bbdccbbcadbbdcdbcbdbbcbaddaacabccccadabddadcacdddacbacacddbcacdbbcacbcacdcbbccbbbbbdababcbddcabbbbcbadddabbdadabcabddddbbabcbaddacbdddcaccddabdcaaaacabbabadcbcccaabdbadbcdcdaccddadaabababcabbaadbacbddaacbddcaacadddcddbaaddbdbbdadabddadbacbbbddbdbadbdddddbacacaaaacadacbbdcadadacccaacacbaabccdacabcabbbdcdbcbabdbabdbabdcbbddcbacabdbaaacccacdcccbaaacbdcadddcdcbacbccbabaaadbdcbdadbdbdcdddbcadbacbdcccdcbcacaacadddcdbdddcdcddaaacbdbcabbcbdbcdbaaadcbcacdcbdcbcaddbbbccbbabbcaccabaaaddddaabadbccbcdbaddaadcbddbbcbbdacbdacabcaacbaabdbbabdbbaadccddcbbaadddbcdacbcdcaddcabcadccbadadcaaadccbcdcddbabcadacbddbbcbaaddabdcaccccbbddcbbdbbcccadcacdaccbdaccabdcbcabdacdbdbdacbabaddbadadbbcdcdcccbbcdbacadbdbcaccdcbcbcdbaaacdcabdaaaacdbcdbddbaccdcaaccccbaababcbdbdabdadbbcdbababcddbbbddbdbbbaccccadacbdabbccddcbbdacdcccbdbddcbcbdccbdcabbacbccacdacddccdcccdddadadbccabbcdccccdacbaadaaccddaaabbccbcbdbbbcabddddaccdacddbbbabccdbcdbdcaacdccadabbabadbcabcabcccaacabcbadbbbcbccacccdabddbaccadcacdbccdacaabcdbcdcdbbcacdabbdbdbccdadbaadbbbbabccabadcabcdddcbcddabccacccdbbaacdbabccdbbabcacdbbacdddaaacdccdcaadddbdddabcbbcdcbbdddbbadbbadbcbbcddbacabcbbbdcacbcbabcabadaddbdabdccaaaabcbdcdabbacbdaaaccccdadcbcaccdbdabbbcaccacbadbcaabbccccddddccdcadbbbccaaabbacdcbcccddbcdddbbcaadacbcabbbacdbccabcddaaabbaacbcdaaabcbaabddacdbbcbbcdbbbcddbbbbbdabbbdacccdabdaccddddaabdaddddddbbadbdcbcaaabcccaadbbcabbdbabddaacdadcbbcdabccbababacddaacadacccaabcbbbadaccbddadbcdcaabdcbccddaccbcbbbdbadcbdbbabacadbcbcdaccbbadcdbcbadcdaaabdbababadbddbdadccbbbddadddcaddabdacdcaaaddcabdaaccbcdbdbbabdddaabdddcacdaadacccdaacdbbdaadbcacabdccddcbaddaacacddabbddacbccbadcacdadadcaddddbddccadcaddacdaadbdcbccaccdbcacdacaabacbacbaddcccdbbacbabdcdccadbabcccaaccdbaddcaaabccaabcabcdaddcbccacdbcabaabbbcdcadcbbcdbdcdadcacabbdacaabddcabbdadbddabadddddcaacaabddaabbcccbbbbdddababaabdcbccacbbbaaabcddcbcabacbdcbbbcaccdcdddbbabdaaaadcacaadacaccccccdaaadcbcbccbddaaabdcdacbdbabbabbbaaacdcbcbaccbdacdbccaabcdcbbadbdbcbbcacbcbddbbbbdadcdabdbaabcabbdddcbddcccacbbbdddadbabbdadddcadbabccabbdababaacacdaaacbbdbbdcabbbaadacaddbcbddddbdabababbbddcabadaabadacdabccbaaaabadcddadccadbcddbacbabbccaaddddbdccddcbbdacacabbacaabdbadddbbdcbcdcbbbcddcaaadbbdcbdbbdaabbdbaacdabacaaabaacbbdcddddcadbdcdbabcbcadcabbaccbbadddbaccadbcddbadaaaccccabcccbcadadbccabcccbacadadbbbdadaacababaacccccdacdbdacaacccaccbadcbaabcadaaddbbbddcdccadbccdabcbcbabbccdbdacbcdcabcddbccdacccbccacababcaadddddccccaddbaddbabdabadccaacdcabddaccbdccacbdaaccccaacbcbbcbcdcdbcaacaabaddbcbcbbccbccaadaabdcddbcdbcdbccdcbcabccbadadcccabaddbadcccacbcabaccacaddbbbaabbcaacbbcdcdddbbccbcddbdbbbacbbdcdacabcaabbabbacacdbaabacdbadbabcbbdbcbdcaabadccbbbacdaadadcababbdddbdabdcaddcdddccbcaddcdbddcbcacacddbabcbcbabbbabccaaacbadacabbbbadbdcbbaacccbaddabbcdcacbadcbdbabaaaccbaabdaacaccacadbabcdddbbadaacdadabddaaddcddcccddbacdaccaccdbaadadbbcbbdbabdacabadcbabaccddacacadbbadddacbbdacbdbdbdbbabaaababaabcccbddbacacaadcddcadcddbcaadcbdcdcddcaadcbcccadbacccdcaddbdcabcccabddbbabbdbbdaccdbbcaabadbaacbcacdcabbcadacdcbaacdbdaadaababdcbbbddccbbbacddadbbdbaddadcbbacabdabcaaccbdbdcbaaddbbbbbbdabbcdbbabdbcabcdaaccaaddbdcdbcadcbbacbcdbaadbcbaddcaddacccdabcdaaacdacdabbcbcabcabbcaacdcdbbbddbbdcbaacbbdadacccdbcddcbccacdddbdacabaabaababacbdcdbdccdddbdabbbdaccaabdacbcbcaacccadccbaccbaadcbdcdbaacabbcccaacbdabcdabcbbbdacccccabbcbcdcdccaabdcbcacbbaccbaccbdaaccdabbbdbdcacccbdacbcadabbcaaaacbdcdbcaccdacbbbcbdcccacddbbbaadcaabaccddbcdabdbcdbcadacbbaccadccbdadbcbcbadabbdcdabaaccdabbbddadacbcacbaadaabddaddcbdccdddccbabadaaccbcbcbbdacdbcdacacdaabdacbccdabadcdbddccadddacadacdcaadbbddbbbdcbbcbbbaadbbbbbbcaddadaadadcdcaddabdbacdccadadcadaacbacdadbcaacabbbbbbdcbccbddddcbaacbdbaacabcdcacadbcdabadbbabbcddaccbbddbcbcbcacbacdbdaddcdbdabdadcacccdcabbadadabdbbddbaddabddacabcbdbabbdacbcbadaccccbdcadcbdbbaaacaaccdacacaaccdcbbbaccabdacbcdcdaaaadbbddbadbcbbbabdbbbdcddbbacabcccbadcbbaabddccaadcbadabdcbacbbdbdbbbbbdaacccbcacabcdaddbdddabdcdddadbababcbcabccbbccbbdddcbcaadbbdbccbcbbdddacccbbbdccdbcbcabccdbcaadacbcacdbbadacdadcaabcabcbbddccbdadccdbdcccbabaaacbcbccddcbcacbbbadbcabbadcbaacbbcbaddcdbacadcdbdccccadccbbbbdddbddadcaddcbdadacbbaccbbbbbaaccccadbabcbcadccacbdabcbacddcdcaaaaadccdccacccbbdcaabaadbbccdbcadabbcacbabdbbbbdaddddbadbdcdbaddaacddabacbbabadcddcddbcacdadabdbdcdcacbdcdddbdaacdacacdabacdaccdbadbcabbcbcbcacdabccacdccaabadcbbbacdbdadabadabdaabbccaaababdbdbbcddddcdbaabcddbbcaabcaaabaadabdccbcdbadcacbcbbdaacadbdadbdcbcadddcdaadddbdaacdaacdaaabcacbacacabccaadaddcbbabbcdcdcccdbbccbacddbacdaadaaaadcbacacdbddddcdcaccddacddbcbcccdbcaaaadbcdbbadbbdddbdccdcaabaaddbacaaaadccbcdbdabbddcbaddcaddccccacbccdadddddbabcdabdbcbacbdbbdaaadaddbccbcdabdbabcbcaaadaacbaaaccdbbcdccaaadabbbddbaabcbddbcadcababcbddddddaabccacdbcadacdbbbacccdbbdcaccbbaddcddcddbbbcdbbdbbabacbdcdcdbdddcdbcbbdddaabcdaabaccdcabdcaadacdcdacccddadacdccbcbadbbdbbcaaddacddaddcadabacbbcaaadaccccdbabcdcbcabbdbbcdbdadadcacabadcdabaaddcabdccbcccadcbcaabcdccaccabcbdccdadcbaabccccdbadaabddcaddcddabbbacaadcdbbbdacbbdacababbbdbbbccbbadcbaacacbadaacdbcbaadcdcdbdbbcdddabcdaabbcaaabaaabcbaaccadcadaabdcdbaaaddcadddbccaddcadbbcddadacbabddbdaccdacdabdbabbcdcdcadcbbdbcdcadcbcbbaacabaabdaabcbdcdbdccdcbabdcdcdadcccaddcacbacdbadbccddabaadcacdacdabadddcabcdadabbbcaabcacadcbbcacacddbcbbddcbadabaaddacbbdadcaddcdbaabbbacbbabdbdcaaabccbcddbabacdcbdcadabbcbabcbdcccbcdacabdbccdcdccbddccbcddaccaaacdcabcbacaccdcbcbddaadcccdcadcccdadacddccbbdabaaabadcdcaabbdddabcddaaabccbbdabcadbccdabdaadcdbcddbdcdadcdcdddababbcdbdbcddbdaadbadcadabbdaabbbdcadcdaadaaabddcacbabddcdcdaabcabdbcdbbaaaadbadcccadbdbcdbbcbdcdcbbcbbdbbbdaaddadadcadbadcccabcabccacaacdbcdadacadbddbbdcddcdbccdcabaaccdddbdccdcbcdcabbccddcacdccdaabcabbaacdcddacadabbdaabdabbabccacbacdcdddaabcabdcddcbaacddbbabdcbbaaadadddddacdcddbabdcacddadabacabccdbbbccabddabbadbcbddbbcaccacaadabbccbdacddcabcbabdccbcaaccdccacdbabaadbdcdabadcdccbcbaabadbadaadacaddbcdabdbabbdacabaaabcdcdcdbccdcccddbbcdbcbcdccddaacbaabadcabdccabdabdbaabcbdbadcbacdcddaddcaadacccdaaddcaaaccbbabdbbbcbbdcdcbddcbdcadccabddcadcbdbddcdcabacdbbdddbdcacaaccadcbccdaabacbccdbaabacddaaccaaddcadacbcaddadcbdbcabdcabdabcbdaaccaacbccbdcbaddaabcbcabbcadadbccdaababdbacdaccdabbbacbaacacbdadddaadabdcbadaaddacccbbdbdcaddaacbbccccbddbdbcccbcacaabcaabcdddadaaacddbbdacacacbdbabbacdcbcccbcaccddcbdbacbddaaddcbbbdcadbcaddbcbdabdabddcdcdacaacdaddddaacddacbcaabcdadbacaacaacccdddbbdcaaccdcbadcbdccdbbcbdbcddabcdbdadaaadaabadadcbbbcbddcaabcddbcccdaabdbabddadabbccbbcbbccacdbbbdccdaacdcbaccdcabbdbdaaabdaccbbbdbbadccadbabdbbaaadcbcdccabbcbccaccdbbacdbbdadccaaacbdacacbdccaadddacaaadbddbaccbabcbdbdaadbbdabcbcdabcddddcdbdcdacddbacbaccbaadbcdcbaacbdcddcadddcdaabdcabdcdabdaccaaddcdbaadacacddbaddaaddaacaadadcbcdaaccbddaabaccaacdaacdbdccdadccaabacddddcdadccddcbbddcacdbcabdbdbdcabdbbddacddccacbddbaccdcccadaddbabadaddcdacddddbcdcaccbaababcadcbcbacccdcbacbcbacbaaccbabacadbdadcacbbbcddbcabcaaaddbbacccadccdddbddcacabaddbbabcdbbacacbbabacbccabddcadbabaababbdacbdcbcdbacabbbbcbddbaaccabaccaccaccaadbdbabcbcccbcbcdbcaadcdacadcdcdadbadaddabaaaaabbadabccabcaaabcbacdccadaadbacaddcbdabcdbdcaacdcaccadabdaabbcabccdbbdcbcdccacbdbdccaabbaacadbbdadcdcbbddaabadbcccbdbddbaacdddcdddadccbacccacddddacaaaddcccdadcbdabacbadbdaddacdcadacabddccabbcddccbcaabaddaacdcadaddaabdabcbdaddbdcddaddcddacdacbdaaaabcaacdabbacaabbbcbaddbbaabcdbdbbcadbddabbccddcccdbdadbabcbccdcadccabccbdbcdcbabbaadddaaabdadbdabcbbdabcdbcbcadabcdaadaccaddaccdacdddcbcccbbaccccdacdcbaaccbbccadccbbdcdabddbdcaacadcdbbaddcbdbcadbcdaabcdddbcccbbcdbbdabbdbbbdabcacadabbadaabbaddbbcaddacacdabbddabdacbbccbdcadbcaacccdbbbbcdcdcdbbcadbaccaaccbbbdabbccbdbacbbacdccdbdbadadadbcadcccdaddddbcdabaddbcbcdcdacacabcbccccbbbabcddcbaabaadabcbabdcccacadadcdaacaaaccaababdabcdbdacbdbcabaadadabdaddccacaabbccadcdbadccbbdacdadbcabaadbdbcdacacbbdabcaadbddbabaadbbadacdbaddddadadbccadaddbcbdbaaacdbaabaaddbabdddaccdcacaacaacadbbacdaacaabadcbdacbbaadbbdaccccaddcaacbacabcccbbdccaaaccddbdaacdbbdbdddcaabacadbbcacbaabadcadcabcdddadbdcbbccbaabaadacbcadbdcbbcaaddcdbadbdbdbcbcabddbacbbddcccdbbcbcbdaaabdbbcabcbbcbccbdbddcbddaaccaaadcbdcdbdadcabdbcbabdaaabbbdabbbcacaacddcdbbdaadcbccadacabdabacccdbdcacbcdbdadaadaccbabbcbdadbbbbcdbbbbbcdcadbacaccacadbacbddcbaabcacbcccbadacdbbbbbdabbcacbcccbdbdaaadcabddabcddccddbdbabddddaccdadddbcdcacdccdaccdacbdccbccaabdbcdccdddcbcaaacdccbbaccacbabcdaccbcacaddcccabdabbdcaabbaabcbcaddcbbcdbaddcdcaabcdaabddccddcddccaabacdbadadcaadaddabdcddcaacacaccbcabddccdcaadccabaaaabacadabbbaaacbbbaabdbdbdbcacadabbcbbaccbcbcaddcadcdaccaddbaabbababcbdcacbdaaaaaccccabcacdbbdcdaacdcadcadcaaccbaddaaaabaacbaadcbddcdbacdbaabddccacbccdcaabbbaddcbcdcbaaadcabbcccbcaacddaacccbacdaacdbdbaccbddaaabbdabbabdcdaaacaabcbadcbcdbadcdacbbdbcddddccdcdbcbbddbdbcbdddadbabacdcbaaabacddbbacbabbadbcbaadcbbadacaadcabdbdcaabcbaccbbacbdbaadccaaacdcbccaddbbccabcdcaadcdacdcccccbdbbbddbdcaadaaabcdbcaddccacdbbbccdcdccdcddcddbdadacbacdabbbddbacddcbcdaababaabddbddaaabccabcbaaccacabaacdabcbadabcbaabbcccccaabdbaddcbdaadadbcacbbdabdcbcaccdddaaaacbcbdabbadcbdbabddbccadcdabdbbbadbacdbabcdbabdacdbabababdadbaacddbcbbdacbddccdcbbddddbdccaabdbcccbcdabcdcdcddaaacdadbcbcddbbbaddaacaddcabdabbacdaacbabaccdddaccdabcdaccbabbcdbcadbacadbbabcabaaccadbbccdbbaacdabcbddddaacadbbcbdadadcaaccabbbcdddcdcdadaabccbadaddbbcbcdbbabaabcbdddddbdccdaaacbaaabcaadcacdbbcadadcdccbbccdbcacddabdabacaaddcbbadacbcccaadcbaabcddacadbaadcdcbdacdaaacbadccadbccdcabdbdbbcadacccdcbccdbbbccdadadcdaacbddbdbdcaabbccabdbbbabbacdacdabdadadbcadddbcbbccdacbacaaadccbbcaaacbdcccadcbadacaccdaccdcdcbbcadcddacdccdaadabcccddcacbbbccccbdacccbcbdbbadbacabbddcbcbacaddcbbaabaacbccdabacbcccdacdacddacdbcddadcdcbacaaacbbbccbdcdaddbbadddbdacbacbdaaadbdcdcadcbbdcddbcabbdbacbaabdbcaddcaaccacbcddaacbacbdccaabbcddcadccabbbcbaababddaadacccdcdbaacbbcadccbccababbcaacabacbbbcdcbdabcccccabacacacaddbbcbddaabcddcbdbcbcbaabbdbadabaaacaddadbddcdcaaaddbabbdadadaaadcaaabcdcadaaabcababcdbdbadbaccddbbaabbccccdabcccaaccacdabacddcadccadcdacdbadcbcdaacadcdbabbabcdcdcbcdbcdddabccddabbddbcaaaabadbaabcbdacdbcbbdaadaadadbccbcdaabccdadbaadbabcadadbdbdcccdcbbaccaacaabbaddbccdddcccbadcadcdcadbbdaaabbbccbdcbbcaccbdbcdabbdaacdcaadbbadadadaabdbcdcbccdbcdcaaddbdcacbccddbbccbabdddabaadaaacabadccbdacbccadcabddadaddbbdcbdaadbcdbbbabccacddcdbbddbaacdbdccbbdaacdacdcdcaaadbabcaaacabbddbbcbaacdacdbabcddcbcdcacbcacccababadaadacaabbbccabaccbaaddabcdbccabadcbcbbaaadaacabacbabaaccaddbbbcbcacbcadcabcaccbdbdadabdadadbabccdbaaabadacaabdaacbcdbacaadcdabcacdbbadbddcadcbbcabdaaddacccccdbcddcadcbbbdccbadcdacddccdcbacbbdbccaabdcabcccddabbdadaabccbbbbdcacaadbbbcddbdbdcbacaabdcdbcbabcbabcdbddcadbaacdddbcaaadacbaacdcbcbcacaaccbbbdddbcdccabaaabddccaccccbcddabaadbadddbcbccadabcdccdcdcdcccbdcadccbddacbccadacdbbadaaccabcabbdbcddcdbaaadbcaccccadaaadbbbbacdadbcdbcccdbddadbaaddddacabdcaccdadccccbbbccdcdbaccbdccbbbcdbaadcccdabccabacaacaacccbcbbabcdcabcdcacadcdacdcdadaaaacbabccbcbcadbdcdadacaaabbadccdbcabdcbadabaacbaaabccbddaddbadaaacabcacdadbbbaddbbacaaacddcadabbbbdadbbbababcabbdabacbbdadbbdcdbbbbbdbccbdaabadcccbaacaddbcaaaaabaccbdbbcabacccbabbbcbdacdbddbbabdcdacccdcacbbdaddabaabdadccaabaaaaaadbababaaddcaddbbcdcadcccbcdddbbccdadcbcadabdabbcddbccadadcdcababcdaacabcaacdcacbdbcbcacacdaaabaddbacaaaadabddacbbddcaacddcadacdadcbadacdcdbbdacdaabccbdbbbbbabcbbdddadabaddcbbbccabadddacdaddbcbadabcbdadcabbcdcdaaaacacbbdcaabadbcdccbabbcdbddbdacccacbdcdbcccccbbccdcadbbcaaaddaabbdcadbadabdddacddabaacddbabaaddadbbdaadbbabcdbbccbbdabbcadacabadbbdddccbccadbadbcaaddcadbbcdaabacdbcbdbbbdcdbaadcaadcacdccdaaabbccabdddccaddaabbcadbdbdadbcbccabbcbbcbcbcabadddcbbaaaaddbcbcaaadccaccacbcbaacdaacacabbaadbacbcbccababcabbdaabcbabadbaaaadaadbaacacbacbdaddbaaadabadcdddcbaabbcabaadabbccabbbbabbdbcddacdbdbdacadcddcdddccdcbbcaddbdcabbcdbddbcbcadabccdbabdddaaacacdbdbddaadcdbaaccabcccdbddddcdcacbddccdaacbdadaabccadddadadacabcbadbadabacddbcdddababbaacbdcaadbbabcbcdcabddabadcbadbaccbdddaaccaaacaadabbddaddabcbcabcbcdcacbdabddbdbadcdcabdbdccbbddacdbcdbccbabccddbdbcacaacadadadbcadbacccbadaadbcacccdacaddacbbbbdadcccccbdcccdcadcaabdaddbdbcaaaaaabaaabcbdaaacdadccadbabadbdccaadaaadacbbcdddcbadccbbdccaadaaabcccccdabbcbcaacdbbbdbdcabccaccbdbdbdadbdcddbdbbdcadbbcbbdcddbabababccdcadbbdbaabaccadddcccaabbaadbdcbccdbdbacdaddddddddddabdabbbdccbbacabddadbcddbbdbccdadcddaacabcbacbbbddadcbbdadcbbcbbacbddcabddacbaaaaabccbbaabcbbcbcddcbdacdacdbacdbaababbccbbcbbbaadbacdaacccaaacbaccaaddbbbccacbaabacabbdabababbddbcbccababbddacaadbcdbbaacaacddacbcdcddbaddddbdacbdccbacbbbddcccdabbbbcbbcccdbbcbccbcbacbcababaaddbdacdccabcbccdbbaadbdadabaabbbaaccdaaadcdbbcccdcdbdcbdbbcbbcbdcadabdcacacccaadbabdabdbcdccbabcdaccbcddbaabcdddbcdbcbadaabddddadcadadcbddbcccdccabcccbdcbbaaabaadbccdddcccaaabbbabacacaddabbdccdbdabcdbbcbccbbcbaabadcdadacddbbbdbaabdacbcaacdaabcdaabbddbbbdadbddbbddacddbbaabbcdcddadaaddbaddddccacbdbcabcabccbcadadaddacadcaadbbddabbabdaabddddbbcadadbdbdbcabdbadabaabbbaccaddcadbccbddabacdccbdabddbbabbacacbbcbdaadaabaabdcacbdbbddbabababdbbaabaaadbcdcacaccdabadbdddbaacacdcdcdbbcaaabbbaabdbcadcbaacbacdaacddcddcdaddadcadaadaddaaadcaccbcccdbbcbdbababacbdabcadcddbddcacbdbacbcbaddcbcbbaccaababdbbacbabbcbddbdcadadcdaacbbdaccbbbbabcdcbdddaacaaccccadccbcadddccadcabcddcccaacdbcdbddbdccdccadddcdcaadcdaaabdddccaabdabbccaccdadbcdaacdccadcaacaccaccdcaacdbccbccbaabdabacccbabcdcdcdcbacaabddaddddcccdbbccaaabacaccbccdbccbaaccaadddacabaccddddbadbccbbacdcbcccacabbbbadddacbbcadcaaadadbaaabbadcbacdadaadabcbdcbaabadbccbddaacaadaccbccaccdbbbcdbbcadbacabdaaccbdcabdaadddacbabacddcdcdcdcdddccbbbdbdbbddaaabdaacddcccbadabcdcabcdbbacaabbabcdcbdcccabaaadaddddbccbdacddadaaccdccdbdcdcdddacddcbbbbbaabdaddaabbbcbbdaadaacdbccbabaccddccabbabaddabdacacabbaccbbabbccdbcaaaddbaaddccbdbdacadcbbcaadbcaaaabdbabcdcbddbcadbcadddbdcbcdabcadbbaadbacddcddbabbdcbcdbbdcbacdacbadbbcacacabcccddacadbabcaadabcccbcdcdbdcbcaddaaabbcdbdacdaabbbdbcccbddabaabdbacababdadbdcabcadbaccdbcdccaddddacdbbcadddabcbdcdaabcccdbcdcccdaacdbdbccdacbdbdaaadbacddbcbcbacdbcacacaabbdbaadabcbbcdbabccccccaccabcbacbabbcdabcdcccaaaaadbccadacbccdbcddadaabcaacccbddaadbcaacbabcaaaadadbaccccacbadbbbabbaaabaaacdbdcadbccccccbcdbabccaabcabcdbadddcbcbdaaacaacdacbcbaadbadcbbccbaaabbacaacadbbbabadacccbdbbcacddbdcdbcacabaddaacdbcccabbddbadbacbabdccacbaddbaabababbbcbbaacbaccbbbcbacccbadbcdabaadcbaabadcbdccabddcdbddadaaaaadddbabccbcaababbcbacaccaccadbacbaabbacadddacaaadbbdaabdcddabdcaacbcddbbcbbcbadaaaaddbdaccacccbdcdbbabbbaacabdbaacbaabdbccdaabcdbabaababcbcbbbbaddcdddadadddbcdbcbdcacadbccdbabbddabccadccccacbcbccdbbcabdbaabcdbcdcbdcbaacbacabdccdcddbbaadaaaccdcdbdaadadadcbaccaabbaaddcbbbbbbaadbbcdaaacdbcbdbdccdddacddcbdddacbadbcbdcbbaadccadcdccbbbbabbddcabcbcdaabacdcbbaadbdaddbbaaadabcacbcdbbbbdddabddadbabdcdbbbcaaaaabddcdaadbdaadaccabbddacbdbaacbaddaadccaadabddccacbcdbdababbcdcabbcbbdcaabbccbdbabbdccddabdbbdcddabaaacbbadaadcccdbacdabccaaacbbacbddcacdbdbdddcbcbccbacbcdddccdddbcdddbbddbacbcdabcdddcbbdadddaaaddcbddaadcdcdbababcbddacadaacdcccaccaaabccdadccdacbcbbbcaaaaaddbabdabcccbdcbbdbacabaaddbbcdabbbdbaddddbcdabcdbcdacdbcacddadabdcbcabbdbbacbabaacabcbadbdacaddadaccbdaddcacbcccdcabddcabacbbabbddddcbbddcbcadcaaaaccdcdcdbaadcbcddbbdbbcadbcdddbacddabbcbabbbddccccbdaadcaabaabcabdabcbadbbbacabdabbcadbcdbcacbabdcaddddabcadcdadabdcadadbddadcacbcabbaacaddccbdbdbcddadddacaabdaabcadcbcddabadadddcaddacacacaaccdbdcadcccdddccaaddaaacbaddccdcbdadadddcaadcadbccdacbbcdadbabcadcabccbdbcaccdabdbaaccbacdacaadcabacadacbbdcabbdbbbbaadcdcbcbdacdaabbcdbbddbaaabcccdabbacccccbacadabbbacdcadacabccadbabccbcbacabbacababdacaacdcbadcdcaaacaaccaccbddbbcbcdaadbdccbadbdacacddcadbcacdcbcbccdadbdaabcbcbdabaccdbdabdbbcddabcaccaccabacbacababbdcddbddbcaaccacdadaabcaadbbcbacdbdabcaccdddcabacbbdbbbadbdabbbacbabdcabdaaccacbaaaddcadbcdbcbadbdbaabdaabadcddcdcacbbadaacacbbbbddcaaacbcacadcdacddcabbbcadadbccdcccabaaaccadcdddaccabaaccccbdadbddabdbbcaaccbabaadadadbaadcbddaabbcdcbacddbdbddcdddabadddbbaccbdadbabadadabcbbbcbccccddddccdaddbccaaacaaacbbbcdadacadabcaaddbabdbdddaacbcbccbbacbdadccddcaadcacdbacdcbabdcabbbbdbcbccbbdbdabdccacbccdcbcdbbaaddbbdddcadbdbaddbbcbacbacabbcccdbadccdddbcacbacbdadbabcbcbbbdbbbabbcbadacdbcbbacadddabbdabdaabddabdacbcccbbacbadbabcacadddabcdcacbbacbccbacdcdaaaabaadcccccaabcbcbaaaaaccbacbbbddabbacbcddcbdcbaadbdbadacccdadabcadcadccbcccbdcbbdbcbbcaddbaaabadacabdadbabaccaddcbbabaababbcdaccbacdbcbccdacabbacadbcbddbbaacdabdbcabdcbddbcccdacbdbcbaccacdadadcddbcacdabbdaacabcbbacbaddbddbdddbacbddcdabbccadbddddbcabdabcaccbbbdcaaaabcadadddcdcbabdcbbccdaccdbbdcbacddcaabddddadadacddaabdacbddbacddadddbbdddaccccbdcabcdcbacabbaccababddbcbcaccbcabaacaaccbaababaddcbabbbbddabbcdbdacbaaccbdbdabadabacdcdcccdccadaadddaaabbbaadbdcbbbdadccddabbccbbbacaabbbbcbcccbdacbbcaddcbbdddddddddbbdaababccadadccbdcddcabaddcbbbbacaacababddcddcbcbacaabccaabbacbdcdbdbccbabdbbdbabbaddabacdcbaacaddadcbadbddacaadbccacbbcbdcbdddcababadbbdcacdaccbcbcbdadbdabadadbddcbcddcbbbbdbacdabdbdaaacaddbdcdcccdadaaaddabcbbaaadbcdaddddccbccbccacdbcddcbcbadbbbdbbadcabcbaadacacdcaadcbdacdcbbabdbaacabcdabbbacaadbcdabdddadcccababcbdacbccdbccdccbdcbdcdcaabdaadacbadcbbdcddcddaababbabadcacdacddcaacacbbbbbdcaaacbacccaddbddcbaabdacdabcadddaaddaccbcbabbbcbdbadcbddcdbdcccacadccbabbbbdacaacbdbaaadcaabcabcbcddccabaacaccbddadbadcacbcddaaaabbababdbabaaacacbacacddccbabcdaadadacdbdadbabccabacbccdbadadcbbcbbbcdadbdabddacbbcbcdcadbcaadacbaacdccbbcacacbaabdaadcbbaadbccdcdacbbaabbbbadacdadadcacaabaddbbbaadbcdbaabdacddbccccbccdccabaadacdacaddbaddcdbcabaabadabaaabbddbdcdbdadbcbcdbbbcdbacdcdbbbbbaabdbbdbddaacadabdcccadbcaaaababacadaadaadbccbabadaaddbcccdabbccbcddccabaaabbcabcbaacdbcdbbaabdaaddcdbadbdbcbabdbcddabbcacbaadabadcddbdacaabadadcdbccbbbaacdccdcdbbcbcdcbbbcaddcdddbcdabccccbdadcbadacbccadcddaddddabdddbaaddbdcccddacabbbacbababdddcabccaabcccbaaadbbaabcbdaadcdbcbaadabdccbdbbaacbaabbbcdacdbcbcdaabdbddabbababddddaccdcaddabcccccbbbabdaaccbaaabbabaccacdcacdadccbdbcbbaabacbaddacabbdddadbabaacbcdcdcdbabccdbcadbcadbdbaabdbbdcaadabdbddbbccddabdbdacacdbaacbbbcadabaccbdaccaabcdcaaaadaddcdaacdccdaaaabcdacbcadbbadaacbdcbbcaaadcdbababbacdcbcdcddaacaccaccbaabbbabdadcadacddabdcbdcacddacdadcbddbddbbdadadaadcddcabdcaaddacacccabadcccacdcbbbabdbcdacddcadbddbcdabbbdaaabbcbcbadadacccbcbccdcacdcdadcaadcdcacbdacbcbcddbbddadcbaabaaadbbacdccbdbabdbbddaabdbcbcabbbccbaddddcaacdcadcaaacaadadbdbcbbbcdaddbbcbbdcabdbcdccdacddcdbabadcddddccdadbabbabbbcacdacacabddbdbcabcdaadcdcaddcaaadcdadabbdcadaadbcbbdbcdbaaccddcbdbcabdcccaccdcadccdbdbdbbddbadccbabdbbcddaacdabbbbcbdcdaddccbbddbcdcabaaacdddcdabaccddbcbcbdacaabaaabbacbabacdcbabdcabbcdbbccbbbbadcdbabccdcacdcdacadbcdaddbabaaaadaccadcabadadabacbbabbaacaaccdcaacccaadbbbbccbbcbadbbbdcabaaddbdbcacdcbddbbcbccadaaacbdabacdcbdbaacaadcadacddcccddbabcbdacdbcbbaabcbdcccccdbcbabdbdcacaaccdcacbdcdaddacdabdccdacacbbdbadccaabcacbdabddbbdbaabccdbccdaadacdbbacbacbacccabdcdbcbcaacdcbdadbacaaaddbbadbdabaabbcaaabaababbbcadadbaabbaabbcabdcaaadddaadadacdbdddddcacabcadbbbccdbabacaccbabaabaddcaaabbcacabdbcaddbdbabbbdbadadacabccacdbaabacdaacdbddcabccdcddccccbdababaaaacdbbadabcbbdbaadcaddacddcdcdacaacbcabababacdcbdbaabaabbacabdbdbdacacdabdccbbbcaaddcbdddbaaabcbbdbaadcaabbcacadaddbcdcccababbbbabddbacaaadddbbdcaddacdbbbddacccdacabccbcddaadabcadcbbddbdacbcadaacabacacadadcacaacbdaacadddbcaacddbabdbaabbacbdcacbadcbcbbaaacdabdccdaacbcdccaddbbbcbcdadcacabbadccbbbbcbababcacabbddcbbcabadddbccccabcbdcddcbddbbadcddcbabccdadbcdccaabadaadadcbcaadcbdcdbddaacdbccdbaddbddbbcbddaabaadccadababaabbababbdbaacbaadbcbbccdcdadbcbcaabcdabdacbacbbacbadadcabbabbddbdadabddadcdcacdabcbadcccbbdcdabdbcccdadadaaddabacdcdbbcabaccbdaaccbaadadbacbcaddbcabadaddcacaaabacbdaababdbcddbabdaddbdaabdccdddcaaaddbcaaccdbdbbabaacccacadbacabaaddbaabcccbabacbadbdadbdabbabbababddccdaccccbcddbadbdbadcaccbaddccbbdbcbccbddbcacbdccbdbdddbadcacaabddadadacdddbdcaddcaaaabbbdddccbaaccbacddbbdadcbcaaacdcdbdadadcdcabdbbcdaabbdcadbdbbbbdadabdaacaccabbbacabaacbccdcaddbccdddcdbbcacaaddcbdcccdbabcccdacbddcadddabaaaabdaacaadaadcaccdcadadababdcdbcbbbbbcbbddbcdcaccbbdadddbccdddcabcaadabcdbabdaacaadacccccadbdcdbdadddabcabdabdcabdaabbcbdddbacbcdacdddcadabcdabaadcaccdababaaaaaddbaddbcbdabdcbddbbaaacbbbaaccbaababdbccccddbabccabdbdbddbdcbacabccdcdcbcbbaccbdbcabddddccbacacbddbccabcbaccdbbbacbdcaccbacdbcccbaddbacdbcabbdadcdadbbabbdabdddaaabcadacdbbdadbcbbacddadbaaddddbdcacccdabbadabadcdddbabcadbdcdcdbbadddccabbcbbdddcaadaabcbcbcddcbabccccdbaaabcdcdcdbbbbccacdbccdbccadaabdbcdaddbdbdbbddcdaccaaccdcdcabcccdbdbabcaadbaaaaccaccccccbccddabddbdbbacbccccbaabdbacabcdadbcacaaaddcddccaddccaddbccbdcccddaaddbbbcadcbbdbababbbcaadcbaaddbdabadbaabcaaaaccbaacabccadbdaaccbbaabbbabbaacdbdabcccdaabccabbcccbcddccbdabdbdaaacdaccaddcdbddbdbbacaabadaaccabbaaaadcbcdbacaacbdbbaabcaabcdcbbbdccdbcaabaddababdbbdbbbacddccadabaabdcaccacbaddddbcdbbdadabccdcaaddcbdaacdcbcaaadaddbaadbcccdbbcdabccdabbabdaadbdcddcdcbbdcbcddcbcbcddbcbaccbbbcacaacdcdadadcadaabbdcaddbaabacababddaaccbcccdbbcbbcaaacaccabbdabacacabdbdcadcbccdcbaaabcddbcbacacacbcdbdcbadcbcabcaababadddbaadabdacaadabacacbccbbddcdaccccadcaacbbbcccacbdcabcdbcabababcaacddddbabbbaddaccabccccbcdaccdbbcaaabaccdabdaaadccdbcdcabbabadcbabbbbdddbbddcbdadbdccbbdcbdcaacddaadddbbcacddaacbabbabbdcddbcabbdacaacccdbcbadbabadddbbacbbccacbaddbbacabcabacaabbddcbacbbaddccbacaccbbbbdcbcbdadcbabcabaddacdcbddddadaaddabccdacdbabbdadcaccdacbaddddcaadccbbbabcabddcacadabccbdaddbcbcddadcbacdacdcaaadbddddcbddcadbcbccdddabdbcbdcdadadcdccdcaaaacabccaaccbabcbdbbbccbacccbcbbbaadbacdaadadacdbaaddccaaccddbbccdcdcbcacabccccccaddadbdcdaabccadbdddcddacdccadbbbccadbdbbccddadbaaddbbcadbbdaccaaddcaadabbcabaaacaadaacdabccacdadbbadcccdaacdbddacbdabacadcbbccbbcdacbadacdabadbbcadbdbbdaabcacbccadbcccbbabcdcdbcdbbbabcbaddadadadbbaccabcaadcadabbcbcacaaaccdaadaabbbdcdaabadcdacddaadcabacbdaabdbdbdddaaaabdcdcabdaabdbcdcdccbcdacbadddddcabddccbdcdaabcccccdbcccbbacddcadccddccdacacbdcadbcadbadcdabdbbbcacbbbacbadcaddccdaabbcbabcaaadbbcdbcabdbdbcbcbcdabaadcabababbababaddbadbacacdcccaadcbacadbbaddcbaabbcbacabbbaccadabbbddddcaadcadbdcadbaadddcaaacbcabacbcabbabcdcbdcabacbbddabbaccaabdabdbbaccaccacbcabdbaaababdcdbaccdcabbcaaaccbcbacacbbdccbbcbccbbdacbdbacacdcbdaacabdcbdbbadcacaccacdabcadcadacdcaccdddcbbcabcadcacdcccbccddbabcddbdbbcbbaccbbdaddcacbcccddaccdddadcccbaacddccddcaccbbdcbcbddbcbabcdddddabcdbcdaacddbdccdbccdaadaacdbcaccccbaaaaabadaadcdbddcccdabddacdddbdbcacddcdccdbcdabdcdcccdcbcbbaabcaddcbcddddadaaccddacbbacbbaaaddcacddcadbacadcaabacdcccadcbadaddbcbddbcadbbdccdddaaaaddccadaabcabadbaabbdabdccbaabadadcacdaaadaddaadcdabdaccbcbbadacdaacdadadaaaccbdccdabcadaabcabccccbbcbaaaaabbbccdaaddbcdbcacdcccccddaaadbabacbaaadccabdadcadcaccaabdacaaabbcadabbbabcbbbacabcbaadacbbbbccbdabadcdbdbdccadadbdbcdabaaabaababdacabadbbcbbabbbcddbccdbdbadcadbdbccbabdacddbacabdccadcaadaacdcbbacacccbcadbbaddbcadadaaabbacbbbacaaabbcabbcdbaddaaaadddbaabbdadcdaadddadaaccabadcaaabbdacbaddbdabcaabbaddcbcabbbcababadabacabbaccbdabbabcabcbddddaaaabbcdcbcdcabccdbaabbbdaabbdcbbcaacbaaddcbdbaacdcdaccdbbcbbbadbaaaacdbacdccddadaccccccbdacdacdddcabdabcccbbbbbdbdddcabcaccbdadabccccbcccababaccdbcbadbbbdaacadbcdbbaadadacaadbcadcccaabbdcbcbcbcccccbadbadcaddbaccaddcaccacbbaccbbadcdaaacadabbaddabbbbabddbdcbcddacadcdbddcddacacacdccbcdaabcbaacaacbababbaaaabdbddbdbddddbaccdccadcacdbbcababdcadbbbbcccddcaaddbcadbaacabbbacaddadaadacbdbdcabacccbbacbcacdcdbacdaadddbbdcbddaaaacbcbbbabcdadddbdbbbcbdcddcbddbaabadbacabadcadbcdacbabbddadadbbdaabdaaadabdabdbaabdddacadddbdacabdababaccadddbbddbaacbcaabbdccbccdcacbdabbdaddbacbcbcccdbabacaccddaadcdcdaaaddcbaddcddbaaaadcbaabbdacbcababbdbacaccdbbcdccbadbdbaaadcccddddadbabdaddadbaaaccaaaadddabadcaccbacbaccddbadbaadaccbdcbdbbcbbaaacacbbbdadaaabbaadaadaaccddcadccbbdbbbdbddbddccadbabadabdbbadabbcbcdddddcbaccbcdcdcdbdbabcbdccdaaacaddccdddacddababdcbdddcdcdcbbdbcdabbddddbdbccddbaaaddcbcdacaddcaaaddcaacbaacacaabbddaddadccbdbcdcdcaacacacaaaadbadcabddadabccacbadbcdaaccccaadaadbbccabcccbcdadabcaccdbaccacbbcdabbcdabdacaaadddcdcbcdcdcdadcdbbcbbcbdacacabababcbacbdbbabaacdcbaacaabccdcdcccdadccdcdcbdbdcabacbbacdaddbcbaacddccabaaddcdccacdcadccbddbcdbabbabdabbccadbdcdadcaccadcdbadcdbaaddcbcdbdbcdadcaaaadadddacaabdbbdcacbcadacddacdbccacddaabaaaacbadbdacdbbabaabcadbacbbdbadcaababdbcdaabcbdcddbbacbaddcbccdcdbddaaaddddaabacbbcccdacacaabaacdcababddcdadddcaaadaadabadcbabcddadcaddcbdcacadbbcccddaccdbddbddcadcabddddaabbcdbacabadddadbccbddcdaddbccdbcdababbdcaddbdaabbcaddbddaabcbddbaabadcdaaabacccdcbdccabadbccbcdbaddbdbcdbbaaacddcdaccabdbcbbaaacacadbdcbddbccadcadbdbdbaadbdbdbcccdddbbcabdccaccbcbbcbaaaabdcdbccccadcadbbbccdabdadbaaacadbacdbacdacddcabdbadbbaacdcaddabdbbccbcccabbacacbbabdcccdaababdcabdabcacdbdbcbccbbaaaacabdacadcbcccdbddacaaaccadddabcdabdadbaccdbbcdcabcadabcaccdcbdaadcbddcaabadabaddadcdddcaadddacaccbaccccbcbacddadddccccacccbabbabccbcbaadcdbccabdbcbacbcccdbcbddbdcadcbdaabcbdacdcbccdacddaabccaabcdcaabbbdaccbccadccabdbacaddddadbbdbcdcbbadbbbdddcdcaaddcabbccaadcddaadcadadcaddbdaacaacbbaccdcbcbbadadaccccdcdacbcdcddbbacdacadaaddababcbccdcdbaadadcdccaddcbbccbbaaaacacccdabadbadabadccaccddbddabbdaaaaacbbbcddadaabcdbaccaaddcbddcadbccbbcbccbbacdbabdcbadaabacddbccbcdbaaaacbdabccdddbdccadbddacdbbccaccdacdcaccbcbbaddabcddbadbbcacacccccaacbcabdbbbcaddaccbcdabdbdcbdcbccabcacccadacadccaaacccbcaabdddacddcaaaccbaabaaccdcbddabbcbcdbdbdaadcabbbaccbaadbaccacbdadcdbddbddaaadbdbabdcdbccabbcddbbbabdbdabadbaadadcaadbcdcddccadcddaabbccdcddbcdaaabacdcbdabadbbcdddbdcaabdbabbbccdababdabcdabdcadaabcccbbccadddbaabbcdcdcaccdabacabaabdbacbdcaacbabdbbcaaaababdaccbacaacdcacddbbaaacddcacdaacaddbbbcbbabdaadcaaadabdccdabcddddadcbbbbbaabdcdacacbabbcbaabcbbaabadaacbcbddbbdbbbddcacbcabdaddbbabaacddbcbdcdcbbddcccbccdccbcaaadcdacccabdaccaddcaaddbdcacadadadcccdbabbdccddbbcbaccbdabbcbcddabadbaadcbbdadadbcbcabadabadaaacaccbaaadcdcbacabadcacaccdccaacabbabdbcbdabcacccdcacdbcccddaacdaaaddccbbbbdbbddaabcbcabcbacbcccadcccccdbbcddcaddcbacbabdbddcbddbccdcdbdbbcccdbbcabbacbbabdbcabacdbbdadbdacadbcbcdcccaacdabacdbbbaddcdbddadcabaaacbbcddddaabbabbbcadaabcddbccaadbbdaaadbcccdcaaababbbbcaaacdbacbdccddbcddbabdccddcdccaddabccacdacbadabccddbdccdcddbcbcddacbdacdccdbacdcadddbbbdaacbbcdcacdadbaccababdddadcadbcbcadbaacbaaacbaddcdbbbaadbbbbacbdadbbcbaddadccbabdcbaacccdbcbccccdccccadcdcbbbbacbddcabcbdbcbbcbbddcbdddddaddbccbadcadbadcdcbcbcacabcacddbccdbdbcbaadadaddabcaadacdaddbcdabccaaabcaaacbbbdbcddbcacabbcadcdbaadbccabcbddbdcabcacdcccdacaabbacddbabcdaacbabccbbaccddbcbacddccaaddbadabbaaccccdadabbbcabbadcdbadbbbdbdbbdcddabdbabcdbbdaaccadaddcaabcdacabbacbcbacaccabdcacadcacaadcdddccaacdcdacdcadacabbacababacbbccdbdadccadabccabdbaadbccabcabcddcdbbbbdbbcbdabbabbcbcbcbbcdccaaaaabaacabbacbdcbabcbabcdcbcaabbaadbabcdcbbbbcbdadcdbbdadaabbdadcccbadadabdcdbddabcbbbccaccabcdbbabbcadcadcddacccbbdbaddabbbacacdabcdddadbdacaaddcabddacabaddabccacccdcbddaabbddabdcbadaddbbbbcbcbaddaddaaaadbbbadababccdaccdbaacddcdaabcdadaccdccccadaaabbbaaaddcdaccabdbbacabdaadaadabccdcabacbabbaaddbacddcdcddabaccdccdaddbcdcddcadbbabbabbbadabbdbadbbccbabdbcdcdbbabcbccdbbdbdbccdadbbaccaddcbadbabbaccbdbbcdbacbdcabccadddaddcdccdbbdcdbaaddacbaacbdadacccbbaccdadbadbcdbcddccbdcbbbacbdadcdacacbcdbcdaccdcdaddbbdbadcaadcdcacadaccabbaaaadbabbcbbcbbbddbadbabcdddbcbdddcabadacddcadcdccbcacaaabccaadbbaccddbbdddbddaacdaccaddcdcdbddbbcbbbdaddbdacbadbdbdacbcaaaaadacabaabbaacabcaddbadcdcdbbddcbcbbbccdcaabcabbdddcacdcddcaaddbcdccddbcdabaadbdcbcddbbcdbbdbacadccacbcbdcabbadabddaaaaadcdccabdbddddccbdcbcbdddabbdcdcabadcdaaddadcbdcadbbdcddaacdbaddaaabcdbacccdaddabccadcacabccccabdbabaadbdbacabdcbbcddaccacdaccdddcbadccabccdaacddaabcbabcaaccddaaabbcdbdcdbddbabcdcdacdcbbcbcdcdadadadcddbaddcbaccbcadbbaaaadaccdcaabddcddabbddbdbdabdcabacddacabbbcccccbadaaabdbcccbdddcccaabdcbbcacddbddcdbbabaadaabdacbaaddcbdbddcacabaaacabbbbdcdcadccbbbbaacddabacdcbdbbddcddbcababccbadbdccbbabbccbddaabaabcbcccdddbdabababbdabadddcbdbdddacadbbbbaccdbbddcbdaccdaadaacbcbccccbbaadcbdabadaabbadadbddddbcbadcbcadacbccdcdacbadcdddbdbbdcbbaadadbcbabbdcdcbabbdcdbdaccccaacacbdbccabaadbbacadbdaddcbaaacaddddbddcdcddcdaabdbdcabaabbabddcdcbdddbcbdaadcdbaadccababaaccdddcabcbdaacdcbcdadcaabacaacacaaacddcbdbdddbdabdbaadacddadcdddbcacddacddcddabdacddcbcddbdacacabccacaccaadadbbbbbdcbdbaaaddbdbddabcccbbdbadcbaadabdcbccadbcababbdbdddbcababaccabbbacdadabdaaddcadbdbddddccabaddcbddcdcddcadbadbaaddacbcdcddbcddaaddabaaddcaddddbddddbdadcaccbccddbdbbcdadcdcacbdaccdbacacbcdbdbabbaaaccaddbabadcdcacadaccaaaadbbaadcabcbddaaabacdbbccbaddbcbcdcacbaaddabbaccacbdadcccaabbccbbcbccabdcabaabbaabadbababcccbdaadacbbcdddadbdbcbbaddbccabdcadabadaacdbdadaacaadaabbbacddacbabacabcabababaaadcbbdaadadcbaacccbdacaabdcdbbddcdacaadbcccbbcccdbdbccbdabbcacddccbccbcacbbccbbcdbbacabacacccabddaabaaccabacaabdabdadccccacabcbdbbddcdcaabbdcdcdbcbdbacbcdbdbaadcbdacdcdcbabbbbcddccdccdcdddbcaddabbcaaacbccddbbbccbdabbdcdddacdbabbababdadcadbcbddbcaadabdbbbaabdbcababddcadbabccaaabbccdcccadbdcbbdaababadadbadacbdbadaaabcdbbdbbcddcbbcdaacdccabbbcadaccbcabbdaccbcabacddcdabbddcadbacddbcaddbbcbabcaaadbadabbdbacbbdbcbacadbdddbcbdbcdcadabbaaccabdadabdaabccccacdabaaaddcbbdaadaccdadadbbbbddadcacbaadcadabaccbaccbccacabcbbcaccacdccacbdcbbdccadbbaadadcdbdaccabccccdbcdabbcddcacabaaadbdadaaaddaacbdacbbadddbcccbbadaacbdcbaaaddcddbddabcccbbacabdbddbcdcbbdaccabcbbbaaaacdbaabbaddbdacddcbadccddbdcdddbdbcbdbcbaccdbaddadcadbccdbcbbabccddddabcbbabcbabdbacbbdaacbbbabcdaadcccadabbccbabdbbbbdcdbccbccddbcbdadadacbbabbdcccdbdbbddaacbddacdaabcabababdccaabddbdddacabacbbbcbcbadbbabadbacaabdbbabaacaacbadaabaccbdaacacdaaaacdcdbadccaabcccccdaacbcccbcdbbcdbbcddbbcbbaabdbbadcdbdcaadbdcbdcbacaabcaaddabdbabbabccdbcbcadbddcbbbaddabcddacadcdbadbbcbbcbadddccabbdcddadbcdaabbccadabacabbadbababdbdaccccacdacadbbdddcdbcdbbadddcbccabaddaadaadaacaabdcabcabdccbdccadacbadbccbdaabbbdaaaccbcbdcaabcbadcbbcacadcbaacacadacacadabacaabacdaaaadbdabcabdbadcbabdbdbdbdcccbbacabbdaaadbbaaadbddcbcdcbaddddcccbdaadabbdbcbaaacdabcccddadcbbcddadabbbabcbcbcdccabcbddabbadddbbcbdbbdbbcddddaaacbbddaadcbccacddbbbacccabbcbdaddcaabccbbacdcccabbacacbcbbcdbbacaaadcbdaaccadddadbbcccdabbbddadcaabbccdcbbcbdbabbccdcabdbdbdcbaaaaaaadbdabaacabcaaddcddcdabadbbabbbdbabbbbddadacacccbddcdbcbbdddcaaacacbcbdcccacdbcdbccadcbcaccaabbcbccbccbddbbcbacbbdcaadadcaacacbaadbccddcdcccaccccdbabbdabaadcbaddbbbcdcdddabdadcccbbdbddccaddbcadbacccddacccbdcbaccbbadddbcadbbdddbcaddcaaaadbcabacdbbaabbddacaacabbcdcccbdddbdacbabcccbccaadcbabcaabdcdadadacdccdbabbacbcacadcbabdbcdcbcdacbcabdcdabbcbabccacaacadacdccdbaacddacabdbbcdacaadccbcacadbaddaddcbabbcddaaacdabbbabdbaccdbcbdaadaaadaabaddbbbaacbccdaaabcdcabbbaabcacdbbaabbbbbbcbdacbdcdbcbdcbcbbbabccdddcdaaacccaccacdccdaabdcbddcbbdbbbbddccbbbbabcaaabbbaabcaddcbdcbacbcbcbdcaaddbccdbdbdbacccdcbbdccdaabbccacbaacadcccddabbdccbcdddbacabcbdbadccbcbcbdcaababaacacbcabdddcddcbdcbbadcbaadaaabddaacdaccdbccdddadbdbcbaccbbcddbdbacaabcaddbdacbcbcdcaababdadadcdcaacbbbcadcabdababcabdddabbcdcadadaccbdbcbdbbdaabbdcbacccaabacbabadababbdddabacdaaaabbcbcbaababadaadcbacdacbabdbddcddadbaddddcaccdcdbdacbbbdabaabaddcbbdaddddbabdacbaaababbababacbdabacabadbbbadccbdcdacabaadddbcacadcdabccdbaaaccbcbdccadbadcccaadbcbdcabbcdccdaababcabcacaccadbcbcdcbdbabcdccabaaddabbaddacdcbcbbbbabbbcbcddccabcacdadbdbbdccdcaacbdbbdabdaddbdcdbdcabcddcdacdabadabbbcadadaddbdabaaccdaacbadabaacccdcabaadcdcdadddaddccaadcadcdabaadabbbdcbabbaaaabcdbbabdaaacadcacbbadaabbacaccdcbbcdcccadcacbcabdbdbaccbdababbacacccdcccbddbddaccabddaacababbaabbbcdcbdacddcbccccbacdcdbbbaabccaabaadcddacccaaabcaacdbaabdcaacbdbcdbbbbcdaacbcbbccaadcdaabdddcaacdbdcaaaabbdcbadccbccbaabbddacdbcadadadadacccbadcbdacdbdccbaadbdadbdcabbdacababddbbacdcadcdabdaabcaaabadabddbbabcccddaaddbbcbacddccaaabcababdbabdcacaccbcbcdbaddbddaacbbbbbcdaacadcacdccaadddccbdaddcbddccdbdaaadcbbcbbdbccbbbadbbabbbbbbabddbaddacabbccbddaccaacaacadccdddaaccabdacaccdccdadadbdaacccdacacdbdcbaaacbcbcccddaabbaabaadccbbdcacaacbadaadccdadbdddbdabadadccdadbdbaabbbddcccaabdcccbbddabbcbcacabddabbbcbbadabdcdbabaacbbaabccddadaabaadccbbbcdbaadbddadbabadbcbabaababaadbabbabbddbddbbccbcddcbdcdcabdcaccadabadaacbcabacdbdddaddbbcccdddaddbbacacabbbabddcaadacddcabacdbdbcbaadaaaddabdbbaabddbacddccdadcdbddbcacabdbdaadaaaaacdbbbdbbdabccdcdcacccccbdaccbbabacbacacaacbdccaaabdbbddbdbbaddabadbcdbabaacadcdcadaaddcbccaaabbbbacdaabacbaacaacbbdadddcdbdbcbcbcdcbcdbaabbbdbccdbddcaadbcbcabbbcdbdcddadabddacdaabbabadaaccdcbbaaadaccbcbdcbdbbbcaaccaccbbbdabdddbdcbacbdaccccdbdbcbddcbdabcddabbccbcbabcbdaddaccbaccaaaacadabacaddaacbdbccdcbdaabaacaadcddbabddccdbdbabbbdbcbacabadddccaccccacdbbaacdacaabcabbbcbbaccdcbaacbbcdcadacdddbdcacabbbcdcdbccbddcbbdccbaabaabdddadcbcddbcbdcbaadcacdcadaaabadcccaccabccabbdbcadaccdabdbcdccaaccccdaaabbbdaaaadbcbaadcbaaddaaccddaaadcdcccbbccabcddcdbbcdbbbbdacbcdccdbdcaccdddabbaddddbcdddddddbcddbaddababbbaccdcaddbccbdbdbbccdbbcbcdbaccccdddacbcbdabdbacbdbbabdcdcccadaddcabaaccbcdcadbaabbbdabdaaacbdaddcdcbbdbcdcbaddacbaabbacdabaabdbcbdadbcdabacddabdcdadccbdabacdabbbabbbdcccdcbaacdddbccdcbcbddabacccdddabdbbbbdaaadcccabaaadbbcaccccbadcbddcaaddbdcddccbdcdadadbadcdbbadcdbabbbddcadcaabacdabccdbbaaddaadaacdcacbdcbaaaabddbbddbaadbacbddacaadbdbbaabbccbcbabbabbdbdcbaddddbdbadadabacaadcbddbbaaadcacdbdbadbacdcbaccbdacbccbdabadaddbdccbcdaaccabacaabcccabddcdccccbccacadbcddbbadddbcadbbccdacbadbaaabcdbdaaabacdabdbcbdbbbdccdaaadacaaddbaadabdacdacccaccdbcccdaccdaccbdacddcbbabcccbcbabacdbcaddbbddbbbbbabbaccacbcbaabbdabccdcdbbcddacdbcdcccddcbccadbaccdccddcdccadaadabbbacdcabacabadababcbbdcdacdacbccdcabbaadddbaadbdcbccadbababdbcbcccbaddbccabcbabadcdacacadccbbbbcbdcbdcbdacadbabacccdbcbbadbdaadbabddbcbdbccaacbcccabdbdcdcccacadacdcddacccadbccbaccbcdbdbacadddbbbbddbbcabadbdcabbaaaadadabccacbacabbcdbacbaabcdcdcdcdadcbbdbbacdbcbdabdcccccbbdadaccccbdcbcccadcdbbabbaaccabaaaddbccdbacbccaabbcbadadbadabdcdddccaacdacbcbadbccbdcaddcbcccbacaacbdacaabdabbdbbabaddbaaadadddababbcbdacccaadbbacaabcacbdcccbbadcdaabbaaaddbacdcbbdaccbaddabccdbbaaccbbdabddbcccdbaadbdbbddddacdbdbacbccacadbdcabcccaabdbdcadcbdabbacaaabcccaacbadcbcacbbccbaacbadadbdadcccddbcddbabdadaabbbadcbaaaaccdbcaabcaaccdaaabccdadbaaccbabdcabbdbaaadcdbbcaadaddbcbaccbddcdbacabbaaabaaabbdbabcabbbbacbababaabdbaaacdbadcdbabbcdcbbaaaadddcbdacdcbbaadbacdbabadddacbbdacbbcdbdaddbadbabaabcabcaddccdbbcbbacddcacabcbccdddbadbddbbddddadbacbadcbbbcbadccbdbabacbabcbbccacccbccbadcaadbcbadbbaadcadccdaccadabcbbaaacaadbacdadcbcdadbaacadddaddbdbbcadddccdcdbadabbacdadabcaabcdbddcbaacbaadacbadbaddcbbadbbcdbbadbbddbabbacbcccbaabdbbddbbacbbbcbdbbcdacbcdccaddbcadcaacaddcbddbcdcabccadbcdabaddadacabbccdbaccadcaabdcbdcaabdaaccbcbacacbcadbdbdcbacdcbcaaacccbdcbacacbabbbbdcbbbbdcbdbdbccddcabbbccdcddccadaddaadbdadddcddaccbdcdaccabbdadadbccbbcdcbcaaacabdcdbccbacaaadbabccddcadcbaddcdadcabbbcabccacdbacacaabbabcbbdcbdbbcbccdcbbddbdccbbdbbdacaacdabadbcdcaddacbcddcabcabcaabddbbaddcbadaabdddaaccdccaccdabdaacacaddcdacabaccdcddabbbccdcabbccacdadcbccbadcbabbbacdddbcbaddbbbbddbccbdbacbadcbbddbdcbbdabdbacbaadbbcacdaddcacdddcbcbdabbccddddcdbadcbdbbabcdddbabddaccdcbdadbcabdccdabaccdbbdadbbbccdddcddbccaabddcacbaadbbcbdccdaabaacabbbaacabcadcbadacadaabcbaabaabccdddcbaddcbacbaacdbacbcbcabbccbbaaaddbbcbcddccadbbcbdcbcbcacbdbdbcbbccbccdaddcbbcddaacadcddcbdaccbaddadbbcccaadccccaacbabcabadadcaddacddbbdadaccbabdcabdbaacaadbcddcdbdcbcaabbaddddcbcdbcbccbdccdadccabcaadccadcdcdcaadbaaccbdccccdccccbabcdcadbdcbdaaaccadaddadbbacbcccbbbbaacddabbacadcddaadcdddaacabcabddbbacddaaabbcccdabaaccddbbdccabdccdcbbdccccbddcdaccaacdbdcbbdcbcbcbddbdbabcbcbbccdcaaabaadbacdabacbbbabbccdcaadbcdbddddddbcbcaaabbcbabbadccbdacadbdbcccdadabcdbdbcadddabcddcbcaabbdddcbcaacbaddacdbdacadbcbaacbaaaaaccbabcddcbbbadddccbdddbdaacdaabaaaaabaddbadccddcbbbbaaacacdbabddcadaaddcbbcbadbabbddabcbaccdcacbdaccdcbddbcbcdccdcacdabbdbbbdddbbbaddbabdbccbacbccdaabddbaccacdacacdadccaddbbcccdabdddbbbcddbbcdccbccaabcddbdadbdacbdbdbdadbbccbddcdabcccbbcaacaddbabcbabbddaacbbaacdabbbccabbbbdabbabdadacbcadccdbbbddcabadccdbdababbcbbbdcadabbbaccccdaaaddcccbcdbddbcbadabbaacbaadbcccbcdbacadcddaabcacbabaadbcaaabbbbcddcbaccabbcdbdcacbdaabddcacadcdcaadcddbacbdccbcbbdccdbdbbdacdbdbdbcbcdabaabbdbcbbdccdaaaadcbabdcbacbdcccccdcbaabadabcaddcadaabaacadadcdcbccdbcabbbbbddbaaaababcaaaabadabaccdcadacaacabdcabadbbbaacbbcbcaddbbbdbcdcaadbadcbdbcddcdbaccbbdcbdddccbdadcdbddbabbaacdcdcaababccacccbbcaccdbdbbbcbccbacacdaddcdcabddbaaadcbdcacacbdadbadbaddacddcbdbdbabdaddbcbdbbdbacbaaadbdcadccddabdabdabdadaccdaaaaacbabbadabddaaabcaacbadbadcdabacbdcaabacccacaaaaacadcbabcbcabdaabbcdcaadcddaddadcabcadcdbaadcbddadaaddbdbbaddbbadadaaabaadcabcaacdddaabacbcbbccbcabddbaadcdcddbcabaccdadbabbabbdbccbcaddbadccabdcbbdcbbcacdccbaadbdbccbcdbdccadcdbcdbaddacadccddcaababbcccdddbabcccddbcbcdcccadddbccdddaabcaaabdddbcdcbadccdabacbbcdbadcbabbacbbbcccaacaddcadcddaaaaaaabaccbccaaccabcbccbbbcadcdccccddabcdccbaabadcaaaadcdcbddcaacbdbbacadcaabcdcbadacbacdadcdbbcabdddadaacdbcabdbbbbdbbcacbdaccacbdcabaacabacddcadcabcbddbcdcdaaaabaccbbbccadbccdbddbcbcbdcbcccccbaabcbbabdccbaddcdacdadcbbaaddcbadcdaabbcddcdacacbaccbadcdbaadbdcddcabccbbdaacdadbacdcbcabdcaadddbabbdbcbbbbbdbbcbabbbcacacdcdbabdcbadacbacabdcdbbccbacbddcbcdadadaccbabbdabadacdababdadbacccdbabadbdbbdbcbcbcccabdcbbabbddbadaddcccddcabbadbdbadadbdccdbaacdbcbadabbdcabcbadaddcacdddbdababbcaccbaaadbbcdcadcdacadabccdbaaddabdbbdcaaaababacbdcacdbdbdacdacbdbddcdaccccdccbdcdadcccdadabbddcabcdaabcdddcabbcaacabacccddbbccaccdaacbcdaaadcbbabcaacccddbadbadccadcbcbbdcbbaccdcbcdbbabbbcbbbdaaacadddbcacaccdbabadcaccaddcbbadddbdbdaaaaddaccdaddcaadccaaacacdadbdcccbcbaddbdbaaccdadbbcabadcdbabdbabddcaaabbcaaabbdabbbaaacdccabbabbabdaacddaadbbcbcbcddddadbdcdaacccdcbaabbbbbdabaabdcbacaadadcacbbbbcdcaabbcddccaadccdbababcdddaaadbdccaddcadddddbcadaabccadcdabbdccbdccdcabadbdbccbdbcabdaaddddadabaadbbcdcdabdddadadddbaaadcbbcdbbbbcadcadacaddbbaccddacacbcdbdabcdbabbdadbbacaccaaaddbbcbbabaacbabcaaccababbcaaabbbcccabbbbabcadabbbacbcccbcdccaccadacaadadccabaaacdbdadcbdcccdbbddbccadbadadbbbacacdadbddcbbdccacbbdabacdddaaacdcaacdbcbabbbbdcdaddccbaaccabbdcadcdcdbcdcdcadbdcccaaabdacaaabacabdcadbcbdacbbabddcddaabbaaadacddcbbccbbaaacdadacddbadccdbdadbacddacadababddbbcadbdcabacdcdbcaaaabbacbccaccbbbbcaabddccaaacadaaccabccacabddacabadadadcdcddbddcbbcbbbbcaadaccacaaacababcdaccbadcacbcdadadbbbcbaaacacbcdbbbdbddaaaacbcaddaddabcdcadcdcdbdabbccccbccdddcdadadbabbbdcdabdcacbcdbbbdcbbcccaddbddcbdbdccdbdbbdcacbddbadcadddababbbacdbdcdbacddbbacccccdcbccbaaaccadacddabddccacdbbcccaddaddccabdadcaaaaadcaaacacaabbdbdcabdcabcdadadabccacbaabbadbbcabddcacadbdabaacaaacbdcbabbdbbccacbbbbcdbaabddbddbdbdcdbbbcdbcbdbbbaacbbaadcdbcbbdadacadcbaaaccdbabdacdbadaccbbaabcadcbbddabadaccbbbbccbdddaadacacdccdbadddccdccdccbdcdddcbcaaccdcdaadbbaacbdacdcabbbdabcddaabbaadadacbdadbddddccdccdcdbaddccbdadbccbdbdaadacbaccbaabadadbaabbababdcbcdccabbbaabadabbbbaddbdbbbacdadcbadaccaccbbdbcbcabdccaaadddbbbdaadbccabacbcdaababcccdcbbbcadcdddbcbcdbbacacdaacdcbbdabcacdddcaddaadbcabaadcababcaadabdabbabacabddbbacbacbcdacbaddacddddaaadbaaaaccccaddcbabdbaabacdddcdbbbabcacaaadcdcbdacdcaccdcadbbdabddacdcdcaaadcdbabddcccbadcdbdcdbabbcaadabdbcdadccabbcbccdccaddbaacddbdbaadbdddbaaacdabcacbdaaaaccaddacdbacdababadaacaccdcdbdadaddcdacdbdcbdcadaabbcadbdabbcdbcdccbbbdacbcbbcdaaddaabcacdbacbbccdaddcabdaaccdbcabddcdacddaaadcbaaaccaadcddbcbcdcddbbcdbdbacddacdacdbaccbdbcdccadadcbacdadbababaadabdaaabbcaabacccdbadccbdccacdbbdcddccbddbdcaacbabdbccbdcdadaddcaccaadbacbdcaaaabacacadddbdbcadbcddbcdabddcdbdabdbdabacbbdadbbcaaacddbddbcacbacaccccabacdaaadcdcaaabbcdacdddadacdaaddddcbccadabcccacbaadbaacdcabbdbaadabacddcdbccbadbaccaabdabddcddcabccaccabddddddddabbbdcdaddbcdcdadbcbdcbaaaddadacacbdadadddabbbbdbbccdbbcbccdcaddbabbcbdbbadddcaccddabdddabccbdaaddaadbcbaaabbcccaabcadadadccdaaccaddbdbccdddaacadbdcddcbdbccddcbcdcaadcabcbcddbadadccaabbcdddbacabdabaddacbcdaaacabbbaccddbccbbddbdcdaacccbdddbcbdabccadbaaabdaddabbcccccacdaadcdccdbdadbcaccaaddcdbbdcabbacaaadadbddacaaabbdcbacadcbdcbdaadbdbdcccaddbddabbdcbbcaaaacadadabcdbcdcadabdbcbdcdbcaccbdabddaddddcdaccbadbdabdbabdbcbccadabccdccbabcadcbadcbbadadcddbbacdccdccadaccacbdabbddccdcaaccdcbcdabadcabcaabacdbdabaddabadabbdddbbdddcdaabaacdbacdadcaacdddcacdccaaaadacbbdcccdccaabcbccbbdcbdccaacacbabbbacdbccbabcbadbabacbcbbbcdccdcabababdcadcadcbdaabcccdbcacabacadacdabadccbbbbadaddaccabcacdbdcbacdbcacccbbbdbbaaacdbadccabcbbbcbccdcdbadcadacaaadcdccbadbddcaccbdbdbaddccdaaddadacbbbcbdcbabdbccccddbbaaabccaabdacdabccdbbbbdcaddcaacbdacbbaacbddbcdbdacccbdbabdaaccdbabbccaaadcbddaddacdabdbbddbdbdcccadcdacddccdacaaabbccbadbcbbaaccdbddaaadcddaadadcbbccbdbbdcbdccdaaacdabaaaacbacbbbccaaadadcadbbbadbaacbbcdddcacdddddbccaabbddcadbaccaddbddddbdcdabbcbdbaaaabbcdabadddbabbadccadddadadbccdadbadbbddbabacbacccdbccacdddddabcddacaabccaaccadcdbddbdddbcdbbcbbabbaddcbbddcbabdaacccddcddbcdcdaccbaddcaaababbbcdddcacbacabdcccdcbabbbcbbccacbacbcddadadcbbcdabacaddbcaacdddabacbbdaddcbaabdcacaaccdbdbddcdabdabcbbbbbbbabccbaaadcddacdcbcdcaaccddadadcaadbcadcdabdadcaaccacdcbadbdaccddbbdcccdadaacbadccccddacbbcbcccadacbdbcadccabdbabddacdaabbbdbcabcbcbcdcadaadaaaacbcaacccbbaddccbabbbbcacadacdaaaadadbddcbaadabddcbadbdabbddabddbdaaadddbcabcbcccadcaaaccbadddbcadcdbddddbdcbdaaddabaadbcdbdcabdbcdbccadccdccdadbabdccddaabbdbcddddcbbbccaadaccbbaccdbdbcdbbbdaabdababccddbaacacbcacaaaacbddccddbbbbbdcbcabdaadcdaaddcccddbabababbcbddcdcbaabddabbabcdcaacaddcadbcacbcaaabcbccbdbacccdbaacdbbabbdbacbddcadbdccbaadcaaabdccbbcabaddccbaccadcadbdacbabbdbddaacbcccdbbbdbabdddcccdadcbdcddbbbbbccabacacbcbbdcdcdbbbdacaccdbaacbdccbcaacabaacbcbcbbbcbacddbbccbcbccbdddccacdbadcabccadbcabaabadcdddcbdbaaadcbbbbbdcacdbbddbabccbacddcababdddaabdaccabababbbdabcadbdbdbbadbccaddcddccabbcbaabacdcbdaabbaaccbbbddbaccdcccbbbdbadcbcabacaacdabacccddaadccaabcadbaccdcbbbaaaaadadadabcbacaabbdcccdaddddbacababadacabaaadcaadbdabaaabbaddbadbdabababcaccbbabaabacbababdcdcbacdddbabdbccadddcdaaddddabcdbbccbaabbdaacadbdcbcdabbdadcddbadbdbbcacbadddcdadcdaabbbbacdccddbbcbbdaddcabdacdbcdaccdaaadbcacdbdaadbdbdccbbbddbdabaacbdacacadaaadcbaabcaabbcbbdcdbabadccbbcaccbaadbbcbcbdadacdbbcabbbdadadccbcacacbdadadcbcdbbbdbdababadaadabcdacaaabbccdcbcbadcddcabccdbddbbddddaacccacbbabaaaaaabadbadbaddcaddcdabbdbbddbbacdbbadadbacbdbdbcbcbbabcadacaadadbcbcccadddbbaddddbadbbbcbdddacabdbabcdcabbaaadabdbcaaacabaddcbcbdacaadbadcacbbbddadbbccdcbbadddadabdbbcdcbcaddcbbbdaaadadacccccbddccacabbdabdadcbbcbbacbccadddcadbacdacdcadaddadaaddcbbaadadcbbbcabadabbaaaabadbddcacbbcaddbdabddbdbbcadbadbbcbcbbcacbcabbadcbabaccdcdddbbabaaacdadddcdaadbcbcaadbbabbbcbcdcddadadacbcabaaaccdcabbdcddbbdcdaddcdbadbcccdbdcdbabbdbcbbbbdbdcbbbcacdcabbbaabccacdbdacabcbbbcaababbcdcbcbccdcdbdbdadabddbbadccbdbbaaddcdabdadadcacbcdddbccaaadabcdccdccdccbddbcccdccaaabbabcdddaaaaadcdddcddadbdbdbbabbcbdbdddadabadbbdcbabbabaacddcadcaddbdacbcbacbcadbabacdbddababbdcdcdacdabdacaacccdcdcacbbddbdccdacddcbabddbadcbbcdcbddbacbbddccbbdcdbcbcbcdddcaabdddcaaaddacdabddadbdcbaadbcddabcddcbddaacaaabbcaadaccbdcbaddbcdcccdcbcaadbcdddbadbccccbacccbdaabcbcddabaaccbacbabdbadcccddbacdaddbbcbbaabcbadbbcdddddccbbadaacabbddbdccbbbdcaccccbbdcdcaccabbcddbacbddddbacccddbdabadaabdcbbbcdabcbdcdabcadadccabcabdbacbbabdcdbbbbabccacbdaadbdbaabcacadaadadccbacdcbabcdbacbccacacbabbdddabccbbacdccdacddabcabaabbabddbbdcbcbaadcabbaccdccdbadadddcccabadaccdbdcdbabadcdcacddbbddbcaaacdbcabccdabcadaabababaabcbbcbaddaacabcccbdbacddaddaacdbacbdbbccbbacbdbabaadcdabaadbcddadccdababdaadbadbbcacdbddcbcdccddddbcbdbdaacbcaaddcdddbddabbcddaabbbcbcbcabdaccddccbaadccabcacddacddacdddcbdbbacabcbdcabdddacdcddcadbcdbbaaacaacaacaadbadccbacdbbdcccacabaabacbbcaadcccbabdcbbbdcbcabaabbaccbdddcadccaccddcdcddaadbcbdabbacbcbccdbacadbdbccccbacbbaadcbcbaaadbdcccabbcaddccbbadacbbbcbdadbbbddcdaacdabaaaaddbbcaacbabdbcccccdcaabadacbcdbbccbcabaccaabcbcbabcbbacbbbdbbabbaddccdccdcdcacbcaccbaaaacbdbdcacbacccbcacacacbacdcdbadbbccdccccddcabddcabdbcacbccbcddcdadaadbbcbcaadccdbddccbdcaaababdadabbaaaaadcccbccddcadbacacabadaaccdabcdccdbdaddabbcdcdadddddbbadcbadbbcacabdadbdaacaadadcadacccbadaabcccbddccacbbbcdcbdacbdbadbddbacabdbadaadbabcbaaabcdadbbdabdbabaacaccbbbaadcabacbccbddadcccacdddcdacacbacdbbcbcbbbdcaaddcbcdaabdbabacddbaadbbbcabdbbacbbcdcddaabcbdbdcdcbbadcaaddbdccbcadcdbaddbcabdaaddacbcabababacbcdbbdcacccbcdbbcdcdcccaddaabbdbabdbbccdacbcabaacbdbadddbddbcaddddbbaadabcbabcadddccbaddaacbabcacdccbaababbbacbadacaacdbdbbbdadccaabdcccddcbaadbabcccdbcbbacacddbcbdabccaaacbabdacbcdacdccaacdaabcbabddbacbadaaaccabdbbabbccaabddaadbdbdccabbbbadbcbbcbbabdcbdabbdcbbacbbdaccbaccadbbbdcaadcbdcbdaaaaaddccadccbdbcbccbddacbbcbcddbcdabbabdcdcbaddaaddcaccacacadbdcbcadacbccacaccacabaabbaadddcabdbbbadbbdbcbbcddaccbcadaacabccddbcbdadbccadbdaaccccabbacbcbbabdaacababcaaabdabdaddbbbcdabbcbbacaddacdaaabbbcdcabdbccdccbaacacdbaaadcaabacacadcdaddcbbdaddcadbacbbcaabcdcbabbacbddcadcabdadacdacaadcccbbdcadcaddcbcabcdbdcdabbcdcbbbbcaaaaacbdcbccdccdddcddddcaacbdddacddcddbddbddadaccadddddbadccdaccacbdccadbbccadccaaabbcaccbcbdaaabcaadcbbdbddccacccbaabcbdccbbbbbaadabccabdddadabbdbaacdbccddbbbabdacbbcdcbccddcaaabcadcbddaadbabbbabbaddcbbdabbacabcdabddaacdddaabbabbbbdbabaabcdbdbbcbcaaccbdbdddcdbcaacbccaccaaddbcacbdcddbdbbbadababddacaabcbbddacdabaaaccddacddbabcaacaddacbbdacddabdcbbabcbbdaacabaddcadcccaccdcdddcbcaccaadbbcdcabcacdcdbcbbcaccbaaabcbbdcdddccbdadbbabadbdcbacaaadadabddcacdbdaadddabbdbdadcbadbccdadacdcdcbbabccdccabbdbaabaacdaddadcacadaacabbadabbabdaddacaabacdddcdcbcbaddddcdbbbcacabcbbaabdcdabacadadaabbcdcbacbbabcabadccbdbacabdbdaccbdabcacbcabdcaacacdabaacbddcdcbaadbbbbbbdcadaabcbccbaccadccbacccaabccbbcdcbbdbcdcddcbdbccadacacaacdaccbcdacddadaccbdbabadadbadccaaacacdbadaacbacbaaadddbcaddadcdabdbdcbaddcaadcabbcbcccacdcccabaadaaabcdacbadadaddddccbdbcbcbabddadaabccddbbdcadbbccdcacdabadacbaadccccaadbdbaabbcbcddcbcbcaacccaccddbaaadbdbcaabaabdddaabccbacddbacbabaabdbcbbbabbabbddcadddcaacaaaabadbbcdcbadaaddbbacddabbbadacdcadccdccbddaabaabcacccccdaaaddcbdbcbaaccbbacdbbbdbccaaccbdcaddccddcbbcaabccbadbdcbadacdaadaacbadbdccacabdbbddbbbcbdbdcdddbbbcdaadbdbbadcdaccdcdddcabdabadcbaacaadcbddaaaaabdcbacabaaabccdddacdadaabccadaabadabbdbbdcdadbbdbadbdddbdbcdccabadccccbbaddbaabcacdcbcaccddacdbbdadbcdabccccddccddddabddacaaadbabbaddcacdbdabdcbdabcdccccbdadabadcdbabbadcdadcaddcddbcabbdadbcbbdacddbdbbcaadbddaaccaabbacdbcaddcdabbbcbdcddbcadcbdbbdccbdadaadcdcbcacdacbcdccaddbaacdadadaddddccdcdaabbcbabadddbadcabbabadcabbbddcadddcbcbbacaccadbaadddacaabbcaacbdddbbbdabdaabaadaabbbdabcadcbaabacbaaddabdcbdddcbbcdcbaadcadbdbbccdbbbbdbdacdabacccbbbacccacddaccabdcdadaadcbbadcacdadbbadadcaddccdcdcdccdddbdddadadabddcacdcababdadbbbaccbbcabccddadccadcadadacbdcdddcdcbcdcdbbdcadaadbbcacdcbdcadcddacdbdabcddbbbaabbaccdbcadbbabcddabbbbccddacabcdcaadaacadabcbabbcaccdddbadddacacdcbcaacbabadaadcbbacaacadadabdcbcbbbcbabcdcddbbddccbdcbdaabcddbabddaacbbddbdacdbbcdcdaaccabacaacbdadcbddcdcaaacccabcddcadcacbcdbaacdaccdcdbaacacdddcacdbdaaddcbbabdccadbaababddbabbbdadbddaabaadcaabcccccbadbdcaccbbcbcdadcadcbdbbaaabaadcddbbadaccccadbcacaaaacccaabcbadaddccbbbbdbccdbdccbbaccaddcbcaabaddbddbcbbbdbdabcbdbcbccdbabbabbcabbdcabccabbdcdbaddbdcdcdcbadbababdcccbabcdbaddbccbcbaacccaccacdccbdbcddaabdbabbaccacbcbcbdbddaaccddcadbadaddaacbcccacabdaacabcbbcbdbcbbaaddaaaabddabbadabacabcbbdbdcccbcdacadbbdbbdcdcdbaacdccddbcbbbcccadbbcddbcbbaabbccbcdcdcccacbddbababdadacacbacdbaaabccdbddbdcdbdbdbcadcbacccaacdaadcccabcabcaaacccbcabcddbcaadccbbbaddbbaacdadadcdaaadbadddcbddcddacaababcdbbadabccaddbcccabdcbdbddccbbdbacabdbdcaccacddcbaabdcadaacddabbbcabbbcdadcaadcbbbabcababadabbddadacdbcbddbabccdbadcaccdcbbbbcbacdcbacdaacbadbbbbadacddadcacbccdbbcaaccbaaabadcccdcccbbabddabdbddbbbccaabdcbcccccbcbacdaccccacaaadbccbbbcbdacbaabdaaddddadccbbbdddaaabdddddacadbaddbabacaddacabcdcbaddacadaacbbdcabdcaaaabaddbaabbbbccbbacdbaccabcdacdbddbcddadcaccbcacbbbdccddcccdacbbbccabdcddbcbbdbcabbcbcbabbcbbbcaadccadbdabbdcbdbcacdadaacaaadadcabbbbdcdbcbbbbbcdaddbdaddcadbbbdbabcdadccdbabcbbbcbaadddbbdbacccddccbadbcdbaddbbccbacaacbdddbbaadbadaacaabcaababbdabccdadacaadbaddbddbbcccadacccadcdbabbabccdcccddbacbabcbabdbcbcdadccbddbccccccdbdddbbcbdcadcbbbdababbcbccddcdbaadcbbbdcacadadcbbaaaabcccbdbdabcdbadbaabbabbbaabacabccdddccabdbddddadcacbacbaadbbabddccddacdadccaddacaccbacaadccaaddbdabdcbbaadaaccabaccbbadbccccbadaddbcbbcaabcbacdaaacabcabbcabdacccbabaacbaaabbdbaabacadcdadcacacabdacdabdbdbadcdaacdddbbdccbbadadbbacbbbcadcccdcaddbcdcccabdacbdabbdbbbbbaddbbbbadcddaadcbddabcdcacddacbacbcdcadcacbbddddcabddcdcabcacdadbbbcdbbacccacaddbddbaabccdbadabcbaccbbabaddcbcdbcaaacdbddbcbdcbdaabdaddbdabbabdbddabadabcacdabcbddadbddbacdadcdabbcabaaddbadaababddcadbacccbdbbacadcaaacccdbbcbdaacddcbddacbacbadbabccdcabdacddcbdaadabcaaacbadaadacdbaadccbadbdbabbcddddccbbcbddacdcddddabbadbadbadbcacdddbdaabacabddabbddabccaccbdbcbbcbdbbcdddabcbcaadcaacdaaadddbbdbaabcbbcdacddaddcddbbbdcdbcdbbbcadcdbabdccdcbdcbcbcdcadbcdbaabdadcabcabbaaaaaacdbcccddabaccabdabbcdcbbdcccdcbaadbdbcabbcbbdabddacdbdccdaddcdcbcbbccbbbacbadadcbacdcddadcddbccacdbccbcbccacbbacbaacdddbcdddaabcbacbdbdaabdabdadadccadcabcbcacdabbcababdddbcdcabddbcbccccccaccdcdbaaacbdadcdacdcdcdcdbabdcbaadbacabcabdbbacbabbdbbbdcdadaddbddcddacabbbaccadbdcaddcabbbaabdcdcabdcabdacdbadbcdbdcccaddbabdabdcdaadcaaabaddaddadbddabbcaaabdccacbdadcbbdacbadcbbddbcccbbcacacaaccdcdabadaaabcdabdadadcbbdbdcbabbdadaccccabdbbdcabbdddbdbcbdddbcbcdccddacbdbcccbdbcdccdbcacababdbaacdbacacabbabdcdbbcbcdababcdbbbbdcbcaadaababccddbcabcbadcbbddcbddabbdccaabbababdbcdacbabcdaadbaaabaacbcaaddccbbccbdddbaaadacdcaadadcabbbbcdccaacabdbccbcbcddaaccbccbcadbdccdbbbdcdcbadabccdcaabadabccccbddbdcbbbbcadcbcdcabaccdacacbabdbbacbbcadbbcaacccadcbcddbdbcddcddadadaabbbcccddddcbcbcddcaccccacdabcbcdadbddbdbddbcacdacbccaccabdcccaadbacbbbbcddbddbcdaaaddbabcadbcbdabdccbcccbccdccdcbbcccabcbbbdbcabacabaaddbcadaddbbdcadddcaaadbdaacbaddbcdccadcbddbbbbbdabcabdddabbcbcdccadacddbdadbcddcddabcacdcdbbdcdcdacbdaabbbdbbbcdaadccabddbcaabacbaccaddbbbccbbadbcaaaaccdcddacaabbcddbccbddcabcaabccbaabdcacbccacbdddabcaaccbbcbddbddbdaacacadcaadcdbaddbbbaabaadbcddbcadbabcabcbacbccaddcbbcdbdccddacbbbacbdabcbdbadbcaccbddddaddcdddacdabdaabccccaaccdaccccbbdbabdbacabccbbabdaccbbdccaadaaaaacabaadadacccbcdbbdbccdabddcccbcbaddcdcadcbbcacaaacdccaaaacadacaabacbdbbdddbdcbcacccdabccaacdabacdddcbdabacdabbabdbcbadaccabbababddacbbdacbcaccddbcbbcdbadacacdbabcccabcccbaddcdabcdbadccdbddaaabbadacacbdcdcdaaabadcdccdbdacdcbccdabbbddbbbbbddbbddcbbddcbddbbbadacacbcbdcaabdaadaccdacbdbdabdbccaaccdccdadbbdbddacbdbbadcabcadcaaabcdcacbccacdbbbdcccdaadbcadcadadccdcabbcbbadcbdcbccdcadaaabbccbcdbbcbccddcdddbbddbdccbdcddbcacdadcabcacccdccdcdcaddcbbaaaadcdabbacacbdacaaabbbbbddbcdaabaacdcaddadddddcdccdcdddcbbabcacdbbdccbaadbdbcadadcbbaaaabdbbdddaddbcbccbdccdabdbddddabbcdddbcaccbaacdbaacdacbbccbcdaadbcccaccbabcccdbadbbdcdbbaacccddcadaaaabbbaaabcdbabdccaabcdcadbcaabdaaaddbcadcdbdacdccccdcdabcacdcbbbbadcbbcdbdbcaadaacacdcaabcbadacbdcccbbdabcdcbbcacdbdbdbdcbdadccacacccbacbbabbccbdcdadcabcddcbbdabadaddcadadcabcdcddaabccabadbbacddcacbdbbbabbbbbdadadccdcaabdaddbcdcbbbccadaddbbbcddaccddacccdbcccbcdcbddadbaabaabcbdabdaaddcccadaadbcbbdcaaaadbdcbbccbbbcdabaacdacccbcbaadcacbbaaccaaaacdbbacdcacabcbadbcccdadabcbbacdcccdacbdccdddbaaabcaabcbdccccdccaabbcddddabbabcbbbddbbcddcdabdbcddacbbaabbdacaadbbadcdcddbcabacdaddacbbdbdaacbcacbaabbadddbaddabbcbcaccdabbdbbacbdbbccaabdbcccbacaaacbdabbccbabaabcbabdadbbdacaabdcabaadcbadabdabbadccaaacddbbdadcbbcccaadacbcbbdacbbdaabbaccbacbaacbacdbaaacdbbcdaaccbbacccaabbabbdcdccacdccbdbaabababbabbaddabcdccbdacbdbccdadcbacbbadcaabccdcbbdbbbadadbccaccabacabddcabbccababddacdadabadcdcdadcbcccacaccabcaacccbbbaacbbddcdbdccbbccacabccdbcbcaaaadbcadcbcddcbbdbadbbccbbadaaabdadbdaccaaadbbcdccbbddbcdcadbdbacbccabdbdabbdbbadbcdaaaddacbcdbcbbddcddbcadbcbbcaaddbdcabdabddcdadcbabaacdaaaaadcaaccbccdbcbbadbbbcabaccadbddaabbbdabacdacbcacdabdccadcdbabcccdadabbddccdaccbdbdaaadbcbbaddbabddcbccaacdabcccaabbdaaabdbbccbdabaddacbdaccdcbacdabaddcdbbdbcbabccccdddddcbbcdcdadacccdbbdacacaacbaaddacdbdcabcaaabbbcccaaddaaddddaacdccadcbdbccdbccdabdbcccaacbbbbcabcbcbbcaaabcdbcdacdcdddabbcabdadcaadadcdcaddbdbdadddcaddddccdababdcdbddacdcdbacacbbcbbbdcdbaabcdbdcddddcaababcccbbdbcdabaababadcacdadbdbdcacacdabadabbbabbabddabdabdbbccbcababcbdccacccacdcbaaaccacbdcadcaaccdcdcddadccadabbcddaadbccbdbdddcccbbddddbdccbbdbacabcbbbaadabddcabddadbcdccadcaabaaaabcbdaaaaadcbbbddccdcbdaaccdacccdcbdbcbaaaaabadcbdacadcdacbbcacaabccbddccbbabccdadbcabbbbadbddddcaddcbbaddaddabbcadbcdcdcdcacbccbcdabdbddcccdddaabdcabadbacacbaaddccbaaabdbdbddbcbabbacbadbacdaaaddadcaccdabcbcdbbcbacaaabddccaacabbdbbadcbacdcaccccdabaaaccabbadcbdbbcdabbbaddbdabbacaaacbcacaaadcaadbccccdccabbdadabaddcdcddbdccdcaccdbccaacdccdacaddbbababcaadbabaddacccacdbbdacccddcabcadbacbbabbaadbdadddaaabacabbbbdabacaadabdcacbadbdcaddcdaddbcbbbdccbcacaacdccadbbbbbcbdccaddbaacddacdacabbbbbcdbadddcbbbdcccbdbabcdabdbdabacbccdaaaacdaaaadbbabcaadabccbcbbccaabdaabacacbcbbadacaaacddcbababbdcdcbadbddaacdaccadbcabccbdbddccddbccacbdabccdbbbbcccccdabbabdcddacaaacdcadadabbbacbadcabccbdbdadbadaadcddbabbdadaadcbbdcacaddadbddcbccccbaacabcbbbbbcbddbdbdabacdddbabdbcdccdddbaaabbcbbbcacbdbddbabcddaaaddcbbccddbabddcabdcacdbbdddccdcbacbaccabaccddbbabdbcabcdaccbacabdacaababcddaabcccadabcbabdadadddacdacacbbbacdcdbcbaaabdadbdbbcbdcaaddaabcbbaaaabdaaabdbaaddadadbacbcccdbbdbddaccdaadbdaaadcdaadcaaddacccaadcabacbaccacdadcbcadbdbdbadbcdaabddddcbbbaadbabcbbadabddaddbbdaabdaaababcaadaadbcdddbabccdcbbcadaaaaaadcdabaadabbaddcaabcddcddaaddbccddbbccdbbbcccbadacacbdccdcbaccacaadbbdddaddbabbbcdbbdabddacaccabaccabbbdcbcadcdadccbcaacdcbbcbbcaaacbbddbbcdbbcdcccadcaabdcadddbcabcbadddcbaaadabcddbabbbadcccbbadbdbbbdaacbcbbccdbdcaabbaacbcadcdcbcacbbdddbbaacbcacaddbdbdacddbcbcddacbdaacbdcdacdccacddaaabbbddccdcbadbaddddbbbadcdcbdababdcbadacaacdcdbcddcbaaabddbaabdabdbbcbbaadbadcaaadbddccbdccbdbdbaabcddabdacbddddccacdcccabadbcbdbcdbcabbaadcaadacacbcdcdddaabacdcacddbacacacddcaaaacadccdddaacddbbcabaaaddadcaacadcbbadccdccddadcdcacccdcdbabdcdcccabdacddddbabddbacdabbcaaabdadbbaaabbbabadabddcbcbccadacddbddccbdacbdaddbdbacbbdcadbacdadbacdadadcbacadaddcacaababbbdcddcccddccdadbdbbbddbcaaccacddabbdcbbcccbcbdcbcbcacacaccdadcbbcabbadabbdaabdbbdaccbcbdbdadadcabddbddacbdcbcacabccabddadabbccbcbabdacdbcdbbaabbcbbcaccadcdcccadcddccaaccacdaabcacdbaaabadaabbccccaaabaccbdcdcaccbbcccacdbddcbabbbcddbabbcbdaccadacabbdcbccadcdaaaadbaccddcdbabaadddccdadadbabdcdabbdbabaddbcaddabddddcdabaaccadcbcbccabdccddbadbccbcdaccddcbaacccadacdcdddaaabddcabbadbdaddccaccbaddaadddcadbbbccbddddadcdacbacbddadbcdbbcccbcbbbcbbcccbcacddabaadcabddbaccaaacdbddcbbaadabdabccdbbaaadcadaabacbacaadabbddabbccccbabacacacddbadbccbbddbcdcbadaaacdddacdaadcdabddaabdcbabdabbcdaacdbcbcdccbbddaacbdcadbcdacbccdabdabbddaccccbacbdbdddbcaadacdbaaaccdccccdadaccbcdbcacdbccacdacddcdaddaaaacbcbccbccadbcdcbadbcdadccccbcabbbddccacccbabddddddbddbccadaadacabbaabbdcbbcacadcdccdddbaccdcaaabbbacbdbabdbaccbbabbdabbbdaaacbbcadbcbdbbaacddcabdddadaccbabdddcacbdaacccaddacadbcbcababdcadacdcbabcacadbbdbbbccdabaccdddbddabbcbaddddddaabdbdabbdddbabbbcdbdadcabbdcaabaaabcccbcdcbdaaaaaadcddcccbbbbadadbdcaaadcbdcccaddcdaabacacadadaadbababdcdbccdccbdcaabccdcbacdbacdcdaadacbbddaabbddcdadccbccdccddcbdddbbdbccddddbabbdabcabcddbcbbadcbcbaacdadbcbcccbcbbcadadddcadcccbadbcbcbdacdcabdcbcbaddcbaaacbddbdaddbcdbcbbcacadbbadabbabdccbdcdcccacbdcdcaccbccccacddcdaadcdccddbbadaaadadccaadbdabaddcadcabdccccdbdcadddccccbbccdaaddcccacdbaccccbcacadcdcdadddacdddbdccbdbaacaabbdbbbbdaccdccdcccbbdbbbcbdcdcbabbddaaabdabbcabaadccdcdbaaababdadabdaaddbdaadcdbdadacabcdccdbdccbbdddbcbaacdabcacbcccdacbbacacacbbbdbdbddacddaacacccaddabbcdacdaccddacdbccddadacdcbbbacadadcadaadbcdcbbacbaaabcbbdcbcbdcaabbddccdbbdabccdadbbbddcdcacdaabbcaccccbbccbacabdbaddadcdbcaaabaddbcbdcabbdbcccadbbdcacaaaabcdbdbaddaaaccbbaaccacdccccccbaaaacabcdcbbdadabddcbcddcabadcacdabaabddbabaddbcdabbbccccacadbcbddaadbdbdbadbabddbbaaabbdabbbbbacabaadddcbcabdddbcbacdbcaabbbbdbccbdcaadbbdacadcccabacacbbbacdcccbbccacabbbacbbcacdbcadabdacbadcadadadacbdadbddbcaccabcacabcbaacadbbbbdbaacdbabbbbccdccbabadacacdcbacbccaaaddbcaccabbbacadcbcadbbdcdddddbcdabccdabdbaadabddddcdaddcbaddabbddbdbccdcddccbcbbacdadbabbaaaacbbacdbbbdaabbdbdddddcdcddbabcdccbcadabadbacbaadcadacddcaadbcbbcbcacdcaccabbdaaaabbbbccdaaaacbdbababdbaccdbdbacadbdbdcbcdcdccdabdddcaccacbbdbbbcbbddadcbadcdbbbdccccdadbcbdaabbdcddacbbdabbaaabdbbccacdcabdccdaacaabcabbdaddacabdbdccbbdabddccccbdbadbccdcbbbccbadbbddbddbcddcccbdddcaaacbdbbddaddbabcbabacabbccbdcddcbadcbcdbabadabaaaabbadbacadaddaabdcccacbaacdcbaadbbdabddccdbcddbbdabcbdcdadcbbdbaacdcacbdabbbdbdbcaaaacbcacdaddcaabbddddaadadddcbdbdbbcdcbcadcddcdddbdbdbbcabcdcacdbdccadddacdabbacaaababdacdacbbcbddaadcccbcbcccadaabcdaccbddcddadcacbbcbddcabccacadcdbcbbaaccbbcdbdddbbaadbabcdbdcadccbddcccbaccadcdadbaddcadbabbdabadccdabacadacaddcbcddbaadbacbdbcbcdadbaadcacbccccdbbcacddcaccbcabbbdadcbddbdaacdabccabcccdcaabcbbcbaacbaabbacabdaadddbddddacabbbcacdacadcbcaddddadccbbaddbadcbccabbbcdbaadbcbaacbbdddcdddacddbcbacaabbbcbbacddbadbdcddbabadaaddcbbcdaadbccabcbaddbbdaadaddcdcccdabcdddadbdccdbaadcacdcbdccdbaaacddbaacdddacdbccaaacbaaabdbcbadccdddacadaaddbccabcbcbbbddbdcaaccdadadcbaacbbdacccadcbbcbdaaddaadccacaacdadaabaabadabdcadadacccbbddcadddacdbaababcbababbabbabccddcaacddbadabccbbaccbbbacdadaababdaadcaccdbddcabdbacbaccadacddcbaadbaddaabdbabbacaacbaddbcadbbcdbbdbbadcacddabdbddcaadbbcbadcaabcdaabccdcbbbccdbbccaacacdccababbbbcadacabcdcddbbadbcdbbbabbaccdcbcbddbbcddadbaabdccbcbdcaabdccddcabdddbaabacbbbcacdcdddaaabbcccaadcdabbbbadbbddbbcdbabdaadbbccdcccdbdaaaccbbbdacccdbbcbabdacbdccadbcbaacacadadaacaadacdcdabcdcdbcaaadcbcbbaddbbbdaadadbcdabbccabdabdacbaaabcbccaadaadabbbacacdddacbbdcbabbcaabbbbadadadaabbbbbcdddcacbccdaacadbadbbcdcdaacbabbadadccdbcbdadabddacdcadccdacbadbccaccadabdbdddbddacaccdabdccadababcbdcdcbcbabdcadabccdaacdbdabaaccbbccaabddbcdcbbadaacdcdbcbcabbdcbdaccbcdbaacdcaadabaabacdcdacdcdbcbbcbdcbacbcbbacbcbaddacaaacdabcadbbbcdccacbdbccbbdacaadaaacaabccdbbbcbabaadabdcabcbbabccdacdcbbcdbabbdcaaadadadbdbabaaabccabdbcabacbcabbbdbaddbdcacdabbddccddabacaaddccbcbbdbcdbacbdaacbccabcdbbbddccbcdaddbbaacdbdccbcbabaabbcbadbabccbcdaabddbcbbdadcccbacbbbdabaaccdacccbacdddababadbcbaadbbdbaacaaddadbbcadabccccddcbbdddddcdcbaaaacddddcdaacbddacdddbbcadcbcabcdcdcdbccacdaaabcbbcdbaacbccccccdadbbbcbdbdbadabccacabbdcbbccbadcbccdddbbbcbaadbdcacccabbdaabcaccadbcddacbcacddadbcaaddcaacdbdabaaacadcbcacadcaaaaddddcadabddababbadccccbccccbbccdaaccbcabbdcddcdccdcbccccabaaccabaccdacdcccddadcabbdadbacabaaddcdcdadacadbdcbdddadccabcbadccdcacadbbbbbaacadbbaadcabbdbaacccbbbadcccacabbcbccbccccbadadadadaacbadccccddcaacbcbdcbcadaaabdacddcacccdddadabdddccbcaccbbcdbacacbadbbaaccccdddadbdaadbdbadbbbbcdaddabdbbbdacacbacadbcaddabbdddacccaabdacbccaaabacaccbdabbcccbbadabddadadbadcabaacacaaabbbccacccaaacabddbddcccbbbbadbaaccdbdcacddbcbccdabdcadaccddcbbbdabbbcdddbdcbbdbaaadbadbabcbadbbddccbacdbbdbbcbadbdbcdabacbcdcbcdcbabbccaddddbbddbbcdccbdadbbccbacaaccbbbbdbcdbccddabbadabbcddcbbcacaddcbdddbbbdcaccaddacbccbbdadaddcdbddcdbadadacbbadbddcdcdddaddbacabbdbcdaaadcdacbbbacadabbbaddbcbcbdbcbccdbadacdcbcadaaddbcbaacddccabcbabbbaddabddaaadcbabdabddccaccddacacacacadaaadacdbbbacbcdddaddbdacaacabacdccbadaaaabacaddabdcadcdccbbcaddbddacbcaadaacabccaaaaaadcbabaccaacabaadbaaabdacaaacabdaabaccddcccabdbbdabcdadcccacbabdadcabbdcaaddaacadcadaddcbcddadacdbabddcbadcbaaacbdcadbbabdcadcbcacdadddabdbabdcabccbadbaaaacbdacbcdbcabdbdcdaadccccccccaabbbbbdcbbccccbdcdcddbacccacaccacbcdcbabcacbbaadbaabdaacabbacdcbbbbccaabadabcaabaddbdddbbdbbcdbcbcbbdccadbadaccabbaaacbbbddbdbcccdbbdbddcdaaccdcabacbabddabbacbadbbaabaaacbcddbadbcbcddcdaaacbadcbadacabbddbccadacddcadbbdaababadbccbbdbdbddcbdccabdddaacbaddaaacacddadadbacdbbacdbdadbcdcbdabcbddabbcaaaaddacddccddcadbcdcbbbbcbdaddadbcaabaabdbbcccaacdcdbcbaddbdccabacbddacbddcbbdcbdbaaacabdaacddcdbbbcabdcddcccdbdaaddbbaccdaadadbdcddcadbdbbdccacbdbdaabcdadddcdccadabcddaccdbadcabdaabadaddcdadbadcaabacdacdcbdccccdcbadbdabdddcddcaddcbbcdbcdbcdaddadbdadccbdccdccdcdbdbacccdbbcddcbdcbcaacdbaccdbcdaabbdcddaabaccbcdcdcbcbadcbccbbccbdcadaacccbcbaadadabaabbcadaccddbcacbabcbddadbcddcaaabcbcdaadcddccdbcdbbdbacbacdbcbbcbdcdddbbaabaaddadadacabdddcdddcdbbbdabaccccddbbbdcaadcdcacbaadddcdaacaaaadccadadddcccdcdbbcaddbcaaccbddabaacacddacccdaadadddbcacdacbcdbcccdbabccabadaabdddcbabacadbbbabaadcdbdacbdadccadbccacaacccbabcacabcccadbddbadbdcccaaccabbacbadcbbcccacbdadadbbddabbbbbabbbaaccbdbacccddabaabcbacacbbcbdaadccbbdccdbdbdadcaaabdcaadcbcdabadaaadaccaadabbbaccaabbacbdbdccbacbaadaacbdcdbdaabdaddbbacacdaaacadbbccddaccddaadcadcaccaaaaabbabbcbcacdaaccbdbaddcbabdccabcdbaacabdaacdbabccabdaaddddaddcdadabdbdbddacbabadcacbbdcbbdacbbcdcbcbbaababbcbadccabcaccabdccaddcbdabddaaacdcbbcdbaddcdbbcabaaaadbddddadadcdbaacaacbbcbcaacbdbaddbdbdbbdcccbcbdccbdaccccdaccadbdccccccadbadcddbbbddbddabdbdbccadcadaabdcbcabbadccdcdcbacbddcaccdaaaabccbdabddcaaacdddbbcaccbccdcbaaddbcaddbdbcdabacbdbaadcaabdbdddadaddadcdacbcdcdadbdacbabcdacdacbbdadbdabcababadadcaabdaaccbdbbabdadabadaadbbaccadaabcaaaddcbdababcdcdaccabacadbcbbababbcbdaaadbcadbdcabaacabacbbbabbbaddddcdabddabacdadacabbbcbbbbbaacacdcdacacadcbccbabdbdbbacacbaadcbddccbbbadbbadbddccaddacabdabbcacaacacabccdcbaccacbbdacabbacdbbadabcbdddabcdbcaabbadbabbbcdbbcbdddccccbcdabaabcbccdabbcdadccacacdcccbbdddcabaccbbbcaccbcdadbcabbbdbabbddbbddbadbddbdbcbdaccdddacabbbbbdccbdbadabbdbdbbbdaabdacababcbcaaaacbaababacdbcaadcdaacbddaacbccbdaabdddcabacdabdacbadcdacbdddccccbcdbbcbbcacabbcdcaabbcbcdccbbddabbabbabdbabadbabdcdbdccbcdcaaacdabcacdabccbdcadcbcaadacbcdaadccbddaabcbadcadbbbbdcaadbbbbcdcdbdddacacdcaddbaccbbadcacbdbcababbbadddddddccbdabaddaadccddddbddcabdcbbcdaaacacddccbdacbddcdcdccbbdadbcadaddbbdcdcdbaacbcbbcddcdbbdccbdbccccbadaaaabbdbadadaababdbcbbbcaacdddbaaddbadcddbdcccadcdddcdccbbabadababddadcddbbcadbdaaaabadabddbaabbdcddbbaaddabddcdaabaabbacaccdbcdbbbacdadcbadcddbaacbdbabcdcbbacbccbadacccacdabdacccacabadbddbadaaaaadaaabdadaccdcacadcdbcccdbcdcddcadcdddcbccdccdccaddbaaccdcdbdbcaaabbccbddcbbdbdccabdacddaadccdbadbdcdadccdaadcaabcdddabbabadacbabccddaadabbbbdacdcdcadbbbbccbdbcabadccbcabbdbdaabcddbbddcdbadaddbdbddaadbcacdccbdabbacdbdadcccbcdcaacddadcddacbdcabcbaaacdacabcacddacbcbdccabdadcdadaacbddbaabddbbdcadadbbcbddabccbdcbdabbdbdcdcdcbbacdadbbabddabadaabababcdcabbcacdcdabbdaddbcddbdbbbcddabcddccdbbbbbbcdaadcbbddacddcdccabbbaaadbccbadaacbbdbbddaddccbbababcabaccbbdcaddadcabdbddaaaaddcdcbbbbbcbaadcabacabdcbaabaaabbddaddadbdaabacdabbaaaddbbbccbabcadbbcaaddbacaaabbdbdbcaadbbabcdcabdadbbadbabacdcbdbabbcbcacbaacccdcacddabbabbdbaccaccdaddabbacccadaaaacdcdbadcadbdcaababcadccacdabbdcbaadccdddcbbdcdaabbbbacabbcdabdadbcacacabacbdcaddccdadbbccbdadcacbccdbccdaddcadbcacddcbcacadabbbbbaddcbaadaabaabccdddabaabbaddcdbabbdbbbcacddabddaccbbdadcbabddababdcdcabbadddbabcabbdcbabbcaacaabddabdaabcacaddcbbcdabdcbcadacccabdabadbcdaacacdacdabddbccddcdddaabbdbcaddabbadadcaacdbcbdaccadcdaaacaaacdadcdaaacbaabdddbcbddcbbacabcacabaccddaaabdaabaddcdacadddbacdbaadabaacbccbcaacddbddcbaabacaacbccadacdcddacbacaadbbcbcadacbbdcadabbadccbcaadaccdddcbdddacbacbbadadccbbdbdbcadcbcbbaccbcdddbbdaacdcbadacdaaadacbbddcbbbcbccccacaddddabdcbdabaababcddaccccdcbdcccbabbdcdcccdbdadbdbbdcbdcddbbbbbccddcbdcbcddcbabddccbcccdadcddcdbcdbbbbcbdbabcddcbcadaacbbddbdbbaddbdcadabddbcbadaddaabcbcaaadcdcdbdccbbcddaacdcbbbdddcacbcaaacadbbdcacddcdabddcdbabcddccdbacddcaccdbabccabbadcdbdadcbadbddddddabcbbdccabccdcddcdbadadadbbbbbdbbdccddabccaacbbbabcbdcdacabdbbddaabcacdbdcacdccbdbbdcbdcadcdaabdabbbacbbbbaadabbadaadadaddbcaccdcdccdcdaacbacddacacbcbbbbbcccbaccccbadcaabadcbddbabacbadabbbcdabaadcdcccbbaabacbbaacaaadbcbadbabdacddacdcdcbaadbcdbccdabdacdbcbcaddacaabdaabbadacaadccaaadbacddbaacabcdcddbdaddabbbcacacbdbbadaccbabdaaccccbabddadbcaadbdcacdabccdcabddbbcdacdcbabcadadddbccdbadbaacbadddacccdabdcdccbbadccabbcdcbbdacbcacdbaddcacadaacccdadadbddbabbbcdacaaabcacabbddddbbcbbabacccdccbbdcaabcbbcbadabddbabcaadbddbbacbaaccdddadadcbbacbbccccbabadccbdddacacbcacbdbdaddbbbcbbbcdddbaccdaccdabcbdadccadacacdbcbdbdabcbbaacdcadacdbdbcbcbbcdcbdbdcdbbdcbddccbadbccbddbdbbbbdccbccacabcdcbbbddccbdaadcabaadcbbcbdcbcdacdccaddbaaabbddcbdabadbabddccdcdacaddbdabdabdcaaacdcbadcaaaabddbccbaabccbbcbbbaaaaabbadbbabcdbccdbaabacaacadaacdababbbccbbacbdbdbcdcdccdcddddcbcaacbcdcdadbabbcdbbccccdddccbbccddbacbdcdcdccbbbabadccdbaccacbcdacadbbdcbabcdccabadaddacabadbddbdcbdddbabbddabbccdcacdcadaaccbadabccabdbbdbaddccabcaddcbcbdaadcbabdaaddcaaacbbbddbbcccbddccdbcdccdabcabccbdbccdcaccbbbbddccadcdacddcbcdcadcccdbaadcbcbacdabcbbadaaaabbcabdcbabbbddbcbcccacacbdcabcbcdcdabbbacccabbbabcccbabcbcbcabadbcacabccbabdadbbbdbcacdbbccdabdacbbaabdbadbdbcdacabdddbcbcdcacdcbcccbadadaacbdaacadbccbdcaccdccacbadcabbbacbcccbcbbcddaacdccbcabadccacdbbbbdccbdcbcabdbdbcabdbdacaadbcabcddbcddccdbcbabbbaabbccdcadbbcdbcaabdcdddbacdbacbadcbcddbbcbccaccabbdcaddcbbdadddbcbdadadcacdabbcadcddacbadacddacbbcccacadcbcbbbccdcabbdadcdccdbdaddcdccdcdbcaacdddbdcbacdcadbaadbcddbacdcdadcbddbdadacabdbbaabbbcacddadcddbbdddacbaadaccaabcddaddcbacbcdcdddbbbcaaadbcdcddddbbbbdbccdddbcdddacbdacddccccccddaddccadddacccaabbdbddaaabdbaddaccdcababcbabaaacbbbbccbaabddaaadacccdbbcdadabcacacccadccdaacadddccacabdcadcabcdcbdbcdbaaccddbdddddacabbcbdacaccddbdccabbbbaccdddbadcaabdbacadbcaaadcbbdcaadbadcbdcdadbdcdbbaddcbaccaadddbaacadbbbdacdaacabadaadbadcccdcacbababdcdbdcacdddbccccaaacabbadcdbabcaddaaabbbbacbccdddaabaacabdbcbbacdcabddadbddddccaabadccacdabbcbbcabbbcbcbcdbcbbbdbcbcbaababcdaabcbaabbbacbbddddabdbddcdaabcdaddabbdcccaabadbddacbbddcccdbcdbccadcdcdcccbdcddacccdcbbdacabddccaadcdcdcddaaddadbabccbacadadcdbbadcccdcaadbccbabccdcbbbbdabddabbdddcccabaaabdbdaaadbdbdcabaaabcbbdcdccacbdcadbbdacdcabccbddbbadbddadacadaabcabbbbbcbbcabacdbdabaabdaddbcaaabaccccabddaaaadbacdaacaacbbcadaabadacbbdabdcbdcadabaccddaadbbdddddcccaabcdcacdcadcbdddccccccdddaadabdcaddcdcbbdacbadcdaabcddcbcbbbaddadcacacabbbbdabccadaddbcbddcdacbccbcbddbdbdccccdabcbcdbbddaddcadabdcbdcbbbcaddcdccaabbacaadbbabdabcbadaaacabdbddddabcaabaaabaddccacaddcbabbcdabdcadbdcccbbddaacbbbacadabdaabcacadabcbcbcbcbdbaacabadacaaccdbbdadbcabaccbbcdcbbbdaccddcddbdcbaccccdcdaddaabaabaddbaaaccabbcdcadabcdadccaabccbaddccdccaabcdaabaccbababbacdabbacacbbcbdbbcaabbdbacadbadcdbdbabbcddbcbcbcaaddcdbcbacadabacbabddbdadcdbabacdacbdccbadadbbacdaacccbcccdcddacbddddddbaabdbdbabadcdcdacbabdaacccbddcabdaaacccdcaadacbcddcbaaaabacdcaaadddadccdccabbcdbcdbbbaabdacddcdacddbddadcaabcabccdbaaaadababacabbdbbdcbdacadbcbcbacbbbdababdadabcadacadadccaacbacdcabacdaadcaccabdbdbacadbbbbdaddadbcddccdcdddbcdbacbddababdddcaaabdccbccccdbdccdaabdabccdbdbacccabcddbabcaddabdaabdbcccacdacadcabbdcbdbbdbacbbccabbaacaadcbdaadbcbdbdbdcaddbdbccdbacaabddcaaddabddaddbbbbbadbadadbdabbbaabacacccababddbdcccdccddadcdcabbadaddabbacddabcbbacdbcccdaccdbbbdacddbadbacddcbcbbdbcadcbcccbcccbaddcdaadadbddddaaabbcbddbcdabcbdbccbaaaccdbacbaaddacabbacccdcbccdbdbcdbdbcdcbabcbbddddcadaaaaaacbbdacbcbdaccbccadbbadccbaabbaabbddcdabbcacadacbccdbbbacdabccdbabbbbcdadbaddacbaabbdaccccdcccdbaabbcbbbbdcbbdadcabcbbddabaccaccbbabaadabcacaccaadcdbacaaaccadccdcccacabcdabdccdacadaaadcaaccbbbbdabcaacdccbacbddccdabcadddaabdaacadddacbadddadcbaddabcbaacbbdcdadbcbaccbaadbddabbcbdbadcaadccdcdcbbdaadcadbbbddaaabdadbbcbadabbcabbacbbbbcddcccdbdcdccbbbbacaacddcddadabcbaabcdbbcdabdaacacadcaddacccabcbaaccdbccdabdaaabdaddcccbcccbadddaadcccacdacaadadccabdabcacabdbbcacdbaccbbabcdcadcadadbaaaacddbbbddccaccaadadbccbcbdaddbdababcaacccadcdcdabbbcbcaabdcbccbcdbdaaddbbddbcabcdbdacccadcbcbcbdbcdacadacbbdaabacadcaabbbdaadddbcaddcdcbbdbacddbcdddbdbababbbbaddcaaabadcdbdbddbdccbaabcdbcacdabacaddaabccddbaaacabbdbadddcabacdadbaaacacdcdbbccdccccbddddcaaaaaccbdbdaaddbdccadddbdcdcababdbdbacaabbaaccacdccdbdbddabdbabcbdbdacbbcbacbbbcbbbadabaccaccacaabbbaaadabacdadadabddbdadbcbcaabaddcbbacccbdbabccaacadcbcaccdbbadaccbcdadaacbaccabdbcbcaccabadbbbabbbbbabadaccababaaadadccccbbcbdbadacabcccccbccaaccbcdbddbbbcacccdbbcdcacccacdbccbddddcabadabcaacbdddbbdbdcddbbbccddabbacddbcacbdbcabaabdbcbcbabccdbadadcddcdaadcdcdccacdbdbcdabdabcbccdbadccabbdccadbbdcccdabccaabadddbacacbdbacdacabbdcbbcbdaabdbdcbbcabbcdacadbdadbbcbcbcdabcdccabaaadddabdccdbcccbcbabbaddadabbdcacbaacacbcbdaabccaccccbbacdabbddaccccbbbccbccccaaadddbdacddcdaddbabbdcdddadddaabaacaaccdcdbcbbcabdcdbcdcdcaabcbccadcbbadbdbaaadbbcdabccbcaadbbcabdaddcadacbacabbccaabdbcddcabbdacbaadcadccdaadcbbaddabbdbcdbccbadbddaccbabddacdbbbadcccadccdaddbdbbbccdcdddcdddacbcacbabccaacaabdaddaacbcdcbabbdbbccacbbdccbddaddbbacbdbadcbaddbacddbcbbbbabacdaaadcabacccdbcbbaaabacabdcaaaccbdacaaacbabbcaccccdbbbabcabcdbabbbaabbbcabccbdbcabddcaddabccabddbbbaccaadccacdddcaaadccacaacbdacaabcbbadcdcadcdadaaddbabcbacdddddaddbdccdacbbcadccccbdcddddbcddacabccccbbcadddadcdaabcdbbaacdadbaabdcaaabbcbdbaaadccbdbaacbddbcdacdabbbdabbcdccdaddbccbcbcdcaabdcbdaddcbccacbbdbcddcadcdbddabdbddbbaddbadbdadabbccddacdddcdabdccaccbccbabbbdbcccadabcadcddabddbcbaddbdaccbdbbddcbacdbdabdcccdabcdaccdbbbcbddccbacabbccabbddcdbbbbdcdbdbbccdaabbddbdbacaacbbddcdaccadacbdaacacbbcbbcbdaadcaaacdcddacbccdbadccbdcdaaadcaaaddaabcbdabadcadaddbbccabcbbbbbbbbddaacaacabcdabcdcaddccbccbcadaabbddaacbbcaaabdababcbbacacaabcdadbdcaacbdaddacdbcbbdbcccdabdcbdbbbbcccbcbcacaacdaccacaaadcabbcdccdaadddbcacccabbbabbcaccddaabacdccdddcbcadbacccbdddbdddccdbccccddcabacdabbbabadcbcaabcdcbdaabdbccbcaddbcabbddcdbdcadbcadcccbcdbbcdccbbcababbdabdabcdabcacdaabaadccbdcbcbdccdabdbbcaabbdcacccdabcdbdcdddabcabbbccddaccdadaccadbbbabbbccbabaaacdbcabbdbbbbadbbcdbaadaaddadddcbbbbddddccaccdadbcaaddaadadbddcbaaabdcacaddadcaaadbbacbbcccbbcdabcacbcbbbababdcbacdccbadadadddddbbaddacbddcdaabddbdbcddddcadabbcadbbbabdcbbbcbadcdadbbbaccdccabccacdabcbdabaabddaabcbbcacdaccdabbccbbaddbaacaacdcbdadacaadaadcddddaccaddaacdcbddabbbababbddacabcadabcbbdcacadaccdaaabddabaaddaddaabdaabaaaacdaabbadbccdcccadccacbbbccbacddcddcbcdbacdddbbddbaaaadcaaccddbddacacaadbbbbbaadccacddcbcaabcdbaacacabbaabdcbaaabaaddaabbdabcabcddbbbdbccbddccaabacbbddaccaaadcbabaddcadadbbbbbadbddbbcbbacadcbcacddbacddaabbabbbcacccbddddcadbacdcdadabdaabcbabdcdbcccdcccacbccabdbcbbdacadcccbcaccadabcacccdbadcccbcacaddbdbbacccacbdbacdadbbdcbcbcbbdbcaadbdcadacdcdcdabbacccdaccabcaccdadcbccacaacaadcdccbdbccdcbddbadbcbabacacdbdbccbddabbccbbddcbbddcddcabcbcabdaddaadadccdccccccddadbdccbcdcaabcabbabddaabbaddcbaadbbacadcacdccabcabadccbccdbbdcaaddbcbdcbcddbbbdcaabcbbbcdadbbacaccbdbddcbbdbcdbdacdcaccdcdcbaddcbabdcbaccacbbaacbdcdbadadaaccbdaaabdaabbdadabcdcbccaabbdbbbddcabacdacbbdccadaabcdaadbbacbacadcccaadbdcbcaabcadcabcababdbdccbbbabbbcddaaacbccacdddbaccdbcdbcbbbccaacaaaaaccdcdbbacbbbcacdbcaabcddbaacadcdcdbbbbcccabaccacadacdbcbcddbacbcbdcacbbacdccadcacaacbabdaacddbcbbadaccaaadaaaddbacddbcbbabaddbdddcdacadadcabdaabdbaaacbdcdddbbaabbabcacdadddbabacabaacbbcacbbbcaadadcddbdbbabccabcabbacbcdcaadccbcbbbadccaaaaccadaabbdcbdcddbbcadbadaacbdbdbadbbbcdccbbdcdcdbbcbabbbcdaacdabbcdabacbadbbbbcbdabdcbaabbbcccadcaccdcbddccbadadaccacccdcdadccadbabadccbaddddbbaccbbacabcaccbadcdabbcdaacabbcbadbbbcccadbccdbdbadabacaacddccdcbaabdbdddcacbadcccacabaddcddbabbdccdbdddddbdcbbabaadbbdbcbbaaabababbabbbbdaabbdccdbdadbcccdbccccdcbaabcabaaacdcdcbcbbcccddbdcccdbaabbcacaabbbdbaabbdbdadbacacdabaabdbabcccacdbdabcbaddbbadbdcadbdcbdcbadddddabcdacdbadcdadacdbbddbcbcdbaaddaddabcbcdabdccccacdadccbbbadadadacaaddbadcdccdbdadcabdcdddddaccbdcaabbbdabccccccbabdbbaadddcaaddabcbadabcbbdbcabdcdcdddcdccbdacdacacdddddbddcccadbddcbcddcbcaddcdbcbdddacccaabacdacaaccaabddcdbdcddbdbabccddaaaabdbdcbcbdcadcbbdbbdcabbcabadbbbcbdbcdcbdcbbdadabcccbcacaccbdbdbbdddaabaababdbcdbabaddcdcddbaadbcaabdbbdacdcabdcbcdadcadbcddcddcbabdbadacacbabdddcbdcbcacddabddacdbdcacdbccdbdccdaddccabbabdddabbbaaaabccaccddcdbcabbbacacadaccccdcbaaadadabadbdaddbaabddaadddddbccddabdbbbabadabbbdcbdccdbabbdadbdccdbdbadaadaddcaabbccbdcbdbccabcbdcdbcabbccbbbbddddaccdabccccbccaaadadcbdacdbabcaacdbccbcdccabdbabaadbaccddcbbcdbbddbccbbcddbcbccbcdbdadcdbbddcddcbcccddcbdcadabdaabddcabadbabdabdabddacbbccbababaddcbbdbcdcbaacabdbddacddbcbcccabacbbbabdcdcdbaaabbcadbcdcdabacbcbabababbbdaabddbcbacbbdbadddbaaabddaadcabcbccdaddcccaabddbbdbbbcbaddabcadadaabdcdaadacabbcccbacccaacdcaddbcaccbbacdaccacbcbdcdbdaaaadcbabcccbcddbddabdaabddcadccbabcbcdcaadbcdcdabdbbbcbdccdcaaadccdbcdbdccbdcdddaddbcabbcbcbababaddddcacdaabcaadacadaadadcccdccbacdaccddbabbcbbccdbddabacadbabccbcdbcddaabccaccacdcabcbcaaddbdbbbdcacccadadbdabbdabcadbdcbcccdcdcaccdbcaccaddbbddcbdbcaaaaabdabbccabbddbbbbdcccabdaadaacdadcbdbcdcdabdddcbdcaddcdcacbbbbbdbdcabdaaaabbabadcccbbabbaaaabbbacdabbbbbdccbaccbdabbdddccbabdaccabddcdddbdcbdcbccacdbcbdccaacbacacbcacbaccbbcccbbbbcbababacdbddccdadddbbdccdbacdbbdabcacabdbadadccadddacdcbbbddcbaabdcabbcaaacadcbbbaadacbaabbadcccdabdbcdacdabcbdbccacbddcbaaaadcdbcdcbcaddbdddcddcbacaaadbdccbcdcbbcddddbcaadbaacbdabbbacacdaadbddbbaadaadccbaaaacacabbbacdcabcbacbacacadaacdccacbacbaccabcccbbaaddddadcddbcccdcacbaacdcaaddacbcacadddddcbccddcbddcdabbabcccddbcccbacbcbcabdcbbdccddcccacdaadbccbdbddcdbaccbbaccdbdbadbdbdcdcddabaaadccabdbabcadbbaccddaaccdbbdbcbaadddbbcdbadbaabccbacdadcccdbcabbcbcbdcabacccbacdcdcddddabbcbbdcddbcadacabadacadccacdaddcdbabdaaccaabacdcdadcaabaadbdadcbcdcacbbcbdbdcbdccbbbabacaccacccdccdddbcabdddbbcdabcddbabababaccadbdbbcccdacabdbcdbdbaabaddcaaccdcbccddacbabbcbccbddbacdcdbddabdaabdbcdddccbdadbbdcacbcbaabbdcacccacbdcbabdbcbccacddcbdbbdcadabcbadaaaddcddaaccdddbdddddbaddadbdcbbbadccbbaabbacdbaabbbaadcdbaaaabcccabbcadaabcbacbbadbdacccbdaddccddaacbbdacababdbabddcbacaccdabdcccabcbabdadabababcdaaccacdccbcddcccddabdccbddbdbaaacabbcccaabaccddadccdabbbabbaddbddabbccbcdcbcdcbabdacabcaaddbbbaaaacadabbbcddbddbdddccaadabcbccdddcdbdcbddbcabcaaaccababbdcbacbcdaccaabdababcacbccabadaaabaacbaaadadcdadbbdcbbbadbcabdcbbacabbddadbabdccdcbddbcdbbcddcaadccbaddcadbcdcaaacbabdcddaddbabadccddbcdccbadbcaacbadbaadcaaaccabccdcacccbabdbcaacdbbbaadbccbbcacccacbccbbdbdadbacbdbdddaddadacdcddcdacbcabbdbcbcccadccbadabdaaabbcaadccacbddabcbdccdbcbccccbaaadbabaadcabbabacdccbacddbcbddbbbadbdadbaccdaacadccbccdaddbbccbdcdbdbdaadbcaadabaddddbdbbdcadcdaddcddcaccabcbdabccbbddbaabbbcbbdbbbdcaadccacaddcaadccddcddbdbbbcbcaaaaccadddcabdddacadacabbdcdbacabacbdacadddcaabbcdbacabbaacbadddaaddaabcdcaaacbcbaccadbdadabcaccdbbcaccddabbcbccbbbcccdbbcdabadccacaddcdccbcbdaacbbdadabadabccbbcaddccdbaacbacaacdacbddbaccdaacaccdbacbabcbdadbbdaddcdcdaabcabccbdcadddbaddddddbdddcadcdaaadccbbaccbbcdacdabccbaaddcdccbcccbacbbbbdcaabbbadaaacdaddbaddccbcbabdbcdcddaabadcbbcdcbddbaccbbbbacabacdcbacacdbdcdbabbdcbadbdbcabaabacadccdabadadbabaacbcdaaacbcaabbaacacccdaaddaabcacabaddbbacbbaadaabcdbcdbcbbdbccdcdadadadbcdacacacdbaddbadbaabbcbdabaadababcacdaaacabbaaddcbdcaadddccaabdaddbbbaabbcccadbaccacdccbbbaaabaccddbabcddaaaaaccbbacdbabcccadaabbbacdcccaddbaacaccaabbdadabcddbcdcacbbcccaacbbcbcbaacdccbcdaababbcccbcbaacacdbbaddacacbdbdbccdcadbcdadbaabdcbdbbacabddcccbbdddcddddacaaaadaaadbcddaaccababaddccdcdccccababcbdabcdaccccbcbaadbbacbbbaabadcdabbaaaaddddacbaaaaddddaaadcabbcaaabdbaaccbccadcbcbacbbadddbdbcdcbadbdbcddabbbccaacbbdbbdbbbbaadcdadcbbcccbacccbccddcabaaacccacbdbddbbbaaccadcdccdbbbdcdcccddcbcbdddabbcdbcadcdbbaadcdaabcbbcdbabbdddcccbddcddcbbdccadadcbabcdaaadddcadccabbabdcdaadbbaacbcddcadabccabadabaccdcdabdddabdcdbdabacdacaacacbadadcadbcbddadccaddaaddacaacaddcdaababbccdddbcacbbabddbbdbcccbabaadccaddbdccccaaaaaccdccdcacadadacacccbddcbddcddabaacdababaabbddddddaaabbaadcadbccdadabcddaccaadbaacdbacacbcdcbbddaddbdaccadbddbaddbbbcdcbbadbcdcbcdbcdabdccdcadddabdaddbccdacdaddacbdbabccbbcbbdccacbcbdddaddadbcbdcddadbddcbaadbdaaaaaaccbccbbbdbdbaadbbcdbadadcacdadbdbcacdadbdbbdddacbbcadaadbdddcccbddbcdccbcacdbbcbddcbcdcadcdabbddabaacbcabddbbadccbbbacacaccdaaddaccbbbdaaadaabdaddadbcdabaddabacbdacdcdccbcdbcabbdaadbdabdaabdcabbdbbdbcadaaabadcdaacdbbbdcdddcbcbbbaccdacccabbbbcdacddcdcbabaaddacbdbadccdbcdcbbdabdddacaaaddbccbadcbbabaaddbbccadddabbaabaaacacaaadbbcbddcbcabdbdaaaacaddbdaccdbdaaabaaaacdbbcbbbdbadbcaacbaddadbdbccdabacbcbcadabcbcbcdcbabdadcabaaadcccbbdababbbbcdbadddbdaaadaaadaaaccabcdacbcdbdabdddbcdaddcdcaaaacddbabdbcbbbcaadddadbbcaadadcbabdabddcbbaabbbabdddaccaabdbcccaadabddccdcbabbbdcbcaaabadaacdcbcaddbdabaccabbcbabbcddcaabbddbdcbddbaadccdbaccdabadddccaccdbcdacbbbbabdbababbbabccbcdbccaaaaccbddadcbbdcabbcbdbadaabbddabdcbdbddbacdbbabdccbddcbbdacaabcdbddacdbbcddbddbbbdacccbbcacbaaacdbadbdddcdbacaabcdbdbddabbaacdabdcadabadaabdabcdcbbcadabdcdadadcbccdaddddddaabbacdbadbcbbbbdbdbbacbcbbccddaabbdacaaadcbdaddabaccdadbdbcbcccdcbcddbddcaaadadabbaddbbdbddbddadbacbccbbacdbcdcdcbcaddbdcacbcdacacbbcdaaabadcadcabcddbbbbcdcbccadaacbaccacacaacdbabdbbaabbcdcbcbdabdccbbbbcadadbdacdbacdacddcadbdbacbddccdababbcbababccddbdccddadacbddbdbcdacaccbdacaacbdbdabbbccbccccadbdccdaacbcadbcbadcababaabcaacabddbadcdcadacaccdcddadcdbbcdccccdbcccdccddcccacbbbcbadcdadbddcbacbdacccbdcbabbccbccccbdccbdacdddbcdbcaabadacbbbaacbddabdbdabcbcadcdbcdbcbabbaacdaacccabcdbabbdacadcdcdbbabcbaadaabcccbcbaccdbbadadbcbcabcbddaccabbaabbbacbcbadbacbacdaacbcadbdcabcdadbcacdcdcdaabaabacbabbddbbdbddbccabdcbcabdcbaaaaaccadaabcbccdadadbcccaacccabdaddbdbcdcabadcaaaacadccbacdcccbbbddbcdbccbdbdbdcaaabdacbdbbcabcddcacccddacbcbabcaccccadadabbbabcdbddcadbadcadbdbaabdddbacdbdbbdbcadbcabcabcccabaddadddccbdbbccbddccbacacbadcbdbcdaadaddbbdacbcaacaabacaabdabbbbbbcbabcadcccaddbbbddbddcabdcbcdaaaabaacbdacdabacbacbbcbdbdcacbccdcccacbabbcdcbdbadbadadbdcabcdacabdbbaadcbbdcbddddcabcbcdacacdbddbcaccdaacadbbcdaabbacdddaabdcdbbcdddbcbbcddddaabadddbccdbbaccdccbdcaccadcbcdacabadbcdbbbaccbddbdaaadaadcbacadcdcadcbddbdabcdbdcccddbaccaabddaccbabdbcaaccdbaadcdbadddbcdbddcdccbacababcbdabdbcaabdccacadcdadcadddbbabcbaccbdccdcadcddcdbddddbdbdcdbdccdacaaacadbcacdaaccbcdaccdacdbccbcdaabacbcaadcbcdbbacbdaabcacabdaabdccbbbbdbcccddabccaabbcdbdddcdbcbccbabcdacabcccaacbbbbccaabdcdbdbdcddababaaccacaaadaabbdbddcccabaabbbddabdbccbabbcccbbaccaaccbbbcacdbbacaddaacccdaddbaacbcdcbaaabdabbabcbaddbadbbbaadaaccaaababcbcabadcdbbcaccacaccbbcaabcdaccbcabbbcdcbbbbdbdcccabccbbaccacbcbddbcacccabccbdaacaccdbbbdadbbdcabacccadadcaaadcbdcabcabdcbbdbbacdbddaabaadacccabbbadacdadddccddcbbdbcaddcabbdaaacddbcdccdaadcddacdcbbbdcaabbbbccbddbcaabaabcbbaaddbdabcccaacacacbbccbcdddbdbccadcccdabcbaacbcddcacddbacbcbcdbbbaddaabdbbdcccacdaacadbabddbddaaacbaabacadcdbacacacabacdbdabababcbbcdccbbdbbbbbaccdaddaabcbbbcccdcababbbccbbcbdbaacbababdaaccdbdadabbccdaccdadbadabadbbdddaaadaaacacbbcbabaccdbbaadaddbaaccadcbabcccbddbcbaaccbddcdbbdaabccaadddbcabddacdddadcccdddcbabdcdabadcddacbddaadcddabbcbdbbcabdcdacadbacdaaadbddcddadacddacbcbacbcbccaadddbddcddbabdabcadaaabbbcccddbbdcacdbaaaacccccbccdbcccaabbaaababacddbbdbbaaaaaadadcabbbddbbbaaacaaabbadbccdccbcabcddaaabacbdccdbddacadbbacbabacaccabbdbdaaadadbbdddacbacadccacccadbccbbccbaddabbdbbaddbdcccdbbcdaddbadadcdbdcbabcabccddbbbddacababbddcdcbdccdabbaddaaddccdbcbbadbdbabddbbcbbdabdcadacacddcccccdbcdbadcbdcdcddddbadcadcabadaccbbdcbbdcacbbbcbcccabadcddcddcbacadabaaaacdabdbbdcbbcccdbacacabdadbadbadccaadbdabacacdcabbcacdacbccbbbbbcccacccccbccaacdadabaabacdbaaddbaacdcbaccdacaadcdabaabdadbddbbacbadcdabaaacadbdaabadabdbdbcbbbdcccbdadaccadaabbacdbadbbcdabccbcbbcbcdccdcbdadbaaacaadcbbdcbcbcbdbadcdabddacbadcccccdacddaabdcbbcdabbccabdabbbccabacddcddadabadcaabbdccbaabbbcddbbdcbbdddcdcbcdbdcbccabcccbaacacbcbbcaaddccbacdddcdabacadcddacbcaadabdbbbacbbcacadaddaacacccabbbabdaaccbcabddcaadaadbbbbccadcccbdaddaaabaaaadbabaaadbbadbddbdacddabcdcaababbccaaccddbaababbdaaaabccddbacbbadcdccbabbaddcbbacbabdddacacbadbaacadbaddcbcdcbdbabbbcdcdcddbcccbadadaabddcaaabcabbdddacaacbdacabacddaadcbddddbbccbcddbccdbcccbababdadabaaddcccacbdbdabddbcccdbabbbaabbbdabdbabdadcadbcadcadcbadcccacadccbcabacddabdaddbccacaaccddccaaadaadcdbaaccabbbabdacacadabbcacbdbacbacdabddbdaaddbccacdcacacbaadbabcdbbcdcbcabadcdcacaaccbaccbaabdbcbbbbadbdacadbbdcddbbccdbdbdaddcaaabcbaaaabbbaccaabcdaacbacdcadbdcaabbdcbdcdcadbabdadbdbcbcddcbabbccbcbcacdbaccdccacaccbdddcbbabbcbcdcbadadbbbdccabbabaacdadccbacbadddcbaddcdadaababaabdadbdaccdccddbadbadadadabdcacacdbbcdcadaddaccabacddcbbdbadabccdcccddccbacdbabbaaaddbcbabadcbdacbacaddacbccaabcaacdbbacbaabacaacdbacacccddabcccddcdacdbabccccccacbaaddaaacccdbbdddaabdbdbccadabddbbcbcddcacabcbdabbbcbbbbbcabacbdcbccddcccddddaabaacbcdacaaaddccacbbaadcbccdcbcdddabdbbaadadccbdcbccaccddaadbdabbcbadddcdbbcbcdcccacbccbdabadbcbacdccabacbccdacdbaccbbddabccadaadaadcadcbcacdbbbdbdadccabdabbcddccaaadddcadccaadcddbbcaccdcacbbcdcddabcbbcdcdbcbabbccbcbdaccdbaccbaadcdacbbcbcaccdabbabcdcdbcbddcbacabdccbbcaadcaccadabbcbcadaabdabaacabbdbdbddcdbadadcbbccbccbcdaabacdcabbcbbaabccdadcacbdcabdabbadbdcbabcabcaacbcdbcabcbdadcaccbcaabaadadabcadcbbcbbbccbadcaaabaaccccddbadbdbbabcadadccdaccbbbbdcdadcdaccdcabbdcbacccdbcccbadabddcadacdbdcbccbaadbcbdbadbbaddaaadaaccbbdcdbcbcdabcbabcdbaaabdbddaaddaaabcdbabcbcdabbdacaaccacadacbdbccbcdbbadbaaccadcdbacaccbaaddddaccbcbacbcbdbdcabacaacccddcdabccaabdabaaabacdcdbcdcacbdbdddcaabbcadddbcaacbdcdbaddbbcdcbbdbdabdcacdabbcbdaadacdacbacdbbdacadabaacbbcacadcddddacabacddbcdacdaadadcadaabdbbcaadabcbcbddcadbbbdcdbaababdcccbbcdabdbbbddccbccbcaadbdbbcaccbcdcddbbaaacdbcabbacddbcddababbdddddbcddccddbcadcdbccdcccabccccadabbaabdddacaddcdccacadacbdbcdccdaaabbaccdcccdcccadcadadbdbcbbdbcacccbdcaadcaaccbdcbaaccaccdbdcaccdbacdabdcbccbcbbccbdacbbbdabcddcadbdcdbbbaabdbacaadcadabcacacdabdcccdcbcbbbbbacaadcacbcbacdcdabadddadccbbdcdcbaccaddbcdcddabdaabbcdbabdaadbbacdcbdcbbacccadbcdadacccbccdbdbadacdccbccdbadccdbabbadadcdadbdcdbcbdddaabdcdddbcdcadcabcddbccaadaadcccddabadcbadbbdacacadcabbbbccacacabcdaaacbccbbdacabadbccbbabdaadcdaacabcdbdbdaacbcdabbcbabacbbbdddcaccabdcacbbccaaccbacadbacabcdacacdcaaabddabdcbdcdcccbcdacdcaccdbbcdcbbbccbaddcbdcbbdaadaccacdacddbacccddbaaaabbcaadcadaacaabadadabaddcdbbddadcbabbcbadcdaddacaddaadbdababcadbbddbdacdadccadcaddccdcdabbdadaadcaabdcdcbddcbabacdbadbdbcacbdadabcabbcbcacdadacabaabcbcbcabcdbddbabbbabbdcdccccdccdccbaaabbcddaabbdddaadcabdddaadbcdcacccdaabacbdcdadccddccababaaddbadcbcadccddacdcdbdaacdabbbdbccacddbacacbadbccbcbbcaaabcabbdaabcdbcaadabbcbaddbacabdcadaccbadcdcdaaabcabbacbaccbadcbbbbcbcbacdaddbcabddcdbbdccabbcaccacdacacdacdaabbbcbcacbbddabdbccccaadcbcbabaacbbaddcddbbdbdcdadcaadaacbcdcbdcbbdabdabbbcadcdabaaaddbbabbbbaaacdaadcbbbbadcacddbadabbbdadabcbcdbbaccbbcaacadabacbcbcdcadaccdcbddbaabdaaccdaaadabadbcaccadbbcccdadbbcdcaabddcaaaadabbdbbccabcbadbdbabdacddcadacccadbcadaabdccbacaabdabcacaccbcdaaacdacacdbcddadbcbcbaaacdbabbcdbbcbbccbcdacaabdcdaccdcdabcbabadbbdddbddbddcbcbccbcdbbacdddabbdcaccdacbadbbacadcabbdbddabdacddbdbddbadbbddcacbcddddbcdbdbadbddabdccbccbcaccbcdbdbcbdcbaaadaaaaabdbadbddaccacbcaabdbcbdbbdddcaabaccbacadcdbdcadbcbdbbaddcaacadcdbdacbadcacaaabdadcdabaacaaadcdcccddbdbdcabbbcbaababaabdabadbddcacbccbcdccdabdbccbdcddadbcdabdbdcdacaccdbababbcccdaaacaddbbaacabddcdbcdbcccaababbadbbadcddbdddabbbcdacacccdcacaccbdcaaccbdbdbcbaadddaaacdadbbbcbaacacadddaabaccdbbbadabababacabdcbbddadcdbdbccdacbcaddbcabbaaadbccbcadbacacbcabcadbdcbbcbccddcabacbdadccbaabaadbacbabcccbdacdcddbcdbbddbddcabdbbcdcbbbbdaaacdbcadbcdcbbdabcddcbacdaacddbbabaccacdbcccbdaaabddbcdcaaabcaccddaccbbaacdcbababcddacaccbbabdcdcdaacbbaaccaaccacbacadbcdcdbcbbacdcadabcddccacccaaacdbacccaadadabadacadcbcdcdaccaddcdabcdccdcdaddcdadbbadcbbcaabacadababcadbabbcbccbadcccadabbaabdbabacbbccaddbdddaadaaaddaacccdddddbdadbbbacadbacbddcacabddcdaaacbbbcdbbcdbbbbccacadbdcbacbdaddbccaacabbabcdddadbbbadcabdacbcbcdaddaacadbccdcbabcacacddddbaddadaaadbccddcdaabdabadacaddbaabbdabbabdcdacbaabbdaddacddaaaabadbbbadcbabcdbaccbcdbddcacddcabbbbcadaccdbbadcadaacccadadcdbdbbdcccddccabcdacddcddcbcacaabbbbacbcdaddbaaccdbabacccbdaacdbcdaaabddadaddcaadbdbbcdbcdaccccacaaaadcabdbadddbabadbdcbabbdadcdbccddbacabcadcdcdbbaddcdbdaadabadddcddaacbdadacdbbabaaabaadddbccaddcdcacbbbddcbbcdacbbdcabaadacdcbdadbccadcdccbdadcabccacccccacdaddadcdccaaabdadddaaddaadddddbacbabcabdabadaadacbacbbbacbdacbabbcaacacbbcbacbbcbadbccddcbcabdadccadaacaccbcdddcaaddaaccbabbbddcaabbaaaccacaddbbbbcccdcabdcadcbcdccddcadcaccbcdbbdcabcccaddaabcadababdccbccabbccdbadacdaccbbaabcdaadbbdcbddcdaddadcbdacbbdbcdcdddbadbabbccdcccdcccbadccbcacbabccabaabdacabcbadbdbccbdccdbdbcdcbbdccbcddcbbbaabcdbddbadddbacdcdcdddacdbadbbabbbaabcbcdddbdddcddbcabaaccbcccdbccabdadcacdacbdbdccaddbcddacbaabdbaadbbacdacbabbaaccbabdacdaabcdacbbdccdacdcabbabacdabacdacdcdbaddcbccdcabbadbcbcaaddbcbadacdbcaadbdbbddcaacdcdcaddcbddcabcadcdacbaaadbdabdacbccbadcbaaabddcdcbbdacccaddcddddadccbdcbccdcbcdbcbdabdcdadccabbbcdbddbcdbcacdacaaccdccdcabaabccadbdcacbbdbabdcbbadadcdcdbcaadbaacdbcacdabbabbdcbccbbaadbddadcabcbdddbdbbbccacbaacdabdbbdaacdcbcadabcacadacddacabacdacaabbcccdbbdcbaabbbdcdbabcdbaacacabbaacbabacdacddcdbdcbdaacdadcbbcbbadcacdaacdabdddacbdabadabcbccaabdcddbacbadbdcacdadcadcddcabcdbcdbdcccdccaccbcdbabdcababccaddbacadcbcadadbcacdaadccbbacbcacbaabcbcacbadabdacdcaacbbcacaaccbadbdadccabccbddbcccacaacddbaacdccacbccbddddcdaabbddadbcdbabddccbadcbaaddcbdcadcdcdcbacbdccabdbaccbaabbacdcccddbababdddcbaaaabaadbbcadddbadcbaaccbbaccdbadcdbbadcabcbddbacbcadabcbddacacbccbdaddcdbbccbbdaccbcbdbabccbaadccbabcbdbcbabdddcaabadcccacddddcbcadddcdaadcddcbaccdbaadaabdadacdbddccbaacddbcbdcdddddbabdabcbaccbcdbcdbadcccacddabbacdabaaaddccadcadbbcdcadbacbdacccbbbacbadbcbaaddabccdbddbdbaadddaadbadcdcaaadcbbcbdcdcdabddcacdabbacdbcdbbcbcbdaddcdbbaddbbcccacdadcdaddabbdbdaadcccbdacadbccacbacbccdbaddbcaccaabbaadaabdbaabccccadcbacbcbbcbccbbabacddcacbddadaabcbcbcdccbcaddcdaacbbbbcdbddccdcccbbacccdbdaaadbbabbbcccdbcacbbbbcddbaccdbbaccadacdcccabdccbbdadabdabcabcbadacbbccaddaaadaababbbdbacbadaccbccdbbadcddabcdbdddbbaacadcbcdcbabdbcbdadbbadbbcbadbcdabdacbbbbaadcdaabadbbcadaadcabdbacdccacbbadabdbcdbbabaaacbddddadccbacdbcbdbcddcacbbaabaaadadaababdbdcccdcaaadcdaaabbcbccdcdbdcababaacdabdccabaccddcbadbcbdccdcbdaaabccbbbcddabdadccdbdacaddddcbcabbaacaccbcacdcdcadbadacadbaccbcbbcaabadbcddcbaaaadcbcacbcadcddabcbadbbbbdabcabbbcbcddbdcabbdcdbccbbdbcbabacdcbadddbaccaadccabbddcddcbdabbbbdbcaadabcddbacbccdaabccdcaddbbbbabaadcbaacacaadabacacbacbdcbbaddbcccbcadcdcbdacaabcbadbaaaccaacdbbadaddcccacbabadbcaccbdccdbcacdccbdcadaadcdbabbdbaababaadccdcdcaaaaccdcdbabdacdbdcbdbcbdaacbbaccdcbddbbdbbcbdadcadbddcbabbaabdcabccaababdddbdbddaaccadcbddcbdbbcaabdcaadcbcbbbbbddbadbcdcccdcabdbccdcdcdbdbdcddbabccdadcdcabdbddddacacacdaaccbcddcdbadabdcbbdaaaabcaaccabbdbbdbbccadcadbcadbdaacdbdbadbbaabdcbbadababdbbcacbadccacbabaddadabccabbbcdbbccdbaddcbddaccddddaddabbddabcbbadaacbbdcbaaaccacaadbcaacbcccdccabdababbbacdccdcbaadcbacdacbbdabdcababbdcabaababcbbacabbccbddbaabacaabadbcbdabdabbadcaadaaddcbccdadbdbacbbababdadacbabccdcbabaacabadabdaacddabdacccadbabdbddbddbccacadccdcbdccccddbbcdabccbbadbbaabaadcbcacdaccdcaacddcddadabaacadbcdcaddaadccacabaabcbbccadaaaddbadddaacdbbcdcaabcadabcdbddaaaaccaabcbdcddcbcccbacaabacaabdbaabdbdcadbbccdbcddcccabbaadbadcdcbdcbabbbbdbacabdaaccdadbbcacdcdcbcabdbcadabbaddaccabccbcbbadbdbccccbbadcabaacccdabdbcbdbdcdcababcbbaabbbbcbbaaadddbbbddadccbbcbcccdacccdadccccccbcabacadbacdbacccdabaaccbcddbadabbdcccbcbcdbbcccbbcbdcaaccdaabaabadbdaaadbdadbbcbdabdabaccbdccadadbcdcdacddbbbcdcdabdccaadabddddcdcccdddbdabddbddcdadcddbbacbdabdbcdcdddabcdcbbaabacdbcaaadcbccdadacbacddbacddabacacdddcadaaddaadcabbbcacdaadaddbcdaccabcdcddbcbbddcccaaabdcdbdbdaddccdabbdbcbdaabbdccabbccdddbdbbbcacccacdaccbbccadaaaaadabdaddaaddacabdcbcbbdbdbdbbdbdbdbcbdbcacabdcbbabbbabacbabcbadacddacacddccdadacabcabdabadaddbcdacadbdbaacacacdcbdacbdbacacddbbabdddacdacbabaaccbccbaccabdadacdbaddaccddaadddbaabccbcddabcaaabacbdcdabaabcdddbabababcaddddabdddccbccbbadacabacbcbcabcaabbddcdbbcdaacbbacdcacbdabdadadadcbdaccadcaabccabaaccddcaccdabaaaacdadcbabbddccccaaacbdbddcaddddbcabdcdcbaaddadbdddadabcbbacbbccaccdccaacbcbccbaabdbdcacaccaaabdbaacddbdaadaaaccacccaaabcaabcccbaccdabaaccdcdabbddacacaaaacadcbdbbbbccccadbbbbbbcbbacdaccbcabcdbbccbaaadabadddcddbccaabcdbcdcdcccbbcbccbdbbaccdbcbbcdbdcdabcccbccabcdacaaddcaabacbbbdddcccdbbcdbccdddbbbbbadbacccbadcbddbcdaabdadcdcddaaacabbabddcacdddccaaaabdacdcbacabdadcacdaacdbbdadabccacadbcdcacccddaadadbcacaddbbbaacadccbcccadbdaddaabcddbdcccbccdcdcdbccabcbbaabacabcacabcaacbabaccdbaacaabbdbaddabccddbbdadbbddccbcbbbbaaabcacdcdbdaabbdbcdadcbacbbdcadbbdbddbbdcaaddbcddadbbbbdbdbaaabdcabbcdabdbccddcbbbddadaabcbbbdcdcdbcabbcbdbaddcadabbdadbaaadacabbccdabacdacbbaccdbaabadabdbccddcccdcdacbadcacaccabacadacddddbbcdacaabacbabdccddbdcbdbbabdddcdbdacbcabcacdaacaacbaaddcabdbadaccbdbabaaabadcadacdaadcabdcacadcadbddaacaccbcdabbbcbbdbcbcccabdcddddbabdddabbcbcabcadadcbadcdbddaabbbbcbaaabaacbabaddabcdaacccacbbdccdbcdacabaadbdadbdcdacbbdccccccbcbcdbaddaccadacdaacbacbbabacdbdcccddbdcdbadadbdaadcadadbcbaacccddddaabaaababbcaacadcabdacacacdadcbacdcdabacacdcbbbcbcbabddcadbacccbacdabcddbdcaccbbdaaddaaadccabccbddcdddcbddabdaabbcddcccabdcbcbcddabccacbbdbcccbddcabdbdcacbdcacbdbcaccccbacbbabbdddddcadcbcadbcbccdddbccdbaddccdbccacbaccccddbaadcacacdccadacbdbdbcacacbcaaadbddddadddddbbdcaadababdabbbbdccdcbddbdaabdacdaddacdcacacacbdbcbdaabdacabdbbbbbadbccacdbbdabdbcdaadadbbcaccabdcadccaabcbdaddacddcadbbcdbbcbcaacbbdcdadbdbdabbdacacacaaccbcacbbbacbbcaccaaddcdaddbabadcaacaccdacbacabbcadcbbdcdadaccbbddcdbbabaddcdcbbbdddbacabbacacadccbcabccbadcbcaaadabadbdadddcadcdabcbbaabdbdaabbcbacdbbdcadbddbccdbddacacaabccacdbcbbccdcccdbbbdbdcdddddacccaaaabdbaacaaadababbdabbcbcbababddadaaadacaacbaccbbdccadadabcbddbdccaabacbabaabbdbabaacbacaadbbabaadaddabdabdccbcbcbdbbbcbbdcbbbacacdbcacddcccdabdcdabbbaaddcbcbcdbbacbbbddbaacbbbbdccbbccdccbcdbdbcccacaaaadcbdccaacbbdcdccccaadbaaddcbacbcdadddbbddbcbbdcabbbdabdccbbbddabcdadcbcaabaaacaccccacdddddcbbcaccabcaccdbbdbcaabdaddbadadcbcdadcabcabcbbacbbddddadbcdbdaabdccdbabbabcaabdcbaddadcaadddcbdbbcdbacaaddccccbbcdbccdbdccbbacbccdbbabbdccbddcadbdbdbacabbcbdccbdbdccdacaddbdcabaacbacaacbbacdabbcdabbbddcbbbcdbacbdbdcbcabaadabbdcdcbcadbccbdabcbbabccdaccadabaddacbbdddcddddcbdaacbbdcdbacdaddddadbbcaddaabdccddaddcadbdbdbbbbaddcdabbbcbbdcacbddacbaccadbaadddbaccbdbadcadbbccadcbbaccddcbbcacacacdcbaccdaaddcdacdbcdddcadcbcccaacdaadcadabaccdcbddadcadaacbdccacacbbccaadbaacbbdcdccadbdcaaabadacdbbccacbcddababdcddbbabbadcadbcdcbbbbacbcdbdddabadaabdccbccdadcdcacdddadddcbcbcbbbaabcddbcaadaabacbcbaaabbaabcddbbdbcddddaaccdaaaddacddaaaddcabacaaadddaaabcaabcbabdaabbdbdcacdddbbadccbdcbdacdcdcbbbcadaddacaaaabacabcaacbbacbcbbcbccdbddcdabcbcbbdcdcbdddcaabddadabbccabcadbdcdbdbbcbabcccabcbdbdacdacdccbdbbccdddadcdadddcdddbbdcdadccbbddadaacdbdbcbbdababdcadcbcbcddcddaaadabbdcddbddbabaadbdbaddaddbadcbdabcccccbbabddacdcbabdddacaacbbcbbdbacacdbcdccbdaaaddacaaaadbccbcdacdbbbbcbcddcbabddbabddbcaaadaaadaaccccdabacddddbddcbbcaddcdcdccaaddddadcadabbcaccccbcccabaadcdcdcaddcbdbaabcbdbbaadbdaaadaabaadccbaabdddbdbbcdcddbaabdadbbdaaadbaaddcbdcccdccddccaaabcbcbcacbbbbdccbbcbccbddadccbdacdacbcabaacbcacdaddadaaddcbaaaccabbcdddbddcadcbaacbcabdcbdadcbcddcbcdbcddcdcadbccbcbadbaabbbcbaccbaccabcbcacccbabdbcacbdaaddaadbccdbadbbdcaacbbcbccdaadcbddbcbddccdbdaccdbabcacdcdccadcbbbadacbccaacbcddbbadcdaddbacabacccbdbbbcdcddadcdabaacaadbcdcdbcbdacacadbbaababadcdcbddddbbbbbabdccdbaaddbaddacccadcaccccadbbddbcdacababbcaddcddddbacddcddcddcaadbcccbbaadabcdbdcccddcdabadddadcabcccbaadbabdadcadbabadbcabacbcbdccbaddbccbbcadcaadbdbbcdbaadbbdbddabdadbaaadadddacaaaddcabcaddbdcccdaddaadcccdcdccbbacbcccccadcbbbddabaaacbdddcbdbacadddbbbbaddbacdbdcaddbddcacddccadbbdcbaaabdabddadaaddcdccdccdbcbbdddaadbaccaaacbadccaaabbbbadddaaaaabbcdcccbbdcccaccbabcdbaabcdcabbbdbdbbbdacddbacccacbdbabcaaadddcdbddbaccadccdbddabcdddacccbcbccdccddcbaaabbacbbdaccaddcbacdbbcdadcdcbdcabcadabbcbcdabcccbbdabdadcacbacbdbccbbdbbbcacbbcccacaaaadaccdcdcbcccbcbcbaadbbbaaadbacdaccababaacbbccbdcdccaaccbdcadbbdcbdbddbaaaccbbcbbdabacddaacdcbabdcadccdcddbabdbcbcdcaaacbcaacdbdabdcccbdccbdcccccbdbabdbbbcabaaacadbdbdcaaabbadddbdcbabbcabdbccaddbbddddbdadcdccacddadcbaababdbdbacbaccdbcdaaccdcbcdcccdcaabcdbbcadcbadacaacbddaddccacbdbdadbbdbabdcadbbdadbdaccbbbaacbcdbdacccbcbcbddadcabcbcccddbdcddddadadbdcaccacabbadbaaddbadacdbddcbccbdababadbdacacaadacacaaccacbbbccadbbbbddcddddaaababddabcdcaaabcddcddbadcbdbaddccdabcbcbdbbadabcbaddaabbbcdbcdcdcabdcacacaadbcaccbbdbdaccbdabadacccdaacacdbbbddcabaaddcacbacbaacaacaadababbaddbcadccbcadbcabacbdbcdcccbdababdbbdadcbbacabdcbdbcadbaadbacccbbdaadccdbacddbdccbcdcdbadbabaccccbdbcddcdccddadcdbbadccbdccbcdccaabdabdaccbacccdadaaabadcabcbcabbddccdbdcbaadbccbbadaaddbbcacbcabcbcacdcdbadcbbcdcadcdababbbabccacadbabcbbdcbbbaccddcbcabadbabbdcbaddadaddcbbbdabbcddcdccdbadbaddaaaddddcacaadcbdbccddabcddacbbadacbcbccbbdaabaabcbcdbbcbdabbdcdbbdddddaabadabadbcaccdabdacdadbbcbcacabccbbaacdabcacbaaccbadbccbabddcdccaaabcadbdcacdadccabcbbdcabdaaaddadcaaaaabcdadcacabcadcddacdcccbcabaaabbdbaadabdcacadbdbdcabccddbbbddbbbaacccbaababaaddbadbdabacadbadcccaaccdadddddaadcddacbaadaaadcdbdbcbadcaccdddbaacdbcadcdbcacccadabaaddbddccbbbbadabaddccadabbbacbbcdaaadbbdcccbabcdadcadbaccbdbccacbabcdadcdcdaadbcdcdaaadddbdaabdbdbbaddbbbdbdddacbbccdcbbacddbbbbcaaacacbbcdccdbccdcaddccbdbadbabbdadbdbdaaacdadadcbdbbbddbabddaababcbacbdadcacbbcacdacabcbcaaaacdccbdbcabdababcdbcbadddddbacabccadccdadcadbbadabcdddbdbbabdbdaaadacbccaacbaaaadcbddacbbdbcacdccddcccbddbcddddcbabbdadacdbcacacdcdadcabbabaaaacddcaabbbbcaacdabbbcaccdbbccbadabcacacadbbcbacbbbaabaaabdbadccadaccbcbdaadbcabbcdababadcdcbbbbccddcabbbdcacccdbdccbacabaadcddccabaddcabcbadbddccaaababcaddabacbddbaabbadaccccaaabdcaadabcdcdaabbdabaaacdcddccacdaacdaddbbcabcababadacdaabaacbccbaddabbdccadadbccdadaccacdcdbdcadadbddcbdbaaddabcbbdadaccbccbadbbdababadcbdbabcbbaaaadbdcabcdadbdbbcdcbbbdccdbcabdcadaaabaccaadcdbcdddccbadcbbacbdbcaacccddddcdbadbbdccabcbbacababccbdadcaadbbbdccdabcdbacbbcdaddcdcddcbabcddbccddacbacddbcdbdbbcbadcaccdbbadbbbdcadadddaabcdbcdacaaabcdddbbdbaccbaddccbacacdbdccdcbbdcbbdaadadccdbadaabcdaccacdbdbababdbacabbcbabaabdbadabaccbdbcacbbdaadaaaacbbaccdaacdabcbbdacacacacbccdabdccccdcdacdbbacacacbbabdabcbdddbccdcadccbdabddbbacdddaadabccbbdadbddbccdbdddabacdcccbcaaadbadcccddbdbabdabdbdbcbccbcaccddcbaadabbbaddbacccddcabbbcccadcbcabddaddadadcadbacddcaabbcdacdbadaacbdbbaabaccdbcdbbbbbdbddbaaaabaadabcbcbbdbcdcccacdccdababdadbbbaaabbdbbcdbaabddbaacbddcbaabbcbdaacdbcabdacadcbabbcdbbdadbacaadaacadddccdcccaaababdcdabadabcadaaabaabbcccacabbccdcdcdcacacbbcacbddccaddccdccaaacbbdcbcddbdacaabbdcdabdcbadbababcdbdcdaaaccbcbabbdccccdbbdbbdcccdbaddcbaabbaccdbbbcbdadcadbbbacabcbcccbcadaaadcaaababddcbbdcadbcadadadcddddcacccbacaccbbdabddbcdaacdbacdcabcaaabcbdbcaaacbcabaddaaacbcccbaacaabdcdbdddaabbbccdcbdadbccadbaaaabccbdddcbdacacdaacabdddbbaddddcadabbbaabdacbdbabddddcabddaccacdabacbcdaaacaacaabcabddadabcacdacddabcbdbbcdadababcaabacbaadbdbbcdcdbabbdccddcdddddbbbacddbcabbabbcaccddbcdbabdacadbdbadbdacdbaccccddbbadcacbdbcdacabccbdbdaddccdcdbbbcdcbcdbacbcadddabbdddcaaaaabdabdcadbddbacbcacbabccbcdbcdaddadbcbadaabbcbabdaccddbdcbdbcbdbccdabdbabbbcabcdaacddaddadcddcaccbbcbacdbaabbcabcbdaaabdbdbbdabadbababcdababccaddbadbdabbcccabdbcdbabcbcdaccbcdaddcbbbacabddccdbbbbabdccdadbcaaacbadaababdabbdabbbbcaabdddbcbdcaabbcdacccadbcbdacdabaaddcdccddcbbaabbcdbdabbbdcbdadbaacdcdcdcbcbbadbbdaaaddbdbadbbddddacdaadbdbdadbaccacabdadcaaaacbdadadbbbcbcbdcdccadddbcadcdaaabbabaccdbccbdadcaabbcccabdbddbbdccadabbdbaabbbdccadcddbacadcadbcbadadddcdbddcacccbbcabcbbbaabbbabacdaacbcdcdbbddcdccbddaabbababdbbbcdcccdbadbddadaaccbbabaadddbddcadcacaabdcacbbbbacbdbcdabcbdaaadacbbddbbddadadbaaadbccadbacccbaadbdbdbddcbcdcdbccbdcabaacddbabacdddbaccaaacddcddbdadbcddaaacaaddbdabaddccbacdcdabbcbddbddabccccbbbbdaaaccdbcdacccbcdacbaadcdabbccabddcbdbaaaccccbbbccdbdcdbcdcacbbcacdcbcbddcadadbdccbccadbbbccacdabcabbcdcbcabadddabdbcacdddadaacddaaddadbbcabdbabdaadabbaccccbcbadaddccaaadcbadabaccabadcadcdadcddcadbdccdaaababbdadccabcccccadabdabdaccaaddababdbbaadccaaadcbbabcdaabcddaaaabcdacdababccaadcbdabdbcabacbbccbdbaddcbdcacbddcbcdbccdbbbcdbddccabacddcaaacbdbcbdbdddaaacadcccaddbcabdcacadbdacbdabdbbbbadabababababcbbaccdaaddcacbaccabbcdbcabbbaacdddcdbbbbbabbabdbbccbaabdbcaddddbddababacadcdbcbccdabbcbabbcbcaacabacdaaadddbadadcababcddcdbdccdacddabbabacacdbbdcdcddabababbdcacacaaccddcaddacaabccdcadbccbadcdabacdbccdcbdddaadbadccbbdbbbbaadacadbaacddcbccbcbbbadcccdccabdddaaacaacddaacdabdbddbacddaccacacbabaaaabadaaacacdbcccabbbcabbdadcbdaaaccbcaccaccaddaaadaddacaaaccbbacacdabdbbadacbcdbdcdddbaacabbaacdbabbaabdbccddccbacbbcbdaabadcabaaccddaacaabaaadcaddbcaddbcdcacaddbbcadbbddaddbcaadbccbccaadccddbdddcbbcdbcdadadcddbdbbaddbbcbdcbdaaadadcbdacbaabacacadbcddbcbdabdcaaadadddddcbcddaacaabdacabddadacdabadcdbaadbbccdcbadbdcbddacadbdbcacabccddcadacbcdcaadbbbdacbcdbcccabcadbdadbdbcabcaadabcdcccacdbabadcccbbdddbabbcadddbbdbbcadcbbcacacdcdbbacdaabcdbbdccacadbcccbaddddccddbaabdbbccabbdcacbaabbabaadddacaddbddbbaaccdadbbbbccbcaadddaacdbcabbbbcabdbdddddbcaaccacbacbbaccabcacccaaaadbcdabbccbcabcbbcabcdaacddabbadacabbbcdcacadaabdcdddcbaddbbddbcbbcbcccbbbbccbcdcbadbbaddbcbbbdadaaddcabdbcdbcabdbbdccaadbbcdadacadcbdccbbcadcabccddccddbaaddcbdaacaadbcdbabddacacabdccbdcbcdcbbccdabdbacdaddcdbabccddcabdbdcddbccbcadbadbcbacbaacccccddbbddacdabcccccacdcacdaacacdccbcbcdcdcbdcdbddcdbcbadaabbdcbbdcbdacbbdddccbcdbcacbacccdadaacdadbabadcdddbbdddbadddddadbcddcbadbabadcccadaacdbdddbaddbacbbdcbabaaadabcdadcdcbcbccbdccacbbaccaccbabaabacadcadddaadadcbcbacacbbbdccabdcdbdbdccadaacababddbcdabcdbcbddddaabaabadaadbcaaccbbcbdabcbcdbdadbcdbaaabddbadadabcdbdaddabdacdacdbcabbbbcbcacaccccbcccacaadbbabdabbbddcbbbadaabddcccbddbcaaaabbaccbbdccdbdccabdaabbcbbdccaabbddddaddcbaddcdaddacccaddcbccdbdcbcccabdadcbdadaddcdccbcabadabdbcccdddcaddbbcdcbdddcbaacbaaadcbbaadcccbadcacddbacdabbbacdcbbcabdacddcdcadabccaaddcacbbcbbccadbdbcaadaccdccccdadcddddadcbccddbabdaaaaabacaaacdccdcaccabdabbcaadccaddcbcddccbdcbcabddabcdbaacdcdcdcaddbcbacdcaaaabcaabadbbccbbcbacdbcbbbaddaabbcddbbbdacddcabdadaccddbaaabacddaccbbaadabdbabdbcdbdddabaaadaddabdabbdcddccbaaabbaadcaaaaadadaccbcccdccadaccabbadddccbcadcdabaddcdcbdadadbdbaabbccdcbcbacbadabadbacbadddaccbacddbaadccbdaccddddcbdcaabaddbcccdcbbbcbaacbbbbadcddbbdbdcddcdbdabcbaabaaccccdbbaddaaacacbcdaadcaaddcaacbdbccadaaabccacacacbcabccddcbdccacabccdccacbadcccdcbddbadbacaccbbdabcaabcdadaadacddabdbdadbaabbdbaaaaabababcbbdcacdbdabcccaadcdadacacaddcdcadacccdbdaccdbabbcacaabaaddbddcdbbcccdbababbcdcccbdddacbbccbddacadabccbbacaadcadacacacaccdcaddabbbdcdcdccddbcbabccabcaacbbbcaadbbdbadadbcdbcbaacbaccccdcbdbdcacccbddbdcabadddbcbadcbacbcdababdccabdaadcbbaadcadcbcccbdcdabadbaaadccbcaacbdcdbdbabccdcccdabbbcccdcddcaccbcabdaccbacdacbbdccdbaababdbddbcccdaddcdcadbcdbbcaaaacdbaadcaacaaacabcadabdcccaaadccbbddcadccacaadaaccbbcddbababcacbaadccbaccadacabddaacbdcbcddbbcadddacaccdaaddaaacbccaddbbcbbbbccdddaccdbbcbcaaccaddddaccadddadaddbaabcbcbcccdbadcdddbdcbbbdbacdcdadbcdcaddacdbabcbbbcddbbbaaabcccacbdacaabbbabcacdadddadcadabbbdbdaababcbbbdccccacddacbdbbaddcccaaaccbbcbbcdbcadbdcbadbadbaadacbbcabbccdaabbabaaccbcbccdaacdccddbaccdccccbbcbdaabaadcaabcbdcaacbcdbaabddcacabaaacbccccbdcccadccadbdaaadacadbaadbcbadabadacabddaaddacaaadbbdadaddcdaadaadccacdcdddddaabaacdacddaadacbabbabaaadacccaadcbdacbacdbadcadccddcbbbbdcdcabacaddabccdbbaadaabbcbadaacabadbdadcbdddcdcaabaacdcaabdcddadaaadcaccaadcbcaaadbdaacababaacaacadaccdccdbccbacbcabbdcaabcaadaddcaacbddcbadbcbabbcdbadabaababbbbcdadaadadbabcdabbacdcdcabdaadddbacbaadbbbdcdaabaaccbdababcbbacacdaadabcbcdaaaadaacccbddddbbcaabcbcdbdabccdacacdddddcdcdbabcdccadcccdccddaddbcdbdbabbdbbddbdbacdbbbabdddddbbaddaabadcdbdbdcdacdbcbabcabbcaaccbaddddbdcbaacaadbabcdbcdccabaabadcaabbcddcaabbcadbdaaccddbaadcdabacaadbabacaaadcacccdbbdbdcddadccbcdabdbbdcbabbbdbcabcdbcbbccaaaccddbbdabccccaacbcdacdbaaaaddcadcdacdacbcbabdaadbbbdcabbbbbabcdcabddabdbdadcdadccdbcdcadacdbdbdddaccbbccccaabcacacdddcdadbbbdaaaddadbaabbbabbaacbcdcbcbbdacbcbadbdabddabcdbaabcccadaabbcaadacacadbadbbbdcdbabbabcacdbbabbdcccabbabbacddbccadabadcddcbcbcadbcbabbabdacbbbabccddcabaacdacddcbbbcacadddddabbaccbbaaadabccbdbbcccaadcccbbdaddaccdbcdbcdaacddccabdcdadbcbdcdcadddddaadcccdadbaaacaddcdbbabbbddcdcbbdabcbbcdabdddbbbabdbddbabcccddabcacadcdddacbcbacbadbbaabaadddbadadcadbbbdbcabdccdcbaabcdaadccacdddbabacbdaadaabbababacccdaddbcacdaddabacbbaaadbaddcbdbabaaaabaddcaadcccbdadbcaabbbbaaddaabbaabdbddbaddabbabbcacbaccbcbbbdacbdbccbaccaaaacbdacacaaddbccdcbcbcbdabbdababbaabadadbbddcbbddaadcdbbaabcdaccbddcbabbcdabdbdbaccdadaadcdcacabdddaabbcdccacbbcaaccbdbcbaababcbaddddadbbdcdcdddcbdbaddccddadbccabbdacbccacddbcbbccddbadddadbbacabdbdbcacbbbbaccaccdcaddcbacdbddbcdabaddcacbcadbcbcbdabbdcacdbacacdbbacbbdaadacbbbdbaaacbcccdddbbddacdcdcdabbddbaaaacaacccbcaacdddcbabaadacbaabbddddadaabbaccabcacaadccdbcbabcdbbcabcbacddbadccbcacbcdbbbaddaabadabaabcddadacabacdcadcbdddcaddbaaadcadabccccbbddcaccdbcaccbdbacadaccadbaaddcbbdcccdcadacabadbcbbbbaccbbdbdacaacbdbaddddbbbdaaaadbaaabcccdadcccacbcbdabccabbbbacdcbdddabcbcddccddcdaaabccdadbacbdadcccdcaddcadcaaaadcbdbbdcdcccdadcdaabaabbacbddbbbdaacbddaaccbbbcdacbbbacdcddaaabacbccdcbaccbccddddbdaacddbacdbcacdbddabbbccbdcdcdcabcdbaacccbadbbabcbdadcccddccccaacadbdacbacccccbbabcdcdcabccccbacbdabdcbacbdbcbbaabaacaddaacdadccdcdabadbcacaddcbcddbdadaaabdccdacbbacbbabdcccaccdbdcabcdcdaabacaacddbcbdddccaddddbdccadccaaacdaddbaadccaadadadaccacaccaddabdcacadaabdadbbdcabdccdcacccdddcbadbddbcdcdcbddddabcdbdbdacdcdccacaddcdcdbbddaaacabccabbbcdaadadadacdacacaddcccddbdbadabdccacadbbcdacabccdbdbdbbcbaccbdbabdadddcddcaaacdcadabddcbcddaddcabcaadadbbbbadbdbaaaabdabdcdcbaddaccddacacdacbbbbcbcabdcddbdbbcdbaaabdcbbaddadcabbdbcabbdccbaadcabaacdcadbccbabddbacddababcacdacbcaccddacdbacdbcdadcccacccdcbbbcddcddcccbdccaacbdbdcacbbdadacdbaccdbbaacdcccadddacbdcbbddcbddcbdbabdadddbdcabadddddbddcbaddbbbdbbaadcaacddbddacbcdccadbacbaacabddabbabddcdaccdcbccabdcdbccccbdbcbccbccacbddabccacdbcaccbbacbbbdddbcacbcadbcadaadddaaadcbbacdaababbcaddcdcadaaaaddbddddacdcaccabbdcddbccabbacdcbaaccbdaadbabdbdbcdaababdacacddddbbcdaabbdcccccadcdadcbcabcbddaccbbcbadbdcdabbcdbddacadcddbdbacbadbcddabdbbbbbaddbdaccababcabddabddabcdbbcbccbcddadcdababdddadbacabddadaddadcdaaccadbdddcbaaadacacdbaadddcdbcdccacabadbabdabdadadddbbacdcadaacbaccbbadabcdbadabbbcdcacdacdbdadbcbcbddccbdbcccbccaacdbcdbddaacdacacabacdbaadcbabacaaddacdbcbccdcadbaadbbcdccbddacddbaaabdbaaaddaaadcdaadcdacadbcdabaabcdacbabccdcdbddabddbdcabaacbadbacdcbccddddacdbaacbcacacdbabbcaabaaababdadadbadbccbabaacbbccbccbdcadbbbdbcabdabbabddaaaddadddabdbacddccbdcccbbdadaddacdbcabaaccccdcbbadcddaabdbaabbdabdbaaadcbadccabdccbbdbbabdbddaabadaccdbabaabcbccadbadccadbbcabcbbbcdcdccacdadcaadddcddcadacbdabdddadcccbacdbaddaccdcbdbaacddcbbbcdcddcddbbbcbdbacdbaaddddadbdbbcbbbaddadcdbddcbaababacabbbacacbaddcacdcaccadbbbaaadbaabadaadbdbdcaaccdccdabdccbccaabaadbabdabbaccadbbaccdacbbaadcbcdcaddbcdcddadaddabaabacaddddcdaaabcabdabddbdbabdbbdbcdacdbdacbdaaaadcacbbcbbdbcddabbdbdddabcdabcccbbccacdbcbbdccccdddbbbddbddbabbbadcdcdddadcbbdbbdcdcdcbcbaddbdaabcccbacdaccadbddccbcbbcacccbbcccddadbccdbcbbddccaccdbcddbabadbdccdabcccdabdbdabbdacdacdbbbadddadbaacdbbcccaaababbabacccbabbdbcaccaaccdddbccaddccdcdddcadbaabcccabbbbcbaabbbcdbacdcbacbcdaddbcaabdabbaccdbddbcdddbaddbbddcadbccbcccdddabdadccbbccadaaccdaadbbcbddcbabaccccbdadcdacbddabbdaaccabdbdcdaabdabdadaababcdadacbcdcbaacbcdacdbaadaddbdcddcbcadbaacacddaaadcaddbdbaddadbbabbcdadddabddbcabadcbcdbcbacdcaddaaadcdaaacbcbcbaccadacbabcdcdcbaddbcccabbbbdadadbcddbacbcbdacdadcdcddadaaacdcacccbabdccbaadcddbcbacbbdadbbdbaacdacddacdcaadbaccbbadccdaaabadaccbaadadccacaabacabdabccdddbacbccddbababccbccaacadcdbbbcbaccdcacdabdbcbdaccbbcacadaddddcdcaccbbdbabacacacbbbacaadcddccbddbcaaabbccbabdcadbbdcbbddaacbbdcbbbbcddadbdabaddacaaacdddbdcabaaccaccbbcdbacacaaacdabcdbcaccaacbdabccadbbbdbccabbbbccdabddacacbdbdccbbadadbddbbbacacddadcbacacababdabadcdbdccdddbcbcbadcabcaadccdbddcdbcdcdbbbbcdacbdbcaddaddddbbdcacbbaadccdabcbbbabbabacbbdacaccccacbdaacababbdacaaaadcbddccbbbbabaacdddaccbbcabbccbacdbdbdbbdddadddddccaccbdcaacdbaadadbdabbcbbdcbadabdbddaaddabdbdbdcdaaddaacdadbddcdbadacdbadababbcabbcdbccddcddbbabcdaccaacacbacccaaabdcaacbbabbcdcccbdabacababbdbdbababbcdaaacdbacbdbbbcbabdabcacdbbaccacddaadcacacccdadccaaabbabdbaccadcdcbdbacdcbcaabadcbbddadabdcacbccccadbaaaacacbabcddacddaacbbbbdabaadbbdcbcdcccacabccabcbdadddcbbcdbaaccabaccbbbbdcccabdbcbcbadbbbdbccbcaabcdadabcbacdabaacbaacbdaabdbcdbcccaabacbbaabddcabcadccdcccabcbccdbbaddaaccbdabccdadadacccdbabbcabbdabdbdaccdddbdddddaabacbcbcdcbbbadcbcbcabbddbbbbccbddcddbbcabaacdccbdbabadcbdacccaaddbadaababcdcdcbccacdbbaccccddaacdddadaaccaaaadabdaccbdbabcdcdbbddccbbddcbdaddcdcbddbbbaadadcbaaccdcaaabbcbccdabbcbbcdaacbbcccabcabbbccdcddbacacaaacadbabaacdccdadbbdabcaddcadbabacbbaabacbadadaabcbbcccdaaaddcbbacbdccaaddcddbdcaacddacdaadaddabaacacadcabbdcabddccbbbabadbbbcbadcbbccdbabccaccbbccddbdccbbaacdccbbbcccdabbccdbccaacadccbbddbaacaaabcbdaddddbbdaadacaabadcbadabbacbabdadbdcdbadcbcdddadbacbabbddbddabbbddccdacacccbbddaacdacdcdddbacddabdadbaabcbdcaabaaaaadbaddccbdcacaadacaddbabcaaadbbbccbbdaacbdcadabaddcadccdbacbaadaabbbabbdaadadadbbbdaacadacabcbdcbcadbdbbadbcbddddbcbdaddcdbdadcbdadccbdadbcddadbdcccaaccccbdadddddadabccadbccdacabbdabbabbddcbaddaccdaccbbabddcbdbdaabacbcaacdacccaabacacddccaddacdbcddaccdcccbdcccddcccbcdaaccbbccdaccacccbabaaacbaaadbdccdaadccddbbacdabdcdccbcadbbbbccbabdcccdcbbdcdcbadccbddbdccbaacdcccabacdcbaaabbcbdccaccbdaabbbddbadadaadbdcadcacbdcdaabdddccabcbaddaadbabaabbabdcbbcaaddbdbadbccdaaacdbabddcadacbcbbbbdbddbdccdbaadcbdbddcaccdbcbdccdbcbcbbcdaabdbccddbcbdbaccacddbdcbcbcabdbadaababccbabaddcabaddabdbdbbcbccbdcaddbbbbbaadabccccaddcbcddccbdcabdaadbdccccaddaddaccbcbbccabdbcccdbbddbccadbdccacbcccdaaccddbbdccabaaaabbcbbbaabdcdacbbaaddbcadcccccaacddcabdabcdbccbacccbbcddabdbacdacaccaddbacbdddadabddacdddddaddbacdabbabcaaccdcddcbbdcddcabcccabdbdbcdbbdbbdbaccbdbbcadddccbbaaccdcdacacaabdbddaddccccddbdcacdaabdacddbbcbbdabbdbcdcddbaccbbabbbcbcbaadbcacacadbbdbdbcacabcccaccdadcdadddccddcacdccadbdddaacaddaacccaccbdbccbbcbacacccccdcadaccccdcacccdcbbcdddcdcbbcdccdadbdcdbbadabcbdcadccdacbbbadbbcabacdbdbbbaddaadbbabdddaadadbcaacbbacaaccabdddacaccdcbdbddcdbbbcbbcbddaaadcdcaddccaacbacbcdbdbddacabadbaccdcdcdacdccabccabbcdaacbcadababbdabaddcacacdabdbdddbdcaacdadaccddbdaddbaadcddbbdcaabcadddaadbddadaabbaacaabcdaadacabcddbbbdcaccdbddabdacbbacccccddaccbaaabcdaaacbdaadbacccddadbdaabdaccabbdddddcddcaacaadacacadcbbbacbaaddcddacccbcacbbaabadcddccbcbadcababcbbcbccbbcdcbccbbdbbcdccacdbddbabcacacbaacbacbdaacbcbcdcdcaccdbcadbcaababddadcaabdcbccbadabcacccacbdccabadadaddbcdabcaddbaaddcabbacccddaaabdcaaccaacddadbddddcacacddccbccbccacaddbacbabaddcbcbdbcababbccccddcdbdcabacbbcaabdddabdbddaabbccadaaddaacabcccdcbaadbacdcaccdbabdbccbbadbadbadaacadccbddbabadbbcbcccccacbcadcbadaddcbbcbcaaacabcaccddcbdcdcbcdbbdabdacccbdabccdacbbcccbcddcadbaddbddcabbddbaaabadcbcacaaabaabdabdcdccdcacbbabccccbbcbdabbabdbbaaacbcabccdadabdbbdcdbddbdabccaacdcadcacdacdaababbddbbcbcbcdccaddabadabbdabddabbbbabcdabbabccaacaacbaccacdcdabddcacccccbddbbbbcbbabcbdcabdbcbbddbbcbccbadacddacbacdbdcabdccbabaccdadcdbcdbbbaabadcabbcddcdadccaadbabbddccbbabccadcbbcbcdbbdabdccccbaadddabcdcbaacdcdaaabcdaacbdbbdbdbdbdadcdddcbcabbdddcbdaaaadccbdbacbbcabcacddcbcbdbbbbcbbdaabccbdcadcaabcccbacacccbbdcccbdcaaacbcaaacddaadbaabdacccccdcabcdcabdbbaabdbdccbdddcbcaacabdaacadadbdabadbdbdbdaaacaacbabdbcccbccdaddabcbabbdacccbadcbdddcabcdacaddddddcdccccccbcbabbcbadaddcddbdacbbbcadbcbbbcbaaddbaccdbbdcdbbaaabaccbdaadabbadbdddbdbadabacdbaacaaddddbcacaacabbacbdadadccaacdcaabbcaaaccdcadccbdbbcbbbaccaaddbdcbadbadcbcdbbbcdadcbbbdbccdbcddadcbaaacbdcdabdccababcddbdbbbdacbbccbbaabcadcbdddabddacdacababbbddaadccabddaccdcdbccccadbdabbdcdbdabbacddcdcbbcaddcbbdaaddababacabbdcdcbadabcadadbdaacddacdcdbdcaacccddabcccbdbbbbdddddbaabddacdbadbdcbccdbdadddaabcbcdadbaabbdccadadadcbbccdddabbcbdbbdadaacbcadbaacbdacbccabbaccacdacdbbdddbabdbdbdddababddbdabddabdbabbccabcbdcaadccbccaddabbcadaabadccbdcaccdadcdccbcdabcdcacbccbcbddaacaadcadacbddddadcdabbdacdadcababcbccdbababddccadacccccbdcbdbcaacadccabccbbbaaaccdadaabbadcaaaabbaadbdcdcddabadcbcabaccaddddabccbdabbbaccbcdbacccabcdccadccbcaddcdaabcbbdacdaaacdcdcccadadabbcaddbdaadadaaddbcbbaaccbdaccdaaccdbcbcbccbaaddccdccddbcbcacbaadbabdbddcdccbadddabddcddcccddbaabbacabcbcabdddcaaacbaabbddcacdcddccdddbbbcadaccbaaddadabbdbadcbbadbdddbdcbcababaddabacccabddcdbdbdabdaabdcdacbdbcacacabbabaadddcdcaacdabbcccacddabdaaadabaadaabaaaabcadbaadcbdadaaaaccbdbcabdddaddbcabaccabdbcbdbaaadacaaabdabbacbdacbacaaaabcbbcbbcdccdbbdccddaccccccccddcdbacbddadaabcabcccaaadcdcccccabadbcbabbcdadacdbbdaacaaabddacdbaddbbcbdcccadcbcdbbdabcbdbdddcccbcbcbbaaabccaaaaaadbbbaccccadaddcdbbbdaaaadbaacacaadbcbacaacbbcadbbdcccddbcacabdadddcdcaabdadcacdbcdbdbcbdacbcdcbddddcdcabddcaddbbcccdbadaddacadcdadbabbbbacbbccdbcdacabbbcbadcdacaabcdbcaaddaccbbbddbaaabcacccdcabbbbddcdadaacbcabdadadbbcdaddaabdcabdcbaabccaabcdccbadabcdcababcaabdabdcddccddbdacdbadadacdadcadbabddaacbcacbccbbddacbcbcbacacbbbabaaabbadbbbacdcdaabbbbaddbaacacaaddcacdbdabacabbabdcbcbdbbcbaddaababacbbbdcdcabddadcadcddcbddcddccaaadaadccdbaacababbdccbcbdadbddacdccddbcdcbdccbdbacdabbdbdacadcaddcaaadbddcbbcabaacdcbdaccbaabbadbdbdbdbdaaabddacbbddbcccbcacbbccbdbdaabcdadaaacbcaacabcddcbadbbdbdabcacabcadcbcaadcbaaadcbaddbbdddadbbdbacadbcbcabccdacaddaccabbdccdbbaadaacdbbdbaccdadaaadcbdddddcbadbbcdadcababcdbdccbcdabcddcabdccbbcbaadbdbdadbcabdaddccabcddaabcaaccadccaccdcabddaabbccabcacabbbadbbbcbabbbdcacdcbccbccdaabaabcdaabcbdbdacccacccadbddcdcccbbaaacbacadabacbbbdcbbdbbcaabaacdbddabaabcadbbaabacabbdcadabccccabcccadadcdadcdcccabccabcddddcdaaaaccacdabcacbddcdbbbccbbcdcacdbcddcdbbadbacdcacbacaddabdccccbdcdbacacbacddcacaabdadadcabcacdaaadcbddadcdbadacdaddccbaabddcabbadcaccccaaabbdbbbbbdbbbbdbcccbacbdbdcbcdabadbbccaaddacdacbbacbaaadbabccacadcdabdccaaddddbbbaacbbdbacadaaacdbcbdcdabaaadbcbbbcabccdcdcbdaddcdccdddccdcaaaacdacdcacbbbbcacddaaababcabcabdddaabaaadcacddacaadadbbbdddbabdacacbdbabdcabdcabbaddacabdacbaddcdbdccaaacaaabdcbbcabdbbbccbbdacddcdacdabdcbbbbabddbbbdcdcdcbdaddcbdaccdbdabdbcbddcdadacddcdbbddcacdbdcbdddbdcbcddbdbadcaadbdabcaacabccdddcdabbcbadabbbcddccdadadddaccbbacabdacddadddadddccaccacccabcddcabbcaabbbcacacdbabccdaacdbbbbaacadbcdaccbaccdcdcababbbbdcdcdacbbdcbdccddbcbccacbcccabdccdaadaccacddbcdbbbcaddabcbdacccdabdadcbcabdadddaabcddddcaabbabcccdcbdbddadbaadccddbaabaadccddccccacbbcbccbbccdadddbccdbccdcbcaabaacdbcbacdacabcdacadaccdddcdcbadccabadacbdbdacdcccbbddcdbbccaaaacdddbadbdabbddcaacbacaacacdbbacbbbacaddcdabcabcddbacccccaddbcabbbaacbacabcdbcbdbbdccdabddaaadcccbaacbdcbdabcbcbadacdcdcbcbcaacccddbadaaadacacdbaabcbbbaddabcddadbdbbbcccbaaabbaaccdaccdbdadaccadcabbcbcbccbdcadbadbacaadaabdbccbbbbdabdabbabbbdbdddacadabddccdbccaabbdbcbabaadabbabdaacaacaabbadcbdcbcaabadbdacbdbbdbadadbdcddccbaaddbcbcdddcdacccbdbcdaddadabadbdaaacbacddadacbdbbaccdbcccbbcdacdcddcccabcabadbcdbbbbdbdccddccdaacadbabddcbbbdccadacccdbdcddbbdbbacbdcccacbbddaaccadddacdcdbaaaabaccbdbbbabbaacabdcaddcbbcddbbdcbddbbbbbabdbbdcaabdbcadbdaadaaadacbacacbcabcbdcbbdcbcacdbdaadadbadacbbaacbccddccdbcacbdabddbbbdbccddadcccccbdcddbcbdbdcbaddacbaddbacdacdccacccacbdcdaaaaccadaaabdbccaadaacbacccddaaaaddbacccbbdbaddacdaddbcbcddbbaadddcddacdadcddbccddbbbcbdbabdacdcbcbadcbdaabcbcccdabbbdddbccabbbabbaabdbaadabbabdbdaacaccaddadcdbbcddddddcacabdcddbbaadabdbaacadaaabbadaadbacaccdbacadddcbbbadbcdcdbbdbbaacdbcbcbcabadddbabbbccabdcddbbadccddacdacccbcdbbabbbcabccdacbbccbbcbaccdbdacdacdbdacdcabdacdbcddcacadcddbcddbcbbbcdabdbdbcaabcccaddaabbcabadabcdabcbbddacdbbcadbbbcdddbdabbdbcbadbcdbdccabcaabcbdadcddccddaddaababacabcbccbdabccccdadadbbbdcdcbbddacbddababbcbcacbcbcddbccdbbbbdbcbddcbcdacaddabcadaabadbcbaccccdbdbcabdccbbccddadddbaabccdabcdbbdadbcdaddbbdabddccacccdabbbaacddcabcacddcadbaddaaddadcccbaaacccadbbdbdbcbbacdbcdbacdbdddcaacbddbcddbbdaaccdaadbcbbdbbcbadabdbdbbcdccdcbcdbbaaadddcbaaccdbbdbdbcbbcbccddbbbddbdbccaccabdddbbccadaaacadddcdcaaacbbbdddaaadaadcddacbdcccbbbadabbdcacdbdccadcacacbbcadaabcdbcaaadbdbcddcacaadcaccbbbaacacbabbbdaccadcbbdbacaaccccacacdcabbccdcabbcbabddaacddccabbacdabcbddbbcbbdbcccaababdcdbcdbbaaccddddcbacabcacbabcbaabdbcdaccbcaabdaadaadcbbcadbcdcbbaaacbabbcadddacdcbcccccdcdbcadbadbbaaccbdbddbaadbccbcbcdbdabcdbbabbcbdaadcdccbcbdccddbaaabacbaadddbbabdbdbbccabbcabcaadcdbadacaaacbddacaccdcbdddbcdbddcddaadcaddccaacddccadaabcbcacacddbddbccddbabbdaccabbdaddcacabcaccdadbddabcbbcbccadccccaacdddbcdbcdcacdadacadddbbacadbcdadabbddcaddbbddccaabdabccadddbadbacbcbcccaababccaadaddcdbaddcabddbcdbbdcdcbbabdcadcaccdbabdbaaddcacdacaacdcaaccbabbdaacadacaaabdaadcbbdbdcccdabbdcabbaaacdaaabbbabcdbbadadbabbdcacbaaddacbcdcaddbaadaaacdbacbabaddabbccadabacaadaddcbdbbddacabaccabadbaddbdbbcdacdaabbdbbadccddbcbbdacbbbbabbddbdabbdacaabccbcdcbdbaacaababdbcdaadcbbbabdccdabbbadbcacbaccccdcdddbaaacddcddbbadccaacbdcaddbdbbcaacbaddddcdaccdbacdcadaaaaaabcdbcbcbddcdcbbccdacdcaaddddcbdbacacaacaccdbbcdcddadbcaadddcdacdabcbddcdbbcdabaaacbacdacacdcbdadbbccbcbbaadbbdabcabbcdcadaccacbcbadcccbdccbdcbcaabaacaadddacaaccaccbdababacbaaccadbbadcaadddaddcdadcdacbddcddcdbacbbdcbbcbddacdadccdcbbdddacabaadadbaadabcbadbbaccdccbabadaabcacacbdbbcbadaddcaabccdaabacbccbbdbccbcdbcaaccabdbdbabaadbbcdbbbdaabaaabcaacbaddcdcbbbcdacbadccddcacdcbcaabacccacccaadbbbdcadacacdababbacaccbdadcaaacdaacdaabcbadbccdbbbadcbacbccaaaabdcacbaccddbacdbbaadbcbcdcadaaadaaabbcccbabcaddddccccbbcaaaaddcdbbccaadccaaababdccdcbcaadcabbdcddacdadaabcacccacccacdbdbaccbbcbdccbcabdcdabcacabdccbaacbdbbabbdcddbdadddbdcccdbcccbbcbaadddcddbbbccdcdccbdbabccbbddabbbcbbdbabbbdcbcbbbcadcbbbcbcccbabbadbbddadcbabdbdccdacdadcbabdbbdadaabcbddcdbcacadbbbdbcddddcacbdaabbdbcdddcbccddcbbbabbcdbbaccaabcbbbcaccdcadccaacabdaadbcdbaabcddccdbcdcadcaddacbdaddaaacadbbccbbbccdbcdbadbccabdddabdcccbcdcacbcdacacccccdadaadddcaaaddabcbcadbccbadaadababbbaabcbbdbdacabaabcbcadcaacdbddbcdacbaddcbaacbacdcbdaadaaaacddaddbdaabdcabbdccddaabdbdcdaccbdbdcccacadbcaaccdabbccadddcbbbabbaccadacdccbabbabadbbbaddbbaababbcbcbabdddadcbabccadbdbdaabbbdbaaadcacbabdcbcdaccccccabcccccbdddadcdbbbdddbbcdbccccacbbabdacddbddcadcacccabaadcabdddccaabcacdacaddcaadcdabcdabbbbccbacaabdccbbbddcccdabbdbabbdaadacbcddbcdbbacbbddbddbcdbcdcbddcacdcabcdaabbcaaadacbbddcdcbabdbdbdbdcbbbaaaadbbccddcbdbcdacacbcaaabbbabcdacdabdacddbdaddcacadbdcbcbaaaabddcddaaababcbaaacbdbcbbcadddabdacdacadbaaddbcdcbdaacbbdbadbbbbbdcbcbdbddbdcabbbdcbaccddadbbdbdbabbaadbdcaddbbabccddddbccacabdaadbbdaacbdcabaaacbadcbbdadddabdadccaaaccabbdbacaadbaacdacbbccabacacadbcdbbaacabbabbdadadbdbadcdbaddaacacdbbbdbbddcabaabdbdcccbcdbcddaacbbbaabddbaacabcaacdbddbcadcbbbacdbbaabdadcbacdbbadaddcbdddbdcaccdbbadabcdddbdaddaaddadbbbbbbabbddacaccbdbdcbddbdcbbaabddaabcdbcbbbcbddaddbadccccdbdacadcacabaadbdaaadbbacbaddadbbadcacadbdacbcccbadabdbcbcbccaacaddbccbdaabdabacaadaaaabdcbdcadaaddacddcdccccccdddaabababababadccbdcbbabcacdcdbaadccbcbbadbddcbcacaaaacadddcddccbacccadcdbccaabdcdcbadaaabdadcbadabbbddccdadbcbbadacdaaabaddaacddddddcddccbcacbcbddcadcdacdcacbddddaccabbcbccdbbdaababcbdcdbddbccacaddcacccdaddacbaacacdadbcbcabbdcccdacbcabcbdccbbcdabababbccdbaacacaaaaadcddabbddbcbcaaadcbcdcacbaddbccbaaccbccbbaaddcddcccbbacaabaadcaabbaacababddcaddcadbcabddbdcacddbcddbcdbbdbadcbdddccbdcdbddbbdcdcdaacbcbaaabadbdccdbcdcacdbddbdbababadbdddbdaccaabacacbbaccadbcacddbbadcddadccbbccabdacdcbbbdbbaccdbcadadbcdaacccacbacdcabccccadbbcddddbadbaabcbbcaaccbbcccdaccddddcdcdadbabdddacabcacbbabdcacdadadcbaccdcacccdbdbcbcbadddcccbacaddabbccaddccadbcbadcbcbdabccacbdbaacdaadcacbbacadcbabcaccccccbdddabdbacbaabaaadcdbdabbddbbddcacbbadcabcacaccadabbabcacdcabcddbcadddabdbaaddbabbbbbcaabdbccdaaacbdbabcaaaacddabadcdacadddbccbbcdbaaadbdbcabcbbdaacdcacdbdccdbdaacbabdddbddbdcbccbdcddbdbbaacccbccdcdcadcbaabdbadbbaaacabcadbbcdacbcdcaaabdcadcbcabadbbcdbaccdabbcbcdcbcdbdcdbdcccadbdbcadcdbcbbbabdbcadaabacbbcccdabbcdabcbcbcccbcccacadccbbbbaccadadacadbcdbcbdbbbdcbdaccbcdacdacaacabccddddcaddacbacadbcddccbaacddbdcacbabbbdcaadadaadbcbccbbadcabacaaccbadcddddcdadadcddccbddbddcdaadcbbddddcddbdbadbbcddaddbbbdacbbddbdccbcbbaacacbdddadbbabdadabccbadddbdcbccadcbbaddddabcdccaabcbaabdbabccaadbadbadacaccdcdaacbbdacbdcabbbdbacdbacadbbbdabddccdcabdddbaacdadcaabccdabbdadabbaddabdaaccabbbaddbdcbdacbbbcabacdabacbbbbabadaabdcacddadddddbcddbaadcacbddbabcbbbbaabbbddaacbdabaddabdbdddbdbbbccbbacbbabcacdbaabbaabacbcdabbcdcbcabbddaacdadbdbbacbdabdacbaaddadcbadabddbaacbbbabdbadcacbdbdccbadddbbcaddbaabdcdccbabccccbaddcdbabadbbdcccbdbadbacbcabcbbdbcadacdcbdbbbcabacddccabcaaaddcbabcdbcccbdcaccaacdaaccccaabbbcbaacdaaccbaabbddbbbaccabbcdcccdbabacaabaaaddcacbdcdccabdcddccbbaabbdcabadadcbaadddcbbaadcabddbccbadcdcbcbddcdbdbddcabadddbaaccbdaacdbdddddbdbbbdddaacbabccdcdbdbbaccaadddddccbcddaabdddcbbacbadcdccacdbcaadabddbbaddabccdbdaaaccacacaabacdaaaabcdcdcbccaabcbddbcaaaddccadbcdabdcdbbadabbdabdcdcccccaacbdbdadaaabdddadccdbdcaadadbdbacbcccdddbcddcaccbbcdcbacddbddadcbdadbabdbbaabbdadcacdddabddbdaacbadbabaccdbbcadbabbaabbccacadbccdbbdaabbddbdacbcabcdaaaccbdbbdadbbacddccbddddccbadacbdbadabdbcdbcbadbcaabbbabbcdacaabdccbaaccacabaabdcdbdbcdaaccbbdbaacdbccbaabcbcaabbbddcdcadadcabcaaaacbcccbabdcdaddadbdbdddbdabbaaacbbadbccaadbdaaaacccbcccbcbcaadbdddabaacddcacbcabcccbabbaabbcdcddacbbcabbaaaabdbdbccadcabdbaabbdddaccbbaabbbaabadabcdbcdabbacdaadcbcccdbbcbabdcbbadcdcbacaabdddbcbaacabdabdadcdbccbdcabaccddcabdbadaabccbcbbaddcbddaddababcaacbcdbcacbaaabccadaccdbbbbbcdaadccbcdcadacabdaacccaadbdbbaacdbddbbccdddcbdbabcbacbabbdccccbdcadcdddbccbcbbcbcbcbcddcaddcbcacbcacabcbcacbcdaccacabaddddabcacbaadddadaadbcddbcadbbbabdcddbadbcbbccdbdddbabbaddbdcddcbccbcbcacbdabdccbddbcccdcbdccdbbdbdbacadddbabcbbcdcaacaccbccaaaabacaadcdadbbccabbccccdddaabbddbdccacdcbabcbadccdbbdadabdcadddacdaccbbdbadaccacdbdbaaabdacdbcacaaadcdbccadcbadabbbbadbccccbccdcbcdacdbacccdabddadabbaccbbbcaadabcacabcdbdddacbdbaacbacacacaccdcbadbdbdcddcabbdabdbadcbacacadacbcdcbdbddbddabbabcdbbbcddaaaddaabdbdccbdcddbbbdbbcaddbcbdcdaccdaabaddabdbcdcbcbbbccdacaadbcbacadbbddacdbcdadbddcacbbbdaadaccdabbdcbaccdddadacbcadcdcaadadadcccdcaccdcdaaaaabbdcaddabbdbcbaadcabbbbaadcabdacbcdabcddaabcccdbaabadbbddccbbdcaaaccdbccabcddcdbcbdbbdcadddcccabddbdbacbcbccbbdbaabddccbcacbdccaacbdccbbadcdcdacdacbabbcdaacabbbabbcdaacbaccdbcabaaddabbdaacddaaacabddacbadcbbcdcaddccacadcadadaacdcdddccdddccddacaaaccccddadddadbcacdccddbadadbbabbdaabbacdbcddacdbadbcaaacbaddccabbbadabaaccdcddcdccdcdabcbbabdbdbdcdaaaadcddcddcbbbcaacbddcacacbcbcaaaccddacaddcaaaaaaaaadcdbdbccbdddbcdacaddcccdbccdcbaaabaabbcddbbcaaccddaaaddaaccdbbcbcabbbaadbadadccbdbaabbdcaaaaabcdbcddabdccabadadabbbccacbccddccddbdabccccbbdbcaccdadabddcbccbdcbddabbacaacaaaabdcdcbddaacabdbccaabcdbcccbababdbdcacaacabcaddbabbaddaaabddbaddddbcdaacbccaabababaadadabaaccdaacaaaddaacbdddbbacbadacbcbcdaabccbabbbdbbbccdbaabccbdccbbbaccccadacacbadbcaadaabcdcbbcdadacbccaadabaaaaadbbccabaaabbbcdbabbccadacddadbacaacaaacaadacdbadddddccdbdccbacbbbccabbacabbcbbdbaadcdbcbccadccccbdadadcbadcdbcbacdaabaddadababdcbdcddbdbdabdddcccbbabadcabadcdadbbbdcaadbbadabcacdcbbdcdbdcaacbbddacdbbdcbdbdabbadbaddcbbcbaadcddaccccaaacdbbadccbadadaccbbcbdaacbbbbdbadabccadbbabaaabccadadabcacabccbaabddbadbaaadbadababddaadbcadcdbaccaccddaddcddaabdbabbbadacbdcdcdcaaaabbbccacbbabccbcddabccdbbddcbcccbdabcdabdaababddbccacbcabbadcbddcbcaccbcaacbbadcbddcdaaacbbbdaacbbaddcbdcaabbccabbbbcccbbbcacdccbaaadbabcdadadaaaacbdbdddadacccaaaacaaacddabdabdbddcccdcaadddadbbaaabdcaacaaccdbdbaddacdabbaadbabcabacdaaaadcbcabbaadcdcadadacdccdccacacdccddccdaabddcbacabbdbcdcdcabbbcacbdcdcddccacadcbbbdacbcacdbcbdbbcbbaabbcdbcdacdbadaabbdabccccacbadaabbacaccaabbaabccadbcbdbcbcaadcccbcbdabbcbaccccaabbdbcacbadbccddcdccdccddcccbcdcddbabddbcadbadaacccabdcdcbbddbabcacddabbdccdbbbccaabdcabcbdbacddaaacbbcbdbaddaaabddacdaadbbdcadcdadacadaacddddbdadbcdddbbdddaaacddbcdcadadddabaaabddbbadbabbacdadcdcbacbcccccbbdcbdcdadabaaadadbdacbcdbdccababbdcaacabadddbccacdaabcdabacbbcadbadcabbcacbabadbabbaadbcdbdabdbcacbcabcddadcadcbdacddcdcaadbccbcccadbddbaadacbcdaababbdbcdbddcbaabccbcbddbdbdbbbccbcaacddbbcbccabdabbbddadbaddaaaacacaccdbbbbdcccdcdadbadabdbcbacccbdacbddbbbacaacacadbbadbaacbbaaaaacdbadbddbddcdcdaccaacaccdddcdaddccdcabcbdcdabdaddbdbbbdcddaababdaacbccbbdddacdcbaacbccbdbadadddaadacaaaddcdbbdcdcccaddcddaaadcdcdccaadbcddcbdbcaabacdbddbbcbdddccbbdcbbbacdbaddcccacaaabddadbdbdccddddcdbdaabadbadbbbbdcabbbbcccdddcdbbbddcccbbbccbbdcaabdbcacaadaddbbddaabbccbbabcaaddcaaccbccbadbabbaddaacccbdabadcdadcbcccbadcbacbddcbaaccadccabaaccdbaacbbccdcadacbdccdaaaacaabcddcaaccdcbdacccccbacbaadacdddbbdaacaadaadbdbabbcdcdacddacddadcbaadcccddccddbddadddbcaadbbcdcdcabbaabcbddaadabbdcdccdcdcbddddcabbdbadadcbaccbbdbcccdabcbcbdbcacdcaaddbdbaabbbbbcdcddbadcbccbcddbdbadbcaabbdccabbadddbbaabbcdcbdaaaadcddddaaabcabbbabcbdacbdbddaaaccbabcdaadcbccacbcabaccacadcdcccdbaddabbdadbaaadcaaadabacacbbdbdadcadbabdaccadcbaccbbddaabdacbccbbcdcaddddacbdaadbddcdccbbcdccbbacbbbabaaddccacccaaaccaadcabddcabacdbaacbbbbbadabaacbdbbddaabcdbbaabacbcbacccacabdbbcdbbdbbaddbbabbddacdcdcccdabdacbdcbaadabaacbdabbcdaacaadbccccbddbadbcadadaddbdabacabbdcadbddacdbdbbdddbabaddbbdabccbccbccaddaaababcdcbbdbdacbabaacdbaacbacaaadcaaccaccccdbacdadccaadcdccadabbacddccbcbbbbbbbcdcabadcacacaccdacbacddaaacdbacaccbcbbddaacddcdbbaddccbabdacdccbbaadabccbaadcbccadabccbdbbdabadabdccaaacbabccdbccbcbacacbdadadcbccbbaddcaddcdcaaabdacacbbadcabadccdcbcaaababddddbaccdcbcbdacaccbcdcabbbaadabaaccdcacaabaabacaddcaaabcbadaccbdcdaaccdbacbbacaccdcbaccdbcbccbbdcdbbacaccadbcddbbdccbddbaddcabaaaddbcdabddbadadabcabdcddbccadadcdabacdacacdddddaddbcdcddcdbacbadacdaddbadcdcdadcbbbacccddbbcbdcbcaacaddabadcabdcbabdadcaddbaaacbcacddbbbcbcbbbbccbcbabbdcabdccaacbbdaddbabdaabcdbddccacbdcbadcbcbaacdbadddcadcdaabcbbdadadbbdcdbcadddaababdbbbcbcbbbacbcddbbbaabcddbaabbbcddbcdbccddccabbbaabdddbdaabcbbababccbaabdaadaabbdbaadaabbadaadccbcaddcdabddcbdddbbddbdaddbbaadadddabdabdaaadadbdabaabacabddccabadcdcacdcdabccdcadcdccdacabcddaabacddbccbcdadaccdbcabcaccdbbdcdbddddaccbbbddcdaaadccbbaddbdbaaabbbabbcacacdcdaacabbcadbcaaabaaababcddddaddddbacbcabddcadbbacbdbbdacbaacadccacabcccdcadbcbcaddaabaacbddccdaaaddddbdaacccbdabdadcdabaccccdbbdaccadcdccddaacdbdddadaacdabaacbcbcadbbabcbdcddbcdcadadddbdaadbbcaccaddaccaaacacabadadbdacbccadaacddbdadaccaadcdaddcdcbabddcabcddcbcaadbdcacbaddcbbbdaabdccdddacdbbabcdddcbaaadbdcddccddaacabbcbdbdccbbccacbcdcacbdcadacbddacacbdabccabbcabbcdadccddbabbacdaaaaaaaadcacdcdbbabadadcaadcbcadaaacdcbbcbdccdabbbdccdcdcdbcdbbdaabdbcdaabcabccaabbbcadacabaddcbcdcbccdbaabdcddcacddcaaacdbadabbadacaabbcbabaacbacdbcbdabdadccdcadbdbaddaacadcddbdcbaacbdabbaadddabdbbccaaaccdccbdbcddadbcccbcdabccbdadaaccdbdbcdabcdcbccacbcadccbbccadcbbdbcdddcabcdadbdbabbbcbcccdccbbccacbbbdcaabdccabccdcdaccacacdcacdbdcddbadbabbbaacaabdcdacdccbdccacbccbbcdaaacabcbcddbcccabcadaaccabbacbbdcacdabbadbabbdaacbbcbaddaadcdbadccaadaadcbcccaddcbddccdabdcdcddcdbcdaddbcbaccdacdadacbaabcdaadadacabadbddcdadabccdaddcdcdcdaadabacbbcbddccacdbaaaaccbccdccabcadbbdccddbddcbbbbbbacaadbbabacccacdddcaadccadcadadcdcaabbcdbdbcacacbadbaadaadadddddbaabddcabbdccbbdaabdcbbdaaddabacabccddbbccacbbcabaadcdbcbacaabdaaaadbbcbdddaabbdcdabbaddcbbdaacbaadbdaddccdbbbdaadbaabdaabcbacdbcdacaaaadadccbcbacabbadbcabcdbdbbddbdcdbbddbdcdbaacdaaddcadcacbbbbbcaadddccbbcbddbbaacbbaaccdbadadaabcbacccabbdcadbbadcbadccdadbcbabdcbcbaabbcbcadabaaadabddbabcdbbbbcbcbcbdbdacccadcbdcadddcbabccdadadbddaccbaabddacdcdcadcaddaacdcdaddbcbbccddcbcabcadaabbababcaabaccbacdcdbdabdabacbcdcdccdadbcdddaccbcbccbddcddcdbabbcaacbacaaabacaabadddddcddcccddabadccbadccdbabcdaacddadbbacaadcdbdcdcbbcdcabddcaadbcaacdcbaccababaccbbacacccbaacdbcbdddcdccccabddbdbcbcbaccccbacaaabdcadddbcddabdbabbbdbacadddabdaaacbdaaacbaaabbadaccadadddacbacbadbadbccccabdbabbbacdbabccadbacaaccbaaaacadcbabaccbcaadbccdcbdabdbcabadaddaacdbadbddaaccacaaabccbcbdacaddcbdbaddcbbbaddacccacbababbdacdaccdacdcdadadbbdcccdbacdcbbdacdbdbdaccccdcaabccbccabccbbaadaddaadbcddccacbcccbbddccbccddbbddbadcdbdcadaabbbacbbbdabcddbddbbbbdbcacdbcdabbcdcbbcaabdbcddaaabdbcdcbddabbbbccbccadaabdccbabcccbcdadbbaaaaddbdadcdabbddbaaccdbacbdccdddaacacdaabcccbbbbdbababaacabdbcccddbbcccbddacacbcddabcdacddbdcdddadbccdccacbdaddbccdbcbcbbdaacdcbbcbdacabcbabbcccbcddcbccdbbdadbcdbdbaccabccadaddcccadacbcddbdaabadcdbdcddcacbbcbaddacddcaccbbdcbddcddcaadbaddbbbabbbdadbcaadbbddbcccaccababddcbbbdbabccdcabaacadcaddcddaacdcadcddabaadbddabbddaabccadcdbdabbcccbcaacddaabdccbcaaadbcacadaccbcabbcbddadbcddaaacaddbbddadcccdddbaacdbbbbddbbcccbbcacbdbdaabacddbabadbbadbadcbbaaacadcadbadcdbdbddbbdbadbcbdacaaabbcdbbddababdccabdadddaadabcdacdbaabbcdcdccbacdabdbcbcdbcccbccdbbbbbbbcdbcdabbcbddacddaddacacaadaddbaaccaadddabbbbbaaadacabacdbcbccbdcaadbdaacccaabbcdcabcbaaabccabcdcdbdcbbbaadcaabcdbabdabddbcadcdcdcacdccccdbaabaabcaacddacbdabadbbaaabbaaacbbdbbcadbcdaacbdbcdcdcbdbcabccbbccdacacadadcddcabcdcbacbbdababababbabcabaacbaddbdcaccdbccdbabbddbdbcccdcbadabacdacdbdacadbdcadcdaababcacaaaacbcbbdbaadccabbccbbbddbccaadccbccacadcdbbbcbdcccdadcacacbadbcabaabcabcadaccdbaaaaaaccaddbdbcacbdaaaddccbbaddadbcabcacaccbadbbcabccbdacaaabdbbacddbbadddabaadccdabdbacbabbaddbdadccbaddabbdcddccbbccddcabcbabdbcabcaacdaacdbbbabbacdaadbadacbaccbcdbbcabccbabbbdcacccbbdaaaaddcbbacdacabccbdbadcaadcaaaaddcbbcaccbcbcdddaabadbdddddadadcacbbbcddbaacbaccbbbdcbaadbbdcbcaabccdbbdaccdbdacadbdddbccdaabbbddbacbddaacdcbabdaacaabcbbaddcdbbbadcbdcdcadcddaaddbbadccacaadccaadaabdababbcacaadcdaccabaadbabdadabbdddddcbccccbdbbacbbcbccdaccbabcadbccdaacbcbcbdaabcbbccdccbdccdddcdcdacddabdaadbddcbbbdcccccaccdcbbdadbdddbcdbddccabadbddccdabdcbbacaaaabacadabddccbabddddbbaabbccbccdcdaacdbcdcdbaacdbaabbdadaccaaccddbbbabadabdccaccdbbcdbcbdadcbdddbbbbccbcccdbcacbbaaaccdbaaaacbdcdacabaadbdaabcdcdabaacabaacbdacbadabbddcddcdacbdbaccdccdcdccacdccbdacdabdabadadcaabcdcbdcbabdbabbbbbcdccdacbaacdccaaabdacbccdcbcadcdcbaddcdbdcacccacdcdacdbcbbabdccbadcaaacdcdcbabacaddcadcdddacccbbbabdbabababbabdbdbdbbaacccaadcddbaddadcdaaabdacbccddbbcbdccbabdacbdcaaccddccbbbddabbcbacdabaddbaddbdaccabaaabbcdcbbdddadcdbdbbbcdabbcdbadbcaccbbdbadbdcadcbaaadabdcbccabaabccabdbadcacdddbccdddbdabcbcacdaccddcbbabdaccdadaaabaaaaababbdcccdbbdcccdbabcdcbabadaabaccbdcdacdcbcbcdbbddacdabacbbdbaddbaabcbcabccddcbbdacbbbdaabaaaaaabbaaaccacbcdcacaabbacaaacabdacacbdabcbcdabcdcacbcbccabaabbdcbddacdbcaaaccbdbbaabddcacbbccaabbbacbcbddddccbabaaccaaccabcbbbbbaabbacaadbdabbdcbbaacdadadccabbbbccddbbdcdbbbbdadabbcbaacabdaccdcbadabdcdaaabccadcabcbdcaacbcdbbaacddbaaaadddddaaccaddbababbbbcadadaaaaccadcbdabcbbbccadacdcaddbbcccbbbccdbcbdbbcccdcbaabccabccacdbdacccadcdccabdbcabcbdbdcacdadcbcbddbbaacbbadacaccccbacddacbddbbcdcaadcddacdcadccadbaccabdacabccacdbabaaaddaaacdbdccabcdccbbdccbddddacabaaddddddddbaccdcabbaccabbbabcddaabcabdbbadcaabcdddaddbdabbdddbaaaccbabddcadddbddbaccaddbdcdbbacaabcddcbabadbabdcbbdbbbacadddbabdbaccadcdaabaddabccdcddcdcbadadabccbaaccdbbbbacddcbcddbddccccaddababdcabdacdbcadadccbacdccbcadadccddcbddbdbacdcdbccadacdabcabbaddddcbbbdddacdacbddcccdbdccadbbbccdbdddbdcadccbaccabcbbdbbcabcacadabadbbcdaddcacaabddaaabdbcdcdaaadaaaddadccdabbcbdcdadbcdacbbbdaaddbdccdbcaacdbdccccbadcdcadcaaddabaadddcdbacddaadabcaddbcbacaaccdacacccaababcbdacbaacadbdaccacadaddcacccbccaadccddadcdddaabbaaccababaaabbcdbbaadacaddcdaadbdddababcccbbabbabdcadcabacaadcddbdbccdbcccbacccddabadbbdaaacbdbbbccadbaaddbacdadbbbadcaaacccadbbcbbcdbadbbddcaaadcdbcaddabadcdbbddcdcacadcaddcaddbdddbddcbaaaacbbbcaadabdaabbbaccabbdcbdccaabbaaddbabbcbcbcbddacdbdcacaadbacbcabacdaddbcacaacdccccaaabacaadccdddccbadacaaaaccbadadabbcaadaccddccacbbacbabbccbdaabdcbcddcadcaabbcdddccdcaadcacaddbdbadccdcbddcbdbcbbbabdcbaaccbdabababcbbdbbbccbaddaacccadcdcbdacaadbaaccacdddaaacaadccacaaaddcdadaccaabdddcdbdcaabcbaadabddbcbcdadbccdbaabbbbadacddcadccadaddbcccabaacadabdbccbddcbacbcbcaacbacbbbdcdbccacbdcbabaaddbabbdddddddaaddddacaccbbccdccdcdadaadaacadddabcdcdbddccacbbdbddcdbcbdbbccbcccbcbdaddabbbdcbcbddbdbdccbcbcadcadaaabdcbccbdaaabbbadbdcdadcbbdadaccdaccccbbabddbbddcaddddcdddacabacbacbdbdbbccaaddaacbcdbabbddbaddbadbcccdaaacdcbbdcabdcbacdddbbddbabbdbbcccbbdabbdbddbbbabccbcdbdaddccddbddbbbdbcbcacdacccdcbbcddbabacaddccddbdaccadbcacdaacabdacacbacbbcabadcacbaccaadaadabdccbcadacdcadcbabdbabdabdaaadcaccdbcacdcaaaaaddbaaabbddbdaadcbcababdbbacababacddcabbccabaaadacdddccdacbcdabcbbadcbbaadbcbbddbacadbabcdadccabdcbbbbccadaacdabbacbadbbdddbdbcbbbaaabcdacabccabbbccabbcaccadacbdaddbabcbadcadadcdbbbddabdaccbadaccbdbabbddccdddcabacdcbabddacdbbcaabdaaacaddbaaadbbcdbcaacbccaaadacddbcaccadadaababaacdcdabacadccabcbccadaadcdacdcbdaaadbbbacdbbbabcddbabcabbbaabccbdadacbbdcacdcddababddcabddbadccbbadbcdcbaabddababcaaacbcabbddcccacaddccdbddaadbbcccbbabdbbbbdbdcabcbabbadaddccdcadddccbbccdcccabaadbddcbddcdbddadbadbbbaddabbddbcdcadddacabaaabbcaaacccaabaccdcccacddcccdcdbabdabaaccaddddbccdbabcbcbddbcbbbadbcdacdadccccabbcdccbbbdbdcdababaadbbcabdddaabbdbcdaadaccbbcabcaddcdccddbbbbdccccccbdbbcdcacbcddbcbcbbdbbacbbacaacddacdbccbaacabbbadccadccdcabbacbbdcdcacccadbcbaabddaccbbabbbccdaacbdaadddbbdcbbdacdadabacacababcddcaabbabbdbddddadbcbdadbbcbacbcacccdcccccabbbaccacbbcbbbddcbccdaaadcdadcacddbbaccdddcacddabaacdccdabadbdbbabdbbdbbdbdcbdaddcbaddddaadaddadaabcadabccdcacccdcdcbacdadbcbacbcbbccbcbcbddadddbaadbbbdbacbbbdbabbbdcdaadaccaaabdbdcdadadabbcabdacbcbdbaddacdaccdccaccbbddcbabcccaabadcbdaadcbaaabccbacbccdcaddabacbbbdbcccbddbbddadccbbdbdbacdcabddcaaadcbdadbbdbacbabcddbbcaacaadbcdaabaccdcddddbdbbdccdcbddcbbccadaddcbdabccbcddaddcdabbddddbbaadcbcacacaaaccababcbdbacdadbadbadadbbdcbcdcdbdaadabdacbbacddabdbbaabcacbdadacdaacbcaacdabdacbabddcbaaaacccbdabadaacccdaaabddbddbdadbddbdbbcdaabcbabccbbddccdacbbdbadadbbddddcccddacbaabbdbbcdbccbbbbbbcbbaaddcdbaddbbaaaabadcadacdadbbdcaabcdabcabbbacbddacddadadadacdaacadaccdddbcbdabacadbbbadacadadadaaaabcddcbcadbccbddaddaaacddbacacccacbddbdcdcdacaccdadccaccabbaadbacddcddbbdadddbbbaadcdbbaddcdbcbbaaabcbbcbbabaacadcdcabdcababbaacccbabbadbbaccddbaaaaabdacacddbacaccacacadaccdbccdbbcbcccdcccdadcddbabcbcdcacddaaadddcaaaababcaddaccbccacaacbcaddbddadcabcbdabdaabbcdadcccdcdbbbdadcdbaadaadaccccdbdabcbcbcbabdaabddacadaccddbadbaddbabdbcccbacccabcccaadbbccaaadcbabbbaccadcaccbcbdcdaabbaccbbbaaabbddaccbcabbcaccaadabacdccaddbbabdaccbccdaadbcdcbccbaaddaabccaccdbababdbbacbdcbcdadcccbccbacdacbacbbdbcaaddbacadcdccaacdadddbcaaddbccacacbbcdccbbbbdaaaaccccbdccdbcabcdccccacdacaacaadddcbddcabdbcadbbdbdcadbcbdaacacccbaacaabaadadbdcacdacaddbbdbdcbcbaddcdcaabadaabbdadabacdccadbbbadcbdaaacbddcbcaacbcccdbcdddcbaddbdccaadaabcdddbaabbadcbcdcbcdbdbbbcbbbcbadabbcdcdccacabbaccdbacddcdddcadcdaabddcdbbdcccbabdddcacadbaacaccddbccccdadbdbccdddcbbdbcbbbddcdabaabcadababbdccabcdbcdddadbbcaccdcabbcaccdbcbcdbadddcddcbbdbbddbcbcacacaabccdcccdcbaccbaadacbdcaccdadaddcdabaadadbadcbabadbdbbaacbbccadbadacbcdacadadccccabbbcaaaaaaaabddadaabbbdbbdcdcbdcdaaacacbacabdcdadaddcdadabbdbdbcccddcaaadbbbcaddcdbbaacadbabdbcbbbbacaaccdccbadacdcdcccbdadbbccbddcabaadcaadbacaaaabbcaaabddaddcddbbcbabbaacbbcdbbccbccbadcddccaabcdaaaccbbcdbdadcbadbccbdcccaacadabccddbbdacadaadbacdadbaadacaabdcaccbddbcbacccccadddaaaaaacbcdaddbbaccadbcbabcabcbadbacadbcdcdbdaccbaadaabdaacadddcdbbddbccdcbccdccdababdabbbddabcaabadabcdbaaadacdabcdbacddcddaadcdbdcdddbdabddbdacdcabdbcbcbdbaddbadabdcacacbddcddbbddcacdabcdcaacaabaabbddbcbabdadbbbcbdcccbdadddcdbbaacccbbadcbcaaddadbddccabaacaddbdadadadacdbcddabaabdccdbdddababdcbabddccbdbcabacaadbdbbbcaacaaaccaabadcabacdcaadcdbcbdaaddbbacacabcaacbbcbbaaaaadabbcabcddbabdaddacaadadcdcdadbdadddbbdcdbbaabdbaddbddbdddccbcbdcbdcaadaddbabbdcaaddbdcadaccbcbadbadddbabddadcbdabbbcadcdbbdddabacdaabacacdaaacdadcccdcdbadccaadddcabbcbcbcdbcbdcacdacbcbdbacdaccddcdbaacdcabbbcbccbbabdacabdddcabddacbcdcbaaacbbcdbaaccaddcacacbcdcccdbaacdbcaddcbcbddddabcbdcdccdbcbdbacccbbabbdcdabacbcdcabdcbabcaabdbcdaadabcabdabdcabadddaadcbbacdbbaacddbcbdccdddbccbdcacaadbbcbbcdadbdabbbbcbdbcabdbdacdadcbabbbaaaccadabcdbcaadbbadcbdcacaaaabbacabddaabdbbcbdacdaccdccddcbacccbbdbcdadabadbaccaaccdbcacdadcbcdcadacaaaaddddaacdbacaaddbcaaacacacdccbaaaaacbdcadbabcbddbdbcbaaccbdcbccdcaaaccdcaaadabbbaacdbdacdcbcadacddbbbbabbacadbdbdcbbabaddddcdbacdaaacacaddcadcbdcbcbabcacabdbddbdadddcabddacacdabbddaddaddacadabaddadcdadccbdacdabdaaabddcbacbcbdaaaacbcbbbbadcabaabccbbabcaccbcbacbbdbbabbbdcadcaababcacabbaadcabbadcabbdcdbdaaabbdcddddbcaddbbbdbdcaddcdbcdbabbabbabbbaadacaaaccacbbcdcabaccabbddddadbaccdcabadbcddaddbdcbddbddbdcccdbdcbbacdabccbdbdccdbadcbadaabadcbcdadaacdcaaacaadbdacacdcbcadacbaccbbaabdabdbbbbabcdbbdbcbacbdcdadbccadcdbcdbcaacdcdcbacdbdccaccbadccadbbbddacadcbdadcdcaadbcacdacadbcccaaaacbdbacbabcacaaabcdaddacbacbabbadaacddaadcacadccabadadaabdaaccdbdccdccaaacaaaabadbdbdbababbadabcaadaabcaddbdabcbcddaabbcdbabdbbacacbaccbbadaccbbdcdaacdddacadacdbabaccbbbccbcaaababbdbccabdbbaddcdbccddbbdcadadccdcbadadbbadcdcbbadccdaaccdbbbbbdcaabaaabdccccbaaddcccadddbdaaddababdcacccccbbcbabdbaaccabadccccccccbbbacaaabadaccbdbccabbdaddbcdaddaacaccabdddcddcabdbcabcabcccccdabddbdadcbcbdbbdbcabcdcdbdadcbdabccbdadddbbdbcbbbccbacbdbbbbbabdcadaadbbcccccbaacdabddbcbabddcbbdbbaabdbbddabcbbabbacbdaadadacaccabdaddaadbddadbaccacbbbddabaabdbbcadabadcaadbdacbccbbcbdadcddbaddbaadbcaabdbacaadbcbbddbcbcbbbbadddbbcddbadcbcbddbcaccbccdbdbacdcbcccddcdcacbdadadbbdbdacccdacdbabddadccadbadbbbacbbccbdacddabcdccadbccaaabddabadbacccacbcaababaccbcdaababacdadabddcbddbaddaccddababcabdcbbdbbbdcbcbaabccacdbaaacccbddaacdadcaabcdaabacccaadcbddcaccdcadbadacbcaabccbdcaaabcbcbdadadadaabccdaaaadadcabdaccbbadbddbdcddccdbdcdbcaadbacbacaabadacdbabcdcacbddccdbaabddddbdddaddddbadcadcababacbbdadbdadcdbbbabbcaadbcadaabdcbcdcaaadaaaccacaddcddcddadcdadbdacadaaabcbaddadbacdacddbdcddcbaacabccabcacddabcbcacaacbcdacacbacbacacbbabdbadaadcdbaabaccaaabddaadcdbddbaababcccdaacacabcaacacaacaaabcaacdabcaccacdcabccacdaccbcacbbdccacbaacacccabcddbabdcbdddbabdabcdcdccbcbdcdcdadbabcddbdccaacccaccbdbdabccbabadabbccacdaccbcaccbdddcaadcbbdbaadccdbbdabbccbbdcbdccbcaaccacbbaabddcdbdcdccdcdadabacaccdbddadbcbbddbaaacddcbadaccadaddabdbdbbbaabaabcbaacdccccdbaaddbadacdabbabcadabddbacacdcaacbaddcaddcdbadcbbcbdddadacccbacacddbcbabbdbdbabbaaddcbdadcaabcbbbaddbdddadacdbcdcbddccddcaccbdbcabdcadabacdddbacccddddacbdacdacbdaabacabccdcabaabcabdbadbcaddcddcbadcacccacddccabacbbdadccbccbacbaabddcadbccbcdccdddddcddcaaadbddbbbbcaabbabadbacdabdcdbcccdbdbdacccacdbabbbbabddabaaaabdbbabcbabccaabdaadcbbbbdccbaddacbabadccbcaaabdcbddcadbabaaddddbaddabcbadbacbaddabbcbabbcbcbacddcbacbbdccddccabacabdaaabadabaadccbddabbbaacacbaddbbbddabbcaabaddddaaadbaabdcbcaaaacbbddaabccbcadaadbdbacbcddbccddbacdbbdbbdaabcbbcdcadbacbaababcbbdadbbabcbccacbdccdbcbdcdddcaaddacacddcdbbcbdbbcbdadababcaddcabdadccabaaabadbdbddaaacaccbaadbbdcaaaabbaadaccdbccacbbbdadbccadddbaaabbacdbcacbdbbcbccabbabccddadaaddcdcacddcdccaaabdbdacbcaadaabddcadbaaaabbaadaddaddccbcccbcbcdabdabbaddddbdcdddbbacbdabbddadbbbbdaabaccbadcbbbbacabaaaadbbbbddbadbddaabbdabbcccdcadccbbbdcdbdcccaabcaaabccbaaddbaaaabacbcdbddabacdabbbbaccbbdbbbbdddcaaabbdadbaccbbdcdabccddbdbdbcddadabaddbcbcbdacaabacccbbabbdabbbabbccadcbbdddacccbdcddbcbdcadcccababddbcadddaabdcddaccdcdbdabcbbbcaaaaccbacdccdbacdcbbdbcdbbcacccbccddbdccaacbdcdaaadadabbccabcbbdbbbccbdcbbdbdaabcdbababcbccbcaccaaccbdadbdbbcbbcbcddbdbbcdaaaabccaadabbadddbbbabdbccaadbcdbbbdacdabbcddcabbdccadcdbbcddbabdcbbdcbabddadbcbccbbbccacacabddbbacbbbbdbdacaacddddcdcbbdadabdabdabaddbcbbbbdbbcbccbbcdbbbaabbbbcccdaccddccaccabdabdddbaabbdadbabdcccbdbdcadaaccbdcbbadbdaccddcccccadacabaadcbcabbdbababcdbaddcdacabadaadccaabdacccacdaabbbacdbdbbabcdabdccddaccbcaddbbbbaaaacccadbaaadaacbdadccaaccdcddbbdbbbadaaabbbabaccbacaaabcbcdcbaccaabccbcabbddcdacaabaddbccaaabaacdddbaabadbcdaaaadadaadcdbccbddcdbbacdcaabbddbccabadaddbcbaabdaddacdaabdccbddcdbdcbdbddcdbdacabcaacadcddbbcbbaddcabaddbcdadcbaccbbaabadbbbbbbddacabccdccccbbdbdabddccbbdbbcaccbcabccdcddbabbbcdcabbaddbbdcbbaaadacadacbddacbcdccbcdbdbabadbdacacbacacaabcdadbbadddbababcaaaddadaaadadcabbcaabcbcdbdcaadaaadababdadddcaddcddaaadcdacdbdccdcbabcdacdcacaabbacbdcdadaccaadbdcbbbbbadacdacdbaacdcbcadccadacaaadcadbdaddddcdbcdbcdcccaacbddabaddcccccbccbdbdbdcdbadbdbcbcdbcdcbdbdbbdabdcacddbdaccbcadcbccccdaadbddbacdbbbbcaccbbdacdbddcbabacaaacdbbadcbbdacabcdaabdacdbddbbccaaaccaaacbbbddacccbdddbdcaddddabaabddabbbacdcbcdadaaadabcbabdbcdcdacadaabbccdddcdaadbadabbbaccabbbbdcadbcdaacdabaaaddbadbcdacddaddbdcdddaaccaaabdbaaabacbadaacddbcbdbdddabaabcbbccbcbccddabccccacaadcacababbaadbcdccaddabcadbcacbabadddddadbadaadacccabbaacddbaaabcbcccacbaadbbaacbdddcdbacabbbccbbddabcbdcdcaaccbbcddddbccccdbbadccddbbccbacdabccaadbcdaaaacbdaadbaccddddabccbddbcddbcaadcbaddcbadaddddccbcddbacccdccacccdcbdddbdabccbbbbadccaaabcdddcdcbccaadddcbbccabcadbbcbcbdcadbdabdabaadcbcababddbcddbcbbaadccbbacdbabbbbcacacdcaacbbadbdabcadcadcdbaabadccdddddadbddcabccbbaabcdcabbcdaabdabdcdbbabcdadaabbdbbaabcbbbdcbbcdbcdbacbccabdbbccbaaacacbcabdadbccabdaabaaadabacbaddbbddcaabccaaaaccaaabdbcccbddbdcabbbcbcdaccbdbbcadacddcbdcbdabcbcdcccadbcddcadddcbdcdddbababaadbcddccddbbcbcaccbcdbbcacdcbbacbabaadccbbcbbadababdbdabaccdbcbcbddbabadbdcaccdbcbadabcdaabcdabdabaacabcdddbdcacccdccbcdacdddbbdcddabbccdcccaccdccaacaacdababddbdaaaacdbadbaddcadcbaabcdcadcdbbbdccbcadcadacdadddcacbaccbcdaadaacdbdaadddabbbcccdadbdadccdbaaadadbcdddccdadbbacaddddbccbcdcababcccabadbadcdcaaabcaccdacabbdcacbdaaacdbdcbcdadacdcbabbbbaaabaccbbdbbcbbbadcaddadaababadddaabaabcabbabdcadabdcabccdbddcacbbccaaccbbcadcdccddccaaaadddcabdccbacdaadddbccddbcccccddbbcaacdbbaadccaacdcaaabddacadbbcbaccabaddadbdddaaccadabbbcdcbcacadcbacdadcaaabdacdbdbaccbbaddabbabaaccacdbbadaccbbdadbbdcddbcabbaaaabccdbcacbbbbbbdbdbcbadbddcdbaaddcabbbacabdbaabaaddadcadddcddabaacaaabdbbdadbcccaadaadadabcaacbbabacdcdddbbacccbdbaacadbbcbcccacaaadbddbbdaccbacacaadcbcdbbcdaaababbdbadaacaddcccdaccbacadcdaadaabdaccdcadbbdabcccbcddddccbaacbacaadadbdcddadcbacdcdbadabaddddabaccaddcbadacbccbbddcabccbcaccdbdcbccbccbbbbddaccaadabbbcdaacddcabdacccddcacdcaaadabcadaaabddaacdbcdddabcbabcacddaabbdaaaacbdcdddaabdcadddbdaddcccbadddababddabdaacdcddcddcdaacdbdbabcabddadababdadacbdacddcdadcabcdbdadbdaabbcacbbabbacadbbdcaddaddaadbadbcadaddbcabcbadbcbaddcaddbcaaaabdacbbbdadddabaccbcbbcaaabbdadbbaaddbbdcbabbbbcbcaadacddabccadcdcddacbbddacbadbcbcbdabdaaddadabdbaaacbbdcbbaddbdabcdbabcdcdccdcccddcacdaaadabdddccabadaacdbbcaabcdaccacccabadadbddbaccddbadbbbbdcacbdadddcacdcdbbdacbbdcbaccbcdddbbcabccdcdcccbbbbbbdaacccaabcddbdbbdcacbdbddcdaaacbcccaaabcdabddaacbbacccbddddcdacabadbbaadcddabbdcddcbadcacbcaccbbcabdcacdabadaccabddbacaacacaaabcbcddadccbbcbbdbadbcaaddbdbbbdbdacbbaabcacbdbaccaccddddcccbaaabddcdbbabacaadbbadbbccdacdccbcbaccbdaacdabcadaddacdcdacdbacaccbdabbcccaabbcddcadbdbbdddbdbbaaddaabcbcdaadbddbdbcdbdbdadddabbabacbccbccbcaaadcbdcddaccbadbbaaaaadcbcacddccdddbcaacaadcbcbadcdacdbbbccdbbdacbababbbbdbdddbdadbbbbacaacbabcbbcbdbdacbcbddcacabdaaaaddbadadddaccdbbdbcbacacdbbccdddbbcddbdcdbcabcbcdccbbdcbbbcbabcbbcbddacdddbdabadacbabddcdadacdcdaaaacdcccccadbdddbcdddcdccdbaaacbbbdcdbcbdbaabdcbbbadaadcadccdcdcdbbdaaddcdcbacbbbddccdcacbdacdadccddadacaaaddcbbbcdaadbcaccbcaccdcbbcbaabdbaccaddabbaddbbbdbdacbbbbdddabdbcaacbdacdababaddcbadacdcbddcbbbdddcacaadbbdcbbdcbdaabdcbaaabbdcbcbcdcbaabbaacabcdcbcbdbaadbbadcbcccbdabcbaaadbcdabacbbbbdcdaacddbddabadaddccaaadacccdbdabbdabadacadcacaabcbbdbdccdbddcddacdabcbbacaabcdaccadaaddcdcbddbcabdaacabaacbdabbcbccbabcaadcdbaaadbbccbcdbdabbadccbbbcadacbabaabbbcdbaadadadacbcadccabdccdcccabdbbbcddccdaaddcaaaadacabdbdbdbadbbcacdcacddccaabdbdbddbcdccabccadaacdcbcdadccbcbddacddbbcbcccaaadaabdcbabdccdcadccdccdaccdbddcbcddcdabdddcbbbbaddabbabadbbbbcbaacdbbbcbabcdbbbbcccdbcdddddbbcacbcabaccdbaccababddbdddcadbdadacdacabbabcdaddddbcbcccccdcacabadaaabcbbdabdcbdabbcbcbbdacdbabdbdacbbcaabadabccbacdcdccdabddaccbaaaaddddbcdadcccbcdcddadaaccdabaccdbdbcdaccbaacbabcbbccdadbbbccccaacccddadddbbaabdccaaccdcbbbcaccccbdababdcdddccbcbdbdbbbbdbdbaabcdabddaaaabddbbacdcacdcbacbcaadbcdbcbbcdbccadabbcaaacdabcccbacbbcbccbaabcbcddcdccbabcdcdddbcdadaadbcbacaddbbbabacadbdaabcbbbdabaddcaccddddacabccbdccdcbacabccddabadabdbabbcdcccbdddbabdcaddbacddabaccbaabdbcbdbbbbdddaaaaadbcbdbcbddabacbadbcacbabcdadacccacdbbadcababccdaadbaaadcbccbbaacbbcbbadcddddbaaaadadccbabaddcdcbbdbabdccabbabbcbacaccdabcabcadabaabbacbbdaaaabbaccdaaadaadcaacabbdacaccbcabdaadaddbbcddabbbbbbaabcbbcdacacacaaddacccdbadddddccbacccdbdbbcccddabcdcbdbaabdccbdadaacdaddadadabbdcbacbbaacdbbcaaabcbdaccbdbdbcbadadaddccbabbbabacbcbcadbadaacccbadcaacdabaadbccdacddbcbaccbdcbbaacaaacdbcccbccbdabcccdbabdccddbdbaababdabbdbaaabacadacbcadabdaadcbbaadcdbbcdbdcddddaadcccbcbddbbacddcdcababadccccbcadcbbbabdddcdacdbcaadcdacabcbaaabdbddcbdccbbcaabbbdbadadadccddaadabdbcabbdbbdaacbabbcbdcbbacdaccadbacbdccdccbdddbabbdbddcaabacdbdccdccaaaddcbcdbaaacccddccdcadcdbbdbdbddabbaadcbbcbbbacccadabdabccaabaaaccdccacbaaccdbbbcbbdcdcaccdbdadababccabbaabdbdabccbcdcbdbdddadcabaacbabcbbcbadcbcbacdbdabcaaadbddbbbbaadababbaddbddabdaabdaadddbabddbdaddbdacaacbbbccccbcdacdccbbccddcbcaacacdadcdbaadbaaddaaddacbabdadadcccbbababddcaddcdccccdcacccbdcccadbcdccbbdbdaadcbdddddaacaaabcdcdcaccdddcbadbdacdcdcbdcdaccbcbdbcbbddcdadcbbbadbbabcbaddcdadbdaccccadbcbbbdbdbdddbcaacabaaabddcabbcbcacbadccbbdaadaaaabdabbdadbdcdcaadbcbacddbabbccbaadbdbcaaacdbadddadbaacacadcbbbcaccbabdcaabccdccccddcdabdcdaaacddbbacdbddbdbcacddacacbdbddccdcbddacacdcadbccbadccadacbcbaccacdcaadcdddacbaccddddadbdbbdbaccbabccaddccadbabdadbaabcbdaabdbdbdcaacdbbccbbcbacaaabcccdbccdcbcabccccddcdcacadbcbddbbbabcababdbdacbdcaacabcdaaabdcbbaabdbaadacbcbcbababbbdaccacaabbabbbacabacadacddddabcbbaddbcbbccabbdcbdabcdaadbbcaabcaccabbaacbdcdcbacddabacdbbccddddadbbadaadcdddcbbbaccddbaabacaddacaccdddaabbcccbcdcdaaddaaccdbcababdadcbaadcbddccbacddddbdaddabdbdbaaaacbdbdbabdbadaaaaddbbccddbcdacacdcacddcdccbddcadaacbabbbaadadabbdacabbbdbaaabbacbddccddaaaccabdbabcaadbaacdabcaddacdaabcaabbbdcabbbccbcddddaccaddacacdacabadadcbacaacacabdccbbbdbdcbcbccbadcdcbdccdabbadbcacdadbabccabaabaddcaacdccccabadacbaccccbacdcbddaacbddadacdcdcccaaabbcccadaaccadbdcacdbabdbcdbbaaadacbcabdccabcccacddbabbbadccddaaadacaacbcbddbbdcdbacbcabbdaabdacddccddacadbbdbaacaaacaabacdbababbccbdcccdacaadbbcbaaccbdccaabddddccdadbdcacdbaddcdbaacabbcbcbbadbbccadbdbcdbcbadbbaccacacdbdaadacdbdbcdaddcbaaddcdccbbbcabaadcddcbccdaabbdbdadcacabbadaccbacaacaaddaabcdbadcbdaaadcadbbdbdbbbbccbbbbdacbdbbbcaaaabdccbabcabbabdcaacbaacadcaadccbcacacbacbadbddaabcaacbddddadcdaccdbdadcabbcbccbbaddbabdcaadccdccdadbabacdadbbdabbbcdadaadcbcdbcddadaccbadddcbcabcdcbddaddccdccaccdbdbcbabbcccbcaabcadcbbaacdcdbbabbcaaabbddaccddccbacddcccbdaadcccbcacbccdacadcbcbaaadddcdcbdbddccdadbbdabbbcdacadbcdcbaddcaababbaccaadbdbbbdbaddabcacbdddddabdcadaacddadbacdddbaabaccbabcbbdcddaadcababdacacdbaabdacaddddccacbacbbcddcabbcddbcdbdcadacbaacdcadaccaaaacacacccbadbcccbdcaaacdcacabdcdbdbadddacbabaaddaaabbdcbcbbdcdaccbbccacbabadcddbddcacaacbcbbdddabbaadaccdbbbacabcadadaddbddadadabccddabbbccdbbaadbbdbcaadcadadaccbbcadbbacdbacbdcbcabbcbdbbdbbadcdbcbababcacbdbadaddaacaddcabbcaadababdbccdccbddccdababaaacacacddaaacabccdbdacdbccdabdadcbabbadcbdbcbabbcccbadcbbabbbbaccdbcacaababbacaddcaadbbaadabcbdcacabbddbbcccddbbcadadcbddddccbbbcbdbbdacbaddcadcdbdcaaabccbdccdddbaabacccdabaaaddaaccbbdbcdaabcaaacddbbdacaccacaaddbdbaadbbdaaccbdabcbcacbddcdacdaabbdcddbbaacbcabccbdbcdadddacdcdbcbacccdabaddddacdcaccdcaddcaaacaabaacbccdbbcacadbacdcabdbccbbdcccacadbdcaacadbcbbcbdbcbaacadddbaccaddbadabaaaadbddbdadbcdaaacccbdbcbccdbbcabcaaaddbaaddcdcbacdabaabbdbaabaaccddcaacabadacdabaacdabbdddaabcbcdbadbdaaacbccccaadcbddabdadacaccdbabcdaaddddccadadbabbbdadbcbabbdacaadaadaabbbbacacabcdaddacbcaddccdcbdcdacdddcdcdacadddaabdcabcddbadcddcbbcdbcbaadbadddccdccbbdabcabdadcadbadadbbadcdcdabdddcadbcdacbdccdbcdcaabcdadddaabdbbdcdabbbbbbaadabdbabadddabaabcbabbcabbcbdacbcbbddbddaadbbaacbdcbddddcadcbcaadcccaabadaaadccdcbcdaccbcbdcbdccdcdadbaabacabdaaccdbcacdbbbdadcabaccacdaaaccbdaccacaabadbbbacdccdddbababaacdadacddbbbdbbccbbadadcbddadaccdadaccdaccbccddbcbdbdcdbbbbcacbcdbadaadcaccdaabcdcdbbabababcabdddcbbdcdaadbbbdbddcddabdbcacbdbdbcabacadcbccbdbbbdbccbcbadababcdcbbcdcbcdcaadddcddccdaacadcbbdaaabbabccadbacadaaacbbdccadaabdddcbcaccbcdcdcbabcccddcaccdcbdbcbccdaaadbadadbbdaabcdbbacbcdbabacabcbcdccddddcbdbdcadaaadcddccdccdabdbaabacdcdbbddbbcbdcdaddcccdaddacccdbdbddddccbdccaddbabdbbadadaddbdbdbccbaaacdbdcddbabcaadbcddbdcdabdacdcbdcbdcabdcbcdbacbcadbccdbddadbcdbdbdbbdaddbcaabcadabaccaaaacbdbddaddddbcaabdbaaddddbcaabaabbdacdccdacdbacdbaadabbbbdaaabdbcbcabbdbbcabcdaccdadbacddcacacbabbacaccdacdacbabadadabcbadacaaaccdcdcabcddaaabdbaddcdddbbbccaacddacaacbcaabdbbbbbdabbabcacbdbbcbccbdcaabaccdbbabddbdcccbccbbacbaaabbbddaabbdacdbbbaaacbdabaaddbbddddcdcccbaadabbbcbaacadccadaabccbcacdaadbaaaccadbbacddcaaccccadbcddccabcaddddbdcccdaaaabdababaaadabbbabbbbabdadbcacdbdccbbbbbabcddddbbbdabccbdcaaccadcaabccdabdaabaadaaabdaacbcadddbbaaaacaaabdabacaadaaacbdaacbdacadbccacbbcdbcbdabbcbbdbadcaaaabbdbdadbcadbbcddbbcddaccdadccdaacbbbdbbcacaaacbccdccadbddbdbbdabdcbacbcbbcadcdbaaabddcbcccabdbcddaccadcadcadbddabdbdcccdaccbddaabbaaaaaaaadabbbdbbaccacabdcbddbdadabdcdadcaacacbbaadcadaaaddcbbdacaccdaacdcddcccbacababbcaccbbcdadbcbbbbacbaaababbcdcbacacadabcdcddabacdccbacbabcdcbbcbbbbbbacacaabbacdddbccacabbddbdcddbdcbaaabadadcccbdcaadcbdbbcbbcbccbcbcdddaddddcdcbbbaadbbabbdccbdccddbdbaddbcabdbcdccaaaccabaddcdaaccdacacabaccbaaacdacccdacbabaadacbdcdbacbaaaadcadddadbbddbccdbddbcdbbacdcbaaadbdcabcacabbbcdacabcdbccaadadcaccabddcbcabacdcbadadcabdbcbcddccdabcbdacacabccbdcdcbadccbaccbcbddbdadbdcbccaccbbdbacbcccabababbaddaacddaaaabbcccbddcdccbdbcbdbaabcaaacdbddcccaddaccdadcbddaabdcdacccbccdacabbcddaddadacccbddbdbcaccabcdcdbddcbbcadbdaabbdacaddbccbbcabbbdddcacadbcbdccdbcacbcbcdacbbbcccbbbcabddbaaccbdbcbaccddbdbcaabdcbacdacadabbdaaccabaadccbdadbbabaccbaacadbbbcbbdcdbbdacdddaacaacdcaaabacbdcacdaaddcdcbcbbcbcdbdbbdcbdadcbbddabdcddcacaddadaccbaaacacdaabaccbadbadbdbdabbacbcbbddacdadcadcdccddbddadaccbbcbabbdbabbccadcacaaccadbcababcdcdcbcadcbbbccbaacdaabacacbaddcbdbaacbadbdbddaadddabcbbabaaccdddbcdccdadaddaddccbabaabbabaacbbbdcaacbdbbacacddaacbdadabdbbacccaabdaaaadacddbabccbdabbcabddcdaccaabbcaabaccbcccbdbbbbcadcbcdcbadacdaabdabacdbbaabaccadccddbaaddadbacbddadcadcaaccaababadadaacccbacbcaabadabdabdbccaaaaabccabdabdcbdbabaacaadaaaccddbcacdbdcabcbccbdcdbdaddaaaabbaaaadddaabddcdabaabaaddbacbcddadcadbbabdbaadadbcccdababcdbabbbdbbbbaaabbaadcaccbacddbaacadbbdacadbadccdaccddacdacddaaadacaacbaabbccadbaacdaccaccdccbabdbdabbbaaaabbccdadbdbbaccddccabadbcbabdbabccdabaccddaaadadbddccbcacccaccbaadabdcbadbbcbdaabadcbabcabbcbbcbdcbdbddbaacccadadbcbdacbcaabcadabdcccbacdaacaddbbdddbcbabcabbdbbbcbddcdacababdbcddaacdbddbaddaacdcbacbbaddbcddcbbbddcddbdbbdaaccaddbbbaaccacbdbdbdabcabadaaddbabbdadaacaaacabbdaacdabbdadbdacaddcaabdabdabbdbbacabaacaadaacdddabcadaacdbdadaaaabcdadbbdbddabaabaaaadcbbcbdbacbabdaccdccadbadddaddcaabaabacdccdbadddcbbbbbadbbddadaaaaabddaddbcdddbcdaadcddcaacdccaccabccbbcbbcadabdbaacccabbccacdcaaacccdacaaaaadcacacbbbaabacaacbadddbbccaacdadaabbddcaccacdacacdaccaccddabdbdabdabcacbbbacbacdcaccacbbbbcddabcaaddccbadcdcaacdbbcaaaadbbadbdcdcbcbbdccbdcdcdadddcadbabdbcbdcbacbbdaabcdbbacabadbdacacbddccaaaacccdbcddcacccacaaddbdccbabbcadbddcaadadadbcacdbbabadbcdbbabaaaaccdddcdccaccdbccacabbdcabcbcbaabdacdddabdbcdaccaaccbcdcaadcaabadadabccaabdbbaadcbbbbbdcccdabbdbbdabbaabcbababaaddabaacbbdbbcdaabdaadbddcbcbcaacabbdddcadbcdbbcbbcdbcccaccccaaabbcbbadabbdbababacacdbdacbadabdccccacbabbbdbdadcabaccdaaacbbdccddcbbbbbdabacdbccaadcadbcbbdddbcdbcbbdacbcddbbaababaacaddabadccacdbaaccdaddbbbdddbaddaacdcdacacacccadbadccbcbdbcbbacabdacaacacbcbbbcbdabbacdbbaddddcdaabdcabbccbbcababaacbabbbbadaadcddbcadbdbdcdccaadabbdbbcbcabdcacaacbababbacadccdcbaddcdbcdabdcaabbcbabbdcbdbaadbacdbbaccdbdaabbcbbabbcaadcbdccacabaddaddbabbdbbbbcbdcdcabbbabadbdccddaadddddacccdabdcdcbdbacbadbbdbdcaacccbbdaadacadcbbddddaabacaadacabaaddcdcaadbbcaccbbaacdabbbdaaddddbdabaacdaadddddacaaaabacabcdcbaddbdbdcccaabbadbcadbdabddbccbbaacdddadbaacbaddbcbdabaacdabcbadcadcdaadabcddcbcaddcbddabdadaabbbcdbcdbbbadcccdaccabbdaddabdbcbddcbbccbbcbadddaabdddabcbbbacababdaaacdddbaacbaddbcdcbdaabdabbcbcbbbaaacbbdaddccaacccaaadacbbcacdcaccddaacabccbacdddadcabbdabcaadcbcaaaaababacccdcdabcbbcdacdcddcdccddddcdbbdaccccadbbbccabccbddbcacdcbddccbcbcdcadcbddbdbcdcaacdbdbdcdadbcbcbdaadccaccadacbbccadccbccccccadababcbacaccdbadbbdbccddabcdbccdaaddadbbddbcbcccdbbcbdaababbdccaabcaccdcdaacaaccbddbddccccbdaacabacacdcacabdddcddabccaababbbcddcccbdbaddbbdcbdbaddbcbbbabcbcadcbbbbcdbcbcdbcbbdaabbcbcbcaacabacbccbcacabbcdbbdcddcaddcdbdcdcbcadbbcddbcccaacdcbdbdbacccddddcbbcbcdbdcddbadcaacaabccdcbdabacaabdabcdbdbdccbbcaabdaabdaacccccdabdabccbaacadbabaacadbabcbaacbddbbcdcdbadbddabdcbccccadcdabaabdccbcccccddacabccabababdadadccbabbbacbbdacdadccbbbdcbbacccccbdcccaadadbcddadbdccacccadbccaddcabaacdbaadbdacbbacdbbdadcabdddcccddbcdaccadcdaacbdcadbcddabdbbacbddbabdbcbdccbddcdaddadcabaaaadccddacdaaabbcdacadcdcdabcccbadaacabccbacdbabdabbccdcbbbcbcabadbcdcdbdadcbcddbccccbddbcddababcdaabacdbbdbacdabdabcdbbcdacdbdbabaaabaadabbabadcbadbabcdaacbcdcccbdbaabadbdbbcbdadbabdcacdbadcdaccbabdaacdccaddaacbacdbbdcdabddcdcacbcbddbbcbabbccbabcaadcddcbabdabdadababacbccabddbaddcacabbcdbadbccdcddacbddabccddddaabbdcccccadababdcbbaaacddcacabddabacbbbbadbacbacacbbccdbbdbdcbbbbaadcaabbbbbdbbcbcbbaadadbddabdccccbbbdbcbaaccbdccdddbcddbbbaaacabcadccbcbcaabbbacadcdaaddcccdaaaadacbbcacccaabbacbbacdaabbacbdaaacdcbddaccbcccdaddbcdabdaddbadbbdcbacbbdbbbabdabcddabdddcbbbabddcababbbdabbdbccdadcdddbcdbddbdbcdcbbbbdaddddddaadaddbabdaacdcdcbadcbbcbcbdabbbcddabacddbaddcadaacbbdcbacbadabbbbbabbdcaaacccadbccbbaccabdacaabaaadcaaaabbbcbccccdcbcdbbdcdaabbdcabcabbaababcdabcabddabdcbddcbddcbabbdbaadccdacccbdaabcbdcadbaabdddcaadadabcddaaaddaccaadcdacbcbccbbcbdaabcbddadcacdbabcdbcdaadcaabdabaccdcddacabadbbdaadbacddccdbbbdcbdbcaabcbcddcbbdcaddabadcabdaadcbaadcdbaaaaccbbddbbdbdacbaacbadcdadaddbbcccbcdddcbdcbdbdccdcdaaadcaaaacdabddccdbaadacabdcdcdadddbbaddcaabdaddbdabddcdacabcaccbddadccbcdbddadccaaadaacaaabddabbaddadbaadabaddbccdbacdcaadaddddbdbbabdaadbacbcbbdcabcabbcbbbaabacdbcdaaacaabdcccbbbaaabdddacaacdaacdcdaacbddbdcbaccaccbcdcbabaabcbabddcaabadddbcbdccaccbcddcabdbcddccaabbaabdbbacbdbdacbbdbacabcaddacadbcbbcaccacaddbabababbdcadbadcbccddcaadacdddbddbddcbaacdbdacbbbdccaabccaccbadbbbccdaaabcacdadbdcbaacbcbbacbcdcacabaadabbdacdaadbcbbbccacacbadbadacbaadacbaadbcccdbddcccbcddaaaabababcabbcadccccabcbbccabdccadbdaaacaaadbadabcbdaabdacaabdbcdcbacacacbdddacbddccbddbbbdbbcbabbbbdbdcbcadccabaadbccdadcdbcbdbdcddbbdaabbdaabaaabcbcbdccddbaaacbccacbacdbacacddacacadacbacaddbaabbbdbbdddacadbaabbbcbacdbcabbddbdbddbbccddccadbddbadabbdacbbccabcbddadbcdaababcbcbbbadccbabcbccbbccdaaabcbdccbcabbdacdacddcadccaaaaccdbcbadbbbcabbdbbbccbbabbbdabbcadbabdcadbccbbbcddaabcbacdddcbccaadadcbcadabbcbcacaaddbcbdbbcaabaacbcaaacdacaccbcbbdbbbaabbdbcadacbddddccabacacadadcbdacbacddcabacddabacaabcdcaaddcaacaabaddcbdadbcbbbcacacdadbadaadbacabdbdbddbcadcdbbcaadaabdadabcdaaacddcccacbdddbccabcbcbdadabcbcacbaaccdbbbdaccdddabcbaabaccacccaddaabbcbabccbdaadbcabaaacbdaadccacbabbcbdadaacababadabccaddbbcaaabcaddddabadacaaabcccdbdbddaaadcdcbccdccacdbccbbbbbccbdcabcddaabacdbbdbacdcadaaaddbbddbbdcdabbbddccaaaddbcdcdacaacabddcddcbaccaaddcdbcadaabbccadccaddaabbcbbbdccadacbbabddacbaadcacdabdbcaddabdaaabdddbcacddddbdcddbabdaacbcaaadddcadacdbbaaaddbdccaacadcbdddcabdbcdbdcbadcacbcdbadccabcaacddaccdbbaabbcdcbbcdaddbaadbbbaabacdcacdcacaaddadcacaabacbddcabadbbdbbaaddcbdddbcadaadbbcdcbbadbbcbdccbdccbdbbddbcabdccddbaabbcccdbdccbabcacaadbadcacccbacdcacbdccabdbaaabdddbaaacdaabbbdacadcadbcbbbccdbbdabacdaccacbcdccaadccabbbaccbddabccccaacccaadbcbabbacabddbcdccddcaaacdcdcbbcabacdcaddbacdbdddbbdaddddacacdbcddddccccdccdbadaaaddabcdddbcabaacddbbcbabdaccabdabbcaaacabbdbdcddbacbcadbbaccdcdcddcbbbaacabacabbddabddcaacdadadcacdcadbacdbddacaadadacdddacdcdcaaaddadddddacadbbbacdbaacaddacacbdabcdaacdadcaccbcacacbaabadabddabcbbbcdddcbabbaadbccdbabbdcdadadcddbdccadbcbbacbbbabcbdaaaabdaacdaaadaaaaadabdbdcbdbbbbcddbaccaaddacdaaaabaccddbaabbaaacabcdcccadcacaabadbdbcabbabdaaaabacbdcacdbdcccadcbcadabdbddaccccddaddcbbadbcdadccabaadbbbcdaaabaddabdacbbdbcbaccadcdbaabcddacbabcbbcbbaacbbacddbbcbcddbddbadabbadadcdcaddbccbcabaadacccdccaaaaddacdacbcbadcaccacdbaddacabacbbcbacacdbbaaacaabdabcccdcaccdddcdcbbcaabaadacbbcdcbdaaabdcadadbaddacbacbadcddbdaadadbbbddbcbcdabcddcddccaddcbabddddcdbccdabadaabbdbdddbbbddddcbbadccaaabdcacdacabdabdabdcdbadbaacabcdbcaacadaabdadcbcbdacbdbbadabbcddccdabdacabbdbddabbcddacaaadaddbabdadbcbdbccbbdbcccbdddbcbaccdbaacbccaabdaddaaddaaaaababdcacbccbdacadccdbaaddbbcdddabaadcbccbcdbcaabbcdaaadacbbdddbbaabbddcdcbbcccdadcbaabaabaacadaaaadcddbdcccccbacccdbcaacbcacddaddbadacdbdbbbcadcbcaacabcabaddacbbcbdadbbdacccabbbdacbcdbcdaacccbcddaaccacadabbccaadbdcddacdcaaaacbabdbaaadccdbdbdcadcbcbbdabbabddbddcadcbbbacdcabcbdaadbccccbccdccabdbddbbcbaccbcdbdabadadacaacbabaabdbbaaabccbbdadcbadbcabcdccdbdddabdbabccdbdddaadcbcdbbddccaaacddccbadcbdadcadcddbcccdbdacdbdaadbbcbbadccbdcabbdddbaaadabaadcbbdbbdacbdbabccddadbcdbcbbdaccccacdbdbabbbcccddbcdbacdabdcaaadcbadbadbadaadbcdbcddbbbdbacadaadbccdbddacdbacbbcbacbaccacabcddcdccdadbcccbbacabbcacbbdbbdbaaabddccabcabbdbcabadccdcabaddcddcbbcabadbdcddcaacabadbaccbcabaaacbbdbbcdbcabddddbcdccaacdbcaccddacdcdddcaddcaacbddbccbbbbcddbaabbccdccbdbcccacdbabcbbcdccadacadcabdbddcbbbadbadcbccddcdddbcaacbcacdbddbbbdadacdaccaacdcbaacabddcbdbaadbdbcaddabadddcdabdbabbabdaacdabadccbadbcabdacbadcdaccacddcddcbdcccbbbcbdcdbabcddcacacbcdaacbdbbcdaddcadddaddbdcadcabdadbcdbbabdcdcdabbbaacaadbbabdaacaaadddacabbdbabdbcbbbbbdcbbdbabaadbdccbabaccdbbcbddbadaabdbdbdacdaabdcadcbaccdcadcabacaccbdbcbbbbaccbcaabcbcbabdddcdabbabdcddaabdcabbdcdbcbdadbccdadcadbacabdaabbdcadacbccacdacacddbdbbbcbabdabdbbcccbccacdacdcccadacbbcccdcdcbcabaabbdbabbddccbcbbccddababbaddadbdbaabaddbabbdcbbcbbacbccaadccadababccbaabacacabddcadbbacbcaaddaccdddcdcdbbdbdcadbcddbbcbacadbadadcacabccdacdabbcdaacaaacdcabdacdcbaddbcccadbbcadccccdbcdaaccdbdcadbbddddcbbbddcdddbcdbcbccbdaadabbcabacdcbbcbbbcbddbaccdcbbbcabcdabbbdcbcdcaccbddcddbbcaacdcbbbbdcadadcdcbbaacdadbccaaddcbaaaabdcdbcdcadacccacbbcdcabdabcadbdbacaaacabcabaddcbbaaddbabbdbcdcabbbbbbbdabacbddbcddacaabbbdbaddbbcadbabdabaacabbccbcddabccabadaaddddabdaacabbbadbbccdbadcdbdcacccaadbbadbadacbbbbbbcbbcbbaccbdbcbcdbcbdcccadaabdacbdcbdacdbabbbacddbccbcaaddaacdbcbabcbaddabbdcdcdabdbadbcbbcdadcbbbbbcbccdabdbcbddcdaacdbbbacabbbdbdbccdcdbdbdcbbbddcbcabcdcbbcdabadcabbadcccddbadddaabbcbabcadbbbdccdabcdcdbacacacbadaaadbddabbacdbbcbcababdacbdaacdddaabaacbabacccddaddbccaababbaccbbcddabbbcccbcaacbbbcdadbaadcaacccaaabdcccbabbbcccacbdbbbdcacbdacdcbabcabbaabaabbdcdabccbcabcdcbdcabdabcbabddcdcadcadacddbaddbdccaaacdaccaabaacccccddbdaddcbcbacdddcbdadcbadddadddaadbdadddddbcbdabaacbdcbbabbbddcbcbacbbabdbdccdcbcbbadadddbabbdbbdbbaaabbabbcdcdaadbcddbcdccbccbabddacdaacdccaadddddcaabcdbbbbaaaabadbbdbabbaccbddadabbbdddcadccdbbbbcccbcdbdbcaacdbababcaddaddcdacccbcdacbcdccdbacbbaccbbabbdaadbacbddcbcacdbdbaddbadcdbccaacdbdccdccccbacddbbaacdaabccaadddbcdbdadcbacaacaccbcccddbddbdcccddacacaadbaddcbabdbcbdadacdcabdcddacbbbccddbdabbbbabdbddacbbdaabdaacacbcbdcacaaabbbacadccacddcaccbaddabbccccccbdddbbcadcbcaaddaccabddcadbccdabcabbcbbcacabbababcbadbabaccaaddbccdddbcacaddbcaabaadbbacadbaccdadbccbbdbddaaccddcabccacaadcabcabacddbdaabcabcbdaccaacbdbabacdbbabaabaacaabbcbcbdaddabcdabbccbaaaabdbcbacacbbbcacaaaddadcbcccbbcbbaddccbbabcaddabcabcccdcddbbaddcdcdadcdbccbbcdcbddadbcbddadaaddddcadcabbadbccbccdbcbbbbaadddadcdccbdadadcadcbbbbdcddcdbbdacaacdaaddcaabbddcbcbccbdbddbbcdcbcbcbddcbdbcdbacadaccdacbccdadabdbdacdccdbadbdbcddcbabcbbccdcbdbacbbacabaaabbcccdadabacbdcacacbdcdddcbacdcccaccbdadccccdcbccddcdbaadacccbbbadbdcabcbbbbcaabaabdddaccbdbdbdbaabbabcddbaabadbbccddbbcddbcbbbacbbcaadacbadacdccccabdbcaacaddbddddaacbbcadddaacbdacabdcdadccbcadbdcadbbbaaacbbadcbacccddcaccbcbacbcacdaccadbaabdbcaadacccdddbcbacdbccddcddbadbbabccdbdcaacacbaddcdbbbadbdbbbbdddddaaddbbabcaacccacacbddbcdcaadbdbbddadbddadbcadcdcacdacddbcabdbdcabdadcaddbcaccdcacaadcacacddaddbbdacbaddaabcbcabcccbdbcdbdaacdbcbcdadcabdbbabdcadbccbcbdaabcbcaccbaccddaaacdbaacbbdcabbbbaaddcbacccdabddcbbbcccbcabdaaaccdaccdbcabacbbaadabaabcdcaddacdcabcaaddacacbbacaaaaacadcdabadbacaadbbbbddcdcbcdbdacaddaccbddccbababdbbbdbacccabacbdbcbcaaacaabbccdccadacdbbbdbcdcaccdddbbcaaccbbcbbbcbcdccdadaaacdbbcdbbcdbdbaaacccbccabbbdddddcaadbdbdcbdbcccdacdbcdbdcbadbcabdccdaadcacbabaabdccbadbcbabcdcacdaddaccdddabdbcdcbdbcaccaaaddddcdbbaaadcdddacabcacccdbababcbcdcddcccdcaddbbdbdcadbabdcdbddcabbddacbbdbaaabdaccdbacbcbdcccdaabcbbdcabcaccbacbddcbacbbbcdcdcdbdadbdddabdcbacbcbdabcbbcacdccdaaccdcbbdabcabcadbcdadddcbadaddacaaaacdcccdbddbbbacaadcbbddaaddabcbaabddbadadabbaacbabbcbdbddbdcaaddcdccaddadbadabbddaacacdbcbcaccbcacbaabcdbbaccccdcaaaccabababcccacdabcbababdcbdbbcddbabcbbdccbddacdcaddbcabdbcddcaacddbaccdcddcbaaacbddcbbbdccacccccdbaccbcbccaadaaabacbacadaaddabcbcbacadcddcdccaaaddbbccdcabbbcacbcbaccaabcbccdbaadabdabababdbddacbcaccaadbbcbdabaddaddcacaacaacabdaddcddccadacbbcaaccaaacacbdababddadbabcadbbdadbcadaabbddcacbadbabbdbdacbdddaddddbaddccabdccddbcacdbcadcaddaddccabdbdcbdbaddaacdbaabbbbdaaacbcbddacdacdddbaababddaddcdccdcacdbbcddbbdbdbbbdcacbcdadaaacabdddcdbbabbdbdabddaddaabadcccdcbdcdaabababbcdbbaabbdbbdadababaabccddbccaddacddadabcccddbbabdbccadabbcabbdbdbbabdabbdcacaccadbbaabdbadbdbdccabddbcacbcbbdacbacaabcbdccbbcaddacbbccbdcacbddcddcabcbbadaaacaaacbbcaaccaabddbcbbbbaacbccdbdaddaacadaadadacaccbcaabdccbdabbcdcccddbabaddbbdcdcdbcbabaaacbdadddacdadcadbdaabcdacccbbcacbcadcbbcdcaabbddddbddcbaccbcddcabadacbdbdacaadbdabadcdbcaddbdbdbbaabbabcbabdbcdccbaccbddcddbabccddacdccdcbcadbdddaaaabbbddddcbbdccdaabbddddaabbdbdbacabddcadaaaabcbcbaaccdddbacaabdcadcbddabbcbdcaaadbbbdcbbcabcbababaacaddbddabcbbabcdadcccbbccbddadcdccadabddbbabaddccbaddddaadcabaaabadbaccdbbabcabcddaadcbadcbddbaaabdaacccacdaacdcddabccacddddaadadaadccbbcabcccddbcaaddbbccccbdcdcbccbcdddddbbdbcaccdcaabbdabbcabbcdbbbbabdaabdbdcaabbabdcdbaaaacaddbacadbbadbccdcbcbbaccacccdcccddadcdababdddbbabbbcadacdcbadbacbdbdacaacdaababbbdadbbbcacddcaacbbaaccbdabaaacababbcaddaabddcdddabbdaaccddcccbbaaccbbbbcdacbcbddbbdbacdacddcadbcbabadddbbbcbdaabbabbacacccbcdbddbcaaddbddcbabaaabababbabdcbddddbbdccbacbccadddbbbcbccbabdbdbcddcaaaaaababcadbacaacabdcdddadcadaaaacadcbcabdcbdcbddaacaccbcbddcbabadbbbdbcbcbbcdcadabcccccacbcdcacdddacbcadbdcdbaabcbcccabccdbcdcddaabbbabdacbbbcaaaaacbcaabdaabaddcdddabdcbdcdcadbdaadddbcaccbddcababbbbbadbdccaddacabdcbbabdaaaacdbcabbcbabcaacbdbacbbaccdcdcdcbaacdaadcbbaccddccdadaddcbdcddbaadabbccddaddbcddcbbdaccbcbcabdcabdcadbbccdbbcadabacddcdddcadaaccabdbcabaccbdbddadbdbccdcdabccbccacaaadcdbbdbbadddccaaaccdbbbcbcdbbdcddcdcaaaabcddbdaabdbcaadccdcbbbaccbccdcacbdadaaaaaadcbcdbadcdbdadcdccbabbccadbccbdaabbddcccadccbdaabcadbbbdaacaaabddbddabaacdccaadacccdabbdbbbaacaadddbcdcbabccbcbdcabbbbcdaacbabbadcddcdaababbabccabdbcdbdaabcdcdcbdabcdcbbdabbbadcabbadacddaacbbddcdcbbdadadbbadbdbcdcbcdbaabbdcdbbaddbcaadcdbdbabcdacbaddababcbbbbdbdaabdacdcccdccdbabdbbbdcccbcbdcaaadccbaacbadcbcdbcbbacaadadcdbdbbdccdcbbdacdbcabadbdacaacccbcdbbbaadbadbdaacbddbabbdaabccdccbbccbcadddadccccdacaacabacbdcaccdbbaabadbcdcabdabbbadccddcdcaaaabdbbadabadbbdabadbaccbacddcabbccbbdadbbcbdabddaccccbbbbbadabbdcbdacdbbbaabaddabdcdcbacabcacaaddbcbccbcacdaadacabbbdbbacdddbdbbaddacacbadabadbbbaadadcbbbdaacabbcdadaccbacdddccaacadcabaaadbccdaacddbbdababdbdbccaccadabababdaddbdababbabaaccdacdcbcbabbbadbadddbdaabbddccabbadbdbccdacadccabaaabbdabdcdddcdadaaddcdccbdadccddaacbbbbdcdaacdaadddaabaaabbbbaaacbcddabdbdddbbbdaabbbbadaacabccdbadaadababbdabdabbcbadbdababacbcabcbbcaaaadaaddcdcddabccbaaabcdcbbbaaddbcdccccadccabaacbdbadbbbaaacdabdaabbccabdaaadaaacdbaaccbacdaddcabacbdacadacbcadadcaaaccdcaadbabadadcaaddbaaacbcdcaaccbbcbbcdabbcbadcccaaddcaccbadaadcdccdddabccdcbdbadddbddcccccabddbcbbaaadaacadadbdacbbccdccccbadababccddbdbacaccbadcdcdabcdcbcdaabdccbaadbadbbabddcddbddbacbabacccbbccccdcacbbbdcccddcdcaccddcaadccbbbaabcdbcddadbddadcddccdcbdddbbabcbbaccbbbadabadcaadcbaabacbaddcdbaaddcccccccbdbddcccabdcdcababaaaadcddadcbcaabbcacdddbccdcaaaddbacdccaabbcacdaabcdcdacddbbbabddcbbccbddbcddcbddbcbdcbaaaabacaabbcccdbbddcbbcdaddbdcddddccdaaabcbddbddaacabaacdccadadbddabdddcacccdbbcacbddddadddbdddadbddaadaddccadaadccacddbabcdbdaaccbbaddddbccddbdcddaaacaacbacbbccbaddbabdbaaacdabdcbcdabbbccdbbbadcdabbcbbabccdababbdbadcbdbcabdcbabcadcbdaabbccdccbdcccaadbdcdddbaaddcadcadccbabacdadcbcbdddcbbcdadacddcabcdbabaabcdababdcdddcbabbcbdbaadbcabddcabadcaccbccdadcdbaaaddcbbccdbdaddcdabbdcabdbbaacccbcdaccbaabbaabdacbacdcbaaabbadbdccbbadbaaddddccccabdbdcdccdbcabbbbdcacdddadbcacbadbacbbdabbddacdacdbadddcabdcdcabbbcdbccaaccabdddabbaaddbcdbaadddcddcbaadddbbbcaadccaaccaccaacaddaccadaaccbaaaadaaaabaaabccdbdcddcbcabcbdaaccbaabdbccbbbbcadbdcaaadbdbcaddabdcccbacadcaabdacbcccbbddbaacaacbacbdcddccbadadaccdbdddcbbcbbbdadbccacbcaadbbdbddddbaabcdabaaabadbcdcdbaacccaacaddbaaddddbadacbdbcabddabaccddadbabbacbbabadddaacddbdaabdaccabcdbbabbbadbacdcabababcacccaaccaadccacdabdbcddddadaaccccdabcdbddadbdddcabaaaaacaaccccdabadccddbbbcdcadbdcbdaabbbccaaabaaaaacbdcbbcddabbadcdbbdcdbbcbddddaacacdacccddbaaddbbbdaccaaadbdbabbababcadcbadcbcbadddcdadcacbdabacdaddbcaacccbbabdadbaccaacbcccddcbcaaddaabdcccddcccacadabadddcbcddcddbddaacddaabbabbccdcaadaccddababdacabbdcacadababacbdddaddbabdcccddbcbddadccdaddaadbbbbcadadaccdccadbcbdadadbbbabddcadbabcbcbbdadbdbcbbdaddabdbdcbadaddddbabbbcabdbbdacbaccaacaabacdabbbaabbdbbdcccdabcaabadbdbcbdbbaaccdddadbcddbbcbccbadcbdddcdbdbbcabdcdcbbdaccabcabccbaaacbccdabadacbccdcbaccdcadadbbbabdbcabdcdbdbcdaabddacbbcddaccadcabddaddbaaadbadbbbabbbcaaddacccbbadabdcccbacbdccaccbddacdadccccaddddabdcdcadaaccdaaabbcabbaaadadacadcddababbcbcddcaacadcacbbbcaadadbccaabdbddabccddaaddcbbcdddbbdcdcadaccabdaaddcdbbdacbdcacbdbcdacdbdbdbbabcdcbadaddddaadbcbcdbaddccaaabbcadcaadbadbaadcbcddddcdaaddbacbdcbdddbbcabcbacbbbdcdaadadcddbdbdacbcabaadddadbacdccbdadacdccaaabdbdabccddaccaaadbaabdabbdcadcdddabdcbcccdbdacaabbbbdbcadcaddbadbbdacbadbaaccbcdccbdaabdccddbbccddbcdccbcdddadbdbdbaaadddcccbaadcaaaccadcabccbabdacdadbbdbbaabaacbadddbdbcdcdaabdbbcbaccdddaacdcaabddcddbcdcacdccadbcaadcbcbbbcdcbabbdaaacdbcdabdddabbbbadcabdacbddabdadcddbcdcccbbaaaaccddddaaaaddcbdddabadcbabddbbcacdacccaadcbdccbdbbcccdcdbcdcadcdddabbcaaabaaddbadbddbbdadbdcbccbbadbcbcdabcaabababcdbabddacbdcbbbcbcccdccbcdbadadbbdddddbdddbbccdcdaabcbddaddadcdcccbccabcadacdddcadacdacaaabcdddaabacbbcaddbcbdccdabccacbaabaacdbcbdcabaccccabcdaadccdcabacbdaaabbccbbacbdabbcdabaabbdaababbaabaccaccbbbbcadbbadacbbabbccbabbdcbccdcdacacacabacdadbdbcaabadabddabcdabbbdadddcbdadadadaacbcabaacadacbcccbabbdbadccaaadbddbdbacdcccbcbaaadcbacbcbcdbbacbbcbbccdaabbbccdbaadaacaccacdaabaacbadacadaadadcaddbcdbbbcbbbadcddcaccbbddcdcdcdbbdddbdddabdabdbdacddacbcaadddcacabbcaaadaddddadadbdcadccdcccdbcbccccabddcbaacaddddbacdbddaacccdcbdcadbaaaacdcabcbcabacdadacaadaaaabdbcdbbbacbdabddbbdcbdacbdcaacdbbbdaadcdadcccbabaaabaadacabacdbcdaccabdbddccdcdcdbdbacaddcdbccacddbacaccbcabddbcdadadbbabbccbaaaaabaacccabdabadbcbddcbaacadaddcbaddbdbbccabcdcbdabddcdadcbabdbbdbccbbacadbbadacdcabccaadcbddddacdabbaaaccbcaabdaabddbcbbaccbddddaaddabbaabbadbacdcbadaadbbccaddbabccdbabaccadccbabbcddacbbacddddbdddbdcdcbadbdbcadacdbdacbbdcdbbadbbbaaccbbdabbaddacabdadabaabcbcdbdadbdcbbbbdabbacaaccbaacbabaaadbddabadcaddabddddabbbacbdcbbccadbbbdcccaaaabacabacdcbddbaaccbdaaacdcbcadccdbcadcccccdbdadcbcbbdaaaabbababbcbcccaabdddddcbacccddacaadacadbadabbbcccacbccdccdaacbbcbdacadacbbadaaddccaacbdccaadabbabbdbacbbabccacacbcaaabccbcdbaacadcdacadabdccddcbbcaccaddbacdbdbdabbcabbcabdadbddbbabacccbdddbcbadcbbcccccbcccbbaadcabbccdbacddddbadbcacbdabcdbabadcdaabdcdabaaccbccdcabbbcabdccdcddabbaaacbdcccbabacccbbacbccbddcddababdbababddcbacbddcbaccdbcbbabdbcaccccbbcabaaccddcdcddaccbbbbacbbdbbddcaaabbdcddbbbdddcaabbdbcdbadddcccabdacacdcdcdadbbbdaaccbbcccdcadaadaaddbdddacbdaabcdcdaacbbaddadacababcdbddadcdabbacbbccdbcbbdcdadbdcbcddbcbabaddddcadcaadbdddcaabcdabbccdcbcbcdccacaacdddbdaacadddadccaabcabddcadadababcadaadabdddbddaaaccacdcddbddbbacdddbaacbddaabdbaccacacdbbabcccdcbddddbccdcabddbcbcdbbabaddcabdcbbbdabdcaacabbbcaaddcbcdbabdacaaacbacbdacacbacddddcadbdaabacabccdcccbacccaabcabacaabcbcbdadaacababbcddaaddcbcbbbdddcbdbcaacbbddcadbcdacabcadcccbcaadcbdcbcbcbcbddbccbbbdacdbcdbdabbdcacddddadcbdddbdcccabbddadbccbdabcdccbcccbddbddddcdabdcaadaadadaccbbadadadcbcbccaaddabaddcbdcbdaacbbcdcddabdadcacdbaaccbbdcbdbdcdcbaacdcadbbacacbaadcbbccbcdabacacadbbcddbddacdaddbdccccdbbbccadddbbaaacccadbaaccaabcbdabdbbbbbabaabaabaabdddbcbbbbcccbbaccdbdccdaaaccabbdbadacdbbbacdccdaccbadaabdbbddbbdaaaaaadccbdadddabcccdabbbbaccabcdaabdccdccdcbbcaacbdabcbdcdbccdcbcdaacddaabdbaaabaccaaabbaaaaccaadbaaccbabdaadbbbbdabddcbaadbdaabaabddacdcddcbabbdbcbdaaddbbdddccdddbdbcdcacbabbadadbdadcabbcddbbabdcccdbcdbbddddbdacabbabaddbcbdabccaadaacdaadadcacbcdbacccbcdaabaccaddacbdabbaccccacadabcbdabacacbbabddbcabccabbcaccbaaabdbcaaacbbcbdbdcbacdbccddaddacbdacadadbdccacdcacdbacdaccdacccdcabcbbbbdbdcabbdcbdabdcdabccaaabddccbbbcadbbdbbabccdccdcbadcbaddcaadccbbabdadcaadccbddcbbbccaacbbcaabbaadacdccadbddbbbaccaadbacbacbbcbadccdabdccdccacbcdadbdabbccddbacbadbcaccbdddadadacddcdcabdcbdadabdaaadccbbacbaacccbddaddbacbdbbddddcacbcbabdbdaacbcddddbcbdabbcdccbdbbdddbacdadbbaabdbcaadaccddaadbbddddabacdacbccdcccaddbaabbbbaaacacdbacccabacdaaaccbbdcabcbdcbadccbddacbcbbcbcddcacaccdadbaccbcdabadbadcbccacbacaadacbcbddddccdaddcadddcacadbbabdbadaaddbddaacbbabdaddaabdabcababbabaccbdadadcabbacacaccccadbaacccdcbbcacdadbddcaaccbbbdcbdbdaddacccbabaacacdbadacccacdcddbcacdbaccbbdbbbbabddbdbcaccddcccdcdacbcacdbacadbcacbccbddbcdbbbddabdccdbacbdcacdcabdbacdbdcbdbbcbcddccbaabdbadddbaadcadcbcaacdaaddbaabbadddcddccbabcabdcdbacbbbcbcccbccaaabadcabaaabdccaaccaddabaddbadabbbacdcccabacdaccccaccccaaabbbbdbcabbbaadccadbdcbbbdabbaacdcacddbcabccbaccabbacdadcdbadcdbbacbcdccbcadacbbcbdaabccaddabcbaaccccccaabbbbdcdddddaddcaaacacdadbbbbccabdccadaddbcaadcdbabcbadbabadcbcccbdbcdadacdbcadacbbddbbaaadcbbddcdadbabcddbcabdaabccabbbbbcadccbabcccaadbccdadccaddcbbdccaacabbbaaaaacadabbabcdbcdbaacaadbccddccbbdbbacccdcccdababcadadabbccbbbdacbbbacaadbaccccdcdaadcdcbbccbbdaadcababcabbbcdcdbababccaacacccbcadaaccaccbbcdaabbdbbbdadaddcdcdcaccbdcddbcccbbcbabdcbaacbccddbbaddadbacbbaaaccbccdddcabcabdddbbbcdacbbdbbadacbadcdabbadccbabbaddddddadadcdddcbbbabbdabcaadcbbcadddacaaccdbbadbcbadbabbcdbbcadbccabbdcaddbcbbaaaaaabbadbbdddccccbaaccdcccaadbbddddbaddacbbbadabccbbcacdcdbcbdccadcdaadabccbbcdbabbbbaccdbcabbccdcabdadcdcabdcbcacccacddacdbabcdbaaccccbcaadbdcbdcacadccaaacdcbcaaddbdbbcadcbadbcdcdbdadbabaabcbdaabbbbcdaacbccbcadbdddbdddcbdaaababddacbaddcccadabbabdcccbbcdadbacdcbaaacddcaaccdddabbbaccaaddbbbdacacacdaccbbddbacacadbdccacbbdaccddadcbaadbcbbacabdcbbcabdbcdbdccaccbdbaacdbbdbdaadcdaacaabbaabdbbaabbbdbabdbacccdbdaabcadcddbacabbdbaaccdbddaadaccbdaabcadaddcbccacbaccdcdacaaabbcddcccdaaacabaadbdbdbcbdbabbaacaccacacddbaabdadcbcdadddcdbaddcadbdacbbddabddccccccbbcadaaccbccdadadcbaddcdadbcacadbdbbaccbdddabbdccdabcbcdbcbcaabacaadaccdbcccdacdbccadbbbcbabcabbdbbdddadbabdcbdaacaabbabcccddccbcbbbaaaacbadacacbbbcbcccbabcdbcdcacbcdaccbbcabdcdddabaadaaacdaaadbcacabacaabddcdbddbbbabbbccaddcadadacabaaadabaacaabbdddbaaabcdaadabbbcdbdbdcaadcdbabadccdcdccaaddccdbcaccbdaadbddddcabbcdcaaaabbbadbdabcbbadddcddaadcbbbbcbaaaccacdcabadabbdbadaaabdadcabbcddbcdcacdcbdccdbdadcddabdbbdadcdaaccccabcacbbcacccdcbabcadaccbaacbdddbadadaacabdccddcabadcdabcdabacaccdbcdbaadbdcaabadcbbddcdbdacdaacaddbdaadcaccbcdabbbbdbabdacbcdcbdaadbbabbbcdacacbbbcbaddcbbbaabcbbaabacacbdcabddddddbcdcdbddadcbbbbccbabdbddddaaacdbdcdadddccdadccbaaddcddbddbdaddcadaddcabacadadaabcbacacaaaddbadabcccdcdddddcccbdcbddcdbdcbcbbdadbdabcdbccaccadccdcdbacdcbadcbbadcdbcabcabaacaaccaacacdbccdaddabadabbcbcaccccdcaddbabcbdbccbdbabbccccdaabadcdcdaadcdbdbabaccccdbbadbacbcacdcbaaabcdcaaacbabbaaabdbabacadcabcaacaaaddcdbcdadabdbcccdcadcbcaacdddcdacabcaddcadaacdcacddbaccadcaadbaaabaabcdaccbdcccabdbbabbbdadcddacccbccccdcaacabdbdacbcbbacbaaacbbcabcacbacccccacbabbddcbaadcdbcdbdabcbbaacdcdcdbaaacddddbbacdddbddcdcccbcacdddbabcbdcdbdabdbbcacadbccbbabacbbddbdbcddcdacaabcbbacbacadbbabbcddbcbadddcbcaccbdbcbdacccadbbaccabaacadcbcbcbdcbcbabbaacdabcdcdadcbdaabcccadadbdcabcdbcbbdaddbcbccabdbcaadbabdbdabcddbadcbcddadabbcdabbcbabddbadccccdbdcdacacddccadabcbadbccbbccbdcccdbccabcccbabadccbaadaccabbaccbddbababcbddabdbacadcdbdbbbadaacbdddbbadabbcbbcadbdcadaccbbcdcbcdcddddccdbaabbadaabbcbcbcbbaccabcdcdacbbddadcddaaccacdcabbddddbcdcbbdddabaabbdaddcacbdbcbacbccccabdcbcdbcdbdcabdcdcbccccadcddcccababccacbadbacabdbddbbadbdaababaacaccccabadbacdbadbcccaccacccdcdbabcbcbabaacacddadccbacbcbacadbcdcccdbcacdacbcbaaabbbddaacadbbbcdcacaddcdabaddcaabbdcaabcbacbaacbacbacbdcbaabcbcdddcdbcdcadacadcacdaadbbabcbcbdcdaaabaddcbdaddbbddbcddbabdcababdbdaacadcddcbdcacdaadcdbcdabbbcaddbcadcbbcdbbbdacbdacacdaabdaddbcdbaababbccddccbbdcbbddacbbbabacccbaacbbddcdbddccbddbbdbdabcccaaabacbbaacbbcdccbbcbccdabdbcaababbdbcdcacadabadcaaddbdacdaadbcbbcabbaaccddaddbbbccbadaaddcabbbccbababdaababccdadcbddbcabbccdbbccbabbddbdbbcccaccdccdbcabcdbcabbcbacdbcdbdbaddadcaaddbcbcacadbabaabdababbaccbbaaadccaacabbddbcbbbcbbcbcdddcdacbccabbbaadcdabcdacdaddbdbcbdcaacbcbaaabccbdcacbcacdbcdaacbaacccddabcaaaadabaadcaddbbbbbabbadbbbcbdccbabbdddccababbdccddccaacabbccaaddbdbacabdaaddaadabcadbdcbdacbbdbbacdbbaaadaddddbadccbcacbcbbddabbdcacaaacbddaaaacabdaacaccbaabcdaaccadbdaacbdbabcbcbcbccbccaaccadcccbbddcbdcaadbcabdbddccdbbbbbccadbaacbdcdadbbcdacdbddabcccbaddddacbacbcbcbcdcddaacddcacacbbbbdacbbbbaacadbcadbcdaccdacbabcbababdabadadbaccbbccabdbcadbdadddcbdabbbcbacbcaadaddbabbaaddbccbbcaadbdcddbabccadcdcabaabbadabcadcaddbdabaaaaccabaaaddcdbcaddbdbccdadcdcacabdbdddccccbcabddbadbcbadbcacaaaadbddcaaaadabbaddcbcdacccaaabbbcbaccaabcdbdcdccdbaacbdcabbcbcabdcdcdcdabbccddacbccbbcbdbcadcccdbdbcbacaaaccdcadbbdcdcbcccddadccabdcccacacbacabbabddaabdbcbacdadcbcdbcbaccdbdadddadddccdcdbdbcdcbdabadbaaaabdcaccdbaadcadcbadccacaadccabbdcabbcababdabbacabcddbaccaadbdbccacaaaaaccbaabadaadddddddccddaacbadabbcbbdabbcaddabbcacbdcaccdbdabaddccaddccbcdbcddadbcbdbddcdbbabcdcbaacadaccbbbcbbaacacbcabbbaacbdbbccdacdaccddabccbdddbddcaccdcadbcbdabbcacbbbdbcbabadbcbaaaacdabcdcbbddcdbdddcacaddcbddbabaaacbaadbacaabacdcbdcabdcaacabcbddbcdcabddcbbbcccdcccbadcacdaadacbbbabdaacddddcadbacbbbdddaacdadbacdadbdcccbaababbbdaccaacdaacaabbbcdccabadbccaadabcddacccdbbabbdddbbddbcbbadadacddddcabdbaadabdcbdcaaaabbcbbaabdbcbbdbdabccadddbddddccdcbdccdabbcabdcaacdbbdacddacaddcbccbcbbaccbdbacaaacbabbbbabbacdbcabddbacbdacbcabacbabbbbbacdaacabccabaadadccbccaabaddabadcadacbbaaabcacbcddccdcacccdacabaabacddcbcbdbcdccdcdabcbdcdabaacdadddabaabadbccacabcaddbbcdbcdcdcdbbbadabdbdbbadaccccbabadbcdabcaaacabaadbacdacadcadcdbdbbabbadcdacdbaaaddcadadadddbcadacacddacbcabbdabcbaaddcdbdddccbdadcdccaacaadbdaaadbbabdcdabdbcabbbcbccdddbbabacdccbacabdbcabcbdcbdcdbbddcccdbbccabadcdcaccddcbcdccdaadccccbbaaddadcdcbcdbacdccaadcbdbacddcdacadbdabbcaacdadaaddcdcacddcbbadaaddbdabdbdbcccdddddaacabbddaccbdcdaadacdbabcaacbbbddbbccdacdbdbddbcdcaccdbdccdcccddbbdabdaabbddbabacbdcadbcddbbacdbbcbcadadccaacadccdbccadaaadcbcdbbdbabcdbbabbbdaaccadcdbabbdbdcbabccdddcbbdcddbddcbadaddcddddddabdbdbdbcdcadbbbacdaabbddbbbcadddbccbbaccbbadcdbbbdbddcdbdadddbbababacbbabcccbbbacbcbcacaabdadcaaccdabcbabdcdcdadcdadcbcbccacbdcaddabcdcbddbccbbdacaddbcbddcabbdaacdaacdaddaaacdcdbddacccbdcbddabbcccbccadbddaaccbaabaddcaddcbbbcaacaddbbdcbcbbdbddadbccbadbcaddbbccdaabddacdbcbcacadbbcdcbcbbbcbcddadbdcccdbdadcdbdacbdbbcccaabdadcdbbdbbcdbbcbbcdabdaddbcdbbbcaabbdcabccaadbbacbbcbcadcddbcdbdadcbbbdddacdadbacbdddbbccaabcbbdddcbcdbbbcaaadadacdadcadbdaccabbcdddbadbababbdbccdcbdacabccddcbcbdbbabbddbdccabcccdcdcdbbabadaddcdbccabcbbcddaadbadabaabdbbaaaccbbdcacdaddaddcacadcdbcbacbcabadccbabcdddcbaabbcbbbcdcdaccaddaacdddbdadccbacdaadbbccabccdbbcaccacbaaacaaaaadaacdbadbabddcabddcdacdccbdaccbcdbcacabbccbcdadccaadaabdcadadaabbdbbdcdcdbadaabdaababddbcaaaadcacbbcabbbdaddccaaaacabcaccbdddbddbddcdbcbbabdddbabbcbbbcbabddaccaacaccbaccabadcabdcaaaccbabcbcdcbcdabcabcadbcbbcadbbcadcbddbcbdacbcccdbadcacbadbacacdcbbabcbcbbaddbcbaaddadaaadcabbdcadbacdcdaabacabbcccbddcacbaabcbcdadbdabcaddcbdcbacddbddadbbcacbcddacaabcbbbdcddbcbcabdbacbbccccaaddacdaddbaaadbcbbbabaaddbdbbcccacbbdaaddbbdcbaddbbddbbbdcabcdacabadcdbadbcdaaadabadcaccbaacdbdacbaccdababdadbdaaadacdbcacdbbaacbccbbdaadacdbccbabbbadacddaabcccacacbbaccacdabdbabadbdcbcdcadbbaccddabdcaccaaacbdabadcaaacdbbbddcdcbcacdbbaabbcddddcdbbbbadcdadcbacaaaddaccdbbccbdccbdddccadabbabccdbabdcdccddbbcbcbbadabdccacabcbcbdbdccbddacdaaaacccaaacaabdbdcdaddadbcdbadbcaaaacbbbcdbdbadcddcabacdccbadabaddccbbbddcbacdbbdddbcbaabbbccccddddaacadbdcdbbcdbbacdbbacdbddaabaaddcdddaabcabbcaddbadcacbbbdbddacbcaddbddaadaddacbbdbcabdbddcdccccddbcccaaaaaccabbdbaddcbbcaabacabaacabddcacaacabbddaddcacbabbbcaddcdccbcacacbbddbcdacdcdabcaccbaabadcabcdbbbacdcddabadcddcdcadddaaaddcccbcbacbdacababacaabbbddaaababdcddcbacbbccbddbbbdbdbdddbaaadccabbbdacbcbcadaaabaadadbacbcaddbbbbdcdcbdacdbddbabacacaddbdabbcbbabcaadaaabdbacbccabdddacccdddbcacdccdbcbdacaddabaacccabcdcdabbbbbaacacddcdbddddbbbacaddcbdabbbbbcbdaddcddadcadadbbacddabbdccadccdacbabccdaadabccabcabdbdbabccccdcadbbbcbbcdccabcdababcbadcadabacccacadcdbbaabbcadbbcbbccbddcadadbdbacddbddbddbaadabbdcccbccbbdacbbdadddbbbbbabdcadbcccbdcacdccdccbbdcaabdbbacdcbacccadbbadadaaacccbcabdbaabbbacbbbddcdabbcdccbcbcaacdbaadbbcdcdbddcadbabdcccbdadacbcdcbdbbbdacacbdabbbbdabaaabcdcbabaaaabdaccabdcbdbaddbbabcbbcccabaccbdbbbabbcbcabddbcbddbabcddbdbbbdbddcddbcdccccaaccaabbbccbcdaadcbbabacdddadaadaadabbdadbbddbadddcdabbcabcabbbacabbacdabbabcbddbbabcbbbdbcadbcdbcdcaabddbccabbcadbdccbcccccbcbccbcdaddaaabcbcbcdbbcdadbbbacbbacaddbccacccabacadbaddacbcddbbddcbddaacbacacdcddcacbacdbcacdacaabcccadaaaacddadabbaabababbcbccccbdbdabcaacabcabbabacbbaabadaccdbccbbccdcbaadcbbaaabccaaacccdadcbbabcbdaccbacbaadaaccbcaaddbdcaddccabaaadaabbaccbdcdcccdccccdddbdbcbbbdddbbadacdadcaadcddaccaaccddbbbabcaaadbbcbbdaccdcacbadbbaddbcbacbadccbcdcddcbccdcabbcdcccccbaccdaaabdaabcbdaaccbdbdcacaadddabcccabcbbccdbdbbcbddbbbbaccaabdccdbbcbbcaabdaaadcddabdbccccaabbccddccadbdbaacdcaaabdbbdcbccbbabaaccdbacbaacbbccbdccddaadddbcdcdbcddacbdcbccdddddccddcdbbbaaabacaabadddbdcdaaadcbbdbcdbaaadabddaaccadaccdbcbdcdaabcbdcaacdacdbcabcccaccbabbaadabdccacbbbbcbabaaccdadbbbbdadabadaddccdcaaacaccddbaaddcacadacccdbcadbdcabdaabadaaadacabdbaabbabcacadccccaaaaddcbbddcdbaabdcdbdadaaacdbdabbdabdddbcbdcbccbddbcadababcccacbbcbbbaaaccdacdbadbbbaabadbadddbdcdcabaaacddacdbccabbbbdaabacbbbbbdcdbacdbaccbbdbdaaaabdcabddbbaabbbbdcacdadccddaaddcabdcbbbabcbadccdcadbcdccbaccbddddabccccbadaacbabbacbbddbccdcdaaccacbddaaadaaacbcabdcacddddcbdcbadbcbbabcaccddcdcdbabaaacdbbacdcaccabcbbabcdadbbadadcaddcbdacbccddcddbccdaabaabdaccadcddacdadaccacdbcaaaadcbccdccbbbdddacabbcdccabaabadcdbdccdaadddadcbdddaacbcbacccabdaccadbabbdccbadadbacbdbabddbdcabaadabadabdcbcccddbcdadaacdcbdabbdcdbdabccbcdcbcacccaababdbbaadbccabcdbdbababbccbbccaaddbacabbabcacadacbcddcaadccdbadacdbccbdbaddbabbaabccaaadadbacaddacabcbdbdbbaaaababaddcdddcabbbcdaddacbcabcddbbccbcaaaaaccacadaaabadbaaadaabcbbdadddccbaacbbabcabdcbdacaadbccbdaaccbbacadaabccbdccccbcdabacdbbccccaacdddddbbbcbccdacbccdadcaaccdcccbbbbacadcbaaadabbcaabbcbcdadacabccddcbbacbddabcbbdcdbcddcabaaabccabbadcccddbcdbabdaabacdcbcbdabbdaadadbaddddbcdaabacbbbddcacdcacabcabbabcababbcdccbcbbddddaddadddbdcadbabbcacbccddbbadaddbbdbddaabacabdbacbacddbdabaabbcaabbbcdccbdcbbcbaaaaddbddcbbccbcccabbbcccbbbcaabadbaadbacdddbcbcdadbbcddaaaabadcddbddacaabccddbbdddcbdabdddbbcbccbcddbbbdbbcccabadcbdcddabbcccadcbdcadabadbadbddcbaddbcddbdbdbbaccadcadccddbbccbaadbdcccdadabcbacdcdacbdccbcdcbadcabcdabacdbbcbadacaccdccacbcccbbcdddabbcbdccccdabacbbadbbaaadcacbbcadcdbddcacabdacccdcacdcacbabcacbdbdbbccdbbccddacddacaaacdcddadcdbcaaadbbadcbcdddccadbdcbcdadccaaacacbbbaddabdadbabdaadcccbadadcaddaaadccdbbdbdcabcdccdcbddbcbccabbdccbbbabcacdcbabadadbdbcaababbdbadbbadbccaddcddbbababbadbaaabdabcbcccadabacdcadcbbcbbcbdbccccaccbbbdbacbcaadcbdbbcdabcacbbacdccbcadadabbcabbdadaadcbddcaacdacdacddbbccacdcacddaacacddcaaadcbddabdcddbdcbddabaaddaddccbacccddbcbddcddacdbcbbaacbcbcbbacdbdabcaddbdbbadbccdccbbddcccddbbcadabcdaabcdcbaccbbaabadbccccacbdbccacbddbabdcbabddddcdbabaacdabcbcdcdabcadaaacbccdacbbddbcacaacbcacaacbbddbcadabcaaccbddadbaaccdcaabcaaabadddaaacccadacaccddbdcbaaccbcababcddcadddaaabdadbabccaabbdacccadccaaddcbadacdbbdacaabdbacaabbcacadccdcbdaaacbcdcdabcbadbacdcbdcccbbadcbcddcbdbacbcacabadcdcdddcdcdbbcacdbccdcabbbcbdbddbdadbcaddbdbdccdcdbaddbadaacdccbaccbabcbdabbbabdbdbbdabcadcacbcacdaadcddabdcbaddbcdadcacaaaaaabdaaabbaaabcacbcabbbcdbbcddbcbdbadccddccbabdcbaabccbabbcbddcdacbabcacdcdbcdcdcddabaccddcbbdaaaadcaccdbbcdcdbdbcadbadbbbdcadaadddababbddcbacbacacabbcbdddddbbbcbbbbdaaddadcacaddbbcddabdcabdbbacabbbbadaddbdbaabbdcbcbdccdadbddcbabbbbbcabbcaccccddcdcadddacbcccdbcaddcadbcbcbddcdcadaaacaabacbdddddbcacaadbdaccbdabdcbbbddcdcadabdcabcdabbddcbbddcccdcdbacaaacaadbaadaddacddbdbdbaccdddbacbacdaacbdadadbcaaaacbcccccadccddbdbcdbcabdbcaaddbddbdabdccddaccabbddbdccdddabcbdcbbccacaddabaddaaaacbcbddcbdcadbccdccadacabbaabaaacbabacacdbdabdaccdccbdddaaccbacdbdcddccabdbdcadbdccbbbddcdadccaadccaccacabcddbcbbbbdcadbbccccddcabdabbadbbabbddddcaabdacbcbdadacbbdacdbdccaadadacabccdacbbcbaababbcddbcabbdcdbcaacbccacdbacdaddbbcacdabbbccabacdbdbaaddacddbaccaaaaacdccaddaacdabcddbcddaccacdbcddbacabbbbabaddbacbbdcaddabadcaccddacaacccacbabbcdadcccaccaabdbaccddbbccaacabdadbcbbabdcababbbdbcbbccbdbbaadaccbabcccacdbcbbadbcacacabbddcaabcaaabbbbaddacdacccaaacbdbbbccbaadddbdbdcadbcccbaccbacbcbcbabbdadbcbddabdddadcadacabbabbaabdcbacabbadaaaabccccadbabdcbcbadbcbccbddbcbcbdddbaabadbbaddaabbadddccbabddbadbcbabcbbdacadaadabccbcbdaacabaabaadcddaddbdddccdcdbdcbdddaadabcaacaccbdbcdacdaddbaaddcaddadcdcddcddcbddaccdbadaaabbdcacabccddacaaadcddaddbaadbdaabdcadaaaabbcadbcbdabdaacacddaaddddaadcdadadcbacaabbbaddaddbdbcbbabbdddabcccadbcbdddbabaabacbbcabaddaacddcddcbadcbbddbdaccbadbbababbadccbbcadaddbccacbbaccdcbccabbabcaacdaadbbbabacbdaaaadddaddabdbdbbcaaccdddabbcbaabadcbdddbdcadadcbadadbbabcbccdddaabcaddbdabaadacacdccabdabbdbdcccbbdacbdbaabcacbadbacbcdadaabbadcabcdbdadcddbddaabbbbccbcdbbbacddabaaacadcaccbcaacdccababbcdddcdccaacabdbbaabddbaadabacdddcbaaabdccdbdabcdaaccbbadbacbcaacacdcabbdcabbcddadccaacbcababcaaaacbaaddbdbadbbdbacccdbaccabadbaaaccdaacddddcacacccbaaadbdcbddbddacabbcccdbcaddadcbbcadcbccddacbdbcbcccaacdbbcadbbdbbdbdbdaccaacbbcccdacccadaacbbaabadcdabdbccdadadcbbacadaccddcbbccbbdcaaddbdaaabaccbccacabadccddbabbddccbcbdacccaddbcaaadacdabbdbbbbdbabbcdbcacddbaabdbbcabdbabcabaacddaccbaccdcabdcbcadbdbcabbddddacacccbcbaddaaababbddabdadbbdccbcbabbaaacdddbddaddccadbaaacaabacdbdacbadbaabbdadacccbbcbcbbdbadaaabcacbaaabacccadbdbccbccbcbcbdccddadaddcadcaacdbcdaccaaccbbacddcdabccacbdabdcaabdcadccdabdcdbacacabdaadddacbcdacaaacdcdbdacbdcabdbdcdcbcaddadcaaddaccdcbaacaccccbbaccaaacbdbadbabcadbaccccadcddcbdbacdccacdabbcacbdcdabccabdacacabaababddacbabccacaccbadaccadcbdacadcbbdacdacaaadbcaaadbcbaadcaaacdababdbabcbbbababdcbddbdddadbacbaaddabacaddcddccbabbacadabccbdbbbdbabdcabbadcaadbcbbbbbdcdbcdaadcadcadadcdccbcaaabaddabbdcccdcddbbccbbccadcddbcdbbacbcbcabbcbadcccbdbacdabbacbcaabcdbcacdbbbcdccadccadcbcdcaddcbcabbcbdbdcbdbbddbbbbaabbdbdcdacdccbcbbbbbbabadcbabcddabacdcccdbabbdcdbabdaddbddccbdbccddbcaadadbbcaccddbdccbddbcadaacbcdbccaccbbcbdccaddadaccbdaacbabdbcadbacbdbadcadadbcbddabbbdccbbddcdcbddcadcaabadabcccdabaacbdddcadacbcdbadcdbdcabbbabdcbbcccdacadbabccbcdbcbaadbbadbcbbbdcbddbdbdadadbaacbbbbbcdaaaadadaaabbbccaadcdaaaddcbcddaccdbaacccaddbcabacccadbadbdcaacdadabacdabbbcbdadcabaaddbcddabaaadadcacbbadccdabddaadbcbddaabdaccdcadcddbddaacacddadbbabbbcaaadacadcdbadbcbdbadaabbcdbadbbccbbdabdbbbbdbddbbcacbabddcccbdbdababbdccdccbaadbddbdcbbcddbbadbacaaaaaabadaabddccdbbbccddabaabaabdadddbccbaddbcbddddcabacacdbdacdbddcbbcbcdaaacbbabdcdbcdcdddbabbcbdbbdddacabaddcadbcdacdbdadbbcdbdddccadbacddabbdbdadaadabddadddccbbbcacdbacadaadcddbaadbacdadbcbabbbdbaabcdaadcacdcdccacddccccdacbcbbcbcdabbadbccdbadbdbdcdbacadcbcaabccadadddadbdababcacdbacdbcddacdbdbacbabdcbaaadcaddabbbdcacbbbacddccaacaadccabbdbbdacdabddbbacdaabbcbcdddcccbbaccacaccabbcdddbacbdaaadbcdbbaaddbcabbbcdccdbccbcaadadaabdcadaacdadbcbdbbbabaaddabadabacbddbbbadcdddbabddbddaabaadcddbbcdbdbcccccccaabdccccaddbccdbddbacdbcabbacaacdacddbdbdcdacbabdcccaccdbaaaabacbbcdabaadbcdaccbbdcdbbbbaaacccbaaadabdcdbbdccdbdadccddabaccdcdbcbbccbbdcaccbcdbacacdacaacdbcadcaccaaacaabdbbdccbdddbbadbddddbaabcbbbbdacadbaabbbbaaaadaddacdcaabddaccadcccdabaaddacbcaddbcacdcabdacddaddbdabdbbbdddcacbbddabaabbbcddcdabddcdcdbcdbbdcadacccbcaadcbbacdccbaacababdadcadabbbbddbaddbacdddbcaadcbaddbacbaccbbbaddbaccaddbdddaabcadabbaaddaacabbaabaabcccbdbcdacbcdabababcdabbbaaadccccddcbbbcacabaacbbcbabbccbbcbabbcabbbaaacbacdbdbdddadbcbbccacaaadaadccacabcdddcadddddaddddadbabcddcddbaddacbbbccaaabbacacbacbdaddaddcccbdcacbcdcbccdababcbdaaacaabbabbcbbacbbdcccdaccababdcacaabcbbccbbaddadbbcbabaacacbdabacdaddbaadbabcbacacacabbcdbdaccddaabbcdcababbdbabcbdaabbdcbbaccadbbbbcccddbcadddcbaddcddbbdbcbacdacdbacdcccdbaaccdcabcccaddcdaacabcbddbacbcbccbbcaddcaaabaaccbabbcbcccbdbcababdabbcadccbdbbaabccadbbccabccaaacdbdbaabbcdadcccbdadcabdcddaddcdaccddcacbdcdabdbcaccdcbccdabdccbbdbaabdbacabccaccaadccdbadacbadbdadbdaacbdcdbccadadccbdcacdaacacacaaaacaababdddaabdcbcababcbbcdccccdabadaabcacacbcaacbbbabaaabbbdbacadbacbccbcbbcccacabddadcccdbadbcdaaddbccdaccaaccbddbdbcccdbdccbbaabcbbcdacaccabddaacdadadabbadcbbbcacabcddbbbabdadddcccbadabddbbbdcdcabbbdaabdcaccaccccdcbacdbbdddcaabddadcdaacdacabbcbcbabdcacddabdbbcdccbddabbbabcbcadbaccbbbacbbdaadbcdccababadcbbcdbdbbbacaacadbbcadaadadcbdddbbbdcabddbadddcabbcdcdcdcaddadbbadabbbbcabaaacbdacddabcdddaaccdbaaabccdaadabcdcdbdddcddacddbbcabdcbbbddabcbbbaadcdcbddcdccdcaabdbcabdcccbcdccbbddcadccababadabccbadcdcdaabacbabbaacdbbcacdcaabbadaacdacdbcccddcdddcdccdcabbcdccdccacdddbbdcadcbdbabbabccdddaabdcddaccaddcdbdadadaadcabdbdcddddcdacabdbdbacdcaabbaccbccabadaaadbdccacdbbcccbcadbbabdcdcdcaaccabbbdbddadabadbaababdbddbadcdbaadbdaaaacdbadbacaadbcadddabcddccccddabdbbdbcadbcaabccabbbdccddbbcddabbaccdacdbacddccbdadadcddbacdcddcbacdbacabdccccbcdcababddacdcdababadadbbadcacadaabdbccddaccdabbdcdcbbbddcaacdaccbacbccaacbaabdcbbbcbdaddccdbcdaabdcbddaddaccaacadbacccbcdaccbcccbcdccbcbadbaddccdcddcdcabbdabbbdcdadcacbdcdaacacbbcaadbaccaadcdabcdadbddadcdcbbdcdccdacabaccdacdaacdcbaddbcbcacaaaddcdbdabaddcdddbcabbbdadcccabdbdcbcdcacdddbadccdbaadcacbcccaddcbbaddddadcccabadcadcbbcbadababbaabaaccacabbddccaacdbdabbbcbaababacbacbbabbbadacdcdacccddacccbbcdcdacdaaacbcbacbbdbddddadbdccddcaacdaccdacabcddcbdbcdacccaccdbdcaacacdcacdcbabacdbbaacdcddcddbbcddabdcbbbbbcadbdbabcaaacbbbadabaabdbbbacbbddadcadbcabbcbaaccaacaabdbabbccacdaabbcccdcddbcdaccccaadbcbbabccbcddaaddccddcddcaacaddadddcdabccdaccdcaddbbcaaaccdddaabcbdddaaacdbabdccbccbcaabbddbbdadbdcabdcabbbbdaaacabccadbaabddacdcdddcbcbadbcbcadbdbbbcbdadadbabcbbbcbdbdbaaacdaaaadcacaddcdbccdacdacdccaacabbadaabaadbbbdaaacabadccbaddabcaabbdaacbbcccdcddbdabdbccaccadaacbddcaadcdddcbdaacddbcccbdbddcdcdbaddccacaabaadbdabccddabdbcdabbbabccbdbddcabbcdcddababdadcbbbabcadaadcacbaadcbdadcbbadddadcbaddcadadaabdacabacbddcbddbaaacbbabcadcbdddbbdcbbbcdcdcbbcababddbcaccdcddcdccddddabdbdbbdadbacaacbbdabdccabdbcacbdabdccbccacbdcdadaaacbdcbaaadddcdcbbdbbbadccaddcbbdbbcacbcdacbcbadbacbcdabcdddbbbabaaaaababadbadcdbbddbbbaddaccaddcddccaaadcbcababddaadccadcaacaccdaadaacbcbabdbabacbdacbdbdbbbaccddccdabdbbadcaabbcbbcdbdabbbbdadcbaaddcaacdbcbabbdabaabacddaadbbaaabaadbcbdacadbaabcacbccbaddddddcadbabbccdbcadaaddaddaadcddcdadcbcacbadaabcaabcccbdbaadcbdcddbddcccaacbbcdcbdaacababbbbdcbadbdbddcdaccbadcbadbddccdbbabdbaabbdcdaccccdbbaaadcbdddccadacdcdccacbabaddabcadddacdadbbbcbabaabbdcaaadabdbcdbcaccaaabbcbccbccbbdbbdcdbcdcbaadaccbacabdbcadcaacdddbbaacdbccddadaadbcaabccbaaabbcdbabddbcbcbacaddbcacadbddccabdadcadcccdabacbdbbdddcdbdcdbdccdabcabbaadddbccdcacddaaadadddaddbbbbbcccbdcababdadcaaabdabbdbacadccbabdbabbacddacbdabdcadcccddcaaacdadaaddbddbbbbcbababbacbdddbdacbbbbaadcbbdacbbaccbacacccbbabddacacdabbbdacbbcccdcacbabbdabacdbbacadabbdaadaddbdacaadbbcaaadcbbdcdddcaabcdaaacaabcdbcbcbabccddbbdcdadacbdabdccbddbcbadcddcdcaabbacdcdbcccccccaaabdaddbcdddcabdaaacbababacbcadbabcbbbdbabcdccadccdddddddcbaccbbbdaabbcdcccbcdacdacbbdbaaddccccaddcccddbbcbcdbbcdccdddccaacbdccdabdccdcdbadaababdacabbddcdacbbadcacaabbaddcdcadabbbadcddbddbcacabdddbccbabcdbdbbdcddbdacadaadcdcabadddbabbddccaccbcbdacdcacdabadcbccaccbaccacdccdcaadcbcbaddccaacbccabdbcdccbadbbabdcbcbbbcdbcbccdccadbadddaabbbbaadaabacbadacbabccacbbddbcdaabdccaabaadbccaccbabcacbdbcdddbbaaaadacacdbccccbcbbcdadcbbddbcbadcacadddbdcbbabcdacccbbdacbddddbdbaadcabcbcbaacbbcadaaadcaaaddcdbacddabbaadbdadcacbcaaacccaccdcbbcdbaaacbbabdabcacbcaaabdbabaaaacadbbdbdaddbacabcacbaacdaaabcadccabdddcdbabddbabdcdcddbdcabbbcccbabaadcbcacadcaaddabddadccacacdcbcbaabcadbcdbacdadbcaaccadcccccdaccdadbddbdcdbccaadadddabadabdbaaabdbdccbbcbcbbdcbcbdbdacadbbdadaccdcaaabbaaacbaccddbdbcadbcbdbaabcbaccdcaddcdcabacbcabbdbddadcbaacbbbccdcccccbbbbbcccccbaabaadabcbbdcaacdadddbaabbdaaccdadbaadabadaaddbabacddcddbddacababdbacbcacbbbdabccdcbacccabdaddcaabdccdacccdbbccbbdadccabbdcdcabcacccbdbcbadcabaaabdbcadccdccbabdabadbadbbdcbabcaccaddaaababcdaacbbbcdacabccaabbddaadaaacccdcdbcdccbbbdbacacbadaccbabbbbbbacbdcadddddcadbbcbbbdbdbbadcccbcabdcddcaddaaadcacadbaccaddbadbdbbbdbaddbcadcdddccbcaacbbddddbadaddcbdbaabcacdcbbcaddcbcdcdbdcaabdcccbdabbdcabcaaaacbccbadbacdcbdccabdcbdbdcdcddaddabcbcacbbbbcbcdacadbaabcaddbbabbcddcaadccdaddcbdddbaadbabadcaccacbabbabacbdbbbdaadadccaddabccbacdbbbcaddadbaccdbccbddcbbbcbbcbcbcaabdacabaccadbddbccbdcbcbacbdcbcdbaccccdbdadccdbaadbdbbbddbdaabccccacbabdadbcadababacaacbcbdbababdabbdacaaacddbbcddaabbbaddadaadddbccababacdbcadabcbabacbcbadddbddddbababcdcdabddacadbddabccbddacadbabdaddbbbdcaaccadcaccaabbbadcdabccdacddadcadccabbadacdbcbaadbcaaddcdcbaaadabbddacabbdcababdcccaddddadcdbaabdbbbccacabbddcdcdcdadccaadaacdaacaddcdcdbccdaaccacdddbcaddbbbcdddcaadabbbddbddcbaccdbdcacbcabaadbdbbcaddbbbcbccdabdccbddabcddccccabdbacacaccdadabcbdcbdbcbbbddacdcddcdccabaccaccbaaacdacdacccbdbaccddadabbdcbbabbacacbcbbdccdddcdcabdcdaacddcdabbbcccbbdacacadbabcbacdbbccabdbaadbacccbbdabccdbcaabacbbbcccdcbcaacaaccbacbacbcaddccbaaabacdbabbcddacddcbbadccdabcdabbbdacdcdbcadddcadddabccdbabbbbdaaabdddbdbbbcbaccdadcaabbdcabdcbbaacdcbadbcdbcccacdaabcdbcdcdbbccabbbcbcaacddbabadbbaccacbdabdcbbabcbcaacadcdddbccbbddcbbbdbbbccbbcadcdadcdababbcdbbcbabdbdbdcacadacdcabaacdccccccacaccbcbdbaacddacabdbcbbaadbcbaabcaddbcadbcbdbdcaaaaaadacbbdcadbddabcadaddacddbdbcdadbaaaccadabcadcccbbbacdabdddccbcdbbacbcababacbdaabdadddabcdbdbdbbcaadbcacaddcdbbbcabacaaaaabacbccbbddcbadbccbdddacddadabbacadbadbcdccbdcbaacbcbacacccacdddcbbcadcbcbbdadabbbacacbbaccabcdcabbbccddbabaaabcbcbbdbabaadbddccdbdbbbaaccadbadbbababddbccabdabcbccccaaaaccddabdcdbcdbbaaaabbbcbdddddcabcdbaddabcdabacacdbcadbabcbaadddbcdbcabddccadcaddbbdbccdacdbccccbbdccabcccdbaaddbbdacdcbcbaaccdabcdbddddccabbaddcdbabbdccbbabcccbaababdaccbabcbaaaccdbbabadcddcbacbbbcadcdbddbabdbcdbdbdbcbaacabdacbdddddcdbabcbaaadbdbbccaacbddddcaddbbbaddbadbdddbaaabaacdbbabdacccbaddabbbadadababcdcdbdababddcddaaaaddddadccbbdcddcaaccdacbbdabaccdbdbcddbcbcddabbacabbacdcdaddadccacdbdcdbbbcabdbcbcdbaacddacaaacdabacbdcdcbddaabbcdbcccadcbddaaddaccdaccbcccbcacbbcbabcbbacacdbbbdcddcadcbbdbddbbbddaccdcabbabcaadadababcbbbadddcbaababaabcbdabaaacdacbabddacacdcabccdbadbddbaaccdaacbbcdcddbcbdccccadbabbcddbcccbabcbcabcccdccbbdcddccdadcbcbaadcdbdbbacbddaabcacbcdbddadbacbaccbbdbaabcaaaabdcbcdbadcdcabadcddddddbcdbbabaaccaddbbdbcdccddaaaaaacccadcbbbdbbbbbdcddbdbbbcaadcabcdbdbcdddaccabcabccdbbaadaaaddccadbaccacabbbaabddbaccbabaadcccaaccbbbcdaaddabbababaaccdcbddcbadbbddaacaaabdacaccdabcbbbbbdcdabdcbaacbacbadaabcabcdadadacbdcdabcadbaacbddaacccbbbbacbdccabbdabbdabcbcadbcabcdcccddbbddbddbbcbdcaacaaacdbbcdbaaccdcbacacaaadaaadadbddcdcdbdbbdbbcdbddcdbccaabbcddcdddcacadabbddccdcababbdbaacdddccdccbabbaadbcdadadaccccccbaacbbdccbaaccccdcaabbdbcadbcbdddcbcccdabcdbadbabbaadcbbadabbccbcaacdaaaccabccddbdacacaabbdcacdbbbbcddaddcbcbcacaabbcbacdbbadbcdcbabcdbaabbcabacbabbdbadcadbccbcacbbbcccdbdcdbadcbdacdbcdcbbcbaaddcccadbbbaadabdddbaccacdbcdabdccdbaabbcdadcbddaabdcadcddbdbaadcdddcdcccccabbaddabadabbcbcddacabaddddcacdbbcaabbdcccccbbddababbbdbbdacaabdadcaacdbbbcabbcbcaabbbcbbabcdcdacccaabddaaaabadbcdcccbdabdbbdacddcddcbdabcdccbbddcdcdcdbbbcadbdcbbddbcaabbcccacbddddbabdcdcbbbcbacbbbdbbacbbccdbcdadddadaccbacaaccbdaadcadbdcacdbccadbddacbacccbcccbcdbcdabdbacbcbcadadabcbbdcabdcddcaaaaacdcccbccdcbdddcccdaadbcadcadbdcdaaacaabdaabbcccabbccbddcdbbdcbccdbcbaabdbcddcacdbabcacdcbababaabcabcdbbdddabdbaaaaccabdadaccbdcbabbbdcdcbcddccbcbbbbacbbdabddbdbbdbbbadbcdccccadbccbaaaaddbaccdbcaabbbcadaabddccbdcaaddbbbbbcbdbabadaddcdaaccabaaabbccddddcdacabadaaabddddacdbaaadbccbbcdbcbadaccacbabcbaddccabaadccccdbbddcdbdacbddaacdcbdbdbdadddccbaabddbaabbdbacbcbbdbcdcdbddacbacdccdbccddcdcbadadbdccabaccbccaabbadaaacbabcdbdbbddcacacbccbdbcdbcbbcdadbcbdbddbabcccbbdddbbbadcbdbdddbcddacbbcdccbcccabbbadccbbddddbdbbdccdddaaaabadcdbbadadcbbccababcabddacdbadacccadddaaccbcbccdabcacadbbaacbcaabccdaddcdbadaaacababdcdbbddcddbddabdbbabadbcccdcdcdacbadaaaddcccadcbdaadddadaacbbddabaacabababbdbcdadadaccabadbdbddcdccbcbcaddddbddbcaabdabcbcbbcbbdbcaccddbaddadcdaacacaadcaadadcddacabacadacadccbbdaaccdbcaddcdbbcaaadabdcdcbcadbddaaaccabacadaddabbacadcddabdcdcdaccbbdaaddacdbcadcbbbaacbdbcbbddcdcacbcbdddccadcaccbaddbbcdaadbbcabcccccdabaccabcbdbbbabadcbdaadcbacddbbaaadadabaacdbbbcbbddbdacdbdcadbbcccbbdaddabcdbccadacabcaadcbbbddabdcdcdbbadabaababdacdbdabcbcdcddbbcbcdcbbbbdaccddcbacdaadbacbdacaabdddcddbadbcbacabaacbccbcddbbdbcacbdadbdccabcaaddabcbaddaddaadaadbdbcbacadcbdadaddadccbbcddbdbdbbcbabbbbddbcbcabcacdccacbccbbadcddbaacdcacdabcbbaaaabcdcddadbbacdccaaaabaddbbbcdabcabbcbcadbbddccdccbdcabddbdcccdbbabcaabaaaddbbaabcabccdddddcdadabadcbbcbbbdcadbbbcbbabdcccadbdacaccaddbccaddaabbcaacacbdabbddbcdabbdbdabcbcdbdcbbabbcccadacadcddbcbbcbcbaccbabdcbdaacbcabacacccddcdaddbabbacbcdccddbabcaadbabacdcbcbbcbadcbbaacdaabcadccaaacdbcddabccdcbcbcbbbcdacbccbcdcbdbbbccbdabcbcabcddbaacccdaadabbbaddcbbdddcaaadcaadaacbacbcacdddcdcbdbccabadbcadddbbcbbacaaccbaddadcbdccddccdcacccbbccdabbcbbadbaddaadddaabcdbddcbabadacabaadcacaacbbdcbabcbbdbcbdadbbbbbccdadacbbaddabdbcbccacbbacdbaccdaabbdaabaccdcadadadddcacdbbaabbbcbddccbcddbacaccdcadbbddbbaacccaccaabbddcaadccddbccabacdcacadcaacdbabcacabdaaacdcadbddbdcadddcdddaacdadcbbbcdababcadcdbbcbbddadcabdacbdacabadcdadadcacadcbdacdabacaacacababdccdaccdaabcdcbcabbccacdaaacabdaacccccbcbacadddbbabbacadaacbbbacaddbaadcbabdddcdbaccccaccaaccccbcdbbbdcadadcdbbbbdbcbabdbaabbcdccacaacbadadacbddbadbbccdddcbdbbbdddbbbbcbaccbcdadbaacbccadccccdbbabcdabcbadbcaccabdaddcaaabdcdacccdccddadbdbacccbbacbdcbadcbbcbacbccccdcadabbcacdadadbdddbdbcaccdabcbcdbdbbcbccdcbdccdbacadcbddddbcbabcaddcddccacdbcbdbdbbbcbbdbcbacdbbcddccddbcaddcdbadddadbdbadcdddcabcaadbccdcdcabdcdcdbdcdaaadaddcaadadacbbdbbbaaabcdcacbaacbccccabccaabbadadddbdacdbcdccacacdddcccabdacbbadaacaabdaabcbbcabcadcbacbbbddbdcdcbcbacdcaabcbcdabbcbcacdacacdbdaddbcaddbcaaacadabcbdbcbccaccbadbddbaacccdbbabaddabbabbdcadccaddbcbdddbbcccccddccdaaacbdcddbdbdabcdacccdaabbdcaabdcaaaccabbddbbaacdcdabbbadbaabcaaadccabbbdbcdbdcadaaaadbdaaccbdddbdcbaaccbcdbbaaddcbcaadacccccbcbcdcbadabcaaabcadddcabdaabddcbdbdadbddcddabcadcdabaadcddaccccacaaaacbcbbadbdbadaadbdbdabaacdbcbddcdcccddacdddbddbaddcaababccaabacdadadddbbdaccaabbccbccdcdaabadaabbcbcdabadbacabdbabcbccbbcddcabdaaccaccdcabbaaadaadacbcdddaaccbdcdaadbcabaaccccdadacacbbcdbabbccbbddaababcbbcdbdcccddbadbcddabddcddaddbcbccbdbbcbcdbdaacabaaccadbddbcadcddcbadabdbdaddadcccadacccdacdcadaccacdddcadbaaaaccbcacbcbcdabbabcbcabadcdbababdaaabcbbcabdcbdcbbcabcbbbbabcacbdaddaddcbaadacacdddbaddcbdbcbbdbcbbbdddbacaabbcdbadbcabbcadabcacdbcdacbbadaaaddcadddbaccbacdbdbcdcbdabbbbabaaacaabbbbccabcdbdcccdacadccacddbbcadbbbaabbcabcbbbabbddacaaabbddcccbdbdbdbcadacbbbbabcabcbdccdaabbabdaabddbbacdacaabacccaddadbcbbbbadabdcbacabcddabbcbdccdcbbdcbccdcbdcddddbbcabcadcbcdacadadaacdbcccaaaddaaccddccdbbbddccdabaaccbdbacabaaadaccacbaacdabcdcccbbbcdbbcdccccabbcabaabcdbaadccdcadaaaaabddccddcaaabdaadbbaadcdaadddcdacddaabbcdddabcadbdddcdcadaadddcdbddabddabdabacbbdcdddacdaaacbdcbaacbdaccdabcbdadabdaaaddbcdacabbaababbbacdbacccccccabcbbcbacddbcdabcbaddabdabcbaadbdbbacdaabdcabaddbcaaccddddbbbabaadabaadaadbcddabdbcbdcaabdcbcaabbdaadcdccdabdaadbcddbaabdaccdddadbcbcadddbcddddbcabadbdabbabbaaabadbddbcadbbdbdbcdaabcdcbbcabcbaadcbbcdcaacccacbbabdbcbcbbbadcabcdcaabcdcbbbaabbabacbddccbbdadadbaabbdadabdaadbcacdccdbbdcdbcbbabdadaaaaaabdcdbdabddcababdbbdbcabcdbdccbcdabcbddbbcaccbbcbacccaacacbdabbaacccdcddcbacaadbaadaaccbdddcdbcadaccdccaaccdacddaccbdcdbcbbcdddcbacddbbcaaaccdbaccdcbadbdddbcdbbddbddbcbcabcadcdbcbbcbddacbabcdcbabcccdababdcadbcdacddababbbabbddccbcdaabcbaccaabdbcdcdacacdcaacddabdacdcabddbcdccbaddcdbacadcabdaddadbaabcbaccadcbdccbdccabbddcacbccacdddabacdbdddadadbccbbaccbcbcbcbdcaacaaacabdcbcccbddaadcccaaadaaadddadcccbadcabaccddcdddadcbcabbddbcccccadcbdcdbdabcbdbbabccddbbddcbadaabdcbbaabddcbaaacbaabbcaddcbbdabcdadbdbbbabbaacaabbbcbabcbbbddcbadacaabcbddccbaaabbbbddaaabacadbcdcbbdcadaaabdcbbaaccbacccddcdaddddcaddccbbbacbbdacadcaddbcabadcacddbdccbccadddbddddbdccdbabbdcbdadcaccdbddbbaabccdbbcbdbcabaabbbaccadbaccaaabdbbaddcbbcbabaacbbcadabcbbbadcbaddddaddbbbdcadccadcadbdccdbabcdcddacbcbdbdbdcbcbbcacaabcbcdccbdccbcbbbccdbcdddacbcadddcaddbddccaacbadabdcaccdcdabdccbccdabbaacdbbacbadcbdbcdbbcbabbbcbabdadbbccdddcbbcabbbabcdcdaddbabcbabbaaadacdadacabbbbbacbcddcaababbbacccbaababddbabddcdabaccdaaaacbbccabbccdcbaadaadaabdaacabdccbaabadcabdbdbcaadabdaabacabdcacacbcdcdccdcdaaaabcbadcbadcadaaabacbcbccaabdcdbcadcbaccddabaddccabbcaaacccbaacaaaaaccbbdabdaddbacacdcdbdbcbdbbdcabdadaabdcdcacdbdabacbbacaadacacabccddcccdbbabbadccaabdadcddcabbbadddbcbaccbddbbbcacaddcbadbdcbabbcadbdcaddccdbdcccdddcacacabcbacabbccabacdccbbccdbbcaadcdccbdcddacabcdcdcdaccdbdcabdbbdcabbdcbbbdbabcddcaccbdcaddddbcbadabbdbcbacaadcbcdaddaaddbdbccadcbddcadadccacbacbcbbabdcbcabcadadbbdddbbdabbbcdcccddcddbbadaadacbabbacaacbdaacdadadcaddaccabadaaadabadacbaaadccdbaaadaacabcbddcdacabacbaabccbcdcdcccdbdacdbcbdabaccdcbaddbbadbdcbcaadcadabcdcddcabaddcaddbbcccbdcbdbbddacdddbabbddabbacdaddbcbcdbccbcdabcadcdbdaddcdbbdcbbddbabddacacddccabcabbccaabacbbcbcddaddcadbdbcabdcdddbdbbdadaccdaabdbadadbccbbdbdcaccbbdbdcdccbaddbdbdaacdbbcbbaabdabcadacbccbaacdddcbcadaacbcbabdabcabbdadacaaaabbcccdbdbdbdcadcdabbbaccddbabaddcccdbdddbccbaccbdddbcbacbdddadabadbdbbcaddbdccdbcbdaadacbbabdabbabbbababcbccdcbbcddcacbacbaabbdacadbcdbddbdcadacaaabcadadbcdbbcababbdcddcbbbbcccbabcbcbbdcdbabdaabcbaaacdbbddabadbabbbcaaccacadcaabbddadddbddaddbbbabbabdbbacabddbababacddcccdababaddcdaabddbccaacddccbcccdbbcbcddabdddaacbbaaaacbdacadbdcdcbcddcdcbbbdcaccadcadbcabcbbdadacddaccbaabaaacaadadddbbcdcbccccbaaddabbdcaadcccdddaabbacdccddddadadbaddaabdbaccdcabccabcddacaccccdaccaaabccadcbbcaacabbcabadaacdbcbcddabdddcababbcbdcbcbbcadcdabbaddccdddaccdacbaabbcbcdaddccbdadcccaadcabbdacadbcbbabdccdbbcdacabcbdddbdacddccbcaddddaccbcabaacbacaaaadbbcdcadabbabdbdbbabbcddbacaacabcdcbbcbcbbaccdbbcdbcddcaaabddaabcdabadacbdabbbcdbdabdbddabbbbcbadabadbbbccbcabbaabdabaddbccabcdbcbabddbbcdcbbdadcdabddaacdccadcadcdddbcabdcbdccacadadbcacaaaddcbacbbdbadbaaabdcacadabaccacbbcaacabbbadcbbaacddaadccbcadabbcdbabbcdacddacdddcabaddadbdaabbddaddbbadbbcacddacbabdbcbdcaddbbaccaccbbbacdbbcdaaddcccbccdaacabadabbccbcdcbabadbdbdcadabbcbcbbaaddaacabcbbbbadacbaccbccabdbabbcabddbaabacdabadabccddbddbadcaacddbdccdcabaaddbdacdcaabdcccdbdbabdcbddabbdbacdbadadcdabbbbcdacabbcbaaadccdbdcdbbdcbbbcbacacdaacabbabcaccaadbcaddbbbcdabaddcaacddbddcabacbcdbbdbbadbdddbcacacdcadcbbacbbbbcabdacccadcbbdcabccbdbbacdcbbdaababbdbdcabbcdaacaaddddaabdadabdbadccbcbbaabcdddacbbccdcccddddcadcdccadacbcbaabaabdccabcdaddaddadbadbbcbddaabdccdadbdbcabbcbdcaadbbbabbbacaadddaabadaaadccdcdbdaaabdbcbadaadcccbdbbabaacabdbacbabcbbadaccbdbcabbaadbdcadcadabdbadabbddcabadcabbbcaacbcbbdbdacddacddcaddddabacbddbacbadabbacadaaaadaccdddcbdbbdccbacccbadacdbbdadabbdbdacaccdbcacadcbcdacaccbdbcdcdabddaacacdcdccaaaccddbabdaadabddacabdcdaacabccdcbbdcbbdaadbadbadddbdbabccbdaddacdacdccdacbaccbbadaccabadadbcddcdcacbaddbabcdaacacadbccaaababdbcabbabbbdcddaabdbdddaacdcbdadadcdddbdddcccabbaabcaaaaddcbacbddaaadbdddaabaacdddddacbddbddacbdaaacabbabadabcdabcccddbbbacabdcdddadcbdcccdbabddcdcacdbbdcdccabaabacadbcbcbbddddddbcddaaccccaaddaabbabbdbcbdcdbccbbabbbcbdabdacadbcbcddaacdcaabcaadacdaddcabccccdcadccadabbdabdaaaccbcccdabcbaadbcddccacaadbaccbbabcdaddcbabdcadaadcdbcddcbdddaaadcbcacbbabbdbbcbcadbaadbbbacdabbddaaacccadabbcbaabbcbdbacaccdbbdbadacbabaccdaabcacdcdadccddbcccbbbdabcdbacdccdcbdabcdaadacadbdacdbcbacacacdcbccbcbdbabdbbcddbbaddccdddcccccacbcbccbadabacadadadcaadcaccdbaaaaadbbabdbcabdcabcaadbcbdddddbdcdddcbadbddacacbaaacddcabbdadbcdabbdaddddacacbcbacdcabdaabcdccbccdbcdcbdababcdbbdadcadaccaaddaaadccddcabdbcdbcacdacbcabddbbbaadcdbcbaccbacaaaabaaadbcabaccaacaddaadabdccbdcbbcbaaaadcccbacaabbadadbcdcdabbbbddbcccabaddbaabbbcbbddcadaabddbcddbaadcddaacbaaabcdbcbbdccacbdddbaacccabdaaccbbbdbbacbdcbbddbddcacabdcdcaabddbbadbbdbaacacbddaabadaddcbdababdabaaadbdbcccbcdaaddcbadbdcccaccccbccbabbbdcacdccbdcbaacccbcbcacbacdacbbcadabadabbabddbacabbacabbbbcabcddaadacdadacdccabacaacccaaaccaaddaaaaabbdadbbcaacabbbacccddadacbcacaddabbbdcdabcccdbddcabccdcadbdabdadabddacdbbacdabcaaccbababdcddcccbadcbbcbcbcbbcdaccbaabcdbadddcbddcbdaadccabacabbddcdccdbacddcaabdabbcbcddbbcdbddbdadadaaddbbcbdcadbcbcdccbdcdabcdbbacbcddacaaccababacbaabaaacdadccccbdccabcdaabbbcadcdbcdcdadbcaadcaabbcbcbbcabdbdabccabcaaaadcdcddcbcbaabbaccccccadbaaabbbbbbdcaccdaacddddadbbcdbadacbbddcabcaaacbacbdcbbbdccbccdcabadbdabadcdababbdbabaaaaaacadbbcacbccbabcdadcbacbccdcbdacdbbcaabbcdacdcdccdabbbbabcccdcaaddbbbbcbdbbbcbbbabdababddaabcdccbbddccacacdddddadcaccdddbcaccdabdbacbdcdcbcadaddcbbccacddaccabddabbacdaccbaaccbcbbbdabdabbcdccababacbbccdcdbccccaaababcacbdcdccacbdbccbababcddacaadbabdbdbaccdbaacbbbbcdaccbaccbaddbcacaabdbdbddacdcdadbbdadbacbdbdbabacbcdcadaaccaaaadccbdcdadcbabacdddbabcabbccddabdbbccabadcadadccccdccbcbbcacbccbddccddcdaadbccdbcdbbabadaacbbdbadadacbcddbcacabbcabbdccdbbbadaaabdddddddabccacdabadbcddcababcdbdbbcdabdabcbdddcaccbacaddccdcdabbaabacccabddaabbdbaccadcacabbbdbcbabdcbcccbdabcaabdcabcacdabccbcadbcbbacbdbbadbcacddacabcccdcabcabacdbdbdbdddbacbdcbcdcaababcdabbdaabaddbacbadaacbacaaddcbbabbaaacdddacddddacbbccdccbacaabbdcadbdddaaacdacbcadabcbdabddacbbbccdbddbdadccadcddddbddaadddaadacbaaacdabdabaabdbbdcdccadbabbbbcacbaddaaccbbcadbbbdddbabadbacdabaaccbbdbcabbcbdaddbbdbbdacddaabdcabcbaaacabaddcdccacaacbbcbcaaddcabadcbbbadcaadacdaaaddddbcbbccadbbcdbdcdadbbbbbbbcacbdbcaacacaadbacbbccbaccdacddabbdbbbbccbcbabacdbdbcaababcdcadbbccddbadadcbccacdbbaaccdbcbccbadaddbbadacbaaccdacddaabdadbccddcdccccabaccabbbdbbcdcdbdcbcabcadadbaccddacbaddcbcccdcaaddacabbbddbbdddcddaacdaddcdacbbdcddbbdbbbcddacacaadabddaaacccccabcbcdcaadbcdadadcccaddacccaabbbbabdcdaadddbcdaccadbcddcbbabbcbcbcbabbbcdbcbdaabbcbdcdddbdaddcbabcbaabcabaabbbadbabbcabdcbccdbaddbacadcdddabddacbbddddbbacacdabcbdabadacdbcdbcaabdacaacbbdaabddacdadccccdcabcaadcbbddbbcabbbbdcddcaddcbdddcdcaaabbccacacdbdddbddccddcdacbddbaaadcddaaccbbcadbabacabaabcdcacaaadbbdcbaadababddbccccaaadddaaddaaddccdbaacbbdcddacacbaadbaacbcaacbaacbabdbcbbadddbcdabdccddbccdcaaadcaabcbaaddcadcaabadbcdcdcdbadcaacccbccaabbaacaaccdacbcbabccadcbcdacccdabcddcaccacdbdacaccdcaabccacbaaaddabbdbddbdbcaacbabacacdcdaacbadddaacccabcaadcabacbadabadaabcbdbcadbcccacccccbcdbcabdcbdcadacabbdcbacabbdacbddbddbcbdddacddbbbddaaadbdbcadaabdabccaabadcaadcacacbdcabdbbcdbdcadbdabdcacbaacbaccadacbcccccacaabddbdbbcacccbdcddadbaabcbdbbbdabadabddbdbcddadabbaccdcddcdcbdbccbbadadbddbdcacbbaababadaccbbbdabbabdbadabcbaddadabdbdbdcdaddabacddaccaadbbbabadaddabdacacbddcbdbbddbacadabbbccccadcdccdaabaacbacdbcbcbccaaaddccccbdbdbbacddabcabacbdddabbadbabcbdacdababcbcbccaaaacacdaaaadcabacbdcbaccdbbaabaaacabacdabcbcdbbadbddddbbaacaaabaddaacdbdbaadcccadccbaddadbbccacdccbdddccccacacdbcbccaadbcbcaaabcaddcdbdcdbabcbadcccdbbcdcaacdabcdcddcdbaacaaddadacacbccddaadbdcabcbdddcbcabbbcbdcaacadbbcdabcddacdcdcdbaddbbaabaacbddaddcbdcbdbbbdadcbcddbcbdcbbababcbadccdbbbadbdabacddddbdccbddcdaaaaadcbcabdadbacdcbcdbcacccdcdccabcbaaacbdcccddaaacdcdbbcbcbadaacbbaccadbbabbbbbacbbddbbcdbaabddacbbcdabcbcbbbcbbbdccadddabbbcbbabcbbdbbdccabacdddbcbabdabbcaaaacaabdaccdaabbdccdcaddbcbcbbaacaaacdccadbacdabbccaaabddcbaadcccacddcbabcabcdabbbccababcadbdadaddcbadcdabbaadbacbcbdacdddddcabaacbbcaccccabdbcaabbbacbcbccaccaddbccabbdddcccbdaadcdccdaacabaaadbbcaabbdddcaddbbaabddcadbbaddbcbadbbaacabdccacbccccbddcdabdbccdcaccacdbaaddcaadcaaddcabdabbbaacbdbdbddbaccadaaaddababcacbbacdbcddbcccbbcadddbddbdbadbbacadbaaadbabccacbadbccbdddcdadbcbcbcabcccccaccbcbabaccaabdcacacbacabbadccbbccddabdcdcbcabaabaccdabcacddbcabadbbbdbcbbccbcbcddaaacabcadcccbbbcccdddaabdddcbdddadbbcabdabbccacbcadabddccddbccaacbddccdacbdbdcccdcbaaccdadccddddbbbadadcbbbcbacddccdbbddaadaddbcbcdddcbbbabbababdbbddcbbddcbdddccaddbbdbbbdbddcbcbbcaabddcacabadcdcdadbcbcddbcddbbddbdaddbcadcabbccccbbbadbcbbdaddcacdbaaacbcbbccaacdbbdcabbabcdadcaccbdcabcabdcdaabcbdacadbdbbcbcacbddcccbdccdddbddaccdabbccabcbabadacbdbbddabcbaaddbbbdbdacaccbcdaccbbdadddadcacdcdcdbcdabacbddbddaabacdccdcccdacbcbbcadbcbbbbbaadbacccacdabbbcacadadcadbaadddacdabacbadabddbadaacdddaabdccbcdabbababdddaaabdadadbaadccccadadcdcdcbcbcaaabdaaabcabccbcaabadbcddcaabcbdabacbcbaabddaddbabbdcccbaadcadddadbcaaacdcbbadcdcaccdddaadcbcaddbcacaabdcbaadbdbabcbabbddadddadacacbcbddadcbcaccacabdbaaabbbcccaaddaacbcdbcbcdcbaabbacbbadcbbaacdabadddadccbddbcddadbcaccdbbbcadbcbddcdbabacabcbbcccbadcaaacacdcacddadddaadaccdaababcacdcbbbcadcbabcccdbbcdcdcddbaaabababbcbbdddccadcaacacababacaabccddbaacdbdbbaabcdccadacaabaadcabbcbaaadacdcaabbcdbdcccaccdcdccabcbadbbacdcddccccbcdabbadcaabbbbcdaaaccddabbcbacdadadbdbbccabbacabccbbddbcdbddcdcdcaacbdcaaabbdcdbbcdcccccbcabacdbbdddcacdbbbacdddaccabddbabcaadacdcbaacbccdbdadcbbdbbbcacabcabcddaabcbbababcdaadddadaccdbcbcadccddcacaadbbadddcdddbaadcacacbbbcdbbbcdcacabbadcbdbcdbbabaaccabdbcbcdcbdcbaccbcadbbacccbababaaacababcccacdccabcdcabacbdbcaacaaabbdbcbdaacadccbababdacbcbacbadacbbcbdaddaadbccddabcdcabaddcacbdccbdbbcbdbdcadacdcbacdadbdbbbabacaaaddbbbdacccbadaccbccabbadcadaaadadbaabcbadbbbdbcbdccacaadcbdbaaaacdababcbbcacaacaadddcacdcbabddcaaaadccccbcbcccdaadacbabbdbddacdaadccdcabddcaaccbdaabddcbdbadbddaabcbbcaadbcbccabcadcadbcabaddcdccdcdacabdbaaddccdadbbcbddbdbaccbcadccdbbdacbbacdcbacbcbbbcbdaaacadbcbacbbdaacaacaacbbbdaacbbcbdabaabbbbcdcbabbbbdaccaacccdddddccbdddbbbacdcbbaacadccabcdacadcbcabcbaacbabcdbddabdaadabbdcaacbcabbaabddbaaccdccbccbacacdbbaacdcddcbcccccccbdbddcbcddcdbaaabdbabcbbdbccccdccdaddaacdbbdbabacddbaaddabddadaadaadbbdacacababbbddbadacccbbdaabbabdaadadaaabcabdaaacdbcbdcbabcbdacbbdabddbabcabdbccbaddbbddcaaaaabdddbdaadbdcaddacccdabcdaaddaacdcbdaadcbacabcddaccadbdbbdcbcdaacdcdccdaadccbccaacbdadcaaaddddcaaccacadadacbacaaababcdbcdddabccaacddbccacbccbadacbabdccccbbcbcdcadbacbabcccbdabccbbcdcaddbabdddaadbbcaddaaaddcddadacbababcbccacdadadaddcccabacadcdcadacacbcdbdacbbbcabdcacaadbcbaadadbddcacbdbdbadaadaaaacabddaaabdbbdbbdbccdabbadbddddbbbcacbaabbcbcacbccbbddcbbbbdaaacdbbbbdacacdadacccccbcdaacacadbbdbbbcccaababbdccaadbcbbbccccbbadbdbccacdadbbbcadcddadacbdcdcaddaaddadcdadabadadacbaccacbabddadaddabddcdabbbaddddbbadacdccdcadbbddaccbcbaadcdabaadcabdbacbaabdcdbdaaddbddbaddaacaabdbdcdabbcbbaadacbdaacaabcccbbaadddbacaddcdcbddccbbadbacdcdcccdaadbddacaaccbdacacaaaacdbbddbddcabbabcdabddbbcadababbcdaaaabdbabcdabdcbddccbaccdbccadcdacbddabdcaddddadccaccbadccdbccbaababccadbdbcaacadbacadcbdcdabdbbddbbacccaadbbcbdbcbcbbcacabdbbcacbcaadbaabbdaacdbbdacccbbcdccdbbddcacdccbdcacabcdccaaaccdbdbacdccaadacbccccacbdabbbcbaacdbdcaabdbaaacdbdcdcbacbaabccdbbbabbdbcabdcabcacacadaddccaccbcdddabdddbdcccaaadaaccacbcdcdbacdadabbcbddababdaaabbdbdcadabdbccabbcdcbcccadabbabddcbdabcadcbddcddaabbaddcbccdaddabcabddcddbaaabccbbcbcdcddcaacbcbacbdbbcacdadbdacccacdcbcddcdaadabaabcabddadaddbabcacbaaccdbdbcbdbdadddcadcacbbcadcbcccdbdacbdcacdcbbaaabbbbccabaacaabcacbabddabaccdacaddcabdbacbcbbaadcdccbcdccbdacacacbcbdbddacccaababbcccacbbbccbccbbdbdddbdacbcaadbacdcccabcaaaaabcdacaccadbddcbbaaddadacbcaacdadbcaccabdddbaabacddbcddbcabaccdadccdccdbcdcdbdbcaacccdabdadabacaaaccddabdabbdacdddaacccbddacdacdaadbbbbcaabaaacaabaddbdacacbcaccabbdbcadbcccdbdcaaabbacdaccdbbadabbdccbdcddbadabadcacbbbdcdbcaddcbbbdcbaaacdcbabadccadcdaccaabacbcaadcccddddbbadccbccaadbbcadcbaaddcbdbacdccdbdcbdcdcacdacbcdabdcbbccdcaacdcbaadccbdccadcabbabbcdacddbddabccdacccddbddaabdbbabacaaaadccbcdbabadcdacabadcccacbbbbdcdcacadbcabccbabacbcdbccdcabacbacddcdcacaddadcabccccabbddccdcbbbaaddbdacdbdacdadaddcdbdbdcaaabbdccbdccbaabcdbadabdcabbdcadbaadbabaabcbcbbdcdcacbcaddcdcdabacabacddcddcbcdbddddaacbdcccdcadcbbdcccadcaaddbbdaabaacdacdacaaadbdaadcddaadddbbcadbcbbbabdcdaabdcbcdababdccaccdabddbadcacccbcaadabcacccdaddabcbcddbcabdbdbcbdbcccdcbdddadbacabacdbaddcccbdababbaabccacbababbcdcdacccacccabaabccccbccbcddaacdddabcdccabcaabdcabadbbdcbbddaadcacbadbaadacddcacadbbdadbbbbadbbbdbccdcdcbcdabdadddcdcdccaaaaccacccccccbdbbbabdbdccbbbaacccdbcbabbcbbabdabbababaaddbbdbbadcbcddddddbbdbdbddabcaabbcaddbccdccaabaccaacbabcccbbababdbbbbddcdabcbacdbbdaddccacbadaaddccabccbaaaddacccbbdbcdacdcacdddaccddbadadbacabadcaadcabadaabdddcbadaadcbcbbbadabbbbbdcbdadaaacaccdbddcddcbbdddcbcaacbabdaadcdbbcadcbccabdcbcbcccbadcdabbadcbaacadaacdacbccbbadcadbbbcbacddabcaadbdcaacbcdbcacadabcadccdbcbdadcabdcbcdbdbabbccddcaaaddabdcdcadbccadcdbaacbbbbdccddddddcaaabaadabbacbcbcbaacacdbcacddaacabbcbbbacdbbcdbabbccbdcbcddcbbaaacccbbcdcaaadccbbdcbdcbdbadcbaddcdaacbccacaabccdabaaadcbddcdacbabdccabbbdbbcddcbcdadadbccacddcacbcaacbdddcbbddcdabcbbdbacadbcddabccbdcadcaabdcddadabaaddbdbdadccbcabacdabcaaacaadcabcbadadbbbccacbabcadbcdbcdaaadddaccbdddbdbddccbcdbdcbdcabdbbaadbacdadccdcbddaaabcdbadadbcbadabbabcaddbabbdabaabddbcddcbaacbbcbdccacabdbadbadcbcabcdadaaadcabbdbbcacbbadadaccabdaccdddcadcabdbcabcdadabccbaadccdddaadabdabcddbbbcbcdccdcbdadbddcdacaacbbdacbcabccababdaccdaaacdadaddabdbbcaadbaaccaccacbddbbbdbbbaccadcccaddbadddbddacdabbdbabccbbaacabacbdaaacccddcadbcdadbcdddbcabddadabccacaddcdcaadddaddddcbacacbcbdccdccdcdddbbccddcdbbdbcadbddaadbdadcdbdacbccdbcdabbadabdcabadabdcbdcdbbaddbdadacbccdcacccbcdcaadabddaaacbccdabcccdbcbaccbdbaccdbcdaddcaaacaacadcccbcabdbdaccbaccaaadddcacbccbaabbcbadccdabbaacaddbbcabbcccaddbacbcbbcdcacbcadbcaabadacabdaadcdcdadbdcbcbbbddadaabaaaacbabccbadabbdddbaabaacbcabcacaccdccbdbbcdbdadabcdaddbbdcaababaccaabccadaccbaddcdbaddccbdccdbbddddaacbabbbadcddddbcaccbbdbaabbcbdadccdadbbdcccaaaccdbdaddcddbaaaddbcbabddaaabacacbccbbadcaddcadbaaadadccadabdacbacdcdaabdabcbbaadccddcbbcaacdacbcadbcbbcdaacdbcbdbdbddcdbcdabdaddcdcbcbbaacbadcbadcddaadaddbcbadbaadcbdcabacddaaaadbaaadcccaddaddbacaadbbbdaadddadbdbdcddbdbbadbddbaddabdddaacddcbbcabdbbcacbabbdddaabcaaddbccaabddcadbbdaacdaabacbcababddbbccdaabdaadaabaaaccdcbbaabdabccbbdaaacdbaaabdabcabcaaacbacbdadbabcaccabdbadcbbabdcbdababaacaddcaaabbcaddccbddbddbccdcbdcadcdcadcacddadddddcdaaddcbabaabbdccddcabababdbccddbbccbdbdcbadbadcdcabccdddacdddcdbcaababaadabacbabbacbabbdabccadacddcbdbbddcbbdccacdcdddaccdadabaacaaaabbadacdcbddaadcbbddbdcbcbcbdacaaccaaadbdccccabadaabbdabacdbcddadbaadbbbcbbcbaddaddbacbdbbaddadbaabcbbbbdbacdcadbdbbdcabbdcddddabddaaacdddaccdbcbaccabdbbbdcbdcbdcdbaaacdcdbcbdbadacabdbccadbbabbccbacbcddbbabdddadcbaabccccddccacbccddacadcdcccdbaacdbccaabbaccbaaacbadcacddccbaccbbdcaabdbbabcbcbacbacadaabddaabcaabddbdcdbabacdcddddcbbbaabaaacbcdaabbbcdcbacabbbadcdcccaadccbacddabacaccacdabbbcbdabacadcbacbccaadbddaddaacbbcbddddaabbcccccaacbbdcabcabbcbbbbacdadbdcbdbaccccddcdbbbacdbcaadcdbabbcaadccdbcaaacdcdcccbcbabccdaadbcdaaaadcddaacddacbadcacadbcbaabdcadbdbaacdadcdbbcacabbacacbdaaaaaadaadbacaaadbddbaabdbcdbcbcaadbcdcdbccacadcddaadbdcccacbacaccbcadbdccbaadaccbacbaaabcbdccbcadaadbcabaaaddacbbacbabacbccdccdacbdabdcacddacadbadbadcdbabbdaadddbccdbcabbcdadaadbdcacadcdbaabbbbbccccabadcaddcdadbcbaaacbdbadbccbaadacacbbaadcbccdbccbdccdaaacdaabbcadaabcbbdaaadbcdcdccaacbdcadbbdcbddccdcaaacbadcbbbaababbbadcbdaabacbccddbdbaaaaddbdccdbdaaabbccadcbbbdcdabcbdbdbbbdaaaaddcacdbdacdcabccbcabdaacbacdcdcbcadaaaaadcababbadacbadccdcddbddbcabacbcbacbbcdcbcddddbdbabcacbccaddacaddcdcacddcdadadcdbbdbbabbbdadbdbccaabacdcccbbcaaabcccbbcbcdddbdcdbabdbaabaccdbbbcbccabacbaadadcddacabdcccabbdccdcbabacddbbbbddcaabbbdacdaacaadccddacacdaababbdaadddadaabacbbcdcbacdcabadaadccaacbccdaccdcabdbabbadcdbdbadaccabadddbccbcbacdbdacababbaddcdddcddcaccbbaccccdcaaaccdacabbcadcddadbbbbdbaabdcccbbdddcccacaaabaadaacdcdcaadccdbbbdcdabcadddccdcaadaccabacadbcbdacdcbbababccbcdbdadbadddcaaaddcdbbdcaabdbbcdccbaadbaadbddcadaabacaaadcbddcdbbdcdabadadcbcdccddacccaccbbdbabdabcbdacdddcdabccccdabbbcccbbdadbaabbdadbaddbdbbdaadbdbdcdbaacbbdaadaabcbadccadadadccaacbbccabaacdbdaccbbdbddabcccccaaadcddbbcbbaccaddcaadacddbdddbcdabddacdcdcbbcdabdcadcacdcbcacbcdccccbdaabcbaccddbbbbabcbccabcadacbcdbdabbcbbdadabbabbacaabdaccbabdacdbdacabdabcdccaabdbdabccbabacbaacacccdaacadbaccbcacddcacadcdabddcddcdbdcbbbadcabadcdccdadacabcdbdbbbabcaadaaadabbbcbdbcaccadbabbadccbdbbbdacccaadadccabdacbbabbbaccddabdccbcadbbabbdcdcaabadbbcddcccbaccbdabdadbcdacacbadbadbbdabbcdbadaadbaadbcaaacbcdbbdacbadbacbdbabacadbadaddadcabccaacabddbaccbbccbcdaccbadaddddccbaddaacaddcbdcddbddabababbdddbadaaabacadbcccabacabacbdbdddabbbabaddbbcaddcacdcbdcdadadadadcdbdddbdccabdbdbbabbdcbdcabbdcacddadcddbdcaabdacdcdcadbbddcbabddadcbcaccaccaaadcdccadacdbbdabacaddbbaccbcdadbacaccacacbdcbbbcaaccdddddccabdbbddccdbaabadcccdadbddddbacdadabacddddcbbcbddbcdaadbbacaabaabdacbbacbadddcbcadbddbdddbaabdaadaaccdbdadabbdbacabdbccdaabaabaddacabdaabbdacdaaddbabbacbcbacbbcdccdccdbcadbbbcbdaaabddaadcaddbdbdbcddccdbbccbaacadaccdadbadbacdddacddcbadacddbbbbacacbababbdacccdabbddacbdaaabdaacccdcdbaabdbcdbcccbabcadacbbbadbddbdacdbddddbcbdbcdcaacabdccbbdccbbbaaacddcccadbdcbdbdcbccccdaddbacdccacdaabcabbabbdcaababdbbdaccdbacbcabbbcbcaddcbccbcaaadbbccdccaacdbaddaacdbaaddaaacdccdbcdccbdbdabacabdbadcaccadcbdbbddddcadbbabdcbdabababadbccaabbdbccbcbbbcddcddbacababbcccddbbbbbbadbbaacbbabdddcdbcdbbccddbcadbdbadcaccdacbacadbdcbbcaacbacddccdcbabadaddccdbdbcbacadcbdcdacdaacaacacbdacabcadaccdcccaacdbacccabbddaccadbcbdbaaacccbccbcaaabccacbdcaabbbbcabaddbcdbdabcbbbcbacddadbbddadcdbbabcacdcbbcbbaccdaacdaaaadcacddddacdbddbbddacadaababbccdcccacbcbaabdaadcaddcadbdcdbacaaacbbcadbdbcacaadddadbddcaacbccacddbcbbaaaabcdadaadbacbdddcdddbbcdccccdcbcaadbcdcbcadaddcdaaaddadaacdcaaaadcdbadbddaadabbabbdcadcdcadcabbbddccabddbbabaacdccccbddacacadccdcdababcbcabcccacaababdaacddabcdddbabdabbbabcacaccdcbaaaddaaaaabcccadddcbdbbbabbbadcddadcdbcabbccabdbaddbcbcaacbbddaabcaccdbadcccdaabdbdabaaccddddcdcadbcdacacddcaaadddbcdbbcddaadaccaacadddacbcbbadddbadadbdaaaacaabccdadaccdccaacdaaddabbcaabddbcccdacddbacbbcacbadbabbbcdadcdabaababccdadbaccbaccbaabcccbccbacbaabddbacaacbacddaacdaccdbcccbcbddcdadccdcbaaddbbbcbbcdbdbcbadabbdaacaccdbbbbccbabaacdccbbacbadbaacabccacadddddcacacbababcbbcadcccbdcbcccbcdbabdddcdcccacdbddcdaabadcdbddbccddaacdcdccbabacdbaaadccdbcbcaaabdaabcacbdaccccacadadbdcadbbcaadabccbdddcbdaababacdbddadbdccabbbccdbaabcbdbdcddaabbcacadcbaabdaacbcbdcdcadbdddccdaccadabcbaadbcaaacabacacabdddbbcdbabdbbbcbbcaacbdabdcaacbcdacccbaaacbcbcbcbbbbbaaadacbbacabaadacbbdcaadcbdbbcbddacdaacddadcaaccdaccbaddbddccccbddadaddbabdadabcadbddaacabcadbbcaddabdabaacdbdbddddabababaddcbcabddcaacabbabcbbcddbbcbacaadddcbdbbadddccccbbccabdaabaabccabdddcacdcccdaadbcaabcccaabddbbadadadbcdbcbaadcaacbabdddbdbdbcadabaaddcddaaaaccacacccbacbbccbabdccbcdbbbcabbcabdbbcabbcdddbcccccacccddcbcadccbadcccaacdaaccccabccdddaccaaaabbcccadbadbbddbdbcddabacbbdaadccaddadcadddcbabbbdaddadcbadabcdcdacaacdbdbaaaacacaabaddddddbbbdddcbbdcddabaabdaabcdbabbbcbcbbdabcbbcacbcdadcdddbdaacacbbcbdcbbabbcbadbcbaacadacbcdccbddcdbaababcacddbdbadacadabbbaaaaacabcdbadbacdcacbcacbcadbbddbbaaacbacaccaabbdcbacbdbdcbadcaddbbacdabcbddcdaccadabaacdcdbbcdbddaadcbdadbcdbcccbaacccdcbacadccaababbacdabbbcaddaddcdbdbadadabdaccaaddaacbccdbdccddcbbcabdadcaabbabcccccadcbaaddbcdadcacdbdadbacaddbbbacddcbacacaaacccadbcdbccdcacbaabcbbdaccbbaabddabcabdadaabcbbabaaadbacddcbaadbbadabcaaadacdabbaddadcbdaacdcabbcddadbcbcbaadcacbdacadccbaddabbddcbcbacbdbbabbddcccadadbdbddcacacacacbabbbcddbbcccbaaacaccbcbddcabadbdbbabbbdbbcbcdaacacddcccadbadcbbadcdcbdcadbdcdbbbdcbdaabbadccadaddddcaaabaddbcdadcbcabccbcccddaacdbacabdcdbbdcadcdddcabbbcacdacacbbdcdcdcbabcacacbcddcacdddaabdabcdaabbbddadbbcdbaddddbcbbccadadbcbadabbcbdcbbabbdacdaabbccaabbcaaccaaddaacdcbacaacaacacbcbacadbcbaaccaadacababcacadaabbacdcdbacbcabbcaaadcddcdacbabddbddacbbddabbacdddcbaccbadbbabdcbdcadbcadbacacaaadcaadaddaacdccdcddbbdcdaaddcdcccacbabdaddbbdbcadaacdaabdadcccbdbdbaababbadadaaadbaabadcadaaaccddadacbaddacdbccaddacabdccabcbdadbdbbdcbcdbbbcbdbcbddcbaccddbbacaabacbdabababddbbcbbcdddcdcaccdbdbadcaddaddcacddabcdbddddabcdcbacccabdaaaccadbbadaacddbbcbadbdbbadcddabcdbdccdbbbbbbddccdaddcbadcaacccdaadaaabddabbcabbbcacaadaacbccaaaacbdbbdccdcdcabdbcbacbdcacadcbcbaddddcbcbaabdbadaadcdbbbdcdaadddbcbacabbdcaadcbbadbbabcadbbdcbaadadddcdbbabdccabddbcdaabbbddcbaadcbabcdcbadcdabcabdccbbacabbaadadbcacddabaddacdacbcbdbddabbcdbcadaacbddccacaaabddddbcabcddaabcaacdbadcbdcaaacaacdcbdadaadccacbbdaadaadcbbdadcbbcbabbccbcdbbddbbacccdbadcbacdaaccbadacbaaadccdbccdcdacbaccccbaddacdddcbbbbbbaccaabbacdcacddcacbbdadcacccbacddabdbbdaacdcbdbcacdabdbaadbdaaacacccdccdbaacbcaaabdaaacdbdabdbacccbdbcdcbdbbcbdbddacacdcacbdbdabdbdbbcdddadddddacaaccbaadadacaddccbabbbabddbcdaaddaabcbcacbdaacbbbcdaacacaccacacdbabbcdddbcbadbdaacdaccacddadbdccbaadabadaacacbaaddcabadbdbaabaddbdabcbdbbdbdcbabdbcacdadbadbddaddcaaabadacbbadccbbadbbdaddcbcabcbbaccacbcbacbadaadbdbbbdccdbccacdddaacbbacaaacdaddbdbcdadbcadaadbdbbbbdcadbbcaacadabdddcabcaaadcbcaccadcbadcdbccddddddaddbddacccdcbbaadbdbcadabbaadbacbdcbbacdabadacdbaccbdaddddacaabbdcdbdbdbabdcbbccadabcbbbacccadabddabdcbaabcbcbbaacbdccadbdabbcdaddbbcbacabdbcabaddcbcbabadcdbcadabbababbbbcadcbabdbdabdbbabdadcadcccbacbddcbbadabbaddbbdcbccdaacbadcccddaccabddddaadaaadbadbdcaaaadccccabbcaabaaacabbcbcbddcdddbddcbacbcbccbbadbcdccdbaabcbbbcdcaccddddddadbabbcabdcbccddaaacbddccabacaaabadbccabcbcbcdbbccbbbaddcaacabccdacabacccdbbaadccdcaccabbabbdcbdddaddaacddbbdbbbbddacabcadcacdaacbdcbdccdbcdabdbbcadbddadbaaccaadbacbadcdaacabadaacddcabaccacdbcdccdadadbbddddaccdbbbadabbadbbaddaadbdaddccddbdadaabdacdcabdbddbbccbddadcdbbdabcbccbcdcbcdccadcccdaadbadacdbaaabaddbbcdbadbbdacbcdddcbbcadabdddbdbdbabcbddcacdccdaddaccaccccbcadccbacdcdbaccdbdbccbbbcaaddabdbbcdcdbbcaddddbacddaddaddcbbadaccabcdbbabbabcaaabbdcacaadccadabadbdbabaddcbbccbbdcaddcbddcdbdaaadcabcaabdaaadacdaacbdabbdcbabbaacbbbbddbdaabaadcdacdcbcdaddcacbbacadbabacabbabdadabbaabcdbadadaaaacdccdcbccdabcaaadbcaadbbabaacbdcdcbcaacddadaabccbcdcdaacadccbcbbddcdacbcdcdcbddbadbaabdccaabcbdcddabbaaaaabaaacccbcdcacdccacaadbcbccadabcacdbcbaaaddbcbbcadcabacabbddacdbaddadacbabbbaacabdbaccaacbdcdabcddddbbacdbabaccbacddcaddbcbdcdabbabbdadabdaccccbbbcbacdcbcbdacdcabcacdcabbcbbcbaaaaddbadcdbdbcaacbcadacacabbbbaaadaabdbdcacaccccbccadbadbddaddcbccacadababccbbdcddaccadaabddcccdcdabacdbbcbbccaddaccdbbdaaadadddcabadcabcdcacbabcdcbabbcdbabbdcadbdabadaabaadbcacdddbcccadcccbbdaadcadacbbbdcacdcbcdcabdddccaadddccdccbbcbcbbbdddbabddcddbcdbdaadbccadbccacccbccabbbbaacaaccaaabccabbcabdbdcdddaabccacbcdbacbcbaaddbadacbaabadabbadaaccddacabcacdaababcbadacdacdcaacdaabaaaaccadbbcbdcdbdacbccccabcaadaaacaaadccbbddacbcbdbbcbaccacaaccbaabbaaddaadbdabaabbcdcabcabdbbdbddcaaababbacddcaccabcbcbaaabdaacdadabbcdababccbdccbaacacbbbccddccccaacabdabdccdddbdccadccdcaddadabccdbddbcbbdcacdbbdddbbcdaadadcbdacbaccbddbbcdaddbddbbcdacccabbcabbbcbddddcdabdbbbcccadbcbcadcadcaacbdcabadcabdbcdbacdbdcbcdbacccdbbdddcabccdacadbdabbdbcbcaabbbaddcbcbbdddadbccddacdaacdcbbdbabdcbaccaadadbabaaaccdddbaabaaddbdaacddaaaaadcbaadcacacaaacdacacdbadbdccdbdcbcbcacdbbabaadcdcaabbdbdbdcabadacdbccbdbacaaaddcbaddabcdcbbcadaabbccadbbadccabbbddbddcddbdaababacabccdbddacacbdacdadacbcddaabcadbbdbdadbbacccdddcddaccacbdbdadbdabccccbccbdbaccaddbdbcdcaadccbdcadadbacbddbddcaadbaadadbacdaddcabbdbaabdcbadcacbdddccbcddabacbadacdadddabcddbcacdbdccbbbcbbabcbdabcacbacbaaddacbcdcaabdbaaadcddaacacbabbadbbcabdaadcbaddadaacabcaddabaccabbcabddcabcacccaadbbbccccbcccdbabbdbbbdcaaacdcabbddbaaabdacdadaddcabbcaadaddccdaabadabcccdccdcccbaaadcdabcdddbbcaadbaaacbcaaddbabaddbbaacbcdddbddbbbdaaadbbccdbbaaccacabcdcbbaadccaaaacbbbdcbadcdaccacdbdbdddcabcdbcadbccacdcabccabdcdbbbddbddbdbacbcdcbabcbacaadcddcbadbdcabadbbaaabdabcdbdabcbabccdcbaccbabbacddbbdcdbaacdaaacdbbacddccbdabdaabbccadbcaaacdadacaddbbacdadcdadcdbdcaacabcccddcbbcccdcbbcabccaabbaacabdadbacdcbccaabcdbbabdbbbdadbaabdddbacdadbcdadbacddabababddcdddbbccbabbbddbabbaccacdcccbddbcadbbcbbcddbcaadbaacdbadbddacaaadcabdcdbcbddcdabdabadacbabaabaadababcccacaaabbbdbaabbdaacbdcdaaacbdddabdbaaddcbbcbaddadbacbcbbcbdccdbbbdddcabcdccdacdccacaccddbdbcdccaddaaadababbbbccdacadacdcaaadabcdadbdbddcdadcbccddbccbbccdcaadbdabbabaccddbbdcadbdabdcdaabcadddbadacaabcbccaadbdcbbbaddaccbaacccbaccbbdadadbccccaadabaabdbbbdcbdcabcbadbcaadcbbddaacbccaccdcdcbccdbadcdcaaadbcdbaaabdacbbcdddcabdddacbdbcdbddbdaadbbcadbacdbacbcadbccdbcdcbbaaadadbbaaccbcadbadcbabaadcdbaabddbccdcdcabccabbdaccbabaadaccdbdbdaddaabbbbcbddddccddbadaccbcdcaabdadcdcdcbcbaabbdcdadadabbabccaadddacdcbacdcccbbcdbbcbdbddcacadbccdbcbbabbddcaaddadcabcdcaacacabddabdabbacadbcdabdbadaacddadabacbddabbacbdcdddabbcbabdabacbbaaccaddcbddddaaddbadcdaccacbdddbbddaddadbbccdbbbbccbbdaabcdddbbcbdcbcbadabbddddcdcacccdccdcdbdbcacadaacbcddabadaabddaaabcbdadcdaccdaadcbbcdcbbcdbdadccacdcdadddadcbcbabcdddcddbbbccacccdcbadcdcbbaacdbccbcacbababdbabcaddcadaadbcbddccbcdcddcbdcbcbbcababaccaaaacdbdbccacbbcacccadbaccadddbbadaaacabbbcbddddbdadacbcbdaabbbcdcbaddbcdcccbbbbdbaababaabaccdaadadbdcdacabccdadacdaaadbcddbcbaccddadadcccdbbddbcbbacabddcdaacddbbadcbdacbcdcbbdcadddcdbbdbaabacbddbadcabdbbbddadadcbbcdcbccaacccdccdbdcdccdaaacdaddbbdddacaccbcaadbadcdbaaabaccacaddabccdacccddbbcdbadbaaddbbbacccddddccadccddbabbbbcacaccbcadbdddacbbcbcdbcdadadaaccbdaddbbabaacbbacdbdbbbbddabaddcadcdbabbbbadcaddaaccaaaccbdababcbacaabcbbcdcacbccdbbdcabbddbccccaadacababbaddaaadbabaaadaacccbcdbcbbbcaadddcbadccbddbbbbcdaaaadddcbdcdcacdddadbbcababbacbdcdaabcadabbdbcabcacdaaaaaacadacccbddaaadcadaaacdcdcabbccdbcbcabbbdabddcdbcccdabbcbcbccbdadbdbcdcbdddcacbcddbaaadccbcbbccdbdcaabdaacbbdddddabacbaabbababcaababadaacbdbdbddcddabbadaaadddbcabaaaadcccacbadccdcddcccbabcdabababcbabaabddaddababdacbdccdcbabdbcbbbbcbcddaadabdadabacaaccacbcacbbadbacbbbdacbabcddccbadcacacccaacdadbbbbdbddadbdbccabaaccddcbdccaaabccdcabdbacbbcaacbdacadcbbbacbacaadcbabcaaadddcbaddddbadacbbbddccdaaccddbbdcccdacacdcddadccbbdcccabcacddddaddaadadcbdadbdbadcbcccabcbbdbdaccccdcdaaddcdacbccbadccbbddcddbddccbdacdddbcbaccabbdddababaaaadbbaabddcacddddcdbdcdbbcababcddccbacbabbdaacacdbacabdcccbabbabbaaacaaabbdbcbdacdaacbbbcabdbabcbddacddccbbbdabddbacdbcaabbbcbbbccbddbabbbcbacbaaaacddbcadbbadbadbaaaaabbabbbcaaacaabbdaadccadacdbbcabadcaddbdacdbbaacdaabdcbabcbbbdccdacdabccaaacdaacbbdbabbdccaaacdcddcdcdacddbcaccbabaaabdbbcaadcdaabbbcacadacbcacbbababcbcbbcdbaabbddbdabadccbcdadcdcaddcbdcabadacabdddccbccacbbdabbabddabdcddabccabddbbdbcdbdbcabbaaaccbaaaabcdbccaabbcbccabaaaccaccddbbaaababccbbcdbdddcbbdcdabcddaccdcdaaccdbbdcbdadabadcbbdbabcadcabdacbccabdbdcaabddcbacbabccddbadbdddbbcaaadbdaccdadbdadaaaaadaddaaddbbabcbcbbdcdaddabadbbaadbccdaadcdbabdcccaaddcabdddcdcdcdadbaddcbdccddccddddcacadbbdbdddccaadbaaabccadcddddcdbdbaacbccbcabdbacbdccaaccbaabddccbabcdbcbcbbadbadbcacbdbdbbbabcbdbbcaacbcdbcacdbacbdaaccdcabcddacababcdddaddcdaaadcdcbcdcacbcabdaccacddcabbacdbbccdbbacaddacacaacbcbabdbacbbabccbaacbabcbdbabcaaccdacbbaddbaccccabccacdcbcdaddacdacacabcacccaadbababdbadcdcacbbbaddbdcbbbdaccacdabdbbbcccbdbdacdbdabcbadcdcbaabcbdaacddccbddcbdbbaabdcadbdccacdcccbadcababddabcaabbcaaabaaacadbcacabdbcbbabbbcadcacabddcccbcacaaabcdcddbdadbcbcccbbaadcddbddacbcbcdddcddcabbbbbcbdbabcbbcdcdcdabbcdbdbcdaaaabadbdddcdbababbccababadaddacacddccdaacdaaaddcacbdaaccbddaacbcdbbbbcddaddddbccdbadbbcbabadacaadddcbdacaaccdbcaccdadacdbababddddbcbcabbcddcccadabbdddcadcbdbbdbcaadbdadbbcddddcdbbbaccabcdabbbcababacbcdcabcccbccbbbddbccbbccaacdcdbccbddaaabadacbdcadbabbbcbbdccdbdaacabddbdcbacbdddaabdadadbccddccbbbdbdbaddcdccdabdcdbdbddcacbaacacdddbacbcccaccadbaadadacabacbdbbabbbdadbcdcacacbacddddcadcbbddccdbaaabcdccadbcadbdbbbccaaaadccabacdcaabbabdcdbcbcdbbdaadddbcdddcdcababaacccddddaaadbbcbbbaabdcacacbcddcadcdbddcdbacddccaacdbbdccabcabbdddbcdaaadbddaaabdccaabbdacbacbbcbddbbccaadabbacacdbaadddadabbcdabcbcdcdacabdcadaadbdadbccabbbbacadabcdaaddbacdbadbbbabdaabbbdbdcbdaacaaccddabaccaccdcdddacbdaacbbbbcdabbabdbcbcdbdbbcdacdbcbacdcbccddcbddbdbadbbbdbdacabdbbadabbdaacbdbdcdadddaadadbaabbbcddcbaddcadabcbdaabdcabbbaddddcbaadccacccaccaadbaddccccabccdcbcbbbadbccbacccaacaadbdabdcddcdcacbadcbacaacdabcdbcbbdddabadbcacabcbbdabbbbadcbccbbabbbddbbacacddccbbdcdcbbcdabadababadabbdbcbbdddcbabcdacbcccbadbbdbbbdccbbbddabdccbbdbbcdbcbbddbbdabcbccbadbaccbddcdcdabbddaccacadbdaccacddabbabcadcbbcacdbaabcbdaadccccddbcdbcbabbbabddbdbdcbdaabbdaabccadbccbbddcbdddbaddbadbbadacbdcbbdcbccbaccdadddbdbdcabcdddbbbbcadbbbbadddabbdacccdcccdadbbaddbabcdadcbdcacbcaabcbcaacccdcbdaabddbcddbadaaadacbcddcdccaddabdcacacabbdccdabdacbbaaadadaadddaababdccaabbdddcddcabccabaccddcdcadaaddddbccdcbadaabdbadbacccbbbbcadcbdccaabaadaadccabcbaaaabdddbabaddddbddbddacbaabbaccaddaccddccdadaccdcababccbabdbcdcdacabbaacccddcababdabbcadaaccbbaabdaabdabaadddbccaaacadbabdcdcbbabddbdbcaabcabddcbcdbadbbacbbabbbcadbdbbcbcbaaaadacbbabcbccbcbcaacdcccbcaabdcbaadbdbcccaabaccbbaaabcadcaacccdbbbdbbcbbacdcaccdbacdcabdcdcbdddadcdccbccaabcbacbabdabbdcdadbddbbccdcbdccbaddbabaccaabbbdcacadadbcaabddbbbaabaabdcdbdccdaabbdcccdccbcddbaacaddbbbacbbdadccdbaacbdccdbdbaaabcbcdddcdcccddabbccaabaddaabccdadccccccbbbbcdabdacdbaaacbadddcbbdcddadbdbdbdaabbdcddddcaddcabdabbaaabdbbbabdcddcdddaacdbacadbcadccacdbbdcabbabdcaddcdaaaccdcdbabdbbdccaaaabbbbccbacdbccbbaccabdcbdcddadabccdbccdccabcacbbcaccacaaccaaadaadacccdcaababcdbdcbbcbcadbbddccddaabdaadcabddacbaabaaacbabbdbddcbadddddcdaacbbdaabbcacbdbccdbdcbacadadddbadcddbbbcabadbbaaddcdbbabccacbbddcacbdaadddccbcddddadacdcbbbadcdaacdbcddddabbacaabdabdcdccbdbbdacdbddcdaddcbddbabdbaadaaaabdabababbcbaabadccbbbbcabaddaddccbaaaababbdddddddadcaacbacababbbbdaddcdaccdaaccaccdabccbccdaadbbbadddccacaccccbccdcacaddbcdadbacccdddcbccacadbaaccbddcdbbccddddcadcaaddbcddaaddccaddcbccbdcbddacbbcbbddddbdadacababdcddbdbabccabddabdcdaadbdbbcdcabacbcdcdbbdacbcbcacbcaddaabccbacdadddcdbabaaadcbcacdadcaadacccacaadabbdacbaacaabcadbacabbddcbbabaaaddaadacbbcabdcddadcccbaacacbcdbbdbcbcdcccbcbccbcaababbddabcaabdbadbacaccdccdaabcbdaddddcbddaccadcdcdadcbbbacdaaccdadccbbbdbbcccacdcdcdbbadaabbdbcacbbbbdcbdabdbdcababcadbdcbabbdbddcaaccabdbdddaadaccbadaacbaccbcccdbadccbabbacaadccdcddbdacababccddabccbaacabcadbbbabadbbadcdbddcdcaddbaabcdbcadbdcdddbadacaccbbaadccbcbacdacbabbddaddbbbdaaacaabbddbdaccdadccadddabbdcdcdadbaadccadcdababdddccdcaaccadddbbdcacdbdbbaacbaddabcdccbbccbccdbabbbdbdbcdcbdbbcaccbcabbacadcbbddadbdbbcdcbddcbacadddaaaccbbbcadbcdddacddbdbadcaaccbcdccabdcbbddaabaccddacbaccbadcdbbbcacabcacdddcdbaaacdcacbdadabcbccbacdcabdccacadaacaaccddcdbddbbcccabcbacacbadacdcbddcbadbccdcabcacbdddbbabcaddadadddcaadbbdbdbcacbcddddcdaacbadacbadaaacacdbcdcbabbbbdacacadcdbbcbccaaacbcdcbdbadcdbdcaaaacdcabbdddbbcbacbbdcbdddbdacdabcdabbdbabaddddbcdcbcbabcacbacbddacdcaccccacbcaccbdadbbbddccbbdbdcaccdcbdababcdabaadcbcdbcddacaccacdaadbdbcbadcabbadddddddccaabbcdbddabccabbbdccaccbcdbdccaccdddaabdaabcbcacadcbadcacdbcdbbdabcbdadcdccdadcaccdcbbbcdacaabdbbdadaaadccadcbdababbcaababbbcbdccabadccdacabbcaabbdaaacdcccbbdcddbddbacdcbdabdcbacbccbdbbbcddbdaaaacddaccacaadbbadadabdcbacbabdaddaccdaabcaacbaabdccbdaaaadaaadcdacbadadcdccdbccdacbdcbbadaccdacabcdcbdaaacbddcdbddcabcbcdccbadabdccbbcbdaacdacabbabdbacaddbacdccbdcadbaccabdddabcbadcccadabcbbaccaaadbcaccbabacacbccabbaddbbbdccdccabbccdbcabacddcbbadaaaabddadcbbcdbbabbcaabdcbddacbdcababadcadbbdbadbadbcdbdbddbcdcbdacdccbaacabcaddcaaaaccdbccacddaddaaaabbdcaaccabbdccacbbddbdbbaacaacdcbbaddbbacbdcccaacadadbacaddcbcbddcccaadcddadccdbbcdcddabdcacbccdcbabccdddccabdcdbdaccacbdaabcbdabbcbddaadaabbaacbbddadcacdcaccdbddadadbdbaacbdcbdadccddabccdaaabcdcccbbbbdcccadacbbabcbadcbbaacccacacdddcbbcbdbcdaddbdbacabbcdccaacaccbccaddcbacbcabdbbcbddaabcdadcabcdaccdbdcabdbddbdaacccbaacadcacadbbbbadbccbdacccadbacdcdbccaaabaaccabdbbcbadabcaaadcaadcdadcbdacdbdbbdcbcdbabacdbbbcccbacccabacdbbadbcacbbdcccdccacdcaccbaddadcccacddddccdcccbddababbcbcdcdccaabbccdddaabbabbdcacaabbccbdcaadcaabccacdcaaadbadaaaacabdcbadaaabdcddbcddbddacbcdbaccacdaaccbadbdabbcaabcbbcbddadcadbbccbdbcbbbbcaddcaccddcbbbbdaccbccdacaabcdacdabcccaaabacaddacbdcaacadbdabcbacbbbbacabdcaaddabddcbdbbaccacccbbbaadcbdcacccdbcbdcbaccadacdbadcabcdaacaddadaabcabbbadcdbdddbdddabacbcbddabcabdaacbdcaccccbcabcbdaadaadbaccdacbaccabcccdadccdccddbcbbcacdadbbcbcabdcddaccdaaabacaacdbaaaddbbddabddaccbdcbaabadddbdccbdaabbcbddabdadcbabdbcababdadbabaddccaaaaccbdaabdbaacdaccbdddaacaabcdbbdcbdcddacdbaaaaacbbaacadaabacbbbcccbacbddbbcadcacadcbccbbcdaaccabbaaddaadbbacbddbcdbbddcccbacbcddcdcdacbcdcbadbbcddcbcadbdaabbbbddcacdcbadcdbbadacabdcdbbdccddcccbcbadcbbccdaddcadbcacdbbaabacaadadaddbccdbdbcadbdddaacbcbadacbabdacadacdaccddbdabababbcdaaacbddcabdcdbbbaacaabcacdddcbcbacadcbcdcacddadaaddcbcbadaddadaddaabcabcaaacacddbdbcadddcdbdaabacccdaabacddbbccbbbccabdabaabdbacddabcdcbbabcbabdcdddcabdccbcbaabddaadcbbdccbbadcbccdabaddbbbcbacaadbbbcadaabbaaacdcdddadcbadcddddddabddbaabdcaddbcaddbdcdadbbaaadccdbbbdabacdaaacdcdadabbdacbadacacbcbddbaddaccddcadbbaddcdcacbcccddddcadcbdcbbbabbabdababbbacdbaddacccbbccbcdcdddccacdbbdcbdccbccbdaaaddaddbddadccdaadabadabcccccbdbbcadcdaacddcbdcabdaccdbdcbbbbdbbddcdabaabdadacadcacbdbbaabbdddadcdbbadbcdddacbabccadbdbbaddcacadccccbaaacbaaadbbbcddaacddacdbdbdbbcddbddcabaaadcadbacbbddbdabcccdacabacdbbadabbabdcdcaaddcadacbbcababdbcabddacababdaccdbcdbccdaababbcacbdadcdaddbccbbcababbcbabdaaaadaddaabdccaccbaddbacdddcbddcddbacdbcbbbdcaddcddaabadbaaaacbacbacaabbcdbdcdcaddbdbaccbcdcaddababcbabcaaadddaccdaacdbcacdcbdabdbacbbcbcadbaddabdabacddcdbcbbabcdadbcbaadcbbdbaacbabaacddcaadbbbdbcbdbaadaddbaccdabbbbbbabbdbdadccbbcadacbdbdaccdbbdaabcabbdcaababbabdbbddaacdaabaaabddbccbabccadbdcdabbcdcbcdbdabdcbabaaabcaddddcccdcbbdcdbddbabacadcbbddcabdbdabaadddbdadcdaacaacadbddcadadccabdaadabadbddddaadcdaaaadddacbcbdbbcddcbbdbbcaadcddaadababcabcabdcdcadadaaacdaccabbdbccccddcdbcccaadcddacbadbaddbababdaabdaaccaaadabadcdcaabbcddcccdcccbbbcbabdbccdcdcbbcdbcdaccaabdacdccdbdddccbdcdbbabdbdcbdbcaacdabbabcaddbcbdbdbbadbcbbcbbddccabdccccdacaaadbbdcccdacbbdcbbbbdacdddbdadaabdabdcccadbacadabdddbdbdbcaabadbcbddbbdbbbbbcccbddbdadbdaabddabdabcdbbbdbdcdabcbabaadabbabdcbabbbccacabccadaddaccdddaadbabbcbcbabbdddbbcaaccdbcdcccdbdbbbbcabdcdbabaaccbdddaddcbbcbcbdddcdbcacacadabacdddcbcdbbddbcabccacabdadbbbabcdabcdbdbadbabddccacbcdccdaacbadbaabbcbacdccddcddcaabbaabcddbcbaabbdddcacdcbadabacaacbadbdadabcaddcbcdadadaadddabbdaabbcdbacdbdccaabbbdcacbcddddddbcaaaabdacdbdddbacbbadacbdbbdcccabccddaaddbcdbbdcbcdcdadddccadcdaabdbbacbbcbdabadbdbddcddcddddcdbcddbcccbdcacacabcdcdccbddcddbadccbccbbaadbacbbcacddcbcdddbccbcdaccdbcbadcddcaccdcacdbadcbcddccdcbbcabccbaacdbbccccdbcaadabcbddbcddaacbcaddcbcdccbddccbaacaaccdcabaadabdcdbbddaaaddbacbdcdadbddddadbcaaccbbcacbdabbcbabaabbbddbbdcacccadaddcdacaabaacacabaccaabababcaccacbdacbcddaaabddbddbbdbbbdccdacaccbbbabcdddaadabcabddcaaacddcdbddadcabadabbcccdcaddaabcaabdacadbbddcbcbadcbcddbaccddbdcacddcabbcbbdddddbbbaababdbddddadaacadcbabbdbdaadccdbbadacddccdbdbcabdaddbdbdcbbdadabbcbaccbbbbbcccaaaaddaaadabbccbadabbadcbddbdcbdbbbbcddccdbdccaaaacdcbdbcdbbbbccdcaaddacacbadcccbaadbdbdcaaaccbbcccdacdbddbcabcccdbcabdaadcdccacdcdadcbdbabcbaddddabbbcbbdddaacbbadacdbdcbaadadcabdddbadcaacddaccadadbcabcbcdadabcddaaddcccdbcbbddcdabdcbbdadaacdcddcddddadcabdabcbabccadadccddcaadabbadbddcbabdacccadbcdabcaaddccdadbddbcdbaacccadbdccdcddbdccdcdcdbdcdaddcdbbadcadaadbdbacbbbacdacccbabbbabaddccccbbcacdbbadccdccabdbbaadcddcacaccacadddabbbbcddabbaacadcddcbaddadbcabcddbcdcbcabddadcbadacacbbacdbcdbddcadcabacdabdcbbbaacaacbdabcddccabaaacbbacbdcbabdacddcccdabdbadadaccbbcddbdcdaaaabcaadadbbaabbbbbadbcbbabacbdcaccbbacdacbdccdcdabbdbdcdaaadacccadbbcdbdcbbdadcabcccaccadadacaabbdbadaabbccdccabacbddcdddaacddadaccddcbdbbccbbccbcdbaaacbbccddbcdadabbacbdacddbadcbacbacbcacbbcacccbbdcbbdbcaaadbadacbdcbdbbcadbbdddbbbbdddcbadcccdabbcdaaabbdbddbcbcadbadcbdabcadaaacbcdddbcdbcacbdcadbaacdbbadccbacbacbabcbbbaadbaacdbcbcadadabbdcdcdbbdcdccddbbccacccaababbdccdcbccabdababdbbbbbaddbbbbcacaddccdcbcdabadabbcdbcbbdaadbbdbbcbbbbbcbcbbaadbcbdcbcabaacccbddbdabacbcddbdadbcadadabcbcdadbddaccdbaadddcddacbaccbdcbbcdbbabdbadcadacaccacdadabbbdbbbddbdacbdcaabbabcdcdbdcacbcbddddcbabdcdccccaaacacdabbbbbcaacbbcbdbacaabddbddcccdadabcabbacbacabdbcbbddadadbadabcadcccdbdddcdcddcacdcbcdacaabcccbccbbbccdabcabcbcdddacbaccdbdcadccbcbaddcabdcbcacabbcaaacbbddcadabdddacbdcacddcbadbddaadbabbabcccbdadadabcdbcacbccdaddacbddacdcdaadcabaddabcacdcdacacadacadacddbcddaccdcdbcadcbdbdbdbccdbcadaacbdacacadddaabadacccdbabadaadbddbddcdddcadabaaddccddabbcbdaaabaabaadacabdbdabccdbdaabdaaabbcdcbabbdaacbadbdbbcbcdcdcccdaadddddaacbbcbbbbddadadcadcaaacaccdaddcdcadcdaacdbbbbacddcabcadccabcdccbadabbcacdcdabbadbcacacbacbbcddbcadbcbaaccbcdcbbbccacbabcbdadbbdccccadddaddddcdbcdaaabdbbcbaccbdbadbdcdbbcbcdbacbccdbdabbdacbaaaccbbbcbbdcbbcacbbadcdadabbbccbbabbdbddadadacdccccddbccadbdadaccdcaddbabaabccaadadababdcaabcbdabccacabbccbbcabdbcaaabcbaadddacccabbdcbdabadaccdbcaccdacbdadbbddcbbacddaadadcbdddcbcbcaddcabdcacdcbbacbbdadcbabaacbbabbacbbcbbccbacabcbaadabcdabacbddbcccaccccbbdbaabaddabccbdbabcccbabcaadacbadcccaccccdaaabbbadbdaabdbcbdbadabbdadcbbbbcdbbdcaacdccacbcbdbbdbabddddcaaacbbaaacbbbcaacbbbabbacacdadbccdbdcdddaccccdcbaaabbadbdddccdbbddcacdcaadacbdbdaccacbbacdcdadbcababcacddcadbadccbcaacaaccdadcddddcdababccabcdabbdcccadcadccbdcbbccbbabbdadbddbddacbaadabaacbddacddaaaacdadcbbcacdddddbdadacbdabcbccdacbcdbbcccbccadaacaccacbcbacdabbaabcbababaaccaaccccaccccacaacdccadaadaaddadbddcdddaaaddbbaabcacbddaaddaabdbbaaacdcbdcbccccdbadadcadbddbabaccaaacabbdccdddcabccadddddaddbcaaaacddcdaaddbbabdccbbccdddcbaddcbdaacadadbddddabddadadadbbcdcaaabadabadbddbbaccaadbcbbdbdbaabdbcbccaddabcbdbadbbbacddcbabddbccdbaaaadacdddbbcbcdbdccabdcdcdbdbbcaadaddabcbdaddcaadbcdaccbaaacdcbbaacbccbcdadbacccdaacbacccaaacbbdbaaabdacbbdcaddcdcbadbdddaadbabdaabcacdacbcadcababcabdcccddccadddababadbdacbbdaabdbcbdbadcadbabbaaddbaadddaadacbbacbbdcbcdbdacbcbcacbbacadabbbdcacabdcdbabdbbccdbbdbacadbadabaddcdbbaabbccabcddaddddbcabdadbcddddbdaacdacccabdbbbbbddcaacaadbccaabbddcabddaaacddadabdbbaccaababcbacdadcdddacbdaacaccacbdbadddccabddcadcacccdcccbbcadcadaacdbdbbaccdadaabddbadaacaadbcadacbcbabddbcdcaaddcbbddaaccbdaccadcbdbdaaddbbddbabcccabaaccbdbddbaaacaccddbbabaadcbbbabbbdcbbbbadbabbbdbacadbbdaabcacbcccbdbcabbbbbbbbbbcabbbdbccbcdbdbacdcbccaacacadaacbdcababbbccaabbbabbcbdadbdbbbadcabccdcabaddbccbcaddbcdddbbbbabcadcdaadcabadbcaccacbbaddcbbdabccdcacbbdcdcbdbccbcaaacdaabddadccadaaaaaabaddbacaccddbdaaacdcbadabdcaadbdbbaadccbdabacddacbdababdabbdcaccccdadabccdbbbddbcbdbbadbcabcdaaabccddcbaaacbcbbcadbdcaaabbcbabadaabddbbbaaadaaadbbadaccacbbcabbbbbdaaddcabbdbdbdbcbdadbcbbaabbcaabdccdbdbcbcabccbabdbcdbadddaabcddabdaacdaabcbcbcabbabdcbdbccdcdbbdcbbcdcbaaadbbdbbacbdccbacadababcccacadcddccabbcccbcddaaccacadccbcaadbcabdbaaddaaccbcacccdbdbdadabbcdabaadcbacdacbdaacdaacdddadbdcabacadcdbdcabcbccbddcdccaabdcddcdabccdccdadaadddbbbaacdabbdadccdcaabbaddaaaaaaadaadbaaadadacdaddbdcccacacdaccdbadcbaababbabdddacbcbaaccbaabdbcadbbccbabababdabddcdbacddabbacdbcdbcdccbbbdbbdadadcacddaddaccbabcdcbacdbdbabaaddacadcdcbabcccbcbacacdbcbdbbddcbbcbccaabdbcdaadbbbabbbddbcdabcbcaaaacabcadbabacbcaabcabdbbcabdddaadacbcdaabbddcadbcddaabdcddaababbabcdcccdbaacbaadabcdaaadbcaadbdbdbabcabbdcadddbabdabcabbddccbdcbddcadadcaadabadcadaacaadadababcbacacdcdacbdbdcabbdcbbacbcdddbdddccaaabcacabbbacadacdcaddcabcbaabdbbbcaabccbdbbaabdacdcadadbbcdbccdcbbbbbbdbaacbdbadbcccadbbcadbdbcacddaadaabcdddacddcdaccacbbaadcadbaabdbdcddcabaaacbccdbdcbabdacadacbcdcdcaaaacddbdbdbcbcabdcacdcdaaacbcdbbcdcaabbdbbcbacbadbcabadcacdadacddcbdbabbdbcdcdcababdcbadaabbbbdadddacdabaccadccbbdadacddacdacccabaaaaadacbaccdadbccbcbbbadacabdbddcdcccbaabcadadbbaabdbccccaddccbadcbbcdbcacccbaaccccdadcccacdbaabcbcdaddbbdbbdcbbdcbcadccdcdcaabdbdcaaadcadcdabadbcacabcacacadbbcabadcdacbcddacabdabcdcbcaabadcacaacbdddbcacddbaaadcaaddacddcccaddbcbcbcbbdaaccbbbbccadcadcaaabacaaaacabababdcadbdcadabbbcababcbaaacaaccdccadbcddbdcdddabdadaabddbaaccdcbabdabdbadcbdcabddccdccdaabdcacddacdaabccccadacccccdacadcaaccabacabdddccadccbcbdcbbbddbbabcbdacbdbbdcbacadcacccbcbabadbbcaacaddbcadcbbaddbdabacdddacacdcbdbcdacbdbbcabacabcacbdbcbbabadddbcdbdadaacbddcbcbcaacdddbdcbddbdabacbccddcdbcccabdabcacdcbadacacbbcdccdbabdcbbbbbbcaccdbcdadcabdccbdabccacdbbbbdccbabccdbbabddacadcbdccbdbdccacacccddddaaabddbdabccbddbccdabcaaaaadaaddbacacacbacdadbccbcdcaaddbcdaaaabbadcbacbcacaaadddcaddaabcdbaabcaccbbdcbddbbddbdcdcbbcaabccbacbacdabadacbdabcdbddaaccdbaccdcaadadcccaabbacdbdbdddcccaacaaaaadbbbbddbbaabcbbbacdcbcaccabddcdcacabbbbdaaabcbbbbcabcdcaccddacbdbacadddddccbddabcccdbbbbacbabcdbbbdaacabccadcdbdcbdadcbdbcdabdacdbcdaadddaaabcccbacadabbabdcdaabcccabdddddabdacbdbbadacbdccbbcbcbaccbcddccaadddcabaaacddbacdaccdcbbdabcbdcadcdaacaacaccdaacdbabdcadccbdcaadabcbbcbaaccbbbccbcbcbbdddaaaadcacdadcbdcaadadccacdbdbddbdcdbccdbaacbbbccbadabcacdadaaadbddadabdccbdbcdbcbbcabbbabccabcbcacaddbaaaccbaadddbbbdbbdaacdabacabccdabbadcabaaddacabaddccdbddbdcdbccabbbdbbcdcaabbaadbabbcacddbdcccaccdbaabdacbbdbbccaaacadadabbbabdcbcabbadbbcddccdccbabccaddbdddacdbacdbbacccbaadaccbdcbaabdccabcbbbdacabadccabcdcddadccdabdddbdacbdbbabaadbbbbaacbbbabaadaccdcdaabdbbccdbcdabddaadcbabbcabcabadaacabdcdbcadbbabcbddbacbcdababdddacacbbbccdcdabbacddabaaadbdbddbcddbacddaaddcdbdbdbcacacadcbbcaaccadcdcccbddbddbdabbacdacbaaaccbcbcdcbdabdbdcbdacaccaacddbdddabbdadcbaaaaccadbbccddabbcdbacccddddbaddaaabadbdbbcbcbacacacaadbacccacabbcababacbbddacdacbccbbacaacbdcdbabdadcddabcaaababbbdadadabdddccbacbbccabcdcbbdccaaabcabcbaddabaaadaacdadddcbdcbcbbdbcdaabacbbbcddddcbcacaaaadbabdccddcdbbdccbaacabbdcadddcaaaaddcdaddabbddccdbdaabbddcdcccdaccbdcbddcbdccddbbcdccdadadbbbaabccdacacbadbacacacdbcadabbbdabdadcabdcadbddaabdacccdcddbabcddbccdcabcddbbdbaddddcaccbdcbbdacccdbdcbdcbddbbdabbabdabccbdbbcdadbaacbdcbdbacccadaaadcbbadddadaaabadccbcbcaccaacabcdacadbdcadccddbdabcacdadccadcababcbadddccaddaabbdaddaadccaabcdcbaddabdaadcbadccdacacaadbbbddaddddbacbbddddccddcacbbcdadabdbbdadcaacdccaabbbaddacadacabcbcbcabbaddbdaacbacccbaababdabcbadacdddaaaddccacabdbabbaccbddbcdabcacbcacabbcacdbacdacabacccbabbbdbdadaaddadabddaadbadabacabcaaabccdbbdcdcbbdcdcbacdacdabcacabcacbbdbdbdacbcbdacaabaadcbacaaadbddbdbaaacaababacacdcbdbbaabbdadcaacacbacdbbbccccbddabcaadaddccdaabddabbbdcbbadbadbbdddaabacccdcbaaddcddbdbcacddddbdbabdcdabaacdaaaacbaddadbcdaddbcccdbcbbbadcdccccacabcaacbdaddaddabbcabddaaaaadbcbbbbabcacdddbdcaddabdbbdbbccddcbcdadaaccacbdaacbadadaacaddccdcabcadcbdbbbdccbbbbbddddacbcdbdbcdaadccbabbbdacacbcdacdabbbcdabbcbdcdabaaccbbcdcacabbcbaabbdcbdbbdbcdbacacdbababcaccadcccddcacabcbdaacacbbddcacddcbbdbbdadabdbbaaaadabbccabbcadacadabbbccabcbdcadbdcbcccdaddacbccdddbbdddaacadaabdbdccbcdcbbccccbadbcbdcbcabaddbabbabcccdccabadabdccaaabbddcabccdabcdcbdddacccdbbbccbdaaacdcbcdbacbcccdabcaaccbddccbaacdcadaadbcbcaaaabbcccddacbabdbcdbcbcbcabdcadaccdbcddaccbbbaacacddddddcacadbdaccaabdcadacadaacbcddbaccddadacbadcbacbddacdbacaacabdbccabbaccddcccdbcabdbdbcabcaccadaaccbacbdcbacdacdccdbdcdcbacbaababdddddcbbcbcdcccdccdcabbddccdcdbbbacbcdcabcdddbccbbcaadcdabccdcabaddacccdaabdbdddabbbdbcddabaccbddcacaaacaadbdcadddbccdddcaacbaacbccaaaadabacbbcdbcbbbbccddbdbabaaccadddbbdabaddbaaddbaabadbbcbcbcabddbddabcabacdacdadcdbaaddaddbabaabbddcacacdacaabdcccdbddcadabcccddcbbddcacaaacdbaaacccadaaadcbbbdcbaabadacadadbbabbbbdaacbcbdabcbcbadbabcbccdbddccccddddaddddcaccccbbbaddbbabbdaccccdcdcccbacbcbccdbbbadbaaacbcbaadbcdadacbaddcabcdabbbaaaadcbccdaaddddddbabbbacabdbbdbcbdcacbcccbbacdcdcdbaabbacacadddcdcccdacdbcbabacbbddbcaaadcddbdadcabadccbdcacbbaccaaccccdbcbcbcbddbabbbbadacbbdababcbddbacddcaacbabacbdbabccdcbdcdddcbdacbdbccbdbacbdbcabdcdcacccbadbcbcadccadbbadadbbccacbaabbabbadcddbbdadadaabadccccdccadddaddacdbbbbcabdcabcbdcacbbdddbaacdbddddbcbdccbdcaabcccaadabddcccacdacbcacccadbdcabbdacdaaabdadaaaadaddcadbdccbcadbbdccabcadaccbaddaacacbabdbdbbdadcccbaaacacbddadaaaaaacbadbbaaaddbddbbcbcbcbcdcdabacbdcdccaabbaacbbccdcabcaadcaccbaaabbaaacaddaabacbacadbdaccabbbaaabadaaaddbddcdaaccdbddddaaaacccdbbdaabacbbdcbdbadadddbddbdcbbdadbadbbdbbcbcbacbcbadacbcbdbababbccbdacaacadbbcaccbcbdacdbbacadadaadcabddcddbabdcadcdabdaacbdcababdabccaabcbaddccaaaaadcdcddababbabbabbadadacaadbdaaddaccacabdbccabbcdabcbdcaabaacddbadbcaacabacccacabdaccaabbbcbaddacdcbbcacdddbdcaabcbabdaadadaadbdccdadddbacdcdcacddbadcaaaaccdacbadadccbbcdbdbbdbbadadbaddbabadbdabbcaabbdcadbcbbcdcdbabdbdbbbbbabcdccdcdabadaacbcdcdbabdbcaadcbbdcbaccbbccabbcdbdbadabacdcccdbbcababdddacdbacdbabcccdababccdcdcbbaaccaaccacbbbdbdccdbabcddddaadbccacdadbbcdbcdcdbcbbacacaadccdbdabccbcbcbacabddadbccbacbcdaabadcdcbdcdcdadaadadadaccbcccadbddabdbbbaadaabcdadaadcdcdcccacabcdacdadaaadadadcacbdacadbbccaacdbbcbcdbcaacaadbcccacadacddbbdbdbdbbadacbabddcbabddcbdcbdabbddbcababccbadbcabdadcbadacadccddcadcbddbdbbadaadaaadbbdacbdbddcdaacabbcbdbdadddaadcddcbdbcaadccadbabaccacaacdadcbdbdbcbbdbabdaacddacaababddbbdbcabcbdadaddacbbbbbcaabcabcaccbcdbbdddabcbcabaadddddbbddaabbcabaaaadbccddcbcabbdacaadbcacbdbcdacbddacbdbccbdbdcdbccdcbdaadaaacadbaaadbccdaacddccbbcdccdadacadccacddcdbcacddaabbcdcbcbbbadddccbdcdbababdbdabacdbaabdbdacbbdddcdabbcdddbabcaddcacdcbdbbbabccabbbbdbdabcccadbcdaadccabacbbbaadcdbdacabdbacccaccbaaabbdcacbcbbaaabbacadabcacdcbadaccaadbacdbdaabccdbcccdccbdbcbbbdbbcbacaaccabcaadbacbcccbdabcddbbccdbdadaddaaaccdbabacbbbbddccddcbccddaacbdcdaadcbccaacababbdadccabbdaddddadbabbadabccadcbababaccbcdbacadbcbbcdabdbddacabbacbccdadcacbbcaabccbbbdaabacbbdcbdddacddddcccbdccabdadddccaabdbdbbcababccadccddadccadcadddbcbbbaaccdcacabdccdadccdbcddabcdbddbabbbbddcadacdccddbabcddababbabbadacacbbadcdddccabbdcdbdbbbadaaabbbdbbdcbccbdcacbbabdaaaccdabadabdaacdaaabbadbcccdabadacaacdcadbbccccccbbaadbccbdbdaaacdcbbbaacbdcacbcbdcaaacbcccabcdbacdddcbbddcbbadccddcbddcccdcacbaabbbcacbbdabdbbdbddccdaaddcbbcbddbbaaccbbcbdbdbcaacacadcdbabbcbaccbacdcddcdcacddcdcbccdacacacdbdddcddacadcdcbcccbadabcdbbaadbcbcadabddbcbcaaadbadaaadcbcbdddcaacadcaabcbdbbdcddbaabccabadccdcadacbdbdbaaddcaadccbaaddbaccadaaadadcacdadbdbdcbdacdcacbabcbaacbdbcdaacbbcaabbdaabacbbddbcdccbbadacbdbdcadcaddcdbabcaabaaccbdabaaabaacdbdbabbddcabbdddadddbcbbaabddaacbdbbacaaacccadacdaadadcaccbdcbacdbbaadbbdbccbabbccbcaacdddbdadaaadddaadbcddcbdaaddbbabbdabcbbcdacdcccbbccbdadbabacdacdcaccadcbbcbaaddccaadbbdddadccabadcbbcdbbabacabbdcdaacdacdabdabbaabdabaacddaddaddddcbbcacaaaaaadacabbcbdbaccabcdbddbadcbacaacdadddccacccbcdaaacaacbaddbadbcacbcbbaadcccdccdbbcbacdbddbddacbacaddbadcbaababcdbdbbaacbbcaacccbbabbcdcacacccaaadcadadabdbaabcbcddcaddadccdadacddbacddcdaaadddcbdbbbcadccbbaccacbaddacdabcbbbaacacdaaabcbdaacdbabdacabccdbbaacaacacaaccabdcdbcbbdabcbcbbdcbcccaacdcaacbbdcadaacdacbcbcadbdbadabadcccddbcdccbacabbcaaccdccabadaaadbcaadddcaaccbacbacbdabbbbabdaaacdccbcdadbabadbbbbabcabaacacababdbcdcbbacdbbaacaacadadadbcaadbbbaadadbacaacddbcaabaacacbcabacacbcbaacddbaaabdbcacaaddaaaddbcbcbddbddcdabadcabbabbccacbbacaabbccdcacaababbacaccdbbacabcbcdbdbddbbbccadaccddcbbadcdadacbabcccadddddaadcabdbcdacbdadbbddcbabbbcccbdcbacddcdabcddaaddadcadaaccabcabddabccacaadbddcbbbccdbbbdcdccbaaaaddddccdbdcdaadcdbddbdcabbbaadaaacdcaabdadaadaabddccdaddbccaaadccdadcccdcaddaabccadccbcaaccbabdaabbcabccaacbcdadbbbdbaaddbdbcbcacbaabbaaddbbcddaadbbdbdcbaaaacdddbaaababaadbaabcdbcbabccbbabacddababcdaaabaaddbdcbabddacdcadacadbcdaaaadcbbbdddddbcdacacadccbccdadcbbddbabbcdadddcdbdbcdcaadcbddbbaaadbcccddbabcbacdcccaadbbadcddbddcbccddbabbaddbcbbcddbadbbddbaadacccbadabadcbaaacadabccdbadbdccddaaaddacbaddabdcddaaabaadbccbccbadcbbdddcbaaabbddaaaddccddababbcabcddddccbaccbbdaabbcabcadbbdabdaaaabbcdaadbaacdbddcabddcadacdddbbcaaacababccbadbccbcacacbdadbaadaaacbccabacaddbcbbddaadcbdcabbcddcbdcbadbdcdbcddabadacbacbccadacddbdbbaddccddabbdcdadcdabcdaddadbddccbbddbcdcacadbdbddddcdbbaaccbcdbacbacabbabadacaaacbacaaabcdbacccaabdbacccbdbaadbcbdbcdbdccacaabadcadacabbdbabdcacccadbbaadaadaadbddbbdadbaacccabaacbabbcadddbacdcabcadcbabdddbbaaacdadcbdddadbbabbbcbbcbabaabcbbaddccabccaacadbbabcddaabadabadadcbabdccdabdbdabababdadcdcbabbcaddaccddccaabbccddabcdbddbdccddacddcbddaadaabbdbacbcdcbdcdcaabbbadabdbccacccddacabaacbcabacbcdabaacdadadaacbbaccbabcdccacbcbcccaadcdccbdcdbccacbcbcacbbbadaaabbabdcdaadbaaaadabaccdaaaccdcbbaccddddcccdcadabcdabcabaabbddcdbbadaadcdbcbcdaaacbcabbbaacddcbaadbcbdcbcbdadaabcadaacbbdcdbbcbdbbaaabddbccbcabdbcdcccdccbcbbdaabbaacacadbdbcdadbadcdbcbbccaaacbdcbbbcacadbbcbabcccdbadbcbdcbaaadddbcdbccaabcbcdadcdbadbbdaccdbbaddccbaacdcdbdddbbcdcbcabbdacaadbccabbabbadbdccddccbadaddadaabdccbaabbdaadbacdddbddccadcbacadaaacdacabdbdbbcdacacbdcbcdcadbaacaaadadcacddcaacbadddbcdcadcabddaadbdcdacdcddcaaacbcabdbbbdbaccbabcbacadbdbcbddbabbdccccbbdcbadbabdcbdcddabacdccacacdacabcdadaacaccbacbddbcadbdcbddbdccbcaaabccdaacdbdcacbddcdcdbadcabcabbaacdbababdccdcbbdacbdcabbacbacbcdacaaaadbbcdbcacbdccdcbcbcccabbbcbccbcbcacacbabcbaccaaddcbbddbccbdccacbacdadcdcdaabadabddcddadbdadbaadaacdcdcadacdabdbbcddbcbbccbbdbababbcabbcacabbdaadbbddadccbcdabcbbbdadcaaabbacbaabcbcaacabbbbddbdccdacbddcaccadacbbaadbbdadaacdacacdbaabdbcccbadccbbbcdaccdbcaaddcacbbdaaadbdcbacdaddaaddcbddadabdcdabbcbacbbcacdabdbcdadabbddabbdbccbbdaaccdcaacccbbcacdbbcdaccadacdabcbbabbdbaaaadbaacbddabdbbbcddcabdcadbddbadaacaaddbbcbbadbbcccabbadbddbcdcbbbbacdbcdabbcabcabacaababcabcccbaaddccdadddcaacdadacddadbbaacdacdabdbacdabcdaadbdaacaadccdbbcbbccadccdbcdbbcbaabccadcacccbabcacdcadbcacccaaaaaccabcaddadcaccdddddcacddbbcbdaadbbadddcbacbdaaccdcabccabdcdddccaabdcdddaabdddacccacbdcbbdacadcccbcdadcdbdbdcddcbabbcddcbcbcbccdbbcdabcabadcbdaaccccdacdbbcaccccdbbbdbcabddacbddaabbbdcbbdacddcbcbcbadbcaaacaacacacbbdcdcadcccbcacbddaacccbdcbbdbdbcadcccdacbddbadaabbdbdcaaaacaacbaccaadcdcdbaddaabadcacabaacdabddcbbbcaacadcbadabdddbbcbdcbadadacbccadaaccdcbdabdcadcdcdbbcbacdbcbcdbaaddbaacdddcacbdccdbdbbbcacacaddcbbdbacbababdddacbbddccbdcccbcccddadcababbbdbdccabbcbabbdcaaacbdbbaacdbcbbbacdbdbbcadbcccbaaabadaaaacccadcacacccbadbccdccdbcccacabaadccdaddcdadadadcbacaddaacbdccbbdcdaacbdcccdabacabbabbbaadacacaaaadcdcddcaabbdddddaacdddbaaadcdcdadcddabbbabddcdcacaaaaddbbddbbdcbacaccabcadcccccaacaacabcbbdadabcbaaabbaaccaddbabbcaacbdbdbdbbbccddabbbbbbdcdcabccdaaaaaadbddbaacaabdccaaddccbcbddaadabaaadbdbddcbbbcbbabcbcbdbdadadcaadaadcaaaddcdccbbdbdacbaddacccbbaaaaddadcabcabdaddbcccddbadadbddabccdbcdcaccdddaaacdcdccaccaccaaaacdadaddcbdadbcbabbaabdbdcdbddcabdbcbdcabbddbbdabdcccadbacdaadadbaddbcdcdbabdbababbcddbcddcccdcacdcdadddacbabdbaadcddbadbcbadbcdbabccacbabcdbcaccbadadacbbadbadcdadddbaabadddbbcaabdadaaaaaaadacdbdcbadcacbbbbdaddcdbcbadbdbadbcaabdcadababddacbcccccadbdaadccbdddcadcccaaadbcdddaccdcbccaadbcaadcdcdbdabadcbadbbdbcbddbbbbdbbcbabdddcdacadbbdddaacbcbcdacaaacdcccbcaabbddccccbcbbdddaccabaddcbccaccaaabdbdccdbdbdacdcccbaccdbbdbbaadadcdbaacbaabccadcccbddbcacdaacaccaadaccbdccadcbabccdccbdbcdacacbbcacdbabdababdcdacdbbadabdcaccbbdcdaadacbaaaddddacddbcbddaacdadaddcdacdcaaabbdaaacddabbbadacbccaacbadbccadaacbdbcadbddacacbaaadbacadbcdcddbddbdcbcbdcccdcdaadbccbcccbcdddcddabaadaadaddadcbbcaadcaccadddbbcbacdcddcabcdadbcbbddcddcdcccddaacbdbaccbddcaadbbabcaadbcbbabddccaabbcaadbccccadaccbcabbcbdddcadaacbdabcacbccaadacddaadacaaccadbdbaabcbdbbddcaadcccabcdbbbbbdbabaacccdccccaacaabcdadcddccbbcbcddddbddcccdcdcddadccbddbcbbbcdcbdddacccaaacbadbdadcbacabacadbbcdcbaacadabbaacbdccabcdcbabddadcbcbbaacdbcbaabaaacbaccbdcbcabaabaadaadbdbcadcbadbcccdabddcbadadbcbcaacadbbbdaadccaabbcbbdbbabdcdabababbcdadcccbaccabaadabcdccacddaabacddbadcbbbbdbdddbcbbbcbadacadcaaacbadbddbacdbacdccbbbcbcbcddcddccbdcdddbadadbdbadaccdbbaacdddaacbacbddabdabadabbcdcdbcdadbbdddadccaddacddbcbabaddababbaabdccbbbacdccbababdddcababdcccaccadbadcbbccaddddcbaaaddccdccdcccdccabcbcdbcbdbadabdcacbdbcbcbdcbcdbaacbacbbdcbcaddcabcbdcddbddbdddddacabcaabcbcccabadadadcdbcabaadcaadbcdabdadddddbdbbcddccbddccdbacadbbbdbddaaccbabaaccccdbddaacccbadacaddcabccbcaddcdcbcabbdabacdccbdccdadccdbaaaaabacbccddbacdadbccbbaddabdbbbcbccaabbacaaccdddbadacadbcacbaddcdbaacaaddcadabbbcbcdbccadbccbdcaddbdcbbaccdabadbcdbcdbccaadcbccbdabacdbdabdaddcbcabaccacbddbdcbaacccdccdddbcacccbacaddccdacaddababbbdabddabdbbbabcdbddabdadbbbcbabcdadbdcaaddbbacdaaddbbaabcabcdaaddabaccabcbcbabbbccacddcabcadaaddccddbbbdaaccbcbababaadbaacacdccbbdcbccdaddacddaaddcbccccacbadbccbdbddccabdbadbdbbadcdadcdbbbbdbccabacdbacccaddaddbdbddcabbacaadccbdabdaaabddacbdadccabcadccaddcdccbcccdacacdcdbbdddddbdbbdcbcbbdaddbabbbbabcabbdcabcacccadcabadadcccbaacdcbadaccdcbabcbadbbaabdabccbbdaccadccdccbcbadbcaacddddcccdaccbaacdaacdbdacdbdbccbdccdaaabaadddadabababdccbcaabaadcbdabdbccadaddcdddcbcdddacacdddcbbddddcdcaadbdcdddbdacddbdaaaacbcacaacdbdcdbdcbcadcbbabdbddaabdbdadcdcdbcaaccbcddacccbdcdaaddcaaccdccbcaadcdaacccaaddcbaccbaccccdccacadbbbbbbbadbdcbcadcbdadadaabcbdcbccccadbaabcadaaccccbacdbbbdcdabddddbdccaabdacdabbcbbcbbbcccbacbacbccbdcadccaadbcbdacadacbcacaddcccbbdabdcdccddacccdccdcccbbadbdabaacccdacabcabbcbcacbabaabbbbbcbaabdccbccdabccacaababdaaabdbadbbcbcadbdaabcabccabdcdaacbbdccbacaddbddcbdbaaabaccbabcbcdcadbcdcccddbacdbcaddbbcabbdbcaadcdbbdbdcbaacbdbadcadccbabaaaabbcacccbadcaaadcbaabddabbabcbcbbdcdcaaaaabbcdddbbbcadadbaadbcabaadcbacbddccacbbababcbbabdcbdddbcbaddcbdcdadacadddcccddcbdaccdabcbcdbbdcbdbdadbbcccbaaddbdcddcbcaabaabbaaadbdadddcadaccdcacdddbabcadacbdaccaddcaccddabbabbdaabcbcddcdbbcbcbbccadabcabccbdbabbdaaadcabbdcdabcdddbcbadbcdcabdaaacdddcdaaccacdbabdccdaccdbacbddbbabcdcbbbdddbadcbcbcababaaaacabbbbabbccbdacddbbbcccccccdadacbabacbcaddcdccdbdadcdccacddbdbaadcababcbbbdbccadcadcdacdacbadcdadbddcaadbddacdacdabaabcbdbaacabaccbabadddadaaaabbccbaaabbdcabbccdddddbccdcbbadabbababcacbbaaadaddcbbddbdbcccdbdacbaaababcddccbcbbacdbbddddcaaabddacbadddaaabadcbbacdaaaacdddbdcabbdccadcdbbcdccccbadcacdacddcaddcaadaccabcbaacdccbcdaaadcbdcaccbaddbdaacccadcdcdddadcabcbcaabbabbacddabbadddbdbacbabacbadddbbacdacabdccdcdccbdbaddacaabcdcadbdcbcbcaacbbdacabdccabaabcbcaddaaadadacbdccbcbdaccbdccbaddbacbbbdcddadcaacbddabccadcbacadaabadcbcddabccadddbaddacddcbccadadcababdbaabcaadcbcbdacbbbacbdaacbdcdadbabccbccaccacbbbbabbbcdbbdacacccbdabcadcbcbccbbdcbcbadaabbcabacbddbaaadabdabccababaaacbbaaacdccccddcacddddcacaadaaddcbbcaaadccdbdccaabdddbbcbbccddabacdbdcddbbdcaaacdadddddbacdccdcbbdbcbccbbbdcccddddcacdaabbcadabacbcdabdaddaabdaaccadacbccbcadaabcdabcabdcbdacaddbccbdbdaadccccbddabddccaabdcbddabdddacdbcbbcbddbcdbccdadcdacdabbdcdbbabacdacbcbcbcabbaaaaadacbadddcaddaccdabddabccaddbbdabdbbbbbbdddaabcadabcbdcbbccdadaddcbcbbbdbbbdccdacbabdcadbaddacbdabbdbadabdccadbccaadaadcbcbdcaadabbacacababbbdcaacccbbaacdacdcdcccdaadbacbacaabbacdcaacbcdbddacaccaaabaadcdbbdddacabacdacdadabcbacadccabcbbdddbddadbcdcdacccbacadbdcbdcbbccaadaacbcaddaabbbcacddadaaabcddaabcdbddcbadbcaacdcdbcccdadcbbaaabcbbcdbdabcbaacdcadbaacbddbbcbacddacdcababcccbbcaacbdcaacaaabdddcbbdbcbaabaacacbcdcacdcdacdbcccadcdbdcddcaccdcdbcdabbdababbacaddcccbbbdbcddccdbbbabcccddcdbddbbbbadcdddcbdacdaaadbdbdacdcaaacccbbadcccaabbdbdbcccabaccaaacccdbbcabbacaaacbcadbcdabdccacdcddcddcacbdcaabcdadaccaacbacbbbbabbbaabbaadacddacbadcdbabbbbdddbcddccdcdaddbdadadbccdababcbcdaabcccccdbcbaabccbbbdbbbcadcdcababddcdadaacdbaccdbadacaadcbcaaaccdbabadcccbddcacbdbadbcbcabdcabcdccbdcbdcacbcdbccabbdbcdaabcdacdcdbdadbdadbabbcdcbbbbddcaaadcccbbbaccccdacbbdddbdacdcdbabdbdaddbcacccadbaddcadbbacccbcbbcacaddadaadabddabcdbcbdacaddbdabdbcaccddbbdbcddbbbccaddcbdbcadabacabbcaabbaaaccaaccaddbdbdcaabadccbaddabdbdbdbacaccbdcaadbacccabbcccbcacdbdbbdadabbbccbdabaaddacacbdbdacbacaaddbccdccbcdaaccbcdbbacabddcbaaacdcdbdcbdddaadacdbdddbcaacadbbdadbdcccaaabdabdbbcdbaacadccbaacddbadbdadbbabacaddcddaaacacdcbacdccabaacadadbdbaacaaaccdbdccaccddbcbaaddcaabbdaddcaccdbbdccccbaccbbdacdcaccadacadcbabbdababbcbdcacaacdbcadcbbbbcdddabcaaabcacccdbcdddacdbdcdbabbccbadcaddbacbdacbddbbbdaabaacdbbcdaaabcadcddddbbbcbbcdbdccddcdaabdadbcdadcaabbdcdaaccbacadaadccdbcbddabbbdbbbdbcdacdcbacabacddbabbbaabcaabcabbaadcabccacdaadcaadacbddcaacacdccdacbcdaabbacacacdcdabcdcbcaccdddbbccbcdcccbcadbbdbdaccacaadddbaaadcaccbdacbddaddbcdbbdccbdadaaddccbbdbacbaacdabddbadbaadcaccdcbbbdbcdbdcbaccaccdbdbdabddabbdbcbdccacacaaccccaabdcbbccddadacdacdbbbcaaaabaadadcdbdcbbacccadcdcbdbabbabaccdaccadbbacacbcccbdddacdcabbbdabcaaabbbdccccabddabaabbadbbaddbbcdbbbcbdcbcabdaaadddccadadbcdccbdaaaaadaadcbaacbbaaabaaddbaaaacccddaddbdcdacbbdddabdabdacbcabddcdbddaacdcbacddcbaadccdbbbccdbcccddbaccabddbcbcdbaccbcabcccbbdcabdbaccddcacacdaaccddadcdbaddbcaddddcadcaadcbccbbadcbaaaccbbabbbadcbadaddadddbdcdadaccbbbdcccbadbbaabbddaabadbbccdddbabbbdbddabadbbbaacbbdcadadacbaaacdcdaaacaaadbcbcdbdcdcadbdbdaccddbcabdcaacdbacbacbbaaabaaabbaadbcaacdabdbaaaccbdcccccaacccaaabcbbaadcadadadabcdabaccaccbbbcabdbcabbcdcaabbdbddbdbadaabbddbcccadbbdabdbabcaabacdbbcaaddcadbdccbbdcaccabdccabababcadbacdddcddcccdcdcccddbdbdadcabbbcbcdcadaddcccddcadcaacdbacdbcbccaccabccdbadbcabcabaacbcbdddcaacacccdcbdaaabbbbcacaccbbabddcbcabdcabaadbadabbcbcdddadcdabddaaadbbbbadbccbcbccaaaaadbdacdcabcdaccdbcccabdbdccdbbdabdbdcddabdaaacabccacabddbddaabdadaadcdbbccddacdaaddddcdacaccaaabadaabccccdacdcbcabdddadccbbacbdbaaabbcddcdbbcdcbccccbcdbadccaaccadbdcdbddcccddbdaddacdcbbbddacdbdaaacdbccbbaddcaabcbddbddaabdbbdaaccccdddaabbacbccdcddcdaccabcdaadcadbcabbbcdccccadadabbddccddbddaaadbabcdcbbdadbbbdddacdbbcaccdbcdbcacccbabbbcabbbcdcacbcbaaccabccaccdaccbcabdcbcddcddbbadbdbdcddbabdcdccacacabbacddbcdbcbaaabbacdbdabdadcbadbaaadcabcdcadaccaacdbdbbccabaddabaaaaabbcdcddabcdbdbbcaadbcbaaaddacdacdadabaabbcbddddbddccaddadbbccacddadcbbdabcaabbaadaabbbacabddacdddabbddbbaaaadbcddbdccacacabdaaaddcdbbadbacdbbdabbbdbbcdaaabbbbdbbaacdbbbcdbbcdcbbabaacdadcbccbcabcbddbbdccadbccaaabcdbdccacccaabbdcbbbacaabcbbaacddddcaaaccbacbcacbbdbcbdbabaabbcabdddbdcabdabcacacbdbbaacdccabbccbbacdcbbabccaabcabadcacacadbbbbdacbcacdcddbaccdbacbbbbcddbadaddbabbdddbccddbadcdbabdaccbccaaacaacdddccdcaaadacabdbdbcddcabaaabaabbbabbaddbcccbcaddbcdaccdcdabddabbdcdbacdaccbddcbadbdbacbcaddcddbdddccbacbbcaabadbbcbcdbcbdcbcddabdbaabbadcbcccdaaabbaaccbdaaccaaacdbbccbaacacdbbdbcabaaacccbccadadaddccdaacbcbdcabaabbbdadadbdcbabcadabacbcdbbdddadbdddbabddbbcabbcdabcdabbaccadddadcdbcdcdadbbdccbbbcbcdabddbbaaaadcdddabbabcaaacdaababadbdcadcbaaabcbccbadaabddcdbbdcccbdbcdaddcabddababbddacbaacdcddbddcccbadcdbdacdaabbcdcbcdddadcbcbcbcdcdbdcacccbadacddaadbaddbdddbcbddcdadaadadbcbdcaddaaabcdbbdabbabbcadaddcdbddcdcbcdbaadbaaacabdbdcdbaaadacdabdbbddaccdcccbadadabbacbbabdccadddddababcdabbdccbbbaddcbcbdcbdabcaddbdacddbdabbdbacadccbbcaacddcbcacacbcdcdabccbbdbbbadcddbacdccacbcdadddccbaacbbdcddaacacddbdabcbadcccdbbcbabaadbacbbacaaacdcddbacbdcbdbddcbbbdddbaabbacddbccbbaccbbbbcddcbddacabdbacadcadacccccdbbbcbabbdbadaccdbddcabadbbadcdcbabcaacdcccbacacbddbdbbcdcbdbbcdcdbddbdbaaccdbaaacdbbaabbdcdcbbaaadcabdadbddbdcaadacdadcbdaabbcbcaabcdaadccbdabdadbbdbcaadddacdddcccbcddcbcdbbdcddddcaacaabddbacabcdacdbacadccabbbdccacabbbbbdbacbbabdabcaccdabcccdaabaddccbaddcbbdbcdcdcbdadcdcabcacbabcdddcadbccdabaaaabacaacbdabbcadbdaccbbcccdcddccccbbccbaadbbcdaddaabcdabcbcddbdccbdcbccadabbdddbbdcabbbdccadbabacbcabcbccccaabcabdaaabaccaddabccdbacacbdaabdacccbccbadbdabacbbcadccbcbcbaaaacabcbadabddccdbccabbdaddacdbaaadcbbddbbbccdcbdacbdcbadadbdcdaabdbdcadbbccaabbccaaaddcbdbcbacbdabcabcabdbccaadcbaaaabaccaacdcabcddbbacbccdaacddbbdbabdbcbdcdaaabbdacbdcbaacacbdacabadacacbdbccdbddcdadcbbabdcdccacaabbdccdcdabdbcdcabdcacdabdbddcaddbbaabccaacbdcbaaaaccaabacacaccbbcccabccbcaadcccbbdababadabcdadadbaacddbddccdbccdbbdcccdbbdbadacdbcabbcdbbdaabacacdbcddcdadaccdcdabdbcacbcdaadadcbbaabbacdcdcccadabbcdaacdaacadbdbcaaabdaadbdbabcbccacaaddcadbbbcbbdcbacdbdcaacabdabbbdbcbdbabdadcdcdaaababdcabdaacccacdcdaabbbdabbcdbadbbdbaadccddbcdbccbccbddbbdcdcccdabbcaacddcadbaaccdacbcbddabcacabcdbdccdbbddacdcdbdccabcbaaadbaddbcbadcbadbcddbaabdcadadabacdddccdbdbcdcbabbbdcddbadaaddaaaacbdbaadddbadddbabcdcbaadddddbcababdbbadddaaddadccdccddaacaccdddacadabbccddcddaadaccddbcbdbbddbaabdbbbbaadbcbbacbcdcdacbbcdddadacdcdadbcbacbacbdcbdcdccadddadcbabcccaddcdcbbbbdbdddbbabcbbabdabadcdcadcbbdacabbbdbbadacdddccccbacbdcdcddbbadadcbcaddbcbcddbdaacaddbbccaaaacccdcbdbabacbaaaabddbaabbcbdcdbccdbcccddaaccaaaaacbbccdbcccccbddaccdbadcdcbcacdabcaddcaaabcdcabbddccbbaaaadabbdcddababdabcbaaccbdbcdacbacacbcbbabaddccbccdaddacbdbbbcbbadabcacaaaaddaadaadcbdabdbccbbddacbdbdacbcdaddbdcdbdcabbbadcbbcdcccbacdbbbbdcdcacddcdbcdcaddcdaccadcdbcbabadbdddbdbacabcbbcdabcbdaadaccdcdcaddadacdbacaacbbadcaadbacbbbdaacbcdddbadbcdcbaaadbbcccadabcaddadcdbcccddadddddcbacccccdbbbdbcccbadaadaaadddaddbdbabbbbadbccbcdadccbdaabdacdbbadddbcadadbcbdababcbcbbbccbcdcdbdadbcbabbbcdadcdbaadaabadbcbbdbacbccacbbdcbdbbabbacacaaaabacdcdcaadadaddabbbacbaaacdcdcbaabaabadadaacaabcdccbcbabcaccdaadbbaabdccdcaabacaaddaccabdaccbaacdcadbcbdaccdddacddacdaadccacacbcdbcbccbcacbaaaadacbdadcadaaccbdccbabbadaacbcccacbacbaacadbcdaaacacaabccccbbccdbcdddacabcbdcabbcabddcacbcacaaaacdbbdbbaacaddbcbbcaadbdddbcbababccadddbabacadabcdbdabbcaaacaddaccaabbcccdbaccdbcdcadbcbcbdadccdbdbaabbadddcddcaccccabaabbbbcdacabccaadbacbcccddadcdcddcbbbcaacbaddbbdcdabcdddbbadbdbcadbadaaaddbcccababdddddabdadcaababccbcabbadcbdcbacdabadabddacbadacdbcdddabdaddabdcbbacacbdabaaabccbdacacaacdacabacddcdbcbcdccbbaabccdcdbdcdabcbccdaadacbcbacbcbabbaabcdbddbdbbcddccbabbbdddadcdaccdaacababbbdacbcadcdbccababcbcdcbbabbdacababadabaadaabddbbcdbbccaccdcbbddabdccabbaccabbbadcdbbbcaddadcabdddaccdcdbaacbdccbcabbddacbacabdcdabddcdbdbdacaaddcccbcaadabbbbabacabdbcabbbdadcbccdbcbbdcbadccdccdaabddccbcdaacbabbcacdacccabadbdbaabddcdadccbbbdacbbacbacdcdbdcabbbaaddcabaabacbbacbadbccbccdcbadbbccaccbaadaabcacdddabbbbdaccadcdadadccbcbddacadbcdadbdcbdacbbaccdadcbcaabccbcbcccbaaaddabccbbdbbdccbddadddbacadacaadbccdccbadadaccbcabcaaacdacbcbbdbdaadadadabbbbdbcccababdcacaccbbaabccddadcbbabcabaaddbbbcabdddbbcbccddccacccaddbccccdadadaccababdcbbdcbbcdacccacbbcdddbaadaaacbbadbcdbaabbcccdcccccdacbbcdbdadaddacaabbbccababaddabacbcacdadcbbccbdabcabddbddcdaabbabbcdbcddddcadcbccaddccbcaacaabdbbbdcbcbccccaadadadcdbdbcbcbbacaaabacaaaaccbddccacddbabcbbccaccbadaaddadbbbcdcccdccdacdaccbbabaccabdcddbcbcdbdcadadddbababddbcbcdcbdaaacccdbdcddbbdcdcbabccccbdabcbbadcadddacacbabbaaaaaabbcbcbcbcbdbdddaccdcaacdbbbaadcdcdacbacdcbacdacaccdbabacaddbdbbdadbbccaadbcabdbdbcbacbbddccabcaaadbcdcdbcbaabadaddcbbbaabddaabdaababcdaaccadabbacaadabdcabaccabbdaddddbdccdadddcdbabccbadcaccbcadbcbabcbcbadacdabcdabaaccaacbaabbaacabcbabaadbacabccdcdacdcbbbbcacdadbaccbccdccacaabbdcbcdbabdbaccdaababdcbddbbdbccbbcdbaaadbcadddabccacddcabbbcdaccacaaaaddadbcddbbdacdbddbcadadadbdacacdababadcdbbdbdcbacdcaacbbacdcacdcdcbdcdababcacadbbcbaaaaadabbbddccaacadbacddadbbcdabcaddcddddcccdacdddaababbccadcabcbdcbbabddbccbcccdcdbdcdaacbbdbabdbbcddbbbbcbcdcbcbbdacaabcbbcaacbddbbddadadddccbddabdbcbaaaccabcaabacdcbdaddabdaadadcbbaccbbcabdcbdbccadbabcabdabacbdccaacddcaaccdcbaddccbbcbbcbbabdddacdcdababbccabddcbbacbcbddaabdbaacbabdbcbbcacdbcccbadcacdbbbccddcdbccacdbadbdcbdcacaddbbddabaaacbadcbcabacbcbddadbccbdbbdddacadbcadbdbcbccaaaddddcdbddadddcaaddabbbbacbcbbcdcaaccdbcbcdaccccbbacbbbbcacdbdcdabdaaaddbddcaccaaaabbdcccdbbbaabbbbdddadabadcaababababcabbbabddccdaddcbdddbbacdcadaaaabcadaddbbaaddaacbcdaaaaccbabbcbbbccdbdacccdcdcbbcbdbdbaddbdbcbaacabcdcaccdaddbcdccdddbdadaaadbabbaaadcddcbaacaaaacadbccbbccdadaaadccbadacaaabbcabdbbbbbabbaddbcbdaacccbdbadacbdcdadcbbcddabbabdaddccaaaabccdddbacdbdacbbaccdcaaadddbaaccbcdaccbdabadbcadbcddcdcbcddcadcbdabdacdadcdbacbcddbcbcdcbdccadbbdddcdabbbcbdbabbaaabdaadacbacbacccabaaaaadcbdadcbbccbadaddaacabdbbabccdcccdbccbccdadadadaabcabacaacbbdabbdcdcadabababdbcdcaaddccccdabbababccdcacbbaaddacbaababcbddbadbddadcdacaadbaaabcadcbadbacbbbacddbadaabdddacabdcadacdcbbcdcddcccacbaddaacdbbdacbcaaadadcacaaadaacccabadaaaddacdccddcacdbcaaaacdbbbdcdcdbcbdabddadadaccaaddcacccdcccbcbdbcbdbddcbcbcbdaaccadaccaaaabddcdcdbcbdddcbbaaadddbbdddcbdccdbbadbdaccccdcaaabbdabbcabaadbdcdcddccbcbcdaccacccdcbbdaacabddccadbbccddcacdbccbbacccdcdaacbcdcbdbadaccbdaccacaaaccbdadbdccaaccaabcdddbbccdcccabcadbcacdcdccbdcacdcaadabcccbbbdddacabaabbbdccaadcdcdbcabcbdccccdacdacaacaddaaadbacbcaaadaadacdaaddbcbcabccdbbadcbbbbbaaadcacacdaabccbbaccadbaaaacbdacbdcbdcddbdcacabaabacacadbaccdddaaaddcaccccbddbadbdbaddabcbdbcadcabaacbdccabdabcaacbddcbdcdcdabbbccacddaccbbadadadccdabaccdaacdcadaadaccaddaaabbdcacdaddcbaaadcaadaacaabaadcdbacbdcaaaaaaccbbdaaabcbcbcdbddaabacdbdbdcdacdccabcddbaaabaccaddbccabbaccdaacadcabbbcaacdddbbbaaabababcbcbcaaccadcabccbbbbccadcdcbdaabccdcbcbcacbcdaababdcdbbdadbbbcbbdabdacdabbbdbcdabdaccbaadddacaacbbbbcadcdbaaacdcaaaaddadddabbbdacbdcbdacbbbbbabcbbcaaaaaabbacbadaacbbbbaaabaadbbcadbddaacbddbbcabaacbddaacddbbbbddcdbabcaadbdcdcbadbddbadcadbdbbcbbccbacccddbcaddddabadbaadbcdaddaacababbadacbcadabcbcabddccaacacccbbdabadaacbccdbbacccaacbdccbdbabcdbcabacbddccacdbcadbbbadaaddabdacbdaccbbccbbdddcddabdcdbbbbcbabbaabadcbdacaaacaaddcdbbdacaaccacdaccadccaacbdcbadadaccdcddbddcbabdbdaddadcdaddacddddddadbcdcaddccabcbbdcabcddbccbbaadcdadabccbdcdabaaddccccbcaccadbccdbcddaaddaabaccaddcadbbccabadacdcdcbacbbbbddcbbbbacbabaccbdbcaacbdbbcdddddbcabbdccdbabdabccbcdddbaacddcbdabbbccaccdadddbacdbabacbacbddddddacdbcdddbdcacaddcbdbaababdbddcadacbcdbaababdccbdbdadccaacabbabddcbadbadbbbdaaddaabbdcdcbcbcbacacbbcdccaadaaacadbbdbacbcbdbdcbbdbbcdbbdcbdbbaabaadbcdcabcacbddbadaabbabbcdbcbabbccdbbbdbccbdcbdbbdaacabbddcdcacadaacbbcbcdbabadccaccdbccaacbccdadcbdcaababbcaddbbcbbcbbbcdbbccacbdbaaadaddacbaaaadadabdcddccbddaadacbdcccdbdbbcbcdbcbbadcadcaaddbbbdcdddbbabcabdcccacacbbdabdbdcacabdaddbcdadcbabddbddbdcaacaddaaadcabbccdddacddccddacadabccdcdbcbaddddcbcbdaaababcccaaaaabbccdbbdcbddbabaccdddadccaccdcddabacaaaadadcaccbdcaaadadcaabdddcaddabaacbdbdaabcacbbdbddcbabdbdbbcbbddbbbbccddbbdddccaabddbddabacbdacbcbcbccdbacdccdddacabbdddaabdacadacccabcdcdaaababcdbbabdddcbdbdcdcddbacacbdcaabcaddccdabccbccbdacdaaddabdababacccccbbcacbdbbbccccadbbdaacccbdcdcaddaaddabbababcdcababccccbddcdccbcdabcdccdaaccbaccbdcbaaccbacbcadcdadbdbabcababbcaabaaaabdccbadcdbcdccabdabcadcddadbaddbdbccdcabcbcacacdabdddbcbddbcbddcacdbabdbaddacdcdddddcaddddbdaaaddcdbbdbbddddacbcabaacbcbaacaaaabdbadbbdbdbacdcbbbdcaacacbccaacbbaacdccdacdccadccdccbdddcddcadaabaaaadbcabbbdbacbadaddbdbccbbadbbaddcbdaadbdabbacbdbadabbbbdddabdcdadcccbbbdccadbcbbdddcacdabdbbadbadcabdbacbabddcbdacbbcdbdcbcadacbdbbcbdccbabbadcbbdbbddacabbcadcbddcbbacbbbcddbadbcbccddabdbacdbbaabcaccaaccaadcccadcbcabdaabcdbadcbabaccabdacdddbaadcbdbddbdccccddcadcbcaabdabbdccacdbcababbdddbbcaddcabaaaadddcdbdacbbccadbcddadbccaaaccdcbaddddaddcbccbbabddaabdacdaadccdaddddcdabbaaddadbacdbbdbdabdcbcbcddcdbbcddbabdbadccdbabadcdbddcbccdbabccdbbbdcdbadbbdcbadbbbddacbadcdbdbddaabbdbcabdadddbacdbbbbdcbcbbcbbddbbabcabbbcdbcccdbdbbadbdbcdcdaaadbaabaddccbdcccacabcccacdbdcbadddccbcabbadddabcdcbdbdddaadccdbcababcbdddbcddccaaadbdcabcccbabaddacabacbddbabbabbbcaaddbabacccddbcbbabdbabcddadcabccdbdaaacdcaddccdabcadbbdbddbcaacccadaddaacbadccbcadccbbcbbcaacdbddcdcdbaadaddddadbccddcacbcdcacaccadbcadbbbcccabbabcdaaacccbbddbcaabacbbccadbaadacdaadcadbcbdcccccdaacbaccdcaddcdcdddcccbadccabcbaccccbbdbcccabbadadbbcbdbabbacbdcadbacdaabbdbacbbabbbdccbbdcdabdcbacccaaaaacbcbaccdccdabbbcbbdcabcbdaccbdcabbbcdcbccabccdbaacacbcbcbbaabbbddcaabddbccdbdbccbcccbadccadcadadbbcbabbbcabdabdbaacaccacdabaabddcdccdaaaabdccdadaaddcacaabdddccdddbbdbdabcbcdddabcdbcbcbdcaabdbaacdbdcbcaddcdabdddcddabadccbdcaaaccdcbaddabdababbdcdabdcabbccdccadddbbbcddbdbcbcadadbaacbabbacdbcaddabddcadbaccacdbdbcbbbaacbdcacabbcbbbbdcdbccdaccadccbdaddcbcccdabddccbdabddcbccaddadcaacaddabdbcacbabddbbcaacbbbbdcaabcbabdcdccabcbdbbabbcaaabccabdcaaadbadcdaaaabddbccbacdddbadbcababbaadaaaaabbdcaaddcbcbbccdbbabddbcaaadacabccdadbddcbbbccbdadcdbdbaaddccabddbabbbdaaaddacbbaaadcabcbbbbabacabbdccaaccdbbbbddbdadcbacadbaacbcadaddcbaccabbccccaabdcbdbbccbdddcbcacccbbbbcdccbcbddbbacaabdbaccbaccbacdadcddbcadccccadcdddbcbadccacacdbdabcaddadabacbbccddbdacdbacacbcbdacdccbddbddccdcdaacdcbdcddddcacdcdacbccbcdaadcaabcadadccbabababadbcbcabaddacdbabcbcdbdaadcdccccabccbbaadbdacaacbbbdcddbcdddbaacbabdaccbccacbadccbdacdcdccaacacacbbbddadbcbdcdacbaccbbcaaadabdacbbdaacdaddddcdcbcacdbbadcadbadddcbdcaddabcdbcacdcabadccdabdaacadaadccccbbadadbbaaddaabddcaccbabcbdbccdcaabddbdbbbabcddcbbbcddcbaddaabbbdcaaacadbdacdcbddbccddbccdbbdcabacdddddccccddabdacacbaacddaccacbdcaccacdccdcadccdaaacbabccbbaaacbadcdaabcaaaccbbcdaddaddbacbaddddaccdacabaaababcbabbbadbaaabccdbbabccbccdaaaadcbacdbacbdddaaaacacdcabaacdbdbbcdcabdccddbccaabbdccaadbccdbadadaacaccaaccbcdcbaaabaacacbdbacdaacaabccdcadccdbacccdddcdbdbccbdbacdbddbbccbadadcdacbdbbcadcdbdbdbacacccaccbccccbadbcddccaabcabddbbbbadbcbdcacadbcddccddbacabcabaacadcacbbbdbddaccccbdccccccbaaddcbacaaadaddbdbaaaabddbacddbdbaacaacabbdaddbcdabaaaabbbacbcaadcacbcdcdabbcabccbccdabdacbabddbcdbbdbbbdccbaacbaaabaaddbcbadacbddcddcbdadbcdbbdcbbadbcabcacddabbcbdddbbbbbbbbdbcababcddcdaaaabcbdacbdbcacbadccabdddaadabbabbaaadbbcaddaadaaaadddcbdbdbdbaccacdcabddcaaadccaacbbdcbbdadddcaabaadcbcdbcaabdcdababacccdddcdbabdbcccddcdaaabbccadcaacaddccbbadbacaaccbbacbbabdbdcdaabcbbbdbdddbdddddaaabdcacccccadabbabcdcabadbbacdbcbaacddddcbbbadbbcdcabcdabaddcadccbbcbaaddcbacabaacdadcccdcccbbddbdadbaadbdaaccccacaccdcabdbaaddbbcbdcdbdadddcccdbabcdcdaabbbbabddbcdcabaccabcacaaaddbbdababcddddcdccdacdccabbdacadaccbccacbbadccbaadabbbcadbddabbdaaaccccdbcdcdddadcdbacadccbbcbbadaccadabbbcbbdbdcdcbdccbcabbacabcdbcbaaaaaabbccacddadcdcccdcdbacbbcaadcdbbcdbcaadcbcbcbcbccdcccbbabcaaccccbdbdcdcbcaaacaaabdaaadbbacbddacdacdddbddcacbbbbaccabdcbacbbcdccbbdcabbbbcdacbbdcbccaacbcdacdaacbcadadadaddbbabcabbcdbadcbdcdcbdccaddaaddcbcbabcabbaaaaaadbabcbcddbccccacbadcadaababccdaccccbadbaddaabbdddcdbccaaacdcadbbacccccbbabbdccdabbadabcdbdbcabcdbadcbbcacbaccdcbadabcbcbcbcdddbacdcccdbbdabbcaaacccacabbaccbcdcadccadccadcdabacabdacdbacccdccacdbaaadcbdbbbccbbccbdbadaaddbdddbdddaddbbdddcadaacbbbddbbddaccbcadddbaaaacadcbabaadbcabcdbdbcdbbcdbbaadbcaccdaaadcdbbdacdaadcddcdddcaabaadcaadbddcddbbaaaacbdadaaadaaacdabdaddacdcbabbdabdddaadbdbccbcdcdbbbbbbbbcccbcbdabdddbdccaddbbabbbabcaabaaabcdacbcbadbaddbcddbaacdbbbbcbaccdbbbbaccdbcaacdddbdabaddbaadddaddcdbbbdadadbbcdbdccbdccaabbaadcbdbccabbccbcdabbaadbacacdcdaaabdbcacdbdbcaaabbbcbbcaaddaddaddddcadabacdacbdadabccaabdaadcbaacabaabcbadabbdbddabcacbbbbabaadcccbabddabbacbaaadddabcccacacdcdaaccaadaabbcacdbbbbadabbacdddcadcaaacbbaccadadccdddbbbccbcbaaddcacddbcadddcdbadaacdcbddacddcbbcbcdadbbcacdaddcbacdddaadabcdccdcccdbabbdccdabcdbddaacccacbdcdaadaccbaabcaaabacbcbddcdaaabdabcaaccdcdcbdcdccbaabbddbdcabdbcaadaccdaccaacdacdaaabddcdaccdbcacbadacbaaacbadaaaaabcabbdadcddaadbbcdcaaabcdcbbcbbdbcadbaacbdddbadaacacbabaadaabacbaddacbccdcacbadbabcacadbaaaccdcbbaadbbcdcaccaccdccdaaccdaddcdcadaadbdaadacbabadccabdbcccaadadcbbbcacccabcdacdbdbcdbccbcadbdaccacddacbabcabbccbcdccddbdaddaccdadddcacacabbdbbdddbbcaacbdccdbcbcaabaacbadcaabaaaacdbaccacbbdaddbabddaccbdcdcabaabbdbcaaabbbacdadcbcbcdabcdbcdbbababaaabddbdcccdaddaaaccddddccbbadcdcbcbcbcbcaadacbdcadcccacbbaadccdcbccaadaaacdbabdbddbaccabcdddcaabadbbccaacbdcadcaaacccdadcaaccdbddabcacdbdabdadadccccddaacdbbdabbdadacadadaaaaadbbdacdccbbaabacbbcdddccbbbaccacdacdabdabadbbcbbbaaacbccdcdcbaabddaabbadcbcdbacdccacbbcabdbbdcbdaaadabdccaaaabccacacabbbcdbddadcbcdcadccbcbbdacabbccaddccbdabbccacdbcabdaccddcabbdadddcaabcdaaccbddcaaaccdbabcbadbdaaacdabaababbaacdbcddcaabbadbbdcbbbcabaddcbaacccdbdacbbbcdcddcdcadaaaaaaadccbbcbbdaaabdcbdcbbcbcbbaababdcddbababaccccdddbbabddcdbccbaccbdbaccdcccdabddcacbcdacbcabcdbcbbabbddadabdcbbcbabbddcbbcddcdadcbcbcaaccaaabbcdaaacdbbbbdadcdadaccccacdadccabbdcaabbdccbaaadccadbbcaccdcddddbccbdcdacdbdacddadacabbcaacbbdbdbadcdcaaabcbacbdbbdcaabbabadbaaabcadccbcacaccdadacadaabaccacdcbabbcbadcbbbdbbbcacbabdabbbaacdabbcaaccccdcabbaacabaccacadabdddbbccdadddbdaaacacbbacdbddacbdcddaaababddddcccdbdbdcbdabbccdddbcacabcaacacaaddadbbcdacbcacbabcabdaaadbaacdccadccaabbcbdbbddbbdbaccdabcdbbdcbbbadbdaaccacddaababaacabbdcaaccddcbabccbcddaacbbbcccbbaadddaaccbcddaddcacabccdbbbdacdbbcabdaabdbbdcbccabcdddcbabaccbddccbccbacaadbdcddadacddccdcbdbabdccbadacddbdddcccbbdbabbcbadccdccdadcbbaabcdacaaaaaddbbbcabbacbcbdcabbcdcbccdbbdbaabbcbdccbcdbcdcabdabbdbcabcababaacbcaccdbdacbadaddbbdaabcbacdabbacdaadadcaadbaaadcbbbdabaccabdcbdabdcbcaccbcdabcbccbbcabdcacbdaacdcdcbabaddadcabdabcccabccdbdaadbbbcaccdabbccccacddbaacadccacbdddaaccbddaddbdbcadbaddbbdcaddacddcdadddbacbdbdbccadbcabbddaabadbbccacbbaacacadaabcabcaddacbcbbdbbacaaaabaabdadbdaddbddbccdbcccddacdcadbadbdadaabcbdcabcdcbddbdcabccadcbcacacddddcacaababbacbcdcacbddaabaaccabcbcbcccdbddbbaaadabbddabdaadbbdbbdaccdddbddbaadacdbccdadcacacdccadabdacdcdcbbabaccbaaaabcdacddcbcaddadbbcbabcbdcddbcadcdcdadcbadacaccdadbdbaaccabaabcdaabdbdadcabccbdcaaddbddbdcbdbbdbbddadacddcbbbdcdcaddcbcdaabdcccdcaaababbaadababcccaadddbaabdacadabccdcdadbadbbbbabdcdbddcdabaaccbaaaabccaccccabadbbbccbbdddaddaaaabaacaacccbcbcaabbacaadbcbbdacabdddddbbcbcaccdccadcbaacaaabadcdabddacdcdccdbdadacbcdcccaaadbdacdddbdbbdaabcbadbbdbcbcbadadcdabcccbaaaacadaaadccdaaabbcadccbcbcbdcbbcabbcccdbbdabbacdabdbabccbcddaabdabbbdbaaabacaddbbcabcccdbcaadcccaaacbabbadbacacbddbacdcacddcdcccccddbbdaccbcccacaadacdcdddcccbcddbcdbabcbccabaaacaacabdbbcdcbcccbadbcccabdcaaccdbcacdcccbccbbabbbbbabbcbbbcdcaaadddbcccddbbbabddabddbbcbbdcacbddbbddcbbacbddaaccabcbcbdbdccdccaaadbbbccacbadddcbbcddcdcdaddbbabbbacaadcccbcbadccabbdaddacabadacaccccbcdcbddccdaadcccabaaddabccdadddbdbbabcdcacdadaddbbaabbbcbadcbddbccadbcababaadddbbaddcdddcadcdbbbdcdcccadcacbcaccbcaaddbbccaaadbaadaadacabacabacdbbdbcbbbbbcbabcbdaaabcbaacacbbaacccddabababaacbdbccddbbbccaddcabcaccdcabddabbbcdddcaacbbbabdddbbabccdcbabbcddcadabbccdbdadbabbcbdacddaabddcccbacadbcabacbdddacbdcdabaacadbabdccbacaaabbddcabbdbcdadadbaccddabdaddccaadbbcbddcccbbbcbbabbabcabcdddbcacccadbbbbccaccacadadcddcdbdbcdcbbaadcbcdcbccbdbdbbbddabccbbdbcdccdbbcadccacbaacacdaadbcacacbbbdadbddaadabcdbcadbcbcdaccbccbdddaacaacbdcdacabddbbaadcccadbbcbdbdbbbdbbddaacbadcadbabdabbbadbabbccbbadcbaccbacbcacbbbbbcdabdbcaabacacbdccacaadaabadccbbacbdccddbcccaabadbdbdbdacdbbbddcacccdabcccaaacddbacaaccacccdccacacadcdcbaaabbbcdccbdcabcacbabaddababaddbbcccbcbdcddacdbcabcbdbccbdaabaddaababbcbadaaacaacbbdbbaacabdcbbddbbdbaabbbdbdaadbbbaacacdaaabcbcacaaaadddbbaddaadbacccdbadcacaccddbdbadabacacddbaddacbaccacdbcbdcadabacbcadcccaddddbabbcadccbbacbabadbdaadadaddaaaccbccbcbbccccabddbacdacbbaaccabddccbdcdadaaacaacaacdadbccdbdacaacdccccdbddcdddaaadccaddccddbcccdbcbadbdbcbdbdbaaabbdbcdcdcdaccabaadcdacbcbbdbcdccccbddddbabbdcacbabbbdcacdbabadabcbdbaaddccdbbccabdbacaaadadbdaccddacdcbbddbbddcdacbccacadcddcdcdabaaadbcdcabaddacabaabdbaaaadacabadcbbcaccdbcbdbdacbaadbcdacabbdddabadbcadcbaaadbacaacacccddbabbbddcbcccabccdbacabcdcbbaadddbbdabbcdbcbdbdabcddccbcbcababdcbabcaaccccdcacbccbddcaabbcbdddbdaacacaccdabdadaadabacaabbcbccdddaacdbcdaadcdcccaacccddbbbdbcdbdcdccddbbacbabbbcbcbdccdbdbcbcccccadbdddccccccdcdcdbccdbabcccbabddcbadcdcadddacbcddabadbabdcdadbcdbabacabccbdcbbdbdddabdcbddaabbdbdabcacacaddddcdaadcbaaabaaadbccbdccaadddaadcccccbcddaddaacdabccdcaabdadacdacddbbdaabbadddcabdbaabbcdbcbbdcadacbdbcbabccdbadbbadabadcddabdccbcbadccbccaabbbcbcdaccdbcdabbbbaadadbdbbbdccacabcbdcdadacbdacccbacbcababddbcccdadbbccdaadcabcbcbacdbddabaabdaaacabacaabbbddbaadbbcdabdacdababbdcbbacdcccdcaaabcbcacbdbacccbcdbcbcaabbbdcabbcbdddbaaaddacccaacddccdbaacdbdaabdaabbcacadcbccaadccbcdcdaadcdcdaddababcbddcdddbbcbccccbcbcdbccaacccddadddbccaaadbaadaacbcccdbbbcbdcbbcbcdadadcdaacaadabdaaddbdabbababadbbbddbdadbcaabbdcabbcdddbabdabaaabbbdbdbabbaabdbbbdaacdcabcdbcddddaddadcccbbdcddaaaccacdbbcaccbccbccdcaadcabababbdabbbadacbccaddbbcababdbcabbdbdbadcbdbcbdacaaacdcddbadbdbadbadccbdaaadbadadcbaddababbccdccdbcadadaabaababbdbcbbccccbcacbcbacdbcbcadddaddbacbdbdabcdccaaacaccabdadabccbcabccabcdacacdadccabcdcadabdbbdbbddaccbdaabbdababaadcbdcacaacabbdcaaddcbcbadcbdbcbcdabdddddbadcaaabdbaadbaacbbccdabbaaacaacbdbcddbcabdaadadcaddbdcdaddcacdaabcabdcddabdcaadbcbdbacaccccdacbddcbcdcdcdabdbaacaddddadddcccbcbcdaabdcdcbdbdccbacbdbaadacaaabbacbabbabbacbcbadbabdbbcddcabcbaddcabcdadccdaadddabcddaabbabdacddbbbacbabbdcdabdaabacbdabbddcadbbcbdbdbbbddadcadadbaaaaabddcddacddcaaadabbabbccbddabcccabaabddacbacbbacbaccbdadabcacdaacbdabdccbbabbcadadbbcaadbdcaabacacddadcddaddccbadbbbddbdcdbbacbaddbdbbddabcdacdaccbbaabaacbaccaddbbbbbdabbdaacbadbbdbbdcdbcddbbcacadcbcbacbddccadadbdbdbdbddcdbbdbdcdbbdabcabddbbdbadbdadabccabcadcccccdbcdaddadcbbdadccbaadadddaabddcaadbaabbdaacccbdbabacbdbbbbdaabccabddbbddcdaaddaabdbbdbcaabaaababcaadddaabadabcababbdacddbcadadcbccdabbbbcadcabccadcaabccddcccaadddacbabcabcdddadbabddbbbbcaaaababcdbccaaccdbaddacbaabaccdbbaaccddddcaabdbcaccdabadbabacbcccdaddbcdaccccabbccaaaccaabddacbaabbaddbcbcabcbdcbaabdaddbdaacbcadbccbdcadcddbbbbdbbcbdcbccaddbcabbcdbabaddadbdacbdccabbaacbacddccddbbddbabdaccaadcdbddbadddbbdaaccdcdbdcdcbcddabdcaacbaadbdabbbdccdabbbddcbadbdcaabaaccdbbdbbdbdcdcccbdcdbdbabbccadddcaccdabdaddbbbdaaddbabaabbdcdcdbbddbdddbdcbdcbbabaacbbbaacacabbabdbbbdbccadaccddcadbaadddcdcdacbabdbccaacccccaccabdbdbcacbdccbccdcdadcaacbabbcdabbcaaddddccdbcbcadbcaccdcadddccdacabbbcddcdaabccddacdbbbbcadcaadbadcabbadbcbcddbcacbdbdaabbddbaabbcdbadabaaccbddcaacacaaaabcbaadaadcddbbdcabcaccabbbacdbcabadaababbacdabbbddddabbcbdbdbabdbdcccbcaadddcbdcdcbddcdbcbbddccccadcaccdaddbddbcccbabacbdabbdbdaaabcaccabbacbbdbcdadcaacbddbdbdccdddabadcbcbbaadabbccccadbccabcddacdcabcbdacdcaaccdabbccaaddbaaabacabdddaccacadacddbdccddaddaaddaacbabddcdcbbddbacdddcdcbabacadacddadbcbdbbcbbdbaabacdbaccdbddabbcaaccdbadcacaaadaaaccdaadcdbdbacacaacdccbaabacccbdccadbdddddbbbaacbdcdacbddbddacbbdbbcccdbaddcdaacadccaccaddcdcbcaadcacdcdbcdcabcabaadccbcaddbbdcbddabdadabccdbacbacabaccaaccbdcbdbaaadbbadbdbadcabbdccccabcbddadabdacdbdcbabdabcddabdabbaddcbbcdcdabddcdaaaaabaadaacdabbccdacbcaabcbdcdcddaddaccabdbbcaacaccaccacbdbbbbcdbcdabcacdccdbdccbbbabbaaaddcbddabadcdbaaddcbabbcdccccbcddcdbacdadbabbadddbabcdbdbaadadbdaadabbddddaadbdabcadbdbdababdadbdcbccbdadadbdbcddcddcabadabbaddccacdaaddcbacbddbdbbacbcbcbdcdcdacbcbadccdbdcddcacdbcdbcccbabadacacadaccacbdaddddbabdcdbcdbbaaabdcdadbdacbabddadbccbdbacbbadbaabaabdaacbdaaddaccdaccdbcbdadcdcdcbabbbbbdccaccaddaabaacdbbadcddcdadacdbaabcbcbccccacacdcdccbdababdcbbbaaccbaccbbcdacbbdccabcacdaabbdccbcdbdabcbbccbadaacdccbdbbbbbcdacabacbcbdbcaddadcaadbabacbdbccdbdbcddddddaadacdbcbdcbdacdadaccddcdcadcddddabcccadbcccdcbaaccbaabdbcdcaabccbaccaadccaddbcdaacbcadabaadabbccbcbddbddddadacacaabaadcccacddddcbbacdccbcccddbabdcdccacddbbabdcbcddadadccdaaacdcddcadccbbdadcadaadbcbccaacacbcadcbbbdbbdbbdbdcbbcadcbadcdcdbdbbadbbdacdcddccacbdbcabaccbabbadbacdbcbbbbccdadacdabcdbdabaddcbabdcbacabaccaadccbadcdccacaaddcabcccbccdccacbbcccddabcbababdbbdcdcdabdaacbdbcddccaadaacbddababdadddcababacdbadadbbdaacccbdabbcdbcbaabcaddbddabccdbdbccdbdbacbbccbadbbabcbdabdbcccddddabcdcabcdbbabddabccdbddcbbbbddcbdabdbbabcdabddbdaadcabdccdbababcdabadcdddacdddccdddcadacaddbcabbdccbdbbddacbdcabbccdabbbbdadabacbadacbcbcbbccdadaaccaabccdadbdcdbbaacadcdccbacdccabdcadcbdabbdbbbccccdbbbcbdbabdcbcbbcccbdcccaccaabbbdcbbdbaaccbabbddcaaabcdbabadacdcbbddbddbbcdaabacacacabadacbcdabccdcbdddcccbcddccdbacaaabaddddaccdbacabccdaccdbaccbddcdccddbbbcaadacdccbbabbadbcbddaacbccacaacbdadcadbbbadbadadadcbaabaaaaadbacbadacbbbcabdcbcdbbaabdacbdbddaddcdddccaccbaaddbbaddcaaddabbcdbcbcbbbadaccacdcbcadbddcbbbabddbbdbacbacaacdcbdcdddddddcdbccdcbdbcdadcadbadadacdcadbbbbbccdaadbdabdcdcbdaacaababdbbaaaaaddbddabdacadcadabaddaabbbdccdabdbdbacdbadbbdcbdcacdbcbabbcbdabdccaacaadcbbbddddbcbccdbcddbdaacbcbabdbcccbdbcdbadaadccbcabaabcabbbaabbbdddccdababcdbbbaadcbdacbddbabccbacdccbbccacbbdabcbdcabbdbcddaddcaabbbbacdbcbcbadacdbddabdcccbccbcdddccdbccadcacaacddbccbbbcddcacadcbddddbacdbdadabaadabcddabbbabcbcbcaacabdcbdcdabaabaacaaaabccdccadbbacccdcbcabbdababddadcbdaccdbcdbdccbacdcaadadcabbdacbccbbdabdddccabcbdddccbdabccbbbbcabcdadcbdbdacaddbccabaddcdaabcddaccacccbacaccadcbbaccbaadddccabbabadccddccdcacadddaccbbbaaadacbadbabaaacacbbdbadccbccddabcdbdadcabacadddabbccdadcddaddcadddbddccdbaabaabcacbacaabddddbadadadcdcdcbadcbbbacadddcadcbbcacccaabddacaacacddcddbbcbbdddbdddaabcdcccbdacbdcdcdccabcbdabdcbdadaaabddbcbaccaaacbaaacddaacaadcdddcacabdcdccdddbbbcabcdcdcdcabbddabcdcdaccddbbaccadccdbcadadcbababcacbddaadcdabddabadaccbdaddcbcbdbcaadaaddcdcdbaddbaddadabdcbbbcbdddacbbbdccbcaacdbbcddccadcaccddcbdaaaaabdbdaaddddbbcdddddacdddbdccbababdabcaabababacbabbddbddabdddadcabacbaadddbcbbaabbdacaacccacdccbaabbdcabdbbbbbbcddababaddcbdbdbdbddcdaaaaaabbbbaacabcbbdcdacccadcbddbaacabdbbadcacddabaccaacaadbdbbddcabacbdbccadbbddababcbaaaadbbcccabdbabddddcaddabdbddadcabaadbadadbabccaaacbccbaddcdbaaadadbcddbabacaccbaabbadcbbcdbddbdbcaaabaaadbcacbcdbbcbccacbacdcbdaacbababdaadcbcbccabaaaccdabaabbcaadacbdabcdaacababacdbadcdcbdbdadbcbdaaaabbbaccddbaaddaadbdcdbadcaaadcddaaacbaddbcbbddadcabcbbddcdadabcadcadcddbcbcbbcbaadbababcbaabcbbbbdccadabbbadddabcddcaddbbbbccbcacbcdbadadcdcbbadcbcbcdcbbdadddbabddaaccbdadbdcbcadbdabdbcbacadabbcacacbacaccabbabadcdadadbdcabbcaaccdbacdaacdcbbdbdccbbbdbccbccadddaabacbaaabcaadadaddbccbccabcbadacbbbccadddcadcdadbaacbdbdbdbaabbddcccdadabacabbddbddadccaadcbacaaccabadacccddccdccdbacbbcbaabdbbaaaaadabdbbaadccdbbcbcadccdacddaaabcacddbcdccabacbdbcaadcadaddbddcaaaacadcccbcddcbbddacaddccdbddcdcbadbcacddddcacbacadadabdcdabbcddcbdacccccddadbcbdccbddadddababcdbbbdacaabcaadcbbcccabcaccbacdbdabcddddcaddcdcbbdcbbcaccbddbbbabacdbdbdbcdbbdbbacdbcbaadbcacddcccdbaacacdbbdbadbacdcdbdcbbdddbdaaddacddcdcddbccadaccabacacdcdaadbaabcdcadcadccdcbdadccacddbbaabdbaaadbaaadaacbbbcabddbdcbbcbdbadbbddbdcddcdabaadddaacdddddadcaabdadcbaabdcbcdcdbdcbacaacacbabdcadacbcadabbcadacaaddcaadbbddcacbbdbdabcdddbcacbaccddcaddbcddccacbcdcddcaadbbbcabbbcabadbacaabbcddccbbbadbbcdcdbacababcbcdaaddbacadbbadaadbdcdddbbdcbabbaaabccacadacbdddbdcacbcabbdbcdccbcbccbdadddcaddaabdbacccbcaaddcacacccccabbcdcdcbdbaddbdaadbdbacadbbddcabccacddcabdabcbbbdbcdbbcbcbaacdadaaccdcccdabdddbdcdbcaabdcdadbadbbcadcccdcbcbdcbacbcbcabbbbcdaadadaadbcdcbaabccbabcadadcdaadcdaacbcdbaddcbabaaadcaccaccccadbdcdcbcdbbdcddcdbcdcccdacbccabdacaacacbcdbdabbbdaaabdaaadddcdbdbcacdbbcdacbcdadccdbdcdbdaacbaadcabdabcacacdadcdbbdcaacacbdcabadccdbdaccdaabcccaaccdbcdccdacdcdbabcdbbdabbccbccddcdbbcbbbbddaacbcacbcdcabacadddaacbcdddcdcbbbdbccddbdcdabbcbbddacccddbccdddadcdadccdcabdabcdcbcbbdbcdbcbdabaabaabacdcabbaaccdbccbcdaaddbdbcddbcbacdacdcaabbbaacbcddaacdacbbcdbadbbbbcaabccbccbaaddaababacbaccddbbdaaaddcdbddbaabccbcdbbcdacdadabbcbaadcdbdcdadcddadcdbccadaabbddaadcbcacbadaacccdbabddaaabbbabcccddccbbbbacdabacadbcabbbaccadddacaccaddccaddaddcbbabcddabadaaadabacbaccacbbbccdcbcaddccccacbcdbadcdbabccbcbbabddcbdaababddaabdabbaabcbcabbabaccaaddaaaabadbaadacdccdabbdbbbaddcdcdadacddbacbdaddbbbcdbadbcdadcddbcbdcdaaaacabccccbcbbcddadabacdbaaabaacbbcacacddbbdcccdccacdaababddbcdcccdcdaddbacbdbaaadbbcccabcbcaaaaadddabdcadbabadbaccbdaddbdaacbbcaacadabdabcacbaccbcbdcdabdbaccaaccadbbbddbbbabccaabddaddbcbccdadbdbadadddbddaaaddcbdcabacdbcbdbacaaadcabdbacbddcdbaacdbdcacdabbdaccbdbbbabdbdddcdcbbcaaacaddacacacbdcbabdccbadbacaddbdabcbccdbcdcdaadbaccadabbdbdaaadbcacbcbccccabaacaadbacbabddcbabaaddaadadcaadabbdbabccdbbcdddacbabbccddabbbcaabbcbacbacabaacabbcddbcbcccbbcbbacbccdaddaabccbdaabbbbcdbadabacacabbcdbcdcadcacaacadbbbcbdccdcbbdcaddccbacccbaddbbbdbccaabcaadbbdbdddacdcbcbdcadadcabdbaababdabaadcabababbbbcccaacaccadbddbbcadbbabbcdbdcabccbadbccbcddcbcbddabcccbabbbddbbbaacacddcacadabbddbdcdbbdacadddbbdbbacbdbccabaabbaadbcbbcccaabbdaadbdacadddbdccddaacbbacdaaaccbddccaabcbabbdadcdaacdacadacacaacbbdbaddcdcbbccaddcdbcdddcbdbadcbadbbbaddddaaabdbccadacadcaadccbaabbbdcbcadbacabdddcddcbdacdbcadabaababccbcdbcabdbbaaacdbbacaaaaccbdccccccadbaddadabddcbadaadbdbddabcccdbbbdcbbdacaacbdddacddbdcbdccdbdbbddacdabababbdbbaacadccadacbaacbbbaddabccdcbcbbbcaacddaababaadbbcbdbccbdcadcabbcbbbdccacbddacacadaacaadbddadccaabacbbdcbadddddcccaddcacacbdcaccdccdcadbbbbacbcdbbcadcccdcdbbccacdbadadacdcdbddabadabadcbdabadbcdbccbcbdddbbccadacddaaccadacdaaddcbdbdadbdacdcdcdbbccaaadddcddbdadbdabacdabcdaabadcbccaabbbbbdadcacdabaccbaaadcaabcdccddddbccbaaabbaabaacabbdbddaabccadadddcadaddbcabcbdccbcadadadccbbbacdaabbdcabcabdaacbdaaabdbbcabdacabbddaabbcbcabacddcdbbbdcdddbddcbbabddadcabdcacbbccacbcbdcbbaddcabdccbbcaadddcaabcdabbdaadcaddcaaccdbbacbcbddbcdacdadbaddbbbbabacabaddcbcbabdadababdcbabbdbbdcbcddaadaccaacbdbcacddcdbaccdddbcaabccadacddccbabcbadcabbababcbbabcdabbddddabbbaccbdcdacbccdccbabdcbcdaacaabdbbccbdacbbccbddaaccbdddddcdaadcccdbadcbdbdcabbaaccadcbbdacaaaadbbbbbadddbcaadbbbbcbbdaddbcadbcccaabcbcdddbdcbbbcadbaabcbcbccdcbbbddadaabdbcbacbdddbaacbbcbaacaaaaccdccabcdbbdbdbccdadbaabbddccdbdcbbbddaccbabbcccabadccbdcdbdcadbdcbbbadaacdaacaddcdadddabdadcabdcbddcccdbddaabbbaadccbcbaabdaddaadadaaccbcbabddbcccbcdacbacdadabcbbabaacbabdabbbcdbcddccaabaaabdcaddbbbddadadcacccdadddbdddcdcdccdbdcbacdaccacaadaaabacaabacbabccccbabbcbbdbdddbaadccdbadddaadaabccdbacbacbbacabaabbddaaabdaabcadcbbcaddacdacaacacbaccacaadbcdbcbabadddaccacdcabbcdacdbadbcbcacadbddcccdbcaabcbcabcbdbabdbaacabaacdaadadccdbabcadadcddcacacccabddcccdbcddcbddcdadbaddadbcdbddddaadcdcbdabbbddbccbddbdcaddcbbdbdbacaddaabcdccabdcacabbbddbbabbabadddaabadcbcaacdaccdbdcacbdccaccbbaddabacdbcdbccdbddbbbbcacdbdccdacdbdbddbcadbbdbbbabcddbcbacbcaaaaacbbdbcccdcbbabbbabccddaddbaaacccdccbbdbbcbdadccccddabddcbbddddcbdaccdcbbcccdbdbbadbdadbbcaaaddcbacbccddadbbadbcbcbbdabddaacddcbbdabbaacbcadddcaadcdadadacdddaaadcaadacaddadcdcdaacadccccddabcdacabaccbdcbcbdbcccaacbbacbccdcbabcaacbdbcacdddbbcdccabbaaacacadaabbcdaccbbdaaaacccddcaaddcbbaacaadcccdabdcbbadbdabdddbddcdcdbacaccabaccabaddcbbddbcccdbdcacaabbbcadccbbcdddcabacaccabccadabdabcbabcdabdbdddaccddbbdaabbaaaadabbabcccbabdadaadcbddcccabbdadddadccbbadddcadbbaddcddadabbabbcaccbbbccacccdccbcdaacbdadcadcacddbbbbbddbdaddaabbdcbbabbabdadddbcbccdbcacbcdcddaaccbaadcbdbdccccddcdaadcbddadccdbcbdccadbddabbbbdccaacbcadaabaccccdccddddbaddadcaadabdcbddbcaabacbbbbcacacccacaccaadbcaaadbdbadaccddacdabdadddbcbcbacdddadcabaccbacddddbdbcbadaaddacaccacbabcddbcdbdbaaddccdcdaaddbdbaaccbcdddadbdccdccbbacdabddabbdcbcbdbaccbaccddbaacdddabaaabacbbcadcdaccbdbccdcadcabdbccacdcacaaaadbbdadaabddbdadbbcbdaadbabacabacddcbaaabaccacadabbdbaddbcbbbdcccbbcccdbdcbddaadaacdbbbbbbabadaadbcabdcacadcbbdcbabdddccbbdcdabdabcddbdcaadababcddbddbcaccaacacacbbbaddadbcbabbddaaacadcddbcdddabccbdadbadbbbdccbbddbbcabccaaddbbbccddaadbcabdbdcacabdccbdacccaadaabcdcabaabbcbaadddddcadbbddbadcbbacbbcdbdbacbbdaaddccddcacdbbbadadadbbcadbcccbccbdcadccdbbcacadaaabbbacdbdabdbcabdbadbdbbbbbddadabbbcdccccdbcaadbcbdcbaddcdcccaabdbbabccbaaacaaaabdbabaadcdadbdabdabbbabdbdbdaabcaacbbbddbdcacababccbdbaadbdbacbadcddbaddbbbbdbdaccdacabbbcdcbaaacbdadbdabbbcbccaccacbbdccbbabbabdccaccacddbbccddbcaadbbcbdabacdccdaddccaddcdcdccabcbabadbdacaccbacddabaaaacdcbdbccacacaddaadbaccacdbacacaccbbacbbdcddbddaabaddddddcbaaaabbcdbacaadcaadbbcbbdcadabddddadbbddaacbbcdabbcccddbbbaadbabbcabcddadadabbdabbcdabaadccbdccdbdcbcbbabbcbccbddbdabaccababddbcacbdbccbdbbbdbcbdaadbddbddcaddcbcbabccaacdbbdcdcdacccbdbbbaaddaaadddadabddbdbbcaaabcaccbaadabcadabbbcbdcabbbdcbbcbadcbbbccaccaddabadddcbbdcbcbbdbccbbacbddbbbaabadccbadddaddbdacbababbaccddaddadbddaacdaadaacbdbbbbaadbbccdadcdaddaddddccbacbcabadcbaccacbddaabbcdcbbbcabcacddcaacadbbacdbccbdbdaaddcbddcccbaaaaaacbcbdcbdadbdcaccbcababcdcbbcacadccdbadcbbbbacabcbbbbcdabcdcbbacdbababdbaccaabdaabcbcaaaacbdbdbcbbdddbcbdbdddddbdacdccaccbabdbbdbbbaccbabbcdddcdcbbbadccbcacddcbcaacbdccbdcbabccdabcdaaadbbcbbdbcdcacdadcaadaabcdadbacbdccdacbccdbabccabbcbadaacbaacbaaacddbcadcddbbccdbacabccbaaccccabbcdadddabaaadaadbcdbbccdcbbcaaacaddadacbdcddabcdddcdccadcddbaddbbdbdbdddcdcdcdcababddddabcacaccadbbbdbcadcdaabcaaaabbabcacdbbbbbdadbbcbbcddbbdcaccccacbddbcaccccbabaadcdcabbcdcbbddbbbdbddbacbdccaacccabacaacacabbdcdbaabdbadadbbaacdbbcabcbabcbacdabbcccbdcabacbddddcadcddabbabbbbdbccdccaaadbacaccdbcacaccbcaacbcdbcadbcbaccddaadcbbcbdcddaddbbbcdbbdaadaabaacbcacaddcabcddbddadabcacaabccacdadbadcddccaaddbabbdccadcdcbdcdddabdbcdcaacdccbbaacbdbbddacdccdddadbbbddaabadcccadadabdbdabdabdcdddbdadadddcdbcdbadcbdacadacddbaacddbdabccadbbbbabcdabbbaaccdccdcdaabcdbbccddaadcdabcbdbccabdccacccdddddbcaadaccddccddcbaadadaaadababdccbdcbbadaabdcbdbcdaaddcabdbadadccaabdbbabdcaaacddcaadbbaaaacaddbdbdabbbaabbacbbacabaaccacbddbbbcdabdbcacdadaabbbaaaccdddcbacabdadcccadbcabdacadcabacdcdcadacdaacdbbbacaacdbcaababdcaadacaadcbcbbccbdccbcadbddbcdbbcbddacbacbbdbbaabadbaaabdaddbcbcbdcccbcdbbbdacaadddaaddbbdabcbaccabcdcdcadbcdccdcdccbbdbdccdddcbbdbddadcabadcddaadbcbbddcdbdbacaccddcdcaabcbacabbddbdaddacdbcddcdbdcbdcdcacbddadbbdbaabaaadcbaccaabbcaacbbddadbddddccaacaacaddcaaacaadcbcbbaaccbabadbcbbabbdadbbdadacbdbdbbcbacdabcbabbaaacbccaaddacadabdadcccbaddcdbadcbcbcbdadbccbdbadabcbdcbacccbaabadbdccbbcbdacdccbadabbdccacacdccbccbdcacdcbdccdaacdcbdcdaadaacaacbdbbbddbddbaccabccadbdacbbdacbcdcbddddcbccacbacdddabdccddaadcbccdddbbcadcbaccdbddcbbadbbcbbcbabbcadbcddbaabdabacabbcdcbabcbddabddbbacbbbaacccbdcbbadaaadddccbbadadacdabdaddcabcdcaccbbddacccdbdbdadadadcdcccdbbacabbdbabaabacacdadbcccdacbaacbbbaccdcdaaadacddaddccbacbdddacaacdabcaabcaddcabaaccdadaddcaccadcdbdddaccdcdbcbaaaabdddacdcabadcabaabcdadbdbbdbbbbbcabdacdbbbacddcdabbabbcdddadcdddaacaccbbccbabacbbabdddbbbdbaabdabbbddcccccddabcdacabdbbcdcbbadabcabddddaabcccacbacddacbdccbacaacccaccabccacdcabbbdababbcabcabbbabbdcccacaaacbdccbacbdbaacaddacdaacdddacbacbbadbaaccacccdacbbadcabccdcaaadbacbbdcdbacddcbccccbcccdcccacababdaaddaddccdacabbdcdacbdcaacadbcdbccacbcccddaddaddcdbcaacaddbdddcbcabbddbbdcdcabbcacabbabbcddbdcdccdcdcbdcdabdacbbbadcdddcaadadabbddcdabdadabaddaacccbacdaddddcaaaadaabaddcaccddbdccdddbddccddcbbbadcdcdddacbcdbaacbadbdcaaccbadaadcddacabddcccacbcbbbbcaacbacddababccdcdabaacbdccbacaaccacabacdcbcdbadabdcdacbcdcdaccaaacdaaadddccdcabcadbdddcaabdabaadabaddbadbcdcddaccbabdaacbcbbdabccdddaabdcbaccabdaabaadadcbbddccbdccbddcccdbdcccccdaddccdbcabbbcdacbbdabbddbddcccadccbccababcdcacdaabcdabbdabdaddccdbcccdbdcabdacadaaaababdcbadcbbdadbcdbadbdbdccbdbabcbdbaaaddbcbadabcbacbbabbdcbdabbacaacbaabadbacaadbcbcabdbcbbbcadbccdaabadbcbacdcbaadbdddbcdacdbccddbcddbaadcbbcacbbdcccccaabdaacbaccdaddacdadadbdacdcdadadcbbcbdbcdccccdacaddbbbaadaccdacbcbcbdaabbaabcccdcddccdaabaacbcdcbbccddacabcbbddadcbacddabbaacdbacbbcacaacddbbaaacabccbdcdacddccaaaabcacdadbdbbdbddadabccccbdaadaccaadcddbdcbcbcbbdaccbdcabababdbdcadbcbdacdbbddbabdacabdbdbdacdccdbcbbdccaddbdadbbdccacbacdcbcbaccabdddacbbbadbcbbbbdabdbdaabacdcbbcdcdcacabbdcbadaadacbbbcbaadccccdccbcbdbabddddbbbdcaddbcabdcbbccacbbdacdcdcdcbdccbcdbcbaddabbabaddaacddbddacababbbcbbdcccabbbbaaddaddadbcbbabcabacdcbdbdbbdadccbbdcaadcaabaaddbcbcccbbabbbcbabdadcdadcadbbbacdcaabdadbcdbbbaddbbadcaacaaabcdcdcddddcdccabcbbadddcabadadabcbdaacbbcbbbaaaddadabdaacdccbcdcccdcbdcccbdcbadaabbaacbabbcddbbcdabcbbdcdbcbbcddcbbabcaddcbcdbdcbaabbdcbcacacbcdadbcaacaababbadbdcdaddccaadbcaabddddbabcaacbddabdbadaddaccbdadddcccacaddcddddccddcbdddcaabbbccdaaaccdbdbcdcbddcdcbbbcdbddcbdaaadccbdaaabcddbacdcdaaaabcbadbbbabdbccccaddccbcbcbdbbccadaacbbdddcddaadcccbaacaaccbdbbacbcbbcddaadbcdbcbddcacacbbadcdaadaadbdbddaacbbacdccaadccbaadcacdacbccbdabdabdbbadbaababcddacadccbcdddcdbbbababdccdcdabacdbbcbacdcbdcddcadccdadcdcadcdcdccbbbbaddcbbaacccdcdcdcdabdcdcbdcdbbdacbcbaabbcdbbaddabbdbcddcdcbadbaaaabbbdaadacdabbbadaaabdbcbbaacddbbbcbbabdcababbbccbacacbbdbccdddbbdbcaadaddcbccbdcadcccacaaadaddbadcdabcababddcaaaccaabcdbddbbcbdcaabbdabdbcdaddbbbccabbabadcbddaddaaddaccbadaabaddbbaabccccabaaadabcdadbabbaacddbdcbbcbadacddbcddbbaaabbdadbaababddbcbddaccbcdbacadbdcddaadccaababbcdcaccaaddbaadcbabbdbababbddbadabdcaccddbbccadcdcdbddccadbccacbbcadbaaadcacabcbadacacccbabdddadacdbabaaaaaaddabcbbadddacbbdbacaabcccdbdcbaadadacacbbbbcabdaaaddcbbddccdadcbdbbbadbdaccadcbdbaaddbccbbdbbdadabbcccabcadbdbadbddbaccadbdacaaabdccbbabcaaaddadbdcdadaadcbdbbdcaaddcdadbddaacdcabbbadaacddcbbaaddacbbbcbbdbbdcdaddccdbdcbcdcabbcbabcabcdbbcbdddccadddcbadcccdddbaccadccabcddbcaabacbdcadadacdbcbbabbcccccabdbbdcaabdccbcccccdaccdcadbcaabbdccdbcdcabadddbbacbcdabcbabdbabbaddadcdaddbcbcbcaabadbbbcdbbcbabbdbacbdcbccbbbbaddcaaddaaccdbcdccccadaaabdddcddbadabbbcdcaccddbcdabbddaacdabadcccabbabcbbadabcdcaaccadbabacaadbcdddcbccadbaabddccdcaabccaaaaaabcbddbbadbcbabbddbcdbdbbacaccacdbacdcbaacacddabcdacdadbaaacacddbacbdabdaccbbbabcdcaabcccaaabadaadabadbddbcbcadbcbddbccbcaacdccdaaacbbbccbadbbaccdcdacbcbacadadcaaaddbdcabccccbadbcdccbbccdcdabaaaadbbbbaccdbbddbccaddcbcaaacbbaadcbdaadbdaddbdabaccccbcdbabdbcbdcbdaddcdaaacdcaacadbbbcadddcabdaacbcbdbdaccabccbbcdcddaccddabadccddbcbbabaddccdcadcabadaabaadacbacaacbddbabcaccdadabccaadacccdabadaaaddbbaabbcdadabdaaaabaacdaabcbcaaddddbdbaacadabacabcacdccdcccccaadadaacddabccdcdbcaabaaacaccacdabadacdddccdadaaccadcbdacaabcaccbcdccddddcdcabdadbbcccabcacbacbdddbabaaaddcbbbcadddaabaacccddccdcbdbcabaaddcdccbdcadacdbabddbacbabaddaaacbabbbadaabaaccccdbbccaaccabaaccdacaaccdbbdcccdcccaadbababddbaabcbcddadbadbacdadbcdddcbcddaddbcaccacaacdacabbdbbbadbcbadbaabcdccabdccbcacdcbbaacdaabcabbbcaadbdcccadacdcdabdaddaadaccdbabcddbdabddaacaddccaccdcabdcabaacbbcacddbabcbcaccbdbabadaacaadacbccadbadabcbdcbcdacdbcddbbddddbaaacaacdaccabbaddaabdabdadcbabcbbbbdbbbacbcccbbdabbaddcbaddccccdbdbcbbccdcbababddbbaddbdcdbbacddabdaaadccbbadaaacaacdbbddddbabaaccacadacaaabdbbccadbbababcbbbabadadcdccddcbdcdddaabbbabddddabccbbdcbccbcaaaaaaabbbcaccdabbcdbccdacacaacbacbcdbadddbcaccccdcaaaccdaabbacbadccccabdcdbaacbddbcacacbcddbddcaabbdaccccbdcbaabbbccdaddbbadbdccdadadbddccbccbaddadbcabbacccdaaaaabbddacadadcccccaccbbabccabbacbadbcbddababbacddbbbabdbcbadcadbdcbbdddbaaacbccadbcdbaacaacbacddddaaaadbbbcccdcdcbcacdcaaaaaaadaaaaaacbdacccdbddabcaaaaaabddadbabcbabbcabbaadbddbbdbaacdbdaddcbabdbbaaccaadcadacddbcdbcdcbabbbccccadbbbcbbbcbaaaacadbbccdacadcaacaddccadcaabbdcadcbaddbdaabbbbcdbabbadbdcdbddccbdbbaadbbcbcbbcaddabaadadcdbcdcacbabbaccaaaccadbbbcdcbddbcdddbacacdabdabbbbadaddbdccbabdbdabadaadabbbdcdbdbacbcddadadbdcdbcdcdddbdbacccadbcacdbcabbdaadbacadbaaabaccaababadbbaaddbadbdbadcdacababacbdcadabbddcaabbabdcdbbadaacbaddabbadacdbbbdbaabccbccaadaaddacbdadaabdddaccadaccbdacdcbccadacdabbdaadbbcdcbccbcbddcccbbadabccabdacacdbcbdccccabdaccbccbbccbcdbbdbcbbbdbdcccbdbcaaacdcccdcabaabbacdabaadacababcabbbbdacbddcbbbbdabdcddacadbabccaaaaacbcccddacdbccadaddaaaddcbbccadbbbabdaaccbddddbdadabcaadbcacbbbddddbcdddaaadbdccbbdaccdabbdcddcacbbbbbbcacbcaacdbbcabadaaacadabbcbacdcdccdaaccadcdbdabcccbcaadcbccdbbbdccdaaababacadcabbdaddcdaabbabbbbdcaddbacbdbdbabcaccaabadaddcbdaccbbaabbaadcbcbcabdcccacddbdbbcbbcdbaadbdcbcdccacbadbbbccbccdbccdacdcdbabccddacbbdbbcbcbcdbdcacdabcbbcacbdbccbdbdcddcdbdbccadbaacdacabbaadbbabdddaabbdddccbbbbabbaccbcbbaccdaadaadcbbadaabcaabadabdcdaacccbaaaccdddacdacdccaaccdbacbcabdbdaacbbdbaadbdcbbcccabdacabcadbaabadcbcbbdbcbbcddabcaaccddbcccadcacadadcddbdadaadbaaacacddcbbcadcdaabacddcdbdcbdbccadabcbcdcadcccaaaaaacacaabdbacdbbbcaabcdabaabdabdaccbbdbdbcbcabbbacdcdbcdbcaaabdcbdbbdcaddcacacdcabbaacbacbcaabdccacabbbabdacbadbbacabcdacbcbddcabbddaadcdbabcbbdbbaadbabaaadacadcdbbcddddbacdbaaabdcaadabbaabaacbcadbbddcbabcadabdbcdabbddbbcdacdadbbbdddcdacaabadaddbdbcdaddbdddbcaacbbabadadcdccadbcacdbdbdcbdaccdbdacdacbaadadbcbddcaaddcbbccbacbdbdcbbacdbdbddcddaaabdabbbccdbacddaadcbcdbbacdadcaaaaaaacbadcccbbdbaaabaddcbdccccbaacabbbdbabccbdabdbbcddbddccbadbabaaabbacccdcabbcaaabbcacccbcdddccdccbbcbbddabccaccacbdabcbdcbaddbbdddbacbbddbaaaccacbcabcacbdbcadacddbbaacccccbbcdacadddddcdcbbadbabddbbadbacbacbcbbccadadadbabbaddcabdaccdbddaacccacdcadbbcdcbddaaaabbbbcbbbbbbacdccbdcbabdbbadabdbbdcdbcbbcaaaadddbcccaadbaaaddbbddcaccabbbcddccacdacdabcddcbdbbcbbbccdcbcdcdbdaaacbbcccdcbcdccacbbdcdacaaabaadddaadbbcccbadcbcddacbbbbdddcabcacdadcdbcbdbababbaddbdcbddbbccabdbadcbccdadbddbbbabccdadaadadbdddcdbabacadbadccdbaadaaadacdcbcbbdaacbbdddadaccddbcabbcaadcdbdabcccbdaadcbaddddadcdddcacdccdcabaadbabacaaaabbccabdddddabdbcabaddabacabadddbbdddcadbaddabacdadacadbaaadbdccaccbbcacbbabdddbdadcdabdaadaacbacabdccadcabaddabcccccbbbddabbcbdabcdbddaaddbcdaaabcdaacacbddbbaddadadadcbdddaccbcdabcbddcaadbacabcbadcdbddbbdbcdcbabaadabcbbcaacbadabdcadcddbacdacdbcbbbdddbcaddbdadaabacacadbcbbbcaaadbaabacacccadadbbacccccbadcbbdaddcdcbaddcbbcdabcabddbacdbcdcbbdcabdcbbbbaaddcdbadccdcadcdacddcabbdcdadaabaadbbabbccadcccbcdadbbcbbdcbddbcddcbcccacddadbdbbcddacbacaccbbccbcaaaddbdcccccdadbbbdbadbcacabcbcbcaadaccbadcccbcdcabbabababcccbbdadcccabbaaabcbaadbcbcdddadcacdabdbcdbdbacbcbcdcabadadcdcababdcaacdbbcdbaddcdbadaabbbadddbccbaacdbcadddddbcaabaccbabaaaddcccbbccaccabcbaddbcacadabbcdaaacbbdbccddcbabbaadbbccbbcdbaaccaabacccccadcabddacddccacdbaddabadabdbddddbabcbddbbcaaccccabbdbdbadacbdcccddddacbabcbdbadabbcdbadcddbaabdcaabaabbaaadcdcbadcccadacaccadbcdbadacdcbcbaacbdbabddbaddbdaddaddabcdbacacddcbacacbaadbbddcbaabddcacbbcdcbaaddaadcbababbaacdbbbccadbdbcdaaacdcbbccbcdbdacbbcdadbdcbbacdbbbdddaccacdcacacbccacdcdcaddccdcccacaccacabbbccbdadbbaacddaadcddbddacbddcacdadcadbbbacbbbbccadacdbdbccccaddcbbaaaacaadcbdabbcbacdacddbbbcdbaacdcbddddabaddbacdaadcaaaacddaabbdacadcdadbacdadbacbacbcdadaabaccabcdaadbbbaddabcdcaddcbadbddacdbcbaacbaadbaadbbabcbacccbbdacccbacccbcacdcacabdbddacbccccdabbadbadaccddcbcaccddacadbcdaccacbaadddbaacdbdcbadbaabbabcccccdadcacdbbcabcaaadbbbdbbcdbbabcbddbbaccdbbdcaddddcadabccdbddaddbadbccbdaaacbdccadadcccdddcdbbabbddabcdcacabbdaaaccdbabccccaabdbcbbbaccaaacdbcaabcccaacdaccdacaaccdbcaccbcdddabaaccacdbdadacdcddcbcbcdcadbdbdacdbacdabbdbdaacadbcabccaacbcaacdbccaadbdbabababaaacadaddabcdcadadccabcccacdbbcdadacbcddcbdadbbacdbbcdbddbcccdadbbacdcdbcdbdbbbadcdcacbddbbdcdabcbddbcacbaadcdcbdadaaabdcbbbaddbbbaacdbbbbbacbcdbdddcdcdacbbcacdcadbadabdadcdaadacbaaabadabccdacabdaaaabddabbacbbddacaaabaaadabdcdcadcaaddccdcadaacaacdbcbdadbcdcdabadbcbaddcccddbcdaccbbcacaaabccadabcbdcdaabadaabddccabacdcaababdabdbbabbabadabcabdadbcbccdadbaabddbdbcdbcccabdbbdbaadacbbdadadabcdddcddbdbadacabdbcadcaccabbccdcbbdddcaddbbdacaaacaccbcdbdacddcabdcbddbabddadaddccbabbbadbcdabbdccadaccbcaddbcbacacabcddbabaddddcacddccacdcdbbcccbadbddaaddcccccbbdaccddbbaabaccaaaaddcabbcdcadaadabbaacccbcbaaccdddacdbbbaddccaadaddacddbaddcdbadbcccbaccdbccdaaacccbccccaddaaaddbbccbacaacdbbbcacdbddbbccacadcdccabdddbdbacdaaddcadbbbcdacbacdaabdddddcdcadcdabcdcaacbbccacdacdadaacbbdabbcdabbcbdcbcdaabacdbaabdcaaccdbdcbddbdadadbbcbacabbcbadadbdccaadabaddbcaaadacbbcaccaaacbaddbbdacbabaaadabdcadbccdcddadbdccbaadcacdbccbadbbaccddbbbabddddbdacdbbdacccdaadabcabddabbbddadbcabbbdbbccadbaacdbddbbdccabbddadaabbcbbcbdcbdacdcccdcbcdbcbcccdbddbbdcacbbbaadbccddddabbbddbbaddadadadaddacaabadccadcbadaadddadddadcadcddbaaacbdbacbddbaddbadbdaacacbcadddddccdcbcdbdbcaddaacdbdacdaacaaccddbdaabaddcabadccacadbbcbabdcacbbaaabcbccadabaaccbcddcbcccbcbdbdcbadbbbbbdbbcadcddbaadcccdcdacddbdcdcaccddabdbcabdcacbbdddbaaadacbdcbcaababcdcaabdbbdabcbdbcbdbadcbddcddababdcaddbadbbbadcbaabcaabacadaacdcbaabdaaabcbbdbdcbbdcddcdcdddacdcdbdbbbdbacccccdaaacccbdbaabaddaaccaabadbcbbaddddadbacbbbacdddddabbbbbddcadbadddcbccdcccaaaaddddacbbaaadadbcadbbdacdcbcdcdbbadcadbddbdabcacbddadbdccadcbbdbbdabcbbdbbbccbdcaddacdacbcaccadabaccacadbaabcbbbabddabcbacdbcdcbbcdcbbdaaaaccccacbbcdbcbcabadabccaacabdabaaabdcddcabbcbddaadbdcbcdccadcadbbcccddcbcbabadbabbcdcccddcaccdccddaabcddabbbbadcbcccdcddbcbabbaaaccbbbbbacccadaadbdddddccadbabdccbcbdccaaddcbbccdddaaabdddadccaabbcadbcdcacccabcabcbbadabbcdbccccccaccbabdaadbbdbaaccdcacccaddacccbbcaadaacdddabdbaadccbadcacbcdcccdadcbcaacddaadadaadbbcaaccdcbcccbdcdcdbbbcdadbacabcdcacbdcadccabdcdaddabaabbccabdacaacabaabddabbdcbcbbdabbcdabcadbdddccbbbabadcadbdccbdadabbdbcddddcdddcbbbbbbabdabcabdbcbccdadadddcbabaaddabcdbdbadbbacdddccaccaacbddccbaccdddcacaacdddacadbaccbacdabdbcaacbbaccdcaabdcbbcdcdabdbbcabcaadccbbaabbbbdaaabddbcaaadbbdabcbbcdddcacadcaaacdccaaadcadbdacccccbbddadcbdbbcbdabccddbadacccdbdbabacbdcacdcdadcbdcdddbcdcbcbadabcadbccccddbcbddddcbddcaddaddcbddabcccbaddbccbccddcbdbacbbbbbbabaacbcabbdbcaababbbdadbdccbbccbdacbcacbcaaaddacaadaaddaaddcadadcdadcdbaababacabcbabdcbdabcbddabcdcaabdddabcabbadcdcbbcbbbdbbcdccadcdbddaadbccbccbbacdabbcdadcabcccaadccdcaabdcacabdbdbdadcdcdccbbabadbdddadcccdbdadcdacccaadacbccbbcaadbadcbbdbbbcdbbdcacaddccbcaacaccbcdbdbbabdbbadabdbbcbcbaddcddbcbccccadcacdbacbcdcadbdcddbaddbbdbcbadcbaadabddcdbabdcbabaacadbbbcaddbacbdddcddcbdddcdddccacbddcdaabcbaacabbdccabbccbddabcadcacbcdddbbcbdbdabbcdccbbdacccdcdcaaadbaddabbccabbdacbadcacdaaddbabcdadddbabbbbbaabddccbacaaacdacdbbbaadabaaabdbaacddabaaabccdbcdccdddabbdbbccabddbdaccddccdabadcdcbabcddacaaababdbddcbcddbcdddcccbdabaabbddcbccddbcccdaabbcbbdbddaacdacaabacadadcadabddbbaddabcaccdbadbaccdbdbbaddaacbccaccdbbdabdbccdcdbbbbaadbdaaaccaabcacccbdcbcbabdcccaccadbcdbadcdababddbcaadccaaccabaccbddbcddaadacddcbdcbdacacabbbdbbddbbddcbccdddbbcdbbabcdaaddcababbccbddadaacbacdcabdabadcbaabccddbdcdbacdaabdabcbbdcbddbaddddbbabaabcadcdabdcbcbcbddcacccaaddbdacababdabbdaacdbcbbcccacdaabcaaacbdddabbdcadcbcdbbddcdadcadcbbcddaaabccdbdbaacabcbcdacbcdabddbddabdadcacdbdaccbdcbcccdaaabadcbbbdabacdabadbdadcadadcdbaccbabbacbcbcabcdbddccccbbcdadbccbbbcdbcdaacbdbcabcaccadcbacbaabbbddacadaddbacacbdcdbdcacdadcdaccaabbdacbdccbdbcacadadadabadccbbabadcbabaadabadddaabdaccdabaabdacabcbddbbdadbabcbccdbcadcabccadcbaabdbdabdbcddbadbbabbccabbcccbdcacbbdcbaddddbddcbcccdcbbbccccbadcccccabadbabadcccdcadbadcdabddbacaaaaccccdbdadaadccacddabccdbabbcabbdbbddbbcddabdacabccdcccdbadbdadcbbcaabcaddcdabcddaccbcaaadcaccdbabcacacdcadabbcbabbcaacdbbdacccccbccaaacabcdccdbcccbdadddcdddabbdbacccdaaabbbdcadbbbadbaacccdacaaddbcadbcbcacacaaababcddaacbaccdbdbbbdcbcacbcacdaabaadcdabdabbbbcabddbaabbddccabccbcbcabccadacbbbbdbdbbaddacdbbbbddcdccadccddcbabdbcbcaacdcadbcddddcacbdccbdaabbcdcbcabccbcdadddaadacaaccdacdcacabaddabbacbcccaacdccddbdabdbddacaabcacacbcbbbcccdcabcadabadacccdcbababbbabbbabbdccabcbcbcacacddcccccbcbcabcabcdadcbdabdbcbacaadbadacaddbcdcdbbdacdccdddbadbbbcadadaccabaddcccaabdadabdacdcddcdacaccbdbadcabcbbcbbccabbbdbccbbbcabaaaadcabcdbaaacdbdccbdaacabbadbdabaddbdbbacadadbccdbcadacdcbdbcaababcbbdcadbcdcbcbcbcabcadaacbaacadddadaddcbdcccbacddadcdccbadbdabadcbdaadaadccdadacdcccabcacdacbdcddcccdbdabbdcccaadaddadaacdcdccbacaaddccdcaadabaaaaaacbadaaacbcabbddbaabaadcdcdaaabcdccbabdacbdddaccabcdcaaddabcdcdaabcacabddbcbcdabdcbabdcdcdabcddacadcddbbdcdddbddbddcbadacccaabdcbdcadaacacbaccdbcbccddcdbbacdcbaccdbccaabbbccdbddaaccdcbdbadacaccdcccbbddcbbbbbdacbdadcaddadbbcaadbbdbdbcbcccbbcaaddbcadaabbbbccbccbdabdaaababaddddcccbcdbddccbaadabbddcacbbbcdbccadcbcbcdaadaccdcbbdaccdddddbccaccccaabbbddccccacbccbadbbccabaaccdcadabcbcdbbcdcdabdbbdcacdbccaaababccacdcccabcaadaadddccccadbdaaaabdabcbabadcadacdccdddcdbaccccdbbdabadbdcabbcdcbcbadcbcbcbcadabcbaabdddacadcdaacacccbdbbbabdcdccdcaadcddddaacdbdcbadbbbdadbbbcbadcacbcdbbdaacaacbdadbacabaacbcbcccccdbacadcdcbddccabddbbadcabcdbbbddcabcbabdcbabbdcadcbaabcaabadcccdccdacdbbaabdddcabaadaaccadaccaabddddbdabdcbcabbdcdbbbdcccdbcdddaaaacdcadcbcdcbbdabcbbddcdbcacdacdddaaaacaddaaccbbdcdaadabcabbbcbdbccccaadcbdaaacccddcdbabbbdcaacdaddaabddbaccddcdccbddddcdcdabbaaacbaacbccdcaddcccdcccbbaabaccabcaddbccbaabbbcdabccaaddbccbaccaaacdcbcdabbbcbdcaaabadbcdcccadbaadabaccdacadcbabdcbacddcabdcabdacddaadcadaccbabbcbdcadbacccababcbcddcdaacbacaabccaabcadcdcbbcddbdccdabbaabbaadcbddcbcbddbaadadbacbabdcacabbdccdcadaadcbcabdbcabcdaadaadadadaacccbadbbcdabbccccadbaaabdaddcdbbacdbdaadddcdaaccaaadcccbccbbabadccdbbbbdcaaaabdbdbdccabdcacdbccccdccadaaadabcdbbaabdccadcccdabdaabcbbdcbdbcddbbccbdbccaddbcdcbacbbdbcbdacbaadccdaadcbadbcddbdcdbaaabbbdbbcabdcbadaacbaacbabacddaccccddcacdcdcadabbcacdaaaabaccbbbadbaccadbdbcbdcabdccddcdbadbdcbcaadbddcbacdabdacdbdcbdadccddbdcacacaaaaaccbbbdddaaaddbadcccccaadcbdacbabdccdbcbdcbcddacaaadcadddcdaaabbacbbbdbbabcbcadaddcccbcdcadbcadadcbddcbbbcadcbbbbbbccdcaadabdccabcddddaabccacabcbbccbbbdbacdcabdcbcacccadcdbdbacadcaccbcdadccbbbcaacbdbbbcbcaaadcdaddbdddddabbadaabdabbbadbabdbbcacaabdcdaaadabcabcccdaabdaccacaabdcbbdabbaaadcaadcddaccabaddbcdcbacbdcbddaacaaddcdadaccccacdaacdbbacbddabbcadddcccabbbdadadaaadcaadccbabcccbaccaacabdababddcbcadaaaccdbdcdbcaabadacabcbcddbdcccddaabbcdcdbaccaddcdacbaacdbcbbdcdcabcdccbbddccccaabdabdbdbccbadadccaadcacddcabccccdbadabcdcabccadbcdacbdabbdadddcacccbcbdcccbdacdbcbadaccdbbdcdacdacbbbccadaadadaadbaaacbbcbaabcdbabbcdabdbcabddcadbbbbabadcbdbaaabbbccaccbcbdbaabacbbcaddbbaabacdbabcadccbbccacadcddcdcbabdbccadacccdbcbdabbabaabbccaacdcdbdadddbcacbddccccdaadddabaacadcbbdabbdcdabddbdcaaacdacddcabbcdddaadcbddccabdaddbdbdbbcadabbbbbadadaddbbcaccacdbcbbdaaaddccadcbdbbbaadbdadabddcbbccdacdcddcddbcdaadacddbdabacdbdacddabdbcbaaaabbddacdccabddacaaacbbcabaabdbccaabcaadbaccddacdcbcbdbcbadadbccdccaddbadaababdaadcbaacccaccccdcabdadbbbbcccbbdaaadadbbbadcdacbcdcabddbdbaaadadaadbbaabbbdaaddccbbbccdbdabaacbbdccabdaabbbdddbcbddcdcbaaaaacdcaacbaddcabbacadbadcbbdaccacaaddcdbcdccabdddddaacdbcbaddabdbcddaaccdcbcbabbaaddcbbdbacdbdccddcdaacbaddadbdadbdaccccadbbdbdcdbccaddccdacadbcaccbddacddcdabdbcacadcacdddaccbcbabccdbcccccbddccbddaaddcdbacdddccbcccbbdaabbacbdddbaadadbbcaddbacccbdcccdddabadacdddaddaaddaadadbcdbbaddcccbccccacababdcacccccdddbcbaddadbdacbcddaddcaabcdabdccdadcddcddaabbbadbcdcababdcbdcbbbaccabdccabadabbaddcdcbdbaadabbcacbccbdabdcbaccacdbbabaddddccdaddddccdddbdcdccdbdbccaacbbabdccbbdacbbdcdbcddadabcbbbcaddccabddacdacbccbdccbaaabbdcbdacbabdacbdaccbaabbaaadddabcbadbdbdcbbabbabbccadcbcbaddddccdaacdccbbbccdccccaadcadaccbabddcdcbbbcaabcdbdacbddbbdabaddbddddcbdaacdbbbbbcdbbcdaabcabcaaccbcadbdacabbccdabbbadcdadcabbbbaacddaaaddbcbdbacccddddadaabadcabddaaaaaabadddcddaccdabdcdacdcaddcacacddbabcdcbdaaacddbbdcdabccdcdabcbadcdcdaacbcbaccbaacbbabcbaccabadcabbacdcdcababbddbddaccdcbbbcccdbcabcbbacbdcadcccdccbcdabbdcabbdcaabaddcdbcdaacbccbadacdcddbddbdddadcdcdddadabccaabdadcdadbdbbaccabbabcacdcabdacbccdbbcabbdaccbabcdaaaaacaaabdcdabcaadaadddbcdddaccddcbdcdbdbbcbaadabbbcbbbbdcddcbabadccddaabddabccaaaacdcaddcabcbcdbdaaddddbccacacacdbccdaaddcdbbcadbbaaaaaabccddbbdccabbccbbbabdddaacaaabaaadcdbccbcaddbadacadaddaaacccdddbdddbdbccdbbbdbabaabacacdccbdddccdbdacccbacaadabcdcddbdccccbabbcccbdcdbcdbccccbcdabcccccbbdadbddabcbccccddacdddaddbacbccddadcdcabaacdcdcabcadaadaccdccaddbaabbaaccbccacbaddaddadcdbcdbdadbcdabdbabadabdabddbadacaabcabdcdbcdaddccbbcbadcccdaddbcbddcbbdaccdababdcbacbbadccaddbbccccdbabbbcbcdaccdbcdacbdcbacacabdcaccdbddbdccdddabdbcbdaadddcbaccbcaacbababddccbcaddaaadddcccbdcdbbdbcccabbdacacccddcadccddbdbbcabaadbcaadddcdadccbabccabdcbccddbbcddbbbcddacdaaabddbbbcacbcbdbbbadddcdcaaaaadbabddcabcbcbccabcababbbaaacaaaadbdbabcbbdcdbcaadbdaadbbdcbbdccdbabcbbaccdcccbbdccbbccbccbacbbdbaabbbbdbbbdcdddbadddcbacbbcbdadbcdbccacddbcbcbccacbbcbddcccaaabddaaadbbaddbcbbddcabadaccbacdcddccdaadbdaacbbdbdbddbdcbcbdddadbaaacdbaccadcdcbaccdabccadbcbadcdcacbacacacdddacadccadabbabbaddcdcdcdadcdadabcdbaacbbcbcddcbdadbbcdaadbaadbbacabababaaccbbbcbddabbaadabbddccacbacadabbdaccdbabdccbbbbddbccbbccdbbdbacdbcadcdbadaadaabbcbadddcdaaccaddcaccbdcbabcdcddcbdcdccdccdbacddaddacabccbbcdacacbddaccbbbdaabbdaabdbccbbcacbbccccacbddbbdaccbbcddbdcddaacacdaaaabcaaddaaaadcbadddcacddbbadaccacbadbbdbcbccccbccabccccbdbcacdccdadcdddadcdadccccddbaaaaaaababbdbdbcbbaacabbccccbcdddabcdcccbdbdbbbbbbdcdabbddcddcaccdbbcddcadaaacccdbadbbabdaaaabdbcbdcacdbaadaccbaaacddbccadadddabdababccbdbdbbadabdbbcaacbcbcbbdcaccbcdababdbcbabdbdcadbccaddbbcdccabcabccbdccbacddcacccdcadccadddccccddbcbaaccabbccaccacacddcabbabcbabdcdbacabacdcbaddcdbbabbabddcbdcaaddbdcddcbaadabcbcdaacaaccbdcbadadabcbdcaadbabccadbcbccbbcdbdbbbabcdabdbddadababbcdcdadcccdaddcdabcbdbddccacabadbacaddddacabdbcacbbcdbbcdabdcdbdcaaaacbbdaaddbabdcbcacccbddcbdaacddacbbabdcdcddccddadabbacbaccdcddbadcbccaddccdadacdcccddaadcbbccdbddccaccdcdbbddcdadbcdbbbabcbacbcdabcadadcadaacbabbbaaccbcbbdcdbdbbabcbdcbccccacacbabaaabaaccadabadccaadaaadddbdbaccddcaccbabacabcdccbabdbababadddabcbadacabaacbabdadbbbcacddccdacacdddbcbcabdacabcdbccbadbcbcbccdbdadbadbacabcbabccacbccccddcadccdddaccbdaabaaadabdaaddbcacadccdbddbcbcabccbbccbabbacdbdacbcccdbdcabcbdbdcdabdbdacacdbccdaadadcacbcadcacdddbccbadcabdacabdbcddaaddcdacdcabcacdadabcdabdabbbabacbcdcbbacbabccdbabccddbaabcaccacbdbdbbcdccdbcbcdaaacdccdaacacbdbdbdbbbababcbcbcdbcdccbababccdbcababcbcccadcbccbbcababaacaacccccbacddaacabcadbadccacbdddbbdcadcdbddadcccaabdcdbadacdaaaadbacccabdabdddaccccdddddacdcbaaadadcbacbdcbbabccaadddaccbccbccbdcbcbabcbbadddaccacdbcdcadaccdccbcaaaacdadddbabcbddacacdbbaabaabbcabdbaacabcdccccbadccababaccddbaaacdddcdbbbdcddbddbabcdbdcabbccaaccbacaaadabaadcdcaaccbddbcabbbdddccacaaddaccbadbbcbcdddbcbbcbcabacdaadbabdabcadbcabcbdbdabddbcaccaadbbbaccaccabbdacbcaacbabaabadddbabccbbcbdbdddacbaabbbdababaaaaccbacdcbaabccbdcbdcddccaabbdccacacdcbdccbcadacddddcabbcbbadaaaaabccaabcbcccaabbacccbbacddcbcbdcdbdcbbbabddcddddcdcbcccdbaadadddbaddbddbccaacddbcbbcbcbcdaddacdbdddbaacdbdbcdbdcbcdcdcbbadacdabdbccdddaccdccaadcdabadcabcbdbcabdbbdbddacddcaccadbddbadbdccacacdbcbccbdcbdabadbddabbbabbcadcdccaaabccddbabcddaadabbbddbbbcbccaaddababddadcbacbcbbbdbdcaaccdbbaaaacbbcaaabbdcacbacbacccbbcddccadabdddcacdbcdcdaddaaadbcbccdcdddabdddabcbcbbbccdaaacccbdaacccbadbcacdaaacbcadbbbcbbbbacdacbbbccabddcabcadcdcbcdcbccadbcbcabcabaaadbaadcbcbcadcddbabbaaddcddbadabdbbcadacaabcabbabcddcbdbcdcdbbabcbaddcdccaadbdcbddcdcdbcdacddddcbbaacacdadbbbbbcaaabbbcbabbaaabcadbaddcaccdbddbddddaacaaababacbcdabbdcbdaddbddadcacbbabcbacdbddacbbcbbddccdccbacdcadadcabaccadbaaabbcbdcacabacccbdddaddbddbcdbcbaabccdcdbabbdbabdacadacacdbcddcccacdbdadaaccbadcdbccacbbbcbbadabcabbabaabadbdaddbbddbddcbdccbcbddacdbccadbbbaacbddbadccdbcbccdbbabccdbdacdbbcaaccbcbbdcadccbddccdcdbddbcbcccaddbbdaadddcbcddccacabaadadcdaaabbaadacacccadbacddcdaacdddddadddbabccadaacadbadddbbbabdbbdcdbaabdcaaadadbbcbdaddbadaccacbaaaacadcbbcacbbadadbdaacbdcbacdccbccbdaccdccccbdbbacdbdadcdbbddbdbccbcbcadabdaaaaaaaddabccddaccdcdbdcdbdcbbabcbaaacdcaccaacabacbababddbdbadabcbcdaadddbaaddbdbbdbbabcccccbadcdddbcaccdbabbabcaddcbbacbdababaddbacdcddcdadcabdaddddcdacacacbbbaabcbdbadcaacabbbdbacabdaccbadcaddddaabbcdccacbdbccacaacadccccdbbbaaacadadbadcabaccbaabcccdabbcabbbaccbadddaccdaacdddcbdabdbbabbacadcbdbacccdcdcbcbacbcaabbaabbbabdbabdcdcccdccddcaccbdadaabddbaababcbcabbdabccdbaccadabbadacbdbdccaaacdcdddcdcdbbbdabadbbcddacbadddbcbbdabbcdbcbcdbbdcababcacdbddabadaabbdbcddbbdbdabdddddaabaaccddcaacdcaddbabcaadcacdcaaccccccbcaabccbbccaacdbdcaadbcdbdcacbdadadbcdaabbbccdbdaabccabcbdcdcdacabaacbabbbcbadbacacddbaadbbdbacbadcdabcbdbbcdcccbbcbaabddadccbcdbccdbdccbdabbadcbccdbccdcbcaadddadcbabdccccaccddbddcccddddbaccacdcdaccdacdccadcbbbdacacbbdbbddabbbdbdbcdcacaaabdbcadadbbccbbbbdccbddbababdadcdcaaaabcabacadabddddaaaaadcbcbacbcdddbacbaadcdcdccacacbbaddcacbdaaaaddbbccadcbbadcdcacaaaababacbaacddadadbbbcabcdaabbcccadcdcbbdcabcddcccadaccbadddcadcdcacdccaadbcabaacadcabcabbbcbbcdabbddbbbbbcdaccabcdcdbddcdadddbbbdacddacbddacdbddaddddbcbdcdcdcbbbdccdaaaababcbcccabadddbabcaccdcaaccdccdabcddbacdccadbdddaaacabcacaacaaddaaacbabcdaaaacbaaddadabcbbdddbacabcaaccbbcabcacaddcbbbacbacbacadcdcdcbbdabcdccdcbcbbdaddabdaccbbcdaacddacdadcbaaaabdadbcdabddbaacbcaaaddcabdcacaabcadcabdadcdbcaacbacdbccbbccacdcddbaacbddaadabdabddbaccbaacbbbbcbbbcbcbcbabaaabaccaddaaddbbbbaacdaaadcbaaaacacacbbadbacddcbcccbacddabbdccadaaacaacabdcacbbdcdcbdabacbcdbcadcdaadaadacbdabbacbbadbbadbbccbddcabaaccdbccdbbaaaddabdbdcbdabdbdbdabbadcddbbdaddcaccdaacbdcdadddcbccdcacbcacadccdbdccdcbaacdcadabcdaccdbcddcdaabaccbaadbcdacaaaccddcbccadcdabbadabdbaacbbabccbdcaaacbcaccaabaabbbdacbaadadbbbdabbdaddaaaacbcdbaacddcbabcadbcdaccaddbaadbadcdcabbdabcddbdbdaaadcabadcaabbccbcdcababbdadcbdadadacdcdacbbbcacddaaaabdcdcbadcaddaadbbabaacdacccdbddcdabdcbcdbcaacacdbbccaacaccdbabdcdbdabdbdcbcaccadbbdcbacdccddddbbbacdbbbcbdccdadcadcaabcddbdabdcadbdddbbbcdcabdaddcdbdacbdacbbdbdaadcabacdabdbdabcdacbbbaabdcadacbbccbcbaabbaabccbadaaabadbdacbaaccdbaaabaaaabaddcdaabbadadcaacccbcdcbddaababcbccdcbbbbcadbbcbdabbdadbcdbaccadbdbabcdbcdbbbdacccaabaddabcadbbbaadddacacbbbcbcbbbbaababbbcacccbbbddcddccdacddcdccddaacbccabdcdddddaadddddcdbbbcbbdccadcacbbddcbbcbacbaaadccacbabccccbbcccabdbcacbbabaddccddaccbbcbbcdaccccdbcbacddddcabadaabbdcacaabbcccddccadacdabddadcdaaaacbcddaaddabbcabcbcabcccccaaddcbbdddbbadbdacdcacdbbbbcacaddabbddcbbacdabdddcaccbddbcaadabadadaabddcadbcbbcdacccdadacabbcdbaabacbcccbdbadcbdabcadabadcbbcadcabbbdbcdaadcbbacaccdabdcdaadbbdcbdaaabdadbcabbbcbbbdbcbaabdcdcddabddaabbbadbcbdbbbbdbcbcdaddacdbaabdbadbddcacadaacccbcaababccdcacacabcaabadbdabcdbdbdbcccdbdccccbadaadbcddcbacdccbabbbbadaccccadcdcacacadabbaaccdbdbcacacdbddabcbaaddbdcaadcbbbcbdabccbdccadcbdacbcadbbbdaccdcaacddbccadccdbdaacbddabbcbaacacdcbbdbbabaaaabbcaddbaadbcbaaaabbcdccccaccdcdaaadcccbacdccbacacadadaabadaabccbbcbccbdcdaaacccbbadadadbbbbbbdcdbdcabdddacbbccbcdaddaadbbcddacabadddacbbabbbdbdaacaddddbcdcaabbacdccdcdbabbcddbccbadaacdcdcdbbdbaaddcdbacdbdadaaccbdcbaccaacaaadcdcbdbaacbbacabdbbaadabddbaabddaaadbcabbabadaadcbbccdacadcccccbcadbdaccbbcbbbbababdddabcdbcdbcaadcbdbabdddccdcaaccbdaccccbadcbcbcccccccbbcddddbbbccccaacabadbcacbdaabaccdaccacadacccbcadaabadbdcdbadccdbababdaabaccddbbbacacdbcdbbbcddabbacdbbaddacaccdccddabcadddaddbbdadabcaadcbdcdadaddddacccbbccaccdcddccddbbdbbdbcbbdaccbbcdddddbcbddbbcdcdcabacddabdadabdacbcccaccbabccacbbacdbccbbaaaadadddcaaadccbddacbaaadcccdddcacdddcbbdcbbbbbbcbbbbcacaccaadcccadaabdcccdacaabccdccaababaadaddcdbabaabcbabccdcddcddcacdccdabcaccbbcddaabaadbcccddccbbbbdaaabaaabccdacdcbadcccbbdacaacccbbbcaddadbddbcddbcdccadadaaccadacdbbbdacabccabbaacbdbabcbadbbcdbdbdbdcaabccbbdcbaacbcdbdcbdccdddaabddcccbdacdabddbbadbabababcadaccdaacbcbadabddaddabcccabaaaccbbbaacdcaabbabbdddcabbbbadcbcbbdcdaccbdcaadcacdaacacdcdccbcbdacccacbabdbdaacaabccaadadabcaacbadcddbdcacaacccabaabddbadccbbddbbdcacddcbaaccbdccccaccbabcadabcbaddddddaadadcbcbdddddddaabbbaacbcbabcdabcdcbcbbcbbcbdcacabbdacdacbcdbacbaaaccdabdbadacacbabddbdbdcdaddaddbdabacaadddbddaadbcdaacaccacbdddadccbdadcccdbdaaabddbcbbdddbcdcacabdaccbbaddacdacbbccabbccbbbaccdadbbbdadcbccdadcdbcaacadbdcddaddcddccadbdaddaacadbbacbaabdbbccadcdacaababbccaadcabcccadbdabcdadbaaddacaddbdddbdaaadbbdbcabdcadcabcaabdbacdcdbddaccdbdabaccbcdbdabccbaccbabcdabcdabaacdaaabdcaccadacaaadabdbbdbbdabbaabbdacbbdadacaacacacbccdcabbccdbcaacbabaccbbdaabacaddcbbcacddbabbdcccaaaabcadbabbcbbdccababcbdcaacdbcdbdbbadabbadcadadabbcdabbadcaccdddadbdaddacbdbbdbaaccbabadbbbbadbaddbbddddbaabdcacccbabccbacacbbbdccbbdddaaabcdcaccbbdcdddaddbabdccaadbbdacdbbababbccadaabcdcaccbabdaaabaacdadacaacccbddbcdbccdddbddbbdccbcacdcdbdcbcccabaaadaddccaddacbdadcacbbcabccdaddbaaabcdbccccaccbbbbdadbbabbcbcbaacdddaaddbaccabddbcaabbdacadcbcdacddbcaabbabbaabbcaacdddbabddcdabdbdccdbabcbbddbaadbaabbdbdddbcacabdbdabdbbcdaabcdadaddcbacbbacadcccacabbbcddadcbbaaccdccbbacaccccadcbcdbcbadacbbbbbcaadbdbbccbbbdbaaaccccbdaddacaaacadccccccbaadabcdbcacbadbccaabcdbadccccaaadcaddabcbaaacbbcacdcddcdcadcccbdbbabcdbccbbbacbcdbddcbbcdbacabddccbdcbacbbcbbaaacbbdccaccadbaabbbaadacbccbcaacbadbabadcbcaacbddabcbdacabbbadddbcabadaadadcacabdacbbdbdbabdddccbbbbccdadbbacbdaabdccadbbdacababdddccbdcccddcbbbcbbacbdaaadddabcaddacaacacbcabaccccdbbccddacbaadcbacdadccdabbbaabbbbcacacdcabbdcabcaddaadddcbbcaddadcadcabbdcaabcacdccadccbdbabddbcbbbcdabcccdccabbbacddcaccdccaacddbccdadbddbddaadbdccdcacbbcaddbcdaddbaccdbbbdcdacdbbcaabddbdccabddcbdaadaacaabadccabbcabcdadaccdcacdcbbaadadcacbcacbacdcabccbddacddddaccbccbbaacbcdccabbcbabbbdcbcddbcbdcdcbbbcabbcacddcbaacaabbcaaccddbabaccdacbacbcdaacdadaacbbcdaddccdabcccbcacddacaadcacbbdccbcababaddddbbcabccdcabbaddbbddcabdbbddaabdabcbbadadbcdbcaadcadbdbcdccccadacccddccabdcdcdccccbacddbbbbbdcabdaacbbdbdabbddcddadcacbcbaabbbbbbcdcaabbccbccbdbaabccbcbcaddbdcdabacdccbacbccdcadacaacbdbddabbbddabbcdbddaacaabdcdabcccabdbdbbabadbadccaaabbadcddaadacadabbdcdaadcbbcbcddbbaabacaacdcaddbcbcaaabbbcbbacbbaadddaacbbcacddcbcbccabcddddbcbbdcdcccacdcdacaaaaaadbabaaabbadcdacddbbccbcbaaacdcdcdbbadaabbbbbcdbcddadddbababcaddbddbbbbabaaabcbccccbbcdbbddabdcadcdacbbadcadacabddacabcadbdaccacddbadbbddabbadddbbdcccddbddabdddacdababbaaabbdaadcbddccbadddacbdababddbabbbacaabdbacdbcbdcbbcbdddabdcaddcbcddcaaaadbddcdbdcbacdacaaccdccccabcbcbabbdaadbccbdcbababcacccbdbbaccbdcbdcbdacdbbcacddaacdcdddbcacbdbabbdacacdcabccdabdbaccbabccabbcccbcddaabcabbcbdbbacbabaababccccccbadaacccdcdbbadbacbcbaaaddbacddcdaabcbccacccbbbcabbbcccccbdadbaaddbadbbbcbccdadabddbdabcaddcddaccbadacdccbcdcbdcacdaddabbcdcddcddcbbdddbdbcadabcdaddadabaacccbcbdbdddaaaababdcbabbaddbbcccbaabbaabcdbbaddbcacbddabdabbcabddaabdcaacbcdacdccbbaaaababdbccabdddddbadbaadddaaddacdacbacdcbabcdddcdcccaaddabaadbdccacdccbbbbddaaccddadabcdbaabbbbabaacbdbdbcacdbcbdacdaaaccdbabddbaacdddabadacbdbcbbacccdccdbdbbcdcacdcadbbdbbaccbadbbacacdccdbdbbcbdcbdabcdbdcbcadaadabdccdacadddbdccccddabacbadaccdaaaaaddbaccbabadaccdbddbdaadbadccdbcbbbcbbaddcaacbbbbdadbbdcdbdabbdbacdcccaaccacbddacbbadbaddbbadadcbbcbbbacdbbbdbabdacccbcbadbcbcaaccabddcaadabbdbadacbbdccccacdaadcaaabcbabacccabaacbbccdcddddadbaaadaabdcadbabcddcbadbacadbdddbcdaaccadbbcddadacabcbbdbdbaaddbccccdbadbdccaabaabbbdbcbcddbcdbbddddbaaadacddadddcccdaccaabacdadccaaddcdbbcddbdbdabdcacdcbdbdcdcabadcdadabcdbaadcbdcaddbdddacbabbcabbddcaddbaccdabbcccaabddddbbbdcbdaadcbacbbdabadcdbbcaccaabaccdbdcbbababcdabdbbbbbcadddbccbaabdbddaabbbcdbabbacadaacbaccccdcbcdaaddccaaccccabcaabcacaddbadacbccadbcbbabdbbbcbcabaaaadbcbacbbdcdacbdadccbccdcddcddbacdccadbcaccbdadbddccdcadbbcacbcdbddcabbcccaaaccddaabdddaadbdadadcabaacdbddbcbaadadacdaabdaddcadbacccdcabdddbdddcbaaddbdbbbaaddbacdbcbcbcccadcaadbbcdaadaccdccbbaacdcdadbdadacbdcbcaaacbcbbacdbbababadcbbdabacaccbbcaadaadccbbcabacaabbbddacbdbdcaabaccaccddddcdbadbcdbdcdcbbcbcabdaaacbccaddabaaabbabaacadcadadddbdcaadaabbaccbaabbbabdcdcbdbcbbacabcccaadbbcccacbdccadadbbbaacddccbaabcbabaadaccabbabcccdaacbdccbbaadabcddccbccbbabccbaccabacaccabbaaddbcbadadbddabcddcbdbabdbbcddbaddbdadbaccaddbbadabdbccdbcadbaddcaabccdcdbacaddbcbaabccaccdacadacacadabbbccbdaccccaccabcdcbbcacbaaddabbdbadbcdaadbcbcbbabacdbdbdabbcccacaaadabcdbabadddbabaaaddcdcdccbadcbcadddbcabacdaadaddccadaadbaaaccdacccaadbccbddabddabcbbdbacccddbcbdadbcddcdbdcdcadcdaaccdbaabdbcabbdcbcbabcbbdbdbabddbdccadcbdcaabbdcdcbcbcaacccabdbdaabdbaabdcadbcbccaaccbdadabadcbbacdcdadaadaababcccbbccaacaddcccacbdacddacdabdddcadbabcacbadbbbcdadcbddcadcdbdbadbcdcaabcbacabdccadccddddaaababdddcbaaccbcacaacdbdcabbbacdbbacdbbcdddcbcbdcbaddccaccdbccabbcbaaabaacabcbacbadbdbaadcdbacccdbaadcaaadddaaaddabdabdabdddaaaaddbaddbacaacbabdbbbdcbccbdcdbddcabcacccdadadcaaaacabdddacacbbbadbbcadcdbdcbaacbabacdbbaadbcbcaabdcbdbdaadabbdababbcbbbbbbdbdadccbabdacdabcbcbcbcacbbccdabcdbdadbdcccabdaabadaacbcdcdccdcdbacbaccdaabddbacddbdadcddbabbcdacccadbcaddcdddbaccdabcaddbcbcaccbdaddaddcdcddbbcdbbbcbdcdabaacdbbacacacddbbdabcbcaddccdababaadababbcaacbdbdbbddacdddaccabcbbaaabcadbcbcdcdcacabcdccbaddadccdacaaabdcbbbaddaddbddccdaaccbbcaaacaadcdccabbaacaaadcbbdaaadbdbbabbdabdaadbbabaadbbcaccabbbaadaabdccdaadccdacccbcdaaabbacbbccaabcdbdbabdcbbcaadaabbdadcaccdaacbbbbddcadcccbbadccabddcadadaddcabacbdcbabbacadbbcacabaadaacadddcbdaacadddaadbabdacabaabaadacdadbcbcabaabdbdcacbadaacccbcacaadcdcbddbdcabadbccacaddcaacabdacdaaabdaccbabdaddcccababcddaaaabbcdddcddbacacddddaabcbcdbbdbcccacababddddcdacaaddabaccdddcdcbbcabbdadbbddbabdbdcddadcdcdcadddcaaadaaddaaddaaccabddaaaccdbddbcddbacbbbdadabcbbabbcdcaabbdbcccdbccaddababadacbdabaadabdbcccacaccdcdcaaccabddadbbcaabcabdaccdbcdcccccccdabbacadbcaccadbadcdbadbdabadcbdccccbacbaddaabcbccabcacddbbdddadaacbcdaacbcdcbcdabadcbdcbdcbcadacabbbadddcdabccbcbdccdbacdbdbbcadccdcadccaaababcddcdbdccacdcbccdbbbabddbacdddcdbaddabdcdabdddacbabbdbcbaddcabaddcaddddcadbacaccbdddddccbbadcbadccabddccaacbcaaddbdcabbbcccbcdddbaccdbdaaacbcddcabbdbcdcbbcaacacddcacbaaccacadadbccbadbdaabcbbbbcdabbbacadaabddadaccbbbcadacbcaacbbbacdddbcbadcdcddcadabcbacdccbcbcddbbadaabcaddadbdbaaaabccbcdaccaacddabcacdaadbabbcaccbabadabbcaadadbddabacadbaaddbbbbbbaddcdbdbcabadcbababacbdbcddbaccacdcaabbacdccabcaccbadbbdbcabaadbdaadcdacdcdbbacddababdbacdabcbcbdadabcacaddadbcbabdcbdcbacbbddadcbcdddadbacbdabbabbbbcacabcaaacdcbcbccabadacadaaabaadadaadbdcaccbdacddadbcdacdcabddbcacabdcbbcdbacccdaadbdadcbddcdacdbabcbbdbaddbcdaccacacbcdddcdaaaccbddcdcbbcdabcadbbaddcbdcaccccdbcbddaccacdcbbcbaccadcabacdddcacbdccbdababbdcbbbbcbddcddbcadbbdddbaddaacddddddabdccacdacaaaccbccacabcdbbaadbcabbadddcbbaadaadbdaadabdaaccbacbaadadccbbaadbddaabbdabdcccdcabcbbcaccbccbcdaaaadabbbbddacbcdccacabcacbcacbabccccbabbccdbacdbdccdbaadbccdddcaccdbbabcbbbdddcaacbabccddccaddcaccaacdbcdadcdcddbadaabaaaadadccccabbbbdadabddddbbcbbbbbddddcdbcccaddccbacdcdbdacdaadcbcbddcccbbccdcbdabcdcbabaadddaaddbbcbcdcccbbacbcddccdcaadcbddabddaaaaccdcbbccbbabcbdabbcccbccdbdcdbadddddacbacbddccddcdaaccbdaadbbcdaaddcaddcdcbacdacdaaaddcbbdcbdbaddccdbddbccbbbdcaddabbcadccbdaabbbadbbbccbbacddaddbbbdcacabaacdbdbcddcdcaacbccbcdddcacdacbdcdcdccdcaccdbbabaaaaaccabbccbdacccaaccabcadbadbacabcdcaaccbdacbbabddbdbabcccdabbbadbccdbdbaadadbbddcbdbacbcaaadacdcabcabbbccdccbbccbabbbdcacaaabacdbdaadcdaaaadabaabdcaddddbcaccbbbbdcacbddcbcaddcbbbabdbdaabacbdbcadbdcbacdaaaabadbabcddcdadbcbbbaabdccdcabccaaccbdccadaaddcbcccababdcdcbadaaabdcbddbdddaccccdbbdbacddbbabccddadbbabbcabbcaddbdabcaacbacddcbcbaacddcacdbdbbbdcdbcaccdaabcbcabbaaaccddacddbbacddaaccddaccbbdadacaadaaaadccdccacddabadbdbcdbaccdabcaacddabdbdbcadddcbccccbaaddadbacbbbdcacbadcbabcabdbdbdadacaaabcdcddcadbadbcbbbddbccddccddccddbddcbdaacdbadbbadbbdacddcadbdaaadbcbcadccabaacdbaabaadadbcbaaaacdddcaccbdbdaaadacbcbdddbacbabbcacdbddcbacdddbbdacddaabacaccbaaadbbaacccabcdcdacddbbdbcdcdbcddacddaaaabbbccbdddadbbcadbacdacdbdcacbdccdbacbbcbbcbaabcbdbaabdccabbbacdbbdccdccddacbaabacadacbdbabacbbcdcbdadccbcaadccbdddbcaadcdaccccbbccbdcabaaacbaccaaccbdabcaadddcccbdaadddcbacdaadbbbabdbabbaaccabbcaddadbdddddaddbacbaccaaddcdcbbaccbacbadbdbccdcbbbdddabdcddddcadbbadbbbdadabcbccabcadbccdbcddcabdbbdadccdbcbbcaacdbcbbbaabacccbddbcbdcdbbdcacddbcabadcbddcabccdacdcbaaccdbadddcdadccabcdbcaaddbbdaacbcdcddbcadcaabadddcddcccbdcbdacdaadbccbcdadddccdbbdbbaabcbdbbacdddccacabbcaadaabacbdacbadbbaabacdcdcbbbbaadadabadbbcdccacdcabbbcdccbcdaaadbdcaaddabbdbcdaddadcdcbacaccbadabacabcdbaacdadbaccabacbbdbcadcabcacdcdcacdddabbbccbdccbbbbbdbdcabbdbaddddccbdcccdccbabbbcbbbdbcabdddaabaabadabbbdcdaadaabdddbbbdaddcbcbbaabcadadbbbbaccbccacbccaabaacbcdcaddccabaabaaddadbbacbccacbaaccbdacadcbdabbacbadbddbdaacdaccabaadbdbadabddabdadbacacbdabdcbdbcadaacaccbabddcbbcbcdcdcdabbdcdcbcccbccabaadaccdaaadaaddcadabdaddaadddabbdbddcddaadbddacbccadbdaddbcadcdccbacccdbbddabdaabccadbaadabbcdaaacbacabdcdddcbbdadcbabbaccaadcacccdddccabdcbdbcdabdacaadaaacacbabacbccbdadbacbbbcbbaddcabcabdacdbaabdbacbbddbddabababdabcbdcdbdaccbcabccddcccbccbdcccbacdabdbcacdddbabbdbabbcdacdcadacababcaadaabdacabddacddcbaddcbabdbbdadabcdcbbabbccdccddccbddbdbbddbdbacbdcccdadacbbcbbccbcaccaddbdadbccbcbabcabcbdadccbbbcacaadcdadbbbcaacbddbaccbacaadbdccddabdbdccdcdabbaddcbbabbadbababccccabdacccaaccdbdadbcadcbcddcadbdcdccabaabadcddabadcccdabcddddaddcdcdcdccadbdbaacdbdbaacdcacadbabbcdadaadacaaaddbaccdddddcdabaadbbbdcadcdcbaaaadbcaacdaacccbdbbbadbbcbcacbbdacccdddacbbcbdbdaacaabaddcbacbdaaabccddbcaaabdccdddadcabadabcdaabdbcbbacadbcdcbddababbacccbbbacdabaccbdcddcbbbaaadacaaacababcdabcdddadaabbccccabaabcbadccdcdbdccabccdcdacabbacabaccdbccbcacccdbcacdabdaacdddccbbcddabddcbccaaabacbacddcdcdbbdbdbdbcbccacdacdddabbbbbcbcacbaccdadcdddbacccdabbcadabcddbacbbcacdcabbccdcccdddcbbcbcdbcaadccabcccbcdcbaaddbaabbbcbabdbdabcdbaaabcacbdacddbccdcbbbbdcbdcaccaaccddabcbadbdadaaaaabacbbaaccacabcadbaabcdadbdcccbbbccaabddcccadaabdddcddaaaccadccaaddbadcbdcaddbdaddbacadbbacaccdacdcbbcddcdadbdcbacabdcadcdaaddcddcccccccabdbbddbbcbcdbdaabbbabadcdbcaccbcccaddbdadddadacbbcdccaacaaabccddbdcbbadcabcdcddaaaaddcdadbdcacbadaacddbdcdbdbdadccbcddbdacddddcbaadacddabbdcadbbaacddbdaabcbdcaddcdddccaaabaacbbacabbcccaadbabbbddcaddbacbbadbcaccaddddacaabbcddcabbadccdadaaadccaddabcaacadadcabdcbaadbdccdddcdccbcacdcadcbbbbdcabdcddacdabcbcccbaaccabbdbbdcacddcbdacdccaddddaaadbcddacdddbdcaabadcbababacbcacbaddbbdbcdaabccaaadcaccbbdabcaaacdacaacbcbdbdbaaabcdcccaadbbabaacbccdcbcbddaabbadbaaacbaabaddcacdbcdabbcddaddadbbccdcacbbdcccdcddbcbbdcadcacadbccbdcddbccdcbdcdabadaabbcbdbcbabbadcbaadbaaccbddcadcddbbabdacadacabbaadabaddabcabccbcdbdbdbcdcbbacabaacdddbdabbabcbbccdbabbcbbcacbccdaadadbdadbdcbddacacadbaacdcdcadccbaddbcbddaccbcbcadbccbdaabdcaacabdbaacbccdbcdadabddddadbddcbcadbaacdbccdbcbddcadadddcacdbcaaacabaacbdbbcdbabaabbdacadadcbdbcbdbbbccadbaadaaaddcdddbaaaddccddcbcadbbacacabcadcbdbcadccbccbdaccdabdbbdbaddaadddbabcdabdaadddbdbccdbadddddbacdbaddcaccbcaaccbccbbdbabdabbdcdddacbbacdcabadcdbdbcbacdbddadaaaccdbcddbbdccdadbabadbddaabcacbaaababdaccdcccbdacdaccadacddabbccbdacadddaacbbabcbbcbccddbadcaddacadadbaadddcbaaadccbbcabadcaaaaabadbcdccbbcbddddaaaccadcccdadcabbdacbbbacccdcbdbbbddaccdbaabbdbccdcdcbcbbabcdaaadcbaddbcbcadcbabdbbadbccdbcabcabdaaccddbdadacadacabcaacacbbbbcbabbabdbbcacccdabdbdcdabbdcbccddcacdbdbcddaaddaadbbcccbdacdadabbbcababdbdadadaabcbadccbbbdabcbcddabadabcdacddcbcccbcbdddccaddccacabacbddcbddabbdaccbbbbbaaadcdadcaacdbaccdbcbdcccadaacdbaccadcdabdbdabddbdbbcdacadabdbdccaacdcbcdcbdaddcbcbcbbaacdcbbadaacbbbccaccdccaccbaacddadbdddaddbbaabadbaaaccdaacbbabcabccaaaaabbadacacbaabacbdaacabcdabddabcaadaabcbdcdabccdabddcbcacacbcdcaabaacbacaaaccbcabdcdacccbbaabddcbaadadbcabcaccaacddbadcccbcbdbdcdcdacacadddbcbacdbdaaacbaccbbbccaaaccdbaccbabdbbcddaacccbbadadcadbababddabbdbcadbbbdbdbdcacaddbbdaacaaabdbaccadbcacdacaccaddbdababdbadbcbbacbccbcadcdccbbcdcaadacbadcabaccaccabadcbababcbccababcdbdbdbbcadddabdcbbacbaddcaaadbbccbbabcbdbbbccbcbaaadcdcabaaccdabcdbcdbbcbadacdcbdccbacdadbdcadcbadadbbaddaabdaccbabdbdcaacaacccaaaccdbdaaaabdcbbcbcdadbbdcccbddbaabbdaccdadababbadcccdbdbdddcbbdbacbcdcacabdbbcbcddacaaddadaaaadacdabddcbbacbbaaacaccbccbbdddbcabbacaabcadcadbcacccccdbbdaacaaadccdddacbcbddbbcbbcbbbcaccacdddbdbdcdcdddabbcacacbbacccadbcbadbacaabbadcacbcdccdacdbccbdbadadaacdaaababbbccbcbccdccaccbbbcbdaccdaddbcbcbdaddccbdacbccbcbaabbbcddcbcdbabbdabddbcbcccabddbacdbbcadaabdbaabadaccaabbbddbacdbaddacbccabadadcbbabadcdbdabcabbbdcdbbcbdcabcbaccaccadbbcdbdbcdbcbddbbdbccabcdcaaaddabaacadaccbbadaccccbaacbbdacbcdabcbabcaabddbcabdaadccdaadddbbaddacddabddaadcdaabdaaaddaaaabccdbacdbcaacbbbdbdcbacccdbbbacbacddccbbaccccddbcdaacaaadcdbabacbaadddbdcbbbbbccddabbdbcdbccbaadcccccbacdcccabaabaaacddbabdabcbbdcabdacbbcddcdbdcbbdcdcdcabdaddadbaddadaadbcdbdacdcbaabccbcbdcaadbbbbbabbabcaddacaccadbaaabaababbaaadadbccbdaabcbabdadadcdcdabcccdadcaadcbbcbbaadacbccbadbabcddbaadbcbcdccbaacdbdbaaaccacacdcdcacdbacbbccbdbddbddadbbaadccacbaccabaabcdbbcbcdaaadcacaaaaccdcaccabcdbccaadaaadcccbcaabcadcdaabccadbaccbaddcabcdbbacdcdadabdbcacbdbdcabdcbdabacccddaabaccaacdbbdcbdddadccaccabdabcaaddddddaaaccabadaccababaccbcccdcddddbbddcbcbaaabbbbabaaddbadcacbdbbdadaabccdadccdbdddaabdbcdaddcbdabbadadadcabadcccadbbdbdcbcadcbdcacacbbdabdcdcbddcbccbbaaacabbaacdcbbdaacacbdbdcaacccadcbcbdbbccccbdcaaaabacdcaabaadddaaddacadbbbbbbbccaaadadacbabddbaddaddaadacdcbabacbcabbdadbaddbdbcbaaabddcddabaadababadcdcdcbddbacbbbadbdbaabddcbbcabbcababbcdabcbbcddacbddbccdddcaccbcdabacadccbcdccdcbabdbadbbbbbcadbbcbbbbcadbcdbbcabcaddacacbbcccdbdbccbbdccbbabbcdbcbacdabacbcacacabacdcbdabdadcbddabdcbdadadccddddbbcbccdbbccdddcbbaadcbcbabccbbbddbcaccccbaadbadadcacbbdbbddbabcdbcabddccacabbacdacbcddbaadbabbdbdbdbcbabddacdbddcdacbcbbcdcdcabaacbbdbaabccaaadddacdcaadcddccdbbbbdbcdddaddbddbdddbaacbddcdcccdbccbcccdbdcbcdbbdcabbaacabaaabcccbbcaacdccacbdbccabdcaccdccddcaacabccdbdabdabdbacadadbaddaddddbbcaacbaabbdacbadddbcbaacaccabdadabbdbbccdbacaccdcaaacaaadbcbcddccbdabbbaccbadbdcddbabdcadbddbdbcbacddbabadcbdadaccbbdaddbabcbddcbaacabcaadbdbcdddabbdddbabcdacddcdcaabdbccdadaadccbabadbddcabcaabacaaaaabddabcacbdbdabdbdddcbdccccdccaacadacbbaccaaabdabdbbbbdbbbaabbadbbdbacdcbdbbacdbabcacddcdbbdbacdccacbdbccaababbbcbabacdaadaccdbacbccaacdbdcabdbbdcbcbdbaaddaadabdacabaacbbbaaaabdbabdcbdbdabddcddbdadabadaadbcaccbbbddaccdabddadbdcbacaaaacddadabdabdccdaabaacacdbaabbdbbcbabaddccdaabdbbcdabddbabdacaaadababaddbacdcadadadaacdbcaabcbaccdaccbddbccaaaddddcbadbdbdcadbdcabcbabadaccdadacbdaacdcababdcdbbdcdcdccddddcaddbbcbaddcbaaadadaddbdddabcdddddcaccdddbddcadcdcccddcadccbdbccdcbaabbcbdabddbcbcaddccabadbbaaacadcdbdaabadccdbaaaacccaadbdbcbabbaacaabccadbbcaacabccadaddcddcabbacbbaacbcaababcbabbacabdaddddabaccbbbadcdaccacdbcdabcacdbbccacccdacdcbbadbcaacbdacbccccadbdbcadbbbdcaccaaccdaddbbbaddabbcbcdadbbccaaabcabaddccadcccbbdadbbabcabdbbadbdbcdbcbbadccddababcbcaaaccaddbaaabaddbdddcbdabbaaadbbcadbaabdcccbcbbbdbccddccdbabbcaaddcdcacacccaabbcabccdacdbbddbacbccbbadadcdacadababdddcbbddabbbbbaccaaabaabdaaadddcbacaaadacdccbdcadadcdcbcdcdaacbcadadbdbaacadabdadddbddbbdcbbbbbabbcbbbabdbadcddbddaaadbaacacbbbbcabcccadaacdaabccbcccdccadcdabddbcdbdabcccdabdbccabdaadcadaacdacacdbbabaccbccaccbddddcabbabddcadddcdadabadbbaabbdbcbccbacbabdcdbbdabadddbacdbbdbbbbcabbcccdcaddadaaaadcdaaadcbbdcccbccdcdcdbdcabacabaabcdaadbaabbbabcbcbdcbcccbcbdbdbdaaaababadaaabcdbbddcdcadaaacadcadadaaaaaddcadadabbcdbdcdaabadbaddbdcadcbbaddacbdbbabccbdcdddabccdddcbddcdcbbbdcbbaccbcdbaddabdcaccaccdbcdddcaaacbbcdccbbabbacadcbccdcabdbcbdabcbcdbbabccbdbbabdccadbbaacbaacbcabccdabdacbbdbadbbcccbcadaacbdcaaddcdbaaddbcbabddadbbdbaaacbbddcacdaabaaabbbaccccccdacddcddacbaccbdbdacbaabaabacddaaccdbaacbdcaadcaddcccbcbddddbdadabbcbaabdbacbbadddabdcaabcdaaaaccadadbbbdcbabbddddaabcbaccabccdaccddbadbacabbbbbdaabdcbabbcddadadccabcbccdabcacdadbdccccddbcbdbbbaaadaacbbbaccaaccaddaaccdccabbbcacbbdadabddcabdaabacdbcbcdaabbaaacbbbbabdcbabccabadcdcbbabcbacaabacbadaaccddbaacbcbdabbcdcbbcabdcbbbdabadbbddcabacbdaccdaaaabbcadbadabaddabdacdcbcdaacdadbccbdcadaababcdcbbbacdccbccbcdacbabbddbbbadbcbdbdcdadccbcabcabdcdbdbbdcaccabcadabbaabacabbccddbcbdaddbbdaadcbccacbdabbcaddaadadadaadcacbdccbcdbcbbadcbddaadbdacdccbadadbddbcbaddacadcccdadddabdbbdddcccdcbcaccabdadaabbddcdcacccacddbdbaaaabdbbcabaddcacacbacacddbddacdddaadacaadacadabadabbaabccbbacdbccdbddcbbdaadaccbaadcbddbbcaabbcabdbacbdadadcdbcaddddcadcdacbbbbdcdbdaacdadbdcdabbdbaacbabacacbcaadaabbbcabdaacdcbdbdbcdcbddadadcdbbacbcaabcabcdbdacddbabbbabcabacbcbdaccdaacbaacacccbcddabadadadbcbcabadddaadbaaaadadadcdabbbacbcbdadacdabbbbbccdaadbaadaacacbbddabdcaabababbcdaccdcddadbaaaddbddcdbcacbbcabcadcbdbbdbadcdbbdabdacdcbbaaabcacadababccdcdddbdbdabddbdcaccabaadbccbcabbcadaaabbccddccdbcabbbaaddccaaccbabdddccbccdbcacaddccacadacacddabdcdacdbabddbdcccadadcbdacbbccdcdcbbddcccbaacdccabccdaccbbbdacccaccbcbabccdbdddcdcdccdbdbabccabdbcbaaadcbdbaaaacadbbbadccaacadddadabcaddccbbdaddabdcbaabcabddbacbabdadbacbbdbcbdbbbbaaccdadacddbbbcbdbbdcdababadbabdacddccdbacababbacddcbdddcccaccadcbdadababdbadcdaabccbbcbcaddaabdcadabbcbadaaddddccadbdccaabbabbaadadccabbaaacddbddccbbcbbdcadacdbbcaaabbddcbabacaadaacdbbdaabbddbbcddddbcabddabdbcbbbcbbaadabcadcbccabaaccdbaabdcabddddadbddcaacccacbcaaadbdddaabdabcdaaabcdbdadcdddbadbbcabbacacdabacdbbcccbcaacdccaabdbdbabbcbdccdbcadcbbacacdcddbcbbdaccdcaacbaddcacdbdcaccbdabbcdcbabcdadaabcdccbcdbbbabbcdadbbadbdddbcaacbdbccaabbbbcabcdcacbcbbcbdadbdaadddddacacdabbaaadbdbcbdddcccdbabcdabdbbcadbabdbcadcdcdcaccbdadbddaaabdcdcbddcdabdacadbcabbadbdabdbcdddbacadabbdcabbaadaacbcaadaabcdccdbacacadaabccdacaaccacddbdadcacbdadbdbdbdadabcbddcccdaaacccbcacaccadbaacadbbdacbdabcdddabbcacbccbaabdbabdbcaadacdddbbaadbcbaddbddaacadcaddcbcabcdbdccdddcdcdddcdbbddbbabcbbadadacdbcdbbbcabbacbbaacacbdbbbdadddbbcbabbbdadaabbbdcaadbcbdabcaccabdbabcabbcdcdbbbaaaaddbdccbdbdcacbdaccaccadacdbddbaacbdccbcdacabcaacccdccdaaaddcdaabbadbbdbdcdbacacbdddcccdcccbadabddbcdbdbddbdccabadcbddbaaddccbbbddbcdadddccaabdbaddbbdcbdbdaddbccabbdbcccccddcacaaccbdabbdbdabcacacacdcddbdcadcdadbcccbaabcbddbbccbbbbdabdcdccdcbdcdbdacbbdcccdcddabbbddbdacdccbdcabdbcacbacaadddcbaababbaacdabacdaacacbcabdcdbcdcaaadaadacadcbcaacbdaccdbdadacccdbdbabbbcccabdbabcdbbbbbdcdacccddbcdbcbdcadabadcbbabbcbabcbbdbadcbaddbabcadcdaccbddbacdccbcaccaabbdddaadbcadacacddcdaadbadabbbbdbcdcadacbcccddcbabbacabaccadabbbdcdbcbbaabdcbddcabacbdadbbdcbabdddddbccbcaadcccccddbcbaddbccabbadcdcbabbdcbbbdbccbdcbbcbbbbccacdaddacadaadbcbddcbdbccacdddbaadbcccaadbbaaabadcbbddcbabccacbcacdcaacbbbcdaaadbadacacdccbacabbdcdadadabccdccbdaddbddbcccdbbdbbbccbabdcbcbdcbcdaabbbdcabcbcabcddccabbcdcbdacccbbbddbcddbcdbcacddadbbccdcabbacdbabdbccaadacdbbcbbdcadadadbdbacaaabcccaaadcaacacbcdbdbcaaacdbdabbdbdcadbbcbddbbbcacbddddadacbccaadbaaaacbcbdcbadbdcacabdbbaaccbaaaddadbbbaaddbabcdababbaaccaacabacbacdccdadabcccdbdddaddbadacdcbabdbccbcdbabbdbbcaacaabddabdaaddbdaadcaaccaaaabdaabbabacccdadbaaabacbbbacdbaaacddddbacddccbdacabddbddcbdadababccdbccadcbbdcdcccdbdcdcbcbdaacabbbbcbdadbbbbbccbdccdbabbcdcadcbaccdadabdcbacbaccbdccbababdbcdcdcdccbcacdcbdaadcdabacdbdbdbddddbddadcdcccccccdbbdabcbbccbccabdaadbacbbacddbaccdcdbbcbdbdaadadabdccacbdbddbbcdbaaddcbbcaadabbdaacdcaabccaddddcbbddccabcaadababddabcdadbcabbdcaadddadcdaddbccbabbbdbacbabddcdcbbccadaadaddbcbacdcbbcdabdccadccbababbbcccaaabdcbbcbdadcbbadbcaddbdcadbddcacdbdaccacccacbdbcabbbcddbaacccbabccdacdcdacbccdcbadcbbadbddbacdbbccadbcdadacdccbbcbdbbcbbdadaaabaadbcccbbdbdccacddccaddcdcccbdcabccddcccdccdbdbaddbdddbabaccdbbaaacbdadabacaddaaadcaddcaabcdbcadbaddcddcbdbabadbbacdcccddabbadcdadadcccccadccdabacdadaabcbdacdbccdcddacbcbddadcbbaccdbdccddbcddaacbacabbccbccaaabcbbcbbbadcbcdbcadaacbcaadaabbcbdaadbddcdbcbbdcbcccdadccddbbcbccdcabacdcbcdccaadddaabdaaaadbcbabdaccbccdcaadcacadbcabadccbcadaabccababaaddbbbcabacbcaabacbbbabcbccadcbacdbbcccabacdadddcdbaadbbddadadcacbaacdbddbdbbbbabaababacabbdddbdbaacbbcaacdbdadcbdcccbddcbdddaddaaadcddcbbddbcddacdcbddaccacdaaccaddcdcbbacbdaddcabdcbcbacdadccdadddbdbaaaddbadbdadcbcbbcbcddacadbccbabdaaaddddbcaaaadcbddbdddadbbcdbaacbcadabcccbdadbabdbdcdddbcccadacccacadadcdcbddacbbcddbabacadccabdbbdabaabcbcbddacbbaaccdbdcdaadbdcbbccacddbcadcddcbddaddcaccbadbbbcdbbdabaaacbacdabacacdccbcbddcbacddcbcbdadbdbbbbcdddbaabdcabbacdbabdcacadcbadbbdaaacbcaddbbdcddcbacaacccaaabadbddbddaaccaacdccaccbbddbdacdacadadcaccbcacdbcbbaddbaabbabbdaaaaadbdaadcdcbabdcccccacccaddbbadabbbdbabdbdaadaacdacbdadbaabaaabdabdbbbdabbddabdccbdcacabbaadcacacbcbabcabaadcccdbbddbaacdabcdbcbdcababadbcbadadbcadccbbadccbbadaacdacbdbcaaddaddbacccbdcbcbccbbdbbbadaaacadcadbcbdacbacbbadbdddacbdddbcccacabcdcacbaddbcdacbabdcadcbcdbdaaaddaaacbacbaccacaccbcbbdccbcadcccacddadaaddcdcccaaacdcdaadccaddbcacddcdaadaddcacaadcacbdddbbadaddcacdbbabaccadbbbddabcbdcddddbaadaabbccdddbaaaaabccdadcbccadbbcbbbdcbddbddcdabdbcabaaaccadcaacdcbdcdcdccdaaadddbcdbaaaabbcacadbdcdbabadbcccaacddabbbcdadbbdddabcdddabddcddbcbbbdaadacbbccacbccbaccddddbbacabdacbaacbddadbdaccbbdbccbcabadabaccadcacdadaaddcccadacdcaabdddcddbdabbbabcbbdcaccddddccccdabbbdabbaaaacacbbacdbdbdbcbccddbbbbacdddcdbbccbbdddcbdbcdccdcbdcacabcbbadbcbccadcaddcaaccbdbdbddddbddbbabbddabdccdcabbcbdbddbcbdabbbaaddaacbcccbccdacdabbadddaababbcddabbaabdadcabcbcdbadcdcbddcbcccbabccbadbbdaaabadbdcbabbcbbbabccaaddadadacccadadadccccadbcbdabcbaddbbdddcbccbaccabdbbccbdbdbbaccdccaaabacddcbddbdcadddccdaacadcccadbdbddbccacadcbccddaabcabbdbdbcacdaddadbbadbcbbbcdbabbddcdcbbbabdadaccdbbbcdacdcaacdaacbcccdccbccbbdccbbabbcabdabcbccdabbabdbabdcdddbddaacddcabddacbaccaaadbbacabbddaaddbacbcdcadcaacdbbbaccacccdacdaaadbddcbbcaacbdddbccabcbaddaabcbdcddcacbabbdbabdbbcbbcddbdcbbaadcbbdbdcbacadbdcddabaaadaababacdcbcbbabdbaadddbadcabaacdcdbbabbdabaabdbcccabadddacbcccccdacddcdcdbccdddbddcaddcddacbcadcdabdbbbcdbcdbcbccbabccbcdadbbabcabcbdcbaccdcdccacaadcaaababdbcdbbdccabddcbbbabbbacbcddcbbddbdcbcccdaaaddddbcdddddcdbaaacadbabcaacbdacadcdabadadcaaccccbdabbcdcbbdabacbabacaadbccbdbbbadddcbbbddaadccbaacabdbdcbcbbaccbcdbcbdaacaddacabdabccccaaddbcacaaaddddbcbdaccaadabdcdacdbbdcabdcddddaadbcbcccadacaddbacbdaacaaacbddbdbddccabbdbbccbbdbccaaabddbdbbbbcaabddcadcbccddbabcadcdcaaaabacaaaabcbdddbcbdadbddbaddadcacbcdccbdacdbccdcadcabddddddcdaaadacbabcdbdabccdbcdbddadbbacbbaacaaababbbcabdbccbaacbbcdbcdaaadbccbadbabddadadcdbdcdbacbbdadbcaddadbbcbdadbbcdbdddcdacacbdbadbdbdbaaabdbcabcaabababddcbdbbcadaacaabcabbbbdddbbbccbcbdaaaddaaadbacdcbdaacddcadadcbaadbcbcbdbdccabbdcbaacacaadadacddadacbadcbaddbabdaaddcbbcadbaacdcbdddbdbbccaaaacbdabccddbddbddaccbababaadcdddadcbbcaddbaadbadbaddbcdcadbbddbcbcbbadbbcdacbdcabbcacbdddcddbddbbbdacbbbcadbbddabcdacbbabaaaadbbbdddabdadcdcbabccdbbcdadbdcbbabcccddbddbcccbbbccacbaadaadcdbdcabddbccdaaccadadaaabbdbcdcbdbccdcbaabdddcdbcdcdcbcacbadcacbddcbcdbbdcddadbbdbcccaaaaabcbcdcbbdbdcbcbbdcabadacbaccbaccdbbdabdaacdddcdcbdcbddbcacbddadccdbbcaccdababdcbdcbacacbbbccabacadbbaababaaddabdadabcaddcbbacaaccddbdddaadccccdcadbbdbcbbbbaabcddabacbcbcccacdbadbadddddabccdaabdcdacaddbdaddaccdaaabbabbbcbcddbbdbaddcadbcbcaaabaacdaddcddabbcbacacabbbbdbdccbcdbaddbabadbddddaccdcddaaddcccdccadccbcdccabdddcdaddddccbdbcdabaadbbcddccbdbacbdabdabcdcbbcbddcacddbdadbaabddddddbaaaccaadcabaccaadbbddabbdcaabcdabddbacdbdaaaabbabdcbccccdcccbbccdabbbbbdccdcccadcaaaaddcdbbbdbbddbaccbdbabdbcadcabcbadbdbccabaacbadadbdcdcaaddccbabcdbbaaaabdaddbaaabaabcadcbdacdabcddaabcaadccaaacaaabadddbbdbacdadacdabbbccbdbbcaadabaadbadbbdbdcdabdbdadcabcccacbdcccdcacdacdabaadadcbcdbdbdcbcddadbdbbcabdbcbdbcccdcbdcaadccbddbacacaabbabcadbaaacbdcbdbbcbadaaacdcdcddaacbdadaacdadabcbdddaaccbcbabacaacaaadddaccddababccbbaddbdcbadaacacacacbdabcddbaacbdbbddbdbcdabbabdbdaddabcaaadaddcccbcbacdcdbbcacbcccddacbacdbdccdadddcddddbccdcbbbabddabbaaccbccaabccbdbdccbbcdbcccdcbdbaababddbcaccabbdadaaacbabcadabcaaddaccdaadacbcbdbacacbbbaddddccaaaabdbccbbcdbacdcbcaaddabcaddbabbddacbcdbaccdcacdaaabdabccbbbccddacbabcbaddccddbdbdabbddbcbbbcbcdbadbddcccbadabdaabcdcbacddabccaaddbdccdcdbbddcadccdcbcdccdddcbacbaaacaccdacdbbdcaadddadcdcbbcbacadadabdcdcddccbcdabbcbccaaadbdbcbabbdccccbcbccdaadaaaabdaaabbdbdbdbaccacaadadbdadcacbadccbbbdbcdbadcddabbabaccddaabaabcdbcdaabbcdbcccbdbacaabdccbbcabcbcbcbbcacacadabdddcaacdbdcdbaabadcdcabbcadcddbdcbbbabbdacbdbacccabdcdcddacbadcbcbdaacadbbadddadaabacddacdaaaacbbdadcbbadbdaacccadccadaccbcacbbbdbcdbcbaadaddadddcddcbbccabcdacaababaadccddbcdadcbadadbbdbbdaacdbcddcacdacabdcbadbcacdcdbbbaccccadbcdbbbcabbbacccacabaddcabdcbacccdabbacadabbabbbbbbabbaadbbddbaccbbadadcadaacacdadcbacadbbdcdbbabbcbbdbccaddbcbcdaccbcaaabccaadcabcbcbacccbadcadddccbadcccbabdbdbdaaadbdaaabccaaaadcbaacdcdccaacdbbcababdbcdaaccbbcadcbaadabaadcaadacaadbcbdddccddaaaacbcbabcadddddaccbdbabcbadccdadcbadbcdaccdaacdbbdcabacadcdbcdbbabdbcdbbddddbbacccdccdcdabadddbcaccbcbdcacaababacbcabdddaccbadbbdddadccacddaadabadccbadbadbdbbddabdccdcdbadacaadddadbbdadbacdabbacacdbabaadadcabddaccabcbaccbccabccbacccacdcaaadaacdbdcabcbacadcbdaaaaccccacdcddbdbcbbcaaddcdacbaaacabdbbbdcbacabdadabbddaabdbdccccbdadcadcadbdbadaddabbdddcdcccbbddbabadccbdbcaadaabcadabcddbcaadbcddacbabcdccdbbcdabcbbdacbaabdcccdbbbacbdacadacbacdcdacddaaaaaddaaaddcbdaadcbcddbcdbbccaabacddadcdbadacdcabbbdaaacbbabaadbddcbcccaaddadadbdccbdcacdaccdacbababdbcaaabcaaadcdddcdacddccaccbaacbccbdbcbdacdadbbbccbdcddbaabcbcacbadbadaabbcabccbabdabbbddacacbadccaddbcabaacbadacbddcdcdbdcbdccabbcadbdcdcbadaaddccddaccdadacdcadbbbbdbcdcabcdcccadbadcdaadcbaaaaddcacacabccdbbadabdabcccabcccaabaadababdcacddddcaaabdccaacbbcbabbcbadcdadaddbdbcdacddcbadcdaabcbbdcadbdadbabacaacabbcdcaaaaacbdbabbaadbaabcbacdccdaadcdddbcdcdcbbcdccbdcacbaacdaabdbabaccaccbaaddbdcbbccdddcbaaabadbbbdcadbdccddaabacacaacadaaccbddcbabdbdbbaaabaacdbcacbbabcdcbcdcabcacbcdabdaccbcaabcdbaaaadbbaadbcadbbacccdaaaccbcdbdaacdbaacaddbccabdbccadaacabcabcbaccaaddcaddbabcaabdadcbcababdcabadadbbddacdadcabdadddbabcdbdddcdbadcaaaccddcdcbbdbcbabdbcdaabdbcabbbdbbdaaccacbbaabbdcaadddabddddcabdacabdcddacccadcbbccacdadbbccdbdadaaddbdccaddaadaccdadddaccdabccaaddcbdcabbaadcddcacbcacccbdbccacaacabbbdadddcaadbbabdcbcaccbdacbaabddadadabdccbbbaaaaacbbaccacddacdddaaaccaddaaddbdaaccbaabbcabbddabcdcdcccaabdcadbadadcaadcdcbacbaaadbbbbcabbbcdabdacccdaacacbdbacdacdcdabbbdabbaddddbbccaaaabdbdcaddbdbabcadbcabbbdbacdccddbbdcdbacbabababbbaabaabccabdaacccdbdbacbcabcadbbadaaaaabccdcaccacacacaccacddccabcadcccbcbcadcabdbadcdbbadabcdbadbacbaabaabdcccdcabbcdbbbddccdbbdccaccdcaacbdaaabbabcccccbbcbccaabcdcadbaacbbacdbbcbaabdbcacbbdddbcddcacdcabdcbacdcadcbbdbadcadcdadaacbbccbaccaadbbbdccacdcacdadabbdcabbdbccdbbbaaacacbdabaaadcdabbddacdcdbdbdddcabddddabaaacbddcadbaccbbbdcdcaaacccacccadacdaaadacccbbbcbcccdcddbaddcaaadbdbdcadaacccdabaadabdbcbabdccbdcacdbdbdcddadbddadddabcaccaadaadbadbcdadbaadbabdcdadaddcdddbccadadacbabcaacbadbbadcaabcacdcabbabbcbdccabacabdbdaadddbbbbdadabdabcadbdbbbbdaabacbccacbabdbdadddcccbcbdcbaaddcddcdcbabbcbcddadcdbaabcbbdbcbccaaaddcacbcddacabdbdbdaabdddcaaadabaddbadbcaccbbcadacaddcbcdababadbdcdbbdccccbadbcbabdbcbcbbadcbabbacadccbddbdddbdbdcdbaaaababacdcbaccbdccdacbbabcdbbaabbabadcccdaacbaddbddcdcbacddbaabdacccabcdddadbdcdaddbaacbccbbaabbcbabdaadadbdccbbababadccdbaabbccccacdbacbcaacacabcccbddbccbacbadddadabcdacdbdccbdbbbdddbababccababddbccaadacbdcccdcbcacdbcabcaacdcdaaadcadccdabcacdcacddbcaaaabbcdbdaadbbbbdcacdbadcadbcbaddbacbddbbdbccbdcaadcadbcccbcdabcdddbaacacbdcbccacaaadccdbadbabddcadabcbccdbdcdcabacbcababbaccbabccddabaddbbbdbcadbdccbbcddbcdbabadaddcdaccdbcddbcdbbaadbacdbbaaadaabdbbaabdbccbcbddaadddbdcadbcbcdcbdcbadbacdcadbbbcaccadcbccadabaadcdcbcbbacbdabdcbaadddcddaaabadbdadacbcabbcbacbdaddbdaacbdadbaddcccdbbabaccbcbcddcaacbdadaaacacdbabccbdcbacdabdbacaacacbbacdaccbcdaacdcbaddbcdbcbcbbcdbdacabbccdabddadbdbbdddccabdacdccdbabdbbdbddcaccdaaaadbabcdadcadaabddbcdddbbbbbdaaaccaacccdbbdbdcbbbccaccadbadbccacddcdcadabcddaadbbbbcbbbdaabbcbdddadadadbdcbdabbcdaccdbbcadbadccccacbadcdacbbcadcdbbdaaabadaddbdcbdadabadbdccbdabaabdbbbcbccadbbbcacadacbaabcbcbbacacacdbaccdbbddacaaabbdcbccbabbcdaadadddbbaacbaabadabcbaaabbdcbccacbdadbbcacadddbdcccbcdcdabdacaaacacbcddbddbbdbaccdcabdacccacaccabcdcadaabdadabcbcccbadcbdbbacbdacbabacbbbadbadccddbdbdaddaabcadbaacbdaabdabcdddbdabbdddadabcddcccdbacacbbadccdccadccdaccaacabdccddcacabdacddbdbddaabdccbcddbbcccdccbbcaacdcccdadcbddbadbccddabdddbcbbbbcbdbbbbaccaacadbdaaccdabdbdcaaccadbdddbdbbbddbcbacbdddbaddbbbcabdbbdccdddadabbbacabbcababbcaadaabbdacbdbadbdbbdcdccacadbbaaadacddabcbdbdaadddbbbddcdcadadadddadadcaabbddbbbbaabbbabaacdaccbbddaabaaccbaccddaaabbaacadcbdddbaacbadcbcbbbcacdadcbaddcbdddbdcdcbdddadddbcdbacbdccbcbcddaaacbbcabcaaaacaaaddbaaaacdbbdbddaabbdbacaacdbabcccccabddacbcaccacbadcbdacbcbcadcdbbaaabbaccaacbbddcccbddcccadabddbcbdbcadbdababacbaadacdbbacccaddacdbdbddacaaaabcaabcbdcbbcabacbaddcabcbdbcdabbdbcadbdcaacadcbdaadddacbbbdbddcccaabccaaaccaddaddadaacbaaaddacdabaabbbbadbbddbdbbdabcbdacdabaaabcbaabbbbbdbccaadabdbbdcdbacdbbcdcadacdbacadcbbcdbacddcbcaccdbcbdbcdcdbbcdacacbaccbcbcbbbbadbbcaaaadaabcacdbaadccaddbdcadcabacdcbbdbbacbcdcaabcdbbbddadaadadbdabaaababccbcdccbabbddabbdcddcabdddbaddabdcaadcddaddcccdababadddaddbaabddaabbaadaaabcbbccdadcbbbcacbdccdaddbccddbbcabddadaabadcabaabbcbdaaadbabddbcbbbdcbbcccbdacbdacaadcbbabaabccbbcddaabaccdbddacddcdcccabaaabddcddcccaccacbacdbdcaaacbdddbbdbccdbdadadabddbbdcdadbadbddbbdbcddcabbdadbdcdbbcdddcbadcbccdcaaddbbcbcbcadaddadbbbacabddbcdbabcbbcbacdcbbdbababaddbccdbbadaacdcdcbaadbcaddccbdcadbabcbbbacdadbaddbcdddbbbccbbaacdcdbbaccadaaabdcbddddacdcacaabbacabdbaabddcccaabdabdabddcabbcbcbdbadbdddadacaaabadccdaabadaddccbcbcddbdcccbbaadbaadaccadccdbcbcbbaddbcbcaacdbcaadbddbbbdbcdddaddcdbccaccddcacadacbaaacddcbdccdabaaaabddbcadbadaaccdcbcaccbbaacadbdcacdaaddcadbcabcadacbacccdacdaddbdaddcbaacaacddabccbacdaabadcccdaddcbadbcbbcbdadbbcbabdadcaadbcaabdccbbaaaababcbdbaabdbcacdcaadbdadacdcaddcbcdabdbdadbbcbdddcdbaabbacadcbcbbbbdcdacbcbaacaacadbdbbdadccaacbbacabcabbccacdadadbabddcbbbdcadccbbbdbaccbacccddbabcbadcbbcbadaddadccadacaacabcddbdbdbcabddbdbcabddcdbdbcadbcaaccadacccdcbcdacdabdccbbcbddadadaadcbddcaccabdaadbbcabccdbbabacacacabacbaadbdbdbcbcdcbaddabcdbcccaabcdabaadaacbaadabcbcaabbddcbacdcadcddcaaddbcdcdabccdaaccbddaaacaabcdacacabaacaaccddbbdbabacdaabcdddccaacbaccccbcccdbcababbbaadbdbcaacdaadacbbbbaabbddcbadcdbbbccbdbcacadbadcaacddcadcabacbbcccdbabccadacdbcddbbdddaccaababccbcadadaadadaaaacbdbaadcaaadcadcccabddbbddadaaccdabddacbdabdbcccacdcaccbacdbaaddacdaacadaddcdbccabcdcdacbabddbcbdbabcdbadbbddadacadddbdddababdccccabbcabddbccbdbcabcadbccbbddddcadbacabbaccabcdaaadcbbddbabdaacdbcadcacdddbbdcbbbdaabaadcdccccacdcabbddcbbcdcdabaaddbcddacbdcacbdaaccaacabbbacdbbdbcacdbaddbabbdcdaabcdcacbaddacbdddaacccacaaadacabcddddbababacccbabaadacabbabdbcbddcaabcbaacbddacdccaccbadbddccbcbabaaaadadabccadadaaaaaabaccbbbdbbadabadcdacdcbaccdddcdbbdbcaadbdcabdbcbbaaacbddddbdacaabdacccaadacacbacaaaacbaabbabcaabbbcadaddaaccdccbccdcababddbcbddddbcbaaacccaaadaacdbabbbaaadddaaacadbdadcbbbacbabcbbacbdcaaacbcbaddbcaadbbadabadcccaabbabcadacadbddbbaaacbbddaaaacadcddbcbacbcbddaabaaabcddcaacdbdbbccddccbdacacaddbbcbdacbcacaacaccadbdbabcdbddaabcccbccadcdccabdcdcdbadbacdcccadbbccddaaaadcdaddbbccabcbcbccddddddcddbaaadbbcacdbdcbcadddbccbabddddaaccdddcbdabaaccabbcdbbaaaadbcbdbbbbdcbbbbdbbcbccbbbdcdadaaabadccdbdbbcdaadcadbabddaaaacbdccddccdbbaccddadbcbaddbbcccbcdcadcbcaccbadaddbcbdbcacbaabbbcabdadbbdccaabaadadbacbbdddabdcddacccdcaccdcdaccaddbbadbcabdbadcdaaaddcddbbdbbcacdbadabdcbbabcaccadabadbdcacbbbcaadabaacccaacddbcbbcbddcbdddabcbaadcbabcddbbcbadbdbdabbbbcabbaaacdbbcdabccbbbcadbcbbcbccaaddcbadaccdcccaabccbacbacaccabaaabccdcbdabddcccbcbbbbdcddcddccdcccbaaaddbdcaacbacaabcbdbccdcddcddacdbcdbcddcaabdcdbcadcdbbbadcaddccdacdddaadbcabbcdabcbbccbadadcbddbcadcbcacccadbaabdccbdbadadbccbdabccaadaabccadbaaadbdadbcbaacbcacdcdbdabbdadbbcaaddcbaadcbbdacbaabdbdbbcccbbaacaaacadcccacacdcdbbdbdbbaadcdbbacdbcdbaabdbbbadababdaacdbdcccbcdcabbbaddcccaddacdccccaddbcdababccdaadbabddabacddddcbddabccadacaabcaababddccbbdbadcbcabdbcbcdbddcabbdcbcddddaaadccaacbcadabdabaaaacadbdadcddcbdcbcbdbccdaccdbaadddbaccdabbadcaabdadcadbdbaabdbaaabadcaddabbabacbcbcadbdddbdcdcbadacdbbaabbcccaddddcccabbaadbbbaddcaccaccddadbaabbabcbcbadccdbcadaabcbccbacbacbdabacdbbacdadccdadccbbdcadaccaacbacaaaabbacbcdbbdddccaabbcaacdaabcdaaabcccaddaabcdacdcccdabbcabbabbacbaabbbadabdddacbbaabadcbcdbbcbdbaccccbaadbcacbcacbcdbcddacddddccbabadbbbbaaaadbdbaabaccdabdccccdcbcbbbddabbccadadcbacdbdccdacbcabddddbdcabcdbbccbacaaadbaccacdbaaadddddddcabbbadababdcbabbddaaaccadacaadadaacbcddadabcdacbaccadaaddbbabbbabcadcbaadaccbcbddabdaacaccbdaabbaadbcbbcbadcdbaccbcababdcdbaacaabdaaacdbcabcbacadccccabbccacbcbaccbbdccadddacdacbbaacdddcadaaabbbbddbdddcbbcacadcddccabccdbabbcbdccbcbadcddccdbaacbdbacdabdaacaacabbdbdbabbacbdacbadbcdddbbacbbccddbbdbacacdbddcbdcacaadcddacbbcbdbbdcdadbcbcbdbbddbbcadabccbcacdbabbbbdbabcacabcbcbbdcabbaaddccbacbadbddadcaadacbabcdbbcabcaddaccdddacabdcdddbbdadcbdabadacdccadcacbbdcbdcacbdcbaacbdaddaadacadadbcabadbacdacaabdabdbabbbccacadbcbbbdacddcaacabbcbabddbcaadcbaaabcdaabaaadbacdbbbbcbccaabdcabaddbcccdbacacadccabcdccbaabaabcacdcbcdbabbdacbcdbddcaadbaddbcaddadaaddccadadddbabdbcccadcacddccbaccdcdbbadaccabdcbddcbbccdadddbaaaadbabcadcacbcabddddbdcaddabadcabaacbacadabdccadaadbddabdabcddbacbddabdadccdabdcadbdccdadacdbaacabdcaabbbbdcbddcccabadaccdddbaddbaacdbbbbbadcdadcadcccbdcdbbadadbcbbdcdadddbddcababdcdccddbadabbcdaacbadcdbadbccbbacdbdbbdbdbccbbdccbbacaacadaacddbbddccddabcddbacbbccacccdbdbccbdbddaadcacdcccbddcbadbabdcbbcdcdacdcaaddbdbbccddbacadbabcacaccbccccdabbadaabcdddadadddcadabbdcbabccdacaabcdadcbbdbccacaaabcddbcacdcbbaccdaddcddacdbcdaacaababdcaadbdddaccacabcdccdbbbabbaddcdbdbcbbddbabcadcbdcbabdababbccbccbabccddadcadbdbbcbdbcbcababcbdcccbadabdcacaadbaaacbaccaddcbacaabcbaaadddbacbdaddaaddcbbcdadaaddbcdccacbdcbcdbaadbadddcacabacdcbccbbddcacadaddbdbbacacdaabbdbcccbcddabcbdacacabbbbccabbcadbaabaaddcaabbcdaddcbbcdccbdabadbbcdcdadcbcacacaccaadbccbcdccdbdaddcacdbabaaaaaabaaacbaccbbbbcbabbdaddabdbcdbadddcadbddbcabcbdbcbacdcadaccccbbbddbdbbcdcabdccdbdbcdbbcdccaababbdcdbacdcadbddcbbbabbadabadddbddbaaadccabbdbddccdacdccacdcbaabacdabacaddbbdacaddddcacbbddaabbaaddabdaabccbcdbabbbcdccbcbccddadadcbbddabddcbacabbaccdacdabbddddaccbadcccacbdabcaabbddabdcbcccddadbccdacbbadcaccaccccbacbabbaaacbaabcccdcddbbaddcccdccacbccbbdbdbbabbabdabcabbdadcdccbbcccccdcbdbbbcdbcaddbcbdaccddadabaabadacdbabdadbbdcdccdddbcbbcdbdbacabcbdabdaddaddcdcbdcbacbdcddacbdbcddccabdcaacbccacccabccdbaacacbacddbddaaadbbbdbdcbdbccabaabbbbabdaaadacabcdccabbdaadcbdbacbaadcacabccbbaddbacacbccdcaaaddddacdccdbbbcabacdbbdaabdddcbbbbbbbaaadcdbaaaabcabcccbcdcbadbdababdaaacacbabccbccaaacccccdaddcadccbbacbbcadbbdaccdcabaddbabbcddacaaccdbcadcbddaadbbdbabccbcdabdbabaadcbadcdcdadcbaadbbabcdaccbbcaddabcdbcdbbddbadaacbabadcbbdcadcaddabbcdabcdbaddcdcbbbacadabaabbdcaaadcdcbbdaddbacbadbccdcadcbdadbaacdbdcccaccaaabbcaddabcdcadbcddaadcbcbcccddadcaaaabcbcacbdadbdcdddbacddbbcddcbdbbcbbddadcbcaddadbadbadbcdcbbbccddbcbbbbcabcdaaaabcdcddbaadccbbcacabaadcdaabaaaacbaddcdddddcadbcccdbcacbbcdbcbcabbcccdcdbddaddbcaaadcddbcacbdabbbbdadddadcabcbcaaaacdddbdbabbddcabcdbccbddacbabadbcccdccabbabcbaaaabddddccbccbcbbacccdabbaacabadacaaddccccbaabcbacadadcadabbacabbddbcbaabbcacacbabadcbddbbcdbabdcddcbdbaaabbaccccbabdcadcccbcadbdcadcdabdbbbdcdaaaddbdcadabccbcdcdaccdaddbdbbaaddbadadaabaadcdabacacbbaadcadbddadcbaddbacaacdabcdbbcadbaabcbcbdccdaddddacadddacdbcdaddbbadadcdaaaaacabbbcaddcbbaaadabaacaccdbdacddbcbaaadcbbdcccddddadcbadbcadcbdccddbcbbdabcbdbdabdddbcdbcdcdaccdbcbcddcabaadabacbddcdcabddcdaacabbcbadabdddadcbdddbacddcacbdccbbcddddabdcdbbdbbdaddccaccbbdbdaddcabaddcbdadaacbbadcaabbddcdbacadbdadbcdacbbbcccccdcbdcbdacbcaabcadddcbddcabddaadbdddccddcacbdaaddacdbabacdbcdddcbbccbdaabaaaccbbbdcdadacccabcacdcdcbbbbbdbcbcabbccbcdccacabdccbbddcdddbdbdcacdccbabdaacccadabbccbdbaddcacbdaccacabdbdacaccccbaaabbdcbdbabaabbbadcbbbcdccaddbbabbabcaabccdabbbdadcaadddcddddcbaccddaaddbbaaadcbcccdbddcddcccaadcddcacdcddcdadacacdbdabcaabadcdabcdbccaacbbbdcdbadcbbbacbacdbddbbcbbdccbbbbbadabbddbbbbccbabacdbdcdcbacadcbbccdaaaaaadabbdcdddccbdaccdbcbddddbddddabdbcdccddacbbaabbbdcdddccdccdcbcabbcddcbadabadcbddabacadbbdcdbbcadaadcadadbdbadbbbadddcbacaaddadacdcbddcbbdabcddcaacacadccdbbdbadacbdacccccdaddbaaaacbdacacbdccbacdadbbacdadababdccabbbaddcbbccabacbddbbdabdcdabcddccdcaccdaabacbabcbadbcbabacbdbbcadbddabbadadadadcddcdadcacbabbbcacaacddadaaddbddbaaaaacdcbdccbdcbcdaaaabaadbcacccbcadadcacaacddbdbcaacdabdbdbcccabccdcadbdcddbcdbadabbbdbcabcdcdcdcdbccadccaccbbccbabcccabcadbddcaabdddbccbdbccabddcbdaaabbadabcccdabcdcddaccdccacccbdbbcdbddabddccccddacaddbbcbadaadcbddababbababbcdcaddcadcaaadcddabaaadccddcabaadaabddcadcddbadaaddbdcdadcbcddcdddaaacacbddaddbdadcdcadbcbdaccadadcddcbdbdadccddacaabdaddbdadaabacaccdccacdbbcdabcaccbcbcbdbdbabbcaacbcacbbcbdadccaddbbaaacbcdcaaccaadbdbdaddaacdccccbaccacdbddaacbddabdcaadabcdbbdccbccadaccdcdcbcbacadacdbcbdbdcabdccbbbcdadccbcbdaccacadcbacddbcbbdccabdadbdbcacbcbdbccadbadbdcddcccaabbdcbcdbacddbabdaaaaccdabdcacddbccbdacbddcccddbcdcacaaaabdcacbbcabbbcdcbcaddacbadaadddabdddbaccdcdabcdadccbdccccdabcccbbcbbccdbbaadacbdbbcabdbcdddbbcaaadbabadddaadbbcabdccbabbccdbcadadadbddcccddddcbbabdacbdabaddbcbddbdcbbbbccbdaaccbaccccbdacbcbbcbccabbddaacdabaabcddbacbdbdcadcabcbbcabbabccacdbacaabdcaaabbdcabdadcaccdccbabdbdaddcddbbbbbdacbddbcccdcdcccddcdacbdaabbaadcacdacabacddbcdbcdcdbccacdbddadcdadccaddbdddbbdccbdbcddbddcbbdaccabbcdadccabbdbccbaabddaaaaacbadacbaddcdbbdbdaddcbdddcddaddbcdddbcdbdccdbddcaaacddcadabbdcbaddadcbcdbdacbabcaacdccadddcbcbaccbcaaacdcdacadcacdcddccabbacbadbdbcbaadbddabcbbacddbbdbbddadbadbcbbdaacadccdbcacbcbccbcaacdddddddadabbbcdbaacddaddacbbccccbccabbbccdbacaaacdbddccdcaccabaabadcaccbaacbabdbcadddbccbcddbabdbdbacccbabaaacaddbdacbbcbaaacdbddbaaaaaaccddaabbacaababcdcacddbccbbcbdaddababadccbabdabcbcbdacbbddddcacdbccbdcbadccbacbcdbddcdccdaddcbabbddddddaacdccbdbadcadcddbcdbbbcdddcacdbcdccbcdddbcacdcbdcaabcacdaddbcaaadcaaabbbaadcddacdddddbbabcdadbcaccdabacdcadddcacbcddbccaadcdabbacdacbddbbabbadabcbcdbdadddadcdaadcbaccaadcdbadcaaddacccbaabdabcbbcbadbcdaddbcdcdbdcdacabcaaabdacdbdcdaabbaaccdbdddcdcaadaabaaaacadbbbccabadaabbadddbdcbacaddbadbbdcbaacdcddabcabbbbddbbacaabcdabdcaddcabbddccdacbcbbadabccdcddbacabbacdaaccbcbcbddadcbbcbbabccbdccdbcabcabcbbbabdccdacaadadbdcbdabadbbabdacabbddbccababaaadbddcbaacdabcbbcbcbaacdcacbbdabadbbbdcabdcdadddbabcdbbcbbbdcabdbacbcadabaabcddbcbccbddaabddaaccccdbcadabbccbccdcadcbaadbaaadbdcccddaccacaddcbaddbbcbaabbdaaaaaabdbbcddccbadcbcbdcacbdcacaabccbadadadbdacddcdbcadbbacddbdbbcbcbbabaddbddccabbdbbbcccbdcacadcaddcbdbbdbcbbbcabdbcadbcaddbcbadadacabaaacbdddcccaabdcbaddbdaccdaccdacbcaaacbdbcccbdaabbacbcabcbdcdadbacadbcbabddbabcaaaabadadaaabdacbbdabaadabbabaacbbbbbbdddbbabadccddabadabcbdbbccacdcbddbcbabbbacdadcbcadbcabcccabadcbbbdddaacbcbcdcccbbdbbbbdcbbdcadacdcaabbbdbbaadcababbdbaddbbdcabccdabcaabcccdbbcbaabbdddbddccdcadcbcbbdbccbbadddaddcccccdcadcdbacaaaddbbbabcbaacadcbdadadbcdaadddcaccbdbdabaadbcddddabbacdbdcddadadabadacdcddcdabddaacdcccdcbcccadadbdbcacbbacaacadacbadaaaabdadbbacccdbbaccbabcbdcbdccdaadbdcccdbadbddbcabcadddbbadccabaddcacaacdcaccadbbcdbacbbbaabbaadababcccabdcdbbabcabadcadcaddddaadaabaaccbacbaacacdccbcabacdcdaddacadbcaabbccbbdccdccddcdcdcdcddcbddaccddddccabaaabbbcbabcabdbcaabdcbdcdcddabbddcbabdcbabbaacaacccdcaaaccbcbcbadbabababdccdaaaaabccbabcddadcddbcddccbcabadddabdaaadacdccacaaccbcdacccdcdabbdbcabdaabaccddcdbdacaccbdbbcdcdddccacbddbcccbbbccacccbacbdaadaacabcbaacbdadababcdcaacccddabdbaabadbbcddcbbaddcabbdcacbdbcddbadcabadabbcdabadbadbdcddabadabcbcddaccdaacdbaaadaccddcbadbccddccccdacdcddbcdacccbaddbadaaabdbbbadaccbdacccdcbacabacadcddbbbddacdaacaccbbdbadddabdabcdbadcbabdbccacbaacccbcbbbbaabbbcdbbadabbbcdacbbaabcadaddbcadccacddbbacbbbcaabdcacdabdddcccccbdcbcbcdbbdcadaacbdcaccddacacaaddcdddabbbdbcadcdbbadbabdabaabbccacadacaaadcbacdcccdbcccbcddbaacdcadccbdcacddaccccabbcdaabdddaadbccacdcdcabcccdcbccbacabcdaccddcdcbccaabdacaacbdcbbdcbcdcbcaadaaabbadcacadaaadddcaaacddbabdbaadcaaadcbbaaddaabbbcdbcbcdbdababcbaacbccdbbacabddddbbbadadaacbacbdaadaadbdbbdddbccabbdadbccadadaaadcccdbcaddbbadbabcdabcbcddacdadcdbcdadcbdbddddabdbcbcdbabbdadaccccbbbbacdccaddbdbccbcabacbccacbdcbdbabdadcbccacbccbddcddbbcbdccdcddccccacdbbaabadaaadaaacdaadaaddbccabccadacabbccccdcbcdaabdadabbadcdbccdaacbbcbbccbbabdadddcbdabdbaacadcabddbdcaddcbabcddccaabdadddbbaabbbbaadadaaccaadbcbadabdcccdaadacbbdddbaddaddddddcacdbccccdcddddbaaacdbbddcabccaaacddaadbcddbbcbcdbcccbbdbabaaccccdaaccbaddbdbacabdddcbdaddcddbddddcaddccddccaddacbdbccbdbdbacbbaaacddaadcadcacaaddbccdabaddbbcbbbcbacabcddcacaccddddcababcdacacaaccadcbddbbcbcccddbbadabbaacacbdacbdaccacddcbdbccdabbbacadcadcdcaddadaaaddabdcaaaddabddbcbacbbacbbabbdcdcddbbbcbacbddbcccbcbdbcadbcdddbcdccdcbccacdcbddddcababacbddccadbcdbdaabddbbabdcccdadbccabdddbdbcaccdacabbbddbbabaacbacbadccadabbaccbdcdacabccddcabadabbddbadccdddaabcacdcdaadbacbbdcdddaddbdbcddaaddacdcdabbabbcddcccbdbbdadcabdbbddacabadbddcaccabbccbaaccbcaddccbaacdcbbcdaadaddadbcadbbdcdcdbaadcdbbaacdbabacbbdcdbccddbcdabdacadcbbacccbbbbacbcbbdbccddcaadbbdbbdbbaabbbabdacaacdcacacdaabacdbbdccddbbbaaccacdcdacbdbcdadbcbdcdabaddbdbadcbbdabdbcbdabacbaacbabcabdcddbbcccbddadbddabaacdaaccaccaccdddddbbaaabdbddabbadaabbaacaacbdbbbbdacdaccdbcabbbcbbdcbadadaadccccdbdbabccddcbcacbcaccacadabcacdadacbcdacdbbcbdbdbbababdddacaadcbdbcdaadcdbadccbcbdcddccbcdcbadcdcdbddbbabaadddcaddbcaccbdabcaabcdcabdbadcabacdadabddcdcccdcaccddacbccaabcccdcdabbacbdaaaaccdaddbbdcccbcbbccdddbaadccdbbabcbcbbbdbdddbbaaabdbdcaaddddddcccdcdbbccbdbbbdcdbaddcdbacacbbcdabdaaacbaaddacdcdbbcbdaaabbdaddaddadcacccaccddccdacccbcbcdbabcabaddbacdbbadabcccbbdcbcacbccabcbcadaaacbaaccabcbcddaaaadccacdaabccdabadbadbacddcabcdaacadcacdacbddcdcdabdccddcdabbabacbaddcacbcaabdcabdaababbbdaadbbacdcabaccccadbcbaaccabdccbddddcccbdcbccdaabadabdcadbbbcdddbbcadcdacddbccaaacddbabaccdadbabaacddacdadcbddacccadabdacacadcbbadbaaadccbbbbaddabdbaddddbaabbccddacdbaadcbaddaabdbddcdddccbabadaabbbdddaabbbaaaacbbabdbdbccddbacddddaddcdbcccccacbbacaadcccbdcdbabcbaabaabbdbcddbdddacdcaadddddbcdabcacddadccadaddabadaadabacaadccdabadcabcbbacabbddbadaacdcddacaadadbbdbadadbaccabaadcbccaadcddadbddcabbbabcbaddccdbdbbcaccbcdaddabbdacabdbbcaaaabcdadbdbadccbbbbbdcdddcbabdbcdbbadddbdaccaaabdacdcccadcacdcbcdabccabdabbbddbadacacdaddbbacbddccacdacdabcdaddcbdcabacadcddcabaabdabaacbdddcdccbcbcadccddaaadaddbdcaabccbbdbcabdbdbabbacdbabbbbddbabcaaccdbacacbddaccbdabdbadaacdccddccccabcaabbbdbadacadbdbcdabdbdacbcccddcccdbcddcacbddbabacbccbabacaabacbdaddbcddcbdaacbadddadbaaabddacbcdaabbbadadcbbbdcddbadadbcaabbcdcccbadacdaadbbddaccbcbbdccbbdbcdbcccabdadcddbccacaaccbdbccbddaababcdbaacbbccbcddadbbdcbdcbbadddcdaccdabdbbabcdababccbddcccaabddbaadcbbcdcaccabacbadadcbdbdabaadcbcacaacbacacbcbaacbbdaabaccccccbadacbddabbdbdbbdcbccddadcccbbccdaacdcbaccdbabdccbccbcbabadbbcdabcdccabbbbadddacdccbabcdcacadcaddbcacdbbdcdcbacbcaaadbaddaabbadccdddacdcbccdacdbcdcbbaadddaaabbaccccccbdabbbaccacbbadaddacbcdbacdcddccadccddccacddccadbaccdbddbdbbaddbcacdabccbbdabbdbdcabcbccaccbdacaddccbcbddacbabcadabcadbadcacccdddcbcbccddbcbbddabccdbaaadcabbdcdacdabddcccbbddcbccbdbcbbdddbcbdbcaccccddacccadbbabbabddaccdcadddcdcabdcddaddcddbdcabdcddcccbcababcdbccbacdaaccccbdadaababdddcccadbdaabaabbcbcadcdabddddacbbacabddcbcacaaaaddbdadddbbbcbbaacacbacbacbcdbddcaddababacbccdbcbaccbdbdbbabadbdbbdddbddadabcbcbdcccdddcdcadddbbcccddacaccaccdcbbacabdaaddbdccacacddcabadddabbaaaaaacbaaccdbcdcbdcdadaccddcdacdbdabbddddbaadbaabaaacbaacbabbdbbdabdbbcbadadadacaaacbccacababacccdbccdccdcbddabdabcccddcbbcbcbbaccaaabacccbdcdcadcbdaddbbbddbbdacbabadbbbdcdbabaddbabbaccbaadaadbdbabdddbdacbcddbdaaacccadcccacaaaabdcaacdbcabbaaaddadcadddbaadbdcdaadbabbbcbbbbbcadadcaabccdacdbcdddacbacacaaddbcddcaabdbaabbbcacbdcdbacdcdbbaccccdbbdccbdaaaaddadccbdaabaabdcabdbcccbcbdbccbcdacbcdadabdddabbbbdcdaaaddbcabddbaccacbdddbdddcccadddaacbcccbdcdcdabbaddacaadacdcaacdcdcacbccbdaddbbbbcdbccdcbcbcabdcbaccddadaacddcdbbddbddcabaddaddaadddbbdddbabadcdacaabaccaddabcbbacbddcccbbabcbddbaadaaaaabdccdcdbadacaaddacbbbbcdaccbadaadacacacacdbcbacbccdcabacbdcbbdadcdbbcbaadccbbbcabcacbaadcdabdcdcbacbabdbdaaadbadbcbaccaabcbccdbcbbccbcadbcaccbddadbcaccdbadcbbcabccddcccdaccddcabcbacccbcabbccdcbdaadcccddbdcdabcbcdcabadcddcddbbbdadcbccadcdacdcccbcabcddccaddbadcdabdcbdbccccdaaaacccdcbcddccaccbbbdcccbaccdbbcddbdccccbacdcabccbbdddcbbacbdacdbdaccddbcdaacddcbcaddcaddccacccabbdbdddaadcccbcbbbcaccbaccbabdbbddcccabaddcdcaabcbbbabcdadbccbbbdbdbbadbcccaddcbcdcccbcabccbaccdbabbadbcbbcbbbadbbbbdaabbdabbcddbcdabbdbcabaccbcbcccbcccaabbbacbdadbaacaaccaadabdcbabddcddaaddcaacacbadbcbdcadccdacbacbdababaabcabbdccdddaabbcadcbcccaddcdbbdbbcdddabddbaccbacaaabbbcbbcabcdabababbccdbcbcbcddddbacdbddaacdcadbcdbdadacddbacbbbbaddcbabbadcdcdbcdbabadabccbadaccbdbbdbcabccadbccacdccaaccdcacbcabbddbdbdbcdbcdaaccaccadcbaccabdabdbcaaaaccddaabbbbbaacbdbcdbdcccddbbaaaaacddbabadaccdabbcbccacccdbcbaccdbaabbacbcabbabcdbbddadcbcddbaabbbccdcdbcadcdaacbabbdaaddaaccdbbadadcdacdcaddbbcacadcddccdccdbbaabadadbdcaabcababbdacadcdbcabdddbbacbaacbcbdadbcbdadccbaacabbbddbbcaacbadcbaadddbddbbabccaadbacaaadccbdbadaaacdbbbaaddadaaddbdbdaaabbdcacbcbaacbacdcadccbdacbbcdddacabbbcbcbdbcdcccacdabbcdadbacbadabdbadaabbdddddcdbbdbbaddabaaacdbaaabdbdccacbabddcdccbbcbddadbbdcdbadabcdbadcbbbcbbbaadbccbdbaddcdbdacccbadcdbcaddddcbdbddadbbdacbbcbdaccbccbdaddadbacbabbbcbdccccbbcaccbabdcbcadccdaaabdbdaddbdbdaacabadbbaacbbaddbaabbadddabadcdcccadbdcaacdcbdadadbccaddadaacbdcadbddcaaadbdaccaabddababbccbdaddbcaabbccadcaddbdccaacdbcbdddccdabbcddaddaadabccbbacadadaaccdcbcadcdcbadbabdaadbadaccdddbbcccbbbdabbcdabbadcbcbbcaadacaccbabbdacdcccacdbacddbdacdbcdabbaabbcdbcbabddbbadadaadcbcdbbbdabdbcbbaaccbabdabdcbcccacaabbacbabbbbdcbcdbbaddddabcabcbbcddbacdacdbcbddbcaabcbbcdbcbbdbdcdbaaddaccdcdccddbdaabcccddaacbbdccbbdcbddbadbbcdcdbccaacdaacddaacdabbabdacccdcddacadabaaabdddddbabbdcccbbdaddddabdcdaadccacaadbbabaadcdabbdbdadabcbcaacbaabbbcaccdaaccaaacdaacbacccdccbcbdcbdcbbcdbccbcdaadbdacbdacdacdcdaaabcacbccbcbadcbcbcabdadcbaacbcdbcdddbabcbbccddadbcccaacabbddbcadbcbbdacbaacabdbadbbbdcdabbbacdcaddccdcadbdaddaaaccabbaabdcabcaacdbcccbcdaabcbbccababacbaadcabccabadacaaabbcdcbbbabbabccbcbcbbcddddabdbdbdbbacccacdcbbcabaabcdbaaddcccdcbaaadbaaaccccdabdaaadcddbacdbdaacabdbbcccddaddcddaacbbacabbdbddabddbbaababcbdbcbdcbddbdaccbbcaddacaaddabbbbbbacbddabcbdbcdabadadacadcbdcbbabbdacabcabcbbcaddbabdcddbbaadaaabddcdbcacabcdacbcbbbddccacbbbcadaccbdcabcdbbbcccccbdcbddddbbddbdcccbccbcbcccaddaaabbbcdcaaadbacddcbbbaabbddbcdcbacdcccdaccabadddbddabcccabaadcbcadbadacbaadbdbbbbacccbaacdcbcdcdbadacaccaccadddbddadadacdaddbbbbdaddabbabbbdaadcabacdddadacbcdcdcddabdbcbcbcccaccaccbbbdaaddabcacddaabadabccdbabbcdcacbcbbaaacbbadcddcdddabddccbaaaabbccbdbcbdbbccbaacddaadaaaadabadccacbbbaaadadaddbcdadbacabdbdcbaddaabcbabbdddbcadcddbacbccabaaaccbdbacbdbcaadaacadbdddcadaddacdbbdbdadabaddaaacccccaadbcabbddacbdbbadbbdbcaddaaadabddadcbcdbcbddbccbccdbdcacbbaabccdcdddabaabddbdbccdabbbbdddadddacadcccacdacdbacbbdbdaadadabcdaacdcabbdddaabdbcadbdbacbdacadaadcdbdaacdcddcadcddabadcbdbaddcbccccbbccdbcdbacdcbaaadacdabacbbaaaadcadbcdcbaccbacbabddbcacacbcadaabcddcabcdaddccadccbbbbdbaacdaacdadbdbdbcccacbbddbacbddabadadcadbcddabadcdaacdbacdcdcadaddadacdacdadcdcbcdacadbaaaaacdbbbbbbaacaaacbccdacbccbbacadbacdaacdcbdbbbbcaccbbcdababddabbbcabddbbbbbddaddcaabccbcaacaacbaabddabbadbdddacaccaddbaccbaccdbbabcccaaabbabbcabbaaadacdddadcaccbdcabdcacdaadcddbacabcadbccaccdcbdddcbcdcdbbadbbccacdcacabacccbacbabbbdcadddbacacbcbcdccadbbcdbdacadcddbdaacbbdbbcbccadbaabddbddcbddabcadabcdcbdbdccccabacbdbdcacbacaadaadcaadbaabcabdcdbccdabccddabddcacdacbccaccdbbddbbdaabcaadcbcacabcbdccdbccdddaccacbcaccdcdbadabaccbbacacadadccdcdcdabbcdaaddbcdbdaaddcaccbadcdccdcabbdadacaabdcabbaaddbaacdbdcadbabcabdddbdadabdbbbabbbbbbcdbdbaadbdbbccadbbdacdadababcbcccacdbadddcaaaccacdabacddccdcdcbacbabbbdaccbccdbacdbbbbacdaacdcdaaaccbaacdaaddaddaabdccadddcbcacdcaabcdbdadadaadcccbcbdacdabacccbccaadcdaaccacdbcbcbaadacdcacbddbcaabbabcbdacbadbabbbabaaccddacbcaccdcabddccbbabbccaacdcccdbbabbdcbbbbbbcacbbcdbdadccdbddacdaacabbcdccacacadbabdababcadbbaddacadbcaaaccccabbbdcdccdbddddadaadcdddabcabcdacaddabbaacbbbdcaacaddabdbdbcbcaabcbdacacbdcdcaacadcacadccbbbcaccacaabacbdacdbdacabccadacddabcaabaddaddccdbbbcdacaaaccbbddaaababccddabbcaddaccaadadccdbcabccdaabaddbabbcadcbdcbcbdabbcadccbadbddaaabcaadbbdbabdabbadccabdcbddaccdcccaabcbcccdabbbcddcaaccccddbbdccdbcdbcdbcddbccbdcccdacdcdbadadbcdadacbdadcbbcadbddbcadbcdddbaaabadccabcaaaddcbcbddcdcaaaabaaaccadcabdddaabdcddbacaaddcdcadcdddaaabdccbdabdabddaacbdbccddbacccdccdabbbbaadadddadcbacbdbaddbcbaccdcbbddbadaaacbaadbdbbcbaccddadcacdcdacdadbadcbccddacbccbdbbadcaadacabcddaaccabadccbaaacadabbadbcdacdadaabdcaacadacddcacbacabbbdacdbbdbdcaaadcaaccbdccbaaaabbddbcbbcdabcaabdbbcaabdcbbadddadbccddddcbdadddddccbcbaaadcdbbaddbdadddcccbccdbcabbabbcbdadacdccdbbcbbbaaabcdbadcdcadbbabcabaaacbbdbaadaacbaadaacbcbccaaaadcaccbccccdabcdccddabbaabbaaadaabbabcbdadcdbdcbadbbcadcccabbabacbdaabbaddabdaacddbcacccaabdbbddbdaabcdaaaadabacbcdcaccddbcbddaadaacabcbabdacadcdadcddabbaacaddcbbbcaccabcddccdbcaccaabbbcbdcbccabdbdcdaccabdbadcddcbaaaadcdcbaabdbbcbadcccddabddbacdbabcdcbccabccbacadccdadbbdaddcbbbdbccacccbccbdbabcdabcaabbaccaccccacadaddadbbdaadbccdaabbacadbcaabdaadabbcabcdacaaaaddadbdaacaccccccbaccbabdccabcbdbddadacbcaddccabccadbadcdbadacdbbdcbdabcaaddcccabcbccdcccababaddabacbbbcdadababdddbabbcbddbabbdbbdbccbdbaccbacbdcbcddaaaddcccbccbbbdabcbdbbdddcaccddabaddadbcbdabbbaaaccbbcccdbbbbcaacdcaacbcbbbdddccddbddbcacdadacbdcbdbdddccdcbbbaadacbdaaaabaccdddbccaabaabadaccdbdaddadabcacbcbccdaadbcddcdaccaacccddbaccaabbcdccaadbbdddcdaacabcdbcdadabacbcadaccdddbddbdabaaabcbabddcbbcdccbdbdbadcbddaccabbbbdbadcbdcdabbddadcbcdcdcadccabccaaabbbaadccbbbadbddddcdccdaaaacabdaaacaaabdbdbacdcbdadccabdddadadcadcdaaabaadccbbccdddabacddcbbbbaabdbbadcbdbddbaaadbcddcbabdacbddcdabcbacadcadbaaaccccbcbcaacddbacbdcccbdcbbbbcdbdcbcaddbcdcacabcbdacadbacacbcadbbcadcadbdcbacdaabddadddcddcbacaccbacdcdccddccbbbccbcbbcbaabbddadcdccadddcbdadaacccdcaabdbdbddacddabcadaadaaddadcdacbbacaacacdaddadccabcbbdbcddbdacbacccbcdaaddabccaadcbcabbaccdabddcdaaabcbadccbddbacabddaadddddbddbcabadbdbbaabbddabbdcdaaaddaaacbdddbaaabdadddabcacbabccaddbcccbdadaccabdacdcbbaaacdacaccbcaabccbaaacbdbbbaabcbdadaacabdaadbaacacbbbbdbccdddddadcddadddcaccccbbcdbdbbcdcdcaacacbbaddbadcdadbbbcddabbaaccbcdcdbdacbddddcaadcbbbaadacdbacdddbcbbabbccadabbdadadacadbacdddbdaacabbcddbbbbaadadbdabccbccdccbccdbcdcdddbcdacdbadacdaabbaaabcabdbdaadccaacbbccaaccdbdcadcadcabbabbadbbbacbdaacabadadabbdbcddcccaaadccdccbdbddccbaadbcaabadacaccbaadaacbcacaacdddadababaccbababcdbcaddbaacdbbbacbbaabbdaaacdddcdaabcdabacddadacabbbbdbbbcabdcabbccacdacbcbbcabaaabadddacbdddcaaaadadcdababbacdaddccadbbbbddbbddaaabccbdcdbaddcdcccaabdbdccacdddbcdbbdacaacdadabcacbbbbabbbacaabdaabddcdabbdbdabdbbcacddbbbaaaccbccbddaadadabcccdaaccccbbbadddbaadacacbcdaadccacbbbcdbbbbdcbabbbbcbccdcdccadcbbdaaddcdccbcbaccbccddacacaacabcbbcadcdccbddabbadbddcdcddbcbacdbcaddbdbdccbcbaddabadaccaaddbabdcddccabddcbdbabbcbdbacbbdcbabdacccbaaadaaacaccdacdcabdbabaabaabadbbacacbbbdbbabbbabdcabddddbddbadcabadbddcdddabbdcdbdcdaadcbdaabcbabddcddaadddccadaaccbaddcbabcbbcbbbacddddccccabbadbbaddbbadacddadcdbcdbabdddcdbbdacacacccdbaccccdccddacdcbadaaacdcddcdcacaddbadbcbbaacbbbdddcbaacbddaccddabddabbcaacacdcbbcaacdddadbddbbbdabbccdbccbcbbadddadaaaabcacdaaabadccbdbdabddacadacabbdbcdcbaccbbcbcbdadaddaacdbcddcdadaddccacbcbcaaaddcaacacddcbcacdaadbddccacdaddbbaccadbdbbdbdcdaaccabdbcbdcbccadcadaacdcccdbbdaadabcbcbbaadcdadadcccdbacddcccdccdbacaccbdbadbcacdcbbbdacacadddddabadbdbabadaadccabddbdccccdadbbdcdbcacadbccadadbcbdbcaadbcbbacbdacbdbcbbcaddcacccdbbbacacddcbdbbdcbdbbddaabccdbdbcbbcadbacdadccbacababddcbbbaddcbbdbaccadbcaacaaabdccbccbcbbdbbbdcdddaddadbcadaaacaababcdcdddbaacaacbadbadbbdcadaaabdabacadcdbaddabcdbbdbbadacbaabdaccadbbcabdbbabddacbdabbdbdbadbbbbcccdddbaadcddacdcacdabaaaabacaccbabdbbcacdcaabdbaccabbdbcddcdbbadbdaccabcacbdcababdcbccbabaccaaabdcabbccddddabcbbcccabdaccdacddadcdcacddabbaddcbcaadcbbdcabdbabaddccbacaadddaaddabbacdbdadadbbbacaaadcdbcbaabcdbddabcadcdadbcacacbabbabdabbacdadcccddcbdbaddbbbabcaccdbddbaaadabccdbbbcbbcabbdaaddacabcadabaccabaddcbbcbaaacbcdbbacacddbcbacaaabaaaaddcaccadaaadacadabadddadbcbabbbcaadbcbbbccadbdddbdbcdcbbbaddcaaddbadcddcacbbcdabccdaccadbbbcdbbbacddaadbcadbbbcdccaaabcbbbdccacbccdbbcccadcadddbcaadbbbbadcacdaacddaaddcdbbabdccabadbabaacbbbcadacadbadaccbbacdbccaacacdbacccdcdbbcbddacaacbaadaaacbccadbadabbbdbbabbabcdcddcdabacdaddabddaaadccadabaddabbabbddcbabdbcdbbcbadbaabdaacdcbabddbadbaccddaccbbaabcaddaacabbccbacbcbdabbacbaadbacaddabcadbcdaaadacdacaaccaaacdabdababcdcaadcccddcbdabaddaaccadbabcdbccaaacbcacaadddbadbcddcdbbbdbbdcdbaaabbbbddadccabdadbbaacbadabccaaaaaadcadddbbbcbaddacbcddaabababcbddbbcacccdcccabbaccccaccbbdaabddacabbcdaccabacadababbdbcdcbbcbadbdadbbadacbacbbccdabccccbccbcbdbbdcbacdadcacdbcadcbaccdbaabccbdcbdcdbadbbbcdababaaaabbdcccaaabadaabbbadbbbbdddadccbdcdaddbbcdbadaaabcabdbadddbdacbabccbcbcaddccabccdddaadacdbdacadaacacbddcaaccbadcdaadccbddbadbcdadbcaddcaadaaaadbdcaadddabaddbdadbacbdccaaaacbcbbadaacdadcababaddacbbbddbbddbacbcabdddbdcabdbcbaaccbdbcacddccdaabcbdccbaadccacadcacabaccbababbdabaadabccbabaababcbadccabdadcabbcbddbddbdabdbccbacccccbbddcbdbbdcccabcdcbddbcdabbcdbbddaadcbdddcbbccdddabdababddbddbaabddcddccbddbdcccababdbcabadccccbdaaccccdbdacddbbbdbcabadcddbdbbccbbaaaadddccaabcdbccbbbbbbdabacbaadcccdbaccaabaadaabddcbddabdabadabcbbdddcdbbdadadcbdcaaacbbbdabccabbcaddcddccaadddbbbdcbbdabcdadadbdbbdcbacccccccacdcaaabbcacdddacbddddbccacbccdbaaddddbddccbcbbdcaddbbcbbdbcbbcabccddcacbcbadabdcdbbbabbaddcadbabbdcaababbbbbdccdabcaabdccddbdaadcbdcdcdabbcddcaadbdddddcbbcccaddaddcaaacadcaabbbccaabdbaddcacdbbbddbacdcabdddcaccbaccbabaddcdcabbaabaddbdcdccddadccacbaabcdadcabaabaaacbdbaaadbdbdddbcccdabcbcdacaaccdcdacdcbddddbbadbaadbcbdadaabbbdbbbdccccacccbccaacbcacbdcdcdaaccacdcaddbbcacbccbcbbddabbcaadddcaaadabdbbcaaaabdacacccbdcaaaccbacabbbacdbaabcabadddaddccacacadbdacaaddacdbaadbcadcdaccdbacdbbccbadacaaacbadaaaadaadadccbbaccdddbdbdbadcabbdabcbcbdcbbabacbddcaccaabbacdcabacdcbcaddabaadcbabbaaaaabbabacbdbbadaabadcddaaadadacadadbcbddabbbdaabdadbcaaabbadddcacadccdcbbbbccdcdabccaadcbcbbddbbbddaaabcabbcbbdbcbacaabdaacbcaccbcaabbcadaacabcbacdbddccaddacdcdbacacdabdbdcdabccdaabbdaadcddbbacbdabaaaadabdacadbbaaddcaddbdccbcbccccbbddbbaaccadabcaabcbbaddcbacdacaaabbdadbacbcaddaadaccbcbaaccdbabdcbacbdbbaabcdbdddbdabcaddccddaabaacccacddbcdcdbcaddacaadbadccacbccdbcdadcdccddbabcdcbbdcaddaabdbcccdbccabbcabbbdaababaaaacddadbdaaddbbccbbcabdcabbbdcdacccabadabbacacdabbbdacdcaabbddaadbbdadbdadbacadbdddcbcdbddbccbdabdbccacdcbcacaadbabcacaabdaddbacacabdccadcccdabccbbbadcadddccdaccdacadbbddccccacddcddcddcddbdddddcbcadbadbabdcbdcdcbdbbcbbdaacbdbdaacbcccacddcbcddcccdccadaabbdaddacdcacadacddacbbacdcacdbddcdaaaccddabbacaccbacbbbcddbcdcaaccdcadaabbdaadbabaddcadbcaacccdadadbcacccbbccdbabadadacbacbddcacddddddddbbacaabbcbcabbaaabcbccaaadccbdcadbbcbdaccdbaaccdcdddcabaaddbaababdcdcdbddbbacabacbabccadbddbbacbbdbcbbcccddccdbbadddddabcacdaadddaaccadbdbcddbabaacccbcdcaaadaaacabcdcadaccabacdabcdccabcddaddbccaabbddcdcdbdbbcbabdccacbadadcadbcababcadaccbdcbbabacbcdaadbabbcbccacbccdbbaddcbcaacadbdcbcbbbdbdcabddcddccaaccaddacabadaadcddcaccacdbbaccabbdadbaacbdbcbddadaabbbaaacacacacdbdccccbcbcbbadcccdcaccdadcbcaaaaccbbadcdaaaadcdcaaccdcdcbdabadbbbdbadbbcbccabdcbddaddcddaacadddcbcbcdacacbcccbacabdbbbbcddbddadaccabbbcbddccacdbadadbcdcdcdccbddadbaaaabacaddacbadbaabbacccaaadacacbddaddbddcabbcdaaaacbddadddcacdaadcbabbadbbaabacadbcabdadcccabbcbbcccacaadcccababcbabbbcdcbacbdcbcbcdaacacaaaaaddbaddbabbbcbbcbdbddcabcbabcacdabcaacaaacbcbbddadbcdacbaabddbbddaadbbdacbccccbbcadbdbdccdaddbcdadddcaaacaabdcacbdbbcaacbcbababacbaadbcbaddddbbdddcdbdddaadddcbcabcbdcdcdcdcddbbdbccabbddabbcacdcbdabddcbcdcbddcbabcbdaabdbcdbababaddabbcdddbbbaaabdbdbdccbdcccbcdbabadbbbcbbdccabcaabdabbbabcdadabbccbdabadcbadcccdccddccaabbabbddcbadbacaddbbddadadcababbdbaadbbbbbddcdbbacbcabccbcaabadabbdaaacdaaddddbbccbdbbbcdbaaaaacdbbdcbbcbcdbacbdaaddbcaaaddadccbbccdcdadbcdabaabcbadbcaaadadcbaacbdadcddaadbcdddbdddbdacaabbabbadacabaaddbabacabaaccbaddadacccaaadbbbccabbdddbcdcaadcabbcbdddaaacababbadbdbadccdacccdbcbacccdaccacabdbdbabdbbabdbaacbbccaccddbcabdddbbbdcaaddccbdcccccaccbbcaadcdcdacdcacbbbbbabbbcccacccbabcbcdacbbdccaccdcaadcadbccbccddaaccbcccbccdddcbddcddaddccabbaaabaabbaabdcadabaccabacbdcbabcadcdaccccaacdbcabbbcbdbacabddbbdbbacacbacccbccaddbdccdadbdacccdabdcacdbabddcaabcaddbbbabdabaddbacacaaadbbaabbcbdbabcbabbabbdbcdbddcdbccabddcacaabcbadabcccacdabdcbddabbddadccaabdddaabdbbdbbcdbadacddbaadaaabcbaadbabbcddacadddbaadbdbcaadaaabcbccbabcddcdaaccddcaababaaacdcbabcabbbbdadbcddcabbdcbbaddabadccdbcabaabcddbdbdacadccdabacdaabadddbcbbcdbadcdcbdbaccccaabccadbabddacadbdabccdcbdbbaabbacbbdbcabaadaacaacdadbdabdcbcdacabcddddabadadabbaddcddbbbbadccbddbcbcacaacbadbcabacbbdbbaaaccccdcdbabdaabbbcdbcadcbdcacccaadcbccbccacbbdcaacbadcadacdbabbababcccdddbdaabcacbbdbbbbccadabbadadaddcaacadbdabdacaabbadabdadcdbbbdcccddacabdcaaabbabbabacdaaccbbdacacaccbaccdbdcdacaaaadccbbddbbacabbcadccddaaadcbacdbcbddcbacabcdbbddacbdccbcbdddbdbbcbbadbdcdcbdbadcaadabdddadadbbdcbaddbcbacbaaacacdaddddbbcddcadbaabccdadbaabbddabbaabdbadabdbbccccbcdcbadddbbdcdbadcdcadddbcccccaadabdaadcbccbcdbabcdbcbcabcaaddbcbaacbbdddbaaccbdabbbbbbaaacaaddaaaabdadadaaabcdaacccaababccdbcdcbacadcdcbaadddbaaacaaabcbabcddbdadbddcddbccddcaadcacccdbbcbcbadacdbcbccbbdcdaadadacaddcabaaabccacbabacbdccbbdbccdddcabacabadcbabdbbcbcbccbcdaadbdbcadccdaaaaacbcdbdcabcdabaaababdddbabaddbdabcdaaccacdaaadabdbcaadcadadccabacdcdacddcccacaccaaabbbabaccaddacacbaadadaabbcabbccdacdabbababccccccbabbccdcdacbabbdcccdcdcbddbdabbabcdbcadbbbacbbabaaacadabcdcccdbdddabdcaadcbadcdcccbccacccdccabddadbbdcbabaccbccbcbacdbaabadcacdddcddaaaadbaddadcabadbcccabaadadbdadaadaddbaadbbdbddaacdcbabbbdbdddbdccabdaccdcbabddbadcbdabbdaaddcbbccdcdacccccccbbbbbdcaccdaaabcacbadcdabdaabdadbdaabcacddbcddbdbddaabddacccbadbdcadcbddabaacbaaabcaabadacbbabadadccacdcaaaaaaccaaaacbbddbcbaadcbcabdbbdcdaddcddbcbadbaabbbccdadacdcbddbaaadaabcacbcbdccadddbcbcbaddaccacabaacccdabdcadcdabaddbddadbdbacabdbccdbcadcacbbcdaabcddadbadbcacadbcbdcdcdaaadccdddcabdabaccbaabbddcbccdddaaadabdcaadbdbcaadbdcbbdcaabacabaacaaadcbdabbcdacdaabccadccabbddcaadabbcabccadbacdbcccdbbbabcdcddadaabababddcdadccdabbacaddcdaccdaadccdddbdbbcaabdadbdabbdcdcdbbbaaacdaadabccdbabdcacabbcddddcccddadcbdbbadbabbbcdddaabbabadabaacaacccddaabbbbacbbaacddbaadcbcbbacccbdabbaaddbbddddcdbbbdbdccbddbcdadbbdcbabdccdbaabaaacbccbbcdddbbccaabacdacddbbadcbaacacbaadbcacbbbdabaddbadccbabccaacbdbddaaccaddccddbcadbdbbdaacbdbaccdbdaadbbacacbbbbacccbaabadaccbbcbdccaabccdadbcaccdcaaabcdadddabbbcadcbcccbbbbdccaddbdddbcdbdccaabbaddbddbbbdbadcddaacbbaabbcbcacabcdcbabbadbccdadcddccccacbcacadabaaabdaabaadccaaabbbdabbdbaadaddcddabcdaabbcaabcdcbaadaddcdcbdcbadabadadbbbcbadbcdbccacbacdccbacddcadbcbdcbdcdcdccdbdddacaacccbdbadbccacdbbadcdcddbcccacadbcaaaacccbcbdcdddbcbddbcdcabacdbadbdcbdbddcbabddbbbbadbdadabbcbbdcadaaaaddabadaaabbccbdcddabacddddbbacacbbbcbcbcadddccdcaccdaabbbbdbdaabdcaabacdbdbaadcdabcdacbdcabbbaacdcbbacbbcbddbaabcdaaacdcadcacbccccdbacabdbbdaababdbaaadaaddcdbdddadddabaacbddbabdddcaacabcbbbcccdaddcbbdacdbabdcdcbcbcabcbcbcbdcdcbacaabdcabbccabaddccdaadcbbcdaacadccbdcdcdadccdaaddcdabaddacdcdcbaacddaaabccdadaaccbbbbabbbddccaccbaaacbabacaabcbbbadadcbaadddddccacbbcadadbadadccdcddcadcbadcdcabadddbdadcdcbcabbcbacbddcaadddaaaacacbdbcbcbcbcdbcbccadacdbbaaaaabbddcdddcbdabaccaabcccbbdddbddcbdbbadadcbbcddcacadcdcdacbbdadaacadcbcbbdcadacdbbaaddaddbdbbcdaaaabaabdbdbbcbbccdbbbabccbbddccaaddccddbaadcccbaddcacabcacadbbdadaccbbbddcbcadccabacdbcdcaacbcaaabcdcdbdbdbcbdaabbcdadcdbcbabaccdbbacbccababbcdbcadccaddcaaacdcbcbbbdcdabacddacbdcdcacbbcaaaaccccddccadacaaccdbacabccacaadccacadbdaaaddbccdddadcdbadcdcdbacacbabbdddcacddcdcccccacadcbdbbccdbbcbddaabdabadaaccbbcbbbdbdddbbbbbbbaacadaabbadadddadbacabdcdcbbbbbcdbdddaddabbbdabbcddcbadbddbddcabdcbddabdbacadbddaacbaddccdcbddccdbcbdaabaadaabdcaadcdaaabaabcbcaaabbccbcabcbbdbcddbbbaadaaaacabdddbbacabadbbababacbaacacdbbccababcdbcddbcbddcaddadcdacdcbbdbcadacadbccddaaadcdbbbbacaddaacaadacdacccdadacbaacaccdaacdadabdabccdabacaacacddcaadbabcbcacbcbddcbdccbdcacabdbcccbadbdbabcbcbdbadbacdabcbbdcbcddbcbdaccdbbadbdcccccabdaddcabdddcddadbaabbaccaabaadccbacbddcbddabcbdabddadaaaadbbccddbcaabdacabdcccdaddcdbdabcabdbdaabcaacabacbbadacdacadddadbdacbaaaabccbabcddccbabadbadbdcbcccdccabdabdadbbabadccaaadabbccdbbddacccdcdcbbcbbbaadcbdabbadaabaadaabadbdbbdbcabbacbbbddcddccbabdccdbcabbcbcdcadaadcdcbadaaabadbdbbbaabcbcbabdcddcaaacbccdbadbdbcadbaabdbbcabcabcabcaacabdbbbbaaabdbcbdbccbcbdbaabbbbdbdcabcbdaabacccddbbbbddcbaacdbbaabadccccbccaaaccccbadaaacadcadddcdcbbbcdbcaaabababbdadbdbbdbdcbdcaddcdcadacdcaaabbdcabbbbbaabdcbcbdbaacccbbbbaacbccdcdcbbcdaabbbbbaabbbdcbdcbdabaadbcbdbabcccabdcdcadcddabbcababaabdddcaaabacabdcbdadbdbcbaabdccaacdddbaaddaaaacccdddcbbcaccaabcaaaacbdaaaadcbcaccdccccccdcbbadabaabadcbbdcaccdcbddaddabbdbbdccdacdaccddcbcaddadcbccdadacddbbcaccbadcaddbdbdabcaaadcbbadbccaadbadccccbdabcbadadbcaadcadbddbddddbacccccdbdcddcacdcccbadcacaccdadccdcccddcbaababbddbdbdadccccdccdcdacaaaaaaadbcaacbbbadbdccccbacbadadbdcacacdbcbdbdddaccbddcccdbcaccabdccccdbcdccdacbdcdcabcaadcadcddadbbacadbaddbccaccbddbbcacadddbddabbddcaddccbbbcaacbddacadabacccdabcbdaabadbadbbcaabaabddbbbbabadcaabadcdcaaaccddccbabddccccbddddacdadcaccbadddbdcbdaacbbccabdccbddabdbbaadababcabcbacbacabaacbbacbbcacbbbdbabbdddcdccbcdddbbdccadbdddabaacdcaabbbddbadaaaccadaccbaaaddccbbbdbbccdadcacbcdcabccdabbbbcbbcddcacaccadabbadddccabcddbaccccbacbabdabaaabbdbaabdccdaabcacaddaacbadcccbbbbacbaabaabcbbbdccaccdddcadacbbbbaabddbcdddcccbbacbbbabcabccaacdbcdacddcdddadbdaaaccbcbbcaaddcabddcbacadcabcbdaaaabcaacccccddacadbccbaadbddcacdadddaccbdccbdcbddbabcadcccaddcdaaaccbbaaaaacbaaadcdbcdbadbbdababbabccaabbcacdcbcbadabdbbdabbbccaabdbdacddcdaabbbdccdbdabbaccbdcccacbbbbbbaacaabbccddbbabadbadcbcaadcccbaadaabccbabaadcbcddbaadbacaadaabbbccdbcbdcbbbcacadcadadbbaacdbcacdccdcaaabbbcccdbbdadccdbddbbdbaacacdcabbcbaddabdcbabdbbdddbaadacaaabddcbadaaddcbaacdabdbdccbadbdadabcbcbccdcadddccddbabacdabcdccdbaadbaadcbcdbdcdbddccbcbcccccdadddcbdadcabbbbdcccbcaabaadddadbbbcbcaababadadbacbcbcaadddadcbdcaccbcddcacdbbabacdcdcdbabbbdaadacdcbbaddcdbabbbddccacadbcdcbbadbbacaccadaaacaabdabcdcabacaacbcababaaadbdaccbacaacbadcddaaaacbbbcbaddadcbdaddbbbdddaaabadbadddabcbdcddcabcbbbaacaccddbaddababbbaadcadbbabaaadbabdbbbddcdbdaadabcdaabaaacbbadcccaadacbdaabdcdbcbddaacbadcaccadcdbbadadadbabdddcbabdbadcacbcccdccadabaadbbaadcaaddadcdbbacccaccadabbbaccdadbcdcdbccddaaacbbdaadababbcddbbbdcdaacabbbcbdccbddaacbabcbdbdbcdbbddcbdbabcccadcccddbcdabaadbdddaaaaaddccbaabdbaaccbbcbdaacbbcdccdcabcadccddbbcbccdcbbbcaadccabdbdbddadcccddcdbacacadccadcaadccaaacaadbcadcadcdbcaacdbdbccbccdcbadbdaccadcccddddcdbdcdcaccaaddaaacbccbabdbabcabadbdbbcdacccbaadadcddbaaacadbacbbaccbcaccbcbadcddabadbaabaacdcbdaaaacdcadcddadddabddadadbcdbdddbdbaacbbdaabbacbdddccdbbdbbbcbcdbdcbbbcbadddaacdbdcdacdbaaabaccccdbddabdbcbdbddccdaacdbadbaacabdddddadbbbcdccbcdccccaaacacbbacdbdabbdddaabbcdadbcdcbabddcadaaaddcadadbccbdbdcacdbccadcabcbbabcddcbcbbaccabcbaddcadcacdbcdbbdcbcabbdbdccdbabdadddabddcdbddcbbcacabdaaadbcbbbcadacbbbaccdaaacdbacddbcdcaddbdbdbbddbadcaddcddaadccbbdabaabdcacdbacccaadbdadcbacbbacacdbdbdbdbdbcbcbccbcbabbcbdcbaaadacaadbbacdcbbdcadabbaaacbddbcdaddaadbdbbacccbcbcdcadddccdbcaadcccaddabbabdaddaabdbbdbdcbaccddccdcdcaccadbdcdababaccdbcababaccaccacadabccbcabdbdbcdddadcdaddbbddbbcabbcdabadcbccdacbcabcaacdcababbadbbdabadccdcabaaabddbccdaabccacccccacbdbddacdbdcabaadcbaaccdcdacbbabddccadccdbabddcbbdbbdadadddcaccddbcaadadbdcbbddddabdccbddcdbcbdabaaacacbcdcccddbaccbcbbccacccbbdaccacbdbabcddccbcbdbccddaababaacccabbaaabaccabbbdbbaacdaacdbcdbddccaacabacdcabadcaabbdadaddacbcbbdcbbdcdcccccaabbbdbcbaccbdbbccbbabbaabacdacbabbbcdabaabdcbbbabdcabaadaacaaccdcaabbcbabcccacaadbacddccdacbadcdbcabacbbbdacadbbaccddbcaddcacbdcaabcccbdacacbccaabaddbbbaddbccabbdccbbacbddadcdaaccadaaadccbbdacddacacdcadabcbbcdccabdaddddbdbdacbbdabdaddadbcdcaabddcaacdbacbcdabcacdcaddbadacadacbadaddacabadabcacdbdaadcabcddbbccaacacbdcaadaacadbbdccadbbccdbcbcbaabcaddddddbbabcabcaddccbbdccdbbaaabbcdabddcdbbcbbbbdacbcddcdacbaddcccbcadcbaacbdcdcdcbdbbcacdbccccacdadadbbabcbaadcaaddddbbcdcbbabdbddcaacbccbbbcbdcacabdbbcbadadccacdbbbccdcdbbdbcacaccdcabadbcacaabcdcbbadccdcbabbddbbbbdcacadacaccbbcdcaadcdcacccaaddbaacabbaaaaaadbbcaccabbadbddadabbaacddbbdaddbcdaacdddcdabcdaababcbbbacbddabbdacabbdacdcbadcbcaabbcabadadbccbdddbdddbaaadaacdbdabbbddbaddccbdaabbacdcadcddbbaaaadbccaddacbdcbdcbdadcbbadbdbadbccdbbccbdcaabaddbdbabbcbdbabbadaababbacddadcabcdbcacdcadbaaaadacbbcaddaabbcadadabbabcbcdcbcaaaddbbdcabadbdcbbccbbaccaadbcbacadaccdbdcaccacbbdbddccaabcbbacccadcbabbbcdbbdadcdbcbcccbaccbaabcbbbbdcbbacaddcdaabddbbdabcadbddddcbcadcdbddcacbdbccdacbbcddccaccbabadacacbadcbbbadbbabbaaddcacccbdaabaabdddddabaaddaddaabcdbcbcacaddbcbdacbadcbadbdddcdbcdaabbcbabdccadadcccabbbccaddabdcbcabadddbcaabaaadbaaaadbcdddabbbadadbdadddccdaddbcbdbccdadbbccacaaabcacdcbdbcadbaaccadcdaddbddbabdddccdacabdacdcacabcbdabbdcbddddabdcdaaacddaaadccbcdbadcbdbadcddabcaaaacdbbabbbaaddcbaadbabbddababbddcbadbdbaacdabcdccacbaacabaabbbdccdcdacdaacdbddcacccbcaaaccdcbcabbacbdbbdaabacbccabdbbcdbbdcbccadadaccbdcbdddccadcacacaabbacacaacdbaaacddabcacdadabcaadddadcacbbbbcddbaccccbbaadabccdbabacbabacdbbabbbaadccbdcbcdacdadcbccaccaddbbdcacbcbcdbdcdaacbaaabdddabbaadcdccabbdaaddcbcbddbccbabdccbbcbbbdcddbbcdaabbcdbbcccbabcacdabcaadcdbcbdcddcccadacbacdccbbbaddddacbdbddcacccdbdbddbdadbbabdcbabbbaadadcabcddacddcdaddabbcbcaaddaaaacadcaacbdaadacddbddcaddaaadadbbcaaddacddccdabaddaddbabbbbccdbaaadcabcccaddbcacdddddbbccaadbbbadcccdbaaaacddddcabddacdbadaddcabaddcababbaddcdcdccddcddbcacdbaadddbcbdcdcdaaacaaacacadcdbbadadcbdcacbbbacdcbcccaaccdddbacacdccbbdddadbbadaccdcdbdcbcbcccdcbcbbbbbacaadbdbddaadcabbbacccabaadaaddcadaaccaabadbdddabbacabcdaccbccddadbdacadbcbbcacbbdcaadbacbdbacabddbcaabcbbbbccbddcadccccccbaddaabdaadddcdbbacaaaacbadbaddcadcdddadbcaddddbacaaaadcadddaccdcadcababaaaabcccbacbccaddacadcacbddbcdacddddcbdabbddadabdccddbbcbcaadbcbddbaacbbaadccacdbcddccdddabdbcdccdbcdacdcbddbadddadbdacdaaddbbdcddaaccccccbacadbbccbbcbdadbbcdadcacddbbdcccaaadbddabcdcbadaacddbbcaacabacbbbcbdcbbbbddbbcddddbdbacddacdaddbbbbbdddddcdccccbdddaabcbbdcccadddabacbcccccdbaaddcbdbbbaaabbacabbccddadaaaabcdacbadbddbbcbcdbdbdcbdbaabbcbcabdbddaccdabbdcabaabdadacbdacdcacaccdbaacaddccccdbadcacaabccaaaabdacbbbaabcbcdcaccdcddcdbadbaadacaabaaccddddcdbacaaaacadccaabdcacadcdabbcbbcbabdcabbbbbacacaaaabcbbdacdbbccbbcdadabccadcccdbadacabcdbcbddccbcdcacdbaaaccbbcdabbcddaddbbbcdccdaddabcbabddbbcbbabcbaabdbddccdacbbcbaccbcaadabccdccaabadaccbbbaadcadbddaccccaccdbdccdbdbcbcdcddbacdbcbcacdcaaddcadbdcbdcaccaccbadaabcbbadcbabbcddababccabdbbadcbcccbdadababdcabdacdcdcddbacdaddcbabcddcaadbcbcdaabcbabbadcacabbccdbcbddccddbbbacacdbdadbacbadabbdbcdaacbccbddbacbaddccbbaacbdaabdaaacbccbbaaaacccbbcadcdcbcbdcdddcbbacdbabdbddcaadbadcaadbdacddbbbcaacddcbbcaddacaaacdcacabbdbcacccabaccadbcddadbadcdacbdbdabcabbcacabbdbcbdbbbddddbddcbcdbbdbababadbddcdacdacbdbdbcddbdbcaabcadcabbcccbdbbacbbbddcccbbbacbcdcccacaddbdddaaadcccaaacbcbbbbccdacbdcacbacdcabcdbaacdbbadbddcbccdbbbaccaddabdcadadabdabcddcbdabbaacaabcaccccbdbadcdcbbcabbbbbabddcbbcbddacbdbbccdcaaabaadbdbdcababccdaaaddaaadaabddbbdddacdbacbccbcbdcadaadabdcdccdcdbdbadbbadcbcbbdbbacaccbdccbbdbadbcacaadaababbdbaddadaadadacccdaccbdabbccdccbaaadaddcbbdcdadbcdcbaabbddadcbdbbbddbaaccacbaacddbaabbcccaaaacbacdcdbadbdcbddccbdbccdababcacabacbaddcccaddcbbcdaabddabaadbbbbdadaaabbbddaaccadacbcccbbccadacdbddacacbacdaabacadadccbbbbcadaccbaadddabbcbaadabcccbbbcdcbaabcbbbaacdbcaadabbbacdbaacbdbcacddabdadddbbcaccaddbddbadbadaccabaacaaadaaddaaaccdddbacccbdcdcdcadabbabcadbbbbabdbcdddbdbaacbaaadcdbbdadacccbccdcbbbdabcbacccaaaccbbbbbcbcbdaaabdaabbdabdaacdbcddbcacdbcbddcbdcccadcdabbddabacdacadcabbcadcdcdbdaabbaabdcbcdddacbabdabcccacadcaaccabcbacdbddccbbacaabaccdadacbabcbbcbcccdccdcdbcabbaaaaabccbbcbccababbaacdcaabcbcbbbdabcaabacbccbcbdacbaaabbccbdcacdaacbbaacbbadcabbcdbadbacdacbbbabbbabcdbdcabcdcdadbcbadcccaaccdaabaabacbadcbacbcccbddcbbdacdbdadddcdddbddadbaaaaacdbadaddaaccbabdcaccbdbbbcbcdaabbadcaddcbbbcdddaaddbcbabddcdccccdcdbcacacbcbdbccbadcbaddcaaabbadcdddbcabddacdbbbadbdcddbdcacaaaabbbdaabadadcdbbbbaadbdabacccacbaaacbdbadcbdcdadaccacadbdabaabbcbdcacbabccdcdbcbdaddaddcaddcddacacdabdccdcaaacdcabababbcdabccdbbcbcdcbdcbaadadbbccabbadabddbbabdcacbacabaadcabccddadbccbddaddaaddabbdbbddcabccbbcccdadcabacadbbaadbabcdcdddbbbabcbbbbcbbdddcccbabddbbdcccddbadcabdacacbdbcaabbccddbcddcbbbddbcaadadabaddbddddbbbdbcdbacaacadbaccddbdcadbcdcbaabbadaddabddcaddccbaadbdbccddbccccdadccbcbbdbdcacababdcaabaaddcacadcddcbacbacbcaaddbdcdcbdcaddbacabcbbbacbacbcdccabcbdcbcbbbababdaadbdabaaccacadabcbccbbbbddcdddbaaadaadacaadbdcbacdbccacbcbcbacdaadaacaaadddacadbabbdcccdaadadccccdcbcdabaaaccbadbcddcbbcbbddbbcbadbddbddbcbdaccccaddbababbdbdddbcbddddcdacbaabdabcbbdaaaabcdbcbaddcbcadbdbaabbaddccbdacdccacabcbcbbcbcaaabbddbbdbbbdcbcbdcdcaabcbbcabbaabaacbcbddaaaccccabaacdcbadabbdadaadcdacaddbcbcdccbbbaabaccbcccbbdcbcaadacabdddacccaaccdacbcccdbccacdaadcccabaccccacccaddacdabccddcbddbcddaaacaabdcccdccdbdcdddcadcddadbdbddcbcbdaacbbdadaaaacadbdbcdabcdbddbaddbbcaaddabcddccabbcbbcaddaddbbadcccdbbcadbaacbcaccbcbbbcccbabccdbcbbdbdabdbacbcccbcbadcdccbbbdcaaccdabbdadacdcdbbdbbbaccaacbdcbbcdcdbcddcbaaccdbcdaabdbabbcddaaddccddbbacdadabdbbbdcbbbbcabdabbdcaadddddaccaddcbcdbccbdadcabbbbbaaacbbbccbccdadadbcddcbaaaddcdbddacabccccbcadaaccaddbddbdabacadaaaabdbacabcddddbbdaccddaacdcabbbaddacdadacdaadaabaccaddbbbbdaccadaabadccbcbbdcddadadcacdababdbaacacccdbdcaaacdaacbcbaabbabaccbdbbcdbbcabadcadaddbaddbaabbbcbacbadbbdcdcdbaadaddcdcdbdabaddccddbaadddbcbddddccaaccacdddaababbcbddcabdcaccacbaccaadcbbaadbaacbdcccaabdbcbcbcbcdbcbbadcadddaabcacbdcacccbadadaacadcbbdcaccacadcbbbdcccdaddbbaadddcdabcadaaccdddbcbadaabacccabdbccbbcdddbdccdddaacadcadbabbbcccbbaccbdcbaabacaacdccddcbabbaddddbddccdabcbbdcccbcdbdbcdbddadcddcaddbbbbaababcccaacdbdddabdbdddaacbbaddbbdcadcabbdbabcdbcdddadbacabcbcbabaaacabadcadcbbcdbadadcdcababcdbacaaaababdabbdaabcdcbdbbdadbbdabdbdbacbdadbccadbcacdbacbbbbccadcadbadabbddcadcaabbcdbbacdaababdacadabcbcdbccabbaddabccbbbbdcbcaacdcbcbacadbaccbabdbccbcdddaacbdbdaccbadcdcbcaaadcdbddbcccbbacccbbdcddcddaacbddaddcdcccbdcbbbdcadbbcccbcadbdabbdaababaadddcbdcbddccdaccaadbbccdcbacabdbcccaccdaaadbacdadcaddbddcddacdaccdaaccdbcacbcdcabcddaabbcddcabbcddbcdabbbdbadcbaabddbadbbdcaddbccbdaabcbadaacccdcadcdccdcaaadbdcbddccbdbcaabdbdbcbbaaddddbbccaabbdbcacbdddcbadabccaaaddbdddcadbcddcaabdaccbcbcabaccbabdbbacbddabbdcbcabddabaadacaababdbcddabdcbdccabadacadbbdccbcadadaaacdddccabbdddcbcdadacbcdbddddaccdacababbbdaadcbcaaaaabbbdbdaaaccbdcddcddccbdbcbdabaabbacdbacabbcbcbbaaccdddbabddabadddabddacccccccadabccadcbbacbcaddaddbadbdcabadddccbcbdabbccbcadabdabacbddcdbddccabaccdaddcbcdcabaababaddcaddbcccdaddcdcdabdbcdcdbaccaaaabdcbabacdabaaccadcdcabacaddaccabbbbcacadccbcdddbcbbacbacdbacccacdabbccabbbcddbdbdbbdbcbdcbdbbcdcbcaaaccacaccadcbaddcaddbdddabcacbbcbcdcbbcacbbbdbaaabbcacaadadadcaaabbdaacdbaccbcbacadbcddbdcabbbabddddaabbadbcdaddbbbbbcbcabcadcbdababaacbacbaacbdcbdaccdcdcaadadadcabdacbccccbcabaddcbbdbabadcabbbcaaaabcbdbdaddbbccaacddddbcacaccadaaddaabdbccbccdaccbbaaacaaaaddacaccaacdacccdcadadccababbbbccaadababcbabdbabdadccdcaddcbdadbcaaddcccddddbdcacdbacbcbdabbaadccdaadcbbdbbdcacdcaabcaddbabdabacddbcdbbdcddccddbccacadbaabbabcdcaaaaccbcbaaccaaabddbbbbccdbddbaccdadcaadaaaadacadadcccaaccabdccdaddbccdcacadbabdaaabdccdabbacddabcbbdadcdbcaadabccbcdaaccadacabdbacbaaacdadbcdadbadcaadbbaaaaaabbdccccaabaaaaddcccbabcccacdcbbdbacdbaacbaadaddbddabaccacbdaababbbbdaccbbddcaddbbdbaadcababaadabbdcdcbbbdadbadaabdbcccacbcababaadaccbddcbacadaccbbcbdabacbdbbdadbdbaabbdbadaadbbaccdabcaaadacaaabcabcaacbadbcdadadaccaacbdabcdcbadadcbbacccbabcddadadbcabacaaddadbaccccabcdbcccdbcaabccdcccbdbbcbcabadadaabacbcacdbcaacadbdddabdabbcacabbacdadddcbcbcbcbcaabdbbbdbbaccccabacbabcadbcccabdcbccddadabdccbadaddcddcccbaccaacdbcabcdccabdcdcdabbaaacbacaabdcdcdaccdcdbabbccabdabadbddabdbddcbbbadabdbaabbcadddbacbdccccccdcbbccbdbaadacbbddacadbbbabcabcbddddccaaadddacbdacdbcabcaaabdccbccabbcaccdcdabaadcdbdbbaacdadcccbcddcbacadacadbdddaccbccacdbdacdcbdabbcdaacbddadaccccbdddbcccbaddcddbcbdcbabbbcabcbacabbbcbcaacbcabdcccadbdcddcabbdabaaacbdbbacbacbdacdbbabccaacdcaddccabaaacddaddcacadacaddddcddddcacaabcbdaaadcdccddbaddcbdcbbddbcdddcbbdcaddabcbdbbbadbaddcaadcabccdcabaacbcbabbccbbacbbcaccdaaaccacbccacbbadccdcaccccdaaadacabcaaaabcbddbcddcbddcbdcabdaccdabdcbdcbaddbbadbccddddbbccdbddadbabdccdcddaadabcbcaacabddbcbadcbacccbcabaddabadbacdbcddbccaaacdaddbadcdbccdbcbdbadadcbbdbdaaaacdaabaabcbdadbaaabcadadbbacddcaacdcaddadabcadabbdbdabbdbdbababadbdbdaaabaacdaccdcdadbdacaadaddacdabbbdccddaacbbdcddcbadbdcabacadbbbbbaadcdccabcacbbddabdbbcbadcbccaacccacdabcbddadbddcabdbacddbaacacddbbcacdcaadccccaddbbcbbcddddccacbbacdbabdcdacbbdcbdddadcddaabdccdaddabbaccdbbbbabdddacbbcdabddbabcbcccbacddbbabbcbbbcabdacdddbbabbdbdbccdaacbdccddabbcaacddcaddbbdbcaddabdabbccbdccbbbababbcdcccdcbcbbdddcddaacaccbadcdaaabcbccabcdbbccbbbbbdbcacabdcccaadbbacbadbbdcaadbcdadcaaacdddcbcdadddaadcdabcadaaccbbcbadabadbdcaccacbaddbdccbbcadbcadcbcbdcddcaccacadaccaaaadadbdcdcdabdccbbadcaccdbababccbdbacdaacbadadabadcdbdccacddcdcbdacbacadcadcdcabacbacaabcaddcaaabcacdabdacadabbddbcbacccacaccaccddbdbbcbbdaabbbacaadddcbccaaccccdbcbddbdcbcbcdcbdacdadccaccdddcdabcdaccabdcccbcabacdbaaabbdacdbccdabccdcacbdcdbbbddddaadcabacbbaccbacbdaabbcadcdcdcdabbdcbbcbbdbcaadbaabddcbbcaddbaabcdbbcaaaaacaaaddadadcbaddbbdbbcadbacbabbaaccaadbaacbccbbddcaadaabcdabdabccaaabdcddbbacdbabbaadcabcdaddacddcacadcdcddbdabccddbccddabadaabdbabdccdadbddcaddbacacabcdabcbdaaacbadcabacbbaddcaddadacddcaaababbdccacbadacbddcdabbbbdddddcaacaacbabbbcaadcbdaccbbbbdadababbbcbbacdccbdcbbadbbbbdddbbccaaccbcbaddccadbbaddaaddbdcdabbaabadccbdbdbadcddbdbcbdddbdacbaacdcadabbabbbbddaacaadbdacccdccdddadccdbadccddddaccdcaddababdccaacddaaabdcdbcaabbbbaadddddbbcdacbcdcabdbcdbbbdbacbacbbdcaccddadcdcdabcbcbdcadaacccbbbadbbdbcbbccabccbdcdcddcbbacddbddcbbbbccbdcacddbddbccdbaaddaaababbbccddbcccdbdccacbdddadaadbbbaadbdcbaaabaadbbabababdacbdadbacdbdacbbaadbabaabddaadcdaadacdaacbcccaacbcadbacdcbbddadadddbbccbadbdaaddbddadaddddbccabdcacabcbcabdcdcbcadacccdcbdadcadcdacddadaabbbaabbabacccdcbdcadacdbcaaabcaacbabcdcdbabbcddbddbccdaaadbbdcdbadaabdcdabcacbbdadcdaaaadcdbbcabdcbbcabcaabbdbaccbbacdccccbccabdaccaddadccddcdddaacbacadbbaaadbabbbdbdbadbbdadddbdabbcdbcbacacdbcdacbcadadbcdacbaccabcdcbdacdcbcaddadbdcdabacbadaacbaaacaadcdccbaddcaccbaaaaadaccbaddadbbcbabccbabbbcacbaaaadbaaaaaaacdbadaccabcdbbcbddcbcdacbadadcbdbdacdadacacdabdaabccadaccdddaccdabdbcabaddddaabbbaccaacdccdcbddadaabcaadbdccdadddcbccddacacbbdbbbaccccddabbadabdcabcbcbbbbbcccbbaacdbbbcccdaacacccaddbabddbdbbbcaaaaabdcaabcaabadaadaccabdaabdcbaabcaabbbbcdbcaccddcacabdabbcacbaccdacccdaadcadbaabcaaaabaabacdbbbbdbaabcccabbdccdcccacacccacbcbcbbaabcaadadcbbabbbcacadcacbdcaabaccadaaacdddbbbdcbabadddabcaccaacbbbadadaccabcbabbdcbbaccaccdcdbcaaccbabaacaacbbddacaaddabcdaccacdcbbdbbaacccaaabbcbcbcccaccbbddddadabaaccabdbdbbdcaacddbdaabadbccadddbabdbadbdcdbbbcdbbddbdacbdadcacaaabbabbabdcddcbadccddbcddbaacdcbabacbbbcadbcbccdddacdcdcbbcbaacdccddccccbabdbcbdcbcacddabbccdddbdbbdccaabacddabacdacccbbdbcbadccccbabbcabbdddaddcaacdccbbaccbddddcdcaaccaaaadbdcadadbdcaadcbababbbabdbabdaabcbdbbccaaddddaddddcbcdcbccabaaacbcacaaaddadbabdbaadbcddbaacbbcadcabaddbaaccbbaadddbdadbdadccaabcdbbbccababddcadbcddacadbbcaaccddcbddbbbbbddacdcadcbccbcdaaabbabdccdabbbbadddadddddaadddbdbcbabbcbdbcbcdbddaccabdbdcbcdabbcbcddbaaccbcbdcdbaccbcdbcaacdaabcdabbbbdaacbdbcddbaccbbdbddcbbbdaaddcbbcccbabacdaacabadbccddccaaadbbdbcddcbdbcaacdddbdbcdacdcacccadbadcdcccaccbadccdcddcdcdcdcccccdbcdabbcbddbbbacdcddcdacdcbadddddbabccdcbcddbcacabdcaabdbbaaaddabbdacadddddbccdcbbcdbbbcbcabdabadcbacdbacdacbdcacbbbaacddddcbcdadbbaaddcacdbccbbabbbcbacbccdccbddcddcbaccbbdbcdddadbdadcdaaaccdbacbccbbdcddaadbcaacadcaababdabcdabcabcaabddadbacabaaddbcaadbbcadbcdaddabdaddacbbdcabaabbaabdaddccabccbdccdcccbacddbcaccdadaccdccbbaddccdcccacddabdbddcaacbbbbcccacbccbbcdaacadbdabddbbaddbdabddccdcddacbaccdbdcaccccadcdacdbdcbaccddbbcdcdaccababbddccaababaddcddabbaaccdcbdadaaabbbadbaadadabaabdbcddbbbddcbbaddcaacdbaadaaccbcdaabccbdcccdadcdbdacbbbacdbbcdabaddabaacaadbbdddccadccbabcbcabbaccadabbadcbdccdbcbddddbbdcddbccdcbaddaabccaccbaddacbabbccdcbbcabbcbcacbdaadccbbccccaadbcaabbabdbdddbccbbaabacbaabcaaddbbcccccccabcddbdadbcddbabbbabdbcadacbadadbcdbbcdccdbbddcabbddbbdaaccbcdccdbbcaccbcaccbddcdabcadddaddabdccdcddacbbaccadacbbacaacbbddcaddaacdaacabbadaabacbdbbacabbdbadacaabacdaaddbdadbcbbbddcacdaccbbcbbaacbcbaddccdbacdddacaaacbbbaacdbcddbabcaaccadbbbaaddccbbcdddcbdddccdadadddbbaaadacccdaddddcccbdcbddaaadcaccdbbbacddabddcdbabcdccccdbdaabbbabaaaccdbdbbdacacaccccabcdaacaacbbacaaabbdcababcacaadaccddaabadaabbddbbdccaaaaacdaacdbacdacabdccdddbccbcccbdaaccadababbcdddccbbbddbbcdbbadacdccbadacbbdcbbbcdddbaaadacdadcaaacbadaddacbacacdbcadccdacabdcbabbbdcbbaabbaccdcacaabbadcdaaabbabdcaadbcddcddcaacaadcbcbdcdcdbbdbcbbdddbcccbddbadcaadbabbcbdbcbadcbdccacbaacbdbcaabdccbacdcabcdabbccacabadccacaaccabcdcacadadadddccabcdbdcabaaccabdbbddbcdbbccbacbbdcbdbaadabbbadabcdcdddbdcdbdabbddccddaabdbdabadcddbccdabacdabadbabbbbbcbdadaabadbcaddacddcbcdadbcdabacbdddbabbdadaababacdbcdabdbdbbbddcaaacbdcadccccddcaaadaaaadacadabcdcddccacdabacbbdccdcaddabbdcdccbbccccbcacdcabddcbbacbaababbdaaaabcdcdbaaccadcddcbacabbbbbbcacddbcabddaaaccacccbbaabdbdcbbccdccadadcbbcdbabbabbacabbcddacaaaadcaaababdcabddbcdbacddddcddcadddaacccaaadbbcddcbccbcbaaacbaaacaccbbddaabaaaadcdadcabaabdbbbcbbdaaddaadbddabcbcaddaadddadabdbdacccbacadcdbaabddabbdbbddbbdcbbabbcaabdddcbddcdbbbdaacdcbbcaccabbcdabdaaacbabbbaaccbacacacccbadddadcdaadbccdcbcaabadabcbbcbdcacbadbcdcccccacbadaddbadcddddcaaaabbbabdaababbbaddacbabbdabcdabcbbdbdcdcbbcccaaddcbaaacbaccbdcbcccaaadcdcdaddbcabdbcadbbddbaaccdddddacbaabdbaaccbddccdcdbbcdbddbdcabcacdccdaadaadbccadddcacbbcaccabaaadabcdcbbbcabaaacdaacddbddabdaabbacaabaddcbbdacaadcadcbddcccbaacabbcadabacaddbbbaaabadbdcbaccabbbcdbdccdccabcadcccdcccbbdadcabbbaacccccdacbdaddbbccdadbbbcdcadadabcadbacbcdcccbccbdbbbdcaaabbbaccdddaddadbcbdbcdabbadbdbdabbacaabddadbaabcbcacddbaddabddabddabcddacdbccdaacacbcdbdbbdadcabacadadbbbbbcddcbcbdcaaaacabbaadadbccabaacdabcadcdacddcccadbccbaadcbabdcabbaabdcbddbaddcbdddadabadbdcdcddddcddcdabadbddccaadcdccdacaddaadbcdcaadaacbcbbaabbcdbdbaaaaddbdacdbccdadabcabbdddabcbdbdcddddccdbcadadcaaacdaddcdbddacbbdccdabdddbccbdcbcdaabddaacbdadbbaacddabadcacaccbdddaccacaaacccbccdaccdbcccbbbcbabadaadcdbcadcdddcbbdacbdadbcbadbdabaccdacaababdbddcacaaabbbbbcddbbadabcbaccccbbbdacccdcdabdbaadabcddcdbcddabbcdacdbbcbbcdcacabbabacccbddbcbddbdcbdccaabdaccbcbbcbaabdaaacbdcbccbbbddcbcbcdcaacbddcdbdcdbdbcdabdcbdbbadbdaddcadddccdabacddacddaacbccdcdbcaaabdccddcbdccdacbdcbdbcbcdcbbcaccdcacbbaabbaccabccacdbcccddbdcbbbcdabaaccdbccabdbbccdcaadbabdcaacdbaaccdcccdddbdbdbbcccccdbdbcdbbadcaaaaddadccbcbdcbcacdddbdbcccabdccbcaabadbadaadbcbbcbcabdaabbaadbbcbcadadcacbbcbbbbbacdbbdabaccaccdadcdcbcdcbcddbbbcaadbbcabcbcdcbbdddbdcdccbccadabddbaaabacacdbdbcbacbddcdcbcaadacbcccdaacdbddcabacbaabadaadadbddbcadbcccbadcdddcaacdbddbbbaabdacabaaaaadaacbcdccdbdbddddbbcccacbccaadbcbbbbbabbbadcdaccabccdabcbadabaddbddcccddadcdacaddabccbdcccaccccddadcbabaaddccbdbbccddcabbcccbabdcdddbcabdcddcabbbddcacbbdaacccadccddcaacadabcacccbbaaaacadddbcdcdbdaaacadbcbbdacbabababbdcddabccdccadbdcddcdcbdddaabbdbddadddbcbcdcccabddbbdaaaacddccdcaabbbcbdccbbacccbbcbbddacdcdbcaaccbaccacabbcccddaaccdbcbacdcdcdabbbaaacadabbdbcbdbbcabaacacbdacabdacbdcbddacadabbbcbbcbcadbcadacdacacbacbcdbaadaabbbadbadcbadccddbcdbaddaaaaaabacabdbdacadcabdbcccbacdacbcdbcbcaccbacbbbdbadbadcabcacadbdcaabbbdadcaddaadaadbbadbbacccdddcacbbcddbaabbcaaaddacdacdbbccaccadbdacccbaaacdbdacdadbaaacdabdcbaadddcccdcdabaacccabddadcdbcdcadcacaccaddbbcbddcbcdbaacbdaccbdaaabacaabcdbdcccbadacdadaaccbacdaccadbcbacacdccbcabacabbbccacdacdabcadabcbdbcdddcbdddcadbdcbacaabbdabcaabcdbcaddabddbabcccbcdcaacdadabbabcddbabadcccadaaddcbaabcccbadcbabdbbbcadaabcaccddbbbdbcacccdcddacbbcbaccbdbbdcbaccbacaadcdbdcaabddbabdacbdddbacbadbdadbaaadbcbadaadbcdadbcaccacbdcacbabbcadaccaabbabcabbcbccddcccaddbdadcaadccbdcbaccbcbbacbbcccbbbbbbdacddccbdbdaabdababdcddaadbcdbdcccaaacbcaadccbbaaccbdcbadabddbadbcbacddabbddbcddbdadbddbbdcaaddcacdacabcdacbbcddcdcabbacbacccaadbbbbbccdcadcabbdcbadaccddababaaaabcdccdccdaaaadddcccacbadcdcbdabbaacdbbcddcdbdcccbcbbaabaccadbabbdadabacaacacddacdbbabbaadbbddbabcdccddddbbadabbbbccabbaadbacacaabadaccccdacabddbbdacabbdcbbcbaabdadbddbbcacbdbddaddacaaacbbaddbcabacaadbbbcdddacadbccdbaddddacdcbcdccdaddbacccbdcddadbdaddcdaaadadddacbaccdaabcabcaccbddabbcdbaaaabbacdbacbbdcccbaccbaccbbbbcaaccdabdbacdddabcacacbbdadaacaacaadddabccabcaaadcaabbababccdcbddbaabcadcacdaaacdbbdabcdbddbaddcbbbcaddcbccccddcadbbbadcbbdccabdcaccadbdbbbcbdadddcbaaaddbdaabcddbbcbdbaccadcdddbccadabcbcbcbdbaabacaaaddccbcddbdaccccccdcddacbcdbbbadabaabbadbcbdcddcacccbdcdcdddbaadcbdddbddcdcbdabdadbddddcabbcbcbcdaacbbbcccdbbbccadccddcacdacdbcbbdcbadcbacbbbdadaadbdcabbdbabdddbcbaccacdbcdcbacdccbdcbbcadcccbbbccdbdbdbdbabcdaaadaaabaabdcbcadbbacaaaaccaacbbabcdcaaaaadcaaadcabcacdaabccbbabaaaccaddacbdabcabcdddccacbabdccbadccccccbbcbdbbdacadddaabdaaabdaddbdccbdcadbcdaaaaaccacabbcadcbbccdcaccadabdacacbcdadadbdccacdaddadccadaadbbdabcdacaaaccdbabcddbbbbabaddabaadddbbaddcbcdcddadbdcccaabdbcabaadabdadadcaabbdacbabaddbcbccbcdbabcaabaacccddcabbacbdabdbdbcdddccaabdbcaddabddcbbacaccadbdbabcdaccdbbaadadccdbbadacdddadacaddbdbaadbdbacbccbbbadcccbcdaadcdabddbbdbccadddaacabdcbcdabaddabcdabaaacadbabcbaabcbcccdddddddaadddaaadacdadbdbaccbdadbccadcddddddbaccdccddbccadddbaaddacacccaaaabccadadbaddbdccacbacddcabbbabbdddcdbddbcbaabdaabcbdcaabdabbcabaddbadcaaacdcbaddbbdacabacaddacbdabcbabacdaacdccaacdbdaccdabbcbbdcdacacaabaadbddcdbdadaabadcabbaabcbaabddbcdbddadddbcddddcbcddabcccccbacadaddbcccabbacbacadcabdcddbcbbbacdaccdbbbbbdccccaacabbcdcccddcbacdaaaccdaaaabaaacddcabbdaacdaacccbbddaddbacdbbdccacaaabcbabccabccbccadbaadcacabdaccaaaaacdacaddbabdaccdbbaacbaacaddcdbccbdbcacdacbcbadbccababdcbdcbcdcccbaaacdccbaaaaddadbdbdacbadddbccdadccdaaaddcbdbabcbcbcdbdabbacbcacacbbbccdddcdaaaadcaccadbbabdbcccbbcadddacaddccdbcabbcadaabcdcdbaaacaaddcbdcdadabadaacbbcbbbcdbccabaddcbcacadcaacbdbcbabdcbbbcbdbcadbabaadbabbcaacadcadadcbcaaabacbcbcbacaacbbcbacdbcbadbaddcccddaddadcbbbcddaaaddaccadcacbdacabbccdabaadabcacdbdadbbcbaadcbdabacbbabdaddcbdccdcabcdccbadbbacacabdacaddbbabaadcdaaaddadacccbcbcdbaccbabbdcaaabdcaabaddababdddbacccddccddadaaacacaccdcabdaabdaadaacbddaacaabdcdcccbaabadbbbdcbbaabadcdaabdbddbbaddbdddcbbbccdccdaacabccdaabdcbbaacbacaacadccadbbbcbbacbaddbadddbbabbbdbadcbdbcacabbcbdccdadbcadbccbbaddabdabcdcddcddbbdddbdaddaaacbcdacddcacdbabbdddaabcccbababacbabadaacbbabbcbababdadccaabdacdcdbbcdddccabcadcacdbdcbdbccbcbdacbcadabacbdcabbbdaacdcadbdbdbccbddabbcddabbddabcbcbbacacadabbcbaabcbabcabdadabacbccbdabdbabaccdcacdbbcccdbabdbdadcbcaaaddabacaddbcabdcccccbdcacaabddadbacadddadacadbdccddbbabccbccbddcbabbacbbcbacaaddccddbcacbaabbcdabcdaaaaacccddacacdacbbbcddcaabdcadccadbcdbcdddacacbcbccccabdbccacdbbccdbcccadbcdabaabacaccbdddadbcbaabaddbaccddcdbcbbddbdccabbdcdbcdbdbcbdcbacbddcbaccaddbdbcbccdcbddacdadadbbcadadbadabccdcbbbcddccbddcacddabccadbdcadbcbccbbaddcdaaddbabaccddbaabacbcdadcccaccabbbddbaacacdcdcddbacbddbbcdbacacccacdcdcccdcddddacbcadccbccbdadbdddacabbcaacccaacababadccdbcbdaccbbdacadcbaabcaccbdbddccabcdcbdcbaabbadacbaabcbbbbdcdabdbccbcacccbccdabaacbbcaccdddbacaadadbdacdbcdabccbbbcabaacddcbbcddcbcadabdbabddcbccadbacdabbbdcbcbabdbdcdaacaaabbdbdcddadcdbaabdbbbdabacdccaaacabaabcccbacbdcabcbcbacaddbdddcbbdbdbaadbacaddcdbdbaddbdabbbddacabcacbadbadacdccababdbcadaaacbbcbabcbadbccccaaabadcaddbcbabaacccaadcccdbadcaddddcdbcccabaadbcccadacaaabdcbaccbacddcccabbccdbaacacbbcddbddddcdaacdbbcbadbcbaabbcbbccaabdbaacacadbaacdbcabbccdbaddbbdccccdaaccaadabaddcadabdcacbdcbaacabbdbcaddabccababccacbdcdbdadcaacdaacbcbbaddadbabbdadacdcbaccdbaaaadbddababbdbdbcdaccdcdcbbbabbdcccbddbcdcddacbacadacccabccaccaaaabdcddadbdcdcaababcbdbdabbacbabadbdbcacdadcbabbdcaadbbcbddcccaccbadccabccbddadccdaadcbacbacdadcacbcdabaaabbdccacaabcaacbbdbadbdbbcbbdbabacdddcdacdabacbddadbcdccabaddbaabaaadcacaabddddadbcabcdcaacadacbaadcabadccadaccaabcddddacddcacdddbbbacbabdcddbdcbcdabcdcdbcadbbbdbcccdcbbdaadbacddbbdbbbdbdbcccabaaacccabbbcbcbcbbbcdbabbbbacbccdbacaaddcacabadbccccaabbaababdaccbdbdbdcaddacdbaabbaaaaddabcaaddcdadcbdaabbaabdaacbcccdaaacaadbcadcbdbaacbcdacbdaddddcccadbaaabbcbabbbbdcdaaadbdadbcabcbbadcdbbaabbdccabbdbbdcacabbabbcaccbbbddcdbcbcbbcbaccabcddbcccdbbdbbccbacddabccddbacabdddbcabdcacbcaabbdabbcadddcdacdbcbaccbcaddabaddbabcadddcbaaaaaccaccabadbdacaaacbaddddbcaaccdbadbdcdbbddbdcadcacdadacdcccbcddcacdcbdccdadccbdbcbcbbadcbabadbadcabadadacaacccacbdddabaabccddbcdddadddcabbbdcdcaddcacdbcdbdcdbbcbddcacbaabccccddbcbcddcdbaadcdcdacccbabdcddcdbadcacbbababacbabccddbcdddbaaccdddbccdaccacabbaadbdbcbabcccadccacbcaadaddbdacbabccabacbdadbbcbbcbadcddabcabdcbcadbcbdcbcacabaaabbccbbcbcabccbabbaaaadbccdadddcbcbdbdccadbaaabcadacbccdcabcadaaacdbbaddacabcccacddababdbccdddbcccadcabdbccbbbdaccacbcabddcadcdcaddbaaaabcbadacaadbacabacbbcdcbdbcadcbcbbdabcdddabcacdddadcbadadccadabdcadbdcddcdbabcdaadcddcabacdabccabcbdbbdbdbababadcbbcdacdbdbddcaaddbbbbabbacbddababdcdbdcbaccaadbddbdabbadbabcbbbaccacdcacddbbddcdacabbdbcbabcabdccdbcabadddcddacdbcbabdcaadaddddcdcacacddbbbabdbcacabcbddcbaccabbbacaaacacddbcbaabaacbddbcbdcccdacbbdadaacdbbabcbabdaccaddbcadabbcbcbccbdaaccbcacdcbccbcbccddcccacbbaddccdbbaabcbdccdcdcacbbadbdbdacaaccacadbaacdbdcadbdbcbaccdaaacadcddcbcaadabdbddaccdaaadbdbdaadddabbdaccddabadddcacccdddbabbdbbcbbbbdaccbadccbbaccdbdabcbbcdacbdacbaddbdbdaadcababcdcbcacdcbacdccaaabbcaaabcaaabbabbbbddbabcacdadbbabcbcddcccdacacaccdbabddbdbacddddbbbdbababbaddcbaaddbbaadcdcdcaddadcdacabbddddabdaabcccbdcdbcbacdbbdaaaaaaddcaacbbbdddddcabccbdcdbddacacbddaaaadaacbccadccadddadbcacddaaccacbbcbbbddabcadcbbbaaaddbacdccdabcddaabbcdcadbadacbbaadddbccadabaacbdcddcacdcbdcbacaaaddcbdcadbacccbdbbabdccdcdcdbbddbcacbdaddcccdbcdbaadcdbabdabcdabcdbaaaacdaabdbcaacbcddbadaadbabdbdaddbbdacaadccabddbadbbbcacbbaaccbcdcbdcbbddadccbadaacdbbcabbdaaaccbaabdabdddbaababbcccadbcadbacadbbabcaabcbaccdcdbdcacabcdadadbdaaaaacdaccccadbcadaadbadbcbbabcbdbbabcdacaabdbdbbccadddcbbbabcdddcdabcdbcaddbadbcadbbdddbccdddabdcacbccbcccbadbadcdbbddbddcabaaaccdabaaaaadcbbdbbbbdbbbaaaaccbdadcdcbdbcbdcbabaabbddcababbaddbdbcdcdcdbdbdccadddcbdddbcbddacabdaacadacbdccdbaabcadbbabcccaaacbabaaccddbdbcdcadddddaacbdadddaacbdbcbdbacdcdbcbddcbcbacadbcccbccdbadccbdbdcdcddcbbdbdddacacacbbdcbbdababacddddaccabacababbbacccaacacabaccbadddabbcdbaacbbaaaaccabacdbdddbbabbbbcdcbcdddacbbadddbdcbbbccdbabcbabbbaadcddcccdbadcaaacbccabbbcdbcaacddaddcadabbdadadaabdbbaaabbaadbbaacaaaaaabdbabcabdaadcdccdbdbccbadcbcbbcccbacaddddcbbdcdadabbccccaaacbdddcbaabbadbcacabaacbdddbbadacaacbcbcdaaadaccacbaadacbdadcbbbbcdcdbabcdcdccaabadcbddaccbacbcadabdacdabcaccbcacccbcabcccabddcbdacddcacbcbcdcaddadabdacdddacbaaddddbdabacdcccbbabbcbacdaaacdddcccacdbddbcddbbbaacabbabdbcbbcdaacdcdcdadaaaadbbadbacdddcbbaacaaaabccaaaadcbddcdddbddccaddbacadadbccbacabddcdbacacbabcaabaaadddcdcadbcbbcdddacbcbbbbdccaabbadacbccacaaabcaaaddccccdbcdbbcababaabcacbdccbaaadcbacaacddccdbadbbbadbbacdbbacdcabacabbcbdcdaabdadcbabbbdcdaadcdbcbcdcacbdddcddadcdbdddbbcdbadcaabbdcaaadaabaccbadbabbbdcbabaccdbcbdcdbabadcbccdbabadacbdbbcddddbcbacdcddbacbdbdcdbbdacadcdbcdbabcbddcbccbbacccdcaaaaaabbcabbcbaabdccabdbadaabacdbdbccababddcbaababcacbdadacdcadbaddcacdcbdaaacadbbaddbbcaddcbacabdababbddadcbcdcddbaabbbdcddbadccbbdacccdccddbadbddacaccdababbcbadadddbdabbacddcbddaddadcdbbbcbaddbdcabadaaccbdbbbbadbbcbaddacaacbabacacaccbbabdcdcbcdacdbbacbaabbddabbaaadbadcdbbadcbcaabacbabccdddcddbcdabacadcbdababbadccccbdcabacddcdbabbccdcdabbdabbcbccdcbcccabbbcaaaacbdacddabadbbcbdcccbaacddaabdbcaddddcdcdabdbadbaababcabdcaddadccadcbabbcccdbaabadbbbbccacbaadcdacdaacddcbdaabbbabcbaaadadadcbcadccbdbabaaaccbdcadaaccabdbaacbdaabccadbdadbcacdadbcddcccdcaddacbcadccdadbacaacdcddabcccbbabdddcdcbacccddbdbbabadccdbcaabbabcadcbcaccdabbaadaddacbcdcbbbcaacacabbbbdadacabdaacacaccabcdaccbdbdddacdcbacbcdadccaddaadcdbbbcbdcabacacbdbacadcddbddbabaabaaacccaabcbcbbadacbcaadbbdbbdbaddbacacdddcccbddacbaaccaadbccbdbdcbbcabcdccaadcadccacaadadcbbadbdbabddbabdcadcdbbbcbbabaabbdaddcbbdcdbdccddcadddbabbcbacddacdbccdcadddcdbcbcccbadacbbabacdddbabddccabbbccabacccabadbbadcaddabadacbbdcadcabbdbdaabcbddacaadcdbbabdacdbddacdaaadddacabdbdadcbbdcaccdccdbcbbcabdcaacabdddacbbdaadabcabadddbccaabbacabcaabcababcbcdcadacaabdddddaddcdbbbdcdddbccdadadadccdcabcabaaabcaaaacddcdaaaadccabcccacbcdbaabbdbdbaababdbabbcaccbddcbdcbcbcdacadabdbbcbbbdddabdbdcbacdacbcbbdacaadcadaddabcddbdadcabddaadcddadaadaadccbbbcacbbbbaccbbcbbcbabddddbcbbbcabacbacdcccadccacaadbaccdbabccdbddcddadadaaaabcddaabdcabaadbcccbaddcdbbbcacddbbdbbdabddcadbacbdcaacbddbbaccaabcbddbbcabcaabcddbaccbcbbaabcaabcadbaaacbccddcbaaaaacabaacbdccbcdadacadbabcbbddcbdcdcbdbaadaaddbbaaddcdcacadbdbdabcddccabdcdcacdcdccbdabcadddccbddbcdbdbabacdacccbbdcdacdbaaabbdcaabbdcaadbcaadbbacbcbacacddbabbaddccaabcbcbdbcbcbdddbddaccdabdcbbddbcacddbbbdcdbdcbdbdaccbcabccbabccbdcdbcbbdadbcadacdbaabbcbbcdbccadaddbadccabcbbdbcdbacddaaaacaccabadabdbccbdbcaaddcdaabcacbcccdacbcbbaabadaccabdcdbaddabdacbcbaccdbadabdcbddcdbcabadccdcdabbbacbabbacaaaabbcbaabbadcdddcdbdcdbccaabbbcaacddbcaccdbddbbbdcddcdcdaabcbabdcbcbccbcccdcddddbadadaadddcccdadcddbbacdabdadcbdbcabdddaacddaacdbdcdbddcbcbdcddaacddbdaddbadccabbdcbbadadcdadcdddcdabaabcaddcbcbddaacdbcbaacbdbdbddbabdbbacaaabbacdddabbbccbcaadcabcbdbcadacacadaabdcacdcdcadbdcabbcdcacadacacdaacbcabdccdcabcddcbbaadcaacddcabdddadbccabcacdddcdaccbdbbaccdbdbcbcbbcbcbdbbbbdcaaacbaaccabbaaacbdcdcdddbdabdccbaabadcbcbbdddbdcdadbaadcaadbbbbccababccbaacabdcdbbdbbcbaaaccddcccbccacddcccbccdaaabababadbdabcabababcacdccbcaacdcbabccccccdddcacaabcccddddcbbacbacbaadbcdadccabcbcddadaadcbcadabbbaacbddcacaaddcbbbcabdcabdabcaddbdcadbbcbbacaacaabbadacabddcaadababacadccdaaddbdbdbbdacbcbbcdbdadaccbcbbbcbbdacccdcccaadcdcdaaaaadadadacdbaaacccadcbaadcbbaaaaabdcccadabccdcadbbccdbcaaacddcadcddaadbbdadcbacacdabbadadbcdccbacdbbbbddcaddacdbadacddbddbcacabcdbacbabbabccddadaacddbacbabbcacbcccdcaadccbcdccdddacbddbabdccaabdbaddbabdabbccbcbacbdaadabaccdbdabdcbcdbabbbcbbbdccacacdcccadacaabaddcabbadccccbacbcdacadcccbdcdcdbbabccbccdbdadbbacadabdcadddadbddbdaddaacbbdaddaccabbacbaacbcababdbcdaaccaaacaccccbdadbcbcdacbccbcbdacdacabdacaddddccabacacaaccdcbdacdcacdaabcaacddbbcbbabcddbbadbbcbcbaaaabacbdddbdadcbbcbdcbbdaccbbdccacbbacbaacaadcbbabcaabdaaaaadcbdbaaaabccbcccbbadaacdbcbacabcadadbcaaccaacacdbcaacadbdbdabbccdbbaccbbdccbbccadadbcbbacacdbddaabdbacbbabccadccbacbcdcabccbddcddcbbdaddccbabcaaadddaaddbdccacaacabbdaccbbdddabdabacbbaadddbcddcbdccbddbacbaabcbbbccbbcdabbcdddabdbcdbdaddbadacacbaddabadddbcabddbbcbbdaadcabcdbabadcacabcacabbcabdacaabbbbbdccbadddbaacdcdcdbbbbcdadbcdacbbbabdadadbdddaaddbddadcbbdaccaabaaabaacaabadaacdcbcbaaadbacdcabbbdddadddbadcaaaabaabdacddbcdadcddbcabaccaaaadcaacaacbdccbdbdddcccaacbadcdccadcabbdbbbbdaaabbbbcdaadbadcbbaccdacaccdbcddccccdbdbcbdcaaddcbbdccabdcccbcbabcddacbcabbbbdccaaaaccccbdddcababcdbbbccdbbbcaaccdabdcaadbdabbcdbccbbbcdadabccccccbaadbdadbabadbbbcccabdabadbccacabbdabacddabcbaadbcbccbdcdcbbdababcdbbbabcacdbcadabcbbdbcbacadcbbdbadcccdaacdbaddcdcbbccaddcdcbddcdacaaadcbaaacbadadccbaaacbcabcbcdaaabcbbaddcacdccddacbdbcabcbbdbabbcbdbddcbaccdaccabdacaabdcdcbbaadbcdbdcababacadcdbcbcbbdacdcbdcbdbdcadbbadaacaacbbddbcbdadbcdbbbaddbabadaccbcdbbcaddadadabcaacbcdcaadcabcccbdddcbaaacbcacaaabbbacddacdbacdcdbcbcbbbbdcaaabbabbdadccadccababdbbbacbacdcdbbdcadbbbbccdaaacaacabdcaadbbdbbcdaabcdaadcbacdcddbccbccdabbabcdbadbbabcccadabacbbccbccbcabcbdddaababbbdcbcccbbdabcbbbcdabbbabbbbbacbbbbabcbaaddadaccdacaddaadcbcddbbbcbcdaddadbaaddaccbbddcddaacbbcaacaddcacbcaacddcabdbdbddaccbbbdbccbdacadabccdcdcaccaadcbdadaddbcdbcaabcbcdcabdbbadcbccadadabdcbcdaacaddbccdaadaaadbbdcbdcbabbdcbdccccdddddbaddbdcdbbadabdacadcdbadcccddadaaacabcbadabbacadcdbbdccaadbdccdddbbcbaababbacdcdcabacbcacccbbaccaaadacdacbccccddbddadcabcccdcbcdbddcdcabdddaacacdbacaaabdaabcaabaaadbbdcbbccabdbddbdabbabbddaddadccdcacccabcadcdddcdcbcbbadcdbbbcabaadccbaccadcbbbcdabdbacdbdccbabbdddccaabadddabdcdaaacdcbadccdbabaadbacbdbacbabbaccaaaabbdbaddcdcdcccdcdaccababcadbadcbcadcbbddbbaabcbaadccdcdcbacccdbabcdacabbddaccadaaaaddcdccbccdaabaacababdcaacccbbcddaadaccbccdbccabacbddcaaaabacccabbdccdaadbacabacababcabdbacbccccccbaabdaddbbbcacdbdddaadbddaddbaddadacaabddadbcccbacabbcccbaacdbddcdcbbccdaabdcbdadcdcabadbacbbbbdccbacaacaadaabdddcbccbaccbbdcbadbacdcbbcdccacdbaaddcaddbddacaddbacbdbdcaddbacaaaadbdcbadccdabdbbdbacdddacaabbbcdacddbbdbbcbdcdddacdbcdddcaccbcbbadaacdaacdbcddbdccdccdaaddbcdccbbcbcbddddabdacdbdcbcdadcccadadbcbdccddcbcdbacadabadabdbbbbabdbcbcccbdcddadcaabaabaddbbcababccbcddddaabccbdcbacaccdaadabdaabbadcdcaccaddaabcbaccccccbcbcdcbbbbcabbadcbdddcddddacbadddccbcbabbccbdaccadbcbbadbdcacbadcabdcdcccbdcaccddbdcdcaccbcbbcadccdddcdbbababcaaacccbdccbbdcdaaadbbdacabcaaaaccddbcdccbbaacabaddcddacdacdbdaabacbdabccbbcaabdcdcabcaadabcaacbcccccdcadbaccdaaaabbbbcdcaaaaadabbdcadababcbaaaddbddbcdaaddbbaadcaaabdcbddcbdbdcadbdbdbcdccbaccccbbccbdaaccbbcbbaabccccbacbcdcbdbccdcbbcccdcabbabdbcddaddaaabaacddbcadaaadbabbbdcdcabbaaabadcdacdacdabcdccabbdbcabdacacadbaddddbbdaaaddaddaaaadccadbbcddbdccbabcbcdcadaaabddbddcbaddcddabacaabbdddbdacacddbdaadcacabdcaaabadbdacacbcbccacbdbaacaaabbbaccaccdcdaacacccccbdbabdddcccbbbcacdbbaddcbaddccaddcbcbbdcddcacdabdacdcadaadcbadcdbddacccbcbcabdbcbbbcabadbcddabdabacadaadccaaaddcbaacbabcdcbdaabacbcadbadaadacdacabcbddbbcacddcdcbababdacbdabaddaacabcdccdaadbdcbddbbacbcabdbabacdacdaadbdacbdacbdddadccadddacbdbbdcbbbabacbccddbaabacccadbcbddccacbcbcbbbbccadbbdacaabaaddccacdcbcabcbadaddcabcaaccdcbcdcabbaccaabcddbbabbabbacbbdcdcdbddcbdaaacbacbcbddacababacccacabdbbbdcabcdcadadabbccbaddaddaacccccdbdbdbaadccdccbdccbdbdbdaddccdabcccadbdddbababaaaddbacdbdabbcbddcdcbdbdbcabbaddcabbddaadaabcbccacdacacbdbdbaaccdaccbadadabcabadddcdbaccacaacdcdababbcadbcddcbcdabccabaaaddcacbcbdbbcbdacbcaacaddadacbcacbacccabcbbadaadbdcacbbcaadddaccbbacadccaadabdbbdddbcbabdcadcbcddadbacaaababccbdccddcddbdcdaabdbcbddbaaddcdbdaaadbadbabbdcdbdcdcbaabaaddaaaadadcbbdcbbccbbcdcbacbbdacdbcbadacacdddbbbbbdcdddcaababbacbdcdaacaddcadcdbadccdadacdcbbbdcccaaaaccdababccdaccacbabdbcddabddacbdbbbbbbcabcccbdbbaddadcccbdcddabcbdbcdadcabcdbcdcadcaadbcccbbcddccacabccabcabbcaacbbcccccdddcacadbaccabdabdbacabaccbddacaccdaccbbbcbbcbdabccdbcdbaaccdddcbcabaacbaddacbddcdcbaabacdbaaaabcdadbdccbdcdbaaccaccdbabbcacdadcacbccacdbacdddbaacaccdbcdbdabddabcbcabbbadcbadaadbdabccbcdcadaabaddadbbdadddbbaacadbbcccbbdaadbdccbaddbacbbadcbcbadaadbddbcbdcaacddbcbadacbdbaccdcacbbaabbdaabdccaddaccbbdccbacacdbdcbacddbcdcacaadcdbcaabbdbadbbbbbdacbcaccbcbaaddcabaadacccaadbdabbabdbdcccabaaacddddddabbaabacbdcdcdcacacdcbcabaacadcbbaabaccabadbbcbcacdcaadbbccacdacbbcbdacbdbaabadabdbdddbddcbaccbdacbbcacbcbbbadadaaabbcabdaabaacbccdbcbbddbbccbbbadabdbccddbabdadbdcbacdccbacbbbdbdcacaccbabaabaddaaacdcbacdbbcbacbbdabbdcdadabadbabbdadabcdabdbbcbdaadddabaabccbaabdddccadbddccbbdcbdcbaacadddaadccdbccaccdaadadbcaabaccacbbaabbcddcadbcbcddcadacbdbcbdcacaccbaaddbaabcbbcdbdbacacdcabcddaabacdcccdabbcbdcbcaaadaabbbaaabbdabdbbdcaabddddbbcacdbdabbdcabddaccadcdcaaabcabdcbaadaabcddbacdbbdddaccddacdaccabccabdccaabcddbdbddbbabdaaadcdaddcbcaaabcbabbcdadbbcaadbccbddadcbadccabbccbbbcddaadbbbbddbacbbdcaccdbdabdccbbcdaaccbcbbadaacacddbddbdaabbdbbadacacbabcbaacdcccbbddcbaadbaadbbabccabcdcadacbcdbdbbdddbbcdbddbbadccccddcbdcaabcadcdccdbdddaadaaadabaadbbcdadbbdcacdccbddabacbbbbbbacdbdbaababababaabdcbcbdbbcdddcabcbcadbddbbcbcbacdbdcadadbdcdabdccbdaddbbbadcbbdcabcddbdbdaadcacdcaddaadabbccbbdaadadbbbadacdcaaaccabdacdbdbdddcadbbdccbaccdbdcaacacaadadaaaaddaccaaabcaadabbcbacdccaccbccaaaaaabbadbddaabbbcbbbadcbdaacccccbdccabbaacabccbbbddbaabcccacacdadcddaacbddbbaabcdbaabaaaaaadcaccccacaccdaacdcacbccababbabdacbaacdbdacbbbadcccddaacdbbddadacccbddacbccaddbcdcaaaddbbbcdbaaccddabaccaacdcacdddcbdcadbbbccdcbddabcacbccdddcccddabcaddbabaadaabababaaccdbbbdadacbbdadddabccaaaaadcbddccadabdbcbbbcdabcaaacddbcbaabaadaaadcccbbaaadbcbbdacdaaccadbbacaacadadcaaddbcbadcdcaadddbddcbcdbcbadabbddcdacbcadbabdbbccdaabddababcdcbccddcddadbaaddbcacccccdcaadbbaacddbddadcbbdadbcbdaadababcccbbccaaddcdcddcbdccdadbcbdcbddcdccccbabacbcadacbbddacadddcbdadaacccbbcadabccbbddccacbdcbaaccccdacacccabdacabaaddcaccdcddcdaababdddcabddcabddcddbadacdbdddadcbdbcabbdcdbbbcbdabccabadaaabbddcdccdcbdcddaccbdabbdbbaabbadadcaaadcdcdbacbabaacbccadcbbdcadaacdaadddadcbabdbadcadcaaddabbdddddcccbdcabbcadbbcddadaadabbcaacbdadacbdddddadadbcadcdcdccaddaaaadacbabcbcdaadddabcbbdcbabcbcadbddbdccaadcbbbaabbadcadaadadaaddabdbbaadccabaccdcdcdcabaacbbbcaadbbadcaddddadaabdcadcbbdacbddabaadabaadcbccbcaaadbacaabddabcacadabcbabdcadcccdbbccccadcbbdcdbbbdadcbdccadbbcdadbdcdcaaddadbdccacbccbccacddbbcadbaccbabdcadbaaadadddbdddadaddbcaccccddcbddaacddcdacabbbdaabbcbbdaaacdbcdcdaccdaccacbadcbccaddabccdaabbbbbdbbaacbaaaabcdcaacdcbdabadbbbcdddbadddcdabdcabcddaabdcacdbbadbbdbdbbacacdcacbdadadbabaaddaccddccaadcdbbbbcacdadacbbbdddacaaadaacbbabbdbaaaadabccaaacbadbcbaabcdbddbdbbaacdadbdadadabddcccbbaabaaccbcdbddabcaabccbddbccabacabdccbbaaaccaadcdaaaddbbaccbcbcadaccabcdbdbddbaaaabaddbabdaabbcaddadadbaabbdbcbaddcdcacddaaccdbbaadbcbaaaadcaaddbaabddabcccadbaacaddddbaacbadbabcdcacdadccbccbddbcccadcbabbdaddccabccddbccabaacccacdbababdbbdbbdadbbbdbdddadadbdacaacbcbbbbaaaabdcddcdaaddbddccacbaacabcddadcdcbbcadaddcbdcbddadddbbcdddcabdddbcadacdbcbababbaaaadbdadaaabccdaccdcdadabddaacadddcaddbabbdcbcbdadabdcaadccabcbccabcccacddabccacbccddcddbabbbaabadddbdccaadabccaccdcbddbdcdcadaaaccbbdbdacadddbabbacbadbcccaddabdcdcbccacabcccdbcdddabccdcbdacddddbdcbcbbcbcaacbdcabdcabbbdabaabbaadcdbacbbdaddccbcbdaaaacbaadaddbdbbdcccdddbaabdccbabcbdcaaccaccbdbdbddbcbcbaabbbaddbcadcddddbccbcdbbdacdbbccaaadddbbdbbddccbdccbcabacaaadaacadcadbdcccbadbdcbdbccaaccbabdccbabdadccbadaddadddadaccdcbdcdddabaadbaabdbbddadbdbbabbbcdcdbadacdbcddbbbbcbccaacababdbadcbdbddbcbacaabddcdabbbaacacbbcadbcabcaabadcabdcaadccdcadadddaaabdbadbddbacaacbbcdbacddbbcbabccacddbddbabbadaccadaacdbaadcccbabcbbcadddabbcdbcddcbabbdbcdbbbbcaddabaddcbaacdbdccbacbdcdadcdbcbddbcdcaadbccdacbddbdacbcdacbbaaacaccddcadddbcadabdbdacdcacdcbababadbdacdacbcbaaccbcbbbadbadcabbdbadbcdbaabbbcdabcadbdbabcadabddccaabbdcdcdabbddaabcbadcdbaddcbbccaddabdbdabbdcbaaacabaddcaaccbbddadbcabcaabcbdccaccabaaacbddacacabadcaadbbdcdaacbbadbbbbaabdcbcabcbacadcccbaababcbabcbbccccbaadcccddddbbaabbddccaabacddbcdcbdabdbdccacaadaaadabbabdaaccbbcabacbdacdcdcadabcaccbddbaddcaaddccdccddaddacaaadadababbcaaddabcdbaddbaddbbadbdaccdbbaddadddabccaabadaacbdbddcdbbcbcbccccccbcacbddccadacdccbcbdddaadcadbbcbcbddaababaadabbacdadcddacabdabbaaabcdacdabaccadddcaaacaaacaccbabcadacdaccdacbbccbabcddcdbaaabdccbcbcacacdcaaaadcaaaabbbbabbdaadcdcdbcbcddbaabacbaccbdaadadddbacddabaacaccadaadcbbbdaabccbbcddddcaccbaccaadbacacaacdbccbdcdaddbddaaadcbccdbcdbcbcdbdadabaacbbddbbaadbdcbbbdcbaadabbabccbcbcdcdbaddbabcbdcdcacdaabacaacadbaaddabbdaadcadddcdbbaddccbdaabbdbcdcadbdaabbdbddbccbcdcdcddbadadbcdbdbcdbbbccaaacabaabbaabbdacddcaaacdbbcbaaddbcbdacaacdcdaaacbcabdcbadbbadbdaaddadbccdbaccbbbbcbddddadcdbacccaacbbcabbbcacdddbabaaaddcabcbbadbcabbbdbbcaabcacddcabbdcaccbbcdbbddccaccbadccacbbccaaacccbbcbbbdcbbbbdbddcdcdbdddccdbabdacababcbaabccadadcbdcadddbabadcddcaddcdcccbaddcbbccacbddacacaddbdabddcdccbcdbdacadadccbcddcddbdbddabdbbaaadbbabcbbddccacbababacaddbcdbbbaabddadbbcddccdaaddaacdaabbccbbcadbbcdbacabbbabdcbaccaaaaacccbcbcbccabcacaaacbadaddddadaababcaddbaacbaaaddbadacabbcdadbaaadcbddabdbacbadddcdcacaaccadaaccaccacdacbdaadabccaacbcbbddcdacbdccbccccdbcacbdbdbcadadacbbaacccccbdcaddaccbdaadcdddabbcdbbbccdbdbbaddbacdbbdadbbbbdcdbbdbddabdcbadaabbdabbaddcbddbbaaaacabbbcdccacbadcdaccbcddaadaadaacacccdadddbccaabbaadcdacaacbbbdcbaaccdbbdddacacabdcdcdabdacbaacadbabdcabccdcabdaddadbcbcdbacdbdaacdccaacbcdbdabbadcabaaddadcdaaadcccbbddcadaacaccbbcbadddbbbadbabbdabadbddcadccdbaadbacadcadbcacbddddbaacddbccabcdbbccbddbdacccbcdddcabadddaaabbdabcdbccbcdababbabdacaacaddbbdccdbaaacdcddbbddbadbbbbbddabcbddbdddaaacdbbcacbcbddacddccaabcddaaabcddbbabbddabcbaddbdbdaaacacccadccbdadaaaaabbcbccaddbcdcbbbcbbaadddccdaccdccccbaacccdadddacdddababbcdcadbbaccbdcbdbcaaaadbabcbdabbbdadaabccbdadbbdadddaccdbacdacacbbcbcdaaccdacddbbcccbbddacccbadbdbdcdcadaaccabbdaaddbabcaabbdcbbaaddacdcadadaaadabcbdbbddddabcdadccbabccacdcaabaaccacdccbbadcadcdccdbbadcabdabbabbbcaadbbcdcbdcaddaababbdcdddbbdabcacbcdbabaadbdcdbcccbaabacbbabadccdbaabcbdaabccccdbcdcdbabdcdddcdbcaaabbdabcddacbcdbdccdbcbabdadaadbdbbabadcccbaaababcaccaaaabdcdccadbbbadaadadccbcdbbcccacadcacdadddbacdcbdbbdbcacbddbbcbabbbbbadcbccdcadccdcbddcdcccdcdababccdaddddbccacbcdcaabbccaaccbcddadcadcddacaadabaadbbbacbdbdccccaddaddacddabdacdaabdbcbcacacddbcbdbdddbccabbababbbbdbadddcbabdccacadcbadadcdadddaaacacdbaaccbbdacbcbcdccbabdadcabbcddbcbcccdccabbdbdbacaddbaadbacddaaadccbbccbbccaaaabdcababbdadbccddacdbccbcdbcbdcdcdbacacbacbcddadcccabbbddcdacdbdacadcbbdabbaacadabadcbdaadcbcdabdaaccbbdacbcaadccddaddccccdccaaaccdddcddcbddccbbaabccbadbdadddddadbdbcccdbdccddaaadbbacaadddbcbccbdbbcdaccbbacaaccadcdcaddaccabbcddabddaacbddcdacabcddcacdbdadaacacdbaadcbdddcddcbdaaddddcdababacbaccdcdaccdcacbbdaabababdacdcbaadcdaabacdbcaddadadaaaacbbcbcbcbdaadcddcdbaabcbdadbdddadbcaddcdbaccdcbbcdbdcacbbbdaccddddaababdbbdabdbcdddbbacbbaaaccbacccabaabcbbabdaaddabcdccbcdbbbcacbcbcdabbcbcaaaddcabdddaadddcbdcdaaccbcababbbdbcdcbcddcdbabcaaacacaddddbdaaaddabaacadcabdcacbdbbcddaaacbbabbddddcbbaadbdaddadabaadadcbbabbdbaadbdbbacccbdcacbcdabddbabaccdabaaaabacacaddddaadbaabadacdbdbbdccdbcddcdbbbcbbaaabaacaaabcbadbcaacbdbdcacddcccaadcbdadccddbaadbacbabbcbcacdcbaccdccabdbccbbaddaabdbdacdbcdaabbacbbaabaabdccacccdcddaabcadbddbbdcccacbddbdcababacabaddbdccdcdbddbdbddbcaaabbcbcadcababacabdbdcdddadbbbcaccbdbadcbbdddbbadddddddcbbabddcabbddadcaadbcadbbbbcdbdcabcbcadaddcdcbabacaccbabbccacadbcdcbddddacbdadacbcdddcbdcddadabbadbcbabbccdcbacbbadaaaccaabccacbdacbbaccaabdbbbabbbbdbcbdbcdcbbbdbcbaadbcbabbddaacdadcaadbabaccdbdaddababbaaddababbbbadcbadacdcbaccddcbdbcadddcbdaaccbcadabdbdbaddcadcdddcbdabccabccbdabddbdbccacdacccdaddccadcadbbbdabcbaadbaabaaaddbddadcccadbcdaaadaabdaaaddaacaabaaabdacadbdcbcbddacadbadbcbcdbabbbadcbadaddcdccbaaacbacddbcdbbaccbddbdccddcadbdccdbdadbdcbbacddddbbcbcabdbcaaddcbaaadccccacccdbaadcbabccbbccdbacbaadacacdaaadabaadadccdcadcbbccbdccdacaddbbaadbacccbbbdadddbdcddcaddcaabcbbddaacdbddbcabcbddbadddbdbbaadbbcaabcaccbbbbaddcbcbcdcbcccdbdacadddccdbaaabccbabaccccadddbcbccdbbcabbbddddbdccbbccaccdcbcabcbacadcddbcddadddbacdabdbaccbacacdaacacbaabacccaccdbcaaaaacbcddcdaaaabbdbbbacacbcbdbaabdacdadbdacbbadabcdcccddbacacdcdaadaacddbcdaaaccdcaacdbcadbadcaadbababacbbabbadcdbaccbabbbcccacbdbccddabdbdccaccdadcabbbcabccddcabdbcdcbacaaabbccccddcbbcbccbdadadadbcbcbaabadcbacbcdbcabdaccbcddbbbcaadacbacacabaccaddbbaacdddaccadbdbcbdaabaaaccbacdbddcbcaccdcccdbdababbcaddaabbdaabdabbababbadabddddcaadcabdddbadbbaacacbaddbcdbbbabdaaccbbdccbadbadccbabdaaccbaaacbbdccdddabdbaaccbcbbdbdbbacddaaacbcbcdbbddacbaadcbbbcbbaddabaadaaaabdbcccbadbbcbddddbbbbadcacbaacdbcdcddadaabdbbcadcacabdbdaddacbccbbdcacdcbbdbcbbbdbbdcbccbccbacbaaddbcacdcbdcbaaabbadcabbabdabcbbcadcbcbcbacbcadcddaadbcbaaababdcbcbaddabdbabccbdaaaababdddddbcadddbdcbbaccaddcdcdcdbccaababdaaddabcadacaddddcbcccdcccbbdbdbaacaaacbcdbbdbcdbdabbadbdaddabbbcabdcabcbdbdcdaaaddacbccccdabaababdcbcacdaddababadbdbacbbadcbdabcbabbadadbcbbababcddabbddbbacdbaacddabddabcbcbacdccdcdcdaaaabadbacdabdcaacdbcbcbdbaddbdaccaddccadcdbbccbadcabdbdbcabbaadadcbccabccacaabaaaaabcdbacdbddddabcadcdbcdcbbccadcbadcdaaacabddbaacadcccdbcddcddadaacdabcccdbadabdabcddbbcabadacbddaddddbabdacbbccbbbbadbbabbacddddabdccccbaacdddacccaaaccdbaaccadddcabcdbdabbbccadacdacbacbddccdcbbcaddbdabbddcbadcacdddcdcccdbbcbadcbacbcadabcbcbdaadaacacabdcaccccbbdbcbacdadaddadadbddbdaaaadbdbcaddcaaabccbdcbcbcddbcccbbbddcabcbbdddbdabdbdabdabbdccaabbaaccacddbdacaddbddaddcccabbaababcaacaddbdcdcadaddadacdbbcccacacdacdacadaacdacdacdbcadcabacccdaccbccaabadbdbcddccbdbccdcaddcdbaacaaadaddbcddcbbcaddadcbdbccbcdadbbddaccdddbaaccdcbbbadaaacbadbaabcccdbcdcbdcdbbabcccaabdaddabcdabaccdcacaccdcdbadbbdbabaacbdcaaacaaaacdcdbdabcacbabbbcdcdbbaacdddbcbdbbbddabbbbcbaadadaadcdbdacacaddbbbbaabbdbdbbbabaabdcabbacadbaccbbadcbbabdcbbcdbbacabcbdddaaabdbaaccbcadbcdcddacdbddbaaabcbbdbbaddbcbcbbccddbacbcaaddaadcdbcccbddacccbcdddcccdbddaabbcaacabcdccddbbbbdccdbaabacbccbcadabacbbdcbdcbabacbdcccabccbcbcbdcacacbdadcbadaaaabbacccdbcbbbccacddbabdbcdddbcdacaaddaccbdbadabbaaacbbcaccacbdcddaddcbaacdabbbcdbaabdaaccacaacacabcdabdbdbdadaadcbcbbcaaacdbbdbcaccddacacdcbccbccdabaababbccbcbdccaadcdabbcacabdbdcdcbaacabbcdacabcababdbbbbcaccdaddcabcdddbdbdbdaadacbbddbdaddbdaadbcdbddabacbccadbcacbcbabacadbbadccacaabcccdabdaaccccdcdbccbadaabddabaccaabadddadcabbaabbababbbcdddacaabdacdcdbacacaabbabdcdbcaddbcbabdaabcacbbddbcdcddccadbbdadcacacdcddaaaccbdbbbcaabacdcaddcaccaacabcadcbccbdadccdddacabdccdcdcdbcaabdbaacabddccadcdbddcababcbdadbacaaddcaccacdaadbbadbdcbaccccbacdbbcabdbcdbdcaddadcdcaccccdddabbadbcdbddadaabcdcbbaacbbabbacdcccccdcabddbcaadcdacabcadaccbcadaaadbaacdbcaacdacdbcdacbcbbaadbbdadacaadabbdbcaabccdaadaadbcacccdaddcdcbcdbbdacaacadbcbbccabcbbcabbbcddadbabdbdbacddcdcbccaabddcacabacabdddacbccbddacaaaaadcbadcabbacdcddcbcabbabdbcccbabcdadbcaccbbbdadabacccadbcabadbcbcadcbcddbacabaaadcadaabbbdabbdccdaadabdcbdbcaccacdadcddaadaaddbbadabcaacabdddaacacaabcdcbbaccacdcaaadabccccaacccdadcdbdddbbabcbcdabbaaccadbadbcdbacadcbdadcdbccdcccaccbddccdcabbcbbddaabcadccccabbbbdcabdccabddacbabbbdbbdccddcabbdccbddacdbcdacdcbbbcaddcbaaddaadaaadaadcaabdbcccbcddcccadbcdadcdccbccbddccdcaccbcdcbadadcaddadcdaddaacbdabcdabcddbcbbbadacdaadcacbdbbbbdccddaaddddcdbddbaaccbbcdacabbdddcbbabccadddaabbdccbdaabddaadbbbdaaacddadbccbdabdbaaabdaddcccbbcaadcccdadcbaabccdccacbbdcdbdaaabdabcaaddbbdbcbcdcbbadcdacabdbbbcaadcccdaaaadadbbadcdbabbaccdbbadcdacdcbcddbcdbbaaabdbdcbcbabbbabaaabddbabbadbddccabddcbcaaddbbdcccddbaccbcacbbabdbaaacdbcaabbcddcbddacbdaaccdddadbcadcdcdbbaacdbdcadccbacdbddccbccdacaaadcbaddcacacadaaccabaddbdbacaabbcdbbbdaaabbacbdbbcabbcbbdcacbadbdcccdbccccaaddacbcbdcacbcdbcaddacaddbadcaccbcdbacabddbdccbaababbbccccdbbacbcbcdcdadbcaababddcbbbbdaababbaaaacbcbaabddabaaacaababccdcaddbcadbddccdccbbbccbcaacdbdbddbcbbdbbadcabdadcccbabbaacbbaacabdcabbabcbdabcbdaabbcbbbdbdbaadbbccccaccbdaadbabbdcdbdabcabdaaabccabcbabcddbcdbbcdcdacabcdadaddbabacdcabacbdcdccccccddcbcdcccddadbdadabbacddcabbcadccbadcdbabdcaadcabcaccddbbdcdbdcbbadccccbaddcaaabddacdcbbcacbdadcccbcabdbbdabbdacadcabdcdcdbaaaddbabccdaaaacddcddadbcccbcacbdaddbdbacbaddabaccadaaaabaaacbaabbaaacbbdcbbdcbddbdabbdabbcbadddbcabcadaadbddacddcbaccbddbddabcacbdbddbcbcdbdcbcaadbbbcdaabbabbcdbabddbaabbddadbcccbdcccaacadadddbbaabdbcbdadaddccdadccbccacdcdadaaabdaacadcaaccddcddcddccaacaccbaaadcdccdbaadadddcdcbdccabcdcbbdbbdbdccbbabbadadacccbbbaadadbdadaaccbbdcdddcdabbbabdcbaabcabbaadbbdcbacccbccabdaddbdabaaadaaccbacaacbbbacdcacbcdbacdbdacabdabbdabbdcdabcabadadbaadcdbcbbdbadbdcadcaadabcdadcacbbacaabbdaacdbdbdacdaacbbabadbbdccacabdaaacdddaaccbabdadcbdcaabcadadacbadaddcbaddccdacaccdbcdddcbdaddababaabaacddbccbdabacbdadacbdcdbccbaddbaacdbadacdddddbcddbdaabcdccdbdcabdaabadacadccacacbbdbbdcdcaabadbbdabaadbdcbdabdbadacccacbabacdbccadbdacdaddbddcbabbbcadcaacbababdaadbaabbcaaaaddccababcccbacadadcbdabcaaddbaaaabbcbdbbdddcabcccaabbcaddccddbaadbdacdcbaddbdcbadccbabdbbcabdbadbbdcbacacdadcddabadbcaacdaadaabcdbdcccbbbdcdbdbdabcbabcbccabbbdadbababddccbabcdcbbbcdaadabadcdccbcaaaccbadbbdcdcbaaadbacabbbcdcbadbdbcabddaccccdaddabccdabdbdbddddacdbdcdcdcaadbbaacdddddbcaddbabcbaadccdadadbbaacabacdcbabbcbbaabacbdaccbcddbccaddddcbddcabdbcdabbaaaaaacbacdcadabbcdddddacdccaddcbcdbaacabaccadbcbdddddaaadadbbaadbacaabbdaabcadbaadcdcddddabdaaabcbbbbdacddbbdaadadcdbdadddaadcdcaabcccdaacdaccbcaacaabadcacabdbbdaaaddddbcdacbbcabccbabbabdaadcbcbbacabddcdadcdbadbcbcddbcaaacdcccdaaddcdcbdaddabcdcaadcbcabaadbcaccddadcadcadbacbbaddadbdbbacbbdcaabcdacacaaacbdcbcbadcbbacacadcdabadadcbdbccdcddaadbabdddcdaadacbbccddddcbbcbbdccacbabcdddbdbaccbdcbbaddadaddcacadcabcddbaaddccbdbbdddccbadabbdaddadbacadddaddcdababaddbaddccddabcbbaadbdabadddcbbabadacbccdbaacbcccaccdbdbbbbccdbabbaaaacacacbbdcacbccdaaddcaacdabaccdddccdaaadbdbababbabaacadbcccaddcdbbabbdccacccabcdddbacaddabbcacdddddbdacbcabcccddcdadaaccdaadcaddcbcaddcdcbbcabaaabdccaccbabbbccaabdabbaaaaddbbadddbbacabcdacdcaccdbaddddbcbdabbdbcbddcaccaddbccbdbbccacdacacbacbdbacaabcbdaabbbadbcaccdbbbacdbbbaaccadccaddbcabcdbdcdacddacaaadbacdacbcdacbbbacbcbcabdabcabdcadbbcccabbbbacddabcbaabbccddaaccdabcbadcbdacccddbcabaadcdbccdadbcababccaaacdacadcdbaccddcabddbbbadabcccdbbbdaaccddbcaabdcbabacbcbacccbdabbadcdadaabbddabbdbdcdcdbbdaacbaccabaabdaccabababdadbdcaccbcddbbcdddbaccbddadcdccbabbdccbddbdbcbbadbbabcbadaddccabcbcdbcaddbabaddabaacbbbbddacabccbabbabadbaaacddabbcdbdbbcbcabcabadcbcdbcbdcbdacacbcacaddccadbdaccaacabaadccbddabdccbcadabdbdbcbdaabdbccbdbdcccbdabddcbcbdcdcdabacdbacdcdacadaacdacababaacaddbbdddcabbbddddcbbddadcbacabdcabddadbaabdbbcaddddddbcbcbcccaaaaddacddbdcdcbabacdcadcdadcccacbcabbabaabaadbcbccbcddccadcbcaaccbcccbddcdbccdcaaaccccbdabcdcbadbacdbbacdadbbccdccabdbcaccdbcbdddbaccddabcdddccaacccabccdddcdbdadcdaacdcddabbbdbbcdbdbbbdbdaabacdbadbacdabacddcdbcbacdacdacadabcbdcaaadcccdbcadcadccdadadaabddddcaacdbddcdacbbdcbdbbabcacccbccabcbadcbacaabbcaadccadbdcccdbcbdbcdcdbbacbaadddbdaddacacaabacbdddccadaadcdabcdbdaccdddabccdbcddddadbbccacdaadcdadadccaaacabbadbbabaabbcacaadcdcbdcbccccddaaadbacbcddbbacdcaaacabcbdcbacbaccccccdaabbcbadccccddbdabdcdbaababbdbdaaadbacccaaaaccdabcbaddcbbdaadbaaaadcbbaabbbdadbaaccddccdddcdadbbbccacdaadabadaacbbabbaddcacadacdbdaccdbbaaccaacddcbbccaaadcbdaccccabcbdbbbbbababcaaadabbdaccdacdbdbacdcadaadaabaacdbccbdacacdbbbcadddbaabcaabadabdbdbdabbacacbdbbcdaaddddbcaabdccacacdbcdcdbaacbbcabccaadccacdcddaaadbcaaccdadccccccbbacabcacdcdbadbdddbcbbddcbadbbacabcbaddcacbdcbcabbabccdbbabaaabcbbdabcacdbcaacaabaacccbcbcadabcbaacdbcdbabcabcdcadccadbcacacacbaabdcacdbdacdddcacbdbcacaacbbccbbdabdddddbaccdbcdcbcdbabcdcddbaabbaacbdaaddcdbddacdcdcbbcabadcbcdddcdcdbabdacbdacbabdbdccadbbccacbcaccccdbaabaccaadbbbbcbcbbbbdddbdbccbaddcccdaddbcbddcabbaabaddaaccccbbccbbadcbaaadaddadadbccdddcccdbcbbbaddbaccccbbdaadabdddcbdcbcacdbaababbccddccccacbadaacdccbabbbabcababaadcbccddaacbbdacdaaccbdddaabaacadadcdddabccbaccabcbbbcbcaabcdadabbcbaddabbdaddbccbbddcdabcbddbbadcdabacaabdbbddaabdcddaddbdacacbdacbdbdbbddccbbddacbaabdddbcbadcddbadcaddddbbdbdabacdbdbcaacadddbbacacaadbdbcbacdabccadcbbaaddcbacbabbcbbcbcaaccacbbdbaddabbbaabdaacdbdccdbaadcdbcbdbbaabdccadadbbdcbbadbdbbbdbacaaccbdcccadccbdbcbdbcdcbaaacdcdbcbbcbcbbcdcdacdbbbbbbbcbbccacdaccbccbcbcadadbbbcdcdddaacdbcdaaabacccbccabaddabbbbaabbcabcbddcbabdabbcadddcbbacddcdbccdabdccacddbddbbbcccdacdbadcbbaababcacddcdbdacbacacadbdacccbabaaaacbcddbabbcddddcbacaaadadddbcbdaabaababddabcddcacadddbacbacbbcdabbadaccddcabbddcdadcbbadbdcbbcdabbacbabdbcaadcabbbcbbbbcadadbdcaddddccacdbdbcbbabbdadadaaadacaadddaadddddccbbabdbcdabbbcdaaccbdabbbbaaacdaabaabcbdcdbdabdaacdaadcabbaaabbadbcddaccbcaddbaaadbabbbdbbccbacbbaddddbbddaacddcdababdddccdccdacbbdcaaacaadcdbccbcccdcccdbacddcababdbbbaacbadcdcbbddccbdbadbbdbccdbbaacdabcdadbacaacaaddbcbccdabacdbdcbbbccadbdbbdbdacbadacaacacdcbabbdcdddcadaccbaacbbabdbbdabcddccbbddbbacaaaacddadbdabbcdaaabccdadcbacdbdaabdadbdbcdcacadadbbcdaadccdbcbdcdaadbbadacddbabcdbcbadabadaadcbcddcdadcabdcacabcbbccdcccadccbaaaaadabdabacdaaccbacbaadbbaacbbcbaccddbdbdadccbcacbbddaaacdcabaabacbcdacdacdabccadcdacdabbaacbaccdaacccabdbacabaccdadacbcbccababdacaacbcddabbabdabcbbcbadddbbbcdbbcaabbbacbaddbadddbcabcadadddcacaddbbcbabbaabacbcadabcccadcddcbdcddabdbccddabdbccdaaaaccdbdcddbcbaadaabdbdadadcdaadadaddadbcdccbddbacadbbdacccbacbdbcacbdbbcadabdcdcdddcaadcdcaaddabccdbddccbacaabdcaadccabbbcbdddacabbccbdabbabcdbcadbacabddbacccdaaccdacabcabaccdadbcaaddddabdcbddbbcbadcabdcdcaabbcdaacccdadbdbbbbbaadccddcccacddaabdcbbcaccabcbbddcbcdbcacbcbabbcaaadccacbabadcbbcabccbbbcddbbcabbaacbbacddadabbbacadbcbcdcdddacaccaacaabdcadbccbaacbcdcdbaccacdbccbabcacdbacbbadbcddbcbcaddcacdcbcbccaaadcadcadadcdadadaaddbacccbabbccbaacbdcbbcdadcdddcccdaaabcbabdbccddabacddcabbbcccbaddbcdbacacbbcbaacddcbcbcddacbdadabadcaabcadacabbddbccbbbacbabaaabbdbbaadacbcbdbdcabcbaacddbcccbdadadccddacdcadacaaacacdbbadbcbddadcbcbdcbacddaaccdcbcddbbdbacacccaaddcdbcbbbbbaaaabbbbcbdcaabdabbaaccdcbbdbaadcabadbcdaabaaadaccbadbcbcacddcabcbcbabdbadcdaadbadcadcbabbbdcdbbacacdbacddabddadaaacdccccdcabbdccbabcadcbbaaddddacabdabbacdbdccdbcacbcaabddadcccaddbdabbcdabdccdcccddadccddbdcdbdbbaaaccbddaadbbabaccdcacdcababbdcaaccbdbcbdcbcabccacbbaabaccadcabbaaabdcabaaabdbbdadddcadbcbadbbdabbabcddadddadbadcbbbaabbabacbadcacbcddaddaacbbcccdbdbddccadaabcccbbdcccdcbabcdabcbbbcdabbbdabccdddcddbdbcbdabcccbcaabcaadadaddacdaabcbbabdcdccabcbdcadcbcdacdbbbccbadbcbaacaadbbabdcbbdbadbbbbcabbddacbbbdcbbbcaddbdbdacbabdddabbdbbdcaddbbaacadbaadabbadadbaaccccddbbcacdbcddaabadbbabdddccccacbbbdcdcbbdacaccaaacdcbbbccdadcdccbcbbaccbbacbbaacdbcbbbdabadabcbacccaaddbbbbaccdbccbaaddbcadbbbaaabcadbacbacdbdbcdcacbcdaddcdbacdddbbddcbacaddbbaadbcbbdbdacbabaaadadcdcdcacabbcbbcbbbbcdaaddaddbddaaaaccdaadacacaacbbddcbbbdbabcdbadbbbbbaabbdbabdbcbaacddadbcdbdaadccdbcadaddaabacdcdadccccbacddcdacacdbdbaadaddabcaddbbadbbdcbbdccbbcacdbadaddaadcbaaabaabaabacabbbdbbcaaabdddbcadadbcddaadbdadcbaadcdccdbbdddbacdbaaacbdddcddaabcbcccdcddcbbabcbaabbbddbcdaaadcbcaccbcbccaddcbbdbadacccabdbabcccddaccbdaddaccadbbdaddddbcbbdbddacadacbacbaabacdcbdcbbccbadabbddbbccdacbddaddcbadadabbcaccadcbdddbcdcddbdccaaccaacccdbdababdcdaccbcbaabccadcacacbcaddbcdbdcdbaccadcbacdaacabacdaadadbccbccccbbaccbdbdadacbdccdbdddbdadbdacdbbcadccddaacddcddcabbbacdbadbbbcbcdacbaabaadacbddbacddbacdbdbaabddccaccbabaacbaadacabbdddcdbbcdccdacdcacddbaaacdabacbcdaabaddddcbbcdbabcdcaaaccdabcbcdbbcbdcddbbcccdacbabdddcbddabaacabbccabacacbabadcacdcadbcddabacdacdbabbccacdadcbdbbaabcbbcbdcadcbabdccabaadaabddddabaaacdcdcdccaacbdbccbbdaabcccdbabbbdaaaabcbbbaabddaaabacccbddaccabbcbcdacaaacccddadbdaaaababcdaaaadbaabaacdcaaadcbaddbddbbcccabcdbadbbbbcdacabbdbaacdbdddddcdacdccdacaabacddcdcaccadccadacadaccbbcbbdcdbbdcbcdbabacccccaabcadbdadbbdccbdddcdadcddcddccbcbdbaaaabcbdbcaadabbdcdbcddbababaababdadacdadbabdadbdaaaabadabadadbdabcbdaacbabbaabcababdaaacabbdabcaacaccbdbcbdcaacabdccadcbccbadbbddaddbbaacbcccccbbbdcbdccbdbaaadbaababbdbaaaacbccddacdcdbdabbbbabacaadcbcbdaccabacdcdbacdbdddaabadaabdcbcdcdbddbdbbacdcdcabccacbbabdbacbdcddcaddbddbcbbdbbaacddabadbbadaabcaaaacddbaccadcadacbdddbddbdadacdbbadcdbacdbdccabadcbaadabdddbddcadddbaccbacdbaddccdabcbabddcdccaacbacbdddccabbcabbccccdbacbdacccadabcadddbbdbbbdcddcadddbcbaaaaaabcaabdddacdbadaabcdbadcdbddacacaadddacdcaccddcbbdaccccbbdcaddacbaaadcaaadadadbbdcbcbcabdadacaddddacbcdcddcaabaddabbadcbadacdddbaccabccabdbcbdcdabbabcddbbbbaddbdddbccaddaccaaaadbdcdbcdaabccddacbdbdcadadaacbdcaaddddbbaddcccbcccdabddadadbabcbdccacadbbccbcddbbaacdddbaacdaadababdaccccbdcbdddadcccdbcdcdcaababddbdbbdbbbdabccaadcddaacacdcacddbbbccbdaaaadcdaacdcadbbcccbcbacbdabbadddabdacdaaaddbcadddaacbccadcdadadbaccccddabcacbcbbdcccdcbbabcbbcacdbbcacdadcbabcabbadababcabddaccbcccdcadbdbadadbbbddabdabdacdbcbbacabdddbccdbcdcbcbcbdddaacbddccbcacdcbabccadbbaddbbcccbbdcddadcddadcdcdcdabddadcdadcacdaacdbbadabcaccbbcabdcbdcddddabdddbccadbdbdcddadaaaadbaccdababdaccdddccdbdaaabbadbdcbcddacdcbacadbadcadbabaacbaccddcbadcdadbacbbbdbdcdaabaccaaaccdababaaddbadcaabdacbdcbdbcdbcabaddcdbadababcaadbaadabbbccdbddaccbddaaaabcddcdcbadbdbdddaaccabbcabaabadccaabcbacbdcdcdbbcdbcdccccbaabacccacacccbdcacadcccbcadadacbdabcdaaabcbababacabacdccdaabdadcbaddccbcccbadbcbdbdabcacdbbddccdaaabaaaacabacbabcdcadadcddabdbcbdaabccadcbdcbccacdacabdbbbbccabccacacabbabbbbcaabbbddabcbbadabccdacbdadaccdcccdddbdbbadabaaadcbdcbdccddbcaccacadbaaaadadacadcdbccddcaccbadacddbddccbbcbdbbccdcccbcabaadcdccbcbdaabacbdacdaabdacbdbabbbcdadcbdacdabbaaaacaddaacadbadcdcbdadbddddadbdadaccadddadcaababacdacddabbaabacccacadadbbabccbdccbcddccbaddacbaabcdcadccaddbaabdabcccbbdcbcbabddcdcbcdccbdabdcadacbbdcdccbbbcaccbbbccdcbbbdcdddabbbadbdaabbdcddabcdadcdbddacdaabbccdacdcddbacacbadcacdadadbdcdaabcadcbdcbadabddddcbaadababdadcbbccdabbadccabcbcdbacacdddadbdaadabcbddcbcacdccadbbaccdcbabdcddbbdcbdaabcdcaabddaacaaacdcdddddbdddbaddaacdcaaaddadcadbbddbbdbbdbbcbbdabbbbbddcabbbaacababcaabddabaadadbcbcdbddcbcbbdbaadacccadcbccabaaacdccbabcccbdccadbabacadccaaabbabcbbdbbadaabbabddadcdadadddddabbdccbcddbbdbcbadbaaddbadcdacdbbbbcbadadbaacdbbbbbacddcabdcccacabcbababbcdadcbdadbcaababbbbdabccaaddbbdabacccadccbdcadbadbcdccbdbdbbdcccbdcddcbdcdccdcabbaaadbccbccbcdbccbacbbcbadcadaddbcdabcaadcbcaabadcadbddacbdcbbbbbabadbbaddccacccadaadcaabbbabbddcabbccbabccaadbbaababbdbcbbcbcacdddccdbdadcdbadccdadcbadbcbbbcdaabcddbcbcdcddbcdbaaccbabdddddaabdcddbccddaabbbcdcdcbdcbbbabccaabdbcacbccddcbdbbdcdaabbadadcabcddaddcaddccaccbddcacabdccadbacdabbcbbbcbcaabacbcdbdbcbbcaadbcdcdaccbbacacadabdcddbabdddccbdabcadbcababdacbbbbccababcacaadadaaddaddbbcccbbcabbcaaccdcabacacbccaabcdaddaddbdacbcacdddcdaabdddbcdccbcbaadabcdbcaaaabbbdaadcdcadabacdbcdcbdadbdbbcbaaabacabccacacdaaadaabcabcadbbcccdbaabdcccaadcbdabccbbbaaaccbadbbcbbabccbccbcbddddabbdddcbdaabcabcdaccbddadccaabcddccbdcaabacdbaddbddcaacbcacbddbdacabddabbbccdddbaddbadbdaacdadbddbcdbcdddbdabaaabdcaadcabbccccdcbcaccbacdadcbacdbdcbbbaaddabbbdbababcacaadcbaadbaaacbddcadbdcbbbbbbaacbbaabdaadcbcccaccacbbbdabaccbdbabaccadbcddabaaacacbdaaadbdcbcbdbdcdcdddcdcacdbccdddcacbbacdddcbaabdbdaaaaddcccabdcdbcdccbcccaddcdbbdbcacdabddcbdbaadabbaabdcaacabacaaadadcabcbacbbacdbdaadadbdccbabaddccdabadacbacbcdcaacaddddcbbcaadabdaaadaaabadbcdadaacacbcaacccaaabcddbadacbccdcdbdddadcaaaaadacdbbabbcaaadddbacbaabccddccaadaaaacbccbacdddadbacbacbababbbaaacbcdccacdabdcccabbbdabbacabbccbbddacdddcbbcabcacdbcdcdcddbccbbccbdacadacdbcdbcabadaccdcaaaaaddabcbdacbbbcbccdbdbcddcdddaadbdcabdbbccdcdddaccdaddbddccaabdabdaddaadddaaccddbccdcccaaddaadbadbccadaddbacabbbdaabcbacaddabccaccbacdcdcaddcddbbbccbbabccddbddaadcdbbcdccaccbaddaccaababddcddcbcbcbbdcdddbdabaaaabcbcaabacabdbcaabdccacdbcdcadccbdbdacbbdcbcdabbabdadbbcbadbaccabbcaddadcdbadccbbdddcbaccbaaabdbacacccbcdabcadacdbaccdbbccbdbdcdddacdbdaccdadcccdcbcaaadbaccbcdbbbaabcdadcabccabcabcbcddcddcaacdabbbcaabbaabcadbddacccdabcbbaadcbddccbaaadbabdccacdbcdadcdbccdbbaadbcacdaddacdbbccbdbbddbabcddcbaaadbbddbabdcabddbaaccbdbbdbcdadbaaddaacadbbcbacdccbcddccbabacadcaacddccbcbaabcccdadbaddacdaaabdccbccaaccadaaccccbcdddcccaadbbaddaacddcbbacdabbdcdacdabbdcddaddccabaacabdbdabdbabcaccbbdbcbadcddcbbddbacdbabadddbddadababcdabdacabcdcdbbbcddacbcbdccdaaabdbdbcbbdbcabacbadbdaadcdcbdbcababbacdcbccacddbdaacbaaadbcadbddcddaaaaabbabacbbcababcdcccaddcbaaaadbcdcdadbbdbaaddacbadbdabbbacdbbcbacbddaaacdccabbcdcaadccbccadbaabbdcaaaaabcbaabcbacabdcaddbcdbdddbccddbbaacaadacbadddaddcacccddcbdccaabbdbbaaabadbdaacddaabdbbdabdadddaccbbacabbdabaaddcadabbdcbcbddbbcdcdcbbadbcdcdaaccabbadbabcaaccdbabcdccdaacccdcbcddddcaadabdadcdbaacbbcbbcbaaddadcdbabccdbadbdaaabbdcadcdcadababbbadddcddabdbdaababbdacbcacbccdacabbbaabccbabdddccaacbabaddcdcbadbbcaaacaccbcdddcbaabdbdaddaccbdcdacbdcaacbbddacadddbcdaddbaadbcaccdaacbbabbaaaabddddacdcddaaccaadccbdbcaaccacadbdcadcddcbcacadbcbccaaaadaaacdcccccaadbdbbbdbdbdbaabdbbdddcadcddacdddcbbcdbccdacdcdbdaabadaaacdacaaccbcabcdccddbadbcbdbbcbdbabdbccacaababbaaadacbdabbbbcaddcababadaabdddbabbdccadacbcdadbccdacdbcdcbdbcdacbcaacaaabcabaacddacaaaccbdbcdaabdccbbdcabaaabbdbbaabbadbacdacacbcdddacdacdcaaaabbacbddcdadbadbaaacaadbcbdbbdbdbbbadcccacccadadabbbacaabbddcbbcdabcabdbddcdccabccbaccabdacaadaabaadabdadccbccdadccaabbdbadbcccdbbddbaaacadaaccbdadcccbcaadbaabdbdcabccdccbdcacaadcdaddaadddaadaddcdaaabdbccacabaadbccdcbcabaaabbdccbdacdbccbabacccdbdaccbdbaacbbcbbbccdcadbbacaccbddbddbcabcbdacabcbbbabccccbcabdbddcacdddbcbdaabdaadcadcbcabddadcacacbbadcddcadbdabaaabbacbadcbcccccdcabdccbaadcbbdcaabbbbadaddddbcabbccdbdccabcdbbaadccbaabdcacbabccbcacdbacbcacdadbdaabcabddadddcddbabdddcaddaacabcabdcbbccdbdbbbbcacaaababadcdbbcabdaccacdacbacaacdbababdcbcdbdcbdaccdabddbcddbcbcbbbdcacabababbcbbcaadddbdadbdbcdcbacadddacbdbbaddbabcbccbcabddaadabadccbcaabcaccbccdacaaadbdccbbabbbcbaddbdbbdbaccabcddbccbdadcaadcddddccdbdbcbbaddaaacbbbbbadabbddcdbababbdccddccdbbddcdbbddddadacacbdcbdcdddcabccbdadccbcbbcddadacaddbdaabccacacdaddccbbdacdadcaadcccaabadabbabddaddadcaaaacbcaccbbddcaccbcddbabcaddcaacccabacabacdcaaddcacbcadcbccdccbcadbccaadcbbddcaacdbddaacdabbbdddaaaabaabdaabdbbadcdcadbbbacdbbaaadccbdddbaacbbdbbdcabaacacdaaaaaadddcabbbcbcdcabbabcabbcbbcbcbcbcababdddbcabadadcbacabbbdccacabdbacdabcabccbcccbacbaaddabccacddcbabdccadccbadbddcacbbbcbccbdbddbdbabacbccdadaccbbbdcabcddbbbaddcdacaacdccbdbcccacdbcbbaccacdabbbcdcddaabcbdbacbcbcbbccdcabadaddbabdccbaabcdaaaccdcbbdaddddbcbabadccbdbcaddccadcbcccaaaaaabcabcdbbacbcbaabcbadcbccdcbcaabcbccbabbcdadbbaacaaaadcdccbbadcbcdaaacdcaabcdbabababcaacbaaaaacacaacccdbdbbdabddbbbbaacdaacacabcabcddadcdcaadacbbbbbbcdbdbaccddcadccaccaacdbacbcabbcdbbaabaabddccdabacdbacbadaccadcabdabbcbacbbbddbbaacccdbcaadabcdabbbacdbbbacccdbbdbcbcdacdcbccaccbaaccdbbdbdaccabadccbbdcacddcdcacacbbdcabdabaacabbddbcbaabddaddbabcbbabbbdaabbbabdabaacbbcdbadadbdccabcdaacaccdabadbcbbaaabdcbbddcccadbddbdabccdadcddabdbacbcccbcbcaaddbacdcdabcbdccddcdbbbddbdbabdcdbbdabddabdcdaadacdcabbbadabadcccabccaadcbdbacdadadaadabbddbaaccdacddaadbadaabbabadabacddabadbcbddddbbdaabbcccaacddabcbbcbddbcacbacaacbabababdbacaabadacaccaddcacbbacabadaddabadadbcabccdcdaddcacdcddbacacdbdcdacacdccbaddacabdccacdcaaaadccbababdbbbddcabacdbaaacdbccdadcabddbccbcadcdaabbcddabcdcaaccdddcaddaaababcdacabaddbcbbcabbadabccdadaccabdcabdaddddabcbdaaacbcdbbbacbbddcabccbacdaacdbacddbabdabcdbcccacadbbdacacbadacbdcdbcdadaacbbcabbbcbbbadbbabbaaddcbdccbacdbbddcaacaacbcacdbaaaaacbdaadcbbdcccddbdcdbcacdadbdbabbbdabaababaaadcbcccbdbadcdaaaaaaddbcaabddcbdcaccbccddaaaddbabadddabbbdddcbdadabbaacbabaabbbddaacaabdcabcbdbcbdbacbadcbdaddacbcccdabddbbbcdcbcadbddabdcdadbadadcbccaddcddadbbabdbcbcaabdadabcdbdcdddacdaadacaddacdbcdcbccbbccdbadbbbacadbabcbabdbabcadaddaabadbbbbdaaaacbbbdccabdcbbbdbbdddddadadbccdcadbdacbbaadcabddcdaccbbaacabcbbdabddbbbadbacbabbbcccaddaaccbccdaddcdbbcabcdcbcdaaabbabdaabddcacdcbabdaaacaacadcdcdaaacadcbcbcdccbcaddbacddadbdbacbdacdcbddbdbbaaacbabbddccbdcddadddbbacbcdbdadaadddbadadbdabdaacdccbbbbcdacbbbbbdbadcbddadaabbddbddcbccdaaccaabdabcbcacdcbbdbcdaccbadcabaabcbcaccdcdcbdbcbdacbbaddacaaddadbccbbdcdbaadcacbbbdaabbcacdbbcdddabdccaababbcbdbcccaccabadddccdccbdbdbcabbbcddccdcbcbdbbddbaddacbdaddddbbbaaccbdcccddbcaddbbacabdbaccabbdcaaacaddbbacbabddabbabcddaabdacddadaaabcccbbcbccddcbbbbccadaaacbabdcabcdcadadcabbdcdbcdcdaacccbbaadbbbaabcdacdbbacddbbaccadbcbddcdadcaadcaaccddaddcbdcaacaaadaabcccbcadddcadbdcbbbbbbabacabcdabacbabccdcaaaccbacadcbbbaaddcdbaccdcbcaddcbdcbcdabdcbcbdcbbccccabcbdcaadacbbbcdbadbdabbbbacdacdccbbdcbbcadbcdbdcdbdadbbdacaacabaddbbdaaabbdcdaaadadcdcdbcdcacddacacddcdccbbdabaacadbdbdbacbccaaadcbcdccadabdcaaabacbcbabddbaccccddabccbdcddbcdacabccddacdbdddddcadcbacbacabbdaacdbdddbbacccdbcccdbcacdcacabbcdbcdccccdcccabdbccadcdabbdbdaacabcacdadaacbbabbdadcadbbbcacbcddaccabacbbbbadbabbdcddacbbbbdccdcbaaadccbbcbbaddbabdadbcabcabadcacbccbcdddaabdbacdabbcaadccbcaccbbcacdbbdadcbcbacbccccadacccccaddccbbcccbbcdabcaabdadcbcbabcddacaadacbddbadaadbadcdadcbdbaadbccbddcddcdcdcadbdcccabbccacdccacbabbadbddccbcabdabbbcdbbcddccadbaaddacbbbaaddddbcdadcaadaaacdcabbbacbbcdcacdcadbabacabaddbcdcccdbabaadcbbdbbbddcccbbbbcdcbaccdbbcabbcddccddcaabdabdacbadbbdcdadacbddcbadcbcbddbbbcdbadacccbaacbdbdbcdadaabdcadaadaccbdcddabdadddddaccacdcdaabcbdddddbcbdacbbabbdcaddcadcbdabaccaaccbdcbaabcbcbcdccdccbabcabbbddcbbddcaddcabddcaddbadabaacbdabadaaaabbbbacbbabbadddcbddbaccbaadadcaadcaabccaaadcdabaaabbdccdbbcccdbacbbdadabbbbcaaabdaaabbacaaacbaaaadcbcbbcbdabacdabbabdcbdcdaaccacbcacbcadcbccaabcaddbcbbdccdbcccadcbcaacddbbcccabbccacdacbaadaacdbbababacbaddcdbcddcbcbbbccdbccaddaadbcbdbdadccddbbaaaccddddbbdbdcbabdcbacaadaaabdbcadaccdadcaaaccadacbaabbdbcaababdaacdbaacdaabcadabacdbdabaddcababbcccdccaaddccaaaacdbdbacaaadacbcccbbdaccbaacddcbbaadbdacbbdbbbacbbdacabbcaaaacdcdbaccdbaacadbccbdabaddadccbcbddaadcdcdcbbadcdabcbddbacbbdcadddcdacdbdabbcdbadcacbddcbbdaaadbaddbcabccbaacacdaacabddbccbbdbccbcbbbdabaddabccaddadadbacbaadbdabdbdaddaaabbcabaabcbcaadcbdcbccaabcbcdacbddbaacccdbabacabcdaadcabcdcdbcbcabaccbbdbaaaccdcdacdacaaccbbabddbbccdbbccaaacdaaddbdabadbdabcabaabacdcacdcddcbadaabacaaadcddbbbadccbaccbcccbcabdddababbacadbddddaadddabdcbcdbcdcbbbdcdccccbacbcdbccaaccdddaadddcbacdbbaaaccdaacadbddacdcccadaddbcdbaddcababdbcdabccaaaddbabdddaccccabdbbaabbbbcacabccdcdddadcbbacccddcacacdabaabcbddbcbcbbbcacbddacadaddcaccdddcdbdabacadcbbdccddddcdccaaabaaaaaddcccbdcaacbbcccdcbacabbadcbabcbcddbbadcdbcdbbbacadcbbcacaabacaacbddcbbbadcbacadcccbacbdcbdbcdacadababcbcdadaaccaababaccaadddacccdbcdbacdbbbddccdcacdcadacbcbdcdacdcabddcdccbdababadbbacbbacccaaadbccaccbadcbdaccaaccddadbcaadbccccdcacdabcdadddacaccbbbdddccdbbddaadabdababadbcbdcaadaacbabbccdaaccccacabdcdabacaddadcbdacbcbdbdccaacaabbdddaadcddaccbabbbcddcbbdcdbdcbbdbddacdccbaaaccbccbdcaacaddabdddcccdbdbcbacbbbabbcbdbcbbaddccbdbbddabddcbabbbbbdabdacadcdddabbcaacdcbaaccbdcabadcdbbddabbddaaabdbacddcdcccccbacbddcbbddabbbbbbacccccdabccadacbbcccbdbcbddbbcccdcccbbdcabddacbdddcbadaadbbbbbabccbbdaddcbdbdcdbbaaddccccadabcdadddabddbabadbddcacddddccbddbdbaddccbcbbdbcbdccaccbdbacaccdcbbdaccabcdcbdaabbbaabbbbbdaccdaacccabadcbcbadaddbadccbcdbcdcbabcdaacbdaacdddcdbdbcbdbcdbacacabbbdaaadbddbadaaacdccccacaccddabdcacbdddbbdaadbcbdcbaabcccacbcddbcabdbbcccbcbabccacbbbcbdddbddaaabcdbdaaadbaabcdadaadacdbbbbcdaabdbabcbbaadabddbcdcdabcaddcdacbcabaacdadbadcddcdbcaaadcdbddcbabdbbbbaabababdadadcdadcdbcbaacaacdacbbbcaadcdbcbddbdaaabcbabbdacdcccaddacaaacabdbbddddbbcaccdbcbdababbaaaccccbcadddabccbcddadaacbcddbabbbaacdbaacddcacabdacacabcdcaabadbaaaacacccabcdabcddababccbccddccadcddbdbbcacabbddbadcbdddbbbbcacbcabcbddbcdbbadddcbaddcdddbdbddabccdcdbdccbbdabbababdaabaaddccbacbabcadcadcacaadcddccbacbcaabbbbaccdccdcacccbdddcaabcabaacbbcaaadbbddbcddcaacdbadbddcbacdddadbaccbaacbbbadbadcaacbadacadaabdddaccbacabdbabcabdbadcbbbdabdddaddcbdacbdcdacbdccdcdbcbcbadcbdbdbbacddcdbcbbcdbacaacdacdaddabbcabaacdacddaaabdccaccaddcbbcaaddcdacccdabacadbbdbdbcaddadbcbddcddbaabaaaacaddcbaaaacadcbcacdcdbbabaccadbcacdcdcbcacbcbdccacbdcdabbbbdbaddcaacaabbaccbabbaddbccaacbdbacdcbacabaaddbacdbacbdaabacdcbcbbdcdaadbcbbabcabbbacbacbdddbbccdaabcbbdbdddcdcbbbbbbaabcaaddbccacbcdcaabbcacadbcbabbbcdcabdbbcddbbdaddababaabbdddddbbacdadbbbdbcabccbdcbcbcdabcccaadabcddaddbdabaacacacacccaaddacdbcdadccacbacbcabddbccaaaadabacabaccdaacbaaabdaabacddcbabcccbbdabcbbaabbdadbcdcadccaacaaabdbbdbdabaadbbcadccbcbcaddbccabbdbdbcdadbaaadbbdbbbacbcbbbaccadcdaadadccdbaadbbcdaadbaaaccabacbdadcadcddcdcbbccbccabdaaaabbcacdccbcbcbcdabddcabbbddbcbacabcdadbdbdbabdabbbdacadabdacdddcbbaccadcbaddbdddadbddddbdcdcdddababbdddddadbcdbcccdcaacdacbbdbbcbaadaddaadddbbddabccbcbddcacdccbbbddaccbbdaaacdcdbcbabdbdacdbdadbbccdacabdacddccbaabcdbccbadadbdcacdbadbdbdcbdcdbabbbdbacabcbbbadddcbdbabdbdbbbbadbaadadaabaadbaddbaabccdbcdccddcbacdaaddadbdbbcbcaddcbddbccadaadddcdbcaaddaccdcabdabddcabbbbaddccacddcaabcbbcbcccabddacbdaabbababbbaadddcacaccabcbdccbdabcdaaaddcacbddacaabdddacbcdccbabcdcdddddbddbcdcbabdbcbaacbbbcadaaaabacacbccbbdbbcbdbcbdbbdcdcbccbbbcaccbdacdbcaccacdbcdcacccbdbbacccaaabbbacccabbaddbdcababbcbadccccbbcaacbddccaaabdaccbadcddbdbadcbacbcaaaabdcacacadbdbdabaadaadbdabacddcdccddcaaddcdaadcbcbaccbcdbbbbcbbdacacadcbccbdaabbdcacdbbbcdddccccadbdabcadcabddaaacadaaadbdacbbccbbbabcbbccbdcbdccdcdcdccdcdccacdddcadadbcbcbdacadaaacccbcaaddbaddaabbddacacadbdcbdbadcccddadcccaabddbbddabbdaadaaabcbbcbcaddcbaadaccaaacadccaadbcababbdadbbbcbaabbdbcdbadbddcccbdababdaaadcdcdadaddabbddcdbdaccadabccbcaaccacccdacabaccaccddbaadcbaabbcdacbbadbdcadbbaddaabbcdbbdbaabbdbcbbdbcbbdbbbcccddbbbdbacdcadcabdbaadcbbddbdaacddcccabcaccbabdcbacbddadcbbcababdabbdaccbbcaaabdaaacacabddccdcadacdabcdbbdbccdddcbdabbcdaacbbadbabaacccdbddaacccccbbbbddcbccdcacdbbccbaddacaaaabdabadabbaaabdabbdbbdcaaabcdabddabcbaacaccbcacbcacaccdddadcbdcabdccdcddccabbdbbbcacacaddbddaccddcbccdadbabacaccbcbbdcaacddabddaabdcabbaccdaadcabcacdabbaabdcdcdcadcadccaacdcadcbddcdabaabaacdacdddddbbbdcdcdccbcccbddaacdbcccbdbcbaacdaddbbccccabdcddcddadabbddabaaddcdbdacdcbdbbadcbdcaabaadaacbcacbacacbccbaddbcccbcaabdacdbadabbcbbcaddcbabbadcaabadccbcbaaccdbbbbdadacdaccdabdcabbbdbabaddcccddbbcdabcbaadbddccadbdcbbdbccdccbbdcdcdcaabdabdcdccabcccabadbcdabddadacdddaabbccbbcbcbbabcaabaadabcbabcbaacbbdbcabaccdaccccccadbcaddbddbcbbdbacdaacbcdacaabcdbadddbcbdadaaccddddbaddadcccbccccabbdcaadcdbabbccccadbcdccbacdcadbacbdadccbcdabdcddbabbbadbddabcdaabccdbccdacbdbcaaadcccbaabcadbbcddddaaaabbddaaaabdadbaabccccccaadcabbdbddbccadbdbcbbdbcccbdcdcbcdbbdcaaadcaabcadbdbaabaaccadcdddcbccacdabbcdcdcdddacaabcabdaacbaabaadadcdcabdbbbbadbbddaacdbdabaaabbdaadcdaabdcddbbdccdccbccababbcdbbbaaddccabbcaabaccdbbdbcadacdbbcdbcbadcbacaabcddcdcacbdcabbabbbdacaddccdbbdaddcdadaacccddccbcaaddccadadabdbdbdbdbdbdcdcbbddbbbcaccadbbaacabcdbbabaddabcabdbbbdbbcccbaddcbadbcbddbdacacdbabddccbdaadccbcdbccabdabdacdcbcdbbdccdacbcdadabbabbaabacacccdacdcbaaabcccbbddbcbbbdaccbbddadaccbdcbacdcdaccabaaabdbabcbcaabdadbddbbbacaccccbdacadabbbcdaabacdcaadabcbbdaadcacddcbacaaabcdabcbaadabddacabdacdabccddbcadabddcababdbcddaaabbcbbcdbdbaddddbbbcdaccadcdaaaccdbcddccacdbacdadccacababaabcaaabcacadacbaccbbcdbccabacccdddaaddbcaabbcdbadcaacdcdbbbdcdcadcaccaddcbabcddabdbdbaacdacdadcdabbddccdbbcccaadabdbbdacbcdcabcbdaaccdbddabdcdcbbabacabcdcaaccbbdcdbbadcadcadbabdbdaccdbddabcccadcacbbdbcdddaacdababcbbdabadbdacdddcbccbbbacdccdbdcbabbabaaadadbddabadadaddcbccadcaabdadacadcababcaabddcadcaababcdcdacabbdacccabcbbadaababccddcbdbaacddbdbcaacdbcbacbdcdcadcadccabbccaaaacacccdabadbaadbbbccbdabdccbcddcadccaaaaccaaddacbbccbdaccbbdcdababcabadababababbaddcbdcabdadbdccdbcdbbdbbdadcdbccbdadddaaccacbddddbccbdbbcccbcbadaaabaaccdabcbacbbadadcbabaadbcccbbcdcbacadadbcdddcbccbdbaddccddacabcbbccbbbbbdacbabdbdaccdbbdcacbdbcadbbcbdaccaadaaadacbcbdcabdbddacbdbabcaadccdcdcbabacbacdbdbdcdaaadccbbacdabdcbddcdcbcacaccadbdbdcabddabbcacdccbcacadacdbdcadcadadcccbaadbacccbbcdadccbabdacbbccadbccbbdbcaaaacbdbacddadbdcbbaababdddbcbdcdaabbadbcabdbaaaddbbadcdaadbcbdcaadadcbbacacbdadbaabdaabbcdabcdabddaccbcacbaddcbbbabbdaaabdbadcbcbcbbbbcdbcdcbccbcdbbcacdabccabcbacaabaabaadccbbccdbdbdcdbbbcdadbbbccdcbbbacbaccbcacbabbacdcbbbbdbbccdacaccaaadbdbdbacdbdccaddaccaddcdbdbcacddbacdaddcaaacdbdabcabdcbcabcbddddcbcdadbabbdabcbabcaaadbbddcdbcdcaccdabacbbaddcacddadcaabcdcabdaacacbaaaacbadaaaddbbcccaddccdcbadbaabadabdcdbacdacacacdadabaccbdaaccaccdccdcbcaccaabadcaacdabddddbaacbbbccbadcbadabdcbdbdadbbaacacdccdabdaadcdcbbbaabccccabcdadbdadbdccaccbddacdbcbaddcabadabaacbabacdbbcddaaaadaddccbbcdaabcbbbcdcdcababcdaaddcadbdacaaadccabcbbbccbbacddbbddbbbbbbcbadbabaddadccbabbdadcacaccbacadbaaaddabdddbaadddcddacddbaddbbaddbbbdcdbacccdccccddbdadcbbbcbcbbdabdbbbabccbadbbddcbbaaabbcadaabdbaacbbccccbcadbaaabcaddbbddbdbbcdcbdaadabbccbdcdbcbdabdabcbdaaddadddbcacccdbacaaaaaabadbccababbadddcdbccacdbadaccdccdaccaaddcdacadcacadbddcccababdabcbaccdacdbdbbcdbdbddbcbbcbdbadbbbdcbcdbadbcaadabadacbbbbaacbdbdcbcdccbdccbcccdaabdcdcdccdcbdbccbabdbbdbaaaabdccacbccabaddbacccbbcacaabbbbbbabdacdbbbcdddaaaabddbddaaabcadbddbbadbaccaccdaaabdcbcdcbaadbcdadccaabdbdddadbbccbddddadbdbdddccccbbaccbdcabbbacccdbbbddcabcdbcddbadadcbcbdbddbbcabbcbaabcbcccbdaaddcbbabaabacbcacbacbadbcbdccadaaabbdbabdbdaadcdbbacdbbdbdbdbccadacbbadcaaddbbcbcaaccccbadbcdccabdcdacdacbcadcccacbcacacccadbbcdaccdbbcaadcabcdbbdcaaabccdbdcadcadbaddbdbbcbbdabaadabcbabdabdaddbccdddaacabcdcdadcbbacdaccddbacaaacbcddcabdcddcbaababbbbddbabdccbbaacabcacbacbdadacadbbbacaabbdabcaadcdbacbbdacaaccdcbccddacbcbccababdcadbbdadbbccdbdbcdcbcbbbacddbacbbdaaacbdacbcbbdbbcdadbbdadddcacdbcaddbcacddcaccadbdbbdddcdcadbaaacbccbdbdcbbcdbddbacbaabdbcaabcdacabdbacbddcdbdbaabcbacdcdbabccbddbbacccdadbcdcabdcaddbacaddbacbadabccbbadbcdadbaababdddabbbbdddabccdacccdadbbdbbccbababaacacbccddbdabbcbcbbacbbdbacbcbddadabaadaabdbdacccabcbabbbabbbacabaadddcadabadaddbdaadcdaaddadbcdbbabaabcbacddddacabdddabbbabccdcdcadadddacaddcbcbbcbcadacdcbacdabdbbadcdbbaacdaddaaabdddddabddcbcaadbcccdcadcbabadddcabddccbdcaccccddaadbddadbcacadcccbdadbabadddcdcdbcadbbbcbdcbdccaabbacbadbccbddcbbcacbcdcdbbbbbdbabdcbbcbcabacdbcbaaddaddbdbbddcbadabddabcbcdaabbaccacacccbaabaaaadcbbcdcbcdddacdddbbccabbdbdbbabacadccbbdabbbdccbbddacadaadadddbcbbcbddbbccadcbbdcccabbdbdcdcdbddbcbdcdbbabadcccdadcddddaacbcbbccadaabcdbccdaddacaddcbccdcbcaadbabddcbcbacacdcabbcacbcbaadabbcbdbbccddbbdacdbabdbccbdccbaababcccbcddaabdadcdadaaacbcdcdbbcdacbddabcdbdacaadccaabcbcaacdabadbcadabccaabcdaddbdcbacddaddbdcbcacaadbaaacaabaadaaabdcbcacacadcaabadabcbdbcadbcbacdccdadadcabacbccdbbcadabbaaaabdddbbabccdbbccdabaabcaacdcddcaabbcdbbcacaacbacacccbdaddddabbdcdccdcbbadabacdabbdbcbadddcddbdcacbabbccabacdacdacabdddbcddabdaadbdbbbdcbcacaddadcdccdbbbdacbbdcddaabababadacaccbbaadcacaabbbcababbdcbdadacbcbaccadaadcdabdbdbaddacabbbadaabaccdbbaccdbbdbadbdacbbcadddbdcadbbaaacbcacccbbbbdaddcdcccdadcbabadacbcbcbddddcbdcbdbdbdabdaacaaadcaaaccbabdcbcbdbdbaaddcdaaabcddbacbcbbbaaccdbddcdaabbbacadbbcbaccbdaaddcadcacabbaccbaccdcdabcbaadcdcaacabaacbccabcaabbdabbcbbddacbdacacacbabdaadaaacbdbdcccdccdbabaacadcbddabacdcadcdccbdddbbdaadacabccbddcacabaadcddbbbdcdcaabdcbcaaaaaacbaaabbcbccccbbaabbdacdccbbaacdccaabacacadbcdadabdbcaacdcadbddbbabddddbacadaaccddadccdbadbdbdacdabdaaaddddbacadbddacbddcdddbaabcbabccaaccdbcbaccabdbdacaaddaacabddbadcdaabcdcdabddbddbdcbdaadbdbbadcdcaacbdccadcdaccdabbcadaabadcbbcdbbcbbcddabaadacdadcbddcabaacaaddbcacbcdcaabdacacacaacaadaadbdbaacbcdbbaaaddbdaabcdbaaabbcbabdbcbadbcbcbdccdcacabcbabdccadaddddcbbaddbccddabbcadcabaddadaaccdbdbcdcddbccbdccdabadbdabcabdabadcdaadbadbbdabcaddbaaccddbcaaaacdcddddbaadbcbbcbcbcbaadccdcddccabdcababaadbadbcdabcbdbbdacbbcbddbbcadaaaddaddbadabacddaacdbadaaaddabdbacccaddcadbbbcabccdcadcadddaaabcccdacbdaccdcbcdbbadbcbdbaccdddcabdaadccddcdcbdacccbabccbbbacdcbccaaaadabadabaaaccabbcaaaabcdddccabbaadddccddcbcacabbbdabbacdadcadabccccdaaaadbbbbcbadbbadaacaddbabbcdbaacddbbdaaccdddbaccbbcbacdacbdcdadabaababdccdadadcbaddcddbaacadbcdacaddabcacbdbbccaadbbabbbccbdaccabcbbacbdbcaadabbbcaaddbbbcabbdcbddcbacddadcccdbddacbbcdbacacacbdcdadaaaabbcaccbbbbbbcacccbdcaaccbabdacddcbcdbbaaaabbcbbbcdcabaccdcdadccacdbaaadbbbddaacacacbdabababadaabbbacbdccccabbcbddddcbcadadabcbcccdddbccbdaddbcdabadcadbcbdbaacbbbcacadaababadacbddabdaadaacadaadddbabcdcacadaabaddcbcaaddcacbbdbabdacdcaccadcdbacadacbcbcdadcbaaabaacdaccdbcddcddcacaccabaadcaaaddadcdaaaadbaccdcccbbdcbcdcbcaaccdadadbacdcdaacdabbcadcadadcbbdcacdbdbcadaaabbacdccbdcbbaccaadcccadcdababdabacdacbdaaaaadacdcadbdcdcdccccabaabacdbdbabbcbacbabddbcabcaccdbdbdacacacdbbdbaadaaddddcccddbbcbaccaaabacadbdddbaddbdaccabcabadaccbbcdcbccdabdddbcbabbbdbabdbbbbcdcdbcacdbbbbcbaabcadcabdccdbbddccbdaaadddaddbddaabadddacbbdcbcccdacddcccabdbbcbcabdbadcbdcbadcddddbbcddabbbcdbbcbcbabdcddcbcbbccbdacdccdccccddacaadddcbcbddbcdcaadacbcaaaddbcabbddcdbcddbcabdbccbddabbcbadbdabddaccaddcaddbccbbbbbababcabacdcbbbcabbccbadabdbdbaadaabdaddaaddbaccbbbccbdcacccaccaaacdcaaaacadccdcdddbddaacbdadddacbbcdcbbcbccbbccbaadccaddcbabcdcddabdaabbacdacbaadcadbcdbbabcbdadbdbabbaacbbccbaabcbbccdcbaaacacbbbcbcabdaabaccbcddbbddcbaaabaacabbbcadddbadbadacbdbbdccbcbbdbddbcabaddadcdabaddacabcccbcdccaadbaadbdcadadabcaaaadcabbababcabadcacdcdcbdcbccbcbbdbcdbaadbadaacddcdccadcaadccdccacddbbdcccdbbabcadcabaccadcdadabdbdadcdcccdbcacdbbcbccdaacccabbcbbabadaacccdcadacccaababaaddcabcbddadcadcabcbadabbdacadabbbccadacbdcdbbcacbdbbcccaaccaccaabcbbbbdbdabddaaaccbadbdaccddbaacdbddaabdabadcccdbdbdabcacabdbaccbddbdcaccbbdcabdacccadbdabdaddacbdaccdbbaddbbdcbbbcbdcbcbdadbbbdacaccbbdacccacdbadcbaccbadcdcabbbaadbbdbaacadcdaadbdbabdabccdccbaabaabdcbaaabbbdbdbbcddddaccbdabcaccbaddadbbdddbdcaaadadbbadaadaacabcaddaaabdcbccbabacbcdacdcbadbacdacccbabdbaadaabaacdbbbacdcddbbadadddadcdacddbabccdadabdcacabdbcccdacdbccdddbcbadabaaddbbbcbcbadbcbaadadbcdccbacbbdbdabadbbbaacdbbdcaccccdccdccacdbdbbcdddbbacaabcbbbbbccdddabcababdddadcadcabbdbcdadbbdababbaacdddacabdddcdacdbabaaaacadbddaddcbbdabbddaabdccdaddababbacaadbadaabddbcdbcdcacbabadbbaabadddcadccbbbbcbabdbcbabcaccdbabaddbccaadcbccdbdbbdbbdddbabcbcbadbdbabdddabbabcacbababbbbdcaaabcaddcbbacddcbacaacacabbbaddbaddcbdcddaadadbbbdaccdccdbbcbbdbaadbcbcaccabacaddabddacbcdcbdababdbaacdbbbaaddaacdababddbacadbddacadddcbdabddbccacbadccdabdbcababdbcbbdcbbccbcdcbabbdbcbbbacbcbdadbddaabbcdddcbbcdacadbadccdabacbdcdadcbaadbacbbcbdcaadbddaabdadbadabadcbcabcbabcbbcbaaadddabbdcdcbdddcdcddbcadddddcadcbadaccabababdbaddaccdbdabdcabacbdccadcddadbabcabcbabbdddcabaabbaddbcacbdcdcbacdccdcabbabdbbccdbdabcdabdcaccddaaccdcbadcdddbdabbdaaccadacaaadcdbaaadcacbabdadadaccdcabdabacbccdacddbccbcbdacaaaadabbcdbabbdcddbaadbccadabdadaabcbcdaddcaabbacdaacdbdacccdabddaaaaacbdcbcccdbabbadcbaabddddacacbacddbbdacaaccbbdcbabacbbaaddaaadbcddadbbdabcbaaaacdbcbdaaacaaaabaccbcbbbbabbaaacdddbbabddbadcacadadbcabccbcccbcbbbabcddbdabcbcabcbaadbbabadbcdcdddddaaacdcdbcabcaabbaadbadbdaddadcabcdcbbabadcddccadbbaddaccabddcddaccdadbaadabaadbdacabbdbbabcbaddadacbcccbbcdcdacdacdbabdbcacdbadadbcadcdbbbddbccacadabdadbbcdabcccdaccdadccbddbcddcaccaaabbdcaabcbcdbcddcbdcdbcabbcbaaddccaabacdcaddbdcddaaccabcbadcabbcaddcbcddcddadcbbbcaabbcacaabadbbabaadbacadcaaadbbadbdabadbadaacabddbbdbcdbcdabacadcbcbacaddddcbbccdabacbacdbbaacddbacbadbacacdcbaaccdcdcadbccaddcaccaaabdcccddcbabdbcccbcbbcdbdbbbdcaadcbdcbbbbddccdcabcdaaaacadbabbadabdabdcdddcdadadacdaddadbadbaaababbaaabccabbbccbcbbbbddadabddbbbaacacbadbdbdcaddaaadbcbccadaccbcaabbacabddbacacbaacbaadbbbcdabadbcbdaccbdddaacdbdbacccbdbbddcababcabddddcdacbacccdabcdcabbbaddacdbcdaaaddadaaaabbddadcbacabdbaaabaccbddadadbaaadadbbcdccacdadbcccbddcccadacadacaddbbabdcddddcaabbcdaccddbacdddaddbdcbdbabdacccbbccbababadddacdbabdbaddacacccdaadbdabdaaabbdabdbabcabadbcbbccbbdbbcadcbacbcdbdaacddbbdcdabacacbcdcacacdabbbdbbdbaabbcbbbdcccaccabadacdccdabbdcdccccaabbddcdabdabddccadcdbbaadadddabdabcbbccbccbccdcddccccabdaabcdddaabbcadbbbaaaacdbbcbaaadbcacdbdbdabcbdcadaccdababcbabbddcaaabcdccbcccdcbcacbababcbdcddcbdbbbacdabaaaadbbcadbbcbaabaccdccaaccbbbbabbdadcbdddbcddaacddbcddacccdadbcdbbacdcacbaadacdbddcdcacdbcccabccaabdadcbaaacabbdbbdbcdadaaaddcbddbccbbbcccdcdadccbbcbbabbbbdcaddcaabcdbbcbccbccdbbcbcaabddbcdcdbadddbcbdbddabaabababbdcdcddcacbaadbccdcababadacaacdcbcacbbdcddbcdaddabadbcacacddbcadaccaccdabdbacbdbaacbccbdbbdccdccaddccbcdadbacccbbcadacbbbcdabdcadbbcaadbaacccbbaccdbdbbabacddbacdccaabaacddbabbdddbdbbdbddaadccbddabcdacdbcbdadbbccbabbbaabcdacbbbbbabcbacdbbbdccdbcacbbcdaaacccdccbcadabddbccbbababcaddddbddaacdcbdbccbcbbbccbddbcbbaabbccbacbbccccacbadcccccbccccbaabdadabdadbbcaaaccdcdaabccddbabbabdddabbcdcbaaaacbccbaabaabbbacacbbbbcbdbbddcdaaacaaadadaaddccadaccccdcabacccbaacddacdcbcbdacaaaddcdcdbdbcbaabbacadbddcdccdabdcdbcccaaddaccbdddcabcaabcbdbbbccdcbabcccbdacacaadbcddacbdbdabadbaadacabaaadaabddcabababaccaaadbdadbcccababbacccaaabcaaadcababadbccaacdbdcdbdbddcbddbccaaaccbcacccacdcdcbccdcacdddadcdaaddabbbbdbbadbadaabcabcbcadbddbdbaadadcbbcdbabdaaadccabacbadbcbcbbbacbacdaddbdabbbabcaddabaddbbccccddcdbbccdbacbdabdaacbacdbccdaaddccacddadabaadaacbbcddcbbbbddcbbddacaaadcddccbaccdbacdaaddbddacbcbbddbaabaacbdcabdadaabccbbcccadbbcabcbdcdcdadbababccbaddabaaaddbaccdaaabadccdadbcabbdaaaccdcccccbcccacbbccbdddbaccdbacdbaddbcbabcdcdaccdcbccacabbdadcadbabbdabbaaddaadbaabdaadbcaadbccaccccabcabbabcddcbbcabdaadcdbbdcbacadbcaaacacdaabbddcddbacbaaacaaaaccbabbdadcacbcdabbadbcbdbddaaccbccbdbcbddabbabddaccbaddbbadcddcccdbcbdcccbdbaccbddbbbcdcccbdcbcccccacbacaccbacdccddcbabddcdbbadcaadadbacdccddbcabaacbbaabcddaaabbadababdaabdccdcbacccdaadcacdbdacbcadaabbdcbcbbdddcadbccbdaacdbdbaddaabddbbccdddadbbaaacdcdddcbbccdbdddaddaccaddbcdddaabdcdbabbcdcaacccaccccaaaaaabcbcabadcbccacdcbbaaddabdcbabdababcacbbabbbddbdacdbaaabccddccddcdabbdcbdbdbccabccddabacbcaddcbadaabaaadbddaacadccadcbbacaccbccabacbbcacbcbdccdaadabbadbdcaabdabcdbccdcadbbbabdbadcbdcbcdacddbddcadaaabdddbbdcabdbbdbcddadcabbddcadddbaadcbcbbccdbbcaccbabdbacbddbacaadcbccccadbddaaccdcbddabaacdbccddbaacacccaadbdbdbdcdddbaadcababbacbddcbdabadabdcaaccbacddcbabbccabdddccadcccdbbccbabdbcaaaacdcdbccaccbdbbbaddcdaaddbcbdaaaaabacaaabbddcdadbdabbcbaabdaadcccccdbdbaddcdacaaadaacbbcbdbadcbddadbcbadadcabdadacccdabcddbdbccdbbcabbabcbbdaacdadbbbacabcbcccbdbdbdbcbaaddaadacccdaabdcdbdabddcbbcdbccdddcbccbbddcacdbabaddcddabbbacccbbabdcdccadbabdbcddcbacdbbdcdadbddbdccbccabbdadcdcbbcbadbcaaddadabccbaabcacabdccbcbbdcacdbbcbdabdcdcbcddbdcccddaacdcbbaaaaadbabacbcbdbbbdabddadbcccdacccbdccbacddccaddcadbadbabdbdccbbacaacddbcddbbcddcdadabbdbbcaacddacccaaccbdddcaccbbbbcddaddccdbbdaccbadbadbcddcddbddbbccbdaadbcbaaaccbcbbbccbcacdbddcabbdcdadabbbcbcabbdcdbabcaddaabdbdadadbbdcbaadcdddbaacacbabcdcbbdddabdbbccbaaaccbbdbdcadcacdcabdddabcdcddaaddcccabdbcaddadcdbbbbcdcabdbcacaddcaaadaddbdccbdcdaaddbacdbacaacaabdcaaaddcbcabaabdcbcccdacbdcddbdbbcbcbcaddbabccadcacccdbbbccddddabadbaadbabbadbcbabcddacacbaaaddcbabcdadcbcdccabaaaacabdcbdacbbbcadbaacdadcdcbcbabddadbcaaaccbbaddcdcdbbdddabbdbbbabbdadacacbbcdbcbddcbcdbabdcbbcdaabbacacbaddbdccbcbcdacccaabbddacbaddabdbdddacadabbcbbabbccbbbdaacdabcbbbdbabbacdbccadcdbabbabcddcbcdbacacddaaaababcccadcddcdbdbaccdbddbcdbabbadccdbacacacaabbccdbbbbbddbabcaddbbdddacbabcdccbaadccbacccbddcacaabbadcabdbbabcaddbabaccddaccadddabcdbcaddcdccbaabaadddbcaacddcccacaadbcbdaaddadcbacbcdcbaccdbbabdbaaccadcccacadccabdbcbcaccadaabbbdadbaabcbaaaabbbdcabdbddacababdabdaabcadbcaabccabbdadacbdccadbbdbaccbacadacdcdbcdadbccbacddbaddbabadabaacdabadbbadcdbdcbabccbdddbcaaaaddadccccdadcdbdcadacbabaacddcabcaaaddabdaaadababadabddbcdbcdadbddddddbaacaacdcbccdaddacdacddddbdbabdadccaaacdaddccdaaaadcabbdbccadbcbadaaaaabcabcbcccbcaacadadcdcabbcdcdaaaaccdcbbbbabccccdccddddbaccccabbcaaddccbcbcaccdddacacdacacbabbacbdcddbccbdabbdadadadaabcdddadbabadcbddbbacbdacdccdbaaacdacbbbbdabdcdcbcddadadbaddcadabacccbccacddcbbbcbcdbbdbaacdcacccbacabaaaddbccaacdddccadccbaabcdabaacddcacaadcddccbabdbaabcadddbbcaadbcdcbdccdbcacdbaddbbbbcaacbbcdccccbadadacadcdadccdabbdacbdcdcbdacaabadcacaacbdcbcaaadacbccbaadbbdbabcdbadbbabbcaddcdbdcdabcadddbabdbcbaaaadcdaacdcbcdcbcbdacccadbdbabcbcbdcaabaaacbdddbbcbdabaccbaadaaaaadaadbcddcddcabcdacbabcbcbbadcdabcbdabaacabdabacabadddbcddcabdbbdbacbccdddbccbaddcccdbcddbcaaaccddbacdaddbdcdacdccaaaacbbbdbbbbcdabcaabaacbdabbbcbacaaaabaaabadaddcdbabcdcbaacacdbbddcaaacaacdaabcddddabbdcbdcdaccbcbddcabbbbacbcbccdcaccbabaaabbdcbdcbbccbcbcadadacadbcbacadadcacbabbacbdbadaacaabdabaaabddbabdabddcbbcaadcdbacaacdcabaadbadccbbbabddccdabdccbbcbbccacaabadaddabcadddbadaabdddbdabddadbcacbcabdccadaabcdbdccdbacddaaabbaadbbccbbdaabbacadbdbaabdcdbbdaccaadcdcbabcbdadbddccbcbbcabbcdaaacdacabdadddbddbbbaacdaaadbbaabdcacacbadadabbabcdcdbbbdabacbbbdcdcabadacabdbdcbbbdbcddcaccabadccbadadbcbdccbbabdddbabbbdaacdbccdbddaaadddabdbbbbacdcbacdaddddaccdcabcadccddbabbccbbdccbabcbccdcbcabcbadadaccbabbcacdaddabbbbcddadbbdbdddaaccdacbabbcaccdadbdbccdcdbbabadccbcccbbacddabcbdcdbcbcbabdcdddccdddacbaccaabcccacadadcbdbcacbabbdcddaaadccacabbbccddccadccacdaabbbabccccadbccddbdcbcdaddccdcbddaacabdaddabcccdabcbacdcaabdcbcdccbcdcabadcabccccaabbacdcabbbcabdacccadaccccdddcdbcabdbaacdaacbadadacbaabcacccbcbccddaccaadbbabaabaadcbaababcdbaaaddacbdcbcddacdcabcdccaadbacccabccaaddbdbbacadcbcbaccdcddadcdaabcaaadabdbaabcbcdcdaacbbacbdddcdcdddcdcabdbddbcabcadacccdaacbbcddddabdadddbcbbdcacbcccdbcbbddddaacdbdcccacdcddacabcccbdadbdbcbabcdcacababdadbdbbcbbcbdcdcdbbdcbcbcacabbbdbaacddacabbadbcabbadbdcadadbccdabbbcbacdadcaadcabcbadbdadbbccdbbabbabbcddbaaccabacccabaaabdbddccbbccaaabbddbbdbaacadddbdbbdcaddacdacdcdcabbabbbbcbbcbcbddccaddacacacbbcabddababddaaaacaccbbcdcccbbdddabcacdababbddddcacdabacdaaabbccbdbbbddbaabdbacbabdccdbabdccbacbacbacdabbdbddadcadabbbdbdaaadcdadbbccdddaabbbdacbabdccbcccbcbdaadcacaabacacadddbbaaddaccccbdbbbdcadabcddbcabbccaabbbcdcadacdbcbcabccadaabdaccaacbcbcdabacaccbcccbdddcddddcddaddddddcacbbacdcaadbaadcbdbaaccaaabccabcbbcdbccddcadcabdddababbbbbdbdcabcdaccbdacaaddcdabcdacadbcdcdddbddacccbbdcacbdddbbadaaaabbbddbcaadadcbddcbddcbdbdaabaadcdcdbbbdabaaacbabcccbabbaaddcbcbdccccbccddcccaabccccbcabdcabcacdaadacdbbbddbccaadcbbbabbdddabdcbabacdbccdddbabaacbbadbcdcdbbbcdcaaacaadbabcddddbccccbabbacccdbcbaabbccbacadacacaabdcdbdbabacaddcdbbdcbdddacbdbaadbdcaccccccbdaadbdabdacddadabbbacdcabcdbcddcaaabcdccaddaccbbdddccdddcadadabbcdbbbbbddcbbabccdbabbacbdbcbcdbabaccccabcdacbccccbdcaababdabdaabbbabcddccddccdabdbaaccbbdbdccbcabdcddddaaaacaaccaacadbdbbdadcbbababbadccbccddccdadbcbadabdabcbcaabcbcbccccbcaacbcddbdabadaabdcaacabacdbcadbaabccabcabdccbdddccdabbdaabbababaabadacdbdbacaaddabdbaddcdccbcaadcbccbbcbcabbdbaddaddbdcbbbbcbbabbbbcabdbddacacbbbcccadacdacddababdccdddddadadbbacbcaccadbaaacaaccadcabaacdccbaddbcdcacdcbabaaacdbaccbdbabdbdbdacdbbadcbabdbcdcbbacbadbbcdaabadaadbddabdddbccdbcbcccaaabdadbdadcabdccddcbcdcbdcdbcaabbbbacbcdddcddcbccbccdcddacaadbdbabacadbddacddacdaaccaaadbbabddbbcabcdbbccdaabbdacdcabbdacbbbbbdbdccdcacdcaadaabaadcadddbcadcbbcbbbdbddccadacdccdcabbcacacdaadbbbbcdbccdbaadabbdbdcdddbddcdbcbadbadbdacacabbccbcddcabcdaacdbbbabcacbacabbbddbbbcdbddccbdaabbacabaccdbbdcacbdbaccaabbabcaccccdbadddbabcaacdabbbdcdddaaccabbadbccbbbcbdcddbcbadddaaaabcdddccdbaadcbdaaabbdacaddcddccabcdbbacbcbcdaaccbbbbcadccdadaaacdcbbaaacdcccbbbcbaabaddabacbdadbbccacbcaddbcabcddbcdddcbcacbbddddabbaccadbabbabadabbdddadaabddaadbaddadcbababaddabbdbdbabbbbbdbddacbcbbcdabcddbacabcadcdbbbcbadacbaadacddbdbbdcdbbdadcddcccdbbcccdcddbdddcdbcacadaadcddbdcaacbcbaaadbadbabccaacadcdccbcadadcaddbcdcccccdddcdbcaddbdbbaaccbaccbcadaadcccabbcdbcdbcbddbbcabccdccbbbdbbaadadabaadaaaabdbaadcaaacccdcdbcaccdddddbddadbdddababdaabaabdabbcdabaaaadccccdcbcacddcaadbccbdddcaaadacddbcadacbcbcdaababbccdccdcbaddcbadcabdbaacbaaaaddadabdbcbbbbaaacaababdcbdababbdbccdddcbaadcaacadaccdacbbabbdccbddbbabddcbddadcbbacabddcbdcdcbdaaadabbdbbbdddcbcacbcdbbdbccdcbbdccaacacddddaaaacdabdddbaddcdddcdcdadaaabdabbdbadababbaacbcbadadcdcacbdbddbaacbbbbaadbdabbdbdcbbcadcddabdaabcdbcdbcaccdbdcddbcccdbbbaacbaacbdddbcbabbbadbcbadddbddcbabdbadbadcccabccdddbdbcbdccdacbabaababbadcdadbadaaccdacdbddbdbccabcbcabdabdcbcbcddcadbbbbccbbdbacddaabacdccaacadccabadcbbdaddbdcbddadacccbdcbbbbbcdbacadadabbddbbbdddbcdaddabddaaabccbaabcbcbbbdaaadbbcbadcbccbdbcccabbbccacbbbabaaabacaccdaaacadaabdbdabdbbbbbadbddcbcdbcaccbdabcabadbacbaadadcbbbbcacaaadaaadbddcddccdcdcbbddaaaddadaacaadbddcbaacacbdbddaacdcdccdabdcaabadbaaacbabbbdbadddbcaaacaabaabbbcddbacaaccaddbaaccbcacaddccdcccbacbdbabbcaaabccccbacbcbbacbccccdcadccbaccbcababacdbabdbbadcaadaddcccadcbcbbddaddadbdddaabadbacdacdcbbbbddabbdbbcbaddccbcacbcbaccccbcbcadaabbadcbbdbbadddabcdbbbddcbcddcadacbcaaabdcaabbbcdcdddcabcdbcbdcaaabbaaabbcdcbcbcdbdbbaacaddacdcacbbbdbddccbcddacdbbabacbcabaccdbbbabdcaaabbcddddcaccacbbcabbbcddaabdadddccccdcccadcdbadaadbbaccadcddabbbabacadccbaaaccabbabcacacbadbacdbbbcacabccdcdcaacabaacdcbcccabcadbbdaabbcabaabcbbaccbbadcdbcbcacccaddbbacbcadaadbccccddaaaabcbaadbdbaacbbcbdcacabdcccccccabdcdacbdcababdcabcaabacbbbdccaadcbaccbdcbcbbbaddbcdbbdcaaaccbbbbddcddbabacaccaadbbcdcacbbccdabbdabacbacbcbaaacdcacaadbccbbbccbcbbdcbbbdccbbacbdcacdcaaccdacdcdcabbcadddcddbddcdcdadbccbcdaacbcbbdadcadbaadacbbdccacabdcabdbbaacdbbbcacccaddbddddacacabbacbadddabadaccadddbbcacabcbdcdbddbbdbbdddacdbacddaabbdadbdccdacacabdbaadcdbdcccdccacbcdcdabcdcdcbdaabcbaadaaabcdaabddbcbcadccbdbbadbcaabcbddccbaabdbacdcbbabcccacaccaacbacabdaabdcdddbdabdcabbdbdadabdbdcaddcdbdbbccdbbcddbcaabcacccdbbdaacccadbdaabddaabaacbacdcacaabbdacbacaadadcdddbcdbbdbcdcdbaaaabbdddbddacadcbcbabaaadcbbcdccdcccdabbabdadaaaacccbddadcadbbbaccdbbadacdcbddbacddbaaccbdcbcabbdcbadbabdacbabdaccbdcabbbcbcddddaccdcacabdcdcbbcacacadadaddbacadbadabaababdddadacdaaaacabcacdbcddcaccabbddddcdccbdcdcbaadbdabadbbaccbcabcbbdbdbdcdaaaccdcdddcbbacacdaadadaccdddabaddbcddabbbbcccabcdaccbbaadbbccaababbacacccabaccdaddccbabbcdccabcbabbabcdadcdcabababcabdcbdcbdaabcaccdadbaaddbbdcbabacbbbacdabccdacadaaadbbdbadccdbdbacaacbaacbdacbacabdaadbdccbadabbdaaddabdabbcabccabcabcdbbdadaccacdaddcbcddaccdbcaccbdacbbaaaaacccdccdcbdaaddcbbdacbcadacdaccadddccdbbcdaabcadacaacbbddabbacadbcdbbaadbbbcccbaadbbdbddacbccacaaaadcdcddbcdccaabcbaadcaaddaacabaccddddcddccbdcaaabccdaccadacabdabbbcabdbdcacabaabbbccbbcccabbadadaabcccadcacaddbccabdcacadbacdbacaabaabdccdadbddcabbccaabdabdcbaccbbdccbaaaacadcdbbcdbabdadadaacacccacdcbddaaccbccbabdbbabdaddcdbbcdcaadaabcbbccbddbdabdddabbadcaabdaaaaccccccbbaddbdbcdccaadcdaccacabcdbaddbdddbabababbabdabcaccbbbdacabadbacbdbacbccbbcacdabbaaaacbbbbdbdbddcaddabaacabdddacaccbcdaabbabcdacbdcbcbdcbadaaaadcbdaaaaadbddbadcbabbddbcbaddbbcbbcababcbddbbcdabcdcbcabddcbcddadddbadbcacaccbddddcbcdcbcdbbabbbbadcbcccabcdabdcadaaacabadbdcdcbacaacaccbabcbacaaacaaabbcbaccabadcbaadcaabacccbbcadccbddbcabbddaacdddbdbdcdbabbbcdddbabdddacbccbbddcdbdaccddbbabdcbddbddcbacaddadabcdbccacadddaacaaabbacaabddddbacbbcccaacdbbcabccbccdddbbbabcaccaabcdabcbdbbcdaaaabacabddcadbccbcbaacdcbdaadadbdcbadcabadaadbdbbbbccbdcbcaacadddcbadacaccbabbaddbdbdbbacbaabddccacdddcdcadbdacdaccbcacdaadcdaadcacdcbabdabbacabacacaacbbdbdcbaabbdaddaacabdddbdadabdadaddabacbbdaaabbcacdcbadccdaaadcbabdadcccacdaabadbadcbcaaabcbabdaaacbbcabaacdcabccbcdcadbcacbbcbbaacbbcacabdcabdbcaccabdabcdcccddcaccdbccacdbabadcbbbcdbddacbadcbbaccbcddabddadcccdcbacbaacbccaabbabbbaadabaddbcbabcadabdabccacdcbabdddcdcdbcdbbcbcdbacccbcdabbaabbddcdbacbabbdcdaaadbadcbaadcaaacbdaddcacbcdbdcaaacadacbababcdcadaccbbccddabccdbadaccbcacabdcdbcdacdcbdbcabcdddcbabbdcbdccccdbdbcadbdcdaccbbacababddcbaccdacbcdacddcdbbadcdabbaabcccbcaacdcbaaccddbddabaaaacdabccbbcbdacdadbbcdcdbcbdbadbbbcaaddbddaaadddadbbcbdacdcacacddadbbdbabbccdaacddbabaaccddbbdddbbbcdabbbacaadcaaadaccdadacdcadabcbacdaacddcbdcdbbdbcdcbdccbcbcdabcbcabcacbacbacbcaacacbaddbcdbdcbabdcacdbaacccdacccadbdcacaacdbbcddbcadcdbddcabaacadbbbccbbadaabababdbaccbadccacadadacbddbdbaadcbaaaaddbaccbbabbdcddabcdcccdcadcacddabaaadbbdcdddbcadbbbcacdddbbbdabbdddabababcdaaabbbdcabbbcabaadddaaddaccbcbcdadddacacbacabbaadaacbdacddaccbadabdbabaabccbabddcdbcbabcddacdcbaacdabbcadcbdcdcdbcadbaddadcbabdacdcabdbdbdbcabcdaadcadcbbbccadcccabcadbbbbacabdbdbbcdbacdcbadbbcdcdaaccacacbbbacbaccbcaddbddcaddddaabcbbadabbdcacbaaccbdabbaacdacacadaadbbcadaccacabbbddcbacadaadddbaddadcadbdbabdcadacadcdadccccadccbbddaadabdbcadbacaadaabddaacbdbaddcacbbadaabdbbabacbdcdcbbabaccccdbccadadcdaacbddadddbbdcadcbcbdbbdbdadbbbdddcaabbdadabdcaaacdbabdbbaccbdcbbdadadacbcdbdbddccaaaaaabdcacabcacddaadcccbaacbcbbadadaabbabcaddabacbdddcdcdbcddbadbbdcadcbcbbcbcacbbdadadcdabcddbcbbddbacdbacbdbccbdbbdbcdcbbaaabbcddbcbbbaabacbbbbddcacbdbbdadbdddaaabbcbdcaabccbbbabdacadbbadbdcdadcaabcaddcccdbccccaaddbddcdbdccabdbabccbcacaddcababcdccdcbcbaaccdacbcbcabccadbbcacdcdbdaddbbdbdcdbadccbcdddbacdcbccccbdadcaadbcdcbadaabdbadacddcbabbdbcaadcbacbabcaddcabbbddcadabcabaadacddcbcaaaabccaaccaacbddababacdcaaddcbadbcadbcaaaadbbcdacabdadadbabbbbbbbcbbcbcdacbcbdcaadbdbcabaadbdcabbaadbacbaaaaaacbbcccdddbaaacbaaacdcadaaddbdbddcdcddcaddaaaccbcdccabbcadbbacaddadbcaaacbdbadddccbacabadcdcbacccaadacddccbbabbacaddccccdabbbaacbabcadccbdcddbacdccbdbcbcdcbbabcccdcddadabacababdabbdcbcdacdcdabacbccbbacdddcabaadcbaacdaccccccbaaaaddcacdacbbcaccabacccccbbbacdbcbbbcbacbcabaadcbccdabcadddbbccccadabcdbacdbddddabbbddbbcabdbaaccbabcaaddbbdabccadbaadbdaacdcabdcccbcbdaaddbdaaaacdcddcbbcbbaaccacabbbcdccddcacddcccabdbabaccadddbddbaaaddbbddadccbdbaadddbababcbbbcdbcaadabddabccabcaaddacbacbdbabdacacbddccddbadcabaaddacdaacdacdcbccdbabdacccbccddcabcdaabdcbaaccdddabbdabadaaacabdabbdcccdabdcacbcabcdddcddaaabcbabadbbaccdcccdadabbccbadbaaadbacadbadcdbabcddbcdddacadcbdaccadddbbccdbccaacdccbabadabaaabdaaadcdbdbcdbcdbcacabcbdbcccaaccbdddaaabaabbaaabbcabdcbdabdbbccbbbaaaadbccbcdaadccbdcabbddbbdadbbaccbdbdcaaccdccdbccacccabcccbdaaddbdbaabbbacddbbabcdddcadbddcdccbbbadaacdacabdadccaadcdacdbcbcdacbaadccabddddbbcddaccaacccccdbddabadcbbaadbcaaabcbbcbadccdadaccbcbbabbdabaaadddaccabcddbadccaadaaabbcadaacaddabacdacbcdcaabccbddcaababbdabaaddadbcddaacdbaccbddaacbcabaaddabcbdaccbcadbdaaddbaabbadaacacdddbcbadbbdaaccbbadccbacdcabcabdabccbdcadbcddcddaaabaacdcabddcdcccccbbbbabbccbabdccabccabdccbcccacbbbbbdcdabcbccaaabaddbcbaccacdaaadcdadcdcdadccdcaccddcbbcadacacbccccdbbcbdadcccbaaacccaaaadbbadabdbaabaabccdbdddddacbccbbacdcdbdcddccaaaccdcbdabacaccccaadbbdabbbdcacdcccaadaabcbdccdbabbbcccacdadcbbdbcbbabcbdbbdcdcbcdbaaacdccacbdbdcbbcbadaccddccddbdcbbbcddababdcdccbcbdbaadcdcaaadbbadbdaccacbccbaabdbddbbbbdcadaadbbbdacbcdbcdadbcdddbabadddaacaababacbbbbdddacadabbacddddddbadbccddbdbddbadabcacdcbbbdabcbaabaabacbbbadddbdadcdcbbdcacaaacdbabbaccbaddbaabbdbbbcabcacadbbdbdcbddcdbbcabdbacbacacccdbdacaabcdccabcadabdbccaddacdbdbcccddcccadbabadbcbbbabbdaddadcaddcbabdbbdacbbacddacbabdddacdddadccdddadcabddddadacaaabbbabbcdcddbcbbabdbabccabbddaacaabbbcbdbacdbcabdacbadaadcbdcbadcdbcaacabcbaccbbacdbdbadabccbbccacbabcdabcabcadbccddbabcadaadcaaaaccabddcbcbdcadabbabdcbcbaaccdbddaaacbcbdadbcdcaccbbabadbdddacaaabcdadbacdddcabdbbbadcaacadbccbbadbdacbaaacddaccaacadcdabaabccbcbaaabccbabaccadacdaaaabcadabdacaaacbdbdbabbccbdabbbacdcaccddbddbbdbccbaddaaaaddcddcdcbbacccaaaddbcbcaaccdabaddacacdacbbbddacccdbacbdaacaccddcddbadcdadcadcdddddbbbcdddababcabdbddcadbaaddccaadbbaccaaaabadbacabadbacddbccaaacbbbccddcacbaaddbbadbbbdccbcbacdadacaccbbaadccaabdaadcdcccacacdaadaaaadddddadbbcadaaacbaccccccbdcbbbbbabcadbadbbbbbaaccabcbdcdcabbbbdbbadccdbacbdbbddaaacbcacbcabcaddcbbbddcaccdaccaccaabddabbbcaadcdaddcaadaadccbcaadaccaccccbacadbaaaadacbbadacadacbbddddbbabdcdddadddccbdadbacdbbcdddcababddadbbcaaabbdabaabaacbabadbcaddbccdbdadacddacccaadbaacddbdbabbbdddbdabacaaabaababbacbaddcadcbbdcbaacaababcacdbcccbacaabdbcbdbdcbcdabdbdacabcabcdacabbbdbdabadbbabdadbabbdddbbaadcbbccbaabbacabbdddcbdcddbccdbdbabcacdbddbbdbabaadcabaaaccbbcbadddcadbadaddcbcaabacbccdaadbcddaaabdbabbbcbccbcacdbddabcacbabbbbddcdaddbddababbcadbbbadbbaabbacacbacabddcdcadbcbadaabdcbbabdcbadbaddbcdcacababdcdaccdadbcddbcbbbabbaabcdcdcbbdabacbacadbbabadcacddabccddcbaaddccdacaddbcdccccbcddcbcbbbbababcddcbdcbbaccbcdbdddaaacaacdcdcddaccdccaccacbadadcaccdcaddcdabdaadccaccaacbbdabcbdbadbaabdbdcdddadaaddcadccbbdcbaaaabbcdbbddbadacbaabaaccbbdbcbaccccbcaaddacbadcbdcbbcbabbadcdcdcdcacddbbcddaadabbcbdadcbcbdbbdadadaabadbcbcbcdcdbbaaddbcbccabcacbbccddbacbddbbaadcadbcdaddcacddadcccdbbaaabdcbababbaaacdbdacdbbaccabcbdbcbacaddaddbcbcacabaabcdbadbcbaabbcaaddccabbacdcddbdbbcaaabaddcabcccdacaadcccdacbcabacabbbbddcddccabbccdccbcbbacbadadbaadabbbddaadbcbaabacabcabdaccbddcbcabddcdadabcbbbaadadaabcccbcaaabbdbbddaccbdcbcbdcbcdaaaadabbbabadabbaadbcabcbdadaacabbddbabbcdcdabcbdbbabaaddaacccddabdaaacbcbdbdddcdbdabcdbdbaabbbaaaabbdcaacdcaddadacababadbbdacbbcadcabdadbdabbcaabbdcbcdbbabbacbddabbcdababbacabbacaddabaaaabdaaadbcbcacbadbcbbaadbbdcdbcdddcaadbbabbccddddbaabcccbacdbbcabbabbbbbabdbdcdbddbdbacbccadaabadbacacbdbdbcdacddddcbacdbdadddbdcbddaccbccbbcdbababaaabdadbbdbbdddbdcbdacaaddacdaddcbcbbdbbcaaadcdbccaaccaadacddaaadddacbbadbbacaddcddbdabbddddcbcaccddcabdccbadcddcdccccdccabcdabddbaaccccaabdbaaccddadbcddcbccadbbcaddbdbdbdbccbcbabdadcdddbcbaddccddbabaaadbcccacbcbbdacaacacaccdcaacadcdddadaacadcbbbaacccbbacdacbabbdddbcccbcbaccadbdbbbabcbbacbaaabdacbdabcbacbaaaabaddacaaddbdcbdacdadcbbdababdabdbaacadaaddabccbabacdabdabaaadbdaaacabddabccdccabbdcaabacadddaadaccbcdadddbdbcbababdcbacbdcdaadcdbdcddadaccadbdaaddcbdccadbdbbdbaabdbdaabadabbbbbcbcacbbdacdcdbcbdcadbabbcaccbdbcdbcbcbaabbbabdbbaddcdbbaabddbacddcaaabbddadbabcadaadabcdcccdcacadcdacaacdbbcdcbccabadcbbbaadbdaacbbbaaabcddadddcacbcadabbddbbccdccdcccbcbcddcddbcbbacaadbacabdbbdcabcaaabcdbcbdcaadaddbbbbcaabdaaabdbdabdbcbbccdbaadadbccbccdccaacdccccdcdbabdaabddcbccddbbbdbbadcabcbdbdcbaaadcacddbbcabdadaacddcbbcdacabdbabdadbdbbdaadabdbcbabccbccbcdbbadcabaaaacaccbadadabdbdbdcdddcbcaaadaddbdabddccdcbdbcbbdcbcbacddccccbddbbbcabbadbabccadbcddcadcaababcaababdbcbdcdbcbbddabbaddcacdbaadbcbddaacdcaccdbdaadacbdcbcdabcbccabadccabadbccacadacdadcdaabcdaccccdaacdbcaccdaddbacadcbbddbdbdbcaacabbcbcccacbaaaabaaadbcbddcabcacddabdcbccabaadbcdaddcbcccabaacaddcbacdcdcbcbdccadbcddccdcdaadbcadaaacaabbdcccabcaaabdcbbbadbabaddcbddddaabdacbaddadabadddcdcacbbddbcdbcadaabbdbccdacdbaabdbcacddbdacbabcbdcacacbaabdccabdacbdcadcdbbbcccbbadbadcbaaccabddadbcbdbbdcadcbabdaadbbbbababcbaddcdddacbcbbcdabcdcddbadabdbbcbacdbacdcddcbcbdbabcbbbadbacadccdcacddcbaabbaacbbccddaddcabdcbcbbdbcbbcaaddaabdadbabbabcbccccadddadcccccdccddcbaccdbcddbcddccaddadccdbbadbdbbcaabadaaddcacddccbbbbdcbdbddcbdaccbadbabdacabaddaddabcdcdbdadbbbadbdccabaaadbbbdcabccbdbdbcbdcbdbbcbcadacbdcadcdaacdacddaddcabbbbddddbcadcdbdcccaaaaadcdcdaaabdcbaaaaaaaaabbaabdabadcdbaacddaddabcbdcaaacbacbaddbdcbadddddbbabcbdbaabbdbbacadaadcdcaaacdbacaacbdaadddcdaadbaaaccdcddccdaccdaaadabccbdbdbddacdbddcbaababcdcabcbbbbadcbcbdbdacccbcacccbdabacadbcddcdacacdacccdacdcccbadcacdbdbdccacdbcacbabcdbabcaddbdaddcacdcccabccabccbababbcabcbccbdcddcbbcbdadcccbdadadbaaccabdbcdbdacacabddbcdddadacdcadabcaaacabcdddadaddabdcbdaadcaadddcbbcdccabadabaacbbabbdbbadbcdaaabdcdcadcadcbabdbdacdacccdbdcaddbbdbbacbcbbcaababbacbbcabcdadcadabcaaacacbdccddabbbdcbdcbdbdbbcbabddbbaadddcacacdccddadcdacbbabbbabdcabddadcadabaacbdcccbddacdacdccdadcacbcbdcbcadcabbbccccbdccccbcadcaccaacadabdaddcdbcccddbbbcadbbbbcaaadaddddbaccacccaacdcccaadacddcaadabdbbadbccabbccbbddacbbccabdcdcdaccaaadcdaddddcadaacdddcbbdaadbaaadadabdbabbaacacddddadbcabcaaaaabdaacdbcacccabbaadbcdbdbacbbdcadaddadbaabbdcdcdaddccdbdadddcaaddcadabbdaddabbbdcaabbccdabaddcddbabbcdabdcccbbcabbaccbaaacdabbdbdcbdddacbabdaadaacdddbdababdccabadabdaabbccbbbbabaabcbdcabbaddadaaccdbadcaddadccdcaddacdcacadccdabdbdaadddaddcdcdacaadccadcdaabcdcacbddaacdbbccdbabcbaaaacbadacbdbbccddbdbccdaadacaadbbbcbdccdbcdbdcdcdacaadabddbdbcccbaacadcaccdacaacababacaadbdcccdbddccddcdbdcbdbcabaaccbbbcddbdcdbaadcdddbaddbacdbbbbdccddbbbcdbdcaaaabbbaabdbcdddadadbccbccbbadacdadcdacdcbaadddddcbddaaddbdacbbcabddbaaadcbbbdbabccbbbddbddbbdbacbcadabcccbcadccdccadbccbcabbacccaddcacdbbddbccbbadcbabbdbccdcdbcdbcddcddacccddabbaadcccbdcbcaaaabdadcaccaadcbcdaabbacbcacaacbddcadadacabbcdcaabdcdaddcccdbdaddadcabddabbcbcadbdcdaadddbcbbcdaaccddbcdbbbacaabcdaaadabaacdbbadcbddbddcdbbabdabaababdabdaaabbcacbcddcbbaacaacabddcacccdabddbababdccaddccddbbaabbbbaaacbdcccdcdbaaddacabbbdccdbccdbadbdbaccdabdcacaddbdbcbaaddbabcbabacbacaabdcabdabdbaddacadabbdcdccdadadccadababadaaaabbdbddbcbccccabdcdacdaadbadacaadbcbbcccacdabccababdbbcccccdcdacddabdadaacccdccdabccccdbdddbabdcaddbadcbccaadadccacddbadadcbadbadaabddbababacddccbdbcbabaabdccacabdddbadbbbbddaabcbccbcaddddbbccbcbbcacddaddcaadacabccbbbabcdbddbcbcccaaccacdcbbaddcabddacdbabbabdbdbdbdcacdddccbaadcdcddacbdaccbcbbabbadaacbbbddbacaadddadbacdcbdcbddcacbdaddbcaacdcbdcdcdddcddcacdaacdaadccabcdddddbdadbadadcdacddaabbdcabcaaacbadccccacddadbbcdccdcabaaccbbcbbbbadabdccccdccacdabbadacdcadbbddcabbaccabbdbcdbbaabadbabcbabccdccdccbabdabaacbcbbdacadadaaddccbbcdbdcdddcaababbacabccbacdcbbcabaabccadacdbdaddbccbdddcbadadcdcccbccdcadcddccddcddcbdccdacbccdbddbbaddadbbbacdadbddcdcbbbbcbacdcaadbcbaadcccdcdccbbbbdbabdcadbacddccdcaddcabcddcaddcccdddacbdddaadaacaadaaaddacacbbdbcddacdadcbbcbabcdcbdbdaaadcbcabdabacccbcabadccacacbcccacbdbabdbbcaacdbdcbddacbdbacbccbaacaccbcabcabababbcbbddbdacddaacbcbdabaaabacacddcbabcabcbcacbdaddaaadbccabadacbacdcbaabbdacdbaaddadcaacdbddbbdaacbadcbabdbddbcccadcdbababbdbadcccdaddcadccbcaadbabccccacbdaadbcacccadbdaccbbcdabddccaadddccdcbaabcdbabcaabbcbbadcbaabdaddccbcbccacbbdbabdddbbdacaadadbccacbaabdabdbcdbdcacabcbadbcdadbbcabcbdacddcbbcbaaaadadbcaacbddcadadabbddcacaccbbaabddabdbdabbcccbaadabddacccacbbbdbbcdbacabacdbcdbbbaadabacabcaabbbdbacbabbcdbcdbdaccccaadadacdabbacbcbaaaaccccdadcbacdcdbccbabdcdaabbaaacddbacbcdabdaadddadddcaadbcbdadcbccbcaacabaddcdcdaadbadbbbccbcdabaddbaaaaacacbbabbabbddbbdbdcbbbdcbbbbdadbbacdcacbbdacdaaacabdbdccbbdabbcccccbdcddabaaadacbbbdbcccaaaabacacbcbddacbaacdabddcabddabcbadccadcaaccbacdcbcacaccadabcccadabccbdbbddcaaaccdaddbcddcaadcbdacdbcacdbccacdacabddaabaaddacccadbdcaacbdaadbccccbddbadaccbdbdbcbdbcdcabbdcabcaccccabaaaccccabbccdabcdcdabddcbdddcdbcddaabacababbdcaddadbddcadadddcabadbaadcbbdbbbdaddbcabaabcbabbdbdbbccdbbbdacbcaaabcdcabaabadccbaaaacbbcbacbcbddabdadbadcbdbadbbdddcdbabcabbdbdcabbaacbbadbcacbadddcccaadacdaabdccbbdadcaaddadcbccdcbbbabddabadbdaadadcdacaaadcbddcdccddacdbadacbaccbcbbaaabbcbdcbdbbaaccaabdadcbdccdccabbbbcdadbbccbdacadddcdaccdbdabcadbacccbadbaccddbddacdcadbaabddbbdcaaddaaddbcbcccbbacdcdcddccaaddbacdacabddcaadacbddbaaabbbcbaaacbbbcdbcbaaabdadadaaacdcdcdaaacabdbcbaadcddcdbdbbbbdacadbbbbbdacdbbdbddbdcabcdcdbcddccabbbaaadbdbabacbaacdaababadcbddcacaaadbcdccccdcbddccbbbabddbbcbaaaabbcabccccadaaaccbddccbacdbaacbcdccdaabbdcdccaacbcddbdaabacbcbccacabacddbdcacbbaddcbcccabaaccdcbcccccbddcddddadbaddbdcbbcdabcbabbbbbcbbcbadadabacaddabbbcdbbaabdccbccbdbdcaaabccbcbcdcbcaccbbbcbaddccbdddacbbccbaaabcbcdcbddcaddaacbcbddbdaadbdddccabdaaadcdbdaabacbaaacaaddcdbadcaccadbcdbccbabcccaacdbadaccccbacaaddcdbddabcababcaadcbbbcadacbbdbbcbcbcbacddbcabbaadcabccddcbacbabcdbdadcbcaadcabcdbcdcbdddcbaaabdcabdddbcdcabdabbdcaddbccaddcdcccbabbcdaabcacbacbbcbacdaadbcacddcdcabbdcdbbbccdcaddcbacabbbcacacbadacaaaacbbccaacdccbccbaccbbbcaccdaabbbbaabacbbbacbacbacdcdbdcccccaadbacacddadaacddbadbcabababbdbbacddabbcdbbbbcbacccbabcdcaccbbbbbbcadddaadbdddbbbddcbbadaadbbcdbddadabacdddbaabdcddbacbdcccccdaacbacaaccdabbcbadcbacaadaaddaccadacbcaddacacbbccbabdbcdccabaacaabcaaccaaadabdcdcaaccdbbddbadaaaaacbaaacaddddcadbcdbacbcccadcbdacddddaccabddccbaaddabcdccadbdcadabccaddbdaaacdbbabdabaabcdbabcbabbdbddacbcdaddbccddadbbdbbcdaacbbccabcdcdddacabdabadaaaacaccbacccbdcbdcdccbacddaaadbbbacbddacadabbccdbaaccdbdbcddacdaaadcaabdbccacccbccdcccddbbcaaadccabaabdcbacababdaddcbdaacdbdccdddcdbabadacadcbdddddcabbcabbcacacddcdcbbaaabababbdaccababddcacccbaaacbdddcbabdccdbdcbbbaddadbcadaaddbbacbdcadbccbaaacdbbcaaabbdcdbbccbccdcccbaaddbcacdaabcdbbbbdbcbccdbacadacabbdbdaaabdcbcbcbbdddcccbdcabbdabddadadbccbdacdcdcaabbbcabcbcaababbccbabaaccacabbdcaaccbdacacadcccbbdaacbcaddddadbbdaccccaadccbbdbdcabbbadbacddcbdabbbdadacbdacdbbabbbdccdcadadbadccbddcbdcdbadcdaaaadadbcccddbabbdadbbabdbbbbddbbbcbccbcbcdaddbbdaacaccddababacccdddbbdcacadbcdaacabdbbccdbcbaddcbabaddcabdbabadcacdcbcdbadaaadcdbadcbddabbcbbabacaabababaacbddddcdcdccaadaaaddbbdadcbccdadcbabdbcacababdbcddcbaaababbadddbdaadbbcbccabddcbdcbcdabdcaacabadacaaacabddaabdcbdccccdbcdacbdbbddcbdbcbbddabddddbabdcbcabcabddcaadbaccbdabddbcaaacdbacbaddcabccbcccbabbcbcadcadddbccdbcdccdcacacbabaaabdbaadabdbdbbbdcaaaadaababcdccabbaddabcdddabbabcbdaaccabcdcddbbbccbcbdbcbdbddccaaaadbaabadacdaabcbcbaddddccadadcddaaaacadbdadcbbcadbccbdadcccaaaaacadbdadbaddcbacdadcadbdadabbbbddddbbaabbabaccbbcbcdabbdabcabbabccadbcacadadbbddddacacdbdcccbbdcbcbdbabcbabdddabbacddbcdbcabadcbcbbccccdddcdacbbcadccccdadabddaacdcdacdadddbbcadbcabaaabcbdaacadbcdbdbcadbdcbbacddbdbabbdbbbccdbbdacbcacbcbcdaabcababbdbccadaccacccdadbadabbabddaabbccbccaadcbcbcaddabdacacbdbddbadddaadcacccababaccaccdaacbadabaadcccdbcaddccaddddcbababbdacddaddbaadcabbcbaccdaaaddbdcdbbadbadddbbbacdbaacadbccbcabdabcbdaabcddbabdabbdbdaadbbcdccabdcdbdcdbcadaacdbaaaddcabaabcccbdbbcddbdcadaddadacccbaadccbacaabbadbdcbdcbdabadccacdccaaccaabcdbdbacbacdcacddacddacadcaadcdcbcddaddacbaaacdadbbadbabacccacbcccccbbcdacbaacdcbacdabbbaabdcabcdcabcbddcacdcdbdccbbcdaaccacaaacadcbadddccdadcabbbdddbcdaacadaabbbdcddcadacbcdcbdaaddcbbbbbbbbcbdbcadcabcaaadabccccbadcdcbbcdcbbccadabdadaadddcbbadccaddacbbbdbbccabadbcdccdbbccbadabadcaddabddcdcddacadcaddbbcbcbbadaccbccbabcbdbcadcccdbcabbcadbcbaacbabbdbdddaadcdcddaacabbdaabcbcbdcdcbcdccbbbdaddaaabcbcadbdbaadaacacccddbaaacbbcaabdddaaddabcbaccabdcdbadabddbaadcdcdcdccbbabdbacadbaabdcadaadcbbcbadcacabcdbdbbbdabaabccdccbdcdbacaaaacdddbbddcddbabcaacacbcbdbddacacdddcdaadcaacccbaaabdcdcbaaccccadadbbaabdbbabcdbdaacddabccabdcccccdaddbadbaadddcdcdbdaacbbadaddbbdaacccbccbcdddaadcaaddaacacdcbbdbaddcaddbdcddcaacbabadacdaacbbbccdcbacbdbdbacabaddaadbabdddddbcaadbbdabdabbabdaaccaccdcdabddaababbbbbdbabcbdcbddaaccdcddcaaaccadcddcaabddcadabcadadbcbbcabbbbcdabcabdcbdadccccbcbddcbdcdabcbcbcabcdbddbdbcbdabbbbcccbbadaaacbdabcdaadddccacbcacdcccbcbdadcdbdabbbdcdbaabbbbbaccbbdcdaadbcdbccaabcbdcabaaccddcbbbcabddcbbcbabadabdbadcbbbcccaabdcabadabcccabcdbcbdbddbaadccaaaccbacbcaadddddcabcadccccdacacadbacabbdbcdbccdadacdbbbbbbccacadadccaadbdbbbacddaabdabcdbdbdabccdaadaabcdbcaddbacbaccbcbcddcdbbdbbddbbbccdcbdadadcdbaababccbaaaacabdcadcaacaadadccbbcbabbcabcddcaacabaabaadcbbdcaadabaccbadbcdddaccbacccdbcdbdadccdbcccbdcdccaddbbacdbbdbcbaddbcbdbadadbcdbbdcabaccabddbcbccbaccdbbcbaaddbbacaccdbaaacabbaddbaabadddbaacbababdadbdadcbccbcccccbcdbcdbbaccdaccacadccacadddbdbddababdaaddccdccbbdabaadacdcdacbdbddbddcacaadacdbdccaadabcaddcbadbddcbdaaaddadcaacadbaddabdcbdababcadccaddcddaddbcbbdcaacdbcbbaabdbdddaabbcbbababbdccdddadbadbaccabdabbcadacdbbdadbcaaadabbabaadadcdbadacbddcdcbaabbcbabbbbcaacdbcbaacbabccdcbbbabbacaaaccddaabaabbdbbcbadbaacddbbbbdadcdcdbcdabcbacbbacabaddcdaaadbbdbaaabacaaddabaccbacddacbbcabacbdaaacacacdcadbcccbbcdacbababadccccadbbddbdddccbccaabccdcddbbddbaadcdacaacacddccbadbacdcbbbdabbacbddadcbaccccdddabbcaaacbaddacbadbbbbdbddbaabdcdaacaacadabddcbdbbbaabdbcdcadbadcdacaaababdbbbcbdcddbdaabbabbbddcbddbbbcbddbccbacaadcdcabbcbaacbbbdcaadcbcccacbacbccccccdabdcadbdcadcbbddabcacabbbaaacdccdacdacadcabadcbdbcbaddbacaddbacbbbdcaabcdddccbcdbaaabbbdaadadbdbabccaddddadaccbdabbacbbccaabadcbabcccaccddccacccabcbbaaaacdaddcacccbdbbbcbccbdaabbbcbabccdacbccaaddccacbcbdbabcacdcccbbbcdbcccdcdcbbbcbacbacdaacbcccddbaddbabddbbbaadccbdbaaccacbbcdbadaddacadbbcbbdcbbcacbdbcaaaadacbdcbbcaacdadcddadddcbbdcaccddbaaabcbdbaacbadcadbacdcbcaadadbbaaacddbcbcddbbbacadabadbbbcaabcbbbbddadbbdacdaaacdbabbadcaddddbbcabcbdcadaddbcdcdcddcbabbabdadbbacaacbbbcbccbaccdaaacabcabcacacbadcdbdcbcdccbbdbaabddccdaccdcbbacdbacbaaacaccaaabccddccaacbbdbaddcbdbcdddddadadbacbbcdacbcdbcadbbdcdabccadaaadbbbdbcbadcbabdcddddaaccbbcabcbadbabcadbcccbacbbbdabaaabaaadbcbacdadddbcddddbdcbcacdbacadcaccbbdbcaadadddacabbcaabbccbcbaabadcdddddaaabcabbdcdcdcdadbdcabcdddbcdccbbacbdcaccbaddcbcacdcdbccaabdbadddadadbcbbcacdbadcdbdcaddcccaacbbbadacddaddcdbbaadbbcbbcdbbcaadcacdbbddbdcdbbddabbcdaabcabdabcdcdabdbbadaabbcadcaabbdacbcddbbbcdddbcdaaabaccadbcaacdaabcacdcbbddadbdcadccdabdbaccdbcadccddaacabadbdbcacccbcbcdcbbdbaabbcbcbddbbaabdacbdbdcdbddcababaccdacadcaaacabdbccddbcacbdacbdddccdcabacdaabadbacaddadbacaababddbbcaadbdcbbaabcbcacdaacdacccbbdcaaacabddabbaaadababdbdcacbaaccbbbbbddabadaabdaadddbbcacbaabddddcdadaabdaabdcccbdbabddadcdbddbbbdacbaccaddbaddcaaacbcbddaccccaaaddcaaacbaadcabcacdbccabbabacabcbadcbdaacbadaabccabaddcbbacabcdcbdcabdbaaddcccdaadbabcccbabddddbadbcadcdddcbaacbbaaddcdaacccacbddcbdadcdacccdbbdcdbbbabcdcddaaaccccbbdaacbbdbbdbaaccabbdbdcdabbdcbcbdbbbabaccabbdadcabbdcbcacabdacacacddabddcbcabcadbdaaaabdbcddadaccdcadacccbcaaacdbabcccacddbbbcadbdbaddacadbbbbbacddcccbbcaadbddadbcddadbcdddcadadaddbbadcaabccbddcbabcaddaaddbccabbcbbcbdcadaacadcdcbbddaaadccaacbdbccbadbdddacbddbcdccccbcdbbdacaababcabcddaaaaddccabcdadddadbccbdaabddccddbbdcccbcabbdcdbacbadcabdadccdccbdabddbddaaccdacbadccbcdabddcdbadcacccbaaddadbcbdbabddaaadcbbcadaaccabdbaddcbcbaabdbbdbdcacabcdcddaacbccddacddbddccbbbacabdbbabadacdbcdcccaddbdabdcbdbcddcaabcadcdaccacbcddcaccdadacaacaacaacbbbccdbbcaaccdcdcbaaadddddddcdaddcbdccacbdabcdccbbadddbdbadcabcbcabaddcbdddbabadbbcbdccddaddaaaaadaaccdcbaddddcbcdbcdcbbcdcaddccbcbdcbcbddcdbadccaaacdcbbccbdcbddbdcdaacbbdadaabcdbcbbacadadabaaabacbcdbdaabcdccbbbaabddbaaadaccaaaabadadbbdcbbdbdbdcbadcccdaddbbdaabdbcccbcbcbcadaaaadbacbcdadacadddcccbcdabcadbdbdadaadcaaddcdbabcaddabacadcbaaabadbbacccaaddabaacdbddaadddcdbbaadbdccdcbacaaacaddcdcaadbdcacbcabaacbdcbcdcabbdaccbaabcdcaaadccbddaaaccbcabdbcaaccbbbcaaacbacccaddbbcbacbdbbadbabbabbbbaccaccacabbddbbddababbcddbcaabdccddacaabcbcbcadaababbcacdccccbabbdddaacdcaabbbaccdcaaadcaaabaacccbcbbdbcddcbccadacabdadcacbcdbadadbccacdaaabaaadacadbaacccdcadbcccbcbbbbabacdcdddbdcbabacabdbccacbbdcccdacbdbccbccddadaaccbbcccbcbdcaabcbbacbadcacabcabbbddbacbddbcddaaabdccbacaadbccbbbdacaaabcbcdcaaacdcbbddbdbbcddbaccdcbddcbbccbbdccabcbcdaabbabcccdcdbdbbccaddbcabcbcdddabaaadbcaaadbcacccbbcccabcbcbdabccabdcadbadddbcdbdbbbaadadddcadadbacadcacbbdaadccbbbccdcacdcaccaaccdccdadbcabbbacaaaaadbdbbbbabdbadacaaaadabaadccdaacacadbbabacaaaacddadbbbdbdccbdbdaaaccbbcccdcbdcbbaadbabbabddadbadcacaabcbbbabacbcbdabbdcdcacbdbaadacbdabacadaadbbdacacbdccababacaddddadbadaddcbcbdaabdbcdabdccaddcdadaacbbdababccbccabbaadacdcaaadccacddacbdaddbbcbbadaadbbdbdbbadddaccbcaacadbdabcacbdbcbdabcabbadcdbdcdaaadbddbaddddbccaaccccccbaccaabdbabbcdbccccaaabcbbabaddccababacdaccaccdbaaabacaddbcdaabaddbcabcbddadccaaadcaacadcaaabacbdbcddcaababdcabaacbacbdacdcaccdcbaaadbcbbdcadadcccdaabcaaabaadccaddcbadddbddddcbacbaacbccbcdaddddccbbcabaadacdaacbdddcdaaabbdddcbbccaabddaaacddbccadabacaaccbacacccbacaddacaacbdbbadddcbddabdabdbbcccbcdaadadcbbbbdacddabaabbbddccadcddbdbcadbbdadbddcdbbacddbcdddcaacababadadcbbcdcdcdbaadcacddcaddbbccdabbcbbcddadbaaacccdcaccdcadcbabdcbbdcbababadcbbbbaacccabbdbcddcaddbbbbbbabdcbcaacdabdcbccaadbdcadcbdccadbdacbbaacdbaddaccccabcacacadbbcbbbdabcabcbbabaccdbadbdcdbbbbdadacbaaadbadadcbbadcaadbabdcaacaddccbcabbbccbcbdbbdaddadaadbccaddacdddbcccabdbccdabdccaabbccdaadaacbabcaccadcdaaabbbadbabadabaaadabadccbcbbbacbcbbbaababcdaabbcdbdbbccdbabbdbbaadcbbcccbbcabacadaccdabddbbaaacaccababdacacbacbbababcbabcdbbddbbaccaadaadcaacbbcddccddbdbddbdabbadaacbacdaabcbdcbbdbcccdabbdbcccabbdcbdddaccbaabcdacbbacbbbacdabbcbbcddadbbbbbdbbbbccaccdaaaacccabbccdcddcbaadbaddbaaaabdbaabcdcdbbbdddddbbcdcbdccdadccdddddadbadaadaaadbcdcbadaddccdadcbbcbdacccdabdcabadcdaabdcabdcbacacdbbababadbdcccccabaacaccdaadaababdddcdcadbadadaccadccadacbabbcadadcccdccbbdcbadabbbbcddbdababbdbbaaaabbbdddabcbadbcdcaccccbaaaaaabcacbbacbbaaacbaabcdbbcaddcadddcbcaddcbbbcbcccbdcbdadbaddacbacbabaacbcdcccbaaadddabcabdbabdcdacbadcdbcccdccabaaddcdcbdccaaddbdbcbadbbaddaacbadaccbacdabcbcdcdbcacdddadbcbdaabacbbdddddaddacaaabddccacdbdddbdbbababccdabdbaabddcbbccdbcbaddcbbcbcbaddaaabbdadaccbcdccddddabddcacacabddaacddccccdabcaccbdabbccbcbbbcdaccccdadcadabdddabccbbcddbdaddaacbaaccacabaabcdbdcddcabdddbddbbcdbbdbbdbbabaddadabcccdabadddbbaadcbadaacdcddddbdabcddcdccddcdccbaabacdddbaddcadddddbbadcdbabccbabaabdbbdaacbcaacdddbcccccadccccaddcaaacccdbbcaccdcadbcbbaacbbadcccaacdcdaacdcbcbdcbcbbbacdbcadbbbadbadcadcbcaadddcddddcbdccaaddabaadbbbacbacbddcabdcbabdacadadabbcdadcabdbccdabadbcbabddbadcbdddbdbabadbdcbdaaacadbabbcdaacacccdcbbaabcbbcbbadaccccccdcddabbdacdcdbbbbdacadcababdcbdacabdddcaadcdadcadbdaaaccdddadcdbbdcdaacccabbadbcdcabcacbdabccdcbdbcccabcabbbbdbdbaddbacbcbaddbbccababdaacbaddcbbdaacddcbddbdbcccbdbbbaabdcabcacaccaaabdbabcdaaddabbbaaaaaddbcadadbadacccdbbbcacdbdaadbacddbcaaacbdacbddadcaabaadbadddcaddabddccbaccccdacbccbbccacdcacbcbaccdaccbccbbadcabbddcbdcdbaaaaccdaaaccbbbccdcadbaddcccddcacdcacaccbbbacdbdacabbaadbcdcccdccddaddaaccbaccddcccdbabddbdcaaaddcabdcddbacbdbadbadbdadabaccbbbbcccccbbdddcacbddbdcbcdaadbbdbdaadcdcaaabcadbcbddbabcbddcadabdcbacdadbcdbaacdadbbcdbbadabadbddbacdcabbcbccdacbbbbbaaccacbcddadccdaadbbcabaabaabcbaaaaabcbababbadcbbbaabdaacbadcddbdadddbbbddccaaaddbcbacbadcbaaaddadcdaacadddbddbcbaaacbaaccabcddbccdacadbcdbcbddbbdbcbabcccbbcadbbdabcdabadbcbddacacbcddcadbdcabcbbdccadbccccabcccdacbdcbdbdaacddbbcaccdcacdccacdabcbaadcdbacdbadaabbbdcbbccbaccddbabdadaabacdbbdbcbacdaccddcccddcbaddacbacaaadbccbbacabdaadbdacdbacbdcdcaaacddaabacadaccbaddcbbdbcaacadbdbddbdbacbbadcacdcdcadacaabaaaccdccacdbbacdabaacddcbddbdabaaabadbcccaacbbddccbdcdcccbddcadcaaabbaabdadbadaddcdccdcdbaacaabbabaadcbdcdcacccadabdaabdbadcacdbbadcaadccdababbccbdccadbbccdbdbcbddccaabacadcacbbacdcaaacacacdbdbdbddcdbbbdcdccacabdccbdbaaddddbbccadbbccdaadaccdbcbbbaaccdbbadadaddbcdbacdabdcccccdcccacaaddcdaabdabadacabbbacbddbcabcdccaacdadbbaadabccadddbbbacadadcadcacbbacbcacaaddabbbcbbadabaaabbbcdccbbadacccdadaabadccccbadcadbaaccccdddbbbbcbccbbdabbdcadbcabcbbdbcacacabdadcdbacdcdbaaaaddcdbcadbccdbcbbbddcadddbdbaacaddbbbcabcbbabbddacacdabbdcccabcdabadbbbdabbbcddccccadadaccdcabacddabacaaadcbccccbcdadbadaadddbacbaddabdadbabbcdadcdcbcbcbbcaabbbbdccddbdabdbbacbdccbdccbcdaddbdaaabbbdcdccbadcdcacabddadbaddbcdadaadacccadbcbbdaddcadabcacbccadabbacbaabadcbdcaaabcaccbdabaccacabcaabdaacbbbdbacddbddddcadbabcbddaadccabcddabddaadbacbaababacacbadadbbaadacbbdabdbbbacdabdadbdbccdaccdabccdbabacdddbbabcccbdbabaaaddcbdbbaababaddbdbcaacbaaaaadcbbbcbbcaaaabcdddbabddbbcdddcabcbccdcadcbabdbbcccbadbcdbabcddcdcadacdcdccdadbacddcbadaaadbabbcabaadbddbaddadbcdcabadbcbbddadccacdabababbdddaabbbccbdcdbbaacabdabbcbdbddddadbbbdcaadbdaacdbcadbadbcdcbacdaacbdbccdbccbbaccbacbcbacaddbdbccaaccbdcbaddbbcbdcbabbdccdbbabdcbcbcadabcbbbaabbddaddcdcccdbdbadccabbbacbbbadbabacbcbccbbbbbdccbadddadbbbbcbbbddddcabcadcdabddbabaacbdaaccbbacddcababcacbdcbdabacdaddbbdadcaddaccbcdbbbccdcabdccdcacbadcadcccdadcddcadcddbadbbdbcbababbbacbcbaacaacaabbaacddaaabbbcccbcbbabcabdcacccaccddbdbbccdcddcdbccaabdacaddcaacababcbdbcadcdcddaadcddadcbadabaaabdccdbbddbbbabcbbcbbbdacaabccbcbbabbcbacdacdacdabddaddcdbbbcdbdbbbcddccddcaddacdccbcbaadbbddacabaababccdadbccdbccccaacdaaaacbcddabdcddcdbaccdcbaddcdccabaacccdadabbadaaddcdccaddbababdacbadcbddcbabbbabdacbbdacbcbddcdbacacccacbcdbaddacadadcccbdcdadaabaaabcbbcbccbacbbccacabcaabcdcccdbccdbaaaccaaddaabcbaaaccdddcbbcdcdaadacdcacaddbdccadaadbdaabbdbccbdaddcbddbadbddddcabaadaabaacbcdacbbadaccdbdbcccbdaccdcbabacbadbdadadcabbdbcbadacaabbaaccdabcacdbbacaacccdabbbdcbaccadaddabacbbacaaaccabdbdaaacbcbddcdbaabdbaaccbcbbacbbbcadbcddabcacdabaadcdbccdacdbccabdabcabdaccacabddcaaabacdcccdaacadccbcbcdddaaaaddbcbacaadaaabaaacdbbacadccaaddbcbacdcbbdaabdccabdabdbbbcbcaaadabccdcbdcccabcacdadabbdabbcddadcadaddcadbcaabbccaabbdcdcabdacbdbaadabccadcabaadadcdbbbdaddaddcbcddacaddcccbddddcacabacadcccddbcbbcadbcdcbbababdcccbcdbccccbbbcbadccadaacadbbbcbcabbdbaacadacdbcccdbccaaccbcccdbbcbcadcbbaabaabaddbccbdbadadacddabaddcdabaddaacdbcbbddcdbcbcccbcbddacdaacacdbdadabdbbdcccdcbdbddddbbbacdbcddbdbadcbadbcdbdcddbadccdcdcdabdddcbdbaabaabadccdabadcbbbdcaadaacaccadaccccaacacadbdccaaacbbdddabaabcbdbcaaabdbacdbccccbaaaaaadaaacbdccbccabbdddcabadbccaabcbaadddacddcccabdcbababbbcdbbabcdaadddccbcddabcadcbbbadcacaaabbccbbbdcdabaacbadabccadccbcdaaadaaccabdddbddbbcbaaabdaabaabcbacbcabdaddadcdcaabdcbcacbbaadcbcabbdbcbabcbacadcccdaaddabaccabbbdcdbbdacbdbdabacbcbbadbabaaaddcabdbddbdddaddccddaadacdcadbcbbcaadbbccaddbcbcbabdaccddcccdaccdccbdadacddcbcdabaacddcabccaadbaabadbabaddabcdabdbbdbcaacbcbacacdccdacddddddcbacbdcadbdadabbddbcacdddaaccacbadaadbcdbcdcabaccbddbcbbaccdcaaaaacdcbdacadbcbacbccdcbbcbaadbabbbcaacddbdcbcdaacadcdcacbddabddacbbdbabaacbbcaadddcabaaaddcdbccabdcacbcbbbcccbcaabcbdcbcbacdaaacababdbdcdccdaccbbadabddcccdcbbbaccbcdccacbcccbaddaadaddddaabbbcdaddcaabbccbaadaaabaccaabdbacdbbcbaadaaaccdcdccdadcaaaddaaabcdccbbbbbaccacccddbadbdaacaaadcdabacadbdbabacbbdcaaadaddadbdccdbdbadaaacdadaaccdcabdbadccdcbcaaccbaacacbbdbcbdaccaddddbdbccbdcddcdbbadcaaabbccccdaaacbccbbcccbaddbdbbadcdbdabbcdcbdccaaccdddcddcbaacccddcdaacbccccdacddaddbaccbcdadacccbddcdbcbdcaaadbdcabcddcccabdadcababcabcbaccdabccdcdabbbcbaabbadacdbaadbbbbabdccaaacacbcaccadbcddbdabddbccadbdbdcddcbccdccadbcdabaaaabbbaddbdbddcbccadcddacdbaacbcaaabacddabbcdbdcadddbbabadaccdabdbadadbaaddbacbcbbbbbddabdbbccadcaccdcddccbcabdbddcabddcbbacbaaacdabdbbcdcaaccdbbbbbaacbadaaacbcbabcbaddccdbbdcbbbbbcbdbdcdbcacbdddddcabbddbdcaabbadddbbacaaadbdbabbbabaacabcacbddbaabbdbbacbbcbdccbddcbbbdaabdddcacdacacaabcdcdacdcbdadacbdabbdbcabaacddaacddbcdbacdcaccddbaddbbbacaaaccadbaadcbbadcbcdcaabaaaddbcbaddbadadbdbabcdbaddbaaacddbacbacbcbadacabacacbbddabcdbdccdcdcddaabcaaacabcccbbaccdaadcbaaddadabaabbbadcaabbbcdcbcccaddaacadcdcacdddacdbcbbddbbcbcbbcddbabdaddbccdcbababababddcaddcdadcadbcdadbaaacbbcbdabbabccbaadbbaadbabbbdaccdbbcccbdabaabbcdccbaadbcbdbbddbdcadacaaddddcabccbdcbadcbccadbdcbaaabbadccabaabcdbbbddcbabcabacbcbabcaacbbcdabbadaaaacacbaccdbcdbbcbbadaacabdbaddbaccdcaacdbcadcdacdccccabdaacdccacadcdddcbdabcbdcccabbdabcadbbcbbcddbacbdcdcaadaddacbcaadadbdcacdbbabbabcbabddcacddabaacdbbcababbdbcabbcadddcbcbabdddcbcdcbaccaabbdbdadbaacaaaacbbaacbacbccdddcbdbbdabbaacbdaaacdcdcaccaddbbdbbccaaacbbbaabdbaaaaccaddcbbdcccaabbdbaaadcdcdcdcdddbdaddcbcabbaaadbdddaadacdbbbcddbacaabcbabdaaabaadbdbbabdccabddadbadaddcbdabdcddadadcabbcaccbcdcdcdbacabdacacabdbdbcbbabcaddbccddccabbcabacadddacaadddccacbcacacaaddcdbabadabdaadacbdbdbcbaadabadbbbdcaacccdabaabdddcbdcabbbcabbbaadbbdccaababdddabdcbacdcaddacabccbcccbbddabddcbcbdbddcdabcbbbabdbdbadaaabdbbacbcdabccbadcaabbddddacabccdbcbabbcaadadaabcdcddbcbccccdbbddbcbdacacdbccabccabcabaabaaaccabdaddddbdbdbbdcbdcbdabaadccbcbacbbacbaaabdabbbadbbbaaddcddaadabbbdadcbcaaaadacbaadbdabacaabacbcdabaadbcdbacaacbbdcaddabbacdabaacacbaddcabbcacbccdbdbdacacaacacccacabbabadbacadcddcbdadbcbdddcdbccaddcaacabdcdaacabaacbcbabbbaddabbabbdbcbabccdaadadcabcddaabacbbbbaaadbaabbacdcbdbaabacddabbbaacaccaadbcbccbaabcddaadaaabbabbdbbacdbcacddaadbcdacbabcddacaacdbacabdbcaabccabdaddbcdbbcbdcdbcddabbbbbbbbdcccdaadddbdadcbddddaabcdaabccabddaaaccadcbddcacacacbdcbcbdcaabcdaacbabddcadabadacaccbcccaaccbbccdacaadccbbbdccbaadbbdcadddabcadccbacbdadabdbcaabbaddaabcdbcbdccdbdcabddbcddbbdaddbddccbcbaaadbcaddcdddabcaddaadddadabbbcbbcaabacdcbbbaabbadbdaaadcbacccdccdcbcdddbbdcadaccadabcacbbbdaddadacdcdacddbcadaaadacdddcaacabbabadcddccbcddcdddaccabacabadacaccacccddbcbddbbbdabaccddbcddbbdabadabbaabcadddaddcbadadcbadddccababaabbadcabccbbbdaacacdccaaacadddcdddabcccabaacbddcdcacdddadaadbabacbbbcddcdaaaaaadcdbdbbdadbcccddbbcddbbccccadabdbdbbadbbcdbadcbddadcabbcaadababaccdbcbcaddabbdbabacabddbdcadcdcdccbbcccaacadbbbbabdbadaabadccbcbcaadacabddbadadabdaadbddbbdbacbacaddaaccabaadcbdcdbbdadcbccbadbcabbbabdddccaabcdcbddbdcadcdacdbcdbaddbdddcbccbacacbccaddbcbacccbdadabbdadbccbabcabbbddbaacdcacaadaddaccbaaaacdbbdacabdccadacbdaccdadbbaadcddbcdbddabcdcadabdbdcacacaadcaabdaacacbcacababbdabbcadcbcdccabdbabdbcacdabbbbccadaaabcaadbccdaddaddcbacbdacabaabadbcbdbaabcdadccaddbdbacdacccadaaccadaacabdadabcddaadaaaabdbdadcdcbcaccdcaccccbbbccbcbdbbaaadaccbbcdabccdbbabcacaaacdabcdbaddaddabadaddbcacbabbbdaacdbddddbdbbacbbdbdcbccacdcbaadccbbcdccabacdccadabbdadacbaacabdbbaacbadabdddaccdcbcdbcaaacadddddcdcbcbcccddcacbdbdadbaabacacbcdacbbbdbbbadadccbccbdcadadaaaaddcbdbbcbacbbccbdcdddddbaacbdcdcddbdcdbbdadabbbabccdddbdcbabbadcdbdaabbbcccdddbdcacaacddddacddaabdccddcdddddcbccbdacdaccbbacbcabcbcbaccbcacdacbaaccccadcccbabcbacddadcbdcdcaddcdcacbaccbdbabcddcddddbcadbdccbabaadbbcdccaabcbbbdbacdbabcabcbaadbaadabdaaaccbdabcbdbbbbcdaadbacbdadacddbdcaacabcbaaacaaddcdcaddcaadbabbdcdbbcaabcbdddcaccbcaccadaadddbdacbbbdbacbaabdbbcbdaadbbcccbabbddcbacacbbddccabdbdaaabccbaabbbbabbaaddadbabbaccbadbcdbbabddcadabbabbbbbdcacbdaadbccbcbbabdbdbdcbaadcacddcddbcdcadbcbcdadbdbccccbbdccbbbbabddbabdbaaacdaadcabbbdaccdabccbddbddccbaadacaadabcbcbbaaddddbcdacdaadcacbbbababbdcbdddaaabcabdbdcaddccbcdadccccaadcbaacccbadadcadbbabbddbccccaddbacdaaabcbcdadcadaabcdcdaacbdabddadbdbaabadbbaacbadccbacdddacacccbacaaadcabcbddbdacaccaadcdaaaaaddbdcdacbdddadadbbdcdcbcbbbcacdaabcbabacdbacabddbaabcdbabaabadaaabcddcbbcaaabaabaabcbbbddaaacdcbcbcddbbcacaabdabaaddacbabdbcdbbbabbccbbcbabccccbbaababdadabbabccdcaddacabcddbcddbbdadcadbbdbccaacccabbaccabcdacbbbadcaadaaccdcadcaabdbbcdcbaaccdccaddaabbdadcabcadcddbbbadddcdcadbbbccbddccbbbdccabcbdbddcadbbcdaaadaadababddbaaacbabcdddcddbdcabdadabcbbdbcddbacabcddaacaacdbdaadacbcbbdcabcbbccaccdacdbcdabccdadcbccbacacddbbaabcbdbdabacaaddcdddabbdacbbcdabbdadacaadddacbbaadadcbdadabbbaaabcdacbdaabbbdbdacadadddbbddbbaacacdbcbaabbaabcdaadcabdabbddcaacddcaabdddaddcbdccaaaddacbccbacdcacadadbaabdcccbdcdabacaaddbaaddaccdababaccaaacacbaddbdbcdcaddadabacabdbdcacddacccadbbbbbbdbaaaccbbacdddbdaabadacdacbccacabbcddcddadadbdccbbabdbdcbabaadbadcdbaacccddbaddacbaaadadcddabccdabccadacbccdabddacdbbcdddacaabdbbaadddddccdababaaabcaddbaacacddadaabbadcbcaacdbbddbacdaadbbbacbddabaabacaadbbdbbddbabcddadbbdbdbccacdabbaddbbdbabcdccacaabdadddacccaadbadabdbbbbabdabdcbbabcdcdabdbbdaaddaddcdccbccaadcccabdadbabcadddacaddbabcacddbcbdcbccacdabccdbbcddddccbbadbcdbbcdddbbdaaccabbacdbcbdbccdbabcdaccbbbccbdadbdaaccaadabdccabbacdcdbccbddabdcbabcbdacdaddddccabaaaabdddbbacdcabdaaddcdacaddaccccdcaccabaddbaddbdcaabdaabdcacacdbdcdcddcababbbaabacbcbacbcdaaaabccccbcbcdbacbacdacddabbabaaadadabcbacddaadbbacacaabaaacacdddcbccbcbadcdddacdabaddcdaacddcccaccbabbbdabddadddbbabacaacdbacbabbcbcadcbadadbcccdddbbcadabaccccbdbdabbcdbaaaacacddabdbbbaadddadbccbccddacbcbcdbcddadaabccadaadcdbdcddadbaadbccabaacdaddbccdbaaacddbcabacbadaaddbbcdbdaccadbaabadbbdddaadbacaccddccddabcdcccabcdbacadacdacbddbcbbbdcbabaaabcbbcaaadcbabdcabdadccbccdcadbaabdabacacabbacdbcabaccddabdabacbbadddccbcaacdccbbccbdabadabbdadabbcbabaccccdcbdbbccbbbcbbbaaacbccccdddbbbbdddbbacacccaaabacbdaddcaaaccbabdddcabaadcacbbdbdbcabbaabadacdbbaabaacddbabccddadaaccdcabddadaaabcadabcaaddcbbaccabbbabddadbdbadbbaddddbbaaccadacdbdabdcdcbcdbcddadbdaabdbddababbccdddcaabcddcbdadbcabdccbcaaabcabdbdcadccabbbabbccccbacbdccabbaadccbabddcdbbdbaaaabcbcaabbbcbaaccddadbadcaacbabaabadabcacaaabbccacbcbaacbcdaacbcbdcabcbcacbcaccdbbacabbcbbaaabbcddccbabaccdbdbdcaddcdaaabdacddcddcdcabcccdbcbaacabdccdccbbdcacdbbadabdcbcabbcabdabbbcacabdddaddaaaddcbcdddbaaddcdbcdddabaacdaadaaabcdaaadcbbcdbaddbbbcbdccaabbcaddbcddaddbbdbdabccdbccadaadccbbabbcaccbbbdbcaacbcaabcadcabbacabacbcbbddddccdcaddabcbabcbbcdccacdbdbacdcacbddcccaaccddbdaaaccbdcccaacbccbbcacdccadbdbdcbabddbbbcdacbbdddcbcdaacadbcddccdcbdacdbbcdaddbacdbbaddcabbcacccadbccbccaadaaccbbcacccacbbdaabddbadcdacabbcbcadddbbabbdbaaabcacaddcdabdcdbddabcbbbacabacbbcdadabbabcdcccadddcdcbaddddadcdddddacdabdcaacabbbdadcdbcbadcbbdcdbbbdccccacdbacaaccddabcbaacabbaddadcabcbccdcdcdacdcdcabbdddabdaaddbccdbacbcbcdcbcacdddbcbadbdcddbadbcbbbaabadcdbbabbabaabcccdacaacaaadaaaabacdcbaccbcddaacdcbcdcbadadcacabccdccbdaddadaaddddaccaaaabbcdcbbdcbaadbaccabcbabacbdbbbcddccbaaaaccbbaabdaacacabacabcbccababdaabacbcdcaddcabdccdbbbdbccccaaaaccdddcadadcacbdccaddadcdadbaccbbddbabbaacbccabadddbbbcdabcdbbbdcbcaccbddadadcbdbaabcdaddadbbcdabdbbcccbcbddddbbdbdbbadccbcabddaddbccddccdcaadcdadadbabccbdbadcbadbbabaaabdcbcbbcbdcccacdaaddbaaccbcadacbcacdbbaaacdcdacdddaddacdabcadccadcaaddaabdbacddcccbbcabbcdbbcdcbcbacdcabbaadccbabccaabbabdcaaadabbbcbbbdbdddabbacbcbcabdabcbcccdddcbbcbdbdbccbcbaaaaadcddbccaaaaccdcbbddcdabbaddbcdadabbdabdbdddbbdddcbbbdcdccddbcadbcdababadcdbcadccbdacdaaaaddbcdbbbdcdaddcacabbbcabdaaacbdbbbcbbbabbdcbccddcbaccadcadababaaadbbdbdacaccccacdaadcbababcbccdcbadcabaacabbcccadbaacaabcccbbdabbcadcacddcdddccacdcddcabdccbaacabdbbdccbcacbccaadabcdbadbcbcbbbbbdcdcdaaabddcdddddabccaacadccccaacdbdbcddbdcbbdccddaddabbcdabcaddcabccacbbbcbdcdcbbdddacddbdddccbaaabbccaccbdbdaabbaaaaadbacbddadccbabbdccacaaddcbaadcbbdbcbabdbbacccbdddcacdbcbabbbdcacadcabbbaddddcabbccdadcccbadbdacdaaacdaddacbaadddcbbccabdaadcbbadcaddcaccccccbdbbbdadcadcaaadcbaddbccdcdadcdadcabcdbdbbdacdddadcbcaacadbbdcccacacaadddcbddbcbaddcdddcbbdbacabbbdcdacddcbcbaaddadabbadadbdacbcdcdbaadaabbadcadabbacbdcabcddcabbccdcdccaacbdbcacbabaccadccbbcbcbddcddaabbcbddcadabcaddacdbdbddccaddcacddbbcaadcbbabbcdbbdaadbcbaaddcabaccbccaaabdcacbaccbbbaadacbabbcccbadcadcbbadabaccadddccddbccadbdbcbccdddaabbbaaaadbddcbbdbbaabdcadaaddddababcaabbcbbadbabbdbccaadccddcdcdaccbccddcdcabbcbcbcddbdacbcdbdaaacccbdbadbccaddbddbcacdcdcababacadbbccadcaddaacadabddaaadddbacabbacbccdabacabbcbdacabbbcdddabcbdccddabbbdaabaaadddaadbbaacbadadbabccdadaadcbaababadacacdaaaacccdacccdaadbccbadcaadcbcabdcddabcbcdddabadcdddcabbabddabdccaaabbbcbcadaccdbdbcaabaacaaaaddddbdcaabacddbbcccaaacdbaabadccdadcabdccadcdbcbabbdbdabaacadadbcbdccdcbbbabbbadacdbccbbdbbcaccbdacdabbbaabdccbcaaddcccacaccabbadccdbdddbdbaaddbdabcacaccadcaadcdbaccccbdcbbdbbccaabcabddcbdaacbdacaaacbadaacbabcacbaaadddcbabdbbbacadbababdcdcaaadadbbbddddaacdcacbbbddbdaabcbdadcdabaadacacdbbacdddcaadaaababbabdbaaadcbadcbddaccdbbcbdcdbaccdbadbabcbdbadacddbbadabdccdbdcadcdddcddcdabacdadbacdbbcabcbdcaacdbbbbaadabadcbbaacaacdccdcaabbdddcccbadadccddabcbaacbddbbccbadacbacdccacdaaacdbacbadbccaccdacdbcacdcbcbbdcbabaaddcdbbdacddccabbdbbddaadabbacabdaabacaccbcbaabaddbbdaccaacdddbccaaadcadbcddcabbcddadaabddabddbcdbbdbcdbddbbcdadbcbddbccadccdcbbabaacbddacaccbaccbaddabdcdaaacbbdcaddbbbcbbabbddabaaccacbbabccdabadaadddcdbbadcbddbcadabdadcdcdaabbcddacbcddcbdabbdbbbdcadbacdcbdddccdbcbcacccdcbbbbaaadccdcbdddacbbdabcdaabacaaaabadbccbbadbcdcbddbcbbcdaccdcdbbbcbbacdacaaddacdccadccdcbcbadbaaaccbccacacdaadcdadcbabdddcabcdbdacdbccccacbcacbbabdaacbbadcadaaacbcddbbcabdcdbddcbdbdbbaaabcdaddacbccabbcdbbdabcaabbabadabbcccdbcdcaacdacabdcddddabaddcaabccaacbbcadcaabbdddaccacdcdadadaacacdabccdccccbacbdbbaaaaaddcdcbdadabdabddaccbdbbbdccccadbbadbbbadadbdabcaccdcbcaabbacdaacacadbcacbacbaacdbcddacabdbbbacdbadbccabdcbcdadacbccbbacbcbcdacaaacbaacabaabcacababdcabaddccadcacbbaaacbddccbbddabaacaadbbddbccccbbbacdbdbccabbcacbbbdddaddcdbabadcabaccacbccabbbabcdbcbdbbbbdcbcadbdcaccbbddddcdddcaccaccbdcddccacdbcbbbacccacaabcbdcdaaaacbbaccdaccdaadcdaacccccccbcbcdcdaabbcdddbccacbbdbaccddbcbbcdbcabdbcaabdbabddcadbabddaabacbbbcbaddacadbdbbdcbcdadbcdacbcaddbabcabcbdacbaaabbcccddcacbbdcdadbbcbdbaaabdcdccaaababdaaaadddbdacddcbddbbabdcddaaccdbaadcddacbbddbccacaccbacaadadccbaccddbdcbcdcdbcadbdbcaccbcdbbadacbcabcdcabdbbabadabbdbddabccbbddaaddbbbcbaaadaabbadcbcddcccaaaddbdadcdcbdcbccacaaacdbaacbdacadadbdcdabaaadbcdbababdabcdddbbadccabddbaaccaaacdddcbbdddcdabdccbbbbabdcaccbccddbcbcbddcabbdbcabcdcbbdcbdcccdacbabcaddcaacdbccacabcadcdbadbdbdddcbbddcabbdcaaaaacbbdbbcbbcdcbcddadadbbabcccaddbbccdaabaddbadadcacdbdccbcadddacddcabdccbcabcadabaddbbddcadcccbdbaabdabbbcbdacbbbaacabddbddddcbdbacadcbdaccaaacbcddccdddaadcdcbabdbbacabaabdbbaaadccddddccdcbdbcccdcacbccaadbdbbbcdcdaabcaadcacccdbcaabbbdddbbdaaaaabdabcbbdcacdadddbababdcdaddabbabcdcaaccbdddcacbcddbbaaacacccbacbbddacbabcbadbcbabbcdadcdbcadbbdccaaaddcabcadaaaacbbbdaddbaacbcbaccddaadbdcbcbccacbdcdcaadaccddbdadbdbabcbaaadcdaabbddbcaadacaaabbbaaadbadbdbaacbccccdbcaacdcbcbabbcdddbadaccdcabddcddacddcaccacbaaccdbdddabddaddbccdddbcddcdbcdbabccdcdccacabdbabaabccbaccccbcddccdbadccaadbacdbdaccaadacacdacdacddbabddacdadcdbdcadaadbdcccaaadbcccddadcdcdbdbccdaaaaddcbdcccdccabddcddbbacbcddbcccdaacbccadaacdcdbccbcadbabaaaabaddcddbbcaadcdbbaabbcaacbccdddabcacdaddcccdcaabdbadaabcabaabbabcabdabbbdbcbcbddcaddaabbabbccbbdbcacddcababcdbaddbbdadaaddabadcadcaababbaaccbcbbbdddaadccadcaacddccbcdaccaaabdbdacdcbdbbdcbcabbbbcccbcaccbcacdaaadadccbddcdbdcbacdddddbdbccccabcabdacabcaacbdbadccdbbabddaadbbadabdbdacdbadbaccbddabacbabdbcbbbcaaadcdccabdcdcdacdcaabaadbabdbcaacbcadbbdadbacdcabddbcabbbddddabbabbcababccdbcdaabcbcaccdccddbdcdabcdbddddddddadbaccdcbbadabcdbcacadacdbbdccdbbdcbadddbabdcdcbdacbcaacadddcadababadddadacddbcdabaadabcbcaddacbbbbcdcabbddabaccaccdddcdbcacdddcadddcbabdabcdacbbbdabccdcddddcbdadcbcadaccddcccddcaaadddcadbadbcdcacabbdcdaabaacccccdbcbdacaacdcbccccabccdddababdddccdcbbcdadadabdaaaabccadabcabdddbadcddcabbcdddbdcaacdcccbbbacabaccacadacbacbdabcadabcbcdcbaabddaaddbbddcccbbdccacccbdbadcddbabcbdcccdcbdbabaacdaaacbadbbcaacccbddaaaacbccbcaacbbaadbdaacbdbdddbcdddcdabbccadadbccbcacbdaddbcabbbbbbacbaadcdddbcabbcdcacdbcacbbcdcdbccabadcbacbadcdbcbadacadbcaabacaccabdddbbdcdbcccdbdcaddacbbacbdbcdddbbadacccabdaabadcacbcbdcdddbbddabcdbccbbbccdcaacabdcddcccdcbadbadbbbcbdacbdbcbccccdaddcacdcaaacdaadbdcbabaddcbdbbbaabcdbdccdbddddcacadacdbbbddbadbdaaabadbcbccddcbbdbdcbcaabaabcbaacacdcbabdadadbadcdbbbccaccccccbcacacbbddbdcadddbbdcccdbdbaadadbdbadbdacddddbbaabcaaddbddccbdbadbacbccdddaadabbcbccccdbdddabccacbdbdbaddcdacddbdacdbbbbdbdcdbdcbaacbbcdacaabaadccaccccadddcbbbdccdccbbccbabcabbacbbdbbadbaababaccbacccaddcbbcbcbddcbdcdabaaccddbdcbaaddbccaccdcccadcbaabadbaabbdcadcbaaddacbcbadcaadaabbbdcdcdbcdcbabbcabcdcbccdbddccaabdcaadbbcaacdadabacbdadbbccbbaacdcacbcabbbccbdbdbcaacdbcddbcadcbdbdbdccccabdbaadbcbbbdabbabbcadddcccabcdcaacaddbcaabbabdaabaddbcadbadaacdadbaddaddcbdbbddccacabbbcacdcbaccabbaaacddddccddddadacdcbbccaaccbadbbcbdaaaccddabaabccbdbacdbcbadccdddbacbcaaaacccbadcdbddabcddacddbabbaddbaadcbadacaabdcadadabdabdccaacdadaccbcaadcdabbdbbaaadabddcddbccbbcacaababdabccdcdbdcbdaccaccdbabccddbabbcbddbcabaacacbcddbcadcadadaabccadaacbcccbccadbcabddcbddababccbbadabcbaababdcbaabaccdcddabaaacddadacdcdbdcacdadddbccbbcdadcdacaadbddabaaddadbbacbacdccacaacaaddcdadbbacaabcbccbaacadcddbcabaccdbcddbdbddcddccacaabbabaddaadcaabdbccaacdcacdadbbcdaaacacdabbbcdbdaddbbcacabcddbccacdacbdcacdaabbabaccacdddbdabaabaacbadacacabdccacdcaacadabcddddccabacadcdbacdccddbdccddadaaabaccddbbabcdadcacaabdbccdcbcdabdbabdcaccadbbdadcaccbaaacdaadcddacbcaabdbbdacdddbccaabcccddcddcccbaabcccdaddcbbcbcaaadccdadbbcddcbaabacdcddbaadcdacbddbdccadcccdabdabddabbdbcbcbccdaadbbbbacbbaaacccccadbababcaccdaabcbbbbbcaccadcadcbbbdcadacbbcccbaccddaccbcdadbacabbacdcbbbaddbadbadadbcbaddacabccbbbccbbbadcccddadcbaabccbddadbbddcadbcbbbccacdacbabbabacbbccacdbdabdacacaaabbbcddbcdadddabcbdccbadbdacdadbaccadadaddacdccbbbccddcdbbadbacdacadcbabcacbbcbaccbdabddccdddcdcaaabdbbaddcbbabbbcdccdadddbbddabcdcdadbbcbcbdadbcbcccccbcadababadccbcdbdacbdabccccaddbccdaccabaabaabdbbabccdacaacbbbaadcdcacabacdddccbccabdbbacbbddbbdcdabcdbdcadcbacbbcacccdcddaddddbcacbaccdddbadbddcccbcbddaccdbcdacdbbbcdcdbbccccadaacdccddbabcacaacdaaccbbbbdbbabbaadcccbbcdccddaabcabccaaaabcabacddbdadbdadbaacabbdabcabccabbddacdabdacbbcbbccdaacdadaacdbcbcdcccaacbbcacbdadbadbbacdcacddcdbadbcccdbbbababbbadcbbddddccacdacdddbdabdbbdcdbccbcbcbabcacabdddbaadaadcadbabaccdcbaccddaccadbdbcadcacbbdbabbcaacdadddbbcbaaacdabcbdccdadaadcdddbaddcddabccbdaddddbaddbdcaccbcadddacbaddaddcdcababcbcbdbdcccabdddcbaccbddabdccbdacbbdddccacbddadcddbabcdbdacddddaabcccbdcddadcdaabdabcdcbacdadabbbbbdcbdddcccbbbbcdacccbabbddbdbdadbbcbbadacdaaaaddbccbadbbbdcbdbaadbdaababaddaccccbabdddcabbbcbdbcaadaabaddacbcacabbdadadbaabcdccacbaddcdaacaadddbcadcadadbadcabadcccddcdadcdbdaddbbabbbaadbcbbdccbddcbaabbccddcacabcdbcdbcdcacaaaabacadabaaccbabbbaaddcbdbadbcdbbabdcacabdbcbadabccacdbbbccdaddcdbdacbabacbbadbcdcdaacabcaaadabbabdaabbbdbbdbbcdbdabbdabddaadaaabdbacaabccbcababababadacdcbbbbbaddaadddacabadcddccdcdcbdcdcddddcadaabacaccdcbabdddcbdabbbaaaacadbadacaddcbdcdacbacacdbcccbcddaadbcacbccaccaddddabddcdadddaccacbdbdaaadbcccbdcabbcbddcacdbbcddccacacbdacdbacbcdcbddadcbddddcadcbaacadbdbadbcdcaaccbddaabcdadbcdbbbbacadbbabaaddaaddcbbaaabcabbbdcdacabacdbcdbdbdcabcdcdcdcdccbaacbcaccccdddccdbadbcccbabcdcdabdcaacdbbadcacdbadccaddbadccacdccadbbcbcdbbcdcacabdabcbbbabcbcdabcaddbbdbadcabccbcdbcbcccddabbdbbbddaaddcdbbcbccdaccccdbcdbbacbbcaccbccaadbbdbaacaaddccccaddbbadbdacaddcbbbbaabcaddadbcccababbbcadcbdbcbcdbcbabaadccadddddacbbbbcaccbbaccdcacacdacbcbbdcacadcdbcbdaddbadcacadadcdbacacdaaccbdcbdcddcdcddbbbdddccaccdaaadaddcccdabccccaadcabaccdbadbcaacadadaabbbababbbbddbbbaaadcdbbcbccbdabdddbcccaadcdaaddabadddaadcddcccacbcccdbcaadadbacaacbbbbdbabcbabbbadcdcaddcddabdbdcacbabdbadacddbdbcccacbdaacadabcccbbcdbcddabaabbbaacbacdbbccabdbbbddacccaacbbddbdbaabdacbadbddbbdababacdaacdcacddcbaccccddaddcaabcbcbcdadbaaddbcabdbdaadaccabaabcddcaddaaabdcabddccaaccbcaabcbabdbdddcacdcbaccbccdddaadbbdbacbabbabdcbbacdbdacbcdacabcadcddaadbcbddaddbcddbbcdcbacabaaddcbcabadbacdcabdacdaaccbbaabbcdacccddddaaccdabdabddcdcaadababccabaccbdacadacacacaaaadaddddbbacddaaabcabcbabaadaadcdacccaccabdaacdbdacccddcdccdababbadcdacdccacbcaaccbdcbbbbcbcdbcdadabbddccddbdcaaaddbabcdcacbabdbaabbadcdbaaadbcdcddbaaddccbcddbbbcaaabdbbabdcccbbdcccacbbbcdbddbbbccbcaddcdaccbccccdbccdbdbbcbcbacccbdbadcbbbbbdcdacbbcbacdacdbadcccbcdccbbdadbdbdacabdadacbabadbdadbacaccbbabdccdbdddaaabcbadbbdacbacccdadbddbdccdcbdbccaacbdbccdbcbdccbdbcacdaaaacddccabdbaaababdddcdcddbbcadccaadbbccaddcdbbadadadcccdbccabcdbdcddabbcdbdacbbbadcadabbadcaacccdddbbaddccabbcdaaadddcbcaccbddbdaccccdbddccacbabdbbbbcabcbdbaaddbcbddadacaccdbabbdbacacaacdbdacaccdbbcaabdadadcbbdbbbdbbbbdbcadabcbbaaccdbbdabdddabdaaccaadddcdddcabcacccdbcdcbccaabababdbbabcbdcbadbcadccdbdbdaaaabadabdaabdcaaddcadaabbdcdbcbbabbabbaccdcbddbccbccccdbdbacadccdccaadccabaaccacadccdcacdbccaaadddcbbdcabaacccdcabacadaabbacacccddaabbccbbabcadadddaabbbdadacaacabcddbcbdcdbbdccdadaccdbcabccaabdaccccccccabbbdbaadaccdbddacdadadbbdcacddaddbbabadbdaadddbbdddadcacaddababbaddacbddccccaadcbdbbcdcdcbaaadaabcbbcdcacbbdccacadadadadcbcbbcabbabcdbbcaaadbabadaccdccaabbccdbbdcabdccadcbdbdddbaaaaacddaacbdacaaaddaaacbbdabacdbbaabbdcdccdddbbdbbdbdabdcdadccdbcdadacdbddbbccccbcaccdcddbddacaaddbcaadadadbcbcddbaadbbbbbddadaaccddabadabbadaacacdbacaccbbadbaabaadbaacdddadaaaaabbabcacdbdbabacccbccdbaacdacbbccdacabcccaabbdaddabacccdbdcccacbbbadbcbcacddacccaacbdcacccabadadbdddddcdadcbaaddccbdadbddcadcadddaadabcdbaccbabbbddaaddcdcdbddbdbbbaacbabadaaaccdadadbbcdbddaadbdbcdaccddbbdacbdbbccabadcbddccbaaabaadcddbaddadbbadbddaacacadcdddccddaaabcdacdcacccaaddbbcccdadcdbdabacabdcbdbbaddcddbddcdadbbdcbacdccbaaaadcccddacdbddbbacdcdbdbcacbbbdcdbaadccccbcacdabaaaabdacaaaddaccbccacbbaccccaabacbadaabddcbdabaaacbcaacbdacdbbabdcbdcdcabacaccbbcdacdcaaddacbdcbccddddbdaacabbbcdcbabddaddcadddbbdbcbbadcbddbddabccabcdddbacbdccbcbbadbaccacacbabbdddbdddcccacacabaccadbaabbccdcbabcbccddabddbbcddcbdbbdaccddbccbbcaadbbbcddcadbacadddddacbccbabcacddddbbabbcbbdabaacacbabdcdbacaddabdadabdbcdaddacbdaabcdbadaccbcadcdccaabbbbdbabbcbbbaccacbaaaaabcacacdbaccacdcdacbccdbddddaadbacddbdcbdbbbcaccbddadbbbddccbadcdccccdcacbbbaacdbcbcdcbdabdbbaacccdbbadbacddbaabddbdcbdadbbbdbaabddccdcccbadbddbabadcadabbccdacdbcadbdcddbbdbdcbccddbcdbabbddcdaccdcabdbaabcaddcadbbaddaccbbdcdddbccadbadaccacabcacbcaaacdacbcdbadddabacdcbdbbdddcccbddcbddbbcdcaccaacaddbabdadcddbdddbbbadcabdbddcaaccacccdcdacbdbccacbaabdddadbbbcbaacabbaabbddacbacdddabbcaacddadcdcdccdcdbdaaadabdabbbcabdddcddaabcaadabdbbacdadabbdbbddbabbbcacbdacdcbadddcdddaacddabbbcbccdccbacdcbcacddacdadbdccbacbaccdbbabcabdbaabacbddaddbadbcdcdbcdbddcdcbcaccdbadbcdadddaaacaacaaacacbcaddcbbcacaddcbcabaabadbcbdbbcbdaccacaadcdcddbadbbbbbdbddbcdbbbddcccbbccbbbbcdbdabccabdbbbcdbbbccabccabdbaccaaddbbbbdbcccacdccaaddacadccbcadcbbadbaccdacbbcdadcbdddacaccaccccaabcbcdaaadabaadddddbaacbcccddadbdbdaaadacdbadcacbbbbdbdaabdabcaadbaddbbacaaccbbccbdcbbabddaddcdccacdddaccaccbccbccbaacaddddbacdcdbabaacadbaddaadbadddaccabaaacdaacabbdadadbabbcdccadbbdacccaddbbaacbbaabbaddabbbcaabcdcdbbddaacadcbabcbdadcbdadbdbbcaabcaadbaaaadbaddadbbcbdabadabdbaabbabcdaddcbcaddacacddabbbdbadcbcdabddbccddccacbcbbbbacbaddadbdabaadabadbbcdbddadbbddacdaaddabbacadbcaaaadbdbbacaabbcaaabadabdcdddbbaabdadabbdbbbdcadbcdaaddbacbbbccdcabbddbcabccddcacbaccbbbdbccdbcbcadcadcdabbabcacaacacdbaabcdddddddabaddcbdcccdbddcbbcabdbdcdcbbdbccdcbdaaaccbbdacddacbddcbabbabcbbddbcddccdcacdaaaccabbdcacadcbdcabbcaccbddcbddbdbbccbdabdabcacaaadbcbddbdcadcabbaabccbacbdaaaccddcdcdacdaaccdaddcbdcdcbaadbbbbadcbaaabbddccbadcbbcaabbcbccdbdddbbcacdddbbdcdaabbccaacccdacddbcdabbaddaaadcbcddbccdcabdabcddcdaacaabcccddbadcbbcaddacbccbcbdbbdababaaabcdacdbcaacdcbaccdbcaacaabdadbdbacbdbcdcacbbdcccbbacbbbaaccbdabbdbcbabbddddcdabbadaacbcdabbbccdadcacbbdaddaccacacaccdaabddaddddaacbacbcaaddcbdacccaabdbdcbdabadccbbabdcadbcdbbadaaaaacdadccdcccdaaadcaadadbdcaadbbddbcacdcdabcbbdbbdcbcabbbbabbddbdbadbadcbdabcdabcaaacabacbbcdcccacaddacccbadaadcddccadcaddccbaabdcbcccdcabcbacaacacacabdcaabcccabaccccababcacbccacbbdacacddddddacabdbcbcacdbddbccababbbbacdcdbbcddbbbddbababbacbcbcacdcaadabddcdabaacacddacadabcaacbdbcaabacacabcadacbbccbacbbcbaadccdcacaabbdbdcaabaabcdddcbbaccbacadbbdcccaccbcaacccccaabccbdcaaadccdbccdaaadcbcacdbddabdbccddddbcdbdcacaddbcdcddcadcadbccbcbaacbacbcdddabadcaaadbccdcaaadcbadbaacbcaccdcdbcadddccddcddcdcadacddcccbcaabbdabbbcaabdabddabacdddbcabddcbddcdbabdababcbadabadcdcdbccbcdbbcbbbccbdddbabcbdcabccbcaccabdcadbcaddadddbcadcabacabdbacccbcaaddcacbcacdcabdddacbbccdbabccbdccbcbccccbcadccbcbaaaabddabdcbddbbdddcbaaabbbbdcbdaaddbaabcbcddabdddbcdbaccdcbaabaddcdcacaaddddddbdcdcbbaddaaddcadaaacbabcabcbadacdcdccbdbadbcaddcbbbcacccbdaaabcbcbcaabcbccaddaccdabccbcccdabbaaccadbbbaadccbdadcccddccdbadbcbbddcccbcbaabbdccabbdbbadaddcaabcdcaaaaadbdadbbaadacdaadcadacaaadcaccddccaaadabdbdbccacaaaabcabddacdcabdcabbbdabbacdcaccdaaababdbdbddabcbabbbcaaacabbbaddbaacabcadbccacadcbbcaacdaabdaccacbadccbacdbdcadaccadacbcaccacdbaadacdcbcbddbccbdbbdcdacdcabdabbdcadcbbcacbbcbcbaaddccabbacbadccabddadbddddbccacaabbaaacdccbcbbbaddcbaaabccdcbaacccbcadbcdcccccabcdaddcdabcddbbddbacccbadaaddacaccddbabbdaabaddabcbddcaddccdbddadaacabcabbddcbccbaacbcdbbbbadadabababdaacbdadbdccdddccaacdabbabcdddcdcdacdbbcdbcacacbaadadbcbbabbaddbadddcadaacbdcbadccdcdabcbcdabbdacccaaadbbdaaacdaddbbbbccacabaadcddaaaddbcddbdaabadcccabaaddbabcaddbaabddadbbbcdabadcddaddcccaddbaaddacacbadaddaddacadaddaacbdcdbdaddcbdadbccabadcbabcaabbcbddbdbcbadcbaddcabccbddbbdbdcdcdbacbdacabdbaadaccccabdacaccaddacbaacccdccccdabdcadccddabacbcadcccadacdcdbdadcdcbbbbdadbadaddabcbbbbddbcaadbabdacdbdaaabcacdcadbcdacddddbabdaadbdadcccccddcccbadcbccbdccbccbababdcadaaccbddbcaccbcdaadbccccbcbacdcccddabbadabdcddddbbcbdbbbabdababcdabcabcbbddcdcdccbdcbababdbaacdbabcddaccadadadcbdcabdbdabcabadabdcacadaabdcaadcccdbdbbcaacdcadcddbcabbacbdabccbbdaaabcaacaadaabacccabdadadcabadadbadadacddcbbcaaddaabccbcbadcdbddacdabdaabcadcaddaadabcacbdabbabdaabaababaadbacacabcdaccabdaddbbaaaddcadaddbcbbdbdcaabdbbacbdcadbcdbbdadacbdcccaddacbbddddbcdaccbccdcbdabbdaabdccdaadccdbcbacdcabbbdbcccaacbcaacdcbdaacacaadbbdccbacacdaddbaababcccddcacaaaaacbcdcabbddabdcbdccacbcdaaaacadbaccdddcdcccdaadadbdbccadbbdaccccaacdbcddbaadcddbccbbdcbdacaadcdccddccbdbdabcabcaabbabadacddcdadbcdbbccbadababadacddbbddbabdcddbbcaaaadbddcaadbacccbacabdaccccdccbdcadaccbaaabaddabdadcabdbadddbaaacaabbbcdcaacabbabbaccbaabadbddddcbaccbaccddbccadaddcbbcacbbccabccabadaadbabaacbbbaacccbbccbaccddbbcddccaddcacdcbbbccbddabaabcbdadbcccacbbacdcacccddcbbadccaaddccabcadadaddcbbcaacddaaaadbbbdbbcdabacbbdadcbbbaacddabcacdcabccdccdcbadcbccdcddbacdcbcbcaddbddadbcbccbadbcacbbaadaddadbaccacccbbaadcbbadacddaabbbdacddaaabbabcdadbabcaabbaaabcbbccdaddbbccacdbacbccdacdcddcaadadbdbacadadbbbaacdddabcaaddabdcaccaadbaaccbaaacacadbbccdaddaaaaccbdccbdbccbcddccddcccdcbdbccabbaccdadbdabcaddabaacdbddbaaaacbdcadbbcbbbccadcdbdadacdaaddaddacbadadbcacabaccbddadadbccddaabaadcabadcbaccaaddcbbdbdbddbcabaddaccaddccbacdddbdbdadcbbacccdcbdbabbbabaddddacbacbdaadacadadcbcbbdbacacccbbabbaabbbadaccabaabbbdbbdacbbaaabdbbabbcbbbcccdcaabbdabdaaababaccdbdcadcccababcadbcdbbbaabccdbcbbddcddcaadabbdcbdacacdcaabcdadbadbdaccacddacdbbabadccdbaddddcccabacbdbcaaccddcabacbdbdaccddddcdacbdbabbbaabcbbbdbaabacaabadaadcbdbacccccdccdbabdabadcababbcbbcdaddcdaadbacadcbadbbdbaabadbaabbacbbbabcdaabbdccbabbbbddbaaddccdcbddadbdcbadbadcccbadddddaadbbccbaadaaabcacdadbbcdbdcbbdacaccadadaadbddcbabbbbcadcaddccdcdccacabadcaaccccbdbdccbbbcaabbbaadcdbaccacbcdbccbbdbcdbdaddacaadacbbaabcaadbabbdcacdddccbcabdcbccadbdacbdbadaadddadbddcbabcbcbbacccabbcadcbcaacdabccababdabcdabcadcadbbaaacbabcabbbbdbddddddcdccdbabdbdddbbcddcbbdcbcdcadcccccdccdcaabaccaaadacacbaaadadacaabaabbdbadbcacbcdaadaadcbadddbcaddcdbcabbaacadcaacbcbdabdcadbccdddcacbddbbaaacdbabacddccdbbdabaabaddbcabbdcabbcddccdcbdcbdddccbcaaabbbadccabaddaadadbcadacacadacaadcbabddadbcbdbbddbdbabbdddcdcadaacbbcdabbdbbdaddadbbadaddbaaaabbcddcdaabdcdccbcabbabbdcdbbcbbbccabcacadcabcbcaabadbdbbdaaabbbdcadaadcaaddcbdadacbbaccbcbccbdcbacbbabacaabcddadcddccbccdbdaabcabaabaccacbaddcaaaaacddcacdcacadabbdacdbbdcbbcabccbaddcacacdcbdbbdbadcbbccdaaacbdadaccadbdaccbadbabdddcbccdcabddababccacbaabaccbadcadaccdbaccadbbbcdcdbdcbcddbbdccacbdcadddbccacdcbdcddaaabadbbacaabadccabdcbaacaadbdcabcaaddcbbdbdbabccdbdbdabacadcbabadccbccccddcdcdbabddcbabcdabbcabcdbcbdadbbbcaabcdcabdacdaddacbbdcbdbcccbccabbccbbbccaadbbbdbcaadccddccbbbbaadbdbaddaadbacdbcbabacbabdcaddbadabbcbbacbaaabddcdbddcacaaaaaacbacacbaaaccaaccbaabadbabaccbdbabacaacdcacacaddcadccdbcccadcdbbcbbdacbadbdbbbcaddaadadcdbdcbcacbccadabdccbccdddccbbcdbcbabbbdbdacdbddbcddccdccadacabdaccdcabcaadddadcdcccbdaacaacbcabadcadbdbdcabdddcddbdcdbddcbbcbdcdbbdccddbaaccadbccdcccccbdbaadbadccaabcbdadccdbcadccdbddaabdbddbbaaddbdadaaadabdcdbcbbcdbdcbbacdbccbdbbcdaddcdbccdcaddaabddcadbbdadcddaaabbaaddcabccdbcbadcbddcaabbbbcbcbddbacbadaaaddcaabbcabcacabbadaccbdbaabddababdcababcddbbbaddcbaaddaaaaacddaaaaddcbbabdcdcdabadcdcbcbbdbacacbacbbddcdaaccddaabaacaabcbbddddcbacbbacacbabacbdbbbbaddaadadcdcddacdaaadacbabbbcbcbcbbccadddccbbbddccbdabbccaacbabdbcbccabadbbbdabdbcacabcdacdcbcbdbcdaacddacddcaaadbaacbbababcaaccacbdcbacadbcbcbccbaaacaabdcadddacdcbcbacdbcacbcaadcdccbcdcaabdbacadccacadbbdadcbccddbcdddacbcdadcaaabbbcdddabdcdbbaaadccbdccaabbcacacbacacacababcbacbdbcdcbbccaaabadcbbcdccdaabadacbbcacaadabdabdcadacddabaccdbadddadaabbddbaaabaaddacbdadbbabdcdcccbbbbddbbddcaddcabbbabdaaababaadbadadbcadabadccdacabdabbbccbacbacadabdccabbbabbdddcadbaaddcccbabdaccbadcbbbdabaddaacdcccadcbdddcdabadbccccdacadcccdacdbccbddadcaccbdbcabddccbbbaaadacddcdbbcbbcbaadbbaaccabdbbabacbcacababdbdbdcddbbdddaadddccbbaccddbccdbddbbccbbcdadcdccbccadbaaaabbacbdccddcaabbdadbbbbdbbdaddcbaabaadcdabadabcbaadcccaacbbaadacaaaaadadddacadcbbdbbbbdcdbdcdbadccdccddddaddcabcdadbdcbccabddaccbbdcbacccaddddadccdabacdbadabcbdaccdabbbbabdbbcbacddacbccbdabaacaccadbddddbbbabbdcddadacdbcdacacdaccbadaaadabbcdcacacbcdcaaccbabddacdaadbbaccbabddcccbdadcdaabdadabdcaacdbbcbaabcddaaadacdcabbdcacaddaabdcabdcbcbbcdacdddddaaaadbbacdadaabbbdbdccdcacdacdadcacbcccabdcbacdcdcccdcddbcbddadcbddabacbaddcaadbddbadadbacaadaccabcdbbaacdbdcacbaacacaccdcdbdbccbbdccdbccabdaaaacabdccdbbacabcddbbabbcdbadaaaacacccdcbbbdacabddacbbcababbdcbbcdbcdbbcbbddaaabacdcdcadccdbcbdcdacbbcddbdacaabacbdccbcdcbdbbdbdbacbcbdcbdaabadbabaabdbaabbbcccdaadbadbabcacbabcbcbadaddcbdcaacaddbdcabacddaaddbadbaddcbdabcdcacababcadaaccadccccbbbbbdaadddbaabcdabacabaaadadabaddccdbbacaaaadabcdbddbaaabcccdcaabcbadabbddadccbbcadcccdbaccaddacabaaadadbbccbccddbdbbcbabccdaddbbbccbadcadddaacdbbabdaadadcadcbccadccabbccdacaababbdbddaddcddbadcccccaabdbbdbbbbddaadadbdcdacbbbccabcdcdbbbbabcadbbadbddcbadadaddcccbbcdcbaababddbaababdaaaabcbbcacbcaacdcdcdbcadbbcddbdabcccccabdacabbccbdadddcacbdddbdadcbcccccddcbdaacdacbdbccdbaadbaaacdacbadbcaacaccdcbbabaabdbbbcbacbbaaadbbaabdcbadbabdbdbacbccdbadacdccbdabadadcacdbcbbdcbdbbdaccbcbccdbbaaacbbbdadbcbcacadbcdabadbbddcbdbccaccbdcccccdbdaaadbdcdbcdacdacdaababaccabadadbcaccdcaddbddbbdaabddbbbddddadddbdcabddacdbccbaccbdcccbcdbcbcccabaddccdbcbadcdbbbdaabdcaddcccbcdbbddbaadbcdcbbabccabdadcbdacdcbadddcbacbddccaccdbccdacbbabdaddbbbabdcabdadbdadabbadadbcbcdbaadadacaddddbcbcbbacddbdbcddbcbbcaabcdbcddbdddaaaadaddddacdbdaadccdbabbbcdbaadabddabdbdacdcbbaadadbcaaddaccaadbdcabaabddbbbadddcacaadacbdbbbddcccbaaaabadabaabbbccbddccaaabbdccdcddcdbabcbdbccbcddcdacddcdccbacacccbadcdcabbacacbdadcadbcaababdacacddcacadbcddccadbcbcadbcbccbabdbadcacdacabcbaacbbbbdbddddaacdddadacadaddddddbcbcdddaadbabdbcacabddddcbababbdccacbdcbaddcccacabaacabdbcbdabbacacdbdadccdadabaaccabdbcbacbbbbaaadadadcbdcddcadbcdddbcacabadabcccdcbaddcdabbcdbccdcccdcaaacbaccccbcbacbcbbcbcaccbbdcdbadcaacccccaacaccdccbacccddbcadadbdabbbbbdcccdbdddbaabdacabbaddccdcdddabdccddcaabccadcbcdbddaaabdbacaddaaddaddaddcdbbbcabddcaacaacccaacabdaadbccadddbabdbdbbdcdabdcadbbcbdcbacadbcbdcdccaddaddaccdbabdaacbdddadcbabccadccaacddddbbbdacdaccbccddcdbcbbbacdadccbbdcbbdcddbbbabcadbdabdaadcbcbdddbbaddcddcaccdbccdcadcacdacbdabacaabbbbacddccddccadbaaccaacdccadddabaccbddaaabdbcdabcdaadcbbddcbbaccccdcdbbbddabdccdadbbcadcaaadbddcaaacbaccdbdccccbcacdddddbcbaacdadadbcbddcbbcdddaabcaacbbcccddbbbabaadadacdadbcabadcdcccbcbadcadacdccaabdcacbbbccabadacddcbdcbbaadacbbcddcacabddabbdcababdcbabbcaaddcddbcbaabaabbbaadacdcbabcacdadbbdabccbcdaddaadbcaadbbbacacaadbdccbbdccbdbdccbaaabcacbccadbccadcdaabcbbbdbbaddabbdcccacccabcadacaaadaacbbadccbdacbdddccabaabbdcdaacaaddbdaddbcaddcdcbabdccacdabcbabbcbcbddddcbccdacdcacaccaababcbadcccbbbdccaaabdcccaadbcddcbdbabdadcadacbbbddaadaaaadcacdcbaaddadcddbacadaadcdabaadbcaaabddbadaaddcaabddbbbaccabdbdcabbcdabadabbcaadcbdcddbbacabdbdabadbccababbbdaadadacdbdbccacbdbdcabbaadacbdddddaddbddbcccbbacdcbdcddbdcadbdaccbcdaaddbbbcdbcdababcbcabbdaacddbacdccbbacaadcbabcadccccdadbdaccbabbbbbbbcbbcabbbdccabacbcdbcaacbaaddcaacbcbccbaabbbcbbadacccccaadcdacdabadbadcaaabdcbabbabadbdacabddcbadadacbbccaccabcdbaabbcaddabbababaabcdcdabadacacabcccbcdaabdccbbaaadadadccdddddbddabcddbbacbdcdbbabdcdacaadcadcddbabadaaacadbbcdadabbcbabbdddcbdbbdabbdbcdcbdcaccacadddaabcbddacbabccbbaccacbbabbdbbbbcdddbbcaacabcaabdddcacbdbcdabaacacbaaaacacaabdacacdcadcbdccaaddddddcbdbdbbbcddcadbcaaddcaabdddacdabccdadcadaaacccaadaaacccadcabcbcbdadbdccbbcacbcddcbabbabaaaadadbcdcbdbaacacadcbdabdaddbaadbdabbbdaacccdabbabbdbaabddabbacacdcadbaadbaaccadbbacbbcaacacdbbbadcbdbbbbabbaddcbdaadaacacabdaaaabdccbcbccddbbccbcaddcbaaadcdacbbddcdbbccacadbabbcbaaaabcbcdacdbcadbbdcbbababcbbccdaadaacdbbbbcacdbabcacdddbacacccdcddcadcbbcbbaaaabbaadabaccadbbaddcdaddbacbdcdacabdccbddbbddaaaacdacdabbadbadbaaaacdabacbacabdaabbcacbccccdccabbabcaacdababadabcdddabaadabacdbbadaccaabaabbdccacccccbbbccdbccaabcbabbbbbdadbbaacbddbacbcdabdccbadacbcdbcbcaddcbcaabddabdddbdbbabbbddcaacabacdcaadcbcbbabbddcaabcdddddbbdababbbccdbddbabdaddabbaacaaadbdbdcbbdbcbdabdbcabaccbabcbcbbdbbdaccaadcaddbdadbaabcbccbcaabcaddbdbdcdaaacddabbabddadccdbcccbabbaacacbabcbccabaddcccdcadabbbabdacdbaaabbacdacaacddbdcacbccbcccdbbadcbdcdacdbcacdcabcaacccadbdbcbdcadbaadbcbbcdccbcbdaddcbcdacaacbdbbabccdddabaabdcdddaacbbcabbccacdbccabcaacbabcadddcabadababcbbadadbdaadadbccbcaccdcccbbdbcbaccdbbdaadadacaabdbbdbdacdacdbbaabccdabbaddddccabdddcccadabaacddbcbcdccabadbabbbadadddacacdbadbbdcddbbcadddddcdacccbbdbddaaaadbcdbbdbcbcdaddaacabccabdabdbcddaabbdbbbdacdbadcbbdaaaabaababddbcacddbbdbbaabbddacccacabcdaadaadcbcabcdbbaacbbdabdcbdbadaddacadabaccacabacccccbcdaabacbccdbdabaabcaadcdcbbaadbccbadddccacbcbacccdcddbdaccaabbcbccbdcacbcdcbcdcbadacacabbcdcbbabdcdbaabcaaacdcbccdcbbbdbadadbbbddbbcacdbbccadddcdadbddbababcbbcbbcdabdcccdbdbbccdbbabdcddbdbcaacdbbaaaabcbadabadccbbaabcaabbabdaddaaadcabcccdaacdbdcbdbcdacadaacadbddadaacabdabbbcaaaccabcdbdbbaacdccccdbdbbabcaababcacbdabbcbbabaaccbdcdcdbbcbccaadbbddababdbdbbdaadadabbcbbdadccccacaaaaacbbcaddabcadadbbdcbcbdccdddadbcbbacabccadcdcbcaabbddadcacbbdbcabaddadabbdacbccccbbbacdddcdbbcaadbdaabccbdcaddacddccccbadbcabddcbaaccbacbdaaadcacdbbbdbdcdabdadcddacbccdcabcddcdcaabbdbccdbcbbbbcdbbdaddacdcbbcacbbcdbddbdacccccadccbbcdcbabbacaaacdcbaacaaacdcccabbcacbbcddbabcaaacaacbabcbcacbbaadbaddbbdccaabacadcddcbdabdcdaabadbbcaadddaadbadacbdacaabadbdacddbaadaaaccadbaccabcbaabcddbdadadcaacdacccdaccdcbdcaddbbabbadccaaadbaddcacaadbdbabaadbdaadccbbdbbddcdadcdcdaadaabdaaaccacbcbbaccabaabdcdcdcbcbaddababbabcddbabacaadcadacdbbdadabaddacaccbadbdbcddddcabcccabdbabaddbccabccdabbcccbdddcbcdadbbcbdcbacbabadbddcabcbdcaabcdbdabccdddccbbdaaddbadbaddbddddadbbbdbadddccdcdacbaacacbbddbacacadbdcbdbbbcddacbcaacbdaaacccaccaacdccdbabdcddddbdbbbacacdabccbadaccbbbbdbbadacbabdaacdcaabdaccbaccabdddcbcbbadcbbbaacdacdbaadcbbcbdddaacabddcddccdccaabadcacabccacabbaddaacaccaccabcabdabacaacabdbabbbcabdcbcccaccddaaddacaccaaadcdccdaddaabbabbcccdcbddadaacdadcabdabbbadcdbdddadaccaabaabdcdbdaabacaaddddbcddacbaabadbdcaaadabababcacddbbdbcbcbdcaddbddacbccadbdcdaccdddddbabdaadabaaacbdaadcaabbdabaabacabcccbbcdbbacdacabadbccdbaaddcddbdbbbcaddbccadbabacaaccbbdddccbaababcababadadcdcbaadddaadcacadcabadaaadbdcdacbdbaddbbcdcaabbaacbdbddbdcdbbddabbdcdddccbccdadcdbcbdbaabccdacbdcbdabcbddadcacdaadaddbcdacbbbaccbcabacdcacbdaabdbbbccaaddabbacbbaddadbdddbddcadadabcdaadbcbdbdcaaabdbdddbcccbaaacabdbdcbbbdbaadadcdccaaccdcccbcccddcaacaddbdabcccadddbcccabcdabbddcbddddabcccddcbddabacbcbcddbacccdadbadabcddacabaabbcbdadabadaabbaaabdcbdacccbbbdcddddbccadcccbadbadccacbdadcdcbcdbacabdccdabdbcddabdbadcbbbdcbbadbcddddcaacababbdcabadcddababccbdabbccbadbabcddbdddacadddbaddcbbabdcbbdccabcadaabbacaabdcddbbdbddabbccdcacbdbbacaaabcddbaaaacacbdabbbbdbbbbdbdbddabdddcacbababbcdccccbadccbcdbbcdaadcbbbcbbbaaabbacbbcbdbcabbccdbbcdaabddbdccdaccdccbcaccadadadbacaaaabcdccddbcdabdbbbaaadccdaacbdbbacdbccbbbccbabdbabdbaabccdaddbcabdbbcaabacbabbcdbccacbddacddcbaaadcaabbdacdddaccbcbababbacdaaccacaaaacadbbbadbcdcbabbbbcbdcddadcbddcdccdadaabbbcdadcbabdcadbdbabadddcacacdbcadbdbbdabacbcadcaddacaabbdbdbccdabdbdbddacdbbacaaabccadabababccadcadbcaaaadbddabadbdcabdabcdcdcaccdbadbddbcdabbbdaabaacdcddbbadacaabdbdccbcbbcddbbdbdddddcddddacbacacadbadbacbbacbabcabbddbcbaaadbcabacbcacddcbcdbbababdcabaadbbacadadbabacdabbcbabdccdbdbabddbdcbdbbacacdddbacaabadadbccadbbdbcdbbbddbadbbdcbbcacadccdaddabbbadccbdaacccdbcbadadcdcaacdacdcbdcabcdddcabbcabbdabbcabccaaddacdccaddabcccaddadccdbbbcbbcbddcdacddcccacdcadcaabdcddbacadddbdbabcddccdababcacdcabaadcbabaabddbadcbccccabadcaddcbbbdbbdbcdacaadbdddbbdcaacbbabdcdaabcddaaabccaaabdabcaaacdcdacdbdabbcdacbdddaabdddddccaccadadddaccccdcacbacdbccabbadabdabbcabcbcbcaabaabbdaaacbadcbcdddcbdcbdccddbcdcbbabcbdaaaddcadbacbbcccdbddacdbcabbbdddcbaadbbacbdcadcdbdbabbabbdabaddbdbcbcacdaaaaacdabcdbaccbddaacadabbbcacdcadddbadaaacaadaabbaaaadbbaaabbcddddbabcbaddddcbcdadddaaadbcacbabacaaadbaccbaaadcddbccaabbdaaacadabdbabdadabdcccaaabcbccadddacacdcbcbbadaaadabcdbbcadbcacbabdcddcabdabdcadacaadcadababcbdbdbcdbdabcdcbaabcabbcbbdaddabdadbaacdccdbdbcdbaacbcbaadbabacccccaadababcabdbdaaabbaddbdddcbabdbbbadcbbddccbdbdddacaacaaddbbddadbaaabaccbddaacdbcbdbcdbaacdaadcacaabcbacddbbdaadabdabcccaacaaaaaccbdadbdbabcdcdaabbcabbacbbbdcdcdcdacbacbcdbadcadbcbaabbbbcddcddabdbdcdccdaacabadaaacaaccddbbbccbcdbbadadcbcacdbcddcddabaabbdddbadbacaaadccdacaaddadbdbbbbabadbcccbbbbdcdbbcbbadaadbbbccbdcdbdacccacbdbbcadccabacdccabccbdcdcdcacdddaabccccddbdadcdcbabaadcdcbdaccbddcddcddbbaadacdcbaaabbdccadcbdadcdadadacaacbcdbdcdbbdbacbccbccccdcdcaaababdcbaddbabdaacbaacbbdabdcdcacddbaaaaadddcaccabbdaabcaadbcddacbababcccabcacddcaabdabdcddaabbdabdabdaaccbabacbbbabbcbdaabddaddcabbcddbbdccddadbbddbdaacabcbdaabcddbbcbddaaabcdcdcdddaadaaaccbdcbdbcaadddcbdaacadbadbabbdabdcbdadaabcacbcdacccdbdbadbcddbdccacbccbcaddccddabbcabbcbbabbcddbabcbcdbddbdbcdcbcaccadaccbadbabbaccddbbdcababacbadabbcbcadadcbbcdcacbaaadacdacccdbdddadbdccaddddddbbcdddaadcacdacdbddaddccddbabbbdadbacdbcaaadccabdaadcbdccddaacbcabdbabdcdaabbaabbadbbdbabbbcadacaddabaccddcdadbaaacbccdbcccbddaacadadccabcbdbdccdccbccacdcdaaadcbcbbaabcaddccddbbcacdacadabacdcdbdbdccabadddbcbcacbbcaaccacaccadcaadbcdbcadcadbaaaabddbdcdcbbdaccabccdccbdbaabcbdacbcadbdbbbcdccccdaaabcabbdadbccdaaabdcbcbdbaddcddbdddbdcacaabadbdcaddddcbdaabdbabbacdbccbaabadbccdaaabacdbaccaaccddbadbbacaddacaabbbadbacacdbabbacdbadddccdcbccaaddcddbbbcdaabdcadbabdbbbbaaacccccbbccdccabbdbccdbadbbdbdddbbddbccdabcaacddcbdbaaadcacdabacadddabbcbddddacbadababaabdabdacdcbbcbdbbccbcccaddbbbdddbabdadbbbaacccaadcbdaabbbdcdccbaaccabbaadbcdbccddddddcbaaaabbbabdbbcabdcbcdddbbbcbbbbacaacacaabaadacbbdacacbdbbbcbacbbdcbaaaaccdcdcccbbcdabaaabccaaadbdcababdbdabdbaddbdcccbadbbccdaadcdbbbccbadcddaccbcaddcbdacbabcdbcdabdddabbbacdcccbbbaacbcdbddacccaaacadcaadbdacbbbbabaaacdbcdbccadabcdaddcaabbbdbccbabddbaacdcadddbdbbbbcdbddbabdbcdacdbabbadbcdddcabdbdaaadaacbdddacabbcdaabbccbcbddbbcccacdbbdbadaadbcccababdaabbdccbaccaadcbdbbbbdcaacbbaccbcbaccabcdbabcdbbcbdcbbdadbdabaabbcababacbccbabaababadbdcdcadacbdaacbbbcbdddccacbababbcbcccddabaaaabbabcacdbabbdcdbaaddaddcdcadaadbaddbaadcdcbaddbbadbbbbcaaabccddddbcbbacddcaacdbaacbbbbbbcbadadcbadcaadcdcdabadacbbabaccdccdaabbcbdcbbcdaddbbabbddcdbdadcaadaddabbcaabadbbbbbabddacccdadbbdbbcdbccdaddbabaadbdcdaddcaaaaabdddddddcabbcddcddcbdbaabadccacbcabcdbacabbbdcccdbbacdbcdcdbcdcccddcacabdbbaabddadadddadddbbbcccccaaadbabdaadbddcbbdcabbdabacbbccadadadbbdbdccbdddbbbadddcbcaadccccbacdabcabddddabcccbacdabcadbdcdaccaacccadbcadbadbdcdddacbccaacbacdabdddccbccdcbabdccdbdbdbccaddbaccabbccbcdcbbcdccddbcdaddbabdaccadbabbabbcbcdddbbcadabcbbccabdbbdbdddbbcbdcabaacabdcadbccdabbadbadcddcadbdaccdbdacdaadccdbcaabbcadaadaadbcadcdcdbdbdaabbddddabdccdabdabbbcddadcabbaccccbbdbadbccdcadcbaaaaccadbadadccdaaddccddcdbbbadcacdacdaaaccdcacccadaabddaadbbdbcddbcbcabdbaccbcdacdccdbdabcddcaacbcdbcdbdbdabbbacbccdcdbdbdadbbdcbcbaabddbdbcbccdcacdddbddcabccdaddbddbbbacababccacddabcbddcbbaddadbbdaadacdbcadaccdaddddccbbdacadbcacadcbbabbbcddaaddbacdbbbadabccdbdcbcbbcbabdcdcabcdcaacacddbbccabbcdcdddcdcacacdabaaadcabacabbdcbdcddcbacacadbdccabadbdbdabcaabbbaabdcdadbacdcaadcaadacdcbabccbcacabcddabccadbbabcaddadcbaccbbcbbabddadbbccbadbcdacbdabbbbdadcacddcacccdcdcadaaacbabbbcbaabaaabdbcddcaadaadacddbcadccdbadabaddaadabcbbadddcbbcdaddbaaaabbdabddcdadbcabadaabcaccdccdcababbaddbaacccdabdbadaadbdaabacbcdaadaaaaacdbddbdbcadabcbdbccdccbacbacaccdcdbbaaaaabbbdacdbdaabbabdcadcdbadadaaddbbdcddcdbcdcdadabddcccdcdbccaaacaaddbadcdbcdbbabcbbccddacadcccbccdabdcdabbaccbddccaccbddcadcdaddbacddabcdbaddbccdcbcddbbbdcbcabdaaadbcaaaadbadaccabdcccccaabdddcacabbbcbbdadacbbaadabdacbcabddadacbabddaaadcbcacbcdbcbdaacaaabccbbbdcbaadcccaabbcdbacccdddbcbbbbcaacbbabadcaccdabbccaadddabdccbbbcbadcdbcaddbdabbaababbdcbaaccddbcbcbaabdaababacdddcdbacdcadbbddacbbabaadabacbadcabdcccbcbcacacadbacacbadacdabccbbcdabacdadbcdabccabbdbcaacdabbcdbcdabdccdabbbbcddcaaaadcbdbbcaaaacacacddbbdcacbcbdbccbaccdadabccdbbcaaddcaacddbabbacbabcaabaacacccabddbcadbbdabbdbdadcdabcccdccbccaadcabcdacbdbabbcaadaccccacababcddbbcaabdcddddbbbcaaccbccddabaccdbcaabbbbccddbbcddcaaaabcacdbdbdbadadcdcdddbdaacccaabdadbdacccadbcbcadcccbcbaadbccbbcbbaadbbcbdacbccbcaabdcccaaaaddddcddbbaaaaccaabaaadcbccdcddccbcddbcdbacdaaabbacaabcaaabaabacbaacabaccaacabbaaaadadcaacdadbcadcbdbdccbcbbcdcadbdaacbadbdddacbbbcaaaacdbbbabbdbaabcddaddacaadbbbccadcdcddabbddadacdcbcacddadbbadbaadbcbccaacadbdbdbadcdadcaccbbdcbbcabbddcbacdbdbbadaabbcabbdbbcbdbbadddcdabbbcbdaaccccbabacbcdabdadcaccadddbdbbdbbabbaccdcbbcbbdcaacaccbacbcdbaacaccbdcacabbddadddbccacddccdcddabdacdacdaddabcdcbcbbbaaccccabcacacbbabadcaddacbdcbbcddccabbadbadbddbaddadbaabdcdaacadcbccdccacabdadadadbdbacddbaccaaaaddbbbddbddacabcbddcbdaaaabbdaadbdcabcaaabbabcdaaaacaabbbcbaaaacccdaabcbcbccbccadcbccdcdcccdcbaabaaabbdcdddbadbdaabaaacbbcdcbdbabccdacaacbccbbabadbdcadddbdacabdcacdabccdacbbbaaadaabbcddcadccbadcbdccbccbdccdbbdbcabadbbdcacdddddadddadbadbdacaddbdbcacbdbdccabaddcbbdcadaaadccbdddbdcbabacaddabcdddaddcbadbdcddbbadcadcbabdbcacacacbbbccdccbabcaddbadccdaacabdacdbdbabbbdbabdccaaabadbaaacbaabccdbbbbcbdcdbbaacddddddaaabacbdbcbdadbcacadbababcddccabcabdbadcabcbdababacbcdcbdbacdddbdbaabdbdddbbddcdabdcacbbdbdbaddbccdddcadccadaccaabccddbddaaadbadacdacacbabbdacaacdcababcbbbbbdadccdcdabcabdcddcbabcacbccdaddcadaadbaddbbdcdcbadadcabcdddacadcbcabaabccdcaacaadbddccddbccccaccdddbcbdcdbdbacccbabddbbcacaabcccbccacbddcbcddcaccbdbcdabcdcdbdbbdbdcaaadbabaabcdbdcccdabadbcccaadcbcdabddcbbcbbbdabbaccddabbcabccccbbaabdbcccddabcdcbccabaaadccbabcccdddddbdbdcbaaddccddabcbdccbbaadbbabccdabbbacdcbccbbccdccbacababcdbacddcdcdaabcabdddcabbbbbbdaadcbdcabacacbcddbcbbccdcacdcccaccaddcddacaddbbbbcdcbdabaaaacdaacbcddabdcccdbbcbcdaabbddacdccbaaddcddabccddbaadbdcdbbabdcdcbdcdcbccbdcdaabbabbddcaaccbaaccbbdccbadbbbccccddbdddadbdbbcccaccadbacdcbbdabcccbaabaaabcddcbcbacdaaddabbdbdadbcdaadbdccbdccbbbbbcdcbcdadbaacacadadcddccdadcacddadcbdcdbbcabbdcbaacbcabdcbddcdbdabaccddaababacdadabccdccdcabdccbccdadcbbdadcddbbbcabcbadccacbbcdadaabaccabddbadacdcbabcacdaaccaadaccaaaaabdbcbbcdddabcbccdcacccbaddbadcdabdcbdbdddcbcdcdbcbbdcdbdaacddaabcaccbdbcdabbbcbadccdabbdcdaaacdcbcddcaadcdbaddccdcbaacbcaaddacaaaadbdcabcdcdadccdbccccbdccddaaabdcacccbdababdccaddddcdcbdaccadbbccadadddbdcddcddcdadbdaaaccacdadcbadccacadbbdbbadccdaccaacbbbddaddcdddcccbdabbabdccddcdcdccabbaadbbbbbdddaadabaabbaacdaaaabdddabdaaddbbdbccabcbdccbabcbabcacabbababbcbcccdbbbcbcbbbccbdbbbddcadcbdabcdaccacabaadcdaabaccaaaabadaababdbbcaddbdbcdddbbacdabbacbddccbdddbbaaddccddcdbabadcbdabdacbabcdbddbcaaacbbbbbdbbababdaacdcbdcacdaadbbbbcaadaadacdcdadabdbcaddabcaacbbbcccabbbbbcbbcdcacadddccacbcbabacabdcabcccddbcbccccabbbbdbaaccadadbdcbabcbcaacbbaaccdbbdaccbadadcabbddccddabbadadcbdddcbdddaadddacbcbccaaabdcbcbccacbdbbcddcbdbdcbcabcabaddcabbcabdcadabacbddcdbbabcadcaadbdccaacdbaaadaaadcacaadcbddcabcdcdacaaacbacaaccaaabacdcadaadcccaddcbbacbdcbabcccacdaababcdcaababcbcdcadbbabcdcabcadaccbcdcabcddcbabcacccdbadcabbabddbabbcacccdbcbccddcaccbcdddbabadabdbaddcbabdabdcdccbbcadbdcacddadcdcaccaadbdabacddbcbabaabbbbbdbabdabdcadccacbacbdabbaaaacdbcdaaccaccacdcccdaddddbcaadbadbbdabbdbbacdcdbdbbbacaaabccaabaccdddbccdaadbbccbcabcbaddabbcdccdbdbddccbbdbddbbcadcbabaacaabdbbbdbbcabcaccdcaabcaadbbdacabcdcdbbdaddddbbadbddacdaccbcbbdcaaadcaddacbcccabdaddabadbddddadadbbcaacbabddccdbbabadbbabccdcccababaaabaaddcddccdbcdcddccccbdbdadccbdbacadabadbbabbbbadcabbbaccbbcdccbbabcbbbcdacdbacccbbdbcaacacdadcddcacdabddacdccaacbdddbaabcccadccdcacadccabccbcccdbcbdacbbadcddbcdbdacacadadbbbcdadbbadccbdbabdcaadbcccaaaaddbcddbcadbbbdcdbdcddcabacdbadddacbbadbcbaadcdcdaaddaddbaaccbdcccadbbddbdbadbccdcaaaccbcacbdacabbccdbbdbbccddbabaaddcdaddcdbbbaabdcdbbbbbdbabacaadbdcdbdbcdbddabcbabcccdbdaccabaabcbdcbbaacbbbddcbdbacdabbdcacddccccddbbabdcbcddbbbdabcbdccabbaadddbcdaccaabcadddabcdcddcaadacdcacacdcbdcdbdcbddbcdabbdccbddcadadbdadbaacbdbdaddabccbabacaacabcaaabbdcdddbaaddbaddccbbcaccdabbcaabccdaabdbaccdacacacadcbaddbcbacbbdcadadddbaaadbbcccbcdccaacabcdcbabdaddabbabacbaaccbdcaacccddbacabaadcbcccdcabdbbcabdbccabacdcaadabaaccaaacbbaccadddaabcabcaaaccbcaaaddbabcbabbacaadccdbbdabacabadabcabbcccbdbaabdacbccbacbdaabbcdbadaabcabdcdadcbddadccbcbcccdcadaabbbcaaaddbddcddadacdccdbdacbcabddaabacddccacdddccbabaaddbcaaaadcbcadcdabdadbdbddddbcbbcbdcbbbdbccdcddcdcbbcbddcacbcadccbdaccacaaadacbaacdadaaaacbadacdccddbcbdadcaccbcbccbaccdabacdaccccccbcddbaacbacdcdcdaadcacacaababdcbdaabbdbaaabdbdacabbabacdacbcdddcbcadbddaaacbbbdadabbaddadbdbccbacdcdadbcbacaadcdcccabdcacabadccaddacabbdaabcbdacbbbcacbcdbdddadbcbcbcbcacadcbdbbbbddcdaaabcdbacadbabbcaadacbcabbbddcddcbbddddbdbcdcdcaaabacaabbddcaaccbbaadccabdadcdaabddabdbddcbbbabcbccbbcbbdbdabdddccadbcbdccbbaaddaadbbaccdcacdcabcadbddaaccddacbacbdcdaacadddcbcbadadadbcabbbbabdcdabbdcabbbcdbaaadbadabbacdbabccbdbbccdbaadbdababbdcaaaadcadcadabbdadcddbaccccbdaadcadccdcacdabdbbacbdbdcaabadaaadccbdbdacbcddbcacadbbdcdcacdacabbadbbacaadcddcabcacadcbcbadacadaddcaadaadaaabbdccdaaddabadbbddabbbbdacdcaababbaaccbadbdadcaaccccdcdacacbadcbdccbcdbbccbbbdcddcdddabbdbacaadcbacdbabcddbdaaaabbcccbbacdddaaaadacdcddbccdcdcabccbabacbdaaaabcbdaadccbbaccbddbaacddcdccabdcaadabdaaccabadabbacbdacbbccbdddbccaccdccbdcaaacacdaaddadccadddcaabaadcabbdacbdcbccacbbdddcbdcaadbdcaadbdacdacbbbadadbabbddadbcadcdbddcbabcbccbcbabdaaabccdacccdcbbbdbbddbbdbbdbadaaddccaaccaacdccabccbcaaaabcddaaadbcacccbbcdadaaacddccbdcabddbdabbdabdcaccdcbbbbcbaadaacaddcdcaadacbcdbdbbbccacbdddaccccadccddabadaaaabaddacdacdcaabaaacbbbdddbbccccdbdcdaacbbcdaaabdbbaabbabccccacbabaaaaddcbdbbbbbadbccbadcacbdbbdddbaadaacbdadcdddbdbccdcabccccddbbddcabbabcaaddddbdbbbddacacdccccdccccbaaadabababcbaaabddcbcbbcbcbdbcbccbdcbbdacabdcddadddacddcbcacacdcbdacdddacadbdbabaccadbdbbbbacdccdacbaddadaccdbdbabbdcaacdaccddabdbabccddbdbdbdcbbaaacddabcabacbddbdacdcccdbcbbabbdacacbbdddbccbaabbddcbdcbababdbbaddddbdcbdaadccadbbdbaadaabbccbabddbbcbdbddbbcabdabbbccccbdcddbdddacdbdbdbcbdbdcbbbbdabbacddcdcbacabbabcccddccbbaadccdbcdcacccdbbadadbaddaadacbdccacaabadcbccabacabbdcbaadcdcdbdbdcddbccbadbbdbabdccbccdccabbcaabbcaaddddadbcabdcabbbcadaabababaccdbbdbabbcaabdbddbbbcdaacdccabaddbddcddababbaabdbddbbddbdacacadcdddcdcddbdccadaabbbacabbcdcdcdbddaaabacbcdcccadbbdbbcacddcddaaabddcacaabaaccadcbcbdaadbbbabccdccddccbbaccdcacbdaaccddaaadacdbdbabdbdaaaaddcbcaabdcbdcbdbbbdbbbdbdccabdcdccdcbddbaadcccbacbcdbbccbcdcdbcdcddabbbabdddbaccbccdcbcddbccddbdabdcbcadbcaaadabdbbccdbadbbadacdbaabadaadddcbcbcaaddacadbccbbcaddaadcacccdddbdadbbdaabbacbddbcbbbbaabcbbccdcacddcacccdccadbcdbdacdccaacdcbcdcbddbcabccccbacdaaadcdcadabaccbbcbbaacaabcbcaacbdabacdcbaaacdbbcabcbacbbdacdbacacbdbbbaababaacdcdbddbdccbcabbdacdabcadbbabadabbcacbadbbbbdabddcdaaacbbcccbbbbcaadcbccdcccabdbcbdccabbcaccababaacbbadbbbcadcdbdaaabadbadcaabccbdacbbadccbdaccacccdacccabadabdbabacbaccdcbdbaccaabcdadacdcdabccaabdabbdcdcdcdabccabadadaddabbdbcbaabadcacddcbacbbcadbddacbccbcdaccbccccbaabbcbadabdabcabddbaaaddaabbccabcbddabcbcbdaaaaaadddbcdbbdddaabdccddbcabbdcbaccdacabaadddbdbcbddbdddbdbbaabbbbaaabaabccdaadbdcbcdcbdcbbdacccbbbdabddccdcaabdadcabcbaaaadccccdcadcadbabcddddddacadabadccadccaabbabcaadadcdbabccdacdbacbcacbbddcbddcccbcdbccabaadcaddcccbababcbddccdcdcbcddaaaadbcadacddbabcaabadbaaddcaccbbdcdcaccdabbdbddbabbcdbcccdbbddcccdddaccddbaccdcacadcdadbaaabababbdcbbddbaacbacdcabbbabcddcbadcbdddbdddacbadcadcdbbacdacbccbacccdadcbabadbddbabbddbcdbabdabaacddcbacdcdcbcbadddbabccadccbbcdcadbbbdbadbabcdabbbadbadbcdaabcaddbcbadabdcbcbcdcbbbcabcacaabacdadbccbbccdabcadaadccaaccabddabbacdccaadbcbdbadcbcbdabdbaaadbcdadccbbcdaddbccddcddbdcaccaddcbbacaaccdcbadcbdbdacdcddbcbcaaabddcdbddcddaacdadadbbbccdddbadaaaccccaabcbbabdddcdbdaccdbaccbadcddbaddbddaaaaddaccddcbadacaaaaabacaccbbccccddbbaabdccdadabcacccacabdddabacbbcdccdadbcaabdaabbbbcddccdbbbaabbcbaaacccdccdbcdddcdbcdcbdbcdcbbbccbdcbacdcadbdabacbbaaccdccccacdbabccbbdddbcacbccaddbdaacabcaadbaddbdaaccddcadbbbbdcbbacaccccaabdcdabcbabcdcdadabbdcddcbbdccdcbaadcaaccabbcbddcbcdbdcacdabadaaacbabccdcbbbbaaccbcbacaabdabacbacacaacacacadccaddabacaddcacaacbcdaaadaaaaaacdbaddcdadbdbdcbcccdbcccaacdacdcdaadabcacdacbcabdaaabbddcabbddcdadbdaddcbbabbcbacddbccadcabccddcacdcadabaddacabadbdacbaabbbbddddcaadadcacddbcddccaacadaccccabbcbcdaccadacdcacabbbacadbccacdaddaacadbaabaabdabddaccacdcaddbbcaacdbdcdcdcacbcacdbdbababbacaddaddbbddddacdcdcdcbbbdbdabccdccdddabbcbcabcadbadbddaadcbbdbacccbdaadcaabbdbdbdacaddadbabdcacbbdadccbcabbcbcddadcbbdbbcadddcbcababcdbaddaadcaaadbbaadbcdcadbabbdbdacbdabccbccacbcbbabddcdaaabdbbadabbddbdbdabdbdbbcacdcabdbdbcccaaacdccbcdcbaddcadbddabcabdbccadbbabbdaaddbcacdaddbbdbcbddcbbdacacdbcabdbabcdabcdabcbdadddcaccbabddacdacbccdbdbdacbabbcdccccacdccacddaacdabcbaadcacaacdbdbbdbcacddbcbaadaaadadccbdaccbadbdaaadadcbdcbdcdbbacdcaaadcdabccabdbaabaacabcbbabbcabbadbccddaacaccdadbccbaaaabcdadbcddccdcaadabbdbcbacbcadabdbcbdaccaabbbbbdaaacbadcbddcbadddcbcacccdcccddabaccdddbbdabccbaadadbbcbddbadbcaabcabddcacaaaaacaaacadaabdcadaacccacbbdddadbdadcaabadcbaadbddbaacbacadbdbcaaabdcaabcbddcbbccaacbbbaabcaacadacdcccdcdddcbcccbddaddabcbcaddbdabcadaadaccbcaabadcbacadaabaccbcbcbbccdbcbabcacaaccdaddbbabaacaccccdabcdadcddccbddbbbabbdacbbbabdddcbcaaaadddcacbacdccadcbaaddbcbcbaabaacdabbcacabaacccbaccdccdccbaddbdabdaccddadbcdaddbacdccaaabbbcbadabdaadbbabdabbdaabacabccadcbccaadccacdcbbcaccaddbadaabacdbcaaddcccbddadaaabcddccdacabbbcbaadcbaadbbbaabdccbbabacdacdacadccdcddbddcadddddccdacaddacadbdabadaabbdcababdaadcabddbcacabacbaabcbdabbdabdbacddacabdccbcdddcbcabdbababacbaccabadcbacadccabddbcbddbbaaccdddcacbdbdbdbaadbdcdbbadcbaacbdbbbdbcbccadddcaddabbbcabadccdcacdbdcaabdddaacaddcdbccdbcadadcbaadcdaabaccacaadddadabcdadcdacbabaadbbabadbdabbbdacccbdcacacdcccbacbdcdabdbdaaddbacaaddbaabdadddcadbaddcbdcbbbacabdaddcbcdddacabccabaadabdadacdbdbacdddaaadacbbbbaaaddddbadcccddabbabaddaccdacbdcdcbbddbddbddccbaadbdbabbccdaccabdccccadaadbbddbabaabbcdbdbdddbbcacabbbbacbcbacbdbbddcacaccabbdbaaddbadadcacadabaaabadbaabbdadccbcdbbdddbabacdbaacdaacababddbcbbaadcbddacadcdcabbbabaabdccadbbcdcadbaacbdddbacbdcbcddbaaaaacdcbcacbaabacdcdbdddabdabdbbcbbaaadccccacccbcbccbddbaccbcdacabacacddcdaadcadaaaacbcbdbddabacbdcdcdaaabaadcbbcccbabaddbbaabdbbdaadcdbbbdcdaacbbacbbdacaacdadccadcadddbdadccbcdccbadadccbbbdcbabddcbabbabbbbdbbdbccabdbcabcaaccbcaabbddbaacbdddbcabcccbdacbaddcbdddaacaacddcccbabcaaaaaaacbacbdaaabddccbccbbabdcbabaadbdcabccaabbcabaddbbddcacaaaabdcbbbcbaabadbbadaacaaccdcabaadabcacacdcabadddbcdcddbcddaabbdbbdabcdcbcbdaaabcbdadaaaadabcbdcbdacdcdccccadabbdbbbaabddbabcccbacbbbcaaadabcacbaaacccbcbccbadbcaddabccabcccbdadcdaacdbdbdadcabccadadaaacbbbacbcaddadacccdbdccddcaabaaddbccdccdbbbabcbdcbbacbdabbdcddcdbdbdabcabdbdddbdacdcbbbbcccdaddbcccbadcddadcadbaccdbadcbbcaadbbdccacabccaddcbadcdbdbcdacbabbbdadabbccaacabbbbcdabaaaaabbbbaabccddaadbdcddacbbbbabcadbadddcbdcacccbbacbcacbbcdadacbaddabbdddbdccdcabcccbdcccabdcbbaadaadcaaababdcaabdcdbdaccaddbaaabacaaaccbbddadbbbaaacbbdaccbcadabcbdcbcaacdbbcadadcbcadccbcdbaaccdbaabadccabddaddabcabcbbbcdadccaabcabdbaaaacabcccdcabbbccadddccdaabadadcddaaacbcbcabadcdbbdacacbdaddbcdbacddbdabbdcccbabdadbdbaaabcaaacbcccbcadabababbcdacdcdaacbbbcabcbcaaabdcaadcaadcbbdcacbdaadabbdabbdcaccacaccdcbbabcdacbdacccddcbdbabcbdddaacdacaadabdbddaaadbcbbadcbcaaadcbdbbccabadccbbdcccaaddbcddabcccaaddddabbccdabdddccbcaabaddcbbabbbddbbbaacccddaaabccddddddbadaaddccaadbadccdaadcdaaddddadccdbacadadbbdbcdbcbdadcdcddbdacbbbcdddbabccacadacacdbabadcaadabaddaabddbbbcdbcaadbdabbbabcdddaabbddccdcbddacbdabbcadacadcbbcbbbdbadcdaadcddddbbbaadacbdacbbbabbbaddbadcaaaabbbbaacdabcbdbbbbccdbacbbbadbdaccaadbacccbdcdbcbdddbdbabbdbacabbaacaaddccbacadccadaadbcdacaabacbdacdcbdcbcbdaaaadcdbabbdabdcbdcdcabbbdddccbadaadbdaadbacccbcddadadbacccbacbcadcabdbacacbbaadadcbccdbaaacabacbabdacddcaadbdbbbacdadbbacddccdbccaaacacadbcddaabacabdaabbdcdddcdbdaacadaadbcbbacdbdacbdabcdbbcdcdccbcbbacdaadccbbcbdacdabbdcadaccaccadacadcabddabbcaacbabaccacccbaccdaccdccbbaddcbacdacddbacdcbcdaabacbbabaddacbdbbcddbadbdcdbdbcdaabcabdbcaadddbccbbdcbbdadbbaaadbdcabdcabdcacddaacbdbdaadaaddcadbacbadccabbadcabcaccdbadcccdbacbbbabdaabdabcadccdccbadadbadadddbdbbbaccdddcadcbddaacdbbabcacbadcadbcabbacabadadcdabbdabccaccbdbdbdadbdbcadacbcadbbbadcbdccabababaddcddbddabbcccdcbacbcaadcbdaadbbacbccbdcdbcccddabdcacabacddcddacbaccbacdddbbadcdcaadbcdbadbccbbabaadcaabccbacaaadbababbadcaccaccdaccaddddaadacdcabbddabaaadcaccdaabdaabcaabdbadbbbbccbdaadbdbddbcdacdddadbacbbcdadcdadcdbbddcbacbaacdbddbacabaacaadbcdabcaabccddcdadbacdbbcccdbbbaacacccdbdabbabbcdcbddbddaacadcdbacdadbcbbdccacdbacdcacdaaaddcacaccaadabdaabdbbacbdddaccaddadbcdabdccddacbccbbcdbbacdbcadabbacbcabdbbdddabaababaacaacdcbcadcbabccbacabcbcaabadddbbddbaabadbddbababacbabddabdababbacdcccccbcaaddadabdabacdcdababadbcbddacdcddcdadbacbccbdbbbdddabddbdabcdbdacbdcadcdcbabbccdcbabcaacccbacbdacabcdacbbaaaddbbbabdaadabbcacadddcababbaccacbbabcdbabbddcaaabdabbaadbcbaddbadbaaddcbabdccdaddaacaabddbadacaddcaacadbacbdaadccaaadbcddacbbbcbadaccbbaacbdbdccdcddcaccadbacdddbdddccbcadccabcadacbcbacddacadcbbacbdbabddddbbdbcbcaccccccbdccbbabdbdaadaccdacacbccddbbdbddddaabbdcbcdccaacbddcdbccbcaacadbaadcdcccbabbccdcabbbadaccaabccdcdacbccbbcdaabacdbddbabaccaddcaccbcccddbcaaddcbcbdbbabbdcaddddbabcdcaccbacbdcbbbcbbabdcbbaccbbcccddbcbdcdabacadddddabbdbdadbabccaccdacbccbbcabadcddccbccdbdccddacacacbdddcbacdbabcbcabcdbbabcbaaccaaadacdccccabbcacaccabaababddbcaabdacabccbacbdbcdbbccbacdcdaabbccdcbbcbbbddabddacabacaddbaccbbbcdcbbdccacaabbbbbbcdbccccddcabcbbbdccbcbcccdcdaacbbcdddcaaccabacadaddbbacddaabbaaaaadbcbabbbaacdbddabcadcccaadcbacbbbbacaabaccabdbdacdcdbddcbbccabdbddbbabbaddcaccdbdaadbabdcacdbccadddadccdbbcaadccddbadbbcabdabbdacdbcddbcadccaaaacccacbbbcbbdabcbabccdbdabcccbcbbdabcdacbcaadddacbdbdaaadcccdaaabaadbabadccdcccaabbbbdcabadbdcabdcdcacbcbcbccdcbcddabcbcbaaabacabbaccbadddddbaacdaabbabddbbadaabbbaadddbcacccddcccdbabbbadcabccbddbbbbcbaccacccbdadadaaadbbaaabbabcaccabdbbdaadddcccaddbcaabaaadbdadbdaaaaddacdccabbdbcadaddccdbcddcaabcaddcbaaccdccccadcdbacdcbdcdcaddadccccbcdcccaaadaabccdacdcbbcabcaadaabbdbadbadcbcbbbaadaaadcabdaddbbacdabdbcdbcdbcdcbaababdaaabadaccabbbadcbddcdcbbdbbddbcbdbaddacabbabbcbdadaccbdaadcccacdabbabcddaccdbcbdbcdaaadbacbbcddccacbdbabacccdcaabdcdaccdaacdbdabaabcaabbcababccbabadddcadbdababdddadcacbadcccadcbbabbadccdddbaaaaddccbacdaadabbdbdccbcdaddccbdccbcadabaaccbccabdcccdaabdacaccabdbcbddaaaacbaaabbaadddacdabcdcaaccaabcaabaacdcaaadcbbbababcbcbcddddcbdadccbdacdcabacabbccddadbcbabccadaacbbddcaadabcabdbbabacdacddcdacccaabdabddcaabbaaabcabbadccdcdbbdbadcbacdbdadababbbdabccbbdacddcdacbaddaadcbbdddbdccbadabbdcdbbadadbdddcbdacbcaddccaccbbbdabadbdbdacaabaddbcdcdddcbbdbccbbadcbacdbacccaacddcbddcccacabdabccdbbdbadaaddbdbbcdabccdddbbbbcdbdbbcbdbadccddbbaacdaabcbcdaadbdbbcacaabdbadbabdcccbacbaccdacbaadddbbcdddcddbbcaccbbdadcadbdcbdccbdbccccddadcacdcaddaddbcbdbdbbccacaaabcbcccbdbdbbbddbccbddcddadbdbdbbbccdcacbccccaacccbacbcdccbcdacbabbddcdddabaaaaacccdbabdcdccabcdddabccbdcacccddccbbcbdabbcdcccdddddadadbbbddbbaabcdbbcbcdacdbdbdcdadbbccbdddcddaabdbcccbbdcdddbaccbabdacadbdcdbcbdbdcdadcbdabbddcdccaaacacbccdbaacdddbddaababababdadddbdcbdddcccdcbcababaddacdbdbccdacbabacbdbbaddcabdcccdcbbdcaddaaddccbdcdbdbaddccabcddbcbcccaacdbddcdadccbbdbabdccdbcdabacacbabbbcdaccacacbabbdaacbdbbdcdabaabccdabbddbddadaddadddbabdcbcacdadadabaccdcdcbcdcdaddcbabcbcbcdbbddbdabbdcdbbccccbadbdabdbaaddcbcddcdbdbaaaacbaaacabcbccbbcbddcddbbabcddabcbaabdccbbcabddbaaacbcbacddccadaacbaacbbdadacabaccddbbbaadbdcadbdacadaabbdcbdcccabdbdbcddcacabdbaadccaabcbddbddbbbbaababdbcadadcbdbdcbddbdcccaabcaacaaaabaddabaaabaccccdddbccaadcdcabccabcbbcccbcdddbcdcdcbacbcaccadbacbddabdaccbbbcbbcaaabacaaaccbaacbddbdcbcbacaadbdddadcdddcdaacbbcdacabccdbdabaabbdcabdacddcdcdacabbdccaacbdbccbbddcccbdddcbdddaccbddadccaadbabdddddcadadabadccaacacbddabcdcddddcadbdabdaacdaaabbaabcbdabdaccadacdcbabacabccdcbcbdbbbdbcbdbabadabdcddaacaabbdaccdcbaaaddbcbcabcdaabcabbdaacaacbccaaadbcbbddcaadcabdbcbadaddcdaabcacbbcbbddcbaadbddacbaaababdadddacdbcdccaabbaccdbcdddcadbbcadadcbaaaadbbcdddcdcbdcbaddbadcacdaacdbcdbddbcbdadcdddbdccdcbbccbadbbcdcbdbbdabbcabbcbdaabcddacacddbcdcacacbcaaacbbbddbdbcdbbadcbcbacbbdbaaccaaddadaddbabbdddddcacbcbbaaccdcaddaacaadaacdbabadaccabcacacccbdccbdbbcbdcbcaadacaabccacaadaddcabacbbbbbdadcabacdcdcbdcbbacbcbdadcbbcbdadbcaacccdcbccbcaabbcddbacaababbcdaaaadbcacdbcadbccdbddaacbcdddcdbbcaacbacbcdcaccaaadbdddcdddcbabaccaacbbbaadcaddabdcacaacbacdabcdaccdcbadaddadddcaabbddbdddaadddaccadcdcbdaabcacdcabadddddabbbacdbcbabadaadbabbababccaddcacaabccbdbdabcbdcabcaacbdcdacdcdcddacdabbddcddadcbccddbadaaabbbdabcdbccaaacbbcdbabbabbcbddbacabdbabdcccbdcbcbacdaaabbcabbbdcbcbacccccccddaddddcdbadaddcabbddddccaadcbcbccdaacccacccbdbcdbdacabbaddbbdbadabcdabbbbbcbcccabddbccbdbbdcccbbdbaccccdabdbdccdabcbbabcdcbccdbccccdbbccadddaaaadddabdcacbcdcddccbbacbbcbbccbdaaaaadcdbccbbbbddbbaaaaacacdcbdccddabbbaccaddbbaaacdcababaabcaabcbcdbdcdccaaccabcaadacbcddbddbccdcadabbbcdcaddbddcddccddcacbabdbdaabbcdabbdccdcabacacdbcaacdcddaddadaaddbdabcaddcdbdcacadcbbabddddabbdbdcadcbccaaccaabbdcacabcdcbdabbdcaaccbcabdddbdacadbcccbadcccdabbabcacbbbbbdcacadabdcccaabddddabbbbacdbbdcaccabdabcbddcdbaccadbbdabdacdbbdcdacbbabaacadcdbdcddabbbaadcdcccbdbacdddacbcdcdadbaaacbccddcabbadcbdcdbddbbbbcbbbadcdbbadcbbdcabaabdcbacdcddacdbbbccbccccabccdbdadddcdabaabdbddadbadddcbbbcbcaabababdccddaaadccbccacaabadaacdbbbabddbcaaacbaaaccdcabbabccadababcaccdbdaacbdacbbcccacbaacccdbcccccacacbcaaabadabdcdcbdaacbbdaccdddbcaacdaacdcbcccbadbcacddbbddbbaddbddbdbbadbbbaacdcabadbbcaabadadbcdcadbacacdddbadacacddbcbccbccbccbbbddbcdbccddccbcbdddddcdddbccabadcaabccbbbacddadbbdbdbdbbccadacaaacbbcaccccadddbcdaddabccbbbabacccabababcdbacaabdbccbdacdaadbcbbaadacdacabddacaadaaddbbdadcdddddacadabaaddaccaccbdbdbbdbbbccbbdabbaccbaadcbdaaccddccadccddddaabadbaabaccbcabbcccbcdbabadbdbaacddbbcdadadbcaababcabbcbacaccdaacccaddacaaaadbadccabbcbbdbdaccbbbdaabcadcbbbdadbaadbbdcadabdccddcacbdddbbbcbdaacaccdcababacacbcabcacdcccbbaaacbdcbadddddcdddabcbdbddcdbadbcaabaacbbacaabbcdcddbbaaaccbbcbababcaabbbcadcabacababddababbbdadcbbaccbaabbacadcacaadacdcdaaaccaccdcacaacabababbacbbbccadacacddaccbaabbcccaccdbdddbaddacadaddccccabcddbbbddcdcabaaddcabbaddcbdcbdbabbacccdccabbabcdddababcabcacdcdbddaacbabaabbabbddddaabcacbbdadaadcacbbacbcddaddbbabcabdacdcbaaabcbcddacbdcadcaddccadaccdacccdaabaabdcbdabbccbbbabcbbdbaacbadaccdbcadabacdcbaabdaadadbcdadccdbcdcbcaabaabbaddccacccbdbbadadbadccadccddcaccdaacbdbdaadadddcdccccadaadbabdadadbddaccdcacabdcadacbcccccbcdacbadbdabaabdccbddcabcacbcadcbbbbdbabdbcddabddababbdaccbcdacdbbbacabbbcacccadcabbbdccbbbacbcbcbcdaabdaaccabadacbadacbddddabadbdbbbabacadbdbcabbabdcccdabbccbadbbbbaccaaababbbdccbdcdbdaaadccbddabcbacbcbccbccadcccaccaddacdbccdcdcbadbcabdccabbdbcccdccbcaadacadddcbadcccccabbccbcbadadcbdbcbadadadbbbabbaabacbbcddcbccdaccbbcbbbcdabcbabdabbabbdbbaaccbdbcdbdacbcddcdbddabdcacdcdaacdacdddcbdddbbdacbddcabdddcbdadacabcbccabbbcadcbdbcaddddadcbccbbabdddcbbdaddddcbcddbabdbdaacadbdabcddbadacbdddaaccdabdbbbcabcbbaaabdadadaddcbddcddcaaacabdaadbcacbccaaadcdabcdbadccacddbbabadabaccdbadcdcbbbcacdccabdcdacddabcbddcbcabbcabbadacaadbcacabaccbbcbabacdbcbacacaabbcdcabaaadcbaddcdccdbaddcdacbcdbccbbabbbbabdbbabdabbdbaaddacdbddbcdbccaddbcccdcaddddabcbabbbbbcaccdcddcbdbcbadccacaaaadcbbaadcabddcabbbdaddbdcacccddcaaaccbdadacddbcadabccababddbdcdaacbaaadcdbdccbccaaadbdaacdabcdaaccdbdccbbcbaccdcddcbacdacadbbdadaacabccddbbaabbabdadadbbddcabacabbabaddcadcdabbabbaddbadbbbbbdddaaadbcbcbaccbbdbabcdcaddaadcacbcddcbadacbabbcadcbbdcacaddccdcacdaaddcbcbdbbaaccdcdbddabaaccbddcbaadddddbbadcddaaccbbbbddaadacccabacadcbbadbbbabcbcbaadaaccbcbcdbaabcccdacacbadbbdbaaacdaadbcabdcacddaaccabaadcbdccbaaccbcdbacccbabcbcccdcadacbccdbbcbabbbabdddabaddcadccdcbdddaaccbdbaacdcdaddbacacabddddcbcadccbdcddadaabbdcaddaccadbccbdcbadcdbcdcaddbbadbcdabccdcabbcadacdbcdbabaabcacdcadbabcdcbbaaccabcbacbcaaaaaccdacbbdbbabcabcbccbdbcdbadcaaabcbcadcaabbccbdadbaacaccbbdaddacaadbdbbbdacaadcbacdcdbadcbddddbbbaaddaabdbdabbacdaadbadbccdcabbcaacdcabbcbaaaccbbddaccaadccadcdcbcbaddbccdbbadcccbabcbcdbbbccdbabbddcccbdddaabacbccbbdccbcddbbdddcbdbabaddbcdbddddbababcccccbcbaddbbbbdaacbaccadabcaadbacbcdbcbbdaadbbbabcdddcbbabbbacdcbadbadcbdbcabadccadbaaabcdbbddbacccbbabcdacbdabdccdbacbaabbcbbbbabaccdbbccdacbdcacdbbdbcbdbbddbabbccdaccaababcabacbcaaccccadacbcbabcbadcccaaaacaaccbcdbabdbcabacbaaddaccdaadcdbbcabbabadbacccbddaacdbcabbcbdbbcbbccbddabacdadcdadccdbdbdadbacddddaabccdccdcdbadaabaccdaadaddacdbcbdccbddcaabbccdbadbddbbdcddabacdccbcbdcaddadaadddbbdcadbcdccabccadbaccdbccdbbbdbcbcadccddcddacbcdbbaadaadddcdccbcbbcddaaaaaaadaabcbdbdaaaccccbabdadbdabcbadbadcdbbdbdbdabaacbadabccbaacccdaaccbdaababcbaacddacddbbcbdddbcdccbdaacbabdaccbbdabcadacbcbbaadbacddcdccbaabbcbdcbbbdccdccdaaccacdcaacbcadabdbccabdccaaddbcaaaacccdcaabdacbddbdbbbbbdaccaddadcdccdddbcbdabcadddadacdcdbbbbbbddcbbddbabbacdcbbabdbcdcdaadddbbaabbdadddbdcaacccacdabadbdadddddaadbdbcadadbcbbcdbdbbabdcbabcaadaaddbdcddcccbadcdddbdacbcdbaabbbcadadbdddbbbcdacdaccbddcacbbcbbcaabdbdbabcbdbddccabbdddccdbdabbbcaaccbbaacccbdadaddadcababcaacdadbaacbbaabdabddabababcbdbbacacdbcdaabdcabddaabbdabadbbbaaacabdbcbbcbddccaaaaacabadabdddbcaaaddddadcdaddddcadcccdbbdccbbddcddabcadabaabaddddbcbcaabacdcadbabbcccdddccbcdadccccdddbbcdbdcddcbbaadcdcddddcbdcbcababccbccadbdcabcbaccdcdccbadbbbcadadabbccabbccddadddcdacdbabcdcdacbbccbbadabbbaaacabaddccbcdaccaabbbacacdcbabddaababcbdaccadbdaacabbabbddddbcdccaacbcabddbbdccacdbdddbddadccddcddcbdcdbcbcaaabbadcacbcdacbbcabddccccddccbdccddcabccaabdcaadbccacadccdbccaccaadcdbccccdcbdbaaabbbadbaccdccdcdaacdaacbdbbdbadbdddbdadabadbbcdadbbbaaacaacccccdcabbcddbdcbacbaaadbbabbaabcccddcdcccacadadcdddadbbcaadaabdbabcabcadacddabcddaccaccaddbdccdcddadbabbadddacccbdacadbdcdbbcaaccaacbaadcbaaadaadcbadcabbaadaadbcaaaaccddcdbadbadaccbdbdbccbabbaaaddaacdabbbabcccacccabacdbccacdabcddcabcbbdaddacbcacbdaabaccaabaabcdbabcdcadbdaadbcdabdcdacdbcbbcdadcbcdbdbaacbcacdbbabbbbacbacabaaddabacbbdbaacbbbcdbbcaadabbddacddbdbbdbdbccbdadcabbbcabdcbabbdacaaadbbddddcbadadbcbdacdbaacdabdccabccbacbabbdcacccacacaddbcacbbaadccadabdadcacbcbbabadadcbdaccacdaaaabacccabddadadcbbbbcbaabcaccadbacaaddbdbccbadaddcaaaddbaacdcdbcaaadcbaddbcdacabddbadcababacabbcaadbacaccdaaadbbcbccbcabbdbdbbdcaadacbdbcccccaccddcdbdacabbdbbbccaaccacadbcaaccabacaddccaabdcddabaaadbdbadacdababbdbdcadadabddcdbdbbaacadcbadbdabdcbbbdacaabcdaddcdcbdaccbaabaccaadacbbabbcddcccddcbdcdcaaaacaaadcacbbaccabdccbdbbacbcbcdabddacbbcdbdbdbdddadbccacbdcccadacadcdbbbadaaadacccdccbcddaacbadbbccbabbcccdabcbdabbcaacabdacdbbddabdcabdcbdacdcadbbacddbdbdcaddddaccbcbddadadcbbacccaccbabbdabbabbbccacbbcbbdbcddbdaddabdcccbbbddacaacbadbadcbdbcabbcbdcaababadcdbcdcddaabacdbbacdaacacacddcdcababdbccdaddcccbcdcadccbacccaaccddaccbabcdacadddaabdbcdaabbcbcbabcadacddbadccdbdcbbdcadddcaddbadabccaaacbcdadccadbbabadcacdabcbccdaacadbcdcbdcacadabdcccbbdacbaacbbbbabbbcdcbcaadbacacbdddacacabaacabaadcbddccddaabdabcbddbbcdbdaabdcaacaaadbdcadaccacdabdcdbbbcababbaccbbacdccddabbccbdccbcacdaddcdcacbcdaacabbaccbadacbacacbdbcbdacacbcbbcaabdcababacabbbcaabdcddbccdcbdacbabdddbddcadccbbbbacddbddabddbbccdbccdcdbcaabaacbdbbdbddddddcadcbadaacadbdbbbadbabddddbdbcbdacbdddbdadbbdabcdcccdddaabcbbbadcaabdbbadcdabdacbacddbbaadaacaadacccdccdbcacddcbdaabcddcabccdbaababbacdcadcdbcbadabaadddbcabbddcccaaacabcaaacdcccdbcacabdcdaadcbaddcbcccccdbdaccbaaabccddabadbbddaddabcabccaadcdbaabadbcacdabdadcdadbcdbcccbbccbddcdbbacdadabbabcdcccbabcccabaabbbbabcbbccdcdcbccbdbbdbdcbbccddddccaaadcdbccdddadaaccbdaacaddbbadcbaaadccadbaccdaadaccbcbcccabccdcccddcdcddcdaaaccbcbcdbdaadcbcbcbcddbcdacbcdaadabbabcbbbcadadabccdabaaaaabaddcdddbadadddcdadcadabbabcdccdcbdcadacdaacbcccddbcaccbaacbcccbccdabbcbacbcadadcddbdccaadcbccbaacadccdacddcabbdbdccadbbaabdaabdcbdcbbdabbdcaabdbbcbccabdbddaacdbbdbbaaddcdabaaaacdbcacaabbcbacbcbaaabcaacddbbcbcbabadacbddaaadccbbbcacaadaaddabddcacadddddacdcabbcdacdcacaabbbcdbdacacdbccbdaaccbabdbddcbbdabbbabbdbbcdbaddaadccbadbaababccabaddababddbbabddcbbdcadcbcdcbcccdacdbccbaabdcdaaacabbcdabdbaaabcaccaaaddcbaaaabbbbaccacdabadbaadabdbcdabadadbaacdaabacbcdbddbbcbbbbaaadcbddbdccbcbacabdabcacbccaabbacbacdcdcaccdcdddaaabbbacaabbdbbdaacdcaaaadbcbbabbccbccdabccddbccddaddddbbdbacbcbadaadcacbcbcdbcbbbbacbdccaaacabbdcbdcdcaaaddbabdadacaccbdadccdabaacbcdaaaaacdaaaccbcabddcbbdccbdcbaadcdaadbbddcdbbcbbbbdddcadbbdcacdbacbcadadacdcbaacbcccccdabdcbdcbaddadadcadabacdcabbaaacbccddacaccbddbdccdabdccdcbcaacddbadabdcdcbbabacbddacabbaabcddbbcdcaacddcaddbcdabcdadccacabbaabdacbaacbdbbacabacbdaaddbddbbbcdbadcdbcaaacccbddaabccdacccaaadcadaacaaabcbbdcabbabccbaadadaacbbdbbbccbdbdbbdcdbadcacbcacdcaabdbbcabacaaabcdbddcccdcccddbcbaacaadbacbbdbbabddbdaddcaadbaadaacaadaaddcccbdbbbaacdaadacbcdcddddcadacaddbcadcaacdddcbabcacddaaacabdaccddccabdabacabdbbaabababbbaccdbbccabbadacbacbaaadcdbabbabcbdbbacdabaadaaadcadabaddbabcbadabccbbddcbcdbbcbacadcdaabdcaabbbcdadcbdccadcaaadbbaabaaddacabbababadabcaddddddbbbabbbaddccabdabcdcaabbdadcddaadadddaaaadacadcdaabbadababddaabcccbaadcaabdddbcbbaddccdddbabdbbdcbbdcbbaabadaadcbabcdbadbaddcbbbbddadcaddccbabdcabaacbaabbcdadbdadcadccaabbcbadcddbadadbcccccdcaddddcbdadadcadbcccbaabadadddabddaadcbbccbabadcbcbdaadcbbdabdcbbccacdddadbcdddbdbbbcdcddbcbcbacbaccdaabcaaaabdbbdaadaaaaacddbacdcadbaddbabcacdccbabcabbccbcabcdbbcaccccbbccccaadcacccccdddcbddbbcadbdcbbaabcdbabcaacbbcbbdcdbcbabdacacddadbddadcdcbabddbcaddcdbcbcbdcbaaccdddbabcddcbdaadadbccdbbdabbddacccddbccaddbdddcddbdbdadaabbaacadbabaacbaababbccbacacaabdbdcdbacbcaddbdccdbbccabbdcaccdddcddacddbbdccdaabccaccabccbbccdbcbadcdcbacbdbcacacccbbbccdcacdcdbdddcdacadacdbbccccdbcaddabdbcbccdcbaccbdaadddbdadddaccdadcaabdcdcaacadcabcbcdcdcdadbacabddabbcacdaacbbaddbcddcdacaccbdadcbcdddcbcbbcbbcbbcbbbddbaaabccdaadbacacabccbcdaddcbdbadbadccaacbbadabcccbbbcababbaddadbdbbddbdacbdddbbabcccbadddbdcaacbcadabcaddcbaacdbbdcdcdabcadadcacdbdbadbabbccddcdbdcababbcbdcaaccdaccbbabcbcacbcdacaabadabddcabdadbdddbdcddaccacdccdcadddbccaabcabddcccaddbdccdbaaddbdcbcdddbdbcdcdadccbccbbbbadaadcddbadabbbcccbaaababcdacbdcccbbbdccbabaaadaacaacbbabacaacaddcbbdccbbcdacadbbdcacadbbbccdddddbbacbcadaabcaddaddbdabdbdddcadcbbbcabaacdcbaaadbacaabccbdcddccddbddbbacccbbdadcaddcbabadcbdddbdadcbcbadcaacacadbdaccabcdcdbdbcccaaccbdacaaacbcacccbcbadbdaaccbcdccaabdaccaadcdadacdcababddbdabbbcccabbccddbbbadadcbcacabdaccaaaccaccaadcccdcbdbbcadddddcadbbabacabbccdcdcabbcdbdbdbacbbabbcbdbdbbbcccccdcbddcbddaaacbacabddcddbcddccccdbdbbddcbacdaabbcabadccddabdbbacdabcabccdbcbbddddabbabbadccbcdacbdaacdaabdcacbbcddbacbadbbccabbbdadddaddaaadbcbdabddbcbbcbbabbbadaabadabbadacdcdcdbddbadcbbdaaabbdadcaccdcbcbbcdaddcabaddbaddcdabacadabcaabbaacacccaccdcdddcaadbbcbdacdaacbdcabbbaddbbccaaadcdcbdaacdbdbcdaabbadbccccaccccdccadaaddaabdccdbabadbdbbaadabadaccbdcddbddadbbabddadddbcaacaddcbddbcaadbbcaabaacaadcdddacdcbcacccaadbcbbaacacdbdaccbadadabaacbacabdacacddcabdaacadcccaaabbcacbacdccdbcddcdbbcbabcdbdbacddcaaabbccdcdbbaaadbabcabbcbbadbaaddcdbabacabddcccccbcbdcadcaabaacbbdcbdbccaadbcaaadbbdabcbbcbccddbbdcbcccddbccccbddbabdddadcbcdbcdcdcacaaccddadbdccdaadbaaaacabdbcdaabddbccbabccdbabdbbdaaddcdcabaadccaaddbaabdddadaddacabbaacdcaadcdccabcadcdccddcdcbcbcbabaccddbaaabacbabdcabcadddcccbccacddcbbcdbddacdbacdbdadcabbbabadcadcccbbdcbbdbaabdabcdcbadcdadcbdbbbcbadaccccacdcaacabadabbcdddcdbddbdbcbbbcbadbbccdabdcaaaccadacaddaacbcabadbcbbcabdaadcabaaabbcbabbdccbdadabcbbbdaacbddabdaaadcdbbabbcddbdacccbdddbacddbcadaddbbaaccaddbcddbccbcacdbabbbbcbaabbbbbcbacddddaddcdacccbdbdbcadbdabdacbccaacacbbadacbccbcbbdacaabcddccacbdddacdbdcdbdddbbaccabbbccbdadabdbaabbdaaaaaddbcacadcdcbdacadabadaaacccbbdadbbbbdbcaaadbaacccbbcddabcbabddcbddbabbaabbcbacabbbacabbbaadbbdbddddabcbabcccdababcdaabdcadbcaadabccddcacddabcdaddbdacadbdbddccdbcacabdbacbaddccbdacdadacaaabcbccbbaccdbdcacbbdbabcaccbabbcccacccbadcaacbbbdccdaacdacbaddbcaaddabcabadcbbdccaadaddddcbbdacbbbbacadbdbcadcddbadadcbbdadcdaddcddcdcdccadaaaddcaababbbaadadcdcabbcbabaaabcbdaabbbcddacbbccaadcddcddcacadcdabcaadaacdbcabcbdadddcdadbddcbdbbabcccaadadcacadadddccdbcdbcccdbdcadcbdcabaaababcbabdadaacddcdbaaaabbcbccbacccddbdcacaaccdcdddaddddaccdbbaacacdbbcddcbadadaddcbdbbdcccaaadbcbdcaccbababdbbcaadcbbddbddcbdbadddbabdbacddabaccdabbbddbcdadabacabcaccdbacccddacdababbcdcaaddcdcadcaaaadcbdcabcdbdbacdaacddddcacbcdbdadbcaccdddaddaaddcbbbbcccbcdaaaabbabaaabdaaadcaacbadddddadddbbabbadcddbcadacddaaddadcbcdbdcdabacbbbcdcaabdaddcccdcccbdddcbccabbbdcdcadbdcaabbcccbdcbdcdddadddddccadbcccdccbbcaccdbdbcbbbcaabccdbacaabcaabacaaaccaacbdadbddbaddabadbbbabcabdddbdbdbcccdddbbacdddcbbabaddccddddbbabdaccddbbdddabbcabbaddbbbdabbcdadaaaabddaacacdddaaccbddbdcbacdddbcabbaadbacaaaabbcbccbdacdcbbdbbbccadadcbcdcddbbdcadbcabcdabdbabdacbdadcadcccaccccacbbacbdcdbacdbadcbcbbcdabbdbaadcdacdbacabacadbadcdabacbaaadaabbcbddbabdabbdbadddbdcadbabaddadacdacdbbadbbdaacbbccadbbaaaacabaccdacdbdabacdbcdddbabbaacdcbdaabbbbaadbbaddcaadadddabddcdbccdbabbbdcaacdacadcbbbcdbaaacdbbbdbcacbabadbcbddbcabaacdbcdacdccccbdabdaccacdcccabcbdaabcdcabcadacacaddaabbcdbdacccbdcabbaccbcbaabcbbccabcabbcdaaadadbbcbbbdddadbccbbbcadacdbbcabbaabdbabdadcbabcdadbdccddcadbbbaabbbbcaaaabacddbabdbccacbcacbdadaccbdcabdddadadbcdbaddbdadcccabadcdbaaacdadcddbcaaaabbaddcbdddbdcabdbbdabcdabbdabbdbacadbcddccaddbcacbcadcadaddaacddaddddbbbdcbddaadcabdbcdddaacbaaacdddbbdbcbdcadaadaaabdddaaddcbdaccaabcaadbabadbabccadbddbdaacadbbabdcdbbbaacddcaadbdcdbdadbcdcbbdcabaabcdadbccccabcbcaccacadcbadbaaaaabcabaabdcddabdbbaaaabbadbcadaabccdabcddaaabacbaacccadbabcaccacdaadcdadccdabdacbcdcaccbaccdaaaacbcabddbbbdacbddabdaadddaacddcdcacabbcdcbddbcbacccbabbcdddcaadacaaabcbacdcabddbbcddcdcbcbcabdbdbcadbacddcaddadddcdadcadadcabdabadabdabbdcdabdbbdcbbacaacbbcccabcdbbcbcaadcaddadcadddcbcbaddbcbababadcbbdddacccdadbbbcbdaabbdbabaddbadddcccbdcbcbddcbdcacdadddbdcdacacddacadbacacccabdbcdbbdbbbccbbbdbdbcacbbcdcdacbdbcaabddcacbabbdcbbddabbbcbdbadbcccabdbbbdcabcbdcbbbbdadcbababbcbccabdbdcabcbacadbdcdbaaddbbdbddadabbcaddcbcaabbcbabdcbcbdcbcbdbbccaddaadaaccbadbccbcdcbbabccbadbbccabdbcaabbaddccbdcadbdaaddbbaddbddaaccccdababadcabacaaabcabcacdcccddbadabbbdacdbcbabdaccbbdacdbbddcbcbaddabbdddcbbbbbdbbcbacacbaccccaccdbbcacacddabccdcccdaaddcaacdbaccdaabcbdabccbaddabaaadbbbaaadabcaabcdaabcabdcaabbaddcdddcbaadcaddbcadaddacacbdcadcbadbcdcaaddcacbcabbdddcacddbaadacddacbabcdaacbabbdadbabaabdccabcacaaddbacdacadcbaabdcadacdbaabcbabccadabdcbbaabccdbbdcddcbddccddbdcbcbbacaddacddacacacaccbddbdaabcdccdcbadcabdabdcabdcaadbdcbbbbccaddcadbadddddbcaabadbcbdcdcadbabdbbbadbcbbbabbbcdcbbcacdcddacbadbabadabadbbddadbdddadcbbcaacdbbddabddbacdaacbdcccbbcdbdcbbcacbcccbddabdabdbacddaadcdabbcdcadacdabddcabddadbabddcdbbabccaccbaababbbaabaddacaaddaddcbbdbcccbbdbddcbacbcddccaacabbdcddcabdddbdadcdbbcbbbcccabdddadaddcaabadcdbcbabcadcccbddbcbdbbcccacacbbadccabaacbacacdcdadaccaddccbccdcbcdcbdbdbbcbdccadabddacbaacbbbcabcdcddcccbddcdcaabcdaabacacdbbcabccacbabdaccdbdcbabbbdbabdddacdbcacacbdbaacbcdcadaacdccbbcdcbbccccaaccdbdcaddbaadbaacbdddadaccacccbdcabbdcdabdacbabaaddadacbccdccdbabcbaabbbdababddbadccdbbdcabdacdabbcbbaabcbdaaccaddcddbcdadcbcdaaaaaaacabbcbdbadbbdcdacbbcabbabcdbdadcbacdccadbcddacddcadadccaadbadbbaaddaacccddbbabaccadaaaacddcbabdabddcbabccadcccbacdaccaabcbbbaaacbdaacbbabaccbccbcdcbccaabdadacbacdccdddababaadcabacacaacccdcadbcdaabcaaddddcdcabadccdabaacaaaaadbcbcbaddcdbddcdcdbbababbbabbbbaadacacbcdbdbbbaaaaaaadbddcbbaabaddaccdadacbbbbddcacbdbbccccdbcccbccdcbdbcdcccbbcaddcacbcddadccccbabccaaddccdaaccbabddaccdcdcacaddddaacbabcbadbdadbaacbbdbdccdccadcadcccbdbdacdcbbdcddbadbaccbbbbcacdbadaadadbcacacadbaabbcacabcadcddaabcbcaccaacdcdabdaaabcbacddbbbdbcacabaacbcacbacdbaaabcdbbdbdaacbaabbdadcddbbdbcbadcaddbacaabacccabadccdaaccabcacacadddbbddbdadcaddcdbabddbccbacdccdbdcdbbcabcccdaaccacadbdbbacadcbacdccacdccdbacadcbbbababdbdbacadccabcadbbcdddaccccdbbdbaacdadbdacdbcbdaabadabccdaacacdadcdbccadcaaabccccacbbdcbabcbbabaabdaddcbbbaccacadddcaccbbdcabbbbcccabacaddcabaacccdaabccdddcabbabddcbbdddcacadaadcabacbdacacacdcdadaacbdbdbbcccddbcbaabdacdcbbcbcccbcadaabdbcbabcaddbbdbbcdadccbbaadbccccddaadddabdbbdbabadcbddaddacbcbdcddbacdacbdcbcaaacccdcbcdaccbccaddbbdbbbccbabcdbddbdaacdacadcdabcdddbdadccbdcdbdbbcdbdadabbbbbbcdcacddcaadaadbcaacaabddadaaacdbbbaacabdbdcadaccadabcbddaccddbcdbdadcdabbbcddcaabdbbadbabcbddcdddddcbcbdacbdccdcdaadcdadcdbdbccddbbcabaccabccccbcccaaadcaddbaaabcdcdcdbbbaddabaabccbacbdbdadbdccdbbcaadcbcddcaacdacdcbdabddddaccacbadccbbbaabbcadcabacbaccbcbccdcbcbcabaabcdcbbbcbacacccdccccaadbbbdaababcdbcaccdcdcababaacbbdbbdcbdccaddcaccabbcbcacdaabcddacabcbcdbaacddcadbccbdddcbaccbcbbaabacbdbabbddddabccccdaacccbbbddaaadacbbdcacdcaaaacbaaacbcdbccacabbdcaabdaabdcdddbbaccdbacaabcbcdcdadbadacaaddbdcabacddaacdabadccabcdabdabadcbbabbddcaaccbccbdbbbdcacddcbabadbccdcdacbbbccdbcbcddcdcbacacacddbbbcdbbdccbbcadbaddccbcdcddcaaadcdaddbbcdddadaaadabcbdcadaadaabbdabccadcdbadcabacacaaccdbacddadbcdbbbbaacaaccadbcbacabdabbbabbadadadabccdaddabbacacbacbccbcbcbbacbcddccbaaacddddcdbdabcbaaaaacddddbaddacdcdacbcadaabbdbdcabdbdbdccbacbdaaadbadbbddabcbcbacdbbadbbbababcdddcadbcdabddacadaccbdbdccccdcddbdcbbccdcdadcadbbbdcadacdaabccdadcbcccdadcdbdbbcbaabcccdccababcacbdcaacaabcbaadbacdaacabaaaaddaabacccdabdacabbccdbccadbaabcbddddadbaccbaadbbadddacbcdadcbdacdbcbcadbbccccbcccbbbbcadcbbccaadcacdbcbcbababdcacdbbacbaacbadadabcdbaadcacbdaacdbccbabddbcabdbbbcccbdccaaacaaaacdbaacdadddddbcbdbcccdbcbccadacdaddcddbbdcdbdddddbdbbcaccdabbcbdaddabcccbcdcdaacadcdbbbbcddcbdbbbcddbbdddcbdbbcbbadccdcabbbdaadcccbaccdaccbacccbdddacbbdbadacdbdbcdbbbaabadcaaacbdbccbbbcdabcbaabcdaaadcbdcccaabbadcbbbbcaddabbcbaaabadbbcbddccdaacacaabdacddaaaaabaacbacdcbabdaddacacbbaacbcdaaccbbaaaadccbabcbbbbbaaadcbcabdabaabcbdbaadbdcabdaaaadacbacacacaabddccdadcbcccdacdabbbcbaadcdbddbddbbbabdbaddbdccdbcdcbbdbdcdcaaddaaaabdddadbbacddbcddcadcdbcaacccdaadcbbdcaabbbacddcbdabacbaddcbccadcacadabbcaaccbbacccbacbbbcddcbdbbcccabddadbaabbbcbdcccacbdbbbccabdabbbdaabadccadbbdaacddcbcbdaaabadbcdbaacdbcdacdbacddcccdabdccdabddccccdabbcbcdacdaccccaabddccaabbcccdacddddcbcbddacbabdcdddabacdcbcaddbbbcdacdddcabbbabdbcabdbcacddacbdaaadcaacbddbadccabcdabbcdabdabdacccdadbbddbababaccdadcddbcacbdacbaddaacccdccbcbccadaabbbbdccdbbdbdbabddabaadccbaacccabcdcdcacddccbacaacaadbbdaccadddaaabaabcacaabaaccdaddadccbacdbaddacbacddcbadbbbabdcdbcbdbbabddacaaacbaaadbcadabdbcdbacaabadadabbadacddbdbbcdabababdbcbababcbdaabdadbccadaddbcdbdadcbcabcbdcbbdddcbbbcacccbbbcbcbbbcdbadcbcbcdadbcdbbacadbbbadbaadacbcabcddacdabdbbbacddbcacbcacbdcbbbadcdcaacbacdccbdccdddbccccbcccabdabbcbbabaacbaadccccccccdcadacbadcaaabbbbcbbbdcaacdbabaccbaacaaaacccbdcaaadbdbdbdcccdbbcdcbdbbabaddcccbbddaabaaccbaabcaacbaabacbddcadcdccdddcaaddcddbcbbcaddcdbcdbcabbdcaacadddbadaccacdbcaacccddddcabcccacabcabacacdaadcbadaddbbbdcdbbddbcccdabcbdcdddcbdcdbdbddccdcdaaddddcccbddcadbdbacdadcdcbddbddccbcadcbdabdcdbbdacdacaccdbddbdcabcaadbcbdabbacacadbcdaabccdbbbccbbacbabacbcabadbcdcbdacabcbcabcadabbbbcdbabcdaabcbddccbabdabcbccddddbbccccaaadcbdddaabdcacdababdddcacabdadacdcacdcaabaddacacdcccbaacbdcbccadbaaacdadcbabddabbcacbdaaadccaacdddabcdadadbcbabdcaaaacdcaacacadaabbaddcbdadbacbbbabbbdabacabbbdbccdddaabbbabacbcabcdbddadaacadbabbbbbbdbccbddabadacacccbbccadabcdcadabdbabccacabadbadbcabdaabbddbbbcaaabaccdcacccdcbcacacdcaacbcdddacbcaadabcccaaadacbcddbdbabadbbcbcdddcaadddbabdaabbcbdacacaccdbadccadacccaccdcbabcadbdcdbababbddbdcabcbacccadccdadbbacdcddacaacdccaaaacaccccabdbddadddabadbabacabddcadbcddbddbdacbdbbbcbadccdabdccbcbcdbbadadcbdddcccbaacbcdccdaadabbabaccacbacdbbcacbadaccbaadabdcabddbabacbccbcacdcabacaabcaaaacadbdcaaadccdbcbddbcabdacbddcbaadccbddccadacabdcaadcdbbadcbbddadcaaabdcbbacabaabbabbcbbadadacdddbcdcbcbadabdabbbdaacdcabbbbcdccbcbcbcabbdaccbbcdbbcbcdcbdbcccdccabcaadccbbbabdadddbbbddcadaabdabccdcbbadcddccbddabccdcabdaaccadaaaddbabcccabbaadcbbadddacddcbdacbdbbbbcaddbccaacbbdcbdbadbbbcbdcdbbdcccdccadadaabadbdaddaaacdddaacadbdcdbddaacbbcbbbdaccbbdcbccdacdadaaadadbadababdbcadbdccdaacdacdddbaaaaccacaadaaabaaaaabbcbcddabbcbdbbcaaddcabacbcbbadabdadbbcdbcdbcbdbbacabadbabbddaccbcbcddbddabacdddaaaaadcaaccbbcabccadaaacdaadbaacbbaaacadaacbcaddcdcaababadcaabacbbccaaaabaaadcacaadabdcbdbcbcbcbdadadcaabdabadbccbbbcbdbccdbccddabaabcaacdbbcbcaccaccdacacdadadbcccbaabcabcaddbcbccccccbbacbbdbadadccdcbbddbdbadddcabadacdcccaddcdaacbabacaacbaccdddaccadbbddadadbacdaadccbcbdacdbaacdacbcaaccbbdaabbadbadadbaadaacbabadbdacacadcdbbabacccdaadcdbacddabbddadcdccacaddcccddbdaaaaadbdaadcccbccbaccddccbdaacbdaacabcdabbabadaccabaaddcddcbdcaadcbcbbacbcdccccbbadbadcdbaacbcccdbadbcdadcaaaabbacacaaaddbacccbccacdadbacbcacabacccaabaaadcdadbabcabbbcaabbabbbbdcdbabdbcbcacaaddcbbcdbaaddbacdcacbbbccdcdbbcabbabcabcddabdcbcdcccdbdbbdbbbabdbbcddbcabcadccbaadacadcabbbbcbdbcbcddbaaabbcdcbbcbcccdbabaddccacbabacdadacdbbddbbacbbdcabbdbacabccabcbbabbbaaabddddaccbacaaccadddcccdcdcddcdcbdbcdddaddccabdcbcbdbddadbabcccbacbdaacadcaccdcdbdabbbbcbddcaddadccdaaccbddbbbbbdbbcbdabcdbcbcddccdbcaddbaaddaabcabbdddccacbdadacaabdccbddbdaaddbaaaabdbccadbccdbacddcdcddddcacbccdcccacbdabacbbcdddbcdcabacabdbcbdccdbcaadcacbddbbacdaddbcdcbbbbbbcbababdaddbcdbcdbbdbcbdcaabacaddcbacbcdbdaabbaddbdbddaddaadbcddccabbddcccacabddadadbaccbdcbcacbadbadabaacdccbdadbcdbccdacdadaabcdaacdccbcbaaaacccacdadbcdccdddddddbcabbcabbacabdcdaacbcdbcadabaadcdcddddaabddbdbccdadadadcacdcdcaabbbbccdadbbbdcbacddddbcbddaaacacbcbccbddabddcdcbcdbbcbdcccdbcccbccacdbdbbaaaacdcbbcbcacacbbbbcbcdababddaccaabbdcbbccdcdbadcbacdcdcbddbacdccdcdccdcdbacbacdabdabaabcbbbdbbddcdddcdabdcdbadddccabbdaacabcbadacccdcdaabadaadbbabcbcccdbcadddbbbbadbabcbbdbdaabbbcdacdbcdbdcdbccbcaaaccccbaabdcbdcdbccbbcabaabdccdabbddbbdaccbcbcadcbacbbbdbacbccbdccdaacbadabccccbbcabdcadcbcabcbcbbbbdbdbccdaaaabdcddadcbdcdcbabdabbacacadcdbdddbdbbaababbbbadbbcacdbcbbadacadbbababdbbbbacbbabbadabbbbbdcdcddcbabacdbdaddacdbadbdccbbadcacadcdbddabdbcabbbdbaabcdbddbddcbbddddacdaccdcaddcaabcacdbbdacccdbbcacbabbcbacdbbabdadddcdbcbbccdadccdcdacbdcbdaadaabcdddabbbacbccbccddccabcabdcadddddaacaabababccaddabcdbacbcbbccbadcdcccadddbccaaaaabddbbbdacbbcbdadcaacccbadccbbabddccbadabadadccddababdabacaccdbddbbdbacddadbbadbcabbabbcbbbbbbdbbbbacadabbbadbddbabdbdcdcbbccbdaaaaadcdbbbadcbdddcaaaabcaccbadbdaaabcadcccadbddadbbacdbdcbccdcdaabbabccbcdadbddbaabcbbcbacaddbacabddcaddaaacaccbccabbcbddbadcadbdccaddcabcdadbaaaacbbaaacbcccddddcabcccbbbccdcdacabaabdaacdbbabacbbbaaaddacbadbabadcaacaccbadccadcaddacdacbcbdbbccdccbccacaaacadbdababddacdadddccccacdabcccccadaaccbddbacccacbdaccdbcbdcbcaabbabcacbabccbdbccdbdbdabcadbadcbcabccacddacccaccdbacadadabbaaccabadccacdadcbbdbdccbdcadadadbcccbbbdbbdbddbbccacabacdcbabdacdbdabdbdaababaccadacbcbaacadabcacbbadcacaaadaaddbaddcdccbbdcaacababcdbcdbddccddbbddbcacdbcccbbadcdcbdddbcdbacaddcaabadbcbaaaacdacdbdbbbdaabaaaabccddccdabaabcaacdaaababbadbddddacbbbabbdccbdbbcbddaadbabcdcdccadcbadacddabbdabbcaabdbcdaababbaabccaadabdcbbbabcdbbdadcbcabcbdbcacacbbcddcbbdbcdaaaccbbcabacadddaccbddabdbdadabccddcaaabbadbbaccadcbddacbdcdccbcdacbdbdabbccdcaaacdbdcbbccbadabccbbdbbcbbddbabcbbabbaddcbdcbdcbacbbcababdbaabbcacbaaaadadcacdcbbdacdcacbbaaadbdbbcadaaabddddddbaaddcbaccaccbcbddbddaabbdabcbbdcbaabdadadbbdcbbaacbcbdccadabbbcdddccddcdddddbcabdaddddaadccaddccdccadcddbacdbcbbccabcdbdcdbcacabdccadacaadbbdcbaaccadcccabdbbcdaaadaccdcaccbdcaacbcccbbcdcabddcadaccacddadaccbcdacadcddccbbaddaacaaaacaabcadaccbbacbaddadacbcddcaaccddcadbdbabbccbacacccbdaacddccdadccbccccacccbccbadacbbaaddbdaddcacaddccdddddbacaddabdcbdacadcdbcdbcabbcaddbdbddddcdbbcbaacdcddcbcdbbdacbdcacacaacaacdccbabaabcacdcbbacbaabcdbaaadcddabaaddabdacddbabcadddbadcbacdabdbdcbadadbdcdbdddccccbcdbbcaacbaccdaddbaadcddcbaaddaccdacaddcadddbcbbdcbabbcdcdbdaabaaababcbacbdbccddadcabcbccbbbdbcdddcadacaacccccccaaccdccbddbaaccdbadbabacccabdacdbcabaaaaabdbacbdcacadbdccdbbacbbcdbddddbcbaadbdccbacabdcbbaadaaadcbccbddbbdbbbacbcbdddcadcabddccccddbccbccbbcdccdabdddbcbcbdaddcbaccadaaadacdbadadcbaabaacbacbdcabacddaccababadcdddcaddbbaaaccdddaccbcddccbbdbcccbbdcabababbaccdbabddadbabcccacdacbdbaabbdcabccdadaacbbbcccdbcbabdabbdccacbcccdbdbbdbbbbacacbcaadcbbcabbbaadabcbbadccdbdcaccddaacadcaacbacdcabbcaabcbbdbacabcdacbdcccccabdddbdbcddbacdacaaaddaccabcdadaadcdadcadbcdbdcbccabbdcbcaabcadcacaccbccbbaccaabcdacaaacddbdaadacbaaddddacbcbcbaccaabbbcdddbdabcadaccdbdddbbaacabaadcadcaacdccbbaabcbaccddadccdacdcccccbbbadcbaadadaababcdbcccbcabdabcadbdbdacabcabbaaadbbdabdbcdadabaadbbcbabcdbdcbbaddcadacbbbadcbbddbabbdbbacacdccbaacccbdbacdcccbcbacacdddbdccdbadaacdabcacddcabadcdadbdcadacdbcddaadbdabaddaacbadabdcdcbccabcaaaacaddcbbcbcdabccaccadcdcbcbaaacaadbcacbcbdadbcdbbbaabcdbcdaaacadacdaccdbcdaaacbacababacddbdbbdaadabdacdccdcdccdabbdadabbbbddcddbbdaddccdcabaabddbdaababccbccacbacbddbbcbbdaadcabcabaccbaaaadbcabcdbadccdbacdaccaaccabbabdcaabbabddadbcdbabaaabcbabdbbacadabddbbacbbacbdadaadcbcabdcddbbbcadbaadbbdbadadcbbdabaabaacbccdaacaaccdcccabcbbaaaccaaaddcbbababbaacdbdaddcddcdbccbadabbcdcabdabcccddabdbcdbddccaaaacdcbbbdbadbacbccdaddacdcbcbacababdcdbaababcbcbbbabbabdbacbacbcbdbdcbaacdcccdccacccabdcbcadaabbbbdbcadcdabcbbdbdbccabcbcadbcaddbbaaadcaabdbdbbcbbccddacbbaacbaccbddacabdcaaabccbacbcaadabcbbbccdaaddaccdcabdbbdccadcbabcaabbcadbcadcdabdcaaabbcccbadcccdbdcbdcbcdaddaadcccbaaadacacdcadddbbccbaddaacaacacaddbdcbbbbcbbdbdbabdcabcbcbaacddbadaddbaccdbbacbbbcdbcbdddddaabdacabddddbdadaabadadddcddcaacdccdddcdccdcaaaddcbcacbbdacbbbabbbdababdbaabcbaabdacbdcabdacaaacdcadcaddcbdcdddadadcadacadabddabddbcaabccbdbdbcdaabbaddabdaaddcbbbdbbbbdcdaabdabddcacaabacdbddacbadddcacdabdcaaccccddccddddcbbadbcabcbadddccbdacbbacdcacdbcaacabbbbcbccbddbbbccdddbbcbaccbcadacaacccdcbdddddbabcadbabbaadaadaaabcccbabdcdcccaadabaaabbdcdaadadacacacdaabcbaddbdabcaadddaaabdcbbacccdbdcaaccbdacacddcdcabacaccdbbcbddbdbddcaddcdbccddcbccdcdbbdddccdadcbacddddbdbcbcdbaabdcbccdacbbdcadacbbcdabbbdcbbbdacdbccdbccaddcdddbacbbbcdabacccabcdbcdacdaaccbacdcadadaabbabbdcdbadcccadcbdadddaaabaaacdcbddaadcdcbdbdcdbcabaacdccabbbabcbabdacaaacbdaccbcbbbbbababaabbbcdbacdcabcddbdbdcdbaabdcbdbaddddcbbccaddbabcdddacabdcdcaadbadaddacdbbbadaadbcbcbadccaaccacaadbbaabcbcdaadbbbddcbbadabdbaacbbacaadccccbadcaaadbcdbadbabcdbaababdcbdbabcdbddbcacbacabbabbddccaacbdddbbcabdbccaddccbdbbdbbcabcacccdaacdbddddacbbbaacaccadbcbaadaacadabcbbcdccccabccdbbccdbaadddbbccbaccabcdcdbddbaddbaddcadabcdbdaaaddccbabaddaaaddaadadabdababdacdcadadadaddabcdacbbbcacdbbbcaadcbcbdaabbbdbdbbccacdcacccaccccdabaddccadadcdcbdcdaaccbdbabcdadacdcbccbddaacbacaaccbacdaabbbcbabcbddaacdbabddcdccddbbbdaabaccdacbddaabadcbbaaabacaacdcdcaacabbcadbdacddbbcbabbbbdaacacbcdcdcadccdcbddaaadcbadacbaaacbdcdcdcadccdbabcbaccbbdccbcbbdacadcabbcacbbbbcabadaccadddcccacccadcdcbcbabbddaaaaadccbabbdbcadbcaacbabacbaaaccdaccbaadbcdbdcbcdcbcabbadbbbdddacacaccacdccdcdbddadccaaddbbcbacdcadbabaabaacabbabbddbadbaaacabbdccbbbdcdadbbbbadccbbbbaaacdaaabaaddcaddbdbcabdddabaabcddcadbdddbcdadbcccdabbabbdbbdbbbbbdcaacbdcbabcdabdbcbdbcdbddbdccbdcdbdcaddbacabdcdacadaadacbdcaccdcdacabbcddbaaabbdccaccdddddaacbcddbbacdccdbbadbcbacaacbabcddbbbbbcccacdcbddaccdadcbdbddcbbbdccddcdabbcdbcccaddacadbadbcccbaaacdbdbdaaabaabadcacbccbbcbacddccbbddbbcddcdcbcdacdcdbbadbbbcbadcdddddabcadcbddaccaabcbdbbcdbccdbabbacdccabbabccbbbcdabacbbdadcacbadabaadbacbcdcacabaadcacbbcbdcabadaccaccaabbaaccdbcdbccdcabacdcccaadccbabdacdbcbddcbbcdbdbdabdbacccbdcccadadbbbbdcbadbdcdabcdccbaabaabbcadbadadcdccaccaccbcccbdbbbcddbacadcbbcaaaadbdbccbcbddaccabaadddcacaabcaabcbdbacabaaccacdaccbdaababdaddbbadddacabacabcdcbdaadabcabcdcbdbdadaacdadbbaaabdcabdbbbabdadccbdbadddbbdaddcabaaacccddabcdacaabddbbabdcdcbdaddbbaddcdacabacabdbadcbbddcbacdbadccbdcaabbcaabaaaaddcdcbacddabbcaababbcadbadcbdbaabdbddaacdadbdbcaddbadbabdbbbaddccddaddadcabdcdcddbdabdddddccbdcbabcddacdcccbaabacddbaabcbcadcccacbcbbcdddcbdacaadbdddccbdbabbaddbbbddcdbbadcddcacbdcdabaddbaaabcacdbdcdacacdcdcdbbbdcbdcddcabdcbcbdcaaacdcbdbccabddbbbbbbbabbcabcaccdadbbbabacdcbdcaaaacccbcdcdbdadccbadbbbaaabddbbacbcbcaadddbbdbabccccbbbcbdbbadcbcccdbccbdcdacbcabbaccacbabaddcabbcbcbadadaddddbbcccadccdbdbcadbcaaacadbdbdcbdcabcbddaacabcddccddcdddaddacbaccaacbcacacbbddcdacdcbdabccaddbdcabccdcacbbcccadcadbaddbdbabcddcdcdbcaddacdabccdcbccbddbcbcaadcaacbacdbcacdbcdccacddcdcacabdadaaaacaacadacbabdadadcdbcdbabaadaabcdabdcdbadcaccaacbacbabbcadbadaddbbdababcccbcaddddbdaddbcbcbbaadcacaaddcabcacdddadbccbadcdbbdddaabacccddcadcbabaddbbcdccbcddcabacdcabdaaddaadadddbdaadddbacaabbadbdbdcaaacacdaaaaabbbcbdadcabcacadcbdcdbaccbbaddcadbabbbacacaacccccaabbaacdcaaddadbdddbccbaaadcbcccbaaaacdadcbdacdddccdadaaaddbbaddabaaabbaacdaaaccaddbccdabbabbddadbabcbcccbbdaccbbadaaabddadaacbadbddcaacaddcbaaaacbddbcbbccbccbbbadddcacddbbccdacdaabdacbcbcacbdaacdbabcddaddcdbdccdbabbdccabaadddcbcbacdbaddadcdabdbaabcdcabaadbabcbaacbaacccaccbaadabcaabcdbaacdacbdbcccdbccbabccbdaacaabaddcbdbcdbbcddabdcbbadbbadaddaaaddcbdabbcddbccdaadabcabccabdddabbdadbcbbdcbccbddcacbcaacbbdcbcbcdaddcddbdbabcdbbcbdacbbbdbdbabcabdcadbabbcddbabdacbcabbabaccccdadcabdddbcdddbcdadcadbabbbbadbddcaabaacdaddacacdbdacdbccabbaacdccbbcbabccbacbdabbccacbcdbccddabdbbdcaadbccdddbdacdccddcbdbdbbcbcdcbddbcdaadaddaddaaacbdbcacdadabcddbbdbbaccdcbdbdabdccaddacbabdcdbbcbdbcdbbabacacbabbabdccdbaacdcbddbbbddaacbdbddbbbaddcaddbbbcdcccccdddccbcbaaabbcbbccaabbcccdaccbccbbccabbdacaaadcddbabaccdddbbaabcaabbcaacbacdbddbbaadbcacbaccccccabbcadabaaddaccadcbabacddcbcdbbcadcbabdddbdcaacbbbadcaabdcbccccadbadbabbbcaaacbdccccadbacacbcdaaadcbdcdbabcbcbdadcbdbaccdbdcabcadbbcaddcbcabaabbacdcbadddbcababcccbcadcaabdaabdbdbcbbbdcbbccccaaccbdbcabcdbaaddbcabaaaaabccbbdaccdabdbdbcaabddcbcabcbccaccbccbcdcdadabbdbabddacbcdcdaccbdbbcbbccbddadbcdbbbbdbacddaaadbadbcbbaacbdadbbabbbaadccbaddacdbcbadccacbbddcdbadccdaddbbbbbbcabbaababbadaaaacdddaabcbccdacbacacbadbddaddddcbdaadcdbbabcccbbdcbcdccaadadbacbdaacadddccbdcdbbbdddadbaabadbbccddcabcadcbacdadabdcccaadabaadccbbaddcbaabadbddbbabcdcccbabacadacbddaacbdcdcbbbbdbdcddbadbaccaabbbaadcbadcdadacdddbcaabbcbcdbbabcdabcaacdbbaacbbcdbcbccdaccbcaadbcccddbacccabdbabcbddddbabcccdddcbccbaaddadaddbaacbcbcdabbdaabadabbcbccddddcbbbacdcdaddbbbbbcdacbbbccaaccddbaabadbabccbddcddddbcabdbadcaddbaccabadbcddbadbbdddbcccaaabdbbddacaacaccacaabcacaaddccacdbbadabdbcaaabaaddaacabdcbbabcdddbbadccbdabdbaddadacdaccbcbaaaababcdaddddcddabadcdbaaabacbdbdcddbdacbccaacdbacbbcddcdddabbabadaabdcdcccadbdcbccccacbdbbadbdbdacababddddabdacccdaddcdbdccddaddcbdabbabacacbbcaadccbbcbbdcabbabdaacccbdbcbacacaddddddabdbdbdbacacdbadcdcdbdddabcdbcadaaabbaabcaacbbbdadbaaabdacdbcdbbcdbcabcaabddbddabdbcacbdadaabaadcdcaaddaabaabadbccbcddaccdacbbdccbcabbddcbcabcccdbdddaaccacdcaaacbabcdccacdbdcccabaadbbbbaabcadccccadddbcabcaaabdccddaadbdbbadbcbcaacaccacdbcabbacaadabdbdccabacaadaddddccbddabdccaacbdddadbabbadcccdddbadcdbaacbdaabadbcabbaabaadcabbbaaacdcbadaadcadabddacbdbcbdcacbdcaccbcbaacdadcbcdbaadabbbdbdbddddaaacacacadcdbdbbcaddadbdaadcbaaaadabcbacccaabaaabbbdbdccaaadddaacabdabdcdabccccabcdccadcabdaaccbdcdcadbcbbbcadbcadcbcbcbdcaaacccdbbcabdbdadcadbababcdacdcdbacbbddaabcdcddcdccbcaadddcadaadadbccacbadadccdbbdbaabadcabcaddadcbadbcaaccdbbdaabcccccbdbccabcbbacaababcbdacbadcbbcdbbddaadbaaabadbabddbbbcdadadbdddadbaabadbcbdaabbcdbcdacddcdccbacaadcdabacdadabbdcbccbabdcdcabaabdbadaacdcbbdbcacaddddcabddadbbdcbdadbadcabdacaccabcdbbabcbababdbdadbadddaddddabcbccbaddbddaaabbaadbbcbbcddaadabbddcbddbadaadbabadbcbabdacadabcabbcbadccccbcccbbbbbdbabaadcdcabccbcbadbdaabdbaccacacadcbcbcdacccbaadaccdcadbcdbdcdbccadccbccbaaabdcaddcddbddabbabdadabaabdcacdbcbaaacaaadbaacccdbacbdcdabccbabcacacaaabdcbabcbdbdadccccabddbcaadcddcbbcbcbccaacbccdcbccacdabbadbcabcdddddadbcddababdbddbbdaccabaacacbcbdaaccbdbaddbccbccdacacaccdccdbdaabdcddabccaaacbddddbcdcdaadcbbcddacadacabaadccdabbdacbdacacdadcbccdabbaabbdbbaabcccdcddddbcaddbdbaaccdbacdcadcccdbcacdcadbcabcbbddcbbddadcddccbababacdacddbbacbdcbdacdadbbdcbdcaaddcaabbdccbacabbdadadddaacbabccababbabaabbbcdaaddbaccbcacdbbbaadccddcaaacdbadabbddbcbcacbbbbcddaaaaaadcbadcbdcbaababbaacdadabadccaadcabcccabbaadbacbcacbaabaadcdbabdaccbbccaacabcabddcaaccdbddddcacacabcaadddabacdbcadaaccadcaaabcdccdcabaadcdcccbbccbccabdcbcdaadcdaaabcbcdcdbdacdbadacdcaadadaddadcddbbbdbcdbbcacdccbdcddbabbcacbbcaccccbbbbcadadadbdcdcdbbdbccbadbdbcacccaabdbaacadacacadaacaadcbbacbbdbcddcbdddcaddcaadbdaaaaaaadbabdbaaacbbdddddbcadacccddcccbaccaddcddadaaadbddcdddaacdccbbadaaacdcbddabccbabbcbdaabdcbcbcaccdddcacbbcdcdabcdaddaadabadcbcbaacdaadcaabbbbcadaadbadadaacadaccddcddcbadbcbaddbdcabaabddabcddddadbadaaaaaacbcbcacdbbacdaaacddbdcccddbbbccacdbbbbdddccdbdadbdbdbcdddbaaaaacbbcacaadacbbdcbadcaadcdbcaaadbbbacadaaaacdbbbbabcabdaaabcbcdbdbdabbddacdacddcadbabaababdcdbbaabbcababbcdcccbcacacabcdcadcbcabbbdcaaddaccacacaaadbacabbcabaccbadaaccdbaadcbdacdcbacbcdacbbabacbdbcbcadbabbdbcaacdccadaddcabddcbcacaddadaacbbdbcbcccbcbdcbbdddcadabcacdacccbcdabddabdbabbdaabcbdaaccabacdadddcbacdcbdcabcdcdcabdcdbadbbccacbdadacacabbbdbddcdbbbcdabddbaadbcddaadddcdcbabbccddcdbdcaccbaddcdaccdccbbdabacbdbbdcccddcaacdaabbbdadcbdcadccddaccadbdacaddcbcbaaabaacadacabdcdabccdadaccdcaaadadcadddbaacddbabaabdddaadbbcadddbcdddaadbbcdaaaddaacbbdddcacbcdbbddbdddcadbadbbcbcaadcacaccadccbcbcacdcbccbdadbdcdbdaccdaccbcbbdaddbdbddbbdbbcbadaabddddccaddadcadadaccbbdccbaddbcaacdcaaabccbddbcbdbaaaddbbbcddbdadcbbacdaadadccaacbdbbadbbbadcaaacababcbdccaddcbcccdbaabbbabccabdbabcbadbaabaacbbcbbaaaaddadbabcaccadccdaccdbddcddabddcdbdcabaaaaddbcdbacdbbadaabacdbbbbaacbaabbdcdabccadcdcabccbacbcdddcbaadaccaacaacbbabcccacbabddaabbbbbbbbbaabdddbbdcddbacabbcddbcbdbacbddadadccdaaacdbddbabddbbadcdadaadaadbbbacddbcbdadadbdaddcaccbcccddaccadbadbbdadadcddbccadcaabdddaacbdcdbccbabcadaabbcbaadabcbbdccbddcdddadcdcabccdbdacacccdaccdbbddbbcddaadcacadbacddddabdcdcadbbdabcddabaabadcaabbdbcdaacdcdaadacabaaacbbddabbdabdcdadbdccddbcbdbaadbbbbdcddbcbcbdaacacaadacabdbcddabddbaadcccaaccbabadbbdcccbacbabadcddddaddbccbacbadbbaddabbacccccbbbaaacdbbbdccdcccdbbcbddbbabdcccdccacacddacccabcbbdbdaaddccdcdbaccbdccadaaaabcabdacacadadcdbddbaacdddbbbdcdadbaccdbcaabccdbdbaacadbabdbbcbcbbbdcabdcdaaabcbccbcbccddcdbcacaaccbcbacaadddbbabadbcacbadbaccccddabcdcccbcbdcbccabababababbabdccdcdbdaddcabccaccacdaadbaacbabbcabcccabcbdaadbabcdacdbacaddcaaaababbccadcbbcdbcadacaccabdbcdcaabbccbbdadacdcbcdbdabcccccadaccdcabbcdddbdccaaccddbbadaadbbaccbcdadcdbabcadabaddbdcaddcdcdabccbbcbabcadcdbbddcddcbcacadcaccbdbbadddbadddcabbaaccacbdadaddcdcdabcbaabccddcbcdabbdacbccdbccadccadbdbbcadaabccabdddabdaabbadaabaddbacddadaccaabbacacacbaddacabacbdacbcdcadddcdbcdadbaaccbaccdbabbbbdbcbacabacabdcdcbddaabbacdbddcdddbcddabdccdbccdbadddaccdbbbcddcaabdcdcbabadcdaddcdabdcddacbadcadddbcddbdcabdbdabbccdabbdbbaaccaaadcdddbacddccaddcdcdcabadbacabaccbbdbcdaadacdbcacbcbccaddcdadadabbcbbabbababbacaaddadbbadcbacabccadacaaddbaacccdccbadbcddbbdbcdbaccbaccbaacdacdbbdbbaabdaccabddbbdacbaaaddacaaaaadcaadbbcaccaddaaabbabbccdbbbbadaaccaaddbccbdaddabbbddcadabcdcbcaddaabdcdcddaccdccdcbcbacddcdcaacacdbcdddcdcaabdbdbdababdacacddcddbbcdcacbabcaccddbaadbdadacacacbcbbacacdbaaddddbbcbbcbbbbbadbabacbccabcdcdcacbcdbcdcadacdbaccadcacbabadddbcbcddcbcbdbacdcddbcdcabbdababdccadcdcbcadbcccbbdacacdccbddddaabbaaadbdcbccbaddcdabaaccbdbbcaddcddcbacdaccccbbcbabcdadbacaddacdcdbbdbddbcaddbdbbcacbbccddabdddbdcacbbdbddbcddbcbaadccdacdcbabcacadcccbdbcdaccabaabbccdddbccaabcaddbcabcadbabcdadbadcabbcaaaadcddddabbdccdbabaacddbacbabdbccccbaddbbddacbabcacdcdbabcadcbcddcbadccbdccdbcabaadbbcdcdbabcddbbdbcbbbbbdabbcbdddcbbadccddaaadbcdbdcbbbddbabddbbabbdcbdbbcabbabcbdccbaaaabbcbbdcabdacdbddaaaccbdccadcabacbbadaabddbbdccbdcaddadddbddbcddbbacadcdcddcdbcdcccacddccdcccccaabaaccacbddccadacddabcadbdcaccccaabdddcaddadbabacabcabbddaadcddadadaabbacccabbddcbbcdddbaabababcdddcacbddbcbaabacdaccdadadbcbbcdbccbbcadddcccbaacaccbdddbcbdacccbabdddcccbbcacdaaddcbdccadbcdbbcaacbcdbbbbcdadccbbcadcadcbdbbdddcacbcdacccddbaadabbbaadacdcddcabdcaaccbdbcaabcabdaacbcddcadbbdcbdbcabadbabacbccbaabcddcaaabbbcbdadddaaaabababdadcddcdadaacbbbcccbbcbcabcacdacdbddadaadaaaadacccbaabaabcbdcbacccaccbcababdbbdcbdbbbcbbadccdabbcdbdcdaadbaacdcadadaabddbbccddbbaabcbbacbaabbdccbbaaacabdcacddcdabbcdbccbdcbdbacabcdcbabaddbcdabbdbdadbbcccbdcbdcacacaadddacdcadadcadbdbcbdcdbdcaaaddaacabdbacbacbccdaaabdcccbdcdaacbaabdaccdcacbaaaabaddcdddbaabcabadcaadcaabdacdbadbaddcddbccaaaddbabbadbcaaabdcdbbadabaabcbdabdddbbadcdcbadbcccccdbcbdadbbddddabbdddaccacddacdaacddadbbdcdcdbcdadacacaccabbdcadcacdbdbddbdddabcabbcbbcdddabbdcdbcbabdacccdbbabaaacdaacabcaccbcbbabccadcacbaddaadbcbcacbaacbaabcccccbbbacabbcbddaadaaabdcaddbbccababcadcdcddacbaccbcadacdcaccabcdddcddbaadadbdcbcabbaddcdcdcaadababbbacddbabdbaccbddaacbddcbaaaabaaaccbbcdacbdaadaddadccacacdabdcdcbdadabdadadbcbaabdbbaabddddbbabdbdacbacadbdcdbdbbcbddccbaabbaabdcdbbbaccaccbacbbabaaccddabdcbddccdccbdaccadccdbbbabdaacbadaccacabaddcaccadaacdacdbbdcbcdcddaabbdaacdcaccdacddbdaabacdacbbbbddcacbbcabdbbcaaccaaccccacaaaadababdbabcdacaccabdddddbdbdaaadcaaddabcdbdbadabbaccbbbbccadbcabbbccccaabdadbbadcccaaaddabdccbbdabcbcbcacbadbabdcbdcccbcdbaaaddccbcacddbbcadabaccbaadacdcbcdaacccbbacccacbbaaacabacdabcbbabadcddaabbbbddabdbdbbddbaabbddbdccadabdbaadaccbabbbdabbbcccbdaabccabcaccccabadbbadbbcadccabdbaaddacbcbbdbdacaabbadabdbabcabbacccbaccdcaddbcbbbbbabdbaccabaaabbabddabdaddcbdbcabacddcdadbccccbbaacaaccabaccbacbbcbacccaaaabbdcccbcdabadccdacbcbbccbdccdbacaadaacdaadbbcbbadcccbdbccbdcbbcdddcabcbacdcadccabcdcccacbbcabcddadbddbbbabacdabddccbacdcaccbcbabdcccaaccbdcadccbadacccbdaadbdabaadcdcdadbaabbbbabdacabdbadcaadbcddcbbdababacdbbdccabbbdccccbacbacbdadbddabacaddacbabcbbbcbbbaabbadbabdcadbddbabaabdbbabdcdcbbbcbdcdcbcacdcdccccbdacdbdadcdbcbcbcddbdbabcbbcbaccbbdbabdcbcbdcdcbcdbdddbdbbbddaabbdddbbacabcdbbacdcaddbdbaddbdcdbdbcbcddbbcbaddcadacbbdccddbdababdabddbcdcbcdddcdabdcddbaaddddacddbaddccaadbdddacccbbacddbdadabcaadacdbacbbbadcbcbdbbaddcdcdabacdbadbdbaabccdbabacdaddcddddbdaaaadddbcddcbdaabbcdcacadabaabccccccacdadbdccabdbbadaccbaabddcccacbadbdccabddacacabaddccacbbbddabddbdbdacabbdadcbcbdaccdaadaadbdbaabdbddcaccacddaacdacadbcabddbdcccabaababdabddaddabcbacbacbdbbccbdccccdcadbcacdcdccbdbacaddbbbbbaabdbbbbcaaadcdaabdbbcababbacbcdbccdacccbcaadbdcbcbaabbcabcabbccbdbdcaaccadccabbacdccbddbaabbadccbdcdcabddabcbbcdaaccaacddacddccdcabacababaadcacbcaccdbacbacdaaaaccbbaccdddccaadbabaddaaabbdcaadadabadaaaddcaaabdaacbadbbddacbabacadadbacddddbbddadabcdbbabaaadbdddaadaadcabbcadddcbbbaacdbcbdabcacbbaaaccbbbcdddaacdddcdabcdadccccdcaadccabdccddaccadbdaccdddacbaaadbbaacadabbccbacddcbbbbddcaaaaaaccbaabcbacdcdcbadabbcabdddddadccbacaaddcbadcbadcacddddcdcbdaacadddbddbdaacaabdaaaaabbaabbdcdcdaddbaddcaddabdadccdbcbacbdabcacdcababbbdddcacadaaaadaacdbcadbcaaadbcbaabaabbcccdbadbdccaaaccbcddcccacadcdcdbaacbcdabbbdbcbbcdaccbcbdcccadbdbdccdacdcdacaddacdacbdaadcddbbcccccdbdabcccdaaddcadaaacbadbddbccadcbddadddccababbdaddcdcbaaacbdcbacadcddbdaaaccdbddbccabcbdbabcbaabbaccbbadcbbdbaacabdaacbbcbbdddbdddcbbdbccbddddccaacaaacaabcdbdccdcabdaadbcbbdccdaaaaabbcddabcbaaddcaadaadcbcbdabccbcbaaabacdddbcbadbdcaaddccabccbacabbdacddcddcdbbbaddcdabdacbdbddacbcaadabdabbbdbaccdbddadcdbacbbcbdddcbdcaaccdacdadbcabccddccdabdbdccdabcbdbbbddadbdbcbadaadddbaddbdadcbbcdadaadcacacacacaacbacbbcabbdadbbaddcbaadaaaacdabadbcacbaddadbbbbadbdbbdccadbdbddbbbdacbabbdbcccdbcbdaaabacdaaadcaadcabaadbcdcaddaaadcccacbaaccdabcadaadbddbabaaccaabacbdddccddcdababcabdcdacabacbbaddcbcbdcacadadccbccbcabbbcdbcbcdacbbdccadbaadbdaaccbbdcadccaabacbdddbbacdbdabaabacddcbabbccadabddcabcdbbcabbdccbbddaadabdcdbcaacccccdcdcdababdaacadcdbabadcdccaddcbbdbcddacdaadbcaccbaddabccaaadddcadaaaccdacabdbddcbcdcccbdabadbcdcdbcbcadddcbcccabcdacdcbdbaabbcdcbaabacdadbddbacbbbaaccabbadbabaabbddbbdcbcddcaacdadcdcddaacbdbaabcdddbaacdabbbcdddabdcbdcbdddcdccbbcbdbaccacdddacccccbadccdcdbadddabccbbdbabddadcdbddaddbddddbaacddbacbdaddbabaccabccdaaabddcbbbccdcabdbaddabddaabddaabcabadcaddadabababbbcdaaccadbbcdcabbadddcaaacadaadaccaaabdbbccbdcbaccbacacdddaadbcbdbcaadcbdaabbaabdacbacdabacddbddbddcdbbadcadbbcabbbacadaaabacdbbababadbdabdcadbdcabccdccddcddcbdcdbcaacabadcddbabcdadacdabadcdaaacdaadbbdcabcdbcadbaababadbdccbbcbcdacdbbdabbbacddddbcbabdadbbbccdbdccdcdcdadabbdcbdcbbbbdddbdcdadcddcbbdbabdacaccdddabbbaaccccaccabcccbababbcbabadcbabbacdcbbccaccdabcddcabbbdbcacbabddaadbccdabcdacbdcbbbbacbadbcaaaaccabbadaababbbacadaddbdadcbdddaaddbabdaabcdcabbccdcdbdbaccabcacddbbdbbbbbcbaaaabdddbdcdbacbadbdacadcbabdcaaaaabdcdbdccdbcdddaccbdcdacddcbbadccbadbddaccdadcccabbaaaabddadcdccbadaccacabbbdccabbadcbcdbcabdbaabaadccbcdbdccdbccbcdbbdacbbcbdaacdcabdacdbdcaacdacddabdcbaccdcacbadbabcddbcdccddbdcaabaabcbbbbdabddbdbdbbdabdbbdcddbbbdcbddbdbaaadaabbccaddaaabacaaadabcbcdabdddacaacdaadaaaadaabcdaadcbcaabaaaccbccbcbadcabdaddacadabcaacccbaabcdaddaaabddbccbaadacbcddbdbcdcdbdcaabcbdcaddddacccbcbcaaddcbdabaadddccaaaaadadacbaccacaacbbbbbaacaadbaacaccddbbbaaacacaccbcdcbcabcbbcbcabddcaabbbcdbbccbcbababadcccdcccbccabbbddbbabaabcdddcdbbdadcbabacbbbbddcdcacdddabcccacbccbddacaacbcacdadccbbdacddaaadcabaccaccbcabbdbbacdadcabcadbdbacdcaadcabcadaccadddcbacdddbbcaccbabdbbcccddabbcaacdbacbcdaaadbbabcabcabbcaacaababdcbbdbcdcabdcdadbdacbbbccabaabbabbddaddcabccbddcbdccbcdccddcdccccbbabababacabdbadcddadbcbbbdcbadababddaaacbddadbaaaadbcddbbbbcaaddbcbacaadcdadbababcddaacdbcbdcdadcbadaddbbdbddbdcabaadbcdbaccdddaadcacadadcdaccdbcbabdbbdbcbdaacbbabdaddddaccabacbdcbdadadddcacccbcbaacbdccbcabadbaddaaabbadddabccccabbcadcadbaabbacadcbcccabbbdaabcdbcabcbadadcaccabbdccbaddabcdbcdccbacdacccdcbadaaabddaccdcadbbdccdabbadcbaddcbddbbaadacaaaccaadccaaccabbadbdaadcdbaababccbcdabadacdbacddbaaadbcdacbbccdcdadabaccaabcbcccbbaddbbcdbcbbcaacdababadbdcbadabacddadccbddbbcdcbcbbaababccaabaddacddaacaadaabbbccbddadbbdcabbacdcadcbaaddbacddcbbbbcdbaddaabbacddabddbcbdadaaadcbbcbdcdcabadcbcddddadacbcbdcbccdccbcbaabbaadbbbdbdcdcbaadcddaadbcbadbacddbcaacdddddbbabbcaadbbbadbcaabaabbdcdaaabbacbadbcbdacbaccdbaabbaaabaaddcaacddcbdddccdddcbdadcabcbacdbddbccdbaacccbdccbdbdbadddbdababdddaabbdabcadabbdaacaaaaabbdcbddccbcdddbacaababaabacabdaddbadbacbbccadbcdbbddaadbdbdcbacccbaddcdccddcbbabacdccccdcaccbacbaddadccdcadabadbcdbcbcbccdddddddcbaabdabdddccaddacbbcaddbdddbbcccbcaacbabcaabdddcbcdbbbdbacabcbabbbbdccccdcaaabbddddaccacbbbbbadddbddcbbccbcdacdbcabccdcbbbbdbacaccdcdacdadbbabbdcdcbdabdbabdabaabacbcdbbbaadcaaccbcaacadbabbabbbbaadddcbbbdbcdcccacbbbbdbdcbdbdacbaacccaabddcdcdddadabbacdcaabcbdbbdcdbbbbacdbdddabacbdbabacdcbddbbbdcdcdcadbbcbbccbabcbcdbcbacccacdcbaacbacabddbbadabcaddababadadcaddbcacabaaadccbcddaaaccbdbbcbddcddadcccacdadaccaabbdabdaaaaaacabababbcbabbcccddcdacbddbaaacbccdabacaaabacacbccadcaabdcbccabaacbbdbbccddcdbbcdbbacaaabbadaaacaabbacaacbdcdcddbbcadddabaabbaaabadaadabcdabbbddddacaabdcbaadaccdccaabbaaacbbccaaccbdbcbcdbbdbadcaadcabccabcaaddadbcadddacddccbaddcacaaacdccbabddcbddbbddddcbacacbacacddddadbbdabcdbbcbbaaadbcaadcabcbbadbdaaabbccabbdcccccabadacbaaabcbdcabbccbdbbdbdaacbdbacccdadbbbcbdbacacbbbccbbadbcddabdbcddccbcbdbdabdcabbdcadbbbdbbcadaabbbbccbddaaacccacccbcdaacbacbcdbccabbbbbaababdddabbccacddabdbbadcdaaabdbdddbdbcddabbbdcbadbaccadcadbdddaadbddcdadccbbcdcdbbaacabacacadcddccbdbddadbdcdabcdabccbcbcabbababbaadcbadabdccbcdbabcbbcdadbcdcbddcbddaacdcaadadadbaddbdaddbbcacbcbaccbbcccadaaaaabdbbaddbdbdcdadbcddabbabaccbbaddbdcaadacaaacabbcddddccbcdddddccabddabaacddcbbaabcbbaddbcbbabcdbdcbdcaddddadadddbccddbbaabcccccbdddaaccdcdbcacbbbaadccaadcbbaabadcbccddbbbcaaaaadbdacbcacdcacbacaadbcbccabadcabcbabbbabaabbbcabcbbccbbbccadaccbacdababbdbbccaadacaddbcbdbdcddbaaadabbabaabadbabdbcbbbcddaadcbddddcbdaadcbdaccbbcdabcaddddadcccbbacbddbcadcbdbadaaabaddcbadaccddcbbacacccaacabcdbdcdacbbccadbcbabbcdbbaddaaddcbcadbdbdcbaabbddbddbdcbdbaabbcbbdddddddaddbbcaabdccbbddcaccdcccbbbabbbbccaacbacdadbdcdabdabdcaccdadbddacadcabadbabbbccdccacdabadccadacbbdddcddddccadbdabdcbcbbbbbaaabccccacbbbabcbbbcbdacccdbacbccbcdccbacaadabbbbbbccddcbadcbcbaaaaccabcdbabadbdccdacbaabcadcacbdddddcbdddaaccaddaccbbdcbabbdaaddadccccbdccdcacbbdaaabaacacabccccbaddcdbccacbdabadcbdccabcdcccbbddaadcaababddbbcaacbbdacbbbdabbbabacbaacddcabcadadcccbcaaabaaabbaddbdbdaaccbabadccdaaddbadbcadaaccddcbaadaccccbbbcacdbddcaadadaabbbbbbccdbddcdcdcaadcacaaccacaccbadbcdbacddcbbdbbccddcbaacaadbadccbbccbddbdddaadaaadbbddbdccabbacddbbacbdadcababcaacdcccbcabbbdbabdacdbccdbcbacddbacacddbaadbdbdccbbaaaaacbbbabdddbddddcdbaccddbacdadddccacababaccdaabdacaababcccdaaabdaddccbddacbdbcbbacccacbacaddcaaaadabdbbcbdbbadbcadddbcabddccbddaaccababcdacadbdbacbbbdacadbababbaccacbdabadbbccccabcddadbbddbccacaadcabccdacdaccbabdccddbdabadcbbaddadaccadcabdcadbdabbdabbabdadddacdcadccdbadcbbcacabacddcbcdaadbbcacdbacddaaabaabcabaaaabcccdabbdadadbbabdcaadbbdaabdccddcccadbcacbcadcacdddbccaaabcbcbabcbcbadaccbadbcdddcdbbacbbaddbaaaabcbcbdadbbadcacabcabdccddabbdaddccbcddbcdaadcdbcaaadacdcaabdabaabaacabdccaabcaaabbcbcbcdbbddaaadaacbcbcbabcaccdddbcacdccdbbdaacccabdddaaaaaaadacacdaacdacabbbdaacddcdabdcdcadcdcbaacabbacbaddcccaddcdcccacdcaacaacdccbcbacbdabddbcadbdbbbcabbccdccccddbcdbdabdbdcccdddbbdccabcadccabbbbadbdbddbaadbcdadadaaababdabbccaddccccaddcadcabbdddcadacabaaacabacdccdabcdcdbacbabddddcddacdaaddaadddabbdabaacdccadbbdbbbaacdbcdcaaadcbdccbbaaaabbddacaacaaddcbdbdadbccddbaacbadbdbddcccdcdadbccdcdcdddccbddbbadaabababcdcdbbcdcccabdaacacdbccabadbadaadacdbbadbabccaaadaddbbbddbcaacdadacbabddbdbadcbdadacaaacdddcacaaaaadacccbdddcdacddacddbcccdbaabbbdaabbcdbccdcccbcddccbdaabbadabbdbaccbbddccadcbdcdbdacacabbadccccbcaaaaaacacbabadcbdacbadcdacdbddacdcdbccaacbbddcbbbbbbcdccacbdddaaddabaababbdbdabbcaabddddabaccddacdaccaddbbabadabcbaababdcddbbcdacdadabdaccdcaccdcabbcadbdabddaddcacaccccacbbadadcdbadbddaccdcaaccdadbbcbcadbdddbadbdcbdaacdacdabbccbaaddccadbbaabaddaacaaadbaaaabcbcbabdaacbbaaadaacddcbcccdddbabababbcbcdbdbbbdabdabbabacdbdabcbddbcabbabccaacabaaacbabcbdbccdbabddcbadcbdaabcdacccaacadbdcdcdccbccdaddccabbcdddcacababcaabbbcbcccdbccbbaddbbaaacccdbabbbbddbacadccbbcbcbdbbaacdabaccbdccdbcccacaacdcaadcccbcbccdadbccbdbabbacdbcaccdadcdcdbcccadbcccabbdadcaadbadcbbadddbccbbaadaabaabaacadbcccdddbbbddadabbbaacadbdaaaadbadabaabaabcaadaabbccabcadcbacaaccdbbbbccddcdcdcabcbdbbbaddcadacdaaabcbddbdaddddbcabccaabddccbbacacaadbccdaccbbbbcbcacdbacdaadcadbcdaaacdbdaacbcbdbacacddcaccacadcddbbaccacbacdcbdaaacadaddbbdcccdbbbcacabcadcccdccbdbadaacccbadcacacdabdadcadcadddccbcabcdbdacacacdaadcdbaabacbcbbbdbadddadadccdbacdaaddcabaabbaaccdacabcacbcbbcaccdddbcdbbbbbcdbaabdddbdbacacdabddaddaacddacaddbdbbacacacdcadadddacbcaabadaccbddccbcdacdabcdccbdcadbcbdbbcdbdcdcccdcaaddacbabdacaaddacdcdacaaacdbcdcbabcccdbaaabcdcdbabaddadbacdababacbdbbadbcaadacddbabdbbbcbadcacbabdbdadddbccacaccbcadcaabdddcbdddcdbcbbbccdbbadbcdacccadabadaddbcabbcdccddcbbaaadbddcadabbbbbdacbccaadcbdcaaacabbdbbdbdbddddaabbaadacabdcacdcbdbadbddcabdcdbcdddcccdbcbcbabbbabbaadbbdaadbbabcdcabacddcbbcbacbadcaaabcbbddccbaacacddaadaabbdddaaddabcdacdcaacdbdabcbadccbdadcbcacabbbaadccdabacdacbabbacddacdaabcdbbbabbabcbcdccadccdacccaaaabccacddcadbcccadacdacaadcccbdcaabdddabaacbadcccbcbcbcccbcdcadcdbbbaddaddaccddabdabaaaaaddadadbaccccddadbbacdaaabdacaadaaadaababaccdddccaddddacbbaadbabdbbcacdcbbbbaaabcbcdbcaddcbcbccddbcabccdabdabddacbccddcdbcccabdbbbdadabbbcccaabadadadabdadbacadbdcbbababbaabdaddcadcccbadbcbdddbaaccbcbabcdaabcccabdacdaabcaccdddcabcabcaacbadcdcddaacdcbccbccddcbdbccbbaddcdddbcbccbabddbbdbacbdacbbcddbbbbabbccdacadacbbdcdbcadcddbaddbcababbbadadabbdccbbdacabdbcdcdbadcabcbcdabccbaacdddbaaababdaaabdcaddaacbcbccbaaaacdcdbcdbbadcbbaadaddddddcdabbabbcaddbdddcdbbabaccbbbdcddbadbbcbdabdbdadcdaccadcddaccabcdcdcdcbdbdbabcbcdbdcbaacadcbbbadcbdcbacbabcacdabdabddbdcaddabbadbbcccaaaaaaaaaabdbdcadbddddaddaaddacdabbcdbadbdbbbcdbdbbbbcdadaadbcbadcaadddcbaacbcbdaddcaaacdcddbbcbacaacdbddcddadabcdcdbbbbaacbbbcbaacacaddccbcdabcadbaddbcabbdacdabdcbcccbadddcccddbbaabcdccadcccaccddacdccbbddcaacbdaacddadabbabcbbdadaaaabdbacccdadcbadaaadbdbdabaaabcbabcacbaabccaabbbabcaadaccbddacdccbbadacdadabccaccbdddcdacadcaadcdcbadddbbadcadacdccbbaddcbaabcadacbbbbcdacacdadaaabacccbddbbcaadabadabccbcaddbabddadadacdaaddadcccdbdbcaddacaadaabadbbaddaacdccdbbcdbcbcbbcbcbbcadbabbaaabcbdccdbcadcabaddacbccadbbcbcdbbadaccccdaddaabdacabbbdddacacddacbbaccdcbcabdddcaabcbcdaabbdbdccdcaacaddabcbcabccadaabbdbdcadccaaaccbcbdbbdbcbbcabdbcacbcbacaabbcadbbcaadbaccccaaacddaaaadaaacddaadacddbacadbbbbdbabdcadddbabacdabbaabdabdaacbcdcaabcaccccadaddbadbacabaaacdbacdbbcaccccbdcbdaadaababcabcccdcdcadbaabdbabcdacbcabdaacbbcbadcadbdcccbaaccaddcbaadbbbabdbabcadadbbcddacbbbcdacbdcaddbdacdbadacbacbbbddbbbcaacdcbbdccbcacdddbdbcaaaccbabaadadcdcdbaabccabbccbbacabccaaaabacabbdbbcaabadadcaabcdcdbcdbbacdbacdcbcdbdcadccadbbadabbadcaccbbdddccabcadbccaabdcbdbdaaddaacacdcaaccbddbbcdbbbcbdccbadacaabcdabcbdbbccacaaaadaadccacabcdbbdcbdabbacabbacdaadccdabaccacbddbabdbdbcdbbbdcbacdadacacccaadddbabaabbcadccddaacdbadcdacdbacbccaacbbdcdcdcbccbcacbddddbaabbbbaaabadacadcddcbabbaaadbacbbdabcbccaacaaddbbdbcbcbccbddabcbacdbcaccdbaacbbdadaddcbcaabacdadadabcacacdcccbdacdaccdbdcbddabcdcbbbdacdcbabaccdbbdabddaabcaaadbcabdccbbabcdbaddcadddbbdbccbabcdbcabaaaabddbbbaddaaccddacdbcccbbdbbddcacabdabccadacddcaaadabccbdabdaabdacccbbcabcbcdcdadbaccabdbcccdbbcaacadcdbcdccaaddadbbaaccacccacaaccdaccdbbbcaadcbcaacbcbbccdcaddccaddcabcbcccdbdccabcbaaaaccaabdddbdaaaddbccbbdbcddccccbccdbabaaadbabaabadbbbddcbadbaabddbacabaaccaccabacdbcacbddadbdbaabdbbcacdddcccbcbbcdcadddbcbcdbddaacbaabacbddddccabccdadaabdbabaacddbaadaacaccddddcdcabcaaccccdcdbbcccbdbdccdbaadaddcbcaddbaccaccadcadcdddddcdccbaabcddadcdcaabbcbbacbbdaaadcbabadcdbbaddcadbadabdacdcdcacabcbaccbabdabddabcbaacccbbdcccabbbcbcdddaabbbbbbbababdddcbccbdcdbdcdcddadcacbdaadccddabbbdacaaadaaacccbbadcdbabdadcdacbdddabdccdbdbbdcaddabcacaaccbaabddaadddbddcccacacacbbcdbbaadacbdabbdbcadbcbdaadbdbadcacbbaadcdddbbbcbccdcbaacbccdbdcddaadaabbbadaacdacaccbabaaadadaadccbaacbcdcbbccaadbacdcbbccdddacdbacbdbcbdacdcccbadbaaadcacbabbaddacdbcccdddacbabcaddbdbabcdddddbaddbbdbcabcdabbbadbccdacbbdaadacddadcadddbbdcabdcacddddbbccabddacdddddbabccbdbbcadddbcdaacdcabbacabaacdabcaabdacdacbaabddbbcdbcadddcbddcdbcdbbabdcbdbbacdaaacacbbccaccccdbaabbaccbbccdaadbdccdacbdcdaddbbcaccdcccbbaccbacbaccadbadcaddbdbcadaaabdddbcbacabbccddcbcbddbdacadcbddbdcdbcdacacccacabcbdcbacdcdaddbcdcbaabcbaabaaadbbdadbaaaccacabccbadadacdbbcbcddaddbcbaddccbaccadabccbabbdcbaaabccaaabcadbccccbacabadaabbdcaddccabcaabbcbcccacbcacabcbbdacdbdadbddcbcbdabddbdacbbbacabdbbbddadcacaaadabdadbadcdacbbaccadabbccadaabacdddddadbcbcddcdcabadaabdbccbccbaadbcdcaddddddabdbabacbbcddcbccababacccbbcaaccdcdaadaadabbaddbaadaddcaccdbbadcbcccbbacddacdbbbdbbabdccddadadccdbbcddcadaccacdcbcabbddcbbcbabcbcbdccabdabdbbbbcbadcbabbabaabcbcadcddcadddbdcbacabdabbaadacdaadaaaaabdaccccbcabccbccbabababbdcacdacacaacadacddbccaabdaacdbbacdababcddcccbbacccbccddccdcbddadcadcbddddbbaaadbbbdadccbbdcacccdcabbbadcadcacbadbcdcdadacccadddccdabcbdcadcadbccbcdbabccdcbaaaccdbccabbddccbcbabcbddacbbcdcdbabcbabcbabdacdaddbbcdaabbcbabbbddabcabbcaaaabccaddcadadbbcadadacabddaadadbdcddbcabcaccdaadacadcbccccccddddaccdccaccdbbcdbcadbbcddadadcadcbaddadddaabbacbacaadacdcbdacbacaaaaacaacaaacadbdadadccaaaacdabcccabcccccaabaadabddaaadcbbcabaaaddccbaacaddccbbadcbacaddaaaaadcbcacdbaabcbaabdbacaadcdaaccbbacbdadddacbacdcaaacdacdbbbacabdacdcacdbabccaabddcdccdbaadbaadbacacaadabbdbaaccbcabddcccdbdbbbbabaaadaabadabccddccdcabbdcdbabbabcddcbcdbcaaddacdaddcdaabaccaaddcbbaaacdcbddcdbcaaddadaaddcbadacdcacaccdcbdbbabacbbdaddcaaaabadadaabdcbadbdadabccacacbbccbbbcdadccbacabddaaadaacdbdddbadccdbbcccaabacdddbdcadbcbababbaacaabdbdbacdbdabacdbabddddcdabbbbcbdbdcdabbdbdbdacddcbbcadbcaadbbadaadcbbbdabcadabcbdbbcbcaacdaddbadcdbcbdaacdcaddbcccdaddcdbcbadcacacbaabdccabccbdbababbdaabdacbacbcbbccbcdbcdbdcaaaaaacdbdadcbabaaccacabdddadbabcbcccabbcdbddbddbdcbaaacbcbddddbdaaccaaacddcabdcacdbbcabbbcddcccbacabdacbbbdcabbdbdbbdddcbbbacdaaaabcdccccacbbbcdbdabdbaadbdcdbdddbdcaababcddabcdacccadacdddddaabdccbbcccadbdaaaccbaacdddadbdcbcacbbbadacbdbadcaddaccddcdbaadccbaaabaaacdbadcaaaacbcdbcddccaabbacdbdbbdddcdaaaddbcabbbabbcacbccccdaabaadbacbccaccadbdddbddbdddaadbcccaabdbbcabcbaabaaddbbadadacaddaabaabdbadcdbbbaddcadbdacbadabcbcbabccaabdbaaccddacbcdbabddcdbdbabcccbcddabcdbcdcbbcccbccddbcdddbacdaccaabcadcdbacdddbdacabddccbbcabbdcacbadadbbaacbdbbcabdbbcbdbdaabcbabaadcdadbddbbddddbcaddcdaddbccadaddbdbbbadcdbdbcdcdcbbdbdbddcaccdbcbbacbababadcadbbcbdadadcbbddbcaabbaccaaadcdbdbddadddcdacbbdbbabdbabddadddcdcddccbabdacaabdbdbddcabaacccbcbaaadccacbcabcaccadcdadaaddddccaaaccdacdbdacbacacaadcbcbdbcbcdbaacdbabcdbcdaaacdbaadabcbcbcdcddadbbadababadaddcddbcdddddbbabdddcbacadaadaaddcabdddbadbbaabdbdcadcccddddcacddadbbcbbcacbbbaaabcdbbcbddccccaaccbddcabdbccadddcacbcadccbcabdacdccbdcbdddddacdbbbdcbadbdcbaadcdaccbacbadcddbdcccbdbbaadadaacdaaadcbdbbcddcaccadddbbbadcdaccbdcadaacbddadabbccaadadbbdaccabaacccbcdadcdbdcbcaabccccbbcdbacddcadbcbadcdcbacaddadcdabacabcddddacbbcadabdbadbdcbdabdddddcbcdabdcdbcaacdbbbccabddcacbdcdaddabcccdcacccdbdcabdbdcdaabbddcddacbbbddcdbdcbabbdbdcdbcccddcadbbcdacabacbddbcbcbcbabbbddbbaacdabdccbaddbbbcacaadcabaccbcacbbaadbccbbddadabcdcccaddabbaaabbcbaddccddcdbccccdadbbcccddccbabadcccdaccccbbbadabbcaaccccbbbbdadcdbcbaccbaddabcdcddcdaccadcdddddbbbbcaccbcbbbbababcdccdcdaabbdcdaabdabdccbacdbcdabcacbdacdcabdcccabbaadbccdadadccabcbcbbabdcdabbbcbdadbacccdadcdccacbdacabadcabdcadbdccdddbaaddbdabcacaddddcabdacbdccabdbbddccbaddccdabccdaccadaddabbdacbdcccaccaadadddbadaadaaaccbbddbbcabdadacdaccbcadcacbacccdaccccacadcaadccdcadadbaccdddadcbdcacccddbcaccadbadababbcbabddcadcdccbbdcdcdadcaababcaacbbaabdbdbbadabaacbbacdcacacbcdbcabbabacdbbdbdbabdcacadddbbcdacccdacbdabbbdabdbcacaabdaacaacacdbdadcccdabdbbcdccbcaaaddcdcccabdbcddacaadbabddacbddaaabccaabddabadbacaaaddcaddbaadbddcbbaccbcbcbaabdcccdaddddbaabdbbbaccacbdababddacabbbabaddbdcddabcadaaacabdcacbaaacacbdcdbbcbabaaccabaaaabaaacdaaabcacbbabcdcbccbaabdcbdbdcacacacdabacbbddcaadcbbcbdbdbcdacdddbbaddbbbabbdcadaaccdcbadcccdabdbdcccccbbccddcbbcacccbdddbcacabddbdbbcbcbdbbddbbdaacdcbdbcbbadabccbadcbbbadacdacdaacccbbcbbbbcddacadbadbdddbddccbadaabdcccaaccddbaccaaddcbaabdaddacacbcbbccaaadcaddcdbcdcdabcdddabaccdccddbdcddcacbaadcdabaadddbbdacbdaadccdbbcdaccdbdcccbdbdcdbddcdbabdacdcbddddcbadabccdbdacdadcacaadbdcdbbacdccbacdcbcbdddacbcadccbcbcabcaacbacddbaddbbddabccccadadbbcccbbcdbccabdacddaadccccdcaccdbbbccbbbbadbbdbbacdcaadacabcbccbcbaabcadaddabdcdabbabcdcdbbddbddbabcdaadcbbcacdcbabacccbdbdcbdbddbcbdadbbddaccdabbabcbbaddcadabdaddabcaaddbdaddbbbccbbcaaababdbbcacdbaacadccbcbcaaccadbcbbaabcdcddcdcdabaccddcdaadbdcadcbdbcbcbcacaccddbdddacbadcbddbcdacadaacdacacaadbdadacaadabdaaddcdbddddbcaccbcddbcbadaadabadbacbaaadacaddaccccaacaacaabbdabcaddbdcbabbbbbdacdbdcabaabacacbadacaabdbdbbdbbaaaabaabbaccdadaccbcabbddacadcbabdbaaabbbadddcaabadabccababbaccdbadcbddacbdbbdddaabbcbabacbbcabdccccdadcddadccddcddbddbcbbacacddcdaddcccdbbabdbbadacbdddccbabadcabcbdbdcdadbcdacdbaadddaadadadcdbcaababddbdaddccdaddcbbadbdaaabdaabbdbadbcccdabcccdccbcdccddcbbbbddcbdabbbcbcbbabddbbbccdaddcbacdaddaaabcacbabdcbcbadabdaaaabacbacadbccdcccbadddcbddcbdbdddaaabccddbcdcddabcadbbdaabcbddddccaddadbcdbacccadacadacbcbbcddaadbdadbbdaacadcbdacbbccdcddbcccbdbbbdbbbdbbbdcabccdccaababccdbcdcbdadadadccacaabbbdbdadcadcccdadccabbdcaabaddabbaabdbdababacdccdbdcdaacddbaaaacccdbcadcaccbabbccdcdbacddcddbabcdbaaadbcbaccbbdabcbadddacaadabddaddbddccadcaaaadccdadaccddddcbaaddabbadbccbadaadcdadaacbcabdbdadcadddbbbdbdbdadacccacbaadabaccdabbacbcccbddbabccaacdbcccdcbbadccabcadbcdcbbacdadccaabcbdcbbdaccdbdabcabcbcaaadccdacdddaacbcabbdcbabdaacdddcdcbbdacbbabcacabcaacabbdaababdaadbddabdbbdacdcbabdbbdaccbbcddbcadccbadbaadacadaabadbdbbdaccaaaacdcacadbccbbdacbcdbbabadbdbbaadcaacbbccbaaccccaabbaaccdcaaccbcabbbcaadabadbdadbacccccaaaccddadccdbacabbccdadbcddddcadabdcaadcdbccdccdbadbddccbddbddcdbbdddacbbabbcdbddcaaaadacccddddbdcaacaadccaddacbadcbbcddabdcaaccdbcdacccdadbbcbaaccdccdccbccadcbaacaacbaddcabbbcbabdaadbabadcbaacdcbadcaababbdcccccdcabdccddacdcdbacdbbaaadddddaaccdccccadccddcdaddcadabaaddabbadbdcdcbbaddccccabadcbbadbcacdbbbadbccadabcbbbaacaabbbaadadccadbcbacabcdcbaabcccaccdbacdbbddddadcadababdacdaccaacadcddabddbddbddbddadaabadcbdcaacaababdbbbdccbaadcbbcbaaacdbbcccbacadccabaccddddddaadadcaccdcddbdcadbdcdabdadcbaabcabdccbcbbcbaadbcbabcddcabacbcaabacdbddccacdaaacbbaccddbbbaaaccbbdbdcaabcadcabdacadbaaaddadaccadbbbaaaababdbcbadbdacccdcdabaacdcccadbbdbbaabdcdadbaababacccbccbacbcaaccbdcbacbcadabdddccbdbbbcbaddacccccbbbbbcbcdadbaacaabcbadcbacbdbcdddccbddcabdcaaddcbcbdbcdacbcdacdbbbaababcbdbcabcabbbdacbbcbdbbacbbaaabddacabcbcabbcaccbbdcaabaaaadabaaccbbaacacbabddcdadbdaabaaddbbbacbbcacbcbbaabacccbaaabadaccadddadcdbbabbdabdabaccbdacbcbdbdbaadcabbbabaddabaccccdcbcacbbacadbcdbcaabdcddacdcdabacdbabcccbadbcdadadbbacdcddbbcabbccaacacdcadadcccbcbbbabcbacaddddadabcbbcbddbcddbbadccdaacacaddbacccdadacadbdabbdbcdbabaddddddcbdbdccbdaccbbdbacbbcdbdccddcacdacbbbdbccdaccbdadddbddcddcbddcacadadbcbabccddadbbdbcccdbdcababdadbabdcdbcdcbcabbacaabbcacdcbabdcbabbdabadbdcaaccdddadccdabababcbdbdddabccbcdbccdcaadcbbddababbdddaaccacbacbaccaacddbcbdbacdcbbaaabdccdcddacbbbadadaaaacaaacadcadcdcdcbaadccbaaaabdbcccacaadadaccababbdbcdddaadcaadbddacdbaadccbcbdbcbaaaccaddaaaccdbdbdddbcccbaddbcdccbbcabdccbbcbbdbdcacccacdbabddcabbcaccdbcdbbaabbccbaaccbdbaddaaadbcbcdcaaddbcabdaccaaddaaacdacabbacbddcaacddcbaadddacabbdacadbccddbbadbbbdbaacbbbbaaacdcaacaabcabccacbbbbbdaadadadbabdcadbdcdabcaccbcaadadbccacbdcdddbdbdcbcddcddadbcddbadabccbadddcbdbcbbcbccddbddabcdbddddbbdcdbcbacabdcabdcaccabadbbdabdcddbbccbbbcdbbababadababcdcddcbbdaccacbbacdccadddaadacadbabbabbcaacccddcdbaabaccabbdccaaaddaabcbbaccadcadcacdabacdcbacbabdbbcabcdaabddacabdddbbabbbdacdbccabddcbdddbacbbbdadcabdaaddcbaaaddbcbcaccdbdbaababaaabbdaaaadccbdabdbcdaabcbdadbddabccccacbbcdccbdadbcdaddcadcccbbcdabdacbdcabacddbbcadbaaddacbbdcbcabbaccdaaaccaaaacbbaadbbdccacdbbaaacaaaacdbadbbaacdbdbaacbdddbcaadbabdbadcaddddbcccdbcbbabbcbdcbdbddabcdbcdcabddadacbaaabaacbcbaadaabcabcadbcddcaadcbacdcddadcbbabdcdddcabccbcdbabbcbcbabaaabdbcdbcbdabbcbdbdbdadcaccddaccddccbaccdddacdcabdbbddcaadaccbbdddbdbcdccacbcabddcdbcacaccabbcaaddcacacadddacbaaadcacdaddccdddadaaadcabdadddcadbbbdadadaabacbcdbbccabbdcaccbdddbcbaaadcccdbdbcdaddabddddacdabacadbacbaabbbdcadaccbaddbbdcdaacbcbcbabababdccaaaabadbacabdaadaaccbbcbccdabbaaaaabcaacbaacdcbcdbbdcddacacbbcdbaabbccabdabdddabaaddacbbdadadccabbbddcdabccccbadbbcddbcbacaaaadbdcbcabccbccbbdadabbcababacdadcdcdbdcdacdbdcbadccdcdaadaabdbdbadddddbcdacbbbbadacdcdcdbddccbcdabaadddbbaddbcbaadddcdccbbbcbaaddddddddabdbbdcbddabdbdaddabdbcacaaadccacaccacdbccaaccaaabaddadbdddbbaadbcbbdaccddbcccaddbddadbcadadbaadabcdddaccccdaddbacdaadddbdaddcbbdabdadbcbcbaababdcbabbbcdbbadaaacddbdbcdabbaddcbacacbcacabdadabcabcbdbabcddabbcbcbbcbcadaaddbabbabcddddbcdbbbabbcadddbbaccaabdbccaaacadacbddbadddaadcdcbadaacbcbcccbacaabddaabbbdadcbaddcddddccddcdbbadcacaaccdcbcbccadbabccbbccbccdbcbccdbbdabcbddaaabbdadddaddabaabaddcbdddddbbbcdcaadbdcdabaddcbadaccdabbbadadbddbabcbbabdcddaddcdcbcddcbddbcadadbaccdabcddbccdccddcacacccdbbbcdcbbdcbcaddcbcdddacbabacbdccddccacbdbccaabbbbaadcaddccbbbddcbaaddddbdabdaaddabcbdcbdbaaadcdacdccddccdbbbbacbdadbbcaccbcccbbabaaccbbaaabbcbacdccdbccddcdabadccadadadbccaabcccbaccbdbcbbccababbbbbbccbcbddcbcbccbbcbacbaabadbcadaadabbcabcabdaccaccaccadcabbbcccdcaaadbdaaabcdbbcaaabccaaddbadabcbdccadbadaabaaacabdabbbcbbcbdadcddddddcaaddabaccacdaacbddbadbbcccadcbdbcaadcbdddababadccdadacdadaddcbbabcaddbaadadacadcddadbaacaccbdbdaccbdacbbcdbbbdadbbcbcadadcccddaadacabbddbdadbbccddcaacbcbabbbbcddbdddbbacdbdcaaabcccdaccdccabdcdbdbdadbbdbbcccbdaadcccbbccbdcbcdacccabdccbadaaabbdcbdaccdacbcdcbcbacadccbdaacbcbbdadccdcdaccdabddbdcdadacdbccadaabadddcccbdccabbadbdbaacacccabcadacbddcbcccbddbdcaabcaadbdccddaacaddbadcccacadbabbaddcbaddbbbdaacdbaccdbabdabcbdbcaababdbbcdbcbbbadadcbadabcccdbbadcaaadccbdadcbbbdcccdabbbbddadabacbccdcabbcadbbadabccbdbabccaaaabcdcdacdcbddadccaacbdcbbdbabbbdabddbbdacbcbccbbacdbdadbcddabdcabbaacdaccbcbbdcbabbdbcdccbbccdbcbbcaccccaccacbbdcbbaadadcdbddaaabcaabbdabcddcccbbacccccccaaddaacabbbbadadadcccdacccddbabcdadcddacbcccbabcababadbcdcacacbaaaaadddacbadcbcccccdbdbbccbaabacbabbddbccaaaadacdcbbcdbbcbacaaadbdadcaddaacbcbbcbdaaaadacbcdddcadaabbdcbadbabcbbdbdccadabcccccabdacaadaaabbbbbdaadcacacdddaaacadbcaddcdddddaaacacdddddacdadaabdcbcbbabaddbaaadacadcccabdcadcddcdbdcdcacadacaccbadbcbcdcbdbcadccacccdcccbbcbcdadbbacccaadbcaaaacbcdddcccddcadbcdbdccadbbddababbdadadcbdabddbbbacdacacaacccabdbdcccddcabdcdbddbdcdadcaadbbcaddbdbbabaaaddcddcaaadcbbcdbdbcbabdddbbdabccbbdddadaaaabadcdbadabcbdabcccbcddcdccbbdbabbdadddbdbcacbbccbcbbbabcdcabddaccacdaddcbdddbacbdacbcaaddddbcbbacadbaabccaaaaacadbacdabaaaddbccdbcdcccdbdbabcbaaaacdbcdcabdaaacccaaabacbccaabcbdadbcabdaccbbdbbcdcdabbabcacbaccaabadaacbcaaacbbaabddaabccbdabcdcbccdbabdabdbbdabdbacdbcaccbcbaabdadbbbbbaabcddccbcdddcdbaccabbcbdddaddcaababddacadcbdaaabadbbbdacbcdddcbbacbddcbdaabcadaaaddcdacbaadcacbddcddcaadbaadbdcbcbdccdbaccbabbdcbccbdcddaccdcababdcaccaaaccdcbddacddabadcbcacaabbddbdcdddabcddcdbcadcdcadbaabdccaacdbbaacacddcbbcdcdcababcacaacbbabdcbbdaadbaacdbcdacdcdadbddcaababcbdccdaabbbcacabdaccbbccbcabcaaaccadbcacaabccabbdcdcaaddbabaccaadabbbcccbbbadbacdccacbabdadadadbcaabddcadccccccdccbaabcabbbabdaacdaddbaccdccabdadbbccdbaadaabbdbbcaabacccacdcbcacabacccbcacacccdbcbbbbccddcbdcccdbccadbdcaccdddcbabbbddcbcdddddbdbbccbcbbbaccbdbbdadcdabddadccaadcdcbaddccddddbadaababcabdddcbcbcbcbdbccdcbbccbdaadcdcccbcccaabccbcabcccbcadddcdddccdacbdbacacdabdbaccbdaadddbacaaaccaddbdacbbdacdcbdcbaccaccdacbaacbbcacbdbacdcabadbbbdbccddbdbbbcddddcdaabdbdccdddccabcccdbddacadbbdbadadcddaacccdbadaacbbbbabdcadaadbdacabdbbcbbbccbdcaabbccabbaaadaabacbbdcdaccdacdbddadccdbddccccbabcccdbadbdbcbadadbaadccddcbdabbabdcdacaaaabcaadadcdababbcacaabdcaadbbaccadacabdcdcccdcacddcdcdaacadcdddcbaddbbaddacccbbcdacbccbccdbadbadacbbdcbbadabaaddbbdccbabaddbcbddadabbacccdabbccdcdaacabadcadcadadddccbcbdccdbcbabbcccbddcdbaabbccadbcdcabcaabaaddcabadadccaccdbadddcdbaacadcdadbdacdabdaabbdcaadadcbbdabbbbbabbbcabcddcbdabadccdacddddabbdccdcdcbcaddaabdadadbadcaabcabbdadbdbdadacddbadcadabaacddadcbcdbbbaaaabbdaddacddabdabdbbcacacdcbdddaaaddbdacbabbbccaddbdcaabdddccabdbbbbbcdcadabdadbadbcbadcabacacabaaabbdcdabcacacbcaacccdadbbaabbdbdccadcaadcdbaacbadcacadbcbadbaaccbbbadabaccadcacbdabbbdadbcaddddbcababacdcacbbbcaddbadcddcbaddaaaacdddcdccacaaadbacbdaddadadbcbccdddcddabaaccccccabbddcacbcbaaaabddaadbbbcbcdbcccbaaabbbaaabbddbbcccdacdccddbcccdddcabcdacdbdddbcbdcccabdcdddcdbbabcccbcadacbccbcadcbcaddbdbbcbadcdbccbacbbabbccdcbccadbbadbdaadacbbdddaaadaadcaddbdccbbddbdabacacbbccadaabaaaddbdbcaddccccdccdcadbbcdcdaabbbccdadbcccacaaadbdcabcdcadcdccaaadbabbbbdcaccdcddbbccdadacbaddadbabbbbdbaccbdbbccdbbdbdcdadccacdbbbacabcdbbbaadbbadbabcddacbcbabcdaacbbbadaabbdbdbbadbdadbaabacdbbbbcdccccbabcbabbcaaacddaacdadccacadddadcabcbabbbcdcdaccbdbcbadbacdcbaaccadbbcdddbdcbabacbdbdbdbddccccadcdcdabbdbdabbcbdadcdcbdcbbcdcadbcddacacccdaabdbbcbbabdaddddcddccabccdacbbccdacdaadadbcabcabdcbadbcabbcabbdccaadccacacdbadcadddcaaabacababaabaaadcbbcadccacbcdacdabcddbcdccbccadcbdadaccbccbdbabcdbcdaccbcadcdccadaddbbdbcbabcaadcbdbbaaaaabaccdbddcadcddbaaabcdbccdbaaaabcaadccdaacbddcacccbdadacbadbbcacbbcbbbbcdbdbdddccdcdccdacbbcdaccddbacbbdbbddaddbacbdbdacbccbcaaaaaaabadacdcacbbbbdadcccaaddabdbdbcadbdcabaacacdcbbaadcabdcccacccdcccbbadbdcddacbbcccacdbbacadbccaaddddbddcbbcccdacbbddbabbccdbbddbcdbcacbdadddddbdcbaacbacdbdacbabbcbbcdbaacdbdbcbabddbdbcbcacbcabcacddcaccbdcadcdcaababdcdccbcbbabcabdabaadaaacccdcadbbbcbaabcbaabdddababcababbbbdadaadadaaaccaadddbcdcdcadddabcbccacababbadcccbdbacbaaaabcadadaaccdacacaadadbababdcbcbbabbdbdabbaddbccdabddcccbacbaaaadcbcbdbdbddddaacbddcbdaaacbcbbddaadccabbdacacbacabbacbbbccdddbdcbccbdcacbccdccadcddcccacbdacbcbabdcabdaabccbcdbbcadaacbacbdaacbcdadacaabbccdadbbadcdcccadacbcbabcccbabcdabcdcccbabacccbccdacbaddbabdadcadaacdadbdcdadbbdbacccdccddcddadadbadabddcbcbcbbaadcccacbddaaddbbbacabccadaadcacaadcbabdcbdaddbbcdbadbaaacbaaaadbcbdbdbccabddcaddabcacbbcbddcdacabadcddcdbdacdddacccbbbdcbadbccddbadcccabbaabaabddcabadbbacbbcabcdabcdccaccbddbabbcadcababadbcdacdddbccacdaaccccdadaacbdbbcaacdaccddacdbbddcbdcddbacccaaabcbcccdbbacdbdadbdcbabdadacccaccbccbcbadbcdbcbcdcacccddabdbdddbcdcbccbabddaadadadcaccbcabbbbbaacadcddddbdaaccabdadbccbdaaadcdbdadaaacccaaaccbddbddbbaabbdcababdbcaadcabccbdaddbbcddcdbbcbaddabdcccddadacabbabdcdbcabbbbbbddaacacdaabcccddcbdbacbbdcdadbcbdccddddabccaaaadacbcbcddabbbcccaadcdbcadbdcddbccaccadcddccabbaccdadcccbbbbbdccadbbdcacaaacccdccbccaddbcdbdbbcdaaabcdcccbbacadbccddbcdabcbdcaddbbbdcbccaccdabcadcdcdbbaaacdccbddbbbacbcbadcdccbabbcbadbabcacbbbbaaccabacbdbacbddbdbacddbaadabacbaccadadcbbddaabdbbabbabdacaacdbcbddcaadbdbcabddccccddccaaabbdbdcbcdabcdbdddbaacabbbbcacdaaabccaaddcddcdadbdacaacadadabacaadadcacbdbddddbcaabacacdcbaaaddacdacacbdcddcbabadbcabaddaddaddddbddcddadaabaabadccababdbadddcbdbcbccbadddcbaddaaabccabdaccddabdadadbcdadcdbbbccbacdddddddacccdcbabbddbcacddaddcdbaccdbcbacdbdcdcbcdccdadaccdaaaccaddddaccbacdbadbdcccdccdbddadaacccbbcaadbddcadddadacadbbdbbabaacddcdaacddbdacaaccdccbaabbaacadddcdcdbcbbcdbdadbddcabdbaadccaabccaddbbacddcaabdcaacbbacadaddddadbbcdacbbdddadbdadbdbccbacbcaccddcdabcdcbaccbadbcaaadacacbcbbdbbdbaabdccddacdbbbbddbacccddcbbababccabdaaaacababbabdcacbbbabacbdadbcdabaaabaaddcadcaccbacadcabcaacabadbdbacbdbadacabaadbabdbccdaadcabbcbbdaddcadddcacbbbabcbbddabbbbacccccacccccacbdccbcadcacabadaadabaabdddaadddabadacacbbbbdabbcccabbaaccaaabcabbbdddccbbbdbcdcdaadccaadbacbdaaccaabdcacbbbaabdacddadadbdcbccdabddbbaaddaabbaaacbcaaacacdbbddbbddaaaaccbdcabacccdcbdcdccadaccadbadddbdcdcddaaadccdcbbcddbaababddaccaacbcacddcadbbcbbaddcbbccaaadcdddacaddcbaccdcdbcacbaaccbbcaddcbbcdbdbdbcdaccddcabacbaccbcdbdcbdadcbcbbbdcbcbbccbdcdbcacccddababdbcaaabbdadaabdbdacdadcababcdbdbbbcddbcdbcdbaabaddabcadadadcccbccdcaabbccbabddbbaaaacbbbdcadabbdaadbaadaddccabdabadcdbcddaacdcbcaadbabadccbdddcbcdcadbcdadaaddbaadbdacdddcbabcbadacbbcbcbbbcaabbbdacbbbbaacaabbcbdacbaacdcbdaaddbccadbccbbdcdcaaccaabaadcbcdbabadadddbabbcdcbbbcddbacadabcdbbbdbadcddcddbaaccabcbdcbddaccdbdbdcabbdbccaabcbdabbcaabbbacbcdbdcccbaacbabcadadacabbddcbddcdbadddcbccadacaddadbdcddbdccdbdbbddadbdbdcadabaabddadaacbcadbdbadbbccbdaabbdaadcbadcbdabcaaadcbbabbbbacbdadcdbadccabcdbbddcdacddbcbcccddbdddbcabbadddccccdabaacdbabbdddadbaddbcdbbabdcaccadaabacacbbacabcbacbacbbbdccbbcdacddccaadadccbaddacddcbbccdcdcdadbcccdddcaadababdddbdaadcddcdaddcbdbdabadbbdacaabbcaccbcabdaccdbbbbbbcaaadbaadbcbadadbdaaacdbaaaccbdcbbabaabdcdadbbdcdbdbdaaadcdbdbabbccbcadddbbbddadcbaabddaadcbbabcccbbbcddcdcdabdbcdddccabcbcaabbbddadcddbbadaccacccdaaabdaabaabdaddadcdddcbdddbdcddacbddaccaaaccccbbadadddbbcdaacbbcaadcdadbcbbdddcdcaacdddddccadadbddbcdcadaabcdabdcccccdbabbdacabdccdabadcbadccddbbbcddbadbcbaacbbccccacbcbadadcdcaccbccbbdcdddbbbcddbcbdddccaccbcacdbddcabbadcbcdbcbaacacbdcbdcacdcdbaabcbdcdcccbadbaabdccadbdaabaaaabddbabddcacccbdbbcdadaacaccaddbadcaccdbabbdddcbadacaccdbdcccccdbaddaccadabbcbdcacaccadabdbccccaaccbcadacbcddcdbbbdbdddccdbabdbcaaaabaaabaddcbbbdbbabbcdbbbbacabaddccadaabaaabadddbdabbddbbbdcadaddbbdaccadadbddacadbdadacdbacdaababbadcdcdbbddbcbdadbcdcddaaacbabbbbcbbbddbdacbccccabbaaadaacadaddcacaadadcabddbdabacdcdcaddbaddcadccdccabcaacdaddcaaaaccbaabbcabadbbdaadbdcabdbcabacdadbdacacbbcdcababaabbbcdbddcbadaacbcdbacacbbabbcdbdabbbcbacaccddadbacddaccbbbddcbcbcddabccbaadadccdaacbadbacacbabdbdcdddbcbbcbacaadbabbdadacacbdcbddbbaddbcaadcdddcbabbcaacaabbbcddacaaacabcbcbcdbbbcbadbcbddbbcaddacbcddacbccabbabdbbdcdbbbaccbdcadbcadaacccbbccccbddddcbbbabcadcddbcadbcdcaaaaccabccbdadcccacbbddbddabaababdcbbdbabdbadaadcacccbccdbadadbcabacbdaabccdabdcdcdbbbaaaaccdaaadcabcdcccdbaaadcddbcbcdbacdcccddabddcdccdadcbadbcaabadcaadabdccddbcabbcbadcddcddadabcdbbccdaabbcdbaddaabababcabacdcdcdcabdbadcdbbabdbacbbcdacbadaaabdddbdcbcbabcabbacbcdbbabbbbdbbacbabcddccbdbaddcacdbacbaadcdcddbcbcdbababdbcadcabcdcacccaabbabcdcadcccdddabdaccdcdabddbbcacbcaaaaadcbcddcaacacdadadcddbcdbdaaaddcabbcbbcdbddcbaaabbdacabcccddabbadadbdbacbdadbbcdccacbcdddaaddcbddadaccacbbccdbdadcacccaaacabdbcabcdaaddddbbadbddabacbccabdccddccabcacaccabdbcdcaacdaaabbcaabdacaccdaacaccdcdbbdaccbaabacddadccaacaadcabbdbcdbadcdbbcacabdadacdccbcbdbaacbccddacccaaaddbccbbbbcbcacbbacaaadddcadabaaadcccddcdcbddacdccdbccdbcbdbdbaabdbbdcdadbcdcacddcdcdcadbcacaadcdbdadaddccdcacaddbbdcbdaacdbdacbdcbcddbbbccdbabbdadacccccddcddacbbcaacdddaccdbdbaaaabdaabcadbcadcbbcadcddcbdaabbdbaababddcaddddddddbdcadaabadccaccbcdabdccbadbbddabaadbbcccbbcdccbbdcbacbabadaadddaadcdbbcdaabbaadaaabbcaacacdcabaacbcdacbddddbbcbbaccbdbbcbccbddcaddbcbdadcbdcdacadbabddbdaddcabbadaadbdcbcbbacadaacbadcadbadcbcdbcdcaadbccaaacabbddbaadacdcbdddbaaabadaabaddcadcdbbcdaaaabddcdcbcaddaccdaccadcbddaabcaddacadcbbcbcabcadbcddadbccbaaddbbacaadbcddccdbbbaddcaddcaccdbdaacacddbcbcabbdccaddbcbbbdacdbdbacaabaddbbabcabaaaddcaadadcccdbdaccbacdadddcabdbbabaaadcadbcdbacaabacdcbbaadcccbddbadcdbddddabccdcbcabadcadaddcdadcbbdabadcddaadacdcbddabcdbcacdcdbabadabbacbccaaddcadaaaaacadadabaaddadbddccabaadccbdcdacbcacacbdabccbdabbcdbcacdbddaadacdbbbaaabccdaccbacbaacbdabacbbccbabaababcbbaacdbdaadcbcdaddacdbaaabcaaaacdaabbcbbdaddbdddaccadcbabcccdbbbcbdccbcbdabadcbbccdcdcbcaadcccacbcacddabaddaabacbccaaaacbbabaccbababbcbaaaddddacabaabbccadcaccdbdbcaddadacadaabdcacabdbdcdaaadccddbaabacacbbccbdccaaaaabbdbbacaddddaacabddcddaddcbcbdaacdacbbbccdaaaaddacdacddbcccacdcdbbdcbcadbabababdabdbddabaacccdcaacadddbbbcaddadbcbbabccaccdcbddaddaacdbaaddbbabbdbacbbabbbdddaabbdcaaabdacdaaabdcdadcabbbcbbcbbdbcdcbbdbcabaacbbbdcbabcaababdaabdbcdcdadabaccaabaacababbdaddbacaacaababacdacdbacaacbdcaabbacadcabdabddbbccbddccabbabccbbcbcbcacbddaddcabadbadccddcbacdcdaaaacacdbcbbcdbadadadcadbbaacaddbcadabdcbccadcbacdacdbcabbddbcdccbddabcdacbacdacadbbbbbbacdbadbbbbccbcccddabadbaadcdccabbcbacbccdabdbaccdbbdcbdddbdcbcdcdabdaadcdaacccddbcccbbdbcbdbdbcddaaadbcbdbddcaaccbdddabcaabaddacbdacabaacdcdddcacacddacbcaababacbccaccddadbdaabbbabddcbdcdcbaddccbbcadabbbaddbdddbbdadcadcddbdbaacbcdcbaaabbcbacbabcbbcaabadddabbcadaadbdbbcaaabcacbccabdbdabcddcdbdcbdcaaabcdcadacdcbbbdaacbaaabcaabbbcaacacbdddccaaaacaacddccbccbbcaadadabacbdccddabcbaaababdbcdcdddbbabaaccdbcbdbdbdbdbaacdbcbbddcbdadbbdbddaaabdacccadabbdadbdaaccabcdcbdcabbadaddacdacddacaccbdadadbbbcdaacdbcadcdbcbaaacacddbdacbbbcbaacbccadddcbaaaccbcacccbcdcbacccabaadadcadddacaacbadbbcdbadbbccbbaccdaadbdaacaaadddabbaacadbdbacbcdbaaddcbccdbcbdcccdcdabdbaadaabaaaaaddabbcaccbbccdabbbbcdbcdacbabbdadbbbbccdaacccdbbadabdbadcddadcacdddaabcbabbbdaddacbbccbabddabbadadcbabaacaaccbccdabaacdadabdccaabbcabaaabbbbbbbdbcbccdcdaaaaabccdccccacadcabddbdddcbaadbdcbaaaadacdbdcdadabcdcaaacaabcbbaccccbbbbccaadccbaccbbcbbabdcccdcbaadcdccddbaddadbcddadbcdbbbadbcddabdbbaabacabbcdaddabdddccdccbbddddcdcdbdbcdacdbcdcdbabbadcbdbaabbcbaddbcacbcbdbccdbadcbaadacaaddaabdacbbcbcdbcbcadaabdbaaccdadbaddcadbaccadababdadabacbbabbbbccabdadbbabaacbbacdabdbabcacaccbcbccdcbadbababdcdbccddcabdaadbdcbbdacdabcbcbbddadcddbcabaccdcabdbbbbcdbcbadacaccdcccabaccacacccabcaadacaddbdbdcbaccbadbbcdccbdaaaaacccccaddbdabddaabdcbcbddccbbcacdbcdcbaaacadccbbbbacccbdbbacacabadbcabcacdccabbacdccaccaddadbbdbdaacbaaccddadddcccbabacddcbadcbdaadcbbbadcbbdbdaccdaacadaccdaaadcccaaabbaacbcbcbccbdadbbccbcbadcbcbcdcccdddcabccdadbcacbbddabbabdbbbdaddbdadcbdadbaaccddacacbdcabbdddcdcdcaacabccaaabdcabdcbaaadbcdbdccabddcacdadbcddbaddcdabaccdbbadacbcacaacabcbccddddacbbcddaadbcdbbbcbaccbdccdadaddacbcdacdabbdacbdadbbadcadacdbadaadaacbabdaabacabdcabcacaddcadccbbcdbabaaacbbcdcadaacaddbbdcdcabadbadacccccaaadaaabaacbcbdaaadabcbdcaccdcdabaadcadbacbbccbbdaabdbacdaccabbdaccbcdddbbcbcdadbcdcaabdaadbadcdcdccabbcdcbbdccacabadcdcdccbbcaadbcdbbcabbbaacdabddacacbbaadcbbbadadbdbcadbcbcccbbccdcaccbdadbbbbadabbdddcadacadaddbdcddacdbdaacdcbbdaabaabaabdccbcaccddacccbabcccccbbbadcbcbbcdcbdadbbcaaccdadadbabcbbcdaddbbdbdcddbcbdcdcaddcdaaaacbadccbabcbaccbddabadaaddcddbcbaacabbdacdbbcdbddaaddadbdcacadccdbcadbcdbdbaddccbaabcbdabacdddadbaccabcbdcbabaaaacaadcbbcdaabbdbaacbcbccbbbbdbabbbbdccccbbcccacaccdccbbcacddabcabadacaadcccddbbdbcbbbdaaddadcdcdaadccbdacdadabdcbaadadbadbcaddbddcabddbadcadddabcdbdbacaabaccdbacbccddadaaadcbdabddacbbdaaccbaddaabcaabcaccbcdbdcacadcdcbbddacdbdbdbcbcdadbcadbdabaadccaaccbdcbacabacddcccccbcbadccbddabcabcbdaadddadbcdcadacaacdccacddbabbcbdcddabaddabbacdcbccbbdbbaddadaabbababaaacdcbbbcbdbcadbbdbbcdacbbbacaaabbbaadbdbaacabcaababcdcabacbaddadbddaabbdbdddcbcbaacdabdabdddacdbcddcadddbccadbbcddddcaacdacccbdabdddadcadacabbbbbaddbcadacbdbcdddcaddddcbbbbddbddccbdccbadabdadacadbcaadbcbcdcbabaccbaaccbdbbdbccaccbaaaabbcbbcaaccbcbbddabbcadacdbacbbbdbbabdaadcccaadbbcabddccdaaadaacbacdccacdcbdbcbabbbadddcbdddccadabaadcbaccbcbabacdaadadbcddddaadcbcdcbbccadcccaddabccaacbaadbdddbcddbadadaadddbbccdddaaadbabcbcdbcddadabbcadbaaddcabcdccbadbbdccbdbbaddccaadccbbcbcdbbcdadddbcbcacbddaadccbcddaccacddbcbcbbccddbcbcdbaaabdcabbcdcababacdabbcddbdbdbaadabbcdbdaddbcbdadbacdcbdccbdbabccaaaccdadadcdbbdacadcbaddcaacbccbacccacbaaaccdacbcbbdaccaddbaadbdddbbcaadddcdbbbabddcadacaaaacabcccdaddadcdccbdbbbaddaacdbabadcbbaddaaddcbadcbbdacdcdbddbbdaabacccbcbabdbabadbbabbbccdbddcaddccdabacaacddabdbcbabbcccacabaaaacdacadabcdbabaaabddaddacdcdadbbadcbaaddbbbadacacccaadcaadaacbbcccddbbabdbbbdbcddadacddcdccdbbccbabdaccdaaaccabbbbaababdccdbccadaccdbacadaacbbccbadcbccbaacabccaadacbaabdbbaddcbbacddbadbccdacacbccbbbbaadadcdccdaabbabaccaadbdbaabaddaddbcacaddcadcbcabbdadbcdacbdddddbdbbbbaaacddbacabcbbbcdcdbbcacdccdddbdbbdccdcdbcdbbcbdaccbddcaaadaadcbcddddcccadbadabaddaddbbaddcacdabccbbdcadccaacaccbcbbbaacaccbadbcbdacaabcacacbacdabbabcddacbbaadacbdaaccadcacbadddddcdbabcccbdcbcddbbdcbadbbbbabdbdabddaadabdddcbcdbabacdabdbaccdcaadaddcadbacdcbcacbcbbcccadbadcbddddbbddcbabadcdbcddacdacdcddbccbcbababbbaaaadcdacbaccccacacbdddcbdacdabdaacadcdbbcbabcaddbbdbbcddacdcaacbbccaaacdacaaaadbddaabddbdabbacabaddcccacdabacaddbaabbddbdabcdadcadbbcbcaadbbaaacbbbbbdcbabbccdbacdbacaadccbcbbdbbdcdddababadbdaccccbdddcadadddadcccbbcabcccaabccdbcbdcbdaccdaaacdbddadabaacacddbcbabadabcabaacbcdbacbbacdabccccadaaacddababdbdaccdddddbbadaacbcbaaaccadcacbdabdadcaaccbbdacabbadbdaadcbcdabcabbccadcabbbacacbdcbcbabbbcbdcbabcaccaddbdcaabbdddbaadadbadacdcbbdaaadaaabbaadbddadddcdaacbddddddcbbccccacccdcabbdbcdaacccbaabacaddadccaddbdbdcbdcdacbbcbcbcbbacddadaadbcbcdbbbccadcdccadcaabdbcddcaacdacddacbdabddaadddaccdcdccaabdddcabcddcaaaaadbcbdcbddacabdabccbcbcadcdbdaabaadccbddaabaaaccaaacbddcacccaadcabbccdbddcacbdccbbcbabbcabbcaddcdbdbacddbbadaabdaabcabbdcbdccdcaccbcacddccbdbacdbcdcbadacaababadddddaacbccdbadcabbabacdabaddbaadcababcccdcdbbaaaaccbbadbdcdbdbcadcbccdabdcdcbbcdadddcddbbbaababadbbaaacdaabcddadbbbbbbadabdaccabcddadcbbabdbbdbcdbcadcaabaaccbcbbdcbbddcadbbaabcaaddccacbbadbadcdaacdddbcbbdbdcdcdbadadbaccdbadcbbbcdbbacadaaaacaadbdabaadaaddaabddacacdcbccdcbdcaddcaacdddbcacbbdcaaccbaaccbbbcccaccabcccacdadbcabdddcababdddcccaaabcbbcbddaadcdcdcdbacdabdccbacdabaabbadcbcacddbdbbcbdabcdcadcabbbdadbbdccaddaddadccaacdabaccbbdaaacbabdaacdbbdbdaaccbbdbcccbbdcdaccadacbbddccbddaadabacadcbddcabcdaccadcdbcbddcdbabbacbcdbbcbdacdcccbaddcacbddaadaddcabbabddacadccacbbdcadabbdcbbcadbbcbbdcbcaaabadbcbcdcbdccdcbbacdadbcabcadaacabcbcbabbcdbadccdbcddcabbaccacbbdabcdbaddbdcadcbdaaaccaaaccbccadbabbbccdaabcdaacbabacaabdbbbaaadcbcadbaadcdbddabdcbccdbbcddadadabbabcbadcbbdabcbabbabdbcacabadacaacaacdbbdbadcbcbacbbcdbccbdbaddaaadccbdcaabdccdabaadcbcacbabccaddcbdbcbccbcbabdbbbbbbaddaccdaccbbaacdbabbabdcccbccabacdbacbaaaaadddddaabcdbbbddaaccbacacdccaccdbbdbcadccbbccbadddddddbaaabcaddcbccdbccbddcbbabbaccbcbbbadbdabbdadadaaacaabbabacdddbddaabcccaacddcadadbdcacccacaccacdbdbccdcadadbddadadaabcbbcaabdcbbcacaccababdababaadbbdcadcbdcdbbccdddbbcbddaadadaaaaabbdabbdbccdacacadaaccbbabccdcdccadacdadcbdccddbcabbaddcadadaddbaaaabcbcabbdcaaabacdccbcbcacdcdbcbdbbdcdadcbcbddccbbbaabdccaddccaabbddbcdccaabbccccbacbdbcbccacbaccaddbcccbaadbbcdbccbdaabddabcddaacadcabacbacbadcdacdbdcccabacbdbadacaccaddcbdcbbcbcdbcdadbbaaaaacbcabccdccdbbdbdabacbbbdacdccabdabcabbcbabadddbcaabbcccdacdddabcaacbccdcbdaabdadddbabbbddabdbccadcbbbbacddbddcaacbacbccdbababbbccdcbcacadadbbccabcddaaacacdddbbdcdcacdcadcdbdddbaabdacaabbcbdacbbacabacdaaaddbabaccaadbcbccdadcbbbddadbaaddabdadcacabdabbaabddbbccabbbdaaacbabddbcddacbaacabacbccddabdaaccdacbabcbcaabbddbabaaaacaaacdbaacddabacbbcabcccbbbaadbddbaadcbcbacbadaacdcbadbacddcbbbacaabaacddccddccaadddbdabcbdaddcaccacbcabdbcbccaccdbcadcccddacacbbddbdaddddbcaddcaababacbdabaacabcdadcdacddadadabcaabdaaabddbccbcbadabaddbaaaacdbbdaabaaaaccbbbdcbadaddccddaabdbacdacadcaaabbabbdcabcdbbcdaccbdabbdcbbbdaccccdcaaabdbbbbbbccdaadcabdcbddbaddadcdddcdddaddcbdcbccddbbaadadbabccabbbcdacbdbdbaacccdddbdcabbadbaccaacddcacbbbbcccabccbbbacccccaabbcacabaaaabcaadbddddbacccdccabccdbbcbddcccdccacabcacacdbacaaabdaaabaccccacdbbdcbadadbacdbacdadcaabcdbcdbbaadcddbcdaccacacbcdcacacbdacbcadabcdacbddbabcbaadabddabbabbadcbaadbccccadbcadcabcbbbdaccbccacbbdbbdbacdcbbacabcdbadbdbbdcdccdcdddaaadddccbbdbddcccbadbacbbccaddbabdaacbbdbbdcdbcaaabcbcdcbcbcdbdcaacacaddcbcdbacccbcdbdabbcbcaadddcadbaaadaabbdbbacbdcddbacccaccbcbbcdaddbaabbababcadbdbbaadaababdcaadaadcccbbbbcddbadbbdbdcccdaccbabbbcccbbcbdbabbcbdbbcdbadaacbccdddcabccbdcbcaacdbbbdbbcaabbccbabaadcdccbbdcdabdbcdacbcdbadcaabbcccccdbabcbbababbcdaaaadccbabcabbaccdbbabcddcaadbdbdbdadcadbdbdcbcacadccadaaccabaadacacabccdcbacbbcadbddbbcdcbaccbbaccdbabaddcbcacdcaabdcccbbbaaacdbdadcbaadadcbddcadcabdbadacdbaacddcdbabdbbacaacabbabcccacbbbbcbddcdcccdaddcbccaadddbacdadabbbcddacbdcadacaababcbdbdadadbcdbbddbcabaccbcabadacabcdcacacdaabdcabbadbaadaaadccdcaadcabbdacaccacadaddcdcbadccbdbcdcaacccdaadababcdaaddaabddbbbbdacacadddaaddbcdbadcbdcabaddbbdaabdcccdaacdbcddcdcdacaccbdbbdbbdcbacdddcdcdabbbbbdbdddaabbacadbaacbdcbcbbcacacadabdbcccbbdddbdcacbdddadbabacddddabcbbcbacabbcbdbabbbcddaaddbbccccbcccdbcaadcccbbabbadacdddcbadacaabacacadcbbbbbbbdbabdcadcccabddbddbcbcadbdcabadaabaacccdabbacdddcbdcbcbdccaacdcabdaaabaaacdacdaddabcbdaacbcdadabbbbdbdabaacbacaddadcccaaddbdbdddccccbdcdbcdcccadcbbddbdabdbdcabccbbbbadadbdbaadabcdbbaccbcdaadcabbacccdacaddbccabcbbbcddddccacbcbcacdbddbaddcbaaacbdabcdabcadbbdbbaacbbbadbbddcabdaccaabdacdadcdacacadbacdbdadabcbdaacdddbbddabdbacaccddbbbcbcbcaabbaadccbaadddcdccdcccccdbdbbdbdaaaadddaaadcdabdcbadbbdabbaaabbcbaacaabdccabddbbacbacadabdaddaadccddddacababccabdadbabacddbbddabcccaaddadddbacbbbddcddcadbddbaddcddcdbdbaaaabbcbbbcbccaadaabbbaaacdcdabdcbcbdbdbdaccbcbdbddaccdddbbabdcccbdbcaddbdbdbbdbbdadcbbbacddcaaaddbdbabaddbcbdcadbadbababcaaddbbcddabddcbcabacacbbdabcdbccabbdaabbabbaaddacbadaaaacbdddaaadadbdddaddabadacabdacadadaaccacbadabbcaacadcacbbbdcbaaaacabccadabcbcbbaaacddcdabdaaddbcbcccaccdbcbcbabdaaaccbbabaaaabbdadadcdcadadbabdcdcaabcbdbcccdabdcbcacadbcbbbaacbbdbdccdcdbaddcdbccbababcbdbdcacbdddbbbccabddacdbdcddcbacbbdbbadbcbdddaccbcabcbddbdccdbdbbcbcadaabbdaadbddccaadbaaabaabdccbaccaacdbdacbaacbbdbcdabacccbaccdbaaaaabccbbaabcabcdaabdbbccccacbcdacccaccaacacadddcdaabaccaccadddcbcdbcaadbdbddaacaadbdbcacabbcbcabdcdcdddbbabdcbdcadbdaddaaabbbbadcadddadaaddbbbaacababdcccbdacbbbdbaabdcacdcadabdccddccddccdbbcdacddcdbcdddbdbaddbdadcbadbcddcbcbdaaccddccdbabbbdcbbbacdbbbbcddcbacadcdbbcccaccabadaadabcbbcbdddcdacbadbbbaacdabdaabdcacdcdbacbacbcbaaccacbcabaccadbcdabcabbcaadacaacccabbdaaaacbaddabaabbccabcccccdbadddbabaadadcdaaddaadcdbabbcccacbbadabdccdadaabdbcaacbadcbcbddcdddcddcdcaabddbddcbddcccccccdcabcadbbdbbbcbcacaccbcbdccbccadcacbdbbdacccbaaacadcbcacddbbcbccdbbddbdadddaabacacbcadcadbacacbadcbdcbbabacccdbccabadbbdadabaabddbccadcbcaccdddaacdbabcbbcdbccabdacddbbccaaadcabdccbbacadbcbaaaacadbdbcabddccdbccccabdbaabdbddadbbdcaabdddabdcdbddbccbcadaadccdaaadbdbbddbccbccdbbccddbcbdcbdabdaadaaacbbdabbcadcaccbabcdbbacdcccbbdbcbccadadcadacdbbabdbacbdcabaacccdbdcdadaddacbadbbbcbbbbcbbacbacddbadddcbbabbabaaabbadcaacbcbdcacdbbcacaccabaccabcacdccdbbbbcccadcabdababbaccababbacabdbcccbdabdcdadabdbbdacaccdadcdadbdbababcddabdbabdcbbaddcabcbddabcddbcdabaccaccddaaadacdcabcabaaacbbdbcadacbabbbbdbcbacbbacacbcbabdbcdbcbbadbbcddbcabdcddcabddcacdadadabcdddccabaccccbdabccabbdcddadcbbbdcdcccaaccaccbcbdbabbbaabddacbccbcbdddaaadbcdbcccbbaacbbbbcdbbaadabcaacacbcabaacbddbcdbccbdadcbcccddbabccbbcbaaccdabdabcaaadbbcabacddbcdbcdccccadcbcccdaccccabbbaacbaccbdcbabcccbdacacaabbaccabdacacbcddccddaddccabacbcbbdcdccbbbaadbcabacccccabcababddcbbccbccdbcacbcaabcdbbddaddaadcdbcaddaaaacccadccabdbcbdabadccbcbccaddbbddbabdcaabbbdcdbdbdaaadbbbabbdaaabddadacbcdcdbccaddcaaaacaccabacddccdabbbaabbcbbdccdcddaccadaddbccccaccacdadbccdaccdaadacddbcdccaaacdaaddbcadcadabcbdcbcadadadbbdadaaacbacabdcdcacdcacacddcccccdcadaabbcbdbadbcabbbcbaadbdbabaaacadcbacbaaadccbbddabdacccdcddddcdaaadaacadcdccccacaaccababccacdbabddddbcbaaadcabcacbdbdabccbdababbcdcaadccdaadabbcaaacdabbaabbbbcabcddcdbccacdcdbddcacabbabbaacbbcbadaccacababcbcbccadcaddaccddcadaaabdddcccabddbcababccdbabcaddbaccdbdcbddaabccabbbbaabbbdadbcbbcbdcbdaadaaadbabdcccdddbdbdcdbaaaccccbbdabaddbaaadabacbdccbbaaadcdbcacaabdaddbbbdaadaabdddbcabbcaadcabbaddaadabbaadadabcdabdcbdcccbabdbbadcdbdbabccdcaacbdddbacbccaacacbbdbbddddcdababcbcbcabadbabdcdabdacaacbdacaadaccdbbddbbdccccdbbcbcddcbbdccdcaccdbbdbcabbcbbcbaadbdccccacdaccaaabddaacbdacbdaabcdcdcdbcbabaddbbaddcbbabdbabbcdbaadbcdadacabcddaddcabbdacadabdddcccdcaaadaadacbbadadacdddacaaadaccdccddbccabbbcdcddbdcacadacbccddaccccbaaddadacacabbaabcacddabddbbbbcabbbabdbddbdbbdabcaccacdcbdbccdbccabbacabcacdbdacbcdbaabbdaccaadcadbcbcddcdbaccdaabacabbcbacdabbdddaaaadbdabbbaaddcdcbbcbbdaadbbbbbcdbbdacdcacabaaadbcbbacbddbbdcacacdcabdabdddaadbdacdbdaacbcbaadbdddabdaabcbcdbadcabcddbaabcabcdbcadadbbdcaaacbdbdddcddcdbdcabacbabdcccbdcabbdacbbcbcbabbdcacabbdccddbddaadcbdccacbcdbdddaabdbcddcbabccbbdabadcbadacbcaaadaabbdbbcabacdbbccacbbdabddaabbaacbdbdaddccbccabbdabddaabbdacdcbabbddcabddaaacdabddcdbcadddadccbaadcdacacbdddacaababaccbacccacddccbbcdbbcdacbcaadabbddababcbaddccccdbbdcbcaabccdabccdcabbccbbaccbdaaaaccaaccbaddddaabdcbcdbacbcbdcabdbdbbbccabcabcbbcdaccbbaabbabdcbaaadacaaccccbbabbadbdcaadccdbbbcddcabbbaadacbccbadddabbbabdaacbbaaabcdbbddbdabccbadddbacdbcccbccddadacacbaccbccaacacadbdbcdaabbcbccaabbccbacddaaaabacacbbcdcadbccaccdacaadbabcbcabdbcdabbaacbbaabcadbcdaabddadcdaadcdbccdacadbbcacdacdabdaaddcabcdacacbddcdadacaaacccbbbcdbbbadcadcabdcabbcddbdbccbcacaaaaccccdacccabbbdbabdccabcbadaabadadcaadccbccdaacbdbaddcdccadaabbbbddacbbddccbbaaacccbbacbacbbacbdbdcabdbdbdbbbcdaaddbcaacdccddaddccdcacbdaacacbbdadaabaacbcbcbdccbdabcdccdccccdacbadddddccbbcaacddcdbcdabcdabadcadaddaddbdbddbddbacdccccdbabacbccaddbcbbabdcccddccbdbaabbcabaccdcdddacbcbcbbacadcbadddacbbabbbbccabccccddbbacbdabcdaacbbbaaaabcbbabddabdcbaaadacccadddddbbaabbccdddaabcdabcccabccdccbaddadabdabccddbbbbdadadbdadabcacacbcdcdccdbbbcadcadbcddbbaaaacbdbdadaddababaccbcbcbadcbbbbdadaddcccdccbbabbccdacbdcdcdddbbbbabbccaadbaccdbdaabdcbacbbdcdddbdacbcaacabacbbbccddbbbccdbaddacabbccadabddccaadbcacdbdcdcdcbdcccccbabadcccaccaddacddbbdcccadaccdabbadcccadaaabbdadcaddccdabaaabdbaadbaccbabccbddccccccadbacbccddabaadbdccacbcabdacaddabdbbddcddbadcdcbdaadabdbacaddabcbacabcdaaaadaabbdbadcccdcadcbaadaabdcbaddddcbdbaabadaacbdcbbddcaccbbcbadcabdbdcdbdbbcaadbdacbddcdccaccacbdccdbddabccdbbcdbcbccabdbddadbacccdcadbdcbdcddabcbdaddbddccbbdacddcadaabcbdbdddbdbccbcabdddacddcdbbcdcaaadbdcabbaabddbbababdacbdbdaddbcacddbbbadcacbbbccbcabaabbabccabaadddcccabaaaabcbcccddbaadcdaadbcdcbbbaccbcbbbbbadcbcccbadcaaacdcdaadcbdbacdaaacbabdadbacbbbcbdcacccbbcbaaaccadaabccbbbaccaaadbdadcacaacdabcbcbbaabccacdcdcabacabdbdbdacabaabaaccbcdabdacbdcbacdabdbbdcbcbbddaaabcbccaaddcacbcbabbcdcdbcacbbcbddccadbcdcacabacbcbcddbccdbddbbacdadbccbaddbbadadaacbacbacabadcbbbddadacbcbbdcacbdcccdbacbddddbcdddadaadaaacdcdabddadcadaddbcdcaacbdcacaccddaabdadbdbacdacdccababcdccccadcaaabbdcdabddaddbddbabaccacbcddcbacbdacadbbddddababcdacabadcccbccdcdacabccbdcaaccbbacbdddabccadbaaccdbbdcbabdadcbcdbcaaadadccaccadcbdaaadcddbcdabdcdcdcddbabddbdbccbdbacccdcaddcdccbbccbbdcbdcdddbadbaaabdccaddadadbddcddadbcccbcccabadbdadbbacbaddaccdbcccacaddadddbabdbbbcdcaddbdabdbdbbacbadadbabbbcdbbcbacbbabddabbadcbdcbcadabdbadcdabcbacabcdcaacdcbbadcccadcdcaabcabdadddcbbbadabddddcaabcabbcdccddacadbddabbacbababadbbcbaabbbaacccbbbabaabdadabcbaadcbbadacdbbabbcadcbdbadabaaccccadcacbccddcbbacacbcdaabbaddacdcbabcabdaabcabaadbbbaabbbadcbbcbacbaddbddbcadddaddbbdccbdcaddccddbcdbdacadcadbdcbcdcdbacbbcadcabdddabbcdddbbbdcbcabbcccaacaccaadaaddcbdcabacdbaaadcacdcdccaadcbdcdcbcdcaddcbbcccdbcbdcddbbdbdccabdddaddcbddabbccbadccabdabadccbaccdabbdaddccaacccbacccbabbccaddcaabbaccabacdaabbddccbaabaaddcbcadacbadbbadcdbabbbaabdbdbcccccadcddacaadaaaaadbadabaccbdbcadcddbcdbdbcaaaaadbbccaadbabbacadabdabcccdccabbbbdbbbcdcacccdddabcdbcbcaddcacbbdacdacdddbacccaaccbbdabddbbdcaddbbdbbbccdaaddcaaabcccacabadbcbbdacdabccddcdbbbccddbbdbbbdabcbcbcdaacbddcbaccdcdbdaddccdacdccdbcddcdaacadcacdbabccddccccbdaaaabadbdccbdddbdbddcbcbbadcabbcbaadbcadacdaaaccabddacdadcadbbaccbddccccdcadccadabdbaaabbdbddcdadaddddbadcacccdcdddabccbbbacbccccbbddcaadbabccbdcbbacdcaddbadcadadcdaadbaadadcaddbcdbadabaccadadbbbbdaccddbbbdaaaddcacdcbacadbaccdadcaddacccdbddcbbaadacccbccbdcaacabbbcbccdabaacaddddcbbdaccdbbabacbadbcdcdbcbdbabadbcdbdcdcbddddccbabdcddcaacaabdbcdacabaddccabaaaacbcccbdcdacacaccdbbcbcacdaacccbbcdddacadddabdccabbbbaabdbbbabccacaccbccbaaccaddcddabcabdbaaabaabcbcabcdbddcdcadaddccddacacacdabadabbbcacacaacbbacddadddbbbbdcdbbdaddbcbbcadaaabdcabbdbcacaaddabcdaadcbabbcaaabbcadbcadcbaabddacdbccdbdbcacbdcdbcbabccaacddbdbacccdacadbadaacbcaaccdccbbcddadccddabcbbbdbadbccaddabbbddcadcbcacdcddabccdbdddccbccaadbababcbdcacdbcccddccdadbbcabaddbacbcaddccacaabdaabdbbcdadabdaaaabcbacdbbdbccdaccbbabcdbbccbaccdbdbbcbdccdaabaccddadddcdbcbcdaaacadccdccbadbdacbcdbddabbcabcddacbbddacdbcdbdaabdcbacddcbddbcdadbbbbadcacbdcbccddbddabddcabddcadadcabbcdabdbadcbcbccbabdcbbacaacacbcdccdcadababaaaadacaabdbaccacdadcaaabbaddcdacbbcadbcabbacaacaacbbcdacaabcaadabdcdaaaccbabbdadadbbadbabcacdbacabddaabbdaadbadbabddabbcdaadadacdcbaadcbcaaabcccaababdaaabccaaddaddbcddcdcdcbcccbdcdacbaaddccdcdaabbcababcaddaddacccddabcbacbcdabbabaddabdbaaccddbbdbcdaddccdcbbdacbcaccbbddcabbccccbcacbcddbccbdabbdaabcabaaabbcadbbdddccdcaaabadababbacdddccbacdbadabacccabbdccbdccbabaadcbabbcabbdbaaadddaaaddddadabbaaccaabaacdddcdabcabaccababbcacdbddcbdcbcaabbdccdbdbcbccaadbdcbaaaddcabbdbbcccdaaadddbdddccacdbbadabaddcaddccdaabdcdcaddaaccbbcaabcaaaaccadcdaddadbdcccdcaaddbbdbaadbdabddcbddbcbadbdabcbdaaabcdccaccadacdccdcaaddcddcdccabcccdaaabcdaddbbbdcdbadbaaadcddadcbabbdbbdbbccccbaaadccbbdcacccadccdbdaddcadcacacaadabaddbaaadccddcbacaadddddddacdcccbccbaaddbacbbcbabcaadcacccaacaadcbacddcdabaddbacdacaddbddadaccdbaabdaccacdddbaccdbacdcacbcdcdccabcadabcbbdcdadcdabdadabddaaacaadabdbcbbabbdbbcaabdcacdbacaddaabdcadcacdacbdacababababdaacbadaadbcababcbaddbcdaacddacbdbdcddacacbcabbddadddcdcacdbdaccccbddcabdacdccbabbbbdaccbdcdddcadbaacbbbdbcbdcdabbcabcdcdcbaacbaaadbbadcbcbcddccaadbddbaacdcdababcdbdbcadbabccaccdcddddbbacdbcabbaaacdacbabccabbcdddddbcbaadbabacabaabdcacbdabadcacddddaabdccddaaddccdbccbddcaddbbbadbdaddabaddcdcaaabcdddaacdabccaaabdbacbbcabdabcddcdcdcaadcadbddbacddcacbdbbabadabdaacddddaaacdbbdcbcbcbcccaabbdabadcbdcabadadabbdacacadbcbabbdaddaddaabacdbacdcacbbabccdbbdbdcbbaaccadabdcdaadbccddcabcdddbacbddaaddcbbddababbdbdcdcacabdbccdbdbaabaabdccdadcabbbbdbdabcccbdbbcdbbaaddbdcaddccdabbdccabddbdacacabcbbbdbaabadddddbcdbacbaacaabbddddccdbaabdddaabcdcbadbaddddcbccbdccbbccdadabdbacbdaccdddbdbdabdcadcdbdcdcabbccbabdcdccacababcccacdbbdbccabbbaaadacdcabbcabaddcabdaabacdadbacadaaabdbccbdcccbdcdabcaabadcacbadaaaaddddbbbbddbbdcbdccddcbabadaacbbacabcbddbcddcdcdbbaccbbbddadaaadaacaadbaaadccdcdbdbbbdcdddcddcbbcabbadaaabcbaacabddccbaccdaadbabacbcbabbcdbdcdcaabdabdbdaabcadcddabdaabadcdaccbabaaadcadcbbbcddbbabdcdabdcdbbcadaaaaccbdbacbcbadbcbcddbbadacdaabdabbcbdcadcccdbdbbbdacccacaabbbdbbadccadacbbbdbdcabddcbddcdbcdbdbbdacabdabdbbabcdbbadbaacbdcabbcddaccbaddcddaabbadcbbbaabbdaabadbbddcabbbadcdabdbbccddaaadbbaabbcdcaaccabdbdbaacbdbcaaacaacddaabcbdbbcabddcbdbdcccbdaaacbbabcabcbdbabaabaabcbbbcbddaabdccaadaacaadddcdcacaabdbdcacbcdbbabdacdddbcbbdbddbcbdaabadbbbddbabbabdcdabdcdcccacbddabcbcddadaddddbdbcbcdabdcbccaabcadadcdacabccabdbbddaadcbdbbabdaddbbbadbccaacdadbddccdcdacccadbbadaaaabbababcbbabacdadbabbcdcdadaaccdbccbcaddbbcdddcacaddcbbbabdadbabdcabccbaabadcbacacbbcbabdcababdbdccadcbdcbadbbabdddacbcabdadaddacbcacdbddbbbbdcdcccbacccaabadcbbbcbcabddbdbbacaadaaadacbcbacaaaccddacaddabcadabbcdbdadbadaaadcbcccbcccbacbbcbcdbbcdbadabbbdcddaadcadbbcbaccdccbcbaaadbaccabcbbdddbdadbbbcabcdaccaccadadcddbbadabcaaacbaaaadadcadcaacaadbbabcbcdcdbadacbcdccbbaabbbbcdcaddbababaccaddbadaacabddcdccbbcacabaabaaacabddcbadcdadbbcacdcabcddbbadbdadbaccaaacddbdbbadabaaacbbdabaaadacccbddddddababaddbdcabccadaabadccdbcdacddbcdbcdbaadbadaddaddacbddacabaaababbdaddcddccbadacbcccbcbddbbbaaaadaddcbacaaddacdadddcddcdaabbddbabdabadbcdaaabdbbadabdbdacdadaadddbbdbdacbabcccdaacbcbccbccaadcddcdbabbabaddccbaadcabbbadbbbdcddbadabbaacdbdcbbdbbdcbdcdabdaccdbaaaaaadcbbbcdaaabadadbbdadaacdcadcddcadcddbaccdcabcdbdbbacabbdcdabddccdbabdbaadadcbbaadcbcdcbcbbcdabaabaababddccadcbddaacddbadaacbdcccacdcccaaabcbadbadbbdaadaadcbbabaddacabbbbaccaddbbcacaaababbaddbccadcbdacddbadccbdccdcacadcacdddcbaddbbcabdbbcbbdcccaadaaacdcddcdbbdbcdbacaaccdaabdaacacacabdbbcdbbbabbabbbccdbbcaddabacddbbbccadabdbbbacadaddaabbbdacccadabadcdabcadbcccdaaaaddbcdaadcbadabcddaaccdacdbdbadcccdbabcbabadadddbdbcdbbdcbcadcbcccbbbdbaaaadabdcadbabbaccddaadcaaacccaddbcbacabaadcbcbabdbdbbbccccacbcddbdbcbdaccbacacbbdcabbdadacacdcbbaaaabdcdcbaaadcabbabbacccdbbccbdaababacbadbbbcbbcdabcadbcabacadcbdbaabacbbcaacbadababaaabbbbbdbbadacadddabdbddddcdbbbdcabbadcaddacadbdacbcbaddcddbaccddabcabdcbabadbdabbdddcbbcbabadaaaadabadbaaaddaccaabbabcbbdddbbdaaaacbdaaabdcabdcabccaadcdacbdbcdbdabaaccbadbbcaadbaddddcddadbcadaadcacbaccbabcdbcdccdbdcbaaabbddaaababaddddbccddcdbcaacdbbdbdccbaadbcbbbabbccdadcbcdcccbaddacbabdcaababdcabcddbcdcbacabaacbcdcbbbdbdacacbadcbbdddcaabbdbbbcbdbccddacbdaadbcdbdaddddcbcacadbdaabaabcabababddabdaacdccdbabaacddbcaddcabdaadaabbcccbbdabbcdbdabccaabdabcaadaddaabdabbbddabacdcbadaddbdcadbcbbacbdaaddadbbacdcccabdcccdcbbbccaadacadcbaacaabcaddabdcaaccadaccbcaaccaaacabdcbbcdaacdaddadcabcdbdadbabbddbdcdccddccddcdbbbcbdbcbacadaaaabaddcdbbbcddcdabbdcdaabacdbcdacaabbdcbacdcacccdcddaabaddbcddbbbcdbbcdacdcbbabdcbabaabbbdacabbbcbcccbadccacdcccbcdcdcaaaaccbcaccbbdbddadadabbaadabadadcdbbcabaddccbbdbdadaabdccadbbdbdbbdcbccccdaccbabadcaadbadacaaddaacaaacaccddcdaddcbabdbbdcabcbdbcbdddacbbbaaddccbdcdbdacabbccdcbadbcabbccdadbabaaabcabddddbdcbcdbccbcdcbdcbacccbbcaccdbbbabbccccdddccccddacdbbdababcdbdbdbabaaddcaddaddbbbadaccbadbaaabdbddcdbadccadbddaddcdddbbaadccbbdcbbaacaadccabbdbadbbdcadbadadbaaadcadadacacbbabbdcdadbccdbcbccccddacbaabdcbbadcbaabbddbdabadbccaaddacdddcddacdbccdbbadcabbabdccadbdbbccdabbcddaadaacbdabbdacbdccaabdbdbaddbabdbcddbcabdadccdbbaacdaaabddbcaadaacdcbbccbababcdabdbdadabbcdcabaabbcccbbcbdcaabadbddcaabdcccadbccbabdaabccdabaabdacadaacabaabdbaddcdccacbbdbdccacaacdbcbdbacdcbaccdcbccabbdbcbddaaccccbcbbdccbddaacbaaacbbcccbdbbadacbdcbcaadbcdacadcbcbdbabccaddbaccabcbcadabcdaccadbdaabbcbdbabaccabdddabaaccabcbabdacbdaaccdcdbabdcbcbacacccccaaaccdcbababddcbcbdbdddadadbaaaabddaaaadcdbadcadcacbaaacaaddcacddbacbdbddaabaadbbccaacdcdabababdacacdddddccdccccbddbbcbacaddddddbccddaadbcbaabcbaddbacacdacacadcaaacaccabdcdddcdabaddbbaabbbdacbccadaabdabdaddadacbcaddaadccbbccddbcbddadddddacbdcacbcacccdcbdcdcdbdcaabdcabdbbbcbdcabcddcbdbdddbadbabbabaddbddbacbcbcbdcabddccddcdbadbabacdbcddaaabdcbbadcdaaabcdabbbcdbcbcbdbbcbadbbbcbdcadaaddbbbbabdcbdabcdbbbccdbdbbabbddaacddbbdaaabccbdcbccdacdcadbddbcbbddaddcadddccabacdccdadbbadbdccdaacdbacdbacadabddbddcdabbaadbdabbbaadbbbddbcaacdbcbbdcdabddcbacaacbacbdcdaaabddbaadcbcddaaaacadbaccccacbbaacbbabacddbaabdaaccbbacbdcccacadbcbbcddbdcdbabdcbacccdcddbaacdbdcacbdbabcabadadbcccdaaccadbbdccacbcaccacadaadaacabaadbbbaacabcabdadabcdacccbbcccbdbbdcbbddaaccbacddadcaddbdabdabaabacbaabdbbcaadddccabcdababdcbdddabadbcacddbdaadbcbaabdbdcbbbadacddababdcdacbdabadcabbdbcbaabcddbbbbaabcccdadcbcddadccabbcccadddbbdbbbbcccdcdbdcdcccbdddcabdababdbabdbdbabacbccaabbccddcbcccccdccaccccddadaddcbabaabdcbdacdcbacbcdccddcdddbcbabadacbdbadccaccbabaddbdaabcbbcdddcccbcbbcdbcdaaccbaabcbbaaadadbcccadaadaadcbcabadcdcdadcbbcccabdaacacadcbccbabbddababbabaaccbdddacaacddaddcabaddacabddbcacdaabdacdcdcdcbbdbbabaaacbbddbbcccbcccbabccbbdbdccdacacddbcabadcccababaccdaddcbabababbadbcbcabdcbcddabaaaacbacdcabaddadaaaacbddabbacbbcdadcbccbadbcbbccadcdaabbcaacbaaacabddccaacbcdccdcabdaddacbacbbbabdadaaabcbbaacbcbddcabdcccdcbdbbbddcbbbdcccbbabddccdcadbbcaddaaddcbccddccbccdbcbcbaccdabcddbacbcacbddacdaabddcbccabcaacdbcbbcdccbbaabadcdbacddadaadababaabddbdccbcccbaacacaddddaccddadbcbcdcbddbdccabadcaaccbdbccdccbdbbcbcbccddbdddaccbcabdccadbccbcbdabbbaaddbdadababaadbcbacdabdbcbadadcdabbcacbacaaacaabcdddbacaccdbadcbbabcccbbccdddacbabbdbaadaaadbcacabbbcccbcdcdbaaadcaddbdbcacacbbdbddacbdbcbcdcdbadbbdadbacbbdcaadbddcabacaaaaaccdabbdcdcabdbacaaacbcbcdcdcbdadbccdabccdbdcdadbbdabbbcaacbbcaacbabdacbdcbbcbabcbbddadbacddccbddddabdcacabcbbdcdddabcbccdddcdbcdadddddcabdbccadbbcccbcddbadcdbcdaabbbaccbacbbccaadacabbdcdbabddbdccaccabbddbacdbacbadacaaaadadbccbbbdcddbdddcccbdbbddbaaabcdccdccccbbdddaacaaabdddbcbcabdbcdcdbcabbdddaddcddcdcbdabaccaaaabcacbbcbadcbacbaabcabcabdbbbcbbdbbabacadacccccababacccdbbdbccdadcaaabccaadcdacadbdbacaaaddcbcbabdacdddccaabbcaacacbdbdbaddcadaaccdaabbccabbbadbdcbdddacdcacacacddcddcbbdabcadccbcabdaddbcbdbacbcdbcbcdcdcabbdddddadbbcbdbcbcccaabcbaabbddacdbdaabbdabbcbcdcccddbbbdaadcaaacddaabadcabdaadadbbcccbdadccbaccbdbbddddbddcdbaddadaaabdbdacabaacbacbddcadcddbdabcabcaadbcbcddbbdcdcbdadabcbadbdcdabaadacdbcdaabcbbccdddbabbcaddccbbdcaddcbdcabdcabbbccdacabadaabbbcddbdabbcbcadbdcbadcaadbcaacbabdacbabccbaabddaddadcdaddcabdcdaadbbdadcdbdcabdcdcddbbcbdaaaadbcdcbaaadbcaaccacbbbbcdbadaaddbabbcbbbaaccccabdaacbccbbcdcbacbacacbdacdbbddaccbcacabdcdaddbacdacabddcabbbdcadcbccbcdcabbdaabcdcbcccaaddbaabdccdccabaaadbdadcbbccdadddcbdaacadaabcacccbcddbdcbaacbbbdacaabdbcdbdaaaabaddcabbcccbacadabbbcbbdddacccbdccdddcbabdddadbdcbadbbdbcbccadacabccadbcaccdcbcacaddaddcaabcbdcdddadbbbacbabdcaadcddccbdcbddbaabbbdbcddbcadabcacdbacbbccbdabadbcbddddcdcaaabadbcbcadbdcaabcbaddacacdbbabdabdbbddabcdcddbcccdaabddaacbccdbbcbccbaaacdcabddacdacbbcdcbcaadabaccbdcbbaadaccdcbcbbcbdaadaddaccccdcbaaaadcddddaaacdccdacbbacbbcbcbbddcbdcdacccaaabcadbbbcdadbbdcadccadaabbdbcbabdccbdddababbdcbcaacddcdddcdbbabddcccdcccadbcadacbbbccdbcdbddadacacdcbdacbaabdabadcabdaaaabbcbdcaaccbcbcdcdbcbbdbabbacddacbccccdcaccabaacdbacccabbbadadcbddbbdcbbaabcdcbbdabcbcdbcabdcdaccdbdccbbaccbdcddbcdcbdaadabacbbccbadaabbdcabaaacddddabdcaccabbabdabbcdbbdabcdbcacbaccdbdcdbdadbbdcbacbdccacdbaababdacabdacdadbcbcadbabdabaaabcaddcdadbdcbadbdbbdcacabcdaacbcbaadbddbbacabcacbcadcdcddcbcddbacdabbcddaddcbdbadadcbbadcdaddacbbddabbdbdcaaaabbdababbbdbaabcadacbcddadbdddbaabaccdcbbcbcbbbdbacdadabdbaddbababcaddccccddabbddaaacaabaaccbaddbabdbaabbbadcdaaddcbdcbbababddcbaadbddadbaadbcbbdbbacbaacaaadbacbcbdbcdddabdacbcacbbcaabdadbadddbacacadabcdcccbdaaadbaabdbbcdcddbccbdcbcbbdbcbbcacaaadcdcdadbddbacbcadadcccaddabdaadbdaccdaacadbdaddcddddcbaacdcdacadbabacbdcbbccbabacacbbaabdacccdaadcaadcbdccccccabaaccbdbcdbdccdcbbbccdadbabdbaccabbdbadaaacabcacaabdbcdbabcdacdddbdbbccddacabcacdabcdbdcbcdbdcabccbacbcbbbdaadcacdcbadbccbbdaacbddcbaacbdcbdcadacbcdabacbadadbbbdddcdadcacabcdcbddbbbdbaabbddbbbaddabcdcbbbcabdcacaddbbabcacbdabbbccdbdbadadcccdddddacbacccbdaaaacdbbdbbbacccbdcdbdbdbbcaccbdccadcadaadaccbcddadaaaacadbbcacddbdbcadbccbddbaabdcabbcdaddbaccaccabdbadaadacbbddbcbdcbbbbbbabaadccacbdadcacbcbacbbcdbaacadbccbcdabdbbaadaaaccbcccaddacbacadcddadbbddbcabdddacccdadcdbbdcccbdadcccccbbcdabdcddbcbdaacbbaddaccdcaaaabdacadbbacdaddcadbddcaddcadcaddbdbbbcacbacabbcbbbbbcaaadcaccbcbbdaabbbcccadaddacddacdaddacaadbbcdaaaabbcbdaccacbcbacbdbacdbcacabaabdcdccbcbbbaaacdbabbddaadbadbdcaccbbcabdddcdcdbbdcdbdddacadbacacabbcddddcbbcbdcdabbdbbdbbbabbdcaddcabcbdaaabcdacaaadacbdddddabddacbccbbaacaaaabdbbacadcadddbbcccbcdddbcbabbddddbaadacaccdddabdcccbccccbcdabcaacdbdabaddaadddddbadaacadbccccbddacdccdacabbbccdadcccbddbbdaaabaadcbcabbccdbaadabcdbbbdbbabaaddacadaccccddcdacdbbdddcbcbdabcdcbcaddbabbbadbcdadaabbcabcdabcbbccbdcbddcabaddaaaaccccdcbcbcacbcacddbdcadcbcaacccdcaaddaabadabaccbccadbbadccbbdcadaacadadbbabddbbdacbdaabbcdbcaacccdaddccbcbaddaaacdddcdaacbbddcdddddbcdccadbcdbabbbcbddbdcadccbbbccbcaadabddadbccbddbcaababbbdbcabacdbaacadbaccddaacaacababccabbdacaaaaabbbacacadaababccbccddcdabbacbdddadddbadadabcabddddbcacbdbcbacabdddddacbdabcacacbcddbbcddddadbacdddbddcdacadcadacbdbccdbadabddcdadaacbbbbcccccddbbbabadbdddadabdbcbadbadcadabbdbbddccdcaaaaadacadcddaabccbdddadddcdacdacdbdcccddddababdaaddbdbdadddccadbaccbdbadbcacadcbcadacdcddbaadbbbaccdcadabbcdcbdddabadcddbabaadcdbddaddcdabcdddacadacbadabaaccabcddabdbaadbdbcbcbabadcddbacddabdcabdcdabaddbcdabbdbcabbbadacadaabacbcbcbccaabbaddabbbcbbddcabdcaadcacabdbdaccaadaabcabadddcadbccdbbcdcadcbaddccaccbaadcbcbccbcbdacddbdacbbbccccccbabddbcdbcacbaacccdabbbccacddbcdacdbdcacbcdbcdaddaaadcaccadbcdaddbdbcdaddabaadcbbbdacbcbddbbbaadbcbdaccadbccbaddaddaabddbddbaacdbbdbcdadbcbdccbbababdbddcdccdddaccbabddaabddabadccdcaccacdddccbabdaacabbabcdaddbaabbbcbdbcabaccacbaccadadaaaccbcbddbccadcabacddabdadaacdcabbddacbdbcdcbbababdcabcdcddccbbabdaccbccccdaddaaabaabccddbccdbdcbbbabdabddbbcccdaacacdcccbcdddcddbadacbdabcdacdddccdbbcaccacbabdbaddaddaabaddcbbaaacdbabbbdbbacbcdbacaaddbbbabcbbcddacabaccdcadbcbacaabbbbccacadddbdbdbcbdacbcccaccbbbadcdadbcddcdadbbcbcddbcdaaddaacbcbadbbacbacdadcaaddcccbbabacadabacacaddbddbbaccadabbadbbabdadbdbbbdcdbcbdcacacacddcdacdcdcbddaddcbbddccccbabdbacbbbbcddcdccbadabcabdaacbdccdbabbccdbacabbbcbddbcaadacddcbacbbcaddaabacccadabcbcaabccccaaddbbbdcaccbccadaabdcabdbadbacbdddbcababdabdadabdbacdddabbbadaabdcdabbdbcdabbdddaddadacbddcbbbbbbdbcbdadcccddabdacdccaadadabcbdcdbdbdbabdaabbdcadcddcdaacddcdbdcdaabdcdddcacabcbcabbbbddddbbaaabdaccadbbdccccaacccbacaadbdadacccccdcbbccdaccddcdbdaaaaabaadaadddcabcdaabbcdcacdbbcacddaacbdaabacabdccdcabaccaabddbbabbbddbacbcabcabaccccaaacababcaacaabcabccacbadcbdaabbdaaadbccacadbbbaddddaddacacdcabbacccdddddcacabaabaadaddadbbcccddbcbbbdadbbadabacbdaccaabcaadbacccaddbabbbccbcddbbbaaaccbaaaddccbaddbbabaaadcbdbddbdbbccddbbccdacbaccdacbdaccbadabbcccabdbcddbbcdabaaaaadacdaabcadbaaaaaabdddabacdaaccdadddadbccdcdbbbbcbcbadcbbcabcdcbddbaaabdccbddbdcbdcbbccabcdbabbbabcdaabcbddddcdccdaababbcddbcaabaccdbadbbacaadbaadacbdaabbbbdbbcadbabddcaaabdccadcbcbdabcbadbdacdcbdabcccbdbcacacbdccaacdabacdbaaddadbadcddaccabcdcdcacccabcacccaddaacabcaaadaddddaacaacdabaacbdcbdddcdacacaddcbacddddcddbdaadabacddbcacbdaaabcdbddbcabadacaddbddcdaaabdadaccccadccacdbccbcbdabdadaaabcdacdadbcacdbbbcdcccbaabcdbbbadcabbbdaacdddacbbbbbadacdbabcddcaaacbadabbbaabcddbdacccdbcbddaabdbccccddbbbaabdadaaaaddbdcccbdccdcbcddcadbbbacdabbbdbbdcdabacbcbaaddcbbbddcadbcadcccabdbcdbabbaabadacacbaddbbdcbcaaabaadaccdcdbbcbabaacadaccdbbbcadaccaccdccaccacabadacdcccbddddbdcccbddbcbdccdddaddabdcaadbdcaadcabdcdcabbcadbcadaadacacdcabddcbcababdbaaacddacdbcccdabdddaaadacbbaaaaacdcaccdbdccabdabcaadaabcdaadbbbbaabadadbcbabcbbcbbbddcbcdbdcdbcdbcbdacdadddcadcddaaabdccbaabcdcbbadbdcbcdbaacbadcbaacabdcccbccdbdbcbdbadbbacaadacabbdbacbbbdbacaaabcbdaadbcdbbaaacbcddababbadadbcadcadbbdacabdaddabcbbadacccbacaccabbabaccbcbccddbbacbbaccdbabbaacdccdddcbabdddccaaccbabbdbddaddacbddbabcdabaddbbbbdcbbcbbddbdcadaacdbbccccaadaccdaccbacdbbadcdbadbadaabcacdcabcbbadaddacaaccadbcdbbbccaaaabbcabacbaddadcaaabaabcddccbcdbbdbbbdbdbacbbcdabadbdcdacdaabddaabddcbccdbbbabddcaaaaaccababaddbbbbdbaaacbddcbddbcabaacaacabdbcdacbdabcddcacbdbdbdcbcdbabbaaaaabacabaadbaaddcdcbbccbcadbcaadcdbdbbbcabccbbdbccabdbabaccbdabdccacddbbabdbbbbdddadadacadbadbccbcdbaaabdcadbacbbaadcbaabbabbbdcddadcaaabacaccdbbaccaaadddacacadadcabaddaadcbbdabdddcddcdacddcdbcbccaaadcccccbbadcdcbccbcbdddaabdaaddcaabcdccadacddabddacbabddddbcbbdcaaabbdcaabddbacacacbcadcdacdbccbbbccbbadaadcdddcaddaadbbbaadaabdbbaaddcacdbaadbdbbcdaabbddbcdddbaadbdbaaadcdbcacddaacaaaacbbabcadaacccdccbdaccaacbdbccbcdddbaadabcbccacdbbacbdcdcacacbdaabbddacbddcdababadbbbcdbddadaabccddaaccadaccdcddbcadcdcaaaccbbdbdacbdcdcdbbdcddadcccbcdcbdbdadbbcacdddacdaaddababbccacacbaaaaddaabccbddddaabdbcaaccaabdbaacbdbcabbdaaddccddacdacccabcacaadaccadbcbbbbaccbdaaacbccbdbadbdcbbaacadcadbdccccdaaccaccbddbaacbcdddbabddcbcacdaacccddddddacbadcabbbbaadbcbccaabbbddccddcbdadaccdbbddbdcbccabddcdbddcaabacccccbabdcbadcaabdbdddcadcbccacaacbdaccacaccadacbabcadddabcddcbbabddcddabdaadcccdbadccadddaadabbabccacdcaabcdbcdddbdcdbbbcbacacbdcaadabbaddabdcccbcdabbbdaccbbccabbdbbdacaabcabbaabaadbbaabacbdddacdacbdcccacbdabdbcbcbcbddddbcaccddbbabbadcbdcdbadaaaaaccbabaadbdcbacbaadcaacccdbbdddcbcdccbabccbadaadbbddacdacdadbbabcbcdcdbcdacdadcbccdabccdcddcccdabaaaadbacdabbbaaaaaaaabacabccbcccbdbabdcddddadddacabcabbcabaddcacadbdbabdbbcaabbddbbcdcbcdbacaccabdcdadadadbbbcccadabdcadcdcdbbdadbcdadaadacdddbcccbdcbcdbbdcabdbabadccccabacdbcbbcbacaccbcabaaabbcdabdbdadadcbccdadcaaacadadddbbabcacdbbadccbbdbcbdaabbbcdddbddbbadbddbaabbddbacaadadcabdbbbacddcbdcbcdadadcdcaaaadbbacabaaccbbbabbcababdadbbaaacadabdbacaccaddbaddaaacddaababdcbdccdacbadbccaadbcdccccbdacacbacdadccadcbcdccccdbbbdcaaccbcdbddccabdddbaddadcdcdabdcdcadcdbcbdbcdaadcbadbbadcbbaaaabdaddaaaadabcddbcaaaccbadbabdccaacbcaaccaaacdcbdccbdbacccaabaaadbbbccddcccaacacdaddabccabbcdbdcbaabbccdbcccbddadcddbdcbccbcccadddacbccdbbadbdcbbdababbaaddddddaddaaaabcbbdabbdbcdbbabbbcdcdcbddacaadadccbaddbaadbcbadbbbbabaacaadaaacbccaacbaabbbbabcdaacbbdbaccdaabddbdaacadaaadddadcbdbaccabbbaccdadacbcadadccccccdccdaadaacbbabbabaddcdacdbaadaddabbcbabbadabaacbcbcaaacdbbabcbcaacabaccbcacbbcbbdcbaabbbacbbacbbcabccddcabddacaadbbdbcdbcdcbaabbcdbadaacddbddadddacdcabddbabbcadcaaddacbacddbdcbaadbdddcadbccaccbadcddbacccdcbadacaaadcbbddddddbcbabbdbbadadbbdaabaabdaccdabbadcdbdacacdcbabdbacbaddacaddacaccbbdbdcbadcccddbadacadadaaaabadddbdcdccadddcaacdaaddccddcbabbaacbbcbbacadadbdacdbadabcbcbacbaaaddbaadcbaacadadbdcbcbcbcbdacdbbbbdcaddbccdbcbbbaccbdcabacdacaacccaaabbddcadaaaddbbcadccbccabadaddcddbccdbabcadcabdabdcabddbdbcddabccaddabbcdbacdbcddccadcbcadbacbbaccbcacacbccbdbcabdaddabdccbdcccadacadbcdcbdbdbacbdccdcccdaacabccccdbdddcddbabcacaadbdcbaaccddabadaaddcaacdbabdbbadcbdbdcacdcdbbbabcddbaabbcdccabcbaccbbacccbadbccdddcdddabdbcabdbdbacbbcdaaadaddcbddbacaacddbcdcbbadddcbacbccdcdcdbbcdbccdadddbbcdbadbcdacbaaabbdccddbacbacddcbdbbbabccddbdacccdcbbbbbbabcadaaabcdcdbcccbdabdcabddadbdccaddadbaccacdaabcbcdcbdcddcaaadbbaddaadaaaacccbdadaabbaadbbbabdbbabbcbadcabbaababadddabdbdaacdbdbbabdcdbbadaddabbcbcbdcbcdcabdcbcadaddcadacbbbcddadbcadcbabbacbbcacccaccccbbbbbcbbcbcbdddbcdadabacddacbcbbccdacbbacbaabbcdababaddacdaccaadabcaddcdddbbdadddadababbabccadaddaaaabbbdbcacccbaaadabbdaaaabbbaaaaababbcdbabadcadaddcbcaabdbabbdbbcddacbcdaccbccaccdccdcdcbdadacccddbbccdbbbcadaabcbadbbdbcccbaadcbabddabcbcaabadaddcdcbcccbbbbddcabdaaabccbbdbbaabaacdacbccbddcbbdaccbdacabdcadbdacccccbaddaabccccbaabbbcdccdadbbaaabcbacaabdcdccddabbbadbaadaadcbcdcbdbbbdabddbbcdbccacbcaaabbbadabdbaccccbbabbdaabcbbaabbbbbbacdcdcbbbbdbbbcbdddcbcacbcbaccdaccbdddabdbadbaadbcdccabaacbdcadacccbabdaddacdcbcaadbdddbcbcddbacabbbdbaaccbaccdacbdcbcddabababccacbcdbbabcbddcbbadcbdcbcbbacacdaadcbadcabcabdabdbaabbdcadbcbbbabbcbbcdbbcdadcdccadbcdbcdbadababadbaabdcbbddcacdaaccdbacdabaccbbadacacaaaaccbbcbdcdadbabcabcbcbbbaabadbddcacdbddacdaddbcaabccbccbcaccbbcacdccabcccabdbbccadadaabbdabdbaaaacbbccbcddbcdbaabadcaabbabaaccddcacadddcabbcbadbdadbbbcbacdbacaadbcdccdcacbbddbcbbdcdadacbacdcdacadaacabbcacbdbbaacaaddcdcbacabacccdadaaaddbdacddcadbbcdccbcdbcdadbbabbcaabbbcaccbcdbcbccdbdadaadcbdccbcaaaccaaabcacbdbcaddbbadadddabcadddccbddaddddbdbccccacdaaaddddddbabbbbbdbdbdcdaccbcaddccbdcccbdabcbbdaaccddaadccaabdcccacccbdacbabacaccdaccdccccbcddbbbddddbcadddccbbcbcbcdcdadaddcdbbbadbccacdcbdacbbbbababaccddabbcdacadbbbcbadaacdbdacaddcbadadcacdcdddbacccbaaabdddcdbddbaabaaacdabdcbabdcdbcbdddddcdccaccccdcbaabccaabbcbadadddabcbbcddaddcbbbbaacbdaababbacabbdacdccbdacaabccabcbcdaabadcbcadaaabacacbcbaaccddbdadbdadcddadbddbcbdacddbdbbdabbababccaaabcdbbcbdbcaabbbadbaadaacddbddcdcabdcbbdbcbaaacccdbcdbabcbbbcabddcddadddabbacdbaddaabbbabbadbabbbbbbbcdabdabdcddaadbcbdabdaddbadcdadbcdaaaadbdbccbbdcdadddbaaacddadadababccddacadbabbccbbaaccbadbddbaccacabaaacdbdacacaadaddccddcdcadacdcacdbadcbbbddccbaaaaaaadbaaacbdacabdabbdcbcabbaaddabbbcccdcabdcaccabacdbdbdccdcccabcdaaadbaabbdcbcabdadbaddadcbddbcdbdcdcdbbddadddbdbdcbbdcdbbabbdcacbbaadcdaabadcbdaddaabcbabdaacccaadccaacbdcacbccbbaddaccbdbadccbabdabaaaacccdbdcadbabddcccbddbbbbdacabaddccdcdbccdadbbbadcccdacadccbbaddacbadcdaddbdcbdaddbbadcddbdacababcdabcdbaaabaaabadcbdacaabcbababcdccbadcdcdaccacdbacdcabdadcbdaadcbacaadaddadbcddabacadcbcbbbcbbcdcbacaabccaddacbaccaddbcadaadbcbdcdabbaacbdbcccddbabbadccbcddbacbcdadcbdcabdaacacbdbdbabadbadccbddaaccdbdbdabaacaaccbbcdccaabcdaddcadccbbdcacdabbaaddabcaccbaddcabadbcaccddcbcdcacbbdcddddbacabbaacaabddddaccbdcbdbccbabdadbdabbbacabaadcdaadacdcccdcbaadbdaabaaacdbdbcaacdccbcbbdbaccbbbcbdcddbcaddbabbcdabcadabdcabddddddadbdccbadadbdaddadbaabddccddbddbcacccaabadccdcdbcaabbdcacccaacdbcbcdcdbcbbdadbcbdcaaaacdccdcacacdadcdacadcadbacbdacbaccacadbadbbbdaaadcbdbcdbcaaabaaadadbcaddbdbcbbbddbcbaabaacdaddcdbbabbcdcacbdbccdcabbabcbbdbcdababaaadcbdbcaacddcbcaaaddcbbaadabadacadacacdbacabcaadadbbdadccaabcdacddcdaabaadbabddcaaadcddbcabacbabcabcddcaabbcbcdbaccbacdcdaccdcadcabbbddabcdcdbcabcdbbcddcaababcbaddcbacdbabdcddabddccababbbbacdcdcdccbdbdcabccacdaaabacbacbbdbcabddadcdbdaddadccaddcdcacdcdddbacacabcccbaddbddaabcadcbbbabdbcbcdabdadddcddbbbdbdacbcbbacdcacdacbadbabcbaddbbdcdbbccaccddbbcdabbacdabddbcbbcababdbababdacbcaabbbcbdcdacacbadbbbbbdcdbadbbdcccbbdddabadbcaaddbdccdbacdcccccacadcdcaccccbbaaacbbcdabddbccbacddadabbccdacbbcddaadadcddaadbbdacaccbdcdbddaacacdcdccbbaadabcbaddcabccabcdabddadcbdaccbccdbcdccabaabbabbcaccbbcbbddcaacccbabbddadacbcbdbbaaddabcdabbbbacddabcccbacbcdbaadaadcddacbcadcaadbbccaaabaaabadccbcddcbdacdbaadbdbabaadcdadcdaddbcababdbbdcdbaabbdabcabbccbbcaccaacaaabbacddcacbccddaaacbcabccdccdadacccbbcbdaccdcdcabbbacccdbaaaaacdbbbcacbdcccddbabadacbaaddaabcdbabcdbdadaabdadcbbbcadbbcbacdcaacaccadcbbbaccadbcbbbbcbccdddbcbbbcdadcabbadcccddacccddcabcdadbcbdbcadcbdbadadbcacbdacbcabacababcbdbdcccdcbadbabadacbbcacbcadccaccacccbccdacaddcbcbcbadccaabdbdbdbbdacacabacabbbbaabccdcabbccbbdadcccdcdccbcabbbcdcddadaabacbabbbababbdaacccbaacddbccdccdacabdaccdabccabbcddbdacdacddcccbdbacbacbaacdccbdcbbbddabdadadaddaabcdadacbdadcabcccadcdaabbdadbcaadadbcbaabaacbabbbbdbcabdbbcbadbdccbddadaddcbbaacbbacababbdbcccdbadacabacadabbabacbbddabaddbacbbbacbddbacaacaaacaaddbcadbcbbdbbddccdccbbddbddabdbbccaaabccaadccacbdaccddcccddbbaaacbcdbabbacbbccddbdccccddddbbcbadcddbaabdcdadbdcbbadbcbcdbadcacbaacadcaacaabcabdbdabdbacacadcdbaaaaaabbdcccbcdaacdcbabddcdaccdbcdabccdcabdadcbcdaabcbddbdaacdbdbadbdbdaaadadaabdddcadadabddbcadcacccaacbadcdbcabbabaccbccabaaabaadcabaddbaacbbcacbcdaadbbbbbbccacadbdbadabcccadcabccdcddbcabdbdacacdbcacabccadbbddadbbccbcbcdacbdadbdcbbabadcacdcdbadcaaddbaccccabaabdcaacdadacbdabcbbbddcabcabcbcbbdccccaacdbbcbacbbcddcacaccbccbbbaaaddadbabddabccabcabdaaaabdbaacdcaacaadcbbaccacbaadccdcbcabdbcadabbcbcbccdacabdccbbdbccbcadccacdbbbacddbcabbabddccccccdbcaccaababdcddaabcacbcaacdbddcdbccdbccdabadbbadcbbabdbaccaabcabcaaaacdabcaaadbcbabacccdddbcdbbdccbcabcdabadaabccadcdbcacaaddbdcbcacbabcbccaccbacdccdddadcabacaacaacdaacadabcaabbbbbccdaacabccdcdaaadaccccaabbaacdcaacddacdcabadccbccbadbabccadbdcadadacaccdaccbcbdabdbdbbdddbabcddacdccacbacccdddddbbcdabadbbcaaddbbaaacaccddddaadaaaccbdabdaaaddccadbbbdcbccbbcacadbccddaabadbbdbaaacbcabdddccddbdacaaabcabaabaddbbaacbcccaaadccabbbadbbacddabdabadcaabbbadccbccbbcaabaabacacaaadabdddbbddbbdacddcdabddbcccbbacddbbaacdacbcaadddbdcbadddcdaabbabbcddddcccabcaababbdbcbbcdacaaccbaaadbaaddcdaaccdaacadcaacbacbdaadbdccbcadbcdaacacdbbbadacdabdaccddcbdcdbdccddcbddcdcdbdddbcadaaddacdcbdacacaccdddbbcbabdbccdcabdcabbadaadacbdaabccbdccbcccaccdddbaddcdbcacccbaaadacadaccddccbdacdcbbbbbbdacbadaccdabcccdaddaacbcadddadddcadabacdbdcdacbbdcdcadccbcdbcdbacdcbadbbdbcdbabacbcaccadccacbaddccbccbcccdaadadadbabbddcdabaabdaacbacacddabcccbdabbcbccbbaabbbdccdaccadbcabbcccdacddabddcbcbadcdaabcbadcaacdbacadaabcadabdcccccbbdabdaaccaaaabaadcdcaaaababcdadddbdabadabccccbbdbabacacdbbdbbccdddcdcabbcbbaadcdabcacacddddaabccabaccbaaabbdbcbcdccaadbbcaaaddadbaddcdddccbccbdcacbcabdaddbbbdcacdcdbcdbaccadaabaddbbddbcccdcccbaccaadccaccabaaaaabddcbdbdbcdbadbbbcaaaabaadbdbbddcaccbdcdddccbcbcacdccbcdaacdbcccacbcbcbdacaddbabcdadbbccdbcacdcdaaabbbaddabdbddcbdddcbbbbacbdadabcabdadccaacababbcbbddbbaccbbbacddaacaacbddddbddaadddabaabcdbbcaddbdbbadcabccabdcacbdcbdcbaadcadbbaaadaacaadbbbbdcdcaadbadadbdcabbcbcdcabcaccadacacbbdaaaddbdddbababddaacdcdbccdbdaaabadcdbbcadacbcbbccadcabbadcaaccdddaadcbbcbdddabaddbcbabbcdcccdccaaabcbbdbdbcaacadaaaccdaadbbaccdaddbdadcaadabcbaaddaaadccacdabcbabbcbcbcdcdbbcaadcbbacdbcaaadbbbdadbabaabcbadccddcaddbbcdbcbcababadccdbcbddacacdadcbddabcbaccaccabcdadddbadcdccbacbadccdddcadadcadbddadcdaadbabbcaacbacdaabcdbbcdcbcadbcdbcccbbdcbaccadaabdcbdacbbbcacacacbaaacdbdadbabccadbdccaddababbdaacdcccccbbddcccaacabadaadabcadabbabcddadabcbdddaaaddcabcaabbbcbacadaccacaccbbbddbbbadbcacbcbcdabbaaccaddaabcbbbbdbdacbbccaadaaabaddcbacbdbbddbbbbdcdacdadcbdccaddabacdccbdbbccbabdbcacaabcbaddddccbddbbbbcaadbccccdbbaacccbbcbdcccbcadcbddbcccabbcbddcdbdbadadcdaabaabcddcaaccaddbcbabcbbccccbcdbcdabddcdcbdabdcabdaaccbbdacddabddddaabbadcbcdbbaadccbacbbaaacddbbbcdcdbdabacbcbcaaabbbddaacacbaccbdccabbbbbcacaabcdcbcddcadbcdccdadabbacaccadccbadddcabaacddacbdcdaaabaacccdddadcacbcaacccbbdbadbbddccddcdbdbddabcbddbadacbbaabcaccabbddcabdabbabbbabbaccbabcaabdacccbbacddbcaddaaabdaabccdcbaccddddbbcbdddacacdbbbcbacadadcacbbbccaddbbdcdcaabddcaacacbcacbbcaaabdbabcdcdabcabbddacbbdbacaabbbbbabaadddcbbddddcdccdbdaabbcadaddcbaaddaacacacdcbadcdbdbcddcbbcbcdbdcaddcbdbccccdcabaadacccdacacaaaacbdcdcbacbddbddbaddddbcbadbaccaccbbaacaccbbabddadabbbcbabddcadabacdbbcabbcddcbbbaadbbcabcdbacdadcdadccaaaddccddadaddbbdbaababccacdbddcbacbdcaddbbcdcbccdbdaacddacacaccaadcbdbcdbacadddaddccabcadcabdbdacbbacdcddcdcddccbaaccabbddbabbabcdbdcbccdcaadddbdabacdccddbdcaaabadcacacbccdccddaaabdbccabdcdcccdaabbcacddcdaabcbccdcbbcabaccdccabdbdddcabaabaddcdabbddcbbbdbbdbaacbdacdccbbdaccbdaabaccbdabbccbcdbbcbbaccadcaadbbdaacacbabacaccabbcdbabacbddbdcdbcbabbbacaaaaccaacdccbbccdbbdcbacbbdcddadcaaaddddcbdacdbbdadbbbcbdcbbadcbbdabbbdbcdcdbadcacabacbadcaccbcbccbbbadbacacbcddaddcbabadadcbaaacbcbdadcaabacdabbddccccccccbbaaabdbddddddcdaaacccacaacabbcbadcadcbaaadabbdbdcbccbcdcbbbdccccdbcddabbcaccadbadadacdacddccdcdbadcdcabcdbbdbdbbbbbadbabdaccdabdbdbcdabacacdbdccdcccabbdadbcbbaadcdbcdbaaddcdbacababdddcbcdcddccddacbdcdadaabbbbdbccbdcbdcabbdaaaddacacbdbbcabcdcdbcacbdbdbbdbaccdddcdbcabbcaddbbabbabdcaabcabaddaaadccacbababcdabddcbbadcddcadbdbacbacbddddbddbdcdadcdadbbaaacccbcdccdcdbcbdddabbbadbadcdbccbdbdcbddbdddaadcbacadccbdbbbdcadbcbddbcbccdbbdaabdaaaccdddbdddbdabbbabcabdadccddcdbabbdddbdabddbbaabbbdccbbbadcbdacbdabbddabdbacadabbaaaaddcbbcbcbdaacbcccdcbabdcbaadadbdacbbcaccdaaabddacddaadbabadcbbacbdbadbaaadbdcbdcdddabadcdababdacdddcdaaabdcbaacbbcdcbbbadcddcaccacadddcddabbcbdacbdaadacbccddbdaacdcadccbccbdddccadddccdbababbcabaccbbdbddadcdaabbcadbdababaadcacdababbdacbbcbdcabbbbadbbddbaaaacbadadaacbdaddacaddbcddccdbacbbddaacaccbabcdbddbbadbdadddccccacdcbbcbdaaacdcabbbddcbacdbddaadbcbddabccccdbdddbddcadcadbaadbcddbadddbbdaaaadbcbcbabcdbcccabbacdaabcacbdcacaaccaacddbbbbdaddabddddbdbcdabacaddaadabcccddbacabdbbdccbccccaaacdaadbdabadccdcdaabccabcabcbbaaccdddddcabbacaabcdabdccaaadbaabdaaccdccbbbbacbabaacbbacbccacdbdaccdcdcacccbdcaacbcdcaddbcbddbdbccaddddddcbcacbabcdacbddbccdcabababababcaddcbabdadabaddcadadcdbddbbccbdbadbacadcacbcacaadcdbbaabdccccacccdabdbdaccbacbaacbadddbbbacbbcbaddbaaaadadacadbbdabcdabbabbaccaaaccbbcddddadbdbdbcccddccbcaacabccbbbadabbbdcabaacabaccdcadccdbabaddbabadbddbcabdcbbcdbbbdcccdaaabdbbdcabddccddccbaadbaaccaabcadbcdcbcaabaddacadbaccadccdadcdbadcbddbddbadadaaaddabbcbcbadbccacddcbbdcdabbcccbacccccbbcbbcabcddbaacdcbadbddbcbacbbbcababacabaacbdaccadabbcbdadcbccdbbdbcdbbaddccaadbdadaadcdbabdbdbdcbdbbacaaaaadbdbcbddbbacbcacbcdaccddcdadbddbbdbcddbaabdcddcabddbabadddabbdcccddbadbaabbacaadabcbcbccdadcbadbbbadacbbccaddcadcbabbabcccbaccdacbdaccacadbbbcdddadcaaabadadacaadbaddadbcbcdccbbdabcddabbbddabbbdabcddacddabcccbcbcadcbcbbddddddaccacbbabccdbdcccbcabbdabdadddddcbaaadaadccdcdbbdaccccddacbcacbddcbadbdacddcaaddcbabbcabbccbadabadcadaadbdbbcdbdbcbdcbcdbabddaabbbbabacaaababacdadabaacbcdaddbadcbccddbcaacabdbcacccdbaabcacdcccadddadaabaadabcaababbadabccdbbadcdcacddaadacbccaacabbcbaaacbadbddacbacabdaddaccdbbaaadccadddcabcaaaacbdbdbdcadbcdcabbdaadcaddcbdadabaddbacbddadbabaacbdbbbbaddbaaaadaccadbcccbbcbacddbadadabdbcaabacaacacacaabacdadcaddabdbdcdaacbaacaddaaddaccaacbdacddbaacaccccbcabadbaccdcbdadddccbdcccadddbacbcbbacdbadccabdddcddccabddaaddabbbddacbbcdcbcadbbadadbaddbaaabcdabcbadbabcaccdaabbccaddaaddccbdacacacddbbdbddbdccbddcaadbbddbbdcdbdcbdbaccbabbddadcbdbadcddcadbabaccddadcdddabdbdbdddcdcdbabcaabdbbbdbbccccacdbdbaaabcddcbdbabaddcbadbdaabccadcbacdccddcbdddbdbabcabdadabcdcdacddabddddcddbddbcccbbabcbadcaddabddadccbdaabbabcdbcbcaccdaddddccadadadbbacccacddbadcdccbabcdaabdccbbdcdccdddccbadcacaddaadadbacabbccdddbbbdcbdbbaabcacbcbdcdabbddaabbababcdddcbadcdcbdadccbadcadaccdcdadbabbacdbcbbbdbbbcbadaddddbabcbbaaadbdaaabaacaaadbbcdbaacaaabaaadddddbbaccabaaabdaaaaccccadacdadcadddddcadadcbcadbcbbbcdbacbbaccdcdcbccdbbbdcbdcccbadaccdacdadbdadbdaabdcaccabcabcaaadcdadbabdaaaddcbacccdaaccacbadcdccbacbacdbcabaaccdadbccbacbadbddcdcacacaaaabbbbbcdddbadcabccddcdabbbcbcacdbcacddaaaaabacacacbbcddbcbacbdccacdbbbccdbcbbddbbcdbaadaabdddcbdbbdccadacdbddaacabdaddcbaabbbddbcbcabcbaaadddbbddcabcdacdccdacacbcaadacdddbcbcbbccdcacbddcdcdcdbdabbdccdbdcbbcccacbacbcdcbadccccadbbdcbddbccbcabadacadbcbacccadcdaacbdbbbcabaaaadbaccbacbadadaadacadcabcadcbdbacddabaabbcccadcbbadbadcdcabbcddbabacbabacdbddbbadacbdaacdcabddacbcdcabcabdbcaaddcdadccbdddcaadddbbbbbaaddcbcbcbddbbdaadbbbcacbcdccacddbbbbadcdcbdbbddbcdacbbdadbbcadcdabcbdbbcacdcdcaaadaaaddabbbbdcbbcddaabadbdcbbdbbabaababdcadcbccbbddbcddadccddabccbdaaacdbddbbdcccaccccbdcccbcbdbadbcbcbdabadcaacdabcdabbbdbdadbdcdbabcdcacbdcbdbddcdbbccbbbdcbdcacaaadbdabdcacbaaaaddaabcaabddababcaaacbdbacbbbabaaccacbdaadcbbdccbdbddabbaddacacbdddcdabacaaaadcdaaaacbbadbaacdaaadabcdcdaacadaccacabddcabbbbbbbbaacaaacdaddabdabbbacbcbdbbcdccaddacbcbacdbbbabaadcdbadcabbbccdbbcdddbdcddcbccddcbbbccbdacddccbacddaacccbcadcbccdcacbbadcbacaadaaadcdaabcdccbbaabcbdaaabbcdbbaaabcabbdbadbdbcdaabadcadbbdadbbbcaacccababcdcdabddacccadbcccaacccadcbbbbdadadbcbcdbababbcbaaddcbacdcbddcdccacacaddcdbdbcadddcbbdcdbacacaacdcbdcccdddadadbaaababccbdddacbaaabcdacdaadaabcaadbcaadbbdbcabcdabbddabdcdbbbddacaaacaadbcbdaccddbabadbdccddaddccbbacddcdadacdcdccdadcddaaacdaacdbacbbdababaddaadababbbabcaacccddaccbcaaaaadbadcaccbadcadaccbcdbcdaababccaadcaadbcdadcabccaccbdadbbddacbbccaadbbdbdcbbbacbdbbdccaddccbcdbcbbbbbdadccbbabaddbabbcbbacbdbddbdbdcaccbaadcbbacbcbabbacdcacabcdcbcbabdaabdaadccbbabbabdadcadcadccccbdcdcacbdddbccbddbadcdcdabbbcadbbccbacdccbccdddcccdadccaccbaddcaadddcbdbabbaaacccbacbcadadaccbbdcbccabcdaddcbbadbbaccdcabadaccbbabdccccbacbbcacccbccdddaabbabbcddccbbadbddbbbaabaaabcbcbddbdabcdbdadbcaaabadcddaaccadbcadbcbcdacddaddddacdbadbbccddabaaaaacabbaaaadcddaccbabcbabbacbcbacccdbbdabbadcacbbdcdcbdbaaacbbabcbcdabacaadbcbabcbdccbdadddddcaaabacbcabbaaacacdabababcabaacdaabccaacbbdcaadadadccbcdcaacbdcdacaccdbccddacdddacdcabdbaaaacbaacbbddbbabbddbdcacdbabadaadcabddcbabcbadbcdbcbdbbbcdccddaaaabdbcabddbbddbccddccdbaacdbcdbdcaaadacddbbadacddbbcddabadddbcaacbacccacdcdbdadcdccbccaddcaadbddacdadaadadcbaccaacbddbbbbacdcbbccaaacaaadbabdcbbbdbdbcdddbbdadadcdbbcadacabcaacdcdabaadcaccddbadbdcabddaabcabbbdbbabdcbbdaddddaadcbccdbcabdddbdccaadabcabddbcdbadadbbaadcbcdccabcddbbdbcbaacdbdadcaaabdcddcadadddccccbabcadcccccdbccadcbccddcaaaddddcbcdabbacbaccdbccccadbdaabddbbcbbccdcdcdcbaadbabbdbaacbaadbdbbabaddbacbaddbadbdbabccadccbdbacbcbacdbbbddaaaadccdcbdaadcadaadacdabbdccadcbdbdadbdbdcdddcbcbaabaacabbcacbdccacaddbabdcacaacdbbcacdbccbbdbcacabddbcccbadabbcdbcbdbdcabdbadbccacccbdbbbaccaccdccdacbaadacccdbddbdadcddcacdacbbcbcbadcdbddbdcbdaacdbaaacadcdbddbcdbacbbbacddcbaabdcbcaadabddcbaccdddbbadbadddabdbbdabbccbaccdbccacdddaabcddacdddaabcadbbbbdabaddaaacccbdddcdadccacdcabcdaadcdbddbaaaacccaaacbcddbccdbdadacbdddaabcadaaaadbcbbbccaabbbdcadccdcdabddbbbbaacacacdbbdbddbabacacdadbcdbdadadbcbdcabcbdcabcddbdcdabdbbdcbcdaacbacbdcdcacbdaccabaaadadadaadaabbdaabdbbbccabcaaabbadadcdcdbccaadccbbaabbdbdbacdabbaaacbbcaaccacbbabadbdbbabbaccadcabbcbaaddacddcbaadcaabdcabcbcadcbadcadcacdaabaccaaddbbababcbabaaaabccdcbcabcbdddcdadbaaccbabdbdcabadadbddabbbdbdbbbaccacdadbcddabbbdadacbccddadadaccdaadbbbbbbbcccdcacdbcaabadaadcbabcddddaacbdbbdbbdbcddacadabadadabbdaccabaadaddbccbddaaadbcbccacdbddbdacdbbaacabbcbaacbaccddbababbdddcacccabdacdbddcbaadaaddaadccaddbbbbdaabddacdcabbbadcddbcbbccccacadbdcbbaabdcdaabdbadbdbacbcccbaacdddaccbabadbbbacbdcddaabcdbbcbbdcabdaabdaccbadaaabddcacddcbdadacbddccdddbddbccaccddbaddddbcdcddaaababcdbdccbbbcbaccbdbccdccaccabadbbdcdbcbbdbbcaddbddcaddbbacbbdaaaacbddcbccaaaddccbdabcaaadbcddbbaaadabdbdbcbddbdbbcbaaaababaccdbddbaccbadddcdbbcbdacbaabcbddadcbdaaadbadcabcbccbaacdccacbaccbbabdcdcaaadaddcadcaacbbbabcaabccbaaccbcbaacbdabcdcbcccdcdabdbccabccdbaaabccadcbcdbcaccaddcababbadbdabdbbdbcbcadadacbaabbdbdabacaabdccbabaccdbaacaaddddaccdbcbdacadcaacccbbaabbcbdacabaddcaabccadddabddbcdbacabacdcbdaaaaaadbcabddbaacccaadbdbddbdbbcbbbdbaddcbdbcabdcaabdccdabaaaaccccacacacbcddcdbcaaacddccdbddadbbaaacdbcbdaabbaaababbdddadbacaabacbadbacabbbbadcbadabdddbbcbccbdbdaaababadddddbbdbdcdbacdccbcbbaccbacbddbdbdcaaabbcacddbbccbcdcccabadadbabbccabaadaadabbbbabccddcabbdbddacdacbacabddbbdaccdcaaaadacdaccaadacbccdadabccddbbadbabcbbbdabccbdcaadbdaccbaacdbdababbbacdbcbdbcabcdcacbbdaaaaadacbdddbbdccdaadbadbdccbdcaadaaadccdbbdccdacbddbbccbdccaabcdbccadbccccdcabdcadabbbabdbbabddcbccdddcadadcdaacdbdaaaaddaaacccaabbabbcdbcddbdcaaaccccccdadbcbdaaaadccbaaadadcddcabbdadcadbbdaaabbdcdbaccadcabbbddcddbdbddbcaccacadccdacbabadaadcadcaaadbdbaaadcdddaacdaacbdaadbadbdbbadddbbbbcbdabdadbbdbaaaccbaacaaaaddaccbcacdbbdabbbcdabcadcbdababbddbacbdbdacbbbcbcaadabdcbcccdbacdabbbcddaddccdabbcdaaabacbadababbdcaaccddaadcadbaacaaaacddddbaabcaadddcabacbdbaaabadcdccbcdaaaadadaacadccbacabbbaabdabbacdcbdddcbdbaacabcabdacddbcadadbbdbdaaaacbacbacbccdbcaaddddabcbcdcaacdadaabbcbaaccbcccbbbdacdcabbbbdcdaddbbbaabbacadbbabcddddbacadbacdacbcdbadbaaddacccccbadbbdadddcdcdddccbaccbdadbacddcccdcdcdadcdbaccdcdcbddddabdccbcbccaadddadbdcdadddbbbdbadbbaaacaaddbbdabdbddacaccdcaabbcddcaccddcabdabcdacddccbbcdabcccddacbbcdbcaabccdaadaacdaacacdbccadcbaadbbbdabdbccaabaccbccbcdccdcdcdcccdcddcddddcdbdcbbdddddabcccdaabddacacbadaccdccbbcaabccdaaaaacdbbbbdcccbdadcacadddcbabbdadddccdaaccbacdbabdbccdacbbdbdbcdaababcbdddbbadddadaabbdcbbacadaaccccadddcbdcddcbbddbdcdacdbcadbcbdcaadcdcdcdbadbacabcdcdcdbaaccbbddbadcdbcadbbabcaccbcbdbcaccddcbbbdcbcadaddbccbabddbadccaabcdbcbbdaccbcaaacdaccbaccdabddbbcdabbadbadaacbcddabacccabcdbddacdddbdbcadddcbdbdcdbadddacacacadbbabdcdadaadcdbaddbcbdacaaccbadbbcbabcbcacdcbddbbdcddbcbbbbcbbccddcbdcbddddabcdbaabdcdbcbdbbcdcadbdbdabdabbcadabadcabdbbdbccaabcbabcacddbbccacaccddaaadcbdbbdbcdbdadaacdcbbdddbbcdabccbdabddcbcbccdcabcabccbcabcddcdbdabacdbdabccbcddcdabdacaaacdbdbbcbaadcdccbdcaadacbacbccbcddaadccbdcacbaddaacbacbbadcdbdcbbaacbcccacbdaaaddccbdbbdadacbddcbcaabbadcabbbbbdbcaddadcdcbabcadaadaaccdadaadaacbcbbacdddcabbcaadbcadbdcbaaaaccdcddbccaacccdabcdcadcabaccdbbdcaadbcccacbbadbabdacacabcdcdbaddadccadadddbdcabcbdabcbcbcdacaccbbcdadcaacabbccbcacadddbbbaacddbaaccbdacdacadadabbbcdbccccaaadcaccdbdaccbbcaaddacdddcbbbcbbbcdaaddaccddcbbdadacdbadcccdcacaccbdddbbcbcabdacacadcaacdcbbabadcbaadbcaabdaaacaabcdadccabadccdcdaaccdaccaccababdcaccaabcaabcbcbccccbcacaadcbcdcdbbbdcadadbdbdddbcbddbdcabdbaaacccbaaabcdabcdaddbadacadaabcacdacabddccadddbcdddcdccadaddcbaacccdddcbacbcdbbdcbcdccddbdcacabddbdcbbabccbabcaddaaabddbccabdbadaacbccabcdddcaabbbbabbaddbbdcabdbaabdbcdbbadaddbcacacaaadcbaccacdacddcbababbbbaaacacccbbcdacddaaddbbdabadccacadaaabacabbadacabbcbbddcacbabccabbddabbaadbcabbccbaddbcabbabdcadccbcccadcaacddbcadcdaadccdcdbbccbadabadadaddabdccbcbdcdaacdabbbcadaadabbacbdacbbccccabcadcbdbbcbdcdacbadcdacbcaacbdbddbabaccacbcabacdacabbccbdacdbdcbaaaccbbcdacddaddbaacbcadcccbdcccabacbbbcaacbbdcabcbdacaadcccdbcdcadbcdadabdacbbbccdcdcadabacdbbcddbbbcabdabdcbabdacdcddddddbcaabacdabcbbcdcabacabbaaabcbcbcdbdabdcbaddcacbbdcdcdaaabcccbbdaabaddcaaacabdcddacdabcdcbddbaaccaaccabacdadbcbcbcbcbbdbabdcadbadcbdbbcbbcbcaaaddcadcbaaaabaadacbcdbdcccdaacccadccbddcadbaddaccdcbbcbbdacbaccbadbdaccbcdcdaaccbdcdbbdddbdbdbdaacbcdaaaabdcbbcbbdbccaccbbcaddcadabacababddddabcbbcdcbbcddddaacacdbdaadbbcbabdacabacabdbadcdcdccaabbaaaaadddacbadabcdacbcdccbcbcbcdcacccdabcadbcadcbbddccccadbbabdaccdabacabdbbbbadcddddaddcbbaadccdabcddcaaabdcacddcadccaacccbdbbdbdccbcdbccccaddbbddddbadbddcdbcadaacaacbcdbdbbbddadadcccbdbacabbcdbacbcabdbabacbcccadaacadbadccbbcdcdcccadaddacbcdaaadccbaadccccdbccbdddcadbabaaabdbcacbbcadbadbbddbaadaddcdadbdbccbcbcaadccdcacdcacdcdccbbcbacccdaabbdadacaabaabdbddcdbcccdadadcdcddcbdcadddddaacabacbadcadcccddcdcadcbdaccdaababcbabbbccbababcdabcbcdabbcdddccdcaadacddcbcdbabcadbbbdbddbcccbaaaccacbaccdcabbcbbaababaacadcdbcacaacbadbcdddbccdbcadbdaaddcdabcbdaddbdcdbdacdcbaadbdccccdabdaabadadbdaabaadddbabdcadaabcdcdbcddacbccbdddbcaccaacbdbdbbadaaaccdddcbdccdbdbddbbcacabbbbcbacabcdddcdddabbcadcdadcdabaaadcbddbadababcdbacaaaddbcbdccbadcdcaababbbdbcbadccacbddddbdadcbbbddddcbabdacdbdccabacdaccdcbabadbdcbdababcbacdddbdababcddaccdcbccacddddaabbaacacdacadbadabcdaddcbbcbbacbbbcdbcddbabccbdddddcddcdbdabddbdbacddbacaccdacaabbdaccabddcbbcdbdbbdabcbacadcdbdddaadbaaacddcbdbcadbddbadadabccadbaaabdbdadddcabcacbbbbcabdcdababddacaabccbddccaddbaadaaaabbcdcdddbdaacaaccdaacbaddcdabcbdbbcccbcdaabbbbbaadcdccccbbbcdbbbadcbbcaaadbaccddbbaccaaaacabccdaaaabcccadbadbadcdbbdddbadaccaddabcbdabbdadcbcdadbcaddadcdbcbcccaabaccaabbcbacabdddddadcbcacdcdcbcbcbccddacaacdbbaddccbbdaabbcabdcbcdcbcaacbabbaaacbabaadbcabbabaaacccbcbacbcadacabccacaacadbbbbcbccdddcdbaabcadbaabdabbcdacbdadacadaadcadbdbcaccaaacacabbddaddacacddadcbcdbbacbabacbaccbccdaaacbdbbdadadcddcbbbacacdcabdbaaacbbdddbbdadbcbaddddcbcdaaadcbcbacadbdbddbbbdcbddabbdcbbaabcdabaaacdcdcbadbccccbdbdaacccdbbbadbdbbdcbbaabbdcadcddaadcdddcccbddadcdacbbdabcadbbdaccbbaabbcdbbadbdadddbbdabdcadaaddddadbbbbcbcbdcccbbcacdcdcdddbdcdabbcbacabacdacaccdddcccbadcdbaabcdcbbaddcbcbdcbadaacdcacdbdbbcaacdbcbddacbaddbaaccbcbaacdbcbccdbccdcbcdbbdacdcdacbdabdbcbbcbbcdaaddcdbbbbaddcdacbbdaaadabacbbaddddbdcadcdacabbaabbabacaabdcbbacaaddbbbacacaacacaaadbcddcdcbbcddbccaacddaddcbbbccacdddddcacadcbdabadbcaaaddccbcbcabbcabcbdcddaccdaccdadadbbccccacdadcaadabaaccbcdaabbcadcdbdcccbbbcadbacaccdbbdbbdbabacadaaaddabdbacbdcbbacacbdabbdcbcbcbdbbdcabcdabbdbadbddcdadabadbacacabcdcadcabdccbbcdbadccaccadbccdddcabdbcabdcbdabdabdcabdbdddcdbbdbbacdbddcbbcdcbbaacdccccdcabcdcddddbbdadcbcadccbcddccaaabdbbacdbdbbddadabaababccbdadbadadbcadbcbbdbbdbabbadadbbbbcbdbcdacbabdadbbcdbbcbacbaadbcaaabbadaccdddddbcabdbddbcaacabbbabbccbccdcadcbcdcbbdacdbaadaabcaaabdabddacbadcbabdbdccacddabcbdbbadcadabaadbdcdacdcbcbbbcccdbbdcdacdbabacbdacdbaacdcdacadbcdaaacaaabaabaaabaabcaabdababbdbcabdacddccccbdcccacccccdbabbccccaddadcdababbcdbbbddbddaccddddcccaacccadaadbabacabadbbbbcacbddbdcbadbcbacdbcdcaabbccdbbaaaaddcddbbccbacadaacccbddabdacaccaabcdadbcddabbbaaadbadabdaadbdbadccddaabdcbdccaccabcaabbcbaaaadbdddddbcdadadcdaccadbdbabdbddbdbcacbdcbaaadccdccababcbcbdabacdcccabcbbabcbadbadbaddcacccdcbbadcaddacadacaaabdbbddcaccbcbaabaddcbbcbccdaccdbdcdaccdccdcaabbbcddcdadccddccdbcbccdcaaabbdbabcdaddacccdcaacaacdddacbccacabaddbbdbdaccabadabcdbcaabaaaabbbccaddddabccccdbdcdacbdbccabbababbdcbbbddbdbccaddaddcaddcbdcdbbdcbbadccbbbcadadadcbadcdaabcdcdacccbddadddbdcbacadabcbbadccddcaabbddbaaabbbbaacccacdcbaacbcbacccbaabcbccdcddadaabdcdccaadacbabccadccdbcaacaddbaaacdacdbbddadabbaaabcbcbcdbadcdbccbacbdccdabccccbdaaabdbbacababdacbddcaacbaaccbaaaabdacadccbbcbbdddddbddabcdbabcdbccdcacdbabaadbdbaababcccacddcbdaddbbbccaccacbccabbccabdbbcadbaaaabbccabacddcbcdacabccabdcbddcaadbaddccdcbbbbdbcdacbadcdadbccdbbbcbadaccbaadadbdadacdaccaacccaaddacdcdbdbdacdaacbddbbddacbacadaaaddaaccbdcccbabbdbdabcdbabbbdcaccdbbbacdaaccabdbbcbcbcbbbcabcadbcccbcadddcaccccdbcbcdccbdccaacdabbccabbacaabbcdaadcbaadbbccacdcababcbdacadaadbbaacacbccbbddcaabbacdccccacacddaadabacdcbadbdaabcbddbbbdadabadccccdaacbdaaaaadbacabddcbcbbcbcbcbadaabdabbcbabcabaaccddbbbaabbdabdbcbcdcbddbcbbaacbdadcdaadcdacccbdacbdaacbccbcdcbbcacbbacabbbdddcabcbbcddadcacdacacbacddacaabbccacacbbaabadabddaaabaacddabbadbbaddbcbaaadccbbaddcaccdbaaccdbcaddcaabaabddbbdacbbaaacdddcdcccadacabbaadcdadbaaaaabccbacadaddaaaadadbcdabddbcdadadcbaadaaadccbadbabacddabacccaccabaabcabcbcaabbacaaaabdddacbdabbccaccddabadaacdcbccbdccbabdabdbcdcaabaadbddadcccbdbbadabcdbaddcbccbccadbdaaaccbcadcbbbaccdaadcbbcdcdabcabdbcdacacbaadadadadaccabaaddabcddadbdddbdddbababdabddabadacbdbacacbbcaddddbbcbadcabbdccadaddacdcdbacabddbcdbdccbbadcaadddbbcdcddddbccacababaaadbabcdbdddccdcbbdaccdbdddacbdabadccacbdcacdaabddddbabaccadccbdcddcbccdddabbcdccdcadbcbdccacdbaacddbcadcdbbcbadadcaddddbabcbdacdbcbacacbbdacbacdaadbccaadaacddbdcbccbbdddcccbddcabccdbddcdaccbadaabbcddbcadcdcbbdbbbbbababadbdbbaddacdbadbddabbcacccdddbcaddbbabddbbbddbbbddaddaadcbdbddaaabaadbbccdabdddbdcaadccbbcbbdcbadbddabaaccaabaaddbbbdaabaacdbcdadcacbdccdcccccbacacddbbbabbddaaabaccaaccbccdacadabddaaadadbbdbbbdcdabbdadadcbaabcbdabbaaaadaccaccaadacbcdcddbbdaadcaacbabbdcdbdadcaaaddcbadcdabcadbbbaccaaadbbccacddbaacaddaabaabacddacdabcccdbdddbaddacacaddcadadccdbdcdaabaacdabbabacbbddbdddddcbabbbadabccaaabdbcaaabbdadadadbacbcadbcdcacbbdddccdbadabcbbdcdcccbdcddbccaccbabaddabcbcaccbaaccaaddccccdcdabcbcdabcdbbbdcccbdadcacaccdccbbcacbdbaddcbddabdabaaccbcbcabaaddcbabadbdababbaaccbbaaabacbcacdaccddddccbbbabdbbbdddddcbbddabadcbcabbbabcdccbcddcbadbbcbaddaadbadbbaccbccaaabacccbbaadabcabbaadcabcbcdbcdcabaddbdccdccadbccbcabbcdadcadbbccbbcdbddadaacbcadbcdcddadcbdcaaadabbbbababacbcbabbdbdcabdadbddcdcdcabbbdacddaadbdbaaaccdcdbcdddddcdadccaddbdcdbaddabbaadababbcbcabbdbaadccdcaaacbbccbddcadcbbabbcdaabddbbdadddaaabcdcdccbcaddbbbccabcbbcdbdacadbaabaddcbaacacbdbacdababbdcadacdcabccacbaccbbbbabadcbcbdccaccbbaadbbcbdbcbbbdaaabacdcbabccabaacaaddcaaaadabcdabdbacdbcbaccdaddcdccabbcbccbdcbcccabdccbaacbddbaabbddacaccbbaddabddaadaccaccbdabadddababdbcbbaacaddbabdaacdadcabadcacccdabbbaacccdacdaaadcbcdacccbcaabcaaacaccddbdccacacaccdbcdbbdadbcabbdcaabacaabbbcdcbcadbdbccacdadcccbbadabbabccabdcdacabdbbaacacaaaddbbacbaaccbbdbcccaaccdbaccacabacaacbacdbbdbabdcbbddaccbccdbaccddacdddbccccbbbdacbcaccdaddaadbddcbcbcaccbcbddcbbdadcdcbddabbaadccadcacabccbbcabbdbdacaabaacbccdcaabbccbcbabcbcaadadbaacbbacdccddaccdabbdadcddcdcbacadbdabbcbaacbacbdcdbaccdcbbaadcbaadbdcbacbbacaddbccacabbadcbccdcddaaddbbadcddbbacabaaccdacddcaaadddddbbbdccbdcabcabcbdaadadccccabcbddcacadbccdbcccadaabbbccabacdbbddabdcdadabbccabbacabccbbbabdacdcdcccdcdbcabdbdcbcadacacdbcbbcbcabcaaaaacacdcdccbdbbbcdaacdcacccbbacbbbccaacdcbddbacbbaabbacdcdadbdcbbcabbdddaabdbbbdcabbdbdabddabacbaabddcdadabadaaddadbcbcaabbdabcdcdbcbbddbbbbaaabbacbcacbccdddddadcaaaddcdacbddacbdaadbccaddddaddacabdbcbdbdaabdbbbccbdacbccdbcadbdaaabdcadcabdcccaddadaacacbcdbaccddaabacdadbacccdcdaabbdcabccdabccaadcccccccabdcdaabccabccdacdbdbdddccbdddbdbbcdcdbcccaccbcdcccdcaabdacbcaaddaccbbaacdbbcbdadddbcddcccccccbabbcbacabdcacabbaddcdaaadcacbcbdbabacabaccdccdcdddcadadddcbcdbccbbdbcacaadaacbddbdadcbddaddbbbdcdcdcccdaabdccccbcbdddbcabdbbdacbcddbbcbcbcdccabbcbbdccbcddaaacdbcabdbbdbbbcdbacddcccdcccdaabcbccddbbbbdbabdadabdbccacaadabbccdbaccaddaccaddadddabcdcdbdddaccaddadbccccadcbcbdbaccbccbcbcbacaddbccbccbbaaddadbaccdbbbadabbabaabdadccbdddaacbcdcadcbabdbcbdadbdccaabacdaaaddacabbbacbbabdccaabbccacbacbdaddcbbbcbdbdbccdcbdcdcacbbddcaaacbabadcaaadacdbacaadddacddaacdbdadccccdcdcdbcadabdaaacdaabbdcadccccaaccccdaabbccbbabcdaabaacdccbdaadddcdcaccacadbcabbcaadcdbdccacdddcdbbcdcaacbbbdbbaababbacbdbcabbdaadadacadaddccdaaadabddccbdcbbcdbaadcbaaaabcdbccbbccbbadbcccacdbadbaaabbbbbbdcacdcabddcccbdbddcaacbbcbdcaacbdccdcbbcabccaaadccbaabacdbddcdccdcbbaddacdbbbbdddbccdbdaaacdacaabaaacaddacddaddccbdcadddbdabbbdcdacacbdbccbcabbdcbabacadddcddbcdacacbcbaacbdcdccdbacccddddcdbccaabdadcdbddbcbacdaccbcadccddadcadbbabdbdbccacababcabcaabcddacdaddbdcbabccbcbabdcccdabdbbccacaabadaadbacadabbbadbbacacaaaabadabaabaadcaddadcbbaabcbabccdbaccddbbaacabbbacacaadcbcacbdaccabccacaababbdacccddcdaaacbdaadbbbbbaabcbaddbdcbabcccccdbaaddacaabcbbdccadcaadcdccdddcdbaddcabcaadacbcbccdcdaaddcbacadbcbccbcdddbccddadbccdaccbabbcdabdabdbdccaabacbdaacacdabdcccddcabcbbdaacbdcaaaccdbdccddcccbaaacdccdbdacbadacabadacbcdacadbcacbdcadadcadbabdccbdcdcadbdcdadbaaadcadaabbcddbbbcccbadadcadcddbacdbbbddbaccacaddbddacbbdacdcadacdbcaddcaacbbcccbaacacabbdbabbcbcaaacbdaaccdaacdbcaacdacddcdddabaaadbbcaacaaaaacbccbcabddccadcabdbbdaccbdbcbbbdaaddcddcddcabcccccbbcbddbccdbdaadbdabaacbbacccabbacdcbdabccdbacadcdacbdcdaddbaabbacabdbcbcaacccccbdbacbdcccbcdccdcdaadcacadabacbddbcdbbcacdccabbabbbdbcbdddbdbbbadccbdcccaddacddacbbcaaccdbbccacbbbcdccaaccbbabdbbcdbabbaabccbabddaabddacadaddacdbcaabcacbdcabbdcdbcbdcaacacdbcbaddcbcbaaacacdcbcabcddadcdcddababaaaddaadacccbabaabaadcaacadbbddbcbabbddadadbabccbbaadcccdaaddadccccbdddacabdacdbcdacbccccccbabbddccaabdcadbdacaaccaacdbadbaacbdacdacbbbadabbbbcbcbcccabccdcddcccdaacaddcdcaaccdcaccacdcdaccabcbcdbcabacabcbadbbddcbbaadaaacdbadaadbdcdcdbbcaaabbdadbccacabbbbadccaddbccadcdbccddaccbabcbdbbcbbcbdacaabdccbcbbaccadbccaadadbdadacbbabcdabdbabbcbdcdcbcbdbdddcabcbaabdbdccabccaacbdadbdbdaacadccdccbccaddbdcaccdadaaaabbadccddbcddbcbccacbddcdacacddcbcddabacdabddccddcdaacdabbbcbbcbacbcddcadadbbbdcccbddbdaababadabbcddabccdacbadcdaddaacdadbabacddabcadacbcabadbbaccaacccbcacccdacabbbacbbcacbbcadbbbbabdacbdbdabcbdabdaadabcbaaaabddcdbbbcabaacacbcabbccddbaddbdbccbbdbdbdbbddcbadbbaadcccadbcadaaadbbdcdacddadcababcacdacacdcdabdbcbccaabddbacbcacbdcacdbcbcbcaadcbcdbbcbcbabccbcabdbdbcdddcadcddbcddabbdbcabbaabcdbdcadacdbabbadbbbbaaacddcabaabbcdcdbcaadaccdaaaabbacaabbdcbdcbaaacacdadbacdaccaaccaababdcddccabbddcbcacdbccbbbcaccdbdaadddcdabcbdbbaacbdbbcababbcabdacaadbdcdbcabacabcbacbdbddadabddbdbddcdabcbbcdcdbbbabdbdbaabadbbdadaddadbcdbbbaaabdbdacadcbdccdaddaddcacdbcaccdaddcbcadbabddaaacccbadbacabcdbabbaabbcdbddddabcdcaaaacaabcbbbdcdbcccbbbbdbacbddacbcdddccddaccdcaaadbdbbaacbbcabcccbddcdbbcdddacbddadcbdcddbacccacccbcddaacabdbbacdcabaacaacdcabcddbcddbcbbbcdacdddaadcccdccacdccccbdbcbcaaddaabbcbbcbadddbaabcdaadacbbcdacabaacabccacbbababddcbcccacddcaabbbdaaaadbacdddbcbababcaddcaccacacdaaacbdabdabbcbcbbbbbcbabaabacccaabacddbbcabdcbdaadaadcbdbdadbdabcaccccddacdbbacbbdaabbbdcaacacaacbccddabdbaadaadaacbdddcbacccbaddddabdddacbdcdcdaccacaaacddbcaacbabcddccdbdaddcbddcdcdddaacbcccdddadcddcccdbacccdcccccbbadbdcaabadcbccabcdddbadaaaabaddbaadbbabcddddacbabbcdccdbdbaaabddddddaaccdacddabdbbbccaabababdcbbababcaaadbaaaababbdddcbbaadbcaccabdadddbdcbcacabdddccbabcccabdacdaaccbbaddbddcaccbdbdbcadababcbadcbbacbadccbbdbcdcdadcbdbadadbadaddcabadcaadcdcccbbcdbababacdcddbccccdbdddcdcbdbbabbdbabccabdcacbbddbadbccbacccbadddbacaccbcdabdddddbccadbccdbadbdcabbdcaccaacaccabbadcbbcccbacaddcdcaaabddbcabbdcbdbaacddaaabcdcbddcbacbaddcccbcbdbddcdbdbbdccaabaddcdabbdbccababddbcbadcddddacbbacdbaacdbdbacbbcdbcadcdccbabbcabaccaacabdcbbbbcacacaaabbccccadcbabcadacdabbcadadcaadbbcbcdcbcbcadbacbaadbdccbccacbababcbcccbdbbddbdaabcbdbacacdadcaccbcdcccbdcabaaabbadbcdddbcbdbdaacbdbbccddbbcadbcbccbbabbcacdbabbcadaaabacdbacaaadabdacacdabdbdddddabdddcbcdcbcabbdbcddbabdbcacbaddacaacaabcadacccbcaccabdacdbdaacbdbbdaaacdbdbadddbcacdadcdcacbabdaccabddcaccacdaadadbcdbaccabbabbbacaaaadbdcdbbdbadacdddcdaacadadbcacadddacadaaadddaccbaaacbdbadbcddddaccbcbabdacacdbabddbacbbcddadadadccdcaaadaacbcaabdbcccaabcbdbdbcbcbdadcbabcadbccaddcdcbdabaddcdabbcabbababadcccadacbbdbabbaccdaaabbdbcaaabbaacdcbbbcdbddbcdbdaaddccababbcbdbdcdacdbdbadabcaadcdbcdbacaddaddabcdbbdcbbdccbacacbbbcaddddccdadacabdbdaccddddbdadabcdcaaacacacdabdcdcdabdcddacbddcdcacbdbbdbdaaddadbaacdddcaddabbcdbbadbbcaacbbdabdadcadacabbcaddbaadcdaccdcccbddbdcabcbcabcdbaadcaccddccaccdadadaaccbdbbcbdbbccdadaccabaacdacccccacadbcccdbcddbcababaacabdabbbcdcaaccccaadaabcbcbdabdbacaaccdbdabcbdbdbaccadcbaabcaaaaddbbbddcdbcbbababacccadbaaabbcdcddadbddabddbcbdcdaccccdcaaccddddcaddbadbcbadcdccacadbacadaadddcdcbababaccdbcbbaacdaccccddddccdccbddaacdbbbbbcdcaabcacbacadbdccdbbaaccccbdcdbcddcddabdadaacdabcadadaacdbcdadabcbcdbbdaaccbcddbbacddcdccdabacbbabbbdddabbbabcddbabbbabcbdadabdcbbdbccbbbcccaddcdaaadcaddbbddbdcdaadbcdbbcdbacbbcbbccddbcabdbdaccddbcbaabdadcbcbdacddbbbddbadcabccdcbdbcadddacaadccccbccdabbbdcdaaabbcadbaaddbbaaaacbaddadbdbcbcbaccacaccdcddacaacdaaaacdbadaabaacdbcaaadccabcccaddaadbcdaddbabbcbcabdbdcabadacbbbdabccbcdadbabcaadbaacdcaaaacabbbcbaccdcbdadbdddabaacaccacabcdacbcccbdcbacdcbaaadbbbaaaacaacdbdbbbccbacdcaabbdbadcaabdcbdcccccbddabbdcccdaacdcaadccbcaddacdabbdadddccdcbbbcacaaabbddbbbabcbaaccbbdbbcbdadabaccdaaaaddddbbbbdacaccccdaadaadcdaabcbcdaadccbdbddddaaacbaabcdacbbbdbbbbcdbdadadbdabcbccdcdbccaadcbaacbddaacccacdbcabababddbbcbacdcaadadadaacccaadbddcaaadcaadabbadcdbcbdddaaadddcbaddcabbddcdbcccaabcccbddabcbccbcbdbbdacbbaadadabddddabdcbcaaddbdbdaccdabadcdddcccdddcddcdacdbcaccdcddddbacdbcbbbadddaabdcabbcabbbdbbccdbcccccddbcbacdbddadacbadabaadbabbbdcccdcaadbcabdbacaddadddabadaddcadbadbdacbbbcddaaacaacadcccaadbcbbdbcaabdaaddbabbcaaabccccadbbabcacbdcadaacdaaaccacbcaadcdabacdaaadbdcaabcccdaabcbdadaddbdbabacbcabbabadddacdbaaadcbbaabcccbaaacabcbaccabddaacadcdccaccbdaddbdcdccadacbbabadcadaddabbabdcbbccacaddbabaacdbdcbbdcbdaabbcbaadbbbabcbcbcccbadabdbacaababbbcbabbcccbddbcbaadaddbadcbbcdbadcdacaddbdcbbbbaacccadaabccabcaacbadbcdacacabdccaabcbcacadcabdddddccadddaacabbdbdadbdacdcccbcddbaddacacadbaaabcadccaaabacbdbbdcbaabdacdbaacbddcddbddbacbacccadcaadabbcdaabdbabcabbabdbbbcccccbabbacbcbaabaaddddabbbdacadabacacbcaacbccaaacadcbdccbccaccbabbcdaabadddbadddbadbbaabaacbadccdcdacdcdacbacbccacabaabcbbdadcddcccbdcdcdbbcaacdaddddabbaccbacbdabddccdccccacdcbbdcbdddabbabbbdddbadcbdddbbcbcaabdadbcdbabdadcccadbadbaabadbacadcccbdabdddbbdbdbcbaddaacbbbcbcbadabaddbdaaacbdacabdadbbbadacadbaaccbcccbdbcabcdacaaaaddbccabaadabdacccdabbdaacbacbacadcbaadbcaabdaadbcbdadacbdddbcdbdaacdacccdacacdabdcacddbbddbadbbacbccadbbdabcacaabddaadabadcaadcaaaacdaccbbaaddabcbccbbadabaaadccabbcdaccbcacbbadcbcbccdadbbdbcdbbcbadbbabacacadddbacbbccaddbbcdcddddabddcdcddbdcdadcdbdbadaadaadbbbbaadacddbacadabbcadabaccdadbbdcddadbdbabdddbbcbbbbcacadadbcbaadcacadbcbbabdbdabbadbdbaadcdbbbcababddacdadacdbbabbddbcbbcaadacdabbdabbbadbbacaaccdbcddadbacaddbacdbcbdddbdbccdabbccabcbbcbcbabaadcbbadcaadbcdadcadbccbdabbcbabacdcdabbbabcbdbbacbdbaabcbccbdbdbddabdbbcccbdabaabaadbcadaaadddadcacbdacabdccbbccccacccbbbbdcabbabbaccccccbbbdaddbbabadcdcacaccccbcbadaacbbabccaacabbbccdbdabaadcbdbbbdddbaadbcabcaccbcaabdaaadcbbcddcbaadaaacaabadababbbadacabdbadaabbbdaaddccccbdbbddbdacdabaabbdddcddcbbdcbdacbccddbdbbdadbdadbdadcccabcdddaabbcbbbcadadaccbbadabadbaddacacaacbcdcbaacccbadcbdcdbddccacacccbbdddaaaccbabbaaababbbaccdcaddcbaadcbaaacababbbabcdbcabaccbcdaddadccdddacccddcccdbcbcdcdbdadcbcbccccdbbadbdcbdbddcabdaadbcddcaabcbccabbbabbbdabbaccaadccbccabbdcacbcadcbdbcabadbabaadbadabccaaccdccdacbccdaccbbbaadbaaacbdbaacdcbcccadaaccdcaccbabbdddadbdcbdacdacbaaacdbdadacabbbcdacadbdbdaddaacadbccbddcaddbcabdacdaddaaaadccbbdcbcdbbbddabccdddadaccbcdadcbacbadbcaadbaacaccdcccbacdcbbacdaabacdaacbbdcdbdabdbcdcdcdcacaadbccdabcbdbdbccacadbdbaadccdadadcddcbdadaadbbbcaababcddbabdabcaabbddcbbbaaacabbaccbdddbbabbcdabdcaddbabdcabacdadbbabaadcbdcbbddcccdaaaacadadddbcdcdbacbdddcdabddbacbacdcccccaadadbddbcaabcabbabbcabdcbdabbddcaddbcbbbcbbccbadadacddbccbcbbccddaadbadbcaaaaddcadddcdaddbcbadbccabdcbcaabcabcdddabacbcccadbbdaccaaccababdddbdbccaddbdcdccdccadddadadadccbbbbcabbcaadadaaacbaddccbaaaccdbbcbbbdddbbcacdabadbdcdcddbaacbaaaadbbcaadcdbabdcbdbbcbbdaccbddbaccaccbadabaabbadacdaddcdcacddabacbacccdbcbbabcbdadbbbcdacbdbabccdccbacbacbabbdcdbbbdaccdababaadcdbabaddbabcdcdcccabbcaddabbcdbdabdbbdcdaaacaccdaddbcdbabdbbbccdabacdababaccabaddcaabcacbacbdcabdcbbacaadabbbcbbcbaabaddddbaccdcbdacdbbaacbaacaacbdaaaaaaaabdbcacacadbdcdbcadbbadcacbdadddacdbdccbcddcddbdaadacaaaaaccbcabaabaaaaccdcabbbdacdabdaddadddcbdaacbcbbcdddddbdacaadbbdbcdcbbabdcadddbbaaacbddaaaabacccaaccbadbcbbadcbbcdcbcbacabdaaabccadabdbacadbbdcaccddbcbccccdaaaabaaadcabbddaddcbdcabbcaadccbcbbcadbacbbbadacdacadbadabbdbbbccccccbccacdaabbdcdacacbbbdabdcabccbdbabdaccacacadacccacddbbbadbaacddbabbdcaccdbcabddcdccbcacddcabadcadacadabaadbadadbbddbcabdbbcccacbddacdcbbccbdcacaacdccbccdbadbbccdbbcaaadbddbbcababadadddcdbbcadabcdbdbbcbcdbadcaccadbcbbabcddcccddcdcdddabddaaaacdabdaacbbaacdcddcdbdcddcabcacccdabcdabcdbbbbadadbccdddabbbccddbdaacbabbccadababdbbdcacbdabaadcdcadacbddaccdcacaababddccdabcaaabcddcaaaadbccabbbdbbdcdaabbcbabdcbcbbbcbbadaccaabcdbdcababbccddbbbacccccaaacababbddbabdbadbaababdddaddadabdadabacadaccdacbbabbbdbadccbbbccbbabbcadcaccdadbdbcbccdcbadcdcbcdccdbbdcadbccabbaadaacdcdacadcccdddaabcbabcdcbaaccdacadbbcbbacbdbbacbcadabbbdaabaacaadbbdbdccabdcaaabdaccadcadcaccdaacdbbcabbcbaacdadcbcbdbcdabdbbbadcccadacbbccbaababdbdaccdcadbccbacbbcbacadbaccaccbcbbabbdcdccdbbaadccbdbbdacabbdbcadbbcbcdacbcbbabbadbcacbcaacacaacddcdddcadcadcbacadccabcabdddabcabbbbdbadbacddbccbbdbdddbaaadbcbaddcadddcbcbcababddbcabbbdcdbaaaaacadabcbbccdbadbdaabaaaaaadcabdcaabcdabacbabbccdccbacdbccdbbabcadbaaccbabcdaadcacaadbcddadacadabcbbddcbbcaacdababdcabbbaadbadbcccaccbbaccccdccdcaadababbcabcbcaaccaaccdabbbcabcbdabcccbdcaabaddbdcdacbcdccdcdcbaabbcbcbacdcbdcacaaacdbabcbcabaabbcacccdcbcababdccaaadddaabbbcaddbbdcbcaabdbccadacaccdbcbcaaaacbdccacaccdbdaaddbccddbbbdcabbccbcccacbbcaabacabdaabacabccacaaddacabcacaaadaccacccaddbbbddbbadaaabadaccdbbadbabccbaccddabddddbdcdbcdbcdcaadbbbbcaaadabbbbacbdabaabccadbdcdbddcdbbbdbbbcaacbdcdcbddabbbaadcabcbaccbbccaaabbdacaccbdddbbddadcacaaadbbbcbcdcccdcbcdbcdcccbccbaababbacdcddabddbaddcdaacacbbdcacaaaddddcbdacdadbcbddaabbabadbbccccddaaccbcdbadbccdbabbbdccdabbabbccbaaadabbdbbbdabbabbaabadddcbbcddcadabdbbaadbcbcbadbcbcbdacabdcacabadabcaccdadadbabbddbbdaabacaccbdbdcaccaadacbacddcabdcccaddacbadbcaddabbbbcacbbbadccbdbaddbbcabbacdacbccbabbbaddbdaabcbbddbdacccdaaadbbbbccdddddddaddabacccbacdbdacdcaaccbbcbadacadcdcbacdbdbdddbdabdabbbcabddadcabdacbbbaccdbbdcdcdbbadcbabcddcbaaaccaadcdcdbbacddcccbddabcaddbcaacabacdcdaaaacbbbdadbabcddbacaccbbadccccadacbbdacbaccdbbabccbdcbaaccbbcabcbadddabaabccdaaaaccbdbabdcbacdbdcaabcdcdaabdbcdbacbdccdcddcbccacbcbbbdccacbddaaddadbdabbbbacdaaabaadbadaccbaaddbacabcaabaadbccdadddbaddccabcbbddcbbccdccbddbadadabcbdcccbabcbcaaabaababacdcbbcbbdcbbcccabcacbdacbddbdddbbddccaaabdcdbbacbabbaccababcbdaabcbdcdacbcccbddacacacccccaaaaabbcacacdbddbadcbcaaaabdacaacabdbabbdadadaacdbdacddbaacadaaabcbaaacacdcbacbcabcaadaabdbbbbccaabbdcacddaddadabbbbbdcbdbcabbdcacbbdaabdcdbcddbaabaabdaaadcaacbadacdbcdbdccddacbaacdcdbddacabcbddabbdcabadcacbabdcbdbdcdcbbcadaacbbbbcbdcaabcbbbabcaddcdcbdbaaaabcdcbaaddacadbdaaacccdbcabcbacacddaadcdacaabdaaababdccbcaccbbcbbbbdadcdcacbdbbbadbdadadabdcbacbcdcabdddddcbcdcdcccdbdcabbcacabdadbdaccbabacdddbddaaccacbdcdbbdabdddcbadcbadadacacabbdabccacacabdbbaacbdaddbaaddddbdabbdaadcabdbbbbdccbcccbccdadaabcabcddaaddacdacbccbcaacdbbacadadbbdddbcdccdadbcababddbcbbbddbcbdadbcabbddbcddddaaadbadaccddbccdbbcbbdccacdcbaaaaaabbdbcddcbdaacabaccddccaaccdaabbbaabdadcadbbccbcabbcbdbdcabccadabcaadbacbddcabcacccdbcccdbbcaaaccbdcdcdccaacdbddcccabdccbbabcacbdcccccbcbddccdacbaccdcdccddcbdbccddababbcccacbbccadcccccabccccccdaaabdabaacabccdddcaababddbddbcabaddadaccaadbdbbdadacadcdadaaddbaddaddddbabaaaaccdaddabaabbbcbdcdcccccbbcacbadacbbacaaadcacbcccaabcdbbcdbbddcbbdbccdcdacbdabbdbadbbababcdadcccabccbacbdadadabbbbcccddcacbcbaacbbbaadbdbdccabdbacabbbbbbdcdabbcdabcbaabddacabacdbbcababcdbcdabbdacbacadacacdcdcbbadbadbabcadaacbaaaaadccbcabdbbddbbbbcbcccaaadddbddbaabaadabbacabbcbbdcadcbcdcddacacbccdcdabbadcdccacbdacdbccbbbadabaddbadcadaadbadcccabbdbadbccaabadbabdacdcbbdacbcdcabdcacddbaaabddbdabddcdccaabcdacbcacadbdcacaccbbbbddcadcdcdabddbcaaabdacbadbaaaadbbadbbccdcbaadccbbbbbbddadadcdcbdddcdccbbdcaccdccbbddcacbcabdcdbdabbbcdbbbbcbbdddcdcadbbadbbbddbaacccbcaaacbadcddabdcbaccdacbccacaaccccbacbadabaccdbbdcacddabbdbcbabaadbdbabcccabbcdcdcacddcbcadbabbbaaccadbcdbabbbdbcbbdbddabacbbcdabbcaddadcaddcbcadaabbaaacaadccaccacbbbabccbaabadbcabcabcbdabaddcccdcbcbbdcccbbaaabacaaccdaabccbbdcccaacccdbaadcdaccdcbabccaaaddaaabcbdcacacdcbbcbddabccaaccbbbdadccbdadcabdddbbcdbabdcbbcdbadbabdbddbbbcdddababccdbbdccadbaaacadabccbaacdcabbaddbaaabcdcaccbccdbcdabbccbcaacaccccddbcaaaccbaddaccbbaddacbddcabcbcabbabbddcbbdacdaccddabacbbdcdacbadbcdabbdbdbcabddbbabdcaadacddbdbbbaadbcdcabcbcbbdddcbaabdabcccbdadbccdbccdbbbcddcddbbaaccabacaadbaddbddcbcbddacdadbbabaccbbcadbbcacddbadacaccaaabcacabbbacbdddccbaddbccbcabdadacbcbddcbdcbdcdbadccddbbdddbbbdacdccddcbcadbacadaddddbbaabdaaacaccbbbbdacccabbdcddaddddabaacddbccacccdcdddcacdcaaddcddcccadccddacadaddadabacbcabcdbbdbddbdcbcbadadacbadbaadbaccbcdddbbbacdaabdaccaccaccacaccaabbacacddccbdaccabdaccbbdbcdcabcabbbbadbdbcbbcbcbddaaaadacacadccabccaacddcdaabaccddaaabcbbacbaaabaaccddababdaccabaaacbabddbcbacaabddabcbabccabacbbcbdcdcdcadadaaaaacbcbdabbcadabcdadaddbaabccadcbdbcdadbdbccacacbcccabbaaaccacaccddacdddcbccbddcadcdbabdadabcbabbbbdccdbdaaadbbdacadcabdabcabcdbdaabccccacccdadcddabcdcdaacbbaaabbaadbbacdcdcaadcbbdaacadcbaddbaaacdacdccbbaabacbdcadaccccbacdbbbdabcadcababadbcaadadbdbadbbcdcadcdcddbacacccdbdcbadaacabacaddbbddacbdadcbddcdcbcdbddbdbabdbdbdbaacaabdabdcdbdcbdddbdbadcadbccabcadbbbcddbbdacbcbbbadbacdcaccabaacbcadbccaabcbbbbcdcbbcbdcdcbbacbddacbbbbbdbdbccacadacdddbcdacbdacddacadccdbaddacaadadcdacabaadcbbbbaacbdbcddabbbbcbcbcaabaacddacaacccbccbdcababdbbdaacbdabadaabcbddcbcccbbcbaaaadacbbbbbbdbcbabbcbdacbcddacadcbaaaddbbcbcdbdcdbbbbddabccabccccdbbdcbaadcdbcbaaadbabbdacccbdcdadadaccbcacddabadabcacdcbacdcdabdddcdbdbdbdcadcaaddcdcdbcdbdcddbdabdbddbccbcbacaadcdbaacbadcdcccabcaadcdddabbbbbdacdcbababbcbabdbabbbdabbcbccbbdbabdcccddbbbadabccdaccbcbacabadadccdccaaadcacacbcacddabdbccdbcbcdbaacababadbddabddcbbcbbcccbaddcdacaaaabdaddddabcbbadddaadcccaccabbdcccacddbddccbbdbbbdcabacbbbddbacacdababbccdabbbdddcdddcdbcccaacaaababcddbaadbabcdbaccdabaaccbccbacdadbdacabcddcadcbbddcddccbccacacbcabcaadabaaaabbbcbbcacdaacdbbcbdaacabdabbbadbbcdbadddbbbadacabddcaadcaccbcccdacabbbcdadbbbbcdbabdaacbcddbdccbcddaacabbdacddabbbdacbcbdbcadaaadaddbccabbdccbcbccbbcdbdcacccccdccbadbbabbcadddbdccbaddcdcabbbcacdddddcccabccbcddacbccdccdcccddbaddbcbdddddacaabccaabbbbddcabdcaadadbbdadbcbdaccabcabaadccddbaaabaccbaccbababddcdddbddbadcdcabbbbbacbdadbbcabacbdadbdccbcccbdcabdccadbbbadcbcccbdccbbbcbdaacaadcdcabcdadabdddccddacbcdabaccbaddaabbddddcbcabdaadcadcabcaddcdddcacdaddaccadadcbacbddaadbbabbbdbbdcbadcddcbaadddcacabdbcdcacdbcadbcdcbabadbbaccccbbbbbbaaabdabadabddbaabdaddcdabbbcaddaaccbaaccaacbaaccdbaddbdbcbdbbdbabcaadbccdbbdabaaccbccdaabdbbbbccddcaaaaaddbdccdcacabcbbdcbdbcccdcaaaccbaccadbdcaddbcdcbacaadbdbcabbcabccdaddadcdbdadabdbcdbbadaacdbbbbcabacdbdcdabdddbddcaabcbbbcababadcdbcdcadcbcbdccacaadcaccdadaacacdadaddddcbbbdababaaadbcdbdbdbacadddabdadaacdcbcaabadbabbdbdcddabbbdbbbcbcaaacdaaadbdcddbdaabcccadccaabaabadaaabccabbbbbdbbadbdabbdacdddaddcbbbdddcdcdcdcaccdcdccdadcdacaadacdbccdcdcccdbdddacbddadbbaddcddaddcacbacababcbddbbabadbabcabaabbdcacbbbcadbbaacdaddbccacbdaabddbaacdadcacbbdbddaabdbdbaaacddabcddcabbaaacacbdacbbaddabcccdcdabaabadbbabbdcdbacababcaabbababcbcabcaabbaabcccbcbccdcdbcaabbbdbdbaccbdcccccbbdacadcabdabddbcdcaaacbbdaddcaadddcabbbbdcbbaddadbdcbccabbbcadbbcdcdbdcdcabdbbdbcacdcdabdcdcbbbcbadcdbddaddbddabcacdbbcbacdcbcbaacbbccbdcabaabbcbcabdbdcbadabdcacbcbdadcddcbbdcabddaabdcdabbbdcbddcdbdaccbbcbdddbacaddadabdacbbacadbccacadaccdcddaccaadcacbcdbccdcddaabddcbaaddbdadabdacaddbaddadbcdcdaabdbcdaddbbbaaabcdadaccbdabbdddadaaadbbccdbbacaddcccddbdcbcddbabbbcddcccadcccbadcaadaabbacaaadabccbabcbbbdbbbbbdadcdabacbddbcbcbcdddadddbbabddcbaddbdaccbcdacdacdcaaddcaacaccbdcbadddbcbcaadbdcddbdbdacdcbbbcaadabcabcddaacddcacababbbabcdccadbabdcccadbcbcdddcabacbbabcbbddabbcbcabbcddbdbabddabddddbbcbbbdbbbcaaacbdacdcaaabdcabaabdbbdcccdbbdddccdabbbdbdccdcaddcacdccdccbcaddaccabadabccaccbbdcaabcdaccbdbadddcbabddccbaabbcdcbbbcabababcacaabacdcbbadccddacbaabccacabcbadabbaacabaabcaaddacdabcddcaacbadbaaaddbdbbcbaddbcacacabdbabdcadbadbccddcaacbbdaaddcdaaacabccdbbcdbaacddadbdaacddbaddabcbcdddbccdbadbbaacabbadccccddddbddbdcababdbcdacaccabdcbbaacdbccdabdbacdadbccbddaabbdacdccadbacdaccaacbcdcadcaccbbccabaaccdcaabadbdcabcddbccbddacbbdaaaaadbbbdddbddadbbcabacaccbbaaabacababcdadcaaccaaccbbccbabaddbdbbcdbabdddacbdcdbaaccdbbbdcbdacdababccadacbbcacdbdccacdadbabbbaaabaababaabdabbbbacabddadbdadddadacadcccbbccbddcbacbabcbdccdcbcdaabaaabbadbcbacdaadbcacaaccdcbbbbcacbaabdacbacdacabcbaadbdbbdabdddcbbbdcdddbdabadacdddcbdcbbdcacdcdbbbdccccccdbbaaabadcbccbbdbbcacadddcaadcccabcbcaacbbcddbbacaaaabaaddbbacbddcbdaccdbcdddadddccbdaadaaaadcbbadbcbccbddccababdbbadcbbbacbcadccbccabaabcddadadddbccaddabddbaadadbabcdcdddaddabcbacaccbbcbdddbbdddddaacbcbdacaddbbcbbbcaddaabcbbadadbbcddddbdaadbdccabababdacbadacdacdaaabaacbbdacdaaddbccaaaaddadbabbbaacdcdaabdbccccdacadbadcccbbbcaabaddabcdcbcadcdaadbadacddbcbabaabccdcdcbdaddbcbbabbccabdaccdbbaaacbadadbdbbaabddbcddacdcdaadcccddcbbcbbabccbcbaadaabdddbbacdadbaacbdacdcabbbbabdacadcaabbcbaaaddacdcdbbcaababcaccadadaaadbbbddbddccddbdbdabdcaaadbcbadacbdbbaccabadddbbcbddcaccbcaddbaccacddabbbccdcaabdadbadbbdbcbdacbbabbbadcabadcabbaaabadabdaaddddbcddbccbdbbddcbdabdcccdcdcaccdadadbabddcadabdacbcdcbcabcccdbbbcdbaaccaddbacadacaabbdcaadbabbabcadcddccaadcbcbbbddddbbbacddbbdccbcaaabbaddccbaaabcaabdcaacbdabcbaababddbdbbabcaddadccbcabbacaadbdddbbdabacaaacbacbadbddabdddbddcbdadacbbacbcddaadddcdbccbdbdacaabcababdabbacddbdbbccaacbaabbcdbbcdcbbaadccaacacdacabdaccccbaddbdadddbbadaabddcccdccdcabbcbaacabdddabcacacbdabbbcdbcdccaacddccbcaacddccdccdabbbccacadbdadccaaadcbdbcbbdbbbddcaabdadbadaacadcdbbdbabcbcbcdacbddcdcdddcbaccbddcccadababcddddcdcdbbacbbdcabadbcbabdaacacdaadccbbdaadccdacaacadadaadddddcdcddcccdcaaacbcaadcaaabbcdadadbadaaccdccccddabddcbdcdaccabccdcbadbdaccccacccadbacaaadaabcdbcdaaacacdbbdbacccdaabdddaadcbbacdccbcaccdaccdadbbcabadcadbabbccdbcddadbcabdabbabbbdbccddacdabcdbcdacddddccdbaabdbbccbdaddcbaddaadcbddbaddccddadbabbccbcbbdcdccbcdccaadadacdacbbdcbdccbcdacbcbddbcbbcccdaabadaacbdcbabbcccddbbababadcdabaabbbabbabcaaccaccccadbbcdcabcbbaababbbabcdacbbdbdacddaddccadbcdaaccccbacadddcadaccbccddcdcaaacbcababbaccdabbadbabbabcdabbbcdcacacaaaababdcabdcaccabddddacaadadbccbbaaaccdbddcadcbcbbbadcdadaacabbcbaadbddbaacbdcdbaccccbddabadbbbdcbcdddaadcbdbabddcacdacbcccddccbcabcdaaacdacdabacbdacadcbcccaccadcabcddbdcabacbdcbabdcadabcdbabdbcbbbaacbbddddcddbaacbaccabbbcddbbcacbbaabbbbcdacbbcdacdaababdbadcdccbcbdcdddcababacdccadccdabdbaaadcbaabbcdcdadcbbcaabccabbabcbdcbccddcabcccbcdacdadcdaacbadcdcbacbcbcccacbcdcaabdcdcbbbbdbcbdcdcbbbaacdcacdbbacabbddcaadbbcadbcccbbcdabbdccdccacbdcbbacddccaabadcadbacaabcacdcbcdaacbdadcbbddbccaacbacddcbdcaacdddddadbadcacdcdaaacbdccaacabaddbccbcdabaaddbdbcbadaccaddcdddcdacaacaacbbbbaccddccdabadbbcbdbacaccadbcdcdcddcbbdbddcbabadccaabbdacbcacdbccccaacdcadcabdbbcccdbdbdbdcddbabccbabcbabbabaaaccaabccbaacddaabababdabdabccbdbdadacdcbbdddabaabddbbdccddbdabdcdacccaaacbcbcdacbdbabbccaccbaccadacabdadcccadbabadccadddadbbcdcadacdabaaccdbbadbadadccaccbacdbcddbdbcdddadbdadcacdadcbbaaaaadcbadccdadbccdccacdbbaadccadadcbabbacaaccbabdacabacbaaadbbbcbabbdbbacbabdaaddaaabadaaabcbbdbdbbdaacdaddacddbabbcbdaddcdaacdbabcddcddcbbdadcdcdddaccdababacbdbdddccddabbdddabbbacdabaccaabadbcdbcbdadbdadacdaadcbabcbdbcbacccdddbcbadbacaaaddcdcadaacccabdabcaddcdbbbdbcacadbdaccdddbccdcabadbadddaacadaccbaddcbbdabadccadbbccabbadcabdcbabacbdbbccbdabbaddbadbbdcdacdccdcddabbdaacbccbbbaaccddbddadcacdaddcbcacabccaccaadcabdcbaadaadbaaabaacbadddccbdbaadbdbcadcccabbbaacbdbcbbadbaaccbdcbdbbacbcadbbadcbcbcbaccbcbaaddddacacdccccacdbaddaccdbbbdcbdbaadcaaaadaaaabcaadacccaaddbabccbdbbddbdcddbdcacdccabbcdbcbcdbdcaaccddcbaadacbabdaaadaaadbbbbadcbabbacdaaabacdabbbcabadbaadccaacbcadabcddbdabcbbcbbddabdcccbaabbdaadbbbddbbacaacbcdcdbdabacccacbcadbddccdddaaddccaddddcaacabacbdddaddcaadbaacdadddcdbcdcaabadddaacbcdbababbbbaadbdababdbbbcbaddaabcacacabbbbabcccbadbdcaadabdcabbdbddcdaadbbbcababacbdcaadabdcbcbcbcaabdabcbcacaddcddadacbddaddbbabdbadcbcaadbccdacdbdadadaacbcbdabadabadadcbbabadcaccbcadccdccabccabacbcdbdccbbccabbaaabacacabacdbbcbcbdbcabbbadcaaccadccbbcacdbbcacbbdbcddccdbababaadabdcacacdccbddcdbdcddcabcbbbbadcbcbcaabacccabababbccadddadacdbbacdccacabbcaaacbbcaabbbdaccbaccabcdbbccdbaacdaacdbcabdccccdccbbcdcdbcadacddbcbddabccacabadbddaadadaadcdddcbbdcbcabdbcabbccadccdcabcbcdaccdbcbddcadcbddbdadabcbdccdadcbcddabcdcdadbbabbbabacddcdcaabbaadccbdbdbdccbacadbabcdccbbaacaddbbcccaadacbcdcbadbacbbadadacccdcdbbcccaabccccbdacbaaddadaccddbaadddccaadbddcabdddadacccbabbacaaacccaaacbbdaacdbabbbdcaddddcdaabdccabcdbbcdbcdcbacddadcdbdcdbdcdcddaaabcabcdacaadcbcdcdbccdddbabddbcabcbcddacdaacdbdaacccbcadacccddacaabadbacdbdbdccbcbccabdaadcccbbadcdbbbacdbcbbbabcbdacbcaadadddcabbdcabacdcabcdbcdcbcbaccbdaabadddacabbabddccacacababccdcabcbcbccadddcdacdbabaccdddcbdcabaaaccadbcaacccbbacadbcdacdbdcabadbbcdcbbaddcbbcbcadabacabbbbccdadcacabbabccbdccdaabcdccabddcbbdddaacbdbbdcbddccabbbbbbbacdaacacbddcbabdacacddcbacdbdbaacdabbdbdddddcaccccaaaadccddbabbacbdbcdcdbadbaacbbdadbdadaaadbbdbbcbbdabacdbbadbbccccdbdddcadaaaadacbabdcccccddadcacdcccdccbbbabbcaabdbbdddaaabcbdbbcbbbacdcbdcadacaabbabdcdaccbcaccbdaaccbcaadcbddcbcbcbcdbbaacaaabacacbabdcdccdbbdbbaaabbccaaaccccdaabcbdbcddaaaadcdacbdabadbabccbdacccadacadcdcbbdadcaabbcacabaccdaabcdbbcabbaacbaaadcdccdaadcddacbddccddcbbadcdadcbcaacdbdabdbdccddbdbadadacdaccabadcaaacacbcddadcaccaccabadcddccadbabddcabcccdddbabcdcbcbaaaddcacabbacdabaccabdaacccbdcacdbacaacadbacacdbdaaaabbbbbaddcaadcadbabdbacccaccccaadaccabbbdaabbcabdbaabdcbcddccbcdbcbbdaccbbbdbcbabccabadadabadabaccdcddcdcaacbdbdbddadcbcdacbdccdcadabbdbacccbbdbacdadbdabbbdcddbbdcadccbdbcbbddcbaccdbaccadaadbccdaddbbcdbadbddddabacaccaabbccabcaacbccdddbbdbdbccaacdddbbabdbdaaacaabaaaacddcaadddcbcbccaddcaddccabbdcdcacdbdcaddacccdbcbdcbbcaabbcbbdaddcadabddbaadccadcbdabddabbbdbccbdbbbdbcaaddadcbabcdccdcaddacaccabbdbbbccbdbabbadbaaacdcbbcdcbdadcabaaaadddaacbccaccccdbbbdadccbbbdbdaabacbacacdaadadbcdaabaadaaadbbdadbabacbdbcdacdbdbccbcddacbbaacabaddacdaadcbdaadddaabcdbcabcdcbbaababbaaccabddcdcaccdaadccbdaacdcbdbdbaddabcdbacacddcdadccbdcacdbdbbdbacdabcabcabcbdaabdacaacabacdcdabadbbcbdbadbdddcacdbdbaccacccbaddadddccdccbbbccbcbbbdcbbdaaddaccbacdabbbaccbbdabcdbbccdbcbadadabdbdbaacadddcacacacccbddabbcaccccbbadbcbccabcabdaabcadcddbbdbcbbdadcaaacbdaaddbdbcbcbbcdddadaaacdccabdcdbaddcabdcccaabcacbdbcdcdabbdcddddabbbbaacbcdbbcbbacaabcbcbcbabcbcddaadcccbbdabacccabccbcdddcdadbbaacdcdbdccbacdbcddcacadabadbbbcdbdcdcdbcbbcbacadadcdcaadaaadbddcaaacddadcbcbcadccdbadacababdaabdbcacbabacacbdcabcadddcdaddcdccbcadabdbbacadbdbccdaacdaabcaccbbabdacbbbcbbadcbaadccdaabbdcbbcddcabbbabdbbababbbdacabddcbbddccddabbdbcdccadcdcddbbcbddddaaababbaddaddcdcadacdcbbaadaacddcbadddbdabbbabccdadcbadbabdcdbdacadbcabbdaccbabbbdbabdcaccacdbdadccbacbbccbcdcddbabcadbabbbadbddbbbadaaabcaabdcbdbbbcbabccaadaccbdbabbbaadabddcddabbccccdbaddacbbdaabbcbcbdbacccdbdbadbbcadddaaccdadcbdadbccadddcbdaabbaaabccadbcbadcacabaaabddadbddbacacabadbadadbbaababccbcdadddbdddbbaaddacccdabadadaadbbaccbdabbcdacccddbaddcddddddbcbabcddbbdcadabaccbbaacadabcacddddbabacbcdaacbaddcdddabdcbdbddaaaddbbabdddcaccaddbbcabcdbcdacccacaccbadbcbbbbbbcbbcabcccdbbcaababdabccaddccddddabbabbccdbbacdbacdbadbdddaadcbbadccbacccbcccacbaadcacabbcbbdcabcbbbbbacbabbddbdacdacabcadbddbcbdaaccaabbaadcbcaddbbdcdabbacbbdbdccabddaaddaadbcbddadcabcbabbddddadcbcdadddadccaacacdbbcdcbcdaddbbcbaddcdcdcdddcdabcabdabcdbcdbcabddaddacbbacadcdadddaddbcdbdbbbcbcabcddbbdbcaaabddaccabdbaccccabbcbddabbacdabdbcccbbcccbabccacdaccaabddabbcbaadaaacdccbadbadcadcacadacbddabdaccacccdabacdabdbbdaaabadcbccccacdaccbbdcdccccbdbbcacdacdddddbcdbcdcdddbcbaacdbaddccabbabbbbddaccaaddcbbbdbdcaddaaccccdabaabbcbddaabbaacabdababacddcdbcdddbcbcdbdbbbddadadccddcdccabbdbaaddddabcadcbdaabcaccdcdababdbbdaddbcdaacdbbabbdccddaddbdcddacdaabcbbadccbbcdacdddaaccdcbbcccbacaaacaccacddbccabbaddabbdbcbaabbbbcbdaadacdbbdbbbaaadabacbbcabbddbcdcdccbacccccbddbabccaacababdcdaddccdbdbbddcbbcbbdadcddddbacdcbbddabbbabacbdcaacdcacdbadadabadbcbcbadccaddbbcdacdbadabdadcddbadbcbbdaddabaddddddbcacadcbcbcaabcaacbccadbabbadcbccbaaccbccbddbabcddcdbdccccbdcbbcbbbddaabddabcadabacadcdcbbcabadabcbaccddccbaccdbaaddbadccadcbdbbbdbddddbaaabbabbbdcbcacacdbaabcccddcccbbddccbbbacadcbbdbabdcabadcbdaddcdacbcbacdccbcbbcdddaccbdbaaabcabcdbbbadccadcbcacaaaacacccdaaaaaccaabdcaabacddcdaacdccbbcbbcccdacaaacaabcdbdcccaacbadddcbddbddaaacacccddcabbdcbaaacdabadacaddabbccaadabbdbdbbaabbbacbcbddaacabcaadbadaccabacbdcadbcddcdbbadbbadadcadccdbabaadbbbcabaddcbcdbdaaadacaabdacabbbdccadccccdabbacbaadbbdbdcbbabbbddbacddabadadcaccddadbbdcbcabbbbaabbcbaadcdacdddabcdcdddbadccbccbdddbadbcaaacccacccdcbcacdbcddbbdbbdbdaddaaccdabcabccbbaadbdacdaacdaccddcacbbbbabcddbbcadccdccacbcccdadcdcaaccaacdabbdcdcbbbbaddbadaabcadcdbdaadbdbacbdabbccdccadacdaddccbbbabdacaccbcdcdabbadccdadaadaabbbbbbcccdacdacbbbcbbabbbdbddadabcbadbabcbcccabdcdbcbbbcbddddadbcbbbaaacbaadddbdbcbbbaababccbbdaacdbdddaddbacaddcccbdacbbcdbcdddacdbdaaccbadaadabacabdcbdbbcabaaadaaaaddcbccbaacdcddbacdccddcdbcacaadcddcaddbdaabbdaabadbcbdcbcbbdacbbadaabbabacbcbbabbdabcadcbbdcbbbabdabdbcbdccdcddabbabcaadbdcaddbabacbbdcdadbcbccabbbcabdbdccabbdccacaabcdadaacacbcbdbccacabdccadabacccccadddccbcbabccbadbacbdcdcbbddaccadbcbacadaadabcdcaacbbbbaddbbaccddccbcbbddacacadcdaabcbbacabaacbdcacbccaacdcddbdcaaccdcadaddbdadcbcacacaaaccacababdddcdcacacacbbccacaaabadcabdaddabadbcbabdaacddccbabaadbadbccdaaabcacadaacadabdaabdbacaacccdbaaadbabcacaccacbabcdbbbdddbcbcccdadababbbaaaabacabdbbcdbbbabccbdacacbdcabbacbdcbaaabdaadaddadacbabdbbddddacaabbcabcdcbaacbccabaaaacdcddbaaaaaadaaacacadadbbbbccdbbccaaaacbbcbdbbdccdcbbadcbddadaaccacdcbdddcddacbacbacaccaaaabadcadbadabcabdabcbadacabbccbdabddbadadddcdbacaaacaccbbdbabaadacabdadaddcbdbbdccddbaacbcccacbaabaaddbaccadddbbddbababdaabcbcdcbbcaccbbbbdbacdacbacacbbccabcbdcdcdbcbcbbbdbdabacbdabcaccabdaadbaababccdbcbcddccbbaadbddbdaababcdcddcadbbabcbbccdcbacccbddadddddabccbaacacbccbbbaccadccdcaddbbcaacdabcbabdbaadbbbadaddcbcccaccaccaccbbdcaddcadbcdcabbadacbdacbddcbcaadabddabbbbcaaccbccdbcbbcabddabcbbbaabbdccbbdadabbcadacbcdbcabaddbabbdbdcbaddcbbbdddbccdddcdcdcbcaacddadccbaadaaabdacbbdcdaaddacccdacbcdcddbaaccdddacdaddbbdcddabacbabbacdaacdbabcdccdbbcdabadbcbaadadbdbadbcaaacadddaaaccacbabdadaacdabbbccacccbbbccbadbbcdabddbbaddaaabbbadabdabaadbdbcbaadbbadbddddcdbbdbcccbdbcacbabdcdbacabdbdbcbcdadadcddabcaddcadbcbbbccdcaaaddddddaababadabaaadbcccaababbadbdcdbaadcbaaaadabbcadabdbacddacbdbbccdbdcabddacaaacccbcdcbaacaddbaaadacbcacaabdaaaddadcadabdaabbaacdabbabbcdcbbaadadcabddacaccbccdcdbcabcdcbbacbcaddbdcbaabccdadcbbcbaabaddbcbabddcbdddcacbdddabbdcdcbaddbabddadacadbddcbdaaccbadabbddaccdaccabaabaadaaabcbcaaabcbdcaccaaabaadcaabcdcacbcbdccdaabbccabdbacbddccabaddddccdbbadabbcbadcbcadaabccbdaccaaaacacdcaadddbccaaccbaabdbbdbdbcdbccdcabbdabdadaabbaabadcdddbccbbccbdcdcadaadabbbbaaaccccbcdcbaabcabbabccabaadccdccbbcacadbabaccccabacbddabdaacdadccabcbdabbaccbdbddaddaadbabdcbbbdcadcbdbaacacaaccadabadbabdcbdacbccbcdbaabbcacaabcadacddaaacbadbdcdccbabbbdcbccddccbbadacccabadccbdcabdcbccacdbbdcbaabbadddcddbadcccccbadddbbbdddabdbbbdcddbcabdaabddabcadbabdbdaaadaaacddbddaadbcabbaadaacdcdbddbbdabdddcdcbbadbcbcccccddbadbcddadbccaadbbdcdbabaacabcbacbaddabdcccdbbdaadaaaabcadcdccdbbacbdaabdddbbccdcaacccddabaaddbcadacbdbbbbbacbcdaaccdccabbbcdabbdbbdcbcdababacaacabcdbacccdbcaabbbdcbcbadabbacabdaaaabdcddadbcbabddcbabdbaadaaacdccbbacaccccbbdabaaddabacabbcbccccddbbbddcddadaddcabdbdcabdbacdabbdbcabdcaabdbbcddcbdddcdbbdcabccbabbddcbdbdcdcaacbbbdccbadcdbbbccbcaacdbcddcaddddddaabbdbbcdacbaacacddabbcadbabaacddcbddaccccbacabdbadbcaddaaabddcbcbcddbbcbbbaaabddbdbbcabbaacbbbacadaadbcccdbbacbaaaacadcdcbbcbcbcacbaacadaddddaabdbcaacbbcaccddddbadabdabadaddcdadaccdbabbacaddcbcbdccdbcacbdabdadbdbbdbcbbcadbbccbababbbabbcbddacaaabbbdbddcdbaccbcadaacbbdbddcdadacdacbcadcddcadbacbdccbbcaccabcbbcaaacadddbadbabcddababcddbcccacccabdbaacccdbadabacbdcaddaadabacadaabdcaaadcbcdddaaaddcaaacadccdbadcdacadddabbacbcbabacabbddcdbacdbacdbababddbcadacdcabadcdcbabdcbabcdccaaadddcddbcabacbabadcbdbddbaabbccbdcaacccbabddbabbbbdaabcaaaacabdddcabdcababbdaccacdadccdaabbccbdbdacdbabcccadbdccbcabaaadabbccdbdbdcccadbbbadbbcbdaaabdacdcdccabddacabbabddbcbbbcabbabdcabbaaddbbcabbdadacdbbdbdcbcbbdcddabdaaabacdbacbdaabaacddbbabbcdddcbbdbddbadbddbdadadcacdbdacdcadaccdbadddbcddbcddddcabaaddabbddabccaccdbcdcdbdaadadbdacbacadbddcadcdbdaadcbdbdbcdbbbaddacabbabaacdbbcadccbcbbdbbdbbdaadcaadadbbdddcddacbddaacdbbaccbddbbbcdbdcbbbbcabadbccaaccacccdaaacdcbbbdbcbddddcacbaadcaaddcdcdbacbcabadabacabcdcaaaadbdacccdbbbdcacbadbaabadaccbbbddbadadbadabddcbcccbbcbcbadadbabbbccbaddddcdacbcdcacdccddddccadaaadbcacbabacdddbabdbabbddbbaaabbabcbbcbcdcbaaaabbdadcbdcbbaacddaddbccbdbabdbbababcdbbacbbbdadcdcdadcdbaccacdabdaadaabccbaaabbdbdcacccadcadbadddbcbddbabccbbbabbabbbcabbccdacbcdaabcdacdddabbdbcddacdcdaadbcaaaaccdbbacdababbcccdbbabbccdadbbbcbcbbcababdbcdabbababdabdabdcdbaabdbbdcaadacdadacbbadcdacaabbcddcbbbdcabdaccccddbadbbdccbcdbcdcddbcbcdbddabcbccaadcadbbcccbadcdcaacbbccbdbbbbdbabaadbdadacaabdbbbaccaabddbcdbddacabdcbaacacbdbcbaddacdaacbcdcdaaabcbccbabddbcdacbbadacaacaacbcbaabcbaacdddbdccddcaaadaadaacbbbdcacdabbccacaaacaadadadaacabbadcbdddcdbdcbdccbcbacbdcadbaadcaadcbacbddcdcbcaddacdacdbaccaabbcaababbacdbcbcddbbcdabdbbacaacacdacbbcdabbdcbabdbdbdcbdddcacaddcdbaaccdbdbdaaaaaddabbbbdbdccbcdbbdcdbadabcaacbcacaddabcccdbadbcbdbaadddbbcaacbddcbbbbcabcbdbcbddbcbbdccadabcacababcaaddbbdacdaaaacabccdbbdcddadabbbdadcdbadddcbdcdadcaddbccaabcdaddddcdcdabdabdccdcabbbaabdcaadbbaacdccbabcbcabbcbcadbcdacacbcacbbbbcdbacdbddcabbbbdcbacbadbddadbdcaaccdbdcaadbaccdbdbccdbcddcdcddadadaabbddbcbdddcbacaabbbabaadcccacccbaccadbbcdadcdadbaadadbbbccdbdaadbcbcdaccdcacdaacdaacbacacaacadddbaababaddadabbdbaabadaababbaabbabdddddcadbcbcccbadacabbccadbbcadddacccbcdbbbccbaccabdaacdabdaaddadcadbbdbcdabcaacbabdcdbbadcbaabdbaabdbdadacbabacbcdbbcacdcbdddaaabddcdaadaabcdabcdcdbadbdbabccdbaacbccaacaacccbaadcdcbabbadcaabdddbcadcabadabbacbcdabbcdccbbdbbbabcbaacbbadcbbddcacccdbbacdcaadbcababcbcbbddcaadbccbcdcbacbabdaccadccbacddbbaacabcbbdaaccabbaccccaccbaaabdbcccadddbcccaabdaccbdbbadcdcdbadcadddcccadbdaddcbbadabcbbdcbdabdcdbbbcacbaddbacdcacabcdcdacaccdbacdddcbbdabbcbcabbabacabacdbcaaaccddcbbcdbbbdcdacaddbadbcdddaadbbcdcbdcdacadabcdadcddcdcacbbbbbbbdbbcdcdcbdaacdaddddddcdaddbdaddccccadbddddddbcbaddaaacabacaccbddaabbabaaabdbadbaddccccbccbadbaaadaabddccdaaccdccbdbbccdadddddacabbdccdbcabbddbaddabbbdbcbbbabbaccacbababdbcbccaccbcdbcbcdbbcbccdcdabaaaddbaacbcbdbdccddccbcbabbaaabdadacbdbabaddbdbddacdadddbdbbaaababadadcbaacdbcbbbccbbbcdbabacbcccaabbabaadaccdbccbcdcacbacacdcbbbbdabcddbacbcbdbaaadbddacdbcbacdcaacdddbdcddbbbbbcdabaabbdabbaaabacbaabcabaaddaddbbcbaadcccadcdcbccdbdccccbadccddcdbcddcacbcbdbdbbbdbbdacdacaccdccdccbddcbcbcccdcdbaaadcbdadcacddbacaccdabdbcbacdbddbbadadbadbbbaddaadaddcbdcdddcbcdcdcdbbbbcadddbbdcbcdcdcaabdccacccdabddbdaccadbdcbbbbacdccdddcbcbcdccccccbcacbdccabcbbaddabcaaacbcabcbdabcbbaabdaacbcdbbacdadabdbbdbacbbbbaddbdaaadbdbddbbacddbcadadabbadaaddadddbdccbaacbbadcddddbdabdddbdacbbabcdcadacbccddcbcdcaabcbcddbbbccccacabdccdcbaddacabdadccbabbacababaacadacdbaadbbacaccadcacbbdcabdabcdbabddbcacccbcaccabacadadcdcabbccddaadaacdcddadcaacbccddadbbbdabcbacacbadcbacdbcdbcdadbcdaadabcddbaadcacdacbdcddbaaacbcabaddaaccdbcddcacaacdacdccaaadabdaabdadaccbaddbdccbbbdadbcccddaaadccbbbccaaaabbdbbcddadaaacdbddccbdbbccdacbbbacaabaaacdcbacbbbaddcaaabdcccccdadcbbdacdddddaabaaaaddacdabcabcbaaabcbbcbcbbdddbcabaadbcaabaaadacccdbaccaddcbdbadabdddbcbddcbbacbbaddcbaddaabddcddddabbaabdadbbddacdaacdcdacacdacacaaaddbcccdddaaabbabccaabadbacccaabccdabbadcdbccbddccbaabaacccddaddabbcbacdbcacbddcccaabdcddccccaccdacaaccaccdbcbddddbaacbacbcaabadbdbbaccddcaadbcaccccdddcbddcaddcacccababbadaacdcabbadaababbdbdcbbdddadaadadcddbbbadbbdbaddaccdbadbbcaccadcbaccaaacdadabdccbaabcbcdcdabadddddabbadcddaddcacdcdcacbacaadcacaccdbddabdcaacbdddbadacdaddbbdccbcacbacbccbbadbadbbcdcdcababccdcabadabaadbcbbccdddcacdccdaaccadddccccbbdabbadbbacbadaaaadbccbdacacadaaddabdadbcbcabaaccdaaccbccdcacaddbbdcdcdadbbaaddddbaabaacddabacabdcbcdbabcaaacbcbbddbbbdabbaadadacbadddbcddbdbdaccdacaccddbabbdcadcbccbcdacbdcdabdacbabbdabccaaccaabdcaaacacbdddcaddaabddadcdddbbcbcabbdcbacbadcdacbadcddbdbcbacddadabbdbacbabcbadadcdaaddccbcbcdadcacdbbaabddbddadadcdacbbbdcddbadbbbbdabbbbdadaccbdbdddcbdcddabbcabbcdcdaabccdcccccdccbbdcbbdaccdbbddbbabaababdcbabcbdccddcbaddaddbcddabadcddacbabcbbbbbaacabbbdacdccbddcdbabcaadbcbacaaccbaabccbbbabcccdabdddbccacbcddcbbdbccbabcbabaaababddbcdddcbdbbabbaabcbcdccbbddcbbcdcbbbdcbccbcadacbbbcdadbddbcdcbbbddaddaddadcccdabddacbdcaaddaddabadbcacddcdbcbbdcbdcadcddcabdcbadaddcddbdcdbdadaadddadbcdbbaaddadbbbddbbbbdbadddbbdcadddbcbabccdbdcaddaccdbdccabcaabbdbcbdbcadbdacabaddbcdcdaabbbacdbbcdbbacaaabbadbccbaaccddddababbdddbcbbddbbaadcbaabdcbadbcbcaabdabccaadbdccdcccccbbbddbbbbbdccabbdcccdadccddadcdbcbbcbaccdbbbcbdbcbabbaccdddaccdaabbdcadcdbcdcaacabdcbaadbaabdbbbbaaacaccccaabababcdddacadacacaccdcadbccbdbddabdababaccccdcddcabacbbdaabbcadacdacbdbbaddbdbdaabadaacbcaabcbcaccbdbbbcadaadabbdbbccabbcacccdccacbadddddadabdadbaadbddbdcdbdcdaacccddcacbcabcbacbcbdcdcbbabaaaaaacbdcacdcbcdbdbccdddbadcdbadaddaaacabddcaadbcbdacbaaccdccccabdaadaadbbcdcababdabadccbadcaaacbbccabacbdcccbaaccbddcadcbbcacdccccaacdbdbdcaccdbbacdbaadcccabcdabcabaaccdbddcdabadcacbcbbbbacadabcbcadbdddddaddaaacdddddbdcbcbacaacdcdabababacadbacdcdadbdccbdccbdddccabbdbbcdbddbbdbbbbdacaaaadbccbcbadcacaaadbcadbabadabdaccadadabbdcaacccbcaccdabbdaabababbddadbcaacadadcadabccacbbdadcbaccbabbccdbaabdababdcaadddcbdbbbcdaaddcccaddbdacaaabcacccdccdaaaabcddaacbccaaaaaabcbbcbdaadcdddcbaadaddbbcbabbbacadacccabcbacccbdddcdacadccdbbcabdcdaaabaccddbdabdbaddccdcadcdddcdcbbddaccaacbbbbadddbbddcacbcaabbacccaddbcdadaadddadbdacccccbbccccdbbadcdcacaadbccabaccdcdcdaadadabbacacbcbdbcbdcdcccabaadbdbcaccddadcdccaababaadcccddbdbdbddcbcbdaccdadcdddbdcddbadbbcadacbbacbdbdcbcadbdcaacdcdcacdacaddccaddaaddcacbaaaaadccabbbabdbbdbbcaddabbcdcabcddabcacbdcabdddcbacddaabcccdabdcbccabcaabdcddddcdccccabadcaccacdbccccbabdcdcaaadbbabbccbbdadcccccdcdcaabcdbbcadcbdbaadbcaabcbccabbbbcdccbcbcadbdbbbabcddadacdbabbdadbcacddddaaaccadababacddcdbbacadccbdcdaadbbdddacbdbdaacdcddcdbbaccacbccbdbddacbcadbabbabadcdacdbdddcaaadbccdbbddccbccccaabaccadbcbcbbbcccccdcabbccbddadacbaccbbdcdcddbdaaabaabcabdadcacbcdbaccaccaadbacbaddbbdcccaadcdabcddacbcdbaddcacddbddaaddbdcabaabccadacaddddcdbbdddacacdcbddcdaaabccadcbccbdadcaccaadbacddabababdaccccbbabbbcccdcbbcccbdcbaadbbdbccdcaaddbbddcabdddcabbabbbabadacddcdbbcdbbcaacbcdaaacaaadbaaddabbadbbddbdbcbaaddbaababadcabbddabccacbaaadbbadbbaccbdaacbdbacddbaacacacdadbabcbddacddcdaaccdbaaaaaababddcbacbbaaabdbcbbccabdbadacdddadcadbcaccdcbbccadabddbabacdbcddaaddbcdadbaacadcaddddbddddacbdaccddbcbdbabdcdbdbbbacaacdcbdbbbdbbadacbbacddbccdcdacbddbbccdbaddcdbbcccbaacbdcaabacdadddccabbbdaadbadcacacdccadccddbbbbbddbdbaaadbaccbaddbadbaabdadaaddbdcdddccdbbbaacdbcdcddcccadaccdbcacdcbadbcabadbbacaaaadaaccdbccbcdcdaadabcdcccdbbadababcabaddccacddddcccdacbcbdacdddddcbdaabcbcbaaaaabbcbdadcbaacdbaadccdcdacbdbbcbdcbccbcbddaddbadcddbcdbcdddbccbbbbddbbdbcbbccbbbdacdcbacdbabcbbaccaacccccdcbbddcbcbcabbbdadddbddccccbdadbcbbdbbbcadabaaaccbcacdccaccadcbcaccbbbddaadbcbbdcdbcadbdcadddaddcbddcddbbcdaabcadcaacdbddaccbcabbaaddadbababccbbbadccdacaacccadadaabddacabcadbbddcddadccdadaabbdcddccdaabccdcacabbdacacbbbcccdddcaabccdbbccadccddacabcddabcbbabcbddadbadbabbdbbddabdaccccddaaacaddbbdbbadccccbcbbbbaddacadbdbbccabaddcdcccbcbaccdabbdcbabbccbbcddcccbadababbabdddbcdadcaabccbbaacabcdadbcdbdabddddcdcabdddbcacbbabbdaacdbaddacdbbbbbcbdcacbbaadbbadbdbbbcaaabbdcaacacadbbdcacbdbbcbddbcdcccadbddddddabacccacaddbdbdbabcadccbccdbbbaddbcbdddadaacdbbdadcabbdaccdbabbdbbacbdaabdcaaccdddbddcbabaacabdbacdaaabadabadcccabadabbdccabbacddbbbcdddcbdadbcddccbddcabccbdcdbbbcdababacaacbcbbbccbbacdbbaacaccbbacbcdaacadbadbbabdbbadbdddacabbcbbabaccaddaacccaaabcaaabbbdabccbaabccbcadcbbcdcdacdbbadcddbdbdacacaaaddcddbadbdbabdacdaaabccdabcbaddadcadaddcbcbabacdcaaaaddddcadcbbbdcbbdaababdbcacdcabbbdbdacddbdabcbaddddbbbabbcacbdbdccbbaccbaddbdadadabdcaddbdccbadacbbacdddcaaacddcdbcdbcacbbdbcacadccbcbaccdabbdabcdccacdaddccccadcbbdccaaccbbdbaccdabdbdcbabadbcbbaacbbabcdbdbbdddddcbcabaddbccadbddbbdbcadbcaddbacbcbaddbcdaadbadcdbdaaabdbcbcbdabcdccbadccbcbbcbdcbacdcdcdccbcacadcbcbcaabbbdadaadbcadbdadddadaabbcccababbbdbbcccddbbbacaacdddabbdcdcbdcadccccbaddcbdbaadcdadcccbadccbccbcdbaaacaabcbddcdddcacbddbdacccaddabddacaadadaaaaaacbdbbccbdaaccadbcbdbcccccaaddbbcccccbaacababdccdccaadbbbababdbcccdaccddabcacdaacdbdabccbacbaadcacbabcccadcbcacdbbbddabaadcadcacbcdcdaacbdcabddccbabddcadddccbcdadabddcabbcaacdccbcacdbabbcdcdcdddacdcbdabcaaabdacdbccdbabadaddccbbbbddaddddbcbcacccddbdbadcddabcacbccaabbcdcaacaacaadddadbcbdbabccdcdaccdcbdcdbacccdcbccdbbccccbabacddcababddadddbccadbcbdbbbdcbbcabcdbabbddaccaacadcdccddddccdcbdbddaccbccbcccacbbbcacdbaccadaccdaccababbbccaabacabcbbbbddcccdabcccbcdcdccabddaabdbcbbcdacbddcdadacaabababbbadaaaadcbadcaacadccdbcdcadbdccccccadacdaadbacaccacdbadcdccaaabbbdddcbadcabdccdaddcbabaabbbbaaadbbcbcddaadddbddbbcabcabccbadddcdbbddabbddacccbddbcddcabdcdacaccbbdbdcbcccdaaadcbdadbdbcbdbacdbbbdcddcdcaacaaacccabcacdbbaddcbadababbcbddcabadbcababbdacabdbadccabcadbcdccdcddcaabacabcacadcbbccacadbcabbcadcabadadbacadbabbacdbdaccbcbbadccbdbacacbcaccbdaabbdaaddccdddbadcbacbdbcabdddabaccbdadcbbaadadaabbcdaaacbbbbaadbbbcadddddbbdcbcbdadddbbadabddcdabddbbcacdccadcaadcabdbcccdbaccddacbcdbcbccbdbcbaacbccbadcddabbcadbdadcbadccdbaadadccacccbcadadbbbdadbacaaacaacdacbdbaabadcdabadbbadaaddababddbdbbcbcbccbcacababadbcdbaaadcbbbbabbcdbdbbbadccbdabacccbacbdaaacbdccbcddabaaddacdacdababcabdcaccadaaaaaadcaabcddaabcdbbabccacccbcaabcaadcabacbcbaaacdbbcdcaacbdacdaadcdabcdcaadbccddadaaabbccbdbacbacbabbacbddadbdaadbbababdbcbbdbdbcbcdddbbdaacbbdbbbacddcbbdabaabddbdccbbccaababaaaadcbdcabadcaadaadbdcbcadadaaccacbdbdddcddbaadaabdbbadcddbbbabcbacbbbbcccdaacbaaabadbdddaacbbaaaaccbadaadaabaadcbacadddaccaddadcccbcaaddaccdbacbdbadacadadcaccccdbbbbbbdabdacadcbddbcbdadbcbabdddabbbdbbabcdacdcdadbcabcacdddacdbbbbcddddaccccdddbbaabcbdbbadaddadabbdbcabcdccbadcbacbababdbdccbdaadbcbcdcacdcacbabadbdbcdacccddaccaccdbbadcbdbcdbbacdcdcadddadccdbcdcbbcdbdcdaadabdadbcdbcdaaabdccabacdddcdcdababacaabaabaaaaaadbdddacdabccccccabddbcacbacbbdddcbacbaddcadbdabdcbaddbcbaaccbcaaabbbbcccacbdcbcdcdbbddbdddbacdcbdddccabbbabadadddabccbcbdbacadccbdcbbbcadabdcabdbaadddddcaacbbbdaddbcddabcabccaabaadbbcacbabccbbccaadaacbddbbacbddbbbbcdccabbcbaccbdadcabaaaddbcacacaccaacabadbabbabcbdaaadacdcbdbdcdbdbcdbbcbbacbcbaacbdadccdcbcbddccbabaccbacaddbaabacaddbbbbcbcaabddbcdaccccadbdadbbdcbbaabddababcadabbcbdabcbddbcdbccbbaaddbaacaabddadbbdbbdbabbabadcdadbbcddbddddbaccbdbcabaadcbcacacdaaabcdbcbcbcdddbbdabccacdbdcaaccdbcdbbaabccddaacadcadccbbadadcaaddcdddcdabaaaaccabcacccadcccdccacddaddacaccccdcddccabdabadbcacadcdbaaaaabadbdcdbabddabcdacabbccbcbacdccdcacdcdddcccdddbdcddaaccaccdcaccddcccaacbadacabbaddaabcbdadaccddddadbbcbdaccdcbbcddadddbccccddcbcbbaabdddbdcccadabbabadcabdabadaaabaaadcdbccdbcdacdcbdbaaacccdbddbcbadbacbbadcdbbbadadcadbbbccacbbccccadaddabababbddadccdcaaacddbdabcaaddcdabbcbcdddbdcdcbacacbcbbbdccddacbbbabcabcacdabaacbcbababaabddcaaaaaacdbbaaddabcbbbbbddbbcbabaaacbbddbbbcbbadadbccdacbdcddbbccbcbacbdaddbcdacddaadadbaadddbbadccddbaddcbbcdadbaaacccbabdddbcbbcaddcbdbccacddddadaadbcccccccbcbbdcbccdbbbdddacaabbdaaadcabccbaddcdaccdacbddddaccaadbadacdcdcbcacacabacaaaabcccaccbbbcdbccbacddcbcbbcacdabddacabbabccccbbdbdbbbaaddbcdadbcddbaaaadbcdbdbbbccabbbcbdabccddabcdaabbababdddddcdcdcababdbcbbcccaacbabbadcbcabdcbbaacacdbcbaaddcdccddbbcccdabddbbadbdcadaddabdbacbcacccbacdbcbbdcbbdabbabdbccbacddaccdadccbbcdbacaadcddaddbaaccccdbabdbcdcccaccbdcaddaaddbbdccbaaacacbcbacacadcbbbbccabccacbdcddccdbcbbaaccccadabdcdbbcbcabbcdbcacbbaaacdbdadbbdcaaabaadcbcadcbdabbddbcdcbcdacbabdabdcbdcdcdcdbbbdadbcbcabadbadbdaacdddcacacbacadaddabdddddabccddcbbbccabdaddcdaacdcbddadccaabadbdbaccacabdacbdbbbbbbabababbccccbbabdcaaaabcbbbabdcbccdbaadcabbdbbcbbbbdababdcbcaaabbdadbcbacadddbdbcbadcbddacbcacaaabdbcbdaacbdcaddccabbccadbcbdddacccbdabdadbccbdbcacaadacbdabcbadabaccabcbdddcccbccdcabcacdcbacccbbbcabccacdccbabccabcdbdbbcccdcdabbabccbdcbbddbcbaacacdbbbaaadcccdbdabcaadccadccaaabacbdcabcbcdcdabccadbaadbcdbadacdcbddaadadddaadcdcacadbaabcaacacdcbbdcbabcaabdaabbacabaaccdaabddbddcaabbddbcbdaadadbdaabddabaccaadddaccbbadcbbbbbacccabbbacadacccdcccddaaadccdbdaacdcbdcaaabbaabaacabaddbbdcdaccadaadbdbbbddcccababcbbaaacccbabdbadbbdcbcdaaabcbcabadacaaadbbbaccbaddcbdcdabdbdbdaddccdbbabaabdbddacbdabbcbcaccdabccbcbaaabcaccccaacdcaabbabbdadbdccacadaddacdadbbadcccbbadcaaddbbadcdaccacddcdcbadbcbbcdaaddabbaabacbaaadaabdcdadccacabacbcabbcbdcdbcaaabaaabacccaacbdbadcccdddcabcbadddbcdacbcdddbbbabbbcbcacabdaadbaacdddbcbdabacddbdbddbcbcbbccbaacdbabdcbddaabdbabcddcadaaacbdaadacaabcdbabcdbcadbbadcdabadbbdcaacacaddddaddadadcddbbccaaaabaccddccbbaabdccbaccdacdacbbbddcdcbddbbaacbdbaacbdbccababddbdddbdccddabbcadaabdbdbaacbacdbccbcadadbbccccaddacaaababbacccccdacaacdcbadcccadbabbcabdccbcdccddcddcadcbbaddbccccddbbbbbacadacaadbbcaadbdbcbdadcdaaccabccadbabdcdcbccabcaabcdbdbdbaaaadabbdcddccacbaddcdbdccdacccccccaacbdaaaaddadbaaacccbdaadabccdbcaacbcacdbdadbcccdaadaddaaaaabaabcacaadbccaacccaddadacccabdbbdabbabaababcccabdcaabbbcbbdaccadcacbccacbaaddaaabbdddbdbababccadcacacbccabbdcbacdbaaaabbbcbaccbbaabbdbbbacaddbdddaaaabaaabbaabbdacaddccdcdcbbccdadbccbbdcbdcbdccacaaabbbdadbaddddadddaacdabcadaacacaddbbcbbddbacacbbbabdddababaabbbdabcdabbdaddacbadbbcddbbdbaadbabbabadbcabaccdcdacdbbdacaaabddaaddacdaadccabadbdacadaadacccbabaddbabcdbccbccadbaaccbccbabbabbdddcddcdbdacaadabdaabacadbdcbcdcadbcbaacadccbacbaabbacadbabbadbdddbccbcacbcdbabacbcadccaaadbccdacdacccbcadcbacadbcccdcbcacbdccabbabdabbcdadcbddddabaddaadadaccccbbbbcbacacbdacaddcaadaddddbacdddcdbadcdbadaddccccccbcddddabddbccbabaddcdaaacaadaabadaacdcdbcbbbbacaabccabcaddcdadbdcbaddbcaaabddabdccdbadadaddbdcaadbaadaddcccdcacbbdbbbcaccbabaddacdccccdbcadbdcdacbdccaadbcdaabbdadbcddcdbddabddcddbcbdcdccbbddcdcbacbccdbadcbacdadcccbdcbbcadbbccccdddccdbddaddacdccadcbaddcccbdbbddbccaccdcbbdcbdddaccbbbbdccacdbdadcccbbabccbadadcabdbbbcccaaccbdbabacbcbccdaabcdccdcadddadbacdbdbadbcdbacbdcbcbbbaaddbabbbdacdcdbdbdcdcbbaddbbddbccbadadccbcbdbdbddcbcdddcadbdacddccbbaddadcbadcdaaababbdaadadbcdbbcddcbbdddbddadcdcccddddaddddadccabddacdacccbdadaadddbbbbccdacbccdabddbcbaccabababdabdbdbbadaabaacdacadaacbcacbaadbcdbcabbcbddbdcdddabbcadcadacaddbcbbbbdbbbddbaadabcdacddcdbdaccadcbbdccdcbdacaadbaaacbdabbabcccaddcbaadcabbabddaddbcaaacaabbbbcbbcdabadaababddaabadcdccacdddbdadbcacaabbcccabcccdccddbcddaacacdcdcbbbbdbacddbaadbaacdaacccbbcdccdccbaaccccbbccdadcadbccaddaaccdbccbcbccadddddabbbadbdaacaacddabccacbacddaabcdacccdbaadddabadddabcacbbcbbadabdcbccdccdabaabccaddbaabcbadcccaacaabdacbaacbadabcdbccdcddadadcaacdcbdbdccccacaacddababbbccbdbddccbdbbddadddddcacccacdbcdaadbcbbddbbddbccbcdadddcbcbbbbdabddbcbaadddccbabdddaddbabacacdddcbabacaabcbcadabadabdccccdddaadbccbcbbccddddababbdaddcbdcdcbaadbabadacadadaccabcccccaaacacbacbaddabbabccdaabcbaaaabdacaadadbddcabdaaccabbabbabdbcbcbdcadacdcdbddaddaccadaddcbcabaabbcdbaaabadbdddccadadabdddbcccbbcadcdddbabbbbacdabdcbddccdcaaadbbcbcdcbcbadcccacbbdcddbcbdaddadbbacaadcacbcbdcdcccccadccabbbdbcdbcdadabbdddbaacccbcbdddbbaadaccaacbcbdddcbadadaadcdabbdadddcadbadbabdacdcbbbbabbbcbacbdaabbcbcbaadcdbcdddcabdaddbcacbdbbbadacbdcdaccabddacaacbdacccbbdadaadadaddbbddcbdabccbddaabdddbabcabcbacaaccaaddbbabdbbcaadabbdccbbdbadbaabbbddccdbdbbcabcddbbaacbccaacaadcbaabcabcdabdcabdcdddaddcccaaaddddbddbcbcaaaadabcbaadaadbdababddaaacdbaaabcddbabbdbbadbbcacbdacdddcbdcbdbdcbdcbbbaacaccbcdaccacbabbaaadacaaaabdabaadbacbcdcdacaaacbabbabbbbbcacbcbdadcdddccaddabdcccabbdbbdbabaaddbcddaaaabcdcdadcddbbccbadabbbcbbddbdcdaadbbddacaadbabbcacbdcadddbacadaddadacbccbbccbdacccabbadbdbacdcadbbdaddcddccadcbccdbccadaaddccabdaacbcabbabcdbabcdabcbdacbabdcabcbaadbcbacdbcadabaaacbaaddbdcaaabbaaaccbbddadcdbaacbdbccdbaabbdbcabbdcccbcdbbddcdadacaadcddbcdbabbdddabdcbdacccdaadbbbcdbdcdacbcdaadbacdccbbbbbbcabadacabbbdbccbbbcabaaccacacdabbcdbdbcadcdbdddbbbbaadbbdcccddabbdcdbccadbabbdcbadcdbdbdcaaacdabbbddbadabcdcdbccdadbcbddbdaacaabcbaccdcccddacdbabdbbcccaccbbbcdddbaaddaccaacdccbbbcabaacbbbabdcabdccdabbdbbdccdbaacaacdabaadcdddcdcabbccdacccbbdbbbbcccbbcccdddccccbcdddbadcbcccabdbbcdbdbcdbbbadadddbddcdadcabbdddcabacabccdaaadaccccdabcbabcadabacdbadbccaabadcccbccbbdadcddbdbccbbbdddcdbacbaaccdbdddbbadabcbddaccdaddcccbcbbbabdbbdcdabcbcbddcadcdcddbbbaddbddcaddabaadcababdbcaacdadcaddadbdaccbccaababbccabaacddcacabbbcdaaabdacbadcdddcbbbccddbcddcccddaddbadcccabcaddcbbbbadcbabcaadcbdcabccbdcadcdccadcbcdbcddaccbddbcaddadabdaccccbbaacbbcddbdaccbcadaaddcbaacacccaabbacaccaacdabcbcdcbdcbbcbdadbbabdbbcdaccdbaadddacbacacdacabbbcdddabcbbddcabbcaccabdadccdccbbdbdaddaaabcdcababcaaccadddbaaadabdcacacaaddbacbbddcddbddaadcbdddbbadadddbaccabccabaadcdbcccdbddabdbcabcaaaabdbcbabbdaacabcbcbcadbcacddbcabdbbcdbcbdacddbbbbdcdaadbcabdddddddaaabbcaaddbccbdbdabacaccbbdcdcbcdacaaabaaadbddabbbaababcabaccdccddbcddacddaddaddbcbbacccbbaabcdaaaddccdccbdbcccccdcaadaddcaddddbccbbaccabdabbddadbbbaddcbccccabbbcdaacabcbdbdbaddbacaacabbacaacdbdadcccadcbddadcadabbcdccacdaabcccccadbbaccacaddbaccddaaaaacbcdabdaccaaabadadccbbacabdcabcdbadcaddccddccbdcabaabbbdcbdaaacbdadbacbbcddccdabdddbbbaabadccaccabddcbacadbcddacbbaaaccbacbcbcdbcbcbbacdbbbadddaacdddbdccaccdbbbcadbabbaabaacdcbbdabcdadabbacdcaabbcabbdbddbbdbcaccdacbccbbabbacabacacaabbcdabddccdaadaabddadadcaadcbabacccdcdcacbaaadacbcabdcbdaabcdbccbcccaddcaaaadaadcababccbaaadbcadadadcdbacdddddcdcbbdcccdabbabdadadbaacddddadacbadcddaaaadaaddccaaccdababdabbdadbcbddacdcbaaadcddaabbdabdadbaadbcddaddadbdabdddbccdaaaaabbbdbddcacdadcbabacaaabcdcccabaabbcbacbadddabbcccbcaccccabaadcdabbabbaadbcbdbbabccbabdaaaacaaccccbcdcbaacbaaabdbdadcdadcabaccaadadccadabcbbdddaaddababbbaabdbababdabccabbbabcadbcbbbabbdbbcadbcccacdadbbdabcbddbadbdacacacdddbbccdddcbdccdbbbddaaccbacdccccbbccccccaaadbdcadabcccabcccacccaccacdcaddaababbabbadacdbadcaadaacddbdacccbccadadaabacbcdddcbbbaacbcaabddbccadcdbaddcadcddbdacbadbcadaccbabddbdbcdddbcdccbcddbbcbabbabadcabcddcbccddbadbcbdbcdcbcbdbacddbcbcccacbaccaadabdcbcaabcbcabaacaddbcdbcadabaddababccddbdddaccaaaacbbbdcaddcaaadbdadcaacbbacdbbcdbadacaadbbddbdabdaabaadadabacbdbacccacddbbcabddbdacdacadbbcbbddbaddabcadbccccbdaadaabdccccacdaddaabdbbdbcdbbbccdcaddcdaddcbcccbcbabbcaddbdcdcacbdbabacacccacbaacbdbaddabbbcdcaccbbdddbbadcdbcbaddbabbbbbadaaaddbcbadaaddadddbccdadddcddcadacacacbcaadbaaadcbaaabccacadbccbacccabadaddabcbdabacaaabdddbadddacbddbdcadbdabcbbabccdaabbacbcacddadccddbabbbcbccaacdbdbabcdadbdcbdbdbbccbbddaddbabddacddbaccccabcdbacaabaccdcaaacabcaadbbdbdddaabaacbcdadbabddcabbbabcbddcdbadaccdddddbadacdacddbccbdabdbdcdbbcbcbbabbcaacbaddddaccdabdbcaabbaacabbddabaacabbabcbabcbcbbcccababbcaacccadcdadaaaaaacbdbddcbaddababbbcbacabccdcbdcdccbbddacddddbbdaccddcacaddddbbacaddccccbdcaabadbacbababadabccabacdadbbbbcaddaabdbbcdbbdaddcacacbbbaabacaccaabcbabcacdcdcbaabdcabacdddaadadbabccdbddbdbdddddbbbaddbcdcdadaacacbccacbdbbabacdbcaddbabaaadadbdcadbbbbbbcdbabaccaadbdcabcbabcbdacadcaabcacdcbcbddaaaaccbababcadcaabacddaaabbadcabcdbbdaabacabbcccbccbbbddaaaccdbccdddaadbababcadaacacbdbaaaadbdabdcddcbdbadabadcbdbcbacbaabacacaccdcbbbbbcbcdddbaadbcbcbccddcadcacdcdcbbbbddcacccbacaacccbbdcbcdaccbdadcbaddbaacdbcbdbbbbcbccbbbbbcbccacbcbcbcbbdadbbbddadbddbcdcaaaccbbcaacbaadcbdacbcacbacacaaccacabacbababbbcbbbbdcaccdadccdbbddcbbdcdccbccbcadbdbdcbcadabcbaddabcbbdaababdcabbbdbabdbbaddcdadabccccadcacbaadbaaaadccccaddbcbdadbddcadcddbdadbbddaddddddbbbbcabacaadcbbdddabbdaabbacbbdcadcaccbccccbbaccbccdbbbbabddddccbaacbadbccdbbcbbcbacbbdcabcdbcbaddbbbbcbddddabcbacccacaacabdcbabbaacacdbccbbdddababcdacaddbcbdadccaacdadabdcddcacbdbbdcadddcbbbacacadaacbdbbbbcaacdbcbdccbddcdaabaabddbbbbbbdbadbcdbbcddadacabbbbadabdbdaabdcaabbdbccccbcdaccdacbbbadcbaabcbabbbbbbccbaadcaadaddabaacbbcdaddadbaaadbcbcccaabcbdbbcddacbacbabaccbaccbcbaaccbcdcccbbdadcdcacddcdbcbdaaddbcabaaaadaabacabdcdbbcddcdcddddcadbcccaccdbcaadaaaabacdadbcabccbdaddcccabbbabbcabccacbdcdbbabbcaadababbbbcabcaccdcbdddbcaaabbacbbbcaccccdcaaabdcbcbcdbaddcddaaaadbaacccdaaaadaddcabbdcddaababdbaacacbacbacbdaabaddacbdaccdaabaddcbdcbbbccbbabadadddaadadddbaadacdaddadaccadbbbdcabcccbcdbdddddbaadbcaaaaabbaacbdbbaccabccdacdaadbaadccbabbdcdadbbbdaaabccdcaaccacdccccdbdccacdbccbcadbbdcbaabdaabbcdbdbacaccacdacbcdbabbccddcbcaabbaaadbabadbccbcccbbddaaaddcbdadbccbdaabbbcabdbdddadcbbccbbbddaccabcdadacacdbbccddacdaccdaaabbbccddcacbbabdcacaaacdbccbadcaabaadcccbaaddaaacdbbcbbbadabaadabdaddddbcbbadabcbdcdbbadcabadabdddaaaaadbcdbdbbbdbbdbdaaccbadaccaccbcbdcbaabdabddaaccccaaabddcbbbcdbabaadbdcddacddabaddbcadbbaaaddbdcaaabcabccbcabddabccaacbadcaaabdbdcbbacdabddcaccddbbcdcaaabddbadaabbdbaaaaccaadaacbccdadacdcdbbccabddccddcabadabcdaaabaadccbccbdddccabcbaccaadcabcbdcabbcdabcbdcdbbcaabdaaadacabdcdbdbcdaabdcadadbbcbdcdadaddcbabdbbbddddabbccbcbadcdadacddbacaabbaabcaacdaaacabdccabcadadbdbdbcdaaabaaacaccaaddcdcbcabaabdbcacadbdadadcddbcabbbdadcccdbbddbcbadbdadabcadbdddccbcbbdcccbcdcdabbcdbcabbbddcdbdaaaabccbddddbbadcbcbdaccbddbbadddacbdaddbabcdcabbacbcdcbbdbadaabadbbccbcaaabacccdaabdaabaabddadbccbbcbaddddcdbccaccacdaddccdbbcbddddcbabdbacbcdcbabbccdabacddddaadddcadbcbdacaccdbaadbbbcbbcccdbbacbdcddcbbbacacddcbbaaccdbcabdbadacddbcbdcbbddaadbcddcbdccdccbabcaddbcccdaadacbcaccaddabcbcdababbcdabacbbaadabdaabbbcdacdcccaddabbcdabcdddbdddbccbbccbddddbbabbcbdbabbacdcaadcbbcdaaccbcbdadcbcdbababadcbcbdcbabdbbadbbaaabdbdcbddcdddcabdbdddbdcdbddaaacccbaaabdabcbbbdbdcbabbcbcadabbbdcbbbacbdbcacbbcddbbbbdcdcababbcabbbcccdcdcadbcddbbbccaadbdbdbdbaaadaadbbabcbdcdcbbacbdbadcdbaccbcaabcdaaaadaadbbbcdddbaddbccddbdabaddbbacabcdbcdcbbdcabdddbcbdcabbdbdbdbbaaddadaacbbbacaadbdbbabdcaababdaaabdddacdbacacadbbdddcabbdcacdcccabbbaddaaaccacdbcbbadaddbacbbdccabddcccbdddcdbabbdcaddbaaabdbdbaabbccccbbabccbcdbccbbbdbabbdaabacbcdbcbdccbbbbbcdabaddaaaacbdabdbbdbaaaadaacdacabbabcdccbdabddccddabdcaacacaacdcddaddcabcacacaacdbcbadcadcdabdbdddddbaabcdbacddacadacacddaacbadbaabacacdaadbbbaaabcbadbacdbacdddbbdadbccabdbabbcdbacaabcccabbaabcaadadccbccddcaddbcbcdaccbbbbccaccadbadaccacbdddbabcdbabadabdccddcdcbbaddbcaacbcacdbcbbbbbbabbddcaacdddbcbbdaababcdbaaadbdabbcbaddcbadadcdaddccaddacccbbaaccabbcaddaaddabadccbcddcdbcccdccdbccbdcaaadbdddaaaabaddadadbdbadaccabdaccdcbbadcaadadcbbdccdcdaabbabcaabaaabaaadddabaaadddacdabbacbcabaccabdbbdabacdbdcdbacdcbbcbcacddadadcbbbbadcbcdcbaadaadcddacdabdbbcbcaadbccdbadbaacabadbcbcdbabcddddabadbdcdaacabcdadddbaadcbcaaaccdadbaaddacacdcdacbadccacdabbccdabadaddbdcbccbaaccacdbbcdbbbbabbbdbacabcddaacbcadcdbcadcbdcdcdcdbdacbbccabadddcabdccacdcbcbbbcbdbdcadbaacabaadbddcccacbbaabbbdcdaababcaabbccccbababcdbdddbdbcababddadababcacdbaddbbbbddddbbbcdbdbaabadddbacdcdadaacccdcdacbcacdbacdcddccbdccadcdadcacddbdadccaaabaadcccbadccbbccaacbbacadacaaadcacadbbacbcdacbadbabaacddbaaadbdadcadabacbaaadcccbbabaaddbbaaaabbcadddaccbbdaddccddcdaaddaadbcddbcdbccbbdccadcdaaaacdccdbabdcabdbbccdbacdccccddadbbcdcaaccbbdcddcbbcbcbbddabaaddabcacbbacaaaabacabcbabdadacabbccacbcddcadabacaaacabaabdccbcbaabcbcdabdcdabddbaaddabbdcababdbddadccacbcacdccdcbdacbadbabdaccaaccadadcdabbdbcaccbcbcccaabcbaaaadabbacdcbacddacbccabadaccddcdacbbccdbdcbabacbaddbcbbccbddcccdadabddbbcbccabaadbacbcdccbbcaaaaddcbccdccbcacabbccbcaaaccdadaabccbdbaabbcacbcdddaacdadcdabadabbcbadaabdddbbdcaabdaccdadcbbdbcbcbbadbdbbabdcdabdccdbcccdaccbbacbabbbcbbacabbcadccbcacddcadabababaaabdaaddacbbbbddbabccdaacdcbbdddccbacdcddcccdcaccddbddcaabddbabdddbcadbbdcddcdccbaadcbdbbcdbbbccadaaaadadcbcccbbaddcbccabadbcbbaacacaacbbbbaabbdcbbbdbddccbccabbacacdabaaaddabcadddcbabdbaadcbbcbacccddbcacaacdbccacabaacddcdddccadbdabddaacdddbcbdcbcbdcbadacacccbccdbbdcdaacccbaddcddcbbccbccddbdbdccaaadbdabbaddacdaacdacdbabdaaaaaabbbdbddccdcaadabbbacdbdbadacbcdadccbbdddddccbcbcdadcadccddaaacacbcdbdbdabacabddcdcbbdaaccbaccdbcbcbbbadbbbbdcddcdababdbcbaccabcdcbccaadadaadcaadcbabcbccddababdabdccbcbbbabcacddadbdaddaabcaddcbbcdadcbbaadbcacabbacadacdbcaddaddaaaacccddbdcdabddacccaccbacdcbccdcbdcabddcbcdccddbdbdcacbddbcacbbcbdaabbadcdcbdbbbcdcddcddddcbaccccbdbabdbddacdddcadadcaacdcabdbdcbbcbcacbacbcabcdbadbccbbcdccaacdbbdcdabcbabbdbdbacadddbadbcdbcbbcadaacaaaabcaccdcbcdccbaaddadcdabdcadadabadbacacdddbccdcabaaadadbaabbadbccaaabdddbbcaacbacdbbaabacbdbcbdaacaddaddaaddddacbaddbdbcdaabdacaadbaccabbbdbddddbabcddacadaadabbaccbbaaacbacbccadbaadabcabdddcacccccacbcddacdacabdaaccbdddabdcdcbbcbabccbdbbcccabddadbbddbdbdddcaacdacbbcadccdbacabaabcdcadbddacdabcbcaabaadccbababacddaaccbdbdbbcabbabccbdccdaaababdbbdbbddbccbcabcbdbbdadccbaabacbaaaabdaaabcbddbccdabacaaaadaddcabdabdabbccdbaaacdadcadcbbaacbdbddbcdaaaadcbaaaadbcabcacbddaadabcaddabacaadcacaadccbbdbcabbbcbcddcbcdaaaadbbdddacabadaddcbbaccdabdddbabdacbdcdcabdadbccddbcddaaddacbabbcdbadbddddaddbbbcdbcdaaccabcabdadacddddccbdbdadbcbaddcbccbdbadcdddcabaddaacdbbdbababdccacaabcacddbddbbcbcbccccacdacadccbbbaccbbcaabdddbdabdacccacaabbcbbccadcadaccbcdccabcabbadcdbcbbdbccaabacabadbcaaddbbcadcacbddbcbbbdcbcbdadcbdcdacddabbbbadcdaddacbbabbaabddacdaaadabdcdcadbcdcbdaddaacbabddcbaaadbaadcbcbbddbdcabbaaadaccdaddddccddabacdacaaaabbdcabaaabdcaaddabdcaaadcabaaadbbadbadbbaacbbacdbdccdddbadbbabdaabdabdcccbabbabababdbcccbaabbadcbdaaddcbabaadbcbcadabddabdbdddbcbbccdcdabbddddbcbdcacadaabcdbabacbabaddcbcadbdbdddaadddacdbcdcadaadabadaabcdcbacadddbaadaadbccdcddcdbaabbdbddddbccbbbbcabaadcaccabcadaaaabcdcddaacbaddbcdcaaababdcaddcabaaabdbadbbdabdcdccbdadbaaabbcbbbbdcaaaddccaadcadbdadbbdaadccbdcdcdacbaadccbbaddaccaddccdaacdabcdacacdcdbacacbdaadaabbabcbbbabcbdcdbbddadcdaaabdbbacabdcbdcbdccaddabbadddddccbadbbbdbdabdcbbabdcadcbcdcdbdcdcdacbcadddaaacaacbbdabcddcddaccaaccacdcdadddabcacabbadcaaddbdacdacadaabccdbabcdaccdcbcbbabccaaccccbcdccbcabcdbabddbacaccddddabdbaabacccababcaabdbbadddbbbdaabadacadcbcbadaccdddccbacbcaaaadcacdacabacccbbdadbdddbcddababdbdabddbdcabbdbddaccccadcdcdcdcdacdaacbaadbacccdddbcdbcacbbbdbbbaacdaccdbdcdbabbcccbacdadcaacbacbddabdbcadbbacbadbdbdddadcbbcbcadbacbcbbcdcdbcadddcaccaadcaabcbccbabaccdcdaadcaadcaabaddcdcabccbbcbacdcbbdaccadbcaccbaaababdbaccdadbddadbabcdcccaabbcbdbadaadccabdbcadacbbcaabdadacabbcdddcacccaabbcdbdabaaadcbadabcbdacabadbabdbbbaadbdbaddadaadaddcddcbdddaadacbaaaccccabcbdcaaacaacdcdccbbddbddabcdcadacaacbdaccaacacaabcacabbaacccdcccdacbbccbbddbcdbbcdadcdddadbdacbcadaddbdcdcbcccdcbacabdccacbcadacbcabcbdbaddbcacbcdacacabcdbdbcdcbabdaccdacbddaabaacdacaabbaddabadcbaaddbdbcccadbcccbdbaccaccbdaabdcabcdddabacdacbbcbddbdcccaacdbbddbdccddacabbabbbccdabadabdcbaaccbbcdccbbbdacacbbabcbbdbbbdbcbcbddbbbdddcdacdddcaababadbbdbddbbcadadaddcaacabaadbdaabaabccbabbcccccccdbdbadbcaaadabdacacaacdbcddcaaaabbcbbcbaaabcccddddcbdddaacbcbcbacdabdbdbcadbbcdbaabdabbaabdcaccabdbdcadcdbacccdddbabdcabbdbbcabddcccdbadcdbabdbaabccdbcbbbbddcacdbbcbacabdabaddcacccbdbbcdddcddbbdbbddaaabbaacbbabdacabbdcbbadacdbaccaaacbcbbcaacababaddaddcccccdccabdacccbcbaacdddddddcadccdcbadbbbababbdabbaabbbdcccdabdbcabbdabaaacbbccbccabddabdcadbbdbcacbaacbacaadbcdbcdcddccddbabaacdbcccdadccabccacacadcdcaacdadcbdcbdcabbabdbbccdcbaccabaddabbaabbadaddbcddaddddcbcadaaadaadacdddccbdccddbcbdbcabbdbcbbadadcaaacaabcadbdabaccdadddbdcbcacbdbbbbccabdccdbacccacacdbacaaaaabadacddccdccdbaddbddabccabbddbddcadbacbaadababdccddcdcbdbdabdaccccaaccbaabdadcdcabcdaaccbbbbbdcbbbaacdadcaddbabadccdddbbdaccbbbbaacbbdcacbaccddcdbaaacbabddbcaddacaddaabadcaaabdbdabbddddbabdcaacccaabdbddddccbabcddcccbaddabccaacaccdabdcdddcadbcdcdabdbadabccaabababacbabbbccabcccddddbccdcbcdacaaaaacccadccdcdacabbdccadbdbadbddcdadbcaadbbcdcddcbaaadccccaacbdaaabacdbddacdbbdcabdcadbbcbdacabdcdabbcaabcabdacdadbcaddaadbcbadacddbcabbddbddbdcdbbdaccdaadbcbccddddabbaacdabacdddddadbdabbbdbdaddbddbbacadbbbaccbabdaacbdccbabbacccabcdbbaaddcbddbdbaacbadbcccabadabbaacdbddadaaaccdcbbabcbdbccaaaaabaaacdddbaabbccbccbabdabcbdabacdbbcdddbbbadadbaacdbcacaacdcdadaaabcabccaabddabbdbcaaccabcdcbcaaacaaddcccaddcabaadbcdccaaddccdbadacbabcbbddccbddbbbadcbbdcdadcdbccbcbdbddabbadbddcddbbdcccacbcaabbcdbdabdbcbbaacdccbacdabddababddaaccabcaabacddadadcadacdbbbaadccbdaaadcccccdadadcaaaddbdddaaccbdaaacdbacadcbbdbdcadbbcbbdccdacadabcdbaddbdadabdcdaddbadadadbdccbccdbdcccbcbadacdabbacabdbcbaccddacddcbbcddbcbbadaabccbbbbdcacdbdcbdbccdacddcaddbaabaabbacccbaadabcbbbabacdacadbbccaccacacabdcddbccddbaddcbcaddbcbdcdacaaacbbdbccbaacdaabbbbdacaabccabcdbcaadacacabcdbdcabdacbccbbbaaadcdbabbdcdaaaaacbadbdccaddcdacabababcaddacbabaddacdaadcacbadaacbaadcddbcadbcddbbbbcbacbdaacdcbcabadadbcdcaddcdacdcacbcbddddbabdcabaadacadadcbcdacbabbcdaddbcbaacdbbbbabbbbaaaabbadbaabaacbdaccadbdadbaaddbdcadcabdcdddbdbaabaacdcabccacadacbbacacdaaabacadaabaabadabbbbadbbabcbcbaabbdbabbacdddaccbaabcdccdacbdddacabbbddbaadcadabdbacbccbacdbddbdbacdcbcabcaccbdcdcbaaddabbbcdadacacaccdbcbdbacbaababcddbccdbbdbabdddbcbadacbaccbbbcaabadbdbdaadbbcbdcdcbddccabbcdacaccdbdccbcaadbddbabddbcbbbacabcccdcbdaacdbaadcaccaadbdadaaddababadacddddbbadbdcddcaadbdddbbaccacddbaccbbabbacddbbdcbbbddccdabbaabddcadcaaccbbdcaaacbdcacaaabccadbdaddddcccdaaccddbcdbacacccdccbbbcadabccaccadcbdbbaacddbdaccbabbcccbbdcaaacadcdbdcbddcabdcdccddaaddddcbaddbddcccdabadcdcbbbddddadbdacbbbcacdcdcdcccaacddbdcddadacbcbabaacadbdacccddcdaadbdacabccddcacccbbbcbdbcacbbcdabbbaddcbbaacacbaaddabcdbacabddacdbddaccbdbdbdcdacaadaccbcdcaaacdadadadaabbbadcdaddcdbcaaabcdacbbcbccdddcbbadbbddccdbaccbabcacbbdbbcabbdadbccdbbadbaddcbbcaaaabaacacbdbbcddbababadbddbbcdacbadbabcdcabbbccbdadacaaddbcbaacbabccbaadbabcbaccbcdadcbbcbdddaadddbbccbccdddaccccacccaccacbadccdddbdaacbaddaccbdabcddcdaabaccaacbacccadacddaaccddccbcddaccaacbacaaaabcacaacbcbbaccdcabccdbbbacbdbadbcdccdcacdbcdddbbccdbdbcacbdbccdbbdadcdcddddabdbcddbcbdabcdbabbcdddbbcbcbbbcbaadaaddbcacbcdaacdaabaaaccaadaacbdbcabbdbacccdbbdacaaacaddcbdaccabddddabddcababbbccabdcbabbdcabacdcbcbabaacadabbcbdddbaacdccdadbbcdcddddddcccdcbdbadcbaccccbcbacdaccdccabaccaccbadbcbddccccbccdcbcbcaaabdcaddadcabacccacabbbdbdbadadccdddacddcccbcdcddcbacdabbbdcbadccbcdcdbcbdaabbaaaaabcddacbcaaddbaabbaabddbcbacbdccaaaabcaaadddbcbbddbabbaccddbbcbbdcccaacbaaddcaddadadacaabdaacdbcaccaabaddbccadddadbcacaccaabbadbddccadccaccacddbbcacdadcccbabbbbcdbcbcacbadabbabcddacbbcdcbbcbbaaccdbcaabbbccbdddbbbcabbbcdcdabdcaabddaadccabcbbaaaaccccccbacbbcbbbcaacaddbdcdcbcbbadaaddacdddddbdccbbddabdcddabdbccacbcacbbbdadaacddacdaaabcdaabdbdbcccbdbacdbcacbdadbaabddcdacdcaddddbaacdacdaaaccdccdabdacadbdddcbcabacacaabbcbbbddcadddacacbaabdacabacbacdbbccbbcdacacbdbaadcacbbadbacbdbaaabccbbcabbadadccccbcdccdbcbcccddabccbccacdccdbdadcdddbcbbdccadcdcaacccdcccacbadbaabbbdacdddaabcbdcccdccdaccdcdbaabdbbccabddbddbacbadabbbbbadabcdcbcaddabbdaadccdbdbadccaacdadabbbcbccadddbacbcbacadddccdcbccbddadcacdcaabccdbbdcbadabcdbdacaadbacdacdcddddadcaabbccdcabbadbbcccbcdbcdbadcbacacbcabbdddadcacacabcbabdbaccbcbaacaaabaddbabbcabbcbaaacadcaabadaddaadabadccddddcdabbdadaaaaadbcdddaadbaadacaadaccaddbcacbbacbababcacddaacdabccacdbbccdbabbdbddcadabbcadbbcadcbaabbcddabbccddaadbdddacdbacaacdabcaccddccdcabdddcbdcbcbbacabbadadabaadccabdbcdddccdbbdaadbcabaaddcacbddbacabacbcabccbdbaddcbcaaaabbbaddaabaaabdacdcabccbcbdacddcabababdcdcdbdccddcbcdddcabaddddbaabacbddcbbdcadddddcdacadbbdddcbcaaaadcdababcbbbababcbdcbcbdbcacacccdddbcacdddaaaccaadddabcadbcbdbadbccbbdbbabbacacabbacddbcbabdbbddbcbcadaccabdbadbaaabcddaccacaaabbddbaabcbbbbcccbbbabcccbdbddcbcdaaadddacaccacbabccbcdbcabdbdcbadbbdcacbcadbdadcbbbcaccbdaadddbbdbaaadddadabdabbcacbdcdabdbabddddcdbadadaaacbadbdcbdbddbcbdcacababbabcdbdaccbccbcdcbbbcdadaabdcddcbdbcbcbbdabbddadbcccbcbbdbddccbbacbababcdcaabacbaacdbdadadaabdcdcacccabacbcabddbcbaabbcadcaaddaadcbcaddbbcacbdaddcdcaabbccbddaccadddbcbbbcccabdbdddabadbadaabcaccabadabaacaccdbbcddaaddddbbbadddbaaabbbbddaacbacdbdcaadabdbabadbbddcaaabbbcbcbcdbaabadcdcbaabcabadcadbacacaddcacdbabcbcbadcbdccdccdccccdadbadbdbaccbcdadbccbccdbbbacdbbbcddbbaccabacbaaccbbdbaccbcccdbaaaccdabbccabcbdbdacadcdbcdabacbbadddbbdacadcbaccdaaaadbdbabcabdcdbdabcdcbcbddadaabcbcddabdcbbcdccbdabbdcbbcddcadadbbcaacbadbdcdabaddbccabdaaccaaddccabccdbabcbbaaaadacdcddbdbbaacdbcbbacaadadbbbcbddcbbcbcacdabbbaddaabadbbddcdaadcddddabaadaabadadddcaadcbbbdbcbdaccddddcaabbcabdacccdbdbababddaaccdccdabaabcbccabdbbdbacacbddbcabcccdacacbbdddbdbaadcbddbcadaccadcdbdbbdbbdaddbaadddbddabbdadbbacabbcbdabbbdbcbdbddcbadbabdddaacadbccdcbcdbdabbabccdcdacaccadbaaacddadbddaccdbddccddadadbdbdcaaaaccddaddaabcaddabcddacaacaddbbbabbcbbcbbcbcabcdacbdbbcdcdcbddaacccbddcdbddbbdacaacdcbaddaaabcdabcdadcaabbbbcdbabdabbabbacbddbbabcbcdaccdadbbcbaabaaaaaaabbddcbcdacddaacaccaabdaaabbddacdbbcabbcbccdacdabbaabdbcbcabacbdccdbbabbbddcbbabdcacacbcbbcdddadacabdcadbcddadacbddabbacacacbdcabaabdadcdcdacbdbcdccbcdcaadbbdcacddabdcdaccddadbddaaccddcbccdcabbccaddadacdbccbbcddabcccddcdcbacdbbdadbdaacbcbbcbcabbaccccbcadbcadbbcdaccdacacdbddccaaccbadcbbdaccdccdccbaacdbcaaadaabbbdaaccdbdccbcabdddabdbdbacddddabbbbdaaaacdddabcdbcaccccbcabadcbcdbdccbadbdcabbadacdcababbcacbdaaadadaabaabdddbacadbacdccabbdadcadcdcccadddcbbbcddccabadcdcccbdadbcaccabbbbcacabcbcbaabdabdacadcaaaccdabaccacabdcccddbaaddbddaccdbcddabbadbcdccadcdbdabdccdddcaaaacbccdbdbacdcabcdadabbadacbcddbbbadcaaabdcdabadddbaddcbaadaaadcacbaadaaacaaabdbdcadcdadcadcbaaadaccddcdbcdadbccbdcadcabaccddbaabbcccccbabbbbccdccdcbcadabcabacdbbcbbaabbacaadbdaadbbccbbbcaaacbddcbddaadaacbcbbacddbcbddabddadacdcccabddcbbaaaaddccbddaddbadddcadbaddddccacddcaaacdcdcbcccccacaabdabbadccdbcacbdcdbcabcdcbbbaddbbdacbddbadddcddaaacdbcdddbbabddcabbcbdcaccaaaccdcabbbdbcacadbcdbdabcbdacddbcbdcaabbacacabaadcbcbbccbacadbbbaddadaaaabbbacaabccaddaccbbbadcccadbdacdcdcacdbddbcdacbdacbdbabdbbadbccddcddacacaadabcdcddcdddbabadaacacccaacdabdacbcbcccdbcacccdacdcccbccacccdbdabaacaadacddacdbcddcccddccbcccbcbcabdcbcccdcdddcbdadcabbabcccacbaaabbcabbbddaabadcaacddaabacbbcdacabaacadcbcbbdabbaadaabcdabacbbbaacdadddbadbdbdbbbbccaaccdaaadcbacabdcbbdbbadbadcdabdbaadacbddaaddbcadccabcacbacacbaddbbbdbcdcdbabcdbabdcdbbcbccacabddbcbabcdaccdbcabddadbdddcccbbcbbaadbdccdcbcbcddbaacabdccabcaadbbbcacbcaababcddbbcbcdadcddacddabdbcadabccdaddbcccdbaababacddababcbdbabbbbdcabaaaccddbacadaaabbddbcdbccabacadcdadccddabcaaababdaccccddacaabaacdbabbbdcdacdaddbdbdaadddbdbcbbcccaddcccdbccccbdbdabaacaccbddbccbabddbbaaacbdcadabddaccadaabbbacddbdabcbabdddadaacbdaadaddaadbdbaabbbadcbbddccaacbdcdacdaddaadcaaabcbbdbbdbdddadbdbbdbcdaccaccddddccaaaaaacbbabbddbbccacaaaacbbdccbcbacbbbbcdcccccadacccbbdcddaddddaadbcddaadacdcbabaddcddbbdadcddbdadccaaddddbcbbdddadabddaaddadaaaccbccbbdaccadddabbacbcbbbbdddcbdcaccdbaccbdccbcbccdbbdcacaabbdadccadbbcddcaccaccdaddddbbbacabcdaccadbdddbdcbbcccbdadcccddadcbbdcdddcbadbcddbbbdacbabbacdbdabcabdcdcaabcdbddbbadbadcdacabdbbbccdabacbcdbbcacaadddccaababbdacaacbbbacbcddaaadbbabbbabbddcdddbcacbadacaaacdbbcbbddbbbcaccabacddabddadbaaadddabaaacaabcaacbbdacdbbddbdbcdbabbbdbaddbaabcbdcdddcbadcdbcddddabbcabddbbcacabccaaaccddccaaaaabcacddbddbdddbcbabdadbdbddccdcaabddabcadcabcddbdadacacccbdbbbbddabcaabbcdaadaaabdcbbcbabcddbdbcbdcbadcbdbadcacacaabbbcbcacbbbacbdbbacabbcadaaadddccbabbbccbbabcbabdddbdbcbbcdaadbbaddbacdbdbdcdaccbbdacbacdcabbbbcbacbdbaacbddcaabacadbcbddcddbdcbcacbddcbbbdbcadbcacdccdcaaadacccdcddccdbbdadacabadaabbbadbcaaddddaaadcbaccadcbacbccbbddacbbdbdabaaacdbcbcadcabadcdcdddccbadacabaacdaaaacbcdddaddabddacbccadcbaaabbbacabbccbccabdaddacbaabdaacaadaccabdcabbcdcbbdadcbccbaaaacabdabcdbdbbdacdaadbbcabddcabababbdcddacdddadabcdaacabbcbccbdadbcbbcbccbbddaabbcaccbcabaaddaaadababdacdaabaacadabadaacbcacaddcbbcbccccdcbdddbcdaaabaccdcaadcbcdbddcbdadddcbbbabccaadcbacbabccbdabbbdaababdcdbcbbacbbdcccabdcddacbccbbdbbcccdadabacbbbcccdbdacaacdbddadabdbcdcbadbaadbcdbacccdcaacadcbccdbbacabcdbbddbbacbbcdbdbcccdbabdbbddbcbaddabadcaabbabbdacadbcbdddcaabbcbbdaabdacbcaadacdccbdcbaacbabadcdcadaddacdbabcdabdcbdcddddcacdcbbdccbdccdcdaabcaddcacddccbbcabdbbbbcacdcbccdabaccaadddddbcbbdcdbdcdbcadabccccabacabcbcabcdddbbddddbddbcccdcccaabdbbbbdbdddbcdaadbbabacadadcdcbabddbccdbacbcdcbdadbdbddccdadbbbbcbacdabadbaaacadbbdcdabdcccaabbdbdadaacdbaaaaccbbcadccbaaadacdaabccaddcdadaaddaaadcacdbcdabadbbdbddaaccbadaadacbcaabcaacdbccaabbbccbdcdaacaadbccdadabdbbbcdbdcbabadbcbdcbdbdcdaaccccddcbbdadcdcdbdbcddbbdaccadcbbacbadccdadcadccbadaddaddaccbbcabbadbdddaaacdddababbccdbaabadaacadcdccdaddacbcbabccbacccdddadbdcbaccadcddcddadadddcadabcadbabcddaddddadabbcbbbcdcbabdbaaadddcddcaacddacbcbcaddbccdbcaaabbddabbbabcdbdddadcddbddadccccbcadaabcbcdcabbcdaccaabdcaccaacabaccadcdcdbdccabccaddddcaacdbacbdcccaaccbcabddabbddbaadabaabbdcdbdcabdabbcdcbaacadcabdcccbcccadccbdcbaaccddadbcbacacdbbccdaddcbddadbaabdcbdaadbabacadadbdcccacacccaaaccdbddcbdbdbbdbdadbcddabbcbddababbaabaaacdcbabbcccbcddaaacbdcdddadddbdcbcadbabacabbdbcbbbadabddddcbdddaddbaddcdccdaddbaaadaaadabdbdcdacbdbaadbdbacdccddbdddddababababcadcbabdbcdabddabdbbbddbddbcdaababdbbdcccbbdadbbddaddcaadacdccabcbbdbbcacddacbbddadacabcddcadcdaaaaccbdabacbaadbbdcdbadaaccabdacdbdcbdabcdbdabccdddabcaccdbddaaabcdccdbbbcbadcadadbacaacdbadacdcbcddaccdcddbbbbabbbbacabbbaccdcddbdcadbaaacbbdddaacbddcdbadbaacadaccbdbdabbcddbcbacbdbccccddddadcdcbccbbaaccbbcdacdbcabadddacbacddcdcdcacdcccbdbaaddbaccabcaaacbcccabadacdbccacabcdadadbbbcbadadcddccdcdabbbdaddaccdbaaabddaababcadccdbbaddaddacddcbbdaababcdcaabcbccdaabdacaadddcbddaacabbaadbabcdddaadbcddcabbbddabccccbbbaabdbabdaabdadcacabaaabcccabdcdaaddcaadaacbabddaccadbaccaaaaaabbabbcdcdddddbddbdacacdacdbbcbdbaccccabaccadbdbdaacabcdcdbbbcbabcbabdacadcbbbaacbcddadcdbdbabdbbabdddcacadadaccbadbcdddbdcaacdaaaccaaaaddbcbcbdadaabcdababbabadcbbbbabcbbbcccccbccaaddbadadbccbcdddcaddabacabdccaddcaacaacbacbcddcbbcaccabaddcacacaaaacbdcabbabaabdcadabdcbbbbacdbdbdbbaddcbcbdbcbcaccbbabbcddacccbbbddacbbddbabcdcdcaaadbbcbdccddddadbbdcaddbbadbdddbccdbdadbcdddaddbbbcddbdccddbddbdadbbdbbdabdabcdcddcdbdbcbbadbaddabdaadaabcbacdcddbcadbcdddcaaaaaddbbddbbdddcdccbaacdabdbddcccabbaacbbbbdaccadaccbbdbcdbaacacbcacddbdabaacdcddadaabdbdccdcabcbaabadacacbcacadccddbdcdcbabccabbdabccdcaccdccbdabbdbddcddbddccbacbcadcabccbdbcabdcacadcdbadbcdbcbabdcadcbdbabbdcdaccabadabdbcdbdbbcabccbbdbaaccddbbabdbbccbcbddcbdacbdddccbdbcabbbddcccaadaccbdbdcbdbbdacadbabaacccdddbbdbadadbdbdadbbcccaaccdbbbbaccadbbdaadaaaadadadcccaadbabaababbdbcbcadbdddbabcabccdcbbbbbcadbaadcdacddaaabccbcdcdcbcbacccaddcabbbabcbbccbdbcdcabdabcdcaacabadadacccbadccbadabbccdadbabcacacdabacdbadacdbadcccadcbdaadadddddbbbabcabbcbcbbcdbaaadbcdabdddabaaccaaabbaabacbdaccdbcdbdccdcbbbdabdccccdbbbbdcaddbbacdddcadabbacddcddcaddbacbdccbcdbbaabdbdacbaacbbadbdbdbdcabbaaacdadaadcbaddbbdbadcdccbcbbadabccbccaabcdcdddbccbcccaadaaaaabdcbaabdbdbdbadbbcadbadbdbdcddabddadabddcdadbcabddccdbccacabbccbaabdbdccbcbabdcccabbcbccadccbcccacabacbbddcdcabcacaaaabababbccbcccababcbdbcdccabdaaddcbabcadddcddacbcbdadccbcbbcbcddbaddccdaaddbbdcaabdaddbdadcdcdbcacbccddacbcbddcbdcbbccaabbadadbbcccdaddbbbbacccaacdaccddbdaccacbddcabbddbbdbbacadbabbccbddbbcdbccbcbddcdbbcdbcdbccadaddacdcdbadabdcbaccacccdddcadddddbabddcdddcccbdbbababadababcacaccbacaabcccbabaccdcdbccbcbabdccbdcdbcbbcbdaacdadddcccaddaaccbbdaccacbacbdaccdadcbdcbbcdcbdacadcdcdacddcaabdcaccbbccabcacdddaabcacbbdcdcbcbdccaaadbcbdbbccdccbdaacbdddbbddcabbdaaabadcadcaccabbdbdccadddacbacadbadacccdaabdaabdccbadcaccbaabdbcdacbbacabdcabbbdadddacddaacadabababbadddaabaddbcaaaadbccacbbaadbabdbcdcbcbbdadddcbddcaacbdbabbddaadbdbccaabacddddbbabbdabaaaddddccaccadabadbcabbdcacdcdababdcbcacaadbcdacbadaabcdbabaaaadaaaddaaaabbbbdccbdbcaccbbbcddacddadabddadcdcdbbcccdcaccadcddadbbdbdddbccbcddcbbccaccdbabbddadcdbbcbddbacbbacbcbdcdbadcabddcdbbabadbddbcdabaccbcaaabdccdaadbcbadaabccbbaddcabccdbabddadbcccbbadbbcdaabcbbcbdbdbadbdbddadbdadbbbbcabccccdacaacadcbddadccbabccadbddabcacdaabdbcdacddbadbdaacdcdaadcdcadddaacabdaadccacadddbbdbccbabadcaadaadcdaddbaaadcbdbbaaadcaababccdcccbbacdddacbabdccaadcbbbcabadaddcacabadccacccddadbddccacdddbacaaadaccdbaddbdcbacdcaabccbdcccadbccbaaacdcdcbdbacadcbbcddadabbbddcddaaccdddaacdcaddcbdaacccdbaaddbdbbddcddbcccdcbddcadccbdcccdbdbbbaddaaccdacbaabdbcdbcdcabbcbacdaabaddcbabdadaaaabacdddddacdbbdbcaaddbdccdbdacbcbbcdbbbacddccbaadbacdcbbaccaabccbcdabccbcbcaacdbbabcccbdddaabddddbadacadabdaddabcaadacabcaddabdcdcbaddabacabbdcddabbbddcbddcbbcacbcbccacacaaccccabccbcacdbabcbcbacaddababcabbdcccadbbcdbccbaacccbacbbdacbccbbbdddadadcaadbbbbccdcdaabccaaabddbacbbcdbbbaabcbabddbbbbbcdccbaadbbbbabcaddcccadcbdcaabdacbdccdbdcaacaabbadadccccacdccbbabcaaccabbbadaadbcaccaadbdaabbbbbbdcdcdaaddcddddddbacabaacaccdbadbacbcadbbbdddaaccbacbdbcdcbcdbadddadbcccadacbbaddbccadadddbdccaaabdabdccbaadbaadacbaaccadbbbabdcdddbcbbbbaabbccbdbaddbabacaabbbdcbadcabbdccbcdccdaddcdcabdcdbbdcccbcdabddcadcdcadddcddddcbabdacdcbcdbddccabdcbdcdaddccadbabddbabcbadcdabbdcdacabbacdbabbcdcdcbccadcbcdcbabcacbcadadddcbccacbacdcddcacacccdaabadabbabcacdaadaaabaacbdabbcabbcdabccdddbdbbaabaadbabdbbbadbcbadaaccbbacdddaccdddccacddaaccaddbadcaabaaccbccddbbdbbcddbbdadcbbacbadcbababdacdcacddbbbaccaaadadaacbdbbabaadaaccbcdbadadbbdabbddcbbabcbcbacbbaaacaaabbcdacdcacdcabbdadddccdabdaababaaacddcaabcabbadacddcabdbdbccbdbbddbcacadbaccccdcdcaddcccaccadcacabbaacdcaaccadacacbbbcbdcaaabcbbabbdccdcbaabdbdcdcdcddbcbbbaaabdddadccbabbbcabddbbcbdcbbccdabccaacbaadbacbcdccbbcddcdccdacbcbdaaaccdacbbdaabbbadcaddddabbdddabbdbaccddaaaabaadaacdaabdcbaababdcdadddaadcacbaaadbbacbbdbbcabcdddcbdddbacbcaaacbdcadcacbcdbbdddcbbacbbddcddacbdaddcdcbbcddcdccbbbadabbdcddddcdaabdddcdbabbdbbacaadaaadaaaacacdcbadbdcbdccacacaaaddcabcbcccaabddbaaaaddbcdcddacdbdccaaaadddcdacbddbaaacbaabdabccabbacddbdacadabcbcddbdccbacbddaddcdaadbaacbcbdabacbaaaadcacacdcbaacbcdddbddbdbbddcbadaddbbdccdccbabacadccdbbbabbdbbabdbbadcdbdbbbbcbdcadaddcbbabbdabbdadbbcccaddaadccdbaddcbdadbbacacaaaadcdbbcdaddcbbcbddcbccbdbddbdbccdaacabbbdccddbabaabdaaabdbcccbadddcbdabadaabbcdbbcaacdddbbdadbdaddccbcccaddbbddaddbbcbdbdbdaacabbbcdacdbbccbbacddacdccaabbdddcbdabbbaaddaabbddbcdbacddaabadcadadcabdabbbabcaaabbbdbacababdbccbdacddddaabcdbdbdcacdcbacabdaddaacddcabbbadaadaaddbbdbbddddbdbcabaaccddccddacaaaabdcadbddababbdcacaaddcdddcbccdaccdbdbddaabbadbdddbbadcbaccdccbacaadcadacdddbbbdaddcabaddabbcccbcccacadcaaccabbcdddbcaadbbcdbdabcabbcdddacbdddcacbcdaacdacadddddaaccbadacddcdacbabdaaaaadddaaabcaaddcaaaababdccbdccadbbccbdbaaddaccdababbcaadcdbadbacaccbabadcdaddacdcbbadacccaacdcbcacadadddcadccabdcacadbcddddaabcabcbbcaacbbddcacbdcbddaddcbbbaadacbbdabbacbaccddccdbcacadddddadababbdbcaabccdcabcbbcdccdcadbdadaddbabdbccabadcddacbbdaabcabcddccdccdbbdbabbcaccbccadabbdcdbcdbdcbcbbdaadbddccdabdcacbbcadbabdcccbbbbcbdbaadabaaddddcaabcaccbbcdbbdddbdbcabdbddddbcbbaaccbadcddacdabdccddadccacbacadadbabcbcbbbbbcddbcdabbadbcccaabaacbbabbacdcacdbadaacabbddaccccbbcbcbbdadcbbbbcdbbdcdcbcbcbddbdbaabdcdcaabaacaaddcabaaddadadbdbbacdbdbcabbbdbbadcadaaccdadbccccccaaaabddbdbadabccbabdbcdaaccddccacaacbbcbabcdcbadbacadccabcbaabddacbddbbaabadaccddadaaddbdbadbcdbbcaccbbdccdbbccacbdacdbbcadbbaabaadddbcacaabcbdcaaaacabcdcaaaacadbcbabddbbdcadadbadbcadddbddcbcdabbaadacbcdacbadbdabbbddabbaaddcbacbaabcadbbbdadcabacdccbbaccbcdcccdccabcababaaddccbaddbddcdbdcccdacadbcbabcaddccabcbabbbbbacadcbddbddabcbbdccccdcbbcbddadcdcdbbdddaacbcabcacadbbabdacbbacaddbdddbccaaaddaacddccaccdadbcdaccabccabacdddadacbbacddccbccaccdbdbdacddaccacccdadadaacbabdaccdacccbaddbdaacaadacdbdaabbccdccbdddbbabddaacaacacbdbbabcdbcbcdbacdabadbbdbacdadddcaccacdabccdcbdbdcadcacaaaabccbaadcacabbdacbaacbadbbbaabcddabdacbcbaacbcbbacdbbacabcbdcbcabbdbdbcddcdadddaadbdbcabcdadbdcddbdbdbbdbcddbcccdacdadbadaddcbdaadbadaabccdbabcbccbcbcdacdbcabdadbccadcacdadaddcaddddddcaccaacababcbdbdbbcbbdddccadbdadbdcabbbbcadcbabcabdcbbcaaabdbddcdcadddbdcbcadaadbdbccaadaacbaaddbacbaabacbabdaacdadcabbacabaabaacddcbcdabcddcdbbacbbdbbaacdcccaacdcdddccddcbbadaddababaaddbddbbbdbbdabdcdabbbbadccdabababbbdcaadbbaddabaacbdcdbdadadddcaaadcbddcccacbdccdddbdbcaacabadabdacdcbabcccadddabdadaadbdabcadcdbaadcadcbaaabcabaaadbbddaabbcbadacdbbddcaaabaadabcabbbbadaabccadccbaacacaabdcdccdbbbabadccaccccddbccdbcdcbcacbbdadbaaccdcdcaccbcdcabdccccbdcadacbabcdadcbddcabcdddabaccdaabbdabcdbddddcddbaabdbacacaababacbbaddccdbbcbddcdcbcdbabdaaadaadbdaddbabdddcbbcacaacbdbbccdccdbccabaaaadaaacadaddcdddaddcabcaaaaadadabacbbdcdbbaddbdaccacacddabdaacdbaddbaacdcddaaabcabadcbcababcccbccabcacabcabdcabccdababadaccdccdacacbdabdbaacadbadabccadaccacccbaccbbaadccacaaacddcdbdbabcbadabcdaacadbcaaadcaccabcddbacbdbdcbbbcdbcabbbbaaadcbaaadbacabcbbcbcababadbddcaddadcdadadcaabaddcdbbabcaaccadaaadcccbbcddacadbcadacccdacbcddacdccdddadcaaadbcacabbaddcdcaabdcddadbcabbdccbbcaaaabbdcdbdadbcccddcaaddbbacdbdbbbcbccdccbbbadcbcadaaddccdbcaaaccddcbadbccdccabcaacabbbdbbababddbcddddcdbacdbaaccdabcdbbaddadabcaadbddcbddcdbdbcccdcdbcbcdacbddacdbdabcbcabadaabdacadbbbddbdcaadcccdbcbcbdcaacddcddbbabbcddddbcdaabaccdcdabcbbbddbbccaddddcbacccdbcbabbababcdddacbabdbbbacddbdccaddbaccadddcbacbabadccbddbadbabaadbbbbddbacbbddbbdacaacbbbcbaacadabadadcbdcdaccddbbcadbaaadbbcdbbbaaabbbdcbdddddabbdbbbbbcdbdddcbcbdccbcccdabcbcbaacbbabdbbbbbdcadbbbabcdcbdbbbddcbadddadcdacbdacbdbbcddaddaabacbbddabdbbbaabbcabdbdcbacaaacabbdbddbbdddbbbdadcccdcacaabbcdbbcabacbdacabcbdbcccacbdddcdaccbbcbacbcababacbdbccddbadbcaabbcdabaaccbcddabbbacddadcaddaabbbcdbdbcdcbdbdaddccbbaaacabcbababbdabbbbbbbddccaadadcbcdcdabaddadaabcbddbaddcddccdbcabddbacbddddcdcdadcbddcbbcddabddcdcbdbbbacbbbbadacdbddbbbabbdacdabcaabbccabcabbbdadaaabcccbabbadcdddcdbabcadccaaaaccbdddaccdadbaaabcbcdccbcacaaabdddcdbdddddacbbbcbdbccdbcdabacdaaaccbcdcddbbcddcbadbacacdcbaddadddccaaccbacdaabcbaacdddaaddddbdbdcbabaabddbbddbbbadbbdbbadacabdaddbdaccdcacbabbbdabcbadabdbbdacbdccbaddccdabdbaabbcadbccdcdabdadbbdaabcccbbaaddcdcaddabbaaaccbbacbadabbddccbcdddacaddaacbabccdaabcbbacdbadbcbadabddacdbbcddbaabdcadbcddabddbdddbaadcdbcdaababdcdbcdaccbaacdddcaddacabcbcccbcdaddccdadccdadbcaddcbbdddddadbbacbbaaddbacaccaaaacbadbaabddaddcdcdcdddaccaddacdbdabcbcbabaadbacbdbcaddcccbabdcbdcdacadccbdaccaccaccbcbaccccaaddbdbabacaacdabcccdabdbbdcccbabcccdcdcdcbadadaddccccaccaddadabcccabababacddcabbcdacccadbabacaaadcacdacbdabbaabbbbabbddcbdbbbccababbaabaccabbcadbccdabaabbacadcaddcccdaddbadbabcbbacdabacacccbbbacbaddbcccacddaccddbdddadddacadccbddccacacabbabdddadcabcbabdccbabbdadddabdaadacddbdaaadbacdbadadacccabaabbaabccdabdbcdccbbadacdaacbdcdddcbdbdcbbcdaaccbbaaadbcbccadcacbccbdbcdbcdbdbddacdbddccabccbbcbdccdbbcbbabbdaabbabdcbcdcbacabcabdcaaaadbdbcacabbbdccbcbacdbdccbcbccdacdcbcaacbccbcbcbdcdcbccccbabbdbadaadbbbbbdbdcdcbccacabbbacabbbadacbbbbbdbabcdabdaacacbbdbdabacabcdccccaaaadcbabcddaababdccdaccddddbdddbbaacbcabdacacaadbcadcdbcaabbaddbddbadccbaabbdbbbcacdbbccdbbbccddbabdabccbababdcbcdacabdbabaadbdaddbccccbadbdccddddaacbbbdaaababadacabcadbccdadbcadbcabdcabbbdcbaaccbbdccbbcabbccbbabbabbccaddddbaddcbddbbcbcabbcabaaddbbdbbdcadadbbdaccaaadcdcddcbdaadaddadbcabccbcbddacbcdcdbcdcccdbdaddcdcbdbbaccaddccdbdcabbcbbcacaabddaaccddabdcdbcacddaaadacabccdccddabdbaacdbbabccadaacabcbdaccbdddbdcdccaacacbcdbcbbcaacbdbaaadaadaddbdabdddaacdacdbccdadbccadbdcbbddaadbbadadddcbaddadadddacaacdbacdaccbdbdabcbccbdcaabdabaccddbabdddcacbddcacbdcddbcbbbaacbabbcdcacdbcbddcaaddcbababaabacdcbdbacbcdababcdddbbccdadddadcbadbbdbbdaacadabcaabbadbabdddcbabdcbdddcaacdbabaaaacaadadadcdcbcaddacaabbbcdaabcbdcddbdbbcbacdcbcbbcdbdaabdaabadabaadaaccbddcdbddabddcaabdbacadbcccbddcdacadcdaadcaabccabbccacddddbacaaddcccdaddcaaadddcbadbdbacdabcbcddddbdcaddaadccccacddadbaaaacdadccdbdbacbcddbdabacbcdccbccccaccdcacacddbbaabbcdabaccaddabbabbbaccdcdcadccdcbadaacacbcabcbccccadaacdcaccddbbbccadbccabcccaabcbbdbbddaddcbbccacdddcaacbcbadccadbaadacababdacabbcaaddbdbdadbacddbaccacbbcbcabdaddcddbdaccdacaaaccabddddccaccdbadbcadaddaaaabadddcaaacaadcdcdbdbcdaaadcbdcaadcababadbbbddcddadaabdcaaabdcdbcbbbccdbcdacaaccaabdccccadcaaadccacbcdbcdbacabdacccdbcabdabcbbdbacbdcaddcddccbccbaadddbddaccdddcadadacdcbbadacdcbbdbacaaacdbbaabbbdaacbcdabbddcdabbbbbabddccbbbdaccddcbdcaadaadaaaaadbdbddacadcbcaaadbccccabadaccbacabbcadbbccbadcbbadccacbabbdacbdaacabdbcddcaacdabaddcddbbdbabcacdabdcadcdcdaddacbdaadcbcbcdbabcbbaaddaccbbcdccadaadbcbcacdbbcabccababacbcaddbbbdcaabadaaddbaaabcddaddabadbddbdadcaaddadabbbbddcbbccbdcadbcbabcdacbbcbccbcaadbcaadcbddccabcacdccabacadaabbdabdbccbddaddaadcbbaccaaacccdccaadddcaaacbabdcabaacccdbdcdbdadcdbabadcccbbbccaccbacacbbdcdddbdbbcbaddbcaadbdbbcccdbbbbccdbbbbaabaccbcbdabaddccdabbbbccaabbcdaddaadbdaaadccadbcbbdbacccbadadabddcdbbdccbcdabddabacbabdaabaaabaacccaadabdaccdbbbdbccdaabdcdcabbbacabdaaddbaacbaadadadcbcacbdccbcdbbcdddabdbbdddbbccaadcbabcabaabcbdbddaaadccaddcbcdadcbaddabbcadccdcadbcdacbccbaabbddbcdcdbbbcdacccabbaadbabdccabcaabcdcbbdabdaaadbaabacdacaabcbdcdcbcbbaaddabbbaaaabbcdcaabbcdccdcadbddcdacbccbccbdacbcadcbdbbadaaacdcababcacaddbdcdbadadddcdaacdbadacacaadaacabdadbcbbddccdbcaabcbdbbabbbccddbbdcadbdadbbbbdbddcaaadccadbcbdcccadcdaadabdbdccbaaddcaaadacbacbababbacdcdddccadadbbaabdadacdbbdbcbdabcaddcbbdbddcdacbdadbaadaaadacdddbdabbdadcbabbaddddbcbdadbcdcbdcbacadbadcccabbdaccabcbdbccabdbbdadcccdadbbbbcabdccbdbbacdddbccbadabcbdbccccacabaadddcdbdaaaabccccadbbdcdbbbadcdbcccbaaabdbbbaabccdabdbabddbadaabcacbbacabadccabcddbcdcdaaddddcaddddbbddacaabbaadbdcbaacbaaccdccaacccdaaabcaddbaaabbbadbacdcabdadbcdadcbadadbccdddccbcdaadbcabcbacbdaddcbaadaddaacdccaddcdcaadabbbaaacbbdacbaabdcbadabdbdabbdbccbbaccbbacadccbcbdabcacbadabacaccdcacdccccbdaacacdabbbbdaaacdccbdadcbbddaacacdbcddcabddcccabdaadbbbdcadccadbcaacbcbdcacbadbbcdbdddcdddbdbbcbbbcbbbccccaacbdbbdbddcaabbcadabdabcccbadccbcdaabbccaccdcbaadbababcaabcaddbadababacbdcddcbbadbccccaddbababdbbbbcbaadaddbaddcbbccdbbbcbacddcabdbbcbcbbacdcadabacacaacaabadcbbbbcbadcdabadacaccbcdbbbaabdbadabaaaddacadbbabacbcdbbcdacadddadcababddbdddacbcbcdddcaaadddbcccbbcccadccdaacadbcdaabcabddbddcabbdaadcaddcababaacbacabbbcdddcdddadbdabdcabdcbcbbacaacdcdccbcacadddccbaadcbcdddcdcadaddadacbcdbadcccaaacccbcdcccbcabaadcbdddaaacdccbddcbcdaccccbcbbaaaaabcbddcbccdcbbbcaaddcdbbabadbcaddcaccdbbbdabdbccaddbdbbdabbbaacbddaaaaaadcacbddcbacaabcbdbdadccacaabbcaddbacbbcbcdbddabadbbabdcdaababcdbacdcbcccabbdadadbacbaabacbbacdcdbcadbaddcdadddacadababadcddaaaddbbdacabdabdccdbbdbacaacabadabbdcaabccbdaacdadddccbcbaabdcadcadcbbadbdcabddddadadbccbaadcadcacccbbcccbdbccdbacdbdacccbcccbcbbbdccbdaadccadcdbdbddcbabdcaabbddacbbdadcbdcbccbdddbacddddbadcaabaadadabccaadacddccbbdccbdadcdbbbdadacacbbccccbcbdbdabacaddabaabddcadacbadbbbcaabcabcacdbcbabaccdbcdbaadbddacbbccbbaccaabbacbdbdcabcbcacadcbbcbbccabacbbdbdbabdacdcabdaaaccabbbdbadadcabaacddccccbdacbacbacadbdbbdcdaacadbadaadcadcbdccbdbaaccbdbdbabbadacdadacaddacdbacbadacbabbcacdccaadabacbdcdabbdbbdcdcbbbaabbdacbbacaddbbbcddccbadccbcbcdccccbcbcaccdcdcdddacbbabdcbcbaccdbddbcbbdabbdcdbbbcbdcadcbdddabacaccdbadaabcabbbaaaddcbdbbabcbdcbadbacdbcabcdaaabcaaadbacaabdabbbbcdcdcbcbccdbcacacdaddbcbaddcadbabddbcdaaabaaccdcbcaaabdabbcbcacdbdcddcdddcbcbbabdabcbbbaabdbdbcaadbdaaabaadcddcbddbbacdbacbacadccdbbdcdcdbadbccbaddadabdccacdcdbdddcdabbdacbababbdbcbcdddccccbababdbdcacdaababbadadaaaddacddababbccbadadbbbdacbcbccadccadbadbdbbbbacaddbbacccbcdbbaaccdbbdcacdabbcbbadccbbbddacbdbbdbbccadcbdadbbccccdcbadaddaabcddbdacabacbdabcabacbcddbaadbdddbcccdaabbcddcaaabdbaadcbdbdbdbbacdbddccabbddadbccdbbbdacdcccbaccbcdccdccbbbddaaddabaacbccdddaddabacdacdcbbabbdbadcdddacdccdaadbdcacccccdddcbaddcacddbadacadaaabcbaacabacdbaaaaaccddabcacabdcddabcbcaabbbbacdadcbadacdacdabbddcbddccbbdccbcababdacaacddcbacadcadddadadaadcbddccbbbbccbcbaaaaacaabacbcaadacaacbcbccbddcdcdcdacbbdbbcdddbdcdacaaabcdacbdbacdcccaabadcbaddaaacdcdddcddcddcaacacbbdbccbbabcaabbbccdcbdbbbaccabbddccaabacacdacdadaaabcdacbcbcadacdcacadccbccbbdcdaddbccbdddbddbcdbddacdaabacaadbccbabbbaacaaddbcbacacdccbccababaabdbcabddaabccaacbabadabddacdbadccacadcacdaaacbcccdabcdaacbacdbcacdabcbdbbaaddcccbccabcdadcbbccacbbddbaaccddbccbcacdcdddaabccabbbadddddccadaadbabacbbcaabdaaaaccbdddcbbbdccdcbaaddccabbbbcdadabdccbdbdbadccccabbadbdabcaaccacddaadacababdccdaacacbdaaadbcabddaabcbacbcaaacabcabacdbdcabbdacabdbbbcbbabdbbcabcadddadcdbaaddccbcdcadacccbabdbdbddacaccbcadaaabccbccbaddbaddcdbadbdcaccacbacadaabcdadbccbacbbcadcddbcbacbaadcaadacabbcacbddbcdbccbdadabdbccacbbccbbbacadbbdbcacadabddccacdcbdbcdbbccaadabccaadbbdabbabcdacdabdabcadccacbdbbbadadadbcaabcbdadaadbcddcaabccdccaadadcbacabaddaabdcacddacdcdcbdcbcbabdbcdcddbdbcbbbaadaaacdbdbccccacbdcbacaacdddbddccacacaadbcdacbdaacdbabaaadcdadbaacdcbaddbabbdddbddbbbabbbbcaacacaaadbacdccadadbccabbbdbbcccbabcabacbaddbbbbbbadbdddacabaccaaabdbddaabcccdacbcaacadcbacdbbdcaddcbbdbcbdddabddcccddbaaacbadddcdaaccbbbcaadbbccccacdaacdaaaacdacdacadacbbdddcddaccbcdbbacdbbbbddcbbaccddcabaacacdaccadadabccbabacccdbadaadddaacbadbadadabccbdcbbcaacadcadbabcacbdddbcdcbbbbbdcdbbbacacbcbdcdcbdabaddbcbccdcbcaccddcdabbcadcabbdbbcacacddabbdcdabdabcbccbdbdaacbccdbcdbbdccddbbdbdddddbdacaabbbcdabbabccdcdabcaabaacbcbddddadddabbbabbbbcbdbbabcdcabddcbcddaabaabdaaccdddabcdcbbdbbbddaadcadadadbaccacbdababcbcddadccbdcbbdddcdbbaacbdaacdbdddbdbbdcdcbdabdbbadbacadacdadcabbbdbbbaddbbacccaadaaccaabccddddabbdcddcdbcacbbbabbadcdbbcaaabcccbabcbcbdbcdbdddcdbbbdbccbdbcacaaddaaabbacabbbddbcbcccddcdcabacbcbdacccdaababddbcddabcdcdababdcaddccbbbaaaaabdacabdadcaacabcddbdbaccdadcabdcdcaabcbaadcdaadbbababadcbddabcdabadbcabacbdababccdbadcacdadbaaaacadcbcbbacaacbcdacbcbabddbcbddabbbabaaccabdbccbbcdaccdddccacdcdcbddbcacbacbbbcdaaaadcaabcccbddcccbadacccbdbbbbbdabdaaccbddcccaaacbdcdcbaabdbcadccdddabadcbcccaddcdcbcdbcdabdcccdbcbacaabdbccabdcdcbacabbabbcbcddbacaadcdbdccdccbddbcaabdbaaddbbddcdadbccddcccacccadcadcdabccabaaabbbbadacadbaadacadacacaccbdadacbacdcabcbcddcdbcdbcddbcabdcadacdaaaadccdadcaadbddcdaabccbcdcbbcbdcbaddaacdbbbdadddccabcadacbdbcdcddacbacdbabdbcdcabdabadbcbaabbbcbdcbcacbaddbdccbcddadabdaacbacacbcccccaadbbdcaababccbcabcccdcaadcbadbccbdbbacdacbdbdddaaddcdddbcbbacacdacdcabdacabcbaabddacababcdcaaadbadabcadbaacbadddbcdbdbbccbcbaddbaccbbadccdabbbabbaddbdbbcddddaadacacacbcddddccabdbbadabddccddbabbbcdcbbdbbacbcadbcccdcdbcdddccbcacdbcdabcbadababbabbdadaadbbadcddacbccdbacbadbaaddcdddcbdcdabcacadaddcbdbbdaccabbccdbaaaccbdacccbccccbadaddaddadcdbacaaadaacccdbccaadbcaacbbcaabcaccababbbbadacdbdbccabddbaadbdcabacabcaadddddaaadadccdabddbbaaadcbddbdccdcaccabcaabbacaacbcacbccdcdaaccaadbbccabddacabdddacdabccbdbcbccdcdacbaaaddadbbccdaacbcdaaabbcacdcbdabaaaabdcaacbadbdaddddaaccbcaccbacabbdacdbbdaddcacbddcdbaabbdbbdddbcaaccdbaddcddbdbdbddccaddbaddcaddcababacbcabccaaaaabddcbccddcdcacdcbcdbddbababdbdabdcdcdcadadddbddabdacbdacdacdacabacdbdabddccacdbbcacbacdddbddddcbdccabdbcccadddbdbbddbcdbaddacbcddccbccaddcdccbddbbbbcdaabdadacaacabadcbcaddccacdcabccbbccbbbdbacdbcbbccbcaacacbddaadadbbcbcdcaacccabdacbbcaadccccddcdbcccbdcacadcbbcdcaccbbacadcacbcbcabdcdcdbbddbbdbbccdacbddcbaddabaaccbdcccaccbbdadcbcbacdcdaacabadcdbccddabbbcbaadabbcaabbdadbcdbcbbacbbcaccccbdadcdddbdddcdddbaccbcadddacbcbcaabbbabdbccddddcdcbbdacbcdbadcacadcaaadcbddbbcadcbabdacabdcccadbabccbcbbcabbbcbbcddcdbdddadccbacdbdabcddbcacddcccdbdacbadaddbaccadababacbdaabdccbadacbcbdaaccccacabdddcbacdabaadaccccdbacbdbbcabcdbadcddbbcadddbbbaaaabcacccabacddcdcbbbababdcdcdcdcbabbcbcdccbcdcbcbccdaddcdcbdaabbdaddcbbbdbcbabacadabbabbbcdbdaadbdddaacbdbcbabdcbadccabbacabcbbcddcacccaaacacababcdbaaacdbbcbccdaccacdcdcdbbccddabcadbdabbcaaddbcdcadadaabcabaacbbcbdddcdbbcdcbbbccddcaadcdcddaacddcbcdbbccdcccbdadcaddbaccbbadbadccacdadcaadbdcabddbbadaaaacaddcdbbdccdaabbcabdddddcbbcccaaccbbcbbabadaababbaddadacbaccacdcdbcbdddabcaaccdddcbaddddddaccccacabaabbdbbcccbbbddabacbccddbbdbbdbdacadaccaabcdddbbccbabacdbcdcdbbcdbccadaacabacbcbdcbdbbbaddabcaacdbccadbcbcbcbcbdbcddadbbaddcccacbcbdbcadbadcaaabcccddbcbbccbddbcaddadbcbabdcdbabbbddccccbacddddacccaabdcacdbbadcacdcbacabaabbccbbcbcbdcbdbbbccaccaadbdabbcaddbaadabdaddcdbcbcbaaddcdbddddacdcdabaacddccbcaabccdadcbbddaccbbdbcbabbccdbdbacbcdaccbaadabdabdacaabccdbaaaabdccbcadbbbaabddabcbdddcbbcbbaacdddbaacdadbddacdddbbadccbbbbbbcccaccccbcacbcbabbabbbadcbcabcbcdccacccbdacabacdcdcccacaaabddccddaddbaccaddbacbcacabddaaccadbdcbcacbcbdacbccdbbcdcdbbaadccbaabccbcadcbbdcaacbbdccaabdabddcccbbdbdcdcddcdbbdbaabdccacdadcbbadacddaadccbddadccaadcbabcdaacdacadacdababdcdcdcbdcccdadbccbcbcdbddcccdbbbccaacbacadcddadabadbdadaacbcdcbbdccadbbaaadcaaadcdbadacbbccbabccbcdbdcdbddbcacdadcbbbccacbcaccdcbdacdccadccabbabbaaabcacadaccbddaaccbbbbbcbbcaacdcddacaddddcdbbbbbdcaccaaddcdbbcddcdcbbbbcddcabbdcdddcddabcdadabaabdaabcbbddbccdabdbbacddcabbdabcdaacabdbdadcadbdaddcdaadabddbdadcaddbcddbbcbdaadbabdadabbbbdadacaadabccddcbdcbdabadbcbabcccccddabcbbabadbaaddccbbaadbacbabcabcabaacdbacbcbabccaccbbbdbdbcdbcabbbabadabcbbdacdbdddadddddcdcbacdbddabbcccdbabbcddabbbcbbbdcaaabaacdddbcacccbccabbaccadcabcbccbaaaabdddadbdabcdbbbadccddcaaaabbcbacccdddbcccddcdabaaaccdbdbcdcdbcbcaaadaddbabbacdddddcdcddcdcbbcbbacddbddacbdbcdcabddabacddbbabddaaccbddaabcaccbdaabadcaddadcdcacbbdabccbbbcacaadaabbbababacddbcabbdbcbabccbbabdcacbcbcbdadcdabbccaabdbddddddaabaccadacacbbabbdacddcbcbcbdaabacbaddccdadddcbbcddaabddcbcaddbdccdadadaadcaaccdcbdabbddbdbccccbdcbddddadcdbadcdaddcabadacacdcadccabbbccbacacdabacbabccbdccbbcbacbabdaacdcdbdaaaaacdcaacbacbdadccccabcdbdbbacbcaabaabcdbbbcaaddbacbbbbbbdbdbadabadcbcacabdabddadcaddccaaccdccbcabdcacccacbdaccacabbcbdcddcdccdccbdbbaabccbbacbabacdabccbaaddaddabbaaaccbabadcccabdcabcbccdaddcbcdddcbdacbcaaacdcabdccaadadbdbacadaacccadcbcdbaccaadbdacaadbbccbadaabdcddcbcccddaaabbbaabacdcdbdacaabbcacabdbdccbcadcbcddddcdcbdbbbacbbcbcddaadbdbbabaccbddbbbaddcbcddaccbddbdbaddcbbcccbbbbacdcccadcdaddccaabaaccbbdddbbbaadadbdacccadbcaddcbadccaabcbdbdaacddaadabbbaacabadcabbbdabdddaccbaacddacddabbdaacbacddddaaabcdbcabbbbabcdcbbaadabdcddbacccdaddadbaddddabddadccccaccacdaacadcdbbadbbcaadcdddcddbbabaabcdbbdabbbdbbbaaddbabbbacccdcbdadcaddbcbabbdbbbcddbdabdcaddacdccccbcadbbddbbbadbccaccbcabbadabdaddbbabcacbbabcbadcddabcddbdaadccaadaaaccabaadabbabcbbdbbcdcbcdcddcddcabacdadcbbaabbcdbacbacbbcabcdacbdadacccbcbddabbdbcacacdbacbdacadcbadbccbdacdddadddccbdccbdadbbaaddbbacbcddddddccbcbddabddabbbddcdbacbdbcaadaabdbdcabdadddccacbcdbddaaddcbbcbcbdcdbabcbcdbbbcccbaadbadbaaabdbaaddacbcdbadddbabbcdbabcaadbbdadcdcdcacddaccbdaadcadcccdadadaccdcddabcabacaccabaababdcadbdbbcccccdadcaddcdcbcdadacacbdbababdcddaacdaaabbcbdbcbacdddcbcbdcccddaddacdbaccaddabbbbddcdbbccaabcbadaacbabbcddabbcdcdababcacdbbcadcddcdaddbacaacadaccbaabccdaaaaaacdabddadbcccdabddbdbacaacbbdccbcddcbadbadcbabaadabaccbcacaadabdbadbaadccabaccdacaacddbbcdcabdabbababacbabddacbdbacbabcacbaddaaaddadcbbdcaddccdbddadaccdcbadaabdbbbddaababcaccbabbbaadabaccdbddbdcccbbabbabdcadbabdbbabbcadaabcdadcdabbaaacddbcddddaddbadddaaddddaaaacacbabdcddacddcdbcdbdaddadbbcabcbaadaadabbdadaccdaadbdbadabdcabdaccdaacaacacacaabbbcaabbdcaccdcddbcbcddddbdbabcddadcdbdadadaddabbbdddaaabacddbbacdddbdcaddbcbcadabcaccadabcaccbbadaadcadaaaaabadacddaacdbbcbcaaddbdcbbbdbbddccdcdcbbcbbdcccbcacaacdbabcacbdcadbdcadcaaabddddbbaacbcdcbadadacdbbaaaddccbbdbadcbdcbdaddcdbadbcbacadddcdcdddbccabbccbacdcdabaacadbcbdabdbcdbaaccbdccabbdcaaabaabacaccbdcbbdbcbbcdbbbcaabdccccacbbcbabcbbcccbadddcddcbddcbbdadcabcbadacaadbccdddcbacccccbabcbcdcbaadcdbcadbcccaddbddaaaacaccbdbbcccabadbcdaabddacbbccaaacbbcaabbaddbadbbabdadddabddcbcbabdacbadbaddadbddbbabddbbbdbadbaacabbcdbcdaabdbcbaadbaaabcccbdddabaaadcbbcdcddcaaacdcadabdacddadadaabaabaccbaacbbdbadbbbcbbdabcdabcdddacaacbbbcaabbaccaabbcccaadacdaccabaccaabcaabaccacbdabdabccabdadabdbadcdcdabdcdcdbdbcaacbcbabdcdbadbcdabdcdcdcaccdaaaadadadbddcaaacbacaadcabccbabcdadbbcdabababbdbcdacbadbadbbdbddadacdbdbbaddcbccaacacaadbdbcabdacddcadaccacbacabbaacbccacadcccbadddaabddbacdcabbbadbbbaddcbdaacbcbbbaacbbababadbadbcaadddacaaabbdaadcddaddccacdacacbabcadccadaccaadbcacdcbcccabcdaccdabbbbabccccdcabdacacbabbdcbaadbababbcbccabadbbbbbdaaaccbcdbbbccdcdacaaacbcdbcddbcdbaadaddbdcbccbcacccbccaddcbaabcccbdcdcbcbbdadadccdbacacabddccdcaddbcaccbacdccdaadadacccaadbcbadbddaddcccbabcdacddaccbacaccacdbadbabbcdabdaacdccadadbbccccbdadbabdcbcbbbcbadbdaaccbbcadcdabbdddaadbcbdaaabbccddabaaadbbdaabacddaadadbcabccabbdadcabaadbadcadbaaacdabaaccabdadbaacbcdcbdaccdbcbbbbaacbbcabcbabcdacaabcadabbccbddacdccaaddabcacadccdaddccbbbaadcdcacdacaabcaabdcdaacddaaacadddabadbddbdabcacddbacaddaccbbcaddddbcdadccbaaabbbdcbcbbaabbddddbaaaaaaadbbdadcdcabcbcdabcdaadbbbdbbdcbadbcabccbbbbcddbccadddbcadaddbbdbdcbcddabbbadcddbcabbdbcadbcacdaadccbacbdacddddbdcddcdabcababdbbbaadabdddcddbaddaddaccbbbbadddddbabdbaadbcdcbdcbcaccabbabcdbdccdcdadbdbabcdadaabcbcbbdadaabdbddbaddccccbcbddacddcacaaabccbbabbdbcbdadaadaaccabbdcddccbbcdbcccbdcacaccaaabbabdcbddaabdbcdaacadadbbcdddaccdadbabacdcbbccdabbdaccacbdbbcdacaadcbbaddccdaccdcddcddbcdddbaddbaaabdcdbcbcbdadcccbcaccadbcdccccbdbbbbccbddadbdddcbbdbbbdbbbccddaadaadacaaaaaacbbdbbcaadcddaccdaaadbcaddcbabcadaacaadcbbabcadcdbabbdbcbabbdcbacaddbadcabbaddbaacbaaddcadaadcdaadadadcbdaaabadbacbccdbdbbbbadbddbacccdadbadbbaccacacbbbbaaabdabaaadcbbcbabdcbcbcbddbbcbcbbdbdabcbbdacbddddbccbadbdbccddccddacbabddbdddbbbdaaaddddcbcdcbccbbaaddcbbdadcbdcadbaaabdccddcaddcdbbcccaddacccbbbdccdaaabbbbcdacadaababdbbadcacbddbdadddadbbbadbddbbdddbdabbacdabbacdacdabdacdbbdbdcbbcdcbaddddacdaccbdacdaaccdaaabcdabbdbbbacbbcdbdcadcbabaacbdbcccdddcadbbbbcbabcbbaaddbaacdbabbdbdddaaaaaacaabadaabbddbbdadccbbcdcdcdcdbcbdacddaadcababaacccdcacabbbdbdcbbbdcaacdddddbabcabdaadaadbacabdbdadaacadadbbbbbcbcdcdbbaacadbcabbccbbdbcdbbcdadadbacaacdababbabcbddbdbbbabdbbbbccaccaccdcdaabdabaccadbdacccaacabcbbcbbaabdddaacbbaadaaacbcdbcaddadcbbbbccdbdcdbbbbdababbdacddccbcccbbaadbcadbcacccdccdbcbbdbbcdabbbbdccdbdadbcdbcdcadcccbdabaaaaaddbadbdcbcacacbcbacaacddaabacbaddabdcacbcdababbcddcdcdcacaccddadcaadadcccbbbdcdbcddbcccbaddaaadbacbdbbdbacbdcbcbbdbabddabdaabbddcbdacbccaadabcabccbddddcdbbddabadaadbdadacbdbbbbaaadcadddccccaadadcaaddcbacdcababbdddcaabababbdcaabacdabdcadabbaaabaaaadbccdabbbabaaaddddddbdbabbccbbcbbcaabbdadadbddcadbcbbbabbcdacdacccdabdbdbcccdcdacdbbcaaaddcaacccbdbcadbcbaaaadadddddbaddacaacdcbcbcbbbcbccbabaabddcbaababcacabbacdbcadaadacbbadbdaabccbabbddbbaddadabdadbdaddbbcabadcdcbdcdaaaadbddcbcddaadbaabcbaadcaccdcaccdcbbbacaacdbddbbcdbbbbbbccbaccaadbdabccbcbdbcbdccdabdacddaaacaaadadcbadbdabcdccbbbdddadbbaababaaacadcababadbcdabdababdddcbddcdbdbcacdbcdcddaadddacdccacabacbccdbbadacacbccdbadddbcadaacadcdbcabadcdaadcdabccbcddabbdbcccdcbbaccccbbcbbbdcbcbbdbdccdadadbcaaabbaddaccbbccccdabbdaddacabcbccbcddbddcacbdddabdbabccabbcdbabcbddcbdcadabdbcccadbbdadacbdadaacddbabcbdadababdabbdbdbcadcdbdaabddbcdbcabddbcbdaacaddacbcaaabbaccdcdbbbabccbbadadadcddabddaaaacbccddbbcdabccdbccadaadbacaaadcbdcbdcbbdbabbdbbabcbbbadbcabccdbdbcbcbbcdcbdcdaaacbacbbdcbabaadbdcbabcabdbdcadbdadaadccabaabbdababbcbbdddcbaabdcdabaadadccbbbadcaaabcccacbaadaaadaabbcaabbaabacbbadababcdbcdaacccadbcadcaaacbcdcbcbbbddcabdcadbbcbdacaaddbbddccdddcbacabbbddaadbbcdbcdadbbcbccbcdccbbdccbadcbacbacdaababcadbdccccbacbbdabdaabbabaadccdadcdbbcbabdccddadcacccacabcdbbaacaccadaadabccbcbcccbbcddcdaacadcadabdacabddccdcabbdaabcbddaabddaccadababcdabaccabbdbdbccabcdaddccabbcbddabccbacccaddcdadbdbbbbbacbdabaacdadabcadaabccddbcdcbbccadcbabacccbcaabdacdcdcbdbccdbabdccadacbbdaaacdbddbbadabaadcccabcdcadaababbacbccdcacababbaabcabacdbaddbbcacaaadccaccbcbcccadbaccbdaacbcdccbdcbaabbacdddcbdddbddbabaabacbbacacaadcdaacccabdbcdadbababbabbcbdbadacddadcdaaabddbccbbaccdcddaaacbbdacdbcddccdccbdcccdbddccaaccdbddbcbdddbbacbcbdbaccbdbaaddadbddbaddabadbadadaabaccbaaddcddabcbaabcacbaddbbbccbbaddaadccaadddddadbbbccbabbbbacababdcaddcdaacaccccdabbadcbdbcbccdcaddcbaacacdbcdddccbaadabbcacadcdaaacadddaadcabaabcdbaadbdbaaadaaabadaababdcaccadcadadbdcadbdcdcbdcbaaccdbdcdddcaabdaaddaadcdcbddbadcddbbcdacbddbbccdbdbdaaacdddcbabaacacaccddcaaccddcaabcabacdaccbcdcbbccddbbadcadbaddbddabcacacdbacdadcacbbccabbabcbdcddcccababdbbadbcdddddaccabadcbdcccbddcdabbacbddcacdcbbdddcacbadcccdacacbdabbbaadbcdbacaacdbbadccaddaaacabdbcbbadccaccdbbabacbddcaaabcbbaddccbcccbadaadbcdcbcccbbabdbbcdadbbdbadcaadddcccdcaadbacbbbababbbababddbbbdaadbcbcddbabacccddaccaccabbdaaacadbbabdcacaddaacdcdacdccadabdabacdbdaaddbbbdaabdaddbacabdbcacbcaccdcbabdcdadaaddbbbccabdbaacaddbccacddaacbcdcbacbacadbddbcacacdcdbacbcdacdabbbbacaadadbaaddbaddbdaddbcabcdcbdaadcddadcadbdbdabcadabddbaccbbcdcadbdacbacacddcbacaabacadbacabdacddaaababcdccbadccbcaccddcaabdbdccabaabdababdacbbdbccccbddbdaddcbaccdbbdddbccaabaacabababadcadbbcccccdabadbbbdcddbbcdbbcdcdadaacaaccaccccabcccaacabcdaabdabdcdbbbddcbacdcabbacabdcbdadccaadadcdabccdacbadbdbbbbcaacabbddddbdbacbdbdacdbdcaacdaacaadbdcbbcbdabbcaabbaaaacacabacdcaacdbdddddddbbbaaaaaddacdcbbcdacccddbacaacbbcabbdababbcbacbdbcabcbdbcabcccddacbdcdabadbbadddcbdaccbbddcbbadccdcabcdabbcbdcbcdccdaabacdbcacaccadccaacdbdbaabbacdabdadcbcacdadaabcdbcbacabaaccaabbddcbcbaacbdacccbbcdbbaddbddcccdabacbdacdbaadcdcaadabdaccccdcccccaddabdcacbddaaddaadcabdcbbbbadaababdcccbdaaabcbadbdabccaddcaadcacbbdaddcbbacccbadcccadadcaadbabbbcbaccacdddbacdbcccbcaabcbccbabccccbcadaccabdcadadabbabbadccdaaabaabdcbabadbbcbddcbdacdacbbdccdbaaacccbddbdbddddbbabdbcacabaabaaadbadccbabdabcdadbbdaabaabddadaabcdbcbbbccaddadaacdbdbcbbddcabdaadadacadabbbcacbcbbccccbaaabcbaaccdacbabbbbbadadbdaddaaaccbccbccdcbcdcacbcdbcdbabcddcdcccbaaabcdbddaacbdcaacdbabccaadabbdaadddccaaacccdcaadacbbaccccddbdccdadbbabaccdbccdadcdcbddcbbbbddcbacddbbbbdbbbcddbccdcbaabaabadbbbddbcaacddcbcdbcdcdbcaddbbacdaacaddbabccdbdddddbcbdcabbaaabaddadbadcdabdcdabdbaadbcbbaadbaadadbbcaddabbababdcacccccadadbdcbdbbbdcacdbcacddcacdaaddaaccdaddccbacabcdcbbbccdcdadaadbdddcbbcddcccbabbbadabdbcdbcacacabaabbaccbabdabccadbdbaaddcbddccdababbcbcdadddabdabdabbbbccadcadabbdadacadadacccabdcdbbcbddaccaadcbdbcaacabcddcbddcbbdadcbbccadabbddadadadaacabaacaadacdcbbbddacddabaaaddbbddabdbcacacddadcbcaccacddaddbbbadbacdbababbccabbdbdcdbadacdacadcdcdcbdbccbdccbccadbbcbcabdabcdcabbaccbddbbbcbcadaaaacdbcabbcdcbaacbbbdbaacbdcbcdddccbcddadbcaddcdcddcababacaccbccdcadabacbaccdccacabaabcddbdcccdbaaacabcabccaddaadaccabcadcababddcbaccdbabdadddbcbadbdcabadaaccdacdbbdbaaababbcbadaadadccadbcddadcdaacbadbdcdcaddbacbbaaccdcbbacbabacabbaaacbdcacaadbbcbdddacaddddcbacccaabaddaabddbaabccaaadacaabbddccbacaadcdcbaccacdbdabdabadaaaaacabbabcacdabcaddcabdabadbddcdcbcbbcdabaaddbbdaaabdcaacbcdcadcdccaacdbddaddcccbbacaabbabadabcdaddbbcddcdddadccdbaccaabdbbbddcaadacddbcdaaddadabdcdadbadacbcccbdcbdcaabcccabbdbdccadadcccacbcbadbdcaadcbdcbbddcbcabbddacadbddabbcdccddccaccbacacabcabdcbadababcbcacabdacdcbcdacbabddabbbbcdbbcaabbacbbcaacdaaacacbbadabcabcddbabbacacddbdadccdadacdcdcbcbaacddccacddbddddbbdaaddccabdcccdcdbdcbcccaabdacbbbcabcdcbdadcbbbcbdddadcacdaacbcadbacaadcbbdccccaddddaabcbcbbacdddacadadbbdcaaabcdadadadcdaabdabcbddadcbdcdcdcdcdccbcdabdcccccacdcdcdcccbbbbdaaadacaaabbdaabcdcabdbcdbadabcbbbacaddaaabbbbddaaaccccbcbdbccbdbabaabbacabcdaaccabccdbccbbaadabbbbcdaacccbcbdbdbcaaacbcdbabcacadacdbcdcdaddababddcccacaaddaababddcbacbbacbadabccbdababdabbbadbabcdbbbbbbbcccbaddcddbcbbbacbacbdadcababdcaadbaddcdcdbcdacaddcbcbcaaacbbdcdbcacdbbbadcbacbdacccdccdbcddbdddcaaccbcdccdbcaabdaddbbacdddbdcdbdbddbaacdaccdacbcaaccadcadcbcdcbbbdccccdcabacdccddababadadcbbccbcbcbbbbdabdbbcadacddcdacadccbcccabcabcaccdacabbdbbaccacdadadccabbdcabcbdaddbcacaabbbcdabaacbdcadbdaabdbdaddcddabadcdcdaccdcbdadaabdacaddcadbcacaaddaacdbcdaccdabcdabadbcccaaccaddbbdbdcbacaabbbadbcdbaaccddbcbcaaacdddadbadccddadcaccaaccbbddbbacdaaacccadcbbbcdbddcdacbdaccaccbadddaccbddcdccbdbaaaddcbdbdacabdcadabbadbdbbbdcbdcbadcbddcddccacdacadcacdaccbadcddddcccbaaabcabdacbcbcdadbdcbdaadacbdbacbaddbddcbbacbacbbabdacdcdabbadaaabcdadabaacbcdddbaddbdaacaaccccacbdabacbbaccddccaabcaabccccdddccccadabbbdbdabaabddbcdcdabdcabcaabaccabdcacddaaadbdacbdbdaadcccabcccdcccbddacdbaddcdbabbddaaccaccbbbaddccbbbccccaacdcddddabdabcdcabadcbbaaaccdabcbabddddddacbdccbaabbbbadcbddccdacacadbaaacacbbababcabcccdadacdcacccabbbaaabadbbdbbccbcccabdbcdddadcbdacabcadcbbbbccdacbdbaabdbaadcaddcacbddbddabcbdbccdacbaddcdccbcdddcbcadccdbbcbadddcbcdbddcabbaadbbcaabacbbadacbdaadbadcbdadbadbddbbbdadabbadacdcadadccacbdadbaadacaddadbabcdabdbbbdbcaccabcbbdbdbcadacccbbcbdbabbbbdcbcabdddcdabbaadbabadacaaabaccadabacbaddadbadbadbcdcadcdccabbaaaabababcdbbdabccccadcbddabbabdddaddcbcbcddccbcbbbbabdadccccbdcdbacadcacdaadcadcbaccadacbaddaabcbbbadcadcdaaabbdcdacaccdadccddcdccdacaddbadcadaabbcacccacdabadbadbcdccdcdacbbadcadccccdbdbabbabcbbcdbbdcbadabdccbcacbcccaaaaacbccccabadbbbcacdcdbaaddaaacacbccbdaaabbcccaabcaaaacaccdbdabcadddaaabdcccbdadadbcbaaabadadacaaaccabaabbabddaabcaadacbbdddcdcaddaadcdacacbbdadbbcdcccbcaadadcbacdbcaaacdabaaabcddcbbaddaccbaddddcadbbcadbcaccccdddaacddaabcbaabcdbcaaaabdaababdcbacdcacccbbcbdbcbddbbdabbbacdcaadbadabcbdcbbbadcaabdbccadbadccdcbddbacbcadacadacdbccadcdbdddacbacbbbcdabaaddbacccdbddabdbdbcbbcddbbbbbcdaaabdbbbabcabaddcbaddbdbdbbacacbccbbddcaddacccaaaadbcdaccdacaaccdacdaacdcaacdcdddabbcbcdacbdaaaaabbaabadabaacdaddadbbcddabbccbdacaacabdcbcdadccbcdadcbadcbbaadbdbccdadccbdbabbccbbcbcdcadaadcdbccadabbcdddabddbacbbacdacdcacddcddcdbdcbcdacbadbdaccdbcdacccdcaabaabcdbbdabdbddccdbcadbdddabcddcadddcdacddabadcccbdabbcdbbcdabacaccdbabcbabdaabbcdababdddabdbdcdddadadabbcddddbbdddccbdbbcbdacacaadacbbccbcbaadacdadabacaadabacbddaccadcccaadabadccdbadbcaadccacccacbaabbcabcdbccabcbbbacdcbdccacacccaaaaabdaccbbddbdadcacbaabdacabdcbbddabbbbdaadaaacdbaabaadabaacbaabddaadaaadcadcbbaaddcdaadbaabaababadadccdbdbaaccaabadaacabcdbdabdbacdbbccdbddddacdcbbacacaaabcdbbbdaaddaadabdbadbdcdcabaccbdbbadbacacbcaaabccbbdbbbcbbccbcbcdcbadcccdbdcdbacadbdbbbcbacadcdcadcacbbdbbbddacbbcbaaadddaaddbccaddbbdbccddcbadabbabbbdbbaccccbabddbbabcadbdbcbbabbdbbcbcabcacdcbbbdbaccabddcabcacaccbcdcdbccabdbcabacbdcbcbdaaddacaaaabbdbaccbcbbccbdabcabacdbcbdacacdbbbadbcadccbbbbddadccabcbddbdabbccddcadddabdcbbbccddabacdaddcccdabcadcccbacbdcabcbdbdbaabdcaccbcbbaaddbdcbcdbdccacacaddaccdcaaddddaadbacabbacdddacabbdaddabbdccaaddbddbdddabdaddbddcbdabdadacbcdbdabbdcbdcdcdddccccabbddbbbbbdababdbbbdccbcbdbdbcbdcdcccddcbcaadcadbcdcdbacabadacdaadcdccdbddadccccacdcbbbcdcaddadcdcbcddabcbabbbdaddbdcaaaccdabdaddccccbaadabccdabdaddbdbcbbdadddbdacadbbbaccaccacdadcaaadbacdccdcbaabddbdcdcbabbcccdbddaccacdbbbdababadadabdaaabbababcacbdbbdbacccbbadabccdcabcccacbccabdbabdbdabdacacdddabddbbaddbbdabcdaddacacddabbaddcbaaddcabbccaaaaacccaacbaaacddadabadabdaaddcbcbbdbbaabbccdaddcaaadadacaddcaddccadaaaaabcaabaaacdcabbbdccdcdacdcdadcadbcdcdccdcabccdabdcacacddbabcccbcdabadbccacdaacacccabbbbdbdcbccccbdcdbbaccbbcabdcdaacbadbcdddbdbadadcdcbaaabaabbcbabbcbbabddcdbdaadbabbdaaddacdbdbccbbcdbddcdccbcacddcdbaaaabcaabbcbabcbddbacbdbcaaaaabcccbcbcbcbdddbaaccbbaccaadadbbaacdccaaaaaabcddcbcdbbcdbabccaddcdabbbcbbdcbaccaaaadbcabbaacbbcdcddbbbcdaacdddacacdbbdbaabdaaddcabbccabdaaddabacadabadabdcddbbbddbcabadacacdbabdccbdddbcabddcbbbcaabacdcdcccbdacbbabcccabcaacacccbbbdcdddcdcbccdabddcdabdababccbbaadcdcadcdcacabdcacbbdaacdabcaddabdcadcdcbacbcbbbdbabcadbadcabccdbaabccacacbcbdcbddbcccbbcdaabdbcdcddddaaccbacdcccbdbbbabacddacacdbacdbddcddcccdbccdcbbdcaabbcdccacbdccccdbbbbdacbdcbcbdcabaacabccacdbbdbdcbcdddbcbabaadbdbccdcacacdccdcaacaccbadacdbdccccdaddbacabaddbabaddadddccbddaaccbbbdbbcccdaccaaccbdcddaabaabbaaadcddcaabddbdabddbbcbcabccbcddbabbabaadbcdbdacacaddbdcbbcdbbdbcaaccdbccbdadcccdbdbbcadbadadbcbddbbccdcbcdacbadcbbadcddddbacdbcddbdddbcdbddaddbcdaaaaadababadbdbddccbcbcaacdcccccbbdabccacbcacadbdcdcdbdddbadddbdacabacaabbbcdaccdbddacabbbadbadcadcacbdcdcbdbdddcbccccabbbdbaacdbbddcaddaacadadcaaddcbcdcbbccacbcbbabcdbcabbbdabadabbdbbcacdbbdcabaabbcadabbaacbadddcdcbdbbaadcccaccaabdbcccdcccaadcaaccbdacdcdbdcdbdbadadbcdbbccbcdbbcaabdcbdddaaabdaacbcbadccdacbbbacacacdcddccbabbaabcdccaacdcbdcbcbcbacddbdbdbadcacaaddbbdacdcbbddadcaccacbdcadcbcdbcabbccbdbaaaddccddddcdcaacbadcbdcaccddadcbbcddbbdbaaacbbaddbbacccccbccbbcabdbdcaaadcddddcadccadacabbbbabbbcdbbdcdbbadcdaadcccaabdccdaacadabcbddbccaabddbbdacdddbaaaaddcdabcdbacdcabaaadabcccadadcbbcbbabbbabddbcadcdbdbdcadcababdccaddccabbcdcabdbddabdbdccbbaccbcbccdaacddbaaaddcadadbbbcdbcadcaaabdaaccbdaccdcdaababcababbddadadabacbdbbacbbddcaaaaaddaabccaabdaadacbadbcddaaaabbbdcbabcbdcddbdddbdabdcbddaacabcadccccaacdbdccdbdccadacbcdcacbbbccabcdaaccababddbbdccddcabdacaddbacbacbccdaddacbdbacacbaddbccdbcbcdddbaadcbddcbadbbdcdddbdbbbbcbadcbbdbbbcdcacaddcdabdbbdcddcdbacacdccbbdbbcbbcccaacaccbbdcdaddddbddbdbddabddcabbbacbbbcaabcddcddbcbbcadabcdcdddbbdabaabcdadcababacdddbcabccbdcdbcbbcadcadbccbadbccddddcccddaccbcccbcccbdbbdcadccdaababcdacbdbccddbbccbddabdabddaadccdddcbacabaadbdddaaabaacdcaacbddbdcacccbcbcbcddbadabdcacabaacbdaacbdddaaccadcbddcddabccaddcdbddcabdccbaaaacccabbcdbbdaccadcdcdcdddcdcacbaadccbccddcdbbbbadaddccbcbbadbabcbdaccccacadbaaddbcadabdcdbbdcdbbacdabdacbdcaddbdadaccccabdccaddcdcddccbcdbbadaaacbbcbdcdbdcbdabccaccddadbbabcaddbadadddccbdcadbbccdcadbaccccbabdcdcdbbbdaddbcabbaaacaabccbaccbadadcabbadcacddbcdccaadbaababcdbaadbbdbdacccbcbcddddaababbdcbbbbaccbacabbcdccddbdbbddbcbbadccccdabdccaaccbdbbbbdbcddccbbabbbddcbabbbbcbcabbcabcdbacdcadcbbbaabadbcdbaabbbbcdbcbcaccccaccddacbdbaaadccbddcaacbbbdabbbbbadbdbdddccaaccddbaabdaaaddbaddabaccbbcabcdcdaddddddcbcbabbccbddbaabdbddadcbadbbccadcabbaaaccbaabbddcaabdcddadbbdbadabdcbbdbdddddcccabddccdbaaccadbddbdaabdcdcabdbbbaadcacdbddbcccdbcbaddcdcacaccdaaaaacbdaaddbaccbababacdcaadbaabddcbdcbcdbcbdcaaacacdccaaaaaabaccaaaadacbabdcdbabadbdbccaaadcabcadacccbacbbcadadbacabcabaccbdcabbbacbdcabcbbbadadbbdacaddcdddcadaacaadabbbbacabcbcccddbabacacbaacaccdddbddbbbdcbdacacaaacbbdabcabcbaccbcabddbbccaaaddcdbcbbccababdaacdcbdabadcdabbdabdccbaddaaacbcbccacbccdcccacbddbdbdcccbdcddbdcaacdadbdabcaccabbbadcbbbacbdacbacacabdcbccdcccadccabdbbcabbbcdcddbdbcdbabddcddddbaabccdbcdccbddabbddadbbccdcbdcbbcaadababbdbbabbadabaabcddacaccdbaabadbbbbcdaaadcddcdbbbbbdccaaabdcbbacadacdacaabbadcdddbaddddadccabababacabdcbacabbaccdacbdcbbdccddccbabcdbbaabacbbcbdcdcccdabbcddadaabdccdbdddaadbdadadacddbcacdabcdddcdaddacccdcbcbabddaddabcbbbcddacabccaccbacbddabccabbbbdbabbdbcdcbbacadacacbdbcaadaacdbcdcbcdadbacdaddaccbaacddadcbcacbddbbcdcbcccabbbddacdbacddccccbabcdcaddaaadbbbabbcccdadcacbdadccdcbccaddadcccdacdcadcbbbddcbdcbaddabbbdadcdcccdbadddbdcddbcdcbaaddddcdbccadcbababaaabacaadbdcacbdbadcccdbdcccdaadcabcaaaddcdbcddbaabddbdbaddcccccabcdacddaabacddbdcaababccbacbabbdbbdddbbcddabccbdacacadadbdbbddcacddbdbadbcaaabadddabbdabadcbdadbcbabcbdaacbbacdabadcadcbdababaccaddcaaddabcacaacaacacabbadcdcadcdaddbdccdbdadabbbbaddcababbdadccdbacabaadacbabbbdcccbbbbdddcacdabbddaadacccabadadcacaacbcddadaadddbbcbabaaccccddaccdbddbcddddbcaacccaadbcbdbcabdcadcabdbccabbbdbdbbaaabcdbcdacacbcacbbbbadbcddbdadcccabbaccaacdabccbbbccacbddbcdadbdaddaababdcadacabaccdcacddcdddcaabadcdbdcaaadcdbcbddbbaabcdcbaddcadbaabcbacbaacdcaddccdaaccabcddbbbdcacbdaaaaabaccdadbbbdbbccdadacabcacdaccadbbcdbbdcbaaccbbdbbdbdbdaacbadcddcdacdaadddaaaccadddcabcbcdbddabdcacacbbcdcddabcddcbcdbadaddbdbccbbdbdcddbaadccadadbdabbbbabdadccbaaccaaccdbbdcddbaccbdddacadbaabcbabbcdbbcdbaccacddaadabaccccdaaabdcdcbbcbbacdaaccaabacbcaccabdacaabbdcbacbddaaddcdcdcdcddbbcccbadaacbcdaddcadaccaadcdbccbbacabcaaabcccbbbbbcbcdaacaaabacbacbbdabddabdbbcadabcdbdbabaccadcbdabddccdacddcabbacabbddddcaaadcdddaaabacbbdcbcaaabdcdbadaaccdaaabbcbaccbdddcacaadddbbbdbaccbaabcacdaabddacdcbdccccdbbcaadddbbabacacaddcccacccbbccabadbdadccadbcccbdadddaaaabcabdaccdbdbbaaacbdaabcbaaadcdbbdcacdcccabbdcbaadccdabdcbbcbcbcddacdbbabbacadbbacbbccaddaabdbadddaaadadbbabbcbaddacdcbcdbdcdacbacdbcdcbbabadabbcbbcdccbabadabccdaabdddadbbaccddaaaaabdddcbbdbbaabcccaacdcabadabdddcccccbbaadcbcdbacaabcbbbabdddaadcbbbabbabbcaadcaadcbbdcccadcbccccabccabbbbddbbabbabcbcabbcddaaadcaabccadbcaaccdbdabbaddcbacadcbdbbacacacaaddaacccbcdaddbdacccccacbaaaadcccabadacbbdcccdbbdacddaaddbcabcdacbdaddcbbcacdbcbdccddcaabbaacacbacdccacbccbabbbbbbcbadcdaddacacdbcdacaabdcabcadbdcbcacccacbbcddacdaddadabcdcacbdddacbdadbbccdbdacbbcacadacbcddbcbbacacdacdbbdbccabbbbbbdccdbccdcbcbadbacdbbbcccbababbbcbcdbacacccbacacaacdadacdacbbabacdbdccdcbbdcbadcbbbbabaaacddabbaacdddbcbadadccbadbccdacabdddbbcbacdddcaadbbcaabdddaabaabbacabcbcbbbbdadbadccdcdaadccccabdabaccacabcdbddbccdaccddadaddaddcdcadaabdaadcacbbaddadbbbddbcabbabcddcabbccdbbbccaaccbcbddaacbabaddcdbcddbbacbbabbdddcdbbbbabcadbdbabcdcdddcbabcbaacbcacadddaccccadabdcaabcdbabadccacbdbdccdcacdccbaaadcacabcbbabbacdadbdabbadbacdaabaccdcdcbbbdaccbdaaadaadaaabcbadcddadbcddcadaccddaabbdabcdbccdcabdddbbdddcddcdcadcccbaadbabbcbaabbdccaacdbdbacacdcbdabbbbabcabdccaaabbccdaabdcdabddcdcbaddabdadcadbdaabbdaadbdcabcaababaacddbccdddcbdbabbcbdddbbcbdcbdabcddacbdbdbaddbcccadcabbabcccadbbcdccbcdaabbbaadcacbabcaacdbcbddbcaabadabbdbcacaddacddadcbbacaadbcdabbdbacddcbbcbddddabbdddbdaaababcbacccdacccddddbaaaddaabdcbdbdbbababbdcdbacbcdabcbbcbcaadbcbdbcddacbacdaaadccbdbbcbcaabbdabdbdbddddbdcddaabacacdacccacbcdbbccbacaadbbcacaccacabcbdadddaabdcdbbabcbbadbcdcdbcdcaabcbaaacbbabcbbcddcccbcdccbaadccadbccbcbaadccdaacbddbdbadadcccdadcaadcddbbcdbdddddcbdcdcdbcdabdacadadadcdcddbdcdccaccacdbacabcbddbcabacbddbadcdcddadbaabdbcbbdcdaacddabcbabbcaababccdaddaaabaabbbbddabdbaccbbbdcbadbccdacbabadadabbccdddbccbaaddcccbbccdcbdaabdabbcaabcababcbddcacdbcadbbbdbcaacbbcccaaaccbbbaccccbcddddacdbbdbbaddacbccaabacbacdbcaabaddddaddbcacacabdcacabacdbcabacdbadbdabbcacbdddadcdcccadaccabcbcaacbbabdbcacacacccbccbbbcdaddcdbbbbcbdcaccbcadabbbaaccccaaaaccdbbacbbdbbdddbadbccbababcacdcbdcacaabaadabadbadbbdcdadbaababbdddbbdcdbbbdcbadaaaabcddbacdabcaabdbdbbdbcabdbdccadcdcbdbddabbaacddccadbcabcbcacdbccdbacbdbddcbbbcbddacbddbbdabbaadcdacdacaabcbbbcabddaaabaddbadcacbddaadddcbcdbbacacdbcccacdadacaabbaccddbcccdabdcdbbcdbbabaddcaabbbddcbbcbcaacccbcbcbadadbddacdddcddcaaaccdddcbcdaacddbdddabacabdabbbbddbcbbcacabcbbaadcbbddbdadaacbdcaacaadbbbbdbdcbadcdbcacccdcbaadddddddabbcccacccbdcddbdddddccdcdbcbccbdaaabacccddbabacdddbbdcbbabddcacdbdbdbacbaaadbcadaaddadcccadddcbbcacbbbbddadddddadadbdcaadcdabacbddaccbaacbaabcdbdbcdbdcbcdbcdaabbacabaabccdadadbcbaadbcadbcacbbbdcbdabbaaadddcbdbaaacbaabcbadcbcbadabacbddcbdcbbcbaacabcdaccdddacddabbcbbcdbcddacccbccdccbabbbcdcdcdaccdadabdccdaaaaaaabaaabcadcdcabbacbbabcdcbbacbcdbcdcabacbdccbddcadaabbadcbdcccaaadcccadadccaaacdcccbaacdacbcdbdccdbdddabdcabbcadbadddcbbcbabaddcdddadddcaaaddadcbcabcdcaccddddaadcddddadcbcaddbcaddcdaaaadddaaddbbaabbcbddbcdabcddbccbadabadcdacadabcccddbccbcddaaaabcbddabdbcdabddcaadcacabdbbbbbbacdddacbbddcaadbbbaabaacdacacdcbdabaadcbacaddbdbccaabcaaccdccdaadccccbbaacccaacbcadadacbdcabdaabbdcddcbdbdabbbacdcccabdbaadaabddbaccdaadacdddcddcdccbcbbadcabccaddcbacabdccbadbccbabccdbdcbdcacdcbcaabcaadcbabbdbaddbaadbdababaacdcdcdcdbdaddaabdbdcacddaccbdbaadbaacbbabdcccbdacbdcdcadccddadcbcddaccbacdbcacabccaccdbbcabaccccbdccbbcdcdbdbbddadbddbcbacdacbaaaddcddabddadbcdcbabbbdcdbdcdabaccadddddcdcddadbdbadacbabdbabadaabdcdacdcdbadcbbabcbdbbdadabaabbdbacdddccbdbacbdcbccbadbabaddbdcdcbbabdccacbbccbcbadbbdaadbbcbabcbdbbcbabbcbabadddccbbcabcbcadddbaadccccaccbbcdbbacaddcacacaaabbbabcadcacdbdacabdccaaccdaabbadacdddbbcdcabcddcbaacdcccbbacbdbbccaccbbcddbdcbcabcbddaacbbcdabcdddbcbbddabdcbccaabbaabaabaabdacdacacacdddbcbdacdaddaccdbaccbcadaacaaccadddaddcadccbadaaaabccaaaabcdbbadddcdaddcabdabaccbcacabddbbdcbbbcddaaadbcbabcabaacdaccbcaaabadbcbcbcdbbdbcabcacacbcadbcaaabcddccabaccabcbcdbbcccabdcbddbadcdbaabddabcaacdbccdaaaacbcadddcabdababdbbcadaadcdabccdcadbcaaacbcdcdbbadbbdcadcdbcdccdddddcccbdccccdbcccbbdddcadbbdccbadcccbdabcabbcaabaadcdcbdbabbabacabaaadacaacdbadcacaabdbddcdcabddbbaaccbadcbdadcdcdbbcbddaccbcbdcbcbcdbaddbccaccbdacbabaabdbbaccccacaabbcaaadaddbadcbdacbbaddbdbcbdccdbaccbcabdabaddcbccdcbcbabaadccaaacdacddddacabbcaadddaccadccdbddbacbbbacbcabbdbcdbdcdcbdaddccdbadcabbbbbdadbdbabdbbbbaccaaabbbccacdbcacbcdddbcbcadabaadaadcbbcdbaabccaabddababacddddbcccaabaabbdcbacdcdcdaacbdcbaacbccdcadacdddcadaaacbabbdddddbdaadcaacddddababccabcadcbabaabdaddbddacdcabdadbccccaccddcbcddcdbddbbcabacdbbaaabbccdacbcaddccbbcdaabdaadbcbcbcbdabbaddcdbaccdccaddbdadcacabcddccadbdacbaaccddbacadacdcdccbbbabbacbcbbacadcaacadabccdacbabcbcdaabccddbaccccdddcbcadabacdbcdadadaabacbbbdabacacabbadbdcbaabddcdbabccccbccddcbcbcaaddbddbacdbacdaddbabdacbabcbbdadbadcdddadbddbcaccdcdbbccdcdbcccccdccaabccddbbdadadbcadbdaccabdbdcdcdddddbbdbaaddccddbccdbcabcabddbaaabbacdaaccdbabdabdbdbabbdddbcbcccbcaacaddbccaaabcabbdabaaddbddbddccdcdcccdaaabadcddbdddccbcdadabcababcbcabcddabddabdcabccbadbdaaaadbbbcbddacbccababcaadccaddcbdcbdabcabddbdaabadcbadccacdcdcbaadcabbacacbadcbcccbcaacbcccddbccdcdbbcccaacbdccbdbccccdacbbccdbcdcaacabdcddbadbcccacbbababbbcbcdabcacbbadbbbddaddcababcdcabacddabccbdcaacbbaaccccaddaacbabdadbdcadbaabbbabacacdaadbbabaaabcccbbbbccbcbbaadaaabcdadadabbdabbabcbcddbbdcbaaacdcbbdbdabaabcbbdabadabdabdaacabddcdcabaaccbdadddaccbbccdabcbdadccbdabcddcaabbadbbdccacaddadaadaaacbddaaadcdbbbbbacbddaadcadadccbdcdaddaacddcbcacacadaaacddbabbaabcacbdcdadcccbcbcdbddcabadbcdbdabbaacacdaabaddcdcbbbdcabaacacbdbbbccbcaaabbdbbddccccddddcdbcdabcbbbdaacbabacdbbccdbbabcdbacbbdccbadbcaabddcccdbaaabbcaccbaddbcaacdabcbbcccdbdbcbbdcaccdcbcddbbddcccdccdccbadbaacbdbccdbdccdcacccbcdadbbdddcdbcbbbcbcbcbbdcabbcbdbaaaccaacacdadabccdaccbdabaaacaaddddbdbdcdcdcabcddcbaabcabdbaabacdcdccabdabacdcbbdccdbbadcbddaccccdcdacdabbddbddcdbbcbbdbabaccbcaabcbaaabcbdbdacaadcadbaccddcdadbabcadcdcdbdbaabaaaabccbdacbabacadbcdadbdbaadababdddbdadacbbadaaadbbbacddddbabbcabcbbdaacdabddcbaadbcdcdaabbadbaabcccadccacddabccdbdadabcbdddccaacacbbacddddacddacbacaabcdddcbabacaaaaccdbbadaacadaaabcddbcdacbccacbbccdbdabbdbcdbccddcaaaaaacdcdacdadcaacddabacacccbaacaddcaccacbdbcaacbbaabcaabdcadaabcdcaaaadbabbcccdacbddcaaadbbadccabbcdbbaccdaadabccdddbacccbbcddbacdbdadbaadddddbaccdbacbacadacdbcdabaabccdbdaadabdbbabddcdcaccbdbbaddabbcccaadbbaacdacdabddcddbabccdcaabcdddddabdaabacdbdadacaadcbcdcdbadadcaaadabbabdccbbbccddccdbdccddaadcacacacddccdbbacbabddbabdbddacddbcdcbababcabbccbcbbabcacaabbbcdcbccabbabdddaadddbbcdaadcacddccdddabdcacbddacccacccbacdacaddcadbdacaacccbaacacacaddcccacbdcbdbbbbbbacbbadbdccacacbacadcacdddddbacacdcacdbabcabacababcadccaacacbababcabaabbccdadbddccaacbdcdbbbdbabddacadacddcabadccbddcbcccdcdddccddadcacccbcbdbcccccbcbabdbcbbdbdabdaabcddcaabbacdaccbbccdcccdbbddaabcbbcbdabbcdaabdbbbacdddbdbaadbaabdddccdaaddcadcbbaaadbddaacbbbacbdbadbaabccdcdccccaabcabbbccbababaaccaabadcdbbcdbdcaacbbbacacdbcbcbcadbbbdccddacbcdcabddbcdcbaccdccacabadcddbadddbccddcaddddbacccbbcabdabaadbcbbdaadbadbcabcaabccaaaaaaaaadacdccbcdcdddcbcbcacaacabbccaccbdbbabcbccbccbccabccacbcabcdcbaaaaccabaabddadddccccbcadcacbbbcbdabdccbccbadaaaacbdbdcdabbaddbabbcaccbbdacddccabbddbdbcacddbddbcddcaacdaaccbacddcbdbcacdccbadadcdcbadaabbabaabbdcbcbdbbbdcaaadaaaaaabaadabbaacdcddaaacbcbabbdaadbccbcdbdacbaabcdccdbbdbbddadabdacbcddadaddaddcbbddbbcddccacaaddbddabcaccbacccbbbbcddbbabdcabcadcbaaccbbdbadcddcdacdaaddadacadacacddaabbbabadbacaccbabdadddcaccddbbbdaaaacbabbacbdaabcadbdadbabcccccbbdbcddbdcdddacdbcabaacbcabaacabadbcbbbcdcbcddcaccaacdacaaccbddaabcdddacbbdabadcaaaaadadaaaabdcddbaccbbbbbacabdccacdacbdbdbbbbaacddcdccbaadacdbadaddaaddacdcacadbcbaaacdcbbaadcdabcdbbdbdaabadbdcdbcbbccaaacbacdbcdabccbbcbddbddacddabbbbbcbbccbdcbabbcacadaadaabcbacaacddadacacadcdaadababdcadddbddadbdbcdcadddbadbddaddadacbcacbabcdbabcbcadcdacdadcccaacdbbadbacbcacaacbbcbcacadaabddbdacddaacbbdcaccccddbcdddaabccbbccacdccddcbdcccdacbdabacdbcbdcbccbcabbbccbcaccaaaadadcacbdaddccdcbbbdaddbaacdadccbcbdadcaacabbddaaababaaadbbcbccaddccdbcccbcdcdcacadbbdcbdaaccdbdccaddbcdcacbbbabdccacaadbacdddabbbdbbdabdadcaabcdcccaccabdacadadcacbabcdbbabbccbcaccaabbddbacdbdaddaacbabddddcdcbbabcddaaddbbaabaabccbcdbcdcdbbbacccabccbaddabdcddaadaddabbdcdcacaaabdcdcbaaddacccdcbccddcbcddaaddacacbbccccbdbcddaaccccbabbaccdbaabbcbbdbbcdaadcccbbccbcadbbddcccccbacaadbdcdccbccabcbbcdbdcdadbacaaacacccbcbcdbaadcdbddccacccdbacdbddbcbdaabccaaadcbcbabcdccbacbbadcaddcdcdddbccbbaccddaccddbadaddcaddbabbbbbbacaddddddaabdbaabcdcddbadbacacdaadcaabddabdbcaabacbddccccaddaccbddcbccdbdddadbaaaacadbdbcdddbabbabaadadcadbcabadabddaddbbbcadadcddadaaadcccbccbcadacadbbcddbccdadddcbddabdcdacbcbddddddccbcbabcaccabddadbadcccddbcdccbdcadadadccabcacdacabdbabbaddcdcabaaabcbacbaadaadcdddddccaccaadcddbddcbacdcacabbcbccdcadacdbdbbcaddbbccbbbabadbaddacbcdaddcddacdaadcddacdbabbbccccddaaddccacdddccbbdbdbaacabbabccbbbcaadacdddbccbabcbdcacdcdcbddcacababaccdacaddabbdacdcbabccbcabbcadddcabdadbadbbccbacbdccdacdccbaadcbcbcccacaacdbbccdcbdadccaddbcdacdbcdccacbbbacabdcabbababacaabaadbcacddcbadccdbaacddcacdbbddacbccbcddbdabddcddadcccabbbdddbcbaddaacdcabcccbbaaadcadabcdbbccdcdbadbcdbacdbcacbbabbbcbabacdcaadadaadacccaccdcbadbcdabbbbbbaccdcadaccaacdbbcdbaccdacbcdcabdabdbcbabbaabbabdacbddbdbdcdddccabcdddacbabcbdcdcaacbcdbcbdcdaadaaacdbabacbcdbdcbcdacbdbcdbbcdcdccbadcddbdadaccbdabdbccbbdabdbabdaddddbadbcadabcbcdadbbbdddccbcbcccdbacdcaaaddbacdabadcbaacdbbbcabcdacbbcddaddbbbdadbbdbaccaacbacadacaacbbadcacadbbcbaaababbcbbbbbabbabcacbcdadbcacadcbccdababacbdbccbcccdbbaabcdabbcbcdacadbacaadbbcdddacbaaabbcddbcdcbcabcdccdcaaacdbddadccbbbaddcaccbacccddabadbcabbbadbdbbdabaabcdcacddcbbbabddbcacdccaacdbbccaabdbddbbdaadaddcdddccdccbccbbacccabdbcbabcbaaabcddbadbadacbcbdbcccdcdaaddcccddabcddacbadcdaddacbddbcccacddcdcdcbdcaccbcbcdccadbbaadbbcabddaacdbccdaaccdcadddaadbbadbdbadcbcdbaadbdbacdbbabcadcdadbcbbabcdbdbadbccaddacbcdccaddddddabdadcbaacdbcdccbccacaaabdacdcbdbcacabcabcbcacdacdbddbdbabaddbcdcbcadbbbccaabbdcdcbccacbcddbcaaabbbadadccadbcccccbacbbabbcbcacbcbdbbccacdaaddcddddbcbbddcbdacbbbbbabddcdccbcadcacbbbbadcccbdacbaaadadccaccacaccdaacbbcbaadbbcadcdbcdabddddcbdbbacdabcdadcdbbcdabcccabdacadbadbbabaabdadbbdcaabaadbdddadcbaadbccbcacaacacdaadacddbcadccbdccbddccbdbdbdadbabadacdccdbadcabcdcdbccaccdcadcaacacdbccabddaddaaaddbadaadbbdadcccdaddbbdaccdbcabacdbdddcdddbbddabcbadadbbccbbbddcadacbcbcacbabdcbdbacbccdcdabadaabdaacbbdbcabaaccdbababacbcbdacbdcabcdbddcdcacbccaddccbbbabacacdbcbcccdaabddcaddabbbcbbabdccbddcaadaaddbbddacbddcacabdccaddbbbddabcdcacdabdbddcbaddcdaadaaabbabcabccacdcbbcabacbccdaacccabbaaccddbbdcdbdacccbaadcaddcdccadcadbababdabdaabacaccadaadbddbdbbcdabdccaadbbdddccdabaabbaabdbbbdcaacbaaddabbbdacdbdacbcccbabacaddcbcbbbcbacccabcadbadbdccdcbcdbaababcdbcbadbdabdbaccbddbccdcddbbabbabbbddcddccbacaaddbddccabbbcbdcdccbdcaaaabbbbaacbabddcbdaacbbadbdadbbacdcddbcbbccdbcacabcdaadcacbdccacdadbabbcbabbddbcbaaadbdbacbdaacabcddaaacccbabddbbaadacdddbcadbbcdbdacabadccdddaabccdcddbcdbbbbdccdbbcdbabbbbdaddcdcbcccdaaadbcabaccddabbbccbbbbcaacbbadbbcdaacacdacacdcbabadcaaaadcaaaacdbdcbaddadccaababccbcabcaacbbbbbdaadaaacdbcdbdacbbbccadcacddacaadadbdcbdaaaabbcbaaddbbccddddccbcddabccddbdaddadadbccbddaacaccddbabbdcbdcddccadccacdddaddbcddaabadaaddccacaacdbdbdbbdcccddaddbddacbaacabaacadcbacaaabdbdbcadcdcdcccbbaaacbbdbcdcaadddcabaddbccdaddcdabacadccdacdaccdcddcbbdcababdbcddcddacacccadcacabbcaadcdccaddacdbaaccbcaddccbdadabdcbdbdaaddbbbacbaaaddbbbaaabbddcbcaaccaccbbabadaddccddbdcaadadbcabcbcacbaadbdccbbdcaccaaaddcbdbddccadbcbdbbdaacadcccbdcdabacdbbacdbaaaabdcbadbabcddcacbcdbdccdaacaddccadbdddacdcbabcddadaadbbbcddcaadaadccdddbdbcddabcdddaccdcbddaacdaadadaadacacccccbdaacdabdccbdbacbbadddbddabcadbadbbabbaaaaccaccadacdbcbbbabbbadcaddbddbddadbbbddbaaacdcbdaadabdababaccacdadcacbccccbdbdddacdbdbdbcbadbaabdddcbdbadbcbcbabadacadddddbddbdbccdaadcccdabacadcdbbabcdaccccbcccabdbddbabcdbcacdadcaadcbabacbbdbbbdddbccadbaabadddcacbddbaaacccddbcdacadddabcacccdcbacacdcadccbdbbaddcdcacbadcadddbdaddcdcdcacadaddcbdbbdbddccaadbabaabddbcdddbbccccaadabcbcccbcbbdbaaabacbcbbccadddcdbaabdabcbaadbddcbdbbbdaadabdbbdcbddadcbbabdcdacdbbadbcbcddccadbcbbbababdbdddaccbdabdccbbdcccbdaaaadddabbdcdbadbcccacdcbdacbccbbabccbbabbdbbacddcaaacdccddcdaaddbbccadbdbcbcaddbabbaabcddbdaaababcccaabcbbcabcccdadbcbcdcdcadbacaacbadddbababacbdcdbccbcaaadccbcbacbbbbcabcdbbcadacbbcdbadadcbabcadddccdbdacadaadadcdddbdcbcaabacaaacaaacacaabaddcdacddadddcbadcbbabddaddaacbaccbbdacaccdadbccbbcbcccbbbdcdacbadccabcbdadbddadcdcaaacdbcdbccdbddbdbabdbdccdbdddbbbbbbadabbddacdbccdccdbdacdaaadcbdcdcccaabacacaaddbabcbadcdbaadddcddbaabbaddaacddccdbbacbbcbdccbdbadcbdaaacdccdcbcabcaacccdcbcadaabbbbdaadcbbcbcbaddcadcbadcaadbacadaddbdbbcdaddaadcabacdadddaadbbadabbcabacbcdddacabbbdadadbbbcbcdbddabddbbbbaabdbcbbbacabbbaddcdcbbaacacbaccccbaadadbbaabacbcabaaadcaabddaacabcccccaccbbbaadbccabdaccdacbacbaabacdbadacadcaaccbaaaddadddbacadcbdddcabddabcabaabaabbbbadcbabdcdabdbcbcdcacccaabcadabdcabcbdccadccdcbbadbcddacdbabbddddabdddcbbaddddddcdcacdcddabdcaadcbbbadbcdccaaaacbdababaabcbdbbbdaaadcbaaaabcbbaabcdddccccdbacbbbaaccbaababcdcdbadbbddbbccbbbaadadcddcdcdacaddcbddbcbcdabdacbbadcabcaacacadddbbcddbdddaacabadacbcadcadadaaaaacacbdaadbadcbbbaaadddddacbcabbaddadcccddcabbaaaacabddccbbcadbbdacabbcdacaaacabcddbcaadaddcdcdcccdccddcbdaacbadaacaddddddadabcbbdbbbdcdccbadccccbacdbddadddcabcaacdabacdbaddbbabaaabadccaacbcabccdacddbbbbddddacadaddacabddbcbcadccbbccdaacacbcbcccbbbbbddbacadbcaaaaaddacdcbbccddbbddaadaddbccbdcacdcddacbdcdcbadcbadabaabdcadbabdcbdaabbdadbdabaadcdcdabddbadcdbdadaacadabbbbdbcccaddbadccbddcadbcaaccdcdbbbccbbcdcbbcbabdbccdcaacabcaddabdcacacbaddcddcddccadcabbdcdaacdccdccdcaabbdbdcaaacacbccabccaacaccacdbabcbbadccdabdbaababdddcbacdadbdcdcbcbcbcbdccadacabbabbacadacaacccbbddbaccbcaaaabcacacaadbcdcabccbcaaddbdcdbdaabbbddddbddacbaccdbdaabdabddbcddaacbdccabcbdabdbddbbccbdbdaddacdccdbbdddcbdadcdbadbdacccccdabcdacccbbbcccaacadbdadcbdddccabadaadcbdaadcdabccaccbdbabaccdbbbcdbaacbdbacdbcdacdcaabbaaccdcdbdbabcdcddcdbddacbacabbccdbbaccacbdbbddbadcbddbbcbcdcccdaabcaaaaadbbacdbccbbcdaacaabdadabcadbbadcbbaaacbaabacabdaadaccbcadbbdccdcbadbadbbbddbaadbbdacdcdacdabdbdcbddadcdcbbdddaccdcabddabddcdcbddbcdcacccdbcdababdddcbdcabdddccdaddaccaaccabdcccaaacddabaabbbbaddccddccadbaabdcaaacacdabcacadadddcccaaccddacbdadccacdaddabcbdcabcaaaddcabadaadcdadccccaadcabdbbbbcadddaabccdaacacbcbdacbbacabaaacdabaaddcbdcabcdddccdabdccbadaddadaacbdbcacdbadbdadacbaabdbabcaccccaccdbccdcddcdbdcaadaaddbddadababdcabcdcaaacbbadbcaaaaddaabbddccadadaddbbaacadacadabdbbdcbcbccddbbddaaaaaddadbbcdabcbbcaabbdabbbcccdcbbccbbcccddccbadabaabbaccbbaccabcbdbaacadbbccddabbcbcccbabdbcbbabdaaabdcbbcadbcabcdccbdbbcdabcaabdaacbcdbcdaddcbcbdaccdccbacccdacdbcbcdabdbddcddaccdaadacbdaabcaadcbcaadabadbabcdccddabcbdbccdcddaccbddbdcddcccdbaaccdcbdbddcbddcaacbacadacacdccbcdabbbcbaddcaadbdcacacbdbcbdadcddccaccdcbbbcadcabbdcadbbdbadacbbcddbcbbbbabaccabbddbcacbabddccbbcaddcbdacbdaddabbadaddbaacdabbaabbadabbccaacbaaaacdcacbdaabcbbabcaacabdadbbccdccaabcdccbcadabdabaadbddcbacdbcddaaddccaddaccbbcdccdaddcbcaaacdaddccccdbcadbccbaccadacaaacaadaacccbabadcaddacdbabadbddbabcdbdadbddcabbaccabcdacabbaddbddcaaaccbbbbcaabbcadabacadcacbddacacbdcadccabdadabdbcadaaaaaccdadddbbbaccccbcaadabbabcdbdddbbcccbbccbacacdcccbcaadccadbaacaacadadacddcddddddabdccdacabdbdccddaacacdbabcaacbdddbbbdcddcdbcbaccdddbbbbabccdbbcbacabbcddbbcdaddcbacdadbbdbccdcbdaaaabddcabcdbbdababaaabadbdddddbdbdbbdbdcacacdcabacdacbbbbcdbdbadcabcdbcbcaabadccbcbcddccbbcbdcaabbcbadbadbadabbcadcadcdbdadddbdbabdbdbcabaddaacbbdbabbbcdbbccbccdacaabccdcccaddccaacacaccdcdcbcaacbdbbbcaddabdababbbbbbcbacdbdcacbbaacacadaabbcadacdacacadbabdcbabdaddbcaabbacaacadadccdbadacdbbbabacbcdcbbaaaaadadadddacddcacbbbddadacbdabbccadbadbbacdcabcacbbccddcacadcccddbabbdcdacdddabaddcccbbacadcddddadbbcacaabcaabaaaddacaabbacbdbdbacaaacadadbacbcabdbdcacdaaaacaacabcaadcdcadccbdbacabcccabdaddadccddcadccbbddbadcbbbdcbcccbbcdabbbadabccdaacaddabbdbcabacdaabadabbcdccbadaabaccbbbdbbbdadbccbdddcaadccacdabccbdcdccdcccddbdbcacdbdbccabaddddacaacdabdcadabdcadaadccbcbdbddddbdababcdccdbccacdccdaddbbaaacdabdcbabcdddbadacaaccdcccdcacadddabcacabdcccabcccdaaabdbccbccbaccdcbaaaaddcdcbbcdbddaadbdbaacbadbcacadaccbdababcaccbbcddbdccbbbacbcbbcbbbdcabcdbadaddbddbdabbbbaabcbddddccaccddcaccbcaabdcdadabaddaadbddaccabcacbbadadbdcddadacaaccaddcbddcdbbbddddcdcbcddadccbbbbcadddcdadbbdbaaaabcbdcabbaacacaccaddbccccadccbbbdacdddcbacbabcbbcdccdddabcccacdcbcacadcdbbbbbddbccacdbcaadacdcdbcacdcabbdbcbcadbcbabcadbdcacabadabcccbbbaddbacdbbccdbdaacbabcabacadcbabbddbbcacddbbababddabdddadabaaccbbabbcbdddbccbdabddaabccadddadcdcbbadcbdbacbbabadaaacbdadbdbaaabacdbbbdcbbbacbacdadbcabcacadbbcddddcddccbdabadddaccadbcaacdaddbbccbcbdccccbbbdabdcdbadbaacdaabdcabddccbddacdbbacbdbdadaacaaaaaacabaadddbadcdacddbabbbabdabaadcbacdbaadabadbadbbccdadbbbbbaadccdbcdcaaaabbdbcbabdcddbcaaaccdddbbcbbddcbcbbbabbcadbbcdaabdacaccdbacdcdaabbbaddababcdcadacabcdaddabddcbabbbaaddcacbabcbbabbbacdadaabbadbbcdbaccdbbaacbaddcbbbbaaaabcbcaddcbcdbadbccccaacababdcdcaccdbbbccdcbbbbcbacadcacddcaacacccbdcadcbdcdbacccaabcbbcbcccccccabbccaaabdccabadccdcbacbcadbbdabbaddbdacdaddcbdbdbcbbabddaaccddabcbcabbdbccbcdcabcbabadbdababbbabbcdacaaddcadcddddcabacbbbaccbadadaabacccdcdabaccbcccaacbcbcaddcddbddaadbadccdbccbbdbcadbbcbbcbbabcddddcdadadacbdbacadcbdbdcabccdcdbdaadbdacaaaaacaacadbdddccbcdabdbcddaadccbaddbbbcabcbdaccdaddacadcccdbaaddacdacdcbbccaddabbbbcdbddbddadcabbcadbdabbbdbbacbbdcbccdbbcabcadaacdaacddaddabdbdbcaadccdabacdbcbdadaabcabaabacbdbcaaddaadbacddcdbcabaddbbcdbddacddbabbabcbdddcbbbcadabbcaacdcddcacdbacdaddbcccccdbbcdcaaadacadccccbdcbccccdbbdbabaabaaabbadddccdbbbbcbddccccddacacdacbbabccbabdcbbbdbccabaaccbddcadbdcaacbabbbaccadbaacdaccdbccbcadaadcbbdcabbdbbddbcccbbacddcabacccacadbabdbcabadbccdbccbcacbdaadccbdaccccdcbcadaaabccbbccabaabbdbcbdcbdcdbabcddbcbdbaacddbbddacdcddbacacaaccaaabbbdcbdcdabdacbddbadbbbaabcbacdabaacccbccbdddaaabddaddbbcccaaddaddadddababbbadbaabcbbbababbabcdacbbbbacdbbadbcbcccdacdbdabcccdbacddcacbbacdbccacaadcaadbcbccccbcbddbbdcbcabbbaabcbbbbdacabbacdbcbcbadcaabddcbdbcbcacdbbbbacacddacdbcacbcccdadcdbddabdadccdccddabcabbcddcddcdbddbacbaaabbbccdbddbddadcabdabdabdbcbaaacccdbcccdcdcbacacdabdaaabcccbcacccacbbacdaacdacacdbccdbadbbabdcacabdbcacbdabddbbbdcadbaabdadbcadccdacdaadabdcbbbaabaadbababacaccadddadbacaacbabcbdbabadcadddcdbdacbabdbcddbcbbbaababcbbadbabdbbdbcaddddcdcbdbadabccacacaaaabcddacdacacabdcdacddadabdccacaaadbdcaacbcaccaaabcacdbbdcdabbccadddbbdcbabcaaabadaddacabadcdadadaabadcddddcbdadbbcdabbdbbbaccabdcbdacaadbaabcabcbcbbcacadbbaabcdacddbdbcaddbdcbdcdbdcdcacccaaacaaaababccdaacbaaddbbcaddbcbcacadaddcabaaddadbccdbbcbbcddadcbadaabacdcbdcadbccdacccabcbcbddaccccdaccabcdbacbdbccdabdbcacbbadadaacbabaadbdbcbdacabdbcbccbcbdbdadaaaabcacbaacddcbaacdaccaddcaabacaccadcbabdbdbbcccdcaaaaaccabbccdaabdaadcaabadcbadabdbcbabaaabbcbdaaabddaabcdcdbaccbccabcbcbdadbddadcbbcdcaaacbcdddaacaaccccadccaadacbaaaaaacdcdacdbdcbdcadddcadacdbcdcbdbcdbcdbdcabbdbcccbdcbddcadbbdaccabcdcbdadaadcdbbbbdbacddacaaadddadbdaddaddbccddacbadaaaaddacddabdacdbabcbadbdadabdabacbbdbbddadbdacaddadccabdbacdcbddcababdaabadbabaabbdbddadbaaddbcbaaccdabdabacabdbabadcdbdbccbbccdabadcdcbcacabcdabcbcbdbacabbdaadccbccdbbbacbadbcbdddabbdaddbaaaabaabacdccbdbddadcccacacbdbcdcaabdbddbddcccbaaacbbabccbbcbddcbbabbdacbdadbaccbabccadcdbacbbbcbacbbaabdbbdbcbbdcaaddaaadcdbdcccdaadcbbccdabaabcabcbdbdcbbcabadbbabbbaabdbbcdcabcbacaddadabcdabccbdacdabbbcbcbcbbdadadbcacdbacdcbbdbaabbcadcdbdccadacdcbdbbccadbbacbaaaabbdcacdaadabbbabdaddbddddcdbbdadabdbaaccdbabacadcdabccadbdcaacbdaaacaccacbbaacacbadacaccbaadcdcbbacbbcbacbadcbbbddcdbbaaadbbcacababaacbdccbcddaacbabcddddbabbbddaababbcccccdabdbcdbabcbdbabcdbddcbdcdbacbbdacbadacbcdcaabcdbbbbbdcadabdcbcacdccbdbdcacccbdccbacbcdddbbdadccbdacbacdbcbbbaaabcdbbccacbcccdccbbdbbccbbcaaaddddccadbbbbcbdcbbaaddaacbbbaadacbabcabadccacaddcbacdbabddccdbbcddddddcabbcabcdbbcbcdcdaacbbdbcdabdacbaacdbbccbcdaabadabcaabdcbadcbaacbcdcddcbbcccdccbdcdaccdaaabbabdbbbbadcdbbbadccbbbcdbdcbbdcdaabbddccdcabbddadaabbcdccbcaddbdaccbcaccacdcccabbdbdcdbbbbdcbbadccdacbabaccacabdbcacbdcbbaacaabcdbcbdcbbbacaccdbbcdacbbdaaadbdcaaacddccabacccbcadacbadcaacacbdbbdadbcdaacacbbbcababddbdcccbabcacbbcaadbbdddacacaadaaadddcbbdbcaddadcbdaadbdbdbbbccdabbcacdcbacccacbbbdaaaccbdcdcbbbcdcddaaacddbcbadcddccbccaccdacbbbcbddabdbaabccdbccbdbbdccbcbdcaddcbbddadbdddacddcabadbadbdcccddabbaacdcaaadcbbbcbbabcbdbbabcdddcdcbddcdacadcacdbbbbaadabbccdcbbaacadcdbbbacdacdbddabadcacddccdacabaddddaacbbbcbadcdbbabcacaadbabbbbdddbcdbbaabdabacccaacaadacdabdacaadccdadddababaabbcdbdcdcaadccbbaadbacdddbbbdacccddddcbcbddbacccacabdddbdcaaacadccdccbbdbcccdcaadabdcbbcdbdcbcabdaaaabcddbaaadacdcabcccbadccccdacaacccdcdcdcdcdbcbbddabdcabdacddbddccbacacdcabaccccabdbccadadbabcbccddbadcbadaddbddacbddcbccadaaaacdcdbbcabaaccdbabcacbcbacdcaaaacbcbdccabdbcccbcbadcdcbddcbbbccdaadaaadacacabcacbcabbabbdcbccdacccbacbccbacacbbacadddadddcdbccabacdbacaccabdacdaabcabbbaccbdabbbddcccacabdbaadaccaabdaddacadadbadaababcacaccdccddcbcadadcadcbddcccddbdbbbbdcdbabcdbcaabdabadcccdcbcccbbcbbdcadcaacbbdbdbbadaccddcbbadacbbdacdbacddbadadbabacacdadbcdcacaddcadcdcccdcbcbddadbbdacbdccacadcdabdbadabbcaabbddccbabdadbcadcbbdcadbbbdcbcccccabddbbdbdddbbaabcdbbdbbcbacaddcbdcbbcbabcabbdbbdbbacdcaddbcdaccddddbdaacccbddcbdcaabbdccbdcbaccacabaacbdaabcbdbcbdbdccdbabccabdcbbcbabbbadabdabbabbccdcaaacccdaaaacbbbbadacadbabcaaaabadbdaddcdadabdabccbdccbaaaabbcdbcdacbcacdcaabbbcacdcdbdabadcdaccbdcbdbadabccbcbaaacbbabdaadadacaddcbcdbdcdacdabdbcdbbdbabacdabaabbbabcdccaaadabbccddcbacdbbdcddabdcbabacbdcdddcdbbcaabddadcdbdabadadbadccdcdccddddbdbdabbcbcccbcdadbbddbbcaccdaccbdbbabccddbbabaaaccdbadcbbdaadacbddcdabadbccbdccdddcadbbcbaaddddbbadacccbcdbbccacbccdccddbabbdddbcbadaddbcbacccabadcbbabaddbacddaacdbabadcccbcccdddacdabbbbcbddabbdcbbdbaccadacddcacdabbddcdddcdadcdabcabdbcdadcaccacacdcbaabdcccddcacbbccbddcabccddcbaaaaadbaddcbccababbbbcabbaadaacabbbcdbddbcabdcdabddabbbbbdacdbaddcabaccdcbcaddcddcabaccaacbdbdbbdbbdcddacadcbdcbbaacaabcddbaaacccdaaccdbadccbdbcdbbbbcaddcabdbbdabdccdbcdbabccdcdaacbaacbadbdcacdcbdbcbcbbaccbdaccdadcdbadbbbdbcbcdacacaabbbaddaccdbcacaacbbabbabbcbacddbdadcdabdcbbcdcabdcdbaaadbabbabcccaddbacdcccbaddbcbcdcbadbdabbbacbdbddcaccbdacbacaaababdcbadddcdbadbbaaaaccbdbddbbcaadccddcbcdcadccaacccddaddddbcdbbddcbbcaadbbcdabacdbadaacddddbdcddadababdaacdcdaacddddbbadbbaddbdbadbcdbcdbaabaccdcacadcabbdabadbacdbabcddbadadcccddbacabcaabaadaaaddcdccabdbbaccbcabccbabdadbaadcaabddaabdadabbcaaccccdbdadabdabdcccbcccbdbdbccccdacaacbcdbcbcccdbdbadbabcacddddaddaddbaaccdbdddcbaadcddadcaacddcacadadbdcbbbcaadabacacdacdacacbbcdcbacabbbcccaababcbbbbadaaaacbddabbacdacbaadccdbccdcdbdcdbbbddbcdcddddccbabddbbdbccaabbabcaccbcbbbdacabbdacddbababbdbaaadbdcbdadaddbbccbaaddbabbabcbababbbcabcbbbaccadbdccccbdcaccbadbbadcddcbcbcdadbcdbcdbbdadadacacccabccaadddcaadcdcadbdddaccddddcccbdddaddacbcbcdcdcdcdbbcbaaacbccccdbcdcccdbcaabcabdacbaccabaacddbabbaabcdbbddabdadaacdaabcccccbdbaaabadacdacacdacdbdadcaacccdbcadbbadbbacbbabadaabbdddacabcacdcbcbcdcbdcbcabcdbddbbbcdadadbddaaaacbaadadcabdccaacdcadccdbabdacabbaaddbbdabcbbcdbacaddcdcdadababcbbabddccdbdaacbdbaaadabccbdbdadabdbcbacbdccbbbbabacbbadabdccdadccbcdcdaddcbadcacbdadaadbddabaadbcccadabbadadbbaccddabdacbccabadaddbcccdacacddadcacddbdbcdaaacbbbccdbdbcccbaabdcbabdbbaacdaaaabbdacbacccddcddaabcbaacbcbbabdbbbadaabccdaadddbadbcababcaccaacdcacdbccdccbcbadbcdcbdbabdddabacccbcbcddcdadaacbbbdabccdadbdccbdaccdccbdcbcadadbacaddbccdccdcaccdbbccdaddcbaadacdaacbcabccaabcabcaabacddddcadddaacaddacccddddacaadacdbadcbbabaacdddcccbcbdbaadbacbbbbabdaaaabadbccdcadbbccdabbddaddbabbdbcdadbaacaccdccbdadbbddbcdacbdabcabddbddbadbdababbbbabcccacdcaddacdcadcbcaddaaadbaaadabdaacaccbbaadbabcabaccacaadcacdbbdccbccaccddaccdbdbdcbabcbacadcccdcbcaaaacbaddbcccaccadadbbcaabcdadacdadcaabaccabdccdccdcbcacdabdadddccaadcbcdbbbaddbbdcdadaabbbacbaacddcaaccdbcddcaadddbdbadbcdcbdbdbcadaddcacadaaccccaadabddbbdbbdaddcbcaddabacbcaaddacbdabdbaacdcbdcbcadabcaabdcccadcbbbbbadcccbdddcaadbbbddcbaaacbdaadaadbdddbcdbcdbcccbcbbacacdbacdaacbcddadbbaaacddccbccddaccadaaaacdacbcbaaaccbabddcdbaddbcbcbcdbdcdddbccbbdccdddbadbdbbcdcccdcacaabacdbcdaaadbcacbdbbbbdddbbbcbbcaddbdddddaabddbddcbbcbbbddadaddcbbaabbccadddacbadaaddccadbcbdaabddccaaacaadabbcbbdadbabdbbbdcdbadcdddcbaddaccddbddabdbaddbddbbbcdcdaaaabbaaaacdbbabcabddbbccddcdadbabdcdabcbbbccdccbdcabdbdcbbdcbadcbddaaabacdddbdcadcbccdccabcdcdbdaaccacccccdbbabcdcbbdbdbbbbcdbdcbbcbdacccbbaadbadcadcbbbabdadcddbbacdcbdcbbbcddcbcbdbddcdabaaabcbbbacabacadccaabacbbdbbababaadccdabaacbdcadbabaccbcdcdbccdcdabbdccbbababbdbcadabdabcdddbdcdacabacadcacabbcdbcaccbbadadbabbdadaaaaddacccdbabdbdcccccdddcddaadbcbabababaacdcadbbababaacaacdbcabacaddcacbdddacaaabbdaddddbdbddcbdcdbbccccdaddddddcaaddccbcaadabadbbbdcdbbdacaabdbbbccbadccbbdbbbaccbcddcbbacbabddadbcaabcbbcbcbacacabcbcabddacdadaccadcbcacbdadaaabdbdaacbdbaabbdcaccaddbddadddacbaddccabcacdcacadacdcbcaaaaccababccbbaadbbddbdcdcdbabbdadcbdbdbadbaaacacaadaaccddbbbdcaccdcabacbdcadabcbdabbcccdbaadaddcddacaddcacddbdddccbaaaacacacddbaadcdddccddacddccbbcbbadbcbcdaccccbabcbbbdacbccbdaddcdbcbbacaacbaddccadaddabcbdbcacdacaaadacbaaddbdabaabdcaaabcdcdcabbdbbadaaaccdddbbdbdbbdaccbccaccbaddabcaddbcdcdcbcbaaabcabadbbaacbaabaabcbdbbdddbdcdababaacdcccbcbdcdabbabbdbbbdbbcdbdccccbdcbddccbacbdaccccaacbdbdbbbadcdddddcacacddbddddabcdcdaabcbcdadaabbabdddcbacbbbbadcaddacbbbacdbacbdbdddcdccadaabaabadbaabdccdcabbaaaddcdcdcddbababcccbcaabcacaacbcaacacbdbccddccbaccccaccccacababccaccaadbaaccbdccdbcbdcadbabbadbbccccdabacdaacbacaacddaadbcdcdacbdcadaabcacdcbabbadcacbbbddcbadcddcdbaacacbabbabccbbdcbbcdcbbddbdbacabcddaacbbcdccadbccbbcbadddcccbdacaaadaaccccbacbdbbddccbccccdaacbccaddacddadaadcdadaaddaababbabdacaccbabcddbacbdcacbdbccddaacaddccdbdbadbcdbadddadcaaabaaadcaaabdaacbcacabdadcccbcccdabcbdacccabaaadcbddaaaccdaaddcbacaddbdcbdcabdabcbaabdadbcbbbcbadcaaabdcbdaccdabdbccbcdadddddaabcaadcbccaccbbdadaccddbacadabcabbaccbcbcdabcdadddadbbdbcbdbcbabacdcacdaaabbddbdccbaccdbccccbbdacddbdbdccbababbbbbdbddbbccbbadbbabcbcdddcbabbdccccdcabdddacbdbbdcbbaadbbbaababacccbabbacabcacbaacdccacbbcdcdacdddcacbdabccacbdbddbcccbcbaaacbbaddbaaccacdbdddbbabdcdadcbacadadcdcbcbbbcddbbaabddaccddaddadcaaccdbdbcabcaaaaacccdadddbdcdacadcacdabadadcdaabacbabcbadbdcacdadadbacbccbdbbdadabdcaddcdaadccbabcacbabccbabbababacbaccabbcbabcaacbccccbbbacbdbaccddcacdbccbbdacadcbbccaaddbabdcdacdbdbdacbdabcbccdbdbddcbbabcdcbcddbcdabddaaacccaaddbacaccaaababbbcddcdcddbcdcdaabcaabbaacbcbabccaaaacabdaaddbbdcaccbaddcababdadadbbadaddcbbbddccadacbdadddaaacbbaaccacdcbdbdcddacaabadddccacbcdbcbabcbbbcbcabaddaaaacbbacaacbcbadbbcabababbcaadcacccbcadadcbcdcacddccdcdcbdbdbbbbddddadbcbdbcdaacabcbaabddbcaccdbcdaddabbaabaadacbdcbdadcbbbbaadadaababcdcacbaaddacbdcacadbcaabddabdbcacacdccbacbbbabbaadacdacdccbcdbcbadcaaaaddaaccdacbbcdadabdaaabdcdabcaddbadabddcdbcccaaccbcdbdabccdbacccbbccaadbadccaaadacdddaddacbbdaddcbcbccbadbacbcaccbdbbdccdcbdccddaaadcaadaacbcdcddaabadddbcbaacdbbdccaaaaacccccbbcaddccaddbddabcbcaaadbadbcaddadadbcbaccbbdbdcdcbcaacbbaaaacbaabbbbacbddaccbaabdaabdadbadaadcdaddcbdcddddadadacdcccaddccdbadcdaddcddcbcadadcbdddddaccccddbcbaaacdbaaadddadabbdacadddbbdbbcddddcccddaadaabdddcdadbdbacdaaabdabdaadcbcccacddccbcdacaaadacadcccdacccdddaadabdadacabdcbdacaddcdbaddaddaaccaabddccbbadcbdddddddcccbccaccdccabbdddadacdbdbbdbdddaccddcabdcacabbbbbdccacbacbcbcaaacdcdacbccadbbdcbcbadbccabdbdbcbdcbaddcbccaaacaaaddabdbcdbbddbaddccdadbccbbbdcccddbbcadbadbdbaabcaacdacbdccadacbaccaadddddbdcdcacbbcbdabaaaaccabdddbbacaddccbababdbcadcdcdcaabbabcbaadbddbcdcdabdabaaaaccaabcdbaccabcbbcbaccacaaddbbbdccccaacaddddddbdadadcbdbdddabaccbaabbbadbdaaddcbabcddbbdcdbdbbdddcbaabcadcdbadbdbadccaccaaacacbbaccbbaaaabadadcbadbbcdcddddcdcdaaaadcbdccabddcddbcbbdacbbcdcdcddccbdbacbdadcdbaadbacbbcbcbcdbacbccacbccdcccabdbadbcdabababdbcdabcbbbcacbdccdbbccbdddbbcbabcdaacacabbacbcbbbbbcdcdacdbcdbbdcdbccccaddbbcbcdbcdbdadbcacacaabcacdbcbcbddcccdacabcbdcdaaabdbabacddbdbbcbdccdddcdbbbaaadcbbdddaacabaabaadbccddaddddccdcabbbaddbdaddbbaadbddaaddbcccccccabccacadddcacbbdbccbdbbbbcdabaddbcccdddaadccbccaabdbaacbdbdbcdcddbbddbbbdaabacacbbcdcdaccbcaabcbaabccdccbcbcddcbbddccabbabbaaaadaddaccddaccccddcbadaadbacdaddddcbbadadbcadadddcdddddbcacacdbaabcdabaaddcbadcacdcadcaccddcaabdddcbdbdbbbacacadddacbaabcbddbbbadadccaabdbcadacdbbbbdddaccadcbbddbbadaaddbbccacacdddadbadcdddabbdcbbdcbccaadbccdbccdbadbadabbcbabaccbadcadacbddbccaaaccbcccdababadccdabacadcabcabacdbbcabcdcadabccacacbbdacbcabbaaabbaabcdcabcabddbcccabdbbabcbdcdaabdaddbcdacdbbccdadaabbaccddbbcbaadaddaaabdadcdadbadcacbbabacacbccddbcbddbaadbaaccaabadaaadaacdabccaabbacdcaddddabbdbabdddabbaacddababbdaccdcdbdbbbccacdbcabddacdcadccabcccbacacccbdbbacccdcddccaddaabdbcadcdbdaddcacdbaddadabbbdadaadbcacaccaababbbaabcdbaccaddddbaabcabadaadcbbdddddadbbbaabccacbdacdbdbdbcaabcbcbadbacbbdbbcacbcaabacacaadadabbcccdabbadbbcdbcccbbdadcaadaacddacbbababcbacdcbadcacccdbbabadcbccadbdddbcadaaadabbdbcccccccddcdccaacdbbaaadabaaaaddcacdccdadaddddbbcdbbaadacacacbccdaabdbaaadbbaccbbcddbbadccdbdbbccabcadaaabbabbccdcacbcddbabccbacdbcddadadbadccdcdcacaccccdacccbaacbaadbaadbbaabdbbdbdddbadcadacbaccdcbdcabbdabddbaacbadbcbdbaccaabcdcabaddabadcdadabccbbcbdccddbcbbcadccadbdbdcacbadaddcbbcaaaaddbacddaadccadbaabdacaabcbbcbcccadccccaacbbcabadbdbdcccddccadcbabcdacbdcbdbabbdbaccccaccdcdddadbcaacddaacbbacbdbbaccddadcaaacdabbacccbddcbaaabcccaadccbccccbccadaadccaacdcabdabcdccdccdccaaddadccdaabbbdadabdcbcabdcddadacbbbcbaccbdcabadaacccccbdaccadadcbaaccbcaccddbcbbbcbbbdbaddadbbbadacbacbbcabcbdaaadcadcadaabdcbaaadcbbababcadbcbccaddbacaaacacddbdadaddbcbcadacaacbcaabbaabdbddadccacabdcbdadaccbdaacdbdabdbacaadcccbdccadcadcadcacacbdabababaadbddccadbabcacbbccbcabbadcaaacbcbcccaaddcacbabbaaaaccbbdbbadcaddbababccbdadddcccdabbcbdabbbacadcdccccddaaaddddbbddbabcdcdcccddbbcddbbbccddcccbcdbcabcbadadcdbadcbddaabacaddabbcbcbbdaddbcdcbbdbdaccbccdacdddacaaabdacabadaabddacacdacacadcadcbcacbcdcbdbaacbcccabddddbaadbbaacbdcabdcacbccbaabcdcadaddcdcdacdadccbcaccacbbbccccbcbcddaaaadbdcdadcbacacbabbdbdcbbadabcdbabcbacdcdaacddcbbbdcbdcadbdababacababbcacbdbaddbabdbccadaaadadaadddbbbcaccdcacccacdacbadbbbcdccdcccdaadbdcdbdbacaabbabbcdaacbabdbbdcdbcddaccbcbbbccbbcdacacddbdacbddbbacddbccdccabacacdabcdacbdddbbccabaadbdcdadcbaccdbcabbdddaabbcbddbcacaabbcccccabdbbbbdcabdccabacdbdcaddaabdcabbdcaacbbbaccdbdbbacccdbdcbddbdccabbababcdcbaddaacddddcacabcdddcaabccaacddccdcdcabdbcdcbcdddcabadabdbdddcdbcdcddadddbdcbabbdaccadacdbbdccaacdadcdccdbcddcddbaaddddcdbdaddabdbbcdcbdbcbaaadcdaaccbadbbdcbdcadabadbacbbcacadabbcbbbdddddcdcbdcdbbabbcbbaaabbaacbbdcbdadcabddbcaabaccdcdbcbcbbbcbdddabdbacddddbadbdcacacddaabcdadbdacbdcacaadbbdcbbdcabcdbbddaabdcdbdcdbdddcaaacbdacaadbacadaddacacbdadaaddccbddbaccaaaaccbacaaaddbaddbadbaacccacddddadaacccbadbaadaddccaaadadccdbddbdbbddbabdaadabbbcbbacacbddaabdbdddaccddcadcababdbaabaabbadadccddadccbccccbdadbbbaaabcdababdabbacabdddacaadadacbcbdcabcdcbbcadcaaabbddacadddabdcdddcbdcadbaababadcdbcdcbacaccdbdaaabcbccbddcbbacbdaaacbcdcaacccbbcddbacddbddadaacdadbbddadcaaacdaacbbcabaabbdabbddbbaacdbaacdbbbabdacddcadacdcdddddbddaacbdbbcbadbcaddabaccbadaaccccddbcccadcaacacaaadabddccdadbbbbcbbdcbaddaddccbaccbaccbaabbccabaabbabbdccaaacbcdabdbbbbddcdabcacaacdbdacdbdadccdbdddaaabbdccbcbcdcbacabdbcabcbcbadcabbbaddaabddddbdaabbabbabcddcbdcdbdabbcdbccddddbaddcccdcaaccbdadcbcdabadcdcbbdbaccbbbbcbadababddacccdccaccbacbdbbdcaddcdacaabcabbccbabacadcdcbdacccabccbcdbcdcdcbadccaabadcccaabdddcacccaadbadbcbbaabcddcddaaaddbcccadadcdcbadadcacbcbbcdbaabaaccdaddacaabbccdabdbdbdabbdbaaccdddcababddadbbbccaccacababdabbbadaadbbcdbdbbdaddbcbadcbdddcbbaadcbcbbbcacbbbaacbcddacdbddacbbacbbadccbcdacdbcbaabadaddbabadcccbcdcdbbdbdaccabacdaddbccacaacdbbcacbacbdbabcdccbdbaccadbcbddabaadcddadaccbcaadbcdbcddacbbabbacadbaaadcaccbdcbbcccaccbbccaadbcccbdcacacacbaacdddcdcadaadcacabdbdcccaddcaddbacdcacaababbdbbccabaabbddcccdcccaaaaccbdbcadaccacbdbcadcdaadcbbbaaacaacbabcadabccabbdcbbcdbdbdcacbbdcacdbabcabaddaddcadcdacbdcbcacdadccbaaacdadcdbdbaadbcdbbcddbcdcdaddaaadbadbddddabbcbccbdbacdbcaccadbcbdccaabbabcdddadcbdcadacaacbaaadbaadaabdbbbcdcabbddcccdadbcbbccdcbadbcbbbadbcdbadbccccbcbdadccdacddcadcaabaddcbccaaccbcaaccdbcdcbbddaaaadabcadbcbbdcacaacabddbcdcbbadaaaaadcadaacaacdcadddcacddcdcbabdbcbdbbdacaacdbaadaadcbadadbdccbabcccccbcbccadaaadacdccbacdadaabbccbcdcddddcccaaadaababcdcbdccdbaaabbdaacabbacbbdbbdaabbacddabdbccacccdaacaddbbbbbddcacadabccdacdcacbccadcabdcbadcacabdadcaaabbcdbbbaababaccdbcaadddddcbddabbdccaacbaaadccdcdbaccacddabcbbbcacbcdbbbbddaacccbaccdadbcddbbdbaaaabaacddbddbbaddccacabbdcdddccaacbaacccdcaddabdccbbdcdcabcaccdccdaabccadcdddabccadbcbbdbcbadabcddadbadbaabccadcdddbdcddddadbdbcdbbcbabbabbbadbabdbbccbbbddbddbccddaaabdccaddabdcbbcdabaabcabdcbdbaddbdbdcabaabbdcbaacbccdabcbbcbcbcacdbacbaacbadacdabadbccbaadaccdabcbcadcaaccaddcabddcccbdcbcddbbdccabbaabaddccbabbcaadcbbcacaadbdcbcdbaabdadccbabbcaaddcaacaacaacacdaccdbdcadcaaddccadadcabbbadadccababbacbdacbbddaacadbcbbbbaadaacdcdabdddacbdabbaddccdbabcbbcabbabdbcddbcaabdbbcaaaacbcaddaadcabdcbcbccdcabacdcccbabdacbbccbbbddcaabbbbbadababddcabaabaacbbcbddbaadaccbaabbdbbddbdadcbaabadccbddcabadbabaaadbabcacacdaddcabdddbcabdcbddbdccaabdcabdbaacccdacdabbdbcacdbdbbbcccbcadcbabdacbbdcacdadcdacbcdabbcdbcadabadacaacbdccbcadddabdabababbdaacdcbacbcbabacdadbcddabbdcdadbcdabaccadaacccbadcbcbcdbacaacacbcadabdaaccccadabdacabaccdcbcaababcdbccbcccadcaddacdbaddadcdcdccaadadbaacddaddbadabdcbcaccaddcbaaaacbcdacabbacbbddccabcdddccdcadddbababdcdcddcdccadbdacbbbabcbaaabbabaacaaabbabbabaccbbddcaabadbcbcbddbdbdaaddcaacaaaaccbbbdbbbddacccadbcaabccdccacdbdcaadaaaabaadbcaaddadcbdaaadccacdcccdcccbdcadccabdcddbcbdbaadcabaccbbadbdaacadbddbbabcdbcccaadbcbaaacbcddcbdacbaadbdadaddccadbddbadacccccbbbdccdaabdbdaaaccaadabaccacdcacbbcabacbcacaddacdcbcbbdadcbddbbabbccaccaddbccacaabcbccdcaccabcacadbccdcadaadaadbdabadacaaddbaaaddbacdaacdcaaadbcadadacabaaaabcdcdbcddcbcccbdcccdaaabadcaddabdbacbcacabbaaadaadccbcdbcdaabbaaacaabbabbbbdcdbbbddbdadaadbcbabcbbddbcdbacadaacbdbadbcabbdbcbdaddcbacbdaaddbcdbdcbadbbbcaccacdaacaadabddbcadbdbbbdcaabbaacbbbccaaaaabacdddbcbadddbdbcdaaccddadcbdbbbbbbabbdddaacabaadcabdcaabddcdbabcbaddbadbdaadbabdadbddbbdddddbbdbccbcacdadcbacdbdcdcabcdcbdbcbbbdabaaadcacabdcabcdbbdadababcaaccabaddddbdbadcbcbdccacabaabaabdacbdcdccddcdadbabccdcacbcdbbddabddacaddacbdcbbacaacdbddbcaddadabbdcdcabbbbaaacdadbcbdbaadbbcadcadbddacbdcdcbaddbadadbdcaacadadcbdbacbcdbddbabcccdbbdbcdcccbbadddbdadcdcbbbacdbdacdcdcbbaadddacccddaddbcddcbccdaacddcacaaccaacaacacadcbdccdacccbbabddbbddddbdacbdadbdccbabadccdbdcddadaacadaabbbbcbbacccbabbdaddbcdacdadbbcdcddcaadbdaddcbdababcdcaaacccabaccaaddabaadadbbcbcbcadbcdaddaabdacbcbbabacdbaaabdbdabaacdbaabcadddbcccaabababdabdcabaadcdabadabaabcaddbabdcbdbdaccbacbaabacacdaddaadababaacabaaabcdabbaacbbcaaacbacbcccadbccacbccddbddbddddbaabbbccbcccbdddcaddbabbcbbbabdadbcabaddadcbbbcdcadccbdbcaadcccccdacbcbccddcadcabacbccadccdcaadaaaddcdbadacdadaabbbcdabbbbbacbccaacdcdbbcdbdddcdacdcdbcbbabccbcccdccaaabaaddacddcbacdbacddbabddacbabacdbbbaddbaabdadbdaabdacdbdadcdbcdddcbcdcddadcdcdabcbabccdcbabccacadadaabbbbcbbacbdcaddcacccbccadbaadabbadbaadbaaaaddbacdccdaccbaabbbadaadadbcbaabbacdbaaabbaddcbacdccadccdcddbacdbdbbdcaccdbadcaacadcbbcbcaaaadadabddadbbdaacbbdabdbdccbccbbaaadddcaadadbadccdcacbccaaadbdabdaaacdddacdbccdcccabcaabcdcadaacabaabcbcdacaabdbbaaccaacadccaadcdcdcbcaaabbaaabcdaadbbbdcabaabbacbdcbcdadccdcbdadcabdbcbcbcdaddaaabbcdacbaaabccdbadcccadccaabccadbacdaabccbcabdbcadcccbcbcbcabcbacabccbcdbbacddbbacbddcdcabcaddbbadbdcacdbacdcdbbdcabdcccdcdbaaabbdbcbdaacabcbdcbdddbbdbdbdbdaddaacbccabcadbcdbdacacdbbabdababdcadacadaaccccbdddcacddddadadbbbaaaaacdbdcdacccddbdddcabbcbcacdbcdbcabbdcabcdaccbadabbdbbccbaddabacddabbdcaddadddbcbdabdddbcdcbdbaabcaddaaabcdccbcdcddaaccdacabbdcdadbccddddcaaadddbdadbcdcbbcccdddbcaadcbccdcbdcddbddabbdacdadcccdacaaaadddddabcdcbccacaadddacacacadbadccacbabbccababcdadcdbbcdaacadabbcbbadcdadcddcbbbbabbccdcddccbcdbacdabcbbdbabdbccabbcdabcababbdbdabdcacaadcddabcdabcdabbcdbabdcbbdddccdcbbccdcdacaddbbcacacdadccacdabdcddadcdcbdbadbbdabddaaadbcaabbcccdaabbcbddcabdbcccbabaddcbbaddaccabacacbdacddacddbaaaadcddccbccbbdbbaabaccbccadddcdadbbbaaabcbaadddacddabaccdbabdcdbadbaadcccdbccbabbccbdbcbcdabacadbdaccaabababcbabdbcdbacaaaabaaddbbcdaadcbbaabacdbaddbcabaccabbaddbbdabacadaccaaadbadaccaabbcbbacccacbcccbdbdabbbacabddaacbbcbacbccdbdbdacdabbcddbaaadbccdccccbbbdbabadcdbacacbbaccabaccaadadcbbadacbbcddadddadaaababddbacababbabbbbdaaaddcbabaccddaaaddacbbadacaddbbbbddaccadcabcbbddbbaccadbbddbcbcbacccbaaddcbdcbdbbdccbbcdacbccbbcbadacaccbccbabccbdcdcabbdabcaccbbddcccdccadaddacdcbddaabdadaadbbcbaccdbddcbcbdbbbdbcddaddadddcbabdbbbccddccdbaadbdcacabacdaddcdcadababcabaddcbbbbcbddccdacddcdcbddbdadbabbdccbbacdbdddddbbacabcbbadbcdbadddaabbaddccbdcadcbdbadcdccdccbbbacdabacbcacbcbcbdbcadbcbddbaababbbbcadaaacbddcdcddcdbbaabdaaaccdcccadbdadccaddcabadcdcccadbdbbdaacaccdcbadadccabdcccadcdabcccdbdbddccbbcdbaacadabcdcaaabbbbbaadaabacdbbccabcabdbabddabccbcbaadaadacdabbddadbddcbacaccacbcdbbdabdcbddbccadacabbacdbbcbdcbabaaddbbbbbdbdbbddcacbcdccadccaaabcdabbbccddbdddbaacabbabcbaaaccdbacadacbbbadadddaabbccbbabbbaadadcddabcdcaabdbacdcdacdaaabcacabddaddcbaacbacabcdcdbcaadaabdbbcacaddccbcaaccabbcdbdcddacbdcdadccbcacadbbdddaccbcbcaacbdbbbacaddbdcabbcdddcaccdaabbbbadcabbacbbcdbacbabacbdcccddbcdbcadbadadddcabbccbadddbacdabddcabbddbabccaabccdaabcdadbaddaacdddcbdbbbddaadadcdaccddbbdcaaaddacacddbbdaacccadcdcbcdababaaaabacbacdbccdddbacbcacbbabbbaadbbcdcdcadbacadcdaaabddbaacdcacdadcaddbdbbadadbaccdccbcaaacbdbbabdbacbbcdcddcdcbbdcbacdabcddccbbbaaadbddcccbbaccdddcaabdacbcaababbddadaadbbbabaddcbadacbdadddbdacdbaddabcadddcbabddbcbaddcacdcbabcaabbaacbaababccdbcdacabaaddadbcbaadcbcdcaaddcdcdadcbccbddccddbbaddbddcdcaccbccbabbadbdcbcdbdcaccaddcdcbacbdbccbadcbbccbddbaaddbacbcababcdbdddbdccbcadcabcccaaabdadbbbcddaadbcddcbababdbcbbcdaacadddaabcaabccabdaadcbacddbcccbbabaadbbcbacbaddadabdddcbdaaadabcbcbbdbccbbddabdbaccddcbbdcabbacbdbcbccaccadbabacaacbbbbdddcbcbabbbdacbdacdbdcadcbccdcbaaddabbdddaadbcaabcbbbbdbddbdaddabbdcbacdbaaaccbcaabcadabcdbaaccdacaaacdcacaadadbbbaccbdcbcbbccdcbabbbaabddbcacdcbaddccdcbddaaabccbdbdcdbabcddbdcddccaacdcbadcdcbbabdbccaacdbcbacbdcbaadadccdddbcaccaabcaddacdabbaaaadbcbcacadccdcbbaacaadadcdbbbbccaccbaadbddaddbccdddbbcaabdcaddacdbbabcacccbcaccadcbddbdadadbadbadaddaacdabdbcdccacbaadaccbdcbbcdbdadbdbbdbbaddcbcacbdbddbbcdaacadbbcbdbdacdabacccdcddddcccddadadbdddaaddabaaabbdcdaddabadbdadcacbacaabbcbccbbbadcbcddaccccaddddacaaacdbbdbcccdcaccdcdacdcaacbacdbccacabbabbaadddacdbdccdbdbdbcaccbbadcddccacddbcbbbccabbacccbacbdddddabcacacdbacababbbadaaccabbbdbbbccacddbdadaccbbdbbdadaabcadccbbcddaccdcbccbadbbdbadccbcadacbddbccbdcacdcacabbdadbdccbdcdaccacacccdbbcbbbbbdbbbcaaccddcccdbcdbbddacdabadacdcacaabcdddddcbacdbcbbbddacaacdbacaaaabbddadbadbddbcbaacbdbabbdcabcdaddcbdcaaddacbdbdcdcbdbdbabbbaccbcdadddbdcdddbdcaabdddacdabdabaababccbccadbdaaaacbcdaaabcabaacabbbbbcbdaaacccacdbbdadcdbdbbbdcdaabdbdabcbbdcbbbcdccabdcccbcccbbbcbdbdadabbbbcbcdacacbbbabacbbcbbcacbdbbcadadaaccbcdcdbcaaaccccbcaacdbbaccabbbaaabddaaabdcccddcbbdacabcdaacddbbbabdccbccadbbaaaddcbcabbcabababbdaccbcaacbdbdcccdacbcbdcbcbddddcbbdcdbbddaadabcbccbbaaabdccddcacccbbbccdbbaadcacbccabccbbdacdcacbbaddcbabdadbbdabccdbdabddbabaddadcdcbccaddacdadabbccbccaccdabadbabbbbbdbdbcddcdbdbdcccddcabddcbdacbabcddacadcabdacdcbbcdbdacacbacaddadcdcaacabdddbacccaabacaadaabdcabbbbcadcbddadccaaddcbaadcbcaacdcabcbadbcdbdccdabccbbbbdcbcbcacdbdabcbabaccbbadacbbddabbaadccaccdcbabcbccbcbcdcdbcabcbcbddcbadcccdabbdcbaaacacbaaddbdaabdbdadaabacbbcdcaaaadcadbdbacbadcbddbbdcabaabcbbccbabdaacabacabcbccbdcaccababddaaaabddabdacadbdacbdaacbcbcabddcdbcacbacaadbaaaadcadbbbddcabaddcacddadcbaabbccbdcaadadcbddbbaccbbbbccdddacacbddcaadddcadbaddbbcaccbdacadbcdcadbdadcaaadbbddcaabcbabadacacadcadbabaabbdddcabdbbbaccbbdbacbddbdaadcbdabbadcbaadcacacacadaaaadbdaadbdabbbcccbcadbdcaadabbcdbcbadbbdbccbdcdcdadadddcabcbabdacccaddadaddcdcdbcabbacddcbbcabbccbddcadbbcbdccaaacdcacadcbccacbaadbbdbbbccbaabddbddbddaabaccbcdbdacacddacadcabdcbbdacbbaddbdacddacadbdcdbaacabaccabadbbdddbddbbdcaaabdcddcbcdcccacccaaabddbcddcbdbbdbddabcdaadccccdbccdabdbabbaddbaaacbaddcadbabbdacccbacdaaccdccbbacbaadaddcbdaccbacccdbdaadbbbcbacccaccadbadadadbbbdadbacaccdcdbbcdabdbdcdbbbbbdccaadbacbbcbbacacacddaacdbbaccdadbbdddacadabddbacbbccadbbcbbbcabcbdbcbbbcddbcbbadbcbcdaccaccbdcbacbbcadcbacddacdbdbacdadcaaddddccaddbccaadbacdadadbbbdcabbbaacbccdaccbcacdddbdcbacbbccdcacdbaaadaaddcbcccccdbcbadcccbacddbcbacdabdcadcbaddcbbabdaccdbbbcdbaccaddabdacdcdccdaaacdbcadaaacddccbdddcabcaaaccccbbcbbddcbbaaaacabdccbaccbacdcdababdbbbdbababddabaadcbbacdbaaacdbcbbcbcaddadddbbbdcadcabddcbcacadbdbddcddcdcbbaabccbdaccabbaaacdaaaaaddbcacaacacbddddccabbadddacacbadcdbcdadbabacdacabbddbdcbcbddddccccdcbddbddccbabbcbbadcbcabbdacabadbdbadccbcddcdddbababbbbacdbadbccddabadbbcdccaaacbdacaaccaadabaccaccdadaaadadccdbcbdcabcbadbacdbcadbaddccabacabcddbdccdabaabbadccabbbcbabdbaabacddabcbdbdccbabbdcbbcbbbcddcaabaaadcdaadcacbcacdcaaccaabdabacbcdbbbbaaccbdcccbabdacccbdbbbcbaccbbbccdcbbbabbadbbaaadabcbaadbababaacdcadccccabadddaaaccababbadbbdcbdacacacdccddcacdaaccacababaddcacbacdacbaadcacddbcbaadadaacadbcbdaccadbadbdbaaddaadbcdcbaadacaccbdcaaccaacaacdaadadabdccabbadabbadacbcabddacabccadbabdadaabaacccdcadadbcdbcdbabddbccadbbaababddacacbdbddbcbcacddbcccbabbdabdaacdcdbadcadadaccccabccdacdaadaadaadbcbbbabcdaaabadababadbadccadbdaacbccccbacdaacdbcadadcbccbbaacdaddccdcdcacdcdbabdcddcbcaaddccbacabcaccbbbbccdaddbcbaaccdbdbdacbcbbabaabcdcadbbbbdadbabcdcddcbcdddddaddccdcdabbbabaacdbaabcabcdcacdbcbdcbbaccdaddbaaccbabccbaacdbbbdadbadabcbacbdddcaacbacaddddbbccddaccdbccddbbacdccaaccbcdbbbacaabccbdbdbccdbbcbdbbcadabbccdacdbbbbcadbbdabcaccabaaadbadadbbbbcbdcbcddbdabbcbcbabaddbdbbaacbbccdcdbbcbbcccccdbcdbcbaacabbcaaddaadcdccbacaaddbbcadababacacdcaabcbbabbccbbdaaaaadaaaadcccabadccbaadadaadaaadbdcccadbcbaadabaddddacdbbddbbaaccbbcadcbbabcbacadcbbdbcddbbcbaacadaddbcadbabdcabbabccbbdaaaddabadddcbddbbdaaadbbcbddccdcbaaadcbddaaccbcdcbcaccabbabbcabbcaabaacaaadbdcadbdabdddbacdababacadacddcacbcddaadccdbacabbdccadccaaabaddbdaacaadabbabbdbbabdbdabbbacdcdddbabacbccbcaaacaacadccacbbadcbdbaabbdcbbbabbbacccccaddadcccaababddbddcdcdabdadccabcdcdbcddcbddaccaadabadabbcaaadabdbbdaaabdbdaabacadbacacddcdcdaaccacdaaacbbcdadacddddaddaddcdcdacdcdbcbdccbaccaddcadadddcccddaadadddadadddbacbdcdbaabcdbdbbdbabccaaaddbcacbcbdccccacbadccaadabddddbcdaaadcbdbbcabbdacbccbbcccdcddbbdaadadbdbadcccdbdbbcdacddbcadcddcaaaacdccbacdbcbdcadadcaaabadddbabddcbdbddbdacabacadddccaabbdbaacaacaaabddacbbcdbaccdadcaabddcbccccabcacabcdddccbcbacacdcacabdcdccdababdcadbddccbabcaccadaaaccadcaacdcdcccbabdbcdcdbcbddbcaadadadbdacbcaddddcbdabcbacdacbabdbbccbcdbccaddddabdabdbdacbcdaabadaaaadcdccaaaccbddbbbbcbccacbbdbddacaccbacbdadccaddcdcbccbbcbbccbabdcabdacbbdcacddccccbaaddbdcaaaaccddbddcbaddcacbcdbadacbcbaddccaccdacbdddacbacdbdabcbabcabddadbcadcaabbbddbdbcacddaacccdbcabccbbdbbaccadcdbacdccaccbbddcccaabbddacbaacdcadbacbbcbaabccbdcacdbaadbacacadaadccbddbdbcdadccbcbacddaaacbdbbadbacabcbcabbdddaccdabdaacdcbddbbdadaaacdbcabbabaaddbcaacddcbcdbdbdaccbbacababccdcbacbdaaddaccccbdadbddcabbbccaccdaddacaabcadcadcacbcaacdacadbcbbbbcdbdcdccaacccccdccacaaabcaaaabcabccddacabcccccbdbaaaccbacabbabacbadabaccadcbaaccadcdddaadcdbadbaccdaddbbbddcccdaabdbcaacaccbccdacdacdbbcbbcbacbdbdcbdcbccbaabbddcdbaaabadcacbccbcccacbadacacdadbabaadcdacbdacdadadbaaaaabdbbdddacccadabcbcbaaddccaccaacbbbaadbabdaadddcaabacdaadbcdbcccacdccdccbcddbcccabcdaaadcddbadaabbaaacaadbacdbbdabaddddaddcaddbdcadaabdacbbdccabbadcbdaadadadacabdbbbbbbbdacaabaacdbdbdcccacababacbaccbbbcababaaadababdacadaddddaccabdabbddcabadbdcccddbdbbdccdbdabaaadbbdccabcacbaadddaccdccccaadaaabdcbbdacbadabdaabacdbadbbdbdadbaaabacdcbbbcaccbbadcacaddccdcdabbcbcbbddcbbbadbcaaabdcbbdbabacdadbacdbdcaabdbbcdddbcdcbcadaddccadcdcaccdaaaddcdcabdcbabaacbdcbbcdbaadddccddcccadaddcacacccbdbcdabadbcbacbadbcccabcaabbadcbcaacabddaabcddbcdadbbcaaadaabcbbcbbdddbdcbbaadccccaccbbdccdcadabdbdbbadbdadcdddacccdcaaddadaadbdbcdaaadadcdccbcccbccdcbdaaccbbaabbcdabbbbadcbaaaadbdbccbbaaaccddbcbccbddcdacdcbcbbbbbcabdcbacadaccdbbbadabdbdcdccbcbacacdcbbcbdbaabaabccdcbccacddcbbcbcdaaddbaaccaabdcaabbaababaacaadddcddcadaaddcaaccccbddbcbcbcdcbbdcadbcbbcbacdcabdbcaaabcdcadadcdabdbaababcbaacacbadaccccbbaccdbacdbdbbacacabdbdabacdadbabcaabadddaadacbbcabdcabaccdbbcddcdadcdcbdbbcdaaabcddadcaccadacdcccccabdbcdaccbdadddcdaaddaabbaccabaaadcbdbbcbddddacaddcbaaaddaddbdddbaacddcbaacacacadbccbadcddacdbdcbdbcaadcadaabcabbbbcbbaddcbcbaccabaccbabdcdbacacaaadbbcabcdadcaacabcaddccbdcaaacabbadabcbddcaacbccdbadbaabaaddaaacacabacbcaaddadddbabbcbbddbaaaacbcdccdabcdaadadddcddadcbcadadbdaccbadabadccabacabdbdacaabadacccacbaabbccdcbacadbbacaadadbbaabbbadbdaadbacdcadabaacacdbbbcadbcddacaadaaddccacbaabdabacddbbbbcdbcccbbaccadaacabbdacbcbccdccddabbaccadacbacddaaabaacbadaccdcbacddabdccabcbcadaacaaddacadcabdbdccdbdcbccdbbadaaadbbaccaddccdbbaccdccbbcdddcaddddcabddadbaabaadbbdbcbdaacbcdcbaacdaabdaacabddcbabdcadccabdacbbcdcdddbcdbdababdcaccbcbbbacdbcccdbccbbbaaacbabdbbdcadadacaccbcbacbbbdbaabdaabddaabbcbbccdaccabcccccbbbccccabcbaddadccbcaacaddcbdacbdabbbddbddddccddcbddccaacdaabdcadacdbbcbdddddbbbacadbbbdddccdbcabbbbddbaaaabbbdbdcccdbccdddcbaccddccbabcbacbabccdcdbdcacadcbdcaccccddddadcbbbdcaabcacdacccacabbbccdbccbbdaddccdcbaccdabccaacdbddacababcbdbabcdbacabaaaddcdcdbbdbbdcbacdcabbdcccacabdbacdbdcadbdcaabcbbdbddabcadcdaccaddadbbccddacacbbcddccadaadcccbbcdbbacdadababbcbabaababdaaaaabcadacbbbdcaabcacabcaadadcdacbdaacbabcbbbcdaaccdddcbaaddbacdadcbbbadccdcdbaccabddddcabbadbcdccbaadddbbcbaababbcbddcabadacbdccccbacdacbaddacaddabcdbccbcbaaabbcbaabdadbcbbccbbbdbcbcabbccaadcabcddaababbacccdaabcbcdccdabaadacccacdccbadcabbadddacdababaabcacaabcaacbddcccbcaaaadacaabcacbbacbbcacdabacaddccabbdcbabbaacccbaabacdbcacdbcdbadddacddbddacaabcddbcdcbaaaddddccddacbcbdbabbcdacaabdbcbacadcbdabbcddbdcabaddcbcababcbbdddabdcbbbadcdbaaddacbabacadbcdaaacccbcbbcddccabcdccababcccdacddbbaababdcddcaadcbdccddacbcbccdabcbbdbdaccbaccaadcabacaaddacabbdbdabdabbdbcdbbadddadcdbabacbcadcaabcabccaaacadbbdcdaccbcdacaccaadbacbddbdabbbaaacbddaaacacccaddbcdadcdccbdddcdbbdaaddabbcbbcbcbcacdabdadadaccbcbabcbbddbbadcdacbbbabbcbaacbadcabccdcababbdacbcdaadaccdccacdcaccbbbbaccbcaccadbaacbcdaccaaddccbcdabdbcddbddbddcdbddddadbaadadadcabacbcbddddabadcaababbaabddbcbdabcdbcdabbacdbbbbbabcbbbcdddbdcadccadcdabdadbcabadaaddadacbcbbcdcabadabdaaddaabbdbaadcdbbabcbbcaaccacaaaadbbbbadaccabcbbadbcadcbadcdabdbacbadbddaaadbdabcddaaabcaabdbccbbbddddbdccccbcabdbbccbabbadbbdbabbbccbaacabdaaacddbbadbdcddbaaacdaadccaabbdbbddddbdaabadbcdcabcccabbbccaabbbaccddaabdcdddbddcbcbdcbdddacccbcbdadaacdcbacaaadabbdcdbabdcbcdcccacdccabadccddcbbadacababaddcbbdcbcddaadabacdddbbaaaaaaddaddcdaabacdcdadcaaaccacbabaaddcaddbbaacccbbbcdcbcccdbcbcadabdaabddccabdacacacccddbbdccbdacaadbaaababdacaaccdcaddddccdcadabcbdbdcbacccaccbccadcbabbbcccbbaaaaaaccbccacbabbbcdcbcbdddabcdcddccdbdcddaddbbcdcbdcdcaccccbadacbcdadaaccadacddbcaadbdccdacdaacabccabcabcddbcabbdaadbddadadccbdacdbdbbaccddaadccccdcbcdbbccddddbabddddbadbaddbbcaadddacdccacbdccbdacbcddbdccdaaabaadbaddcadddabadaccabaababbdcacdddbaaccdababcbcacbaaccbdcacdabdccccbdcacabbabaddadbaccbdccddcabbbcbabccbadaccddddacbcacbbbbbcbbdaaabbccaadcbbcdcdbbacbbddbbacdcadbadadddbbbaabaadbdddaadcadcbabadabbcdadbbadcbdadccbddbabacdadbbaacabcbdacbdbccbddaaacbbdbabddcbaacdbcccaddcdacdbacaaaabdcddccdaacbccbccacaddadddacbbdaaaaddcddbbbcacddcbaaccdcdbcdcbdccbcccdddcbadbbdadbadbdbcaddabdcaacbdcbdcdbdcaccccdcdbdccaadddadddaaddacccbdbcdbabdbdaddbcccbdbbdaddddacabccdcaaadaabadcabcadccbbacbdddbbadcabcabdaddcbadddcbadbbccbbaabcacabddcabcdabbaccdcdddcdbbbccdcabcadcbddacbdabcaccdddbddbbdccbdbcaaacacdbacdbcbdbbaccccbaababdaccbaddadabcadaabbcabcccdaaacdadcdbacdbcdbddcadbbbabaddbdacbccabadcdadbdaaadaaaccbbdccdcdbaacddcbbbdabadaccccadbdaaadcadbbcdcdbbaacadcbabccddadcdddbcdbbaacccacaacbbdbdbabddcadddcbddbabbddaacbdabaacaacadcdbacddabccbaddbbaccdbaddbbaaaddabdddbccdbabbaabbdcbdaaccbcccdcbbbcabcddadcbcaadbbaaabdbccaaccabbbaaddbcdabacbabadbaccaccbcaddbdaacbdacadcbbacabbcbdcaabdbcccaddacdbdcabdbcbcaccadadcbdbbccccdcdbacbdbabdccdabddacdacaabaadbcababbaacbacccdaccccadabcababadacacdadaabbaddcdcdbacaddcbbcbaaacbacdcdcdaaaabdbbadcaccdbdaccaadaabbdbdabcddaccadcacbcdacbabcadadcabdabaaaccdcaaaccbcbcacbbadcbcbabcaddbccadbcabacbaabddbbddabdcbcdadbdbcacbcaabcbaaabcdacdbbcbdbcadbdbdadaaaabbccaacdcbdcaaadcacbcddcccdcacabbdbcccdcadccccbaaccdabddabbdadcdacccdaabccbddcdbdcccaccbbbdaaaacdccabbccabbdabcbbdcbabddabdbadbabdaabadabcbbdcadbbccadaaddbaacbddbaadddddccabdbaaacbdabaccdcbdbbdaccddabcabbdbbcddbbadcdcaabcaddbbaadcdbbbbbbadcabcdcacdadccadadcbdabbddbbbbaadcdaaddcbcacdbbbaddacdcbdcaabdbcdbdabacbcacbcdcabaccaaccadbabadbdbaaccdbaacbccdcbbbcadacbadddacddadbdaaababbcbadaccacadcbbdbdbabcccbdaddbdccbbacababdaaaabbbaccbaddaabdaaacccbbaacccadabbddcccdbcabbaabbbbcacbcbbaabccaaabbbaadbdabacdbccbacaaaacaabbdaaacacadadacbbcacadbbddccbcdcbbacabccbbbcbabcadadddcacacadbdcaabbccaddcaabcababddbaaababbaaadcbdadadcdbdcdbacabccdddbbcbaaabdacbbbcdddaaccdbbbdccdbbdbcdaccbccbbaaadbcbaddcbdbdccabaaaddccdcbdbcbdcbbcacccabdcbbcdcaabdadddcaaaddacbbdcdaacdccdddbbcaacaacdbbaaddaabbbbcbabbccbacbacadbcadaaaddcdbccbbbdcaacdbcdaabbacddbdddadadbbcdbbadacaaccbdabddbcabdaacbcbdcacdbcccccdcdbbdbbbdacadcdbdddcadaadcbcbaacadccddbdbddbaaaaccaacbdaccabbbcddbbbddabccdabbbbdbdbdccdcbcdcabaabcbbaabadaccdcbddbadcbbdcddacdadaddcbddbdbaacccadcbbcaabcabbdabaacccadaabdacaadabcacdadbaabacbccdbccaaddddcaadbcbbacccdabccbcdadaccccdcadabcdcacacdbdccbbbaacbaccdaaddcdadbdbdacbdabdbaadbccbcaddbbadcdaaccadbacbdbcaaaabaabcbaabdadcddcaccbccadccddacacbbddababdaabbbbacdcdbdadbabcaadbdbbccacabadcbacbaddaadcdbcdddbadbcbbcabaaadcbdddcacdabdcbbdbcbcbabbcdcdbbadcbccdbccaaabbacdcdbbbbdacbabdadddbaddbdbaddbbcadcabaaadbcddbdbaacabbadabbccabdbdaabcacdddcdaaaabbabddcdbbcdddcaccbdccaadcdcacdcbbcaddbaaacccacadccccbdddcaaaddaadbcdddadbbaacdcadacccccabdabdbdadadbadadbccbadcdacadcdacadccdddccdbcabdbdbdbbddddccdcabbcdcdbadbabbaabdcdcdcacacdaadccdcabbccddbcbabdbaddbbbbabbdaabdbbaabdcadaadcddadadcddcbcbbbcbdcacabbabbaccaaccdabbbdaddacbacdccccaadbdcbdbdccaccadbcddcdaddbbbccaadbbbcbaccdcdabdacdbbbdcdccdcbddcbddbaccbabcdbaabadcbbbbacacdbdccccddbbddbbdbdacbbdbddbadcadddbdaccbcaddcabbdbbdabdcbcdaddcdbadabccddadbccdcbdaddcdddcbadadcdccacddaccbccccdbbbadcdbaabaabaaabcdadbdadaddabccbdbaddaaaabadcbdbcbdbdcbcaaaddcbbcabbddadcadcacdaaaaccdccdcaabadddbcbcbadcbcdbaabaadabdbaaaadbabbdaacabcadbccabcdcabcdbbabbbdcbdacbcabcdddbdddcbccdbcbdbcaaaadacddbdaddcbdcacbcdbcdbabaacbaaccbddaccbaddbdbadabbacdbabaadacddddccababdddccacadcdbabccabcabdbddadcabbbaccbabdcbabbddbdacacaddbcccbabccddacbdcbdcbdccdaaccaddbcbbdabcbabdabbcbdcdacaaadbaccdaccdbbdbacdbaddacdaadadcabcacaadcdbdaccdacbbabadbbcabddbadabbbccaddddbcbbdcdbddcdabdddbaaacacacddbddcdcaaddbababcdadaadababcccbabddcbcdbddbdacdbaddbdcbcbcabccbcbaddaddcdbccbdbadaaddbbccaadbdbadbdbaacdadcbbadbdacdabbbadcadcbdadadcdcacddccbaacdcddabadcabaaaadbbdbbcddcbcdacabbcddaaabbbbaabbcaaaacacbccdaacacccaabbbbcabcaadbdbdbdcbdaabababadbcdbcccdabcacadddbcbcacbbdaacccaccacbdccbadccaccadbabccacabcadddcbddbcabbbbdbcabbcdacbdcccadbacccdadacccbcdccddadbcabaaccdaadaabcbacaacdacbcdabbddbadccddcaadaabbdccbbdaaabadcacbcccdbccbbaaadcacdaacdcddbcbdcbbccdbdadcaabaacbddabcadcdbbcdaaaddcaccadcbadbabaddacbbdbcaaabddcbabbcadcabdddbcdbbacdbbbbdcbaadbddcccadbcddabbadccbaabbdbbdcacdbbdccbabddaccbdcabcadbdcadbbbabaabaaabddcbacababbabaacccdcadbcadcadbcbdaadacbbbdbadaccdcbabdadacddccaccaacaacdcaccacacaaccbaabbbdbdbcdcaadbdabcbdbabbcdaababdcbaaabdccccaacbbccadcdaddcdaaadbcdcddcbcbcaabddcdaaccaddbbddcccbbcbadcbdbbbbdabccccdcdbbcdbabbdaacadcacbcbbaaadbcacacdbbdaaabccdabcccddaaaaadccbddacdbcdbacaabaccbdacdacbdbbddccacadccacdddabbdddddccdaadccbacacabcbbabacacaadbabcdbadbdaadddcdadccadadaabbdbacbadcbdbbcbbcabcbdaacbbdaaccbdabadcbdabdaddabdaccdcdbbcabdadabdbcddcdbccaaaabbcbcdbbccbcbdbdbaadadcadaacacaccccabbbbcbbaabaccaaaadcccddbaadddccadcdaddbbdaabcaacbbddacadacdadadbcbaaaaddbdbdbbbdcddacddacdbabaabcdbccadaadccbbdabadcadccdacabdbdaadbcccaddddbcddcddccacbabadacacbcbcdcbbbcabababadabbbddacbdadcbacaabdbddabcbdbbdbabcbccddbdcadaadbadaaaadaccbdccbdbabdcdaabaddadabdadcaacadcbabcadcdcacaacdbbcaddabbcdbbacddacddbbdadccbbbbcabdabadcadcaacbccaaabbcabdcabcdaadcaacbbcabbcbabcadbcdcababdbabdcacdccbcdaababdccdadbcaccdabbdbbcccddcacdcccadcbdbbacabdcbdbcbcdcbdabddbcddccbbcdcbbcdddbacdabccbdddcbcdbdaccbaddbbcdabdbcbcacdbbadddacdcdbdacdaddcdbcdcdbccbdabdcbccaabdaaddbacbdbdddaaababccaccaabbbbbcbdccddabbddbcdcabcccdbdbdacdbabbbdaddbcbddcbddbbdcaacdadcdccbaacdcaaddabbacacbcacbddbcbbbdcbbaccdbaacaabcccbdbaccaacbbcaacaacdabbddbbabbaacdcbdbdbbdbbddcbbbbbbcbcdcbadcabbcabdbaddaacbaaadccddabadaccaaaacdccbbabcabaaadcdabcddcabaddbacdcacbccdbccbacbbbdbcaaadbcadcdcacaabcbadcdcdcbcdacbacdcbddccbbbbdaddcccbdbbddcbaacddbabdadccbdddbddacabdadbcabadbabcbdbcdacdcbabbdcbcabbbccdadbddaaccabcbcdcdcbbabcdbbbbdaaacabbaacdccbcadbcabbbcdcdcddacdbabbadcddbadccbdbcdddadcdcdbbbbbadadbcbcdcabacdcdddaadbcbbbcbabbddbccbdcbaccdddcbabcbababdaacbaaadbdbbabbcbccbcaaabaddbdcacbcaccacbbbddcaddddbdaabdabddaadabddcacddbdccadbcdacbbbbabaabcadbaadbccadcadcbadccccdbcdabbdaaaccabaddabbddaabaabccadddcaacdbdcaadcbcbcdbbcdadcadbbcbbabbbbaadcccacaadadcdcbddbbcdcdcaadccdacddbcbbdaadbcbbacbcdcaaaaadcbbdcaabdcaddccdaaabcbabbbcbabadcdbcccbcdabbbbcccaccdbcaccdcdaaacbdbbdcadbbbadcddcacbaddabdadaabbdbcabbadaccabcdbdacbdcdbbbbacbbaacdddacddbbcddccdbccaabddddbdcbcdbdabbcdccbbcbabadbccccbdbaddcaaaaabcdabdbadbadddacddcbcdaaabbdbaccdaaccbabaadaaabbddaaadaddcbbccacdacdaadbcabadccdddccdbcbacbaabbcdbddacdbadacbdbdcbbdaccaadaaacbcdbacdbcddaccdcadcccbacbacddabadbddbdcadcdccbdbbbdcaccdbcbbcbbabddbacabdcbbaadaaccbacccabcbbbcdcdbddacdacabaabcdcabbbcdacdabcdbddcdbdaabacddcbbbcdcccbcbdadcbcddddbbaacdcbddbadbccdbabdaabcbccdcbcbacbcccddcadcccdabcaacacdcddcddadcbccabddcccdadbdccadccbdaaddaadcdbaaccccaadbabadcaadabdbaaabbdddadbcccabcadcdaacdcdbbcdcddbcdbbcabdbcadacbbcbbacccccddcbbacdddbddadccbdbabcbbaabcbdbacdbaaaaadabdbacccbbdabddacaddcdcabbccccdcbaadddccbaaaccdaddbdcdadbacbdaadbccdbabdbdcdacadbadacdbcabbdccdcdcdabdaabdcbbbdcadbdacaccbaaddddabdddbaddccccdcaabddaccbbabcaabcdccaabbccbabaddacadcadabddccaccbcccbdadccbbadabddccacdbbcccdbbbcdcabcabcccbdbcdcbcdaacddbabdbdaccdbacdcaddadaabbcbcbdbcdbcacbdbadddddcdacdcbdbdbdddbbcadbdbbaaccdbbdabaacdaaaaccdbcabdccbacbacddddbcbcbccbdbddbbcbdccbccabbcddabcabccdbdccbabcccdaaddbbbddabdcbcdccadbccbacabcacdbacabbdacbbcacdabcabcacadccbcbdbacabaddccbbaddcddabddcdadadcbbbcddbdadcaabbbabbccbcdaddccddcdababbcbbbbddbdddcacbbdadcacaadbdbaadccacbacbaacaaccdbdbadcddbbbbbbaccaaadaacbccdaacadacdaaaabbdbcdcabcaabbbddbababcbacadcddcbdbbacabddcddabccdadcbabbcdcaadbdcacadbadddbbbdbdddabadbddbdadcdababcdbabbbbccdddabbbcdcbbbcbbadbbbbcdacccabcbabddbbaccabccaadadaabaabbbbadaadbbbcbabcbbadaadbcdbddadbcbabaacdbaaaaddbdcbabdddcdcdbbcadbdbdabbddadaddbbbaadddabaabdddcdbbbbabdadababbddbccddbabdcbdacddbdbccbcddabcbbdadaaabcadbdbccadcbbdbaacaadbcdddbdbcdcbaddbdddbbdacaadaaacdbcdccdcbbbababdbcbacbdcadadaabbbacbcadbbcbcbbabbcccbddadbbcbadbcddabdacbdabcbcdbabdbcbcabbdcadadccbcbcbddcdcbddacadbcbdbbcdbbbddbadaaaacdadbbdacabcadbbccaddbcbdcccdacbbaddbdcdccaabcdacdabdadbddbccababacaabdbabdabcbcbabadddabcddbdddbccddabbddacbbcdabdaddcddadbbdabbbdbcbbddbbcadcaacacacacaddcccadaddadbbacdbcdccdbddadaacadbcbbbdcbbdcccbababbcabadbadcbdbdcbabdadcacbccbaacbdcabcbdbdaacacbdcaadddbcdacaabcbbccccdabacbdbbbbcaadbadbbbccbaadddccccadabbbcdacabacdbbcccdbadbddbbadbcdcacbdabddcbbdacadddacdaacdbbbddaadbaabdcdbbcbadbcbbdadddcadabdbaadbadbddaabbccaacdbdbccaabdaaccaadbababbcbcdbabacbdcbadcdccdbddddcacbabbdabacbddbadcaaabbadcbabbabaacbbcbcabdaccbacbddbddabdbdcacadcbbccdcacabcddcabbbdbacbccbbadcbadcdbacbbcbaddabbabbbddcdbdcbacdccccdccdbabcaababacdddcbdbbccacccddbcddcbcbbbcbccbabadddaabcabdbdcccbbaaddddbcacababdaacdabcbdcbbbddadabcbbdbaccccbcdbcdcdaccdabbbcdbaacdbdcdacddcccccccbdbbbbaaadabdcacdccccbccaadacdabbccbdbacddcabbcdddaabaacdaaacaadcdababbbaaacddccaabddbbcdabcddcbddadcacdccbaaccaddbadcaaabbcddbdadcbccdabadbbabdcdbbdbbadcacdbbaddddbaabbdbccaabcacbbcbcdaccacbdbdcbccbcabbbaaccbcbdbadacadabdccadabdddddbadbadcababbcbabbbcdcccddcdccacabcccaabadbdabbaacccaaabadbdddccdaaabaacbadcbaaadaacadcaadcdabbcacadabcccbaaccdbaaabaaddcccddbcdbbccbbcbaaabddbadcbadcacadacaabddcbdccadbddccdcdbbbadadcbbabccdbabcbcadbcccccdccdacaadbbaacccaaccddbdcbbbcadbabcccadcdaaaaaddcabcbdadbbdadbaccdaaadcbcaadabaaddaadabdcccacdbddaccdccbdbccabbdacbdbcabcaccdcaadadcdddccccababdaaaccadaccbdbbbdbcdddcbbcdaabbabbaccdbccddbdabddcabcadbdaabcadcaacaacaddbcadcabcbaadcbcccbddcaadadcbabdcdccbcbcdabddadaacaddcbcadcaccbadbbadadcbacdbabbadababccbababcaaccaccdcaadccaadacabcccadadbccbbdadcbaadacbaccbbccaddcbcaacabdccdacadccacaaaaaabdcbdbbcbabaccbaaacbaddcddddaaaaccbbbaccccaccabdbbdacdaacdcadcdabddbdacabcddbaadbaacdbccbbddadbdcbbaddbacccadaddbbbdccdaaddcbaaddbdccbbaaabbcbbacccddadacacdacdcacabdcddbbcbadbdcbbcbccbdcdbcdbbaccddbacbdacccddbaaddccdccaadbddbbcdbdaccdcdabdaaaadcbccaccbdcccccccdaadcbcdcdaddddacabbcdbabbaacadddddbbadbadabaccdddcbdbabdccccdbbcddbabbdadcaacbddbcdbadcaaddaacccaacbabbccaacbabcacaaadbdcddddcdccbbacaadbbacabadadcccbbadbbbcbbbbdaadaadccaddcbadaadbadacbdbcccdcdbbcacccdccadccaadacabbbabccadadcbcbcbcdcdacbaccaccdadcaaadbabdcabaacddabbcdcdcbdaadddbbcdcddaaaddccabadccbccbbabbbbdacddadbabcbccdbbdbddaccdcbaddaadabbbdadcadacbaacdbcbccadadaadbbbdcbcbaadccddcacccdaaacbddbbaaddcdcbbcbcabacbdbbabcaccaaddaddaaabcccabbbccccbbcccaadbaddabacabcbaaadcdabcbccbddbdcaccbbcbdbabccadbddcbccbdaadadddacdbcdabcbabbdbaccbddddcacdaadcbdbcddaddbbcddabbbadbcdccbcbacbdcabccabddaaabdcacbacdaaaabdacbdbddabadbabadacddccdddbdcdbabdcabcddadaadadababccdccbbcbcdccbdacbadddbadbcadabbadabbabcaaddbcdbcdcabbdbadbbaabacaabcabdaaaadbaddcbcacbcaccabbcadbabcbcccdbdccdcabcdddaddbbddcdbbddddcbbbdaabbadbbbabacdaaaacddbbbddbccaabcaacacbdbbbcdcddccdaccdcbcdaddcccaaadbbbdadacbdddaacabbcbcdaddadbcddcddcbdbbbdadaccabaccabadcbbdbabbdaacbdbcbcbadabbbadbcabbbdbcbacbdadddccddbcbaadccdbadbdacaaaaabbaaddcbadbabcaccabaccdcadaccbbcbabacadbaacbcdaabddbdbacbcdddddadbdadcdacadcbacbcacdddbaacadbddaaaadaacbdccddaaacdddcdbacbdacbbcabdccaabcbaacaaacacaddabbabaaadcbcbadccbcdddbcbcabcabcaabacdcacbbcccabddccbccacdbdcdabcdcaacbdacbcdacaaabbdaacccccbcbdddbaccabaddbcbcbaabccbaabdccacacccbaddbdbbacccddadadcbdabbcaaacbcdcbacabcababdcddddbabdbddddaddadbdaabdbbbddcabddddaccdaabbaacbbaacabbbdacccdbcbabbcbddbddcadbccdaaddbcdcabdcbaaababcdbccdcaaaadbbbabdacaccbdacacdbcaabcddaccccbccdacadbcaadadaabcccaadcabcbaaacadbcadcdaacbabddaacabbdaaccbbdaddacbbdbbcabbcdaccbadacabccacccddaddbbabdacdbcabbbdbaddbddcbcbcabbdabdccdcccdbabdcbbcaabcabbacbbcbbdabdcbbdbdbdcccbaccbabacbbcbdabdbbbdbbcdabbddacdcaddaccaaabbdddcbbabdbadacbabcadaaaabdbddcdccabddddcaabacbccdcaabddcdcbcbcbbabbccccbababcbdaaddddbccbbdcbddadcaaabcddccdaaddcaaabaacbbdabcbdabcddcccaabdaddbdbbdabddddcbbddbabdcddcddbcadaaaccadaccaadddcaadccdbdddabcdbbccdaadaaaadbccbddadbbdaaddbbdaabdacaabddacabbbbadcccbbbaaadbccdbdddbcccacbcdddabdabbdbdaacaddaccdacaabbcddbcacdddcabbdbcdcdcbbbcbaaabaaacdcdbdcbddaddbaaadcbadadcccaddcabbcacddadcaacbdbdbdaddbdaccbbbdbbcdabbabcdbdccaacbbccacaddaacacdaababbbaadbbabbcabdadabaddcaadbdcabbbdbbdbccdcaadaaddbbacdbcbdabacabadabcaccaaccdbbcbbdddbbbcdaccaacababbcaacbabadcdddabcaaabbabbcdbdabcabadaccaabcdcdbdccdcbcaccdcbcdccbdcbbaaaaaacbdbbbbbbacaaccbdaaadcccdcdcaaabadabccdacbaaadbcdbbaccdaccbccbdcaabcacdbbdbdbbccaddbcbacbccacbcbbcbcaccaccdbdaaaccbcccdcdbaacccdacaddccadbcdddaaccbaacaacdbbbdcdaccabbcadcaccccddbccbdabababadbacaabcacdddddcbccbacabbbaddcadbbcaaacdbdcbdbcadbadbaaaddcddcbcbaddababbaaacdbcccaaadaccdcbaaabcabdccdabcddbabdbdcdbbdccbddabdabbadbcdaaddddcbabdadbaabdadaabcccdadacdbcdcdcbabbcccdbbbdacaadbccbacbcdaaababbdadacdcbbcbbbbccadaaadabccacaaabbbdaddcdbbcdcdcabaacbbbaadcdbabbdccddcdaacdcbaabbabbbcdacdcabdadbbdaabcbbbdbcbcdcadcabbbdcdbbbbbcbbadccadcdaaccbcdccbacbdbccbcadbdbabbcccdabadbaacddcdbbcadbbddcacaaaabcbbccaccbdcbadbcbddbdadcdbcadadcdadbccbcbcdbcaddadcddccadadabbbcbcabdcdabdaadbabcbacbcdcababacaddbabcdbcadbbaaabbddcdadadcdbadbdbdccbdaacdcbdbdaadcdbacdcacdcbadabadadabacddcbadddaacbbcbdcdcddacacdcdacbbacbadbdacababbacbddbadbdacdcaacdcbdabaadccdbdbbbdbbaacaaabdbdbbddbbcdbdcabcbccabbcdababcddaadcacadbdadacbadccacbdcdabdacaccbdddbccdcabcaaaddbadcbbddbababababcdbaacdcbbabacbbaabdddaaabcaddddccbdbcabdaadcccbdcbbbaacbcbcadaccdbacbccdabcacbaadaddbacacdbbaddadcaacccbdbabaaccdbcdcbabbadaaadcddbdaabaaaadbbacdadccaaacaddaddaaadcaaaaddbcbdbabbdcdcdcdacddbaadcbdacdbbcadcadadabaccacbcccbabdccccbbbbbdbcacdcbdccdccdaddcdacaacdbcbacbccddbbbbcbbaadbbbadbcbaabcabbdaddcacadbabacdabbdcbadbdbdddcdcacddccdcbbdcabbabbaccbdcbaabcbccaddbadbdbabdcbaaacaababacbbcadadbcadbdcccdcaddacabdbaadbcdcadcbdcaaababccbacdabdadccadbcbdbaabadcadbbddacddccccabbdbcaadbcdbbbaacdbbaaddcbcbbdaccaacabcabdabddcbaccbbcdcacddddcabccabbaaccbcadbcddadbcbccaccbcdabbdaadaabbcddaaaaaadcddadddcbaabbbcddcddbbdcdbccdcacbdddcabdaaaddcddacdaaacccbdcbacdddbddabddccadbabdacbccbdaacbdcbaabccaacababdcabdbcbadaccabcdcaaadabbaddbbbbcddbadbcbccddadacdadbabdabccdcdbbcaccaabadcabaaabbbdcdddababcccaaddbbcddcabdbccdbbccdbcdcaacccacdaabcddbcbbdbacacabacabbbcacbbbbacabaadbacbaabacbbddbabdaccdacdbdbcdbbaaddaddcadcdcbbbddbabacadccbbbcbdccbcabccadabacbccdbacadcbbacbcadcadbdbdabaacaaccbabacacccaddaccdcadbbaddddbabaacaadcbccddddadbbbcdcbcdbadcdbddaadccbdddcbcdaabbacdacbdcddaddcbacaadacdaaacaddddccbcdcacdcbdbdaabcbcbbacadabcddcacadbcdaabdbcabcbcdadbdcadcabaccabdacdccbccacdbcddbdbccbaddbdacdabaaddaaadaacadadcadddcbaadbaccdcbcddaaaacaacbbddcdaccccabcdbbdabbdbbcdbababccccdcddcbdbccacdccddddacbbbaabccabdbccacacadddddcacadaddbddcabcdbbcadcadaabababbddabaccbdadabbaacdbadbacacccdddbcaabdcaccbbabcadbaccdbaacabaddcacbbdddadabcbddddcbbcbbcdcbdbaadabcdaaddddbbccbadccbdcdccbdbdbaabbdcaacbbbccbcbdbccadaddadbbddcdbddadbbbbbcaacbadccaccbcbbdcbbccacbaacbbcbddbcbacbabbbaadcdbcbbcbcacbcdaddadabdccdbaabdbaaccccdddcbbacaacdaddccadcaabbaacddaabaacabbddababbbaadbcadadbbabbdbbbcaaadbacbadbaaadddbdcbcdcaabbcbdadcadbbadaacdadcaabaaacddccaaadaddcaabddbbcbadacadbadbdbbbcddbaaabccdcbdbcaddadcdbccabddbcdcdcbbbaabbbbdadbbddbdaabacadabadcabadaadabdbdbbacdcdcadbbcddddbadccbddcdddaddcddddbbbdbabcccadaabaacbcbbabcabacbbbadabdccdaadcadbacdcaaaadbddccdbcbadaaaddbddabadcadbccddddbadabcccdcbdbdbbaaabdadcadcadcbdbccdadadaaababbdaddbcbdcbccacddaabcacdadacbaabdbaddbddbcbcdaacbbbbddbaacaaaddbcccbbdbcddadacdcbadcdbbcddccbdcaddddaabbabccdbbcdccbbcacdddbbbddddaaccbaaacbadcddcdbadbcacdabaaaabcabbcdcbccbccccacdbbbcabdcadcabadacdddccaaccadbcbdddbacdcadbabbcdbacdddbdadbdbcacdaacaadbbbbdbbccccdbbadacadcaacabdcacaccbacaccdacabccabbabdbbcdabdccdadbadcbcccdadbdaacdaddadccbdcababaabdbddbdaacabcccccbbcdbabadacacbaddadcdcddcdadcddcccdccaaccbaccadccdadadcbdcbadddcddacdaccbcdabbaacaabaacbdcaabdbdbabcadaaacdcbacadbcadbccdbccdabbabdcbcadbbacbdccaaddbdcccddbdbdcbdcddccbbacdbacdbbadcccccdbadddccacdadbdcdacbddcbdcaacabaddcddbddcaaacbddbdaaccdddabcddabcdcdacbbcbabdcdacacdbbddbdaaacbbaacbbbbaccddcdcdabadddcbabcbbbdcbaabadcdcdcdbdcabcdadcaaaadaacaabacbadcadaabddbdbaccdcbcbcbcccadabaabbbdbddbcddccbcdbccabcbaacdbbddabdbbbccdadbbdacbdcbadcadabbabcbbbbdccbdcacddbacaaccdcbacddcaaddaaddccaddccadbcababdbaaaadbcddbbdcbadacadccbcbbbaacadcbcaabbbbddcbcdcaccdacbadaaccacacadbbcdbcccabcaacccdbbbaccbcdaccdcbbcccbaaacdddaadacbbbaccdcacddbdbcaaaaddbcaabbaabccbadddccacddbdccdbcbcbbadaabcabdcadccaaabdacdbdccbdddbbcadcadddaadaccbdcbbdbcdacdbaaddbcabcbdbcabccdabbcaccbdddcbdddabacdbaaaaccacdadddcadbbadcdaccdbbccccdbdcbaddacdcdadaaaacbdbdbcbabcdccbbbdaabcadadacaccaccaccbbacbbdbcbadbccaabbbadccddababadbdbbbabadddbcbabadbddadcadbdbdbccddcdcbacdccbabdabdcdabcababcbadbdddbaabbbcaacdcdabbdddacbbbdaddbdcaddabcdcacbdaacbcccdcbdbdccabaccbabddabbadadcadacabddabbbcabcbccdaccacabdbacdbbccaacacddabdaadbdddaaabacdcbabddcddddcaadbbbcbcdaddbadacbcadcabcaadcdcaaaacbabadacdaabababcdbaccddbbddaddaaacddccdccbacccadadcbddccbacddcdadaabcdabaddddacdaaddabdcaddabdadcbdbccbcddabaacddbbacacbbcacbbaadddcaaaacdbbbcacccabcddbaacdaaaaabbccaabaaaccdcddaadccaccaaaaaaabacccddacdabdcdcadbaaccbaddddadccbcdadccbdbbbcdbdcbacacacbbbabcbdaacabcccdddbacdbdcccbaabbbabcdabdabacdcbdcbccaacdbbcbbaccdccdbdadcbcccadbcaccdaddbdbbcbdcbabacdbcaabbaacbcacdbdacbcbdbaacdadabbacbcdcbaaaccaaacdbacddaadbdcdcbbbcdcddbddabcacbbbdbadcaadcccddabacdaadccabbccadaccaccaaabbcaadadaabcbbcbdcdccadbdbadddadbcabadcabbbdbadadcccaacccbcccbabdacdcccbbddbccbabadcacddaabacdacccaabdabadcabcbddacbdadddbcddabbdbbbdddacacddcbbdcabdbdddccadbacbccdaacabaababcaccccccbbcddbdcaddccbbddbccdcdccdcdbdccaccaccabadcccababdaaddbddcbaabbccdaccaababbddccaaaacacdbabadbddcbbddacccdaaccbbdbaabbdcbddaddcdaadddbbcadccaddacbbccbabaacaadcccbddabbaabcbddcadbacaaddcaaaadccccbdadbbaccaccdaacacadaaaaaacbabaadddcbabbbaabbbaaacaaddccccddccdbddddddbbabccdbadcaaadcddabacaddacbaaddbdadbcbccddbbdcadbdbadaacbdccbbbbcdcddcbbcbdbabaccacccdcbcdaaccbaabbbddbbdcdbcdabdcabababadabadddaadbbadabcadbccacbbddcbaccadcbbdcbbcbcacdacbbdabdadbdbdbadacaddbbbbabbacdabcdadaabddcbdddbbccabbdbbcbcdbaaaacdbccdaddbaaaacdadcbadccabdcdcabcccdbdbbadbdadcbaabacdcaadbdbdbbdbbbabdcbaabddbccbcdbdadaabaadacdccababbaacdbddabdbdacddbcdbcadcbddcdcabddcbcdadacabadbdcbccaadbdaacbbbccdacaaccbdbdaadaddcdcacadcadcbcddabccaddbdbdbdcbdbcaccbdccdcccbcbbcaddcccdcbcbdbcbcadbbabdbbacdcacadbaabbddabbcddcadcbcbccdbdcdbddabccbdccdbcdcdaacdddbcbbacadacbbaddcbadbdbcaacabbaacbbbbcdbacddcacadddbbddbaccdadacbbdadbcbbaacacabdacabdabcababddaccddacdbacabcccbdadaadbddaacabbdabdcacacaaabacdabcaaadbdabdddacbbbabaabaadbacbcabcccbdabcccddacdabdcbccbdbcbbdacbbcdcbaaccddcdaacbcdcacadacdcdaadbbbdbbaaacbabadadabbcccbbadcbdbcadabaaacddaaccdbbdcacbddccdbbcbbbdbaacbdadcdbdaaabaacbcaabdcbdaababadabdcbccbbadbbdadbdddddbbbdabbddacccbdcabcdddddcaabdddddbcacabddabbaaabdbbbcdaaacaaddcdbcdcbcdcbaadddcacaaddadcabaaacbdbaadbcbdddddaacacaabcddccbccadbcbdaaadbbbdbabaccbaacbdcaabbbadbbddaaccdabcdbaacdbbbcbacaaabcaccaccaaabbbcaaabbbbcabcabbcdddbcddadabbbbcaacacabcaabaaaabacaacadacabbdddadcdbbcdcdcbddaddbbcaaacdaddbaccddababaabddbaaadbadddcbcdddaacdaadbcaabcdbbabbcccacadbabcaaaaaacbddcbadbccbbacbcaaabbbaabdaddbcaabacddddbbabcccacaaacbbdcabdcbccbbbdcadddacadacbdaabddabbaadadaaabbbacbdccaaabccacbbbdbbdcabbdccadbdbbbcdabadabacaaaaddadcababaabdbcababcbcdbbcdddbccbbdbcdcdcbabbddbdabcaaddbbdbdccadbcdcbdcadaddbbdaabacdaabcbdddddcdcbabdccdacbdcadbadbcddbbacdccbddddbbabaabcabcaaddcaabbabcbcaaaaddddbadacaddddcbddacdbabdbcacdcdaddbcdbddcccdddabcdbcdcbacdcabbacadcbccbdcdaddcdabccddbcbdadbbacbdccacdbdabbbaaadaabbcaacdaddcddddcacbadcaacbadcaaaaabdaddcccccbbabdabbaddbdaaccdadacbbbcbdddddcdddaaccabdacadbcccabbdddacabadcadbadbaacbcbbdabdacbbababaccddcdabdcbaabbbdbbccabbbaadadabaacabddbbbddccbbcaadaccadbbbcbddbbdbaababcbdccbbbbcacaadddcbdcdbbcbdbdadadbadabaddcbabdbbaccbdaacdbbadabdddaccccdccdccbbccaadacaaaabdddabdccacaadabaaddcaabcbcdbbcadddaccdacabdddccdbabbddcddbabdbbbabdadcbacdcdabbdbcbbdbbbbbbbccdccccabaabadddbdbbacbcdadbddbbacbcbbcbcddacbccbdcacbaabddaadbddbcbbcbbdcacbaddccdadabacabaadbcacacbbaccadbaaaabdaccbbdcadcbbddbdbbabdadbcabccbbbabdcadadddccdbdcaacdacdbdacccdacadcabbccdccabbdacbcbccadaaaaaadadbbdbbbbadcdaadaabdccccadaccaddabaacbaabbacccabcbdccaaaacdbabcdcbaabbccbabdcabbcaadddbcdbcdaaacbbbbbbbcddbdabdcbbbdcdaaaadaaabcbcacdbacdaaacadcaccbcbdbcbdacbbcddadadcaadbdcccddcdcaccaddabdbbccbacbbdaabadcbbcbcacaddbcbadccbddbbcaacaabaddbdcacddbaadbddbcddcdcabbacacdabadddabcbdbbadadcdabdcaddbacdddbcabacaaadadaabaddcaabcddbcbbbcbbbcdbddadccaddaabbbcacddaacdbaadbcbdabdabbbdaacbcbaddabcdbbadcbcabdbddcacadcddbaccdcdcabddabdbadaabcacabbcaabccbacacbadddadcaaadcbbabdadbbbbaddaabdacbbbdcdacacdcccadbadadbbaccbcbbbdbdccccddddbcadbaddbbbdbadbbbbadbdbbdddbaaadbdaccabdcbacbaccdabbbaabadbdbbacddadccdbaccbacdccadadaddcbcdcbcbccdbaacdabacdcabbacabbcbdcdccbdadaabdccadacabccddbcdcabdacbdabacdbdbcbbdbbbbcadbddbbbdadddaadbcbaabdbdadcbbaddcdcabbabbbcbcaaddbadabcdcccbdbdbcdcccbaadcaababccbaaaaabbdcbdddaccbbcbacbbabaddaaddbdbdcbaadcacadabbaddcddadcaccbcbacadcbaadcbadcabdbbdaddbbdbdcbcdbdcadcbdcdcbdddcddaaacdccadabdddaabaacbdcbbbcdbbcacadbadbbcacdaaadcbbadcdccacaabcbacabaacacabbcdbcbacbcacdcabbbaaadaadccaddcdbcabadaabdddccacbabaabadacdcabccbdddcbccabdbcabddabaaddcccbacdadbdabbbddaaacbdbbbabcbabaaacddddcdddabccacaaaadcabdaddbdacddacaaacbbbbadccbbcccaaaadbbcbaabbdcccddbabbbcbcbdcbbccdcbbdacacacaabbdcdbcbaaddcaaddcccbbcdacccbcbcbcabcaacaabddacbcbbdcbdcbbbbbcbaacdabcaccdaadcaadbbbdbcbbcbccdcdaaddbadabcbdccacbbccbbdbcbdbcaadbdacadabdaabbcabadbadbbbaabbbdaddaacbbdaacbcbbcabdcdcdcaccbdabbccaabbbbbcccbabcadccccbbcdadbdbcadbbcdddcdbaccabacaadaadacccdbbcdaaddacddccdcadaccccdddbcdccdadbaacbcadbabcbcaababdbbdcabbabaaddacadcccdbdbadbbbabdadbadadbbaabddaaddabbadbdcbdbcdccbaaacaabaccbaabbbcaccdcdabbdbbdcdcbaaaaaabadcaccdcadbbdcbbbdccaaccbdcdacdaaaddacabccdbaaaccbdbabdacdddacdaadaaadabcaadbcdccdbabbbabcccbddccddaaadbbbcbbbdbbcaadacaacbccddbdcdccdddcbddadabdcaacaabbdbccdbdaaccddddccbbbcabbaaacadadabcbacbcbdbccbbcddbcbbbbbccbbabdbacbadbaddabadcbacbbdbbaacdacaddcdadaadcbbabdaadcccacbacdcccddbddbdadadcaaccbabbdbaaaacaabbdbdbbdadacadbdcaaccbdbcdbaddbbcdbdccdadbbcbdbacaabbddbdccadcbacbcbcdcadcbddcccbdccbdbdcdbdcdacabbcddcbcabdccabaaaaddccadbddbdbcbaacdabcaacbddcbbccbbddbcbcdabbbddacacccdbaacaadcbaabbbdaacbbacbcaccaacaacbddcdaacacaaadbcdacaadccddaaabbbccdbaaadcbbcdcacccdcbaddadabccabdbaabadcbbacdcadcacdbacbadbbddadaaddcddcccbaabbcdacaadabdccbbcaaacadbdaacdaadabacaddbaabaccccdddcbdbdaacbacdccdaddbcbbbddaccdbdaccccdabddbdcdabbcbddddbdcdcacabbcabbcbcbcabcdbbaddbbdadbddbdcabdbacdbcdccbcabdcdbaccdddbbcabdddcbccdcabcdbdcccbcabccbbbbcaaacacabdbbabbbdbddbaaaaadabdacccccaaacbbacbbdcaaacddddbaccababacbbcbdaddbaaccdcadbacbcbbabaccbbadddbacdbbdbbbcdcbdaaddaacdddaacccbcdbbcaacdcaccbccdddadbabbabccaaacdcddcccddcacabcbbdabcddddbcbdaccbddbbadcaccbabdadaddddddccadcdaabbbaacddbcddcdadcacbcbbbcacbcdddddbcacdbdadcbaabccadacdccbbaccdacbccbcdacdddaddddbabaacbbdcdbaccadddcbcbacdabddbcbdabcadacaddaabddabcbbcaabaddaadabaabcbadcdbacccbdcdccddcbdddbbcabdccbdcccbaacddadcbccaabaaddacaddacdbabbdbaabaabbdbabcabcccbddbbccbbbadbdbabacbcaabbaaabcddccdaaddccabbdaadcbabdcdddccdadcbadaabaaabaddaabddbcbbcccbacdacddcaabaadaadbbcbcbabbbcbcbaccbdadabdaaadbaadbdaccdaaacddaabddbbacaabdaacbbdcaabddaddabbbacbdccaabdaabcdcacbcdbacccadbcaaaaabccdbcccbbdcabbdaabcddbddacdbbabbbbcbbababcacaabcdbaaaddcbbcbbdbbcdadcbdbcbcdaccdbcbaaccdbabccaadbbbbbabcadadadccbddbacbbcdcdadbaacdbcdcdbaddbcbdcaadaacbbbdcaccacbbbdabcdcbbdcbacaadccdaccbaddbbdabdaddbdbabbcaddcbbdaaadabcaabcbcadbacabbbdbbcbdbadadadadcddadadcdaabbccadddbdacbaabcacaccbbddddaaddcbcacaaabadbbcadbaaaabbcbdccdccaccbabdccddddacbbdcabcadccacaabbacaccbbdcdadccdaadbcbbaadbcbabcacddcbacbbbdcdbbbbccaccdddccdbddcbcbdbaaacbbbbcbdabcdcbdabbaccadcdacacbaddbbacadaabbabccddccacadcacdcccbdbabdddbdcdcdddaabbbddcbaabdbdbacdddaabdaacdadcbdbdbdcabbbbacabcccbddcbccdbbccabaddbbdadacbaacdadcdadabbcaabddcdbababbcbcbacabddcccacbbacccdbccabaabadbbacabccdcacccaabacdaccddcadcabdadacddbaccdaaccabbadbaddcddbdcbcddccacdadaccbdacdcddbdaabdcadccbaabbbddcccbcdbdbbbbdabcacbbadddaadaaccabcbcabddacbadbadccadabcddbbddcabacccbadddccdbddaaccbaacbbaacacbcdbabcccaccaadaccaadbbccccbcddbbdadbdbcabcbacaccbdcadcbcadbcabdaccbbaaddcbccdbcdaccadccccbbccbaadbcadababcadcaabdccdaaabbcddbaacaaadbcbaddccdcdaadbadbbaabcbccbbcccdbbadcbdacdcbbdabbbccbdbadadcdccbdbbabcdabbbbcccacabdabbcbdabdbbbcdacbbabddcdcccaaaacadcbaadabdaabcdcaadbdbdcabdbdcdadbddadccdddcaaadcbbdbccbcbbbdcbcadcabbcadadcaccbadadccbaacadabdbbcbdddacacdabddcccdacacdadbcbbacdccccbcbbcaadbbdccadaabdabbbbcacdbcbcacbbdccccbabccbbcadccaabcacadcdcbbcddcdcdcbacdccadcaccddccbacabdcacbbacaacaddccdbcababbcbddddcbcacdacbdcccbdddcbaccdababdcaadcdcbcddbbcdccacbbccadbbbadaabcdcacabdccacdcbdaacdacccbcbdcdbccbadbaabaccdaccacaadabbadbddbbcdacabbbdaadbdabbadcabbbaaacaccbcdcbcbbbadbdcdacdddddbadbaaadaaabddbdbcbdbbddccacaccdadcdccdadaadabdcdccbadaddcddcadbdbdaddbdccacbccdddcdbbaadbaadadacbdaddaddadccacaabccbbcdbadbbaabdbccdcaacbbbabacaadabdddabbbcbbbdcaacaddabbdadcccccabcabaabaacdacbdddcaabccccdddaadcdccdaabbcbaccdcbddcbbbbacdcdaddbabcdcdaacbaccacbacadcccaabaacdbdbcdcbdccdbccbdcdacdccbaadbaaadabbdbcbbbdcaccdbddbcbdcbdacabddcadadbdccdaaadddddddabbabbbddabcabdcacaddabaddaadabdccbbcbdaccbbcababadbcbacaccdadcdbabdabddbacacaccdadcbabaaabcbbdccdbdababbdddacbbcbaabbdbcbdcadcddcdccddcacbbbbacbbbddddcdcdcbddcddacdcdadaadccaddddddcddaddaabdbbabdbcadabccdddacbddddbaaadacaccdbaacadbccbaacdaacadcdccaddadadbdcdacdbbbdbdcdbddbacbaaacdbbbcbcdccbbabccbdaaaadadbaaddbdabbdddbbbbbadcdcaddabcccbdaaadadccadcbadcdccbadabcdbcdacdaaabdbdddddcdabcbadadcccadaacbcacacdacdddcbdbcaddadaccdacbbcdababbdbbbbdbbccbddbdacbdcbbabddadbcdcacbcbadbcabdadaabdcadccbcdcdabbaababccabacbadacdbbbbdcdadcdaabbdbaadbaaadbdacdbdddaddbddbddbbcbcacdabbccbaadccbbbbbbaaaacabadcbbcbccbdbabacbbbbdbcbcadbabccbccbaacbbbdccbdabcdadadccadccbdaadbcaacacaacaadbadaacddddaabddaacbacdbadcaadddcccdabddabaddaaadcddcbabbbcddcdcbbdadbbdcdbcacdddbcdaddbcdcbdbbacadaddcdabdbadccaaddcbcccdbbabdbccccacbbabbdccbdbbabdbddcdbaadabcdbbadddcdbcaacaabaaddadcbccbdaaacbbdcdbdddaabcaddcabaacacaadadbcbdcdbdadbdcdcbbcbaacbbadcbabbaacabdccddbdbadaabbbbbbdddbcbaccccccabdaadbabdcacbcbacdadacbcdcdabcbcbbddaccdbadaccadaccccbcadabdbccdccddcccadadabdadbdaadbbacbddddccbcabaaaadbbaabaabacbdabaabcdbdadcabbaddddcddaccabdcbdddcacbcacbdcbbbbdbadcabadbccccaacacddaaacacdbbdcbdcbbaadbaacadbcbdccabcbbdadbcdccdaccacccbcdaddbcdacccbaddbbbdccccadccbadadddaacdbabbdbbbcabdcddddbdadcaccbddcdbcdababdbdcacdabcdbbaaabcccaadadbddbbdcbbadddcbbaacdddcbacabdadcaaabacbaabcacbcbbdbaddbacbcdbdcbbdbcbacdcabcddbdbccbaaadcbdbcbdbabaccdbbddbbcabadabbbacddaababccccccdabccddbbcdaacdabbadbadacdcadcadccdaddaacbcdccaaabbcdaddcdaaacabddcccdadabdbdbcbcdaccbadcadcccabbcadcbaaabbdbabcdbadbbdddbbbcdbbaacbbcadcdcdccaabbbddcccccdaaaacbbbabaabcdabbdcacccccdaddadbdcabcdddccadddaabcbaaccbabcacbacdbcddbbdaaddbcadbddcdadbbabbbdccdcbdaacdbdadcacbbcdabdbbddbbcccadddcdbabccbcabdddbadbccccaddcdabbdbdcbaccdcdcabbcdccdcdbcdbabadabaaaaaabbacacccadccbbaccacbdddcbcdaccdaaacbbbaccbcbddadbabacacbbdbddccbccbbcdadbabbbadcbbcdbcbbcdbbdabccddbcadbdabacbabbddbccbbcbdbcabacabbdbaccadaacbaaccdabbaccbdcdbaccdbcbddcacabbbbbdcddcdbddcdcdaaacabcbcdcabdaaacccddaaddddcaccdccaccdcabdbcccabdbdcaddadbbbcccbbabdccbbddadaadabdaadcbcbabaabcbdcaadcacccaccddbdddaababaddbadcbcddbdbddcabbbbddaabaaabdcdadccadababdabddaacbdddcccdccdbabadbbcadccbcacbdccbccbbaadcabcacccddcddcdcaacdbbaccaabcddddabcaadddaabbbbacacccbbcddcbcbbbadbacccddbcddacacdccdabbdbbabbbcdbadaddaadbbccbcdacbaaaddacbcbdbcdaddcacacdcbbcdbadccbbddcbbbbaaddbbcbabccacbaabbaddcaaaaddadbaadddbccadbcbbaacccdbdbabaaadccbbdbbacccbbadaadaadaabdbcdabcacdcaaddbbbcacddcdcaaaacbdcaccbabcbcadcbdcabcabccacbbdbbdcacbcdbdcacddbcdbbbaacccabcdcdacdbbccbbbcccadbadaabdbccabcbaddabdbacbdddadbabbccbcbaaccbbdabdaacabccccacbddcdbaabddbbbdbddcacbbbbbcdacdbdcadcbddbcacdbdbccdcbdcadddbadacaaadbdaaddcbadbabaacbddadbcbcddbabacbadddddaabbbddddcbdcbcdbdaabdcadbdcbcddbababcabcdcaababbbbbaaccccacacbcbbbddbacbababcdaadbbadbddcbacadcacbabbcbbbdccddcacaabccdbcdddabcdcdadaacbdbbadcdcaaaaddcbabbcabacacddaaddbadaccabbcdddbbbbdbbdccaabddccaaadacadbcaabcaabcddccddbcbaaadcabcbacbabdccbabcddaabbddbdcddcbccaaadadacacabcacbdaadcbcababcdbadbaadddacbcdbdcacccabcabaacccdcaaabdabbacacbdbccbdddbdabcdcbdddbcdaadbadddabdccbdbcdbbaccdbbcccdabaddbdbcabbbacdaadadbbbabbcbcdddcbbdcbdcccddbcaabbcadcdcabbdbdaabbaabcddbcabcdcdaaaaabbbaabcbdddcbccabdcbccaddccdcdcacadabbaadcccdcdacbacacbbbbdbbcbcbbcdcdbccbcadcaadabaabccddcddcdbcbddadddcdaabbcdddcababcbdbbbcdbdbcbabccccbccbbaabcdcbcbadbbbcadcbbbcbcbbcccbcccacddacdcdabbbaabbcaadabadaadbadcbddbdcccbbcbcdcdadcdcccbbbcddadbbdabdbbcdadadbccaabbcdbadddadbddbddcbdbdbddacbabbcabacddaddbcddcaacddddbbdcbdddaabdbbddbcbaaabdcaaadaccdcaabaabdcbcabccdaccbbabdabcaacbcdbddbacdadccadabdcccbdcbadbdddbcdabdbcbdcbadddcddcbccdcccadbaacbdaccaccdbaababadcdadaaaccbcddcbaddadbbcbdaadccadcaaccaacacabdaaabaccbbbdabdabbdbcbdddbaccaadcbcaddbaacdbcbccaabcdaabdbbdcacbbdacdddcbcabcbccdcbbaaaadccaaddccbdbcdbcadacdbcdbbbbdddcddccbccccdccdadcacdccbdabacdcdbbbcadbcbaadbddaadababbbacdadcccadaaadbcbbcddadabcdbdcbaddbcddccddddadbdabcabbdbbbcbcccdbddacbbbcaaadbaabbdaccccdaaacadbcdadaabdaadccbcbbdbbccbbcbadabdbaadbcbcbadbcaadbdbcadacabaacbbbcabcbbccaaaacdcbdcbcbcabcabdbdacbbacddccaaddcaccdcadabacbbcbdccdddcabadcbcadaadacbbdacdadddbbdbcdabacadabbdbbabacccdbbcaadcabccddabdbbbddaaaacbacacacdddbaaababdbbcccbacabcbaaababccdabbcbddcacbbcaccdcbaaacccdcccbdbdabccbdbdbbbcccbdbbbcaacabdaadbddcaacadddddabacbaaabbacdaacdacbacdcdccaadadaccddababbaadaccaddbdccaaadacdcabdddcbbcaddcbdadaabccdcaacccadcbccbcaabbbccadbbdcbddbbcdbbdbaccbaabccbcdacbbcdbaddadccaccbabbdacccdacbdcadccacacabdbdcbcbdcbdbdcdddaadacccbbacbcbbcdcbdaaaabbcdcdadacaacdcaaddddbacdadaaccacccbbcbcaacabcdbdcbdccbddccbbbdbdbabccbbbbaacdbcdabcaadcddddddbcccdccddcdabdaddbdbdbaddbbcccbabcdccddccabacbabcbcbccbacaabdacdacccaacbccaadbdccbdbadcccdadbbabddbccabdccabbadbbccbcdccddbbbbbbcdacbccbaaacddccdcccbdbdabcabacdcadcdaadaddcbbccdbdcbbdbbdabbadbcbcabbcdbcbccdbccaaacacbdacbacaabadcaaabbadbdbbacccbdccdcdcdcdcaabcbacccdbbdcabbabcbcdacacacbaaacddcddaadadcdbcccddaaacdbabbdcaacabaaabbbacabbcdaacabaaaacccdbaaddbaccdcbddbbabaaaacccbcdbcbbaadbbcccbcbdcbcbcdabdbddddacdcdacaabddaadcaaabbabcaadabcdaaabbaaddbabddacdaabdcaccadbcaaccaadbaccaabccdacdabbbcbdcacdcabbbbabdccddadcdcbddddcbdddddcddaccdadbdacabccabbcbcddbddbccbbaadacbaadaaaccbcdabaabcdddbaacbbbccadaababcccccdabbcadbdbabacacdbccccbddcbaddbbbcbaacddaacbbdcddcbabadbadbcacbdbaabcbbdbcdcdaaddadacdbcbcddadbbccbbbacbacabdabdadcbccdbccaaccdbaadbcadccaacbaddddabccacadcbadccaadbdcdbccaddacacacddbdccbbdcbdddbbabccaccacaaabdbbacbbacdccdbbbdbcadadbcacbadddcccdbababbcccacdcbbdcbbcbccacaddadccbdaabddbacccdbbadbabcadabbacdcdcddcababaccaddbcccdabaadaaaabdabdcabbacbdcadbdbcdcdbccdddbaaadcdacbbaacabbcbbcaadbacbacaaddacadbbdcaadacdaadabbccbdbddadbddbdadbcbbabbdccaaabdbacacbcaabaabbdbbdbdacdababdadaaccbcbcccddcdaadbcdbdcdddbddaabcabdccdcaadcbadbcacabcbdddadadbabcabddcbbcdccbccbaccddacbababacdacadbddddabdaadadccbbdcbbddacbbcdaacbcacdbbddabacdaccdadcadadbabccddcbccbadbcddbcbbcacaddddbdcbabccccdbbdabaccacaddcdabadcbabcaacacadddadabbccadbddccadbbdaacdacbaddbdadadcdcbaacdbaabcacdaddadabdccbdbaddcdbcbacdbadcbbabcbdbaaabccdbcbbcaacabdbaacdcdaadcbacdddbcbbbbdabbabbbbdbdabdddbbbadabcdaabbbbccabdbacbdbcbcdbdbddadaabaaadccbccbcadaabdbbbdaabddbadaabcaaccbccbbdccddbaababdabcddacdcbbbbaddbbcacdccccdbcaccaacdbccacbabdbcddacadccbacdbddaadbbacccdcbbccaccacbbdbaccbadaacccbdacadbadaadbbaddcdaccdbcadcddacccaddaacbdbdaccacccdcdcbdbdcbcadbdcccadcabdadcaacadccadcbabaabdbbddabaaaddbdbdbbcbdabacccbdcbcbcacbacbdccdbdaddadbcdbccbdbdbdbdcbdcabccdcacdbcdbbcabcacdcddccbbabcdcaabcddccbdbcdbacbcadacdbabbdacdabacadaccdabdaacbdbdccabcabcdaccabacabaabccbdadcaddcbcdbddaccaabaadccbbdadadaabddadbcbdcdadcaccbdddbbbaabdadbdaadcbcbbcccababbdadbcbcdabbaabbbbbaabcaaaaadaaaabcbbcbaaccdcaddbcbaddbaacbdaaaacbcdbdadcacddadacbbdacaadbddaccdacdbdddbcabcdbaccbdbccaccccbaddbbaacddbbcadbccaccdcdbdbbbcbcadaaadbbabcbccdacddcadddcdcbacbddcdcdcbacbaacdaddbbadabdabdcbabcccabccdcbdbbbbdcdacacdbdbadacacadbadaddbadacaaacbadbcaaacbbccacddabbbddaccabadbcdabdabdbbbabadadaccadbbddcddabbcccbbdbbbabcbabbbcbccdacacdabababaccbacbcabbddcbddbcdabcdbdbdaaadcbacbccbabbdcbbddbcadbdaabcdcccacaaddbdbbcbbcddddcbccddccdbaabccccabcddbcdbbcbbbabaddbcaacabababadacccacacabddbbabcccaabaaacdbbcaaababbbadbddcbdbdddbaddaddbcacddaaabddcbcabcdabdaacddddbbdabbbdbdbbadbdacacaaadaabcdacabcaaadbaddcdddbdbcdbacddcbacadaacdddccdddcdabcabbcaabacdbabacadbdaadaddbdadcdcdbaabdadacbdaccdabcdddadbdaadddbddadbddbbabccdcdcacbdbbcbcadacabbcdcacdabdacbacdaadccaaaaabdaaccadadcbbaccabbbdddbcdbcdbacaddcabaadbbbbbabcbbadabdaaaccdbaddbdacaacbdacbabaddbcbbdbcadadabadccdcbacadcadbccdbaaccdbcbaabcadababcbaaadbcdabacabbacdccacadbbadbcaadbccabcacabbbbdcdabbdccdbdcaadcabdacdbbdbccaaabdacccbdcdbbdddbdbdccacbcbcbbbbaadbcaaaacccacbaddabbbaacadadcdbcabbdadcccdbcbbaabaaacadddaabacbababadabddcdddbdaadcdbcbcbbdddcbabddcbababbacabbbbbabcadacbbdaabbaaaccbcaabaccdbbaccccbdbadabbdaaccaddcdacaacbabbabbaaaadcaacabacccbdcdcabcacdbbbcabbdbbcdbdababcaaccdcccbbddbdabcdacbdaadbdbacdccbaaacbabcaacbbaacdddabcacddbaddcbddbdbccdcddbabbddbabcccaddacdbddddbbbabcadddaddabcdaaabdbdcbcdcbabcaadbcdaababbcbcdbccaabbbbdbddcbcdcbdccbbbcbcccadadbaddccaacdcacdadaacbdbddbdadcbccccbbbadbbadabdcbabaacababbdadacdcbcdadbbdabdadcaaabcacaaacdcadabbcddacacabaaaccaabbccdbcabcacabcddaabbadaccccbbbabcaabcbabbddcdddadaaccacbaacbabbabcbbdbadaddabacadbdcadbddddccbabddcaccdabbadbabbcadddddcabbddbadacabcaabcacadcaacbddbadcdabcdcbacbbaadcccaddabdcaabcdadabcaabbcacddbcbabdddadddcbbbbbbdcdcbaacdbabcdbcadccbaccaaaccddcdabdbccdcbbbdbdaabbacdbdbaddbddbbdbcabccbadabcbbbcccdbdacaacaacaabbccdbccbbbddbacccaccacccacbdbaadbbaddbcdccbcccacbcadbcabcbccbbbbcbadaaabdadaabbbcdddadacababcbbcabbadbdacdabdddbbbcdcccdcdcbcbddcbabbdcccdaadbabccddadbcdbcaadaabbdaddcddcbbbdcdbdbccbbdcbdbcadbbaabbdaaaabbccabddadcdabdcdccbcccccbbbcbdadadbcdabcbdbcccbbbacacadbcadaabddbbdaacabcdddacaccacaccaaadcddbaadbbcababaadcbdabdbdcacadaaacacdaababadcaabbaddbccccdddddbcbbcdbabbbcccacadcabcbbbbdccbcaaaaacbbddacbddbcbddacbcabadbbbaccbabbcabaddbdbdcdbacbadcccddcadacbbabbccbbdbcddcccccbcabcaacbccbcbacdcddbbcadabdadbbdabcdcdcdabadddcdbbdaadaadacaccdddabdcdbdbbcbdaacabdbbbaccadbbbabaddccababbdcdcddadbaaccbcdcccdcabdbccdcbdaddabcccbcdadabdbcdabbcddcdcbbadcaabddcbcdcabdaacccbbbbabcddbcadbaababaadbbacaaacaddbcddcdcdbccbcbbccbccdaccbadbbcbcdcbbaabcbccadabcccabddccbdbadadbbbadabbddbadbadaaccdbadcdbdaddacaaadcccbbbbccaddbddcdddcbdcaacbddaccabdbcdaddbdddcadacdbbccbbbcaddcbaadcdadabaaaccbbaaabcbbbbddccbddbdaabadcbddaaabcbacdbbddbababcaccdbdadbabdbbccaaabddbdbdcbdcdaaadbadabaadadababbbbbdcdbcdcacbdddcdbdcaddaddabbcadbabcdcbdacdbacdcabdcaddaacbbcbabcabcbabbcbcdabbddcbabadbbabbcbcbdbccbbbdbdbbadacacababcdcbcbdbadbcabddabdbcadbaacbdaabdbcddbadabcddbbdacadbdacdbacdcadacacdbbcaddbcbdbbbaccababcbcdbcabaaccdcdcbdddbdbdcdccaadddccaddacbbbdaabcaabaabadadadbbadaaadaccbaadadcbadcaaaabcbdaacdcccdbddcbdbaacadacaaacdbcacddddbadddccdadbabacbdcaccbdccabbbbaddbaddbacabdbadcababccaaddcdacdbacabbccccbdcdaacdbddacbcbadbacbcacdaddbcddddddbbcdbcbbcadbddbdaccbccdbbccaaccabadbcdcddcbdcbcbadaacabbaadababacccdaadbbacdddcdcdadbaccbdadbaddacaadbcadcdbddbabdddcbbabaacdddbdabadccbacdbcbbaccdbcddbdabcbbdacabbbbdcbcadccaabadadabdcbaadacaaaccdbddbbdcbabbcbbdababaaaddcaccbacbdaccadcacadbbbcadcbbdaaccdbcbcddcdbcbbdddbcbbcdddbdddcdbbaacabaabdababbbbbdbbcdcbdbbbbbdcccbbdcccddbdccacdcabddccbcacccddadacbcabcbdbdccccdaadaabddcbcccdabbdbcdcacbaaddcdadadcacdababacbcbaadabdbdbbabdbabcccdbcddcdbcdbcaacdbcbdbbdbbccdacbabdbdccacacadddcdccacadcbbddbcccccbdddcbddbcbaadaaadcadcdbaddbccabacdddbbbcdabaaaadcccbcabcdbbacdbcbbbcbdaacabbabcabccbdbbdcddadbbcbdacbaddbaaabdaccccacbdbbbbdcbbbccddbcddaddddcadbbbddbdccaddbdbcabcdccdcbdcaccbbcacabbacbbacdcaadadabbadbabaaaccbdbcccaccdacabbbddbcacbddcabccbbabaccaccabdadcbcadcabcabaaabacdccdadbccabaaadbcadcbbadbbabbbacbcadabccbddaadbcdbcdcbadddccabacdabdcadbabcccbaccdbcaaacdccbcdcbdaababccbdbcacaacabacaadcbdaadcccabbdabddccababbabdadcdbadaabbcadadcdadcabdcaccccddbcaabcdddcbbbcddaaaaacdbaaddbbccbbbadcdabcdbccaaccaccacdddbcbbdcabdcbddbbacbacadddaacbccabcdcbdcdaaacccabbcdcbdaccdadbcdbabaaacaccbaabbbcdaadcdbcbadbddcdcddbddcdbbaadcddcdaadcbaddaddcbcabdaacaadcacdccadbdaaadacbdaddcccdbdbdddbdbcbddbcbdacddbababadabaddbbdabbbadcccabaabbcbccbddcbaacbbaaacbaaacadaadcbbdddbdaaaadbabaaaadacdadabbbddaddbacbccabacbccaadcacbcaddcdabcbbdcbbdbdddccadccabdacddbcdaacaadcbbbdbcbabdcbdcddababbdcddbadddbdcaabcbccbbcdaaabcbddadaabbbacbabadbaadaadaadbdbcbcabdcadbdadbdadcaddbddcbcccccbcaddabcdcbbcddacabacadaaabbbbadbdbabbbbdabdccdbcccbcbdbdbbdadbbaaccaaccbbcdbbaabadcadbdadcbacacbcdbbadcaccbbbbdbaaaadbacdcdbbbcbcccababaccbddddccbacdabadbdcabcadabdbddbdddbbbdbaddacabbdaaaaaacaababbddcabbdcbbccddbabccaccbabdaccdacbdbdbddbcbcadbdbadcbacbbbcaccaadaaddbdcbddcbcbbadbbadadcabdbdccccdbdcabdcaabaaabaccdcccaabbbbaaaabddaccccbdbabcabbbcccdabbbbabdaabbdcbcccbdbcccbddbdabbaaaaaabacdccbbcccbabdbbdccadbdcbabdaaadabbccadbabcdbabaacacddccbbbdababdbbcdbaacbddcccaccddbdbcdbddbcbbcccaadbbbabccabcadacaadaccbccbcddbbdbbbcdbdbabbcccababcbdcbcdcbacabdbddbbcdbdccddbdadbbbcabbbbdaaabddcdddbabcbbbabdbdabaacdabbccdbcbbabcabcadacbcabaaacdadbabdadcadcdbacbdbcabadadbddbaddbdaacdcaddddbabbdaabacdabcbcddadaacddbccbadcdddbadbbaabbbbbdddcdcbbabdcabcbcabbccaacbddcaadbadbbdadbcbcdabccbdaaddbddddadcddabdbabcdacaaadcccbaaddbbadccbadbddbbdaadcdaccddcccaddccdadccabbabdbdacbddacdabcacdbdbbdcbccdcaabbdbabacbacddcdcdaaddccbcdbccacaacbbdaccbddabcbadcddabdbbacbacbccadacdbabadccdbcdcdccdbdadbbbbcacadddbbbdbbdaaaddabcbccabccdcadcabbdbbaccacbddccbdcdaacacbdbaaccccbdbaddccbdcbdabbacbdaaddbdaabacdacdbbadcbcadbdcbccccaccaddcdbcdcbdbdcddbabbaabbacdbbaababdabbcdacbcbbbcdcbabbcdddddaabbbbddacbcdddadbddaccccbabcdddadcbdbbddaacddbaacccdacabbaddbabccbabdadbadcbbdcdbbabdbacdbababcccabdaacbcdcacccadbdddcbabdbbababdacccadaccbdaccbdbccbcabcbabbacdbdcbcddccdaabacccbcaddcabcddcbbbdcccaccbcdbdcdcabddaadadbbbadccbdbcdabaddacccdcbbcacdadbcbbdacbdbcdcbbbbdddbccbccaddacbcbacbadadababdcabdccddddadddbabbabdadacaddcddbddcdbbcddabaaadbacbaddbbbbcacbcabaabbcabcbbddccaacdcdcbcdadabdacacadbdccbabcbbbbbbbcbaddcdbbadabcadcbdcbcccccadbbbadcbccbabcdadccaccdaddccadcdcadbbaddadaababccadabbbbcacddabddddaccaabdcabdddcbbacccadcaaaaacccdadcdcbdbdcbcaaaccadabadccccbbcbdbdddcaccaddbabcbdcbacdcbcacdcdaacacdaaacdbacdaadabdbdabccdbaadbdcbaaadbcdabcacadbbacdcdadacacaabbdaacdbabccadcbbaccdddbaaacdadbcabcbaccaaccaccacabbabacbcbcdaddaddcbcbadcdccccdbbcaccaabbbaadbcbaaaaddaaaddbdacdcbaadcbabcbacbdcacbbadabcaddaadbdddccdcbaaadbacddabddadabcdaaaaaddacbdcccbcabccbccbbbbdcdacdcadbdbabdadbdbdcadbdbabdbcadbcadbcbbdcaadbddbabccdcadccbcdbaacabddaabccbaadcbdcabcbbacddacacbccbababadbddadaadababbbadabbbdbcbdacbdadcdabccabaaabdbcbdacccccdbcbdaddaaaaadcddccbcaaddacdbacdcacdcccaacadabdbabbaaaaaaadbdcbcacdabcbcdaaddcbcaabbdaacbaddccacbdcdabaacdbbddcabdbcaaaccdadddaabdadadccabcbcddcccabaccabcbcbcbdaaddcbbadddddbdabadabccddddadabadcaddcdcbdbdbdcaaaabadddddcbcacadbcbabcdbabcbbbbbadaaacabacddbcacbacbbdcccacacabdbdcdccdcababababdaacdddabbaaddbbdabcdaaddcabbdbdabbbaccbbbaababbcaabacbacbddcbccadcbaaabdbbcbcaacdcacbdbbddbacbdbccbaaaddcadcccbddaabddaaaddcddcacdccddabbbaadabaaadbbbcdbdbaadbcddcdaccbadbccaaaaadbcaaababbcdbdadccdabbdcdccadcdbdbdbddcacadbbbaacdcaccccddababccddbdddcdcdaaaabaccadddadabbbdbccabdbdbcabcccdacadbcdbcccddcadbcccdddabdbddcacbccdadbabccdccbcabbdbabdaaccacdbcbbbbccaaccaacaaddcdadcdaacbdcaccbbccbccdaaccdadcdddadcddaddbcadaabbdddbbbbbadddbaacabbaaccbbbddcbbdccddbcbcbcacadcaacdcaaabcaccaddaaccbbcbddacdbcdbdcdabadcacaacbcaadacabcbdadbadcbdcbaccdccbdddadacdacacacbaacacbacaddbbbccacccbbdbdbababcbdbddbacbbacacadadcbbcaacdbbdbdaabbacadbbbcbbbbaaaacccbcccabbddabacabacadbaaaabdcdcbdaabcaaabddadccadcbccddbcdcbcbdddaadbbdcdccabdccdddacabbbdcdbdbddbaaabddbcddadabddabddcccbadbabcbbddbcbaaadcbabbbbdccbabbbabdbcabbcaacdcbaaadbdacdbbccddbcccbdaccbcddaacbcadbadacbbdcdddabcadadccccdbdbabdbabdcdccaaacdaaddadadabcbdbcbbcadbccdbcdbaacbadbcabdbadddddcdccadabdbabadaacabbbadcdabdaabbddccdabbdacdaccbddcbaaabccdccadaababdcbbbdadcbcadcbaabcddaabbddabbbacbbddbccdbcbaddbacdcaadacbdcdcabbdcdbbdcbbabcdcbbbdbcbdadaaacbdadacdddbbcdaabcdbcacdbaacaabadabcaaacbcbdcacdaccdadadadbddddcbbcadcccbdcacadbbbacbcdadabccabaacccaabdcaccdddccccdbcdacbcddbdcddcacdaabdddacbcadcdcccbddcbbdabbacbbcdacbbbcbaadadcdbadabcbddcacaacccadbdcdadcadcabdbdbbabacdccacdccdcadcbcdbbccbccbcdaaadcddcabbcccaacabcdccbaabaabbccdcdaaddccaacabbbbddcdaaaaadcbdcdbddbabaabcabdcabbdabbdcddbddadbacdacdbaababdccaaddcdcacaadddccccdaddaacbdcadbbbaadcdcddacacadbdadabacccbadbcbadabcaccbdaccdabaaabcabbadbbcdbcadccabaaddabaddaddbaaddaaababcdccddaccdbbadcadccbdbdcbddaddddcbaccadddcaddccabaadaadbcccbadbbdbadacdabdbacbcdbdddacaaabccbdbbbcaabdaddddbbcacacaddacddbcaabbdddbbacbcbcbdddacbdcadcabbdddaddcbcccbdcccdabbcccccddbdacadcbaacdcdcdaacdcbcdcbdbcadcbcdbcbdbbcabdddaaabbadbdaaabbbdadaadccaaccabacddbddbdacbadabacdddbccabaaccbbbdcdccabdaaccdcaaaacdaaacadadaabbbcbbcbddacbabbccbcabdbcacdbdbacadccddddbcbcaacccbaabdabdaaabccdcbabdbabccddbcbcdacdbcaaabacacaaaaccbaadbcbbdddbadbaccaaadccbbbaacdabbdcacdbaacbcbaaadcaabcadcdcaabccbccccaaaabcdacdabdbcbbacddddcdbccdbcdcadabdcbdcaccdcdcdccbdbadaadacbbccadbacadbbdcaaabcabdacddcbdbacdcabccbabcbbcccdcaaadcbdbaabcabaacabaabacadabbaabadacdbbdbdddbdcadcbbbaacbbadddcccbbcabdbabadbbbcadcccbdabbcbcdabcbdaacdaddacbbcccabbdcaacadbacddcddcaaababcabaccccbdaddaadbdacababdcdaaacabcadbcbadbbaadabbadabcbabaaaddcbdddcddbabcdaabcdcbbcdccbbbdbaaadacbbdcdacadbcbbcbbaccdbbadaddbaadddabdabadbdacaddabaaabadabdabbacacdbdaacdacbacdbacbbacccbdccdccccaddaccacdadbabcaaaacddbcbdcbcaddadaccacddbadabcdacbbbabbaccdabacbcbacdaadcaddccbaaccababcbaabccbabdaddcdadacadbdbbbabadccddaaadbbddaadacabcbbabbabaacadacccccbbabbaccbabadcdbdcbdddcababaaddccccacdbbbdccbcdddadddabacdcdbdddbddaaaddacddbdcbbaccbaccbaadbccdcdcbbaadbcdccdbbbaddbdcaaddcddddbaabdbbadcdabccacdacccbadddcbdbbadaadaadbddbcdcdadabcacdbacbbbcabddacaaccdcbdadbddaccdcddacbccccbdcdabaadbbcbdacddcdacabdbaadacddbbcdcacbccbcccdcdddabbcdcdbacbadbaabaadcadcdbabddbaaccdbddbadacaaadcdcddbacddabaaabbdbacaababbadcabcdcddadadaaaacadbcabdbccdbbcacdcbbdaaaddccabddacbaccbaaacbaacbbcbaadbbababacdcccbaccdbdabdbddbdcbaddadddcabacbddbbbbabdbcaacaaddcbaddbbbddabbcddbcbdcbbcccabccbdbddcacaadaaacbcbdcccddbdadbdbcbbcbcdbccbbbbcabbcdadcdcccadbdbbbbbdabcbbcddabdbdddcadaaadbacccdccdbdbabbcdccacccaddbaddadabbdcbaabdabbadabbbcdcbdaabbccabbaaccdbbcaadbdacddacdabbaddcbdaacabbdddacdcbbcbdbabdcaccbdadddccddccbdbcbdaddcddcccaadbdbccbcbbbbdbcaaabccbcbbbcbabdcacacbbaaccabccacdbbcacdcddbabaacbddbaabbaddcaddcaaabaccdcddcaabbdbdccdcbcadaadcbcbcbabadcbccabadcddbaacdcddbcdbdddcbdbddcdaabcbbadbdcadbdadddadababdcbacdbcbaababbcbddbddcbdcadaadbcdbbcadabcddaadbbdadbdbbdacaadddcadaadbcabddbbddaabcdbdaacadaacbdabbcccabcabbdacdaadbddcddcbcddabcbddacaabdcbbbabbbdabbcdcdcadbbdbbbabccadbcacbaddbcbdbaadccdbcbaaaaddbdcaaaabcaabdabcaabbcadccadbaddbcacccdbccbcbddadccdacbaadcadbcabbbadbdbaadccdbadbcabbccdcbabccdbdbcadbaabdcbdbbbdaabbbcdaaabdcbbaabccdcccddbdbadbcddaabdddacbabccbacbbbadbbadababcbbcdbbbccdbdcdcdcbdcabddbbacdbdbdcbbddcadccabadcacabdbdddcacdadacdbbccbbbccaadbcccdddcdacbccbaabdbdcbdabaccdabaddabdaddcaadaccacbcbdadbdbaadbaccacbadbdaccdcbcbabdacabcaaadabacadccacbdcbbbabcdcbcbcabbcdabdbdbaadabaddbaabdaabdcaaaddcdccdbbacadbbdddacabbbccdbbbbcacdbddbdbcddcacdcdadcbacddbaaabcbdcdbabcdcbabccababbdbddccaacaacabdbdbabbcacdbabbdcbdaabdacadddcbcdaddabcaacddcbcabadaaaccbadbdabbbcbaabccdccadccdadabbbcadcdcaadacaadbcccbbbddccabadcabccabadaccababcbbdbddabaaaddcdaadbdbbaaadccadbaaabbcaadaaacacabdabaabcbdacadddadbccbddacbabddaddaddbbcbbcbabbbdbccbacddddcbcbbcdbcabcbcbdbdcdcddacdaddaccbacaabadacbbcdbadcddddacacccbaddadddacdabbcdbadacaddadacabaacaacddacbbbcbdacdbccbccadabaaccbccddabdabcabdacaaabcdcbacbbbdbcaaacddcddddbabcbbccddcdaadabbccabacabadccbaddcdabccbdabdbadacaabcaddbdccdccbdcdabcdcaaccabbabbddbadddddcddccdddbbacadacaabbcbbcdcabcdcaaacadbcbaccdbdadcdbbcdbdccbaadaabadbbbbcadacbdccbdacaababadbdbbbddcdddcdacddaacdcdddaadbbdbbdbaccddcbdcccaccdbcdaacdaabcdcabdaadddabbabaccbbdaabccbcbabbcdccbbcbbddabbbaccdbadccbddcadbbdcadcbcbbdbcdbdadcdbccbabadcaacbbdcaddacaddacbbadcabddcadadbbbbbaddddbaddbdacbbdbddcbdabcdadadbacbbcdbddacccacacccbbdacccdbacbdaacbdabccddcbabcacdccdcbacababdbcacbcbaadaacdbccdcaabdbabaaaaddaccbaadbabbacacbbdbbbbadcbacccddddabaacbbdbddbadabaddcdcbcdaccbcdbadddbaddbcbbbdacccbcabaacacdbbacddbbdacddbaccdcdadcbdcbddbacdadcadaccddabcccdaddbbddddccccbdccbaadcdabcdddccdbaabaaacbdcbcdbbbdcaaabdccbcadabdcddccaadcdddbabdbbdcddacdccdbbcdbdadadbdcabddaaabbabdbcacdabadcadabbcbcddbccbabdcdaddbadbaddaaddbadccbdaaabbdaccaacdadcaabdcbacadccccbdbbcacccddcdcbbbadcbaabddccddccaacbdcbbddbcdadbcccaaddabbbcddccddcbbbaadcdcbccadadbdbbaabbacbddcacbdadcbccdcbbbbaddbbabcdaccddcdadccaddacdbcacdaacbdbbcbbaddabaacdbcbadadbdccbdacaaccdcdabcbabbdbbabbdcbbdccbcaccadaddacacdcdadddbcaccabddbaacdacbbcacabddabddddbdcdabdaaddbcdbaaddabddaabcbaacdcbcbdcdddbdaaacdccbbacbbddbdcaccadddcbaaaaaaadaaddaadcbdacbdbdbabcadabcbdbcaacbbccbccababdaadcddcababbaabdabbcdacadcbaacbaddddbcdcabdbbbdbcbabdcbbbbabbccabcbccbcccbcddbdabaccadbdcbbbdbbcdbcbaaddbccbadcbddbbacabdcdbdcadbccbdaccdcddabaccdccdbadbbaabcccdcddbbbdababdabcdbddddbabddddbcacacbcdacacdbcddacddbbabcaddaadcddcbbcdddadcbadcbbdabccccacabbcbdbcccbdbcadcaaacaabbbbaaacdaabadbdaacdbbddcaddacdcabbbaaaacbccaaddccbababcbccdbcbbbbbbadcbcdaacabaaaacdbacbbccdbddbdddbbddbdbcaabdcbbccabdabdabcbccdabcbabcdaabaaccdcacddcaaacdbbbbbccdcbccaacacccbbbcbbdbdcabcdaddbacadbbbaadcacaacadadbbdcdaaaddddcbbdbadbacaabdbdcbbbcddbbbbcdadcbcdddbbbccbddcbbcacdbddbcbbdbddbdbbadbbaaacaccbdcdcddbdcbbadcaaaabcdabcdbdccddcabbdbbdcbbcbcdaaaabdbcbbbbaaabbddbcbdcdbdddcbbcdaadaacbddbabcaddabdbcdcbaadacbaacbbdcccdccbdcabddbacbaacbbcabaabcdccdbabaababcacdaddbdcaaaddddbcbbaddaabbdcdccbdadcbbdadccbbccacacaddcdacbcbdbadcbcbdbdbacbadaaacdaadccbadccdaacdcdcdbcdcadddabbbcbcdddbadbcacacaccbdcbaccababbbaabddaadbbcbcddaaadacbbaaabdaaddbbacbacacacabacdbcbaabcdaccacddaddbccababbbbdcdbbcabcbdbaaabdabdcbcdbbbaaadbbbaadcdbddbddabbdcadababbcdaacabcddcbccbdcdcabdacccaaacbcbbbbcbbbabbcadbadabdcbddacbcbdaaddbdadcabcdbbbdcadacbcbdbaacbccaaabaabbacbcaddadbababddaccabadcddadadbbbbdadbdddbbabaccdaacaaccbdadcadbbcdcdaddaadcabbbcabdabcaacbbdbbdcbbccaabcdddccdddbbcbacbcccacaccddabbbbacbdcccaddcacdacadaaaaadcbaaaabbdccbdbcddaadddbaddbcaaabacdccbbdcacdccadadbbbaaacdadddbabdbdaaaccbdadcccdddddadcbddbbabdddcbbaaccacdccdddaaccdbacadabbbdddcbadadbbcdbbddaaacbacdadcdaccdbcabbadbbaddadddbcbdacaadcadabaabbabcdbbacbbabbcaabcdbacddcddcaabaadcbcdaaacaadadcdabccbcdcacdddcdcadddcdaccbbbdbadcaddbaaaddbbadabdcdabaadcbaccaddcbddccbdbbcdbdcdaaadcdcaaadabacadabadbdcbdbdabcdabcddbdbbccdbadadaddcbdbdcdcdabacdcabdbddcccbacaaaacbdabcdacbadcccdbababbbaacadbbbbdbcbddaddcdccbccbcdbadaacaadbcacbadadcccacbaabcbacbaccccbdabddaacbccbaaaadaabddcddcccdbbacdbbbacabaabddaacabbcbcddbddbddcbabcccacbbbdccbdaaacabbcadccdbadbbabbbaadbaacbbaadacbbdbccbdabcaabadaddbcadaddacdbbaaacdbcacbacabbabddaadadabcbdaaaacddaadbdccbcbaabaadbcdbaacbdaaababacccaddbadabcbdcbdaccaaccdabcddacadbbcbcbabbbbacacbcaaddabbdadabdabbcabbbcdbcacdcdaaddcddbcadccdabcdcddcdcaadaddccccbdbdcbabbbcdccdcbcabadaddbbdbdcdcbbdacbbccdccabcbccbcababacdacaccccadabaaabcbacbbacaccdabccdcbadadcbadcadabbadabaaaabacaccbbcadaababcdacdcbbcbabbdabddccccbcadcaadcaaaadcadaddbbadddccbaccadaabbabbdcacdaddabddaaacdbdbbbbdabcaacdaddbaabdaaaabaaddabaacbdcbdbacddbbbbcdbbcdbbcbbabdbacaddababcaaaccabdcbcdbbcadcbddcaabddddadccbaacadaccbdddbabcaccaacaddbdbbadbcaadbaababdcbbacdcdbcacabcacabaaccbcbadbabddaccdacadaaaccbbccdccdbabacadcacddccdbbbbdbcdbacccccddaaadcbaddcdcabcabbbcdcdaadaaadccaccbaccccacaacddaaadcacdaacbbcabbdccbcbdcaccdabddbcbdbcbaaaadaaaaacdaccccdabddddabbcbcbacbdaabdbdbdcbbbcbbcdddcdcdbbdadccdaaddbdbcdbcdacaccccabbadccddcaddabccbccbcbabbdbdddcdbcbcbabbbadaabcadadaabddddbadbbacbdaccbbbddaaabbbabaaadcabddddbadadabdabccdbbccddbcccdcaaabcacdadabdaacabdcababccadbdadadabdcdaaabdbbaadaaaabdbccbbcbcbddacddddbbddbbbdcbcbcdaadbcdacdacdbccaadabddcbddcdbaabddcdbbcdcacdddcbbaaabdccbcdaddddbaacdccbcacaaabdadbabcdbdcbadcacabbaadbdaaddbccbbbcadbbaacaddbddbccdbcadcbaaabcbacdcdcaadbbccdddcbadccadcaddcddcaacddbdcccadddbbbbdbcddaacadbdbbbcdacdbcabbdcccccdbdaaacdbbbbcdcadaddcabbccddddbddcccdaacdbdbbacacaaddddbdadabcadabcacaddbbbbccccadbdaadbacdccdbabadaadbbcdacdbacabcaddcbcddcacabbbcacacbadaaaadabcbcdbcbbadbdddabacdbbddddabaacddcdacbdaacbcccccdbbaccdcbccadaadaabbbcdddaaabbbaaaccadadcccdadbcabcbdbddacbacbbddbddbadcdccccaadbdcacbdababbabdaccccdabdababccdbdbccdabdcaaaaacbbdcccbabaadbaabadddacaaadbccdddccadcabddabcdcacadcdbbddaccbbbbabacddadcddadaabcdacbcacbabcddbbccdabdcadbcccdbdaddbbaabadaccdbbcbddadadcdadcabcbacabdbcddabdccbbaadaaaaaababdbaacadabdcdbadcabcddcbcacbdbdcabbbacbddbdadcbcdccccbaadaccacbaacdabcdcadacbadccbbaadbdddaaaaacadaabbabbddadbbcdbbaabaabdacddaabcbadabbbddccbddaaabcbdccdbacbacbccdaababdbadacbcadbcdbcbccbcccdccbdddcdccbdbbbbbbcdccccabbbcddaacbaaaacbdbdcbcaddbaacaddadcdbabccdbadabdbdcddacaaaccccccccdbbdccbdbdadcbaccdabdcccaaccbdabcdbcacaababaacadacccaadbaccdcbdcccbcbadddabbccdbaadbbaadaaababcadbcacabbacacadbdbbdacccaaccbadccacdbddbdddaacbbbbbbacaaadbaccadccddbdcddbbcabbdccadbaaddcacdbdccdadccbdbddbbdbddcdbcaabcbdbbcbcbddbaddbcbbbacadaaaabcaababcdbbcbdcabcabaacbbacadbdacbcaacbcdcbbcccbdbcaddabbacdcabdbcbacabdbbadcbcbacbaacacaadbcabccbaddbdbdcdcabcdddcbcbaabdbbdbaacbcadacabddbaaacccbcdccdbdcdaadcabcbcabacacadacbcddbcabbaaacabddabddbaaaadcdccddbdacacabcdcccbcbddccbaddccadaadbdcacbcaabccabacaccdccaddcadbbcdcccdcbadcdaaadaadcadddbabdcccdabcbdbbbcbdacbdaacccdddaaddbaaccadabdccccdccddcccdccabccdddabbbcdbadacabbaccbbccadddcacddcacbddcdcbbcdbdbcbbbdbdddbdbcddddabadbaadbcdcabbacdcabcbcdcbbbbadaadabcdaaddccbcdccbabdadcbbbbccbbbdcdbdcdbabadaccbbcbddadcbadbddddcbcdaadcacddcacadaccdadabacbccadcccaaaccacdccbbaabcbadccccbbacccaadabdccdaaaccbcacbbddbabcaddbaccdcabcbdcbaddbbbcaacacdbcdcabacbdddcaaacabbdadbdbabaabccbbcbacbabacdbbddbbcbdcbaadacddcabdcacccdacddbcaacabcddcdaadaacdaadadbbddbccbbcccadbcbdacabcdacdcbbaacdcdcabccbabddbdccbaacaccadcbabaadbdccbdabbdccadabbabcadaadadadacdadcbcacbaccddcbbbccbaccaddaadbbcacabdbaadbbdcdbcdaddcbbcbccdbdbdacccbcdacddcbbacbcaabdddbabcdacadbdbcddcaccddbaaaabbdddbdbbdbdaabadcaccbbbaccacdabbcbcbbaacaddabacbbdbdbdaaabadbaadbbddacbabcacdaaaadcbbabddabcbadbdcbbccccbcdddcdaddcbcdccddbcacbbabbdaaaddacdbaccdcdddabddacdaaccbcccddcbdaadcabadbbcbabcbddbbabaddcdcdaaacdbbbdddaaacbaacacccdddcbbacdacbcbdcdbcbaabcbaaccbaccbddcacaddabbbcdcdbcdadcdbbbbccbcacabbaccdbbdcabdbdcbcadadbdbbdcbbacbdcaabcadacbaabadddbbbabbcbdbbacddacababccadbdaddbdbbbcbdccacbbbabcacdbbbbdbbdbdcbaaabadddcbabdabcdbcdbdbbbaddcddacbabacbcdccdcdaddbcbbcbbbadbcdabababcdbbcbacbcdaabaddcaacabdacadbbacaacccccdcacdbcbbddbadabbbdbcabcdbaacacbdddababdbcbdddcacadacacbaadcdbcdcbacdcdabdbbcaddcdcbbacdbdbcdbbdbbcdbdbdcaaaaabdcaaaadbcbcdbdcbcadababaacdbacadcbadbdaddbcacbbcbacadbbdccbbdbcbcbabadbcababacbbcbddaaccdbbbbaddabdddddcbddcabdbadcbacaabdacccdadccdbbbccbbcddcbbccabddbbbacbbadabbbcddacabbddcdbabcccbdacdccdbcdacdabbcdbdbcacbcdaacbbdcbbddcddcdcdcccdbadacbaaaabbbbadbadacdccdcdcaadddaadccaaaadcddacdcbaccdbcdbcddcbddccdbacdcaaddaacdbaabcbabdcabacacadadaadacbdcddcadccdbddaabddbbdcbabcbbcdaabcdbaaacabcabccacaccdbccabcbbbbacbaadaaacdabbdaacabacdbcbbdcbadaadcbcddcbdacbacaaccbdbbbbbcbcbdabddbadcaddaddddabddddcbdaabcaccccacbbdbcaacabaddddcdbbddaddbcaabddadabdcacbcddadaadabbaccadaaacbbaadcaabbdaaabdadcbdcbdbadbccbbbcdaaddcbbbaabbaccacabdabcddadcadbbcbdadbdaccbcaabdcbabbdbcdcbabdaccaddbaaaccbaadddbcaaaabcdadaccdcdbaadcdbdcbcdcbcbabcbdbabbdaacdcaccdccabaddbddaacdbdddcadccadcaaabcadabbbaccaabdadbbbabcdaacccaadccdabbbbababdcbaaddccdbccdcddccbdadbbbdacddbcccaabadadcdbcdcbdcadabaccbcacbbbcbdaacdacdbcdccbbccdccbbccdccddcdcbbddbdccaaaacbaddcbcddaabdddcbabcaacdbacbbdbaadbacabdccbbdcbbcdbcccbadabcabbccccacbcdaabcbdbdacccbcdcbbcbbaaaaabadadcaddddaaabadacabccaacabbaccaaaaadacaabdcababaccdbdbcbccbdaccbacddaaaaadddcdcabbcacbbcbdacbdbdbbdaaaaacdbbacccaabcbdbccaabcbcccaacbaddcbddccdacccccacdcccdacabacdaaccbbbdbacbccddcbdadbabbbacabdcccbdaaadaadbdcbacdbcacbcadbccbbcabbabdbcbcbdbdacabaccdadccabdcbaddcaabccacacbabddccadbcbbdabcaccaccbbbdccbaacadcbcddcadcdbbdbcacbcddcadcadbbcabcdadcabccacacccbcacaadddddbbdbbcbcdcccaccdcdaabcabcbadaacccbadbaabcbbabccdabbbbacaadaccccbcabdadaabaaacaaaaadabadbccdcadaacaaacabbaddbcdcbdcccdacaadaaabbcdadabdabddaddaabbcdaaabcdccabccdcddddadadbcbddcabbddbbdcccacbdbabbcddcdcaadaaddaddcdbbbbcbccbaaacdddcaccbbabcabadbbdaacdccabccbcbcadbbbdaaacdbcdabcdbdcddabcabddcabbbbbcccdadcbdbabcaaacababadbdcddbbbbadcabacddccdbabbaaccaccccddbbccbdddcdbbdbbabccababddbbbbcccabacbddbddaccdacccaccddcbbdbcbbacdaaaabddbdaaddacdaaadcabcbcccdacccacaacddcabadddbbbaaaabbcbccccdbcbcabadddcabbbbcbdbcaadddaccddddaaaaccdcbadbbcdbdbabaabdcbabbdcabdbabdabbbddbabbadcddaadaddaadbdacabcbccccacbcabddadacdaccddbabcaacbcaabacdddacaabcaddcaccdccdcaadbcccbaabdddacaadbbacdadcbccdccabbcdbbbccbbdbcbcccbaaddaaddcadbdcbaacccbacccbddccdddcacbcadcbcbbddccbbaabdaabcbcbbbabacbdcccbbbdbababbdcbadabcdbdadbacbbabdbabdaccccbadbabacadaabaabbbdcabbcdddabbabccdddbbdcacdccbbcbdbdcadccaddddabbdabcdbcbcdccccdaddcbddbdaacbddabddbcadbbcdaacaabbdbdbccbccbcddacdbbacaaacccabaabdabadaabcdabaddbcccdabdbddddbbbbaddbcadbbbcbcbadccabadabcdbdabdaccddbadaaacbabdbddadadaacbbdaaababcbacdcaaaadcdacdccabcbddbbdbbadaddabbbabacbcbabcbaabddbcbbdbbbddcabcaaaaaaabadcabbbaadaabdddddcbddbadaabadaacbcdbbbbbbdbdadabbadbcbdbbabdcaddadcababddcdaaaabdacdbadadccbabacaabaacddddbbaaaccaccbdababbdcbdadaaaaccbbcaaabcccdccbcdbdbdbbdddcbadbbaabacadcdbaacbbaaaadbdbbdbdbdcabcaaabbdacaabdddddbbbcdbdabdcaddccaccccbdbcbbbacbcaacbcbdadbbbadbdddcbbaaaaaaccabbcbcdbaaaccaaabbdcaaaacaddcbbababaddaaadbdacddabaaaadbcccbdadcacdacddabacdccbdcdccdccbaccadabcababbbdddaabbbcaddacadaddbcbddbcbaccbacdcbcabcdbcdcbbdbdcbaabbddaacdbccaabacbacadddaabcbcacbcbbdbdbbdbadadcdbbdbdcaabcaaacbcbaccabddcaaddbbabaddbbdcacbbaaccccddddcbbcaccccacadaabdabdbcbadbdaadbaabdbbdbcaacddaaadcdcabaaccccccbaddcdbbbcadcaccbdcbddaccdacbaddcadcaaacaaddbccadcdbbccddabcbbdccbdbcbccdbdadbccacccbccbabbcadddadbbabacdcaccbbdbacdcdadbacabacbbbbdddbbdacbdaddcacdadacdbbbdcbcbadcdbdcadcdbdcccdadbbbcdcaddcdbadaddccabaaccdcdabdcdacccbdbacbbbacabccabcadcbcdacbacaccbccbbdbbabaddaadcbdabacadabacddadbdcbcdbabbacbccbcdcbbacaaadbdacaddbcbcbdcbbdbcdcadacbdbdbdddabadcaddbbadcdddddbdbbaddaaaddadaccbabbdbadadacdabdbaddcdabbcabccdbabdadbbcacabaaaadabcdbbacbbcbbaddccbacbbcabcadaddbadcdbaddaccadbbccbcdddcdbbddadbddbadbbdcccccbccadbdcbdcabcbbddadaccacaacbacbdddcccbddabbabcbcbaacdbcadaacbcccadacbdaaadcbccabbbddccdababcacbacdbcbccdbdaaccdacaccccccbacbccdddbadaaaccccbdcadddcddbbabdddcaaaaccacabccdaaaddcaddaabcbcaccbbabcdaacadbddbbaacabbdbbcbdabbbacbdbabdcbabcbbbbddccbbbadbdbadaaaddcacbdcaaacccccddbddadcdbcbcddacddadbdacdcadbbbdbacbccbacdcbbbbaddddadcabbdabcbddacadbabbabcacdaaaccdcacbbbcdbaadbcdcbdadcdbdddbadbcdababdcaacdacbccaacccabcbccdcddcdccbacccbbbadcdbbddcacbcbacbaddbdadbcdccdddadbacacbdacdabbabbbdcddabbcddccdcdccdaabcbdddbdbacbcbcdacbbcbcccacdcaadcddbdcbdadaabdaadacbacdccccdcdacbadbccaccdcabaadbdbcadccdbaadbdabdaaabdaddbcaaaccdddcdbbdddcddcbddbbbcdcbbdaabcaaddcdcdcabbaadbbbcdcbcbabdccadcdaaaccdbdcbdcacaacdbbaabcdddbabddcccbbbcaadcdaacdcacbbabcdcadbbbbddcaadbabccaaadcbcdccddadddccbbbddaaacdddacadadaccbdadbaabcbbbaadbbbcdddaadcacddcaccacbcdbccdbcdaadccbbbcbbabbabbbddabdadaaddbbcaaabcdacabbdadadbacacbdcdacaccbdddabdadcabcbddddaabcaddbcdbaaaacdcccaaadcdbcbbccbabdbcbcddcdcbccdccdbdbcdcdcadbbbaabadadacadadbacaabddaacadbbdccdbddbababcddcbdaabaadcadabcbbcbdcbadbbcdbcadcaddcdddbbdcdddccdadabbdbbbabdcdbdbbbcdacdadaddadbbacbbdbddababcaddabcddbdcddbbcaccabdccdaabdbccabaccabdabdcadaabcacdbcdadddcbdbdccbbdbcaabcaacabbdaccdbbdabbbacabbddcabdaadbaaacdbdabcdcbbccabcccdadddcddbbbccdccacaaaabbcbcaccdbcaacdcaddcccabbdddadcbcbcbcbccdcbcaddcadcabdbdacdbabbcdbbabddcacaadaabccdccbbbadbaadaabddadccaacdadbddbddbcadbcbabdaddcadabdcabccddcacaadaddcbacbdbaabadbcbacdadabdbbbbccdaddabacddcdcbcadbbbdaddacbddcccacadddccbddaaabcbcdccddadacccbcdcaccccbadddbaddcdcadbcbbdbccababbbcccbccdacbdbdaddcacbcccadadbdbccacbcbcccbcacbbaacdabcdcbabbadbdbaacdddbdddbccdaacbcadaabcdcbacdbdabacdababcabababdddcdbbbaaacbadddbabdacbacdbbaccbbdcbbcbdcbdddbbcbbcbbdaaaadbbabbadbdacdbabcadadbadbbbdccadcbcaaaccdaadcdbbdbbcaabaaacccbddccccbaadadadccccdbcbdabcadcaccabcccaaccbadbddbdbcbcdaddcdadbddadadcdcbaccbdcadddbadabacdabdadabacabababdbdcaacdbadcaacbabdaaddbbaacbadaacabbbccdaabacadcacbdbbbdcccbbaacabadaaacdaacddbbaaadccabaaaabbaddabcadbaacbabcccccdcccddcabccaadccaddccbddbddccabbdccddcbabbaccbacddbcbbbbdccbaccbdadbbbdcbbbcbbbabbbbdbbdadaddbabdbabdaabccbbcaccbbcaacbcaaaccadacaddddbdcdabdbcbacdcaaababbaabdccccabcacdddacdaccbcdabbacbbbdabbacabcdacddccdcabddbddbcbccdaddcbdbbcaccbdaadbacbadaadcccbaabadbabccabbbddcdaccacbbbbaccabadaaabaccadaabbbadbddbdbdabbccbcccdacadabdcacbadbadbdddbbcbbacbcbcbcbcbbacacdadaccabcddcdacdddddbcbccadabbbacbaccbbdbbddaacaaaabdbabbdbdcaccbcbbaaddbbdcbdadbaacddacacdcacadbabdcccbbadabcbcccbcacdcdbcbbabdaabbdbcabcdcaacbbdcccacddcddcbacadccbbcbccbddcbadcaabcdcbcddcdaadccaaccbdabdadcdddabdccccbcbdcdccdccacccbdacddccaadbcabbdadbbddddddccadabcbbccddcbdbdcdacabcdaabacacabbcadbcabaaabbddbccdbdadaacccbcbcbdadaaacdacdacccdacabcbbcdbcadddbdcccccbbabadadaabcbaaaaaccaacdcccacabbbbdcadbddadadadacbaadcabbcabbaaabcacabbcdccabdcccdcbbddccddaddddcaccdacccccdbdaddbcacacbdcaaaaabaadcacaccabbadcbaadbacdcbdbcabdbaaaddbcdabddddcaddbacaadacaacdcbaaadddacdacccbbdaacddaaccbbdbdadcdacdacabdbcadaacaddcccccbaaccabddcabcaaaccbcbabcaaaabdacabbacbccdbacbcbdaacdabbcddbcdbbacbddaabbacbbadaadbaccbabcaabacddbbdbdacaabcaaccccbdaaabdadacccddacabbcbcddbaaabbdbdbdbabddadcbdadccaabbdcadccdddbbabdbccbaaaadcdbacacacbbbbcdaaadadcaabacadcaabcdbbaaaabbcadbddcccaabdcbcabacaacbdadbaabaadcbdbbddcbbddabdadddaabccbbabbadacabbabbdcaabacadccbabaaacaabdabcdbcbbcddbacccadbbdbadddacdabdbdaadabdbacaacdabbabcdccabdddacaaadadcdaabdbcbabacabcadbdcadbcbdaccbbdabdadbaccddcdbbbbcbccbbccbcacbadabaabacbadacaaaaccbdbbbaabdbaacbbadaccbadabcadbcbbdcdcacdadadcccbdbccabcabccacacadbbcdacacdacbdbabdaacccaadcccadcaddccbbcbadbadcbabbdaccaccabcdbccddaaabcdcbcdbbadaacdcbbdadbabbcababbdbbccbaabbadacdacabdcadbcdadbadbaabaaddccdaabadccccbbaddbbccaccdbaabadcdbdbddcabaccaccdbacbddbbbdbcadacacccadbdcbbbadbbdcbabbbccdbdbbccadaadbaabddcbbdaaaabbdbadadddbbabcdbddabacbbccbbcbdcaaacbcaccabdbbadcbcdbbddbddcabdaacddacdccacadcccbaadbcabdcdcacdaadbcbbbdaddcbadbccccdcbcabbdccbaabccbdbbddbdcadcdabaadabdbcbabdcabacbbdbdbacbdbaddddddbaaaadddadcdadcdacabcdbbabbcbddcaabababccabbcdbcabbaaaadbabcaddbbcbcbdcbadcdccaddbabbbdcaadbbdbadaacbabadabacaadbddcbbcdadacabcddcbdadabbdacdbbaacddcdbccbdcadcbcdcadbdbcadcbbbcdbbcddcbcdbddaadabccddadddadbbbddaccadcdbacbcdababddccabccbdcabbbdcbddcdaccdcbdaaddccaabdcdcbcdbacbcbccacdaacccaccacaaaccacbcbdadccdbadbaaccadbcabcdbccddaadadddbbdacacbcaccdbdbdbaccddaccdabadbbcadadbbabdabbccabbbccadbcddaaacbdacbbbdabddcaacdadadacccbdacbaacbccccabdaccdbdccaaacadacbabccdadbaddcabbcdbacabbcaabdbabbcdddcbcabadccabbbbbccdaabacccdddcaabcdacbabadbadabadaabbbacbbcdbbadccdaabdcbddcdabdcbbadccbbdbdabcbdaccacbabaadbabbddaddacccdddbadcbddbdcdbddbabaccccabbcdbcaaaaaabcbbbcddadbbdaabcccddcacddbaadbddbbaaaabdbaadbdbdbddcbbddddadbdaacabbaacdaddabbaddbaacbcadbaabcdabacaddccadddcbcdcaccabdcabcabdaddcdaadaccbbbddbcacbbdcbcbdaacbcaaddadbbbccaadcbbdddddacdacbbcabacadbaadbdabccbbbcccdbcadaddbbbddaadacdacbbdaddcadccdbaccbaaacacbaacbdccbbacdbbdbbddcaddcbbbcaacdbcaddcddcbdcabbbbadcbccabdbbbcbabaabdaadaadddbadaadbbacbaccdcbabdbadaddbcbccdbccaaabbccdbdccaadbcacddcbabdbbbdddabacdcdbcddbabbabdcddcbdbaaabbbbcdabccbbaacadcbaccbddbdbddbccbbddaabdaaadddcbdcaacaacddaaabacbdcdcdcacdbdbdacaabbacccbacbbddcacdacbdbcbbcddcaabcaabbccbbdaccadcaccddcccabbcbaabdbcdcacdabcadccbbcbdadabbdaacbddabcdbddccbaadccdbaacbcbccdcbdcababbcdcbaacbbaacbbddbdcaaacbdacdbdcdddbbcbccccacdddccbcccbbccacaaacbbcbadbaddaddcaaadcdabdbabadbcacabadadbbcacdbabddcbddaacadbdaddacabcdbabdbabbdcabaacbbbbcdcbbdcaaadbdabcbdadacdbddcbbbadadddcdcbcbbbacbcdcaccbddadcdbdbaabdbbacdccaaadacdacbadcdbadccccdcaabdbdcbbbbacdbaadcdccbbacabcdacccbddadcbbdaaadbcdbaddacaabbccbcbbdbaabccddbdacacbdacbcccdabbbddcaddbbbcdadccabadcdbacacdaccbdbdcccbddaccdcddddbabcabcaadcdbadbbbbbaacdbbdabcaabdddabdccdaacabcbcacadbaaadaaabaccacbabbcbddbcdaccabacaacbacccacaaddcbbccdbadbbcdccbbbbdcddbaaddcbbababdccdcbccaabdbcabcbbdcdccddaddccaadbbccbcadaaacdacbdcdcbcaacbbbcdadadaaccbacadccbabccddcbccabddabaacacbdbccbaaabacacacdbbcbbccdaaadaabddbbcdaabaccdbbddcadcbbdadadccaabdbbbbacaacdacdcbcdbbaabbbabacddbbdbaccabaaaddcdacacddcbbdbbcbdcaddbbababadacdbabbbcacabbaaadacdbbcabccbdcbdbdbddadbaacbdaddaadaccaadcaddcccbaddbbbdbbbabbcbbdbdaadcbbdbbaacddbdcdbbabbdbcdcdcadaccbbaaabbadadaabbcbbaadccdcdcadcbcaddbdadabbaaccaaddabbccacacaaadbcadcbbcbcbabacccbbccabdcbccadbdcdbdccadccdbcddbddaacdcaddbadbcdddaaaddacabbdbbcaacabcbbcdbcaadccdaddaaddadacadacdcdcabaaacbbdcacbcaaaadcadcbcdabdccacbbdcdabbdbabdcaddadccacdbcbdbbcccbbabacbbbccaddbcaccadbbccddcadcadaddabbbccaadbbdcbbbbbadcbbabdabaddabacdbbdbcbbbaaaacdacddcdccdcabaaaacccbacdadbadaaadbcbacabbdacbcdbaacbcbaacccbbddcddaccbabccacbacddadabcdbbdddddcdaadaddcccaccbcadbdbddbdabdcdddbcddcbabdcbdcaadbaccbadcbaccadbddbcacadaabaccdbaaaacacadaddcaddbbccbbdbcaaabaaddabbcdaccbabbbcaabddbddccabcccdccaddbaaaacaacbadcbccbcccdbaddacdccbbbbadbdcdcdaaacdadaccadadabbcacbacbadbdaadbacddacaacadacdccbddaadacbadbbbcadabcacddddccbaacbaccddaaccacdbbacabdcbcaadcbbabdbadacdbbabcbdbadcbcdbdbcdcabbbbcdcaaabbacbdaabbbbbdcbcccaacbcdbacbdacccdddbaaabcccaddacdbcdadcbbbacdadabacdcabdaabbcdadabadbbbaaccdadaabcbaacbdadccddbccccbabdbbdccbddbaddcdcbddadadddaaabababaaddabccddbcdbcaadcdaccdbccbaaabdadbcddcdadcccccbccdddacbcbcdbcbacacdcadbaaadadcbbaabcdbbbbccaaaaaadbcccdbabbdcbdaaabcbbaabbbcccbdbacbddbbccadcdabcaacdcbaccbcadaabdaabdbbdbbdddbcdcccabbbbaaacccaadbbcccdddddaaaabdaadabcabbbcaaccaddaabddcdbbacbaccdaddbabacbbdabbbadbbdabdaadddbdccbcbabcbbbcdcbcdddbbaadccabbdacccbacdcccddadbbddbddadababcddadabccdddcadbbbdaaadaacdaaccdccacdaacbcbbdbabadcdccaacaadbdacdabbccadaaccabbaadbabccdddacbadabaaabcaabaabadacabdabdaddcacbdadcbbdbcbadccdbbcdbacabaddbbccaddacbbaaaddcabdcacdcdcddaddcacbaccbcaddcabacbcdacbcddbdbbdcccbbdcbbaccddccbdcdcaccacccccbbcdddabcdcbacbcaabccbabbbddcababcbbacabdbcadcbdcaaaccbaccaadcccbadbcbbdcccdcaaddadddaccdaccddbabcbddcabbcaaadcabacdbddcbdadcaadcbdbacdcbcabcacbacadabdbdcdccdbdbabbabbacbcbbbaaabdcbdccababdbcadcbacbbdbcccacabccadbddabcbadacbbaddbcadaacdcabacdcacadcdadacdaaaddcababccaccbbaddadbccaaabddbbaadccdcdaacabcdcdccbaddddadddccaacadbccaccbbaadadacacdcccccccabdbbccabaaacbbaadadcaaaacaabbbdccbdbcdabcddadbbabcdbbacbbccccdcdbbaabddddbbbcdabdcccabdbcdcddbacdcdaadadbcbccdbdbaddbcabbcaddabddccadcaddadbacbacbbaaaccdacaadbddbaadabcbdaaddbddcdacadbabbcdbabdaadadacadcacabcdbcbbdccdccbadabbdadbdbccadcbdbcadccaadcdabbdabadacddbbcdbbaccbadbccdcbdacaddcaadbcbdaaacadcdcdbbcdaaacdbbaaaacadccddacbbdcadadbbbaccbbcccdaadbbadabdbbcdcacaaadadaacdbabdddbaabdddcacaadbbaccddcdbdaabdddbbbdabcdcbcbbdbcadbabadbbcaacbbabcdaadacdbcbaccdcdcddadabacbbdadcacccbcdbaaaccdadbacbbadabdbdddcabccbacacabcdbdacbdcdbaddbaaaadbacadcddcdcaaabbbdcaadcaccdadabbcacbccadcbbccbccbbadabccdccaddddbadcbbadccdbabadcdccadabcdadcdbaadadcdbdabacbddbddccbddcaaadbdacdbdcbdbbabcbdadbbabdabbbcdbacbcaacdbadabdbabdcabcbdbaccccbbcbbdcddbaadbdcabccabadbabacbbcdcbccbcdbccacadcccdacbddacaaadacbdcabcbbcbbadaaacddbacdccbdaaccbcddcdddcadddccdbcbbbaddadbabdaabdbaaabaabbccbdcbcbcadbbccaadcbcdbbdbabcbababdaaccbbdaadcaccdcccbacdddadddbbbacdabbababbcaddbacdabbacaaaccbbbabaccbdcdcdbbbcdbbddcbdbbdbcbdabaadaccacbbdcdccbdabbbacdaadaabcabbbdcbcbddcbbadbacaacdbdadaadbbccbaacaadaccbdcdbddaacabcbccacabdbccbcbaaadabdcbdbbcdcddccbababadcdbdcaacabdadbbacdbaaaccacccaacbcdbadabdbacdbbbbdddddaabababbbcabdcccbbcbdbcadabadadbbadacbdcbccaadbbbacabbcdaacdbaccdbdddddbccababbcdbcadbdacbadadabcbabcbcbaddbcddadacdbaabbbccbcdcbbcacaccbdcddddcabbccaccddcbcbddcacaabdcdddccdbdcaddbadabcddbadbdcdddaddabbbadddbbcbcccdadaccddbdcbcbaaabbabcdaadaadbbbdbcaaaadbdcbabbbcdbddddadddadadaababcddddbcdbcacaaaccdbbbcdbdbcbaccaddcdbbdcdcbabdcabcbcbdcadaadbadadbabbbdcbbdcddcbccaddabcadaddaaaddaaacbdaabbdbdaccabdacabcbdabbacddaddcbcbddbdbbdaacbbabddcaddddccbaacbdbdbcbabdabacddabadbdadbdabbbbdacacbbbcdabdaaacbacccdccabcadccdcaacbabdbacdaaacbaadccdbbcaccdcdcaadbbbacbbaddccddaaabaabbdbaaabcbcabdccbbdacbcdbcdcdaacbddadacdaccdcddadbdaaababcaabcabcabccaacbabbdcbbcdcdddabcacbcdbdcbabacbbacadbbcddaccadaaadbbcacacbdcaaddbbabadabaacddcbdbacbdaaadbbccbddaacdbccbabdccbbbadadadaddbdacadddccaacaccbacdbbcddbbabdaaccacbcabacabcabbbabbcdbdcdaccdaaccaabdadcacaaadccdbcbbdbcdcacacccbcbcbbcaaacbdddccdabbaddbaddcaccaaaabbdadcccdcdddaccddbcbcdcaacaadbabdbabdbbabddbdddbcbcadcdbdacaacbcbbadacaabdccddbdabacbacddddbbabcbcdbdacbadbdbcddbaacacdadcacbbbcbdacdbcaacbbbabadacbdbbbccccdbabddabccbdcbabcdbdbcadadaabbbccbddcdaccbdcdbddabcbddbdbcabcacababdaacadbadccdddbcddacbdcdbadddadcbcbbbbadccabddbbaadcddaaddccdbbcabbaccdcbbaaaccdcdbcaddbdcbcaaabacdabbdbbacacdaaaadbcbbbcbcadcacadcbdcbcabdcacadbadabaabcaccaaadccdccaddbddacdcdadcaaddcccccbaaacccacdcaadaccabdbdbbdbaccbdddcdcabbdacddddacdaddadcacddadcabaccacdccdadabadddbdbcdddccdddcbdacacbdcadbaacaabcbdcacccabadcaabcdddbccacdadadadadbdbbcaadaabddbdccdaaacccdbddbbaabdcdadcaddacabcdcbacbadbbdddcaabddcbbddacdcbabaadacbdabbbddddbcbddcbbccddbcbbacccdacacadaaabcdbccacdcbabadddabaadcdaadaaabdadabcdccdacaaadbdabbdaaaaacddaacddacaabbaccbdacaaccabaddcdcadadaaaccdaccadcdbccabacdcbdbbdbbaddacbcdaabdacdcdaabadadbcbaabdabadabddcdaaabaccadadcdaaacdcacddabacaacdcacdbadddcbaaaccdbccaaaacdcddbcdadcdcacddcabdcbacaadbadbadcdbabbaaadccdbacaaadbccccbaabddcadbddaddcdddbdabadcbbcddcdcdddadcdadbcabbabadcaabdabbdccddadbaccdccbcaadaccbaacccbddddbddadcbdcdacccdbaccacadababcdcadabcbbcaacabbabbacabddaaaccaadbacbbabaabcddaacdbccdaadadaabcbaacbbcdaabcccaabadccacacbcacbddacccadacaddbcdddbccacdcdaadbcdcaadbadbabbdbaacdcdcaaaddbabcbcdccbddacadbbddcadcbcbcbcaccacdcacdadbccbbbbaddccadcbacccaddacaacbbcbcbbbbbcbabdbdbaddabcddbacccdcabadabaaacaddbdbababcbacadcabcadcadbdbaaaccccbbbbcdbbccdbdbabbdabbbbbdcbabbbbdbcdaccddbadbcdbdabbbbccdbddcadaabcbdccadcbcbacddcbddbddaaaddcbbbdbabbcdccdbcadbacdbddcbcdcddabddadcbbaccdccdcadacabdaabddaadacabdbabbaaacccdbabcadbcbacbaddcbcaccbbdbdcccdbcbbcadbaddcdcdabbccdddbbaacdaaaddcaccbabcabccdbcbdbacabbbabccbbbccddddcdadbdcdcacacddacddbcbabadcbdacccabcdcdbabdcacabdcabdaacbbcdcaabbdbbcccbdcdbcabdaabdbdddbaababadccdddcbdabaacaabcdbbbbdbabcacbbdcaadcaaacdddbbcdcbdcbdcdbdadcdbbdcbcccddabacbabbadcdacaaccacccbaabcddabbabbdbadcadbcdbbcccbdacbbcabbdddbacddacabbbcdccdcdabaaaaccaaadcabcadbcbbddbaadaadddadabdbbbccdbbaaccbcabbcbbabcadabcccdddcbacbcadcddcbbcddbaacbcddcdbdddbacdcdadbcddcabbdabbdddbbbaddbabbdbcbcdbaababcdcddadadbadaadbdcdbccaddddcaabcbdaacbabbddaadcddcdcaadadcadcdddbbaaadcdadadadccabdacbbcdddbdcabbdbdacdabadbbccbdbbdbcbdbbbdbdaddcbabdabccbbacbddcddcbadbcabbbbbbbdddaccbbadabbcdabbccabcdaddacbddabbbdbacdadbccabbbcaccdbddabbdcaccabcdcacadcaacccbcccccdaccbcddacdabdbccbbbadcbdccaacaadbbccaddbacbcbdbbacaaabdbcdbadcaacdcabbdbbdbdccbcaaadccdabcadcbbbcacccacddccdbddbddddcbaaddcbcbcbcdcaccabcccdbaaaadccbbbbddbbacbadcbbbadddcccbaaccdbbabcccbdaadaaaddcbbdbbccbbcdbacdbdadddadabdccabadcbdbbbacacdccadaaaaababbaacdabbdabcabccddaccbdccbcbdcbccadbcacacaaaacbbcabaccaddadccacbbabbbcabdadaacaacadadabadcacdbdcabdaadbcddbcdbbcabdbdadbbbdddbddddcbccacdcbcdcadbccacadacaacabaabacdabcdaabbbdacdaaacccacabcadaaabccaadcacccbcadbcddbcaddcdddadbdbadababcbbcdadbccabdaddbaaacdbbbccadaacaabacdabdacbddddcdcbbdddbccbcabbcadcaabcadbabdccddcaaacaabbadbbadaaaccddcdabbacdcaddacbdbacbbbbcadbbccaddcdabccabcbccadbcaccbbcbabaddadcadcbdbaaaddccadcbacadbadcbbaabcaaabdcccbbbcbbabcbadcbacaadbcdbdbaccbcbdbabbccbdbcbcadcdcdacadbdbbaabbadaddbddccbbbdadddcdddddbabdbbaadbbcacbacbbbbcbaaabbddadadcacabccbccadbcacbccbacaddcaaddbbcacbcdabccbacadccbddddababcdcbdcbcdbcabddcccdcbcacccddbaacaacaaccdbbcccddbdbabbddabdddacbcbabbdcdcbccddcacbbacddadacacdbbdcddccaabdbabacddccbaccabbaacacbdadddbacabdcdcdaacdaadadbaaaaabacdbbaacccadcbabbaabbbadaccddabbddcbbdadaccdbcbacaccdbaaadbcddcaddcaadcccbddddcbddbbbcdbbbdcbdcaaaccaaaadabcaaaadaaaddbaaaddcbbdcddcdbcdaaacddbdcdbcabdabcadaacabadacdaccccccdcbddaaccadbcbadabbddcbaddddccbcbbcaaadcddcddddddbddbbdddbdadbbbcaaacccabdcadbddccbabdabcdbcaadabadaacbcbdcbadcdbdcdbdcacbccadacdbdadccdbcdddbcbcdcbdbdacdbdcbabbbbdbbdccbcabcabaddaaaddcdbdadcbccbcbdaabcbabddbccccbaadabbababcaababaabbbbdbbccaadccaadcbdbcdababccbbdbaacaacddaccaadddadabaccdbdcdaaaddbdacabdbacabacdccbdccbcabbdbadddcdbaabdadaabadcaaacaacaadadadabccdddddacbabdadbacababddcbbbbbbabbcadacbdacaccadacdacabaabddbaaccabcccbbddbaaacddbdbbbadaacdadbdbcbaabadcbdaccbacaccccadbcdbbcbbabdabcaaaaacdabbbcabbadacbacdcddbddabcbdaccabadbccadbbcdacddadcabdbddbabadddbbcdccabbbdcdccadcbbddabbdbcbbcbbcdbbcdcddadccaadadaddabcdbcddacccacccadadbcabdbdddbabaaabbcddbdbbcdabcddcaaabbccccdacbcacadbbdaccbbbdddbdcdcccdddadcbabbbdbdcdbbaaabcdbacadadbbdaacdcabadadbbdcadacadbbbdcddbbacdbddabcacdcdabadacdccdabdcbabbbadccbccdacbaccacbcbdacaaaacbcbcbbccdddadacaacacdccaddbcdbbdbdadcbbbacbbabdadadcdbdbcccadccbdbdcccacdcbdaadcdcdbdbcdccacdcbcadbbcadcdaacbcadcaaabdccccccaddaabdcdabcadcddabaabdcabdabadbcdcbddaacadddbbbabbdaacaaaabcddbcdcbdccdaabcbcbdabddcdaddbbadbabddaacbccddcdcaadcdbaabaabbddddadacccabdcababaccdbabaaccbacdbcdadcabdddcaddddaaabadbcbcccbcdaacabddbaacbcbbbbbabcbcadcabcbcdadaabdbdcaadbdcdbdbdacbadadaacdbddacbcaaddaaabbdbaadbbbdaacddcbdababbcbaaaacbdacacbdbbdadcddcbadcbaccbbcabaacdbcdcbbcaaadbaaadbadadaabccbbcccbbcdcbcabcddcaabbdbbbbaccbbdaabdbbaabbbddcacccbcbccadbcbcbddcacdbbcccaacbaddbaacacccbabbcadddcccabdabbbbcdabcccaadadacadbaccccdadbbdcccdbdcbbcbaaadaacdbccbadcbbdbbbdaabddaabdddcaaadadcbddbddcbabaacdacdbccabacabddaccdadddccaadbdccabccdbdbccacccbcdcccbdcaabaaddbdbaabdaaabddbdcbbcddbdcbaccdaadccacadabddacbbababbddbcbbdccdaddaddbcdbccddbdddbaababbacaadcdcddbbdbbabacaadbaabaaacaccadddbcdadaddbaacabaadacbacadddbbccbdcccdbdabbcdabdaababbaaaccacbcccadbbabddccbdccabdaddbdbdcbcbbdabaccbacdaaabcdbdbccdcaaaacabbadcbbcadcacbcdbdaddaacbddcdbcabaabacbcdcabdcbbccbaccbcddbcaadabcacdbbdddccddbcdaaadbdcdabcaccddcbaadadbcbdaccddaababadcddaaabacbcddbbdbccbacbddddabaabababcbbbddcaccbbccbbdabcdcacababadabdccdbdaadadaaabaaddacbbdcbdadddddbdcabbdccbaabaccdbbbdabadbadacbcddbaacbbdbddbdcbbbabdababcaaacdbdacdbdaaddbbbddbcaccaabbaababbabbadcbbddbccaadcdabcdcddccbacbbadbdbadbcabacdacbaadababbccdddbaadaddadacabdddbcdaccbcddcdccdbbcabcccabcdbdaddcbadccacbacbbdacadccbabbbdcabdbabcbadbdddbcdbadacadcaacaddcbddbdddccbbddabbbcbacabbcaaddacdaacdcbdaadaaaabdcadcabbcadabaaccdaccbddcabdabccbdbcdcdccdabdacbacddbbcdabbccabdbbacadccbacdbcccadbadbcbabaadbbbdaddbdabcbaababdddaabcdadcabccacbcdddcbdbacbadadddadbbacabbbabccbcbbbcdbdacbbcccdacabdcbcbbcabcbdbaadbaddbdbcbcdaddbbcbdabaccdbdacbcbbcdaadaadccdccdcbccaaaadddaddddddcbbdbdbddbaacdbddbdbdbaccdacdbabdadadaaccbcbbdbacddacdddabadbccbaddcaccabcacdcdccddcbababdacdddacdbddbdacacbcabdddcabbadabdbcccabccbdaabcdaabcabdcbbabdbbcbbbdcacdbcdbdabcadbdcccadcbbaaabcacacacbabadccddbaccadacbcdcaabdbbbbcddadcdaadbddadadacbadbbcccccbddccddddaddacdbccabadbabccacdcddaabacddcacddcbadccdadcacbdacbdaabcabcdabccdaccdbdbbdaacbadaaaddbbabaaadbaacacaabbacacdbbdacdbcaddbbbbccbcbdbddcaababadbbccbdcbacccbaababcadabbcbdbcadaacbaccabbbbcdcbdaddaadadcabbdacddadcbaccbddaacaacaabcabdabbccbcddcabacddbadcaacacbcbaacacdcadbcccccacdaaadabcacdccadbdddabaddbadacdbbbcddbddacbbbbddaadbbdbaddaddbacdbabcababbcccdbcbcdbdbcaddbbcbdccccaacdcbcdbdadaaaddbdaccabcdbcddaacbbbdbbdbcacdcaabbccaaacbbcacdcbbddbbddbdbacdccdcbcacddcacdabdcaccaddabbabdbaccabdabaccacdaacbacdddcbddcabccdbdcaddddcaacabaccbdabaaabcbbcdcdcbccbbaaaaaabbcaadccdbdaddacbdddcdddaccaddcbdcddcbdabacccdbdbdcdccbbaadcbbabacdabdccccccacbadcdbaacabcacaccbcdcccdcbdcbabdaaabbcacccdcabdcbabdabdbccbcdadaaaabbacdadddbaabcacaadbcaaaadbdbccbdccbdaddbbdbdccaccdbddababdadbdcdbacdddbbcdbccaaaaacddbbaacbdcabbcdbabbababbdbcdccbdaadbbcbccbaddbcbabdbcbccabcbacbbbcdcadcdcccaadcccbadaaabdabbbcaaccdbcadbbbcdbbbbbbcddbddbddbddccbabdaacaddbcbabcbbacdccdbbabdbacbcaccbddcbbaabdddcadbbccacdbbcbaccdbaacaccbdacccbaacbddaacabbcbaacdbcacabdcbbcbbcdbccaaaccbdbcbbcbdbabbcabacabcdbcccdacbdabdcadaddabddabbcdcdbdcbbaaddcbbdbadbbadadaddccccbaccadacacddcdababccbbbdddcdcddaaacbbbccadcdcdbdacaccabcadbaddcddaaaabdcbdaadbbbccbaadcacbabbcbabbccbbaadcadadcdbdccbddccbbadcadacbcaaccccbabddbbababbbbddbdcabcaaddababcdcddbcadbccaddacdccbcdddcadbacdcbadaacccdaadbaadcdddddcacccbadacaccaabbdcdddbaacbaddbaadaaacbccadcabcdcadccbcbbccaabacabbbddcccccaddbabdbcdccacabdcbdcdbddcbacdcbcdcddaaddcaaaddaacaaaccccdaabacdaabaddcbdcbbabacdaacbaddbbbbcccbdabbaccacddacadbdbccddacdbacbbbcbaaadcdadaabccaabbbbdcbccacbbbcbcbbdabdddbcabacacacddbbdabdcddccbddbbdbbdcbdadbbddccaddbaccaccbcbcdadaadbbbdadaabdbabadadcadcbcbddccabbabadbbcaacdaaddaccdddacaaacaaaacacacadacbadaadabbacbcacccdaacccaacabadccadacdbdabcbdcaacaabababbdbdadbaaaabdbaabaabaabbbaddbdaadabcaccbcddcbbadaccbccaabbbdbbadbbcdbddacbcdacaaacccbdbdddcbcadbbdadbacccaddabcdcdbcbbabbdbdadacdaaddbadbddccdaccacadbaddaabcabaacbaacbacdddcacababddaadaacaadddbaccdbabbbccdbadadcdbabddcdacbadbdccccbdcddbcaccbddbbcabdccdcabbccbbbcdbcccaaaddbbaadcdbacbadadacccdbcabccacddcddabacbadadacacadcadbccacccdabdbdaaacaadbacdcbdcbdcccdbdaccdbccbcbbddcbbdacabddaabbaadadcadcaccaaccaadabacbbbdbaacaababcbacbddddaadaaadaddbadbadabbbabbacadacbadddacadcdadcadbadcabdcdcdbabbdcddcaacabccaabaabcbdaabbacccbacdbcbcbacdccdabaccbbddbcaaabaacdacbaabababcbcacbbcbaccbcabdbdbdbdacdadcacbdddabdbabababcdcdbbddcadbbcdabbddccabdcdddcbbcdcbdbadabddbcaabdabacaadbbdbccacacbadaddbcadbadcbccddaadaabbaaccdacaabdcbbabdbababcbcaaddccbbaadadddaabcadbdbcacdbdabdacddaadcdcabcbacdacadbcacacbdbaadbaadccddcbcdabadbbdcbddddbdacbcddbaacadbccdaacaacaddddaacbbdbcbbbaacdbbaccdbadaadccabbacdacaacdbccddbdaadbacbabbcddbbccdcccbbcbbcabbddabdddbcddaaadbcbdbaaaaddbdadcccaccccbdcdcdcddccdcabbcdcbcadcbaabcdabcdaccabbcccccaccccbaacbcbdcbadbccaaabdbdcacdadaccabacbaacdadaacdacbadcbcbdbdddcbbdabaabbdbbcdaabcdacccbcddddbcbaadbdbddabbddbbaacdaccabdbddadcaddccaadabbddacdbcccbdabababbbbaabbcbdabbdbcaddcddddccdcbdcadcdccbaaacabadabcbadbbbdcabdacadadcbaccaacaabbddadbdbbcaddbdbbcdaaaabdaccdcadbbaabbbabdcabcddbacacbaaaacccabcdcbbadbdcacaadccbdccdddabdcbbddacbccbbacbcbcabdbdabbcdbacaadacbaadccddbdadbcdaddcbcbacccccdbbadbcaddacdccaacaabbdccbbbababdabcdbcdaddbdcadcaabbacadddbabdbcbdbbbdbacbcbabcacbbcddacacacddcdbbbccbabbbdcdacdddcdbdddcbccabbbbdcdbbcdacccbadbbcbaaadbbdabddacdbdabbadabbddcdcbbcacdccacdacbbcddaccdabaaaadadaaccabcdcaaaccadcbbccdaacbcddabcccdcdbdbdadcdccbbbcbcbacbccddbdcbbdbcadbcbacdbdbcddcaaababbdddaabbadbbcaccadaccbaadaddcbadaacdabacbacccbcbdccdcbdbdbcaddccbcddabadbbddbbdbbcadddbbcaadccdddaccdcdccbddcccdbaadddbbbcccaccdcbcccbbababaccdabcdbbaadabdaacbabdbadddababcaccbadccacccdcccbccdadbcbcbccccddbaaadcdaacdacaaadbbcabdabccddbdbbabbccdabcdcaabcccbccbcbdccbaccacbdcbdbcadadcccbabadddbcaaddbddaabbbdcddabadcddacadaadbccbdcdacddddbddbababcbcdbaadadcbccdbdbdababcaaddbbbabaaaaadcbddbbccbcadcdbddadadadacddbbadddacccbaaddcbdbabbacbcbdcaadbdacbcccdbcdadadbcaccababccdabcbbddcdabcadabbbdbdcbcaabdadaabcbaddadacdbabdddbcabddaacaabcacaacdbaacadbacabddcaadadbddaccdbcabbdababcddaadbbbdadbbcccacabdbcadaadcdccdadddbabaadaabcbcaabbbaddcbcbcdcaaabcdccabbdaaacbdadacdddcbacbacddaacbdbaddcddadbbdbcbcdaabbabdadbdacdaadcbcccccbabbdabaccbaddbadadcbacacccabbadccbbadcadbaaccbdbcaadccbbdadacdcbdcdbbcabdaccbdadacbdbddabccbbdbcadbdabbbbaabdcbadcabccaadadbbacaabbcbbbbcddbbbaabdbadbbdccbbbabbcacbddaddcdbabdaccabbaddcdbaadaddcccccbaabdbcaddcdaccbbaacdcdacbdbbcdccccacddaccbddcbddbbadacbcbabbbcadbaacddadacccbacacdaaabbaddcbbbcadcdcbbbdccababcbcbacdaabababdbcdaabbccadbcbdddbccbcdbbabdbdcadbbcdadddbccdaddbbbdbdababbcddabaaacbdbadadaccbaccdbbccacadccdcacdbdddbcaccaaacabaadadcdacdccbcbdbdbbcccdbbbbaaccabbbbcccaccacbbadbbbacbcdbbacdbcadbdabdbbabddcabbbbccaaccabbcbbabbdcbdaaddcabacddbcaacdbbadccccccaacddbdccbbdccdbdcadcaacabdababbbdaacbaaccabdcddccbbabdbcbdbdadbdbadaddccdaadbcddbcdbadadddcabbdccdbadacbcbdbaadccbdccacddbdadaaacbcdacabadddbdbdaabacbcacbbaabadcdcabdcddbcdbacbcadbbaabbbacdbbccccbbdababdddacdaddddcdbbbdccabcdabdcdbabdaabddbcaadabcbdccdccacdadddccacccaabdcabdadccabdbdacddaaaabaaacabdcbadbaaccadbcbbcdccccbdddddddcbdadcdbabbcadbbbababdcbddbaaaaabccbdcdbcdccbccdcbaacdcddcbcdabcccddbdcabbcacacddbbdbcaabbbaccbcaaaddadcaaaaacccdcdbdaddcdcbaddcdcccbaabbbdccacddbccabacaaadbdbabacaacdccbbcccaadacacacbdabcddbbdbddacdabdaddcaaabcdabdaacbcddccdbddbaddaacdabddabbdaaabccadbddabbbdbdcbbccbacdbdacadcbcaddcdcdcabbacadbbdcdbbdacddccacbaacccdddcaaacbccbdcbbacdcddccdcddabbbdcdadbddcbbbaddbacdcdbcddbdbcccccbacbbcbccccccdbbcddcaddaaababbabbacaaacbbdabaaadadbbbcaccbcacccbbaccababcaadaacccabbccdaacacdaacaaacdabbdccdbcadbbcccdbcdabbbbabdccdcaccacaababcaacccabdaabdabbbaddbdbbddccbdbbdacbbaaabcbbcadcdabccbacdcadaaabdcadcbbaaadadcacbbaabdabdabbaacdbdbbababdabcbbbddabcdacbbacbabcaadddbcabcdbbbccbccdcbdbdbbbccdacadcabcbbcddbdabcaabdcdcbabccccbaaadbdaaddabdddaaabddbbdddccddaaaddadbccaabdbacdadcbdadbbcbbdadcddcaaabbbbcbdbcdcdbadacabdaabbaaabbcbacdacddbccdcdccabacbcdcccadcbbdcbadbbdddbabddcaabcdaaaaababbbbdacbaccccddccbcdcccabaddabaaaaadbaabccdabbadadcddcbabbaccdcadbdaabadbbbacabbbacbbbadbcaaababdaccdbcdbddaddccbcaadaaacaddccdcdbcbabdbcaacbbbddabbdbbbbcabcaadabcaacabcadbdabccacccbddcdacaacccdbacddccccccdbabbcdcbdddcbabbadbdcdcadaaadcaabbadaccdaadbbddcdddaadcbabddccbaddbacdaaabcddadbaaddaccbbbdacabbbadbbaccaaddacabdcacadbcbbcdbaaddbabbadbdcbaacbbddbccdcaaacbcdcdbddcacbbadacccddbcccbddaddaacdaadabbdbcacadcdbbcdcccaccdaaacccdaccccdcbdcaaabbbacaacccadbadddacbdaadcdbcbcdbacdabdbddadbbbddcdbabbcabcbcddcddbcaadcbbbbaddcddcacbcbdabacacbacabaccadadcdcbbcabdccddacdcbdcabcacdbcabacbdbbbbcabbadadbdacdcacbbaabbacbcbacbcdaabaddbabacdabcadcbbabbaaaaddabdccdabcbdddccdaadbdccaccccbcccdaccbdddcbbddccbabccbbcaddcadbabcdcdcbabbcccbddbbadbdbaadbdddbdacaadcddcaaddaadbccacbaacdddabcabcdacadbaaadccabdccbddbbcdbbaacabdbdccbdadacdacaccbbbcdbdbddbadbcdbcaadaabdaaddbabadadddcadadadcbcacabcdbdbdadcadcadcdbbaabbcbbdbcabbaddcaacdaacbabdbccdadbbaaacbcaaaddddaaabacbccddaaabddccababbcdbdbdddbdacdaacddbdbbbbcbcbbdbbccacbdbbccbcdbcbaacaaccccacbadbcddddacabdbbababdaadcbcaacbbacabdbbbdabcddaddcdabbdbbccbcdbdcabbbbacaddbdccdbcbadcccbbbadbcdbcabadbdbaccbabbacdacbabbbacaaadcdbdcdbcdcabbcbacacdabcaaddcadbabbbcbccacbbbcbadcbccbdabdddbccbbbacddbdacddacbccdcadcabaaacdcccddabbacdbcabbccdbabbcaadcadbbdbcddddcacaacdacddcaaddaacdcadabdcbbabcaabbabadbdbddcccabadbbbdccdbbddaaddccaabdacdcabbddbbabbbaccabbabbbaccbdbccdbbadccaddbdacbbabcbddbacbdddcccdbbcbaaaaccaadcadbacbddabbadbaccabccbacdcadbaabcdbbdcddbdcabacbbdcdabbdcacdcabcbbbcbbdadcbaaabbbdcdaddbdacdcbdcbabacddaccdbadccbcacaaabadbddcbddaadaabacccaaaaadadbcdaddddacbdcdaabccdcdccdcbdcabbbdacdbcddaacdbbdadbdadaadacdbabcbaddabbbaddbcddbccccadbbdddbdaaacaddcbcbdabadcdddaddbabacccccccbdadacbdcbabaacaacaaddccdcdaddcadabbabbddbcdbbacddccdbbadbacbcabbcbccadadadbdbddcacdacababcbcbccbabdccdadcbabaccccdaacbabbcbcbcdabddcadcabcdcdbaaabdacccddbbbdcbcdabdbaabdabdabaccdadbaaacdccaccdddddaabbcdcaaccdabbcbdadabbdacbbbaacaacdbcbdaaadccbdcaccbcdcacbdaddddbaacabcdbbdacdcdabcabddaccddcabababaadcbadabddbadcccadbbaadbcccddbdabadbadbadbbdcdacdcdbddabddadaddccacbccbbbbcccadccbdbddcbbbdaaabcabaacdccbbcdadcdacbadabcbadcaaacbcaadcabbadbbdbabddbdbccbdababcadcabadabdcdaddcaaddccacbcccdbadbbdbabbaabddcdabbdcbdccdcbbababbbbbaabdcbcbabaccdcaabbdcaaadbcccdccbaabaadddaccdabddbaccbbddddbbbabcacbcadddcacbadcacabddbbabdbdaadaababaaadaddaadbccccadbdacbbddcacbbbaaabadbdbbacadadcbdaaccbdaaacdabdaaadcccddaabdddaaabccdbbabcabaddbbccdccabacccccbcacdcbccadbbbccbdbcabdbccdcddcadcabadcddcdcaabdadbbbccabdaaaaccdbbadcdacdbabdcdadcbddadaabbdbbcdbbbabbbdaccbaabaaadbdaddbbddaadcdcdaadbcbbbdccdacddadcaacabcbacadaaacbdbccbbdbabdaaccaacbbbbaabcabccbccadbdcbdabcdcbbdddcddcbccbddcbcabacdbdadcdaacadbcdbbcdccbdaddabddacdddddbbcadbdccbccacdbdbaaccabcdbaddacaccbcddccdcbadacbaccccaacaacbcacdcdcccadddbcadaacdbcacdaaddbaaadaaccadadabddbcdbacaddadcdccbcbaddcacbaddbcacaddddbabaabbdcdddccabbdaddbacbcadaabdaddccbdabbabadcacbbcccdadcdbdaaabbdbcdabbbdcbacbbbacbcdadbbbdccabbdabbddbadccadccbdaabbbdcadccdbaccadbdbcbdcbacbcbcbbdcbdaabccabbaaacdddccddaaadbdcbacbdabcaccbaccccabbddadccddcbacbdabcccadcabbbbacbaababcbcbacdbbdaabaaaabcbddadcdadcbabbbcadabcbbbdbaaddcbccddbdcabacddadbbcaadbcadbabdddcaadcabdacdbdcdbcbaabcaccabaaabbbbdaacdccbbdbbdbacdbcdcdccacdbadddcaabcaccdbcdaacbacbbbdbbbdacbbddadaccbdacbbbcbdaadaaccbcacadcccacbcbccbdababddcbbbdcadacbddabbbdbbacdccaabacdbacddadabdcbccccaabaadacbcadbaadccdacdcabcadddabccbdbdccacaaaabacacadbcacdaaacaabaaaddcabddbbabbbdcccbbdcbdcadddcaaccadcabdcacdbdbabbaabbbabdabdabbdbbcdcabccddbdcdabdacccdcaccdbdbaccbaaccabdbbacbcabcbabdbccdcccbdadccadacdabdabdacbdcbddabdccccaccbaadcaadaabaabbdadcdcbcdadbbcadcaccaabaaadababcbdcbddbacdbcddbcbcbcabacbcbdacaabababadccbbdccacbdbaccacbbbcbdcbbcbdccabdbcacccadabbacbbccabcbcaadbcbaacccabdacabbddaccddaacbabdcbadaccaddbcbcbbcabcacdaaddcbcbdcddaaaddaccdccdcbbbabaadbdcbcbdccddbbcbccadbcacaaaabdbbcdcdbcbdcdcaccaaacabbaadbbdaaadbadbccddccdbbcbacdcaacadbdaaabbbabacdadbccbabbbddbdcccbdcdbaadadcaadbdbbbdcccccbddababddbdcadbdbdbcdcbbdadccaccbbaadbcdaccabdaaabadbddcdaccccdbacadddccadcaddcdaadcacaabcabbcadadcbcacdbadabaadababacaabddaaccacbaaacddccbabcbaaacbbacaaabacbaacddbcacdbdcaccbaabdbddcaabcabbddcabbaaaacbcadaddccbadaacddaaabadcabbbbcdacbdaaddbbcdbbaadaadbddddcdaababbdbabddadbbddadbccabbbbbdccaaabddbddadabbbdbcacdbadddbcbabdcdaaacdbbdacbdcdcaddadcabbadacddcacaccdbccccdcbacacbdacbacabadaabccdbaddbcacbcdabbbdcadbccbaccbdcdabdbcdaabdbcbcccdabcaabbdbccdbcdbdbbddaacaacadbcacbdcdabcbdaacdcdcbdbdbbaadcbabdbbcacabbdaaacaddbacaabaccdcaaddddbdbdbcdcbadbbbcbcadbbadbccbbbacdcbadbadddcbbbcdcbcacadcbdcddcbbddbbccbcaabcbcbacdadbcccbcacbaabbaabcccddcdbddaacdbcabcabcbcbcccbbaccdabbbdcaacdcbabdabcbacacabdcabbbbbdbbbcacddabadacabccccaadbcbcadbdbcdcaccddbcdaddbccddcbabbacbbdbbdddcbbbabccbcabbcbcacccbccbcdabcbccacccbbcbaccbabbcdabbbacdabaaccbdddacbbcbadcccdcbaabdccbdcddacaccdbcbbdbbcacaabcaaadcdccbcabdddbcdacaaacabcbabababcdbbbcaddbaacdddddcdcbacdadcbdabbbdabdbcddccadbcddadcdccbdbbcbdacacabcacdadbdaaabdaccbabbbbdcabcacccdacbcdabddabadcacbbdccbccbdbbacbadabacabddcbbdddcccdccccddcabcbbbddbbdbbabaccdcacccadccdcaddcadaddccacbadadcdabbcdccbdddabdaabcdabbcbabdbdbddbbbabcbdcaabbbdcbadacddcacdcabcacababadbbddadbdbdcbcdcaabdaaadadbccccaabdbbacadbdbcacdaadaccbcbcacacaabbbddbaccdacdaadbcbbdcbbbaabddaaacacddbcdacbbdaddcdcabccdbbbcaaabbdcbcddbaaacaadcdbacccbaabdacdbbddcbbcaabccabdacdcaddbcaaabcdadaccdaacabdcbabaacbcdbdbabcbcddabcadaccbdcaabacbdbadaaadbbdadbcddbcdccdbadbdcabcadbabadacdaadbcdbcdccdbaaccdabdabcdadbdbadbdbbdaacbbccbdbbdadbccbccbabbdbddcddacbbbdcabddcccdccddcdacccbcddcaaacadadcbbacaadcbcbbdabacccccbdabcaddbaaacbcbdaaccaacdccbaccddabccdabccbdcdadddabbccddcdaddbdbdbcddcabadbdccbacdbcaabccddcdcaadcbaaccbddcddaccabbadddddddccbdbccbbbcbdbadcdaadcbccbbdddddbaacdcbcdcdaccbcddccbbbcddbbaabbacadaababcdcdddacdbbdcbbdddccaabbacdababcaabdccbccabcdccaadadddddbcaaaddabdcbbbdcdcdcbdabcbadbdbaccccdcbbcaccccccadbacdacaddcdcddcdbcabdaacbddcbdaadbacaadaaaaaacdacddadacbaaaddbdbaacbbdccaaacadcdcbdbbabcdcdcadabbaacbacbdbaccabddaddddbbccdbddabdaddddaaacbcbcbddcccdabdbccbadadaaccbaabbddadccccbbacaddddccbaadacbbadacabcabbaadbdbbadaddcbbcdcaccaaddcbbdbaadcadbdbdcbccacdabbdacdcdbbbdcdaaabbcdbbbcccaadcdbacdcdddcddadacbadbdcdcbbaaababdabddbaacbaabcddaacdcdcddccbaddacccacaababbcddbacbcdabbacaabcdaacccddacbbbaabadcbbdababddbccaabdcbcaddddadcbcbdcdbadabbccaaabddddccddaaaccbddbdbccbabdbabadccdcaadbbccdcddabcccccbaababbcddcbabcbbaabcddadacdccbacbbbcdaddbabcdccdbaaacccabccabadbbcdacddbcbdacadcbcadcaddcdcacdbdbcbddcabdddbaadbccbacbddcbbdddaddcaabcccbadacdbcdbdbbbadddacaccbbabcccaabaccdaaaabbbdbddcbddbbacbbbdddadcabadbbddbcdacaccccaacacbbcdabcbacadbdabcdacabbcdbcacbacadbccacacbccddacdaacdabbbbbadaccdcabababcbdcdaadacdbabdcdadabccbabaacccdaaaacdcddaddacadbbcdcdacbddacccccadadcbdcccccdaccdabcdaabbbccacbacdaacddcadccbbabbcdbaccacbdbbbabcdacbaacddbbadcdabbcabbcbabbabcbdabdbbcadbccaaabcbbccddcdcdacdcbddcbbadccdabbbcabadabacdcbcbdcdaabbabbdcacccacddabaccbcbcdbddcbcbbcadbbdbbccadaccbadcdadbadcaccbbddbbdaaaddcaabaddbcbabacccbbcbaaaaababdaacaaacaccccbdbbccdbabadbaadaccdaacadadcabdaacdbcabdabdabdcccdbbcaadbadbbddcdcdbacacadddcdcbcdabcdbacdbabbddacadaacbcaababcdddadadbaacccddaacabcabcabdaaadbbccaaabdabcbccccadacbbcbbcbbdadaddadcbdccbadddadcbdcdbaaddcbcbbccdbdaadadbcbcddccbbcbaddaaadaacaddaacbacbaaabbbddacbbdaaaccadaccabacaacbbacadcacddabadadcccbaaadabbdcbccdacaaacacdbaaddcdcbbaacbcdadaadcadcabbddccaacdbbacddddcdcacbdbddaccaacbccbdbcdcaadcccabdadcdccbababbbdaacbcdbcacabbdcaadccbcadabcababacaacaacbcabdaddcdabdabbddcbbdccacdadacbddaaadddbddccbdddbcbaabdadbbcdbdacdbdbbbabbaacacbabbaacaccbbabaccdbbbdaddbdcddacabdcbbabbabacabadcbdaaaadbdaacaabcccdbccdbbbbdbbcccbbbcdddaacbdbcbccdcbbcbaaabacdbcddcdcacddaaacdadbcadcacaabbccadcdcbabbaaddcaaddabdcccdbdacaabddbadbcadbbaaaaadcaaabcdacadcbbacdcdddcbccacbabdaadbacacabccbbcbadabdaaadbbccdaaabababbdbccbaddcdadbcabcccbbadabbddbacdbacddcdbcacacadadaadacdcbddbdcaacbdccdcabcdbdddcdbbcacabccbaddbbccabdadabbcdabdaaddaabcdbabaadbaddcdcbcdacbdcdbdbbcbadacdabcaaacdcadcccacaaacbacbabacbcdcaaaaaadaddabbbbabccbabcbbddcaaacdabbaabbabaaaabdcbacdbbaadabdbbaabdcabadaaccdbcbcdccbbcdaabdbbabaccdcbbbcaacbcadaccbbaddccbdbccccbabbacbbcdacdacbdacccccdbbbadccacbccaacacacbdacddaacacdcdcbaadaddadabbcbacdadbbccaaadbdabbaacacddadbbcbcbcadbadaabdbcdabcdcacdabcdaaacbabddbadbdbdddcdcdaacbdbbcbcdcbcacddddadbdacbbabbbccdaaaadababaddcddacbcaddbdccababbcacadaccbaacdcdbababbaaccddaadabaaacdadcccbbbdcdbcadabbaaccbdbbdcbccaccbadbbbcaddaccaadadacbcbcabaabcaacaaadcadcdacddcbbbdcddbbdbadadcdbadbccdbcbbbccbbadaddcdbcdccddbbdabbaabadabbcccaccbdccbcaaacacbbadaccadbbdbccdacbaacbaddabcddbdacbabdbdbdcbdaddbdabbbbadabddcbcaabaabaddcccccbcacbaaabadddaadaababdcdbcacddbccbbacdbbdaabddcabcdbacbbcdddbcbdabdaaddccaabbbbbdbabbcddabcccbcdadadbbbbaddbbbdcaacbdaadcacbdcbbddbcaabcaabbbdbcaabbcacacddcaaacbcaadddbccbcccaadbcdddcadaaccbbdcbdbbacabcdcaabccbbacabccdabaaacccddabaaaaacdadbddcabbadbcbcbdcdbbcaacbccacaddcaddaaaaabbddbbdcbcaaaddaccdcdaadbbadbcddcbbacbcdcbcdddbdadbbdadcbccbcaccbbccddcbdbcbbbcbcdbabddbbcbaccbddadbbbbdcdbcdaadcdabdbbbabcbabdaacdbbdcdbabbbdcbdcbdaccdacbdccdddbdadaacddbdaadcccdadcdddbdbdcadbcbacbdaadddcacdcababaddcbddaacbccaadacdcadcdcabcacdbbaaddcdcabbbcbcbcaabbbbbbabdddddddbcdabaadddcbccbacacdbccddcbcadaacbcbbdccccdbcccadcbdbadcccaaccdaaddaaaacaacdaaaccbbbbdcaddbdacbaaadddaaadabdbcdbcadcbbbddbdcbddadaddbaabdcdabaaabbdaaddcdbacccdaacdbcbdaccbcacbbcacbdaddadbaadddaabbbadddbadbbadcbbadacaccadacbcbbbccbbcdcaacdcacbacbcabdbcdabccabbdbcacbbaadcdbdaddcdbcbaccacbcdbbcdcbcbabcdddadbdccdcbcbbdcbdbbabbadcbbdcbcaabbcdcbcdabaacadbadabbcbcbdcdbcbaaddbddbbabddbbcbbbdcbacddddabbbbaabbbababcdccbbaadbcdadaadbbdabaaaadcbccdaacdbddccdbcababaabaaabaadcacbcccbacddbcddcdddbdbadddcdcdacbdddccbcdddcddcbbabddbbdbababacdbdbcdaccadbaaabaadabaccdcddcbdcbacbdbdbbcaaadddcdbddbbababdadcabaddcbccbaadaccabbabbbdcbcbdbacaadbdddbccccaadcbaadddbcbbaddbcadbdccddbbdacaccdbbacddcdabcdbbdcabcdccccdaaaacbddbbcacaadddcdbddacdcadacdccccdbadaadcddacabbcadcdcbcaacdbbcabdbddcdaccabcbbcdbccbcbdcbcacddccbaadabbdbbcbddcbdbbaaaddabcbaccdcabcbdcbcdadcaccdaacbcddcbbcdccdddbababcdddbcbdbcbdbbbddbdbccadbdbcbabdbdababdabbabddaadabbccccdaabddacbcbaadbdaacaccabdcdccaaccacaddcdadadbbabdabbbddabcbddacdcdacabdbdbaaddcadbcccadaaaaaddcdadabbadbcdccbadbbbaaddacbcacbdaaacaacddbdcaaadaadbdbdaadcabbacbdccababdbaabcaccddcacaabdcdaaabbcccbbbccaabacbcdbabdcbbdadcacbddcabccadbddcddadacadbbdcdabbbabcdbcaccddddadcbcdaccdcdbaabbacacacdabaacbdadaadbcddaadcaadabbbbbaddddabaaadcdaacdbaaddcbabbbbdacddddababdcaacaabccacccaabdcbcacaaadabaabbaabdcbadbdbcacdabdbccacbadcddaabbbddddacaabaaaddacdababbbbbccadbdadaaddcbddcadcadbbcddcbacadbdcbacdcddbdaccdbabdadacdcdabdccadbadabbbcbddcddbdbaadcddcddaaaccdbaabddaabccbccccddbacdbbdbcccbbdcdccbbcdcaababcacbcabdbcdddbddacadccdddabbcbdbbbcabcbcdaadabacdaacddaabddaadaaacaccbdacccbdbcddadcaddbdbcbbacaddccdacddccaddcbacbcaaccbaccdbdccdbdacacadbddddbaaddadabdadaccdbabaabcacadbdacccaaabadadccbadaacacabdabcaabacdcabcacdabbadcddbddccbddccdccbbcdbbaddcadccbcdaddcddaccccbbccbbadaaadadcccbacacdbbabbbadbcacbbdacdbcdacddcbcbccccbadccaabbcddaabdbdbdbabbaddbabdabddddcbdaacbacbabccbbddbaccdacabadddabdbcabdddadbbcacacbaccbbdddadaabddcabaaccddddaaadcbcbbcadcaabdcacaacddcdccbbdcddbacbabcdbdddbabcaababdabacdbaddbbcbacddcbcadbbacbbbcaaabccdababccccddabbddbdbaaddccbdbcbdcacccabdadcbabdadacdcacbcdadbcccbaaacbbdbbbacdcdabadcdddbdabbdadbabaacdcdabcdbdabcabacbaabacaaadcdcbaabdcddacacbcbacaacbdccdaccbbacddaacddababbbcbdccdaadcdcdabcdabcdadbbbbcabdbdadabcbdaaccdadcddcadbccdadabdcbbcddcabbdccdbcbbacbdbadddddbaabcbcbbbdaadcabbbadcddacdadbcaddbdcdddbccdcbcdccccadbadcaddccacacbccbbdbbcdaabbbdddbcadcccacdbddaaadcbddadabbacabdaddcbdadddcbbbddacbccdbbbbdbbacabaadcbcbcbbbdbabdbdbbccbdccddadddbdadadccdcdadaadacbadaaccbdbdcbdbddaabbacddddccbaabddbddcabbabdbaacbaaaaabbaababdaddcbbbaccdddcbdbccdbcbdbdbbcddbbddcbdbabcaabddbcdcdbcabadaabcaddaacbddadbadddcdbbbbcdbaaacdbadcacdaddbabcdddcacbcdabacacaccbcaccbbcdbbabbabddcddbdaccbccaaacbbbbacccadcbdddbcaddcabcabcbaadcbdcaadcddabddddaababdaddbdcdaacabcaadabdbcbdaccdcbdcbabccccadbabbdacbdcadccaabdbdcadbdcadccadababcaccdbcabacdaccbdaddcccadcbbcbcddbcaccdbdbdcbbdabaccadcaaddbcddbbcbacdbbaabcdbadcaaabaadcddbacbdbbaacdcdaadbcabcddbbacbcaabdddacdaddddaaabaadbdccbcaacbbabbcddabacbadbbcbadabbdbddbadabccaaaaacddacdaddaccbcddcbaaaccdddbbdacbccdcadcaddbcaadcaacbddbbddaddddadcadacdbbacdbdabcccaccdddabaddadbbdddbddcddbbbbcbbaccabbaaaaaccacababdacdddabdbddaacadccbacdddcbcaabcbdbabcabadcdacabcbbacdccddaacdabcdabdbcadddcccaaddbcbcddadbcbbadcaaacdccdcadbdcbdddcdccdcccbdacdadbccdaccaaabcbbdbdacadaaabccabdaaccbccbadcccdbddbcbadcdcddadccbccbabdbdbccccbdccdbcdadbbaccabbdbcabcadabbbccbabbbcdadbccdadcbcbccdaccbbbbccdcbbbbcaccbdcbbaddcdbddabbbaadabadcbcdccdcbcbbdcbcadabcdcdbcbaadddbadbabcccacddbadbbcbbacccddbdcdcdbccccdadabcbadbacccaddacdadbaacbdbccbddddddaddbdaaabddcccbdcbbaacbabdacccbabddddbabbaacddccbbbbcaadbdcccbdaaaabbcbcccdbadbacddbbabdababdbbdbbcdbdcddadcadabaccabddbabcbcaddcbadaaaddbdbdbbbcbdcdcbbdddddbdaaccbaadddacdaaabccbacbdadccbcbbadcdbccbccabdcbdddacaadbdcdbbaabaacabcccbbbbadcbbdcabdaaabcaaabadddbdbbcddcdbbdcbdadbcabbabbccccccacacaabaacdbddaddcabbbabcabdacbddbaaccbddbadcbacdcdbbccbdcdcacdcbdbdbabacaaabacabdbacccabdcabbbdcacbcbbcccbadadbabddccadccdbbabbdbdabbcddcbdcdbbabcbdbbddbcababbdbdddabcabadbdcdcbcddbbbcdacbddbbabcaadbaaacbaccbbbccabcdaaabadaacababcaacdbaacaccbdccbbbbdabbcdaadccacdcdccbadcbbcaccaadbbbadbbbcdacccbadcdddcddcaacaacdbaacbbabaadaabccbadcadddcdbaacaccacdaddcbcbabbcbbdadddcddcaabbcccdddbdcdbccdabadddbacbbcadbcbcadbdccbadadcbcdcbaccdbcbdcccacabdddaabdadbacbaccabdcdcaddbbddcdcadcbbaaabcddacabddaadadabccacbbcddacbadcaacdbcaaaadaabbabdddccadcabcddbdddbdaacdcaacbadacdabcbbcdacdaabddbbcaabcbbabdabbbdbbcbcbbdcdbbabdbaabdacccdcbdbdccaabacaaabbdcadbdaddcbbbbbddcdaadccddabaacccbababcbbdccabdbcdbcdbcdcadabcddcbcdabbccabbaacbadbacbcdcacddbbcdcaadacdcaadabcaccdbcaacaabaaabdcaadbabbcccbbaccdcabbabacbaabbcbbacbdabcabcbdcccccbcbbaadcbbbaccdabbcddccbdababcbabcadaabbccdbacabbcdcaadbcdbbababddddbcacabbdbcccacbdbdbbdbdccbcdcbcadcbcaccbcdbabbddbbcbbbbdbabcdaaaccddbddaaadddcdabbbabccbbcbcddcbadbdacbabdddbabacdddadcdcdccbbddcbddcbdbabaacbbcacaacdccaabbaddcbabddbcbcdbbadcaabccdcbcaaacbdddbdccbbabdcbccbaaaabcaacddadabcbcaabaabdbaadbdaccadabdaccdccbadccbadddabbabbcaabcbabbddaddccaccbddacaadccbaabbdbcbbcbcdaddcaadbcbabacdbdbcdcaaaaacbbddcaabcbbbddcbbaaabacdcdbdaddadbaacacdcdbcdaabaacadabadccabaccccdabadddcaacbbdccddaabbbcdaaadbaaadccabdddadddbaaabcbacbaaaccbdbcadaddacbdadbcdbbabddbbbcacccaccadcdcacdadbdaddccbadbbadcbdbabaabbcdddcacbdddcbbaabcdbcdbbdcbacbbadcbabbcdabcdbdddbbaaaabbdcbabbaccabcbcabdaabdaddbbaabadbabdaaccdaccbcadacdabdcbdbaabacacaaccbcdbcdaaadabaaacbaabdbdabadcdacadcbadddbcbabdbbaadbbcdddabbdbdaddaaadabbddadcacdaccdcabbcddbacddbddcdabcaaabacbadddbbbabbdcadbacadbaababddaccaacaacaaccccbdccababcabbcdddbdacacbbaccdbdaaaaadaaacbdbacbbbcbabadcddcbdadbddccdcdaddcdccccdcbacccdacdbcddbcaadaabccdddccccbaadcbbaaddbaadcddccccbabdcabdddcaadbdcabadbdbdddccaadaaddcbbdacbdbdccccbbbbadcabadbacbbbcababcaabadabccdcaccbcbddaadccddabcdbcbacdcaadaddacbdcadaadddddadbbadcaabbbbacdcadacdcbababcdbdcdcdcbdddadddcadbcbdbacbbcacaaaaacacdabbbcccbdbabccabddddddcdcbabaaadaacacdabacdcdbdddbaadbbdbbcbcacabdddadbacbddbbdbbcbdaabcddaacdbabbadbbccbcbbcdcbdacbcdcabacdabcbbbdbccbbaacababdbabdbbacbdaacadaababcbcbdacdcdcaacabccaadaabdcdabbdcbdccacbcdcbccadccdaaababaddcbcaccdbccddbcababdcaadcbccaddddddcdddccaddbcbaccbbdccddccbddcadacbdcdadcabbdabbbbbcaddbabbcacdddbbacbbccccabaaacaababdaacbbbbacdccadcdabcadccacbbccbdbcabadcdabcddaadbbdcadcadadaaddcdbbabbbadddcdaaaacabcccbababacdaabbbcbcbbacdabdccddbbabacccbdcdadcbdcdcdbabbadbccaacbddbcbccdddbdbaaaaddaacddabcaacbacdbadddbbabdaacbcabcdcacbcadcaccacbcabbcbcbdbacaddbacbbcabaacbacdaaaddabddadccaccdbcdbacabacbacbccadddbbccadcbbaacadccbdcaaabaccdcbbcaabaaadcdcbdbbcbcbddbacadcccdcdbacabccccdaadbdcadbdabcbbcacbbdacabddcdddcabcabcdbdbbbacadacabbaadcadddbccddddaacbdbdcacadcccacdcbadbbabacdcbbbcabacbbbbdadbbabbccccbcbabbbdddaadcbaccccaacaccacdbdccccbdbbacdcacdddabbdcddccaaccabcbdcbabcdbbadddcbbbcacacaaadbabccabdadabcccadcdddbbcadaccabbcbcabdddbbcdcacdccdccdbabbbabcabbbadcdccadbddbdaccaabbabdcbbdbcaabbadcacdcbbaadbbbaccdbacacbbdaaacabdbdbbacdddbababdaabdaaadacadabababdccdaaccdacddccdcadddddadabadacbcbcbcdacadacbdbdbdddcbddabadcdcdcbcddddcbcbaaabaddaacdbaacacaddcadbbbaadcbdcabacdcdbccbabdcaccadcccbdccabdaabbcbbcccdcdcaabcbacbbcbaccdccddcdccdcddbbdddcbadaaccbacdddaacbddcabbadccbabbdcaccaccbcdbcacacbbbcadbcdcdbcddbbbbddbcdbdbcdbcbbbdbcbddaaaacbbbdcbdabdaadccaaaadddaacdbcacbdaabdcacbaacaaadcdccbdbbdaccbadcbcdcbcabbabbcbcdccaaaddcaddbdbbcabbdabdddbaacbbbddbddbdbbbccccacdddcacadccadbbdadacdcaddcbbaadcdcbdaacadcbbbbbaddcdacaabcabbabdadabbbabadcdcaddcadcbdaacabaddddddacbcdaccbbcbbdccdbcddbcbcaaaaabacaddbbcccacbdaaabcadadaadccacaacbdbcacacdcacbdaadaababccbdccdccabdadcddabbbacbbdaabbacbabbbbbcdccdacbacababdbdcddaabaabcabddddbbdcadcdccababcaacdbccbcccdccbacdddcaaacccbcbabcaccbdcbcadbccddaccdaacaaadddadaddccbbaadaabababccbabddaacbacbcbdccddacaddadbdcbaacbbaadcbcbadbaaacdbcaabaaccdccbaadcbccaadaadcaddbccbcbbbbbabadadddacbdcdbacacaacbdaddbdcbcdcbcabcdbcbccabdaaadbabdacdadbdcbcabdbdabacbaccddcddbcdabcbdcacdabaacdaaaaacbcbbdaabbcacaadcdaccbaaddcbbcddbbaadcdaaaacdddccadcbdaddabdddabcbbabacaadacdbdacdcadadcdbcbcabacaacbabcacbbbabcbbbdbcacdadbdcccccbdabbccbbabbdbbdababddadbcaaacccbadcadabcbbcbbccdddaabcbddacccddccdadcabdacbbdcbbbbdcdbdabdcdcdbabdbcbdadccabdddcdccbdaacbdacbadaacabdadaccdbaddbaaaabdcbcdabcbdccbdcdaabacaacabddcaadddbbacddcbabcdabadddbdbdcbdbadcdbbadbcbdaadccacddccdccaccbdcabbabacbbaccabadbbdcadacddbbdacddbacbbbcbcdcddcccdbcacacaaddddadacaadcddcdbdbbcbccbbbdacbcaaaabcbcaaddadcaacaacbbcddcbccccdaaaadbabdbbbbbdbdccbaccdbbbcbabacddcacccdaacdcbdacdcccdcbdccbddcbaaddcbdddbccdbbddaaaadcadacbcccccddaaddcbabbbbdcccaccbccadaddbbbdddcccccacaabbcadcdbccddddddcbbacbabbaccaddabbdaaabbdbbbbdbacaaddaacaabcbadcbabcbbbcaabccbcdcadcdbdcdcccabacdccdaddaacacaacdddcbcbccadaaaabddbcbbcaabbddabaaadddcbccbbaadadcdaacdcaabdbbbadabaddcbadabaaaaddccabcbdbabdbbcbccbbdbdabadcbbccdcddcbdadacdcbadaaddbcbcdbbbbaacbbcdbcccbdbdccabddcbcadbdddaaacacbbdaaabbbdbdbcdadadcdbbabbaddadaccbaacacdababddcaadbcbababbcabdbabaabbccababaccabbcccabbdddbbbadcbbcdabccabcbaadddbbcadcbddaabdbadaabdddbdacbdbbaddacacdadbbcaccdbddacbbacbdadbbccadaabbadcaabccadacdcadbaaabdacbcbbddcdacadbabadcdaaacaccacddadbbbbbdabbabcddcaaacacbcbcaacbbcbcccbddbdbddcbacaadccbdddbbcaacacbbcdbccacbbddbdadabcacadabdacadcbacacacbcdccababcaadbdacabcddbbbdcbccdcbdbccbadacccddcddccbbddaacdcdcaccacadaadabddbadaccbacdddcccabacadbbacaacddddbcaccddddcabcbcbcdbddaccdbdabcbcabcdccbbcccdbcacbcaaaaadacbddabdabdbddacdabdacbdacbdbdcbbcdaddaadbabddbadcdccdbacabadabdabcabbddbadddaadccaacbdadcdadbbbccbbdcbccbccbbbbdcabbcdacabdbdabbabdcdabaccccdcaabbddbadccbbbadbddddaaabdbaccaadabcabcccbcdadabaaaabcaabddbbdaaaabadcddcccbbdcddbaccbdbadcabdbccddbbcdbccaacbcadbcddcadbdcccbdbcacddcccdcabadaaacabdcbdaacabcaaddcdadcccdadbbaaacaadbacadabdcbdccdaaacdcbadcbabdcaabbdddbdbddbddbacbdbbbdababbadbbaadbdaabdbcbaccbabcdadbbcaaaababddcaaadabdaddbaadaddadbbaaadcbdabdccadaacacdbdddddbaaddcdbcdacddaccabaddbcdbbcadacdddcbadcccdbbacdcaabdcacaaccaddcadccbacdbaddbadabddcadadcacbccdcdbcbddbcdabdbabdadaacabccdcdcbdaccbaddbadadbabbabcccdcccbdccccaadabadbbbbcdabaadddbcbaacdddddccbaadacadbadcdccacdbaadcbcabacdbabcadbacbacddacbaacbdbdabcbaddaddcccacaacbdaababadcadddddddaaccbcaabadbacadbabbddbacdcadcbcabbddadadbacbbaaccdabacaabbdbdcbcdccaddbcabdccccbcbbaaaaacbcbabacabcdccbdbbbacddbaababaacddabdcdbbabcaadcbdbcbcdcadcacbdaaabcacbdbdbcbadddccdbbcdcbddadabdcddcacdcabbaaadabbdcadbadbaddbdaccccaabcbbccbbdcdbbddbbcdddbbabddbcbcbbbddbdaabcaddadaddadabdbcbdbcabacabaddbbaadbbdaacaddbbbbdccdcabcabdbaddcadbdcbdccabdadabcdcdcdacbdccaccbbaaababacbcbcabbbdaabbacaabdacbcbbbccdccddccabcccdddbbbabcddcdadacdabccabaababacdacacdaababdcbdbdbacaabcddaaabaadabbbbaabcdbdaccadbadadddbbcadacbdacadbcaadcadabdcabadcbabbdcdddcaaaabbaacabcdabbdccddaaabddabbbbacbbddadbcdbddddadccccccdaddcdddcbdbcdaabbbdbdbdcccaaabccbcabbcbdcccaaddcbbddbcdaaababdabddccccdcdabddbdbdaaaabcccabadbdbcbabaabbaaaabbcbababbaddccdbabbbaccdcdbdbcbbbacdcbcdbcaaaadcaacdbabbabbbccdcdabbbaadbacbccbbdbabbbbbdcbbbcbddbaaabdbdcaabdccabbaabbabdacadbdcdaccdaacbbacbadcadbddcdadbdccbadbdbdabbaabcdaccbacddacdacaabbbcbcbaabbcdbbacccbcbdddbadadabdbcacdababaccdcccaaaabddbabddbdaaadccdddcbdddcddccbccbaaccdaccabaddccaddddcabaaabdcbabaaaccbbbbacdbabdcabbdbbddabddccdbddbaaacdbbbdbccccddccabcbdcaacbaacaabbbcbabdcbccbcbddabdbbccbcccaddccaaddbccddbdabaddcddcbbbadbcbdcbbcbcdccaacbbcdcdddccaddabdbcaacbacdaaacbbacbacddbcbabcabccddbcdbbddbbbdddbadabbbbddcaddabddaabbcdbacadcaddabaadcbccaaabcbaaddabcdaadcbadbadbcdaabbbaabddcbcadbaddbaaaaadacdcaddbacabbbbdbbaaaacccdddbbbdbbaddaacaaadcbbbbcacbbdacbcaddaccdcdadcbabbbdacdaacbcdcdadbcbcdbcadcbbbcdccdcbddccacbbbbaaccbdcadbcbcccddcdbcdccddbbdcbbddbacdcdabccbacdabdabcabccddbdccbcbadccdacbbdbadaddcbdbbbacdbcbdbacbcadadbbdcdaabadbcbbdacaddccadbacdddbccccacacdabdbabbadccccbbadbbcadbdddcccadcadacaabbbdbcbcdcaccccccdcdaddcaddbadbdbcdabcddcbddabaabcbbddcbdcadbabaddccacaadbddacaacbdadbacbcbbbbcddcabdbcdcaccbbdadabaacaaabaaabbdabbacacbccdbbbccaabacacdbcbdadadcccccbabacdbbdaacaddccbcbcdcbdccabcadacaadadcddcddcbabdaadbaddcddabcabbbabbcbddcdcacabdadbbbcbabbbadbccabdcccbbbbbcaaabdbcacadddbdbcbadaabdddabacbacdbababdbadccdabaababbadbadddbabcbccccabbcacbbbbbbcaabddabbcbdcbcddbcaddcbdbaabbacbacaacdaccaaaadbadccdbdaddbacdadbbbddbbccbabdabbacabddcaadacdcdbddadcbddcadcdbbbdadbdcdaabbbdcdadccbbbbacacaabadbddcacbdaccabbbbdbbaddaadbbaabaabaaaaddbabdbabbbbcbabcdcdcabaabdadcbabacddabdbacbcdccdadbbabcabbacadabbcadbcbcbbcdcbccdcbbddabbcbaacadbbddcdbdcdcadbbcddbabadaabbdcdddbdbdcccaaadbcdbcbbcacabdaccbccddcbcbbbbcddbdadbabaadcbdaccddadbdbdccabcabcbaaadadcabcaaccdddbdcacdbbaaabadcadbaddcbaabdcccbcbddcbdbdadadbadddadaacabdabcdcccbaaccabdcdddccbdbccbbcacbbbbbbacbaabdbcbdcbcdddbbdadddcbdadaaacdcddccbbbdcbdbbcdcacbbbacdbddbbbabcacdcbcbababcbaadbcabadabbdbcadcaddacaddbbdcddacdcdadddcaabbcbdacacbcdbbdccbdbdddbaaabcbddadacdcbdcbdcbddcadcddbbcababbbdadcbacabaccbcabddbaaabbdbabcaadbaaaccbadddadaadcbaadacdcdaaacbabdadcabcddaacacadcbdabdaccbbdccbcbabdccdbabaadbbadcdadcddbacaacabcabdcabacbccdbddacadccaabaddbcdbcdccaaabcbdbcdcbaadbadaccbadbcdcaaacbdbdbddacbabbaddabdaccbdbabacbccdcadcbdcbacbacdbbdbcdadbbcaaacdbabccbddcbadcadaadaacadddbdcbaacdadaddbacbbcbacccdcdadadbbbbdaaddacaabadccaccaacbcddcbacccababdbacdacdbabbbaabadaddabdbacbdcbdacabdbaabdbdbdbcdabacaaaaaabaddaabcbdadbbcdabccdbbacdaccdcdbbdbbdcacdccbdbbcbabadadadbbaadddaacdaabbcbbccbadccbaabaadbbaabaddacbdcdacdccdddbaadadcccbbcbbaabdcdddddbdccbcccacdcbcaccbbdbbcddaddbccbbabdcdbbddccbaabdccbcaddbdbacacbbdadabbcccbabdddddcbdcacadcbdbdcacabcddcdbcbccbcdaaabdcaaddbbdbacabdcbabacaaaaacbdcaaabbabbcbcddddadbbcdddcbcbccacbcdbbddbabdacbcccbbdabbadbbaaabccbcbdaaccacbbccbdadddbdbdcdbcaadcccbdcbbcddcbacacbcdadaaddcaccdacacccacddbdadddddcababbdcbcccccbdbdbaaacaadaaacdcdccabcbbbdbaacacaaacbcbbdcabbcbcbbbacbccacadcacababcaaddbdbbdbaaacadcbacdccdccdaabdcbcdddbbbbcbababdddbdaacabdacccddaadcaddcbabcbdbacddadcddcbaddcbaabdcdabcdbabdddcdcbbdabdbddabcbacdacbaddcbbdcdcbcaaddbdbbccdcdcbaddaccaabbdabcaaacccdcbcbbdccbacdabbddbaaadbdbbbbaaaddbabdaaaacdbcdbbbcbaadbbdcbabacdccbcbdcddcbacdacdbbbbacabaaacbcacaadcdbabdadccaccbacbbdbadcdbdccacdbbacabaabcddbbabbcacdddcadddbcadadadacadbcbbdccbabddadabbadbadabddcdacdcbbdaabddbcccbdaccbbdacacbdacacadadcdbbdbacacdaddddbbbcdbbbaacbbdcbadaabdcadabcabcccbdcbdaabacddcdaaccacacccbcbcdbcacaaacbdbbbbbadbdddcdbcbdaddbbcacacddcdacccbbbaaabadcbaadcbbdaaaadbcccaaccbbdddbbcaacacddccbbacbcdacdbbccabdadcadccaaadbcbddcaccadcbcbdacbaabacccbdbdcaadcbcbccdcadccddbdadcdaabbdacbbbacbacbdabbcababcbcacbdbdabbcabdbbcabaacdbddccbbbbabbdccccbdcabdcadbaaacaabdadadcdcbaabbccabbddabccccacbbcbcaabacbcabccdabbbaaaccbaaaabbdccadbaacbabbcbaaacdaabaccdaadbaacbccdaaccbaaadccccadbdcdcdbdadaaaadbcccbddabadbbabdbdaabcdbcacabbbbdabbcbbbdbdbcbabbcdaacaabcdcabbaadcdcddbccbcdabcdcbcadadcaadaacbbcaacdabccddcaadbbacddccabccacabdaaabdddccdaacdddcbddcbccbbcccdbccaaacccbdaaaadcbdabbcbddddaaddbcacdddadbddcdbaacdcdbbbcabcbaadbaacbcdddbdbccdcdbdcbddbaccababcadddcabbbadbaddabdcadaaabbcaaabdabacdbaccacdabdcabaaadbadcbddaadaddbaaddabdccdccacdadadcacddddbaacdbdddadcdaacdabbabdaccbcdccccbaccdadadbacbcdcaaacddcacdccbcabbadccbbbdbdaccacdcddadbbaddbabcbcbccaabbbaadcbbcbccdcddcdddcbbcbbaacabccbbcadaaccbcccbbcadaadbcaaccabacdcdbbbcbacadacbbcbcddbbabbcaabcbddbccacbbabbdcbbdbcdddabcbccdcbadabdbadbdbbacdcbcbdbdcdcaabdcabbdacbbbdacbbadbcddbacdbcadabcaddacacdadcacdaddbcdcbabcddddbddcbacbcaadddabbdddcccdccdcdcdabcaaacacbaadcabdcbaaadbaccbbdbdabacddaadbdabbaabcaacaccaaccbddaaadacdadcddccdcdcccbddcdacdadcdbaaabbdbddbbcabcdadbcccadabacabaaacbdbccccbcbdbaadcbacddbadccbccdccccbdcdaccdaacababbdabbcdbdcbbbccabbdddacbbcacdaabdbcacdcbdcdbabcbdcabcdaacbbdcabaadacabbdcbcacbcdddccccdcbcbdddbcadacaccababbcdbbbcbbbacdabadcbdcbccaddccccaddcaabdadcbacdbadadbdadadccccbcabacdcbdccabcbdabaadaaccdaadcdbaacabacadddcbbcbbbbcdcbbcdcccdabcbacdcabbbbdccbcababaaaaadcacbabcbddbaaababaddcaadbcadaacacddcbdcacccbdcdbaaddbcdcbcbccadbccbbbdccbcdbadaabcddbcddbbdbaaabbddbdbddbddddccbcdbcbcadacaaaaadaaaadbcdbadbdcbddbaabcaaacdaaacdabccddadbddbcacdaaaabbaabdbdbdcabbadadccaabdabcbbacbacdccacdadbcbadadbdcdcacbbbddccdbcaaaacacbdababbddddbabdbbbbcdacccacacadbcdbbcdadddbdaadcdadaddbaddbaaacaaaabbcbdbbaadabcdabbbdcbbccbdabdbcacaacaacacacbbbddbdccbaabbadaaaccabacacbdccccbbcdcdbcbddcbdcbdcbcbbbdcdadbbcbcccddbccbcdbaaccaabacdbbcaabaccbbbdcbcadbddabcadbbdaababbdacdcbbaabdcbacbaddbdccabdbdacbdadcadbbbaaaccdbcaccdbddbddddcacadbaaaacbdadacaabddccbdcdabcacadcdbdaccdcbdddcbdbcaadaddacbaabadcbdbbbdbacdaabbdabdbacdbbbdbadbbbbcaabacdabdcddcdcddaddddacabadabacccddcabaccbcdcdcadccbbacdcbbbacdddcdbddbcabdbabcccabbdbcbdddcbbcdbcbacbcbdcccbaadadbdcbaaadaaadacddddbccadbdbabddbccbbadaaccbadccacbbbddddacbbbccdbddbddcaacbaacacbaccdacdacbccdaaddcbcbbdddbbaccadabbcdaddcadbdbcaddcbcbacccccbccaddbbbacdcddacccadaccbbaadbbdcdccacbdcaaccccdcbbcbadadbddbacdcdadadaaaababbddddcaaabdabcaddcdccaadacddbbaaacbbcaadbdaadbcbacbdbdbcdddcdcccdbcabbdbabdaaacbccbcdcaabddaddabadbcbadbbaccaadcbabadacbabadbbdbbddbdbddddccacdbdccdbbcddaadacdcaddcdcbbdacaddacbccaacadcbabababbdbccabdbcdabbbaddbbcdcbacabdbabcdbaccdabdcdadacbaadbdddcdcddbbdbbcddbaccbdaaabdbabcbcaadaabbdacaccaaaabddcadddbabcbdbadbdabacbaadccbaacddbccddbadcabcbacbddbdaddbcaacdcbcdbdbbcacbccabbdbbdaaaacaabdaabbcdbcdbabadbbbdbbccacbcdcddccbccacadbdcacdbadbccdaabbaadcbbabbbbadaabcbacaddcdcddbbbdcbddaaaaaddcbbbcabcbcabaccadddcbccdacbbabadacbcddabcdcddcdbcdcacaddbaccccdcabbbcbabcaadbddcadddcacabaaabbbbbdbccccaabdcccdddabacbcadacdacabdaccdbbcdabcacccabcdcdaaacabddadddcbcadadabcaadccadbbccbcddcbdabcdacddbcabaaddabcdbbbaacdacbaabdabdcccaccccdcabbddbadccbdadddcbacbbaadadbaaadbabaaadcdcbcdbaadbddacadbccdcabddbdcabcbdbbabdbbcccbadcdcbbbcccdbdaaababaaadbcdbbcacddbdcdbdbcabbdaaccadcadccccbcbccacbaabbbacacddbcaddaddabdaddcacbadbbcccdbbbbabdaddcbbddbbcaaabcbcccacacdadadaadbdaadadccdbddcbaacbbaabbbdcbdbccdabcdcbdaccadaddaddbddcbbadccabbaacacacabbacccadaabaccdcacacdcabbdbbddbcbcccbddcbbadccbbacbdadbddadbddaaaadabbabaacbdccdcbacbadbacdabdacdddabcdbcdcdbdcadbaacaddadadadbcadbacbababbadcdadbbcdabcaacdbdbcdabcdcbcdabbbbacbabcadadcadcbbbcbddabdbcdaaaabbccbadcdbcaaabaddcbadadacadaadadbbbbcacbdacbacaacccadadaacccbaadcdbdcabddadddadcaccdacbbabcacaaaaccbbacdadaacdcdabcbbdaadacdadddbdbadcddbbbdbadcccdaaaacdbcabccdcabbbbcdbcbbcdabacadaabdbbbbdcdbacbadbbdcbacdcdbaacdababcdddcbcbbcddabbdcbbaadabbbbbddaadcdaabccdbcdbacddabcdbbdbbccaaaddaadbbdcbdbbdbaacdcbddbcabdaddcbbcddabcbadabddbddbdadaadabcaaaacacaacaadccdbdbbabcbcdcaabacabcaaaaccabbacdccacbacdbdcbdccaadaaadbbbcbddacdadcabcbbcacabaadddcbadcbdcbcaabacbbdacdbdacbabbcacadbbabbadcbabbacaddaacbadbbbcbcbdaddabdcbdccacdaabbcaacaaccaabcdadbcaaddcbcdbabcbdddcbcdacdcabcdaccdccbccddddadddabababdcaacccaadccadccdadacbbccdcbcbbbbbadbabadbcdcbbbaacdccddbadaccadbdddaacacacbcacbccaddaaabbaadbdddcaacbdcbbbbddbbcadbbbdccadabccbbaaacdcbcbacacbaaacbdcdbbbcadadacbaaddbbbddaaabccabbaacdabdbdcbdcbdcbcccdadbbbddaacaccbcdabdcbbaaadacdbcccababcaaabbdbdccabbcbabaddaddacbaadbdaacdbccdcadaadabaddcaddbccdbdadacbcadbbbabddabdabcccbbadbcbbadbddaababdbdbddacdddcbdbadcdaacaaabddaacbbcdccaabccabdaaccbacacdcacbaddbdcbabdddcdbddcbbccbdddbccadddbbbcdddacbaadacccdaabdbbcaaddcdbdadacaabbdcbdabbaacaadcaccaabaddbbbdcdbacbbcdbdbaaddabdcdbcccacdbbbcbcacbacdaccacccddbdaddadbbcababaadaabbddadcbcadddcadcacadaacacdabddcbbbbaabcabddbacaabacdbbcdcdcdcbcbdcacdbcbddbbadadcaacbadcbadbaadbdcaabbcbbdaaabacbcdcddccdddabbdcdbadcaacdbcbaddcddcabccdbccabccacbabdabbbcdcbdcccdbbddbdabadcbadbcdddaaadbcbcaabdabaccccaddabaaadcddccacbdbacbbdccaacdbddcdcadcabbadbacbcccbbaaabbadbcaacddcccddaaabbbaddddbcddaaddccdbadadbaabbaadcccddabacbadbabbbabadcaacdaccbbbccccdcdbbdbccbdbccdcddbcbacdacbcdddbdbbacddcbcbacdbdcaababdaddacddbbaddcacddabaaaddbbddaacbabaccdaccbbccccadadccccdcdbcabdadbabcdcaccdcdcbabbabcacbaaaadadcbabbbacaadcaabcbdcaabbabbaaddacccbbcccbadbbddacddcdcbacbbdabdbbbdacddbdcbdacbdccdacdbccbbcdadbacabacbbcdbcabbbccdbabbcdabcbcdadcdcaabbadbdcbcbaddcbacabddacaaddbbaabbcdacbbadbbbdbdadbcabbdababdbddbcacbdacaabcdcdaacbdacddcbadadddbabddabbacaaacbdbdbddbbaaddddddccccabddbccabdabcdbbaccdbcbcacddcadadccbdaccaadaadbbaaddbdbddaabacdbacdcaacabacdcabacddbcaabacaacbabadbbbbdbacdcabbbbbaccbdabcaabdbbbdabcbbaabdadddadacacbacbbdcbbacbcbcbcdbdabcbdddbadabbaacabdccbbcccdcbcbaabccacbaaaabcaccdbadddbdccddbdcadbddbcddbcbabcabbbdcbaabcabbbaccbaaabbddcdccdbbdabbadcdaadacbddcdbabdacbcbddacdabbcdacabaabaddbacddacdccbcdbbcbacbdbcacadddbcaadddbcdbdcabcccbbcddcdacbbadcbbbbdbbdadcdabcbdcababbabadabddababbcaabdbabcaaaabaddcababaddccdcabdabadbabcadabddcccabaccadddacdbbaccaaacacabcaadaaacdaccddcbaccbcaabdabcbacdcddabadbacaccdacccbbccccacbdbbaaabcbccccacbcbddbbdadbbacddbdddcbbdbbcbcaccdbdaccccdbaacadddaccbddcddcaddacccbdbbbaadadddacbdbdcacdacbababbadbcbddddcadbdcdabdbcdbdbcadaccdcdbcbabadcdadcbbbcacadbabadbdcbdcdbabaabbcbcbaabbcbbcaaaaabdabacddaddaaaccdcccaccbccddcabccbdadbaaccdaaaabacabcbadbcbcbcccaddbdbbdddcdbabdacabdcaccacdaddacbbcaabacbbbdaadaccbddadadadcaaaadcdadbdcdcabacaddaaabcaddbbcccaacabcdbdcdbbbbddabacdaaadddacccdbccdbdccacdabccbacabdbccbbdadcacbcbbdbddacdbcdabdabbacddbccdccddcabadcaadccddcbacbbbcddaadacaccdcbabbcddbbdcadbcdacdcbccabbacdbdccdccadadabaacddcddacacabbcbbbbbcaabcdcabdbdcaccdcadbdabbdaddaddcadcddcdadcacddbaaaabdaacdddaadabdbbbbacbdaabbcdcdbdddbacbccbcbdbcadbcccaabdbdbdcbabbcdcdbcadcaddbbbdaaccbbbcbaccaaacdaddbccdcdadaccdadbddabaaabbaccbbbaccababcdabcdaddcabdcdabbadadcdaaaacbcdbbadaacabdaaaabbcbbdadbbddbdacdabcddacbbbcacbdcaabcbcbacbdccadccdbbadacaaabcdababaabaacddaabbacabcaacdacbcbdbacabaaddcacccccacbaaaaaccdcabadbbdabbbddbaddaadccaacccddaabccbbdcdccbaddddccacdaacdbadccbdbbdbbbbaabadcbcccacdbddbbaabdaaccdabbbdcadcddcabcabcbdbcabdbabbbbadbdacbcbcbaaacdadcbbccbaabdbbdaabdbcadaddaaaabdadbbbaccadcdbcccaaacdccbbacdbdcaaacaacabbdddcabbaadabcdbdbabdacadbbabaabbdddaacdabbbacdddbbcacbbdaababcbcddbdcbabddcddaddbbadcdcdacabccbcccacbbabdccdcaaccbbcbabaccdcbdcadddcaddaabbbbdbdbdcabcbdbdcaadbdcdbbbabcbdcabadcaccdacdbabccbdacbbabcaaddcbcaccabcaaacacabdbbcbacccbadaadddccbbbbaccbcdacdbcdaaacaacdcdacbcdccdbdcbbabcbacddadbdabacbcbbbdcacaababcccbbcccabcccaaacbbcdaabadccabadbabdddcdcccabbddbdaadcbcbbbadbcbccbdaacbadcbbdabbdcdcccccbbdbbdbdddabccabaababdddbddadbadcabccdbdbddacdaadaabacbbadaccbabbdddacbddbdbcdcbddcddcacdabaddbbbacbdbdccacbdaddbdbcdbbbbcdaaacccccaacbbdaadddbdabdacaaacacdcbcdaadddaddabdadbaabbadbcacababacabccdabababdcbdcdaccacbcbbbaaacbaabbbddacbaacddaadadbabbcabbcbaabbbbbcaaadccdddacaaadacdaccbcdcccdcbaadbdbddabcdcddcbcccacadabbaccadccbbabaaadadcaadaabcdcdbdabaddccccbbdacbbccdadacbcccbddcdbcdddabdacdbbdadbadbbccbbadbcdbadcdbcdcbccadaacaddcdcbcbbbcbcbcbdabdbadcdaabbdbcaabdcdbaaaacdcabaaabbadddddddcdccddbbdddbadcaadbbcabcacbcbaaabcbbdcaacadcbcdcacbcbabbdacaddcadcdbdddaacbddbabdabdbccdcbadbccadbbbadbbddadbadcccacaadaadaacbdacacdcdddbbbdbbdcbabccacdbcbbddddcbdbdbdabcdccdabbdcadbccdaddbbcccaababcbdbccccdddabadccbcacdbbdcdcccaabbdbacdbccddaddaabdbbccbbaccdbaadbadaabbdbbcbcbdcccccabbaacdcbbdbbabbcbddbddddaadadcdabbaadabdddacbbbcccbacbcacbddbcdbddbabdcddcdcbccbbdcacbcbaaaccbbcbbbbdccbadbcbdbbdacbcddccddadcacaadcadddbbacbcbdacadbcdbadcaadbdbcddbabddccdbbaacccabbacadacbbddcadbcdbbadbadababdbccddcdcbbaadcccccbadabdddadcacccccdaacdbdcadbcadcadbdbbbcddccbabdbbbacbbdddaaaccacabbaadacbcbabdbbdccbbcbabaacadaababadabdbbadadccaabdddadaabbbdbbccbdbcdbaaaaddbaadcbdcbbdbdbccbcddbaadbaacabdcbbadaddabaadaddbbcdbabbcbaddddcdcabaaacddbbcdbaadadaaaaabdacbccbaddddacbcadbadadbadcdcdcacccdddaccabdcadaaaddbabcccddcbdcdacbabbbbdabbadacbabcabcdcdbccdabbdbdadcaccddbdddadcdddbcbbddcaaadacbadbbadadbbbacddbcdabacbcadbbcdbabbdcddcaadcbcccdaadadabaadcbaccccdabbdacddccccdcdbccbaacbabdaacdddcabcbcadaccabaadacddcdcccadbbdbcccabaccbcbaacacabacdcbbadbdadcaabcabbddaccbabadddcaabbdccbbadcaacccbaaddcdbdddabcaaadcdbbbcacabdcdccdcdbabdbbcbdddbabdbdbcaacaacacbcddadacccbbcbbddcadddcaadbdbccbbaacbabdbbbacadcaaacaaaaadbdabccbbaaccaccaddcbbaaadabadabcbababddadbbacdcbaddddcaadcaadbdcccbdddcdccccddcbaabddbaaacddbbbcdbcccbabdadaddcdbdbbcbbaaddbdabaddddcddbabbaaacdddabdbbadaabadbdbbccabcbbbddddbacdbcbccbbdadccabcdcbddbbabadbbdaadbdaaadccbaabdcbabcddabaabbddbbaddaddbabadbadabcaabcccddddaccaaddcaabaacadcadccdccbcbbcbccaccaadbdacdacbdbdcdcbbbaadcbdcbcadcdbaddbbabcdbdacbadacbacdcdcbddccaaddadcadccdbccbcbacbbaadbcdbaaababadacccadcdadcbacbdbabdcbbdbdadcbaacacbaadcadaacdbbabbabdcabcaccddcacaddabaddcabbbccdbdbdcdaacbadbcdcaddccddbadccccabddcdccbaabbdcbabdddcbadaaacbacaacbadcbacaadcabaaaccacbdabcbaccdbdcbbadbbadabadbcaaaddbacabbdddccbcddbbbabcadddbacddacbdbbdbdbacabbbbbaadaabccbacdbbaaadaccbbcdabdbcbcabcbdbcbbbbbacbdbacdbbddcaccdcdcabbabcbbadccbcdddadccacdbdbadacbcabcbdacbbadcdacaacbcbbdcaaddbadbcbabdbdcccccbacacacadbdbbcddddabcdabdcddcacbdccdaccaaccbccaadabdbacbccdcdbbbaccbbddddbbdaacdbccdadddaacdcbabccaacddcabdacacbcbcccabddbbadaccbdadccbcddacabbacccdaabbadccdaacabaadcadbbbaddbcacaabbbdcbaadbdadbdadadaabadadabbddacdbbbadccbddcdaadaadaaaabcdbabbadabacababacadddacccdccacbaacccdddadcdbcabbdbaaabaacaaccaaabcdabbdabbcaccdcaabcaaabdbdbccddaccdcacabacccdcddcdcabcaccbcdddcbaccdbcbdcbccdadbdcdbcbcbacadbddcaccccbccacbbcbcaccadbccabacddcddadacdacacabcabdaabdbbbdbbbabcdbaaabbcadbccaccdaabbaadbaaddcbaabbcbcbbcaccbcaabaaadcddbccccaadcaaabdabdaacccaaaccbbbbbdacabdacddbbaadacaabcbbccbaacbdaccadbdcaacacdcacdbbbcbcaccabbccbdbcabdadabbdbabbcbbdabbabbdcacbabadccbcbdcaccbdbbcdbbcacbbbbabbcacabccccbdabcdbddbcbcacdbcdaabcdadddcdcdbccbbccbbdccdaccbbcdaccdbadcdababbbcadbdbabacdaaabddaadbacadcccccbaaabdbbdacdddbccaadabccddddddcbdaacaddcdcadaacdacddacacbaaaddcccabbabbddbadccdacdccaaacbabbbbccadbcabbaabcdaacddcbbddbacbbbaacbbcbabaacadcadabbacbaacdcdabbbbacccbdbdaaacacabacbbccaaaddaccbccdbbcbacbbbcacbddbdbbddbbcacdcdcbacbbcbbcdbdccbbcababbbbdbbbdccbcaccaaaaadbddcbabdcaddaabbaacccacaabbdcacddcbdaaacbbbaaddbbbddcbccaaaaadbccdbddadbdaaaadcddcdabbcbcabddabccbadbcadaacadccddcabcaabcdaabbcadacdacaaaacdabdcdadcdcaacbdbadccddbacccacdaacabbdcbdaabcacddbbccdbaadbbabbaccbdbddbacbdbccabbdbcabddcdbdbbbccdcccddbacaddbdadddaababccccbbddcbbcdbccddcccbbcbadaccdabdddbaabcbaaadccbaaaabadddaddaadddacdbaccdacdcbbbdcabdaddadadabbbcbaabbbdbbcacdcabdcbcdaaddddcccbcdcbbdcbdadaacccdbabdccabccddddbcbdbdcadadbdbdbdcdbdddcbbdbbbcbbbdbaaadacbccbbdacddadadccccdcbbaabacaccabddcacbacaddbdbababbdccadadbdacaabdaccabcaaabbbadaccbbdaabbdcbbadbcdbdddaadcabadcaaccacbacbacdadadbababbdbbddbbbcadadcbcaadccadbdadabccaabcdcadabbdabdbaccbbcbbddbdcddaaacadbccddabaadabcacbaccaccddacbacdbadcabbbdcbccbbcbabbcacccacddacacdcdaacacbdcdcdadcdaddcbabbbaddaaccabadccbacbaabbdbbdbccaaddaaddaddcdcbbadadabaccdcbdcdbbadddaadcdcdcbabacbdcdbaccccaccdcbbaabcddbabcabaccbaaddadcacaccbbdcabddabdddbdbacbbddddadabbcbcbbdccdcaacccbcaabddbcdcdbddcdcbaaccabcdaacbdcccdbacbcbcadcdbbcbddbaaadabbacbbbcaccbddcabcdcadcabdaababbaddbdaabcbbcbcddadbbddaaadcdbbababcccdcdccadadbdcbcbdcccddcddcccccabccaabdcadcbcbbadabdacccabdadcbcaacccdacadaacdcdcdbcadabcbacacdcaacbcbdacbddaabbbaccbcadaacabcbbccccdadabbacdaddabacdbbddaaacbdcbddddadacdcdbacadabccbcccaddddaaaacdccdbddabbadbacdabdacbbcdddabaaaabaddddddadbcdcadbbaaddadcdbaacdbcbcbabcbbacbbbcbbcddbadbaabcccadabdabddbaaacddddadacdddcbbbcbcacaaadbccccddacabbcacddddbbbbcddbbddcddaaadcccadaabccdccdddcabddbbdacdbcccddadaddabcddcaadddacbdcbabbcdcbbacadbddbcbccaacccbcacdacabdaacccbdcaaabacbcccdaababdcccbacadbccdacabcabdbdadbcbbcbcbcdbcadbbabccbbcbcdddccbdadaccadaaabbddcdbbbdbbabbcdccccaaadbddabadacadbcdadbdcbcadcbbdacccbbcadbcccbccbbdcbbcbdbcbbacbdccbcbccbccbdbdddaabaabdabbddddcdccccabbaabcaadbadaabdddaacaacdbaccdcdbdddccbbdbabcbbddcbccbbacabcbbccddccccdabbbbbcddbccbacacbbdbaabacaadddcbbbdbdccdababcbbcacaaacdabadddadcbcccaccdaabdbccdadbbdbbcacaddaddabdcdccdacdcccbadabdddddbaadcdcdabadaacacdbabbaabbbcddaabbacdbbdabacaabbaadadadbccbccbdadbabbacbdbbcdcbadcddccabddaddadaabbbccddbcddaaadabdcbdcbbdbaaadacabcbcadacadaadcaabbccbdddacabcdacbcbdcabbbadbccadadbdaccdddcbddacbbadbdcccaabccacbbcacabbbaccbaddacacacbabdcdbadccbabbaddcbabbadaaabcbaddccbacbbcccdbdadcbcbdddccaaddbcdccbabbbdcdcadaabadacbbddaadbbbcbbddcbdcddbaddbdadacccddadacddaaabbccbdddcdcccacdddcbbcdadddcbbaaabcacbadadbbadaadacadbdadbbcdbbaacacacabdcaacdcaabaddddabdccbbcdccdaadbdabbdddbbbcbbadabaaddaabbcacddcbadcabaccbaacdbcaccaacbdbdccdcbdccdbaaaacbdcddcbdacaaddbabbacaddbbbcbddcddbdaaacacddabdbcbbbaaaccdbaabadbdcbcacddbccadccbacbdbcccdaaabacccabdbdbcdcccccbddacccbbddabbaaacaddbacdabdadddaaadcbabbcbbbaacbacabddcbaabdbacacdbdacdccdbcadacdbbdbccaadcbcbcbcadddbbdacbdaddcdcbbcbcdbbababccdaccbdbcbccaabccdadcccabbdbccdabccddbaadddbaaacbbcaaadcbcadadaccbaadccacaaccabbbbbcdadcbdbbddaddcdcbccbbabccbccccddababccdcbabcbbcadddacacbdaacddbcbbcdbbacdddbabbbadaadcddddcbcaacdccdcbccdaddcabaccddaabcbbbdbddaddddaaabbdbabbadbdabbaaabbcbaddcbdccdcbababbccabbcbcababaaccdcabaccabdcdacdabdcdbbabdcbdbadadbabbbddcacbadacaacbdaaadbabddccddccbcaaaaaadbcbddaacdaabbbcabacdcdccccdcaacccdcbccaadbdabbddddbdacaacbaacdacacabddcbaacaacabcadbcaacdbdccabcbadbbaddddbbccbdcdbdabbdbdbacdacaccaaddbdaaadacadccccdbaabccbaaacaacbbcbbccccadcbdbdadbbcbcdcbcdbdcbdbacbcbbdacccdccadcdabaaddbaabbddbbcdabadcdaacddaddcacdccbadbcaacccbddcdcbcbbbbdaaabcdddbdcaaaadbbdbdadbcbaacbdcaacbacbdadaddbcaadacbabadcabbbbdbccbbbcacabcdacadaaddbbdcdbcdbcaacacaabdbaaacdbccbababacdaaddbcdaaabaadcbacdddcdddbbbaccaaccbbdcabbdbbcdbdabaadcccaaadadadcdbcacaacbdcccdabcbbadcdbabcddbaabddddcdabacaaabdadcabcbacddabcbababcadabbdcabaaaccbddddcabcbabccddbcdbcdcbdbcdcbcddacdcabacdcbadddababbacbddbcdcdbcbbaaabccdbacdcbabdbbdcadccbbddacdccbabdccadcaabcbcaaccddcbdaaacacccbcdbbadacdcddcddaacddbaacbacdccacabcacdcbdabdabdbbdbccbdadddaacdbccdbddbccdbabbabcbbaadaacabdbcbbdadcbbddbbabababbbdabddcbcacdbdacabaccccabdbbaddabbaabbddbdbbcabbdbacdacbacdbdcacbcaddcacdacabdddbcdbbacdcbbbabacaacbccbccccdacdcdbbdddcabccddddacbdbddadbcddbabdaaadcaaddaccabbacabdadcabcdbcccbbbcdabdbcccdccbccbddcadbdbaadbccabcabdcbddacaabcdcdddaabdcbbccdaaddbaddcbcadccacbabbaacbbacbcdccbcabcdddcabcccbdcbaabadcccdcbcacadacacbbcdabdbbabbacdbdddbdaacdcadbbccadaaabdcacabaaacbbddbbcaaddaccdccccbcbbcbbdadcacabcbacadadacabcbbbbcdaaaadacacccdcacadddbddbcbcbdddbdacbcaacdccabaacbdbccaaaccbcccadbdaaaccabaddacadbccbdbdddccadcccbcbddddadcdcdcbdaabbddcbadcbbaccccdbcbacbccabdaadcacbaccdcadbcdddcaccdccdabbcaccdbcbddcadadaddcdabdccadccddbdbccbcdcbbbacadbdccccbbdbadabccbacbaaccdaabdaccdcbbaacbcdbaccabbcbcdcdccdadddbaabaabbbcabbddbddaabccdbcdcddabacabbabcaccdaadddbdbbdcaacadadcbcbacddaabdbdabcbaabcbadcbabbccabdbbcacaadbabbcbbbaadbcdbbacdaabccbdbbcdadbdcacddbadbcbbadcddaccbddcdccaacdbbabaddcbdbbcbcadcaaacdccadaabcadcacdbcadadccbbbaabdacbbdaccbccaaacdacbcddcddddadbbaaddcddbcbacddbadccabadbaaacbdcacadbabdaccdadacbaddbaabdbacddccabacbbbccbddcaadadaacdaddcddbdbcddbbbddcacabadbcbdcabaaccabcbaabdaccbdbcbbdbdadcbdaacccdbcdcdaaadaaccadcabccccdadbbabddaacbcccaacccabdddbabcdbdaccaaacccdadcabcbddbcddcaadccbccddbccdbacaaabcacadbcbabdbcaabbdcabddccbacdcdddddcadccabbcbdccaadadcdbcbaacacbbdaaadccddcaabdabbadcdbbabacdcacddaddddcaacaabddcbdabddadbbaaccbadbcbadbdbcaabccddccbdbcbaabdbdcadccacddbaabdbdaaccdcaddcadabdbcbbcdcacbccabbdaacacbadcdbcbdcaabbaadcadcccacbcdcaacaddcdcddcbbcdabbdccaababcbccdadddabadbcbcdbcaccbbcadcbadbbdacdabbcdcdcbcbabdabcbddcddacbddacbbabcdccccdcccbbcadbcaccddaccbddabbddbbccaadcaadcccdcaaddbcbcbacdcbadacbabcdbabcabcaaabcaacaabbcbdaabccabdccdaddbabcdcbdbabdabdadcadaaaacdbadccdaddbdaaccdcacacdcabcbcaccbbdccacaadcadcccbcdcdaaacaddbacdcbbdbdbdccbddcbcdccbdadcacbbcaddaacbbdddccddcacadcdadbcbbcdbbdadbdbbdddaddcabbddaadbcccabddadcaddacadcacbcbdabbbacbccddcadddaaadbddaddcaddabccbdcaabcbdccbcacaaaabcadabcccbbaccddccacdbdadbdbabdbadbabaddaddcaadadacccbdccacdcbbbacacccddcbdbbaadbcacaaddadacdcdaccacbcccdbbbddcdadbccababdcccbcdddcdcabbdbddadabdcbccadddabbdaddabadaacabdccbbcadabadbdaddbbcdbbddaddadbcdbbccdcaabbadabdbccbdcbcabcbabbdbccbcdcaadcdbdccddacbacadcdbadcaabcbadabdbbbbbbbddababccbdaccacabbbcbacccddabbdcababdabdbcdcdcdbbbbabaabbbbadbbbaddbddacaaaacacbaacabdbdbabcdccbdaabbbbbabbadabbabacdbadcabacbadbddbcbcdaaaddbbccbaccddabcbddcacbbacbbdccbbdbbdaabccddababcabddcbbddcaddcadbbdcdccbdbabccdbdddaadbacbbbaaacbccabdabaccbcbdabdcbdbacabbaabdcadacadcddaccbbadbbbadccbccbcdbabacaaddcddcdccdcadbbcdddcbcccabaccdaaaadaaacaacccaadabdcbbcdacbcdababbcdadbabacadbcbbccdbcdacbaccdaddabdbdbbdcaabbadacbbdbcdacdaaaabdccdcaacdccdbacbadddcdcadabddcadaddcabbcdbdbbbbaddccbbbbddcdaabcccdddcbddbdddcbcaddcdcbabccdbaabdaadabdbbcaaadbcccdacdddddbaaccbdccbcdbdcbabbaabadbcbbaacbccaabdadbcdbbbccbdaccacbbabddaddaccbdbdbcbabcdbaddcdddbbcbabbbaaacdaaaabccdcadacdcaccdbbaabaacabcaccdcbdbccadcbddbdaaacabbcbcbaacdcabbdcaadccbccaaaddabcbdcbdbddbdadddacbaccdbddaddddbdcddadddabbabcadabdccbbaddaacadcacdbbabdccdaacccadbbccadaccbbdccaddbdcdbcccabcdccddbadaddbbabdadabdabadacddcdbdaaadbcabddccacbccddbdcdbdddadcbddbcbdadcadccabaaabaabdbcabcccdbbcbbbbccacbcaaacdcccabbccbaacdcdadcdbdddcdcabcbacaaabacccdadbddabdaaacbbddadbaaadcacdcdcbddacdbaaacadaacbbbcdaadacddccbdbcdbbcaadaacaadcdabadcaacdcacaacbcacdcaaddbbcbcbdaadbbacdcaabbbbacabdabccaddcdadbbcabbdcabbcacddbacadcbdbbadcadccdabdaacbbcbcdabbbbcccacaabcbdbdabaddacabdcadadabbbaabbacbbacdcddcabdddcacdcaabbccbcddcacbacbbcacacbbbadbdacddcdbbdcabddacbdacbdcacbacbcbddaabccadddbbdbaacbcddaaaaaddbdbccbbbdddbdbbbbacabdabdccaddddddbdbabcdaadadbaaddbcaabaacabaabacddddcaabdddadcbbabbbaadccdbaacbccbcacaacdbbdddbacddddbbdbdbdcbcbbdccaccbbccbbabddcccdbdbddbcaaadcdadbccccabdbdacccbcbdbdccbcddbdbddcabccdadacdbadcaddbaccadcccccbbdcdbabccaaaabdcddabddbaccacdabccbdaabcacaccbbddbccabaadcadadbaabacbccbbbcdbacccddcddbddadbbcacabdaaabcbaabdcddcdbcabdcbbcddabacacdcdadbdabdadcbacbbcbadadaadadcbddaccdbacbcdcadaabcbacbaddddbbadacccbbcdcdcbabcabdbbbbbcbbbabcbcbdccbccddddbbbdadcdaccaaacdbcdadadacdbdcdabbdadbbbcababadccacbcdcacbbaaababdcacbdaabdabcdacadaabcbbcbbddbccddbaddcbbdaddcbabdbcbdcdaacbcdacbcdbdbdbbdcaaddaabbabcddbcbbddaabccbddcabcdaddccbcbccdabcbbcabaaabcabacbbdacddccabaaccbadcbdccaadcadddcadbdbdcadcadbbddabddabbccadadcdbdbaccddbaaaabdbacadaabcdcaadcacacdcbdccacaaabddbaabcadbccbaaacbabaaccccbaacbcddcabdacccacbaccabaaddbdddadbccbcddbdbdbccccbcdacdcddbcdcaacdcbabdadbcdccaaddccacacccbbdbcbdcabcdaccdaacacbbdcbccacbddbaccdacbbaaaadddcdabacacdbacdddccabcaabbbaddabdadcbbcccaadbcadcdcbaaabcdbcbaabccdadbdabdbcadaabbcdaddcbbaaddabbcdbccdabaddcdbbdbaddddddbbbabadbcdaddcddbdcdaaddabcdcabdbdadabdbdadddaadcddbbcaadcbdadcdaddbabcaadadbaabccdcadddadccaadbacaaaacddcbddbcdccaabccccbdaddcaaadabbadcbadadbaabcaabdcbcbabacbbcaacdcbaadccbbabadaaddbbdadaccabadcbdaaaaccdccacbbdbdbadcddaababdadbabbbabccababcbdbbbdbbddcbddababadaabdbcadcdbbcbcdabcaaccdbbcadadacaddbbabdcdcaadbbaccbcaccaabcdcbacdcaaacdbabcaacabcbabbbcabaabbcbbbdbcdbdddbbaababdbbdbcacdcbccababcadaacccbbbcddaadadcaddbbdabdbabadbaaadabbddbaacaacdccbabcdbdbbddbbdabbcddcbdcabbdbcdacacbbaadcbdcdabadaabaadbdcdbbdaccddbccbabaaddbcbcbacbdabddcbabbdacabccdbcdabdcccaccacdbcbccdbabbbcbccbcaadcddadccdbcabcabbccabaacbdbccaaabaadbacdbadcdbdbacdbdbccaccddddabadbcbdbcaadcaaacbcdddaabcdbabbacabbdcdacbccacccaacacdadcccbcbbabdabadbcdcacbacadbccbbbcbdbacbbccbaccbabdccaadabadbcadccddccddabaabacbdababacbdccbcbaabbbabbcadacaadacdcdcbbcbdaacdcddbdcbcaaaddadccddbbdadcbddadaacabdddddadcdbbabbbbaccabbbaddcaabaababdbacaadbacabdcacdbcdbbdcaccccbddcaabbdaabacdccddcabdcbbadcaacabadcabbdcbcdcdacddbddddbacdbbaacdcbaabacdbcddddcbbdacbddbdbbccbdcbccaaaccaacdacadcbbdbaadcddbccaddbdcabcacbcddaaabbacbaddadcbcbabcabdddacddbcddaabdbadccadadbdaacdbbacaacadccdbdaddcbbdcbcdbcabbcbccccddadbdcccbdbbcaddbbadaadbccbbcabbccdcdadcaaabaabbbcbdbaaaadcababdddbabaddbcbcddccbddabdddaabccbaabddcddbbccddbdbdcabccabbdbdacbdcdbcbcddcbaadadbdacddbbdbaccacbabaddcdbcaabaadcdaadbabddaacbcbbbbbbccadbcadcabcdddddacbbbcadbababcabbabdcdbbacaadbbcacbdccddacdbcaabbdcadcadcaddccdaaadbdaabcbcdbdbbcbcbcaccbddbcbadabdaabcddbabbdcdadbbbcbdbdccdcdcdcdbdcbbcaacbacbbdbaddabbaaaaadadadcbbbaaaacbcdaaacdbbadadaaaacacdbdabaddaaccdabbbbbcdabcbbacaadaacddccadbdbdabcacccbcdddbababbbabbdbbbabdacbdbdddcdcbbcadaddbbbdcbabaadabababddbdcccdccabaadddadcbabbcccacacdbdadccddaadbabcdbdddcdbabdaabdcbcaadcbbcdbaabdcbaddadaccabccdadabacdbdabbadbdccadbdbaccdbdaabacbcadcbbbdbbcbbbbbdbdbcadbddbadddbbccdcaadcbadcabcddcbbabbaccddbcacdbbcadcccbdaacccacddcdadbddcdccaaccadcabcdccbcaccbdaccbaaaadbbdacabdaaabbcdacdadcbacccabbaabdbabadbcadaccccdabbdbccdcbccdddaccabcccccbdbadcabbbdbcabbacaadbcdcaabccabaaabcbddbbbbbcddabbadbcbbdbdabdabaabaddbdcbbacdcaadbdcdbcdcdbadbacbabbcdcccccbbcdabdcdbbcacdadaccdccccddcadbbadabbbcbcddbddbbabddadcaababcdbdaccbabccbbbdabcacbcddbdddddaabcdcddabdbdbbacbcacdbddcccaabbdbacbcabbbdacdabdcabcddcbcdbdcccdbbddcdaaacbcacbadcbaadccbcbaabcccddcbcadcaababbbccddddbcbbccabadccdcbbcaabbbdddadbadbaabacbcaaabcdaccdddbdaaaaccccccbcdaabccacbdabaacacdacbcdbbcadaaadacdaddcbcddccdbdbbddabddbbadcdcdcaadacaaddbccbaccaddbdcaacbbddcdddcddbbaacbbaabaadddacdccdaacdacadbabadbadadddabcaabbcaddcbddddbadbdccaabbcbdbddcabcccdccdaacaaabcababdcaddbbdccabdbabddcacdcbacccaccbacabcbdaccdccaadbbaacacbaacacddacbdbbabdacbdccdaddabdacdabdcccbcdadbbacbddababbabacdbbcdbcadbddacdbbbbdccbadaaabacbaacdcbcabcdbabbdddaddbbbadabcdababacddbcdccdbaddadbdcadcbdadaddbdcacbccbddbaabbcadbcacaddabdcabdbbdbcbabacdaaacadbcccdadbbcbdcbddbdaadbbbcbcdacbbbdccccadcbbdbdacaaabababdcadbcbcaadbcaccccadcaadbdcaaabdadbadbcaaccdacdddbbbdbbbbabaddbcdabacdcdaacaddddcdaacacdcddaaabcadbcbdbdaccdccbbaacabbcdcbaadbaaacabdbbadbddaddbbddaddbddcbbaccbbadcbbaacaadbbaccbacdbaccbbdadbcbbaccaddbdcbcbcbcaddabcacbbabcadabdcdabbcaddbcbccbadccddacdcbcadddacbcacbabcacdbcdbdbcccabbadabaacddcbbdbacbbdcbaabadbaadccbabcbadcacddccbcbcbadcaabbcccdcddbcabcbadaccadbaccbddabcbbdbcbbdbdbdaccbbbbcbcaacdaaadbabbbbdadbdabcadcdcaacbbadcbdadbbadcdbaccacbbacbbcabadadbcdbdbacbbddbbaddaaccdccccdddaaaabccdbdabdbbbdbabbcacaddddaabbdcdbddbadbccbbbacbdaadcbbbbacbcddbdbbcbbcbaaddbaccacdcabcddaacccacbbcbddaaadcdabbccadcaddbabcdbdcdadcdadacbcabdadbabcdcbbbbdbabcaddcbdccbcbbaadacbccbaabbddabcbdababbbabacacdaaacbacabdbccaddabababaccaaadbdbadcabcababcacdabddbadabacdcdbdadbabaabaaccabbccbbccdbbaccacbbcbabdbddcacaccdbbabbbdaddbbcbdddabdbcdcacbadbccbababcdcdabcbbdbddcdbddcdaddddddabadadaadbcdddcccbbcbddddadbdaabdccddcddcaaaabacbaccbcccbaccbaadaadcbbcdbbadcadcdccbabdacabdcddbdacdccaacbcadcbbadadbabababddacdabccadbdcbbbabdcbadbcaaaddadaadbcaddbdadaacccadbcadaadadcabadaabdabcdcccbbcdcdbbaaddbcddbbccabacadbaabacbdcbadddcbdbbacbbbbcaccdadaaccaadbacdbdcdadcccbabdadabdcbbbbacaabbaaaddcaacaddcdbdbbbcbcbcacbdbccbdcdadcbcddbdabccbcbdabbcadaddcbacbcbbabbdbbdabbcdacccadcbdbdbccddaccdcdcdaadaaaacbcadbddbddbadbadadccdcabcbbbcbcdbdccdbbcbcacddcbdabcccaadbbdcadcdacacddcdddaddaddbdbabadddcacaacdbccccadbaadbbadcdccdbdddabccadddccdbacdbddbabbacdcaaaacdabcabdcdcbddbabbcaadbcbadcbacdccadacbcbadcadbabdcdcacddcdcaadddcbabdcdbadbdddbdbccbadbadcadcccdcdaabccccbdcdbdbdaadcddddcababdacbbbcdcccabaabbcaacddadabcbddaddddcdaccdaaddbaaadcacbbcdccdaacbcaaccdbadccabadccddddbaabcdccbaacccabadccadcaacacacbbcbddcacbacbadddacbdbbacddaabdabadbdadcbaaddddaaddbcbdcbadbccabcaaddacbbabdbbbdadababadccaadcbaabcbddbddcadcadbbbabdbaabababddccbbbdbbaaccbcbbcbdbcdddcbcbabddddabcdcabccabcdabdaabdccbabadccbbddbaabbacbaabdabbbbdbcadcbcbdcbaabdbaabcacccaaabdcaddbcaadcaaccbacabadbcdaccaaacccdcdaabdaabdacabdcaacdcaadddbadbcbbadaddaabbadbcbbbaabdabdddabbdcdacacdcdcaccdaadbaccdcdacdababbdbcdcacbdcdaddcbccdddaababbddcbcbddcaccadacdbadadbdbdbabcddcbacddbaadacadbccbbabcacaddacdbcdaadaacbacadaaaacabaabccbabddadabccdbdcbdbabdbacaaddadccacdaacbddcbaddaadcbbaaddbdababbbacacccabdbbbacddbaacdadbdcaccababdcbdbdcaabbadaababdabacdacaadcdcbbcdccdccbbaccaaadacbbbacabacddbbcddcdabdcdcbaabdcdcabbacdadcbcdbcadbdcaabcacbcbdbbbdcccbadccabdbddcbcdddbbcadbdbcabddaccaaabdbadcdbbcdcbdbdbcdddabbdaccaddabdbaaabcdcacccdcbbbbbcaddadbcdbcdbdbdacdadcabbdaabcaaabcbcacdacdddcdbccdbdddadadbcdcbddbcdaabdcddbaadcdabbacccabcaaadbcbbccdbacdbadccbddcdcadabbddcbdcbccacbbabaadcbdbbbbbadaaccbcdcbbdcbcbacabaaabccaaaddbbaacdabdcdbcccababdaccdcacabcdddcbbdadddabbaabdadbcadbaadcaababdddacdaccdcddcdcabdaadcdcddccaadbddbdacacabdabbacdbacabcdcbccbccccccdabdcdccbcaacddbbadadabcbcabbbbacbaddbdabcaddcdacabacbbaaaaaacdbbdbddcccabdcbcbddabaaadaaadacaaadabacbcbaccccbbabbadabaabdaadadcaabdddcbadcbdcdcabaacddccadbccdddababddcdcaccdadacabcadcbcacbddcdbdaacacacddaaabdccacbaabdbadddbbccaaaaddbadbdaaacccbbaaadccbbbcaacbdbadbbbccbdaddacccbbbcdbabbaaaddacbbabaadcabddacbbcdbcbadbadabddddadbbaabbddaabbadaaacdbcacccdddcabccdcbdaadabdacaadadcdabcbbadcbabacccbabcaccbcbabcdbddaccddcabbbbccaccbcbbdbbaddababbadaacadcbaacaacaddadabdbcbddcdcbdccadaaacdcbdaabccbbaacbbbdcbcbadcbddacbbcccbdbcacabdbaaaacadccddbdabdbadabacdccadbdbdddcaadcdbcacaddbdbbaacbdbdadcdbcdaddcaaabadcacbdaddddbbdbcaacadaaccbdddadddcbddcdaaaaacbbaacbbcbcabacdddacacaacacbadaabddacadcacadadadacdbccaacccacaabcaddaabcdbbcacbbbabdbacbdcdbdbccbcbdaabddadddccbddcdcdcdcaaaddbdadbcdadcacacdbbaabbaacbdcbdbbcbbcdcdbbcadaccdddcddddbaaccbbbbdbbadcdadabbdcbccdabdddcadbddbaabdbacaddbddddcdbddbccccbabcbacacabbdbdbaadcdbbdcccabadddacccddaaddbdccbdcddcdacbccbdddbdcbabccaaddadbddbcdccdacdacabcccbbbacaaccabaabcddadcdbcbddaaaacdacaaaaaccaaabbdabadabcabdbccacaaabaddaddddbdacdadcdbabaacdbcabaadadaaaabdcdcccbcbdcccbbabadddaabababdaacacddabaacdccddddbbbadbdabbbdbddcbbacdaabdaaadadbabdccbddabbacaddbddadadacabcbdcbbcdaddbabbccbcaaacbbacbbcbdaacabbcdadadbcbcbbcbadccbddccaddcbbddadcdbabbccacdcacacacccdabdbacdcccbaacbabadcabcdadccadbbdbddcbbadbdbbccacbdcdacbdcacaadccacdcccbadccabcbcdcddbccaaadacdadccabdddbaacdabdbbadaabcaaacbcbcacdbcadaacbbaabdabaaadbdcbcccbacbccdccaccdccccdabddacbddadcdacaaacdbdbcdcaccdaaabaddabccadadbdbadbbcdadacabdcccaababcbabccaddcdacadddcdaaddbbcdccdcddcddbabdccadaddacabcaccabacaccdccdcabaddacbdacdbdcbabababbabdddaccdcdccdbccbdddbbbcaddadbddacadcdbaaaacadcacabccdabcccdcddbdaabbcdaaaddaccbcbbbdddbacbdcabdabbacbbcdcdddbdbaabbdcadcbbcdbcccaccaccbcdabbddbabbcbbcbaabcadcadabaadabaaaaddabddaaccdabdcacdcdccbddadcdcadcbcbaadbcdaccccbbabaddcadcbcabacbacdbacddcadbdadabadccdcddcbdcbbdbbdaacccbbabdbcadcaacdbcabdcdccadccadcadcbadcdcacbadbadddcbdacbcbadababbdbbabaabccadccaddbdbaaadabaaaabbcacccacbdcddbcdcacbbaabcaaadcccbbdddcacbcabddbbbdcadacbdcbcbbadccccdccacbdccadcbccaccddaabdabbaccadacbdcdabbaddcaddccdadaacbdadbbccbaacbbccbbcabacdcbdadccaccddbacdbbcdcdddbcadccdacddbdadacababdacaacbcdacbccdbcbcaaacbbbcabcbdaaaacbbcadacdcacacdddcadbdddabbabacdddbdacdaddabdbcdaadbcdbcbdcbdbababbaddcbdaccbaaacccbbaaaaaaaaadbbabacadcdadcbabbadbcdcacbbddabbacccbaaaddabaabbbdbadaacacabbdacaacacdcdbadddbcabaaabdbaddddcbadddaacbbbcbdacaddadabbddaaadaadadcdcddbaaccdcabacaaaaddaaccbccbabbbacdccacacdddcdabdbababccbbadbadabbcbbaaabaddbcaddddcccbddcadabdabcabbdcbdbbbccadbdadcdbbcccabdbbcacdadabdbdbcbbbcbccddccaaadaddabcbabdddcabaccabddcdaaddbaddccccbacccdcbdababcabdacbcdaaccabcaadcdbdbdadccabadcccccaaacadbbbdcbdcccbaaadacdcccacadcdcdcccddbbbbcacbbcbadddccaccbdddadbdbccabcdbdbbcddbcbdaadbbbdaacbcabddaacababccbabccabcaddabcaccabbddbadbbadaadababbdcbbcadccdcaacdcabbcddbdbdbbdaaabbcbccacaaabcadacddadcbbbaccaccbbcdddcccdadbdabcbccadcdccdaccacdcbcbdbdcdaaacaacadcbaacacbdbbbcadcbbbccbdbcabadcdbcbbcbcbadcadccaabbbbadddadbcdbbbdcdcdbdbabacaadcdbdaabddcbbdaddacabdbcddadcadacbddcdabbcbbddaabbcbdcbbbabdcbbaccbcdabbcccadcddcddadaccbaaabbbacadbdacdcddcdbadbccbbcacaabdaccccbcaacdbcbdabccaadacabdabaccbdaddacdbcabdddacdcbcbddbdbbddccbbcacadbccbdaadbdcdcccdacabccbdcbdaaaabcdbccdbdaacdbddddbdbbcbdccdacaabdcbcaaadabcbcadbbaddbccacccbcaacdcdacacaadabcbbdabcccbbccdcbbbbbdddabcacddacdbccbbcdacbcdddadbbaccdbacdaabdcbdddccabdbcbcbbcdccbdccdabbacbdaccabdabdbcdcabbcbcdbacdbbbddaccddccbbbdabddaaaadddccabaadacdcbacacbdbacbcbcbcccbbbdcabcbcacbcbbbbabdabbdcbdcdcbdbdccdbcdcbaccaccaddacaacddbbaaccbaaabdcdcbcdacddcaacaadcdbbdaccaaaabddcdbccdbccadbccdbbdccbcccacadbadadacdbdbbabdcadacacbaabcbdcbadadcabbcbccadbbadacccccbcadbbcdbdccdbdaadcdbddbbabbbcbaaddbdaacacacadacbcbaabcaadcbdcdcabcdadaacdacbdadaccbdcaadbccddcacdbabaddbcbcabcdbcadbabdbbbaaadcaaddbabdacdbacbaabdababadddbbacacdaacdddbadaaababbbcabaadccaccbccdccacbdcbdbadbbaabbbbcbdadbcacdccdbccadbbdcabadccacdadcdcbdacbacbbcdcbcccabdbaadcbbaddbabdadbbddbdcbdaaadddabcbdacccbddcadbacbcbaddbabbdcdddccbcccabcdabaaddbbcbbdbaaaaddbcdcaabcbdabcdbcababaddacddadaaaabdabcbdaaccbdbabccbdddddbdcacaadacdcadddcddacddadcacacabdaaacabcbbdcbdcdaadaaabcbcaccddbbdbabadccdddcbbbaaaaaccddbaadabadbabacbcbcdacadbbcdbcbbbaaddcdcaaccadccacadcacbbcadcddcbbbcdaaaddacdcacbadabddaadbbccabbaccbccacdababbccdcbcaadbbcdbddabdadddbadbdaaddcccbdaacaccbbbacbaaddbacbbcabcddcdccbbccaadcbcabbbbbbabacabdaacbacdcdaabbcdbdbadaadcbbcbbacbbddcaadbcbaddcbbdcccddcccaddbaaacccdbdaddacdccbcbcaacbdcddddbcdaadaacdbbcbbabbbcbababcddcccddaabacbcbacddddaabddbccccbdcbddbdabdbbccbaacccdcbdadbaccdcdaadbadbabbcdbacababbccabcacaccacccbcddcaadbcabacddaaadbbdddccdccddbdaccaccccadaccbaacbdddbcbaadabdacbcbabdbaddcdbadbacbbbbadcbcadcdcaabddbbacadaccaadbabbbaaddabcbbbcbddcccacbbbddddcdacababdcddadabbccdcaabbaddddbbaabcdbdbbbdabadcdcbcbbcabdbbbabbbacdddbcadcaddbacbbbacdadacdadcdbadddbdddabdcabaabbabddcabcccbadcaadbcdaaaadcbbaaabdcddacabbaddaaaaadbabacadbcbccbbacbabdbacaddacdbbadbabcbbcccaacbcddcdbcccbcaccddcbadbdabbbbbdaaaaaddcadccaddbdcbadddcbbccbaacbaccbaccdddbccbdabccddcdddbcbdbcdbbcabacabbaabbbccdadbcbddacbccaacbdadcdccadddcadacccbaccbabcaacacbdcabaadddddbdabcaaaacbdaadcbdacbbacccdccadcaabaaabbbcbbdbabbdcccdadcbcaabdcadbcadbddbbcccbadadddbbabbbacaddcdcbbbcbcbbacbcaabcdbcbcccdcadaacdddabaaabacaccacabadbcbdbcdddaacbcaacdaadaacbdccdbddbdacdddacaacdbccdbaccbbdbacaaccddccabbcbcccacdbcacbbcbdbcacbaccabbaadddcdabcabcdabcaacbcddabdcbcccdcbdcdadcbdbabadacccadcacdabdaddadcaccccbdddccdabaccdcdabbcbcccadabacdcdaacaacabddadcccbaccbaddaadacdbaccacdccdcadccbcdcacbaddccbdcccbcbaadaabcdaacacdaddadcacbabcbbbdbbccccbaabadbcbccabaacddbcbdbbbdcdcabccbbbcabbbbdcacdadbbacabdcdddbddacacabddcbccddadbcadcdaadcbdcdcdbbcaabaabacbabddddbadabbcdbadacdcdbadcaccabbccadbbbadbcdcdddbdbdadacadccdabaddccabbcaadabadbddaabcdbaadcddddbddbccdbdcbcaaadacaacdddcdaaccaccbdaccbcaaabcccddabcaaccdbbcbabdacbdbdbacdcacaccdccbadacdadccbbbccacddcdaddcacddbaacdbbbbbcbcabcddadacabcccbbbcdcadbbbdddbccadbaadaddaadccdcadaddabcacdcacadbcabbaadbcbbbabdaaadaadbcaddbccdbdbbcbbdbdacbacaaddbccaccaaacbabbdbbaaccadcbabccdadabbcbdadbadcaadcbccdbaacbdcccddbdcbdabcdddbbddccbcbbdcbbacddbdbddbbcdcdbdcddabdbbabaddaacbdddaacdccdbcdacdcbccadcccdddaaaddbadabbcdccaaaddbdbdcadddbbdbaacbcadaaacdaccdcbcddaaacacbcbacbcaabaacbbbaccbbaccabbabacdaabbcdbcaccacaaadbdbabbbcbbbadaaaaabdbbcbcacadcbbabbdbbddaabdddaaaddbdcadccabcddddddddabcadbdddadcdadaabaddacbdabaddbbaababbbdcccbcbbaccacddaabdabcbcadacdacaacddccbccadbcccabcdacadcaacaadccddbabbcbadbddbbdabdabdbdbdacbccdcacbcabacacddadbbcddacbcabbcdbccbbaacaaabccdbccbabcbbdaddacacaddabdccbbccbddbacbcbabcbadadcbdccbbbbacdbccbdaaaaaacbabacbbacbdccbdcbdddbcbcabdcacbbdcdccdbdcacbbdbbacbdcaadddcdbacdbbddbaddcbcabbadbbacdcbacdabcdcbccccbdacdccddaacaabdbbddcabbacadbbdacbcbaaaadbcaddbaccabdabbbdccacddcadbadaaccdcccdbdadaabbaacccddbaadbdbaaaccbadadbbdbbcbddaacbcddbbbcccbcdaddbbdbcacbaaadabcbabcbbcacacadddcccabbdbdbadbbccabbdaaabdbbdcadbdbdacbdbbdcabbdddddddcacabcbdbbcdcdaddbcbcddbabbbaadadaabaaadcbcaddbabcabacbbddcbdadcdccdacdcdabdccccbbbcabccbaadddccbdaababaaadaadbacabbcdccdcabdbbdcbbbcccdbdccaaccaadbbbaaadcacddbbcdddcbcdbaadcdbadbbcabccbbaddbbcdcbadcbbbbcbddbbccbcdbdcaddabadbcdcddaabaaadbacddaddaadbadbabdabadbbcddadbcbddadccdbbcbaacdabbddaddaacbbdddbcbddabdcbbbbabadaccbdcbbadcaddabbddbddbdbaacacbbaacaabbbabccacaaaabdaabbbbdbaacaddcdbbbcddbcacdcddddcaccdbcdacdabcddaacbbdbabdababdbaccbdcadbdcadacbaadddacccdbccadccabacddadbabadacccbadbbbbaabbadccbbcbdbdacacbbbbabadbadbaddbdabbadccdbbccadddabbbababaaaababbbcbcdbadddabddcddacddadcaaabbcdabcdcacccacdbccccacadcdccbbdccdcccbcbdbabddcdcbddaccdabacbadbabaaaacdbbdcdcdbaacacbddbabccabbabdcddbcbacabbaaaabadbcaacccbdcdabbbdbbdcacbadadcabbdadabcaacdddbacdbdabdddcbcacbbccdcacbcbdacdcacadadcadacddbdbacbadcaacdacabdabcbdcbdadcbdbabcacbdbbdaddcacadccbbbdabacdbcbcbbabdbcccdbdbdaacacbabdbcaccdbccdbdcdcbbacbcddaadaaddabacdcaacccdcabbaccacbacbddcbbcbadbbbcdbaabdaddcdccababcccbbccbcbaacbacaabdabcccccabadbdbcdcaccbcdacdadddbccacaaaadbcdcbaccbadddacccdcaadcbdbdaaaddbacdaaabddccbbcbccdbababdabdddaaabcabbaabbcaaddbbaabbcbbbdbbaadabbdaaacdabcabacdcaddadcdbaccccddccdacaddbcacbcdcddabddadccdaccdacddacddcdacccadbacddddcdcdadbdbabcdbcbaadbcddbaccacdddcabcddcbdcabcbaaadbccacacdbabadbbbddaabcacccaacbbaaddcbbacacccbdadcabccbddcccbbcccbaaaddbcbbbdabbacacabdcbdadbbaaddadcccdbcdbadbddbddaacbddbbccdbbccabaccdbacbcbcbabaddaaadcacadadccadcbabacccdccccdcdddabdaaaadcdadcacdadadaaaabbccadcabcabdcadbaaabbddbaaaaccdbcbdbbacadccbcdadbddbdddaddbcdadaabcdacbaaaaabcbddcabaababababcbcadacdaddbdcbbaaccdcdbaddbddabcddaaacdcccdbacddbcacbccddadbdbccadabdadcdbcacdcbabcabbddadabddcddcbcaddcababbcbcdadbaaaabdaadcaaddbaaabbccbdcdacaddbdaccaacadabccdaacdcacbbdcbdaccddbddddaabbcbccdbdcacbacbdaabdabaccaacccabdcccddcaacbcdcddbcadbdddbaaabdcccbabdaadbbacbbccdaddbdcbdbcaccbddacdcdbdccadaaabdacabddacccbadbddcbcadbdbdbbbbbaacbbdcdaaaabbcabdcbbccdbaccdddaddbdbadcdaabadcdacdbadbcdbadbcbbaacccbdadcabcccbdcdcabbabccddbcddcbadddccbcacaabbcbbccbbabbacddcadcabccbaadcdbacccadaddcbabdbadcacccdbbabaaabdbcbbbcadbbaacdcdcbbadcadaddcabddbbbdddacdbcdcbaccbdddaabbbdaaccbdccbddadcdcccccdacacbadbcbdbcdddbababdbdddddbadcdddaaaabcbadbadbbbabacaadbaacbcdbcbcabaabacbbcdccddbbcbbdbcddcaabaadbbabadcdcbabacddbcdbddacccbdabbaddadcbccdcbdaacdbbddbcbababdbcdcdccabbacacadbcbdcddbacddaaabacdcaacddcdcacabbaadbcbccbbdcbdcdcabcbabaacdaabdabdcadccabbaddacbddaabcadcbdcbccccdadcdbabacdaadbccadabcccadbbaaabccacbcdcababacdcbdacbdbcdadddabcdbbbacacdcdcbbbcbbcacaaabddacaabdcabcbcbcbddcbbbcdcbccaaddacaddacbdbbdccddbacadacabccacddadccbcbbddaaadacaaaddabcdacbbadcacaaadadacdbaadbbababdccadadbabdcadbdcacddcdbbadcababadababaaadadbcdbacbaadbdabdcbdddcacdbaabacddbcbbddaacacdcacacbddadcdbadaaadcaccbbadadadadbaabdbdbcbdadcbadbacbddddcccdbcccbcbadddbcdadcdaddadadbdccbcbbdadbcaacbadbbcdadcdccbaacaadacabacdaaacadbcbdabcbacbcbadacabacbcacccdccdcdbadaadbacdccabdccaacdddaabcdbbcbbbbccaacaaacdcdccadacaccdbadcbbcdbbbbcbcaaaddcbacddbdbabccbcacbbbabdccdbaccdcdbdbbacccaabdaadcbbbdaabcbcadadbacbbdddbaacbadabbbdbcdcdbcccdbbbcdbdcbbdccaccdcbcdacdcdadbbccdccccbbddbaacdadaadbdbbbdbaddbdabbcbbdbaaabdccdbbabddaaacdddabcdadddcddddadbbbdbdcbbbbddaccccabcccdabadcdcaadadccbcdbddcddaadddacaccbdccbacccccdbddaaddbcbcdbadadcbaadcdcddbabdacacccbcbcabddbaadcdabdbacddcadaadbdbdbcababadcabcbbadcdbdbccbcccdbacababbaacccddadcbcdbbdbcdbcccbaaacddaacdbaaacccbbaacbccadccbddacaadcdcbbbdaadddccddcdadacbacbdcababacadbdbcdccbdbbabdbdaaddbdccbadddcaabaaabdcbbbcaabcdbcbaacbcccccaccccdbcadabbbdbcacbbaaddcdbdbdacbbdcacabbbbadabbddacddabcbcbdabdbbcacccdaccadabbbabbcaadcdbadadacdcdccaccccdccacbcbaaacbcaddadcbddddbabbdddbdcddbacbccabdaadcccbdbddabdbcaccaccaacabbcabacabccdcadacdbabbcaccbadadbcaddcbaddbbbbcadbbbdbccdbbaaccdbbabbdacbadadcccbdddaaddcddccbccdcbcddbddababdbcbbacacccdcacabaaacccbadcdcaccbadabcdaabccacaccacbcabbaddaabbabbadbdadcadaabbcbaabacbbbdcdadcbaaadbaaacadccbdabacbabadaadaabbdccbcacbcdcbabbccdcbccaacbcbbbdbdcbbdddbbcaabcdcaacbcaccadadbbddcbbdcdadbbddabaddacbbacaccbbdddacadbcadaadbaaacdbbadddccbdcdcdbcabcdcdbddcaaccddbacdabbabddaccdbabacadaacdbcbcaccccadddcadbaadcbbddcbacadaacbcdbbadacbdbdbcabcbbcbcabdcbbbcaadcbbbdcabbddbcbcbddabbcaaaddcccbdacccbdcccdbbbdbccaadddadcdaacccbdbaddcdccaadbaccbccdcbcbdbcccaadacaddbbaaddadadbdcbabcbcbccdcbbaabcaaabdbcaddbbddbabbcdbdcbbadbabbcadddbcbccdaccbabcddbcacdcaaacbaacccaaacbaaabdabbdbdbaababdbabcbcdcbdcbbdbcccdcacaaaabcbbdbdddbabccdcdddacdccabcdcdcbaadadcccbdaaacbddbccdcdcaabbcabbadcbcdbaacbabcacbdaabadabbcbabdccdccabacccbaddddbaadbadcdacddcbdcabccbdabccdbdacdddccbbddcaaddcdbcaddcbaaabcdbdbbadbccacbaabbbbaccbcbbddbbabbacacdbdbaccbabdacdddccbaddabbdbddaadbbcbbadabbbdddbcdabcdcddbbabcdcdaaabdbbaabcbbaabdccbdabdabadaacbacccdcbcccdcddbbbacbbdbacdabdcabbacdbbcadbadabcdabcabbabcbdcbdacbbabdbabcbdbbadcddbbcccccccdabcddccdaccbdacbcaabbaaabdaacbdcbacbccadbdadccadbcdadabcbacdabcddbcbdaccacbcbaabadbbadbbcdbcadbabbdbbccaababdbdacdcacdcaaccdccabcbccbbabbcdbcbddabcbccadccddcbcabadbcacdbcddadbdcddddbdadccadaadbcdbbabcbabcaacaadaacabdbcadbacdbaccaacdcbbcdbadadbaccaabacbabccddcbdcabacbddacabcbcbbcaaacacbbdbaaddaddacbbcbacdcadccababcaddadacacddabbbbccddcbdbaadbacbcadccbadcdcbdddbbbcacdaaabacdcacdaabdcccdbadcabdbcdadbddbbcddcddaaabacbbabccdaacbacbabbbccaadaabacbdaaacdddabdaaabdccccbdaaaddddababccdaaaabcbdcacccaddabaddbabbcbbaaddaabbdbacaaadbdaabcaadbcabadccdabaaabcabbddcbdbcdccaadacdadadccddcdbddbaabbcbccbaaacabdbcabdddadbdccddbbdabcdaccabdaadcbbdccdddacbddccbcdbddddbbaadbbbddbabbcadcdbccccbbbcbbdcdcbcabdacdadcbddcdbdabdddadbcbdbbbbbaccdcdaccccccaaacbddddbdaaadccccdcccdcbbcbacacaaccabdcacbdabbccaddbbdcbabdccdccaacccbdbcbbbcadbbbcdacadbbcbbabaddcacbbacabdcbbcbaaddabacddabcbcbdabdbdacbcabbacaccccacddccadaddbaacacaaaacddcacbcacabaabddaddbbddccadbbcbabbdadaccdaccacacbccbdbdbbdbabcddccdadaccdaaacbabddcdbcccccdbddccdddddbbcbabdbdbcccddbdccabbbcaadbabcddbaccaccccccdddddcabcbaacbbbdcbcaabbcbbabdcdbacdbccbaacacbcabcadbddacdbbdccdababdddbbdbbdaacaacbcaacbcdcaacbdcaadbaadaccdbaaacadaaacbaaadcdcbdddcadcccdacdcbddbaadabccdbabacccdbcaacbbddcadbddbdddcbbbdaaabbcadcdcadbcdaccdaadcdcdaacddbabccbdbbbdbcbcadddcaadabadcadbdacdbcdddbbcdacccdddcbddddbccacbcacddcbcadaacaabcddbbbcbdcbccdaadcbccadbadbdccbddcbdacccbacbcaacaccbcbaaadcdbcccabddcaaccddcaacdcaacdccdcdcbcbdbbbabacaabdcdaaccaaccddbabacdbbbbbcdacbcbddbcaaacbbcbabdddaaccccbccacdaabaadbbadbaababbccadadbcabbadbddaabccaaacbccbccaacadccabbcdaacbababdaaabcbcbbbbbbccddccadbaabacbccbddadddbcdddddadabcaccddaadbddaaccbcbacdcdccdadcdbbdbcdbadcccadcaadbccdcdcaaacbacadddbdddbccdabbcbcbcaccacadacdabcbbabbaddaabbdcbdcbbabccdbdacacddcbadcbadbbbbdacacacaadcbdaadbbaaaacaacddbacaacdbaddbdbbdcaaabcdacdcdbdaabdcdabbcccbcbaabababbccabdbaacadacaaddbdcbddcaaadbbcdbabadcaadadccbbcdbabbbbcabbabacdacccdadcdbaadacccaccdbaaacdaddbdcabcbabdabaccacccadadbccbdcdddcaadcddbadbdbabccbdcddadadddacabcddddcacdacdaadccdababdbaccbbadddbddaaaccdadacddadccbcbdabcacaaabcacaacabcaccdcdbbdddaaddabcaccacbcbadaddddbcabccdcdaccdababbaddcbbcdadbaacbcdbccdccbdbccabdbcdacdcddbbcaccbdccdbccaaabbbbaabcdbbbdbcbabadadccabacddacdaaddbdcbcbcbcddbdcaddddcaabdacacdcccabbbbabdcdddbbdcaddadaccacbbbacbacbbcbcdbcbcddbbcbbdacbbaaccaaddbaaccddabbcaabbaddbbaddbcccacbacdadbdbbbcacdaacbbabbcbcabbcdaccdbdcddcccbddbabcadcaacdbcdbbdcbaacccdbdbadbabbddadcaadaabcbbdcbadabbadbcdacabcbbaaccbabbbcdccccdddbabdccdddcdbcacbabdcabbdadccbcadbdcbabddcabcadcbdabacbddccadbbcaadabadcbcaccbdacbdbbadcbcdbccabacbcddbbddbddddbdbdbddbaccacbcddcabdbbbcdbadadcdadcdaabdaddbcadaacaddcdabdddbbbaaacbdcdbababdccbacadddcaaaaaadddaaccabacddacbdccbcdbdbdadadddbcabacbbaddacdccdbbdddaccbadabbddadbdbbdabbdcbcaccabccababadcddccdcacbdbccddccdabdcdcbabbddbaaaddbcbccadbabbcbdcdcbacbdadbcddcadcdbddabcccbacdccbaacaabdabccdaacaddabcabdbcbdcbdcccadbdccbabbdbdddcbadbdcdbdbdcadbaacdcadabbbbbabbbabcaacabdddacbcadbbaaccdcdcbccddbaadbcdbdbbacdbcbdcababdcabbbbdddcbcaaccdcadacbabdbddccdcbcadcdddbaddcdcdcbbdabcbddacadbbadccaccabbdbdaabbbcacabbcdcbbadbcadccbacdaabdcccdabadcdbdbbaabbcbbaabadadcaaccddadddbacddaaadcacdadacddddacaabaaccabadbabbdaaabccbabadababcbdbccdbddadacbdadbdbbcbdddacbcdacabddcccbdccacaaddddcacddddbddccdbdcdccdadcbadddabadcbbbdccaadadbaaaddddacccbadbddbbadcbddcaabcccbbdbbbddacacacbcdaddcdbbdcbdddbbcabdadcdbccaccbdbdbccbadccabdaacdccccccdcbbbaacccdbbbabbbacbcbbcbcdcbbcabbdacdddcdddbbbdcdbddddbcccdabdbbcadcdddbbdcbdacbadcdccbbbadaacdcadbdcabdcaddcaccacacdddbcbabaaabccabcadadbcddaacdaaccdddbbbacacdbbbadbabbcdbdacadcbbcbcdbcabcacdcadabdaccdcbdcaacccdddbdcddbbcccacdaacacdabcddaaabbcbcbadadcdccbcbdcdbcadbbcbcbcbcdbbbccdccdddcdbcdbbaddcadabadadbccccaababddadbcaabcdbcacccacbbabbadabdbdaaabdaaaacaaccdacccbadccbcdcccbbdcbbaadaccddadaccacbccbccabdacdbbaaddaadababbacbaacdcaabdadcbdbbbbbbadbbaacdacbbcbaddbcbdabdbdadbdaaaaaaaddabbbcabacbaaadcbdbdbccdacbdccbabdddadbaadbdcccccabccbadccadcbbcdabdaabaaaabcdcdaadddabbacaabaaacdaabdaaaaadccccbaabbcdbcbcaddbacabccdcbabadccbbacdaadcccbbdccaaacababcbaddcdabdabcaaddbcbcdadcdcddabdcdcdcbddccccbcbbcaddccaacdbbbcbbdadbbdabcdcbccbcdaccdccccbaaabddcbadbadacddbcdacdddddacdbabaadcbbbdaaadbcdbdccadcdddaaaddbcdcaccdacbaaadcccdcbaccccaacbadbcbcacabdccabcbddaadbbbbdbbcdbcbbbdadbcddbcdbddacbbcabcadcbccccbbadcaaddcddbbdbcaddbdcbdaabbbdacccabcdddcbdaaabbdabcbcdbcbbbdcaacadbbbdcaaacaabbbcbdbaabbaaaacaaacbbccabcbbbdccabbddaaaddadcadbabdabdbcdbcbdcaaadaadddacbdbadccbdacacbbcdacababadadbaaaabcabdbcbccbadacbbcdadabcdbddcacccaddbdacbdcdcbcbacdccacdaacbddddbdaabcaacbaccbabbacdbdbbdadcaddaacdbcdddbaabdbcadcddcbdbbdbacccbcccbdcbbbdbbcbbdacbacccabaddadabdcdacadbcbbaadcacdabdabdaadaddddddacccadbacbcdbacaacddacbcbabbaacdcccbdccdcdbcaadcadaaaddcadbdbcadcaadcbbbdcbbabdccaddacccbbbaddbbdddabbadccbbcbdaccbccabdcaacdaabdaababadccdcbbaccaddbbbddaddacccbdabbbdccdabcdddccdaaadbbbdbbadccbaaccbcadddcadcaddacdaadcbcbaddaaadacbbdcdadbcdcbbcababbdcbbcbdbcccddaacddddbddcbcabcacbcacccbdddcaabbacbccbdaccdcbdbadbddadababcbdcddcbddbabcbabdaacdddbdcddbdadcbcacbbcacaadaacbaacabbbbcccdbaadadcddccaaccddadcdabccbdcacaadabacbacdcdbdabacbbabccdcbaabddddaabbaaaabacbcbaacbddcbbdbdddbadccddaaabcdbbacbabdddddbabaddcbbcabcaacbcdcdadadccbdddaddadabbdadcdabacbbbcacdbcabdaddcdcbddaadadcbcacabcaaacbdaacbadccdbdbdadbababcccbbdabccaaaadddaadadcaacabbaacddddcbdabcdddccadcbbdacbabdaaccabacdbcbbbcdaadadddabaabbaddbbbbccabccdcabadbabadcdbdccdabdddddcdaddcdabccbbabbbaacbbbdcdcddbcabdbbcdcaaacaddcccbaacbacabcdbaabddbbbcddcdbcbddbdbaacaadcccabbcdbabacddabaaacdbaadbabbadbbcbdbdcdaabdbcdbabddddcbdccadcaadacddddaddbbaaaaacddcadbaaccabbdbaccbacdcadbaddbbcbbaabcbacccbdddcbcddbccdabbccadbaabbbddbdbddcacddcabacddccbcbcbdcbcacadbccbaabdcdcbbdaccdaddabcbbcbabdcccacdcbbadabddacbbddccdaaaadbbbdbbadaacddbcdaaccdcaddadcdcdccbccbadbcddcabbadadcbbdcbbcdcbdabcdcdbacbcccacdbdcdccabdddddccddddaccacdadcdddddddcdabcadacacbaacccccddcbabbbdacddadbbdddcbbcadbcbaaaaabccddabcbabdbacbbcdabbdcbdaaccaaadddaabadddacbcdddddbbbdabccabcddaacddacbdbaaaaadaacbcdabcbbbccbadcbadbdddccacccdcacadbbaccbdcdabddcaabdcccdcdaccacadbbaadaacaaaaadbaccbcbcabcdadaddaadbcbadcbcbcaaacbdcdabdcdbcaaacaaaadaacbbddcdbaddaabdacbbbbacacaabdbabccbddbcbbacbabbbddcdaaaddbcacccddabbbdcaddaaabcdddabbccbbccddbccacbadacccdabdbadcaccbdaacbdaddcaacdcdcbdcbcbddacbaaaadabcddbdccdccdcbdcdddbbdbccdaddddbdbcddbabdacbddccddaacacbdcaccbaacdadcbdaccdbcaddbcdaabcbabbbbaaaadbaaacbadaddbaccdbbbbddcdbaacbdaadadcdaacaaabdddcbabadbacabadababadaddaabcddababccccddababadaacbcbacdbddaadccddadbacbdbccddcccaacbbdadcadcaaacadbacdbdbdcdcdadacaccddbbbabddbbbaccbcbaacabcaadcabbcbdbddccbdbcaddbaaddcacbdbdbaababdccacddaddcdbdcdacdacbcadaddcaaabccbccdcbbcaaaabcbaadaaadcbcacacaccaacdacccaaacadbdbdcddabaabaadbddbabaaacadcaddcdcaaddcdacdbdccdddbbaacbbcdbccdaaccbbcdcabbccdcdcabcbddcbddccbdbcbcaadcccbbccccadbbbacdbdaadbddcdcccdbdbababcaaabdcadcdcabccbacbdcbdbbdcdcdbcbbbcadcccbbddbbddcdadbdbdddcbbaadccbbdaadbcccadcbdaddadaadcacaccabdbbaadcbcaaccbdcababaaaabcaabbcbbaccdbcabadccbcccbcabbcddbabcbbcaabaaaadadbccbbabccaadabcaabaacccbaddabdddddaacaabcdabddcacacdadbcbcbccadabbaccbaabddddbabccccadbdccbcbcddccccbabadacabcdbccacbcaddbddcbbbcacbacdbbcaacbadbabcccddbdcbdcccabadbdcddcdcccbbdddacbddccaabbaadabcdcaddbbdcbcbddcbdbabadacccdbdccddaaaadccacababdcdcaacccbddcbbdbcbddacbbbabcababbbdadacdadabcdccabcbcadabcccaccbccbabbbdabcbaabdadabcdbbcdabacddabcdacdbabacdbbabbcccacaabcaddcabddbbddcbccdacdadbaabaccbdaabbdcabdbbcdcbadbbbaacaacbbbaddbdababddabdbcbddbaabcbdbadddcccacaacdbcadddcbacccbbcccbabaaabddacaaaddcdbcddccbcdddabbacdcccabdddbdbbadbbacbcbabbbcdaaacbbaadbdcddcabcbabcaccdaccdbadbddbaadcaabcbabccbcccdbabaacbccabadcadbdbaabdacabadcbdbddbadcbcabbcbaddbccbbabadacaccacddddaadadabaadaaadabcadcbcbccddbdbabadaabdccbdbadccbaadccdbccacbcadbadcaacbdcdcabdddadadcbbadcaabddcccabbbdbcbcacabdccadccaadbcbbcabacdaadcadccddaccadbbaddcaadbccddcbbabaccbdababcdccadadccdbbdaaacdcdcccaaaadacadbcacacccadaddcdbdbbabcdbbdbbaaacdbcabbdacdbdbbbdddbbcbbabcababbdddddacbbcaabddbcbdcdabbbdbccbcdacbdddacccccacddaccdcaabdbaddaadbbbdaaabdbddaaaacaccabddabdbbbadabdbaadcdcddcdcaccccdcabcdbdcbabacacdcaaababccdbddbbdcabbadadbbdcbdbabddbddccaddbcbbdacddbcbbacdacabcbadbadacccdcaddcdddbbadbbbdaddcbabdabdbccdcdaabaadcddcbccaaacdccdabdcbdadbdacaccadaadccbbaabbaacccadbcbdbdaabbbaabacaddcacbacbdcbabdddbacddbdadcbcadcbaabbadabaddddaaaddbbacabaacdcaaacdcbddbadddaadcabddbcbacdcbbbbacbbaacdbbabcbddddbdacccacdbaabcdacbcabdaddbcdacdbaacadacabdbcbdbdbabdadcdccbabadcdccadbdddbadadcadccdddaacdcbbdbccddccacbaaaadcccaccaaabddbdcabdbddbbccdcbcccdcbbacbdcaacbacbbacadcbdabbcccbcbadcabbbcbabccbadcdacbcdbdacddacbbdcddcadaabbadaaaccbcaabdabbbbcadbdadadbdacccaabccabbbabcdbacbcbbcddabadaaaabcbdddbdcdccdbcbaddbaccaaabbacbadbacccbdacadbcdabbdcdabcdabcbcbdbacbbdccdcbdcdbacabbdabdbbccdbddbcacdcaabddaacacaccddccacaaaccbbbaaccbbbadaccdbcbcbcdbdbdcbcccaacdccbcaadcccdcbbbcaabcabbcbaddbaaddddcbcccadbdbbbcbcdccbacccccbcdddaaddacbbdbcbaaaddcbccadbdacbbcabdcadbbadbcdabbaaaaccacdcddaddcacdacbcaabdabcbcdaddaabadcadaadbaababdddcbcabcaacabbbdcdaabdbcddcddbcbcbdaddbcdcdadbcdaddadaddbbbbcaddcbabdddcadcddbbbabdacbdddaddcbbdcdbdadcbbdcdccaddbaaadcbcaccaabdcbabbdacccdccccadbcbddbbcbdbbcabddcbdcdcdcbcccdcabbbdbdaacddabcdbaaadaababddbbabaaccdcaadadabdaabbdadbbcaccdbddcaacadbcdcabdddccadabbcccadbdcbdbacbadcdaadabbddcdacacbcccaddadaacdabaabacadabcdbdabccbddbcdbbaaabcbdaadbabccccdbcababbddcdbaabdbbcdabbacccaabcaccdaacdacbdbaddbddaccdbaaccdbbabadbdbcdadabcdbcababbcccdccccbbcccccaaccddaccbbbcccbccdddbdacdcadabababcdbaaabdaccacdaddcbbcbababbcadbacadbabcaaddddabcddacacccadbbddbccabcdcaacbadaaaccbdcbacccabddcbbcddcccbccaadabdbccabdbacbadadadcabcbcbaabdcddcdabaddbabaabadccabbdcdbbbdaabbadccdaadcdbbabddcabacdabddbcbbabcbdbabccaabbaaaacbabaadacbddbcdcaadcacbbaaaabdcdadbdaccdbbabdcdacddaadcccabbccdcdddbabcdcddbcbbccddbddcadcdbccccbabbacbbcabdabacccdaabcbbccbabbabbaabababdddabbbcdacacdddbacadacdddaadabddcbababaccbdbbcbaddcdcdcbcdddbcabbcabbacbbacbabdbbbabdbacdcddccadbddcaabbaababbdbdbbccbddccabdadadbbccbdcbbccabbaacaccccbcdbdadcbabbadcdddcbbdcbddbcacbcadcdbcabdabcbbaddccccaabdbcaadadabadaaaaddaccacdabccbabdcadbdbaacbcddcdccdadaddbdddabbdcadcdcbdaccddacddbaabcdbadcdaabadddbadbcbdddabccddaccbbcbccadbaaddcbdbbacdbbacddddbdabddaabdaccdabdbdcadabbaccbbbbdaacdaddbcbdbdcccdabdddcdaddcddcdbcbdcccadbbcadbaabdccdddcccccbbdcbacdadabcbaaadaadbacbaacbbbbcdadccbdbdbabccabddbdadcbcdbbcccbccbabddadadbdacdbaabccbbbdabcdbdbbbabdabcababdcddaddbdcbbdcdaccadcccdaccabbdcdcddcbacddcabcbbcddbdadaccdadcdabcdabcdddbcaacacddbbaadccbbaabdddbcdaacabdbadbcabdbbddbadacbbccbbbcaababbbbdbcbbcabaabdcdaacadacbbdcbdbbbdddbbdcbacdcbcaaabaadbccbccccbcdadbaabdddaaccdbadacaaaacddbabbcdbcdccaadbbaaabadcdadabacaccbaacbaaadcabcdccadaacccdacddcccbadababcbacaddadbbabdbdacccababdbaaabbdcaccbabbaaddacabdbbdddbcbcbbbccaabcacbcdcaaadcacdbacdcadbbcdcddbdcbcdabadacccabdcbadacbddbdbdadbaababccbcbcdcacdcccccbccdddaacacacdbcabddacaddbcccaccbabcddcdbbcbcadbabaaaaabaccbccbdcbcacabbbbcabdaddacbabbccdbdccadcdbbadbadcabacadcddabbbadbaabdadabaccaacccbddcbbdbaabaddddaadaacdccbbcbccdaabcdbbbabbcbddacddacdcdbdabbbaabcaddbabcbadcabbbdbbdacbcbabdcddadaaaadddccabdaaadcacabacacdcdacbacdbbcbddaccccbdaacddcbaaddaacbabdccabcabcbbdacacaddccbaddbaabdccaacadbcacbcadbccabbbababacddcadbbccabacdadbaadccabaaaaaccadddcdaabdbbabbbaacaccbbdcabacacdcbadacdcabbccdddddbadbcdbaacbacccbabddcdbdcbbbdbabbdcadbadbccbabadcddccddabbbbcbbbdaaaaaadabdddcaadadbcbbbddbcbddcdbcdabbdbbccccbcccaddaaacaadcccaadcddbbdddaabcccbddadddbdbbbcabdddcadcdadddbbcdccadbbbbddcaddaaabbababdbcbcaaabacdcbacddadbbbbdbcbbadcdabaaadadabdcccadbaccdaccdccbcabbadcaadbbddabaadbbaabbdbababcaaabdadddbaacdddbcadabccddadddddcdbdbbdacdbadbcabdaadbbadcbbcbabbacbacabcdbbcdcbccadccbdcacbcaaadacabbccaddbbcadcabbbcadbdcdcbdcdccadacdcdcabdabcaaaacccbacdaacbacddcccaabdabccbacacbaacddccdbdbcccdbccabbbadcadadcbcaadbdbbaabbcbcbaccbbccaaadcbcacdadbaabdbbccabdcbcaaabdaacadcbabcdacbcacdcabdcbccacbacbcbbdddaacbcbbdbacbccabcbadbdbcbabbbbbaabcccbbdcacabbbcacdccdccadcaddcdbcdbcdcdcabccdcccaccdaaaadbbabdbaaadacaddbbbacdcadbcbcbcdbdbcdbdccadaadaacabbcdcabbdbacbcbbbbbdaaabcacacddcacccbbaccadcccbaabcbbaabbcdcccacccaccdcacdbdbbabaacaaaaacadcdcabbabbadbbddacabddbadadbbdcdcaaabbbbccbcccbbdaaababbdadcaabacdddabbaaacddabacacbcbcacbcacadcdadddddacdbbaaacabadaaacdcaabdccabcaddcabbdbaacbcadacaacdcaabadcbdcdbdcdcdcacbbddbbbdbcbddddbdbbcbabbabdbdacbdcdcddacacdaccabbcbdacaadacbbdcaddcaabbdddadcccbbbabbddbbaabdddcaddcdabbcdcddacbdacadbdbcddccbdccaacbcbddcbbddadcccaaacaabcdcdccdbababccaaccbcdbdaaddcadababcddadbbddcbcadacacbabbcdddddaaaacdaabcddbacddbdcdaaccddddcbccabdacadabbbbcdbacbadcaddcdbaabbbcaadabbdaaadcbadbdcdaacdcdbaacbabbdabcaddabbcccdbbcadbddbdbccddbabadddcccddbadcdbbdbbcccacbcbbbcbddddaddbaaabbbcbcbaccababdaaccbbccbcbcdcbacdcdaadbdaaaaabcaaddcccdacbbcbccacbbccddadabdbabdccdbaababaddacaabcdddcbbadcaabbabacddaaacdcadccbddabcadbbccbdddaababaaddcdcddabbbcbccbdbbccdcabbbabdcbbcbcdcdaaddcbbbbbadbabbabdaccdbacbcbdbaddbccbcabdcbcbbcdadbdcaaadccaabdccbbaaadcdacdbacddcabdacdbdabdabccbdcdcbcbcdaadddbcddbddaaaddaddabbdddcdbaacdddaadcdaccdbdbdabcdddbdacbabcbdadbbaabaaddacaabaabadddcacacbbbdabddbcbcccaacacdadcdcbbcabbbadbbdcdcbcaadddbbaaddbbacabcbdcbacbbbcdccbaabbdddbdbddbbbbabcacaaccbcbcbbdbadcccdabdcacbbacdabdcacbabdcbddddacbbbdbdbbadadbcdaacadabdaaabacbcdabcdadabdbbacbbdbacdccbbaadcbaabadbbdcaaaaaccabdbdcbbabcabbabcdaacbaaabbbacdcbcdcaccddcbcadccbacbdbdcbbbdadbacccbdcdbabdccaacddcacbabaaabdbcbccdacaddacbbaaccdcbccbcbabdaddbccdadabdacbbbbabddadcadaacadacaaccbbdccdcbccbabdbddbadbdbddabbbbabdcbdaccbbbbbaccadcacbcdbcdbdbdcaadccccabbdadaadccccbcaaabddbdadddacdaddacddcaddddcbdcdbcdcabcbdacaadbcdacacccccacccaccaaacbdacbbcccdbbccaacabbbbaadcdbdccddbacdbdddddcccbdcabdddddabcbbcbadbcccbacbbbabbadbdadcbdcbdbdcbadbcdabaccacbbccadcdadbcdabbaccbbdbacdddaddadbbacabbbcddacddbabadbaacaabddcbaddcccddcaacabaadabaccaacddaabdbcaabddccadcbcaadcadabcabbcdddaabcbcbbacdacadbdabdabbdaadbbdccdaabddabdcacaacaaabcbcbabcbbdaddcdccdababbdcaabadacdbacbddccdabbbaadccacdcbdbcbdacdabbddcbddbbbababcbcadcdddbdbdabbcbddddcdacccbccbaacbaabaccdcaacccbcbbadddabbabacbbcdbbaabcaaacbbccddadbccdcddadabaabcacdccadaadbabbccdccbabbbadbdccdaadbbdddcbccadcacdcabbdadbcccabbccabdaabcadcadccbcdbaaddbbacbdabbddcbabaaaabbdadcddaabdbccabdcdbbbacbddbccbdadcdacddadabbabcdcbdadbcdbdbdbdbbcdabbaddcadbddaabaabcabcaabaddbaadbacddaababbbdcadbdccbdbadaadababcddcabdcbcdbccccdcbbadadbcccdcbdbdccadcddcbcbbccabbcadbbbdbcbdacccbcdcdaabaabcbcadbcaaaacabaddbcbcddcaadadadcdbdbcaddcabacadaaccdbcccacaacddaadabccacaabbadcdacbdcaddccdbbddcbddbbddbdaadcbddaddbcacbdcabdddacdadacdbcddcbbbadbabbababaacddcaccacadbacacbcdaddbcbbabcacadabcdcacbabadddbdcaaaabaccabadcbddccbccdaabdcaabbdaddaabccdabccaaaaadbcbaccddddbddbbbacabaadbbabdadcdcddaacaadbaacadbbbcdccbcadaababbacbbccaaadbaabbccdaadbccdcdbbaabccaabcbadbbdbcccadcbdbbcbaccbdbaccddcaccbadbaabcdccbccbababbddcddababbddcbaaacdaaddbbdbbbbbdacbadcbdabdccadccacabdabbabaaddcdccbdbbddbcaacadaddcaabcbacdcbbddbdaabcbdabccbabddddbbcbbbbccaabbdbaddbbcbbdbbdcddadbdbdacbcccdaabbdbdaabddcadddbdaaadacaaaccbcaddddabcccadbccabcbcdcbdbbcabaadbdacdcabcbbddbbbacbadbcaaacbccbbbdabaaacbdabcdabaacbbdcddbddcbbbdadcdbddcacccbcabbdaacbbadacacaaddbdcbbabbddccbcddaadcacccbbccaddaadcacaacdadadaaaabdadaaacaacbdadbbddbcdcadacadddcbabbbbacabbdbcbdccdcabaaccaabaaddaccdadcadadacaaadcbdaabdbbdcdddbcdbbcbbdadcccaabdcbcadbcdcbdbddaaabaadcdcbbdabadbaadbdabbdcbdddcacccbabcccdbcbaadacadbabdcbdcbbdcbccdcdabbadabaccbbcddddbddcdbbaaaaaabdcdcbccdbaacdddaaccaccdbbcbbccbcbbdabacaabcbacccaadcdbccbbcabaacbcdcaacadcbaaacbcabcacadbdbbcbadcdbbbcaadaccabdadcaabdacabdbcbabbcccdbcddbbabddccbccacabcdcabbdcbdbbbcdadbdadcacbddaddcdbdacdcdddaacbcdcccaaacbdcadabcadbbcccbdadcadddbcccddacbabbbcbbdcbaccabcadcddaccddaaabdbdcbaacbccbcdbaacdddabaccdcddabbcdadcccaaacbbdcdbbbbcbccccddbddccdccdbdcacbbbcdcddabaaabdccdabcbbcdbcbbaadbbddbcdbdaaabcacccaddbabbbcbacabdbaccabbabddbcadbacbbaacdbadadacababbdcbcaaaacbaadaabbddbadcdddacababbabbdcccddacbadbddacbcacccbabddacbadcacbaaddbbbccdadbcddbcbdbcbdaabbbbdcbbccacabbbbddbdabaccccdbdaaacbbbadbabccacbdbbdbbddaacbdcbadccbdcadacbcbcaadaacbaccdbaddbadbbbbdcdbcbdadacdbabaadcccbddaccdbdaaaadcabdcccbbdbacdcccbacdabcdccacbaddbaacaaacbcdbccacacbcadbaabaddbbacaacbacdaabcaabadbbbddccdcdcddbcabdcdadcabbbdcacbaacdaccabbcadbcbcacbddddbdbcdacbadaadcbccadbabdcbccccaadbdcabdabbbdbddacdaacbcabcbbadabacbbdccabbcabcbbcbdcacabdbbbdddcacadbcbccaacccbddcddaacdbaacbdbddbadcbbcdaabcbcdadadcccbdadbccdacbacaabcbbacbbcbccccbcdaaadbddbdbbabcadacacbcccaadccdacbdddccabcadbbaadddbccdddadabdddadaddbcbdabdacadbaddbcdcadaddcbcbcbadbdbdbcadaaaccabcdddcbacadbbbcdbabbaddddabccddcacddabccdcacdabbcdaaccddddddadaaabcbaadcabcadddccabbadacdbbdcbdcbbccaacdccaddcdccacaabbaccadacdaadbacbadbcaabddcbdcbacbcbababdbdcdacbddbdcbbdbccbcaaadbbdacacadcbdacbcbccddccabdbaacccadaaacbaddccdcbcabaaccbdcbccbaacadbcaadcabacbcbadbccaabacdadbadbdcbccdacacbdaacccddddcaacaddbbccdbccbbcaaabaacddddababdadadcbadacdccbdabaaabbbaaaccdbdabdaabcaaabdabaababbdaaaddbcdabacababccdaacdbbdccaacadccaacbddcabadacccbcacdbaadcccdadcccabbbddaabcaaccabddbdccbbbabcbabcdbddbaadcaaaddbbcacbbcccbbdccdabddddacadadbacaaadabccdcadddcaabccdbacbacdbdbcbdcadddcabdbbbcaaababbdabdbbbaddbbabbbabcbcaccacbcddabdbdbdbdbcbadccddaaddacbaabdbaabbaacacdbbddddbcdccbbcbcdabacaaacbddbcccacbcbdadcacddbabccddbaaccdcdddbbbccaccdbcbbddaaabaccaaaadbbaacaabababadaaacbcadbaaddcdcadcdccbbccbcbdabcacddaddcadcbabccabadbcabdacddbcdacccbdaadcdcbdddabbcccbaaabadcccdbbcdabadbdbdcabccadcdbcddcdacbbbdbabdacacbdcbdbaccabbadbccbdaccdcbddaacdaaaaadadbadabdbcaaaccbbbadadaccdacbbdcbdcbcbbacbaccabbddaccddaadaadddbcbdcdadcccbddaccbcdacdcdcbbbbcdbdaacdcccabbacabacccdcbcbcaacaccbcadbabcadbbdcadadcadbadbcacdabcbbabdacaabcbdddbaabcdbaadadabacbbabbacadadbbabacabddcccbcbdbbaacaddabbccbabbbbbabaaabaccaabacccaacaddabbbabcdcbabddaccbadccbbbadbdaacddbddbdacbcdadccbbabcbbdaadbdcccbcbcdacbbddddcbadcbcacaabbdbaaadaacaaccaacbbbdcabbddcdbbbcddbdbbbabadabdaaddddcbadbbcdddaadcddcddbddbdacaaacbcaabdbcacbbcacccbbcabaddacdddcbddaddbdaddadbaddcccbbdbbcaacacbbbaddaaacbdacdcbbacddaddcaaaaccbabcddaaaddaaaddcdbaddcccdddcdbdaddaacdbaddaccadccbdddbdcadbabcbbbbaaabadadadccdadbbcaaddcaadbcabcbddabcdadabaaadcbdcabdacbcabbbaabbddabdaabaadcccdaaabbadaddaabaddbdbdaacabbcadbcbcacbcbdacaabdabccbdacdcbcdddcacbaaababadbdcbabcbcbbcccdbdbabcccbbbabacbddacdabcdbcbbdaadacabcaaaadbddbbcddaaabcaadbccdbdcbdcccbdbacccaababcdddabbbdbdcdcbcdaabbacbccabadbcdcaaddccaabddabcbbbdbbdddadcbabdbbcaddadacadbdbbccddbbdcbdbdcbaaccbdccddcccbadbdcddacbaaadbccabcbbdbbdbbaaadddadcdabcbabaccdaacbdbaddbdabadcccabbbadcdbbabacbadacbbcdaadcdbcaacaabaabddadcddbcbccabdcdcbcdcbabbadddccbabcdabbcdbccddbcacdabaacbcbcaaacabdcbdabcabbbbbbdcbabcdaccdbbcacdcdcdbccdbdadadddadcaabdcacbcdabbaababadabbababdaccbadbbadcadcdcdcabaacbccbcadaccccbaccbdddbacdcccccddcdacabdbbcabcbcbcddbbabcaccbdbccaccdcddcaddbdbdbabbbcadddbbabacbbcdbcabdabaababbbddabcadaacdbcacadcbcadbaddcdacacbbdbddccdbbdcbbabcbbacacdaaccaabccbcaccddbadacbdcaccadbdddcacacdaadaacddababacdbcdcbbcacabbcabbcadcbabcaaabbcbaadbbcdbcddcadacbcbacaadcddcbbaacddbabbcacaaacadcadabccccadbdacbdcadcdbdbbcbdccbcccacacbbcdbaaacadcddbcacaddacacddabdbbabaddcabdaacdcdbcdbccaabdbacbdddbdddbddbdabdbbbbddacadbdcabcdcadacbbabdbcdbacbaccdabaccaabdabdcabadbdbbdcbdaabdadcbccdcbcccdcbdccbbbbbaaaaadcbdbbbbcbbcacbdccaadccdacbaabbaccaccbdbacdaadbdacacdcbdabbdbcdcdddbabdccdbbabacadbaaaacdacadcdabbbcdcccddbdabaccadcbaccabdadabbcadbdababdbcadddcaadbaabdbaddcacddddbcabcddbbbadacbdbcabcdcbdbdcbccacaabadabdadacbbbcaaaddbabbcabcbdcdcbbddbcdbacabbbddabbdcadcdacaacdcaabbadcaadcbcbccddcbcabacbdacaaabdabacdddbddacbcbdbbcbabdbbddaaaabaabddcccbbbadddccbcddaadcabbdaababdadcbadacadcdbbaddabccdddacddbbaddcadadadbdcdaabbcbdbccadcbbcdddabcbcbcddbdbcadcdadbddabbadadbddccbdaacabbbbabdabddaadbcbddaabcdcdbaacabdacbdbcdcbadbcdaaaadbcaabcacdbcdcacdbdbdabcddbadaccdbcaadaabbbbaaacdbaccdabddbcabddaccddccabacdabbbcabcbdcdbaddbcdcbaccbdaccbabbdcddbabdddbadadddbabddddcbcdaaadcccbbbcdacaaabcaadcbdcbdbcddddadacabbaccbccdbabdadddcdacadadcbcbdaddcabbbccadbccdaaaabccdabccaabcbbddabddcbcdcbacdcbdcbdbddabacccbbcabccbadbdbadaacbbbabdcbbbdcdbdabbcacddaacdbbacaabacdcdbcacbcbcbbdccadbdbcbaaddbabddabccacabcbccaacbaabccdcddcbabbadabdadbcdabbcdccbdabddcdbdaacacabcdacdbdbdadbdccbbddcbaaaacbbaacaaaabbccaccadbbcdbacaaacaaaaddaabddaaaddbcbcbdddadaadbcbdccbbacacbadcdcdababbdacdcbbaabdbcabaaddcdcdcaaaccbbbabbdbcacaabbbabdbbddbadbcddccdbbcdbbdaaaaadaccbdcbbbcabbdcddadccdcadcbcbdcaccbbcbddcdbcdabddabcbbdadcaadabbbdcaabaddabdcbdcddddadbddadcdaabcacaaccdccbbcacbabbdbccbdacdacdcacbdcdaadcbbdadccacdabddddbabadaddcaadbdbdaacaadaabbcbababbaccbddccdbcabdcdcdabbddbabbaaccddadbcaacabcbabdbcbbcddccbdadbadacaaadcbdcdcdcbbdcaacdddbbbdbdbbbacabcccaabcbbaddabcbdaadbbccadaabadbcadbaabcacbadbccababccadadbadbbccabbbdcdbabaccbacbddcbbcbbbaacbcbdabcbaccbcaccabaacbcddabdbcdabadaddaabcadbabdbcddcadcbbacbcdacbdadacabcbaaaadbcabcbaaaddcadddccdcbbbbcbaadccabdabcbacccddabdaacbbbabbddccaddddcddbdcdbdcddcabcbaadadaacaaddcaaacccabdcacabbcbacaacbbbacdbccacdccadbdbbbcbadabaaadcbbabcdadbaddabdaabbdbdabcddbadcbadcaacaccbabcbdddaacadcccbbcaabaabaadadbcadaababbddbdcbddaccaacbddaacbccddabdbdbdcddacaaccacacababbaababdcdbbabcabadbbddbcbdaddabcbabacacbcbbdbaddbdbabcaccdcadddbccbacaacdcbaccaadbdddddabdbdcbcadabadaccbbbdcbcbaabaaabdddcdccddaaaabccaabdcabbbcbaddaaccabaacddbbaddcadbdbbcdababccaaabbcdaaaddcabadcacddacbabaaccddbdcccacabababdaaacbbbcccbcbbccdaaabaaabaaacadcbbbddbdccabdaddbcdacdbacbdbabcbccabddacacccdcabacdacaaddababcbccbdcbabccadacdbdbbbbdcaabdccddddaddadccdbadddadcccccdbabdcadaddacadddabbadadcaddadcbddcaacaaaaadbddaacbcbbbbdaadccaabddcaacdbbbabbabaccbcdbcbbdaaccdbbacdbcdddacddbbcddccbccaaddbacacbbbbadcbdccdcbcbdbadbdacadcbcbacaabcdbbcdacdbbacccccbdddbddaacaaabddaddbbccaccadbcabcdcbacbccacacbdbaddaacbaccdaaaccbddcaadcbbccbccbccaacaddcbcacaacaabcddbccbabdbdbaababdbbbacdcddbadccbbaacbdababccccccabdccddaacacdadbdcaacabbbaddbbbcacdcdbadabbaddbbccbdcdbdbadccaacddaabbcdbcdcaadbabbbdcddabadcaddbddacbbbaadcaddcbdacdcdadadaaddcdcbbccdbddbdaabbbadbbcccacadcbdaddbacaadccbabdaabdcdaddcbccbdacadccbbbccccaccbaadddccddccaacbcbaabcdbacbbdbbdbabbbadddadcaddbcacbaaacdddbbacdbaabddadbbdbbcbababacdbddcbaabccccbddccbbdbbdccccbbbaabbacdddcdabcbdbbaacbadbdbddcddababbacbbbbbbaaacacbbacdcabcdbabdcadacdbcacadabaccbbbadbbdcaacacbabaadbcbdbdbdabcacadcdbbaddcdcaaddcdcbcbacadcbaccdddddbbbcdbdbaddcaadbbbacabdcddbdcacdbdbbdccacbbbbcdcccddbdcaaaacbadddadbbadbdbcddbabaaaadbbadddbdcdcbabbaadddaaaabaaaacccaddabbbbadcdddcbbcccaddcabdbdcbaabdadcbdccdcaccdcbbabdadadadbadbabcdddaabaaddcdbdcaadaaacdccdcdaddacdbaacbbbccdaddcdddcbbddaabbdddccbadadbdaabccacccbbaccbbcccaacadbbacccaacddababbaaddabbddbadbcbbdcbacdbbbadcddbaadaaadcababcaabdbbccacbabbdcbdddbbcbadaccdacaadcdbcbcdbbcadabddaacddbdddcadabbabcaddadabbbadaabcbdbdadcbadacbcdadddcddacadbddacdbadbdaaacbcbbcaacddcbadabaddbcabbbcddadabbddccaaddbccbaaabdcccdcabbdddcdccbddbbdccaddbbdbccbaabdacddcbbccacbabddcbdabacacbddddcbbddddbcdaccdbddacacaacaacadddaabbdddababdaadcdbdbcbcaabbaadadaddabdabbddabcdccbdcabccaddbdbcaccbacbddcccacddaadbbbadcaacaadaadabbdadbacabbdbdcaccaabccbaccccdcabcdcddccdcdadbcacbcbdadcbadcddbdbcbdbdcacdbdbccadaaccbbddbcbcdabdabdadbcbcddcaaccaddacaadbcaabdbacadabdabbdccbbbdaabababdabbdcbbbdabadcbbbcdbbdccacbaaddabbbcbdcccccabdadcaacaaacaabcddbadabbdaaccdaaacccbaaddcaaadcdbbbbdcdcaadbcdbbaacbcadaadcdbbdbaadbcdbdbdcabbadbbbdddadccadacbcdbdbbacacbdbbcbcabbabcbddddccdcbbbdcbcbadadbcbbabcbdaaacbdcdbbaabcddabaabcdacbbccadddabbbdcbddbccacbcdccbabbbaccadcadbbbbbaabddbdddaaccdadacbbccddcbabaaabbddddadcaaabbccabdacadcdccdcbdabcdabaadcbbbccdbcdbddbdbddccadadadadacbdacaabacbaabadabbcbacabaabacdcbcbddcdcbcabacbabadadcccabacddbcccacabdcbbdabacacdbaacbdcdbdbcdcabaaaddacdacaddbdccaccdcdddbbaadabbdaaadacdabbabbbdcdaaddddcabdaaccddccbbdadaacadcbcabbbdabdccdbaddabcdbadcaadbcaccdcabbccdbccacddadbacbaaaaaacabbcccdccdbcdbabdacbbcdcabdccaadbaabbdadaaacbacaaddcdaaabcbacbcacdbaacddcddaddddacbaaaddacdcdbdcddbbbbababcaaabbaaadaddbbcbcaaadbbaccadbabccabaccacccaacdacbcccacaaaddaccdbbadbdbbcdaacdbadbbbcaaacdbcddddcddbbabcaaacbccacbbbdbbdccaaaabacacabacccccdcddaacdbabcabccdacbddbadaaadcbaacdcbcddadaabdcdcddbdbdbacaabbacadbddbcdbaacbddcaadbdbaddadcdbcccbccdcaabcdcdcbadaaaabcadbbbdaabccbbbddacaababbabadcddaacddbaaabaadaabddcccbcbcbbadadcddcbbdcaabacbcccabbabdcabcabbdcdbbcadbdddbbcbcdacddcbbbbacdcadccadbddcbaddddaaabaddccccacbcaacdcabacadbdbacdacadabbadabcaabcdbbaccdbabbdcdaaaadaccbabddadcbcabadadddcabbbaabbbaadadbdddbaabaacadccdcacacdcdbcdbaccccacdbbcbbcddaaaabdbaadbdbbdabddabadaacbdcaaaddbcbbbcadcdcbdcabaaccacbcbbdbabbadababaabcccccacbabaadcbbdcddacabdcaacadcdcdbbabbbcddbabbbadbdaddbbcbbdaadccddcadabbbdbbbbcccadacbcbcaadbbacdacddbdddacacdadabbcaddbbbbabbcdcacddbbdabdbacbbdbbbddcdbaabacacbddaadadbaabaddccbdbaccaabacacabdadbdcddaabdbbaacbbbcbbcccccabccdacaaccbaddccadddbdaaddbbccbaadabcdaadbadbcdbcacadaadaaadddbdabbdbbcadacadddbddadbbaacacdcacbddadbdbcacaaaddbdbccdddbcbbdcbbccbacbccaddbbbcacbcaacccdabcaddbcacaacdccabdccbcdaadccabdabdabbadaabadaddcaacaadaccabcdbdbbccbbcdddddbdaabcabcacdbcbcbcacccdbadbabacdbcdcdbabddddbdabcdaaddddbcbdaaaacbccaabcdbcadbdbabacdbacdbccacbaabdbcdadcdbdbaaaddbddaddcdcdbacacabbbcadaadabbbcbadcbaabdadacaabaabcbcbdcaacacbdaacababdbcccdcbdcbaccdabadacbcbcaaacdacbdddcccadacbccacdddddbddbbdddacdaabadcabcbccbcadcacdddadddbacdaacdcacdabaacbacdacbacacbacbccdddcbccaadaacacbadbcdcdcdccdbdcacbbcaabaaccbcdadaddbdbcaadbccbbbccddcaacbacaacadbdadcdacbadcddbcccaddddcbccaababdaabcabbabdbabdbcbcaabbacdbdcdccccaaaabcbccbccbcbacbccacbdddadcaadbddcaaccccabbdbadcadcabbdccdadcabbcdcbdbdabbbbcbdccdadabcabccabbcbaaadacadcababddaaccdbcdbbaadabdbaabbcbcdacbabbdaabaddaadcdcbcdccbdcacbcbaabcdaccabdcbccbdbacccabdddbdccdbdaccadbdcbacdacdbaaddddcbbadddacdccabbabdcaaadabacadcdabcdcccabbbaacccdbccabccccadcaaabacdbbcdbcdababccbaabcadbbbcacaacaacabdbddddbccccabcbbbdbddadcaaadbabcaaccdddacadcaaacbcacacbdadcbbabbbdaadaccaacbcdcaaaabcccddcacbabdcbcbdbbcddbccadbddaadcddcbbaacbddcaddbabcbadcccdcbaadbdbcbdbadabbbbaaacacabdddacbbbaaaacadaddbbcaddcacaadddaabccbbccbdcaccdabbadcccbbabdcadabdabbdbbcccbbabababcadcbcddaddabbbcabacdacbbadddcddcddbbccdccdaaddacccaddabaaabbbcbddccdcdcbccbbdcdbaadccdcaddbaabadbddaacadccbdbcdacdcacdcaaaadddacbabaadbadaabbdcdddacaddccbaabcaacadabbdbabcaacaccdccdcabbabdccbaabcdddbdcddbccbcaabdcababacccddcdcbdacacccbccaaabcbadcabcbbbcadddcbddbcbbbddaabbacbcabbaccdabcadaccccaacdadbdcaabdcddcbaaccdccdbdcbddcccabbaacccccbdbcdbdacdacacbadbdcdcbcdbcdbdadbbabdcacacabbbbabcacbddbdbbbbcbdcbccabacdbdbabcbcdcadbdbcadabaccdadaaddddabddbcacdbacddbdcbbdaabadbcdaaacaadabbaacccbdadddbddbaddcbcabbabbbdbbbaacccacadbdbccbadcdadcacacacbddacaadcccbadcbabaaddddcaacdddacdbacbaaabaadadcaddddadbbaccbbdcdaabbbabccdcdacdcaaacbcccacccadabcabcbbcdcaaaaaccdcdbdcdbbadbacdbbbaabcdaacdbaadcbadbdcabcdcddacadbddbbdaacabbabacdcbbdbadaddbbaacccaccbbdbdbcdcdbdcabacdccdabbacddacbbcaddbbacaaddaacaadabdbbadabbacaaaccadabdbdbddcbdabdddccacbabcccaacdbbbbdccadabbdadacadcdddcbabbabcdddbdadcbdacabbbdadabcacccaabacabdccbbcbbbbbbacbcdbbdcdaacbddcdccddacbaadaadccabdccaccaabadbccdbcacadbabddbdcdaacbdbdacaacbcacbddbcdcbcbbbcdacbbdbccddbcacaddbbdbbaaabcbbdbacbabacccccbaaaddaaaabacdccadcdaddbbcacbcddcbbbbcbdaadaccccbbdcdaccabcdddadadbabacbdbaacccdbcdaacddbacccbcaacbcbcbbcdaadabccdcdadabdcdbdbcbdadddbbbbaaacbddacdcbabdaadbaaacbaabbaccddacddcbbdbaddbdbcaaaddadacdccacaaaddbccaccaddcbcdbdaadbababcaadaccddaabcabdbcaacbaacaccdddaaaadcdcddbdacabddacbcddbabcbaabdccadadcbdbbbdcadbabadbaddcdaabbbdddcdddabdbdbbbbbdaacbabcddccbbbabbaadacacadcdacdabdcabcbdabadbabbadbddaaacabbacaadcddbdcadcddadbdddcacdacbddabababcadcbacdbcacbcdbcdddbbbbbbdbcbadbbdacbbdacacbbbaaabaaabcdbdacbabbabbabdabdddbdbcdbadabcaadcbcddcaaababcdcbccccaacdbadaddbbbdcdabaadbdcdbcbbdccbcbdbccabdadbbdaaadcabbbdabdabccdcadcbabbabcbaddcaadcbdbcaacddbbcbddadccdbdddcaababbacddccbdbbaacccdaadbcaccababcabcbabacadcbaaadacbacbbdbbdcddbbdcaaaaabcccbbdcbcacbaccdcddadcdabcdbdcdbabadaddddcabbbdcbacddbacaaddbabcbabddcbcbbaacdacdaaaadddadcadaccdcdcbadcdcadabcbbcccbbbabcbabaacbbaadbbbbbadcddabcbbdbaacadbaaccacbbbcbccacbdbcccbaadcbcaaaadccdadaacabcdddbacababccddcdcacbbbbaabdcadcbbbbcbabbaaddacbbabbcbcccbadcdddbbbddacccdacbcbdbabaadccbcabaabbbbbcccdcbbacddaaccdccddbabdbcadcbbadacacbdbddccddbcdcabddaabcbbcdbbabcaccbaacdccbbdddcdcaabdcbddcdabdbdbdbddcdbdcbcacdadacaddccdcbababacdaccbaccaacddacbaaacdaddacacbdaaacbccdcacbdbdcdddbcdabccddbcbcabdbbabddddbbaddbbdacdbbacccbbcdcbdcdbaaabaadadbbdbddcbbcadabbadaadabaadbaaaaacabbbdbbaacdaacdbcbabcadbddabcdddbdcccabcbcdcbccdabadaabbbdddcadccabbbbbaacccdcaddabbcdcccdddaabacbbdbdabadbabbbdcbdcacdacdbccbdabccbdbbaabdbdbcacdaaccbbaacdaddbaddbbbbbcdbbdccbdbbdbcbcbadccbcdccbddbacbaaaacddddddbdcdddbdccabadcdaddcbdbdddacddabccbdacaccbbbcddbcadcdbbdddccbaacddaadbaccbbaabdaabbdcccbcccbdddcdcdadbaadaaadcbaabaaadcbcadcaadbdbabcddaacabdcdaadbadbbababbbcdadcccdbbddcadcdbadcadadcaddbccaddbcbcbacdbdcccaabacdddccbdcbbbaabdcbddccbbbcdbadabbcaadccccabccbcccbdbbacadbcbabbccbdcadcbbcbabcdcdcabccadaccadcdaddaccbcabdaaccbdccdcccbbcdaaabacdbbdcddccabccaccddbcadcaddbcbaabbccdacccdabaabcbbadbacababbbbbdcadcaaacdbdddabdaddacbcccaccdcadddcabccdcacbbbdabdccdaccacdccbadddbaaacccddddacbdbbacaccacacdadbbdbabcacbccdcccddddbbcbacdadbdccbacddddacdaabdbddabacaaccadadbccdcdcbaacacdbadaaccbbddbbbaaaccdbcdaacbcbdadcadaaacadadadaaadaacddbbabaaccbbcdabaadbcaaabbdabbbdbbccaccacbadccaaaccddaacbacbbaccdbbaadabbdcccdbccbdcabaaacbaabcbcaadadbadabcdacdddcbcdababbacdabaccdadcbbcdbaaaaadcbbdccbccabbcdcbbcccbdbcbbdadcdabacdcdcabdbdabdbaddbadaaccdbabddbdbcbcacbbbabdcacaddcadabaccdbdadbacbdbccccdaacdcddbabccbdddddddccdbbcaddcdcbdcddbabbcbcbaaaddadbdcbcdccadaabbcabdcbacdddacadcabcaddbdaacadacbbbbabddbcdacbacaadaabbdcddbccadbbacadbcaaaabdcabcbcbbcdbcccdbbacdbcaacbddbdcbcbdacadabadbcbdcabddccacdbbcabcddcbabdcbdcabbdbdbdbcabbabaadcdcbbddcdbaabcbddddddccdbdcdcdaccacacdabbadaccbdbddadcdbcdacababcddacddbaddabcdcbabcdbddacddccadacbbdbbbdcdacbbcdabcbacddddaabdbbadbbaacddbddaaaababdcbdbccbcbbacbabbcacaacdaccadadbdababcccddcbcbadcbabbcdbbacdbccbacddaabddbcaaacacddbabaabdcacdacaacdbadaccdbdccbdacadccdcddbdbdabbcbcaaddbaaddabadcddcddbbbdcdacabcacaaabcdbccacdbbdbbadbaadcbdabdaaabcabbbcabdccbabbdbadacacdddbbacdabbdbdaabccdbbbacdadbddadbdcadbadbdddaaccddbcdccadccdcaaccbcbadbccdacacbbcddcbadaaacdbbddddbddbbabacacddadacdcadcbdbdbbbdadabcbcddaaadddbdccbaabbbdccbabadcabbbaabbaacbaccddaadbbbdcabacdacadccadbaacdbcddcbddcaccbcbddbbbddddbdbabdadcdbcabcabadbdbbcdbdcccdaacccbdacbbaaddabcccbcdacdcdddccabddccbdbbbbbcddadadccdbacadbcacaabaacaaddbaabdabccabacdbbaacddacadbbdcbaccabacbaaadbcdcbabcdadbdcbddccbabcccbddacaadbbdcbdabbddcdddabbbabbaadbccccbdbaabbccaadcbbbcaccadbaadccbdbddaacbdabdcdacdadacadbdcdcaaadbdbdbdbdadbbbcdcabccadbabadbbabddcddbdabaddbbaddddbacbacbccadcdbcbcccdddcccdcaacbbdacabbdabccadabcdcadbacddccaaadaabdcaaabaccddbcccadabadcbcdcbadccaaabccdbdccdbbccbddbcbaadcbacaaadbbdbdcbcdcbabaababccdabaddaabadcacbabbacdadabdadbddcbddbadaabbdacdbdcdcacaaaccabaccbbbaddbacccdccbcddbabcbbccacaccaadacbcaccaaccabcabdcddcaacddcdccbabdadacbcacbdddbaabdaabcdccacbddacacacbbaaadadabdaabccbdaadcacabcdaacbbaabcacbacaadacabcbdadcddbdadcadaacbcaadabbdccdbaaccadaadbabadbdbaddddadccabdcbabcabadabcbcccddacbcdcaaaaacdddbbbcbabcacabbbaaacccbbcbdcaaadabadaaacbbdabcdcdbdcbadbadcbcdbccaccdadddcadcccbbbbdbaccacbcbddabbdbbddbbdaccccabccaddbccdaccacdccbacdcdcbcbaadabbcaadabdccbabdcccccbccaaaacccdbaccbddbcbadcccbbdbcadbcbccbabdcccccadcaacacdbbbcbbcccbbcaddcabcadccccabdcaddbaaadabbdbbbaddaadbdbaadbccbcdbbddbccdaccaaaacbdabaabdddacabcaccbdcbdacababbadcdbbdaddcdbcbbbacbbdcbaccccbaddcdcbbbaadbbdcdcadaaadabcdccdcadaccdbcdddcadbdbdccdaccdcccdddbcbbccabbcdbabccaacbadcdbbadaddccbbaaacbccabaadbdcacbcaccababbaacadcdcdacdbbddbbdacacddbbcaccddcaabddbbadaadbacdcbbacaddadcadcdaabacbbbdabcbaddcbdccbcbdddbabddaadbbcddcdaccacccadcacbddaccabdbcbadbcabbbaabbcdaabcdaacdcbcbbbbdaccaccbaccbdbcbdcdbbcdabbcddcdcabcbbbabbcacbaccacdaccbddaaacacabdbabdaabbbdabbbbbacaccbadcbcbbbabadaabaababcbdbdcdaababdbcbacabdccbcaccccadcdcaddaaabcbacadcdbaaccbcaadaabdcdabcaddcdcbcaddcaaabcbccddccbddddbdbaabcddabbbbdcabbdcbaacaaaacbcccaaddbbcbdaccbabdddbcaccdcabaaccbaadbbdbcbccbddbbdddcaacdbbcccabdabbcdcdbcddaaaabdccaadccdccbddbdddccdaababadbcacbbadbccdddcbcdbcbdbabdcbbbcdcdcdadcbaabdadccdaddabbacaaccccaabdcbcccabcbacdaacdabdaabaabaaabcccdaddaaacaddabbbdacbddcdadcbbdaddbcabdabcaaddacbcbdbacddcbacbacdaddbbbbddcbcadbdcbbdabdaacabacbaccabadddabdaacdbabbccadadaccbdaadcaccbcdbdbadcdbbdadacccbdbdacaaabdddcacdadbcbadacccaaacbaabbdcbcddbdbadbbbcdadaccdbddacdacbaadabbcaacbddaaadbdbcccacdbccabadabcaacadadabdbabbbdbdadaccdddadcacaabcacacbbbdbaccdcababdabdddbdcbdcabacadcbbacbabacccdacccabddabcabdcccdbcabddcaadbcbdaabbcaccbbbcdddaccdadbcabadcaaababdabdaddacdabcaadadccbdaabaacbcadbadbbdccbabdbbbbcbaccbabbddbaaabcacccaddbbbdccdcdcbcdbdcaccdccdacaadccdbbbcdbcadabbcdcacdbbaaddccdcadabdcddccdaccacdaabcbaaadcbbcbddbdabbcdbccddcdcabacbbaccddacdacccabcdcbbbddaddadddcdbabaabdcdddcdcddccbdbacacdcaabcadbcabbacccacbcaabdbcbcbbbbcdcbdcdddabccdaaddacbcabbdbabacbacdbbcacdbbaaaaaadcbcdcddacbcacbddcaddacaabccacccddcaddcaabbdccbdcbdaadacadbccabbaacdddccaddbbaadcabcadaabcdaccdabadaadadadcddcbbcbcdcdadbdcbcacadacbacaacdadbddcdbbcdccbcdcacdcbacddcbacbcbbcacabbddcdbdaddccbdaacbaacadabbaabdbadcccbbccccccdaddbddcacbadccbadddcdcacdabccabdaabbcaaaaaddaabbdbaaddcbabbcdbaccacacdadbacdbddbbcaccaabadacaddddbadabcddcaaacccbaaadbdbbddcaccadaabcbddbaabbcbdcdcaaabbcccadbcdcdacbbccdccabdcdcacdbcacdaaaccbcabbddcdcaaaddccadddbcdbbbbbcbcdbdacacdddcdcbabaaaabbbbcaddbbcabdccbadcabddacbdaacdbcadabbcadbbdbabccabdccdabdabccbdabcacbbdadbccacbbdccacdccdaabcaabcbdbbadbadcacbccccabdbaabbaccdcbadbaadddbbdbdabddaabdcbabddbcaacacbcdcbadabbccabccccdcadbcdbddbcdaacbcabbcdacbcabbdcbcbaabbdbacddcaaaadadcdbbadcdcbbcabbbaabaacbacbcbccbbccdadacdcadddddbdadadcdacadacddcacaaacabdccbdccabcbaddbdcbdacaddaacaccabaddcbbaccdabbbddbcdbcabbcabbcaccbacdbbaabcbabdaccaabdcddaacacacccdbdcdbcddcbbabaacdbcbaadbbdaacbababccdcbabdacacbaccccaddbdaadacbabbddaabcaddbbbcbdddadcababacacabcdbbdccaabcacbddaabcabccdbbadbaaaadabacdcabbaccdbcbbddaccdccbccbdcdcbaddbdddbdacaabbdcdcdabdbddbdaaabdaccdcaccbddccbccdaabdaabbacdbddcdababcaaacdabdacdabdadcccbadbdbaababadcabbcadabbbcbdabcbdaaddbcdadadaabdaddddddddacdccdababdaadadddacaabacccacaacddbbadbaaacdaccdcbbbbcccccdbdadadbadaaddddddbbdabddbcddacaabdbadcbbabccacaccbcacdbbaddbcbdbdaabdcdcabcadcccddacbcdbacabaacdabadacdddccacdaaababcbdcbcdcbccbbaadcdcaacbdacaacbbdbaddcdadbbccbbddabdbcababddabddbcdaaaaacdcdaadadbbbbbaddbdcacbbccacbcadbdbaccaadcacaadacbbbacbacacabccdbacacdbacaabbddddcbaacabbabbcbabcbcdcdcbcaccbddbadabbdcaabbdbcadbacaaabbdbbbcbdbcaacbaabaacaadcdbacbbadbabacacbbcdbbaddadbbacdaadbddcbcdbcbabbccdccbbcbbaabbadcacaabdaaaaacbbbdadcabcdbbacdadacdaaccdccddabaabbbdbabdcadcbdccbccaaaacbaddbaababbcdcacbaadaaacccaabacbcddbbcaddcbbdcbcbdbbdaabcadbbdbabdbaddacccccbbdbaabbdbbbacbccbcacdbdbcdcddbdbbbbaadcccbaabdabddcbaacabbdbaaabbacdabaaababcdccbacdcbaddacaabbdbdcbaddddcaddddacdacabaaaadbbbacbabdbacbbaaaadbadaadbaddcbbbdaacccdaacbcbdadbbadbadbbdcdccdbbaaacadadccdddacccbcacbdcbdcddbccacababcadabaabcccacdbdbcdaadcabbcdaadcadcabacadccaacdbcbdcadbbabcaaacbdabbbccdbccdcadcddbdacadbaabacdabcbbcacaacdadaccbbbddcbcadcabcccbbbdbbcacbbbbadacabbcbbadaaddccbbcbbaddcdbddcbaabbdacccabbcccccdadccdbbdcbdacccabdcbccbcbbbadacccbabcddadcacaacabcdcdabcdbbdcbbcddccdddcabaadbcaabbbdbbadacaabdbaabccdcddaadadaccbcbbbbcabbcbaaaccadaaaaaaabcdccdaddbbcbddcbbdabddabbcdccdaadcbdaaacdbcddcaadabcbbbddababcdbbaaaacadddadbdadcdaadbbbadcdadbabbbcbbdccddabadacccabdbaabdacabdbbddadabdabbccdabbddcbbcdaadadbdabcdbadccaadcbccccdaaaccabadaacbcdadddaacbddcaabddcccbdbaddcacbbccbdadbdabdacdacbdccabaccddbbbbcbbcbabcccdccbbbbaabcdbdbbdbccaaaaccdacaadacdcdadacdcbcdaabcdccdbbbbdccbbdccadbbcdabbccdbdacbaabbcdacdacccddbadadbcabdccaacdbdcdbdaccacabdccadabcbdabbdbcadabbcbcdddaacdbacdaacadcbdddcabbcdbabbcccacababcadaccdaaabdcaaddbdbcdccdadaacdcaaaaabdcbddccbaaabdcbadbcbcbdccdcccbdcaadcbcbaaadbdcdbaacccdababadcbdabbacdabaacdbcacdcadabbacdbbddbbcdcbdabccdbcbddadbadaadcbbaacdcaacdcbdbdacaccddcccbbacdcbbcabdbaccdcdabacbccaddbccddabadddbbbbbacdaddaaaaababdcaadacbdacdadccacabbdacccabbbcbcacbabadaabacbddaddbbcbbddcbcdddbaacdaabddadbbaadacbdaaabaadcdccbdcaabdaabdbaadcccdaadadaaacddbddbbdcdabcbbdadcccdbbcbabaaccdbdbbdabccbbcacbaddabcaddcaccbadcabdbbcdbbcbabdcdacdbadbadbdaadccadacdadcbabcdbacaadbacadbcabdaabdcabcbbcddbbcdcbddbdababacdadcdbcdbacabaabadbbcaabcacabbabbacacaccccabbaabcbbadcaccbcdbcdbabbdbbbbbcccaadbddaacbdbbccccdddbbaaddacbccbabbdcbbddadabdabddccabbdadbbdaaaaabdacdccbabbcaadcdbadcdbbbbdaaacabbcdcbdacaabaccadbcbcccbdcaccadcbcbadacbbcccadbbbbdccdbacbdbdaabdaacbacbccbcbaddcccdbbbddaccaccdbcabdaaadcbbcdaabcabbbacddbdadbddabbbcbbbdcdccdaddcababbcbabadacdcababbbbcdccbcacacaccacbcadbadbcadbbddcbaacdadbbacbddcbaabbcdadcdadcccccabcbcbbbbdabdbccbcdbddccdcadcacaabcadabbcabadbcdadadaaaacddbddbabbcdabcbdcdbcbcdcacadbbdcbabaaaaacbbabbaddaaccccdababbccbcdaccdcabbbcbaababcbbbabacabcbbdbcabbdbabcacbbccabddddacccdcddcaddddaccbbcdbacadbccbcbbaabdbacddccbcaaadbbdddbbacdbdbcbcdabdbcdccdadadddbcacabddaabbcaaacabcdbbcbbddcacbadccdccbcdbcdaaddadacccdabbccdbbbabacdbbacadccccccdbdcaddbbdddcdadbbddbadbabdcbdcdbbccbadccadcdbcdaacddadbdddbccbbadaaaadddaddcbaccbddddbcdcabbcddcaaaddbadacbbcbcaccbbccbdabacdaddbaadadcccadabdcbcadcddbdaadadaabaadcabcbbdbdbbdaddcabbcbaaabcaddabbbcdbcaaacbdbbddbdbbcdbcdbdccccdbbaddadaadcdabcccbaadadabdadbabcaaccccdbdabacdddbdddadcbdabaccdaadaaaddcdacddcdcbacbccbbadbabddddbcadddcdddbbcccbbdcaaacdcbdcadcdaabbcbbcacbaacbacadcbaadadaccbdadaabcdadcacaddaabbabcccaddccbcbcdccbcaacacbdacbaabbccdacdbdabcaadcdadcaadabdacbcadcdadcadccdbcdcbcabdbaddbcdddaddbbcbddbdcdacbabcbbaadbabdbababadcddadaaaaaccababbaabddcacbaccbbcaddcddbdbcacacccccabdadccaaccdbacaabbbaacdddccdcdddaacdaacababcdcabcabdbcbcdcabccaabadabdbcaccccbddaaddbddddbbbbcccddcdcaddaccddbbaadcdbabcdddcdddcbdbcabcabdddccbcdadbabdbcbdaddabacdbbabaacbcbdbdbacacbcbbadbcdcdaacbcadcbcbddcccababccdcbbadcacbabbadabaacdabaaccacacddabcbaadcbcbbcaaaccadabdcadcbdcbabcaccbabbadaddcbbcbcabccdabcdaccbdaddccdbbaadbdaaabdaadccddbbadadcbbddbadbcacddddaadbcadbdddbabdcdcdbdadbcdbbdacbacdabdcabddaabaccbacdcbdbacbacbbadbbbadbbddcbcddbdbbcbccdddddcbcbcbdccaaabadbdaababcbcacdbcacdbbdcbadbbcbabccbdadaaacdbdccdacbdcadcbcdabbccdbcbaabadccbcbacccdbddbcadcccacbdaaadabbbccbdadbdbbdccbbcaccadacadabbabcbdbdcacdbdcdbbdccbdaacdacdccdbdcbbbacbadcccdacadbaddcddbcacaabaddccaaaaccadcbddcdbcabcababcaccbdbdbabdcdbbcaacdaddbbcadbbbccccbddccbcdcdcabcbaadbaddbdcbaccbdcdacabbccadbaaaddaabbdcdddabccadacbacbcabcadbbccbacbaacddabacbdababcbabbbddddcadbcbbaaacccaddacadcccdbdbcadcbdcbcbdcddbdbcababdadcababcabbdbbadbcabcdcbdddbcccaabdbabbccbdacdacdcbaadbdabdaaddaccaccddcbbaddbddbccdacdbdcbabbbcbaabccdbdbcbabcaddbdbabdadcdbbacaaaccbbdddbdbdcbddbdbbbbdcabdcbdacdacccabdbadcdcdacbdbbacbbcbacdbacdcdcaacdcadbbdbccdacbcacdcbbbbbacdbbcbbadbbabcadcdaacddcbbdccadbadbaababbdacabcabbacbaabbbdbdadcabbbdbdccdbdadcacbbdadababadbacddabcdcaaaacdccdbcddbdaccacadaadbbbadddaabdbbdbabbdbdbbcbbabcccbdcadbbbaddbbddbcacacccddacdbbdcbaaaccddadbaabaacbdbbdbbdacadbdccacbbadabdcbccddaadbbccdabddcadabcbdcdcaaccabaabdbacaaccaadddadbdcabacbdcdcdcdbbacddcbcbcdbbadbdddbbcbcdabcbacacccaccdacdcbccabadadbcdccccdcbaadbdbdbddabddccaacbabaaacdabbbdccdcaabdadaadcaacdbcabcabbdbaddcccdbccdbbaddbddccddbcbbcdacdbcddcbbbdbadddbbabccdbbaacbaaabdcdcadaaabbbbbdcaddcaaaccbdddbbbdcaacbccdcbcacaddbcccacbcabddccabbabdddbdddccaaccddbdcdcabddbadccdbaacbbbcacbddbaadbcbacccbadbadadcaaaccdbddbdcdbacdbcdbadacdcbbcdccdbcddcbacbddabcddcdbcaadddadcbaddacbdaccccadcbabaaaadccbaacddbccdcdbbabaacccbdaabcdccdaddbaddaadabcadcaadacdacbdbccbdddbdaacbbdddcabadbccccdbddcdacdcbacacadbcbadaadcdddbbaddcbbcdaacdbadcacadcaacbabadbaccbbbdcbadbddcdbbabbabcbddbcddddabacbaaadbbcadbbdccbadadcbcbabcbbbaacdbdbcabcdccdbaabbadbbbbaaaacbadccdabaccbddacccbabaccaadacaabcdbddadcaaaddadacdbcaaaddabadabcababdcdcdadbaaccbdbbbacdbadbcddbbaccdcabbcadbbddabdbbcdcdddddcdcbdddddcabdcbdaabadcbadbcabadaabbbdadcabddbcccabdbcaddabccadbdabacbcbdbcbdcbcdccabdcaaabbddbcdabcbcbaaabddbcdcaaccaaaabbdaabaaaaababbcacdabcddadacbdcaddaccabcaccbcbbbbbbbadcbbdcddbbdaacaadbcbaaabbbbbdcbdabcdaacddcbdcbcbcaaddcbbdaaddbabdadccbbdbdaccaaaccddaaadcdcdcdddbbdaacadbbdccdcaaaacccbbbbcbcdacbdcaababbdbccacdacbdbbcbccbaddaadcbcbccdacdcdbcacddcacbdbdcdaacbdaadaadbbbcacacdaaaaabaabdacabcadababccddbbcababcdcccccddbabccabadcbabcacbccacdacaaadabbababdbbcadcddadcbdacdcbbcddbcabbdbdbbadccbabbaabdacbdcdddbdbcbcbcacadddadccacccaaadadacabccacddcdaaaadbabadbbabacbddbdabbdacbacabcacacbcacacbddccbcdccaadabcabadadadccdbddccccabaadbacaabcadbbaaaaabaadcdcaabbccdadbabadacabccbccadbadcbaccdbbbadabdaacaabcbbdcdbdbcabcabdbdbcaccabcccbcccbaadcbcccdcbcaadaacbcbbbdbdcacaaadcddaabbbdadacccdaacadbbcacdbbcacdbcdbccdaaadadaaacbdbbabdcbddcdaaaadccacacbdaddaaabcbcdbdaddbbddbadaacdbbcacbabdddaddacbcacabbddaaaddbdadbbaacbaabdcabbbabccadbbaacbcccabaabbacbbddbadbbabddabbcbacabcccccbbcabdbaacaaacbcccadaaccbbdcadbcbbbabdaaddcddcbcabcdcddccbacbdbbaabaadcdddddddcbbdddabbcadabdadddcbbbcbdcadbdcabdabbcabdadcbabbddddbbbbadacababcbdaccccdcbcdaacdbbaadacbabbabbbcddabbddcbbcdcbbdcdccddaababbabbdcabbbbcddbdaccabcbaadabcadbcdabcbddcaaabcbcaacccbdabdaaabddbadcdbbbabdbabbcacabbcddcddcbbbdadacdccadbdcddbdcbbcdbcaacdabcacadbdcbcabbdadccccaacbabbddbdcacdccccadbdabbccbaddcbcbadcbdddddacbbabcbccbdadbadbdcbbdccdcbcacbcddcbcddbaabbdbaddcbbbbdcbcddccdbbdbadadbcbcddccadddbababddcbabaddcabddcbaacdbddadacadaabaccdccbcabbdbbcacdaddddadcdbabacdbbaabcadcbbdcdcccaaacbaacddcaacddccadaddaacccdcdcacbcdcbdbdacaccdcaddbcdaababdbbbdbdddcddbddbbcbcacadcbbaabcccaabbcacabadabccbaabdcbabbdcdddacddcbdcbabdcababbadcbadacdabaabdccbdadaccccdcdaccddcdbdcacbbdcbdbbbacaabbbcdadbadbcbbadaddcabbcccdaabbbbacacdcabbdabddddbccbacbbcdcccaccacbaccbbdcbadaadbaaddbcaaddadddccdcabbaacbcdcdabdbcdabcdcbbbacaaaababaaaabcababbbcbdabcdcdccdadacbbbadbdccacdcdcabaaacaddbddbacaacbaaccccaaabbcdbabcadbcacbbdaccadcadccbbccbbdcabdcbbbdcdadbcbacdbadcabbcbabacabbdaaddbdddcdaddcaadbbacbcdcbccbccdcacbcccacbcdccbbacbadaccccdbabbdabbaabdabbadbbccbcbbcbabbaadaaabaccdaccbdabcbdbaaacdadaccaacadbcadadccdcbbcabcabdcdcccaadbcadcbccbcacbcdbdabbbbbabbacabbcddbbdcdbadbdccdccaabcbdbcbcdaadaabaabaccddddcbdabbbbaaaacadbaadbadbdcdabdccbbccdccacbabcccbbadcddccadcbdbcabbcaddcccbabcccbacbaaccdcdbcbbadaadaadbacdbdabbdcdaacbaacccdabcbaabdacadccbaabcbbadbacdadbabcbbdcbabdcddccccbcadbcdcadabdacdadbccdddbdcaaddcbdaaccccccacccbbdcadbdcdbcbcabcccbdbcbaaaadbcbadccdbbadbdbccdcbcaabcccaabadbaacaacdddcdaabadcaabbcadbdccdbcabcbdaabcdbdbabddbbadbcadcdadaddddbaadaccababdaccbbbcabaadcdbdcbdcababacddabcacdaabbdbdcdbbcdcddacadbaccdbacdbacabaccbdcabccbdddbcbbddbcadaabbacbdadccddcaabdadcaacdbbaccddabdbdbbbbcacacbdccbdbbcbccccdbcdbbdbbcaddcabadbdddbddbadbddccbaacdadbacdcdbabdaddabacaaddcddcddabbcbdadcbdaadcdbacdaddcaaabaababbbdadbcbacdbbbcabbcbadcabdcdabdcacdadbbbcabdaaacacaacdbdbddaaaddbaaacadbdddcbccadabcbdabacabadcddcaccacadcccadcaccbcdbddaacdaacdddccbbaddcbaacdcdcbabdbdaadcaddbbbabadccbdbbabbcbdcbaccdacdadbcdadbdccdbccbdaccadcbbacbaddabdbdbacbbadcbddbbcabdaadaabbcdcaddacabddacbaccaddadccbadcdacabdcadcccdcdbbadbbcddcbcbdadbdccbabdcacddaaaccbdccbdadabdbcbbbbabdbbdcbdadddcbccbddcdadccdcddcdacbacaadcbdcccdbbcbadaacacddaaddbabacdcdadbdbaaddccbbbacaabadbbdbbdbcbadbcdadabbccbcbbdddcbdadbabcddabadcccccdcaabdccbccabcddddbaccabbabbddcacaadcabcbddbacabdbcbbaadaadacdcccadacaccccbddcacdbdbbcaddabcbbccdabcadbdaddaccadaababbdacdaabdcddbabdddbabdcdcdaddaabdbbaabcaddcddcdacccbbcbddcadbcdabacbcbdcabccbbdbdabacaabaaabbadadccccdadacaabcbadcbbccbadcbbdcdcdccacaaacddbddbddacaabdadcadcdaddaababdacdddadacabddbacaaacdbabddabdbbabcdbdddcddcdbcabadbaadbadcccaabbdbdaaacbdddbddacbbacdccaabccadadaaddddaabadadacaacdabcabdabbcadbddbdbdcdddadaadcacaabddccdbbbdbbbbdabccabaaadbaabddddadcbcdccddbcbabccdccabcacbddadcdbcadcbabdcbbcddbdcdccbbabbbdadadbcccbdadacdcdabbcdadaccbdadcabcabbaabcabaddcdcadaddbbddaabacacaddabbaccbdbabcddcadbbccabbdddccdccccabbaabacbdbdabccacacbcacdddccdcdbcdcbddcbccbbdcbddbcadbabdaabbcbaabadabbcdbabcbddaadbabadabadbaddbcabccdbbbabadabdabadcdacdbaaabdddbccddadbccabbcabbbbadcdcaccbbbacbcadccccdbbbcacbdaddadcdccabbadacccddbbbcadcbccddbbcddbdcbbddbbdcddbcbabcaaaabcddbadbbaabaadacaddbaaaddbbbaacacccccbdbacdcddbaacdaadbaabdddbccbdbcadbbccccbcdbbadbbbdaddabaadcccabddddabcddcaaabaccdddbacdddaddbacbdaadcdcadacadcbbbdcdccdbdadaccbdcdbbcddbcdccbddaaddbdbaadadddbdabaacabbadbbbbbacbdddaabbbbcacadbccddadcbabaccadbbacdddabdddacbdbcbccbdddddbdbdbdcbacbddabdcbbdcaccdcdcbcbbbccdcdcdcabccbcbacccbabcacadccddcacababdcdbbabbcaabcdcdaccddbadccacbcdbacbccbcbccbdbcdbadcbbbdbdaabcbadabccabbdcabbcaddcacadbcbdcbabcdcdbdcdacddaddbacdccadcabddcccbbbccbbcbaabdaaaaacaaadbbddbbbbcbdbbacacbccbbcbabdccdadcbcabdbbcdbacbadcbbdaadbaddaccbbdabcbbdadaadcbddcbbdbdadaaabadbdcdadcbdbcbacabbddddcabdbcacaccaadadadcadacdbbdabaddccbabbacdbdabdcbcdbdddbbcacddbbbcacbdbbaddcaabbbacdacbdbadaadddcddcdaccdaddacacbbdadcbcbdcbbbddadbdcdbbacbcdadabbbadabcccacbacdbcccabccbacddddabddacccabddabaacdcdababacbbcbbdbadccbdcddcbdbcdcadbcddadaabbdddacbdcabaacdbcdbdcbbbaacadaccccdacdccdddbcbdddbbbcabbdadaadddbabdcdddddccabaddccbdbccacccdcdcdbdbcdbbabdcbbaadbdcbbcbbabcdacdacaacddbaddbcabababcbbbcdabddadddadbbccdaddbcdadcdddcdadacadbbccaaaccccdcdbadabdbdcadbabacccdddaccbddddddadcbbbabaaacabdbccdaddbbccbdbbacbaadcdcaadaddbcbbccadccdcbccbaccddbddcdcabbcacbabdcbbcddabcacdaadabaddcdaaabcaaabbdabbcdccccdbddcdabdccacaddbaaddacacaddbabdabaaaabbdbddddbaddbbcdbbbddabbaacabbdddbaacdabcadaabdbcabbbaadadaccdaabcbddaaaddacbaadbdaaddccacbdbdccdbbaddbcadadcabdbcabbcdcccaaaccacdbabdbacbccdbdadbacbcbcdbacdacccbcbccacadbdabdbccbddaaddcdcdacdaaddaaadcdabbabaddbcdbbbcbdbccbcdddbbadaabbbbadaacacdddbcbbcaaaaddaababbdcdcdddbbacbaddddcbcdcaddaaaabcbbddbcdbcdcbabacddaacccabacddbcdaadabcaababaacdaccabcaadbabbacdbacacbccbdcbbbcdbadbdabaabcadddbaaaabbcdaabbccaddddaadcdcbaacabcbbbacaadcaacbabdbbcbabdcddbacbcdcbddbcdaaaabbbbddaaacacdaaadadcabdccdacdbdcbdbdccaabcacdabccaadddabcbcdcadcdccbdddddabadcaccabdcdaccaadbadabaccaccbadbdbcccbcadcbacddccacacadbdcabdadcadcdccccdcacacbbcadbbdbddbbddddbacddbaccbbcaacbacbcbaadadabaddcbdcddbbdcbcccadbdbdadadccbdbcaccbdbabdccdbadbcbdcbcdcacbccbabdccdbbbaddccbbabcacabbbbdacbdbdbcbdadaaabbdbbadacccaaabbbdbdcbcdbccaddbdcababcbaccdbdaaccccdccdbbcabadbaccdbaabcdaccaaccddbadbdababdccbdddbacabcabbcccacdbaddaaddcabdcccbcbdabdaabbddaabbaddccdbccccdabbcbabbdaaabcaccddddcdaacdbbbbbdabdcdddddaccddadabdbddbddbbdcabcadddcbcbbdaadcabacbcbbbaaabcccccabbbbadbbdaaddcaaacbababdacccbdddabadbddbdaacddcbaabccaaddccbbccbbcdcabbbdaacabdbdbcbcbadcadcaadcddbcabaddbaacdbdacbbbccdcbddcacadcaacdbcadaadabccaabcddcabcdaddcbdaddbbaabadbddbaaccbddcbabacdacbabaccbadbdcaaabbcdbdbbadaddadbbabbbcdaadadccbbbbcacccbbdaddcbbcaccccabcabbbacdccdccbbadabdcddcabcdccdddbbddbbcbaabaaacadcbccdbdaddddabcbacbdcdbaaaddbadccccddaccdacaabbddadbddbccabbbaabcacbbcbaadbdaabbcddbcccbdddccbbadabdcdbdabbccdabaaaacaadbaccadaabcdababbcacaaadcababadbccbaabcbbdccbcadbabaddabdbcbdadacbdbaaacabdcacacdbacbadcabdddabacbabbcdcaaadccdccbaadbddcacccccbbacaccacbdadbdbaacadbadbbdccbacabbadcaaddddcaddadcdbcbdbaacbcbccddccbccbcabbbabccbdaaabacbabaabcaddcccdcbaaddacacbbcacbadcdbbdbddababadbbdacdbaadadcbbbbbadacbabcaaaaaccaabacbacbdbdbabcbbcdadccacdccadcaccdbacadddcaaabdbcccabdcbbdbcdbbabddaccacbcdcbdbabdcccbcdbcdbddabbcdaddccbaaabacbcbbcccddaabcaccaddabddbcdbbadbdaadcddaccdbbccccbabdbdcdbdbcbdaabbdbdacacddababddaabbddacadbddacbbbaabdcbcbabdaacbdcabdcabcbcbcbabcdcabcbdbabaacadccbddcadddbaadaaaadcccbcdcdabcdccbdacbbbaaccbcccdccabdbdbddababadaccbdbabcaacbcdbcdcacaaacddacdcbbadbababdaacabaadbacbcacbacbdccaabbbbdcbacbacbddbadbcdcdbdddbbbadbdabcbbcdcbbdbacacddbbdacbbdcdbaabcbcdcbddcacdbdacdcdabcbdadcdbaadddbbcabdacaaddadbadbabdbdccabbdbbdbcdbdadbacadadbaccdadbbacadcccdcdddbacacccbaabaaabdbdbbacbdbccbddbdabbcdcdadcbbcbadbdbaddaccbbcbcbabddbcdbbaccacccaabadbdbcdabbddccacbbdbddaabcdadbdcdbbbdccbdacdcaabcbbddbbddcbdaadddcddbddaabaaacabbacbaabdcdcdbbcbacdcbbccbcdcabababdbcadaddddbdaddbaccadbdbbdccbcbdbabcbbbcdcacaacdcbabbbddccadccbbabaadcbbacccabdadaccdabcdacdcccaadbaabbaadbaaddacddaaaddcbccbccdbbbddbdddcbbaabbadcbbcbcaccdcddbbdccdbbdcdcbadaacaccbcbcbdcbaacacddabbbddbdaddccbcbdbbbddadcddbdcdbdbdbbddbdccdadcbdabbaadaaabbcacaddddbbaabdaccbbbaacdcabcccdbcbbbabbaaaadabccadccdacaadbaaadbbcddbcbbcbbdbadcbbbddcacbadbbcdcddababddbaccdabbbadbccaaadcadacbddbccccaacaaadccbbadcdcacaccccaaabdcbcbbaaadcbbddbdbbbaddcddddaaabbcadbaaadcbdabdbaabdbaaacbcdcbddddbbcccdbcdcdcbbdcacdaaabbbaabddcbbacdaaccbddbababdacaabbaaabbadbdddbbaacabadaddbbdbcadacbabcdadcdccccdcadcacadcbddccbaddcacaabdcadadababadcaabbcdbdbcabddabbdabddcbacbdacadadbdcdbbaadaadaabcbdbaabcbcbcaadbccbaccbbdbcbbabcddccabddadcdadbdccdbdbaaddbacbabddadbbbccbbcbcbacdcdcdbdddbddbababcadaaddacddbbbaacbddabdbbcbdcbdbadacdcddcbdccbbaddbcaabadcbdcbdadbcdbbbdababbbbacbdbdccacbdbacaabaacdaccdadbadbbddcccacbabdbdaddbbcdbdcddcabcbabcdccbbabaccaccbbbabacdcabbbaaaddcdcddcbbcddaacdaccadbabbaabacaadcbdcaccbcaddbccddbabcabcdabdbcccddcabbddbdbbdcdddbbccdcaacacacdbcdaabcbdcccdbbcccdadacdbccdbcddaaacdaacddabcaabaacbcdddbddcaaddcaabaadddcdacdabbcdbaddcddcccaccbadbadccabcdbdbdcabdbadcbccadbbdaacddccbbbdcdddcacacccbcdcabbcdbdcdbabaccacdccaddcdbccbcbdbdbbdbacdadcadddacbcaacacabadaacabdadccbdccbaaddbbbaaaddaddcadbccacbdddcdbdbccbccaddccbbacadbdcdcaabaacaadccdcbdddcadbdbdcddacacdacbaacabdbcbaabaccbcaaaccacddbddbcdaddccbbadbabcbababbdaabcbdddbaccdacaabcdbdaabddcadaadbbadccabbdabbbaacbabddddcddcbdadccadccbbccaaaddddbcddccbbcccdddccdbdcbdcccdaaabcbaadabcbdbbbaccacadbadabcddaacadcaccacaccabbbbbbadccccdbaaccadaaacccccccacdacbdbddabbdabcddadcabdbbadacbcbdcccbddbbbabbbbccaddacacbababbcbcbacbcacddcdcbccdadabbbaaacdcbcddccddbdacdabdcdacccaabbcdbaddbdddbcbbacbbbddabdcbbcbadcccababacabddbccbddbdddacccdabacdbbacabbacbbcccacbcabcacabbacbbaacacadbcccdabddcbabbccbadbcaabadbbbbdcaacacdacdcdaaaaaacbbbdacccbcacddbbdabdcadcadacadabddacaadcbccbccbdcaadadcdbadbbdabbdabcdddbadcbaaccaddbbcdcbdacdddaddacdbabbddccbcdbbbdaccddbbabcdcbbbbbdddabcbdcbbabbacdbcdadbdcadbdbabbbcdcaaccadccdbbaacdcacabbbbdbaddbaaababdcccdbdaddccaadcabdcdccdbcacacacdbcdbcbbbdddbabcbcdbdbcbaabadcbbadaddaabababbcbacadaabadccccccddaccdabccdcbccdddaadbaacaabacaccdaabcbdcdbcbbbcccddcbdadbdaccdcbbaacaaddaaaddcababbdcbdccabdccdbcddbdadcaddaddbddbbcbdbadbbaaaccdbcbdbadbcbcddccdaddbabaaccdbddbbcddcbabdaddddcccdbbdadbabdbbbbcbdbdcdccdbaccdbdbdbbdcbadcdcbaabdddcbbddcbdaccdcaabcccbaabbdcbdbabbddcaccdbcbababdcbcaccadbddccadddaaaabbcaacdccbaabbdddadccaabcadbaddaabcddadaaaacabdcaaaadccdcdacaacaaccbbbdcbdddddbaccccaacdabddadccadbddbadababcbaadadacbcbbabbdbbcdaccbbcbbbacabadadddcabccdbcccacaadddaaadbdbaadddadccbaaaadcbbbccbcdabdbadcbaaaadbccccababddcdcbacabdcdccdccccbaaaabbbdddcbddcdbabcabdccbdcccbdabcdaaaccdabaccddaddbababacbabaabbddbbdbdcdcccaaabcbbbddbdbaabcdcabdcaacdcbdddbdbbabbbadaaadbddaddccdaacbdcbacdcccdccbbdabbcdbcbdcacabbdcccdbbdccbcccaabcdcccdadaddcdbdcbabcbbadcbaaabbdadadbcbabdbccdcdcaaabcabbddddaccdbcdbcacaaabcadaacbacadcdcbabadbccccbdddddbbcabacabddaddbcbdadbbcaccccddbcaabbadccbadadcabcadaccbbcdaadaaccacbaacacdcbccbcccacabacbabdbaadabaddcacdcacabbacdbabaadbabbbdbcdcccbaddbacccddabdccacaccbbaacdbabcddbdbdcbbabacbabaaaabcbdbdcbaabacaccbdabbccdcacbacbbaddacaacbcdaabdccacccaccabcdabbaadadbddcdabcbbbbacdccccbccabcabadaddbcdaaacbbaabbcbcabbcbacacadcbadbbbbbaadabbcdbacacabddabbcdbdbbdbdbacbbcababdcdadbcccabcdcaddcabbdaabdbadaacddaaadcbbcbaadcddddabbacbcdabdcbccdabcbabdcacdcaaaadaababaddcbccbbacdddabadddcbdabccdcadbaadccddcaabccdccdcaaccaadbcdcaaddccbcdcdbaabcbcbdcbccbcbabcbacadbddcdccddaaacddcadbddccbcccadcccbdbabcabdddcabdbcbdaaccabbaadddaaccacadcdaacbcdcabbdaaacdbaabbacadcdaadddbacbbcbabcbbddccddddcbadabbcbcbbbadbcbbbbdbcbbdabbcacbcbbdaccdcbdacddbaddcaadccaaadaccaabcabaaacacdbbddbdbcbbcccabbdcaadaaccaabadcdcdbabcbdcdababccabaababbcaabacabdaaccdbcddbdcdbdbbbbadddbdbdacdabdbabbabbbacaadbbabcadbbaddcabbbccbccadbcaddbbbbcbccbaabaccddcbdbcdccbabbdbaacbbbaacbaaabcbabbaabbdbbdcaacdbcdcbacbcbdaacdadcbcccddbbbadcccbdcdaabbaadbbaddbdcbdbadcddbbcbbaccaccdbdbacbddaacadccbbcbdcbdbccdadcabacdddbcbbdbbcbdbbdcdccdabbdbbdacbdcbdcdbccdddcdabbabbcdabdacbcadddccdcbddbccbddbdcbbdcbdadcddaabdbacbadcdadbbbacbddcbcacabdbdbccabcccacabbdccabbddcbbcadabbbdaacdbdaaabbbbadaacbbbcdbacccdabaababcdbddbacdbcbdacbcacadcbacbbbbacdddacbbdddbcdcbcbbacdcbacddacbccacbbbacddcabbdcacdddccbacdcacaccacbbddbbdccbccabcbcadbacabacbadaddbcabababcdacbddacabcdccabbaddaaddbccabbbccadaabcdcccacbaabaddbbdcdbacdcdbbbdccacbccdaddabbbabcdacdbaacbccdaaddaddcaaaddccacbabccaadcbadaadabbadacbdccaccdaaadccaacddcddbcacbacadbaaacccaccdcbacdcbdcccdcddadbcaababccadbcdbddabbacbcddaccdadccdcccadacabdadcdbcdbdcaabacbdcdcbbdcdabcbddccdbcdbcbdadbbacaadddacddccadbaadaddbdacdaaaddbadbbdacdccdbacdbcbbdbdbadddaadccadcbcaadabdbddccdcccdbcadddccadbbddddbdbcbaaaaabbaddcdbdacbbbbbddcacccdcdbdcabaadaaddbbdadaaaadaacbaccabbaacadcacdbbdcacdccacaacbbcacaddcbcbabbcccbbdcaddbbccdabdadccbaadbaaacdcabdcbcaacbbcbccdaaddbcadacabbdacbaddbcccddbbdcbbddcdadaabddccadacaacdaacbdbbbacddbabdbbacacacbdadacbcdbabcddcaacccbddccbcdbdadccdabccacbbdadaccbdaddbcdaaabdcccdbdbdacdddcdddcddcacbaabcadacbaadadcbbaccdbacbcbcdaccadddddabdababdcdddadaddcbdbacaaabdbbdcadbdddddbadbabababdddcabcbabcccbccccbadbaabdbacaccbbdbbddbccdaabacaadcaccbdcddbcbccbbdacddbababcbcdabdbcbcbddaccdcdadcacdacdcccbcddaababbabddccddcdcbabaadacdbcdcbbcaacbcccccacdabaabcdbccddbaaaccabbddbabdcaccbdaacbbccbddbacdadbcbbcdabadabddddacaddaabcddcdbadbaccbddadcaddbcacadaddacdbcbbaaabbcaabbbcaddbaacadcddaccbddbbaabcabadbadbcbcdcbdadbcbaabddbabdbadddcbdbcbabbccbdbaaccddaabcdaababbbbcccbdadaddcabdcbacaadbbcdaddaaaaadaabaadcdabdbaacdacdaadadcdbdcabdababdacacbbcdccccacacccdccbddcbbadccbccadbaadddcdbcabcaadddbcdbccacbbabbccbcaacdbbdccaadddcbabacdaacbdbcddccbaadaaddddcbbbaacbbabbadababdbabcddabacadbbbbaccadabcabcacacbbdbadcdccdcbaccabdabcdacadccdcadccbccbcdbdcddaabaddcdccbcbabbbcaaadbbaaaadacbccaacddbdaabadbaddcccbcadaaadabdcabdddbddadddaddbdaadbcabddacaacdbbcbbbbadbdbcdbacddbabbaaabbbdbbcacaccabcbbbcdcddbddcabddacbadadddcddcbccabaaccadadcbccdbcccaabcccacbcbbbcadcdbdacbabdadabbabccdcbcacabaabdadccadbbdacaabacdddbcbbabacbdbcbcddbcbbabcccdddcacdaaaddccadbcacbcbabccbddddbbaaaaddddcbdbdaddacacddbbbabdaccbcaadcbcadbddababadaaddacbccaccdadbbcdbbdcdbbaacadcbbaaddbcadcdaaccacdddbcbccbadbaaccdcddacaacdbdbaadbacbdadbabbccbcadacbbdbbbbaabbaabccbdadaaaabbcaddbdabcdcddbbbaacddadbcbadaddaddabccaaccdbddcdbcdabbacbadacbddacbcdbdcaaaaadaabbdcdacdbbbadbacddabadcabcbdbbbdadadbbbbdbdaabaacdbadaadcccaadbbdbaabcbbabcdbabcaccdacbccababbbcdbcdccacbdbaddacdabdcbbaadcacadcbababdbdbcbaabddbdacdbdaacaacdbbaacadbbdabcadaccbdaacbadcaaccdddbdbcaaaccaddcdacdccccadbadccacddcadaaacccdbcacccdbccdacdadacaaaacddaccaadcaccdcddbcbbdbbbddbcdbdcdacacddabcdacaabadcaccdbcadcdddabccbaacaabbbbcbaccdccbccbbcdbdbdddccdbdacdadadcdbababbcacdacbdaabbacdbadbbccacdddcbcbcabddccbdbcacccbdabacbadadacbcacdbdcdabbabdadadbbdccadcaccdabbacddaaaddbacbadbcaaabcbbdcdcddcbabcaaccdcbbddbaaadcbdcacdddddbbbdcccacddaaccbdaacdcddaddabababbbadddadbcdbcadbccbbdbdccbadacbcbccacadbabddabbcccaaaccdcdacdcbdbcbcabaaaabacadddaaabcbcbaabcaccdddbbacdababddbdaadbcbbbacccdcacbcbdddcadbcdddcdaccbabcbbdcadbbcbcdddbcddabbdcdbdccddcacccaadabcbbbabcbacbccabcbddcdcdbcdcacbcdccacadbbdaababdbadaaddcbcabcbcccadbbccdbdcdcdbbcaaabbcddaabcaaadcaccadcccadadcaabaacbcddadbdbacdccdbcbdbccbdddadbabdbacaabdadbacbddcacadbacdbbcdbcabccddaadcbbcbbbbbabccadccaacabccaccccbaddaacabcccaaaddcadbddbbddacbcaacccddccaddbbbddcbddaaadaaadadbccbcbdadbbcbabbcbbbabbaabababcdcdcccccdbcdbbddbbabcdaaaadbabddabacacbbdbaabbacbabbdadaaddadacaddaadcdbacdacbaaccbdcdcbabddccdcccbdbcbcbbcadabbcdcacbaccdaacdcbbaadddbbccdaaadaccbadddacdccabaccccbaddbcdabccabcdabcbbdbaabcabcabadbaadbbdacbbdcdbbbbadbcadcdcbbbaaaaccdddbcccdabbdcadbdcdbddcaaabacbdcbaccbcbbaaccdaddbdbdabcbbbbdddccddccbcbdaadaddabdbdabcdaacaadbdbdcbbcabacaabbbbadcabdddccbbaaabcddcccadaacbcbdacdacdaabacccaddaddcbacabadbddbcabddadddccbbbacabadbccdcbdbcddcbaadccbbdbcdcccabadcdbbdabdcbdabcbbcabcdcaabcdcdadccbdbbddddabbccdccaaddcbccadacaaddbcdabcaaadcabbaadcbdbcaccccdaabbccaacaabbcadcabddddaddccbabaadacadbbddbcacbcdaccddbbdabbabadcbabacbbcdbddccdcbacddddaabaaacdbdccadddddcbcaaabbdbdbabccbbbdcaccacbbadaacdcdbaaabdcadccadbccdbdcabcabadcbacccbcaabcdbdcacaddbdcddaadcadcbbdabacddcbaacabdaacbacadaabcacddcdcabcccaadbdbbdbbabddbbadadcacaacccacabbbdbabbacaccccdcbdcacbdaddacacbcaabdaaaaabccccdcbdacddaabacaadccbbbcbbbbdbdcdadcccdbdbdcbdbdadcdaababdbbccbaacbbdbcdcddcbdacacabbadccdccabcbbbcbcdbdacdccdadbdcbdbdcdcbcabbcaadadbddbcdcaaadbdbbbbbdabbadcadbbbcbcdadbddbdbcabbcdcdbabdcdbdddaccaacbcdbbddadacabbdaddacdadcdaaaabcbcabaaddadaaaabbbbbbcdcbddddabcdcadabcccbcbbdadcdbcbbbadbddaacabbcacbccaadcbddcccdaaacdccdbcacdbaabdbcabcbdbbabdaacccbadaddcdcadddabcabdcdbdbaccabbabdcdcdcdbbbbdcbcdacaadbacccbbdbccaadbcabdaacdcaadbcbadbacbbabbaacddbcbabcabbcdcaadaddccdcddcdbbbbaacabbcccbdbaabcdcabdccaddddbcbbaadacababbaddbbcdadddaacadcdbaadccbbccbbdbadbcdcabdbdcbdcbcdbabcbacaddcdbabacdaaabaabdcaddbabbcabbadbaadbbadbdaabdbaddaadbcdadccccddddbcdbdbcdbcadbdbaacabadacbababccdbcdabbacbbcdacadacaabbabbccaaabaaddbdbcccaadccddbdddcdbdcddaabbbddbcdacbcadddadbdcddadbddbcdabccacdcbcdacdbddcdbbaabccbacabaaacddbbbadcabdbcbbdabddbdaaabbabaadcbccdbbcabcaddbadadcdbcadccbaadcaddaabcdbcdbbabacbbdddcaddcabbbadcbdadacabaccabaadbcbcbcccdbbbccccdacbbdcbabcdadbcaaddbccbddcabccabcaabcbadbdaddbcdbabadcaabbcdddbdcbddcddbccdcdbbcbaccacdacbacbbddcbacdacccacabacaddbcdacbbadacdadabdbbbbdbbacdddacbdadbccbcbcaadadacadcdabbbbcaccadadbcaadaacdbaaaacdacdabcdddcdabcdadbdbcddcaccbcdaddbcbbbaacdacccabbadcddadbbaddcdaadccbcdaaabacadbcddddbbdaabacabcbcddaadbddaacadaccaccbacbbacbbcdaddbdcbcccbddcaadccbadbaddddddccdcdbdadcbcbdaccbabacbbddccbbcddcddbbdabbddcaabbddcbcabadcaaadcbadbbcdabdcddbcddbdcaacddccdcddcbaabdccdbcaacddcbbbcbcbbdaddaabcdcbdcccbbcbccdbbdbbdbbdbcdbaadadaadaddcdcbdcdadcadbbacadaddaccbdccdccadccadadaabccdadadbabbcaabdbddcdcabdbbdaacaadbcabdcbadccbbaccdcbdbaddaacccdbdccadbadcaabbddacaddaccbabdabbaaddccccddbbcccbccdbdcdaaaccbbadbcdbbdddbcadbaaaaccbddbbcadaddbbcdcbbcacddbabdabaaadaabddbcdbcacdadbdcdbdabaaaabacdaddbacacadbddaabdadddcbccbdbaaacbddbdbcbdddbbaaabacdadcbaddddaaaaaaaccdccdbbdbdbddaaacdbdcdcaaaccbabdacacbaaddababbbaaccdbcbbddacdcbbbaaacdbcbadaacddbcacbcbbaacdcaacbbabddabdbabdccabaaaadaccaddccbbaacdbcdcbadbbbabbcbcbabbcaddbaabdccaddaacbbbdcddccdcbcacabcabbabcadbcdbdbdddcbcccacbabadbbaaabbaddcbacaabadbaacdaaaaabdbdbadabaabbcabcddccccdadadcbbbccabbdbabbaaabadbdbcbdaabdbcdbacccdbbbdacadadcdccdcdcbdacdabdcaacadbaccbbadcbdaaddbbdcacbcacadaccbabbcabbcbbccbaaccbbbdddbbacacdcbddbadbbdbbadddaabbdbccbccbacbcaabadaaadbbadbabadadbcdddbcabddcbbaaaacbbaccabdabcdabdabbabbccacdccdabbccddcadcbbccbcccdbabbdabccdcdcbdcabbdcbdcdbcdcbbdacdcdbcdcdbbacccdcaddbddbacbcbcacadcbddabadbdaacaaccbbacbbbcaabcacccadaaccccbccbaddbcdacbdcabcdccacddcdabbbacacaaadbccbabcabbacdacaddadccaabdbacbcdabdccbbcbccdcbadbaacabdadbdacadbadadabccccbdcacdadcdcbbcbadcaddcbadcccdcbcdcbdaadabdacabcdaccaabdaacccbcaccdcabdbaabcdadaaadaaacaddaddcbdabbcdaadbccacdcccabcacabacdbaacbbabbbbaccddaddbdbacbadaccadddcaaddacdadcddbbcaaabaacbaadbccbddcdaabcccaaaaadadbbddbcbccaccacadbccbcbbbbcdbbcdcbbaaabbcbbdbaadaabddbaddbdcdacccdcabbbbaabbbadbcacacabdddbbadadacccdbcdccccaaccdccabdacdababdbacdbacdbcbdcbddbdabdabccadbabbbbacadaddcdadacbcbbccaaabdabcbabcaacbddcdccdacdacddadabbddcabccdbcdbdbbcccdcbdcdaddbdcbacaaacbabbcdbbdbddccdccbdddabcaacdccbcdbdacccdaaacaaadddabacbcddbcdaadbabacbcbbcbdaacdcaddadcbdaaddadacdbbdcbbaaccbcddaabcdcbbccdcbcbddabbccbadaddbbcdcdbddbbbdcdbdabbcabaddcddccbacddbbbddaaabacdddbabbabbbaabaddabdccddddddaababbcababcbcccacababbbddbcaadaccbdcaacbdbdadbbaaadacddbacdccbdcbaccaaacaaaadcddadabddcacdbcbcbababbaacaaadcdddaaabdddbdcadadcaacadbccdcbbcacbabcdcdddaccabacbdbbbaaddddcbadbbcbdddadadcdbacaadbdcdcdcbddadcbdacbcdabadaadccbbbdacbdcbccabddbabbdbaabbbacaaaccdcddcbcdacaabdcadbcbdbbdcabbadbadaaabaabbbdaddcdcddacdbbccaaadcbadddcbdcabcacdacbcdcdabadabadcddadcabaaadcbdcadabacbcbaadddadcddcbbdbddadddddaccacbccccbbcacabababcbcdcbddabccccbbbbabadacbbaadccbacdbcddbcdbbacccbbdbcbbadbaabdcddddbbddaccdaacbdbaccadcabbbcdcbcbbabcddbacacccdddbaccadcddbcbbdbcccabbddbbacccabbdccbacdbaaabbbbbdcdaccdadaacbddcaaaabcbbdbbcdcbbacccaacaddacadbabdcaadabaacabccddbbbccbbadaccdcabaacbddbbacccbbbbdbcdcaddacdbccdcaadcbaadabdcbdddbadcaabdbbaabdadddcadddadaacbbadcddbaaccccabcdbddcacbcdadcadddaacddddccbcccaaccdbacaacdbcadaddacdcdaaaaccaabcbadaddacbbdbcddadbbbbacdbaacddbcdccbcbbcdbccddbbdcdcaabbbbddbbabdcaccdaabdabddccaaadbcadcdaadadcbadbbbabbdbbabaabbbddaacbccacaccadbbcbabdaacbaadaabadbcdcacacdcaabbdaacdbccbcdcbcbbcddcaabacaddcdcbcdcdcbcabbbcaaacaababaacbbdbbdbbcbacdacbbccbdccbcaccbadccddbbdaaaccacdabacccbcddbdddaadbcdddcccbdcddaacaddcdaaaabaaaacacbabbabdabacaabccdabbbbbacbdabcccabdabdabcdbbcddbadcdabddbacbdacbbbaadbadbdcccbcbaaabbdcbcaccbcaababcabadbcaaacdbabdbcddbcdcabcbcacccaaabddcbacddbbadcabaccdccdabbddaabbcadddcadabdcdaabaccaabbcacdddccddcbcdcbcdddcbdcccdddbcdbbcabadabcdadbabbaacbadabbdccacbadaabbcbcdadcacaacabaaabdbdbbccbbdbaacbbbdbacaadabaadbbadcacabbbdbdbbacabbdcddbabcdcbcdaabbcdacbbaddcddaaccabbbbaacbbabccabbddacbaaddcabcbacdbbdaabbccaddcdabbabccdccaaaddcccbaababcbcaaadadbddadddbccabadbaccacbcdcdccacacbbcbdacbdadcabbbbabbabcadccbcacadcdbcdcabbcdcbbdbadaacadcdcdcacaacbcadbbbaaaddcddacbbbbccdcdaccdcbacbacaccaaaddabbabccaaaaddaaaadbaacdcdaccabdddbcddcaaabaddcacadadadadaabdaabcddbcccccaccdcbdcaacaddddbdcddbacdabdcdaadaabacddbaddddddaccddadadbacddaabbabbaaccaaddaabdccbbcabcbcadabdbacdadaabadaccabccdbcddadbddbcaacdadcdcacaabdbaabbaadbadccbacdbdacbddbcbbcccdcacbcdcbabdbbbadcabcdabccadccaacdababcbabbaacadbbbddccdababdbbbddddcbdadadadccaccddadaddbcacddabacbdbcacbadaacdbdddcbbacdcdbdadbcabccaaddcbdcdccaadacbbadbabdaacbdbbabddcbbadcbabdbaaccbdacbbdaccaddddbcaacabddcbadccacdcacbdbdddcdabadbabccacccaadacbabbbbcccdcbdccdcacddaaacbcdcbcbbbddabbadddccbcaddddbbdccaaaacbdacdaddcabcbbcacdacdbabdaaccbaccbcadcdabdcdcdbadccadcccaddbaaabddddbbdbbcaabbbdadbacacaabbbccdabdccccacdccaabdaadccaaddbccddddcdaddcbdbadadcabbbddcddbbdcccaaddbadbcdcabccdddcaddcdbacaaddbcdbccccaabacddcdbacabdccacbaacadcacbbadacadccbbabdbcbdaaabcacaddbacabccbbadbdddaacdcacdabdacbdcaadaaabaabddacdabdcbdbbbcabdacbbbbbaabacbdcadaabbbbdbbdacbdcccbaddababbbbcbaddcdbbdcabbdbcdbbcbabdabbddcaabacaadadccbacdbbbadcdbbddcdbbcdcddcabcccadbacdbadbcbccaddcbaaabaddccacabdacdadbdcbbccdaddbccdbaaaaababadddddaccbdcabbbccdcbdcddabdcbccbddddadbcaacdcaadccdccbcdddbccdabadacabcbddababacddcaadcaccbacaadbbdbbacaabbbdaabacccaadabacbabdadaadbdbacbaccacbdddbabcccaddbdbaaacacbdcdddaccbdddccbacdadcdcbababadbbccbaddbdbaccbbdbdcccddcaabaadaadcbdcbcdadbbdbcdaaadcbbaabaabdcbbcdaaadacbbadccaaddbacacbaabdcacbaaccaabcbababcadbcccacbcdddbdbdbcadccabacbddccccadaadcaaabcababbdaaacacdccbaaadabbadbcbbaacaddbcddbcdcdbbbdddcdcbbabbcaadbcddaacacdbcaacacbacdabadcaabdbbbdbbabdcaabdbcacdabbbccaccbddabdcaaaaabdaccdababdabacdacaaacbcbcacddbbdcbcdddcaabadbdccbacdadababcbbcbdaadacaabdcbbadabcaadabdbbabcbdbbbcccadcadbdbbddbaabadbacacabccbccdacbaaddcccbdcbadccaadcacbadbcddaaadadabaaacdcabbddcddbcabbcdbccdcccccaabccccabaadacdadaccdacbacdccdaadacddbbdbabbdabdbdbcdbdadadccbbcdcbdabccbbacdbddabbbbcccdbacbabdbcdcdbaadadcbcdbccdcacaadabcccccddabdadddbcbbcabaddaacdbbadcbbcccddaaddbacdcdbdcaabccbcdacacddadabcbacdcbdcdcadaaadabbadabbaccdbdcbbaadcdaccaaaadddbbccdcbddbbacddbdbbadcaabcbcbdcaadbdccccbbbccbbdaaadadbddbbdbdbdbbbbbbcbdcbddacdcadcbaabcbaaccacbcdacadbdbccadabcddabaaadddcddbbdbdabbadbddcaadcdacdbbabdbccaababbbaacdbcccdacccabacccccadcdacadbcabbcdabcbccccacaabadbcaccdcccdaacdcdccbacdcdbdcadadbcabbcbccadbaccbbbdbbcccdcbdcbcbbbcdddccadccbdacddbccdddbabaabcbdccdbbbaabadcaaacddcabddbcaaabaabcddabadadcbbcadcddbbacacdadaaadcbdbddcbbbccdbdadcddbbccadddbacdabdcddaabaaaaabaddcbddacddcbccdaacbcadadcdaabaabdcddaacdcdabcbacdbabcadbcdccbddaabcabadababbabcdddaabdcdcdcdbdabbddcdcaacccbcabdbcabadbdcaaaaaadcadacdcabbccdddabbccdcacacdadbccdcaddcdbabbccdadacbddabddacadccbcbdbcbcaddadaacbdbbdbdbabbbdbdbbbdcccadacdbaadccaaddbcbdbdadccaccccdddbcaabbdcccdbbbccabdcacbbdabacababdaddddcbbddddaadbccdabcdbddcaadaaabcabbabdcddadaccbbbacbcdbacbbcbadadcdcbbaaadbbcddbdbdbdbdbaacdbcbdccacbddabcdabdcadbcabdaaaccdcadacaaababbccadabdbdcdcabdcdcbababccddbddcccbbacaacdcbcbbccbbadddbdabacbbbcbabadaaadbcabcbcddadccdccccddacbdaccdabdcadccbddcdcadcadaaccdcbddabccbacbdbbdbdcbbaccdcbcdacbddabcbddadcdabacbdcdbabddaaaacaddbdcbdaaccdbaaaaadccbcdcbaaddadacccaacbcaddabddcbdcdcccbccdbadbbccaddbbacdbadcbcdacabdbdaccbbcddbdcca cbddbcbdbc