cacbddacbcdaccdccbccadabcdcacaacdbdabcddaabadcccabadcbdadbccdaababababdcadaacabbbdcbdccbadaacccaaaadcdadbcccdabbcadbbacadcdcccdddbacbcbcddbaccbcbadcdbccccacbaddbcdcaacacabbdbdcaddaaddcddcccdbccbcaccaacddccdddbbdacaaaaacbcbcccdaabadddcdbdccbcbcbabcbdddddabdcacaaccdbbaacdaccabdcbbadccbcadaaaacddccbcdddcaabcdcacabacccddabbcbbcbdabddbdcdcddbdccaacdaddadccdbcbcaaccbcababdddbacacaaacacaabdcdadbcbbacdbaadbabdcbcadbbdcbcacbcaadcaabcbdddddabbccbccaabadababddacabbdbadacbdaddbacacabbabdcaabcbbbddadcadcccadcbcbddcccbaccacacbbbbbbbcabccadaaabcdbcdcbdbacaabbbcbaababcdbacccdbcbddcacaacdccbbcccabcdabdadbbbbbaddbbabdadddaabdaabdbbbdabcdbaacacdbdbccadbabaabbdcdabaaccdadccdddadbbacbcdacaaaadbbcdaddbcbdbbbaabccdbbcadabaddbaaaadcababcdaddddadcddddbcdbdcdacaabbdadcccbdbcbddbbcdaacacddadccacbbbdccdcacccbaabacbdcbabcddaccccaaaabccbbbacdbbdcaaaadadcdbbadaddacaabaadabcdaccdacacbcbddadbcacbcbcadaccdcacabcadbdbbdccaccabadcdcddaaaccdbdbbaadcaabddcadbbcbbdbbcaaccabaaddbadcbaddcdaababdcadccaaddddbadbdcbccccdbddcacadcbbcbbbbbdadabcbdaaabaddcadcbabdcaabbbacdcababcdacbbcbcdbdcabbccdaadaacdddaadbdaccdcbdaaabacccadabcabacbcadadaadccccbdbbccccdcdcddbaacbdbdcccacacddbabacdbaaddcddbcabbcbcbbbcdaaabcdbabddaccadbdabadadcadcdbcddccacbaccbcbccbdbbcbacbcbdcbbdcccccaacbbadabddcdcccccaadccbacccbcbdaddbccccadccddbcabbbcbcdbdcbddcabadcbcacbccddbcdccbadacabddbcabdddcbcadbcbdacabccabbcacaadccabddcdacabdababcbcdbcaabcacdcccccacacaccabcbdcbdacdbdbccacdbcbacacbccdddddccaacadcbdbaacacacbaccccbbdaddcadbacbbcdccdbbdcbccacccdcabccdaaddaccadaabbddbdcdabbaadbcbdaccaabacadbaccccdcbbddcdabcdcdabaaacbbbcadacaabaaaaaccaadccadbcabdcbaadcddddcdddccccaddbacaaadcacdcdbcbbacabacddbdaccdcaaccbacacabddacddbbdcbccaaaaadbbddcccbbbadbcbbbcaadcadddcbabaccbabbacbbaadcbbdcaadbdcaacbcbaccbbbcdcdbbbbdbdddcddacbabcdbaadcaabbbccabcbcbbbdbadcadbcbadcdabaaacddddbaadbddbcbbddcacacdbacbcbcddbbbccacdbcdbcdaddaaaccccadbddbbacacbddacccabacdddaddadcaaabdddbbcdcdacacaccdbadabddacdcbccadccadbbcbcbdcdadcddcbdbccacabababcdcbdbcbdaaddcadaaacdcacccbcabbdbccaaabcacbdabadccaadbccbbdcbbabbcadacaabbcbcbaddddccddadbcaccbbabccadcaddabccddcbbadbaacabbbadbbbbbccababdacddbccbcabbaadbabddaadabdbbdcdcbdcadbddbadbcdbcbcdadadabaccdaacacbdacdaadbbccadbaadbdbabdcdabcccbbabbbaabbacacacdbacaacccbdcdddccbcbcacacbdadaccddccdccdacccbaaaddcabcdacdcdccbbacbcbbbaadccdbcbcbdccbcacddabaaccccbacdcacabbbbacbcacbabadbcacabccbabbdddadadcabdbdbdabcbbcbddbccabbabccbbbbbcdbbbbbcbadcddbcabcacdccadacacddcacadbbadbbbdddbbdacbcdbaddcddcbcadabcaddcdacdcacbacbdcdcccbaaddccbbbadbbabbdcdadadcccbccdcdaabcbacdbbaabcacabadddaadcaadcbaddbabcbccdbccbdcdadcddddbabddababdbdabccdcbccacbbcacddacbdcbabcaccdbdbcacdbddbcccdbbdaadadcbdadcbadacbacbbadcabdcbabdbdbbccdacaddcdcacbcbccbdccdbbbbcddadcbddcbaadbbdddccdabbdcccccacccabddbdbddabaabbaaacadccdacbbabbdbacbbbdacdbbddddcddbdaaacbbbaabcdadbdcddaabdbbcbcccababbcdadacbadbbbdacbbabcaccbdcbdccddbaccabcaddbbbddaadbddacdbddbabbbddbcadddabcacbdddbdadbcadbccadbabccdacbddabcaabdbccdccaddadddcacbddcaadccabdaccdcbaabdbaadbdddbbbdacabcadbdadbbdcabcaaadddacccabdbbabdcdadcaabddbbdbdadbcacbcddabdbcbacbdbadcaaaabdbdbcbccbdbbaacdacccdbdbccdadbbdadcbcddbbabcdaccdacdaaabcdcdbdbbdccbdabbdbaabbaaccdacbccabcdbaabdcbbadbbdbbacccbacdabaaddbbbacdbcabacbbcaaacbddbcdabacacabcabbadadbaaadaccbbcadddcbbdbbbdabcbdbdcdaddcbddaaddccaacbbdaabddcbacbdaaaccdbcabbcbabaadcbaadcabbcbcdbbdabcbcdacadddcdacdbbddadcdbabbdcdaddcaabbbcdccbacabdaadacccdbcdcbacabccdabdbbbbddbabddcccdbdbcccaaabdcbddcbcaabcbcdabcccbcbdcbdcaacaddabbbbcabdabdcabddadadbddabbbacbbbacdaaacaccbbadabdbddbaaddabccbacbccdbabddacabadadcbbababbabdcaaadcababacaadccdcdbcbbcddcdcbbcbcddbabcbcdabbaaadabccccbbcaaccdbadadbccdddaacccabbcbcbaddabacdbcdddabbbaccadaabcadbdadccdcccdadcaaabdcdcbadabcacabbaabcbcccaaacbbdcbdbdadbccddaabbdbccabbbbaabbbacbbbccdaaacbbbbdbcbcbbaddabbbbadbdabadcaccddccaccdbabaadddacbbcacbcdadbadabadaccacaadcaddbadbcbcdcddcbacdbbcdcbddcccddbcbdbaaadabaabccadcbcaabdcdadcbccdcadbacdaadacabaddbacaaabddabaadacbdcdacbaaaaddaddbdabacbaaabcababcadcaddbdcababbdaadbadddcddbdcdccdabdcccdadadcdadcbabdbbccacbbbcbdbaadcbbcdbbddbbbdadabbaacbbdccaadcbddaaccdbbdbdcbdbaccdbdcdcdddcabcbbabcdaadcdbaadaddddccaabcabccdacbadbbcbbaacdccddcbcccaaaaadddbdabcdacdbaaacabbdccabbbccaccbbbdcbcabcbbacaddcddaddadaccdacdbbcacbbdadcabcdacbccbdbabbbadabdccacccadbabcbbbbccbacbabcdcdbbaccacddcbaddcbdbcaaaacabaaadbbbccacdaaabdbddbdabdcdddaddbdadcaadcababbcbbaabccdbcdbabccaacbcbbcbcdacdbbabdddbcbcadcbaacddddadacdbbccbcabcddadbcdcbabdbcadaaccabbdcadacdbaabaccbbccabdcdabdbdddcdacbbccaddcbadaccbcadcdbcdcbaddccaacaacaddacddacaabacbadcdccdababdcdbcccbadbbacbdcdacabcbdcacabbbbcddabaccdbdaccbcadaabbcbaabbcbbcbdcdbcbbadabdcacdbddbabacccbcdbcdcdbabdcccabdbdbbdddbbdabbdddabcdbbadbcdadadacddcbbcbcdabcddcdcaddaccbabacdddbddccacbdbccadbdbdcbbbbacbbacbbadddadababbbdacacbaccddadddbbacbcadccdcbaaabccaccaccbaccbbadddddddabcdbbddbcbbbcbcaaabdbddabbaddbbbcbcbbccbbbbcbbccccbbabcbbbcdbbbdcdbdbbdcacdcbdbbdcbadccbcbccbdabbdabbdadaddcdccacbaacacdacdadccdadccbbbbccaadacdbddcbbcadacbaacbbbadbadcabdccdacddbbacaddcdccdaabcbcbcbbdbdacbbcaddcadbaacbcdacdbcccbdacacbabaacabbddaadccbbbdbcabcdbbaccdbabacdaccccadbbdcacaacbccccdaaaccaadddccddbbcbbbbcadbbcdbccabaabbcbdcbdbdbbbcacabdbdacccaddbccbbbadcacdddaabdabdddabccbadcdcaddccbacaaddcaabaaadddbbcdcbbcacdccaccdadcbcbbaacbaaadadcadaddadcaccdcadaadaaadaabccdbbcdcddacbdbadcbbdbaddbcbddddbbddaadadabccdbcbcbaaadcdadcdccdabbabdccbacdddccaddbdbabbdbbdbcbbbaaaaaacdccaddbabccaadadabbdddcdcbabdadcabbbdbcbddddbbaaacddcaccaddaacccbadccdcadbdbacbadccdabdbdacccdbaadbdbcdddbcaacbdbbcdcddcdbdbcdbbcbbaacdaacaccdcbbaddacbadaadbbbcddcbdccbcbcbcadcbdcdcccdbbbcacbcdaadcccaabddadacdbcadcaaddaacbcabbaaaabaaadcabcbaddabcbbbdddcddcdcbbcbcaaddabbaddacbcdbdbbcbddaddcddaaccbabaaddbcbcbdbdccadbcccdcbdacdabddabcbbbdbdcaddddaaddadcabacacabcdbbaaabdbccabbabcadcacdadcabcccbbcdbdadcbcdbbcdacabdcabdccbdddacbcdaadbaadabbbcaddbbadbcaddaacddccbaddbbccbbbcdacbdbacadbbbbbadbaabcbababcbbcbbcccddcbcdcadcaaaaadaccaadcdcaaddaadbddbdbdbbcccddcaaabbcaabdacaddadbbcbaddddccccabbcddccdbbbdacadbcaaacddcdbdcbdbcbdbdaccbcccddcddbacbccccaddccadbabaccbabbdbdcbbddcbaddaacbcdbdcbdbbaadabaaaaabdbadccbabdbacbdcccbaaacbdabbcadccabcaccdabcccdddcbcbbcbbbcadbccbcbbcbbacdcabbcbbdcddddaacbdadacadaabdccaadddabbdbadaddacbdacbdbaaadcacbbaaacdbadaacdbbdaaadddcccdbbbcbabcacabccaabaabcdabbcbabbacacbbcdaaabdadbcbacddcaabbddccdacbcadcccadcccadbcadacaacaccadddacdcbcacdacaaacdbacadaababbbcaabcadbbabcdcaddcbbddcaaddcbcacabccbcaacdadcccdcaacbddddabaabdacbaaacdcbacdacabbcabaacbadbcddbaacacbcadcccbcbbaadadabcdadaabadaccdbdccdcdcccccbdabccdaabcbdcabdacddcabddbdacccdcbdaacdaacbcccccdcadcdcccbdcabccccbbacaacadbbdcdbcccdcbaadcacdbcbdddadddbaaadddbdbdcbcbcdddccdaaaddacadbdbaaaccabbccadddbadbcccdadcdbcaddbcabacbaabdbaddbacbbbbddddbbcaaacdaabadcdbdcdaddbdadbcbddabcbaaabcbcadcbcbbaccbcacaabdacdbddcdaccacacbdaabbaccaabaaaaaaccdacadccbadadcbcddaadabadbbdbacccccdcababdbaddabbbbcbdccaacbbabcbbaabdcaabdccabaddabaaccccdcaabbaadcbadcabbadacdbccadccbccaccdcbdbbbccdccdabdacccbcbdcababcbdbbbbbbbabcbbbdbcdcbacadaacdddaacdbbddddcdbbdacaacaabcaccdadbdcbbbdbcbabbbddcdcbbbddcddcbdacabbcccccaddbbcbaaabcaddcdbadacacbdabcdccbcabcabcddbddabbaaabababacdaaddcdcadadbddbccababaccabdcbbbdbcdccbccbcaabccdaacbabccadbaaabdccdcdcdcbcddcdbabcccabcabcccbabdcbcdddabccdbbbdbbacbdbdbacacacdabdbcaaccadbccbddbaccdbaadcdcacdadadcaaabdaadbdcbdabdcabbadabdaccaaadbbdcddbdccddbcdccaabbbdaadadaccccbdcacacbadcbcbccdddaadcdbabdddcdbdaccaacdbbbcdacccdddbdaaddbdddababbdbcbadaaaadbbccaaadabbbccdbabbdbbadcdcabcbdbdcdcbbdbaaacadbbbdadababaaaccbbbcacbdacabddcacccababdddcdbacbbdcabdbcaabdadaaabadabaddccdaabcbdccddcbccbdacccdbbcabbaabdbcbddabcacbacbdcccccdaccbaaccdcdbdcaccaccccddbdccdccccadaaabbadadcaaaaacdbbdbadddcdabdabccdbacaaddcdbcbdbccaaacddaaccdbcadbbbcdcaaacbdadcdbcababaabdcdddccadcdcbaccddaaadbdcaacaddddbddbabccacadbabdbabaaddccadcabbcdcadcacccccdddadbaababbdaddcdbdaabcadabdcadbacdbaaacbbccdcdaadbbddccbbcbcddbddddcdbcbbbccdbacbabbbcaccbaaacddcddccddbbccdcdccadaccbcddcacdbdbaddcadabccaadbcaddccdaaacccaddbbbacacabadaddbcbaacdbabcaaaaabbcdaaabddcacaccacbcdcacadaaaadaacacccbbadddacdbbbdbbddcadcbadacbcaacdbaaaacddbcaaadcaccddabaabadbddbbabaccbdcadacccbbddcccabdacdadaddcbacdadaaccddddcaaabaadbdcaccddcdbddacaacbbabcdddaccdabbadadcabaddccbbccabcacccbccaabdadcaadbccdcdabddacdbadbadaadbdacdabccdcccdadccabcbddacbbdcbdbacbddabcdbaadcbdbcdccbbcdadcbbcbcbddabbdbbabdccaaaabbdabbbcdaaabbdcaddbcdacadccbbbccddabbaadacaaccacbcddabbcaabbdddcddbabbdbdddddbcabcbbbaddacdbdbaabbddaabcadbcdaadaaaaaccccddaadbccabbdbabaccaddccacdbabdadccdcbbabdaaabbdbacbbcacabaacccabbbbbdcdcaaabcddccacabbcbcbaabcdddbdcbcdbcbccbacdcbdbacdbdacbdbacabaadcddbdccdcabcbdcddbdbdcbcbabaababcadbbdbccadaadccaddbddbadcadbcbdcbccacdaadbcccccbbccdbaddddbbcdcbddaacbdaaacdbabbbddbbcbaddcaccabccababbbadccadabaccddaaabddcbddabdaddcbbdcbacdabbdcccbcbcaccabbdadbbabccabdbabdbbddcdbcabaaccaacbbabdacbdbabbadbdbbdbaabdbcaabcabbdbdcacbcadbadabcaabdaaddcbcdbddaacaaaaccdbcbcadbadcbcacacbdcababbaabcbbdbbcacddcbcbdcdacbddcdddaacabcddacabbcccbdccaadabcbaabbccdcdaaddbccaccbddcdaaabcddbddacbcacddabcdcddbcdddcaadcaacdadadabacdabdaabacbbccbcadbcdcdbcccccbcbbbdddcadbacdcadcccaabbcbacabccddbdadbbcccbabccbbccabbddbbccbbdbbcdcdccdbbbabcaadcdccaccbbaadaadaadcdabdaaabddbacaaccbcababbcdaccdadbbcbacbbcddaadddbdbbccbccdbccdccdabcaccacaabaccbaacaddacacbcabbcaabcacbddabcddcccdabaaccdcbcbdaabddabbdccbcaabddddaccdcbdbbaacaabadacdaacbccdabdaccbabbabbabbdcbadbddadcdcdbaadaddbcddddabaabadadabbaacdbddbabdcdcdcbdabaadcddcaadcbcddabddbcddcbdcaadaccaccddcccabaabdadadcdcaadcdbdccdbabccdcbcdcbdccabbddcccdaacbdadabadcdbdccabbbddabcdbdaadaddddadbcacdcababacaacadcdcdccacaacadacabaabaaaadbabaadcbabcacabddcdadaabacddbacbabbdcbaabacacbdcbababaddaaccdabccdddcccbddccadcdaacccacbbcbcccccbddaccdaaccdcccaccbdccabbdbbcaacdadabaaabadccbaacccbcdbdbbccddabdabbccbbdcbddbaaddcdacdcccdbbcbdabbddcbdaaacacbdddbbbbaccdadbdabaaaadbadcccadaabbacabcaddaddbabccbcccddadacbddadbdcdbdabaabcdcdccacaadccbbcdadcaddbcdcdbabbcbbdbabadbdabddcacdcadcccbdcdbbabbbaaadcbbbccaaadbaddbcbccabbcbbcbbdccdbbacaacbbaccbcbadcbddbdbccdddacbaaccbaacdadbbadaadacbcaadacbbaabbaaabbccccbadcdcdacdcbbabacaabbdaaacbdadcdabccbcbbdddbcdaddabadccadcbccdcbbcdccdbcdbacdcdaabaddadbcbadbdcccabcacaacdaaabdddcabcdccdddbdddcbdbabdbcaddabadaaacccaadaacbbcbdbddcdcbbbcdbdcaabdbdbdabaddbdcddbdcaadaababdabccddcdcdddccbdcbcbdadadbbdabadcdaccaacababadcdaabccdbadbbcdabadbcbdbaabcadbdddddbbcbbdcddcaddcbdccaaccaadcbbdbbbbcdbccddacaaaccabccdbdbdabaddbaaccacbacbdcaaadaccdcdcaababcdcbdcadadbbdbbdddabcdcdcaaabacbddbdcacaabdbcccaaaabaaacabadacdbdbdcbcbcbadbdbbbbbdcbbccddbbbbcbccbddaaddaaaccddbacadbabddadacacbbdbccaccbddabdbdcadbcdcddaabaadcaaabdaddcdbdbcdbdcadcdcbddbbbdacbaababdaabcaadbcdacccdaabcacdbccbbcabdbddacaadacbbcacaaaaddcdbaaabbdcbbcdbcbcbdbcbcccbcbdccdbacccaccddadadbbccdddbaabddadcddbbbdcddcdcbabadcdccbbbadbccdaaaacbacbbcbdcadabacdadbdaababadbabacddbaddaddcddabaabdaadcadadaabacdaddbbaaddbadbcadaaddccccbbddddccadaacdadbacddbbacbabacbabccddbadcdaddadcdabbdabdccbcbaaddadabdabdddadbdcbdbdbcddbaaccacbabacaacccabbdadbaaccaadcdcdbdabddbdbbacaabcacadaaaacaaccdaacdcabccdaddaaadcbbcddabddcbcabcbcdbdcbcdadcacdaccabdbbbabcaadcbbbcccababbbaccbcaccbdadabdddabcbadbdbbcbadabddbbbaacdcbadccbdabacaddacdaacacbcddcbbbdadddcdcdcbaddcdddbbbbcccdacbbcbdccbddbdcbbadcdbdadadbcbacacadcdddcabbadcbdbcdaacacccddabdcbcbcbabccadbcbadbadbabbcccaccdcdbcbcbacddddabbbdcbcbcbbcbadddacdccabdbdabadadadaacdbbabcbcdbadabcbcdbbacccacabdbbbdababaabdaaaabdddbbcaabbbbaabddadddaabccabddcaaadddcbddbacabbbcbbccdaabdcabacccabbbdbddcdadacbacbacddcdcbadddcddcbbabdbadacbbddbbcadccacacaacbcbcccbbabdacaacadaadcdbcccbbbddcacbcbcbbaacbbbbaccbadddcdaccbaccdddbbdbdbbbcbaccccbaadcdcdabaddbccdacaabadaabcbdccaaddabaddbcbbcbaddabdacdaaabbcdbbdddcdaaccaacbbcbbaccacdcbcddaadccadacccdbbcaabccdbdbaabdaacdbbabbddcbcbacbbaabcbbabaabdcbbabacbdddadbbbcbbdbacbacdccbadcdbdbbaaabbabcccbaacbbdcbcadadbaccbbcbccacdbcdcbbccaccadbcdbcbbcdaabcabdcddbdadabbdabbbdacccaadabcccdbdaadbcacdadbacccdccbdacadaadaccbcdaddcabccbdbcbdbadaccdabbdbaacaccddddbacaadadcbabccbdbacddabababdbcaababadadaacdbaacbcbbdbbacbababbdbbbdaadbcaccabbaddddddadcdccdbddbbcccbdccdbbcbcababcababbddccdbacadababdaccbaadbdaabcbbcbbcdaacddababdbdaabbabddbbabcbbddbaabadcadadcccddadbdcdcdbaacdbdacacbdddccdaadabdbaccbcdbbababaccbdaaadcdbdddabdbaddadbbdbbacaabccaccbdcaadaddcbcbbaaddbcadccdbdbbaadacdbcaaaccbbabcadbbaabccaaaccdddcbbdbcccccbbaaacbcdcdaaabbbaaacccdbadadbcbbacbcacddbcdadddbbaabbcbccbcbcabdbdbbbcadabdddcdaaccbcacaddbddccbabaabbabcddaacadbcdbdbdababccbbcaabdadabbcaaccdbaacbcbabdcbabbcddcaccddbaaccbaacbaacbaadadcdccadabdcdccdccacbcccabbdccdccaacdaacaddcdabcbadacbbcbaaadcddabcccccabcdddbddaccbabcbabbcdcbbcbabcbacadbdbbabdacaabbabacacaabacdddbbdbbbacdbacbcbadbbbaacdaccccdcacddacacdacabcdbbbdccdcbaadaacdadaddcacdcbccadadaacdbdcdadadccaadcacbacbbdcbaadadadcdbaddababcbdbbcadcbacbbbdbbcaacbcbbccabcdbdddbdcccccdcadcbadcccaacbcddbcbbccccbdadcbdbdccbacaaabacdcdbacaabacaadadaabdbdbbaaaddcbdaccbdacdaaddbdcabadacabbbabdacbcddbbbabcacccdcbdbaaaadabdcdaccddbacddaaabcbcaadadaacadaabccbcbdcbbdaaccdcbcdbbdcabdabbaadbcaddbcadcacbbbacdbacbddbbaaaddccddcabbbbbcccaddbcdbcbbbccdaadcccbddbdbcddacadbcccdacabbadbdcdbcababbddacdacdccbcddabadacccbbdddabbbbccbbddcdbabbaabdcdbaababdcbccacdcabacbababcbdcaacabccdbcdacdbdbcadddacdadcdadabbbdabcacbacbcadbdbbadbbbbcdbbaadbbabacadbaaadbadadaadbdddbadbcadaadbdadacabadcbcaabcaaaacbaccbbadaaddcbabadabbaadcdcbcaacabcccddbddaddbdbbabbbdcbdaccadbaabcbdcdcadadcacdbbcdbdcdccddabaddbccbbbddbcdbcbbccaadaabdcabdbaddbdbbbbcdbcadddbcdcaccdbcacdcadbcabcbdcccdbbacbcddbbcaabcaabdcbacadcdbaaddddabcbadbbdadabbaaaddacdcabdbccadbdcdbbdbdbadddacdddbbcccabdcdddcdbcdcbdcdbbaaccdccbcabbcdcdcacadbdbdbcddcbddcdadcacdabdcddaddaddadcdaddbdcbaccbbbbcdcbcddccbcdacdcdccacddabccdaccbbdbbabacbbbacdcbcbacbcaabcbdabcdddbccdadbdcadcccadadabaacadacddbdcccaccbbcabbacdbbbadbdcadbacaaddabccbdaddabbbccbcdbccdbddcbadcdbdbcdbbabbdccbdbddddadcacbcbaadccacdbcdbabccccadbdaacbdbcbcdbababbbdcdcadcbaddbdbdcbaddddcbcbdabacbadaadabcdccddadcdccbcbbdacadcbdcaacadbcdbddbcccdbacbcabaabacbcdbbabcbdadbcddacbbcccadadbcbcbabcbcbaddcddddcbbcdbadcabacbcadbbcbccbacdcbcdbdababccadaabdbaadbcdabdbbdaddabbddabdaabbbadcaacbbcccbabcdbaabbabddbaaccdbbccccccbabacbadbacccadccadaaaccddcadcabcccbacabbabbcabccabadcdbddcdabadddccaddadbbcbcbadabacadbcddaabbdbdadbacdadcbadcbdcaddcdcdbbcdaacdccdabbddcdbcbbaaaccbaddcdaccabdbaccddadbcbdaccbcadaaccbadaaadaddbbbbacabdacaabcdaccbbcdadadbdbccbdadbbcdbadabbbbdbaddbccbbdccddbbacdddadbbbdaacdacbccabdaaccdddbddaaabccbcbcaaccbcbdadbbacbbcbbaaccccdbdcbdadcbbbbcbdcbdbcdacbcabddbaabcbacbabcaacbabaccddcbbdbbaddcbcbaaadcddbacdbbacaacacdcddbdcdbddcabbbbadaddcaddacaccadbaacaddabaacccbbdaaddaccccbddbadcddabacbdbcdbbcdadaadbadbaadbbbccaabbdbdbbacbabbaacbbabaacacbcdaddbdabdddcddcabcbccccddaddaabdaccddbccbabcdcabdcadbddadacabdcbbdacbadcccdcdadcdccbdbcaacbbcbbabddcbddadbbcaadbabbbddbddbacacaacdbadccbacdcbdaaddddcbcbdbaddabbacaaabacaacbdacadbcddadbcdddcbdcaacbabbaadabcdbbbcaadddbaccdcbcbccbbcbbcdadababdacdabcbdcccdccbabddccbadccbdaadbbcbbcbdaaabddccacddbccdcabacacbaabbacbadbdbdbaaaadbcadaacccabcabaddbabaccdbddbdcacbbabbbaabdcbbbcaddbcddcbacbadacadbdcabbdabacddbbbaadbacaababadbbdaaadacadddbbccbbccacdbaaaaacdbcbaacbbccbbcdbbabdccbdaabadaccadcbcdbbbcbacbdcbaddabdcbdaabbcccdcdcaababbdabbacbbcacbabbaaacadaaaadadacadcbcbcaadcbcdcddcacabcddccccdcdccccdacdbaaabccaabaadabddacadcddadbdbbdcdabbcbcabbaccbcababddddbcaaadbbddddacaadbcbdcbdcbababdccdddacdbaacabaacabbbbcdcacaacbaacaadbcdbbdddabadaabbccdcabcbdabcbabcbcbcadbdaaacaaccdacdabaabccccaacbccaabbcccbbccbdacdabdbabcabddbbbdbaabbdcdbdcabdbacdcccddbcacccbabcabcacacdacccabdddbdcaddababbbadccdbddaaaaadbbbddaabbdaddcbdcadcaacbbcbacdbabbbdbdbbdadbccaadaccaabdcdadaccbccbdcccdbdbcbadccabcdbccccbaddabadbbacdccaacbcaccadcacddcdaabdcaaabdcdcddaaabdadaacddbbcbdbdaccdbbabbcbbcbdbbdddcaababacaadaabccacdadbcbcadabcacdacdacddbdaddcaaadcddcdcacbccabbaaaccaaccbcbddbcbbbdbdabcbbcdbaadbcbddbddaccacaddcaaccdbdddbbbccdbdbcddbccdbabdaddcbbbdadddddadaabbcdbcbbcddbdababadccddcaadbcdbdccdcdcdddaacaabcccbbaaabaacdaccdcdaacccbdddaddacaaaddcdacbdcadcadacadaccbaaccbadbcaddbdbcadbddcdaabcacacbdaaaccbdaacaabcaabacccdabaddbacdadcbbbbbbadcbbcadcadababbaccabadcabbddcccbcbccccdcaabddcbbddbadbdaabaaaadddbaaacbaaaaccdbcdacaabbcadabdcabdccadabbbdcdaaadbdbcbdadaadcaaaabbccaadacadbcbabbdacbacdaaacccbdbacbbcdcdbdcccdaaaddaccbaabbcabdaaacbdacabccddcdacabdcdbbcabddbabccbabdbcadcbabdabcbbbcbcacdbbbbbabbdcacacacbbadbbadcbdcdaccadadcaacbadcdddbcdcabcdcdacdbacabbabcbbbcbabbabdbabbdadddbcccdabdaddacccdaccbdbcacdadadccdbdbbbccccdbbaadaccabbabdbccabcbabddbbddbbdabdacdaaacdbabdbdbdddddbcbadbdadbcdbaaabadacdcabcaccaaddbacdaccaaadacdcaacacaacbadcdadacbcccbbaccdbadaccbbddccdcaadbaaaabdbbdacacddcadddcdbccaaaccbbddbbbaddccacbaccaaccddbbdbbbdadccaabbdabcbcccdcdddddadbabdbacacbadbdcbadaaabbcccbbcdccddbbcddbccbadddccaddbcccacdaccbadabdcddddabaacaddbadcdcacaabbadbdcdccdacbdbbcaccabccdaacbdabbdcbcddacabcdbabcaabcbbbacacbaacdcbaddaccbddcdccadccaababbdcbddcddbcdacabdabdaacaabdbddabaaaddbdacadcdbdbbdadbbdbaadaccdbaddbaddabadadcbaaaabbbdbcdccaccbaacaaabbbbdabaadaacacabcddddbacbbadaaababbbaadccacadadbbdcadcdcbddbbddcbcdcccababcadacdcbdacddbbbdacdccadadddcadcbaacddabddddbbadcababaacbddabcbacccbabbbabddabdcdbadcadddbbbbbdcbaacabdcbdcdabcccaaaddddcddbdabbdaaaddddcdacbbbcadbcddbcaadbddcbdbaacdbcacbaabddadcbcbbdddcadcabbdbcabbdcaacabcadabdbbcdccadbbbcccdbcccdbccacbacddabdacbcabcaacdbcbbcabcdcdbabcbccacaadccbaaaddbcdbacbddccdcbbaaadbabdcccbcbcdadbbbdcdbdcacccbbddbcdbddacadcbcacdacbaacbbcacbcdabdbaacbaddddcbbbdaadccbcbdacbcaabdaddccdaacddbbbbbdaadbbbddbcdbcaaadbbabcaadcabccaccacddccbabdcabcbbccabdaaddabdbddbaddaddccbadcabdadbcabcdcaaabddacdcbdaabdcadbcbcbdcccaabaddadcbcbcdbbbaabbbdbbcbacbdbcaccdddcaaabaccbdabcacabaabaaccabacabdcbadadbdbabcbccddbadcbcbabbcabadbbdaadbccbadacaaddddaadcdbaabcadacaccdbdbbddccabdaaacbabddabbcbdcddaacaccdcdcbbccdddcdddcaabacadabbacccaabbbbdadbcbccdcccdbaccadcdbbcaadbabcdcdaabbddabdabcccbcdacddcdbadcbdadbbdbdabdcdabddcdbdcbdcadbaddbdabddccadaadbcaadabbaabcdccbcaccbccdaaddddcaaccccbdcabbdabcabaacdacabcbaddcdcdcaababbccdcadcdbbaaaccdbdabadccdbccdbbbdaabbcadaabadccaccbaccadacbcacccacacccbbbbdcbbdcabcabccddcacbbbcabddabbaabbababacbabbadbdadaabbdbadcdaacbaabbcabdcbdbddbcbdcbacabacbdbdcdbdcdabdadaccacdcbdccdabbaacaabbabcbababbbccadbdaddcbbabbbdabbdbcdbdacddcdbddddcadabadbcbdbcddadbabacdabccdcdbbccdbdbaadabbcccaddabbadcddbabdabacacdbbaadaadcddcdcbaadcbdbcbabbadbaddbbccdbbdcccacccdccddcddcdbdcabcbbddbdaaacaadcdabbabdddcbdaddbaabbdaadbacabbadabcdaacaabbabccbccaaabdabbbdcadacabbbccdacbadddabccdcdbbdabacadcadaddabbdadadbbbabdbcaddadccbdcacbbacdabdcbcdcbbddcddcbccddcaacabcbadbdbccacdbaddbbabddbdbcabcacdbaabacbddddbcdadbcbbbabddbdddaddabaadacdbacdbbddbcccdcbadbddcbdcccdabcababdacbbadbcaadcadccddbbcabccabcbadbbbcbbbccacaddbdbcccccadbcdcadbcaacbbcbdbbabbddcdbabccdadccaaaacbdbccabcadccacdbccdcddbdaabcddddaccbccaaccacddabcdaaaadcbdadaadaaacbbacbadccddccaadbdcddcadababccbdaccdbbbacdbbdadbdbdcdcbcbccdbcbcacbddcbccabbcbcadbbbccaccacdbdbacbacbdbbcbdcbabcbdadacbbddbdcbadccaabdadcdaabacbbbcdaadadccbdbcbdbabaddbbbddccddcbbdadcadcbacdabdaabbcaaaabaabadcdaccbcdacdabcbcaaabcbccdaabccdbdaaaddaddddabdbcddbdbdbbcacdbbcacaabcadcdabcbbaaabcbdbbaabddcbacdcaabbdcdcbbdbdadcdbaddcdcbddcccbcaacbaccbabbcbcdbbbaadbbacbacdaccbcdbdbbabdabdcccdddadadccadcdaadcdcaabaabbacaaccbbabbdbbddcbcdaaadadbbdacabaaaabacaaacdbdacbbdcdbcacabbbdadaddacccaabbabbcdcdbcaabaaabacbcbbcdbccabddabccbbbabdacccbbbcacaaaabbabccbcdcdbbacbacdbdddacadbababccbbdcdccdbccdabaaaacddaccccabccabbbdababadbaaaadcadbcaccdbccdccbcdcdbcdbbcddbbdddcccdaacbcdacdbdadcbbddabbdddabccdcdddbdccaabbaabcdcadbabbcabacdccdddccddacbbccddabcbdadbccdbcdbaadcbbaaabddcddadadcccadbdccbcdcabaabdaabaccadddbdbabbccabddcdcbcabbbbcbbdaccaddbadcdabcaddaacacccdbdcacbcadbccccaccacbcdcaddccbdcbabdadcdcbccbabdbcdddccbbccadccbdcbdbdbdcadadddaabcbcbbbddddabdcbdddaabbbaadaacadcdbcbacabaaadccadbdabbcccddadccdddcdbcdaaccdcdaddccbcabbaccaabdddcccbabbabcbdbbcbbbdadadddbdabcacdbcccdbabaddcbcddddbcddaadbbaabaaaacacdcbdaaadcdabacbdbbbcdbaacbddcccbaccaaaaacddcddaacaacacbddbbbccabccacabbddbcdcbcbbaaaacbbbaccadbbdddcdbbbaddadcadcaaaaacbddcacdccdbddbdccbadacddbccbbddcacabbcadabbdcdccadacdbbaaabdabbdbaacbaaacbbbddadcadaccdcdabcadbcbdacbcbabdcdbaabcdbbbbaadccbcadcddcbaccbaabcbdccbbcaaacbadaccadbacadaacbadaccccacaccbbacbcddddbbacaaccdbaabcbaabcdbdddcddadbbcbdcdadacabbdddbcadacddadaababdbaddcddbcdbbdbccdcdcbcacaacaacdddbdbcabcdccabcbbccdabcbdacabdccacccbdbccabddaacbdcbaddaaabcbdbdbdcccadbbbdacdbabcbcbdddddcabacadbcbbdbacbbbbdaddcdaacaabcacbbbdcbabcadddabdadcdbaabbacbbbaaacdcbdcababacacadabaadbdaadabcadabddccaacdaaacabbbddaaaaadbddacbddbbddadaaddabadddacbcaddbdbabcacdbabbaaaddbacbabcdccccddbccacccbcadabdcdccdcadcdbaaaaacbdbcdcabadcaaccdcdcdabdaabdcddbdbaabbcadcabcabacacddababcbbcdacccaddbbacabdbcbbdaadbcbcddcbcaccdccdaaacbdadbadbcbaadabcbaddaccbcdddaccbaacbdddbdadbaaacdbbadadddccaddacdcbcbdaadbbddadbbcaccdcbcdaabdcacabbadddaabbccbadcdadddcabbbdbddbbcdbbdadaadaddbbcddbabddcadddddacdccdbbbdbcbcbddcdbacacbabbddabddaaacacadbabbccbcabaabbaacdbcaacacbacbbbbaaaccddcbabdaabcabdddbcbbdbcdabbbdcccbccdadaabbccddaccbbaacaadddaddbcbabbacaccdaccddababadbcbacccdadbbdaabdccccdaccbccacabbbabadddddadbdababdcaabbacaddbbbcbbcaccabdddacadcabbadabbcbcdbcdacdbcdabdbbdcabdcabdcadbbbcddbaadddaccbcdccbbdcccbdbccdcaccacadcdcbcacaadcdaabadadcbaddccccdcdcaabaaabbcbaabddccdbdcabaadbcdcccdcbaacbbadcadbbbacbbbcbbbddbbcbcbbccacdadacacadbddbbacdadcadacddbbdcaadbcabdddabcbcdcbdbbbdbaccaddcddbabbddcacbccaacdbabdcbdbcacabbcbdadababdccdbaccaddacddaaccbdbbdcdbaacddabdbcbcaaabbbccbacaaabcbdcadacbacaadcdcadcdbabbbcdbdadaadcbbbbdbbdbcacdbcdadacdbadddcccbcbdccdccbdbbacbaacdaaddbadaacbbabcabdabcdcbbcaabbcddadcacabcbcbacacdabdcccbcdcddcbbbacacaacdbaccabcdcadbcbbdcbacccbcbabbabdcbdabaaacaccaababdcbdbbdbdbacccdbcddcabadcaaddbaddddcdcddabdaacdacacadabdbabbdadcbcbcbbadcaaaadabaccacbbcaabdaacbbbbaccdcacabbaabbbdcaacddddadabbacbddbadcddbabdcdbbbbbbddaabaaacbadaccddbdbaacdaaddcbbbbdbabbacdadbdccabadbabdcdabdabcabdbdbaaabbdddadccabacdabcbbdaababdabaaacdbadaccdcddcadbabbbabcdddaccdbaacdcaadabadddcaddbadcaacddbdbcabcbabbaddbbdddacaccabbbbaacdddaababdbdddbcaaccbcbaddbadbdaabcaccbbbaccccbccbddbdddbbcacbbbadbadacccdabaacdccadbcabdadcaabbdbccaacdabacdbcdbaacbbcccccdccdcaacaacdacbaddcaadcdaacdabcccdddbadcaaaaabdcbbcacdabadabcbbdcbabbccadaaabaaaabccdcccabaddccbcaabadccadbbbadaacbcbdbccdbaadbadbadadcdbcacbaaabbdacdabdadcbbcabaddcbccbaadbbaccbaaabaddbdacdccaabbcbcbdcbabdcbadbcacdbbcacccaaabcbaaddaddbabcbddbdbcdbdccadbadabddacbaaadcddabdabbbaaadcbcdbdabbdabdcacaadcdbdacdbcaadcbcadcabdaccabadaadabcacbdbabdbaaaaddddacabdbdcbaadbadcddadacbdbbcdbcabdcbdbadbcddaddacacaddbbabaaadccbacaacbbdcbccabbaccaddbacddbccbbdcabbbddcbcaccddabddccacbbaccaaaabcdbbaccaccddbcdbbdbdacdcadcddadbbdaacbcbadbbdbaddadccaccddabcbabaadbbbcbbabcabdbcaadcbbbaddaacddbdaadbcbbbcacbbbcabcdbbdbcadcdbccacbddddabacdcbbdcadddaaabccbbbdaccaaddbbadaadddacacaabacabadaaadbcbdcbccaabbbacdacdddbddccdadacdcbaaaccbccdcadcccacabcccddccdababdcdaaadbcbcdaccdbdccddbadbdabcbbbbddccadddccdadbbddbadcbdaabbdddcccabdaabccdbdabbabccdcbbabcdcccdccaadcbaacdbddcaabdabbbadcadbcdcdaddcacbccbaacacbdbcddaacddccdcbdaacaacdacdbccbabddbaddccdccdacaacdccdccdbbacddbcbcaddcbbacccdababbccabdbaabcbcbcabdcbabaacdccdccccdbbabadabdddbabccacbdaddddcaccbbdaacaccadcdcaaabcbcdcadabbcccdcdabcabbabdbdcccbacbadcddccaacbdbacbdcdadcccaddcdadacaadcbbacddbbcdbddccbaddbdaaadaccdddbacbccabaabacddbdcccadaacbbdbdddaabdcdbaaaabddbabbacdcaccccddcbddadccbbacdccadaddbacdcdcaaaddaddbbddabbccabcddacabcaadbaaccbddadacbaccdcdaababcbbbddcccbbcacbabdcacccbbbdcadbabacdbdbdddabddcbadacbccbdbadaabccddadaabdaccccccadcccccddadcaadaddadccbbccbcbbbdbddbcaaddaaaadabdcbcabccbdbabdcdaabbaddaddcbbbabdbbbababdbabbddcaaccacccbddaccdcbbbbcdcbacaabdcbbbddddccdcbcddacaabcdbcdabccccaaabababdaadbcbcbbaabdcacdaccddaacacbadabdbcdbdaaacaabdbdaabacabaabcbdaadabddcccccadaddcbcccadbbcbadbcabcdacacaddabddcbbadabbadaacaacccdddddabdccccdcbbbaabcacbcacbbcddcaaacbccbbdbdbbabaabbbaadccacbacdbabdabcdcabdacbdbbbcaacaacddbcdaaaccaacdcaddcdacddabbcbdbbbaabccdccadacdbacdaacccdddddbbaadbddacacbddadcdacdcdbdcbacadadccdccdacbadaccdaddddababcabdcbaddaadbdcaddbaccbbcbcdcbaadbcdccbddbcaaadcbdccdbcbaacaabdabdbbabbcbccccbccbbcbddabbbdabbabadaaddcdccddbdddbbcdbdcdbdcbccddaadcadaadcbbdbcbccadabaaadcbdabdadacacbaccbcaaadabdabddbbadcacbdcababadddbcacdbddbaaadcabaccabdbacbddabbaaacaddacdbcabbdadcdbaaddbbbadacdcadbaacdcbcdcbaccdabaddddabcaccbabbcbdbadbadbbbdbcbbaaddbcadacbdcddddacccaababacdcbbbabbcdabcbdcdcbabadbccdbacdabdcbdcadaacbdbbbdddaacbaadddddbbcbdabcacdacccbbcdbbbddbbdabdbacbdbaddbbcadbcabaddbdbdbbcaababbcaacccdcdcdcbdbcdcccbbdccacdadadbbabdbcbcadadcadaabadbbcbdccaacbdcdaaadcccbbadcabaddcacdbcaaddcaabcbbdacdbacccccbabaaaadbddbaaadadbadbbabbbcdcbadcdccddbdadcccccdaddaddaacdbcbdcbdabbcccccccddbbcdbacbcdbddadbdacdacdbcbcbbbcbdbdbddddbacbbcbdbdccbacadcdbdddbabadacbabaabadcdccbaadbcacbbcbccabddaddcbbaabdbaccdaaadabdadccdccccbacadcbbbddcaacaddccddaabadcdcdddabcaddcddcbbbcabbbbbccbaaddcbaaddcabbabbabdaacdcdbacbddabccddcadcaccadbaddcbcdccbddabccadadcdddbaaacdacadadddadacccbbddcacccccaccacccadbbacacbdccdbccdaabdabdabbddacdccdbaacdddcdbadabddbddbddbabcccdccbcddcdbbbcaaacbcdcdbdccabbdbcbadbbbbacddccadbbaddacaddcdbbbdcdbcbbdaaacadbccbabbbaacbcbaababbbabcdaccdbdcdbccaaddcccaacacabaaacbdcacbcacabbbcacdcbddbbcdcddcdabccdaacdaabddbbbbaccddaadccbcbcadbbccdbcabbacabcacdadbbcadaddaabaabcbbcaababcabaabbabbacbabbbcdccbcacbbbaabbaaaddbdcadabddbcabbadcadddbabcbbdddcaccbbdddbcddbadcdbcadddccdaaddccaacbcbddddbdcdbbabccdcdcadcdadbcbdddcbbcbabdccdbabccbcbbbddcddddbaadbabdaaaccbabcddddabddbcaddcaabdaaacdadcbaabbdcbcbacdcdacbdacaacdcccbdbddddcdccddbdccadcdadcaddcdaddcdccbdcdadddbbdddddbaaaadbadbabcbdcadbbadcbdbbcccdbaababdabbbacdddbcaabbcaaacdccbcdcaaaddcadcaabaadcbbabbabcbbbbccdcdabaadacbcbcdbbabcdbbdcbcdcbbcdbdbbbbbacbaaabdbcbbdbcdaaddadddcdbaccdccddbbabaacacdbdcabddbdaaaadacdcbbbccdcacdbddcabaacacabdbbabbddbdbadcacbbadcccaddcadbbbadbccaaaadcdbbddbdbaaccdcbadddacbaaddabaabadbdadacaacabcbcacbabbdccdabbabbaadbaabcdcddbbbaacaaacbbacadcdcaacccbdabbdddbacbcabacbbaaaddddabbbddaddbcaabbcdabcadbcdddacaaccadabcbcdbbcadbaacbaabcaaccdbdbbbcdabbbcdcaadaccdccabdcbacdbdddabcdbcacbbdcbcbcabaabaaddccacbaadbabdbbcbbadabaccbadcbbdddcdcccbccbdcccdcabacdacabddadaabcdcbdcdadadbaddccdddbbdbbaadddaaaaacadadabacdcaacbbdcadccadcbbcbabacabbbdbcdabadaacbdaadabcdadbbdcababddcdbbddcaccdddbaacbcaaadcbadddcbabdaddbcdbbcddababaaccadabcbdbaccbbbdbcadabbcdacbaacbcabbabcdaaadccadbcacbacacbcbadcbdcbdbacbcbcadbdaccccaadaaddbabdccadabdbcddabaddcaacacadaddabbaadccdcdcacacccdcabbcaadbbcabbbdcdbadccacbbbddccbcbcaacccddcdcabcdaadcddcbcbbcdbbcbbbdcadaddddddbaabcadbcbcabadbacccbddababdaacdccbdbbacddbaccdbbaabaccdddddcbbcbbcddddbabdcaadcacdbdcdbbbddcdadcbabaaadbbabdccaccdcbbcbdcccdadaccaabcdddbddabccbcdbcbddccabcbbbaadbbddcbacacdbbaabcdababcbdbdddbdaaaccddbdbbcaaaddacbcaaabbcabcdacadccdccdccadaddcacdacabdcbcdbababbbacbcccadcbaabbaaadacadaaabaadaccadabdcdbacaccacdbdabadbbcbbddbcbbdddabaaddcbdadabbbadadddcbaadccbbdadabdbbcbbcadcbcbbddbadabbdbbccdabcbcdaacacaabadcbcadbbaaaaacbbaacabbadbaaddaccbcabcbcadaddbbcdacbcdacdaabcbbbcdbcabdcdabdacdbabdadcdddbaccdacbbddbcbccadacdcbddabadcaabbaaacacadddadcdccbbdddaadbaabbcdaadabaccdbaabcdccadcddaccaaaacadddaaccabddabdcbbddbaabdbdcdadddcaaddccbbbdbdccdbbdccabadacccddcdcbdbaabbccacabbaaadccdacacbbcabcaaaddddbcdadcaacacddbcdbcadbcacaadaabaabbacbbdaccaacddababadbadabdaabddcadbaacaaaacbdcdbbbbcbdacdadddabdbcdbcaaadacdbdbbbdccbdcccbdcddbacdadbdcdababbcccabcaacbbcdaabaacbcbcabaaccdcdcbccbccabacdddcbccaabcccdcdabacdadddacdaadcbdaddccccccabbbaaacbbadbacbaadaabdcddabbcdcdadbabbcabccddcddabaabbbcbacaccbadabdccacacabbcbdaacccddbcbbdbaaccbbdbddaadaddadbacadbdbdabacdadbccccbcdacdccdbadaaccadcaacbcaabbbdadcbcadaabdbbdacbdbdabdbacaccdaaddacbabddababbbdbdcbdbdccddddcdbcaaddccdcadbbabbbbbaaacadabdacdbbaabcabccaacbabccbbddddbcbdcaacbbdbdcbbccadbabcdddcddbbdacddadcbcaddacaaaacddacabadabccdaacaadbbdddddcbaabadbadbaaccadbbdcbddbbaaadabbacacbdcbabdbcabccbaacbbabadabcdabcbabbadaccbdaacbcaddcdaadccdbdbadbcadbdbccdbaaaccdccbbcacbcdbbdbcaacdbbccddbbbcbdabbacbabbaabbdadccacbddbacbcadccdbdbdbaabbbcbdbccbadbdabcdcbbdccbaabdcacdbaaacbdaadaaabaadbbdddbcbaadbaaacadaaccbdcdcdcddaabdccbcbdcdbadccbdccbcbddbbcdcdaacabaadcbccdaabaddbddaddaccdbbddcadcdaadcbabbcbbcabdcaaddcaccaddbcadbbdbcaccbaadccadacdacabcdcbcaccdabacbaadbbbbabacabbbabbdbbcdbccdcdbadabccccacbbabcbcacbbcdbddddcccddbdcccdacbcacbcaaabbbababcbcaadbcbadddacccdbdddccdcacbcdbcaccacabaadcabaadbdddbcabddadadaddadbddaddcbababcaccbcacccbdbbaabaddbbaaabbdbbaabaabbacbcbdaccbaabacabddbcabcbabcacddbbabcadadcbaddbaababbcbdbbbdcdbddaaabbccabbbcddcdcaddacabcccabbbdbdbacdaadddbbbcbbbbabbbabdcdacbaadbccbcbdddcababdccacbcddbddbbaacabccbabdcddbbbcdacdccddccbdaaabdadbbbcbddbbdbdbccbacaabcbabacdacbbdadbbacdaddacaadbcabaddadcddbadbdcddacaddbbcbacaabbddddbcbacaaabdadbaaaaaaddccbacadabbbdccacadcabccaddcbbadcadaadcdbddbddadbdaaccdbcccdadcdcbdaccaadbcadaabcdadccdcbbcbacccbdbddabcbdbbaccdbbdccbdddacdbcdbcdcdaccccbaadcbbcbabbdddccdcdccdbacadcddacbcccbbbcaaddcdbbbacadacadacadbcdccdcabcccaacbbaddaccbabbabacdbdadabadabddabaaacbcddbaacaddadccbbbbdcbccccbabcbbcbdbbcdbbbaacbadcdadbaabdaccbddaabcbbacdabcdaddbcdbababccadddacdbbabdaacbaabbbadccaccccccaaabbccccddbcbddbdcacccdccbacbdabcdbbacdabbacbddbccddcacdcbcdadabacabdbaccbadbabdbbaacccbbcccdacacdbbaabaabbbaabaadaaaacccaccaacbbacdbdbabdcbcbdaaadaadbbbddabbabdabcadcdbcaddbccaabdabaacdadcbdadddabccacbdcadddaacccadacbdabdabcaaccccbccddbdccbcbacccaadcdaddacbadbcbcaaabaadacddccbbaadcdcbaccbdacbbabdcbdacaaaaaaadcdddaabdddaaadbadadacbcddbdabacbaabbabddcacaacbdcbadbdcbbdccbabdcddabbdbabaddcbcbaddcdabbbaaccabbbdddabbacabcaabcccaaabddababbddabadddbddadcbdadcccbadddbdadbccabdcaabddbcbbddbcaadabcdaacdbadbbbdbcdcaabadaaabacbcdaacadcbccdadccabadcadddbcdbcaabdabcbabcbadddadbacddbbcdbddbadbcaccbadccacbdaddaaccbaabbddbbbdbdcccbbbcbbdacbbbdbdbcadbdbddcdddcadbadcdabaabbbbddcdaddbabcdcaadcdbaaababdacbbbdaccabddbaabbdbbcdaccdccbbbababcadbababbcccaddcddbaddacddbbdbabddccabbbbcadcdadbcdcdddacbdacdabaacdbaadaabdabadaddbadaaddacbcdadaabacadcbbbbdbaadbaccdbdcbddcddbccaaadacdaccdcaabdacbabbbbdaadcbccdcbbdbbdccadabccbaddcdadbccdbbbdabcabddabcdadcacddaabcabdcddabcbbccbdccadcdbdacdcdadbaacddadccbddabaabbddbacccbcbcababacbdddaacdcadcdcbccacdcbdbbbdaaaabdcdddccabcbbdcadbccabbdccdbbdcbdabbdabaccbccbaaabadbdbbdacdbddcadaddcabbdcccbabdbbcccbccdcacbcaabcdaaaabbacadabcacbaadabcaacadcdcdbabbbdaabdcccabdcbdaccdaaacaabcbdaccababdbacdbbdbdbdbaabdabccdacdbddcaaabbdbbaacaadbddcabbcdbdccbcaccbbbbdadddccbcabddaadbbdacccdcbaacddcccdbbcaaacbcaacddccdbbbddbabbcdbadbdccddbdbdcacadaddddbaabdaacaaacdccaaadadcbbddbacdddddababbddccccbcbccbbadbdbcbdadddbdbbbbdadadabbabdcdcddccbadcbacbdacbcdbcbabacbbaddbcbbbcdbaaabdcaddaadbbaabbbbbbabddbbaccccaccacbcaddccbbadbdbbbdabdbaaddccbcdabcacdccacacacacdacbddbbcbbcbabbdcccdbccddaacbddbcbdbdcaaababbddbcbcaacddcccdcbacdadacacaadcaadccbbdbdddabbcbbbcbdcdccccbacdbbbadddbdbbbcacccbadabdbabbaccdaddcacacbaddbcbbcbabcccabdaabbabaaacdaadccbbacdbacabadcbbbdaabdbddcadccbaddbbdbccacadcbbdacabccccacbdcdcabbaacabdbcbcbcbddabaadbaddadcdcbdcbcbacaadbcddadbddcdabbadcaaccdadbccbaabddcbcdbabbcdddbdadbcacccadaacadaaacbabaddababdbadcccabdabbbcbbbcddcabdbcadcdbaadaadcdacccdacaadbabdcabdbcdbccddadabbbcbaccbdabacdbaadccaddccddadadadcaccccbbbdabdabaadcdbacacbbbcacaccaadccaccadbcddadacccacbacacabaaddccddabddcbcbcdddccaacabbcacadcdabcabbacbadbdabcabdcdcbaabadabcdcdcccdacdddccabbbadcaadaddcddcbdcbbbbcbaabbcbabdaaabddbbadbbdccccaaacddaabaaaddbbdacadaabaccacdbacddcabbadbbabadcdacadabbabbaacaabcaacbddcabdbaabcdadbbdbccdbcbcaabaacbdbabdabcbbcdcdacdacbddccdccdcdccbcaaaaaabdccacaabcaccacbabbbdaadadcadbdabcbbadcaadaaacaabcadcdccbdccbcadbcbadcaaaacaabcbbadbbbcbddacbdabaabddadadacccddcbdcdabdcdcbaabdbcdbbaadccabcacdbadbaadbdbadacdcbadbacdbaddbddbbddbabbaaaabdbccddcabcaddacbddcbddcaddcdadaccbaadaddbacccadcaadbadabcdaabdccccbddaadccbadbbdcdcbabbdbacdddcbbbbdcdaacdbdbcaddaabacccbbbbcadabbdcdaadcbbbdbbcbcbcccdcabbbccccaaacabaddccbdaaacdaddbdadbbddaddbaacaadbdddaaaacbbbbdcdddbbacabadccddcbdaabbcbcacbccdddddbddbaadaccabdadabdabdbaadaabcbbcbabcbbddabbbcbabbccbbcabdcddaaacadaddabaadccbddcccbcbadaacbdbcacdbcccaddbdabcdddccaabacbaaadaabbcbcbccaabccdcaadcdadccdbbbabdbabbbbccbbdcdbabadabaddabbcabddacababcadcabaddacddbbcabccbbbddaaccbccbdbbdabcdaddacaaddcabcdadadcbbaadcabcbadcccbcdadbccaacddadbbbcdcddacabaccdadcbddbddbcdcbbbbaccabbbacbccbcabbdcbddabaadccccadbccabbbcbccbcabdbdadaddbbaabdcdbbcaaabdbadabccdabacaddddbadcbbadcdbbbccadddddabaccbcaddcbbbcdadabdccbacccbbdbbbaaddbabaaababbbcbbaddcddbdaaccbaaabbdbacccdbcabdbcaaccaabacbdaabdbdcdcabdddacdbdbbbbabbcdacdaccccdaadabababbbcdcbbcbababdaaacbdbadcbdbdbaabdccbaaccbdadbadaddadacaacbaccbaddbcbbdbdbacabdbcdddcbdccdcccaaddcdcbabbabbbcddccbccaaacdaabddabbcadacdcbbcdbbbdbbdcbdbcbaddccbcbddacdaacaadaabdbccccbbbdbdabdbdadbbcdbadddcbacddcacbbbacbdccabdaabdccbbadcddaabadbdaaababdddcacddaabababbccccbdccaabcddcbadcbabdabddabddacdcacbddcbcdbcaacababdcdbbbdabadddddcbbccdbcdddaaacbaacaaabbddbbbbcddbccbbaaabbdddacbbbcbdacbddddcbabaabcdccbaaccdcadbcdbccbdaabbabbbdbbccdccbcbcccddaabdcaaaccdbbdacbadbadacdbacdddadbbacabbcababbdccbdcaccccdcddbadaacdcabccbcbcbdcdaabdacbdcbbbabacbcbdcacbddbcbdacbaadbbabbddbadccadcaabbabadbdbacabbdbadaabcdccbcbcbbbcbbdbbbcdcabaadaabbdcbaaccbbdddabddbcdabdacabcacacccabddcbdccdbddcddccbcdbdcacbacdcbbbadabbbdbdbaaabccbadddbabdaaacadcabcdccbdbcdbcddcddbddccdaaaaadaacdbcdcbdacccbbcddddacccdccdadcaccdbdcddbdbddcdcabadcadacbaaddbbabaccbddcddddacccccddcdaddabcbbbdcbdcdbbcdacddabbbbabdbcdcaabaacdbababaaadbacacaadcbadabbbdcdaacddaadccbbdabbcbddcdabdcccbbdacdcadbaaccaaacadbacdabdaccbcbcdcbdbcbdbccabcbacbccbabbdaaacabcccbdbabcdcbaaccaddabdbdbabbabbbbdddcacacbddcbbaadadabdadcbccbacdddccdbbdacacddcccaacdcacbbccdcdacccccbbbadbaddaadbcbbbbbaacadcbaabacbbcabbbabbdbdabadabcaaaabbcdbdccaccadbbcbcbbcabdaadabbddbdbcaccccabcbcddccbaaddcbbaddaadcdddddacaccaabbbcbabbbccdcddcbbbcbcaabdccabaabdbdbacaddbdaaabdbcdcbdabdcadcabddacbaddbaaacdcbdaaccacccadcdccdddaddbcacddbbbbcadbcaddacdddddabaddbdbaacadbbbbadbabbdaabddaaaabcbacdcbcdbcbbacddcabbaadaaabbcbbcdcaaabadacbbabcbcdddadbddacdddcaadabcbacbbbcdadbcaddbbcbdbdbccdabccdadabcbbabbacbdbccccdacdaaccabdcbcbbdbbacaccaaabaacaadcaaadbdacdbbbcbcadbcbbbcdcabbbbddaacbbdcdddabcddacbdaacdacdadbbaaabcacaacaadaaacabbbbbcdddacaabcbdcbaaabddacbcbcaabcdcddababacbccdaccdacdaccccbaaccbcabcacdaacaddccbaccbacdccbbdabadcdbbbbadccdcacbddccbddcdbcbdadcddcdcabddaabcbbadadadbbaaddaaabbbbdcdcdcdaaddcdbbbbdbabbbaccdbcabaadabdcdaaabacbcaadccdacaabdbaaaacbddbcacdbbbacbadbcbcbadbcabbbbbbbcdadbaabcddacbabbdabccbadcccbdbcaacacbacaabcccbcaddabddadcddddbbcabddbdbacdbabdbdbabddbbadabddccdccabababdababbbabdbcdbbdabababadcbaaccddbcbccbdbcaacbaadabdcdaadabdcdbbdddbdabcbccabdcdabbdbddbbaaabdddaaaccdcdbbcabdccdcbacdaaacaaacabccbaadacdbbccdcacdbbbbbabccddaacbaccabdccdbdccacaabcdadccacddbdcccdbcddaddccdabdcbaaadcbcadddcacaadbccddabcaabbaccadcaccbddbabacacdabdaaacdacbabdddcdcdbadacaadbbadbcaccdacdaabbcacccbabccdbbbbadddcbdbccbaaccbabbacabdddcadcccccbdadcbaadcaadadcdddddccabddabcaddccddbdbaddddccbabbbbcdabdccaacbcbbbbddcdbaccdaabddcacbdacdacbdaaaababccdcabbdcbdbbbaabcbcdddbdbddaadabbcacbcbaabdacccdaaaccdaadbcabaadddadbccbdcbababcbbadbcbdcaabbcacbcbccccbaacadabdbabcaacddddddbbccdbacabbccdbdacbbbbbabbcbcbbdcaadccbdcdbcdadbcdbaacbabdaaadabddaddbaaddadbbbbbccdbbbbaacadadcbcbcccbcccdbdcdaabbbacdbdaacccdbaddadbcababbbcccbbbcbbdcacbbbdddbaacdcacdbdbddcbdcdcbbcaadbcabaccdcdaacbabbabdcdcadccdacadcaacbabcbdaacdadcdadddccabcaadccbddcababcdbcaddbcaccacdbdddbdcaabdcdcdbcacbcbcbbccacccbbdbdbaabaabbdbacaaacabccacbdbbcbcbcadadaacababdbccccddcdcbcbaadbaacaccddcaaaabbbbbdaadcccaaadddccbbcddcbdccaacbcbcddaddabcdccdbbcaaccdccddbadadacadbabacaaabbabacadadbccbabddcaddabbdbbcbccadbabdcaaccdbdaddcacdccadaadcadbcbdbcbbbccbdddacdbdaabbbdcbbbdabbdcabdcbcadbacdcdaddcbbcbccdcaadabbcacaaaadcaacdcddbbbdccaacdbadddabbdadaccaaabcccabcddbaabbdaddcaaadabbccdccadccabddbaaabbacccbbcbaccbddddadcbadcdabbdcdbddacaaadcdcabdbdcdadcddacdbbdddcadbccadaaadaddbadcdddddcbabcbabbadbaacdacabaddaddbccdadabaddbacccaabbbcbbbababbdbbadddabbccccdbacbcbccbbbcaddddccbaaddacccbbbcbbccdacdbbbacbabaccbadcabddbcbbaadddabccabbbabcbdbabdbadbabbacdbbddbdcbdabcadbbbabacbccdcbdbdaccabcdbbaadbabaccaccddcbaacbccdcdcbbabdddddacbbabddcbbcabddcccacbbacaadabdddbdadbbcdbdbbccaccaccbdbccddddbdcbdaddcadabdbdabcdbbddbaddcccaadbbcadccdabdaadccbadcbccbcdcadbadabdcadcacbcbbccdbcaddddadbcadbbdcccbccbddabacbdaaaabdbccbccacbadbadbbcdbcbacbacbadbbdbbbcbcdaaaddcdcbdbacaaadcbcdcbbacacaddbadcdbbbabccbacaaaaddbcadcbbcaaacacbdcacdcdcbadaaabbaadabaccdcdcccabaaabdbbcdccbdccbccadbaaddbadcdccabbcadbbcbacaadcdbcbcadcbdacacdbaccbcdddadbdbadabdaadbabbcdabbabbdddcacbacabbddacbdccdddcdadccaccabdcbccbdbdaacbacdcccabccacbcabcbabadacbcbbcbadbadbdbbcadcbdbabdbdcccabdcaddadddbdcbcbcabdbbddcabdbccbadbbcddbdbcabadcbcbdbcabaabacccacbbbbcaccddccbbaacabbbdaabbbcaaaacddbaadbbaaccabcaacbacbbcbcadccbadaaccacdbdaadcabbbccddadaaadbcbaaaacaaabbcadabadbdadcaaaadcabdacacbbadadbcdabcbdcdbdbabbdcdcbbddbdbaddabbdabdbacccdcdaddcccbdbbbaccbbbcdbadacbdcddbadadaacabbdccbdaccaccbcbaccbbbdabcdabddacacdaaabcbcdaaabacbcbcccbaccdbbcaaddbbddaddbcdcdcdccaadbabacaddcdbccadaccbaabccabbacbbdbdacdcbbbaccbbdaadbbbdbcdbaacadbaaddbddacbbdcdbddddbdcacacababdcaaaabbbabdacaabaccbbcbcddabacaabbaabcdcaddadadcdcabacdbbbdcadbadbddbaadbddabaaccbbbdacddbdacaabacaaaacadbbcbdddccbdbabbbaadcdbadabbdbabbcaaccbcccaddaacbacdddababbacdccdbaabdadadddbcdabdbdcbbabddcbcacccaacabcaaaccbcbbbcbcdabdbbdcdcdcbcaabacdbaddcbdcbddaacdbaccabadcdbcdacabdadddaaddccdabdbdcbbbcdddbabdbbbbccdcdabdbcaadbdcbccbbcaccadcdcadadcddbaccdddcbabdccadccdbaadccbcbabbcbdcaadbadabbbbdbbbcabbaaabbadaaccdcccadaccbbdbaaaadacbbaddadccabcddccaabdccaadccdddbbcabaadbcdcbcaddbaabdccddcbbcdbaaadbdadccababcbbcddddddabacdbabdaabdacdcbbbabacaadcdcabbcbdcdbaabcddddabcbcaacbacaabddcaccdbbdbbdbabdcbdcbbddbcbbdcbbaadbddadcaaccabbacabbcdcbbdbaddbadacdbdbbcabaddbadadaddbbdcccddddbbcdacdacabacaddbaaccdacddabccdaabbcbbaaacccacdadcdacdcdbacdbcaadadbdacbababbcaabdccadabccbcdaacdcaacddcdbdccbadaaddcdcabcbcabbddddcccaabccacbbadddacaadcdcabdadddcdabacaacdcaaaccbbaacdcaadbabbdcdbdbbbcddbaaaccadadaddadcaacabaadbdabbcabacdddcadadbadadcdddaabbbcbdbbabaadadccacdabbbddcdbcccccdbadbbbdacaccaddacdccdabdbcdccabdbadbcadabadcbabbaccdbdaaadbabcadaccbabdbddcdabcbcaddaaadbccadabbcbcacbadbcddcccddcaaaabcacbbddcbabcdbddcbdcacabaacbaacdcaacbbcbbcdbcbddbdadabcdaadbaadcdbccccbaddcbbacdcdbcbcbadaccaccdbaddbcbcbacbabdbddbaacdbbacddadaabdccabdbadbcccabcadabcabddaccccddddabbcaacbbaaaaccadcccbbbbcbacddcdbacbbacbdcdbdaaadbbadabdbaacaaaadccdcdacbbcdadbbbdbaabcadacacdcadcaabbcccaccbdbbbacaddbbcbdcbadbbbbbddccaabcdcbcddcdcaacbcccacdbaddaabadbacdccaccbdadabadaddbcdccdbcaccdccbccdcaacabdaabbccbcdccbcddcdcadddbccaddbcbcadddbadacaacdcaaaaaabdbddbbacaaadaaabadcccabdbdaacbbabdcbbbdcccbcdccbdacadccbacddccbdcbbaaddbbdaacadbaccddcacadbcacbdbbacddccddccdcacdcaacabcaabbcdbaccbabbccccddbabaacbdbadaadbdcabacdcbdbaacadabbccadaddcdbbcdbdbbcacadddabcccbcddbcbabbcaacaacccaaacdcdabbccdbabdadbaabbabdbadcdaddddddcbdccdbdadabbcbbbbcabdddadcdbaccdcddadaacdbcdadbdbbcaaabbccdabcabbdacadcadccbcddaccacadbdacaaaabbcabcbbccdddbcbbdacddaccaddabddcabbdcbdcbccdbdaddbbcdbbabbacddabbcdbbdbadbabdaadcdcbdcdaddcccdcbdabdcacacaaccccddacabcbbabbbdbcdaabbdacaadabcbccbcaacacdcdacadabdcdaddccdcacdbabccbadbdddbacdcdcacbdcaccbabcbbcdbdaacbaabcadccddddadabccadddacdacdcbbaacddbdddcdadcdbaaadbbaabbabadcccacbacbabbcdaddbcddcddcbaaacdcddcdcdbacdddaadddbdbabbddddcdcadbdbcbbcdbdcccdabaddccacccdaacdddccdaadcccaccdbdbbabdbdddddbbdcacbdacbbdccbdaaadacbcabcbadaacadcadaaddddcaabadbbcaacadbcbbddcbdcdcadadbddaadbcbcccdbacacdbcddbaacbdabddcacccabcabaadadddcaddbdaadbcabbcccdacaccdcdbacadabbbbbccccaddbbabacddcdabccbdbdcabaddddbbbadbabcadddbbddaabdbdacabcdccaddbbcbddbdddadcdbbbbbcbbbacbacdbdcbcbbbdacdbddbcbabbcccabdaacdbabccdcdddcbaccdbadbdbcadbadcababdbbdadabbbdbadadcdadbbcdcacadbdcbdccccacaabdbacccbadcdcdbabdaccbddadabcdbcdbbdaddbcadabcbaadaaccdbadcdaddbbacdabcdcbbbdbdaddbadadbccadaccadacaabbdaacadacacabaaaddcddddcddaaabbcdcabacdccaababdbcaddccbbaccbbadbacbbdabadacdaacaacdbcabdabdcaabcbababacbcaacddcabcaccbbbabaabbbabbcbaacccacbbadccbdccbddcaacadbaadbbacbcabaaabaccbaacaaabdbbcccbdacddacccbbbcaddbadadcabbdbacdaabdaadbdbcbcbdacbabddaadbdcbabadacdaddacaacddbacccdbbcabbccbbbcccdcdba dadccabccdddabbddbacbbcacccdddcbbbbcdbdbbbddddabcadabbaccadccabccadaabcdbdadadcadccdbacbabcadadacdacaccdcdccdabcadadadbdcacccbdbbabcbccbadcbaaabddbaacaacaaddbcddacdcccbaaaddbbbcbddabacdadaccdcbdccdcaaacdaaabaacdaaabdabaddbdbbabcabbbbadaabdabcabacccddcddbbaabadbaaadacabdaabbaaabaadccbaacddadbcadcdacdaadbaddaadcaacaddacdacbbddccdbdbccbccdcbabbcccdabcadbddcabcabdcdbcbdddbabcacbaaaacbdadabcadbabcadaaadbdabaabbccacaaadbbaddaadbaacdccccacbbaccacdbdcbbdcbbbcbabaaabcaabcaccbcbadbdbdcbdcacdabccbdaabdbadacdddabccdacdbcbdabddbaabcbcbcbdcdabdacddbbdbaababccdbdacbacabbdadbaccabdbaddcadcdacbcdcddbaaaacaabdcadbddaccdaccbbdcadcaddbdbccbbbdbadccdddbdcddccabdaddbabdcdaacbddbdbabddacdbbadcddcbcccddcccadbaccbbbbbbdbdcbcaacabbaacdaabababcabddcdbcdcbccabdacadbaddbcccdbaaabcccdccdcddacbcbcbcccdacdbcdcaddccacccadcdcdabcaccdcdabadadaddcaaccacdaaacbacbdbaacbbaabccddaccddaccbcdbcaacbbaacdbacbbaaccdbacadcaabdbccbdbdbbccddcadbcbbcadddaabdaaccacabcbaabddcdbaabbdacabaccbaaadacbdcaadcaaadaddbabadcbdcdccdadbcacadacccadcbaadadddaddbbbcddcabcddaaabbbddbbddbddaccbadacdcaaddacdcacdacaabccabadbddbcbaccbdbadbbcaabccdaccbadcddaddcacadbbacdabaaadcbbacbdbbacbadcdacdbdcbccaadabacadddcbbdbddbbbddddaccddcbdbaabcadcbbacadbacacbacabbaccbddaadbbccabdbbaaaaddcabdbcdcdbcbcbdbbbdcacaaaaabdcacccabdcbcccdbdcaaccabbbdbbbacdaadbaccbdddccbbbcaababccbcdcbbabbbbccdcdbbdcaadacbddbaccdcaddadacbbcbdaaaaddaacbbbddddbccbabdadbbcdbacbabccacbbadcbbcadbcabacaaaacdcaabadaccddbabcadabdaadcddcbaddbbabaacdbacccccdcddbccddcdcbabadaaabcddbadacdccdbbcdbadccdaadabbcaabdcbadddacdcbcccbccbccaabdbbabdbdcbaccdccbbbbbcccbdabbbcddabccbcaadbbbacbbbddcaccaaabbdccbdacacdbbadddbbccdacbacbbacbacbcdbcabbbabbccbdcaacbbbaddcabbdbcdcadadcddacdbdbbcddbbdbabbabbcbcbcaacdcbbbcbabacccbbddccbcddabbabddadbbabbcaddacdcbadbbaadbbaacabbcabbcdbabacaabbddcbbccccdcacdccdacbdccacacbcbbdbcdcccaabbdbabdbccaacabcddbadcadacaacbdacccbcacacdcadbbdcbcdaabadaaadccacdcbaddbdbcccabdbcddacbcdaddccbcaddbccdcbacdddcccddcbbccbbcadabacdccddbbdbcccdcbcadbbacccaacbbabcdccadbbdaacccacbabbbabdbbbdbabbbcdcbbdcdacbaabccaaabbcbbdbcacbddacdccaaacacaadbcaaabcbbbcbdadcbadcadbdcbbabcdbacdcdbacbcdbbbcdcaadadabcacaccadbabadaccdacdcbabccccbadbddadbdaccadbddbabdcbbcadbdcccaadcdaccddbcabcdcaabcacdcdbaddddaadbacdbaaaaccbdbaccdddcdadbcdcaaccbcbacdadcadbdabdaaacdcacbacbbdddcbcbbacddadddccdccdbcccbaacdcdcdbaabdcdadddcdbaacbdadbdadaabdcbaaaaacdcacaccddcadaabdbdaacdbabaabbbcdbababbddbbcbbacadbabdacbaadcdaadbacbaacdcadacadadcaaccaccbdbcbbaddabcccaaabaadcbbbbdbdaabccabdbacbbadadabaccdcbbadcbcdbbdadbccbcabdcdbcacbcadaadcddccdddbcdddadbdacabccbddadddbdbcbbbddadbbcbccdabbadcdbabaabdcacacadcacaabcaddddbaddcccbacbdbcababcabcdcaaddbabaddccccdbddacbccbdddddcbdbabdaabcaddabdabdcdbcbcaacdbbddacaabbaddacaaacabddacbdaaabdccbbbabadaddbcdaaccbbadcdbabccabcdbdccbbbabbbcddcadcbcaacdbdcdacbabbdbdabbccccaadbbdaababdbdadaccaaddaddbbdacdbbdcbaaddbaaabdbbcdadbdacddcdadadbcccbdcadbddcabbacdaddbdbbacddcbadcbdccdccdbadaccdccbdccddabdaadcacaaacbcbacbacacaabaddaddbdccabddbbbddadaadddcbcaccccbaaaaacddaabaadbadbabdaabdbcdaabacbbbbbcaddbcdadcdbadcdcdbddaddaadaddbccddbbaacbbcbcdbacdaddbabddbacdabaccddbdddadcaadcabddcbcacadbcaccaccdaccbbacbdaadacccabbdabcdcdaabcdcaddccaaadaacccbaaacbdcacaabbbadbddcadbabacadbabbddaabbaccccbcaadbcbcaccdccdccbbcbcddddddbbccbdcdbccabadbaacabacbcadcbcdcacbbcbddaaaccdcbddadccddcbbbcccbbbdcbbbcddaaccdcddbabdaaacaaadabcbbbcadadbbcdccaabbdbcbbbdbdbaddbdcdabcbdcdadcadcbbbaddabddccbbbadccabbbcdccddadacaaaabdadcbddcbadcacaaadadbcadadbccccdacccbdcabacbdcbdcdabdccacdbabbacbdbaaabbdccdbaaddcaabbadbadbddaabcadaabbcaabbdcddadbaadabccbdccaaacddabccddccbdddacdcddadadbadddbbdbdacccdaccacabaacbcdcbacdaccdcbbacddaaaccababdccddbacbacccdbdcdbacdbbdbcbadbcddabcdbbbbddccbabbccccaadaddcaaaddbabbdcdddaacababcbbbdbadcaccbcbbbbadbbbbdaaaccbabbbadadddbacbaddccdbadbbcacaddbcacbddccabbaaadadbccdadcbccdccbaddbbcaccbbadabcdcbcbaabacdabcdddcbbbabaaacddcbbcaaaacbbdaccbadbaacdbcdbcdbbbbdbaacdddcadcddadcaabacbacabdbdccaabaaacaabacbdaaddabacccbbcaddabdbbccbbacbccbcdddcdabdcaababddbcbbaddabbbdbdcadabcabbccbadcaaddbccdddbabadbbbcccccbcacdcbdcdcbabbdacacdbabcabadcbcbbddddccddcddddaaaabdbbcbddabbddadccaaadbaaaaddcaadccbcbaddacbadbaacabdcacabcbcacdcdcbacabadbcdbcdcdbbcdaaabdbdcabaccacccdccccacccdcccbdbadacddbacdccdbabbdabdbacdacccbbdadcdccaacaabcaaababcddcadaddccccbaacdddcabdbbadbbabbababcabacdacdabaccdabcdbabadcbbddbdbdabbbbbdbacddbdbbcbbccdbadacddcbadccbabcbdbabbdbacdbbdabddddcacddcbdaddbbcaacbdaccabdcacdbadcabababbdcdccadbadaccbbcbacadabaacbbccccccbdadabadbdcdaccaddbbcaadcbcdadadbcddbcccddacacaacaddbbcccdaaaadaaccbccbabcbdbdbadbcdabbadbcabcbccccbbddadaabadcbcdbaccdaaccbdddabadcadcdbcdbaaddaccdaccdccbadbbdddbbcbdaacacbaabaddabadbaaddacccddababcadcbcabbacabcbacbccdccaaccaadbddccaababbdddacbccaaddaccbddcacbdbdccbabcbdccaddcbbdabcdacacbbdbbcdcccdddbdddaccabbcdcabbdcdbdcdbabccbbdabadbccdaddcbcbadaadcccbdabdbadbbbcbdaaacdaccabbbbdbbbaddbaddbadcaabdddadbdcdcbddbcbacdacbcbdbbddacdadadbaccccbdcbcabdaaccdcddcaadcacadcbbcdabaaabdbcbcdacbacbccbcbdbbdaaabacddccbaabaccbddcabbcdacbbdbbabdbdabbabbcaaaadbdbcaadaddbccacdadccddcdadcbadbacbdccdcbbadbcbcabcabcbabdcadbdcdbddbdbbddcdaddbcdadddcddcbbbacbabccdcdcabbcaadaddabaddacbbabcbbcdbcbbbbcdadcdbccbcaabdcbacbccddddbcbccadbacacaddbddcdcbdcdaadcbcbbcbccbbcaaacbdcdddbdcccbacdaccdadddbcdddbaaddddcbdcdbdbdccdcadcbdabccdbacccadccdcdcbddabbbabaddbcbcdbadbadadabdcbdbcbdddacdbbcdbacbcacbcdcacdccddadbdbcaabccdaaaaaaacbdccdbcdaacabbaaabcbccdacdbddcbacbdbdddbadcdcbbabadbcabcdadabdbcaddcacabaabaabbbcdadacabdadaadddabdcbcdcdabbcdaaccbbacacdbbddcadbdcaddcbbbddabcacbbadcbacbbacabddcccabcbdbcbdbcdabcdaacaadddcbddcabadaddadaacbbbdacdddbccccbccbcdcadabbcacddbaaddacdadabdaacdbcbbbddacdddaaabcbbbdcaaaacdadbddbaadcdcacccaddadacadbbcbaaccadabdbbcbacaccacabbdddacbddacabccdcbaddbdbbadaccdcbcadccaccaacdadcdbaacabdccbddadbcabdacdbdcdbbababddbccdbbbaadabddbacbccbcadbccbaabababbadadccccaabbbccbbadadccddccabdadadbdcbcdccacabcacadcdbadabcdaadaabdaddbdaadccbccddbaaaabaaabdcccacccdbbbadaaadcabddddcdacaccbbbdcacbdbdadbbbbbccdcddaddbdadbdbbadcdabbabaaabcccadadabacacadabdaacbbbbbcadadacddccdbcbacbaadbccdbbdaccddbcdabccddcbdacdbabbbbdcdbadadbbcdddbbccdadbdabccaaccadacbabbccccacdbbbdabaaaabaaccacbddcbbcacadbcaaacdcaccbcbdbbccbcccdbbcbdcddccbbcdbcbdbabcccaabdabbbbbadadacbdacddddcaacbbdbbacccdaaaaccbbdbcdbddbabcadbcabbaccacdcaadbaaadcbacbccbbdaddabbdbbbdcdacacaaddbacaadaccdaaaadbdbacccbcbbabadaaaabbccbbcbbabdddccbbbccdcbaabacbbacacabdbbcddabcdcbcacddccaccdbdadbaaabdacddbddbbccaacdccbabdbbcabddbddddbacabccbbbbadcdbbadcbbbbdcdbdbbbabbabddcaddcaaaadabadacaaabddbcdbcaadaabbcdcbbddbbcadddbadbadbbaaacbaddccabbcbbbcbaacdbdabddddababbcdddaddadaacddbbadaaddacbabbcbcdaadddcbcdcdcacccbccabbcabccbcdabcabaabbbbaabbccddacaadcdadcacdcdbbacdddcddacbddabaccaaaacbbcbadbacababcbdcacbcdbaddacaadcddddcbcaababcacbbcbbbabddcdcdcdbcaccbddbbdabcaacbadadbbdcbcdccccbaaacaacacccbcbbbadcbcbddcdcaaccadbbbcbaccaaadddbadbbdbadaaccaaadbbcaaccbacbcbdacdbccabcbddadcabdcadbcdbdcccabbddbcabbaabccadccaddbddadaabccadabaccbbcacadbbcbbcdcccdcdaccacaabbbcbbcddcbbcdbbcdabbcdadaddcbacbadbcbaacbaaaadabcbcdabddbdcbbcdccbddbabacbacbaacacdddbbddabacabbcaacabdddbcbbbdbaacdbcdcbacbbccbadaaddabadabbbdcdcbbcacbadacccaabcdabdbdcadbaacabadcddaadddaacbabbbadadbbcddacdabcacaadddccdabacdbdcacadadbbbaccdbabacbcadddbabcabddbccbaddaacdcabddababbdbdacaaabddcdacaadabccaaabddbddcbabadbdccbccbcdbadbdcddcacccdbbabadcaaacddabbdacdbddbcadacaacadddcccdbabaaaacbbadabadddcabbcddbcaacdcaadcdadadcdcdadbcaabdbabcccddccbbddacccdbccdaaacddbcbdbabacaaacdbaccacdaddbdcbcdddaabacaabdabcaaccdabcbcbdcbbdbcacbbbbccacbcdbdaccddbbccadcbbbdbacbdddcbdddcdbaadabcacdcccadcababaabbbbccdcbabdddadcccdaaccaaacbbdbabcadbabcbddbacccdbcadbadabdccbbdbbdcbabbabadabacadcbbadbadddcaacadbdaabdaaadcdbcddbcaddabcacabbccacaaacdbaaabcadbddcccdcabcbaaacdadddadbdbddddcadbbcbbaddbcdbbccdcaaddbbccdcdbcbdccaddbbdcabbadccaabdcaacbaabcbddcdacbdcbadcdacdaaaadbdbdadcbadbcaaabdbcacacadaabdaacacbbaaddadddcacabaddcdbcdacbbdccddcabcdacccacabddadaccacaddacbbccacacbcccdaabdccaabcdacaabbdbdbcabbcbdbcadaddcabcacbbddbcbaadbcdcdcaacdadbdbabdadcbbdaadbddbacbdabbaacabacdcddddadccdcadcbcaadbdcacababddbdcbabdacbadbdcbabddaddaabccdbaadabccacbbddadcdcdaabdbabadbbaaddaadccabbaddccabaaabbdbacbaaadddddbabdcbbacbbcbcbdbbacdadccbadbcbbdbdcbabbcdaacbdbbacbbbaaddbbcdbbbadcbabcbcbdccdcccddbcbdccdaccdadccbddbaddcbbaabddcbdcccaccbcddbbaadcdaccaaddbacbdbcbdcbadbabcbbaabbcddbadcdbacdcccdbacbcbbaadaacabdadcabccbcbbbbacdcbcccacbccbbcddacdbaddcbdbcddbbdbccdbaaaddaabaabddababdcdcbdcccdbdbbcccbdcbdbbabadccdacacbbbbbdccabdbacddaddbbdbddbdbaaaacacadcaabacdacdcdadcabbdddcbbacccacabadacdcdadbaacadcbabdbaddabddcaabbbbdccbcbdcacbadbcddcadcccddcbabbcaaadcaaadbaabddadaaaccaadaaabadddcdabadcdbdcddacbabadddacadccbbdadbbcbdcddbcbbaddacbdbcbacbcdcbddbdaccadccaaaccadbddabdaccabacadccbdabccaabcccdbbbabbbabcdbdcbccdadcabbccaabbcabdcbaddcdddadadcbcbacccbaccbabadaddbdabbccbacdacdbdbddabddcdbacadbabdcbbabbddcaabcbcacdcacaaaadbcdabdabccddddbdbcaddbaaadbaccbcaadbbaddddbabbabbdabaaabdddccdbbdcacbcbcbbbcbcaddabdbdcddbadaccdadddaaccaabcdbadbadbbcccdabbdadaaacaacacabbacdacbacdbcbdabbbbabacbabdbbabadbdabbaddbbccacdbaadddabcdcbadcabdcdccccbdbdbdbddabbbbaacaaccaacdadbdddabcbbdcbbbdabdcdddbddbbdbdccbbdccbaadddbaddadccbcbdbadddcdddadbbadcdcbbcadcdabbcabadcacaadcbbbdcbdbcbbabcdddaaabcccbbdcbabdbbaacbddbbaaacccbcabadaddaaaacdbdadabcbcacbadabdbdabbaabbddcdbacdbcdcbbbddbcacdbddbbbbbccabcdbbbbbbbdbbdbadcbdaccbbaabdadbbcaabcadbccddcdcdcdbacdbcbbbdcacdabdabbabcaccbbbbdcaaddadccadabaddabccadcbbadadacbccdcacbcbdcccdcddaacbbcaabbdaabadacdccdadbbaccaddabdacdbddaccadbabdcdbbcadccdbdbacbcabbbadabdbccccaabcadaaaadbbabcbadccbadcaadabbcbdbccdcbdcdcbaadaddcadddbdbbbabdabdaccdcabcaabdccbbbdbbdcdbddbcbdadbbaaccdccaddcaaacbcbcdccdacdbccbbbcdccbbaddaabcccabbacbccdbcddcadbcabcaadbdcdbcbbaadcdbcdbbbcadcabbbaacddbaaabdccdcaaaacabcbdadbdcaacabcdddddadbbdddbdacbdabbabcbdbcaadbddcadcbcdddccaabdaddbdbababdcccdbcdababbaacdcbdaccdbcbdbacbddbbbddacaadbdaaacaddbdaabdddcaacacadbcdbbadabcbdbadcadcacdbdccbdaadbaadadababdbaacdbbbbbadbbabcdadcddddaddcbabbbdbdabbcdaddbcacddabaacbbababcddbbbdcdddbbcadbdbacbacacaddcadcbaddcdababaaaccacdbaaddbbacaddcaabaabdcddbaabddbcabcbcadcbbcdddcdaabbaacabbccbcacadadbaccdcccccbcddbcaccaddcccdcddabcbbadcddbcdacbabbadcccbdbacdabaccabaacbcdbbacbaabbadcbbbdbccbcdcadbacadcaccacbaddbcabcbcbaaacdacddbbdcdabaaccaccbcccbacddabaacbbdcbccbdabbacdccabcdbbdadddcdcbaabcbddcabaaccadcccdaacdcadacaaccdacacddcacbbdcdadbaadcabccdaadddbacdbbcbaaaddaccabaadacccbadcccccbbcabcacbbcccacbcbaaabdacdaabbbaabbaacbbcadaababbcabdcadabddbdcaabaaaaccbccddccabdddadddaaabbdcbcbccadaaabcccbcdcadbabccabccbdbbbbbdbddadcbdbdccabcabbdcdbdcbccabbdbbaccbcbdbbaaadbabbadbcbdcaddccbadcdbcddbbbbcbaaaadbcdbbadbccbccaabaccddcbbaddbcaabacadddbbaabcaddbcacabbcadadcbcdbaaadcacbbccdbaacbaaaaddbabaaddbcaaaaabbdbdbddbdbbbdbcdacabdbbcaabbdadddaaabaddbabaabbcccdacddbccdabcabcbbacaabbadbbdcaabbadabacccaccdabababbbddcbdbdbacdccbccabdbcdaadadaabbbdaaadbbbcaabbbadbbbccdacaaacdccbddaaaabaadadcccbcbadddcddabdbbdcdaaadcdadcdaaadbdcbbbccbbaacdbabaacbdddcccbababccccdbaabcadabcbbbcbababcdbddbaddaaaddbadbbbbdacaacbdbacacbdacdbdaaadccdcddcbdadacacccaadaccbbcadadabdcdadacaabadbbadacaabcbaadcdaabdcbbdccbbaabcbadbaadaadccdbadbdacbacaaadcaadaccddccdacbdccacddbabdcadacabdbadccacbccdccdcabbcbbaccdbdcbadbdbbaaccccdabababddbadcddaacdaddaddacabcbbbccddbccbbdabbbabcdacdbaabbdcabacccbabddadddbabddabddbdccdaadcccbabaaadbdcdacaccaacdadacdbddbbbdcacddcdabbadaabddcbaddacbcabbbcabccdbccbadcbdcbbabdacbabddbbccadcbaccbbddbabdadbdcabddaabbcddaadbcbccddccddaaddbacddaddbdbaaccbbcbadbabdbbcacdaaddbaadcdbccdcbadbccaaadaaccdbddcbbbcdbaddccadbbadbcbbcaadacbcbdaacaaaccabdbdacdacbbccabacbdbddbbbabdbbacddbbdacadadababcbcbdccacbabcbabbbdcbdcdddadcadbbadddbcbbcddbabbcdcaaabcbaccabaabddbbccaaccaadbcaccbbdccdabddcbdddabcaaacdaaaaabdabaaccaacddcbabccaacccbaddcaacbacbdbcaaabccbacdccabdcbabbbdbdcdcbdcbddbadadacdbabacddbbbbacbcccbdcddccdddccaddcdbadbbcabdbacdaaccbddbcdbbdaadcddadbcaddaddaaabbabdbccdbcbcbbcddbacdbacbcbadbdbcdabcddbaddcacaddaacdcbbadbcbdcddacabccdbddbcdbcdaaacbdbaadcbbabdcbbaacdddbbcacaccadddccdadadaabdbaddacddbbcbcbbaaacddddcababdaacbdadcaabaacdadacbaabbacacbcacdcbdccacdcabaadcbcacacdcdbcaabdcbdacbdbbdaaccdbbbdbbaabbcbdcacaccccdbadcaadcdacabdcbacacdcbcdbdccadaaabccacbbdcddcccbaacaaacdcbcbcaddbaabbaacabdbacbbbaadcbccbcddbbadbaacdccacbdcacbbcbadbaadbbababcccacdcddbdbdbdbccacddbacbdcbbcbbcbadbbbdabdaabdbcaaabccdcaddacbbbbccbcadbbdbcccbdbcdaababbcbdbacbbddbdbcadccdbdcacbaadcacbddadcbaacddbabbcaddabbacbabcadbddcbaacadabbdadaaabcbcbbcbcdcabccbbaacdadabbdcabdddabcccccdddcdbdcadcdcabaacdbaaaaccacadcdcdbbacccabdacaaabdbcabdaacccaabbdadcbcdaacdaaadbacdbdadddbcbbbbdccdabdbbabcadabdccbbcccadabdacacacdaaccabaaddadbbdbcdbcacbdcaddcacabcaacbcacaabaabbcadacccadbacccacaadadcaabdbddaadcbcacdbabdcacddbbbbccaacddbaddabbaaccdadcdddaccadbabdcddbabbaabaaddbaacacaabbddacacddabdcdcdbdadccbdabcacccdacbcadcccccbddcacbdabdbcddcdccdbcaadccaddbdcdadabbdbbaddbbbbbdbdcadcdddcdacddddbddbdaadcbddbabdacdacbabdcdbcddabdadcdabcdcabcbabcadcaabbddcdcabccddcadbbbaadaccdadcdbadccddabdccdaaddbdbaddabaadbacbacaaaddadcdbaabaacddddcacdcaaadaabcababcbaabbcacbdbdaddcdaabccbabcccabddccbbdcabbdbbdddadccbcdbabdabccaddccacbbbccaabddadcabcbbbcdbdcdabddddbbdcbbabcabdcdcbccddacdcbbdddcacbbcdbddbbbdbbbbbdcbcabadcdbddbbbbccbcadbdcdcdadbbdbcbdccccccccddccdacbcadadbbbbaddbcaadcbbcabbabaabadbcbcccacdadcbdabbbbcacbdabacaabbabddadbaccdbcccdbcbcdabbbdcadbdbdcddcabadbbbbcbdabdadbdcaadaacbdbbbcbaaabdabcdaaccdbdcaddcbddbacccbdadbaacdccbbdabbadbaaaacabaaccbddabcdbbbadacabcacaadadcaabbbacccbacbcdddcdaaccbbdbbaacdbcdccabbdcacdbccbbcbdbccbcccbddbbaabbcaccbacadcbdadddcbbcaacabbdccdbabcbddbadaaaaacdabdcaabbcabbdbacabdccdcbcbddcaddbbbcbdaddcbddbaabddcccdcdcacdbdaddcddacaddabdbcdcdddbabbdccbadbdcdccaababadadccdbaccbadaccbbbbbccdcaccaddbacddaaadaaddbbabbabdaddcbabdabdbcacbbcadcacaacaaddccbbacdbdddccbbdbaabbbdbaadcadcdccaddabbcbdcdacbbdbbdadbdccacbcccdcdcdcdacabadaaacbdbbcdbdccdcaccdbacaccdbbadbdccddbaabdadcdcadbcbaccccaadcbbdabbdaabaaaabcdbadbbdabacaacddccbcddbcbcbbadccccbbbabdbcddcdcbbccbcccdddbccdbdadbababacbcacbadabccbabcbcbcdcdabcaaacadabdbababccddabaabbabbcdccadbababacbbbdcdcdcddddacbaabacdbacaaabbaabaddaccccdcbdcdcbcddabdaaaacdabccddbdbbdbbbcadcaaaabaabcbcaabaacbbbacbdadaadbccdbacaccbddbbcdddcbdcbcbaabadadddcdacbdbbddbbacbacddaacbacdcdbbcbddabadbdcacbccabaddbbabddabcbaabaaccbbabdabcdccadacaabcbdacbbaabcdaadcacddbcbddaccbaaaddcbdbcadcadcbacabdccccabbccddcbbddbcacadaabcacababbbdccccdaaadcccaadabccaabcacaccbdbadabbbabdaaabddadbdaabcbdadddbbcaaddbdabaacdcbbddacdcdaaadbbddcbbadcccdadccbdcaddaabacbcdbbccbdbcadbbddcabaadbbbddacaccdaaaaabdcdaabaaaadcbabacadbaabccdabbdcddaaabaabababbddbdadaabcdddbabccbdabddbbaacdcddabacddbabbbcaaabbccbcdbaaddbbaadaadadbdcbababdbaabbadcacdacaabdadcdaddbccadcbdaabdddabacdbadbdbbbcccdbaaaacdcbdacabbbaaabddabdcccbabdddadbddcbdabacdccababdbcbbdcddbaaddddbddddbacddabbadbbccbcbbaacabaabcbcddbccdaabddbabbbaccddacbadbadccababddaacdbbbcccadbbbbdcbbacbccbcbdaaccdcadadbabcbccabadcbabbdacdcabcbacdcbadbdbabbcdaadbcbdaacadcdcadbbbdcabccdbdcbdddcbdbdadbacadadaadbbdacadcbdaccabbcaccdcbbbacbcacbbdbbbdadabbbcbcaaacdbdbadccbbaddabcdddccdbddcbbcabbaaadabdaaacdaddcbcabcbddadadabcbbcdbccbabadcaabdaadaadabdababadbdcdabcbcaaddacddabcbdacabbcacaaacbaacbdbcadaacbdaaccaaccbdcddbbdbccabaacdbbddcddabaacdbbaabadddcbbbcbcccccdbcbbdbacdccbcbddbcdabbcbaddddaddbaaaddbccaaabbbaababdcccdcabbabdbcbccbbdddbabaabcacdbaaaddaccddcdadacaaaadbdabdacccaacbaabdbaabaabcdbdadccbaabcccadccadabbcbaaaaacdbddddbbbdcdcdacbdddabdddacdcadcbacdaabddacacacdbbbdaadcbbcacdbbadbaacbcbcadcdcdcccdbdcdbaadbbbbbbdccbdccddbdcadaaaabadbbbdcbcaacabacbbadcbcaacdacbcacbbaaacbdcccdddacaacaabbaccbabaaadcdbdcbcdaccbcbbabcdbcdacbdcccdacbabaacadcabccaaadaaddbdadcadbabcbbcdadbbddaacbacacdabdbbbdcdbadddcbddbcddadbdbcacdbcdbcadbadbccbdcdcbcbdabccbdadbdaddacdabcdcccdabccbaacdabdddadcdcbbdbaacbddaddddaaadbddbbdbcadacbacddaaadcbbbddaddbbcacdaaadcbaadccdadadbbaaadbbbbbacdacdaacbdcccbadabdaabdcabbcbaddbbccdaaaacbdadbdabcccacbcabbccadccaacababccdacaacbbbbccdadaacbaddcbdcadcddaccdcbdddcdbdaadacabcddbcdcdbccbabcbccaaadcdadaacaaaddcccabcdbcdcdacbaaabdbccdccbbcacaaccdbcccdcbbaacccccdaabdaacbcdabcbbabbccccbccadaaacbdbaaaaaaadadcdabbdcabddcccbdbacacddabaadbbdbbadabcdabadbacccadbbbbdcdbcbdaadddbababccdaabacbdbadacadcdbddcbbbbdcbccdbcdcddaabcccddbcbbbdcbdabdaababcacadaabacbaccadddbddccadbcbaccadbdbacdbacdcabbbdbbddbbacdbbccaaddbbadadbbbddbbaaacabbcccbdbbcbabbdcdbddbabadabaaaaddaadbcdbbddbbbcbccdddbdabdcadbdaabbdcccacdacdccbabcaabbaadcaaaccbddbcaacbaaaaaddbbcbcbbdacbbdddbbadbdcbababcddbccaddadacccbdadacadbaadaccbcbbdadbbdbcacbbcababcbdaaccdddaccbbadbbabbbbddbcaacdabadccacaaaccbdcdbdbadabdbdbdacdadcabbcbabcdccdbadbabaddbccbbaaaaccdccacdbaacdcbccccaacbcdcbaabccdcabcdcbaabbbdcbdcbbccccddbdbbaacbabbcbbdbcbddbabccdddcbdcbbdcaccdbacbaacddacaaabbcacdbdccbdbcbcdbaabbbcadadbabbcddcaadabacbaaddccccabcdcacccdcdbbccbbadaccddbcadcbcabbdaddacdbcccaaadabcccadddcbcdaacacacaddcabacaabadcaadbaaabbbdabdcdbacbbdbbdcbbbcbcbdddbacaddabcaddbcddddddabbaabdacdaaccbbcbaabcdcbcbbcbcbdddbbddccaaaaccccccbcdbaaccdcbcdabdabcdcccbbdadaaccaccdadbaacaddbcbbdcbbccbbcbcdabaabaaabacbcabdbcbdabddbacccabdbaadcdbcdbadddaacbdaabdddcdcdbcaaccdccadadbabbacaadcccddccabababaacbbbcdbddadbbbbcbcdccbddbbbccdcaabbbdbcabbcdabcabacddcbccbddcccbbdbbadccdbcddbcaadaaacccdacbdcdadcdcddbbbbbcdccaabacaacdadbcbdbddaacbcbcabcdbabacadadccbbcbbaacbcddddaaacbdcddbcdbacbccbdbbdacdccaababcaabbaddcabaaacbbcadccbbddbcbcdaaadadaadbccaddddaabbababddcdaacdbcbacccbccbdaccacadacbdcccabbcaaccddbdadacbdacaaabacaadacabbbbbadccbbbacababcbccbdcddbbcdcadaaaddababdbbbabbdbcdcddbdadbcdbdbddadaddccdcacadcccddabcdccbdaabacbbcacbaacdadbcacacdcdaacdcbabadcdabcbdcacbddaabdcaccbbcabdbdabdcdcdbabbcdacdbdabcacddbabdccbbaddcdbcddadcadcaabccdabaccddbbdabbaacdabaacbbcbcccabbdaddbbabcacabbcbadbcaabcccbdacdcbbbdbaccabbaacccbdadbddaaacbcbaccdddbcbddacdcabcbbdacbbddacccaaaddbdccbcbdcdccabbacbacbdaadaaddcaddddbcbdcdbbacdabbbdabaddddbcbcabbcbcabaddbcdcddcbccbdbdbabbccbdbababdcbabccbcdcbaccbcabcabdcccdbcbdcaabaababbbacaccccdadccdccdcdbaccbccacdbadcbddcdccdaacbddacaddccadcadccbadcccdcbaaaddacbacacdcbdadcbbacdadaddcbdbdbdcaabbcbdbbdadddcdababdcaacabdddaabbadcbbbaccababdcbdcbcddcaabbddccdbbaabbcabdddcacabdcbddcdaaddacadbdcbbdbbabdcbdaabacdcbcbaccdcdabacdcbcaddbadacacacbdaacabccbcccbbbdbaddbddcacacbbaadcacccaaddbcdbabddaccadbbbbddbcbbabcaabcdcdbcdaddcabdbcbaccbcabbcbaccdacdcabdadadaabaddcdaccdbabccacacbcdabacaaabbcabbdaadbacbdabdccccbabdbadcaacdbdbabdbbabdddbcdaddcdcaaadccbccdbdbabddacdbadcdcadbddcdddacbcdbadccadabadacadccbcacacdddbcbdddcdcccaadbcadababaaaadcdbabcdbdbdddcbbbdcbcaaacadacabdacacaccdcdbccabbdadcdddcbcaaaccaddaabcdcabdaadaabaaabbabddacbacaddbaabcaaadbcdaaacddcddddbdacadadbdaaaddcddaabadaccddaaccdbacbaaaccbbccadccdbdababdddbdddbcccababaccaddddcdacaaaacbaabacdacacacddbabbddabcaacbadbbaccadccdcbbbddbbcaddadccadcaabdcdbccbbddaaadacadbbdcddbcdbcaadbcabaaabcccccdbbddccbabbddbbbbabaacbdbcdaccdaacadbdaacabdacadabddbccabbdbdcdbdacabccadcdccccbabadacacbdbadabccbbbacccdbdaabddcbbabddcacbcacccdcddccccddaacadaacdbabddcacdbddccabbbaddcdddabcbacaccadcdabcddccbbdaddbcabaadbdccdaacbbdaccdbcdbcdbaddaccadacbdcadbdacdbbcbddaaabbcacadaccacbdcbaabcbbcaaaccbbdcacaadcaddcddbbaabbccaaccdaadabcababbcbbacaddbbbdaccdbbcabcaddadcdccddbddbbbbbbabadbabdabcccbdccddacbddcdddbccacdbdbbdccddacccdbdacdabbbbaddbccdaabbddbbcdaacdacdcaddbacabbcdaddbdcacbcbddddaddddbcddabdbbcadbcccaddbcabcbdbaaccccadabcbdaadcdbdcdacbbddcdcaabdabaddbabaddbadbaabdbbbddbabcbbcaaddbddcadbbdddabdaacdcdaadbbdcddabadcbcbaacadccbbdcababdaabbabbccdcccdadbadccdbacbcbacbcbcbaccaadacabdbbddddcdbcbdddcaacccdbcccbdacdadabccccabbadbbaddbaaabaaabbcbabcdbccabdacbabbbcbdacadcbacaaaadabaaaccdccbbabccacdccadddcbacaaaddccdadadbdccdcabaaccacdbbaaddccbbacdcbacdadabcddbcaacccacaadbbbadcbbbaadcdabbbabbabdadabbaaccdcdbccdbcdcdababacdccacdccaccbacaacccbcbacdbadddccbdbbddcdbbcccacdbacccdbddcdbbaadddbbbaadbbbdcccdabdcabcaaabacdbbbdbcacadcadbcccbdcaacacbdbadcccaadcdaabcbaddabcaddcacadabddcbddbcddbbaaadccbcccacdbddbbdbcabddddacbcdaacdcdacdbcbaaaacbccaabacdddbdbcbcdadddccdbbaaddaddcacbbacdbbdcdcbdacbcbabcaaaaddcaabccaabbdaccabcdcaccdbddaabaaddadacccadacccacabccdcbabacdadccababbddacbbbbdacabaddacaabcddbdbcbdbaabadddddadcbdbdcacdbbadddcbadbdadcadaccccaadccbcadbbbddccdcdccdcaacbbdbabddbdccbcacaadcbccadcdbcadadbbabdbcbbcabcbccdbcdcadaadcadbbdbadddbdbbbadbdbdcdccdadbadaaaabcaacbddbccdcccbacaacaadbabbacadaadcbcaaaabacacabbcbcccdddadcbcdcbbbadbcadcbbdbcccdadabcddabdcdddadcdadabcabbacbbcaadcaadaccbbddddbacbbddcaaadcaaaabdaddbcccccbdcacdcbabcdbdaaaabcaaababaadbbbbaaaddbbdbcbabdcbaccdaadabddcdbbabbcdbbcadaaacadaacbcbaacaaacbaacdbadaacaacdcddbcbbdbabbabcaddbacabacaabbdbaccdbdcdadacbcabcddacbcddbcdbdacbdccdcdaabbccbcbbadbbdbbbaadabaddcadcaaaccadcbbcaccadddbccbdaaccccccaacdddaacbdaacbbcbcbcdcdddcbbaddddabdabbcbadbacadcbaabbdbdbcbdadaadccaaccdddddabccbbbbbcaacadadadabcaddcbaabcaaadabcccdcdbbdbccdadacacbabdddbcabcbbcaccdbdddacbacaaadbdbacbcbcdbcacbcbcddbdadacacdacbddcdbbdcdbcaccddaddbabcaddbabaccbadcbdbacdcacaacdcdddbbbaabacaccccaacaddcadcbbaabcdadabdcdccbaabdccddddcaadcdddbddacdbccccccdbccaddbbaadaabddbcbacadaaacabadaddcabbddababdaccdddbcbaccacccacdadbdbcbcbacabcddcdbbdbaacadddbdaccddcadccaaacccdbdbbccbdbbbbdbcaaadbabacabacdadbababcdbcbaabdddddbdaadccbdacdaccadcaddccaaaccdbabbbcbbddacbddcccaacccaccbabbabbabacdddabbcdbccaaadcacbcdbccbbbdcaccadbadbacbaaaabcacdcbbdbadcaddadbaddbcdccdbbcacababdbddbddcabdaacbcbbbabcccdbbdbbabaaccbdabcabadcabdbbccddcddcabdbcbdbddacadcbbcbacbbcddbcbccbcabbbdcbccbccbbbcddcadbddcacacdcacbbaabbdcdadcccdaabdbbaabadcbccddaabbdcdaddaaadbaadaaadacacdbcbcdccadcdbccaabbbdccaccabdacdaabcbcdbaaabcbdddaddbadbbbdbddababbcabddbbcaabbdcadddbdccdcbccdbdadaacbaddddbddaadbbcbccacabddccbadbaccbcbbdbbcdbabdcadcdbdcdbdbddbaaccbdccdcbcacddcbcabadbaaaabbaacbabbcaaacbdcbacabddaccdcbbcdbdccccdbbcbbbdacaddbbdbcbbbadcbdbbbcdddacacdbcdddadbbccabadaaabaaacdbdcdacccabccbadccbbcddadddcdcbaddbabaadbbccdcbcddcadcccaaaddaabcbdbdbcdbbadbcadcacbadbdbabbbbcdddabbdadbddaaccbaccbabaaccababbadcadcccdcdddbbbbaaaaaadbacdabbdccbdbcdaddbacaddddcccdadbdbabaacbdbbbdbdcbcccabcdabdcccccccbdacadcadacabcdbcdccaaaaccabbccbabbaddbbdbcbabcdcbccadcdbadbbccdaabbbabbccadcaccdddcbbdddbadacddbabbbdbcabdcbccacdbabaddabbcacabdbabdacdcabddbdbbdbddabdadccabcbccdadddacbcbcdadcadaddbddbcadbbacabcbdcccadabccadbcbbdbabbcddaabdaadbbdabdabaaaacadbbccbcacdddabbaaadcdccaaddcdbcdbbdcddccbadbacaadaddcadbacbddbcabdaacaccdddabcbccabddddadcabddabdbcddcacbddccbcaaccbddcccaacaadccdcbdbbadbdbacaacaaabcacbdddbddbcabacdcbaadddbaadcbbccbcdacadaaababbdcbbbaaaccabbcdaccbaabbbbdcbadaadcaabbacbbccacabadabbaababbcccabbbcbbaadcdbbbccaadcbcbacdbbaadddcbccbabbcaaaaadadadaccdcdadcbbdabccbabbcacbaaccdbcabcbdcaabcdbccdcbdcacdcddbcdcdbddccccbbdaccbdcaddabacdaccdbabbacbbbdcbdbbddacadaadcbdadacbcacabadddccabacbcdddbcabaaaadadbbdbcbcaabdbaacbacbcbbdddbaaadcbbbbcbabdddabdddbaacdaacbdbbbadcaccdbcbbccadbcdbbadccbbaccbdcabbbabadbbaadbdbaacdbacdabdddbdddcccccbccdaadbbbdbbcddbdbdccaaaadbbacaadbaaacbdbbddccdaadabadcdbcadacaddbdbdababdbddcabddabcbbdcbddadbcadbcbaabcbabbcacbbcbcccaaadbcbaaddbdcdcacddbadadabdbccacbcacadbabbaaccaacadaabdccdccbabccbbbaddbbbcccccbdcdbbadbcdadcbbdaddcbddacccaacdaddabdaaddabadcbbbbbccaadcbbdbbaadaccdbdbddabdbbbddaabcccaccbccabaaacdcdcbabdccacabdabbddabcabcaabbdbbaccbdbbaddaccdccabaccaadbaabbcbddbcdaaabcbaaaadabaacbbdbddbcccaddcadcbdbbdbcbbcdcbaabbdcacadcccddbdbcbcacaddcdaaaacaddabdadacdbbbcabadbcbbcbcbabdaacddaabcbbbbdaddbdaabaacdddacdccccbdbccddcbddacdbacabaccbbddccdbdbaacdcaddaccbcaacbcbdccbdadbdacdbcbadbaaadbddcddcdcccbbccaacacacdbaccdacbcbccadbbcbdddaaadbbdbabacbaadaccbbdccacbddaaacdcdcddabdcbbcbcddadcddbadabdcadaaacbddbaadbabbaccbcdbbbbdbccacbccdcdbbcbbcabaababdabcacdcdaacaddbbbdbaadacaaddaccacabbddbaaabbcdcaacaaddabcddaddbcddccbbddccabbdadcdbbdacccadbaaadbdbabaaacddadddbbabdadabaddaabbbcddabaadadccdcaadbdcbabcdbaddbddaadbbdaadbcdcbcdbadcdccbbbbaabdbbbbcdcddaccdaabcdcbdcbccaacbbaadcdbbbacaabdcbcbabccbccbbbcabadcaccabadddaddbbdddcbbacbddaccdcbccdbcbadbbdaacdacdacdbabbcababddcbdbbdbbbaadccbbdcbdcccdcdccdccaaddbdcdbbbcbdcbbbbcaabbdcddcbcbbabdcdcbcabcbbaabaadcbabacabbbbccbdddcdbbccadacbaaddbdbccbabcadccdbcbccbbacabcdcdcdaaaddcdbcbabbccacdbbcdbabbbcbcbcaadbbabbcdabdbdcbcdbdcbdbdbbdabcaabbadcddaaaaabbacdccdabcaadacdbabbcaacdcdbddcadccbbbcdbbaaaadcbacdabcbbdbcababcbdbabcbdbcaaddcadaaddcaaccdbccdbdaabcdddacbdaaaaddcdbdcccbbacdcdccbcadabbcbbaacaccdaacadacddbdccaaabddabdddcdddabcdcadbbbcbacaabcdbbccdddaacbcaadcbbbbbbdbabcddaddbbcccdbdcccbdacdbcdbadccdbbdadbdadddabaaaabddaaaddbcddaccadccccaacbccccacbaabadcacabbcdabcaabbdbdcadcabdbcbcdabbdbabccabbddcbbadaddbcbcaabbcaacaacbddbdabdcadabbabdbcdbadaddbaadaddddbacccdbcdbabaacaaccdcbdabbdccbacadddadcddcdcbcbccaddcbcabdaccacbbdcabbcaccdacbbadbcdcabbcacbcbdddcabcdcdbcabaadacdadbcaacbdbabaaacadbdbabbbaabdaddbaddcadbcbddabdadbacabbbdbacadcbabadabacbcdcabadadbadaaabbcadcdacdabbaacacabdadbaccbbaaaadaddacccbdccdbcbacbdcaadbbbccadddacbbdbbdbccbccbabcaadbaaaddbacdcadabcccbcbcddccdcaabaaaacbabaaaccabbdbcaddcdabaaddabdbcddbbcadbcbcdaccadcdbabbdabcdbbadacdababddbbdcaabcbcadcacbbccaaacabbabadbdcabadabccbccddbbbdadccabdcddababababbcdcdbadacbadbdabcacabccaddcdcbbacaccbbccacabadbdadabdacbadadadbcaddbaccddddbdbccabbaabdbcdcaddababadbddabbbcabbabbdcadccdabddacdbbbdbdbcddaabcaaaacdcdccacdcddadaaddacbdbccddbcbbbbaaaddaadcaabbbcbccbcbdbccbbababadaacdbdbadcbbacdadaadabbdbdbdbddcddcabcccbcadbbbbccdaccbbbdbdaaddbcdbccbcbddddcabaaacddbbcaabaadabbbccccdccbbdcdabcdaabcbacdbccdabdbdcdcadcdbbaddbdccadccdcbaccdcdbcdbbadbaadbbcaaddabcaadadaabaaacbabdadadaddbcabdbcbbaadddcddcbadbcaccaaadccddabdbacbdaaaddbadbdacddbdcbdccaddcacbcccacccdbacbaaaaacbcbcdaadcaacbdabddabcbcbadcadabbbabbbbbaacaddddbababadaaabdddbcdcacaacacadadbabacbabdbbadadbbdacdcaabcaddbdbdcaabdcdabddaddcddbabcdadbdbbdacabcdaabbcbadddbcbadcabacddabbcbcbcbcadbabbdbcccadcaddcbabbdddbbbbadabacdddabccdbaccbdbadadddaaacbdcdcdaacbddcdcbadacddddbdcbaacdadbbdbdbccacadbaabbaadaadddacddcdbddbbdaaddaaaccabdbbbbbdcdcdddabbcbaaadacaddcdcdcbcdcaaaaabcadbdbbddaccbbdabddbcadccbaddcdbabbbbdaaddcdaaadbbcdadbdbcbdddaabccdccdcabcaacadadaacaddbbdabaabaddacdcdbbddcdbcbcaaacbdbdbbbdbdbbcadabacdccbdacbbacbcadcdbaccadcdbdcdbbadbbcdcaaaaabccddcddbbcbabcbcaabdbccacbabdcabaacbdbdbccbcadbbcdcccaabadbadddbadcdcaadddcbddbdbdcccccccdbcddbabbbcdacdadcacbdbbcccdcbbcbcdacbdddacdcaadbdbbdaddccdddbcdabcabacccccbaaccbcabaaabbcabbcacccabcdacbbdbdacacddbacbcbbccadabcbbddabaddaaabaccbdcdabdbbbbaccdabaacdcacccbbcddaccdbabcbaacbbbbadbcbcdabaaaabadaaaacdacadabdbbccabadddcacdcaaccdabbdbdaabaddbdcccaddadbdddcbbcbdcadcbcdaabddddbbbbcddcccbdaccadbbbbabadaccbabaabdbbcbbabcdabddabdbdcdcaabacdbdcdcdbabddadbdbcdbacaccaddbddbcbadadaabbbddacaccbbadbbcaadbaccdccaccdbbddbcbbaacbadcbaadabbcbcadbaddbbaaaacbacadcddddacaadbdbadccdcccccababcdcabbbcbaadbadcbcadbbcccbdadbcbcdabdccdcdacadbccddabbabbdaaabbacabddadcabbbcbdddbabcdbcbdcdbababbaddddcaccddddadadaacbbdcacadddbdbdaacbcbdacbbaadaacdbccdcdcccdabbbcdacbcaabddbacabcbabadbadacdaaddbdcbddcdcddcaccdcbdcdcadccadddddbbdccbabcaadadddddbbaddcbdddcdcabaacddddbaddaacdbcccdcdacadcaadbcbadcdbdcddaacdaddcbabdbcaacdbcaaadcdbacdcabdbcddbccdbdbbaddbcaadabdbcabcbcdcdacdbbcdbdadddddbdbdbddbcdcadcabdacacddbdacdcbdbdcddaaaaaddbbdbadcacbbdbdbdcbddddccabaadbacbdccdaddaccadcddbdddadbcddabbaabddbabbccaacadabccbbacdcabddbbcbdbacbddddadccaadabcdadabcbbbdcccdbabdbbcbbbbbddbbaddbacdbcadcbbadaaaadaaaddddbaacbdbbbadbdadacdccbdbcbdaacabddadbbddcbdbdbcaabdaaccadcddbbbbbaccaadddcccbacdcccdbbadbaaadcbcbddcbccbdccbbadccadbbacadbbdcdcbddcccdadaccccacaaadaabdcbcdacbbadbbcccddbcdcdcccacbadbacdcbadabcbbbdaaaacbbacaacdccaadbdbdacbdcdcdaacccddbdacdacdabaabbbddddbacaaccbdbdcaabdddbcbdaaabaabadbbbcaaaccdadabdbdbddacbabcaabdadcddbaddbaccdcdcadabadaadcacddbdbcbcbcdadcacdcabbaadbabbbdadbdddcdbccacddbbbcdbdcabcbaddbbacddccadccbccdbabdbbccdcdcbaaaaddaabacdbddccbcddbadbaabcddaadccbacbbdbcccbacccccddbcbcabdaacddcdbccbbacbcaabbabcaccadadcadbacaacbacdacdcdabababcbddabbdbdcabdabbaccddbacbbacacbcadabcdddccbcccbbccbdbdbdacbdbbdddcadaaaddcdcdbdbdcababddaaddaddabdddcbbbaadbcdabdadaddccbdcdcccbbaddacdcdcaddcdbdaabcbbddddcbdadbdbccccbdcdbdcbcbacdbdbcddcbccaaababadbcacacabcdccdcaacddbccbcddcccccdacccccdcbadaacdbcdbdaddbabdbdaadbdbaccbacccaaaccabdcdacbaadaadcdbabcdbaadabdadbdcbdcadadddcbbaaddcccbaccbccadababadddcddadabbcdcbdaccbbcdbdbcbaaabbadbbadcbaacbcdcddacddcadabadaaaacbcaabcbcacabcddadcddbdccdbdaabdcadcbcdbddacacdbdacaacdddaccabbabadcabadcbabdcbdccbadbcadcbcacaccddabdbaadadbdcdcddcaddaccccdaabadcaadcbbaccaaaddabccadddddbdddbcaacacaabcbbccbbbdbaddabdccbccacbdcccabdaccaaaadaacabbbdcccbbcdabacadaabbcaccdcdddbcbccdababdcbacccabdccbcdbddcadcaddaacbddbcdbaacccaabbacaabdacaacbcccaacdbaaabcdbdcaaacabacdbacddbacbcddabdcaabcdbbcacddaddbaabaaadbdcaadbbaddbcabddadcbbcacbbacaaacccabdbcdbacabaccadbcdbbbaaabdddbcaccbcadabadbbcaaccacabacdbdcdaabcacdcbdcacbadbbbbcacacdcddcaccbbdabdddacacddabaccabadcdaaccbcdabddabdabbbcdadacaccaddcabccacbbccbbddabdcddbcdacbbcadccbaccaccbdddcbdabcbbaacccbdacdbcbdccdbbbdcaacdabcbdbdbcdbccbabacbbbabddccdbaaadccacccabcdcacadabaadcaabbaaddbbdccabbcaadcbdcabbbddacdbccdcbcbbadcbbadbccdcdaccabcdcdabdbaaadabdaccaabadacbccadabaadbbcccdaddcbdbcabbabdddacdadcbdbcddabcaccccaacbcaadddacacdddbbbcadcaadcdbbcdcdabcdddcdcadcadbbdbaabccccdbcabcadbcaababacaabcccbdcccbdabbbdbddccbabcacaacbbaabcddcbdcddacbcaabdbcbabadccbcbccbcadbbbadbcbcbdbbaddadacdccdaadadccdcdaacbcdcdabccbbbabcddddccdbbddacbabacddaaabbdddbccdcdcbaabcbdacdaaabcccbddbabbcdbacabaddadddabadbbbcadadcbabcdbdbccbbcdcdddbbbdccadcacabacddaabbccacddbccccbbcccbdcccddabbbdccccacdcdccbaabccccbacabcbadbddaaddbddacbcbbaaabdccdbdcdabacbabcbabddbdbbadbaacbacdcdadaadcbdaccdadcaadddaacdcacbbbabcbbcddbadcdbbcadabadcddadbacbdabbabdbcbaacbdbbbcaabcbbabdcadabdcbbbbaabaacabcbdcbbbcdbcbcdbadbaacadbcbccabbacbaaadaacadaddabcadddababadabadcbcaccddbdcccdcacbbadccdaccaacccababccbbdccaddbbadcaabbddaccacadcacbddacadadaaadbcdccbcdabbadacbbabaaaaddbbcdbcddabdcbaccdccbbdaddaadcdddbbbbbaaacabcdabdacbbbdbccaddbcccddbddcccadcdbcdccbdbaadaabaababddabdaccdbdccabadbcdabdcddcacbcccbabcaddbdddbacbcdccccddcbdcbcdadaccbddbdaadcbaadcacdbbbbdbcbbbacccddbdabbbcacaacabcadaaabaacabadbbadbcbccdccbbcddacdacbcddbbdcdccdcdabdaccbcaaacdcdbadcbbdaaaababdaccddcdbcdaabacdadcbcacdbabbddbccadbabdacbbcbddccddbcadabcacaaadabdccddbaadcbabddcdbadacdadcbaaddbbdbbdbaabdaabdbbcbdcbadaddabcbcadacdddcbaccbdcadabdbcdcadbdbccccdaabcbddacabddcdbabbccdcbbccdccdcadacdccbabcadbdacaacbcbdddcdacdadacbcadddbcacaccaaaccabccaaabcdaccbacdabababdaadccdcdabcdaadadbaabddcbcbdaaacaaddbdcacddbacacadccccbdccbdccbaaababcbcccabdbdcbddaabaaaccbdcdbaddadcbbbcddbddbddcbddccbaaaaaaabcdaccaacdcccdcdbbbcacaabccbaacccdcdccddccccdccddddccbcdcccdacccadacaccadbdadcaccadcbaddcdcddcabccabccababaadaddbdcbbdbdabdabaddabaddccccddbbabdacaadccdbabdcbbdcccbacbadbcaddabdaaccbdbaadaddabbcdcdcdccacabdccdbaadbacbbdcdabdacdddcabdbdcbcbbdbccaabbaddcccacdbcdaccbddacbcbdabddddbaccadbdbbdcddddabbbddbbaaaddaaccdccccdbaccdacddbcbbccdcadcacacccdbdbcacabdddbaacddcccbadbdaaabbcabcaaabcddcbadadbaaddcbdbbaadbbcbbbaaaccdadccdbdaddbddabadcdccbbdcbbbabadbabaabadbddadbabbabbbabbcddaccdadaabdcacbadccacbaacdcaaaaccaabbababcddacdcdcbbbadabadaddabccbcaddcbdaaaddbaacacbccaccacdcccbbbbbbdaddbaacbcddbbababccaaadadcbcabadbcccacdcaaaaccbbbdaadbddbaabbdddcbaddadbacacbdcbaddabcacabdddacbbacacdaaacdbbdcaccdadaadacacdaccdccbbdabbdbddadccbaabdcbabbacccdaadcaddcdcdcdbadcadadddacccdbdcdabbadddbbcaababdacdbadbbaabbdcdbccbbbbcbbbadbcdcbaabcdcccaaadaadadccdcdbbaabccbaabdcdacaccdcaabaadaabbddcbcbbaacdcdcacaddbacdddadcabdabcaabcdcccacadbaaaabbaabadbcbdbdbcdaccbbbcacddbccbcdbadbdabadbcdddccdacabadcdaccdabdbcadbcaddcaaabdcdabbacbbabcccdbaaccbacdbaabbdaaddcbaaccddcccdabdcacbdbacccccbacbbcdcbcbcdccdccdddaadcdadbadbbbbbabddbbadadbbaabbacaacacaccdddaadbbbccdbbcabdbaabaccdcbaaaaddddbccdaaddacccabdbacdbbbdaadacadcacdcacabddcdddaadaacbdcddddbaaddbacbcbddcbccacadccaadcbaabbdcdacadcaccbbabcbbbbbcacbaddcbcacbdcadddcbbbdcabccdbaddbcdbddabcdddaaadcdccdcccdbacddcdccdccbdadbccdccadaaaabbdcababdbabbcaddbbaaabccacbabaabdcabdcacbbbadbdccbbbdacbabbdaccabbbaaadddacccdcbcdbdbcddbbcbbcdabccdcbccbdbdccdabbbcabacdcbdaadbbccaaddabdcdbadddbadddbacdbabdbbdbddbaaabdadcdbdabdbbbdacbdbabbcbcccdbbcdbaccbcdadbaadccaadbbaadcdbdbcddcdbbdabadddadbbdcaaaabcbbcabdcbbbdadcbdabdbccdbcbbdcbacdaacbbdbdcdbadddcdccbbababcdababbcbabddacaddadadddddcabcddabbcdcadbcabdaadbcaacabdddadcabbdabbdcdddddadbadadddcadbcddddccbdbbdbaccadacdddadcbbadbdacdcaaabaaacbbbaaacacadcdcdaaaddabbbaabdbacacbbbddbccddbaaacbacdddabadacdbaacdbcbdcbbcacbaacbdccccaaaaccdbbbdabbcbadacadabaacabacdcaabcdcbbbcdcdbadcdccbddcdbdbbcabdacaadabddbdbdcabbccbddbbcbbbbbbddabdbaddcbabadcdaabbabcbaccacbdddddadbcbcacbaabccccdcaddbbdccbcdccbbcadbbcaddbcbaabcbbddddadbbccbbadcbadbccbabdacddbaddcddbddadcacccddaddabcabdddcdcadbcbcdcacccccccbcdcccacdadcbdbabbdaaabbdaccaaaadaccabdbbdbbcdbddabacadcccacdcbcccaadadcccaadaadcabdbccdddddbaaccdcbbbcdbaadacbabdbdcabcdaddcdbcdbcdaacaabccbbbcbcbcbdabbaadadbabacaacddbcbcbddbcadcccacdaddcddcdbbcddabbdcbcddbacbbbcaddadadadcdaadacbcdddbcdbcdddcbcadcdaaabcddacccaccbdcacacbdbdbdabcacdbbddbacddcaacbddacbbadadbdababadbbbcabbacadcabcadbccbabcabddbbbaccadaacaddaacdaddbbcccabbababddddcadbdbdcbadcdcddaaabbadacbcaaadacabddbbdacccdabdddaaacabbaacaaabcbccacdcbabbbbaccddbbbabcccddacbccaccbadadbcdcacadadccacbbbdbacccababcbcbbbddcccdbdcabdbcaadbdddbcbcaaadacbdccadbcacdbbcababbbcbabcbaaddabbcdcaddaadcddcabdddaccdbccbbcacdcaabcdbdcbdcadddddabddcbbddadacadbddbddddaacaddaddddbabbbccbabadbbbbbdaccacbaaadabcabcddacbdbbaadacdcacddbbbdaabbddacdbacccdadbbbdcabadacdbcbcbbcadaaaddbadadcbddaabbbacadbbdbaaaacaacbcddbdbacbcacbcbbaaddbadbccdadbadbdddddaaabacbbcbccabaadacabbcdbabcadbacbdacbbbdccddadabbaccaaddccdcdaacaaaadacdcccddacbdcbcccdbddcbbbdaadaaddaaccddadaddbabddcdaadbdacacbaadbabcddbbacdbaaddabbbdddbaacccbdbdbcbabaacdcbbdacbcdbbbbbccdabbbcaadbdbddbdcdadbdbabbbbabbdbdddccbaaabdacccaccaadbadcbabdcdbbdacbbbbdaacdbbbadbddaabcbbcbacaaccbcbddcadbabdddccaadddbcabdababaadcbdababbddaaaadbbbcbbacadbddaadacaabdbbdccbcdaaabddabccbabadbcbaaddccddbcdbdddcddbbcabadbbacddadabcaabdacbacbabbacabdabcddadddabaddbcdcaabdccadcacbdcaabcdacbbadcacdaddccdabadccdcdcaabccaccbcaddbbbbccabcccdabbbccadbaacdabdbaddcccddaabccbbabdbbddbdcdaabccdbbccaaadaacbccacaaaaacdbcdcccbaabdacacbbccaabbcdbacdabbabbbbbddddaabbacddbccacbcbddbaaddbdacbcabaddadccbcabbbccacbdccdbdbcbbdddbcccccadadbbbcdaaddbdbccdcdcbbcdaaacadcdacdcddcbdadcacbdacabdcacbdbcbbadaacaddadbcdcadaacacadcdcbcbbcbcdbaccacddbabbaddbaacaacbadbacdcadcddbdabbacdddddccddacbaaaaccdadcaabbdcabbbdacbcccaaccdcbaadbddbcddbcbcccbaddbabcbddaabbbcaadcaabcabaadccadcbdabccadddcdcdbddbccabaccbcddbcacbcaccaadacdbcbbddbbdccbcabdcacbccbacaccacbbcacdbbcdbccacadbdcdbacbabcdbbcabbaadcdacaabbdbbbbddacdcdbacbadcdbdbdcadbcbccbbcdccaccdbdaadcdcadabdcaadaaabbdbcdaabdbccdddcaddbbabcdcbbccddadabbaacddbddcaadabbbcdaacaabdcdbdaabcdadaacdaaadbbadbbdabababcbdabcabbcbdccddcdbacdadacdddddcdcccaaadbacbdadbadddbbccdcbdbcddaacabaccdddcbcddccddbccaaccddccaccdadaddacccbcdbbadaddbddccbbabbabbadabcabbbcaacbdbbddcdbcbccdabddabaccdcbdccdaabbaaacaccddcddacddaddabcdbddbdbbcbddcbbdbaabdbdcdbccdbbcdbdcaabcdaadddabcbbddadcdcabbcaabccaddcdbbcaaaabddadcaccbbdbbcbabdabbdcddabcabddcbccbccbccadcbacaabadadacbbabaacdaaaabcbbcbababccbbdacaacbcadadadcabcbbadaadbbadcdaabcaacdaadcadbbabddbddaadddbcbbcababadadbbadacaddacbcddadcdadcaddbccaadddabbdcababcbadacaddbcccaabcdacabbabaaaabacdbdadbcbcbdbbdbadadaddbdbbdbabdbcbbcbbbbacbcbbadcbcdbdbcaadababbcbdaacbdcbccadcbbcbdbdcadcbcbcbaabbddabcddaaadddcaaddbadabbdddbdccdcdddddcaabddabbddadddbddcaddbccaccdbbdababcbbbcbaddcbbdddcdacaccddaabcabccddccadcaacbbaadabdadddaccdcabccaadcabbbdbdcaaaccccbddabacabcbbbbacbadddbabbccbdbcdbaabaacbcddcdddaababdcaabacadacabcbbcdadaddbdbbaddccdabadbaacdadacbccdccacbcbacabcaadbdadbadddcadaccbcccbbbadcccddbbbacbaacdcddbccdccdccaddaccbdbbdccbddcdcbadcaacacddaaabdcbbddcbbdabaccbabbabdcdbbabdccbbccbbbccddddcbadadabdadccbcbdbbccabbbdcabadabcddcdccaaacdabaabcbaddbadcddadccdaddacdacbdadabbcbaabacdcbacadddbcdbdbbdabbbcaaadbcdaddaaacaaadcacbcacdbaabcbabbbdddbbabbdccdcacaadadcccdacadbbcacacabcbaacadaacadbbabbcbcabcddaadadaaaddcadcdcababaccabcbadabddbbdbcbcbadabbcddacbaccdabcbacdcacbbcdbacaaaaaccdccadaadbaadcaddbbddbbadccaccccdacddaabdbbbddbcddacacabcbaacbbddbdcbdcadbbbabddadadbbcbcdadcadbabaccaccaaabcdadadbbbcbdcaacadbdbbcacdddbbbbcbbbdbcbabdacacadcdcdcbacacccccadccddaaccccdcddcaabbaabbbddaacbdbacbcaababdbdccacddbddcaabcacadbacdadaabbcbbadbbbcabaadacacdacadbadadcaacccabdcbbcbcabbcdbbacdabdddabbcdbdacddccdbcacaabdbbabdccdbdbbbbaadacbbbccadccdacdcdcacdcdddcdcaddacbdddbddaababaccddaaacbbcaabadaacccadaadadcbcbadaddcccbacddabbbbdcbdccdcadbabcbdabacabbcbcbacbcbdaacbaabaadaabcbbcabbadbababbcbdabaaccbbaacbacdbabbaaddddccaaaaddbabbdabacbdaaccbdcbcbdcbcddaacbadabaabadabccabcaddcdcbbaababcabcaaabacadcacacdaacbbddbdcbcbdbbdddbccabacbbddbbadadacabcaacaccbdbbcdbdbabbbbdbbddabbdadbcddabaabbbadccdaabcaadcdbcdcdacadcdabadbdabddbcacccbcdbbadcccdddbcbcccbddcdbddcababcaaabcdcbacaccdcbabcaacccbbdadcbaddcabcbdbaabdabbdbdcdaadcccabaaadadadcbaadaaaccccdddabdccdcaddcaacadccbadacababacdcbdbdbadaaadbccbadcacdabbdbdddaabcadcdcdcbcddbacdcbacbacbccdddbddadacdcdcbdaaaabcccadcdcdccdcbaaabdaddbcacabcbabababbdaccbcdcdacbabcdcdaccbdddbdbcacccabcbcbbcabbbbcaaaccdbbccccbbcaabaaabbcddbcaadbbbaaadcaacbdbcccdccddabbcadbcbdddbcccacaadababdcbdcbdaadadcbaaadaadccbcacbabdccaaccdbaddbdbdbbdcdcdddccbcabdbbdbabbadacdddcccaadbdcdcdccbbdccccbddcbaaadabddcbddaaaccacacccdcbddddcbbadadabcbaacddabdbbcbabbcdcaddbbaabcbaacdccdcbaabcabdabbbccdaccaaadabbddbbdccdccbddbdadcdaabbaddbabdddaccdbbcddacacbbcabbdaccbccaadcdcbdccbbcdccbcbbcadccbcbdcaaabacccdccacbdcbdaddcbadacaccbbbccbcdddcbbdccadcdbabacbddccdcddbdacdadccddbddbacdacdccdabbcdbcadaacababccabcccabdddbbabcdddacabbacdbdabacbdddaddcabdbabbabddcdabaadbcddcacdcacbabddabccacbbdbddaaaacbdbbabadcbcddcacbdaabcbcbcacdbbcbcbababbdacbbdcdccaccbdcbcbccacccabbacdbddbccbaaaaaabadaddacaaccdddcaddaccdcdbcbcdbcbccaaddacbdbabcbcabddcbbacabbcdccdccdabbdaabcbcacabbccbcaaccbcdccaacbbcbadbabadddaabacadadacbbdacabdbdcaaaddabbabcacbddcdaccbcbcbddcabbbadacaaabcacbaabaccaccbdbbcddbddcadbbabaadcdccbbaacdbaddacaccbbabdacdbbbddccbcdbaccbbcddbbbddaaadccacdddddccbbbdcdadabbbcccbbbdddacbabacdccbdcdbdaacdabaaaccbbccdcddcdcdbcacacccdbabcaaadabbddcdbdbaacaaddcbcbbccbcdaabbdbacdacacabcbcddccdbbcababccdbbddacbbdcdcbcadcbccdaadbddaacbbddcbbdcbbdcbbabadaddbabcadaddaddbdcdddbccaddaddbbdabbdbaadabcdcbabdccdcbbbadaabcdddddbcdaaacaabddcbcdcbccdadccdcbcdcbdbacaccbcabdbbccbcbdbdbbcbdaaaccacccbdacbdcdcbacccbbdabddddadbdaabdbdabdbcdacccaddadcbbabbdababaadbdadcddbababbdacadababaddbbadbdcbdccadcbbababadacbaabcbcdcaccdbadcbdcccaccdbbdcdccddbcdacaaacadddddadbadcbadddbbdcdaacdccddddcabadcacaddcbdbbbcbdadacbdbbcbdbbababbcacaccbbbaadcabddcabdabbaacadbcbabdbcccbcabdcdaacccbcdbdddadcacbbbbabcadabddaacbdaabbbcdcdbbababbdbabbcddcdcadccabbddadcdaccadbcabccbbacdbaacdbadbdcccbdacbdcaaccbbbaaddaadbcccccdddbaacdacdcccddabbadddcaacacdaabdbacdddabdbccbacadacdbcbccaabdabdaddcdaabcbabdddccaaabccccddccaadacbccbbcadacbbcbcadcddbdadbcbdcbcbcdcadbbdbcddacdabdacacdbaaabdabadababcccabcdbdcbdcdbacaccbaccccdaccbbaccbcbdbacbbbacbababbacaaacbacdbabbacababdbcbadcdbbcdbbbbdcbddccbabbaadcbcbabccbbadadcdbbdbcdddaacaabaacaccbcccadcabddbacbbcdcadadbabadbdaccdacadaddaabcbaacddcccaacdacdccddbbabbcadbcacbaacaccccdacdbaaacdadbddacdbdadbacdbcdcadddaccbdcdaaccdbbcdbbcadcbdbadacbbaaaabcdcbaccababccbbbaabdadbcacddbacadaccacacbaaabdaaaccdddbcadaaadacdadcadaccbbddaddcdbccdadadbdbacacacdaadcaadabadbdabcadaabaabaabadabaacadcbddccccdadcdaaddcdabdadaddbdaabcddabddccaccbcbdcccbdadcdcbdcdbbcdcabcdaaacddabacadbadddbababcbbdbabdaacadddbddccdbccbdacccbacadbacbdbbaabcddcabaabcccddcdacddacaadcbadacacdaccbccaddcacaaaabadbdcdcbbaddbdacdacbcddddbacabbdcacdcdacbcbcccadadbadcbaacacadcbaaaadcdcabcbdcbabbabcdaddaabadaddcdccabdbadcadbbdbacdacaacdddacbdcdbcbbcbdcdaccbcdcabacdaabdccdddbabacdcdcbcdcdcbaadaaaadccdacbadbcbdcdbaccdcddcbdadcdacabcbcddbabbcacbbacdabcaccabaabccaabcabbcccbadbbdccdddcbcdacbbccbcaacbbddaccddddddcbcbdcbacbdddbaddbabbbddaadbadbcdddcbdbccbccdbcddbcbadacaadabcbaaaddbaabaccdcdcbabcbdbacdaabbccacabacbdabadcbadcadbaadadaccdabbdaddabccaadacdccbbbddcbaadabddbcacbddaabacdcabddcdbabbddcbabbbabaaccccbdbcabdbbcdabddccdababacacddcabaccdacbabccccacbaacddccaddaaccbdaaabacccabbdabdcddbcabbddaaacaabbbcddcdcdbbddcdcabaccbdccdccbbddddacadcabadccccdcadcacdabdcdbcaacbbcdcbdcbcdb bdcbcbddaadccaccbaadcdcbbbadaacbdaccbdbbdbdadaacadacaadbccccbabaadbaabdbddbacbbdbaabcbbdddccabbaabddddcaacbadaabcbdcacdaccdababbacbacbbacccddbbccacaccbdcbccbbdccbcbbdbdcdabaacabcaaadaadbcdcddddaabaabbcabddaacddcbcdadbcadbacaababdbcadccabdcbadddadabadaddcacdbbdccdccbcaadcaabaccdbbacbcccaacaacbdbdbbdacbaddcbdadcabbaaaadcdcacbaabccbdbbbcbdbbdcabdbacdaabacdaaadcadbbdcbccbbabcdacccdbbaaacbddadcdcddccdccdababcbcabdabcdcadddaddcbcaaddcbaddcabbaccdccdcabbbcaaddbdaacddadbcbdbdcbbccbdcbacacacbbbbacdbabbdddbcdbcbaacbcbddacaacadbdccbcccbbcadcccdbaacdaadcbdcbabdbacadbccabcbdaacccbbacbdbbcbcbaccabbbabdbaaaccddccddbdacbbbbbdacdcbbdccddccdaccbcaddcabbcbabddbadcdacccdcbdcadcbaabcadcabbccdddadadbbcbccabccbdccdbdcbccbbbdbabbbbababdbadcdcdbbadcdadaadbdbcdaaddddadaddddabdacbbbcddbbcbbabcaabdbadaabacaccadabccdcdbccbddcdbcbcaaaacdbbbaccaaaabdbbacdcadcadcbcbcaddaaabdacbbdbcbbdbccccdadbdbbdcbbdbbacdaccaaabcbabbccddadbcdcabcdcbcdcdcdbacabbbdbbddabdabcbbcddddbbdcddbbccdddccddcabdabcacbcdbcaacccacbbccadacadbcacbdadddaacdbdddcbcdbcdbdbdabdddbcaaacadbaabcbcccbaddacaabbbbbacccaabbccabaadcadbadbbdccdcbdacbcccacaccabacddbbabddbbcadababddcddcadddacacdcbaddbcdacddddcbaabcbaccbdaddbbdcdbddbadbdaadabbcadbbbcadadaabbbcababbdaaccdcacabddaccbccdccdcaccaaadbbcbcbdbbabbcddbdabacdcdbabcdbdabdabdaacabaadbbbadaadadbdcddbccbbbddbbddcdcaacdcccacabcdccdacbbacdcaacaabddbdbaadbbddacaaacccddacacdaacddacbcabaadcccabaaaaababbccdacdccdaacabcbcbaddaadbbacdacaddadadaaabbdbbcdddccbbbcbbdabddadabbdddcaaabaabdbbbaadabdcadbadbabdbabddcbbddcbacdbaacacdbacaadabbcdbdbdcabbbddcabbdbbcdbbcbdddabcbaacbdabadccccccbadccdbadbabcbccbddbcbadbccaadddcdcddddadbbcaadccaacbacabbcbbbbaaacbbbdcbbbbddacdabdbbccdbabcadbcaddbabcccadabbbacacdcababbadbbbbccddbbabdbacdcbccabdcbdabbbdddcacbdccdadacadddabbbaabddcbbccdbcabbbdcabdbcddaadabdbcadaccdbcaacbcddcbcacdbadcbcabcdcccdcdbdacccccbccadbdbdbdccbaccbadcadabddbabadbbdcbadaaacdadbcdadabdacbdbccbcdcccdcbccbcacbccabaaacdddabcabaabdddabddcacdbdababaddacacccddddaccbbabddbccbcacddbcdcbcaaccaaccabcabdabbbdacbcacacaaaaacdcbacabacdacbbbcbabdadbcdbddbbaacbdabddbbbabdadbbdbdbbdcbadababdcdddccbddacbabddccaaddadbbacbbbbcaccabdbdaadbaaadacddbbbddccaacccbaaddbdcbddbbddaaccacccabaddbbccabcdcdddadaaaaabacbcacbdbdcbacadcbabbbccdddccdaddaaccdaacddcbaaaddbaacdddbdabddcbabcadaaaabcbbdbaacbadadbdbbccbacadaddabdcaccdbddbcddabbdcabccadcdaabdbcdacbcdbbcdcccbdbdcbbdadcbaabddcaadaddbaddbbcbccadcaadaacdabdbcabcabbdbbcacaabcbbbaacabdbadacaccabaccacbbabddacbaacbaabcbabadcbbbbcccacdaddbddcbbdbbbccccabcbbabbdbdbcdaaaacbdccbabbbcbcccbbaddbdbabaccadbadadcaaccaadcdadddbcbcdbabdadcabdaacccabdaddbabaaadbadcbbdaabcaaaaccbadbcbcbbdcaabcdcbdddcbcccbcaabcadacbadbaaacccccadcbbdbcadcadabcdddbbbaaaadaacabccabbbaaaadabdcccdbacdaacdbbacaadcacbbdacdbdcbbcaabadcdccaaadbadbccacdbccadbbdbcdbabcaccdaddbacccdddacdddacddbdcbdaabcabdcdbcdbbdacdccdbcdadacbcdcddbdbbaddcbbbaacdacbdcaaddadccbbbacbcadddcdcdabacccadacadbdddccaacdacaabdbadcdbdabdcbbdccdbdcdabcacbbdcbaaaadcccabbaddcdcabdcdbbcabaaddabbdaacccccabbacccaacdacdbbbaccbcdbbadbcddbddbdaaddcbcadbcdccddbcabbaabcacaacbaabaaddcbadbcabacdbcdadbbbcaabdadcabbcadbacdcdcadddbbcbaabadcdcdacccbbcccaccdcbdcacdbddaaadbbbcbddcabcdbdbcbbcbbddbcbdbcadcbabacacbcdcddaacbadcdcbccdbcbaccabbacddcbabdbbaaaabbadacbbcdbabdbddacaccaaddbcabbbdcbcaabccdcadaabbdbddadadccddaaadaaadbbcbdbabccbdddbbccccabacdcddadddacbddbadaccdbbacbcdadabbccaabcabcdddcdabdaadacbadcabaccacabcadabcaadacadcadbacbaacabcaaddbabbacdbbabccbbcdaddcdbddcddabbaaaadbbddddcadbccabcdbcbbdabdbcdcbaadadadbbcbccddadbadaccbbbddacabcbaddacddacccabbccdbabbcbaddbddcbddbabdcdbdddbdbdddccccadccadbcdbcddaadbdcccdbcaabccbbccbcbcbdcbccbacababbccacbadabbdcbbccdbcadcacaacdcadcbdbcbdcacadacadabcababddbdadcaddabccbbdbbccbcdcbcbcccddbacabaadccbcccabccacdacabdaadacaaaadbabcbacdcacdaabacbcbdabcddadaccddacacbbabccdddbaabccbadaacbcabcbdbdaccbbabbadaadadcbbadcacdcbccbacbaaccddaccadddbdddaddaadaadacadbcdccaacabbbdbbadabccbcaaadcabaacbbccabbacbdbccbabcdabbdbbccbcddcddbbbcabcccadbabdbcccddabdcbaaabcddadaccabcbdbadbabaabccababacccbcacdbaabaddcadbdccbdabcadcdadccaadaadcddaadbbdbcdcbacacddbdacbaaccbcaacacdbcdbdacbbcbdcaaaacdabacdcccbcaacaaabaabcbbabdacbdaccaacdddadcbacaadcadddabcdbcbcabdccbacdbbadbaddaaccdbcddbcdcbacccdcccddbdbaacacdddddbacdadbacdbbdccdcaccbccaadacbcddabaddbbbbdcacddbcdbaddbdacddadaacabbcdaaaabddcddbbddbdaabcdabbbbadcababbabbbdccbdcbaddaaddbbacadaadbabcbcddcabddacccbdaccabacacadadcdcddacdcdbdcaadcddbccdcdbacccddbddbdacacbdcbdcaccdcadcbcdcababdccaacadcbaddbbcabadabbcbdcccdabbabaddcacdcacbcbaacccaaddaadccabadbadcbdabcabbccdbbbbcbbcbadabddcdabdabcdcdbbbcdcddabbcddacabbbaabaaaabcacdaacacaccdbdaccdbdbbcdbadabcdccbbbcdcaccbbcaadcbdadbbccadadccacabadacbaadadcaadddcdbbdcbddcbccdcdacccbbaccbdcbdabddcdacaccbcabcadddaaababaddbadabbadadbbcbbccbdbbddccbccaccaadcdabbbabaccabdbcbbbbcbdbbbdacabdccadacdbdbcccababaabdddbbccbccdadacdbbcbbbcbdcdccdacddbcaabcddcccbcabdddcccdbdbbbbccbcddcdadaccbdcbdacaaabdbacbcbcddccadaddacddabcbbbbdaabddddbcddbcccabcbcbacbbbbadbacdbddacddaddcdadacdaccdaaccaaadddabbdcdabdacabadccaabccaaabcddadaaacaddbbccbbcdadbacbccdbcbdaddaaaddaabdccddaabcdcabacddacdacbbadccbbbcaadaababadddbacaddcdadbcbbcabbcbddbaaacacbccddbcaadadcdbccccdccabddbaacbadabcdbaabbdbdddacadbdcdbacddddbddbdcdadbaaddcadcbcabadadcddcbcacdaaaddccddbaddcadcacacadbabaaabbcdcdcccaaaabcadcaaabbcccbbabbdbadacdcbdbcbbbaddbacabccdddaabaddaaadacdabbddadabaaddcdbccbddbbcaaadddcbccbcdcaccdcccababaaacabcdbdacdddacbcbaadcdaaaacdaabbaccbbcbbbbdbdadcabbbadabcbdcacccdacbbdcaadddcbddbbbbbdaadaabbdbbdbdcaacccddbcddbdbccaacdadcdccbbbbdcccbddbaccaaadacccbaabadbadbbbbbdcaadbdaddacaacaddcbabdaacddccaadbdbccdbabccadaddbabdaccbbbcabccacbbdcbbbdcccaabadbabddadabcdbacdcabdcdcbcadacbbcdaccccbbaddcdbadaadcbddcbbcdcaddccdbbbdcbabddbacbdbabbdcbabddddbdbddccbdcdaaaaccbdbbddacbbcdcbbcdacaaadaabaccdcadababdbccaaacdbabdaababbcbcacbaadaacdaccacddadadcdbdbbdbbdaaacacdbcdaddbcdccddabcdcabdbcaddbdddcacddbcaabbdcadcbaabbbcdcacacadddbacccabdacbcdcdcaaaaadbcbdbacdccacbdccccabaadabbdbbcdbdcccadcbcdbaaabcabadacbbccbdcccbbbdadcadbcbcbdbdbabcbbacabbabcdbabcaaddbbdabbbdbcccaabbbbbacaabdcaaccaababbaabcbaaabdcdbaacacbcdbdacbccbbbaacbdcbcdaddddaacddbdddcdbabcadaddadbadacbbbbbdcacdadbcbadbbddadadabcabbcadaacacbbccdbadbcdbcbdbdaabcbcdccdabdddbaaccbdbcacdccabbacdcdaadcdbddaddabbbdcabacbacdcbbabcdcbaabddcdaaabddcbbdcaaacabacbbbdaccbabaaaddbaabdadcdcabbaccaabaccdbddadcdabbcadbdbccbaaabbccddcbadabaaadbcccacaaccdaccababbabaaccdaacbcaadbaaaaabdaddacccacdcdcaadacbdbdcbccaabcaabbbdbdbacbccddcdbcbbccbbdacdbbdbdcbdccccbbbddaadcbcabbcdbcaaacdccacdabcccadddcddababbccddaabddccbbdbbaaabaacdcbccbdbddabddaabcbcbacdcbdddabaccabbcaddddabddcddbdbcccbcbaaaaabacabcbcadbbccbdbaacccdccdbddbcaaabdbadbccbabccdcdacdabdacdabcaccadbcadbcadbacccdaacbbaaabddcdaddccadddcacddadbddbdbadadcdbdbbadabbcbabadcbaaddddadadbbcbbbccdcbbcaaddacadbcbbacdadddadcbbdccbadbacccbdcccdcccaaccdcdccddbdababdbdbacaaccbdabadbabdaaccadbbacdbcaaabcdcdadcacccacbddbaadaacbccaadbdcddbbdacbcadcacdbdbccdcababcbcaddacbddbaabdaabbddcaccadacbbdaabcacdcdbbbcccddcbdbbbcdcadbabdcbdbbadadbadacbcccdacababbadccccaccacdbdacdababdacbaaadddcdcaddaddcaccbdcbbdabbaacbabbdccbcdbcabcdadccdbbccdaabadbdbcdcdcbdbdabcadddcdadaadcccbdbdbbdacbddbcdadbacdccadcbdddcdcbccbcadcabcbbbdbddbbcbcadcaccacacbdddacdaadbcbadbbaacbaaaadadaabcabbdabdbdbabcacbccabadcdcdccbadbbbbabcbddbdccdbbcabbdccccbddadbdbccbbcccadbbdaaaababccbdcaacbadaacbcadaccccccaabbcbbbdcbabddaacacbbdabbaadccccacbccbdabacaddbcbacbcadabcabcdbcacacbbbccaaabaddbcbdabcdccabbcbcabcbbbdacbabddadaadbacbcccbcdaaabddacbbdadbbabcbaaadbaacbadbbdaacacdbcdcbccbaaccaaabdbddbccccbbdaaabbcbcacaaacdbbddcdcbaacbacabbcdbddcccbddddcddcaacaaaccdbdcccbacbabdddabcbbdaddbacdbcabadbbccacddbbdabcbdacdacbbdccdddddaddadbbdbbdabdcbaadbbadabbdabcdddaaacbadbbbbbcadccdbdabcbabcdccadcbccddbabbbcbbbbcddadddbcbaaddcdbbcbaddbacccbabbdcdcacddacbbacbacbabadacdbdcbbbccabdabcabadccdbcbaadcddcbbaccbddcbbbcbaacabdaddbbccdcdcadcbcadcbacdbdaccdbdddbbbcdcbbaabaacbcdcaacacdacaddbacbabcaabdcbbbadaabcabcccbbbadcdacabccabcadbdbbadacabdacdbbadcdbadbcabddbcbabbabcdbdcacbcacbbbbaaaabdbcacadcbbacbadaababdcaccdacdbcadcacbacdaabaabdbdbaaccbcbbbaddcbdbbdccadcddbccbddbaacbdaacddccadbcccaadcdbddaabcaaddbdccbddbbbbcdaccbddbddaacdaccacabdadbadaabaccabbdcdcbaccacbaabaddbddaabcdcbcbbacccdccbcdbcacdbbadcccbaabbdaacabbacdcccdbdcccdbcdaccacdbadacddbdcaaaabcbdadccadbaaabbbcddcccabddbbaaccbabbaaabdbdbbcbdbcbabbbacdcadcddbbcccbdabdaaacaaddababdadcbbbddcddadbadddbdbcdddaaddabcbcadabbbacdcdabddacaddaacbacabcdccccaaddbaaaddabaccaacbadcabbccaaadddbcabbcddacabccbcddadccbcdadddaddbbadcbbdacaadbbcabcccbadbacdadabaadbdcddcbbdbdcacdaabbdaaddadcabbdbbdabdacddcbcaacbaaddaddabdbbdaddaddaccbdaacdcdbaadccbdddabcbccddbcacbbcdcdcdbcadcbcbbdaddaddddaccbcbabcaaacbcddbdcabaaaadbddccabbdbddbadadbbbcdcdadbabccdddadabcdbccbcacadddcbdcbadaaddbbdcacbdcadabadddbaadababdbbadccbdaaccdacaaddcbaacabbbabddaaacbdcddbcbbcbdaacadddbabbdccacaaabbcadacbbbbcaacbccbdadbddddaadcaabaddccbdaddbabaacbdadadbbbaabaaccaabccddbcdaabdbcdbbacbbddcaababdcbddadabbcbcdcccaadddccdbdcbcadbdddcccadbacbcbdacacaaabcaadcbabdcddcacbabbcddaababbcabddddddbadddddaabadbbabaabaddccddcdcccacaacdbbaabbbbabcadcdbcddcacbcadabbccbaabaadcccbcacccbcbcacbccaadbbddbdddcaabddadccccdadcbdbbcadcccaaaaddadcdaabdbbcdacdabcddddbbbcbcbcabbacdcdccbbcadbdabddaabbdbdcbabcacdacabbbdbbcacabbcbdbcbbcdcabbabcaadddddbabaadcdddbaccdcbacdbcdabdbdbaabcaadccbabccbabbdbbdddaaaaabcaddddadcccbbcdbdcdbdccdaadbbbdcddccacaccbcbbcccbbaddbdcbdacbcabcdadbcabdcacccdbbdbbdaacdabbbddbbdadbaadabdaabccdcacccbbcddaddbabdacbdabbdddaaaaaccbbacaabdbdcaabadabdadacadcbdbabaddaddabdcbabddabaaaabcbcdbcadcbaabbacadbaacbddccdcdadcbbacdaddcaacdbbbadcaddacdcbbdbbcabcaccbccdcddddcddccdcaabcccabccbcbabbaadaddaacaaaccdacadacadcddaabbadbabbadccacdcddbabcbbbadcabcababdbdcbddcdbbbabcabcaaccbadbdcadbcbcbaaacdbdacaacbbbadbcbddbcacbdcaabccbbbdbaabdacdbccabadacbbaacccbabdadbacbbdadcdadcbddabcbaaaabcdbddcbccdcacbacbacccacdccbbaacdbabdcadaaaabdddbbcbcbdadcccbccdabcdcadadcbcbacddacbdabcadcadbabbdcacccaaabbdcbbaaaaaccdcabcdbdabdddccdacccaaccabcacbdcacbaaccdbacdbcbaacacaccdbbcbccdbbdddadadadcacdadddccaddbdababaccbcacdcdbabadbabbcbaccdcaddbbdcadabbbadddccbadbcbaadbdacdbbaadbbcdccabdacbdddddcbcbbbbacaacbbbabacbaccbcccdadcbadaddaacabadddddabaabaabbdacdcadcabccdddddddaaccdacbdcdacaabacabdabdacdcdcccdcacacaaaacbdccdcacaddcbdbadacaaacbcbabdcbcbbcbadaddcbbacdbdccdcddbcaabaadccbbcacbddabbbabcabaddaddddcbdbadcccaadbbdbaaddaabbcbadadaaabcdbaadaadcccdbcccccddcbbaadcbbaadbccbccbcabbdadacbdcaabcddaadbadbddbacbaadcdaddcaabcddbabadaaacbbbdabdbabaaababdddccaadbdddddbddbdddbaccbdbdcaddacddabbcabcabccaabdaddacbbdaaadacbabcaacaacaacbcdddaddcdaadacccdbbbdcdadacaddbccacdcbaccccbdaaddbaccbaabdbaadacccadacdccabbbdbacddcbcccbbdcdcbbcbcccbcdabddacadacddbbaadddbbdbdbcbbbdcadbdcdbdbcccdbdadcaaccdadaadabcddabbdabbcaaccccbddaabbaddcdcdbaccddacdbccbdbcdbdabaccdbabaabbcbbcdccdbbcbcdbcbbccbccbdcbcccdaddcdbdcccbbccbbbaacadbabcaacdbccbadbaaacbcdccaaadbddccaaacdaacbadacdbaaaddabbaaddbbdcdcaaaacadaccbcddadadbadabacdcaaadccdcbcaddacbcddcdcccaadaaaacbbacbcabbbddcbcdaaaabcaacdbaadbbcabbbdabadcbbccadcdcbdadabdcabdbbdadddcacaaaadaddaacaddbadabadbaadabaadaddcadabaaaccaaaaacbbbbacbacbcdcadbaccbadcaccdddacbbcbcabcccbdaaacdbbccdbbbdaddcdadbbbaadbadbbcbbadccbccbcdccccddadabcbbabdcdcdaccbcdaccadcdadccdacacccccbdcbbbcacdccacdabbaabaaadacbddaddaaccbcbbdbdacadbcaacabbbbabdadcccddadbdacaadbcbbdbdbcaccbccaacacbadbdccbadddbaadbacccbacddbbbbadaccaacacbbddadcbaaabdcbbaabcbbcbacababdbbdbcdcdbdcbccaddabccbccbbacbbcdadaacccbbdbbbdccbdbadadbbdddcabccaaacbdcdbcbdccbbbaaaabcccaabaacdbbccdabcdbacdaaabdbbddbabcdcdaccdbacbbdcbbcdbbddacacccdabcccdadbbabddaddbcadcbdacaaabcdacdbdccadcdcdbcbbcbbaaddbdcbbacbcaccdccbabcbddcbadccaaadadddcddcadddadbcbdabdbcaababbcdadcadababacbaaddaaaccaccbbaaabbbbbdbababcbdadbbdccadbaddbadccdcbcbdbcccacdabcbabbdcabbabcdabaccadbcbcaadaccaadbddaaacbbdcdbbbadcbaaadcbcabaacdaccdaabcbcbbddbabcdcacbddcccacdbabccdabdcbbdcdbccbcdabbbaddbacdbdcbdbdcdcbadcadcacbdcdcdbacabddddbbabbaacbcaddbabcacdaabcbaadbbdbdbabaabccbbaddadadbdbdddadbccdbbaccdbcccadacbaddbdcccaaddcdcdbbdddaadadbcdabbadaadcdccdaccdcccadbabaaaaaacbbcdbacdcdbcbacbdddcaabcbcabbdaddcaccbdaacbddaccbbcbddaaaaadccdccdaaaacbcadbbadbdacadacccaadabadcbcbbbaccbcaddbddadccdcadddababddbbcdaaacaabcddcdacdcaaddbcdcccbbaccaadcbdbdaccbbcdabcbcdcacaaacabbbddaacaccdbbbaabdcdbbbccdbcdabdbaddaddaddbabaadbdabdbcadcdacbcbcccbdcdddbadcbbccbbbabdbabbbcbbabddbabcadacbdbddbdacabcbaccdccaacdccaaabcbbaadcababcccbabaaadcbbaddccababcaccdccdbadcdccaacbabccaccddabcdcdabbdbdbbcbadcdbaccbbbbbdccbbdbccbacbbaabddcdbcdcdbabaaccdabdcdabdabbcdcccdacdbcadabcabdacbcabadaaacbddabdccaacdcddbabdadcaabcbadbbccbbbdbdbaaabadaddccaaabbacbbccdabbabcbddacbbcdaddbadaabddbbbbdbaaabbddbcaabcadccaacbbcacadabaaadbbaaddcccacaddaccaddbcbabdddaadadcacbbccddbdbccbbbaddabdbdccdbcdbbbaaaacdabadbbdbdaacdacdbacdbdbbabbcbbccbdccabddbbdaabcbcbacbabcabbcaadbacbbdbbbbdcadaccccdcabdabaaabcacdacdbbbabdacacccaddcadddcadaacbdabacadabcbccdddbcdbbdccdabbcbbdcdcdbcbbddadadcddcddbcbdaaadcddbbcdddadabcbdabaaabdabbadcabaaddddddbcccbbbdccbacbdcbbabbcadaabccdadabacbccdbcddaadaabcbbcccdcbdbddcbabcaddbdbdbccdcabbdddaacdccacbbddccacaabbabaabacbdbacacabcbdabacddddcdabdaddacbabbddbadbbdcdbbcccabadcdbabbcaccabdcacabcacbdbddabbaabdcbcaabcbcccacadcacaddaaaadacdbbaaddadbaccbcccccbbbdbabcabdaccbbcdbcddbbdcbcddccaaaacdcadbbdccacadccddbacbcdaaadaaccabdaabadcdbaabdbbbbdaabdbcbabcddabbdbbaccaaaaadcbbcbacbacbbddbaccadcaaccbbbabccbdbdcadcbcacdbcddcbbdccbcbabcdabcdcbccbabddcabbdcdbaadabbaddacacbacdbacacddacbbbddaddccdbdcdaccacdbbdaccddaacccdcabccbdcbccbbccabaddbdcaacbdcdbaddacacacbbcccdcacddcbacabcdadccaddcbbcadbdacbbbdcabbabbbcbbaccaaacdcbbacbbbdbabbddcadadadaabbcaddcdcadacbaddcaddcdcaaccdadabbdbcbbadcddabbcbaacaabaabddaccaadbadabbadcbccdccdbcadbbaadbddbaacdbaccacdbddcbbaddbabdabdbcdadcdbddabcbdcbbaccccbcbdbcccbccaccdacddadacbabcddddbdccbcdcdbdccdacaaaadddaacadddabdcdbdcdbbbcccbcbcdcdbbacdcbaaabdddacaaaddadbdcdacdbddbdbcbbadbcbbacaaacdbcaabababaabacaabaadcbcbcdbddcdbdddcaccbbcbaaccbbbccaccbbcbbccbdcdcabddcbbcbdbcaacdbcdcbcdbdaaccbcdbabadcbaacbbcbccdcacccadacaabbbccddbcccdaadadbaabdbcdddbcccacacbdabbaaacccdccccbcccbcadabdcbbacddcdcaaadbcbcaddbdcdaacaaccbbdbcddcbcadaacccdabdaddaaddcabbbcabacccdcaaccacacddcbdbbcdcbcbdabdccabaccbdabaabdbbacdbcbaabadaacbacadaabdbaaccdcbdbbccaaaacdcbdbbbcabacbbbbbbaaddcbdbabcccaddbdbadbcddbaadccbadbabbadacaacaabacabbddacdddabadadcabddbbacdbabbcdabaddadccdcbdddcacaabcdcaccbddaccaddcaaabdacdacdadabddddcbbadccdcbccaaaddadaddacbdbadaabdcdddcccdbbaadacccbdbabdbabdbacdaddadbcdddbbdccbaabddcbccbcbdacababcbabcaabcbbbdcdaacbbdbaabaddccccadcddddcbcdccdcaccdacccbbdcbadabacbbcabddcaabbcdccbdabcdabaacdacbcbcddbaaabdaccbcabbdcbbcccbaddbddddddbbbccddddaacdcaacadbdddaddcbdcabcdaccbdabccbdcaacddaadbdadcdababcbdbcacbddcbacbcaccbbdddccdddabdbdaccbbcbbcccbbcbbabbbbdddbddbbdccbdacacbcadcdcabbbabbacccaabccbcabcdbadacdbaacddbbcabcbbdabadcabaaabcddbdcadbaaabbdddbabdcabcabcdbbddddcddaacaddcdcbdddbbadabaabdcbacdcdbbbcbbabdaaddccbbadadcbddcabdccbcadcabdbbbbbbbadaaabbcaaabbbacbababdcdaacabcbdcbbccbcaadbdbbdcadcbacadccaddcbcadaabccacbcbaadcdcbaadabcccbbddbcccaaabccbdbcdbbcdddbbbcaabcbccaabcbaaacaabadcabadddcbaaacabacddbcadbbcaacdccaacdbbabcdabbdacbacccacdadbbcbabbbcbdcdabbdbadcddabaddbcbadbaaacdacdbbcabcdcbcdcbaaabacbdaaccdacaacbacdbddcbaddbdcabaabbddcbbccaacccacadddcccdccabdcccacacdbacacaadaaadbacbadabcbbccccaadabaacbcdadbbadacbbbcbcabdcccabddbcaacbbccaccdabddaddcccbcbcdbacbcbccdddbaadaacbaabdaaccacbcaaddbccccdbadabacdadaaabdcabdabcbbdacbbabbcabcbabaacbabbaabdcdababbcbdbadccccacbbacbddacadcaadaacddbbbabdabddadbbcabdcbccccabbadcddadccaccaddbabcddcbaadabacddacccabcdbcaabcdabadbdaabbcdbcadaabcdccddcaddbadacabdadabacbbdaabaddcaabcbbccaacbdddcdcdbcbcbdcaaabbdadbadadcddbdadcacccabbbbcadaaaddbcdccadbacddbccaddaccadcabccabcbddcddcbbbcbacaccabdacaadbabaadbccadddcbcaccdddcddadbdcdbbcdabbbbccbdbabcdbdcbbabcdbbdbadadacbcccabbcadddbcadcabddabbbdbbcdcabddbcbcacbdaccacacacbbcabcddabdacaadbbbccaccbbdbbacaadbccdacaddcdbddccccabaaaddcdbcaabbaccabdddadcbbdaadddaccdbbbdcdbbdaaddacccaacbccdacbacaddaacacadbdbabaaaacbbcabbdbbbdaddbbbabadccaacbdaaaaabcbccaaddddcdcddccbacacdcabaaacaccccabababccbcadadaaddcbadcbdcabdcdacdcbcbdccbaacdcccdacbbbcadbaabbaccbbccccccbcaaccbddddbddbdcdbaaddccbacacccabcacbbaaddcdabcdbdaddbdbdbdbdabdcaaccdccdcbccadddacddaabbdcaacdcacadbbbcbccaacdcdbbdaadddadcbdababdbdbbadbbaddccacaaabccdcccdcadaddddcbdacccbaaacacccdbdddcbabcacbccbddabaadbdbdcbaacdccdcbcdddbcabbccbcbbbdabbaddccbdacbdbcbadcccabbcacaadbaddcbaaccacddbdbadccabdbcddddbdcadadbccbbdbcacdcdcdcaabcbbacbaabadadcadcdcbdbbacdaabacaadabccbadbbddabacddcbbcaadcdacbccdaaacabacdbdddbabbdbabbbdcbcbaabcbcacbadddbcabcccdcccdaadbcacdbadacbbabbadabdddabdbbacbcadbcacdacddaababcccdcbddcabcbdacbbaddbaaddaabababadbddddcccabcabcbbadacbdbdcccdbdbddbbaddbddbacdaababdddbdcbdbdbcbbaaddaabcaadcdcdaaaddbbdbccdbdbadabcdbccbdcbacabcdbcadadcbbcbabcdadadddabdaaaddbcccbadbbabaadaadcadccccdcbbccdcbcabbbcaaccbaccaddddbbbdaabbcbbbaaccabdbabbcbddbdacbdaadbccbaccbcbadabdbabccbccbbdbbcdbbdcaadbcacbbcdabaccacddacdcdbbcbbdcacbcabcdccdadabdabdcaaddaddadaddcdbbbbbbcaddbdbbcdbddbdcbcccabbabadbacabcdccbadbbabbbdbbcdbadaddcaddcdbacdcbadbbbbdbbcdccbacccdcaabdcabcbbcaabababdddaadcadabcadadcbbcacdaccbbaddbcdbdacbacbbacacbabdadcbacbdacbaacaaccaacbccbbbbcacddaadbcdbaabdcaadcaadbaadababddcbbabaacbdddbadbbacbabcdabbcaddddcaabbaddcbaccadadcbccacbdaaadccccadabbdacacdbaabbcbdddccccdbabccadabbadcccaccdcdcdddadbcccddddbbbdbcbaaddcabbbdabaacabaccaabaacbbdbbacaaabbbbdccccadaaaccbdbcbaddaadcabbccdcdbdcddaaaaacaacbbabddbcababcabcacbbabbcdccdcbcdccaabcccdcbccddccdbcadaabbbdbabaabcbbaddcaadddcdcbabbdcacdbdacdddbaacabcdaaaddbbcbdcbbbabbccdcdcddbbcddadbbadabaddacccbcacbccccddccadacbcbabcbaabccdbcaabdbcbcdbadbcbaabdaaccdbcddcccaabbddcddcaccabcdabaabdbbaadbcdababadccbbadbcdcbadddcdabacddbbdaabacccdadaabdbcbddabadcaacaacdadccccbddbcccbdcddcdbccadcaabcbbaddddbacddbcccdcddcdbcacababaaccbbcadaccdbbbcacbabcddabcbdbaaaacbadccbadacccddbaaaaabcbddcdbaadcccdababcaddcbdddccacccbbaacbcbbbcbcccdccbaadaacabbddcbbbccacbdddacdbcacdbbddbbcbdcabbcacadadbcaaabdacaccccbccdabdabddddabbabcbcbcccdadccdcbcbcabbbdcacbadcacacbbcaddcbbddcabacbabaababdbbdcbddcbaacdccacacbdbcacdaaadcaddadddbbaadadcbccbcccdaaddcddbbbdabbcaabccdbabdadccdacccaccadcacdcbaaddcdcaabdabbdbbabbcacddddcccacabcacabaccdacbaaadcbdaadbdcccbdcaddbcabbcaddccbadaabbcbacabbbcbcaaadbdaabbcbcbccddddcaddbbcdaadcbadcbcabcaabcaabdadbdcaadcdacdbbdbcbcadacccabcbaaaaadccddacdaaabbbdcbbdbbbccaaccccdaacddccbbbccaaabdcccdcabdcaaaadcbcbbcdaddcbbddadbacdacddcabbccbcccaccddaddcdcdddaabbcadbbbddaccabdcbacbabdacbdaaabaccbdbccdbcbccaddcadbddddadaacbabbdadbcddcdcdcadabbcabdcadcccbcbdcdcadbdcaacdcabdcbbaccbccaacbaddbadbbccbcbacacbdbccacbabbcdaddcdcdcccdccacccdadbcbbabbccadcbbddccaaabcaacdabcabdbcdbdbdddbcaadcaddacaadaaddcdacadbdcbdadcccbabcccacacbbbcddcbaaacbcabbbdbadbcdaddcacdacdaadaacaaddabbbbbabbdacdadcabdddccdaaaabdddaddabadbddacadaacacaadadbcbadbabdcbbaaccbcbddcaadaaaabdddddaadabaabcdcccadcadaccdabdaabccccbcacdadbbcbbdacbcbcbbbacbdbdbbadcbabcccadabbdaabbaddccabccdcaadabcadddccabdadbacbbddbbbdbacbdabcabddcdcdadcacdcacddbcdcbdcddcbccabbbdbcdddcacbcdadcbbddbaabcacacbccbccccaaadbdbdcaadccbbababcabadcddcbdaaaddaccabdbdaadddbbdadbdccddadabdddddcccbacbaabbacdcccccbbdbadcbbcbdccdbcccbccacabcbabcdbbbbccdacaddbddbaccdcdccdbcabbabccaacacdbddddbcdcdaaddcbbaadccbaabbadaaaaabdbddbbcccdcbcccddadaadcccdcdbbcaddbcbbcacacbdbaacabbbcacdadcabcadbadbcaabdcbaacbbbdadcabbddbdddbadaddaaabaacdbdaaccccdbacdbaabdaaaaabcbaacacbbdbaccccbacbccabbcaabbbbcdcbdadcdacdccbdaadbccbbabbbccdccdadbbbcbabdccbcdcdaaabacaabdaaadbbabcdcbdcccdabacdbaaccdcacacddabcddababcdccbccbdcacddddabdabbddbcadcdccaccbdbddbbbcbbdbbadbbbacabdacccdcdbacdcccdadbccccaabbdccadaaabcdaabdcabbdabdabaccbbbcdbdbbdbbabbbdbcccccdaaabdbbcdcadcbbbcaabdcdcdbbcdadaabcbcbdcddabddabdabddddcbbddcdbcdbdabbdbaaddcbddcbdaddccabcbadaccccbaddadbdcaaddcaadacdcabadaadadbcaabbcdccbababaccbbaabbbccccadadadabbaadaccccacbcccbddacdbcbbabcadabbbcbdcdbbaddabdbbcacbbbbdcaacdbdacccbdcbacdcdcbacdbcccccccdabacbbcdaabdcbccabcddcbadddcacdbbdbdcbdbbcdddcdbaabcaabadaaaaccdbcaacacbdacbcacacbcaaccbabcaaddaddbcbcbcabcbcccbcacdaccabcbcbcbadcbbddaacdcddcacdbbdcbbabcadabbabcadaccaaacabcdcddbcadabccacaaccbbbcaaabbbddadaccdbcaddadcbdabbbdbbbdbcddcbbabdaccddadbdacccccbcddaabbdcbddbcaddacaddbdbbcdabaddbdaacadddacdaabaaddabcadcbbbadcdbaaadbdbbacddaabcdbbccbddbadbddcaacbcbdbdabcabbbdabdcbcaaadadacbabdbbaccbacdbddabdabbccdbdddcbcddaccccbaaadcacddcbbddcbccbdbcaaadbadddddcabadcbbadbbabadaaaaaddbcaabcdbaaddaacacbaaaaddcbccccdabcaddbbdcdccccaadacbddabbcaadbdcabdabdcabbbbcbcddadbccadcacccbbcdcdaaacacaabbabccdbdcdcbbcabdddabbbddabbacdbcbbaaabacddcadcbcbcdccbacdcadbbccdbdcdcddddcbbdbabcacbcdbbdaaaaaaccddacbdbccddacabdcccccbccdcdccadbbaddcadacdabacdacbbdcbcabbbabcaabaacbbaabacccccddaccccbbdbabadcdcdddcdddacadabbcccbdacabbdddacbaabacdbcbcccdddcccdccadbdcccaaacbbdadbdacacaadcadadccdbbacdbcbddadabbdcbccbcadadbaddabdbadbbdcbcdcabbdabadabaaaddbcdbbaddcaadbcbcdacdbaacdbddbdacaaacadbbcadadacdbdcdcdccddbdddccacacbbcbbccacbdbbbdbcddbdcaccdcdcdbababbdbcbcacddddaadadcdcbbacbbdbddaadbbbbcccccabbadddbbbaaaddccdaadcaddbbdcdcdaabaabcdaddaccdbbddaddaacbababdbacbcbdbbbccbcbdbabacddcbcaadbaabccaccdcddbacbcadbbddacabaadbdaddbabbadbacdcacdcccddcaaabdacabbcccadcccabccadbcadcdbacbdadabaadccdcddadbbabccdbdbbbbadbbdadaacccaddbbdacbaaabccababddbbbcdddbcdaacbbccabaadbbbabccddaddbaddbcaacbbbccbdddccdcbddcaaaabadcbadabccadacaabdbbbadadbcacadabadaabdaccaaadbacddbabbbabaacbadaaaaadcbcdcbccbacbbdabdbcbaabaacddababcbaacbdddbbcccdcccbcbccaccbaaabccddddacbdcdcddcccdbaaaaddcbbaabdddcccdccddabdacccbdcbcbddcbadbcaacdccbbaaabcddbcccbcdcacbcacbacbccbdaccaacadcabcdbacccbcbdcddadcacabddbcdaccbbacbcbddbddaadcbbdcddadadccbcaaaaabdccbcaadccdbcaadddbdccbdbbabcaaacabaccdacaccddbddbddcacddaaaacadcabaadbabcacabcdaccaacbaadddbbaccdbaddabcabbaddcbadcddcdadbacbabcadbadbdcdccddacdbaaaabacdbaccadddcddcaabcbdcabbbbcacddcddbdcbacbaccdacdcbdcbdcbaccacccdcdabbbaadadcacbdbbbadcdadccbdbdbaacbadacccbcddcbdbbbbaacdbadccdbbbdbdcadbdadadcbabbbccbbabcbddadadddbcbbbcaccdaddcaddcddbacbbaacbadaddbccdbaccdcbdbbadacdcdbadcabdbdacbddcdaaabacacbabcabbacbccdabccbccaaadbdcbdbccaabdcaddaaadabaddbddbcadcddcacabbdcbdadddbcddbdcdbcdcbcbabdcdccdcbacbacaccdbadcacbcacadddbcadbaabaaacadcdcdbcaccaadbcacddcbaccdaacacdbcbadcdcacdbcbbcbdddbdccccdbddaaddccbbdbcccabbcccdbbbbdaacbbaccbbddbcdbbdcbdccdcdbaddcbabbddbdacabbadbcccddaababbbacdcbbbbdbbbccdbabcbacabadbbbbadbcabdbdccbabacdabcdcadacacbccadadccaacacbaabccabcacbdddadabaadddcacccbddcccdacbabdcadaacbababbdbccaddcabddbddcdcbddcccabcdabcaabdbdabbbcdcdabbbcbdcdcdddcbddaccdbbaaccaabaacdadadaddbbacbcbdbaadacddbabddcbbcddbccbdccacabdadcccbddccabbacccacdacbbdbacbbaacaabdccadacaaaacadbdbdbcbcadbbbbcccbcabdbbcbddccdcdaabcbdbbccbbcdadbaababadadbcbdacccadbacbacaacbbacaabcbbddcccabdaacabdbbcbdbbbbdbaccdcaaaddcacbcccbbadacbabccacbccdbbddcdddbaabbdcbdaaabcbccbdaddacbbcababaaacdabcacadccbcaadcdbdddbbdbcdbbbddcdcccdcdabcaccadadadcdbbcbdacbaadcadcaabbdacbddbcbadacdabdbcabaaabbaaddabcacadcccdaaacbcaccccddadabcacdbbacadcddccdbddbadadbabadaacbddaaadcbcaddbaddacbbaddcdcbccdcadbbacbabccccacccdbccbbbccbabbddadddbabddccacbbbbabdccbaabaddbcdaaddbbcaddbbaddaaaccdbcbbacdadcdbaacbbcaddaadccdacbbbacabaddbcbcdccdaaaaaabcbdacbcabbcabdadcccbcbdbbadadbccdcadacbbcdaaaabcdcdbbdcbdbbcaadbddaccaccacbcadcadccaacdccadccbbacaabadbbddbccbdbccdadccacbaacbabdacaccdbcbaacbababaaccadddaaaaccdabdabdbcbdbaacbbddabdaabcddabbccdccbbbdddbdabadabdadacbdacdbbabacabdcbcbccdbbcaddbabcddcdabbdadbbdaadacaddcbabbaadadbcdcdbccaaaadddbbcddbdccbaaabdbbadadbcabaaadabcbdbbdadbbbddccbbdadbbacbccadacacccdaacbbbddbababaabadbbdbcbbacabccdbcbdaaadbabacbabadaaabbcccdcaccbcbbabaddbdabcccaadacdddddacbacccabdbddbaabdaddabcacdaddbcacbacdbabcbadcbccbddacabbbacbcdbabddcbcacaadabcdcdbaabbbacddbabccdcdbdcbacdaadddaadbbbbcdbdccaadcbcdacaadcadbdbcbbdcbbdadbbdccdccdacdcaacababcdabbacbbadacddddcbaadccbdadacdcdcbabddbddacbaacdcdcbdcbcacaacbbdaccbdaababbcaddbcacbacdddbcdbabcdbcaabddddaaaabccdbbdccbbbbddbadddccccdcbdaadacbdccbdcadacabbbaccbabcacbbdbbbbaddadabdccdabacccacbbcdbabdbdadbadbbccdddbddcacccbdbaaccdcadcbacccccaaddbbcdadcdaadadbbdcdddbdacbaabbcbacbdaddbddcababcbabaacdaddacdbddaddcddadbbdbcabbccddcdaddcdaadadbaaacddbaacdcdbaaacbabdbbdadbbbbbbcacaaccbdbbbabbbcbadddbcacabbdccbcadcccadddcdaddcabdbaddcbdaaddcadccbbaaccabbdbacbddaadbdbacdbdcaccbdaaddaaddadbdadbbdbcdbbccdacbddcbccddddaacbcbbdcacbabbacadbcbdadcacbbdbabccddbabaadaccdacaccdbdbaaabcdddcdaacdcbccdbbdbbdddbbbdadabccddacbcabacbbccbcacbadabaaaaaadcaddacababccdccccdbcaaabadacbddadaababbdacdabacaccdbbbccddabcdbccabdbadbaddcdaabddbdbacabdbbbbccdbcdccddaaacdccabdaabddbaabcaadbccadcadcddacabaaccdaccbccbdaabccdaccacbacbcabbadadcadabaadddadcabcadbdbdbbddddaabdbcdccbcccacdabbccabdbbabcdcddcdbbdbdadabdbabcadabaaddadbdacbcddcbacaaacbdadadbdcadbddcbcdccdacabbdcbbcdbaddaaaababcddbaaabdabdadccbbdaacaaadabadacbbbaccbbccbcbadddbdcbdcbccdabaacdaadaadcbbbdadaadadacbdaaabbaaacacbccaaaadadbacacdccdacadddabcbaaddbdddabbdaaaddabbadddbddacaccbcacaaaaaccadbdcabdccaddcabbbabdcdbcdcbabbdbadbabbaaaadbbcbaccdbbdbacdccaadcadadbabacaabbacdcdddacbdbdacdaacbbdcabcaadbdddbcdbcbbabaaadbaacabbacdbccdddabdbddadacbdbabcccccddddbaaccbcbdaadabcddcacadbcbaaaacccbacbcdbaaaccaabbcacabdbcdaddbaaccdcaacaaabadacccccdcccbdcbdacadcdcccabdacaacdcbccdddbcabbdacbcddadaaadcbddacbacacdbacbadbcbcaccababcccacbabadabaccdadbdbacadcaddddbdbbcacbdddcbadadacbcabddcaababcdacdaccabaacdbabcdcbbabbddacbadabaaccbdabcdadcccacabaacbabacddbabddbabdbbccabbdbabdbdbcbbbaadaaaadaabbbccdadbcbdaddbbcbcacdbaaddccbddccbacbdccabcbabdabbdbbdacdbcabcadbbcdcbcbcbdcdbbdaadbcdbddcccbcbbcccbccdcbbdddbdccbaddcaddcaadbbdbacbbaccbdcdbcbbbcbddcbbdbbbcaccdddcabdaabdddcccdbaacbabadbccacbdabbcabbacacdcdcabdcbcaabbacadcbcbabdabaabdbbdaacbdddaccdbccddcccdddadacbabaddbcddaaabccaacbdccdbdddaaadccccdacacccaaaabcdbabccbddbaddbcddbabbcdacababadbaddacbdcbcdbababdabdbddadaddabcdbababacadbdddcaccbcdcddcbadcbbbcaacbbdbbdbbaacdaabdadddcbbbaacccdcaabcbdababddadcaddadbbbdabbbcbbdabbbcabcbaacaccbcdbccccbabbcabcdbcbdddaadaaccbbcbacbbbabdbcabbccbbbcbbaddcbbdaabacdbadabdabbacbaabbadbbdbaabdabdccaaddacacddcddadcbccdddabcdbacaadbcdbcadacdcaaacbcdbdcbbbbdcababcdbacbcdbabbbacabcbbccddbdbbbaccbaabbacbbdaddddbdccbddbdacadccadcccdcbcbbbcdbbcdbddcdcbacacadcadbdabcddcabbcacbabdaaabcddabdacdcabcaacbbcdcdcdcadabcabdaaccacbbcbcddacabdcbdbccabacbddbcacbaadbadabdcdadaacbbbbdbbcadbacaabddabddccadbadbaacacddcccacbaddaaacadaaddbcabaacbcadabbdcaacacbcaabdaccbadaadcdddaadddbacbddccccccacadcdbbdbccbbdabbcbcbcdbcaadacdadcddbcabdbacbaacdddacbbbcdddaddadaabdcdcdcdddabdacdadbaaddbdddbadadabcdbddadabcbababaadbbddbdabbbdcbdcacbbdccbbcddaabddaabddcdacdbbdccbbdacbdccbbddacbdbadbbcacddcacaccddaadbacdccdbaaabbcabbddbdbcdcbbcaadacbbccabdbcbddcbbbabdcadbbadbbbabaacbcbadcadaddabacdbdbabdddbadcbbabaaabaacccdaadbcdaabbbcccaaccaacaabddcbabdadbbaabdadbdabdbbcddbcbacaacdcbddcacbaccdbbcddabddcbadaabaadbdbaccbdabcbbbadccbdcaccbdcbadabdacadcddbbabcbdbaaadccacaacccaaaabddaadcacbbcdbadccbdbacbdbdcbdbccbddcaabbaccddbcaccbbbbaadbcacdadacdcdcacccadbdbbbbbcadbdddbcadcdddacadbbddbcccacccbdabbacbddcaaaddcccdbbcbcddcdadccbccccddadaccadbbabdcaacbddadbaababdccdcabbbbaabbdcccaaaacddcbcabaccdacbdcbcddbdccbadccdbacdbcbdbbbbdadbbcbabddaacbcdbabcabbadaadcbaaccbcbbdacbdddddadaacddaadadcbcbabbbcdaacbabdaddaccdacbaddabbabccdbbcadcbaaabdadcdddcddcddbbcaccbcacadcbddaddcccccdddcabcccdaabcddcdbbacccbdcccaadbddbbbccaddcabdbdaccbaaaccddabdcbdccbdcbdcdacdbcccbccddcadbbdcccbaadbccacdadbabadaabdacaccdaaccacbccbccdcdcdbbdadcccdcbcbdddccaaddcdaabccbcaabaccbccdbaabdadcbaccbbaccbbdbccdbccdacbcbdbbccaadccddddadbdaddabdcaddbdbdcdccacdadddbbccacbcacddbbdbcdaacbadbabdbbdcabdddcdbdbdadbaccadcdabbcbabbbaddbdadcbaacacdddbcacdaabdcdabaaddcdbaacddadcbdaaadddaadccddccdbabcbdaddaaccacdddadcdbaccbdddbbdccbcdaddbaccabbdddbdcbcccbcacccacbcccdadccadabdcbbcddbbbccdccacdbdcaabdaddbbbdbdbbacdbbbcdcccdcabadcbadbacadccbcdacbdadacbdcdacccdadbbababcdbdbddbacbcbabddabdadcbcddddcbacaabacabddbacaacbcadccdbacadddbbadabddaacdbcdadbbcdbdadacbaaaabbacbdacbbbbddcacbddaaadabacdadbbddcdcbdabadbacabcabbbdadbdcbdccaaadcdccbdaabaaaddaddacdddcbbdadadacbbcadabaaadacbbdcabacababbcadcbbbbbdadbdbddaadbabbcacabbdacbcbbcccdacbcbccaaccdccbdbacbcabdcbbadabbacbdcbbdadbabdbabadbbddbddcacdccbaabcdddbbbcbbadccccacabbcddbcacbdccbababcbddadccbadcdaccabacddcdbcadacdbdcdbabbadaaddaaacdaaabacabdbcddcaabaaacacdcccaabaccdcddabccbadacbcbbcadbdbdbadbdbbcdbaaaacbaadddcbdcacdbcbcdbcdadbbaacbcbaaddddacaabdcddcaaaaadcacbcabbcdbaabcabcadacdcdbbdaccaabdbbccbaabdbbbdbcaabdcabbbcaddcccbcbabaacdabbddccbadacbcddbcdacaddcccbcccdaadbadcdbbdacadabdcbccacabccddddbbaccabbcbcacababddbbaabaaccabdaccadcbbaacbbbcaccdabacabdaadababacdddcadbacaadbccbdabaacaccbdaadcbadcaddaddacbabddaddcaddaabcabbadbdbbbdcdcbdcbdbdbbcbaabaacaddbcaacccaababbaaadcdbddddcbbbbbdaabbcbbacbacbcabbcacdabbcbdcccccdbaacdabadacbadadacaabaabbabaacddaaccbbdccdcdacbdabaacbcaacbdabcbddaacaaabadbbadbcaadcdbdbacdbddbddabddccbdcabbabdddbccabcdadabbcdadbaaddbbbabbdddcbbbdcadbdbbcccbacaadbacbcbdbacbccaabbccbddddcdbbacdcdbddaddaddccdcdaaaaaaccddcadacddbcbacbbdbcbdcdbadcdadbdccdcaabbbddadcaabaddaadcccdddcccadcccdaabbddadaacbcabbbdbbbabcdcccdbabaccdaddbbccacdcccacacbaacadabcdcadabadbadcccbaabcaaddcccbaddbcccdaddaababdbbbbcabadcaadcbadbdbbbabacdbabacddddabdddcadbcbdcadcadabcaddbdacbccbdcacbbbccaddacbbaadbbccbacbacaabbcdbabbccdbbccadaabacbbabcddcaddbbbdaabcddaaddcaaabdadaababacbaaaccacabdddabddbdbcbbdcdadcbdabddadccbdaabbbddbcbcaddaacbdcbdddacadacbdaccacdcbacdaabcdaccccaaddcbccddddbbabaadbbbaacbccadaaabbdbcbcdcccacbadbddcdccccbaccccabbbddcbcccbabaaacbdcbaaddacbaccdbdbaacdbdcaaddbccbbbabacddabadcddaddcbaaccdbddccbabcdadcdcbbcbdabcdaaadcccbcbbbdaadccdbbbbdccabddcbacbbdacdacdaccccacbbdaaadbadaabadbbcbdcbdbcacaddbbcbbbdbbcbdcabbaabcbdddccdbaabcaccddccbdcddcdaaadabcadbbcbcaacdccbaabcccacadbabcdbccddcbadbbaacddaaacbcbacccdddddcdbdadcadadcbccabdbdacbcdbcbadcdccaaaaddaadaaaabbbbcaccdcaabccaabaddbbbacbbbbaadbbaddcdcbaabdcbacbbdbcadbdbcdcdbdadadcbdbcbacdacdadaccdabbbcacadbcbddbdddaddddbdddadddcacbabdaacbdaddacbccabcacbdabdddccabadaddbbdbbcdbbbcbcdaadbabaaddddcbbdaaadbcaccbaccbccbcbcdbcbdabdabcbddabcdacbcbadccaacacabcccccacbdaacaccdccddacbabdaadcbaddcbcdcacbccacbdaccabcaaaadbdaadcabaaccdbbdcabddbcadbdacbadbcbcbccadaddbacbabddccdcbdbabcbbdccddddddcababcbacadabddbaaccdbbadcdababacdaacdddaabdbdbbdbaaccdddabbbbabbddcddcbcdcacacbacdabccbacdbcdcddddccaababbcbadcdacbddabbddcaaabcbadbadacdacbbaabddabddaddcbaccaaaccdcabbdbdcbbcbaabcbacbbaabdddaabcbcdbadcdbccbdbcdcbdcddaddbbddbbacaaddbbcbccaaabdcddbbaabddcaadbdcacaddcbcdcaddbaadccabcdabdbdccaccdadddaaacaaabddbccdadbccadacadacbcddccabcbacddabaadcdcbabbadddcabcacbacccdcabbbdabddbccccacccbaacbaacbadbbcaaabacadadcaacdcbdabdcdcaccaabdababacbddddcadcdbcabbddadaadbbadbdbadccdabcbbbcacdcdabdcbdcddcdcaccabbbcbdaaddcbbcbddcaadbccdabdccaccbcacabccbccdbbbbacacdbbabaacddbdabaddaadabadcbacbdcaddadccbacdcdbcdbcdcbcadbacadacaacaccaadabaacdabaaadaadcccbdcbcddadadbccdbbabaabcbaabdccbcdccdacdccccdabadacddcdbbcadcbdcddaaaacdcddbacbdbdbaacaadadcadabbadcdccdcddccdbbbdcadaaacadddcbdabddabaaacdaaacbbaaaadcadacacaddadbadcabcddacbdddbaddadadcaabcccbcbaacdcdacbacbababcadcacdcaaabdaccdacbdcdbdcdadbdaddaabacacdbbcddabbbbbbbdcaddacdabbdbccbbbcdcddabdacaadcbdcacaaacbadadccbcbacdbcdababcacdbaadbdbcbbcbbcccdababdbcababbaaabcadcdadabccdabbddccbdbdaccaadbacadbaadcccaabcdbdccbadcbdccbdbcaadddbcdcacdcacdabcdabbdbbaaadcaadbcbabaababbdcccabdaaacddddcddcdadbabccdbdaacbbaabdababcabbdacdcccaabdaaabbbcdcccadbbbbdabacaacbbadadbdddbaababdbaccdcbbddbabcaccdcbdbddbdbccaaabdcaabdbcddadcbaacaccbabddadcdbaddbddbbdabadacbbdbcaddcaabacdbcabdacadaccbcbcaacddacccbbabcaacbdcddcdbacddcbbcbcbccbabaddddbbcccddccbabaddaaddbcababacadcdaddbdbcdbdbadacbabcdabbabbcabaacabbaddcddaacbbbbcbbbcadddbdddacccbabbbadbcaaaadabdbddcccadbdcacabacccccddadaabaacabacaccbadabccbcbbbcdddbababcbdbdbabcabbdcccccdbababdaaddacdcbdcbbacddaccabddaacdabcddaadcabdacbccccadacbabaccdaaaccddabacabcddbbddbabdcbccddddbdacccabcbbbbcbbddbdcaadccdbdbacdbbbdadbddcdcaccddcdddaccdcadaaddccdacdcacbcdddbbcabcccccbababdcabdaaaadbbdccaccbdddabbbbddccacdacaacbcdbacdbccbddbdadbbacbbbadcbdcddccabaabccacccadabdbdbbaacbdbbabddabbbbacacbdddcdccbcbabbbbccddccdccbcaaaddcccddadcbbcbdccbdbdbcaccdaabcdadcdbdaaddbddacabacbbbcabdaacaaccddbbdaddcbcaccdbcaacaaaacbdbcddccccbadaccbadccccadacacccbccbcaadbaadbbbbabcbabdbbbcaacdacdbbabbccdadccaaccdbaaacbacbaccbbbdcbaaddbccdcccdcbbdacabcaaaabcbccdaaabaababbdaaccbabbaabdcbccdcdabbaaadcdadadbdddcddbccdbcddcdabcdbcbbccccbbccddaabdbbadabadbdadaccbdaaadaabdcaabcbddbbbbdccdcbacbdbcbcdcadbdcdacbaabdbbadaaaadcdbbcbcdbdccdcccbcaadadadacdbddcaaccabcdbbdcbabaccadcdaddddcbbbdbbdbdddcdcccbadcdcaadadbbddbacccdcbddbbbaaacbaccacbabbddbbbaccdbbddcbdcdcabdacddbcdcaabadbcadbacdacadddbccaacdbccbbcddbaddbaacaababbcddbabcbddccdbdbaccdccdadddadabddbdbbcccdccdaadccdaccdabccdababaadcbdcbacdcbbdcbbbbabcdcdabcaacadccdaddcaacbcbdcbdcbbdbdaaaccaabcbdbccdbbdbcaaacdcccacbbdacdadcbdccddcbabbaabcbabcccadadccdbdcbabdddbbcdabcacadbacbbdbcbadaabbaaabbdcbcccbabaccdaabdabcdbdbbaaaddabcbdacadbdbabacccbddacbcbdcdbaaacbcdbcaacddcbaabbdadbcaabcbccacabdbbbcaadabdbbabcddbbbcaacaadcbcbacaddcddcdacbacadaadbdddaccbcbadbbbdaabccabdacaacdbabdbbdbaaadddacbcbbbbdccbabcbaaadbccdaacdbbdadbbadababadadabacdbbcacbcdddaaddccaabdddacddabbbdaacdcacbcbdbbbdacbddbdabaacadcdaaabbcbdbbcabcdbbddabcdcdcadccacdbdccccddbdcdacabddaaccddbadcccacbdcaaadcaaadacbbabcdbdadddbadbcbcbbccccddadcbcaaabadddabbddbbbdccacbcdbacbcdcaacbdddacdbacbabcaddccaccadcbccbcbabcbdbadccbacbaaadbbdbacabbcabbbadacdaacdbaabcdbdbccddbdbbbdacbbbcdbacaadddadbcdcbbbdabaaabacacaaaadbaccdccbaacdaccddadbbaaccddadacdcaddbaaccadbccbaddbbcadbbdcbbcdcaadabdcadcbadabdabbbbacacabadcbacdbbbcacdbdbdbabbcabbdbdccbbaabaaadbdbcbaadacdabdccaddaadbcdabdddbdbcaababddbdbaabdccddbdbdcdddabbcaddbbcdabdbbccacacdbccdcacdbabaadbcdbdccaacdcbbacdadadbbdabacacbcabadccabbacaacbdcabccbbdbcbdadaaaabaddadbadcdbbacadbdbcbcaacadcbcabdcbacadcbcaabaabbcddacbbabcddbdccaabadadabbcacbcbaccbbaabbaddbccbaaddbcbbbccacbdcbbbaaaaacbcadccbdccdcdcaccbdabaddcbacdccacadcbccdabbdcaccbdcccbbaaccdacccbadcbcdcdcaddadddaacdcaddabddabaddcaacbaadccbbcaadcadddbddcdaaccbbadabddbbaacbdcacdcadcbacbcdccbbccdaacbadacbdadddacbdcdccbbabbdbcabadbcddcdccccbdadcdddbdcddccdaabdacbaadcacdaaccacddacbbbaabbcbbcaabcbcadadcadddacaccdddcadcaccbcbaddabdbdcccccaddbcacbdaabaaccacaacacbbbbdbdbadbbcbdabdadabadbccaaadccbdddbdbcbabdadabacbbdbadcbcacbaabcaadbbccccaddcdcadbdcbacdaadbadddaadcbccdbbbadbbbacbbcaababbbddbbabbbcbaaadabcbadacadaabdcbcbaaabdbaddccabaccdcadaacdccbaabdcacdcbdcdadcaacabddbaddbbbddbacaabcabddbcbdbaddcabcddbbcdddacccbcccbcdacadcddabadbccddbbccdbcadcbaadaaababadcdcbdddcbddcbcbabaacabccddcbdabdacacaabcaadacbdbacbcadccbccaadbbcdcdbdadbdbbbbacdabcabcddaaaacacdbaacbbbacbddcdbbaccbaaaacbccbccabcbbbcaaaddaccadbdcdcdcccdcdbaabcacadaacbabddabaaabbddbbcdacbacbaccdddabccababbbdbbdbdbccbdabdcbdacdcabccccbcbdcbcaccbcbacabccbaaccddbdacbbaaabcdadcbadbcadaddddcacacacaabccccbbdbbddbbdabacaaabcdccadcccabcadaaacaaccacaddccaddcbbaaacbaabaddcdcacbaaadaaabaccbadadccdbadabccdbcbadbdbbadcccadcacdccbcdaaabbbcdddccadcbcaccbbdcaaccbbbdddcdbcbabaabbbbdacababcdcdbdcbabcacabccbbccaadacbdacdadcccaacdbdacaacccccddbcdacccccccaccacbadcabddccbbcabaccdbbcdbacddaadadadacbdacdcccadbdabcabccbcdbddccccadbbaabaddbabcbaabcddbadccbababdcddadbdcdcadddadaabbdccdbbccabbcbabdaddabaccbddbaabcabdacaabddbacbcadaccdbaddacacbdcdbcccbabcacddddbbcdbabbbbaccbcdcbaddcbadbbabccdcacddadcadadcbbabaadbaaacacccbcabcabddadbcdbbcaddcccaccadacaacdcabaccbbddaddbaadbbbdcdcdaddabdacddcccdaddccbaabbcdddbccbdcddacdaadbacdbcdbbacadacdccbbadacdacccdbadbcccbbdaacbbbcaddadbbbbdbcdcabacadbbdbcdaaaaabaccaaacabdcabccbcdcacdbbacaadbadcdaaaddbbcabaacacbcbcadddacdabcbccbbdadcabddacdcacbdcaacccaabdbbacabbbdbaacabbcaaadbbdbdbacdaccbabcdcacbadbadbdacaddcabbacbbababcbcacbbdacccccbaccbcdabadaaaabaadcbcccacabccdabaacdbdaabcbbdccbcbcdaacccadaaaccdbacacbdcbdbdbaadbadcbaadabcbcbbbddbdacbbaaccbdbaadbbcbbcadaacbbcaacdbcdcdbadccdaaadabbccbbdbccddcdbdbabacbddadddddcdaacdbddbaadddadaabcdccbadaacdabdcbccbadddcacbdabcbddbcbbdcdaccbdcbbccbadcccacddcdadbacbdbadbddbdcbaacdbcdcdcbbbdabdaaccadabcbbddbddcdddcbdaabcbbdccadcddcabccbdaddbcdaccabaaadadcbbcdcaadbcbbddbadddabbdadbabdbbddabdbdaadbdccadabacbbadbcddabbaaacbdaccdcbbbaabddbcbbabdddcbadddddccdbcdbdccdddbdcdcbbbcabdabbcccbbccbbdccdbabbcbccdbcadbabcaacadbbcbbbbddcddaaddbcaaabaaabbbccadcdcddbabbbcdddcdadbacbcddbcddcacccccacaabadcacaddbcdbccadacadcddbccaccbddcdcaccbbbacbccbacdcadbaaddcbadacdaaccccdcbbbbacdaccbacddcddbbcbddaadccbaacdbbcbdbaaaccbbcdbaacdbdbccdbabadcdacbbbadbdccddacbbdcbbbbaacbcbbaacdbbbbbccacacaacacccacdabdbcaccdbbccabaaabbbcbaacbcbbccdddabdaacddabcdbcdccbdbbccbaccadbbccbabcbdddbddabcbcbcccaadcacacbdaddcddbcacdabbababbcccabbbacccdbbcccbacccddabdbbbdaddcaabbbbcbbabadddcdcbaaadaabcaccadabbbadabadabbbacadcccddccbbdacbcbbdcaaadddcbcbcddddacbbcdbabcdcccdcbcbcdacaacbaabbbaacbaccccabdbbdcacbdbdcabdacabbbaddadaadcababdbdddbbabddccdbababcadababdbbcbaccbabdbbcdcbbadabbcadccaddccbbcdcbacbbabbaddacbacabdcbdbbbadbbabddaaddabdcaddbdaacbcadbabdbcacbaddbdcddaddadbccdccbddacadcbacaccbbddddabcbcbcaacbadaabbdabaabaabdbcdcccddaacddccabcccbcdabdacbbccadbcbdddcbcaabaaacbcaabcaacaddabbadddcbcbbbacadabdbddbbdababdacaacccadbdaadabccbabbcaadcbaabdcdbcccdbcddacddcbadcadccbcabdcbcaaccddbadcbddccaacbcabacadbcaabbccdaabbacdcddaaddaabbaacbdaabaacacbbddccdcbacbcaccdbdabbaacbbadacddadcbacddbbbabbddacaadcccdacbaaddbaccbacdccdbbabdcdcabbdbbbddbcacabdabdccddbcbdcacaacccbcaccbdaaccabdbababcbcdcdcaddbdcbcdcbcccadcadaaabadbaccbaaacdccdaacbccdadbbbcdcbddbcbbcaaccddbbddbbacdbddccaddabcaadcaaabcdbbbdabbbbbcabcbbddbbdaadcbcddbbdddcbaadbbdcbdcacdbbbcddcbdaddbcadcbcccacadadcadcaacbababdacbcbdaaccccbdcdddcadaaddaaaddbaadacbaccdbcacbdabbddcaacdaccabbadaabacdbaabaabbbccbcacddacdcdccdaacbdacbdcdcbacacdabcdaacbaadbdbaabbdadccbacdcadaabdbcddacaacdacdabbbdcacbbadccbcadccbbdaaaccdbdbddbaaaddabababbcacbaabdaaccdcdccbbbdaaaadbcbcabbdcabadbbcbbdababdcbbccbdbdcdbdadcaddbdadbcbbadcdbdbdadacdbbcadcabdcaccabbddacccaccbbccdcadbdbddddacbadbbadabdbcadcbdbdadcdacaddbabbbcddbdccadaadddcbbdbbbdadcdcdbaacbbccbbdbcacbdcccbbadcddcdaaccbacbbdaddbdcadbdccdcbacbbaccbcbcdddbdadaacacacacddbdaacbdcadccdccdcbacccabcabbcacdbbbcddadbaabdccccddcdbaccacdddcacdabbcbccdcacbdccaacacdbaddacadbdcbbadbdcaabadcbbdaacbccdbaabccbdcbcdbacaadcbbdbabccababbbcdcdccdcdadbcddccbbdababccadbcaaabcdddddaaadacadbadadbcbbdacbbbbddbdbadadaccbdddbcabdbbbcacdbcabbdddbbccabadcdabbdabbbacbdacabaaacdccccaddabcaccbcdbabcaddccdddbabcabdbdbdabbddbcbbaabaccacdacdbdcadbaadbdbcdbbdcdbdbbcbbccdbabdddbacbdddbdbbabadbbcacaabbadcdbdacbcadbdaaccccddbbdaacbaabccbbddabadaaabddbacbcadaacbccbbcbbaacbbdbdbbccaabdbdaabcadadacabaddcabcdbdddabdcdbadddddcaadbdcabcacdaadaddacdbbaddbaacadababccaccbaacccccacadbadaaadabdaaaacaacabbadcaacbcabdabdcbcadacdaabcabadabcdadbcdcbcdbadbbccaadadbcddaadbacccbbabddabadacbaddaabcaddabbaacacbaabcbbacbdcbdbbbaabadacbbcbbdaaaadbdadbbbabbcdbcbcdcbbccdbdcacabaadabbcddcbcdddbcaaddccadbccaccaaabaddcdacbcabcddbaaddbdcccddbbcaabadbcdcccdacadabcaaaaccadccbcdbcadadcddaabdadccaaadbdccdacaacccacccccadcdbcbadacaaccccddcdbacadadabaccacdcaddddddddaaddabdcdbabaccccbaacdbbadccdbccbcbbcbacdcdddbdabadcabccccdbdcabcbdbbccbcaabacbddacdddacdcdabcccadbacacadaadbcbaccccdcabcabacadbbabbdcacccdcbbbcabcdabbddacadbaadcaacbdddcabacbbdaddccabccbacbbbbdbcbbddcaabcdacccbabdbcdbdbbabadbbcccbdddcbdcdaaadabbddccaccbbdacdaddbccadbdacddccdcacddcdddcaaccbbccdbddcbdbadcabaaadccdbbdbccaddacbcdcaacbabbbbbdabcadbbccdbccacbdbcaddadcdcaadbaacccdcabaadcaacbbcaadddadadbdacabaadaabdbaabcacdadaaacbccaddcbacadaddbbcbcbabaddacbddcbabddcccccddadbddbaacbdaabbbabbaaccbccbcabaadcbcabcacdbdccdbadbdbbdbbaaddccbdacaaaddccacbbcccacbbadbadaddbaabccdcadabdccaccabacaddbdcdddadadadabdbcbabbbdcaccdacaddadbddacbdbddaccbacaddaacbbcabadadbacdcbddddbbadccabccabbcbbbbcdacbaccabcbdbbdaaddcdaacdcdccbaddddcccbcacdaadadccddcdddaaacddacabacbcbcbdcdbdcbabcddcbcdcdcdadabcdbbbdbabcacbcbcddaabcbbccbccdaddbacbcbcbdcccadadadaaaabdcbbcbdacbdbbbccbbcbaabddddadcadadcdaabcabbbbdabcddaacaccacccdbadbbbbcbbcdcdbbcbbdcccbdcababbacddacbdbddcaaccdaaadcadcdcbbcbabaaadabdcaccaaccbdcbdaabbdcbdadaccdcaabcbacadbdcddbcbaaccbcaabcdcbbcbbddccbcabcdaddbabdbbcdcabdccbbcdabbadbdaacdcaabddcbbbaadcacdbadbadcbdbcaddddbccddaadccaacdbdbabbcdbdbcbcccaddddabbbadddbbabcddbbcdbdbddcacbabcccbcabbbcaabacabbcdcabaaaccdbbaacabcbbdadccaabdadabbbaccaadccbadddabaddcadbaabbcbdcdaccd dcacdbaccaadbcbbacccaabdbddabbbbbcadabbcbbbbadcbcbdbacbbcddabccadaabbbcbbcbcbccaacababbcdaaacbcddcabcaaccbbdadaabcbdaacbcccdbbbccddcdacbbaaccbbabbabacadcbcbcacbbccbadbdabdbbcabadabaacddbadcabbcaaabcbdacbacacccdddacbbbbdadcabdbcccbbbcaabcadddcbcaaabacaadcabcbdaddbcbcacdccadaacbbaaaacaaaacbdaabccbaccddcdccbbdbcbbcdcdaacddabbcaacbcccbddaabdcbacbaddbcbcaabbdacccdddbaccccadccbdcddcdcabbddadbabacbcdcddbcbadcbccabdadbcdcbdadcbacacbccdabbacdcabbdbadadbacccadbcddacadcaaadcacabacbdbababbaccabdbadcabddbccdbddadcccbdcdbdccacccababcccdcdbbbdacacbaddccbaabcdaaaddacaadccdbccbbbabcabbbdabaadcdbcdcaabababcdccdacddcbcbadbbcabbabbabcabcbcbacadabcdcdbbaabdaabcdcabdbccdbdbbbdcbbdcacdbabbdcabbddbbddcadaaccacddbcbbdaccaadaabcbbdaccbbcbaaadcccdcdddddacdccacbdaddcdcaacdabccdcbaaaabaacbbbaacddbbbcccbbcbcadddadbccbcacdcddccaaacbcbbcdbdacbbbaabddaadababdbbbbacabcabdddbbdcbbcacbbcbbcdacabaddcbbcdddbaddbabccdcbbbbbdacaaaacccadadabdcaaabcaaabdadbadcbdabbcaabdbdbdacccabbadccdbdaccbacbbdcdcdbadadadddacadacbbaccccccaddcaddaacadbabbbbcbacccadcdbbdbcbdccbadcdbbdabdcdbdccbbbdcadddaaabdbbdbbccbddcbcbbbadacadcdabddcdccbcdacdabdcadddabdcbcbbdbadbcddbbbabbaacabadbacbcdccdabaccaabbdcbdbdabcacccadacbaaadcaacdaabacacdbdacdacdbacbacddcadadcdcabcddcabacabaabdabcdadddabcddcbbdabcaaabadadccacbbdcaabaaaabbbacaaccacdbabdcbdaabbbadcccaabaaccdbdabbbadcbbaddababaccbbbacccccbdabdabbdcadddcbabcabbcadbccdcbaaccddabbbbdcabacabcdddbdcdbccddbaddbbdbcbcddabdbbdccccddababbdcbaadcadbadaabddadcaaadacabbabdbcdaacdadacddcbcdcddbbbadababbdbbbaadddbcdacdadabdcbbbcacddaddccdbdbbddacdddadccbbdddddabbcabbdcdabcdccbccddddcddbabbbdcacbbbbbbbabadabccadbcaadddcacbdbdaabcbbaccaccbabcdabcbacbdddbaccccadacdcabbaaacbcbcddabbcbdcacbabdbadacaadccccadcddacdadaabbcdddaacdcccadcabcabbcbcdbdbabbcbdcbddbaaacaaddbacdcbddbacacbdacbdadbcccaccaaccbdaccddbbaaccbabacccaaccbbbdbccdddcaccdcbccadacaacbcbabcbbbbaabbacdaccaacccdcddaaacabcadbacabbccadddbdabdaddcbcdbbccbbadbbbddcaacdbbdcbbbbbaaccdcdccabdccaaaccbacadcbcbcdaacddbaababdddcababdbacbbabddcdccabaccacdbdccdbcbcdcabbddaaabddccbaccbccccaacdbbdabcbaddbdbbbddcadacacbabcacacabdabadbccdcbcdaddacbacbcbaacddccbbbbddaddbdacbbdadcddddbbdcdadcbbcddadbcdadcbbcccadcadccddddaacaccbbdcbccdccacdcaacbcddaaadcadccadbddacbdcbbdaabdbbbccdbdacaddcacdcdacbbcccdbabacbccdaadbbabcbdcbbaaddddbcdadbdddadaccddccbabddaacdbadcdbccabaabdacdddbbbabcdddbaaadcdabbdbdbdbaadbcbdbbcbadbbacbbbcccabcadacbdccaccadcccdcdcaaacbdbaabcdbaacdaaaaaabccbbcabdabbddccdcbbcdadcdccdcdcaaaccaaddbbbbddddddcdacbbddadcdabcabcdadddccababbddbddabacbbdbaacdccadccddccdcdabcbbcbbbcbdcdbcacdcabcaacbdddbcacbbadacdacbaaabbdcabbcaaadadacdbbddaddbabacbccbdbbadddaaddbcbcbcbbdcccdacaabaccccdcdaddcaacccddadbbcccacdbccdabcdbcbdaadcddcaadddccaccbaddacdaacdbbabbbdddabdcadabadadaacccccdaddbbcbdbbdabacdcacaabbdcdcdbcdacbcbdbabaddccdccbbdcdaaaabbbdcadaacdacbdcddcaccabdaddbbcbcdbbccbaadbcbbbdccdbaddccaacdcdabbbababbacddbaaaabbccbcbcaadabbdacdcbdddcddcabddbdbabdcadddbccdbbddaacababdcabdbbbcbdbbabdbcccccbaddcccbdbcbcdcddcadaaccdadbabbbaabcbcacccbccacdadaacabacdacacaababaaddadbdbadddaabcdaddcabbcbdccdbdcbbdabacdbdbdadabbdadcbcbadabcdcadbdcaabbcadbddccdbcacabcadadacbccdabdacabcdbdaacbcaddccbaadacdaabadbadbbcddabcbddaaccabccbbdabcbbdccdcdddbccabaaccbcdbdbccdcbacdbbcdddcabdadcccacbddbccbbdddcabacaabbbdcdcbddaaacdcaabdadbcdccabdccaabdddbbbaacaddcdcadaddbccbdcbdcabbabbaadbaaaacdcadaccbdabcccabcbaaaacdcdbccdcdbcbaacdadaadcddcacacbccddcacbcbcadcbcddcdadcbddcdbcdbcadddacdcadbbcbbcbcccbdbddddabaddaddadacbddcddbdacbadcaadaddabbdcaabdbaaddbadbaddcbadddadcbbbaabdcbdbdadcabadccbdababaadcacacadbbccdcaccabaaadabcbcadbbdbcaaabbccbadcccbddbcbcadcadcdaadbbccaaddaccbbccdbcaaadbdbcadcaadabbaabdbacadccaccbcadcabbcbdadcdcbddadabcbdadcdbaacbabdbdbdcabbdbcddcdddcccacbaacaadbdbdccbbadbdddbbaacdacbcaabddbaccccaacdccbcdbbcdadacdabaadbcacdcbddcdbccdcbddabdadbcabababbcbaadabddacbcddbdbdcdabcbdbbbccdbccabbacbdcabcaddddcbcacbadbbdacacbcaccbcaaacdabaadadbbbaddcddacacbcaabdacbadadbacaadaaabdcdacbaddbabcbabdbaddcdbdbdaaacdcaaadadddbbacdbabcbcbbbbadacbcdacacaaadcccadcdbbbdbabdbcabdbdbddadacddbccabadaaadcdbbbddbaabbcdadbcabbabbcbbbccbcaabdcbdbaacbbcdbbbacdabbbdaadaaaacabdbabacabbbaadaabbcbabddaabbddacbdcbbbddccddbaddacabcbcaaacaaacdddbcbcbddbaaaadabdbbbbdcbbcbdabdbdbdaacbccaabcdbbdcbaccbddbaddadcccaaccdbaabaddbadbbcadacddccaabbbabdbaccadaacdacdbbacdbcbbbcdddddaccaaddcbccaaccccbcbbdcacdabddabbdbacabbdbcabdbabcaacddbccacadacabdbcddbadaddddcbcbabdbdcacbabcddcccbdddacabbcaadccbcaadbdcdbdddadaaddddaabbdbabbdacbcaadbdacaaddbcccbaadaaabcdcbdbddbadabcdaaddccabaacdbcbbacaddabbdccabddacdacdacbaabddbabdcadbacabdaccdcaabbbccdbdbabddbdcadcbbcdccdbbbddccadbdbbadbaadaaccbbccddbbddabbabcdbcbccdccbdbaacccabddaccdbcdbaabadaddaacaaccccccbcbacbcabcdddcaddaabdcaadaaacddbdacaccaddaabdddacabdabccccbaacddabbccaaccdabbdabdadbaacbdbccdabaacadbdcdcaaaabaaaacdaabcaccdbacdddbaacdbcdcacbbddddbabcdcabbadacadabdccaadadbbcabcbaacbcbaacbacbbcacccaacbcdccdbbaacaadbaccaaabcabbdadabbaccadaabcbadcdcbbdbaddccadbcbcabbccbccddadddabacbaddacbdcdcbdcdcdcbddbbabdbcaccaaaadacdcaaadbbdddacdddcabdababcddddbccbaccbaacbbbcbbbccdcbcdacddbcabdcbcccdcabdbadcbdbbbbabcbbbddaddccbcddbdaddbaaadcbdbbbaaddababacaddadbcbbddbdaccbbaaddccbdadcbdababcdaacdbbdddbdbbacccbadcccbbadabcccbccbcababccbbddadacddacdadabcbcbdaddbdaddbddcbdbbdddcdcbdacbaaaddcaccaadaccdddbdacbdddacaadaccbbaaacccbbacccadddabcadbcdbbbcbdacccacdbdbadbacdddcadbbdbdcacbadddbbadabbcdcbaabcdbaadbdbabcaadcaacdaaccbbbaddcdddbdacaaccacdbcaaaabdcdabbdadabdacdcbbbbdcddbbcbdaaacacdcdabaaaddaccbbaabaadbdccbdaccadadcabdcdcbcdbbbbaadbbcddbbccabddbcdadbddacaabbcbbaababdddbabdddbdbcddadcbcbdabaddbcbccaabdccccabdbcbaabdbbcdaacacdcacbbcbaaaaabadcacadbdaccbaaadcbacabadbabddddbbaddcdbacccaaddadaddadbbdccacbcaacaddcdbdbbadcddbadacdbabaccbcacdccdbcdcddacdadbabbadbaccacbaaacacccbacacadaddabacbabbbbcdbbdcaacddadddcbdbbdbbacbccbdbabbadcdbbbbcbdbdbccdcdddaaabadcdadcccbacdbadccacdddababcdaabcadaaabadababcdbccbdccdbbadbbabddccaaaacbdccaadbbbadbbbbcabaacdddddcadbdadcbcdacabbbbcdbbbcbcbbaccccbbbaaccacdcbcadcbddabbabcaadaccbccdaccdbabbbdbabbdcdcbbdbbbdcbbdacbabbdbbdadaacdccacbccbcdbaacbdbcbdbbccacbddacadababdcdbcdaabdcdaacdacabdcaddadabbccddcdccbaccacccbbabcbaadbadbbbddbadccdbddbaaacddcabbddddddbbdaaabbdcabbdccdcdcdadaaadccbaaaabcabccdcbacbdbadcbbccacacdcababbaddbbddaaaaabcddcccccdbbdbabababcdbaadcbbcdbbbabcdddadaccacddababdbdcbcaaacdbcdccdbddacaaabdcbdbbbacacbdcdcdacdbdcdcdaacababdbdabdcaadaccadacdbddaabaacbcdbaacbcbddcbadcacbdadbdbbdadaaacccbbcbdbddddbbdbaadbadccbbcdababcadaddcbbcaddaaaadbbadaaacaabdacddddddacddbaaccbbabbcaacdcbdbabbbdbcbabaadbccaabcbcabddaaacdcbddbdddbdabacacdcdcbdbcdaadaccacbbdbaaacabddaadbaddbbbdddacaccddcaccccacdbbbacbcbdbcbdabacbcbcdacdcbbcaaaaacabbaddcabdabddbadbaaddbbbddacbcccdccaabdcaadddbbdddbddcbccbccbcbdaaabccdacddbbbadbdcdacddcccadbddbacbacbdcbbbbcdbdadccacbadbaabacbaacdaddaccdbdbcbcacaacaadbcabbdcdcccbcdddaccaccbcbbddcabcdbcbadbcaccddaadaadbcacdcacaabdbadccdcbdccdaacdcddcdbcccadcddcddcccdaadbacaadbdbdadbdccbbccadabadddabbcaccbbcbadcddaabbccadabaabbbacbbabbbabdbdacdcdaddbadacddbbcccaddbddbcabdabbcdcdacbbbcdcaaabaacbacccacaabcbccdbcaaccdbbccadbaaacaddadcddacababbdcbaaaacaabbaccdcddbdbcaaddcbacbddcdccaccdacbcadbadacadacacaacbbddcaddadcdbdaadcdbcbacbbbbccbbdcbccdbbbdcadcbdbcaabddadccdacaddddaccdcccabdbaaccacdcccbadcacccdaaabdbdacdaaabaccddbcbabbbcbbbdacadabdddbcddcbaddccdaabaaadadcbaacbcbbaccddadcdaadbadddbbbaabbcdcacacdaccbacdbadbdcbacacbccccdaaabccabacaabbddcbddcbcbbddbcbccbadbadddadaaaccccbbbbbbacbdabccaddcacdabaacbdbaaaadddabacacbcbbdcacccacadcdddbcdabcadddddddcabdbadbabdbcdacdaddbbbbddbccddcbccbaaccacdcbcdadcddbadacbaccddabbcccbccddbadbddaaadccaaacbabdaacbcccacdbcadcddbdacbcbaabccdbdbcacbcabdadbcaacaccacaabcabaddbcdcddabaaabdcdcdabadbabaacaacdbaccbdbcdcadddbabcddbacdccacbccdaabbcabbaccabcabcbbbbdbaccddcdbdaaabccbbbadaddbbaadacdaccadaaddcbacbdbbabaadbacbdcaacdbcabbdbddaaabcdcddbcaaaabadbcaabcacdaadbdcaaddcdbbddcaadddbbdbbaddadcaccbacacbdbbdbbbcdbdcaaacaacdbcbdadcbbaaacbbadccddcdabdbabbbcbccadcccbbbddbccdabddcbbccccadcbabbadbbccbdccddbdbcbabccbbcbccdddbcccdccbbadacccddbbadcdcbdaccbbaaadcddcbccdbbbbbabababddadabadccabcddcbccdbdcbbddacdbcdcadbbcdacddadcadbdadaacdadacaaddddccabddcadbaabcbdabddacbccbdcccadcaccaabdbabbadcababdcdbdbcbaaaddbcbdcdaaacdbcbbbbabaccacdcdbbcacbbdcbdcdccaaacbbbadccccdcbcaaabcaaacbbdabbdcacccbadbddacdccddbacdaccbaddccbddcadbcccbcbaccbbacacbbdacbdabcaaacaaadddddcddabbacccaccdaacacaddbbbbaccbdbbacbbbdcaccaaddabbabcbadacdbabdbaacacabcbcacaadbcaabcdccadcaabacdbacdcbbcdcbccdbdccdcdddbbbacdcbbaacadadbdaacbababcacddbdcdbdbacbccbbddbbdbabbcaddaddcbcddcccbaacccdddddcadaccbacdabadccabaadcaabdddbbdabaabcabbaabcbadcccccddbbadccaccbbabddacacaabcacccaabbcdddbddcddbcbbbdadadcbcaddbdbcabccaabcdbcdbbccaccbddcaccbaabddaddbcbddbbacbbccdcaacdabbbcdcbbbbabcbbdccacaacdddbaadbadcaccacdccdadcbbccadbdbadddaacacdcdbdbaadabbbbdbaabcababdacccdbcbacdccdcdcbcabbdaabbcdccccabaacabbcbbdaaabdaddddcacddaadcaabdacbdbcbddccaaddacacbbdadbaabddcdbbdcdcaddcabacabdacdcbacbbbacaadaadadddccddbbdbdbdacbddabdcdcddbaccdcaaabbbaccacbcbdcbbabddccaddbdcaabbbdadadaabcadccdcdaabadaacbabcadbabbbdcaacbbacbccbddcdaccccacddbdcddadaccdccdbcbbcbcabcdbdadabbdbaacccacbbabdbbaabddbdbccaacbbbccdadbbdbbaabcdaabaacdaaddccaaddbccabadaccabdddbacbbbacacbcbbbdaabaaaccbcababcbaabbcccdaabcbbabaddadbbacadcbcdacbaacaabbaccabbacdadcdacbadaddccccbbcaccccdadaabddabbcdadcadcddbbdccbbadacccbdbbcadcdcbcddcddcccdbcbadbddbcbaaabaaccaaadccbdcaabddadcddacdcbaccabbdabdabdacbccdbcbcaadcaccacccbbaddccadcadddadaddaddbbaacadacccdcadccccdbbccadaadcdccbcadadcdbcdccbbcbbadcbcbdbccccddcaaadaccddbabdcbbaacacddcbcdbaddacdcddccbdbcdadadabbbaadacdcbccddbdaccdacbcccdcdcdbbaccbccdabcacadcdacadcacaccabcdbbccbadaabbbbbccbdaddabcdbbabdacbccdbbdadacaadbaddcccdaccbbbbadcbdabcdccacdbcbcdcacbcdcacdbbaadbabbaadbbddacddacabbcdaaabdcabbbbaadacadddccbdadaddcdbabccdccbbdbddabbdbabdaacaddbbbcaabcaaadaaabcdadbacccdcbdbbcdaccddaaabbdcdbbadccccccacbcdaabaaccdddacadddcabdacdacbaddaccabacabaaabcbbbbcaabbbaacdaabddbaddddbbdcddddbdcbbcbadbdbccdabcdbbccacadbadbcacdcdabccacbcddbccaadccbabaacdcdbbccdbbdbbdcaacabcadbabccbcacdacbabaacbbabaaaacbdddacdacbcbbdbbddadcabccaddcbdbaaabadaadadcdcddbaadcdbcabddbdccadbccdbddabdccbacdadbccdbdcdcaaadbcdadacdbcbbabdabacdbbdcacbcbbbdbacacbcccbbcabaacbaadbacdcaabcabacbdbcccacbdbadcbcbabcbdcdadbcbabacbabbbccdbadabdabccbbdbdbcabacbddccbbbbabaabdddcaddacdcbdcadbbacccddbaaabdccaccacddcddcbcdbbacbbbaacbdadbabcdddcdcdaaddadbbcbbbbdcbcbbbddbccacdbaadabcbbaabcacdaaccdbacdcdabddbadacbccabcdaccbabdabcbcaaccadbbcdcdbadbdccddbbbdbccbcbacadbcbabcddcddaacccabaddbcadaabcbcbcbccdadacbabdcbacabcdbdbcddbaadadccbdbddccddbdbcbacababcabdcbababacdbaacbddaaaacacddbccbbcacdadbaabcbcbacaabcccdbccbccadbaddabcaabdacccacacdaabbcdbbbbdadaddbdadaababbaabdcacddaacdccccbbbaabbadbbcccdcddcdcacddccbcbcbabbdacacbadccbdababbabccacacacaadaadbcdddcdbaccccddabddcccacabbaacdacddcdcaaaadbcbbbdaaccdbbcbbabcccddddaddccadabcdabbcdcbdacddabcacadadbadaccbaacaddbaddadcbddadacdaccbacbbaccdbbaabcdbbababbcbbbdcbcabababaacdbcacdccbbaaadaadcbacdbddbbbaddaabcacbdcabbbaacbacabdaacadcaddbaadbdcdddbdddacbdcbbbbbdcdcdabbadbbdcabcaabcdcdcbadbabcccbcccccbbdbaaaacbcbcbabbbcaaacdadbdbbdbdbabacbcbdcbcaccbabaccabdadbbcdbaacacadbbcadabcaabaadaacbcdabacaccabdbcdabbccdcbaaacdcbadbcbdaabccdcdcdcdbacbccacdddbadbaadcbccaaaccccbabcbdaaabcddacbddcacbabaaabbbdcadadabbdcaadadcbabdaaaacadcbbdabaccacacddbdbacbbccbbabbaaabdaadacaaccabbaabbbddbcacccccadadaaabccdcbbbabdbaadadadcdadbbbbbcdbacaccaabddccabcaacdbaddcbaadacbccccabbaadabbbaccdabacacdcaaabbcddaddadbcdbbdbababbdbaaccabcbbcbaabdadaccaadacdcdbbbdcacacccacaccdbabcbdaddcabdccbdcdbadacbddbadacadaccbaccdadbbbbbcddaadaaccdcbcdcdbbcacddbdcbcadbcbbdcacacddcdbaccdadddbbcbacbaaacbadadbbaaadcaacacadddddddacdaacbcccdabdabadbdcaccdddadccdcdabdcaaabdadbbacaccabaaddaaacdabcdbcbdddddcbbddcdbcbbbccdbccdbdddbcdabdccacabdbdaacbdcdccddbabcdccaabcbaabbbcbddcadabcaccccbddabcbbdadbdddccdaabddacbcdcbbdccccbacdcdabcbbbbcbabbbbdabdbabcaccddbcbaaadbdadbbddabccacabbcbaacadddbaabacaaadccdcadbadcdabbcaaaaccccdaadddcabddbaccccbcbabddcbcbbcaccdccbcdabcaabcacadadbbcbdacadadacbcaabacacdacbdbddbaacaacdcbababbcccaabdbddccbaccdbbacbddaddbddaccaacdccbbdcbadcbbabccdcdbacbaaccbbbbdcbdbadaaaabdbbacacbaddadddddbcbcdadbcccdcbbacbadcdbaccdddcabacdcdabcaddadabdbacddaabccbccabbbccbdbcaabadbcccdcaaacbcdacdcadacbcbccbaaaadbddaaaabababbdccadbdbaaacacabbdcdcabdccbbabbdacddadadddabcccdabdcdbbcaacbdbcdcbcbacbabdabbaacadcaadadaadbddadcadadbaddbaaaaaccaddcbcdbbabaaaaaccbaadcaaadadbcbbdaaaacbaabbdacdddadabdbadbbacdcbadacadaabbdabaadcbcacdbbdacdbbbadacbdadbcacdaacddacaccbaacdbbabcacdbcdcdadabdaccdacabaaaaacacacaacdadbadbcabdbdaacabdadcacadaabbbbbaaccacbadbdccacacadcaaaaddbcbbacbdcaddabaabddbadaacaaabacdaabccbbcaacbccddbbdbabcddccbdadbcaaccdcacbdcaaaabaddbbabcdababcdcccadddacbcaccdcccccaaccbaacbdacdbadccbabbbbabbbaaaacbbdcacccbacababdaddcacdcabbdbcaabaccaadcacacdbbcabbddbadaacccccbddbbaaadddcbdadddaccbacbbbadcdcaadcddcaddccbaddbaccbdbaccadadcaadddababddddbdbbbabbcadcdabdccbaccdddaacdadadddbdcbacbdadcbabcdcccabbbbdccbdbbdaddbbacacabdcadadabbdddaacabdabdabcbbcccaaaacbdbbddcacadbbcaaacdcabbbcbbcbacccdbbbddababcacacaabdcbcdbbcabadaacbaacbddadadbabcbabbadbdaacacdcdcdabadbdadbccbbacbcccabacaaadacddbdaacccdacadbcdcbaaccbdaaddbaddcddacbcaccddadadcbbbbaabbcbdacaaddcdaacbacbbcdaabbaddcbdccacdddcbdddddaacdcdbcabbdaadacddccbdcdbbccbcdbddbabadbacbdbbdcbdabdadabcbcbcdcaabccacadbcabccbddaacbdccbdbdcdbabcdaaaddcdddccddcacacabdcaccaaadbabbbaadadacacadbcbcaabbaabaabcaaadcccbbacdabcababaaddcadadddccbaabdadadbaadacabbcdccaaaadcabacacddddcadacadcdcbdacacdaadcddbbbcbcbacdbdbdbcdaddadbbdaacddcdaadddddabdddddadcbabbdacdacabaacbcacabbacacbddcbdddbbbddbcadabdcbbabbadacbcdacbbabcabacadcadbabaaadccbbaadddcbddcddbabcbcbaaadaababccdadcabddccdacacdcbbbccbaccbadcbbdcdadaabdaadbabcbabbbbdcdbbcdcdbdbcdaabadaacaddacabbcadbadcdacaabdbdacabdbbdaaabddbccbcbadbcbadcbcadcaddcbacdbadcdbdbddaabcacbbabacadadaadbaabddddabbcbadbbadccbddbbbaabcddbaaaaacaaacdbbdbdbbcdccddcccacbaabcaddcddbdcadddbcabddbbbbabbdbcccadddccdabcbdbabbccdbddadaaacdcddabcbcadcbdddbcaddcdacaadbadbaabbdcaacdacbbdddbbccbdbbcabdbbdcdddbbdacbbbcdacadbbbdbcbdacbdaacbdcdaabcadbbcdaccdbdaabaacbbcbbbacadbbaccbaacdbcaabadccdbdccbdbbbdddbcacdacbdbcbddbacdacccbbbcaaacdbddcdbabcbaccdbbddbdbcbdacadabbcdbdadcadbdcbaccccdbdbdadaadbddccabcaaabdbdaabcbddbcbadabbddcdabcaabcabcccdababdbddbaadbcddbdccddccaabcadaacdabdccdbaddcbddbddcaaadcabcdccbbdddcabdacdcaddacccadbbdabcdcacacdacddcbcbdcccbcaaddacbbbaddbdddbcdadbdbabcbbadbbccbbaaccaddbccdbbadcadbcccaabdacddadcdccbadccbacddadabddbcdadabcacbbbabcabddbbcbabdcddbabcbbaccdddabaadcacdbccbcaaabdabadcacdaabcdbddddbbdcdbbaaabdbdaaacccdbadbbadaccdadabcdaaadadbadbaccacbbcddddacdbcdbacdbbcbcbdbbcdddcadddcabcccacaaddcbcdbdbbdccbbcdaadcadaabdcdbbcacdcbcbaddcdcddcdbacccbacdcdcaccbaababdaddabbabaddadabbdcdadabcddcccbcdaaaaddaccaabdcbcbdaabbbccaaacddadadcbbcdcabdabbbcdddcaacbccdacbdbcbaabaaabcbacccdbabadcbcdacacddccdadaaacccaddbadbdbcbdaabbccddbdaacddddccdddcadddaabcccaddddbdadaddcbbcddddcbdbcdcbacaabbaacaabdcdccbbbcaddacadabcbdcbcdcbcaacaccbacbbdcbdadababbadcabddabadbbaaabbdadbdcccbcdccdaacbadaccdbabcbadaabacbdcabccbcacdcbbdcacccdbbcdccbcadbabcadccccbbcbbdbcdcadcccdacdcdacbacbbdbacdcddbccbdcbbbabbdbabaabcdbaaabcbcbabcbadcdbddaacadddadbdccbaddabddbbdddbcbcddccaddbaaccbadbbccaabddbdbadbdcaabdbababbbacdaddcdabccbabdccbcbbbbaaccdacdaabcadcbddaddccabaabbadaaacccccbbbdbcdabcabdcccacddbaacdddaacaadddbadacdaddcacbbabbcbbcbcaabcabddacaddbcbacdabcadaadbdcdddcbcdbaacaaacbdcdaddddaadcadcdababddcaacabbadcbbadbdaccccacdcccbdddaacabcccdbdbbdbcdbabbbcbbdbcbaccbacdcddaddccdaabdabdcdaaccadaddadabcabddcdbbbdadacbadccabbbbcbcabddaadacdabbcbdabadcdbdacbccaacddbacbcabdccdcaaddaacdbabcdbdbbbabcaddaacbbadcbcaadacbabdabadcbbaaccaccacbbcabbcaccdcadcbabaabcdcdbabdaaadcbddcadbabcacdadbacacddddabbcdcaabdbcaadacbccddadccddaddadbabdaddcbcdbacabdbbdcdcaaadabdababdcdbaaacdbdbddbbbddbcddbbbcdabddcbdabcbcbcabbaddadabcdabbabacbbcaadcdcabbbdbbaacadbdaacbdbdbaddddcaddcaddcbbbcbcdcdddbcacadcaabbcbbbddcadacbaabadcccdaacaacaadcaaddcbbbbbbbcdabddbbdadddadacccdbdbbcddcbbdddadaddaaddddaddaaaaddcdadddabdddbabdbddbacabadbddbadcbaadadaadbcddbcddbcbcbbabaacadccacabcabcbaabcbaaddddaaccbcabdbbaddacbcadccadddcbdcbacdbaabcabbddcacbbabaabccdadadaddbdbcaddacbbacbdccadabcabdaaadbcacadcdccacddbbccbaadddbdacdabddcaabdcdcabcaaaacbddbacaccadaaaabcccaaccbbbaabbddaddddacbddabdaacdccddadbadbdbdddacacdbdbcaaacbbdaadddcbacabbbccdbcdbbbcdaadcbabacbbaadcaccbbaccdcccbbbddabaddacabaacaabcbadaddccadcccbcbacbcbbcbacaabacbccbcccbccdaabddababbcadbdcbaddbdcbbdadbbbbddbbccbcbcdaabdadadcccbabcbabaabcddcdbaadcabbbaacbbdbdcddbddbdadddccccccabaacbbdcdaaccbcbcddbbbabadcdbcbacdddbdadbbbbddcccabbacaacbbccaaadcbaabacbdbdcadcbaabcdbdbcaaabdccbdbdabbbdaccadbddababbabdbdabddaddccabccacaabaddcbbcadcbccbdddabbadbaadadadacbadbabaaabdddacadabccbaaaccdbbcbcabdacbaccbbccadacddccccdcccbacdadcbbcdadddbbbabbabaddadaccbbcddcbbcadabdbddadbbcbbabbccaadcdccbbdadadbdbaacbdaaabadbcabcdbbcdadddbdbacbbbbccbbcbacdcacacdabddcccdbdaacddcdacbacabcbacdaaaddabdbcbadabddabcacdbacdbaadbbbcadabccbdccbcdddacbbddcbdacbbccabbaadcbbddaadddabcadbdcacbdddddcbdccdadcdcdaddaddaaabbadabacbacccccbcaaccbabaccbbccbdbbdbdbddaaabbacccddaccdbcacbbcbddadcbbbbaaaacddabbaabdddbcacbdacccabbabdbadbdadbdbcaadaaabbabbdcadaaaacbbaacbdcdcaadcddbdbaddbbadcbbccadabdbadbddccbcdcccccdbdcbaadcdbdcadbaaadcccadbcddacbaacdacaabcdaaabbbadaddadddacbdaadaddaddcabacddaddbabbbbccadbcbcacbccdbaaccbbbcddbdcbcbbcadbcadbdcccbacaddcccabdcbccabddbcccbbbaaabdddadcdacacdaaccdccdabcddadcddcacaddabcccdbcbdadcabbaccddbbaabcadacbaaacbaaacbdacbcaccacaacbbbcabadacabcacccabdcacbccdcdddaccdacbddcdabacbbaddbbaccbbadacacdaadaccabcbaaabaccadbbbbcdccdbcadcccabadcabcacddacdccadcbdabbdccacadacbaaadaddccbcbcdabcbccdcbcaabdbaababaaaaadbcdaabccdadbacdbcabbacdbbdbcaaabadbccabccadaaaaabacbabaaadbacdaaaaddcaccacbddbabdaaabadccbacabdadbbbcbbbdcccbbbdbdbadadabbbaabcccbbcacbdbdcccaacddaacbbbdcbdaaabcbabdacbbdacdcadccdbdcbbdcaddddbbbbddacccabccdcbabdbabcbbdbcbdadbbcdadcccdadacbadaddcaadacaccdbcabdbbabcaacacadbccddcaaccdccccccaabcacbaadcbcbadabbccbcdcbddbdcaaaaabacdcdbdcbbcddddadbaaccaddcdaddccdbaccdbaacdcbbcdccaaaabaccddccbadcbacddcbcabdaacbaadaacaabadbdddaabaabcdbcaaadadbacdcdadbdddddddcdadddbdabadcacbccabbbccabddbbbbabddbcaccaccdacaabcbdbadddbdadcdddbbabadddbbabbadbcacddaaaaacbbddadcccdacbbabdcbcacadbcdabaadacdacdabbdbbcddcccdcdcdcabccbbabacbcbdbbdaacdcdcaacdbadddbdabaadaadaccdaabccadcdaacbdcccdbaabababadabbabdcdaaacdacdaaadcdbadabbbcdaabdddbddcadbdbdcacacabcdbdaccaacbdaadbbdcaabdccbabacabcbcbacccdbccbdbadbcdbacddcbcdbcaacccbddbabbdbaabbdabaaccdddbccbcbcaaaadbacacadcbadadaabbbccbabdcdbbbabdbcaaccabdddabcaaabbbdbccbbdbbbcdcddbdadcbccccbddaacccbcdddaabdcddbddcbabacdadbdbabaddbdcccacbdddbcbcdcdcccaadddacadbcacdbbacaaacdcdbbbabdcaddbacdbdaccdbcbcccdcbcdcbbaabccdadbaabbadaadbcaaabddacddccdbdadbbcdacadcadbaaaaabcaadccaababdbacaacaaaabbdbaabaaaacbcccddcbcbacccccabddbdcbbbabcdbcdaabdcaccbbabdadbdaacccabbccaabdacbdddabacccadbcbabdacdcdccdbabbbaacbabadcaabbcccbdbaccacbbbbdbbdcdaacacbdcdbdcdccbbaacbacddabacbacaaaaabbbcbdccdcddbcbbabdbccdacbcdbacbdcabdcccaddaababccbddbbaaddadabbdbbbbabdadddaabdcadcdddacaadcccabbabbaabbddaababaacbcaadabbacabdbdcbbacbcdaaccbdacbbaabcccaaacbbdddcacacdcbcbbdadccabdcdacccccddabcccdbbacacaacadabacacbccccbccacaaaddcbbbcabdddbddbbacbadcbcadaccabdccccabbdacccbacaabbcdccdcbdbbddcdcaadbacbcaaaddbbaaacdbcabcbcbbadcabcbccaabbbbacccdccbdbacaabbabdbbcaccaddcdabbbcaabcddcbcbacdcbbaaddaacdacaaadaaccdbcbaccbdaababcdbbcabdcbdcbccbdbcabcdaabaaabcbaacdadbbcaddbadbdcadbbcdabdccbadbdabaaddabcbaddadadbbcddbddcdbaaccccddbcdddabcccddbacbbdabcacbaadddaabbcddccbcaccaacadabbcddaccddbbbabbdcddbdbbbbbdacdadddcbbcabdbdccddbbccdacbdabccbcccccaaaabbccbdaacddbdcdcaacbbaacabdcdbcbaabaddcdbcccddbdcaddacacdccaaacdddddbabacccdabbaacacddadadccdabbbdbadabdadaadcabadbdcabdbcadbdcacdccbabbdbaabacdadbabbdbdbadadcdccdcdacbddbdaacbccbaacbbdbbdcbacbdadbadaacabccbdaaaaaddaabdcbbbbddabadbbccadbcccabdcdddbbddadcbbacaacdaacdcdddcbaacbcdcaabbcccdbbadbbcdbcbbaddbadcabcddbaaadadacaacddbcbddcdaacdbdcdbddbbabdacdccaaccaddcdbcadbdcddcbdbddbdccdbdaccdacddbdbacadacbdcbcdaccdbccbbadabdbbccaccccaabdadacbdcbadacacadbacdcddccdaddbddacabbadadbabcadbbabbbccacdabbcacddaaadbaaccbcdadccddaababccbbdaacaadbbabcccdabbdbbcadacabbcdababbdabbbaccbaccabcbcbcdcabcdbccdcaddaadacbdababdaaaaadadddbbbacbdcabacbaaaccddadcacdaabbdbcbddaaadcdaaddaacddbbddaaddbddababaabdddcdaccbabaacaaddccbccbccbabcdbcccdbbdcaccaadacdcddabcaabcbddadcaddabbccbbbdbddaadaabdaabaabcdacaacaccdcaadccacbbcacadacddaccdacadbbcdabbaaabcdccaabadadbccdbbcddbaadaccdbbbbcaabadbddccaccdcbcabccadaabcdbcaadcddcddcddbadcbdbbcbababdccbcbbdabbbbcdccdcbcbcddccabdbbdcdbababadbcdccbabbaccbadabbcdbbdabbadbaccbcaacaabbaaacdccdbcbcbabaccbabdbaabdcdaabadabadbaacddbbaaabccadbcbcdcbabdbaacdddbbcdabdbccbcbbbbcbdacabacdcdcaccacbababaacaccacbcacdccdccccbdcdccbadcdacacdbbabcbccdcabbdcadcddbadccdcacadbadcdcdcbbccaabcdaabbbaaadbbaacbabccaaacaddadaaaaadbbcaabccaabaaacaadbaacddbddaccabcbcdcccdcbaadccaaadabdbddaabbcdbcddaaddbadbbdccbbabcabaaabddadbcddbbadbcccacadbbbddddcaabcbdbcdccccbdcbaaacbccddcacdacbbcbbdcdaadaaabbcbcadbbcbdbabdbcdccdababaacaccbaaddabcbacbbdababdcddaddbdcdcbdbcdbbacabacbaaadbabddcdddcccbadddaacccbdcbbdadaacddaddaddbaabddcaccaddcaadadcbadbbdbdaabbbcadccaadccabcbddcbccbcadaccbcaddccddcccddaaaadcbababcabaddcdcaccddbcccadbcbabcdaadaddbbbdabcbbcdcbaacbadaabaddabaabdabdcababccdcbbcbdadcbdbaaacdacaccabcccdbbbacdabaabbbdbbbadbdcdbdacbbcdcbcccaaaccbccaddadbdbbabadddabdbaccdbdbdbcdcbbdbabbdbaccbccdcdbcdaabbababbbaadbadadbcbcbddbcdcbabcaaccacdcdcbabccdaabdcbddabcdcbdadbdccdacbdbbbbbddaddbabbacbbadbaaccaaccbaddbddddabdaabbcacccaacdaabdbdbcdcbbdccaacadcadbacccbcaababaccdcdabadbacbcbddbddbbbcdababacccdcadbbdbacaccdbdaaaccccdcccacdcbcabdbdbadadadcbdbdddddbaddaabbddddadaadbbccbbcccaabbdcacbdcdbbcbcacaddbdaacaadbbcdbdbacbdababbccdccbacccdbcbbabdbdabdbacbabadbbdddbcadccdcdbccdaccbdabcaaabccdacabdaaddacdbdbbcaccbcaddacaccccbbabdcccddbaddabdadadbdadaaadadbaabdcaaacaabbcbcbddaabbbdccdbbcbabbdddbabbabadcdcbabaadddcbdaabccccadcaddadbacbcdcabcbdbccdcdcbdcdcabbdcbbcbbabbcdccdbccbacbcbccdcabcbbddccbbdcbdacbccbbaaaaddbbbbaacbccabcbdcabbddcadcdcadcdaabbdcbabcbbcbabcddbcdbaadadccbbcbcdbcdbbbcbdbadbdbdabbdccaacadcdcaccaaacddbcbdccaaccbababdbcdbbdbddcaccdacacbccccaccaabccabacdaabcbbcccbaddabbcdbbadacdadabdbadabcbacabcaacdbdddcdaccbadddaaacdcdddcaadacaadbcbcdbbbcdadcbdbddadcbcdbbdddccabadcbaadbcdcacbbcabccacadabbadddbcbbbababadcbbabbbddddaaabcaddadbaadbbdbaddcbabdbcbcbdadcacacbabbbacddcbadbdabccacaaabbcdbadadadcdaacbdadcbdcbdcddaaacaababdadadcabbbbcdddbadadaddadcbbbcabaacdbdbcdcbcbcbccabddcdadabdcbcdadabddcaaacacdbdddbcdcdccdbccccdbbbddaccddddccdbbcbbbccdaacdbbacccbbbadbbdcacdddaddaabccdbacdcaaacdddbdbbabcbcadcadcabbabadcbbbabbaddcdbdcbcaddbbddacbaacacaccadadaaaddcdbcaccacbccbabdaaadddbbacadadaddccaddddcaadcbbbabcaadcaabbbddbdbdddadcaaaadccbababcdcbbdaabcaccdcbccdadbaaccbbcdcbbdaddadcbbcdbcabcccddabddbbbabccaaccaddaddcaacabadabbccbaacbcaaabddaccdaabdbdccdbccabddcddbbadadcaddccdaddcdccdbaddcdcadbbbcbdddaddbdcadcabaadcbabdbddcccddcdaaadccaddbadacbcbdcaaddadaacabdabaddaacaacbdabdaddabccdacdbabbdbcbcddbcdddbcaaaccbcdaaabdbccbdacabcbdcaaabaadbcacbccbcaadabcbbacdaadbdadbdcbcaabcddbdccacaabbbbdcaccbcbadcdaadbdcabbcdcdcdbdaccdcdcbcbccabdccadaddbddcadcdcddbdddbccbdacaacddcbbbbbbcbabaabdbbddaaadbaabddadacdcdacdcddbbaabdcacbcdcdbcaadccbdbccdaddaddabccabbcdcdbdbccddcdbbddcdaddbbdccdcbacbcbaaabbcbdbababdccabdbcacadbbbaabccbcdbdcaadabddcdcdcaadbcccbabdbbbcdbdcbbcbddbddcaccdaacaadbaccbcbbadaddccbbdacbaabdbddccbcabdacccaaddcdacbddccdaacccaabbbaddbdaaaaaddcccadababcccdddcccaaabdcbcbdaddcadacabbdabcbbbddccddadaadadacdbdbdddacbcdbbbabccaadacacbbdbbaadcdccddcdabbccacbdabdbdbcdcdaaddaccdbcbcddaccaabdccadadcdbadcddabbacaabbdccaadccadccadccbcbabaacbcdbabaabaacadaaacddbaabaaccabccacbbabcdadcbcaddadcccbabbcdaaaaacdabbbdbbcaadcdadcddabaddadcdadcacbdbddcdbcaccddcdcacaccdcabbbddbdddcabdcadadcbdddccabcaaaabacabbcacabcacdabdddbaabadccbccabcbcbbacabadaacbcbccabdbabcbcbaaccbacadcaddbadccbcbcbabdcbbcdcdadbddacbadcadddbddaccadaddaacdabdbbbdbaaaaabacbadcbaaaccadabbdaddaaaadbcbadbdbaadcacccdcababdcaccdcaccbcbccdbdbddcccbbadbcaadbcabccbbdbacdcbcacdddcdbcadabbdddcdacaaabadbdccccbcdbabcaabbdcabbcccdadaccbcbccacbccdaadadbaddbccaabadabddbacdbcddccbdacbbdacbacadddcabdcadbbddcccbbaabbacdddddaaacbbdabdadddaabccbaaadbbdbdabbcacbdaaabcacddcbdbabdacdcddbbcabcabaadabbcdcbcaaaddbbbcddddaaddbbabdcddccdbabdccdcdbadaacabacdcadcdcdadbaccacdaabdabcabdbdacbbbcabcbabcbcdddbcdacadcadacbdbddcbddddabddccbddcdcacbdcccbdcbcbccbdbbbdcbdacbccbdbcbcacdcbadaccdaccccadcaaddcbccbbadcdcbcddccbabadaccacdaaabbdbbcbbdbddcdddbadbcaacbdccdadbabacbcbacabddabdbabaabbcdcbbdaadddbbdabdaddaaccbccdbacdbdcbbdbddddabdacbbbdabacaabdacabacbdacdadbaaabddcadabbddaccdaccdbadcacbabdccbbbbcdadcbddbcbcddcccbbcabacdbdaacbdbabddbdbdcbbbcabbbddaaacdbabbbabdabadbabddccaabaadacddababacacbdbdbdabbadbbabcbacabcdbabbcbbcbbcbabcbbdbadcaaddddabadabbaadabcababaacabbcdaabcaaddbddcdcadddcabadadcadaccdadbcdabbbdaabcbdbacbaaacbcbcdccacbcabbdbaaacaaddacddcabdddcbdbacbdcaccbbcdaadbcbbcdddaadabdaabdbbadcbabdbdabddcddbaadbdbbbbcbacadadccbaacabdabdcdaaaacbdbccadbdadabdcdcdddbabacbadcbbdbdbadcbbbbadadbcdcadcbccbcdabaabbcbabaadaddbcacbadbaccacbdabdbbdaaabdcadacdccdcadabddcdadbcbdabbcaddaaacbcbdadadcdadadcbbabbbbaddabdcbacdcadacbddadaadcabadabdbcdcdaacbccdbdccbdabcdbddbcbbcddbbcdbccdddcbaccaddaaadcdabdccddcdbbdccaabddaaaaaadcdcadcbdcaaacbaacbcccaabbacbacdaaadcacddcddacdaacdcbabdbbabcdcbbbaacbbcbddadadcbcdcacbdabbccddbdbcbdcabcbadcbadbacbbababddabccabaabcddbbabdaddcccaadcbbabcaacdbdcaabbcbdadbcaadacbccaadcbcccbcbbddddcacdbcaccdabcaaddabcbcbdbdaadbcbddabdcbcddddbdcbbdaaddbaabbddcabbbcbdddbccabcadaacdbccaabbbdbbcccdaadadaccaadadbcbddcaddaddccaaaabdbadbcbaddddadbadbdabcadacdbbdccdadcadcdaccadcdcaabbaddbddcbbadadcccbabbdcabddcaccacababbdbabdbbacddddcbcbbacbbcacaacbdccacbbcdccaaaddbccbbcaaaadbbdcbabbcdcadbdabddabcbccbdcbdccbdddaaccddbdbddcadcddccaddcdccacadabcbbdbcdbbbabbacdadaaaabbcbbccdbcaabbdaadcdabacdbacbdbbcbcacdbaddbcadcbaaababcbabaadbdaccaddaddcdbbadbbcbddaccbdcdddbbdbbdcacaccabdcbaadcabadbccbbbbadadbdcbbcddcacccdcaccadbcacbdabbcbdabbbadbaccadcddccbcdabdddaccbbbdcaabadadaaddaddabcbcdcdbcabcdadbaaabaadcdbbaadcbaadbccbddaddadbcccdbbaacabbdaabacdcacadccddcadcbdbdbdccccbdacbccaaacdacdcbbdcdcaabdbbdbacaddcdddccdbadddacbbdabbadcadcbcacbdbacddbcdcabbdddccbdcaccdcdcbddbcccbcacbbbddaaddaacabdcccccabdadccaddaaddabddcdbaadbccdcbcaacbadabdddadcadbadcbbcdbadbccddaaababaccdcddbcddcaddacadcddcccacbccccbcbcacbadadaccbadababbacacdabbaaaababaaaabcabdcccdaaccdccbcdbbcacbabbcbdbddbabcddadacddcaadacdcdbbbbdacccbddbbbbcaccbdadbadbadcdcdbaabbbcabdccacdccacddddabacaccadccaccbdabddbbbcdcbccddaabacdadbcdadcdadadacbdbcccaccaabcabcdccdaaaaccadaaccddaaaddaadbcabcdbdcdacdbbdddbdccddbabdbacdbdcabaaabbdacaaadcdacdacacabcaaacdbbbdbacbbcdcdddcbaabdbbcccccbdddbbccddbcbbadbacbaccaddadcabdcdddbdbddbcbdaaccbcaaccdbabcbcaadaadbaaabdbdadcbaacdabdaaaadcbbcdcbddcabaaccadacaacbacabbabccdbacccdbababbcccdbcbccabbddadbdbcaabddcddaddadbddbbbaccdcdcaccbccdaacabcbdadacbcdacabcabcabbdbcbbacccbabbabacadaacddcccaaccaadadbbdadddbdbcdaddabdccbdadbbdbbcaacacbbaccaabdbbbdddaabdbdabbdaabdcdbcbbadddbcbbbbbcbccddabdaddabbdbcdcdcbaabbaccbdabdbaabababbbccaccdaaaddcccdccabcaababccaaadbbbcbbcacccbbabcadbacbacbcacbcaadccaadcbdacbbdbdacbdbbabccdacacadbcccaadbccaccdaccdcaaabcdcbbdcabcbaddddddcbaddacbacbcdcddcaacdcbacddbbaaadadaaaabaccdbbaddbbdcbdbccdccccbbbdcccadccccaabdabcaccddacbcdbacdbaacbcdddbabcccbdbdadbcbccbaccccddaaccbcacbdadcddbcadcabcccaaadbdcaddababdbaaabcccbbcaadccddacdbcccadbcacdaabbabcacdbabddacdbbdcdaadcdbdacbadcdbcdadddadacabdddddcddbacacacaddcbddcbadbabcaacbcbaccadcbabbbdabacdababcabdcacddcdadddadcddcdbdcddbcbbbdaaabcdbcbbcaaabcaadbdacabcbcbaabdbdddaaaabddccbcaacddcdbdaacdadcdbbddbbddbcdbcabcccabdcdbdbdbbbbbdadcbdbcbdabdcccdcbcabacdacaaccbbdcabcaacccbcabaccacaccadcbabcbcadaaaddcaabdcbcaaddbbaabaccbdccccdbddbcacabbacbbbabdaacccaaddbbdddcbbaacadcaaccaabbddbdddbcbaaccddbcdadaaababbbbbcbdcdbdcacadcbdbadcbcccddaaaddabaabbddabbdaadcbbbaacbbdaaacabcaadcbcdbabbbbcdccacbbdcbabacaccddcbdbabaabcadbddacaacdaabccadbcddbadabbcacdabdcdaccdadddcacadccabadcbbcaadbbabaacbaaccdcddbadbbabbdabcacdbcdbccaccdbdbbcdcccbbdbcacbabdbddbcbddbdccbcaabdcbbdcbbcdcbcbadccccdddbdabaacaadccacccddddbcdccbccacacdabbbbdcaddcbcccdcdddccbaacacbcbddbacbabadbbddbbadabaaacdcdacbcabadbcabbdddbcabaacbcbbbacbadccabbcdbbbbddcbacdcdccadbbcdadcaaadcdddcdbbcdbabdcbacbbbdddddbadccacdbadbabcdaaacccbbbbabbdbcddbcccbbbbabcadddacbdabbdaccbdbbadbdccabdacadccdbbcbadaddbbbacbacddbdacddbaccacdacbcdbddabaacbdddaaabdaaabdaacadcabbcdbcadacdaccabdaddacdababdcdadaacaccbaadcccbbdabdcadbbaabaddcccbdcdbaaadadabcbdddbabdbacaaaddbbdabdbbcacbadacabcadccaddacadabcdbdccadcbbbbadddbccbaadadbcadaccdbcbbaabccabbdddddbccbdddbbdabdacccbddcdaccbacdaacaacabbaadcdbacdaddaacdbccbbcdbdbbdcbbcbbaadcbacdbcbdacdabacccdbbcabadbccdbacbdadadbaaaccdcbbcbadadabdddccdddbddadcadbdacaabbbacccdcaadbcdacacdccdccaacdcacdbadcbcbdbdcdadaabbdcbadadcddacdcbddbccbdaadcbcaccbbbbccbabdccdacbcacaabdbddbbaacdbcccadcdbbcddadbabbccacaababaddaabbbabbbaccdcacbcddcaaaccddddbcbdadaabaaabdcaacbabddaccbdcdababccddbbcdbcdaaadabcabbabdcbadbcbddbdbcdbabcdbbabdbadbacbdcbbdbcdbbaacbccbdaccbcddccdabaadacaadaabccbbbbaccaaaadbacddbcdacdccabcacdadcbbababaccdcddaabacbabddcccaabdbcdcbaabdaabdddbccddacbccdcbaacaadcaacbcadacaaacacaaaddddbaddbacdacdaabbacadddacdbbcddccddcdcdcadcddcbdbcbccddbdcbabccadccddacdbadbdbbdadbadcacdcadbdbabdbabcdbcbcaacabadbaabcddccaccddcdadcdcdddaacbdbcbbaddcdddbcddbdabdbcabbabdbbbbacbcdcbdadbdabbcbdcdcabcdaababddaabdbdccbcddaaacbbcddcbabbdcdbcdcacabddccbccbabbabadccbadbdadcddcbdcbbddaabddbaaacaaabaabbabbabdbacdaddbbdbcccaccbabcddcdbbbadbcbbdccddbccbdcacddcbcdabccaccddcdaadaacccdbcdddbacbcacdddaabcadcbbbcdaababddbcdcacbacbcbbcddbcbcbdddcdbdacbbcbaadbacaddcabcdbadabaddbbabbadaabbaccacdadcbdbdaacabdcbbddcdbbdbdacdacabdccdcadbbbbdabcbdadddcdbbdbbbcbbcdccbcabdcabddbbdaaabadcbdbbadbaaabcdacdcdbcaddcbdaccbacbaabbddacdaacdadcbdddadddaacacbbdbdaaaaacbdabacbdaccaddadbddcddbbabdcdaabcbaaccccadbdaacdacbaacabdaababbdbccdabbbbcaadaaccaacabbcdabccccbadbcbccbcccaddcadcbaabbaaccbdbabbacbcdcdaadbcaabdddcabddbcbdbdbabadadaabdadacadbbadaacddadacbdddaacaacabdbdcadcadbddadbadcdadbcbcaddbbdbadcbaaccdbcbabccdcadddabccbcbaadbdadbdcdcbbdddbbaabbaddbcbacbadcabcdbccddaccccdccdcbabcaadabcabcdadacccdadaabccdaabdbcccbbcbbbbcdbdabbdbdbddacabddacaccdacbabcdaddcccdadbddccdbbadcabaccddbabaddbdbcbabdcbbabadbbaaadaccadcaadcddadabdddccbddcadcabcaadabdbddcdbcdbaaabbbcbcbaacbabccbabaccdccddcaccaaddcddbddbbadabcccbcbddbcacdccccdcacccabdbcaddbabdacacdddbcbcbbcaaaccddcddababdaccdcccdcadaddabdaacdbbcdaadddcdbcaaadddacaccccddcdaadababddcadcabdbbbcacbdcdcdaaddbabaabdaabcdccccabbcaaaacdaacdddbcdcdcbdccccbacbdacaabdaabaadababdabddabbddbbbaaabccadabcabdbcbaddbbcddbbbcdaababbbdbaaccddccdabacbdcddacdcabaabbbaabbcaddaabbcdadbcbdaabdabdccbaddcccdbbabbcbcbaaacbdbaadabacdccdbccdcaacbbbdbdcddaacdbbabadacddddaddbcaacbbdcbabcdacbbccacaaabdbacadacbdaaaacaacadabacbbaadbadcdbcbabadaadcdbdabbbaaddaacbaadbadbdbdbacbcbbbccdadadddbbbbcdbadbbbccdddccbccacbabdadcacdcccbaacbdbcddaaabbcbaabbbabdabccaababcbbaadacddcaaccdbbbaaadcddcdadbddadddbcbcbbbdbcdacabdaaabdcdcbbadabbbbdabbccbddccdccccacabadbcccbabcdcadbdddabdccadbbaaadcaacccccabbabbccaccacadbbdddaacdaacacddbbdabadaddccccadddcaacbddbbbabdddcbbcbacbacccccadbbacabaabdbbdbaadcbcabbdaaddbbacacddacbcddbabaacbcabddcccdbcddbdccadcccadddbbcbacbcaababcdacbdadbcadadcdbabdccdabddddccbaadacbabbadcaadccdadbaaddacccadcbcaacbdcacbccadcbcaaaacacaaddcadabbbbddcaccaabdccdadccdabdbbbabbcbddadbabcbcacddbbbdacbcabbcbccdcdbdcbbabbdabddbdaababadacaccaccabbbdbdacdabaacdaddaabcdadbcacdbaacaaadbdaacdbbccadbadcbbcccdadbdbdbaaacbdddbcabdcdadadbbbbbacdcacbdaddbdcaddddbcbbabccaccdacadddbadcdacbbbcdbcbabdccddcadddcccabadbacdcdcacacbcdccbdbccbcdacbcdbbaaccabcccacdddbbcccccbdbbcadbbddbbcbccbbcdcbbbcadacbbdbdcdacabdcddcccbbdcadcdabaaaabbdaacaaadacbcdbabaabacbabdcccccadbdabacdcbaccaabababcdbccdbabbdbdccddacbacdacdcacabbcdcdaddabcaaacbbddcacdbdaddbccbdadabbadacaabaabcccadbcbdcbdadccbcdadcbbcaadabbbcaadccadbbbdbcbdcccabddcbcbbbaacbbcabadadbccbddbbcbddacaabadabccdbacacddcbbbccddaadcbabcbbbacdddbdbbddabddbcbccbcbbddabbdcdbbacbbbbbcabaabdddbdadadbbabdcacadcddbbcdbbcccacacbdcddaadacdccddccabdaccacadcaddddcccaabbadcdbccdacdbbbdaddbdabcdddbaaadaabcbccddaabbcaaddccaccbbbcbbdadcddcacaabcaabbcdcdcbdadcaaabcbddbccdbaaaabcaadaacacdddcdcbbbbbcbdbcdcdbaccddcacbbdddaddacaacdbbbcacbacddcbcddadabdabcabdabcdbddbacdbacdbacbdddabbdccbbbcaadabaaddbaaadbdaabacaacacbabadacaccbabccdcbcbadcbbaaaababaccdcccddadccdbbaabdbacdccbdabaaabadccaddcbacbdddcadddadddbbddadaddaacabcbcacacbdbbddcabcbacbcabbddbaccbdacdbbbcdadabadbdddbdcaacbbabbdcddbbacadaaccabdcdbadbdacacddadbcbcdcdbaabdcaacbbcabbccaadbddbabdccabbcdbdadacccdddaadcacccdadbacbcadcaccbabacbabdcdddabdbcbccbaddddbddbdacabdabcbcabdcbbbaaadadbaabaadbddcadccabccbbdcbccaddcdacdbcdabaddaccddabbcbacacdadadcacabcdbaaadababbadddcacaccabdcaacdabacbdaddbadcaaadadcddcdbadbcdcccacaaccdcdbadbddbdbdcaaabdabbacdcbaccbbdcbbbbababbcdbccabcacacbcdbdcddbcbadadaddcbaccccbcdcaacaddaccdbccaddddcaabacacddccdddbaccabbbbcbcddcadbbdcbabbdcdbabddddddbbccdcccadcbcaabbdbdccabccbbaddddbdcddcabcbdbaacdcbdcdbabcdbcdacdbdbdcccddbbbcbaacdcabcdaddbccdcdbcdcccabdcbcaababbacbdcdddcdabbbcaabdccabaccbcdcbbbacbbdcbaccabbdbdacdadcddcbbddbbbcacaacddddccabbbccdcdbdbbbdaccaadadcbbdcbdbccdacaadddcaaaadaadbbdbbbddacadddcbdcbcaaabcdccabaacbdacdbcbaccddbdaaccabcdcabdabdccaddaaaaabaabaccaccabcadcbbaccbabccabcdaaabbbdcbacccccdbaddacabcdcbcdaddbadcddaacbcccdccccdaabaaacdcbbaadaccdcbaacbdddcbccadadbdaabdccbdcbdcbcbabdacadcccddbcabcdbcbaddacdcbbadaadccbddcaadcccdcbbdbcabaaccddadadbadcdbadcbdacabddacaaacccdadccbbcbbdcdadbbdbdabdbaacbdcbcdbbcadcccbabbcdbcdddcccbadabdbcddbcdbacaccbabdbcabdaccbadacbacdbcaacdcbccbcdacadbdcdbdccccbbbbcacdbdbadccbdcbabbcbcadbddabdacdbadbdcbdabbcbbcacacbbddcdcccbaadcaccaddbadaacddcaacbbdcabbdaaddbacdddbbadacaabbcdbbaacaddcaaccccdabddcaacaabbdabddbdbcabacbabbcbddbccadadcbddbdcbbcbaacaabbcdadcdccbdddaddcdacdbdaccbadddcbbccabbdbccbdadddacadddacdabddbdacbabdaacadbbbbcdcabaddbacbbbcccdaadddbcaaccbbddcbccbbbcacaccdcacdcbcccbdadbadaaccdddcabcabbbdbbaabcbcabadcccaadaabacbaaacacdaaabbaabcdcdbabcccbdadabcaabdbaabbdcbdbcdaddddbbaacbbbaabcbddbbdcbadbccddbbbaaacdbccdaabdbcddcdaabaddcdabaaabaaccbadccabdbbaccdbcdddcbacbdababcbbacadaadccacadbdabbccabbaabadbccaccabcabdaadcdbbdcbbaabaabcaccabaabaabddcabbdadacbbaddcaaabcdcddaacdbdccdadadacdbadcdccabaabaaaabddcdcbcdbbbdcdaacadbcbbbbacaaddbccacaacbabacccdadabacbcddaaababcdacddcdbdbaaadcadcbabbaaccadbdcadbabcbaaacbbabcbcaccbaddcabbddabdbbaadcbbdbcccbcaabbbdcadaacdccdcabbdbaaacbccaddbdbbbccdbabdccccdbbdcddcabacaaaabbadbbcbaaddcabaacbcbbdcababacccbbcbbddbbcddaacdabbcacdaccbdccaadbbcbcadcaababccdcdadddbbaaaddacadcdbacaaadddbacbdcdcabdbdbbbcdbbadcbcadaadbdcbccdaabbcbccdbcaaaaaacbaaaaabbcbaccbcbbcbaaddaadadddbdbbdaccbbccccbcdbadacdaadbdcdbabccddcbbcbbadddcdbdddcdcdbdcddbbaccaacaaadbbcaabaddddabadcaccdbadddbbbbaabadabbcaccdabdabcdaaaacccdcdcdbccbdadaddccdbacabcaabbccacadcbcdbdabdbcccaccdbdbccdcacdccdadbccbcdbbaaaaacbcbbadaaacbddadcbdacdabcacacbbcdbbaddcbcddcbccaccaaabbbbbcdbaaaabadddccdacadacaddabbacccadaaddbdbddcdccdddccbaacadcabdcdbcdabacdbcadbdddaccaccabbdabcccaaccabacbbabcabbcddadbdddccdaabaacbcabdcabccaaabbbbbddccbdbbcacadbbcbabcababdbadcacbcbaabaabcadcbcaabcbbbbcdcdacdbadcbbccbdbacbbdcaaddadabadccbdabaadbbdacccbadbaabdadccaccdbcdbddcddadaaaadaaddadbbcdddbcddcdcbccbbabaabbdbbbddabdbabdbadaabbccbacbccbaddbdadaacbcdcccbadbcdbcbcacadcaadacccbcdbcdbbddcbacadbacdcdcbbbdacabdbbdcccbacdcaacdbdcadbbcddcccacbbcabdacddbcbabdccbbdddcbcabacbdccabadabadcaabcdcbbbbcdacaadcddadbdcbdcbdddbdaddccbbdacbcadbabbbbcaaaccdcdcabadddcddabcdadbabadcdcbdaabdcabcdbadbacbccadbdddbbbccadccbbbbbddadbcdacabcaaaddabdddbbddbcdbdcadbdcbbddacbdacdcbbdbdbddaccdcddaccaaabababadbdabaaaddbaacabcbcbddcdbdadacbcbacbccdcbddadbaaccadbabcccbaaaddcbacdcbbacabdaccbbaccdaddbcabdcaaaaadcdccccbdbbdcccbcbdcbddcdddabadcbabaabbdbcbaaaaabcbbcbbccabdadbadbcddaaaaaaabbddabdcadabdbbcbdbcabcabdadadddadbdbdbbbbdcaddadbdbaadcacbabdbbbdcdcbcadcdccdcbabaadccbdacaddadaacdbbcbbaddccdbdcaabcccbcdbcbaabaaaadcacbadddbbaccacbbaabbccdcbababbbcdacbbabbadddacdddddaadccbbadccbbacddcddcdbccababdcadbbcdaabbacbacaacbdcbbadabaadbbcdaacbcbabbbdcccabcacbcbbbcbcaaaddbbacaaaaacaacaaacbddcacadbaabdaabccdbcdbcddbbcabaabdccabbbabdcbcdbbdbbdbbdcdaaabaadabbabdddacccadababdbaacddbdadcbddddcabbaacbddcbbcacbbabdddbabdaddbcccacbdaadcdddccadadccdcdddcdabcaabdbabdaaccbbaaaccacacdcccadbacadacacdddacabadbbddababbabcdaabccabccdbbddddcaabbccbaadadacbddaabdacddcacdacabcbddacbcbbccdccdaddaccdcdacdccddcddcadcdddabaadacadddccddcccbbdbacbcdbbdacddcbacbbbdcdaddbbbacaaddbbbdabbdcbabdacbbbaabccbbaaccadadbbbbdbabddcdaababacbabcbdadbbbaddadcdbaabdcdaadadddbbabbbbdccbdcdbcccaadcdabbbbcdbbdacbbaccdbcccabcbadccddbadadcababcadbcaccabaaadbdbbbbabaabbdbaacbabcbacbbabcbbabaadbabcbbbddbbbbbdccccbdcbdcdadbacbddcbadbddaaabdccdcdbcdddcabbbdaccddacccabaadabacccbbacbaccdccbaddcddcdaddddaababcdccbcadadabddcdabddbadabaddabdbdddddcadcccdbdaddbdabccbbcbbbabdcaabaabbddcdccacabdbacdbbdbccccbcabadddaabacabdbbacdccacacdbddcddbbdbdcbacaddcbaaacbbacbdddcbdaaccccbabddbbdbdccaabadcbbbcadccbbcdccdcbdbcbcaccacdadacadcddbaabcddcddccbdccdababbdddccacccaddcacbabaccaaadbcddbbbdcadacdcaddcccbbbbcdddbbcbbdaccddabcdacbdabbbcaccaacbcdadabddacbdccadccdaccaabdbdddabcdddabaccbcaabaacdbadcabdbbbcdabdacaddbadadacdccdccbbaacadccbdcdbddaddcbcdcaadcbaddbbbabaaadaadbaaabacdcabcacdbbcbccdabadbabcbcbdcbbaabbbddbddccbbbcccccacbcbcdcabaccaddbacbaacbaddadcdcacdddbdabcdcbccadbccbcdabcbddbacdcdbbabddbbacaabbbdccadacccbadcbbbadcdbcbbdabddabbcdcdccaacbcdadbdcaadddbdacbcddabcadccadacddcdabcccbaacbdacadcacadadcbadbadbdcadadacbdbcaaaaccbccbbdcdbaacbcdbdabbcdcbbaccacacbcbbcddccbaababacacaaabacddaccbddacdddbabdcbaacadddbbaadadaccaaabbabacdabccbabbadaddabddadddbacbcbbbbbbdccdacbdadacdcbdcaaadbbcdcdbccabaadbddcabbdcaabddccdcaabbbbbaddaddabbbbdcdbaccbacabdbabdddbbabcbadcdcccbddcdbaacaabaddadbaaabcbcaaccdabbbdbbcdaadabdadbbaacdadddccbddbbadcacabddccdabcdcdadbdbbbdbcccaabbdbddacccbbcadacccddacdabcacbaabaabaacbcbbacabcacdbadabdcdcdddcadaaacbadccddcccbcacbcccdccbcaacbcdbabdcacaacabdbcdcbddaddbbdaddbbbcdccbbadbcbcdddcbcbbbadccbaaddbcbcdbddaddacbadaddbbdcbcddbddaabcdadabccacaccdcbadacbddcccccaddccacddcbdccbbcaadacdadacbcbbddabcadabcabccdadddabdacdbabcdbcabdcdbcbabbbdcaabcaddbbdadaacbcabadbbcdcbaccddcccacacbbbcbabaaddbbbccbdccddabccbcdcaabdccdabaacbabbcaaccccacbbbccaacdbbcdbaddbbdccdbdbabcbbbaccbbaadddbdbaabddbaacdcbcaaabbabadbdccddaacacddcccbaabcacaddacdacccbbbbdabcbaccacabbdabdacbdacaccbccdccddcaddbcaaccabbcdcdcbdcbcdbccdbbacbdccaccccadbabddddadbcabcbbbcdbdabdacccbcabdbdddbaadbaaadbabbdcabcbdbabcdcddaaacdaccaddabccdccadadacdccaababadaadaacdcabbbadaaccdaaababcdcabcbbbcabccbadbcbbaaaaaacdddcccaddcbdcadccbccdbabbcddababcbdcddacdaabbabbcdccdddadcacaadcbcdbaacacacddadbccaaabbdaddbdccaaddbdbbccbcbbcbdcacbdbdbcdcabcbdaaaadabcabaabdcbccaacbaccadaccdddbcbadacbccdbddbcadbdbcdbdcacaabccbbcadcdbbcdcdddbdbadbdbaabbbbabdaccbbaabacbddcdddddcccacbcdbcabddccdacdaaccadcdaaddbbbbdadbaccaddbdbaddaacbdcdabbbabbddbcabbcbadacbbcaccccabbcacdcbcdaabccaccbddbbbbbadccdcbdcbdccaacbddbadbbddcccbcddcacadbadcdbdacdaadccaddcdcbcdabcdadcddcbcaadbccadacbbabccbaabdbdcbdacbdbdaabdcccaabaaddacadabddbdaccabddaabbdddadbcddcadcddccddbcbaacadbbdcadacbaabdbdbdccdddadbdaadcbdbcdabaddbaadccdbacabdcccadbccbcccdccbddbbbdadccbdcccacbccaadbabababbccdbaadadbabdcbaadbaadadbbddababccacdccbadaabccdcbbdbbcbbcaabddbbacbabccbadcddaddacdbaccbbacaacbbdacbddbdacaadccbaacbcabcacdabadacaabcdcadccbddddcdcacdddcddbddabdaababdcbcdaaaacaddcdadacaddabdbbbbaaabbdbaaabcadacadacccdddcdcdadaccbdadcbbbcaaabdbbbaabacadabdacaacacdccbacdccbdbbbdacdbbcbcbcbbcbdbbcbbadcdcdacaadacaaadbddccdcbbddcccddbddccdccddcadadbcaadccdcacdbbdacdadcdacabbddcdacbcbadcbbdccdcddadbdddbabdbbcccddaacdddabbabacbbcacdaaacdddbdbdcabccbbbdddaddddcdddcdbabcadccbdaadadbbbacdcdbaacadabbdbbddccacdaadcdbabbdddabcabaabbaadbcccdbcbdddadbbddbdbdaadcaccdadcdcabcaddbcbddcabcbbcaccbdacdcbbcbabbdcbdbabbcacbbddadcaccddbbbbdadcacccdbcbdccccccbbaadcacbcdddbaacacbacdaacbbaddcbacbccbabdbbdbbcbdbccaabdaaabcbabadbcaaccbdacbccdabcbaabaddadcaaadbdbbcdadbddcaabddbaadbbbcabdabdababcaaaadccbaddadcddbbbaababaabdcacbabbcadaaadddaccbbabdddcacbcacbcacbdabaabacdaaaccaddcbbcaadcddcdcabdbcbcdcbcdbbcdcccadabbdccacbbcbaaddddbadaaaad