbbdddcdbdcaaadaacccbbabdcaadbaddbdcaabbbcbadbcaabdcdcabbbabdcddacaaddcbacadbcaaddbbccdabbcadcdcddbddcbcabdabbdbcaddacdaccabaacabbddbaaccaacabcaccbbabacabbcdcdddbcdcbbdcdbabdbcacdaaacbadcbbdaacbcaacdccbddcaabdaabdbaacdcbaaaccdacbcabdccdcdacbaabccccaaddacddbadbadaabbadccdacbbbcaabadcdaddabdcbccaaadaddcaabbccaccbbcbbaacddbbacdadcbabbadadcbddcacdabacacbbcababbbaddbdadbdcdcadcbaacbadaabdaddaaaabaabbabdcbdbdabaaabadadbbddbdcdbdbbbbcdcbdacdbddcbcbbcdcabadcacbdabaaccdaaaccbcdaadabadadbaadbdbbcbcccccbddbdcbaadbadcddaadcbabaaaddddddbcbadbbbadbdbbbadccdcaabdcdbbdcdcccdbcddcbadcbcacdcbccdcbbbdacdddcdacdcbdccdadbcabadbbadbbbccddacacbbbcdccbcadaadcabcdccbdbbdbccaacdbaadbdadbaadbcdbddddadadcadbabaabcddddccbddbacdbccaccbcbcaadbdcddacbadbdbcabcdddbbdcadbacacbbbbcaccbccacadacabcdcdaabcbaabcdccdbdaabdcbcaadbdbadccddbdaacddbccccacddcaabbabdbaaddadccbddddbadaadacbabbbbbcabcbcdcaddcabcbcddbbdbdaaabaaccdcbbcbbbbbdcbdbadbdbdbaabbcbdddbabdbccdbbcddcbcbbadadacacdadcaccabdcbaabdcccaddcdbdaaadbaaaaacbbdcbdbaaabdaadacdbadcdcadbcaababbacbddcbbbbcacccacdadbbccbabaacbacccbcadacacdadadaaacabbaacaadabddddadacbacacccaacdaccddbabcbbbccaabdcccaccadcdabbbcadcabbdccaaabaccabcaddabdaddddbadcccbbcbcbbabdddccbbdacacacbbbaaaddbaddaaaaadcabbccdabbadaabcdcadddcdcdcddadbdbcbaccdacaacadacbadbcdbaadccdbcdbabdddbdddccdbdabbdacbcbcccdccbbcdcdacdccacbdcadcbaacaabdbacbacccabbdcabbddcadacbcabcdaccbbadddccaddddcbabbacccaccccdbddccdddaaabaddccaadaadcabbcabdbdbcbbbaabadbdcbbbabbbadacaacbdbdbbbcbcbaccdbcccacdbabadcccdbcdbddbdcbcdccddadbbcacbdaadccadbbdadbdcbaddcdccbbdadbdcacccddcdbadabbcbbddadaddddbacccccdbcacbbdcbddddddcccbcdabbadaacbccabacccbddbadadaaacdabbbcddababbcaaadadbdbdaadccddccdacdbcddadcbbacaacbbbdacdccbbdcdbbdaddddbcddbadabaccbaaaabadadbadbbdbaabdcccdbcaddaadccbdadccaacabccccddddbdddadccdacdadabbadbdcccbcbaaaabcaabcbbdadcdacadbcdadbaabcbcababbdacdddcbdcdacacacbabcadadacbdddcdbdbdccacdcdbbabdbbabaacabdbaddaddddbbbddcdacccdaddacaacccdbbbcdbbdbccaddbaaacaddacaadbabdcdccbabbbcbddaccdaacadacabbbdacdcddacdaadbcbddcbddcaadbbcadcbddcaddacddcbcaacddaabdcacddaadccaabcbddbaddccabcadbdabacbccbdbcbabddacdadadcdacdbaaccdbbbacccaaccadabcabaadbaccdabcaddaaaadcbccdbbbaacbbcdcacdacdbdcabbcbcdbccadaccbcadbcabdabcdcdccdbcdcbdcbabaacabdddcdccdadcbcadcdaaabaddadbcbbdaacccabbaadbcccaaabcbbcaadccdcdbaddbbabbbaacbbaacdbbdbdcdadcbdbbbadbaabaddbdbddbdabacccdbcdaaabcdbbcdddaaaaadcaadcdbcdaabbbcdccddcdccbbdcdbcdbdbcacbaddcaabaaabddccdbcccaabbaabaaddddccbdcabdcbcccbaddacabcaddaaaaadacaaacaadcaacaabcacdbacbabdbbcbbccacdaacaddbabacbacaccbddbadacdcabccadcbacbcddcccbdcdcdcdcdcadcdcdadcbcabdbacbcdcbbaccadbaadabbacaabbabdaddddbdcacdabcaadcdcbcbcbbdbbbbaacbddbcadadacddddcdccbdabcadbddbddbbbacaaaabdbcdcddcddddbadcacbcbdcbadbbadbcddabaadbddcabaadcacbabcccccbbbaadcbbdcbaabdaaacbdacabaabcaaacdaabbbabadacbacdcbaabcabaddcacddacbacbccadacbcdcaddcdadbdaacabadddbacaabdddabcbddadbcabcabdadccacbcaaaccacddabccbcaaaadbaaabacdcbaccabaccdbdcdccacabdddabccdabcdaacbbcacabdaaabbdcaacddccaccdbcabdbabdadaacdadacddbdbbbbccddcbbadcdcdacddcbddaddbcabdbdbcbcabadbccabaaacdcbaddcdbabaacdbabcdcbbdcddbabcacadbaaabbaaddcbabcdabdadaccbadbcbdacbdadbadccbbbdaacbabdddddbbadcccdbdbacbabbdabbadcabbabbdacdcdbcdcddbcbdbbddabcdaccbbbabbbcacbbcbdabcbbacdddbacbcaaaaaabbbaacdbcddaccddccaaadcccabbddbadcdbadadcabdcbbaadcdbbdccbbaddddbddddbdcbcdabdddaddbcbccbddacaadaadddabaddbcbbabadcaabbadbbdbcccdccabccabbccaccbdbbdabdcbbbdcddbcbcacbaddcbddabdbccbbcccdbabadddaacaddcbccaadcdacadbacabbbdccacadbbcbbdbbdabbdbabdacdcaccacaddcdaacdbaaadddcbcdbcbccbaddcaaaabaabaaadcaaddaabccbbdcccdadbbbdaccccbbbcbacadbacdcacacddbcadcbaadbccdacacdabaacadcddaabadcbabbdacbbaabdcdcbcadddbcbcbbdcbaddcdcccddcccbcbbccdcbbbadbdaacbcdcbbdabdcdacaabbdddbdcadacacddbbdccabbcdbacbcabadbacabbdaaabacbdbbdbbcbccaacdbaaddbcbacabdbbbabaddcbdbbcdaddbbdabaccbcaacccbcbaabacbccdbbaaaaaaabdabaacacdbacadabbcadbbaccccabcdbaacddbdcbcccdbcbcccabcabbccdaaddbbdabdacdacbbdadbdaadadddcaddcbcbbdcbdabdccddbbccddaadabdbcccccccadbbbcdbacbbcdbbadcbcddaaaaacabcccaaddbcbdbaddbcbbabcaaaacabcbdbadcabcdddaaadcabcddbcbdcaadcddcbaacccdbadddcabadbdbbaddbdaddcaacacacdacbaacacdcaacdadccadddacddccdccddcdddbccdbdcddaabacabcacddccababdadccbcccccbddddaacccbdadcacdacdbdcabdacbcdcdbbbdadaddcbabacabddbdaadbcbabdbbbdcdbcabacddcdbccccbdbbcdbcdaabcadcdaacabaddddcbcaababccccdbaaaccaacccdbbadbdabaacaabccbbbcaddcdbadbadbbcadbadcacccacacddcdcdcdbbcabbcbadaddbdbacaaabbdaabadcbcabdbabbbadbdcbcadcccddcddabdcbacdddccacaabcbbddbadddcdbadaadadacaaaabdaccccdabcbbdbbabccaaaddbbcdbcaadbcadbccbdcabdabababbcccbcadbccbdacacbbccadcdcdabdbbbccacdcdbdabcccadacacbbcbcdaacabacadbcccbaaabbddddddbbacbcccdbcdbbbbcdcdcbbaabcdbaabdbcbcdccdcdacdcaacabccbabaaacadacbdcdaacdaccbdbdcabdaddadadcabbbaaabaccbcbadccdbdbaadaddaaadaccdddaadcccacdbcbcaabcaacaaaccbddcdccbbddbbdadbdcdacacbddbbdbddadbadadaaaadcaddabddccbbaccddcccbdcbcaadabbdbdcbcdbdbcbcbcbbbbbcbcbcdaccabdacccabcdbcddcacdaadaadbbadaacacbcbccdadabccbabcbdacadabaccbadabbbaddccbcbbcbdbdbadcaddbcbdcaccaaaddddcaadcbcddbddaabdababbdaaddbcabccdacaaccdbbbdbaddbdadbdccbacdaaaaadccaaddbadbbbdcccaabccacadccdddddbabbcbcddbdbcccccdbbbbaaabbaccaddcadcabbdcdacabdbbdbdacbadccdbabbcdaacabcdcdaddbaddacaaddcaaccabdcbcabadccdcdaaaddbccacdbdccdabdcadcccabbbcacdbdbdacdbcdbdadcababdaaddabccacaddabadddbacbdbcabcdbacdaacccdaaabdccdabcddcaccadbddadcbdadbacbacbadddcacdbbbdddaacbbbdcdccdcddcadcadcabaacadbbddacbbacaccbbacccadcccbccddbdbdbdcdcdcacdadcdacbdcaabccbdbadaaddaaadcddddccbbdbbabbaadbbadaaacdcddabdddbbbbaddbcbdcdbbddbdcdadbabcaacbbcbdbacccbcaccbbaddabcbabcaadabaaadcabcbaddabaccaaaaccbdbcbdaccccbdbbddbbbddabdbcaacddabddadccdbdddbbbabbdddbcaccdddbadadbcacccbbdbcbccbbaccdbbcddbdbbbcaabbddbabdbdcdabadcadacaaacabddadbaddbdcbbcbbaadcdcccbbaadcaaccbdbabacbbdddaaaddaadacccacacdddcaaccbcddddcadabccabaaaaddabadbcacbadabcdcaabccccbbbddccccdabdbbbcacdcdbdabdbbdddcdbcababcdcbdcddbddbcdbacbaacdddadbadcccbdabdbccaabadabbcbcbbaadcdbbbdbbcddbbcccdbbcbababbdaabccbdbcaaddcdadddbcadadbcdbacbccccaddcbcdbcabbacacaaacddbadaaaaaddadacbdcccabaaadaadacbdbccaaacbcbbbbbcabaddcabaaabbadbcbabcbaabcbbcdcbbcccdbcaabbbabcaaacbccbaaccbacdcabbabcdbcdabbcbddcadaccacaccbddbacccbccbaabcadabcadaacabdbcaddabbbddaccabbccddccababdcdbbdbcabadaadcbbdbcdcaaaccabaabdccaccddbdbddcabddccbbbdaccbadcbadbbaaaccabacdcacdbabbbdadcabdbdabccbcddaccabbddabcaaaabbdbabadbdbcdddababddcddacadcdcbadcacdacdddcabcdcdadbbacabccbbdadadbaaacddcbcacbcabbaddaddcbccbdcdabbaadadbbdaabacddddbcacbbaddbaccbdadaddbddbdcbabddbcbdaabcbccadbaccaadcabacbdbdacbcacabcdccbcacbacddcdabbadcaaccbdcbcaacbbaccccbcabacabbcbabbbabdbdbadcbddaacabcadbbddddcbaadcdcdcaadabccdaaadbcddcabacbcbbbdccdbdbbddbcbbcadbacdacaddddddcadccddcbadbacbdbcdcdcbbbdbabdbcaacddcadbcbabddacdbbdddabdddbaadbabddacacabbacacdcbdacaccacadcacccabdacbaddcdabbaabcddbcbaadadbbaccacbcbbccdadcabaddbbabcbbbbdcaababadbddccddcacbcbabbbdcaaacdabbcdadadcbdbcdabcbcadacdcdadccdddaaaacdcbbabccbaabcbbacacdcbcbcacdbdbcabbcdcadbcbcaaaaacddcdddbcccabdadaabacddbbcccbcacadaadbbcdabbaddbddbbbaacbddaddacbbcdacddddaccccccbdcadcabdbdccbcdbddcbcbdcbadcdabddabddcbdddcbabcabcacdbdabcaaacddbabbabaabccbbaabdadcbccbcadadabdbbcacacddadbacdacdabaccbccbdabcababccadcabcabbdcbcdabcdcbccbccabcdcbacdcdcacdaddacbaaabdbccdaddabdbdaacbdaaacdddabdbadbacdbdcdccdcdabdbcabcdbabaccbbdbcbdabacbbccddbddaddbadcabbcccbbadbdadcadacbcbbccbbaddaaadbdadcbdddbabbdbbdaadbcbdbaaddadadcdaccaccbabcbacdbadcbbdbbbaddbdcbccbccdccacbcddaabdddaadacacbcbadbbcaabacbadcdcbbbbccbadbabdccabbbdbdcbbbbcbabdaabdaccbbacdbdcbddccccddacdabdddbbcbcbadccbcccbaaabbadcaccadcbbdadcbadcbdccdbacddbacdddacddaabcbddbcadbaddaacbccbddbbccabdbbdacccacaddaccdccdbacbcdcbaccabdcadccccabdcdcabaaddbbbdbdbdaaacccccadacdacddacadbdadddddabaaaddacacabbcaccbbaccadcadccaabddacdaddcdcccbcdddaccccabccbdacdbccbaaabaddbcbbaacbdccdcabbcabbdddaabcccccbdadabbcdbcddbabbabccabcacbcaacaabababccdbbdbdacbdbddabbadddbbdbabcaddccadacdadcaabcbdccbaacadadcbcbdddacbdbddccdcddcbcbbcaacbabacdacccbabddcacbdcabbdacabadccdcccaabdabbcdbadbddddddaddbddccaadbacbcdbcaccbddadcaabcdcdcadbaabdccdacaabcccdacdbdcccbdcadacbdcadccabdcaabdababdbcddbcdaadadcabbabadcaaaaabacdcacbbcdbdadddbadbdbddcdcbbaadcaabcdbdbbbacabcddbaccdcdddccbbcdbdbdbbdcaaccbdbcdccadcdaacbdaaabcbbbcbaacacbbaccbdddabcbdbccdbaabdbdcccacdbbcddcdacbddbcacaaacdbbddbdccdcdbdadaddbbabcdbcaddabccabbcabcbbbcaaababddacdbacddadaabaddcbdccbdbdabbbbcabaadcbaadddcbccbbdbbdabdabdacbaaabccbccaccbcccaabcbdcccbcddacbababadbbdbbcbbbaadbadcabbdabacbcaddadaadabbcbbccdcbccdabaacaacadabccccaacddadddacdbbbabaacbdaabdacadadccaabbbcacdacdccddcbcbbbccdcdddbbacbaaddcaccdcccccbcabcbacccabdccbbcaacdcbadcaddaacdbabacbcbccaadaccdccabcbdaddbccdbcabaddbccacaddbbacccabbbbacdbbaacdcbacdbdbccdcbababbbbdccdacccbcacbadaadcaddbaacddbdadbbcbbdaadcaddaabbcbaddcbdadccbddbdacddcdaacddbbccdbdcbddbcabbdbcadbcdbbdccddcaacdacbbcbadadcabacbcdcaadbacccaaababacbbccadbdaadbddbbacaadadcadaccccabddaadbdcabaacacdaccddaddcaaccacacbdddbbdcaddbaabdaabbdddcadbababcdcaaacbcddbbbacadbcacccdcdddcddadbdccbddcadbddabadcccdcbaccddcaaacbdcdcbabdabadaacbbabbcabbadbbaddaaccbdbcbbaccacacccaabaaabbccbaabacadbcdbccaabbadaccbbcadcbdcdbcdadcbdaacaacccddbaaacbabacdcccacacbcdaabadcbbcdabbcbbdaacabdadddaaccaadbdcbbabdbbbddabbaabdcbacabccbbdacabcacadcadbdbcbcdaaabbcadcbdbdbddbdbdbdaaddabbddbdacaaaccbcdaaaadcbdddadbacabcadababdbacbadcabaaabdaccdddcdababbcbabacadabcddacbcdbbbcbdcdbaddbdababaddacdbcdcdadbaacdacbacacdadacdcdabccadbbaaddaccbdccdcbddddcadabbabdcbbcddbaccdbdcccdbcbdccacdabccbdcccaadcbbbcccdbbaabbbacccbbcaacdbbbbdcbddcacbcccabdcaaadabaabbacadbaaabadaccabbccddcdcacabdabbaacdcdaaddbdaaaddabbdcacaaccabbbcbcbdbcbcaccacdbbabadaadacddbdcacdbaabbaacdabadabcbcddbbcdbdddabacadbbaaabbcbcdcdbbcbbcccdbbbaacbdaccdababcadddbbbdbcdcababadcbdacdbdcdbabacaccdbadbbbabdddccbddcbcbddbadbccaadbdbcacbdaadbddcaaaddaadadcaddcdcaaabdbaacbacccccdbaaaaaabcbccbddadadabbcbaacacbaaaaddbddbcaaabdcdcacdaababdccdaccbbdbbbadccbbaccacbaccdaaaacdbdcdbbcbddcaadbaabcaacadaccaccdcddacadcccbbacacdddacbcaacaabbbaaacabaaabdacdccbcbaddaadbacaddbdddccccdcdcbdcbaccdabbabbabbdadababcccbaddcddcbcadcdadddbaabbdbbddddcbbabcbcaaadadadcaccccabdaccdadccdcccddcaacabadcadbaaddbdddcadabcdccbbcbbbacaacdbbcaaaddcbaaddcdbddcacadacccbdacdacbacabdbccddbabacdccadbabdbbddbbacdabaddcadadcbacdccbcacabcbcacccbbddddabcccdbbdbaacbcabbcbabdbbadbbddaccdbccbcadbbdacabcdbdabbcdcdbccadaaccbcacdadbbbcdabcabcdcaaadadbbaabddddbabccaadccaabdbabdccbdabccdddabdabacdccabcbacaccaddccdcacdccbdacddbcdccdcdaabcdcacdacbaccaacbcccbddbdacaabdabcaadadabcdcddcdcddababbdbddcabcaaccaacbabdbbabdabdadadaccadddcbcdcdbcddcdddabbbbddabaccaabdbcdaddcbbdaaacacdaabbccdbbcccbcdccaacdadbbbaaadaadbbdbdaabcadabddacdabcbddaccabbacadbaaaaddbbdcdbdcdddbacbcdcbbacadcdbbadcbcadabaddabbddbbdadbacbdcbbbcbcdacbdaccdbaadabdabbdcabdabbdcddcacdcbadcddcdcdbcbcabdaddbbccbdaaabccdabbabbdcccabdbbbaddacdbbabbcaadadddbdcddabcddacbacbcacdccccabaabdabddadcabbcdccdacabbcaaabcbcbcacddcaaddadadcdbdaccdbdddadbdccccadbbabcdaccccbadadaacbbbccbaadbbbbdaaadcddacbbadcbdccbdaadcdacddccababcabdadacdacddbbbbbbabbcbaccadadbbbdcbcccbddaaccbadcadbadccdadbdbbabcdbddddddabaaddbbbacaaddcbadccbcacdacbbcdcdbdbaababacaccbcbbaacabcadbbccabdddbddacddbcbcabcabddbabdddcbacadcabaadcddabdaddbabccbaccbdbbcabbcddcacadbbdbdbcbdbbdccdbddbbaacdcadaddcdaaddadcbcdadcacbbbdbabacddbcdcadcaacccbadaacaaabccddacacbaacdbbbcdacbbdabadadcaccbdaccdababaaaccbadcdddaaaccddcaaacccacaccdadcadabadbaacaaaddcaddcabbbadbbbbbbbdddbadabcaadbabdacdbdacbadaabaadcabdaaccccdcbcdbcbddbaacbdabbaccabdddacccaddcdcdadbdabcdccaccdbdbcbcbbdddbdcaaabdacdbdccdcddaaccaddccaadccbbdccadddcdabbbddabcbadddccbdccbbacaaaaadbdacaacdbdabdbbcbadccccdbdbaaacdccbddadbadbbadcddddbbbccdbcadaaadabbbdbcdccccddbbbbddcaacbadaaabbddaaddbbadaaadccadbaccaacabcadabdcdbdadcdcdabcbdbaacbbbdbddabdbcbdadddcdbdcbadccccccbddccabaddbcbbabdacbbccaddddcdacbbddcadbdacbbacbaababbbdcbddcbaacacadaddbdcaaaccbabbaacbdcadcdbcccdaccdddaacacdcaaccbcdcbaddaddccccaadabcdccdbdbbacccadcccbabadacdcbcbccbcabcacbddaaddcacabaadbaccdbbdbbcadccabccdcabdccdccbbdddbdaacdccdcddbbaccabdcccbccbdbdcddddbdaadcccddcaacabcbadccbabaadbadbabaabccbccadaadaabaacbacacbcbcbacbbcadbbaddabbabdadbbcbdddbcadcddccadaaddddaccadbdbcbccbddcaadddcabdbdcccacacddabcbdddbcbddacbbabbadcddacdaadbbcabccbbdabcccbcbaabaccbdaabbbcaacdaaaaccaacdcabdaccccbacabcbcaccbdaccacdcbabbdbdacaaadcdacaacdaccaaccabbbadaaabbaccbcaadabdacbaccbdcdcabdcdcaadddbcabdcbabcbdcadccbbabacaabadadbabdcabadadbbabbcbdddaacddcbdcbaaabcccdaadaddbbaadadaabcbbcdadcaaddadcdbadcbcadddbddaddcabcacbbbcddbcdbacccbbcbbacdcbdbcdbcdcaaddcbcbdbbacbddacbaddaacaaccbddbcaddaaabcbaddcbccacdbbbcbcddadacadccdbdcdbbcddbddcabcddcdabddbcabbdaaccacdcdabdacabadcdddabdccbbdabccbdcbbcbccaaccabbbdbdadcdbbccbddcadddbabbdbabcaaccbdbcacabcdacacaaaabbbdbdaabcdbadbcabbbbadcddccaabadddcaccaccaddbccadcdbdccacbcdbdddaccdccbadacaabbdaabacbdadcaabcbccacbadcdccdccddabddabbbbdddcdabdaccbbaaaddabdcdcaddddddacaaacccbaaacdbadcacdbdccbadacddaadbcdcbcddaadcdddcccdbcaaaabbddbacabaaabcaadbadcddcdadbacabccacbcaabbbdadcbaccabdddbdccaccdddbddcdccdacbdbabaddcadddabbcaacdbcdabbcbbaddcacbbabccccadadddbdddcadddbcadbbcbdcdbbabdddbabdbddbacbdddbcdabdbcbcabdcaddbdaaddddbaabcdacadadaacdbaddddbbccaadddddbadabcbdbbcdbdacddaacbadddcdcacbacacbbdbdabbccdcddddbbacccdbbdaacabaabcacdccbcbaacdbaadabaabdccabcccbadbddcddbccaadccacacaadbdbaddabcdabbbbdaaccddabaaadcadcabddbaaaddabaaacddaddddacbbdccdcbcadcbacdadcddbcbdddabaadcdcaabbbbbbdcbdcbdcaaddabaddcadaacdabbbaaadbdbbadbaacadaaaabdcbadcaaabacbcacadddbbaddbaacaaabbbcbacabdabccbbccdaabddcacaddadaaccbdcacbddddabbaddbabbbbdaacdaccabdccbccbdbbcbabacdbcaadccdabbdddbbaabbacdbbacbcbbbabaddccadbbdaacabdbaaaababcdaabadaaaacababccbdcbcabbbabbbccbaaadbbddcdcaccdbdabbccbadacaccabddbabdbcdabdcddaaddddbcacaabaababdddaccdadddaaadabaddcddbdcddbbdadbbdddccccabdcabcbbaadacaabadabcbbcbdccadcabdddbdbdacbacaaabaacddbbcadaacbbadcbacddccbdcbacaaabacdbdbaaacaaaabacddddadabbdcaccdacdcabddccdaabdccaadbbddbdadbaddcbacbacbadcabbbbcadaadbbbcadccacbdcbaddbdabaaddbadcdabbabaaaddbaadaddcadaadaaadaaadcacbdbccabadaddddabacabdbcabcdacdbbbccbadaacdcbbdaaabdacdddabdaaaddbdcbcbadcdbdcbdbaccbacdacaaaccabaabdacaccbdcdacdbbabcdddadacddddddcabacadccabadcadccbbdddcdacacbbbbbcaccbdbbdbddbdacddacbcccbdbdcbbbddaadccacabadccdacaabacdcacadcbbabcbccccaddabaddddbabaaaaaacbccadaaccccdbcdabdbadccabbbbaabadbbdbaccadcbcabdbbbbbcaddbcdadabccdaaddbbbbcbbaabcaddcdbdadaaaccbbbacddadbddaaabdadabdaacddddabbdcbadbaadbcdddadbdbddbcddcdcadbcbabdabccaddddbabbdcbdbbaabdaaaadbdabacddadbacabaadcbbddcacdcaacbcaacacbddccdacbaadaabdbadddcdddacbcabdacbcbcddcaaadbaacdbaddbdcbbbabcbbdcbaacdbccbbcadcaccddcdabaabdacbcdabacabbadababacaabcabdaababbbbccbddbabdcbcabbcacbdbcccdaacbaabbbcababcbddababcdabdccdcdabbdadaadcddaaacbbacaaacbddbabbbadccccbacdcdacabbcddbbddbadacccacbadabdaddbdcaabcddddacaaddddddacddcdbccbcccaccbbbaabcccdddabdddcbbdbacdaacbbcdcbbcbccbdcbcbdadadadabdccccdacacdabcdddbadadbcbbcbbaccdbdacbcbacccbbbdddbcccbaabcdaddcbbbcdcccbabcbcbdbdccadacdabdabddacbddddddabdabacbaabddcadabbbcbbbdbccdbbaaaabbccbaabdabcdaadacadcdaddacabbddcaaccdaaccbcdacacacabcaccdcbadddbdcdaabbabdabbaadbdcddcadbdcaddaaadadbdbabcbadaacbcbbdcacbbaccdbdccadbbcbadbdbddbbddddadaacaabbbadddbdadcbdbbdcbcddaaaabacdaacdbdcdcccaddbcddcdcbbbbadbdcbbccabadadbdaabcbbcacaaabdbdbbdbdbbdcdbccbbbcbcbabbadcbdddbccbddcbabdbbbdcdcabaaddabccdaabcbbdadccbccbbabacddbaabbdbadaccddccacdbdcaaadacaacdbaaacaaccdbaddadadaaddabaacdccadbdcbbbcaddcccbbbabbbcbcabccadddcbadaabbbbdcbdcccdcbbdaccacbdbcdabcdccdadbbcbbbdbcccadbccadccbcccabdaaadbddbcbabbaddddaabbbccbcbcdacdcddcbadaaabdcdddcabcbcdaabcaddaddcdbddccaadcbbddbbacadabbbaaccbdbbcadaabcddacbabdddaacaabcdcbacbabacdccbadbbaaabcdabbdcbaacaaaccbbbabacadabccccbbbcbdacbccddcbaacdbabcccddcdbbdaaccbccccdddddcaaccccbbdcbcadaadbadbddbbdbcddaacbadccbaccdcbdaacbbabbccbcdbbbabacadbdcbcabcbcabccbddcbcacbbdabbcacbcccacbaabcaaccdcbdddbadcbdddbbadbaddacdabcbcbcbbadadaadbdbcdddcbcacaaadacaddccccabdbbdccaddadabcadadcbacbdaaccacccabddabcccbcdbdbcddcdbaaddcdcbcaccdaaaadcbcdbcadcbbacbcdddaabaaadbbddcabbacaadabadddcdbcdcdbcdadacbcbcdcaddccdcaabbbddcdddccacadccbdcbccdccbddaabbacdcacaaaddaabdabbbbadbbabbcbacbaabcbddbbabcbddaccccdddaaadcbacdabdcdccacdbadbbbccdcddaabbbabacbcbcdbbbabdddddcaacbcdcbaaabcbcacbddbaccbdcaabbaabadbaadcdbdcdbcadbcdaabaddaacdbcacadbcbcdbdcdbdbcbcdaccadadcabccdcccacacdadbdaaccabbabdbadddcdbdbabcacdaddddcabcbbacaabbbbdbddaccbaadbaddcdacbacdcdbdddbbccabcabccdccbadbcdddddcbcbaaaabacbbdccacabaaccacdbcbbbbadbabcddadacccaddbcccbaccaabccccddadbddcccccccbcccbaaccaadccaaddaddcbcccdbcaaddadbdbdbbbdbcbdbbbdadadaddabcbaacbaccbcccbbabcaccdbacabdbdccbdbaccbcdcdccbabbbddbcadbdcdcababccdacdbddbaddbdbcbabadcdcaacbdadbccaacddaddccddbbacdcbaabccbccdbddcaabcaccbabccbcabbabcdadddcbcabdaacbbacabbccabbbdcbbdcabbdccddddbcdadabdbcaaddbacbcbccadadcbbcaaddbcbbdabbbabbaccaacdcadaabcccbabcdadaaccbcdbcbacacbbcccbaacaadbcbababddcdbbacaddbdbbaaacdbacadbddbbcccabbbbcaaabbbbbaaaacbdbbacabddbbdcaabdbbccbccbbcaacabcccbdbbddabdcddadcdbbaaadcaabaabacbbbbacabbcbdbabcaabcabbdbbadcacdcacbaadabccbaacbaabadcacaacddabbdbadddaacdcbcdcbcbdbbbdddacddccacdbdccdddaacdbbbbdddcbdacccbdcbadcacdbadddbbbdcdbadadacbccaddaaddabdccabbdbcacdadddaaaccdbbbbcacdaacddbdbdbddadbcaaabcdccdcbdaacddbaddbddbcacbacbdcbcbaccadabdbadbdcacdacadcdbcccddacbcbbabbddbabcababacacdcbcccdcaabbacdbdbcaadbabbdbcdadabbdaddbdaadcaacbaaccbbdcbdddbcbdcbcacacadababdabddcaababddadbdbcdaaccdbbcbdaccbcbcabbabbcadbcaccacbccdabbccabaadabadbdbddaadccbcdbadaabacbdcbbdbbdbaccbcddaaadbaccabccabaababadbcdddaaccbbcbbbcadbccdccadabbbbabbabdcabdcdbaaaadbcacaadcccababaadccddddadcbbbbddbdadcccbbdcdbabcccdcbcdadbcaacbdbcdddddbddacbbdbcccdbadcbaaacbdddcdbbddcdaadddacabcbdabaabdbbbbdaaadabccaadddaccdcdadcbacbabbbbdabbacbaaadbacdbdacdddaaabddaaabbdadaadadddacabbdcdcacbadcaaaaaaaddbbbdcabdccabaddbdabdddcbdadbaddaddcabdaaabdcaccadcacdbdabacbcdcddcbccbdbcadcacbbcdddccbdaccababacabdaaaacccdddabbacabcacddcddbdadcdadcbaddcbdacbbbdccbbccccddabbbaaabacbdcbadbdcdaccaddcabcabcabdcdddabbdddbbccadcbbcbbacdaaccdcdbcaadaadbbbdabbbbbdabdbbdbcbccaacdaadcdbaacbbdbccbbdadcbdcccdadcdbcddaddcadcbbbbacabddcdcacdbbbcccadcabcdbbadddbbbaaaaaaabbaadbcddccdbdacaabdcacdcdbcdccadabcdbddaacacdbdcccaabbddcccccaaaddccbadbbcbabccabaadcdddbadcaddacacdacbcaabcbdacaccdbdbcdbbccbcaadcacbccbcacccabcdadaaccabddacaacabddcccacaabbccabaccbcdbcbdcacabccaddcabcaccdadabacacbaabcbccbbbabacaddaaccdcdcbabaacccaacaabccaddcddaacbdabbcabcbbdccdbbaabdbcbabdccdbbadabacdaadaaccaaacbdcbdabcbcdadacbbdadbddbcadbbcccdabbadaacabdbdddabdcabbcdaaccccccacaadcadcdbaacaabbbaadaaaadcadcbadddbccbdbbaaabbacadddadabbcaaaccbcaadcacdabbdddddccdabcaaaaabbbcccbcabcbdcbcbbbaccbdcbbccdcabdbdcbbccabddadbdaaadbaabdcadbdadaaabcbbbabdacbcdbbaddddbbdbcdbcbbacaabcccddabcddbbbbadbdbbcbddccbabbabbdaaaddacbcdcbaaaacbbcddddbcadbcccccdccddcaaadbacdccdcdcddbadccdbbbaabaabbdddabbbdacdacccdbcabddcdbdbdadbbccddbdcaddcddacadadcccbdaacdcccdbcdacdcadcaabccadcbbcaacaccddababdbcbcdaddddadccddcadddcdadbbdcbcdadcbacabccdaaadcaddbdabdbcddcbabacbcacbacbacaaaddacdbcbbacbacccbabcbbcdadacdcbdcaadaddacccdbcabcbaddbbdacadaaacaaccdcbbdddbabccdbcacacbaacabbadcadaddcabcbdccdabdbdbacbbbccdabbacaacdcabbdbabcbbadadbbbbdaadbbdccadbccdbacabddbbbbbaddbccbbcabaacbdbcabcddbbcdacbdacddaadcbbbbdbbabaaddbcabcbabadcdacaddcccdbaacabcabdaaacddbabdbcdccaddabacbaadcaacdcbcdcbdaddddcdddcbdabcbaddccbdddcbdcaccdccddacccaabcbcdadabadbdabdadbccdbacbdaddabbdcdcbababdcacdbadbcbbcdabdaabdbacdbadacccbcbbadaacdadaadbadbbcacdcaccadaabdabddcaaccbdaabcbdbcbdcadaaabdcbbddbcbdbabaddbbbddabdabcabdcababbcdbacaaaacbabcccabcbdbdcbbbcbdbccbddddaadabdadddabcbbccaadccccdaacadacbbdbaddcccdcbabdccbbdddadcdcbccabdbdccbbcabaadcbccbadaaddccdcadbdbddaccaacaaacadabdcbdbdcadacbcbbdaaaacccadaabccdddbdccaaacbcdbcaaccdbacababbacdccdcdbdabaababdbacbdccacaacccaaccccabbbbbabdacdbbccbbbababdbcdbcccdcdcbccbcbbaabbacdaabaddbcadcbabdccdbacacdcaaaaabaaabdccddccaaccbcbbbdaaaccccaddbacaccaddbadcbcdcccabbadcdaccdbcbabdddbcddcdbbbbddbdabbbbaadddbacbbacdddddbddcabbdabcaccdbcbabbdbcabcbbbacbadbbacabbdacddbcbccdcabbaaaadaadcbdccbadbdacddbcccbbbccaddcadcaaacbbdcdaccdbdadddaabaaadcbcdacbccabddabcaccbcdbacdbadadaabaddacadacddacdabbbacabddbbcacdaddbcbdccbabaddcdcbbbbbbaddbcbcbbddadcdbadabdaabbbcccbdbdcacdbcaddacabcbbdacccbbadcbcbcbcbadcbdacbbcccbdbbdcbdcadccaccacadcabcbaddaaaacacabbcaddcbababcbbadccbcabdacadddaabcddbaddbbcddcbabcbdcccacdbbbcdddacdaddccbaacdadcadaaaabccccacaaaaaaacbbbbdcbbaaccdabaccdddbbbdbabdaccdcddbabdccbddacbdccccdbdcccacbadabdbbacbdccbaadccdccaacbbcbabdbabdccababdcacabbcdbbdcdabbdaccaadaddbcaabbcbbccbbabdadddaacdcabcbaccdbabaadbcdabbdcdaacbbdccccccbdcadabbcccccacdddbbccbcccbdabcdacbcabaabbbbcaabcbdccbdbbdddcadaaabbaaaaddbaccdcbaacbdabacccadacbdaddbaaabdbddbacdbccdcbbadcaddcdbabacbbdacdabdbbdbcdacaaaaadbbbbadbbaddcaabddcddbdcbcdcacdbcdabbdadccccddaaabdadaaaadbbadccabcacaabbddabdcdbcacbddbccbccbdddaaaabaaddbdcddcbdcdacacacabdcdbbddacabbcbbbbbadabadbbdddcaaccaadccdabbdccbaadbaaabcdcacdbbaadcaaabbcdbccbbbabdacbacddcbacbddadcbadbbcabbcdcccddcbbdabbcdabbaaaabadddbbcbcbcdccacdbdaabbdbadbdcbaddabbcddccbbdbbddabababdbacaddbbccbcababcbcadbaadcdcdccbccccabbbaadbcbaaadadccdcbbcdbbdacbcadadbbcbbdcbaaacbdbccbdccbccadcaacdbdabcbbdcaacddaaabadbcacccbaaaacaabdcdbcddbdbdbbadcadbccccaaabcddaadacddcddaddabaadbdacaccdcbddbbdcbadbbacabdcdcacadbdbababbcccbbdabdbaccbdcdacbabbadbacaddbbdcdcdcdbdbcdabbabcccbdbbabcdbbdbcaccbcbacccdabccccdbbdbbdbdbccabbaadacacaaadcabcbbcddccdcdaccacaccadcabdbbaabbcbcdddbcaaddccaabacdcabcaacabbcdbadbdbcbbdccbbcbccaadabbddcbcabdabdcaacbbcddcacbdaaddcbaddadacbdbadddcaddcddaabddbbacacbdbacdddadbbdacccbbbacaadaabbaabadacdcbdcdccabbadddddcaacdcdbcadbcbbbacbbaddcdaccdccbcbcaddababccbbdcbcdbaaadacdadddddbbadddadbaccacddddbadbabbabaccaadababbbcdaadaabbcbdcbacaaacdbaccaddabcccbcdbcbccabdacaaabcaabaabbacdbacccdadbdadaabbdadcddaddbbaacddacbbcccccaccddabccccccaadaacbadccccdcbdccaadcccacbacbdabbaaacbdabdaaadcbdadccdbcdcadcbbcaccadbddddddabbbcabccabbabbbbacacdccaadaaadcaadddbcbcabcbcccdbabdbbbcadccdacaacdaacdadddaddccbcdaddcdaacbcabbaaacbadabcbbdcddcccdcbcdbbcaabaddbdaadcaddcbaabbbcadbcbcabcbdadccbcbcbacabccbababbbccdbcadbcdbbdacbdcdcabccbdcdacbbcdcabddccbbaabdbcdccadccacacbabbabcaccdcabdbdbdddcdacabdccbbbdcbcbcdbaaddbaaabdbdabdacaaaadbccdacddcbcdabbbdccbadadcbcdcccccadbacdbdacddbbdcaabbabbcacabdbaadddddbdccbddcbbdcbcaaadbbcbaadccbbdaabadbbbbcbabadcaabccabddbddcadcccaaaacdcbbcddcdbdccdbbdbbbccdaabcbababbddaaccccbddabbdcbadbddadbdaddccaacabcdcddcabbcdadbabacacbacbcdadbaddbdcbaadbcaccddbcabbbcdacdbbdcdbdadbddaaabbaaaddccaacbbaaabdcbbccaaadbaabaaccadadbdaddccdbccdbdbacdadacbdabcaaadadddcdcdcbadabdddadcaabcbddcacddbdcacdacadacaddbddbaabdcbccaccccccbcbdbcbcdcadbbadbcbbbababcbdcadabaccdbdbccdadaddccddccbbdbdbbbbddcccacbabbcdbbdadbccddcbcadadcadbbbccccbcbcdacacbabddddcbbaababcdaccbabddaadbcdaababcacccabbdccbabbcacbaaccdaddddbaadbbaccdccdcbdcaadccdabbaddbbabbabcdbacdbbabaddaaaddddbccddadacdcdcdbcacdbcdbacadcdaaaaaddbcaadcbabbccdbcacabbdbbcbbcacccccbbcdbdbbcbaacdcbbcbcdccdaadddbadaccaddacaddcbacdabdbcacacbabbbcacddddaaccaccbcbcacbcacbdcbdbcddddbaaadacbdbcdbabdbbdaddbbbbcddcdbcadabbcdaadadbdcabbbddadbdcaaabdabcaaccccbdddccdbbcacbddddbcaddadbcaacddaacbcdcaccbadaddcaaadcaabdcdcbbabaacdcaadbbcbbccacdbaadbcdacdccabddcdabccaadcbbdbddcbcdddabcabadbcbacdaacdcdbdcbccdddcadddbcbbddcbcddbbabacddccdbdddadbcbcadababacabbbbddacbaabbbdaccbcbaaaabdbdccbdaabdaacbcdaaaaddbbbddcdcdbaacbcabcccbadcbabdacaacbbdcbadaacdcbdbabbcbbccdbdccdcccddcabaabddbbabbbcbdcdaaccbbbbcaddbbbabddbccddbdaadbadaccdbaaacbdcbcddcabdacbadbbadbdbdcdbaccabccdbabdbacbadbbdacdccccbccdddbbdcadcdbcdcbdacdcbcbabacbcaadbaadbcdbaacaabbbaddcaabcccabacbbdcabbdbbbaaddaabadcddadbcddbccbbacbcadccbdbbccdbccdbdaccbacccdbbddaabaaadabdabbabbdcadcaccddaadbccdcaaddcbddbbbdccdcaadcbccddbbbbbdddaabadabcbcaabdddcccacccabcccbbcbdddabdcdaabbbcdcdadbcdcbdacddadaabdadbaddbbaaabbacaaabbcbdaabadcadccacdaabacabaccacaabdbacbcdadccacaaabcaaadaaacbcdbacaacbdccbadddddbddccbabbbbcdcbabbcbbcbcddccbdcbdcdabcdacaadcbccddbdadaacacbadcbabccdccdbccbdcdccadbbdabdcbdbdcddbadadaddadddaaabdaabaddbddddbdcbcccaababcabbabdcbccaabadddccdcbdbddabdacdbbcbdabccccbcadaaabccdbcdadabbdbbbdbbadddadcbbdabccbdbdcabcbaaacadcaddbdcaccdacbcdbdcadacddbadaabbcddabcacdcadbccbabcabadbcccdbaaaaddbcbdadbdbdabdadbcdcbacacbaaacabbccddbadcabbbaccadacaacdcbddbbbddacaaddaddcbaadcdddcbdabbaddbadbabddadacdaabdcbddbcaaadddddcabbdbcccacaccacdcabdadbbbbacddabcddcbbdcbabacddcdbdacccbbaccdbcacdaabaccccbbddbbdbbcacabcbabaaccaddadaddabcddcbacabcbacdcddaababaadccddbddbabdadbbabbdcddccaaddcaaccddadbbdabdbaabcacbabbbcdcababccbcdcdbabdbaacdbcabcbdccacccdbacdbaadbccbbddcdacbcbdccccadbcccabdaadddbdcdbacacaadcabbddabcdacabbdddccaccaddbdacdbcdbbdbdcbaabacbccacaadaacdbdddddbbabbcadcacdddcaddcadccbddcbbacbdcadadbacdabdbbddacbddbdadadbdcdcdabbcacababbccbdbbbccbdccabbdddbdaacccbcaacdcbadbddcccacbababccbccacddcbccccdbacddaabbbbcbdababdabdbabccdccacddacdddbacbdcbbcdddcbadbbbbaacdcadcabbbddddabaadbaaccbdcaccccddbabdcaacbdcbdcaccbbbcbcdddcddacbbcaabadcbaacbddacbdabccaccdddcbabbdadcbaccccbbcabbaaddcbbbdbddcabdbbddbadcbccaaccddddbccdcccbddbbaaadcddcdddcadcbdcdcbbdabaaadbabcabbddbcccddacbbdadccdbbcdadbacdbdbcbdaabbdbaddddbcadcbadaaadcbadacdbccbbbbcadddaddbcddacaabadcaabbbcacaccccbcaddaadadbbbabcabbdaacbcadbcabcabacbddbcacabdbdcaabccadbaaddcdbaaadcbbabadadbcbdcbcddbdabaabbbbdbaacbbcdbbdacbacbdbbdabadabccbbccdadbbcdabbaddccbabacccdddccdabbababbbdbaacabbddacddbbcbbcbbadaabddadcbcdbaacbbadbdbcaaaaaabbbbcccdabadaacbcddbaabacbcddddbcacbbddcccbdccbaccbcbabdccbdccbaddddcccabbbabacdbccdaddcdccdacbcdbabadbcddbdabaabccaccdbccacdbabbddaabbbadaacbcbacccbcbdddbbbbbccccacdbababbacbddadcbaadbabbdabddddbcadacbaabddbacbacaadcddadaddaddccbacdcddcddabbacbdbacddccbabdbccaaaddcdbbbaadcbccadababbcbacadbacbcbaaccbbaabdccdaddcdbbdacaacbbcdacddcdaddcdcdcccadadccdcbcdbcbdacbabadbabcbbcccacaabaddadbdbcdbbdcdbdddacbaccbacddccabcbbadadbbcbbbbdcddadcaacbabcaccbbbaabddbdababdbdadaabbbddabdbdadcbcadcddaadccadbdaaababbdadadabbcdbbabcabaaabadbbacaaacbbdcababdaabcaccdbddcdcadacabbbadbabdbbddbbaaabdbccabcdbdbbdcadddaccaccbcaaabdabaacbbcdbbdacccdbbddbdddbadadabacadcdbbbccbcdbaaacbbdcdacabdcdadaaaaccdbbadbabdaaacddbcbdaadababddabbcbddbcabbdbbdabdcdadabacbbbcbacaaaaacbbcdabadcaabcdabbacaadabacbdcbcacddaaadacbdbcbaadbaddadabadadabbbaaddbbdcadccadcdcaadcdabadabcacababdabadddccbabbacbcacdbbddbbacacbaaccdbddccccccdadbcaacbccbbccacdddabdbaaccbdcdccddbcddacdbaadaaabcacdddacbddbadcdddbcabaabcccbdccaaddbcbdbaacbbbdddcdbbabbabddddcaaccdccdcccbcaaaadbdcccbcbabdaabddabccacbddbaddcdcbacbdaccbbcbacaaacbccdabbbaabbcddbbccbbadbbcacbbadaaaccccbcaabddaddbddaabddacdcacdcbdcddaacbababccdcdcbdccabadaaddbccaabaddbdabcdbaabadbaddaabcaaabbbcdbccabaabbbcdbacacacdabccdcbaddddbadabbccacdcaddbdababcdaddabdabdddccdcbccddaaacdbcacadbbbbbdbdacbdcadbcadacdccbcbddbdadcdcccbdbacbacacabdcbdaaaadbacdbbccbbdbbaaaaccbbcaccccbadadcdadbcaccbcdbcddddbddbddcaabdcacdababbacacbadadbdcbbaaaadddbacbcbcdcaadbccdbaacdacbccbbabacaddabbabcdaacdddcaddcadcbbbbcdccdbdbbcaadbdbccdbcdccaaaacdbadbbbcbbdcdbadacbccaaaddaddbbabdadbbbdbacabababddbbbdbabcdddcddbdabbddacbaabaaadcccadbadadcbdbddbadbadabbccddbddabcdddbabaddcdbbbdaadbcadccacbccddaacacaacdcdccbcaccccadcdcbaddcaadcdcccbcadccccacabbabacadabbbabbdbaabdbcbbbbbadcaadbbcbbadbcaacbbabcbdcdadaaadcabbcdccdcbcbaddabbccddbbdbccddcaddacbcadbccbdcaaddcadadcbbddaaadcbdcabdddbbacbdabbddaddbaccabdabddcccbaccbdbccccbbacbadccadbdabbdadbdadaacbaddbcbcbacaccdbadbbdcdccdadccbbbdacadcddccbaadaadddacacdabdcaabdacdacabcbccdadcbbddbdbbadccccccdcdbacbbdddacbaaaaadcbcacccaabadccadacabadcbbacadcdbcdcaadaccbbabacbbddcdcaacbacccdcccabcdcdddbcbdccddcdaaadbbaaadcadbbcbbcddaaaccddabbcdcdabbcabdadbcbabcbabbbbaaaaddbdcdddcdabddaabacddbbcdacbbbcccadcbdadddacabdaabbdbadaadadbbbdbcbadaabcccbaaaaabdaccdccdadbcaadbcdacdacbdabccaacbdabcdcdccccadcbccaabbabdadbdcacbbbbcabbccbbdcadbbcdabbcbabbaddbbcadadbdbddbacbdacbbacbabbbbbadacaaddbaacabbabcbbcbbbbacddbccddcccbacbccccdccababcccabaddbbcdcbcdbdacdcdadbcaaaabbabbcdcdbdbaccbbaabdbccbacdbadcaacdbccdcbcdcaaaddababddbbbadddabadcdccacbaaaaccaaabababaaabbcdbcccbcccddabbbcddadbabacabcbbcdcbccbbdacbbcbaccaacdacccccbbbcdbbddadadccbbcdcaabaccdcdadadbddaccdbabcacadabbccbbddabcbaccbaacbcddbbcadbacadbdbbbdbbbddadabacdddbcbcddbbcddccadadbacbaddddaacbbdabcbaabbbabacaaabdaabbcbddcddbabcddccccbcadbdbcdaabaccccbabdcddcbdacaddaacbcdbdcdbddadababcddcbbcddccabbbbdabacaaadbabdbcabbbaadccdacdaacbabccdccbdabbaaadcdbcaabdccbabaddbbacbbabaadddacbcdabacddaaaaaabaadcdbcabcdbcccbcdccaccacdcacaccdadadcdaaddddbbdbadaccabdbbdaaaccdddaccaabadddbbbaccccabacccbbcdbbcaadddbabadccddacddbdcaacccadcbcdbacdddcddbacaaabacbdddccdacacdbadcbcdbbdcdbbcbccbbbbbcbddbdaadacadbbbddbdabbccdcabbcbaccbcbcaaccbdabcdaabbdccbabbabcbcacdcdabdadbddaaddcabcacdcbadcaadbbadabcbabdaadaccdccdaccbbcaacaddadcbbbdccbcabdadbacdddbcdcccadaccabdbccaddbcbccbadcaaabbbcadcbcdacbabcbbadadbaacadddcbdbabdcdcccabcbaccadcbabaaadccdccbaccbaaaaadaccdbcbdbaadbabbbcbbbadbbbbbbcadccdcaccdadcccbadddbdccbaddbbaddbdbacbacbdcddbbdbcbcaccbbaacacbcdbdccabaacbcccdcccbddabbddaacbdccbdaadcbaddaadadddbbdbdaaacbbdcadccacdbacbbacbdddcccaadabaddadcadddbdddddbaabddaaaccbddcdbcccdbbbbcbdccddddccaacdccbbcbccacbbdabbdacaacbccbabdaaddaddcccadbbbadbccababcacdacdbabcabbdcdcdddcdbbbbbaabacccbddadccccbdbbbbcccaabbadbbbaadaccdbdadbaccacddbcbdcbbdccdabadbbbacbbbacdccbddbddddaabddaaacabacbcdddbabcdabaadacdbcbdbaadbcbcaddbccddbadadddadcbdbddbcacccbbcaabacbcaccdacdbdaccabdbbaccadadaadacdcdbddacacadbddacddcbabcbaabbaabcdccdcacdcddccdacabacadcdbaabbbbbcdacadcbdbdbccbabbbdacddddbccdcbcccaacbdbcaaacaaccabccadbdabbcbdddabdadcdacaadabbccbdbbaacbabddbbbbabcaccbacbcbcdbadbcaabcccadacbbacddbddaabdabbddcbaaddaccdbabcbdcbcdbcdadacbabbccdadacdccddaacdadababbccacbcbbdcbcdbdbcaccabccbcdadbabbbdbddddadcdbdbccdaddcddcbabacbacbbcabbacccdcbbcadcbcdaacabdddbbcaccddbcdacbdaadccaabbbacccdcacbddbabdcbdbbbbccbbccdcbabbdadbbaabdbacbdadadabacbcbcddbbadbdddababbbbadbadaacaaacabddccbbbccbbadbacacbbbabbbdbdcbaddaccbadddbcabdbccabbadacaaacdcddaccdbadadaadbcacdbcbdbcbcdabdcccdcbdacccddbacdbddcadcbabaddcdcaabcccbdbadaaabdbcbcccccdcbcabccdbdbbbdcbadabaababcbbabaddcbbabdabaccbaccbddbbabbacddcaabbcaddbbcadcacbbacadbbaddbcccbbcbbaacbdaadbcaaacdabaccabdcbdaabcaccacccacabcbdaabcbdbdbbbbdbbbcbdbddcdbdbacdadadbdbbaacdcaddcabcddccddbacbddddcabbdccadbbdbcbacbabccbaaddbdbdbadbddbbdcbcbabdbadbcacdaabcbdbbcbcdabccbbccabcccbbbddbdcbabccbcaaabdcbaccabcbaddbcdacdabcdbabbbabdcdbbdaabdccdcaaacbdbdbdccacdcccbbcabaadacbdadaaaadbabcbddcaabadddccadddacababdcccdcbabbdcdacabcbddcadcbbdccaabcbddddbadbdcaccbcdaaaaaacadaabcccccccbbcbbcbccaacadcacbaddcbdaadabddaddcbaadcbdddaaadbbdacdbcbaddbdbbdcbbaaddbbaddcbadbcbdbdddbabbdcabddccdbcddcaadbaaadaacbbaccadddbabaddadcdcaabddadbdcbbdcddcdccbccbabdaaaadcdbaabccbcbbaabacbddcaacabccaabbdcbabccbbccdbdbcabcdaadddbacddabcadbddbcabcbacbcdbbbcdabbdacdddbbcbacacbbaacdbdccbbbcdaddcabbadccadddbbdcbadabdbdddbdbdbbacbadadacabbdbaccabbaddaadbdcadbadbdaadcabdaddaaacadacdbaaddcaadcbdbccbcaadcdaaadaacdccbadcdcbcacdacbccccacddbdcbbaadddcadaadddcdbbddcdddababbbdadcacaacaabbdadcdddcdaccdbbddbcbbbaaaaaddcbcbdaccbacadbcbcdbcdaadaaacabcbdcccbcacbcbbdaacbccbddddbbdccaccadcaabbaddddbdcbbadcadadddcccdacacbaccadcccbbcaacccdcbcdacdacaabaadcdcdaaddbaababdacccbacdbbabaacbabdbdbcbbcbabbacdcbdcdabbcacabcdcbacdabbdbcbaaacbadddbbbcccaaaabbacbcdbdbaddcaaaccdaccccddcabacdabbcdcdcadadaaddbbadbcaddadbbdccbaacbdddddbcacaccadcbaccaabcdaabcdcdaddccdcacbdaccddadaacabadaabdacbbcdbccdccbcadcbbacabdbbbddccacdadabdcdaddacaaddcaccacbdacaddcccabdcbbcaacacaaaadbbadadcdaadcabbacaadcbcddadbbcbdcdcdadabccdbaaacdadbcadcacbbcacdcadabbdcacdcabbaccbdcaddacacbcdbaacddcbcabaacdabaccdbdddbaacbddbdcadbbaadabacadadbabcabbdaaabcabbdcaabcbbbaabababdabbcbdcbcbdadbdadccdbcbbbdacbacbbbaccbdaabbccdbcbbcaddabdccabadadcababadcacabbcdbcdadadcadcbccccdaabddbbdbcadcbcaabdcbcddbabbbbbcddbcbcdcbaacdacccbdababcdcbcbcdbaabcadcdddaddccbdbddbacccdcadbabacbddddcadabbdbabcaabdccbccbdbbcaddadbcabbdcddacaddcdaddcadbbcbbccacbaaacbbcbbbdaabaddadabddaabdcdbdbdcbbaadccdadcacdccdbbcabccdbcdddbdabaddddbcadabccdbacaadcccdacbbadcdcaddadccadbbbcabddaabadbacbacaacdadcdadcbbdcabadabcabbabcbcdbcdacbddaaddbbaccadaadcaaadbcccdbcbabaadccaddddaadddacbdbbbdabddbaaacacbcdadcdacbbbbdccabaddbcbbbdbdaccddababbcdbdddcdddcabdccccccbcbdcacabdadbbbcbadcdcacbccaaabdaaacbcadbccdaacdddbdcacddbadaacacbdbaadcbacbcbbdbcbdadddacadcddbbbaacbcaddaaabcddacacbaaadabbddaaaccdcabdbcbabadcabcabcdaddabcaacaabbdcbcaadddccabacdadcadbdbacaaabcddbbbcccacbbaadcccabbadacbcdddadbadcdabbdcccbadcccbcadacddccbbacdbddbaacadaacbbcccdbcbcccccdadcdbdaaacbaadbdadbdddddccacabccbcbadccccbdcdbcddacddccbaaabcaadadcbddababbbbcbbbdabbbabbdccacbdababdababdabdacbbdddcbadbdbbddbcddbdaadcadaccbacaabccbdddabddcbababcddacdbdabdbacaccabdbcbcaccccbcdbdbbacdcdbcaaddccdccbacddaddccadcccdbdacaacddccdbdbbcabddcbacddcaaddaacdbaccdbbcabbdadbbbadbbbabccbcccbcbdaddbabaaccdddddbcadccdddbcdccbdaaabdbadcacadcbccbbddbaacccddddccbdbbacbadadbaacccabcdadcababdaccdcaabbdbcdadbaaadbbcadbabccddbacbaabcacbcadcbbbcacaabdabbabbdabcdbdcddbcdbdddbdcccaddabcddcbdaccaabbbdaacbbbaaadaabcbcdbddcdcdcbbbbcaccdccabbdcababcdcbbbbabdbbcdccdaaaaaaacbcacbaabacacbbcbdacacadbabbaacaacbbdcbbcdcaadaabdbacdabadcaddccccbbcdaabddcbbcbbbbbaaccccbdbbdddaacbdbbcbbadabaacadaacbbbbcbbdcbbbbdacaabddacdbadaabdbcbdacbbbbdbcdbdcdbcbdadcaadcdcddabcadccddabcdccbddcdbaacdddaacbbccccddcadcbadcbabcddbdcbbaaaadbcccdcabbdcdacbabcdcdbbcbcabacbcacdabddabcabbdabbbaaaddcdccaabcbcbabadacddbdbacccdbadabccbcbbadcdbbdaadbcbddcaaadddaccadcbcbdbcabacbccbddaddaaadbacacddbdacbbbcaaabcacbacdbbbccbabaabdabcabddaddbcbbaaaccddcaaddccbbbacddcbaacdbdadbabccdcdcbabbdabaabddccaaabaacbacaddacdbddadccabcdddbdddadaccdbbcbababadcadbcabaccdbaacaadbaacdddbdabdbdbacbdacdadabcdcacbaaabcdbddbddabcbacbdcbaccaaacdbbabcdaaabbbaaabdbdddacaaddadddcdadaabbdbbdbaaacdbbcaccacbbcbabacdbcadcccacadcdbdbbabaabbccbbcbbaaadcbbaaaacacccbdabbddccdbbcbbccdbbadcacacaaddaddccccdbbabbccddbabcdddaacdbbbcaabdaddacddcbdbdbdcbbabdacacbddadddabdbdbdcdcbccbdbadcbdccabbacdbbbdababacaadaccbdcbbdbababcbcdcbddbdcacbaddcddcacabdbaccdddabbccabcdaacababacdbcbabaaaadaddcbacbaddbccdaaaabbdbbcbbbdddaabbccbcadacddbdcdabbcbdbbccccabdaabbdbcadbcadccdbdadadadcddaddbaadabbdadacccacacdbadaabbdcbbccdadbdccdddaccdaacdbcaccbbbddcbabbbabaaccdcbadabccdaadacbabdadaccbaccdcaabbdbddabbadccdbddcbccbdcbddabbabadcdddaadadabccaddbbbbbddbcabcbdcadabdabddbaccbacdccaabcdbbbabaaabcdccdbbbadcbcdbadaccbdaabddbbbadbcbcddbbabcccccaaaadcdbcbbdabcaaacbdbcbdaaabbabcdacbacbbdcbcdacababbaadcbcadcadddbbccccbbdcacbbbcbbdabacccdaddbbcccdccbbcdcdcabbdacbcdacaadcabaaabadabbdaacaadcbcaaabaadccaaabdaacdaabcaadbabbcbddacabddaaddcaacbbbbbddbbcbcdcdbbbcccbdadaaaddcbacabdcacaddbbbbabbdcbccacbdadcaadbabbdacbbcacccdcdcccadacdbdbddcbdcdababddbaaccaaaabdaccabaddddbcbbccaddddacdcddddbcdabbccddcdacdaadbbdbdbaacacdccddadcdcdacbaadbdaacccabacaaaabdacbdbcdaaaacaadbababdddbccababaaabcdcadcdbbddcccbabccddaadbbbbccbadaccaabbaaabcadcaacabaccdbbbaadadbcdcbababadabcbbabccbadaabcbccdccbdbbbaaddaaccbaadacbccacacdbbdadbabdcccdabbabaaaccbddacdbdadcdddbdaadacccbcbaacdccbabbbaccdbdacdcdbcddbcbbdaddddacdaccaabcdbcbdbaabccdbbcabddbbabadcdccaacdadbacaabacddcdbdcaadbbaabcaabdacdbdacbbabcdbbaacdbccddaaaccdcaddccacbddaddcabccbccbdbdaccbaaacdbbabbcccabadccdacabcadbbdadbbbcaaababcbccadaaccddddabcdbacccbdcaaacbdaabdcaadcacbcbdadbbdcaccbbadcbddbbcabcccccdbdbadbcbcacbdbbabddbaaccacbaabbdcacbdcacccbcdcabbaaadbaaaabbadddbcaaabcabaadcbbcadccacddbbdabbdbaabaacacbdcdabdbabdddddabbcbddcbcbabdaacccdbdadabddcdbacbbbdcdddacbddcccbcaaaadabbdddaaddaadcdaacbcdbbbcabdbbcccbccdaaddcaadadcccaddbabcbccbbadbcdadbdabccddccbbabaaadcccbcccababcaabcbadccbcdbbdccacadddcbcbbdccaccacccbadbbbbdabdabbbbcadacbbbdadddbbdddbdbccdcbdadddbadbcbbdccdcdcdabdcbdcccacadddaddaadbddccbdddcbdbacccbcddaadaabcadaddacdbdddbbbbcbcdcabddbbccdbcbaaabccabccbacadaccaccdbcdadadcdbaadbbcadabaababcbcaacbbbacbcbaccaabcbcdaaaabbbbcacbaadccbaddccbadcdbccaddacbcadcbdcbbddbdbccddbbbbbadbddaddadccabbbababbdaacadbdcaccacbaabdaaabcdacadaabacabbcbacacbabbbccbdaaacabdacddbdadbabcaaccabbcbcdabdcdcabbcbbaaccacdaaadccabcccbadccdbcccbaddcabbccdabaabdbbcbddbdbaaabcdcdcacbdbbddaaacacacbddbadcdcadaabadbadacdbdddcbbabcababaacacddbccadbdcaadcbdbaaacbaddbbdcdcacabcaaacdadaccaadaddbabbadabbaabccbacddbcadbdbaaccbbdbbdabaaabbdcdabcdbabbcdcddaabcbdbbabcbbcccdacddabddaadcaadbbaadcaabcdbbddaaddabaacbaccccdbcbdcabdbcdaabbcbddbacccadabbcccbbaaaabbbbccdabadddbaadacbdbacaabcdadcdddbccddabaaddbcaccbabdcdbcdabccdbdbcaccbcbdbdcddabdddbdbdaaddcdaccaadbaadcaccaacbdbddacbbcaccadaaaacbbbbbdcddaacdaddbdadcaccabdabdcdcbcbabdbdacdbabdadaabbabdccdbddadcabacdddbdddaadaacccaaddadcaddbacdcbadaaaaabaaaaaabdbabccccaabdcdbadbcbdbadacabcdcabbcdaababbccdcccadbaaccddbcccbbbbcababbddcacbabcbcabdcdbaadbaaadadacdabdadcabbbcaabadbcaacabdcdabbaabbbdabacbadbdcbdddbabadbdcbcadaaadadaaabbdbdabbbddabdbcbcbdcbadcbacadcaaddbabbbcbbcccbcaaddcbbadbdcbbcadbbcbabaabcccbadcbabcbabdccaaddccaacacadacacbdbdddadbcadbdadaccacacabccaaabcbccabcdbccccccdaabdcdbdbcaddabddbacadbddcddcabacadbbdbbdbbbacddbccbdcabdcccdddaacdcacdacdbadcacacaccacddbbdbddbccaccdbddaabbaaabbccbbbdbcabacaadbcdcaddbbaacaaaccaccbbdaacccdbadbdacdbaaddaacadcadccdadccacaadcacbbbcaabababdddabaabdcdcaabaccbbaccaaabbaadaadcbadccbbdddddccbdaabdbdacdacdcbaddccddadbbaadcabbbaabababcaaaccbcaabadcbdcbcdccabbbdddadbaddcaaccdcadadbcccacbbadbadacbdddabcaababccaaddabcbadadacbcdabbbdaacabbaaabcbcaddadccdcddbdabdbcdabaddcbadadbdabdbdacdcbbccbccaddddadbbaddbccaadaadbddbdbcbcbaccbcbbabbbdbcddabddadadadaadbadcbacababcbbdbadcababccacdccdccaddacbacccadcdbbcbdaabddadddcddacadaccddbbbabdcaacbbbabacacadacbaaadacbcdccbbdbcacacaadbbbdbcacccdabaccdacabbaaacbadacdcdbacccdabaddacbbdccacbddabdcabbbbadbbccaccaabaadcbcdcabacbacddabbacaaabccdbabdcddbaccccdbadadbdbbdcaabaadcabdbbabdbaabacccaccacdbbcccababbdbbadbaaddbabdbdbdabaadbbdddddbabcccbcdbbccbcdddbbbcdbaccdadaccdacdccaaabddcbddaaddccdadbbaabbbbcddcbddabcdcbabdcaacbabbcaabbcdadabdddcccaadabcacdadcdbcadbddadbbabccdadacadcbcbdaccdbddbdcacbaadadcbccdbabcadbcaddbddabacdbccbaaadadbdccdcdabdbaababaadddcccdabccdababbcccddcbdadbccddacbdbdacbbddbccdadccdaccddcbabcaddacacbdbcadabdabbadcbcbcaccdadbdcbcbdcabbdcbbcdcbdccddabdccadbdcdbbcaaccdcaacbcbcdcddcddabccdbdcddccdcdacadcacbbcccdbbbccbdbaccdccbcbdaccaaabccbcccaddcdbcdaadbaccdbccbcaccadbaabadcabddbbadaaccbbdcadacabadcbacabdcbdbadbbcbcbcbaaddaddabbadcbaccdddbbccddcdcdcdbabcadacddcdcdaadcdabbabbdbdabadccbddacacbccdadadcdbcaabadabdadaddcabbcabbdddadcdcbbdccbccdbadddddabdadbcddadacdcbdbbbaacbbaaaaadbdabbaccbcccdccbcacdccabbacbcabbcdadddcdcccddacbcdcdaddcccbdaabaabaababaabacabbaadccbabdbbdbccdbabdbcbbcdccbbabcabadcdacabcdaccbdacaacdbadadacaaacdbcbccbdabdbbcbccccdbcaddbdddbabdbaaabbaacaddaacdbcbbabdacdcbdccabdbcdadbdddbaaddbbacbcccdbbccbacccdbdcbcadcbabbccccbbbbdcadaabdabbaacddbcbdbdabccbaddbaddbbbcaabbbbbcaadbbdddbdcbcbdbddcaccaabadadcadcaabcdaabadbabbcbdddccdccbdbcbbdacdaabadbdcbbccbccaddbcacadabddddabbadccdcdbdcbdbcaccbdbbaadccbddaacdbbcccaccbadcbcbcccddacdaddcacacdbdbccbdccbadabdcbabbdaaacbddbbcdbdabacbcbdcbcbababdddddcdbbbcabbabbdbbdabcaabaccdcaddbabcbabbabcdcabccbcdbcacdcabadbddbbdcbdbabacbbadacbcaacccdcbabdccabdcdbaddccbacacdbdadbdcdbbaaacadcdaaadcddcbbcbdcdabcbdacddbbccdcabaddbbbacacacdbdbdbddcacbbadbbbbccbdacabddadcacaacaadaaacbddddcbabdacddccdcdbbcaadcddccadccbadabbdcbbdcacadbdccaadaddadbdabdbcddbabacbcabbabcbaacccdabdcacdcabcdcdddccaacdadbcadbbabaaddbcacbaddbdbaaaccbcabcdabcaabcdabccdbacbcbaababaccaadddbadaaaaaccaadcaadbdabdabbdacddccccaaddcbdcccdcccbabbbdbadcccaacdcbddbdbcadbaadcbccdabbdbccaccbcabcacbdcaaddaccaccbbcddcdacdddcdcaaddcddabbcabcbbcdbabccccabcbbacddccbbbcddccbcbbaccdbaabcccccdacbdbdaddabcddcdbcadbdcbaaadabbdcdcdddaaddaccdaaaadaccabdaadbdddabcbaabdbbabcaabdccadacdddabaadbddcddbbcbcbbdbcacddcccaccadcabdbcbbbadddcabbcddbabdccdbdbdabcbcbdbcbaabbbbcbaaadbcdcbaadcacabddccbccadbcbbddbcdadbdcabacdddbccaaccdaaadbccacaaadbcbcbadabbcdddcbaddbddabcbacdaadcabdcbaddbbcbabbadaabbcdccabdcbaabbcdcdadcdcdacaabacdcdcccbdadddaddbcbcaddbddddacbaddcabcccaaaaabdabbadaacdbaccabacbabcbccdbdcadbbbacbdbbacdbcaadbddadbacbadcbcdcbbabcdbdbddbacdcbdbdaadbcdbaabbdadaaddbbcbaaddddbaaaccaddcddaabcbcbbcbadccdabbdabddabcdaddcaacabacbddbaccabdbcddccbadbaaccacddaadcbbbcaadcbcabbdcacaabbddcadbadacdbdbdcbcccabddbbbbadcabbdacadacddcaadbdaacabbdcdadaadbaabdaaacabcdccabdbcacddcadcaadbdacdacdacbddbbcbcdcdcadaddbdcddabcdcbabdaacdabaaadddbbdadcddcacbacabbbcabdcbcabbcbdddcbccbababaabddccbaadbcadddaaaadbbcdccbdacbbddaacaaaccddbabccdddbcccbadaadccbdbdabcccdbddacaacabcbabccbdcaababddddbcdbbcdadbadbaccbdcbdbbdcdacdbabdabdabadddcdabccabdbabddcbcccdccbbacdababadaddbcbcdbbdbadaaaabbccabdacddacdcbadbccdbdadadacdcaddcaadacbcdddbccbcabcbcddbbcdddacbaaabaccddabacbdaabdbdccacabbbabdbdddccdacadcdadadcdcaddcbdaaddbacddccdddaddaabdbdacadbcddbaaabbbdacddbccacdbcaabdcadabacbdcdcddadbaacdaacdcabcabbbaddcdcdbdbaaadbadbaddcdcdcaddaadbdcaacdcddccacdabcdaccdacbdcbccacbcbdccaadcabcdbabacbcbaaaadacbddbcababbadbbbbcdccdcbccaaccbadcbadbdcabcdbdadabaaacbccddccccabdaaadbcbbbbcccbbdabbcbdccbcddbbbbbcbbdbbcaababbcccacdacabbdbdbbdcaacdbcdaacddadbcbddcddaabaacbdadbabbdbdadadaabbcaddddbdccabbcdaddbabdcbbcacbcdcbbdbddcacdcacaccbcabbbdcdabcdccccadccccdccbddbcadcacbdcbccbccdbbdddcbadadbbcbcacccaddbddacdbbacaacdccacaaacdcdbaddabddaacaadcdcabdadcabcadbbcccabbbdddaaacccbbcbaacbcaabcddabdddabaaacbdabccabddadaccddabcddbbbdcbcccaacbbbadccdccccacccaaabddababbabcabbbacadbbcbabcccaccdacdaacdcdaabdcabaaacaacbaddcbbbdbbbbbacbaddbbbbbdbbadbdddaddbbcdacdcdbcadaadcbdcdbdbdbcdbbddccbccbabbcbcdacbaabacdddaaaadbbcdbccabaaddaaacdbadaccadddbdaacadcbddddddbaadcabcacdcadacaacadcdbabbddbdabaadaacbdbbdaacbadcbdcccccacbdcadbbccdddbcdabcbbcdbbcdbccaadbcdbccabdcaccccbaddaaacacbcaccbbdcbdadcaaadbbaacacbadbbacabdcbcdadbaddabdcbbbadcbdcbaabaaddadbdabdccaadcbdcabbbdabdbcbbdbddbccaabbcdacbdcbdbcdcccdcbabcbabbabdacbcacdacabcddbbcddbddacbcaddbbbccdacdddcddcbdadbaabbbbcababdcdadbddbccccacadabaabcbbbddcdcbbabcccdcaadcabcabccdabbbddcdaccbbbdbdbdaccaadbbaaabccacdcccaddccdadccbadddcadbbccbcadaabbccbdbabbcabbdbbbbccddbbdadbdcddcdaacbaadbcdbdbbdcabdbbdaabbdabdcbbdaccaaabababdaaaabadcbbcdabdaabcbdddcbcabcbdabdbddddbdcaddbabccabccbdcaddbacddbaccddcabdcbbaabacbdccbacadaddaabbcdaaacbacbacdbdbdadccbcacbdacbcccadabdbcbcacbbbcaccacdcdacbbbbbacabcaadadcbbcaaacaccdcccbabdacacabdbdcaabdbdcdcadabaaadcdcbaaaacdddcaaaddcdbccbacaccdabdcacbdbbcadcbbcaabaddccddbaaacaacbccbabdabadacbcbbbcdccbccbcadbbdaddddcbdcdccadadadbadcdddcabdcddbaacbaababbcbaccacaacdacbadccaadacdbcddcddaacacbdcaccbdaddaccccabbdcbdcacadadcdbcbdddcccdccdcbcacdcacccbccadcdcdcaabddccbbcaddbcbddacbabdbdcccbbaacbacabbdaabbadabdaabbbacbbadcbbaaabbbbaaaddddabbbccabccdacaaadbdcdabccdcabacbdbabcbdbcddabddadcdbdccaaabacccdadccbbaadadabcccdbaacdadbaabdbcddccdbadbaacbdcdacbabbddcacbbadcdcaddbbddcacdccbdbbdcacdbdcdadccdcbbabddbdbcbaaaacdcaddabbdabbaababccddbacdddabbdcadbdbbdbadacdabadcccaacbdbaaaacdcdbddcddbcbbabacdcadcbdcaccdadacbccdabccbdaaccbcaaacdbaccbbcaaccdbcadabbaaabacabcdbcbdccaabcbaaccabababddaaadaccdabbaccbdbdcdbcdbaabaaaabaacbddaaddcabadbcaaaddbaccdcbddbabcabcbbdbaaccabbbaccacbbdaaabbcccdacddcadddbbdabababdbdaddabccacdcaabdddabaabdabbbaddcadcdaaccddbdddabaadbccacadabbcdddaacddbbdcdadaabdccdaabcaadcdbbdcddbbdabdcddadbddadacacdcbcbadcaabcbddbbcdcbdbadcdbaaabcaaabdacdcbbdbabccdababadbdcbdcbbaddaacccdaaacdacbccadccbbbcdadbadbbaddacadaddbbdcbdabbbbaccabdadcbbacacdbdabcabbbccbcbddacccccadcabcabbcddcccddaabaccbadbcadbbadadadbdcbababdcadadadcbdccaabbabbcabcbcbdcabcdcbbddabcabddcaacdbdbcdcdcccaadbdaadaddcadadbdbddcccabdbccdbddbadbaccbacbadacacbabdbadcabddcdabadccabdcbcbdcaabdabbbccbbdccdbddcbabddcbacddcadbbbbcabddabcbcbccbbddaccbdabdddcaacccdbabbbabdaababacacbdbddabcdbdbbbbbcdcdadbdccdabacbdbcabdbbddaddaaabddabadbbdddabcaabbabbbadadaadbbabddbbcaacaabdcccabddbaccaddbcaadcadadacdcbabaccacaddbadbdcbdccaaaabcbdadadccbbdcddbccadbdadcdbabddacbccdabdbbadcbccbcdbacbdbadbbcdaaabdbdbaaacbadcbbbcbabcbbaacaabbbcbbbcaababbdaddddccabbcbdaacadaddaaccbccdbbccacdbddbdbccdbdddccabddaccdabaaacbccadcdadbaadcabcbbbbcacdbadabcbcccabacdbacbdccadbbbcaddbcbbcbdcbbbdbdadbdddaadddacabddcbbbbabbacdabdbbabbbbbbcbadcbbbbaddcacccbaaabbbbcbccddbbcbcaccbdacbbadbadaccbdbaaabdaaccabcdbabcaadbbcadadbcdbcabcacaaddbbadadacccdacdaabcbccdcbdabacccdbdaacbdbdacbcababacbccabcbbbdaadacbabdbdccacadbccacddccbdddbdbbadbaacddbdccccbcaabdccccdadbcadabdbacaaaaadaadadcdbdbbccddaaaddabdcdcdccccbabaadaacaaabbabacacbbddccdbccbacaaabcdaddbdbaddcccdccddbddbaacacabdbabaddcbdbbadadadddddcdbdcaaabdcbbdcdacbabbdcdaadcdabaabbbbddaadbbccadbbabdcacabbcbbcbdcadcabbdcccdcbdccbcdcadccbcacddccbdcaccacadbdbacaaaaccbbcdaddccaaccbcdacabbdbcbbdaaaadaabccddcacdbdabcbcbdcddbaddbbdabcddcbbbabdcaabccdccabadaccbdabacccddcdddcaddcdadabcccdaaacbdcddcddbcaaabdbdcaadacccadacabdbddccbcddcaacaaccabdbbdcccbaccccdbbbacaacddadbacdbccbbddcbaaacdcbdaccddbcacacbabadadbaabcddcbccddccdadbdcddcdcbcdcdbdbccabdccacbbdaabaccbddadbcbaaaddacaacdbccaaadabdabdbaccabbcacbdcccaccaccccbbbbaabccccbcaadcbadcbdabdccdccdcdabdbbdcdbbcbdcaccdaabadcabaccacadcbcacccdbbccdadcbdabdbdbbcadbcdadabdcbddcdbdcabcabacddddccbadbadcbbcbdbcddbdccdaaabacbddcaadccbdbbadcbaccdcbbdaacababdbdcadbaabbdbaddaacbdbbcacdabcbddddccccbaabbdccddcbadcdbbdbacacbabbcbbacccadbcdadaabdddacaadcbdbdcdcddcbbcdaabdbddcaadcccaacdddbbdbddcdddbddaaadbbddaabbddaadaabdbcbacddccbbbbbbddcadcdacbccccdcaadaaacdcadaabacabddaadbbdbbccbdccdadbacadcabaadddcbacabaaddadabdbbaacbcbaaabbbdbacdccacbcabddababdbbdabcabbabcbcabdcadcbdcdddccbdbaadadddddbdbbbacdcaddcbbdadbababdcbaacabdacbdddbbbaccabbbaadbcdbbdccbcddbcdbcdcaddbcdddccacddbcadaddcbbdccbdadddacaaaccadacbdcdccacbdbdbcdcabadbbabaaccbbddadddacabcaddaaccacbcdacbccbcabdbcdaacbdaaddddbdcdddddadbababaccddddaccddbcbbcbdacabadccaccacccbcdbdcddddbdbabbcbabacbadcabdcadbcbbccbdcaaaabadaacbadccdacabbabdbccaabbdbabadcbbbadacdaccacacbbdbdccaacadcbccbdcdcdddabbdcddcccabdddbadcdddccabbcddddcbdaabddaaabcadacccdbdcaacdcbbabbdbddbabcbcddacbaccccbbbbdaddbcccbdbabdcbbaabcbdaaabccabaababcddbbdbbcacdbdccacadacaaabcdcadcbaadcbbcbcaaacbbdbadcabbcdadbcdcbadbbcdaacddbaaccacbcbbacbabdabadbdaddcdcbbcacdcabaccaaacacdddcabccbdabcbcccacabbcacdabadbcdcabdadacaccabbcabaabcabcacbbbaabbccabacdddaccddbdabbbcaadbbbdacabaabccacbdaccddadddabcdadcbdddcabaccacadbcadcdacbdbcdbbbcbbbdaabdacdbbdddbdbaaacbacccbdddbcbababaaaacddbdbcbcccdbcdddbbaadddbdadabbdddabccbaddbccbbbdabcdbcbcddcababaabbaccdbaaadaadcdbdaacdaaabdccaaabddcaaadccbbabbbaccbbbddaabcdbcdbbdccbcdbddadacbddcdcaacdbdbcbcbcacbcbacdcabbddcabcdaaddcddadcdbabbddcbcbcccdccbcbbdaaacdbcababdbdcbabadaaacbdbbacbccadabaadaccdcbaaadbabaaccaddcdbabacbbcbbdcabbdcdbbcaccaccbaaadcdbddcacdbbcbaabddbcacbbaabcbbaccaabbdcaccddbccaccbaaccbbdccdaccccbdccdbcacbbccbbcccbdacbdadbcddbacdbbadaabcccadabbdbddcadcdadcaaccdbcbadbdcbbdddbaddcdbbcddbbbdbcdcbdddcbbabccdabdccbbdaaabbbbcbcbddbabaaacdadcaabaaabdacababadddcaabcadcbcccdcaabdabdadcaacdabdcdbbcaaccbcacdaabbdcbdcddbaaddcddcbdbcdccbaadabcaacddadadbabbccccbbbdbcdbadcddbddbadadbbbcdbaacabdabcadcbcdabbbadadadbadabadbcdbaadbbadbacabbdddddcaabaadbddddbdcaddbbdddacbbcddcbdbccadcbadbacbdacbabdacabcdacadadccbaccbbcccdabbcbbbadbcadadababdacabddadddddcabcbdbadaaabaabcbabbbcaddbabdadbbcacccaacacdccbbcdbbacdcdacadbaacbdaacbdabcadddcdadaaacccabcaabbadddadcbaaaacacbcddbcaabbbdbcaabdcbabdcbcadcbcbdbacacbaababccabcbabacdcdcdbabdbbdbbcddccdadadcdcbbdabdadaabcbccccccabbacddcaccdbaaabadaadaaacababdadaccbabbccbcadadcdacdcadadacdbabdaabdaddcdbabbbdbbddaacbcadbdcaabdbbbbddbbbabaaabbcabdaaddaadbbddcdbbbdcbddcdccabcdbddcdaaacdbdaaadcbcdadbdaadcccbdccabbbdcadbabdcaccbcbdcdccbdbbdccbbcbbaddcbaddddbaddacabdbcdcdbacacabbdbaccbdacabcabaadbcaabccadbbdccddbbbddcabdbadacaadbcadacadbacdbcccdcbbbdcabcbcbbddcadbcabcacadcdcdadaaccaacadccbdcddabbcbbbddcccbadbdaabadccdddadcbcdddccabadcabddbdccbcbadadbdbddccbbbddbcbdbccbabcdcddcbcbbbabadaaaabaadbcccadbbdababbaabdabdbdcdaacbdbaacbbbbdbbccbacbcdbbbaaaacbaaabbadddaaaccbddaabacbadacbbccaababcaacaddddcadddabdaadcdbbdbcbbdadbcabbcdbbdccaabadcdbbcabacaccddbbacacacdaddddcbbdbacaddbcaadccbdbbcabdccdabccbdbcbbcdccbdbdddddadcbaacccacddadcbabdcaababacccababbdacddbbdddbdbcddbbcbacdccbabdbbaabdaabdddadccbcadbaabbbdaaddbabcabaabaacadbbdabddbaadcdbbadccdabaacaaddddabbcbbbacadabdbaacaccaacbbcdadcadaccbddccaddbbbbadcccbddababadabddcbabbcccddaddbaadbaddaccdcccaccbccbcdcabdcdbaabcddbaaabdccbcbadddcacdbddbacacdbdadbccccbbabdcdacdbabcacccbbabbadbbbcdbadcdcbdcaaacbdcdcdccdbccadddddccddacdcadabdcbacdbbbbbaabcaacacaadccaacbbdbcdbbcadbbacbaaddcaaabbbdcabaadadadbccccddaaccbcbbcdbaaccacacdbdddadaadcdcdcccbbbbddadcbdccbdbacbbddccaabbcdbdbadbcbbbdaaaadbbbabbbbddbbcdadabcbdbcdbdabbbdcbcbacacdccadcdbacdabaabacdbbacbaaccbdacbccdabacccbaabacbbaaadbabdadbcacccacadcadcdddbbacaabbcbadddccddbbbbdadcccabacdccdccaddaddddacbbabbcdbbcbcaddbdadbabbbddcbbbddabcddabbacaacaacacbadabacdbcadccbccdbccdddccaddabcaacaacdcabccacdbdddbbadddaccdacbcccbaacbdcaddbcdcdbacacdddcccabbcacadabcbdbddbadcaccccdaadcadbbdccabcacbdbcbabbcdbdacbdbcbacdcbcbdcacddbcbcaadbabcadacdacdabaccbabdbccdadbaddaddadcacabbbdcbaacabbbdddcdcdbacaddbacdabdabcdaaccdadadacdbbbcbbbbbcbaccaaddaaacabbbbdddbdbcdcbadbabababdabcbaaddcacadcbcbdbbbadbcbbaabbcdcbddccdadbdbcaacdccddabdccadbbcbdbdccadaaaabbdaddbadcaaaadbabcdcbcacbbdacbcbbbcbdbacddcdbabccaadccbadcbacccbdbacbdabdbcccdcdcbcdaaaaadbabcccabaccbbbbbdaaabadcbdccaabcbdcdbcdccabcddbccdcadaabdbcdcdcdaadddaccabdccaabdbbaaacdcdcbdccaaccccccdcbdaacdacacbcccabcdbddabadcbbccbacacadccdacdddddccaaaabdaccdcbdacdaadabbabcdcaacbcbdbacbdadacbabdcccaabdcaadccddddbadacacbcbcbdbcaaadccccdcabddbcbcaddbcadbaaabbdbbcbabdbdcacadacdadbbbdcccbdcaabddddbaadadcbbddbccbdcaccddabcbbbcaabbabbbbbacadadabdbcbcdcccacabccbdcccdacbddddababdbaaddccaacdbdcbacaaaaccbcacbbbbdbcdabcbcacdccdbbbaacbddaacdbbacbacdabcdccbdaaabbaccbdbcddacbdbdcbabccaacdccdaccdbabbbbddbdcdcabadaacdacaabcdcabaccccbacabdadcbbbbbbdddaddbcabbbadccbbcabbdbacaacbbcabdbbccacbacdcccaadaddccabdddacadcdbbdbcacbdbcddddbccbbcadadbdbdcbadababacbbabcbbcaabaccddccbbdbddbcdaacbabcbdddbbacabddacbcdbbacdaadcbcabcbacddabcaddbdbbccaaabadabddadbacbdbabddcdadaddaaadacbbacdccbbcbcbbadbcbaadbddcbcbdcabccbdbdadaabaddabdadcabcbbdcbcacabcacaccdcacbaadadbcdddbcbcdabaacbcacaaabdcccdbccabdccccccbcaddababcbdbbaccccaaacbacbdccccacabadcddccdaaaaacdadbadabaadbaaccdabaabcdabdcdbcbbdddabdaddbbacdabbdcbcadaabaacddbdbbdbabaabaaabadcacdbdcaccdcccaacdabbddcdcbdccdbcaabddbdaadcdbcbdcdbabbcbbccdcdcbbdabbbcccdcaacbacbcbcbcddcdcbdcacbccbcdaaaddacbbdaabbcbbaadacabbaabdddbdababacabccababbabbbddbccdcadaabcabccbaabcdaaccabadddbbccacdbaddbddbaccdbbcbaadbdbdacbddcbccddccdbdbbdbaddabbadaccdadcacaacbddcccbbcaddbabaaadbcabbadbbbcccdcaaaadcdcaadbddbbbdabacaabccccddaabababddabadcbbbabbcaacbbdccbcaaacbdcbadbdbbdbdccbcddcacddabbdbcbcaacdabdaadbbcdbcaabcddbadbdcbdbbccacbbcccbdabcdaaabaccbadcbcabbbcdbbabdddcdabadbbaccbbcaacbbbaaaccbbddbdbacbcbbbdaacdccbdbcbbadaabbdddadbabbbcbaaabcabdbcacdbaacdbcaababbadcdbccbaadadcbbcaadadabaadaddbdaaadbdcaccdbdbbdcdccdabdaabdddccdaacdbbbdcabbaaababdbbcaccbcabbacababbabcbadcccbdcacdcbaaadbcbdcbccbdcbbccdabbcdadadcadbaacbbcabddcaddbbbbcdabcdbabcbcbdbcbaabbdddddddcabddbbcccaaaddbbadbdcbadddaddacaccdacbbdbbcabbdbabaccabdccbabdaddbcdbdddaddbabddbbbccdadccdcdbcdaddbdaccbabaaaccaddbdcbccaabbbbcbaaaadbadddbbbbaaddbdadccbbddccbcabccacadadadcaccbdbbbbbabcbddcbabbcbcabadcddbbabbdbbcabccbdbdbbbccdccabaaabcbcadaaddcdccbdccdcddbcacdacddcddaddbdbdabcbccccdddbadddadaadacbddbcbaddcbabcdaccdababccbcadddacbaccdcccdcbacdbbbbddbccaabcabaabdddcbddcbabbcdbcdaacbbadbaadabcbbdaadcdacdcccdadbbcddacdcbcaccbcdbadbaaaacaababcdacdcdbabaaabaccadbbbbcaccbbacababaddabbaddcdcaacbdbcacdadccaccbadddcdabcabacbdbadbdcddabbdccdadaabcddaccdbddccabbdadccadbbadaccadaaddddacacddccadccaababadddccbadaaaddbcacacaccbccabdcacbaaacaaaacccdacabbbdbcbcbbbacccacaadbbadbdccbccddddccbadcadbdbccacdbabaddbabcdacddbddcaabbdaaabdbbcbcabaaabcbaaccbbaddbbcdcbccbddaddbabbbacbbddcbbdbacaccacbacbcdacaabbbbcabbcccccaadcadddcbdbcaaacdababddaacdbacadbcdbbacdcbcdbbcbdadccdcdbaccdddcccdcaddccbbcbbdadbcbaadabbcabccccbaabdbaacacdabbcddbabbcaddcddbbdadbbacddbdcaddcdaddaddacdddbacccabababbdbdcbcbdbbbaaabdcaabdbdbaadddcbdaaaacdbbccbbbbdadcdabacacbdadadacdbbbdbaccadaabcbccdacbbdcbbddcdacddcbcadbcdccddcbccbadbdbcbdccdcdcaddacdcccaaababcbaadaaaaabdbdbbababdccccddbacbaccbbbdcabbccbdabaccdadadccdddaadadacbdaabacbadbdcadaacbdabbaabddaabadbabcbacddabcadadaabbbcdbdbbddadabbdaabcaabdbddddaaddcbbacaaaaaaccadacccbacbdabddadbcaaccbbaabddbbcbdcacacaddbcabcbddacabddaadbabbaaaaadabdcacbcaddbabbbacabbdbabbcddbdddcadadcbababcabdcacabcbabccbcbdddbbbddbdcbadcccdcdacaabcdcbdbcccddacddbaabddadacdccdcaccdccccabcbdadaddadbbdcbbdadbabbdbdccdcacdcbcbbaaaacdaadadcddccccaddaaaabaaabdcabcabcbbbddbcabdacdbdadcddbcdcbbabbdabbdadccbadcccdcdabdccadbddacacaadbadbadabdabcbadcacbdbcbdcacbccabddaacaaaaadadbdabbcbdcabdbbddcbcaaccddaaccdbabacbbbddacbabaddcccbbaadbaaadbcaddbcabbdacbddcabddccdddcabcbcdbabcabbddcbbdbbcadcaddddccdaccdcbcbcadababbacccccdaadaccaddcbaccbbaaabdddcbdacacbcaccbcdcbdddaccccdadcddbabaccdccabadbacbbadccddbddadbbdacadcabbddbbcdcbcdbbccdbabddcdadbaadbbacdaddaabcbbdcbacabcdaaddbcbaaabbcdcdccabcabcdacdabcdbdcbdabdbcdccabadcdaabdbdbabbdabaabadcdabadabdabaaabbbcdaaabccaddbcbbcabbadbabcbcbcbcbbbbabdaacddbdbdbcbbacccdccbdbdadcbdddbbcdbaaccddcadadcadbbaccbacbaddcaccadaaadcdcaddcdbdbdadbbdbdabbcdacbcaabddddbcabbaaadbcbcacdaadcabbbdcdabcdbcadaaadbcadccdddbadcccadacabdabcbabbccabcccacdbdadaaadbbacdbcbbcbabccdcabbaabdcdcacbaabbccaacbcacaadcabccadbbaccdbbadabdcbdacaabbaacaaaccdacadbddacacbdacdbcacabcbacdddabaddccdadcdbaccaabcbadcadcdaccacdbdcccadbaabdbdabbacdcbacacdabdcbcbcadadaabbdadddcadddacbcbdcbacdbcbcddabdbbcaacdcccadbdbdcbddbbbcbdcbbccddcbccdabbdcaadbcaadcabacaaacabbaccbbccdbbabdbbdddbaabdabdbbdcdcabdabdabcdddcabacdcbcbbabcabddcbcbbacddaadbdcbbdcdbabacacdadacdbdddabcdddbccadbdbdaddbddcdbdcdcdcdcbdabbaadcbbbccacbdbbbdddbcbdbdbddccabccdccbddcbbcddaacabaaddcdcdcccabdbdadccbcdcadccdadbacacdbddbaddbbdcbdbccaaadbbadddacabdadadbdcbaaabbcbacbccbdddccbcacdcbcabcbcbdbaddccdcdcaacabdcddcbaadcacaccaddcdacacdbbdcbcbdcbdabcdbbdaccacbaddbbcdcbdcdbadddabccddbdcbdddcbcdcbaabcdbbaddcabaadacbaabbdbabccadbbcbbcaacbdbbabccdaaabcbdabbbdacabadddbcbabadababdcadccbbbacbddaacaadbcabbacadaccdacbcbcccbadcdbcaacacabacbdcbbcadbadbcbddaabaababaadaabbaaacdcdccabdacbacacdddacbcacadcadadbdbccacabbddcccdbcbcadadcbadcabaaadcddacbdddacadcdcddacacccadcdaadbdcccddccdaabbdccaabaddbbcbbdaabbdbaddcbbacdabccdcdaaaacbcadcddcbacacccdccbabbdddaadacccaacdbdcdaacdadcbbaababbaabccaadddcbccadacaababddacabdcddccbadcccacabbcbcdaddaddaacaadcbdcbdcbcdadbdadccbabcbdddbabcbccaaddacddcabadbabbcabbbaabbaaddcccaacadbbacadbdcdcbadbbdbdaabaaaabaaaadddccacabbcdcaccbccddddbbccddacddccccbbdbbadacbbbcabdadbcdbcaabdcddacccdabbddbcabcbccdcbdddacabcdababcbcbbccdaddbbbccbbdddabbccadbadbcccbbacdbdacaaccaaabbacbcaaddbbcbabbccccdbadcbbaabcdcbdcdccaaaabbaccdbcbbabcbcdadbccdccbbcadbabcbbcbcbacccaccccdbcddddbabcbdcdcbdadbdbddaddadadbcdbaaddbccbdbbdcdbcbaabdabcadcbcacccabdddccbcbdbccbdaadbaaddabadddabdbbddacdacdaacdcccaddaabaaccabccddddbbbcdddadbbdbbddddbcaadbbaaddcabcdcbddbcccdaddaacbadadbcdccccbdbaacddaacabcbdbdcadbbbadcbdabadbcbdacbabadbcdbadbcdadbaacddbbdaadabcaacbddabdbabdcddbbaadbaddabcccabacabababbadcbcbbbbaddbbacdcccbbdcdddccabcdbadbdbabbdcbdbddbcabbcdacacbccabbdbdaddbabaacadadcdcbadbabbcbadacacbdbcddcdaaccacccccbcaaacccbbbcbccdabadababccbaaabdbbdaabaaaacbadaccdbaaabcccabcdbacbccacdccadbddbbcdaadbbcdcadddbcddbcadcabaaabaabbdbcbbaadcaaaadddcdbaddadcbcbbddbdcaccacaddabbbbabdcabdcadabbdadadcddbbdbadbdcabcabcabdbcbccbadaaccacbcbcacabbddbbbbbcccddccbdcbabbcacdccadbacdccacdacaabcaacbdbbdbadbbaadbabcccccaddcdcbdbbadcaacbabdcbbccbacbcddcacacaabbcddbaabcccbbbbdabdbddbaaaaaaabaacadddcccbdaabdccdabbabadbddcbbcabdadcacbabaddbdcacaabdbcaadaabadbaabbcdadbacbacbbbbdabcacaacaabcddaabcbdabbcbbddadbbccdcdabccaddbcabaacdcccbdcbdbadbcdcdadcdcababcabbbabbccacbbdbabdabddadccbdcccdbaacbabbbdbbcbcddbcacddcaaacbdcdbcdccdaadccdaadbdbabbcacadbcdbdaaacbbdbbdbaadcbdbbbdbcabcdbbaacdbccbabdcbcadddcdaaacdabcdabdbbdaadbdbccdadbaddddabbddabdbbadbdcddbcacbdcbadccbbbacdcabadbccadbccddbdabbcabaabababcaaaddccaaddcccacabdabacbdacacaddbbcccaabcabaabdadbdcbbdaaacbdbabddbccadaabcddadbadcabadbbadcbbbdaaabdaddadcbbcbabdbdddccabacaaacaaabcddcbbbbbdccaabbbbbbbcaccabdcdaabaddcaabdabdadccbcccdcccabdcabbcdbdbabdacbbaaaabdabcbabcadddcacdbdcbaacdabccdcacaabbcbcddcbcabddbaaaabcbbbccdaabdbdbddabdccbbabdcabcbbaccbabcdccaaacdbddcbcacdccaacbadbddabadcccacaaacacbdadaadabcdcbcbbadbbbbbacbbdbacbdddaccbabdbbabcbcdcaaaababaaaaaadaaccdbbbcdababbbadaaaabcabbadccaadbcdbddccacdbbbbbacdbaadacdcbaaaacadadbdcaadcbacacaacbbbacccddcaabddabcadccbbbaaadacbdbdccdbdcabbabccacbbacddabaddcdbcaabdddabdcddabdccbbdaccaccdaabbddbaadddbacaddaccbbcdbdadaaabcabbbbbdcbdabccbccaadbdaaccbcbcccdaaabbabdbabdacbcacdbcabcbbadbbacaabaccbacbcabbbcbccdabcdbbcaacdcdcaadbdcbcbacdacbccdaccbccdbacacbcaaccccddbbbdbcbbbddddcdbbadbbbcddacbbbabbbdbabbadccccdadabcdcdbcaccbbabbbddbababddcdcdaccaadbbbadcdcbabddbccccbbbcbbbdbdbcdbcadcadbbcbdcbccbbbabccdbddbbcdbdacbdddbdacabbcddadcdaaadbdbabacbadddbccdbdbdbaabcddcdbbaabbaacdcacacacbbdbbbccbddbbaaadcaadbcbdccdddbaaddbccbbadcdabbabacabacdcdaccbadadccabadbcaaaccbcdddbddbdbbdbbdddccacbadacbbbbcabbabbcacaacbbaaccbddadacbaccccdbbbabbccbacdabdabdbdcdcbdbbdacaaddcdcdabcdcabaaacadcdadbdaddabdddbcadbcbbdaabaaadbdabacabbbdbdaddacdaaadabacddbaabcddbcdcddcdccbbabaaabcdaabdbbadbcbadddcbadacbbaacddccabcbccabbcdccbddbbccbccdcccbdadcbcddacbdcdbbdaacaacdbbdcadcbbcccdbdcbccdcadbdbabacbbdcdccabcdccccdbdddcacdcbdcdbcaabadcbbdbdbdaaacbabdacccadaadacbcadbccbcabdbadaabddacabdbbabacadbddcabbbabcbdbbaadddaccdcccccccbdbaaabdcddddcadadabbaaacbbacdcddaadcdbabdbccdcdbacabbcbdbdcacbccabcccaacbaddbdcbbdabbabadcdbdddabbacadbbbbbcdbdcbcdcbadbbcdacbccaccabcaaacbadbccdccbdaabdddaabcbbdcbdcaacbddaccbbaccaaadbdabcccadaddccbcddacacccacdabbacbadbcddddbbdaacababdaddadbaadbaccbddaddbaaadcdaccccaddccdbccbcdbddabbaabcbacbdadbbadacbcadbddddacabdadcccbadbbabbdcacbbcadbbbcaacdcaaddbcddbbdbcacdccbaaadcdcadccabcdccbddaabacccdbbbbdabdddadcbddadbabaccdacacbabdcdcdbccdbccaabbbbabaaabdcdbaacadcaabdbdabacbacbcbabadadccdbdbcacacdabdcbddbdbdabacbddcbadcacbcdbbcbdcbbabdcdbdbaddcdabadcbbcdcdbbbaccdcddbacdacbdacabaacbdabcabaadcdabccdcdadbcdaddbacabdbbabccbaacdabdadadcbcbcdccbdaccdcadcbcadcdcaadbbdbbdcbbadbdcccbcbcbaaabccabcdcabdcbdacacabccdbabcaacaadbbbcdbbdcbbdbaadbbadbcccbccbcbcbabcccbdbcccbbdddcdcbaadabbbabbbcdaaadacbbbdcdcddcbbbcdbaaabcbbacadddcccabacaccbabbacaadacccdcdabcabaadbabdaddbcbaacadaaadcbcddcdaaaaabdcbdcbacbccdddbdbabbaabbdccaabdddcdccacccdcbbbaadcaacdddcbbcccbdacdbbbcdcbabcbbdacaaacbddadbcddcddacdabcbcbdbbbabcccabbccdcabcabcddabcdbbcdadbddbaaadaccaccacbdbacdaaccdaaaddadabbcabbcbbaacbcddacddbcbbcbdddacabdccbddadabaadabcbcdcdbbdbdacbcbbddababcdacadcbaccdadcccbdbdbcddacbdacabdcadbbdbbccbddcbcadcdddcddcdaddcabccdcacaccdbdcbdbbcdacdcabbddababbacddadddbdbbcbadbadbdcbdccbdbdabdbaaacccdbccbaaadabdcbabcccdcacacbdacaddabcaacbcbcddbbacddbddbbddbbbaaadabadabcabacadcdbcdaaccccccbbaccccdccdbacaabbccbcbcbdbbbcddabccccdddbaadadacddcbddbcbbcabbbaadcaaadacdbcbacddddbddbadddccaaddcdbbaaddbbddbdbacdbaacbddbdcaabdddbacccabbbdbbbbdbddcadbdcbdcdadabcccbdddddddacaabbccccbaacbcbaccacddcabadccabdcbbaddccbddbcdcbaccbcbabbbdbacdbdbabdabddaabdbbddbccdbadaaacacccbaddadbdbadabdbdcbbdcdccaadaccdabadaadcbcadcbbcaccbcdaadcdcbbbaaadbacdacbcbabcadaaccdaacccabbbacdbbddbbaaccaaababaddcaacccdbdddbbdcbdcccbaaaccabacbccccdbbcaacddbdddddbdaddcbaabddcdbbabcacabddabdccccdcababdccdbacadabccddbaaadabaacadccbcbddbdbddbadbbdcbbbdbddacccbacdadcdcbaaaccadbcdabcbddbadcccddcabcbaadabdcccddadadbdbdadbdacbabccbbadbdcaaaaadcaaabbdcaabbddaaadabcbdaaccacabbbdbacbdcaaadaabaadcbacdcdbbaaacbadcbbcaaacaaaabbaddcadcdcabccdcabacccadbdbccacdabbdaacadadcbcdcadabdaadcbddbabbddbdadddabdcadadabcddacaddddabdddddabadcdcbdbccadabdaaddababdbbccdbbdacbbcaddccdccaadadcadaccabbaaadadaaabadaacbbabcabcbbdccadddbccbdcadabadbbadadabdbcaaaabbcacbddadddddabaababadacacdacbbbdbcadcdcdadccdbbacbaabbdadcbbaabddccddaabcbbddbddcaabbbacbbcaadabcabbcaddcaaddccbabdcccbaccdabbcbbbbbbcbabcdcbacbbbcdabcccadcadcbabcdccbbadbacbaddcdaadbbabccccdcadbdcdbbbadcbaabcddaabdacbcacaaccddbacbdbdcabddbdadcdbddddcdacdabcbdbaaccdbdbbaadbcbdabcccdcbacbdaabcadadddbbabccdcdddaadcbdbdbcddaddbbdbdbabdabaabaaadbccdaaabdccddaccbcacbbcbbdddadcbabbaabaccbdadcbbddddaddcabbbbbadddbaaaddcbdbaacbccaabdcadddbcbbdcbacccdbcdadcdccdababbdcbbbdbbabbccdacadabadcadbadacbdacaaaddcadccdacdadbdcadaabbdbcdadcdcbadadadcdadaabdcdcabdcddbaabadcbddcabcadaacbbbaaacdddcabdcadbaccdbbacddbbddcdbcdddcccbbbbcccaaccdcdbbbccadbdddbccbbbbcbbdadbccacdbbacacdcabacbbdcbabdaaddcabbacbdaacbbbbdbcbcddcaddccbadbcdcbdaadcbcbadaacdcacbabcdabbbdcabadcaabbbddcabdbcddabaaaabdaaadcdccbddccdbaaadcddcccbbbcaacacbdbdcbdaadcdbdadbadbabaabccabdcdcabaccdbbdbbbabaacabddccdabbbadaccdbdcdbaaacabadbdcccbaababadccadacbbbcbddcbacbaaaabddbdacdadddbbbccbaccaddbcabdcdcdadcacaadabbcbdaacbbbacbdddabccbaddacaabbacdaaddbdbbcccaabadccdcddcddddbcadacdcdacaabdcdcccbdcdadbcbdcbcadccbaababbccbbadcadcbabdabddbdbacbcaaccbabdcacaccdabbbdbbcdcccaccaadccdcdcdccacdaaabcadddaaaacacadaabaadbbdccaccaabbdbadbbacaabacdcdcacbcdcbacbdcabdbbcaabccaabcadbccababddbdbaaadbabccdabdbacabdcdacdcbcdcdbbddaabaccadacacdaabbabdadcbdbcbbbabcbdddadddabbbaabcacddcdacabdaccbabcdcdaddababbbcdddbccbccbddbbaabadcdcacabbacdcbcabdbadcabdcdbbddbddcbcdcaadabadacdbdaacabadacdbdaddaacbdccbbacbaaaaabacbdababbadcabaccbaabbbcbdabdacacabaacdbabdbacbbcbabdccbbbbbcdaabdacbaccddccacbbcacdbbcdccddbbdcacbcbbcdbdbabdaabbabcaacdbdddcabddcabccaadbbbdccaacdddbdcbacbbcabcccaaadcccbccccbdbadbccadbacacabdaddcbbddcbcaddcbcbcaabddcdbadabddcbddcdacabdbccbaadbacbcaabaadacbcbddaaabadbdcdcbdabdbaacbbabacadbbccdcbcccdbabbaabcccabababdcaaadbbadadcbbababaddcddcdaccdcadcbbadbabbcbccbbcbabaaacbbbabacbbbdbcaccdaadbabccccbbcbcbdadbdacbacdabdbdaccaadabbcbaadbdaddcacacbcdccccbadcdbaddcccbcdcbdcadabdbcdaccdaddbdbbdccdcdbcadbdddcbcdbadbcbaacdbdbbcdbbdbdccadbacbcdbaddcdadbcaddbccddaacacddbdabacdddbcaaacadadbdcdccdcbdcdbbabbaaadccdcadcbbbcaaddabacbbcbbbbdadbccdcbabacdbbabcbdbccdcdadabcdbdabbdabbdbbdbacddcbbbaadbbaddcbdbdcacdaadbbcaddddccbacbaccdcbbbbacccbcbacdaadcaddbcabaabcccccaacbbbacdcbcbaccbadbddaadaaccbdcabbddccbbcbbdbdbcdadcadbbcaadcdbabacdcabbcbcdcadbdbcdacdddbcccbcbbbdbdddaacacadccadcbbaaacabaddabdbbcccbcdababbcccaadbbbddcbdbbccbdbccccacaaacbdbbddadcbadacdccabacacddcdaccbbaabadabbbcabdcbcaadbbbadbccbcbdacaacababaacbbadaacaccdcccccabcabbddcbdbcaadbbaccbddcbaadadadcbdbdcdcddbbccacdabbbcdaadbaaacaddababbaddaadcbaabaaadbbcdabcaadbabaddabaaddbdbdbddaadcaabcaaccaababbbbaaabdbacccbcbadacddbccaadaadcccdbacdacccbdbcdcbddaacacdaccbbabacbcadcddcdcbbadbadcaabdccddbbaaaddbacbbabcdbaccabcdbddbcccabadcbddbcbaadbddbacdbdcdddcccdacaadbddcbbbbcabaaccdcdababdcbaccbccccdbaadaacaaccddadbddacabbdacdbbaaadaabbabacbabdbaaadaaaacbacabccbcbcbbcbcbbccabcbccabdddcadacdbabbccbadccdabdbbddaabababcdabbcdbcdcdcdccacabbdabddddddbdcaaacaabacdcabdaacdcadadcabdacbaabbdcbdcbbbabcbbdabccaacdbadadbbccdadbacbddbaacdcccaacbadcdbcacbbdbacccddcbbbdcacdaaabdabbaaccadddbacacdbdbdccbbbacbaababdccacdbcbcbdaabdbbabdddccbbbadcdcbbbcdaaaabaadacbadcbcbdaaddcbdbaadcdabaadcabbdaddbbadddabbdccbddccddcdacaabbbaadbcaabacdacabbacdcbbcdacbaacbadcddaabbccdddcdbdbdccadadbcaadbdbadbacbcdbcaaaaaddaabbaadacacbacabdadbbcadccdbcddcdcdaaccdbdacadccbcacbdbdbcacdbcdddababacabcadbcddbbacdbaacdbdcadbcdbcddaadabccdccbcbdabdbacacabbbcddbbcbdcbaccbacccbcdadccacbdcabaabcadddbcdaaaabadaccbabbdaadbacdbbbbdaccadabaaaccaccccbbbdbcbdccbdacdbbcccaccbcadadbddcacdcdcddddacaababaacadbbaddbabbbababdadcacbcaababacbaabacdddddaadcdbbabdddccbcaaadabacdabbcbaccdbddadddadcdcbbbadacbdabcccbddbbcbdabbdaababadaacabbcdabadcdacbdaacdbabdcacabcbdcdbbddaddddbaaabadadabdcdbccbdcbdcabdddcadcdbacdadbbacaddbcdcaaacaddbdbaacccaccaadcbddaaacbbcdbacdbbbcabdbcdccababbbdcacbabbbaccbcdcacadccdacadddbdddddcaadaccadabdbdcabadbcdcacdbbaaacbbaddccaaacbbacbdaacddaadbadadccbdccbcbcaccacbabdcdadaacbccaddbaaddbbbdddaacdaacaaabaddccabdcddabdcaaacdbcdbddbdcacbaaaabcbbcdbdbadbccabbbcbbbbaabbccaaaadbdbbccdacabcbbaaccdaaacddcadadbdaaabcbdaddadbacbbaaabdcabcaaaaaccdbdaadacaddabbbcddccddccdbbbcaddbadccdcaabadbccabbaaabaacaacbabbbccbadadcbdcdbddccdacabcbbcaccbcbdccdaabbccccdaaccacdbcaadacaadadddacdaacdccabbddcabaaadaabcaadadcadabccdacbbbdcddddcdabdabaaacabddccddbdddacbdabdabbdccdbcacdbacdcbddadadcddaacbdbbbccaaadabccaccbbacbabbdccccbcdcaabcbbbcabdbcdbddbdaaccccddbdaacccabbbbddcdabacbcbdadcbbadbbaabdaaccddccbdccacdcbbaccdadbdbdcdbabddcbbaacaaabaddbdcdccaacccbccdbbbadcbcaddcbdbbcbaadbabdabdddbaccaaccbcadcaddabbadbbbcbdddcddcacbcdacabcdadcdaabcacabdbccacdddaacbbdcabbaacbbacaababdaacbdbdbabcaabbadaddcaacadcbadbabaacdadbaabcdabdbcabdccdadbaacacdacabbbaabdbacbddadccdbbdbdcaacbccccbbbbcabccbbcaccbcbdbcbbcdacbacdcacddbcbccdbdcaabcababdcaadabdbcccbdcbadaabadacdcbbabcadcaabbddcddcadddcbddcbdbddaadaaabbccbccaabcabcbbdacccbccadbacdcadcbadcbbbacdcabcadbbbdadccadbaadbbdbcbcbdacdbcdbdcaaadbacabbbdaccabbcddaacbbbdabcabdadccaccabddcdddaddacdccccdcdababdabddddbccbbbadabcdcabdbbadacbdadccbbaacbcbccbcbddddaaadbdaccbaadbdabacabbadadabdcdadccadabcadabccdaddbaabdadcbbccbcaabdbbacadbbbdacbccdbadddbbabcbbabbdcacccaaadcadacbbdaaabbbcbcbcbdabbbdbacacdcbbdccbcbbdcdbcbdacbbbacdaabcbbacdcabdcdbaacddbabbbdbcbaddddccaccadadcaaaddcbbbdcacdddbcdacbbbbdadaabbadaacbdbcbacdcbcaaccdbbbbddcddbcbdabdadadabaadbdcddbdbdbcacadaabadaabbdcdcaaaccdcbdccbbbbdbbaabacdcbcdddbdbbdbcbdbaaacadbcbcacbbbabcaabdbbacccddbadccadbdbdbcbdaabbdcbbabbbdbbbbbadbbdbcaccbbaabddabbdddbdacbabaabbdbabbadddccbdbccaaadcbcdccccccdcadcaababbdcdcdaabadabaabcacddaabbcbbabddbcdbdbdcccccdbacdcbdbbcadbabccdaababadbdababbbdcbcccdbaabccdabcabcadacbdddaaaaadcbbbcbbdcaddccadcccccbabbcddaddcbdaadaccbdbacbccdddcdcbbbdcccdbdcbaccdbaacabddaddcacdcccaaadccaabddccabbccbdaccdcbbbddbacadcbbacaabadbabcacaabbabadbbcbdddcaaaacbadcbababccbdaacaabbcdcdbdbcbdddcaabaccbababcdbaabbabadcaabdabdbdcaccbdadbdcbdcbabbdddaadaddcccacbaccaabdadcaabcbaabbaaaabccbaaadaccdbcbaacdccbdcbbdbddbaccdabbddbadbdcacabaacddcccdbddadacddacdcaaacaadbaaadddcdabddbdbbdbdbbccabdccbcccbbdcbdacacbababaaddccbacadddcbaaabcddcdabcacbdcdcdbdaacacbbcccadcaabbcabcdadccdbdcddadccccaacbbbccdbacdbbdbcaacbdbbcdaabbbcbbccbcaacacdaadacadadbbabdcbcbcaddaacdacbacaabaabadbaaadadcdaadccbaabbaaaaacbbccbccdcacdbbbadaaadadcabcaadadcccbdcdcbabcdadccaacaaaabdacaabacdbcbbacbbbdccddbddcbabcadabadbbbdcdcaaabacabdbacbdccccddcbaadcbdabddbabcadabbcccbacaabaacbdacdabcbdbacadbbcacbadcbccdabcdcccdaadaabdddabdbaddaaccccaaabbbadadcddacdacabaddbcbbabbaabbccbddccdccbaadcadbdaabacaabaabcadcdbbdcdcacdccdaaaccbbdabbcaacaaadbdddcbcdcabcdbbadaabaacacdbcaadbbcbcacddbaaddbdcbcdcbdcdbbdbbcbcaccdcccadacdccbaaddbacbbdbccbadbbdadbbbdaadddcdddaddadadbadcbdacbcadbbdbdbcadbccababbccbdbbdbcdbadbacabdcbdadbbcbbbdacaccaddbbacbdbdacdcdbcbbababcacbabcadcddaabaaaddacacdcddcabccdaaacdcacacaadbabababacbddacddcdaaacbbbacadaccabbddcddaacacadcccabadbbdcbacbdcadacbabbaadbccadcbbdcddbaccaddaccdabcbdbdcadccdabadcdabbbbbcaacccdaaddbdadccbadbdbbdcacdaadbaabddcaddbcccacbbbabbcdabccabcabbdacdaaccdcdaddddccccbddbbabdcdabccadbadcaaaaddddabcbcbabccddbabbdcbadddddcabdabdcdcbbddaabdadcbcdbdbddbcccbbaabccbaccaaccacadcdbdcbdaddbaacbcccacdbbabaacaadbbdbccddaaccdbbdadbaadbabbbcbacabdbabdbdadadddaccbcccaaacdbbddddabcacbcbadacababaddbdaaacabddcabccdbcccbddacbccccbaacdbbbabbababbdbdbdcdabadcdadaddcdaaddadadbbabbabbbcdacddbbadbacbbcdadbcadbbddcadbdcbdddacacbbacbdaddccbbdbcdcbadacdacaacbdcaddaaacdcdabaccbbbcdddbabccbbddababbabadccddcaacbbcbacaaaabbadcbcbdabaaccbdacabbbaccdcccdbdcdcdbcdbbdbbbdbcdcddcabadadbcacaacddbaaacbdbcddadadbbdddccdbabddccaccdabacadbcbcdcbadbdcccbccaddcdadcdbabcbcbbccacadaadccdaacddcdcddbcdccbbcabcbcdbbbddcccccaabdcdcdbadacbabadcbddddcbcaabcbadbdabcabddccdcdaaccaddcabddcbbddabaacbbabbaabdddbcbaabdbccdbaaadaaddbdccdaadbcadcdcdaadbaddadacddcbdbdaacaaddcddbbdbbbdcbdababdaddcccdcbdababdbdabbadaabbcacacadadaabbbbadacbbcdbbbaaaccdacdbccbdaabbcdbbbabbdbbbbbddbabbabadbaaabdabaabdabcddcaaacaabdaacaccabbdbbadaccbcadddcbaccaadbbbababbdcdadbdaabddbbdbcdbadacdbbcabacbaaddbdaabcaccbcabcdddadacccdbabccccbddadbdacabdabbcbbcbdadcdacabacadabacaddabadddbdaabdbbbddadbddcbbbaddabbcddacdddbabdadbcdccbcaaacdbccddaacbdabcdbbbcbccccacbdbbccadadbabdbbabbcdcddadbdcacdaccbccccdbacabdadcabdddabcadbaaadbbdbabbccbccabddccacaaacddaaccbbbadacccdbcdacbdddcbbcadadaddbbdcdcadcdaddbddbbdaaaacadcddbccabadaddccdcdcdacdbabcacaaababcbcdbcdcbbdcdaddacbacdbbbbcccbdbdaddadadbaaddcdbdbcdbacdbcdcabdccaacdcbbdbadaaababcdacdabadcdbdbdbababacaacbdcccabccadcadbdbdadcabadaaddddabbddcccccddbcbbdcacaabbadbcbdcabdcacddbcbadccddbacbbacacbaaccbcddbbaaddbdaabcdbbbabbbcabdcbabbdcbcbccadacdbbdbdabbcbcddbddadbdddccbbadadbddaccaddbbdbababadaaaacaaaccababcbccbcbbaacbdbcbddbcdadcddbccddabbdcaddcabcabcbdcbbdbcdacccdaddbbcbcdcdbaabcabaacccacabcacaddaabccabadaddccdddbadadbaddcadaddbbcbaddbdcadddcdaaacdbcdccabaddaadbaddaacbdccabcaadcabdcdacccacccaaccbbcbaabbacddbdadaaaabbcdbcbdbcbbbbdbaaacdddabbbcaaacccdbdaababdbcccacadcaaadaacdacadbaadddbbaabccbbaaccbddaaccdaaabaccabbbaabdcdcadcbbbdcadbdcccadbbcdadbdabbcacbdddbccdccdaadbadbbcaaaaccdbbbacdadbdbababaabadcabcdbdbabbbabcbbcaadcaddaccdcaaccdddbacccbddbbbbddccbadaadabaadbaaaadadcdbcdbdaddbbadccdcadabcdbdcdcddabcdcdaccbcaaadacbabccaddcdbcaabbdbabbacaddabbabccdaacbdadacabbbddacbccacabbabaccbcbadbabaadbcdacccabdccbbaabcacddccbcaccccdabbacacdbbcdccbbaddccbccbadaddcdbbbdccbcadbdbcaddbbcadadcdaadccadcccaaadbbbabbdcdbadcdcbabddccddcabaaadbcacdabcbdadadbbcccdcadbccdbabbcacdbccdddbbadccdccbdbdcdadaacccbcbbbbcadaadcbcdbadbadbdbbbaabdabbbdccddbacdccacbddcbcdadcccbacccadcdbaaccabddabcbabbbbdbaddaddabaacbcaabbabaacdabbccdcdbcdbcbddacabcdbadcacacdcbabcaacbcbdadcaaaabdacdcbdcbccdaccddaacdaaccabababbabcaaabbadccaaccaaaddabcdddbbcbbbbababcbdcaacccadbbdaccbacbacddddccadabdbbbdbacbcbddbbddbbaaaadcdaacaaadabbaacadddbacdababcdbbbbcaacccbcbdbbadccbccadcaabdaaacacdccbddbbabdbbbadbcbacbdaccaadbddbbdbbadaccbbcabbdbdcbddbccbbdcccabddcddadaaabcccabcddbdddcdcbabaaadbaccbdcddbcaaabcacccbacabbbdcbcddbadabacbdabacdcbccdbdbacbdccbaaadddacadccaadaadcdcdbdbdcdadacdaaaccbaddbbbbbbdcacbadacadcdbabaccadcdcdbcaaaabdabdbadbadcadabadcbbccbddbdcbdbcbccccacdddbccabcbbdbccdbdbbcabbaccabdccbcacdbacacccaabadadddbdcabccaabddacdbbdcbdcabdcbbbadccdabbcbbbccbcaacdaabbdcbbacdbcdcacccadaadddcdbcbdddbaddddccbdabbadaccadcdcacccacbbdbaddacadcadaaabcdaabcbbbdabdbbdacaccbbcbbacdabaccdddddbdadddbcadcabdbaccbacdcddadccbadcdccabcaaccbabaadabddbbbdbadbcaddbcdbccacacdddbaaddacbbbdbbcadacaaadaabcaacdbaadcadbbcddadadbcacdcbcdbacababadadbcdcbbdbccbdbbadbdadbcadaaacbdcbdbdcbadbabadcbddddcadbddacdacdbadaddcaddbdcaaddacdababdcddbddbcbbbbcbbcccadddabbbaaccdcdcdbbdccccbcaddbaacbbcdcbbdcdbdaccbcccaadaaddccbdaacbdddbcbbabaddbadaddcbbbaddbbdaacdccdadcbbbccbcaaaaadccaadabbdbadbdcccdadaacdcabbddbcaddbccdaacdadbcbbdaacdcaacdcccdbaddbdbdbabcdadabbcbabcccbbcaadacdcddadbcddcbcbdddbccdaccdaddcbcbcdbcdcbbdbaabcacacbdcaccbdabbbcadaddcabdadddcbaaabbbcadbbbdadbaacbadabacbdabcccaaddbbdabbbbdacabcacddacdaacdadbdbccacaaccbacdcdbabbdcbcaaabadbaacbcadcbbcdddcabcbdbdbaadaaaaabbabcdbbbdbbdacbbbdbcdaaaaacdddbcacdbbdaaadbaababddccccaabcbbcaabccaacaccdddbaccadddacdcaccaadddbacdcabdadaadddadbbbdaaabadcccccdabbdadccdcacbbaccdacabbcbbdbcacbdabbdcdbbcabdacbbcbccadaccdcadbbcacdaadcbcadcbdcdcaadbaccdcbddbaccbbaabccdbddbdddcbaccdbddcbcbaccbccbaccabdacdcddcbbcabcbaabaaabdcbddbaaaaacadaaabddacbbcdcccaaadcbaccacaacbdadbcdcdaababddcdaaabbbccacaabbdbaaaddabbcbdcaadadddbbccaadcbcdcdadcadadcbabbabcbbacbaacdbbdabcbddddacddcddcbdbaabcdabdabdbcbddccdbbbcdabbcbaccdddcccbccaddcbacdbcaccbcbcbbdbabdcabdcbcbdbaacadbcacdbaabdadbdcdabaaacbcccccdbccdcaddaabddabacadaaadabadcaabaabbcadbaacbcddcaadbccbbbcbbabbacbcabddcdddacadaddcdcadcaaacadadbbddcbacaabdbcdbcbddcaccaddcaabacbcabaddcddddcdadcdacbadbbdbaddbddddcbdcabbcaacbddcaccbbbdaccdabdaaadcadadbdcadcabdaccacbbccbbbdbbcdabcbaabcdcdcdccdbacaddcccaadacbdbccacbcddacbdcadbbaadcdbdaaabbccddbddddbccbacdaadbdabdddbbddbcaaacaacabddcbcaacbbaaddbaacddcddaadcbdaaddaddccddbbdbdddcdcadacdcdcbcadcdbcddaadacbccacbdcddbddcdacbdbcabdcbdbcccacdcccbcaacbadbdcabaaadcaccabccddabbaacadbadbcbcababdadbadabaccdacabbdaabcdbdaacdacbcdcdcdaabdcbbacbaabbbcbabbccbaaadccbcbbaddcbacbababcdbddaaaadbdcdcbcabaacddabdadddacacacbbbbdccbdbacbdabccaaabaadcbaadadaddddcbcbcbbcdbbaddaabccbccbbcdbbccaccddacbdcabbddbbbdbccabcabcdddcaadccbdbbdddacdaccbcbaccbddabdacccbaabdbdaadbdbdadbdaccabbdcabaaddabadaddabaaddbbaaaabccccacdcccdbccacaabbdddbcabcddbcbdadaacbaacbcadadaabdbbcdcadbdababcbbdcaaaadaaddabbacbbdcabacbbaccdbcbaddcbaadcdbcccdbabacbbddcdbadcaddaccbbbbbadccacdbbcbccababdbdabcddaacbccbcaadcbcdcbdccababcbcbcddddddbcaacdadbbbcbbaccdcdddccacccbbabacdbaddcbdddbccdabbcaadbdbcacdbdbcbadcccaaabbccccadaacabccaadddadaccbaaacbdcacdadabbccbbbbbccdacbdbbdbcbadaabccacababbaccdadadadbbdcbdbdbddcaadbbbcabdcabbdadcabbcdccaabdbbccddccbdadcbccaabccdddaccdddcbdabdacaabccabacadadcccaaddccaccbdbdadaadabddcadccccdddbaaddbcacdddabdcadbcddbbccdbbdbbccbaaadacaaaabccacbccbddcaaabaabcccdbabaaabdccdaadabbbddcabacccbaaadcbdbcdbbcbcdddbdbcacaddacdacbbdcddacdbcadaaadabbbadddbdadcdcbddbccccabdabbbacdcabdbadacbacacdccadbcaccaccadacbcdccaccdbcdcbadbabbbbababbabddddaabccacddbdadbdbddbdbdbbcaaaccaadcbcacccccbccadabbbcdbacbbdcbdbcbbdcdbcaccadadcacbcbbdbbadbdbcddcaabdcdacbaaabacdbcdcbdcbbcaacababadbcccbccdadabaadccdbaaaabdacbbcadbdddddcbbcdaaacdcabdccabcbcdbdcdacddadbccabdcbdacabcdbaddadadacdcbbbabdcdabaacbdabcdbcccabaaaaaddccaddbbdbaadacdccabbdccdcccbbaddadacdbdddddbbbabbdcabccaddaacabdcdabbcbcabbdadcdacbccbbbaaaaabddcdcbddabccccdacbddcdbbcaaabdccdacacbbaabddaddadbbcdababccbadbdaaaddabcdadacbabbbcadaabdcaadadbbcbcdabdcbdccbcdcbdcccdddcccacacdbcbbccbaaaabcdaaadadbdacadaaabddbbdccacaabbbccadcaaddbacbcdbccaadccbcbdcbaaacccbcacbddaaabccdacdaccdcaaaccccbbddbbbdaccbadabdcdcacdddcaadadbbbbccaaddddcccacbccacdddcdbddbaccdddabaaadcbcdcddaaaacbcddbcdcbdaaddacdbccbccabacdcadacbbdbdbdddaabdbcaccbaabdaddbbdcadddadcaddbababdaacaddaddccbdccaaddabbbdccaaaabdbaaaadddacbaaaddccdbdbdbabdaccabaabcddaddcacdacadcabcaaabbcddccbdbbaabddbcbdbbbbbadbddcbddadcababbcdddbbbacdcaaabcbabaddcccbdacccbabcacdaadbaccddccddcbdabdaaaadbbdcdbabaabacabcadaacacacdbdbadbdcdcbacdbbdadacabccbdbaadaababababbdbbbacdddadacccaaacddadcbcbbcbbcaabddaccabdcbbadacbcacddcdcbcaacacdabcddddaacbaaabbcbcdcbccadabbbcbcabaddbcbddbbdabccdbbdadabdadccabdddddcabacbbbadbadccbabaabaaddaddcddadbbadbbbcaadbabcadbdcabcaccccbbdaccdcdbacadcbcdcbcdbdcdbaaabaccaabcddbbabbbcdcbbbabdbbdabacdcbcacbcbcabadbbccbdcacbdacbabdcdbbdcbbaddbcadaadabbbbbcbcadabdbdaccbdabccbacdababdcaabbacdacbbbdacabbcbdbdbdadccadabdbdcdbaadadbaddbcdabccccdcdcbcbcbcdddadcccdcabbccdbabbdddaccccbbacbdadddbdddccccdadadddccddadaabddcadabbaddadcdcadbdcdbccddcabccbadcbdcadaacadbadbbadccbcbaaccadadcbdddddabdcbbcbadbbabcdacddcadabcbbaaccccdbbcbcbbadcadccbdadcdacbaadbaccaadacbcddabbbcddbaddbabcbadcddcddbbbadbdbcadcdbdacabcdbbcacdbabdbbacbabcabaccbdacddbcccbabcaccdadcdbaccdadabbccaabbccbbbaacccabacaccdbcdbacccadbbcbcbaaaabdbadadabcdacbdcaddbabdcacdbddddcdabacaccbcbbadabbdaadcaccdbdaacdabadbcabcddabaadbcbcddbbcddbcbbccbbddbcbabbcabcabdcabcbabccdadbbbaabacdbaddbdcddbbcbcadddbdbbdddbcadaadddbbcdbdabbcdcccaababcbdbdbcacbbbccaccbabbaaadabcbbadbacdcdaaadadaddbababcbbdccbdbadadddabdadddcbcdbbaccbdcdbaabbaadddaadcbbccbdcddcbaccdbcaccbccdcdaacdccbdadccbcaacddbbbabdadccdbcbdddccaacbbdddacbabdbdbcdcdddcabbacddcdcbbcaacdabadcaabaadbcbbbdcbacaccdacabbcbacbacbcaaaddcaaccbbaccbdcccdbcbdbcaddacabdbbcbcdcccccbdcaabbbacbbacccaaabcdbcacdabadcabbbbcbddcdaaabdbaaccbcabdbdcaddbbadacccdbbcccbadacdbacbabbadabbbbbaabdaddabaadacadabbcbbddccccbacdcccbccddadccdacdcbaaabbaadbcdcddabbbadbdbdacadbbdacccbabacacbccacbacdcdaaccdbbdcadaacabcacbccababdddcccadcaaabadaddabdddddcbcabccdacbccadcacbdbcddabddcbcadacbcaaabababbaacccccadabcccdbdaaaccdbdaaddabddaddadcaadbadcddbbadbbbbcccbdcadccbbaaccddcdadcdbccdadaccbccbbddcacddcdabbdbcaaadccdbabddcbdbadadddabddabbacacdacdcddcaddaabaccccccddbddcacacbaadddddcdabadadbadbcaaabacddbbccdbdbcadacdcbaabcbbdabcbcbbdcaacddaadbcaaadccbcbcbcdabccbaacddcdcbccbbdccaadabddcaccbadbaadcaccacaababdcbcbabbabbbbbabbbdbcbbabbbdbdddbadbadbbccabaabadcddddadadbdaccddcddcaacdcaadcdadcaacccdddccdabcbcbcccbacccccacbacacddadabccacbccbdacacddaaacacdbbdaddabcbdaddccbcccddbbbcdadaaccbdaacabbdcbdaccbbbdabdbdbdadcbcbccbdaaccdaabdbbdaaaaaacbaacabdabddaaaacbabcacaaacdadbabccbaddcdcbadaabdbbbdccadacaaacabacacaacbabadcaabccbbcdbccaaddadddcbdaccdccbdcadccccccddadaaaabcdadbcbdccbbdaadccaccccaddcdacabcbabdcddbbcdcaccdbbcbaabddbabbcbbacbadbbcacaaabcbbdbaadabdbbbdabbcdbbcbbabcbdadcdacacbbcccccbcccaddadcbbcccdcdbdbcaddcdbabdbdbadaaddaaacbbcbdbaddbaacbdaddadcccdcbddcbcbdabccccaccddbacacbddaadacdacdbcdbdaddddbacaaaccbdbcbcdccabbabcdddcbacaccdaccdddcadcacbacbadcbdacbbcbadccdcdcddbaabdbabbdbbbccbbabdcccabddbbbdabcacadacbdaccadbddbcbbddbabcadcbacababdabcbabbbcccbddadacbacabcaabbaddaaabcbaaacaadbcccabbbdcbdaadbccdbdccbaaaacabdaccaddbccdcbcaabccbdcabcbbdaaaabadacbddabbbdbbbcaaabdbaaddcaababcbacccbdcbdbbababacccdccccbcaddabcbabccdbcbabbcabcabadacbbcabdddcbbadddbcdabacdadcbcaacbbbaddacdddcdabbabcdccaddccddbcddadbbaacbaddbaaadbabddccaadaccbbdbbaccdaaabaddbbbdabbbcbabaadcabdddadbbbcdabadabdbcabacaccdaabbcbbadacdcdcdcadbadacbdadbaacbcccddaaababbaacbbdadbdddadccbdbddbdacadbdbadaacdddabaabdabbaadbbaaadcbdcbcadbccadcccbcbcbddbccbcdabdcbbdbbcabdaacbddbddcbcddbbabbaccdcccddbcaccadcddbbcddadadacdcaccbbbdddbaacbdaddbbcbdabaccbbabbbddbbdcbddaacbcadbdaabacaacdbbbabaadbdbaaaabdbabbbdcdadaabbcbbddbadaadaaaabbdadcaccdbadbccaaadcbabdcbdbdccdcaaabddaadcdccbcdbacadacdaaabdbdaaadcbadbbcbabdacbccadbccbadbadbcbdddaabacbbdccabddccdcbabbccabacddddccbabaaadbacccaccbcccaccdaaaddaadcdadbbbbbcaadcaddcbdbcbbcbdbaddacccbcbbacdcdadbbaacaddacadabdddcbcaabdabbbadddacbaabbbbabbaddbcdccccdcbbbcbbdbaccadccbaaacbdcacbbabbcbcacddcadbbabdbacbbaadcaacbaccdbcaddcaaacccadcddcadaaabdbcbcdcccabacccbacdbcdbaabcbaadadcbbdaacccbdbcdcdbdbdbccdcdddcbbaaccadbcabbabaaabccdacaccabcdcdaaacdccbdaaaacaadadaabdcdcdcdbddbbdcdddbdadadddaaacabadbacdaacabccadbbdaabbbcbaacbcdbddbdcabcccadddddaabbabcbbdaaccddcddadcdddaacddccbbcbaabbcbdccbacbcababadcaabbadacbbbccbaaaddcbadbbbdacdbcbdcbbdbcacddaddaadcccddbdcbbaaaaddbbcddcabcdcbcabdddbdcddbacdbccadbbbcbddbccdcdbdcaabdbbddcacbaadbdbadbcabaaadacacbdcacdacaadaaaccbaadbacbbbaadbbabbbdcadadbccddbdcdccdbaaccabbbadcdbadadddccdcaddcaddcdcadcbcbcdadccddbabdbcbbccdccddccbcbbbcccaddadbaabbdabbbacbbdbcdcacdabbdaccdacabacdbaabdacddcacbccacdbdadccabadabccdddcbddbccdaacdadbbaaabbaaabcbcbbadcadbbccacadcdaadcdccacadacdcbbbcdcabccddbadbcccaabbcbcaaaddaddcbadcacaddccabdacccdaddbcbdbbcdabcdcddaadbcaadccbbabdcbaacddadadbbddbdaabcacacaccaababbddddabacdcdcbcacdddcdcaadacabbacdadbcacaadddddbdddacbbadabcbdbdabadaccdacbdcdcddbcddbbdadaadabaaababcdcbaadabbdbbbbcddbbbadcccbbbddcddccddccbdcdcbaddbcaaacbddcacadbbbbadacdcbdaacbadadbcccbaccbbcdbbbccddbadaabccddaadbaabccaaaacbbcddbdadbdbaadbccddacbadacacccaaaadddbadccbbdcbbacadbabbdaaadaabbdaacccbbddccbcabbacbdcdbadaccaadbdacdbdbacbacdbbdddbdbcabbcdacbaccbcbaddcdcadbdcadbcbcdbadbcbdcaccaabccbbddbdaabadbcbbdcbdabddaddddbbcdabacabcdcbcccacccbaddbdbbadccaddacdaccdcadcbddaccaccabbccdbbddddbbabcdcaadbdcabcdcdcbaadbcbbdbdcccbddcbcbbbcdbbbcddaacbabdcaccabbbbddccbddccdcbbddcaabdbbadadbababdcabbbccbddaddbcbdbdabaabadaabaabcdcdcabdcadbacdaaaaaababbdadbdaccddbcaccbabbbddbbcdbabccabbaccbccbcbaaaabbbdaddbbbabbdcdcbdcadabadddbdacabddaaababdbbcacbaaccadcbdcbbbbcadcbcbcbabadaabcadbcbcacdcadaccbdbcbdccaddccabaaddbdddacdaadbcaadabadcacdbadddabdacddadbcbababaccaadabbbddcdbdccacbbbdccacaacbbbcabacaaadbdacabacbccdadbabbbacbbccaadaddcdcbadbbadacadbbcdbbcbcccbdcdbddabcbdacdcadabbdcccdaadccccccbaadaaabbbabbadaadcdbaddbabbabbdcdadcdadaadbdbccaddccaaaccdbadaaabaaacdabbcabccabdaabbcddadaacdcbaccbcdbcdcadddbacbacbacadadacddbabacccddcbbbddacdcbbbbacdbdcacccdcccccbdccaaabbbdbbccbabccbcdcdcdddcaaccbdccadcbbababdadddccacbcbbbadcbdbbcbabbbbaaccccbabdcbaccaacbddbcccbbdadaaaddbbddbbbbdcababbbdaadcbcacadccacdbcadbabcdbbcbdabacccaaccdadbddaaccadabbdabadacdcbbcdacbdcbbcbadccdbbaadcdbcbdbaabccdbdaccbacabbbdadaddcadccdcdccbbbbbbcabbdbadcaaadacbbdadaccacdbacbacdadcdccbcccaddcccaaacbabdaacaabdabddccabcbccdbdcdaacdcabddcbacadbcdaddbbdddadbbdcbaddbacbcbdcabadadcbcaccdcccadcbddacddbbdcadaaabcaaabbacdcdbbdacbcddcdabacdadcaddbbabcabbcacdcdbcdaadcdbabcadddcaddddddbbbbcadadbcadbcdacdcdddccbbadcacccabadacdbdbdbabbdaddcdbaadadacddabdbbccbbcbdbdccdcbcabbdabcddcaccabdaddbcdbbdccbacbaacccbdccaccdbbdbcccdbbcbadadddbbdcccaaacaddcdbccbabdbabdbaddcdacaddbcdbdddbccbadbcadadbbbdbbddcdbcdbcabbbacaccbcddbacababadadabbabdbcbaadbabdbdddbadacdccbbccabdcbcabcbbdaccbcbdaddddcdcabccdccbabccbcadabdacaccccbdbbabdbcdbdbdbabacbddcbabacabadabbbacaabbdbbcdcacccccdbddaccddaaddcabdccdcabbbbbcbdbcdcdadddabbbddbcdbbbbbcbcdadaabccbdacdbdddaaacadcbbdadbbcdbbbadcbdaaddacaaddbdbcaaadacbadccabddacbcadcacdaaddbdcbddcdccccacadcbbadaccddacdcbccbacbdcadabcbabcbdbdbadadbadcdcbbcddddbbccdbbabdcdccdccbbbcdcdbdabcddabdcccabbdacbdaaaadabacdbcdbaacbbcdbabddddcbadcadbabdbbcbadcadacdcccaddbcdbdcdadcacbdaccaadcdcdccdacdacbccbbabccbbaaccdaccbbabcbabaccdadcbccbdbdadbdddadcbccabcbdcbcadadacdabbaadbbbaaadcbddbdabaabbbdbbbcdcbcccadcbcbbddbbdbbcdbaaccbcabccccbdccacdaccacaacdaabbcbddabadbacaddccadbdaaaccbaacdcdcabaabdaddbbacbbdacadbabbabcadcbcadbadcbadbacbdccdbcbbccbbdadcbcbdbdbaacabcddadbbbdccbdcbccccdabbccddacbdabcbcdabbbbcdddbabbadaaaaccaadaaaadaacbbcdabbabbbbacbabcaabddcbacbdabddbdcacaccbdbbcbdcdbcaabdccdbbcacbcddbbbaadcdccdcdcdddaabdaaabcdcbacddddbcdaadccbccabddbadccabbbbbbacdbabdcacdcdccdccdadabccbbbdbbbabbcbddccdccdabbacaadccccbaaccbbdddcccaccccdcddccacbbdadddbddcdacadbbaacbcbccacdbdccacabaacbadccaabbcbdcaccacbcaaddcccbdacadaccbdbcaacaacacccdbbccbcacbddabbdacadcdaddadacccbdbdbaaaaaacaacbbddccddcaaadbddbbddbabdcadbbcccabcbabbddbdbbaacacabacdcbabbcbabbdaacdbaaccbacaaabadabdcddaadacccdcddccdbccaacbaccdbcabdcdaadcdcaadddbacdbdadccacbccabbcaccadbacaaaacabbccabcbbaacadcabbbcccaaaddddbaaacccbcccccccbbbdbadcbdbbdaaabbabdcdcdadbcdcaddaadbdcacbcbcaaddbdbddddbcadccddacaabbaaacaccbbcbbaadacbcddccabcacbbbdabbbbdccdaacddbdcaddbddccbcbcdcccaacdbcaacbabbcccbbabcbccaaddadadadddabddadabcaaadadcddbcbddcdbcdaabdacabbaaddbaadcabcaccbbdbdbaadbbcccabbbabcdddddcabcaaaabdddcdaddddcaabcdbcabbadabbabdcbbacbdadbcabacabadbacdddaacddaddbaadbbcccdbbaaccabbbddccdaccbacdbcbadbdadaabdbcabdddcbbdcaaadcdaabbbccbbbbababcabcbaaabbcabcdabccbcbccadcbaddbcababcabcacbdcbbcacabadacccccaccbbdcbbbddabdcabacbbdaadbdbdcabadbdbabbcbabdcddcdddacadbabddcacabcaddbcdaadcbabbdbdcdacacaddacccddcbdaddcbcbacbadaaccbbbddcbccdcacbbdaddbbdccdcacadbabbbcbaabccddacbddbcbdddaccadcacdbdacadcbbdbdddcbcccddacbdbaaddcbabaadcdbdcadaabcbaccdcbcdccadddccbbababaaadcaddababcbcbacccadccbaaaddabbbabbabaacbdadbaabcbcbbcdbbcbbbddadbdcacbbaaddbdbcbbddcbabcddbbbdcbdbadbcdbcdaadaadcbcddcbbdcbbccdcccdcacdcddbdcbcaabddcaabdcabacdcdbacbadcdbcabddbcbcccbcacbccabbabacdbabbdbcbbccaaacccdacdaddcdcdddabbbccdbcddacdaadbaaabbbbcacaacaaddbccbadaaccabcdbcbbbccadbaddbdbaddcdcacbbdabccaddcababadacaadabbddacccbccbdacacdcadacbbdcccddadcbdabbcbbdaaacbdbdddcbcbcdcddacdddbbadddacaabcbbcdbbbabcdbadadadcaccdbacacbdaddcdcdcdadabacdacdcaabadbcdbccddabbaaadabadbdbbbcccacdbcadaacabddbbbacddbbdcaadadcaabdddbcbcaccaaccaaccdcdbdabdbadadadcdbbbadacbcdbdcaadcaacbdcdccbdbaabdcadcacdcccbcbadbbbbddcbdaaabdcabcbcbaccbccdcbbdaccbbaddcaccadaabcddccbbdbabaadddcddbbdccbadbbaaadcdcddcbccdabcacacaacddacbbbacdacbdcaabbaccbbcbcbccbcdcbddcaadbbacdbbdbccdcacccbcbcbbddbcadababcaabdaacdcbcaacddaadaacabdaaaabaababddbabbcdaccacdbcbcacdccdbabaadabbbcacddacbbacdacacddaccacbdadadddcacadbdadbadbcdcbbbcddbddccacbabbabbbaaacdacddcdbcdbcbcbbaabbdccbdaacddacacaccadbccddbbabcbbdddaabdaadbdcbdddbadaddcadacbbdbddabbddaaacdbadabdbaabdcbdbcbbdcadccbacaaabbbcdcbaacdccdabcbacddbdcbdbccbaaddaacdccdccdbcadcdacacbbaabbcaacccadccadabaabdcdddaccdacbaaddcdaabdadcbdddacdaabadbddbddcbaddbcbbdaccabaadbabcdddcbddaacbcddbcdcbcccccaddbbcddccdaabdabbdbadcbaccddbacdadbabbcbacbbabdadcbaabbbdbcddbdcaaabbbadbaabdbdabddcdbbcaacdbbcccadcdbdbdbdbabaddcbdabdaadaadddbaccabcbcadbbadcbdcabccccddcadcabbbbaacdcbdbdbccdddacddbdccbbcadccdaabbadccbdcbdcaaadbbbbbdacddbdddbdbcaccdbbddababdaadacbadbcabbbdccbdaddabcccbbbadbbbabcdbbdcbbbaaddadaddcdcbddbcdaacaacadadccadddabdcdbbddbcdadbdbcbbcabbccdbbddabaacdaaaacbcbaabbaccbddaaadcbdaadcaaabcabccbdbdbdcaccdaaddddbacdccacbacadbdccbdbcacabdbaacdccbbbbbdcdcdbabbbbabcdddcaadcdccabadbadbabdaadaccaccdccabcbdcddddbbaccddbbcdcbcabddbcabababdabddbaaccabcddabbddaabaaccccbdbbbccacabdcadddadcbaabaccbaddadbcabcdcdacadcbcbdbbbcabbcaaccdadbbdddccddabbbcbccccdcbaadbbccbdddccbbddabcccadaddcbaccabaaadccbdbaaddabddddacdddcbbbaadddbacabcccbabbdaaacdddbccaaddcaaadcabbdabbdbddbaddccdabbbbaacaadbbababacdbcbcbbcccddadcddbddcacdadaabcaddabaabcdabbaadabcadccbaadaddbdcacbddbddccabbbdbcdbabaccacbdaddddccddbdccadbbcdaaacdaddbddaabcbcbdaadababadcdadabdcbcddcacadcdbbbcaabadadbabccdadbcdacaccccbcacccddbbdccdabaadadccbdcccabbdbdcdabdacacdccaaaaacdcdbaccaadaabcccdbacdcdbbacbdbdbdabcddbbbaabadccaddacddbdddbcababcacacdcbadddcdbcbdbcbcadbccabbabbdaaacabadabbbaccdcadcbacdcbdcccbaaacacbadacddbbabbdccbdccbbadaacdbcdddcabcbdabcaccdcdaadaddacacbdaaadccabbdaabbabaaaccbabdbacdddacaabcabcabbdcdadcddcbaaabbcdcdcadcaacbcbadacaadcbbddcbadabcacdabcabccacdcdbdaaaddbdacddbcdcbacaaaacccccbbdaccbaccbcadabacdbcdbbbcacdccdcaacacbddaddbbdbbdbabaabccddbcddbcdbcdcbdddcddadcadcccabccabbdbacaabcdbbddadddacdabbacdddacadbdaadcaacacbacacaccabbcbadbdbcccdaaaccaccabbaccccbdcbcbccdaacccbdaddabdaacccbadcdcabdbcdbcaadcbdddadbbdccbbbacbaaacbdcccbababbccdbccaccbcbcabbaacdadbcccdbadababcdbccdbcabadacaddbbbcacabdddacdcbbcdaaadabdccccacbddcbabbaccdaacbccbbdddbddaddbbaadabbdabbabcddacccdbaadbcaadbcddddddbaacdcbacbdccaddddabbaaccbbdcdcdcdacaadbbbccbdccccbdacababbdddcbccabdaaadcdbacdbadbdadbbabaaadbdabadabdadbcacbbbccdbcaacbbdddadbccbcbdccdbbbabbcdacccbdcbbabbbabaabdccaacbcccccdcddcbdddabbacdccbdcbbbbcbccccbcaacadaddaadbbccbcddadcaaddbaaccaccabadccbdacccdbbbcbbbcddbaddabcaadaabcadaaabcacacdccacacbdcbbbcbbdcaddccaacbdadcdccadabdbdcabcbabcabccaacabcddabdbdadddacccabacabacccaccbbcacbabdcdadcbdcdbdcdacacddaacbcaccccaccdbdacabbbdbdddbacaabdcdbadccbdbccbabcbbacbbabcacdcbbbacabbacaaccbdabdadccdcbacdabccdaadbdabbacaabdbbabaadaacabaabbbbcbbdbabbdcbdccdacbdccbcdbcdadcdcdaaabccabbacccdbdbdbcadadcbbdbcaaaabcabacbdabbcabccadaddbdcdbaaacddcacbbacccbdabcbadaacbcddcbdcdcadbccdbdaacbdbcadabacaacabbdbdbdbbccabdadabbbccabbbdccbdddbbbadcbbdcbbcaadbcbdccbbcbbacdbdbaabbcdbdbbbddcdaacbabaccccbaaaddcabadcadbbdbddcabbaddddaaadcaaabcaabddadbbbaacdccadddbbdccabdcbcadbdcdaadacadacaddabddadaccbaccaabccabcdbacacaaaaabcaccabadddccaabbabcddbcbabcaababbaabbbadbadbdbbaacbbbaddbacacacbacbdcaaddddbcddccadbccbddbcaadbaacabcaaddabcdabcacbbadaacabdddbaadcccbdcdbaadaabddbdaadcabacbaabcaaabcccbcacdcbcbcacabbcabbbdacbcaacadabaccbcbbcabddbcadcbadaacbddbdcbcdcbdacaccdbacbabbccbcabdabccaadbacdccbcbdbbbdbccdaacaadcbbabdddbabcbabdbcddccadbdabbcbacdcbabbaadccaabbadaacbabaaddaddaaabccaaabcadcbaccbabadaacbdaabbbadcbdabcbdcabbbcdabadbcbbcbcbdcbccbabdbabdcbabcbbacbbcbdbacbccbacdbdbccdadcbcdbbcadabbddaadbccdaddbcbdcadbabdbdabbbbbdccaabcddaaddcdbbdccabcadccaaaadbbccbabcbdabdbaacdadbdbacbcbbbbadaddccbbcadccdbddbccbcbccbdbbcdcdbddaacbbdbcdacbcbdddbbcbaacaccabadadcddbdbdbaaaadabaacabbbccbdbdbbdbbbdbbbdaabbdabccddbdcdaddadbbbbcdaaaaaabadbaaacdbcccadcddcbaaccdcbcdacddbadcbadabcabcccbbacbcdbdbbbbcacaccacaacbcacbabbaabbabaddcdaddddcacdccabacbacbdbbaddcbdaccbbccbbdcbddbccdacdcdbbdbaabcaccccbdcabccbbcbadcdbbcaccdaadcbddbaabdbacbcbbdcdddccbbdcdbbbdcbaabadcacadaabcbcbbddacddabdaaacdadbabcbcadccdbdbdaadbdcddbadcccccddaaabccabcbdadcaaacbddbaabaccbadacdbacbbddddaddbcbccacdbbbbcabbdccbabcbdaadbaddadcccaaadabcbbaacaaabbdcbaccdaaacabcbbcaaadadbdaddbcbbddccacbaaabbacdadbddcbcaccadcdcadadccbddaddcdbdbcbaababccdcddaabacaddaadadabbcddaacbdbacddddacaabdddddcdabaacccbcdcacccddccddbaddabaccdccdbddbacadcdcaccdcaadbbccadacabacadbabcdaadcbdbacbccdbbbccddcbadaddcbbdaacaaacacadadabdabbdddabdabdbdadcdaabacbcacaabadccddcdbacbcacdddcabcbcabababbbcbadccbccadbaabcaacdbbcbdbaaabbcabbdadcddcccdbcaadbccbacbaaddbcbdccdabaccbbacbaacabccdbbdadbaaacaccacabadddcdadbdbadccdadcccbbdbdabbbcbbaaccdbdcdcbacacddccadabdcddaddabdcdabdcabacdacdcdabcbcdadccddddacccdbbdbdbcccbbcbbbcacbdbdcaabacbdabadccdbcddcbcbaaccbbabaacbaaadacabadacdcbbbbccadabbacabbadadcabcbaddcabbdbbcbadabbbcdaaabaabddaabbcdadbadabcbddacbdabadbbcadbdaaacbadbabbcdcccadbcbadaaacdcbbdbaddabcbabaccdaccddccabcbdcbcdbadcbdbbadcdccdddbcadbbdbcadadcdbdadcacacabcdbdddaddadaabaddccadacbbababbddcdbacaadbaddcadadabdcdadacbbddbbbbdbadaaccaccadcccaadcadbdcaadbbdbbbcacddbccabcccadcddcabddddcabaadcbacaddccdababcddddabccbabdcddaaacadcadabdcacdbdadcbddbbabbaaddcabcbcbcdcaaacdbbcacabcdddccacabdbcacdaadddcdadabccbbdbddcaabbbdbcacaccddbcbdcbbbcbbcdcccdddacabbadcddccccbdcbdcabcbadbdbccbbadbdcacabcdaabadcbbcddbababbcacaadcdcacbbdaacbaabadcdbabadadddabdacacbaabbacbbddacaabbcbaacccdbbbdabbcdbdcddccbabaabbadbabacdcadbbcacdbcbbadbbbcdbddbbcacbdcddddcbbcdbbbdbdcbdbadbbababcdcdcdccaaddcabdcdadabbcbdbcdcdbcbccaaaccadabaaacccaacaaaccbcddcaaacccbadccdcbcdbcbbbadaadcdacabdbbbbbdddbaabdbcbbbcdbdbdbdabcbbadaccdcacdbdadbddbababaadacdacabcbcacaacdddddcdddcbcaaadadbcbcbadabccccbadabbacdbaabbaddbadccdddadccdbdacbcdbcbcbcddaabddbbbaadcbcacbbdaabaabbdacacbdabaadbccdcbbbdbaaabadaacbaadaabbadabacabddacbacbaccbcdbdbadadddcdccbcaddccdbbbabdababcbcbdabbbccdadadbcbcccccbdcbadabbacabbabbcbbababcabcddcbdbacbcdcacbdcbbbbbbacddaadadbccddccdbaabcbbaccbadabbcabadacacabcddcdaacccabacbadcadddddbcaacacabbccbcacbbacccbbaccbddadbaabaccbadbabbacacdcbcadcccccdaddcadcaaddbcaadbccbcdbaccadcbacaababcddbdacacdaccbadddcdddbacbabdcacdcdadacddcabccbccdcddabcdbdabdccacdddbdacdadcdcdddcdccbccbcbdbbadbbdcbdcdbbaacacbdbabcacbcadcdcdbaabcadadccbadaadcddadabdbdcbdabdaacadbddadcdaacaabcdbbccddbcccbcdddcddbdadbadcdbbdbacdcdacbbadacadaabcbcdbcdccbacddccacacbadcdbaadbdbcabbdadabadddbcdbadaaabdbaccabdacdbaadbbdabbddbccbbdbcdcbdadddcccbdabbbdbbddcabcbbcbbccabcdccaadaddcddacdaaddcdbaaddcdbacccaaddddcddcabccddcdadddbadbcdccbaabccbbabcdacacabaccbcacccbbbcbacaaccccbaabcbdbaccbcbadaaddbacadccbbbacaacdcbacdcdbacbbcabdabddbbddaddbabadadcdacaacaadcaacbdbdccdcacadbcacbcbddbcccaaacdccaddbcbddaaddbaacadbdadcbbdbccbabbcbdcdccbcbbdcbabbcbaddccdbcaccccbbcbbbaaadddaabbcdadaadcdddbccdbdcddbaaccaabdcadaaadddaddbcaaccabbaacdacacacdbbcadbbcdabddcdaabdcadbcddccdbccbbbbaabbcdbabaabccccddcdacdcbbcccbabadddcdbcdcdccacaadbbccbbdbdadbddaaaaddddbcdcaacdddcaccccababccbaabaaddacbacbdccdabcdcdcaababdcaacababacadcabdbadddacddccaaccdbadddaaddcacdddaaabcbadcbaacacccbcddacdaaacaddabdbbdadadbbabadbacdbddbabacdbccaadaaccdadacabdbddbabadbccbdcadbcbcaddabadddaaabbbcabbaacccaccabaabdbcbcadcadaaccbbbdcccdaddacaacbdbaaabcdbcbadccbbabbcbcdccdcaabbcdaadbababddcddcadaaaadbcdcccbdbdabdcdbabbdadbabbbdbbabadadcdadacdbababcdaccababbababaacbcaabddbabbcbcaccacbabdcaadbbacaacadbcbdddabbaddabbdbcddabcdadcbaccbaabcdcbdcacccbdccdddaadacdbdccdcdbbcbccbadcbaadbcaabbbbbcdbacccccdcbccadabbdbcbbdbdbcaacbcdabaadabbddccccbcccdccdbabcdabdacdacccbacbadaabcbbbbbdcacaabcdccbaabcdabccccdabacddaddcbbaadddbcbdaccdcadbcdcbbbddddacadcbabaddadaabcdcbcbcccdbdcddcaacdacdacacbbbadadaabdddcaddccaccbcddbabdbaaaadbdbccccbdcddbadbcaabbabbbcabaaacbdcbaddbcdcbcabacbddddaacaacdacaacbccabacabbdacccdaacaadbacabbbacdabdbcbdbddbbdbdbcbdabbaadddacddcadcacdbcccbbcbabaccacbdcadcbabdacbabdcacdadccbdabddadcadddacacbbbdacdbaddccbbccaacbcccabbbbcbcccbababdcbadccdbcacbdcdbabbbbabbbbbabdddbbacacbabbccdbcabddcacbaddcaadabbadbcbdbdccbbbbacdaddcbdcbdbcdacdcacbdaddadbcdacccccdbbbddcbdddbcbbdacacbddcaccabacbccbddaaddababaabccccaabbbbcddbcccbabddababcbdbdbabadadcdaadaacaddcbbcddcbbdcdbdbbdadaddbdbcdaddbcaddabaadcdaddddddbddaabbcacaaacaabdbccadbaacaaaabadacacaddbdcccccacdacdbcadcbbdcdabccdabcbcbbcddcadaccaccbcbdcdddaaabdbcdcbddbbacabcccbbdbdbdbbddcacaabcdadaacdcaccddaababcddadbacdccbdacccabadaaacdcdcbdbdbdccaaccdccdbacbbcabcaacabdaaabbcadcdbdcaadaaaccccccacdbadcbcbcdcbdcabbcbbaadcbcdbdcbdacaaaabdbcbbccccdbbcddaadbacaaabbbacbcdcadcdaadccbabcdbddbddadddabcddababadaccdccdccdaaabbcbbbadaaacabadcbbabdccddaddbdaddaaaaabbcbaccabcbcdaadcaabadbcdcaacbcbbdccbbabdbcdbccbdabddbdabcaacdbabacababcbabcaccdcadcadccbcbbddaddbdbdabcbacbddacbcabadbadbdddaddcdcdcbbcddcdbadabccbcccacbdacbaaacabababaaaacacacccadbcccabbbccbadaabddcccaaabacdbaadbddcdabcdcdacbbbbdabdbacaacbacacadaaadbabbcababbababacbbdbdabbddadbdcdaccbdbbaadcdddaaacbcdcccbaabcacddacaaddabaccbbdbcadddabdbadbbabcdccbcdbbdccbddcbbcbbbbccacdcdbcdbddccccbddcbdcdcbadcbcbdbababcadccaaaacbcdabdaaccdaaadbdbdaccbacccbbdcccdadcddcaabbbbbabbbcddacdacbabddacdccacbccbcbdbdadcdacdadcadaaccbcdbdbbadadaaadcdbaaaccaabbbcadabccccacacccbccbacbbcccdbbdaacdddccabbdbabbbaccaacaaccddaabdabbddadabdababbadbcdcabdcccaaaaaddabacdabdbadcbbbdddcdaabbbdcbccbcddaadaaddcaaddbbabadddbcbadacddbdddaaacacbbbbabbcbbddddbadabcbdcddcdadbbdadccacaaddabdaccbdbaaadccadadddccbabbaacccbabccccdacaddbcbcbbaccaaacdadcbcabbdbaaccaadacaaabddcbbcbdcabaccaccadacacbacdabcbbcaadbccdbadccbaabcbdbbdbdbbdbbadadcbdddcbcbbbaabcdadadabcddcaccdccdaddccaaabcbddaaaaaaabcbcaaacddabbcbbbbdbbcbbbadddaabbbbbddcbacdbbcdbbbcbadbdaddbcadcacdadbccbbccdabddbbaaacbbaabcadbdcabcbaccbacabdbcbdddbbdbbbcaddabbcdbbbcaaabcadddadddaaacabcdcdccdbdcbabbccddccaabaabbdbccabdacabbacbdcdcdaccdcaabbbdabaaccbacbcddaccdbaddbbccabdbbcdaacbbddbbabccbdbcdacccbbdddaacdccbcabacddcdaadaddcabdcbdaacacddbadbbbcacccaccdbcccaddbdccbdcddddccdddcdaabbaadaaaaaacdcbbccbbdcababbdcccdbcdddcbdbacadcdbcbbadaabbcaacadbbacdbbaddcdaabbcdadbbcdcabbadcabcbbacddbccbcddabcbadbabcabcbdbddcbacccccddccabbbbcbddadabbccbacaacddadcadbcbaaadaababaddcbaacddbdbdacddcccccabdacaabccbdbcddbcccabddbbbccadbccdbacaccbaccddcadbdccdddabccddaabcdbcbcddcdaadaabdcbdabcdadccdbdacdccbcadbdadadddbcababcdacdbdabdbcccaaaadccdbbaacdbbacccbbbcbaddddaabdaddcdcdccdaacbddccdabccadbcbbbcacbaabbcdbbbbabcddbdbdbbaaaacbbcacababababbbcabdbbacbaadcccdccbccbdddcdcbbbabbccbacaadcaabdaaadddbbbacaabbcaadcadcabcccabaaaccdbdadcdabbdcaabadcdaabddbabbbbbacaddccbcacdaacdbbbbbcaccdacadcdcbdcccbadaaacaaadbbcacbbbaabacbaadbddbabadcdbacdbaacdabaccacabadcacbbaddccaacbcbbcacbccbcbbcdbadabdbddcabdadabcdababcacdaabddacbababbcacdbbdabbdbabdadadccabdbdbcccddcbcbadaaccaadaddcbdaadbdbcccdddcdadbbacbcbaabcdddcdbddaaabdcddbdbdcbcbabccbabadaacdcacdcacdcdbcbbbddabbdbbccdcbadcdcddbdbbccaadbdccaabbcababcaabdbdbdaaaccbcbadbcacaaccdbbabaacabdaccbdacdbdacbbbbddcbdbaadacdaabdccaabddabbddbdccbcaacdabdbdbadabbdadabcaccdbccbcabacccddddabcddaaccaadcccdaacddacddbaddcdcdaddaaabcbbbabdcbdaacacdccccacddcbbcbabbaaaddcbacdcadbdbdbcabdccbaabdbaabbacaccddabcaaaddbccddbdadcddacaaabbdbadaaddbcbcbbcaadbabdccdbcbddbbddacabdbbdbbdccabdaadbcdbabbccadaaaddbabadbcabdcdcbbccccbbbaadaabcabbcbbbaccddbdadabbbbcdbdddcccddacdadbdbbcacbdaadbbdbacaccdadbabbaabcaccaabbaddbbbdaaaababcbcbdcbbbadcdcabccaaacdcbbcdaaabcbaaadcaccbabaadcdcabbbadbaacdcacddadbacacadacbaabddbcacdbacdcdbbddcacadaaacacaabadbcacbdcbcadadddadbaadbcdcdcdaccadaaccacacadcdbaacadccbbdbadaacbacbccbbccabdabbbaabadbadcacddcbdacaaaabcdbcaddadcaddaddabcddbdcbbadbbcdcbbaacbcacccacaaccbcbbbbccdacdaddbdabcabaacaccacdbcccbdabbaacbccccbcdaaaddaacdacbabacccabbccddbcbdbdcacaabbcadddaccdaddacccbbdbdaddbdcdcdababbdcbdacccbdcabaadcadcdcbdaaccbacdcacbbabbdadcabcbcdcdaccdbdaaccbddbacbabbddbcdbabcbdbbccbaccdcdcbddadacbccdcbdabbadbabdcddcadbcbcaadbcccddaacacdcbcabdcaabacaadddcaadadbcbbcaddaabcddaccaccabddbacbaaddbadcbadadbcdadaadbcaccbdaacddabbdaccccbbaadccdbccababcdaabdcaccacaddbcbcacbdcbdccbdadddddabdbababdbcdccadcadcacdddcabdddcbdbbcbddcdcdacaabccbcaaaddabdcccbcadbaaaccadbcbcbbadadcaacccbcccdddbcccdcbbbbbdbaddacddaddcaddcaaddcacacbaaddcababcaabaccccbdaacaddaccbdbbccbabbabbcbcbddadddcbbababddbaabadcbcccbcababbababbdbddbbadbacbdcbdaaddadcddabbbdddcadacbcbbacccdcbddcabadbbdacddddbaddccddcdccdccacbbacbacbbaabccaabbcddcabdbcabadcabbabcbdccbddbcdbdaacdcbaaacbdbaaacbbbbbbddbbdabbdcadadbdbbcbcdcaaccbdadbaaaabbcbbbcbcbccbcbcaabcdcacadadccdddaadccccbddcbbcbccbbcccaccadbdcbdacbdacdabddbdaaabadcdadcccbcbacdbaccadbabbacabcadabacddaccaaccbccccbabddddbbdbcbaddccbcdbabddbdcddccdbddabccccabaabcdbabadbddbcabadbcddcbaadbdbdccdadcddcbaacbbbbdcdaabacbacddccddaabdddcacbcdbbdbcbdcbacddacdccbdacdbcbddddaacaabadcdcbdaacbdcdaabdbcbdaacccdddbdbdddcbbbdabbbdadcaacbdbcddcdbdbacacaaadbbbaacaadcadadaaaabdabdacbbadabdaddccacbddaaacbbdadacaddaacacbcaaacbbbbbaccbccabcadddabaacaadcaaccacbcbdabdddadbcddbccbaddccbadcaaddddbbdabaddcbdcdbdcbabdadbcaaccdbcdbccccbadbacabadaadccdccadbcbabbdbacbdaddacaabcdbaabcbbaaabcbdbabbabdaabccdadabacaadddadadacbaacacabbbbabdbadbdcaacbcbdcdadbacdaabdccdaccdabcadcacadabadcdaaccbdccdbacddcdcbdadbcbcddaccaccdcacaadacbccdddbddcaddcdbbbabcbdabcbabdabbccaaccdaabdddbdbaadcdadbbadcbaddcbabcaababdcadaccbacdccacbaddbdbaddbaacbcdbbccdbdcddaacbcabaacdabdabadbdbcabbaaddcadaaabaddbdacddbcbdaddadabcddbbdbdacaaaabbbdcabadbaadadbdabccccaaacacdbcccabbdcaddadddbaabcdcbbbaacbadbbadddbdacdccdcddadbcbcdbdaabbaccdcdcbbbbcdacdccbbdbbddcbcbcabbacabbdbbabcdcbdbbbcbdbbcaadadbbaccbabcbdadbcabbabadddbcacadbabcbadccadcbaccacbdbddadadddbcbbcddabbababaddbbabadcbbbcbddcccbccadabddadcdbbbadcbcdbdbbcbacdbacadaadccdddacdbcacdadacbcabcbaacccccdcdabcbcacbaababcdcbcacbabbcacdbcbcacadccaabdcbcdaabacbaaabddabaabadcdacacabdbbdccdcbbbababdcbabbabacaaccbadcbcabcdbdbcdacccbacaaaabbbcdcbcbcdccccbbadaacbadbdcdbadacdbabadbcaaccbdadcacaadabbaadcdbddcbbadbbbabcdaacdbbcabdcbaddcbadccaccdcdcabccabaadddaccbbbccddccaabcadbddbcdccbaacbcddbccadacaddacadabbadabbbbbccabdccdbdbbcbaccbbbbdacbadbdbcdabbdbbcddacbbccdcbbbaabaccddabbaccddbaccabdbaabdaccdddcbadaaacbcdacdbbcbdbaddcbcdcddabacddadbabcbadccdabddbbbbccaadbdcabdddbaaadddcbadbbaabcddcbbdbddaacbbddabbcbcaadcabbbdaccdbacbcabbabbbcbcddcaababbadcddbccabbadcaccacadaaddaaccbbdaabbcccdddaabbdcbcdaaabdabdbcacbbbddaddadccccdcacbdacddcaadbadaaaaacccbcdbddccccabbcacddcccdbcbdabadccbdbdaadacbabdbbcabacdbcdaaaccaddbcacdcddddcadabccbbcaaabdcaaadbbaddaaccdaabddaccbbcabaabacdccabcdacadbbadddcdadaabcabccbaccbdbaccbdbbaddbdcccacacdddcbbcbdacdcbbdabcbccadcbcbcdadccbdaaddcbbcdddcbdbacbccdaccaabbcbdadbddacbdbbbbaddcbcbbaaabadcbcacacbddbaabdadacbcdabdbaacbbcddabcccacbdbdabdbabcbaddcdcbdaddcdabcbcabbbacbdcacacddbbadbdbcdbdbbdbcbbcbcddbaacabddacadcbbacaacabbdbbaacccababdaacbcbdadadddccbdbadcddbccdccccdabbccccabdcbdadbadcaaaaddaaabdcbbbccdbbddcaacaccaddccbbdcdadaadcbaadccaddabbacbbacddbbbbbbadabdcacbaccddbccaaadddabbbdbdbcabdcbbbadcccbcdbadaaccdccbbdcbbbaaadadadcdaacbbcacadbabadaacaadaadbaaacddaadbbcdccaddbbccbaddbdaabaacddbcdccbcbcdaddabcabccabcbaaaaaaadbbbdddddddbdadbcdaddcaadacdcadacabcdddabddacdaccbbabccbdcbcaddaacdaaddbbbdcbdbbbaaacabbacbbdbdbbaacbaaccbbcdacabaddddcccacccbadddcddbcccccadbadbcaacdcdddacabddacadcdbdadacacccdcddbacdcadcccccbbadabbcdbaadcbabaadaacddbcabddbcbbbaddcabbdddacdbdcdbaacbcbcbccbdbacddcdadabbabaadbbdbcddabdddbbdadbddbadacbdddcdaabbcaaabddcbbcbdbababbdcabaacacddbdccaadabcacbdddabbadbacccbbcbcbdbadcdbbcbccbcacccbcccabcbdcbadaddddabdddcdbcaabacdbddbbdcacacbddbcbbdadacdbadbcccbccaabbcbcbcccccdabdbccdbcbcbadabbbbdaaacaccaccccdababbdbadcbcbdbdbabbddacddaadbddabbdddbabcddbbbccbdbabbbacccccbbaccabbadbdacadacccdaabcbcddcabbdcccacaadbaadcdadbadcabaacbddacabcbcbbccccdcaccdacacbbccacccabdddcabddbaadaddcbcaacabcadddacbdcaccdbccbcabbcaaacdbdddbdbabcbbbadddccbccbabbdaccaccacdbadaaddadcdcddabaccddbcdabcacdacddaccddcabdaaabdbbdcdbadaddaacdacccaaaddaaaabddccbadddcbbbdaddbadbddabdddbdaacbccdbdbbcdaaaddddaababdbbabbdbdadcadabcbcaabdaaabaaccabddccccadbbbbbcadccbccdacdcacaabbdaadccdbdabbabaddddcddcbddbdccbbcdcbacacbddbdadddddcbbbacccdbcbcabdcbacadbcacbcdbcbddbdacadaddcbbbdabaaccddbbdcdbdcddccabaddccabdbaccbdababcccaacabccacadadbccababddbcabbacadbbbcbbaabdbcbacdbcdbbddccbbaaaadbadcbdacbbbbccdcabbacaacbbcbcabdbcbcacddcacdacaacadabacbaadccdcdddcabbadabaacacbaddaaadacdcbaabaadababccaddaaadaabacbbdcbabcbbbdbdbcacabdacddabdcadabddaddaadddacdcacccdadbccbacdcdbcdbcdacbddcaccbbdcdabccddaccabcdbbabaabdabbdccbdcadcdbabdaccbcaadbdadbcaabdababddcadbaabbcadaadcdaabbdadadaaddbaaabadbabbcdbabddaabcacaccabcdcadbdcacaddabddcbbcbdddbcbbacbcbcabcccdcbbacdccaacabbcccbacaabaadcddbabbdcaaadbddbaacccbbccbdcadddbbadabacbcbdddaaacadbdbbdaabbbddcbacccbcadbddbbcbabbacabbbacdbaadacbdbbbcccdcaadabcbdbdcaacdbabaababadabbccbcacbaadccdabddaabbcaaaccabdcccccacacaaabddcccdbaccbbddcabbacdddccddabbdaaaddcdcacdaabbabdcddbcddddabdaabaccadbdcaaaadcbbbcdbbccabddcdabdaddaabdcabbcbdbbacdabdccbdccbcaddabdabdadbbcaacbcadacaaddabadddadabaccbdbdbbdbaabbcbcabbdadcbdccdaadbdbdabacbccbcdacbbdcdbcddccbcbbaccdcadcddaccddadddbdacaacdddcabdcccadbadaabcaaccadaccbacbbdcdcabbcbacbaccaaccaaadbdcccbcacccaaacdbccabdbbaabbaadcddbcadbbcabcabadaddbbcaadcbbcabaaadbccdccacbacadacabcdddaabbbdccccdcdbabbbcabcdbbccaaddaaaddddbccacabdbdddbbbdcccdbdbcbaadbbcdaabbbaacdddcdbadcacaacdbdaaddbbbbadacdccaddbccddcdabcacaaaccbcaabdbcadbcabbbbcdacabbccdcaabccbacbbbbabbddcadadbbdcbccccbbcadabaaacbadcababadbbdcdccadddbbddbbaadbabdbbcdbdabadbbdacdbdcdbccdbcaadbcbccdaacddaadadbddccdbaadbbacbacacacbccadbcdabdabdabdbcbccddadadcbabbdaadcccddddcabbcbcddbcbadaacdcdbacbddccdcbdaccabdaccabbcccbadccbbcbcadaacaabbbbacadbcddbadaabbbcacabbcbbcbabbdbbabdcacdcbcccbdccdcdbddcccacccbbacaadddddaacacccdacacadcbaccdadddbddbaadadccaddaadcaaaacaacbcadbadaaadbddaaabdddbacaaabdaabbbcaabccdbddacaacbccbbbcbbbdddbdabbabddaddabdaddaccbbadbbbbddbcbadcabbbcbcbacbadacbacddadacbaddbcdccaabbcccaacbabbbbdacbabadabbbabdddadddaacbdccabcccbaaacaadbcddabbdcccacbbaabbddaddcadaadccccabdaadbacdaccdcdbcbaabcbaaacdbdcdbcbccbdabddddbdbcdbbcaadcbbcabaddccdaddcdaabadbbcdbddcbcdbaaaccbcdcaabddadbadaacbbabbaddbadaadbbcbcbbcbcdddcbbcadccadddbbdacabddbbbbddcdbbbdabcbdbbcaabbcadccdbbbcdbcabaabbcddbbddbdbddbdcbcabdddcccabbbababbacadaaaadbbcdacdbcbcabdcadbbbaabaaadaabdaaaabdbcbbddbdabbdcbcbbdbdccbaabbbaaddbbbbdbacbbcbbbcabcccccacdbaaccbdacdabcbaacbdbaacdaddddccabdcabbddbbdcdabacdcadcdddccabdabcaadcaaaacaacbdacdaaadbcbaddccdcabdddaddbdcbbbdaaaadccabbdacbbcbadaaadbcbadabbbbcdbacbbdbacdcdccbcadbbcbcabacbddbccaaddddadcbdddbbccabbcddaddbcdddcccadcbcaaddbbaddbcbcabcbbacccadaadaadbaddbcbddaccbcaccadaccbdacbadbadcddbadacabbcbdadaaccdaddcbcdaabbdabcaaaabdabccdcaababcbcacdbcaabdcaadaabaaccabcdcaadabacdccacdccbaabacbccccaabddbddddaacdbbabccbbbcdccacdaadbacdccbbcdcdaaadbdcabacadbbabbdacacddabbccdcdccacccabdbbbadaadbbdbdbacdcbcdacadccbabdcccccbdbabaacdccbcdcabbaabbcccbdcddbcbdbcdcdaacaaaacbccabdcacbdbcadddcadacadadcabbbaadbbdbdcdbaaccadcaaddddacbdbcdccdcccbbbabbcbddccddcbdadbbbcbbdadcddabbbbdcbdcbbbbadbcabcabccccdccbdcddcbddaaccdcaadbbddacacbdbddbcadcbbbdcdaccbaddacacbaacabadcdaddcabbcbcbaacadccdbcadbddbddcbacdaccbddabadccababddadcddcbaacabbcccbdacacccdcdcdadddadbbddaaaababacbdaabcaccbabbcbdbddcddacdbbbcbbacbcdcdbbacaccdcdadacabcbcbbcdddacaddbacdcaadbcaccdbddbcdbcdcdcacdccddaacabddacbabddcbdaddcadbbbccaadcbdbdcadaabacccdccdbdadbdadbadbbccbcaaddccbdccbacbdcacddcdcddbbdbaccdabbcacabcdcccddadddabbdbabacdbbcdcaabbdcdbbbacaaabbbbdbababbbaddcaadccbdaabadaadaddacddccdbbcacaadadabbaccacadaddbcbddadddbbbcdbbabbddabcadcaaddcaacccbbadaacdbabaadbacdcbcccabaacdacbdbccbbcabcacddccbcdabbcbdbadbacddbcbaaddaadccdcdacabbaaabcdacbbacacdddcbaabdbbccbaacdcdabbdbbbaaadcdbacacdaadaaaddadabbbdbdbbccdbaaadabbdbbccddcacadcaaddbcddbbadcbbcbdcaadcbbdbdcbdbdcbddadcdcdccbdcbdbcadbacddbdbbcdacbdddcacabcdacbdcbbdabcabacabacccbcdaabbbaaadabbabbdbbadabdbdcacabcadcaaddacdbbdddadbacbbaddaacabcccbbcdcdaadccccbadcaddcdcdbbdbdbabcadcabcadcbddabacddbabaccbccbacbcdacddaaccbbabaaddcabacdadbccdcbbccbacacbabcabcaabbbcddadccdaacaddbabcaabcadcaacacbbcbcaaccccddbbacbadaddbcddbaaccddbaddcdbbdcabccdbbdbddddbbacdddcbadcdddacdcacdabbadcbabaabacdbbcadcccababcdcbdabaabbadbdccbcadaaadbccbdabdcdbdddbcbaddaaabddabdcbadcdcbabbcdcbdbdbbbabacddbdbaaaaabbadcaddcbbdcbaabbbdcadbaabdcddaadadabbbccadaacccdddbabcadbbacdcaacabcdcbcbcccbbdbaabdcdddcdbbddbaccddbdabdbddaabcbdbbaaaacabccdacadbaacdcabdcccccbdddbcaacddbbadcacbcdbbaddcababdadcccbcbdacacbacdcabbbadbaacbacbbaaadadcdcccbdbabacdbaccdabcccbdcdaaddcddaaacbbabbcbdbacbabbccbbdcabcbaacccdbbbcdacbcccabccaddbdcbaddabacbbcabcbabbbcbddadddaabdbdabcbdaccacbdbccdbdcbbddcadccbacccbcdacbdbcabaacacabaddcabcddddcaadaddddcbdcccacbddcbabaacbdbdcccadaabdbccbcbdddccdbababdadbaabccadcaaadaaccdbaddccdbdccadbbbacbdcbbdddcababccaddbcdcbcbccccbcaacbaabbcacbdbdcacbddddadbabdbaadbdbbabbcabbdbdaabcacdbccddaadadcddabbbbacadaddabdbbdbaababdcadcadbccbccdbcabbcacbbcdaccacbdccdcccddbdbccadcdcccdacbabdaabdcaacbbacdadbccdbdcaccadddcbcccacdcacddaccddbbaadcaacdcabdabdacbdcbaaabadaabcbdbbcccbdbdabbaccddbdabbabdcdbccddbbcaabcdcdbbdccdcadccccccaccaaaabcaddadbaadddbababddbbbabdcabadaaccbabdccdbbdcaddabaadcbccbcdabccadaababacaadcbbabcababcdadbaaabbacdbacbddabdaccbbbcdbbaddabacbacccabcdbaacadaddbdbdccdbbcdbbaaaaaddabcadadddcbbababaccbbbcdaacbdcaddcccaddcacbcbcdabadccbabbccbdaccccbcacabcdaacddcbcccdbbcdacadadcbaacbdbcaaaaccdaddcdabcbacddbbadabdbdadacddcacababbccacacdabcabcbdbadcbabbccdcadcadbadbaabdbcaabccacadbbdbbbbababcdaacbdcdbdabcdcbcbcababcbacacdcccadaabdcdcabbabddcbbdbcaccdabaacccaccadadacaacdcbadbbadabbcaddacdabbacaadbbdbcdbcdbcdbbcbaadbabadcdcaccbcaaabbbdcaabadadddbbdbbccbcdbaaccccddddcdacdaadcbbaabdcabcdacdadbadcccccbcccbadcabadcdbdbaaaaddabbacdcbccdadccbadcdbddccdbbbadbbaaaacaadcdbbdcdcdbaacddadadddcdbaacdbbcacadccbacaaacccdcaababcbbaabbbacabaaccabbacadcdbacacacacacddacdcbabcdbcaddababbbcccdcbcbdddbdababacaadcbbabccbddccbacdbbacbcabbbccdabaddcdcbdbdacdbabbccbccdbbdaadcabdbaddacdaaccbcdbdbbcdaabcdbabcaacadbbbcabcdbdddaadadbdaccdacdabaaccdacdadbcddcaabcbabbabcdabdbdbcabacbbdacdbddadbaccccbabccddbdabbbdcbcbcadddbdbcadbcbccabdbbccadbccacdaacbdbdacbadaaccbbdcdcaaccbbadcdadadcbabcabbcbbabbcbdcccaccbddaddaccdcbbcbcbcdaddcaabbdadddbdbbccdbbcddbaacbbdbbddacccccabbdddbddaaadbddbaabaabaddbbdbccbacdbdbdbddcaaabddabccdaddcacaadadcdaddbcbdaabcccbbdcaccbaccddaabbddbcdbaabcabbdbcbcbcbcbcdadacbbcdadabaccaccbadcadbdaabccdaabbcbbaadccccaadabdbdbbbddbcdcdddbbddadbaadbacbcdbbcadabbcabbdbcdbdcbddaadcddbdddbddbadbbbaccbdaababdabccabccdbadbbbabdcdadbbcbabcdbadcdadbbcdcbdcddcdcbbadbddcabbbadaaaacaadbdadadbbaaacadccdcacbbcbababcbacccabadbdddcdbbbbdcaacaaaaccadcabdaabcddcddcacadadacccddbccddbadbdbddcaadaadbbaaaccbbabccdcbcccdabcdbdcadaccdbdbacacddccbccbbbbdcbadbacaddddadadabacabbcdbdddcabdbdcccadbbdbadcdbaacccaaaaadcacabdbbcacbcbbaddabccbcdcdaabcadabbcbcaadddddbacdbcbdbdddaadaccaacbaaacbcadcbbdbdabaabddadcadadcccddaabdddddccdbcacabcaccdacacdccaaaacadbacdcdcbbaccddabaddddcdcbcdbbdddabbadcdcababbcadcbdacdccbadadcddbbdcacbccddddadaadaacdbdcdaaddaabdcbdcadddcbbcdcabdbcaaadbacaddcddaadabdbadadaaadbbbadcaaaaccbdabaaccdbcadccbdaccbdbbbccdbabdcacadabddacbcbaacdcaacddbcaabaaddcdbdacdbbbbdabbaabcbccccadbbcdbdddadbaacdbcaadbdbadabdbcdbcdbbbaddbadcbcdbccbddddcbbdadbcacabccccdabcddcaadbadbbcdaddbcabbbdbddccddcbadbcadaaaaccddccaaadccdcdcbacbbbcabdaacdaccabcdadbdbadddccccadbabcdadddadccdbadbbdcccadbbacaccbaabccddcaaccccabadcccabaaacadaabaacccacabdbabccbaccacaaabbadccbdabcacbbbbdaddbccadccdcddcbaabcbccacdcbdacaaaddcabbadcdbadaadbaadaabaddcacccdadcbcbdcadcabacbddcddaaabadddaacacbcbbcdaaabbaababdddcbbbdadaadacbcaadabcaaddbacdcddaccaaabaccaaabdcdddbcadaabdaababcbcddcaccdabbaaacabdcdaddabbcbbabccccacaacdbcdabdbacaadadddddacccbcbbdbcccaddcbbcbbbabdcbaaddcdadcdbdccaaaadbdbddadcdbaadacbbddacacbbbddbdcbccbbaaabdbabcadcdabcbbccadccdaadbdddcabcccabbcaaaddaaaabdaadadbaddbaabdabccdbabdadddaabbddbaddcdabacacccaadbdbccccccbcbaaccddcdccaddcaadadcccccbbbaadcaadaaaaccdcddaabbccbcabdbbcdddddbcdcccabdcbddcadbddddadabadcdbdbbabacccadbaaacaadccbccbbaadcbdaccdadcbdaabcbbcdcbadbbcbcabaadccddbbaaacdcdbbbdccbbdbadccdaddcaaaaddacdccddbcdaddaacdbccbbdcbbdaddccabaadcaabcddbabbbcbaadababcccacaaacdcacaccabbbacddbabccabbddddccccacaabcbddbccbbbcdbadbadbbcdcababadbcdbaccdcbdacdabaacaccccaadddddadcdbccbcbaddccbabddbacddddcacadbbaccbabdaacabbaabbbddbdcbcccdcaabdbaaaaadabbccbbddabdbdaabaaabdcacbdababbccdbbbbacbddbacaccbccbcdacadbbdddcbdababdddbcdabbdbbccbacbbdccddccaaaadbdacbbbdaccacbaccacbdcdbcbdddacbbccabcaadcbdbcaaaddbbabaccbcddacabaadbbbbdbdaaacbaadddccdaaacdcdbcdcdacdbcdaadcccbabddadbcdccccbdccbbbbbbbbabbabdbabdcacbbdbbbbdbbdbacacadbaaabcbdbdcaddcbbbcbbcbadbddbdcadcadbcbdddbadaaacdadcbcaddbccddbaacdaabcadbbdbccdabcbcaabbcddbbcadbdddcccbdbdcbdccdcabcbabcbdcbbcacadbbdccddabbaaccbbadbccadddaddcbdabdddacadddacdcdbacbcadbaabbabdaaddbdcccccdbcabbddbbaaddabbacabbabccbbddbacdccacccccbadbacdcbcbcbdabcacdcddcbbddcdbaccacaabccbcababbdcacdcadbcaabdbabbbaacdddbaddaccbbbabcdcaaacbddaacbcccdbccaadbdcbddbadbcbddbddcccbcbccbdcddbbcacabbdbbaaddddadcbbaababcdcaccdccbacbbcbbcdbccdbccddabbdbcddabddccaabadbcabdddabadbccbddbcaccbbbbbccaaacbcbcdacbdccccbbdcbababbbacaccbadcdcccadcddaacacbbadcdddaadcaadddadaddadaabccacdbcdddcbbdacddababbbadbdcaacbbdcdddcbacabccababbcacbcbddadabacaccccbbdbccdbadadaadcbacdccacdcbdaadcabbaadbcbdcadbadbbbbbdbdaacdbddaacbabaaadbacddcdadadbdccbbaddcdacaddaacaddabaabccaacdacbcdccddddbabdbadcbbadbacaddbddbbbdcdcbcbadccacadaddcdcdcabcabcdadcadadddcadabccbbdbbcbcdadbbdacbbaabbbbdacadabdabcaabbadbbbdaabdcaadccaccdacddbadbcdcadcbccaacdbcbaabdbdaddddbbabdbabdaddbbdbbcaabbbaaddcccbadbdbaddbbaaabbdcccdcddcdddaadbbcadcadacccdddbdcddbdcbccacbcdcbcdbabccdaabbbdcdcdbcccddbacadcbbbbabbcdaaccdbbacbcdcaabcaaaabbdddbccdbadddcdddbccdacdddaacacdbabbbdcdacdbdaaaacabaaadacdbcaaaaddcddccaddaaabaddddddbcbabcddacdbadcdaacdcaccadbbaabcddbbdcddcbdbcabbcacadbdbbdcbbaacdcccdaacaddccbddabbadadbbcaadbaaccccaacbbbabcababcbccadaddcbbdbabaccdaadaaacdbbbacaaddacadbddcdcaabcbcdccddaacdaddacddaccaadbddcdabddbdbadccddaacadcccbccabcccbcdbbdbbacacbabcdbaddcdadabbdacddacdcaccbbccbbbdaadaccddbccdaaacbdcccbbcabdcaadddbdaccbacbcbbdbdcdcadccaababcbddbaacdabcadbcddcbbccccbaccbabbabacabcdcbcbddcaddbcdabbacbbdbbdbacdcdacdbaaccbbbcaadcccaccbcadddcbdbcbcccdcddcddccbbadcbcccbcdbbcbdcbbacccabbddbbcccbbcbccbdbbbcbddaabaabacdcccdccdddddadbaaaabdbbcabcaccaacdbbcacbbadbdcabbabcdcbdcbcacacdbdcdbbbbcbbccddcbbddcddcbddacddcbcdbadddcbaccbdbcbccbbbcbbdddbbbaaddbcddabbdaddaddccbacddbcabbbaccacbaacaaacabbbbacdcbcadcdddacacadcaadabddbbcdcdcbcdbcaaddbdadcbdcddcddaddcbbdcabdcaaaacdcdbcbbdddaaadaccdcbdddddadbbcaabbadcdbabbbaacdcaddbcddcddadbdcacdcddbcdcdcbbdaabdbccdcacccbaacabbcbcdaccdbbdccdbdadaccddddbdcbdacacbbccaddbccbdbdbdadcdcbcbacbdcbbdabdbabbcdddaddaadbbaabaaadcbcdcacacccdbcbadcbadbcddccbcdcadbbdbcbcdacccbcbabddbcdcdccbaacdadaabbcdbadbadacbbaaabbdadbccadadadcddbbccabbccbbbccaaaaacaacacabdbadaaaabaacbcbdcabaabdccbccbddbbcbdacbcdcdbcbcbbadbbdcadbbccbcddacdddbccbbdddcbccddcaddcddbbddcaadadddbdbccbccabdbacbabbdbcdbdcdcdababbbbabbaabdbbdabbcbbaadabdadbaababdcbddcccaaccdbdaacaccdbdaabadabbcaddbdaccbbacbbdabbbdacdaadccdadbbadbaabddbbadddbcaddbccaadabdbaaddaddcbbadbddabdddbdbabdccbadbdbabaddcacbacadadcdbdccaadddcbcccdbdbabdcbccdbaccabccccbbbdbaacdabcbccbdacaadaaaddbdcacbbcbabdcdddbdaacacdaddaaaaaacacdddddbabbbccacbdbcccbcbacaadbbabbcabdcbacacdbbdddddbacdbaabcabbaacccbccbcdbaadbbbcabcbbdcdaabcabbbcccbddacaddbdbccacbcadacaaddcadddcbcaadbdcbbaadccacdddcbdbadcaacacacccbdcacbcbcaddabdbbacdaadcbcddcabdbdadabdcaaaddcdbdcabbcbbdbddabddccdadcaddabdccbddacccbbcadcdcacdbcccabccdddbccddbdcacddcbdcaddbbbbccbcbaccaadabddaccddccbabbcabcdaaddcbabddbddaddcabccbbacdaabacccacbccbcbbcabcbcbaabbbdcdabbacaddabcdcbcccccdcddcaccbdcbbbaabcdcbdddbcdaccbdabdcdbabbabdcbbbabacaaabdbdacddcbbbdbcbdaacaaadaadabcbabdcdabdabdadacbacdcbbbdbcbababbdcadcacdccccbaabadcccdcacbcbdcbdcbdbccadccdcaacdccdbdbaaadccbcacaacbbadcbcabacdaadaabdabddbdbddcbbcbbbdccabaadcacaaccabbcdaacbbdbbbaddaccbadcbbcadbadacdadbcbdcccbcbabdaccadbbcbbcbabaabdcbbbdbaacbbacacbcadabbdddaadbaccddbabbcacbdcccddcddddababdadaddcddaaaabbdbccdbcbbdccbddacbbcbddcdcbdcdcaabbbdacbdabdaccdbbbcddbcabbcdbcacdcdcaccddddaaaacaabdaaadcbcdbbcabadaacdbbcacabddccaccdcdddabccdaacbbaabbcddbabbbaabcccabdbadbadadacbbadcbaccddbaacadcaabbbaaddbbcdabcbbbbdccdcbcbdbdadbddcadcbaaddcbbbcabcccdcdcadbccbdcbcdaccacccdbcbbadcabcacbbdaccabcabbacddccbdcbabbcdaacadbcddabcdcddccaabdbbddbdabddbabccbccadccbdbbadbabbdbadbbaababbdbaaaaaddbbbdbddabcccccbbdbddabcbdcadbdcbdbbdbcabcdbbcddaddccdcdadbabcacdcaadadbcbaadbadacbbbbdbcbbcdbddaacabdadacabbddcdbdaabcbbbcdbbadddccabbaaddbccbabaccbdbaabdcdbdcccdaaadaaaaccabdccdadcdcbbadaabcbcaaadadbddcabcaacbbdaadabddccbbdbcbcabdcccdcdbcbbcacadadbcbbccddccccbdbbacdbbddcccccbcbaccdcbbcbaacabdbcbbbadbbbbcccbcddbacdacacadabddbbbbbccaccaccaacdabcbdcbdbcdbdbadccbbcccbbdcccacbbcdbbaacdcabddacdbbddcaabaabdadadcccaadddacddbadabdddbaabddcddddccadbcccddbbbdbbcccdcdbccccbdacbdbcabcbdccbddcdabddaddabbbdcabbaccddbdabdcacdbcbacdaadaccddbdccbaccbaccdbabbcadabbdcbddcbacabacaccbcaccbdccbbaddabaddcbcbdaadddacdaccddaaaddcdbbacdcbaabcbadcabacdaccabababaacdddcaccbbccccddabdbbbbbbdbbbadbcbcadcacbdcdbaddbabddcccdccdbaacbcdccbbbdcbdbcabcadacabdacaacacdbacdcdcadbcccbbccbdcbccbdabbdbbdacdbbbaacdbbbdcacbbdcbcadacbadcdccbdbdadbddabdabaaadacaadabdbabadcaabbadbcacacabaabdacaabaaabadbababdbadcacbccadadbcbbaacbbccbcbcabacccddbbcadcacbbbccacaddaddbddbbccadadccaddabdcbacdcbddaaddbbdbdadadacbdbcbcadccdcaabaadcdabddadcbcbacdaaccbacccddababacdbdcddcdabbabbbaabbcbdbccbbbdadabbbdbdabdabdaadcdaacababbbacadabccaddcaaaabbdacabbaacbaadaabcbbdacadbaabbabbdcadcdbaddabddaadabcdbdbdccdbacbaabbbabbbcdaddbcdaaddaddcdbdcbcdbdadaabbdbcccbcbdbdcaacaccbbccdabcdddacbdbcabbdcddbaabcbbcbaaaaaaabdaadbcbcaacdccbccdbcbbababdaacacbbabbadcdabaaddcccddbbaababcabbbcbdddaadaabbdcbdcabcacbdbaaaaccdbdaaabccdbacbaaabdcbadcabbbdcdcabdddddbbabaaadabdccdccdcbaadcdabbdabaaabcaccbbcdccbdcbcddcacbdaddddacdadaccbbadadadbcdcdbbdccbdbcabbabbbbbdcbaabccadbddaddbcbadcbdbbbdddccdadbddddcbacbbbaddbabcbbbbacadcadcaaacdbcbcccdcddcdbbabdabbbbdabaccdbabbddcacdcbbdcaacdcdabddbdcdbddcbabddbcdcddacdaddbccdacaaabadcddccddbdaddaaaddbcadbbdbbacbadcdbcbddbdbccdabacbcdcadbcabacbacabccabdaacccdbddbaacbbcbbabccdcbcdadbbcabdadcadbddcaddadbcdcdaddadbcadadbbbbbcbadbcbccdacdadadddaabdcddaadbccddabacacaaddccaddbbcdacdccadcccadacbdabbccdaaadadbcbdcdbccbdcbcababcddbbdcaabdadbabcdabbbdacadccdbbdaccdbaaddcabaddddacbdaadcabdcacbaaccdbbcdbcaadacbbababcdbbaadcaaddcdadaadbadaaaaddadcdcdcbccadbcccbdcdddbbabdcdddaddbcdddbcaabbdabbbbdbdcadcbdbaacaaacbdccdadcadcacbabbbbccbbcdbbbcadbdcbdaaddaadcacdaadadabdadcbdabbccaddddcdcdcbabbdbadbddabccdacdaddacbacbbbcaabcabdbbdbaddcdbbbabbcbcdbbbddbccdcdabcdbbcdbbbbbdbcbabdccbbbccacdddcddaaddcdadccdcbbcaadabcbaccabdccdbabddcdbbbabcaaddcbdcadaaaabaacbdaaabadddbcdabdbdbbcacbbdbddccdddabbacdbaadbabbbdcaaabadaccddcadaadacaadbbdcdccbdddbaccadbcaccbbcbbbdbdbadadddacddadbbccdcdabcbacdadaccadaabadbdaddaccbdcccddbbccdcbbabdaaadbddbdabbddacbcabbcbacbaacabdbbcbdcbacaaabccbabdcdcbddbdccdddabacabababcacbcdcabaddbcadbdadbbcaddababbbdcbadbddccbadaaacdbabdcbbcddcbdddcdbabdbcaaadbdcdaaabacaccccadbacaabadbcacdacdcdcdddbbaddbacadabcccbbbccccddcbabbbbdccbbcadcdccbbbbaabbbaddcdbdadbabddbdaacadbbddacaddbacaaaccbbadbbbcddcbdcbbbacbbacbdbdcdcadcdbbddadcabbbabbbcacabcbdaadbdbcccaccadbddbacdcaacbaadadccbdbbcbdabbccaccdbdbcbaabcaacccaaadaddcbabaacacaddbdabbaabcdbaccdbbdcdbaaddacaadbcacbbaaababcbcddddbdbbaccddcaddbbabaaadcbabdddadaaddbaabccccaccabdbabbccbbaadddadcadddaabddccdbcbcacddaaababbcdbdccbcaabacbaabacbddabcccabccbacddbcdbacccbbdadcbabaaccdbbcbdcbcaadbcbacbddbcadcddaddacddaaabbabacaabcaaaacacbcdcdaadcdabdbabaaccaddacdbcccdabdcaaadcbbabaadcddccbaabaccddabbcdbcddccbdbbdaccaaaaccaaccbcdcbacbbcccdadcdbbcbbddbbdaabacabacdabcabcacccabdaadcacbcadbadccbdacbbadaaacdbbdbdcbaabddbababbddcbcadbccddbbddcaddacbbddaaccbbbdcabaabdabdbdcaddaadccccadcbacaddbdbbbbcaccbcbbbdcadacdbdccdacbbbddbbacbaddbdaddadbbddbbddcaccacbdabaaaccdacabdbaacacbdcdabaccbaadbacccbbaaadbdabacddbabdaaadbbaddbbacaddcaabdbbdbcbcddcadcaccbcdaccacbcdcacdaddabbbadccabcacccbbabbdaabbdcccdcccadacddaaccdbdadacaabdbdddcabaccadbddbaddbbbcdbcddcdabbdcddcabdbadbdacbdbbbabaacdadadabdaacabcaabaadbbdaadadacabaacbaacbaacacddbccdadcacacdddcbbccccbcbbabdcbdccadabcacbccbddbabcdaaabbcdbbacbdadaaccdddccdadbabbaacacdbabccaaaaaadcddbccdcabbaabbdbdccbdcadadcdcaccdbbcdacbabbadcacdbdbbccbdbdabaacdadcadcabbdbdbdcbdbbcbbbadbabbbaabcbbabcbabaaaaabbbcaddabccbcdbaaabbdbbdcdbbabccbadbbdbdbabaacbbdcabaabdcbdcbddaacbdccbccbdbbdcdcdbcbbcbddacbabaccbcdbcacbbcdaadcdcbaabccdabcadababbbdcbbcdbcaacdbabbbbbccbdabadadaddbdacccdbaadaddcddadbddcaabbadbadccdacadcbddabaaabdcbbdbdbbbddbbdbcacaababbdccabaadcaddddacdacbacaaacbacddbcbbcacccbadabbbabdabdababcaacadadbaadccabdbadbbabbaadbcbccbbaccdaaccacbabdaccacabbbcabbdcdbbadbbcbcbbccadabccbcbabddbcbbcddabddbbccdcbababdbdacbdacabaaddaadcdbcabaddabddacbbaabbbacaacaacdaadbcacdbcbaaccababcbddbbcdccdcdadabbbddbcaacaaddaababcdcdababcbacdbcdabdddcaacccacaadcbddcbcbbaababacdabbdbcabccaaccdccbdbbcabcbdacddcdcabdbbbacadbbddabdcaadadabddbbaccbadddccbccbcabccacdaaadcdcdaddbacdcddcacddbcdaacabcbaacbdacbadcbdabdaddcbdcbadcacbbabcbcaaacadddbbccbdccabcdaaddbddbbddabbdbadabdcadbbdddbbabbacbaacbabdabcbcccacabdccccdababaacdcddacbabdccbdcbabccbbabbbbbccccbabaadababadcacbbaaadcccddddcbababcdddaccadbccbdcacddbaaadbadccbcbddbbdabadcbdddbbdacaabdbbaddbdaaadcbdabaacaabdcdbbcbaabdaabaddaccddabddacadbdcdbdaaadbabbacddaabdaadbaabdbbcabdabbcdaaacbddabbbcaabdacbacadbabdbdcbbdaabadadbcbabcacbcbbbaadbbdccdbcccabccdabacbbaaaddcddbabbccdadcbbcbcabdabdbcdabadbaaddcddbabcbdadbddacbbdbaaaabbbbdadcbdbbadabbbcccdbccbacabbbcdaccdadbdabdcdcddbacacacadadcbaccaacaabccdadacbadbdcccccbacadcbbcbdbdccabdbacdbaddabccddadadcdcdabbbcccddacdcacbaddbadaddddaaabccbbddddbacddaaaccadcdcacdbddcbbccdcacbdbbcbabbaaaadacadbcbdbbcadaaadbcbdbbdbdaddaaabaaaccaccabdbdadcaaacdadadbcdbbcbccbbbaabcdccbadbbdacbabbadbbcddcdaaabddabacbdabbabacdaaabdabaabdbcccadbadddbadacdcdcacadccbcabddbbbbbbaadcbcdcdaddadbacbbadcaabcdbaaabcbccdbacbbdcdaccdbbdabbcbcdddbcdabbaabbbdccccdcdcccdcaccccdcdcadbaabdcbdbdcbabcacabadbdbaccdadddcdccdddbadbbaaabcccbdacacccacdbcbadddcccaaaabcaacbadaccccdcbabcacbbcbcabdddacdbdcbcdbbcbbccccacccccaaaaaadababddbaadccacbbbabddacccbccbddddddbdadcccaaccdbaabbbcdadcdbcddaccdbddabadabdababddaaabbddaddbadcacaabdcbdbccbcbbbdabbaabbcbbabcdacdaaaabacadaadbcddaabbbcacacbbaddabaacaadacbcaaccbddccbacbadbadabbadcaccdaccddaddbbddcbcaacaaabbcacdddcaabbadbacaaabbcdcbcccadcdabddbaccbabbbdbcdabbcabddcbacabcbddbcbacdbddbabcadddcabdaaabddbbdadacdbccbdcbaddadaccdbcbacdabccbccbdbacdbdcdddaccbbbadadaacdcbbbcadacccdbabccdcadddbaddaacaaadcabbbbacdcbcdbbccbbbcbcdccdbaacaadddcbccdcddadccbbbccbadbbaadbadcacadaadcaacdbbabcdbdadabcacadcccaddbddacdaddbcdacddbdddadbdddcdcddaabccdcdcabdcacaddabcdaaabdacbabcccddabaacccadddcbcadbaddadcbcbbabdccaccadcddcdbcadccccccacbbcdbabadbabbcdbcbbdbcdcababdbabbbbadbddccadbadddbcaabbcddcddcddccbdbccdbdcaabbbbbcbbaccdccabdabbcadcadcdaaddcdbccadabbbbdaddddbccadaddadccdabcdacdcdaabddadcdcbadddbbcbbddbaadcacadabcbdaacacccbabdadcbaddcdcbcdddaacdacdcbdcdcadabbdadcddbbbcdbccdccbcbadbabadcdadbcbddadaaaadcbdcacbbadcbcaddabcddaacadaacbbacaaacaaccdbbdbdcdbabaaadbdcaccbadcccbcadbdcadcadddbdbaddbaaabbadacbbdbccbbdbbbbabccdbadabacbabaadbbbdbcbabcbabdabadaddcacdbddbbdaccddbadaaabddbcbdddadbbaaccbcacdcddbbabacbbabcacacdddbbdddcdabdcdccccacababbdadbacbddaadcabdbabaaaddcdcbcdababbdbdaddbbcbadaabbcccbababcbabdbbbdaaaabbabcbcbbaddbdbccddbaabdbbdacadccdaadacbabbbdcacadbcdbadaddaccbbabcdacdcdbdcbcccdaaacbcdadbaabbcdcaaddabbabbbbbdcdcadcdbbacadbbdcbdababacdcdcabcbbcabacccabdcdcabbaabdacbacacbaadbadcaddadbacacbdcdabccbcbdcadabcddcabbaaaccccbaddcaacdbabadccdadddaabbcbdccdaaccbaabccacbbacaacaccddddbadbcdcbddcbdbabcbcccbcdbccbdabcdcaaadcbacbaacdaddddabbbabadcdadcadccaadbbaadcdaaabddbddbbbdbbadcdbbbaccaaccdcacddddccbbccbabcdbdcbbdabcbaabdabadbdacabdddbdddbabdcbcdcbdcdabbbccbdabcbbbcabadcdcacdddbdcdbcbadbccbcabbaddadbaacdcadccbaaaadddcbadabcbcbadcabbdaadddccbbbcbbbdbaaabddbdddbdbcabdbcccabccdabbadaacbaaacabaddddabaaacbabdabddaabccdadbbaabcdbcbaadbbaccadacacccadbddbbbcabcaddabbadabdadaaadabaaadabdaaddccdcacddacacabbbdcacaadcaaacdbdabaaaaacccabccbccbacbabbccdccadaadcacdadccbbaddcccdcaabdcbdabdbabadacdbbbbcccdcbddbdbcacddacbbdaabdbbcbcbcaaadadcaababcddbadcbbbccabbbabbdddbcaabcccdabaadaabddbbabdcbaabcccddddaaadadbdacaabdadacadabbdbdabdacdaadacacaabbbadabcbbdacaacbaacdcaaddbbabbabdbbbcacacacccdbdbaadcdbaadaaccdbbbabdaadcbbddcdaaadcabccccaaddacddacdbcdcacaccabadbdccccacbccabbbbabbccaccccabdccccdcbabadbdcadcdbbaccadccddcacdabcaccdbbaadaabbaabdcdaaabcddbcbbcaadabcacdcddbbaacbdbaacaabbbdbcacddcdaaaabdabbccaabaadcdcbddacbdaabdcddaaacbcabaababddbaadcacccdbbcbddcbcdbcdcbabbccdbdaabccddccbbaabaccdabbbccccccbcabccbcbbabacacaccbabdaabbadcadbadcbbcaabbcbbcaadabdcbcadcbaddddacaddacbccbccdbaccdcbcbbbdcddcdbbbcccbbbbdddbaaadcdacababbdcddbcabbacccdabbaaaddabcbadbcdcaabaabaddaccacdbdcbdccdbabdaacbbdcaddaddbadcbcdbddccaaccbadaabbbabacbdcbccdcdbaadccbbcddccccbbcaccacdcaddddbcbbcacbaacabcbcddadaabadbbaabbdcbbabaddccdbadbcbbccdccacbbcabaddcdbdbbbdabbaddaccbddbcccaaddacabbabaccccacdbddaddbccbcdcdbbbccccbcbbadaacccbbbbbccccdabadaabbbcbdbacaccaacdacdadccaaabdbabaccacdcdbabdabdcbbaaccccdbabbadccdbadbbacdbdcadccbdccadcadbcaabcdacdbdadcbbbcbadcbbbbcaabbaddbbddacaaabdadddaaddadbdccdacdbcdbdbadcdabdbcbcccbddcccdaaaabddacddcaccaaadcabaaaaaaaadddbbdadcadacbababdbdccacbccbdbdadcaaddcdcacbbdcdccaaadaaacacbaacaaadaaaddbdbccbadbdbcadbaabcdabcbabacadabcdbbcacabddbacdbcccaacbddcbbadcccabcccbdabdcccbdcdccaabbdddbabaccdbcdbcdcbabaccddddccabbddcdbbddaddccbacdccdbddaddacbadabddacabbcadabaabdbabccdaccabaadcaadacadabaddaadbaabdadcaddacbabdaacaabddaabccbbccddbbacadcacbddbacabdcaddcbbbcdaacbbadccdabdcadabdccdcaaabdddccbbddbacadcbacbdbdaabaacdcaaacbbaabaaadcdbbcbdaccabbdaadabdcbaabacabacbdbcacacddbddcddcaaacbabaaddacaababadddbdcaacabccaddccadadcdcacccddbabbbbddbddcddbacdcabbacadabdacdaaaaacccccdbdccbadadaddacbdcacccdaddddddcdbbdbdcadbbadcbcbcdcdabbbcdbbcdbcdacbcacaacbacdccdbccabcccacaaaadccbdcbccccdacdacabbbcabacdccaddcaacabbadaaacaaadbdcdaccdaadcdbdbbbaaddabcddbabbccbbbbbaccccabdbcddbbbbdddaacdcbcccdbbadcabcdbcbcbcddbdbcbaaabcccdcaddccbaddddbbbabbdcaacccbcbcdbcacdbcabccaccbbcbdadcdacadbcbdddbbbddadabcdaadcbdaabddbccaaabaccacddbdbdbdbdcaaaabccbdcbcaabbddbcaabbbcbcaddacaaabddacddacbbabbdbabcacbcaabacbddcbddbaabccbccacdccbdacddcdaadaabadaadcdbabcdcdcadcababbbccdaddcbdabaadcaacddaaabbddcaccdbbcdbbcbdbbddcaadcbbaadacbbcaacdabaccccbabdabdcdbababbcbdcdaadbdadbddbabbdbbbccbaddbcacdbcbdabdcdaaadadabdccdadacbaadccdbddbcdccddabaacbaddacbdddcdbadccacdbdcbddbbbabababdccbbaacdbbcbacacbcbbddacacccbaddaabdbccbdcaddbabcdacccadabdcbdbbdaaabbcbbcadabdabaaaacdbbabccdabdcddacabadcccdacacdddaddcbbcbcacdaddcbdaaabbacdcdcdbddbddadbcaadacdccaacdacacbcccacccaaabbbbcbcbccdbdcacccaadadaaccccddaabdaabdcaadaccdbbadbbddccdaaccccbdacccbabbccaaabaacddcccdccaacdbacbcaccbadbddacabbdcccabdcadbcbcdabacddabdddbdccdcacddbabccdbdadacabbcbbbdcabaabdaadcbdbbabddbdaddcdcbdaabddcdcbdcaddbdacbccabcbbdbcabacddcccccdddbcbbcbadbbbacccbdbdaacadbdacbcabdacacaadcabcbcacabbddcaddbdddaabccddbaadccbdabdbcddccacdaadbbacccccbcdccdbdbbdcadcdadadcccddcbdacaccacdddcadadabdcabbaacbcccdaaabbbbabbddbaabaddcbdcaddbdaacadabbaadaabdbcbdaaaaadbdcabaabcdbdbadaadbcbabaacccbdbbbaccccdaadddbbbcdddcacdcccdabdddadcdaacbaddddbabbdaadbaddbacddabdbcaadccabbdbbdadddaacccaabbacadcbdbddadadadabbbbdcacdddcbadbbacdbdabbbaabcabbbbcccacddacabddadbadabaabadcccccbcbacbbbbaccdbbbccacdddbcdddbadcacaaaacdddabcacdbbacdbcaadadadbadcbadccadacadbddababaadbdadbcabddcacbaddaaabbcdbbccbccbcbbbadbabbbaabbabacccbccddaaaaddcdaacaaaddacbdcccdaddadadcbabcbbdacbbbaaabbdaaddbaaaccdabbccddcaadaaadabcdabcaaccccacbcabbbadbacbcdabdaabcaccacabdacdabdaaaacbabadaccdbcbddcdbcdbbacdabcadacaaabaabcccadbdabdbbacdbdabdcdccbabdcccbcabbbaacdaaabbcdabcbadbbddaaaccdcdabaaccdbdbaddcbacdcccddaaaabbcaddcdbcacbcaaacaaccacbbbcddddaacdacdddacdabadabddcacaaccadcdabcddbdbcbbbcccdddccdabadccbaacdcdcabdbadacaabbaadacacacababbcacccdccdcaaadabcadcacdcbbcbbabcddabcccdcdaabdaadaacbabbadbcdacabaadcdbbbbdccbaccabadbdcdabbcdbddbbccccacdbcdbdddddaddcdbbcbcdabbacdabddbbabdaacabaddbccaabcbdbbbcbbccbdcbccbaabcbbadaccbbaddaacabbbabbaabacabdbbaabaabbcadcaacbadcaacacabadcabbdcaadcaaddbcbcdcacbaaaababbdbcbbccacaccccbbddbbdbbdaddcbbdcccbdadaadcacdaaaabbbdabacaacddabaaaabcbaaacbabdadddbdaaccbdcbbdaccacbaccddcabdaddaddacbbacbdcdbbcacbbcabdbdacdbbccabcaddcaaaccaadbadcdccbbbbdbdbdaccbacdbbacbaaddcadbdcccbdbdcbdccabcbababaadacccdbccbacddcbcdcaababaccdbcdcccddcbbcbbdabdcabddddcdaaccdadbcdacadbbdcdccdcddcdcbaadbdacdbacbdcabdbbbbabaaaacaaadcbbdabacbaacaddcdcbaadababcbbcabcdbbbacdadcdcbaacbbabdcddcdacacaabbbcdcdccaddcbbddddaadbdcbcaacbabdcdcbacbabbccaaadadbcbdadabcdbbddbccdadcbcaaadbacbbbdcdcbcbabcbdcbbbbdbdcdaccacbbdcccbcadddbcdddacdaabdaabdaccdcbdbdcdbacddcdacccadabcabdadddcbaacbdbdcadcdabcacacbacddabcdcabbdadbdbaaddabaaadbaccaacaabaabaaadcdbaaacbcabdcbbcdabbcbbcccaddaddaddbdbcadabcdaadcabddcdaabbabbdbbdcdccbcbcbcdddcbddcabaacbcdddbddbcdcaccdadbdacdddbbccacacabbbbabbbccadddddbcadbccccdbcabbdcbdccaaabdcbcddbbcaaaaabdababcabdcddcccdaabbcdaccababccbcdbcbbbcabbbcdadabcbdcddadbcbcbcabcccddadddcacbbcddbcdadbdabcbdcdcbbcbdbcdabbddcadcbccbadbcbdcccacaaddbaacdcacbdbcddacdbbaccbcaccadbdaccbddddbaadbcccbbcddddabbddacbdcacdddacccabbabdcbcaacdcbadbaddccdaadbcadbcdccdcadbabbdddddccadaddaaaaacadaadbaaddcddbcbdbcaabcbdcadcaadbcdbdcaabadcdaadbbcdbcdcacadbcdacbaaccccccbaacbdbabbcdcdacdacdccaaddabcccdaccbdcaddacddcddaacaacdbcccbbddadaddcbcdcbdcabdabbaaddcbbadcbbababbbadcbaabdbabcaddaaabcbbccadbccbdacabbddddbacbcdbdbbdaddabccaabacddabcbddacdbdddcdccaccadddcbddbababbcbaabdccbbcdabdcabadccdbbcbcbbcbddadcbaaaabaddaadacbddaaccdabcbadbddcbbbcddbdddabdbdcdabbcbacbbdadaaadcbbacabbbdacabadbdcaddaabddacaddccdaaaacccbaddbcbbbcdadacbdddcdacbadbddbdccdbddcaccddabccdbbaaabbccbaacbabbbdbcdcbdabadddcacbdbddbbdddbacabdcacaabdadbacdddacbdcdbdbcdcdcaadabcdbccabdbbcdbabddacbbcbbcbaccaddaaabdbdcacdcdbddccdcbdcaadddaaacdbddcbacbdccccbbdcbccaddaddbddabacddabaccccdcbbdbbaacdbacaaccaddbddcaacbabccdaadcdcccdabdccadacaadabdaccabbdddbbcdacbcdbddcdabddcdbcbabaabdaadaddcbdbbadcadbcddaacbaadaacabaaddcacbadbdcacbcabcababbcaccccdacbccaadbbacbcbabddbdcdbbcbbbbdbbbbcbdabadbacdcccdaaacddbbdddccccbbaccbbddcdbddddaddcdcabdbabdcdaadcbcbabaacadadccbddbdabacbbddcbaabcbdbddccbddcccaabbaddbbdbcabcdbbddccdccdbcdcddbacdccddbbcababbaddcbdadddaccabbddbccbcbddbcaabdbacaadabaadccbdcaacccadddabacdbcbbcaccdacdacadbcbcbccabccabcdcbadcbabaacaadaddaaabbcdccdadccacaabbdadcabacdbcaaccaacdbabbbbaaacaaadcbaadbabbcdbbaaacbcacddbcdaaccdcaddccdacacbaaddbbabddccdcbccacbaccbacdbddcdaddaaadacbdadcacbcaabacbbddabdcaaabcaaabbdadaaaacdccaccdbaccdbbabddcaabcbbcdaacabdddbddcddcadbddabadcbdbdaddaabaadcdbcccbbabccbdaabbbacddccbbabcccdbacddccbbddcbabadbaabacbdbdadabcbbcbdccacddbabaaaccdbdccbacaacbbcbabddbaabcbdbabccbccdbdddbbadbbccbacbdbaccdadbdcabbddcdabbaadbcaabddbcadacddabbbdcbdcbabaccabddbcbbadcabcabaadbcaacbcdadbaabadcddcdcbacacbcabadddbdcabadcaacdbbaacddbcbdddaadbabacaccbcdbabacbbacddaddabdcbdabbbcdbcbdcaabacaaddbdcddbaacdcaacbddbaadcdcadbccdabbabbcccdabbadcacbaadddccdaadcaabadbaacbdbcaadacaddcabbddbbaabcbdbcdbcaadbabdbbcdcdbdaccbccddcacdacbcabadddabbdacbbbbaabbabcacddcbaaaccdcccabbcbbadccbcadaaddcbadcdbabdabbbdcdcbccdaacacbdbccbbcdaccdacccccbabdabdbcccdcbbbcbacddcdcddcdacbdadbdccacbdbcadaadbabcdddcabdddaaddcbabbaabcabdaadbbbcccccccbbdcbcccabdbcdbdbaddccbacdadcdcabadcacdadabcccdbaacaaccbaabdacccbaccaacdabccddbbabbbadbdabccdcbddccabbdcddddcbcabbbddccacdababadbcadbacccdbbbdcaaadbbcdacddaddaaacadabccacbadabccbdccabacdbcddbbbbacbbbdbdadabadabacadcbabacaaadbddadcaacddaaddcabdcccdccccddacabbdadcbddadcbadbdacbcadbddbdabaacdadbccbbddbccaabdaaccbdabcddbabcdcdddcaacdaaacacccacbbabbbcbcadbadcdbabcadccaacdbccbacbcddbdbddcdadaddbdbbbbbddccbdbaacbddacbacddababbccbadbccbdccbcbcddcbdcbcdbcbcaaabcbbccbdaadacadaacdabdcadbdddabdcbddadcdbddcdabccacbccaccbacaddbcabdadccaccdbbaddccdadadbcabcbaaddbacadbccbccdaccadbccadcacabddcbbabbcacbaabadddabddccbbdbcabbcbcddbdadcadddcbbacaacdcbaaaacbdacbdadcccbbbcaddbdaccdbbacddaaabcdcacaacccdacdaabdcddaabcbdaacccabbaacbbbbbbdcdabcdadaddbdddacacbdbadcbbbaddacdbabadbccadaadabcbccddacccbdaabaabbacabccadcbcddbccdbcbacababdabbcbccbcdddddbcdaacdadadbcacaccbcacddaccadadbabdbcbcbccabacddaaaaadaaccbbcadbdccacdcbdabcaacdcccddadbbcbcbdacdcdbaccdabcadaaaaacddacbbcaaddbcdcbbbbbcbbabaddaaadcbaadacdacddadddddbbacadccbdccaaababcbaabcbcbdaaaddbaccdaccbaadaadcbbbcbbbbcdbdbbdbdacbabbcbccaadadbcdbbadaaadadaacbdaaaacaaccddbcacdcbbddacbbdadadbbccaabddcdddcdabdadbabbacbdbbdacacdbccacbcbcdcdddaddacbdaaddcbdbacdccdcbaabcaaddaccabcccabddbdabcdbbacdddbbdddadbdadcdbbdbaaaacdbdcccbbcbcadbccbdadadadbdcaababadbbddbadbbdcccaabdccdccdbcbcbdbaddddbadbbccabdbbdadbdbdcddcacbabbbbbdbbdaccddbaaadcdadacadadbbacacbbbdaacdccbaaddcadbdbbbbcdcdbcdabdacdbdadadcbabcdbdbbcbabaddacbacdaaddbbbaacdbadddccdbddacddbdbdabcddaccabcbcbcbbacadaccbbdadcacdccdddcbaadaddccddcbdcabaacddcaaadabadcbacdddbabbabdcacddadbccddacdbaccdbcddaacbacaabbacacdcadccbaabbadbccdaaaddbbbcdccdcabacddadcdcabbacaacddcdbccddacddbbdcddbdcbcbcabdcdccadcbabcdcccdbadbbadccdbcacbdddbcadbabadddbcbbadacadcbdbccccbbbcccdcacaadccdcbadcbcabbbdccbccdbcaaaadaccaaadaaccdbdbaaabcdbdbdacbbdbabaddccadcdbcabdbdddddddbcaaaaccdadbbdcdccdcaadcdadcdbdbddbadadacbbdadaadbabcbcbddcdabbcdabcacaacbbbdacabddcdccacabbbdaccacddcccbdcdaddcbdbbbbbaacbacacdcdbaaacddccaaddbbdcbdbccadbacdbcccabcddbdacacddccaabbbdbcdcdbddbcadddadbacccbabdbcaddacadccdbccdcbccbbabadadadbdbcabacdcddcdbababbadbddabbdddbacaadbdcdcdaabaaaaddcccabbaaadccbcbcdbddabcdbcdbdacdaabdbdbbacadbdbabccddcbbbcdacabbcbaaaccbaccdbbbddcabababbbbbcdbddbdbbdcacbaacabcabacbcaddabdddabcbaabcacaaabababdcdbbcdabdcaadbcaddbcdccdbcbbbacbcabcbdcaacddaabbacbcbccdccbdccabbaaddabbdbccdcbadbbcdddcdacadadcaddaccbaadaaaadbdbbdddccbccdbdcbbacdabaddbdacdaabadddabbaacabdbdadbbcabddccdabbddbaaddaddaddbbbdabaacbaadbbbcdacacbabcdabcdbccabcbbcbdbaadbddcabcabcbbdbdbbdccbaadbdacbbcbcccddadacbcdbbacbdbcaaacdcaabadcccccbcccdbabcacadccadcdccdabbbaadbadddcbbdcddaabcabccccdbddcacaabbbabdddddabcdacabbadcdcdbbdcadadbcbdccddadadbbdaaadccaddddbaacdbddaddaaddabbbdadbaaaccdadcdddcbbdcdbccdaccdaddcccadcdaddbcacadbccbbdbacbddabcdcccbddbbbbcacdbaacdbadccacccdbbacacdcdcbdcadaddcddabbdcbdcdccadbcdcbdcacbbacdcdcdabacbcbadbbcdccabbaadacaabdbcdcaaddbcddbccdbbbdcdaacabbcbaaacbabdbadaccccbacbccddccdccdabdadcbdbdacbcbabdcdabcbddcaabaccbbddddcbcdcccbdaabadddddacbababcdbaadababcadaabdacccbadaccdbdbadacbddcdacacbaabbcbbdcdaadacbcdddbdadadccacaadcadadcddbdaaddadbbcabacddcddcccbbdacdabcbcaadddcadddaaddcaccbccbaddcaccbcbbdbbbdbbbdbdddabcbbdacdbaacaabaadadcaddcadbdcbdadbbabaacddabddccccccdcbdabdadcdbdadcccaaacdcdbdacdabcbcbcccccccbddbdcdcdcaccadbbcdddcbdbabbacbacccdcacbcabdadbdaabcbabcdacddbaacdaddaacadbabbdcdababadacccbcaadaacddbcacbbaadbbcacdbdabbcddaaacaccbdaacbddadbdabdbbbbadcddacddadacaabdadcdcddccbabddddccdaaaadcacdbbaadcddbdbdcadbaabbcddbbacbcdbbcabadacaaddbdbcaaadaadbaadacaccbcdccabbdabbacddbbcdcbbdaabadbdacbdbccdadcdccacabcadabcdaddadbcdcdccacbbbbccdbbdcccdcccaccaccbbacbbadbbbbcddddacdcdadacddcbdbbbcbbdccacdadccabdbacdaacbdcdcaddaaaadbcdadbaadbcacbaaacdcbbbaacbddbdbbddbdbbbcabbcdacabdcdcaccbadacadbcdbccaadaadbdacbdabcadadbdcdadbbccdaccdabacdbaddaacabacbbbbdbdacadaccdacbabdaccbdcaacddaccaabbabacdadbaddcbccacdbbaababaacdbbbdcacabddbadabbcdabaddbccbbabadaabbbbddbddabcadddccaabdbcdbbcbaabaddaadcbcdcaacbbacdaadabbcadcdbacccbbbcdbbbbcaccbacddcaacdcacadbbcdddbbbaabccbabacbcdaabdddbabbcabadcdaddcbcbcabcbbabcacdbaacacbbbbcddacabbcbdbaaaddcbacdabdbdbccaadadbbdcddbdccbdbbccaadabbbddccbacbbdabddbcbabbdbdbbcbcadcddbcaaddcbaccabdadccacaccbaddbcdddacccdbacabcdcbbbabdbbbddacdbdcdcbddacadbdbaabdbddccddabcaaccccdbadcadccadccabcddbbacccbbddaddadbdcbcddabaadaaddccccacdbbaddcdcbddbabadcaacdcabbddadcdcdddcdbbdbccaaddcaaaaacddacdbdcbabcacdaadaadbdbcabcdbabccdcacdcddcaacbadaaaccabaaccbbaaaabaacdcaaacccacaaaadbbbcaadaadccabcbcaaacbdcacbbaccdbdbacdcbaaabacbaddcbcabccbabdbbdbcccbaadaacabcbadacbbbadaddcdbbdacdadbccbabbdcdaacdccdcdcbaadbbcddcbcbbdbcacaabaadcccdacaccacddaaaaadbabbcdcadccdbdbadccdbcdcacacbcdcbacdcccbabacaabcabbabbdbdbbdbdababacbcdbcbabdaccbcbabcaaccbacbdabccaabdababbddbddababcaddbdcaacabbdaacacbdcccddddaccdbcdcbbbaababadcbaacdcadbbacbcbbdbdccdaaaababdbaaccbbcbbddadddbadcadabcccacdbdcadcaadddbccbdaccdbbdcdabdabcbbdabacbadddccacbaccaabcacdbdccdccbbbbbaddbdaaaccbbbaabddcbabbbacddbdbacaabacadddccadccaaccaddbdbbbadaaccbcdbcabbbbbbcdddccbcccbdbdbadbbbacadababbcaaadabdadbbdadacacadbddcadccccbbdbbccbbbdbccccacdcddcdbdbadbcacbabaacccbcbdadabdaddcbbdddddabdbcccbadbbdcbddbccdddbcccccdbcbabcdaacbdcbbbccaabacbdbbabdaadabcbaccdcabccaacddbbadcbddadabbdcdaddcbdaccaaaabddcdccabddaadbdadadaacbcdacdcabbdcacddcaddbbcbcddddaaaccaddcabbdadccacaccbcddacdbdabaaacbbadcddcbcabcbdcabbdccccaabddcdccacbacacddcabacdadbdbbabbadcbccdcabdcbbcbabdccddacacbadbaddcdabbcdbcbcaaacbaadbddcdaddbbabbabcaadbdcbaaadabbcacaadbbcdcabccbabccbdbcbcdaaabcbcdcdbdbbbabcaabacbacaccbadcccdacccbbbdaddbdcdbcbbcdbaadbbdbbcadadddddbaaaaccacbadddccdcdcdcabcbcbbaddcbabbccdcacacdaacbbbbdaadbddcacdcbbadbbabcbbaccaaadacdcdbbaaadbacdbcccbcaacbcccdaadabdddbbbbadbccbacbbccacdbadbbcdacdacaccacdbbcbbabbccddbabddaaddbccdcdcddadcdaaaabbdabaaddbdbabcdadbacbaccacabadbadcdcbcbaccbadcdcabcbabdbaccbcdadcbaadabbabcccbbadccbbcdaaabbdabacaaacadabdbaaadbacbbcddccbaacaaaaabcbccbadcbdcbdbbcdbaaccbdbcaccdaddcccdbdbcdacbbadaaccdbaacaacdacdaaaadbabdcadacdbcdaabadcdccbacddbaabdaaabdbbadddbcccbdccbcacbabadbaadbaadddbbcdcbcdcbdcbbdddbccccadabcccbadaadbdbcdccbcacaabbdddbdbcbaacaccbabcbddbccdaacacbddaaccdcadddbbcdccdabdbaadddacabdccdcccadbbbbdbcbccacdbdbbcdabdcabcbdddcddbbadccdaddbcdbadbbbdccaabdbaabccbdccabbacccbcbcdcbdabcdcbdaaacabddadacacbbcbdccbdadbcaadddbcbabccabbadadbbdbbacaabbabdcbdbcddcadaaccaabbcaccbadacbdbdbcdbbbbbdacbbccaaccdaaacddbcacbcbdcdcdcdbcbbcbdccabacbbadddaacbcabdccdbbddaadcbbbcdbdaacdabaadbbcaadddbddbbadabbccdbcbabbabbddbccbacccabadbbaaccbdaddcbabbdbcdabddaabcdccbbcddbbccaaadcdbdcabdccddbccbddcbacbcbdacbbcdadadddbaddcbabcdccaabaccaacadbbbdbacdcbdbbdbdddcacbabccdbdacccbaaadbcdcbbabcdaadddabcadbacacbccddbdaddcddbbdbdbbababadaddcabccaadaddccaacadacaabcddcccbbcdbbbdaacdacdaabcabdabbdbbacdbddabbadadbaccabdaadcabddbdaabdcdcdacacabccacdadbbcbbacdaacdbbbdddddabbbaaddccacdcccbaadabdacdcabccdbdabbbacbcadcaacdcccbabdbabadbbcacdacbabacdabcbddbbdddbcdcdcaddcabcbcaabddcbadcaacddbdaababddcddacadadddabccabdabccadbbcbbcccddcbddcbccbdbbbddccabadacbbbcbddaddcdadaccadabcccdcadcdcbadcabaabdacadcabcdbdbacacccbaadaadaacadadcbbbbbdbcbadcbbbacdaadadaadcacaaacabdaadbcaccdbcdbcdbcdccadbadbaddaccdcbcbbddbacbbcacdabdacdbcaabcccdbaadcbbadabbbabdadcacdcbdabbcdacccaadcabccacbbbddabbdccbaadcbccbbcadcacbbbdcbcbcbadcdaadbbabaababcdbbbbbddabcbbbccdbcaadaddcddabdadcdacababdbcbaabbacbcccadbacaadbbacbabddbaaabbaccdbbdcdacccbcbbaaccbadaadbabbdbddddbbbccdaabacdddddadbcadccbbcddbcbbbaaadcdbacdaaaadaccacacdababcbddbbaccdabccdcdbcdacddcdcabbcbbcaacdabdaaaadccddadacdadbabadbcdacaacaacbabcbbbbccbbcbcacccaababbbdadabcdbcdddcbabbdbabadbccbadacbaaaaddddbcbabbccdbacabcdcddbdcdcdacbddccbaabcdaadbccbdcddadccbbcbacdbaaaccadadaaabccaaccaacbbadacddbaadcabbccbddcdbbaabdddcabbbddddcbdcdacbbdadbabcdadacbdbdcdcaacdcdbadcdabccdaaccdadacacaaccbcdabbcadcaacabdcdbbacdcdddadaccbbabccbbbcdbdbccbddcabdaabcdcbdcaaadadbbdcbddacdacbacdcdabccbabbddadcbdbdbcabcccbadbbccbddccbadbaaadbdabdcbdadbcccacabdbabddddddaadabbbacaadacccdbbacdccdacabadbabcdbabbbbdaaababbbdbaaddbdcaadcababbaadabbcaccdaaccdcabdaacbdcbbbdbbddcacaddddcccbccdabbddbcbcdccbacdcddadccadbddaaadbdccddbcbcbbcbddaaadcccaddcdbcbcabcdaccdaacccbcacbaaaccdcdddbadcbacacbcdcbbccdbcbcadddcdababbdbbdbdbdbbdaddcdcdcdabdbdbbbdbacaacadddbbacccbacbbcacdabcdbaddccccacaabdaadcabadcbbabccdaaabdcdcbccaacaaacaadbabddadbcdcdccacdbbcccbccacadabdbddcacbcdccabdabacbbcadbcbaddbcadaaaabcabcaddddacdcabdbbabbbbdbdbcbaccaaaabdbdaddcbccbdbadbbddcacbcbdacdcbddbcaaadcddcdbbbdbbaadbaaaaddbbdddbbdabaccbddcacbbdbacdabbbbddbbbcaccccddbdbddaaccdbcbcaabbbcbaaaaababcddcbdbdacddacdbdcdcaacbdbaabbcabcbbbbdbddcaaadddddcdbbbcacddaadddaabcacccdccbacccdbaabcbdccdddccbabadaadbbdcaacababaaaacacccdacadddbabcadaacddabcbbdcaacbdbddacdacdabbabdddababddbbdcbddbaccbdddcddccddbddccbddbcbbcaaabacbcbbaaabbabcdbcaabdbadccbbcdaadbbdcbbdbcbaccdbbbdcaadabadddccdbadadbbddbabbadbcdbabcddbdbdabaabbdaaadbcccdbabcabdaccbbbdaaaacbbdadbcabcdbcccadabdbcaacdcddddbdabcdcadadbcbadcbadcaabbdbbdccdddaddcacbbacbcadbbccaadbddbdbacddabcdacdcabadabaabbcccabcabdadddabbdcadacbcddbaaadccccddcacaabccbdbacacccbddbbdadbdaabacddacbdacdcaadbaadbdabcaddcdbdaddcaadbcbbddbbdcccbaabdadacdabcbaddddacbcbbbadccbbaaccbcbacaaaabaabbadaccaddbdbbadbbcddccbabbcacbcdcddbadcaacbbbbbbbabcbcbdadbbcbbddabddaaaccbccaddacabddacaaaadaabcaddcddbddacbcdadcaacabbcbbbbbbabdcdccabccdbdcdaddaacacabccaccabcbdbadbadbbbbdcbdabcdbbdddaccbdccabdbdcadabdacabbbaccadcadccacccabaaacdacdbbbabdccdcdcacdacaddbdcbbcdccaabbcbbabbbdaabbdaddcbcbacdcacdbdddccddbaddadbbdbccdabacdddacccaccdcdddbcdbdddbcdbbcbdcaabbcbdbbadaaccbabcdadddbacdaaaabbbdccdcaadcdddaacbddcdcacadbaccbbbadaacacaababdabdbadccbdbddcdbbcdcbbaabbcabdbdcadbbaccddbdbbdbdcaaabaddcacacbbadcacbccbacdacaaacdacbcbdabccaaaaddcdcbcddbddbcdddacbcbbddbdbdaabdbbbacbcbbdcaacbbcaccababdacaaaabaabacaadaaaaabccbbbbdabcbdcadbddadbbbacbacaddbdabddacadcacdbbbadaaaccacdbbdcbadbbcbcbcdbcbdbbbdaaccdbddcdcaddabadacddccddadadcacccbccacbadacccdbcdacdbcdbbbdbabcaaadaabdbbcbcbdbaaacacbbbcdadbaabbccbacaaaadbcdbbaacaabcbbaacabdcaaacbdaadbadcbdbcbdcbbbabcacbabdbbacdadddaccadcccbcdabdcdcbadbbabbacbdccddadbcbdbcccccbdcadabcccabcadadccadbccbdacabcbbdbadaddddacbcacbcbcdbcbcabbacbacadabdbcacbaabbcbbaabcbbbdabcdabdcdbdcdadacbddaaaabccddddcaadddccccccadabbdcbddddadbacbdaadbcbdcdbcadcbdbdbbbddaddaddaadaaddabbbaacdadcbdcbdaabbaddbbdabbadddccbbacdbcdcbadbbcacaadbcccbccccbdbadbdadacdcbabadbabddaadddbddbbbcbcabcddbdbaadadbbdbddccbdcbabababadbddbaabaadcbccabbdaaacdccdbcdacdbcdcdaacddbabdcacddaaabbcccababadcbaabcbadcdddadcdbbadabdaadcdbdbdbdaacaabacbcdabdbbbcbcbcabccbabaaadddcaaacdddcbddbddaddcadddbabdcddbbbdacaaabbdbdabcbcbddccabdaaaddbdaabdabdaaadbcaabcaacbaaddddaabdcabdbcdcbccaddadbacadbbbadaddbaacdcccbdbddcaccaccdbbcbbdcccbdaacadbadacdbaddcccbcbaccddcbdabbdbdcbacdaaadbbdaadddbaabbbbdcadbbdbccaabbabdbccdcdcdbcdaddaabcbbdcbabdadaacdbdabbcaacaddddcddaaaaddaccbdbdbcddbbccbacddabcbabaddddbcdbddbccdcdbcacacacacbccbadddaddaddccaddadbddabbddadadccaababaadbadbacdababbbddcbbaaddabbbbddbadcabadbaddbadbdbbcbdaaaaacaacacabadcaddcacdbdacbacccacddbcdcabccbdadccddcbdaaabcdabbabbbbabbacdccbacbadadabaccdaccaccacdbadbdccdbbdcacdcabbccdaadbcbcaddbdbcdbbaabddadcddcbbabbdcbddddcadbccaabbdbbcdabbdcacabcbdadbdcbaccbdbbacddccacaadbcbbccdabddbdcbcdaccbaccdbcdccdbbabcadddcdaabaaaccdddbaadccbdbccdadcadadcddbabbbadddccdbcbcdcbdadcdadcdbbdcddbaccacbbacdabbdddccbbbaadddbbbccdcdaadaacdbbacabccadadbbccaadcccabdabaacbdcbcaccbcabbccdcccdabcbcacaacacdcdddccdacabdbcccccaadbddabbcaadaabdcbddbbadcbacacdaccbbdabccbdbcacabdddbcdcacdabccdaaaddcdabadcbcbaabbdcdddbcaddabddccddbcaabadbbcbddaaacbdccccdbbaccdccadabdbaccccccbcaddaacbcadbdbaacbcbdadbdccbbcbaaaddcbaccbabacdddbaddbcdddaabacabcdbdcddcbadadcccacaabbaabddcdadbdbddccbbdcabdbacdcbbdddaddccdcbaadbddcabcdacacbaacdcadcdadddadbddccabadcaaacccccdbddbbdaccdbacddbacdccaccdddbddcdacccbddcdbdbacaccbacccdcbaadabbdbbbcaccbbcbbbcaddbacaabdcdddacabaccaccaadbbcdcdbdcbbdbdddcabacbabaccacbcdcccccdcadbaaddaadbdbbcbabcabbaadcaadcabadbbbaacabaacddacbadadaccdddcdbaccdabaaabbbdbcbdadaaabcaacaaddcbacdaabcbdadaacdcabdcaabddbdbdbddabccccaaccccacbdcddccccacbacacbcdaadddbcbcbcadbbdcddddabbaddadabccadbbdddcbcccbdcccdadacdbaadadcccddabddacdacdcbaccdddacdadadcbdccaabcdaabcbddacccabbcddcdbbdbdbaabcbabdbbdacbacbdcdccbdadaaaadbdbddccaabbabbbdadcadaccacabdccdadabcddccacbbcdacaabcbaacdadbacdacacbaddbaccacabdcaabbcbbcdccaaccdbaccdcddaacadbbddddabbdbbdacbcdbaccccbaccadcbbddadbbccddcadcadcadadabacbacadbdaaadcddbdbcbdaadabccddabcbdcaacbaccabbdadcbabcaadaadabacdabbdaabadcdacacdaabdcadcbdccacbccddaddbabdcdbcbcdcdaaabdbbadcabacabbdababbcbaacdabdbbdcbdbcaaddbababcdbadaacbcdbcaccccddcddcdcccddbbadcadbbbcdcaacccdddacdaacbcaabdbdbddcbdcdcacbcbdbbcadbadaadccabaaaaabcddabbccbdaadcdaadcabababbcdddccccbcadbadaaccdbdbbdbdacadadcaabcaaabcddadccbdacabccccbdcbabacacbcadbdaaaccbdabdccdaabdcadcbcbbccccadbadaacbbddbddbbdccccadcdcdabcbdcaadbabdaacbadcdbbcdacbcccaccbcabdccdcbddadcbcdbadaadcdcbcddabcbcadddcbdcdcdbaccaabbaaabbadcddaabaadadcdcdbbdbcdaabbdcccbddbdcbdbbabbcbcabdcddcdbaabbcadabbbabacdcdacdabbdbabbadabababdcdbabbcbdccdaccbccaadbacdacccccdcccadabdacaabddcaadbabbcacacaaadbbacaaacdcccbdddbddddaabaabdadaccdabbdabbbcbbccaacdacacbbabcaadbbacbcaddadcddaacbddbbdcdddbdaababaaddddcacaadccbdccabcdbdcacccdcdcccdadbadabbbadccdabaacabccdcacdcbdcdcddcdadcabcadadabaddadcdccbacbadaabaadababdacccdacacaadbcddccacddbcbdbdddabcdabcdcddabbadddcbdabbaabdddadbcccacdabdccccdbaaacbabbdbbccbdbadaccdaadabdbbbbcaadcdcbccbbcadaddbcaaccdaaaabbadbdcdabbacdbbcacbabdcdcaabdadaadddbdabadbddabdadddddcdddddabccbcacbbbaabbaaaadacadbcbabbcdaabccabbcdcdbcbcbcabaabdaaaccadaddbcadbabcaadbdaccbccacdcabababacbabcbbcabbbdadcaadccdcbacbbdcccdbdbbcacaddcadaabcabaadbddcabbbdacabbcaadaaccdaccbcddcdcbacabacaabaacbddabdaabcbbbddadbadcbcdacdbabcbadbdaddaddadaadabacabbdbbadbdabcaabbcccabbcdccdabdcaaddbcadcdcddcaadbdbadbdbddbdaacddaabdadcddabdbacaddbbdcbbbddaadbdabbadddbabaaadccadacdaaaabcabdddcbbbabbddaadbaabddbbccbadacccaadcddddcbacbaddcaacadadbccdbbbdabbddbacbcabacaabdbadcabdddaddabccadcdbdbcbcbabccbcbdcbcbbddcbbdcabddadcdcdcaacaccadcdbdcbcdcbdcbaaddccaabbaababcbddaddabcdbbabbcbbaabbccccdcdcdaccacaaaadcaabdccabccdcbaacdaabbcaaaabcaadddcbdaaccbcbdbbaaddbcaacacddacdbbcbcdcbdbcabbcbbddccacbabcdbaaabadabccbccbdcddabddddcdccdabcddbcbbdbccadbacdbcdcbcbccbdabcdacadcbcddbadcdbdbaacbdbadaddaabbabbbcddbadccdcdabdbcacdbadbacabdbadddabbcbbbbdbddacdcabcbcadbdcaaadcabadccdbdababcdccadacbbbaccccaaaadddcbadbaacbdabbdbddadcacbbcccdccdbbbcddbbbaabccacbdbacadcbaadbbdccdccbbcdcbcdccbacddadbccccaaadcccbdcaaddaabcabccdccdabacbbbddccadbccccbcdbadbcabbbbdbdaccbababbbacaccddbacdcccabacccccbabbdbadcddbaadbcbbabbcbcabdccabbccbbaabdbcbccbabccbaaabdaddbabdadadababcbdbcaaaabcbacbddaaccacdacccbdabdaabdbaddcdbdbccbadcaacccabaacddcacabbabbabbcbacccacaddaccbcbadbdcdbbdaaabccccbcacdbdaabbaccbadbcddaacbaccabbdccbdabccdbbbcabbdadabddacaaadadddcdaabcdddacabacdadabdadcadcdaabdadddcdcbbaccbadcabaccbbabcbccbcbbbdabcbbbdbbdaccababcdcdcdbdabadcbbacadbbdbbbaabdcaccacadacdbbcbbcbaacdaaadbcacabdacbbbcdaadcdaadcddacdcbdbaccdbdcbbcadaddacadbcbbabadcddbbabacabaacaaaacacbcbbdcbdcaabbbadccddcaccacadcbdddabbdccbdacabacaddadcabcdabcabbccacdaacbcabdaccbcabdccccbdccdabadcdbcdbcdcddcdaaddbcaadcdacdbdddacdbbdcddabbcbbabdccdcccaaabaddcaccbaddcaccacddaacabddbcdaddcdcbbddddadbdbcccdbbcaadabadcdaabcbcbacadcdbaddadadcbcbdaabddddbabbbdacaaaccadcadbcdddbcdbabcdbabbacddbabddabbdcdddaacbbdaaabcbaaddccdcabbdbccccdddbcaaacdacbdbdaaaccabaacabdbcacadcddadabdbcbaaccabbdddbbcccaababacdbadaadddcddacdbcbaaacaabddcbbacddbcaaadbdabbbacaddcaacbdaacbdaddbcdcaacdccaaddabddacbbbdcbdbcbbbadcccdccbccddcaadaabbcbdbdabdcdadbccaaadbdaaabbacbccdcdcbccbbcdbdcadadbbddbcdddaaddcdbaddbacbdaaabadbbcbbdbccbbbcacaaabaacdccbcccabdcbaaaccdccbdddaabdbaacacdcacabbdcddcdbdbbcdddccaacdadcbaadaabdcddddabadbcacbbadcadbbccddadbdaadadcbcadcabdadaacbbcaaaacdcbcccbdabbccabdaccbcdbbaaaabbdbadcccabdacdccddbaacabababcdcaadbbbbbccddacdabdcddadcbacdddccccdbcdcabababbcaddbdddacacbabcdbbadbcaacaddcadbaaacadccbadabdddbcbaaddaabdabdadaccccaccabdcdacccaddbdaabcabadcbdabbbdbcadbccacccadbacbdcccccaadbbacbacddaddbcadcdbdbbbcbdabcbbdaabbacccdadcddbbdadbcbbbdacccdddabdadabcdabdabbaaadabbaaaccabdadcbbccbdccbbabbabcbcbdbbdadcdccdcabbabbacdcbdaaccdadaaabaaddcddadddbaddaadabdbcaadacdcacccadcacddbcdcccccdcacaccdcbbbcdabdadbbbadadbbccadcdaacabdbacdadcaadccddbcdcbadddacabbcabaccdbadbbcacccaacbacacdbbcabccdbcaabdbbaaadadbcaccbadcabbaacaacbbcacbbccdbacbdcbadcbdcbaadcdcbdcbccdabdcdccbaccbbccdaccccacdcddbcbadcdaadcbbacabbadbdacaacbbaaaccdcbddcbdcbbadbdabcabcadcdadcbbdaadbadcabcacccbbbcdcaabadcabbdbcaaadacbaaabbabadbccbbbdccdccdbccbbccdddababcabcbadbbdadccccdaddbaccbcacdddaaabbaabbbcbabaddadbadacccacaadbaccdbcbddbaccbdcaabbdbaabdaddaddcccabccdcbdbbabadadbdbdbdbacdbdbcabccdbdbdddbbccaddaaabdcdddabcddabbbdababccccbccacbadcabddaabaaacdabcbaabdddddadbbcbcacddddbddbacaddbabccdabdccaacdcaaadbddaadbddcaccbabbaacccbdbdaaabcbaabbdcdddbadacababbdbabdcbcdbcacbdbbdadadcbccdddddcbabccaaabdabdbcaadcddbbccdcccdbcacadadcaccabbccdbddbdbbcbcaabcbdcaddbaccbcddbbcccaaadbccacddacbadbbdbdddcacdbcdadbcaaadacdddadccdbbacccaaacabdaaaddadcddbcbbdddaadbcbbbadaabdaacabbadcbdccccacddbddbadcadbbdcccbdaddadcacabcdabcdbbabacbdcaaadcadcdacddcabdcaccdbbabbbddbccdbbbadaaaaadbdcaacbabbadcaaaaaabacacccdddcacadcbccbadadaabbbdccccdaaacbcbdaaccbcccbcbadbdbdbcbbdacbdacadbbdabaaddbbbdbdddbddbacdccbdaaabcdcabdadccdddbbbdcdccdcdcdcccbabcddcaabbcabcacababcaddcacadadddddaaabbccdbcbdccbaacdadacddaabaabaccccdccccdacbcacaccbdddbabcdddacddcbabadddaadddcbdabbcacbcaddcadccccddacbaadadcddbbbdbbbdadbacaccbcadadabbbddaabcacabdabbabcabaacdcdcadccccdbbbdcbddcaddabaadcbbbbabccaacacdcdabdaddbadbccaadbcddaccddcadcdbcccddcacbaadbdbbcadddaaadcabdcbbcdadcbdbdbcddcabccaacaddbacddcaabddaddbacbdcbaaaccadcbbcccaddbaccaccaccdcaacacbbaadddabaddaaacabbcddcadddccddababaabcadadaadbbcabcdbdbcbdddcaaacdbdabbaadcbdbabbaacdcacacababbaabcaccacbcbddbbbbcdcdddabbdcdbbaacaaadbbbcbabddddaaadbccdbdacbcaacadbbbdccaacbddbcddbbbaadbccaaccddccbabdcbddaaccabadbbdacbdaaacabbcdaadaaabcbbbdadcccdcdddbbcccbaabadcacbdaaabacbaccabbcababababcdcbcdddadaaccbdaacccacccccbccdcbcbbbaabaabbdcbbcbbddddacccdbbdbbcababcabdaaacadddcdbdcdcdccadbbadbcabdcbcacaabacadcadadaaabddbaadcbacbadaadcddaccaccadcaaadcacccdabcbacbdcbcadcddcdbcddcdcabdbccddcbbcbabcdbaaaccacdbadaadcaadccddbbcdbddddadabccddbcbdddadaaaadababbdcdbddbdbcaddddbababccbadbcbdcbcaaddcadcacabadaccbdbdacbacdbacbbcdbcadabbdacddcddcabbaccbcaabcbccbdaadbdccbdbbbbbcaadcccdcbadadacaabbadbcbdcbdbdbccbaabadcadbbcaabbbddcacccacaacbcadbddbadbcdabcddcdadaccdcaddcacdcabacbcbaccdbbdabccacaddaacadaddabbcbddcaaaabadcaababdbccadaacabacdcbbcabcabbcdbccaccbdbdccbabbdcadbadaddcbbbaccabaddadabdcabcaadbddabbdcdcabddbaacddddcdcdcccadddbcaaddadcdabdabdcdbbdabcadaabacabbbddaaaddbcccbacadabdaccbcaabaadcbbbdbbbadbbccdbadababcaadbccdbaaadadadbaaabcbddcbcbbbdacbdcdcdcdddbdccbaaaccdcdcaaaacdabdadacdcdcdbbabdcacccadaacdbcdbbbaadcdddcacacddacbcddcabdddbbaccccbcbcbaccabdabdbbdcabaccdbdcbdccdacdcdcbddbdabacdbddacbdabbbccbcbadadbcadbaacdabaddbbbabdbbdccddccadaaadbaacabcaaabcacababcacacadcdbcbaabcacbabbabcaaacdcdcbddabcbdadcbbaaadcaccddcdacbcacabacbddcaddcdddbdddbbdbbcbcdadcacddcbbcadadcddcacdbcadccbdaddaddcdacbccbbdaccdbcbbdaddcbbaacadcaabcdaccbdaacccaadcbbbbbbbdbbbacdbbcbdaacdaadadcabccaabbbddbbcbcdadcdbaaaaacbabcddcbcbbdaaccddcaababdadaccbdccdacacbacdcdaaaacdcdbabccdaaaaccacccaacdbcaacbcdbabdcaddadbbcdbdcdbcbbcbdacabdbddbbddadccbcdcddbdabbaddabddcbddbadbccccabadccaabcbdaacdcaacaddacbdcccdcccbdddbbaddbaaabadaccdbcbaaaaacadbbbdcdcadbbbccbbabccddadbaadbaccbbbdaccadccdddacccdaaccdcadcabaacdbcbbcaccddaacbcabacadaabcaccadabadadcdccbccdcdaabadcbdaaaaabccbddbbaacbccccabdababacdabbbcacdbddccccadcbadcbaaaabbacdaddccdaddcadacbcddbaaddbadcdccaaddbacddaacadccbcccbaccbdadabbabdacbcadcadadacadcbdabbbdacaccbbabbccbbbdbdcdacbabbcbcbbdccaadaaacddddacbccdbbbadbbcacadbcddcbccbddcdbdccbbaddccaacbabbbadabdaacadbabdcbcbccaaddcabcdbbaccadccdddadbcddcaacdcbdaadacdbdcbdbabcaabbcbddabdaccaddacdadddbbadbddbdcbbabcaddcdabaabcbcccdbcbcbccdaaadcadadcbbaabcdadbacbbbdbcdcccbaaddbdcbabaacbbdddbdcbcacabbcdcdacdbabbcaddbcadcccbdadbcbbcabcdabdacddddcdacdaababdbcdbbbdcabdddbacdbdbabdadcccbdcbddbababddccdacccccdddbddcddddacdaaaacabcaaaadadababcbccdbcccbdbdbabacdbcbcdccbaaabacbaaacccbaabcdcbbdabdccdcdcdddbcdadaabcaadacdacdccbdbcdcdbadabbaacaccbcbbacdaaaddaadabcadcdbbbdacacbdcbbbaacdbbbbbdddabbabdbabadbbdbdbccdcbacbdcaacaddaaccbddcbdaccddbdbdcbcbacbdcbaddcbbbddabbaaccbccbbaacbaddcdbabbbdbbbdbbcaaaaadbababbdbbbcbcbbbbacbcbaaddbacbdcbacdbdbbcbdadbbccacdbbaadcaacbcababacacdabadadbdbcdcadabaabdcadaaacdbdabacbbdaabadbccdacdadaaccbccacabacbbddddaacaaddbcdbcdcabbcabadddcaacddabacbaddbcdabaacdacdbbcdadbbbcbbdcbdacababadcdadddbdbaacabcaabadcbddcdddcacddabcbcdbcbccdabacabcbddbdbdcbbdaccbdabaabcaadbcdcaabaaaacabaacbcdbcdacaababacadbbbcccabbadbcccbbacabccacbcbccacacabcddabadcdacdcddcadcddbbdbcbcbdbbdcabacbbabacaaaaadbaddadacdacaacbddaacdbcdabdbdaadcddccaddababbacbbcbabbcbacacaddcbdbbdcdbaadacaadcbacccadaaddcacbaccaaccccacdaadcdbbbcaccdbbcccacaddaddadadcdbdaadbccbbdcccadbdbadabcdbcacadbbddccaabbbcddacbbbacddacbbdcdcaaadbddbcacbcabcdbdadcabcbdbbbccddaababddaaabcaccadacadacdadcadcdcaddbaabaacddbbdabccadabdcdacbacddcdbcdbcbcbbcaabcbdabcbaadacadabdbbacbcdbcbbcdcadaabdcccbacbcadccbbdacabbddcccddcaacbbbddccbbadaccbbcabbccdadaadbcadbaaaabbcaabbadcbcacbabcdbcabdabacbbcccbcdbdbdbbaaadcdbdadadbaabcaabcdabcadacbacddcdcbdadcdaadbdddddbdacccbdaccbdbddcdcdbcadaaabaadacdccadbcaabbbadcaccabbcaccbdbddbdcdcbaadcbcddabdbbabdddbaccbccbdbbbbcadbcabcababcbdccccabcccabbbdcccaacccbbdbbadadaddaabcdadbacadccabadacdcdcbdcccbbcbbddbcbbaabaccdaccadcbadaabaccccccacdccbdaaaccaaccdbcaabcbdabbcaddadccddddcccbaccddcdadcabaaaadcabccabadcacadcbaacbdcabcbaaaacaaccdcbadccdacbbcacaadccbbabbdbababaaccbcaaadacbbabcababaabdcbdbdabbbacbcccdbbbcccbaddadcdaaaaabdacacbbcaabccbddacbbacbacbdbddaaaaacbdddbccaddabbcaddacccadcaaaacdaababcdaaddcdbdabccdbbbddccacadabddcccdbccabbdcbdacdadcdadcdbacdabcdbbadccbcccbaadbcdbbbabccbcabbbdabacddadadaccddbbdddcccdcdcdbdbadbaadcbcaaddadacabdcadadcaccbaaadcdaacacccacbbbbcbbbbbbababccacbaaddbbcbbaacbacbacdbcacddddccdbbacadaccddcaddabcbaccbbbdbdcdaaacabbcbdccacbbdcaaacbbcddadbccdabcacddccdcdaadacacdcabcacdcabccadbddcdbcdadbcdddcdccabdaabbdaadabddcdadcaadddaddcbadddbcddbaccbddcabddbdaccadccadcdbbdcdbdbddacadccdabcbdcacacdacbcbacabccbdcdbcdcabddabbbdcbaacdccdbcdbababccbacabadbcdcbdcbbbcbbabbacabcaabaacdbabbdccbcdcdbdcccdabababadbaadbdbcdbddcabbcdaadbabacacdddbabdbacaddabcaadabaacddcddcaaabddcdbdabaacaabbabccddccacbcaabbddcbabbcddbcbaccababacdbdcbddbcdabdddcbacdcadaddbcdbadbbacccacadbabbbddbcdcbccbbcbaacaadbbdaabdbabdcbbacdccdccdddbcabadaccacbbbdbcddbcdcbabcddcdaddcdcaccbcdaabbcdcbcddcabddcadbdaaddbbddbdadcaccbbbabcdadccdbbddbbaadddcccdbccddccccbadbaababcaccccdaaacaccccbccbcdadccdbddcbcbabbcaadadddbbbaacaccacbaabbdcabacbddcbbdcadadcacccdacbdabbabacdbddabddbdddccdcaacddcaababbcddadaaabcbcdcadcbcddcdbadabbddcaabbbabaaacdacddcccbbbcddccbcccdacbbabacdcaadbcdccdbdbcacccdcccabdcdababacaccdacdddacabdddcbdddccabbacabaccbbabcdbdacdbcdababaacbbcdbcddabcabbacdddccadbcbbccbdbcacbcdccdcaccbdcdadddcddccabdccdaddcbbdbbdaabdccacbcbdcaacacaddcaaddccaabddbabcaacdaadddbabddbdbcbdccadbddcacabcbbccabaadcaddaddcadbcbacbadbadaaacdaaacaabadaabaccccabadbdaaabccbbdbddcaddbddadcbdcbccacbdaaccadcdddccddbdbbcdccbdcbbcdcdbdcbccaadbaccccaddcccbabbbdacaacdbbdcdbbbddaaadbacdbcadcccddabaacdabbaacababcbaacddabbbcdcabdddbcddbdcaabbbccdcdabbacdabbcbcdcbaddbababbcbdcbcdcabdabcbdcccccdacbacdbdcbdbdbddcaddacabbcacbddadaaddabbcbaabccdaadddcbcbaabdcdccdbdadcacdbbbcabadbcbbccbdadacdcbccaddbdbcabcdbbcdddbddbacbdaaadabbbcbbcadabcccdbbcabbbcdabccaaabaaababdadbbadcacdddccbdcacdcdadcdcbdbaabacddbaccbcbdcbabbddcbcccabddbdddadbabadcaccaaababddadccdaacccabdcacbbbbccbcbcabcbadccddbadbadccaddbaddbacdddabbaddaadadccdbcbcabbcadbbcccddadacbcdaaacababaaaccdbaabcdbcccabccdaccaaaddbbaddadcdcbddcdbbdaaadbcdbcdcdaccbcdbbabcabcbdbacaaabddccacbccdbbaabcadadaaddaadaabddcddaadcdbddacbaccdbbdcacccbdbcbdabbacabaccbcbbdcbdadacbdaacbdddccaddbcdddaccbddbcdbbbccaccbadddabcbbbcbdacdcddcbabbcaabadcacbcdcbaaadddcdadadacdadcbacbdbaacabdccbcbaccccbaabcaaddbbcabbbaabbcbbcccdbabdcbddacbdacbdabbdbadcabbaadcbaaccabbddadadacdabbadabacbbddcabbadacdbdadcbaacaadbcdcccadccdbbbaaaadcaabdadcacacbcadcadaaddcbcbbbbcdcbccbcdaddbcbbacaadbadbbbdbabdbbdcbcbddabbdddaaaccdcbcacbccdbbdcddadcdccadbdbccdcadbaabccbbcbdadbbabccbdbcbcdbcaccbbdbbbbbbbbabbcdbbbbbdbacaacbbbddcddddbdccbccbbacaccacabbbbcdadbaacdaabbbcaadbdaacdcabacdadbabdabbdadadbccabccbbddcaddadddaccbbcbbbdccdcbbbbcdbbabbabcdbbaaadaabbdbcbabaddadbaadbdadbabadbdbdccabddccbbccdbbccddcccdbcdcbcbdddbdbaaddcbdaacbacbcacadbbcdcbbbbdcbcaccbdccaadbbaabaaadddccbcadcacbbcadbbdacbadccabaaabbbcabcababacbcadcadacddbcadcbacbaddaddbabdaaccbddaacccccdbdbdabaacccbbbaccbbbdddacaccbbbabacdcadccaccbcacccacddccaccaaccdbdccaadabdababdccaaadbbccadcdbbabccbbbaaaadbabdbcddbcbbcbddcaccaaacacbbaddccdbdcbcbcaababaabbaabbddbbabcadbbdaabbadcbacddcbdabdcdcbdcddbbbacaabbcaddbdadbacbacaadbdacdcdcbcbaddcccaaabcbddcaddabdacccacbcddaccadababdcabacbddaddaaacccdddadbbaabbcababcadacdbbdcaadcccbadadcdcdccabadddcbbbcbabcaccbddbcbdbdddabbddcdbaddcacbccdadcdaaabdbddbbcdcabcbcbacbdadcbcbcbabbdaadabcdbdadbbdabdbbbcddadbcddbdbbbcddabcccdababadddbcccdcddaaabdacbdbdbddbdaddcdabdabdaaababcabaddbdacbacaaccccbcaccbaabbaabdbabdcbddbdaadaaaacbaacabbbdbbcbdbccdacaaaadccadaabbbdcacdcbbaaaddccdabccdcacbbcbaadaadcadaaadccacbbcbbbbaaadddadcacdacabaabbcbcbdbadbccaabdcdddbdcacbbbaaddbdbcdadbaabccdddaddaabaaabacadacdaddddacdddccbcaaaadcdaaacacdadbbbcabcddbbdacadcddcbdbbcadccbabbcdadcbcacdcaddcddbaabdccabaadccbaadababbcaaaddaabbaadbbccadcdddababbdabcaacacbbbccbacbcbdabbdccbaacbaccabdaacbddcdaddcababccdacacabdabdbcdacdabbbcdacccabbabccabaacdcadbaaaccdacdabbcbbadddaddaabbbcaacdcdaddaadcbbabaddbddbbdbbbccdbaaacbacdbdcdbabdaadddababdbcaacdbbdcdabcddcadcaddaabddaccbdaabcbcbcdbdbbadccdddcadccaddbbcbcacddbdacbcabaadbaacbcadbdaabcabccccddbdacaccacacadaddcdabbadccdaadbbcdbbcbbabbddbddcacbcaaccacddadcacbabbdcbaaaccbbcaaaddabbbbacdaddddbaaadbccdcabddddbbcacacdddbaabbbcacdcaccbdbaddadccbbcbaadccbcbabcdddcdabaacaaacadabaadcdcddaadbbcdbcbacbbbdcddbbbdcbcdaaddddbcbbcbaabbcdacbdbacaaccccaccabcacabaabacbbcabacbacdbcbbcdacdcadbbcbbcbbbbbbbdcdbacadbdbdcbdccbccdbddbcadabaaabcadcddcaadddcadbbcababdcacdabbdddcbcbbcaacdacbbaacddbaaaaadbdbbcbcdabcdcaaaabbdacadabcbdadbbcadddbaaabaccbcbaabacdcdcdbbbcbbbbadbdcabccccadbbcababcbcdbdcbcbdbcdccabcdbaaadddaaaaddabcbddbabacccacbadadaccacdaaabdbdbcbcbcbbbbdccdcabaaddaabbdaadabaccbacabacadbadddcbbadcababdacbadcbdcbbdcdbcddadadbddddbdbadacdddabcbccadcdbbadadbbcdcdbadbaacbcadcdaadbdcbabbccdbabaccacccdacdcdccddccbcacddcbabcdcaccbbacdaaaadccbabbaaabdaccaabdddbddbdacbbcbbdcbddadddbbadcdccccaacdabbaaadabbcdbcbbddddddbdbdddaaabcadbbaaacdbacccdcbcaaadbbcdcdcbddddcdadbddbcbddcdacdccddbcabdaabbaadcbbacaabacdccaaabacccabacdaccdacbddcadbabaacbcacacaaccddaddbcddabcabbdabdbdaadbddbacbdcaccbabbababbbcaddcbbbadcaababadaddddccadbdcccacbadcddcadbaaadccaddaaaaadbdbccdbbcccaddbacdbaddbadabbcbcaabcacabcbccccaddaadaaaacbcdbbdbbcdaacbddcdadbbddbcacdcabcabbcdbddcadccbacabdaddbccacccbcbacaadccabdcddbbcaacadacdcbacacadcacacccbdacbadcccabccbabdcaccccbddcbabbdcbcdcccabbdcadaaadcabdadddcacaddbbcbadbcacdcabddcbcbbaabddacddcbabacaaacddcdadaacddacdbaccdbbcbcdbbaacbcaccdacaacdbdabcdaabbddcaaaabdcdacadcbbaacdbcdddcacdbbaaacabaaacbccccaaabddbbcbdddddbacacbadcbbdcccdcbdacbdbdcacbbcabcaadccccdadaaaadacbaaaaadccccbcaccaacdaaacddadababdadaabddabcadbdbbdcbbdbbcdcdcccbdccccabcdcdcbcadccabdbbbddcdcbcbcaaabdacbaaacbabbacdbdbcaaadbcbaabcccdadcbbbabaddaadddcabcbabbddaaaabbadadaadacacdcccbbbbacacabccbdddcaaaaabcdbaaccbdbacdacabbcadadabbdbddbabbdabaaabdaacdabababdbbcabccadabbcacaddddaddcdcabdabccbdaacdbdacddbbbdcabddcbcdddaadddbadddabbaaabadbabddcdcbcbcbaaadaddbcbbdabaaadbabadddbcacacdbaabaccacbddcadcaaacccbbdbadaddabdbbddabcdcadccaadacddccddbcadddbccdcabdbcbcbacbbcaccdbcbddcdbabccdaabdcbdaddbcbbaabcccbaaaacaadacabcacabdabdbadaddbdcdadccccdbaddcdcaccdcddcbbdacdacbccdcdcababbccbbddddcadaccbcdcbccadadcabdccbadcaddbacaabddcbbbadbadbabddcbbaacdccdbadbdcaadbdcdabacbbdcccbdcbbbccdabbcadbcbbdabcdaccdbcdbdabacbccaddadabcadcbaacabbbbdddacaabbbddcbadcbabdddbacbdacadccdcbabdacacacbddcaccabbbddcbbbbcdbcdbabbbcdbcaaabdbababaccabaabbcbcaadaddcdbacbdbcdcbcaabccaddacdcabacdbbddbddacbaccaacbcdbbdabdacabddddcbaadbacdcccdcadbcccacddbbbdacdbdbbaccbbbdababbacabdcbacddbabadbbdadcdbbbbdacccbcccaaccdddaccbadabbabcbabacaddaadbdcccdbcbcbadbdbaaccdbaaabbbbdcbdbadcbaddcccddaacdcdabadabadbbadaadbcdcccddaabdbdcadaadcdacddaacdbdcabacacbbbacabacbdadbcddaabdcadbbddcbddadccbbabadbabdaddddabdbccdddbbdcdadbaaaccdbacdbdbbadaccdaabbadbbbaabbbddababccdaabbcbbbabcdbaddaaacbcadadcacbbddcadcadccccbdbcbdbaddcdccabdacdcadaacddbddabccacccabaabcddacadcbbdbcdacadbdccdcccbccbcbdbbbbbbddbbdccbbaabaabbaccacbaaacbdabddacaadcdcacabbbcaabbddaaacbbdadcdccddccacccbcdddcdbdbbadcaddcdbaddcbaadcbcabddbcacabcbdccbdcbbcbcabdacdaaaadcbdacacccbccdddbcbdacbacbadcabdcabccaaddacbdbcdccddabccabdccdaaacabddbdccaabdddacdbbcadacbbbcddccdbadcdbbdbcaabdbaabadbaabadcdcbaccbddbccbaabbacadabdccabcacddbbaaadaddccaccdbbdcbdbcbbdadbcbacbcddbccdbcdacacacccdabbccdaacbadcaacdcdabbccbaccbdbbcbacaacdadcdabdadcdcabaccbccbdbcddaadcdcabdccbcdddcddaadbbbcbbbcbabadabbaccbdaabcadadcbdabcbbaccabadadaaddaabdbccadacccdbabccacdadacabccbadbbbcacbcdabadcbdaabaaabcbcdbdabdcddcbdbcaaabbbddcbacdbacaccbbbbdabcbcaaddbaacddbcbdabaddbaadbdabbbacacaacdccdaddbccdacbcdaaacddbccbbbbdbdbaddbdbabbbbcadcaddacbdacdadcadacacbacacbdaaaadbaccbabbabcaaccddaaacacccaabcaccbccacddddbadabaddcdbbdbdbdccacaabbadbdcdaccbddacacabbabcabacacbbaadaddaccccbcdbdccdbcbadcadabbcadcaadabaddcabbbacabaadbbdcdcbbaacbdccadcdabacacbdccabaaabcbacdbbadacdcdddcacabccdcaddadabdbadbcadabdcdadbcbdbcbccdcbdababdcacbbcbbabbccdbabbbaacddadaaacbcddabaadaaddaaaddbbbccbbaaacddbcacccdbbccdadcccbcaabccaabbbdddbbdadadbbdcdcddabcddddaddbcaababadbdbcbddaacccdcdbdadddbababaadcdadbcccdacbcbcbccddddacccdbcbabcaaacbdadaccddcdcdbaadabccabaabcadddcccdccddbcbacbddddcdcdbcddbabddadacbbbbbabdacdaccacdddabdabccaddccabcdddbbbbdaaacacdacbbaadaabaacacdababcacbcaacbadcbdcabdddccacdcacbacacabbdabbaccccdbaababddbbdddbbcaadbccaadddcccdbdbbddccbbccccdcdadccdcbbdbbddaacdddcbaddddddcbadbcbdabcccdacccdaccdbcbacaaabacbadddbabdbcaaacdccaacdbadaadaacadadcdaaabaccbacdbcbabaaaaacdabadcbbddaadcdccbbdacabdbdcccaccabdcbbbdadabacabdcdcbccdbddcdccddadacbcccbbadccdbbbcaddbcaadadacaabbabddabddaddbbccdaabdabbaddbcadcabcdbdbcbcdacabacdccccddadccaaaabbdabcdccddbcbdcbbaadbabdcbaaacbaabcaaaaacacdcabdabcccbdddcdccabbdcadaccbcbbadadbbdddbcbadddaacdccbddcaaadbaddabacdccabccaacabcaadbcbbddccdccabdbabcdbbccbbbbdcddccbaabdbccacddcacdbdccadababcaaaadabcdcccddcbcccbbddcbbbadaacdacbcccacdcdaccacccacccdaadbdbcacddddacbaaaccadbabcaacbadcdaddcbddbabcdabbdabccadbcbbbbbcaadcddbaddbcdadadcaacbcaccbbbbcdabadaabbcaddaccabaccbcbcdbcccbbdcdbdacbcdabaadbbbadcdddadabccbdccabbbaacddddbbdbcdbdbbaacbaadacdaabdacabaaaaaaddcddaccdccabcccdabbbadbdccddaadacdbbdabcbbbbbdabbcacadadcddccccaabdcabcbbcabbaccddbbadbddadbacdbaacabbacccddcaccccdadcadcdcaaccabbcbcacadbaaaccddbccdbccdcdbddbddacbbbcccabcbbbacddcbcacbcdbaaccbdbdcaadccbccbbaddcaacbcdacdbaaaccbbcbcbcbcabadaabcbbabadbdacdcdcbbdccaaabbdaaacbcccbbcbdbcaabdcdabbcdabddcaddadddcbbddabcbbcbdcddccbbbbcadbbbcbaaaaccacdddaaabbdddbcddcdbcdcddabccbddbccccbdbabacabaaaaaadcbbdbacaabbdddcbadcdaddddadadacaccdbdacabbccaacacbddbbdddcacaaaabddacabaaccdcbddbdbdcabccbdcabddaddbadcadddaaadbbaaccdabaabcdbdabadabcccaadcabcbbaaaadabdadcabcbcdaddabacccbcbacbccbdbcadbddbcacaddbdcbccabaaccbbcaacacabbdbddcbdcadadabacacbcacabdaacdababbacdcccbdcadbacabccabcdbaccbaabadccddddbdccabcccdbbdbccdbbcaccbcacadabcbbdaccadaadcbabcbcbcadabddbcbaaaadccabbbdaaadccccacbdaacdabaccccdccbbbabacbbdaddbcadddbddbdbdbdccccbcabbdcaaaddaaaddadbaaccadaacddbdadbcbbddbdbdcbbdcdccdacdbacbcbabdadbcadbddbbbdaadbddcacbcbcdcccdadabcbbbdddcdadbcadcdbbbacddbaabcbdcaacccaacbdbbdcdcdbcaadabcbbabaabdccdacbbddacccaabbcdddadbdcaadbdcbdcbaacabbadacdbdbbdaabcaaadcabccabddaabdccbbdddaaabacdaacdccabcccbdddcdcbccbbbbcbcbbcbcbbadadacdccdacbdddacdcbabbadabbddcacbabdbdbcadbdadccadaddcacddcbdbbbcddcaabbabacdbbaccadadaddabccccbdcbdcabaaabdbdacadddddbbddbabccabcacdccbcaccabdabbdaddcbcbdbbdcadaccababcdadabccbccdaccbdbbcaaccddadbcdccdadbbcabdbadbbcadabdcdbabbdaabddaccacdacdabbddbbdbacabcdccadbcaacccabcdadcbcbcbcabdadbdcccacbccbdaaaacdbdaddcddcbcdbbadacdcdcbcbabddcbaddcadadbdacddddcdcdcdbdbdaddabdbccdbcababcababddadbaadacdadbbcbddbcddaaacbbbaaaaabdbaacaaadccacabbaddccddadbcbcabbbdcbcdcabccbcbdccbbddbbbbacbcccbccbdcbdbacbdcabcdcdacbbbabacdccabbabcabcddaacbcdbaabddbbababbdcdddcbcbabcbdcacdabbddaddadcdbcdbbdabdcbdbadcddcccaddaccdbcdadcbddbdbacccdabcadcdbcbadaadabcdbbacdcdcdbabbdababdabdadccccabadcdcacbadaadcdcdccbaacccacaadcbbcdcccdcacdbcbaccadbdcbbddbaaadcdcccaddcdabddadddaaccaadcacddbbdaabdbdbcdacacabacaadcdbdbcdddaadcdddabaacbaccbdcddaabddcdcddccdccabdaaacacacbabcadaabbbdddddacccabcbbacadaabaacabaacddbaabdbbbbddabdaccdbaaadaacdbbbbbddbdbacbacccdbbbcdddcabbdcababdddabdabcacbbbadcdacdaaacbbbcbccbdacdcdcabbcaaaabddbcdbcdbbbdccbbcabbbdbadbbdccddbabcbacbbdbccdbacdadcdcadbbddccdcdacdccdbcbcdcbabaaccbcaaacdabbcabdadbabaccaaddacabbdccaccaddcbacaadcbcabcbcccbcbcbacbdbdabadbdabdbbdbccdbdbdcbcdccbcbdacbbdcbacbabbabbadbcdaadccabbbbccdaabcaabbbddbbbdbdccbbaaadadbdbcdcadccddabdbabccabacddbcdccbadbbddddddbaaacbaadbcbbcacdaadacbdbabbdbdbadcbcdbbdddcbabcabbaaaaccdbbdcccadbdcacaaddaacdbdbdabcbbdacdcddcabdccaacdacadbadadbbbdddbddabdbcbabdaadcaadadcaaaddadbadccabcbdcadadaabacbddbbacabadcbcdcdaabdabbcaddbcbdbcaaaaddaddbcccdbaddbbbaadababbbaadbdbbaccaddbbcdadcadaaacaacadcbdbdabccbaaddbbcabdaccccdacdcdbbbdbddccdabdaaabdddbdbddabaaaaaaadcddcaabaacaacacdcdacbcacbccacadbcdabdddbabadadadbcdadaddacbdcdccddcdccbdbcbbaaaaddaadcaaacabacdbddcbbddbdaacdccccbbccabddcadbaccccaacbdabaddbcdbbdcabdbcbacbcbdcbdcdcacaddcadbdcdcadbadbdcddcdaadabccadcbcdbddcabbdcabdaddcddcbdbcbddcbdaacdbcabcdababaaccaadaaabbdaccabaabbccabdcacadbacadcaaadbaadcbbbbdcbbdaaddccacbbabacdcdadbcbbbaacdadbbbbbaaddaadacbbbbdababbbbacbacbbdaddacadbaaccdaacabaaadcacbcaaadccdbcdcbadaaccabddbcccadbcadbacbdacddabddbdadcccbdddabdcdddbbdaccdabbacabdbddcdcbbdcbbdbcaccccacbadcdacdccbdcdcbbddbcbadddbaddcdbdcaacaccdcddababbaddccbabcaaaaacbcbdcdbbccbbcaacabdddbaaaddabcbddcccdaaaacaadaabddabdadaabccaabadaaabaddacbaaabbdbdbccbbdacadabaaadbbabbcbcdaccdadcdabaadacdadddaaaacbacaaacdacadadcadccbdcccbbddbdbabadbbacdbddacbddcaaaaadabcbdacbbbbccdcdccacdcccbdbddacdcbcdbabadcbddbcddbbddacbabbbcdadacdbcbddbaaadaaabbbbdcbbdacaacccdaccbbabcbcaabaccddbbbacbbcbdbbaccdddbbcbbcabaaccadabcbadcdbbabaddbddabaaddabbbbdcddbabbbabcbdbbadcdabacabcddccdbaabddbbaabbbcbcadcbbbcbcacccbaabddadaabccbbdabaaadcbbaadbabcbcabcaccbbcaabddaacdccacbddccaacbdbddacccbcbbacdbbbbbdadccbbdbddbdcacbdcbddccaaacdbbadcdbacdcacddabdbbcadcbdaccdcaacdadbcbadbcccccdacccdccccddbcdcddabbbcbdadbcbbccbbcbbcbabcdbddaaddbbabdadacbbcdcaadcadbdadaccdaaccacacccaaabdbccbacdacbcabaabdcbbbadccdaccbccabccbaadcbbdaacdbbbcbdabdabbcbbdacbddcaacadaaabcaaabddabdcaccacbcacddccadbaaaabaddabacdacdbccddcdaadcbaaaadbadcdacbdbdcdbcaaddadacbddabddacddbbccbcaaacdcbbbcaddcabdbdcadbcdddabcdcdcadabbccbbaaadcdbcbccbcbbdddbdaacaccbbbccbdbcbddaadbbaaaababadcccaaacbdcdaacccbcabcaadbcabbbbcdcbccbddadcdccbbbdcbaaaabbdbcbaacbbccdcddaadbaddbdacabdaacbcdadbccccccdbdbabacdcaabbbcbbaabdccaddadaaaababdddbccdbacccacbaabccadbccabccdadcadddabcdbaacbbabcccadabacccacabcaaddddbadbccddbddcddcbddacbabcdddabbabccbdbaabadbccdcddbaacdcaadadbcbbcacdacbdcaaaaaabacdcbbbadbcbddbcbcdbaadbabcdbabcbbdcbcaaccabadabbbdacdddbbcbddadbdcaaadcacabdabbbccddcbbacdcacbdbcdaadbadccdcaacbbcdabaddabdcbbcdabbbdbacdcbabadbddaadbaddddcccdbabbbcadbbddaadcdababadbcaacdbdcbdbcdcbacddcaaadbaccbdbddabacdcaadabcdbbddbdabcaabbcbcbccadbdbabddcbdcccbdbadcdcbccbbbdbcabbabdcdcadbabacbcdacbacabaddbcccccbaacddccaccbacccaacabdbcdaaadbbbadcbcadbcacddaacbdbbacdccbaddbdabdddbcaddbcdddcdbbddbddcbdbbdddababdcdbaadbabdccabdbddcaabadbccadcaccbaabcdbcbdcacccccbbcaacacdccdacbdcdbabcabccacbddccbccdbbdddaacdacacbbaaaadddaabccbbbbcbaccacdbdbbddcadccaddaaacbdbbdcbbbaadddbcbaabdadccdddbcddbaabcbbaddcdabaacbccaaacdacccaadbcccdabdbcaadcadbcbbdbccbbadbbbcdacadcbbadcdbcabdcdcbddcadcbcbadbcbaddccbdadbacdcbdcabbddccdaaaabbccaadabbdabbcdcaaabcbdbbcbababbabbcbaacdcdcbbdcabccadbbdacccdaccbdccdacbbbdcadacadbaaddabdcacdabcabadabcdacbcdccddabccbaaabadaaddccbbcbabdaccbcdaaabbaccddcbdcadaaccccbbbaacddabcbdccbccacdbdcaabaacccbdaccbacccddddaacbcbccaaaaabbcbbddcdbdbdddaddbdbcadbcddabcadbcaabdacdcccdbdcaacbabbadabcbddabadbcddcbbcbcadbaddcdabcccbdabaabbdcccbaabcadcdacdaccbdcaddbbdbbbcbbcacccdabdacbaacdcbddabcdbbadcdbdbddbaabbabcbcaaadccaabcbdddaabbdababbabaaaccbaadaccdcbcddcdaadaccbabbbdaaabbaadcbbcdbacbaccabcddbaacaadbadcaddbaabadaacdccbbbaccabadbbcdaabdbcdcabbbdcbbccbcbcdbdbdbcaccadaabcbadbcacdcbbcbccadddddcccbdccbabcabdbbabbcbbdcabbdabdbcbdccbcbdaacbcdabbbaabacdbbddbadcacadcdccccaccdacaabbcbadccddcabccadabdbccaddadcaadacaddccaddbcbcbdcadbcdcbbaccadcaccacccdcadccdaacbdabcbdbcbdadcabcaabbdcdcaacdddacddacdcdddbabaddbacbbbbaaadbcaaccdcbddbdcadddcaaccbadaacdbcbaddadcbcaddcaaadbdacacbcbaaacdcbbdcccaaddacdcddaaabbdacbdacbabaddaacbcacacddccaccdcdcadcdbbdddbacdbabdbbdaaaadbbaaaccadbcccbcccddcdabddccacbabcdbccabcddcacdbdacbccbdcaabaabaadcacbddbbddcdcacdaaabcbcaccccaacdaddbdcaacaabcabcdbcdccbcaabaacddddddcddcbddabdabbbdddbcbaabdccdbbcadadbdddadadadaddbccadbbaadbbcddbccbcaabdbaaaaadbbabbadacacbcbbddbdadabbbaabadccaccacabacaaccbababbddccbddcdbdcdbdababbcbcadadbdcdcbaddcbddaccababacbdcacdccccccbdaacabcbbdaacaabcdacbdbacbcbaddddbbdadacbcaabdbdabddddacbdcdbbdbdbbbcbdaccdddaaadbadabadccbddbcaadbbcbabdabbbabbdbabcdddacacdabbbddabcbccbaddddbcadcdbddaaadbbbcaabbccbbbcaabbaacdbdabababcbbcdbcdcaaadadbadcdbdaabcbdbddccabdcaaadcadacdcddadcbaacbaabcdadcdaabbabdacdcbdaadbaabdcbdababaddcbabbabbbccbabcddddabbbadadcbcbaddbdcacacbaadababdcadccccdbaaccbcbcbdccbabbcbcaddcccbbbabdaaababdbbcbbaddbaabbcbabcdcaaabbbdcacccadbccaacabdbccbbccdacabdcdcadcbcabacbaadcdbaadaacaabbbcbcdabdadcddabdadcddddcdcbccaccaadbcbdbdddacabababbbabadcbabaacbdcdbabdbbcbabdbcbdadbccaadccdcadabdcaaacaacacdbcacbcadddddbabdaddcddccbacacccdcdbacabcdbaccdcdccbdcdacdcbdcbdaddbccdabaadbbbdabbbcdbbddbcadacdbabacdbcccccbacbcdbadacbcdabaddbddbabddbccacbabaadccacbbbadacddddcacabbccdacaacddddbbddbbbbabbacbbcdcbbbaccabbacaacdabaabbabcaccddaabdbdaddaaacdaddadacbbccbadbaddcbcbddbcdbbbcbdbcdbdabddbcdcbdaaddcbbbccbbabcbdbcabddbdacaddccdddbaaacdcabcdabcdddbaaabcdbbccbdbcabcbddddcabcccbaacacadcdbddacdabbdbbdccacbddaabaabdadbabdccaadbcadcbdacdcadcadddddaaddbbdbccaccdbddaabddcdaccdbbcddbadbddacbdcabccddddcbcacacbdccbaaddadaadbbcbddbaddcccbcaaaacccddbcbbcddcdcacabcbbccabdabdcdcbaababdddddaacadbbcaadabcdaadadbacabcaaabbdbbaddbddbdaccbbbdcaabbdaadcccbdcabddabddabdcabacabbcbccbbbaccdaddaccccacdaadcabbcbdadabcacadabacdbdcadabbbbdaabcbacdacdcbbbdadbacccccdbddbdbddacdcaacbabdaccadccacabcacbbabccccdaddbbacbbabaaddaccdcbbcbbbddcdbcbabcaaacdaadcbcaccdbbdbddbbdcdddadbdccbcacbcbabcbddbbabcacbdcbacdcbdbbdabcbcbdcbcddbdabbaacdcbacaacabdbcccdddbddaccacccdbaccdbaabbaccbcabdcbdacbacabccbadacdadddcacbcdbddbdddbdaadbaacbdaccdcbadbbdbabdddbccdaaaccacdaccbbdabdabcbaabdadddbcbabddddbadcbbcbccbbcabbacccdadbdaadaccbddccccaacbcccbbdcaacbacdddbacdabaaccadcdaaddddaacadbddbddcdddbdcdbadbdcbaadcbdcccccabcdadaccbccbabbbaacabaaabbbcadcbabdddabadacdccacdabcbcadacbdbbadccccbaabadbcbbacaacadaabcbcbcdddccabbbcdcbcdaaacbaddaaacbdcacdbabacacbcdbababddacccbabacadbddacbdbabbadbbaacabcdbcacbbdabbadbacabaabccdabcdbdaabcdabbdaabcaabcabcbaddacdadabaaccabbacbaabdddbbbadabdccdbcabdccdcbcbbaacacaabaabbcddabbddbbaddcbbcdcdcbcaddcbcdccccbdcdbbbcbdcdccbadabddabadcbcaddaacdacabcbaaacdadcbacdacbcabdbcadcdddcdbbdcdbbacdabadcdbacbdbbdabaacdddabcaadcccdabbbcabbcdbcddbcbcdaadddaadacbcabbacbcdcbcbabbcaaacbcacaacaabbcdddddcbccdcbbbbaddbcaadacbacdbddabacdbabddcbdadcdddcccbbdbbaaddacdddaabdcdaadbaaacbacacddbdbacdaddaaddbbdbcdcaaccaabdadbbacaabcdbcbdabcbbcadacbcdabdcaadaaabdbbcdccdaabaacdcabcddccabaabdbbdbdbcadcdbaabddcabadadacbbbbadcabcabcdabdbcaadaddbadbbadddbbadcbcccadcddddacdccccbcbbbacddccbdbbddadccbddcbaabaabdabcbaccbbaabcdaadadcdacababbccddcbbcdadcdcbddaaacdadddaabbdaaddadcdbbdadcbdbdacdbddddcbbddddbacbbbbabcbaddddcbcdbdbadbadcabbdcabbccdddbddbcbddbdbcdbddcdbcacbdaccadbacbdacaaadcbcdbadbabccabdabddacdabbbddcccbaadbdcbcdacbadadcdaacdddcbcbbaccbbbcabbbcdbabddcdbaccabccbbdbbcacccbbccbdcbaacaccdbacbdbabababcabcaadddcdadccbccccadcdddabdcddbcdbcddbccdaccbdaacbcbaaccccbcbbbbbbacaddddadbdbabbdaccdcabdbaacbdbdddbcddbacbbdcadbcccbcdbbadbcbadcbadcdadcccaabbcbadbaaadccccdbddbbacdbcbdcdbdbbaddcdacbdbaabcaccbcbcdaadaacbdbacacdadaaddabbddaaddacbaddcbbdadadcbaaababdaababbcbabcabccaccbbdbbcababdbbcbcdbabacbaaddbcdbcdcbdbccdcbdccdaacdbccbddabbdccddbbadddccadbabbdcdadccacdbabccdbcdcdabdcabbdbdcdbbbdbccacbaddaaabcdaacbcbcdacaabbddbdacbdaadcbbdbbccdbdcbaddabdbbdccdbdadccdcdabdcbaacdadababcaaababbbcaacdbacccbdbacddabadcddbccdcbdcdccadbadaacdabbabadbccccdbccacdabbbbbcbccbddacdbacbdddcbaacbabaccbbabdcaadaadbadccadcabdadddbdcbdccaacdbddabbddadaadabbbdcccbbabaabbbabbdabacdcccdaadcdaccccccbcbacadccdcddbdbdcbcabbbccdadaddcdabbbdaadbaabcaadbacbbddcddabdbcbabcadcdbdddaacabdaacdaabaaacaaaabcbcbdabbbdaaadcadccbbdadaddadcacaaacddccaabccbcdbddddcdcdcacacadddcadbacabbdbcaadbbadcbadacacaacbaadddcbaccdcdabdcdbddacacaddcaddcddabacbadbbbdabdbdaddcbcbbbacdaaddddaaddcbbcbbaaaddbccaacbbdddcbacaddcdcddcbcadbadbdddacabbaabbacbdacdccccccabdaccabdbdcdddbacbdccddcdaddbabcabdabdbaaadacbcddccddbccabacdcccccdccdcdcaaaaabbcbdbaacddababaccabccdcbbbacaadbdbacaccccbacadbcbacbabdcccbbbcdcbddcadcaccabadbcdaddbbaaaadcdcbadbcaacddcacccacbdcaadaaaacaccaabccbaaaccdbacabbadcdbcdbdbcbacdcbccaadbcaaccbbabcbbabdcacbbbaabaddbcbaaabbcccabccccdcddaaccadabcdadacacacbbccdbabdacdccccdcbbabbababcbdadadcbcccabdbacaabbbaccbbaacbbdadadbbddcbadacddcccddabcbbcdaabccadadcbdcabaaabbacbdbbbbcdcabbadacdbaaaaccbadabccbbbdadabbbcbccabdbddcccaabbabdacccadaccccdccccdddcabaadbcbbbacbacbdadbcdcaccdccccacabddbadccdbbbadcddadcbdadddacacaaabdaabacddabbccdbcbcadaaccdcdddcabbcddbdababbdbacacdddbacccdcadaddccacdcdcabbdbbdcbacdbbabbacdccdddacadbdabcbbbddbcddddcbcbbccdcaadcbdcbbdcaacdabcbcbdaacbababbbcdbdcccdaccdbdcbcdcdbdccadbaddbbccdbaadadacbbbabacddaddaaadabdbbdbcdcaabcbbdbbcbbcbabdddbabbdcbcaccabaccbdbabdccbddadcbcacbbacdaadaddcbdcdccbddbbdccddbbdcbadaaaccbcacadbbadddabaabbdccacdbcccadbdcbaadaacddbaadccdcbaaaddccacccadbddcaccabcaaaddabaddaaababddaaaddddadabbaaaddbabbdbdcaadbcdadcadccdbbbddbcabddcddaabacabccacccabdcbdbcacbcbcddcbdcdcbadbdbdcdbbdbcbddababdaddaacabdababaadcabcadcadaddbbaaccbabcdccbabcdcbbaabdcdbaddbaccaacdacdbdadcbcdadbdaddabcadddbabbbdbaababcaddbbdcccabbdcdaccbccbcacdcddcabdddabaadabbbbaccbcdbddacadaccbbdbcddbaadbaadaccabdcacdbcdddbbdcddaabcdbbbacadbaddadcbbbdddcbcdacdbcbddbaabbdcdaadcddcbdcbcbcddbcabdccabbcdcbadbcccaccdbbcccccbcdaccbbcdccbbdbacabdacabababdcbabcaddcbbcbccccdacdcababddccdbdbabcdccbcdddabbcdcdcadcccadddabbcacdadcdaaabbbbccbcccbbbdaccdbcdacbdadddacbdacaacadbcadadbcbbbccbbbcdbcbccbbacdaddbcabaaaaacacddbacaddaaddaccabbbddbcbabccabcaadcabacbddacacadaacaabaddccdaddbcccadadcbbddcaabcdbcbddbbbbabccaacdcbacacdcddaacddcbbadbaaccadbcaabaadadcdcaaaabdbabcdcabcbdccbccacabcbabdccabaddbdcaacdddccddadccaaccdadbcdadddccaadacccdbaacbbacaaadbaabbbbccbbddaabdbabcbbcccbccaacccbabaaaacccaaabaddaabbcdccdcdabbddbcbccdddbabdbdbbbbbddcbaaaaddabdbcdcabdbadbdbcbcdadadababdacdccbdbdbaaabbbcbbacbbbdcddbccbdbdaaacadacaadbbcbababbadcbcdacbcdbccaaacdcbadabbbbbcdaddaaabacacaaacdbabadcbaccdddccccabbaababbcdadcacdccccaaaaabdbdaddacadacbdabbdccbacdaadabdccdaaabcdbdbbddcaacddbcabbabcccccadcddbdaacacaaadcddcbccddabadcbdbcbadcbbaddbdbdcabddcbdbaabaddddaaccbaaaadabbcacccacdddbdabcbcacbaaccabaddacadbacdbcadaccaabcddacbdbacacccbaadcddbdcdccdaabbaaadbdbbddcdabbdddcdabbdcdabbcbdaabbdbababccccaccabdbacbbbaddcbadacddcdcaacdccbdcccccdcabbbadccdadcdbabacbacacddbbdddadaddcdbdaadcaacbdcdcccaaccadcabdccbdaccabddbccbabaacdabbbcaaacaacdbddaccbbcbacbdbcabbaaddcdabdddadbccddbccbdaaacbdccdddabbadcaddabbaadcbbabcbadbcabbdcabbabbabcadcbbbbcbcdaccbbdbccdabaadabddbbdbabcdcdcdbbdcdcdabbbbdcdcbbadbddadacccdadadcdaaccdddabddcbaadcaadacbbdadcaccccabcdbdbbcdaaccadcabbbdbdcdbcdabacacdbdddabdcdcdadbbbabcccbdbddbdcdabdacbcdccbacacabbbdacdadccbdbcccdaacccdabddcacbbbabaadaacacddcbabcdddbbcdabcacadabdaaaddccacacdaccaaacddbadcdacacdbadadccadbaabbbaccbabcaddbbdbbcdcbbdaaaccaccbdbcbadbdcdbddbdddacdabccaaabddcacacdddbadccabcccccbbacabdcaabadacbbbccccdcbcdadabadcbadadbcddbaddcccdbabbddaaaddbcabcddcaaccbaddbbcacddcdddbacccdcdbdddaacdbacabbaacbaadccbadbbddcbbddaccbdabacabbbdcdcadabddabdbbdccbdcbddcddaaabcabcaccbabdadcdabcdddbdaddbccdccacdddbddbcbabddcbbccdbdabcbcbaabccabdbadacaaaabddbcacdaacdadddddaadbddddcbbbbaddacbbdbcdcbadcbdccdcdddabdccddcdadbdaaddcbddbccdcadcccdbcbaddaacdcaadccacbbbccabcdacbabbacbddbbaabddcbcdccbdaabddcbcbbdbbdbaccbaacaccacaccbaabdcccdaaaddcccaccababacdbddbdadabddbacdbcdcdbdcabccbbdadaaacbbbcbdcccdadcbbbccaadaabcbdcccadbaddaddddacaabbcddccbdddbcbbddcbabcadacabdccbadcaaacbabaadabcbdacddaabbcabccacacdbdcabdbaaddababccabbcdaaabbadaccbdcacbdbcabddbdcbaadbadbddbbacbadbddddbbbddbcbccadbbaccacbdacbddbadacccccbcabcabcddddadaaddabcbdacbaaaabdadcdbbadaabbdabaababddbbddacdccbdbadacbbcdcbbdbbcabcabcccabddbcaaaacabaddccbadcdabbadcbdcbacccabbdbaadcccacbabccdddbaaabbcbdcdbdddaadaaaddcbdaddadaaacddacbbdddbddccdcababcdddccdabbbbcddaddcdccbaaaaabbbcadccdbbadccccdacbdabbddcbbdbacaadadadcdaddadbcdcbcbbbadaadccdcbabdbadadcccdcdaabdccbacbdccccadbddbaabcabdaaddccbcacaadbbdcdcadabcbcdddbbbdbbdbdccabdadaddbadcbdbdbadadaccdbcbbdddbddcaaccbbccccacdbdcbabaddccbcbbccacdcbaabadacabdccbddddcdbdbbdacdaacacdbdcababccbbbdabccacbaacbcdbaccabaccdcdacacdbdcacbaacdabcddcbbbcdbddabccabcbcddccacaacacccaababadbacabbdbdaadcbaabbbadbbdcabaaadcaccabdabbcdcdbcdadcacbaacbcbdbaccddcbdddbadadbddcadcbdcddcbdbbcadcdadcdddaadcbccdcaddadbabcadcdadbccdcdbcaddcddbbcacaccabdbccbdcbdddddaadbabcbbcabadaabcacbabcacdacbbbbdacbddadbbcbaabcaadaacdbadbbddcdacccdcdaadbbadbbabbcaddddaccddbddabadbdacbdaabddcbabaaaabddbdbcdaddacabdbcbcdbbcadcccccccbccabaccccaadabaaaccaccbdbcaabbccbbbbadacabccbdadaabcacbcbbdcdcadddcbdbbbcbaccaccdabababaacdddabcdcacbdddbdccaacdbbaddaadcccbabcdbcbccdbbdaddcbdcadbbadccccadadccaadcdabacbcccacbcdddddcacdacaaadaddbcacbdadadbcabdddddaddbdbdcaaccbacdadadbaccabbbbddbbdbaaabaddbcdabccabacbdacccddcaacadddaaccbcbcabdcbcbbcaabcbdabadadaccaaadadcacbbdabadbcdddcddcbdccbdccdcbadbcdcdcddbbdbacbdaaadadbddccccccdacbbaadadaadccdddaabacbbddccbddcbdbcdbadbadcdaddcdaabcbbbadddbbbcbadbbaccadadbddbcbdbbbcadcabcbbcdbbcbadbcbdbddabdaccbbddbdddabdcbdaadbccacbaddbdacbccacbddaabbcaacccbdbbcddbccadaaddcabaccdbdbabccddcaacdabbdaaacaaddadbddbbddbbdbbbacbbcbdadbdbcbccabcbabccacbadbcacbcabcdccbbdbcabdbdacabbbdddcacbbdccccdbbddccbdbbccdacdbcddaaddcaddbcbabacdacaadbbacaadababaddbcacaabadadddbaddabbddbcadcacadbcddacbacbabdcbbccacabdbcbdccbabbbcdcbadccdbddcbdbddddabaabdbddabcacdaddcbbccdacdadbcdaaddcaabddabbdaddbccddacdcaacabcbcdbdbcaaabcacdcadbcabccabcadadaadcacdcbadaadadcacaaadadacabbdabadbbdacccaabdddabcdabddabdabcbbdcbdabcacdcacbcabddbadbbcaadaadbcaabccdccccdcdabcccbacabcabdabadcdbcdbadabccbaaabcabdbcabcbccdabbbaddadccccdbbbddabcdbaaddacabaaaadbbdcdbdcadacbcbcaaddacabbacaadadababdcbadbbdadcbbbadadcbcdababcdcadbacadccabdcbbcdabcbcadabaacaabbddbcddadacdbcbdaaadcacddbbbdcaaabadbbcbcacabdaadcbcdcadbadbbcabbabdbbdaabcdddaabbbccaabadcdaabadbacddaddbdddbdbdcaddcadadcdcbcadddbdbbbbdbaadccddaccadcaadcbdcdbaacbaabaabcdbdcaadcbabdaadbabadccdddaadbddcdddadddccdabccccddaacbbcaccbcddadadbbdbbcadbaccdcaabadabbccbcbddbcaddadbcddccddcacabdcdadadaabdcddcbbbddaacbabddcdacacbdbbdcbbbacacabdbabdbcbbadcdacdddabbbcdabacbbaaacadbdddbaadbbabdbacbabcbacbddaabcacdbdadabbcbbccbcdddbcadcbbcddacddcbdaacbcbcdccacdaaabdcacacbadcccbbdaccdbbbcdccadbbbacdbbcbcbaaddccaadaadaadcdacbaabacdbabdbacbcdcccbcacadcbabbbccdbcaadbdaadaabbcdcdadcbccdabcbccbcccbcccacbddabdadddcbbcbbcbcaadadadccadadcadcdcddbadaddbdcabcdabacaaacadcbababbcaddcacdbaddacbcbabacdacddcabadbcbcbcadbabdcbbbbbaabdddadbabbbccadddbdbdcbbcddacdbdabbbdbcbddccbdbdddcaadcbdabbbdddbcddccaaabaaaddbcccbdcbdadcbbaacbacadcbaaabbbbbccbdbcaabddbabaacdbddccdcacaadbacbccdcabbdcacaabacbbbdbbcbdcbbaaabdaadbdacbbbbbaadaabcddabaacaabbdccdcaccdaadacaaaccabcdadddbddaacadccccbcbdacdccadddbcdcdcbbbdddcaadbdbabcabbdcdacbaadacccabcadcdbcbacdbccbcdabdddadababcacabbdcabccababcccaddcccabbddccdbbcbbcaadcabadcdabcbbaaacbadcddaacddbdccbdbadbacddadcbcccbbdbacddddaadacbabdcdadcaccaccbcdbdcbbdbcccbaabbcbbddcbbbabccbddcacaabbcdacacbbbcaabbcabadbddabbcacdbdaabbcdccdbddccdbdacdaacbdccbdcaabcccabdcddaccbdcbadcccaddbcddbcadcadcdbcdaacabbadbbbcacaacbcdccbddcababcbccccbbcbcbdcdcdababbaacbacaddbdbaddccacdbcdbdaacacbbdbccccbdcacbaabcbabadbcbbadddacbccdacacdbaacbaacdbcbdbcacadcbdbacabbddccababdbccbbcbacdddbcabadabadacdacdbdccbccccdcacbadccdadbaabbabcbadabacabbaddcdccbcbbababbbbbaacabbbaaaacabadddddddaaadcacbabbbacabbdbdddcdddcccddbdbbdcbbdccdddabcbbdacbccdcacadcacabaabdbdbaadcbbbdaabcdbdccaacdabcdbddaacadbdcabddccdbcccaacdcbdcaddbbddbadbaaacbaacabdaadbadadadbcacbadabaaaacbdcbddcdadbcdcddbdbaacdbbadbdcdbaaccacbcbdccdcdcdcbcbababdcdacabbdbaabcddadadcbcbdabbcdbdadccbbcababababcdbaaadcbbdcacbdcdbaabadbddabbbbdbcbbcbadaaaddbaabbbddbdcdabdadacdddcbbaaadbbdacbbbcdbaaddccadadadadcadadbbddabdcbbbdcadadadacbddddabbbaacabbabcbdaccadacaaddcdbcdbcbabcddabbcbddcdbccdccadacbbdbdadababdaccaccdbcdaddcdcbdaaaaadbabdcdbccdaccaadbcadddbdcaadbbddcbcbdccdbaacaaccabdadccccdaabcdddccacdbbacbdbccccacacbddbdabcbabbaaacbadddcccbbccabaccbaadaabccdaddccddbbaaaabcbdbddaadbcbcbdadaadaaabbcbdbcccdbcdaabdabbdaabaacacddcbbdbcadbcbaacddcdddaaaaacdaadbbaccbcbabddbbaddbdcddabadcddbdbaaacbaadccacbbcdaaadbbaadacdcbabadaabbdccccaddadddabaccbbbbddddbcbcbddcdcbdcdadcacbbcbbbcbbdaaacdbabdabdcabacbbbbcccddddcbddabcbcddaddcbadadbdddcbaddaabbbbbdccccadbddacbdabbabbdaccbaacbadcadaadbdbddcabadacacdcadbdddccccadbbbdbddbbcbdbddbccbccccbccbbbdbcccbddbdbaacdaccdbcadbcaacabbccbbcbcabdccbbcacdddbbcbbbaaacdadacbcbcaddcaddaacccbcaadabadcbbcdddbdddbadbdddcdbadbaabdbccacbaabdbaddbaddabcbcdabdbdbcdcabbbcbcbcdddcddcbdccbccaabbcaadccabccdbbbddbadddcacdcbcbccdbdbbbdbbbadbdbddbacaaccbbaddcdccbbbaabcddaababaabdbbcbccdcacddbbbdcbbcccabaaacbadadbdbccdacbaaadccccdaacdccdcccdbaabcddcdaddbdddddccdcacaadabdbbbbbddbbddcbabdbacdadcabbabadbbbdbaacdabacbdabaabcacdadcbabdbbbdbbcbbabaddbbbbadcbdddccbadcccdccbadccddbbabaabbdbbbaaadadcbcddadadcccabcdadddbcbdcdbcacacbadcddaabdabccbaaabbdcabddaccbadabccacddbdbabcddadbbccdbccbaaacaacaabaadbacbbdcaaadddacddbccddcbbddcdaaccadaaadbcabadbddccbccacbdadaacaaadcddbabdcccdcbcdcaabacbaccbcbdabdcccbcdddcadbadcdcadadbbcdabcacabbdacdbaddcdcccaaabdabcbaccccbababaaabbcccccbbadbabbdadcbdcdbbbddabccbbdcbcbbcbbdddcccabcdacdddbddcabbcdabbccdcadabbdbccdadcdcccbbbadbcbcdcbddcdbccaaddbdadbbacdcdacdcadbcabccbbabcabbbbbaacdbaddcbbdbbbbdabddcaadbdcccccdddababdacdddcaaaddcddbbaadbbdbccdaccbcbaaabccabcaabcaacbbbacacaacabaabcdccbdbbbabcadddcdabbbdbcddccbdcdcdaadacadbacaddaddbbaabdcddcdbdcddcabddbaacacccaacdddadcacbbddbdabccdaaccacaaacdaabbcbbccbcbccccbaadcddbdbbaaccdbdadcdbaabdccdaaabddddddbdcabacdcddcdccdcdbadbbacadaaacbbaddabbabcaaacdaacccbabddcbddbcbcabddaddacccaccaddabdcdbdbabcaacbacddddabcbaabdbcbddacdabdcabadbacbbdacdddbcdcacabaaddbaacddccbaabcaadcbcbaacdbdbdababaabdccdacddcaacdaabdacdcbbdabbbdcbccdcadccacaadabcdacccbbdddbdccdcdcaddccdabccbcbcaabdacbdbcdbbbdbcbdaccccacbccdcacabbbcccbacdadbcbcbcccddddbacbbbcaddcbddccdadbbbbbcdcdacaaddcadabdddaddabbdcccbbcbabbbcbadabbbcbbcacaccadbcbadabacaaddacbabbcdbdaacbaaddaadccddcaadcadcccdaccbcdcbcacbdbbbabcdbcbadbddcdaabcabcdabdbacbabcdadcbdbbbbbacadaabbbcbbdaabdbdbbabcbcbcaddabccdacbdbaddbbcdaadbdacadbbdbaddccdbbadbcbbbcdaccbadacdbbcdccababaaccacaadabbcbaaaaabcdbdacbdcbbadcbabdabccabdadcadbadcdbcbdccddacdcbbabdddcbaccadbadbbadbbbdadbdbabaabcaacababadcddddaaaabdccdbddbacbabaabbbdcbcddabcccccddaccbcacacbddaabdaaacaadbcdacdabbcbabbbccabaccbdadcaddbcdbacaccadcabcbcaddaabaaabdbbbaddadbaccbdacbdaddbcaabacdddbdadddbbcdbcbbdbdbdcbacdbddbdacbdbbbdbabbdbaccdaacdaacbbadddbcadbddbcdbbdabddacddababdaccbaacbbdadbcbccaccdbccaacdcdbcdabccddbbccacbabbdadaabcdaaaabbccdcbabaabcbaabdacdbdaaadccababbccaacdcbbbbdbcdbdacadcbabadabbdccbdaacaabdbdcadbdddccbcbddcbaaadbbcdbbdcabdddcccadbaadcaabbccdabdaabbccdddcaccdccadbbbdaabadbcadababaccdcccddcadbacbcacdcbabdccdcdabcdacddddbdddababcaaacdbdbaadacabadbccccdabadadabbcdcabaabacabaccbcbbbacddcbbaaccaaccdbbacabdddbdbadbabcccaaabbaaacbbbdbbdcadaadbbdcbaabcadcbacdcbaaddcacddbbcbbdbbcdbbcdddcdcccadcddacacdcbdccdabadaadccdbccddcadbdadbcadbcbadacbbddcadcaacdcdacabdbbbddcadbdbcadabbbaacdbadcbaabccdacbbdbdbadbdbbdbddaabaabacbcbdabccddaadacbbdbdabbdcccbccbdbcbdcdcbacabdcbcabcbacacacddadcdaacabddbbabaddbdbabaaaacdabcbddcdddcadbdbacdcbcbabaddbcaacdbaabcddbaadcbdbddbbcbacbcbcabccdccdcadcdbcdbadacdbbddabacddcdadbadacdbbdacacabadcaabcdabbdabdcbbacdcdadadaaaccbcdbcdbcabcbcbdbabcccabdacbbbcabdadabadcdaacdadaaabbccdcdabacdcadcdaddccdbdbbcdaddcadbbbdbadcdabbacbabbcdcbddbcabddabcdbcbbcccbdbdacdcbabdcacadcbbbabdbadbacaadbbaaddabbcbaddabbdacaaaacbbadcdddbabbcaadbadbcdbddcaabccbadcadccbaddbababcdacdadbcabbccbabaacbbdaabaabcaacdbbaaaadbacbdddbdcccccbabdbbbdcabbbcadadcacdbaccbcaddcadcaadbcbbbcddcdbcdccbdbbbabdaadaccccdaccdbdbcbcccddbbadaccddacbddcbdbabbabcbcdcdacbbcbbddbcadbacbdacbbdcabccbbadadacadbcadadbdbaabaddcdcbdaadaacdabbddcbabdbaadcbddbacadaabbdcaabdacdbacbbbaddacbbdadcadabdcacbdabcacbaaacbccdacacdcbabbbdbaacbdacacbcaddbccadcbbacccdbcababbdcadcdccdaaddbbabdcaddccdcccbbcadbbdbbadadabacbdbdbbcbdccccdbdacccccacbccbbccdaadbdccccbadddddabadadcdbddbaadcacdacbabccbadadabcacddcbcdcdbabadbbdddcddbbdccdabaabadbaabdbabaadbbbcabdabdddacccaacdbcdbabcacbbbbbddcbdbbadbbdbcddcbdaadbaaaccbaabaddaacdcbdcbcbbbddcacadabaabadddbbbbaccabacbdbabbbacbcbcdbbbabdbdcbdbadddacdbdbdaaacdcbabdcdbdbacccddbbcbcdcbcdbcdacacaaadbbcbadabaacdaccdadccdbbcbbaccdbdaaacacdbdaddbccddabdcdabaabcacbacbaaabadbdabcbbccbabbdcabddbabadbcabacbbbadcdcbbaddbabdbcbbbacccbdacabaabbbcbbbdcbcdcbadbddabcccaacbbadbbaabbcabbaaababdabcacbabacdbdbdcabaaddccbdbbadaadaccaccababcabccaddcbbddbdbcdcaaaacddaadaaaadcaccabababacacbcbcddccbdddbaabcabbcadcbbdddbcbcbdbbcaabdaabbdbabacaddabcbbaaaccbcdcccbabcbdbcccddcdbdaddbaddacbaabaddbdccddccdbbcccaddaddbacdccdbcdababbaaccbddacaadddacadbccddbbdbaddbcdadcabcbcdbddbbccdcaabcbcbccdcddcdbbabbabcbccdcccdccdbdbbaabbdabcdddabcdabcccbdddbcdaddbabbddacccbcacabbaacaaacccabbbdbcdcccbbbdbdbbdcbaaabbdacbacdaccabbbbcabaddbccaacabdbcadcdcdcdccbaabcddabcaccdbcaccdbccbdcabaaadbabbcadbbcdaccccbaabbbcbaadbdcccdddacdabccdaaacdabcdbabaaddaaabcddbddadaababcdcdacbacacaabcabdccadcadbbbdaabaddacacabbddacdddcbbabcdcaacbacbbadaccbacacacdcabddbcdbdbaacacbcddddcaadbbdbacccddbaadcddcbbaccdacdcbbbdabacddbddbcddababacccbdcadaaddacaaadaacbdaddacdcbbddcdbcccacacdddbaaaacccbcaabbbadbadaadbcbdaabbddadddccbaddbacdabbbaddbccacdcddbcbdcacbddbabbcdcdaaaddaccabdbddcdaabbcbacaccddcdbcaccbaddabcdcdaaddbadddaadccdcbdabbcaddabdbbbaacbabbaddbabadcaacdbbbbaadcbdcbdccccabdcbdddcbcabacbaacabdbacacaaabcaddbdaccbdadcaccbaddcdcdcbdabbbaccbaadbcdbcbacabacacbbbdacdacbabbaaabbddadcdadadccbcbcdcdbccbabdaddbdbcabbdcbdacddbbadccdddcddbdaabdcbbddaaddccbcbcbdadcbcaddabdbcbccdcbbcddccddabcaadbaaaaaddbbcbaadddbaabcaacbaddcaddcbdaaddaaadbababdddbbaaacbdbbccdbcaaabddbbdccaabbdbccaccdcbbcdbabccacddcdccdaadacacbabbbbccaabddcabcadcccababbcbbadadacadaccdbcddaadcdbcdadbddcdcdcdbabbdbbddaadbbbdacadcbbbabcdbaaaddcadbaacabcadcaccbcdcacccdcdddbbccadcdbbbddccacdcacbbdbacacbabbdddbbacaccbbcccaccbacacdcaacbdbcbabcccbdbacbcdbaddcaabadaadaabadcdbacbccacdcaabddabdccacdabcbcdabaccccdcbcababbcdddaddbbccbabbccbbdaabacabdcdbcdcccccbcabcbacdcbaaabccbbaacbcdcaacddcaddaadabbcacbbabcbaaccdbdbccbabccbbdbadaaaabcdabcbddcbbccacadacdcadbbaddcbabccacacdbcdabdbbbcbdcbacdcacdcacbcbbaddacaacabdbdcacdabdbcbdccaccbdccaddbcbcbcddabbbcccbdaccacdcdbacbbcdcccbadabbcbbdcdaabbbddddbbabbcbcaadacbbdbbaacddababacdbbacbcabaabadbbacbddabbbbcbadbaccccddccdadacbdadddbcbbadccacabcaadbaabbdddbbbcdcdddccadabdcbbacbdccbaacdbdcdbadcaddbcdcbaabdcaacccdcaccdaacaaacabdacadccabacddacadcbadacccdacdcbaabcbccbdddabacaabddabbadcbccdbacccbadaadcdcabcadbabbddcabbcdbcdbbbcbdabbcdcdcccdadaccbbdadbddcbbddacbabcabbacdabbcbababaacabcccaabbdbaccabdbcadcaabdbcaaabdbcadccadddabddcdcdbacccdadbabcaaabcacddabccaccacdbbcdccbaadddbdcbadcbdaccbcbbcbaddbaccbbdbdbdcddcdadcababdbbadadcddabdcdbbdbacdabdacdacadbbcdddabdddcbaabacbdaacaddaabdacadbdbcadabbdabcdcabdccaccaadbdccccbcdbdccabdbcadccaadccadadcbcaabaabbbbaabaacaabbacaacdabbdbccabaccbaccabccbcbbcbccccccaaadbcccdddbacddcaacaacadbadbdddcbdbcbdbdcdabdbbbcccbdaddcbabcaddcbabcdabbcabcdaccbddcabddadadcbdaccdadcbcabbcbccbcadbccaabccdcadbbdadbaadbbacddcccbdddaabaacbdcccddcacaababbdbbddbbacdbadcbbbaddaacaccdbdabdbbccdcabacbcdcacccbdadcaddcabbbabbacacdbcbbddacdbdbcacccdaabdbcbbdbdbbcadaacbccadcbbdaddabcdbccdadaaccababddbdbbacadbacadddddcaccddabbaacdaaabbbbbdabcabbcdcccddaccdbdabcdccbbaaddccabbcdbbdbcbdabbbcadabdbdcaaaabadacdddcbcdacaacdabaadabbcddccbaabcdabcbabaddcdcacdbacdccbaccdaacbccccdbbcbbcbdaaadbcbcbddcabcdcaccdacaddacdccdabcbbabbcaacababbdbbadbdbdacbbaabdbbdacdcbacaabbadcdabadcdbdbdbabbcdcbcbdabddcbcdaaabbddacbcdadadcdadbbccadbbaccabdbbdcccabcbcccbbdabdcadddccbadcdbcccaaabdacbccccaabdacbbacbcdbbdaadcacdabccaadcaabddbcdcddcddcabababaddacdcadccccbbbdabacbdadddcacbbdacbdbcddbdabdcdcaadddbadddbccabdadacacbbbdcdacdddcdaabdbccdbaabdaccdccbddddcbbbccacbbcbcacbcacdddacbaccaacbacdabdccccdcbcbccabcdadcdaacbdabccddcdbaabdaadadcdbadccdbbddabccdbabddcbaacdcddcddcdbbcbcddbabbbcabcdabdacaaaddaacbdacadbdbaadcdaddaccdaacdcacbcadccdddcdadbabcbacdccbddbcabdaacddabcabaadabaccbcabdcaabcabadaadcabcabdbddcdcddbbccbccdacddccabcacbdabacbdbcbacadbcbdaacabcabcbddccdcdabccdbbaaddcbbbcddddcdbbdcdcbcdccccacabccabbaaaccbdddacdbaadbbbdbbdaacdabbdccbcaabbdcdbbcbdabcbdcbbaadcbbbadabbdbccdaacbcababcadaabcccdaacaaaacbcaaddacadbdadcbbddcabacdaaadcadddcadacbaababdacdcdabbbacbddbadaacccaadbdddabaacbdccbaaabdbcdccddbcddcadbdccdbacccaacbbacdccdbbcdbacdccbacabdbaaccbbdcadaadabbdbdcbbbbcababdccbaaccbbbdbbacbcababbdbddbccadbacbbbbdccdbaabbabdbacacdbcbdcdaadbbabadbadabbcabadaaaddcdbabcaabadaaabacdcccdbcaccdbbaccadcbdabbabdbcdddbcbbbcbbabbadabcddbacbdbccabddbdbabaadcbdbabaccdbcacddcbccacdcadcabdbabcacacaacbcacdaddaacbcadabadbdcbbddcddabbddbdbdacdddaabbbccdcacbabaaaaddcccdcacdccccdccdcbbbacccaabcbcaccdcdcacbccccbcccabdccabbbdbbaacbbcbdcdbabbaadbddaccaacbbdbddbcdcaaabbddddacdccbbabbbccbacdbbdbacccbdaddcbdaccdbbbdacaacdcbcdacaaaaccbbbbdaacdbabcdabbbcddbabbbdbbbacadbcdcbbcdadccddbdbcdabbacabacabbcdcbdbbaadcdcadacadcdcbdccccccdbabcbbacabbdadadcadbabcddbdbbdbdcbcdcbbbbcdcaccbadccdbdaaadaccdbbdbdbdaddaadadcadddbccacbcddbabccbcccddacddbbccacabdadbabcddcdccbddbbadcdabbbacddbadcdcccdaadbadbcccbadcdadaacbcdbdbdbcddccaabaaccddbdacdbbddbcdbcdbabdbbbbaadabcdaccddbcdcaccbdccabcbacbbbdadbdbbbdabdcbdcaddcaabadaaaccabcabbabacbdcaccdacbaabaabaadccadabbadddccbdaacccdddbdaccbadacacdbabacdddcbdccbacaccccbbbbdddccabccbdcccacbaaaccddcdaaaaaadaccbcbdbaadccaddccdbdddbdbbbdcddccaccbcacbcccabacdcdbabbcdbcaabbbdbbaaabbadbabaadcdacadbdcdbbcddcbbacddbaccbcbbaccbbcabbbbddddbdcbcbdabcbaaccaccabbaadaadadcabcabbdddcdabdbabcacaadbccccdababcacadcaabaabdadabaaaaaddccdadbaacccdbcbabcabdddcadadacadcabbdbabdaababaccadaccccaddbcccdbacaadbcdcdadcabbbbcddabdcdcabbbdaddddbdaacdbdbcacaaacbcaaaccdabbddcdbbcddbbdababbbccccdddacbadbdaabcabcdadcadbbcddcabbbcabcbbddaadcddccbbcccabbcdcdacaaaddcbbdabbacaadabccbbbaadaadbcdcaabbbdaacdaddcbccdbbdbbdcdadaccddcdcbbdacbbccbcccaccacdaaabdbbbcaaccaccaabbcacccbabbaabddbddcbbacccbcadbaadadbadaaabaabddcbcbdabaddaaadcddcadcdaacdbbaabcacbcddddccbbaaddbababcbcccdbdcccaaababddccacbcdbbdcadbcccdcdcaababbddbdbcdccbdcbadaaabccdddbcaddcddcbbbdbbaccddbbadaddabdbabadadaadbaacacabababacccaddddacdacbdddbbcabccdadcacdcbdacccddbdccadabdacddadcccdaaadcddbaddcbdbddabcbabdbdbabbbdddbddbbadddaacbdcaccdcdbbcbaddbcdacbbdcdcbcdbadcacbadcdaacacaaadcccbbddbbcacabacaccdbcbaaadbabdccaabdcbbaacaccabccddabaaadddcbcbcccdccbdacdcadaacdadddaaabacacddcdbbccbcaddcddcacccbacbcccdccbddabddcabcddaccbbbacdbdaaaddcaaacbbdcacdddcccbbbddbacbcdbccabbabadbaccdbddacbbbdaddddbcabcdddccabbacabbadaaacccdbbdcdabbddaccadaccdadacacccadabbbabbbddacdbdcdcacccaccaccdcdcaccbcdccbdbbdcdccddaaabcdbcacbaadccbaabacdbbcbbbcbccdbcddadaccdcaaabadccdacdcdacddddbabcaddaddadadddaadacacdbcdbaaaddaddacbcdbacaacaddbcccaacccabdcbccbccbbadddccdaddaccaacbbabdbdbddbcddbcadcccbccbcbdcabbadbdacdbcadbddadbbbacaaadacabcbcddbaadbbbcabcbbcabdcdbcaabdcacccdaaccbccacbcacddadaaabbdddbbdaadaaadaabccdaadaaddcbbabbddadabcdaacbacaddcabaddccacabcbdcddccbcbbaacaacdaacdbcbbcaddcbddaabdbdcddbacdacabddcdccdcbbbabccaabdcadbbcdcaddadadccacbbaadddcabdbacaacbbddbbdcdabadadbadccdddabacacbabdbbbcaabdbcdddccbdadcadadcdaccbdbddbbbbaccacacadbaaddabbacaacaabaaaacbddadabcdabdaacdaddbaccdadababdbaabadcdabbabdddaddcaddbdbadcbbacbbbddaacdddaddbbacdabcadbccccbadbaaadccaaadcdbccdccccdbcabcccdbabcbaddabcbcbbbbadbadaacbdadacbaccabccdbaabacaadaabdcaddbadabbcbdacdabdcddddbaaadcabbabbacadabaddcacdbcbdbcbcdcaadadabcbbcccbccccbddaccdbcbaccabccacabcadbcdddcbccbbcbccdaccbcaccdbcadabbacbbabddbbcaacdbaccaabaccccdabccdbcbddcbcacdbdacadabcbccdddcbdddadaadabbcdcaaaacdcabcccabdaddacbdcdcbcaacadcddbbdbdcadbbdbbcccdbbcacabaabdccacadadacbddccacdcbaccabbcdbcccacdbdbaddbaddcdcdadbddcbddcddccdabdbdbabadccdddddaadacbcdcdbbcbaccdbdabcddbcdbdcacccccbbdaadcadbbaabbbbadcacbbaddabbadbacdbcdaabcddbdbccabdccbacdcddaddcbacbdcdaacdbddbabacdbadbadccddadaccaddcbdbbaddbcdcbaaaabaaabbbabbccdcccdabbbacdcbaabaccccdcddaabdbcadaabaababdacddbcdadacaaaabddbabdbddccaabbcacbccbbdcbccddbbcdcadcadaadbdcdddbdddbccacdbacabcdaaccdcbdaccabacacdadbbdadaacacccaabcccbcaddddadccddbddcbaabcddadbbbcdabaaabacccccbbdacddbaabcdabdbdabaccdbcdcdacdcbdcbaaadcdbddbcddaabbacbdccbbbdcccdccadadccbcdcbbddbdaadaccbcadacdbabcbdaddcbaabbbbabcaacbcdcaaaabbdbdccadbbdacaacddbcddbdaabddddcbcccdbbcabcadcabacbcacdabbcacbdcbdbdbdaabbbbcbdbbaacaadaaacabdacdcbaddacadcabcdabbcddbcdbddddbddbaaaadcacdccadcbcbcadabdadccddacccdaddbdadcadadaadcbdbcdcacbbadcbdcaaaacaacbbccdadcbbbdbcaaaaacbdadbacabdddddbdaccdaabbbcadcadbdaddcdcacdcadcdbdccaddaddccbabaadbbaacbcddabdddadcccbbabacccaabcccddddcabccdcccbdcdddabddcddaadbbabadadaacbbbacacdbbcdddbbbdbbcdadbaabcddbdabbddacddbcccbbabdbccbaadcabdcadcbcaddbaacddaddaaacddcbbdbddbacccadddbcbddbccccdadbbdaddaabcbbbccaadbcbdbabcdaddaadbbbcbcddacadbbdbaadbacdccdcccadcacddcddbdbbcdacaaaababdddccdbcdadadbccdbbdbbdbacdcacbbdcccacbbbdbaabaaddadacccdccdaadabcaddadacbdcccabbcbcabbcadaacabbadcccdacaccbdabbcacdbcdabbcaabcadbaddbbbbcddabcadadcbabbbbcaabdabbccaaccacacdbcaaababbbcacbabcbaccadcbcadbccdccdabdbbaddbbbadbccbacddcdbddcdaaaccdabdccacabacdcaaddbbcabdadaabddbcabcdccccbabbcdaaadacbdbbccababaabacdcbaccbcccdcaaddccccbcbbddbccabddabcacabcadbcbbdcacbbbdaaacadcdaacdbbdadbacbadbccbdadcccabcaacacccaabdccccabdcbbbdaacadbbbdbaababaaabdaccddccadaccdadbbbcddcccacadabccabacadaddbdadcbadbcdadbbdbbddcbbbbccabbccccbaabdabbbaabccdcdbadbbccbabbbdcbdcbabdcbbabbaaacaccdcbdcaadcbdadadabcaaacaddbdcdacbdcbccdddaccccbadaddacbaddabcbddadcbcdddaaddadccdadaabdbbacbaaddccacbddccabbabbaddcaacbccabbccccabbcaacbccacbbbcdbacabdadacaaadccaabaadcddbccbcdcdaaaccdadddbcadcbccabccdaccadadcaaadddbcbbcbdbcbdcdcdaccddabbcccbccccadcaabbabccdadcaddcaaccdbdccddcbcbadaacdbcadcbbcccddcbbaaaaabddbdbabcbbadadbcabccdcbbcaabbcabcabaaabdcaaabdadaadbdaccadbbbacdaacabdcccdbbcbdddcbdbbdbadacbdbbcacccbbabacbbbbdccadbcdcdbdbcdbdabcbbdacdcccabacdbbcbacdcabbaccbbcacddabdcdabadaabacdcbdbccdbabaaadbdaabababacddaabababaaacccababcadcbdccabccccddaadbddababcdacddadbcadabcccdaaabcdaadcabbdbbbacbdbadbbbcdacbaddbcacccdbdcbdccbddcabccbaadbbbddbccbdacabbdbbbbabaddcdbbbadaacdcdabbbcabddacaaaaadaabbbcaaddbabbdbcbabbdbbbdddcdbabcddabbbbdddbabaabbaccdcadcbaabdadbdcadbdcbdcacccdbacdacbdbcacbbcadcccbacbdcbbdccacdcdacacdbccdaddadbcdadbcddadbabcccaccdbcddbccddccdaabbababccdcbbddbadabdcdccacbddbcbcacbcadcbdbbcbdbabbdcbdddbcdcaadabaccbababacdbbaaddacbcdbcbbcbadadddbabcdccccdcbacabdabdaabcbcdbdddaabbcdadcaddbaaacdaababcabccbcbdcaddabaacddbbdaacbdacabaabbaacbbbdabddcbddabdcbdddabdacccabbdbccbdabcadbddbbbbdbbabdadabcadccdbcacdadcaddcdbccbdcaacdcbcdacddbbdaacccddcbddbcdbadddacddbcadbbacacbacddbbacaaabaaabddcbcbadbcaddbdcbdcaddabbbbbaccccdccbddbaaababcbaaacbdddbdaddadabacbcdaabddddccbcacbaabbbcbbabdadbdccccacaabbccdcbddabbdcdabcbbcbdacdacdaabaadbccdcdddbccbcbdcbdadbbbdcddcbdabdaabdcbccacdbdaaccdbadbdcdcbcdbcbcdaaaabaddcbdabdadcacbbbdbcbacbccccccacaaabccadcdbbdcdbbabaccadddabadbaacbdcbbccdabdcbababcbdccbdacbdcbbdcdaacdbbdccaadcacacdcdcabbacbcbcdbdddaccdabbacaabaabbccdddbbdbadddaccadaddcbcaadadbdbcdcadcdbaaadcbbbcadcaaddbabccaccacaadcbabdaccaaabbbaccbddccabbdbbcddabdbccdadbbdcdcccdbbabcbcadcdbddddddbcccdadbbacdbcbcdabdddcdacbdaaccbdacdabbacacaccdbbddddadacdcbcacbccdbababccbbbbacbbdcdbcdcbbcdadaaccaaadbabcbbbddaccccbdababdcadcccdcbbbaababcdcbbcdbacdbddbbdbcdccddbadcbbdbadcdccdbccdcdbaccbcaacdadcaaabdbcbacbababaaaadbddccdbcacdddadaabcacaabbbccadbcaddccabbaadcbbcdbdbbadbddacbcaadbbaabadbcbaddcaddabcdbaccbdbdadddcdbdaabcbcdbcccbaccdbbabdabaddaadbddcbccdcbbccbaaddaccbbacbaadcaabaaccbbbddbbdddaccbdaccabbadbabdabacadabdadabdcbcdbbdbdddcbbdacdccccdbdcdadadaacddaccdcbbadbddbcbbbbdcbacccdcddabcabccdcaabadcbbadabaccaacdcadcccaddcdbdbdcbbbdabadbbaacdabccaaadaaaabccbcaacddccabcdacacdccbddaacdaadacadbdccaaaacddcdcdadbcdacbbadccddadacddbddaabbbaabbcdcadadbbacaaaabdbaabcabcacbdbdcccacbbddaadadabccdcdbbaaccdbbaccccbcacbdaaaddaddadbdaddbbdacdbacabdabccacabbcaabdaadbbcabcdcddcbdcdaabadaabbaacdddbcdcababcabbdddaacbdabbbddcaacddbccdbddbdccccbddadbbaaddaabbbccaddddbdbcabcbabadadaccaabcdaddaabcbabababacdddbdacdacabdcadaabddbdacbbdadcbcaccdbcdcbadcddadcaaaacbacacbacbcabbddbadacbaaddbbdbcdbadcdddcbadadbbbdcbaccdacdaadacbcdbdcdbcacbccbbbdbcdbcbaccbbcabaaccbdddcdcdbbdaaadccbabdacaaddaadabcaabaddcbadcdbbbaacaaaaacdcbdbdbdbcabdacbbbdacbdbbdbabacccdbaccbccddadaacadadbcbcaccaaadbcbaaaaddbcaccabbcadaadbdabdcbdcddaccdaabcdbccacbcdcaadcaabcadddbddabbdbbccbcbcdbcaaaaabccdadccbcabddcbccdccdabcbccdccdcbcdbdcdadcddaaacbbbcbddddadaababdcbbdacbdcdabdbabadccaddbbbaccadabadbabbbbbbbcaddcddbdbcdbbddbaabbaaacbadabbdbadcdcaaaccdcdbbacdbcbabdbadbcccbbcdbdccbcadaaccabdbccccadbdbdaadccabcacaddddbaaabddbadddddadacdbdacacbaabadcbccaddcccaadbccdaccdabaacdccdbddcdabadbbccdbaabdbabbcdbadcbabdcbdbdccabdcddbadbadaccabacdaacabacbcdcbddaadccababaacccbcadaccaacacabcbbdbcbdabbcddbdadcacacccadabaaadabbbdabaaaddaccbcbdbacccdcddcddbcbdaaddddbacbbdabbdbcdadabacacccacabaaddcbccdbadaaaabcbdacccadabdbcbbcababcdcbcaddbabbcadadacdacbbcaddccbcdadbbdacdbddbabaabbcabacadabbbbdbabddbcdccacbcddbaadaabbcccacabddcacdcddacdccbababddbcdbccabcbaabadbcdddcabcabdcbcabdbbdbbcabaddcabdbdcccaababaadbbabdbcbbadcbcabdaaaacaddbdcdcabccacadcbadacbdadadcdcaadaaacdddcdcadabbacddbacbbabdcbbdddacadbaadcbbbdcacdadcbdcacdabcbbadadcbcbbabdadccbdddddbcdabcbcdddacddaddccabccdcbaaaadcbdbaadabbbaadbcdcaaadccdbccbbadbbcacadacadbdcdcbabbbdabadcaaadacaaadacdaadabbdccdccccaadcbcacbacbdcdcacbcaaccbcddcacabbaacddbacbacaccbbdacddcdbbcbcacbcbbdbcaabccbacacbbcaaccbdacadcbababadcadbbcddccbbacbacbdbbabcdcbdaacdabbcadbcaacadcbadccacabbbababcbbbddadadcdcbcdddaccccbcacacabbbaddaadddabaadcdbbbcaccbddaaabccbbccccdbadadadbadaadbbcbdbacdcccdbbabccaacccbcbcbddbdacacbccbbcbadaadbcbcdcbcaadadbbdcacaabadabdcbdacdbdcddabadabbcabdacaadaddacdddbdccbbbaaaabdadccdacdcabccbccdcaddcbdddcbdcccaccdbbcddcbddbbdcdcadabdaddabbbdbbaaaccddaaccaabdbcccddddacddcabbbccaccbcacbbcabbcbcbbccbdcbcdccbcdbacbdaadadcddabccbdabccaaacddbcaaacbadddaacdbadbdacddcaacadcdbabadcdbbcbbdbdacbccacbbcbacabbaacbbdaabadccbbcdbbbcdadabccdadbdcbcbcadaadccdddbcbaabbbddbccabdbcdaaddcbcbbccabbbbcccaccdcdabcdabacdbdbbacccbacadddccddbadbccdccccdaddaaddbdaacbaabbbbddadbdabdbbcbbabbcbdabaadcdabdcdbcdadcdbcabcacddccdabcacadbdbacabcbbbdcdddbacaabadcbabcbacbaadaaaacbacbdcdccbdacaacaddacdadbacbcbdabbdadaadcacdddccbbadcddddccbdddccddbadcababbbbadbdcadabcbcaacccdcadaabbdcdbadbcdddabdaadcadcaacabacacccaccdaadbbadabddccdaabdbbcbdcaabcacabdacdbbabcdbdcccbaabbaccddcadcdababbaaccaaadbacbcdacbbdbbacabcdddcadddddcaabcdcddccdddaacaabbcacdadacadababcccdbbbbbccddbcbdbdcbcdaaadacdbcbdcdabacddbabdddcabcabccdcdacccaddccbccaacdbbaaabbdbdcdbacccbbddbcaabcccccbccdbdcacaacbccaccabdaacccbcabcaccbacadaabcccbababbcdcaaddcabccdaccdaccccaaddbdbabbcbcaddcdcbdabdcdbdcabaadabbcadadadcadcacacaddcbcadacadccdcacaadddcbbdccdabbdabcbcdcaacbbdcccddbacccbdbabbabbacadbaaadcdbadadddadadacdabcdabcbddbadbadabcccacbddadcbaccdcdaacbdbdcbdcbdcbadcabdcbcaddcacabcdabcaaddcbccdbabcbddadcaaccccdbccccdaaadacccadaabacabbaadbbdcdcdcccbacacbdcbdabbabaabddcaabbccdddccbadddbadbabccbbdcabcdddcbbdbbcdcbddbcadbcaccbdaabdbcbdbbbdccccbddbdbcccdaaaaccdacadddccadacabbcadcbdaccdbcbddbcdadbabcdadbabdbcdccbcbcbccdbadadcaddbaadaadabcbcabcacbddbadacbcdcddcbcbaaaddaaccddcdcbdcccabadbddcbcacaacadacdbdbdadacabdddccacadcbadacbdaccbbaadbcacddaddcdbcabddabcdbbcacbcbcdcbacbaaacccacdaadbddbdcaddccabbcbdbbadaddccdaacadabaabcaaccbdadcdbdcaabbbdaacabcbbcbcdcdabddbcbbccaaacbcadadbbdcbcccddddbdbbacaddbdacddaabaaabbcddaabbacbbaccadbbadadaacdccaaccacdddaacabaaacabbcaacbbbbacbdaccdbcccdacaabcdaaccbdadbadacabbcbccddcdccdcdaabddacabaabdcaaddaaddabaabddadbcbbabaabdcdaaacdccaacbccbababbbacdcdabdaadacbddccdbabaabadcadcdbddcdbacbacdbcadbdcddbcaccabbdcdbbddbdcbdddbaccdaabbdcbaaadbcdabcdacdcabcdacadacbddbabcaddaccbabbbbbbbdcbbddcacccbbabddbccadbddaabcadccddabbdaabcdddaadcdabacaadbdaacbabcadadbbcbdbadbcbcdddadccbccddabdaadcbbbaabbcbaadcdcbadbaacabccdcaccaddadccbbbcddcaaadbabaabbbdcabaccabcadbaacbdadddaaacbbaccaaccbbbaddabbbbddddbbcdbaadaccaccaccbbdabaacaaccddcdbbacabdbadbdcadadbdaccdccacddadbacbcaadaaccaadbdbcabbcdcabcdbaacbdadddbcdcdcadddacabbcdbcccabcabbdbbcdbccbcaccaddadacdbabadcbabbcbbadccccccadbcbdbdadcdbbcbdbdacddbacaabcdcdaddddbadadbcbcddaabadccddcadadddcacbaabbcbabcbadccaaacdaaabbaabdbabacdbacacabbcddaaddacdbabbddbdacacadbdabcdcacbaacbaddbaccadddacbcbacaaaabbcbdcabbcbbaaacadcbdcacacccdcccadcdccadbadddaccdbaaadaadaddaaaddcdddadbcbccccdccbaaadbadbdddbbbdcabcdcbcbbaacdadacaabbabbcbdbddacccbbbcbbabbadbdabccabbbcadadacbbdbbbcdcbcacdccabcccbadcdbbacacdbbdacdbddbadbacbacaddcbcdcbccdaadbbdbddbacdacadddbbabbcbababaabbdddabcdccddbcbdaddbaadcbaacacabdbacbbbdcbdacddbbdbaddcdaacaacaabbbcadaddccbaccbddcacabcbbbddcbabdaaacbaacdcdbdbadddcacbcdbbbddbcbccbacacbaccdddbbbdddbcbdcbababbbdcbccddadadcdcddcbddbddadddacbaabbbbbdbabaaadaabdccbbcaadbbccdbbccbadbacbbaadccdcccaadbcaaadcbcccddbbadabbababcdcaadccbacbdbababdabbbaabbaddaadccdcccadbcaccbcbbbcbacdcddbdadcdddcabcaccadbaabddcbacbbbbdcbcadacdacbdcbcbaabdcdbbdcabccddabcaccadabcbaccacaacddbbccbbdcbbabadbdcaabdabacadccddcbcacbadbbaacbadbaacccbdbadaccadaacbabaaadaddcadcddcaaddbcddabaaccbcbababddcdaacaabbdbdddccbbbaaaddbbddbdaacadababadaadadbbcdcbaddbacdabddaacacacdaacbabbbbaabcbcdbbaacabdabbdbadbacbbbccbbbdcaaadbdcadbaaadaaaabbaddddadbbddadabbcadbbdaaacababbdaaacaaabccabdbbddcadaaaddacdddcdbdbaddadddaacaaadbdbacacdbacaabcdbcbcbddacaadbbdcdbcbbdacbbaadbdbcbbdcdcddcdcdbbdddbcdcbcdbaddcacabdcbcccdcbbdbbbcddaddabaaadaddaaacbccdccccdabddbadbcbdacadbabddacdadbcaadaabcbadbbdbadabdccbdabccaaadabacbcbbacbcccbbccacbbbdcbaabdabdbddbbaabdbbabddbdabbbbcddcacdccadaccbdbbbdcaadbbbadbaccdbabbdbbbbacadbacdcbdddcacbdbbcbcdacdacbddcadabbbcdbacdacdcdbbcbcdaddddbacdacdbbccccbcaacccaabcdcadcacbadabcddbacdbaacdbbddddadcbacbdcbbadcaaacddbbdcdaadcbabdaddcddabadccbabaaddbacddacccaabcbdccccdadbccdbddaaccacdacdccdacadbbcbdbacdcbbadddcdacaccaaaadccbcaadadcacbcaddcbbbcccbcccaadcbddddcdccdabdabcdcccdacbdacbaacccabaaccddadbcaadbbcbacbadabaacbbccadbacdddacaaccbccaababbaaddbbabccaabbaaaabdbdbbddacbacbcbadabdbccbbdbbcddabadacddcddcccddcccaccabdcdcdabbbbdbbccdcbbdbbcabdbbcccdacacdbbdacccadaadbacdaaccdcabcdcbaadddaddbbcdcabaaaabbbbaddbcddcadcccadadcddacbaabacbbaddddcbabdcbcacdabddbccbacdaddadddbdcdddbabbdcdccdacbdddcaabcbadbaaccabcdcbbadabaaaddaadcddacbdcaacbdbdacbbcbcdcccabaabaabbabdbccbbddbdcdddacdcbdabdbbabdadadadbbadaaaadcbcbcbcccaaccdabbccdadadbbadcbcaacbadacacdbdcbbcbbbbcbbdddcbababcbaabdaacccdbcacabbcbdabccccadbbaccccadcaddbddabccdcbcccddadadabccbcdcccccbdcadbdbcbcdbbdcbbdaddbdddbdbbbacababadcddadbddccaddbccabcaaadacdccacbadacddacdadbcdcccadccdddcabdacbdadbbcadcabddbcabacabdcdcbdbdcddbcacccacacbcabbabbcbbcbabbdcacbdcacadbbacaaaadbdcbbdcadccdcbddbabbdddcbbadccddadabadddcccabccddcbbdbbbbcaabcacdadbdabddaadabbcacdddbdbbaaaabbbdbbbcbaaadbbbabdbbbbaccacaacbabcdaabbbdcacaaaaadddcccddcabaaaaaacaabdcddacdcdcabccdbccaacdbbbbdcccababddcbbddcabddcbbabbbddbbabccddbaaddcaccbdbbbbdadbbdbbaaabcdadaabddcbcccdbadacbabcaacbabaabdacbdbbcddbcdcbbbcbcbbcccbcbcbacbccbcdbbdcabbbcbbccbdbbabdacaaacabcbadcbadddacdacbbbbbbacddaddacdbdccacbccbcdbccdacbcdcacddbcdbaabdabaacccacbbcdbcabddadccddaacddbbcddaacddacdbacdbbadaaaabacddabddcbcdabadbcdaabbddaaabaccdbcacccbbbabdaadaadacddddbacabaacaacdaabbaaaabbbabbcbcbdddddbdbacdbbabaacccbdbbbdccdcbbbbbababdbcdaaabcdaabbbdabccaaccccaadccaacdbccaacabacdbaddbadbbaccaadccbccbdaadabaabbcdaacbcaccdaaaaaabcbabcabadadcacadbaababbacadbadcdddadbaaccdaccabcadbbccadadbdcdabbabbcbcdbbddbbccadaddccdabcbcbbcaddddbbadccccadacbccbdbcbcbbcaadabbdcaddabdbabcbadbbddbcbadaddbadcccacadccacdaccccdbaabdcdccbaabacbcadabbcddbbaaabcabbaccbbadddacbcbaccccccadbdaadaadbbdcbdddbdcbcbdcababdbdccacdbdcbbbbbbaadddddaddaaaacadcbdddacacccddbbbbbbcacdabacacaadccbbdcbcddabbccdcbacaddadadbdabbcbcacccabccbbddabaacbccdadaadadddadbabbbbbddaaaddacbcbddbbabdddbbbcabcccdbbdcdcacbddddadcbdcbbbbdccabbcdbbbadbcdbdbbacbadbdccbbaccaacbcaaadcadacbccadbdaaababdcadbadbdcdbbadaaadabaabcacadacdbaabaabcbadbcccadbadbbcadddbcabacbbddccdbaabcbccdcdbbadcbbdcabaaaaadcbbbbadbddbdaadbcbccaaadbaacdaddbbbbabdcdadbcddddcdcdabdbdaccdbbaaacbccdbbbddabcacabacbcacbcaabdccaddadabdabdbbaacccdcbbaddacadcdddbdbaabdcbbbdbccbaddccccaabbdcdcdbcbcabdbbdbacadbbbcdabcaaddcbcccacdbdbcdcccdadacbccccdcbaabdbdbccdccbabbcaadbdacabcaddcadbcbacbbccacdbccdaaaccdadbbddbdcbbbdaacbbbcabcdadccbcbcdbddaadcdccbdcadbdacaccbbcddccacdccabbdbadabacbbbbdddbcbdcabaccbacccbacbbabacdddaaadccaddcabdbcbcdcaabbbbbdaddbaaaacbccbbccacdcbabbaaaabdbcbaadacabcdacdabccabbbddbabaacdabbcbdddadbbcbadcccacbbcbacddcdabacdadbacaadcabcabdccccbbabcbcdacdadbcbaadbbbcaadabcacabdacddaababcacdcbacadcbabbaddddacddacaabdaaabcccccadddbbacbcbbcbadcacbdadaaddccabdadaabddcacdbbbbccbacbccacabdbbdabadabbadcabacaababacaabdccbdcacdcbacadcaaacaddaaccdbbcaabccbcaddcdbbdbdbccacbaabbdbdaddcdcdbcddddcdadaaaddbdcddccdbdadabbdbbbddaddbcbbccdadaadabbaadbbdcadbbccaccabbcbcdccccdcdbdcadccddcaacbabbbcbdbddbadcdbbabdccbddddadcabcaaddbaaccddcacbcaababcdacbbddddbbcabacaddccaddcbdabdcbbbcdcbccbadaaadadaacadacccbcbabcbaaadccdbbacacbabcabadaddacaadcbbdaacbadbaaabbabdcdcadbbaaddddbbcdaddacbadbcddbbabbcabaddadbabdccaddacacdcbdccddccdadbabbbccadabcaacdcdbbaccbaacaaaaacdacbddccabcbddbadbbcacdadbcccaabdcbcbabbcaccadbadaddabbadbdbabbcdbbbcaabdcccbcbbdcadcdccaacacbcdbbabbcababddccbdbbcccadacdacacbabcadabbaabdaccabccbadcabbcbdcdacaadcbcbcaabbbbbabdbdcacaddbdcbcbcdccaadabbacacabacbaacdbcbbcbcddbcdbabaabaadbcaadaabbaddcadcbcddcacbadcaccadbbdabbdccacdacdacbcbadbabbbacccdbabddaaddcbdbbabadddcacdcbadbccccbbdcdcddabdcacccdbbbbcddaddddbacacbacadbdbbbaaabaccaabadbcdaccddcaaccaabaaabcdadaddccdabadabdddaaacbbadccdcbbddaaacaacaacccbacbabcacacaadcaaabcaaaadacdbdccbddadccdbaaacacdaddaacabccdaabdaccacdccabcaabddabdbcbdcccddcacbdcacbdaaaddcdbdcdccaddcbcbddcddbcaacbbcadbaaaaaadddcbbbdaccdbacbcbcbdddcabcbcbaabbbdccdbbdddcbbacdaabcbbcacdacbdaddadabdabcbdcbcaccbddaddccaaadbdbaabdcacbddccacadadddcdaadcccbadccbadbaaadcccacadacddaddcbdbaddcacaaccdbccbbacaabdccbcdbcacdaacbddddddabbabdcadabccadddccccbcadbdabaaadbccdcadcdbdcbcccaabcbccdbacdbccacaaccaccdbdccbdbaddcadaacacbdbbdadaddcaabdcbdcccbbccababddcccbaccaccdbdcdddbaadbaabcdbabccdcdcdbdcdbccadcdcdaaccaacdaadaaadbccccdddacabaadcdbcaddbbcadbddccbcddadbadacbdcbcbbaccadcbcbadaddbdcadbadbbbccdbaadbbacdabdbcbdbdccdacbbcabcdbbcadcadcccbdbcbdbdacacacacbddbccbddbacccdabbabbcbaabaadcddcddbdcdacdadcbdbccccdbdabacbaabccaccddacdddaacadcddacbadbbcaaadcacdbabccbbdcadccabdddabbcdacabdcabbdbcbcdaadacdbacbaaaddcacbbdccacbcccacdadbbbdbbdcacabbbdcccabbaadcdcbbbcbbddacccacadcadacbbdcccbdabbdcdbdbddcccdbcaacbbcdcabcabdddbdcbcbbaacddcbdbcadadcabcabbbaaabcadbabaccbccbcbbabbaaccddcadcdaaaaadbcabcaddabccaccbaddbddaaacdccdbdccaccadadbdadbbbdbbdcbabbdacdacdbddddbdbdaaddcccaaabbadcbadbbccbbdacdacaabbbdacadababbccbcbbcdcdaabcbcdcdadccbabcacbdaccbbcaccabcbdcbbdcaccddadbadbbbcbbcabbdcabddcdcaabbbcaabcbbbbbaaaaccabbadbbbcacddacbbaaddabddabbcddbacdcdaaddadcbabdbcbccaadddcbbbaaccdcaabcbbdbdbaadcbbbdaaddcbacbddbcbadcbdbcccadcaadddadcdadacbbdadddaabbbbaabdbcdccdbabcbadccdbdbbbabdbabbdcddbaabbccadbacbdddcdaacadcbcbccabbddbbabdbdbccddddaaabacaacdbbbbbdbcadcaccbbcabaaddbbcbaaabbccccbaddcbddbdaccababbcadcdbabddbbbdbaacddadcbcdbccbbadcdaadcccddcdcddbcdcadbbdabddbbbbbaabbcbccacdcdbdbccbcacbcbbdbbdccdddaadbcbdddcabadaccbdbbbccdcbabcbddcddbcaddcbdbdabcbaacdcaacbccaabdbdddcbdcbbcaddbcababbaccbbccbbcdccdbddbaccbcdcbbdabbbddccccacdbabbadbddddbccddbcabbcdabadbaacbabbcddcabadadabbacabdadbcbacaccdbadcbdaaaddcdcdcddcaadabbddadbdcabdcbbbbdbbacbbdadddaddabaddbbadccdaaacbcbaccbdddcbbcbacbbacddaacbcdbbcccdabddbabdcbcddaddbaaccdcddacbaacdbbaabdcddbdcccdcbacaccaaabcadacbadbcaabdcaacbbdcccdbdaaaabccdcabbbacbcaacabcdbbbdbcabdadbbacdaadabacbcbcbbcaabcabbccddbacaccccadbbccaabdcbccdcccbbbbacaabbaacbcdabdccadbadabbcbbbbadbdcdcbbadabcacaccacbdcbbbcabcbcccdaccbacbbcabcadcdddcbcabcaaaacadbdabdddbaaddbadadccbcbbcbdbcabbddbdaaabdbbabcdaddcadadbbcdbacabbcdbaaadbbbcddbaddddbddcdaccbdacbbcdbbabcbbcbcdbbdadbdbdacbabcbdbbaabcddcccaacbbacdadaaccaacadaadbbdbdccbacaaabbddabacaaaacadbcbcacbabbddbdbcbacabdcdcbdcadacbaaabccacacbcacccbbcabaacacaaacaadbdcccddbbbadccbbbbccbdaccabdddcaabdcbadbdbccabcacadadccbaabdadabcaababbdddcbcaccdacadcadbdbcaccbbcccbcdcaccbddacbcaccacbddbaaadccddbbcadadcabaddaabcdcbcdbdccbabdaddacddadbaaddbdbdccbcdacbbadcbcccbbcdbccdadddabaccaccbcadbddadccccddccccdbaabadbaccddddddbdbdadabbcccccdbbcbbdcdbacbaadcbadbcbbdabdbcccaaacacbdbcacbcdcbdaabcccbaaaabbcadddddcdbbbbabdacccaabbbbcddccccdabbbdcacbbdcddadcdaaddbabbadbdddcaccdbbcadadcadcbdcbcccaddabcbdacddbcbcbabcccacdbcbdaaacdcdcadbcbdbbbdbbdddcaaaabccccdabbbcabcaadbdabdcbddbdacacaccdddcbacbaddbcdbbbccaccbaabaccadcdcabcbcbcbbcdccaadbadcbbbaddcbdbccddcadbbbaadbcccadabbaaabaaccbcdcddbadabbadbdacdbbacaababbdbbdbbdaaacbbcaddaaadccbdcaadbadccbadadcdccdaacaccddaabadcbdadbacbabdccdcccacdcbabdaaddbacbacbacbddbaadbaddcbaadccbdccbccacabbcdaaaabcabdcbadbacccbbbdadaddccbdddbababbdccdacbbdcdbddddbcacacbccbcdcadcccaddbbbcdabadcbcccababcbcaccccdbabaabadbadadacadaabaaabcacaaacababbcddbaadcabcdcbbbbaddaccadccacadcbcbaaacdcaaadbdadacacbbbddbcccbcdbaadabcacdcabdabcdadaabcbabdddaddcacacaadccbcdbdccaabbbccbdabddababcaccacdaabdccdcbcddacaaacbcadccabbaabcdddacadcddccbdaccbbbacbabaaadbdbaabadcbadabdadcddadacdbcacdcbdbabbdcdabdcdccdabbaadaccadcbabccddccabdbdcbbbdcacccbacccdccacbdadccdaddbcbdbbadcbcccaabdccdbbcbcbbaaacbadbcadbdccacdccccadcdabacddbbacbdbabcaccdccbacbddbcdbdaaddcabaaaabbbcadacacbdbbbccaadbdccdcbbdcabccbcaaaacbaabbbbbdbacbcadacdcbdddbacccdcdaabddabcbdbcdcddaadacaaaadabcabbdcdbcbabcdddaaabaabaaadaddbadbdbcabadcdcaabccccaddddccacbccbbbcccadadcbdbcaadbccdaddccbdcbcdadacbbcddaddcbbddcabbdbbadacccbcaccbcbbbddbcdaadbcdbdabacbccbdaaabadaddbbacbbadcdcadabbdadacdcadcdaaaccaaaaaccdbaaadaacbacbdabbbacdaaccadcccdaddcdabbabbcabddaadadddccabddbaddacadbadcaccabbacaadbacbacdbddddaadbcaddbdcbacbbcabbbbddadadbbcbcaaddcccbcbaacbcacbccabcadccdacdaaadddcddbcccacdcaaaabaabbbdbcabadaabdbdbcbdadcccdcbababdbdcccabdadbaadbabaaddadbccadadadcabcbdadaabbbcdaabbcaacdaababdcbdaacacbbddbaddadbaaaabdddacadadcdaabacabadaadbbbacbdddcababdddbaacbaccabccabbdbbbcdddbcbddaabccabbbbaaaddacaabbdbcababbbdbcacbaabccdcdbbcdbdccaccadcddddcddcaacbacdbbbcbcdaccaddcaadacaaaddacdbdcdcbdcdacaddabadaacacddcbcdbbcadccbdbbdbaaaaddbcbccddacabdabcbdbbacaabbabcddccccbabababdddbbaaabcccddaccbcacdbcacdbcbcdacbdbabcabaddcaccdaabdadcdcadcdcddbaccdcaadbabbdbdbdacadabababacccddcddcbcdccacaacddbdddccacadbbacddcdbcabdbcbcadaacabacadcadbcdabacbcbaababdcccdddbbddcbbabcacbdcacbbdabaacabdabbbbabbcdcdaabdadbacbdbaddbddbbaaddcdadcdcadcdcabdaaadacbbadbadcacbdacacccdbdabbcaabaccccadabcacacacbadccbbdcaacbdcdaccabdcbadbcbcbacdbcadcdcddddbbbbddbdbdadccbaaadcbabadcdacaccadcdababbcbcdddbaabaddbdaadcbadaaacadaccbcbbbadcdbbacbccbccaaaccabadbdcdcccddadcadadcacbbbaaccccdddacbbcadcccaaaaddcabddbcddbdabbddcbdbddcabdbaabdbddcdaaaaaaaabacabcdcdcbbbbdaabdadcbbdbabacadadcacccbdacaccbccaddbcaacaadccbddcddddaababcaddbdaccdddcdadbadaccacbadabbcdaabbcddaaaacbbbabbadabbdabaaaddccacabccacdddbbacacbcccdbddbcabaabbcbbddbdacdbcbdadbdddacabcadddaaaadbacbdacaabdabadbabdaacdabbaabadcadddbcdccdddaaddbbbadadcddbcacccaccbdcaadcadcaaaaadbdccbaccabaaddabdbbccbcdbbacbbbaabadcbcdcdbaacaaabbbcadadcadcddccadbcdcbcabcbdaadadbbabddbddacdbaacddbaccccdbddcdddddcdadbdccdbcadaacbddccccdaaddaccaaaccbdddcbbbbdbbaaadbabbddbcabbcbcabdbacadacbabccaaaaaabbddacdbccbababbabaaabddbadbcaabdbcbadabdcdbbbaababddbcbccbabaadbdaabbadddadcabdadbdbccabadccddabbdddccacdaabbcabddacadcbdcddcdddabdddcccaadabddadddddccbbdadaacbdadacbdbccadaabaccaabdbcdccdbacccdadabdddacadcabbcdadbccdcacbccdbbdbacabccaaaaccadbaddabdbccadabcabbddcbbbdbbdcdcdadcbdaccaabbaaadbaaadbbabacdccdcbdabadcaccccdbabdbacaacdacdbbadbdbacdaacabcdcdcaddcdbabdaadaabaacbdbcccbcbdbbdcacabaccdaaaaaddabccdbbccddbcdcaacadbbadccbacacbaababbbaadabacadaaddcdaaccacdcdcabaddcdabddaaddbcbbdbacacadcaadbacdccbdbabbcbbbcddcabbccddbdccdabdbbbbaccaccddaccabdabadbcaddcacddddbdbadabacabdadbcbbcbacaaaaccbacaddaddccbaadacbbddbcbddddcdabadbdcabdadbbadccadacddbdccbbcaacbbbabcacacacababcdadbabbdddbdbaacbddbcdabdcbacbcddacbaacbbcbaacacdcddccddddaacbddaababbcacdcaababbddbdcdddabdcddcacdcddcabacbcadcadcadbbcdcdabcadbdcdcbbadbadccdbbababccbaabccaddabcbcaccdbccbbbddddcbbcacacdddddbddcbdadbdccabdccbcbdccaccdacdaabbcbdddbbccdccdaccddbacbcbabcdbbbcdbdcdbdbcddcdcaabaadaadbbdbdcdbdddcbbcbabccbacbccbbacbccacbdcadaccbbbaadcabbbabdaaaaddaccbcaabadabadadacbabcbbaaaabaccaacdcdbbcabbccccacbdbcdcadadababddccbdadaadcacabdcacdbabbaacbdcbabbdcacbdbdacdcddccdcbbacaaadacdacbddddacacdcacacdcbbdddcbadbddcdcbcabdaaccbbdbdbcddcacccaccbbddbdcabbdcdbddcccadabbcabdbdbabbbdccabbbdbbdaacccddcbccacbdaccddbacbcdaddbccbdbccbdbdacbcadbaddcdacdcbccadddbaabddaabbddacabdbaadddaaccdadcaabdddabdbbbcbddaddaadaabdbddaadcdacccbacadbbcabdabcaddddabaaccdbadcdaddcadcbcbbcdbabbbaaccaadccbbbbaadbadacbdbcabacbbbcbcdcdcdcabdbabadcababacacabcccaddaddcabccccdbbcadcbcaaaccbcbaccdbdbcbcbcbdbcacccbbbadbcbcabcddccadbbcaaabddbcdcdcabbaaacccdbaacdadcdcacabaacbccdcdacdacddaaddcdcdbbdaccaaacaacadccddcbbbddbcdbbddbbcdbadabcbadcbbbbdaabccbbdbdccadbaacabadbddacaabcadabbadcadbdcdacacabdbdcbcccabcdabbaadccdabdddaaabbadccdbbcbbdacdccdaabbcbdabddababaaaadcaccddaaadbbbaddbabaadbccdacbbdcbccaabbabccacadccdbcbbabadddcaacabcbbbadaccbcaccdaadbdbbccbccdbbabdccaddbdddddcabbbbdcdbcacbcddbdaddbbdbabdddcaaabbdbbdbadabaccabdcadccbdadcdbdbccbbbabaabaddbadcadbccbacababaaadbcdbbcaabdcddaaabadaaaabbbadbdcdabdadbdddabadadddcbdbbddcbdaadbdcbaddacdcccacbadcadabbbdbbdbcbbccdcdacbbbddccbbdbdaabccdcbcacabcccdcaddcddddccabdbacdcddbdbabcbbabcdabdacaacabbdcdccbdbcdcccdcaaaaaccdbcddcbacacdbbdcdacbaacbaacaacbcabdcadaacabbabbbbdaacbabdcdbbdccadacacbdccbcabababddaaccbbabadcabddddddabaccddbaccccddddbaadccacddcababbbdabaacacaacbaaadaabccbdaaddaacbbcdabaccbcdabbcddbdcaaaddbabddccaacbbabbadaddbcaaaaddadccadcdbabbadacaaaadbdcbdbbababccaaacbdddaabcbabcaabcbdacdcadddcdadabbdccdcbaaaabcccbdbcdbcbbaccbccaacabababbaccaddbbdcaaaabdacbbdaacbcddabdddcbccdcdaabbcbdacccabbccaccacbbadcbadccadabdbbaccddabdbdaddcdaddaabcccbcccabdccdbddaadcaddcbbaabadaaddbbdbabdaaaaaadbaabacccaacbcbbacabbcddddbaacadbbbdbdccccadacbcddbdbabdaadccdaacdbcacbbabbddcccdcdccacbabbdacacbaabcddadaadadcbabddabacbbbccabbdbadadccadacbbbdbbbbbbcdcabbbdbbdbdcabdabadddbabbbddaaadcadddbccbbcbaaabbbadcabdddbcbccbbadcbbabdddbaabacbbabacabbabdaaaaabcadbbccbbdcbcdcbdcbbbaaaacaccabbbbcdabbbcdcdbadbcadcdddbcdaadaabdaaadcbdbdadddadabaaccaaddabdcabcddaacabaabbdbcdacadaaddcabddbbdabcdabcdcabaddccaabdddabddadaccbbccbbbdcbcdbabbdbadaccdbadacdbcaaaacaccddacbddcdcaadcacbbdabbbcccdabdbbaabdcaacbbcadbddcaacdaabbdbcbbcaccbabddacccadccccddadbdadaaaddacbadbadcadadaccbbcddabdacadadacdcabdbcbabbcccccbdddaaacbcbbabbbbaccadcbcaccbacdbbbbdbdaddcbbaccdacbacdabdcbcabdbaabacaadbabcdadcbddcbbcddcddcdcaacbdabddbabcdcdcadddadbabaadbdaacccbccdadbaaabcbbbdccbcacbcdadcbcccbcaddddbdcbcabccbcdcaabbbbbcbaccbacbaaacbcbddddbcadcdbaabdacaccadccdcccacbbddadaadccccacbbcdbaaabbdddddabdababbbcacaabbdadcddabcdccdbbabbabbcbabbcbcddcdbaaabdddcdababbcacbbbbbbbdccbdadccaccdbdddabaabddaadcdccdadccbcdcdddadbaadacdbbbcbbcaddbcbdcbcccaabddacaccbcaabbbdbdbdccdabdbadcccdcdabadacbdabcdcaacabaaabcadcabbcccdcbadbcccdabcbdbbdaadcacddcccccbcaaaaadcbccccaabacbcbcabcdcbdcdbdcdabadabbcaaccdcdcdbacdbcbcaaabcbaaacbdcbaddccaaddcbcbabadbdadbdccddacaabdbbbddbdcccacaacabcadcbbbcdbdddadbcdcbbcaaacdacccaaccbbcdbcdabcbbcbdcacaacaacadddcdbbabbacabdcdcccbcccadbcbdcadaabddaacbbbaddbbbbccbcdbdcaadccbdaacaccaacbaadcdcacabadadbdcaaccaddabbdcccabaaacacdbbcbaddddaddaadddcbcbbddadacaccdcbbdabdacadadcbbdbbdcdbdaaacaccdaadcdabbbbcccbdcacaaadaabdabccdbaacbcddbdbaddbabbdcbdbbdbbbacabbcbccabdddadccccdbcddaddaaadbdadbdcccbaadcdbbabcbbccbddbaadddcdbbbcaacbdbccbabdacaddcbdcabdbbddacccbabbcbbccdbbbaabbadcaaacadbcddabbdbccccdbcbabccbcdbdccbbaadcccaddaccbcaacddccbbcdddbaddddbadcdcbdabbbcdccbdbddbabacbaabdcdacdddcadadacaccccbadcbccaaccddcabdcbdbadabacdaaabcddabbaaacdbcccadacddacacbbdcaacadbddbcbcaddabddbadbddaacbdabcdabbddbbddbdbabdbcbcabbacccbdbaacabacabcbbacbacadacbdbcacdcdacbaabacddaaaddcbbaddbddbadbddcabbcbadccbccabcbdadaabcaacadcbbbdadddccdadbbdabcbcaddbccbcbbdadcdcccbbbcccddaddbbbcdacbcdcbdabdcbaddaadbadcabcdddbacdbaabccddbdcaaacbadadbacbdbbdaabadccdbcbadbcbcbbbbbbcdbdddcaabcacaaacbdaacddbdaaadabbacadacaaabcdabacbcaacddccbdcdbacbdaddbbbadbdaccadcacdadcdaabccdcaccbacacccacddcddbbcadccdcbaccaccbdbddccaabbccdaaddabacdbababbcdcadddbdbcabbcbbddcdcccbaadbacaadbcaaaabddbcdadbbddccabddccdbdbcccacdcccadbacddccbccadbcddababdbcabddcbdbaddbbccdabcbaabdcbbabbbadbdbcbccdbccabbcdadadbbdbccabdbacadabcddcdcdbdbbddbdbdaabdbcbaaacccdccdadccccdcddacaacbcaaaacacadbbdccccccadcbabacaabddcbbccabacbccbcdbbcbbadddcbdddbccadbbcabbcccbbbcddbccbaacbdbacbdcbbddacbbbbddbcbbbcaababaaddbcdabcdbaabbdcbdbbccaacaddcdcaadcdabcbacbdaacbadbcbcddbcaccbabdcbadaabdbbbcdddbbbabadacbdbbdbbcabccaddbbcadacbdbbaabbacddcdcbcbcaccdcbbaabddbcacccabbcaadddbbccaaccadbcdadbcbdaaaccdcbcaabadcccbdbbbdbcacabcddcabcdabcbddccdbcadbddcdbddccadabdcbdcdbcdcdddbabdbcbaaadababbbdccabcabbdcbbddcacbbbcddddcbacdabccdadcacbcaadcdddaabccadaabccddbbcbcaacdccbccbbccbbaabaaadabdcabccdacaabddddcabbbdabccdddbdadbdcbbcdbdccaacdddbabaaabaaadbdccddcdcaaacbcdbaadddbdcaccbaaaaadcaaddbbbcabaaacdbdddbddcbbbdbcbcacddbbdbbbadacadaddacadabcdbddbcbacdbbddbbbaccdabcdbcddaaccdccacadaddccaabaaaddcdbaddabcabcadcacdbbddacbaabacacabbbcaadbbcbbadbabcdadbbdcbbabcbcbdabcbabbcddadaddcdbdbdabdbbbdabbadcabccbdcdaaccbbbbacaccdbdbdaacadacbdddddcdccaddccbbacccdbacacdadbacddcdbbdaaccaaddbadbbcbbdaabaadacbabcacaaabdcbccadcdddbbbdcddbcbbbbbbbacaccbccccbdcddcddacbccbbcbcbadaaadadccacdaccdadcaadaaddbacaadaabbddccdbaadbcbcdabddbabcddbaddcdcddccacbdcacadbaabcbadcaccdcdabdadcdccdbdbcdbdbacdabcdbcadaabdccdddaacdcabbadbbacacddbcbcdbddbbdabcddbdcdbdbbdccaabdcbddbdcdbdadaddcaabcbcbdbcabdabdbcddbcdcdcacdccdbbdbbdddbcbbabdabaadaddbadbbdaacadabaddcacababacaaaddccdbcbdcddcaaadaaddadcbddacbccdaddbbabdbbbddbcccccababcddbbdbccabbdadadcddacdccaddbcadaacbbaaadadbbaabbbacdcccacaccccdbcddbaabdccdddccaacaabddccacccabdccaaacccacabcbdabbdabacdbdaadabccdcdccaccbacddbdccddcacbadcbbdbbdbbbabaacbbbcdbacacbcdabdcbccaabdaddadadbdadbddacddbbdbbbbbadcbddcbdcadcbcabcabbcddacaddbaddacbddabbddaccbdcbcbbcabcbddabbdbdaadacabadcacbbdacbbdbdcbbbbaacbacdacacdaccaccbdaaabccabddabcabbaabdbdddbbdaaaabcdbccabcccabadadabbbcbbaddbcabdcabaaccaadcacbacdcabbccdbdcaddbcadbbbadcabbcacabbbcbadadcdcaadbcdbbabbbcdaaaddadcbcaccabcbbdbbdbbddbdddbcabbddbbbbdacbaabcbcbcaabcbcdbabccaadadcdaaddaadaaabaccbcadbaaaacdbaccdbddaccbadacdcdbaaadcababcddcbdcaccccddcdcbbaabcaccbddaaadcdccadaaaadabaabaccbdbbadcbaddddbacbcccbcddccddbcddbadaabcbaaaaaadadccdddcddddacdaccbdcbaaccbbbaabddadabdbaadbadcddcbacbabcdcbadbcbbabcbddbcaadcdddcbdbcbdddbdddcadcabdccbacbaccabbbadbdaddcaaaaaddbbabcdbcabbcaabcdaacbdbaddaddabcdbaaccbccdbbccbbaaccccccdbdcdbabababaccdbbacbdbcacdadddadddcddbbbaaadbbabcaddacadbadbadbbcbbcccbbacaadcccbbcacccabbdbcbcadddbdacbbcddbbacabbcadcadcddbbbbaaaddcaddababdcdadbdbbacdcbccaabaaddbdaacdbcbbdcdabccbddbacdcbbdcbbccbddccdabacabaaaaaccccbdabbaaacbadbaadccbdbbdcdddacbbddbabbddcddbcbcdcbcaaccabaaaabaabdcccadddaccaacbccdcbabbdaaaaccdbdcadbcccacabbbacdbabccddbcdcdaccadbbbaaacaaddbabbcaacbacbbccabcdddaadabdbcdcbadbdcaaccdbaabcababababddacabaadccacadcdccaadbddaccbabdacddbdccabacadbdacdbabddcdcaaabbcbcdaccadccbbdaadaadddcdbcaacccacbccbbbcaddbccbcdddabcbaaccaddccdbacccbabbdbdccdbbcdaaabbccadcbacabbcabdcbcdddbcdcabaabddabddccbddcacbaaccacabddaadbcbabacddcbacddabccddddccadacdadbdacdbccbaacdcabbabcaacbbdccddddcdbcadaaddddbcbcaccdbadcdaddcbcbbddabdaccccdddcbacaacccbcdabdaacdbbccdcbbccdaccdacbdbcdbddaacbcacdbccdcbdddcabdddbccbabdbbdabbdddbcccbdaddccbbccabadadadabcddbacddabadbaccdcdddcdbbdcaadcccbbbdbcddaaccabbcaabcdcdbccabadcbdadccdccdcbbbcabbbbbbacadbdccaddacaacabbcbccdbdadddbaddcbdaaabacbbbdacccccdbadccdbbaacbbbabbcccabcacbcccddaacadcbacbcbaddcadcaccabbbcdcababccdaaaabcbbacbbdcbabcdaabbdddabcdaabbdcabdbaccbcbbdccbbdabdbcdbcbbddaddcbcadccadcbbcdaaabbcadaddaabdadacdacabcaabdcaabadddadabbbadcbadbdbaccacccadbdddcbabbddbdadacbcddccacacddddbdababcbbadcbcdbddbddccbaacbaddbaccbaabbbaccbbadbdbbaccbcababaaadcbabadbaaaaacdbccbbcdbbabcadcdbadaddcaddbddddccdadcbccdbdabaddacbdbcabaaabdbbcbbbbaaacadbbcbcdbbbcccaacdbbadccdcdabaadddabddccbadcaccccabbcdadadcdaddccadcdcdbbbcdbdababcbbdddcaaacacacbacadbdbcbaabcccacaadbcccbaddcacadddddbbcdddabaaabccbbdcccadcaacdaabaaddadcccdcbbddbccccabcddbbbdbcacccbaaabbadadcacbbddbdcddbbddccadbacdadcdaddabbbcdbdddbcabadbdacbadacdcccabadbbddcdbccabadacbabdbdcbabdbabddcbcacccbaccbdacbababbaaaaabcdbacbbaddcdaddccdaddddcacdabbcaaabdcacbacbdccdbccdacdcbcdaadcddbddacaabbddcbcaaccacaabadadbddadbacbdadcbbcdadaddddabddacdbbbdddbaaabaccdbacbbabacdbbbdddbcacbacaaaddcbbdcbbadbaababddbadcdbabcddcdcbcabcddbaadbaacccdcdacaaddcdddcbacbcdbcdcbddcdabcccdddddccabcaadadbaaabaddbdccacbacbdabbbbbccbcabcbdabaabcbbddbbbabccbbaaaaacbcdabbdcacbadddabaccdbcbdbacdbddabbcbbbccbccdaccaabadaddcdbdabcbbbbdaddccaaacdabacdbbcbcadcadaccadbcbbbabbabaabbbacdcbcbdbbcadaaaccdcbbddccacdddddddcbaccbdadacbacbcbadcababdcbaabcabbabdbadccaddadddbdabbcdbaddbbabdacabbbaadadbbcdaadbcadaadcbcbdbddddaabaccbdacbcdabdcaaddbdbbcccdbddadadcbadabbbcacabdbadccacaadaddbbcdbbcdacbabdacbdaaacddcdcabcbaabdcdddabacacbbdbdbcadadddaadacaaaccaccacaddbdbaddcacddbbcaccaaaabadabaccccaccdccbdaddadcdddbcdbbbccacbbcbcbdbcacabbbcbcddcadadaaabbbadacdacdbcbadaaabdadbaaabababaaddcdbddbbabdddbbbcbcdbbddaddcaadadbaaddcbbaddabacdcaddaccbadcabacdbcdbbbcadadcababbbddbbdcdbdbaddadccaadcbadacbabbddccabbcabddababdaaabbacaadaadcdcdacdbcbaabdddcccddadbbdddbaaabbadacdbcbadacddbadcaddabaddcababadccbddbcaccdcbaadbdcbdcccbccdcaaccaadabdabccbddcdacdddbdadbdbdaddabccbcccacbbaadbdaccccbdccddcaadaadcbbadcbdaadcbdbdbbadcbbbddcddabcddabababbbcbbbbdbdddcddccbbadaadccbbabdddbcbbcdaddbcadacbbbdbbbaaacadddcdadddacddcacbacdbcaccadccadddaacbdabbdaaaccbcddbbdbbcdbbbbacccaadadbbdbacabaccabcbbccbbdcaabaaccdcaadcabddcbbbbdabdbdabbdbadbacaaacbccbddababbbcddbdbacbcbacddbbccabbacdabbdaacaacbbcdbdabdcdaccbacbacccbcabbaddcacbcbbbccdbcbddbccacdbdbdaadacbbcbdacdbdacacdbcbaddccdaccccbcbbdbbbdcadddaccddbdbccbcadbbcbaacadcbdadddbcadaabbdbbdadcdaccdcdbbdcbababcdcddddadacccdcccabacadccbddbdbdaccaacbaaabdcbbacddbdadbaabcbbccbacbaaddcbdbabcdddaccccdacaacaadbbaadcbdccbabdbddcdcdddabaccacbddaaacbbdadaacddbcdbdadbcbcbacbddaccdadbbcacbbbadbadcbdaabdacdbadccbadbcbbddccbcbbcdddaacddbbcbccaaccccbdaddacdbcbbdcbdcbbbdbdacdbcaccaacdacbbcbacdbbddbdbdaaadcbabaadadbdcdcdbddbdcaacbdbbbcadbacccdcdcdcaadcdcdacabdccdccddbcacdaabdcadcadcaaacaaabdabdbbdcdbbdccabbcbabacaabbabbbacddbaaddbabccdadabacabbcaabbccaadcaddcbcbdaccbcdcdbdcdcbccbdccdbaaaabccacbbaadcdddccbaddbcabbdaccaadbdbaadcdbabccbcabbabdccdbcdbcdbbbbccbdcdaccadbdbdccababdbabcdaaaaaddabcbadbcadabdcdadacbbadcdbbcbabaacccbbbcdcdabdcdbaaaadbadbaadcddbbcabdaacdadabadbdadadaddbccbbddbababcabcababddbbcaabadcbbcaaaaadabdacbcaddcdaacbbcdaaaaaacacdbcbbbbaabbcdadbbcbaaaaaddccbcabcbaaacddcbccdaddadaccabbadbdcacbbcabdccdbdbaacccacbddaabdbdcacadccdbacdcbadadacaccccdbccaddddccaabdbbddddabadbacbcddccbddacbbaabbdadbdcdccbbacdcaabaacddcdbdbdbccdacbbccabcacdcddbbdbddbacdccdddcbdddbcdcabdbdcabacaacaccddacbcbcbbabaacbdcabdaccacddbadadacdbbcddbcdbaabaabbadabadadabcccaaabddadbdbcbbabdabdadacdbbccadccddcaacaadadcaddbcdaddcdacddbcbdacbbcdadbcdcddcabacdaddbdcaadbbcdadccaccddcdcdcbadcaadcdacbcdcbaacbdcbadabbaadbbdbcbdddddcdcadbadbaabaadcbabdacdabaaabcccacabdcdbdaabcaccaadadcbadccdcbddabbdcdbaabdabbaacabcadcabcbaabdccaacbdbccbccbddbaddbbddcabbcabcdddaadbcdadbbacdabadabdbbdadababddbdacaacadacbddadbcaaacbcbdabbacaadbcdbcbaccadbbacaaacdcddaccdadcbcbdadcccbdcadcbadabdaaabaadaabccbcdcdccddaccacbacbbabaabbbbcbaacbcabddaadbdddddabbdaacadaadccaddbabcccadcddddddbdbcbdcbbacaccbabccccabdccdababccababddddcdcadcbdbadaadabdadaababbcccaacbcdabaddadcdbddddcadddccbdcdbdabbdcabbdbbacbcbbbaaadcadbdcaaacbcaadacbdbdcadddbaabdbacdaabaccabcadbadcaacdbccaaccbbdbaabdbacbccbdccbcbabaaaddacbbdaccdbdbbccaaabdddddcadbccdacbdabccbbbdccbacdddadbddcaacdabdcbdcbddbaccabcdbcdaabcadcbcddacabbcdccbcadacabcbbddcdbbaccadaacbacbbdcaccabdcbccbcdbacccacabbdababcabbbbdcdacdbbccbacbdcbabcbbbbcdbdcbabdccabaaaacbdaccbdaacacdcbbbaacadccadbdcdaaadbbbdcdbdbbcbdadcbdaccacddbadcaaddcaabcdcbdaaacccbdbcdacbbcabbcaddcccdcbccbcccdabccdcadbcbabdacccccdbdbcbddbcdbcaadbbadddcccbadddcabdadbacdaccbcbdaaabddbcbdacabbcccdcddcbcbdbcacbdddcadbbdacbdabbbbcbdaaddbccdbdadaaabdabdbdaaacbcadacbdaabdbdcbdaaabbbbdbdcbdababaddcadbaacbdbabacbbbcbbacdbabbaabcddbddbddacabdcbbdaacacddbcadabccddacdcbdbcdadaccabcbddadccdacdabbddcacaadacccbcaababccaacdccaabcdcacdaadadabcdabcbdddacddbcbdcaadcaacaccddcabccccaaddacdbdcacbaddcaaabbdbcccacdaabdbabbcbabcbbabadbcccaaccadcabadcbdcbbcdcbbacabdbcbcaaacbdbdababadccbbdabcbaacbbccaddaacacacdbaaaddaabdadacbaaacddbcdddbadaccbaaaaddbabcabdbdddbcccbadcdaabadacdaddabdaabaccccccadcababdadacbdbcdadabddbddaaadbaaddaadddcdacaacbaadabaacdaacdacbaaadbdaaccadbdaccaabccdbbaaacaabacdbdaaaccdbbddbadbcbccabaacdaddabaadbccaaabcdddbbbadcbdccdbddacababccabcdcdddabbadbbdbcbcddcabdcabcaabaaacdaddcbbcdbbcbdcbdccdcbababacbabcbcbccabbccbccbaccdacbdacaddbcaddbdcbcdbcccbaaddacdbdbbdbbaaaacbbdbdbbdbcbbadacbdadacdadcdbcabcccaaddcddbaaacbccbaabcdadbaccbdbdbddbdabddcbcdddadbdabbbbbbbbbcbbcaccdacbddbadbbadbddbdbdccacabaabcbdaaddbddaacdcabccabcabbdadabbaadcdbcddbcdbbbbbdabbbdcdcdcdbcdabacdaaabddbbdcadaabaddbccbdcabcdaabacdbbdccabbbbacacacaabdcbcdadcccbacbcdccaabdcbdbbbcbabdbccbbadcdacadbbcbbadaabbddcdaddadadbaaacdabcaadaaabdabdadadadbdddadccbccaaccadcbbccabcbbacdbabcbbdbabcadcdcaccccaadbcddccbbdacabbadbdcdbcbdccaaabaddacbbcccddcdacaadaddcdcaaaacadbbbdccbbcbadaabbbbbdabbbbdacdabadbcadaacbbacadcaaddcbdbacdabbacdaabdaadaadcaabadbbabbacaabcbbcaaacabdbcdbdbabdcbadbbabaddadccacdbabdbbbdcddabbaabbcbcdcabcdabbabcdacddcdbcbdcacbabcbbbacddbcdbacabdcdcddbaacacabcdcbadcbcbcadcbdcaccbdccabdadaadbbadacbcdbbcbabaabbddbabcbaaddccabaadadbcbcccdacadabaaabcdadaadabaacabdcadabbbcbbccccbaccddbddcaacacdabddcacbccddbbbaadccdcadcdaddabaaaccdacaabdccdbadddddcabdbcdcadbdbcaadabddcabcbbbcdbdbdbcbcabccbddacccdbabadaacbdabddcdaacacabdbddcdccbacadddaacadbcbdbbbcadcbbbdabcbabccbcbdbbccbadcdbababccdabdbcaccdabbadaccdcbcacaadabdbdbbcdadcacbadccccaacdabccabbadddcdadbadbaabcaaabbaabaddcbbabbdabcadddddabcaddcbbaabbdadbcccbbcdbcbaadaadacadabcbdbdadadacddbaccabccdccacdadcbbadadacaacacbaacdabaacbdbdaaccaabbdbabdddbccabadcaccbbcdadbbaadacadacdcbabcccadadaaaccddbcacabbddbabccbcacacacbcadadbdadbdaaadacaddabababbbccdcbcaabddabdddaddacadaacdcdbccbcbcccacdddcbcacadadabcccacacbacaabdbadbbdaaccdccdbbadbdcaaccbcbdbbaabdaadccdbbbdbdcdbcacabbccccbcdaddbcbdaccbbbcdbccdabbddcaabddcddcbbdddbbcbaacbcccadbbdabdddcccabbdddadcaccbcdadaabdacbcabcdcadccbaddabbcdbbcdadcdcbccdccbbccdddbdaacbccabbaadcaccbdcaaabbabbacddbdcdbcddcabaccaaacaabdccdccdaddddbcbcdcccdabcbcddaaacbcdaddcbbadcccdbccdcbdbcdabcdcbbcabcbacbbaabbdddcddbcabacaabbdbdcbdcbbdacbbbdadadabadddaabadaacbaddcbccbccaaaddccaaabdadaacabdaddadbaadbdcbadcdabccabddbbbccacbacccabddcbabcbdaabddabddcbcccbcbbccabcaabddbacbabcabacddbbddbcbdbabbbadbbbbabaaadcbabbcddbacdcaacdddcdadcdcdbdccabacaabdadabbbcdcbdbdbabbbdaaadaaddaadbddbbbbbcacaccdcbaaaaccdcababbccdacbbababbbaaaaccdaaaddcdcbbbbbbacddccdaacdbadcabbaaccacdabbcbbcdddccbacbdcbadacaccadbbaccbbcccccadbccadabdddcdbbbacccadabbccbccdabcbcbcaacacabacaaaababcdbdadddaadacabbacdccccdacdbdbabbabbadbdbabaadbbacdabcadbadbaacddddcabacaacaadbdabddcddcbadcbbaabdcdcaabbaabcdaabccaadaddddcddcadbbabcdacaadadabbbcddbbcddbbacbbadaccdccdbbcbdbdccaadaccadadacaccbaabdbcacabdbbbbadccbaabcacdbccdbbdddbababcbcaacdbbacadcacccbbccbaacaaaabaccabcbdcdbccacbcdcdbacaaaaadbcbadbcdbcdbddcadbccacaabcabbdcdcbaacbdaaacbcdbcccccdaadcbacabbadadbabcbbccaabbaacdabbaaabdacdbacddcdbadacbcacaaaaddaccdcbaadbddbcdcddbdbddabacdbdcaadbbdbdbcbbdaaabaaabadaaaaadbbdcaaddbcabbdbbaddddbbadbabbddbbaabcacbaaabacccdddcccaddcaacbbdccdcabadbaccdaadcdbcbdbadadcbccdcaabcbbaaddccbddcbabadbabcbdbdccacbbaacbdcdcdccaacbccbbcdcababdaadddbbbbcbaddcbcdaaadccbcbaabdcbbcbbbdcbcdbabcbabdcadbbdbcdaaacdbbdabbbadaddaaccccaabcccadddacaaaccbdbbbaccddaccbdabcbcdabccadddcbdbbcbbadadbbacbcdbbbcbcdbbcdaaacbddcbbcdbcadbaadcadaabdddddcabcbdbbaccaadddaabddbacbcabdaacbaabbcadbcdddadababcbbcbbdcbcbcdbdcbdcadbbcbabdcbcdbbddbdcdacdcdbbabdabdbabbbbbbbabddabbbcbccabbbcacadcaddcabddacbbabbcacccdbaaabbdbcbcdcbcaabdddabacabaaacbdbbdacdaccabccdacbccababaddaacdbcddbacadaddbcacdccdaacbccbbacccabccabbdabacdddddcdadaadccaddbbcaacdcadabcbdcdcdcacaaabdacddabdaaccbccccbaaccaabbaddcacbbacccdcbbacacabdcacadabbcddcbdadcbbaccbbdacadbaddcbcabbdcabaabbdabcaacabacbddaabdbbaabcbaaaccadbadcabadccdcdbdbaaddcbdbddcdaddbccacccadbbaccacbbcdaccabddddcbcadcdcbcbbdabdadaababdacbdcdddcbacdcadcbbcdabdcdaadcbbcdadbbcdbcdcbcdaddacbbbcbdaacdacddccbabccdbdbdbbddcbaddcadccbabacccdabccbaacadbcacbdabdaabcacdabcadadcdabbcbcaabdacacabaaaaacbddcddcbdabaabbddcbdddccbdcacaadaaccadbdaadcbdbdcadcaadaccbadaaccbddabdcbdbccddabdbbcacddddcdabcccabddbbcdccadcaaaccaaaaaaddcacbaaddccdaaabcdddcacdbabccbcadbddcdcacabdddabcbbabdbcadcdacddbadcbcccabbcabdbcaabbdbddddbbbbbcdddadaaabcbbaabbacdbcbccdbabaddadacdcbcbdaadddbbbbddaadddbddaabdaabaaadbbdbacdabcdcdaabbacdcdaddbbdddbcacbcbbcadcacbdcacadcaaacdacabdccddacdcdccdccbcbcadbdbacbcbcadbbbcabcbacabaccadacabddddcbbbdabbacaddcbbbbcbadadddacbccbaabcdbaacdaaaadcbabccbcaaccccbdaaaaabbbcbdccdbdaacaacaddcbadbbccaddadaccdcccadaaaadacbdaabacdddbdabbbcdcccbdbbaccacaacaaabbbdccbcdadbbbbbabbaadccdabbbdcbbdaccaacaddccdcababbababbaaaacbadcadbabbdbadcbbbaadccaacbbaabbbaccdaabbcdbadccdacadbadcdabbabcbdbaabdaabccdbacbbabdbdbbccdbbcabcccaabdbdbbbbcbdddcabcacabdaabccbbabdbbbdacaddcabcdababbcbbdbcbdcacbaccdabbadddabdcdabcabcdaddddbadccabacbadacaccdcbdcaaadddbdcdbabbdacaccdaaaccabcbbdaadaacdccdcbabdbdcdddbddbddcdcdddbbbccddccaaadaadbcbcdadccdbdbcacbaabaacdbdbddaccdabbabbaccdcabbbcbcbddbcadcbbccbabdcaabcadadcbddbabdccbaaaacdcbbbabdbdbbcdabaaaaacabdacbbdddbabbddaccdbbabdcadbcdccdacaaddccadaaddbdcabdaaaacbcdcdcccadbdadddcbcdabacbddcaacbacbbbbcadddccddccccabcdccbadadcdaabdcdbdbadacbcadcbccbaacbcbcaabbcdabaddbdadbaaaabbabadacbadccaddbcdddbaaacddaaacdaaadccbabbdbddaadccdcbdbccdaacabbdacaaddadccccbdbcbddcaadcdddbcbacdbadddadacdccacdccccdabbbbbccdbcbdbabacbabcbdaacdabdbabbdcbbdcaccacbbbcbccabbcdacdabcadcacadbdadbdcdacbddbcccacdcaaadddbadacaaddcdaaabcadbabdbadacdbadddaaaaddbcbccdddcdcaacdbccccbdccbddbaaadbccacadbbddcbcbcdbdcdbdcbbdccdaabcbacbddcdaabacbdadcacbabcdbcbdcdbcccacaacaabdcdcdacccdbcbaacddcddcabcbdddcdabcdaaadbabaadbdabbdccabdaddddcabcddcaacddbdabacacbdcbcadadcdbbbcaabbdcabcadbaabadbcdaccbdcccabbbccdbdaaadbdabbabcbbccdcdbbadcbbbccbdbbacbadaaabbdccbaaddabbababaaadbcacdcacccdbbbcbaddaaaddcbbabacdacbdcdadbdddaaddcdbaccdadacaccabbddbaaadabddaabdbbbbddbcacababacacbaaddaddacbddddcbacddaccacadccccaacdbbbbabdababbccddacccdbcbadcdddcbbdacaadccabbbaddcccacbcbcccbdadddddcabadcccdbcacdbadbbdbaccddaabbaaabdabccddbcbadacacbddbbdbdabdccabacdcdabccaabdbadbcccccabccdabbddddacaccbcabbcccbdbdadbdadaabdadbddaabacbdbadbdcdadddddabddbbdcabaaddccdccacaccbbbbddcbddddbadcddcccbcccddaadcdcabcbaaadbaddbadbcddddcdbddddbcbaaddcbdcdcacaccbdadbacddbcadbdddadadcdaacddbbbdababcbbdabcccbacadcbdaccdbcdcdbbdbdcdabadbdcdbcdccacaadadddbdcabbdcbcccdadaddbbcccadcdabcbcdddcbabccdcdbcbdcbdccbcbbcccccaccaaacddaacdcaddcbbabdaacabaddcbaabcddabcdcacacaabcbbaaaaababddbbbbbbadbabcadbdaaaadbcacdbdbdcbddbbbadcbcbaacccabcdaddabbcbbbddddddcbdcbdbddbdddcdbaccabcddaadcacbcdbbbabaacddabbbcbaabbabbcdddaccababbaacbadccbcacadbcadbbcbbbabdddcbcbdddcbbdbdcdcabddabdadaabbacdadcdbdcabcddcaabbbddddaabccbcbbdbbbbaabbabacbdbbbbadbddbddbdcaddbcbcbbaacdbbadacddbcbcbcababdbddbbdbdadaaabbbadcacaadadacacbccbbaaaacbaddccbcabbcbdcbacaddddacbbbdacbddcdcbbdacdabbddcdaabacccbdbccbcbabccadabcadcbcbaadaabbbdbadabaacaaaaadaaadccdbdccbcacadcdadcaaacdcaccabcacccbcbaadbcbdadcbdbbbdccadbdbccbddacdbbaadcdbcadccdcccdddacbadcddbcdcdccaddbcccdbdbbdddcabbcadddbdaadcbdddbdcbcadabccdbbaaaddbadbcadbbbacadccdcaadaaddabbdcdccccdddcabdccacbbbcdbcaadcbbbddcababddcabcbdccaacadacdbccdaaddabacdccaabdbaacdbadbbbbcdacaddcbbabcdaccabcdabdbbacaadbbcacbabdbdbbdcbbdddbdbbcdcabcbdccdcaadcbbadbaabbbdacbdbcbcccbdaabbbbdadcdaabdadddabadaadadccccdcbaddcadacadbdcdacddacaacaadcbdadbbcaaaccaacbacddaacabdadbcdbbdcddabdcdcaddbdbbcababdcdcbddaccabcabbdcbbbccbcdaddddbacbbbaaccacdcbaacbaadbcbabcccbbcaaccccabababdcacaabdaacbddabccdddddaabddcccbaabcaabbbbadbdacdbbcbadcdaacacaddbdcccbcbdacdbccacbadbdabbccababbadcaddcbbcadacabddddabbcbaacbbbdddbbcdbcaaadbddbabcadccdacbbbdbbaabcbccccbccdbdabcbbcdaabaccbbdcbdddbcaaaccdaabccadbbdcadaddddbbbacacbbddbcdaacdbbaddccbbbbbbaaabbccbabcbaadaadbcdcabcacddaaacabcdcddddacdcbbaaccddaddccbcabaabcbbdcbcccddbacbacbbdabaddbbdbcdacddcbdadbcbbcbaaccbbdbaddaacccaabaadacacacacbdccdddaaddddcabddbabccbbababbabdaddacbddacdbdabbdbbdbadcbbacdbcccaacbdabaddbdddbbcaacdddbacbcaadbbacbccaabbdbdbdbaccadacdbbdbdabdaccbccbabbccdddadcbcaccabcaaddbcbcdcbadbcaadabdabcbcdbaddadcdaccabdbadbcbacdacadddcddcaadcccacbbabacabdbcbdaaaccaddadcddcacbbcddcadbccbbaacacbaaccabdbcaaccdbbbbbbccadacbdcbbbcabdcadccccdabcdbdcaddbbbdacabdccbabbbbabbabdacddbbddcdddacdacbcddddbdadcaddbabdadbdcdadbcaabcacacdbdccbaddaacaaabbccbbcacbcabbdaccdabbbdcabcbdadccddbdcaccdabaabcddcaabdccbaabcdabdbdabcdadadaabccbcbdbdddbbadbacacabbaccaddbcbadadccbaabcbbddaadbcabddbabbbbbdabadcbdcdadaaacaabddbdaacdbbbdbdbaccdbcbcacbabbbbdcaabbcabcddddaaddbacddcbadcbacccdddcbddabcdaacacbdaccaaddccbcbbaddaabbaaddbcdabccbcdcccadbabddcbabccbabdcddcbdbbcccaaabaabdcccdbcddabcdddacdadaddbacaddaaaabbdaddddbaacbddbaddbcbbcbaacbadbbdbddabccbbadddcccbcdadcbddcdbbaabdbcddbbcaddbdcdccdacdacbabcbbcaccdaaadcccdcbdbbddadabcdcddacababbdbdcaadacdbadbdcccbdaaaddcabcbdbcacdabaccbaddbaccdcbadabbcccaaadcccabbbcdaabbbacacbbbccbbaacbbdddcccdaddbacdcdddcaadabcbbcabccbbcbaacaccdccacccacdcbadbccdbcccdcbcbddddbaaabdbadbbccdaccbbadbdabccdbaccdadcccacdbdaaccbaaacbaaaabcdddcddddbaccdabdcdccbacddddddbbcadbbcaaddadcdbcabcbacbddcccbbacdcbdbbaadaacabbbaadbacbccadcbabcbdbcccdaabadcbdbcadcbabbddcabddccbadbdbbdcbbbdcbdbbcdbadcbdcdbbbdadaadbdabcabbdbaabdccbbadabcabcdaaacbcacdcbadbdccadcacbcadacbcbdbccbcbbacdabdaabdbdcbbcadbacaabdbbdbcddbaaabababbdcdbbacaccdbbcdccdbbaacccbddcbadbbdbdabbacccddcacbaaaaaabaddadacaaabcdbadacbcabddddaacdcdbaadacadcddbcddabcbdcacbdccbbddcdbcdbbcdbbcbddabcdbddcdcdbcaddbaaacdbabcdbbaabcaccddbdcccadddccdddabbcbcadcccaacbaacacadacdbdcabccbccdcbddcccbdcdcdccacabacdbcacccbadbddbcbbdcdbddbdbbdcbadabcddabaababdcdbadcbdbccddbbdcdaddddccbbadbbaacbdcbdaacbbaddcbbbabbcbbbdaccdbdbbabbbadcadcbadabcdbdbdacdcbcddabaccdbacdbbdbabacccdaaccdbbbbaacbbcabbabcaaacdaadabcabcbdcadabcddcdacdddbbabbbadddddbadcbcdbccccaadadbcabccbddbaccaaddddbdcbaaabdacbdadccacbadabdbbbaabbcacacaccbbddbdcacdadddcaaadbbabdbdbcbadaaddadcbcbadacbbbcbadcdbcaacacaababacbbdabcabcabbcacaaccdbdcbabadcdbbadabcaddccdbcdaabbdccdaabbdbddcaddaddbabbdaaabbcbbbaccddacadddddacadbbcbdaadabaddcccbbddabacdcddbbbbbbcbdccbdcbdbbaacadccccbbcdcdadbccbacddababbccbdcbaccdadbddaadaddbdaddbabaabbbccaaaccdcbcadcacddbdbbcbadcbbcaccdcdddcadaabcccbaadbdddabababbaacdbbddabbdcdabdcdaaaabddabcbbcbaacabcaddcbccbaddcadcddbccabacaaaaaadcababaaaddaacddddabdbadacbdadabcbdcacddaabaccbdbcbbcaddacbcbaabcadbcccdbcbabcbbadbacbbadddcccdadcbbccbaabaabbaacadcbcabaaccdcccddddadbccbcdaccadbbadabcddcaabdabdcdcdcbababadddddbcabacbbccbabddbaacbcbdaacbddacaddadadbabacdcabccdadbdcdcadcacddbdbcdacbcacccdcbabaddcdbdccbaacaccccabdbbcaadbbcdbbaaadbaadadbdbaaaaccadcbadbdccdaccdbdadabcbddcdcddaaadaaadabbdababcbddddadcacacaadabdaacbbababaabbcbccdbbcbacdddcbabaadadaddbaaabbcadcdaadccccbdbdbcccdcbbccbdaaabadcbaabdaababdbbbbdabdcbcbcbadcacbabadccbccacbadaddcddadbacdacbaddababbdcdadadcadccbdbbaacdcaddadbbadddbababbcbcbddbaaabdaddaaabdabbdbabcbbaaccbbacdbcbabbabaaaacdcacaaacacddabcbdaaacacbdbddacbdbadbcbdadadccadaaaadbaddadcbdcbbcddcabcaaddcadcdddccadbdddccaacbabbbccdccbbadbabdaadbacdcdbbdbadbacdbcbcdbadcdcddcbacacbdbcdadcbbadbbaaacddccabcbbccbdaddadabdccbbabacacacccabddddcdcabcbccdcbadbadbdacdccaaddaadcddbccdaabcabdccdbbddaadcdacddccbdacaaabcddbdaabbdbddcbcccdcdadadbcadbcbdddacbcccdbbaabaadaccdcbbadadddbacddddddaccccabbdcbbbcabcabcdddbabddababccaacbcadcabadabdddbcabcaabbaaddabdcbcbabccaabbcccabddcbaddacaaacaacdcbdaaabdcadcbdaadddaddacdadcdacaaacbbcabbdccccddcddddbbcbaccabcaaccbdccabababadbccaccddbcdcaaacababddccddaddbddddbdbdcacaaaaadcdbddaacbaacadabdaccdacdbabcdbaaadccccbcaaacbabdddcabcbdaaaccdcdbcddadacaadddbadcababdcbccaacdcabcacacbdddaabadbacccadcdbcadbbddaabbbdcddcbcaaabdaacadbbcdccbcbdcabbababcababbbabcabdbabbbbbcaddcbdcdddacdcbbdabcbdcbdabcabdbccbdbbdabadbdacadacddacbacadadabdbbbcaddddbcbabaaaddacbbcdcddabbdddbbdbcabadaaaabbdbdcddaccbdbdcacddacdbaaabcbaacbbdcadaadbcaadddccacbdcdaccdccdbccdacbaddbababbbccdaaddcaccdccdabbcdaaaadcbdacbddaccddaccbcbaddbaccddbbbaacabcdadbccdcdccadadcdccdacacbcbdcbcabdcadacbbbdcbbaabdcccbdbddbdcacccdaadbacddcdccbccdadccbcdaaddbbbdbabdaddacdaddcdbbbbdadadbadbddaaaacbdbcdacadadbcbbcacdccbacbdadcddcabdddaaacdcaacbccaadadabacaccdacbbadbacdcbbcbcdcdaccdcaaadaaacddbdaadcbaadbdbdccabccacdabbbbccdcabcabcacadbadadbacbadccbaababcccdbdcaacbabbcdbdcbcddadcadbbaaddadcababdbbaaacabacadbacbdcddcdbbaadabccadababccccacdcdaadbdbbdddabaababadadabadbcdcddaccdcdaadaabdbccccdabcdaaccacbabdcbabcadacaddccbbbddbdccacadadcabaddbcdcdddacdbbdbdaacaacdabbdbddcbbdcaccadadcdcccdcbbccbcbdccdccdbacdadcdacbbaccbdacadbbcbbacddbdcccbdadccabaabcddcbaaaacdacdaaacdcdcaadccbbdcbacadccdcaacdabadaababdbaaadccccdccbaddadababbdcdbcabddccabadbdbbcdbabccbcbaadcacdabaacdbadbdabdddcaaadcdabcbadaacbddddaaabaaddaabbddddccabcdaabdcddbacbbaaddadbdbdaadbddbccbbccaddadcaccaddbcccaaccbccdccbadbcdbbcbabdacbdadbcaacdadbdaccabdbdcdbdcdadccdbadddcddcccdcbbbcdbdabaccdbbbcddaaabdccabaddddbabbdcacccdcddccbbbbcbddbcbadabcbcbbacbbaacaaabacbbcbadadcaacacdacdcbbcbcbabddbacadbadbbdbabddcbcbadbabdaacbbbcdbdcbadaadaacaaddbaccdbbbbccbabddbdcdbbcccdcadacaddacddabdbcccbbcbbbbadcbdbcbacdacbbadddacccbaabcbadaccbdcaadabaadcabacbabdcabdacdbcabccadbdbdbccbdabaccdcbcdcbbadbbbcbaaabcddbabdddddccaadddaccbcdcdbdcdabcdabcdbdcdccddababdbdbddabcdbdbcabbadcdbbacabbcdbcdacbbdacbddaaabddcbccaabcdaccdddcbbbbdbbacaabcbadacababdabaddbabdccbadacdbacdbacbacbbdbbdccdcdcdcabaadadbcadbabcadbbadabdcadadaadadbadbabdcccdccbdccbbbdabddcadbcdadacbccacbbdbbcdabaababbaccacddbcdcddbbbcbaacbccbacaadabdbaaaacbbdcaabcabacadbdbbacacbaacbdbcbbdcbcadbccdbabbdbcadcccdbbddbccbadaacababcaccacabdcaccbbacacbbdbbdacbacdccaaccbbadcadaabcddddbcdcbbadcbaddabbbbcdcacdbdcddacbdabcdbbdaabcbdabadabdcdbcccbbcbdaabaaccaacbbaabddadbbacddbbabcdacaababbaabaccbcbbbaaddbcdcddbbdcbdabbddcaaacbdcbabcacddaddcaadaccdaabadddbdbacbdcacabbcacacbdbbbabcbbdbcaaccaadbbbcaadcaaadddbaadbcccccdbdbbaadbacdcabacabcdabdadbdcacadcbcbaccadbbcdcaddbacdddbdcbbdabcdbccbacbbacdbddddacbcdbbddabbbdccadccddbaacbabccbadcacbacbabbccdcaddaccbcbaaccccbcbbaaacadddcbdaaaaccadccddacaaaacccbddccabdbadbcdddcacaaaacdadccddbdbbaacdbbbbdbcaccdabbaccdacccadddccdcbccacbdadcccbaabbddcdbdabcccdadbacacbcbcbcccabbbbdaccbacbddccadccdcddacdbbaaaccbccddadddcddbcabdaccdcabacadababdbdddabbbccdcababbdcbddacbbaddaaccbaabddabddabaddacbdddbbbdaabdddccdbcbbcaadabdbaddbcccbcddcabcaadccbcdbabdabcdddcaabcbccacabbadbddcccbaccaadabcababcdadaadacbabddaaadccbccabcdabbbbccbcaadbdacdbbdaaabcddcbaaddbdccaaadabbaadcdabcabaaccddcacdcdbdcabbdbbbddacccdbdadbbccddabccccabadcbcddcbcbccdbdbddcdabcbcdbddaaabcbbdbdaacdbaddccbaddbdbcdbcbcbdbbdcdadabcbcbdbabdadbacddbdcccbaccaabbbbcdcbbcdbdbdaacabdadccbdbbadbcadacadacaccddadbcdabcddcbcbdbacaddbbcdcccdddcabcaabcaaadbbbcabcdbccabbcabadacddbbadcdcdbdacdccdaaabaccacadddbdbddddcdbbcabdddbaddbaadcbbdcbaddabdcdbdabcdaaabdcdadaccbbbbbccbdacccdcbddcbadcbdcbbbacbdabcbdcbabbdaddbbbabdaabcbdbabdbcbcbaadbdbddcbcbbcaaacbccbcabadbdbaababadbbcbadccadaacbdbbddcbcaaccabcadcdcccddbbacbbaddabbbcddcacacadadccdabcbbdcbbdccbbccccaadadbcadccabadbbbdaccdddaadcccccdacdbbcabbcabcdbccbacbabcddcdcbcacaaddacbaaccccadccbccdaddbddbdcddcdbbaaaccbdbbbcdadacaadbbaacdddbcddacccaaabccbadbbacdababadbddbbacbdbcdbdbbccadbbbaaaddcaabaaacabdccddcbcdbcddcbaadaaabbcadcaacbdbbdcabdbabbdcbabcbbacccacbbdadbcaadcccbcabbbabbdccaabacbcddccddcacdacbcaaaabbadbcdbcacdcbbcbaacbbbacccbacadcddbbbdccdbbabbbcbddcbcaccbccdbbcacadbcbaddccaadacacacccddabcbdbacacddcbabaacacdcccdbdcddccbccabdcacbabddcddacbbcddcdddcddaabcdddabddcbdcaaabdbdcadbaddcbaccdacacbcccdbaccabdbaccbcbbaaccccbcbcccdcaabadbacccddbadbdbbddaaacbdbddcbcdaaaabbbcdabdabbdbdadbddccdbcbbdddddbddacaabadaccdadcccddadbddabbabcacdbabaddbccccbabcdbcccaccbcbccabaccbabbdcdcddddbbcaccdbcdacaaabadaccbcdbbcdadbdccccaabbccabcacdaddbabcacaadddacacdaaaaaabdbaccddbdbacadbabcdcadbbbababcadcababcbdbdabbaddbdbddbdbbddccdadcbcdbaccaddacbdaddcbcaaadddbbbdcccaabcccacbadbbddcdbacbaaaabbdcbabbcdbcacadbdbbaaaacaaacbcbbbacbabaabacdaadcdacaacccdccbcbbcbcaddbcaadbaabddacbcaacabcbcbdadcccadaaaababaaadabdbddacdcaccaddcaccaaaabdadabbadcaaaacbbbacddbadaacddbccddbddbcacaacccbbcddadbdcdacdbdaaaadbcbabcbcbcabbbcaaaabbacbcccbcccccbcaacbcdccbacdadddacaccdbabadcacddadbaaaadcbaacabdabacddccaacacddddbdbdbadbdadccabadcdcdaabccbcdbdbdcdaddbbdbaaccdbbdbacdccddcbdccbabdbbccdcdaabdcddbccccbdacdaabcbdcadddbcbbbcddbcadcdcbcadbbbccadcbcddaccacaabccdcadbbaccaccbaabbbdcaaddddccddbbcabadbcdcccbdbbbbdcabcbcddddccccacdabcbcaadabdcbadabddcbcbbddcdcdbbadabacbbadccdacacdcabbddcadbbdddadcbcdddbcaabacbcbdbbcbdccdaabcabcaddabacddaccaaacbddadcbadbddaddadabccaababdbccbcdbcdbadcdccdadadacacdbdaddabcaacdcbcbbbacbcacadbaaacbbaadbaccddbbcbbcdacbbbdacacbbccddcacbdcdbbadbcccddacbbdbddbbbbcddaccdbddcdbddbabdacdcbcbdcdaabbcccadbbabddddacdaccbcdbabaccadabacbdcbcbccddaccbdaababdaadbcdddbdcaadcacadbbcbdacbabcdadbdaddccacccbadaacdccdabaaabdbcdcababcabadcacdbadadabbdbacaacbcdccbcaaaaaccbdcbbaddbacbccbccbbdcaababaaccdbaaddbbcabdbbaddaddacdccbaaddcacccccdacdbdcdcbabbaccdacacaadabbcccbadcacbbbcacdacdadcdcbdcaaababbbbacacadbaabdccacbbdcbaccdddabdcbdacdcdbdabbcbabdadaccdcbbdbdbdccabdbbdbadccdcadaddccbbbdddbdccbaddacaacacdabaababbaacdbcddddabdadbacbadbadbcbabcdbbbdbbadcacaabbbbaccbcbaccddcbbcbacaddbaaddbabcabbbabdacdadcdabaaaddbdabcddadacabcdbadbbaadbaccadccaccadcadbacdcbbacaaddcdcabbbaacccbaacbbcdbbbaaadcabbbccddddbcaaabdabdcdaaccadbabbbbdbcbdbccddadbacbadcbadabacdbcaabdcdaabcbbbcdaacacbdbabacbdacabaabcdbdcabdbcaabccaaabbccacbcccdcabcaaaababcdabbccbccabacbadaaacaabcbccccddcacdbcbabccacdaaccabbdbdcadccbbadcaabacccdbccdcdcdddbddacbcbdccccccdbbdccabbddbdbbddaabadadcaaadcacdadcdacbabccdbabdbbacdddbaabcacbddcaabdddbccccaaabdacbcacbdbacadbcdccbddabadaacdcacbcdccbaddbaacacdacaaadbdcdcbabbcdaadaaaaadbcdcdadaddbcaddabccabacacdaddabddaacacdbdcabdadbaaaacdbdabbcbbcdbbbacadbcdbdabbdbcddddaadcacbacbacabacccadaaadbdbcdbcdadabdbbcccbbbcdadcdbbbaaacbcaadabadacdbaadddbacacaabdabdcccbdbbabaababbdbbcbcdcbcdabcccbdcadabacdaaacdadcdadaacbbbccbaabdbcdcccadbabdbddbbaddbcbbccacaacabaddccdbbadddccacbcbdccbddaadddcbbadbbcbbccabacabadcdbabdbdddbcdbadbcdbbabcbbaaaaaaddadaacbcbdcadabadcdcdbddcadacabaaaccbbdcaabccddaddabddbdcadadacbddcbbaaabddacdbcbbdbdbdaaddbaadacccbadbaaccccdbabdccdadcabdbbadbcbcaddcccaccbbccbadcaccabddbaabccddbaddbbddcbadcccadbddcbbacaccddacccbabcbbcbaccbdaabdbdaadbdacdadcbbcdccaacadaadabbabcacbdcddaadcccdddbdccbdaacccdbcaccbaddbcbadbcddbcdacbabdbcaaaacaadaddbacabbbddccaaccabbcdababadabadbcbdabcbacccccbacbacbbaaadbcddbbdaccbbdaddadbbccadccdddcabddccbabdbbaaaddcaabcabdadbbddacbbbabdddddacbbbccbdaaaaacbcaaadaabcaadcaacbcdbbdbabcbcabdbbaccdcccbdbbabbaddaaadbbadbcbdbaabcaaccdddabaddcdbdabcdcdbaccdabdcbbdbdbccbbabbbdbadbddcdccabbbbcddccdbbdbddaaacbdbaaddbdabacccddddcdadbaabbcbbaadccadbbdccddbdbadcabbdcabbbabaabcaabcdcabaaabbdddacacddcaabddbbdcadbdacaaaaadcacaabbadcabbbccaacccdddcccdadaabbccbcdbdcabacabbcccaddddabdacbbdbabcccccadcabdacbaccabddcbadcbdcccadaadacadabaacaadacdbdcdadcbacdacbdcbbbcdcacdabdcdcadacddbcbcbbccacadcabcacaddabcbddbdcbcbdcbaadabadccdaabcbccbddacdabdcdbcbcbaacdaabbabbbbcccbddcbaccabddadabbcdbdcacdcabbcbacddcbaacadacdccbccbccbcabccdadbcaccaccbacbabdbcdaabcdbcdddbbddabaaddaabdabdabcadaacdaddcddcdddbcbcccddacdbadcdcbdaaccdbddcaabbabdbcadaadccccaacabdddcdcadbaabccbdbcbdcacdbdaaaabddadabbbccabccabbdbaadbabcabbbccdbaaacccbcabadcbddcdcbadcbcddcbbadbacaaaddbccdcdcabdacdaadddccaccbcddacbddbaccabaccaacacdaaddbabcacdadabbdbcbbacbaacabcdbaaadcdaccbdbaaaddbadadacdbbacddbbaaacbcdbaacbaabaccbcdabdacdabbbddbdacddacaabbdbdbcabbcddaadcbdbcbcbadbbbbbaacdccbcabcadbabacacdbcbdbbacabadabcddabbdbabbdbabcddadbccdbbcacadccacabaadababdabdadcbcbbbccccadabbbacdcdacbacdaabdcadbbacbbaabcddcdaadacaddadacdbcacdddadadbadbbdacbccddbbdadcbddcbddcbadbcbabcabbccaadaaacbacdbbbaadbabbbaabaaaabdbbaaabcaaadcabcdaccaaaaadbddcdadadbddcaccbcccaaddcbacabdadbcaacbcbacadadcddadabdcccbbadcbbdbcbacaaacdbddbadbabbccddbcbdddcdbbccacbbdaaadcbbccccadcdcbcdadaabadcbabcbabcccbacacabaadabcaabbddbdcbabddadbbdbdcbabdccbdbbbcbbbbbdddbbcbbcbaaabcddacbbbcdabcbdacbdbadadbadcbbdacdcbdacbdbbcacdadbbbcdcacadccababcdcadcdbdcbbbcabcabacabaddbabdcbddcbccddabdbdcdcbaaacdabbbdbccabdbcdcccbbaadcbadbbbbcadcaacdcbddaaabdaaddaaaabdcbddcadbddcaddcdadccbdadbabbdaddabcbdbddcbcbbcdbcdbabadcaacabcdadddacddbcbabdbacddacdbbaccdaacaabccabdbccbbbcbccbacadbcbcdbbcabdbbdabadcdacdccccaccccbababcbaccbbbbdbbcddadadbbdadcdaabdacbadccdcbbbdccabcabcacbbcbcbaaccdcaabdbacdbddaccbdabdadbcbaaddcccccbbbcccacccbdbbdaabaabcadcbbadcccdbccbdcabbcbaabcddcaadbdadcdddbccabbddaadcabcbadabbcaabbddbadddcdddadaacababbbacbbcdcaacacaaccaabcaabdbddcbaaccdaaddbdacaaadadcdadbcbacdcdbcbbcadbbccdabcaccbdcdbaaadaabacacabcabaddadacadcccacdbbbadacaaddbbccdbcbcccbcdcdbbaddcbdcacbddddacbcabcddccbdbdcbcddcacdbccdaadbbdccdbaadddcdcbcbbabdbbbabadbcbabaadccabaddacccbbbbbcbaabbadcdaabaacbccccbdcbcacbcadadacbccaaccccacabccdcdadccaddccacdcdbacddddaaabbbdbcadaadbadbdbdcabcbbbddadababdcddbbcdadacadbcbaccccacdabdbdcbdcbacbaacadabaadccdddcbdabccaaccbbbddacdbddbadabcdccbcbacabadacbabbcacadadbcabbbbaaddcbabcdbadaacbcbbcbadcadadbcaabdbdacddcaadcaadadbbcabbcddbccbadcccbdcadadbadbcddcadadcdacabdcbcaadbacbcacccbbdbbcddcacbcadaccacbaccddbcdbbabadaaaddbabbbbbabbabcadcdbdadbacbcdcaccbdbaacdccacdccdbcbaadbcbdbbbabdbcbccabaccdadbcccdabcadbddbccdadbcadccdbddcbbcbbccaabccdbdadcbadabaccacdbbaaddcbababddcadcccaccaacadabacabaddbbbbbbbbdadbcbbbaccdbababcdaacbcdbcbbbdaabdbdababaaadcccaddacbdaaabbcbacdbbaabbbacbbcdbdcddabdcacdbbbcdaccacaaabdbbccaaaadbdbabcdbcccbadacbdcaccabcdccddbacdacbdcacdcbaaadabddbddbbacadbbabbabaacbdacbacbabaacaaaccdaabcddacacbbbacdabbbcbcbaccbdddacddabcdddadabadcbadbbcccaabcbbcdadacabddadacccbacaadadbaaaabbacbbcaadabdacbdadacdbdabccdadbbcaddadccbabddcdababbcacaacaadbaabcdacaabcbcdbbadaabbcabddaacddcbbacacdbbddaabddbcabccdcadcabbcbdbaaacbcbddccbcadccadcbbcdcdabadacbdaddcadddcccdbbaacbadbacbadcadbbdadbbacacbaabdbadcaccbbccbbccabbcacdbdaababaadadbddccbbdbabcbbcddabadddaadcbbbcbabdccacbbaccdbcdbaadaaddacdcadcbbdbbdbbdbcacddaabbbadacbacaadcdcbbbccabdcccbccbbcbacaabcdcbcbacadcbabacaaabcadadcdcaccaadcabbdbdcbcccadbbabdaaaddccdddaadccbdbbadbcbdacdcddccadaacddccacabdacbcccbccbacbdadbbcdcaadcccabacbcbaabdbdbdcddbcdaaaaaadabdaddbcddcacbcbbcacbbaabbbdbdddcacabadcabaccdcccbbbabbcaddcdacbdaddabcbccbbbddaccadbbcabacbcdbcbadaacabbddaadbcdccbcacadacaadbacdaccaaaadabcbbdbacbbbdbbabddcadbdccbbccaaccccbabccdabbcdbcbdbadacbbcdacdcccabcacdccbcccccacaaccbadbadadcbbccdabdcdbcacadcdadbccddabbbaacbccbdabddbcbaacdabbbcadabadadcaccacaaddddbbdcacabbcabccdbacbaaabcdadcddacdbdacccbaadbaacdacbbacbadcccbcdcabaacbcaccbcdddadacacdaabaabacbbccdbbaacbbbbbcccdacabddcbdccddccababcadbaabddbcbbadcbacaaddabaadbcacaaddcddbabcdacccabcbdcdcdddbcdabdbccbaabcaaacacbcbdcbddcaaacdcdcbdabbcbcdaddacbacbbcbddcbdcddbdcddbcabbbbbaaaddccbbaacdbccdbcdcabccdcddbbdacbdacbccbddbabdcccacadbdcbdbacdccddcdcbccbcdbcdbbbcbcabbcbdaacdcbcccdabbcbcccbcccaddabacbcabdaacbdaadcbbbdcdcdabaabcdaacbabddccaacbbbcbadaacbabddcbcbbaaacbbdcdbdcddaccbddadcbadbcdaccbdbdacdccabadcbdcbbdccdbdccbddcacdbdaabdabadaaaccdcbaaabdbbacdcbaaaabaddabadbbdddbdbbbbccbbddbbbadbbbcdbbdadccccadddbadcdadbdcbdaddaadbbacabaccadadcbacdadcddacbcbbabaaddabaabbdbbcbcbcbaadadddbdcddbaaadbcccdaccbadccddbdbdcdcbcdcdbddbacbdbcadbdadcccaaaabdccaaabdcdbccacdaabdabdbdcbaabdaacadadbcdaacaadbdbdabdbabbcabadccbbddbbcacbcaccacdcaabaaccbddaaacddabbdabbcbbaaadabbabaaddbbbadbbdaaadcaadccabdbbbaaccbccadcccbcdbabbbbdacbddcadccdcdcbadbadcbddaabadbacdabdbddaaddcadacbbcababddcbbaabdacdaacaddaddddabbccaadbabbdaabcbaabbdddbcdcdcaaccdbabadcaadbdadbbdaadabbddbcccbcbbacdaadaaaaaadadaabdadbaaacdaaabacdddbcbdddacccdabbcbbacbabcabdbaccadcdbbbcadddbdcbaccadbcbacdabacbbcdbccbdcccadaaaabadccdcacbcdbccadaacdbdabbabadccbddbacbdcbdbabddabcaaabcbbdbcbbbdaadbbdacccdcbddababdcbadadddcbbdbdcbaadbbbdcbbddcbaacccbdaccbcccbaabadcaddccbcbdcababcabaacabcbcabbbbbddacdabcaddccdcadbcddbbddadabccbdacaaadccdbabacccbcddbdcbbabddabaabddadcbbbdcbcaaaddcdcdcabdcaddbdbabcaacdcccadbabbadcaabadccbdbcdcdaadabbbbdddaccdbdcbccbbcddbadcccacbbbcbbdbdbcdabadbcaaddcbabdbbadadadbcabababbbbcadccbdaaaddbdbcdddccbdcbbdcbdccbdcdabdcdababacaaaddddbcccbdbccabddabcbcbadacccdabbbdababbbcbacabcdddcccbcdcaabcbcadbabdaacdabdcacbcbbcdadddbbbdddadbdbcdadbcaabcccaacdddcbbbbcaaabaddbdaaccccdbabcabbccbdbcabcdcdbdcabbaccdaddadddcabacdbabddababccdbcccaadbcddabdbccdaadcacdcacadccabcbbddbcbdcacbbbbaadcbbcbabcbddcbddbccbbbcbbdbcdddccdccadbdaccbababbcacbbddcbbbbacdbdbbdabdaacbaddcbdcadcbcbcbbddbbbdcddbdacbaadcadcdbbbccadbbbddbddaaaaadbdbddbcbbccabbcaccccbacacbadadacbbdbbaccdcbaaaaddbbadabccbccdadabdaaccaaaaabddddbbbabddabddbcadcdadddcacbadaabbacbbcbdadbbdacbdadabadbddccabdcabaacccbbdccdbcccccaaddbddadbacbdccbdabdbbddacccbbdcabaacbcdbbdcadadcadacabadcbacabdbccadbadbcddbcbaddbdacbbdbdddbcadadbacacbcdbacbccaccbaadcdaaaccccbccccbddacdabcaccdcdbacdcbbbdaccdcbacddcbddbdbcbaaadacaacbdaabbdbacaaabababccddbbbdbaaadcbdaddcacdddddbabbbbcadbdbdcbbddbbcacaabbddcdcadaacccacbaaaabbcabcadccddaccbadcdbadcacdcbdaabcabbacaabdccaccabaadbadcbddbbcdcbcddcdcabacdbdbdcbccddaddadccbadbbcddaaaacbdabcdcdaabbcddaaddabbdacdadaabaaddbcdcbcdddabccbcdcaaddabaaccaadaddbcbbabdbcabbcdcbcaababababcdaadbadcaadcaacbcdbccacdddbbbbddbdcbcbacbddcadcbdccabbcbbabdabcbacaccbaadddbababacdcbcbcabdbccadabacbdbdacbbddccdbdbdaaaddaddbaaaaadbbadaadccdcdcdbbdbdabbcdadbbcbaaaababcdaddccaaddbbdbcbdbdbbabdbddddbbadcbdcccbaacabdcbbabacccaccaacdadadddbadcaadabdaadbdaadcdbababddbcabccbacabcbaccdcacaabddbbbbbdccaabbbadccbddabaaaacdbabdadaabcaddcaadbbadcdbdabbcdbcbdbdbbaacbbdabbcddbaddddddddaccbaacdadcdaabbcbabcddddbdccaadccdacbcbcbbbdbccdbbcacdadcadacadcbbbcabbcabacaddadabdbbddadbcaabbabaaacccabdbdcbabdaabbdaddadbcabacccbdcaabcbbbbacabaabddcabdabaccbaccbadcacbaaddabcadbbdcdccabacaaccdaccdccadaabadababaccdcdacbabccbcaaaabdcadaacdacdadacabaccddbabbabadaddacddabdbdbaacbcdaccbbcbbabcaadddddbbbcdbabbababdddacddbabbbacadbdddcbaaaadcccabdbacdadbcdaddbcbcccacbaccdacbbcddcdddcccaabdbbbbcbabcccbadadcbdccccaabcccbbdcccbaccdbaadaabbddcbbbcbbacdadbddcabbabcbaddaddbadcbdbadbdcbbadcbdcdcaaaabdbadbcacacddccacabdcdadcaaddcbdacdcaabdbcbcbacaabbaabaaacccbdaaaadcbdbdbcbacbbcdddabbaccdbccabccdbddcbacdddccdcaadbbcdbdacdcdacdbcdbbabbccdddcbddcabbdcccbcacddbddbaaddbcacabdaaaddcdabbdddabbdcdcadcdccdcbddbcccbbcccabbaaaabbdbbcacdaaacdbabdbaaadcacbdbcbbbacdbdcccbcbbaaccbcdbacaadaddcddaddccccaaccdcdaadaacacbdaccdabcbaddacdbdddacbabaababaccdbdbdbbccbccdbcbddacbcacdddddcdbcbddddcbdadabbacbbbbccbadbadbddcadaaabaaacbbbdcdcacaddadbbcadcbdaacdcbdabdccaaadddaabacddabdabaadccbadbcdbccacabdcadbcacbcdbddaadaccdccbcddcadbcacdbdcbbcdbdcdbbdccabdabdadbcaacabcbdacbaabaccdbddabaddabbdbababdbbdccdabacbdabdabbabcdacbdddbbdaadbccccbbcdddabadbcdccadddcdadcccabcacdaabdcddddcbdbbabccadbdcbccdaabdacbcbaddbbdcdabcbbbddacdbddbcdacddddcacbddddddadddadddccababadaabcbabddcbacabdbcabcdcbbbacdbbaadbccbdaddbabbcadbacdabccccaabcbdaaaddabbaccdccacbddbcaddcdcddbbdabcccadbcbbcdddaaccababcbcabbcbbcbdbcbbbbadbbadbbbdabbcacdbbddcbccddddbddabbbbcbcdabadbccacbcdababbcacadbdbddddabdaacacdddbdddcaaccadddbaacaaadbddcbdddcbaaddadabcbdbcbbbbdddbadaaaabaddcaacdbbdcbccccdddaabbcaacbcdbbcbcaaddbcbacdcabcabcbdcdbacbbbdbaabdcacdcaddabcadccbbccdbbccadacccadababcdbbdbbadcacdbccdbdddbcddcbdccbabccdaabdcdcddaddacbcbdabdabadcbcadcdbbcacbbaaddadccccbbccbbcdcbbaabccabcaaadcbbaaabbdcbdbbdbdcdbdbbcdadddbbccdccccabadbaadccbbcdbbbabdaabcbaabadacccdccbadddabaadbcabdcddaadadcdbcaaaccbcadbdcabaccbcccabbadbbbddcccdcdabdbdaddbddaacbcbbbcdbdcddaadbbaccabccacbccddbdcaacadcccacbcabccdcadcdababcbbadbddababacdcdcadbbddcdbcadbaccaccaccdacddadbbabbbcbaaabddddbdaaaccdbadcbcbcadaaadacbcdacdcbbaabdaddbddbbdcddbbabacbcdcccbcbddcddcbaddadbabbddbaddbbbdaabccabddaddbacbadbbaacddcdaddddadbddbcdbdbacccdacdbbcadcbdaccaaddbddadabbabadbcddbccdbcadaddddbddacbcddbcccadbdbdadbaddbadcbbccbbcbaacaabbbacddddcdbdabdddabcbadbacdcdaacdbbbacbcbcccbddbaaccacdaababcdbdabdcbbaabcbcccadacbcccaddabcbbbddcabbddcbabdcbdcdcaddbacbaddcddadbdbdbadddcbccdcacbabbbaaddbdcdaadcbbcccadbdbbaaccdcdbcabdddbbcadccbccbcbbdacaaaacbdbacccabbddaadccdaccbbabaadadabcccddbbbbacdaddbacabdbbaddbbcbaadcdadbcacdababcdcdadacddbcabbaaadbabadabdbbdbbbdddccbdaabbdaaacdbddccabcbdaddbbaddacddabbaabcacdddcbbdcaccbccdadacabadbbdcbccddabddbacddccaddccaadadcbcbbdabbcdcabbcbcabaccbcbcccddaaadcccbbcdaadbbaddbbcabbcadabdddbddabcbaddccbabbddcbcacbdcdddadbbdcacbcdadcbdcdcdddddbacbdddbbbddcdbcbacabdccbaddcaaccdadacbcdcbdcdadabbbdabddcdcaadabcbcaaabbddbcaacdccabaadcbaccacbddbbcddcdbcccddabdacacacaabccaabdaaabccbdddbccabdabdaddbbdcbacadbaabaabbcdabcababadaccbccbadabdcbaaabbaccaddcbddabaddcbdcbcddbadadbacccccddbddcaddadcccaaacbacddcdababbbaacddbaddcdbbddcbacbabdbabcbcaccdcacbaabbabbddbdbbbcbabaaaabacdacccadaadaddddcbaabddbddccdbcadbcdbbcbbcbbdbdddcabbbdcdcddcbdbaddcbbdbabcbdabdcaaabcbadddccddcadabadcccccddddbddabcccddcbdadcadaabcbabbbcaaaacbabdcdcbcadbdaadcdaabbacdbdaddbadbbdabcbaacbaabcdbddcaddcabdcbbdccccbabcbbccaaccdccaddcdbcbcddbcbdabcddaadcdabdcbcbaaccabcdbbabdbaadaccbcabcdacccdaabaacacbcadbbcdbcbddddbbccbaacbabaabbccccbbcaabcbccdbdbccbaacdbbdbabcddabcbdbbacbbbcabcbcddcbbdcdbacccdbbcaddccddbacbaaddbcdbacbdacabaccbdadadbbdacbcbdabdccacdcadbbaacacccdbadbbddaddbcaabbcacdbabadbbaccbdabcacdbcacdcaaababcdbccbccddbbdddcdcbbdadcabdddcacbdcadcaddccbacbdcbabbaccddddcbdbbbddbbcbbbaddcdcbcbcddaadbaccbadaaccdadabdcdbbacbccdcadcdbcbdcacdcdbacbbaadddcabcbcdbdaadcabadbdccccbddabbccdcdcbacabcddbcbbcadcdbbddabdcacdacccdccbbbadbdadaddaaadddbddbbccdbccdbccadabddbbddbcdabbcababdacccbabbcaadddacadcdcbaababdcadcabbdbcacdbabadadbadbddcdabdcadcdbddbbacacaaddaacbdbcabbadacbcacdbcacdcddbccddbccddadadaaabbbdbbcadbdcbbdbbdccaddacaadabcaddaaadbbbbbcbacadbdadccdcdaadbdbadccabccbaccddaccacddbaaadadbabcbdadacddbdadabaddcabaccbdaaaaccaabbbcabcdbcacaacaccbabdcabddaabddcaabaccabbdacdabcbadaddaccdcddadadbdcddcacadabbacaaaaccccccccadbbdcadbbbcbacbddccddbcaaddacdbccbaaabcbcddbadbcccbbbbbabbccdbaddbbbabaadaacbbcbdbaacaddabaaacddbcadbbdcbbdcbdbacbccdbadaababbccabccdccaddcbdacbaccbbbcddadccddababaadaacabbbcccdadacdbacdaaaaddacadddaadbdbcaaadccabccabbccbdddbacabddcbdacabbcabababdccbbcbdbdbdbdbbdcddcccbcbbcadcdbabcdbbccaabdadbbaddbcdadcbbbadababbabacccbcaaccbbddcbbbbadadbdbbacdccbdbcaadadcabdcccdacbdcccdcadcccddaaddcdadaccacbbbcaddbcbdbadcdcaddddcdacaaaabbcbabaaacdbdccaabccccbddbccbbbdcbcdcbccbdbbacbaababcabbddaadabbaaccccbdabdbddccbacbdadcccaaabacbdbadbcabbddbcbaacccccaaddccdbddccbbcaadaaadcddccabdabcbadbcdcdccbadcbccdaaddacbbabaadddcbdadbcadddcabbdcabbcdcbacddcabdaaccaccccbbcaccadbbadaddadccdacbddbabcbacbbbcddbdbccabcddbbadddcbadbbcaadacbcaacbacabbbacdbccbacbadacdddbdcdacdcdcdadcdcadbcaccdcadadadbaaabdccbacbbdabbdabcdcbabdaabbcadccaccbdcbcdcaaabaccaacabbddcdabaaadadccbdddcbabaddadcbacbbacbaacbbbbababdbccdacbdbdbdccdccdcacacbaddcbbaadddbaacdaabddacdabdaddbddacaadaccacabbaaaabbcdddbbdadabccabdaccdbdccaacabaacabaccbbaadbdcdcddbbabbbbcaaaaadcddccdadccdbcbbddbdccaacbdbbcaacbdacaabcadccccaacddabadddcbcbabbdbbbbacdcbaaaadcbbbcaaadadbbdcababcdabbaccbdbdbbbcbadadcccbcaaadabbddbbcaabbdaccbcdbcdaaccbcccdbdddccbccaaaddccbbbcdbadaacadabcddbcabcaacddbcbbabdddadddacacdabddcaddcccdbdcbdbadadcabddccbdbabaacabbdbcabdcccdccacbcacdccbdcbcbabbdaccdbdcacacbbabddcabbbdaacccacddadbddbaddbdbddcbcbdaccabbbcddaacbdbddaddacdbbdacbccaacbcacbcdbdcccccabdacadbabdbccaddcadcbadccaabddaacccbcaacccdbbdcbdbbdcbbbccaabadaacdcbdbacdbaacbbacaccccdcddbabdddcdccbabdcccdcdcadcbcadddcacadaadcccccdaacdcdaacbadbdddcddbdaccbdcdbcbddcdcdccabbcbaaaaccaaccdabaaccbacdadcddddbbddcbbacdabbacdcdccbbddbbaadacaccdcbcbcbbcccdcabbabdabbcbabbcadacdaddbdcaacdcddabdbaccbbbaddccbbbdacacbacbadccadbdcbacbcabbcadcddbabadbbcdadabdbdcdabcbbacacdccdacddcbcbbaddddaadbbdacbdaddabadadbcdbdcdaddddbacccccbdcacbccdccadabacaacaacaddabdcbdabbdcdaaadabcbbdccabcdddbdbbdbdabcaddddbdbdaaddaccdbdcdbbdcdbbcabbaabbdaacaaaaacacbbcbcdcddcccdbdbbcdadacddcbabcbbbbaccadccabdbbbbcbcaccdbbdbcbcdcaaaddaacadabdbcbccbdbbbdcbbaccabcadadbcbbbdbdccbddabdbdabcabcbdcddadaacaaaabbadacbacadcccdbabcbbdaaabcdadcdacdaaabadaababdbdbaccbaabbcbccacdcbcaadbbcdacdbcbdacbacadabcbdcbbdbbcdddbbabbbabbabbadbcdcdabddabbdbdaaccaabbadaaabaaabcbbcabadcbbddaacaddcacbbbadbbacbacdcaddaccbbaccddccaaaacbbabddacdccacbacccddbcacacbbbcccdabcaccadbaabcabcdddcaaddbdccccdabadbdacdacdacaaaccddcdcbcbcaabaddbcbbacccdbcdcbbdcbcabababdddcbccdddcadbdccddadbdcaddccbcdacdabcaddcbdddbccacdacccbdddabdbbdcabbbdabddcddcaaadacaaccbbbdbcacbadbddbaaabbbaabdadadcabccabadadaddcaabbdcbbadcacbbabccbcaacdadadaaaaaddbacddccacbacbcadbcbccbaabbcaaabbbacbbbbddbddbcbacdaaaddbabcbdbcbcaadbcdbaabcaadbabbdbadcbaabdadbdbcddbaccbdacddabaaddbbdbacdddcbbdbdabcdbcccbbccdcdabaababdadbdcbacdddcaaaaabbdbcdcccdddcaddcdabcddccabcabdbcbdccdcbacbcddbcbadbbdbcabdaabaadbcbadaacabaddacdbcadcdacacbccabbcdbbaabcdbccaddccddccdcdccbdaabdaaacacbdabaadcabaddccbdcddaccdbacbaddbbbbcdccabcdbcdbbaacbcacbbcadccddbacadabdbcbccbbcadcdbabcaabbbbccabccabccbaabccddccbbdcdaddbdbbbabaabadcadaacdbbabccbdcbabccddbcbbadbadabbbcaddbabcaabccdcaabccdcdddbddbcdcbdddddaacdcdaaddabdcbaddddbcbcdbbabcbabcdccbdabcabaabbaddadcaabaadbcdadcdaacabbcbacdbadcbdadacbcbbbbdacabcbcdadddccccacadcbabddacbdbaccccaabbbdccaaaacbbddaddaaaddcddbbcbabcdddabccdbabbccddcbbbddbaaabcaaccbcbbddbdccbdcaccbccbdadadbccccccdaccdcdbddbdabbbcacbbadcddadaccabdbaaaadddbbddbbbccdddcccacdadcdcbdaccbcccbdadcdaadadabcdadcddcdcdbdbccdcacabdcdadaaacdbacdadaccccabcbacdbcabcadcacdaddadabcacccbdbbcbdcadaabadacdbdbcdcbdcdcbccadcdddbbaadbcdcbaddadcacabbbacabccabdbcbaaaacdabaadacdbbbcdcadbaccccbdbbcbaadacbbdcdbcddbcddadadcdccdadcdabddcdddbaaadabbdbaccdadddaddccdccabddabccbbdadbacaadddcddadcaccadccbddabacddcdacaacaddbacbcabcddccdbdcabbddccdaaccbdbcaaabaabaabcbbdadbcbcbdcabcaddccdadcddccdbdabdaacdcddcbacbacdacadbadabccbcacdbbdbbdcabdaabaacaababcccdcaccabbbddcaadcbadbaaccaddbdccbaccacabaabdbcdabbcabcacddbcabdaccdbddabccbbadaccbabdcccacdaabbabcadccacddddcdcbdbccbbddbcdddccdbcbddbbadbcbbcdaacbadccccabcccaddbddacbdadbcaadbdaaacddbcccaacadbadcdcaabaaacbaccdcdbabddbcdcaddddcddddcdcadbdccadccdadaaddbaaaadddddcdbbdccbadadbcddcdbbddadbdbacbddbcdddbdbaaadcabccbcbddddcbbcdcacaacacacabdcddabbddbbcddcdbccabdddbddaacdbdadcabbbbdcbaaccdabcddcbdbadabadddbbdcabdcccacadddacacbdddbbccdababddbcabaaaabaccccbbbdbccabcbdbabbdbadcdaccbcaabbcdbdcbaaacdbbdabdbabbbcbdddbabcadaadabdaabaabdadccaaacabcbbbabacbaadcbaacccadcdacadadacdbcacacbaaadcadcacadbdbacdaadbcacdbdddcdcaabaddccbdbcbdbabbbcddacdadbdacbcccaacdbddabbadadccbddadabdddcbdcbbcdcadcbdaaaadbaaddbbdadcdbbccdcbdbadcccaccacbbacaccccbcacbdadadcabdbbcccdabcbabddccaccadabbccbcaaabbaadcadacdddadbcadadaadbdccadbcbcaaaddbcdaaacbcadbcbbacacdadbddcdddcbccbdbbacaabcacddbdbbabbbcdaaadcdddadbbadbcdcdbbdbdaccabdcbaaadbcbddcbdadbddacabdccaddacaaaaabbdcaabaaaaaddaacbcdabbabaabdbcacbddddadbaddabadabcbaacbcaacadcbacabaddcaaacdaadbbdcdadacdbbbdcccadcbbcacccbcbbaabbbadcadcccbcdaabbbbacdadcabddbcddadaaccbcbbcbdabaaaadddcdacadadaaacbcadadbaadcadbacdbaacbcbaaadbbbacbcabccdadcbadabbbaccdcacdcbdcabcacdcdaaacddabbaabbabbbccddadbdbadaccbdcbabdabbdccbdaaddbdaadbddcdacbcbadccdacbcdacdaaccbdcbbbddbdacbdcbdccaadcbbcddbcdaacdadcacddbacbddbbaadcbaddccaabdaddacccadbacbbbbcdbbccadacdbacbdabccabbabcabbdbbabaddbcbbadbaabccdcddbdaacbcdacbabaacbbaaabbbcbdcaabddcbddbbbaacbabdbbabccccccaccbcdcaccddaadbccdabdbdddcdbddcccbacaaaacdcddbacddadacdbdaccbbbabdaadacdbdbbbbddabdabaccbacddcacdcaabcdbdddcdabccbddaadbadddadcbddcdccddaacaadcaaabaaddaaacddbaddaddbbbcdcddabaabdaadaaccbbbabdbbaabdccdadacaadcdaaddadddabdbcccaacdbccaabddbcdbaabbbbbbaddbaacababcabdcdbcbcbdaacacabacbaaabacdddbaddcdbcccacccdaaadadbabccadadbbcabcbddbabbccdcdbdacacacdbccddbabbddadddddabaabcccdabbcddbcaaaccbcadccdccadaddbabbabbdacbccbabbaabcbbbccbdaccbbabbcdddcdacdcbacbaccdabbaacbbcadcdcdaddcbbcbbddaabaaadcbbbcbdbaaadbdcbaadcddabddaabbcdccadddddcccdbddabaccdaacaddadcdbbbdabddbbdbcaddddcdbdbacadaccbaaaaababbcacdbcaadcbccbcadcbcdacaacbdbdccdaacdbdbbbdaddacaabdcbbdabaabbbccdabbcdbcabddccbcbddddbdbdbbbabdddadcdbddcbbcbabddbbbbabaadabcbccddbaababcbdabbdbdaccdacacadcabdbcabbaacaaacbdcccccdbadbbdadbbabacbaaccdaacccddcdbcbacdbaaabccbabadcadabcadcdbabcadcccdacaacbbdbcadbacccabdbccabdddabbaaabbcddadcabddcaaaaabbaabbbadabbcabadcacabcbcddabcccabbcddadcadddadbabbacdbaddbccadccdcccdaaccacbbddccaaadccccbaccdcacaadcadaaaabddacddcbddabdbaadbadadbabcbccdacbbaabbadccadcdccbaacbadadccdbacddadbcaabcbdabcdaacbbcdccbbbbacbaddcccdbdbbaadcddcababbcabcbddcdbcacdabbbadcdddddaddbcadbaddacbdbabaccacaccdccbbcaddaddcdbbcdbddaacccbddaaaadbaabddbadbdbcadaabadccabddccccdcccadbadcaaccdacbacdbcbaaacadaadbdcbadbcddbbbcddaaccadcbdccbbdaccdbacbbabadbadaaabacadccbbacdcbbacabbabcacbbcabddbaadaabdadbbaaadbdbcccdddcbbcdadbaadacadcabddcaaddcabdbdaadbacabbadabbdbabaadcdacacbacdbdbbbbbcdadacccdbbcaddcbabdabbddaabadccbbabbddcccbdcabccbbbbdabcdcdcacabcbbcbcabcdaaaadccdcabbaabdccbbcbacdacbdbbbbbcdcaaabbbbaabcccaacccbdaacaccdabcabddacbcacaddbbabcbcccddbbbcccdaacdbacaadbadbcdcdcccabdaddaadcaddcdcbadcdcaacabcbbabcaadcdabdbdcccbbcbbccbabdbcbbcacbbcccbbbbdbacbbaaabccabadcabababbcccdbadcdcadadbadaabddaaaccabddacdcddccacbcaacbdadbabbacbabacbcadbbbbdbadbbacdbccdaacbbdcbbaabadabdacaadabaddbdbbddabdcbccccbdacccaababcbdcbabbadcbaccacdbbacdaaabbcccccbacaaabdbaacbbcddcdbcaaddcabacabacccbcdcabacdadcadcbdbbdbabdaaddcabdcdcbcbddccabdabbcdcddbbbcbbdbabaaadcddccaaccaacddadabadcdbacdcbacaabddaababdadbdbabaaaaccddcacdacdacdaccbacbabaadccdccbddcccbbadacddbdacdacddabccbabddacbdcdcbcbaddddbbdbbbbcadbbdcddbcbbdaaaaadababdaddbcabbbdccbacbcdccccbcabcadadcccbcdbcddacbdabaaddbaacccbbadcadacbaacdcadacbbbaacaababbadbbaacdabdbababdadaacbcdaacbbcabaaaadadaadbcabdadddaacabdcddaadbbcbbabadcbdddcadacdcbcdbdcbdbcacdcdcbcccacbdcbdabcacdcabaabbacddbccacdddababbdbbbcbcbaadadbccccaadccbcdbddacbdaddcddddcaabdcdcdbadabbbbaddddddaccdbacdbbaaaabacaacdaaddbccbaddcdadbabccdbadbabacbbccbacadbcdacdcddcbcacabdcbcbdadcdcddccbaaddaacaadbbaadaaadadccdcacbbacdbcbbdcaabddadbbaabcacacccaabccaabbbbdbabadcddacaddbbbacaddcacbbabdcaabbaaabaacbccccbacaaacddccbacbbbdcbaabbbcaddddbdcbacaddadbacaccdcabadcdacdcbacbddccaaaadaccbdddacdaccbcbdbaacccbbcdaddabaccccbdbdbaaaaaabbaccddbdaacddaabdadbbdcddcbaadbbbaadccdccabbaadddccabbbadbacaccadabcacacacdbbdccacddbcaaacabadcdcabbbcacddaadcababcbccabdacadbccbbabbddbaabdcbcdcaaddaabcbddabcbbdaacacaadcccacbabcbbcdccadbdbdbbaccbacccdbdbdadccbdcacaaacabaaddccdccbbcdaaacdbdacdabcdabbaaaadcaabbbdbbdbcaacdacbcbbdccaccdddcaadbcbccdccabadabbcadccbaadcdcdbacbcaaacbadabaacadbadbccadddcbbdadbddbadbabbadcaabaccabcccbabcccaaabdbabdcbdcbcadaabbdaaaaaadabccadcaadcbbdbbababdababcbabbbdabcbdcdbabdddadacbcdababdcababdacdbdcbacaadccacacbbcacccadcbaaabadbcbdabccdcbccdaacbccbdbaabcdaddddbcddbcdcaccbdacdbddccdbdcbbbacbdccccdabbbaabaadabbcbdbdadbdacaadadaaaccddbddcacdabdacacaacccdabbbcaabaccadbdadbacdcbbadbddddbbaabaddaaaabcdcddbabdacdadaccabbdcdbcdaaddbcabbbadddababbbcdacddbddcaccdbaddcddbcabadadbdcbacbbdbbacddadaaddaabcaacababddcabcadccacdcdacbdcbbbdcabccacdbcabacdcabadabcbbddbdccabcaabbbbabdcaadcbdbbdbbcbbdcbcdccdbbcdcbcadbbcddcdbdddcddcdbcaaadcdbaaabbdbccbdadcbbdbbacdbcdcdaccaabaccbcdcbcaaaadcbdbadacaddcccacdccaabadcbcdbadaabddcabbdbadbbbdccbacdbaccdcccbadaabbccdadabcdaadcdadaccadabdbdcdabcbddcbbccdbabacddccbaddddaadaddbdcdbdacccadcbbddbdabbbccddaadbbdbcbcbabcabadbbaabcccabbdcdaccdddacbadaccbbabdcbdacabdcdaaddaddcdacadadbccbbdbacbbbdbdaacabcbddcadcddacbadcacbbabcadbacdaccbddbccdbdbaddbbbbbcaacbdcccdbbbbdbaacccbdbbadabddbbbaadbdbdcaabcddddcacdbbdbdcbccbdccbadbabddabaccabbcadcbbbacbacbaccddaccbddbdbcbdcdccaadaaabdacddbcccccbbccbcdccbaacacddccacadacadbbbcabbddcdadaccbdbcdccbaaacaabadccddcdaccacbccdbcabcdcbadbbbcadadbbaabbddaadddadbacdadabcdadabbbbddbaacdcadcdbdcacccccacbadabbadccddcdcdaccabbdbbcacbddcdddbddbcadabcbdadbcbacdbacdcbdcbacacccbbababdbccbddaddacdcacabbadbcbdbbbcadabcccdcbcaacabbcdadcadbaaaaccbababadcababbadcdbaadcdccbbbcaaccaabdbadbbbbcacbacbdaabbcbdcccbdddcbadcdabbabbadddccccdcacdbbabcbdcbcabcbcacacbdbabccbacadcdadbdbdacdbccbccdcccaaacadadcacaccabacbbccbccbcbdacaaddbadacadbcadbddbbaacdddccacddaabbbdddadcbbbbcbdcdbbdcdbbbccbacadbbbadcbaaaaaacbdadcdbcdbbdacbdabababdadcbbcdabacadcccdbcddbadacbcdddccddacddbaabbacdbaacdcbbcbcbcacbdbbcbdcbdaaaccdcdbbdcdcbacdbdbaacabbcadbbaaccbcdbcbccbcaddbbbbbbabcddcccabcadcaadcddbaddcdcbbabcdcdaabccdbdcddabcbadaddbdcdbabdcbdcddaddacddaabadbdccdaabbadcdadbccddbdcabcdcacacaabcaacdadcbdcbbacbdddcbccbacbbcccbbabddaaddacdabcadbbacbbdacbaaadacbbdaaccddbcbacadbcccacadcbbcbbccdbbbcdaccacdabdccbdaddcbbbdbdcacdccddbcdaaaadcacacaabbcdabddccbaddadcaabbbdbabcaaacddcaccccddadcacbbcbbcaddabcdccabbcdbbdadcbbaccbcadbbcddbbdcaddbcdbdbbacbaddacacccadcdcbaccacdbbcdcbdbcaccbdcddcadcddadcddcdbcbcddabaabdadcdadcddcababdddbcbcaabbadcdddabccabdabcdbdbbbdddddabddcdddaacaacabaccdbdaaaaccdddddbcbdddabacbcbddcdccdbacbdcbcdacdcaabadcbcdacbadcadbbadbaaaabacbdcaacaacbdbaddccbaddddcbdadbadaaabbbdadbdacadadcdacabcbdccaabcbdbddcbadbbdaaadacadcccbcacacdacaaabcddbbcccbcbbdbdcacaababaaddbdccacddbdacdabcacbbdbcccabcccadadccbdbaacbdcdabaccddddabcacbcbbddbcbcacaaddadaddcddcaddaabadabcaaacddbaadcdaabbaddaddbacbdbdabdcdbaadabadddcaddcccacbdabdabadbdabdaaadcbbcaacdddccbcdbacbacdaadabcbdadabdbccdcbaddacdbaddaacabadbaccaadbdcbbbabccccadccbcbcdcccbdbcccadcbacbbabbaccbaabacbdddadaccabadddacadccbacbcdaccdadccbcaadcbcbdddacccbabdbdccdcdcaaacdbcbdcacacadcddbbddddbcdcdccaaaaadbcacbacabddbdadccdaadadaadcccbabcbaccabbdddacaddcdcdbcbacdbcabbdbbccddadcbcadabdabdadddacadbaaadddbaaabacdacbadcddcabccacabbacbaabddaabaddddadbaadbcddcabaaabcddcaddbbbdbccbabcbaabbbbabccbdccdbdcbdaacdaccbadcadadacdddaaabcaccdcacdbccaaaaadaabdbdbcbadcccbbcaaadadabbacacbdcbbcddbdbccaccaaaaacbccaccaddadbbacdabdbaaaaabcbdddaacbadddbcaadabcdbadaabcdbdbbdbdabdcdbdacbbbacdbccbacbbcbbcaaacbbacbcbabbdbcaacbdcbdacbdaadbcbababbdaaaabdcabaddacaadcadbdcccbaabaccbdcacccbbacdadbbdaadcbcbababbbabaadcbacbcadabacdaabbdbbaaadaaaabddcaddcbdbcdadbddacddddabbadbddcdccacaadcbcacdbaacaddddcbbbcbdcaaaddbbcadadbbddccbbcbadcdacaddcdaddabddbcbddacbcddcdcbcacccbcadacaddddabddcaddcbddacaadbdbbccbcdbcbcdabbccdacbcbabbabbcacccbccdbddcccaacbccdbbabacacbbdcadccaaaaacbacabcacdcdcdabdcbcbbbacccbdcadbbacdaaacdccabbbcccadcadbaadcababaccccaadacaaabbabcdacabbcadcaaacbbababcbbddcdbdaacabcadacbdcccdabcbabcccacacdbbbcdbccabddccbdabacdbbbbddbcdabcacdcadbdbabddbdccdcdbbacabccdbadadcacadcdbadcdcacbababbbcdcacdbcacddacbaabdcbbddbaddaccadaccccdbccdacbbacabbbccadacbdadcbcaadbbadddabaabccaccbdabdcabccabbcbcddaaadccdbcbadcaaabcacaccbccabbccdcaaabadccacbbcdbadccbcbcbdadbccdadaccddccadccbccdbbbbdbcacdaacdbcdbbbbcabddcdadcdaaacdacdabcccbdbbdbbacdaddcdbdcadcbcadaccddddbcacabccbacbcdaaccaaacadcadbabdbcdbddbdbddbaacccadcdccdbdbcabccacbcacbacadadaaacdadbcdcccbccbbdccdbdbccbddcccbdcbccaddbbbbddaddbbcdabcbdbccadccacbdacdacbccadcccbbdadccacbabdbbabbcaabcbdaaddacbbdbccaacdbbabddacbacbcbccaacaaabdaccbcdaccbddadbabadcdcadbadcadddadcddcacccacacdabcbcacacabdccdaaadabbddbbabbaaabbbcbdcccccadbadaacadcbaadcaacdabcbbccacbabccdcccababbbadaacbdadccaababacdcdbcdcdaadddcaadcabbbccacbadbdddccacdbadcadaacbaccdbaadacbadddbcdcabbcdbaddcaddddaaadbacccdcdcdbadbdacaacadadaabbddcaacdabaaadcddbbccbdddcabddabaacdbdbbaaaddbcaccbbcbddbbaddbcbbdcaaaadacaddabdbdbcbbccaabdabacbdcddbcdbbadbbacbadaabcbabbcadbadbabbddaaabcaacbabbdbbcaddbbbabcddcaabcacacbbbdbdcdccdcddacabddbcdadddbbbdccacabbbbabadabccbaacaaaacdabbaadcadccacadccbacbaaaadabdcdacabadcdcccdbccbddaddcbbbabcbcaacbacddcabdccbccdbccaaaccdddadbcdaacddabddbacbbcdcabdaacddacbaadacdbbdbdcbadaccbbadaaabdaaacdbdcbcaabaabbadbcabaacdbbdaccabacddcadacabcbbddacdddadcabcdacdabaaaaacdcacadabbbbddcabbacbabadbdbccaccbcadbdcccbdabaacdaccdbdbcaddabcbddcddcdcbcacdcbaaaabadaadbaaabacccdccabadcabbbdbbbbbcabcacbaaaddaadcbacbcabcdcadadaabbaacbbccaddcdaddddbdbadcbdcbbbcccacadabadbdcbabdcadcdbbbaaacbabcabbccdcaddbbdbadcbcabbbaccccacbabccccabbbcaccdccddaaacdabcbcadcdaccdcbbbdbadacbcdcddccbcaddadccdabcbabcbaadacdcacadaabdbadbbabbcbbaadccbaacbcddcbbddaddcadaaddbbaacacbccaaabccdcdbbadbdababacbbdbdcbccdadcababbdcbacdbabcadadbcddabbbbbdabbbacbaddadcdadadbcddccbdbdadbcbbbbcddadbcaacccaddaccdaddacdbdbacaadbbadbcbaccadadacacbbcadcabbbccacdbdccabcbccdacaabdadcdccbbabacabbbcdbadaaaacccbabbbcdbdccbcccdabcbddcddbdbccccaacdcabccaddbcdacbbaadadbcaaccbaccacbaadddcaaccdccabdbccdccbcdcbdbbbbcdcadacacbddaddabdcacbbbbabddbbddadbdacddddddcbcdacaadbcddccccbaccccabaadbababddadccdaaacdabbaacdbcbadccbccbdbabcaaaabacbbadcabacccbacaacababcccadabdcaaadccbadadaaccaccdbacdacabccdbbdcdbbdcaaddbbacbcbbadddcacaabcdcbbdabcbbcdcabacddcbbabdbbbdcbcabcdbcaccadabbbcbdaacccbadccbadbcbcdbaccbcbccbabbcaabadbdccaaddadabcacdbdacbbdbbbcabbcdcbabdcccbbccadcdcbccccabbcadacdbcdddacacdcabddcdccbdbdcbadcbddadcababcdbdbdaccbadcacacdcccabbcdbaddabdcccdaddccacdccdabbcbbabcdcbdbccadaabdadbcacddbccbdddbbbacbccadccdbcabbabcdcdadacbcbccaaadcdbaccdbdcacdcddadbcbbabcbcbadbbddbcaccdcccabcadbcdabbcddcbddaddaaddbbdccadbdcbbbcbcabcbcdbcbcabddddbdbabbccacbacddbdcdbbadcaddabcdcabcbbcddbbccbcbcccdbcaadacdadbbabaaaacbcdddbddaacdaddacabaaacbaaccbdcdbddabcdccdcddadaabaccccdabbcbcdcbbacccadcacbaabaadbcbdabccbaccbbdabcaadbddbcabbacbdabbcdbccccadccdddacacadbdbcacccccbacadbbcacadadddbdabadacabacdaacdadaaadcbbcccbdcaacdadbdcbccacbdabaabcdbabcbcaabbdbdbdaccbcdcaabcacbbcbacccadcbbbcaddaadcababadbdbdabbbacbdbacdaaccdbccdbcaadbbdabdbdbdabacccdccdadcdcbcbbabdadabbbdcddbcccbabadcbbbdadccaabbcdacbbababbabcbbdcddbddbdadabbccaadcdacbbcbadcaacadbabaacacaddcbadacbcddadcbadcabacccccaacbbaababaadccabacaaadcabcddcdcaaacadbccbbacaacccbaccccdaaabadadabbbcdacbdccadcccabbcccbdacdbdbdcabbbbdbadccaaddddaaddaaaaadaadccabbcdcabbdacaaddbabbbddcacaccbdcdadadcccddddbccccbbadbdcdddacadcbccbcdbbbcbbdbddbacdbcbbbaabccdcdababddbabddaadabcaaadcbadcabbababaacdcdcbbcabdbbcccbbabcdbadbaacdcddbbcbabacbbdbaabadbcaddbcbcddabadaacbabbabbbadcaaaaaaacdacbccddccccddcddcdbbbcccacdadaddabdbcdaaadbccbaadcbbddbdacdadcadcabcdacccddacbdbabdadccdcacadaabdddbbacccdcaddbdbcaddccdcacdbddddbdccaccdbcaacbacbadddcabbabbcbdbcbbddcdaabaccdbbbcccdcacabccadbcabbacbadadcacdccdaaacaabccabbadccdbacadadccadabdcacdddcccdacdbaadcbadbbccbbccaccbaabdbabbdbaadcacdabbadbacaaabacbbbbbcacabbdacdadabaadcbcbdabacacdabbbacbbbddbbaaaaabadbbdbaaabdaacbbbaabbabbdccaccbacddaacbdacdadaadbaddccccddddadddbaacaabbcdabbcaaadadabcadcdbcabbbddbdbddabdcbaacacaccccbaabbcbaccaadbadccabdbbadbbaaacabbdddccaadbaacdcbaaaaddadbddacdaadcdbbcadddacdccbcacddddbdcabcaddddcbcbddbdbddaacdaddacdbcaabcadbbbabcadacdcbadaabacbdaaaacbaaacbdabdacbbadaaccdbdbabaaacabaccabbbddbcbbbadaacbbddcacbdacbacadccccbbacacccbcbbbaabcdadcbdbacbdbbbadabdacccababacbcccbdccdcddbbbaabbbddacdabbdcdabdcbddccbaaabaadcdacdaadcabbbdaaaabdcbcacbcbbcbcadadbcabdccdddbddacdadadcacbbabdadabadcbddcdcbadacbcddbacdadddcdadcabbbcbabacbbbdabaccaadacabddcabbcddabddccbaddcbdbddbdabaababccbaaaadcbdabcbcdabbacbdabbbacbbcbcabcbccabbcadbbabaadadaddccadabdddbbcddcabcbadbbacaaabaacababbacaaddccbdbabcdababcbcdaabadabcdacddbccccdcdacbdcdcdccccdbbccbcabddddcbbcbcabcbcddbacbccdacbbabadcdcccccccdbacabcababadbdbcdcbcdcbbacbccdbddbcbcabbbabcccaaabdcabdcdddbdaabbbcddbdccdbdadbbacdacdbddcadbdddbddaddaaaadaddacdcbcdbccccaaabacabddcdbabcbcddbbbccdcabbdbaaaacccbabaabaabbcacbbacdcbaddcabbabcbcacbddadcdccbbaadbdccdbbdccbacddddddddacbaddacdadcbdadbbacbabbccbbddcbbabcabaacdbcdadbddcabbdcbcadbbccababadddaccbbbbdaaacbaadcbbbaabbcbcbbaaadcaaaccdabccbddbbdcbcccddcdcababadcccabcabdcddbcbabccacbcbbadabbcdadccccccbcdacdccbdcdcabaddadabcadcbdbbdcbbbbbbbcdcabbddccacbbaabcbbbabaccbddccdcbdcdaaacbbababddbdbccadcbbacccbadcbadaabbcabaababcaacdaababcacabdccdbdcccabdcdbcdcdccdbddaabccacbbcdbccbcdcdccabccddaabababbbadbbacadbcbdbbcdaadadbbbccdddcddadbcdabccabacccdcddaaccaacadbcdddcdacccdbadbaccbabbddaaaabacacdbcbcdddbddbbbdbcadadaccbddbcaccbabdddcdbdddcdccdabddbcbdadbadcadcccabdaaabdbccdaacdadcbcddabbacddbbadbabcdcddbbabacabbdbbdcbababbcdaaaccdaababbcbadaddaadbacdddbaaddcbccbdcccaaacaaaaacdbaccbbdcaacdcaddabaddddabdcadacacccbbbbcbccbdccabddacdbcbacacddaddacabbcacacdbbcdbacbbcdcccabcccdacddbdabbdddcdaaadacddcadabbdccdbdbbccccccbcaacaaccbcbcaacbbcabdbbcaabddcbbdbacdbaccdddddabbbbcadbdadabaddbababbbabcdcaadcacaadbaadcdcdadbbaacdcdccadacdddacacacdddbbddabbadbcbddacbcbbcdbadabdbbacbdbdbadadccbabadaababcdadbdbabbabdaccabdbccdabccdaddbcbcdaddcdaaadcdacddabacadcddcbcdacddadadddbbcdaaabcaaaabbcbabbacaddccdbddaadddccddbcaaddccdcdcdaaacabdabaabadacdcbaacbacbaacddddbbccacbcdcadbdabbddcddccbaddacccdbacbcdcdcadddccddbdcacbbbaccddadbadadbdccaddaabddddbbaacbcbcdcabcdbcccaaaabdbbbbccbcdacacdbaddcdaaaaabcbacdbbbcbcdcaaadbacacbdbdcadcbdccddaadadcbcadbaaacaadbccbcdbcddccbdcbcdbbbddbccbacddcabdabcbdadaaaabadaaccbbbbacbacadbbcbbdbbcadadbacdabdcdddbdbacdcddaabdbbcbbbcdabbaaadabadbdddbbcabbdaaacbcdbabbcbddababcccabbdcbcacdddcbaabcdacbdbccacbacacaaddbacdacbadadacccabbbbcccbcadbadddabbcbbddaaaaddaddbdbcbbcbbabbadcaaaacbaddcdadccbccabcbcdbadbbbbbdbdbaabdddcbdaaabdbcbaabbcdbbaccbcbccbdccadadbdcadadddacdaaaaacdcddbdbadaadcababbcbdddcadcdbddacbccbcdaacbabdcdbadcbcdccaaadabbaacbdbacadbaccdddcdcbcbababaaabadbddacdddbabadaadaddcbacdccaadaccabcadcbdddccacbdababaadbddbcadbccaabdccabbabdbbacdcbcbdccdcccbaabcadbcacabddadaddcaadbbadadbbdbdbbabababcbcadbcaabaabddaabadbccbbabdaacddcbaaadbbbdabcaccadadddacddcadbbcbcddabbccbcbbdcadccbaaccbababcbccacdacdddbdddccaccbddddacbaddbbdcacaaaaabbdaacabcbadaddaacddddccdcadccbcdccaccccdbdabddccbabcabaacaadbcdcaaacbdadbdbaddbbabdbabdbacbadcbbddabdacbbbdcacaacbcabccbcbbdbabcbdcaaddbcbcabaaacdaaccdbaaacbddcacdadbcddacbccdcddddddcaabbabacccbccacadbccccdabadaddacdbabcdcbcddbabcadccaddcbcbdbdbbdddacdaddbadcdbcaccbddabbbbbaaddacccaabaabcbabbddcacddaadbcccdadaaaacdcaabdabcacbbbaadbdbdcaccbaddccdaaaaaacbabacdbdaccccdaadabaadaaabbcbdddddadaddadcdbdbabbbcdbddcaacccccbabadccaabbdcbddcaccdddbabdcbbdcdbdacaaabadbbdcdddccbbaabddcbddbacbcddaaabcbbabcbbddccbdadcbbcdbdbdabddacabaccaacccdbabaacddccabcdbbaaacdbabbcadccdabcbdbdddcdbdcbddbbbccbbbdcbbdbdcbcbcdbccdcdaacaccbdababaadcbaccddacbbaccbbcbbcbbccdbcabacddaddbdbcbcdabdddddcdbacddcddadcdccbcbbbcccdddddbcdbccdbbcabdbcbdabbddadcaaabcbabbcbaabbbaabbcbaacdbadcbacdadadadccacbbcaababdcadcbcdababbaadacdccabdabbccadaaacccdcbbdbdbbacddadaabdbbccadbcddabdbcdcacabbaabdddbdcbbbdaadabdccdbabddabcdcbbbbddccdaadbabadcacaadadbabbcccaacabbbbdbdaccccdddababadbbddddaaccacbabbaaabdbadcddcaabacdcdcdccbcccdddbdcaadddbbdadbbcaaccaaddacdcdcccdcadbdddbbbdaaddbbadcbaaccdacbcbadbcbddcbaabbdaadbcbbabdaadbadbcccaccccbbdbddcbbcabdcbddbadcbadbbcabdbdacabaaacbabdbdcdbacbcdadccbcaaadbbbdacacabdaccdbbcddbcaacddabdddcdcabbdcaacdacacacbdcbbddcccdbaadbdadbaabdbadcadcadabccaccbccadbbadadacdabbdcdbddabbbcdaadabbdcddadbcdccabccaabacbcccbbabccccdcbaaccdbbbdccddbbccdabdbaadbcdddadddacabcadcbdcdabaacabbbacbadcbcdbbacabdddcbbabaccacdbdcbcaaacaaacbacaaadacaccaddddbcadacbccaabbabddacdcdbaadcbcabccccbcdcbcccabbacbabadbdddabacddccdcdabbddaccdadcbbacadabacdbdacacdddbdcbcdcdacaccadbcdbbabccdaaacbdbbdccbcddbcbdccaabdacddbddcaabcbdcbbccaddccbcddcadbbcbbdbdacbcadaccbdbdbbbcdadcbcaadcabddcccddaaccddadcadbcaddbdbccbbcdacbdbbacaabdacbddcdabadcbbbccadbaddccdbddbaadbbdbdadccaaaababbbcaacaddbbdbadbcaccddacdbacddbccccabbabaabdacabdbcdcdbabdbabbbaadcbddcabcacababccbacaadddcdaacdcadaacbdbcdacbdbddadadcadbabadaccabbdcdccacccddcbdaccbaabbbbdbbadabacabddbcdbdcbabbadacaaabaccaaddacbcaccdcdbcdaaaccbbccadaabddcdcccadacabbabcbccccbabaabbccdccbaaadcdbdcccbbadadbbcbbaabdacabccbcbdbaccbbaacacdddcccacbacabdbcbbaacbdcbdddbaabbacdadbcbcbdbcbcbdcabadaabccbcaacacdbadbdbaacabbdadacabbadccadaabadbdabcdddccaccbcbbacadddbcccaaccddabcdbaadaabcbbdddcdddbdcccadacaccadadcccbddddcbdadbbcbbdadbdacdcdbbdddbbcdccbadaaccadaadaabacadbaadabcbdcbaabacccdaabcddcbaaddcabdbbdbdacaaaaabadbdadbddbadabcababbcbdacadcabdbddabbccdababdddddcacbcbcdadabcabbdbcdbcccddcabadadbccabdccdcdaddccbbdbdbabccbabdbbaacccccabadbcaacbbdbdaadbbddacbbddcacaabaaacbdabcababbaadcccbdcabdadddabdbadadabbddcadbacccaccccabcdddbdaaabdaadadccddccadccdacaddcaccbbbbaccdbdccacbcddccdbacbbacdcabadcdccadacbbaccdcbcacbabcaacabccdbdbcddbcdbdccddddbccddbccadccdcddbcbddcbadbdcccddadddbdddbbbadbbabaacdaaccacdbdcbbdcdcbbcaabcbabcabdacacadcadbbdadcbccadcdcbddabbabacbabdacadcccdadadbdcaccdaddcbdcccaccdadccdddbddcabbbbbabadabbdbbdcdcabdcaabcdbdcadddcdbaabdccbbbadcbacbaddcaccabaaccdaacdbddabccddbcdaabbdddbadaddbadcaaaadcbcabdaadaaabcdadbcacaadbcccacbdccdaabadcbdacdbadadabdaabbbbddbcaddbcbdbbcabadcaaaabaabbacccbcaddadcabadbddabbdabadcbbcaabadbdddbaccbbdabbbbabbcaabcdccdbdaabbacddddccdddcdbcddbbdcaacbccaaccaccaddbadcddccadaabaabdcadcdcbcaabdddbbabadbadcdcbdcddcdabcbbccdddbbbdacccaadcdcccdbaddbacadbbcabdabcaadbaabbddbabbbdadadadbdcadbbddcbdbacabacacdcbacaaabcccbaddacdaccadbddbbaadabcdbcaabadcadaddcacaacdccdbbabadbadcdcaaaaabcbcccacadccbaaadaadaacddccbabdabdabbdddaadcbbbadbcddccdcacbacdbcdbdcdcccaaacbbcccbbcddcbdcddbccaacbcaccbdadcdcdbdadababbbdbcdddaccdddbacccbaddaadcadacadbacbaddbbdadaacdccbdaccbbacacaccdbbabdbdcdacadbdadbaadbbbcadababdcdbddbbdbaaccbdbcccbbbadbcccacadcdcacbdbcdcbcddaccdcccbcccbddcddacadbaadacdbcccaaabcddabdccaacbacdbccdccbbbaabdcadabcaabaccdadbccacdadccacccaaaaddacacbdaddcbcadbbbcbcbdbcccaccbbdbbdbcdbbcbdbbbbdcddadbcadabbbcabdbdbbbcaaacbdaaddccdadcccbbbcdddbdaadbbabbbcbbbdadcadcaabddbacbabbddcdbadaabccabdccbcadccccbcacbbbbacadabdbaddbdccbcaddabbcbaadccdaaaabbdccdcacbabccabdcaccadbdbbdbadbaacdadccddaabccbdadbabdcdccdaccacdccdcbacdbddccbcccccdddbbbbbcbcabbdddddcadabdaadbdadbbbdbbcdaaddabbcbbabddbcaabbcdbdbcbdadabbcbaadaaabbbbcdabdcdaabadcabbbddbccaddbdabdbaddcdbbbbddccaccabaccdddcbaccadccdbcbaaddbbacbccdbcbaccadacdadaadbcbacdccbbcdcbdadcbadddacbabdaccdbcbdaaddbcccdcdccaabacddcabbdbaccbcdbcbcbcddadbdbcaaacccdabbbccbcdbdadcdbcacdcddadaccbabcdbdcdaaacacbbbdcccdccadaacddacadccabaadaddbddcacadccbdddabbacbcccabcabdbccdacdabbcadccbccbcccaccbcccdddacabbaaaacbddaddcdaabadcbdcbabcacccccdcabdaddcabdbdaabbcccaddadbaaabbdadbccbaccdaaddcbddbbbabbdbddbddbdccdcaccbcdbbcacaccbabbacbdbbbadcdacdacbabadcacddddacdadbcaabdbbdcacbacdddbcaadcdbdbdccacaabcbadaddcbcdcbbbaddcbaccdbbababbcdcbccccddbbabdbacdddbcaddddcdbddcaabbaacccccacdcbaccddaddacabdadababadbdcbcdcdbdabcbbdcabcdbdcdcbdccadcbbaccadbbbabaabbbdddacbcdabaabdbdbaaabddaccbdbccdbdbcbbdbbbaacdcaaabbbbcbbaacdbbaacdbccaacabababdbdbcbcdbddadbdcaadcadccccaaabaadabbbcbbcbdaaabdbabbbadbabaccccddadcdbdaabcbdccbbabbbdbcdddbcaaaadadcabcdbbddcbccdbcbccdbddccaadaaadccbdbcbaadbcdcacbdbddbbaabddcbadcacabcccdbadbbbdbabbdbccacdbdbcaddccadddcbbaacdadbdcbaaaacdbddbabacccdabdaabadcababbadcdddccaaadbbcbdbdbccabdcbbddbccccddbcbadcbaabcadabaacddddbacbdcaccddacaadbddbcbdddbcacacbdcdbcbcbcbcacbacbdbacbdbddaaccaabbdbadacdddcabaccabaadadabccdccdcccdacccddddabbaccbcdcccaddadadcbcabaccadbdabacadbbbddbacdbddacdacddaaacdcaccaacdbdcbddbccbbcbacdcadabacccaaacbcdaccabbcbaabcabdadcbbbdcbabbcababaaaacbacccaabcbcddccccdbcaddbdbccdbababbacadbbdbbdbaddbcdacddbccadcdddccaabcbbabddbddcbbdaabdccbaddbabbadcdaaaadacaccbacddadbabddabbbcccdacabccadddddbbbbddaadbdcdbbdcbbccbbbbbcadadccbdadadccdaaaccccdccbbccddcabddaacdcdcdcdbcbbcbbcbcabadaabcbdabaccabdadbcadcbcaccbaacbabcdbacbacbccadcbbcacbdaabbdadbadbacaadbddbbdbcdbdcbaacbbbdbdbccdddbbadadcacbdbcbdbdbacbacbdddaabccccaabbbadadccacccbabcbddbdacdabdaaadacbbbccacdcdadbdddddbdaaaaabadcbbbdadbdcbacccbadcccabadccdcbaabccadaddbddbcadabdcadadbdbbdadaacbdaddaacbbbbdcddbdbbccadbbabacddacbacbacbbabbdabcaccdbdddacdccabbddbcabbcdbabcabdbbdbbcbcdacbbdccdcacabaacabdbdcbdcaaadacddcdcaddcbabadddcadcaaadabcadabcacabacbcbdbdcbbddcdaccbaccbcccbdbcdcccacdabadacabadacdbbddaababbaaccdbdbdaddccaacdaadccccbddabadacaddccdddbadbcccdddbbbccacbadbaacbbccaaadcdccbdbbacacdcccbcdbcddccdddcbdbabccbcacadcbbdbbccdbdbacabdddadcdcdbaadddddacccabbdcacddaddbbbbcaacacacbdcbaaccdadadadcaacbadbcdccbbdbabdabcdbadbcbbabbddddaadccdaacdcdcddccdcbcbdddbdddcdccbcbdcacccadaaaacbbabbcdcadbcbcddddaddddadadddbbdbaaddddbcbcaadbaabacccbbbdbadabbabbbcbbadcbcbcbaacacdbcdcadbaabadcccddccdbcdddbcdaccbaacbacdbaadadddadcccadcdaaacbccdacccdbbdbaabaaaabcdcdcdbbbbccadccabdaadbadcababadcddccadccbbacaccacdbaaccaccbdccbbcdccbcaabdbbbababccacdaaddabcbcabccbbdbbcdbbdaccbadddcdbdbcaaccbddcacadaddabdbbbdcaaaaccdbadcddadacbcddcdcdcbcdcbaadcaabaaadddcccbacbcaabbabdbcacadacbabcbaccbaaccddbbccbdadcccaacaccbaadbcbadcbdbacbccbdbbccdbddabcdbaabddadccdbadcabddcabcdbcbdabaaabcaccaacbaddaddccaacdadddadccbbbbbdabbbdbcccbdbbababccacabbcddddcaabbcbcaabbdccbcbcadabacbcbdbadcdcdddaadabbaabcbccbbbbcadacabadcddaadbcadbdabcabbdadccbadadbcddbdcdccddacccadaacdddabcccdbbdcbbdbcbbcdbacdcadadcccbdcbaccbbccacbdcbbbbbdadbddbadacbcdccaaabcdbacacabcccddabbaabdbbcdbbbbadaadcdacbdccdccabcddcabadbbdcbdcdbcaaadbbadbbaadaacaabacdddbcaacdccdacabbbdddbadbbdcdcdcbcdbdbabbaadbbbdddcbcddcbaabcbbbddacbbabcbdbbabadcccccdbcbbadcadccbbcabbbdacdabaabbabbddbcabcbbbbbcddccadaccccacadcdbbbdbcdbcbaaacbbabaabcbccadddcdaaccbaddbccbaddacdbdbadaacadcbdcaabbabcbddbbbcdbaddabbdbabccdcdcadbadbccdccaabcdbacddccdcabbddbdcccdabcbaabcacccddddaabbbaabcaaacabcdcdcdacacbdbdbcbbaaacccacbdccaacaaaacdddacccaaaaddbdbdadaccacbbdbcaacdadddbbbddccdccbcacaabdadccddabddcacabcbadbadcbdabcdabbccacdbccaaabadbbcdddacbbbdbddddbdcaaddabbdcabcbdaaacabaaacadddddcabaaadabbcaabbcddbdbcbadcbddaaabcbccababcbdabbdccccbdcadcabbadcbcbbdabdddbabdccadccabddcccaadbdbcbcccdbbcaababcdddcdaabddbbddbbdabdbddcabcabcaaddbbcacccdacabdcdaadbdbaddbcdbacddbadadbbbbbcbdaadbdddbdbbbdbcacdaddadddcacadccaccaccbabdbbdbcdacdbdaabdacccdaaaaccaaadadaabcbabdabdabadcbdcbcbdaabbacbbdddbdddabdcdbbccaddddaacdaccbaabacadcadcabbdabacdbbadcccbbabbdabacaaccdbdbbdbbadccabcaacccccbdcabbdaadcadbbcbccaaadbbddbadcbcccccddadacbabbacdbcaacaadbcbdacdabababcddcbdccadddddccddcdacbcdabcaddddbcbabbaadaabcabbacaddabdcddddacdbccabdabbdaadbcacdaccdaacabaabbddcacadbbbabcdbddddbcdbbbababcaabacdaadaddccacabbbdaabadcacdbcabaabccbacbcdcdccbabdbcdabcacbbadddddccbcddacbcdccabccbcbccbdbaccdbcdabaabcdcdabbdcdcbcaaccbccdaadaaaaaacaddddbcbaccadadaacaaccabcdcbbddadcbbadaadacbccabdbadacadcabcdaaccaadbdccbdabaadbdbcacbccdacdbddadccaabbacaadbcabcdababdcbcaabadddcccbbadddcddaabcaaccadacabacaabdccaccbacdddadaaaddbbddcacccadacaababbadbccabcaaabaaaacccdaadabcdaacddcddddbdddacdacbbadcbbbbacbbdcabccacddbcbcdaaddbccbccbdaabbdbabdbdddabccbadcbdbcdcdddaababbdccbacddcbddbccbbcadccaadbcbccddabdcbccdbbdbdcccdccbcdadacdbcaabcbdcddccaabcbdbddbacddccbcaddaaabdddcdaacacaccdccabddcbddcdbccccdcaaaabaacdaddbcabcbabccaacbabcdccdaaabbbbcccbddddbccdcccacdccccaadacbbbabdaaddcadcababacbccbcdcadadddddabbdbbcabdccabccaacdcadcdaacdbcdababddccdddabdddadbcdbacbcbadaaaaabdcbcaddabdacaababddcdaddaddacbcccbbcdddcacbdabcbbdbabbcdcbcaacaaabcababaaabdabbcdcbaabbaadcbaccbbbcdcdbbdcdbcacbcadcdaccdddcadcabcbbccadcccacaacaababbbbcaabdbacbdbbadbdccaabdabacdcadccbcbcdcbdccddbcbacbcbbbccdcaddbcccaaabdcbdacaabbcacbbdccaddcacaabbdacbcacddcbaadcbbadbbcddadccbbcaadabbaddabbcdadddcdcabcbccbadaabbaccbbbcddcabcdacbddbbbcbddcaadadcdbabbbddcacdbaacaaadabdccabbabbdbcdbbcdcbbdbdcdbdaadccaaabdbaacccabcccaddbbcbdbcaddbdcdbccaadbdaacaccabcdabddccbcbdcbbaabccbcbbbaacdaadacabbcbaabaabdabcadacadaccbbdbddadaddadadbdaabdbabcaabbdbaabbcdccbccddcccacdcdbbcabbbdacadbaaaccdbbdbddcdacbdacbdabbbbaabcadbddabbdcaddcaadbbbbacbacbacdcccaabcdcddbbdbbccbcbabbbcbccaddcdbdbbabbccaabbabcbdbccdadbddddcababccdcbcccdccbdbcdaaadccccbdbccbbcabddabdaabaccbabbbbaacddbdcdcbcbdcbddddccadcccbbacccaadccbbddcadadbcdadbcbdabcdccaaadbccbcdaacacaccdadaccaaaabbcdadabdaadbcccdabadacabbcbaabaccaaddcbbddbbbdbbdcbacbcadaddaacaacdbccbcbbbadaacbaaddadaccccddbacbdabaccaaabcacaccbbdccbbdccaddacbabdadbadddbabcbbdcccabdcaddabbbbaacdaddddbbabadacdbdcadcabdacaaaadbdcbcdbcacddaacddbdaadaadccdcabddbbaddcdadcabcbabacdcabddbdccbaaaadddcbbbaadabbabbbbddcdcbdbababbcababbacccbbcabdadcccddcacadbaabbdbacdbcabbacccdbcdcdbbcbadaacdaccbddaacabacaabcdcccdbbbadadbdbbaddddaacbadabbddcddcadadcdbcabcdbadbdbbdbaaccddaabacdbbaaddcccacddddbaabcbcdcdadcccbadddacbcddcabcbaacbdcdcaabdadbcbbbadadadbccaacbbadacadacabcaaabacbccbababdadddbcdbcbcdcadbcbbcdbddbcbdbbcadcabbcdddbbbababdaaadcbaaddcbaccaadccccddabdddbbabdadadddcdabbccdbbccccbddacdacbdacbbaabdacaadaaccdccadadddbadbacbaddaacbaadbcbdaabcabcccddaabcdbcabdacacacdadaccbddbbbbbbdaaabbdbbbcdbcddabcbaadbbacaddcbdadbbadadabadddbbbbcbcadaaacdbbbdbdbbabbabaabbcbbcdaccdadccbcdcdadacdbccdbcccababcabccbcbabaacdbcababbcdbacbbaccadadbbddccbccbcabdccbaadcdbdacadadabbddbccdddbaabacccbdacabbbbdbaccdbadcadcadaabccdccdaaccdbbdbdbcdaddcadaaacbcbddcadaaaacccaaabdccbaabacdbdbbaddcbbabbaadbbcaadcbddaabbcdacbbbbdccadbccbdbbaacddbdcacadcabbcddbbdddbcdadaccacdccbbacbaabbcccdcddaadcbdbbaacbbdbbbabcdacbaddacdabbadddcaacdaddaccacabbacdccddaabccdabaacccabbbadbadcbaaddaacdbddcaaabcabaaabcdbacdbdddbddacbadcdcdacacaaccadccacaabcccaabdabbcadbccbbcbbcbdaaabbddaaaccacbadbcaddbaccabbbbcbaababdddddbcaabbddadcbdddbbdbdcacababaccbdcdcbccaadbcccccacbbaaddcdacbdcdcccacddcbacbbaacbbacbbbbabcadbdcbabbacababbadabdcacccabaababbdbdaccccbaaaabdcdcaddacaaccbacddbbbaadbaaadcaabaabbdccaabdaddbdacacbadddcaddaacadaccccbadaacddacaabdcdbbdcdcdcaaadacacccadddcdaddabddcaaacadaabdccadccdadbcccabdacabadaadabdccbadbcbbacbdbbbbccbcddcadabaddddccacadaccdaabcbdbaacdcdcdadbaaaddbddbcadaabadbccddbddcaaaadadbbbacdbadcccbcddadcbbcacdbbacdbdddadddcabbcaaaadcddaadbbcbccbdacbbcbacadcabadcccacbcdbcdadcbdbcbccdcdbdddccdabbdabacdcadddcdaccccdbdbdcacddbddbddaddaabaaaaccdbbbbdbcbddddacccaadcbcdaacacbbcbacbcdababcbbbbadadbabbbccabbccbcbbcdaaabaabbcddabbcbcbaaaaddbdbdbdccbbdbaacdaacbcbaddabdaddbdaaaabcaaccdcadabdbaadcabccbbaabdabcadbcadddcbdcddaadbcdabbccdcbccbddabdbbbddcaabbccbdcccbbadccdbcbaaadddcacacccdbbcdcbabaccbcaaaadadaabdbcbaccabccdaaacbbdbdbbbcddabbbbcbbacaddbdccccacadcbccdbacbbaacbdbcaaaacacbdadacaadacccddbccbcbcbbdcbccbbddddadacbdbbacccdddccddcaadadabaabcadacddbcddcdbbcaabbabbcaabdbdbcccdbbccbdabbccaaabdcccadaccadcbbdddcadaacbcdaaadaadbbcabcadcdcadaaabacbbcdcaacdacbdbdbbccdaabbdbcbadcacdccddcccadcbdcadaddcaddbacbcaddccaabcbcaaacabbaacdaaadbddbddaabbddbddcbcabbbdbddbabccdadababdaacbbcbbadbaddbadcaaccaaddbadbcbadcbaacbaadcbacccadabbbbbdbaaccacacbbbdbacdcbdbaccbcbbaddacdababcabbbcdadddacdddbdbaadbabcbadcbcbcbddcdbdabaaaabdabdadbcabdbbbcadacccccabdbcabcbbabdacdbcabbcccddbbaabbdaccdddbbdcdcbaaddddcdacabbbadbdadbaadcabacbcadcdabadbbcbdaaabcdabbbadcdbaddadccddaabcbdbbccabdbbdaacadccacdbbadddaaccbadbbdaacabdcacadabadcbbacbdabcdbadbaabadccabbabbbdbbdcdcdadbcdacccabccdcccbbbaabdbbbcaddcabbbbaaaddacdbcdccbddcbadcccabcabcabddbdcddacabacabbbcdbacbdadcbbbdcdababaabadabdbabbdbabaabcccdbadbaaabddddaadbdbdbabdbbbacddaadbdbcddcddabaccccadbbcaaaddbcaacbccaddadbacbccbcbdcdcacccadcccbdcbabdabccacaacdbbccdcccddabbaddcdabdadddcdabccdbaaaaadbbbdaadccdcdacddbbbbccaacaaaddcbcbbcbccbbbbbacacabbbaabccabadbbddcabbddcbdbcaaabdabaadcadbbcddcdadbbdcaabddaaccaaabdbcadbbbaababdbbdbbcccadaccdaaacddcbcadcadbaccccdabdcccdacabdaddbdcddcdbdaddbabaabdcdbccbacadcddddddbaabacddcdacbccdbccdddaccaddcabcbbccdccbbdbacaadadbbcbbcbcbaaacbabcaaaddbdcacdbdbaacaddacabcbabcbaadcdddabbbaabdcacdccaaabcbbdbacbcddbbcabcaaacabcbcdcdcaaabbbadabddadbbcdcaaabcbddddcbaadbbcdccbaaadbcadcaabaddcdcadacdbbbbcccccdbddbcbbcaadccabcbcdddbccccabdbcdcbdcbbddaacaadddbdbcbbaccbdcbdcbbbaaaddcccaccdacabbbaacdbabbdbbcbabcdbcbdbddadddcadabbbbcacddbbdbadcdcdacdadccdbbaccabcbddadbaddaddacbaaacdbabbcbccdbccbabcdaccdcadbaadcccbddadbadbdbcbdcdbdcbdaacaabadaaaccbddbbbadcaddddcdadcdacaaaccbbcdbccddddcabdaacbdcdaacbdcddbcdadbddbcadbabcaabccbdabbdbacbbcbdaddccbabcddaccccbbdbcccabcdaacaadddaaabacacacbaaddbbdcaddbcadbadabcccbdacbdcddadcabaaddabbbcadaadbcbbbdabddcccbdabdabddacacbddadcccacccababbdabadcdbbcbabbcccabdabcbdadccbcbdaccccaacbdbdcacbaddaabbdbbdbdbcaaddabbdcbbcddacbbdadccacbccdddadbbbdabadbbacdcbccdbbabccccbbccdacdbabdaacaccbadbacdaadacacabccacbbbaacaddabdadcaabbabcbbdaabbdabdabbdccbddabaabbcbbcccadccaddbbdabcbaacbdaddaabaadbbbdcbcaaadadbcadbcbcccbabccaaacdadadbdbcdcdddcaacddddcabdcaababcdcaacabbbadaddcabcacbdaacdcddccabadbccdabbddbddadbdcaabacbbdbaabbbdaabdcbdaccaadbacdbccadccdaadbcadbbdcadbccaabadabcbdbbcbdacdccbcdccbabbbadcbabadddcbdbaaaadacdbbdbcbcdccdcaddaaabdcbadabddbabbcbbbadbadbbbcaadaaaaababccdaaccbdacdcbcddcababaccacdaacdcdcbdcabddaddbabdabddbcddccdcbaaccbbdbacdcbbbaaccaacadacdcabccdadaaaaacadadcbcabcbabbdacabbdcabadcaadacabcdbdddaaddcdabbbaadabdaaaaccabbcbbabbccdacddbdcbaaadbddbdbcdbbcabdcdbadbcdcbdcdbaadabdadadadadccaddadacaaaaabddccdaabcddbbcdccdabbdcdbbbdbbddabbacddccccacbddbdaabdaabaddaadaabdbaaacabadcccbadcdccdadacdcadcdacaddcdccbbccdbbbddccbcaacbbabddcbdbdcdbabccababcccbcbacadbaddacdccdcbbccbbccabdbdadbdacabccaabcbddbcddddcddbbbadbbdcbddbdabbbdcaccbcbbcacaddadcddbaaabcaccaaaababbacbacdabbabdddddbadcbdbbccddccccaadbbaccccbcaacccdaabbcabbaddbcccabcababdaaaacabbabbcbbcaaaaaaadaacbddcdcaaadacdccbcdcaccabbadadaacabbbaaacdadadddccdbcdcdbcadadaddababaaccccbbacbbacadddddcbacaabcaacdbaccbbcdbadacccaaddbbcddbbbccabbccdbdddcdcbbccddadddbdbbbddbcabbaacacaabbaacccbdcaaaaabdabdcbcddbddcbcbaadccabaddbdacdaccbbcbcbccdcadabdcddbbddbabcadcacbacccabdcdcdcacdabbdcbcdaadcabbdcdddcbcaadccddcddcdbadbbabbaddcaabccabbddbdcdbabbbcbcaabcdbabadbabcdaaaddddadbbbabcbaddbcadaadcddddbaabcdabbcaaadacacaabddacbacacbbdbadabbbaacdbadbdbcdadaaaabdbdccabcbcbcbcdbbaaccaabdcbbdbabbcbabcddabdcadccbaadbbdbdbcabcdadcccbbadcadaddcddccbbdbaddbdadaccadabbabccdbddabbaadaaacccbcbbacbbadddabcacacbbdcccacbacabacbbdbcbbbabaaaaabccabcaabacdaaabddbcacdcbdcaddcaddbcbacabcadbaabdcdbdbddacdcbddcdabaadaaccdbbbbcdbcbadbcddacacbcbbddcdacdbcacdbbdcbcbdbabaddccadadcddbabaacacabdadbdbbcadcbacacddbcbcabbdadcacacbabcaddbdadccaaabcbdbdcdcbdadbcacbbbddadddbbdbbbaabcadddaddacabaaaaaaabcdcacdccaadaddccbcdadabddbbdaaddbabcaacaabbbaccabbbbbadcddbbdcccccbacaaddddcbbbdbacbaacbcbcdbabdbbaccbccdadddbdacbadabdbdabccbaccaaddcadddbdacbbbacbbddbadbcbccaacdaadbdaaabcadadabdbdcbdbadbdabdbbadbacccbbbccccabbcdaadcdddcaacdababdddccabcdbcdcbdadcddccdaddbcccbaaccbbdaaabcdcabaacaacdbdccaabcbbcacbdbcbbaaabcbdbcccbddaaacbdbdbbbbdbcdabcdbdbdbbdacabbdabccddbbcdbdcacaaacadbbbccacaadbacdabacdaacdacdbaaacacabbcbaccbdbdbbcdbbbadaddabacddcddbaacdcbdadacacaccdcbcdcaadabcccbdacadddabbcbdbaddddacbbcadadaabcdddcabbabcbabbcadcabcdadcbabcdaababacbbaadabbcdbdccaacddacccdbcbcbcbccbcbadccadcdabccabbadcdaabbacabdddbddcdcdabdaaaccabcbbdcbcdcbcdbdcdddbacadbdbacbdbccccdcacadbcdadaaddcdbddbcbadbaadcdcdabcadcbbdbdcabdaaabcaadaddbbdcabaaddcbccbbbaaccacdbcbccbabbbddbdcdaaddbcccdcdbcccadadcddadcabcabaadcaddcbcadddadccaabacbadbbdbaacadcdbccbcbdbacacbcbdabbadaaaacddbcddaadbcabbaabbaccacddbbbcaabcaccacdaaadddbccadddacdcbaacdccaccdaaccdccbabbbdcbbccacccabbbdcbdcbcacabdcbbccdabaaaaaabdbdcdacabbbababdacabcbaaaccbbadccdabdbadbaddcacbdccdbcabcadbbadddccdaccabdacbcbbcbdbaddacabadbaabbcbaddbdaccabaadaacadacadddabaaadaabdadaabdabcbcabdcbacbdcdbdcababbdbdcaabcaabcccdbaccdcacbccbdaddacdcabaaacdabbabadcccdbdcadbbccabbcdcccdbcdbdcbbbdbbccaddccbbbcdcacaadacbbddacabbdbdbbbbcabdbbddababdccddbadbbbabdcadcdccacdbdcbccbaaaabacbcdddaaabdabaccbdcdadbbbaadcbacabdbbcddaccdaadaaccacccaabbabdcdbaabccdaccbccdbbcaacbacaddaddabdbdddbbdaccbbacdcbadbcaacbadadaacccdbbdcccadbadacbccdbabaadaacdddaabacdcaabaabadaadacadccccadadddbacaadddbbdcabaadbdaddcabdacabccdbdbbaaccbdacbddbbdadbcdbacbabaaddadcdcbdabcdcdbdbdbaadbbabbbbdaacbdbdcccdbddaacdcbcccabccbaabcddbbabaacbbcddaacccacdaadcdaddcbbcbdadddddccdabdacacaccaaddbcaadbdbadcaacbacbdbdabcabbbadcadaabadbdddbdacbacadbddbbdbddbccbbacdcaadbadbaadaacabdcadabdbdadbdaadadcbcacbdcdcdbaddacdcbcadadbbdbdcbbcbbdddddbbaabcdadabdadbbddbcccccdddcabcccbdadbddbcdbdbcddcdddabbdddcbadaccacdddbccccbbcbcccabcdaadaaabbcadaadbcbacaddbababdcdbbbcdaadcdbbcacaaaddaacaacccbbccdddaddddcbaaabbbabcbcabcabbadbabcacbbbcccbdbbcbbcdbbbaadacbabaabbdbbaabacbbcadaacdbbcabdaadbcdbcdccbacabbcbbabaaabbdbcdadaacbabddabcddcddccacbabdacabbcdcddaadbdadadbdaccaddbbabaadbbdacccbbcdaabccbbbdbdbacaacaccdbbbacbabcbcddccaddbdabcddccdccbddccbdabacbccaabcadcddadacaccaaddbacddbabdcbdadabbbbbccdaaababccacddbcddaaccadbddccccaccccdbccbabccdcccaaddcbcbbdadddbaadcaccbddbcbbacdabccdcbdccbacaadabacddcbbcbabddaadbbdabcababbadcdaabbdaabacdbcdbcbcadbaacaddaacddaddacdbcaaaadccdccbccadcaadbdaddacadabbaabbdcdabdcacaaacbadacabcbddcbcaaddbdadbaabbacadcdccababcbaaacbabcdaddcdabadccacacadccdbdbacdcdbabcacdaccdaccddbcaadcadbdbadbcaccdcabdddcdaccdaaaabccacdcdbbcadbcdcbddadabbcacdaadabbdbdcaabcadbdccdcccdcdbaccbacbbaaaacccbbdadcaabcbbcabadbadccaccdaabdddcbcccbcdadcdadbacacacccdaabddcdacbaaddacccdaadcbbabbcddadadccaccdcdabdbaacbdddcaccbacdbdaacdbdddaabbccbcaccbdbbccbadaddbddcabbaddcccadbccdddadbccdcddcbbadabddbbdacbbccbdabddacbdaabaccdcdbbccdabdddaddbdccabddbabbaccacacbcadccabccacbcddacbbaddcdcaabcdaacbdccadcddabacddacdbbaddcabadbddcacacbbccbcaaadbdaadbddddacddacabadcbcdaaddbaacccaaaaccacacdddbbdccbddcabbbabdaabdadcdcadbbccdbddcbdcabdacaaaaacccaaccddbcdbadcabcdbdcabadddadccaaddbbdbdacaccbcaccaacadbaddbbdbcbdbaaabcabcbdbbbddcacbdabdadacacaabaaaaddbdabcddddbbaddbbddcddcdcddbbcacccccbbccdaadaabcbddcacdccbcaacbbbbcdbdaacbabcdadcabdaadccbcabbdddbbbdcdbddbadbcbddcbbaddcabbadabcabaddbbabddbdacbddddcaccbacdcdbcbddbaaaaabcbbdbcbcbddbdbbaccbbaccaaaddbdccbbcadbccccccbcacdadcdabacdddbabdbbcdaaddddbbcdaabddabddaaacbdbbdacdabdddcdabcdcbbdbdcbbaddccacddbbbaaacaadabcbdbbdacdcaabdbbacbabcdccbccbaddbcccbbdcaddbbcdbcaabccaaccddbbacaddabcdddaadbdcbbcaabcdcadabcaaaaabcbdbdbddbacbcdccbbbbaacadaacabdcadddacdabcdccdadabaacabdddbbabccbbabadcadaaddabacdcaccbadbcdbdbabcadbdddccbbdbaddcccdbbcabcdbabcdbbccbbdbaddbddbdbcbbccdcdabcabbcbbccddabddccbcdbcddcaacacacbbcbaabbacbbcaabadaadcaabdcdbbdcbcbddaccccbabacadccdbddbdaaaabcbcadbddaaaadcabacbcdaacdaddbabdbcbdcbbbbcaabdcbddaadcacdcdcbabcccadaddbccbcddcdadadcccaaddccbbdaddbcbdbabcbadcabbdcccbbbbacbbdbccbdacbadbacdccbddbcbbbaacbadccaccadacbdabadbdbdddcccddccdcbccbadccdbabbbdabbccdbadcadacdcbadddcbcdcdcdbbdadcbcababccdadaaaacbdbcbbdaacddadbddccaccdbcbadadadaabaaccdabcdbbdcdcadcdabbdcddcbbcdcccdbbcdbdcbcdaccbcdddadcbbbabbacaddadbadacbdabcaabbaccccdcbacbcdbdaaacbbdacbbbbadbdbdabadcbdabcdddbadddbdcbbbcbaacbbdddbacdbdbbbaccccaaacadadccbcbbaaabaaabdadcacaacdabbdbdacbbabbbcaddadbdacacbcadcaddcacbbcbcddbbddacdcaaacddcbbbdbbdcabacacadacddadcaccbabbbbdaddcabbbbacccddacbabacadbddcbadcacdddccaabddcbabbcdacabbcbabaadddacbacbcdbdbcdbaabdaabddcdcdacaabbcbdddcddbadcbacabadbcbcdcbabbdadabbababcddcadbaadbbdccbbdabcabaabacbddbcbdaabacccadcbdcbdcbdcdbacadabcdaaabadcacdcbbaabbbcdacdbaddbacaacaabadbdaccdccaabbadbdabcababbaddbbacbcadbdcdaaadaddddacddbaccdddbcdbacdccbccabccaccbbdadacdccdadcbbcbcddcaabbabcdaabbaacdbabdbbccdaacbbccacdccaacbcdbdabbabcabbabbccdccadcaaabadbccadbdadbccadcbddacbaaadcdabadcbdcddcccabadbcabbbcdadddcbaccabcddcbbabcaddabacccbadbcbdbbcadacbccdccabacbbcbbbdadcabadadaaaacabbddbbbacdacbbcbccabccaabaddbdacadacacdbacadbbcddbabcdacbcadaaabcdaaadbdabcabbadbddbcaacababdccdabbbadbcbaccaacbcdadaccadcbdccaaaabcacaddddaaaabbcdcabaaadbabaacdcdbbaaacdbbaccbcadddcbdcdacdacadbdcddcaaacddccbaddbbdacaaacbbcbbacdbbccdaaccbabaddadbbdbcbaaabcbbbdbdbaccbcaaddcacdaaadadcbbcaacaaaabbdddcaddbcccbbcaacbcccccababcccabbacbbacdaadaacaaaabcdabdaddbdaacdadacadcaabcbbcddbbdbabbdadbadcccbbccabcccccacbbbbcadabdbccdadcdbaddadcddaccbbcadcbddbbdaabbccaabbdaccddddcbccaaadbcadacdbdccbbadabdaddaddbbdbacbdaabdcdcccadacbdacbcadbddddbadbbdadcaacccdccccbcdbdadbbcabaddbaaacdcbbdbddccccdbaabcaccbdbcbcdbaccbdadbdcdaccaddcabacdcbcddabccdddbdacabbbadaccbbbcdbadcddccbaabddcaabdbaabbddabcacbacabadacddadddbcadbaabcabcdcabadddbdacabbabbaadacdbdcbabbabddddbbbdbcbcccadaddddcdcbcdccaadabcbbacadbbccccdcdaddabcbacdbccbddddbdcbbcbbbbdcbcccadabacbcbaaabbacdccaaabcabcabcabdcaadccadbbbacdbabdaabdaabddcdddbcbcbbbcdcbdbacdaaacdbbddcbdddabdacdbaaadadcbacacbdcbaacbccacdcbcaaacadaaabccaacabdddacaadabccadcaddcbaddbabbaccadcbbadcdcacbcbbbdaadadbcadbddbcbdcabacccacaaadcdcadadadacacbcabbccadcbdaacadadbbddbcbdddaadaccdacddcdbbadbcbbbdbcbcdccdcbaccdaddcbcabcbccadacbadacbdbcaababcbdccbcaadacbdddaabdcdbcbdbcbccdcdacbddaddbbaddcbccacccbbdabcddbbaabbcbacadbdddadbcdabbcbcaacaccaacdddccacaabaadbaddcccbdcababbcbdbbaddaccacdbddcadcdbccaaabcdaabbbdcdacddaabadbbcaaacabbdbdcccdaadbdbbabbcbbbbabcbbaccdbdababdccbbcbdbabddbbacabbbccbcbaaabbcdabddadbccadbccdacaabccdbaaacdacacbdbbaadbcccabacbadbbcccaacbbdccddbcddcdadbcccdcbbacaccaacdccbbbdabbbddacbaccabddcaacdddabdbdddabcdcbdcccbabcadbabdcdbbaacabdbbdbbdccaddbadbbcbbadaccddaaacdbdacbabaabcabdbbabbcbbdccabccbddcaaccabcbacdacabbdabbdcbbaadaaabadcbcbaababaddccdbcccbcdbcddbdacdcbdcadcadccdbbaabbbdcbcabbccdbadcabdcdacccdbdccbbdbaabcdadabadbcddabdacbacabcbabcabcdaccddcbacaddacbabacccabaabbccadccbdccbbaccdadbcdabdbbcbdcaacddddbdbdbaadcabbcbbdcbbdcdcaacccabbcdbaddddababdddcaadbabacdcdcadccddcdbdccddadbccdbdbcbadbaadbccbccadcbadcdbcdbbdabbacaaccaaddabbddadadbdcdbdbbbabbbbcdcccdbbaacddcabcacacbabacadbbcbbdbbddcbadaccabccadbaaddbdbcdbccdbcbadddaddbcabaadbadcdbbbdccdcbdcbbdcdbcbdcabdbcdbbaddabbadbccabcddaddccccbddababaccdababbaaddaabcbcdccbdbcaaccdcbdcdabcccdbcdbabbbbcdbcbbbabbabdadccccdbdcaabbabbbbddbbabacabccbbdbbcbbabdbdadacabababdabdbbbacddbbbdaabdcabbdccdbbcacacbaccadbbbcdabcaccbdacccbcbdcaacbcbcbdbbaabdbbdbbdccccdbdaddbdccbbbddabbbabacdcdabbcacabacaacaaacacacbddadacccbaabdcabccabcaacaccdddbaabdbcaccabcdbccdacadabacaccacacbabbcddbcbdbdcdcdcbabaddcababdbbaacaabddbcdbbcacadaddbbaacbcddccadbdadbabcdbbbbcababcadbaabaabbddaaaacdadadbcdbbdbbddcddcaaabcdbcccacdcbadadbdcdcadcbbccaabccdaacddacdabbdadbcbbdaabadddbbdabcddabcbdbadaabbacdccccbbdbccbbbbadabdbacddabcbdbabbbdbaacbdbddaaabadbbbabbadbbcddbbbaccbcddcacacdaccbddcddcabcbcdabcdadccdaadbdcbbcdbdbcbbddcbddbaddccabcddccddbdccbbcbccdacbbabcbcaabbbbbacdbadddbddcaccadbabadccabcccdcbacaaddccbdddcbdcdbcdbbcccacbabbccaabddabdbdaccbbcbdcdacabbdbaabdcdbadaabbadcbcdddcccaadcaccabcaaabadaabbbcccbbbbcabaacdcbadcdccbadcdaddddcbaacdbbdcdaaacbcdddddcabbcccccddccbadaaccbdbbddadccaabdcbbdacdcbbcdbacbaacababcabacdbcbdbabdbaccbcccccabcdadcdaaddcaacbcabccbadcbdbaabadadababdcacbbacacdbbccdcccdbdbaacadaadcabccdccbdcacaabdaaaacbdcacaacdbdaadbadadcbbcdcbccadacabcbcdaaddbaaadaddbdcdcbcddaddadccdbdaaddabdaabbdadadcadbcddabcddacdadcbcbcbbdaddabdccbabdddcbcddacdbcacbaadaacdcacdbbddbdddcbcddbacaaddbcdbbbcabaadbbaadbaaccaddbcbcabcddcbbbdcabdcdcbccbdcdcabbdbababbbdbddbacbbdabaabbabaaccdbdbaadbcbbdbccacdcccdbabcabdbcaaabdaadbdadaabadabcadbbdaabcdbbdbccbbbbddddbcbddccadbcdadbadcbaccadabdcdabbbabbacdabdbbdbbdccbaaddadddbaaadbdcbcbcdbbaacddddabbcacdccacdccaadbacddcdcbbccdaddbdddcadccdbadadcabdddbbddcaccbcbdcdbdaacabdbcbdacdabcabadcccdbcbcdcdacdcdcaabddadabddbaaaaddbcbbabccbadcabbdbbbcaaadbdbcacbddacccdcaadbadadcbbdccdacdbacacaadbcbaddacddddcbcbbbdcdadbbaabcddadacacabbcdadbbddccddacbabacbbacbdbbcdcdbbdaaabcbcccabccacaacaacacdacdbcababacccdaddbcdaaddbbbaaacacaccbadbdbcbcbdcbdacdababcbdabcdcbbbbccabdddbababcdabddabcccdcbcabdbbacdacbaacdbdccabaabacdacccdcdbcbcdddddaabbbddabadabadbbaaaabbdcccbcbcbabbcbcdbadcadcacaacbaabcaacbaccdbdbcbbdacccdbbaacbaccacbcbbdcbdbbdbbbadbdccdbbcbdaadaaabdddabdabdabbdabcbabdccbcbbdccbbadcadddbadaacddbdbccbabdcddbaacdddbdacccdadcdbaacacdaccbbacadbadcbbdbbdcbcbbadabcccdabdcdcabcaabcabbdcddbbdaabdbcbdacabbbcdbaaabdadbadcadcbddadbddababccaabbbbaaccbcaacbbdcabacdbdbcdbdabdaadabacccadcdccbabcbaadaaccababddbaaaaadcaadbccabddddbdbacdbcccbbbbbbdaabbcaaacdaadbbcddbdbddbabdbdccbabdadbccadabbbbbbddcaababbabbbacadabdaadbadbcbbbcadacdbaaccabcaababbbdcdaaaabdcaaacdabcbadaccdbbaabcaddbcacccddacdabcbbdadabbbddccaabdcddaacdccdddabdccccacbdccbdcacbdbcaaabccdaabdbccbdcccadabddaacdbcbbabacdaacbaadbacddbbabbdbddbacbcdddadbcdaddadadaadbdaccdabdcdabbcbbaccbdcbadcbcbcbcaccdbbcaadbccacdadcbcdaaabcdbbbaccbcddcacaaadbacacabdbbbdbacbacbaacbabdbbadddacbcdccabcabcbdbadccdbbcdccadcdcadddabdacbacbcbbadbcddadddcddddacbddbabacaaabccbdbacaccadcdcbbbbaaddcbbcdadcbbbaaabababbccbcacacddabadccacdacbcbcbacccbcdbaadbdbaadddbcbbabcdbbaabcabadcdbdccbaadaddaccbbaddbdabdbcabcdaccddcbbdabbaccddadbbdcdccdabacacbbdddaacabdbcdbadbacddcabbabcccbabddcbdaabdacbbcbaacbccaccadaaddadabaadccbbddccbaadacdabcdbdadbbacaadbabdccbbbbaadaddbcddcaaaddaadddaddcccabbbcccadacbcbddbbcdccbbddcacbbdbbbddaaacccccdbacadbbbabbcddaaccadabbccdccddddccaccdabaaaddcdbdaabddbaaccdcabbdcdddaadbbddacbbcdcbacacaaccbadbbcaaccbaaaaabacbcbacbbbbbdadacaacbbcccddbdabbdcdaaddadcbadbabbcdabddcdcbacaabddacadadbcadabcbbcdbddcbbcdaddabcbcabbbcaccbdcdbdaacdaaccababcdccccbbddcccbacbbbabaaabcaddadcacdacddbcbbcdbbabaaabdcadabbdcbdcbdbcdddaacdcabbcdcbdcdddcabadddbcddbdcbadcddbccabdbcbbaabbbccbdbaabccccdcbddcadbdaabdccbaccbcbbdaacdbaadaacdcdbcbadbbbcaccadbddacadbcbccacdccdbbcdcccacbcdddadadcbddbccbccbdadadcddddadbcabcccdcccccbddcbaaaadcbdabdcbcbacddccdbdbcbdcadabdbacaaabdadccacdadaddcdadaaddbdddbcabddcdbaddbbbdccdadaabddbacacdbccdbcaaaaabbaababbcbcaaadcacadcabdccddbbbcdcbcacdbdadbacbbadcabcdadbadccbbccabcbdcbdbabaccccdccbdddbbbadbbcaaadbabadcaaabdacacbabacbdcccdbacbadaabdcccbdbcdccadadcaadadbdabbcbdcbdbacbcaabbcbdddbbdbbdaabadaaadacabcaabccbbdccdbcbbadccbbbcaadcabccdbddccabbbbabdcacdbaadbcbcacccdabaaadbcaccaaccbddabddcdddbbadaaadddbbbabbdabddbacacbbdcdccdcadaccaabdbbcbddcabbccacdbabbcbbdacdddacbcddbcadcdaaaacbdbccbccbabadcbdaddbccbdacacacadbbdddcdcadacbbadbbacdadddbdbdddbcddcaccdbcaacabadbcadadbcaadbcbbbdccaddacabbaacdbbdbbacddadbdcbccaabdcacaadbaaabccbddcdcbbabacbbdbbccddcaabcabdaaacacdbcdcbbcabbcaadacabcadaaaabcaaaacaccaabdabbcabbbdbbabaaddcabcdaabddacadbbcbbdcdbacaaddddacadcccabccacdccccdbcaabccdbdcbdddddbaacdbccdcbbabcccccddadcdcdcbcbaaddcabcbdcdbdcbaabcabbddabacdadbcbdbccdadadaaaddbbcaaaaabcabaaabddcadddddcbabcdaadacbdaacabbacccbaababaaadbbddddbadaaaadacbdcababacbdacadabcdbbbababdadcaddbcddbadaaadbbaadbadaabaccddbddccccdbdbababdacbcadccaaccbaddcdcbdcccccbdcdbbdcacaabbabaadcccdddabcaddbcbddbcaaaddccbcadaacaadbccadabacdcbccdbddccdbadabbdcccbccadacbadbcdcacbabbaaabdbcdadbdaacbacccccccabdccbbcbacadcbaacabaabccabbadaaaacdbacbcababbdaccdbdcbbdaabcdaacdadbcdcddcacaaddccdaddcabcbdbaccdabccaaccbcbaaaacaabcbabbaacaddcaaaccaabbbbdcabdbbdbbbcaddabbbcabcccbbbcbcacaaadbaadbddbcbadabbbacdadaddbdccdbbaabdabbdddcdadbdcdbdccaaadadcdccbddbdcbbcbabcdcbabadbabcddacbbaccdccbddccadaccbccbbddadbcdbbcdbcbdbbdcdacbcbabcbbcddaccaaadabbadbcdccdbadddbdbaadbacaaadadbcbdccbdcdabbdadbbbbdcdccdddcbbdcdbcacdccdabbccbadcbbacaadcaccabbbcddbccbacabbccabddbaaadcddbccaacaabdbddbcdcdabdadcacaadabadbdccdabccccdabdbbaadbcdbddcdbabcddddabccbddabbcdcccacadcadabdaabacacbddadbbbbadbdccbdccddaabdddbbbbcaaaadbccbdcbdaccdaaabddbabbddcdbbddacdbcdabcabdbcbadcdbcdbadccabdacccccdddbadbccabcdbdbbccacbccabddabdabbcbccaaadcdccdbddbcdadbdabdcdcbdacdddcbdcabbcdbaaaaacabacacbdaabbbacdbcdabbcdddddbabcbdbddaabadaaaabdddcdddabaaaccaadbcccbcbaddbdbcadcadddddddccddbadccdcbcccbcdadcddcadabbdddcbdcdadddbcabcdddccaadbccddbcdddbdacadccadbbddddcdacacbdbabacccadcdcccdbdcdbdabbbcdadcbbdcdabaadddaaadcadcbaaababaaacdcadacdbcccacddcdcdbddaabadbadadbbddcccacabadabbcdcdaacccddaddbadbabadacdddcbdabddacabbbdbabcbcdbabcddadbdddbbddbacdbacddacbdddbcadadaabbaacdacaacababbccabaaaccbdbdcdcacaddcbcccbadadcbacbabadcacbbdaddbcabbcbdbdaadbaaaaccbbabadabddbdacadbbbbbadcdaadddcacdaacdbbccdabdcabdadccbcadbabcabddddddaadbdadddbbbcacdadaacccacdbddcdbabcdbdbdbadbbdbcbdcabadaadcabbabbbadcaddcbbbdabddaadcdaabcbabaabbbdbaaadccdacdbacdbcdadaaccbbbdcdabccaadbbdcccdadbddabcbdadbadbbcaacbdbccbcabcddcbaaccabaddcbbcdaccdbdbcdaddcacbcdbdcbcdabdadaadadcbdccdbaddaadbcdbdbbdbbabccaddcdcddabcbdadcbbadbcdaddbaabadccdbdabbdbcbabddccddcdbbccdadaaacccccbabbcaccdadbdaaccadbdacdbaadcabbcacacccaddbaccbabbadbbaccbacaaabacccddccdacdbadadbdccabdbdababadaddadbcabacadbccadbaacbcababddcabdddcbdaadddccdbbcbccbbbadbabbacddcabbdabccadcaabdbadadaacdaccbbcbbdaddcccdacccbcacccdccbcddbbcbbbabbcbaacaaaabbdadbadbdcbabbdacbcddcaaccdbabcacdbccaddcccbcacdaadabccbcadbbdaabcacadcccaccadabdbadbbcddbcacabdcbcadcadbdaccddddccdcacbacdcacadabaccccabbdccdcdaacacdddbcccdaaccddcacaccacdbbbabbdccdabccbbbbbdbcadabddcdbdbacbacaaddbbabadbdcaabaccccbcaacdbdabdcbababbcaaadcddcbdccadbccabcbdbdbabadcbdcbbabbacbbcaccabbcdbdacdaddadadaacbdaaccbccacbbcdbbdcdbaaccbbbdaccdcccaaddacbcbbcdaadcbdacdbddbbcaaaccacbdbddbbdabadadcccbadcdabacdbabcabdccbbcdbcdbccdcddcccbaccdccbbbcdadcdadddacaadbdbadbbabcdcbadcdbccdcccadddcaadbcdcabbdcbbcdacaabbcdbbadabdcbaacccbbbdcdbdcdaabaaccbacaddccaacabadcdddcabcbdddcbabddbcdddcbdcddddccaaddadcabcbabbbcdcdabacaabbaadacbbdaaccaaddbbccdbcbdcabbacbcbccdaadabdabadabddcbbdbccdadbbacccbbcdababcdddcdacbddbcabbcadbadabcaaaadcdabddcbabcbddbabdadcdbaacdcaabbcdaaaaacbaadaabaacbdbcbdbbcdacdddcbcddddbbcbbacaccaadaadaddbddcaaacbadddbacbadabddbdcbcbddcddbabcdcabddaddbaadbdcacbcbbadddbdbbacdbbcbbacacadcdadbabaabccdcddbbabcbadbdddcdcccdbddccdccacddcaaabadcddbcdaacdcbdccbacaddbadaadccddabcbcadcacbdadadadacbdababbddbcacdccadacddbdddcbcdcbdaadcabcdcbadaacdaccaacacabccdddcccbccadadccbbabccbabdbcabacdababbbadaddbacdaccdbaaddddccdbdccaadaaaaabdaccbbabdbadbbdccabcbcbcddadcdadbbbcaaababacabcbdcabbacdbdcaddabbaabccaddcccdacaaadaccadbbddcdbabadaddabdbbadbdddbccdbacbcddadccabcbbcdbcbdcaaacacccacaadcbcaababbccbdadcadddadcdcdaaaabdbadbbacadddbcbbacdcabdbdbbcccccbbddcdcbacaaddccbddaabdbaddacaddbacbccdbbbbbcdaadbaababbddadcadcaabbddcbdababaaacdaacbadacdcbcccadcbcdcbbcabbbccadabdaaaddbbbabccaaabadddcaddcbccbbbcabbcdbdcdadcddcdaccccacbccadacabdccacdacbaababdbdaccccacccddcadbacdadbdbdccaddbabdabbacdaaadbcabbdaddbddbbbbcccbbbabbddbdabcddaabadcbaadcacdbbdddbcbcdaccbbabbcbbcbcbcacaccbbbbaaabdababcbadacaddcdadacccaaacbadddacaaadcccddbcdbcdbcdcacbbcbabbbddcbdbabcabbabbdcabdccbcccccbddaacadaaacadbbbcccbdcbaabaccaddacabbbdaddacddbbbbbddadbccddccacdaaaaacacdabcacacdcdddbddcaaaadddbdbddabbabcaacddcdbdadacdaadcdbcbaabaaabaabadabcccbbddacaacbbbdcdddaccacbccbcadcdbddbcbcbdbbabcdaacaddcbabcacdcdcdbdcabddaaccabbdbbcddcbbbdabcaabbdbbaabcbcacdbadcaacbddccdbbcdbbcabacccddacbabbabccdcdddddbbbabdbbbacccbdbadbaccbacbaddbdbbdcbccbcbdbaddbaabcdaadbdbbcbabdbaccdbdabaaaabbbabdabcdcaccbbaabbaabcbbabacacaddcdbaccbbabcddbddbcadbaadbadaaacbbaaddbaccabddbacaddcdbbaadcbaaabcbccbbbcbadbaaaacbdbabcccdccbacaaadcbadcdbcbabddcbccddcbcaabbcdbbbcbdadacdabdcbccadbdadabaabbcddbdcdaaddbdcdbbaacbcabddaccbbcccdababdcccbdaabbbabbccdbdbddaaccadbcabbabbbcbbbcbbdabbcacdbbdbacbddccddcbdcdabdbbccbaccbbcdaabbbbccccadaccdaadbaaddbcbdbcacccbdddcbbabbbabbbdcbdccaadaacaaabadbcacbcaabaaacddabbbbdacdbbbbaaddcbadbdbaccaccacaabdcacbacbcdadaccacaabacdbbabdddbdddaacbcadabbcbbadbccdbbabadddaddcbcdcdabcabadcddcdaccacdcccdbaacbbcdbccdddbadbbbccbbaccccabdcdddbbbadababaccdaacbdacdaddbcacdacdbcaaabdddacbcabddbbcacccaccadbbdcaaccadbaccabdbdbbdaccbbddbbbcbbacbbbbbacbabacadddcbcaaddabdaabcccacdaccdbdddcbbcbbbdbbaacdacabbcdacbbcdabcaaccaddbbdaddadaababccdcdcaaaabddcccdadddabdccdbccbdddaaccbcdccbdaabdbcccdaccbabadcdddababbcbcbdddacccbcabddaddadcbccbbcacaabcddadabcaadbbdabcdbcdacdbdbddccbbaaadaadbbadbabaddbdbdccaaabcadbccccacbccdbdbcaaadcbddbdbabaabbddccddbdbcdccbdacdcacbbdcdaaddcdcbdadbdaaccbbcbcbcbddbcbcbdbcabcacddcbccbcaaabbcacaaabaacbddcacdaadcdcaddaaaabadaabddcbcabaacddabadabdaacabacdccbadcdacbaabdcbbcbaadbbcdddadbbaddbdacdbcaabcdddbbbdbcacbcaaddbcaadbabcccbcbddbadcbdbdbdcaadcacdccaadcdcdacdacdaaccdcbcaaaddbcbbddbddbdbdcddcaabacdbccdcacdddbaabddccaaddcbdcbcdbcbcdadbdddbaaadacacadbdbbddaddbbbdcbccaabddbcabccdbadaddcddcbccdddcaadcbdccbaacbabcabbabbdbcbaaadcdcbbacaaccdcabcdcbdbbddbdbaacbbcdbbbcdababbccbdacbdcddbaddcccabbaccbcdacccaadcbabcccacbaaddbbaaadadcccbaddccbccbdccabcdbaacaacbbdbcadababbdadcadbbacbaddcdcaaabbddcdababaabaadadbacdadcbddcbaabddcdcdaaddddcaccabbacddccddddbabbdccaadabaadbdbadccaccdbccaabcdbcaadcdbdaaacdabaabcbbbbdabbdcadaccbbaabaccdadbacaabccbbdaadababbabaddcccacdbdacbabacdabacbababbcadcdabdcabcadddccaabacbbdbcdcacbbaaadbcdcbbccacdbdadbbcadbccaacbcaadabbcdccabcdbdaabacdadaaacddacaddccdabbdaccccdcadcabadaddcdcdbdbdbbbbbdcdaadcdaabaadbddccbbdcaadbdaaaacacddbdadaccadcbcbabdcadbadbbbccccddcdcaadbacaaaaaaaacacacacccbacaadcdcbcddbabccaaabbcdcbdbdbbaccbdacdddbaaccdadadbbabcbbcbbbaaadcacdbaddbbdaaacdbdadbbcddbadaacccbdbcbbdabdcbdcbadbaddbbbcbdbcdcaccabbbbbabdcbbdabddaabcdaccbccccccdcbccbcbcdbbdaadabdcdccccddbdacddadabdbcabcbcddccacdccdbdbbaacccadbcdbccbbabacccbacadcdadaadddaacbddcbbdadcdbdbaabccabcbdbbaabbcaddaadacbcccacadabdcadaabbcaababccbabcdbadddadcbadcbacdaaccbddddcaacbddbabbdacaddabdacccdddcbdcccccddcbcaacacbabcccbbaacddcdadbbccccdddccaadccaaddcbcddbcbadbbbabddbbaaabdbabacdcacdacaaaabcacdddcbcdaadbaccddcdbbccdacdddccccacbabdbbcbdacbbabbabbccdbbbccdabaadbacbdcabaaabdbabdddcbddaabaacccbddabcbdacdaabddcdaaaaabcdbddccbcaaddbcdbdbcdbabdcddbddcdadddbbbbabdbabcdaddacabadadbcbddbcacdddbbcbbccbccdbabaabadbbdcbbbbcabcdaacadadcbcdacacccacaaccacbcdccdcabbacccbdbbccbdbcaddaabccbacdbabacdaddabcbbbabaabbdabbdbbcabbcdbcbcbbcaadbbbbadcbdcddadcabdabbabbaaacddadcaadbccacccddbdaccbcdcbcbaadaacdcadccdcbbbdcadbacbadcaaccccbdabbaccbdbcdccbcbdddbdddbacaadaadaacdddabcdbadcccabbadbcbdbdaacdbaacabdbabaccdaabdcaacabdacabbaabbccbabccddabcbadaddacdadddadaacbccddaadacabdaccccdddbbcddacbcdccadaaabcdcdaaabcadbbcdddcbcdaccbbdaabbabbcdbabbdaccdbcaddcdadadcdbdabaaacbbadbdabaddbbbaacdcabbdbcabcbdcabaccccbbaaadcdcacacaaccbcabaaadcddccadbdbcdaaabbadbbadacacbdacdaadaabdaabcdbcdadacdbacbcdbcdcbcbbaadccaaabaaddabbcdddbbbabcbcababdcccacdbbdcbbbcbcacddddbaabbbddaccccabcbcabdcaadacdbadbcadccacaccbabcddcbcbccbddbbacdbdcccdcbdddcbaaadcbddacaadbaccacdbbdcddccdcbcaadccdcaaaaadccdbcdabcbbddaaccdabababaccddbabbbbdaaaabcbbccddaadbdcdcdbacccacdcdcdbccdbbaccbbcddadbacaaccddddbbbbbaadadbbcbbaaacbcdbcbdcaccaadadbbbddcdccbabaaadddabdadcaddbcbadadbcdabaacccddccccabbacbcbcdcbabccaabccacaababbaababcdaacdddddbbdbaaacbddccaddadccaccddbddabcbacbababcdbdbaddadbcdcdbdabdabadbcabccddabccabccbbccdbcadcaddcccacdbdabbdbaacdaaccdaccdbccaccddcaacacbcbdabdbbdcbbdbacccbaabdbbdacdbccdabbbaddadabccaddabbdcbcbcdaadbdabaadcdcacbbbcaddbcacbbcaadcdabbdcaadbdddadbbababbdacddbadbbbacdacccaadadbcbabcbdbaccbbdbaaaddbacddabaaccbbbdcbbcabdcdacacdabbddadaaccaddcacaccdbdcaaabdadcccadcdccbcbccdcaacdcabababdcacbbcaccbccadaacacadabdbbcacaacbacbcccbbdbcabcabbacdbccbcabacdcccaacacbbdcabadcaccbdabccbdccdabdadddbaacdcdcdcbacdaadcbcdbaabcddbcbcaaabccccddcdccbbccbcdaaabbbacabbbcacdbddacacbadbbacddcddccbaccdccbadcbaadddaacbdabdbbccabacabbcdaadcdabccacdcdcbdaadababcdabcbbacaabcdaabbacdbbaddadcdbcaadaaccdadcbbbddccdcdaaabacbbdaddcdddbaccdadbaccccddaddbdddcbcaabaabcdacabcbbcadcbbdbcaaaccadccabddcdbcbbbbdabaaadbdcacddbcbbcdcddcdabcaccbdabbcbacaaacccdbacbbdbddbdaccddaabdddbdbbbccdcdbcaadaaddbaaacddacdbabdddbdccaaababababadcacacabbcbaaccacdbbddacadbcccdbbbcccabddbbbdacacbacabcdaaabdbcdabbbccdaacddacdacbbbacbddbbcaadbdadbcbabdbadccdbbdaadbdbabbdbdbabcaabccbcaccdaccdacaddaabbccdacccaabdcbdcaacbadcbbdbdaababbabaaaddababddadaacbcadbdbbcdabccaaacddbadaddcddbdbbddbbcadbcabbbbacacdbbdababdabcbbacaccaddcadadbcbbddbbcabaabdbbabddddadbadbdbcdadcacdcbcbabddadbcdbbcdabdbabdbaccdddbaddcaddbdabbaacbbbddbacdabdadddbcdcbdcadbcdbbcbaddbbbcccbadcdddabbdabcdaacbbdccbabadccbcbbcbcddcbbbadbbaabbdbcdbcbcdbbacbdcdbdacdcddcaaaddadcadabacacccdabcadbacabcbdacaccddaccacdbadcddabbdcacacbbcbadcdccbdbaccdcaddacbccdadbbcbbcaabacaaabcaddbaacbbcabadbdcadcdddbcdaddcbcadbccdcdbcbddadccabbcaadcbbccadcdccacdabaabdbdbdcdddbbaabcccadbadacaacbabbdbdbcbcdddcaaabdddaacbdbddcbccaacddbabcbaaabaddcbdcdbadcabababbbcccdccabadccbccbcbbbcbbcabcddadacbaababcdbadbdcbadabdaadddaababddabcbbbcaaacdabdbddcbcddddbacbdcbaccdaaaabbbbbddccbbcbdbdbabbbbddbccdbacbaacdbcccbbdbdabbbadaaccbbdbbbadcbdabaccaddadbdadaccdbcacabbdcabcabcbcaabdaccdbabbcadabbccdaacbcbaddbbccaddcdccbdbbcbccccdcdcacdcdddcddbcabbcdbcaacbbbadacacccaabbadabddcbbbadcacaccccdcaabcaddcacaabdbcaacccdcdbcdbacdacdbbbabaabbddcbbddaadcdbbabbddccccdbcbcbdadabbdbbcdbdaadcadcbcbadbdaddadcbcdccbdbadbcacddacbbccccbaaddaacaddddcaabcbbcdaaccddbbcbacbdcbbdcddaccacbabbcbcaaaddbbabaccdcbcbddacacadcdbdacbacbbdacaabbbaddacccbcdcabdaddccaccadababccacbaabdabcbabbdcadbdbdcababdbaddabddbdcdbcbbcbadacdbdcacacacdbdcbacddadcdaacbdbbacbcbabdbdbccdabcaababbabaabaaaacbbacbbacdbcdadbdbccdddbabbcddccddbbdabccccdabaadacdbacbaacbbcbcddacbababdaccdbcdacbacadbcdacaddbdabbddccdcbaacdddbaadbadbaabddacbddbdcadbbbbcbcabbbaadbabdaabccbdacbccbadbaacbccbdcbbbbabaaaacbdccdcaddddbcaabdbcaacabacdabaabaccbcbbdcacdbbaaccaaaacabdcaccbbbbcccbabbcabbccdbaacbbacaccdacdbacacdcbbbacabbdbcbacbbdcdadbdcbdcbaaccadbadccdbdabadcadacadbacaddabddcddbcdbdddbddcabccdbbdabccdcbbcccdbbacdcccbdbdadcabaaadadbdacadacadbcacbbbcdbddcdbdbdadadabcabdaddaddadaacccbbbdbdbaacbbaabcbbcccacbaccacbbdbdbaccddabccddbcbababcbccbccbbabbbaddaadbaadcdcccdbcacbacdccccaacdbcbcbdbcaccddcbababadddbbddbabcadaadabdcddadaaadaaabbcbdddcdccdaacdcbccadbdbbacacdaaadcbcccbabacacabdcadcdaacdabaddcddddcbcaddbcddabdacdabdadacdbcbacdbadcdbadbdddcabcddddbbdddddbaccbbadddbbbdcccbabddacaccbdaacaacbddbdccdccacbbdbccdcabbdddabaaddbabadcdbccdddadacadaacddccddddcbbddcbaadaacaacadbcccacccccaacadcbdbbdcadaacacddcddcdacbcabcdadddbcabcbbabddbdbbdabbbcbdddbbdacaddbaddaaaaacaabbcdabbcaaadababacdbdbdbdccbbddcbcabdddcabaabcdbcdcbcdddbcabbbaaaaccbbbbdaccdabacbddbcbabdacacccbcddbbbdbcdcbadaacdcdcbcdadccdbddbdcdaaaacacbdabdcddccdbadacccbdcaacdcccabbcccdacadbbabbabdbccacdadacacadbcbbadbacbcacdbbbbaabbabdbbbacdabcdcbabbbcdccddabaadbddbaadbcaddbdcacabcdcbacddaadaabaccacaabacabdbcabdcaabadbaadabaaababcbcaacbcdcbcbdcdccbaadbccccdcdbabbcdadbbdbcdbacadbcbdcdbdccaaadbbadabbcdadbabbbddaabbcccabcbccaabcbadabcabdccbbacbbdabdccddccdbbbbdcbadbdaccdaaabddbacddabacacddabcddbadcabbcabbdbcabddacabbcdbccaadbdbdccadabbaccbdbcaaaccddcabacddaacabdbccdcabacbaaadcadabbacbbdabcbdbdcbbccdaacbcadbbddcbcbdabcaabccabbcaadbdcdabaddbababbbabbdbbdcbacccdcbbbbddbccabcdaddabccaaaacabccabcaddaabddcbbadaddadcadcaddcbbdcccdcbcacadbbcccaddccddbbdbbaddbcadbcabdadcdababcbcacdbbdcacabbdcdcdabbabbbbdcabbbaddbbadbbbaaadbbccacccaadaacaadaaadcdabcdbccbadcaadabbdabbcaaccdcadaaabadaccacbabcccabaadbbabbbdababdcbbdbcdcdccacdabbcbcbbccabcbbaaababdbadcccbbabcdabbccacbadbddbbcaabdbbaadbadddccaddcccdaabaaaadccbaaaabdbbaacaccbdabbacabadbbdbbadaabcbcddabdacaaccbaccadbdabbcadbadbabccbdacdbaadbcdaddadbbdcdcaddbbbdbaacbcbadbacdaaacdcddcdabddaacdaabbaacbdbbacbcbcccbbbbcaaaacbbbaabdcdcabbcaacbdabadcabdaadbcdcddbdbacbdcaccddadddbadcccddabbdcdcbdbbbbbbacdadcdbadbccadbdbdcdadbdddddabbaabdbcbaddaaaabaadccaabaacdcbdabdbbaaadbbccdddbbaccdbcdabdccddbadabdddbdcaddcabaccadbaccabcccacabbdcbcdcaadadbcbdaacdbaadccacdaaddbadabbcddaddbcccbaabacccddbbbdcacbbcadabddcdcadaaabbbcbcdadbcabbacbcabbbcaacadacccdbbcdbbdbdaaadcbbbaaadbadcbcabdbadaabdadabcacadbdacabadaadcacbaddaaddcbbdddbabbddcadacadbcbbcdaaaddbdbdccdcccaabdbdccbdbccbcbcddaadcbbbdccbbaabddaadaddadadbddcdcaddcbdabacccaddadddddbcabbbabdbccbdcabddccdccccacdabbcbdddadbabccacaccaccadaaacbadadaccbdaddbcdcbcccadcdbbcbabbaadaacbcdccabccadddcbcbbdaaddaacbbccbcabdabaadcddaaacaddadbbabdcdaabbdacbacacabdabccdbcacbaaacbcabcbbadbbdadbcbcbabbdcdcdbbbbaadccccdddbadccbdcdcdbdabdaaabacacdddaabcbccdbddcabdaabdbdabdadccccbaccdcbcaabaaaabaabcdabacabcabbdcabbaaacdbdcbcdaabbacbaaababddbacaaaabacbaccdccbdddcccbacbabacabdabdaaadccdbdababddbbaaaabcbbbdcbdbcbbddbcccddbbdcdbbcbbdabdbdddaabdadacdcabacbdbabcdabbbabcaadcbabdbdbddbcababbbbbbdcbcadbcdbdddabdbcaddccccbadaaddaaadaaadbdbabaccabdccbabdababbcbbcacbcdaabddacdaaababaaabdbcbdbacaaaacaabadbcdcddababbbdccaaabbddcabbaabcbacbaaddbccbaddbbdbcbabacdcddbbdcdbdabadcaccccbabddabacdccadcccabbbbabbdcdcbdddbdbbcdbaaccdddabdadacddddbabbbaadbcaadcaccbadcacbcacddbacddadddcabccbbbaaadacccacdbcbbacbbadacccccabcdbdaadadadadbcbcdaabcabbaabddcbdddbddbddacbcaacccddaddbcbaaaccabdbdbbaabadadccbccdaddcbadbdbdccbddabcdabcbcaabbcddbadbdcdadbbbdaddcbccddbcbbcdaaabcbdcacddbdbaaaadddbbdbbbbabdbaabcdaacabacacdcdaddacbbdabbbbacbccccabbdccdcbdaaddaddcdabaccdadcddcadbdadbcaadcbbdddbdacabadadababdccdbacbdbaabccadcaaadbbccaadcdadddcbcccadcacdabbcdddbcadbddcbdadcdddddccbcabcadbcdbdbbaaaabbccbbdddaccaccbdadaaabadcddbabaaccdcddbcadbdcaabaacbabccaccccabaaaccadcbccbdacddbbdbdaaccdbabdcbbcdcbcdddbbacadcadabcbbdbabcacbbdbaaacbacbdaaddacbbabddabcadcdbdabaababacacddcbccbabccdccadccccccbabcddabbabcbccacdabcaaacbcbbcbbcdadcdadddabbbddbbdcbabbdcdabacdccdabbddadddcacbcadcdccddbdaccbcadbcdaccabcbcaabdcdabdaaddbdbaadaccdadcccddcdddcacdadbcdbbcbaadacbcaacdabacaccccdbcdabbacaddcbccbdccacadadbaabdaabadbcdaababbdacaadbbbcddbdbacbabbaabdbddadbaabdbbbacaababcabcccbdbabadccbbdccddbcabdaddddaccadbcbcaaddcbcbbdbcdacddaadbacdbcddccccccdcdadadacbdcdbddbdccbabcdbccadadaddbdcbbccddcdacdadbbbdaabdbccbdccadbcbccbbbdcddbaabababbbbdaadddddacacacdabcabdacdcbabdcadcacaaddcbbbaccbbbdbcdadbcddbbdaccdbcdaabdcbbbaadcdbabdcbcacbabacdddccdabddbdacbbdabcaaaacacabadddacaddbdaacbabcaccabccbddabddcdcddddcaaacdbdcadbbdabdcbcadcabdcdcddbcdcbcacdaccacddcaabaabdbdddaddccbcbbdabcadadcadcdbaababcccabdbdbbcccdbbaadcaacabbbbadbddcbdcabbdbadbdbbadbbcbbbcbcaadcdaaaadcabcaadadccbddadcdaacdcdcabbdadbdcdbcdcdccdcacbbadddaacdbccbcdacbcaacdcaacbbbcdccbdcadabbaccdbaabbccccacadbdaaaaacddbaddaacdaacaacbccccdcdadcadaacdbcacdcbdccadbcbadddbbccbabadaacdbdbddbdcbddcaacdccccdbdbbbcbbbabbabddacabddcaadadbddabdcdabcbadddbadccbbcbdccbdcdcbdcbbccbdacacdacbcddaaaddccdbdaacdbadcdbcdacddbacbcaaabcacbcdccbbdddaaababcdadabcdddcadadabcdcbdbabdabaaacaddaccddcabdadaaacdbbabdccbbcbbcdbabbbcdddbbdbdabddadcddaacdbacaccbcccbddcbbbcbcbddddaccdcabdaababbcbcdacadacabcdbabcadadbacbdabacabccccdccabcdbbccccaadcbbbddbbdbcbcaababaadddbdccaabcddadbbacddadbaacdabaacabccccbdaabdccacabaccbbdcbdadbbcdbdbbaddaacdaaabcbcdccaccbccccaabdbdcbabbddbaadbbcaaddbbbcbadcabbbccbadccccdabdbdcabcbbcddabdabbbbbabadacbcbbadabcddadcdbaabaaaddcadaadacaababddabbabbccbbdbacddaabdadcbbbcbbabaacabadccdbddadbdcdccddbccccdacbababdddbcdcbccbdacdacabadcdcbbbcbbdbbbbadbadbdcdadabcdaddcbacdabacbcbddadadbbbbdbcacbddacaacbcbbdbaadbaabbdccccbdbdabadbbbcacbdbbdaaaccabacdbcbadbcabcabbccbabbbbbbdabccabddaccdacbbdcbdcbdbdddcabdcadaaadcaacdaadbbccaccdddabcbabbdcbadbdadbddacdbaabacaadbacdaccdbdcdabcbaacdddacbacbcdaabbcdbcdadccbbdcbdacddcadadbccdccdcdbbdaabbbcddcacbbbbdadadcbaadcacabddcdcbbbbbbdbbbdbbcabcaaddcdbcddcaaaabaadddabbbdcddadabaadaaaddbbabacbbdccbadccaabcdddacdacddadadbabadbcdccccabaacbbaaadcdaaddbbddcbbbbbcbdabbdaddbacbbbbbddcbcaadbccadabcddaaddbdadddadcadcadbcbbabacabacccccabbccaccbbcbcaadcbacdcccdaaabbddcccdbcdbdbbcabbdaaaabdbadbacacaabbabcbbbadbadcdabddddddbacadcdadbccaabdcadbbbcccbcdabcbcbdadcdacbbbbdadbbddbdacbcabdaabbbacccacdacaacacbbbdbddbbdcbacdaaaaadcbdbbaaadabacdbbbaacccdaaacacbcccaccccbdcdbcbbbabddccbacbbacbcbcdcbdcacaacdbccccdaadaadcabdabcbdddacbaaadcacdcdbbaccdbbbcdaadcbaddcdddadadbbbdadcadadabbdbdacadadabbdadcaccabcdccbcaababcacaacdaacdbacddddbacccddcdbccbcaacccccbcccacbaabaadbddabbbabbcbcbaddcaccbdabdabbcadabbcaaccacbbcdcabcdcbcddddddaadbaadddbcdcbcacddadcdaccaadcbbcccacbdcdaaaddbcdacdccaccdcbbdacaacdbdcddcdabcbdbbbdaacdaacddbdbdbdccccccdaaadddbdaddabccaababcdbddbdadcadcaadaddbaacaabccbddaaccdacbcddcbdbbbbcccabbccabbdcabaccdccbcdcbdadacdbacdccdddcbccddcadabccddcaacabcdbdadacabbcbbbacbbccacaacbcbdabdddabbcacdbcacbdbcabcbccbbbcbcbaccccbdbcbccdadaccbccaaaddbdcdbbbcdaddabdccdcdcdaaaacdabacabcbccbbacabdccbaabbaaaadadbbcadbbdaddadcdccacdcaaccdaadbcbdbdababbbaddbacadabaccaddadadacabdbdbcacdbccbcbbcbbaddcdccabaccbadaccbcacbbadcdbadababcbcbbaaccbcddddcbcdccddbdbcddbcdabddccabddcbababcdbacdcdcabdbdacccbbcdccdbadbccccdbdbbbbbbaddacaccdcbacaaaddbdaababddccbcdbbdbcddcbacdcdccbdabddbdadbaadbcadacaacbdddbccdcaadcaaddcdcdadbbabdabaddddbbadbbcacddbbbdadddcaabcdbcadaadadadbccccbabdbcdddbbabdcaabddddacdcdccddbbbbccaaabdcadcdbdabadadddbdbbadaacdbcacddcabddbdcbbcbdadaccababcaacdbbdbdabbacabaadddcbcdcbcbcaacbacccadbcdcbcaccbdbacbcdddbbabdabadccbdccbbccabcacbadcacccdadadacaccdbccdabadadbabbcbddcadacccaacbdadaacaaaddadacdadadbbaaaccabbcdadddcccbddccdcbdbdcacbcdbbaaaddbbcbdcabbccadbacabbcaccaacacbccbbdaacccbdbaaabacaccbabaacacbdbdddbbcbcdddddddddbdcddcdcccabaacccaabccddcadbcacbcddabcacaccdacdbccddcbccaabccdacadcacbbdbacbbbcbbdcdbcbccabbcbbbbadaacddaabcdacaaacbadabadccddcdddcdadbddcdaadbdabdddcabbadbadbbcdcabcdcbddabaadccdbabcabdbbbccabaacdcdbcacbaaaadabdcdaaacaaadbbdbdddcbccaaccadcabcdcacbbcdcdccacbdababccdacbdcbbdacdbdabadbdbaddcdccdcbbbddbacaccdccdcdadcdaddabdbbcdbdcababbcbbbddbdddbabaabadbbcaacbaaaccaadbbcbadcdbbcabdbabaacbcdbdbbccccaccdccadbadbbaabacccbccbbadcccbbaaccddbaacbdaddbdddccadadaddacaabbcdcaadccaddccbdcdbabcdbbaccaaadccaccdadbcbbabdabcbbdcadcdcdcaaabbabbbdbdbcdcabaccddadbabbdcddababcdcbaccbccbabbaaabcdcacacadbdcdbaabcadbbcbaddbcbbadddbacabdabccdbabcbdabdaadcddacacbcddbdaccdcbdaddabcadcdbaadaaddadacdbbddbbccddbabcbbbbbddcbabadaaadbabbbddcbcdbbcdbbddcbacbadcbcabcdcacacbaabddcbacccbbcccbdabdcdcbdbabcdacdbabcbbddddddbacabdbabacbaabbacdccbdcbbbccaadabbbdcbdcbcccaabbcbccbaaadabbcacdddabbcdcbddbcbdbbdcabaadddacacacbaacadbcbccacdadadddcdaccdbdbcbcbacdbbccddcabdddcbbcadddcbccddbbcbdcbaddccbdabbaacdccbdcbbcacdddccbccaaddbbabcaccbadccdddcccaadbdbacdadbadcaccaddcaacdbdcbaabbaccdcbdbbcdbcabddbbdcdbaaabcaacbcdcdddcadcacaacccdcbdbadaaaadacbbcadbdcdccdbcabababbbddcddabadccbcdbcbabbddcaacabaaddaaccdbbadcdbccdabcabbdacaacabcdbdbcddddcbdaccaddadbdbbbbcbcdbddcbcbddcbccabbaacdbbbdddabbbbddbbdcadaadcaabcadddccbaadcbbbdccbbcccabdddcccbaddddbdbadabdbcabcbcbcbdddacdabbdaacddcaccbabcaadacbbdcabbddddaaabbcdbdadaaadccacaccabcdadbddcbadaaababbdadbdadbcddcbcbacdbdcbacbaddbadcdaabcaddcbadacadcbbbabdcdadacdbadccccabcabddcaaaabadbdcdcbdcdadcbbccbdccadcbcacdbdbddacaaccabbaacdadaadacdbaddabbadbccaabaacabdccbcadcaabddababdbabccacabdadaaabaaddbaadccccccaddacabddaabbbadccdbbbdcdbcbdcdaddccdccdacbdbcccdddaabacbdadcbacdbccacaabadadccbbccdabbccacdbaddabcdddbacacabadbdacabcddbbbcddcdddaaabbabbbbbcaddcaadaaadacddccdbbabdccbdccabddacdccbbcabdcacacbbbccaacdbaadcbaccdbaabacadbdcbcdbcaadbbbdccdbacdadadddcaccccbddcbbbdabababdcbdadbaccdaabaabccbbaaadabccdbdccaadaacbacacadcabdddabddcccdadbdcdabaddbabacacacadcbabadddbbdcbaacdaaabbcbdddcbaadaccabadaacabcbdbbbaddbaabbaddbbdacdcddbdbdcabcbcbcdacdddccddcadcddccdcadbaccbccdbcccdbaadaaadcadabdadaadbacddbddcdccaccbbdbdbbbbbacbbbbadaccadabbcdddcaacbcdbabddbcdcbdbbcdabccabaaabbddcdcccbacabbadcaabccaadcdcabcdcbdaccbdabdadbabaddbaddbbddacbccddcdccacbbccccdbccbdaaadcbccbabaddcaadcacbcddbdabacccccbbdccddcbbacadcddcccbcacbdccabdcadccbddddaddcaaccccacacaccddabbdbbcabdaddbbadaacbdbcdbdaaabdbcdaaadcdbaccbcdcbdacdccdcadcadbbdabcdbacddabbdaabdcdddbccaccbdacabbbcadbacdbdadacabbdbacaaabdaacbddbbbdccadbdaaacbcaaaabcababdcbaccbdcaacdcdcacdbcabbbbcabdccbdabcdadadcbaddbbbcdcabbdcbbaaaccadabcdabaabcdaaadbabaccbbaaaabcbbbbcbcbacabdbddcbdbbacadacbdbbbbacbdadbacbbddbacdbddaabccbcdddcbdacabdccbadadadadccbbcbaacdadcaaadaaacaddcdabababcbdcdcabdacaadabdcabbbcbcccdcccaddcabbdccacaaaadddaccbdbcddcbbdaaddcacddcdaadbaacdbccdabcdcbdcaaadbabbaaacbcabbbbcbdcbaaddcbcbacaabaaabadcabbccdccddcbacabdacadbdbcbbcddacdddadbddcaaabbbdadddaccddccaaabaddabbbcdbdbaccabbbdccccaaaaccbbdbacaaccdbbdbbaccacbbdcdccbbbcbaadacdbadddbbacadbdcadbadcbbbbdbcaadbaaaccbbddaccabbdcbdcccaaddacadbbdabadcaabddcddabcccccaddddabcdbdadaacaacbabcaabbadcacabccacddcaaccaddcabaaadbdcdccdadaacbbacdcdbcaacdadcbddbccadbdaadcdaaaabdbbabdaacbdbcaacdcaadaabbbaabbabcbaacabcdadbacdddadacccaaaadacbccacbdbbdbaacdbbcbcaaaacbbcccdbaccbbbadcbcbbadadcccacdccbdcbbbcdcbbcbadddbbadcbdbbacabdddbaddacdaddbdbcdbdadbbbaaacbccaadccbcacbadccccabcdccddbabcddcdababcdbcdcddbdbccdaababbacaaddcbdadbdbcabbabbbaabadddddcdaaadddbabbcdcacdbdbbcaddcbdacaaaaadcccacbbadabaabcacabbdaacbabcdbbaadacdbcbabdbbaddbaaacaadbbadddbddcdccbbbbbdadbbdcbccabcacddaacbcbbaabbbacbaddacadaabaadcbccadbcbccbdbadbbadacbabacabdabbbbccdcccddbbdacadbbdaabacccbbdabacbbaadabbbbaddacdcccaadabbccadddaacbdabdbdcdcadbbdacddaaaacbdcdbbbbdcdbaabbbdddddadbdbabdaaacdbcccdacbbabccbabddaadbccdadbaaccdaaaddddbddbbdcdadcdcacbaaccbdbdccabaacadaacabddbdcdcbdddddcadaaaacdaabcccbcdcdbbdbaabbcbdaaccbcadcddccccadbddddabdccdccbadcdcabcdbbdcdbdaadccbcdbaacbdcbdbaccdbccccabbddbcddccacccabbadddccddacabcbadabaabdadcdcdddbbcbbbbdaabdbabaddbdcbbcbaacbadbbacdbbdcbddacbcbccadbbadbcbadcdbacbdacbaddcaadbcdbcadabaacabcddbbcddadabaaacbdbbccbaaacabdadcabdaabcccdacbdbaddbdbacadbabbdbbaabaaaabccdcbbcaccbabbddbcbcbacadcbbddcdcbaddccadaaccaacdccbadbbadcdbdcbcaabdcdbabccbcdbbabdbabbbcbbbbbdbcdababcaccbbdaacdabddabaacdccadabbadbbcbbaabbaccddcadccbbccaccadadcbbcaaccacdaaacdcbcaddbaaddddcadcadbbabccbcbabacbbadbcbbddcbbbacaddbadcaccbdcddbdbbdbbaadcbdababdbbddccdbacabaabccadabbbacacbbcaabbbabacbcabbacdcdcbaabcbdcbddbddaacddcadbcccdcbdddcccdddbbbacaddadbdcbabcaaaacccabcbcbcbacaabacdacabacbdacbcbccdcacbcbdbcbaadbbddcbbaddadccbcadbaaccbcbacaaabdbddabbbcdaadadcbabccadccdcbdcbaccabdddcdcabdbadbcaabdcbcaabcdcacbdddcddcbbbbccacbddacddbdcacdbdbcccacdabdcddcdcdaadcadadaccbacbdabcdaaaadcbdcaaabbdbcdddcccdcaabbcbcbcaddaabcadaadddadccbbadddcbbbaddaacacabcadababcbabcbadaacdbdbbcdbabaddbddadacbccdddccabdbacdabbbdcaacabcddabadacbaaadbadcdccadbacdcadaddaccddcaadacdabccaccbbbdddbbdcbcababdbccaabdcbcbdbbaadccbddcdadcdbabadbbddcabcddbccdaabacdaadbbababccaabccbadaadcdbbbdaddbccddddccdbaccbbccaadabbcbccccbccadaddbacbcbaabbdcadccbcdddcbcddccbbdbcbbccadbbcaabcaaccaddbbbccddcccdcacdcaddccddcccccccccacccbdcacacbadaccdbaaacabbbdccccdadbbdcdcdcbddbbcabbbbacacdbaadcadadcbdabacdadcbdabdcadcddbbdcdcddadcdaabaadbadbaccbbbcddcadadcdcdccaabaacdcdadadccaccbbbdaadacacdcbddcddcbcdaaaaabaccabbccbcdaddbcdbcccddbadcccbaadabccabcbcdccbccdaaccdacabbdcadcabdbbbdabccdbcbaccddccbdadbbaabccaddcddaabbdccccaaacbcbdaabacbcabccdcdbaadadbbabbcabaccabbbababdcddccccbacbaadbdcaabbabccbbdbdbacdaacbabbdbdbddbaacaddbcbccbdcdccddbdddaacadccdccbdcbdccadccbccdadcdbdcbdbcaccabcaabdcbdacbbcaaacdaaddcddcbcbababbbbbcdbaddcabcddccaccdbaacdcaabdcadabbbacadabdadbbddcacacbcddcbdbdaabbbdabcdbbabccdbcbbbcdacbdabaacbcbbdbdccbcdddbbcdbccbdcbbdaabcbdbaaddabababddcaaddcbabbbbaabcdcbaabbccdbacabcabcdbdcdbadddcaadbbdaadbdaccbcbdaaaaddaccbbcacbbacbbcbdaabccbbbbabccdaaacdddcbaddbdbcabcbcbdcbcbddbddadabcdaaabcdbbdcdccdabbdaaccbbabbcbaccdcabcccddabdbcabbadbddcadaaadcccacdddcdadacaabbcbddacaddcacdadcbadacbbaddadadbdabadbabbdabbabccddcacddcdddbaddddadbabbbacdbcdbbcccabacdcacdcaacdaccbbaabccbccbdccacdddcbbdcbbcbbbadaaabbdbbdcccbbcddbacdccaabcadccddaabcadcadbaaaccdadbddccabacbddddbccacaccacbcbaccdbcabcdccadcdabdcadcbdcabbadbcaccacdddabcbbdcabbccbddbbbddcddbacacbdaaadaadcaccabbdcccbdaabbbcbdbadcbbcaaaadabcdcbaccaaccdadbcbbabacaabcbaaddbdabcaabdbbbdcbdddcbcaabdacdaaabcccadcabcacadbccaaddcadadcccdbabcaddccddbbdaaabadbacbddbababcdcdacdcbdbdadaadbdbaddbddcdccbacaadbdcbaaacbaaadcbabddbbccbaaacddbdccabdcaddbddccabbabadccdabababbacadddcadbbbadbadcacddddadbdbbbdddcbcacacaddcddbdaddbcadabbadcbcaddcadacbacbadaddbabcbbccabcbbcbbabcbbaaccdaddcdbdcdbcdcddbdcabcacbdcabaabbdcdbdcccdccdabcbcabacdacdcabacbaabddbbdbadabacccbabddddaabadabcbccdddcccbbacddccadbdbcdbadcadadbcdcbabcabbabcadacadbbdbdccdbddabcdcbdbcbbddcccccbbdccbcbbadbdddaabdbbdbcacccaddbdccbacdaabcbdcddcdaaaadcacddadbbacbcdbadcacdcdcccaaaaddbcdbbccccbdcdccddacbacbbaddbbbbcdadccadcdcccddcdbdcaddaacbcddbadbacdacaaacdcdcaaabbdbdcbaabbbaccdbcacaaccbadccaaabdbacaaabdccbadbcabbabdadaddbccdbdaaccaadadcdaaccdddbcdadabcddbdbaabccdaccbbdaccbdaaadbdcdcaacdacaadccdcadccaaddbbcacdbbbbdcadcbbdcdabdcdcacdbbcccacdcdbbbbccdabaadacdcadcbdaadaadadddddccbddbacacdabcddcccbbadbbaccbbcbbcbbcbbaddbdcabddbccdaacdcadbcdcadbbabddabddacacbbabbcaadbacdacaccbdbbcdcbdbdcacabbcadbcacbaabddabbbccbddbbaaddddabddacdaaabdaaadbcdadabaccdbdccbdaadabccbbbccacbddccacbacdacccdbadabbcdbcdaaacccdabcbcacdbcbcddccccccbcbadcccbacdbacccacacacadabbcbcaadaacbccbdbdcadddacccaaadcbdccbcadbadabcbbdcccbdbdbbbbbcddccdbcbdcbdbdbcaddaacbbccadbbcadaabccdcaaadddabaaabcabacbcbbcdbccabcbaccacbbddbababacadbaabcdccdbadcbccdcabcccbcdccbabccbaadbddacaccababdbddcbaddacdcbcbadbbdbdaabdbdccdabaccadbbbbadaaabddadccabbcabaaabdacbbdaadbcadcabddbbbbbddbadcaabddbbcaadadbddbacdabadabbdaadabacddcabdabbbbadcabdccaacdddbdabcdacdacaacddddbdbbbbabcdcaaccdabaddcbdcadccdcbabbbaabccabdaacdacaacdcaadaaccadacaaabadccddabaaacccbbaaacbadddacbdcbcddcccddacdcababbcacdbcababbcdaccdaddacccddcacccbbacdcbbcdcacaadcadadbddbcddcbacadcadcbdbbbcbaabcdaaacccddddccdcbcaabccddbbdadbdbadcbaccbbcbbcaaadcdcbadbbbbabdcabcadbcdccddbddcdbdddccbdcbadacababccdbbaadcbdbacccbbccddccbdbbaababbaadbdaacdacacdddacbdcdaddabccbddbcbcabdadaaaddaddaacaaaddabaccbdcabcdadadadacaddccdcabdcaddbbbccacacccdbbddddcdcbcaabddcadbaacadacacccbcbabaccccbdacdcaccabaadaadccccccccccbbdcabcbcacbbaccbdbcdbababcddddbbbaabdadbaccaddcbddbdadaccbaadccdcabadabccdcbcdadcadadccbdbcdcbacadcdcabdaacbaddaddbababdbddbdbbcbabcbbcccacadcadababbabbdccaaccadabbaabcccaddcdbdbddddaaddaaacddbcbacbcadabdbdbadbdcbacbdaacdcbbccbddadadaabaacccdcddbdbbcccbdaacbbcbcaccacdabacccadddbadadccbaadbcbcbaaacdcbadadbdcaacacbcdbbdaaabdddcabdcabcbadddadccdbcdbdbaaaddaddcddacbbaadcbabcbccdbcdcbdbbaddadccccbbddbabbdbabdadddaaacaadcbbdbcaddbaccdadaaaacdbcaacdcbcabbbacccbabdbccdbdabaadbdabaaabddaacbdbdaacdcadcccaabacbaddddbacbdbacaddcbaacaccbccadbcdbbbdbaaccabbacaccbbacbcdcdbccccdbbbaaabdabaaaddcacabbbbbcacccbdcabdcaaddcbadcddbdbadddcdccbdabdcccbacbbabdabaacbccdaabcacabaadaaaabcacddacdddaddacaddacdbbadbcacbbbdbdaaacbbdaaddbbbcbadacacaaabcbaddadccccdbdaacddadacdcacacaacdabcdbcaaadaabbcdcbbadcccccccbadacccbcacccbabcbabdcdabcccbcbccdaacaddcccabbbadbddbbbbbcadbaadcaacdcddbcbbdcdbbcdcaacaacabbcaddbabbacbbacabddcdcddcdbccdacccccdbdccabdcdbdadbdadadddcadbbadddbddcbcbabacbdbaacbdcdddbbcbdcddcacbaaababcaaaabaabbbbadcdacbadbdbbabdbcaddadccacdbbdddaacacdaaaccbdbadaacbccdabbcbdcdaabbaacbacddccccdbcabccdaadbbdddaababaadcbcaaadaacbdcbaabcbdbbabcdaddacaaadbbbcccaaadaabdaadabcdaacaabcabcabdadcbdaadcbdadadbcccaabbdcbbdaddabcddbdcadacccdaabaababacbbcddabaaadcdcbdcdbadcdcbbbadababbaaccddbacdccaababdcadddbbaccaadadcbcbddabbdcbbdbabcbbaccdcdbcdccbbcbaacadadcbacacddbbdcdbaacaaaddbdbacacdcadbccbaaaccdbbabaaaabcabadbdbcaadbbccbbccacdcaccccdddbccacdbdaaddbdbbadadacaacdbcbdaaaccbacdbacadabcccbddacabbcccdcadbabbabbbcbdaacdbdcadaacbadacdcbcdabccdccdacdbabdaababadcbbddabcbcadcaadcaaaddbcadbcbccccadbababdbccabcddaddcdcaababdbddbabcbdddcbdcdccdadccdbcdadabdbbdbadccdcdbdbbbbccacadddcdbbacbbadaddcbabcadbcbddbbccdbdbacbdcbbbabacdcccdacdcdadbccdbabaccbacdaacddbcacdccaacdbdcddbbbcdabbabdbabaacdaabbadbdacbddcdbcbadbbabbbbacbadcabbdadcbdbabcbbcaaabdcadaddcabcdcdccddacdcbcabcdcbccabcaabadcddabdbcadbbbcccdccddbcdacadcbaacbcadcbdccadcddaccabbbcdbdbbdddbcdadbdcddbaabaaadcbbcdcbcdaddabddbaccadbcdbabbbcaadadcadcabbdaaddbaaadadbdddcacbdacabacdbadcbdcdaacadcbadadddcaadbbddccbaccbbcdbcdbdcdbdbaacccbabdcbaaabaddbdabbaddcbabdccdacaaadddbabcaccbadcdcdaacaaacbcbbcabdacccacbdacdacbcaadcabacbdbbaabbadadabcdcdcddadbbbadbcbaacaccbdadbcdcddacbdcabdabcbbacdbdcabcbbcaabcbaabbcabddaadbddcaddababcbdcddbcdddbdbdacdadaaddcccdddbcdcaacaccccbaabbbbbdddccddbbadaacaaaabddbccbbdadaabaaaaadccdbbbccadbdccdadcbabbacabaddcbcaddbabaadbcddbdbddadbcdacbcbdadcacbadccacadabbdbadaadbccddacddbdbdaddadcdcacbcddabacabacccdbdbbabbbbcdabbcbdccdbcccaadcbdcbccaabdcbadbdaacbccbdcacacbddaabacaccdcbbaccbcbbcddacccbcbccbcabbddbbbcccdacabacbacddbaccdbbdccddddabcdddbccacbbbbbbaaddddadadbcbcdbcaadabddbcabdccdddcdbacbadccdcbabababadabbdcbacccacdbbcccabaaccbdbcbdcccbabbbdacdbdcccdcccbdcadddcaadbccbabdcaccddbacabbbdaabcddbaaabbbcdbbaaacabaddddbcaabddcdcdacbadcaddcddaccdaacccbdcacbadbdbcdaababadadccdcbccbcccabdaadcaabaccccdccacbdcdbccdcbbdccdcccdbaabbccaadadacbbcbccdccdbacdbdbcadaaacdabccdcdcccdbdbbdaabadabaddcacdcdabcbdadbbbaacbdbbcdcbadcbcdcbcdcbcdcaabccadadacabbadcbadaccdaddbdaddacdcbacdbacbaaabaaccdabbcbbacbcadbdbcadaabbbabacacdcadadccdaddcbcbdcddbdcbbaaaaadacccbadbabdcacacdcbdacacdabccbdcddbacbdbcdaadbdcdcaaccabbbdadddbaabdbcbcaaddcbabacddbbadbddccdacbdcbcbdccbcdcbdbcabcaadacdbabbddcdbaccdddcddbcacdaaaabaaaccacbcaaabbadabacbcaabdddabbbcbbccadaaadacbaddabbbdcbabbbacdaaddbbbabacdcbcaccdbadacbdcabaccabcbbccbcccdcbcddcacbbcdcabaaaabbbbcaadabbaaddaaddabbdadadadcabcadccaaabaddacdabbdbcaaaabdacacaabdabcbaadcddbabccaaadbcabbddcabbddcbbbcbacbdbcabcccdacccdbcacdbdcbdacdabbdbcdbaddddacbcabbbbaddbcdaaaccbbadcaddaccbdabadcacadbbaaacdcccbdbdbaabadccbbbdbbddaabdbbbddbddbdcaddbccbcdcdcdadcaabdbdcddabbddbdbbdbdabdcbcdabadddbddacadccdaddbbcabcbddddbbdbaacdddaccddcdcbbddaaacaadcaddccdcdbaddacbddabbacbbaccbbcaaacbabacbcbdbbbdddbcbabcadacdbbddaccdddaccaaddacabababbbddadacabbabdbbbacdddbdabbadadcbcdabbcdcddaacacbcddadccbdcddcdbabbaddacbcacdacabadccbbaccacbdcdaccbbcababdbddbcabcbbaacdbdcbbbbcbdbcccdadccaddccaddbcbaacdcbdcdbcbbcaaabcccbbccadaaaccdcaaaabbacacddddccabbdacddabcdcbcbcacaacdddbcbcdbdbbaaabbcacbdacacbcaaddbcbbacdcbdabcbacbaaaccccccdbcacbbabbdacaaaaaaadbacbaccbbbcadbdadaddcabaddacbcaabadbdbccdadbdabcbdbaabdabbdbbabadabdadcbcabdadbdcbcdbcadcccaabacaddaacdbdaddaccaadbbaaadbddccbabdbcdacdbadadcbcacbbdccdbadbabdbbbbcbbacdbcabcddcabbcdddcdaadcbaccababdbdbccddacdadbbcbcddabdccdcdbcbdbdddbdbccdbabddaabcdcabccdaaabbccacccbdacabdcdbddcbbadcdadbabddadbdddbacbbbdbbbccdbaaddaabdcbddbdcdbabacdabdaaaddbcdaccaaadccbbbababbdacabbdcdadbabcbcbbabdbbabcbcacdbcddbbbbabbadcdddabacadbacacbdbabadbaadbccccbacaccaaadaddcbbcbabbdbaacddddddcbbdacacccaccaaaddaccdabdbdbbabbdbccdbbbcabcbdabdcbdabbcdbbacbacdccbaccbbacccddbcaabbdacdcbbcbaabdcdcbabdcddacccccbdcdccddbaaadcababccbcadcccbdddbaadcdddadddadcccbcbccabbbbcbdaaaabaaacbbdbcbaacaddbaabdbcbdbdbacacaddddcbcccacddbcdcdcabbacdbaacbcaacbddabaabccdbbabadcdddcadcdcdbbdbadaccdbbcabcabccbddcabddaabdaadbcdacadbcbddacdabaaddbdaacdaccbaccbccdadbcacbdaabacccbcdadcbcbadacbaacaaddaacbaaadbbccccaaaaaaddbdabbcdddbabbdcbdadabaddadccbcaddbdbaddccdbabdcdcccccddabadabaacbdadcabccabaaccccccbdbabbcaaaadcbdccdabdcaccacadaadddbdcadcbbcccddadddacdbbadcccdbcacaaddcaabcbaaddadabacbadddccbcacddaaabbbabdbacbabaabacdddabbdbcdadadccbbdcbdcbcdbabcbbcabdbdbccdcbaccbbdbdaccadaaadcdddbcbcdabcabdbcacdbdcccbdabdccdccbdadbadcdaccddccacbdbdbcbdcbcbcdcbabdabcdddabcabbcdcdddbcccacddbbbdccabacbaacbdabbbdabaccbcbdabccdbabbbbdacccbcaaabbbccbbcdcdbbbaccbbdcacbbbacadaadcaabcbbabbaacdbadcadbbaddadbbabaccabdacbdcbdccbbbcdadbddadbbbccaabcdcacbcdddbcacbbdcdcbbcadabbcccdbadabcccdcacbccddbbbccaccbcaaadbacdbaddccdcdbbccdadcdacacdbbabbccbadcbadaddcccaddcadcacbdacbabcdcccacadcbbdcaccadcacdccacbcddbcccadbdbacbcbbdcddaadcddcacadddadbbcbdbccdacabbdbbbbdbcdbbdcbcadcaacdadcacbbbdacdabaccbadccccddcdaabbccaabacacbabcdbdaddabdcccaacdaccdddaadaabcccdabccccdddbccdbddcdcdcdbabbbdccadbcaddadadabacaacccaddaaaabaabcbaabdbcdaccabdabbaccbacdddbbacbdbcbbcdddbdcbadcdabaacdaaddacdbabccadbcadcdbddbdddccdabaaddbcbacacdcacdcbcbdbadcddadbdbccdbbdccbdcbbbabbbdccaacdcacadbcdadddcbbddabbddaddbbadacaaabbccbcbbcbdbbadacbcabcaaabbbdcbbabbaddabbcdbcdcdbccbbcadadbdcccdcdccabacccbacabaacadbacaabccadbcddabddabbcdbcadccddadcadbcdacacbbccbdcbddcbcacaacadcdcbbdcbdaacaddccdacdabcaccdcdccccdcadaacbcbbdbdbcaacacdaabbbdccdadacacddaadbbabcbcbabddddaddddabdbbadaadcacbcaaababdacccccbadabababbbcdbbddadbbbabbcacbdbbacccdbdabcccbbcabcaaaaaabbccbbcadaddddccbcdbadbdacdadabbdbaccabbdadbbbbbabcacaacddacdddcbcdadbddbdcddaddbbabcbabcbacbbadaabaacbdbccaadcabadbbcbaacbcdbadcdacdccbbabaabddcbcadacacdbddcdbcccbcbcabbaaacccbdaacabcaddcbcbcadabbcbbddadbbcaddddcbdaabdcbbadcccbacacdccaaacddadcadbadbbcadbdaaabcbccccbdcaabcbdbddbdddbcacccbbbadbabacbcacadaabcacbdddabadbcaccbdadbdbcaddacbabcdacaaacadbacbbaadbcbaacbaacbbddaacaadaccdccdcdbadcbcbcbaddaaaabadaabdccbddaccdacdaabbbdccddcabaaababccbbcadcbdbbdccacadbaaccdccdaacbdbbdbbdbababadaccdbcdbbacdcdcbcdbaaabaacbcbddaaddabbabdcbabbcccadcbcdbbabbdcccdabbbcbcaaadbcdbcdcddabcbbaaddabdccdddabcbacabcccadadbacccccdccddbccbbaadccbbdcbdccaadcbdbddbdccadccdabdbcddbadabddccdbcbcdaacaabcbcdcacbdaadacbcccbabcbbbbbddbdcdbbcdbdbadcdcdcabcaabcccaabaddacadaadaacdadbbbbdabaddbdddcabacbdadccddacbcabaaccdbddbbdaddcdbdcbccadcbdcbbabbbdadbbdabbccdbcbcaccaadaaccdddcdbcabbadcdbaacdacdddcdabadcaccbdddcdcacbabacadacdcdadacddccbadbddabbccaadadbcbadabdcdbdadbabdbabbaccbcaacdabbccbbcbddabaaccbdaababbaadacacbcababadcbaabadadddcdadaaacccbaccddcccdbdabbcacbdabddbcabcbbacacbcaaabcdbcabdbacadcbaacbbaacabadaaaccbddbaadabdcadcbcaaacaacbbdaaaaacabbbacaabcccdaadbbddbaacaabbdccabbbcccdaabbadcdbcbbddadcbdcdbcdbddbacabcbbdbdddaadddcdcacdacdbbaacbcddabaacbacadcabaaadadddbcdbccbcdddaacbbaddbacbcdabbacbaabcdababcdcccccbccdaddccacdbbbaddadbbcadabacbabaddbbaacbbcabcccddabbbabdbbcbcccababacbdaacadbacabaacbcdacabcdddadcbaaaccdccccddddbbdcbdbdcaacbaaaaddaabdacbaabbbcdccdabdbdcacbdaaabbccabcadcbabbacdcadcabbccbaccaadbabbadcabdaaabbcddacadddcbadaacbdbabacbabbbbdadabbaacabcabdddcbbbadddacadcaddaadbbdbaacaacaabcbdcbbdcaaaddddccddacddcadbabababcbbdadbcabadbbdcdcccbacccbcacbbdacccddbadabaaddbbabacbaaddbbcabbcdddadbbcabcccabbacdaabaabaacdcdbaadaacdccccdadddbdccdcdacaddcaddbbdadaacdddccadcbaacadbdaabdbdbccadbaadccccaccdcdbbbbacbaadadabbbadabbbcbaaaadbbbbbbccdadbdbadbaaabddccbbcddcdabdddccddabdcdacbbadcbbabcdcdbcadadcacabcbddcacadadcbdaadcbbabaabbbadbbccdacbdbdbdcaaccaccbbddcbabbcbcbcdadcbabbbbdababdccccbdbbcdcbcacbaaabccccadcadbbbacddcbdbaabcbaddcdadbcabadbcdcccbccbadadccbbadacadbbdcbcabbbdbaaaabdccbbddddcabdbdddadcbdcdabababaddbbdcbbdccadacdccadaabcdbbbdcbbbcdcacdbadccadccadbabaccdabbbbaaadcaccbabbdcbdcbcccabcabadadbbbaccaaaadcbadbcacadbbdddbdddbcdbdadadcdcdddcddbbaadabcbaaabdbdbdccbbaaddcdddbdbdcccbdddaabbcabdabdcdacbdbcbadddcdacababccbacdaadcccdbccddcdaadbcbbbaccbadcccabbcaacaacbaacdbbbdddaaababadbadabacabadabdabbbdacaacdacddbdabababacabbdcbddabdccbdcaacabdccaaccddbdcbadadbaaabcbddbaddbcdcbbccacbbabaaacbbdccabdaacdababadccdcacccdaadadaccbdcdbbaccdaacdbdccdbddadaadcdddadaaadbaadcacbccbcadaacbdadaccdacabcdbbabadccbcdacbdbccbbdcdbdbaccaddacadcdcccbddbddcaaacbdabccbcabbabdcbcabdabcdbdbddabdaadaacbcaacdcddaacbcbcbacadaabcacabbbcaadabbdcdaaccadabbddcacdcacdadcabbbdadbccddbadadadaddacbaadbddabddbcccbaabbcdbbcccdccbddcbdbdaadcddccdcddadcddcbccacacbcabbcbbbacaccdaccbabbccddaccdbddcdabaabccaddaadcccbccddbbccdcbcacaaccabccdddcdcabcadabadcadcdcddabadacbadcaacdbcddccacabcdddbcadbcadccacadaaadccabadcdaccbaacbbcaddcccdabaabbadbbcabdcbcabdcbbbcbbcddbadcdcdcacbcbdddcaccdddddabbcbbbcabdacaaacadcdacdadacabdacbaababcbacbbacdbbcddbbdbaaddadbaabcaadbdadaccccbaadcbcadacacaddcddcbacbdcacaabadaacbbbbddaaaadccdadddbdddadbccdcabcdccdddacbddcaddddaabbaabbaccbadcaadcbbdccaacabbcbacbddbbacacbcacdcbdbbbbccbbaacdcddccdaaaccaababbbacdcddaaaacabcbacdddcacdadbdabbcabcabacddabdccbbddacabbaaccbadbdaccadccccbaddbacbdcacccaccdaadabbbbddcddaadbbcccccdcbdbbaacabbbabcbddabccdaabbdbcdddacddcdcbbaadabdccbdbbabbbcaabaddaadbabacbddccdacbcadbbdacccabbabbbdadbbcbcaddcdbbdbbdbcdbabcbaaddbdccbbaaaacabcbbbbddcdacccdadccacacdddccbadaaabcbcbdabbaacbaabaadcbaabacbddbbdddddabaddadbdddcddbdcbdbddbdabcdacacbbdadacdcdabdcbadccaaaadacccccbabdcbacbcadccabdacbababcacadaccabdacddaabadaaacbbdcdcbcacdbbddaacbbbcadddabdbadbdaabbcbcbddbabccdccbcacabacddbcacddcdabccbddbabaaaccadabccbbbdcabbaccaaccccdabdabadcbdbdabbcdddaacabbbacbbddbbccdbadacdadaacacabaadbababbcbdcbbddbbbadddccbbabdadcadadadbbdbcbcbcbbdbdddddbadcabccddbdaccabdbbcbccabaaabdbccdbdccccbbcdbadcccbbaaaaaaacacaaabadabcacacddaccdbcbcadaabdcccaddbcddcdbadaaccbdcdacacdcbbdcabbcbaadbcbdabdcccbddacdcdaabcdcbbdcababacbcbacbdaacabcacccdccaabccbdaacabdddbcbbcbbbbcdadaacbcabddacabbddcdbccabaacddddbaabcadadbdcdbdbadabbaaabbcdddadcddaabaddcdddaaddbdbcbbdcabdcbcabddccbdbbcbdcddcbdcdabdcddabaacadbdbbbcbcbbbdcdcaacdcacabbcdbaabcaccdbacbcccadcddabdccccacabcdabadcaaaacddaacbdaccacbaacbaababcdccccbcbbaabdcbcaadabdcbdadddcdacccabcdacbdbdbaadcacacddcacdbbbddccccbacaadbbcdcbcbaaccbbdabbcaccbacdcbadbdaaacacdacbadbacbacbcaddcccabaacdddaccdcccacaaadbdccbcdcbdccbabcbabbdbadcccabddaccddbcccbcdababadaccbcbbadbcbcadabddbaddabdacbdaacbbcaddaccbcabcbadbcddcbaddacdbcadddbccbcbacbadabcabcdaaddcbccbaccadcbbabbbbdaadcccadcbaabddadabcbdcbcbcbaccbabccabadbbcabcabbcbdacbaccacbabbdbabdcbbbbadaabadabbbbcddbadbccbcacdbdabddcdadbbcbdddbbbacaaccbbcccdbcacdbaacdcbbaddcbcbabbccbbdccaacdbaddcdaadccbcaacddcccdbaacdaddccbbadadcccdcbcdbbddcababcacdbdbdcbabbcbdaccbdcdbcbbcaddaabdcdbbaddcdbcdcacaaadaabaccdbbaccdccaddcaabbbcaddbdaacabcccadcadbcaacbbabaaacbcabcaccbbbddbcdadadaabacaadbbcdbdbcbcdccbdababbdcbbbdacccbcbdddccdabacdbcbbacbabccbcbcadbbddbdddaccccddccadabcdaacbdabdddccbdcddbdacacddadcadddbbdccbbddbcaaccacacabbabcbbbabbacadacaccdbbbbcabaddaabaccddcccdccccccbbdbcdcadcdaaaacabdcdabdbbbdcccdbddadaddddbbcddabcdcacbddacbcbddadacabadcdcdbcbdbcdcabcbcdcbcdbcacdbdbaccbcbccacbdacbcadccdcbddaabacdbdadaacbdcdbbcbaadcabcabcbaaddaccbcbdbabdaabdbbdcdddcbccdcdabcadccddbaabcbbcacdcbcaddaaccbdcbacdbdacacdbdcddcbcabdbaaabbccbbcbddabbdcdcdcdbbaabdbdbabbbbacbacacbbaababdccadddddaaddbdbabbbbccadcbbcbdcbdddbaaabbdcaccdccaddadbcdcdcaabddddbdddbddaabbdadbaabddccbdbacdcbabdadcbcbcdcbdccdddbabdbccdbaddbddcdbddabacbdbcabdcbbdcabababadbcdadcdbddbdbbaabccbdadabdbacaabdbbdcdcbabdccdadbadbbabaadcabccadabbbcdabaddaabdddbadddaaadcbcdcdcddadbacadbbdcaabccdaaddbddccabacadcddcdbcccbbddccbbdccaadbbbbacbcdbdcdacaadcddcadcaddcdcbaaabbccdacbaabadcbbdbccbdacdaddadacddcaadbadbdbbdadacddacbddbcbdabadbbaacdbbbadbbdcbcddcaaaddacddbcabcbcbdcbbbcddaababbbcdbccaaddcbacacdaacacccbdbdacbacabbbcdddabcaacdbabdbadcbbacaaaaadbbbdbbccbacbcdacddacccddccacddccbddaacacaaabddabdbbbcabacbbcdadcdbdcbcbdaccacbabbacabdcccadacaccbdbbabcdbbbaaadcbcbdbbbaadaadcdddcdcccddbdcbacbababbbbdabbddcdaadcababbdcbddddcaacadaaddbcdccacddbdbadacbbcddadacdddbbaaaadabddabaddadcdaddbabdadacdabddabbabdbcbcadaaccdcdbbcacbdcabcdcdbacbcaccadadacddbacdadbbcccadaacaddbbdcbdabcbcddaaadaabbbddcdadbdccdddadddbdcbcbdcadddaacbccaabddbdbdcdcaabbcaadadaccabcbdbaaacabcdaacaacbbccaccdcbcdaaabdbbabaacabadabbcccdbbbcdcbdcdcaadcdddcddcbcadcbcbaddaddcaccbdcdcadaccabccbdadccbbcbaccdaabcdacddcadaccabcabbadbaddcdcadacdcbddadddcaadccaddccacbdbcaddcabbaddcddcdacbcaabbcaabcacadbddccbabbbabbdadddcacdabcdddbbdbadbddbdabbaacdccddaadbdbdabcccddabaabdadaaddbbbccbddaaaacbccdcdadadcbdcbbbcbdbaaddbacddcbbcdaddcadcbdcdbcbcdbddccbccadabcabaadccccadcddadcdadcbbabbcddacabcbbcdcdacbccaddbcbddacbcaccaadddbaddbbcaaadccdbcdddbbcabaaaacccbbbbbadcaadbcdcdcabbbccadcccdcdbbcbdbbcccabbccadbddddccdabcbcdadabcccdcbcbcdabbbaacdcbcbabcaaddacabdcddddbbdadccaccbadccbcddcabbcdbcdccabdcdbabcbabaabadccddacaacbcdddcaccbaadaabbccacdbddacdbdbbdddbcaddbcbacdbbdacbcddbbbdbacdcdcaddcaccccaddbdacbacbcdaaddbcadcbdbaaddcbbabadbdbbbccbdaadbbbcdbdccbbaccaabaaadbadaacbbccaacbdaadcadbaaaaabcbcbaabddbcacabdcabdaccacdbcabacddcadbcddbbbcdbdbddcbaacdcaabdcdcbdabcbbddbccdddbdbbdbbacaabdbccccbddbcbddaaacccccdacbcaccabdcbbbccbbdcacabbabcacdaabdcabbbdbcabdbcccbabdddbbaaacabacacbacacbdadadccdbdbccccccabbaddaabcacddacddabbbadbbdadbbdcbacdabaccadbacadddabcabdcbdbcabcaaabccaadbcbdcbaabaababdbbbdcdbbaccbdcabbcdbaddbcdacbddababcccddccbdbbddabbddcdbccabacdaacabddbabbaacdaabbcddaabbdaacccddccddcccbacabcdaccbcddcddddaccbcbddaabacdbbcacacbcababcdcbbdadcdcdbadabdcadaaccbccacaccdabaddabadcbbdcdbacdbccdbddbabdabcabdacbcadacbcdcdacbbdcacbcdcbbdddcbbccdddcddbcabdadcddcdaabcbbdbcdabddbdcbabbabaadacdccdcbcabdbddcddabbbcabbbacdbabdbdaadcacbbcdccbbbdbdbacadddacccabdbcaaddabbcdcdadbbdcbdccbbbacdaccdbabcbbacbbacddadddbbcbaccaadddaabadbcaabadccaadddadbbccacaaaacbabcbdccacaacbccddabddabbddaccbacccbcbcaccbabcababddaddcddddcbbabcdabababbddbbaccabadbdaccddbdacaaccaccddadcdcadbdacbacabadcdbabdccccbbabbcdbabccdadbbcbbdaadcbcadaabbcbbdbaabbcabaddabdddccddbcaacaccbccdbabbcbdaddccdaabdacddbaabdccbdbcbaaddccdabcddccccababbdaddabaababcdbcbbcabbdcbcdddaddccdaabbbaaacbcbacacaabaddccaadaadcacacbdcddccbadacbbcdadaacaddaddadbbbbadbdabdbdccadcbabccdadabddbbdaadccbdddbdaccabcbaacbccbaccbdaadcbaaadadccbddacbababdbaaabbcdacbadbabcdbacaabadbbdadddbdcbadddcaacbdacabdccabadccccaadbbdabdddacabdcbacbcbbdcddcaaabbbcacdaccddccadaabbbccdadbabaaccadbbccdddbacbcaccbaadaababbaacacdbbacdaaadbbbcdcddcbdbacbabcdcbbdbdbabddcbbbdbcbdbacadcabdcdabbccdbacadcdccdaccbcccbcdadadadbcccacaccbacdadacccdbaccdaddcbbbbacbbabddcacaabaaddccdcccaadcdabaabdbadabddaaaacaacbdacddcbdabbdabaddbdaabddbbccdbbbbbdcacdabbaaabcacaadddabccddccbdbbbdadacbcaddacccddcadcbccacacabcdacddaccddcdabcdaddcbcbbbaaacadbddddcddcdbbbaccadbabcbbaacbcddcbcdadcdaabaddcdbacddccacdbadacadbdcadddabbbcaccacdaaddacbbcbacacbbacadadbdcaaacdcccaadababbadadbbdacacacdaacbcdbcbdacbaadddddbdcbcdbbdccbcccbbcbdcdbddbbdbaabbbbbbaccccbbcdaabaaddcabccacddcbacabbcbbacdbbbcdddcabcbcdbbbbddacadccbddcacabdddbcbbddcadaddbccadaddbaddaccdddacbcbcbabadadbbdbadcccccbccdaaaddcdbbbbbdaccbbcccbabdbabccbccdbaccabdacbbddbdabbbbdbcbbadaaacdddabcdccdccdbbddbcacdcbcdaccabdcadbcbdbdddadcaccbbbdbdbacccaaacbdcadaccabcabcdbcbddbbcccaabadadbabdbbcdbddaadcdddaacbcddccddacbccdabcdcbcadabdbddadbaacbbccbccabdcaadbbbdcbccbaaaddaadcbaaccacacdcacdcdaabcacbdbdcdddcadaaacdacdacbababadbbbabcaccdbccbdbcabbccbadbbccbcddacddcaddaabdcbccbbbdbaccacdcadcbbbddacdcbbbcbbbbbbbcdddbacabacbccdbdaabdbcadadbaaddcccdadaadaaaabdcdbabaacdaacdadaadbbbbdacbbbacaccbbccaacdabdadbcadcbdcdacdbcacacccbbccbbdbbaaabcabdbddcbbaaccbcbcdbdbcbdbbbabbaaccadcacbabacabccbbcddbcbacbacbcdcdcadaaaccbadaacbdbaabbaaaaacacdaadbdcadbcadadbccbaacccbccbdbacaacbabdaadaccbbbcaabacbcdbabbdbddacaabbacdbaacacaaacaadbacaabcccddbcdbbdaabcbacadacccbccdbbccbaabbcdaaccddacdcdadcccccaddaacbabbddaadbbdbbcadddbcdbdccddacdbcaabccbbdadbdacbacddacbcbbacaabbcdcdcbbacbbabcdbabadccdaaacaaddadbadddaacdcbcabbabddccccaacacabadaddcdadcdaddacdadcdacdcbcacdccabaccbdcbaacbbcdadbdabbccccdabccdcdacbbbbbbdaadbccbdbadccdcaaadacbdccbbbacbbdcdabbccadccdddabdcbdbdbdabcbdbcdcddcadccabbaabdadbabacbaacbbccdddcddabaacdcbbcdcbcdcdaabcdacccaddccadcbbadbcbbacadccbbdcbdabccdcccdaaccdbcbaadbcbdacbbdcbccdbadddabbccdddacdbaacabbcbabdbabdccdcacadacbddbdacdcdcbccdcabbabbdccbadcdcddcddaaacbcdddaadbdaacdbbadbbbdabacadbadbabacdcacababadcaacaadaccdbacdbadbdbcabbdbcaccdcbdbcbcccccddccbbbcabcbdabbbcaacdacabbbdbdddbccaabbaaddcdcddcddbddaaabddcdaaddaadbcbcbbdcbcbbbacdccddcdadbadbacddbcabaacdbaacbdabbbdcbbacbdcbccdbabbcbcbbbbbdaacbccdbddcadbacbaddabbcabbdabcdbcdbccacbbbbcbccbcdcadbcbbcabcbddaccdbdcbdacaacccadaabbcadcbbdcadababdcdaabcddddbcccaabaadbcccadcabdacdcaaddabbbdbbdabdbddbcdcacbbdcbaadcbbccdcbdbcadbbbdcdcddacabbdbacddbccdcbbacbdacacdccdccbbadabddbbcbbbddaadabdbcdbdbaadbbbcaadcbbaaabdccdcadabdbaaccddcabaaadaaddcddbcbbcaabcadacbdbdddaaabadbcdbbddcdccbabcadbcdabcacbbaababccbacdcdacdbbacaacacacabdacbcaaaccccbcbccbddbabcadbcccabdadacacbcdaacadbbaabcacdbaadbcccdbacccbbacbaabacbaacbbacadbcccabbdcbaabcdddccabdadbaccdbddcbddbdabbacaaddaccdcbacaddacaccccdbacddcdcdbdcbdabbbacdcdaababbdcbacbbabcacdcbddbabdcbcbbdccbbbddcaabcbbacbdcadabdbcdacdadccbdbcbddaacbbacbdaacbadcbaddaaccddadcaccdbddaabbacbdbbadbbbdaabbaadcbcbbcdcbacbadcbdaacdcacdacdbcccabdadcbdbbacbcbdddbdaabdccbcbcbddcdcbabbdcbddbcbdaabbddaaccdcaccddbbaaddadbbacbadcdccbcaaabcdaccdacbbdadabadcccddcabdabdbcacbadcccccddbadbcadcbbabaaabcaaacbbcdadcabdadcbddadccaadddcacccdbbbaddabacdcbaddacaccaacaabdbdabdcddbbbbbddddbcbdddbcacacbababdbbdacbcdaacdbcadddcbcbcaabbabadbbcabbcacdbbbaabbbbaccbbdaabacacbdcbabaaaaabddbbcccbadabbddabdbccaadbdacbaabcdcccbbcbdbccabaabdcbadaadbaadaaaabbccbaccbdccadbadadaabadbabacaadabcaadbdcbbdaccddddcdbbbccdbbabdadbbccdbdddcbbdbdcbccacdbdcbbcabddcaacbbcbadabcabaccbbadaabaadacdaababbacadbddacccbadddbdcadcbabcdccdacdcdbacacbbcabbbdcacdacbccdbdbcdbabbbcdabadbdadddcbbdbcabbaacbacaadbbdabdcadabcadcacddadaddabdddbdaabcabbdbbadbbaaadcbaaadaaabadcaabccabbaaaacbdabdbcacadabacdbabbabdddaddbdbadacaabcdacdcdababbcaacddaaabdaadbcbdaabbcbcdbdcdcbacdcacabadabadbcdddbdddbbcbbdbbcbdabcbddaddbacababacdcaddaaadbbdcabadaabaacbdccdbbaababcaccabcbadcbabbacbddddacbabbbbadbcacbddbddcdbabcbbddaacddabdaabccacbbdbcdbadbbcaaabcbdbbbbdacbdbdbcaaccdaabcdaadadbdadbdbcacacdcdcababbcbbcabddbcabddcbbaddcbbdbcbdbcbdabdaadacaacdadbbadbcbadbabcadddadadbddcdccacdbbbcaadabaaccccccadbaadddddadccacbbacdccdadbddabbdddddbdaccdcabcbbaccbcaabcddbabbaabacdbdbaccacabdbaddcccccbbccadbcababdacbbbadadddbadcbcacbbcdcddbbcabdbdbadcaaaddbdaabdcbcababbaaaccaabddaabaadbacabbacbdabdabcacdbbcbadaadabaddcdabcacaaccddaaddcbdcdcbdababdbcbddddbadadbaccadccacbddcbcaccaddbcdacdbdcaacaaaabdbdcaabbabbccdcbdadabddaccaccdcadabdaaadbbcdaddcccbcbdabcdbacbbcaabdbbbcaabbabcadccacbcbcaaccdcadbbabbdbcacacbaabcbcdddacaccbbcdabcaaacbbacccdabbddbabdbbaaaabcdcbcbdaacdcbacaabababddaacacddaddccdddcbbdbaddacacabbcbdbccbcdcacbdbbbaacadbcaaccbcdbaacbbbbdcccabadabbabbbcabdabddcbcbcbdadcbcdccdddbdbacadbbbaabbdbdcbddcdbbabdbbcddddbddccbcadbbdcbbacbcadbaacdacaccabadbbbabaacaadabdddccaadbcbbadbcbbbcbbcaabaccaacccccdcababdcbcbddcddabbadabdcdacbdbabdbabdaccccaabbccabbcabadcaaadacbcacdbccbdcccdbaaccbdccdabadbdcbdccadbabacdcabbcaaaddddcdbdcdccaacaaddadaabcaaadbabcbaabaadcabbaaddabbdbbcdccaccdddcccbdcdbcddbcaacbaacbcdccaabaacabdddccddacdbbbdabbcdabcabaabdadbcbabdabbbcaaacccdadbbcaddabacccabcbcdbacabcdadbccaaaaddabdcbcabbddbbcaabccacaacddabdddabccdacacacdbaaddbacbcaabcbbbbaadcabaadddacdddadddaddcbbababacadbbbddbcdccdaccbacabcbdcbcddbaddbcaabdcccbbaaddaabcccbcbadcdbabddabbccbbabddccddccccdaaabcbbccbaddccacccabbaaaabcdabbddccbbcacccaaaacdcadbbbbcdaaabcdddbbcabdbcaddddcccbcdccddbbcddbccbcacbccbbdcccdbaccbddaacbdcddccdccccdbdbdbcacdcacdbadadaaacabadacaadcabbddbbcbcbbaabacacdcdbcdadbaabbcdddadccdbadbadacdbdcbaaaaaddbccdcdacdcbbcbbdbbbdaccaccaadcdcdaaacdbaadcdaabdcbdacdabaaabdbabbdcdcadbdcdbaacadbdacddacbdcddcbabcbbdbbbaccacdbcddcadddacabadababbdaadccdccddcbbdbabaabaabbacabbbccbacacdbddaabaadccddcccbdcaaddaabacdcdadacbbaabbddbcbaaaabbbcbbaddacccbcbdcbdcadacdddaaddbdaaccbbcaacbbbcdbdbcdbcbbaaccdcaabbbbcccbcccdabcccdadbbddcabccccbbcdabcaaabccadccacdbaadcadadbaccaddbcbcbcbbbccabbdcdacbbadbccabccbaaddbdcdacabcbadcadacdaabdbbbadccccaadbcaddabdaddcdcbcddccbacbdddaacccacdcbbccbabdadadbbdaadddadabbabcadbccadbddbbdadabdbcaadabbbcdbccddadadccbacadaabdccdacbccdcbddaadbadcdddcbcbcccdacdbddcbcbdabaadcdaadaccaaddcacacdaacdddbcddcbbcddbcddbbdcbcccbcbbbdbadcddabbbcddadddcddbdadccaaadccddadbaabddbacddbcbabdadadcaadcbacaccaccbadddbddacaadacaccbddaddddbbccabdbbdcadcaccdcdbadcddbccccddccdbbacdcaaabdabbbabcbddaaaaadccdbcbbadadbaacdbcdacdbcaacaacbbaabcaadcccdadadbcaadbadaacacbcddccaadabddbdcddccaaabddccbabacaabccddcdcacadbacddabcbdbaaaccdbcdcccbaabbcbdccdbccacdadddbdccaadaccbddccdcabbacdbbacacccbbcdabdcadaaaaabccdbabccadacdccdbbcbbacaacdbbcabddacddbddcabddcddabbbabdcbddccbcdcdbddaaaccbdadadabdcbdcdaadbaddcadacacaccdadaaadcdcddaacaadbdcacdcaaabdddbbbbdbbbbbbaacccdabccccdcabdddcaaabbbaccaddabbbadabadccbcaacddaadcbdbabaabcabbdadddbbaaaacacccdcabdcbbccdccaadbaadbdababbcccbbdababbbabdadacaccccacbdcbdacacdacbdadaaadbdcdadcdccaacbbddcbcdbcaccabcdabdabbccbaaaaccbdbbbcdbdbbaccdcdabbbbaccbacacaccbdddbdadadddcccbbccbbcdcbabaaaaddaadaabadaaacacaddcbdbccbccbbdacdadaabdbdcdddcddcdcacdaddbbabbddadbbcdccababdbcbdbadccdacacbcccbbbdcbcbbbdcdaaabaccdbbdbacbddcdbbbabcdcddabcbdbddbbcbbbbdcdaccdccbdcdacbdbdabdadcccbbddcadddbabbabacbabacabcdccddabddabccbcaaaddcbdbdcccdbcccaabbaaabbbabdaacbcdaaddcaddcbdcdcdadbacdbacabbddacbdccddadacccccbcadadcddbdacbabccccbdcacbcdbbdcaadbcccbccbcdbaaacbacbbccddbdbcdabacadcdcadacbadcacccbdaddadaccabbbccbbabacbabaacadcbccdadcbbcdcaabbaabdbcccdcdbaddcaadacaddbbdbbaaaabccdcdaddbdbbbabcbaaabbdbaaccddbbaadaaccccacdbdcdabbddbcaabddbcdaacddaaaabbabcdabbbacabcaaddbacbcbacacdccbcaacbcaaabcaabcdbabdbcbbddacabdbbdbdaaaabcddbbbcbbadabcddbdbdcbcaccccabbdbcdcbcdbacdcaaaabddbabacbdacccaabcbcbdbbcbabcdaacdbbbcdbbddadbccccaccbdcaacdaddcacacacadadbcdcabbcacbbdacdcccbbdadadbcabdddadcbdacadbdadcdbacdbccbcdaccdddcabdcabaabadaaaccbdbdbddbadbacbdbacbccadabdbaccccbbcdbccbcbdcdcddbccccadcccbccabadddaccbccabcccabbabdcadcdcbbabcbbdbdbdbcaacccabcbcdaabbabbddbddbccccbcabcdbcadcdbbdbdddccdbbcbadbccabbacbdbabadbcaaacaaddbdccaacdabbdabaaaacdcbddbabbdbcdbdbacdcbacabadbabdbcaaabacabacbbbaadadbdabdddbddadbcdcbdcbaccdbbcadcabbcabcaaabccbbcadabbdcddbcbabcdbbaacabbbbbcbbdaddcdcabbaabbbcdbbccadcacdadcbabcabccbdddaadbdbcdbcbbcdabcccddddcbdddabccdacaaabcadaacccaaacccddcddadbccdbddadabdccdbccaabaddbbdacbbcbcdcbaaadcbcdcdbdccbcabcdcdaaccdcdbcacbccbccbdadcababadccabddcbbbabccdcbcabcddadbbadccbadbcadacaaadbdabcdbdacbadcbbcbacbddadbbbbdadcabdaaabbdaabcabcbccabbcbbdddbdbaacadbbaacaabcabcbabcadcaddbabbbdabadbbcccdadacdcdddbdadcadbdabcdaccdbdbadcadbcbbbdccbbaacbbcacbdadadaacccbdbbccdbdadbdacbacdcddbcdbcabccccbbccdbbcaadbaacbdaaddddcbcdabdcbaaddbddacbdccbbcdcbbaacbcddacadcbacdabddbdcaacddbbbcdcacccdcddcaddddabbbbbbacdddabdbbddcaadbbddadbacdddbdcabddaaacbccdbaaaddcbcbdcbddcdbbacadabdaabdcdabdbbcabdbccdccdabbbacacaccabbdbbccdbaadacbbbdbaaacaddbadaaabddcacdcababaacbbddbdcbdbddcdbbdaabdddcacbabccdbbadcaabadccdabbddababcdbccbabcbbbadabaaaaabdbadbccdbbbaacdbaabbbadaabbbddcaadadaccaabaacbccbaabaabcddbcccccccdabbabacdbbcddbcdbdbbbacaaabbbddadbcadbabadcaadddbacbcdcbaacacadbbcdccddccdacbacbcdcaadccacdaadadbbcddaddbcadcabdcadcbbabcabbcdadcdabdbbbcaacddadccacbcabdccdaacdabbbbdddcacbccabbccbbcdccdcccacbbbdbbdbcdbddadbdcdbbbadbdaabacdcabbcdcbbacababccbabaababbdbcbbacabaacccdddccbbadcdaacbcabbbbcdccbccddabbaaddccddababcbbabcacdbbcadccbcabaaadacdaabbaacbacbcbdbaadcddbbcbbdacadbdacbbdbbcbccccdacbbbacdddcabadbccbbccaddccabbdbaaccccbbbdadbcacdbbaaacadcccbdcaccddccacaaabdcabacccbacdaabcccbdbbabddccbbdacabbddcdbccdcdbaabdccacabacababcddcacdacacdccabbacddbdbccaddbbaaccaaaddaadbcdbbabbdccbadbababadddbddadaabadccdbbbbcbcabbdcadadcbbddccbaadbbcccaabddbadcbcaabcabcdddcbcddabdcbbcbcdcaaadabdcdcbccbccbadddbccabbbbcdbcaacdabdaaabddbacaccbdcbdabcababccccacdcadddacddcccaaaadbdcccbabdbaadddbaabcbccddccbdcadbacbcbacbdaabadaabdacaadcadbdddddbdcbcadcccdbbdcbcbdbbdaaadaadbcadcaabcddadaaccbaaccacdccbbcddbdacccdadabcddadabcddaaadaaccaadabccacbcaaccddadbdcaadbbbdcbccdabcbacbaacaacaccddbbbdbbabdbdbdbcddadbdbcaccccdbaabdababcbaadcdbcadbbbbcabbddacaddccdacbbbbdabadaaddbaaacddbbbdbbcbadbdbabadbdbbbcadbddadbabcdaabdaabcadaacbdabccddcccaabccadcccaaaaaccacbdadbddcdbabbdcadccacdacacdabcbdcabacbacdcccacaaccadbabdddbdccbddbaddadccbbbbbdaadddaadaaaaccbadbcdbcadadcbabbcbdaabbacabbadccdbbaaccaaddbaadcadadaaaaccabdaaaabdacccbdbbcaabbcddabdcbdaaaaacadbcbaddadbcbbcddcdddacacbaadbacbccacbbadabbddaaaccbbcadacaadcbcbbcccadaadddcaabddbdddaddabdbcccdcadcddabbcccabdadbcbcdcaddcddcbdbdcacdacdbbdbbaaaaaaddaddbabaccdaabcddbbbdaaccacaaaddddddaddaadcbdccccdcbbdcaadabddcacaabaabaabacbabdcbbcaadcbbabcdcabdabdabcdbdccadddcaacabbacbcadbaadccdbadddabbaacacadacbdabaaddcddaccccaaabdcddcdabbdbbacddddcadacaabcabbbbadbacbddbccadabcbdacbccadabbddcdcacbbbccddddadacbadddcaaadadccddaccadcbcaaadbaabcacbdbabccadacaadcdaccdddbadbdcccddadcbaacbcbbcdcdbddabcbdbddcdcabdadaabcdccbbdcabccbddbcbbabdddbaabddabadcddcadbacbcbadcdcadccbacdacbdddbaaccbaaccbccabcacccddbdaccdaacdaabbacbcccdadcbbbbddbaabcdcdbcbbddcaabacbadacadcbbbbbaababacbbdccaacbccabdbddbbabcabbbbdcbbdbbadacdadacbcdccddacabddddbdacadacababdbbccdbccaddaaddaacabbbaadcdbdabcabcdbdaddaddaacbccdccaadbccccbbcdbcdabaddcaccdabbacabaacdbaddbccaccaabddaadccbaccaccabddabcccbbbdccbcbcbadbcbbddabbdcbadddbaaaccdbdcbabdacdaccdadccbdabddabbabddaaababbbdbaaadacdbcbbcaaccdccbbbcdbbcbccbbcdbaccdcbcbcadbccdaadbbaaadadbbadccacdcaadabcaabcabaddcbbcbbbacbdbbbadaacdbabbacbdaaaccabdacaddabbdbcddaccabddcdccacddcaabdbaccccbaababbaccddbdcbbcccbdcbccbdccbcaccdcabbbabdbccaabddbddbbcddaaaddbdcdbadbadbcbddcdaddbbabbcaaacbdcdddddbccaddacbbacbdcbcacbdacbbbacdbdaacdcadabbaabcdbcbcbcbbcdabdcccddbddcadaaddabdddadcbbdcdcddbdaaccdcbabcaacabaadbdcdaccddcbcadddbdaabaccbcdcdcdcccbccacbddbbdccaacbdaccdbaaddbdbddbccdccdbcabbbbdbcabcccacbabbdcdbbacdcbbcbcbacbbccabbcccccbbcccaaadacbacbaacacbddabbaaababddccddcbaabdadabbbacabdddbdcabaaaccbcbdcdababbbcbacbbccacbbbacbdacbbbaacaaaaaabadbccacbcabbccacbababcaacaacacdccddaacabbabbdaadcdcbcddccbbbcabaacdaccdbbcbcbdbdcbadcdaadcdbcbadcdbbcbccdcdddbccbbadacbabadddccdaaaacabaddcdcddbcaddbcdddaaddbcdabacbcbbacadacddcabaabbbbddbdabcddbcbbcaaaddbdadcbcdccaaddaaacbacacdabdddddbdbdbbdaaaccaaccbbcccddcbdaacbbdcbcaccddccbdbacabcdbadcabbcddddbcbbbdaaadccaaddddbccddbdbddaddbdbbcdbcdabbcadbcabbbddaddcabdaadcbddcccacdadaabcdbbccabbddddacdddddcdbccadcdbcdddbaddbcacdcabbbcdbacddabddabaadacabdbaabacbadcbbddbbbdcbbadacabcbccdbcccadbddabccbdbdcabcbdabddbbbddbdadadccabadcbcbabadaabdccbcbcbccbddcadaccbdacdabcdbdccbbacacadccacbdadbdacacabaccdaabccbacdcaccdcdcdacbbdbbbadbbcbddbbbaccaddbdbdcbbbdcdbdbdbdcdcaadbabdabcbcddbdbaccaaaccbcdaadadacbdcdcbdaaddbcbcdbadcdbadcdcbbbccdbaaaaaabacabaabdacadcdccbddbddbbbccadbbddbadcbdcaaaabbaabdcbcdcbcaddcdcccdababbccaabdbccdcabcdbaccacaabcbbaaccddaadaaabbbcdabbcacdddadcbaabbbdccacbadadddcbdaddbabbbbdddbdcbbccddbcbdababdcabcddbcaccdcbaadbaadacacbdaacacbadbbcbaacbcaccccacddbcddcdbacaadcdacdbcbdbbcddbaacdacabdaccbbcbbddcaadbdaddcbaaacbcadbddabadcbdaabdcdbaadccbabacddddddbbdaaaccaabbadbdadccabbccbbcbbbbdcbdbbaacbdddbaacdacadbccbccaacbdcccdddcccdbdacbbdbccbbbdcbaaddbccddbdcccdacaddddadccacbaadaadcddcdcbcabccabccadcadddbddabbdabdaabbddaddaabbbbddcbbbcdddbdccbacbcdcbcbbdcbbddadadcdbcacaaadacaabacaaccacdabcacacbddbcbadccdbdbdbcddcbacaccbbccdcbbbdbdcdabdabcadacdcdbdaddaadbcbcdcccacdcdbcadbbddbcbbcdbbaacbcacabddcacbaccababbacdbdacbbbccbbdcbabddbcacdabbacdaadddcbbdcbcabaaaacacabbccddddbbcbaadbcbcccbdaacddabaacadbcadadcbdacaacaaabaccadadccbccabdddbcddccddbadcdcadddabdacbdacccadddcbbdabacabdccbdabccbbbbcccdbcacccbbdbbdaadaaaddbdcdcdbcaaddddccadababdbddcacbdaccddddbadbaccbbcbdbdcabaadbcdacbbdbaccbbbabcbbdacbddcbbabdbddbdadbdcbcacddabcbcbaddadbcdbcaadbacbbddabdbcbbbdcadbcaccdaddbbaadcdaacacadababdbbddaadbccabacacbbcaadababccdbbcbacdadcaabbcdaaccabbdcacabdacabcddcbdaccbcddbcabddcadddcddcbdccadadacdcbccacddcccdcabdbdbcdcadbcccdbacdcadbacaddbacdcddbabdcddadcccbaaaabaaaddbcadbabaadababdaabbdbddbcabadbcddcabbbacbbbdbcbacccdadabdabdcbcadbdccadcbbbadaaaabbbbdccacbbdbddaadacdaabbabdcdaadadadaddcbaacbcaccccccabcbccbadbcddaaacbcbbbcdabcdbabbadadabcbcccabbcacbdccbadaaccadacacbbcacaaacadcddcbcaddaabccdbbabacdacdccbbcdadacbcdbdacdabdacbcbbcbbcbadaacaadccddddcbdabacbcddcadcbdbdcabcccbdbdddcbbbbbdbbacbadcabccdcdaababdababdbadaadaacbaadbbdcccabbdddddbdcbabbbacdddadbccaddbaabbacbdcacdbbadbcbddddabbdddcabbbaabcabdbdccdccccbcababddcddabbaddaaababdbaddbdbbadddbabcabcdcdbdbbbcbddabbdbcbdcabcaabdbbbccbddbccacaababdbacbcaadccadbdbcabcadbdcbdaaddcbdbadbbbcbcbdccbaabbaadccdaccadabdaccaccaabdccbabcacbabbbcccdcbbcbcabcaddbdcbbbccddddbbdadbacbddccadacbdcacacadbbdcacbbdbcdbaabcddbbdddbabbdcbabdcaaacdbadcabdbcadbcbaacbabddbbdaccbcdddbbaaacacdbbcabcbbbadcaaddbbbdbadabacccddcdcbbddadbddaddcdbcabbdccacbdaadbddaaadddbcdacabcabddcccddbcbbbcdbcdaaddcadcbdadbbcbbabbcabacccaddcabbdbaddbbbdcbdbbcabdbaaaccabdcacdacdddddbdaadabaccdbcbcdacdbbcbcabcaabdadadcdbacacadcaabacdcaddbbadccdaabbdcdbcccddcbabbbccaaabacdddbcdbaaabdcccaabaadbbbcacdcacaaacdbbaccdcbdaacbcadadcadabbcaddacbdbbcaddacbdadbaabccaccaabbbbbdaacbccbbdaaaccbdbcbcabdabadbdacabddaacccbcabccddaccdcdadbbbbccadbdbabdadcbdcbcdabbcbcaaacbcacdaacdabcccadcdbadcbcdacdccabccaddbacbadccbbdcdbbabbcbccdcabdabbccaddbbabcdbadaadcbdcbcaaabbabacabaccaaacdacbcadcdadbbbaaabbbddcaacdbdbdaabaccbdabaaadbcbdaabcdacadcaddbadbdbccabbbcbdbcbdddcdadbdddabdbadabdbcadcaddcdbdbccdbccbacababccbcdcbbddcdbcddaaabbccaadbdbadcdddadcacdcadaacacbdccccaddabdbcacdcdcdbdbcaacdcbabcddbddbcadabddacaaaaaaddcdbbacadbdaacbbdcccbbdbabcccadbaaaaaddcbbddadacddbcbadbadbcddaddacdabbdacdbaaabbabbbdbabcdadbabdbbbaddcdccbcdabcadccadbbaccdbdbdbaaadbadcabcbccdcaccdcddcddbdcaabbcccbbbdaddcdbdabbdcbbdbcbcabdbbbbdbcbdabacabcacdbacdbabbcabdacddcbbcbbcddccadccabbabaddcbcccbacbddcccbabccbddbddabbcbbcadbacdcadbbbcbdcdacababdabaaaaabcbabadcacababcaaabdcacddbcaadbbbbabcdbcbdadbbcacbaacabddacdacbdbccddccbcaadddcdbddbadcddadaaccaaadbccadcdadbcbcbdbdddaadcdccbcadabddcccaabdcbacdbddabbdcddbbcabdbdccadacaadddbbdacdaccaadddddbbaddccdbabbabacaacdaddabaabacbdbddcbacddcbadaacbdddbcacadbccadbdbabcaacdbabdaabbacaaabadccabcdddbcbaaccddaabbaddbaacabbdbbddcdbbdabddabcacbdacdbddcbadadadbcdbcbadcadcaadcdcadabcbdadadbccbccacadaadcdbacccdbcbabcdbbaabcaabcddbdaccdaaaaaccbbdddacbaccbcbcaabbddbadcbbccbbadbddcbabdcccccdadbdcdbdabadabcbbdccadacdcdbddbdabcbbcbababaadbabbdaacabddbcabbcdbcccdcacdbbdbaddaaabcdadbdcdccbaabacbdababcacacbcccbccdddccaadaacccaaddbbbdcbdcdbdaadabddadcccbabdabbbbdbcbbcbbabbdbbacddbbbddcbbdababbdaddcddcbccbaccacdcddcbdcaadccaabaddccbbbdaddddaadddcbaabddccbabccbbbdcdcaddacbcabbbabbbadaacbbdaaaddcdcbcbcabdcadccaacaabacabcbdcadcddddddccdacccbdcdbcdbcadbccccbcdbdbcacaadadbaadbbbbcdadccdbbababbcddcabbccbabacbaccdcbbacddbbacccdacdcadaadacdaaaacdbcadbdbbdcdaaadaabdddbdcacdcdabcbaabbbddcbcacbdbcddcdcadccdacdadaaabddbdddadbcdccaacacabadcdcbbaadbddcaaacdbbccaadaabdbcaadcdddccccbabdcacdacbaacdbabcbcccdaadabbaadcaccbdbdbaabdabdddcdcabdaaadcddabdabbbcacacbdaadbbdccabbbabbadaccdbdbddddbbabcadbbbcdbbccbcbadcacabbbdbaccaacdbdbdcddacdaccdbcabdbaccaaabadabdbbbaacddabacbbcbadcccbadbbddbddbabbdcaabdacaadabccccbbcabdcadabcaabadcbccdacddaaaaccdadbccacaccdddbddbdaccadbdccabaddccbdbabdabbadaaaaaacacdbcbcbbdcdbbdadbcbbdbadacacabbcddabacdadddbdbdcccdbaccdaacdddccabcdcaacdbbbcadabadadbdadcaacdcbadccdbadaddcdbadbccbcadbdadccdcbbbdcbabbccdcaacbccaabdbcddcbcacddcdcbbbabbdaababbaccdcbbdadddacbddcdcadacbcbacbdbcbdaccddcccadcccbbacacdbaccbcabbcdcbacaadbbbaaacbaaccdaacabdaaadbcaadcdacdcdccbddbbbdabdcaccadbaadacaddbadbcbddccabadcdccccbcbdcbdbbbbccdddcdbaaddddcaddddddbacbbccdbacbcabddcdccaacabbacdbcccddaaccaadabbcaacccadbbcdaddbcdadddbaacadcddbacbdbbdadbcababddadadddbaadaabacdbcacccacaaabcdbadabbdcaddcaddaabcdbadcadddcdabaaddcbaacbaaacccbbdcadbabaaacddbddbddbbcdcdaacabddabccdbaddbdacdcadbaababcbacddbbdbbbcbdacccccdcdcbababbcdaaadaaabbbdacbdbadbdaccdcacbadbbbdddbbadacdaddcaadcbbaccbadbcaacddbaacabaaacbbacbabbdabadddcaacbaddcdcbcadcdadaacccbcdcdddcdcabddbccbcccadbacdbbdcadbadddddbbaaabbbbcdcccbadcacdabadaddaabaadccdcccbbdcbaacbadddbcbacaccabaddcbacdaacbbbaaaacaacdbcbcccdcbddcaababbcbddabbacbaaaacdbcbdbacddcbbbdacaacabcaadacdddbadbaddabcbacdaababdbdcabadcdccacaabdcdadacaabdbcbbbddcbdbadddbadabcabcaacbcbcdcddbcbbabcaccbccdacccbababaaaabccdcdbaabddbcccbcddaababddccdcbbabcccbaaaaaddddadbacadbcdbdadddddacddaadabcccadddbdacdcbdbdadbbacacadbdddacbdcccdaddbccacbacaadbbabccbcacdbadcccbddabdcdacbddaccdaabaacccdddaabdccdbadbcababaccddacadabbaaadbcddcddaddbcdcdaddccdcbaabdacdcadcbddbddbddaacaabddcccdaddaddaabdbbddcdacbabdcaacabdadcddaddccacabcdcbccacaababadbdadddcccbacaacbdcdcbcbddbbcbabbcacbccbbacadcbbcdbbbcaddcabbadccbdcbbbbcdcdabdbcbdabbbbdbbababbadaccbdddcbbdccbcbacdabbcbcacabddcaadbcbcaabacadabdaccaddcbcbccadbcbbcbcaabcabbccbacbacdcaacbbbcbbdaadbbadcbdabcdbcccabcaabacdadaabaddbaadbacacaabdcbabbdbccaabbdbcaadbababbddacbcaadddadddcddabdacdbdccacdbddbbbbdcdccabbabddcdccdcbabaadcbcbdbbcddcbbcccdadccccdabcdadbdbcccdbbbabdaadabdcbabdcccaccbdcaadaccddddbbbcbdbcabadcdcbbbbcacaddadbbcddbccdbaccdcddcddadcaacdbaaddbdcdcbdabdccdbcdddbadcbdbbdcbadcccbadabbdaacbdbdcabbcbddbdddddbcdbddccabddbdabbbcddaadcbacdacadbacaabacdbbcaccbccaacdacdbdacabadbcdbcacbdcdccccccadccabaadbdadcabdaddaaacbcbadacbbcccccbcbcbdacdcdcadaccddadddbcbdbdcbdcabddaacacdcbadaadddaadadbbccadacaadabddbbcdabdbbbabcacadabcdccddadcaaacddacabbcaaabdcbadaaccacdaacabbacdabddabdbaccbaaddddaaddcdddddccbdbadddacdcdddbccbbbacabdddbbbcdbacbbddcacbabcadabdbdbcddabbdcaadcddacbdddccbaababdcdacbdbbbcdababbcacccddaabcddacdddcadcdcdcdbaadddcbadabbcdbacdbcdababcbdacadaacdccdcbbdcbcdcacbcbadaacccbbcacbbaacbdabacbdadccddbddbbdaddbcdcaccaddabcbabbacabbcddbbbadbcadcdaddbbbbbdbacbaccabcaaadbbccabbcdcbadddababdcddcabcddadbdcdaabcbbddddbdddbbdbbbaddbdcdbcbcaaaaccabdddcbadbcdcbaccdbcbdbdabacbbcadbbdcadbbddbbabacaaaadbcacdcbbddccccaacbddbdcdaadbdccbccdbadbabbbadddccdababcdcadcddcbcdbcbcdbbdddccddabcbbadddddbdccbdbcddcabbcdacaccbcdcbdbbdababbdbabbbbcbadcddbdccbacacbdcacabcacddddcdabddabdcdaccacdbbcaaabcbdbbcabbcacaabadddcbabbbdabccacbadccdbbcaabbbacaaddbcdaadaacdcdcadaacacbadbddabdccaabaabaaaacdcdaaaababbacacbabbaacaaddcdaaddbabdddadadabccddbcbddcdddddcdabcbccabdabcdcbbbbdbdcacddacccbcbccacdcbabbadbbcdbbcbacadbbababdaabdbbadbbadabababcabcbcbdaabcbadcdbdacccddddddcdbaadadcadadbbaddcdbcbbbcdbdccaacacdcdbddccbddbdadccbddddadabbcdcadcabdbcdbaddcbdacddbbccdabababcabbbbcacaabacdbaaaaabbddabadabcadcabbdbcacaccabadabbacdbbaaddcbcbdadbaddbacdddbcbdcacccbcbdcddbadacccdabaacaabbabdcadcaccbdbdcadaaaddabbccbbccabdadddbddbbcdcddcdaadccaabaddbcaabcabcadadbcdabadacbcbccdddbdbcdacaddcbcccadabbdcbddbddaaccaabcacabdaadaadabcbcbbccdacdbdbdadddcaadaaabaaabacdbacdacbcadbdbcdcbbbbdaaaacbdddbaadadcdbdcdccbaadabaaabdbbbbdacadaabbcabcadbabcdbddcdbbdcacbaccbddbacadbaabcbcdbcacaaadbdbbbddabcdacdbbcccacacaddccccbbcddbbaaadcabcbbdccbabcdadbbaabbbcbcdddaddbabbccccadbdabcabdcbdcbbcbacdbdddbbccbbaadaabbddabcaccdacdcadabacbddbabaacddbcbadcdcdcacacbbcbbaabbacaaaadbaddcbdabbccbccacbababdcbdddbdaccbbaadacadcbaccdbdccaaaccbdcaaddbccdddcddaabacbcbcddaabbdccccccddaddccbcbacbcddabcddabbadcacddcddbacbbadcdddababddbbbaacacdabcaaabcbcacdbddbadabdadcacdbdcdcccbbaacbbaadddcadcbbbbbabdcbabbdabccadabdbdbbaccadcacadcdbbddcddbdbdcddddaadbdcccdcdaddcdcabdbbcabddbcaccdaccbcaddddcaaddbdcddcbaacaadaaabdbcbcbccddabcdaacddbddcbddccabdccddccdcddaccbabcbdddbbabcbcbcadcaaabcbdcdcbdbaaabbbdaddbbddaacaaabacdbddbabccbadaabbdcabcdadccddbcadbaaddadccbcdbdcacbbbacdbcdbbddacadbddddaaadbacdaaccbbcdbbaadacccabcbacabbbabcdcbabaabcddcadadccadabdbbbacbdacbdcddcbaabacaddbacdcdbcbbcbdcabaabdcababdabbdcaabdcccdabaccbdccddcbdcbbbaabadcddacaaccbdaadadaddcabccbddbcddabccddcaacdabacbacdbbadcbabdaddddcdaaadcccbbdccacabdadcbadcabacbdacdccacbdccdacdbdbddcabcaacaabdaacddcbacacdddaaccddcddabbddbdabcaaaaadcabdbadcbdccccaaccddbadabddcdaacaddabdbcdccbdbaacbadabaaabcabacaccdadbcdbaccaddcbabaacadabccacdbaaabacaabacbbabccdbdcacccccaadaddacbadadadbabcddabddbdaaaabdbdcabccdddbbddcdabacdadcdccccbcadcddbbcacaccbcccabbaadbadcaaddbabcaaccdcacbacdcbadbddcbccdaadadbbbbacddbbaaacdacabdabbbcaabacbddbcbccaaddcbbaccccddaaddbaddccaaccaacddcbdabadddabadadbcbcdaabacaaaadabbdcacdacdbacacccdaabdcacddabbbdbadbdbcdbacccccbdabaddccbdcccdcabdbcaaccadbaaabbaddbaadbbcbdaaacccdaddbdbbbccbdcacdbcdbacdbaccbbaaaababdbdabdcbdaababaddbcabdcbcbbdccbbcacdacbacdcbdbbbcdbcddddabcbbacdbdbcaddbaabdbabddcccddcdcccddaababcdcadaacadbbcbcbbbcdddacaaacddcbadabdaadacccdbdaddbcabccbcdabcddcdaddbaaadbdcaccbbadadcbadacadaddbbaacdaabddcaaaddddcabaadddaccbcbbdbbbdcdaccaabdbadbbaddadcdcccdaaadbdacaacaaadcddbddccddaaccadddbbbbccaabcabbaabbacbcdbabbdccbbcacbadbdbbdcaddcccabdabaadbcddbaabdcacabcabddaaabcccccdacbddcabbdbdbacacddcabdbcbcbdddccddaacbaccdabbbddcadbdbdddacccdbdbcdadcaddadbcabababbbdbbcdabccbbbaabcacdcadacadbacdbcacbdabcdddaddbbddbbbaabdccaccabbcdcdbdabdcbccbaaddbbcbddbccbabdcdddaadccccdddbdcdaabadccdddaddcccddabbaccbdbccacbabdbdddbccddddcccaddbbabdccabdcdaacddccbbababcdccaabbaccdbaccaccbaabbcccabccdacaddcbcddabddcdcdcbcdaccadbccbabccbbdaacbcabdacdbccccdbdbadaacbcccaabdacbdcdcdababccbcdbddbccdadcddddddcbdaadadbaaccbcdccabbbdacbabaabaddaaaccadaaddacdaddddcdbacdcaabdbdbccbdcbacacdaadddcbcdabdabcbdbabbbcccadbdbbbbdcccbdddaaddaadccdcddacdccccdabadadacabdaadccbbdaadcabaacadcccacbdcbcdccddcdddcbdbccaaccddbcddbccabbbaabadadbdcaacadbbcdacbbbbddbbbcdabaacdddbdbbbdaaadbaddcdaacdadddcdcccbdbdbcdbdacadbddaaadcdbdddbcbaaabbabddaddabbbbddacacdbccdababaabbdcaabdcbdbccdddabaccddddccccadabdbbcddacddcccbbaabbaccddcbcddacabcbacccdbcbdacddadbbaabdcbaddabdabbbacbabaddcbdcacdabdddbcbbcccbdccdddcadbcdacaaacdacccdaddcabbadbcadadbdddddddaabcbaccbcdabccacccbdaacdcbbcbacdaaabbcbdcccddcdaadbcbabaaaacdbdaabbbdadaababaadcabccbcdcccaabcbcbdbddbacacbdcbbabacbdccabdcaaadaccaddcdadbdccbccbdaaacabcdbcdcccbadbdcbadbbacddbdadaaaaaaadbdbbcabcbbcdadbaddbacaadacbdbccaccdadbbdbbdbbaddaadddcbdacbacdcdabacbabddcabcdcdadbcdacbddcbddccacbddddcbdbcbbbcbcabcddddbabbaddcaacacbdaacccdcbabcdbcbdadcaadaddabcdbadabacbbddccdbbcbacabdccacdcddbbdababccaababadbdcdbbddcaaabbaddadaaadbbcdcbdcaacdadbcabbbbabadccacadccaccbacbdabcbbdbdcdbbbbcccbcddbabdbaddadbbacbcdbcbaddcadbcbcbbbbdccdddbdbdaddcccccbdbbacccdccaaaccbdacbaddbdbbdacadaccabbddbdccdadcbcdaaddabbcbbadbcdabbacddddbaddccadbacacbacbbabcdcdbccdabbbdcbcbcdabcabaadcdddcaabccdddcdacacdccddaabbbdabbcaacdabcbcadcadbbcacbbadbdbddcaabbbcdbaadbadadabcacbbddacdddbadcbaacabadbabadcabdddadacdbdabcacbbddacccddadcddbabdaadbbacbaaccdcadccbccbbaacacdcabbcdbbdcccaaadbabacbcccdbdcacdcbaaccdddccacaadcdadbbbabacabadcadcdadadcbaabdbccccdbcddbaacdbdbdbdbcacaddbbccaabcbccaabcabadabddaaadbdcccadddbccbccbcadacdcddcdabaddccdbddbdadddcaaabdddddabdbbbcdbacdbddabaddacadabdbcbaaccdbabadacbbddabcbadbbbdcabccdcddbccdcdddbadaabdcbbcdadbacbabbdbdbaabccdbbdbaddbbbccdacccabaaabcdbdcdddabcbccacdacaadaabbcabbabacbdccdbadabdadbabdcacdddccabcaacaddadabacbdbbbbadcabacacbcdababdacddbcbbbdcacdbbdbcddabaabdbaaabcccdddcdcdbcadadbcbacdbdddcbcaacaabcdbcdabaccddbabcccbbaddbcbccbccacbacdbbcdbcbbabdbccdcbcdbbbddadadcabaabbadaaaadcddbdcaaadbcccbbadadbbccbadccbacbdacccbbdaabbcbddddacbbcccaabcbdbbbbddbcccddbbbcbaacbdcadbbbbcaddabbcddcaddcbddbababbbccdccddcaaacdcabbcbdbdccacdaadbaaabadacdaddacbdcabdadbdccaadabbadcbabdcdccabcbdcadbbacbbdabcabcdcbaddaccaaabcccdbabcdbdaabccacdacbdadccccbbcdaabdacaaccbbdcddcdcbaccbabbbaaccccbccbcdcdcbdccaddaccacddbbdaacbbbdbccadcbadabddacbdcdaabadadacdacbdaaacddcdcbaadacdcdacdddbdcadddbababcdbdcabaaacbbabaaacabcbdcdcbcadbbbcdddddbdccdbaabacbaadacaaccdaababcdacacabddbcdadbccbccaabacbbbbbcbddcbcccaddccabccbcbccbabbcdababbdbabadbacdbdbcbdbacdbcbccdadccaabadcbaaccbbbbcdaadccdabaddbdacddcccdcbabcbadbbdacbcbdabacbccccbadcdddbadbabcabbcbbadaabdcabaddadadddbdcddaaabbbcbdbbacbccdadbaabbaddacbcadcdccdbddbaabdbbbbbaababbcdabadaccaaaaadcccbacdddadddddddddbccbadbdbcdaadbdbabaabacabdccddcabbacdddbbcbadbbacacccdccabcbababbbcdbadaccbbcdbddbddbbbcabbcaadbbdcbbbadbdaadadaccddabdbdbdbdcaccbddcdabcacddaccbdaccbaacdbbdcabbdaccbbddabcaddadddaccbcadbccdbddccdcbdcbbbcdccdcccddcdacdaaadadcacbcccbcdbaddaccabdcbdbdbbabacbbbccbbaddbcdbcbbdcacacbdbadabcbababcdbbbaaabbabadaadbdbbbbdbdaadcdbcacbccdacaddbabcbabdccddcdabaadbbbcccdddbdacbcdaacccccddbdcdccccccaacabcaacaababbdacccadddabbccaddbbadbdcaadaaadbcccacdadaddcdbbdbdcbdccbdbabadcdabadacacdbccbacadadccddacdcdccbabcbdbcabcbbcacddbdbdaacdcdbbacdcdbaccaacadadcccaadcbacddcddccbacaccdacbbcacbcadbaaabcacbbdadaadacdddcbbbbdbcbcdcadbadbcababadabddbaabdccccbbcdbddcaadbdbacbddadbbaaccacdbccddccbdcbcabcabdcaaabccdcaccbbbddbaaababbadabaaacdabcdcbcdcaaababbcbbaacbcadaacbaaccccdcdcbbbaccadbaabdcdadbcaddddadddadadadadabdadbcabddcadbbcadadcacaadbcadcbbbccbacaddddcbabcabcbcddbaadbcbbaadcbcbdcdaddabaacbbcbcbcddcaadabcdaadbdaadabccdcccadabdaacaddbadacccbacccacdcabacaadbccbadcdbaadccdbbddbcbadddbaacdababbdcadbbccdcabdbaabbdbcbacccbaddcbdbbaddcdbbdcacccbacdadbbaddabdbbcaadcdcbcdbbdddbccbaaaddaaabcaababdbadcccdcdcbcdbbadbcdadaccbcbdcdcbaacdcbddccbccabddbcbbdbdadaadbbcaccdcbadbcdbabcbbccbbaadaaddbadadbdbcbcdaaddcdbbcccbccdddbacbdddbcbdcbcccbdcabadbbababcdcacacaacacdadaaadcababccbcdcbadccbbbdbccabadbbabbcadbbddcbddabbccdcacdacdadadddbadadcbdcbdbcacabcdcbadddbcbaddbdbccbdaccbdaabbbcaacddaddbddaabbacdcbaaddbdbaaabbaabcccdbcbbdcdabaabcadacbbcacbadcccadabcabdacbcdccbdbcacaadddaddadaaccbccdccddbdabccdccbaababcdabcccaddccbcddabbdccdaadabbdbbcddbddddcbdbacacadbacddbdcbacbbaabaabadabbdacadacdbacaaaaccabdadbbbadcbcdcacadcbccdcdabccbbdbadaabbcadbaaadabcdbcbbdcbbaadcdacdcabbdcabbadbddbdaaaccbbccdbbbadccababcaaacadcbdacddaaccabbbaccddbcacdacdccdbdbcbbdcdcbcabcbddabcdadbdddabccbbcbbaacbcbccabdaabcadcddaddbcadbdccabcdabbababccbdbbccddaacabaadaacadccbdcacaabdadbaccbdabbdbcdbaacccaccdbbdbdcabbabcdadaacbdbccccddcaacaddacdcbbcdbccacabbdddbbaabbaabbbddaaacbaadaacbacaaabbdcccbccbadbadddbdcbbccddcbbdacccdbacddccaaabacabcaddbcacacdddbdabccaabcaaadbdcaddaaddcadaadacbdacdcdcccbcbdabbabcccabdcbaadbdacbbabcddbacbcdccbabbacabadabbbadbbcdadcacbdabaddacdcbabadddbabcbabccdddcbaadcadccacdacddbacaadacddbcadcddbbadbddcdbdbccddadccbcdaaddaadbdbddacababcabccddbcddbaddddcdbcddbacacabbdadbabcddccdbbcdcbbdddbaacdbdccdabbcccadbdccacbdabbcbaddcbbaacaddcbcbbccbbdcabdddaabbddbdbacdbccdbbaccddacaabcadadbacdddcbbbdcdabadabcdabaadbccdcacbaaacddbdbccbdccacddbbcdaaddbcacbbddaabdcadcaacdcadcaaccdcacbadcadcbacacaccdbbaacddcdbacccbdbbcadabbbcbcadaccbabbbaccbbbdabbbadaabccddabcbbcadacdbacabacbaccaaddcabdcabbabdbdbaddaddadccdcdbbdaabccdccdabacdbbaaddaabacdaddaabdcccdddbcbbbbdccbbbaddbabdaddddbadaacbbadcccaacbbbaaadbccdaaadbddbaadcadbbcbbaaabdbcaaacacbddcbabaaccadcbdbabbadabcbbbcbbaacadacbddddbadacddaddcadcbbdbcbdabbdcaacdacabccccdcbdbacdcbacdadcdadbabcdcacacbaaaaacacdbbcabdcabcccbaddbbdaaaabccbdcddabadacbbbdcbbaaaacbccbddabdcabdcaacdaddbdcdbdadbacabddbcbcabdccdddcaddcddacbcdcadcacbdacdcbdbcadccddddabddadcaaadccaacacdbaddddbcbcaadbadbbdbbdacbdccdbdcbcbdaacdcdddadadcbbabbcaddcbbddcaccdddcbabaddbcadbacccdabdccbcdadccbdacbcbcadcccaabdbcdcccdccbdaacdaccaadbdabcabaccaddbcdcbdbacdabcbccbdcddcabcdcddacaddaccdacbcdabdadcacdacacaacaadbcdacaaacabadbabacccddabcdadaadcacdacdbbcaaddabbaadcbacbdcacacaadcabdabdbbbcbbccdcadcbddcccaadbccdacdddadccdaabaadaaaabbdbabbbccbbaaccbcdbbcbbbbbcbdcbdcddadcdccddcdbdbaacbddaddabacaddccddbcbaaacdbadaacacbddbadcbcdccbbcdacbadbaaaccdabcacdabaaddaccacabbbbbccdcccaccaabcdaddcabadbcbcdbdacccdddaabddadacadabdaaacdcdbccdccabbcddccacdccdccadbacdcdabcbcadcdababbdabaccbbacdcdadcccdbccacbbbaaabadccabbdcbabcabbcdccbdddaabcdacdcadacdccccdddddacacccbdcccbcbddccbaabbcccbbadbbcaabcaabbdabaacbcccdbaabbbaddccdadbacbaacdadaabaabbadabcccbbacbbbccaaaacaccbbdaccccadabbcbcddaabacbbddadbccbabaacccaacaaabbaabcdbabbdbaaadadbbabccddbdcdabacdaccaacdbcccbdcdbcbaddaacbbbaaabdbccbddcbabdadccadcdbdaacbbccadabdcdcddbbdcaabaccbccbabacdcbadbddbaccdacccadbdccdccadbccdcacadcdddadcaadabccdbacdbccabbdbabdcdcdaddcaaadacabcbbdbcdaabaadadccaaaccacdbdcadbdddbcbcabbbbcbacacbabbbaadddbbbaaabcaccbabcbcdcbcabbddbddaaabddddcbdadacaacacbbddaababbdacabccbbcbcaabdcccbddabddbcdbacbaacacbbbcbbccbbddbccdcddababbdccdabbabddcdbacadcaadaabbcabbddcdbcacabdcccdcbadcaccccbdbddcbcadcccadaacdbdcaaddbdbdbaccdbccbabacbaabcbccbdccdbadaadcbdaadbabcdbbdbbddaadadccbbdbaaaccabaccbbbccabcbcabdcacbabcaaabcaddcccbacaacaacddddcbdabdccabbabccbccabbadcaaaabdbadcadacacdcbcbddbacbbdcdadbcabadcbbadbbbacddbdccdcdcaabbbcaadabadabccbcccaddacccbcccdddaaabbabaabbdabcaacdacaacbbacddcbaacabddcdcbcbdacababaccdbadbdcaadadcdcadddaadbbbddabdabaadabbdbabbddcabbbccaddcdcdababbbbcaabcaacadbddcbddddbacaadddbccaadbbbaacacaacdcadaacaaccdccbbbdddbcaacccbdabdabaaadbadcdcbcdccbdacdadaaadcdcabcccacadbabdaadcbbbbdddabacbddcbabddaaabddcbddabdbcdbdacaabdabcdadddcdcbdbbabdadcddabbccacdadcdbdadccdddaacccdadbdcdbacbdcdccddbbaacdcdabbdcaddccadbdadddccddbaacbddccbccbbcbbccccabbcdcaacddbbbdbaaccdaaaddcccaddccbcaddddbabdcaabbdccbddbdbdbacadbcabdbcbdcaacdccadddccbbcbcccbcdabdaadbbbbccbcdcbaccbadccbcbdaacdaabdcacbaadacbabaddadccbdaccbcbddccbccadabacaccaabdbbbabbcabcaacabcdabbadbdabdcaadabdaadbcaddbbbbbcbaaaadbdccdccdadcdaabaddbbbdbccacdccbdabdaaccbdddabcaacbbcdcbaaddccddcaaaddbdddbdbdaccdbaddddcbadbacacbdadbdbcccbdccaaacabccbbbdbcababdcaddcbbbdacabbabdcbadcbbadbcacdacdcdbaacaaddcacdcaccdadbbddccbbaaaaabcdbaddaaadccaddabbdccaacbbabcabcdacddadacdcbccbbaabcdcdbbbccdcadabccbabaccacdbbdcacaccacbaabaaabcbbabdcdaacbbaaaabdddadabdadcadabbcadddbcaabccbadbcbbabadddabbbadcddbabcbcbacccaddcdbddaacccccdbadbccadcaacadadaaddddbcabcdacadbbdddcdacddccaaccbbddcabcabcbcccdbbbcccaddaaaadbbdbbdaabadcbabdacdbccbadbcacbddccbcaacdbbaacadcdcabbaadcbadadcaabdcacdadcbbbbddaadccbbdaabaabcaabbadaccabbbcdcdaaccbbcdadccaaabdbabdccdbbbdbbacddbdbbdcacdcaabbbdabcbbbdaaacccaabdbcdbcadcbccaccdcdbcaabcbacddddaacabbcaabdcbbcdadddccbcadacbacabdabcddddbdccddaccccbadcabddaacdaabdabdbddaadbdcdbbddbcdbadbbddddbabaabacccbbdbbccccdcaccdccdbcccaccbdabdbcabdbcccdbcbdddbbbcbaddcaaadcccdbaddcddbacadcddccdcccdabcaaccdadcbaabcdccdbabcdbdbaacadbbaadaddaacbcbdccdcccbacbdcbbaaddcabdddcadbcaabdcbbdcadababaaaccdbcccadabdbbaaaadbdcbcccddbdbbccbcaddbbbbddddabdcacdbddacbcdcdabbdcccbaadcbcacdcdaadcbdcadbdabdbdcabcbadcbdaccacccbcdbccbcadcdcacbdcccdbbbdbdbcadcdaaadadddabacdacadcadcbbbbbcbcdbbcdddbaadbadccdcdadbdacbabcbacdbdcddcdaddbdcbadaadbbadbaaabdbbacdaabaaaacdabcbdbbddcadbbdbcdccddaccacadacbaacdddbccddcabddabaaaccbdacacdadddbdbabccbccdbcbbbaccaaaaadddcdccdacdaddddddcdabbbccdadbbdbccdbdbdbaaadcbdcdbbbdbdbddccadcbcdcdbcccccacddddbdcbccbaccbcaacaacabdabcbcccacbbabacbcbccaadcccbbddbcdcdaacdbaadacaadabaacdcacbccbcadbdaaacbabcdaacbbccbaacbbaadbcaccaaadacaccddcdabdcbacbdabcaaaddbabdaddcadbbcadbccbaadacddbcdcaadbaababacadadbacddcddcdddacdcdcbdbbcbcdcddcccdcdbbdbaadbdcadddaaabbacbcbcbadbddaacbcdccaddcbacaadaccdacdbcbddbbdabdccbbaaacbcbdcbbdccbadacbcbcacbcdcaabadcdabdaddbacddddabbcbdaacbcabaccabaacbbaabcbdbcbbdabadaacbdbcdddccdcddbccddbcbddddbadcbacdcdccacdaaadcdcadbcdcadbababccabdccbabaabdbadaacdcddbbddcddaddbbcdcdbcacbaccbaddbcacdadcabbabaabbddbacdddccbbdaadcdbaacabccbabdabddbccddccadaccaddddcccdbdacbbdaabddadbcccbccdaaacccdbbbcdbadcacabaaabadaacdacbbddbcaccaacdddbdbbddbaabccaccaabddcdcbdbbacbdacbbcabacddbbaadabadccbbddccbaabdbcabbccadcacadddabaabdbdbcaababaacbdacabccabcadddabdcabdbacabbabcacdddaaaddccdddcacbadabacdcdddcdbbacdcaababccadcdaaddcdacabcbccaddaadabaaabaaacddcacdbcdccaaddcdcdccdbbbbdbabcdaacbdaddbadbdcaabcabbcacababdabbaaaabcaadbbccadaacdbaacacbaacaccbddaddaccbaabdacbabaaadbbaaaabdbaccdcdadcdcdcabdbccdadaddbdcbdabbdbbcaaabbabccddcbbbdcacddbaababbacbdcbbdcbbacadcbaccbdccaabbccbbbdcacddddccdcbbdcdaaddbdabcabdcabacaadbbaddddadbbcbaacbbcaaadcbddaaabcbbccbbaccdbbcbcbddbccacbabadcabccdddaaadcacdabbbcadaacbcddadcccddacccdbcbaaaccdacbcbacbcdacbaccdcaacadddacbacaaadaaaabddcdaaccadbddcbbdbdddabdddbbbabbdbcbcdddadabacdddadacdaaaabdcddddbbacdbdbcaabaaccadbcbcdadbcaababdbcdbabadcdabcbacbccdcacdbdaabcbccacbbdcbbcdddcacccdccdccabbacbbccbcddaaaaabddbbbadbbddaabdbbbadbbabbbabddccccadbdcbabbdddbdadcdbaacdcaabadcbdbbcbdbacddcbdcbcdbbdbaaaddcdbbaaaabcbaccbdbaccbadcbccbddcdcdbbbaaabaadabaaacdccbadccaaabcaaabbbaaacccaadacacbdcbbddcdddcaaadbbcdcbddbcdabdabaadccabcddbdbcabcabbbabaacbbbccbcaaccbccaccbbcaacccaabccacdcabbcabaabbaaadbdbdcbcaaacbaaacddabcaadbadabccdacbdbbcddaadabcacbbbcddacdaddcaddddaabcdbaacabdaabaacabcabcdbbabdcdbccdbddababdbbbccdcbcaddaadcdadddadbabcacccadabdcadcccaacdcacbaccddbbcaadbbbabcdadcbbaccdbdcaadcacbacbccbcdccabdbdadbcabacdcbdcbddcdcddbadbbaaaadacdaddbbdddbcdddcbcdabbcdabbabaacddcccbabbbbcadadcccacacacbbbbcaaabcdcccdbcccadaacbabadddadcacadabcbbbbdccabcacbcbcdcbcddacbbbdbcadcbcdabcccdcbbabaadcbccadcbaaccbaacdbbadaccabdadbccdbbcacaddcacdbcbcdaabdacaaaddcdcdbbdcdbcbdccbddccddabdbbaabbbaacaccbdadcbbcdbcddadcbcdcbcbbaacabbdacabccdcbbbbbaabddbccaccacbbcdaadaddbddadbabbaacabbbddcaaaacacbcabdadbdbaaccbabcdadcbbadcdbdabcdbcacbbbbdcabccbabbcdbabddbcacbddacbccadcccdaadadbabbbbabbabaaacbdaaacbcbcabdbbdbbbbabbdabddbbdbcdadaadaabacdcbcaaddbbbbbcbbccaccbdbdbccdccddcaddbbcabcdbcacababdddddddaabcdbcabbcbaccdbddddadcbddccdadccdcdcbdbaadbcabdddacbabdcdbdbabcadbddacadaaccacbcaabcaddbabcbadcbdbbacdbcddbbcddcacaaaabbcabbcaaadbaacaccdcdbbdabddacdcdcdadacccdbcacdcabcdbcdcadbcbbaaabaccdbcaaabbdcabbacbccaddbbcbcacbcdcbaaacdcbbbcbbaadcccddacbbadcdcdbdccabbbbcadcacabdbccdbccabcddaddcccdddacddccbcacdbadcddcbbdddabcadbadddbcadcabdcbdbdaacccbcdbddbaacacdcadabcccbbaaadddaaadbbbdcdbcddbaccaddbcdaaabdcdadcbbdccccddddacdcbccaaaacacaaabcacaddacdccacbbbbabdbadbadcbbdbbaaacbdacbbbcbccbcdacdcbdbacbddadaaaddcbdbbcacdbbbaaacbadcabcccdcbdbdcabcdabaddbacdcccbcbdacbaaabbbbadabbabddccacaacccbadbbdbbaccaadbabbdbacdbababdcababbaaddcdacbbdaccabbccbcaadccaddddcdbcdcdccaacbdbbddcacaababcbbdabdacbcdacbcdcbdacdbbabacadabcdacbddadcddcaaadccabbaadddadbabaabdacccadaaccbcdacadaccaaadbcdbbbccadbdabddddaabbbdbbdcdbcdbacaccadaaddbabcababdbcddabacaddddabdcdccadccbbdccddacbadacdabddcadcaacbaaccdadaccdbbcdaddbaccbccbbadbdcdbbdddcaddbbcdadddbccbbdddccbdbaadccbaaaacbcdccbcddbcadabadbcdbbddadccdcdddaddbddcccdacbabadccdadacddbcbdddcacaadabaddadcdcbdbabcacacaabccdcdcabdbddcccabcacabbcdabdadddabbdbcccbcaaabbbdddcdcdccabbacaaabcacabbadbabbaddbdbbdcacddabdcadcbcdcdcbadcbdbccbcdacdcbddaabbcbaaabcacdbbbcdbbbcbbaddcbcbccbddcbbbacbcadcdddabdccdadcbdbcbcaddacdaacbddbddbcbaacaadabdddaaacadaaabcabcacddabadacccaccabbbabbbbddabccbadbbdadcbdbcdadbdaccaddbddcdadbacbadbbcdcadcacccbacccaddcacbabaaccdbccdaabccaaaddddccdcdadaddcbcaaaabdcdbbcbbddddcacbdbaccdbcacdaaabbbcadcacbcbbabadbbacdbacdabacaadaccbdadadcbbbaaadabaababdabaababdaaabcaaddadcdbabcabccaabaabcccbdcacacbddbbdccacbaaacdcbaabcaadaddccdbacabdddcbcaaacbdababaabaabccdcadbcabadccccbbddaccaddcbcaabacdccbbdcdaabccadcbcdcdbbcbdaaabdcadbbddbbbdbdddccacbcbddccbcdcadddccdcbbadbdbacbbcdddaaccbbbdbbbbbddcbcadcbbaaababdccbcbabbcbbccdaaccaacbacdcbbaddacbdaacaacdcbddbdccbbbdcbcbddddcdddcdadcaabccaabcaacbbaabcabdabdaabcccabbaadcbbabcaaaadabacdbabcacccaabaacabadcdadcabaadacbdbcdbdccbaddadbcacaabcacdcddcadcdabcdddbbdbcdacacddcbdbcaacdaaddbbdddacabbaadacadbdababccadabbbddbccacadadcadacbadcdadaadadbbadcdbabcbdcccabbccbacacdaddbbbccbcdbdbbacadbdabcacbcacdcccadbaacbdbbcccdbbdbcaacaadacacadcddabdcddccbdadbcdadbaacaaabbcaababcadaddbccbabddadacbbaabccbdccadbcaaabcadcababbbccbbbaaaddadabaddcaadacccacabbaadabacbdcdcabadacdbadabdabaddbcdacbdbddcccdbacacabccbdddadababbdabcdcbdacaabdcdbcdbadaccacaababcaadbbccbbddcdbbccddacaabacabdbcaccdbcbdaaaacabbadbdcaabdadadcabacaadadcdbcdddacadaaacbdcadacbdbdddcbadccdacdccdddcddcddddbcccacbbddcccdcbabadddaadacdbaaaabaaacbbbadaaacabbacddaacdbbbadabddabaacdadbbdccbacabaabccaddccccdcdaacdbabbbbcdcacacdbbcbcaaabcbccdbcaabbaadacacddcbacddbdbbacabdbdddbbcacacaadcdaacabacbcbccacbddbcddaadadcbdcaacabbcadcbdacccdccbbaddcddbdaacabaaabcccaccccddbdadccbdbaadbacbdcbdacbdddadbaccdabbcbcccabdcbcccdabcdccdcababbabacabcbdacadccbcbbcacccaabdacadbdabccdcccdadcccccabdccadabbbbcbddcacdccdccbcbcccdacacabbdabcabaddbcddadcbcabcddcadbdabacdcbdbcbadbbcbbbbadccbaacdaacdbdbbbdcbcbccbbbccdcdcadbcaccdbabcadbbccacdcccaccaddaaddbcbdbcddadabbcbacaccddabdcbbdcdbbddaacabbdbcadadaabcadbdbabdababdcababdcbbbccdbccadabbbacdcdddabccdcbdddcbbacabbadacdcdabcbbddccbcaabbadbadccdcacadaabcccbbadcaacaaaaabdddcaddccabbaccccbbcacadccddabbcaccbccadbacdbdcacbbddabdacaadccacddbabcaabdbcabcdcdddadadbaccccadbbaabdcddabcbaadbadaccbacaadccabacdccdbcbcacbdddddadcbaaddccbbcbdbddbcbcdabcccaacddcdcacacbacbbccbcdcdaacbdabbcaabcbdbaabbaaabccccdcbbcabbdbadbaccdadbaccbdbacbaccdcbbbdbadddbdcdcbaccadaadcdcbbaaaabbdaacddcacadcdcadabbabaacdbabdcddadcdcaabbadcbcdddbbcbccbacbbcdbbbcdabbabdcbbbaadcdacccabddbcdcaacdaadcbdbdabcadadabadaddbbabdccabdccbbddcaadcbbcbccbdccccbaaddabccdddcbcbddcccdbbcdcdbbdccddcbbdcbbccbabbbbcabcddaabcbccadaddcabbdabbdcbbacdcdbacbaaaddcbbdcaabcdbcdbbdbacdbddccccbdbdabacbdbdccbbcadbabddddddbaaabcbabbaacdbabadccabbcdddcbddadabacdabcaacbcaaaddccdacdbcacabcbbbdacdaabacbbdbdbabbbdbacdaadcaaccbbacccbdaaccacbcadabdadcdcbbddbcacccccacacadcdabcbcddadacbcccdabdcbbcddbadaccbddbdcdcacabcddcbcbadadccdcadccacddbcbbaadbbacbbdaddcbccdbccccdccacdcdcbccdadbbdaaacadabbcdcabcaccacabcbbacbbdcbbaddcacadbdaabadaccdaaabdbbadcadbccccabdaabccdadbdddbcddbbcadbbccddbbbbcadaaabddaadbdcaadbadacaddbcdbbaaadacddbbabadadadbcccccbbcbadbcdcbdbacacbcdaaccbcbabdbabdddcdbcdcdddadbbbbbbbadcdacdabdddbddbcaacdbbaaabbcaadcbdbdddddddbbbacdddadabcbbdddadabcbadbddddadabacbacadbddddbbabacbcdbadabcadcbdaabadbcbdcaddaccbaadabcbaabacdadbbdaacddcbbbdaddcbacbcabbbdadcccaabdddaddccccabcabcbacacdbddcdbcabddadaadcdbadcadbdbbcbcabcdcccaddcccbbaaddaccdbbdddbcaaaaaabdbcddcdadcdbdcbbccacbbcdaadcdabdccbdbaaddbaadcbdbcaaaaabbdcadadadddbbbbccabdbabdcacccbdbaabdcaddacdabdcacdadcdbcabdbbabccaacddabcbcddbbbaaccdbdcbadbccadacbadbddaddbacacbacccdaddacdbbcbdccbdacbcccaaadaadbcbaabbcdaadbdadbdcdbcbaabccddacbbcccbddcaddddbdabbbbdccddbcbdddbbdbacaadaacbdbcaddbcbddcadddcadddcaabccacdbdbbbcabcbaabcdddcdadcdadcddcccaabcdcbcbcaaddabadcdcbccbdccaacacacbdaadbcaacbcbcbababddddddbbdbdaaacbbbabdcbacbcabcbdddccbcabdabbcdddcccdbcccbbadccbccabbadcadcddcadcabdbbbdbaadadaadbcdbdcdcabbbdaadddcacddbabcbbbadccdcddbbacadddddaacccbabaccdbacbacdbaaaccaacdcadccccdaaddacdbabaccbcabdbaccabcbaacbcbcdcddbcdacabbcdbddbaacaacbaaacbbdcabdadabdbaadcbdaabccdbbacdbcbcdaddcbbcaccacbabcbcbbbbcdcadbadcabbadcbbdbcaddbddbbaabccadbbcbbbadcdccccaacbcdcddbdddabbbbabbcccdbcbadcbcbddadadbcbdacccdbbbddcacaacdaabcbaacadcbbdbcacaaccadadcbbdcabbaabdccbcaaaaadabbcbbccdbdbaddacbccbbdcabbacbadabbdbcbcdbdbcabbdadabbcadccaaacadcccbabbacddcbbdbdadbacddabbcabbbcdbdcaadbcdcdcdbdbdddabcaccdaadcadbbaacbbadaddacabdadacdcbcddddacbabbcaccbdccdccddacdadcaaacbcbaccaaccdccddcbdbdaaacccabdaadccdddbdcbbccaddbbddcbadcdbaaacaabacccbcbdbdccbccbbdaacbbddbcddadcccdcdaadbdcbbbbababacbcbbbaddccabaadcbcbaadcaaabbcdadaaadaadbdbdbdcadcbbaacdbbbcdaaaaabcaaaacdcaacabaaddcbdaabaaaaababadcbddacbabaabccaddcaadbcabdacdaccdccddadaddaddaadbbdbbdbaacbadcabccadbbadcabacccdcbaaacddabcccabbabdbbaadcddbccdcbbbdadaacccdaccabbcbbbaabbbdbabcbbbaaddbaccbdcbddacbbacacbcdabcdccdbddaccddaddddadabddaadacacbdadddcdddbbbcbaadbdcaabbbddbdcadacadcdcbcbccddcdacdcbdbcadddbbdcbadbcddbbdbacbdcaaacbbcadccadbccabddbcccadbbbbcdaabbdbbcbadbcbccdcdaccddaadacbddbbdbbdbcbbcbbbcdccccdaabaabdccbaadbadbcbddcdbdcdcabaccccccaacdcdcddcadaddbcbabcaaadbcdadaacacacbaaacaddddbabbaabcacacbcdabcacaadcacbcaddaaabcdabcbaadacbbccddacdddcdacdcdcabbbbcccaabdcabdadcaadaacbcdcdcddbbdbaaccacbdbdacaaacaccbddacadacccbbcccbcbbaabcbdccccbaccbccdbcacdbddcccadabbdccbcaabdabbdacbbcacbbcaaacaaabbacccdbbaccadbbabdcdcacccabbbcadaddaacdbcaaaccabadbbddcaabadcbbcbbddcabbdacaaabcdaccbbdbbabaccccacdcdbdcbddacbcacacaaabddaccdcadcdaaacacdbaddbccbbabcddaaadabbabbdabddcadbddcdbddccccabcbaadcadbbcdccbdaaadcbdcaccdcacadabdccbbbdcaccdbdadddaadbbacbbcdaaddcbdddbdbabaacccbcdbcdcdcccadbacabccdabbbcadbbabcaaaabddbabbadaacbcddaabdaaccdacacbbacdbbcabcaddcbadbdcbbdbccbcdcabacbbaaacddcdadccdcbbabcabcdadaccddadbdaadcbdaaddaadccaddabadcbacbabbcdaccbbadddddbccbabcdabbcdcbbbcaaddddbbabacdbdcaddacdbbdddcbbdccbdcdaaaddaaddcdbcbbbcbdaadabcaadbddccbcdabdbbadcbacbcaddcaccdbaadaaadababaddabdbacdaabccbacdbcbcadabaadbdaaaadcaabcdacccabdbddaaaaabbcdaadcadcbdadcdcadaacddbcbcadbababaadbbdccaabaaabdadbbbdccbaabccacacabcdaccbadaacaccacdabbaccbcbdccdbcabaadbdbcdbdabdadbdcdcadcdacdcadbbbbbbabaddbcdbcbbcddcaadcccdcbdabbaccbadcbacbadcbcdaadcabadbbadacaaacaaddbbbdabdcccbcaabbbcdaacbbbddaadbbdbadbdddadbdbbddcdbabaaddaacdbccaddbbcacdbabddbcdadbcdbccaaaaacacabbcadcbccbdadddcbcbdbbbcbdbdbbccccadaccddccdbbccadddbaabcdbdcaccbcbcdbbaddacdcbddcdddbccccdcabdccbbacdacbcabdbcaddadacccddcddcacabbcbdadbcdddacadcdbddaadacdcbdaddadadcacdabacaccbdcbbdaaccccbccbcacddddbabaddcbcccdcbadccccccadcaaadbdbadabdacbabdcdabddbdaabddccabdddccaaccdbacddacdddcbdbbdadbcbcbcbacadbacabccdcccbcbadabdbaccbadbdadbbaccbcaacbbcbdacddbdbddccdcbccddaacddbacccdabbbbdcdbcddacbdcdcdddaccadcbbabacabbcdcdbbccababdcdabccdcbcbaaadaaccdcbbccddcadaaacaaadbabaddcdbcdadaaccddbdbdbddbbabbbacbbcbdaaddbaaddddcbddbccbbaadcaacabddabbcaacaaabcddbacacdadcccddcabaadbccddbcadaabcbcaaabaaacbcdcdabddaacacdcddddcaddccddbdbdcbddcbbbcdcbbbdabbccccdcdaddcaacbddadaaaacbccccbaaddaaaabcacbdbaddcbccbdccaadadbadbaaabbbcabbbbbbbccadcddaaadddcdbacdbdcdaadbdcdccdcdabcdbdabcbaadddbdcabdbccbdbdcbbcbbdbabbdcdccdccbbdaccaddcaaccbcabadacbbccbcbabbcacaadbdabdaddbabcaccbbdbadaccdcdabcabbaddbbabaaddbbdacbbadcccaddacdccdcbdcacbcbccddaadcbbdbaddbaaacbbddbaacacbbccdbccbcddddacbdaadbaabacbabbcdcbadbcbbbbdbbacbccacddaccbbbabacbdcccccdbbaaaccbcaacdbbdaadccaabcdabddcadbdddbbdbacbadcddbbcbcabcccdabbccdbadbcdbbdaadaabcdbdbadbccbdcdbadadddcbbcdabbccbdcccbbaaddcdcddbdaadccdacaaddddbdaacdacadabbbbcabdbabacddddbddddbcabcabdaddaadbbbaccabccacdcacaaabdadddcdbddcdadddaacbbabacdaaacdcbdaacaddbdcbdddccabccdbdaabbbcdadaddbaddcbdabbbdcadacacbaacbbddcbddccccabaadcdcbbdbdbbacacbcaabbbddddadbdaaadcdacaaddbdcaaacadcbddbbacbccbddabccccdbcbbacbcbddbbbbacabbddddadaabcdbaaadbdcbccbccccccbcbbcaadccdcdcadacbaacaccadabbccdcbdccbbabbcbbdcaccdbaaccdaddbbbccbaacdcbcbdddbdbabbbabacbcdcdadccdcccaacaabababacdccddcccccbccccbbbdacabbacbcdcaadbdbcbdbdbbabacaddccaadaacacbdcbddbbdcdbcbdbcddcadabdccabdacaaabcaccddbbdadaccbbcabcdbcaccbbcddabccbdaacbadbdacbbabdcabdababcaabacdadadacbbcdaddabbcaddacbdbcdcbbcadabaacbaacdcddcbbacbdacaabaabadaabbacdddcddaacdacaaabdbdcdddabaabacbabcaccadbaddcdabaabccbbbcdbcaacabcdacabddbddabcaadcbcbbdbabaabaaacacadacdbcbbbcabdcadaaabcccbaabcdcdbccdabdccbacbccdddacaacbccdcbcddbcdcacddabcaadbdadbdadbcacccdcbcbababaddbdcbbbccbbcccddddcbcbbddcdcbacddaabcaccbacbbdcabdbddaabacccabddbacddddadddbdacbdaaccdcdccdbadadabacddacdbacaddaddcbbabbddcbddbacdddbddbdaccacdccbbbcaabdccdbacaddbccdcdbadbbdcbabbbddcddcdbdddddddaadbcdaabbccbddbdcaaacacadbbcbabcbccdabbaadbadcbabcccccbabcbcbdaaabaabcaabbbacbbcbcadbcdcbbcdcadbccddcadabdaacddababacbaaaddababaccdbdccdcddbbccaacdaaacbacbbadcdbccbdababcaacdcaabdbcaacdaddadaccccdbaddbdbbadacaabbcadbababadcaddbadcdabadbddcabbcabacaacbbcadcdddcaccababbacdbbbdcaabddbddcdbdaadbabdddbbadacaabdaddbcdbcbccabddbddacdbacdaacccadcdcccacababcdcbcbacaaddbabaadbbdbddbdbccddbdbdcccaabbdbdcbabdabbdacdbadadccbccbdacddbcddddaaddaddbddcdacabdcdbbccaaccaccddacaccdaddabddacddabbcdcdbaaadcbdbbbdcddcacdcaadccdadabaddbdcdccdcaacccaacabdbaabadcaddaddacbaaaaacbdbbcadcdcdddcadbdcbcaaccaabbaacaaaaabbabcbacdbadbddacccdccdcadbaddacdcbdcbbbdcaadcabbcacdbaadbcbcdabadcccabdddcccccbbcdabddabbbcabdaaacadacdbdbcababbbabcddadcbddbdccadbdcbabcbadaddcddadacbcbbcdaddaadddacbbdabaababdabddbaaabdddabcccaaacbccacdddaacdbcbacdccdbbdbcadbcdbcddacccddddcabcbcbcabbcbdadacbccddaccddbbbbcddcbdcccbcbccacabdacadcbdbbbbacaaaddbccbbdccacdccdcdbaacbcaadbdbbacdbbaacddcdbccabbbcabacdadadcddbdcdddcdabacdadddaccbdcbcdabbcddcabcbbbacccbadbbbacbbdccaddbbddcdabbaccccbadcbbdbcadbadcdacaadccdccabdbcbcabbbbcdddbbbbdaddacdbcaacbbcacbdaadbcabcdbababaacacdbdabdbaddbbaddaaddbddcddbcaccbacccdbaddbadaddbbaabadbbbdcdbcadddcdbdabccadddaadcbaaacabdcdbbbccbdbacacdbabccdddaadaadddacdbcbbbbabdcbcbdaacaaccccabccdcdcdbdbdccdbbabbdcabaddbbccbbcaaadcabdaddbacdaaacbdbdddbadbbcadbacdaaaadcbbcaabaaddaadddbcbbcaaaadcdbadaacadcdbdacacaadcdacccccddbbbcdddbbbddbabcabbaabbadadcbddcabbbbbcbccaabbcaabdabcaddacacbcdddcbcbaccbaaccaabbbdabdcaadaabcddddbabbdbdcacabdcdccbdbdbdcbcbcbdcaccdccbdddabaaccacddbccbcddcabccccabdcadbacdacbdaaaddddbbbbcacdddabacdbabddaaababdcdccbaadabddcddddbddacdbccdbbdbbabcddbdbccbadbbaaacadacadbdbbdabbbabacdadbbddbcdabcadccbbbbcacadccdbacbcabbdcacdaddddadabcbcbbacbbacbbacacccaaddbddbbcdcbbadaccddaacbaddaaccdadbcddddccbdadccbbbbdccacdabcccdbcdcdbaccbcdccbbcdcdaacdcccaabcdcbcddbbdcabaddbdbaaadbdacaaddaaaaabcbcbcbcbcbacbbdbcbcbdbbbbaaddbacddbaaccabddacabcacabbabdbbbddbbaabdadcacadadbdbcdadbdcccddccadcadcacaaaaacdcdccbdbdddbaabbbcbcccabcdcbbdddcdbbbcdccdaddddadccdbcdcdbdaaacaabbdcaabccaabacbdddcdabcabacabacddacbacccccacdadbdadaaddaaacbccaaacdbdbcccadacbbabadbadabaabadcacdddcbbdcacbbcbadcacccddddabbcbadbcdccadbbcbacaadaababdbcdaddabdcaabaddbbcbcccccabdddbbdabdaccbacccabcddabbaddddbacbccbbddcbcddabcbaacbbcdaabbbdbaadaabccbddaadccbbddacbbdbaacdbbbdbdbacbccddabdbbdbbaaccbadccbacbbbacccacabdadcaccccdbaddccabaddccbacdcabcbcbbadaddaddbcadadcaabaabaaccccbcbabcdddbcdbbabacbadacbdbbdbacbcbbabcbcacabaaaddcadcabcaadbdaccbbcccbccababcbccbdbbaccdddacdbbbbbcdbcbdacabacdcdcdbcccdacdcdbaccbbaadcddcdbbcbacbbdccccdacbaabadddbdcdbcaabcaacdaabdbccbccccabcbdbaddaadccdcaaaadabaccadbaabddaaddaabbbaabcdbdadbcbcbccbbccdbcdaccbdbcaaacacdaaaaadddbcdaaccacdbaddabaacacddcbaabddaddbaadabdabcdabcbbaccdcdbbbdacbcabcdbcabcdcbabbdbbabbbdabdcbbbdabbcdbbadcbbcacbcaccbddadcacdcbdadabbccaabbbcdaccdadbcaaddccbddddcaccbadbbbddbddcbcdbacccaabccbabbbbaadbdcbbdababbcbbddabadddbaacdbbcabcdadddadbaaabccabcabaccbabadadabcaacdbadacddcbccaaddbdabbbaddcabdcdadacccccdddcbbcbcccadddddcacddbcadbbbaacdcabadbabdccbcdbcaccbbdcabdaacacbbcdcadacbddbcaacbccccacbccbacabababbcccddddabaaccdbaacadcdadcbdddbdcccabcdaaddbdcabdcccddaaabbbacdaaaabdabddcababadcacbcabbbddadcddcacaccaabaccdbbdccbaaabdcbaabcaaabbccbbaabbddcbdbdbbbadaaddaddcacabdbdcbcbacdcbcdabdaaabbaabcbabdbdbbddcdbabdccbacaabccbacdcccbbcddabadddbaaddaadabaccbccabbbccadcadbdacbacdccbadcdaccccabcdcabcabdcabbcbdccdccccccaacdadacddabbddcacdabbacbddaacababadacdbadbdabdbccbddaabdbddcdbcdadabbbcbbdbabcbdbbdcbbdadadaccddccdbcbbadabaabaacccddacbdcacadbadbbbaaabdcdbbcabcdcaccbaabcadcbddacbbaccbaaaadcccbdcaaabbbabdcddcdddabcacccbadccdcaadbbadbdacabaddbcbccabaabdccbcdcadaabbbacbacabcdccbcdacddcccabcbbdbddbdcacaaabddacdbbaadaabbdcbcbdddaacadcbaaaabcaacbccdccdbbcaadcdbadccdcddcabbccaabbcabdccdbadabaabaaaabdbcccddcccbccaabcacadbadcbcabddcbbdbcdbbdddaacdccbcabcbaaccdcdadabbdcdabcbcdddccdaabcacddcbcddaccaaddbcdaadacdcdacaadcababddaabcadadbbdcdacadabababacdaaaaaaacaccadcadbbdabbcabdbaacbaacbdbdaadaadbccbcccddaccdcdbbbddabaaddcadabaddcabaadbcdabddbbbcdbbadccbcdbddaddbddcadaadcdaaabdcbcdbbcdccbacbbcdacbdbcddbacbadcaacacdccdcddbbdcbccddbddaccabadcacbaaaddaddbcdccababbbaaddbcbaccbbcdbdbaabcadbccaadaccaacacddabcddadddabaacdbccbccabbaccacdbdbdccabdcabdccabaaaacacdbcccbbdaaaaadaabdcabdbcdbdcbddcccdadcbcaaacbccbbabbdbadbcacaccbaccacdadaadcbdbacbcaabbcabbdacdbdcbddbdabbacadaccddcbadaabdddbcdbbcbdacbcdbdbaddadacaadabccdbcbdbcbbccccdcdbcaccbbbaadcaccadaaaaddaaaddccdcadcacacccddcacdbdcdccdbdcddbbcddbabdcbbcbddbbaabbcaadbcabcbdbbdaabcdcdcbcaccdbdabcbccaabddbdaabcdadcbdcdacbadbddcabacaadbdadcdcabdadaccdadbbdcbccbcdccddadabcbaacacbcacbabbadcbcdaccddabbabcbbccacdbbcdcddccbcbaacdbcdadcdacbccdbbbccbcdbbccbddacdbababbccccbbcabcbadadadcabbcbcbadaacdbcdbcbacbadbdbadbacbccabcbcadbcaacbdadbadccddaabccbadaadcbbdbaacaacbacbababadccdacaccbccdccbccbabadcbaaddbddcdddccdddbcdcdcbdbdacdbcdcdcbcdacbbadbbdaacbccccdcadadbddaadbaadbabadbddacdbabcdabbddaaaaacbdadbdbbccbabdabadbcdbcadcaabddaccccbacabdcadbcbadbdbbabaaadacadabbdcbbbbacbdcaadabdabcacbccbcabbdcabacbcdadaadbdcbbbdddcbcdaabcabcdcbcabaabdbabdbbcbcbdcacbdadabcacdccbcbabbcabadadbdccbbcdcbdacdacccdccdaacbcdcbcdadddbacabaacaadaabcddbddbdcaabbabaadacbacaababbaacadacdbdbbbdbaaaaaccbbbbddadcccaacbccdacbbdcbcccdaaaddacdcccbbbdcaabbdcccadcaadabcccdccadcbddabccbacdcbbbadaacdadbabacbcbcabacdccaaaacbbdabbbaddaabbbcdcdacbbdbbaaabaabcbccbbccbbccbcdaaabcccadaababababcadacbaccdbcacdcbacadadacaaaabbdabacabdbbbccaabcdcdaaabcdccddcdadcabbcdcabbabacbaaaddcddcbdccbdacdcdcbbccbacaccdcbbcbaddacbabaacddccbdaababacacbddcdcccdbbcaacdaaddbcccbdbdbcabdbdadadcdccdaddaacaaacdaaacdaadbbbbbabacccaaaacdabdbadbbcccbddaccdddcaabcbdcbcbcaaccdaabcacdcabbbcaababddbbbcbcadcdadbbddddaaadadbcaddacbdbacadaabdbbcadabadbbaaaadbdacabcdbcacdaaabaabacbcbcdbbaadbddccbacbabbbaddddddcdddcbcabddbdddccdbabdacbadacaacbddabbaaaadbdccaadaabcdacdcccbcdaadbbcbdbbdddbddadcdcbbdcabbccdabcbdaaadcbadcdddadaccaaaadbcbccadbdbdbcacbacdbcdcdcabccbbabbcbacdacdacdbaaacddaadcacaaacaddbdaadbbcdaabbbbcbcacbbdcdaadacacddcabaaaadbaaadcadbdacddacccccbacdbddbaaccdaaccaaabcabbdababcbaaaaadccadcacdaabadabadcaccbacbbddaaccbaabaddccdccabdadaccdabdbbabbdadcaddadbbabbdbbddabbacccdcdcdbcadacbbcbcccbbcdbdacdbaacbdccbcdbbcacccabcabbbbabccdccaaabbbbddaddcacdccdddadcdbddaacddcbbaadbdccbccbaaacccdbbbdadddccccbdbcbaababdbaaabdaddaccdbdbdabccdcbacbabbbbcdbdcccdcaababbadccdadcdcaadaaadcabdbbabacaaadabaabcdabcabcdbcddbbddaccacbcddbbcbcadadbccabcddadcbaccccbaddadbabccbcaabdbbcbcaddcaaacacdbdaaddbdbabadacbcbddadbccdbcabddcbbbbaaaddddbccadcccacdcbbadaaddcbcbbdbdcbbbacdadabccbabcbdcdacaadbbcacdcabbbddacbcbbbcdbbcaccadcdbdcabacaaacbcababaabaaaaaddbcdddadbddbbdccaacbabdacbacadaddadccdbbabdbbcccabdbaccbcdaaaabbcdbdcdcbdabbdbbcacddbcbdcdaadaccddacdccccdddcdcaccddbaacccdbbacbdbbdaadcddaddcbdacbcddccabcdddcbcdbcdaacdddaabbdaacacbdaababacdaccbdcdbacdaacbcaccdbbbccdbcacabdbccddcbaccaddadbdddcacbcaaaddbbcdddcdbbbbccdccbacbccbcaabddcadaabadbdccdaccaadcdabaccdbdbcddcbdbcbbcdaacddbabdcadacadabccccbbcbcdccacbddddbcadbcccddcaccdcaddaadaacdaddcbbaccbcdacbcbcbadcbabdcbdbabbbbdaadbbbadcbacccdcacdddcdcddbbbaadcdcacaabcaadddcddbcbadadacbbbccdcdcdcdadcbbbbaccdbddacaadcdcabdbaaccbbbcbddcdccbcbaadcdbaabcacbbdcddddaaccaaccdaacbadcdabaabcbbacadbdbadcbdbbabacddcabbdbbaabcdbdbcdbdcdbdbdabacdbdabaccbddddacadbbccadddaddcacbdcbaccadbccdbdbdbcadaccaaacacacbdbccbadbddddacdacabacaccccbbbbacddccdcaccacbbbccacddaddccdbcbaadddcacdccacdabdddbadabcdbbbcabdadacccddcdabcccdddabaacadbbbaaacbacdaccbbcbabcdacbaaaadbaddadbbddacdbcbbdbbacacdbddbcacaccddbdbcccadcdccbbdaadaaadbcaccaddbbbbbabbcbaccabbbdcbbdbcddcccaadadcbaccbdbaddcbdddcbcddcacbbbdbdadbcccbaddaddbadcddcddcbdbaadbbababdabdcbcdcadadbbcaabcbdbddbcbbddaabcabcbdbccbcabbcbdbbdabaacdaadcbcbdddaaaabdccadbbdbcdccdbcbcdabbadcddbbcbdbadbaaddaaccbdaaadddbabcbdaaaacaabbadbadcbcacadbbdabdabcdccdbcaacdbcddbadbcbdbaaddccabddbcddaddadcdddcbbcddacccbdddcabcdcdacbadaaaaaaccbcbbccaabccbaaccbdbbbccbbccbcaddbcdcaadddabbdabcccddbaddadaacdbcdbbbacdaaaaaacbaabdcbbbcdddadaaaccadbbddaacbcdbabbcdcaadaaacbbadbaccadcbbcdbacdcabacdbddaadbcccdbcaddccdbbddcacabcdcccbcbcddccadcaaabdabbadabbdbdaabcabccddcddccdadcbbdaabdcbbbdaddcaccbcabababccccdcadadcadacbcdadacdcbbacbcaaadaadaddcbcdbcaddddbbbbdcdbaddabcdddcbdaabdbdcacdabcadadcbaccdcccccbabbcbcaacaabcdaaadcacbbbcacacddcccbddcadaacbdcdacbdcbcbcbbddacbcddcbcdcdaadbdbdacbbbdbddbbaaccccaccbdcadadcdaaddbbacdddbccbadaaccbbcdbcdadbcbcdbdacabbcbcdadbccdcdabbbdcaddcccdcabaadbadadbbacbbccdcaaccadbdaacadcddacbadbbcadbbbbadaabadccadbdacbbcddbcbacbccaddcdacddbaaacabbbbbcaadddbdcacbdcbccbbcddcbadccccccbddaabbaccbcbadacdacabadadbbbdddabbbccabdcdaacabccbadacababcaccbbccdbbcacabaabbbaccbccbcabbdacadcaddcadccacbccbaababababaaaaaababaaabdbccddabbcddccdbacdacdbddcdadadbcabcdcaabcbccbadabcdbadcccbbcbccacddbaadbcbacbcaacdbcdcbbcbbcddacbadabcdbbabcbbdcdbdcadccbacbcbdbdddcdddbacadbdacbbbadcacdbbaaddcaaabbcacbbbbdbadaabbbbdccaacbdccdbdacddcbbadadacdadbabdddbbbaacdaacbacbccabccacbbbadcdcdbdcdbdacbddabbdaccdcdbbdcdddcaccdcaaaadcbdbcacabccccbadadbbacdcacccbbcacbcddaabacacbbcabdbadcdbbaabdcaadacaacacccbcadabcbccbacacabbbcbbdccdaaadadbbbdcaddabadaadcabdbaaddcdcbbabcabbbaaccdbbabdabaddbdacaaaaaddddcdbbcbcbcdcbcbccddbbcdcccbdbdcacdbddabccdbcabcaaadddadcbcaddcaacdacbdaddbbcccddbccdcdadcbddbdadcababaccbccadbdaabcddddacccabababbabadbaaadcdcadcadbbaaaabccdabaabdababcbbbbbbacbabacabaccddbbbcbcacadbbdaccbabbaadccdacdbccbbcaaaddcdbabdcaccadacbdcdbababcdbcabacdabbdbdbbaaadcddcbdcdbcdcdadabbaddacdbcccabcdaddcaabcbcdccadcdaddddcaaccabbabcdcbbdcadaccacacbbbbdadaccdcbaaabccdbdcbbcbccbaaadccabbbdaacccaccbbcacddbbbadcdaddacdcacadccccbadddcabdddcbbdddcbddbbdaabaccdbcddacbdbccdabbcdcccdbdbadcaddccababdbadbabbcbbadbdbdcdaadabdcbcddddcbcadbccbdcbbadaddbdbcacadacdaccadccbbdacbacbcddbdcccccbbbccbacadcbbbccabdcbabddcccaaadabbbdcbbddacadadddbbbdaaacaccacbabbdbdbacddcdacdbbdcadabadcdacaaddbcbcabddbccdbdaacddacaacbcbcdbbcbdcdcaadccbaddacabddababcbadbaaabbacacddcabdaabcddcadbcdcdbbbbaaacccddaadadbabddabaccadcddddcbabdcbddbbdddbcacdcdbbccaddabcbcdacadccacadcabbbcadaabbababadbadcbdddabcbcdbbcaddbcacdacbdcccdbdacdddacdabaddcbddadcabdabcdaaaabcbbaaadbbacbcdcdcabbdacbbaacbbcddbdadacabccaabcdcaccbbacabcdbdbbabcabdbdadbddcabcaaaacccbcaabaadaddaadcdbdbacbcbbddbacbaacddbdacbbacaadcdbcbaaaacddbbbbaddbcdcabcbccbbdabcbaccacdaacaacdcbcdcbadadcbabacbabadabdadaabcacbaadadabacdcaacadcdabaccdbcdcbbaaacbbabdadaabcaaacbadccccbcbdbcbabbbbadccbbacdbbbbbdddddcbbdddabdcddcddcdbabadcccabbcaccbcccaadcbbcbccadbcbbdbcaaaabaccbadcbaddbdadabdddcbcadacbbbaaccccaacdadadcbdacaddccdcadccbaccabcbcbabdaacdccccddbadaabacdcdaaabaabadbaaddccaacaddbdbcacddccaddccdccbabcdcdbcdbbcbdcaabbadcdadccdbbaccddaaacadcadcdcbbcbdacddbaddcabcbbdbcabbcbddccbaacabdbddcabadacaccddacccdbdcaddbbbccdbcdabdaacbdbcacbadcacaacbaaaaadcbccaccbddadcdaadddaccddbdbbacacaddbaccadcbdadddddaaaaababccaddccabdccaaccdbabbacdcccbdbbdbbacdcadaaaddcbdbbcbbaccdddbdbadbccbbccbcaaabaabcdbaacacadbdccdaaaabbbaacbabbbbcdabaabdccccbabcacbdcdcacdbaccdbabacbaabbaaddbacccaddcdabbcddcacbbbdddaaabcccaccdacbadadcdcaabdcbdccbabdaabbbcdabacddbcabcadcdaacbccdbabcbaddcbcbbdbabcdbadaacdadcdacccdddcccaaddaddacadaccbdcbbcabbcbcdcbbccbaddbacdbbcdacccccbcdcdbaccbbbccdccdacbdddabddccacdccbdcdaaadbcdcddaccdcbcaadbaaaacbbbbaaaacabbbadbaadabbbccbdcbaccabdcbcbbdbadccddcdbaddcbcbccbaccaccadacacdbaadbdabaccacbbbacbcccaddcbdccdaadbacbbbbaaaddadaddababdadbdaadbaacddcbcbabcbbbdddadcaabdcaddbdcadddcacdaccadbbabbabdccdacbbadacaadbdccbbcadcbdcdbcbdbcbdbcdbbdadccacabbabdaabcbbacaaacdccdbadcddacaabbbaaacaacadbdaccdbbbccbcbcdddccdbbbbcaabbaddcaaababaaddddddbbdbbcdcbaabbcbbbddadcabbdccbdadddcddcacbaccbadcdbabbcdbdcddbdbaaddcbdddbaacadbdabadadbddcbaccacccdcdccaaadccbbbaaababbaccdadaacdaaaadbaabdbabdcbccbdaabcadddbacadbdaabdbacabbcbabddbacddaaababcbccadcbaadbbdaabbabcbccdbaacdabccabbcddbddcadcbabaaacbacdcdcbcdcdacaaadbadabbaacbbbdbbddcdaddbdbcbdbccbbbaadddabbbcbabbcabbcbbddccccccbddcdcacabdccbdadbaddbccbacbcbdadccbcdbbccddbccbbaddcdaccdbdbbacabadccddacbdccaabaabaabcaadcccbababbcbcbcbcbbccaabadaabccdbbbbdcbcdcaaddcbcbccbcdabaadaccacbdaadbabcabbaccacabbddaaaaabbabcdccbcabadbbcbbcddbcdccaddbddddbdcdbadbbacbcbbdcbdddaadabcdbddbccdbdcbaaccccdbddbcdddcacdcbddcdccaaddabcabbccabaaadbcbadadbddddaabdcaabbddbaddaabccbbbbaabbcadbcdbdcbbdaababbaccccaadddddbccbcaaacadaaddaccdaabdcbacbcbbcbccdbbacabaaabcdbaacddcbcbdaacdccbdaacdbbcbbddaddacadcdbccabbaaacdcacaddbabbabbcacbdbcbadacbcbaaabbcacbabcdabccaadcdaacaacbdccccbddccdacddcbbaddcdacabcbadbaacdbbacbacabbababcbcbcddaadbcccacccbdccdaabbbabddddbcdccbcbcaaaabccbdccbaadbbaddbcbaabbbbcabcacbbbbadcdcaabacaaaccadddbaddaddddbabdcaaaaaddbbcdcabbbcbccdaabaacbdddbcdbaaaaaccbbaaddaddbbdaddcbbbabdbabacbaaccdaaadbdacdaabbdacdbdbbbabacdbccacbbdbcacabbbbaaabdababbccaccccbcbbbbbabdabbbddcdadbadaadcdddbdbddddbcabbacacddacbbabaacabaacdadacdddbbdbcdcccabddcdbbddacabbcccabadadcbdbbbdbabaacadbadadabbadbabacdaaccaabcaadaacbcdcbdabbbaddbaddbbcbabcdddbbddbabdbcabcabdbdddcbcdadcacdaaadcddaaabacccaaddaaabadacbddcaacdcaababbbccccbaadadaaddabbaacaccddaabacdbcbbabbabbbccdbbacbdcaabbdcdaaacbbcadaadcacabddddbadbdcdabbdbabddcadbadadbadaabcadcdbcaacabbbadccdccacccadbbbcbbaadacdcdabddacbbacdadbcbdbbddddbacdaccbaaacdcadddabccaaaacdaabbdcccddcddbabcbdddcccbdbabadadbaabdacadacddcdabbbabbbacbaccbcbcdbcddcacdbdcbbaccbdcbbddaccadbadaadacadadddbbdaaacbcadbdadbcaccabdddabcbddabcdccacdabacdcbbbccbcdbcadcdcadbccbbcacccbcaababbbddbcbbdbabdccddbdabbdcbcbcadbbbcdcaccdbadaacadadbabadacabccacdcddacbabaaabcdddaddbabbcbdbddcbbcbdccbdddcaccaacccddddbbbcdbabccbacaadacdccdabaddddcbccddbaddbadbdaacdabdccccdcddcaaccdaabbdcadccdbcadbbcbdbdbbbcdacbdcdccddbdaadaaaaadbdcbbbddbcbddbadacadabcddccddcdddbddcaadabaaaadbcdccdadacaddadcacaccdabcbdcdaddacbddabadadddcabaaacccbdbcddaaabbadbcdabddbbaddbbacddcdbcaabdcacabcdabaaccacdbdccaaccbddbcadcaccdbbbcbaabcacacdddaaaddbcdbdadccadddcacabcdbdbddbabadbdddadbabacadccbbcdbcdcdddccdddabbbcddbbaacbcbcbcacbbccbccaaadccadcdcadaaccacbbdadbddadddbcbbcdcbbbcbacaccacbdbaaacdccdbdadbabaabacabbcddbbaccbdabdcbacdaccbdcdbbbbddbbbbcdcdaabadcdbbaccddcaacdcbcaabbbaccdaabacdbaacaabacaacacaacaccbcadabdbdcdaacbcabddbbbdcbbbcbabccbcccacbbccababbdbdcdddddaabdcbcbacbaddbdcadcccacbaaabdaddbcadabaaccbbacbccbdcddaaacbabccdacadcacaacaddccbbbbaabcbcdaddbaddbdbddbccddcbdddacacbabaaddadbcaddbbabdcdacbaaccdbaacacdcbbaccdbccbbdadccbbbdbcaabdcaddcabdaacaaadabaddbacabbcddcadcbaaccacadaddccccbdbbdadbcccacbabaabaadbcbacddabacddbcadaabaddabccddbbbddadaccdabddabdadccaddddbcabcdabaaaaabbacddbdacbcaddddbaabaaaacbbbdddcdaaccbbcbacccdccabdbbabcacdccbbbcacbaccaaaabadbaacdaaadcacbadddbabdccdbdaaaacaccdabcbccacbccbcadbdbdcdabcacbbbbbcbacadabbbccbccbcbdcabaacbcbdbaddcbbddcadcdbccadbcdaacdcdacbdbcaababddcccbdcadccbcdaadadbbdacbcaabdacbbacabdcaadddccdadbccdbccbbabacbdcaccbabbcbdcadacbaccbcaadcdddcbbdcbaabbdcdccacbaddcbbbacbabdddcbabaccdcdbbacdacbcbbabdbddbdaadacbdcdababcdaddababdabcccdaddddcddbccbaddabbacbdbdaccadaabadaddacabaddaddddcadaddaaabdbdbddadaaabcccbabdaccdbabccbdabdbbaccbdcdccabadcdcaadbdbbaacbdccccdbcabbacaddcdbacaacbbdbcbbdbbabddcdcaddaadcbbacddccbcdcbcadacbbbdddababbbadaaaaabbcabccbabaaaaabaaabbadabdadcacdbdaccdbadacbddcacaacbcdbbdbcbbaaccaaadcdccddabadbcddddabbdacabdcabdddcdbdbbdbbbacdbbadcabbcccaaadaccdabbabdadccdccbabdbdccdcaccaaadaabbcdbadcadcacbcaccadbbabdcacaabbacacdbabccdcbaabdabcbbabdcbdabdcacbbadbaabbabcaabcadaacbaadabacbacdbbadabadbbdcbbdaabacbbaaadbcdaaadcbdacdbbbaaabbbabbcddbbaddcaabdacdaaccddccaaadcdadddbbccabaaabdbdbacdbddccacdcbacdbbdccccdbaadbbddbaadadadcbbaccdbddabdabbdacccbccccbcddbdaadbcabccdbdaabcbbdcaabdddadacbbbaacdadcdcacdadaccacaadbdcabdbaaabaabdcbadaddbbabcbdcccacacaacbbddbddcdbddbcabcdcbbcccacbaacbaadbcbbcdcbdcdcbbabddcabcbdaaccacbbcbddbcbabaddaadcbabbdbdddccbadadbcdcdbccdddaccbccddbddaccdcdcbacaabadddbbcdbbabdcacddbacadacabadbccbbadaacadccbdaccdcacaaabcabcabddabdccddccbdbcdbadbcbacacccdbcbcadddbcdcdaacacddcbabaaccdaadcccbcdddbcaadadcbcccaddacadabddabdcaddbddcdaacaccbdbdddabdacdcdcbdbacbcbabdadabddadcadddbdccbacdbabddcccbccdbcbbabcaabbcabbdaccbbdbcdbbbadcccbaaaaabbdadcdadbabbddcaccdbabcdccaaccbdccabbbbaddabaaccbccbccdadbddbbdaadccaaacdcacbaaaacaaababdcdcadcbbbbbabbcbacdccdbbacbcddbddbdadcabbcdabcaadbabcbdddadacbcdddcdccdbdabdabcdbbacddbbaddbacddbccadbaabdbccadaccbccdbdddccdbdbdbccbacccbdbcbcbabbbddacddcdbbdbacaaccadadbbadadacdcabdbdbaadbdaddbddccbadcbddaabdacabdccccdbbabbcbbcabdccdddbcacacddadbddadbcbdaadbcdcaabdddbcccadbddababdadcdcaaabddacacdcaaaaabbdbdcddbbdcddcdcbcdbacdaaadadcacdcbbadabccaadcadccbacdadacbbdcbcbaddadabdddaccccbdacdadadcbdadcddaaaadcbacabcabcddbbcbbddcbdccbacdadadbdcdbbacbaaaccaadbccddabdddaabaacdcdcabaddcbaabccbaddaabbcdadcdacabcacacbcbdcdbbbbcaabdadbacccbbcaacdcbacbdcadbcabbcaadabcaddcbddabbacaddbdaddaadaacbdbdbcbbcadcaadbccbcbdcccdbcddbbcadaddddbcdbdbbdcdbaadbadcdabbaccdabccadddabddababdbaabdacabbbcaabccdbbcdcadbddcdaccabbacaadadcbaacbadadcccaddcbcdddbbdbcdcdcbaabdcbcaaaacdabbddadabcddcccdbaccccaadaabdcdcddcdabdbccbbbadcdacdaabdcabdabaccbaddcdbbbcdbbbbdbdabcbcaadcacbbddadcbbbbabaacaaabbbacdabadaababacdbaaaabadadbbacbbabbdabcddbadaaadadbcabdacdccabddacdcacdaacaacacacacbbddbbcdaacbcbcdccdbdbbbbdbcadbcbdbcadbddbacbccabdbbbdccdcacdacbacaabbacaccabbbabdcdcadaacccdaadcbccdaaacdddcdacbaccbacdacabbabbcbcadbadcbcbaacdadddabcacacbcaaacdabcbccbbdbacababbadadaacaccabaacbbbcbacbdabadbcddbddacdbcbdcaccdbcaccdccdddcdcabddccbbbcccdbccbccbdaabbcbdccaabadaaacaacacdccbcdccabacadddabcbaccbbbbcdaadddbdbadcaddbdbccccaaacbbbcadbbbbacdccdbbabcdadadabcdccccdaaadbdbdbcaddbadccbbabbdcdadbaddbacdcccbbdadbabbdbbdbbccdaabddddaadcdbdabbdacbbcacbbcacbcbdadabababbabdbcddcdcabdcdbbacdcbbaddcccadaabaadbbbccdcaadaddcabcacbbccbdcbaccdccbddccbdccbbaadbadcaaaddbdccaacdbadcabdccaccadacddaccddacccacbbbbdbadaaccdaadccddabdabdaabadbcdcddcdadadadcdcbbbcacdaaccbdbdbbaddbbcbcbcbddbdacbccccdcadaabbacbcdacdbbcbbdcccbdbabaadaddacbbccbcdbbccddbddbccdbbaccadcacdadaabdadbdcdabaacbabbdaabbdccdabadcaccdbbccacdddbdbbbccddaadcdacdacbdbbaabdcbdaabbcdadbabddaddbabadbadcbadcbdaadcdcbdcacadcdbcaaccbabaaacacbcaabcbdccbbbcaacbccdbbcccdcdccbcdbdcbdabbccdcddaccdcbaddbacdcddcacaccdbdcacbcabaacdaacbddcadbadcdabbcbbbbccdcdabacabcddcaaacbbddadcdacaabbacdacbbbdcdcbbacdabdabcddbaadccbbaacdbaadcddabcbabbadcbdcadbcadbdcacccbcbadbcdcadadaddcccbbadcdabccaaccbacbccdadcddbbcddbddcdddccbcccdcacbaccaabcabddbcbadcddcdaccdaccccabbdacbcadbcccaccdbaacacbccacdcabcdadacbcccdddaaabbabcdbdbbabbdababdcacdbdbbdcdbbdacacdadcbcdbadddccacadcbcaadbddcdcadaabacdcacbabcddccaddbadbbaaaddcddadadbbdaadcdabcddcbdbaccaddcdbbbbddacdddadccacaaacacbdbcacdababbdbdadcbdcaacddcabdacccdcbbdaadbbaddbbbcbdcadcbbbaabbbbadbdbcdcdbbcaacabdcdacddabdaaabddcdcbbcdbdcaaaaabbcaccccabadcacadbbabdccdcccddbadbcbcdddcddbbabaabcadbaaaccaacabbdacccdaabcdacbbcabcbdacbadcadddccbbacabcaadaccabcaabbcbbcdadbacadabddbcbcbdabccccadbdcaaadabbdbdaccaddaacbcadcbbcdcadacccdabcbabbdcaddabbddbddbbcccbbccddabababccddbaabddaccaacaacdcbdddbccadbbccaaabacbddabdccacaccbabbbcbdabbbaaaabababccbbccbccbccacabdacbccdadcaddaacccadaabbdadaddbaaddbdcdabcabbdbabdcadbbdaaaacbbcadcccbcacddcdbbacdbabccdadbabddabddabcbcadbbdacdcbbadabccbbabbbcbccdcbaddbccaabacdcdccdbdbccaccdcaaadbabdaccacadcbaabdabdacabcaaabacbccbadbccbcdbbcaaddaabacbbadcacdadbdcccacdddaacdcbbabbccaabbbaccbcabbdbdbdbbadbbacddcbdcdddbdbdaadbccdabcbcaadcddadbaddaacacaaccdcaacbbdbabbdadbdbcdbaddddabcbbbddcccbcccdbdcdadddbdccadcacdbabccaccdbcddbbbcabdbccdabbdbabbdacbbdbabcdccbabdacdbdcaaccbaaabcbdcbbdadcddcbccbcdbaabdcbbbddacbdaddbccabcdbdadaaddaabbddadbcddcaaaabbddaaaccdccccbabdaaaacbcbbcaddadbdbaddaadbabaacddcbbcaddaabadaacbcbbacbbcdabcbaabcaadcbbbabbbaaacdbcbacbddbdbddddbbbddbdbcbcbccccaacbaacbacacbccdaddbaaaccaabaaccabcddabacaacbdacdadbdbaabdccdbcadcabaccadbbcbcbdbaccbacbababcbdbabdbbaaabbbabdacdbddaaacadcddadaacddabbccbacdddabddbcbabadbabcabdcadbbcabacbccacdcdaddacdcbaccabcccbaccbababbbdcaaadabcdacadabcbbbaadbdaddacadcdbbccdaccaccccbcacccaacdaccdddbaabadddacdbadaadaddcaccadcaaabadcbbdbaadbbcadddabbddbadacaabcdbdbaddcdcddaccdddacdddadcddbcdddbbdddadabdddddbbaddaddccbadcaadccbccadcabbcadadcddadccccdadbacdaabcaaccaaaddacaccaadbdacdccabbaacaacbaddcbbdddaadcabddcdbbbbbcabbdbbcbaacddccbadbbacbaaacccaaaddddadcdadbdaadccddcbbbbdabdbabbbaddddbcbddabdbdcccdabcaacadddaccaabcabababdacadcaddabaadacdccbdcbcaaaccdcbbcaacabadcadacdcbbbdaabbbdadacccbbdcacbccbdbacbcabccadaaadddabcbcdacdabdbdaaabbbddadadddcdacbcaacaacaaaaacbaaccabccbaaaaddadbddaddaadadbcaacdadbdbaababdcbbbcaddbacccdabccdcaaacdaaaaadbabbdddabbdbbcadabbacbabdccbacdcbddbabccaccaaddabdabbadcbbaaaadbbbdacbbaadabbcacdccacbcbdddbabbccddaadcdbcdaadadbbddbbaabbdbbdcdbaaadbddabddcaaababccddccdaddaadabccacadaaccdaacdbbbdcdaddcddccdcacabbcbdbaacabcacabccccabcddbaadddbbbbddddcdccabaabcaddcacccbbddaacabcdbbcbbdbbcacacccbbabdbcdcabccbaacdbbabbdcabbddabaadccdddddabacbacddddacbcddbcdcbdcbbbcdbccbcdddddcbccaadabacdcbdcbbbddaacbcaccbccccbbdadcdccbbadbadcacaaacabddacbdddbcadbacdaccbdbdcbbbadabadcdbdadcbcbabdbadbbacaccbcbaadddcccbaadbbdbcccbadbacaabcdacaddcaddabbdaaaabcbddadccccbdddcccacaacbcadabaaabdaaabcbcaddccbcbcdcccdaabbcdacbabbabaabdadbbcbbcbbdcbadbcccacccabcdcbcdcaaababbdccabccadddcbdbbbcbcccdaccdadabddabadcccdbcddaccdcaaacbadbddbccdddcacbcabccadbbcacabcaaaaabcbcccbcbbababcbabdbbcdabcbddbccacaadbdcccbbaabbcbacbcbabbcccabdaccbaacddcabdccddcbccadcdbdccdadaadaccbcabbdddbabdabcaaadcaaacabadcacccbcddcacbabdbadddadbdbabdcdabaddcbabbbcdbbcabbcccabbdcdbbadbbcacadccabdcabaaccddbbdbbdccacbabcaabcbaaaaacacdbcccdacdddcddcbdaddabcbbccdacabadcaabdabdadddddbdabdcdaaadcabbabbdbabcadaababddccbaaadcaddbbadbcbacbcbcbbccbbcdacaccccbddbaccbacadcbaabaabbddbcddbdbcacaadbdabdaddabaaadacbabcadacabcbaddccbaadbcadcadbcddbdccbdddcadabcacabddbacacbbcbadacdbdbcbcbdddbcdbaaddbacaacdcaaccadbabddbbbbacddcdbdabacaaddcbbdddbadcbadbccdbdcbabbdcadddcbbbaadadddccadcdbbabcbbbbbbbbccdaaccdcddacabcccbdaaccccaadcbcdbdaabacabaacaaacdabbddbccbbaacbbaccbcaabcaabaddaccbbccdccadabcdaacbacbcbdbcbcadcdbdddccdaadbddcbdabcdccaadadccccbbaaccbcbaabaddacdbaaacbacbbaabbcbacdcabdcadaababdcbdaaadadadabcbdaadddcddadbcbcccacadaadcbaddccbcacaddaabbddbdccacacadabccabbacbadacdcaadccbdcdcbacaddcbbcaddaadbdaccddbcabadcdadaadabbcbabaaabdbcbccccacbcbcbcbdaaaccbbdddccbdbdddbabcaabcbcdcdcbbabacdaadbadbcbcabcaccadddbdadbbdbcbaccdaabbcdabbccccdaaddcdcdccdadcdabcbccbdcddbbcabdbddbccaadbdddbdccdcbbdcdbcbcdbacdbaaaacdcacbaadacdaaaadcdcbdcbcbcbbdadcabccaadaaccadcccdbbcdbaccaadbaaababbddacbcacddccdbabbbbbcacadaabbcabccabaaaddaaacdaaacacbbbcdadbbddccbddbbbadbbbaabbcdcbdddacddcabacbacbaddbdcabacccaddcbcaababbbdbbdbdabccdbcaddabccbaccaacbcabdbaddcbcbbaaddcccaaadcdbbcccdbbccdbcdcdcdaadcabbdcbbcdddccadabaabcacadaddbdcddddacddabacdddcdbbcbbbdccdaabbabbcbbcaadaddbbcaadcddbabbadadbaadddabcacbddadccacacbbdbadcccabcbdbcddccdccbbbcbcccbdbadbbcbbacabbadbccdccbdccacbcbcbbcacbbaccaabccdbccadabaacacddbcccdbbdaabcacaaacbcccbbccbaaacdbcbadddabbbadcbbaaacabdcabdcaccdbcadaddbbcabccbadbcdbdddcacdbcdcdcadcdccabdadabbdcabbddccdbdabdabbccaabcaccacddcbcaadbacbdbbaddcbbdcbbbaacdadcccdabbbcbcbcacbacbbacacbaabcabbbcbbbacddbabaaccdabbdcacccbcdbcdacdddbbaccaadcadcbacdbdcbdbaaddbddbcccdbcdaccaadcaacccadbcbcacacadaccbaabdbdbabdabaadbdabdbbabacadddccaaadddbbbbbcddcbdcaddaadabbcabadcccabcbbdbabcccbdcaccacbacabbcbdcbcadccabcdccdbdcbbbbccacdbcdaaaacacabddadbbcddcbdaccdbccdcbdbbcadabbdccdcbdbbababdaacbcbbadbdaddaaccbdabaddbccabbcbcbbcacdcddbcbccabaaccacdcdbdddaabdbcbdacbcbcddddacbacbabbcaacbadbadddbbbbabdddcbbcdcadddccddbdcaddabdbccabbbbbdbbcbbbaacdcbbcdcbbcadabacabaacadaadbcdcdabbdadacbbcbbaddbaddddbccacbdbaccbcaddcadadddaaacbdcdbcbaadadbdadbbcaacbcbcabbcaaacabadcacbdaccdcccbdbbccccdccccaddbbadbcaddbdcccaacacddabcadadbabadbdccccdaacddbdabdcdaccbabbbdbcbacbdcbcdcddbdcaadbdaacbabcbbdcbcccadbbaccadaacbddbbcaaadcdaabbbcccdbcacdaddccbcabadddccacdcbacacbbcbccacdcbcdcbdddadacdcbadbbdbcabcdcaddcbacddadbddacbbddbbdcacacccdbabadcbddbbabdbddabbacbaadbcddcccccababbcddbabaddbcabbdbddbbbcbddccdacabdccbbcddddbdabaadcdcbcacbbbbbaadaddddabbdadddabbdaacacaccdaaaacabacdcdbaccccbbcbbbdbcadbcaabcabddbcccacdbacbaacccdddccadcdbcdccbbddbabcacbcbaacaabccdcabbcbaadccadbddbbbbacbaccbadbcdaabcbcdacbdbbcbacdbcabdadbdbbbaccbaacacadabbcdddcdacccaddbbcddbadbdacaabcdcdddaccdacccdbdcddcbbaddcdabbbccddbbbbaccddbadabccaccbbbddddbbcdaacbdacacaaacaccbbabcbcbdbacccbdbbaadcccbdabbcdcccadbcdcababbddcdacbcddbbccddbabaccddccbcdcdccbbabcdaadaaacaaccbccccabcbdbdadcaabdadbcdbcbcbacacabbcaccbbbcdabaccaacadcacaabcddcbcabaabbbdbcaacbcbbbcbbabccddbacddcadbcadcadbacbddcdbcbabbcccbbccdcbcaccdadcbdbddbdacababdabddcbadadbbdcccddbacdcbbaacddccdcccadcadcdcccbdadabdaadadababbcadbbddbcbbcaaaaacdaabddbabdabbdadbaaacbcbaccbdbadadccacbccbdaacaaccaddddbbcaddbbcdbcbcbdccaacdcbadbaabcbabdabbcdacaadbddadbdabadcbacaccacccccdaccabcadddbbadbdddacdbaaabbcabbbcbaccdcbbabbcdcdbbaabadccbdbaacdaabaadcbcdbbdcdcacbbacdbabcbbaadbcbcabadbadcbaccdcbccdacdaabbbbcdcbdcaadbbdbddbcccbdbaaabdddabacdccbcacccdabcdbbccabbdaaddbdcdacadcccdbaccddddccbabddcbcadddcaadddcabcbdbddbacadbcbccbabcccbccaaacbdddcdcbbcbabbbadaaddabdbacccdcabdcabdcbbadacaccaaabcbddcaaddcabdadcdccbcacadaacbbddaaaacaaaabbdcbabadadbdbcbdcadddabbbbdacdcdbabacababdabdcbbdccadbcbcacbbbddcdabaababddccacadbcddbbdabcacdcadabaaaddbdaadbbbdaaaaabbdadcdaabacbbabbbbbbabacdccaccccccaababbdbadbacbacaabbcdbcacbcadcbbaabaadcbdcbbadcdcddbbcdcdcabdcddaccdbaddbccdbdbaddcadbadcacbacbdbddccadcaadcbbbcdaacabacbcbaaddcbdacbbdbdcbdbadbdbcbcdddcdbbccbcaddaabcddaadbadcddbdddbaccbdcdcddbdbccaabdbddbbcacdbacdbdcdbadcaaacccbddbddbbacabdbadacdbcaaddddcddbdcacbcacdbbbaccbbbadcbdddaaababacdaaaadddadbdccccadaabbcaaabbabdbdcbcddbbddcadbbacbcbcbaaccbdccddadbadbdbbabddccbbddbbbdbbdcdbbabbadcdbbaadcabcbcbdcbbdababdaadadcccdcdccccababccbcdadadbaaadcbaccaccbcddbddddadcaaccccbccbbbdbcacdaadbacdbdbbbbcddbdcdcacdcadababacdbbdbbacbacccbdbdcaaddacdcdaaacdacaabcaabadddcbaaaaaccccabacccbbbccbccaadbabcccadbdcadbaddbcdcaadbcbdcdacddabbbdaaabcabcdcdbdccbaacbdbaaaaababcbbccdbacbccbccddbcbbdbaabbadbcdbccacbbccaaddadbbaaaadaccbccdcaccdabdbdbbccbaadabdadbbadbcacbdbbbcbddddbcdbbacddbcccbcbabccbcbddadababbcdabdcbbbcbcaddbbdcadcddbdbcbbdccdddbdaabbccdacbcdcccdacddcbadadacdbdacaaccadbcdbabadbcaababadabbabbdcabbbbdadbcbbdddacbcaaaaccdaddcacaacccadbaaadaaabbabcdccbdadbccdadcacbcbadcbabaadddaaabbabadcbaddccccbacdbdcadddaadadacbcbccabbbcbaddcdadaccadacbbccdbbdaacbdbbabbcdabdabcdcaaddabcabcdaadbbcababbdaacaabddabdbbbcbcadbbbcdbaaacdadcbadbbdddccbbbdcbdcdaaccdadbdcbcdacbcaaccccdaabbacbbbbbbdbddbdadabbdcbbcddacdbabbabbbdcbbbcdbddcbaaabcbdccabdcbddbaaddcbbdabdabccbbddbdccadadabaabdcbbdbbcdadddaabacaabccadcbababccbdcdcccdcbaabdbbbbacdcbaabcdcabdbadbdcdcddabbdaadbddacccabaadcaaaaadbbaddabddaddbacdbbbcdcabbadbdcccbddcccccdcddacccccaabdbaadcdccbabcdaacdbaacddbcbaadbaccdcdddacccaabdcacdbaacdcdcbcdbaccadbacbdcbcccacaacdabbaccdaaabaddabadabcbaadbdbdabaacaacbdabccbabacccaaddabcbddcacbccddcbabcbbbddbbabadbaacbbbddbbbbabadabcbabcaacacddbdcbbacbdcacbdadddbadddbdbbbdaacbcdadadbcdddaabbcccbbcdbdbcddbbdccbbccaacdbbbacbcdbdacadcdaaaabdbabdbadadddbbacdcdaaaccdbbcacddcddbabcdccacdbbcccabacabdcabdbaccbabdcdccbdcbddcbcdddcbcabbbadccacddbaddabcdbcacbabababcdddbabadacdbabaccccbabbcbbbabdbbdcbbabcbddbcbdcadbcbbbaacacabadabdcbacacbbdabcdccdaddbadaabccdbaaababbbccaacccccbbadccaaadbbdcdabbcaabcdcbabddacaacbbaacbabaaacadbacccdcaddbcccdbadbddcdbcbbabdccccbddbcbbcdcbbbcacdacccdbcaddaacdbccbbdbdbcaabadbbdcbcdddddadccbcbccaababdcdcbcccaabacdbdcacbcccacabcbdadcaadcabcdddaaccaccccbbcabaacdababdadbcdbbabbbabcabbbabaadcaaacdabdaaacbaddacdbaaacbaacbadbdabbdababacabdbaaaddbdddcbcbcaabccdaadddabcbcabbcbaabacdabacdacbccbbabddabdadadcacbbbbadbacadadcdbcaabaacbcdbabddddacadbabdbadbabbdbdbdbaccdaabadaadcdcaadbccdccbabaddcbcacdbbcbdabbcdacbdaabcadadccabbaccddccdadcdacadccbbbaddacbbadbdbabcbaddbccbacabccdcbdacbbbdcadacbbbbbbddbbddcaddabbcabbcbccabdbadabbcabdaacbabbabbccbbcabdcacdccdcddbcdadcbdaadcdaaacdabccaccdddcbaaacabdabcdadbbdcaacadacaaddaabcdbbccbdbbdbacabdcbbddbadcdcbbbabcaadbadaadccbcccbbcbbccdababbacaabdbbdcbccdcdadccadaadbbdadddadcdaaaacdacdcbabcbccadcbdcbdccddaabbbaacaccccadcaccccdddadabcadccccadcbcdbcdbdcbbadacdbacacdbbdbbbbadcdacddcaacdadccdcadaddcddcdabccbbadbcacdddabddcbaabdadadbabacaabadaaccbdabdbcccabddbadbacaadaddcaabacbbcccdaacddabbaabdabcacabcbbbcacdbdccaaabaabbacadaaadabdbadabdcbbcdadcdaacdcaadbcabadadbadbaaccaaaadcdccaadccbbdabccacaccccdacbccbdbacbabbcbcbcdcbcabbadbabbaacbbadccbcbcadacccacabdaadadbcacbbabddbbacdadccadbccbcacdbaccbabacccaaddbaadcccccabbdbddabcbabbdadacbbdbbbcccaacccdbadacabadabdaadadadcacbdaaddcccdacdbbdcbddaabcdbddddbbbdaccddbddabbddcdcbbdddadcbbddbadacacbdcccbadcbbdcbbcbabddcaddccadbccccbcbbcaadccbbabcbdcbaddbdbcbcddcadcbdbaadaaadadadbaadddbacacbcccbcccdbbdddbaccabcacccaddccdcdcdabbdaadcdadcdcbaadccaaddcbadbbbdbcacdcbcdbbbdabcccddacddcaaaaacdbbcbcbcbaaadcbdadcdccbdbcacaaddbddabadccbdcbbbabaabbdccaabdacabccbdbdccabadbcddcbbacbbabbbbdabdcbcadcdbdaccaacdcbcbdaccadcccdbacbdadccbabadcdcbdadccadaacaddbbacbbcadbbbdbcdcacbbddaddabbcdccbddbddcdbbbdabcdcbabdcaccccdbadaadcdcbbacbcbabcdcbddaadccacaaadcacdababbbcacaabbcaadbdaabddadddcadccabadadcdadaaaacbbdacabbabadabadbbbdbbdbdaddaddacbdcdaddabcdadbaabcdbaadaddcddabdccccadbddbcbcbcdbadbdbaabcabdccddddbcdbdbccdcdcaccaadcbadcacbacbdadcbccabddccdaabdcbadbbdcaddababacbaddcdccdbbdbccabbabadabbdccbcadacacddaddbcadacbaccddbbbbadcacccadccabaddaddddadcacbcddabbcaacbbadccbcbcbddddbabcbbabddcabaccccabbdbbbbccbdcbcaddbbadcbcbaccdddaddbdcbcbcabaacacaaccccbbdbdccbdbbbbcbbdcdacdcddaaacdbddadbabccdddadabccccababcaccdaaddaadbbadadcdaacaddcbdbbdaaccadababdaaaddccbabddcddadbbaacadcdbaabaddcbcdccccccbddcaacdcaccadabcdddbddcdabdcddbdacdcaabdbbbadcbcbbdbdbaddabbdbbcccdcbcdcdaacdaabdbabcdaabbaabcabdcdbbaabcbabbbdccaabadbbcbdadaddcddaddbdacacdddbbbaabdddcbcdaaaadcbaadccddbccbabdccabbbcbcccbbcaaaaddadcacbaaccdacccdbddbbdcbaadbdbaadbbababcbcbcadbbdbcabbbddadacccbaabacbdbbaadbadacdcdcdccdacbdaaadbbacbddbadaadbbbcdadddbbbadbcbddcaddbcdcdbdbdadcbdbabacdbccbcbbbcccdddcaabbadadcdbddcadabacdabacccddbdbccacacdbbbccdbacbcdccdacccbbdbcdadcddcdcbabbdabdacaacbdbbacdccbaaaaaddbacabadddbdbdaccdcbcbbdbbacdbdabbccabbbbdcdcdcdaabcbdbddbddcaaaacbaadcdcbdccbdcacdccdbcdaacabcdcdbdacadabccabcdcbcdbdbcbbccbabdbccdcacbdcaacbccabbcbdbcadddaabacbbbddbacbbccdaadabbabbccbbbcdadcbddabdbccbdcdbcdcbcbdabdccddbabaabbadbccbaabaabdcaabbcbaddbddabbbbbacbdddcaccbbbcabbcbcbcdaacacabadaaddbbcbcccacdcbdbdcddaddaabbddbdabcbaaccbabbcaabdcacabbdadddcaabbdadadcbbbabbcadbbdabbbabbdcddcacadbcdbdadcadbaadadabdacddddcabdbdbbacbaadccbdadcbadaddabbaadbddddbdabcbcdbdddbdcbacabdddaddcbcbcdbccaabacdbababbcdbaaccdbcaabcadbbbdaccbbdcbbaaabbccadbbaacddddbbaadcbabbccdacabadcbabbcddacaccdaaabaaadcbbbadadaaadbcadcaababbaaccbdaabcacdbabdabcabbbaacacbddabbbbdbabddbbaabbcabbaccbccdaacbcbaccdaaadcbaaadbbaaccabcdccdaacdcddadbbccacddbabccdddbcabcacaddaddbababadcbcabdddbabacddcaccabaabbabdcbdacacbdcadacbbadbdbbdbdaadabaddbcadbacccdaccaccaccbcacabccdabcabdddcbcaddadbadabdccbcdadbcdcaacbbcbdbbbaddbdccbaaabdbdabacaacdbbddbbcabddcdbabbccbbabaabbbbacaccbcaabbbadcbdbddbdaacddbdaccdabbccccbaacaddcbbacbbcbaaddcdbdcdbaadddbbccbdcdadadacddbbbaaadddbbdbddbadcddbaabaadbcdcbabcadcdbcabdabacdcadbdaadbbbaaddcbbcdbddddcbdacdbcbcbbcdcddbabccaddbacdddadbbadaddcaaadddadbaacdcabaadbbcdadadbadbccdbdbbcadddbbcccadadcccdcbaacdbddbbcddadcdbbdacccacadcaaddbcdaaacbcacadaabdadbabacdddbadccbddddccbccbbabcbcbdccdadaabbccbcddacdbaaccbddbdcddaaacdddbcdccabcdadddcabcdddbbdccaddddcabdcccaacbabaacbbdddbbbaaabacbabaaddaddaddaccbaaababdcbccdacbcaaaadcdcdcddbbaaddccddabaaccbdaaaabdabdaaadadacacccbcbddbbbdcddabbacadcdbbbdaddddcabdaddcddbddbcddcdccddbdadccbbbcaddcbacbadbbdcdaacbdcaaabadddaaaabadabdbbcdbddbaabacaddccaaabcabcbccaaaacbabbccaabcbdabdbdacbdabadacbadbcbcdbbadabddadcdbbbadaabbbbcaadcdbdcaccbadddbcddddababdadbcccdcbaaaadccdbdcaaddaccdabddccbcdbbadbcadcbccadbaaadbcdcdbadccbbadbbdccbbacadbdddbbadbaabbcddcddbcbdbaddddcdcccdbcdcbacbbdabdddbccbbbdcaabbdcdbaaacbcbaccababbabbadddcdbdddbbcbcaaadadaccbbdcacbcccdbbdbddddabcbacaddaacacdbbbaaadcadddddbcbdcbadadbbbcbdbaaaabcbabcaacbaadadbcccbcbbaccabbabdcddcbccbabaadacbaddbcbaacccdcdccacbacacbbddaadaabaacdbdcbdcbaacdcdbbcdabacbccaccddaadadcacccaaccbcdbdaaadadbbaabbaabaaadadbccbacccdbccbdcacadcccabaadddbdacdcabcbccadcbabbdadabcaccbadccabbbadcbddcdcdbcdbabcbaabbacbdcbddacabdccccbbdcadddadcaaabcbadaabbddaacddbddbacdddadddcccdcadaccabdbaadccbacdcdbacdbdbaadccddbcbbcdabbdcdbdabdcabbddcacdadbabaabdcabacadacdacbdddcddbcdbcacbbdabdbbabbdabbcbbdddcbdbaadccdabddbcadadaacbacbcdaaabcabcbdaabbacddbdababbcadbcbddacadddabcbdabcdbbcaddcbbabbcacbcbcccddacacccbabbbdcddbbcbbcdbaabdaddcadccaaabacbccccccbccdabbcdacdcadbbdaddacdccadcccbcbdcbddcbaaaddcdbddcdbbccabcacdaaaccbacbccbbcdabbcccbdaabbcdddcdbaccaaabcbdadccadbacaddccbbbcdbdcacdcbdbcccabdcbadaaccddadcccbabbbcbacabcbabddbbbbaaadddcccacdccdcddbdaaaddabbabbacabdabadaadcaacdbaccbcdadccbaabcdcdbcabbabbbbdcaddaaaccdaaddbdcbabbcadcacacadaabbdbbbccdcbdcdcacdbacdadccbaddddaddcaacbacadababdcdcccaacaddbcadcabbbbcbddbbbdcdcadcbacdcabccdbacbacddacdacaaddccacaacababddbbcccbdbacddbbcaabdadcdbbcbbacdcbcdddbbcacccbababcddabcaabbaaaccbdbaabacbcbacbacabbababcbcabbccdaacdbdcdbdcadcbcccbdaaadbbdbadddbdbccccbaddcdbcdacbdabdbaaadabccadcbcbdcdadabbaaddbdcdbaadaddadacccbcbaaaacdcccdbdababbbddccbaadabbccbcdbdbacabcabcdccbaccbadddbcaadcbcbcbbbdabcdddcacdaadacbcadcdcbcadbadccdadcadbcbabdcadbcababacdabcabbcbcbbadcabdbbbaddbbabcbacdcdadadabccbbdddaabbadabcdccdbdaccdbddabdbabbadbdaacadbdaabadcbdabbadaccabddaabddbbadccaddbcdaacdbdbddcabdbccdbdbadcbdbddacbdccbbbcacdcacbcbadabacbcacdbadabcbcdcacdbddabbbcaacacbadabddbaaacbaaadcbbddbcabaadbacdacdddadbdbabaccdbbccdacabdccdbbbdabccdcacadbdbbdbcdbbadacdbbcaccdbdbdbabddbaccdabccbbcababdbccaccaddcdbcbdcacbacbdbaabbadabcbbcaddabbbdbcbabccbcadbdcbccddddcbacabcbabbbcbcacaccbbcbdbbbdbcdbddddccbaacadbbcdaacbdccabdabaddbbccaaabdbdcaadacdadcbbddaacbbcacbabddbbcbacccbbcbaabdcccdadcbabddaabcdddaabdacabacdabdbdaacaddccaddbbaaaccbabadcbcbcaababdbccadcdabaabaccbbbdccaddccbadcccbddaabacacadbbdcadadccbbccdbbababbaacddcccabdccabdcaaacbcbbdbddbdaddbbabcbbaadacbbcdddadcbdbbcbcccaccbcdcdaccaaacaadccddababddbcbcdbdbaaaadbbdbacbdbaccdbcdbcdadcbadacdbabbcdadbadbcabbbbacccddbbddbadbadcbacbbcddcbdcacabcbccacacdbcbccdccacadbdcdbcbbabadbdbacdccaabbbdacddcabcddaacdacdcbcbbcadababdaddcbabdbccabdaccbbbdcbdcdccabcbbbbbbbcccdcaabbabbaddaccacadaadacadaaddbdddccbdcaccacbdcadacbdacddbbdddbadcbbcdbddccadcaaabccbbbabcaddbaddbcdaabdbbdbbbdcbadcabcdcbcdabccadddcbdbacddabcabbdcacbbdcadddbadcacbdbbddadaacddbaabcdaadcacaddbbbaaaabcdddaccabbbadccbdabcaabdcabadadaaaaaddcccdadacaaacbaacddaccabcccbadcadadbcadcddaaddbccccabccbdcaabaabbddbcaadacdccdaadadbadbcacbcaadcdcadabadddccdbbdcacacacbdadaadccbddbbddcadccadaaaadaacddccadabdadbbbadbcdaaaaccccdcbcccccbacddcccabcbcabbdcbabccacdcbbcaaaadaadbbadbdacccdbacacbbaccabbadcbabbddadadccaaddbacbabababdbadadadaabbbdcbbacadbbbdbaacababccbcccbbdbdbbdacbadabbdcdccbaddaccbadabbccbbcdbbccaccaccdbdabadbaadaadabbbbabacdadccaacbaadcbcadacccadaabbadcccacaababdbabaddbabacacacdbbbbbabcaadaabcdbdbaacaaccdccacccdaabdddbdadadccbddaaacbcbadabcbccdbbaacacccdabadcacbbbdabcbacabaccdcaabddbcdbdbabaacbcadbaddccaadbbdbabacaacbabcbdbbadabcabadbbcbabcaadcbacbccdccccacdbadababdcdcdbddaabcccacbbaddadcbdbccacbcadaabaddabacddbbaacaaaabdaddaacdcadbbbcadbaccaddbbbadadacddbcddabbbdabcddaccbbcaaddbaaccbccbdaacadcdcccbcbcbababadddbbcbddbdbcdccaabdccdacaccbbaadadacadddcaadacddcacbdbbcbdaddacdacddcaacccbbcaadadcadcccbddccccdacadabbcdabbcdbdacaddacaddcbcabbbdcdacdbaddbadddddcbacbcbaadcdaccdabdcddccccaaddaabcccdbddbdaadaaadbacbcdbdccdcaadaddadcdccdaddcccadcbbccdaaadbbdbbbabcdccbdabacdadddddcdbbbcdcabcdcdadcdbdbbcdddadabaacaacaccdaacadabbadaabbcdddbcbbcabdcbaabbacccbccdcbbacbbadbccdbcababbbdaacbcbaadcadbbcabaadcbabbcdabcdcbbaccbcdaadbababadacccabcbdccddcbcbbbbdcaccdabdcccaadbcbcabbbdbaadadcccccbbddddcacbccbcccddccbacbcaabcabdbaaabcdaddacbabcbdccdcbababccbaddcaacddbadadaaddbbbadcabbacbaddabbdcbcbacbbcdcadcbabbaabbdadabbcbcaadcbaacdcbcbccdcdbabdccddcaacdcbbabcddcdbdacbbccbcadaabadabcbcccdcccbcdcccbadddcaaabcbbaadccdacbccabadadadccbbcbbccdbccabaaaaaddbcabbdbadbccccadbcbbbcbdaabbaabadaacbcbccaacacbaaccbbccacacadaaadcbccaadcbddbbcbdaadabccdadaaccbccabbaabbbdabcaadaacdbabbbccddbdacbcdcacabbaccddcbccccdbddddaaccbabbbaccccabddacddacbbccbaacbbacddacaaddbdccbcdbcadbdbaadccbddbcbcbdccdddbddcddccdacaaddbbbadbcabdaddcacacdcdcdcbcddacacdbcaddbbaddadabbddcbdabcdaaccabaaddbbddaabbbbcacdcaddbbbcacddaacadbadbcbbdadbbccaababaacdbdccbdabbcaccdbbcabcdcbadaabbcbccccabdbdadadddbddcbaaddcbcbcadacadddbdbddaabcddbadabaabcadbdcbcdaadabccacdbbcddbdbaaddabbcccaabdacbbabbacdcaaccbacbcaabcabcbabaabddcadbbadddbabdbdbddabdddabcbcaaababdabdadcbdadcabdddbcdcdcbadcbcddcaaaddbdcbbaabacbcdbcaddbaadabcbaabbbdaccaaacaaacacbcbadddcbdcacdaccdbcddcbbabadbcabcccccadcbdbbdcdabacabdcbbbbabaddbcdbacbabdacbcbddacdbacbdbacbcdcadddcccabbcaccdcbacadbcabbacddadcbaccdbaccdbaaadbdacbabdcdabcabadbdccdadabccbabbbdcbcbbbcbccdabdbdcacaaadadbabbdbdbbbbabadabdabdabdadbbdcbbdddcdabdadaadacabcdcdacbdddbadcabbbcdccccbbabbbaddbaadaaccbbccdccbbabacdbcadabccdcbaabbdacaabcabccdacaadbcbabccadbabdbcaaaabacbadbbadcdabbdadcccaababbbddbdbdddadbddcabbdcddddcddcdcadbccdddbcdbbdbbacbaaabcbddaddbbdddabdbbddbbcbcddaaaacbccbbbbdaddabaaacdabdabcdaabcdcaadaabdacdcdaaccaacaabacbcddbadcddbddcdacaaadbbaddcbdbdbaadbddddadabcacddbcccbbaabaadcbdbdadcbdbdcbcdacbdcdaacacaadbbbddbaadcbbbdcbcaccabdadccbbddaacabadbdaddcdacbdcdabbabcabddbdbadaccaababcbbbacadddbcadabbbddcbacdcddbadbdbacbbddcaccbaacaddcbdcdadbdbaacabdaaccccdcabcbcdcbccabccbdddddadcdacccccbdcabcadbcbaddcdbbbcbcadcdbbbdcabddabcccabcbabcaaabdaadcbbddbabdcabacbcbddacabddaaddaaabbcbcdaadaabbabcdaccdcbcdcadabccbbdabdbccccbaccddcbabbddcaacdddcbbdbabcbbbacadbaacddbcdbcdccbdbcbbcbaddabbccaaddddaccbbbacabbddadccccbbacddabacdaddacddcadccadacaccbdaccadbdbbaccdbaadbcccaabdbdbdbdcabadccccbbbbccddadadcbabcbcbadcbcccbddcbbbcbacbcdabccbbbddabcbcccbacadbacbadcddccdcbbaabcddaaaaddadddbacccddbaddccccccacbbabddbbadcdbdcbdaaddbccabcddabbabadddddadddbcdadabbbbddbdcbdabbcbcdbcddadabcdddadccccacabaacabdadadbcaaccbcbcdcaadabcbcbdcddddacdbbcaaabddaacccdaaddcacbbbcddbaabdadbcbcbdbcdbbbdbdabcbbccadcdccaabddcbadbcabddcbdddccbddbdccbbdaadbadbcbbddbddccbadacdcdaaabddbcbbdddbddcdadddcacdbacacbdbcdcbcccbcbcadbdaaadcbddbadbdabbdacdbabbabacbddbcaaddababacacdbacadbbcccbdaccabdaaadcbcadaabcdbbdcbddcbdbccadcdacbbbbdbbddbaadadbabaaabbdddaccbaacdcdabbcadabacddaabdadcddccaccacbaaccacbaabdaacacdddbddccddcdcadbaddcbddacddcccbabacdbcbdddbaccdadcadbdacdddcdbbadadcadcbcabaccdabacaaabbaabbdbabddabdcacccbdbbadcabdcbddbaddcdccaaabbdcacccccaaaccdbbbdbccababaaccbdcbbbddccadbcacaacaabbaccadaaadbcbcaccdbdbdddbcbaacdabcaddabddcdbcbaacaabcabdcddccaadcdaddcdaddbacdaaaacbcacababcbcdbdabcccaacdcbcabcdddcacadcdbbbdbbcdcaabbabcdacabccdbcaaaddabadddcdbdcdbbabdadadcadaccbcbbbcdabbadcdbabbbdddaddaddacdbbbaabaddbcccaccbadbbccbdacadcbadccdbaccbdddddcabcbaacdacadaacddcacbaacaacabaadbcabccacabcccbcbcbdadbbcacdadcdccbaccabaabdadcbbddbabacbcbcdcbacdadabcdabddcdcdcaacabdccdadbdabdacbdbaacbcdabbadbacacbbdbdddadacababcabaddcccdabdaabcaabbcdacdaddabaaddbbbacaddbcddcabdabbaaaddabdcabcbdaabbcbbbdbadcbabaaaaabbdcadadcccababbbbadbaaadabbcbdbdddcadcddbdadacbcbccadbaacbbaccacbdddcdbabbadaadcdccbbdaccdbaaddacddcababcdbcabdbadddacdbdaacdddaabbccbbdddddbcbdbdacacdaadabaaacacdcbdbcccdbaaabcaacbbcbcdbcbabcdddaababcdbabdbdccbacbccbaabcabcddbcdabcbbacdcdbbdcdcdcbabcaacbbbccbabbddbacaadbaadacacbccccbdcdadbcacaabccabcadbddcaccbadcdbacacbaaddcbbdddddcaaccdddbdababdbbcbdbbcaadacbcbcaaacbabcabddcccbcabcccaadaaabbbbdbcbadbcddcadabaabdcabbcccdddcddbdaccbdaadcadccddddabdaccdbacddaacbdccbcccbaaadbdaddbccdcddcbbbbdbaddcdbbdcccbdbadbaacbbadaaddaacbaaadacbdaabddbccacaaadbcdccddcbbaabddabbdddaddabbbcdbabdcddcbcdcccabacddbabdadadcdbdaddccdbaadbdcbdbdcccdbccacccdcddbbdcbccacdabbcaabcabdabdbcaddcbcddcbdbdacbadcbbddabacacbcaccadcdbcdcacacbaadbabacdabdabbbcbcccbcbcdacabaaacdacdabbdadacadccbaddbabacdcbbcdbbbabadcccdbaddddacbbcdabbdbdddabdcbcddddbabccdaababbbaddbddcaaccaabcabdaaccdbcaaaccadcbdcaadabacadabcbacbcbcaadcccddbbdbaacbadabacabcdaabaaaadbacdccababadddbccbacccbcccbbabddcccacdaabcddcdbbccbdcdbdcbcdbdbacddcbcacddcbcdaabaddaccdbdabcdaaccbcddbacbbbbbaaacbcdaaadbadbbdaadddcbacdcdcbdbcbadaccabcdcabbabacddadaddadcbcabbbacadabacbdccbcadbcdddbadabdcbbbcbadccaabbdddbdcddadcbacaddadcbddacbdbdaacaddcdaaadbdcbbdbbcbcdaccadcbbcdbabccaaddadabcaabdabcbbcdacdddbbccacacaabacbbdbcdddcbaccabbbbcddcbadcaccabdaadddcdaababbaadccacddbdbddabcdcdacccccdadacdccdcadcacbadbddccbdadcbbcbaacbacdbccaddaacdcbbabccdabddadcddcccbbadabbcdccaaacddcdbbcdaadcbccaabcdaabcdadddccbbddbcbcbcbbbdcacbdcccbdcaabbacdabbcdabbdcdccbcadaacabdbccdbdcdadadbbcdcadaacaabcbcacbacadaacadccadbbcdadcbdadcadaabbcbdaadaddacdaddbaadbdbcbdbcbbcdcdcdacbcdaaddacadcaccdbaddbacbccbddcacdbdaadbbccdcbaaddacdbdccbdacabbabbdcdaadccbacaadaddaacdbaddcbbcababbdbaaaadbadaccbdacdabcaccbcadadccdbcaccbbbbddccdacbbabcacacbababacdcdbcbbdabaaabdbbcaabdccaadcadcbcadacbabccbdcdddacbdbacddadcdcbcabcbcaaddbcabaabbbdacbcaccbcdbddabbabdcbccbbaabbddacbaacbadabddabbaadbddbaadcbcaddcccaadbcdaadcddaaccdbcbbbdaccacdccddcbbdaacbcbdaacddccbcccdbdccabcdcbbdcddabacccbdbbacacdbbcacadcabbdccdacadbddabcbadcddccdbaaccacbccdccabbdcbddbdcabbabbdcadddbdddadcaacdaddbccdadabcacbbccdccccbbdaaabdcdaacdaaccdacacccdbabbbbddbcaacadcacaaaacadabbacaddbbbbdcdcdabcaccacdbdbabdbccbaccbadddccadadadbaadaacdbcadabcaccabadbbadccbcaacbcababcaccacabcbbcccbcbadbdabbacaaabdaadccaadabdcaccbdcabdaadabadaaaccdccabaabaacdbbdcbddcdcadccbddaabcadcaaaacdcacbabbddbdcbacbdcadbacbbcbdcdaadcccacbdaacaddcbdababbcacabdbaaacdbbaaaccbabccddbbbabbcaabdbdcadbddaabcbaaaccccacbbcbbbcccdbabcacddaabddccbdadcbbdbacbdbaccbddbdbcdcbacbcbacdddaaabbddcbccdbbcccdbabccaadccaddcddbdbcacbdcacdbdaabccdadbdddbadaacbdbcaacaddcddddadcdcbbcbadcdabccddbdbbcbdcdccbadbabcbdbdcdbacacbccadcddbdcbccdcccddacddadacdbaadacdabbabcdbadbcbbacccdbcbccbacdbaaabdcdcaaccddccacaddbcdaaccbbdcdbccbdcabcddcbdccdaaadaacbadadbdcdddacbbbaccbcdbbbdaaadbcbddbadbdcbcddbabbaccdbbdabccbbdcacaaccdcbcaddacbbaaacdbcddbaaaabdbcdabbdcdcbbbbddacbcbddbcbcabbdcbcdcbababbdaaabdaaacacdddbabccdbbbbaddbcabbccbcbccdbbcdcdbaacdccbdaabbacbcddccdbdcdbcaaddcbbcbccddacdabdbbcbcadccddcbbcbbbcacdddaaaddbbadbaccdddaadbbcdaddcbcabaaabcccddcddcaaaacbddbdcacadbbcdadcdcdbcbbacbdbcdcbcbabdddccadcbdbbdcacdddbcaaadacabacbdadcbbbccabccadccadcaadcbcabaadabcbdddbccddaabdabbbbdcdbabdacdcdaacbadaadacdbbddaddcbbddcbabcaabbdaabcbbbcbcccadbacdadacbdbdddaaaccaacdadbcbdbdcddccdddbcbdddaabcdbabcbddaabcdbdabbddcadbdcddabcdbaddaaacbddccdbadbcccbdabdddadcbdbccdaabdcaacadaabadbccdbbaadacbaaadcabbbaccbbdaababbdbdbdbacdabcaacdabbbbbabbbaaacaacbdacadbddbaadacddaacbdadcbbddabdccddaccbaaacadadbcbabaccbdacddcdaaabcbbacbbabccaaaadacbabbaaacacdacbbcadccbbccccdaabbbbdcacdbbabccbbbcbadcbaccbbcccbadccbabadabbadacacdacdaabbcacbdacbdabdbcbcddbbacabaddcdcbbccbbdacbbaaabccdcadcacdabacdadcdcaacdbddcdbbcbbbabdacadbdadabccbbbdcbbabaaabcbdbdbdcddaacabbacccbccddbabaabaacbbbbcbaabacaaddbcddbcdcddcaaccccabbbadadbccbbcbadbcababdabddaccdacddbdccdaadbbcabcaacbaccddbbadcdacddbdaaadbdacbabbcabccdcddbddbdbbadaabbdacddacaababcdcbbcdaccdadddaadddbbddbcabcdabdbabcddcbdbddcabdccbccdcaccdcddcbadcabdaaccadbdcbabbbaacabdacbdbbacadccdddaadcaadbaaadacdcacaadddbcccbcabbaadbadaccdbbcadccdbcbdadbaaacdbccdaaacaacadcddccdacdaccbddddacbcaaadccbdbaddccbdbdabbaabbcdbaababddbddaacdacabdcbbbbdbbdadbbbbacbbccbccdcadabadcdbbdbadbacaaddbcabcdcadacadcabcddacabaddddccbdacbbaccacdccaacccddaccdbdbdadbbcbcdcccabdcaacbcadcddbcdccbaddbdaadaadaacbccbdccaadbccbbaabdccacdacccdacdcbddbacdaadcbbabcdcabaadacbabcaaababbcddaabbdcdcdbabaaacbcbdcaccdcbcaccadbabbbaacdaddaacdbacaabcbaaacbbcbbacbccbcddbcbdadcaadbcbbccadcbbccacabccbadcccabacabcdccaacdababbbcacadbcbaaacddddcddaacbcdaaaacbaacacacbbcadcccaacccadadadbbcbbdacdababadcadaaddddaaacdbacdcaacbabcddbbdbdaacddadabaadbabcacccdcdbdcbccababcdddcbcbddadacaaadaacaabccaabbbdcdababadbaacdacabcacbbaabdcbdbbaabaddbbadaadbcdbbccacacccdbadaaaaababddbacdbcbcdddbacaabaacddcbbacbddccbabbbdbcabdcacbaacdaadbadbddccbacdbdccadaaaababbbcabaababdbcacddacadddcdccbbbbbacbbcbbdddcbdacadccbdbcbcadacdbaadbadddabbdcccabbaaaaaddbdaddabddadddcbcdcbacbabdccabadcaabbdbabacacddaacdddacbbbdaacaddbaacdadbaccdabdabacacddadcdcdbdbbadbbaccbdddaaadadcdbddbdccadacaadcbadccbcbacadbacdbdcdacaccbbdadccbbaccbbaccccbbdbdcbbdbaacddbbdbdbcacbbdbadcaabdbdbadabadbbcacacdddcaabaddbbcbaadabaabacddbdacdcacddcaccdabddacbaadddaddabdbacbcbbdcbbcddcdaadadabcdccaccdaadccdcaabadaccdabbcdccbadaddddcaddbddcdbcacddbabaacdcadcbacabdaacdabacdbcddaabdadcdaacacabbbbbcaabdbbcbdcaddabccacbcbbadbbdcbadacacdaccdabbbadcdbcaccbddadacabbddaabdaadaadabccdbaadbdbddddbdbadadabacbcacdccaadbbddddbccbcbccadddbbdbbdddabbbdaabacabcdbcaabcadcabaabbbcdacdbcdbbdbdacadbdbbcccbcdadbcbdbccacdbddabcdcbddaacbddcbacabadcbcdbabcddbcdaadbdbcdacacadbaabbcaddcbdacaddaabcdbddcddbdcdacaddbdbaccbbcdaacdcbbcdaadadccabdacaaadcbbcbddcbacbdaddbbaacdbbcddbaaabcaddaabacbaadbdbcccddacacacabcbbcacabacdcbdddcabcadaadcbdbadddbadbbdcddcaddbdcaddbdbdbcdbaabbadbaaadbabaccbcccdcddbcbdaacdddbbaddbdadcaaddcccaaccdbdacadcbdadbddddbbbcccdbacdddccdcccadcabaaccaabdddddacaabdabaacacddadabdbcbaacabbbbadbcddcdcaabdcaddbdddcdaadbcdccbcabddaaabbaccabdabdacdabdcdaaccdadbbaccadddcabbdddcbbdcdcacddbdaabdbaabbdbcdddbdacbadcabaccdcbccaadbdbaddadbdddddccaabadbbadcdbdacdbccbcacabbbadbdccaadbcccbcdbaddddcbddacbdabdcaaddcaacaddcccbadabaccbddccdcbaadbbbbbddcbbdaabcaaaababcadbddadbdcbdbbcacdbdbabcdabdaaacdcbbaaccacbbaddbaadadbdaaacaaddadaddcadbacddbbbdacaaacccbcddaadbaacbddbadccaaabcdcccbaabcdadbbbaacbcaaaccbcbddbadacaaadacbbdcdbcdabddcbabadcddaaccadbcbabddabbcaadbcccaaccddadcccbcabddacbdbbcbbdcdbbbcbdcdadcddaddccdbccbcbbccdbabcbaacbcacdbbcbbacccdcadcadcdcccaccaddadcbcdbccdcdcbdabbcdacdcaadacdcbcdadabbbaccdbabccacbcdddcbaadaacabddcdbcbdccccdbcbcaddabbcdaaccdacbadaaabcdbabbcbbbdaadcaacdbcabbbcaccabbaabbbbcbdcaabacdbcdbdddbdcdadbdacccaccbbbbdbcbdcabddbdbdccbbdababbccdcaaacdcdaccccbabccbbdcaaccbbbaacbcbdcacabbadabccacdabcdcabaaabcacbaabbabcdaabcbbbcbbaccdddccdddcaaabcdabbdbabccabdacaaabccdbdaaddadacbccdcbadbadccbcbcbbdbcbccddadcbabacbdccddacccdbcbccadabbabbbcddacbbdabccccdbdcacbbaaccbdaadbbaabbcbddcdbdcabbccacbbccbbbbbbacadbdcdbbbcbccdccacdabbbdabdddaabccdbbaadadbccaddadadbdcbbcdbcbdbabdbdaccaacabbcdddcbdbcadddacdbdcbbdcaadcadccccacdcbbbaacbcacddbbbabbadabbcdacbadbcadbadcaadcabcbdaaacdaacdbbcacbcdcbcccccbbabaadbaaddcdbdaaaabbabdcccbadabdddbdacccbdaaabbaaadbbccbadababdcadaaccbaaabdbcaacadcbaabcdbdaacaaccccaacbaaaacdadabbccddddadcccbcddacdbabbadccbcdbdacdbbcddadacdabbbaacdbbcbaaaabbdbadbadcbbbcdcdacaccdbdadbbbbcbdbbcdbaabacbcbbcdacdbcccadcdadabacdbdcdaaabcdcabdbcdcdcdadbdcdbdbaadacbdcaadccbdcbaaadaacbdaabdbbbdabdddbdbdbcadcbdaabcbddbadcdbcabccccbcadabbccccdadabcbcddbabadaccbcbaabaacbcccaabdabdbbcadadaddcccdadbdaaabdaacdbbadbbaadcbddcbccbdcbdcbadddaccddcdcccddababcbddccacbbbddadbbbacbdcaccabbdcaaaabddbaaddadbcdccdaaabacccacddcaabbbadcdbcdaadcdbadaaadddacaacaddaacdbaddaccddccacddacdadbbabcadbabadddcaccbdbdccddaccdddbbbddbabbabbbdbdcabddbbbdcdbcddacdcbcbccccdbdaabcaaadbdbbcccdcdbabdaccadabaccbbaccddddccbcdaddadaddacdadbadaadbdbbdbbcbccddaacdbacaaadbaaadcdacbadbbbddccabaadabcbddadbccadcdadbacbcacdacddbdbabdbbcbadcaccdabbdaacccbbdadbaaabbcbdbbbbbcbadbddbcbdbbdabbbddcbcbbcbcbabdaaddbacababdacdaaaadbccbaaadbdadaccdbcdbbbcadbbcbbacbccbadbaccdbaabbcdbcbadaccabbbddbbbbccaacbdcbcbcbabababcbdadacbacbddddaaadcacaaaddacdcabaadbbcabdaadadcadabbaaadabbbadcabbcbabacbdbabcbbadbcccccacbaddbabbbccccaddaadcbdcbcdbddacdacbabadbadbcccaacdbdabaadcaadcabbddaabaaabddcbddcadddddbaacbccaabbaaadacaabbbcddacacbbcadccaccdacabacbcbabbabacccbaddcaabdcbcbbdaccbdcbbcacccbbbcdbdacaddbdbabbbbaddaddaadabdbabcbbcacdabdbcbdacbdbdaaabadccdddacacacbcdadacbaabbdcadbbabdaaacdbadccccaabbbccbdddcaaadbaacbdaabcdcdaccdcbbcabcadadadcbdcbdadcacbdbdaaaacaadbcbcbacabddabcbdcabcdcbbacdbbcdabacacaddbadcccaabbdccadcaadacdacddcaaddbbacacadcbcccdbdbbdcccddddbccbabdcaacbbddccccaabadaddccccaabdbdccbdcddbbccbbadbdadbadadaddcbcacacddabacbbbddaccbadabaddabcdcbbddacaaabccaabbbcbbbacdcdcbadabbdacddbacdaaaabbbdcddbcbadcccbdcdbcbcaadcbbdaaacaccabcdcbcdccaddccacaadadaabbdbdccbcacadcabcabcdadadcbbabbdabdcccabaacaddcbdcccbcbbcbcddbacbdbbabbdbcabdcaccbccdadbaaabbcacbaddaddadaaacaaacccbcacbaabcdcbcbcdbccddcdcadbdbaddcdddacdbcdaaacbcdccdacbcabcaaacacdbdbbaabdaaccdbdcbbccacccdcdbbbdaaaacdaadadabdcccadaabadbcddacabdbacabbacccadbacdaacddaaabddcbcdcbbcbdbdcbcabbabccacbcababaabdbdddadbbdcacabcbbacccbbaaaccccaccdabcadbaddcbcdcbcdbaccdddbabbcdcccdcbaaabbaaacdcbbbaccbbbcbadbddcbacdacabbbbcbdbcdcadbddabdaaabadcbbabcdcacadababbbadabbcdcbdacdbdabdcaddddabccadbabaabaddacabadacbcddccadcdcbadcdadbdddbcdbaccacdddcbaddbbbacaacccddbcadcbcacababddacabbddcbbbdabccbadbbaaabacabbcaacdccccbbbabbcdadbdabccacdcdbcbdbbadbbbaddbadbddbbadbacaabdcdbdccaabbadacbabacdaddcbacbaadddabbcbdddaaddaabbdbacbcadccdbbbbbdcddbcaddcbcbaacbbcadaacdbdddcabbaaaccdcacdbabaabddacbbbadddcdbbccdaddbddabdccadbcbbbaaaccaaabdcdadddbdbcabccbddbcdaaaadbcadacaaaacaaaacadabdccbdbcaaaacaaccddcbabccccbbbcdbbdacaacaddacccbdaddaadadccabaaccadaccacdbdbbaadcdbdbbaddcdacacbcdcabacdaaacacbacbccbcdcdccabbbabddcdadccadbdaacccaaccabadbadbdcdbbccdccbcddbcdcccddaacbaaadadabadaacbabcaaadbccbcaadbdacadddbcdcddabbcdaabbdadabdccbabbdaddacbcbbaaabddaacbdbaaadbacdccaaabdabcabdaabadcdbbabdcacacaaababaabddabdaacaddbbddcbadaddbbcdcacdcbaadaaabaadbddcbaaacbaccbbdddbdbbbcdcddbdaaaaabbcbdadadbcabadcaccdcbabcddcbccdbaddbbbdbaddcbcbccadabbbcadcbbaacacadddbacbcddaaacadcbabdbdcbdabcbaabcdadbdadcddbbccddbacbaabcdcabdddaacbccaaaabcdcccccdabdcaaddcbadbcacccccdabdadcaaacbdbccccddadbbdcdcccccdabadddacbcdbcccbaaaadaadcbaabadcccdbddcaababababbcdaaabaaaacdadadadabbbcdaccbaacdacbbbcbbdadddcababaacddbadaccadacdddbdbddacdbccbbabbcacbcdcaddaaaacacdbbcbdccdbacbcacbdbbcbacabadcdadbcabbadbacadbdcdaabbdababbdaaacaddcaddcaddacbdabdadbcbcdddbaddadcaadbdcdbaaddcbdcddbacbacbdaaddbdbccbaaccccaacdddccaddabcdabdaabddcdaaabbacdbadcbacccaabbabcabdcaadccdcbbcacdaacabbdbccbcababdbadbbacdddcbcbdbccaddabbbbbdadabadcbabdcbadbaaadddaabdbccddccdaaadadddddbcccbaaabbcdbadbcaaacaabadacbdbcdcdccccddcaccbdbccbdcdccdddaaacdbbccdbbbdadaaddadcbadbccadbadcbdbddccbdadabaddabacddcbbcbaaaabcccaacabaadacdabababcbcaadaaaaabdccdbcaaddcacdcabbcdcdbaadabccdaacaaadcbdaabbdcdadccddddbdbacddcaabbbbbbbabddaabccddcbccbbbacddcaadbbaacbcdcbdbcdaddaabcbdaaabbadadccdaabadcbdadaaccdcdbaacccbcacaaacbbbbacbadcadaabacadddcbbacbbdabbdcddadccdbacdabddcddcbdacdbadcdaabdacdbcddbabdacabbdbbcbddcdcdccdccdccabcbddbddabccdbadcbbdddbbbbbdaddbcacacddccdbcdccbaccaddcdbbdcaaaddaddddadaadcbdcbbccdddcddadabaacddadddccadadcdcbdddadbdddadbddccaabddcbdddcdadcddcabcaaacdcadcacdcbaaacddbcdabddbabbbbdbddddccccdcdcaddaabaabcbdbacabdabdbddcddacadbbbadbacbabbaabcadcdadcaadddcbdaaacabdabdcacacadabbadacacaabcaaddcdbbaacadadbadcdabbadaccdddadccdaabddabddaadbdcdbdacbbacaccabcccdaaaadaabcabaccddaabbabdccbdbddbdcbdabaddddcdbcacaddbadcabadbbdcbddddcdbcdcbbdbbadbbbccaaacddddcabdcbcaadcaadddddcdddaaaddccaabdcadcddbccbdcaacbabcaabbbabadbccdaacaddddcbccddadcdcbbbbbcdbbacaaabaabcbbdabcccdacaaaacabbcadcdabaddacbbbddbadcccaadabcdbbdbcaabdadabcbaadbcddcbcdcbcddddddbdbcccbcddaabcabdcdcacaaccdbcbdabddacdacccaabbbcbcbcdacdcdabbcadbbddcaaccabccbcabbadbabbcccbcbaccdaadacbcccaadccdcaccccaaddadadaadccdcbbdaabccbccaaccaacacdaadccbddabdacdabcbbcdaccacaacddbcbbcadcacbcbbbbcacbadacdcccacadbaabbddbbcaabcbcbdaddcbdadcbccbdbadbdbcccacdccbabcccbaabccacdcaaabcdacabdbaabcccadadbbdcabbbbdadccaabbbcaacbaaacbaacabaacaddacdaddccddcddcaadaccdadbddaaaddbbbaccacdadaccabadbcadbcabddbccddccabdacbcabbadacaabbbacdaaaccddbabdbbabdbacadaabdbcadabdadcdbabdccaaabadabdccacadacacbccaddbacbadacdaabddabaacaddbdccdbabcdcabbabddbabccadaaacdbcaddbbdcdbcddcdaaacadadbcaacdabddbabbcabcdcbacbdcdbbabdcbbdaadadcdccdcabbdcbdabaabdbbddaacbddaadddcbbbbaacaabadddbdcccbddbdabdcdbadadaddcccaaaaaacaaccdcaadcbbcabbcaaabbababbddaccabbcacdccdbcbcdcbdacdcaddbcdbdaadbbcdbcdcbbdabbdbbccbaacbacbdabcacdccbcdbcdcdbabacaccddadbdacdabcacadcddbbbbcccadadbaacaacbacadabcbcbbaaaddbbddccabbccbbddbbbddbadabdccaacdcdbbcaabcbbdbbbbcabccbdccdccccadcaacbaacaccbccbbbbbcdbcdbddbadccdbcaccddccbbacbdbbadcdacdbabccbcaccaadddddcbabcadbdbdbdbcbcdabbcaacdacbbaacddbadbdcabccbdcbdccdcaccbcbcbdaabbaaababadcbddadcdcddcbdbcbabadbccbcdaaccdbdbbbbbaccbbaabccaadabdababbdababdbddadacbddcddcdcbdabbadbabddbbababbabdabdcddccadbbbcadcbbacbccbaadaabcddadbbacbbbdaabcddddcbcadbacacbcdccdaaddcaadbbcbbddccbddbcbadbaacbaccadccdbccccabaddbdcacbbaabbdacadabcbdaaababdabbbdcddbdacbabddddbbbdcaaadacccadbdacddccbacccdabddddddaddabbbaaadbadacaaadddcbdcdbabcacdbbcbcabaddabacbbdcbdbdcdbdaaaddbdcabccddbcabbaddadccdbbcddaccadaacaabbdcdbddacacddddcadbcbbabdadbcacbbdacbdadddcbcccabcbaabddcbddcacadcbbddbdcbdbddcddcbcaaddcdccbcccbdadbcaccadacdbabdbacbccbbbadcadcbbddadcbbcbaccdcbdaacccddccbbbdaadbcdbdbbbbbccccbaadaccdbbababbdcdacabbccacdacdbdbdddbdccddccbadbcdcabaadddcadadccddbbaaabaabacdcdbbcdbdddcbbcbcddadbcbbdacaabccbcbdddbbbbdadbaabdbaddbddccadbcbdbbcccbdbddaaaadadbadcadccaddcbddcbacdbaaadcbabadbbdaabbbcdadbaaccbcaacbbdbabbcacbcdbdddabababdaacababcadcacdaadccbdacaabacabdbbacdbddcaaccbbcbccbccbcaadcbadabdaabbcdabcdcccbcbcabcdcaaadcdabdaadbbbabbccabcbbacddbdbccdddabdadbcbaaabcdaaadcbaadbdacbacccccaadbdaddbbcbdbcacbbbddbaacbbbcbacdbcbddbacbaaaccbbaacbcabddccdcddadabddcdcadaadbcdacacdcdbaaacadbbdbbdcaddddacdbddbcdcaddabaacbcbabbaccbcacbcdabcadbabdaddaacaccabbbbcccdddbabbbacbdaccaaabcccbaddddabcadbcabbbbdddbabbddadcdadbdddcaabacaacccabbdaddbcbcdaadadccbddbbaaddbcaaaadcccbbcadbcbbcdbccbcabbdbbbdadbabdbddcbbdcdcccacccaaadaccacdcbdcddaacccdaddbdbacdddcbddabacaddddaacdaaaadadbcdbcacabddaadbdbabbccadbcbbccaadaaaabcbccbddaacbddddaadbdaddbbbdabacdbbbdbdbabbdbbbbbbdccdacabbdaccaaaddacabcddbacdaaadbabbbcaaadbbcbacbdccddcddcadbbaabbabbaacbdcbddbadabdabdbdadadabbbbdccddbcadabacdacdaacbdbdaabbbacadcdddccacbbbcdabddbacbdcaaddacabbbdbdadcacdcbcbadbdbbabaabadadcabdbdddabadbadbadadcadabbcccdbaabadcacdbaddbddaaabddcaaaabdbdccacdddddddbdcacadcbbddcccdcacadccacadcdbabddccacbddabbbabacdcbbbddbcccdbccddcddabbdbcdbdbacbabbddbaccadaccbaaacdabbcaadabdcbbcdcdbdabcadcbcacdcbccddadabccbaddaddcddaccaddbabccdddaaddcddccacabaaddcccccadbacdccddbcaddabdbaaaadbaccdcddcbcbcbacddbadccccdccdbddcdabdbbaacddadabcbbaccaddacaacaadcdacdcadcbddbcbdbbcddbabdbcacccccbcddabddccacacbccbadaddcaabccbbacccabdabacbbddabdabcdcacaabcdcaabdcdcacbcdbbdaacdaabdababddacaabdaaadcdaadcdacabaddacbaccacbaaddcdbbbabdacccddacdccaccdadbbdbcbbaccbbabccdaacbdaacccadccbadbbdaccabddacacabccdaadccccdabacbadabacdbdadbdbbdaaddbcbadbdbabaccbbcccbacdcddbddabaacbabdabcacdddaddbaddbcdadccbbcddcaaabaabaaaaccbaddccdddacddaadadacdddbdbadddaccacbdabcbabcddbbaddccbddcadbacaabcbdaccdccbdccadbadbbaaadccdcdccbaccdbcabcacbbcbaadbdbaacdddcababaaabbcacdbabdabdabbadcadddadaadbbddacbbbbbbcddcdbaaccabdccccdcccabddcddcdcbdcdcdccbadccacbaccababbcbbdcaabadcabcccccddacdbaacabcaabdcaccbdacacccdcdcadbabbaadacdddcbcaccbabacccccbdbdbdccbddbdbcdccdbccbdcbddcababdaabaacdbdcdbbbdcadacbabbdcbdabbdaaddaadbbbbdbbdadabdbacbddbbbdbbcdbcdbccdcbbcacdcbdacdbbdddaadbabcaacbbcbdabacccacbacdabdbbbadaadcdddcacbbdbbadbadabcbcdbccaabbbacaacbaddcccdbcbbacbccdbbcbadadbcaaadaddcddcaabbbdbccaaabaabcaddcccaaabaddccacccabbbdaadcbdaacacacbbaccacbcdacbbabadccbaacadacadbddbccdddbcccacbabcdababcbcdbaaadddbdbbcdadccaccccadccabadbdabddcdcbaacabcbbbccbcaccabadccdbcbdaddadbaccacbddbdacdacdddddcccbabcbbbbcaadaadcacdacaabcdccbdbbbcabaacbcbcdbbbacccbabcccdbabbacdacccabbabaccdcddbaadcabbbddbdcddddbbabcccdadbccacdabdbacbbbbcbcbbdcdbcadacddacbccbabcaaaddbcddbdbadbddcbaadadadadacbadcbddabadcacdaaacdbbdaaccaaacdbbbbdcdcbbbacddaddadaccbaabdbbcacbdacbddcdbdbcdbbbaddaacabbdbdcbbdacdaaabdadcabccddbcacbdbaccbbbcacaacaccaacbdcdacbcddacdccbdbdacdacccabaaddcdacbdcbdacacbabaadcabcdbdacbdaaaccaabccdbadadcabbaaabcacbbaadadabacbbbdbbadadaaabacaabbccdabbccdcbbddcccacbbbaadaadabbbcbdcbcdcabbbadbcacbacbdacaddddabdbcddadabdcabaaaccbbddccddbabcdbbbdadbcddccbacacccbabccddccbcaddccbaacaabcbcadadddababbabaaabdccdbbaadaadcbadcaaacabaabbadbcbdcdbdbaaabacdcddabdadbcbdacbcdddbccdbcdcdcddcdcaadbabaddcaccaabbbddccdccddabccabaccbadccbabbcabbcaaabdcbaccdbabdaddbddccdabbacacaaabbcbacbacbaadacccbbdbacdbaccdadadadbbdcadadadcddbccbbacdcbbbacddcdbaaaaaccdaccdbcccadcbbddbcabdbcdabacaaabcabcddddadadcbbcbccdcdcadbaaddacbacbabdcdcbbdcbbccdccacddaccaadbbdbdbbcadddbbccbadabcaacaadcacccdbbdaccccdaaddabbaadccadbbdbbcbcabdaddbddaadbbbdcdbbbdcbddcadbbdbccccbcdcccdaaacbdaabccdadcadabadacccddacacbdbbcbacdcdcdaccdbbacccaaddbbdacbdddabccdccacdaabdbcabacaadccdacbdcacbbdbbdacabdbdabaabcdaaccccbdbcddacacdaaddbaaccdaacadbcadcbbcdddabdddabddbbabcbabbcbcaabcddbbcbaacbcddcbddacddcabbcbddbacbabbbbdacdbacddcadadbbbaddcaacaaabaabbaadbbdabbadbaabacadcaabcccdcacdbddcadbcbcdadbabdcbbbcaddbddccccbcdcacacadbaccacbcbdcadabdadadacbaabbadbcbdcdbbbadcacbdbcdddddcbbbaabadabacaaadbbaacaccaaaaacbabdaccdcdcddccdbaabcabccddcbbaadabababcaaccdbdabdadbdcbaaaadbcabdbdbaabdaadbbbacaccbaadcabcbbbcbbbabdbdcdaadbcabcadcccdaadbbbcbbbbcabbabbdabaadcacaadacbdcdbabddaadbabdbcbccacddbcddbdabddcaadbdabcdddaaabdcabbcadccbaddcabcdaacacbbbadbdabbbabddabdabbcbaabbdbcbbbabcdcaaccaabbdbdbbccabbcacaadacbaacccabdbddbdcbacddccaacaaaacaaaacdcbcacbadbcdcaccddcbababdabadcdcaacacaccadddcddbccbdbbcddcbbdaabdcbddaccbabbbaccbadcaaaaaadbbaaacdcccddaccadaacaaccbdbddccddcccbcaabdaabddbbbadcbdcddabdacdccabcdcddacadbcbbccacbbccbdbddcbabadacaaacbabddddbdbbbbcadbacaaadcaaabcabbbcadbdbacccdbacccdbdaadbdaaacbdcdbacabcbcacdaddaccddddddccdabbacdbbcbabcdbbbdabacaabcdccbcababdcbdccddcabcddbbbbaabaccccdbddacdcbbccddacdaccbacbbccdcaaaabbcaacabadaccddacacbcbbdaacadcbdadbbdcccdabcdbbcbbbbadabbcbbbaddbacaacddcbbcaadcbbccccaddcaaaabcccbacdbcdddcdddbadddaccdbbbcdaaaccdddddbccbdaabadcdddabacbbacaacbcdacadcbcaadbdbaddcbdbbaaddadaccddbbabadbcaaadbbadabcccccbbdbcdcdbdbaccdbdbcacddcdddbbdbbaddcddccbcdbabddabacdcddaacddbabccaaaacdabbccacdbabcbdbdcccbdddcdbcdadcbbcdcacbaabbdabacdddbdacdadbadabbdabccbadbbccdcbaaaaaaddbbccabaddcdbddbcaadabcabaadbadbbaaccadacdabbcbadabbdabacccdacacdbbcdccacabbbbacccbdddbcdddacaadbacdcddbcbdbbabadadbbddcdbaaabcddbcbbbdbadddcbcaadabdcbcddbacddcabbdcdcddcaaaacdcbcabaabaabdbdbdcdbbdacabbacabaaabccbbdcdcdcdbcdbbdcccbabccdcaabdcbcaccbabcdaabcadbacbbbdcacacbcacdacabbacdccbaaacababbaaccdacbcdcbdaccdbcaaabaabdbbaadabcbbdbccbbdcabaacadabcdbbabdcbbaaacacddccbddbcadbcaabbdcdbbdadccadaccabbbdbabddadbdacddbbdbddccbbacbbddccddaabdcadacbccaabdbdaaaaaaaccddaccbdadddddaacbbaaacbdbbdaacbabdccabbdabbaaaccbbcaaaababcbcaacbccdabbaaadaccbdabbaaabbccbcdbadbbaaabcadddcccadaaadadbadbdbdddcbadcdbadccdaaabcacbabbbdabcdadabcadbadcdcdbccdaaabacbbcbbbacababbdbdcabbddbadccdddbdbdbcadbdcddaabbcaabdccabacaacbcadddcbddadcaadcabccaaacddcbcdddcbdadbaaaccdaccdbcbdcbdacbbdbacabcdcabcdacccbcbdadbcdadccdcbdbdbadbbbaccbbadbddbbaadaababddcaaaadbbcdbdaabccadbadccaddccacccbdcbdbaaababbbbaadbdabbabadbadabdccbdaaddbbbbcaacdabdcdcbaacbbabbdbccaccbcbbcbcdaccccaddddaabbadcbaddaccdcbdbccccbcdbddbdcaddcaabdcdacbabbabcaabcaddddcdbdaabaabadaaccbadabcaabbdcacbcbcadcdaabdadbbdcddacacddacacbcccbddbdabcabdcccddaadbabcaababaacdcdbdadbdbdbaacbdcbbdabdadcbbabacddbcbaabddbbbdcabdaddcdacddaddadadbbaddcddbcabdadddacdbbcdddbdaaadddaaabcbddadabacddccdbaddbadbcdcbabcabdbcbaacdccbbbabbcdcbdbcacadadcadbbdbabccbcbdddbbdcccabccaabcdbccaccdaddbaadcdccbabcaaabdcabbaaaaacbcbcbbccacadadcbccaddaaacacadbcbcabadadbdcbadbbbddacdbbbadcadcbbcabdbcddadadadccddcbadaaabaacbbbbddbdabcbacaaddbbacaaabdcadaacdbdcbdbdcbbcaadddbdbcabaabbbcacbbdcdccbdaccaccbccbccaabdbaddacccdadcdcaaaacbcdcbabcacdbaacdcdcbadcabcbbcaccbaaaabcccacacbdbdccdbcdbbbbbbcbcaabbaddadbcbdccacdabbddaadbdbcbbcdcbbbbbcadcbdaddabdbbaddacbcbcaaadbacccdadacdabdcbadddbcdddccdbaaabbadcdbcbbddcddcacacaddaccdddaccbdddbbcdaaaccadacbbddaacadbabacbacccacdaadacabdbcdcccadabadaaaaadaaadaadbabaddcadbbcccaabcdadabdabdbbdaccbcbdcbcbadaaabaccaaacbdcabbadcdcdcbdcdbbabaddcadcabbbcdcadcccdadbacddbbaaacdaccbcacdaaadbbdbdbbbdbcaacccadbbabaccbcaaabbcadaacddcbbcbcbadbddcadacdbaaadabdcbcddcdbbaaaccaaacabcbdbcbbbddadbaddcddccbdacdbbacbddbcccaccbaacbbbbdbbcbcbcaaacaccccbabacdaaadcaacdbbdbccbddbcbcbdcdcbbbbbdbabcadcdccbaabbadbddbacdbccdcdadcdcddabcbaadcadaaababbdbdccbccbabbddbdbabadadbcdccbacbdcaccbabcaaadddabaacbdcadbcbdcaaccaacacbadccdaabcaababdaccdbdbbadadbccbdccdbdadbddbcadbbcbbaaaadabbccbcabbccdbcdcdaacbaccacbcbaccbaadbacbddbacbbcbaacdddbbdcdbddbdcaadddbabbbbbdbccbdabadcdabaadbcbbbaabaccaddaddcbababaabdcdadbaaddccdbcadccabdcdabaaddbcbdabcdcdccaccaabccdbbbabadcbacbbccbdadcdacbcbbdabbbbcadbcbcaacdbbdacdaacbbbabbddcddaccbdbaabaadaadacabbcdcbadabadcabccbdabdadccacdcadabbdddacdddabccbcabdddabdbbabadcbcbdcbbcdbacbcaccbbcbbdaabacacadddcbababbabaacbabdbddadcabdaaabdabcabbaaddcabcbbcaacbcabaaddbddbddbababaacdbcdcccaabacaabcdbaabacdacbdbbbdadcbbabadacabdbcdbdccccdadccadbabcacdaccbbbabbdcbbbcdbcabdbaddaddddbbbacbcbbdbabcbbbaaccbacccdcbdabdaddccaccccdacbbaaddcdabacabadddbbcabadcdbaddbbabdcbbddbccabaadddcdddaabacdabdadabbcdbcacdddadcdcadddccccaccbcacbcbbbcdadcdccdbdaddccdacabddcbdabcaddbbccbcbccdbacdcdbbbccabccdaccddacaaabbdbacabdbadbbaccbccacccdbbcbaabbddcddbdcccaacdcddadbaaaabaaddabbaadbccbaddabcacdbcdbbabbbaabaccdacbdbabdbacbabdacbabdbccbccdaadbcdbcdabaadaadbcabaadccbadccbacaddbbabdcccaddcbdabbcacadcdcaaabadaaadcaabaaaddcacacddbcbabdcddddcbdacabdbadcbacadcccdbcccbcadaaacadbbbdcabbadcbbdbbcabdaddccbdabdccbbabdadabdacccbdcccacbaddccabcabdbbdbcbbdadbacdbdbdcbddacacdaacdaaadcdbccbccaacdacbbdcacadacdadbdcbcbddcdbdddcadaccbdbdabcddddcbacadcbaacabbcccadacddbbbbbcbdadbabbbbabcbaacadadcbdacacabccbdcbaccbdbcddbabaddadacbbbdbbaaaaaccbbbacddaddaddcbacccabaadaccabdaaababbddacdcdbbcbadbbdddbacabdbacccbbdabacadaaddddadbdcadcccdcacbbcbdcbbdbbbcadbbbdcadababacadbabcccaaaaadddcccdbdaddcccdbbccdbdaabcdbbdcbcdaabdbabacddddacabcadbbdbadbbcddbdadbaaacadcabdcadccbaacdcbacbccbdadcbaccbabaccaabcccdbcaabddaccabdbbbdcdddaaabacacddcdddbdbdaddbbabababaccbdbddaaabdbbaacdbdbcdbbcabbadaaaaaddadbadcbdbddaacbddacadcbdabdddadcaabdacabdadabdcbbcdabbaadddbcccaabcaccbbbdddcaaabadbacdbaadcddddadccaadacaaaaabbadcdabddccbcccacdbbabbccabababacdccacddabbadadbbacbacaaabbdaaadddbdddacbbcccbbabbabcbbacccbdadbdbbcddddbdbccbdcdbaddadaacbadccbacdadbcdcadcccbdbdaaccacbdacabaadddcdcddbbacbabacadddabbdddcbbacbdccddddccacacddbdbadcddcdadccccbbaabacdccabcbdbbaaacddabcdcbaabbdaacbcbcdbaddadbcbacaaccbbdbbaabdaddadabcddbabcaddbdcadaaabcccddacccabccdbbdcadcabacbababbbddaaaaadbbdabdadccbdbccadcabaabaccdbcacbbbaadbabbcadabdcdcccadccdaddbcaadaacdcdbcbcbcdddbaabbacdacddbadbaccbbadbbcbddddabcdddadbabcccaaacaadbbdbbcccbdcbdcdbccdaddabbaacbcdcbcbbdcbaadbbababbcaacbbadcdddacdbcdbccbcaaababdbbdbadbdacdcbbaadaccbabcbadcbddbbacdcbadaabadbdcadaddcbdbbbdaaddadadcdccaadddccacbdaababcdcbddcaabacdbcccaadadbdadaaadbdbabbbcabaadbabdbcdbadaaddcdbdbaacaccdcddacddcadabdacaabdacdadacabaacabaddccbbcbaccccaabcaddbcbbdcbbaabcdbdcbabdbbbbbbdbdbccabddcdacbcddbbaaabdbcbbbaacbacbaaaadcdbbbdbcabcbccbacaadbdcadcaaacdcabbdccabbcddcbbdadacbbadbaabddaadcccbbadcbccdaadadbdbdcddbccbbaacbbaabdacbbaadcbcdbabbbcaacaabbcbaddbabccdcbaaddadabbbadbdcaaabdddbabbacdcddadcbcbddaababcaacbaddaaaadabacccdbadbbdddcabbbbcdbdbdadbaacacdacbbadacadbabddbdcdadaadccdbcdbacbcccdbdabdabccaadaaadcabbcacadbdadacdcbaacbabbbcdacdccaccaacbcdaccaadddbcbcacddacdcbdccabdaddbaadadaacdadbbaadccaabaddbbcaadaaadcddbdbcbdaaabcdddabbdabdaaddbddbaccddbcdcdddcacadbaaaabaddbaacadcdbbdbadacbbdcccbbbdabcddcaacccabdaababddcacdabbdddbcbdcabdadcddbcaccdbcbcbcdacabdadcbaacbbaddccddcdcabaacabaaacdcbbccccdabcbadbdaadbdcdbdacaaaadcdbcacdaacdcaddbcaabcdbbbadaaabccdadbbbcdbbcadabccaabadbbbacbabbbcabdacacabccddbcdbdaacdbabcbcccbaccbcaaccababddbccddbccbadaabbddbcaddbcdbccdcaccbbddccbbadbcbcbaabdbaaababbcbbcddaaabbdccdbadcaaacbdbacbbabdbbdbcbbaddbcbddbcbdabcacbbabdcdcabcabbddabddabdadbdadabaddcbbbccdcbaaacbbaacbcbabdbcbccdddbdbdabccdcddcbcacdbcbcdbdacaddcdacacdbadcbcabaccbbcdacbaaaabdbbabcdbdcbaabaadbbcdbaabbabdababdbbddacadcadddaacdccccdcdcaddbbbbcccdadbbdcdcdaaacbbaaaadddbddbcddaaadbbdbadcddaabddcbcbadaaaadccbddbdaddaadddddddccaabdbccbbcbcabbcacadacaabdbadabdbdacbbaaadbcbaaabcbdaaabdadddcbbcdadccddddadadcbbdabdcabcccbcddbdaaabacbddaacbdccddaacbabcdcdbddddbdadcdacacacbccdcdddaabacdcbdacaabbdacadaaaacadacacdaacbadbbcdccddaddadabadacbabcddddadabcdbbcdcbbaaabccadbabcacdcaddbccdabacabcbdabbaddacbbaddcbbaadaddabcabaababdbbcaccabdddaaccaacbdaadbbbcdaabdccccbbdccbbcdbccdbbccbccbddcaabdaccaabddaaacaabdaacabcbaddabaddbbdadbbdabccdcadcaabddcaadcdadcbccacacbcdacccacadbdbabbbaabcddbcdacdcdbdddacbbdddbbdbaacababbcbaabdddbbbabddbabdadcbcaaaccaaaaddbddccacaaaaacbdcdbacaababbaddbcddabadbccbdcbddababdabbbdcbcbbddcdbdccaddadaabbacacaadcdbdadbacaccabdddccdadaadcdcabbaacbacdbbdadccbdcccbaadbabddbccabadccbbaaadccccbacbacdbdcbbaacdddbdbabddcbbddbaadcdccbadcdbbabdababbabddabaadacbabddbaccdcccbccbdabdbdbbdcaccdddcadcadbdbddbdbcbcdcabcbaccbadadcabcbdbbbbcdcbcaddbdadbdcacbcbbdcbcaacdacddabacbdccbacbbbcbbccbabcacbbbbcaabbbbbadcbcddcdabcdaadbbddbddbbdcbbabcabaaabdcdbdabaadbbacaaccabcdaacdbabddcdddccbabdbddddabbcccbcccaaacccbadddbcbadbbdbdcabddbdbcbadcbddcaaaadbbcdbdadbabadabaadbcdcbbabcaddacbcbdddabbddbadaaacacaaadcbbbcaadcddbdaadaabcaddacbbccdcaacbbdcdacdccadabadcbdaccbdadcbbccbaadacdddcbdcbaddaddaabbdcbccdddbcaabbcdcaabbdabcadcaadabbcabaaaaddabaddacaacbcdacddbbcdcabcdaaaabcaabdccbdaadadadcbcbbacdcbcbbbcdddadabddddcdddaddbdadcddcbcdacacbababaddccbddbdbcbddcbaabbbbabadbbcbaccdbddacbbdababcbcabcadbabbbcbbcbdbabdbaccccbaaaccdcacbcccabdbabddbbdcbacdbbacdbcdabbcbbdaabdcddddacdcbbdaaacccbddadcaaababbcaaddaddbabbaabcccdacddaaccdadbcadbdadacaacddbdbdbababcabababadcdcccbcadcdacccaacaaaabbddcaaacbbaabddcdbbcaddbadabcdcbcbacaadabdbdcdacbaaddadabdadcaaabacbbbbcdacacbbbcdaacbcbbaccddacacccbbaaaddddaabadadbaacaadaaacdaddccdbcbdaccbcbccccdaacabcbcadbbacbbdbaccabcbbaabcbbccdbcbbbbdcccadbdbcbdbabaacdcccacbcaabdcddbabcbbbcbcadccdabccadbaadabcbbcccdcaccdaadcdadddcdbadcddddddccbdccacaabdaccacbabcadccdddabcdbbaadcccdcdbaacaacdacbdccbbccdcdadadbbddcbbadddcbbadabbdcacdddbdcdccbadcdbabccadccbaaaacbbabaddcbabaabcdddbdbaabdcbcccaddddddabdbdccbdbcadcdacadcbddccbdcddcbbabbdbabbdbcacdcdbadcccaaabcdcabbaadbcdcaacdddadbccccddcacddcdddddabdcadcccdbabbadccbacbcadbbabaadaccbadcbaabbbdacbbaaababcccbcbcccacdbaddbcadcbaacbbdcabbdadacaaacabccccbacddcdcabadcddabdbaadadddacdcccccbbbacbdbbbabbacadcbaaaadacadcabcbdbddcadbddcacbbcbacaaabacbbccaadacbbdbbbdbdadbdaccccccbbabacaabbadbadbbabacabdbdcbacbaabddbabcaddddbbdacbbbccdbcdabdaaabbbddcdabccbdcadcddbadbccdbbbacccbcdbaabbcddcabadacbcbacbcdcaccdbadbbdcdcadbcdaabbcdbababbadaddcbadddbdbdbcbcdccbdddddcabbddcacccaabdcacbacacadbbaaccdbdabcacbaaccabacdaaccdddccaddcbadcddbacddbbbacdadaddadbccbadddacdadddbdaaabddaacddddbccadbbcadbacdcbddabcbadcdcbdadbccdcadcddabbcbbbcaadaacaabcbabddaddcacdbacababcacbbbaadbadddddbacdddcacadbcbacccdddcabcddbcaabcbbacacbacdcddaababdccddaacbaddcbcbadcdbcadcdcddcdcabcbdcaadadacdaddbabcaddaccabdaddabccbaaddaacbbbbcaacbbaabcabbddbacaaabcaccacdbdbabbddaccdbaabaaabcadcacbbcacdccaddbbcaacdccddaadadbaaccccdbcbaaabaaccccbccccccdbacaacdddcaabcabaaabbbaddaadddcbabbcaaabbbcdcacdcdcdbddbaaaadbbcbaacccadacdcbdddabcddcaaddabababaacbccadadbbdbbadddcabababbcccabbccabaccdadadbacbbcbcdbabbcbdcaddbdbdbbcdccddadacdbbabaddaddcaccdaaccddcbabbabcbabbcadcaadddcacdcdcaabcabaacddaabcbaacaccacaadbccddcddccbcdabcadadbadddcaacabaaccabcbdddacadbcbbdcacaaaccbacbbbaacbbcaccaacddcacadbacadadbcbddbccadddadcbcbaacbbcaabdcabadabdaaadaaddcadcabcdddcdadbabddcccdaadbbbbaccbacdbbcdadbcbbbaabdbdacbcbcdaccaddacbbddcdddbddddadbacbbbaccdcacdaccdadddcccbcbdaccbaddadbabbdcdccdbdcdadbcbdaccadbbbddbcdacaccbbbdbdaadacdcbbdaacacabbcbacadabcbabdddbacadcdcbaccbbaddaabcbadbcddccacbdcddabcddbdbcdadbdbdadcbddddbcbcdcbbacccadbdacdcbbcdaaaddcdbacccbaccababaadabcbccdaabaacdacdabbaabdaaaacbcadacdaaaaddaacbacdbbcccdadcbbdcdaacddababbbdacbbcdbbcdbdaabcadcabcabbccbacabbdcdbdcccddbabbdbcacbbabdccdccdcbbdddbdacbbbbaadaabbdcaababdaaccbdbbbbdcddbdbbcddbaddccabbdcabdddcdbbcbaabaacddbacdaadddadcacadcddabaaacccabadcbdabbcdbddbccabbbdbaacccdbdcdcccabcaaadbcadacacbcbcbabdbcadaacadbbbadccccbaaaddcbaccbbdabbaccdbcaddabcbbcadacbababbdacdcdbddaaddbdccdbacaddbdbccbcccbaacdaabcdaccbaacdaaccbcabcacdddccdbaaaababddadcbbccbdcbdacbccbbdadaabddddcabdbcbacacbbdbcbdbdddbccadbbbcdbaaddcbcbcccdccabbddacadcadbddbcaadcababaccaadacabddcabbbbaabbcbaadcbdcabccdababaabdbcdcddcdcdbccdbbacadcaccdbbabadbcbbdddcdcaacddcacccdbabdbccdccbcbbdbbcaaaddbbbbccbddcccbaccbbaacbacdccaadbaacdddbcadbbccabadbcccddcaaacaddcbddadacaadaaddbaddcdddddbbacddddbccdddccbbcccddddcddcbdddbabadbbdcbdadcdacababcbbdccccccccbccddbcaacacccccccbdcbbadcacbbbbcccdbdabdaaaabbcbadbccdbbcdcadbccbbdcabbcabcbadbabccaadaacbdbdaddacccadaabbbbabddddcddcbbbbaddcccadbadbdaccbbaddbcbadbbdaaccbaacddbbbcdacbddaabcbbcbbaaaaddcaabbbadcaccacccacccbcdcccbbbcaabcaccdadabdacababaabccbcaddbacdabdacdaccabdbbaabdbaaaabdcaadcbdddabdaddcaccadbbdaabdaadccbbbabadcccdbdcdccabbccbdababbbbcaaddcabcdadbdbdbcbddbbcdabbcababdcdadcaacdbaddcbcadbcbddcdadabbdbbaddacdcdaaaccadbcbabbacacbbddbbbcadaccbdabccbacdbdbbbbbccddcbcbabcdcddbcddcccaaaacbcacaacaddddddddcaddcbbabbcacdbdcbabbaacacdbcdccdcbdaaaadaccbcabbacbdccabacabdacdcbcacaabadbccbaabcaaababaccdcacccbcabbbcdbadaddbbcbcaaacdbbdacbcbaccdbccdadbaaabbbbdcaaaaacbbadbcdbdcaaadaacaacbcabbaddacdcabbdbaacbacadcbabadcbcdbdbdbbbacdbdbcddaddccaadcdbadaadcaddcbacbdccbbcdcabcdbbdbadbabdcbdcbbccbbdadbbadcbbbcccdbadbbadccaacbbcdaacabcdcbbdaabbadccbacdcaddaacabcabaabdbabacbaacabbbcdcdadacaddabcabcbabadaaadbabcaacdababaaacdccdacaccbbdadaadabbdadaaacbdacddcbabdacadcbcabbdabcadbcadcdcbabdacbbaacbbdacadcdccaabcdcbdaadbdaabcbaabcacbdcaddbbddaabadcdbbaabcdcccbddadcbaaccbdadabcacdacccbbbdccccaacdadbdddabbdbaabcaccdacabbcacaabdcddccdddcddcbabcbbddcddaabaaacbcdcccdcdacdaacbbddccbcddddbacdbcbbdadcdadabbcdadbcbabddadaadcddcdaaccaaaccdbcaadbcdbbbcbcadabccdcabbdcacccabbdcdaabcddcbbbbacaaadadddccdcdcdacbddbdcbbdcabcbdcabaababcaabddabaaadcabccbbcdadadccaabcccaacabcddcddcbdcbacbbcddbbbacbcacaaccbacadbababdbbbadbbaddacdbdcabcbcdbdbccbdaacdcdbddddabacbacbcbbcbaacdcdbdccdcadbbdbbbcabcddcccadbdabbdbdcdabcdbadddccbbbbabccdcbbdaabdcccbccacacdcaadbdbababcbcdccbabaaacbaabacbdbbbbaaacbbcbdaacacabcddabddcdaacbcbbaacdadaddbadaddccbdcabcdbabaddaaaacacacdbddabcbdddbbbcbbbbcabbcdbadabcacdbbcbcdacadaababadadabcbdcabdbacaadcbcabdadbcbbddadaadcadbaabcbcdabccacaacaccdadccdbacadbacdbbbccbacbcadbdabbadccddcccddabdddacbbdcbabccbcababdaaaaaacbdbdbdbdaccabacdbadcbacacdcacbdaccdcbdcaccdcaddcbcabdababaddbdcdcdcbdaabcdbdbdbcddaaddbdbadbcdadbdbdaccccbbcddadcaaccbcaaddbdbcdaccdcadadddccdddbaddcbbddccbabaaccddcbbbdadddcbccccacacaacbdaccdaccacbaacabccabacdccdccaaaadabcabbcacadbadcaccacabadbaaabbacccdabbcccaccadccdcacccadaaccbcdadbcbbbbccbbbadcdcbbdacadbcbbdabbacdbdbbbdbdccacbbacbccaaadacdcdbdcdbadbbabbabbbccacdbbdcccdcbdbbadaaadbbaabdbacbbddabbdddbdcacdccbdcbabacdaccccccacddbdaacbddcbdacccbadbbbbbccbcdcbccbaadbcdbbddaacdbcbbccaddbaabadccadbddbccadcadbbdbccbdbbdcbdaacdcacbdabcaacbcdadacbababacabcadbddddcbcbcccbbadbcdcbdcbcabbacdaccdaadabdbadcdacddaacadbdcdccdcbdbaccccaddbbdcaabaadbadbabcbadcaadadcbdcddcacacababbadaacabbdbccacbdccdcadaadbcddbbaadbdcccbccccacbddbdbcccacacdaabcacadbdcaabdaabcbdadddcbacdcacbbbdccddbdcdaacdbbadababccbadbcbdcacadccddbabacacddcbbcccdadcbcabcdbcdbdcbcdaddababbcbdbdbbccbbbabaaaaaacbbaacdbaacccdddcccbbaccdbcbabdbbadbabcbadabbbbabbcbadabadbbbdcbdadaadbcbdbbdacbbccbcbabdddabddadbcccacbdaccccdbcbdbcccbbdadacccccadccbccadbaabbcadacdbccddbddabbbaabcabaadcabdbbdabbabdabbcaaabaaadabadbbccdcbdcbcdcaddbdaadacabdccabdabbabbbddcddcbcdacbbaddaadcbddccbdbdcdddcabaaacdacccbdcbdcaddbccdcdccbabcaadbbacaabadadbcddacaacdaacccaccbdcaddcbdabaddbacdbdcccccccdbadcccbbdcdcabdbadccadddaaadcccdaaccdacccccccbabddaddabbddcbcacaaddcaaaccbabbaabdddadcdcdadcabdcbbadbcbdccccccbcacccdcddcdabaadabaaadcbbbdaccdaaacccdcdbdccdabddcddababcadddddacaacbdbcdaacbadbdacdbabaccdaadcbdbccbdacbcacbdacaadccaadbcbcddcaacbbbcabaaaddcabbadacbabacaccccabbbaaccbdbacdadabbdcbaddbdacdcdbabddbddabcdbaddddacbcdbabccbbcdbbaddcbdadbdbddabdbbcbdbbabbccaabcccdcadbbdbbcdcaaaddbdcacdcbadacaabcbddabdaddccababccbdcbcbaaccbacbddddabdccccbbaccaaaabddcacabdbbddccadbdabbbdababccbaabababbdcbccaaacabadcdadbabbcdadcacaaccbcaccdddbcabbabcbccaddadadcacdbcdacddcbcbaaabaaacbccbddaddccddbbbbcaccbbcabdbdbdaadadcadadbabdaaddcbacdbcdbbdcbcdbbbdbabbdaabaddaadaaabacbaabbcaaadcdbaadbbacaabbdbcbdcbdcbbabbdbadddbddcbcbcbcadbbdcbabcaaacdbccdbbadcdbdbddcdaacdcacabddddbacddadccccdccdbcabddbbbcdcaacdbdaabcddcbbdcccdddbddabdabbbbaccbdccdccdbcbcbccacaacaabbacbcdcccacbcaaaaccdbbbcbdaccabdabdadacbddbdbbbbbadbbdbaaadcbdbbaaabdcdabbdbdbdbcadddadbdbbcbdbdbbddabacbbccabcaddcbadcaccbbcbdbacbbcdbdadaacbdbcaabcdbcaadacabbbaadaacddbdabbddddddabaddadddcddaacbdadabdbdbbaaabbdabbbacacdbcdddaddcacadbaabbccddbabbccadabaaabbdddddaadbaacbadccbabcccbdccaccdcbbcacaabacdbdcdbadaabbdbcaaaabdcddacbbddaaadcdccaccdabcbdadabcabcbabdacbaccaacdbaabbadcccdadbadbcccadbabacdbcdaacbbcbabbbcbabbdcdbddddcddbadbcababcbdbbcddadabbddaaacbacabbaaddccbbadbcbadcaaabcccbaabdcccadabdaaacaaaaacaabbdbdbabbbdcbcacbdbbdbcbacdcbbaccaaddaabdbcccdadababababbcdcbcbcaccbbbacccacccaabdbcacababbbabaccbbbbbaabaddcacbdcdaadcdddacacabcdbbccaacbcdaccadaadadbbaadadcbddabbabcbacacdadbcacacbdccbbaabaadbcabbccccacadabdcadcaddcdaadcbbcdbcdbcdadbbaabcbbaaaaccaabbdbbbabaddbdaaaaacbccaddcaacdbcbccabcddcbaaccccdbbbcbaccddadddcbabbbaccaabacdaabdcdcbbbadabcccdddcbbddbdbdbbdbbacaabdadcbacdbccbcbcbdcbacdcbbbddcbcacbaccddcaacdbdcdcdaddcdbabbcdcbbddadaccaaccbcadadbdadcbdacdcbddabddabbbcbbdcdbbdabbccbcddabaacdcaabcdcdcddbcdbbddccdcacdddbcdbbdbaddcbbcdcbbdcabacccdabcabcdbbadddddccdcacbacadadaaddbdacaddbcdccbabadddadacaadcbbccdccadccaddbcabacadabaccbbcadaabbdaabcbcccacbccdbcaddddadcaaaacbaabcccdbddaacbdbcadabbdabdacdbccddbaaddcdcbbadabababcbcbdccadbccabbababcaacbababccabcdadacdcdccdbdbaccddccbaacaacaacccbbddbbbbbdccabbccabaadbdabcdcbcbccbdaaaccaadabddcddbaddacddbdcbcbdccbbaabcabcddbacbcdddadabdccaccbbbbcddbbabddcccdbbcaabccadddccaccbcdbccdabbcbbbbdacbddacbddcdadbacbcabadaccaddcdbbdcbcbbabadbbbabccbbdcddcddadabaadccddcdddbabacbcdbdccdcbabbdcdaadaabcbdcdcbccdbccadadbbdcdcbacbcbaaabdcdbcdadcbaaaaabbcadcbacddccdcaacdccdbaababadcbdbaacacaadaddcdbcbacdabddbbaddabddccadcdbaddbdcdbbadcbcaaccddbabcccbbadbcdddaddcacbcaacaaacbbbdcbcaadbbbdadbdbcdccdadddcdadacccbbaadbcdacaccddbadcbdcbcbbddcaadbacdcdbcdbdadcabacdbabdbabccaadbaaacabadcbacabcddbccaababbadacdacddabbcacccaaabdaaccbaabbdccdabcdadccbadbaacdbcbcbddddaddacadadcdbabaadacadaabbbbbabcbaacbacadbbaacadbaccddbaabbcaabdbdbcdbbbaabddbdcbdacacdcbababdcbccccddbcbccccbdaaaddbcaacbdbbdacacbddadcdbdbbdabdbabcdddaabccdddbdaaccbabbabcdbaabdadaccddbcccabcdbababbadacddddcbcddbaddddbddaaccbdbabdbdcaacadcbdddcbcabdaabdbbadbcaaadcdbaddadbdaddaaaabccbdcaccbbcbbbddccadaddadbdcbbbdadcbbabcccacbcacbbddbadbdcdaacbbbddacbaaadddacddabadccdbdaadbbddbdabddadbbddbcbccccdbbdaadbcbcbdccbabbacadccbccadabcbcaadbcbcaaddcdcdabdcbdbccaaccbcbaadcbbaccaadbadabcbcacdbcbaccbddabaccbbbbcdbdaddbdadbbbcddaabacabacccccdacabcaabbcdbbddccdbbccbcbbbdcacbcdabcacbaadaacaccdbacdacdbdcadbdcabcccccddccbbdbaacdabaabbdccdbdadcbdacacaccbdddbaadcdaabaacbdbbbdcadcaabbacccdaabbabcaccccbadccbabcadabadcdcdacbbdcaccbbdcacbcabcbbaaaccccabaaaadbccbabacabcbbccaabadbccbcabbaddddcdababdbabdcdaccababaabbccddacdacbbcabdccddbbbccbadddacacdadacccccadadaccbaddcbdbdacacddbddacadcddacddbcdbaadddcbdbdbcabddbaaaadaacddcbccaaaccbabdaccbdababdabaacdccadadcbaaadbabcddabdbacbcdbbcbabccdcbcbcaabcabbdbdccdbcacaaccbbddaabbcccddcbacabcddbaaaddbcacdbcdddabbdaabcaabcddabdbbbaadcdcacbbdbaabdacabacbbadaaacddabadddcacaabaddbabcbadcccdcadddabdbccadddabbbbddbadddcdbdbbccccccddccacadcadbdabcadadabcccbccbdaacaaccbbaccdadbcabddbdbacadadadbbdaadcdbaabcaadbbbbcdcdbdcabbcacacababbabbbbddcdcdcddbdacabcdbaabaabcbaddacbcaacddaddacbaddccdcdabdccaadaacdaadadbccdbcccbbccadbdacbaadabbabcdadaadbbcbbccadbbacbacbbbbdacadbcdbbccdbaaaddbcdadbdddadddbccbcbbdaccdaadbdabadbcadabcbbcabdccbccabcacaddbdaabbcccbbbadcbacbcdabcadadbaddcdaaddcadabaddcaadbdddbbadaabaabcbababddadaccbabcdbbbbbabaccdbdcddbaaccccddcbaccadbbbabbcacaacaaccdacaddaaadcacadcdddcdadbcbcbdaabcadadaacdadccdddbcbccddcccadadbdbcabdcabbccbcdaacabdddcacbadddbaabababdccdadbdcbbdccabccadcdacbddabdcabddaaaddabcbdabcabdbbadbbbdacdbcdacdabdcaccdacaadbbacacbabcbdcabbaacbabcbddbcddbbcacacbabcbddaddbdcddcdbbadcabccccdaaadcbcbdccccaacadbabbaddbaacdbcccbbdbabacacaabdbabbcabcdcdabbbdcddcdcdbdabdccdccadbcaadcbdccabbccdadbadabcacdaaaddcccbbdcbddcadbbdcbcdacadabbddbdaacccbdbdabccacbddbadcbcbbbcdadbdaccdddccacdbcdcdaccaddaadacbaabbdbccaabbbabacbabaabcbdcdbbbdcdadaadabbdbcbbdccaaadacdaaacbcbbadadcdcadbbccaabdcaddbcbadbbdccabbbbdcdbaabcaacbbababbaadcbadcadbdcdacacaccbbbbbbccdccacbdbccdccadcabdcabcacdadcdbcddccbbbbbbcdbbdccdacbdaabdbbdcabcadcbbabcbdadccbbacdddccccbcaadcbdcbaabcbbbabdbcabddbbbadbacbcbcbdbdccbdbaccabbdcdabccdabbbcbdcacabbccddaabdacbcbcdcdcacbbbbcabadbcdcdcbadbaccacadaddacaaacdddacbacabdadbbcdccbcacdaaadbddcbccdbbdcbcdadbdabacabcbacccbaaaaadbabcadcabccdaddaabdacbaacddcabdbcdabcbabddcaaacbbabdccbddabbdbcbcdddadcddbacdaccdddaacbacabdcabdcacabcbabaddbcaacbcdbcdaababaaaaddcacccddabcbcccbadabbacdbbcbddcacabbabcdbbdbaacdabdacccdcacdcacdddcaccbdcbcbadbbbaacdbbcdaadcdcdbcbdcbbcbacbacbabdaadbaccbbabbaacddcbbadbcdaacddcaabbccdcaadbcbdaabcccbbbabbdddcadbbacadbadbbacbdddccbadbadaccddaddcaaaddcddbaddacabcaddccadbcacccbcaadcdcbcbddacdcbdccacdcdababdbcbcccbaacdcdcdadcddddacacdcacaaacddcbdacdbbdcbadbccbadcacabbdbddbdcbccbbacbbcdbadbbabcaddabacbccbaccddcbabadaacadbdabbaccadadddcbbdbbdcdddbbbcaaccdcdccacdacddddcdbddcccdbacbddcaaccadcddcbdcbdaadbbcabbdbcdabcddcddbbdbbcacaccdadcccdabcacdcbabbacacbaacadabbdaacddbcaaccbbadbbbabbbdcddcdacbcaaaadadbdbbacbdcadddccbacacbddccdacdadbbdddbcabbacacaababcdadddbddacdcabcbddbbacabcacbabacdcdababdaddadcadccbaaddddcacbbaacadbbbcbbbacbbcdbbcddaabaabdbdbdcccccbddcaadcccacdcabcabbdbdbdcaddbbdbbdcdddbddbabbabccabcbbabbdbcdbaabcadbdccabbaddddabcbbaadacdbaabdadabbacadcaadcacccabbadbaacabccabdbbdddcbaaaabacbddbabaacbbabaccbdcbaabdcdaadccbcccabdcdccdcacbcdadaddddbcbbdbaccbadcbcdcdababbabdbdddacbdabacbbabdbabaacbaaaccaadbcaadaadaadbdcacacbccbdcddcacbcbcacbacbccbbaaccbdcbdaaacadabacacabcbaaabccbadcdddcdaaadcddcccddbcacbadbdaabcdcdadcddcccbdbadacacaddcdabbacccccdbbbcbbdbbadaadcddcaddcabdcbaaabadcbaaddcabbcdbbcaddcdbcdabaaabdcbbbadaddddcaadcaabbabcbadadaacddcdbcbbddcacdbbcbcbaddacacacdbccadcaacbbcbabbbaabdaaaaddbdcaadbbdcacbccbdabcbdaadacddbcacacccbbdbcdbddbcabbaddcbcdbaabaddccdbbbadbbacddbcbdccdccdccdbcdbaccacdabacddbcbabcabaabcacacdbcbcbdacaadaaddbcccaccdcdacaadccbaabccabddcaadaccccdbabcadccadcccbcdcdbbdbccddbcacabbbdbbabbdbcdbcdcadaaddacdbcddcadadcdbcbccdbaadadcdbcdcadbcdabbadddabdddbacadcdcaaddacdbcdcdaccbbccddcbbdbbbcbabcbaccacacaccccadabcbdaddbadbdddcdabbbdaadabacddcbbdcddaadaccaaddbdaaadadccccaddddaabcbbdabaddabaacaababdbddcbadcbadaccbcadcacadcbabbdbcdcadbababbbaadadddbaacbcaddbabcadabcbddbcdddbcaccaadcccbadabcdbccabbadbadccddabcadaacbbadacbbccbdaccdcaadbcbddddbbbcabbababccaabcdddcbcccbacbcdccbaccdcdddbbdbbcccbbbbdacdbcbccbaaddccaadddbadbbccdbcdcdabdcdbbbdcbcacacaadadaaabadaacbadaccbdabdddcadbacadabcccccdcacaacaabbddcbbcbdcadabcaccddcadacadabacddccdbcdcbcbadccadcbbddcabacdaacbccdcabddaaaadadcdbddddcdabcadabddccbcdabcccdddcabdbddbcdcbcbccbdbddccddaaadacaababdcdccaddccddcccdacbbddcdbddddccadbaabccdbaabbaacaddbcadbcbdbacbbdbaaadabbdcccdacbbdbcbadccbacbcccddcaccdddacbacdddcacddacbcbbdabddccbddadcbccdbaddbdcdcbcdcdcbbabaccbababdcdcdbcdbddddaaddcadcbdcbdcddaccbbaacdcaccabadadadccbcbdddadaadcabaccaabbbdcdbdabddcbbabdcabaccadbdaaabcccdcacbbacacbcacacbddcdbcabbcdaddaabddbdbbbcddbdabcdbdadbcccdbbbdaaaacdbdcbadaddcacbbbacbbdbaaaadddbccdcbbdbbabcbadaddbddcacbddbaddcddabbbadadbbddaadbaddacadccacccadabdcdadccbcdcbbabbdcdaadddbbaadaaaaabcdcbdbabbaabbacdbbcddaabbbaddbbbdcabcaaacdaabbcaaddbabadbccdbaacaaadcbccddddbdbdcbaadbbddadbbccbcacccacbadadddaaacdcababcaabbdadbabdaabacadbdcbbddddacddbbcddabdadabbaadbcbccdcccccccbababbabdabbddbbcaaddbacabdcabadcbaacdbdaddcabcdabcdcdbdbdcacddacaaadbcddbcbdababdbdaaaacacbdcbacbbcbdbbacaccccccbbdbabaacacccbdacadcbdbccdbdaddadadbbacacbabaccaaaababcdccddccddcabcdabdccdabcccbabdabcbdabacaaabcaddadabacdadabbbccaacacccaccbddcabddabacadabccbbbabbdabbabdcabdbaacadaccbaaabcbcababadcddaccabaaccbbdcccbccdcaddbbbabdadcdbcacccbcdccbdacaabbcbbcbddbabdcabbbccdbbbcbddbaddbbabcabacabcdbbcccdbcbdbdcbbbaadabbcbbcadbacabdccabccabbbdbbccbaaabcbdbbacbbacbabbacaccacdcadadcbabddcbddbbbbacccddcccccabbcacabccbacacacdcbaaccbbcacccbbccbbddadcaccadbbdcabbddcdbbaaababaaadbbcaabbccbadbbabdccdddbdabbcbbdbddbaabacbcabcacbbdbcccdadccdcdaabaddaddccbdabbabadbbcadadcdadcccaaadadcababdcccbcaaccbdbdbaddbcdacbdaabdccaacdbdbdacbdbddcbbdccdddbbcdcdcabcccaadcdadbcadacaacacabdcdbbdabcacdcbaabacdddcbddcbaacbdbcdadaaaabcddbaacddbbbabbcaadcacddbbcacccbdbdaaacbcadacabbacddaabcbaaccbaacddbbadbccdcbdbdbddabadaccdcccbabcadbaabdddacaabcadaacbaabbdabcbdabaaddabbcccaccabacdcbdcdaccbadacaabbddcacacddccbbbcccbbcddbaddaadcacbcbbbabaadcababaddadcbbbbdcdcbdcacaababaaaacdbbaaabcdcaccbaddacbabdabcbbcdbdabdddcccdddbddadcabdccdbcbadbddbccdbcdacdcdbcadacbcbacacbbdbabdddbcdcaddcdccbcbddcbccaadaacbbdbcddbdcbcabddcdbbdadaaccaabcdcaaccddacdcbcdaacadaccbdccbccabbaacdbcdbdddaccdbacaacabbababcdcadcdbccadacdddcaccbbbcddcddccdcccbcddbdadcaaddacbadaccbbaadadcdcabdadbdbbaadddccaadcdaacddcabbcaaaddcccbdcabcacaaaccadcbdaddcbabbbdaaccdbcccbbdbbccdbdcbbdacdddccabbcdccdcdcbbaaacacadabacccadabadbdabdacacdcdbaadabcaacbccdcdabdcbdcdaadbaaaaabddbaabcadacdadccbddabbabacbabbdccddadbaabbccaacaacdacbbbddbccbddddbbbcbcabcdcacdbadcaacddddaddacccdbdcbcbdabbdcbabbbddcccbbaddcddcccacbadbadbaaacaccddbdabacbabcbacaddacacacddbacbdaacdabcbbccccbbbaaabdabbbadcbdcdacbdcbaaccbcaddbccdbbaacbcaddbbcabcdaadbaaaaabdacabcabadcccababadaaacaddcbadcaaaabccbdacddcdddcccdcbcddadbcbbdbcaaadbcbbbcaaabaadacbcbcabcadbacbadbcbccbcaaadaccabbbaaccacdbdbccaabcdbdabccdbbbcddaccddbaacbbccddabbabdcabbcbcbdddacdcbdbbdaadadbdccbddddcdcbacadddaccdadadabbbbbaacddabcacdacaadaacaccaabcbcacadcdcddbdcdcbaaccbaadbccdcddaacdaadbbdabddccbcabdcaaadbbcaadbccaaaadbdbadbdcdacbbaadbaacdbccbcbcbdddbbacabddbadcaaacdcabbcabdbccbdaccdbaacdbbdbbabddadbddabcbbaaccbdadbbaccbcbbbdcdcdbcdddacbbddacabaddbccabcdbbdadccddabababaabdbddbdcbbdaaaacccdabcaabababdaaddcbacacdacabdcaabcddbbcaacabdddbbbacdaabbaababddcacadcdaacbbdcbbbbdbaabacbbabadbdcbddabddacacdbddcbbcabcbadcaacacdbddccdddbabbadabcabcabaabdadcdabbaacadcaaccddaabcdcbcbcccdcbdcdadcbcaabcdacacaabadcbdbbaccdadccbbbdadbbcddbdbccdddcadbbcdaabcbaadaccbbaaddacbdacdbcccaadbcbabcddaccbbcaacadccabbdccbdbcaaaaaaaabaacadcdbacacbdbddddacdcbdabdccdababaabddabbcbadbacdbcaababacacbcbccbabaddcaccabbadabbccbdbbdccdcccacdbccaddbcddaccddddbcadadddddadacbdbacbccdaabdaddaabbdabadaacccaabdabbcbbbcccdccadbadcadbabbadacdcabbadddcbadcbbabcbaacccbdbbbccacbddbdbbbaddadabcbcbadbbacabbcdbccbcacbacbabdabbccdacbabbbabbbdcbcaacacbccbdcbbbaacdcbcbaacdcadbaacabaadcabdbccdccaddaccabadbcaacbbbbcaababccdbccdccadbccdbabdbadadbdaccadabadcbcdbdaacbacdcbaacdacdccdbcdddabaaaaabaadbccadcdaddccbbdacabcdddabbdbbdddcbdddbdadbbcabbadbaadcdbacacadcdaaacacbccaadaadbacbdcbcdbadbadcbadccadcdddccbaddacaaabadcbccdcccbbbacbbdcaabdddcaddccabbadcdbbbdcbadcdbddcbcbbcbbcddabcaadadbbababcacaccdaddcacabacddcdcbbdbaadbcbabbddbadaccadaacbadccdcbdbdbbbdadadddacacbadbcbcbadadaabdaababbbddabddbdbaaddcdabbddbcbaadddaabcdbadcbaabaacbbcccaaaabadaabdbacaabbcbbadcacbadadcdaddbcadbadcdddcacbbaadbcccacbddcbadadcbcbcadaaadcddacbacadbcdabaacabdcbacaccaddccccdcdbabcddaabccadddaabacacdcbcacbaaacadabcdbcdbadbddddbaacaabcdcccbadbacabdbdabdbbcdabdcbdbabacbabdbbbaadbcdadbcbcccbcabddaacaabaacadcbbbbbbbbbccbacadbabcaaadccbaacccddbbdbaabdadacbdcbbacbccddcaabcbcbdddcbabbbaddcbbbbbbaacbdbcddabdaaabdbacbbcdadaadbcccaddacbcbbcdadabadbdcdbaccaddcadadcaadaacccddbcdaaccccdbcccdbdbcccbddaadacaadbacdcbdcbaccaadbcbacbcdccbdcdacdbcbcbdcbdbdcabddaabbbbadccabccaddddddadaaabcaaaccdcbbbdcddcdabcaddaaaabcdcbadcdacadabcbdacbaccadadaccdaaadbbdcbccbbdaabdacddcbcbddcbdbbabbddcdbcdbacacdcbdccbaadbbabdadaadbccbabcdddbdbcbbbccbddddababccdbadcadcdcbccabdabcabbdbadaacbabdbadbcdbcaddbbdacaabcadcabbacabacaccbbdbcbcabbccbcccdbdabaaaabcbaaccdcdadadabdddababacddcccddddcabbcdbabdababdaaadcacdabdaadcaabcdbbaadbdcbcddadbcabddccdbcadbcbbcaddcbbbcadcacbddcabadaacaacadbccdcabcbdbcdcccbacddadddbadbdacdbaadcccbbbcbbdbddcddaabdadcbcadacbcacccacacdbcabdadddbddbcdbadddccbdcdbbdbabbcabdbcacbddadaababdbaacbbbbadabdbdcbadcdacaadbbddaacdccbaacddaacadcbbbccdcdadbdaacabbbaacacbbccabcaadbaaaadcadbbadbdadadbdadcdabaacacdbacddaadbadbaadcabadccadacdaddbcaccddaaabcdcbdbcadadddcccbbcdbdcabdcdbaddacadbdcbbbbdcbdbcbcadcbdacbbdccdabbccaaaccaccbdbacdacddcdbcddabdcdcaaacbbbddabbababcbdbccddbdbbccaababdcdacadcaadadbadbdbabdbdcccbadadabbdbcabdbabacdbccabdcdddcabbccdddbacccbacdbaabcbccdbaaaadbadabcbbacacdacddcbabaaddcbcdbccaddbadcbcbdcccdadccdbbdabadcddaaaabacbababbbcccbabcbcddacbbcaabdbcabacddccaabdcdaaddddbcdbccacccdacdcaddbabdaabdcbdbdcabdcadccbcbdcabdbbdbcbadadabdbadcaaaaaadacbbbabbbdcdddcbdababdddbcabadcdcadbaacbbdbaabcacacbaccbcadcbdcddacccbcbccbbbabcadcbcdcccdacddccdcbdcbcbdbcbbaaacdabddcbcbdccdddcadbdbbaabcdcdcdcbadbddddbbccbabdaabcaadacacdcaadbdbddbdabbdabbdacccdbaabaaaddcbcbdcbccbdbbcabbbacaddbcdccbddccccadddcddcddcddbabdddbcbbacdbbdcadcbabcccbabbdbcccbbabdcdccbddcccbdbddaacacabcbccacaccbdddabbabcadbaabcbbacbaccaaaddacdaabbbdccdbccbbaaaddbddbddbccaaddbbcdaddadadacdabacaaabbcdddddcddaacbcbabbbcaccdaaccdbbaaaaccdcaaccbacaadbbcdbddbbadabcdcbbacaddaabbcbacccbcacdbddccbbccbccdaddcaadcadacdaaccaccdbbacccbadacacdbcdbbbaadadacabbaddddccbcaaacdcbaddadcabaadcdcbdcadcadbcddbaabdddcaccadddaabcbcbdbbbbbbccddbbccbddbddbadbbcadbdbabdbbcdddbdbddcacdaaacabbbabcaadbcbcacacbcbdadcdbabdcdcacdbaadadababaacddabcabcbccbbccaacbabccdcacdabaadcdbadcbddaaabcbddbabbbdddbcbdabcacbdbdcacadcdcaaaabaadcdbacbbdadcbacaacaaaacccdaacababacabdacdabbcdbaadcacdcbaddccdabaacbcbbcdbbbdddbcbbbdacbaccdccabdcdbdbcccbccaabaadbcdddcdacbcaccdbdcdadbcbbccaabddbdacacbadcbdbcdcbddbcbbcdcbbbaccaadcaacdbdacacbaaacbcaccbccacaccabaaaddacadcddaadcddcbdabcddbaaabdbaddccbcbdbcbdcddbaddccbababdabaccbccddababdcbaaddddcbdaacbcadddccddbcdabdddadccdaccaddbabdadbacdabbdcaccbbccbdccabaabacbbdcbccabcbdcbaddbbdbbcaccbcdcdccdbdbcdacbaddaacadadacbbdbbcacbcadcadbcddbbbddddadbcccbdabadaabdabbdcccddbddbddbcabbdddaacdcbbbcaaabdcaabbdcaaacadbbdbdbdadaddbdadadbbdcddadabbabccaccbaaacaddbabcdcaaacdcccbbdadcdbbcbbbddadbdabababdbddbddcccbbaddacadbdbbbbbcdddacbccbddddbcdabbdadbbabdcccacdddaabdbbcbdabcddacadacbcabbabaaaddcccadccbcabcdcbacdbaabccdcbadcadcbbbbabaccbdacdadbcdccadcdcbdbacbadcaabaaddbabbabbaadaacbaddcbadcbbacbcccddbadbdacadabcbdacabbcabaaabaaadddbbabaccaabbbcbadaadcdbcbaddcabcddadbacaccaadccdcacadaaacacbddbaacbcabbaacadcbbdcbcababcbcbcbddaacdaddbcdbdcaaccbdbdccbdccbbcabbdcbdddcdccdaccdacbdcdcbccabbbbcaaabbadbaccabdbababcbdaccbbdadccbcdadcbcaaaddaaabacbaacccabdacdddcdddabdbbbddcdccaacdaabcadddcddaccaadbbbcdbccddacbababdacddbdbcdbcabaadccabdcbccccdabcccbcadcdddadaccbddaacdaadddbcddcaccaddaaacadacbdcdbdcbbbbaacdaaaabcdadddbdcbbacddbadacbdbcabccaabccdaaacdcccdababdbadbdbbdadcdabbdddcabbabddcdccbacbdbbadabbdbbacddccaadbcddbcaadbccbadccbcdadacbbaacdacbaaaabcabbbaccdacbabcdadbbcabdacddaaddddaddcdcbacdcdbcbadaababddbadbacdbabaabdddcbaaaacdabbbcadabbabcdacbcababcdccbabaccdddacbbabbabddacbcbbdbddbacadccdaadaacdcbadddbaabaaccabacabbadccadddccadbaacddbaaacdbdcdacbdbccddababdabbcdbdcddcccbaacbcabbbabcabbcdcdccdaaacbacdaababaccaacdaabbdabaaabddbddbbbcbccbbbdaaccaadbddcbccbabbaabdbccbdbdccbbadcccbabddcdbdacdbbddcaaabbacdcacaddacddacbcbaaabaaaccddbadcdddabaddbdbcaacbdcddbdabcdaaccbddabcdacddabbbcbdbbbdddaacccdcadadcbbcaccdabacccdacaccacbcbadcddbaadcbaddbcaddbadbccbadacababcacbccbcccabbabaabbdbddbacbadcbbdacaadacaacbdadccacdbabdbdacdbccdadbcddbbbcdaaddcdcdabbbbbcbbadbdbcbaccbbcbcddcdcadcabbadcacacddcddaddababcbdcdbbdcacbabdbddddccabbbcdacabbcacbdbbabdbbdabcabcccddbdaaccbddaabcacbbabdacdcdacddddaddabaaadcbdddbcdcddddbabccaccdaaddaaaaddcaaaaddbbcaccaddaccbdddbcdbbbbcccadccbdbcaadcdcaccdbbdabcbdcbacdcbbabdbcbdbdadccbabbaadcadabcaaadcbccacaabccadbaaabdddddbaacdccbadcbaccabcaaddaabdababadcbbdcbaccbaacdaaddccaadcdbdadcdacbadbacaacbadaccbcdcccbccacdbbaaadcdaababccaddbaaddbabddaaaadbaaaddcddabbddbbaaadbdbcdcccdddbcbccadcbcddaadbddabccbccbaadbcbcdccdaacaabcdaddccdacbcccbdcddacdaaccccddcbdbadddadadbbdcddbacbbacdccdcbcbdabccabbaccdabacbdbdadbbbadddcbaaaaddbaadbccdadcbbdcbbddbdcdcbbabbbcaccdbababdddaabacacdcccdbdabcdbddcddaadaacdadbbbbadbbbcaddddbdacaacacbddbaccbcdbccdcaccabddcbbbdabadbdcdababcdbcbdadacdbbbaabdcdbbabdcbbbacaabdaddbadadbabaadbabdbbdbabaaaabbddcbdacdcbcabccdcabaaadbdacdcabdcccadabcdbcabcccabbbddccdcaccadccdcaaacbaaabdacdcccdbaacbbaabdddddbadbbcbcbadcbabdaabbccacadbbbccbaacadcbcbdcbcbdddbccccaadbccacbacdacdbbaacbcabcbaadbccbacdaadabadadadcdcaabcaccdcbaccdbbddddbbcacadccddbaacbbaddbcdacabcdddcdbadabccaacadddbbaddbadcddddccacbbabdaadbbdbadbdacdbacabaadcdcbccbbbadbababbaadccbbcbaabbccdbaacaacacbddbdcddaadcdbaaabbacabcdaacbcdadcdcabadbababcbcbccaadbaaadcbddbacddbdacaccacdbddcdddbaaaaccbaadddadcdbcbcabddaabcabbdcbacdaaadadaabddcaabcaababaabbbaadbadbcdadccccbcdcadccdadacdaabdbadbbabdcbcdadbbcadaabdadbbdcacbabbdbacbbbdbadcadccbbcdcccaadadbacddcccabbdbabbbaccdbbbdcababdcaabaacadbdabbdaaacccadaacaadbaddbdcbbcaacdcdaaccccacbcdcdcccdbcbdcbbaacadabacdddbbddbbddacbacdaabdadabdaabccaacddadcbcbcdaaabaccdddacabbdadbcbdbaadddabacccacaacdacbddbbdcccacdbddccbbddaababdabaadbcbbbacdcddaaddbbcdddacdbdacdbabacdbcbcdbcaaaacbadbcacccbaacbbdbaadaacbaddadabccadacbaddddcbaadcbccbaaccdcbcdddbbddbacabbabbddbddaaddddcdbacacdddcaaddcaccabdcbdaddaccaccbdcdadbbddacdcaaacabccaccaacdcbcbadacbadadadcdcdcccdddabadcacccbbadbdcbcabcbdcccdccdbdaababaccaaddddddabdbccacabcadbcabcbbcbaabddbcaaacdccdcdcbacbaadddddbcdadcacccadbccdbaabaaaddcacaddadacbdcdddaacddcdacbacdcbbabcacdcdbdbaadddadaacadaccdcabbdcbadbdadbcadcdbbaddcaabdbbcbbcdabadbaaadbbaddbacdaddcbdddccbcbbbdbcdddcdcbbaacbaabdacbdabcbcbdbbbbbacccbbbcddbdccbdacaadcabdbbbbccabdcabbccabdcabbcbcdabbacbdaadbcdcddddbadabdacbacbbcbadcdacdabaabacbdcdbbcbbcadddddcdaaadadbaadabaaccdabcbddacbbaaddbbdacddbcbbacddbacabcdcdadcccaaadabdcbbbbcacccccdbbabcbaaddbbaacccbcdbabaabdaccabaaddcacbddacccdcbcbaaadcdbadcdcbcdbdbbdccaaacbadccddcdaaacaaacbaacaddbcacdaddaaacbdaacccaccccacddccdcbbcababbabcaadcddcbcddcdccbcadbbddabcccdadabbaacabcacaabbbcabdbbdabddbcccdacacaaccacaddcbdbbcaacbcaaaccccadccacddddaababbaadacabbdddcddddbaadcdbddcaadbdcddccddcccdbdadcbcbdcdabcdabadaacbacdbdbadcccdddcddacbcdddccdbacaaadaadbcadaadadbbdccadbdbbcbbbbadcacdbdccadbdbaabbbbcabbdcaabbcccccdadbddcadddaabadbcdaacdccadadacbdbadbbddadbdcadaadddcadabccaaaddbacaccbccaacdbabbdadaccadcbcbcbbacbbdcaddcdcabdbadaaaadacbbadabbbbaddcbadbcaaabaacbbbacacdadaacbbccbdadbbccddbbbbbdcddbaaacadcdcbcabdccbcdaaacaaccbcdbcdaacbccbcddccaacadcddbdcccdbdaddcacadadbbaadacdbbccdccbbacddbdbcacbadccaaadaabacbbaacabbccccdbddcdcdabbcbddaaccacdddbcaaccdbacadbccbaadbdadccabbaaadccbbcdcbcabcabddccbdbbadcdbbccdcaaabddadcbdcadcccaddbdabbabbabcbddcbcddcbccdcdcdbabcadcbcdcdcdddbcacacbdbccaccdcacdadcbdcdccdcbdbabbaadddbddddbabdddabccbbdcdadbdcddaabddadbbccdcacddcbdcbdccdaabdcbacbbcddbddbcbabbcddabdcdabbcdcdbaabbddbdcbdabdccddccbccbbbcbadddaabcbddcbcddacaaccdbacacadddacadbcbbbbcccbcdcbabbdcbddaaabdadcdbdbdaaabcadbdcadabcbcaddbdcbcbaabaadddcabbcdaacbabcdcacdcdacdaacdcdcaccdddcaabcbbdccabddabdaabbccbcdbbabcccadbaccabbadabcabacbcadbbccccbbdababcbdbdbbdbcbbbccbcccbdabacaadbacbacadbdcacbabababbacccacddcbacdbbbadaaaacdababdaacbadbacbacdbdcaaacadbbaccddccbacbdddbdcbcabacbabadabbdaacdccabcacdaacbbddacddbacacddcabbcbccccdaadbbcdbadcdcdcbddbcadbbdaddabcddbcbcbabcaabbbaabcaadcdcdaddcbdbaababdcaacbcccabbdbccddaacbbccdbbcbcdbcbbbcdbdcdaccabdaabddcbabcbacaddbaacddadcbdbaadaddbbcccdccbabdcdcdcdbddadcbbbdcbcdcdbcabadbddabcaaccdcbbbddbabdcdddacccccacbcddabbacbdbdbadabbdbdcbbcacaacaddabcdcabaaddbdacdbacdcccadcbaccadbbbcdccabcdadaadcadaaadbbcacdaabacbabacbaaccdacbdabbccbbaaccccdaadaadadbbcaddcccdccccaabbdadabbbadaacdcbbaddbbdcdbacbbbddaacdbcdaadaccdadacbcaacbadcadacadbcacdacdaadbbaccaccabacbbcdacacbbdcbaacdcdbcdadaaaaacbcbbbcdbbcbdbbddddcddcdddababbdddadbccbbdccbcccdbdaaadcabdddbacadcbcdcbcccbdbababbbccaccccbabbbaaabacacbdcdcadbcbcccbdddbbaabbcbcdbbaaabbdaaccbacccbaadcbacadacacacccddcccacaacdcbccddbcaacdadbdabadcacdabdbdbcababcaccddcddcbadbacbbbbdcbcbccbbbcaabcadbbdbcbbdaccdbcaacccdacdcadbbdaabbcacccccaddcdbdadaddadaadcdabacdcacacdcabbbaaacabcccdbaaabadabcbddcbadaddbbddadbdbdabdddaacbacbaadacdccdcbddbadbccabaddcbaacbbdbcabbdddbcaaccbdadabdcdcaaaadaabdccadadcddabdbbdddbcddabcdbdcaaacaccdbdccbabaabadadcbaccbacdaadbbddcdcbbdabadddbbadbbaabadbbddbcbbadbdbaccacdcdbbbdccaaacbbdccacbbacabdadcadcbaccddadbdaaacaaccbabdbacacacdaaadddaccdbbdcacdacccbdbdabbcababcccbbcbbbcbbaacbcbadbdcacdacaaaddddbbabcbcdcdadcbbbacbcaabbabdbadbdbacdbacddacdaaabdacbccaaccbaddbabdaaabbbccabaddccdcadcdbabaccadaadacddcbaaaadadbbcbcdbcbcbabdbdddccdbbdbbdbaaaaccabacdccbbbbaabbbccddbbcdcaadacbdccbddccaabaacbbcccdbcadddccbcdaccabcdcbadabdabddabacadbccddaababbabacaacacacbbadaccaccacabcbdcccbcbcadacbaccddddabdbbaccddcaaabccaaadabcaaacaadaacabcdbcdccdcccbdaddabdaadbdcbcccdccdadabbdbaacbdcddabacbbcaccdaccbabacabacdbacdcdaacabacddadbbcdbdccdccabacabbdbcbdbbdccccbddbdaababadcbccbbbbbdcbdcbadcbbcdbdbdabdccacddbcbdabbddbccbcbbcdbcdaaabcabddabdabdaacbdbdaaabcdddbcaaabcdbcdadcaabccdcdcadbcacacbaacdccbbdccccdddbddcbdddbccbadabacbdbabdcbccacaaabbadacaadbcccddccdaaddadadcbbbbdcbabaaaadbacdcccbccabcadcbbaabbbdabdcabbbcacbdcabccabadadcadbcdcccbabccdcdcbbaccccdaacdddccaacadbccaaccdcccaddccadbcbbdddbbcaacbccbaaadaccaadaabccdcdababaccaaddbadabdbbcbbaadbbbacadcabbbdcadabbbaaabbdabddcaaacccbcccaacccbbabddcbcabbcdabcbacddabbdadbbdcdacbaacadaadcdcbcdbcdbaddbcadcaabddcbcddddbabdcbbacabadbdaacbadccccbdcbcccdcbacdcacccbabbbccbddbdcbadbaddabbbccacbadddbdabbdcdcdbbbbabbcdbaabbacadddadadaaccdcdabbcdbbaaacbdbababbbabcbbdccaabadbcacbcdabbddbcdaddadddababdadbdbcaacdccdcaaacbbcdacaadabcdbbdadbacdbdcccacccadacdcbdbbdbadadcdbbcabcdaaaddcbbcbcacbabaddccddbbbbcaaaacaaadbaadbccdadcdcababadccdadacbcadabddbaddaaabaaabdbabaccddbbadcbddccbcbbbbcddbcdcbdbabbbbcbbabddbcdcabbaacbabdbbcbbcdabcbbaadadaaadccbcaccaccaaacddbbbbacdbcadbabcaabdaaddbbdbaaadbbdbcdbcbdcbddbddbcacacdcdacadaadcbcadcbdaaabcacaddbcdcdaccbcadadabacabdadadbccadbcbbcadbddcbcdbdbbbbaabcacaccabbcdadcdbcaaabababcbdabccaabcdaabacbdbabcadabccdadddacbaabbcdcaddccaabdcbcbcadcbabaacbbabcacdcabbcbdaccbbbbabadbadcdccdbbcbcacacdaabddaabdbbbbdbdcdcdcacddcdbbcbaadbaabcacccaccdbddbcbacadccccbddbadcaadbcccdabbbcdabbadccabbddbbbbbbacacbcdacccbacdbaabdbbcccdcdaabcdaacbcdcdbcccbcddacbacaaccbdcccbaabcaccdbcacacaddbcbddcdbcaaacccdcccacdcdbcaaadbacddbacbccabbdcabddbbbbdbbbaadcdcbacbacccbbcccabdadbadcccbbbdbaccbacbdbdbaccddddcbcbcdbacadcbcbbcadcababbbbabadbcaccbdddddbbdcacbbcdbbbaddddbbdabcacbddbdadabcdacbadadcdaccbbabbdcbaabaadccbcbcbbdcbbdcabbababadcbdaabdacabbbaaabacdbbbadadbbcadcabacdcbdbaacccddcbcdddbaaabcadacccbdbadccddbbccacdddbcbbabaaabcddcabababccbbdaacaddbabccbdcaadbbaccddaabcdabbdcadcbcdcdaaadaaaaccbbcaacddaabcaadbcddadbababcdccacdaddbcbaacabccadbbcbaadddbacbaddccccacaddbaabdddcddaacaccaaddadbaddbadbddacdabdaadabcdaaacbcdccddcbcdaabcddbaacbaadcdbcdbcbcdcdabcbdbdcdbcadccaaddbdabbcbadcdbbccdbbdadbccbabdadbaacddcdddccaaddcbaddadbccddbaccbdcbbbcabcaddbbbbdaabdcddadaabdbbcbdaccabaddcabbcaccbaaacbcdababaddabdbcaddddadbadddabaabacadcccbbcaaadbdcaaaaadbbdbccdaccbbcddbaadbdacabccdbacdccadadbadcadcbcadcdbdccdcdbcacdaadccadbddacccababadcbbdabadbadaccbbaadddcaaddcbacaaaacdccadcbddbdcbcbabadbcabbaddcadddbadbacbdbbadacdbdacdcabacdcbacdaacbdbdbbbacbcabcbdbdcbaabdaadcbcbbddddbbaacaddaacddbadddaccacddadadbcdccaacddcaddbccbcaadcdbabcaabbbbabdabbbbaacbadcaabcbdddcadbaacbdcadcdcdbcadbadbaabbdcabccccabdccabdcadaaabbccaacdadcacacaabbccdadbbababdccdbdbabcadaaadbdacbdbdddcabcdcccbbdddcbcdbaacbdadbabdcababcaddbccdcdadccbcbbdadccadbabbcadcaccbcaccacdcbbabbddccccdddcddacadcddcdabbbcabddcbadbaddadbccdcdcbaabddcdbdbbdddbaccadacacaacbdbdcccbbcddbdabbcabddbaaabcdbbabccaabdabacadcbdccccaacacacdccbacbbaccbcaadddbacacdadcccadcdaaddabbdaabdacaaabcdcddacddaccbadcdcccbacaadadbdbdcacadbdbaacaddbddbcabcdcbaabcbaccabbddcbcadbbbdbbabadddccdbcbacdaabdccbcbcddaddbbdaccbbabcccdabdcbdcabaccbaccbdcdddbcbaaabdbacbadabaaacbdabcbbabbadbbdcacdbabcadbcaabadcabdbcddcaadacaacaddccabadcbcdaccddbbbadbccabddcabbbdadabbbbbacacacdcabcddcdabbacbaabacabbdabaaccacabaacccccbcddbddaddccddbccdaadcbcaaaddddadbccdcabbbccccaadcdbdcaabacbddbcddadadbdabbcdccbdaacaccdddcdacdcdccadcacabcbbbcbccbbabbbdbcdddaadabdabcbadddccdcbabacccdabdcdabbabbcadbcaabbcbccbadbbcacbbbddacbadcbdcdacbcaaccbbbadccbdbdcabbccaccdcaaaadabddcdbacbdadbbccabcaabdabadcadbbdbcabaddddadaddcabaaaccbabdacbdaadbcdcddaccdabdbccdaaacadbddccabbaadacdbadbdcdbbccdaadcadaaddbbbdddccabaccbbdcbdcbccdcaadcbdadbbdcddcdcbcabaccaaaadcadacacbadcaabcbabcbdbbbbacacbbcbacbcaadadcbadbbbadaacbbbcdbcbdcacbabdbdcbdbddaadaacdddababbcbbbbcbdcbcbbcdcbbaaaabdbaaabacadabdcdcaccbcddbdcbcbbcdabcbcbacdadacbbcddcabcaaaaddbcbbbacddbbcbdbbabcbaadddcdacbaabacbddadddcbbcdbdabaabddddddaacdcaaccadbdbbbacdcddcbbbbbdaddcdcdbabaccdcaadabdadddbbbabbddbcddbdbbcddaacdabcacaccaddaabcbabcacdbbccadaabcdadaacdbbaadacbaccbababaccddcdbacaaddcabbccabccaacbcdbdddcacbcccddadacacbbbddaacddcbaaabaddbcaacacbbbcddcdbaabbcbaddbaccbabbcacdaddacdccdbddbdacccdddababbdcbdcbbcacddbcdbaaccbcdcdbddddaddddccaabccdddbddbaccdcaddbacaddcabccddaacdabaadaaabdaddbbddababcdacbccccbddbddcabbdabaacdcdbaadcabbdbdabcccdbacdcdadacbdddabcbacbcddacacccdcccaddccbbcdaccabdcabdcbcbccbbacccbbdcdcbcdddccbbdcadbcaccbabccbcdbcacbdacbbdcbadbabaabbdbadaabbbabcbdbaaacccaabbacdccaaadbccaccbbcdbdacabaaabbabaaaacccadaaccaaddadbbdcbccdbcadacdaaabdbbdccaaddcacdcbacdcddcdbaacdcacdacccccdddadacaaaccaacdbdbdabacbdbbbdacdccbbddbcabcbcaaadacbbdacbacbcaadbadccbcadbabdabcadccdaccbdcaadcbcbbbcbdaabcdccdcaabababcdccacbaaccbccbcccdabdcddadadaaccacdbdbcbaddbbadaddbcbbbabccdbacdcbdcccbcacdcdcddcccacadddcccbaadadbbdaabdabbbabbbdbcbcdcdaaacacbbdcdbaadcdbabcdbcdcddbcbaaacdbbddbccacdcbaaabcadbdbbcddaaaddccccccbcdbababcdcccdbbdadadbacddbcbcdacaacbccdcbdccbdddbcdacddbcaaabbaaaccaacccddaccabdcdadbcbaaacaaadddaacaabadbcbdabbbabcbcdacdbacbbdbadbcbbacadbabadcbbdabacacdbdadccddcbbccbcacdcccaccaadcbcdabcabcdcabbdcbdbcadbadadacadacddcabcacbbcabcdcccbdbaccbbccacacddcdadbbdcdaddbbcacabdbdbbdadbaadadbccbcdbbdcacdcaabaacdbcdccacdbabaadcccabaacacabdcbddcdcddbbcdcbddcbbaacdcbbcddbbabcacddbbabcccbbdabbbaaacbacbbcbbdcdaadadacaacaadccbdcddbbabbcccacbbbcabbaadbcbdacbbcddddbdcdbdcaabcbbdaadddcbacdddbccdbccbccccdbccccdaabccaaadaaacbadbbcabcddcbdacacabadcbbcbcbccbbdbabaacccdbcddabdaddaaacbbcbdbdacbabcdcbbcdcaddcaacbdaacabbcbbbbdbdabbcccbabbaacabbdcccdaddbbddaaadbdabcccbbcacaddaabadccddbdbaadbcdabaccbddabaccbbccdacaacdbaddcbbacbccaacdcbbaabcdbbabccabccabbcccbdadabcdaadaabdcbccbaccbaccdbbaacdacaabcdbbdbcbddddbdaaccbcbacbabaadbabaaacadaadbaaccacacbacdccdbadcdcaacbdaddbdbccadddbcbadbacacddadbbbbdacabcacdcdaccbcdaaddddacdabcacbdbbaabaaadabccdbbddacabdaadaddcabcdcbcdbbacbccaabdbdcdcbdddccbcdccdcacddabacccaadcbbddccdcddbddacdbbddbcbbadccabbbddcadcddaddddcbcdddccabdbbcadabdbdacdaacdddbdacbccadcababbcdddacbcacbbaaddbdaccbdcacaadcddccdacacdcbcacdacadbdcddbacdababadcccbdcababbccdacaaacdbbbbababacaccbacccddbbacdddbdaddaadbccccccdadcccbbdaccdcacaaaccaacaaadbbddacbbbcccbbcbbccbadaaaadccaccbdabbbcdbaadaccabcddcbaaacbaadabcdaadbaddbcbbadcaacdcdcccbcadabddbcabadbcadcbababdabbbccbbbbcdbbbdadbbdcbbcbaabbccababaaadbcdbddbbaddcbdcbbdbdcbcaacbabcbbaddaadbdddadcabbadddbbcbcdaabcabddaaccbcbbdbcddabdbdcbddbabcadbdbbbbbbcdadacdbddbbbdbcdddbbdddcaabcacbdbaaadddaccbaacddabaabcbdccddcdbbdddcacabcbaaccaababdbaaabbacbcadbbddbcdaadacccbddbbdacacbcbbcbadcbabdcdcdccbacdbbbdaabcdcdddddbacccdcdbcbadddcdbcabdbbbacccbcaadbdcacaddbbdbcdaadadabcbabbbdcbdcdcaabdadaadbdababaadcddcbdbdddadcadbdaaaabdbcdbbcabbcbdcabaaaacdcbdadcbbadbcacdbccddacbcbcabcdcdbcddcbabacbaacccdaaddddccddaabbdddacacacacaabacbcaadacdacbbdabdacdacadcbbadcaddabbdbcbbdcacbdaaccbbcacddbdbdbdaacabacbdacdbbdddacdbcdadbaddcadbdbaacbdcdaacdadadacbddbcbacbcaccdbbadddbcbabbccadcdbdddacbcacddddbbddbaabbdbdbdbdbdbdddaccbaaaadbdabdbdadadcbcccbaadaccaaccddccabbadbdbbbacdadcddbbabdddbdbcdcbabcbddcbddbbcbccdddccaaabcbabbacabdbddddadccaadbadaaabbbdcbbbbbbacabcacadccdabbcdcbbbbabbaaadaaacbdccdaacdbabcbccabddacdddbabbaadccbbbaddaddacbdbcbdbcdbbcbdbbcdacaddbacbbcdcbdccabdcccbddbbaccdbaadbbadbbcaadbaccdacddcbcdabdcbcdbdadddcbccdabaccbbaaaadbdaadaaacdaabbcadddbdccddabadcddcddcddaacccaadadcdcccdbdcddbcdbabaababacabaddcaacddabbbddddaaddcccdaddbdaadaaddbaabaccabddccacbccddbaabdaacdadaaaaaabddcddcbbddddcdcaccabbaabdbdaddabbbabccbcaccbcabdacddabcccaddbdbbcdbbacaacdbbccadddacccaadacdbccddbdbdccdbacaaabbaabbdadacacddcbadacdacbcacabbcccbbacbcbcbbddcdbcdabaccbbdccdadaacdcbbbcddbadbbaaacabdcbaddaddddacbcbaccadaddaabcadcbacabddbbdcdbbcdbaaddacdaaaccbbaaaddcccdabbdaadaadbadcdbabccddabdbccdddbabdddababdbccdaadcdbdbccbdbbbbadbaddadcccabdbdcbadbcbcdddcbacacadbcacaabdcbbbccadaacadbcddcdbcacacdcbbdbadadaadcaabbadbdcaabcacbdcadcbbcdabbaddacbcbcbadcdaccdbaddbccdcabddddbbbbdadbbaddbbacbdacaaacdabdacbdcbbcabdbccdbcaccccdcbcddbacaabadbddaacadaddabddbbcddcddddacddcaaabdcabcdcbddbdbababdaccccccadcdddaabbbddbbacbdabdabcdcbccbbdcccbaacbaaacbbaadabcdbdbdddaadcbcaabbbaaccbbcadbcbdbdddddbaaabcaabbddcdacadadabddabadddadccbcdbddbddcacaacdbdacdbbcadacadbbbcbbcbbccaccabbaccdabbcbaaadadacdcbdadccdadddadddbdbcdcbcadcdadabbdaaccaabdaabcccbcdaabcddaaacadadcccbccaacddbdcdbdabaaccbdadbdcbbaacdbacbacdccbbbdbdabcbbbdadacddbdcbdaaabacabbaccdcaabbcbaaabaabcdadccbbbddbbccaacddacdabbbabdbdbdcbbbcacbcbbddadaabdcdbdcdcbdbacbacbacdadadaabcbcdcdbdadcbcdbcabadbdbdccccbddabddaadabbabddccbdcdabcddaccdcaddadadadadcdcaabcabbbbcddcdbcabcdcbdddbcddcddccddabcbacbcbbabcdacaabdbbaaccdcbbacbdbbdccbbcccabbaddcacbcdcdddaabcddccadbdabcdacbacddacccdbabdddcabcddadbacbcaacadbbcbadaabdbbccccccbababadddcccdcaaddabbaddbcbaaaaadcacddddcdabdaaccbdaaddbcdcbcbbabcdaabdacaadbcbcacaaccdacacccbdddddcbcbbadaccbbaabdbababdacdddcacccacadbdbabdccdcdbdbbccbdcabdadbbadddbdbdbcdbddbcbdccdabbcbadbcddddbcbddbcaabadbcadcbdcbbdbccaaabccdbcabaaabdcadbbccaadaaacdcddcccdcbdcbcaddcddcbccdbcdcbcacdadbaadbcadcdabadbdcbdabdbddbbcdbaddcadbccacbbadaddbacbbdabaadbcbdcbddcddccaaccacabbabbbdaddccbdaccbaaababdabbccbdcddbdcacbcccabaccdcaadcbbdbacbacbaadbabbcdbdddccbbdacbcbdaaadbcaabdbbddbccdbdbdbadbddabcddcbcdddddcaaadabbdbdccabbdbdbccdcbacdbbbbcdacdcadcadbcacbddbccbdacdcbdcdcbabbbbdabcccdadbccbccccdbdabcbcccdbabcaaabbbacbbcdaacbdddddbbbdacbbcdcabbcccbbabbcdcccbabdcbbcddbbbdcdbcdabadcaadcbbabbacacabaccaadddcacbcbaabacdbbbcccaacabccccdddbdadcacbdadbbcadadbcbcbbacbbbdabbcbcabcadcadabccaadbadaccdbdbccadbabddaccaabdabdbbbcaacaadcbaacdccdbdcbdcdabdbbdcddbaacbaababacbbaabbdbbcabccccbbacaacbaacbcadaabadaabcacbbabccccabdcabaacbaabbbdcbddbbdacdbbadabbaccabdadbbdacbbbacdcdcabdabbdabcbacbdbbcdbbddaadacbcadaaccdabdddcadbddbccbabdbcdbddbdcaaccaaddabacddaddacdaaacbdaadaabbadabcdcadcdbdaabadcacccadaaacbdddcbbadddabbdcaccacacacdcaccbddaacabacccbccdbdbaaccababacabbabcadbdcacbbcbddcccbddbaacbbbabdcdbdddddadabdadbcdcdbbcaacaadaaacaacacbaddccadcabadddbaadabbadcddcbccbcdddaabbcbdccdbdddaadaacbcacbbdbcacbbcadcdccaabcadcbdacabbbacdabaaabdcbccabbadcbcbdaaddabcacbbbcaabccdbcdcdccbcccaababbbdbcbcbbacddaadcdddbabcdccdadcdcadaadbccbbdcdaccaaaaaabbdcccbbbbbdcdaddbdccdbadddaacdaaddaccaddbcbbbdbcdbbcacacadabbdbaaacbbbbabbcbaabaacaaaccdbbbaddaaddbaccdbabaacbddbdaccbcaddaaccbaccdaaaaabacadccbbcccaaccbbaabccadbddddbadddbbaadddadbbcadbddcbddacbddcbadbadaaabddddabababccdaddbbacaacabbbcddbbcadbdaabbbdabbdcbbccdbccaacbbaccbbbccbcdddccadccaabaabccdcdbdbbddacccccbcacbbcacbdbbdbcabbbbdbcdcabdddcdaadcabbccdaadcccbdbbabccbdaacbbcbbbddccccdbaaccccbacbccacbcdddaddddabaacbdbbabcadbadcdcdbcccdbbaaccccbbcbbbdcdacdbccdabdabdbbababbadabbadadddcabacaddcabdbcdcbcababbaaddacbddbcdccdabcadbaccaaccccacdcdcbadcdbcacbcbdbdcdbadbbddbadcddcabdbdddcbbcddccdacdbabbccdabbacdbcbadcbdabadbbaaadabcccadccbcabbdacabbbdccdbbddbbdabbccbaccacdbabccddaaacccabddcbcbdcddbcaacadcdacaadaabcbabdcbbaaccaabcccaadcaabccbdbcabbacbcbdbcaadbbcbaaccdcdbbcbabaacbcaaccbbbaadbbdbdddaacdaccbbcdbbdabccabaacdabcdabccdbacacbcaaacdbcadadbddcbbacdaadddbddbdbadcaacbddcdbbabddadcaadbbccaacbacbccbbcdbbddadbadbacdcdcbcaccabdabbbdaccbcdccbabcbdabcddcccccbcddaacdaccbbaabddabbcdcadaabdabdaaabcddaccaccbaccdbbdacdbddcbddbbaabaaacddcdccbcdaadbaabddccccdbacbddccaabbbdabadabadadbcbbbbbbaccdaabcbbdbdbcacaddccccbdabbbddcbbacadbbaddadbcbdcddbdbbadcdcbbacaccdbabdaacbcbbaabcccbcbbbcbbbbaaddccbcbdcabadcbabdbcddbbcbbbbccbbdcbbdbacbabcabcbbbaabdbbddaddadbcadbcaabddbacadacaccabbbdddadbdbdddaabbcacabaccbdcbddacdcdcaabaabaacdbbdbddbbbbdbadbabdcdbaadbabcbacadbbaacaccaaacdddbadbabacdacddaadabcccbcaaabbbaccbacbaaccaabaacabbdbcbcddcababcbbadbbaddcbabccbcdaccbbbcadbbbbddabcadadabaaacbbcabcbacadbbcbcbcabbaddaccbaddccbccbbabbcdbaccbbababcbcbbbababbcbaaadccacdacaddbaaccaacaaadcabaddcadabaadaccacdbcadccbdaaabaacaaccbbadabcbadbdadbadcdbbbaadabdcdcdbacbcdbcbbabaaddccdbaabacacbdaccbadaacadcbcdabbbdaddbddacabbcdcbccdbbbaabdbbcbcaacacccddbddcddbdaccdccbacaccdaabaacdbacacaabdacdcaaddaaaaadbbdcdcaadbbddcbcbbdcacdabbbaacababcbcdabcbbdaababbcbaacabddcbbddccabbbbbcccbbbbdadbdbccddddddbcbadbcdbdbddadbbcdbbccaacccadccccddbcbbbdcbbdddaddccadbbabccbddbbbdccccdbaddbcbcaaaaadbbcaacacdbbdaacdcabbddccdababdbabacddadbbbaacacaddcddcdbbbddabdddcdacdcadcbdcddcdcdcadadbdcbabaccdadbbabbdcabaacaccacddabdadbbcbcbbcbdcbaddcabcaabadacaacabcccddcccaacbcbabcbabddbaaccbcdbdaabccadcdabcccdcbccddabbddcdabbbcdbccdaadcacdadbcdcaadbcaaaaaaadbbadbaacadcaaaaabccbcadccbcacbbddbcabdcccabadadcbdcbbdcddadbdbcccbaddbcbdacbacaacccddcbcadbbdddcccaddbbccbdcacdcdacaddcddacddcabacadcdaacbaabdcccbaabcbcaccbbabcddcbbdbdbdcdcdddadbdaccdccbcbaddaddbdbcbbbddacbcaddccddaddabdabbbaacdadacbaddaaccbacabbbcdbdadadaddacacbccabdcabacbcbdaddaabdccaaddbbaadacaaaaccadbbbccbbdabcabbbadcabccbcaddadbbddccacddbadbcdcbdbdcaadbddcaddccdabaadbdcbbabcddaabcacaaacccbabdbbbddcbbbbdcbddbccdcdaaacbdccccbbbdccbccacbbaaaadabaacacddcabbbbccbaddbadaacdadadabdacbcdacbaaacabbaddadcdacadbabbbcbbacbbddabaddbdddbdbcbcdcddadadbabacbaacbacbcbaadcdddbddadabbaabddcddbccaabacabcddadbacddbdabdaadadcccdbbbcdcabbbcabdbbaadbcbbacdacdcddabdcccadabbcabadbccbdacbcaaabadccbbacbcaacbaacadadacacdbbcdadbacbdcdadcacdbcbbabacbacaabdcabbbaabacdccbaabbdaccbcddddbcabdbaccabbcbbaacbbddddbbbdccadabacdcdbbcdbaaccdbaddbdacacbbadbacadcacbbddcddcccadbdddbaacdcbdbccdccdcdccacbadaddbdbbbccdddabbdbabcbdcbdcbdbdbabaacbadcbbaadadcbdadadadbbaddcbdbababbdbddbbcacddaabbabdcacabcddccbcccabbbbcbaaadbacaccbbcbcadaaccbdbbadcbbcdccbbccddbbabcdcccbccaddbcdbdadbbcbdcdcabcaabbadacabcbdbcbcaabccbdbaacbcccbdbbbdaaacdcabcaacbcadaaacbaacddabbacadcbdaacccdbcbbadcbccadbbdbbadcabcaacbaacaddbabadcbabdbaccbdacaabcaabbdcdbaddbbccabcabbddbdbabcddababaadadadacbccabcddbcdcadbcccbacacdccacdbdabcdddccdbbbadaccadacdadabbabaacaabcddddbabbdccddbddabbdbdbabdabddcddbaadbccadacabddabacddccabcbccddaadbbadbadbbdbdbdbcacadacbcbbadaccdcbbacacabbdabdcbaaadbcdcbdadcbdadbacaacacadabbdbdcdbbccddcccdbdbdcaccdacbacdbdbabacbbacdadcaadbabbbbcbddaddcddaacdaaccbaddacbcaabbabbcbdcaacadaabdbdcabacccdbbccaddcdcccdbccbbbdbcddbaabacacbaddaccbdcbdcccdddacbcbdadaadcbdbaabcbdbabcbabbcbdcbbaacadcacddbcdacddbaacaadccbbadbbdbbdaacccdddcbacdbcbccdccdabaddacaacadbdbccbdabdccdbaadabacbcaccdcbdcaacbbdaccbbbddaccadbbccbbadacbccacbcacbabdbabcacadabccbcaaaccacaaccaaabdbbadcbdcbdbacdadadcdddcddacaccbaddadbccadbbdbacbddddddccbdbbdacccdcaacddbdcadaabbddbbbcdddacddddddabddbbcadcdcabaaabbcbabadabdaacccbbacaacdaadcbbbbabdabddcddabbcbadbdbddccdbabddbabbabcddcdcbddadacaaabaccbdbccacaaabdaaaacdccbdcbacbaabdcdcabdcdbdbdbbddccbabdbcacdbadaabddddbbcccacddcccaadacdbacaadccdaadccadcbacdbccdbbdbdcadcbabcbbbcaacddbdcaadccacddcaacdabadaacaddcdaababacaddccadabcdcabbcadacaabddbbacacbdbddbcddddcadaccbbadccacddbcdbbaddcaaacbccadcbaabcacbcdacddabbcaccddabadcacaaddcddccacbcadbbaadadbbacdccabccababcadccbbaaaadbddabcddbcdaadcddabbabadbdbdaddaaacbacadddaacbcdbccaacbbdccabaadddbcbbacacadaddbaaddcbdbaabbddbcdbcdabdadcbdadcaccadaddbdcbddccacbbbaadcbbadcbbccadcaaacbcdbbaacccbcdaaaacadadcdacbbdbcbbacbcabadbcbddbbbaccadabcacaaaddabbdccdadbccaabcbaabddcdababdabacdddcdbcabbbaaaddaccbaaabcbbccdaadaabbdddbbadcbadccdcdbabadaccdcaccbcdcbdbcbbbaccdaadcadadbbabbabcbacbcdbcbcdbadacdcdaadcaaaddabccaccbdcdaddcdabacdccddacbaddabcdddbdaaabbdcbdbcbcdadbdaaaaacdcbadbcbcaaddaacabbaadcadccdbacbaadcacadddbbbbbcbdadccacaadccddabaccbddbaadbadbacbbaaccbdaaacbcbcdbdacbbbbadbddbdaadbcbcddaaadccbbcccccaaaccdcacdcbdaadbdabbbccbcaddaadbccbababdcdcdabaabcbdbdcacacbbcbcbcbaddcdadaaacdadbbcbacddadaabdcdaacbbcccccaaaacbaaabbbbcaddaaddcacbdcbdccbaccbdbdadbababdddbddadacbcbbbabcccababacbbbaaccdddbdbdccddbdacdccccccababbbdccabdcbaaaabacacbbddadacabbcbcdaabbcabcdabdacbdddcdaabbcbdbbdaccaadadbbccdacaaaddaddacbbdadbabcadddcbabcaaacdddbbddaccdcabcbdabcdbadababacbdbbdbbdbbddcdccdbdabbbacdccbcdbccdbabcaabcdddbcbabcbdddaddbacaddcccccacaacbbccbaadbdbacdcaacacddbacddadacddabcaddcabdbaacbadabaadcacddabcbabcdaddabbdaaccddddbcccbadcaacdddcdcbdbbcdabadacadaddddaaadbbccbaaacdaabbacacdadccadbbcacdadababbbbdccbbaaacacacdbaccaddacddbdddcabcdbdbbddccddaaacacbbaadacdbacddccddbbadadabbadcdcaacccbbabdabbcbbbaaaabdbaadbabcbabacbadbbcadccbcadcdbcbccabbccddcbccccabaacdbabbbbbdcdadbbbaddaacaaddbcbbbdbabcdccdaadaacddacdacbabdaddbccbbadbcbcccacadaccacaddadbcdacbbaacaabbdaadbcbbabcbdbacabbcaadcbddaabbdcabdbdaccdccbcbacabababbcabdcdaddbdacbdaacbaacdcdcbabdaddddaddaddabadaaddaabbbaaadccaabcbabddcaacbcacbccabadddaddcbbadaddbcdbbcdabbdbadcadcabcabaddaaadbbbaaabcbcdbadcbaccabdbcaababddddbdcdccdbaaacbbdabdaacdcbddcbdbabcbabadbccbdbbbcabbcbdaacdaabcbabdbaacbdabcacbdabccacadcbcbcbcbdcadbaaabcddacddcdadbcadacdabbdadacdbadaacbbabcadcbcccbacaccacabddccdacbdccbaabaaabbdddcbdabcabdabbcddaddbcbacababcbbaacbccbdccdadcbdbaaaaadaadcdadcabacdbdcddababbacabbccabbbdccbbddacdbdbaaccddccbcaadccbbbbbadbbddcaccacdbbcdbdcbdabbbbdaabcbadbccdbdbcbacccccddacadacbbbcadddadaddadabdacdbdbaccbbdbabbdaddadcdcbcbdccbdbdbcbdcacbddbcdcacdccabccccacaccadcdcbaacaabcdddbccbddabcacaccdcacdaaacaccdbcadbbacdcadcaacdcadaccacacbdbdaaadbbcdcdcbcdacccadabcdbbdcababbbdcabbdbdbddccabbaacbbdabaccbbdaaccddacdbabbdcccbccaacaaaacccdcbbadbbdadcaddadbdddacdbdbbdbaccaabdcdacabbacbbccdabdadccaacccbcaddbcadcccbdbdbdabcccccdaabbaaaabbcbcadcabcbcccbdcaabbbaacabcacabbaacdcadbadbbaddbdcbcccdddbadbcbbbcaaddaddccabbdcabdcbabddbcbdbaddaacbcdaadababcabbbdabbdaabdbbbbacbabcacdccbbbdcccdddcbcacbdcadbbdcbddacbadbdbbcccbaacdbaaacabaabbadccaaccaaddbcaaaabdcbccaabbbbccdbdcccbacdaaccacaddacaddbdbadbcdcdbddabdababaacccbcbadaabbbcadadcddabdbbbccbcccbdaadaaaabbcaaadddbaacabbdcddaacbadadaabbdacbcdaabbdacbcbcadbdcddaacccabdabadadcccdadcaddabdcddbacbcccdcacbaaaddcccdcadddcaaabcabcbabaacbadcbabbadbbbbbddcdacaadaaabcdbcdadbadbccadbdbddbdbbdabddcdadcdadcbadcdccadddaccaacbcaddbbbcdbdbcdadabacddcacdbaabbcadbddbcbacdaaababacdcdbadabbdbdaccddabaabdbacabacabdddabbddbbcdbdccdbabcdccbacbcbaccdbadadddbaabcdadccdbdbccacdcadaabcbdcbccacbabddcbcdcabcdaabcbacdcddaddcbadccbaaabadbbacbabbcccbcccaabaadadacccbbaaaabbbbcbdbabddbbbdcabcccaaabadabaddddbcadbdabaabbdbaacbbcadbbccaaadcacdacddcdcccddbdcccccaabbbbbcccbbdadaadcbcaccdcaaaccadbbccaddadabbbabacbcbacdbadabbcaaccbddabadcddbddcbcacccccbbadaabbbbbddabdcbbbddacbbbdadbacaacddacaadaadcccdcbadbbcaabadbbdbddbdbdaabaccaaccbcdaadcbcbdddadbabbcbdacbcabbbdbddcbdddbadcaddccacabcbcdbcdadaadadbcddadbdadbbaadaabdcbbddddcbdcbacacdaadcddbabdacbcdbcdcdaddccbabaccabcbdaabdbddbddbdbccacbbccbbcbacbbacaabdaaccaaaccdcbbabdccbbddcdaacdaadadabadcbccbbbcdadcdacdaccccdbacbdbbddccaaaccadacacbcbdbbdabcbacdacabdbdcdcadcbabcdabcbdcdcbbdadadaddbcdddcbbccacadabdcccccadbdcdaadabacaadaabdccababdaacdadcdbaabcadcdbdcddbcadddaabaddadcaadcacdddcdbcccbadcbabddaccdabaccbadcdabbaddccccadccdaaccabdbdbadaaabadbbbbadbdadcdddccbabbdddcdbaccacacbcdcdadadbabcbdcaabdbdbcdacdddaddcabdabaacdbbdcadbdbbaabbbbcbcacbbccacbdcabdddaccdaaaddcbdabbddbccadacbbbccbbbdadaddbabdcabacadccccbdddccbdacaddaccadcbdadcdccaacdcdabdabadcbdbaacbbbccaabdbababaadddadcdbdcdcbbbccaaccccbabdacdbddaacddabdddadabababbdcbcbadaabadcbbbdbaabaacabadbcbaacababcabbdcacbaaabdaaaaccbcdcddaaacaaccabdaadababdcabdaacdacabbabadbaccdddaadcaaabdabdbdbdacdcccdbaadbcbdacacabcdaaacadbbbbbbbadcaccadbbcdcdcaaaacdbdabaacaccddcbcccdcbbcabdabdbcaadbdbadddbcdccddbadbabdacaacdbabdbdabccaaacbbabcddaabbadccbcdcadcabcbbcabbaabbbdabcdaaccabacbccaabccacbccbabcdddbdaccaaaddabaaaacbaccbabcacbbadbcabdbcbbbcccccacaddbdbdbbcaaadaaacaaaabdabbabccbdbdcddbacbcbbacadbbbbdddaacabaabcadaabdbdcbcdabbaabcacabddcadcdbbcddbadbdcdbbcdabbaaacccdbbcdbccbadbbbacbbadbadabdccdacdabdabadcdcacbdcadcbbbacbaacccbabbccbaadaabdadbabacaaacdbaabcddadbdbacbacdcbaadbcccdabcbbbdccbabdbaccdaaaadcccaddabaacabadabcdcacabdcadcabddcdddddcddaabcdaccbbdabcdbdadbdbbcccdddaaaddbcdbabddbabadadcbdddaccdababddabacadadabaabcdbabdcabcdddacddccccdcbcadabdabcabbacccaccdaccabaaaabaaaddcadababdbdacdcbbaadabdaccbdcabbcaadbcbadaaaddcdcacbbdcababbaadcbadacacdbbddabaacabcbdbddbaddbbbacaabaadcaaddbaacbdcccaddbcacbbbddbcbcccbccbddaddaabdabbbcaaccaaaaabbabdbcaabababacdabbdcdabbdaaccbcdcabaabadabcdcccdddbccadbcbabbdbdcdcbadbdbadccacdbdbacadbcabcbdcdbccbbcbbcddccdbcdcdddcadacadaabdbcdaabaacbabcaaaaadcbaabcbbadbcddcbbbddbabcacdccbcbadcbacdacbdbddccdbdddabcaabcabbccabbadacaadbddbacbbdcaccbcbcabadbdaccbdadcdaabbdbcacabcdbaaacbddadccadacdbdbaabcdacdbdaccabdddcdbdadbbdaddcddcdadccbbbbcbadbabbcaadcccdcddcabccbcdbcccdcadabbbcdbddcbbddcdbbcadacddcdbbbbbcaaccdabdbdacccdbdcacbdbdabcbcbdbbaababcdacbccdbbaaddbdcccbaacbbcdcccddabcacbdbadbaaabdadabadcbdccadacdcbacbbdcbddabcadacaccdbbdcacdbbccbdadadbaccddbccdacadaccdbdccadbccdacdcbdbddadcbdddcbadcbadbcdcadcdbbdaabadacdbdababdcccaabbddbbcdbdacdaddcbaaadcccccbacaccdabdcacddbbacabcccbccbdcbacddcddbddcdaaddacaaaababaaddaaabdccadbadbadcbaddbabdadcbdaddcaaccddbddbdbcbdbabacabcadcaadbdcaaaddcbbdacabddabcbddaccdacdbacabddbdbadddbacbdacacbcbaadbcdbadccddcdacacabdcdcabbabacbddcdadcbcaddabbbccdcaccdcbbbdbcbbbdcbccacbcadbaaadbddddacacaaddabcbcacdcbbccdadbdcabdcabadcbdcabdcdbabacccbddadaccabbacdcbdddbdbbdadaabaaddbadddcdaccabbbdbdacdacddadddddddbbabbcbaadadccadabdcdbaddadbaadabccccbaccdbbdccdacdaacaadcbbcdbcbcaabadbcaaabcabaacabbdbbdabdbdadbbaacdabcaddcbcacbdbcbcdaacdccddcbbbddddbcccdddddaddbdcdbaaccbdbacbbbddbdccdabbbacbacbbbdcaaababcbddccbdaababacacbcbbabcacbacacacdbbcacbdcaadccccacbdbbabcaabdcdcbcabaadadccdccccabdabaaacaaaabbbcbcccaccdbdbbcbbcabcdabdcbbcbbcbddbcdbccdabbccdcabddbccaaccccbdabbdcdabbcbbcdcdddbccabdabadddcbcddbddcdbcddcabcbcacaacbcdbaaacdbcddadaacaaccdbacddaacbcddabcdacaabbdbbcabaadccdacdbccdacdbabccadbbdabaabbabbdbcccaabcdadcdbbdbacbbccadbcbcacdbdcddaadacaddaddbadcabbdbaacbadacabccddabbdabcabadcccaadcbacdaaccbacccdccacccdbbdadaddddbabaccccacabbcdbdabcbbbdabcbbdacddbaadbacddbcbaabacdcbcccaddaaccddacdaabdbdcbabccbbcbabbcabbacaabccbbcdaccbaaadcdaaccacdbaacadcabddbaadbcddacbaccddcadabcdaabbadcbbbbdbdccacdcababbccdabcdbadaabdddaaacbbcddccaccadadacbaabdabaaacaccddcabdcadbbbdbbdabbabcbbacdcbdcdcbcabacbbcaacdcdbadccdbddbdcdbbbcdbddddacbbdcdabbcbbccdabaabbcaccddbdddbbccccbbdccdcaddbbcabbcacbdbdabbcdbccabdacdadddadcacccaabcdaaccadbbdbbdbdacacbdaabbdcacaccdacaaadbcdbacdaaaacdcbcadbdddacaaaacbdcdababccddcbcabadabbddbdbcbdbcbbbaaabcadbbcbcdbccacacdccbdddbcbddaaddcbbcbcabdabdabcbabbadabaadcadacdacbbbadacbcadaadcbdcbcbdbadcbaddcabcbacabcbabbcdbcdbabaabdcdcbbbcdbcbcdbdbbbcadcdacbaddccdabbbdbbacbbabbdcaddcadbcdbabdbbddccadbbdaccaaabbbccbacabbdbbaaaddcbcdddccacdcadaccbbaabababdbbdcdbdcbbaacdcdbdcccaacdcbbaddcbbbacdbddbdbdbcdcabdbcaabbcababdabdabcaddcbabcddaddbbdbdabcdcccdbbaaccdacbdcdabcaddaddabaababcbbdddddabcabcabcdbbbacadbcdcbaabbdcbbaadbcdabdabbaacbbdddcaacabadbbacbdddcaddccabcbaaddcabddabdbacadacabddbdaacacbcdcbdaacddddaaddbacbddcdccabdbbbbaccbbcdabcadbcacaddacbbccbbaadcdabdcbbabccccbccdbdabbcdcbadccdcabbacadcbbddbadddcbacabadcbcdddaaadaadccabddabdcbaddcbdcbbdabcaadcacaadbbdcadcddbbdddbaaabbdbcadbcdacdcddddcbcacdcbbdadaaddacdabdcbabbbaadabddbdcbccaaaabbaaccdacccdaccddbddaabadccdbabdbccbdbbbcaddacacbacdbdddabaaadbbccdbadcdabdcadbbcdabdbdabbaacaddcccabadbddbbadccabdbbddbbbdcccccadccaddadddddbbbcccabacddabcbbcaacdcdaaccdbbbaccbaadaacadcddbcaacccdadbcabbadcaccddbadbdabbcdddcbcbbcaccabdabacbbdcbbcbddcdacabbacacbcbdadadbadcaccadbadaadadabadbcbcdddcbacaccaaabaacaaaadcbcabdcbacdcbccdadddddcadabbabdddacbbaaddbaabbdbbabdcddcbaccdcabbccbdaddaaaaabcddbccdcaadddbcbaccaddcccbacccccdadbbdbdabdbabcacbbbbbcabcadbbdcccbbabdcdbdabcbdacbdbbdbaabbcdbbbbdcccabcdaddaabdbcccbdaaaabccbaadabaddbbbbcddbbbaadcbcadbdaaaacbabdcddddddbbcccbacadbccaacddcaccccbcdcdddabccccbbcaaaddbdddacdcaccccbcddcacdbbbbbcaddcadbbcabcadbcbcddcaaabccdaabcaddacdabadbdbcabbacbcaacdcbaddadabdcdbcbabaaaabaaadcbcbdacacaaccbcabaccbcbbbddbdcddcacdacbdbbcbdbdbabdccdcadacadddcbadcbddbbccabbbbcdcbbcbaddbadccbbbddcadcdbdbcabbcbbcbbaccdbdbdcacbbbbacadcabcdcacddbcccbbadcaddcddcbdbdcaabacbdcccadbabcdbbcdabbdacdacccadcbcdcdbbabddcbdcbbdbbbabbcbccdddcacccbbbaccbdaccbdcaddaaaccbadaddaaaccbacbabcacdbbbccdabbbadddbcbadbbcacbcccdbabdbdddddababbaadadaacdbacaadcbaabcdacabcacdabbadbdbbdaabacbdaddbcabccabbbcdacbbadbbaabbadbbdbbcbbbbcbbcbabaaddbcbdccbdddcbcadabbaddccabadbacbaadcabdabcdaddaaccaabcbdbddbddabbbcacbcdbbbaccaabaabbabcdcbcdaadaadcbddbcadabdcdabdbdcdbbbdacddabcdaabddccbbdbabcbacbabbacdaaddbabcddcbacbaddbdcacccaccdadcbccbaddcccadcdaaadcadabdadaacadcaadacacdcaccbcbddaabddbbbbdddacbabbdcdcdbcaabdabccaacbdacbabcccddcbbbccddcabbaccbaacccadcdcaaacabadaacdaaadccbddccdccbabdbdbccddaaddbdccbbddaabdbbadbacbcabcaacbcacababdcbbddccbdcaddaccadbcbcaccbdabbcabacdaacdcaaccdddbdaaacabbdaabddccddaabaabbddbdcdbbcddbbbdcccdaacacddbdcaaacdbacbaadccbacacddcbcdccccabddadbbabaabccddaacbdcdadbadbbdabddbabccbdcccbcdcaddadbbcddbbacaaaddbcdbadadabcacadadcbaadcaaaaaaacbcbabdacbccdccabbdccaaabbdcdbdcabacddcccadaababadddbabcabdccddabdacabcbadbbaabdadabadccdbccdccdcdaccbacbdcddbdbcdcabcacdcccaddabdbcbbcaccbaabcadccbbadacbacdbdcccaabccdbdadacdababaccdbaddbddabbcbdcbcbaadbabbbbdcdbcccdcdadcbbdbcdbbaacacccadcadccdddbabbcbcbdcabccbdccacccbdcbcaccbccddbcddadbcadddbbcddbdadabacddbccddabbdaadaaabdcabacbccabcbbacddacadbabcbbcaabdaccabcabdddcbdcbabdcbcbcdabbcbabdcbcbbcbdbcaaadabacdbdddcddaadbcddbcdbdbdadbbbdcbbccadcbbddaadaaccadcdaacbcbbabbddcbccbbcacdcaacddccccaacaddbccaabacbcddadccabaadaccadabddcdcbcdacadadadbcbbbcbcdcdbcdabdbbacabdadbdbadbcdbdcbbbbcdabdbbbdddccbcabcbbbddcbaabdbaddcbaaabcdbaacdccbabcdbaaaccccaaaccdbdaddddbcabadcbbcdbccabcaadbcbbcbacacbaadcdbbddbcbcaadbaadaabddabacacdabdcccdcdbcacabddcdcbbabacbdaacabbbddabacaaabcadbcabcbacdacbbbbcbbdbcbbdcdcdcbcbaddabbdbcdbccbcadcdbcdabbccaaaadbccbdaddbddcbbaacddddbbbacbdcbdabaabbbcadbacaaaadcbadbaabbddbcbabbdabbdbcbdddabbddabdbacbdbcbcadbcdaddbbdcaacbaabacccbcddccabbbdaaccacbcddaaaadbcbbbcdbdbadbcdbadbdbaadacbbdbcbadaccbdcadcbabbddadcabcbbcbbcacadbdcbaaadcbdbddcabdcdddaabbbaccdacdcccdcbacbccdddcdbabacdbbacbdbaddddaacabbcdccaaccbccddddcdaabdccbcbaaddbacbcacbaadbcdbcddccbaddabaaadbadcdbcadbbccbcacdacbbcdbcaadcbcdaacacddcbbcbcbcdbddbddcbbaacdccabaaaaaddbbaaaddacaddcacdababbbdbaababdabbcddaccabbdacacbaaadaddcbcbcdbbadadacabbcaadddadacbaccccaaacccdaddacdcadcabbcbdcccddbdccbbcddadbabacccabaadcdabacacadcbdcdddbdbcacddcbdabaccdbbbbcaadaadaccdaaccbddadbadbcbaaabaddcdabbadbcddbdddbcccaadbddbadcdcdbcabaabcabcdbcdacaaadcbaabccbdaddcbaaabdbbbbbcdaaadadcddabbdcaaccadbdcaadbcdbbabdbacdacbbdcccdbcdadaddaacbaaaacddcdadbbcbdbdbbacbddcacccccbcabcddccdcbdbcaacabcbcddadcbcaddaddbabbdaaacdbbcabbdddbadcbdcccabddacdddbdcaadcdcddcbadbdacdbbbcbbdcddbbcbddbbbcbccabaaddcacdccdcbddbdadaadccbbdcaadcddddbacbcbadacdcccccdadbaabcddadaabbcacaadbbcacaaaabdbcddbcbabadbdcabcdcbdbccdbccbadbcbddacabcaadcccaaadadacacdbccccbbabdddbaaacbbaabaadccdbccdbacbdacdacbdcaabbaccbaacadbcdaaddacabacdbcdbbdabbadbdcadbbcbdbbbbacdcddbccadcaabbcaccbdaababaabbcbdbabcbbccaabcdadadcdadcbdaaabbdacdababbcdaccdbadcbdddcdadaadabbabdadcadaaccbcacaaddbcacacbbdcbccdadbdccbabbcaacccaaacdccabcacdbddcdabcdcccdcabcabdacaddadaddadccadbbdabdbcbcbcaadcdccddbbddabccdbdbbadbbddabaacbdbaccadcddbcabdaccbadcaabddaacddbacccacbdcbabcdbaccbaaacddbcdbbdbbccadabccacacbccacbadddddddccccdddbabcdaaaddacdcdadbbacdbdbbcbacddcbabadbbbdbaaaddaadbcbacbcddddbdcccbccbccabcdddbccabcdbbcbddbcdabcacadcccababcbabcaaccabacacaacdbaccbaccdbccdccabaccdaadccadbbcbbadddcbccdbddbbbddabbbbacabccbdbacabcbbcddcdccdacbddaaacbaacdbcbcdbbbcacdcbcdabcabccacaacdadabbddcadabdbaabaddcbbaacdcacabdbacaccabbbdcdabcddabddaabccdbbbbbdcbcaaddaacdadcdcccacdccabaacbdadbaddddaacbccdaaaccdadaabbbcdbcbbadacdabdddbaddbbdabbcdcbdacbaddddbbccbbcaadcbdcbaacbacbbbcadcbbcadddddcaccbccddcddbcdadbbbbbadcdaccdddbdbdbcabbcbbdbbbbdddbcbdcaacbacbddddadbccbadadadaadbacddbbdabacdcabdbbccdadddcddaaabcaaccbbcdabdddaccdbbabbbcdacdccbdbacbccaabcdabccabbcdacdacdabaababdbbddccaddccbdabbaccbddaaddabddcccdaabbdaacdacbdadbdaabcdadccbbbcaabdccddcddabadbcdbcacdcddbcbcdccdaacbaddaacbadbcdbabddbbcacbbddabcadddadcbcdaccaddcdbabaaabbacdcddbdbbdabaacdbddcbbccabdbcabbcbadacdaaaadcdacbcbbbcadacbdaccacdabadbaddaaaadbdaaadcadcbaacbaaddaadcbbbcdaabcdbbbacdbbaadacaddadaaadaacabddacbcdaadbaddacaadabcadbcadadaacdbbcbcbdcbaaadddbcaadbdaddabcbcababcacbdbbddcbddbdcaadabddcbbacdaadaaacdcbdbdbbbbadddbdabdbacbabdaadcbcbddadddadacaabcabbaabbaddabbbddbbbbaccbdccbdbbbbcadcddabccadbdbabddaaadbbbcaaabddbaaddbbaccccbaabdddbdabccbddbbdaaccaacbaaabbddccbcdcddbbdaaaddddaaaacdbdbbbaacbcdacbcbcacaccdccdcdcaadaaccbacdcdabacaccaabccbabdbccdbacbcbaacabbbdcbdcabdcbaccabaccdbadcaaaacadadcababbdacbddadaabbacdadcabcbbdddccbdbddccaddcabcccbdaaabddabcdbabbbaacbaddcbbddbaabddddcbbacbacabcadcabbdbddadabcbaddccdcdadcbbcbbbccbddacbaccdcbabaaddbcccbadacdbcacadcddacabaaacdddbacccdabdbddddadddabdbadbbbacddbbbaabccabacadacabdcdcbdcbaacdaadbcacaddbacbacbcbcdadcbbcbbdcaabccbdccbbdabbccddadcaddaadababbcabbbddabadddcdcabacccadaccabdabbdbdccbbcbcbcdcababdcbdbcdabbbcaaccaaaabddbbdcabbccaadcdcbcaddadcdcacbbabadaccadcbdadcdcadaadccbacadcabcacdaddcbdadcdbdccdcacbbaadaadabacbdadabdbacaadbabcaabaccbdcbdbcbadccbdbcdcdacbacddbbbacaddacabbccbddcbadaccccadaaabadcdbcddcacbcdaadbbdcdbcbacadcdcbbcbbbbbcbdddcbccaabbcadccdbcccbddaaccabcdcdcbbacdbdaabccbbababbbbbbcdaacadbaacbabdddbddabcdcbddbcbdcdddcbdcccadbdbabdcbcdabaadbaabbaadbaaaaabaabbbcabbcbcabcdcbadbbddaabbbddacdbcabacbbbbadabbacaababccddbdcbdaccaccaccbbdbcaadacaabdbaccabacadabcbaabbacbcbcdadaacddadadccdabddcaddcacaaabcbdaabdccadbdddddcbbdccddbaccdbaaddcddccdbdcabcbbdddbbcbcbdacabdadddbabbaaaccbbbddbdabbbaaaabdcbdaabccaccdbbccbcbddaadcbbbbdbdcbcdaaddbdbddbccbcaccdaccdbcacadacdbdccaacbbdaacaccaaaabccabababccdcddcbcdbcddaadcccacaabddbbbdcaadcbcabbddcdcacaadabdbacabbcdacbadbcbacccccbccadaccbbabcabbcbadccdbacdddaccdbacbdaaaabdadccccaaaccccbbcbdacacdbaacaadacaaaddbaccbadbabaccbaabccdbacdaabbabadbaadbddcabcddcbcabbacadcdbbcbcddabbbabcadbdabbacbdabdacacbcccdaabaaddabdaaadabacbcdadccbcdbccdbadadaabdaacccbaccbdcabdacabdcbadcbdabcddddadacdbabacabaacbadaabdcbdcbdbccbcdcddabcaabdabdccdaabcccccbbcdccaabdcaacbadcccadaddcadbddacaadbbacbadbdbacbdabacaccdcadadbdabdbcaacbabbdccaaadacbaccbcbcbbcdcadacbbdaccbaaccccadadacbbdbbdbdcbcccabaccdaaacbdcdaaccdbddbbbdbbadcbcacbccabbaccbcacdcbdcaaddcaccdcabccbaccadbacabacbcddcdcbddacbbacccdbcdcaaddbcbaabadabcccacdadadbcaaadaadaacccddcdacdcbadbcddddddadaddcbabacbacddccdbabaddbcaaababbbcbddbcccddabcdaccacdcccccbccacbcbcdaaabccababccdacdadddabcddbbcddadbbadcdcaaabccdbdcabcddbbdaabcdcdbdabdcbdddbdcdcdadadbdcdabcdbbbbddadaaacbbadcacabbbacbacbadbacbcdcadcdcadddbabcaaccacbbbaaccbdbabacaaabdcabdbbcdbdcbaaddbbcdadbbddcddadcdcdaabbcdadbbddccdcbddcabccadcacbcdadcdbbcbbcccddabbacaddcdadacadcddcddddcadbaaaddacdabbacdddaccacbbaadaddcabaaccbdbccbadbdccdbccdcbdbbbbcdbabacadddcbacabacbcabaaacadaababaadcddaabdcdbabdaddbcadbcddddcbbdabbadabddcaababcdcaaaddaddcdaccbabdabbdcbbdacccdbbdbabdbcbdcbbadbcbbcadbcabaaabbccbdccdbcacaacddbcbdddadcaccccccaaccddcdbcddcdbdbdbdabcbbbdacadaddbabddbaadbccdddabaadbbccccadaacabacbcabbdaccddbccddccdbbabaabdaaadacacddcdddbaadbbbdddccdcabbadbccacccadcacabcdbcaddccdbdaaabaccbccaccaccacdaaabcdcbcbcadbadaacbbbcdaddbcabaccbcadabdadcdbadaabdadcdbcabdccaacacccbbcdacabbadbcccbdababbabcccacaacccdadaaaabcdbbcdbabbadbadbadabcacbbdbbcbddcbabcbcbbbcdbabbbcadccbcadbaddbbbbdddadbbabddcddbbddcdddcddcaabbdaccbcdcbdccccacddbcabbdcaccaaccdbdcddcbadbcaccdacadbcacbcbbdacadcacbdacddbcccbddaddbadbcacdccaaabadbccacbdbabdcbabaccdcaaaddcdaabcdbcdbcdcaccbbaabcabccdbbccdbcadbdbdacaacddcddbcbacbdcbbadbbcbdbdaaccbbcaadacdbbdcacaabacdabbcacdbbdbbbcabdcbcddbaccbbbbdabcabbdbddabcdcbdccaaddacacdbbdcccbcaaaabbabbabdaabadababacdcccccdcbcacbadadaccdadaccdaacaaadbbcbaccddbadaabacbdbabcddccadbdcaabdbbcddabbabcbadbadacbaaddabcbccbbdcbdccbbdacccabbbcbdacdcdccccbbcbbdccdbbbacdadcadcadcdabaabbdbadadcaaccacbdcbcbaccddcccabcdabcacdabcacaccbdcdbbdccccdbcbdacbaccaabadaaacbcbacacbbbbabdbdcaaccdaacbbdbacccbbadabcadaddddadcabbbaccdccdbcaccbadddcbcbbccaadcdaabcaabcbdcabcbdddcbcbccdddcddcbbdbbdddbacbcabdcabdaaabdaabcdbbbbbacbcabbcccdcccbaaaaaacacbcbdcabcaadaacacddaabcabbacaddabcacddcbbcabbcbabcaccdbcaadcbaacdabbbbdccaaaddbbadadbddcccddaabcabbcdccdcddaadbbcdadcdbaadabbbcaddadbcdaddadadcdabcddacdcbbdbdbabdcadcdddcbacbabcbdacccadcdbcbabdcdabbdbdacaccdbccabcbdaaccddbaaabdddabdaadccbadbcdaadbbcbababaddbcbddcaadbdacaabbddadabdccadcbacbbadaaaddbbdadcdaaacabdccdcbbdadacabcbabacdcacccadddcdbabdbbdccbdcbbcaacdadddaddaacddabbdbcacbdcddaddbdcddddacabdaadbaddbcbabcdbcccaddbbcbabcabdcabacbbdbbbcaddcdcbacbdddabcbccaadddcdbdccbbcaccacbcbdcbbcbadcabdcdddbbabbddbbdcdacddaadbddaaabcaddabadcccaddbdbddcccbbdddadcbabcbcdbaadbddcbccaadcaddaabbbacaaaaadbccaacbabadbddbadaddcccbbdaccdadabbacadadaddadcababbcdcadaaacbdacaabaddabdccbcaadddadcaaccabadcaadbbccbccaacbbddabbadabbcbbaaddccbaabbdcbccdcdccabcbdbdbacdabaaaddddaadbdabcbbacdabbaaddadbcabdbaaaddddabbbbabdcacccacbcdcadaaadbcbbdbaaaccdcbaccccdbccddcccdaaddbaadcbcdadbcdbbaaaadcccbddddbbccbdabbaaaadadcadaabbdbdbccbdcdbbbdbcddcbbcdaccdaaaaadadbddcdbabaabaabacacbcaccdcddddbcbdbccaddcbcaddbdadacccadaadbdbabdaacdadccbdcbcbcbdbcdacacdbaacbddbacdcbacaddacbbacaabccbbabaadbcaabaddcdabcccbacbccdddddcccccadbaccaccbacdadbbcbacaacccbbddbcdcdbcdbaaababaaadddbadbdcccbdcdaacdddddcbdabbbaccbbbccacdcdaadddddadddbadbccaaacbbccbbcbcbabcdadadcddddcdbabbccbabdbbbcdabbabccbaacaddacdcbbbbbacdbcacbabbaadbbbbcddaaaddbdbddcbbdbccbdcbabcbadcddcaaacccbbbbccbcdabadcaddadbdbcbdbdcccbbdadaacddbcdacccbacbbdabccaaaadbcabbbacddbabcbdcabddcdcdbacaaacbcbadbccccddbdcabcddcbdbaccaacdbcbcdbaaacadbcadabaccddddabdbcccdcdbadabddaddbaacbacdbdbbcadaaabadcbccddcdbdaaaadcccbcbacbacadcdaccaacabdbacaddcdaccdbbbabdbbbcdbccdadacbdcaccdacdaacaccddcbcaadaccdccddabdadbbadadbdbbcbadcaacccbdbbcadddcabbdcdbbcaababaadcdcaaacbcabcccbbcdcadcdabddcbabdaaddbabbbaadcabdabadbabbbbaaacdcbabcbcaacddbcddbccbbbbaddabbbdabaccdadaaaccaddcaccaddbbaaacdbcdbadcadcbadbcdabcabcdbacbcdadadaadddbcbcaacadaaaabcdcabdbbdbaaaacbddaacdacbaaadccbabbdcaaddacdadbbaccbcdbabbadbcaddcdccdbcbbdddcabbadcdadacbbbcbadccabddabddbaaacdcabcaababcccaabcacccccdcacaddabdbadabaacbdabcbbdabdcbaadbbaabcaabacdbadadadadcdaabdbdcdaaacdaaccbbbdbcbbacbadbdbaaccdbcbacaccabacbddacbdccdacabccadcccdbacddbdcdcadacccdacdbcbabadbadbdaabccaadacccabbccccabdabbdacabadddbdddcbaddbbdcaddacdcdccbabaadbbdccbcbadacbbdcdcadcacbdcdcbbcabbaacdababcccbcababddadacacaadbdddcdbacbdbcaadabbbbddaacbccbacaabbaddacacccaadabcaccaddbdbcddaaadbdcbbadbdabadcbdbbcacbcdddabadbcdbbbccbcdaccadcbaacbabbaadcbbddababcddcbbcbcabaadadacbdbdddbcdcbcaccbddadaabbcdabcbbdccbacbdbdadccababdbbdcbacacadcacbcbacaabcddccbbbbcadcccadcabddacccadacdcdbbbacadcabadcbddabcdbddaaddabcbcbcadcadbdadadbdacbbdbaddbcdaaaabdabbdbdaabccaabbcbdbcccdcacccddbacbcacdabacbccbdadcacaabdddccbbcdabacbbccaadabadaaabddcaadccdcdddbbdbadcbabdccccbddbccbdacacabcbbdabbadccdaacbaaadaccdbbbaaabbdbcdabdaadcccbdbddbbdabdacdaddcdbdcbdbbcabcacbcaabacdcbcdaabccaaaaaaadbbdbcadcbcdabbbcdbdabcdbaabcacacdadccdcccbccdcadadaddabdcbcacbdcdbbabccbbccbddbcdadbdaacbaaaaaabccbbbdccabbabbacbbbbdacadbadbabaddcbadaaddcdbcdbcbccadacbbdaaacacdcdddbbccddcbabbbcadabccccabacddbadbbaacdabddbbcbdbcdbacccabcbbdadbcbcacacaabccbbbcbaccaaacadabdcbdaaddaaaaadaabcddbaddbbcbdadbdcbddcdacdadddaaccbdcccdbbacdbbbdbadbabddaaadadaadbbcbbacabaaaccadabbdcdcbadcbbcdcdcabaaaccbabbcccdbaaacadbacbdcabdaacadddabdddbbcbcaccadcadbabdaaccaacaadaaddabcbbbbcbadcadccacbbdbabaddaaadaddcbccadcccbabdbbcdbcadacbcabacddbcadcaabdabdaccbddcadddacdcbadbbaaccbddbcaaaadbbacdaaadadcdcbdaccbadaccbacaadcddacdaacccaddcbdbcbbaadbbcbdddccbbabcaaababaccccbbbdcbbbcbbcdddbdaacacaaaccbbadacbbadbbccdaacacbacdabaddabdbaaacdbabdbbadbcbaadcbabbdadaddadcbdbadccddbabbadcacabcacbcdacdadcabdccdbddbcacdabbcabbadbabaaddabddcacccbaacabdbbaccbbcccdcacaaccdbdcbdbcbccdcacacdacdabbbbccaaaabcacbadbbabcbaddcabbdaacabcdbddbaabcdcbdbacaaaacaaddcbabcdbbdcdcdaabddbacddbbbbdbddadcddcbacaddcbdccaaaacccdbbdaacbbadddcbdadabcdbabbbbcdcddadcbdabaadcaadccacdcbbbbadcadccabcacdababbaabdaadbaaaccbcabbccccdccbbbabcbcbbccddcababcccddcdbddababcdbbdacdaadcbbcbabbdbdadbdabbcadadbddacccacbdadbadadabbdcdddddbbbdabbcbcbbdbcbcbccbbbbbdbdaccdbcaadaaaaadadcabcabdbdbcbcddbadbdacbddcdcacadbbadbbdbadadaacdacbaaaacdbccaacbdcbcbdbbbcbbbcacccccadcbcacbaabbbcbaacdbacbbcacddccddadaabbabcbbdcdbcaaacacaabacccdaaabccabbadcbadacacacaadbbbcdcccadcdabdcbbbaacbcccbdbdccaacbcdccdcadadcbdccdcadcaaaaaaadabbbcdbacbbbbdabbcddbabdcabbdcbacddadacabaabbbaabaddccccbbbcbdcaaacbabbdaadbbdbcdbcdcbdabadabadbdbddbdbcaaacaacbababaadcadbbbcaabbcbbcbbadbdabccbabdabbbabdddbadccbcdcccdddabbdadbdbdbbdccdcbcbbbbbaacbacbccaccababbdbcbbcbbbbabdbadbabbcaadbcbccaabdccaabdbdcdacababdbdcdbdcacaabcdddcbbacccbccdaddadadcccbcbadadbbacaababdbcdcbddcbddccbbbccccdbcdadaadaacbcabbadbddbaccdbcadcaaccadccdbacdadabacdcaaabddccaacabacdadbbadcabdabaacbcbacacbddabdcdadddbcaacacccaaabdcdbcbcbccccddbaaaaabbdabdcaaddcccccbaccccbbcbaaddcdbabacadcdbcaabcadbadbddaadddacbcadcdddadaccabcbbbbaacaacbcbdcbbbaccdcaccdcabcacaaadbbcbddccbbcadbddacccaccccddcbabdbcacbaccacabacbcaccdacaaacdcadddadcaadcddabbbaccccbdadbdbcdbaadacbdaadaccccbbadabdbbdcddcdbdacbbdcbcdaacabcabddddcdacabacacccdbacdbdacdabcadaaabbbabbadaccdbadaabbbdddbcabdcaadabcaadacdabbbbabbbbbabddcacccbbbcdbcbdbbcabacccdaadbbbdccdaaaabadcdabaadbadcdcccccabccbcdadcbcdabdaddbdcddccdaabadbbcbacbacdbcdabdbcbdabcbcacadcddadccbaabccdacddccbabcacaacdaaccdabaccaabdccdcbbccaadddcbabdcddabdddabbbacbdcccbbccbdccdbacabcbdccdacdabcdbcdcadbcdbdabdccbdbdcddbbabbccddccbdbbaadcdacaacaccccdccacaabddddddcdccbabbbadbbbbacccaaabdaccacddcddbcccbdaabdacbdddacaabdcacbdccddbcdaabdddadadadbdaadcbdcdcdcccddcddaadddaddcbcdabcdcbddadcbbcaadbcaccccadccbbbccdcbdccadadadcadcadaccadbacbbabbbcadccbbbabcbaabdcdababbdcdabaddbbdacdadccddabbadabaaddcdcbadccbbdacdcaddcbbcbdaadadcddabbdabdacaddbabaccdccabaccbdccbadbddcababdbdaddcbabdbbccdbbbbdadbacbdcbbbdbabbddbcdcabdbaadddbbcbdadbcadbcbaacccbbbabcccbcbcbaddbcdabdccaabcaccdcbcbccbdadaccbacacbabbddbbdabddcabcdacbabbdacabcbcbccaabacdabbcadddbccdbaddbabbabddabbbdaaabddbdcaacdbaabbbbddcbacdabbacdaaaabbcddbaaaccdddcbbbbabdbbcbcbbadbdcccddbaddccabbdddbacbdbabcaadcccbaadcdcdcacbacbdbcbcdcadadacabdabbdadabbdadabadccbaccccdabdbdbaadcacbaadbdadaacbbdbbddaccbacbaaccbdcaaadaabcabbddcadddcdbcaadbbcacbaacddcddccddcacccaadbaadbaddbdcbadbbbdcbdabcaddbcbbbbdaccbadbdabcdacaddacdabdddabcdbcbcbccaabdadbbddbacbacaacbcacabcdcdbcddbddcbdcaaccbcdcdaaddbcbcbdaabbabcbcdabadcddbbcdcdbbddbdbccaddaadcabadccbabdbacbcddbabaabcaaacddddabbbadbaaabadcacadbcbdccdbcaaadcdcabcbaabdccdbbabadccbcddbaacbcbdabcbcbbcdabaabdcdaddcdabcccaabbcbbcbcbcbdcccdcbdabbccbdadcdcacbdcadbcdccabbddbabddbbcaaddaaaabdddccadbacabbcbdbbcbacbcdbdaccccacdddccaadbcabbdcbbccddcccddbcddbaadabbcdbdddccaccaadadcbdcbabdabaccdadcccbbdbacbabddcdccacaccadbadcaadcacacacbcabbadaadababccbaddcbcbbcaaaaaabadbdcdabcbbcadcdababdaacbabbbbcaddcbcdccbbbdbaadcacddccddcddcdcbcdaabdddbaacbbadcbadcbdabbbdcdcbaaccacbcadddaabbdbbcbadbaaabaabaccbcabcbcddccddacbdbddacbdbabbcaaaacccbababbabbbaaabbbcbbdabdcaadbccdbbacdddaccdcbdccdbcabcddcdabcdaaadadccacadbbccabacaadbcdbadabbdabbdacddbddddbbdadbddccbddacaccbabdbaabcdbabcbabdcdccdaabaaadcacdaaadaddaaadbdccdbaaacdbdabadacbcbcaacabcdbbbcbdcdcbcbddccbbdbcbddcddcbaaccdbbaacabbbcabdcbbddcbcadacabddcbaaabdcaccabdbccdbdbbdddabdcbcbcbcabacdadcbdcbddadcbbaccbdbbddccddbdcdbbbbabbcaadcbcbadacccaccbcbaddaaacaadbbdadabbbcbcdcccadabdabbbddbabbcbacabdadbaaaacbcdacddaaaababbdbcacbabdabbacccccaabccbbbcaddcbbdcabdacaaabbcbcdbcaaccbaaadcaadcadbbbbcabcaadcdcbaaadaddddcbbdbdccbcdababbcbdbaddbcdcbdcdcccbbabdcccadbdcdacdccddaaddddbadbdbdbabcaabcadddaaddcccabbdddccabdadcccbdbdccdbaddcbdccabbdadbdbcbdddbacccdddbddacbcbcbcbdbdccbadbbaccbbcaabcaaabdabcddcbacdcabcbdababbccddddcddddbdcbdacddcddaabbdcabcabbcbcdccdcabdbdadadacdadabbccbadbacddacaaabcddaadbbdabacacbdbdcacbdbbadcaacddccaacaacbcdabadadbbadbcccdcbdbccdaadcbbddabaaadacdcdabbabadbdcadacdccdcddcdadddcabccbbcbacaacabaacbdbaabddccbddcdabaccadcdabdadbdccccabcbdacabbbcbacadbdbcbccdabddadbabbcacababdacdabbdcabddbbbbbbcacdcbacdbccdcdacbdddcaccaabadbdcddbbccbbbccdddabcccacabadaadbabaaabbdacdbcbadaaabcbaccacbacdccbdcbdcdabbcdbbbacbddcbadbacaabcddabbcdbddddcacabcbabcdccddcbccacabddddcbddccdccabdacddaadbadacbdcddadadcdcccdaddaaadaddadaadabcacdaddaddcaabdbacdbadddbbbabdbadaabacbdabccabcdcdcdcabcdcbbdaccbcccdccbbadadcaaacbbabbacbcacbcaaaadbababcbaccbbdcdcdbdbadbbcbcddbcadbbbcacaadaccbcddbdbbddcbacbbabbaaaababdacadaccdbbbbbdcbaabdcdbacacdbcdbcaaadbdbaddcadcbbaabbdbabbdcdbcdcdadacbcaaaadbccdbdabacdabddcadcbacdbaadcaccbcbaababdaadadaacbaccddddcdddcbcbbcacccbbcdadbccacddccbddcbacaccaabdbacdacaadcdddbaacbbabbcadaddadcaadcaacdccbccbadabdaddbadcbadcbdabcadbccadbadadbbbadbadabbdddaddbbbaddcbdbdadabbccdbbdcaddddbbdcaacacdbccadcdbbdbdcbdbaccbdbcacabaabcadaddddcdbabcddbabaabbbdaadcdaacdaabdbbabbbbdbacddcdadbbadcdccabbdbbbbcbdacbcdadbcdccdaadbacddcbdddaccbdadbcadaabbabcdaccbbaaddaabaabbbaddddcdbcbdbcbacbcaadcaccdcabbcbcababdcddcdacbadcdccddccbdbdcdaaababcdbbadccdacdbdcdcddcbddcbccbadcaacdccbacabaadbadbbbacccbaddcbdaaccdccdbcadcbacaddbcbbdcccbdddbdcdcbaacbddacbbddbadbdacdaddadbddbdddbdbaaabbbdbbbddcbadddcddbcccddbdddcaacadaccdbbaccbbadabaaaccdbbabbabbabddcaaabbadcaaadddcabbccaabbddaaadacdbddbcbdaababbbdcadbcaccdbacacaaabacaccbbbbbbbaadbbcadaadacaddcabbcddbadcdbbadabdcccbbadbbcdcaabddcbcaacbddcdcddbbacadccaaabbdcbdacdbdbbabdccdcccabacdbcbabaccccdadcacdbcdcbdcccdbacabbcbdcbadbaccdabaccaccadcdcadbccaaccdddbaabddbdadcccbababaccbbcdacacbdddaabbbcadabcbdbaddbadbdabdcdbdcbbbdcdcbcaaccccbaacbcddddbcabcdbdcaaccbcccacaaaacbbddadccbaabddcdbcdcbaddcbddccbaddadbcbbcdddadbbaaddbbadaacccacbacccdddababbccdaccacaaddcdddaabbaabbbacabdcbdcacbbbaddddbadcdcadddddcaaabbcccbcbcdbacdcdabdaabacdddababdcddbbbacbcdcdcbbadbcdddaccabcdccaaaccdabccdabacabcdbdbbbbbaaccdddadaadbaadcdaabbccadadddbabacbaadaadcacaaaddacdcdaaadbadbdbabacadbabdbcbbdcdbccadadbacaacbacaadacbcbcdbdddabdcdcdcaababcabcdddabcdabccbaadcabcaaaaccdaadaaaccaccbbdbcbcaaddccdddbacadcadbacbcbcdccdddabcbdddcabdddadcdbaddddcbdaabadbddabbcdbdbcdcaaaaabdcbdbdacdcabdaaabcabcccaddbacabdaabbccacdbaacdcdcccbbaaaabcdddaaddcddaacdbbdbbaabdaabdcadcbaaacaddbbddbabdaddccccdaadbcdaacaadccdcdcaccddbdadaabbdbbaccbaaaabcccdcabbcaaacadcacbccbaadacbbccdcccdbabaadabdabadbcaddaadbcddccbbbaddcacbcddbdcaabbadaaacdcadcddacbcacddbabdaaccdccbabcdcbbacaadbbcccacaccaacddcaaacacadcdacaacbcacacacbdccadbbabbddbccbabcbccbdddbadbabbbdccadabdbccabcdabacccaabaadabbcbcbdcbddbcdaabcccddacdcbbbadaabdbbababcbbcacdcbbbcddaadccaabbcdcaabdccbaabdbcdcdbbdcbdbadcbdababbccbaddadadadcadbccdacbdddabbdacddbabadbbaadccdddcacdbdcaccadbaacdbbdbcaddbabdbadddabccbabbbcadbdaabbbaadadbabcadaccdacbbacbdbadccbadcaacacbbccaacdddbabbdbcbdabaaaadddaabaddabddadcddaaabbbbabbbbcbabcacadaaaabcdbabdabcaabcddacbacaabbabcbcdacaacacbcabdbbacdabadbaaaaacdaadbbbaaadabcddaddbaadddacdbbcacaaabdbacaadccabccddacdcabdbacacabdaaddabbbcdcbadbacdadbbccaddbdadbddcabadaccaaddbbbcabbacadcdddcccbdcdccdddbbcbdaaaccbddabdbaccdbbaacbaabccdaaacbacdadbdcadbcaacbabbccccbdcdbccdccabaccaadabbbbbdddaaddcdddabcbbcbaaadcacccaababadbbddaadddbbbbbcdcababcdcbbaaddddbcdaaddacacbcbcaccacacaddaadaaaabccddaacddbaddcdbaaaddaabbccbbcddbdddcdbcbdadcbddbabbbddadadabddacdadcadcbccbcadbcdcbaabcbbccbdbacdddacbaaccdccbccadbaadcddddbbbcbacdaccabaccbccbcbdbcbdcdccabacacdccbabdcbdbacdbcdddddadaddaaccccacacaaabacbadcdcbabdabbddbdcdbdbbbacdbbccacbccacccadddcacdbaaddaadbdbbaccbbaccacaaaddddcdaacccddabacbcbaadaddccdaadddadcddbbbddcccccdadadaabdccadcaccdcdcadadbcaccdabcdabbbabdaddbaadacdacbccaaadcdccdbacaacdabccaadaabbcdbcabddbddddddcdacaabababaaabcdadcbcbbcabbbbcdbaddacaaccccbbabcccddbccabbadabdcdcbaddcbcbdbbcabcccbaccdccacadcbddaaaddbccddbdcabbabbcbdccbdbbbaadccccdacccdbdcacbdcaaaccbadccaaacbdbdacabaadcbcacbcbcdbbccdcadadacbbcbcabacdcbcbdaadabbacadcdcbbdbdaccbbbbcadcbdbbddbadbacdadcacbcccdcabcacddaadccccdcdaddbbbdbccadcdbabdbcaaabcacbddbaabbaacaabdbcdabacaacdcdabddcdcadcaccccbcbababaabcdcdaadbacdcbccbddaadcabbddbacbccbbdccdbdcdbdcdcdcbcddbbbadacacbccacccbccbadabbdbddbccdabcdcaccbababcadcabdcbcbddabbbdbbcbabdabaddbbabbabccabacbcabcbaccacdaaadabdbcdcccdccdcddbaccbaabacacbbcdcadddbbcdbacdabddadaddbddbaddacbbccaddadadadccaacbbcdcabadccacdadbacadbdcaadaadccadadccaaacdcbbbadcbccdbcacabbacbdacbcadbcaacdadbddbaccdbdbabacbbddadacaaddcbccaadbbdacdbacdaddbdcaaaadbdacaaaacbddbbddccacddababccdcbdddbcdcbcbaccaddaabbaddadaabaccaadbbaddbddadaacbaadbaabbddbbddccbcbcdcdcbdbdbbbdcabbcccdaccbcdcbbcbcdbcdbdcdccdddcabddbadbaaccbdbccabcdcdbadbbcacbabcdcbdaddacbdbbaccccbcdadbdbbaaabacacdcddbbaadddccbbcddddbddabcbcabdaabddbabacadddcbdcccbcadcbbcaccbdbccaddbcdacacbddbccacbbcabcacdbadccccaaaaccdcabcaadabbdcbaabbabcccdbdbadccccbbdcddbcbcacadcbadbcdbbddaaabdbadbddadaccdcaddddcbdacbabababaaccaddddabbbadcdbacdacbdbacacdbacadcdcbdaddcacdbcdaaabcbbbdcbaacddcccaddabadaabdaacabddcaaacacdcdcbdadccaabbbbcdbbcccadaccbbccccaacbdbbbdcdbbdccdcaaaabbacbbadabdacaaabbacacbaadaccbdbdcadccaabddcdaccdbaadaaaddbdadcaabaabbaadbbbbdbdbadaddcaccdaaacbcdabcbdbacbbdbadcbcaddabadbaaaadbdbcaabbbccdbcacabbaaddcaabdddacbaaccaaadbbddbcbabdbadbccdbbbccdaaabcaaacaccbbbcbcadadaacbccbdbcadadbbacddcddcaaccbbaacbbabbbddbbadadddadbccbbdcdbccddcdaddadbdadbacacccbaaabacaaabacdcdaaadaddbccbcdcaadcadcaccdbdabbabcdcdbbbbadcadbdbdbbabacbbdcaadbcbbbbddabbaccbcadccacddccacadcddcbddaacbcabbdadbdbabbdcaacdadadbbcbdcbcdcdcbcaaddadadbdbcddaadbbccdbacabaccbbbdabacbaabacdadabdaabcbbacbcaddcaaaabccabaccaaabbcdabddabcbcdaccdcdbbdbbbacacdcdaddcaadaddbccacacababdcdaccaabdbcacdbaccdbddbcbbbcdccdcdbaccddbcdcdcbbcbcabdcabccdccabdcbaccdbabacbbcdddbcbadddaccdbbdbbdbcccabaddbbdcbbadadacbcaadbadcdacdbbbcabbdbcbbdaaaabdbbabcbbcbcdbdbdbcccbbaacbcaccbaadbcadcbdabbbbdaacbbbaccbdddabcbbcadababaddabddbaaccbdabdadcbdbacccdbbcabdbaccdcaadbbdccaacbabddccaaaadaaabacabaddccdbcabbadbdcabdacadaacdbddabdbabadabbcddddaddddcabccbdbdbcdabadaccbcbcdaacccdacacdbcabacddbdcabdadcdcaaabcddbacdbcccdbcddabacabdbadbbbaadcbbadacaccbbacdbbddbdadddacbdbddbbcdabacadbdbcccbcdccdcacbdabddcccbbcadbbcdacbabdabdbbbdbbcbccaaddcbdbabbacdbacbabddccdadaaaddadcaabadabccacccdbabacccadbaccaadbacccadadbbdddcccdbaabbcadbcababbaccbbaaacdccbdbdcdaddcbcacbbccbbdacadaabbbdccdbccbccccbabadadbbbacabbacbcbadbcaddbacddcdaaaccbcbcadacdaababbbcacacdbbabcaadbdcacbddcaaaadaccbbddcaddcdccacdbbcdcbdcbccaacbddaabbbddcacbbadaaccacdccadabacadacadcaacaccadcdbacbdabbbbcaccabaacbdcaddadbbbadcbacaaaabbdbcddbbbbaddcbcdddcdcddddcaabdcaaadbbbcdcdbcbddcbcbbccdddadbadbcddadcbccbabcdabcbacbccaaacccaaadadcabdbdabaabcbabcdbcdacdcabdacaacccbabbadbddcabcabaccaaabbabddbddcabcadbcccdcdcddbbdddabbcaabdbcbbaccaccccdacbbbadaabddccdababbbcbdcdcaabcadbcabbbcbddadabdaabdcdacaddcacbdddccbbccccbdbdcaccdcbddaaccbabacadbcbbadadbcddaabdbacbdbbacabddccbccbadaaddbbbdaddbcbccacacdabaacaccbcdaadabaccddbbbabbaacaacdabaaabcccdcabcdaccaabbccccabadcbbccbddbcabdcacaaabbdabaddcdddadcbcccbbdacbabbccdabdaacaaaabacbbaacdbacdddaccbcccdaacdbdcbacdcbbcdddbdbaaaabcadacadcababaaaaddbbdbaabacdcbbbaabaabadbbbcccacbbccadbcaadbabddcccaaabddddddaaaabacbccdbbaadadbbaccdaccbabdcbddabbaacaacbdbadabadcbbccacbaabcddbcdbacddbdaddcdaabcdbacbbbacbddbacbcbdbabaadcacacdbcdddbcaaaabcaaddacbcacbbdbbcabcdaaabdcdbdacaaadbbbccacacbcccbccdcdacadddacdbddacaccccddbcacacbcdacadbabdddcdcaccccdaaccbdcaddabbbcaabbbcdabccdbbaaaccccadddcaabbadcdbccbddacdaccbbbbbdcccdcbcadbdbdccabbdcacadcacadbdcdcdbcbcabddabbaddbbbbcbadcbaccaccacbcadadbadccaaadcbbddbbbcbbadadbabdacbbccadbbdbdbccabcdcdcccddcdbcdbbcdbccbbaabcdbbaddbcdbddcbbcdbddbabccbdcbdabacadbbbacdbabcbbccaddcdcdcadbcabbccacbbbacddbabcbbacdabdabadbdcddcacdacbcaacbcaaaacdbcacaaddbbcdbbaadcddbddbacaccadbddbbadbdbadccaaacccaadbbadaccbdddabbdbaaadbaacbacddcddcbcadadabbbbbbbacbaabbbaadaabccabbdabadaaaadabddddcbdcbaadccbdcbdabcadbcdddddabbcdcdacbaadbbbacdbabcabddaadbcdbdaaadabaadcaabcdccabcdccccdadbcaabddcccdbcacccabdcaacbdcbdcccababbccbbdbdbbdccccadacbbadaacaabacbdcbbaddbbabbbddddcaacbcbddcacbcdaaaacabcaacbbdacdaaddaccaadbdbadbbcacadaaadbdbdccbcddacccaadbadabbdcababdadabacbcabdaccadadacacdaadbacbbbbbabadddadaabcbccbacdbccbabcbcdccaccbbbbccabcddadacbdcbbaabbdacbdbbabccaaccbbbbaadcdaaabbbadccbdadacaadbabcbbcccccaacaddaacacccabdbabdaaddbadddadbaaacbabdddbcabaaadabbcbbdcccabdadbbbdacbcaccadcaaaccbddbcdacccbbabcaddacbabadbcbdbcbacdbcddabaddaadcacabccbcccbcddcaccccaaaddacbdcdaabbccbcbbbcdbcacaacadbbaddbbdccddbaccaabcbdbcccbacbbbcdaabdcabdcbaacccacccacbccdcbadaddcbbdaaabbbdbbddaddaccdcdcdcccbabbcbbccbcabbbbbddbdaccaaababddbbbbdabcdbbbbabcbbadbadaaabcaaccadbdadcabbdabccddabcbbbcabcddbbbbaaacdcbdcbbbdbcbabbadcccdbaabacbadcdabbbbcabacacacacacdadbababdbcbbacaccdcbabadbcdcaaddbaddcadadbcabacbaabaccaccbbcbbbdbacddddacaaadacccabbdcdbcbabbbacddcdcddcdacadccbbbcccdabbccacaccbacaccabdcbbdadcdaabbbadcbcadbbccaadadacbbbcdbddbbddcdbcbdbddadbabadcbbdddadadaacbacddabbbaadcbbddabbbdbbadcdddabbcbccdbbdcdbbcdbbdddabbaabbddcdcbbadaaddcbaabdbbbdbcdaadaaacdcdbbabbdabbbccdacbdaccaabaabaababccccaddcadaccccacdbdaadcbbdbbcbbcbdabdddadacdcacaabbaaaadcaaaaabacbbbdccadddbbccbacbcabdadcabdcbbdbaaaaaddcbaccadacaaaaddbacbaaabbbbdbbddbaccabcaccbddacabbaddbdacbacdaaaaadbaacdcdaadbccccccddacdbddabdbaaabbaddbcdccbaddcbdaacaabbbbbdcbbadccadabdaabdaacdadcdbadbcbbccddcabbabccdbcdbddcbdddadacacbcaabdcabddccbaabccdabaadbaaccdcddcadbbdcbcaaaaacbaaaaabacabcabacaacddbcbabbdbdcbcaabdbdbabaacaacacccbdaacbccddcbadaaabadaccbabbbddbdddccbccaddadbbaacdbacdbdbaacdbdbbcabbbacbadcdbcbbbcdcccccccbdbcbddbdabadbcbadcbdbcddaaddacbdbbddcbdacadddabcabbdcacacaccadcbcbaaadccdcdcbaccdbbcbacbaabaabbdbcaadbbbbaadcaaccddccacadaddddcdbbdbdaacbbabdbcbabdaccdcdbcdababbbacabdcccbbadbbbcddbbbddddcbbbdbddcdaaadbabababadabaababbbabaabdbddcdbcdccaccdadddbbaaddacacaaddababaddacadaddbbcbaabdcdcdcddddaddbddcacbbbacdaddddcbbcaddaddcaadcdbdadbdbcacaaadadbbacbddadcbbadbabbacbccdaaaacbadacaabacaacbbdabbaaadadbdbabbadbacdacbbbdabbbacbaaddaacaddbbbcbabcabdadcabcacbaaddbcdadccdacaabaaacdbcbdcaddabacccbccbdcbaaccdabdccacccabcadaaaabbcadaccdacdbacdccddacadacdbadcddbbbabcddbacadccbcaaddacbdaaddaaddacdbaadbccabadbcbdbddbabcddbacddbdbdadcbadaabdabdbcdddcabbacdccbdaabddbbbddbdcacdcbdbbdbcaaadcdabadbcdbcbacbadcdbacbdbaacbbccbdaacbdbcdcaaacacbbdccadcaadaabcbcbcbbcbcbadbbaccdacaccddddbcdbdbddaacdbcbacdaacddabdbadcbdabddcbdadabbcdcbccbabdbacbbadabaabbdaaabcaabdbbbcccbddaddcbaabbabdadcbacdadaddcbbcbcccbbaaaabddacabaaddcabacddbadbbaaaaaddcddabcdcdacdbacbbcccbacdbaaddaabdcbabbbaacbbaacbcdbbadabcdbdcaabcbbcbdbcabadaccbababcaaabcbdaddcaabbbdccbcbbaaabbcadccbacacddacaaacddcdacbddbbbdcdbccdcddaaadcbbcdabccdccbaaabbabababccddcbbbcdbdcbadbcbcdadbdbcababbadcddacdabbbabaddabdabadccabcaaabbbcccbabbaadccaadadbddbdabcadcacdcadadddadccccddcdcdcbacbdadacdaadbcbcddddcacadcbdaccccdbaaddcacbccbabcbcbcaaddaaccdabdabcadddbdadabacdabbbbbddddddbbcbacabbbddccaabdbcaabbddbcdbccacaccccdcadcbbbabbbdcdaadcaddcdacdddabdabbbbdcbaacbababbacbaccaddcdddcbddddcadcabbccddcbbbadcbacabbccdbabccddbbacacaabdcccccbbdbcddbdbbccadaacabcbcbcacabbccddcdadbaababbaabdccbadadcbcdbbcabdcadaadaaadcabaaddbacbcaaccbabaaaaaddcdbcaacccdbadaabdbadbccabaccabbdbcabddccacbbabdabdcbdadaadcbacddaacadbabdabcdacbbccbddacdbdcdaaababbdbdcddcaaadbaddcccbccabababbbbdababbdcbdbcddddddabccbadabdaaccbbccdaaabbdcdbbdbadaabacdacdbccacbbccdbcdbbccacbdacacbccdcdbcaacbcbbacbadddbcbcbbcbbcdddbddbdabcabbaadaaabaccbcabbcdbabcbcbbddbccdaabbabbabaabcdcabdabaddaddbdaccacbdcbadddbcbdbacaccdbaacdcacdcabdbbaaadadccbdabacccbcbbcabccdaddbdcdbadbdcdabdadbcbacacbdabbddaabcbdcadbcadcbcddbacdbbdccccbcabdcccbabbabbdddaadabdadcddcdadbbddbaaaadccbdacdbcddbbadaccaacdbbcbcdbaacdccdbcacacdbcdaaadbcbdbdcbbcbcbdcbaabdbbcaddccbaabbadbbdcbdbbadccddacacdbddbdcbbcaaaadcccdcdcaaadbdbbabcdcaddcbabcdcadadcaadbdcabcbdacdcbabbbbdbcbbcadbcbbaccacbcbcbcddacacddacaddccaaddbdccaddbbbabadacbabbaddbbdcddacbdacbbdbbaddaabbaaccdbabccddbaddbaddbdababaabcadaaddaadbdcdcaaacddcbccdaaddacdadabbccacccabcaaabcbcdddadadbdcbbcadbbbcbcdaaaaccddccddcdabacadbcabcbaacbdbcbabccdacdaabbabbaaddaaccbacadcdcaabbdbaabcccdadabddbdccddcbbdbdcddbacdbbdbbdcddbbcbdbaccccdaadddcdbddaadcbddcabcdaadcccacdaabaddcddadaabdbbbbdbdddbddadbccadbdadbabdaccbdcdcddadabcdccdbadcaadbbddcaccaacabadcdcdacaddadbdcbdcbacddcacddbabbbaddbabcdadaadacaabccbaaddaaccdcdaccaadacaabdbcbdbdbddbadbbdbdddbddcaaaadbbdcbbadaacdccdbacbbcbaaadacabdddbccbcdacabdcbccbbdbcbaacaabbcabbddcbaadccbbcdbcdbdccdacdbdcbddaadbccbdacbcbdccddddbdacacbdcbabddcbcddabadccdbdabddadbccbbcbdadabcabadadcdddccbcabdcccbadddccababbddbcdccccddccccbaaddddaccdbacbcaacaaaccbaacddcabcabcddcddaadcacbccccbdddcdadaadccdcbaaddbcdabbadcaddbdbcabcccdabaddbcdbdbbadcccbbccbbdbdacdbdacaddcbcddddbcdbbbadabaaacaabdcdccccbadabdcdcacccdbcbbdbadadccddddccddacabdaccbbabaadbccaabbcadaccabacbacabddcbbcacdbccbabacddacbcdcddbccbccccabbccaadadbacabcdbacadabacdccbddbbcabdaccdadabddaabaaddbcdadccbbabacccbddddbbaacadcaadccadcbddbcdddabbadacadbddcdaccaddbdddddbbdabcadbbcdbdcbbaadcdaacacaccddccccadcabdbdbaadcdacbadbddcdabaddcdddcdabcbbabbcdadbbcdcacdcccaabccbbbaacbabaadaccdcacabcbaadadadbdcbdbdcacccbddadcbbbddbadcdaabcbbababccbacbaadbcabddccdbdacbddbdaccadaabdadddabbdccdddddbcadbaaacccbabbaacbadcbddcccacacdadaadcbacdbcdababbbcacbbdaacddaaaacadddaddcbcdabdacaadbbdaabaaddbdddacadbacacdadaaabbbbbbddcadbbabcbaaacdbdcbacdacbdbbcbccacaacbaaccdccabacbaadbbbbdaaadaaadccdbacbdbbacacaaabbdcddccabbcbdcdbaacadcbbdaddabcccbdbddadccdbabadacdbdbabacaaaccabccababcacbccccccadbabccccdcccacabbdbcccdbbadbadbbaadccdabbabbbcbadaadbadcccadcaaaaadcddacdddbbaacbaaabbbcbcbadabdddcbdcaabcbddcabcbabcbcdaadbcbdbcbbbbcbadcccddcbcabdcdacccdcbbccdbcacaddccdcddddcbdaccadbcaacbdabbaadcbcdcaacadcdaddcbadcacbaacaddbaadaabaadcabcddaccbdabddbdacccbaaaacbaccaccacacbbcbbabacdddcdddcaabbcabdcddbcdbadaacccacabcdcacadbcaacdbbbdcbbaabaacbbdaaddcccbcadcbdabdaaacdaadcacdddaaddaccbcbbdbccccdddbbdcbdccbaadadbdadbccdabcacbdbcddaadbbdbcbcccaaacbbcbbbcccddaccdaabbdaddcdacdcacdaabdddccdbbddbbacbbcabbcbcbabcdbccacaacdcacccaabbcabdddacdacbccbaabcddbddcdcddcacabdaacdaadbbbcdbacdbdddadbbcbbcabdbcddadacdabaadbcacdcdcdddbddcaaacbaaaabdcdcaccdddabdaabcdcacccdbbbcbdbbcabcdbaacbddbddacdbcbbaadcbdcdaddaaaadcaadddbbadcdbccccaabdbbabaabdabddaaadcacdccbcdaddbbbdaabbaabdcdbbacbdbdcaaadcbdccacacbbaccccbdbadbaabaccaadcbcdacdbabbdbadcbadbbabadcbabcdadcbccdcbbbbcddbdbccabcbacccdadbcbdcbbddcbbddbbdabbbdddbbaddddddcddcaccadcdacaadcbcbdcccdbccdadabbbdbbabccdbcaaabcabbdccadbdbdbbbdbcccacabdbacdcbcbbadcabdacdaccbdacbdbdadddbaacbdcbbbbddacadcabbdbbcbbadcbaacccdcacbddaabacbbddbbbbabddcdacbcbbbdbbcaadcddcdadaacadcccabadccddabbbddbdbadcaabaddcdcbbcbabdccacbbcbdccdbbdbbcbcaddacbbcdcacdcbdcbdbcbcaddbccbaccbcdabbabdbccbbdcabbabbaabdadbdaacbbbdbacaadaacaabaddaadaaacacddaacaddbacdacabbcbbdcccbcbbcbccbbaabacdbddadbcdbdbbcbcdbaabcdaadcaaadbdccddcabbdbdabaabcdabbabbabacadaaaccaabaaabdccaddbabcaaaddbbaadaacbccddadaaccaaaadabaddcdbaaccbabbbddccdcbdacddbaaccabcbbdaacbacdbcbdabccbbdaaaaccacdbabdcbaddbcbacdacaddcadaccccbaabadacbccbcabdbbcadadbbbaddbdacadabcbcacdaacacabcaaacdcabbbcacbaadaadcadddccccaaabacaabddadaabdabdddbcdbcbcbaadcabdaddcbcbdcdcbaddbccdcdbaccababdbbaaaadacbdbbabdcaacaccbdcccdcbbdacbaabbcdbbacccdbdabacbcdcbdbbaaddcbccadadbadacbdcdababbbbaacbbcdaadadbddbbcbdcaacbabababcaaadcdbdcbbdcdbcdddbcaadbbcbdbbcaccdbdacdbcacbbabbbcbbbcdcacacdbbcddbabcbbdabbbbbcaadcaaacabcaddabcbcacabdccddacaacddcccbacdacdccccbddabadacbadaadaaaccbbdbabbaccbbbdbaacbcbbbacaabdbadcbaddddbcdbbddbcccadbcaaccbbdbdaaabaadbadbacbbcbcbdcddaacbddcdbcdaccacddcaccbdadadbbdccadbbccddaadbbddbdcdbabdadadadaabcdacccbdaaccabababdcaadaccdccacbbaadadaacbdddcabacccdbdacbaacacadbacbcadbbccdadabbccbadaddcaabbddabcbccabbddacdaccadababdcadcbbcdadbaabcadbdacdbddbcccdbdbbdbadddaabcdbddcacadbcbdbcaccddcdcdaddbccbaadddaabbccddbddcbbaaccccbdbcbaddbaadcacadadbdabbbccbcbaabbcddbbabddadcdadcbbbadbbdbdaddaccdcacbdbcccdbdbdcdcddcccaaacccccbdbbbbcbddcbaadbcabdadaabadddcdaccdcccdcdcacdcbdacadaaadbabaabcccdbddccddadaaaccbcaccccdcbbdccccbbbbbcaaacbcbadbabdaddabdbbcbbbacaddbcabbabacbadccaaccdcdbdbadaaabddddcdccdcdbddbbccabcdabaaadabcddddcadccbcbbbcddbaaadacacdddacdcbaddbdddbaacacbabbdbccaadddbabbcaabddacdccabcbbddcdbcbdadadadbbcbddbbddabaadddaaaacacbadcdddadbacadddaadacabccccadaadcdcdacbbbaddddcbaaaacdcddaaccaccbbadbbccdbbccbddbdabcddbcdabdaacbcadddaabaabacbaccbdccbbabcdbddbadddbbbbbbbdbbbdaddbcbabcadacdbabcadbcbcbabbcccacacacdbcbcdabbbcccddbdaadcadddaaaababbdacacdddcbabccabdabaccabccbccdcbaadcbbcabadadbabbcbcabcaccabcdccdbbcabddbdcdcdcaddabbcabdcdaddacabdaaaabbacbaaadadbabbcadcdddbadccabcbaadaadcdbcdbbdbcbbccdbddacdbdaaadaabcabddcacddddbaacbadaadddbcbccaacadbbbcbdddacabbbcddbbcaadcdaabdbdaaabdddbacddabdcdcbdbddbbbcdaaacbbdddbcdcddcdcbdaabcaaabdbcdbabdbbcddbbbbccdccbcddcdabacddcbdaaaaacdbddbaccadcdcdadcbabdbdaabcadbaddddbdabddccdcbbabbaacdabdbcbdacacbbbdccddbbbbcbdbadccabdabaacababaddbcadcadaaadbdacdcdaadcacabdabcdbdbabdbdcadadddaabacabbcccbbbddacacdbbadccdbddabdcccbdddcdabccddaddbaccbccaabbcdcccacaacbdccdabdaadccbbaadcbdbdadbbbccccdbcbacdddbdcadbcdbccdbaacdbdcdcadadcabccdbaadadcadadaabcdccaadccacaadbcbddabaccbababbbccbabdabddbcddbbcacbaaccccbbdcabcbcbabcdcdbbbabddddcaddbaccbbadbdcabaacbbcdaacaacdcbcdacdaccbbaddaccdacbacbcccbcaacbaaaadcccddcbcbdadcccaaabdaddccbaaacdcaacaadbacdacadaabacbdbcacabcbacdcbcacdcbcbbccdcbddccbadadcdbbcabaddcbccaaabddaabbadcababcdcdcbbbadbbaacdcacdbaadcacccabbaaabadbcdbbdbcbbdcbcbcabdadcadcddbabdcdbaaddacdcbaddabdadcdaaacabacbbcccbbaddcdcbacaaaccccadcbabdcdacdabdcaddabcbbdcddbdbabdcbcabbbcbbddcaaabccaadcbbabbaddcaabbccbaabddcabdcccbbbcbbbabdddbbcdcacbbcabadbccacadabacdccadcdbbbabccbccbbcbdacabadabdbbcbacadddacadaacbacacdacbacacbdcaaaadcccbbcbcdbdadbaccaaabbcaadabdcadbabdbdcacccdbbcacddddbdbbbadbdaddbcbbcbdaddbbabaddbcaabcabdabdcbaddabdbbbcdbcbddcbbadbbddadcabbcabccacbccaadccaacbaacaaadbbdbbdadcdadcabcbdabdbbcabbcddddcbbbccaddaacabbbacdbcddbcabbddaacbcbbdbbadcddacbabbddabdcccdaaadddabddbdddabddababdacacabacabbcdcddadcdcbbabbabbdbcabdbbaaabdaacdaddddacdbaddcadadcaccacbcaaddcdbcadacdcabddbabbabbcccacdadadabaddcddbdcbbaabcaabbbdcacccadcddaabbddcccabacaabbadaddcadaadbbbdbcddadcaaaacbaacbbbdaccdbbddacdcdabbabddacbdadaacdbdccadadabaadbadaacdbcbcbacabbdadabdcccabbadbdbbbacbcdadaadcacbcdabdddcdcaccdbaabcccccabddcaccbccbaccbddddbdaadcbbcbaccadcddadcadaabacdbacdabccdbdaaaaacabbadbdacdaadbcdbccdbcccddaaadcccacdcdaddaccdbacdababcbdadbaabcdcbdccababdbaadcccccddbcbabbcdbdccabbbacdadccacacabaabcbccaadabbbabbbaabdabcadcacabbabcddbcaccdaccbaadcaddaccacabdacdaddbadabcdaabccdbdbabadabbcdaabdddcdaccacaabbbadabbbaadcabcbbcbbabbbababdccabadccbccbbdabbaddbdbcacbbcbccaacdbbcccbdddddadbacaaabcdcbdcadbcccbddacbdbdbbdcdbdaabdcdadbbaaaababddddcbacdbddababadaddddcbadcbccabaaacccabcacdabddcadcddbbbaaaadcbcadacaacdcccaaabacabddcbaadaddbcabbadcccaaddcaacccdcbddbabbcabccbbdaaaaabbcdadcbdadbdcbdacbcccabcccaacbabaabacdbbacdcaadcdbbbbbbddbacbccaadcbdcbbaddabbcdccdcdaadbbabbadcbdbccabdcabcdcacdccccadcadddbdacabadcaaacbcdadbcdbbdcacbcbccacdabadaaadcbcbdbcacacbbcbabbcbacacbcacdcdcdcdbbcdaaccaddddccbdadcbacdcabaaaacaabdadbdbdbdbbacbcbcdcccaacadbaabaaabddadcdadabddccdaccbcccacdcabaaaaacbcccddaaaaddccaacbacdcbdddccbbbdcdccadacbbdbaabbcdadcbaaabbacbdcadaadcabbdadadcddbbdbacacdcabaacadcbacaadabdaacbccccbbcdaabaaddbbcabbaccaadcbdbcacbddabdadadcadbacabccccddbbccaadbccaaabbcdbaddabdbaabcdadddabcbbcbcabdcaacbbdccbcccdbccacbdbabbcdabbbbcdacbdaccdcbabbacacdabaabadaaabddcacadbcdbbdbbacabbaccddabbadddabcdcadbdcbaabbbcdcdcadbcddcddddcdbbdaaababacccacddcadbddaacaddbbdaaaadacbaddbdabbaaadbaacaacdcaabbbadbbbbdddccaccdaacbdadaaadababcdcccbbabbbbbdadddccadbdcbbccbcdbbbbcabbadbdddcddbdacbbdadadbdcdbbdbccaddabbcdaaccbabddbbaabbcabdcbabbbcabccacdcccbadbcddcbbcacbdcbdadcbddbaaddcdddaacddbccddccbddcbdacdcbcaaddbccaacbadbddabbabdbaddababbacdbccaddcababcbdcbacadccacbadadccadcbdacaadbbadacaccbbbbddddaadccadabbddbbbacacbdbadadcaddddcdaaccdbdbacbbcdadcbccdcdbbaaaacbcabccdbddddadccbdbadcadcaacbabbdaadacccbbcbbcbadaccabccbcdadddabddbadbbcacdcabbbbaaddddbcacbbbcbcccbbcabbbaaddabcbacdabcddccbdbbddaddcbaddcdabaddccbbcdccacdccadaadddadcbbccdcdabdcbaacbbadcabcbadabacdabadbbaadacdcbabcdcddcbbadbaacabdbcababbcbcddaddaadcbaaabcbabacaacbaacbadbcadbcaacbccabcbcdaddbbdbbbbdbccbdbdaacdbdcdbdbabcbdddbddadcbccdbbbddcacccadbbcbadbdbdcbcccababdaacddcdaabcdccddcadcdadcaadadacdcbcbcbbcacdbabdccbcadacbdbdaadbcaaccccaabbccacbabaadcbaabbccdbbcaddabcababcdabcabaacaaaccbddacbcddcabcdccbdccababdbddcaadaddbaacaabacdacadadbdcdaababccadbabaacaadbcaadaabacdcbbcacdbdbbcdddcccddcaadcdbdcdaadabbabbcbdbbadcdddbbddcdbbbcabdaaabbccddcabaabdbcccdbbdaccacabaccccdbabdababccabbabcaaddddcbdcaaaaaaaacaaabaabacaccbdaaccdabbdbbdbaccdbdaccbddcccbacbcbbaadbbabacabdaddddbccaaacdcdaacdcdacabaaacdbbbcdaddddaacbbcdaabcdadabcccdbdbbdaccbcddbbadbadabdbdcdcaddbdddadddcccbbdcacabcdaadcddaaadccbbcacbbbbddcabbccaabbabccccbbbdbcbdbdcacdacdaacbdcccabaaaabcccdccccaabdbcbcacdadbdbacdcdacbcbbbacadccdacbbcdbdddbbbcbadddaacacbaacacbaaabbcaccbbbacaaaddcbbddccccbbddbadabdccabcabdccacbbcddccdcbdbdbdcaccaadbcdcabddcaccacadcbddcbbbabbadcacbadaccdbdbbdccdbcdcbcabadabccaaddbbabcacacbaaadaadddcdbdadcbcbbdaabcadcadaadcaabbcaddcccbdddacbabbdaaaaacddbddbacacdabcacccbdadabbdabdbbadcbbcaddbccccbaaabbddbdbddcacacbaaacdbbbcaccbbbccaadcccbddbdbdbcccdaaaabdcdabddabbdcdccdaadddbbcbcbcacdbbbddbadaccaabddbdaadaaacdbaaabddbadccdcaacbbbbdcbaabcddaccaacaddadcbdcdaacbadbabadacddacdacdacadcdbdbbcaabdcbacccbbcddaaccacdddbaddccbdcadcaacccaabadddbcbadcccdabcabdddbccdcabcbcdcbbcbabdabbdddbbcaaadaaadcdbccacabbbbbbdcacbcdcaabbbacbdbdcddbddbabcdbdaabcccdbaddabddacaabcdccadccccdbcdbdddcdacaacdcbcbcababdddcbdacadbacbddcacbbcdbbbbdcbcdcbbcabdbbaddcabdbdacbccadcbdcbccadcdbdabbbbdbbcbbadbbdbddbdbabaaccbccbcccaddcbbcbddddbccacdadbabcbbcaaccdbbabcbcdbcacbdddcbdddccaabcbabadbdbbbbdbbbcaaabdcddcbaccacdbaaaaccbdcbbcdbdddbcbbadcdccaccacbdaacadbdbcdbbcbacdbdbdbdbabdbcaccbabbcbcbbbbaaacadbbcddcbdabbaadccbddaddcadcdbbdbcaabdbacbdccdaadbbcabacdcdacdcabbdaaaaccaddbaddaaadcabbcbbdcaabbddbacbbcbabbabcbadaadbbaabddbdbccddabdacdaaacccacbdcdbdcdcdcbbaababbacaabdaabdddaacbddbcccdbdabbdddacaddbcacbdcdcdbbbcbadcddbaccbddddbabddaacbdadddbabaadabcabbabccabbbbbbcbbccddcbdbdcccbdcdabacdbcdbdcacddacabccaddabbcadbdacdcdcbadadaaaccacdbcbaccbbcccddbdcccdbdcabcbdbdcaadddcbadaaacadcbbabcbddccbdbbbddbadabccdcaabaadacbcddabaccbdccadcbdbcacadaabbdbbbccbdaacacadacdacbccdccabadbacdabcaadabadaacaaadbcdabcacccbbcbabbbbdccadabcbaaadcbaacdcccbbaccccabbbbcabadccddadabccbdccccaaccadbdbdcabbdcbbcacdbbbabadadcaacbcbcadadbbcbcadabccaaddbcbdbadacbccdbcbcddcdadaacbcadadabddddccbadacadddcccbcaacacaaaaabdbacdddabcbddccacddcddddbadaacbcdbbbabdaabbadddabdddadccccadcdbadcccaccdddcbacacccacbdbbbcbabbbbcaabacabcdddccbadbcdbcaabbdbacaaccddbdbbabaaaaadaadcdbcbbbbacbdcabdabddbcaaddacddacaaabadcacaddaacacbbcccdbbcadddbabbcddbbdcbbaadcbdadbbddcdabacbdaccdbadacbcbadaaadbadbbcccabbaddcbcdbaacbbdcaabbdcabacbaccabaacabdcaabbddaadddacbadaddbbaabbcbcbdcbddbadacdbcbdacaddddbbabbadbcdbcbbbadbbddbbdbaddcbdbcdbadbbbbadacdadacdacbaddbaccbbcbcaccbcabccbbcccaabbabccdbcacacabacccdccdabbbaacadccdbccbcbabaabcbbbbaaacadcbdbcdbbccdccdcdacaacdaccaccbdbcbcbddcbacdaccccacaaabbddaacaacbcacbdabdadcdddcaddadbddaaacaaccacbbdaccabbdadcccacadbaabcdaaabacacccdaaaddbbccbabaacbddaccaabaacdcadcbbdbdbcbaddbbbcbcccbbbdabcaadddcaddbcaabdbbdddbbbaccdcacddbbbaaaaddcdcbcccdbdbbdbbbcdbbddccbbabbdaadbbcdadbcaaacdbdcccbdbddbcbaacbbcaacbabaaadcdccddaddbdbbcabdbdddbccbbbdaddadbabbaddadadabcdaacabcdbbcacadcdbbbdbdbbaddbdacdcdacadcadacdbbcbbbccdcdaaaaaccbdaacaadbbbbbdcdddabacddcdbabcdbacdcbdaaddabdabaddbdabddbabaadaababccbacdbcdccdcbbdccdabdacdcadaaadbcbabbcbbbbcbaadadabccbcbcbcadbcddacbbcaccbddadcdaaaddabbbaacbaacdcaccdddaabdbcdcddcaccadcdacbadbabddaaccdbcdbdcadbcccbaaabcadbaadaacbdbdbcadbdcacccacbdcddcbccbaacabaccbadadbaddacbbaadaacaaadbdadaaacbddbbcdccaaccbacdbcdabaaadabcaadaddbadcabcbcbbccdcbbcddacbadcdcababcaccabacaabdbadbcccbdabbadcacdaacbbabcaaabcbbdcccbacbcabcabbcdbdccaaabbcaccaacbbddaabacacdaadcbbbddbdbabbddbcaacacbaadbcdaababddbdacbdbadbbcadccbabbcabdccbbbdcdcabdacbcbccddbbaddcabcaabbbccbdbbcbddbacbbcdbdbdbacbccbbdccbadddbbdaaabcabdcccbaddbbbbbaaabdbccdadbddaccbaaadbbbccbbacbbaaaabcdbcaddaaaababacadddbaddbbcdcdbbbbadabadbacbddbabcbbcaadcccccbccbcdcbbdbdcccdcadacadccbcdcbccbddbabbcaabacabbabaacddddbaccdbabbdcdbcbabcadbbcbacdbabbbabadcdcabcacbaacdbcabacdbacabdccbabbddcdbdbbbbdcddcacbbaccacbabcbcbbabbccdaaaccacacbaaddbdcccdadbcabdadaabbaddabbaaaacacaacdcbbbcbadcdadcbbdcadabadabdddcddbdbdbdcdbdadcdbdaccaaccccbcaacbdcccadaddabbcaccdacccabadcaccdbadbbbdbcacbddcddcaaaacccbcadcdddcdadcacbacabaaddabcabacddbaccabddbcbdbdaddcaddbbadbcaabbddccbbcdbbdaabbddacbbabaabadbbddcacbdbcaddaacbbbadccbaccabadaddbcbacdbadbdabbaccbdcacdbdabbcdabadbcbdcadbcabcdddcbacabdcdbbcacbccabcbbcabbabcbabddababaacdabcbbbbcdbdbbbadbacdcbccccacbcdaabaadbacbbbddcaadcadacadbbccbdacadcbbaccaaadabacbccadbdbaabcdbcbdddcaccbdbbdbabcdccdaacbbbaddccbacddcacaacbdaddcbcaaddcaddbbabbcbbaabadabadcbacbdadcbdbbcaaccbbccdacabbddbbcddcddcdcadbbccbadcbdbaaddbdcadcbdccddbdacbcadaacdadaacdbddcaaccabdabdbcdabccaadaababddbdcabbaacbdacdccdabcbcdbaccbacdccbaacdacbdabaccdbccaccdaacbdcacbbcdabdbdabcdcaadbaddbdccbdcddcdcabcbabdadabbabddabddcaadbbbccccdbcdccacadabbcbadddccdaccaadbbddccdadaccabccabaccccacddaabaacacadaaacbcbaacdadbdaacdcdcdbbaddddacbbdaabbdcdbddadbcaacdbbabcabdbdcacdadcadadbabcabcbbbcadcaadbbbdcdbbbcdcccccddccccccbacdbcacacbaccabbddacbadaabaacccbbdbadbdaabcbcddcabdcaabddcabdabddbbcccabbacbacbddcabdacbdadcdccbbacacacadacabcccbbacaccaacbaaaadbcabaddcccacbdaacabddcbbbccbdaccbaddbbbbcddbbdaddcabdbbbadadbcadddadccaddcbacabaaabbaabccbabacdccacdddbcadbacdadadcacccabbddcccdcddddbadccbaccbacbdaaddcbcdcbbbdabcbcdadcaadbdcabcacccabbabaacbbddcaadcddbabdbabcccbcacbaadbbbbbcdbcaddbdcbcacbdbdcdcbdadddcccdabacbdddbaadacaaaacdbdbaccbdddcacbccbdaadccddaddabdddacccdccacbbbddcccadccdbdbabcdccadbacaabbcbdadcabdadaddcbacdadddcaabbaaaabbbbbdcbadbddddbadaacaadabcdddcdbbddcddaaaddaacddddbbdbdaaabbdacbaaccadadadcbaaacccbacabdbbabbdbdbadbbdcaaabbcccaacacbcbbabbbcbcdbaccdccdbbbcdccccbbcdaddbdabbcacdddabddccaddaadbabddbcbdccabaabadcaddabdacdabdbcdbbbccbbbbacaacdbcbaaccddddacccabaaabbbccacdbbabdddbcadaccaaabcddccddbbaabdabbaabcadadddcdbabcdbbaddcbacabaacddbaccaadcbccddaaabdbddcccabaabcabddcbacbcacccaabcccacabbdaaccbcddbcbadcaddaacacddbdcbbbadbdcdbaadbcacacabaadabcadacdccdccddddbabdbacacacabdabdccbbbbdbbabbacccaadcabdabadbacbcdbbcccbdddabcdcdbabcaaccbddadaccabaabddbdcbacccdbdbadcdaaacaddddccdadcbaacbccabcdaacbbdcacaccaadacdccbbddccaacbbcadbdbbabbdccaaaddbbaadababaabbaacdaaaaccbcacacddaddabbcabdadcbaadcccdcaaddbcdadbadcbcbdacccdddddbdababccbcdababacbadaccaccaadcbbaddadbdbcaccbaacccaabcbabddcdadcdcaccadcaaaaacdadcbcdbcdccacbaabbaaccccccbbdabcbabbdddabcbbccbabdbbcdddbabcadddaaabcdbddcbacbabbdacbacbaacacdcadbacaccbcccbdcbbddcacabacbcbcadacbccaaacadacbaaabddbbaabacaadccdbcbacbbcdddccabadbabdbcbaaabbbabbdacccbacaaadcdacacbabadcdbdddbbabbcabacacbaaacadcadbadbdaaadbadccdbbbadabbcadbbdbcdbacdcbadadbddadddcabccccaaadabcbbadabadadadbccccbdacbdcdbdddacaaacdcbaccdaddacbcccadabcadcdbadcdbadbbdacbddbbaccdcbdbaadcccbcabdacdccdccccdbbcbabddccaadabcbbcbdcddaacacbddcabaabaabcdcdbdadbacccccdbacbcaccbccbbcaaabddcdabdacbdbcdabcadadcabcaacbddabbabcaccbabbbadaadbccddbcaadcacdaddacdbbbbcbbabcadacadddbcabaaacdbcaaddabbdcacabacccdadbcabbddbdaccdccccdbdacbabcdacacddccdccbdcbbccccdaddcbdbcbccaabdccddbaccdcbbdabcaccdabcbcbcaabbcbaacbcaabacbaabadaccbdbacbcabcbcaabcaddbabdccbbccadaabacdadacadbbaadaddcbabcbbdcdadbbbaccdcdcdbacadccaabacddbdaacaaadcbcdcbbdbcaadaaadcdcacaabcddcababdadabdcdddcccdbbcbcbdaccaabcdccdcbdcdabbabcaabdcccbbccdcbbccadbbcbbdbdcdbacdcbcbdccadcbcbbdacaddbbacbbabccdadccaabcbbdcadbdccadacccbaaadaccdbccdccddbababaaacaddbcdadbaabddccdbadbcbccbabdcdccccdbabbcddddcdbcdddaaccbcddabbcdbbbcccbbaaaabababcbcddadacacacddcdcbabbbcaddcdccdaddadbbadabdabcabbaccbcacdbadbacaacadcdcccdcdacddccbdaadcddbdaaaaacddbaacabcbddcadccaddacaaccaccaaddcddccaabacbcccabbdbdbbdadbdbacabddacdabbdcbdcbcbbabdbbbadddaddabaccadadbdbccacacbbdbbdbddaacccbabbbbcacddbabbdcbbacabaddadacbcdbcccbbcdddcddbcdbdcacddbdbacdbadbacaddbdcbbbcacaaadbbacabbcacdabbbddcadcadcbabcaaabbccacaadcdcdabdbdbbccddbbadcdbbcadadcacbbbcbbdacbbabccbddcbbaabdbbbcbabbdaddbbabbcbcbacdcabbdbbadaaddbaababcdabddaaadcdabccbdcccdacbbdccbadadbdaaccdddaacbbddacbadcaddabbddcddcdacbdddadbaccdabdcabcaccaaabccbbcabbcbdbcdbccbbbccdacbcdcaababcbbdbcddbdccccabcddbbdadbaabcdbcacdacabacdbbbddbbadddaaddadaddccdccadadcbaddccaabaadbcccccabdcbbdbabddcbbcbbcbddabbadaccabbcdabbdababcdbcddbdabacddbadaabbabbdccdcbcababaabcccadcbbbbabdcccccbadbdbdbacaabbcdaaaaabddabaaaddbabaacaacddcdbcddadcdacbadaccacbbbcbbccadbbbbbbcdbcdbbbaccdadcbdbdcbbdbcbdcccdbabdcaccadcbdabbdbcbcadcaabbacabcababcccabbbababadacbccaaadaacdaaabaacddbcacaacdcbacddcdcaddaccbdcbabbcabddadbadccbdaabbbcbcacdcadadcddaacdcbccbaacbbccbbbadcbcbddadbdbcdbaabadbbadbccbabbddcaacdbbadaabcaabdcddaddbcbcdcbbbbdaabdbacbbbaacaccdbbddcccdcdaabadaccdaadbdadcdcaacbccdcdbdaccddcccbaccbcbbbdcbddccccbbbadbdcacacdbccdaacddcabdddbbcbabbacdddccbdbbcaadaaccccdbdcdcbdaccbcbbadacbaccaadabaadcadbaabcaacdaacdbbbacddabcaacdccadaddbcaddababdcccbdcbbbbcccbcabddabcbdddbbddadbaaabcaacbbbbaabacabacbcabaaabcacabaaadaaaccacbbdcbabcdbcddbcbabbbdcaabacacacccadddaaaadbadaaaabdadccbbcdcadbbcbbddaadddabbcbdabdacdccdbdccbcddbdbaddabccadcddaadabdadbdbcccbcacddbbbdbaabbabcbadaaabacaacaaccaaccdcbdbbdcdabcdcdbbccdccabacdaccdbdabccbabcbbaccdcababacbbbddaccdddccbddccadbccdcccdacbddcbdcdaaccdccccbcaddabbdacbdadcddccadccccddadcdabacaacacdcccbbacddbbbbbccdbbcdddbaacdcdcabadaadcbdddcbcdbbdbcaacbdbaacbdaacadcbbadcdcdcdcaabacbcaabaccddcaabbaddbdbacdcdcaaaaddabbabddbcadcbbbcddcbbcadcbdabbcbaabaacbcddcbdcdbdccaacbdcbbdcbccadabccadccddadcbacccbddcdacabacdacdbaadabacacccbaaadbdddbacacdcabaddddabaacccdbddaacbadadbaaabdbbddddcbdaacbbaddcaaabdcabcadaddabdacbacabdabdabacbdacdabcbadbadbcdbddaaaddaabbccbcaccdbbddcbababcabddccbcaacdaadbbabdccbbddaacddaddddbacbcddadddabbddaddaacabbcacaccdacacddbbadbbbabacbddbbcdaacdccbdabdbaccbddabdcaccadbcdbbabcbaadddacddcadaddcdabadcbabaaccacbdcbadadbaacddddcbabddbcbbdddcadbadbddcaacabbcaddccdbccaacaacbcbddaaddbabaaadccbbabbbadcddcacddcbcaaddbdccabdccabbbbbdbbcacdcabdcdaaadaadbcbcdcadadcdbbdccaadabbacdcbacccaaacadaaadccbbbabcddcddbdbdbdcacddddbbbccadccddbccbadaadaabcdbabbbccabddaaaaacacbdabaddcddddcadadddddccadbddacdbcbcbdacabcdcccbdbaabdccabaadbbdbdcabcaacabbcdacdcbacddbcdddbdaabbcbcddbadccacbcacbdcdccdabdadbcdccbbdbaacbbabddddbbcaddbdbadbcdaabbaabdbbadcbcddbdbbacbadcabccdcdcdabbaabcaaadadadddaaaabaacacdbdcddbdbbbdbabcbaaababaddbacdbabaabdbacabddaaccabdcbababdbbddbcddcadbbddcdccbaccbaacccabbdcdcdcaaaabcbcaccaaabaddababacbdcbacabddacbaccccbaadadacdbabbbaabdabcabdaacbaaadddacdbccabbdcdbcddddcabdcccddabbbaddbddbabbcccaadabaadbdcdbcacaaccccddaaaddbdcccccdadddbaacaaacbbcdcacabbaadcacacddaabaadbbccdabdbaadcddaabcdaacadcbbdadddabdbddabcccddbacdcdbccbadccbadbdacbbcacacacccbbaadcdcaccdbccbaaaccabbdcddadddcddadadddcdacdbdcdbddddabbbddcbbcccbacbcdadbdbcaacdcbcccdacadcabbaddcadadaddacdabdaabbccdaccacbabbacaaddbbacccadbcdbbbaddbcaddbadcbdcaadaabbcdddccbcccddabcabacccddbcbcdcbadccadbddbaaacaaccccbccccbcddadcacaccabdcdacbcdadccadaaacdbaccdbdcabcbadbacccddacdbdadacdabacddcaacdcbaacadbbbacbdabbbdccbcccabdbabccccdcbcadccdaabdcbcccdcbbcbaaacdcddbcdabccadbadbabaacadddaadbdcadcccbbabaabcadbbbcccbadcabbbbabdacddbddadcdaadbddbbbcdbaadbdbbdbdbdacbcadcadcaabbbddcdddabddaadbddccdadabaaacdcabdcbdddadacdaabdccabcdcaddacadbcdabaadacbbbaacadcbccadbbadcbdacbdccbdcacadbcdbcdcaabadadacddbdcddbccacdaadaaacdcaaccadabdaddacbabcdbbdacbbdbcdabdbaaadbcccdaaaabbaddaabdcdaaacccacdcbdcaabdddabbbdadbcacadbaacbccccacccdddabdccacdbcbaccbddddbdbccadadcdacbcbbbdbddadcabcddacbdbcaacadbaccbcabdaddccbcdbcdcbaaccdbbbcccbccbaaabddbcdddabaccbcacdbadcbabaacdadcbbadbccddacbdddbddacaabcbcdcbaacacdacbcdcbcacbbbdadddadaacadcdcabdbbdaddbdadddbbbbbdccccbcddadacbbbdbcbbdcacdbacaacaddabdaccbbbbbacbcccdccabcdadadbbabbacadcdccaaaacccabaacdcbbdadaabdcabbacabcbcabcacddaddabdadccaaacbbbcbdbacdabdbdabadaacccaacadbcccbbddbabbdcbddcbbaadcbbadccbaccbdaacbbadcbbbaacdadbdddabcbbbbbccbbdbccbacbcadddbaccabdabcbadabdbadbacdbdabdcccbbcbabbdacdcaacadabbdacbcdcabbcabababbccbbcacbbcdbaacabbbadccdcdcadbbbbababccadddcdcdacacdcbcdbccacbaacdbadbdadcdabcbdccdbbacacddcdbabbabbddbdbccdaddaccaacababdcaddadacccbddbbcdddccdbddabaabbcaccbaaacdbcbaaddcadbabaabbaddcbbdcacadcdddaddbdccccacadbcdaadbaabddabaadbdaacacbdbbbacccbdcccbbadbabbadaddcccbadddaabcdbbbaaaddaababdccbdbcacdabdabadabddbadbaddcbbbadbccbdadbacbddddccbbbdcdbbaaabcacddcdcbaccbdbbdcdaabaadbdaadaaaacdcbbdbacdadbdddbbadcacbadbbacaccabaaccbacbbcdabdaddcaaabbcabbbcaabaaacbbcccaabcddabaaaacdccdbabdacaaacbcdbdbbbcbbdbbadaabdbcbaaaadadbabbcaabbcdacadabbbdcadacbaabbcabcadabcddbcccccbaacdbcdbdcbdbbcbbaddbcdcddbacadcdcbbdccddcdccacccbabbcbcdabaaaddadabdadacabcccddcdacdbcbbacdadccbaddcacdbbbdacdddbbaabdbbcdbcdabdcadaaaabababadaacbbbbddacbdbdadabdaacaacccbaccdbdbacbdcbccbdcbddbbcbcccbdbdbcdbbcdaacadabbbddcbabcabdaabdcbdddcababbbbddbcbdabbcaccacdcdbaacabbcaccadcdaabbcccdbaabcaabdcabcadababaabbacbbaadadcdcbccdbdcdbaaccaccdabdacccabbbcadacbcdbbbaadbdcadaabdbadaddbaaadbbcadbbdaadbcdadbbbdccdbcaaaaaadbcbdcddaabdcbacabddabcdcccddcdaddadcbcdddbadbbcdbdddbadadadcaadcacbcbcbdcbbcbbbacdccdbaddccbddaababadcaccaccdaacbcacdacdcacacbbdadabbdaacdaabdddcababbdcadaccdcadcbddacacdcbcdcadcbbaabcaacadddabcbdccbdbbddcdbdccaaccadddabbccdaccdbacbbaddbaabbbbdaadababcaadbdaacbdabddcdcbdbcabbacbdabbaddbccadadadadabaddabddacdadbccdcdcbbaaadcbaddbcabbcaccccacbadaadaddbbbbaaacdbdcaacacaccdaaabadacacabcaddcbbddabadcbaacbccdccaacdabbbbdababbadcdddcbbdabdccababdabdabdcacdcbcbbdabbccbaadabbdcdbbabcbbbcabbccddcccbddaddbadabccdabaaddccbddcabcadbaacacaadcccbdbdbcdcbdddcdcdbacbdadadcdddccbcddabdaabdbdccdddacacdccbaabbcbdbaabcbcccdddaddabaddccaabcbadbdcdbbbdcabdbcccbacbcbdabadddacbadaaacbabababadddbacadcdcbcdbbcbaacdcbdbabccdbbbcccccbdaddbddaacdacadbcadbcdadcbcdbaadbacbaadbbaccdbabaabdacdcabaabdabddacbdbdbbbbdbdbaddcdbacbdbdccacbccdacbacbddbcbcddcdaabcddadacddbcccaadbcbdccdcbddcdccbadcbccadaccddaacbbabdbcdcbacacdbdaaadccbbccdbccdaaabadadcddcbbcacabbdcdbccdacaaacbbdabcdddbabdcccbdabdccbccacdabbbdcdcdbbdbcdbbadadcccbcdacaabbaaaaabdaacdcccacbabadadcccbbdbcdcbcaacdccaaacbdcdddbddcabdbcbaaaacddbacdaddcbddddcaacaacdbabbcddadbadabccbbdcdbdcbcbcbcbccaddadadaaddccaaaacbddbadccaaabaabdbcdbadbabbccddcbcdcdccadbacadbdccacaccdaabcbadbbcbadbcbddbccddcbcbcacdcaadcacabcabdccaadadadaccacadbaccabcacaddbbbddddaabddadabbddcabbdaadabbcdcdcabcccadcbcbacddaacccdabbdaddbccdbccadcbadbcccdbbbddcccbadabacaabbdaadadbcbdcabcaaadccadbdcccaabddcdabacaccaaabddddbbbdacddcadaabbaabdadcadbcaccdcadaabadaaadcbdbdaadbbcbbdcbdabcdcbcbcbabaadaabbccdbbddbdcbdccdbbddddbdcbaaadccaaacbdabdabbacccabcadabcacadcaaccddcbcbacbdcdaccadadcdbabadbbddcbcdddcaacbababbcbcaadaadbddbbabdaacdbdbcdbddaacacadcbccbabdcccbcacaaaaaacabdacddcdccbddcdccabaacbdbdcdbbdccddabdcbddcbcadcbcddaacababbccdcabbbaccddabcbdddaacadbaadaccbbabbadababcdbbcdaadbdcbdbcdcbccddccbadcdccaadaabacabbccbacdcbaadaabbbcbcacbabdbbdabccdaccdbbacdadcbdacbdbbabdcbbacabdccdbddaadbcdbdcdbccbbbbaabbabaaaddddaacbbacddccbcaaaacdaabacddcdbbddcadccdaccbccdbdccdbbddacaabacabadaabbcdcaabcbbbdadcccccbcddacddacaabcccbdcabcbcadbacbadcbadbabcddbccbacddcbacabbbdbbbcadcdadcadbaabacacaaddaaccddddbcaddcadcbdbcbdcbcdaaaadbbcccbbdbacdbadacadddcbadabdcccdadbbdbdcccccacbaaddddbdddabbdbbdcaadbcdddbddbdadbddbbbabcbdadcdacbbdcdaddacabbbdccbadacbdccbcabcdcbcdbcbabcddccbaadcccddcbaddbadacddbcddcccdccadbdcaabcbddbbdaaaacadacabbbdccaddbadcdadbbbbadcddabdadababaabbacdccdccbdbacdcbbcaccddbdccccbbdcdddabacbbabdcdaddabcbbaadbbabccbccdcdaabcccbdcdbbccdbbabccdabbcbaaadbabccacbaadbcaabdcbdbabcadbbbbccbccbbbcaaddbacddbcccbcddccabbacaddbddaccccbccacaadacdcacaacacbcbcacccddadcbcacccadabdcaacadcdbdadaacabacdadcadcdcbdcbbdaccbbdacabcabbacddbbaabdabbddddadbccaddcbcbbcbddbadbabbcccbddddabdccaaaaadbacbbcaaacbbbcbcacdbabcdbdababdbadccdcbbdcbcdbddadacaabadadbdbdcbacbdcacdbaddddabbaaadadacadccadcacdabaaacbdbbdabbbdcabbcddddcdddadbcbbdddcbbbacabcabbbcdaaccbbdaaddddacbbabddadcadacdbbadababbbcbbbcaacbddacddcdcadcdcbcbbcbbccaddcdcadcaccddaddaadaadccdbbcbdadbddbcddbcdaadcccaccabccdbdaaabbccabacaacdddbcbdbbcdbcdccddddbcbcbcaaddcbbaacdddbbcadaadccadcbdbbcdbbababbdadaddacbbdbacdbdbadcccbcbcbbdcaabbaadabaabddcbacaababbabccdcbdddbcbababddaaccbacbadcbaccccaccdbabdbcadccbbccdbaddbbbccabccacdddabdccabcabcbbbddbcbdccdcabaadbdbbaccbddbbddababcbadadbabbcdabaccdaccbbddbdaacdbdbaddbaadaaccdcdcddcaccbdbadbcbbdacabdaccccbbbcaabadbdababbdacacdbadcabccbadabddbaabbabdacadbdcdbdadccadaadadadabcaacbabcbdbddbacbcbcacadcaaadaabdcddadcaaadcbcddaaadbabdabdcdddabdbdbaaadaacaabacbcdbdcadcaaaadaccddcdacbccdbbcdbbccdcbbcabaabaadacdcbbbacccbdabdccdbbccacabcbaacadabdcbaadaabcbcdacdccbcacdadbdcbdbdcaadbabccdddaacaccbbdcbbacadadabaaabacdcdbbaddbbdaadadbccaacacdbabddaaadcadddadacbdbcdbddbbddaddcdcbaccdbabcacbbdadcdbacddbabdccbcabbabbbababacabadddabbacbbdbadbbadcacccadcbcdddddbbcbcbcdbdbcbabbddadbbcccdbaacaacdacacbbcdddddbbbccdbbdbacbbdcbdccacbaaddaaaabdacddaccabaabbcdbcbdabccdadbdddbdadbddcaccdcdcdddacbdccabbaacbbbcaabcbacbbaccbbdddcaacacaccddddabcabcadbbcbbaacadcadbbcbabdcbddadcccdbdbbdadbbdcdbdbdcbdababbcaadbdbbacdcbdaacccddbdaabbacccbaaacbccccddddcaadbccacbdabcaacbdadbdbddcabdcdbdadabdcdcaccdccbcaabaddccbcdddaddbcbccadcddacbaaaadcbaacabcdaaadaaadcabcbdcbabdcbdadcdbbadcbcdaaddcdcbddbaaadaabbbccabdbddacccbdccdabbaabbbcdddcdbaabbcabcccdcbcdacbcdadcbbacccdbaaabdabbdcbabdcbcbcdbcdaaaaadbbaaabdbbadcbdcbdbddbdcbabaccdcabcacadbdaacddbcdbdcdaaabcbaaccdbbbccaaabccdccabdcbccaaaacdabbdddaaadcdbadaacbcddbabacacdddaabdcaadcdaabcabbbbaaaaacbdacdacdcddbbaadbaddbbddbbcbccbcccbcabbbaaddcaacdbbdcadbbbbbaccddbbddbbcaccbabaccabbbcaccacacadbbcacdadadbabdbbadcccdbdabaddcadccbacbcabbdaacdcaaddadacabccadbadddddbdcbddacacbbdcdbdadbbdcbadddddbddcdabdcdacbdbbbbcccddcbaaacddcbacdccdcacaccadcdbdccbaaccdbcbbcabddbdccadcccaacabdbdacacbbbbaadcbbdbbcdaaaacbcbdcacaccdacadcacdbaaacaadddbdaccbdcdbbabbcbbdccabcadbaabbdccaddaacabacabbcddacbaaccddbbbcaaadaccbabaaddcdbdadaacbcadbcbbddcaaaabbaadbcdddbbdcdccaabacbdbaadabccccaaaabcbdcbbcbaaaccbdabdaccaaaabddaadabadbdbdaccdbcadccddccccadaabcdddabaaadcbbbdbabccbbaabdddddabbbbdbabdacdabbccdcddadbdbcdadaaddcccadcaddbbaddcadadddbacabccdacbbcaabbdcbccacddcbbdaabaaddbdddaccdcccbbabaadadbcadbdcbbadcdaacbdaccabbadccdabccaddadbadddcbdcbdcabccdddcabcabcbbcccbdbcadbbdcdcdcbabadcacabadbdaadddaacdcdacddccdadaadabababcddddadddacbadbbaadadcbcbbacbdbdcdadbdbcddccbcaccdcbdddbdbddaaccabbcdcbdccacdbabdadcaaabccaccbddbaadcdaabadabacaaddaadacadbacbccbcdccbbbacaacbdadcdaaacbabdcbaccbbdbcadbdbcdddacbcbbddbbcaabccccdbcccbcdcabcabddbcdddcaabaabccbaaadccabaadccddabbdaadaabcccaadbddccaccbbcbcadcddabacbbacbdaabcadbaddcbaacbaaadbcbcdbcbacbbcaccdabddddcddbbabbcaddaaacacdcacaabcdccbdbcdcaacbdbcccabaacabbcacddacdcadadccdccdaccbbabbcbbcbddcdaddbacaddcdbcaadccccaabbbbdacccccddaaadddadcdabbccdcacdcddcdadcdbacddbaaabcaaddbdacadbcdabaadcddddcbbdcbadbccacdbdbcdbaaabccddadbbaacabcccdcbdcccabbccddcbcddddaaaddbbbddcacdbbcbcccdcdabcbbddcabacbbcbdbadddabbdcaacdbaaadabbbcdabbaddabccdcdcaccdaaadbcabadcbbacdaaaccdabcabdabdaccdbdcbbaabaccaaddcbadcdabcacbcdacbadbbdadccdbabdbccadabcdcbdccaddcbaabdbcdccaccbbadbcbddaababdccbddacaabdabacadbbacacbabbcccadccdabdddcacccaccacddbbbadaccaacccdcbabdcbdaabaacdabbbcdcddadacccbabccbcbcccbddbcabbbdbabcccddcacbaddcadacdbdacbdbbbadbbdbcaabcdbdcbaacadbcbadaaddccbddbdbcabdbacaddbdaaccacbbabaacddabbbbcdcabddadacbccacddbabdcaccbdaddcbbdaabaddabaadaabaaabcdddcdabadcabddabdabccbcbbccccbbdcbdaabaadbdacdbccbdcdbdbdcddbcaabdccbcaabcbbcdcbcdbbccabbccadddaacddaadabdddacbbacbbbcdbcccdccbdcccbcaccbddcaabcdabdcbcbadddcdadcccabbccaaacdcdddcddcacbdadcdabbdabcabdbaacaabdccadccbcdddcabcbdabaadbcdbbbbdbabcccbccbadddabacabdadaaddaddcbbbacaddbbccaacdcbdbaacddcaadbabddcccacdbcbadadcbabdddbbbdcaaddcaaaccdadcbadcdbcbadbccadacddadbaaddabcccabacdcbccabbdcdadcdccbacdaacbcbcbbcacdcbabddbcddaadbdacbbbaaaacadcacbaaabddcaabdadcaaccabcbacdbbbaaacdcacadbdcddcbacbddbbcbaadbddbbbdcaddcbcaccddcccdaacaabaaccdadbdcbbaccacddcbbccdcbdaacabcccbaaaaadddbaccbdaccdbacaaadbcbbddaabadaccbbbbddcbddcddcccadbaddbdcbdcbcbbacbbaacaadaddcacacacddcddbbdaabddbddbaaccbcadbaddddcadddcacdddbadbbdaadabaddbdababaabdbdababddcaacddabacbcddbaacccaddaadbdbbcdabcadadbaaccadccdbccdabbccbabcddaadcbcdbccadddabbadadbbccdcbccabbcbacdbadbcdcbccacbddbccaaadcababbbcbcbbaadccacccacdabaadaadacdacbdaccbabbbacaacadbcdcbabcaddabacaadcdbadcabadbccbbcdbccaaabcbacccbdcdddcabbcddcbacbbdaccdcacbacdbbabdaadbacabdcaccbacbaccdcdacddcbadbcacdcacdadacdabacbdadabbdbbccabbcbcbadddcdaaaaabdbcadbcdabccbcacacabcbdcacabbbbaaaddbbaadccadddccabacadcddbbcaabbbadcdbddbbddcabccdacddccccacddddadcbaadbddccbcaccdcbcacbccaddcacbddcabbabbcaddadbabaadccbcbcbadabddccbdcbaacdcbabddadccbdddcdccabcbaadbbbadacabddcbcdcbbbcaacbaccdbddbaaabccabbbdcbdddbbadaccbcdbadbdcaccbacdbabaaabcabcacdbadacbabacbcbcabdcbaccabbabdcbddbcaaacbccabacbccccacdbadbbcbcbbabdaabbbadcdacaccbbdaabadbcbbdabbdcacbddcadbaccccaababbbbadbacccdbccdaacdaddcdababcbcccbdbdbbddbcdaccccbbbdadadcddacbaddabcdabdabcdabbccdacaaaadabbdccddabdbbbbacadcaddbdcaaccaccabccdbddbbbbdcdcdbccbbcacacaccadbaacdaabdbbcaacdaacddbbbcbcabdbddddbbbddbcbcbcdbdbabdcbddaddbacccbbccccababbcdaddcbdbdaccabaaadaacdaaaadaabacadababdacbdaccccaccadaaadcdccbccdbadacabbdabacabaddcaacaaacdaacabbdbdbdaddacddbdcdbddbdbbbbccbcbdcdaaddabdccbcbaabadbbcbbbddcaacaaacccaaadddacdcbdcbbcdcdababbbaabdbcadccadadbdcbdccddacdcadabdacacdabccdcabbadddabddabddabdcbbccdadccaaadacbbacbdbcaabdddaadbcbbbabaccadaddcadcadaacacbcdbdacbbdcbacabbccbbabacbadacbabcacaaacbcbddcdcdbcbbbbadcbacbbcacbcddadaadacdddacabacdcaadddacbcaccadacacbcbbcabbdbdbbcdbaacaabbcddbcbdcdaddcbcdcacdcacbcbbcdccabdaadbacadccbcbacbbdccccbcdbacddccabaaddabbadadbaacddadaaddcacabbcdabdaddbcabcaccabcdbbbadcbbdcadbbddcddaccdbbcccddcdcbccbbddbabcbacabbadacabbdbdccabbdbbdcdaaddacbcbdbbdcdaccdbbccccbddddabbaddbbdbbadbddbdabbddaacbbaacadcbbddacadcdcbdddddcccaabbaddadadadbcaccdbddccccbbaccaddbbbbbadccbcadbbdbaccddaabadcddaddbdbcbaccdbdbbddcdbdaadbacbcdbddbdcaacbabadcabbaaddabbdbcdaaccbddcbddaaccabccdadacdbabccddddacdbaadbacaaadbadcbbaaaabccdcabaccabbdcaaddcabbdcbaacdcbbbacbacbaddacbcabacdadacaddacbdaaccaacadbbacdbdabcadaadacddaaaddaadbddddbadadccbcdcdbaaadddcabdbabbbaaabdbddcdbbaccadcdaccbdaabbaaccaabcdaaabccbadcacbcddadcdaaabcaaaaddcbbcddddacabcdcdbdcabdbaccdabcbcdddbcaabcbacbddcbcbcbbbaacbaaadcacbbdbabccdcdacbcadcddbddcadbdcababdbadbbdaabbdcccdbaaddbddddcbcdaabbabadcccaabddcacaadbbbcadacdbabcccabcccbbdbcadbdadbbbcaacacacddddacaccdaddbcccaaabbcaacdccdbcabcdbbdcadacdbdbbbdbcddcddabccadbbadbacbcccaaccdccaaaaddddcbacdacaabdbabbcdbbcaddbbcbcadcbaddcdcbdacacbacbbbddbcdbbadcacbbdbccacaaccaadcbdddbadbadaacaccdbcbdccbbbdbbaababacbcadcddcdbabcacabaabbacbabdcdabbcbbccbddddabcdbccadbcadbdadbdbccadccbccdacacdbababcdbbcadbbdbddaaaddabacabacdbcbadccbaddadbcaddabcbbcadbcdddcacabbbadcdcbcdbbccbbadddaaaaddcbcbaadbbbaabaddaadcccccbbdabadadcbaadbdbcadccacbcbabbacddcbbadcddccbccabadcdcdaacdcabddcbabcccbcaccccadbabddaccadcbdcdaccdbcccaaabcbaacaaabadcbcbccddbbbbacbbddcddcbcababccbddbadadbacccdaaacabbbdaacdcccccbcdacbcabdabdccdaccbdabbaaaaccacbaacbcabcbcddbddcbbcadbdcbbbbbadcbcddbdbcabdcbcdacbdaaabbbccccadaabdacbbbaccabbdddabadaacbacadbbcbbbddbdbabdbbaddbaacbdadcabdabdddcdccaacdaabadcdccddadcaabaababdbbdcacbaacadaabbdbabaabbcadadacaaaadddcdcbbddccadacaaccaaabccbbcdaabdcccdbbadbbcbdbcadabbcadcabbbaaabbcdabcbbaccbbacddadccbdaaabdabaaaabbaacdbbabcbbdabaaabcdcdadbdcdbddcdddcacbccccdbbaccadacddabdaccabbdccdcbccccaaddabddcdaccbcccbbcaadcccacadbdbbddcdcbcddcdaccbcbaccccbbbbcaacdabaaabccbbaadabcaaacdbadabaaddaacddabdbadadadbdddcaabcadadaabcadbcbdaaacbaacabbddbcbcddbcbcbcabbabddbabbdbabddcccccdbdbcaabbabcbcdbbbacbbabbccacdcbdcbdbcabababdccdcbbbbdbaddaccacbaacdaadccbdddcbabbdddcbdaaacdaabcacacbbaabbcadbcdacbaaddbdbddbddadbddbccaaccdcdcbcddbbbcaadcbcacddbaaccbbcaddcddcdddaacdcdcbccaaddddbbcdbccccbbcbcbbdbabbcbaccccbcadabcccccdcbaddcbdbadcbbabdcdbadbbdacbdbbacbadbcbdbcbaccabdbdbddabdcabcccbcdbdaaabbacdaccdcdbcbadbacbbdbcbbdddddddcbbdbdccbcbbbacbbacadacadacbbbcabadbbbaadaddacabbabcbcddcababacbdadccaccdcdbabcccddbbdacbaddaadaaaadddaacbaabaccacccbacdbccbcbacdddcabccbacdbcddbaaacacdaacbabdddabbaddcadadbdbbabaddadddbcdacdaccdddaaacbdaddcdabbacbbbddbdcdcaaacdcccaaddcdaabcaaddaaabbabaaaabdbcaadccccbadcbbcddabcdcbddaacbbcadbcbdaabdddcbddabaadabbadaacccddbaacdadcccbdbcbbcdadbcdbbabbcaccddbadbdbdadbbadccccbcaadbddadaadccdbacbbcadadaaccaababaaabdaacbddabcbbbabcaadbaddaacdcbcdbdbcbbbddacbcbdadaaaadccdacddaccdbcbdbbcaaadaabcacbdcbdbbbccbcdcdddcabaddabdddadddbddccdaadddccaddbbccabdbacacadaadccacdacbcbbaabadbccbcbddcdbdcadbbacccbaacabdcaaccadcabdbcdccadcadaddbbaaddcadaccdddbaaadabdbaddacddadaaabccdbdbabdaaddcbcadbacbdabdddcbadabcccddcbbccadabdaccbabacdadbbabbabcaddbadadbdddcabbbbccbcacccbbdcccabadcdacdaacbaccbcbbabcdbdaadbaccbcbaabbabbaadbabbdbddcdcaaadcbbdccdabccadcbdbdadcccadcbabaabacdabcdbacddacccacacdbacbdabdadadcbabdbbcbcbcacdbdbbdbcddddaadabdddaadacbbbaaabccdccbccadadadcbdbaaadbdabbcadbdcdbcabcbdbbdadddcaaaaccbbcadbdacdcbcddccdddbadbacbbaddbabbdaabaadbcbdacccbaddaaccaccbbbccbccbabbabcbacdddacbcdbbdabcadcadcdabbcacbcacbdaaddbddbddbbcdabcdaacddabbccdadbcbcbdbccdabdbcaacdbbabaabdbcbdbccdddcaccaabcadcccacbcaccbccbddcaacbbdccaaaddcabaaacdabccdcdcbddadcbdccdddddabacbbcbbadcbcdddbcacccbccbdbbaaadacadbdbbcdcabadbddcdacccdbbddcddbdaccbaddabbacddacbabccadbdbbadcaacabddbcdbdcdbdbbbcacbabacccbdddbcccacbadcdccccdacaddbadadbbcbadabbdcbadadcbbabccaabcdabbddbdabcabdadccddccdcdabdaddcbcabdcbcbcabadaabbaddccdabcbaacbcbbaddccdadbbddacacccabdbbaabcbbcabbabacacdaacddabadbbdbbdacbbdbadccbddabbcbbacaccdadddcbacdbcdacbcdbaaaccdbcaacccdaadacadccdabcdddabccabababccdddabbadcababadcaacaccbbccacbcdaacacacddbcaccdcbddabdaabddadadaadaaaadddaacbbcbadcdaccaddbadbccbdacdddabaabadacaccaddaaacabbaddaaddbcaddadcaccbcddabaacaccddaccbaadbcbbdcdcddacabdaacbbbabcbdcddadcbbcdadacacdbdcccbcddacbdcddddbbcddcbbbcbcbaadccbccdbdbdabaacabdbbbadbcdbbdbcdbdbaccaccbdddbbccaaabcbbccbddbaacdadabbdbdbcbabbbbbabcadbdabacaddddccdababbddbddaccacbadaaaccadcbbbbaabbaaadaccbcaaaabcdbbacadacccbbbccbdadccbabcabdbbcabbacbbdaaacddadcdbddcaccabccbcabdbbcbaacbbcacaaccbdcbadbdaaadbdccdccacccadcdbbabbddbdcbdcbccbbbacacbcbabdcbcabccdbbaddcbaadcdddcdabccbbdbadabbdadacdbcbbccaacadcddcbcbaacbdcdabddcdccbaabaadccccbadaaccbcbaadaaaaaccaadddcadbaddcacdccdaccbbdabacaaacabcddbaabbbbcdaabbbbbaaabcbacccbddaabacbaddbcaaaabddcabbdabadcacddabadddaabccddaabddbdbaacacabddaaabadbdbbdddbbacdcdcdbcdbbbbbbbbaadcddbbcdbadbcabddbccadddbbdddcdbcbaacaaacbaacadbacbbdbbbdabbbacdbdbabaadddddbacaccdabbadbbbbcacddcdadadcdaadbcbbbbcbcbacbbdaaacaacdbdcaddaabbbaadadacdcaccdcdbcaddbabcddaabadcaacaabdadabccbdbadcdcddcbcaadaabcdbcdaabcdcaabdacbdccdbbcbbbacabbdddbababdbdaabbccbabbdddacacacddcaadddacccdddbbcbaaabdbccacdaaddbcddcccbddbbcdadcbaabdacacdbbbdbdbaaaddcadccbacaabdbaccdaddbabcaacdcbdabbaddddcdbbdccdcbaccaaabdacbddaadbbcdcaaccabbadacdcabccadccdbacacbcdbacadcbdcddbdccaadaabcddddbccddddcbcbabddcdadaccdddbddacbbbdbcbdacbcddcdadbdcbdcccbdcdcbbaababcddbadbcbadbbacbdbabbabdadccddaaccccccddadacccbbadbaccabcccbcddcbdcddcbbabccbbbadddddaadbaabdddcbcbbccccbcaaaaadbcbcdbbcbbcddacbcaaddadcdbddcaaabcaaaadcadcccbccabcbaaadaddbbdaabdaaabbdcbddaddbbcaadbbdbcadddbbabbdabcbccdabbcadaadcabacdcaabdbdbdacbbcacbaabadbbbaacddacbccacbddbddaadccaadbaaadcbadbacabdcccaccadcbaddbdcadcdbddcbcdbcdbabcdcddccbccbbdbbcdacdacbccaacabaccdbcbbdaacdcbdcbbdadddadbcaabcacadccaabccaaaccbddcbaaadbdcaabddbbcacbbbaccccbddcdbdbbdcccbcacbadbddbddbccbbacbcabdaabaaccdcdacdabbdbdaabdbabbdddcddccdbbbbacbdacbcbaabadbbdbbdadadbdbbbadbacddcdddcadabcbcccddbbdccdccaadbcbcadcacacababcbcacbcaddacdbbbcaaadacbacadaddabdbdbaddadcbaccdaddaadbcddbcdbcacddbcbaccabcdadcdacacdcddcaadbadaaaaddccccbacdcdacdacbbbbadcdabaadabacbdccbbddccdccdcabcdaabcaabdbabbcbdaadabdcaadcbbcdcbbcabbbbccdbacacdaccddbacadcacdbbcdadbbdccbdcdbbacdbbbcdabdbbadcbdbbddadacdbacdbddbbddaabcbccbcdcdccbcddacbddaabcaacaacccbcaacccbdbabddacbbbbdabbdccacccaaacaddabadbbcbdcdcddacbcddcbccbbadcbbdabccdbabbbdddbadcadcbcdcbdddadbaadabaddcddcbbdacbbacddcddbcdbabadcbdabdaaccabddbccbaadcadbdabbcabacbdbaaadbadcddcaccdccbadabbdcaabbdbbadaaccaaaccdcbadcbbbccdacbbaaddbbbcddacdbdbcdabadaababdbcdbadddadbacbbdcabdacaccacbaaaabadadadaddaacdbbcdaddccbbccdaddbabdcbccccddcbaabddaddcdaaadbabbdbacabaababbcccccbdddcdadccdddcdcdabdaabbccadacbcdabddcbdddbbabbadcaaaadbaccabddadcabbbbdddbcaaabbdccdddbabcbacbabacbcdcdbaaabddaaddacbcdabbcbabcaccacbddacdddcbdbabbbcbcadaabdbabcdcbabdddcaaadcabbbdddcdcbbbacbdabcbdbbbbdacbdddbcbbdadbbbaacddccbdcaadbcdaccbccabbcdcdadacddcabbcdbbdadcabbcdcbdadabcccbbbacaadbccdbdcbabbdbacabcbbbcabacddbdbabdbaaadaabcdbdccddabcdadbadadbdacbddbbbbddcdacddbaacabcacdacbaadbdabbabbcbcbbbcadccbadcaacdadcadccbccdddcdacdccdccaacadbcabdbababcbacabdadcbadddadbbbaccadabcccacdbddacbdcabdaccddacaadabbcdcbbdddacdadbbacbcaaacccacacddabdaabbdacdadacdcbdaadbbdccaacdbcdadcacabbcacadbcabaaddbbcabacabcdacddcccdcccabdadbbdacabbadadabcacdcbdadbbadccaddcccdacbdbcabaddcdaabdabdcabcadaaacdcdddacccaccdddbcacbcbdaacbaaababcdacddccbbbbdbddcbbccabccacccabbdbddbacaaccbadaccadccdccdbbadccaacabbabbacddaabaadbddcdcdddddacbcccdaacbacabbdbadbdbdccacdccbabbaddccacaaabbabacccabcabccbdcdadbbcbbacccbbddcaadcbddaaaccacccbcdbcbbccacdaaabbdcdcabdbcadabdddadabcdadcbdcbdcddcbbacbababbbbacdcdddcadcaadddcbcbdacccdcacbaaadcdbbcbcadbbadddacbcabbdddbacdbbbcbbcabbbcbbaddcdbdbcbacdaadcdbdcdddbccdbaaccbbbccbbbddcdcacbbbcdbbbcdcacbcccacddbcddbcabcacacdaabbccddddbadccbbdbdcacbaaccdcaacccacdbbadcadcadbbcccaacdadaacbadabadbddcaccaadabadcaddbddcaadcbcadbcbdabdddaddabadddccbbbddbadcadabaaddccdbbdcabaaacddbcabddcdabbaaddcbdcdbbbddbbbbacdbcdcbdbabcbbbcabdaaacbdabaabccbbabaaacbcdadbbbdcccbcdbdbabdbbabadaadbcdbbacadadaadadabababdbcccdcbbbdcaddaccabaaaccdaddbcabbcccdcdbdacabdbcdadbbcaaabbbcdcdcabdacbabddbabbadccaacdcdacbdddacabaccdcbbcbabadcdbabaccacddacdbcddcaadbddadcbbbccbbddadccccbcaaabacbadaaaaababbccdadcacbcdbdcababbdbbaadbcadaabcbaaccdbbcbabcbbddaaaacdccccccacdaccaccbdcccbcbbcacacbaaccdbdbcbccbcddbcaaddbabddcdcdcabcabdadcdcccbddbccccacbdacdbbadddcbcdacbabcdccbddaccdadcacabdcddbadabaccaabcbcdddadcaaaacbddddccdbbbccbbaccabbcaccbcdacdbccacadacbdbabcdbbacddcaddaddbcccdadadaaacaadabaacbaddbcbdddcdbaabaaaadcbbaadccdcbbdcdabcaccbbbacdaaaadbdbaaabdaaccccdadabcdcdaaabaacaacdcbcbbccdcacdbbbaddbddbbbbcbbddcdddabcaabaccbcadcdbadcdcdddcddbadaadbccdadddcddcaadbacdbaacacadacdabdccddadcbabdddcccdcaaaaccdcbbaddddbcbcdcbcddccabadcbcdcdacbddbbbccbaabdcbbdbbbccbbdacacdaacdbdaadabbdbdadbddabdabbdaacbcdabddbcabdbdddbdbdacabbddbbcdcbbdacdbbdddcadadbaacbbabacabaadbddddccdcbdcbdccdaccadcbbaaacdcbaccccacdbaaaacabcaaabcbbbdbdadcdaacdbdcadcdacbaddcbdbccabcacbccdbbacbdddbdcbaaabbcacabdbcadbdcdbdbcaabdaaddbaabaabbaadadcdabcbaaacddbbddddcabbbdbabdbaaccacdcadabdcbaaabbadaacdabbaacbcdcdadadabcabaabcaddcddddaaadcbdbddcddcdbddccbcaccbdadadbacdcbabcddacbccaadabddbacdcdbcdbddcbcaadabaacadadbcbacdbcdadcbbddddbbdcdabadadbcbbaddbbcaaaccbadcbaaacbcacdaadaadbccaaaacaaacabacabdbacdabdbaadcdccaabdababcaaaaadcaaadbdacbbdcacccddacabbbcaaaddccdcaabaabaabccabbdaacabdcadaccbcccbbdddcadaacdadacabcdbaabddcadbcaabdadcacccabccdcacaadabbbacadadcbdbbbccdbddaadcdddabbdbbcbdbccdbbdbbdabbaabdabbacbacaccaabacbcbbcabcddbdcbdbddbcbddcddcaaadcdacdadadcbddcbadadbdddbdbccbbaaadbdabadaaccdbabcbbccbccbcbddccbcbaaadcbcdbabbbcdaaacbbaacdabdcbadbadbabbbdacaabbadddbaadbdaacdacccbcadbcdccbcdacbacbbbddddaacbdacbbacbacdaadabadcbcabbdacdacbabdcdbdbcbabccdadbcdcdaaadaaddbccddbcbbaacdadaabddbdcdcaccbccdadddbccbdacbaabacdbccbcbdaccdcdaabacbdabadbbcaadacabacbabccbcdaacbaacddbcabcaddacacdccbcdabcbbcdbbbacbddbbcbdbdacdadabbdcbcdcdcdbacdcaaccacdcdaadccadacbbacbdbdadcbcddaacccbdadbaaadaaaabbbcbbdcdbbddaaaccbbaadbdccbcbaaddadcbacbacaadddbdacdabdacaaccdbacdabaadacdabbbcdacbcbaccbacccccddcbcacbbcababdacdcbccadcddddadcdadbdcadbbbdccbaadcbcbdbdcccaadaaadacbdddaabddacacadcbbbbbdcadadcaccbdcdbcdabdbbcbbdbaadbdadcbaadabccdadacdbaaaccaacbccacaabdbbacddcddaccbaabcabbcacbacdbcddbddacacdccabdddddbacdcdaaacbbdddccacdcbaddadbcdacbcabbbbacbbbcddabaabbdaabbbbbdbaabdcdbcabacbbcbbabaabaaccdbdaadbbdbabdabcaaccdabdcaaddcdbcbabdcbdadbcdaaddaadaddaaaabaddaabcdabcddccbaadbcadbaccbdacadadabdbdbbccdcdadbbdbbdadccbabaaadcbadabbadcddbbacbaabdddacbbbccbcadabaadbbdbcdcbcbdadbcacaddbdcbcbdacaddbbbacdcbcacaadaccbccbaaaabbbcdbcbbaddadbdcbccdbdbdbadaaaccdbcaababacabaddadccddcbcbdddcdbcccbddddbabdcadadbccdddadbbccbdbdacccdabdcdadbdbacadbdcacbabccbabbcbadccdbbdbcdbccaabbabacddaaacadbbacdaabbaaacdcaabacadaadcaadcbcbaaaddbbaadddadbaaabccdaccbdcbdccaddbaacababbdcbccadadddcbdbdcbcaabbccdabbbadabccadccdcddadaaabcaccbdbddcdcacbbaddddbababadbbddccaadadcbdcbcaaadaaccbbddabdaacbbbbabcacadbbabbcdbbaaacccdcaccbdcdbbdaabddcdbdbcabcacbadacbadadaccbbbbdbcbccaaacbccbcbcdcbbacddccabbdbbdadacbbaacddccadccbbbcddacbabcbccdbadcaaadaacbcaacbbabdabdaaabbacaddcbbddccabcbaddacdcabbbbccbadabbddcdadaaaabbabbacdbacacadddbcdaccaacdbcaacddaddbccbdddcbbbbdadababdbbdbcdccbbadcaadcbdbdbbcbddbccddabcadbbacdbcbdaccdbdbacabbbacbcbdabcaacddadccabcacbcbbacabbbbacdabcdacacbbcabbdddccbacaadbacdccbdddaccabbbcbaacabbdbccddcdbaaaaaacdccacadacbadbcdabbadcccdbddcccdaabcbcbaaabacaacaaacccbdabbbbbdbccbccccbaddaadbdcadcbddababacaaabdbdadbbaacccaadbdcdbbbcbddabadbabcdaddcdbcdddcdbdaabdbcbaaabdaaabbdbbdadabcadadbcbdcdcbcaabdccaacbcabdcbccaabddcdcadcabdcacbcbcbbacacdadadbacddccabdbadbadbbcdabbcaaacaacdaccbbbbddacaddccbacabcbdcaadbacadbdbbcabdabaccdacbdcddcddcbaadacbcacbcdbddcbbbdccbdadddcbacbbaaddacbcccdaadbbbcbdbdabbaabaccdabbbdddbbbacbdaaadaccdbdaadcbcbbcbdddabcddbcdcaddbadbcaaadbcbbdaacadbbbcdbdacbacadaacdaccbbaadbbddabcbdccacbdaaccadcacbbcabdbaaabbbcbdbacdbadbdbbbdaacaabbaadbdcaaacbbccbaadccdddacbccaacdddbdbbddcdcddcdcacadcbccababbacaccaabcaddcbcdabdcabbcccbcbabccdbbccbcbacdbbdbcdcbddccaaaccbaacdbbaaadcaacdadbcaadabaaaddadbadacbdbaabddaddcbacbaadbadbbdacaddcbdbdcbddccaadadbaddbdcbbacdacbddbcbccbdcacbdddabbcdbbdbbbbddbabdaccdacbdaacaacdbabdbabaccacdbabddcbdcbddbadaddabdbbccbacabbadbacbcbabbcbcbadbabbccccadadaadddcddbabcaacdcaddcaddccddcacadaddddbdbddabaaaabdbacabcacbabbbbccdababbbdadcbbcdbbbcabaabdaabaabbdaacdcacaccdababdabbbadaccddaadaaacdcbcacbbaddacaadbbabccdbdcabccdbbbdbbabdbbbddacdaddaaaddbdabaabadbcddcacacbcbdaaaadaddbbbdaccbccabbcdcabdbdcbcabaaaadcdbcacaddcdcdcbdbcddcaabbddaaddbadababdbaddbccbbadaaadabdbaabbcbaacbdcbcaabccdbddddbddbcdbdbbcbbdaaaaccaabacaadcbccccbbdcdccaaddbddbbbadbdaaacdcbabcbdaacaaccddcdadacadcddbadcdbaddcbddccddadcddabdddbadabaccabadadaccdcababbdccaddbcddaabddcdbcbacadcadccbcbcbdbddcbcabddbccccbbbcbcccbdbbbaaadcccaacabdddadddcbabdbadacbcdbccaccddaabbbdaabdbcdbcdbccaddbdbbaacbaaabbbdadccdabcacdaaabdcdadccabbcdccbcbcbbaddccdcacccbdacdbccabccbdadbabacacdcdacdcdcbcabdbcddcdbdcadadaadcbcbdbadbbddbacbcaadabbbacbcbdccdcddbadcbdbbcaaaaddbdcbbdcdaabaabcbadabbdaabadbcdccbaababadccbabbcbbadacbccacddcbbcddbdcbcaabadabadabbbbccdddddbcccbabaccadabccbcccacdcacbabcaacddcbbddbbabdbccbcbaddccbdbcdcadbabcbbcbacbdabdbdbbdbabadbdabcbbacbbacadadcbaccccabaaddccabbddbdcbbdaccabbcaaaddaaadddccddccbadcacbabdcdabcbaddaacdbbacaacdaddbbaddbcacabcabcadcbdaddadaacbabbcbcbaacbbacdaccabcaaccdcacdccbbddccccbbcdabbcbbcabbbcbdabadcdcaddddcdbababacbadbdcbcddaaadcddccdaccdbabaaacccdbbbbdacabbcdbabacccdacdbaadbdcdbddaaabcddabdbdabcacaabcdbcadbdbcbabdacbcdcaaaccbccaaadbdbdccababdddcbddbddccdadbacacbbdabddbddbcdcaacadbadabcbccdbddddcbbcdbcdbacbddbdabbacbbdbbbbabdddcddbadcbdcdacdbbddccbcbadadbdbbbbdcaacdcacbbababaccbbcdddbbbcbbcbaddcaddccdbccdcbbcabcabccbabdccdbadcbdacbaadcddddddabcbccbadccadbdcdaccabcccadcddacbdcbdacdcaaaddcccdbadaccacccdbcbacbddadbabbbabbdcaaacabbcdccdbbabbddbabbbbcccbcbdcdbabacaaaaaacbdbbadbdabdabdbdadcababdbaabcdaacbadaccbacacabacdbcaacbdddaddaaabaccabadcacdccaabdadcdaccacdcadabadacaadbccbcbbdccbdabdcaacddccaabbdacbcbabbdcacaddabaaacbbdbddbaaadadaadbbddaaaddcadccabadcbdbaadadbbcdabbdcddbcbbadacabdbbcdbaaabbbdcccbabbaabbbbddacbbddccddcdaaaaddddcaadabadbbccdbdccaddbbcabdadbddcbdbbaabacdcabdbbdcccddbabdaadbcccabababccdccacdbcccdabacddcbcbbdabddbbadaccaacadaaabbbddacbadcabadacddbddabacdabcdcbbcaaacdbddcacbacbddabbbcdcbbbccbadbabbdddabdcacadaacdcdcdbaddcbcacaacadbbcbccbcbcdcbcbacbcdacbcdbacddcdacdaabddabbabcadbdcbbabdacbdcbcacccbabbbcdbaccaadacabdbbcdbdbcbcacdcdbcbcbabddddcbddbbbbdbbbbdacacbdcddbbaaaaddccdacbcbaacabddbcbdbacacbccbbdbcdaddaacaacbbbbdcdadbbbdccbbcabacbccdbabaccaddbbadddddabcbacacabbccaaadcadbadbdaabdbdbadaccbaacbdbccadadbdaabbabcabbcdabcaddcbdabdadddadcbbcbabbbdaaddcbbdddcbbcacaabcbcdcccaacbdcdbbadabaacbadaabccddacdabbbbbbbbdcbbdabdacabbbcddcbccbabcaddacabadbbacadcccbdacdbcdbbddbbbbcccaddbababbbdababadbabcdbbdaddbcbadabcdcbbccacccaaccbcbcccdadbaaabbacaabadbdadadbbcaabdcabccaadacbbbdccbcbdaccdddaddddbdcaccdabdbddbbbcabadcddbcaabcdcccdcdabcdacbccdaccbcddbbabdaaabdabdbabbccaabbaccabcbcbccaadbcbadbbddcaaaaddbbcdbbbcdddbcaacacbcbddddaddbcdbcbbbbadcbbdbdaacbbdcdccdcbaccababccacbcddbdabbddaaadcbbbacddcddabdbbaacadccbdcbdadbdcabbdbcdacddbcbbabbbadcccdbbdcacbdcdcbabcbbbbdddcdbbaadaccaadbbdcbcdbacbdcabcbaabcbcccbdccdcabcbccddaadccbaabdddbccbdaadbdcaccddabbdcbcacbdddbcbbcaadadbbddabbadbcbacddbdbddbcbdadcbabdbadbbddbbcdccacddaccccccbacbbdcccbadacabcbdcabdbbccbdbdbaabcbcaabadccddbaaabdbdbddabbabcdaccadbdbdcbbdbbddbddbbbabcdcdaacaadabccaacbcbbcdcaaabbccaccaacddddbabdbddcadaadacbdbcaddbbcadabddaacddabdaaabdbcabbdcdbcbdddbcbbbddadcccddcaadaacbaacccbadacadadbacaaaadbcddaaacdcbddacaddbbacadcaccacaaddbaadaaacacaabdbaaaadabbbbdbadbcacccdccbbbdcadccadbcaacdbbccbdbbbcdcabacbbbaaddacbadababdabcdaabdcbbbbabddbcaabcccadbbbadbcacbddacdbcbdacbdcbabbacadbbbbcbbbcbbddacbcdbcabbddbcdbacccaaddcdbbbaacdcbccbcacadddcaaccccbaddabbabadabbaccccbdadccbcddbdbadaadccdcdbadcdabaadccddddcdbbaadbbabababdccccbbbdddbcdcaabbbbabcdcbacddbaccdbbcabdadacabbacddbdacdcaabbbaababdbaccadaaaccccdcbaaaabcbcddaaacdaccdcdadbadaccbdadbbbbbdacccacbdcadbbbcbadbdcabcabbdcddcbddbabcaddabaacddacabadcadbdcbdbcddcddbcbaaabbbdcbbddabaaccbdccbddcdbccdbdcddbacacdcdccdbabddbcccbcdbaccdbdcbcacbdcdccccaabdcacacdcdcaddcbdcbaccccaddbdcbcdccccddccadbcdbccdcaacdbbdcabcadaddcadadadbadbbddbdcbbdbbbcaccbdbbadccaabbdcdbabaabbdababbbaabcbdbdcdcaccddadbbaacbbdbcdcadbbbbdbbaaabcacbbbdaccdadcdcbcdadbbaccccbcacacdcdcbbacbcbaabbcccdaddcbccaaccdcbdbcbabcccacccdabaccccccbdcabcbbcacbacdcaddbdbbbddcbbbdbadadacbdcbdadbbbbcccddddbaccdddccdaadaaccbcaddddbdaabcbddbbaadbbaaadbbddacbcdcddacbdbbbcccdcacabddcabcbbabccbbbcadaccdddcbcaacaccbcdacaadaaadadbabdcddcbaacbbbbbdaaccaddccdbbdaaabddbacbdcbcbaddacbaaabacaacddcddddccdcaddcdacdabcbabcbcdacdcbaddcaacccbabdabdcbdcdbbccdcbcbdcbcadbdbbabbdbdbacccdccabbbaacbccadbcdaccabbbdcdbcbabcadaaadcdcddbadcdbdcadbcabcbadadcdcaaadabcdcddabdbddcabddbbcbcbbdabacadccbdccabcdddcaadacadadbbacdbbacdccdabbcdcdbcdddbbbcdbcdbcdbadbbcaabddadaabbadddbcaccabdadddbbadbbccabdabadabdabbabcdbddbacddbcaabccacbadaabaccacddaacdbbdadddbabaaaaddacdcabbdbcccbcccdbacaadcdcdccaabdcdcbbddcacddadaabdbabdbcadaccadadbbcabcdabbccabbabcdddbdbdbacdabdbbadbddcabccbabcaaadcaabbcaadcadcaccdddaadcdbcddaccdbcabdadabcadcaabbaaddacacdcabcadddbbabcacbcacbbabbaacdaacabcaabbbbdacbcdbcbdcaadccbdbcbbcdbabadabcbbdbddccbacddabdadadccdcdadbccadccdcdaadcdbbaadbbacbdcdaacdbbbccccddddddccdabacdbdddcbdadbccdabbbabdccddacddccddabcbdbbbbbdbcbcababbdcbaadddccdcbdcababcdccbaaadaacbbbbcacacdcadcdcddaaababaaccaaaabbcadbccccdcaddbccdaadcdcdabddacabbbdcaacbbbdddccaccbbacdaacbabdabcacdacdacdccbaadbaacbabcaaabccbccbababcaadaabcacdccbdabdaddadbddcddabdadacdcabbabacdcbadccbcbdcbdcccbbabcaaabcacdbdcbabdcccddccdcaadadcadaacccbdaacacccdbdbddcddadddcdcdbdcadbcddbbcbccbcadccabbabdbabcbbdcddaabcdcbddaacdbdcbadbcacddbdbbadbadaccadbbcccaaccadbcddcaadbdbbcaacdcbcdaaddcdbcbbbddcccadacacbabdcadcdaacbdbacbaccadbbdabdaabcaaddbcaacdbdaddcadaadaaaacbcbddcdaaaabdcaacbddbddaabdbcdcbcbaacaadaddcbaaccdddccbdcddaaddadddaaaccaadddaacbdabdcddbddbcbdddbbbaabaccdbdbadbdcaacdbbacaaabcccdadbadcaaaddbdbaccbcabccbbbdcddaddacadcdddbbbdddbaddacdddcaacdacdcbddbbabaabcbcbbbcacdaaddadccacdccabdaaaabdabdcaababdcacacbbbcaccacdabbdcddabcdcbccbacccbabddbbcaacddbbababaaabbbddcbdcacdadddaadcaacbbdaddadddccaccbcdcdabbacdabddadbdcdaadbdcbabdbadbbdccaccadaccacbaccbbbdadacbbbdbcccbcbaccdccadcddacddaabdadbdcbbbdaccccdbdbabaddcbcdccdcbcddadcbbbbbcadcccadccbcaabdaccdbbbccabbccdddbdbaddadabcbdccdcccddaccdacbbaabbccbcbbbbbabadacaaacbbbaacdbbccccbaaabbbabdbbabdcaacbcdbccacdaccbddaacabcaadccbcdbccdacbbacabddadcaadbbbbdadadaadcacccacdaddacbddbaacbacbbbdcadbdabbdbbbcadcabcdcbccbdadcdabcabacbbaccbcacbdbdbdaaaddcabcbbadbbcabaddabddaddcbddcadacdccccbaacbcbbcaacaacbacbdcddbbdcddadccddddadbdcaccbabbddabdcbbdbabadacdcacdbcbdbcdbdabacbdcaaaadcddcbacdbabcaaabddcabcddcdccdadbabbbbcdabadacabdadaaaaaccbbbdcbccaacbaacdacacbbbdccabacccbcaccacddcbcadbdbdacaacbdbbddacbdddbcbdabaabcbdcdcbbaacbddabddabdbbaddaaddabadcaabdaddcdbbdcdcabdaddddcbcddbcacddbddabbaccbaddbbcccdcbcdabcbabbdcdacccacdadddcadddabcbdddccaabdcdcdbbdcdbacaccddbadbabbcbdaabcbacbbcbabbddabcdcabcccbbdbddbccadbacbcddabdcbacbcaacbbddcacacddadbaaddcabaaaacaaaabcbcbddbdadbddbdaddbcacbccccddadbcddcbddadcdccbcbdcababacdccdbbbbdbacaadcdbbadcddabcacadbacdcbacbcdbdddaacacbbddbbcccddddabdcadacadbabbbabbabbbcbbbccdbadbbbcabaddcddcdbdbaacaacbdbdcdccabcbbbacbdbddbbccbbaddadbcbddacbdcdacacbbcbbcacddcadbadcaabbdbbabbdbdacaadbbadddcccddddabdccdcacbdccbccaadbbaaccccbddcbbbdadcdaabadaabdabbabcddbaacbddccabdbabdcccdaddddcaacbdbbcbcbccbbddabaacbaacababdadacccacaaaadcdbacadbabbdccdacbccccbabccddaddaabbbcbbabdacbbdbaaabbdacdadcbcbdbddababbcbbdaddaaaadaaadbaacadccdcddbacbccbaacccaaccbbdbddcaaaaccccccbcaaaaddbabbccbdcabccbbcacbddcaadbaaabcbaddbabdcacbbacbddacadacddbacdbbdddbdbdccacbdbcadadddcdabcbadbcdadaadbbabbbabdcbacdddadbbcaaddbcdbbabaacacabbcbcaadaabccaccddddbcbbbcdbbccbcaaacbdacacccbbbdaaccadacacdaaabbabaccbdcdcaddbcbaabcdaddaacaacbdcaccacdbbbbdaddbcadbddbdcbaabcadbcdabdcdcaacadcacbdcaadddadacccbdacbbdbcdcddbdadccdcbadddacbdadddcddcbcdcdccdcabbdcddbbccadaabcdadbbbbcaabcccdbccbdbcdcdbacbbbdacabcddabdbdcadcdbaaabcabaddaccabcccaaccdbcbdbcdcdcababccabdaabbaaabbaadcadacaccbcadbbadacadbbbdabababaadadbaaaabbbcacdcbadacccaadaccbdbaacccadacacdbbdadbbbddbdbadbbadbbadddadbabcdbcadbbbaadcabcbddcdbacdabcbcaabbdadbaabbbccbabdacdbdddcbaaddbabbcbbdbcddbdcbbbdacdacbbaaacabbbccccbaadadbdaacdcababdcabcdbbdaaaabdacabaacbdbcbddcdccdcaccbaddbdccacdcdcdcacbaddaabdccaaabcacbadbcdbbbbdcbaabacbcccabccacdddddbcbaddbdbccdaaccdabbbbdacabacdcbaccaabdcdacaaccadcbccdabdccbdbabaddcdddccdaccbcacdaaacdaaccdcdcacbabdccdbbdbccadabccdbaadaadbbccbadcacccacbcaddbbcabbdacaaddcbdbbaccdbadbddbcdbccdadbabbcadbdbbcdbaabcdaabccbdcbbcbcdbdcbdcadbbabacccdbbdbcccdcabbacdaabbdcbcdcbbcdcbdaaaabddcccbcdcbcdabbacdadcdccbdbbcccbadcbabcbabbdbdbbaaaaacdbaabccdbdbdcddcccbacdbcdbbcabcdcaaaacbdaabdddbbabbbcdabdaaacacdbbbdbddcacbbbdbabdbdcaddbbcbcabbbcbbaccdcbbccdadaacbcddddbddbbdadcacdacaacbdbadbcccacacdabcdabadbcdbaabadcdacccaaacbbaadddababbccdbbbcdbbbdbddcaccacdccaabddadcdabadbcacbcdaddcabaacabacbccbabbadbadccccabacdcbdbbbbbdccddbabacabbadddadccbaacccdaaadacdacaddbccadccdacbcdaccadcacbbcdcdcadcaaadddcbcdabacbbbddbccbadadddcdbcbdcdcadcdcdcaabccbdaaabaaaabddacdcacdcacbbbacaadddcbbbcbbbacddddcbdbccdccccccdaadbaadaacbddcadaababadcddadcdccaaaccbbabbcdabaacacadaddadbbdcdbdabacbbcaaaabdbaabccbabadcaaacdcbaacbcabbbabadbbbdacdcbabdaadacacbcddaccdcdddaacadcaccaddbbcbbaabacdbcadcacbaadbcacbadaddacccabbccddbadaadbbdbdaabdcabbccdcdacdbabdccaccabccbaadcbcacdbdcccacbaaababaaabbbbdaabbaacbacabcacdcbdcaacdcadddcbcbbcaadbabbbacdbbdcddadbbdbbccdbbcbacaccbddacbdcdbabcdaccabbcaccdadabacacbbcbacddbaabcbbcadbcbaddbbaabbabcbdabbaacaacaaabdaddacbacacdccaabdaaadcddadbcdcccbddcccbbacacbadaacbadbcadcdbbacaaadaabbadadccaacbadcdadcbdddcbbddddbdaaddcaacadcdbcbabbcaacdabadaabbacddcbadabacbacbdbcdbbdcaaccacdcdbdbcdbddcdccbcdaadcbbdbddabbbacbcabbbdbaddcdcbcdbcbccddabbbdbcdabaddbcbcaaacaabdcaccdbddbdaaababdbdcdcadbadbcbbadcdacabcabcbadccbdbccbaaabacacaddddcbbcacbcbacadbdbdcbdbaacccdbdccdcbdababbdabdcabdaaadacdcbdcaacddccdbcbcaacacccabadbdacbcdaaddbcddaccbcadbcdbcccadcdbddcaaaababdcdabcbbdddcccccddbaabbdbabbadbcacbcdadcaacccdcacbccdabadacdccdccdcaaabbdabbaabacdcacbddbaaddaaccdbbabccdcacaadbbadbccbbacbacdaadbcccdcbadccadcacbaacdbaaaddbccbdcdbbacaabbbbcbabbadabbdcaabbadacddcacacddaabaaccabbdcbcabaacdbdbbbccbddccbaacdcdaddacdcccacbabbbadddccdbcdabaacabbccdbacddcdadbcdddcbabdcdcbdcbcdcabbaaadacbccdbbbbabaabadcbabbbdcddacdacbcddabaaccbbcbbaadabbbdabbddbcbcddbdbddccccdaabacdaadccbdadbadabdacbabaaabdabcbbaadbcaabddacaddbbccdcdccadddadacddddbddcddddcaabddadadbbcdcdacbacccbcdabdccbadaccacacadabbbbabadbaadcddbaaddabdaadacaddbaddbadabbadadabbbcbccdabdcbbbcababdccdaabbcdaaddccddbdbcaccadcabbadadcdabdcbbbbbacbaddbcaccaddabacbacaacbcbcbdccdbbdcadababccaaaaaaacbcdaabbbccaababcddccccdcdaacbdcdbcadaabdcbabbbbbbbdccadccaabdcdcabaaacbcdacdaccbabccbddbcabaadadbdabadcdcaaccbddbdcccdccaacbbadbabaddaadbbccabdabdddaddcbdbaaacdbbadbdbdaabbbccacadccabadccccdcdbababbaccddcaddadbbcaaadbbacaccabdcabbdcaccdbcacdccaaaacbcbdcdababddcbcaaabccbcaabbdbadcbbcbadbadccacdcdcbadbcaaaddcaabdcdcdadbbbddabaaacacdaabbabdccccccddcdbccababcaabcadccbdbaaacdbdbbbaccbdadcbcaddbbddccdddadadcccacbdcaccccbcbcdcbcbbadabcccbbacaaccdcbbaacbacddbcabacdacababbdaaadcaccaddbabdbbaabacacccbdcdbaacacbbabbbcbacdbcddbbdaaabcacdbcabbcddbbbaabbccbccadbddcbadabaadbdcdaacaaabcabbacbdcacbddccddbcacbadddbcbbabccddcbdcaacdbbbddaddbcbdacadcaabddadacbcdbdbbacbabddcadddccadbdcddddcbadcbddbbdcddaadddccbcbadccdcdadabbacddaabbcbabbaabaadadbbacbacbdcaaabbbbdbcbadccaccccdbbadbccbdcadabaddadbcddbdddcbdcdbaadcbcbaadabcddcdcdbbbcdddabdccaaadddbcadcdcdcdbbbadbbbdacccbddcddcbcacabccacbadacaabdaabbcabbdbddbdccdddbbdcaaaaadddddacabddddaadbdacaacdcbdbbbddccaabddccacbbdbdaaccbbdccdbaaabaacbbcddcdcaabadbbcaabbbabdaacdccacdcabbacabdcbdaabdbabdccbcdbcaccaacabbcccdccbcabdccbbaaddbbdbbdcbdbdbaddacdbbcaabcdbddbacacbdcbabaaaaaabddcdbbdadcbaccadcadabdababaacddbccdcaacbcdddcbbaabcbbcadbbadcadcbcbbddcdcaacccbbcbbcccbbbbbbaaaccdacccbbbbdddddcaabbbdbacabccbcbdcddabbbbdbdbbbddbbbbdadaabcdbdbaccbbbbbdccdbbbddaccdcaaadcdcabadaaadbcdccbcccbcbdbbcdccacaccbcdbbdcbbacaacbdacccccccabbcbdacccdbcbcacaabcbcdbccddacacdcbadabbbdacbacacaaddddbaddaddcdaccbbaacdddcaaccdadabbcccddbaabccccaabadcdddccabbbcbccddddabddbadbadbcbbbdacacdbaaababccdbaabddacbdcddcdbaadcbcbabacbbacbcaaacadabddcaaabacdcbddddccbdbaadadcbdbbaabbaccbcdcdaaaccacadcabcadbdbcdcabdcdabcbabcddcdcccacbadadcccdacbdbccbcccacaacacabbbcacbdbdcacdadcbabbbcdccadaababaaaadbcdbacbabdbddbbdbaccabcbbabdbbadbcaadccdabbaaabbacadcbdcabccbdaabcadcabdcabcabccdcbabacdcbbbbcdadbbdacbabadcdbdcbacdcbcacccbcacbcbcdacabdbabacdacacccbcdcaacacbcacabcddbccbabbccacadacbdcaadbbabdcccaabbddbcbcdadaacbacddbcbcbbbdccabcdcaccabbacdaaaacadabcabdacbadbaaddcbdaddbbaaaccaacbcdcbabddccccdcacacbdcadabbddddaaaddcbddacdbbcbddadccadacacbbdbcbddcaccbdabbadaaacdddddadaaadbccbddccbacabbdbcbbdbcacacaddccaacabbbbcabababbdcddbbcadaddbcccccdcbccbbbcbbccdabccaddbacababbabbddacbccadcbbcdccdbbcbdacdddbcacaaabcdbacbaddcbccabddcbcbdbacabadaaaaaabaaaddbdbcacacadcacadccdcbaccdcdaaaddaadaabdcabcbcbaabbbbaaddabaddaacbadccbabcbcddbdcaaddcdccdbdcddabcbacdbcbcadaaddacdbddcbdabccabcbcdabcdcccccbdaabcccabbacdadbdccccbbddbdbddbbbaadacddbaaabaddbbccaccbdaabccbcddadbdcbcdacabddacbcbcaacbdbcdaabdccaacbcbcbddddccddaaadabcdbbdcdaaabadaccdddabdcdbdaddbadbbacadcbcbaddaaacddbabdbdbdaddbbdabdddbaaaabbcdadbbbdaadbabcaadccaabaddbcccacbdadbbbabbaabcbdbadccccbbdcbbdacdcbbccdbacababbcaabbccdccbdddbcabaaaadcbddacaddadccccbdcbdbbddcccdbdbdbdbadcdacbcdccdaacccccddbcbdcdcacdcddaabadaadacdadaccaababacbbddbbcdcbdabdbccdaadabcdcdccbcbbadbbdcadccadbdbdadcbacbdbbaabbbbaccccaddcbdddbddacdcabcacccdcadadcbcaaaccddcbbaccbccbabaacabacbdcbdcdddcadadcbbdbacdbdababbacdbddbcbaaadcdbdadbdcacdbdcbdbbaabbdadabcacaadcabacbaadcdaaaaacbbdbdccbcadbbbbdccaddcbbdbcabbbdbcbdcaabddaacaabcacdcaabdaacabaccdcdcbcbdadaacddcadaadcabbbbaddbaccdcacaccbbadbcdbdadaddddccbabdcaadbacbbdcabbaccdbbdaadacbcdbcbddcdbcccadaaadcbcdadabbbdcdadbbdaccaacdcdadbaddbadbaacbabbacadcdcdcbbbdcaddcbcccbbbbdaabccbcaccdcdbdbddabaacadadbbcdcabacbdaabccdacbbbacaccadcbdddacbbbccddcccbcbdcadacddbaddddbcabdbaaddcacaaaddbcccbdbccdaaaccdcbabacdcccadaaddccdbcddcacbddcdaddbbbaacadcdbcdadddcddccbcbbddcbcbdbadbbacbbccabdbcdddaddcdbbababdaaadabdbccacbcaaddbbcdbddaacbdbdadcdadddcbcdcddadddcbddaddcbdccddbabacbddbccbcaaaacccadbaaacdadbbcbbcacbcabcbcacccdbadcadaddadddaabccbbddcdaadcdbdaccbcccaaddacacdacadccdbbdaccdabcdbaccdbaacaadbadcbacacdcbdaabadcacaadcbacbdacaddbbcdadaabacdcbbaacaddcdcdcdabcddcaabaababbcadaabbcdaaacdcadaabccdcdbaccccbbdcbacdacdcdbdbdddcbbddcabbabccbddcabadadbbccdbacbbcccbdcabdabacccadbcbabdaddbddbbdbbbbccdadbaddcaadabcacadacabdccdadbcbccdacbccdcaccbbabccadabccdacdbadaddbdcabcadadcbcbbadcdbbcbbdbccdbdcdbdbccdbcdccdbcccddccbbabcddcdabdcbcacdbbabadcdcadacdaacccbcbadccdcaccbdadcdcabaccdbdcdcdcdbacdadcabdbcbaadaaaadbbccbadcaacbbacccbbadabcbaaadcbbadacbbbddcbcaadacbcdabacdcabbcbaaaccadadacbcbcbbbbddccbaaadabaccaaddcbddacccaabddabbcbcbdaadbadcacdcdbadaacccbbcdcaabbccbcbddcacbaaacadccdddbbbdcbbbccbcabdcaaabadacddcddadbcaccbdadbadadcddaadcbdcbdccaacaabcacadbbbcccdbbbcaacadaadaadbddbdcdabbdadbddacbddaababcddbcbacbaacbbcacddbdcdaaabbbbadbabcddaccbccdcbbcabbabcbacbccabccbdbbbccbdccacbcaabbacccdcdabcaacbaabcddadbcbadabdababbcbccaaacabacadbdcbdbcbcbdbcacccacabbbdaadccdbdcabaadbbbdbaacccdccdccbccbadcbbabdbbaacaddcabcbdadcccdbcbddbbbcdcacdccbabbadbdacaaddcbdadbabbabddcbdcddddadcdccbdbccabcaaadaaaabdabaacddaadbdababacbcdcabbcabcbcdaadcdcbbbbbbddcbaacdcbadadacbaadabdccdcabacbaddcdaaccdbdcbcdbdaaababbdbddabddbbdadcbcbbaccdbdbddcbbdbbaabdabcdbcdcbdcddbddabaaacaadabdbddcbddabbcabbccbcadbaadbbbbbabddccaccddccbbcacccdccdbcbdddaacbdccabcbabccdaacdcbccdacabbcbcbdacaaddabaadacbcabcbabdcadaacbbdbdddbddbdaddccddaacdcbaddaacdbdbdbbbcdcccbabcbbadcaaccbcdcabcacccbdabbadcbcababcbbacbcaaddbbabdcdbaddabbdbbbcccbddabadacddbddbabdbccbbdbbcacbcbacadddabccdcadcbbbcabcabaadaccdbbaaabbbaaddcacaddaacaccddccdcccbcadbbdbabaabdabdbdccddcabbaabdbcccdabdadccbcaddaaacccdaaaacddbabdbcbccbcbbabdaccdcdadcdbdaddbdddaccbbabaddabbacbcdcccdaddbbcdcacddabbabdacccbadcdabdcdacbbabcbbcacddbbadbccadcabaaabbaaaabbbddbacdcaabdbbbdbcbabacaccabcdcbcccbbbbcbbbbbbccbbcaccbdbadccbbabdbdacdbcddcaaacbdaabbdccabbdaabbdaaadbacdadabddabadbccddaabcbbabddbdbdccdcdccaababdbaaccdcbcbadccdabcdccddaaccccbbcbbacaaaaacabdbccdcdbddbbadacdadbacdddabcccbcdbbbadbcabcbaaadcacadacaccddcbcdcbacccbaaadcbbdbccbbcdccaadbacdadbabcbdbacdbbadcabcacddbaaaabdadcbddabbaacdbdaddacabddbbbadccddacabcccbdacabadbcbaacbabacacaadcbbdddaadbdadcabdaadcabbbdcbaaabcdaaccbbacaaacddbbddcddabaddcbcdbacbdbdaabcbcdbbbdcabddbcabcabbccbccdbcaabcabdbbdabaaddbccadbdbcacdcbdacbddcaaacdbabadcdbaabdbaabaaaadadbdaacbdcdabccbcaaccbbadcabadbcbdbbadaabcdaddccdcbbbdbdbabdccaabadbacccddbacbbbaabddcbcdacbdacbbcdcbaaababcbcabdbdbbdbcdcacddcddccccdddbbcacbcabbdbcbabddddcbdcdbbdbdbbcccdaacbcbbbaccdbacacabbacacccbdcdbcddcbcadcdcdcbdcbcbdaaadcaccccaabcbcbcacaccddccddbdddabcdcbdbdaadcababcdcbccdbdacacadaaabaccbcacdbbcdccccdbabbdcdaccadcbaddabcdbdabaaadcbcadbcaccacddcdddcadcdabdcaaaadccaacddacdbacadddaadadcacacdbbbcbacdaddcccbacccccbccdccbabadddcdaccddddbbdbdabcdbcaccadcbbdbbdbdabdbdcbaabdccabacbdadcdddbdcdccbdaccbbbcbaaaddcccaddccdcccbccadcdddcccbabdabdaabcdbdcdaacdddbaadbdcaadcadcaacbbbbdbacabdcabbabbdabcaabadabbbdbaaacdacbbccbabccadcbdaccbbcdcdbddacbdadacccaaaaddbcacdbcbbdddcdddacdabdacddacbacdbccddadbdcbdabaddcddaaccddccabdddddaadbaccaacddbbcbbcbdbababdcddacddadccbacbccdcaaaabdbbccbdbaddcdadcdccdabddaddaaddbadabacaadcaddbadcbaadcdbcbdcadcabdabacccdddcccadbbccddacdcdadaaadccaccbdbabbcdbdaddbccddbacddbccbcabcccbacaccbdcaabddbdbacaadbdbaadadbacdbaaacbbaabadbcdbbadadbdbaacaabdadbcbadddbbadcaccadaacddccaacadcdbbabbababdbdabcadddccadbdaadccddabbbdddccbacbcadaabaabdddcbcbdaddabcbaaaddcadcbdbdbcabdadacbbcabddadcbdaaaacdcbbaababdabcaadaaabbdcdbaaacbbbaadadadccaacdccdddbababccbbbbbdbcabbcabcbabddaabcadaacadcdcbdcddbabbaddaabaacbcddcacdadcbaadbbbdabbddadbcbcdacaddbcdbdbdacacdcdbaadaddcadbdacbcddccddaccaddcbcdbccdccaabbbacaccabacacbcdbbbaabcbacdaacdabcdaadbabcddddadaabddcddbccadbdbdbcdaacadbdccdabcdcdcacabdacaddadcdabbcdcbcbdbcbababdaacddaaadbdcaccaccbcdacccbdaabbdadaaaddadaadddddadbdaccbbabaccdccbdbababbbcadbbdcdbbaacbcbcabccdadbacdcbcbaadbdaabbbdcdddbabaccdbbcdcddacdbacccdcaadbadcdacacadbcabdbcabcbcadbcdbbadbbcadaddbadbccaaaaddbcccdbacdcdbbdccbbbdbdacdcccddabdbcccdbbdddbbdbbdbbcacbbaabcdcbbcddbcbcbdddddcdacddcaadadaacddcadbbdaacdacdabdcdcbccccccdcdababddcddcdbccdcaaccdabdddcaacaaacbccbbbdcbbdbccccbabaaadacbccccdbcbccadbcdcdddbdcabbbbbbbacccdaddbbdabbdaadcadadbbadbaabadbbcddacccaaadbacaccaddcbbcadcaabcaddabcccabbaddcbaaabbddbbbaadddcbbaabaabdddadadbaccadaddbdbcbadbaccababddbacbbdbbabbaddaaadbccbdbccacbabdcbaaacacddbccabcbddadccaddcbcbbddadbdbbacccadbccccdacdbcdacdcaddbccbcdbadadddaabdbaccacddccabcbddabbacbdbbccbcabbdcdbacbccbabaaddccbacaadbcbbcbbbdcdaabacbaddbdcadccccbadbbbbbbcabcdadacdcdabacbaaccabcccbbbacaaabdabddcccbbbdbbacdaddadcbaaabaadaaadabbaacbacccddbbaccaddcbbcacdddacbbdcddacadaccbabbaacabbdbccaacccdbbddbacadbcdabbbcccbbabcdddadadbadbbdabbdddbbccadccdcccbacbcbabdbbcbdcacbbbcabccdddcaccabadcddbaadddcddbdaaacbaacacdcbbcdcabcadcaaaabacabdbbccbacadcccacbcbabaacdbccaccdccacbaabbbaaabbbdaddaabddcddddabdbcccccacccbacccdabaacddcbcbadbacaabddacdaabccbdadbccadcbdabdaabbdabaaadadaaaccacaddcaadcbbddabadaaddbcbaabdbdddaabddcccadcdbacacdcaaaabcaccccbcaaddbcaddaabcdaddddbcabcbbccbaababbadacddbadcccbddaacbdadaadbcabbbacdacbcacaabbcdbbdababacabbccadbbddbacddcbacdbbbdcdbcaddcacabdacbcaddbabbccdbbacdbcbdbcdcdabcadcdabaccabbcddacaaabaddadcaabadcccddadcacabbdbddcbadadadaccadadaddcacbdcdcbcdadadadbbbadbabaddaaaabccdadbcbdcbbacacdbccaacacaabbdadbbcddbadabcabcaccabddbccaacdddbcaadabdadcdbcabcacabbaaccadbdabcccbbcdbabcdbcbdcbcccadabcacbbbbddddadcddddccbcdcdbbacbacdadcbcaddcbacbccddccbcaadabcaddaadbacacbacddcbcdbbddbdbadcadcaacbaacaaddddcbadbdbaadcddcbaccacbdaaaacdbdbbbccddcbbccbddbbbdddadacbbaccddadcabacdacbabdbbcaadbadbbbabbadddbbcbacadcabdabdddadccabcabbbcbbadccbcdcaccaaacbbbdadbadaaabdaabdbdddddcaacccbabaabdbbcddbbcababbbddcacbabdadaabbdbccdddccccabdcddaacbcbbbabbbaaccdaacbdcdcbaaddcadbbdaaabbacdadcaacdaadddcacbdbadbbddcaccbabccdadbdccadaaacaaadbddbbbcbddbcbabcdbdccddcdcaacaaabbbdaadadaaacccaddccddbccdbaccaacdaadaadccabcbaabbbbdbcbacaaaccdbdcdacddbadaacabbccabccbabcabcbbcdbbdabcaaddadbdbbabcabcbddbdcbddddccccabcadbcbdcaabcdabbbaaabcdabbddcdcaaadabdacbacddabbacaadabbccadacdccacbdaabddcabccccdaabdbddacccbcdacabcaaabdcaabdabbaabaabcbcdccbbcbdaadcbcdcdcbdaaccdadbbdbcadbdbaacdacbbbaddabccbbacaabcdaccbddaccadadcdbaacbbbadbbbacaaacbdcbbbddacbadcaabccaccabbbddacdabbabdaaccbdaacdbcbcddcaadacbdadaaabbdcbaddbaabbcadabbbbdcaabcaccbdddabbacddcddbacbaccbbabddadbddacbbdbdbabadcbdbbcdbaaabddadcdcacdcdaadcaaabacbdcabccbbdcadacbdcbabadbacccaaddcaddbdcdcdbbcccdbdddaccbdcdaadabbdcccaaccdcbcababacbaadddbdcabbbcbdbcaadadaddcdbdcdcdbadbdcdabdaadbccadbbdcddcdccbcdbacadbabdaadccdcdbdbccdabcbbbdcababcdbaabdabbbadccabadadcdbdaddcccdbdadbababdadbdabcbbbbbddbcdbdcabccaadcaaabbbbddabccbdcacccadbcdcdcdabddaacadbddbbcbbacbbcbcbbaddccddddccbddcdbaccdabbbcaaddbdaaadaadccbcccdcadabdbcbdabbacadaaadadbddbcdadbcacbdbdacbbbccdacccdabbcdccddcddacdaadbbdcacaabdddccddbabbdccbcabdccdcaaddcdbbcbcdaaadabaccccbacdcddbbbcabbdbbbdcccdddddcbadadcccabcaccdbaddbacddcdbdacadcddabacbccbbdcdcbddabacaddbccabbadcbcdccacbcabbbbcbacadbdcbaccdcabdacdbaccbddcdbacbbcdbabbcddacbdcaccddcbbccadbcdcddbbbccdbdaccadbdbdddcdbcdadcbccadbcacbccdaacdcbddcdbbcabcadbcbabdabbbcadbdccdaaddaabaabaccbdcccbaccdaadaadacccadabcaccdcbdacbdbbddaccabdabaacdbbaadcaadbcaaacaddcccacbdadccbbbcabbbdababdaaaabddacaadbacdabbdacbacaadaccaaadccadbbdccbcbabadcbbcacccbaadcccbbcddbbabacdababaccbdacdddbaacbddbadcbbbaadadbababbcdbddbddcdaaccdaaaacacbbcbbaaddbccdcdbacbbdaadacaddbaadcbbcddcbaacdddcadacbbaaaaaababcddcbaaddcbaacbdcdcbbbcddccdadcbbaccddbbccaacbbdbdacbadaaabccbdcaabdbaabacadcabdddbcdaddbabbccadabcbbbcdadcabadcbaabbcbcbadbdabccbaccadbadacdbaaadaabbdcacbadcbaaddcbcabacbdabaaabbadaccbbdadccccaabcbcccaaddadacbcccabcccabcdccddcdabccdbcdcacddadccbcacbccacabcdadcdadcdaaacaaccddbadddbdbbcbabbddadaaaacbddccccabdcbacadbccccaadcdadccbcacdadbadbadcddcabdbbaaadbbddaccdbccbdcacabacccadbbbcabbaccabacccacbbaadbadbcccadcbabcdabbcacadcdbadbccdbcdacaabacdaadbbddadcadddaabaccdacaddadcdbbbcdacdaabbaaadaadcabcbdacaacbbdadbcadddcddbbbbdcbccdbbcbdbdabbbcabdacdddccddcdccdccdcdcddcbdcbbdbccbbabdddcabdcbaabbabdbadcdaadadcdcbbbdbabaccabbbddacbbdbdadbdbbaaaccaadadbacccaababaadddadcccdbdccdbddacddbdcbaabadcbabcacdbddadabddbbccbbbdaddbdabcbbbcadabdbadddabbcddccacbabccdaddcbddcababbbdddddacbabcdaacbcbccacaacbcdbcccdbccddbbccaddcbdacddaaaabccdadccdcbacadcadbabbddabbdbdbbaabddbcbadccaddadabdcddadacbbddbdbaabccbadccaccabacdddcabddbaccbbdbddacbddaddabcdcababcddadaacadccbaabdcddadacddbcddbadcbbdcdddcadcccbccaaddbddbcbcbcccbbccdabcbabdcdaabddaadddaaadcbbcbcbbdcbbdbaacdbaaddbcadbccadabdbdbdbabbcbdadcaacaaabaddddaaccbbacdaccbcccabbdbcaaacccaaadbbdddcbcdcaaabbabbcdbcaababbcbdadaacadcbaccbdadbdacaaccdbabdbdbddbdcddaaabccbcbaaaadccbccdbdacabaabddbabadbbbbaccdcdbddacdcbadbbdcbdabdbbaadbdaabcdcbdccbccaabccbaacbacbaacdcadbabbbadaadabbbcaddbdccccabadbcbccdadddababdbdacccabcacabbcacbbccdccaabdaaaabbdbcdbaabcdddbacdbbacbddcbadacaccccbbdbbbacaccacbdcbdbbddcdcbabacbdccbdabdabacaccccadccdcccdbabcbcdcbcbaababbbbbcddcbcbbadcaaadddcdbdbdccddacccacddbdbcdbbdcccdababaacbcddcbaaddbcbdcdabdbacdacaddcabadddbaaacbddbbbbaaddcaabbcbdcdcdbbdbcaaadccdcddaaaabbcdacbaaabdabaacdcaadddcddbcaabdadddacccdabddbbdcaacaddaddbababcbcbbddbaccbcaaddbabaddcbbdcddbdcdabadddccaaabaccbdbcdaacccacbbbdbcacaabaddabddadddbdacbbbbcbdbdccbbcabbaaababbcdddbdaaddaccbcdaadccdbccbcadadbddcbbbaabbbcccbaaadabbbbbcabcddcabdccadbdddcbabdcbcbddacddccacddbacdbcbaaaacdaddcccbcdcdbbadbbadbcbdadcdaddbbcaaaddbdcdcdbdcbdaacdcbbacaabdccbccacccadbcdadbdbadbddcbcaaacbbddaaccaddcdcbbaccbaadcadddddcbbbbdcdbabddadacbcccdcdcdddcbcdccbbdbaadcbabcdddadaddccdbdbbdcaabddcacaccccbadbcbcdacbddccadbaabcaabcdacdcaacdabbdcacacdbbcacadbdbaaadcabdcbdabbadddcababccbdaabdcbaabbcdccddbaacaaaaaadcccadcbcccbabccccbcaccbabbbdbdaabbcdbcaacdcccdbbcccadbdacacaddcadcbdadddacdcbbdadcccdadacbadbababbadbbabccacccaccbaadcdadbcccddcabaacdbcdbabaacdcddccccadbabbccbdadbadcacdaaacacdbcbaccbbbadaaabcacddaddaaacccdaccbabbcabcabcdacbdbbbdabbabacdcaddabddbbacabcddbabdbadcacacdcabaddabadddbbbccbdbcbcaadacccdacbddddadaccdbdacadbbdaaaadcaacadddcaddaccbdbcdccccacaadccdacbcaaaccbaddbabdaaddcbcbcccccdacbbbabbddadadcbabddddbdaadacbaabbbdcabaadccadbdbdcbcadbacdbddbccacbaaccccdbdaabbccabddcccdcdadabcdbbabcadcddbcbbbbdacadcabcdcaabbbcdbcabaaadbdccccbaaaccacdbccbacdaaabdcbdadaddcdbcbbdcdaadaccdcddcaabdabdacbbdaddbbdcabdcdcbadcdadadadadcaadcdcadcadacbccccbccabcabbdbcabcaacccdaaabcddbbbdbcccbdabacdcdbacbadadaaccdcbcddbadacaaaabcdcddaddddddcbdcdddbdbcacdccbdcacddabaccbcbcbccddcccaddaadaaddbacaacccababbbadbaadcabcaacbbaaabcaccbbdddaaddbbadccccbacdaadaaadaccdcabcbaabdbcccbacaacbcadddcdbacdbbabbbabcbcbdacbabaadabaadadcbccdaacdcabdddddaaacacccbbdcdadacbbbaacccbaadbbdadaccbdbadccbcabdbacabbcddddcdacbbabbdaaacabcccdbacaddbdcdaabadaddcbdabbadbcbcdbbdababccacbadacdbcbddaacbabdddccdbbcbcacbbbbbdaabacdacdbcacbdcacbaadabadbbbbddaddadabcbcbaaccbbbbcbcccbacabbbdbaccdaadcadcdbaccaddaaabbadcdddcabdaabccccabdbddbbdccdacbbbadaddbbcccbcccdddbacabcbdbaabbbacbcddabdacccacdcbbdabcdacadcacaacdbdcabdbbddbcbddaddaddadddabaabcbcdacdcaadccbbddcccacabbbdccdabbcdcbbcacacbacacbddbcdbaadddabaddbdbbcdccdaaacdbcccabcdaabcbdcacdadcbdbbbadadabccaadabbcacdabdddacaabddababadcccbaaabcdbaadaadbccabdcddacbcaccdccbcdbdcdaccbaccbcbbabdcabacdbcbbcdccdaacaacccdcbcadadbaaadadccbbbacaadcdddacbbbbbcabbcbdcdbcdbddbcdabcbbadadacccdbcdadbbcbcabacdbdbbbcbabbccaabbdbccdbbdbbcbddccccbbccabcdcbbbbbcdcbbbdadbcaccabdcbbdacbbbbdbccaddcbdaabadacabbcbcbadcaccadcabcadccddbdcacdbdabdadabcabdbbacdcdbabaaaaabbabddddacaacbabbacabbabcbadbdbbbbdbadccbcadcddacaabbdaacacdcaaccbbcabcacbddcdcbcbaccdcdbcbbbbbbbcbdddcacdaddbddacabbbdabccdadacbbbcabdbccdcbaacdcddacbcbccbddaddcadcccddcaaddcdccccabaaacdbcbabdccdabdabcadaddddbbccbaaaacbcdabbddcabcbdbcdaccaaddbaadcabdbbcbbcdbbbcbabcdbacddbabcbababbaaaadcabddcbabbcddcdbddbbbadbdbacbcdbdbbcccdabbdcbbacdbbacaccadcbdbbdadcddccdcabbacabdbbcbadabbbbddabaaccbddcdcaadcdcbdcbbaadccccacbbbdcbdcdbaabdaacabbcccddbdcadcbddbacbbabdbdbaaaacbdadaabbbdbdaabbadcbcbdcacadaddadccdcccdbdbaabbdbcdccdbaacacbdacdabccaacdabcddaaabbcdabcbbaddbcdcdacaababaacaabbbbdddcaccbdcbddadaababacbcacbcaddcdcdabcaacbcaaabbcabaaccbadcdaabbdaccddbcbdaccbdcadadddbbbcacbbbcdbadabdcccdadadaacaabbacbddddaccbbcaddbdbababababddddbbacbdbbdabbbddacdabcdcabbdcacbbdabdabccaabcaaccbdbbdbbdbddbcccbbbcacddbcbaaadacbdccacbaddbccdbcbcbcbaacbccbccbddbadcbbdacdcacbaacddcadbbdabdbadaaabbccdabcccdabdbbdbdcccddacccccdacabcbbabbdaadbbbbdaccbaccbcbaaaccdcdaabccddbacddcaddbdadbcdcaacabacadddcadaccaacabcaaabdbbcddbbccacacbaaaadadddbabbdcbcdcccdcdcccbcbbbcadcddaadacaddbcdddbdccbbaccbdcadbbadbcccdccbadccabcdccabbabcdaadbabdaacbbadcadcbacddccabbdccdadcacbcabadcbadbbcbccdccbbbabccbccbabcddaabaabbddacacdabaaacbabbdaaabbddadaabcdbcbbacbdcdaaabdcddccaddddabdaddccdcacadccbdaabbbdccadacddbbcaadbbdbdcaadcddcdaddbcdcbdccccbcacdcccbabddbbabdbadbcccdaccddaabbaddbdaccdcadddbdbbacdabacbcbaadbaddabacdacaccadadccaccddacbbaabccdccdaabccaccbdccddcbbaadbdacdacacdbcacbcdbbabbadbbdccdbbdcbbdcaaddbdccdbdcbbddbbcbdcbaaddacccccababcccbadccddbbbbdbccdbbaccbddddbccdaacabcbcbbbadbdcaccdcdcaadbccdddbadaccaadadabdacdbddbcaabbcbcdbabdcadbdcacacdbddcdcdabdcbcaaadcaadbdbabccdcaacdcacacaddddacbacccabaabbdbcacbbdbbcadacbbaabaccbcacbcdaaccdadbadbbabdddaabaacbdcbdcbdcacdccdcbacdaabcabaadbcccddddbdadaabcdababacbdddcbbbbdcbddcabacccbdccbcccaaddbcbbcbccbcadbcbddbdcbcddbdaaddacccdaacaadaaddccbabcdacadbabbbbcbcabbacbdadbcccccadccbcbbbcaaddcabcabcabdabadbbbdaccbadacabbcdcaadabacbadabbadbdaddcacbddadbdbaccaaacbaccacaabdadaacadaaaadcdcdcbcbacccabbaddcdadabcdadcdbbbddabccdcaaaabadbdadbacddddacaabdbaabacabcdbcbbabadadbbaacbdbccbcccdccacacdcdcbdadcdccbcadddddcdbadbcbaabacdddcbdcdbbcaddaaaaadabacabcbaddbcccbabccbbdbbdacacbddbccabcbbdbcdddacabdcaaadacdbdcbdaadcbacdccacbcdbaccabccddabdbbbabcaaacbbccabbddbaaaaaaabbddccddaddcdabccabdbadbdccadcadddcbddadcddbcddcdbaccabbdbdaabccbdcbadbcabdcdababcdaacacacdacbcadccaacbbccdcbdababdcccacbcdcbdbabccaaddbdbadddacdabcacbcbaddbcadbccdabdcdadaadbcdbcdbaadabbacdccbdcdcddbbcacdbdccdbcacaccaddadabddaacdbadcbbdbbbcbbbbbcdadadcbabadbbbcbccabdddcbcaadbbccbbbbaccacdbbdbcaddaadacabbabcabadabacbabbdaddcdbdcaddccbadcdacbccbacdbcbcbddbcbbcbbacacadabbdadbccccaaabdacabbbbddcaabcbcbccaddacbddaadbdcdabdcbccdbbdcaaacdddcadacbdbbacbbadddbaabacbaddacbcaddcdadbbbbadcabbcadddbbcaaadcaddbabbcdcdbbadaacdcccdacabacccbcacbcacbbabcccadaddbcdbdbacccdadbdcddcaaaadcccbcddadcbbccababcbdbdaacbbdbcdbdbdacbdcddaadbadbddccbaacdbddcacdcbdadacdbdbbcdcdcccdbddccdadcddadddbbdadbcadaadadddaaabadcddaaddccbbdabaaabdcbcdaabdaaddddddaaabdcbdcbcabaaddbddaaddbcccdbbbbdbbacacccadbcbbacbbadbcbddacdaadccccddacadcddcbadbdadbdcccbbadcacbacccccbbcadadaacacddaadbacdddcabdbbcbdaabdaacdbbcdcdbcbbabbddcdaadcdadaddadbbdabbcbdacdcbdddcdbddbdbbddbaaababaacacacbbcadcabbaacdcdcbcbbbdbabddadcacccccbccaaacddbdaaaccbcbbdbddcbcdccbddbbacabbbccaabdaadcdcbdbdaababcbbcdcccbcbbadccddaacdbcddcbcbcacacdcabbcbdadddadbdaaaddbdbdddbbadacdbaaabaaabdadbacaccadbbaaddadbcaccbcbaacdbaaacdadbcdabdabcdddddbccbaccdcbacdbdbccbbbaabcdadddaadbacacadadadbdddaddababadcdbacbaadbbbcbadccbcacdabcbbadacbcdaadddbbbacbbcaaacdacbbbaaccbbadccbaaadbdbbddabaabdbcaaaababcbddaddcdabcbddadbcdadcbbaccdbcccdaabaccddadbbaabacbcabdcbccbbbcbabadaabbcdcdabdaaadcdbdadccbddacbbcdbabdccdadbadcaaacabaadcccabbadadaacddadddaacbacaccdadcdcddabdcdccdabddbbcbadcacdcadcaabccbdddbbaaadbcaaaaacccbccbcddcadaaccccababbbcbcccabdcbbbdaacaaccbcdcaadddaddddcdabaccddbbdbdadbaaaaccbdccdbbcbbaadcdadbcbaabbddbaabbbadcccaacbcbabdbbddccbaabbddcacbabadaadbcdabaccbdcbbdabcadcdbbadbcabcdbaacbcbdbdabcaabdacadbbbabcbcabacbdabdbacaadbbbdcbcdaddaccbacaddbbdcbcadddcbbbcddddaaadbdacacccadcadadbcadcdcccaacbbaaacbbccbabdddadcccbadbbaaabcdcdddddadaaddabacdcaadddbcbaadbdadcababccddcdcdadbdbdbcacaadbdbcdbccabacbdbbaddccdacddcdaccbacdcaabdcdccbdcbbadabbbaaaccabbacccdabdccccadbaadcbcddddbdbdcdbdcacadadabaddccdcbdcbbbbbcbdcaabdcdaadcadddbddcacddcdaccacabbcddbaaacddcbdbdadbbbcdacabaccddbacdbbcbdcadabcbbccbddadaabcabaaaddddcabcbdaaacabbacdabcddddbaadaacbacabdabdbbabccdbbbabdacdbbbddabbddabdbdcbabdcdbbcddbccacacaaaddcacdddddabbdabaabcaacadcbacdaddcbabcddbbbbabbccaccbdabdbbabddabbcaadddcaacdbadcdcdabccccbdddcdddacdddccbbbaccbddadbaabacdccbbbabdbadbccdbabdaacbdbabbdaccabbaddacddcdbdcdabcccacccdcccaccdaaacbaaddccdbddbbadabcabbaddacdcadacbcbcbcbddcbbcbaacbaacdcdddababaaddcbdbaadddadccabdcbacaaaccbbbdbcacaacadbbcaddbaadccaddadcccdcccbdadbdcddddaadddcabcdbcbcacaacdccaaacbabacdddccdddbcdcdadbbadbaddcaccddddaaaccbbbabdbbbddaddaadcaacdabddabcccccaccabacccddcbdaddbbcaabbdbbadbccdddcbaaccaaddcbbcaddaddcdcdaccbdbabbddbdddadaaccbdbbddcaccbbbddabaaccdcadbadaadccdacabdadcdaccbbacacbccbcbbcbdbccddadcdbbbcacaccaccbdabbcdaaaabcdabbabbddcbcddccbaccbcbcdcbaccababdcabdcbdaabccbacdacabaaccbabacacaaccbdbcdcbabbccadbabbcacbcbdbbddddddbccbdcabcabdabbdaadaabbdddddbddcaabaacdbaabacccdcaaaddcddcdbcadacbbdddcbadddabbcaabddcccdcdddddbccdaacdccabdabdabbcdcddcbbbabcaddbcaadaababbbcbbdacddddddccccccbaabbaacbdccbbdbbdadacacbbbdbdbadddcaaddbcaabacacaadbaabbbbaaddcabdacccaccdcbbabddddccadacdddddcbbacbdcdccacaccdacaaabbadddcbccacccdddddddadaadbdcacbbdabdbbaddbcbacacacadacacadbcbcaddadcbcacddabcdbcadaccdaaaaccdacdbcddddddbcdbbbcbbacababbcddbdaddacdacbbbadadacdbabbccbddbbcbbbdaadddbdcdbcbadabaddccdcaccbbbdcbbddbdabbbdaadbcddcbcacddabdbdccdbccaccdcdcacaadadadadacccdbdcbcaabddccddcbdbaaddbddcdcacdbbbbcbadbabcbaccdccbabcacdadcacbdbaccacabbbdbdddcdbddaccdbbbbbcdaadabcdabcccccaddabababddbcacbcdbcdadbcbbdabbdcddccbdcbdacccdacbacddbcbddddddbabccdadbabaaadddddccdbcdddbbbabddabdcabaaaaacbbadcddacccbcddadddbdddbbcacdbaddacaddcdaddbaacdbdccdcbdbddccacbdbcdbccadaabbcadbbdbdbbbdccdbcdcacadadddcbdcdabccddbdabcbacbbbaaccdbcbbcdcddddabdcbcaccacddbcadcbaaddabcdcdccacabbddcddcaabaadaacbdcbcbaddcdbbdabbbddbaaccccdaaccbbcadbbbcaaddadbdcacaadaababdabdcaddcadabbcadabcddacadcdabbabcdcddcacabbcaadbbabccdaabcdddaccccaddddbccccbcccdcacbbabcdcdcdbcdacbaaabdddcdcbbcabbdaabadcbdbaaabbaabcdcdaddcdbaabbddbcdcdadbcddddddcabcabbacbbcbbacbbbdccbacacacadddcbacbdcbacabdbaacddcddbdadaaadcaaddbcdddabbaababbbacabbbdccdcbaacbaddbcabbdbddadddccdcbacbccbaddbdddcbcddcaacbdaccdbcaddababcbcbaccbbacdcddcadcabacaddbbaaddbbaacbbbaabaacbaccabcbaaaaadadbabaacacadabcdbddaabcdbbbdbbcccddbaadcccadbabbcdcbaaaaadcbccdbadcaabdcddbdddccbddadbbdabdbabbddcddbccdccadbbddacdadaadaaaddddbbbccbdababacdbadabdaabdabaabbdbcacbbccccdacdaaddbccdbaaacdbddbcdccdbcbbcbadaaabbadaabdbdaddcbbdcccadddbaccbaaabacabddacacacbddcbccbcbacddaaadcdabcabbddadbccaaddadccddbbbccacacbccbcbdbcbbaaddcabaabcbadcbddadbcccdaacbaacbabcdcdcadacbccbddabccabdccaaaaaabcdadcbacddcbcbbcaadcdbcdcbabddabcbbcddddbcadcbcacdddddacbcddbdbaddbdcbadbadcdcaabbcaaddcabcadabbdcabcbcaddcadcaaabbccdddddabacbddaacdbcaaaabddabcaaaadcdbdabccbddcbabcabcbbbccabbcaddabddbddccacadbbdbbdacccdabaadbaaacbbccccadcddccbcbaccbacccbabaacbbbbbcbcaacbcbbdbdabbccdabbcbdccaccccbdacddbcaacbbdbdddabaacbccacacdacacbdaabcacadadbbdababccbaddbdcccaadcdcababbcbaaaadacabcbbdbdbaccdbbdcbcbabbcabdbdadabbcbbaaabbdcbcdaabdccdcacccddcddaaaccdddcddbdbaacdabcabcddcabcdacbaaccaaabbbdaacbbcaccaabcbbababbcccbbdbabbbbcdcabddbccabbcaddcacbdbacbbacbabadacabcabaaacadadcdabddaddcbcdbddbcccacbdbdddbdcbbbcbabaabacdcaaccbccccdacbadccaaaaaacadddacdacbaccaadddbcdabdbdbabadcbddccccaccaabaaabcabdcdbcdbcdadabdbadbcbccbbcdbabacaaabdcabdcbcbbaadcabcaddabccdbbdcdcadbbbaccacaccadbabdddabccaccbdbcabbaddbdbcbcaaabccaacccccbbbcabbbcdbcadaacacaadaccbdccabcddbaccbdbabdcadcdbabbbccaaaabbbdddbacacadddcbbccdadcadddaacdacddccdbcabbcaabbbbddccddcdcabaadccadddabccbdcbdbcccbcdbbdbbabacbacbdabbaaabdadababcddbcbbadbbdbddddbcbabbdaddabacddcdbbdbcdddcbbaddccdabbdbadcdcadabddccabbaaddbaddcdcbdaadaaabaaaccbcbcdbacbacacbaacccdcccacdbbbbaabbcbccddbdabcbcbdddddbaacbbbaaccadaccdacccdaddccccaabdcbcabddcbbbddabdaddccccaabaaddabaaaddbbdbbcdccaabdbbddcabacbdbdbcabddabccbbadacbcbbabdababaaadaadadaadaadadaddbabccbcdcbbadbbabdacadbddcddddadcbbddbdddbdabdddccddabdbadcbcdbaadadcdababdbaaacacbbdcdccccdbacbdccacbbcccdabdabdbddcdbcbcadbbdbbbccdcbaaccdbabccbccacbcddbaccdbbacbaadabacbbacabaccbcbcbcbdccabaddcaadaadcccddbaadcbdaddbcdabbaabdbdbbddcbacddabadbbcaabdcddbdabacaabaccaccbabcabdaadbbcacacadabdbdcdcdadbbdadbdaacacaabddbdabcbadbaccbacaddaddacdbbbadcbdabbbcccccdbdbccdbbcadccbadccbcaabacbacaabccaadbdaacacaacadccdcbadbdaaadabbcbacdbaabbcbddbcabdadddbbbaababbbbdccbdbdbabdadddcaaabdbdcbdbacbcabbbbadbbaddbaaacdbddabddbacbcbddbbbbbbaadacccdbaaccaaacccbbabacbbdcaddaccbbadcdcdcbcaabaccdbbcccaabddbdabacccaccaabbcbdadbacbadaaabdddcaadcabdacdcadddddddbccacbdddaacacdbaaaacbbbbdbbbacabbcbaacbacbbbbbcbdcdbbdbbbdcddbdcbdcdbadbcbabbaccabbdbbdcddddbaddaadabdcdcccbdababdcccdbacaccacabdacaaabbbacbbbdabacbaddddbaabbcccbcbdccccdbbbdbddbdcccadcacacacdddbdbdcccabdbbdcccaadcdaadcadcadcddaddbddbcaabdcccdbbdbabacbadcdbaaaccabcddcbddcdddcdaadbddbcccbddcacadbcbabbbabdbacdacdbdbbbdbdaccdcbddcabdcaddabbcdcacdbacbccdbaddcdbacbcddaacbaccbbbdbcacabdcbbcabadaddcdbcbcdbdbcaabbccdbabcbbccdbbaadccbbdddbcbbdacbcdccbbcbadacdcccdacbdcccadcdaacdbaabbcbaddcdcacbbadaddcacaacdabacaacaaacabcdddbbaaaaadbcdcbabacacbbcccdbcbcacbacdcaaccadcabadadaccacaabadbdbbbabbcadbcadbaddbddcdbddbcbdbdabdbadacddcdacabacdacacdadabcbbdaddaabccdcacbdaadcbccbacbdccdbcccabccadadbdaaaadbdbdbcbdacbdbaadcabaabaccdaddcacacbcbcbcccdabccabdccadaabcdbdbcbaabacdadccddaccadcbbbccbcbbbbbdddbccccabbaaddbbbbacdccdcdaabcbbcbdaadbdbbbdbcbcacccccddababcabbabcdadccdaddaacdcadaddadcbacdacacdbbacdbabbbdadcddcadbbbbbcdbddcdbbaaadccacccbbccdadbdabbddacdabccbbbbbbcbccccadccbaccadadcdaadaabbacdabcbbacbdcaababadcabbbbababacbbcbdbbbaddbaddcdcbbdcbdacacdcabbaabdbcbbabcbacabcaccdccaadbcdbddcddaabdadcbdccbdbcccdcbaadcdaaaddcbbadbdcdabbbcabbacdacbdbbdabbbbacbbbadcaaabbcbcdbdbcccdbadcaacdadacbadadababccaccdcaaddacdabbbdabbcabadddabbacdbbddcabbbdaaadacbddbbdbbbcddcabaddaaaacccdcadcbdcaaabcccaaabadcaaccbbbbaabbcadbcabdbbdacccbbcbaccbcbbbbdacaddadbcbddaaabbbdacabcbcadadbcdcbbccabccdaaaacaacdbcdabbbdaaabddaaddbbddcadcbbcbacaadddddccacaacdadcbdadabbddabaaddcbddbccdcaccaadbcabbccacdadabdbcabdbddbaccaadbcacbaacbadabcadbdccccdaababbdabacacacabdababbaacdddccbcadbadbddbdccddbdacdccdbdbacdccbbdbaacddadcacccbabbddbddbcadabacadabdbbbadadaddaabacdcbaadccaaaddbcdbdaddddccdcbcabcdabddadcbbabbcabdabdbdcdaddbbdadbbaacaaddccccabaccabbbacdcbdbcadcdcaaddcbdaadababdcbbcacacccdccbcdbdadbcaadacdacbaddcadacbddaccabdabbdaacdacadaccdbcabcbcdacbcdcdccabcbcbbdcbadccbcccadcbabdccadacbcaabaacccbdaacbbccdcaddaacccabdcadacdbccdbaaaabddcacbadabcbcdaababdbddbabbaddcbdcbcdcbddbcaacbdcabaacbccbadcbdbddbbbcdcdbddbaadabdaacdabcacaaccabcbdabdabdcabcbbaabccbcadddaddbbacccdbcddabdbcbdbccaaccabcbacaabbdcdbabbcdbcddaccaacbccadcbbaacaccdcadcbdcbbaddcddddacaccbddabbcbabcaccbcbacaccddcdacadbacdbdcdbdddbccdabbcccbbcbaaaccbbacaaddadbccdbcaabcbdbdcadabcbcbcaacccdddbdaadccbbdcbccadadbdbaaccbacaaaacdabbaaacccddddddbbbbdcbadccdacadbbcaaddcacddaadbdadbbbcadbaaabbdcdbbaaaaadcabaaabdaddbbbadcccccdcbcccbdddccaabdcccaacdbcbaadcbdcccabacbddcacbdacccacbdccdaacabdabaadacdbcadbddbcaddcddccbaccbacdbbddccaddcdbaddcabacdadaddabdddbbcccdaadcccacbbbbbdbaaadabdaccdaabccacdcdbbadcbaccbddcdacddaccddbaacccddbcaabcdbdbbaabcbbacabdbdcccabaabcacbccdaacaacbdadcbdcaddabcaadddbacbdbddccadadaccccdadddcbcbbdddaacdcccddcaaabdbaabdaccdcabaaababababdbdbaccbdaadcabaadddccaacacadcbccbcadbbdcbadabdbcccaabcdacbccbabdbabacaaadddacbccbcbbaacdcaadccbbaadbcbdbdcacccbbdbdbbdcadbabbaccacabbbabcacacadcbaacbbdcbdcaccbbbacbbbccababaadbbcbbcbaadcbcaadbdccdaadbadbaddadabcaaccaddacbadbccddbcbaaccaadacabacbcdcbcbadbdcaacaaaabacabacbdbbaacadbccababadbcbbccddccbdcabbaabddcdadbcdccbcbccdabbbbbaacbbdbababdbdcabcaabccbabbdddcbdbcabddacdabcdccdbbaaaddcbaadcacdabddbdddaccbabbdaddcaadcbacbbaadbbcacbcbbbacaacccabddbdadcdcabccacccbcaacdcdcbdacaddbcdababdaddaabdadacadabdacddaadcacdbbbbaacbcacdbacaabcdaabdbdcbdccdcbdacbabbabdaccdccddcacdbdabcccbddacdbaccbcdbdcbaabbadbcacdbcddcbaaacbdbcdaddbbcbbbddaabaacaacadcaabcabdbaddacdadddababadbdadbddbacabbdcadccaadcadccdaaabcbccccccbdadbccbbdddabcbcbcbddddbcbdbaaabccbcdddacdcacbcdddcbddbadadabcadcdaaaccbacdbaaabddcddabadaadbaadcddabbbdcacbdadbbdaccccdcbdabbccbadbadabccdcbaadbaaaaabbcbbcbaaadaccbdacbcaacbbcaaaacbcbccbdbaadbbcbbaabbcddbadacbcdddcccbbddbccadabdccdadcacaacccbddccaaaadcabbbdacacbabbabacadaadacdabacbdaacadcabadcdccadacdbbbdcdbcaaaaddddaabccdbddbacbaacccbdccaaaacccbabaadabadcbdbaaccbcdbacddcddaadadcabadddbdbdcbacbcdcbcddbadcbcdbcbacadaacddddaabdcdbabdccdcacbdbbdaacddcabcadaadbdacabdaadcbbbabcdbaaaacddcdcbadcbcddaadccbdbcadbdabbbdabbacabcabdccadabbcbbaaccaabcdcacccdccacddcadaabdcdabbdacdcadbaadccdbdcccbdaaabdaddaadacabdcddabdbacbbabacbcddadbddbacbdccbbcbaddbcbadbdcddabbdbadbbdcabcddacbbbcbadadaddddcaacdcdbccdcbcdcdbdcdbcbcabcbcdaccddabddbacaccaccaadcdadbdcbdbcadbdbcbdacdddcaaccacadadadbabdccbadaaccdbcdcdbaddcabbccdcddadccaaabdccaacaddaabaddcadadcdacbbacbcbdaacbaadbcbddcddcbdcbddbcbadbacabaaaaddbdbdcaadcaaabcbccbcbbdadbcbbbdcacbbdbbbbcddadabbbdbbbaccadddbcaacbacdbdbacaadcbacbbbadaaaccbaacabadabcbccdaaccdddacaabdddbacbcbaabccabacbadbaccadbbbdcdadbabccbcbbaccdcbbbddcdbcbaddbdaaadcbacbacdaaddababbbdcbcddbabbccccbcdcaabdbdadaabaddaaabaabbaabcadabbccbcdbaabaacbcbcdcabcbcdcacbacddabdaaccdcbddccccabdbbdbaaabcaadaabbcdbdaabbdbdaaabbacdddcddacaabacbcdadcbabdabcaabbabcccabddbccadbbccdcabcbabacdadaadabbbbbacdbacddaacddbdcbcbdbbdccbccccccccdbbbabbbdacbaababadabdadaabddddacaadbdddbadcccddbabdcdcdddaadccbbddaaccdbcaddaabacccbbccdbbcbcbbddabbcacccaadbcdccbacdbbddcadbbcccaaabbcdacbbbbcdcbdcbacadaddcdccacaaababadaacabbbbacbbbcddbbbacdbdcdbabacbcadbcdddbaccddcadddabbcbdcdbdddbaacbcbdbaacdcbdbdccbdabdccbacccdbbadacdcddaaaacbaadcdccbdcdaddcbbdcdbdacbccbbabdcbdbabbabbcadcdcbaabcbdbddbdbacadaccddbcdddbbccadddbbddbcaadbbccbaadabbcadcabdccbadcbcbcccacadbdddabaabbccbcaabddbcccdabddcaadcbdcdcddcdbabbcdacdabbcbbaaadbddddbdbccadbcdacadbbddcadbbbdacddacddacacdaadcdbbcdbaaddbbdcbcdcbdccccccbacbdbabbadcbabdbadbdbddbdcccbcbbdccacbdcddabdabacbadabbdcadbbddcdadcbdcbcbadddbbcacdaadabcbbabddaaabddccabdaddbcbabaddcadcbadabcccbcdbdbacacadbbaadddbbaadbbaccbdbaababbcadddaabdbbcbbdacdbdccbbbcdbcccacdbcbcdcdaddacdcaabadccccdcbdabdaabcbcbdbcbdadadacbdbcbdcabaddbcbdcdabdaddcdbdaddddcbbdddccdbcdbaadbcddbdbdbdddadbcbbaddaaabaddcbcabdabbcdabbbcbcbabbddbdcabaddabbbacbddbbaababdacdcddbcaacbcabdabcaaaaaabddccabcaacaadcabbcbabbccacaabddbbdbdabbdbbaabddaadcaacbbcabdcacaaccabacbddacccbbabbddabaacbababbbbdbdbbcaaddbdacaabddcbbbcdbdbbabdadbabdbccdbacacdcdcaabaaaabcbbccdbcddbacdbdcdbbdcbcccdbbcccdabcaaccdddbcadbbdcabcaabdacaaaabddbdabdcbdccadcadbcbdbbbacbbbdbaddccddaadcdbcbacadabcddaacbccbbbacdcccabdbcccdbdcdabaabdcaccbabadccddacdccdaaaadbaddcbbcbdbbdbdabdbabbdbdbadbdacdcbcbaaabadaadccddbbcaacadbadcadbdadcddbbcaaddcbabacbddacbbbddabccbababaaadbdaacbbddaacbcbabadcccdddccdbaabcbdadbcaccdbbdadcbdcddcddcacdcadbadbcbadccdcaadbadcbdcbcadaabadccbadadbdcbbbcbabaadccadccddbcbccbbcdaacdadcaddbcaacbaaaabdcabbcaabaaddaaaddbcccbccbaadbcdacbddddcabaadddcacccbdadbdcdaaabbddbdbdacbaddadcaaddcdbdbbcccadabddbcadccadccacccadaadbacbbbcdccaaabcdcccdddbbacadbaaddbdcaacbadcdddcbdadcdabbdddbdaddbcccbaccbccdcbcbcdbcbcaddbdddacbacadbdbdddcbcaddadbaabcbbcacbcadacbcbabdcdabcbcacabacccdcddabdbdaddccddbacdabadbdacadbdddababbadbabbabbbdddadaabbbabadaddccaabccbaaadbdbcaaabbcbcdbcaabadbaaaacdabcdaccbbcddabcbcbcbccbcacbdbcbdbbcaadcaabcdddcaaacacaacccbcabdccbcabadadcaddcccabcccacbadadcbacacadacdbacdcdbbdbabdbbcdccddddbddaacdaaccdadcaccbcacadacbcdbbccdabbacdcdbcaacbabbddcbaabdaadcbadbbbcbcbcdbabcdaddccbacabdbdababbcddadcdcbccabccbaabcdbccdaadcdadcbdacccaadcdacddcdbacbcbaacdacababaddbbcdddcbbdcbbadbbdbdcccadacdcacacbbddabddccadabadacccabaaccacbcadcdadccdabbbdcdadcbbcadababdddccbdbcacaddddccccdaaababdabacbaacbacddcaccbccaccdccdabcdcccabdbccbbbabbcacdcdbcacbbcccadbaacadbbbbdacbdddadcddababdccdbdbbddcbbcaacbacaccbabcbbbddbbadaacbdabcbdbaaaacdbcbbacbbccbdbcbbdacdabcdbcabacadccdadabccdaaaadbaaaaabdaadabbaddabddbadccccbaccbadacbdadcaabacadbddacbbabdcbcdadacaadaabcccbdadbabbddcdcbbadccdadbcaaaadbcbccbcaaccccdcdcdaadddcdbcdccaddccbbabdaccaadacabacbddaddcadcacbcbbccdabbaacdbbcbbacddadacaccbcccccbcbbcabbbdbadbbabbccbdbbdcaabcdababbbbdccdabdabbddbaabbdbdccbcacacdacdccdaaaddabbabcbbcadadbcacaadcaacabbdacdcabcdbadccdcaaacbbadcbaabadcdccbacbbbabcbddbcaaaaccbbddacbbbacbbdddbacbcdaddcbacdccadbddabcaadbcbdddbdbaddadcadddaaabbbdcdcaddcddcbbcabdcaddbcbdacbcbccbdcdbbccdbadbddbdccbdbaddaddbdddaddccbbcdddaadcaaaccddcacbbdbaaaccadcccccbaccccdbccdcaababadcbcabcddababadcdddabdaddbccddbabcbacabccadccacccdbdddbbdcabdbaccbddbbdabbbdcbbabddaddddbddddcccdadddcaaccddbccaabdddbdcaabcdddacaabdadbcbbbdcccdcbcbacaadcbcbcaaaaabadbcadcbbbaddaddbbbdcdadbadbbbbcdadbcddaccbbaadadcbdbcacdaacaaabacacdaaccbccbcbcbcbcbbbacbdbcaaacdabaaabcbaaccbacdcbbcdaadbdaaccdadbdbcbcbabaccdcadcbaaccddcbddbcadccaccbcdabbaaabccdcbcaacaaabbcdbdabcdbdaaaaaddaabccbcddaddbcadbadccdddcddccababccababddaaddbdddabadcbdacdabdbabcdaaaaaabdacdbaabbadcddabddbdabdadddacddbbcaacdcdcdcaabccbdcdacbbacacbdabacdbdddcbbdccbddcbaabbbdbacbdbcccdcccbbadbcddddccabcccabcaacddabdabdcccbadacacacdbdcbbddddaadbcddbcddcbaddbccbdcdbcbbbcacbbdcbacaaabcdabcdadddddaabdabddbbddaabcdccacacbabdbccbcccadddbabdddbcbadccbccbcdcddbccdbaccdaaccaccdadabcdabbdaaadadcabaddcbadddddccaddaaaccddcbbcdcadbdccbddcabddccbabaacadcadaacaddadabdadccadaaadcabbddcbbbbccdcbcddcdcbcdcdbdbdcdccacbdadbaaabaaccaabadbdcadabaaddadbcbdccccacdddccddabacdbdddbbbcabdbbbcacabbddbcbcabbaddcbcbbaddcdccbaacbbbbbbbcddccbaabcdbbbbcbdbdbcdcbbadcadbcbaaccadaccaccbcccddbbddddaabdbcccdbbdbacbbcdbbcbadbadbccbadcccbbbdaddccadcaacaaaaaccbdaabbcabbbcddabcdbcdacccdabcaabcbbbdccccddcdaabbaabbddbaaabcdbcbabaadabbbcadcabbadcaabddcabadabacbdadaccbcadcdacdabcdddccaadcaabcadcbdabcdacdbacccdadccaccdadbdacbbadabdabdcdbbdbaabccbaacadabcdbadddcbcbbbadbacddcbdbbcccbbabbdbcbbccabdbcbcadccbbaddcabcddccbcaddccbdcaaabdaccbacbdbacdaabbbabddcccbaddabcbcbacddbdcadcbcabccdaccddbcdbbaddccabbbdcaccbacdabbdbbbdcdbbabdcaadbbbadddaccdccdbaaaabcbcadabddbdaaccaddbdcccbbbdccadddcdadcbbbabccdacdbbcdddbbdcdadcccabaadbcdabbcbcbcabaccaacdbadaddadccaddddbdaaaadababcbbdadbdabdabcdbcabccbdcbadcbdaadcccddaaddcccdabddccaadccaccadcbdcabaddbdbbddabacbcdaccdcccdadbccdbbddddcbcabadadbbacdcdbddadbcddaaabccccdcdbcacddbccbdaadbadbbdbccbdcdcdcabaadcaabcbdbcdcbccaacabbacdcdbddcdadcaacbdadbbadcababbbcaddabaabacdbcaccbaddccdaaddbcdacaacccaadabadadcdccdcdcabbdcaaaabcdabdbabbbdddbbcaadcbcadcbabcdcddcbbcaddbdabcdbaadabbcbcaddcabcccbdaacdacddcccdbaacdabddddadaadbddbbaabaabcadacddcadaddcacacdddbacabbcddbdbdcbddabbcdcacabcdbcccadbacbdcabbdccadbbbdbacdabddcbcdacddbdbabaccabbcaadbddcadbcccdcdcaaaabcccbaccddbbbcbbabadaacccaccadddcbdacccccbddbbaabcabbabddcadbaadabbbdbbabcbdaddacddcbdaadaabcbacccbadcaaaaacbaddacdbbccdaadacdcadabddcbacadbadadbcbbbdbacaadbbdcaadddadbccabcbcbcddabbbcadbcbaacadadabbadacbccbaaaddadbacdccbacbbdcabaacbddcdadabcdddbcdbbdddbabdbbcdaaaacadbccadcbacccccbaadaaccbbadaddadccaaabacacbdbcbadddcaccbbabbbbcccbaddccadbdaacaacaacaaaddabcddabdcbddabdabdcdbabaddaccdacccdbbcacadbdbabcdcccdadcbbbaccccdcbcbbbccaccaabdcaccacbddcdcbcdcdcbacaccababbacaccaccabcdccacacdccdaacababddaaaddaaaccdaabaabacccccdcaacacbccbcdadcdbbabcddaacbdccadacdbbcabdacabcbabcdbaccbcbccbdbcbababcadbcdadddcdcbbcdcadbadaaacbcdcccaccdaccbadddddbaccdcdadabaabbccbdccaadbcbccdcbdcbbdaabdadabbacdddcbdddbbacadcdbadcabcdbbdbcbbbcdbdabbbcddcbdadddbacaabbacbdaadbcbbbbadabdcccaadcdcdddcaaadbacbacddacabdbcdddbdcbaccaacaadcdbdcbadaccddbdabbaabbddddcbdadbccadbabcdcbbcaaabdbcccabcdbcacaacdacbdbaaaaacdacacbbbbcdccbdababcadaacadcbcbdcaaadaaaccdaccadddcdadadabadcbdbbccccdcbbcadabbddbadbbaaaaadabcddacadaabcacdabbbbccbaacbabccddababbcbacbaccddcbccbcaadacaacbcaacbabbbddcbadaabbbabacbadbbccccacabdcacadcbddbcbdacdacadadcaccacbdbbaabddcbacbcaccccdbbbdddcbbcbbaaccdadbdbaddbbcbcaccccaabdcbbacdaddcbbdbaabbabaabcabccadcbddbcdadbacdccadbbaccabaacabbccccbcbcdbcdaadcbbdcbcbdbdabdbabbbcbcaacbcadcdddbaaabbdacbbbcdbadcabcdabdccddaabbcacdbdadbcadcddacddabababadacdbdaddababccbdccbdcaccdbcbbcdccaddaccddcbaacabadbbcabcdcbdbdcadbdacdcaadbbaadaaaacdacadaacaaaddadbacacddcacccabcbbacbcaabdccaabdcdacdcddadcbaababbddadddddcdbcadccadbbbddadbaaadbcdcdbabdccaacccaabcdaaddcabddaaadacabdcdabbdaccdbacdadbbdcdabccabbdaddaacccbbabaadaccbcdbaaadcdddcaadacbcbacaadabacbbccacbcaadcadcadcdcbcaddbadaccdcdbcbdaacabddacdaabbbdbdaadbbbddcadacccadacbcbdccdbdaabbbddcdcaabdbdacbcadadbdadccabdcddbdabaabcabbdaddddddaaaabbcbacdaabbabdccdadabcddcdbbbccddbbacabadaccbcdcdcbcbcdcabddcbacccdcacbdbcaaccbaadccdbbaddcaaaccbbdaddabbcddacadbaacaaaadbaaddbdcabcdbbcabbabadbaccbdddbcdcdcbbdacbccabdcbddbaabcbabcdcbbacdcdcaabddaaddbcdddbaddddaddcabbdadadbdbcccdbcdaaccccaabcaccbadcadcaadddbdccbdaccbaaabddcadcbbcddbcadcdbcbbadabddacacbcaacbcccaddbbacbbbbdbbdabcdcccddaabbadcbacdacdadbbdddcbccddbdabdbdabccbcacdbbdaaccdcaccdbdcbcbaaacacddbacabadccbaaadacbadbdbbadbabcdcabdabcabacddaaabaaacdaddaccdbbdadadaabaaaacadaaaaddbdbcaaaadcdccdbcbabbbcdaddcdaaacacdbcbdddadbcadbdadbdddcdabddccbadbdbdbddbaaaadbbbaddcaccadcdcbacbacddbbadcdcbcabcddccdbddbbccdcbbcbaacdadaabcbcbaaaadcdccbacbadbbcdbadadacacdaccadbdcdcddbdbdccdbcaddcdddabdcbaaadccadcdadaabddabaaccbcdbaadddddabcadbbbaabddbacdbdacabacbbaacdadcadbcddaabbdcbbaaadddbdbdbdbdcbccabbacbacbcabcbdbbdccaaaaaddaaabcbccccaddcbcbacacbdadcdbdaccacdcccacaccdadcdbadaccbccbcccbaddcbcacadbdbadcbbcbcdacbddbadcaccadbcabcdaadcbcacdccaaaaaddddaacaccadddbabdbaaaaaaacddcacdaacdbdcadbddbabbaaaaaddbcaaacdadadddbdadaacbdabdadcbacbbabadadbacbdbbdadccccbbdacddbbbcbabdccabaddbdacbababdabbdcbabcbccbaaaacdcdbdadccbcbaaacadccabadccdaaabdadabaacdcadacbcaabaabbdcadaddcbacadacacabccdccacbcbdaadbcaccaccadbcdbbcddabbacadcbdbbcdccaabddccdacdbacddbccbaccbdbcbbdcddacdbbadbdbacaabdcdbdbaaadadbdccabccbbddbccdabadcadacbabdccacadcccadcbbbbacbdbbcbbdabcabbbcbbbacbbacbdccaabdacdbdbcdddacbbaaddbadddabcbcabacccaddccbdbbadacdbdadbaabbadcdadadabbccacabacbddabbcbbcaadaddcaaddabccacdcdcbdabddadacaccdaacbdabddacadcdbcbaabdabcbdcbabadaacadddbddbdccdbbcdacbdbccdbdaddbdbdbbaadbacdcabaadcadacbcbabbddcdadddccbbccdddadacacdbccabcabccdabacdabaccbdcbdbcadcacacbdbadbabaabdcacadbccccdbccdacaccbbdbcaacabaadddbaadabbbbaccbdcbcbaaabadccdccbbcaaaccdaccacdccabcddbddababacbcdbabbdadddaadcbcdabbcbdbdcaacdbddcbbdbbbdbcbdcaabbddddbcabdbabbdcaadcadadbcbcbdabbaddcbadababbadbcdacaadaaacdbbcbdcbaacdbbddccbdcbcbddcacdbbacbabdcbcbdaccaaaabaddcdacababcbbcbcaacbaadaccdacccacdbcaabcabdbddbbbaacbdbaccbcdcadcddbababdaabdadabdddaddcdcccdcaadccdcacbdbdbabadadadbbaaadccddacbdadbacacdccdccddbbbbdcddcbdabcdacbaadbcacbcdbbbbabddabdcbcbbccaaccacbcadcadcaabbaacbababcccbdbbadabbbdaadbaddabbbaddddbbcdcababdbcbcadcdaadcbadccbcbcadccbdabcaaacbdbacdddddbbaccaccaabdbccbbbdabbbbdcdcaaaacaccbadcdcccbadacbdbbbcadbccbbdbcbbcbbbdbbbbccaacbdccbcabacdabbdddbdcbdbcbcbcacadaadcaadbdbbcdcbddbdcdbaabcabbadcaaabadacabbabdcbcacbbbddddaaccbcdabccccaadabaddbdcccbcacbddaaddcdadbcdcadcccabdcdadaaadabaddcacabcbacabbabbcbaacbdcdbdbadaddcdbaadadaaddbadcbdadbcdbccdcccbcaadadadddcdcabdaccbbabbdbddccacdacdadcabbdabbadadadcccdaddaabaaabaddcacbdddcbddbbadcbddcabcddbacadbcddaadaadababccbcadbaaaabddaaddcabbbabbbcccabbaacadddabcaacacadaadbbbbddcaabacccabbbdcadaadaabdacadbaadcbabacbbccacdcabbabacaaacbcddbacadabdcacbcabcddddbabcaddcdbdcdcdadadbbcdddacbbabdcbddbbbbadbcabdabbbbbccbadacadbbcbcdcbbbacaadaabdcadbaccddadadcdacababaacadbddcbcbdccbdaadaddbcaacaddcdbaadacbbdccdbdccaabdaadbcdbdcbbbdbbdbcabbbbbdbabdcccacddacbbadcdcdcacdaabddcacdbbcdabbcbccacaaadcabadcdaabdccbbbdbaccbaadccaacabcdacdcabbababdbaaaddbadacbbdcbccdcbddccadbacadddcccdcbbabadaaabbaaacdcaaddcbdbddbdbacadcbbababacccdaaaacbdacbddbcbbaaadbccacbcdcbbcbabbdabcdcbdbacbcbaabbcbdbccaacacabdaccbcdbcbbccbdbaabcaabacddaddcaabccbbdabbbcacbdaaababddabdcbdddbddcdcabcbbcbaabdbacccdcaadcaddcbdaacdabaabbbbabdabddcddbcccbddbbcdbbdbcaadbcadcdccabdaacbcaccadbbabbabbcdaacdcaddccbbcddbaddcbdbdccaacbbabdbdcadbaadadddcacaadcbcdaabdccccbbcbbccaddadbbdaaadaddcaaabdbccbaaadccdbcccacdacaabbadddadbdcabcddccccbcdbabddaaaabaacaadbaadcacadadddbdbdbbbbcacdddbdbadaacbadbdbdddddacdadbaabddabcbcbbbdbbddccadbccbcaabaddbdbdcdabcbcbdccbcacaaccbadbdaccacdbbbaadcaadbddadcdbaccdbccaabaacbdcbaabbbccbbcdbbcadcbabcabccbdcbddaddaabaadaacaaadcbaacdbabdbadacabadcbaccacdacdddbbdbcccccdbcbabdccdccabacbbbcacabdbabdbaaddcaccbbbbdcaaadccddaddabbcdddbccbcdbacacddbaaddcdbbbbddabcacabbcabadcdcbccbdcdbbccabcdabdadbbaadbcbbddabddbcbbabccccadaccdcccabccaabccdcbdbcdabacaabaadcdaccbcbdddacacacbabcccbadbaacdddbacccaaacadbadddadccbaddcabcacbdcbaccdcaacaabdcdbddbdbacabbbadccadbdcdbbaacccacdbccddcadddddbacaadacdabadbcaccdabaddccbcdbcdbbdaabacdbdadaddbcbddbbdaacdddaddccacbcabacabbdaccdacbdddcbbccbaadabbadccbadacccaccbbaadaaaadcdcccdbdbacddaaadaddbdabdbcabbbadcababccbdcccdbbabddacaaccdbadcaabdcacbbabdbbcccabddabdacabccbdcdbdccdbcddbdddacdbaadcbcaaaacbdcdadaddbdcddcabdabbcdbbcddaaacbacbcabcddbcbbbbcacdcaddacdddabacdccbcbccbdbbbdddadadcccacccdcdcddbbadbccbcabdcbdbbdcddbabcadabbdddbbddcaadbdbdcbadccbaaaddabaccdddcbdbcdacccdccaccaccccccbbdabdcbbdddbbcbbabacaabbabdcdbdbbdddddadcbdbccdccccbdcbbbccabbcbdacbddbdbbacccdaddccdcdcbaadbddccdacdadddbacdabbcabaddacdbdccddcbaaddabbcacddcaacabbcdccabdbdacbdabbcadabcaabbbacabdbccdbaacabbaadabbcadbcdcaabbcdbcdcabadbadddcaabbcdaabcbddbcbdbabdbacdbdadadcdcacbdccaddadddbbbdadcabcbcabaccacacbbcccaacaacbdacbabcbbaccbcbaacbdbdabcbbcbdbdcaaabaaaaaaccbcabadddaaddddcbacadcadbdccaadcbdadbdbaababccacdaaacbcbcadcadbcdaddabdbacbdbddcbcadacabbbadabdbabcddbcdbcadbcccabdcdbaccdcbbcbadcccbdcbacdaaaadacbdcabaaddccacdaabcbddaddcdcadccbdbaaddbdadbddacadcaccbcbbdcdadbaabdacdbadbddbcdaccdcabcbcbaacdbcdcabaacabaddcccbbcbabdabdddcbadabbbbcdacaaacdbaddcabdadbcdbdaddbbadbaccbaddcacabccdabadbccabdbabdbbccccdccddccbdaddbcacaabcbbdcdccbaaacaadcadbbbdaaadddabccddbccacacacdbddbabbcacbaaacbdbdabcbacdcaaddddcabaaabcdccdabdcdcbccdacdabcbcaaadbcababcbadbcadbacacdadccccabaddccdaaccadadcaddaadaabbbcbaddabbddcbaddccddcddadbbcabaaaabcccadaccdaabbdccdbcacccabccbadbbcabdbaaacabaddaadddabbadcbcccacadbdcdcbcdbacbdabaccbaaaacdcacbacddbbddddabccbbaddbcabbdadbbcbbbdabadacdccbcbdbbaaabacadcdcacabcbbabcbadbcdcdcaacbabcaddaacabadbccbacaacacdbcadcbdcccbbdabdabcdddddbbaccddcdcdbdccdccdbcdccbdcaddccdbaacbbcadcdaaaaaddadccaabbcadaabcbababbbdccddbcabdaccdbddbbabbbaddacbadcdccabcbbabdacbcdaaddbaabdcdaccacdcabdaacdbbcaadabbababdbacdaddadcadacdbdacacbbdbbabcbadbabcacdbbbdccdccdddcadbbdcbcdaddbdcdacbbbcacdbadcbbbcdcadabadccabddbcbabaaaddacdccbabbaadbcadddaacdacdaadadadbbbacddbcdbcbbdacaaabdccbddacccabbbbdabcbcadaccbacdccddabaadddabbdbdadcccdbccccabdacbcddccbbadbacbcbcbaacdbaccbbaddddbbadbadacaabdaccadcccaaaadabbcacabbbdddaacabacdccdbcbddaabbbdabcacdadadbdacddadbabdbdbcdabbcbdcdbdbcbaabbcddabaccbaabaacdbcbbcaddcabaddcdadbadbcbbdaacdaddbdbddbcacbcdbcbbcacadcbccddbcccacdadaaadcdbddcbddaacacaaabbacabcbbddbacbaaababdbadcaabbcaaaddbdadbbdcaaadcbdcdaaabbdccbbdbdacbcacddbabadddbcaccabddbcadbabcaabddbdccaadcbacddbcbbadcadcddcabadccbcbaabdcbadbdaadbbdbcababdbddcddbaacbdaddbcacdbaadccddbcaacbaaacbbddddadabdacacbcbcaaccddbcabbcbbacbddbcdccdbbdcadaacabaccadddcaccbaacdcdaddbcabbaadaaabcaccacacbdbddbcadbbdcdbbdabdbbbdddcbacccbbbbbcabbbbacaccdbddcdbccaadbbcddcaaadaabadcddaacddcbcadadaacacbbcbbdaccdbdcddcddcbdaddacdaadbcaddcabcbcadcdbcbabcbacdacccbacbdaaacbcddcdcbadbcbcbbbdddcddabcdbdddbbbabdbbdabbadadaaaaccbbbcacbaabdddaacdddaaabcbabbcaaaaaabccdbabbaacddabaadaacbbcbdadbbdbacdccbcbcaccbbcababbabdbabdababccaaacdcddadbaabbcbacbdbccbbccbabccdcbcaccbbbcbabbabcddadbcdbabcccdbcadddcadaaacbdcdbaddbbadbaaddddabddcbacbdbbdaaacbbbdcdacbbbdcaccbacbcabdccdcdddcdbadcdbdadbaadbbbdaaababaabbcbdcdbcdbdaadadbabababbdacacaccacbccdbbbbcbbbbaacaabbbcdacccdacadddddcaddabcacbababddbbcacbbddabbcbbccccdbadbcddbcbbcacccddbbcccdcadcaabadbbbcccaadacacbbbbdaddcacdcbccdcdcacdaacbcdcaacbdadacdadccbabcdcabdabcdcbacbdbbbaddccacccbadccbcbabbbbaaacaaddbcadcccdacdddcccbddbdaabacbcadbdbaddddcdbbdcadccddbbabdbaaadccccdccdcabdbbdccdacbadbabbbcdccdddaadcbadaaaacaaaddabbdaccdbdccbdbdabbdcccddcdadadaaabbcbabcdcdbbddbbbaaacbddabaaacbbdcdacadabbaaadabcdcacacccbbaabcabdadacbccbdbbaabccaaabcdbcccaaaaaccadbacbacdbacdbbbbccaddbcbcbcbccccdcdcdbababbcdaddddacbaabddaaabdcdcabadcabdbacdcbdddacbbdddcdbbdbbdabcabbddbabadbdabbccabbdcbcbbaacdabcbddbdcadcbabbabcddddccddbabbabaacdbababcdaacacdaabbbdbbdddacacccacdbbadcbadbaacdbcdadabbadadcbccababadbaddcdbbacabaabbbbccaabadbbcbbacccacdcbcccdcbdabcaacbbbaadacacbbbdccdcbdbccccbcbbdccdcdadbacaaccdadacaccdcabdacbbcdcaadbccddbbbadbbaaccbcacaadabaadaabcababaddbbdbcbdaacabdddddacaaaaddaadccacabbadccacadddbabbbdcdcddacbcdadcbaccbddbcdabbbbbbbddddabababbcdbccadbdacccaddbaaccdcaabcaacdaabaddcadcdbacdbdcaacddacbddbacccadbabcbbbbbcdaaabbcacbbdaddbabcbaaacacaacdbccdbdbaacbcaaabcbbdcbdbdccaadacdcadbcaaabcdcddabddbacaaadddcbbbbdaacbddddccabbabdabaacdcdcbdcdaabadaadddbbcbbddbbadbccbacdcddbadcbcadcadcdbbcddaacbacdcabbdbaaabbdaacacaacaabbbbcadadbacbbabcaadadcbbabbcaaabcdadccccacdcdbddbbddabddcdcdbabccaabcbcccaddaccacabbcbccabadaabddddcddcabcdacbcababcccdadaadbaddbbabaaddabbbadbdcadadccbdbaaddbcbaabdbccdcaababcbdbccccbcacbdbaccdbbaddaadbdccdbdadcbccbadacacddadcccabcdbabaddbacbdbcdaadccdcaabbcadacbdabdbbaddbddabdcdbabadbcbcdabbabcacacbaabbbcabbcacacdddcdaabbdbdbccccbbdbbaadbabcbdacdabccdbdccaadaddabaaddbaadaddaaccacdbaacacbddcbbdcadaaccbdbbaabadbccdaaacdbadabdddcbaccccbcadccbabaabadacdbdacabbdcdabbddcaccdacaaabddddaaccddbabdddbacacaaabcbcbaddbaddbdccabbabbcbcccabbbbcdabcdbcbaccbcaccadacdbcccaaddcbccbdcaacaaccbaabbcccdcbdaddbbbbdaabbaabcabcdbccacaddddccbbcaccccdccbacabbcadbcacbabdcbaaddbaccaacccaccbddaadcddcbcbbbcbbaddaaaaabadcbcddbbbccdbccdaadaabcbccdadadcdcdabddcbbcccbabcddccdcdaddcabcbacdcbbbaaabdcdabdbadaadaadbcdccacaadddccbbccbbbdcadbacbdcdbcdcaccccababacbdccbacaababadcbdbdccdabcbdbcbdccccaaccaadbcdcacbaacdacdbdcbbbaaadcddbaccdadabcbbbbabadcabbcbbbbcdabccdacdadbbbcacadcbaadcdcbbabaadcbccaabaaccadabadcaadbaabbabbdccdacdccacabbcbddbcdcaadcdaaabdcdbacdccdbcbbcdabbcaaaabddcdbccaabbbbacdbddcacddabaabcdaacdddcadadbadbdabddccbbdacadacddddbdcabdabcdbdcaabbdcbdbbdaabdbcaabbddaabcadddaaaabdaabacddacccbcbbdbbbcbdcddbcabcccdaaabadddcbbaddacdbdacddbabcacccdcadbcbcabdbcdacdcdcbbdabcddbaaacccbdcbdaadbdcbacbacdadbccdbcacadaaccdacdaabcbaadcacaacadaacccdcdcdabbccabddabaaaacdccbdcdcddaadbdcacbbccbbacdaaddadabdbaaaddcbcaabcdccccdcadcbbbccaccccdbacacdabddbaababccdbbabbbcabccddaacaacaddbdcdadbacbdaacbcaacaddaabccbcdaabcbdddbacdbcdcdcadaacdadcbabdabdbadbbbdcabcccddcdbbbabcdcababbacacacaccddababadbddccbcbdaadabbbcdcbdacadbbbcaadadbdccdccbcddcbadbbacdaadabddaaabbccadcbdabdcbcaacadbaacabdcabadcdccbbacdbdabbaaccdbdaacdbdabcbdaccbabdbdcaabccdcbdadbdcaacacbcdadbabacbdccadabadccaddaddabaddbbdcdaadbcacbcddbcabcbccddbadadabbbcccbdababbbbaacdaddcdddddccccccbddaccbabacaccdbbbddbcbdbdabcdddbcdbaabcdcadaacbbbdbbacbdaddbbbbbbcccdbbbbaabdccacbdccbbcbbaacdacbccdabadaccdcddcdcccbdccdbabaaabddaccaacdaadaaccdbbbabcbadccbcacddbcbbcdcccccbcbbccdcbbcbdddbacdaaccabcacabcbbddbadcbbbdbadcddacacbabbddbadbdadbcddbabaacabbbacdbdbcbadbaacaabbddcdbbbdccbaccadbddbcadaabddaccdaabbaddaabdbbcdabcaabddbddbdabddbbbdbacbbcabaaddbadbcadccbdcadddbbabaccacdadbdbdacabdddcbbbccaaaaabcbaadbbddaadddabcabbacbabbaaaadddacabacaabbaddbdcbababdcadddbbcbcaddcdcdcdcdaadccaddddaaadbbbbbabbbaabcbbaabbcbaaacddaaabddadbcdddcadcacacbabacdcdcdabbbdaaabadabccbbdabaaadaddacaacadacabdbbadbbadaccbdcbbccbccdabbbacbaaabbdcacbbdadbbcbbacdcabdcadbbdbbbcbdcdacbadccbaabcacccddaddbbdacdaddbdaccacbaabbcbbbcddabccdccdccbcbbddacabbbbdabbdcbcdbdabcaabbbddaacaaaaacdbbdcdbabbcdaccccdccadcbadaddbdcacadccaddddcbaacabcddaacadcaacccbcaacadbbbadcdacaacdabddaabaccbddcdbababdbaadddbccccabccaabddbcacdcbdacadadabdbabdbcaddccabcabcbabddbaccabaabdccaadcbbbaacaacddbcdddbbbaaadabbabacbcdadbaaddccabcbbaddbadccadcbcbcaacdcdccbcbbdcdadbdacbabdbbcbddcbddaaadaddcccadbddcdcbaabbabbbbddcdaddacddacadabdaacdacbabaabccdcbabbdbaaddccaadcdbaaabdbacddaccaccdbccdcababcaaadadacddaaaacbbaabcdddabbabccddbadaadccadadabbbcbadabbcdacdacabcdcacdaabbdddddbcacbadcabddbdadbbadcdaccabcadcbdcbabdacbdcbbcacbadcccdcccccdcaccabcdbdabcdddabadaabbadabddcbbcdccbcacbdcbbbdbddadbdadcdadccddbdcccbcdabdbcbadbcdcdadddabaabcddadadaadbbacaacbddadaccbcdabbaaccabcabdbbccaddcddcddacccdcbcaabcbdddabaadadabadddbcbbabdbababaadabbcdcccccabcadacbcabcbccbbbadcdbcabaccdbbdccccddcadbaaabcccbcbacdbabadcdbbdbabbddddddacadabbcadcaabccbacccdbccbbadcbdbacadcccbbdadadcbaccaaccaabcdcddbaaacadcccabbccabccaaccbcaadaadbbdcacbdaaacccbbdbbcbaddbaccddaadbbdabbcabaadbdbcccaabccbcdbcccbabccccacbcadbbbddcbcaadcddcccbaaccdbabbcaacaaadadccbdaacabaaababdcaababaadaacadacbbcdadacdcddadbbdabacddadaabcbabccbadacdbdcccbaadcdcbadbbddaacacbcadbdabcdddbbccccbcbdbbccdcdddaabbdbdbdabbcdcbccbccdaddaaabacdabdadacbdaddabadadcdcbbdbddacdddddcbbacccbcbcbcbdacabdbddbbbccadbaccddcabbadddaddbcdabccdbdcbadbdabaadaabadbbaccaccaacbddacdbccbabdddbadbdcddadccacabdccdbdcbcbbbbbabaabbbacadadccacbddccdbcbbcbcbcacaacbcbdbacdbacabdcbababacddbdaaaabaadacbacacddbcbbbbabdcdbacddcbbbbddbbcaacbbdbcdbbbbdbcabcbabbcbbcbaadcadaabbbabdcacddbbcabdcdbbbcbcaabcbbdcbaddcbccbbcaccccadbcddacbcaddbadadcbcdabadddbbbaaacdabdabdaadacabbcbbbcadabccdadacdadbbbbcababccdcacdacbaddacccbddbbdbcdacdccdbccaaccabcbabdcbaabaadbddccdabdaadbdcacbbdccaacbadabdaabdcbdccdacadcddbcbcaaadcccabaddbcdacadcacbdacbbbaddddcabcabbbbcccdbdcdaaadddccccbddbabbdabbbaddabcbbaacdabaddcabcbccbaabaacbaabaabcbacacbacadcdbbbdcacbdbcccabccddaabaacddcaadcadaccbcdbcdcacadbcdbbaaadadbbbacaaacbcdbbccacdabbbdadbacababcbcccdcdccbbbaaaccbaccabccbbbcdccbcaaacdaabadbaacbdbcadadbcdcbacbcddcbcbcddaaaddcccbcdbaccddacdcddadbbbadbdddcdccdadacbdaaacbdcdbdadccaaacddbcddabcbadcaacdaddcdcbccbddcdaacdcdaababadcacbcbdcddacadacaccabccadbcbcbabdbccacddabababbdbabccbccbcabbadddccbcacacabcdaacabadcbbcbbcdaababcddbabbacabccdaadccbcaacdacddcbbcbbdbbbcdadabcdcbbbcaabcbaadbbcabacccacbbbbcbbbccdcbbdbdcccbdcbcacbabccbbadcccacdbdcbccdccaaadbcacdccdacbcbcbaaccdbdcdcdcddaccbadbdaaadbbcbaabdcccabaabcabdbcdaaabbdddcbbbaddbbaacdccacbcbabcbbdcdccdabbcbdaadcbaaaaddadcdbbadadcbbddccadcadabdacbaccdcadcabddbabaaacdaccdddcadbccabaadbcabcbabdcabbbbdacbbdbdcaabbcdcadacccabcdccdbcadbacabaaabcadaddadcbcdadcacddcbbdaabccaaddacabdcababadabcbcbcbabdbbccdddcbccbcbbbdbadaccdcdaabbbadbccbadadccbdaabcbaccbdaacabbaccbbacbcadcaaabbcccaababaacdaabdcaddbabcbbadbaabadbdbcbccccbdcdbdccbccccdbadaaaaacadbbdacbdacbbccaccacacbbdddccbbbaabccdbcddaadcbcaadbcaaabacaacbcdbadbdabacbcdacbddacccaacdaacbcbacbabcbbcabddcbacdbccadbccddbaaaacbbdcbccabddaaacbbcabcbdddaabcacbcabddccaababdbcccbacdddcacbabaabdacbcbaabbaacbbdddcaacdccbbdbdcadcbbaabadcaddacbdbbbdbdacdcdcbbadddcabccdbbdbaadcbabcacaadbdcccadcddabdbabdaccddabccdbccaadbaccccbadccbbaacdccaaaaacddccdcdddbdbcabcbcbaddcbdccdadabbccaccdcbdbbbdbdbbbacdabcdabccadbabaabacbbbcdcdbcaddacadcadcbddbcdaabdbabdcdcddcdddbdbdbcadcccbbcccdaccdbcbbbdcaaddbcdccddbbcccccdaddcacdadbbadbbcddcadcbbabdbadadcaccbabdcdccacaabdabdbcadadcaadacbcccbdbcdacdacabaacbbdcdcccbcbcdaaccddcbcbadcbbdababddcbabacadbabcdcaacaacdccdccdbbbbbbabaddcccacbabddaaccbaadbbbacadddcbbacacbbbcbbbcadcacbaadcbcabdcdacddbcdbaaddbadcccdabaaaaadbcbbdaccbccadabbacccdacddcbdbbddcaccabababbcadaacdbdbbbddbadadbddccaaabcadabdaddddcdddbcddabaccabdacbdcdbcddadbbabcdcddcdbbcdbbddbbbcbcdbaabaabdbccbacbcaddbabdcbbacbbccbccaddddabcbaabaabaaccbcacdbbbcbaadccbababcbaaabddcdadacdadabacbdcbadbbaddddbdcaadddbadcaccbbaabcbdaddbadbbdbcdbaccadddcbdbdcbcdbbcdcabcddcccabddaabadbadddbdcabacbababadbcdbcccaadccabdaccadabdaabaddacdbdbaddcabadcdbcbdcaacdbccaacdacbcccdcbcdadacabcabdaadcbadbdabaccbcbdacaaaccaddcabccabbccbcbcbcbbcabdacadbabbbdaadbbccacccccccadaadacccdddabbaadbdcddaacdcbacbaacaabcdaccabaacabcbbbbbdabcdcdabcbadadcdccbabddcabdcaabbbdcdbdcbdaccaccabdaababbcdddcabdcabddddbbabbdcadacacddcbadadcacdcbdddadbdbbcdacddacdaccccbabcbaacbcbcbdcbccabbdbbdccbccacabaacbcddabcadbdcabbdbaccdbbabacaacaaaacdbccccadbcdccdbaacaaaccbcccbbbbbddbcabbccacacbcdbccabcaadcdbccdcacaccdddccaacbbbaaadabcbacbbccdbbbdbaccbbbbcacaabccdabdddccdbcbbbccbdcbacbbbadbcacdcccaaadbdcccbbbbcbbbdcabccabcbadcdaddcccbadcbdaaadbbdacdbaddddabadcacddddbbdbcddacabdbbcdcbbcaabbcabdcbccacdadcaddadbbccbccbabcacbcaddbbdcbcbcbdbbdcacdddccdcacdbbcbaccdadbbacddccbcdabaddbdabadccabbadaddcbcabbdcaabcabaabbadbdacbbcbbdacaacdaddcbaadbdcbddccadcdbabbdcccbcbacaabccdbbdabcdcdabddddddbcbdbaccdbaaabbcdbacaaadccdddabacbbbcadbccaddadadaabbcaababbbcbbcdbddbbaccabbbcdbacdbdabbaacadcbcdcacbcddcdbdacdadbbdaaabccbbbbabdbccbcaacbcaacabdbcddcdabbcdabddcdabacabdadabbccbcdbbaacdcadddbbaadbbbcbbcbdcdcbaadabdcaddcbcadccbdcdbdccdbbcbaacbbbdbcabbcacacbddabbcacddddcabadacbaaadbdcadcbbabdbaadbcdccacabdcbbbbdadbcaddcaaacddadabbcaaacbdcadbdabdadbbdadbcdacbdacaabdbdddbdabccaabbbbacdbdbbbdabddacbcbdaaacccdddddcbccdcdcadacbbbdcacdabacdcadaabbccadcdddbadabccaadaadaacbccddcabacabbdcbdbccabcadccddbaaabbdddacbddbdcdcabdbddcdccbdbacabbccbaccccdaddbbbadbcccdcaadddbbbbbcbaabcccdabadabbdcddddadbdddaabcdbdbaccbdaaacaabbacacabbbdbabadaddcaadcdcabccbabdcbbbacabcaabdbbdddcbcdacbdbcbbababbbbaaccadacccccdbaadabdbadaddadbdabcbcbacabdccdabbcbdbcacddccbabcbdaaabdcccaddadcabcdabddbdbbbcccccdddbbcadbdbddbaacddabbadababdaadbaadbcaabaddccaacbdadaacccbbaddddaccbacabcbddabbdabbbddcacddcbdbadcbcccabaaacadbcdbacdcaabbacacaaacbbbbcddcdaabcadcdadbbcbbdcabbbbcbdcdbaabbdcaaaaacccabcdcbbdbbcabddbdacabccaaacbdadabdadbbbbbbbadcccacbdbcbcbabdcbabaaaddacaaccbabbcadbdbacacbbbaadbaacdbaacdcaddbbbddabdcbadbbcccdaacaabaccddbcbcacdcbcdbaaaddcddaccbabbbadcdbabcaadacbbdcbdaaacddcddbcbcdababcddddddcbcabbabcacdcacddbbbdcdadacbbdadddbcbbbcbcdcadaccddcabbcdacbcdadccdddbbbbcabdbadddbdbacbdccacbaddbbbabbbddddaaccbaddaaaabdcbbaacdccadaaaccbbbbdbbcbdcadcbabaaaddbcbbbdaababcadbbcbdbaadcbddcdddcbaddcadcabdaaaddcbdabbbdcdbcddcacacbddadbbcdddcaacbaadadbccbaabdcbabbbcaaadadaacaccabaaccbbcdcadaaabdbccdbabcdabdccbadcabcdcdacccbbddcaccaaacdccbacadcaacdacdbdcbbcddbddbaabcbacacccdbddcdbbacaadcbccacddbbaabccddbddaddcaacdddddacdaadbbccbbbdaadccbdccaddddcabdaacdbccdbccbdadacccdbbacbcbcbbbdcadbaddcddcaaabcdbccaacdcabcccbbdcaddcacddcacbcdcdbabacbbabcbdcbcbcccdcccbaabcaadadbddcbadcbbacbaacdadcaccababddcdacdacdbdbdbacabdaadaddaacaadadabaaccccaaddcabbcadbbabbacdcacabbbddbddbccddcdcbbdbaddbdabbddabdaaadabddadcdcbdaccbabcacdbcdcaccacdacdcbabbcabdccdcababcbabbaccbbbdddcdccaacadacdddaabcbabadbbaddadbadbbdbbabcdcbdacdcbcabcadabcbdcdddcccbddaadaddcbabdbcbcccdacadadddbabcdbaabadcaabbccddccabbbdbbaadccbabdadadacdbdbcaaacdbabaabbdacdaacdadccadbdbccacbabadddacbcbacbabcddbcbacaababddaabcdaaddbcdabcccdabbbbaacdddcbdabdaaadaadbccdadcdaaccdacdacaacabadcdddcadabbaacdbadadcbaccaaabbbccacdcbccbcdbddccacacadbacbcdcaaadcacbbbabaaaabdcddbbbbdabaabaabacadadbdacdbdcbcaabcbdadccbadabbaddcbacacdccddcddbddcdaabdaabaaaccdaaabcccdadaccbdcbcbbbbaacabddcdbcbbbacbacdbccbadbbacbabdbabdcbbabbbbacddbdabaaabccdbabbaabdbdcdadabcbcddbbdcdcaababbacadddccdccdbcacbdccabaccbbbcbcbdabdaaaccbdcadbcddaacbcadabadbbabaacabbcdcbbdaadcdcacbbcbccaaaaadcbcdccdbbbbdcbdccbbdadabdaadcdcdbbcbdcdbdccdacabdadbccdbdadcccadacaadcabadbbdbcdcdcbdadbdbbbccddcbdcabcaabacdcccadabcacaacacbddcbddbdcaccdabbcdccadaacdcdbcdccbbccaabdbadcdddbaacddbdcbdbbaddbcdabbdbdabbbdcddbdbacccadaadbcdaaabdbbdddbaccbabcbcddcbbdcbadadcdacacdbdccaaddbbacdcaaaaabbabaadccdacdabacdcdaaddaaaaadbaadadcdcaaaabddbdadcabddaadcdadaaababacdaaaabacdcbaaccdaabcabcbdcbaaccabcacaaacdaabdaddabadbbdaccadcdbacacbadbcdabdccaddbaacaabdcbadcdacbdabcddaadcaadbaddbaabbaabccacadccbbcadbcbbddcbbbccbcadadacaabbcaccaabbacdadbabbacabdbdbccabaacadaddcacadbaacdacbdadbccadabadadbdbbaaabdaddddcbabcbdaadadccdbddaacbddadbcbddaaadadacbdabdacddcaccbbdbccbadadcdacdbcbaacaabccccbccccccabcdbadbdbbaddbbbbdcdacacbddbacadcdccccdcdcdacddabdccbccbaccdbbadccbaddcabaaacaaccdcddcdabbbcbababacbbbbbdadbbaabdbaaadbcdbbcaabdbacaddcdcdadbdcddbcddbabdbddbccabdbdbccaccaabadccabcadaddababadadaccbbcadaaacdbdcaaddadbdbababddddaaabbcaaddadccbaaccdcbccabdbcadaadadcbdaabbbacddcccbbdcdabddcdaccbdadcbcadacbbcdbcbccdcbbdadaadcccddddbcbcdbcabaaddbcddcaabaabdbbaddcacabcdaacbcabbbbcbacddcbcaddcdbdbbcaacccddaabaadcbccbdddcdadddaaadbbddadacacccbbcdccccadbadcabadbcddbdacaacbdaaddccdddcdbcddbddadddaccacbaabdcbbbdddbbadcdcaccddadddbbdacccadcadbadabababacbccbbddaddbddaabcbbacdbddcdcbccadbabbacdaaaadcabdaadbaccbacabdcdcdbaacccabdcabccbbdbbbdadadbaabcabadaacbcaddabbcaabaccbccbdaddbbbccdcbccbcbbabcddcaacbbcdbbdbdabcacbacabbcbabaaccddcbcabddaadcbdadddcccabbdcddbacaccacbadaadcdccaaaddbcdadbcacbcddaadaaccdcadabddbadcccbcadabdcccbdddcdcabacdbbbcaabbbcaacadbbacdaaddabbdbcddaacabdcdccccabcaccbcbababbdcdbdaabbbcaccddabaadaadcacdcccbcdddddababcbcacbcbbbacbadacbcdababcbcccadacbaccdbdccbabacdbbcbbaacdacdcacabcddccacdbdbbcbdcdccccbadaaadccbddacdabccbadbbbbbcaadbdbdacddbbcadccaddbadbbaaccdaccdddadbbacbddcacbcbccddccccabcacccdddbcbcdaddcbcaadacaabbdbdccbdcacadcdadcdaadbcddacddcaabacddbbcbcdabbadbaccadabdacddacbacaddcbcabcdcccccccbddddacadcabadaaabdbbcadcbbccabbbacabdbdbcbabbcdbbdbccadacaaaadcdaccddadadccdacddcdabbacdcbbcbdacbbacacadaddbcadadddcbcbaaaadadbcbcbddcbacdacdddaccdbcccbabcbdcdbdabaddccccacbdcadbbddadddaaacadcccbcbbadadbcbdadccdcadcdbbccacaddcaadcdaaccbbacbdaddabcddccbcbcbadddddcddabcbcabccaaadbbcccdbcacddadddacccabbbadcaabacbcbdbbcddbaadaaddbacddaaaddccbcdbbdbcaddccdddaaaadcababaaadcdbcdcadcacdcbaccdaabdcbdbbdabdddbdcccbdabcabcdbbbbadabbccbbddbadcbbbaccbbdcbdaccacdbadaddbccadcdbadbcbdadbadabddcbbddadabadbdadadcaabcddacadaccbbaaabaddbdbabdccacadbadacababdaccbadabdbccbdcddbcacaadddaadadabbbacaadabddaddccdaabcbabbcadadcdccaabdccaaacbbacdbaddacccbabcddccadbbcadacabdbcaaadbccacbdbcdbbdcccdddabaccaadcabcccacbcbadcccdcabcdbaadbbdbdccabccbbcabadbdbddbbdacddcabccbccacddaaadbcbcabcbdcadbbadddcadacacdbcbcbbdbbddcacddabbccbbdbacdbacbccbcddddbdcabcbabdcbcaadbacdbadcbccdcababcabbcbadcacacacabbbccadbcabbbdddaaaddaadacbaaaddcbdcbcabccdacdcaabdabccaddbbbcadacdacdcbcacbddaabbcaaabaabddcacaababadaadcbadacadabbbdaaabdaabcdbaabaddbbabccaaddadcaadabbbbcdacadbacccccaaccaddccaabccdbcddcacacdcabcccbdaaabcbcdabcddcadcbcbbcccaaacbcccabacbbcbbdcdaadacabbdcbcbdccbbddcbcaccccbdddcacccdcbabdacbcdaddaacddcbcdabcbadaacbaadccbbbdbccdbccacadabcbbcadabaccbcacdaaaacbcbacbcbacbddacaddadbbddaabadccbbbabbbdacaadddbddcdcacacdabddacddbdadcadbdcabdbbbbabaaddcccbaacaaacdccddcadbdabadadadbdbdbcababadcbddaaacdacccdddbdacbdcccdbcbaacaacbaddbacabbcbddadacdabacbdacadabaaddcbcaadccabaadbdcaddddabaadaabccdbcdbdbababaaaadcddbccabddccddbbccbbbbcbcbbdacbadbdacaccccddabbdcbadbcdacbcaddbcbcaacaabdaccccdddbcadcbbaccbdddbcddadbadcdbbccddbbbccdddabacdddbbcdcdcacddbbabacdbacccdddcccabdcdcacdcbddaacbdbdaccbbcdcdacccdabacbcadbdccdbccbcdcaabdbbbdcbbaaabdbadbdccdaaaacbbaddaacacdabbbadabddabaddccbcdddadbbbabacbdcdcacadcadddadcdabadaccdbabbcdacccdaddacddcbccdddacdbbccbbbbbdacdbdcbcadaadbcdbababcbbaaaacabdccbbddbaabacabcaddbcbcdddacbdadaabddbdbdcddabccdacacdbbdcdcdaaadbccaccadbacdbbdcbacbccbacaddbaaabbabbaacadcbcdbdcaadbcccbadcbcccaacacdbdbabaccbaacdaaabdaacdbbadcdbbdbcabdcbcacabdcabacadadcbdacaabcacabbdccabddadadbcccdaabaacacaabcbacbdbbdbdbddadaadcadbdaabcacadabaadaaddcdbabdcbabdcaddabbaccaccbbaabcccabadcbabcdbcccabbbacdccadacbbbcccddbabdbbaccaaabcaaadccabacadadaacabcabccdccccacdbbadcabcddccbcdbccabcaccbcadbddbdddaabbccccbdbbcdbdbcdaabbccddcddbbddbdabcabbdcadccbccbccabddbccaddaddbcacdbdaaabcbabdbbddaaababcdabcddbaacbdbdaddcddcbddbcacdaacbcbdccdddcbacabdcbcaabcbcaabdbdbabbabaccaabddaadacccadcdcbdccadcbdcbdaccdbabdadddbcadabcdbaaccbadcdbacacabdccddaadcacccbbcbaabcacbbdaabbacbadaccdbadaabdbdcbbabcaccabdccddccbbddadaacacaabbccbdbdbcccaabdacbddabdcddbaabadcdaaaccbacbbcaabccabccdbacbabbdccaadddbbdcaccaaccbdadddbcbadcbbbbacacbddccaccbbddadbabadadadcadaaddcdbbcddbdadcacccdbbbcdbddcacddbccbcbdddccabcccdadcbacddcbadaacddbcadddaccabcbdcacaaacbbbbddacaabdbdcdcaacacaddcdbcdbdcdbcadbdbcacacdcbcbabbddcdabcaabacccadaaabadaabdbbaadcdbacdbabdccdcbdaaaaddbdabbbaadbdabdcddcaaaabbddcdbbcaadbcbccbbdcdcbcbbdaabcdcbbabdddacbccdabbdddbbdcccdbacdcdacccbcaacdbcadbcdabddbdcbdcdadacaabaabdbccbcbbaadacbcaddbcdccccbddabacaaabdddbccdcdbadccbbddbbcccabaddcbbcaadadcddccdccbbdbdadcccbdaddddacacdddcdbcbacdacbadacdbadbdadcbddbaadaddcdcdbabaccacaddbcdbbcabdaaacddbbdddbdcbbdbccbccabdcaadbbcddbbdabcadcbbadbccbddbcccbadccbbbbadddbcccdaccbacadccbbaaccbadddcbbacaccbcdadcdbadacdaabbddbabaddcccacdccbbcdbacbddcbaaddadbcbbbadbbbdaddccbaccdbbbbcddaacbbabcbadaabbcdcccbaadbacdbcabaaaaabaabacabcabacabbdbbadaddcddcbbbadbdcbcdbcddcbbadbacbdcbdddddacacacdbabbdcaacccdaacccabcdadddccaacccdbaddccadcdddcddddbbacaaaacbaabbbbcacccbdbcddcdadcaabdddcddbbdacaccbccbbcdbdabcbdbbdadcccdbaaabbabbdbadadcbbacaaaddccadbbbbcdaaaadcbbcabddbbddcaccbccbacdbcdbababadbbacbaaacdcbccbcbcaaaacddaabdcbdbbdadacdcdcaabbdbbaccbbcbdaaabccadcdddddaacbcbbdaccbcabcbadadbcddcabbcdbbddbdbcaacdcadaaaccbbbacbccccbdbbdccbabcbabdabbdaaaacbddcaccadddddbbadbaabcbcbcabcbcccaccacdadbbdbbbbcbdabdcccbcbadaabaaadcbcbdadbadbbacabcabbacbcccaaaddabcdacbbabbdcdadabbbbdbacadbaadcbdbccadcabccbdbabbbdddbddbbabaabbdddbacddacdbdaaacabaacdbbccbcdddacdddabddcaaacbdaacacdccaddcdddbccbadaddbdcabdacdccdcbaabcacbabbbdbbcbacadbaacbdabacacbbbabbbaccdcccbbadcbbdacbaddaacdbdacacbccacacabbadbacbaaacdaaddbacbdcdcacccdadadbbabccdacddccbbcbaccaaacbddaddaacbcaacababbaabadbaabbcbadadadcbbdabaddbbaaadaaaaacbaddabddbccbaaddabcaaddbbcbaadcbbcbbdbdbacbbcdccbddacbbdadcacdbaabdddcbdacabadadaaaddbacdadadddbbbabdbcdabcdcddbacabcbbddadabcbadadbdaadddbadaabdababbdddcddacbbcabcdddcaccbcddabaccacbadbcacacdbdcadaccccbcacadbccdcdbcbacdadadcacadacbdbaddcccdacccddccdbcbddddbbdddbdccadbcdbcbacbacddbdbcddcaccaccddddcbacccbbcbdcabdbaabdbadccdaaadcbcccccabdacbcbacddbbcaccbaacdacbdbadbdbdcdbaadaccbcadadbbaccaabcaadadbbbacabbbdcbbcbabababbaddabdaccddccdabadaaddabddbccdbdcddccaadbbaacabcbaadcbbbacddbddcaaddaabbcbcacaccdaaccbccaabcdabaacabbaddbacbbcabbbdddadadbabdadbbddccbabdcbbcaccaddcaacccdcadcddcadbccabbacbccdaaccaabcbcbbcdadccabbdacaadbddbbdacdcdddcaaacbbaaaaadbbcddccbababbaddcadbcababdaaacdcdbbcadabacdccbdcaaacbdacbddaaabdcaacaccbacbaddbcdbcdbbbbcabbbdbdcbcbbddadccdbcbacdcddcabcddacbbbbddbcdabcbcdcbddcdadcbacadcabbadadacdcdadaabbddccdddcbbcccabbdbdbdbcdcaacdcdaacabdbacdaadaadcabadccdddcacaddddaaddabadadabdcbbdaabcdbcbbaacbbaaccbabacbdacbbcdcacccbcabcbdbcbcbcdadcaadbdaaccdacccddbbabbbbdcabbadbdacdbdbcbdaccbcbadbcabcaabddadaabdcaadbbbdbabdbacccbaaaaadcbaaaccbbaadbacaacabbbbbcbbcabbbdacbdbcadcdbbaaadababcacdcbbddbccaabbcdacbcccbdbdccbdaccacccaadacdbadacdcccdabbbcccaadacabbbdcaaacdcabdcaccaaaccabadbbaadbacdcdbaccdcdcccbaacbdcdbabaadbbadbbacbaddbbbdbaadadccaabdbcdadacbbadaccabdacbcaadbbcdcbbdadddacdbabcbddcaaacaccabaccdddcdbddcaaddcdaacdcdacadabdbdcaaadddabadacacbbcbdbcdaddbcdbababbdbdaacabbdcbdbdcabbdacdccacabbbcdbbddbddcbdbacdbbcbcdccddcadcaccccacabcbaadccacadcaaacdcbcbbacbadbaabcddcbcdaabaaccbdcdbcadbddbadcdbdadacbbaddbcddaacbbdaccadccaddacbcbdcdabbadbbcdcccbcacabbbabddbccccdbcbcdcccdacbccdcaadacdaaacccacaddcdcddcdcdccbbadddddbbbdbacdaddbbdbbaaaaccdcdbcacddbaaabbcaadddcbadcddcccaabddcddcddcddccdddacddbacaacabadcccccccabddcaaaacbcbcdccabdabbdbaddcdccbadadaccabddaccacdbddacdcdbbbbdcdddcadaaacabcbabaddbccbacaddcaccdacadbaabbacbaacbcdcdbccabdddcaacabbabbcdbcddccabcbcdaacdaadacdadcadbaabdbdbdbdadddccbacbbbdcaccadabacaadcbabbacaccbaaaacaadddbdcaabdababdbdcdabbcbcbadabdddaccbbbcacaaacabbcbabdbccdddaaadbddcadbbabdbcadbdddbcbcdaacbdadbcabdabaadaaaaadcdbdbacbbbcaacdbadbbcccdbcdadacbdcbadcbdacdcccaabddbcdabccdbcdcccdcacbdddbddddaddcbaaddabacacbbaacabaddaccacaccdabaddbbbbacdbbcaccddddcdbcddccddcbcacadcbabacacacacbbdaacddbbacbbccaaadabccdbdcdccccbaacbddaddbdcadddbacdcccbbdcbbbcacaabbbbbcadbccbbccdaaddbcddbcdccbcaacacbcdbccddbddbcccddadcdbcabdbddcdabbaccbcadbbdbbabdbabddddbdddabccadddbbdddbadcdccdababbacbbdabdbddcdacabbbddcddaaaaaddbdbababcdaadaacaacabcbdcccbbabbbbabccacdbcbbdcaadaadacccdaacbdbbcbacabdcbacabbaabdcadcbaaaacbcdbdcdadbbbbdbdbadbcaabaccbccaaaaccbddbcbabccbacbdaccbaadcacaadacdccddbcddcbddaaaabcbcacacacacddbccdbbbcaccadcdcbcddacabddacbaaaaaabdbadddbadbddccadabcdcbdaddcbbdddbdbbbbbaaddaadaacbcbabbcbaccdccdaccddddcbbacaadcdcdacdbdabccdbcadacaacdcdabadcdbddaacdcacdacabacadddddcbbcbadcdadddaaccddbbdacbabccdadcdddadccdcacbaadbdccccabbbbbbccbbdcbccdbacbdacbcbbcccddbaadbbadbbaacbddadbaaaacaacbbabcbaddcdbbbaacdbdcbdadbbbccabaaddcddbbdbcddccbadbcbcbcaacdaccabdcccacdaabaacbddddbdccddbddbcddcddacaddcdabdbcbdddbbabcddccaaddcbdcdadbbdabcbddbbcbabbcdacbdadccbbcdacadcdbcdbccabaaccdbdbcaaabbcccbbabddcadacdababccddbacbacdbbaadabcabbcdbdccccbbaabdbdcbdcadbacabccdccddbadbcbcddbdaccbdcbdcbcdcccbadcabdddbaccbdbdabbcdccbcadddbddbcbbdaabddbccbabddacbcbddbabdbadbbbcccdabbdbdbbdbbcdbaadaaabdbcbcddbddbdbcbbabcacdddacbabddbccabddddbdcccddcccbccccbbbdabdddcabacbdaadcbdbadacdbcbcaddbcddcdaddcdacbbbacdcadaacbdbadccccabadadbbcacadccacbdddbbbdcdccddadbacadabbbcaaddcabccbdcacbddabbabdaddcacabcdbccbbdcadaabbacbcacddadbdabbacbbbccbdacbadaacabdbadcbacabacddcadadaabbbadbadadcddccdbbbbddcaddabbbbadabdbaccdbdbbdabadaaddbbbdacbcbbbccbbaadacbdacdaabcbddbdcccacccaadbccaaaabdabccadbbbabcbcbdaccbddcdbbacdbbcbcdacbabacdacacbcbbddabbdbcddbaaacabaddddcbcdcbccbbabdaaabbdacbbdaaabdadbdcbcddacdbaaabcccbdbacbacadbabdbacabaddadcbcdacacdadaddccabdaadbbbabccdbcdcaabbcbbcdbcdbbccbbdbbdadbadabaaadddbbdbacbcababcaacacbadabbbbaaacbccadcdadbdbddadddbabadbbcabccbacccbccdbcdacdbcdcbaabdbdbcadcdaddccdaaaabdccdadcdcbcdbdccdccaccabbcababbdbaaacbdcbcbbdbadcadbaacddcbadbcdadcbdbccbbdbdacacaabadbacacbcabbdccbbdadacacbdbacadcadbbcbdccdbdbdbddcbcadcccaaacbcbbababccabcbbcccccdbddbdadbbabbdcccacdadddaaacabbbdabcbbbbcaccacaabcbaabcdcabbadcadbcdccbdddbbacccbbddddadacbaacdbbcdbccbadcdcdcdcadabcdbcddabacaccabbcacdcdddddcbbddccacaadabbaddcadcadcbcaabbcadaccbcdcdacdcdbadacbaddaaabdbbcadcabbccdadbaaadbbccaaaadbdcaaddacbcbabaabcccccabdadadabcabbdaaacbdbcbcaccccdacbcbcdabccbcbddbccabbabbcadacdaccbadddbbdbcabbbabbacaacdbcbccdddaacbddbaadbbccbaadabbddcacdddbadbdcdacccbbcbcccbdaabbaddcddcbdccacaadaddbbcdacdbaccbacdccbaccddcadaccbaadabbbddbacabbdaabbccabbcdcbcccdadddabdbadadbacbdbccabaadaccaaabbbbabddbababcdcbbbdbbdbdadddabbacdbaaacdcdbdaabaaddbdaccbdbcdcadbababddbcdddbddadcbbcccdbdbbdcddcdddcdbcbbadccaadcaccbbbaccbdabbbacdbacaabcdddacbadbbddcaddabcccdccabcaccacaaddcdbcadbbcdbadddbaabdcccdaddcaddabddbdacccaccadbccbccaabadcabacadbcacdabcbbbbbdaaaaacdacdaabbdbdbadadccadcabaacbbdbcbaaaaacdcdcdbcbaccadbddababaabbacddbbdcacbcccbacacbcbcadccbadabadababdababdcccddddaccabdacbddddaabcbdacadacddbbcabdaccbcaaaccccdcdaccdcccdbcbacbababdbadbcdacacacccbdaadbddcdadcabdaacdcacddacbaaddcdbdbbbdddadbddacbbccbbcbddddddbcdabcbbbacaccbbdcccabbbcdaaaabcabbadbaadabdddacbcdbbbbaaccdbbccdcdcacdbcddbcbcbcaababccbcacaabbcdaacacdadcdbaaacaaabdadbabddddbadabbdcabddbdbddccbabdbdcaaaacacbbbaabbaddbdbbabbbbcccbbddadcddaabbcbdabcdddabaaadaddabadddcacdddddacdcabbaccdaadcdbbaaacabdbbbbcbccaddaaccabbcddaadbaccddcddcdcdabdccbbadacaccacbbcadaaaacccdaabcbddbabccabaacaadabacbdcaabccabddcbcbdcccaddaccaabcdaadbcdcccdacbdbcbbcddcdaddddccdbaaadbcddddbacdbcbdcdddbaabbbdadabdbbdcbbcdbbaacbadabadbabbcbaddcddadaccbccdaaaccbdacacabcdaabcbcbaddbbcdcabdbddabbabadcdcdccadbbbdcdcdabccccbbdbbdcdacbbacdababcacdaaabbdacdccbbaddbadcbaaaabddbdbabccbbaabbbdcdcbabcbdcdabadbadaccddddacbcdaccdacbdbcaaaccccdcadabdddcddaacdcbbdaaabccacbabadbbddabdddadcdcadccaabaaaabadbaddcacaadbababdbbaddbbaccdadaacddacddddadddbabcacbbccdcbccaaabadcabcbccdaabaadabdbddbaadbabcbadadbbddbaaccdcdbcaddbbbabbbcbcaabbbccdcadcdaddabdabcbaaaadbdbbdbaacabcaacdddacaaacbddddaaabcddbbcadddcbadcdddabcdbcacbaccabacabddcdbcdddcdddcabbbdbbaababbabcbcaacbaccbbbcbdcdadabaabdabccbcdbdccacbbbcaabccaccbcdbcacbabbcabdabdccaadcdbcddddbabdbbaaacddddcdcaabaabaaacaacccaaaddabcaacabadbdaccbdadaadbcdcbcabaacdadacbccbdbdcacadbcdadcdabbbcbbadbdabcccbccabbcdbdddbacbaacabdcbbaccdcaabbdbdcdccbdbdbcacdadcadbbadbaaadcdbdcdbbcdddcaddcbdbbbadcbdbbcabaacabcbacbccbddccdacaccbcbcaccadaddbcaacbbacacddaaaadbccdcbbdbdaaabaaabdbcacbdbababbdacdbacccababcccaddcdcabadccacbdbddcdbaddbdddbcbbababbaadcdbacaacdadbcbdadaabdaacddbdcabbaabbdbdadbcbdcbcaaadcadaadcadcbcdccaacadabcccaaabbdadcaaaccdcbddddbbbddbcaabbcacbcaddcbadddabddadbaddbddbcbbcaadcbdaacddaadcbbaddacddaaabdbbcddcacaccbdaddcdaabbbbbabadcbdabbbdacbbdabbdccacdcbccbdbbcbdcdacdaacabaccacdabdccbbcdcbcaaaaabdbdaacbdabbbaabdbcbbdddabbddbbdbaabadbddbbcbcacbdadcbcbdcbbbcdddddbdaddbbdbcaddcddddbaaaccaccddadaabcdbccdbabaccddcbbcddabbcbadaabadbaddabdcdbdaacdbbaadbaabdcbcbbdabaadacddabddcaccddcccdadbbbbaaadcbdbbbcbdaaccdcabcabcbcadcbcdbdcdaacacaabccbadbdbaabcdcbbcdccaadbababbdadcddbbabdbdacadacacaccaddcdcaadaabbadabbaabdabdbabbcdcabdcbdbbbbcddabdabbbcadbdadddcbbddcadacbbbbabcaaabbbdbabdcdbdadbbbbdaabccaaadadaacbacbabacdbbdabdadcddadaadacabcacadabbcdbadcdaddcbdcacbabdbbdcdcbbbaaadcaaabacdcddacaadacacdccacbadabbdcdabccccccdcbacbbabbabccbbaddbdccbbacdaccdacccabccdaabdacbbdddcdcacadaddbabbadaadbbcaabadddaccdadcbdbddddbbbcdddbbbcdddbbcbccaaddbaccbccbabdaddcddadddacbdbbccaacbbcaadadccbdacbccccbdcbbadddbddbcbdcaccacbabbdbcdddbabbdbcbabccccdbddbbadcacddddbbdbdccababbadbaccbdabbcbacdaaabbcadacbdcdababbcaabcbbacbbdddaabaadabdbaadbbdccccadbaaccadcadadcdaadbadcbabdadcdbbbcdaddacadacbdabaddbbaaacbddddbbadccaaadcaaaabcbaacdaaccdacddacaabdddbccaabbcababacdbdcddaaacbaaabcaddddddbaabbcdcdcabaddadddbacbcbabbcacbbbcdcacdcdcdccdccabbbbdaaabdbcccbcccbdbaacdddcacbdadaadcbdabaadadaaaabadbbcbadabaccaabbabbdbddddbcbbaadcaaaaadbadbcdccbbacbabcadcdddbcddaadbaadbbacdcbcaaacbdabdbcdcdadddbadbccccbadacbacbddbdbbcddcabacadcbbbcaabbbddabdbdbbbcdddbaadcbbdccccbbccaadacaadcbddbbbcdcacdcabdbcdccdadadbdbbcbbbccccdaababaabacbcaaaddabaacbdcaddaddcdbbcbcacbabcdbdcbacdbddcccabcaadcdcdaaacbdaacaaaacccabadcbaccbcdadbbddcbabdddacabaabcdbabcdaacdbdbbdbdbcccaabaddadacbdcbbaccdcabdccaadcdbcdadcabddbbcaabadcdaabccdcaabcbdbdcadcbbbdacbaadbbdcdcaddacddcacacdbabcbbaccabaadadbbbbaaaadadabbccbdccbaabbbddaaadddcdccddddcbcdabaccbcbacadcbcbacdaadabbdabcdbaaccacbababcbbdddcbacdadaadaacaddadabddcdbabadcbdbbcdbddbabbcbbaadaabbacbacbdcaacaabadbbcbcacdbddccbbbcdacbbdbbbacdbbdbadccccccaacbccddcabbacdcddaadccdddcacacbbddbcdbbabdcbdabddacbcdcccaabdadbacacccabbddaadbcddabdbbbbbccacbabdccaaabdcbdbacabdddaadacbcbbbddaacacdcdcdbcdbdddbdbacaadbbabddbabcabbdccdadcacabaddaaddbbdaccbabadaaacccbddccdaccdadcbcbabcaaadbbacbbbaaccddaaadbbbabacdabcabaaadabdddbdccaccdbdaaccdacdddcbbdbacadbabdcddadcdcbaddcabacadaadaabaabcbadaddddddcbbaaabddadccacdadcacbbbabbcaaadbdcdacabacbcccddcdaddccbbaaaacbdcabbccdacacbbaacdaddabcdaabcbcaddacdacbabbbdccccbbbcabaacbbddaccbccdcbbbbdabbdbabbdadddaaaacbadddadbcdbbbbdaccdcbbbbcabcabbcbadabdcaddcaccdbddcdccaccddaababadabaaacadabddbdabacadabbbbabbdaddbcabddcbaabbaddbcabdbbaaaaccacabccdcaadbcacbddabbadccacdddbdbdcdbdabcbdddacccaccaacccdabaacddaabadaacbbcdcabcaacbdadabadbabbbacabbcdbcdadacccbdccccadbccdabcbdbccdaadcdaaacbdbddcbadcddbbaaccccbdacbcbcbbadcdcbbdbbaacadaadcdbadbddbdbaabbcabbabcbcdbaaaacaaadababcdaddcccacbaaaabbdcdbbcaccccdaaabacaadbdcaacddaabaadcbbabdbdaacdaaccddccaaddadabcbbacaaacacacdddadaddddbcadbddaabccbdbcdccabbadcbcdcbbcaabbccbaaaddacbbadddccabaabbdbbcbccbabaaccababdddcacdadccdabaabbbaaadcbadbcacbcabbdaadabaccdddccbdcacabdacacdcbbabddccdaadbbbdddbacbcddbdcabaaccaacddababccdbcaacbccdbccdadddaddbaaabacacdbaccadddcbcadabbddccdaaabcbaadcdbbacaaccddddccccbbaacdcbcbbcacabccbcabcbaaddbcbabadbcbcaacadaadacacccdbdadbcabdbcccadaaabbcdaabbacddcaaddacacacbaacaddbdbadabcabbbadbacbdbbcccddbadbaddaabdcbbddaabcbdabaddaacdbdcccdbbdbbbaacaaacadbcdadbcabdbddbdccbaccaddcbabacaddacddcbdacbcaaadaabccbdacbdbdcbdaccdbabcbbbbadadcaabdcbbbcabbdbdcbabaacdacdbadbacbbdcaaacaaabbbaddaaaacacbcaddabaddbbbbdacdcaadbdabcdabbcbdcccaaaabdadadabdabcbdacdcbddaccbbabcddacbdbbacdaacbabccaccdbabdbabbacabbbdddcadcdbbddabbdccbbacdcadabaccbbddbbdaddcbadcabcddacbbaadadcccbcbaccadacbccacacadcbcadcdccabbbdadcbdacbddbaccdaccbcbaaacdcabcbdddbdbddbadcbcdbaadccbdddddcacadbbcadccadbdbacdcddcddadabcdcdddcddcacadbcddddddcdbacddacacdddcbbbcacbccabdbbacccbbabdcbcdbbabcbcbccbcaadadadadbcbbdabbaaabbaadacbbcabddcdbccbdbadbdbdcbdabdabbddbaabdbbbdbbaaddadcbdabdccdaddadabbcdcaccccbbbdcdccbdcbaccaabbcaddacaacbbdbbbdadddccaaaadbdaaddbabbbbaadbdcacdaadbdbcdacaadccacbcdcbaaabddcddaacdbcabcabbaadadcadcddbcabaabcaadcdcabbccaabbadadbaaabbbabccdbaccbbdcabaccccacddbbcdcadccaabaacaddaacbbdbabddadcacdcdcabbcbccdcacdddbbdcbcacdaaaadacdccdbadacaabcadabcbdacdacbcbdacdbdaddcaabdabdbddbdaabbbbadaccaacdddaabddccdcbcadbdabadcdaadcdcccdbcddbadcbbdbcbacbdcadbdcacbbdadcbcaabdccdaaccaddcbcadccabdddcabbaadcacdadccdddcbcadcbaccdaddadbbcccdbbbaddbadcbddacbcbbdbbdccbdcbaabcbdcabcadcaadcaccbdabccdbabaabaccdcdadbdaadadaddbadbaacdaaaacacaabdaaccbcccddbbbbaaacdccadadadacadbdabdbdddcdadbadcddbbadddcccdcacbdabbdadddcabcbdbdbbddabaabaccabdbbcbddcadcbcbdbdcdbcadaabcbbacaddbbddddbcdadcdbadcbbdcacddbaaccdddcaacbcccbbdcbccbbabbbccbbaccdbbbcaabbbdcbdabacbabddbaddbcbdccdddbbbbadcaddbadbbdaddcaccaccbdbcdcadbabcbccadbcdbdcadbabbdbadbcdadcdbbabdcddacacabdaabdddbccdddcbbcbccabcdadabcacddbacaacdacdbdddabcbcdcaddabbdbcbaddacbdabcbaabccaabaabcaabdcbadaddbbcaaabadbdccacbccabbdbaaccccccbacdacbbaddccdccbadbdccaaccdbddccbddbadadcaabdbbcdaaadadaabbdcdbdadbadaaddcddbabddacddabddbbccccdbbbddbcddaccddadabccbabddacacaaaaddabcdccbddaaccabaabdacdbbacadddccdddbbadadcbbbdabcbadddddcadaacbdccbdaccddbbadadbbaadacdabcbcbadbccdadabbdbbadcdaddbcddaabaccacaabccccabbbacaaccdbdacccbccdcbbcdcdbddccbabaababdcbbccbbaacdcacdacaacaabacdcbddbdcadacabcaccccbcdcabacbbbbdcdccdaabcacbbdcbbdcdddcadcabcdaacdaccbdddabbabaaacacadbacacddacbcbacbaaaacbaaadacbbbbaddaabaaccccdbacabcdddcbcdacccdacdaaaaddacacdddccbaddccdbaaadbcabdcdcabdaccdcadbbaacacdcbbdbdcdbaabcddcbbdbccdbdaacdbabbaddbbcbcdbaddcacdcabdccdbdddcbbdcabbaddcdddacaaacacaccabcbbdcabdbaaddddacbdbcbdddcdbaddabbbbdbabddaadcbdcacbcaabdabcdadaadacacccdbabbcdbaccdddccaddacabdbcddbdbddadbbbdadbcbabcbaabadabbbaaaddcddccaabbababadadaacbaddcdbabaacabadcccbcbccdabcadcaddaddddbabdacbabbcccbcbbdacaccacccdabcddbabdcacdcaabdddabacccccddacaccbadaddacbdaabbaacaccacacdaadadcbdbdaaacbadcddaabdcbbbdcaababbaabdddadadabbbbcbbdacaaababdbdadcbccbcacdcbacbdadababadabadddbaccaccbcaaaccaccbaabadbcacbabbacdbdcdacabdddcbbabdcbbbbbbaabbadccccaccddabbbacdbabcbdbccdbabcdcbaaddbdbdcbaadadcdcaabccbcaabdbbbddbdbddabdadcabccdbadcdcabcaaaddbdaccbcacabdbcaddacdaadbbdacbcababbbdbacdabcdcaaacbddddcdbdcdadabcacddabdddaddcadadbdbddbcbbbabdbbaaadbcddaddbbadbaadadadcacdbdcdabcddbbccdbcdbaadcacbbdcabddbaabcdcacbabbcccaccdaaabdccbababdcbacadddbcabaadcbbdddcddccdacadbdcadacdacddbdbbbdcaabcbddbcdcbbbacdbdbbaacdacadcdacdabacdcdbbccdbcccdcbadcddcdcabbdcacdddaabdbdbbcaadbccadacdadaaccabbdcddddbbcacdbacbdacbadbababdabbdbbcccbbcabdadddacdcbdcabbaacacaacacddbcbaaddbddbadbbbaaaabbcdcbbdaacccbcbadddcccdbaadacbaaddbcbbbcdcacbbcdadbdddbcacadcadcabdccbcdccadcccabacabccdaaabbbbbaaacccdacdccbabbdbcbbcdccbbccadbabdbbcabcdbacacadddbbdadcaaadccacbcdaddcaacbdcdaacaccadadddbabcccbbdbabddbccccdbaaabbbaddaadbaddbbdbccbdbddaaaadbcaccbcdaabdcbbaddaadcbcbabcdbabaccdbddbcbcbbbadbdbbacddbbccbdcabcdbdbbcdccaaaadbdddcddddcbbcaabdbbbaddadaabaddddbabbdcbcdbcadbdddcacaddccbdcbcaabcdbaddbccdbabdabdbbdddccbcbcadabdbbdbdabbccbacddbabcbdbdbadacdcddbccdcdabdabdacccccabcbabaaaaacadccdcbcaaadbaacccabdabbcacacbbbbbbddcdbcabdcaadddaddaabdacaacbcccdbadaaddabaaccabdccccdbddbcdadbddcadccbbabdccdcaabcddbadcabccdcabdbcabdcdddcadbbcbabaccbcaaccbbaabcbcadcddacaabbdccdbdbdbdabdcaaddbcaadbdaccacdbcaaddadaaacdadbdddccdbadbddccdacccbabbadcccdcbaabbbbcbdaddddbccddbdcadbddbdcadbddbbbbccabcbcaaabbddbbcddabdabbbadccdccdbacaccdadbdadbccaaddaacbcdcccbababaadcbaacdcadcabdddbcbdcbccaacbdcdcbdaccabdddacbdcadcccdacdacabacdcabcccdddcabcbbcbaacaccccdbcdabacabababcdaabccbddbdbacbbbdddcabcdbbbdcbaaaabcbadadcadbdbbbcdabcbcdcaababaddbacbbdbbcbcdddccadadcabdcaaccbaddaddaaaccbadadbcbadcbaabaddbaabbabbbbbabbdcbbbccacadbccbdaddadadbbddadadbcadbddaaabcabdaddcadabccbabaccccdbacbccaaaddcdbcdddacbdacadbadcaccabddbcdaaccdddabadbdaddbdadbcbabcacdacccbdbddddbdccbcbcdacabcbcdcadbabbbbaddadbcaabcaacdcdbdbaaccbccbadcacbdacddcdacabdcbcccaadaadcdaccdaccdddddddbbccccdccacadddbddcdccacbabaaabdaacaadbcadacdcdbbaaadaccadacbcaadbdababddcdbbdaaaabaddaabadbcbdabdbadaacccaddbadaccccabaacabadbacdabadacaadcbdacccbabaccdadcdbbbcbdbdaadccaccabddacaddabcccadabcccbcacababbdadaabccccaabcdcbbcabcdaadbbacdaaddbadddbdcabdaaadbaddaddddddcbdaadaaacbabbbdabcadcddaaccdbdacdaaddccabdbbbdaaaddbdabcabbbaaaabdaacacbbdcbaacdadbccabaabcdadbbbbcbdccacacdbcabadbbcccabdbcdbccdbbcccdbdcaddccddbdbaacdcadddbaddcdbccdabcbbdabaaccbdcbadbddadbdcbaacdcdacabadcbdbdabadbcadcdbaaaaddbaabbaacbaccbddddbdbbccadababdabccbdacbdaaadadcdcdbcbcaadbbadcaaccccdacbdaadcbcdbaacddcccbcdcdcadcdccbdbcbaaaacdcabdddcdcbadcccdbcdcbddabbaccccddaddaddbaadbdddcacbdaadaddaacbabcbadcdbacbbcbbccbdddacaccabccbdcdddbbbacacaabcdcacbcdacdabcabadbbcdbacdbdcbadbccccadbcadcbbadddddabbdcbbdadcbdbcccdbabcbcacbdbddbdccbcaaabaddbddbbdcdcbbdbcaadbcaacabdbbaadbddcccaddbabbddddddbccddbbcbcccdababdaabdbbdacccdaaaaadcaddabcbaaddccabdadaddbabbdcdbbdbddddbaaaddcaccabcbbcbaccabccdccacbacadbaacccbcbddbcccadaaddcadacccbcbcbccbaccaccdddccdbaacaabdbddcbcbabbcbbdbcdbddbdccadbbbcbdcdddaaacbcdabaacdbdcaddbaadcadcbbbcacbbdcddbdaacdccccddbabcdadbdadcbddbababaabcdbbbbdbaacadbccacccbbdcbadbcbbadbddaacadcbdbaccccaccdadbccccddadaacbadcadcbbddddcccdbdddccbdaacccbccbbbddbadaacdbcccdadcdbbadabadaaacacacaaddcacacdbbabaacbcdcdbabcddbcbaaacbaabdadcadaadbcbddbbacccbdcabaacadcdadbacdcdbcccdbbccddbaabbbddcbcabbdabcbaacaadbbabdacdcdabdbdccadbddcdaaccdabbdbacadaccccaabcaadbcbcaadbbbccbbbaadbadabdadadcabadacaaddcacbbabbacddccbabaaaddcadccabbdccccadaddabbcdddbadccbaccbaaddbabbcababcdacaddbbddbaccadaaccabdcacadccbabaadddccbaaabbabadccbcbbdddbdacaabaacaddccaadcccaabbbbcdddcbdcbdbacaaddcabcacdbacddbbcccabdaaadacdbbbcaaadbdbaccbcdbcadcdabbaacddacacbdbcdbaabdbcbbcddbcbcbcbbcdbacacadabcacbcbcaddaaccddbabadcdbdbcbdabccdacbdcabcdbbcbcabcaacdcdcabdcacadccbbdcbcdbcaacbddaaaaddabcdddbccaacdcaaaabcdcdbadaaadbabaadaddbdcbcbcadccabccccbcbabbacadbbbbbbbbaaabccacaccadaabacdcacacaddbadaddcdacdaddddacaacdbaccbbbabccabdcddaaabccaaaacaacbbacabdbbbbcddbdbbaaadaccbdcddabdbaadcbbcddbccccbccbbbdababbdbdbababbaaadddbdbabadcccbddbbadbbcbcadbdadbaddbbcbabbddcabcbaaccadbdccbacadcabbbdbcbdabbbbdccadbaccaaadacacacbddcadcababdddbcdcbdaccaddcaddadaaddbdacdcbccdaccddcbabbdabcbacccdbacdcdadcdcdcbcbaddaccadacbadbddccacccabbdacddadcdbaadccdaccdccbdaabacaadbbaabbcaabdabaadbcbcabbcabbbdbbaadcdbcbbdcddbbaaabccbcbabcadcdcbbaaabcbdbbcccbbddcdadddaddcdcabacddadaacbcacadaaacadddaaacbcacbdbdcbcdbadcbdddcbabaabdbdbbadbbbbabbbbddcacabddaaacccabddccbbcdccbcdbcbccbcaabcccadbdddbbdabaddddbcabbccccabbcdacacbbabbdbabacaaddccccaababcdbbcbbcdabaabadcdcddbcaaccbbdaacddcababbacbbdcdbddadadababddababdddddcccccadcccacaddbcccaddbdacabadbcdbccdadcbbacaacabbdbdcaadcccadccdadddaaccdabbbabcdaacabbbabaabbaabadabbcbbaacbdaaabbdddddabcdbadbcdcadacdcccbcacaaccbccabddbbdcdbbdbbbdcacbcabbbcdccaaaacacbcacdabbdacdcbbdcbcddbcdcdabbbdbabaddacdadacaccbcdcdcabddcbabbdddadbbadcaddcbcbcaccbadbdbbbacabacbacbadacadbacdbbcbdabccccbbdbcadcdadcccccbbddabdaadaadccbdabbccdbdcbacbcbadcacbaadddadcbaddbacdbbacdccacbbbdacccbcbacaaadcbabbdacccbdbaddcdcddcbdadadabbcaddcdbbcbccdbdacbcbdbaccbabcdbadacdcdaacabddcbbadabcbcacdababbaccdbbaaacdcbcbdaccbbcadcacbabcdbbcabbdddddccbbbaadcccdddccbaabbabdcdccaaddbbabdbddbccccdadcddbdbbbaadcabadbacadddccdbccbbdddcacdaabdbadbacbcbabbaaaacddbddbaabdbcaacabdbcadcdddcccdaaacabadaaccccdbccdcaadcccdbccdccdbadddcbacabacdcbcbaadbaccdcbbbaadcdcccbbddaddadaaaaabbdbaccabadccacacabdbadbbdcbbccddcabaccdcaaabdaacdcccaacccabacbadcccbbbcdbacbaabababbadbcaaaadddbddbaadaaaacdabddccabddabdcccbdbbcdcbdccbcccdaabaaddabcadacbaddacadbbacacbdabbdbbccdadcdcaaddabcddadcbbdbabbaacacbcbccaccbaabddbbdcddbcbdbbdddacddbbdbbddcbbdaabbbabccdaaaaabdabbdddcaabdbaacabaabcdcacabdcbbdbaadbcbdaacdadbcadcbdddccbddaacadbbccaacbbbbbacbddcccccbabcacbdacacccdcbbbaddbaadacaabdccdacabdcaabddaadadaacaaaacaacbcdabddabdadbcbcbbabbadcdbddcdacbcccdddbcbaccdabacdabddccbbcacddadddacbdbdccdccacbcacbcbdbbacdaccbccdccdacddccdcdadbccccdaddadaddbccdbddbdcaabccbbdaccaadcddaddcdcbcccdccadadbccbbdbdbccaaabcabdcaaabbbbadacaacaddddbbbcacbadacccaddccaddbbcbcadbcbbdcadcdbadaccdcdcadcaccccddbabbddbbadddcbdbcbcdccaddcbbcdbaacbbacabcadacdbbcbacdddcacdccdcbbbddbabddcddaaabcabaddccdddbdabadadccbadcabbbdcdaaadbcdcddcbcabbabaabcaaccbcbaddaaaacaddbdacabdcabbbcdaacdbcddbdbbdccbdccdccddababbbaadbcababaccddccbdbcdcaabacbbdbdcbddccaadbabbabdddbabaacccddccdaccbbbabcbbaaabcdadbddbbccccdacadaddcaaabdddbdadbdabcddbbdaabaaccbaaabbaddcadbacaaacbcdaaaadcdcccbdbdbaccacdddaadabaadababcaadabbdbbacdbabbdabacacbbcdddbcaaaccdabdbaddddaccbdbdbdddadaaccdccbacabdacbbdcdabbbcaddaccaaabacdddbddaaccddbccadaddcacaaacaacbdabacbabbdabcccdbbbdddbaaddbdacddadddabcbabbabbcdcbbbbbbdcbdbabdbdbabaaadbbadaaaabaaacadcabddbbdaaccdabbdbaaadcdbcabccbbdadccaaaddcabdcccdccadbddccddadacbccadabccdcbccdddcadbbdaaadddabcdbddccbcbddbbaabcdcccdddcabddbbdccbddaabaccdaddbdcccbaabcbdabbbdbcbdacadccccccddbcdddccbcbabbcbdbcadcabcddabbcadaadaabcbbbdcddabdcacdccacaaccdbdacaadadbbcabadadbcbadbacccaabdbbabddccbdbbcbdadbbcacdbbcadbaaaabdbbbbaccccadaccdcbbadddbdabcdbbacacdcbadaacaccaabdbdacaccbabdaaaabaabccbaaaaccddaacdaccdbbdacddcdbbbdacdaacdcdacaadbabccdbddcbbccddccaaaadbabdbcccbddcacccaacdadabdbbcdaadbbcaadbbcbacdacbacbaaacccabaaacbdccccccdbadcaadcadbdababbcbbcddbbcdaccacdbbbccaadddcadadadbcbabbcbddbaaaadbdcbacccbadcbaacdddacbadbacadbbbbadddbbadcddcacbcadacabdccddcdaabbcaabdcbabbcbadbdaccbcdbbacbdabdbbbacdcacdabbcacdbcddacaaccbcdbabcddcabaaddbcdcbdadcccbdbcacddabcdbadcabdbadcbaaabbbdbddddcccadddccbadbcbbadcdabcbdbddbbbbdcccabcacbbcdbccaddcbcacdbcbcbbdabbaddcdcdadcbdcdaaabaadddcacbbdbaddcadacabcbdacbbbcbbdbddbbbdabdcbcdabcdbacbcbdbbdbacdbdcadbadcdbddbcdadaacbacadcbdbdbabccacccdcbbaaccdbdbcccdadcbcdccdbbbadbcabddbcdcaabbbdaddcbdccbabccdaccddaacdcbdaaccaadaccadbcdcbdccbbabcdcbbdaacabcacbbddcdbbdadccdcbbdaaaaaaaaaddcbbccdaadabcdcadcbaccdbbacaababbaacacaadddcaadbcaabcccbaccdaabcbcacbcaacbaaddbbcbabdadcbcaabcdbcbdadadcdbbcacbbcdaccddacdbcbcbdbacacabdaaaabcbcbabdabadbadcaabaabdbbadacdbadcaabdccccddccdaadabddaadcaabcaaccbaabacbddacbbaddddbdabcadcaddccaaaddcaccccdcabdaacdcbbddddbadbadbdcaaddaadbcabbaaabababbdcdbdbabdcdbbdcaddcbdadbdabddccacccbcbcaadadaabaaaabbacaccaccaccdcadaadccbadcdaccacbcacadbdbbaddcdcddcdccbccdbaccbddbbbadaadaccbabaabdcacdabbabaabdacadacccadcaababdbcaaaccdcdcbbcadbcadabcbabcdacddcdcbdadcddbdddadacabcdcdabbaacddcdddddcadacccbdaccbacdbacbdbdabadadcaadadadabaaaabbacdcabccbaacabbbadbcacdbcdabbacddddbadabbcadadadddbbbabdbcccaaaaadbdcdcaccbadbdddaaacdccbbcbadccdcacbaccdcaabbddccddbbdcbcbdacbbdbbdbdacbacacadaacadacabcdacadaaadcadddcdddadabacbbabbabbacbbcaabddacdacadaaaddabdccbdbaacabdcacddabbbccbaaadcddabcacdbacacaacdadabaabdddaccdabdccbdcaaddcbdaabcbabbaadbadabaadadbbcbbadbdcaaacdbcbcccbddbbbadbcbdacbbdaacadadbbdcaaaabccdbbbccccabbbacacabcacbaacdacdcdddacbdddcbccacdccdcacadcbcbdcbdcdcdabccadacabadaccccbdadcbadacadccbdbcdabdaabacacdadaabbcaaddcbbdcabdcbdbcdbcddacbcbbadababdbbbbcadcdbdadacabdbccbabbbabdddaabbacdabbcabdabdcccbcdabaaaabcdacccaacdaaacadadddbdabcadddcccadbcbbdaddbabbaaadcbbbcbdddbccaabdccdbbaccdccadcacbcccdadaabbbadccdcabbdddabdaccccbbcbadcbbaccddaccacbaaabddbcadcccdcccbabdccdbddccbabcadcbababacbddabcbdcaaccdadbadbbaadccabdbaddcdbbacdbdddaaacbcdccbdbccadbbccbbabcadcdabacbcdcdcaccdaacdbdacabacddbaccbcabddcbaadbcbaadbbbadcacdaddcddbdabadbcadddccabcadbddcadadadacacbadbbdccbaabadbbccdabbdbaacaacccdcdbcbdccbcbadccdadcbcdbaacbbdcddcabbadcbbcadbdbcddcadaacddcadbacaabddabdacbcbdabaacccdadabdbddcbbacbccbaabbbbbacdbadacababbdbdccabcadddcaaddcaadaacababddccacbcdaaaccdbccadcaaddbcdbcddcbcacbdccadcbbdcdcbbcdcddcadacbbbdadcbbaccdacacddabaddabdbbcbacccdbccaddddadbbabbcbadcbddbddadccabdcbcadcccadbacbdaccaacaacbcbbaabccdbbdcbadbccdabcadbcadcaaccacaaadcbdbbddbdadddbcdccbbbccddcaacdaccbbcaaacbabccbbcaadbddbbcbcaabbbaccadbadbbbadbbaaddadadbacdbbdbcbabdbacabcccccaddababdcbadbaccacaccbabaaabcaabbddbaaabbdbbcbdacaddcabbdcbcabdaabadccdddbbcdcbacdacccdcaabadacbbdadbbbdbcacdabcdddaadadbacadaaaacabcaacbddcabcdaacbddcacaabdbcddbacbdbadbdadabcbaddddaabbcadbbadcbcacbcdcdcbccaacdddaadccaacdcacaabbcbdacdbbbacacbbaaadcdbacabadcdcaadcbddadbcdacaacaacacabbdabacacccbbbdcbacbddaababdcadccddaaaaaaacacaccabadcbaadbbcbcaddbbbaccdbacbccaacddaaaddaadcabdacbabbcbdbaddcccacaabbadacabddddabbbddbbaddccddccccdccccacdaabaccbcbdaabccacbababccbdbdddbcdbcdcddcdbcabaaabbcaccaccdcdccadaabbcadcdadddbccbacbddcddccabdaabacdaaaadacacbaabbbabbddcdbdadaaaaddcdddabacaccdbbbacbbddddbdaddbcdcdcbabbcaabadccdccaadbddccabdcddacbddbbbcbaaacbacdacbcbbcdccccaaccbdbadbccdcdbbacacdcdccacabacacbbddacddadbddcbdddcbaadbaddabdbbcdbaabbbaadddddbbcbccbdccddbdbcbcbcbdcccdacdccddadbabddcbdadbbdbaadabdccbabaaaabcaddcacdbddbacacadcabdcadcddbdadabdaddaadadbbaadadacdacaccbbaaddabbdbdabdcbdccbcaddabacbddbdcacbbddbbdcbadcdacadcaacccccaaddbabddbdabdcaacbcaadcdacbbdcbababcaacdbddddbdabadddcdbaaacdbbdbdccabdcdabbaaababaccdbcbcccbbddcdcdbbdabdcbbaabdbcbdbaaabbcabdadbbdadabbbbbbbbdcbaadccaddacdbaaadaaadddbdbdbaaadabdabbddbbcbbadaaabdddaddaccbadbaadadadaacbaadcddcbccbdcdadabdddcabaacbaccaacbcccdbbadbadcbdacacbabcdaccbabacbddcbbbcadbccbddbbcacbaaaaaddbbddcbaacdcaacdcdbadaabbbaaaacccaadbddbbdcdbbcbcdbaabbadbdcdbccbdaaddacdbbababbadbcacddbdaaaccabacccdcbdbdbbbdbdddbdabbccdaaadcadddbacddbdbbacbcddaddbbbdbbcbacdcabcdbcacdcbbdbaaabaaddbbdbacbdcacadcdcdccbcaddbddccccaadcbdbdacbcbadcacaccbaacdabcdaddcadcacabacbacabcdccbddcabdbbcabdbdcaabbaddacccdbbcdddbddbcdaddbcbbbacbdddccacbaaaaadccbcadcaddbaacddbdcadbcdcddadbacbbcadddabdbcbaadcababdbdcaabddbdbcdacbddcabdccdbbcddddbbcbacddbbdbbabcbdddcbcccdbcbdcbaadbcbdbdbbccbdcdaadbddbaaadabbddcabccaaacdccbdaabbbbddcaddddbabbdadddadadddbcacccbbdbabcbaaacacbaccddbcddbbccaaacbbdaabaddccabdcbccabdabdabaadbdddbbdaacdbbbdcacdbcddabbbaaaddbcddbcbcabccacacccbdbcbacacdbbbbbdccddbcabbbbdbaccaaccadcdcaadcbcbccaacabcdddcadcccdbabadccbbcdcbcaddabbaaacdcabdddbcabdcaccdbdabacdccbbbaaacdabcccdcabcabcacdcaddbbcccdaabcadacdacbadcdadccabdcaaddbaaadaabbcbabdadbcdccbddbdbabcbddcccbcaaacaabbbcadadcbbcccbdadcbccdcacabbaccabddaabcdddddddddabdadcadccbabbbaaacbcddccaacdaaccadbabddbdbdbaddbdcddcbddbcccdcbbaccbcbccbcdddddadabcdbaacdcddbcdbadadbdababaabbacabcaccacacdacadcbbdbcccabdadbabddcabbcddadababbbdcabdcaccaaadabbbccddddaacdbaccbbcbccacdadcddcbcaacccdbbcacaadcbbbbbadabdbadddccdcababbbaaaccabacbcbddbababdcdacaaadccdddabdcacbdcaccadadcdaddacbddcdcdcbdcacddbadddccdcbbcccbaacabcbccacdbbdcdbcdaddbcdcbcbacccbbbcadcbdcbccdababacaacacddbaccacddcdddacbbddddcddbaadbddbdcaabdcdcbcdcbbcccabbaacadbcbbdaabaabadabacadcacdbccacadbbcbbdccabdbbbcbbdcbcaaaadcbaadcaacddaaccabadccccbddcaddaddacacbbccbdabadaabbbabaddabbcbccabdcabdbcccadbdbcbccbbcaddddcdbdbdaaaabadabdbbddcdabcabcddcbdddbbbacdcdadababacbcaddbadcdbcacdacbcdadccdbbdaaaacbdbdcbccaddadbbccacccdbabacdccbbcabbccdbbdddcddcdadabcaabbddbdaccabaaacdabcabbbcdcdacbcdcaaabdcddbaabddbabddaadbacdcbbadaccccbaaadcbaddcacbdbdbbbbcbaadccbaccabbbadacdadcadbdabadddcdbbdbdbacbdbbaaaabdcdaacabaccdaccdddbaabaaabaacbcbbbddccaabcccadacdcacdadccdcabdbdbbdcbadcbadcabdabdcdddcdabccacdcabdcdbbcbcdddaaadbbabddddbdabbbcccabbacbcbbdaccddcdbccacdbbcccadaaddaadddccaccbcdbacccccdbabbdbacddddddacaabcabadbdadcdcddbddbbabaccadbbddcccdcbbbbdbcbdcddbaabbdbcbaaccbcbddccbaacdddabcabbdadadbbdcabaddcaabcacdbaadbccabbdacaabdadadbaccbdcdccaadabbabccbbbddcaacbcbbaacabccdaddcccacbcbcbccbbacbaccdcbbbacdbcddbbccdacdacaadcbddcbccbdbadcadbccbccaabaadbcaddbcaaddcabdaacccaabccbcddaccaddddabaddcdaddbdcdbadbdddbdcdbdbdaacbbcdbcaadcaabcaccddadbcdcaadacaddddcbbcadbaabddddcadadaccdabadaababbcabababcabaccdbabdbbdabbddcacbcdbdcbbcadccbdddbacbabdcacddabaacdcbcaabdaacdaababadaabbbbacbdaacabcdcdabbadcbacaddbbddbbccabbbdddcdcbdbabdcccddaacdbbbdbbadaacbbcdccdbbbbbbcddddaaadccdbbaddbbcdaaaacbbbaccccdbbacbadddcdabdbaccccddcdcbaaddcddabdadaaccabaacaacbbabaddabcbacadbcabcaaadbcacbadabbddbbababcbabddddaabccadabadddcccdddabdbbcabbbccccbcabdcaaccbccabccddddabbdbadcddbaccddacacddccddbcdcdbaabbbbccddaababbdbaadcbdbbdabccdbabdcdbdbdcaaababcdbdddbabadbcaabbddddabdddacaacbbbabccbadccacdcaaddcacacdcaaaaabcacaabdbcddddbdcbdacbdaccadabdaddccdcbbdccaaabbbabbddbcdbbdcaaccbbbccdcdddaddaddddbaddddabcaacbdcbcdacbaaacbcadbacdcacddcadbdcddbbcccbdbcaadaaaddcdcbbbbdcddbbababcbcbadbdcdbdbabdacabbdabcdaadcbbdbcbbaccbaacbcabbdddcbddbdadcbcbbbdcabdabbdcdcbadcbadbacdcdccbcacbdaaabcbadcacdbcbddacdaacddbddadcccdbcdbcdaadbcdcdddbddcadacabccaddcbbaadadddadbbcddaccdbcacabacdadacbdbbbbddaacdbdbbbcdabdddcdacbaacacbadbabbbdabdabadbcbaacddcbaacdcdabdbaabccaadabcbbdabdabbacbadaadcbcdbcdaccccbabcbddbaabccbdccabbdcdccdacbadccaadbdacabcdbbbdabdccacaaaaaddaadcdcdcdabacbdaaacdddddcbdcadddadbddacdcabdabccbdabdbacacdcabcaccabdbbcbbacbddaadbabccbccbadccaddbdcbbaddddbcccacdcabddabdbcbaacdbbbcaaacddbbddadccadbdcddbcadcbbbcaabcbbdadbdbcdaadddbcbdddcbcababacaadacacbabdbaabadccdabcbbccdbadaabdbaddcbbababacacbcaadcddadbdbbdaabcdaabbbdaccbbdacaadbcbdcdadaadcbbbcccdcbbbccacaccacbbbdddbaaddacddaaadbcdddadabbbdcabcadabadbcbbbcbcbdcccacabbccdcddbaababddbbccddbdbbbbbbbbbdbdcdaaabbddddaddbdbadcddcaabdbccaabbdbbaddcdaaacaaaacbadbcbcacbacddcabdcacbcbaadabbdbbdaaddaccbbbbbccbaddcbbacadbccddacddbabdabdadacbbdaabdcbcaabcddcabddcadacbbdacbdbcbcacbbaabccaabccbdaadbdaacdcdddcdbdcbacdbacacdaaaaccbabacdacbcacbacadbabadddabdcbabddddaccdccbccaccbabccdcbacadccaacaddbabcbbdacbdbdbccbdcadbaabbcdbaabcacadddbaabacddaccdccdabdaacddaadccdcccbccdcaacbcdabcbdadddbbddbcaddddcdcbdcbcaabacdcbbcbcdddddabddacbbdbccadcaaaabccbcbacabcdacabcdddddabdcaaaaabcbbadccccbbbbadbccbcdcabcddcacddddbbcbccdacabbcabaaaccbbcadaabbaadabbcbcbaacadabbbadcccbddcbbdaabacabbdbaabddccadbcaccdbabddaababcbadcbaacccbdaccabbabcdcadcdccdbbabbdbbdcdaaddbabbbbaaaaaddbcadccdacdacbdcababaacbdaabaabcacbaabaaacbdaccbdbdbbabbdbaddbbdacdbbbabddbaccbacdbaacaadaaccabdacdbabbdabccaadddbcbaaccbbdddbbabdaacbbdaaccaccbdcabadadaaabdccdddccdacacbcadaccddadcbbccacdbbbacaddbdadbcccccdbbccccdccbbdcabadadccbacabbdcbcbbcccbdccdacdccbccdbdbaccbcbdaabacbaaddcbacbcdadadbdcaaaaacdaddcdabdabcadbcbcdddcbbdadbaabacdabcbcababadaabbcbbcadcdbacccadadbabaacdccbdabcdbdcbaabaadbcabdbdccacdacabcadacbaabdddababbbbdddaddadcccdbdccadbaadbbcaddcabdcabdaccdadababadbcbabacacbdabdcbaaddaddcbacbdddaabaacacabcddacccdacbcbdcbcdbbcabcadabbdbddbaaaaaabdccaadbbbbdccbbdccddaaacccadccdcbdabcdadcbcbbbbbaccdbadbcddcdccaaddbdbacdaaddbaacaadbdbdcdccbacbddbbdbbbcbabdcdadbdaadbcabdbadbbcdbcbdababccaadcbcabaadadcbadacaadaccbacacacbccdddaddcbcdadaabccbabdccaabbdbacdcbbdacccbadbbdcbbccacdddaadcdbdbddbaaacdcdbdadbadaddcaaaabadadcbcccdcbcccabadbcbccaaddddaadaadadadcaaddccbbabbdabccdababacbcbadcbbdcbccbbcdddbdadabbaaacdccccacdbacdcdcaddbacabcaaddcddaddcabbdcbacabaddbbbcabccaaaabccabdccbdababcdbcbbabdbaccaacdadbbcacadcdacccaacaabcdbbabcaaaaacdbaadbbdaadaadabdbcdcadabcacbbbccbddaaabdaddbbbcdbcbbccbbdaabdadcabbcdccacacaddddddaaaddabacbadbaadbcddcadbbaabcadbcbdaabcddcdbacadcabcdbcababbddbacacaabdbbddbbcdddbadcabcadcbacdcaacdbcbbacccdcbcbbacadcaddcaddcaabccaacdbdccadadaadccdaaddaccdbbcdccdddbdcbccbdabdbbacabdccdddcaccaadbcdaabcdbabdcbdacadaccaadcbaccaabbdbabacdadbdddcdbabcbcacaddbbbbdbbbcdcbdaccbbdddcdcbacdddcbcabdadddbdcacbbcdcabacbaddddcccbccaacacdcdbadcdabdbdabddcaccacdbdaaccbddcbaacbdddbddbaadcaaccabbabaddbaddabacacabdbabddddbbbcabdbabaaabaccbadcabacaaaadcaabdbddaadbdbbddababdacabbaddbabbaacacccbcadbbbcccbacdbcabddaccbdccdabadadacccccdbaadbcbccaabcccbcccdbabcddddcaaccddadaadcbadbbdcaddbaabccbabaaabcaaccabddabbdbaaadcdaccbdddadcababbdbcacdabcbdcddccdddcbcddaacaacbcabdbbcaccbddcdcababbdaddddcbacdcdaabaddcacbcaacabbcbcaadddbaaddcabbadcbbccbbaacbdaacaaacacdadbbbddaabcddcbadbcaabddcadacbbddbcabdbdaddbdcacaddcaaacadcbdbbbdaaaaabbcbbcacdadcadabcbbbdcdccdcbcdaabaccbcdbccbabdddbddabdbdacdabcbdabdcdaacbdcdacbacdcaadccdacabcadbcccdbbadcdcbbbdaadacbbaadcbbdbccacdcaccddbadbcbcddacdcadbddaabacdbccbaabdababdbdbccdbacaabdbcddbabbdbabddbdbadaddcbaddadbdccaaccddabbbacaaccddcdcdbddcabdbacaacddcdacddbbddcababdabdcdadbaddcdbababccaacabdabbcbdadadbbadcccabadbaadababbabdbccaabddbbdaccacbbaccabaacdacdcaadbcabbbdcadbbbacbbbcacccdbacbadbdaacabcdbddadccddaacdabdddbbbbbcdbbccbbcccadccabbccaacbccbdaddbbadcaacdccdaaababcbbadccdabccbcaddadacaddcdbddcddabcdacaccaacacdabbcdbaadaacbdccbddbaccbcdbbbcbbaddcddaddddccbccdabddcdaaccbbccadcadbbdbcabacdcdcacbbccdaaddddaaabdcbbcdadabaaaaaccccaaacdabbbabcbdabbdaddbacabbaacbcaabcdaacdccccabcccbbcddbcaabbacbcddccadccadbccddadadaacaddacaabadbaaaacdacccacdbccdaacddcbccbaadabcbcadbaccbdbabdbccaccdbaccbbcdcaadbabaddbbcdbacbaccdcddbaadbaaaccabaaabcabadacaadcccddbdcbcbbccbcdbadbcdadbcabbbdcdacbabbadbbccabcdbbcbddcbaaaaccbbadabdaabaabaabaaacdcdabbaadaadbbcaabcbcbbbaacddaddcdabbadabbdbaadccbdbabdccaacbdbcbddbdcabcacbddbaabbdbdcaaacaaaabbbcacdcdcddcdbdddaddacbcaccacaddddadcaaccabcdcdbaadbdadadbddcbbaabaabbdacbbbaacdacdbddacaaadbdcddcbacdaadcdaaaacadaaabdccabcdaadddbdbddbbadabdaaaadddbdccdbadccbdcbdbaadbcdbcccadbaabdbadcbdbabdbcdbcccccdbccdbaccbccbabcddcbbaccdbdcacbdadbdccabbcccbdcacddcababdcbcacccbabdbaaaaaddddcbcbbddbbdbdddaddacbcaadbddcdbabacbbacbabdbacabdbdbcbabddbcadadbbbddcdcbccdcaababdccbddcacaaadabbcaabaadcbbbaaabbcdcacdcbdbdcaaadaacacdadccbcbabcbddcabdaaabcbacdddbccabdbcccddaadbcaacabddadaacabbbbababcadddddbdbbdaacddddadcbdddbbabcdbcdcacbcdaaadbbccdcaaccabdcdddacdccacabadccabbbcaddadbcdbaaacdcdcadaacbacaacacaacacbcacacacaddcdabcccabadbadaaabbcccbdbabccbabdcadcccabbcaacccabdcbadcbdcbdcddacccbacccbdbdcadcbbccccbaadbacdacdbcccbbbdcbacbdacabadcabbaadbccbabdbbacabcdccadaadadbacdbcacbacbdcbadbbccddcdaaddbbdbbdbcdcddbdaaaacbddcdcdbcaabcdbdbbacacdcddcccbcdaacabbdbdddbccabdababdcbaaaaccbcdcbaccdcadbcbbabcdadaadccddabbaacaadabbcaabdbbbcbadcdddabbcdabaaaadccddbbbddacccddccbccbdbdaccaadadddcdaaadddcbddacbcbaaacdcddbbacdbcdbdbbcdadbdbbbdbdbcabbdabacbdaccdbadaacdcbacdcacdacdabacaddcaadaacddcdcddddbbadbbbcacaaccaadaccbdccbbddabbbccdadaddcbabbbcaacaabbbbcdccadcaacbbbbcadacbaabbcbbacbccbaaabdbcdcccacaadacbacddbacaccdbdbdddabbaadbaccdbadcdaabdaabdcbcccbbaccdcdbcacdbacdabcbddaaadccccbcbdccaacaadaaadabcbbccdabaacabdbcbddbacaddbdacdcadadbccadaacbabcdcddbdbdbdababdbddaaccbcccbdabaaccbacaadcddbbdabbadcdcadccddbbdddcdcadabcddacbadbdbadcbabcbcccddaadddbbccdabaddccdbbadaaccacbabdadcddadbcbccdaabdaabdcbbdddcaacaadcbbdabdbabbdabdaabaaabbabdbaccbccbdbbabacbdbddabbcacddccdbbaccabcbbddaccdacdbccbbbbdabdcaaddcaadcbabcaccaaabdababacaabbcccbabbcddbdddccdbabbbadcbacbbdccacbbacccadcadabcbdccacabdddacbbdadddcdcdcccdbdaaccadabadabacadacbcdbbbadabdcdccbdaacbdbbabccbcabbbababdaddcdcccbabbdccdbcccaadccdbaadddddbdcabcdbdbcbdabdbababaadabcdddcbccaaccadbcdcdbbabadbabddbbcabdbdaadbccabbcdbdcaccdcaddaabdadccbdcdbcccddbacdbaaacdacbcccdbacdcabdbbbaccbccbaaddbadccdbaccccddccabcadaaabbbcdabbdbdbadaacbddbddbabbcaadcadcdaabcccddabcdbaabbcabccaacddccbcacdbcabaabbdcdbdcdbbacaadabcdbdabcadcadbcaddbcadcaaacccccbbbdbcccdddcbadcabacccccaaabbbdcdbdbddadcabcaaccaadacdbaaaddaabbdbddbbdaacaccabbddccccaabcabadbcddcbabcabdddbcdbdcbdbaaadcdccaaadddbabdbbacbbcdaabbabbabaadacbbbcdccbccbcacbcabdcabadbdcadcacacbaaabbccbabccccdcaccbaadbcccaabbbabbcbbdcccbbdabcbdbcdaaccbabbdabbcbbcbaacabbcdcbcdabbdaccddbacbaacdccbabbcabdccaabaccddbdacbcbdadcbacdcddadcbbcaccdbdababdacababbacddacdbdddacdbbadcbbbbdadbbcabdcccdcccacadbddbdbbcacdccdbcbdaaaccadcdbacabaccdcdcaabacbccbaaccdadcbbdddadaabddcadbbadaadbcdbcabaacabbabbdddbdaddacaabbaccdbcbcdaadcdaadcdadabcbbccadddbacacadcdcdaaabdabdbbaacbbcabcdbbcccaacdbdbbddbcddcacbcaacbcdaabbadadabbdcadaddbcbacdcacccbacbcabacdbdddbdbaabcbcbdcbbabaccacbaaaaccbdbcbbaaadcaaccdcabbabcadccbccdbcbbcbdacadabbcbbbbddbaabdabcdaddadacacaabcabadcdcbdbbadaccadcddaadbbbbbccabcacbdbbabccababacacbcdadbbcbbbcdccdddcccdccdcbadddcbdbaaaabbddbddbddacbaaadadacdcacdaabbcbdaacbacababdaddacdacbbdddbcabdbbbdcbdcbdccbdbabcbacabdbbbcaadabccaccbbabccdcdaadbdcbaacdcbccccacadcacbdcaabcacaadbacdaabcdccbcbbcbadacbdddbaaadbddcdabcddcadbcbbdbacacccabbababadcdbadaabadaaddacabdbcbbbdbadacbcddbabccaccccaabdbaacbccdcacbabdbdccaaccbaccabcdbaabbbcbccbadbcddcccacddadccdacdcbabbabaddddbdbdaddcaadbccbaabdcaacbbddacabdddcddbdbdbcdcacacbccdbdcadbcababcaaabdaaccdabdcacdcadbabaaaaaadadcddaaccabcdacaaabbdabadbbbcbcccbbbbddddddabbcabacdcddccbbbadacacadbaabcabbcccacbbcdacccbbacdaacccdbacbcbdcccddbdccbcbcababcadcadccbadcacadcdbbadbaaaacadaabdccadcdcdbcdbbddbdbbdadbcbaaacdbbbabcdccdabdabadbdcabdbccbccbcbdabadddbddccdccdaddbaccccbadcccadddcbddddcdccbdcbaaccbdddbddacdbccacccbacabccccabcaccaaddcacdcdbbbdbdcdaabdcbbaaadbadaabdabbbbcabcbbacaadbddccaaadcaadcaccbbdbacbdacbbbadcddbbcbdbbcbdcdadacaaccaadaccaadbcbcbcaadddbcdcdccaddaccbddcaaddcbddcaaddbbcbdcabcbcdabbdbddcbccbddbccdddddbdabccdbdcacddcbccaacbadbcdbaaacadacbcdbaabcbcacabdbdccbdbcaaacbbccaddaacbacadcddddbadbddbddaccddbccaadcdddcbdbbcaccbbacdbdbbdddbbdaaadaabddbdadadbaabbadcdcbbbddbcbbacaabdcdadaddcdbbbbcccbababddabbddcabbbcaacadcdccababadcccdcbbbbbdacdbbdcdadbdaabdacdabcccbdbbdbabdbccbbbddcbabcbdadbbdbdbababbcbccaaddbcabbaadbccdacdddddabaaaddbbbbbaddbcbaddacaacaaaabdcbcbddcdcbddbdbccbcdcdbbcbabccaabbcaaabdbadcbccaccaadadbabccddbbdbddaacddcaaacadaabbddadabadcbbcbcdacbbddaccccaabdcbbdccdcbadbcadbadacbabcabbcccdbccabddbdcadacbddaddabdccaadaddbdaccabbabbccadcdddcbcdbdcbdcabccbbcdcccdbdccdcacbbbdabbbacdcbaabdaaacdbabcdbabbbccabbdaacadbdcdaacddcaaacddbccbddaaaadcacbcbcbcbaaabbbcadadbbaababaadddaabababaabcdbcdcdaabccdbabcccadcdaaaabbdaddcbccccdcaadaccadcdbababdbccdbdccdbdbcbbdcbcaadccbacbaacdadbaaaacdbbdcaadbccaaddcbbbbaadbdadcccadabcdbaddcdaaadacdddaacabaaccacadcaaadbbadddcbbbaccbcccbccddcddbabdcdcbbcbcdadacbdacaadccadcddacdcccbabbcdadccabdddbacbddcddcdadaccccccbcbccddbcbacbdadcabbbaaacdbabbaaccbacbdbccbcbcddddcabbdddabdabdccccbbaacababdcddddddbbcdaacdcdbcccdccaddbcdaccaacadbccacbabdacbbbcbdcabacbdcccdcdbddcbaddccdbacbcacbbcdbdbacccacdaaadcabdbdacddabbcbbcbbbdabdabccdadacdabdaacbcbcdbccabddcddabbbcbcdabcbbaaddcdbacccddbcbbdcdcadccddcbdadccbaaadadabbdcdcbcdadbacaddabcbacbaadaabccbabababcbadabbdbddbaabbdabccbdddbabacbcdbccbddccbbbaadcbbdddbdbccabbbdbdbdbdccadbbabddabcdadbacbbdcbcbacacdddcccbdcdcbdbaddcddbdcccbbbdcddbbdacbadacdcdadbdbcdbcbbdabbbbdccccdbbdaccabdcbccccdaadacaaddccadbdaababbbdcacaccdbbcdbcdadaadcacdbbcbaaadabacddcbbbdcbcdcbcadcbbadbcddadbcdabdbbbdadaaacabaccbcbbbacbbcdcaaadbbbaaadbcbcdcbabbcddcddadbbdacbbbbacdcbacbaabbdacdbdababdcbbccbccbabcbbccaaadcbdabdcabcddaacccbddacdcbdccdaabacadccbbdbbbdcdddbadcbcdcbbdbcaaddaddadabddadddaadbbbbacbbcacdaacaaacacbcbbcabadaabbdacddcbbbcbbacbdaacbadaccadcdddadbddccbbdbcdbcdbabcabaacdcccbccbcdbababdcaccaadabbdaacdcdcdabbdcccbbadabbbdbcddbcabbcaabddadcaabddaacddacbccadbbbdaccdabccacdcdcacddbdabadbcacbbccbaccbbddbddbacdbbbbbabbdddccdacddbbbdbcbabacccccdabbddcccdccccccdbcacdcccadbdbbbdaaaadabdbccbacbdaccbbdcdbbccbdbbcaadbacccbdbbdcaddddacdddddaacdbbacdbddbcddabdccdcbcddcdcbdbcdaacddaddcccccdcaacdacdbdbbbadadadaabcaacdcbdcbbdcdadaaacabdaadbaaddbaccbcdcbdaccacbdcaacdbcdcdaacacbcccbaacaadabdcddaccddcccaabcdcaaacdaadbbbaccaacbcdabdbbcacbaaddbbbacbbcbbdadcddddaaacabaacdcaaabbccbdcababddbbaccaddaacbccbdddaabaabaaabbacabcacbacacbcaddcbacddbaadbcabddccdaacbadcccbcccbacaabdabbbaacbaccbbdabcaacccdbabbcbddcdcdacbbaaaacaaadbacddabdddbbbbcabbbdbabdbbbaaacdabbbcdcbbaaabbabcadacccaabbbbacbbdcacbdbbcaaacadaadbdaaaaccacccbcdbaaacbddbccbddbabbcbcdbcabbdcddcdaaabcdbdccbdadddbbdadbaccbddadcadacccadcbccdbcdadbabbddbccaadcaabbdbaccdcbbbacaccaababdaacbbcbdbadabbbabcacbcccacdccabbddaadccbbadacbdbabcccacdaabbabcbcbddccadcdcdaaccadbddcabbcaadcccccbccaccdacbadcaacbdddacaabdaabaccabcdacaadbddaadbabbbccaccadbabadcbcbabaaadcdbcddadabbdcabdddadadabaaaddbabcdccadbcdddaddbabacdcdcbdddabaacbcaabbcbaaabcaaadbbcbdbaacaaaddaccbbacacccbacacddcbdcbabbbcabbcadabadcabaabdbccdbcadddabaaddcbcbcdbaacddbbadddaabccdaabbbbcdbabdccbbbdddcbaaddddbadacbddbdbcbcaadcdcdacbbcbbcccdbaabcbddcdbcdacbdccbdabbdbddbcccacdcbbbcdabacbcaccbacacbcbbbdcaaaaccdbbaabddabbdcddbdcdbcacdbdcdbcadddcdabdbacaabcccbcacddcacdcbbcbdbbdbdacbcbababbabadbdacdbbdadadaaabccadbdcdacbcdddaddcbddbcaddadbadbcddacabdbdddcbabbacbbcdacbadcdbbaacdcacbaccdcdcbcbabbaddbbbdaddbccbbbcccacdbdbcdbacbbbccabccabddbdacdbcacadcbdbdbcdaccbbadcbbcbddcdcccdacabbdacaaaabbbbdcbdaccaacdbacbaabbcacccaadbddccaabddbdcbabdabaaabddbbcccaaaddcacdbacccabbcabadabcacadbdbabaccdccbacdabcbdcbbbdadccdbbbabdcdddadddadbcdcccabbbddacdcdbccdddbdcbdccdabcdbdaddacccaadbdabbdddadadccbbdaddbcadbabccbcdbddbdadbdacccdaccdaccbdbbdbacdbcaacbccccababbadacdbbbdddadbbacacdcadaacdaaacaddadbadccdababddaacdaabddaccbbbcbdabbbbbbddcbabaabbcbabaadccaddcddbdccdbccbaaadbcbccbadcdacdbaaabbbdcaccdaabcdbbbacaccacabdaccccdbcddddabcacadbdbaadbcbbbbabdacbdbaadaacbcddddaaabaadccadcaaaddcadcdcacaadbbbcacaaaaacaacbbcbbbbadabbdbcddacacacadcaabcdccdcdcadadcbaacbadacdbccdaacdbbdcbadaabcacaddcacbdadcbcaabddddbbcadababcaddadcbcccddcbbcbacabddbcbbcbdbcccbcaadccabbadcbadacbcbddbaabbdcbdadbdcdbdddabbdabcccccadacadbdacaacaaaaddddbccdbcbddddcacdaaabbacccbabbdccabbacdaccdbacababbdddcacddbbabcabcdcccbdcbaabaddaddbacccacacbaddacabdcaacdbadabddddababacaacbdcdaabdcccaddcadddacdcdadaccbababcbbcaaadacdbbaaabcccdcacdbbcacbbbcbcdcbcabacaacddababacbdabbbaaabdadcddabbacbadcbcaccbbbabacbdbaacaaabacaacaaacaacaadbcbcaaabddadddacacddbbaabdbddabdcbddacaaabcabcbbadabbdcddbbcbcaddabbdcabdbdccbdbddadaccbbdbbbcbdabbbbdcbbaccdbccbacdddababaddcadacdccaaabdcbdaccbcdbdbdddbacadbcbccbbdbcbdcbcabbdaacaaadaacdccbdbdaccabccabccbdcdbacbcabbcbdccbccddbcdadbbcaaabbccacacbaddcddcdddbcddabbbdbccaaddabcdaaccddacccdccddccddacdaddcddbcabaddadabbdbddccadbcadbccdbcdbccadbdaaaabadbdacdcbdcbacbcbaaccaaddbccccacdbacacaabcbaaababbacaababdcadadcbbacbaaabdacabdbcdddcbcbddcdaaabcbdcbcdadabaddaaabdbaacacacbddbbbbcbdbccaddbccaaacaacdccaaacbbadabbbcbcdcddbbadcdbabadddddcdbddccdabdadbbabcacccbccabaccabbacaacabcbdcdcccbaaacaaadcbcddbcccdcdbdabdacdcacdbaddcbaaccdcdacaaccccddcabacacbdabdcbbacadaddbbbbdbddabadcacaccaccdbcdbbbcdadbbbbbcbbbbbdbdbccbadaabbcbdaacaddddbbdaabbcadcacdbbbbbbdddabdbcdcbaadacbaddacccdbbcacadccaaaabddadcbdbddacbababbdaccbadadbddbdbccccabcccdadbdbbbcabdbabbadabcadbaaabcdbddadacbccbabbbdddcdcaaadbccdcacdabaccbbbcddddacbcddbbbacdababdcbbcdbc