bdadabbdacabbcaadccbccdcccdcbccbacbbbbccdacdbccdbbacdabcdbcccadcbbdbadddbbdaadacaccbdcadacdddcacaaaaccbacabbdabbcdcccccccbcbbdcbcbcadaccdababbbbcadaacbbcbaadabddbddbdcdcbbaaadcaaccabbaddbdcbdbcbbcacbbcdcbbbadddcbdacbbbdacdcacaccdddaaddbdabddbcdcddbdadccdcbaddcdababdbbbababbbcbaaaaccbaabcabbcdcccbacbbdbddabbbdbbdddcabbbcadaabbcccadccdacdccadbccccbcabdabccbacbcdaddbcaaccdbdabaacadddacbbbccaccababdcbbddbabddbbddbbcccdcadabacdcacdbdcbdabaabccaabbddabaccabaabdddabcbdaacbbbddbbbdcbcdbbcaacccccadbbcbbcbadaaabddacdbababadcaaddddcabdacbadcbcbbddadcabbadddaaddccddbdbadbacbbacddddbdabcccbbcdcadccccbcbbcbdddabbbdcbdabdcbbbdddaabaaaabddaabccbbaacbbdbdcdcbbdcaaaabbcacccbdbdcccbdbcccdbaddbacbabddaddbacabaddaadccaabbacccddabdbabcbbbbacbcbdddbcdabbacbddcccbbbdccaacaddccdbcdabaadbdcbcbbcbdaccbbccdabaacbbdabaddaccdbadabaabdbacdbccddbbccaacdbdacddbabbccddbddbadbddcbdccadcaaabbbbbcccbbcbccbacbccacaddbcaddcddadacadcccbdaaadcbddaccbcadcddcadadbbdddbbdcccddcbdaadbddbbddbbacaadddaccddcdbabdbbbdbdddacdacbcdbaacaaabbadbdaacbcbdbacdcbddbbadadbdaccbcdadadcdaaabcababcdaaddaadabddadcdacbcaadccbadbbacbbaabdbaadbcccccbaddddacabbadaaadacbbbddcaddbcdbddbabaaaaacbadbbccccccddcbadccbaddbdaaaddcabcbdcacbdaccdbbddccdddccaccbbdbcaaabbadaadbadcdcddccccaddccbdcbbacbcccdccbbabbcddacbaddababbdadcaabaccbaccbbcddaaaaddacaadbacbabdaddcabacabddddacaaaaddbbcbcaaadaaaabdaccabbcdcdddbdcbdddcdcdaccdbdbbaabdccdbccabbdcbdcaaaaccadbdddcbdbbcbdadbdddccbaacaacbabbaccdcbbacbcddcacdbdacadcdcacbbccabbccabdacdcacaccbadaddcdbdccdcbadccbcddbdccdcdccdcccbbbdcadbcccaadbacdbdacbbdcacdabddcbcdcdcbadadcdcccbacdadacaddadadddcbccabcabaacdadbadbdabaaabdbabbdbbcdabdddcdbcaccbcadddcdbdbaadcddbddbaacadccabaaadadadaacdabaaaadaddabdabbdcddbcacddbadcdaacabaaacbdacbadcabddaddcccddcaddacbacccbdddcacbacadcddaccbabdcbccabcdddbababcdbbccbddcdbdbadaacbacccaccaddacccdbacbcdcbbadccdbcbddababbbcccaccaacadabcdccbdaaabdabaccdacaabababbaccdbbbbccdbccaabdddcdcaddcdbcdcbbdccabaccbbcccbadddbabdbcbbbadbaddccbdbdcdcccaccacbaacdcdaccdbcbcacadaddabdcaaaacdcbccbbbdacadabcdcbabdbdbdccadddbcaadaaacdddcbacbabaadadcccadcadbdaadacdabacacdbbbadbacdddcacdbacddcbaabdcddaaaaabccdacbdacdbaccacccbccaddbadcbcccdaaaaabababbccaabbcaabaadbcaaabbbbbbbccbdbcaabacbdaacdbbcddaddcaaadbccabcbbcdbababdbbbcaaaacbccaccddddbcdaadbdcdcdbdadcacdbdbdccbcdbbbbddcdcadadacddacdbdcaaddcddbdbcbaccccdbccdbdabbbdaacbacdadbdbdcacbacdbcaddcaadacbcacdaacabdbadaddaaaccbdacdccddabdcbcaaabbbcdcdbcbcdbabaacbbaacaadcadcaaabcbababdbcbadaccaccaabacaaaccabcacddaaaddcaacadcbccbddbabdbdbcbccbbcdabddbdcbcbbaadcbacdbbbcdacdcbaccabcbcbdbbaadabbacbcccbabccbcbabdaacdabdccadddcdacabcadacdaaadddaccabdccacaaccdbdbcabbadccbbbcbcbcbcaddbacbdcddddaccdbbcbcaddadddbbacccbaadaadacadadcacaabaabbaaadbdbcbdddbdbcbbaabadadcdbdbcacabccbaaddccdcbbcabaccdbadcddabaccadacacabdddccabccadbbdbdcaadccdbaadccacccdbcbaadaabcabbcbcdacaacbcccddaaaadcccdbdcdccbdacdcaadabadcbbcdadcacadbddbcdccbaacadaddccbdccabdacdbdddbddcbadacbbccdaabaacadadccdaabcabcacbaacbdcbdbadadddacdabcdcbaabcdbdcdcdcbbbdaabaacacbcbcdadaadabaccddacabcaaddaabcccddbacabcbcccddbdbbbcdaddccbcbbdcaddcddddddcacdcabdbcdcdcacbbaacacdcddddcadcdacabdbdadcbabdbbcbbacababcdacddadacdbdbdabdcdbbadadadccdccbdcccdaacdbdcdbcbacacabadddbcdcadcdadcabcbcccccbabcdbbbdbcccdbddcadabcdbbbbaaaddccbbbdacccabaccdbbbababdadacdddaddccdcacbdabdaaacaacaaabacbbdbdccbadbacbddbcdcbbdcccdbbababddbbabddccbddccdccaddadcbdddcbaacdccadaacbbbaddadaccccaaadcbbdacddaaacacbacdbbdcdcacacbbaadacddaaaacadbacccbcabdbddadacddabddcbadbbacbdabaabcccacaccaaacbdbaccaddcbaccaddacbcbadbcbcdcbaacdbbbbccabababbccbbdcaddaaaadcbbdbbcbbdaacabaacaadcbabcbcdccccccbbbbcadcbcccbbdadddbbdaaabaadacbcddddacccdbdaacccddbcbadbdcbadadccdbcbadcabacbcdbaabaaaccbccbbcbbdbbcdcdadcdcccbaadcbdddbcbccdbcccbdaddccdabadddaaccbcdadcdbaaaddabbcacdaabcdbabcdcadcaddcdaadbaccbdbaaabccacbbbbbbbacdbbababcaaadccdcadccbbbdddcadacdcddacacabdbdbcbcccaaccacdbdbaddadcabdaacaacdaabaacccaadbabacdcdaacbccbbacbaadddacdbdbadabcabcbddcdbbaaddcdaaacbdcbaabbabaababccadaacbdbbcccddaddcddccddcbddddcacbadbbdaaaccccdcabdcdaddcbdcbbcabbccdadccaaadcaabcbccbbbaaccaaacbccdbcdcbbabbabaadaccccbadbadadbbcbaaaaadacaabcccbbbbddadcdcbddccddddacdacdcbbcbdccbcdcabcccbddaddcdaacbabbcdbbabdbaaaccdcacddbccacacbddadbbdbddacddadcbadaabdacabbbabdbbcdbdcdacdbbbdcdcabcbacaaccdadaccbbaacddcdbccdccabdddcdddaddbccbaabcdcbdbadcdddaacdaabaabbcbacacdddadbdcccabaabccbddadddbcdddccabccadbacccabdddccdddcddacdbdcccacbdadabacbdaadbbbcbbcdcaacacddbdbdbbbddbbbabddcbddcbbccdacdbdaabbccacbacaddbbddcdcbbcccbbacdbacdaacbcbbdcdbccaabdcddbdbdcaaabdcdcabcccababbbcdbcbabdbadcbcbbdbcbccdcacbbbccbbabcbabdbcdbccdccacbddaccddabadaadbbcadaddccbccdacbddddbccdcbccdddbdcbacabbaddbcadbaaabaadbdbbbdddccaaccbcdabacdadbcaaaccdcaaacbddcbcbbddacdbcdcbdccdaabcadbbbcabcaadaadbabdcccabcddabbbbbbcbcaddcccaabcccaddacbaddddbdaabacccbaabcaabbdbbdadabcaacabbdddcbdabbcacccacabadaaacbbdcdcadcdbbbcacddaadccabbdbadacaccabbbdbccddadbbcaadcacdacbacbabbacdddabddaddcdddacaadaabcbcbbbdcdddadaaacddcaccccacbcbddbdbbaacdacaaaccbabcdadddbddbbacacbcbaddcbdddcaabbaadbaabdbbabcdcaacbdadbabdaadccaaabbdabbbdbddcabcccadabacadbcdddbcdaacddddbbcbaaadbbcdadabbbababdacabccabcbabbacbdcabccabadcabcdbcaaadaacdababaccdadbcadbcdccccbabbadddddabbccabaabacaadccddbbdddbdcdadcbaaaabbdaaaaadacdcbbcdbbadabbadbacccaaaddaadbabcccbaccbadabbadcdacdcbbdbbaaabcccbbaddabcbbcaccaadabdaaccdccccdbbddccbccbcbdbacddcbcbabbbbdabbccdabadadbabdaddccbccaddbaabddbcbbcbbaabdcaadcadccdcccdaabccbacbbdccabccdaabcacaaaabccdbdaabdacddccbbaaabaadcbddcacccddbcabdddddbdababdadbdbdbcdbdcdbccbadaadaacbcbdbbdbccdabbdcdacbddbcabbdbddadddaadbccadbdbcaaabdccdddcbaadcccbcaddbabaddbcbbbbdbcbadbdaacbcabbbcdababacaabbdccbabaadcbcacaccbbbdcddacbbbabacbcccabcdbcbabbcdbdcbdcddbabbdbdadbacaacdbdabdccdacbcdbcbaaddcbdcbcaadabcbddbaabbdabcaccadddbbadacdccaacadbadadbccbcbacdcacccddabdccacccbdcdcddcbdaacdbdbacbaabacaabaacbdcdabadcdbbacadcbbbbddbabdabbddccdbcbadadbdbdbbadddccadadaaaacdaddbaadaddacbbccabbcadbdddacbadcdbcacaddbdcbddcdbbdaaabadbbddbabbbdbbbbccacdacadadcbaddccdbcaabbaddacbddbadbccbddccaaacbdaaaabccddbcadaaddacbcbcdbbbcabccaddadabbacdbbadcbbacbddacaaadddbadccdddbbdaaddacbcccabaabbcddcdbddbacaddcbcdaaabbddccaabbbdadacbcbbccdabccddbabbabbdacabadbcbbddaaabaadacdacadaaaaaddabcadcabdbbabdcccaccbacbbaadbdaaacdcaaaaccbcaadbbdbdbacabbdbacaaccbdbbdbbdbabcbbccbcacaabaccaabbaaadbcddddcccdbdcbdaaaacdcddcaaabdccabbbcdbdadcbdbbcdaaadcccdcbcddbcabdbbdbbbbabadbdbaaacaadcbacdddbdadcddaacacccbaabcbaabbdadacadaacddcaaacddaadbdaaaddbadcccacbabbdcabdbcbdbbacabdaabbcdbdcaccdbccbdbbcbacbdbcdcdbdddbddabdbaacccdcbdddcbabbddaabddbbdabdcabbbabacccddbcbdbbbdbbdbbdabcabcddaddbbadaadbcbdcadcabaaddbbcacdcbcabdbabaabdaccadabbcdacddbbbccdcdcdacbbbdabddbcbaaacabdbbcaacadbbaabacdadbcdacbbcbbcdbddabcadccabcdbdcbabdbccabdbbbddacbdabcdcdadddccdcacaccadbacdaccabaaccdcdcdaaaaacbbadbddbadaddddccdaccdbadbdbadabcaddbaabbcdbacaabdbdddbacdcadbababccdbabcdbdccbaccdccbdadcdbbadcabbbcdbccbbdaaaaadbdbccdbaadbadbbccaaacdacdabacacbcbbcdccbcbbbbdbcdaadaccabcbcababdbaadababbacadcababdbcadcdaacbcbbcbbccaacbaadcdbbadbcadbbcbcbdbcacdcadacbadccbbcbadaadbaacbacdcabbcabacdaddddacdcacbbcccdadadcbbdccaaccbaadaaddbdbbacdbbcccaabdbbaacbbdcdccaccbbbdaddcbbdadacbaadccddbddcbbdbbdccdcaacdcddbbabbcddccbaddacdbbacabdbcbbbdbccbcacbcbacdccaaddaaaacdacccbacdbbbbbdcdacdcadcbaddadabbaacccccadcccbbaddbddbcdaccbcdbddbbdbbadaabacbddbdbadbdbaabddaacaabddcbbbbadcadcdaccaaddadbdbcdbcaacdddcbcbdccabddaaadadaaddadbacbabbcabcaaabdcabdbddbbcaddbddacadccdacdcbaddbabbcbbccdaabccbdbcadbccbddcdaabdbadcaddabbdaadacdbbcdcbdbadbddabbccadaacccbabbcaaccaabdcadddabbacbadcbcccababcacaabcbbcdabbdaaadcaacdcdbddacaabdddcccbabddccddbcddddbccdbbbaacbdcccaaabdbbbddaacdadacddccdcadadcccbbababccccadabdacbbcdbdcbdacbbadbaadbbacbbbbabbddbcbaddcbaabdabbcbadacbdbdacdddacccaddbcbbadbbdacbbadcbddccbddcbabdbabbbcadbcdcdddabbabcbcccdcdaddccbbdabdbaadaacacaddaabdddcaccccabccaacabdaaddaaadddabbdadddaadbbcdaabddabcadabbbabaaabdaaacaadbbbdcddaadddadadbcddcddacdddcbbacabccaccbdcbabaabbbaababdcddcddacbaadaaabababddcdadcaaaccbbdcbacddbacbbcbaaabbbbcdbcbccaadcadcabbdcaaacdbcadaadabcadaddaccadacbddcddbdcdaccbdddacabdacddcadbadacddbcbccbbcdbbdababcaaddcbcddddbbdcdaaccdacbabdbacacacadcacbacbcadacddaabdddcaabcbdcadaacaabbdddbadccdbcacccdcaccbcbcaddcbbdbcccaacccdcacbaadadcaabacacacddbbdcabcdbdbcdcbbbddcabcacdcbaccdcaadbddcaccbcddbbbbbacbaaabbcbabadbbddcacaddaadaaacaccbdabdaadcdadbaadacabbcddcdababddabccbdaaaacbabbadbaabcddaaddbddbcddabbcdaaaddbabdbaabdcaddcbaacbbadbdcbdcadcbaacbbdddaabccdcbacdcacaddababacdadccabcaccacdaadcaadadcbbdbbcccadcdadcbdababbdbdbddaacddcdabddacbbbcddbcadadccbcabbaaaacaaacdadbbacadaaaabdcbdbcadaadabddcaccdbacaaadbacdcdabaddadacdcabbaccbddabdaacbddcbbcdadbdcdbaabaabcacddacbdbaddbcdadbbdabddcabdcdcdaabacadacadaaadacccadadcccddbdaadbdcadddaabdabadbdcdbbcbbcccdbdaacabacadbbabbdbacadadcbcbacabbadcdcabbbaacabccbbdcbadccacddddccdadbdcabccdbdabbacaccdabbccbcaccaaaacadbbbccbbaaacbabcccacbddbaccddadcbcaacdbaddbbcaadacabccbbbbaadcdbacabbdccbadbcdacccddcbacbadaacbacbacbacaaadbbcaaaaddbcacaadbddadabdccdccadabaacaabdbabbdabddbbddcacaacbdababadaaaacbbbacabaccccabcabdbbbdcaabaabadcadbdbbbbbcbbcbbbbdccbbdcbcacbbbadaddacdbbacaccbcbbdcccdbaccacdcccbbddccbaddddcddcdcbcdccbcbbaadbcccbddaddbadaddabbbbacdaddacdbcdadababcbacdbcaacdbdcddaabdbacadabdcaaacdabdabaaaabbddcddddcabcadbbddbbabbcadcaddddbabaacaddbbddccbaccaddbcddaccbcbdcbdddccaabcdbbbccadcadacdaacdcdbddacadcddbacdbccbabdbdaccaadcbacdcadcaddaadabaadbbaddbbbdbabdabdcaddcbabdcdcccabccdbbcdcaccbdcbbcbaccdadbdcbbdbddddaccbbcadccddbdbccbdddbcdbadcabdbacbcbcababdbabdbbdabbdbaabdcdbbbbcdadcdacadbdbcdcacacabcccadacdbbbbbadabaaaaacdbccbbadaaccbbdbddcbaacdcadacdcbacabbaccdbacbaccbadbadcacccacddaaacacbddbacdbdacadddddbdbcdbbbcbcdbdbdaccbccdbccddbbabcdcddcaddbccbbadaccaacbbddadadbbccacbddbcbddaaacbcdcdcaccbbdccccbcbddcbdadcbdabacabbcaacaacdcdaabacdabcddcadcbdcccbcdcbcbcdcabcdbaaaacbcdddcbbacbdcbbccacabdabacccdbbbdadabaddadbbabababddaacbddcadabbdbabbcddbddbadbdbbcbcddbababbaaacddccadbcbcadcadbadbddcdbccdbdddbcaaddddcdccbdabdbbcbbddccdcbdaccaadcabaaaadddbacbddbdabdaaabaddbaababaabdbbbdccdaaaabbbddbabbabbcbcdaadbcddddadbbaacaadbaaabaacacdacabbaacbbccbcbaddadbbabdbaabbcacdaabacbcbcabdcccbccdccadddbabcdaacdaadcbaccbcbccabaccbdbadcbacbdabdbabaccdccdcdaddbbdaacbbbcbdadabdabdbacdcacdbabdcdacacbddccbaaccddbddadbcddcdaccabdcbbddcaaadaccabcacaadaadbadbddbabcaccddcaaddcaadbbdacaaabaaccdaddadbbdbbaacabcbdddddaadbcbcdbdbbaadcbcaddcdbdabdaacbaddcbdccabddbabbbbbddddbcacacbddbbbdbdcadacdddddcbacabccabcadbabcddcdbdddddbbdaaadaccadbdacaccdbbbaccadcdbccdcadcdbcbddacacccbbdacdcdabaabadabbdacdbaaacbbbacbbbdcbcadcddabadacadbdccbbadcddbabcaadbccaabaccbbbdaaabdacdabdbaadadcdccbbcdcadcdadaabccadacbdacaaddbaaacbdbccbbbbdbdbaadcaacdcacaccddbaabcaaacbbbaddaacaddbdbdccbddbaddcbcaadbcaddaacdabcbbdddcbbbaddbaabcabdaacaadbbcbdabbabcbcdddaabcddadacdadcdcdbcdcbdcbaaadabdcaaabcaaaadabdcacdbaddddcbbacdddaadabdcaadbcabacbaacbdadbdaddacaadcacbaadcacdddbcabacbdbbcdcdcbaccbdcdabcaacaaabbbcadadbdadabccdcbbbcbacaababacadabbcbabababcaadbbcadadddccddabccbabddcacbaacacacbbbccdccacacbbcccbdabccdadcdddabbdbbbbaaabdcccddbdcbcadbcddcccbbaaadcaccadbbbcdcdbadcdababbdddddcdacaccadaccabcdcddadacacdbdaddbaadccdadcbcdadbcddbdbbbdabcabdcaabbddadcbcbadadbacdbcccdbcaddaaabbcdcdcdbbdccdcaadaabdbcdaacbcccbadcdbabbcaddacaabcddbaabacdacccdbdabcdbadbbababccddcbccbcbcbdcaacaccabdaccabaadbbabbbcadccdabdcacbdbaadabdddccbccccabcdccadabaabbadacbbbabdcbdddacddddaadbdbbcbdcbdbcdcaadbbacbdcbdadabacbdddddcaabaacaadaadaacabcbcbadddaacddadcdcdccbcbcdcadccaabddcbbdbddcdacabaabacabadabbbdabcbcbcdcccdadbccabbadbacddddbddcbabdddcbcabacdaacbddbccdadcdccacadbcdccbbabcacddccacaaadbaccabdbacddadabdbbdbccaadacbbaacddcbbdaaabadccdbbdbdbaabbcaacdccadcbaaaabcdaacadbaabccdaaaacaaabdaddcadbdabbdabdcbbbbcdcadadcccbaccbbbacddadabddadbcdabcbdbbbbbdcbdbadbbbcdcccbccaababbaadadadbbddaddcbdbdcdbccdcaabddaabbabccbaadacacbcabbccacdcccaadbdbadaaddddbbbcdcbddaccbadbdcbbaaabdddcbccaadbbcdbdbdbcaaaddccbbaccadcbbcdacdbbddbccacdcdcdcbcdaaddaadbccbcbdcbcbcdaacdaddccadacdcddbbaddabaaaccddbbbbcdabddbcdcbddadccabbdabbbddbbbbaadbcaacbbdaccccaadbbbdcbadaadadcbccadababacccacdabdcdbcadcadbaddcbcbaaaaaadaaccdcddadaccdaadabdcdccaddddaabcdcdbabcbdbdbacadcabdcaccadbccadcdddaaddaddccadadaddcccadbbbaacacccadcaabbabcdcadcaacbbcdaabcaddbcbdbacbdbadaadddcdbaabccdaacdbbbcadcccccdaacbcddabaaacdbcbaccdbddcbcbacaababdbaabbdabddacbaacccdcabbcacbbdbcacbdbcabdaddbdabddaabddbbaacdaaccdcddbabddbbcadaacddbbabbdbadadbcaacdaacacbccccddaccbabadcbccccbaacabacddcdadabbadccadbccaddbbdadcbaddbcbcadabbdcbcbddbcacadadbccaabacaacbcccddabacabdbcacaccadabbdabdacbdccddaacadacbddacdcabdbbcbaacdaccbaacbdaddadaddbaddcbdadddbdadcccaadbcbabdbbcdadcddbccdbdacdcddabcacabbadddbddaadaaccacacdddaddcbdccdbbccadbcacdbacbaabdbdaddcbabbccbadddcacacdbddddaadccdbcadaacbadbbcbaadadbdcbcbbcdcaddaddacddbadacbdcbacdddabbbcbcaccababaacccbcbaabdccccaaadcaccdacdadaddadbacbaadbbcdbaaacdcccdabcaabcbdcbdcbcaccccdacacadcdbadcaacbdcbcabdacababdbddddddccabbacbdaabddbacbbbbadadbdcadacdabdccbdddbbcbbdabdacacacbbcccaadadcdcabdabbaaddccacbbbbaaccacbbbdaadbccccabaadadacbdaadcccacccbcdadbbdddcccddbaaddccaccabcbdccdadcdcccdaddcdddccbaaadacabdccdccabaaacbbacadaddbddcdabccbdcdcaaaadcdaaadaabdadacbcadbdbdcbddccacbbccaadbdbccbdbcccdcbdacdbdbdcabdbbbdcbccabbcdacdcdccbabcbbcbddacdcddbabbadcddcbddbdadaabbacdccdaccccbcdcadacadccccdcdbaabcababcccbddcadbcccdbdabbdaadabaccdddabcdbaccdcbbdcdbdacbddbccabaccbdbbcdcdcccbdbcbacbbdbacccaddbbddbbcbcacdbadbddcaaaabcdabbddabdabaabbcdccccabbadcdcbcbcadaddcbcbdabccaaadaadaadaaccbacaddbbbdacdbcbaccdbcbcacacbcbbaddadacbbacbaaaaabbcaabbadddbbccbbdbdbbcdcdacacdbcbcbbabcbdaaadddcdadbaddabbbbabcbddbbdabcbdaaabbbbacccdccadcccbcdabcbabdadbdcacacabaddcadcbadbabdabbbccbccddcabcbbabdbddbbaadcaaddbdaabbbbbacaaccdababacdabacddabbbaddddcadbbacbcabacdcdccbabcccbbbdaadcddbcdcdcaababddaabbacddcadabcbcadacddccdacdcbdadbbaddcddcddaaaabdccdadabdaccccaabbddddbcddcacaabdbdbbcbcbcbaccbdbbbbbcdadaacdabaccbadbbadcdaaaccbbadabbcbddaadccccdbaadaddbdabdddcdcdddadacdddaadbddacddbddbddcdbbccadacacaccbdaddcdbccbbdbabadcbaacbbabaddbcbdacdcaadccdaccdaddccdcadbbbadbdbdcacabadabacbcbdbbcbcdbccaddbaabbcbbbccacdccdacdccdcbcabdbcbcaabacdacbbbcadbadaabddacbabdbadcdbbdbcabcccbcdcdcbddcccbbcbddcbaddadaaadbbcbadaabdbddcbdbbccdbbbdbbbcaaaacdcccdddbbbcaddbaabcabbcbcdabababaccdbbcabddbdcbabdabaccbcbaabccbcabcdbaacbabdddbaadadcccadacdddcbaddbacabbcacaabbccbaddcbccbcccdcbacddacabdadcccbbcccabadbadbccdbbbbbbbacbcbbdadcadddadccdacbdccccbcadbbdddddacbaaddadadbdddadcaddcccbacbdccbcddbaaaaaacabdbaacdaccacdcdbbacaabbbaabdadaddacbbbbbcaaacbadaacdcdadaabdabdcbaaddadbbbabbcdbccadbacbbabbbcdcbccbbbccbbdbbaacbaccbbabbdaaacaadabcddadadabddadbdbcbcddcbcabacddbaaddcdabbbddbaacacbdbdbaccdbdacbadcccdaadcddcdbbddcdbcbdccdbcabbdbaadbabaadcadcbcaacbacaddacadbbbdaacaadccaacacdacdccdbbabbbdddbabaaadacbbdbcdbbcddbadaddaccdbaaccbcbababacdddacbbdaccaabbaccdbcbbcbdddacdbdcdbbdccbabcabccdaaaacbdccacacccddcacadaaccbaabadadaadaacbcbddaabdacbdccdacbddaccadbbadcacaaddcdacadbdcdacbdcbbdbcccaacaddddbddbccdbbbaaadbdbacccaddbcccbccdbbdbaaabaccbcbacbbacacdcbbbddabdbbaaadbcaccabcdbbdbdddabaccdaaccbaadaadcddabdadbabccbdaddadbbaddcaabdaadbddcdadaabcadabbbdbadbdaaacbdbbddabcbacbbdadcbbbbdbbaaaababbcaaadbbbaadbcbdbcdaddbccddcadcdadbacaaaadbaaabacadadcdaabadaaadcaccacbbdbdcacdcacaabbadcdaaabdaddcadcaddaabdaaabddbcaaadddbadcaccbbbcaddaabcdbbbbbdcaccdddddbdaabcdccbcdccccaacadadbbccdcbddddaabccadbdabdacdaacdcdabcbbaadadcadabbaddaababddbdcbaaddabbbdcddcabdcddcbddbabadbbccbcccccbbadaccccabcaacdabaccdaadaaacaaadddcadbaccdaddccacabcbdbcabbccccdcdcaaadbadbdcddcacababacdbcbcbddbccacbcabbdbcabbdabcaadaacdddbbaaadbcbacacadabadccbbacbdcccabaabbcbabaabdadbadabadcbdacaadbadcacdacbcdddbdcaabadcdcabcdabdbabaadccabcadbacbabdbbdabdcdcdaaadbdaddcbcacbcabdcddabcdddbccddbaabddabbdaacdbabbadabcdadbdcdbddaabdbadcacbcccabacddddbbcbabcaaabdcccacdbbdabbbabdcadadbdcbbcbddcdaaacadbacaabaacdcbcacacabaacacadbbaabddcbdbdaddabcbbaaccaacddbccdcaddccaadddbabdacaddbbdbbcadcdadbadbdbaababadccadbcaadbdbdcbbccdbcddbacccdaaacbbaacadbaacbcdbcbbaccdbccbccbccbabdcbaadacabcddbcabdadcdbaadabdcabcddddadbbdcacddaadbbcbabacbaabdccccdbdacadcabbbbcadccadbdadddcdadadbabbdbcbabcdbdaacccbbbdddccbbdbdadccacadbddcccaccabdbbbabbaadddbcbccbdbdbddaadbdcdddccbddccdbdcbddacdbbdabcddabadcbbdbbdadcdccbbdbcccbaaaaacbcdbdcacdabaddcbdaddabdabbbcbaddbcdbccbbcdcdbcbadcacdbcbcddabddcadbbdcccddbbbaaccdcbabdbbdcbdadcbcbdbbdacdcdcddaaaccbdacaabdbdcccabababdbaccdbacadcdacacadcbddcdaaacbcabcbcddcbbbaccacaadddbcddbbaaaadbcaccbbbdadaacabddddaccaccdabaccbdbbbadaacabbaaadbddadccbbdcabddaccbdaddbbadacccadabcdbdccbaddbbbbadacadaaabdabbcacccbacdbdbbdbddbddbacbddbbddbadcdacabddaadcaccdaabbbabdabbdbdabbadaaabdbcbdbadcccdbacbddaccdccbbbdbbcbbddaadcdcabcdccdccbabdbbaacbcdcbbbcccaaccbaabdbdbbdacbbbdadaaccaaaacdcbbcccdadcbadbbbcbdbaccaadccabcdbbadddcbcdacddabdacaabbcadbbbdbdabaacabcadcabddbcbccacbcacadddcaccddabdcdaaaabbddaabaabdcadadbbabcbdbdcdddabaddadbdbcabaddaaddcbddbcccdbddcaddbbcadbcbcadccadcadcdacbcbccaccbbbaabddbdbcccacbcccbacbbadddacdcdaaadcccacabadbbccaaaddcbbbbdbcdbcdccdddccaccbddddbbdcbcbadbdadcacaacaabcabbacdccbcddcabbbcacdabadddcbcddddabdabcadcdaaaacaadaaaacacaaadcacccabaabbbaabcddbabbaabdaddcbdcbbaacdaaaabbadaadcbddbccbcbabbaaaabaaadadbbdccabdbadbaacadacaababdbccddbcddaacaaacacabdabdddabbcbbddaaddcdcaaacbaacabdabbbdbaddbddbdbdadcbacadbbcbdcacbaaabcdcdadcbbaaaccdbbcbdccddacdcbcaadbcdbadcdacadadddadaddddccabcdbddcddbcddbbbdbaabaccaabaabbbbcaabcccabbdcaabcbbdabcdbaaddccddcbbbdccdadacabdbbabdddbbccbcccdcaaabbcdccddcddaddbcbdaababccbcabcacadcadacbbbddbccdcddbbbddbdcddaacacdcdccbbbcbacbcaadcabdcdcccaccdadddbbaddadbbbabacddbcbcdbaaabcadaccbabaadaccbcdaddbbabdbcccaadacdcadcacbbbcddbcdbcaaacacbacabcbcbbcbaacbccdaabdbbbdcacabacddcadbcdbdadaaadbbdccbacdcdddaaabbdabbbdbaadababccdcacaadaccdcbbbbacbbaabcdccabaadaccbcdbbbdabddacaddcadbdcdadaccaaadbdbbcaccdadbacacacadbccbadbdacdbbaddccdbddadbacddcdadaaddcddabccdbbacacdddcabacdcbcaddbaadcbadabaaaccbabaaaacbcababddbbdabbdddacaddaddbaaadbccacbbcbaacaccabbbcdacddddbcdaccddabcaacadbbbcadcbaadaacadbcabcbcadccabacabbccdacbbddccbacbcbdcaccaccdccbbbbcadacbcaaddbdcbcdaadaaccdddbbaacdbccaadcbdaccdbdbdbcaabdcbbdcbacbbadabddbdbdbdbdbdacbaaaadcdadcdbcdbbddabccdadccbbdbdcdbcaadbddacadcdcacadbcbdaacdbcbbdbdcbbaccccbbdbcbdcbadacbcababbacbcabbcabadcadbdcadcacdcacbdbddddcbaabdcbbdcccdbaabbbcdcdadcdddddbadaccbbaaacbadbbaaaadbdbbcbcbbbcbcbabacbcacacddbdbdcacbbcacddcabdcbbdbbbdccbbbadbdbcabcdcbaaaadacbbccadddadabbcacdadcacdccaccadabbddaddcacadaaccdadbbdcacbabcccaccddabacdacbadaccaacaacbccdabcadacbbacdbdaaddcddadbaddabccccccdcccbccadabcbbcdadabaabcadbcdbaabadbaaabdcddcdcdbbdbbdaaaaccccbdbadbacaaacbdbddbdadacdbdccaaadbaddbaaaabcccdbacbccbacbabdcdaaccabbdaccddcabcdbdcbdbcadbbbaccbaadbabbdbbabcaabbbbbdacbcbdadcbbacbbbababddddaaacdacbbcdabadcabacbbacdadbabbcdcaacaacdccbacacccdacbbdbbdbdabcdbddcabdcdbbbdbccadabdbaacadddabbcdabbcababdadaaadcddabccaadccaacbbcbabbcadbddaacdbdacbdabdaadccdacbddbdcddaaddcadbbacdaaaccdbcadbbddbdbcaacdcccccdcdabdcdabcbaabcbdbbbadabbdcbdaabbadadcaabbcdacadcabcdbdacdcabccbbaadababbcaccccdddbbdadbbbbcbccabdbabadddadadacdbbacbbcdcbcabbdcdbddddbaacbdbbbdbcddbabadbbddbccdbdcabbbcacbbccdddcdbacaadcdcdacdabcdcbdaacababdbacdccdadcdadcdabcbaddabbcacabcbbdbdacccabbbaabbdadddadbbacacbacddbccdcdddbcdcdbbccaaddaaabadabcdaabaabadaadddddaddadabdcaacdacbacddbabaccadccdcdadaaddabbdbabbcccccccadcdcccbdabcccaadcdbcddacbbbdbadcccabdcccdadcbdbdcaaadacbdccabcbcabbbadaccbdbbaadcabacaacadaabbdabcabbaadcddccbbbccbbddadbbccccaadbcacbdbbbcbacbbccabaddbaddccbabccaccabbadbbbcdbdccdcadbcadcaaaadbaccdbcddabbdbdabdbaaaabcdacacaacabbdcbbaacaababaabcabcbabdcbabbdccbcdccdbcbacbccdccdccbdadaaacdabbcddabdadbbbadbdcbbdbcbbadcdbcdbadaabdcccdcbddbccdacbcacdaaacbdcdbccdbbbbaccaddcaadbdcacbcabaaddbbdcddddcddccaddbbcddbbaabbdcbaddddaadaaacbabddadddcaadddbcccaccacaaccdacacdcdddadaddabacacdbddccdccddbbaaaadaccddddabdabbdbddddcdabdbcdbacbacdbcaacbdbbbaccabcbbdaaacbabbcdcaadcdcdbadddabdbabdacbbaabdccdbadbdabadbcdaccbaadadacddbbbbbcccadcdcdccdcadcbadccbbadadcadbccabdcaabdcdcdaccdcbdbbadccddbabccabdcabdadadcaaacacbababacaadccaccbcbaaacdabbaaddcabbcccdccaadbdaadcdccbcdadbdcdcabbbcaabdabbbbcbbcbbddcddabdcabadddababacdabdacdbaaaccaddcdabdbaabacacbacaaabdadbcdcaadacabbdbaababbdbcdbabdbbacbbdaccbaddcaadbadbdbbdbdccaaddccabdbdcbdccabccbbdbbdbdbaabcbcdccdabadacaaabbcbccddcacbbacacadcbbcddbccbdaaacbaabcbacadddacdacabdacdccdabcbddccbdcbcabbdbbdaaaacccbcdabcbbbbdbcbabdcadadbbaccccbabdbcabaccdcddcdaabaccccbccaddacccddcaadccddbdcadabdcdcabdddcbdcdabdcaccdcadddbcbdddcbbacbbbbcddcaaadbbdabcdcccbbacadbbabaaabcdaacacadaabdbdaacddcbcddcadcacacacdcbdcaccdbbdbddbcbbcadcacdbcdbabdcaabacccdcccbbdcdadabbccbcccddbabaadbcbbaddabdccacbaccbacbccbcdddbbdaababcaadbdcbadcddcaacacbbababaabaaadcbaccaacaabcabcbbadcddddcddcddaaadccbdbadcddabcdabddabaddbdbbadaddadccdcdabdcabadadacacddaaaabddacddcbccababbbcdcadcdadbbdabacacdbbbdaaadadcddcddacddcccdcddcccaacdbdbcbcbdccbaabbbdbcabdbdcccababacccbbbbbcaaabcabbabdbaccbcdbabbbdbbabbdaddbccadacacbbcdddbabccacccaacadbbddbbaadcdacddccccabdbccadcccbcabcdabcaacdaccbbcdbccdbaacadbaaaabcbcdddaccbcaaaadadaadbabdbbaccbdddccdbdcdbdcbcacbcbcbdcdbcccbbacdbaddccdacdbabdaadcbacbccdaaadaccaccdbdcdaacacdddabddabbbcbaababadcdbbddaaaaacdccacacaadacdadbadbabcaadcbbcbdabccddaadabbbcbaacadbdbccdddbbbababcddcccddcbbcddabadacdacdbcbcaababadcaacaccaabadaacacddacabdcbbdcbacddbcdabbddddbacccadcdbdadbabbbbbcdbddbbdbaccadbbccaaacacaccccacadaacdbdbbabbbbdaddbcccaadcabacbacbbdababbcacaaaccdbaabcadbcdcbcddaaaaddabbccaadbddbaabdbbdccaaabaddccabdbbaacbbdbcdcdcdbcbdcaaaabddcbdadaddaabaddbdadbbcbbaaccadddddccdbaaddcbdabbbabdacbaababccbcbcbdadccdaaadbccdbcbaaaccdcbbaaacdcabaccccabcabcaccabbbbcdbcdcbacbdabcaaadbbdbaaacccbdbdddbbdbbcbdcababbcadadbbbbccdcaacccccbbbabbcabdbccbcbbacaabacbdcdbaababcddcbbcddbacadbbccdccbaddacdccacdcabccbccddbacbcaaacddbdabdadcabacaccaddddbdccbccdcaadabbcbcdcbdbaadbcdcbaaccaddacbdaaadbadaccacaccccddbbcddaaadadabbdcdcaacbbcacabdcbacccdbbbdcaaaabaaaadacbbababbcdbbadbcdbccdbcbbccaddbcbbabdacbbbcdbababcbbdcbddacccacbcdccbdcdddcacadbaaacccbacabccacdbbdbcdbdcbbdbaabdcddcbadabbcccbbabcccdbcccdbccbbaddbabbcdabcbbdabacacabcdcbdadabcbcbaddcbdcdaccbcdabdcaadbaabbabcadadcccdbbdccbbabdabbdabccbbbdcddcbcabddbabdbcbdcaccccbbadddadcbaaddbcdcdcabaddcadbdbbaaddaaddabbadacbcbcdbbbddccacadcabcccbabaadcdcbdacbcddacddaabacadcbcbadddbddbadaacaabbabaccddcaadcbcbacccdcbadcababbacccdccdddaadacbacacccbcccabddcdbbccbcbccbccbdabbcdcbadbbbddbbbbbadbcabcaacdbcdcdbcacacbbbbacddbaaacbcbaaabbddcacdaadbdbddadbacbbabdbdcadaaacddcadbccacbdcdabdcabbdcdbcacbacbaadacbddbcbdbacadcbddbddadbaadddccccdaadcdabdaaabcaadddadcacacababccaaabcdbcbaccdcddadaacdbbcccbdbcbbcbbcccdacaccacabbdadbacaabddcbaaacdbdcbdbbbcddcdddcdabcabddcdbacbbaacdcdadcbdbcdbbbdabcacdcaaddcabaccccbccacdcaabbdbccbdcdcddadddccbadabdcbbacadccadaaddddcbbdaccaddbacadccdadbddcdaaaacabadaaadaaacddcbbdcbababdabdcbdcaadbdcbdddbbbcdabaadddbacdccbdbadaadadccbdccabcccaabdcadbdaacaccaaccbddbcaacdcbccacabbbdbdccccdcaccaddccacbdadbdaacabdabcdaacacddcaabcbcdddbbbddbcabdcddcbcaaadcbabbacbbbcccdccdbdabcadbdbcbaddcacbcbbbacacadbadaacbacadabbacacbbcccbbdcaaabbababbbbaadacaadcdacdcbcaacdcbaadbaabacadddaacbbadcdcabbbadbacdbdaccddbbaaadaadbcdcadaccbcaabcbcbbcbbcbbbbacdcbdabdabdddcdddcbcdadcbacbbcdaacbbdacaccdaaadbbddcadbdcdcdddcdbdbcdaddcbbcdabbabbcbabbdbcadcbddadaacdadaaacdcdadcccbaccaadbbccaadbcbddbacddddacdcacdcccaccdadbcaadcbbcbdaaadbadcbdadaabaadbcadcdaaddbaacbbdcbacadadcdaadbdacdbcadadaadbadddccddccbbcdaabdadadaccbcdabbddcdbdbacccbccbabbcddbaccacadbddbdacdbaddbbcbbdaaaabccacbdbdddcaccbdddbdbabbcaabdbcacbaccaccdccaddadbddbdacddaabcadaccccbaaccaddbbdcaaaddcdcddcadbbbccadcaababdcbdcababdcccdccccabdadaaddbbcccadddcbabbaaaddccacbacbcdbddbcbcddbdbbaacdcddbbaaadadbcccbdaacdbccadccbaaadbadaacbddcabbdbdaabacccacdadbaababdcabaddcdbccbdadadbaabccaabdcbcdbdcdcdbabbcacbcaccbcbcbdcccabacdbaaadccabdbdbdccbddcddabcccddaabdbacbaaccccaccabdccaccadbccbabccddccbbdabdcddbaccbcbbbacaabbcbadabcaccccbdcdcbbababbbdcdbbbcabcdbaadcabdbddbbcaccabdcaabddbbbdcdbcadccdabbadadccbbdaaaaaadadbaadaccadbacacbddadbacabdacbaaddbdaaacdbcaccddcbcbdbdaaccdcdaccbddbcddadcccaababaabcbdddbcccdccaaacddababbdcabcacbdcaacccaddcdddcdadacdbacaacadcdacccdbcbccdcdcbbcdccdabbccbacabdbbabdbdbbcbddadbdcccaadccacbdccbdadbabacadbbbbadbddcbdcbcaaabacacdcbbcbdbddadcbccbbbcbaaabbabdaacdcaadcaabacadbcdabbdacdddacccdcbcccccabadadbdaccacbcddcdccaadcbdcadcacbbdaacbcdcdbacbdbcaadaccbaaabaddbdbddbaaccdcddbcadabddbbbcccbdbaccdaddabadacacaaddabbcadcbcdbbbdaaccabdaacbcddabdacadbcaaddabdcaacdabccaabbaabbddcbcaadbddcadacadccdcddbccabcdbaadccdaaacaabcbcdcddabbababbdccbdccdcadbbaddacbcaaaadcacacdbdacdacdabbccdaccccbbdbdcdcdcddbbcbabcaabcdcdddacbbdbbaaabbcdbaaadababbadbaddbbdcadbbcbbaaaadbcabaaabbabccabdacacadabcbdacbabadacaabbbcbbbadbadbadccbbaccbaddbbbdcabbdabacccbcbbddbddcadddaacadbdadbcaabcccaccdacdbbbaabbdbaadbcdaacbaddacddabcadcaccdbdbabcdabbccbcdadccdbbbbabdaabdadbccbaacbaaadbddadadabbcddcabcbaadcbddadadcaaccaccbacadabddbbccbdbadcbaddbbdddbacbdcaddccaaacbdddbadbddcdabdccdcbccbaddcccabdacbaddcaacdaccdbcdccaddadbdcdbacbaababcbbbbaddabcaaddddbdccbdaddcacbdacccccbaaddcddcbabdaddcdcabacbaacdaccbccabbbcbdaadbbadcaccdacdaccbaabdccbbccccacbbbbcdacbbcbbbadaddbdcbddaaddabdcccbccdccdacbdaabcdbbdcababdcdbacdbdcbcddbaadcbbadbcacbaccbcadcacdaabcdcbbcdabcacabbccbbdcdbabdbadddaddbaacabacdacbcdbbaaaddbacddddbbcbcadabbcbddbcddacaccdaccbdaddacccadadbcbcabbcccacacbdbacbbcaadcaccbbaccacdabcaddaccbbbdacbadcbbdbbdbdddccdbccaacdadadcddaccdadbdcdaddacadddadcbbababbabacacbbccbbbbcaabbaacabcccbaccccaaacdccabaddadcabcaccaccbbbdbbacdbbdcbaadabdaccabacabaadbbbbaacacabdcaabbaabcabaddcbdcaddcbaaccabbadcdbdaaddbccaadaacacdbdcccabbbdcccbccbadddccbbddbddbddcabdccaacbbacbdccbdbabcadabdadddabcccdbbaaaabbbdbcddcbcaccabcbcdaddadbacbbbcddabbbbcbdacbdbcdcdddcdaabbcbddccccadbbdbacacdacddbbddaaaccdcbdcbaddcdaaaabacaaacadbdcbbdcacdbcbacadbaaaccdadcabacaddbbbddbbbbabcccbddcacdddddcabcbacabcdcbddcdaddbbdccdbbdbcbadacdbccadcbcbbbabaddcaadadbbaadcdcaadddbdaccccadbcabaacdcdcbaccbbcabbbbaccdacbaacbbabaaccddcbadcddbdddcabddcdcabdbbaadbbacbbbaddbcbbdaacdddabbabbabcdcaccccbcbdcccdadbaccdcbaabaccdbcdddcdddbadcbdbabcbbddbcdabcbdbcadcabacbbdcbdcbbbcdaadccbdabcdddcadacadddcddccddcbdcbdbdbaabdcdadaddcbacdabdcdbcabbddcdcacaccdabcabacadcadbbddccabcdbbcbabdabcacdccdacdbadddbbbddbcdcbbbbbcdadbacadadcddaddaaaacbcdccdaccbbbabcbcdbcacbddacbcdaccabcabbbbcbacaaccaaadbdbadbbbbcbabbbdcadaabdabcbcdbadcabacadaaccbbbababcdbccdddadacbdbabddccadbcdaddbbcccbccbdbaccccbbbcdbcacdbcbddcabbaadadacddcccdcccbabdabdcccbaabddaaadcbcbbcaaadbadcdacdaaaabacbbaddddbcbdbbbcadbabcbaabcabbbccdcdbabcbdaaaabcaabdcbdcbcaccabbadaaaadcaccdacaddabadabdbcaccbbdabbacdbbdabdcbbcdcdddacabdadaddaadbcdaacdadbabbcccdcdcccbbbdcaaabccdbdbdbdabadbabbcacbdaddbabbcaddcbbbbdbdcacccdacddcaaddcaacdadbdbaabcbccddbcdccbdcbdbbbcbdcabbaaaadcaabbccddacddaaacdaacbdabbadbadcdaccbddbbdbdbaabdbcbabaabbadaddacabdadaddcadcdabbdcabdacdbdbdcdabcabdababcbccdaaacabaacabadaaddcccacbdadadccbaccadadbabccbdbdcbdabbccddcccbacaaddbddbdddabdccbbbaabcdbaddbbddbadddcadddccbadbbccdcdcddbcbbaadcbcddadaddaadbacddcdcaacaabcbbadcabcbdaabdbacacbbdddbbdaaadbccdddcdabcadbaccaabadcaabbcccbbbacbdaacaaadcbadabddddabddadbbcaadccabcbdcdcaadaabddbbdcddcacabaccdadbdaaaacccdaaccbdbdaddddbacadcddcbcbcdbbbcabacabdcbaadbaaacdadaaddccdabcaaacabbbcbcaaadcdcddcacaaacdcbaddccdddbabbaabacdcbacbcaccddbdccdadcdcbcabddddddbabdaaccbdcabccbdadacbdcddadbaccddbdbbadabbbacbaabbaabdbbdcbbaacccccbccbaacacbacbccaaccdacbbddacbcaaccbdcdddbbddacacbababadbcbaacbacaacbabccbddbbaccdcdbbbdaccacdbbbaaddccdcbdabaddbbcadddbcabbacccddabcabaacbabdaaccadddbcbaccddcadbcdcbbadccadbbbaacadcaacdaacaaddbbcdadcbddcadcbbcdbabadcaccdaacdddbdaccbdcdcdccbcdbbcbbddabaacacbccdcaddbdddabdcaadbdcddcdbaddacbacdaabaadbcdddadacacbdbabbababdcdbbcdddcbccdcbaddbbbcbbdbaaacbbddabadcaccbacdacccbbbabdaddcdbdaadadccacbcbdcdaaacccddbddcaaadbaaacacbdbbdbcddabdbcbdcaabcbbccbbaadcdacaccbdaddacabacbbdbcadbaaaadaaabdbaadddbbdaacbacdddbcadcaaddccadaabcbdbddbbbacdabdbddaddccdcdcbabdadacbbacdcbcbcabbbdbcabbbdacbaaddbdcbbabacbaabbbadbddacaaaacbdbaccadbbbdddbcaccdddabcadacbcdddccbbaadddbccacbadbaacdaabaadbbdbbcdbcdddcacbadabdbcdadccdbaccbbdccbdbdcacdacdccdbcbbacacabacdbbabbabbaaababdbdadbcabddabcaddbababccbacccbbbdbadcdccbdabdcbdcabcadaccbcdccccacbcabbbdcaacccacbaadadadcddacacddcbaddcadbdbbcccbdaacdcbadbccdbbbaddcccdcbdbbacaaabdddbcddcdaadcbccbdcdcadccabdccdbbdabcbbccbcbdddcbcdbbaacdbcbdccddcbababadddaacbdccdddddbdbcbabdccddcabcaadaadbccdcabbccdbcbcbcbcdbbbccdcddbbdacabcaaccbbccccbdcbdcaabaacdbbbadadacbcaadabddabbcbbbbabdbdbdcccbccacdcbcaabcdbbbcdcbdccbcddddacacdbcbacbbccacdcabdbbbbcacbaaabdadcdcdcdccbbbdacacaadabbaccddcdaddaabbbdaddddcbbcdcabdccbdbbaacacdabbbabdacbacbbdbaacdbaaacbcdbbdbdccabbbaacbdadcddcdbaabbcdbbccbadbdbadbacccddbcdabcbbdddcbacabcdabdbadbaacbadadabaaccacadacdbaacdcdadaadbcbaacabbddbccdaccacbccacbadbcabbcaccbdcdcadccccaabdbdcdaaaabaaaccdabbabcddcccadacbabcababadcdcdcacccbcccbaddadcdacdbdbccabbabdabaccdcdaaacaadcadbddababbcdabbcccacccdabadbdbdddbabaadbccacdbaadccbaabcddababdbaaddadaddaaadaddadaddcbcbcaadbcdabddabbacddcbabcaabaaddbdaaccabaadbdbcbdbbdadabdccbcbbdbddbdccddabbbdbaaabdacacddbaccbbcabbbadcadcdcddddbabbcbcbdacaccdbcbdadcacdcadabaabcbdbacabbcbbaaddadbbbdaabbbbbbdacbbbcbdcaddbbbaccbdabbcbcdbbbcbaabbbdaacabbdbbbccbcccbbccdbccaaaabdccbbadbabadaaadbdacdaaacabbcdccccbcadadbdcbcadbcacbccbaabdacbadcccdcdaaaababdaaaadcdcdbcbbbbabacaadabcbdbcdbddacacdddabbaacdbbbbaddabddadbccdbdbaabccbdcaddcbbcacadcdbcadddcbdcdbcbdccdacccaadacabcadadbdccbccdcbbdbccabdcccadddbcbcaaaadbdddacbcadaacdbdbbcadddbacabcaadadddddddaabcdcaccbdacabcbbbbbcdbdaccbaabcdcaddbdabcbababbbdbdbdcbdccdadbcacdbdacbaddbaacabdaabadbdcabaadbbbacabbdcdaddadcbbbcaccbddcccaccbaccccddababadddbccbacdabbacbcbbbbcbdaccacbbbbabddabaadaccdbbcdddcaaaadadcdbaadcdcdabaadddbcccacdaaddacdabccaaabdbddcdacbabdacdddcdacabcadbcccbcbddadbbdbddbadaccddbcbbaddbcccbacdaadbacdcddcadacbddcbdbccccdbcbbddddabbdccdbcdbddacdbcbbadabcadcacbcccbadddaadabdbabdaddccddcaccbdddaddcbcbbddbdaccacddccdbbddbdbcccaddbcccadaccabcacaaddabababcdcdbabcdddcbcddbccdccaddabbdbdabacdadabbdcbbbaaabcbdbaacaccabadbacaaaacbabdbabbcbbdcdacadaacdabaacbbbcabdacbabaddddcbadacadbbbcacddcabddcccbccabcacdbabbcbdabbdbacbdbcbdadcbdaaabaacdaadddcdaccdacacdbadcbbaadadddbaabcdadcccddccababaaccbcbaadbcdaacbaacccbadcdcddcdabcadacbddccaaabbbaacdaacabdcccadbbbdaaccbbdadcaabcdbbbccabaaacbcacbdbadcaddbacdbdacbdaddcacadcacccaaacdcabcbaadacbbadccdbccbaadddccabbbbcaddcddcabcacaaacdabcccccadbdcaabdacdabdacbddaccabcdbbadacabdbadddacbcaadacbaddcbdbddacddbdabaaadccdabddbcaaacabaacdcbbadbcbccdcdbabcabcbaacdabaadbbbddadbdbdadaadacdacdcdacadcaddbbaccdcccbdddccbcdbcdbabbcacaccabdabbbddbaaabacdadacbaaacacdacdcdaabdbadcaabbcadccabddbddcbbbabbaabbddaaabaddaddbbdbbcabdccdbdbddbdabbbaabbaccdacdaadcdcdaadccabadcaaacbddaaccabaadaccbddcddaccccbcacdbcbdcdbaaabcaabadaadbdcccbbbbddbacacdcbaccdbacbacadbbcbdccdbdacadcdccadcbdddadccbaaabdaacdabaadcddddbbbdcabbbdddddbbcaacbaaadadcaccbcccbacddbcbdbddbadacbbdbdbdaaddbbdabdaacbadbbccacccbaababbdbdbdaadddadacacaadcbbdbbbdbacbdcdbddbadabcccdcdccdabccacbbabdaaaadbdadabbdadabddaaaabadbdbddacadacdbdadbacdadcbbbacccdcdcaadbbbbcabccdabdcbaaaccbbdbcabbdbbdccbbdabadbbbaddbdbdbcadcadacbddcbddccdaaadcbdcdabcbaabbdbabbcddbcabbdadbdbbacccdbadbadcdacaacdccaaabbcbbbacddaadbbabacccbdcbbdbdcacbbccaadcacdcbdddcdadaacdbddcaaacbdcbdbcbbccbabcaaaabbbdabddcddcdccdadadababbacdaaddcbcaaabdcadbbcccbaacabcaadcacbcacbbdbbaaabcdbdccaaaaddaacdbbbaccbbddbcbabbdcdabbdccadaddcdacbabbcbdcbadddcabdddabcdcacbdbcacacaccadcdddadbcdcacdcddaddaccabccabcaacdccaabddbdbccbcbabaaddddcbbcabcadacdbbbcddbdcaaddddbdcdaaaddddcdcbaaacadcadacdacbcaacbdadbabbcccdcdbbacccdaaaddddbadabbdbdccbbbdbcabbabbabcddbdacbcccdccaabdabccacaccbbabcdcadbabddcbadaccddadcadccacccdcdaccccdadddbcbaacbcdcbaaacacdbddabbcdbcdacccacadcdabdacaaddbabcdabbdcacaccaadacbccaccdbabcaacdcbcaaaabdacdcddabcabdaddadbcbddcdbbabddcbbbbabbdbcacdbbadbcddacddcbabbcdbbbdbaabcaabcadcdbbdcdbaccbbaddccdacbdbbdccadccabbbccacaccdcbbdcdabbcbaccacbbdabdbadcabacdcaaacdaddbbaabddddbcaccabacbcaccaacabcbbabcddacbccdbbdacaaaddcdcdbbbbcccdabdbcbacddcbbbbcdccbaacbccacbcdacbaabddcddbbddaccdabbbcbbaddadbabcaabacdadbcccbabdacbdabadbbdacbaadcbcbbadabdcbccbdbdcbcacbadacabcbbcdddbacddaadbcdcaacaacacbaccbdddbbccddadcacabbbacabbacadacddcbccadbdddbabcbbddbaacababaaadaabdacaccacaccdddbbdbbdbadadabdcbabdcaaaaccbadcccddddcccadbdcabbdddccadccadbbbcdbaaddbbabbadacbbdbacdcbcccbcccbabdbabcdbdaacadbadaabaacaaabddbcdbaaccbaadcccdccacaaababcdbccdccacabbacdbacbcbbdbcdcbcaaccdbadadbcdcbbcadaacbadacdbabbaccaadbdbdcbddabcbaadcaddabcccdadcadabcbccbbdaaccaaaaadcacdadcbdcdaddcbccdababcaaccabaadbdbdcabcaadcbabaacaaabdbcdcdbcdabaacbcccdababdcbabddacccbcaaabdcdacaccdacdcbbddbbdbcbacabcacdbbbabbcdddbbaaacdbdcbcacdbccaadcbcddbdbdbbbacbbddcbddbccccbdccdcddcddbdacadbcadaccddbccdabdadbaaaabadaadbbdacabaaaabbcdadbccbddcbdbccccdadcaababdababcbbbbaadddaaacddabddcdbbadccdcdaccbbddddbbbccbdbaadadcaaacaaabaadaaadbaabccbabcdddbaaaacccdbadabaacddacccdabccdbdcaddcaadbcbccabdadabcbcacbccdbddbcccbbbadcabdddcaadcdaabcddcdaaccddbdbabccddddbdbcdcbcdcdadcddbabadbbcababbddabdcacbcaaccadbcccdcbdbaccbbccbdaddddccbadcacbbbbcabbadddcbbaccadadbddccddddcbccadcdbbcacaabcdbdcbcbcbdacdbdadcbdbdbbcbcbbadbddcaabdbdacbabbdbacadabbbccabccabdaaadbbdbcbbcddabcabbcdacbadcbacdcdadabdbaccdcabcdadabbdcaccacccbbbbcbdcabcdbcbdccdbccbbcdbabbbdddbbdccdbabbadbabcccbaaaadabccdbdaaadccbbdddccaacdcdbbbbcdaabcbbbdddaccaaaabaabbbbadddddabadcaaccdbdcdcdbabccdcbbccadbaaaabbdcdbdbabaadaccaaadacabbdaccccddbdbdbbbaabddababadcbbddbddccdbbadabaacadbbcaddbdbdcdbcdacacbccabddbdbccdbbabddbbddcbcddaacbcbbacaaabaadccccccbbdccabaabdbacdcbaadcdabbacaadacacbadcbbdcddcccdcabaacdaccbbcbdcddaadaabdacbbddbddbccbbbbaccacadacdbcaaabbaabaaaacdacbbacdbaadbbdbdcaacaddbbadcdaaacadcccaccdaadaacadccabcaadbccadbcbddcbaddccccbdbdcbbcabcbdccdbddcdbadcdcbacabdadbdbcacdbbdadcbbaadcbddccacaacdadabaddbdaddcacbadaadaaddcbdadbccdaabbacdbacbacabcdadcdcccddbcadcddddddacdcaddbddbdacbacbcddadacdcdabdabacacabbdcddbaacddddcaaacabadadbbaddddddcdddbaacadacbbdbcccdaaaccbbbbdaadacdddabbbddcadabdcdabdcdabbadddabcddaacdcaddabadddabbbddcadbbddbccbbccbdaacbadabaddacbcdbddaccdbabdbdcacbdcbaadddbabddabdbcbdddacbccdaaabacccddbcaacaadaacccdadaccddcbccbabcaccbccdcaabdbaacacdbddbcabccbcdaaadbcbbddccaccbbabbbdbabaccadcddbdbbacbdbdabbbaddcdaddaaacddccdddbbcbadbccaabacbbaaccadbbaadbbbdddaacbdacacbabcdbbbcaabbaabcbcbdabcaacddddabdadbacabaccccbbcdacbcaaaccacabacaaacddddadddbadadbddbcbcabadcaddaabcabbbccbcddabcbdbbbaababbaaadadcdcabbcdaacdcbcdcbdbabbcdcacbacbadadbbbddcaacbdbaabcacdacbccbdaddbaacbbdaabdabdcbabbdadddcbbcbacbcabbbbbbbacadadbdabcadacdbcdbaddcbbbacacddaabddcddcbbddbcdccccadbcacdbcccdcaaddccdcadcccaddbbdbddcbadbacbadbdbdbacbcbbcdacbbdddbcbdaabbbaccbadadcdacabdbdbcaadcbbbdaaddabdcdacbcbabcdbccdcaabcbabacadddaddbdbcbcdbcdccadbcabdabcaacbabbaabbadacaabcbabdabacaaabaabababababadadbcbbccdbcccbdddbcbaaaaabacddddcbddaaaddbaadbdbbaddbdaccbabbddcdcdcadadbabcacdcbbacdcacadabcbdbabcdbbdcdbaabcdccacdababbaacbcdbccddabbdadcdbdadddbacddabcadcabbdacabcdbbdbbbcdadddabaadcbadbacddbbccbbbcdcabcbcbbbdacdcbbadcaccbbaaddadacbaabadabaacabdbadbdbbdcacaddbcdcbcabbdbbdcaadbbcbcccdcdabacccbbacdabacdacaacdadccabbaddbdbbbdbadbaaaabbaadddddbcabbbbbcabbdbbaababbbbddbadaccbbddcbbaddbbbadabcddbcbdacbbddabcbabdcdcbdbdbadbcddbdbcaccacaadbbbdddacccadacddaabcbacddcaadcbdaaadcbbcdcddcababddddcabaccdbccbdbbacabbcaaadcdbdabbbcbbadcbdbdcaabbacbbabadadadcdcaaaddcbcaadbbadcadaccdaabcdcbababadbdcbdaaacdabccbdaaccbdccabdbabbdabdccaccbdcbabaadaabaacddaacabcccbdbaacdadddadadacabcaaaacbbbcbdbadcbbdcbcababcbcdddccbacdddddbbdddbbaaacdddbadacaababcdadabdcaddadbacbdbcdbbaabacbdabdacdbabaaacacadaadcaabcddcddabcadabadcbaabcddbabcddbbaddcddddddabbcabcdbbbbccdaacccdaabaccdcaadcdcddbdccbddbbdaadabdcdbcabaabcbabcadddbcdcbdadddbaddddbbcaaababbccdccbaddccbacddbaadddaadcbccdcddcdbcbcdcdbdcdaacbbbcdbdcabcabbdcbcdcccdcbabcddcabadcbddaaaadababcabaddcddaddccaabadbdcbabcdbccbadbaabdccddabdbcacadccbdabdcabdcbbadccdcbdcccdccdbababadddabdabbcddabccdaaabddcacbabdbddadcdabdadbaaaacbabccacaccadbdaabdbacbdbdbbccaabcaccdadbccaaabdccabadbadadbbcccdadaacbdaccaadddbdcdcdabccdccacaaddadccaaabdadabcbddcbbcddbbbabbaacbabadddaadabbbbcbdbcabbcbbdcadccbabddcbddddbcdabaaaabcbddccbacbcbdbbcccccacccbadabaaacabdcabbcdccccadadcacaababdddbabccbbdadcaabcaaadadbadcbbaadbcbaccdbdacdbcabaaacaabdcddadcdadcadccbbabbdbbabdccccbbacdbcabbadddddadbadbbaadaddbdcababcdddacbcbbdcadabdcadbbacbdaabdcbbccbabadcbaaccadadbbccdacabaacdbabacadbbaaddcaabacbdacbbacaccabccacabcbcccdcdccaddbddaacdcbcdbbdccbcadccbabbccbcdbddcddadbccdaccdbddddbcacdcbbbabdabbacdadbbbdaccaddaadbdcdcbcdaccaaacdccbadabadcadcdadccacbbbaddcddbbaccbacddabbcddccbacbbabdccacddcbaccaddccbabcbbbbccdcbcdccdabdbddcdbadacddbcabaadbcabccbcdcdaacdddcdadcacacbcdcaaacdadbdbcacacaadcbbcaabbaacbbabdacbcaadbacdacadaabbbabbccccbddbacbacccbacbdddbbdddbcdbbbcbcdadbdacbdaabdaabcadcdcccdddcbcdabbcccdbbccddcadcdaddbdbdcbdbacdbbcbdddcaaccacabdabdbaaaccaacdadbddcdaacddcaccddadcbccacdddddccacbacaacbacacabdbcbdbcddbaaabcadabcadcbcdbbbddbcdccaabaabaabbdabccdcccbbdbaacddddbcadcbcabcabdaaadbcabadddadadabcbaccdbdacbabaaadbdbbcccbdbdccbbcbccdddddbadddbdbbcadcccacabccdbadabccccbcbbbbcdbbdbcdbbadbbabadadcadadddbdbbadaccbdabbcaababdabdabaadcbacccdbdababddbcbcaabdccbccabcdadaddcdddcccdbbbabbccdcaacddbcbaabbbbcccbbddcabbbccbaadbccbbcadbbdacacabbcabababbaaccacbaaadcababcccdacaadacbddabdbdaddbdabbcbbbcaadccacbcccbcbdcddbbaaadcdcbcbbadaaaaaccbddaacaadacbabbbcdccaadddcccacaabbcbdbcadbaaacdadabbbadaaacaadadabcdbdacdbcdcbbbabbadadabbbacbbbcccaabbabbcadbaccdbaadaaaaabccaabbbbcacddcdacccdcccbccdadbccbcadaacbadcdddbdccddcadabadbcbdabbaabbaabcbacdaababcbcbdbcdabbaccaabbbdacbddbccbadabdbccbcddbabadadcdccabcaabbdbdacbcbbbacddccbbdcdddcaaabcbabdbdcddbacdccdddabbcbbabadccddcbdacaabdbcdcbaddccababbacadadacbacdabcdbbbdcccccbbcaacddbcbbabadcdccddbcdaacbdccaadabccacacabaddabbbbccdccabbbcccbccbdaccaaaabdcaabdbdbabbaadcbccaddbdbabaccadadabccbddddcdadbacdadacdcbbadddcdabcccbaabdbdbcaaacdaabcaaaadcbdbdcddaabcbacaadbacddbdccbcacdcabbabcacacabaadcdababbacdaadcbabccdcccacbbbdcbcdbcaadcabddcdcbdbbbcbddadbabaddcbdcdadbacacbadccabccbdacabbcdbaddcbcdcbdbcacdacbbddaddddccaabcaaaadcddaabbbbbcbdcccdbadbbcbbbdacddaaccbdbcccdbbccbbacbbacccacbdaddbbabcbabddbcadccacdbcbacdbcbbadacaddbcbbbcbbdbacbbabaddcdbdcbadcdbaccbdddbbbcacadccabbabbbabcbcacbccdacaacacaaabcbabcababcaabcbcacddcddbdcaccabbaacdbabcdbbdadbacdbadabaadacbcbadaabddabcbdabddccbabaadcdadabdcabddababdcacbbaadbbbdbccbdbcddcbdddacaccddcaaabcdbbbbddbadbcaddaaccdabdbbdaaadcdabdabbbaacaddddcccbcadaddcabbdcaacdbdcccadabbdaccdcacddbbacbbadbbcbadadcacccdcdbbbccadbbdbcbbbaccdadbcbddcaddccbbdcaabcaaaccaadaddacaadccadcccccacddaadccababdbaccbcaddacdabcdcadccdcccbdbabadcbdbcdaaacabcccbddabaaababaadcdbccddbacccddbbbcbccaababdadbcacdcabdddabadcabacbaacddcbcabbadcdadbcbcaaadbbacacbbdacbdddddaaccadddaccccdcacddddacbcdbcabdbacbbbaadbccacaccdacabbcddabadcdcdcaadabbcabaccaadacadcccddbacdabcddcdaabbbcabaaabbadacdccaadbbacbbdcaacbbddccababbaadbbabcdcdbbadcbcbcacdcbdbcaccaddaaadcabcbbbcbaccadcacdbdbbbdaccaadacddcdacdbdcddaccccddaabdacdaadaacdabbbbcbbbdacbbbddcdcbbbabccdbbaadbdbccbdaddcdcbaabaccdddbbaaadaabdaccabcacddbacacdbcacddcdcbacdacbdddadcbabdbdaccdaccabaddcaabbcabadabccabaababcbcbdabbadbccbacabcdaddadccdcbbdaaccdddccbcaacdaabaabbabaddabcbbabadaacaddcbcbabcbbbccadbcdaaddadbbacbcbbcddaaaddcdabdbcddcdbadbdcdbcdcddcacdbaddaddbabbdbdcaacaddbddacacdcbddadcdaddaccdbcaadbcbdcaabdcbcbbaacacdcdaaaddadbaddbbcccaaccbaaccaabdcddadbcaaadddbcddadcabbcbbcccadccccabbbbcbaccaabdcdbcddccccbcdbddbdaacaabdddacaddabccccacdcdbbcadabbcbadababcddcddbdcaccbadcacdbbacaabccbaadbddbbdddacaabdaaaddcdaaccaabdabbcacccabbcbadabcaadabcadcabbdbcbcddbdcabbcabbcdcbdbacddacaddbabcaabacabdacbdccdaacadccbdbabbdabccadacacccddcbabdadabdaddaadbabcacbdcdcabdacdcaddbddaccacdbacdaccdabaddaacaaadadddadabaadaadbabbcabacdbaaaddaccddabcacbdadcdbdbabbadacdabbdbcdbacaacddbcdabbaacccaaadcdabbcaaadabacddccacbbdccacabdcaacbababcbdabcbbdbaaadcddddbcdaddbacaaddddccdbcdadacbacdadabbcabcabaaccbcdbccbdddcbadbcbdbddbcbcbbabdbacccbdbaacdabbcdadadcdcaacdcbcadbbbcaabdbcbaddcbddcdcabcacbbdacbdcdacbdbadcaccdbacddaddaaacadbdbcadabcddcdcaacbbdbbacabcbcaababcbdbaddccddabbcbbabcaaaaadbbacccddacdadbcaacbcdabbdbbddbbadbaddabbcacadcbdaacccabbcbccdaabbbbccdcddaadadadbcddacccddbbddbdacdccbbddbddcddabcdbcccbcaacbbbcccaaaccddaccddbabcabcbdaaabbabcbaccbcbdaaaaadbdddcbacadabbaadbdddddbddaddbcbbdadadaccadbcadaccdbdbaabdbbdbbcaccabbadbdacadcaacbbbabbacbacacaacccdbbaabacaaabccddddabbaaccbcbbacababacccddabbddddacacadbbbbbcadbacccdadaddaaddacacaccaaabaddbabdbbbdadcbadacdaddcccdaabdaadbdcbcddbcddccbdbcdcaccadbdaacdcaadaacbbccccdacdcbccbdaadcbdcbcbacccdcdddbddbcdbadbdddbaddbdcdcbbbbdcaabdacbaabbabdadbbdabacdcdbdccddcdcdcacaaabbccdbdbbcbbbaaccbdcbaacbdcddaacabbadcbcdcbdbbbbbddddcbccdacacdccbacbacabbbcbaccbcddbaddaaacdbaacbdbbacdabbccddddacabacddbbbccacabccbacacbbbbaacbacbabbdbcbdbababccbcdccbdbdbdcaabdddaabdcbbbdbcbcbdacdadcdcdaabdcbabdbaddadabdcabbcdaddccddcabcbbaaaaabcaacccdbdccadcdddacdbcddabdcddabddccbbbbdcbbabbcbdcbdaacadadccdddddaabbadcddddbcdbccadcdbadbcabacbadcacacbacccddcdcbaddacbcbcaaacdddbdbcbcdbacdaddbabbbdaabdbddcdbcccaddbcbcbdcddbcdacdbaadabbbbacaacadbdbbabcadacbdabcabbccabdccbaddadddaabbdbbabaddbdbaaadabdcbdbdcdccbcdcacdadbbdaaaaadacbdcaadcdadcbabbaccddaccbdbdccdcbcbbdaccccdadbcbdacdabcdbbcbaaaaabddbbcbdccdbccccaabdbddbadabcbbdabdcbacbadddbbadaabddcbddadcdabbadbbcdcbbabdcccbaccbabccabccdadcdcbadacbbcddabadadcdddadcdcddabbddccbaacddbdcbbbcbddcdcadaaadbbcbcdbdbacaaaaadbcdcdadbdacdddcdadadabaddccbbdaaaddcddacaccbacadcacacdcbcdcbdbbccbcbdaddddcbcaaacbcbcaccaacbddcddaacabcdcbbbdcdbdccaddcbbcccccbacbdaaaabbabcacbadadcdaadcbabcdbcbbadcbabbaabcbcacccdbbacdddbcccdacadaadabaaacdbdbccbdadbaddbbabcaaadcaccbbbcdbdacccdcdbbdbccacbaacacbaacadcaabbaabbadbadcddadbbbaadacbadaccdbddbdaaaccbcbdacdcbccaadabccaccdbdbcbabdbbaaabdcbcdaadacddccbddcbcccadcdbbddcdcbcbbbccabbbdcccbcbdabaacbabdbcccadaacbddbaacdbcaabbbabaccbbaccbbaaacbabdbbacdcdbcaccdbbbaccbbddddbbdaccaacdcbbcbcbcdbdabbdbdbdcdbaccdcddbbadccccbdcbcbcadbccaacabcdcdcdbbadbaadcbccdccbdccdcdcddddbbcacbcbccabdccdcbbaabcdcaaadcdbaadbbbdacabacdcacababbdabbbcdbbdaddcaccbbdaabdbbccaaababacbbadbdacccdcccabadabacddacbdbdacabcbcccdaabbadadccdbbdbbdcdbadcabcccaaacbadcdcdadcddaddcddddbcbbcaabbdadbccabdbbddaacbbdaabbcdabbcbabaaacabcbacbcbbbcbdcddccaaddbcccdcbacbcdabdcdadabdabbdaddacdcbccadabbacbacbbcbdabdbbadbcbaadbbbaaccadddddbcacbccccaddbcccaadbadbacdbdaacacacbbdbbbdaaabcabdcdadaabdadcdaddabddbabdabbbbdcbababacadbacbcdbdddadbbdbdacbdccbababdaacbdcaaaadcbaaaccadaddddbddbbdabbcaacbacdccaacaddcbdddccabcdbdddbcdaadadccbcdacdddcadcbcaaababacbaaabbbacaabdaacadacdcdcbbddcababbaccabddcddcaaaacbdacccdaadcbcabbaaadccacdddbbacddddaccdaabcccbbbcdabcbddbadbbabdaccddacdbcbbdcccaccabdccbddbacddaadbdcdbbcdbaacdadddddcdaaadccdbaabbcdddbccddadbdacbacbabbadbcbabbadaddabdcbbabbcdbdcdaccddbbaaaddddaadccdcdcbbddcacacdacaccddbdbccaaacbbaccbcddbadbcdddabcdbbcbbbbaccaadacbbbbbadacbcccaccddbabbcdaddacbbcadcdacdddcdabdadaaddacbddacbdcbbbaaabddaacdbcdbddccddbcbddbbaadabccacdcdcbcbbbacadccccaabbacabbcaadcccbbbcbacccddddddabcbaaabdadbcacbccdbaadbabbbddabababbdccccbdaaacacaabcaadcbcdaaaacabdccddcdddbbdcdcadbbacaabbaadacaaacadacacabdbbddcacdccbadcccadaadaccdcdddacbdcbcbdccbabbcacdabbbbacaaadbccbdadbccaabacbdccacacadcadddcacaaadcabccacddcadacbcadadaaacbabbdbaccbacaddbacbdccacbdcbdcbcaccaddbdbbccbbbdddbdacaadcbaccdbcbcacdcbcdcacdabddbdddacccbddabaddbcddcbaadabbcbccbcbcdcabaddcbcbacbddacdaddcabbbdbdaccacddacbbcddadabbaddcaaccbadcdabacabaacaddbbbccbdaccacdadbdccdbabddbcdcdccbdaacbdcdddddacccbbbbcbbdbabadcadddcabacaabdcaabcdcdcdabdcadbdcadbdcadcdbcacdacadccadbcbdcbbcadcbbccaadcacbccddbacaadddabadddbccbcbdabddcaadbabccdabccadccdcabcabcabcabcbadbdbccbdaacbadbdddadcddaddbcbacadcaccbdbaaabbcaddbadbbacaddbbccacdccadadbcbaaaaabbcccadbccddbcdbabbadbbcabbcbdaccbaacdbaacabbbcccbbbcccabbcccaaadcccacbcacaacbbdacbadcbbcabbadcddbcdbdababdcdcadcbbcabcaccacabcbbabbbbadccdaddcbbbdcdacbccbbadbbbadadbdbbbbbaaaddaccbdaaccadddaaadacdbddaddbdbacbbbdbcdcbaddcbaaabbaaaacdacdcacddbadccbacddacddadbdacccbbcddddbabcacddadbbddddadadcabbdadcdcbacbbddbdbaadddabddcbaacaabaccbcdbbbdddbadbbaadbadcbdbdcabddacadadbadbbbbbcccaadbddcadbbacdccbbbabcadbbccdbdcdabadcbcdddcbcbbddcaddbccdcaaacacdabbddbbdcdddabbaabcddcaabacaadcadbdbacaaaccadccbaacbbcbdbcaddcddabbddbccdcbabcbccbdcbcccbabadabadabadcabbcddcadccdbcaaaccdccdadababbdadccbacdcdcaabbaaaccdbcdbbbaacadabaaadbdcbcabaabbadcdaccaaadcbaccaabbcdbadaabbddadaddbbdcdbdcdcbbaacabddbddbabbccccddcbaddbcbbaaddcbdacdabbcdbabadcdcdaadbdbbbaacdddcaaadccabccacabcbcadddbbacdcadabaabcbcacdadbcbcaaddbdcbddaaaababaadaaddbdbddabcabaaaabcaadcacadcccbdcbbcacaaaacadcbdcacbcacbadddddbacaccddabddccbcddbdcaccaacbdabdbadbcbbccaabbaccbcabbcdcdcdbbdcadbdcbbdbccbabaadcdaadabdcdabaddcbacdcddadcaacddcbcccbabcabbaccbdbddabddadbadbddcdacaadddaddacdacdddddcdccbddbbacadadbaacadddddadacbdabacccbdbdabadbaabadaccabbacdddcccdcacdbdbacdadcadddddcddabaacdbdcaadddcccbdabdaaabbcabbcbccccbbbbacbbdadbdaabcccbdaadcadbaaadabadbdbbcacaddbddadcaaacccabcdaaacbcaddaaddbbdcdbcbcdbdcbbbdcccadbbbcbddbcdddbabaabcdcdbbcadbcbaabdacaacbbdbbcdcaddabbbcdbaccbaaccdaaabcbcbbdddcdcbabcddccbbbcaddaadbacadbcabbbdddacbacadabbbbaaccabdbbbcddabccaaddbdaaaccbbbcbdbcacbbacddacddabcbcbaddabbbbcabcdadbaddbbcbdccadababcbccabbcacdbdacabaacbadbdbdadccdcdacababacdadccaadcbaaacdbdacadacacabbdaacdcbdcabcabaadbadadaaddbcdbbadcddadcbabdabdbadacddaadcadbbabdbcdccbbddccdabccbabdbdaaaccbdcbaddddcdabcbabddccccbadacabdcccdbbddacbddddbadcbaccabdacbddabbacccaabbdbccacadcbaadabacacacddcddabaaabbaddbbcbdabcabccbdbdbbadadaddbccdbdcbdccbcccbabcccddcaacaabccbdcadbdacbacdbcbccaccdbcccccdbbcabaabaddcbdccaddbcabdabdcdadadbcbadcabbcdbcacaacacdbbbabcdddcccbbbadabcbccbacbbababbdacdcdcacbbbbbadcbabcddcbcccdbbaccacbacdbcbcdddacaadbaddaadcdadccabcdcbccacabdbbcccbbbabbcabaaaaacbdcccacdcbbbcacbdccccbcbdbddcbccbbaccbadaadcbddbaabbbaddcbbacdbdbddcbbddbbddbdddbcddbbdabaccbbdbaccacbababacadbcadbabbbcdbbbcacccbdadacabcbcacddbcadabcadccdabcdccdbbdadbccaadaaadccbbadabbdcbdcaaccdcddcabdaabcdadbaddabbdcbacacdcabdbcabcacdbabdaaddbcccaacccdbdabbcdcadadabcbdbddccdccdbadababcdbacddbdbbccdcbacdadcbaabcdcdacccaabacbbdbacabcdcdbcababbcbdbccbcbdcaabcddbadaacdcbaabbcbcbcaaaabadaccacaadadbccbcbbcccdaaddbcbbadadaacbcbdadbbddccbbadaabcdcddaacddbdddbabcdabdbaddaabbacadbbdacacdadbadaabcbbaacbcccacdaccbbbaaaacdacccacaaabddddcbcbbbcbddcdaaaabadbccdddbccabdadddcbbcacaacabdaacbabadacabddddcabcabcbaadbbdccaccdbdcccbbadbbddbadaabaaccbdadcbbbbdcdaababbcddbddbccbdcbbcbcddcdabccbcaabbbaabacabcbacbddaabddacdaddabadcbaccacbdccbbbabbababcaccdcdacadaabdddbdacacaacdbbcdababccaccacdcccbcacccdcbbcdbdadbbacbbbcccadddcaadbcbcdcbbbdcbbdbcccccadbbcacdabccccdccabdaacdcbdcdcbdccacbddbcdbdbbcbadcababababddcccdbabdcaddabcdbbdbdcccbabdabacacabcadabddaaddbaddacbdabccacdaacaabbcbaddcdcaddacddadaddabcbccadbccbcadabbccdbbdbbddcddbacdadbcccdcbcbcaaaaabdbacdacadbbbdccabdcdbcbddadcdbbbadddccbdadcbbabadcdaccabcbdcbdcaabccadaaacbccdcbacdabcdbaddabdbdadddaadbdcdddcdddaaadacdcdbbbbdbaddabadaaabcaddbadbcacaccddcbdcaaaddabdcbcadbbacddbcaccadcbdbdabdddabbacdbcdbbcbbadbdcbccdbdbacdaddbbddcdcbcddcacdccacaccaddddbccbbdcbdbdbcddbadbbbdcdbabbdcbbacacbbbdcbdabdaacdcbbbbabbacbdbbdaadaddddddbabcadcbcbacaddbabadbcacdddbdadbacbcabdbaddcddcddbacbddabcccdbcccbabcdddaababdbababadbbcdcaaabddadbcbaaadddbaadddcbacbccdbdcdcccacdbdddcadcccddbbcbbdaaabbbaaabbbbdbdbcbaadaddbdddacdaccdadbdabbaadbdcabcdccacbbaaababdabdadbbddcdacbdadbcccbcacdaccdadccaddddcdddaddcbcdbcdadddaaacacdbcbdcbcbcdaabaccaabaaccababdbddacbdadcddcbddcdcdbbbdabcbacaaabbbdbbbbcbabdacabbdbcdcabcddcbdaadcddbabccbbaabbddbbabbbccbddabdbcdcbccbabcdccaccabbabccdaabacddaacbacbdbbadabacdcaaacdddbbcbcdbaddbcccbacdabbbbacccbcbdbccdddcdbbddabcaacadcaacadbbdbdcabbdbcbaadacaaadaccddbdbbabbcbdbbabcadcbcbcabbdbddabdcddbcbbbaabadbddadccbdbaaabbbcbbcbbbbacaadacddabaccbbaaacaaadcbabbcdabbabadaacacdccbabbcdbdadaaabcbcadabccbdbdacbdddaaccdcaabcbababdbcabababacddadbccdcbbbdbdcacdbbdacabddbdbacbaadddcdbcadcabcaacccbdbdbccdddaabdbcabdacdbdcddcbcddaaacabbddababbbbabddccabddabacaaddcabdacbaacbaacddbaabbdacbaaacdddaddddaaddaacccccacdcbcadbadcdbdadadadccdbbcbccadacdbcaadacccdabdbdcadddbcdababcddbccccbaccabacaddaabdacbcbdbcdcccbaabbdcccabdcbdabcabdaaccadcccdbbcdbaaabcadaaadddcbcdaddbbcdbacbbbdbccdbbaaabbcbccadcbacbcaacbbacccbaabdadcdaacdadabdaddccadbdaacdddadcababdccdadbdcccdabbccabddabdabdddadcccdcbbdbdabbacddcbcbaacabbccbdcddacccbbabacbdcabddbcaabbbaddbcdbcbbadcbccbcadbcdccaadcccdbdabdbbcdbacabadaabadccdacbdcdcdadaabcbcbacabbdacbabbaaadcdacabacbcbbcdbdddcacbaacdddacdababddcbdbaaaacdabbdcbaddacddacdabdbdcdbbcbcdccbccbaccaadccacbabbbaabacadddadbdbdcdcdcadccabdbbabbcdabaadcabbadccbbdabcaacabaaaaacbdbaddbdcaaccbacdbbbdcccccdbbadbaddbbcbdddabcacaaabacdcadcbbbbabadbddbacddabbcdcdcdaddabcabbbdbacdaddddccdccdcaabadabdbbabbdcccbacdbbabddcdcdcdcbdbcdcbccadbdcaaccaaaaadbcadbaadacdababdbacbbadbdbcacdacbbccbbbdbaacadabcdddddcdadcdcdaccadbccdccdbdcbbccdbadddbbccbdaddaabacaddbcbaadadccdaabdcabbcdbccababdbbadbdcaabdddccbdacacadddcdccbbdbcbccadcaadcccadccbcbbbbdddbaccadabbdbbdccabaccabdabbddaabddcbddbaabbbdabaabacdcdcadbcabddaccbdcacaccbdcbbbbaabaabbadddcaddcddbadbacdacbccbabccbbdccbdadcdbdabcbabaacadcbcbbaddbcbddacbccbabaccdbacdcacccbaaccaabddabcaddacadbdbbdddccdccccdadbabbbbaaacbdadcbbacbbbbccaadcdcbacdbcababdbdbdcaacaccabcacacbcdcbbdcddbdbdaabadcdcabcabdaacbbccaadabadbddaadbaaccddacbccacadbbbbcdbacbbddbddcdaadbdadbaabcaddbbbaaabcbbddabdabdbcadcbaccdbdacccaaddbbdcbadaacadcdababdadbbbddcccadacabbbadadadcacabdadcdbdbaadcddccaccddacbddacacaadadbdbacbbcbbdcbacccdbaccacccadcdbbbadaaabbaabcbabacccbacbaaadcdcaabadabdccdabcccbdddabbadcaaabddddbbddadbdcadbbcbdbdcdbdddaddbadaabaabbcdddadccbcbdccbcaacaabdacdddabbdcccbccaadcabbcdaccbbcbbcbaccadabdbcdacbdddddbdbadbadcbcdabaacababddbcbbdcddccaaababbccbbcbcbcdcbbdabadacddcbdacbcccabddabcadbcaccbcbbbbcbbcbadddcbadaabbaddcaaadabbdcccbccacdcaddcaaabacaacadcccbbcbcabbdccbdcaccbaabdddcdcacaabdddcbadbbaddcbbcbaaddcccdabbcddbaaadbcddcdccbcccdcbdcccbcdcbdcbcbbdabbdaadaadabadbbcacaddaddcbbddccdadcbddcdadaacdbcaabbbcdaaacbdacbabbbbacccadcaccbabdccdbbabdacbcbdccaccabcdcdacdaacbcadbabddacddcaacdddcdaabadddbdbccccdcadaabdccddadcdbcbacacbddcdabaaccdcddbddcdabdccdbbcdbdaaabbaaaddbdbaccacdadaadbcdddbbccddccbbdccbcbadcaaaaccdbadaadacbbccabcaabbcccadddbcacbcbacbdbcddddbaadaaabcabbdbaccbdddbdcdcbdcadaccdadbbaabcbaacbbabcdccbdcdcddaabddbcdbdadaddadbcbadbbdcbcacdccadcbbbbcddcbddbabcccddacbcdcdbbdcdbaaabbdaddbccbabcbbddccababdbddccacddccbbabdbccbadcbdbcadccccbcdccdbacdbbcabaccdbccbbddaacadabddaddbcdcbbccabbcbdbaddcdcaaccbbbcaccadcccbbbbddacbbadcbcacddcdaadddcdccbcaaacbddbcbcdbdbcbaccbdaccaaccacccbcacdcdaaaadddadacacdcbacbcaadcaddbabbacdabbbbaadabbccbacbadcaaabaadcccbddbcdbbcbaabccabaacbcdabdaaacabaabcdacccdcccbcbdcdaadcbbcacaabaddaddbacdbcbcbbccacbcbbddbddccbaccbbbbbcdaacaaabccabbbbdacbaccbadcaddcbcbbababddbabacbaadcdabdadabaaddddcacbbdccaccbcaddadcdcbdabcdccbcdccdadbcdcdbdccdacbdddbcbcabcdcaacabcdcacccbaddbcbddadcdcbaabdcbbdacbbdcdababdcadacdacbcacddbaddcadcbdaabbdbcccbbbabcbaaaabaadcacdbaaadbbcddcddcdbcdddccdcbcabcbadaabcccbaadaabbbcabcabaabcbcbbddbccbcbdbdadcacbabcbbcdcbadbdddacdcbbddbccadcccaadbaaadadabcaccabbcdbddcdbdccbdbabcdcbdacdbbcbaccadaccdbbcdcdbbbbadaabbdabbaabdcdabbabbbdabaacacdcccadccbadcddccbbdadbdccddbbdbaddcdbdbbabcccddcaabbbacdbccabccccdddaabcadcadabbdcdccbcbbcccdadbaaadddddcdcccdcdcbbcddacbabacaacddbdabcdcbaaabacabbbcbabbbadadaaaccadccdadbcbddcbbadccbbbcbbabacdcacbdbcdcacdcbacaadbcaccbcddaaccbaadcacbbbddddcdbabddaadccbaaababababcadbaacccdabcacbaaabadbbadacddddbbcaabcdaacaadaddcdbbbcacccdcdadbdbdccaccaadbddaccacbbddccbdbdbbddaaccabddcaabdcbcddacdbadbdbadbaaabdcbadbcdccccbcdcdcbcaccdaccacdaacdbcbbbadbbababdccbbdcbcbdddbcadbbbdbaadcddcdcbdabbdccdbabacccbbcadcadaadbcdccaabcdbcbabcabaccdcacabddaaccdacabbbaadcbbbbcbbcbbbaabcbbaadbbccdaaddabcaaccaaaaadbccaadcccccacadaaacbaacbcddccbcbdabdaacbbbacdcaccacbcdccaacdadddccabacbcccddbaddabcbcacccccbbbccdbdabbcbbcdbccddadbbaaacadadcadcdbcabaabcdacbcddcdccbdacadcdaabcbabbbaddcacaadbdbcdbccaccddbbcddacdbccabbdccaddacbcdaddacbcadbbcaaaaacbacddbbbdaddababddaaddbbbddddcddccbbbdacaaabdcbabbdbaaadadadaacddbbbaacbabcdbaaaadcabacbccccbdbdcdaadaccacbdcbdacccaddacdadacbabcbbdbcdbdabdaddbbdbaaababdddddcbdbdddcabcadccbacbdddbccbadbbbdaddbabaaddaccdaaaabcdabcdbcabbbabdcbabcbdbbbacbdabadbbdaaacaabbdcbbcccbbdbdbccbbbbdcdcccabcbccacdacdbccbcbbcbdcaaccbaddcabcbcacbcdbbcbcbabbdcbcadcbbdbdacbbabccbadbddbbbccaccabccabcdacabdcdbaadbdddcbdbabacbbdbcccbddcdbddcbcccadbcbdaaccbccbcbccadbcbdbbcdaccadadaccaabcddbbcdcbaadcdaadbaadabaddacdddaadbacbcddcccdaabcdbadaddacddaaabadbbcddadcbacbbddcadbbbbcabbccddbdbbabbaadcbdbadaccacbdabcdabbbbcddbcccaccdbcdbcabaabbadbbcdcbbbbcdcddadadadbdccbacabcdaccaadcacdabbdcababadabdabcdaddababcccacbbdcbaabdbacdbbcabbcbdabdabbaabbbaccccddcabbccccccdacadbcdaaccabaccdbddadbbdcbdbbcdccaabadbabddcdbdcbbdacbbbbdacddbabddaddbbdaacdccbaabdbbaccbdbcbbdcddcdabacdabadbddacbdcbaacdaaacadabccadbadaddcbbbbdccbcabdcbaadaaababdacaddaacbdabcbdadbaddabcbcbdcdbcddbbcddaddaacdcacbadbacdcccdcaaabbaddababdcbadcdccadbdccabdaabacdddcccddcbacbaccacaacddbcdccacddacabcbccdcbdcabdabadcddabcdaaadaccaddcbbcacbbcbdcbcdcdcadcadaadcaabaabaaaaaacbdbacaaaccdaaaaadddbcbccbccaabcadaadcabddbbaaaaaacbbbbbbadbaaddacaddcdacccdcaadbbdbdcddbadaddbdbddcadbdbdbcdcdcddcdbdccddabaabaacbdadccdacddaddbcbbbdbaadaacddabaacdddaabdabdcbcbbadcccdbbbbdaacbcddbbaccbddbdddaaaaaacbdbdbbbdcbbdbdbccbdcabcbaddcbabacbdccbcaacbacaccabcdbcaabaaccadadbbaaddbaddabaabddaaaacbaccacccabcdadcbcacdccbcddaaadbacbadacaabcaacbdabddbabababbbccacdacdabbaabcdbddddacbdbadbbbbbdbcccccacabcbabbaacbaddbdaaabdacbdcccabccaadcbacdabaddabbaacabadaccacbdbaadbadadadcabacbabdcddadcbabcbadcbcbabcaaddddaabbabcadbaccdcaddadbacddcdcbbcdcacccaabcdbcadaacdccddaaacbbddbcaabcaaccddddcdcaaabdbbacadacbccbdabbdabdabdaabbccdccbbdcccdaababaddcbbcaabdddcdbabbbbcadbbccacdcdbcaccabbbcddcdadcbcddbabcbbccbcacbbaccdadcbabacbbabdbcddbdbadcadabbccaabaabbbbcddaacddcbcacbcdbcbadddbbaccbbdddaabcdcbdcaaabcdcaabababaabdcadadcbccccccbaacacaccdbdddccacdccaadcacccacabddcadabccbbdbdbcccbcbbbccaaaacabccadcabacbaaaddbccbdacadbaaabcadabbbddcadabcaaacdadbbbacbacdabdcbaccdabbdccdabbcddabbaaaadaadcabddaabadccdbccccaccbdccaacdcacaddaabacbcaaacabbcddbdbbbdaccdacacccccbbdddbbdadabbcdcaddbddbbbbdacabdabaddbbdabccdbacbccccaddbbbdbacbaddbbabcccdcdcbdbbccbccbbbdcabcbaabbacdbadabbcbccbccadabadcddddccbccbbadbcabddccaadbdddbacadacdcbccacbadabcacaadabacaaaaaaccbdaadcaddacabcabbcdbbbacacadbcadbddbdbccddcbaaaaacccdcbbbcdbabadcabbdadbbbbcadadddadacdbabaaabaacbaacdbcbaaccadcdacccccaaaccbbacadcdddbaadacbdcbcdcbadcabbababddcddbaaabddbbcbbacddaacdcdcdccdadddadacbaaddbaaacbbcbbbdbadbddbddbcabccbbaaabcaacdbaccccccdddabaabcbbabdccadcaacaadcacbaabcddbadccbdcbbcddacbcbbadccbacbbbcdcdbbdbdcdbcbadabcacbcbbbacacccddbadcdccdcadbcaddbbcaaabcddbaaaccbbbdadbcaacbbacbabdcbdcaadaabaacddccdabbbacddadaaabcbcdbbccbdaabdcbddccbacbdbdaccddacddbacbabdcabbdbdaabaabaaccbddcddacbbdcacbccdbadbdcbabbdcdababbccaabcabbcccaabdadcbdcaabcaddcacddcbcdaaacbddcbddbaaaccbbccdacbbbadbdadaadcabdbaccdadcacbaacdbcadacdabddcdadaaadddbababbbadcdcdcabcaccdabaddadadaacdbdbbbaadbbacdcdcaccccabacacbdcaadbadccbacdaaaababdcdbccabcbdacddddacbabdcbddbaaacbcbbbccbcdadaabcbaddbccbdcdaacbdcccdcdbbaddbacbdababbcabacaaccbcabaaaacbdbdaccbcaabadadcbcabaccddcbabddbbdcdadaacbccbdcabdcbcdacbabcdabcbdbcbdcabbadcbdabdbbcadcbdccaabdadadbcdababbcdddcdacdddbaabdbcadaabaaaacdccbdcabbdcadddbbcccddacdbdcaaadccdaacabccddadbcaccbabddcbaabdcadacbacdcdacccababbbbcdbbbbbccccbaadbbacbaabbccbcccdacabbddddddbcdcadbcdbaacabcdcdddabbdbcadaabadaacabcbdacacbcbddaaddabcddccbcabbbcbbacdbdcdccbdabadbbdcbcbbcabccdbbcbbdbcaaaacbccaabaabdbbbddabcdcaabacbcdabddccbbdbcccccacddabbcbdddddacabaaddbbbbadaacdaacdbaabbcbadbcacdbaabbcadcbacddbaadcaaccbbdaccaadcdbbabdcabaadabcaccbcdbacdacadaddadcacbcdbacdcbabdcabdcbdcdbabbbdacbcccddcccbdbadccbdacaadacbdadccccadcbabcbdcaadccabcddccdcaaadbababacdababdaadabbcababdaddadccccbacbdccbaaacabdcbccbcbbbcbcbcabbacdabcbadcadbdcbcdcbbdbcbccacdcbbbdaababddbdcacabbdaadaaccdddacaabbaaaacacaabcabbbbabadcbdbacdcccacbacccaadadaddbdadaabbcbccabbcacdacadbbbbcccacabbcabbdcdddccbabadbddddcddbdacdcdcddadbcccdbccbdaadcbcdcbddccbadcadcdbbbaccabbbdaccbcbacbdbadcdbdadcbdabdbddccdddddbbdddaccabadaabdbbdbbdabdcbacbcadccabacadccbbacbdadbbaacbcdabdcacdacbbdbcdbcaacbabacdbbbbacdbbbdbbbbbbbbddabccdbbcdbbdccbadabbacdadaabddabcdcdabcdcacacbbdbabddabaacabacbcbaabaccabbbccccdadabdcccdbbcbbabdaabbcadccdcdcdcbcdbbacbbbbdbabaaacbdcbaaaaadaddbccdcdcababdbddaacbcdcbadbbaabdbcbbccaacacdbaccddbccdbbccddadbacbadddbddbabbddabddbacabacdbdddadacaabbaaccadcbdbcaaabbdaadbacaabbacadaaddaccadcaaaddddababbaaaabbdccdcaabcbadadddbcaadccddbdcdadadbcccabcdaadaaaccdddcccbbaddbadddbdcbbacbbbdbcccdcbdcdcadaaacdbabdbaacdbddbddcaaadacabbabcdccdcbcbdbadddaacbacdbbbdacbcbcbbcbabacbcccabbadcdbbdadddbdbcccbcbabcadbcbabacddbcaccdbcbaaadadcdccbdaabaccadbdaabdbbcbddcabdbdacaddabdabcbaabbbdcbddcbdccdbdddbadaababcaaadcddcbaaaddacbddcdcbdccdbbababdacddcdcccadabadbdadaabdcdaababddbbacbacabaaabdbcacccddaaccddddaaaccaaddbbacccbddccabaddbabaaaaadcbadbdacbdbdddaacdadddbdbaadcddaabbacbcdbdcccdcacbbcddcabaadcdcdbdbbdcabbcbdcabdcacbdbbcdcadbdbddcbbbdddaddbaaabbbadbdbdbcdbadcdccbbcccbbdabcbadcbabdbacbbaaccadccdabcbdbbdbbdbaaacadccbbacdabdcabdcdcabbbdaacbccacbaddbdaadddcddbbabadcaaaaccdadaccbdabdcacaaaccbdcccdddcdbbbbdaddadaccaddddddcbddabbadccbbbdbbcaccddababbabcbbaadabccaccccadcdabbcddcdcbdaadbdcadbcccddaaccdacadabbcbccaabddcaddddaabdcaddadcbcccbbcccadccbcbbcccbadcbdbbccbddbdbddadaddcaabdbbcbddbdadcabcbcbabdaaddcbacaabbbaabdbadcbddaabdcbbabdccadddbcadcdbababaaacbdacdbbccbcadcbbacdabcaabaadbcbacdbaabcabdcddcddbbbcbbcaadacdddbcdaddbbbabcbcbbadbbccdacaccbbdacabddccbbdbbacdcdcccabdbcacbdbccbcbddbcdacaccdcddbbadbbacabdbbbdbabbbbdddbacaadbcdddcbbcbcdcbaaacccbdadabcdacadcbcabcacbaadddddcdcdaabddbbaacccdbddcbdbdabcaddcbbabbabddddcbbabdadaddacccabbbbcadacccddbdcddabcbddcdaacbcdcbbdbaddcbadadcabcbaccddbcdcbbcddcbabbddbdddadcaacbbdccbadcbcacdddbaaabcbabbdbadbaccaabcbbcaabcdbddcaaaccaddaabacddabbbabdbbadbbcaddbdadcbabcdcabaccbcdddddddabaabbccbccbddbcbcddbbdadaccaacdddddcaacdcdcdcbdbaddcdaccabcdcdabdddddbdaaaadbdcaacacddcccbcbacaaaadabaaaacbcdadcbbdadadaabccdcadbddbbabbbbdbaacdadbaddaabadbcdbaaadcdacccdcccdcadabdabaabdcbdadaccdcabdbccbadadabcdccddacdacdccbccbcccdcaaccbcbddbbbbaacdbaabcabbccdaadbbbacccbbbbadaabbabbbaaabacabcddabddadccbbbcbbbabcbdbaaadabcbaabcdabaaddccdbaabbcadababdcddddabcbcbcbdadbbdcdaaccbbcdbbbccaadcaadadcdbbabaabcacadadabaacbabddaabccbcddccaccadbcbccdbabbbccdccddddbacdbdbaabddadaccadadabababddcdcbbbcbdadabdcbbcbabcdbcbbcbbdccbdbbbbcccbbcdaadcbcbaaaacabbdbdcadbcbccbaaccdbbbadddddbcbabcaabacbdccabadbdadabaabaabaadddbacbaabcddddcddcbdbacddbccdacbacaabcaddbcdbdbcdbccadabbbbddadbabdabacacbaddadcddaaaaddddddabccdbaababcdaaddaaabdaadadbbbaddccbaabbabaaabacbccabddcbdacacbddacdadddaadcaddacabaadcbacdbaccaccdadcabccbdbadddaaababbacabddbbbabbdaacbdbcdbaaacdbdabadbcabcaaadcddccddbdddaabdbbddacbcabacccbadbdaababdbdcdbbacadacdcaaabaaddbacdcddcdacdbccddcdddabcccaadbadddddccacccbacbbbabbdcabbbcccdadcdadacdcbdcddcdddcccbdaaabdabbbcaaadcaccbaddccdaadbdcdadddbaddaacaaadabcaabdbbcaaadbdbcaaccdbbadabcacccaadddbaacaddccabcbacddbadadbdaadcbcdadacddcbbdcbcdddbbddbdbbadbabcccddcdbabbcaabbdbcdbcacaacacabadcdabbacdddabaadadbacadabcddacdadbddcdcabcdccdcacbcddbbbbbbadadccaabbdbbaabdddcbbdadbbabdadaabddcbdcdadacdababcdadddacaddadbcdcaaaadcdcbcaddbcbccddcbbaabaaddacacbabdcacbbcabdcacaaadaddbbdccbddcabddcdbdbadbcccdbcdbadbcbbcbbbbadcbbdacdbcbabbbaadabadcdcaacdadababaccbcbddaccaabdccadcaabdbacbbccbacbddaaabcadcacbcdbdbbdabcdabacbbcbcdadabcacbdadddddaadbabbabbcbaadadaacddcadacbbddddbccccbabcacbdcabbadbcbadaddcdcccacbaabbbcadbabbbddbcdbddacadbcdbbabcdbdcdacadcdbbbacbdbbbbadbddccaabadbcaabbcccbabcdbadcdbaadaabbbccbcdbcaaccadbadbcdbbdccabdccaabbaddbcaacdcbbcccccddadcadbacbdccbbddcaadddccdbbcdcdcbdddcdadcaddbdadbbcbbbacbbaabdbccabdcdbcdcbdcddbaabcbcadcccbadaaaaadccbadcaccdcccabadbcabababdacaadaaabcaaababcdaccddcbcdddcbadccabdabcbbbddcbacbdacaacaabadbdaccbdaddadabadbdaccbcaddcabbaccaacbcacdddacccbaddbdabaadccabccbbbbabbbdbadcbdaddababcbcdaaddbacbbbdbdaccaddbaccbcdaccbddabadadbbdcadbdcdbbcbccacdbbaccbbbabccbdcaabdcbdabadbcadacccbcbccaadaabacaadcaaacadbdcddadadabaabdbbbcdadbbcaabccddccadadddaacbbaacaccaabbadccaacbccbcddcdaabbbbaadbbdcbbcbacbdabbcbddacbcdcaccbcccdbbbbdabcabcccaabbccdbbccacabadcaabacaaabbbbdcccabbdaddbcdcddbadccbaadbbadbacaadcacccddacbdcbdadbacccabcbbcbdbcacdaabddbcbdabcabcdacbcaccabdbddcbcaccdacccadcabcaabbcdbdbdabcccbddbbcbdccbddadbbbbcbadadbbcdcacdddaccbcdbcbddcdabccabbcbbaacbbdaacccaaddababdccbbacdbccccacbddbbdcccbcbaaadbcddcbbabaacdabdabbcbdcdababaddddccccabadaccbaadcdadaaabcaabbcbaabdacabcdbacbdbabccddabbaaddadcaadcdabbdcbbdcdbdbcdbcbbbbccbdddacacdabcddddbbcabdddcdaccccbaadbaadbacccacbbdbabbbbadcaabdddccdaaaaddcdbaabaacdbdbabddaaddadbbcccdcdbcadcdbbbbbaddadacbcadaccdcdaadabbcccaacaddadadbbabcabdcbddadbccaadcdbaddbbaadababdacbacbdaadadacbdbccbdaabddbaddbabdcbccbaaacbaabadaddcadcccaaadabcdcdaddcdaabcddbbcbccdcaccbbaaddbbdddcdbadcbaacdacabacacabcdcdbdadabdbddacabdcaadacacdbbcdacabcdcdadbbcdcbbdbcdacdbabcccaccdadbacaababccdccadbcbbccbacbcdcabaaaddbdcbccababbacccbcbabdccddadacccbdcdcbadaaabbdadbbabddbddaacabcbdbcbddbbdbbbaaacbbdbabdbadbcdbacdbaabacccabbdbbacabbabaddbccbaccbccbcaacccbbddbbadacbdbdbcadcbccdacbdaaacbdacdadcaccdaacdadbaabbdcaadbaaccccbcbcdaacacdddddccdbbdcccbababacdddaccacadbcdacbdbbdbdbbcbdddbbaddbdbdabcdadcdbabbbbadcbcabaaacbcbddadbbccddbdbcbbcaddddacdabbcdaabdcdbdbbbcdbbbcaddbbbdadacdcddcbdbbaadbbabbdbcaadaabaabbadbdccddabdacdcbcaacacbcccabcacdbbbbcdddddbdadccbbddbdaadabacccbcaaadbcaacddacacbcdcccdcbdbdddbabdadcbacaaacacdbacbabaaccacccbdcaacdbddcdccdbbadbdcdcccbcbdaacbddcbbddcaabdcdaddcaabaaacddcdcbbbcdcdbcabcbabccbccbdaacdccacbdcccabcdadaccbdabbacabbcaacccddddccddbcdbcabacdccbccbbabccdaacbdccbbcacbdcbcddaddcaccdcabdacaccaabdcbcbdbaabadcadcbdadbdacbdddcaccbaddddbaccbbcbbaddcbabdbccddadcddaacacdccddcadbbdddacbbacbbacdbaaaacdcddcaccadccadcbadccdacadcddabccddcdddbbdaabdabdadacbbbbbdbdddadcdcdaacdbcbdadababbaacddaaabadbbcbbadccbaccdbbbbbbcccbdbdddddbbbcdbbdbacbbdcaaacbabadccaaaccdcdacddaabaabaadadbabacddbdcbbacbddccacadabcccabbadccaddaadaaadcbdacbbabbadacadcaaddbdbaccbcbccbaadbabcdcdcadabadabccabdbbabaaadcabdddabdbbccdcdbbbdcaababcbdadaabdddddbdadbdbcacccdaddccdbbabbcbdbdbadccbdcdaccdbbdababbbdabcbbacdcbdcbcabcdcadddacaaddaadbcaabcddcddbaccdccdbbccbcddacddbadaabddbdbcabbabccdadbbbccdaddaabbccdbaddabbadaabcacddddaabababacadcdcadddaccbbbddddbaddaccadcdabdbdadcbbdcbcbaabbcaaccbbbdcdaadbadabdbccbddbadbbddadcdcbbdaadabcbaabbdccabacbaabaccccddcdccadbbdadadddbadcabaadcbcbcbcabdcbdcbddbcccaaadadddcbababbdbdddabaaaaccbababaccdcbabaaacdddbbccbacabaccdbacbdadcadcdbbcbbcbbcadddcdbcabbbaadadbbadabddccdcbcccadbbacbddacdddccaacadcabdbadbbddadaadbabbbadbdabdcbdaadcbadcbddacdddcddddabdcacadaabddcdbcbcdcbadbddbbbcbdacbbcbadcdbcabcacdbacdddabcdbbdcbabbdcaccdbbacdbbaadcbcdcccddcaadbbdbcdababdcaabdbabbbabccccbdccddadbaccaabdaccacadcddbabbdbdaadcbadccadcaccddccbccddabaccacaacdcdabdcaababddabcabacdaabababccbaccbbabcabdccdbccacdadccccaddcdabdcadabaddbcddcddcadbddcdcbcbccacadbcdcddcaccadabbdcaccadbbdcaacadbabdcbadddadccdacdbccadbcaacccccdcbddcabbbdaccddadcaccbaddacbbbabdcacdaacaaacdcbabdccdacbdcdbabccbabaddbdbcbccacdacdaadbadbdbddbcbddbcddacbddcdabbcdcbdabdabdadcdbacddccacddbadcbcbdccbdcddadbdccdaccdbdccacaadbcdabbddadbdadabdbbdadbbadaadcbbcbbdbcccabbdadaaadbdbaabdbdccabcbbcbbcaddbadbadaacaaaccacdcaabcdbcadcbcabbdbbbbcdaaaaadbbbcadddbbdbbccadccabbcabbbcabddcdcddbacbcbacbaabbbcabcacadcabbccbbcdcdadcccadbaabccbbccaccbdbcccdacdbaaaaccbbdddccbabbcacbddbaacaabdacbdbdbbdacacbdcaaacccbaddddcbacbadaaccbbcacbdcabadcdcaacbdbdbaccacacbacabbbaadcdbabccaabbacbbbaacabcaaabdaadbbbaccaaddaabacacdabdbbddaddaacaacddcbcadabcdbbbdccbabdbabbdadacaccbcccdcddbabccaabbcdbbddbaaddaacddbcbaaaadbcbdccdabbcdaabaaaaadcbcbbdbdaabcabdaddcabaabdaabbbaddabaddabaddaaddbdbacbbacddbdbdbcdabcdbddbbbbcccbbbacccbdddccbcabbbcadbdbbbacbaccdcabadadcddbddcddcccbcbdabcbbdaabbbbadbbddcadaacbcaddabdcadcabbcbabdadbdcdcdccacdbbbbbcdcbacbaabccdcbabbadacbbcdabbacabaccccdabcdbabcdbdaddccbcddabaabcadbacaacbadcdcbbbddcdbddbdaabacccacbabdccdbacddbdaadacbbccbacdcbabcdababbaadbdbbaabadcbdabacaccdacdbcbcdabbdcaacbcbcaddcaacaaabcabaabbcddbddbcadcbddddddadcaadaabbadaadbbcbbdbabbbdababdbcbdabccaadadacccddabaabcbdddcddcdabdadadcaabbbacbadbcadbadadbbbbbabadbacdbbddddadbabaabbdbbbbcbcbccbabdcadaaadabadcadcbccbadcbcdacdcbbdccbabadbdbdddcaccaaaddbbdbaaadddacbddaacdadcccddcaababdadaaaaccbdabcdcdccacbddbcaadbbcccdcaabccdcccccccabcaccbabdbbbbbbcaaaadbccadccdcaacaacaaddcbdadaddbabdcbadcdddbbcbbacbabadbabcbcdacddcbdaacabdddbadabbddcdaddabcadcbbcabdcbacddcdbbdddbacdbadcbacdbdbcbdccaaaccdccccadaacacacadabddcdbdcdaccbcdcbadabbabcbdbddcaacacccbdcddbdccdacaddacddbbdcbcaaaabacabadbbaabccacdccaabdbaddcdccddddaabcacabcccdbbcbacbabababadacdcddbbcbddbccdcbadacbbabacdccbaacadbaaaacadacbbaacdacbbbcbabdbaabdcacdbacbdcdabacaadabdcbdaabdcdcbadcaabdadcabcbcdddaadbcbbcbdccacccccadcabbdacdabcaabccbbbbbbccdacbabdddbcbcccddcbaccbabdcdbcdbccbcdddacdacabcbabdbcbaaacadbdbabcbcdbccbacddddccdbbdcbdbbcbcbaadadadbcaaadccbacacaccdabbbddcacbcabdabcacdccdccdbadadadcbdbdadadbacbdcdcbbcaaacbcbabdbdccacdbcccdabdcddadadabacbcbbbcdbadbbacdcccabdcccaccdaccaadbaaddcdccbdabcdcbacaccdaddabcddcbbccddcccdccccacacacddbabcaaacdcdddaadcadbbdaabbcabaadbaaddbcbcbcbccbbabdbbbbacababdccbdaccdabddacbdbbdcbbcbacbacbddcccbcacaadacbabcddbdaaabbabcabdcbbbdbabacdccbcbdacccdcddddcbbbbbdcaadcaacbabacabdcbdbabbabaddbadcdcdbdddccacddcdaccccabbcabdbcbcaaabbadbdabcbbddbbaadaadcbddcaabbacdddbbcdadbdccccacbccdddbaadcdcbdbaadcdabccdaaabaaabacbbbcaaaabcbabdaaadadaaddadadcdadcbdacabacbadccbbbbbdbbdacbccabddbdbcadbbbbacdbaaaababdcdacdabbacaadbdbabcdbbdaacacadabcadacdcaadbbcdacbddbdacdbaaaadadbcbaabaabcdbcdbbcbabdccdbcdadaadddcddbaabcadcbdbcbbadddcabddddaddcbabacbacdaddadbaabbaaddddccbbabbbcacbbdaddcaabdcadcccacddabbbccddcaacacdcbcabaccaaabdcacdddbadccdbacccaaadabcbaacbdabdddaddbacbabcdabdbaccdbdbacbccdbbadaadabbdadcacccbbcccadabdadddcbbaccbcbdadadacdbccddcbddbcadabbcbbabbabaccbcccbcddaabdabcbcabcbaccdbcdaadabbbabcddadbabdbdadbdddcbcbcbbaacbaaccabbaadbaadcaaabaaaadcabaaacabdacacbbabcbabdbabbdadaacdbaaddcaabdaaacaadbbbddadcacbaaddbcbccddbdcbbaacdacbdcccaddaddadcbadbdbcacaaaaaadaddccacdaabcccabdcabbbbdabadabddcddabdddacdccaaabccadddbcbdcabcbbdddccbcadcbdaacaacbdacbdcaccdddcabaccdcdbbbdabaaccbcbcbcbacacccaaddcdbbabaccbaddddbbabcbadabcbcadcccaccaaadbbbadddabddadadcccbabccadcdcabdccdbabadcbcabcabbbaacdbdadabdacaaabdcdcdbadcddaabcbbbdcbcbaccaadadcaadaacabddcabaadabddbdacdadcbbacaacdccbbcbddddbcdadadadbccacbcbddbaccadabbcdcabadcbcaabbdabbadacaabbdabbbcbcbccccbbbbddbcbacbaaabbacddbbabaccddcdbdabdadbbbcdacabcadccbdbdcdcdadccdacabacaabbdcdcbdaaccbbbccacbbbacaddddbdaaacddbdbcbbbcdddcccbbadaddcabccbdadacbcbccbadbdbbdabdbbbacaabdcadbbdcbcbacccaabadbcacddaccaadcbbcbccddbbcbdacdabcdcbaabbbbdadadacdbbdbdddddaadcbdcabbdcbdccdaddcbbcbdcaaabaadabcbdadababbcacbcbacbaccaabddadddabdadddabdccaacbdcadbddbcadbcabaabdaddadbdcbcaabaddbcddbbdacabaabdbacdbadbbcbcbaadcdabbcdcadaaabccdddbcbadddaacacbcdcbbdaddcaaaabcdbcddbbbdcbdbccbacddbccadbbccaabccadaccbcdaaabbddcddbbabbdbbbcacaccaccdcdbbdbccbaddcdbcdbadbdadadaaaaddcabadccababaccababccccccabcbdcaadbadbdadaddbdccdabdadaacbbcdcdbcacccadcdcdaaacabbbbabaaacdcdddddbabbddabddabacddbadaaaaddbdbabdcabddbcccbadcbcacdcadccbbcabccacbdcabdbbccddadccbbbacccbaddccacaacadbbaaabadddcaddaddbcbabdaaacdcbbcdabbbbababccdcbdadbdadccdcdddacbdccbccbbaaacaabdabbbcccbdbabbddbcaccbbcdbcdccdacdbcaacaacdacdabcbdacbdccacddcdcdbddbcbaddbbcadcdaacbbccbbbcabdaccbccbdddaacaacaaacbbdbabbdbaaaddbbbdcdddbbbdcabbbcabbaabcdccdabacbdcacbcdcccdaaaacdadcccbabacdabdbdaacbdaccadcbbcdcdcdabaaccbdccdcbcadbadddabdbbadcaddddcdbcddbccacacbdadaadadccdadadbbcacaaddadadcadcccccddadcbaccbbbbcbbcdaaaccdaccaddaacdbbdadbcdabbbadbdcbbbaabcabbbcacbcbdbacbdacbbddcacabaaddaaacddccddacdaabccabdccadddcbcbdbcccdddccbaacdbcdbccbdcdbbdbbcdddaddbcacddabcdbdcababdabbdcdcadccbcadbbabccaddbcdacdadccbdbccdccbdaaddbcaadabaabdaacaaccbaacddcdddaccdbdbcccddcccaccbdcdbccaccaddacbdbcacaaabcddbaacaccabcaaadddcbdcbacdcbdccddddbddbdbbdbcaababcbbabbccadcadbacdcbdcbbdcdbacdaabcbcccaaabbdabcabbdbbacaaddbaabacccadcbbcbddbcaaaabcddbcbdabbcbdaabdcbdcdcdddcdaabdacbadddcdbbcdaadddbdbbbdddbcccdabdbcadcaabbcccaddccddddacbdcdbdcacccbddccacdcdabbaccacabcadacaabbdbdaaabdbbdbbdadadddcbbcadbdcabdddcbcaaddcdbbddbadddccdccccdcddbcaaaaacdbcdaaabacddddbbcbcccaaacaadcdbccdbabdcdaddcbadabddcbdbdabdaaaddcdddaaabdadacdbcbdabadaabcdcdcadadcddbbccbbdcdcdaabacbcdacbacbacaaababacdacdaddbcbbbbcdaaabbcccbbabccabbdddcaabbbdbadbcbacadbaaadacdabacbdcdbdadcdcaacbcdaabacacccaabcacbacdabdcbaccbddcabdcadccbacabddabababcacbdacabcddbcdcaaadbcccccdbdcddcbaadbbcdcccdbbddcabadccdabdccdacddbcbcdbbddcbbcddcdcbdccaddccabbccaacddaaacadbddbdbdbbacddacccaabdcabaaacaadbadcabdacdddabacdadbdacaacdcaaabbbddbabddcabdadaabbcbdbcbaaacdaaaadcdcaabbdbadccbbacbbaababadcadcdacadadcadcdabadacdaddaabaadccacdcbbcaccbdccacaddbcbccddbdbcbbaaaaccaaacbbcacdadbcaabcddddacbaabccccccaaabbabbabcbacaaabacaccbabdaaaccbccaadbacbdcbdbdcabccddcbdabcaacaaaabdbaccbccacabadbdbacacbcbcdacdabcbcdbcabcddbcdcdcacbbdcbbddbcaccadabbbcbdacbdaacccdcbacdbbbdaddbaccbbcacadbaaadacaaacbabbdadaccaababdcbcccacbdadabccccdaaadbcbaabcbdbdbdbdbadcbaadccbbadabcddcdbcaccbcbaaccdcacdaaaccbddbccadcbbacdaaddaadadaccdcaabadcdaacaadcabbdaddbddbcdbdaabddbbcbcabbddcbaacddbabcacddcccccbdaccccdacabacbdacadabdbcdcdbadcbddacabcbcdcccdcdabdbdaacdbaacadacddcccadaaadccbccaccacaddaccaccbdcbbcadabcbdadcabbdaaacdbcaaaddcbcbbbccadaaabcdabdbdbbdaddcadaaabbbabdcbcbdaacdaaddbcbcdbdabccddacbadcbcccaacabcdadacacbaadcaabccbcbbaabdacdabccbcdbbbdacbdccdaaaccccaadaaacdbacaaacccccddcbcbabaabbdcdccdcaddacbccbbbdbdbdbbdcbbccbdbdacdcdbddcbdddcaacbbbbabdabcccaddbcbcaaaacbbdaabcbabddacdbbdadabbdbaaddabdbcabdbbbacaacccaccabaabcacbdadbdcbbcccdbdbbcdddcaaccdaaaabdbbaadccbabaadcdbabbcdaadcbbdbadbdabaccddcacabadbdababaddbbdbacbbcddbcbbccbdbccdaaddacabdcdccdbcbccdbdbdccbbdbdbadcbdbddbabbabdddbacddccbbbcbbbcaaaaacccbaabbbabcabdcabdabcccdabccbddaaddbdabdaadcbcddcddbacdcaaaadcbacdaabbabaabdbcbccbbadacbcbddadabccdcacadcccaadbccdbbcadbbadcbddccadacbcdcdaacabddcbcabbaacddcbbccbcabaaccdbccbbcbdbababdbcdbaadccbcabaddbcdbcdcccdacaaacddadaacdcabcbddcadbcacdaacbdcadbdcacbdbacdababbbbdbbcaaccbadbabcdcbcbbcbcccaaddcaaaaccaabbdacaccddaaacaccbdacbbcabdddababaaabbcdcaadcadcaabcdcbabcdbbdcccbacdbaabcbbccbcaadcddccddcadccacababbabcbbbcadbcadacdcdccdadcbaaaaadacccadbcbabdcacdddcadaddababbcacbababcddcbdaaabacbccdaccacbaaababdaccadadaacaadcbacbabbbadaddbcdbacaccdcdccdcbcbabbdbadccabdcbaccabadcdcacabcbcdadcddcabddddbdabadbcdbabbccdbadbddccbcbaccddbcbbdacdbabcdcabadaadaabbbcadcdabbbddbbdcabacbaaabccbaabdcddacacaababcadbbcbcdabbdcdddccbacbadbacabcaddbbbcdbddcabababcddcbbcdacbdaddddcbbddbadcadadbcbccaccdcbcddaaacabcbbddabdbddacacbddadcccbbadcdbbcccaaadcbabbbbaccdbcabddaabaddaadccdaabbccacbcbcdbdabbbbadadadbaddccbbcaaaacbcdddcbbccbdbcbbbbbadacbbddbdadcdddacdbbcccacdbdbcbdcdddbdbddbcabaccdabccbaadcbdcabbdbacaaacbbcacbbbdbcbbdcacbccabbdddbacaadcdbbbabdcdadbacbaabbbcdbddcadbdcabcdbaadddcccbacaabcabddadbdaaadcbaaccbbabdcdcbaadacdccbacdacdacddcabdcadbdacdcdcaacbdadacdadbddacaacabbbabcdbbcdcdcacadbbbacaacdddddaccdbaadbddbcdcbcacccacaacdbabdadbdcbbcddbbbccdbcaaadcdacdcdcdbdabaccaadadbddabacbdbbdabdcadadcdbdbdcdcccdccdcabaabcdccaaadabcaccbbdbaddbccccaccddbccdacbabdcaabbbcaaaaabcdaaaadbdacbcabaaaabcbddcacbcddbdbcbbcaccdaccaabcccbccbacdccdcdacaaccdbddcddaccbacccaabbcadbdcadbbbdaddadaccabbdccaabcaacddaabddddaaacdbbcbbddddbbabbacdcccbbaaacaccbdaccaccbdcaacadddbdaacabbabdadaaaabcbcbaccadbacadacddbbabaacbccccdcdaaabcaaacdadcbabbbdcdcadbddacaabaccdabcdbdbbdcdbaccdbdabdbbcdddbdccccbcddccaababcacabadacddbdadddaabcccdadbaaccadacaabbacaaabbbdcbcdabdddbbcbbbaaacdaacddaaadbadacdbadbaccaccdcbaccdaacaabacdaabdbdadcdbaabadcdaabbbbbdddcbbdccacbbdbbbcbcbbdacbbabcdbadaddddaababbdaaaabdbbdcbcddcdcaadbccbccacdddcbaaddadcaabddaacbbabcdbbdcbccbdccbadbadcdaacadbccccdbbdbddcabccccbbdcaacbdcabacbbdcdadcdbadacccdcdabaccabcacdbacbcbadacbabbdaacabbabcacbdccbbabbbdddbdddbadbdacbbbcdbddcdbdbaddadbcabdcaddadabdbdbbbcdabcdcbaddacddbacbbcdcdbccdcadcbbddbdcabadbacadabbdacdcccddbdbbcaaccbcdccadccdcabcbdbdcaabbdcadcadbbbaadbbaaccdadcbdabccabbcbaadaddbcdbcdbcbbaababddaadadacdcdacbbcdacdaccdacadccbadcddbcbdaadadbcaaddaabccacdbabccdccaaaabdccdababdbadaccaaaadccdcdadddddadadbbaaaadabbbccddbcbdacadbbdddaaacadacacbccdcdbdcacccdaabdcaaacddddacddadabadbdddbbcaaddbdcddababbdcdcdbbdacccaadddddcbccacdbdcddcdabcbadcdcdcaacaacccdaaadaaadccddaadbcdbbccbcaccbbadbcbbdadaadbabdcdadddabcaaaccdacbccbcccabdbbdbccabbcccbdccaaadbabdccbcdcdabcbdccbadbabbacbbbcddddbcbddcdcbaacdaadaccabbadababaaccbcdabccbaabcddacabbabdbdbabdabbdbbbaadbbdaddcccaddbcdabbbbcaabbcdddacddbabbbadbdbbcaaddcabddbbccbadbdcdddccadbbacbcbdcdaadccdbddcabdbbdbcdcdbcdbbaddbbbbbdadbccccabbdbaddbdbbbdbbaaabbbbabcabdcdacbcccbdacddcadcdbcabacbadaacbadacdadddddadbabdaaddbbcabbcabcdcaccdcbbcddcdbdbbaaadbddcbcbcbaccabbcabdadacdbddacbcdbdbdbcdbddbdadadadcbaabccdcabccdbbcacbacaabbdbadcddcabacdabbbbabccaaccbbaabddbcddbdbdcabdcbbddaddadabacccdccabdcbbdabdddddaccdcdcaadcabcacdbbbbdbacbaadadabbaacadcddaaabbadccdcbbaaabbabacaccdcbdaaccacbdaddbabadbaaacdbbbadadcddcbdacbbabacdccbbddaabdbdcbbadacadaadddbadbdacadcabccdbcaadaaaabdcadccabdabccccbacaabbbdacabbdbccccdaddaaacccdaadadbbbadddadbcbdaccaccabdbbacccabcdccccbdaddbdacdaccacdadbbddbadccdbaddaaddacdbcdcdabcaddbabcdbbadccbdbcdaaaabccddcddbdccadbcdacbcbacbbcbdcbbacddacaccacdadacadabadcccaacbdaaddccccccaaccdbaccaacbcdadaccbdaacdadbcacbbccaadadabaddabcddaddbbaaccacadbbddcacbbbaddaadadbbadaadcccbdbaaaaadddcaabbccccaccabbbdcbbacadcbccddbbbdbcbccabadcccaabaccadcaacccdbdbcbbabcadbbaaccdadabcdbcbdcdcbaabcaaddcdbcbadababcdddcaaaaaaddbaabcbddacbbbdacdcadcabcadabbadabdbbbadcdadacadadbdabdbbcccabcddcdcbcdbadbccdaccaabcdddbabbcbbcbdbcbdcaadbbcbcdcbaaabcdbbbcbcdcbdaccaaddbadbadbbbaadcabbdabccdcbdddcdcddaabaabccaabaabcdbdacccacaccbbcdcaccdbdcbdbccdacbadbcddbdddcbaaaaaccacdddbdddcbaabbabcabaaaabbddcaccbbccabdcdcadbacaacccdbaabbcacbbbdcacbbdababcacdbaaaacccdcbddbbcbbcbadcaaacabcbdcabcacbdadacccccdccdbbbcdabbcbcbddaccdccbbbababaadcdbbccbdddccacaabcbdbbaadabdbabcaadbaddabdacdcdbdabddaadcbbadbcaadcadadacaaccacadacaadccadbbbcababccdaabaabdbdaacbbccabdbbcbddabcadcdabbbdbcdadcbbaacbcdbcccadbadabddaccccabdcbbabaadbbaccabbacddcaadbbbaaabaacdbbdbbdadaabbddddadbcaacbcdaacbccacccbbabadabcbdcadddcabcabacdbabddadadbacdabbccbaabdacddbcaaaabacccaaacadcaddacbddcbcabbdadbbccbbbabdbdddbbabbbabcddbcadcdcaddcddcabdbbdcdcaadddabdcacbaccdbcdcbbcbdacbddaacbacbcabadbcadcaaadcbbabdcbdbaadcbacbdbcbaadbaddcbbdbbddcddddddcddadbcddcbccbdaaadabbaadbadbcbbbdacbaaadcccabcddccccdaddbddadbcdacdabddccddabcadacddbbadcbaccddbcbaaabcbdacaaddcdaaaacadbdddbaadcdbdddbbaccabcabbdbdacbbabbcbbcabdbcadadbadcdbaaabdacdcccdbcdbbccdbabbdabaabbdbabcacbbbabcdbcbcddaacbbbaabdbdacbbdcdacaacbdcadbaacdcbacbdccacdbccbcdaabbcbadacbbaabdbcacccbbddddccdacabbaddabdbdcccbbcacdcbddadaaadbdaddbacdbbdccbccbdbacdadbdbdddadabbccdaaabbcabbcbccdbbacdacdbdddbdcdadcdddabcccbcbdaabddcbbbdadbcbddbdddbcababcbcddbdbdccbabdaaddaaabccccabccdbbaaacadbbdbbbdcbcdddbdbaadcbbccddcbcddbbccbcbccccabddbcdbbcdcbdcbacbcdabbcddabddbbbccaadcacdddaabaadcdaabdbbabaccdacdbcabadbcbdacdbbdbdbbacddccdddbddcdbbddbbacababdbadaccbbddaddcdbcbbbababccdacbabadacccdbbabcabdcbbdccbcdddccdccbdcbaccbcbbaddcabacabaccccdabcdbcbcdcbadcdbaadabcaccbadccdaddcaddccccdccaacccadcadcadcbadcadaddbadaadabddbcaccacbddaaddbddcacbabcadbaabcbacdbcbadcbabbddadaadccabddbddcaabdababcaacabdabaddcccabddcbbbbcdcdaddddadabbbdcdacabdcbccabdcadabbcabbbadadaabaabcabdccdccdcdccdababdbddabccdcaabaaadabdabcdbdbbbadbbcdbbaaadcaacabbcbdadaadadacdcbacbbdacbdacbdbbccbcadacdabaabbcadddcdcdcbabbccbcdadbbaaccabcdaddcbadbbcbddbadacbbdabcdbdcdbacaadbdcbccbbadacdbdddabcdadbdacddabcccccdddddccdcacadcbaabbabbacbdddccaacccbdadddcdcbacbcdabdbdcbbbcbddcadcdbccdcadacdabcdcbadcabbaaabbdadaddacaccacccbacbcaaddcddbaaacaccadccddaccacbbaaadddbaadbbdcdbcdcccdaccccbcccacdacddcbbbccdbacddaacdccccbcdaacbaadcaaddbbaabdaaababccbddcdcbdbaabaaadbdadabcdcacccadbdbbbbccbcadbaddacdccbbcbcadcdaddcdcdacddacddabadbaccbdabbccbacadbcbddacacbaddbcbcdcbadbaabcbdccdddbcbbbdcbcbcaaabadadabdbaaacbdbdbaabbbaabbcdbaacbbdaddaadbbcbbacaaccbcbcbdabbddbdbccadbbdadcdbdcacabcabcabcacbcdacaabaabbcaadbacacaacacabcdddccbacddabbcacacdbcdcbbcbcdbcaddbaabcadcaccaaaabcdaddadcaddbcaabcbddacbcbabdabccaccacccbcdbaadaacccbabbdabdcddbababbabbcbdcbadabbbacbaccbccaaadbcacaddbdcdbbcadadddcbbadaacdacdcdcdbbdcbbcbbbcdddaddbdccbdaacddbdbdaadabcddcdcacdddcabacaabddddbbcaacadbbbbbabbacdacdcccdcbdadcaccccdbadabcaddaaacccacbacccddaacadbcadcdabccbbacbbcadbcdaaddcabcdcdccbbbcbdbdcdbadaddcddcaacbdaddccbabaabdaacbababcacbcbaaacacaacbdcdcbdaaaabbaaadddcbdcdabdcbadddbbabdbdbcdccaaabdcadacdbadcbcbbbcdbaacccccdcdccaadbababddabaabdcbaaccbccdbdbbdcbcbbabcccabaddbacaccbaaacabbcdabcbbcacbaddadcddbcacbbbabbadaccababbcddbabbbdabaccabbdaaacaccdcddddbbabaabbcaddcbadaacaccacaabdbbdbcccbbbdddadacaadcdbbdabadcbdcbaacadbaddcccacadcdadcdabcbbadabdccbababbacbcaaadcdbcbddadadbbaaaabbcabacbbadccbbabcadccaadbaacaccbcacdbdbdaacddacdcddcbbbdadcbadaaacaccacbdccdcdbabdaaabcddadccbbdaabcabbcadaccbadbcbcccadabdcbaaadbacdccddcddadbbcdcbbccbbbcbabdbbdcbbbadadbdbccbbbbcbabcbccbababdddddbdaaaaccccccbbaccaddcaadbcccbdbbbbccbbcdcddccacbbcaacbadabcbcdbdadcadbdaabdbaabcbacbddbbdbdcadabadbbdddcabbdadcabbdbacdacacddbcdacaadccccdaadbdbabddbbccabbdacdcbdaaacbcbdabcdcbddcbabacdaabadccdcbdbbdcdadccaaababcabbaaadbbdadbdacdbdddbcbdbdaacccabdbcdbaaaacdbbabdaabddbdcaaaddbaacdbbccacdacdcdbbbcbcbaadcdbdbacdbcdadbcccbdaccabdbcdbdabdaddcbbbbabbbbcdcdbbdcbaddbcdbbcdadcdadacbdbadbcbbdcabbcdacdbddaddbaddcabbacbddbacdccddaadacdbabdacdcacdcababaaacbbacbaaabcababdaaaaccadbcdadbadcaddcdccabbacdacbadabcbddbbabcdcaaaadcbdacdcccbbaacacdddadbcdbcdbbbdabbacdaccccbbcccadabaacaccabdcbbbcbddabbbcbbdbdbbbacbcdbcdaddadabcbaddddcabddbdbaacacccdbcdaaadcbdcbdacadddbbbdccdadadccdcdcdadcdadaadbdadccabbacbddbdcccbcababbcaaacdaaddcccdcbacabaacabdacddbbcbacadccbabcbcddbdacbbaaadcdadbbcacbbbdcdbbaaaccdcabaacbccddccabbaddbaaacabcadbbbabaadaacabcccabddaadccddcbadadbbbcdcadcdcbbdbabbdddccabdcabbbabcbaaadbbaacddaccccacbcbacaacdcaccdccdbbacbadccadcabaadbacabadcbabccbdbccccaddadcbbacdabbacbccdbbaddbcbbdbcdcdacddccaabbddbddccabbcbaadbdbbdccababcddabddacaddaaccddabbddabbbdacccabadcaadcdccdabbcdcbbcdbcdbcbcacdbcdcdbcabcccddbdccccbcbddacacacccadbbadbddbdabbcccddacdcdccbacdabacbbccaadcaaaaccadccbbcdcabbabbbdccbabbabbabdabbacbbddcdaadcaddbcbdbabbaaacccccadacbbbdababbdcadccbdbadccdccdcbbaddbbbaacdcbbcbbcaacacbdbcbbdbaababbcababccbbdddbcacccaadbdbbcaadadddabdddcddbbadddbabcbbcbddabdacdabdbabacddccdcbdcbaddbaddabbdccbcdcdbccbaacdddcbbcbacabbcdbcadbcccacdccbbdcbaacbbbcbccadddbcaddccbdccdddcccbdaddcbaddcdcccccaddcbddddaabcbacadbbcbaddcbddccbcabbbdaccaddcbcdabacacddcadbaacaadacddccbdbadaaccacbdccabdcdcdbbbcbbdaabcbbccddcccbddddbbcbacadabbbcadabcbdccaaddccabaddddbbccbcbacacbacaadbadacbcccddcaddbaddcabbbadccadaccdcccadccccdbcbddaddcbcbaddddddbdbddcabccbacbcbadbcdbbaaddccdbaaaddabcbbadcddaabddbcacccbbbbbcaccbdaccbcadacbccbacccbbbadddcabaadadcababcacbbaddddadababcdaccdbdcdabbabddbbcabbddddcaddddbadacabbadcbdbbcaacacabbcdacacbbdabcbbacaabdcdcabcdddcdbacacbdbdabdbccabdbbaaadacdcacddacccadabbbabacaaaadcdbcdabcabcdddddccbdcdbabadcaabddcdaddcbaacbcaddaaaabdaabaacbbcbddbcbbcccadabdaacdddcacccbbcaaccdbbcdcdabdbaaaddcdbaacdcaacbcabdacdacdcacddaddabdccccccdbcbbcaccbdbbccbcdcdcdccabcccadaadbbabcaaddddaaabdcdababbcddbdbbabacbcccbbadcdcdcdcdcbcccacbcadaabbaddcacbbddcadbbdcbbcdbadcbccbdccbcbbcbcadbdccabbabaacccaabcabccaabbaccddddccabcdbdccbcdbdcbacbbabdddcaabcbdddaababdbcbabacabadcaddbddbdcddaaaabcbcbbbbbddcabcacabdbcdbaddcccbcabaabacddbadbdbdabbcddacbbbadbdadaccdcdccaacccdbacbbdbdadbbdadbcdcdacddcbcbabbacacbaccbdbbcbcaddcbbadaaccccaddadddcbdccbddcadccabbcacaabdaaccccabbaccaccbdbabbcdacbbaddbaadcbddcbacbdcdacbaccbbacabbaaadabdcdababbbabaddcdacccbaabbdbbbadcccdbacadbbccbcdcabbdaccbbddcacadbaadadbbccbacbbadbaccaacaaccbcbddcbdacadababacabbbdadacbbbccddacbcbaadcbdbddcccdbbadddccbbadadccddcabccadbddcaabbaddbbacdcbbbcdddbdcdbcbcdacdbbacccaacbcbbabccbdccbdccabbdbcbdddcadbbdccaddccaddbdaddbcbabcbbddbcbbbbddaacacdbccabdaddcbbdabccbdbdabcddbdabbcadcbdcacabcaaabadbcbbbaccdcdbacbbbaaaabacbcbcbddabcccdaaaddadabdcaccdcdacdacadcdacbdacadadaccacbdbdabccadcdccbadadbcccdbddccabcddbbbcbadcddadbabadbadcbdbbacbdcbbcaaddddccdcabbacddbddbcaddcbbdbddcdbbdabaababaadbadaabcbddcacbcbbbabdcaabcbcdcadbdaacbbcccbaddadcbdbbaddcbddbdbbababbbacdadcbdbacdadbbddbabcacbdbbdadabcadabadcbcbbdbbcadbdcbbadacaaabbbdbdacbaadcacdcabcabbadabbcbdddbbdbcdcbccddccbabbbdcacccaadcadacaacbbbdabadccbdbbbbbbcadcdbdcadbbbcabbabccbdaaabdcbdabbacbccccacbbaddccdaababccabcdbdbdabccadbdaaabcbbbdbdabdcdabaabcabcbbcacdabdccbccdccacccaaaaddbdcbbadacbdbaadddcdcccbcacdcddccaabccdbbdcbbcbbcbddcbadbbabadccabbcbdaddbddaaccabdaacddddcccadadbbcbddabdbaacdbabaddabacbaddabacdbabddabdbdbacadacacbbbbccbbdacbbbddaaadbbbcbdbadbbdbacbaabcadbdcbccabcdaabcccbbcbbcbbccadbadadbabbbdacbbbbdabdabbbacbbacddadbbbcacacddaddaadabcadcddbcacbccbdbacaccddabacccaaddbdabaadcacbadabbabbaaabcddabdddacbdbcbbbbbbadaabcbddddaabbaabdaccabdbddabacbabadcbbbcdbccacbdcacaddbabbbbbaccbbabdaddabdbabcbcacabbbdadddcbbdcbbbabaddaaaacbcbdadaadaddbccadacccaccdcdccabbbbaacadbaabddcdadcccdcdcdbaadcdaccdcadcbcdcacaddbbbdcccdadddcbcadbcabaadcadcccaccbaaaaadcccdccdaadababadacdcdddadbcdabadccacdabdcaccbbdabbcdcadbbbbacaabbaabddccaabacbbdaaddccacdadccacdcbcacbbbbcdacdcaddbccdbaccdaddccbcdbcbccbddadaadcbdcabacdcaabbabcdcdadbcbbbacdaaaaddcadadcacdbcadaccddabdddadcaadbbabaabbacdbcdddbaadabacdaadaccdcbbabbaababccaaaacaaacabaaddddccddaddcdddabcbabadaaadbcbabbdbdbabadbdcdddbadccbdabcdbcbdadbbcabbbbcaabbbbcdbcbbdbdaaaddbbcdabaaaacdaaacdcddddacccadaaddbcbdcaccddaadbbccdadbbcbadabdbadaccccbddddacadaabccadbcdabaababddccbabdaaadaacdbbcdbadaabbdcbbaacbbdbbadcbacdcccabdbdbdcdabdcacbccacadaabbaddabddbcdbcaccacbaacacbccdddabdaaabababddcbcadddadcaabaacbdbcbbddccdadbdabdbdbddbcbbddacdbdbbcdbadbacadacaccddbcbbabaaabdaabdaddbbbdbaaacabdccdccccdbdcdacdcdacbbdadaddacbcbcdcdddccdbadbcbcdddccabacdcadbddbaadccdaadaddaacccbbcbaccaacadcbaadbdbddacbdbbdacdadaddacbdbdddbdbbcaacdbddacabadbaccadabccaddbacddcaabdbcdbddbaacddccdddbbbbadbcacacbddaabbcbbbddcbccaacabcddccddaabcccacdbdddabacbcdbaadbdddcabacabbbdaaabcabdacdbccabaddbcbbdddbcbbcbcaabaabbabacddcdbacdddbbbcbdbddadabcddcdacddbbaabacaacddacbbbbaddbbabbdddabcbaccbcabccddabccccbdacdbdcbccadbccdabcddbadccabacaaddbababaccadaacdcddcdaaaacdaacbabbcbadadadddccbbacdddcdacbcbbbacddaccdadacbccbcbcbccacbdcbaadadbdaaaaaddcabadccdccbadabbcbccbccacdccdbadbcbddcbcbabadaaabbcabbdbaabaaacbdcddaacacdbbcccaaccdabcbadaadbcbacdcddccdccbbbadbdbdbaabcacaddcbdcbdabbacdcdaddaddcbdacadabbcbdbcbdabbaaadadcddcccdbbdacdcbddcdacbddddccdadddabaadadaddcdaaddadbddacbabdabdbdacbdddbcbccadacacdbdcacdbdcdaabdcccdaccacddbcbbaabaddcdbbdaaaccbabbbddadddbccbadcbbbcadcddcdcbbcabacbbccacbababccabdaccbdaddbdadcaacacbcaadbddcabacbddcacdcaaaacdbadbbddbdbbccccbadbdddbacdcdabcbdabccddadaaacabdcbdadcadaccdcababbcabbccccdcbdccaadbbcbcdcbbacdbdbbccbabbacbbbdaddbcabcbbbccccacdccdbddabadcbdbbdbbadcbaadadcdacaaacddcbbbcdaccbdacbacdbbaabaaacaaaabccbddadababbddaaabdbbcaadacaccbdabbaabddbabdbaabaccdacddbadcacaaadaaaddcbbdadbadccdabddbcbbabaacaacdadacbddcdbaccdddcabdcabcaabcadcabcddcccababacaabbacbddacdcbdddababdcbbcbaaddbcbbbabbdbbaddbbdacdddacdbdcbabdadcabbdbbcccdccbddacabddcbadbdccbbddddadcbdabacdbbabcaabbcdccbccacdbabddcadcbdaaaadadaddcdbccabddaccabdccdcacabaccdaadbaadbcaadbbdabbdacadaaacbbcacadcaadccdaacacddbcccbbcbcddcaadbcbcdabcdaaababbabccdbdcdddcabbbabacdbbdacdcabcacdbcddccccdbaaacaaccbabacbbcdcddbcccadbbabdddabccdbbdcddbcabaddaaabbcaadbcacdbadabbbbacbabcabdacdcacdacbabcbcacdccacdccccbbdbabdbbaccbdadcbbccdbdccaddaadadcaddabccbaadaabdacbbaabbacaabcbacbabaddccdcacaaabdbcbdcdadccdbccbaccacbdbccbcbcdbbaacbdbcccbdaadcdaadbcccdbacbcbccbcbccdcdcdacdadaddddccbcbcbccbabbadaaddacdadcdbdacbbbcadccddabadcabcbddacabdbcdddbcdbcbaddbdbbbbacbaaadbdbbccaabccdccbcbbcdbabdddcbdacaaddbbdabcbbacabdcbdbddaaccababcdddbbabcdaadbdcadadddcddcddcdabbcbdcdaccaabaddadacbaabdbbbcdddabcaaccabdacbbbcabacccdbbadcacdaaabbabaccbbdddbbbdbdaaabbbbbcbcadcdbbdcdccdbabaacadbccacdbcdaaaaddaabbbacbddcaacabcbcddbacadcbbcbadbabacacabcabadbbcadabaaabacdacabdbcabccaabbddadadabcbcbdcdccabbadbabbbaddacabadbdaaaccddadbddacddbddbddbaadbcaaaaadbcdaddddccdadbddaccaccacaaccdccbabddcacbddacabddaacaacddbacbadbdbcbadaabadddcbbabdabbbdbcacdccbddabcdccdbbbdcabcdabcdabcdbccabdcadcdbdcbacbdbcbacbbadcbdabaadccbabaabababbbaadaddbabdcdbbaacbcbdcabddcccdbdabbababaacbdcacbaccbbbaaabdccbdddabbdadddbdccccdbbbddcadbaccbaabbbbbdbcaabbdbccbbcddbcadbbbabbddaacadcbbdabdbbabaccadcbacabaddbaabdcabdbcbabddbdbdacbbccadcbbbbbbabadbddacdcdbcdcdbcabcbcbadccbacbdbdcbccdcdcbbbddbcbcdcccbdadacdccbbbabcaaacbbcddbdbcbbcacccadcabcdcbddbddcddbcaccccaaabaaabccbadbaababdcdccdcbccdaaccaccbbcdaadcbcbcaabdacdacdabbabbdcaccaabbcdabcabbbbdddacacbcbbbacbcdcbbacdcddbacbadcccdabdcaddbdbdbbbcdbbbababcdbbdbcdcbcdacbbacdbabcdcabdaddbbbadcdcaaabbdccdddbdacacdcadcbcadbadcaaccdbbbabdcadaabcdddbcbdbbcdcabdcccbcddabbabccdcccdbdabdbbdbabaddcaacbaabacccdadbbcaabccccdbcabcdbbabbccdcdabcccbbdcccaabbadddaadbbcadaabdadcaadcbcadbcadcccbaabdcdacabdcabbddddabadccbcdaccdcddbaadcdaaacdbacadadadcabacadbdabdbadbaabbcdaddcbddbbdcbacccbbddaaaabbaadbcaccbabdcdbdddbdccdacaaadaaccdbaadbdddaaabdabdcaadbbdddbcdbdacddcbdcacadacccdccdadabadcbaacadaccdbdbaadabadacbadbcdcbacdacdcdccdcadcbdbccacadbcaabbbacbdccbaccacbbcbdccdabcaddcadccbbdcdaadabadcccdaaadbaaaadadbcdbbccbbdadbaccdbbadbdcaccacbadacaddddbdabcddababdcbbbaabdddcbdbabbbcbccdadccbccccbddaccaabdbabbcbcadabdcdaddaccaddcdbcabbabbdacccdddcabbabbbdbadbbcabaadbbadaacdadbcccbddcdbdcdadccdabccabbcacddcbcdcadddcabacdddaddbbbaacbbaaccbcbdbdabddccdcddcabdbbdadbcbdddcdacccbabdbcbabacdaabcdaacbbcbbdddddadbabcdccbccacbacccddaadcbbdbadbccbcabbcabbbabbbcaddabbccbccbbcbdabbdadddacdbcadbccabadaabacbbcccddaacbbbaccbadaaddbdcccdabdaacbbccddcbdbccdabcbaabbcdcadddbcbdbadbabcccdcaaadcacabddadbccdcddbbaaddabdbcbcdcccbaccdbcbddbaabcbdadbdcbabacacaddadbbbbabcbaadbbbabbddacbcccbbccbbbdccdacaadccdddcddcbadddddbbaaddcaaccadbabdcdaddcacdddbbaaddbdcbddacddabbaccabccacabbabaccbadbdadbcdcdabdcbbbbdccdaabccccaabacdcddaabbdabadaababbbccbbdbbcbcbdcaabdbcabcaddacdadcdadcbacddaadddaacabcbacbcbbdbcdccccccbdabdccdbbbcdcacaaaaadbdbdccbdcbcaddaaddcabdadabdcbaabddbaaccdccabacdadcdbabbcaadccccabaccdddacabacdcbcdaccbddbbdbadabcbdaacaddadddccdbdacbdbbcddddccbacadcaaccadababacabcdbabcbdadacccadddbcbddddddcaccddcbcbacabbcbabbcacdbddbadbdbbcddbcbbacbbaddabdbbccdcbdcacaadaaaabcccadcbbccbcdcddbbdcdbadcbbbcaaccdaddcbdaaaabcbdcbadbbdacddcacaadcacdabdbbccdadcdbdacbccacbbbdcadddaddcccbadccdcdaccbaaaccbdcddbcdcacbdbbbdccaadacadacdcccdacbdaabcacbbdcddcbccacadcbcbabbbabcbacbcdaccdcababaaccbdbdcbadacdccaaaabcdabdbadcddcdadbcdcaabcbaadabbcacdcbddbabaddbbaacbddadabaddcbcabbacacccaaddacddbaddccdbbdbcaadacbdcabbadbdbcbcadcaccdabccdcdaccddbabcabdcbbddaabacdbdcabadddbabdcbacdcdaddcacbccaadcabbdaacabcccbcbabcabdaabdbadbbcbcbdcdacdccbababdcaacaaababbacadbddccdacbcbaacbacccddaccdcccaacabbbddcbddcabcadabcddbacdccbbdcaadcbabaaccddadddbdbcbdddbcaccadbbadacbbddcbbddcbdbcdadbbcbaadcddbcbaabdddaaaadbdccdcadabdbbcacacabbcadddaadcbcccddbcdabdddbdcdbcdbdcbcbaacbdbdaabababcabbdcdacbddcdadccbcbdcadadcccdcacdbcbdddddbbaccdbcaadaacdbdcaacbdbacdabacaabddbcdcdaddcbcadcdcdabadbbcabababbdcbbacaaaaacbcbabbaacabcdcbbdabbcadcddccadaadaacbbaaccbcadcaadabaabdcadacbcabcaccabdaabbbdcabcbbadcbbbbdcbbcaccacbdbcbbdbcdbbbcacaaabdbcabbddcbdbdcaddcccbcaaabcbbaaccbcabcaddaabbdbadcdcaddaababdbbdcaacdbcbbdccbcbdadddcdbddacbaccdbbbbaddabdddabadccaacadbaddbcdcaacdbccbacbbcddbdadadbadcbdbcabdcaabddaaddadadccacdadbbcdcbaacddccadbcbabaaaabcbdddabbacaccbaaddbddbadbcbabdcacbbabcaddbbaacbacdbaadacadadacbaccaabcababbccdbcaadaccbdcdbdcaddddbdbdcbcbabbadabbddbddadadadbdddccdabadbbcbbddddadbbcddabbaabbdbccaaabdaccacbbdcaacdccdaabddcdbaacdbbbaacacbccccbbbaaccdbdcbadcdcdbcddbcdadcddbbdcccdddbbdbaaccdacbdcddcbdbbddaddadccdbbdcbcddcdbddcddaccbdcbcbcaadabacddcbbaddbdadaddccdacccddccdbabcadaddaaabdcabcddddcdddcdbdcbbcacacacdbddacdbaccbadacbbcbacddabbcdcdcadcbcacddbccbaaccdacdbaddaddaddaccaaadbbcbcdcbbccddcdbddcbdccabcddbdbbcdadcbaabaadabaacdadddbdcaaccaddbcaddcdaaabacabcadabacadabcccdcccbbacababbbabdabcbccbbdbaacbaaadaacbabcbadadcaccaaaaacbcacccdbcddabbdaacabccbcbccbdbccbbaddaddcabccdbdddabcaccacbacdaabdcdbaabcacccbcbcdddaccdbaddabddccdcbdccbccddbdbddbbbbbaacdabcbcbaaaabcdabcdddcacdaddcdbbdabcdcdacddaaccabbbdddbdbddaaddcdbdbcdccbaabddcdcaddcdaadaabbabdccdcbbccdbcbcbddbacbaccacccdbddbbdadcbbaadbbdcccbcdaadcadbdbbababacddabbaaaadaddacbaaacbbaadcaadccdcbbbdacacabaccbbbbcbcaddbcbacccabdddbdcdbbddcabcddcddcdcabacaaaccbdadbccadacddabaacddccdbaccacbabbbddabbadcddbbdadacaaadcdbaaccdacbcddcaacaadadabcdbdbcccadbcabcaabcddbdbcacaaabbbbaadaddbddcbadcadadbbdbccbdddccabdabbdaacabcaaaddcadaccaabdcdcbcdcdacbdabadcadddbddcbcbbaadcdcbbdddcbbccdbdddcccbcbcddbadbaacdaaccbcaddcdbadbbcacbccbbcaabacbcacddabbcddbcdccabdadbbcdccbcabcddbabaccddbdbabbacbbdadbdaacdadcbcccadbabbcdcddababcdbddbbadccabacaaaaacdadcccabdacbccbacbbdbcdaadbdccbbbccddacabccdacbbdacadbdaabbbabdbbcbaacbadcbbabaddabadcbbadadcbabcccdbaabadccaddadbcbadabddcbcbbdcbcdadabcadcbdccdccabadbcdbdadbcbdbaabcadabbddacbdabdacbbabdabccdbaacddcddcabdcadabcacccaaccdbacaccbdcdbdddaaaaccacaaaadcdaddacbbcbbaabaadaaabdaaadcabaaddbbadaaccdbdbbacbdbbbdacbddaabccdbddbabdabcbdbbdadbdbbcbaddadbcdccbccabdbbbcbcbdcccbcbcccddbbcbacaccbdbdadacbddbbdcbaaddddcaabdbbbaccdbbdccbdbacbbbccdaadbcbcdaacbdadbcbbcbdbbbcbadcbaadcaddacdbdddaacaadcabbdacbccbddcdabcbcaaadddbbccdbacdbbbdabacdadcdcdcbccdddbaccadadaababdabaacabacdbcdcaddbcbdcbcadddabbaccacbabdbbaabbabcbddcbdbdddabacababacdddbcdacadccdbdcdcbdadddaadccdccbdbbdabaddbbcadaadaadadbbbabcddddbabdbbacdbdacabdccabcddabccbaaabddcbbdadaaaaabcccbadcbddbdadddabcacbdbabdcdcdbbbdcccdbdccbddaddcdddadcdcdadddddadcdababcabccdcaaacabccddaacccbaccdabcddcbcbadabbbccabbbcbcdacdccbdadbababadbacadcdcbacdbddacadbaadccacbacaddcbbdbcaacccdddcbacdbcdddbaccaddadacbbdaacdbaaabdabbaacccdbacbadcdccdbabddbadaabdadcdadbbbdcbcbddbccacdabdbabadaaddbccdcbcdbdadbbcdcdccccbacbabbccbbacacccbdccbdbcccbdcbddbdcaabdcbbdcdabaabcacdcbccacdadacacaccbddbaaabadbdbcdcdddcdccabdcbdcbaaaccadbbbcaacdbcadacacccbdabbacbccbdcdaddbbabdcaaccdaabbbcdcaccbcdbdbbcbadddaddaaaabbbcababcaacbbaacadddbcabcbbcbbddcacdcadaddbcbcbdaddabccbdbccbcccbadcaabacddbcbdccdabbbcacbadcabbdbccbbaaaadabaaddcaaadcbaadacbaababaddbacbccdbadbddbcaaadbaabdcbbdbbadabbddacbaccccdbacdbddbabccdabcbadaaabdcccbadadabbbcbdcbcbdadbbcddcddbaadcbadbabacaddaccddcacaddaadaaddbbbdabbaddaaabcddcabccbaabbaaadddbcdababbaccadacacbbabddaaabddacdbbacbcaccbabddcacddabbbcdcddbacbddaacaaadcddbbcbaabcbcbbdcbbadaacbcaccaadabddabddbdadcaadaaccdbbcadcdccccaaadabdccacadbbbadbabcccbadcacbcdbbdcdbbbabbaaddaaadbcadccdcdaadcddaabddbcbbadcadcaadadcadacdbaddcdcdbccbdbbabccaaddabbdadccdbacabbaadcaccdaaabdbccabcdcbdbdddaaddbcdcadabccbbdabddcbddbcbdcddadccaaaccccbaacddadccbcacdbbddabcadcadbacdcaaabcbddddbabdabcaccbbcababadadadddbcbbddbddcababddbcbaaadcbaddbdabbadddcadabaabdbcadcacabbdaacdaddbaabcadbabdaadcaaaccdcdddabaabdbcaacdcdddcdbbababcaacaabacadacccdadbcabbbcdccdbdccaadabcbbabaccddbbabbdddbdacabacbbdacabacacbbcabdbcbcccdabacbabcdaaabcaddccadccdbacdbcaccbdcbabdcbdbbcbdbdbbadababadbbddabadabbababddbaaaadbdcacddbcbaccaabdbadddaaacaccbddcbabadbbacdbbccaabbbcccdbbbabcbccbbbcdaaabbbbaddbddbdcbabbcbcdabacdbacdddbcdadbcabccacdccccbaabbabdadcadadbbadbbddacaaacdabddabdadcacdcbbdbdcbdcdbcdadcccacaadbabbbaacaaaaabddacaddaabdccccbaabcbcddacbdadcdccaabbbabacdbcccbabcabdacaadbddbaadbadcabbcbabbacabbbddcbabbbccabdccccbcdcdacdcacbbdbcdbadabaadacabddabdbdccacdccdbcaaaccdacdccdacdbacbbbaddadaaabdaadcadbadadccaddabadccddbadabccddadbdaccbadadcddcabacabcadbbacbddbdcbdcaabbddbcabdbcbdcdcbbbdbdcdbadbcacccbaadaacdccabddbcadddcccdabbdbabccbbabbbdbcaaacdbdbabaaacacbcbcaadcccdbddcbdccabcbaccbbaaacdacdadbddbcbcddaaccbddbbdcbadbcacccbdbdccdadcbcdbabbdbacbabacccabcbbaacccddabacddcbdcddcbcbadabdabbcadbcacadcadaaacaacbbbacaddcccccccabbdcdbbcdabbdaadaadcabcdbadacddbdbdcaadbdbcbdddddaabadadcddcddaaaabdadaaacccccacbdbddcdddddadccbdbcccabcddcbcacbabdcbddbcccbbaaabaaacdccdddcddddcdbcbadccbaccaaadbacddabcbbcbabacddadaabaadacbdcadbaacddabbaacbddddddcdcbacaaacabbcaacdcbbaacbdadbcbdbcabacbbacbabacdbadbddabadadbaaaccdaddaccdcaabbddcaacadbabacbddacbbbccbdcbacacbcbcdcbabccadcddaacbbcbbccbcabcdccadddcbabcacaabcacbdbdbdabcbddacdcdabdbabbaacdccddcbbbdbcaccbbcdaabdabdccccbaddabbabaccaaacccaaccdaabddaababccacdcaacaddbdccccdddbbcacbcbbcaaabbbdbaddbabdacadbbdbddbacabcbcbbcdbdadcaccdbadbbbdacaababcbbacacdbdcbcbbcbdcacbacdaabbdadababdadacbbbccaaadcbbbddaabdbbcbcdcbbcbbabdbacbcdbcdbddacdaacccbcbbdbabbbdddddbadadaaaaddbbcccaccadbbaaddbdddcdcddbaadcccabbdbdcbcdbddcdabcacddbcdbaabbddaddbcdddbbaaabacdcccdacdbcdbdbbdccbdcaabbbdccbbcdbadcacdbdbccdbdaccabdcdaadacabddcdcadddcabacbadaacdccddddaabcbabbabcdddcbabcbbbacdddccacdadaadacbccabcdadbaccaabbddddadacacaddbabcaacdbbdcdadcccaadaaaadbbccbcbcbacdcddababaabbadccdabbcbcbabccdabcadccdcbdbbccbdbadddcaddcbdaaacacbbcdbdddcadcabbbdacabcdbcaddadcbcdcdbbcabaacbabcdddcadccbcccbcabbbcabaabaddcabdacbcccaababdabdcdacdcdacbabccbaddabccdbccaccdbbcaadcccadcbcdbdcbcdaccddadbddbbbdcbaabbcbaddcabadbdbbbdccabdddcccbdccbdcbdabcdddddadbcbacaaababcbbabdababbadcccdacdbcbadbbacbcccdcabcbcddbbbdaabbabbbadabcadddbdddaaabcbccdcabcabacccabdcccddaaaabaaacccccabddddadcacddddcaaddbaacbdbcccbabcababcacabbababbbbabcbbaccbcbdbbdcdcbaddcadbdaaacbdcbccadcbcdbdaaaadbbbcbdcdacbbbdbdcbdbcdaaabaccbdddbcdacddccbddcccbacbcdbdbddcaaadcdbbdabdabbbddadbacacadcadccbdcdbadcbcbacdbbddcdcbbbddaddbdcbacacddbccdabdcaabdaaabdaacacdabdcbaccbbabcdccaadddaaccaabbadddbaaabdbbccdbbdcbabaadabcbbdcdbccaadaabbabbabcdcdadaccbcaadbbbcdacaccddbcdcdaacaaacabdcdcbbabbbbbcccdcdbcacacaacbcddbbcdbabadacbcbcbacaccabbacaacbccadbabdbbcabbbdbbdcbcdbadaaddddacbddbdbaaacccacdbcacabdaabddcdaaadadcadddcabacadacdaddcacbbbcbabddaccabdbcaadbdaabcdcabdacdcbcbaacabbddcbcdbbaabbbacdbdcabdabadccbdabdcdbbbaabadadbbabddcdcaabdddbddcbbbbadadbdbbacdabddccddbabadaabcdbbaccbdabcccbcabcbdbbdacadbaacadadcddaacdcbbacccbdcacaccaadcbbccbdacbbdbdacbaacadacaaaadcccdbaccbaaaddcbdbbabbbdbdcadabcdbcacbdccadabcadbbbcdcccddbdcbbbdcbdbddadbbcbcbadbccaadbddbccbaacbcdbcbdabdddabccadaaddaccdabaadaadadabbcdcdcbbabcdbcdbbbccdccadcaaacdddcbabadddbbbcaaaabbcdbbccbcaadabcdbbcbbcdcbdddccadcbaacddbcccbcddabbdaddcbcbacdcbdbdaaabbbbacabdccbbccbabcdcaadbaaacbcdcdbaaacacbdbcbaaaabccbccbaaadddacdbdcdbddaddddcbaadcaaadcddbbbaccdbacbaaaabcabdddacdbcaaccaccacccadcbacdcbaaddabacbbdabdbddacaabbdccaabbaadbddbbcaaadcadcbacbdccccbacccddabacadabdddabadcdabbdcbadbabbbbbbbbcbccbabcbbddccbdbbcacdbdadbdbcadcdadadcacccbdcdadbbbacbaaabdcbdbdcacdabcbacdabbdcaabcbbbabdaccaabbacacbaccbbddbaccdbaabcaddcdcdbbcbdcbcaabacaaabdaaabbcdaddbdddccdabddbaccadbaccbcddbaabcaddacadbbcbaabbcdccacbbaabdddcbddaacbbcbbcddaccaabbccdcccbaddabcdabacadbcbbcdaacddbcbcbbddcababacbacdabcbddbbbdacbdbddabcacbdcaccabbbbbccbbdabcddcdccabbdddbacbddbcddcaaaabcbbddaddadbacbdbabccdbdbcbdaaacddbaaabdddddabbcabacbbadbcbbadbaacaddcbadcbaadcdcdcbbddbcddbdabcddbbdaaadaaaadacbddbddcbacdadbbadbadbadbdbbdadbbbddcdcadbabbcbbcabccbccadcadbabbcbcaddcbccbccdcbcbccacbdabbaaabcbdbcbcdbdcacdcaaadccacadcadabbdacadcaccbccdddacbbabbadcaaaabcdaddadabbbccacddcadaaccbdcbcbcaabadbbcdaadacbcbddccbdcaadbdadbdccaddbbbabbbcddbdddccacbacadacddbadbbbcdababdcddcdabccdbabdbdcabaaddcbabccadabbdadaccdbbbadbdacbdddcacbbdacdabccdabcbdbbbbdcdcccdbbbcdaaaaadaaadaaadcccbcbdcabcadaccadbdcaabcaabcacdaadadddbbbccddadabcbdbdbbdcbcdabdabccccbbdccbbadbabcaaaaabadabaacbabccbbcbadacdadadbdaaabbbcadacabbbaabccccabcbdababbdddbdaadabdadbccccbdbbcdcaacadabddbddacbaaadcbcdaaaadacdbbcbdabacabcbdbabacaadacbbbddacdbacbacbdbcbcadaaaddadaccdaccdaaddccddcaaaddbaabcaccadaccdacbdadcdadcdddcbdccaabaaabdaaddbdcabccaccdbacaabbcdbbdabdddbdaabdbcddbbccdaadacabcbbccbdbbbdbcaaacabddddbbcaddbbdacccabcccacadccdccbdddccacbcdcaabbccdbdcaadbcdbbdabcaacabbcbdaccbdbaabccaabbbbcbbaacbbdcbdcadbdaccbdddbdbccaccadbdaabaadbbcacdbcddddcbddabacbbdaadcddabbcadbdcbcbdabdcbbdbdbbabbcdacbcacaddabbcadcacbdccadacaabcbbcbadcbaddaacbcacababbbbbdacdadbcbccabacbbacbacadaabacdcdbababcdbbdbadbddbdbdcdbacbabcbcdaddacdbababbbcacbdcbcbadcdabbcadaaaacbcabbabdabbccdaabdccccabbacacdcdcbcaadbadddacddbbccdcaccdccdabbbbdbcdbbcddcbccadbccbdbcbcdadacbbcdbbabcdcaacbcaaadddddabddbdcdcccddbdacadacddcadabaaabaaccadacbacabbdcdabaaaacdccdccadbbccacbaacabddccbaabdcdbdccadadbacdcdbabcdbaddcabcbdbbbdcadbbadddacadaaadcdbdbddcacbdcdcdbcabcbdbbdcddaabacbabccdaabdbdbcbccaddaacddaabcbddcccaadabdadaaacbcddadaadbaddaddbdaddddadbcbcbdbbaadcdcbdddabdddadabccbcbadacbbdaadcabccbdbdaaadabcdabdddbadbbccadaaabbbccddccbdcdbbadbdacbabacdacaadcdddbcbabddbcdcbbcacccdacdbddadbddbcdcbcccacbbaddbdcacdbcbdadbcbbbbdddcaabcadcdddccddaadacaadddadcbdccbbbdbdacabccaccbdacacadbddcbcbbacbaaacddcccddbacaadcdbddaacddbbaadbbcdacbdcacddcbddccdabbcdadcccbcacbddccaddabdccbadbbcbadacccbddbbbcdbcbdbbdcccbbcbbbaacacbcdbdabdbbdddcddcccccbabcacbddcbccddadbaaacbacbcbbabababcbdacdccccadcbddcdbbaadbccacbbbaaacdddaadabcadbbacabccaaccbdcddcbccaccdcadbdaacbcbdcabcddaacbdcacbcabdbbacacadcbbbcdabaabdbbcaacbccbbadcddacababadccdcbdcbbddcdbbbbddadddaacccbbddadadcdcaabdddbcdbdbdddddaadcbadccdccccdbdcddbdbccbddcbabbcdbbbcbadaddacbabdcbcbbadcacdacdabddddbbbdbcbdddccddacabcbccaaaccaaadacacaaacabdbddabaaacbcbbdaacdabaacdaddbbbbdcabcdccbcadbbbacaadadcbdbabbdadcccccabdccbdabdcabdcbdcbadbbddcacdddbadddbdaadbabbadbaccddabdcbadcbbaccbabbddaacdbbcbcbaadaadababcaabbdcdabbaddcabcddbccccbcddbdabdcccbcdcccddddbccddaccadddacccbabbcabbacdbaacacccdbadbcbdbabbdbddcccdbccbaccbbcccaddabdbcbbadbabccaabdbdcdddcbadddbbdccbaccbacaccdbbcbdaccbcbbbdbcdaadbbbddcdbdbdabbadacabdbaadcbcacdbcaaaddbcdbdcacacbabddcdaccbabcbacabbaaccddaacbcaabbdcaaaddccdccbdddbabdcdadcbbdbbaaaddabbdadbdbdbbcddadbbabdcbdddadcabadbabaddcbbaaddcbabbcaccaacdaacaccabdcaacaabcdbbadbdabdccacdddcacdabcbaadaaacaadcadbdbccbcabccccccaddbdaccabbcadbaacccdbadacbcdddbcabbbccbbacdddbcaacbbacdbabcdacbcddbbabccbcbdbcbcddadaacbaddbadbcdaddbcdcccddadccaacccadcbcdbdcabaaddcaadbababbcaccacaaccddaaaabacbdadcbbaccdbcaabbbcabdacabcabadddcbdcbaddbabbdbdccbbbbdbbbaaabcbcabacccacdcbabbccccacacdddcddbbcdcbdbcbddcccbabbbcbbbdcdaaadccbddcdcdcbaadddbdbbbbaabddaaaacabdcbcbacddabdccdcaddbbdbccaaacdcbccaadcbcbbdadcdccbddccabbbdadbdbdbddddbddccddcddcdbbcbaabddcbcadadacdcabacbdcbadddbaacabddcdbbcbcdadcccbcdccabaabdabdbbcacddcdcbacabadbdbaacbadbbbcaabbdbbcdbabddcccdddaaccdcaacbbdabbdbbacabaaadaaabaaddcddaadacbcabcbaabcabbadbababbcdcccdacacacddadbabcbccddbdbdbdbbaddbbbcdcccdbaabcabccdcbbbddcaadadaacbbabdaadccccbcbacbccbbacbcdcadabdcdbdcdcaababddacdddbabccdcccadbddbcdbdcccdddbaccaddddbbdadabcdbcdacdddbacddccbdacacbaabcbdadbabbabbcdbacbcdcddaaaabccaabbddbbaddabbdadabddcdcbdacbdbbcacbaacacdacbbacdbbcdabbdbacbcadabcadabadcdbabadbaccdcaacdcbbbcabdbaaccdddaaccbddaddbacddbbddbabbdacdbdccacbddbbbddacacdbbccadbacabbdcccbdadcbaddcabdbcdacaadcbbcaadabbbbdbabbbaccdbdacaabbdbcaacdddcdcccbadcaddcacbcbcbaddabdddcbbcdbdddbccccdaacbbcbcddcccddddccccbcbdbadbacbdcaccddccbccacdacacacadadadacdaccbbdccbaccddbdbaadaddcbaadbdcdabadadabcdacadbbacbcbbcdcacbcaadabcadcbdbadacccdbbcdabaccdcccdbcabbacdcccddbbdbccdcbcacdbddbcbcabccbddcbccaacdcccadddcdcccaccbcbbddcabdaddcdbccbccaabdcbcacaacddcabbaababaddbcdbbcadcbbddccaabcacaccdddddcbcccccbbbcbccbdbacdccabbbaccbacdcddcaadbdbacdaadabccaacbbbcdcdcccacccddbbcaaaccdacdccddbabdbcdcaabadddbcaaabababbadcbbacacbcacdcbddadabcbacadcacbcbadcadddcbbbaccadcbabcddbbccddbabcbbdddcbabbcaaadcdccbddbdbbdadbccddacccbdbbbcacdbcbaacbacbcdaaaacdccbaacdcdcccbdcabdacabcadcdbccacaaddbabddadccbbcbdcdcadddddacddabcaccdacdabbabbddbdbdcddbcaabcdcdadababbbddbcaaccadaaadadcbddddbccbbcdcadcdbcadcccccdbdcbcbcaddcadbabbaacaaddadcdccbadacabadbcdcbddccdcadacddabacabbaadabbbcbbbadcdbcdaabcadacdbdadbbbbaaacadcacdbabbacbbdbcccacadbdcbacdaadbacadbaccdddbdcbccdadaabdcacdbcbcadbadccacdddbdbdbddccdaaaacabbbbbbcdcabcbbbbdcdacdbddcadbdbaabbacadcaabbbabdcabddcdbdadcdddcacadbbaadcabbbcbbacbaccadcdabbdbcbabdabbcabccbcadcdccdabbaccbadcaddbcdadbabcadabdccdadbbcbcddbbbcaddbccccccbdcbdadcccaaddabdbabcbcbaddcbaacdcddbaacdcbbdcdacbcdabcaadcbcbbadbdabcddbbdbdadbdbbdcabdaccadabdbdbdcabccbadadccadddbdbbbdcaacbcddadcbdcbadddbdadbaaacabaabbbabbbbbbbbbadaabbbdcbbbadbcbcccaacbbacadcabbbcbadccbaadcdbcaccbdaddcdbbabbaadbdbdcbdbdbdcddbacadadadbdadacdbcdaddaaddcabacdcdcabcbccadbbabcdadcbdcbbccdcaddaacacdabdabbaabcbadbdcbbababbdbdcbbcddbaccaccbddadabaadaabcacaabdcadcdadbdcdadbdadcbdccadbcadbabdacbcbdbaccccabbdcbdcabddbccdcdaddcdabddacaabddbddddabbdbcdbaaccacbaadbaaabadbaadbacbaccaccdbcabdbdccbbadabdbabaadccddcddbddcadbbdcbbaadbdbbcaacdbdddbabdcbcabcddcccbbbdcccdadbcdbdabccaddbdababcaaadcdadabccddabbaabaabdcbbdbbcbcdcdccbdbaaccaadccbdcbcabaacbcddacbabbbdbdabbcbbcbacacbcdcbbadababadcbbbcaacbadddabaadbccdbbaadbcdccbdbadacacacbdbccaddbddbbbddaddccaabacbbababcabcadbdbbcbcaacdacdabcbacbbbcbdcacdccccdbbbbaaacabbbbbcdbbdabdaddabccbcdacacddcdacadddcaacdbabdbbbddbcdbbcabdccbdadccbadadabbcadabcddabdcdbdcaddabbbbdddbadcacdcaacdbbaccdcacddbcabaddbcaaacccaacadbccdbaaadbbdabcbdacbcdcdbdccddbbdaccdbcbddaababdbdccbdaaccbdcccadddbabcbddbbddddcddbabcbaaaaddcdbcdadaabccdcdcadddbcadacbaacbaadbccababaabdadbaddadbcadddbcabcdcaabdcbbdbaacbbbbacddbdbbccdddaaaddcabcbcbbcbaabcdcdbcbbcbdbcdacadbcadadbddcdbabdbdbabddaacbdbdaadccbbdabcadbbdacdbbdaabaadaccbadaabdaabbcdabcdcdddcaaddadbaadddcdcdabbcdbdcbdcababddcbddadadccbddabacdaadcbcbbdcccdccdbcacdcdbdaccbadbacbcbdbdbdcdbcbcdcbccdbdadbdacdcacbdccdabbdaaaadabddacdaddcccccbabddcbcbbdaabaddcbbdcadbbababacacacbaaaabbdbadbadbbaacaddacccadbcbdaacbddaaabdaadcbcacdaadccbcdcbcbddccdabdccbcaadabadcdaadbbcdcbabcccaadcdaadcdccacdcaaddcbaabacdcdbdbaabaadcaaabddcbaacbbcbdbdcdddcaacccdaaddabadcdccaabcccdacadaddadbbcccddbabbadbddccacacdabaadacdcaaacdacdcaadddabaadcdbcccbbabacdbaddbcccbccdddbbccbababbdacbddabcdadabbdbbcbcdcaadadccccdcdaabadadccbcddbcbcbbbbcabdddbcaaddbbcdbdaddaaaacacbcdbdccacdccabbbacdbdaaaaabaaacadaadaabacbadaaabcdddcdaccabcdbaccdaabbcabacadadcccababddcccdbabaacaadcacccccbbdaadddbccbbbddcaabacbbbbddcadcbbbcdcbbccacbcadcdbaacbddbbddccccbacddbcbdcddbbcdaddcabbdbadbbabbbdccacbdddcabcdddbddcbcbbcaddbaadcabbdabdababccdcbdbdabbccadddddcbabccccbdccdbbaccbaccdbbaddbabadbcdaaaccaacabcdcdbdbddbbcaadbadddacccbbbabbbaccabacbabaacdddbbcdcabdaccddccdaccdbcccbcbcadcaaccadbcdddcdaacbbbcdadbbcdcdcdddbabddcccccabadbbbdddaadaacccbcdbbaabcbbaaacabddcacdabdaacdcbddccdadadbcaabcaabaacccdccdbbddadcacbabccdddddcbcacdbbaabbbcdbabbbadbaccaccdaccabcaaaadbcaadcbdabdbabdddcdcbccbadbbdbcacdccadccabdcbcbbbcdabacbadabddddcaabcacbaadbbacbcaaaadbbbbdadcdccbabcdccabddcbcbddddcbdbbabdccdddaddadaddadbacdadbacbbbdbdacddcdbdaddbccbbaabdcdbdcddddadcdabdbbbaabdbadbbaadcbaacabdcababcabccbbabdcbcbadccbddbabbbabcccdbabdbddbcdbabcddbdabbcbcabdcbabddbacdcacdacdacabbbcadabcacbcbdaacaccbaddcdcdabcdacdbdcbabadabacbacbcdcaddabbabdbdbacabbcdacdabdbddbccddadccdaddccdcccddcacacadbcbdcbcdddbadddbaacdcabccdaacaacbbcdacccbcbccaccbcbdcaaccacdacdaacadccccbdcbaacbabbbbbdddaacbbacccabcadcbcabaddbbcddccdddddbaddaadadaaddcbaccadccbbadbbbccbbaaaaccbbdddbbbacbcadccdacbdddcdaadccbbbbdcbdaaddcccadcccaacccadabbbdcabcacbcdccbadaddbdbbbcbcbccabdccbbbaacbadcaaaaccdcdbbcbddbbbccbdbdcddbdcdcdccabddcdcbddcdbbcddbdcbdaccdadabcabaddbabdcbbdbcacabbbdadbabbaaaadccddabcbcccdcabcdadcccaaacaddadbacccdcbdddaaabddcbabdacbcaadbcabccdbdbbdbdbcbadaddbdbdadccbdaadcbaaacacaadcbdcbdcdaddbdbadaacdaaaacbdbdabcdbbbbcddaccdabbabbbdbdcccdcbcccdbdcdacdbaabcacdcaddcdbcabddbcacaacbcaaabdbdadbabdacbccaacbcdcdcddbdaabbcdcbbdacacaadadbbdbcbcdaaabdbdaadbadcbdaaadbccadabbdcbaacdbcaddcbaccbddbddbddbacbbcadddcdbdbadbbbdacadacaabdabddbdcbbddbcddcabbbbcdcabbabadbcdccbcdcbacdaadbcbcbdcaadaadabcbabaabbacbaddcbbabbdadacabadacccbaababcbddbbcbcacdbdadabadaaacdddccacbdaccbbabcccaccbcaacaccadacdcbaaaacccbaacdaccabcbcadcadcababaadadccdadbddcccdbcbcdddaadbbacadaadccbcdddaddcddaaadaddcbddbdabcccdcaacacdcabaccddcadbdcacbcbbdcadcdaaddccccacabacccbaabadcdaacdacaddbcbbccadbbdbbcdabccbdbbbbbbcbcbdcbddddcacbdbcadcdcbdadabaabdbcbddaddbddcdabcacddcabdcdbbbdaadbbdcacbdddacdacbbbacddcdccdbcbbdbadaadddccaddaadcccdddccdddadcccccdbcbcbdcdcbdbbddbadcdacdaddcdacdcdddbaadccbbbdbcacccaddaddadbacbdaabbbdacadaabadddbabcdcdabcddbabaddaccdbcbdbbbbdcbbddcdbccbdbdadbdacddaccdbcdcadcdddddcddaacbdbdcbbcbbaadbadcaccbcabbddadadcaababbaaddbcabcbcddaaabcabcdcbddbbdaaacbbccaabdaacdddcadcabcbdaacdccabaacbddcacbcccbddaaadaddacabdbadabbbbabcabacccbaacacabdccdcdaadabcbaacaadbbbcbaadcbaaddaaaaaddcbabbbcbacdcbddbddbcddbaacbbdbccddbaaaaaaadacbcdddaddacbcaaaccccacbdbdcacdccdaaacdacaddbcadabababdbcacdbcdaabbbacacbdbaccaabcdbacdadacdabcdddaddbdbcaccdbadadadcbcbccdabdcdbaacbbaadcacbbcabddbacbbaccddbbbadabdbaddaadabdacaabcdbcbdcabbbadbbdcddbadababcdddcbdbcbcbcabbccabadccabddcdaadcdbbccaaadacdcbcabddcddbddbcdbcdcdbbadccccaddbdabcbcdaadbbdcdccacdabbdbbcddbbdbadddadbbcadbcdabbbddcacbbadbbacddcaabdcaacdbddcdcdbdccdbccadbdbdaaaddbcdcddadddbcdbbcbcddcabacbaabbcbcbdadababcbbbcadbabbbcdddccddbaaabcccbaadacdcbabdbacaabccbcadcbbaddddcbadddcdddbddadbbadccacadacbcbadbcbcaaadccbdddaabcbcbcaddddbbaccabddbbdbabbcccdbcbbbadaaaddadcdbaadbcbbbcbbccbdccdbadbacaadcdaabdbadabdaababacbdbbcdaadbdabacbddacbcdcbaadcdaaacdbccbcdcdcbdcdddadccccccacabdccbddcaddccababcbcaacdbdadaddcaddacbbcdbbcdbaccbbccccbdcbadddbbcbcdaacddadabdadabcddacdcdadbdccaaaaccaababdbbcaaddddbabaadbdabddadcabbaadbbaadaacddcdcbadcbcbcbddaccddcaadbadbcdbdcabdaaadcbbcdaccbdbccbaabaaaaccbacbdcbdbcccdddbbbadaaaccbbbadcdaacdcdaababbcccacadcbccdaddbabcaaccacacaaaabdcdcacacbccacbabdacababbbcdbacaddaacbcbdacadacabbadbdcabbadabcaaaabddcddacdacbbccbacddddaadcadaabacdaaabbabddcbbbdadaccbbdabbabddabdcbcbcdcbbaacacdaccabcdadbcbdaddacbbbbcddabcbbcdacabdcccbdbdbdaaaccbcaabcabacbbbdbdacaacaaabdcacadcdbdcbdaddadbcddddbcbabbdcbdbaadcbdbdacadbcdcdcabcadccbccccdadabccccadcbbcccdbbbccaadccdababbbbbbcccadcbadbcbdddadbbbcbbdbddbaabdbbdcdbaabbdcacacdaabbddddddaccdbbcaadbccdbabcbcabbbaadddbadbdbccdddbabdddccbaabaddcadaccdbaabcaabbdbbabadbdddbabdcbdaccbdddbdabbadaabcdcabcbbbbcbadddabbdcdccbdcadcbbbcbcbbacbcbccbbacabadbacdbddbdbcdbcabccbccdbadacdddadcdccbaddbaccdbaadbbcbbcaccadcaccbcdaccabcbaccaccadbbbcdbbbcdbabaabccacccaddbaaddddcbabaabcbbdcaddcacdcbabdadbcdcadccdbbabcbbaaadadbbbcaccbdaaacbbcaddadbdbbbabbbccadbcbbcaabdccbddcbdcadbacaacccccdaacbdcabcbbccbbddbccdcadacbabbdbbbadabccdcabbcdcdcabaccbbdcbabbcacaadbcddcabaadabdbabbcbccdbdcbddaabccbcacccbbbbcbbdbddbcbcdcccbbccaddadbadbbddbbccbbdcdbaaccabcbacccccbccbbdbbcbcccccbddbaccbdbadcbaadaadcbcbcadaaabcdcddbbcadbbbabcabddaccbbcacccaccbdddbbdaaabccddddaddaaaacbbaaaaabacbbcccbdaacacabcaacacdaaccadcabbbddadcbaacbbdbdcbcbbbcaabbcacccdaaadcccdccabdbccbdaddcbabcbaccabacdbcabadddbcadcccbcabdadadcdbbcadaaccaacbbabadcccbbcabbabadccdaddaaadcbbabdbcdddadaaaaabcaadcabbddcbddabadcdcacbaabaccacdacaddbcadaacdadbcbcdabccbadadaaaccbabbdacdaddddcdbddcabbbaadacbcacccadaadcaccaaaadccabdddaabccdbbcbbbcbdcdcbdadacaaddaccabdbbabadbaddddabacadcbcdbbadcdcbbcaddbacddcbcdccbdbacdccbbbbccdcababcacaabbbcacccddcbbaabdadcdddbcbccddcbababbdabdcbcaadccbddcbdcbcdadaaacdbccdadbbdbbaddacbaaaddbcaadbadacccbaacabcacdcbbcbbccdaccbbbdacacdaddcbadaacddacbaacaaabbdcccbcaddbcccddbccbcbdaacdcbddcbcdabccdccbddcbacaaaabcbdaacabacbadbcbbcabbdaadacbabaaadcaccdcbaaddcbbbcdbbdbbdddadabaaadbdbcccadcbbbaacadcdcbbdddadbbbcccbbaaacdcdcaabcabbcbddcbcabdbbdcbdabdddddddacaabcccdacbcdbcdbbdcdbaccccdadbaaccdbbbbbbaaabdabbcaaacababaaacabadcabadddadbbbbddbdcaaddcbbbacbcbcabcbbbdaabdabaccabdabbdaacbdaadbcbcbbbddcbdaaadbacbbcaccaaaaaccacdbccbbbddddabcaadbbdbbbbcdbdadbdbabdabcabaabbdacdcaabadddcbcaddcdadcdcbdccdbaaddacbccdabbcabcbaadcbbcdaacccdaaabaacdaaaddcbadcaadccdcadbcdcaacbcaaaacdcddcaaddabdcaddddbdbcdcacaaaddbcaddddabdaaabdbdaacabccbddaaacbcbbdcaacdcbdcaaacdcadbaaadcdabbccdbbdcaaadcddacdbbabacaddadabddcccdcbcdbdcdcdacaaddadbaadbcbbaacdcccbbdbdbaaaaabcaddccacccbadaadadadacbadccdddbababdbaadbbccbabaadabcdbdbabdbacdbacdccbdbcadbadcbdcddbddcaaaaccaacbccbcacbcaacbaadabbadacdbcbbacaaabcdadadacdcbcababbcdcddcbbabcadbaaacabacddaadddcbacccbdcdbdacbbdbdddccccbddabbdbbacbacabadddabdabbcccbaaacbabadcdddccccdbcaabccdbdbbdcdddccdbbacdccababcadbbcdadabdcabdacacbbbacdbcccaacabdbacadabcbacadbacaaabbadcaddbabbcccacbacadddbccbabdbcaccdddccabdbbbadcababdbdbabddbccbcbddabddddbdbddbbcbadcdcdbbdacdddcbabcddccdbdcdacbaaaaaccbdcdcdbdddbbcbbcdcadcbabbbbabbdbaddbbcacadcdbbddbbdccdaababcdcdccaadaadcabcdcddbbbbcbccaabdbdaccdbddcaddccdcdddaababcacadccdcbabdabddaddaacdcbacacdcdddcabdbbaaabcbacbadbbdbbbdcdacdaacadddabababdbbdcbbbbabbbbbcacdacaaacddbaaacddcbccdbcbacddddabbccbccabbadcbdbdabcbacccccccadbccbcbcaadccbaddbdccbbccadacddcbcccbccccabbaccdbbbdacdcdadabdccddbdcdcacbadbbcdddbdbbbaadbcdcdbcbdcdabdcabaadacccdaccacbcdcddcacbdbdcaaaadcbbdaadaaacccddacbdcbaddaabbbdababbcbcbabcaaabdbdbadddacadcbdddccbbababbdcbabadbcbcccbdcabaaccbbcdbcaacabccdbdcdcdbdadaadacacddbacdbdadcddbaaccdddbbbbbdcddcbbcadaabcbaacaccbdbadddcdddadadacdcadbbddadcadabcbbabbbbcacacdcbdcadacdacacbadbabdcbbbcadcaacdcdcbbacbadbabdcbbdcbcccbcdddcbccadadaacabcbadbcdbadcbdcccacbdaccbbbcccaaabdddcacddddcadbccacdcacbdbbbddadaadccbcbaccaddcdbabadcdaddcbddddcdbcdbbdcddcdbadabdacbdbcacbaabdacdbabbbaabacaaddacccadabbacaddccdddacddcababcaccdbccdacbdabcdacacbbbddbacdadaaaaddbdddddabbacdcdcdacdcbccbccacacadbbbdacbdcaacacaabbdcacdbdcbcdcaccaaddcccdbdcbcadccaccabdadcadcbdaacdbbcdadaccacccdadacccadcaabccbacbdcdddbabaadccbbaabcaacccadcbaaaacdadbbddbabcdbbaddabdbaabddcbacacdbcbddbbbbdbadbcbbbabbdbdcadbabcdabbabbbbcdccdbdcccdcabdacccbcdbccdccbccaadddbbbbbcbadddacccdabbbadcacacaddcbccbdbcdcdcccabaabacdbcababcccbacbbcbadadbdaadacbdcbdbcabacbbbbdcadccadcabccccccbdbcbaccdcdbbdaccdbbcccdbbbbacdbcabaabdcadccdcbcadcdcadcbaddddabddaddaaadbcaacbbdabbbdabbcddcbdbbaabddbdcdabdbaaabcbaadadbcabdccccdacaacddbcdcbdbbdbdcdcbaddadcbaadaababacadddbdaabcbbddacbbcacccbbcabaaadaccddadaccadaacacaadadccacdcbdacadbcbbabbcdabbcaddbddadccbbbdcdcdcbbcddacccbbaacccadcbcbdccdacdcbdcbcccdcbbaabdbabccacbddddbdcbbccdcaadaddacbbaacbcccacadccdbbdcdbbccbcacdcdbcdbabacaabcdaabacadcbabdbacdbbddcccbabcbcbcddbbbacaaaccdacdcbabbdbcadbdcadabdabaaaabdddbcbdcbadaddacdcaababccbcdaabbdcadccdccbdbaddadbbdddddbbdccbacddcddcdbbbacadbcbaacdaccabccdadbbbbcbdbcccacbbdbbdccbbbaabccbbabccdcbcaadaabcababdccbabdacbcdcacdabdbdababacdcaacaacacbcabdcdbbadcaacacbaabcbbaccadbcddabcbdcdbdbacacadbccbcccaacbaddcdcccaacdbacabbcabbaddbadadcadccddaacbdabdcbabcacdbaaabcddcbcddddddabaaaccbbcbcddddaadacbddbddaadacaddbbddcbccbaadbabdbcdcddadccdabccdbcbcbadababaabcdccbddbadcbbacdaaaaaacccabbcbcdbcbdcdabccccddacdabcdadbdddcacddcdadbcccbabaccbbdbbdbadabcccaaadbdbbdbcacaaaadbccdbadbdbdacbbcbddaaaddccbbaddadbbaaddcbdadbdbccabddbdcaccdcbcccbcadacaadcddbadbbcbaddccbacdabcbccdbddbacaccbcbdbdbadccdaaccdbbbddccaacbaabdbdccbabbdcbdaadccbbbbcabddcddacbccbdddbddaddcdadbbabbadcdccdcccdcbdaccaabcbbdccbdccdbdbadddcbcdcacababbbacacabbadadaaacbcdadaccdccdbbcbdbcbbdaadcbcaccbbacddadcdcbaddacdaccddcadaccdbbacadbbcdacbccaadcabdcdbbbdbcccdbdbbbaaabbdadcbbddbddbccaccadccacacdccbcddadbbdaabbdabbbcbcadcbaddcbccaccadabacbcccbbcacddddababddbdccdcacdcabacbabbcdbddacddabdcaaccccbbcacbccacbaccdcbaabbadbccbbaaaccabbadccabbcacdcccbcaadbaccccbadadcaabaddadadcbddaabaadbabdbadaccdddbbdddacddadbbcdabbcdadacbbaacbaaaddabdbdcddaadcdbcccabccdcabcdcadcbadbabdddbcdadbccddbcbabcdccccdddcadcbcbcbbaadcbbcdbadbbcabbacdabaddcbcbcdaccbbcadccbbbcdabaddaabcbacbcdddccdcadbbcacdcbacbccdbdbadaacadddaccbbccaabdaaddcabdbbbcbcaaaacdacddcacbcadaadaccbbdbddadcdbcaacdaadbcdbcdaacabbdbbdbaadcbdbbadbbbabbbcababbccdabcddbcaaaabbadbdcddddddaacaaacdcabbcddacacbbbdabbbcccdaababbacaabbdbcaabaacbdbaabdbcbacdbbdcadacbcadbaddbaacaadaaadbaaaaccbcdadcaddaccdcaddbbbacddcacccacbcccacaabcaddddababcdcacbddbbccadabdcacaddcdbbbdbcbcbbaaaacbccbdddcdddcaaaabbadddaaddddbdbbcbcadadbcacbccccabdbadbacadcdaaccccdccabbcbbcdcdaacbdadbddcbaabbddaabdcbcadaaabdddadabbadccbabcccaddadbccdbddcccccdbacdacddabdcbdbbcbaabcbdbbdbdbbcdabdcaacbabcdcbaabbccbdcbaacaabbabbaabdaabacbdaadbbdbbacccbbdbbbaabdabbadcadcbdbdcbbcadbccaadbcccaadabcdacddcacdabbacabcdbdaadabaaadaaccbbadccdcbaddcacbcabaaacaaadcbcabaddaddcdccacbbddcbababbbadcbbcadbababbadcccdabddccddbcdababaccbcabaacaccdcccdbcddcadadadbcccbddaddccbacabbbccacbbcadbbacaaccacbbaaabbcbcabbdbabdcaaaccbbbbdacbabbddaaabcacdcadcbcbaccddbdacbccbdadabbaddbbabaaaaaabbbabbdcadadccaccdaadbcacbddccbdaaddadbdabcaaadbbcaaabcaddbabcabaccaacbbbabbbdbbdaaabddbbbcdddbbdcabaabbdaaccaaccbaacddbaadbcaddacaccbddbcbcaccccadccacdaaacbdcbbdbdbdbddbadbddadddbaaaddcbbacaaccadbaacccbdabbbddbbddadddaadcdbdcaacadcdbdcdbdaccdbdabdbabadacccdbabcbbbcddbcaccaaabbbbaddbaddbaadcbcdabbbbaaccdbddddcbccbdadcbaadabaccbddacaadcccabddddbdadaccabdddcadbdacddabaabddcdbacabdaabdbdabaccddaaadcaaabdaacaadbadcccaaccddacdaabdabcadbaadabbbbbdcacbcccdcccdcabacbbbbbbcabdacddbdaccaacbbbcabcaacbddbdcdacdbadcadacbaccaaaadbdadbbdbbcabdbdbaddaacbaaabdbbcbbacbababdbadabbbdcdcbdabacadcdccddacccadbcbcaaacacbbabaadaaabdacdadcadbdbbdbdbcbcbbbbbaddaabccdadbccbaccdcddcaccbddcaaccaddbadcabadbbdbbbbaaaddacaaabddccdddccaccbcbdbadbcbbbddbcbdcaaccbcbbaacbcaadbaddbabdadcaaccacbcbbbddccddaacabcbcacccdacaadcccabaccadadadbdabbbdaddbdcdbbccccbaabdacbdabadccacdcbcaddbcbdabbbdbdcdbdcbcdccbacdddaaaabcdaacdcbcdbccadbbdcaaccdbcdbaacacbdddccbcddcddcdcaacaabcddaabdabbaccaaddccdacbdaaacdadbcaabbdadbcdcadbdbacbdcbdbcacaabcacbbacbcabdaacdddaadcabbdcbcadccddacdbccdddbbcdabdadcbccaddbcdaadbdddaddadcbcbaacdbacbadbdaccbddadcdaacbadbbbccbcbcdddccadadcdbaacccddddbcdadcbbcbadbccddcdcbbbbcadadcdccdbddbacdabcbadbbdacaaaabcbabcabacbdacbabccbcdaadabdcdcbcbbbacddcacdcdbdcabadccaaddcbabcddadacbbdbddbadbaacaddbdddabbbabbbcadadddacddbccbdbaacaadcbbaaabcaaadacaaacbdbabdddcadaacacbcadbacbcccdcbdadbdbcacaacacbddcbcadababdaddccccacadddbddcbcaabcbbbcaadbbaccdbdcdcdcbddcdcbdbbdccadddabbadccacbcdcaadddbbdadddddbaabcbaddddbdbbdcbcbcdbcccdbbbbaacdacbcacadcbbddaddabccaccdddadacdccbdaacabcccababbccabccbdadacbdcdccbccdacbacbaaccddbcababaacadccdcbbabcaaaddbdcbacbacbdddcbbbdcbdaadbcddbadcbaabcaddabbbadbadbdddadabddcdbbbddacdbaabaadbdbdaadcaacbbbcabdcaabadaaacabdcbdbbcbcbcdbabddbbadabdcdabdbdadcbbdcadaddbdcbbaacadcbbdbababbbbbadbddbadcbbdcbbdacccbcadabdababddbcabbbacddcbbaaccbdbcdbddcbabbaabcaabaccbcbbadcdadcdccddddcbbbdbadbbcaabdbaabccdbcdadbbaaadcccdbdacabbddcccddcccacdaacaacadbcdddaddcacddccdabcccaadbdaacaabcbcabadadacbdcbbcdaccdacbcadbacddbbddbccdabbbcbcbacadbcbdcaccacbbbbcbbcabcbddabdaaabdcacdabdbbbcaaacdbabaacdddaaadbcdabacccbbabcacdbacbbaaabaadcccabbcdacbccccabacddddcaacdadbbabcdcdbbaacbbcadabadbddacabcddcbddcccddcdaaaccbdadccdacdddadcdabcbddcacadabbdbacbbddaaccdbbabcccdabdbbdaaddcbadddcbaccdcaaababddcbcdaabadaddaccdbbbcbbbdcbbddcbbdccaacddabdbcbbcbaaddccbbaabbcdbabbbbacadbdadbbbcabacbcbdadaaabcdabbdadcddbcadcabbbddbaadbbaababbbbbbdcbccacddcadbddabcccbbabbccacaddddabbcabcdabccdbdaadbcdbdacaaddaacaadbaaabdabdccabddcddddabcbbdbbddcdcabadaaaacddbdbabcababababcbcdaadaddcddabddddcacabcddcacbbbadbadcbcbbdaacbcaddadcabacbbccdbddbbcabdcadccabaabbdcadbdadcbbbdbddacbbdadaadcaaddbdcadabcccbadbcbbcdcbbaabbbccdaccdaaddcdadccadddcadcdbadcbcaaaacadabaddabbadcdaccdcccaaccbaadcbdbcaddaacaddaadcaaabccbbbdcaddadbadcaabdddcaccdcbabdcbbacbdcdabdadddccddccadbcbcacbacddbbccbbdabccbbdabaccccdacaadcaccbbbabddaaacaacbdbcbbbaacdccbbcbbaccddbabbdbbccddcdddaabbbbdccaaacabacabddbccaaabacddbddadddaccacdbcadbcabcadcbbabdabbdabccabbbbbbdcbacccdbbddcdccdbdddadaababdcbaaabadacccdababbcabdabddaccdbacaaaadcdbbdacbccaaacabdabadacdbcaaccdcbabcdbbcdbcaadbacabdbdcddaadacdbdbabadbcacacddccabbcddcdbdadabadbbadcdbdbcdddacccabcbddaccacaadbddabbbabcacccaacbbcbcadccdabbcbcbaaddcaccaabbcbacccddcaaaddcadacacaaabddadbbababaddccbdcabacccdcbaccddcbccbbbbadcccbcbcabadabccbadcacccabcdcbacabbbcdaacdacddccdcabbadccdcddccbdaaaabdabccbdddaccaccbdbddadadadaaddaabbbdcdbbbaddccadadccacccadabadaccaacbdccacdcdcbbcbddacadadacbcbadbdbbacdbdaacddadccabbabaaddadccabdddcdbdabccbddbcccccbccabadcadaacdaaacbbadcabcbcdadaaacbdbacdbaadcadbacbadcdbccbadbdcddcbdcddcbbabbbbaadcaaabdcbdbbdccabcbbcdbaddacacdbcaccccddaaaddabaaadbcdbabcaddababcdbbdabaadccccaadbdaabadddbccabcbbbdcabcbdcaadcdbaaaddbadddccbddbabdabdcadbdadbbbddbaacccdabccacbccbddbaabdddbddacbdccadccadabdacababddaddabbcdddbbadaddadcbaaddcddbccdcbcdaadabcaccdcadaaadccbbcbacacadaddcbdddcdcbaacddadbbcbdcbbbdadbcabbaadabcdabbbdcadbababababacccdddadaabdaacddabcdcaacdbdcdacdaacadcaabbbadcbdaabdbdaccadbabcbcdddccdbddcbbabbbabacdcdcdcbabbbbbbbacbccbcbccaccdbdccbdbcbaabddabdcdabbacbaabdcdcaccaddccdaabadcbdbaddbccaccacdadbdbdbbbaabdbbabacdbcadcbdaccadbbbadcaaaabcdbcdbbddadbcaccbcbcccacdcdbbaddbcdaabacbabaacbabbbacccadcbbbbcdbaabddcadbcbcdacaaccaacdcddcadbdbcacdadcbdabddaacbdabdcadccccbbccdbaadbccddbddadbbccadddbdabdaaaaabdcacdddaabcdacdaadaaabdddddaccacbbcdcccaddbbbcdcddaddbbacaadbbbccdacabadbddbdbccacccadddadcaaaacdbacbcadcdaaccccdbdaccbbbcccdacacdcdbdcdababcacabcbcbbcddbcabbadddcbccdddddcdcccbddcbbcacbdbdaaabbdbbbcddbcabccccbddcadbadaccdcbcbcdbddbcbaaadddbbcabcbdbbdbdccdbbbdccabcbabdbddababcbcbbbdbcdcbcbbbabbaacacddacbdbbabbacaaabbbacadbddbddbcccbdccacdabdcbcaabcaabddbdcddacbbbabcdaaccdcdbaaabbacdcabdcdaaddcbbacdddbddbacdbcddcbbbaccacadabbdabcbacdbdbcbabbcbdabcdaaddcbbacddcacccaaddddddbbcdbdcccaacbccddccdccddcdbabbbbdcbcdacbcdaabbdbbbbbbdcdacdcbdacabcadaaaaababdadaddccadddccbabacbabdbddbbaadaccabcbaadaaccddadadbbacadadccbdabaccdadabdcbbaaabdcaabaacabbaaaadbcbcddddbbccacbbaaccbaadbabcdbddbadcdbabdaaabddbbdabcbcbcababbabadabcdcbccbbbadbadaabaadaabcaaccaabcbdbbbdbccbdacbdcbbbaaaddccbadaccbcabaddddcabacacacacdcdcccdaaacbabcddbaddbddbbadaacaabbdaddcbcaccbcdcacdadbaccdbabcbdababbdcabacbdacdcbdabbcdcbcccdbdbbbbcccadbcbdbdbbddcdbacdcdcbbcadbdddcaddbdbdbaaadaaacbbbcbbdbddcacbadcadddcdbadbbaccaabdabbccdddbababcacabdbadabadaaadadacccaddcbadcabbacbadcbdaabcabbcccdcccbbbdddddabcccabcdaaabdabaababbbbadadbcbcdaccaccbadbdbbcadcdaaaccdabbabdcacbbcdaccaacddcddcbcacbdcdcdbccccadddcdbcddbabdcabcdbacbbdcddcadbbaadbadcccddadbdcddbcccbaaabaadbaacbcabbabbbcdbacdbdabdaccbbddaddbbddccabcbdcabbbdcdbddbbdbdadddcadacadcabacaacdbcdabbdcdddbbcbadddcbccbbcdcdddbdbacdcdcdbbcacbdbccaadadcadbdcacbabbbcbdcddbdcddcdbacddcacbcdddbbdbaccbdbcbcdbdbcbcabbcbcabdabacbdbcabdcbdadbcbcdbdbbccbcbcaaaddabccdaaadbbbbdccdadbdadadbdbddbbddcdbabdcbcbbaaabccaddcbdcbabddabdccdcbaacbbdbabcabbdcbabaccccdadddcbcbcadcdddbcbbbdaccaddbcbcacddbdbacddbdacbcbacadaacabbcdbaccdbdcbccbbdcaadaadddacbcaccaddabaacadddcccddbdcddabdbbadcddbdcadadcdbddcdbadaadaccccbaabbdccbbdddbabbdabbbdabacabbabbdcddddadbbccbadbcaddaadbbacbdacbdadddbdcacdcaccdacaaddaacbadbcadacabaccaabacdbabbdabbbaabdcbbcbbcabdcdaaadabcbbcbccbbbcbcbacababbaaaacaabbaaacbdacadaadddaccadbabaacbbaaabccbabbdabccaadcbbccddcaaccbbbcdbadadccbddcdaacbdcadbcacbbbabdcddbbdbbbaabcdddcacdbdbbaabcbdccdccaadbbcacaddaddbacbcaabbaaddbaabcaddbbdcdaddbabdaaddbbaaccaddabcdccdacbccaabbaabddaaadccacbabacdddbcdadadcaacbacbbcbcacbbabdbababcabddaddbabdadcddaadbbdbcaccdcaaaaacdcccbabcabacbbaaabdccacaccaddcdcbdaaabbabbdbcdabbaccbbabcccabcbcdbdbbdcddddcccbaabacacadbccacbbcdaabdcabadbbbbcabbcdbcddbcdabdbbdccbdaddadaddcacadadcadbcbadbcccbacacabacbabadcaddbbddaacbcaaccacdccdbdaddcadddbbcddddacaaacdbbddcbccccacddcccbdddbcbababbdadabbdcaddbadaaddcbcdbbcdaddbbdbcbadcacbcdaacaaacddbaacccbdbbcbdcaacccaabdacdaaacdaaaadcdccccbacaccdbbacacdbbdbabbbcadbdaadabbbcaacccadccabdbbbdacbdabddcbcdccbcbdbbacdbaadbdcbbdbadacbbdbcbbcdbcabbbdadadaaabddbdbdacaaaccaadbdccbddbcdcdccdbabcdcadacdbcaabaadcdadcddcbabddbcbacccdcdbcccadbddacaaccddaadbcddcdbbcdabcbbcdaccbcddcbdccbcdbdacdadcbccacdddbddadaabdbdaaaadadbdcbbdcdabdbadbabddadaacdcddaabbabcadacbdddaaacadabbadbdcdbdabbcadbdabddadbbbbaacabcbabdbdbdababbcdcacdacdaccaddccadbddcdadcbaabadacacbbabadccdacadbcccdbdddcdabdddcbcccbbdacdcccacddbccdcbcdbbddaaccccbbbadaabcdbbcdabcadacbaadabbadddcdacacbbcbdcaaaccacddacbadbbdaaacababbdccaccbbbcabdcbcbaccccdbcdadccaaddbccbdcdbcbbbdbcbadcadbbaadddbaacacacabbbadabaaabddcacaabaadacdcaadddbbbadbcddacbaccccbcbbcaadccacabbadbbbbaabacbbdadcbddcdcdbddabcaccabbcdbaddaccbcacbabacbcccdadadacbcdadbabacbdbcbbcccbdaddabcbcdbadcdccdbcdadbccadcacdccdbbabdcacdadbadbdacaccbcbadcbabadadcdbbcbccabbcbaddbdbdddadbbcaddcbcbbcdccadbbbabbaccbaabbcbbccbbcbbabdcdabdddaadabdbabccdbbcacbbccdabcabadbabcbbadbdbcdbcbabddbabdaaccdddabaabacbddddcccbbcddadbdccbbbabdadaaabaccdcdbcccaabbcbabdcdabdbddcbcbcaddadddbdbbcbcbdaadacabcbaddbadbbaaadbdbaaddbcdbbaccdcbbdadcacbaaadddddbdbccddaaccccdacddcccaccdcabddbbcdcddacbdadaacbcbdbdbcdabcddcacbadabccbcbacdaccabbaaaddadaaaacccaddbbdbdacadbcaabbccccadadbabaddbbaacacbbabbadbbacbdcdcabdbbaccccdbdddcabaaacccaaddbacdabbdcbcaccdcadcaadbdddcddadbadccbbcccbbbacbcdadcdbdbacaadacaacdbddcddccdaddbcadadcbbaccbbbcbdcbadadbbaacaadcbdababccbacddaabddadadaccdcdcabddbccbdaccccbbcddaacdcdccdddbdaaabddbdbabbabddbdcbbcdaddbdadcaaaddcbaabddaacbdcbbdbccdbabccbdcbcccaccadcdacdbbbdadbbabacabcbabbdadabccaabbacbaacbcdaadcabdbbbadcbbdcabbdbaccdbaababccdcbcdccaababbdacccacbbbdabbadbcddcbadadcaabcccacddbaaaaccbaabdcbdccacabccbddcacacabdabcbdcdcabbdbbbddcbdadbcadccdddbbdbbdcdabbccadcbbdcdbdcadddcbbcbccddbcabdbbaabdbdbcbcddadabcabbccdaadcadccccdbababbdddbaaccbdccdbcbdbdaabbabdbcdcbbcaccabccbadabadbdabcbaddcddbbbdbaaaddabddcadaddacddadcddadcbbaadbdcdbccadabaadabcbdbabbdaabddcaacbdaddcaaaadabddddaaaacdaababdaaacbabbccbadcbbcbaccbcbdddcbababccdddcdcccaadabccabdbadbccacdccadbbbddcdbcacddbadacdadccccdddcacaccaaddbcdbddbccaddcccaadddaccbadbadbdabcdaccdacdcbaabbaabcdbacdacdbdcdddacbcacaacadccaadbbacdadbddabcbbcadabdbcdcbcacccbacdbaadabbdcddcabddccadbcaddbbdbddcbddcbdabcdaadacadabacdbdabdabaadadbdaaadcdbbbadbaacddbadabaddbcbacbaadcacdcbdcbdcbdcbbccdbaddcaacccabdccacdbcacdbddcdbcbababdbdbacddaabaabcaadaacacdbacacabaccdabccdbaadcbaababbcdbbddaddadcabddabbabadabcddabcacbbbdadccbcbdaacabdaccbdacdcacdaaaddaabacddbaccabbdcadcdbbdaababdcdccacdcaabdbdbbdadcbbbdbcdadbccdddcdccbbccaddddcbdcbdabbadbccacdccdabdcbcccdaaabcbadcabbbdadbadcbcaccdadcbdacdbcbdbaabadaabaccdaacccabdbaaadbacbdbbdbdcddacbddbaacadcdabdacaacdcccbbaaabccdcaacccbadbbbacaaddabadbacaacdbcdadbbbbbbaccaaabacabcabbacbdbbaddbcbdbcadcaacddbccbdbcccdcaccbddadcdddbcdccdcadbcdadbdabcaaababaccbddadbdcdcbaaaacdaccbbbcccbdaaadddccdacbbddcdddbbccaabbddbdbdbaccbadcbdcadababcbdccaaaabdbcbddcbcddcacbcbdccbbddbcbbbadbcdbcabbdddbddbbdcabbdcbbaaabcdaaaadddaddcbbbadbacbdcbdaacbadddddbadbbddccdddacabaadcacdbaaddbaabaddccdcabcacadbbcaddacadddacadabbcaacbadaadaadaaccccabbcadcbaaddcaabbdbcacabaacddcdbddacbadbadabccbcdcdbbbcabacdbbcacddbadcbbcabcbdbadbaaaddadddbcddacaccbbbccdccacbbadcdbcbbaccadbcddcdccdbbcbbddcadccaaccabcccddbadbddddbbcbdaaaddabcaadbaabacbacacdbdaddbdcbbdabbbbcbdadddbbdacaaaacadadadddabbcbccdabcdaabbdcbcabaadbbdddacbbcbcccbbccadcaaccdaadbabcbddacdddcbcacddaddbdbbacadaccddbddaadbabcbcaadcbcdbbdbaaddadcabdcadbdacacbdccdcdadbaacdadcdadbdacdcbdadabaccdbbccaaadcbadacbcacddbbcbcccbaadaddabbbdbcacddcdcdbbbccdadacdcacddadbbdbccaaccdddddaacbbbcccaaabdacabbdabccbbcccdbdbbccbaacbcdbbacaabddabaabadcdabddcaaabadaaabcaaabcbaaabbbbbddabaddabbbbdbbbcddaccadbaadbadaabdaacbabcadaaabdbabccbdadbbbdccababbaddccdbbbbdcbbbddcdabacbcaaacccbdaabcddbbbdccdbdbdcbddbbbaacdadccabbabdaaacccdbccdacadcabdcadcbdabdbcbbcdccbcaaabdbaacacdadbddcdbacdbbcbccdabaaaacaaaacbbbbdabbdbbbdbddabddcbdcdaccddcbdacacabcbacadabdaaabbaabbdccbdaacdcdcacdaadadcdcbccbbbcabddcbdcccabddddaaabbaaaddaadaadbccccabbabbcdbadcbddcbaaaacaacadacadcaaccbdddaddcacdadbddddaddddacbdaaccdddccdddbcbdcdacbbcdcbdccdcbaddacbbbcbdbcdccabddccccacbbcadddbdbadccbccddacabacbabbcabcddaabdcdbdcdbacbadbabcadbdcabaaabadccccdcbbbddacddddacccddcccbabaaaacadbaacbccacdccaccdbdabcbadbbbbdccdadbaabbbcdabcdcdccdcdcaabcdcbddcdcaddacbdcaadabaacccbbcdcbddacabadcbcbdcaadcddbcbabbdcaadaccbccabbccbabbbadaaacdcacdadacabbddbdbcccbbdacacadcddbdcbaaddaacabbbcadccccbaaaabcaabacacbcaadcabdccbadbbcddacdbaaddaccdccddaabcddcaccddbdcdbcbddbaaccdccadcbabcadcbcaabcbbbdcdcbddccaccdbcdaadabbbcbbaaabdaaddbacdddbcbcadcabdddbcbbacdbcbccbcbbbccabcaacaabaaaacccdddbadcdbdccbabbddaddbadbddbbbcbcadaddaaacdddcddcbbbcddbbabddbaaacbbdaadabcdaabdbacbdcbbcacaddcdbbdbbadbadbddddaadcdabaabacabddddacddaabccdbaaacbbbddbddcbbdcbdddabaacdbdabbcbdbcdddbdacbcadacabdcbcdcddcbacdbbdbbaabdadccbbbcadbcdbdccadabdcdbaacbcccaabdaacbbcabbccdcdbadadcddaaddbccbbadbbbdaddadbdacbabcadbbbdccaadbadbbbabcdbbdcbbcbdcbbaadbccbdcdaabdacabdaabbcbccbdabbcabaadcdaadaabddaabaaaaccabadaacabaacddccbdddcbcbdaaadadbcbcacacadbcbdbccbabaaacbdbaaaacccddadabddaccaadacbcaaaccabbdcabddccaddadacaaabcadaaaacabbdcbdadbddccaadcdbbbbddbbdcbdbaabdcdbcdadaabcbbdcdcbcadadbcaaababaccaaacadcbcdabdbacdddaabcbccbdadcaaadacdabdddcadbbcbaacbcbdcdaaaddaddaaadcadadabbcacdcbdadbbadccdacaccddbddcbaabdbbcaaadcddddabaadbbccababbbdbcbacacdbbdcadababcaacccdbbaaadaddbbbdbaccacbdddcaacdacddbaadbcdacacdbabcababbdadccbdacdcadccdcabbdbadbbbadaacbbadcdcbdcbabccadccdadcbbcaddcbaabcccddbbccbcbcdcdaddaaccbcbdcabbcdbaddddcccaaabdbabcdadacbcaddddbcbdccbcaabbbdbdbbdcddbdcbddcabbaaabcccadbaadbdbaaaacdbbccaabdcbcbcbabadbabcbddbbabbaccddaadcbcddddcdbcacdcdadbabbadcadabbbdbadccddccdbaaddcaacabcadbcdcaddacdbbdbcabbdabadbdbcaabdbcbabbddcbabbdabaabcadabdaaddadccdabdddabadbddacaaaacacbdabccbbcbaddbcaabdbaaabcbbcdbaacdcaddddbcbbddcaabcccdbcbcaabaacbdcccacacdbbaadadabacacdddcdbbcdbacccdcabbbadbadaabdcbbccadcccdcaabadabccccabbcbddcbddcbbadbdcacddbababdabdcbdbdcbbcadcaaababdbdccbdcbdababbaddcdccddcddcbdbccbbdbdcaccbabcdaccaacbdcdddbccaccbcbdcacdadaacccaddccbadddaccdaaccdbcbddbcabccbcbadacadabacdcccbddacdabbccdcbccadcaacaacaddadcaccabacadbaabcbdbcbbaabbabccaabdbacddaacacdbdbbaddcccddabadcbcbabcccccdcbccbdbbbcddccdbddbabcbacaaaababbabcacbccdabbaacabadddbbbddabcabacdbadadbaabbcaaabbccaaadcdccacaaabdaacabcbccccadcddcdcdbdaacddaadbcacdcaacaccbdbccbcaacbddbcbdbcdcabdcbabbcaabdbdbbcaaccacdbbccdaaabbaadaacbacccbabdbabdcbddbdddaabcacbdcbaabdaddcccbdddccdbadabdcdcdadccbadaababcdaabddcabcadadbbaaabcccdabddcdcbaccbabbdcddcbadadbadbddddadddadbacbdbdbdaddcccacadcdcadcdddcccccdcbdbbdbaabaddccadadaadcadccccacbbacdbcddddccdcccaabcabdabbabababccbbbbcacbbbbbabbbbabbabcabbcbbbabdbbddaaabcbbadbbdcdbdabcadbcdcaccdccdccabcccdbbabdcbccadcdabaddcbabaaccbdcbacdabcacbbdabacbcdaddadadaabdbbbcdcaabbcdcaccbadabcaacdacaadadabcaacbcddccadcbbabbdddcabaabbaaadcbdcbacaabdcadaacdbadbdbacaccacadcacbabcaaccacacaacdaabbbccccaccaddaddccbababddabadabccddadcacdacccdadaabaccacadaacadccdaadacccababccbbabbadbcacaccabaacbadccdbbdcdcbacdbbcdbdcdbadbbcbdabcacdadbcccccacacdbdcbacdddabaadcbbbcbaddbbdcadabbcadccdccbcdabbdacbbdbabbccdcabbcbcbcacdcbcdcdaadadacbcdcdcaccddccabcaddacadcaacbbabaaaaabaadcacccdacbdbaabcddabaddbaaccdbddaaacbbbabdcbddbaacdbdbbaabbdbbbadcacdacaddccdccbdcaaaacbcabdcabdaaccbdcddcaaacbccacdddbbcaacccbcbbbabaadaabbdcddbcbddabdcbcbababdaaaaddccacdadcdbabdaaddadbdadabaddbadbbbccbcdabccbaaadcaccbdcbddddcddcadaacdbbcddabccaacbbbdcccdbcbbdcdccbbcbacbacdcdbaaddbbddabcaabbdacbdbbddadbdaadccbbbcbbdbabddccacccbbdbcdbdccbbbbabdcddcdddbacbdcbabbdbbaaaaacacabddbccacdbbbcaaddacbacbdaacbdcdddacdaacbadcbacddccbbaddbccdbdcdcabbbccaddcccadcbdddbbdddadbbbccadccdbcdccdabbbaadcbbbbbdacacccabbbcacbdcadbcbbbbacdcdabcadbcaacdbbabccbaddacbacdadacdbdddccdcbadbcbaccbaddbbbbcdcbdbdbdcbadcadbcbcdbbaaaabcdcacaabbbaaddcbdaadcbdddcabdaacbbcddbcacbdcbcbcbaabdcbacacabdcaccbacbabbdbbccbdcbabcacaadcbcdbccadcaddccaddcbdaccacdacbdadbdabacccddbccaacbdbcadbdbacbcdacccabcdaddbbcdaabdbdcbaabbdaadccabdaacaaabcdcaddcdbbcdbddddadcbbcdbdadaacbccbdbcdacbacddcadaacbdbccdabccbccdadccbabbaacbcdddacbbababddaacccbcddcdbdbabbdcbcbccaccddadacdccadcadbdccadacdccddcdddccdcaacbcaabbdbbabcbcbdcaccbdaccbbcaabcccabaabddbdbcabababdadcdabbdbbaccddcbdacbaacddabddcdcdaabcddacdbcbccbdacccbcdcbabadacaacccdcaabddcbbbdaabadacabdadcaaaadacbbabcbbdbcdacbdadcabdcdbabdbdabadaabbabacdcddaddadbcacbbbaccbabcacdadccdaccabbacbbabaadaaaadacdababaddbcdbbcdbcbadbadbdbbddadacabcdbbdcdbabcbabcdaadbaddbcbbbadbcdccbbdcbcdcbaabbcddabbdccccbcbdbcccacdadabbcccbccadadbdabccadbaaabdadabdadcbaddababccadadcbaaadcbcbcadbbcaaacbacadccbccabdcabbdcbabcbacaaddadbcabbcdbdddaaabcccddcdacddacdbddaabddbabdddcbdccbdbddddcaabacaccccaccdbdabbcaacababbddadaccabadccbcddbbabdaaddcbdcacbacbdcccdcadabcadbdddaacbdabdbdbcbdaabccabcbcccabdadbcdaacacaddabddbbddcbadadcacdaddbbcbdaabdcabcabcabcbdadbddabcbadcdadadcdbbaccadcdadabbadcaabadbddbabccaacbdcbabdbabaacccccacdbdaacbadcdaaadddadbccbbbbdbccdddcabadbbbddaadababacabbcdbbbcbddddcaaaddcdaaababcbaabaacbbcdadadbaabdbbbabbbaabddbddcabdcbcacaddadccaabbdcbcaabaadddcadbcbdcacccccddbccdaadbddacbcdbadcdccabcccdddbbccbbadbaddbdbadabccdcdbdbdabcddbdddbcadbbaaddbaaaccdcbadaaaaaabbbdaccddadbdaababccdbbbddaccdbdddadbddddddbdadcdacdcacbaccddbdbbbabacbccbccbadddcdabbadddacccaadadcbbbbbbbabccbdbcabacaddcbacbcbbdbcbbbadacbbbccbaacbbddbbbbcbadaacbcabdbaacabcdcdbcbdaddacaccaaadcacadbddddbbccccadadccdbcacbcacbaabbcbdcaccdbadcbaabddacdcacadaddabbcdcadadbdbbbacaddacaddabccbbdcdadbdacbcccaccdabadbcdcdccadcdaadabcacacbbaccdbbdaccaaccddcbacbdaabddbcbdcbdbcaddabaabaadddbdabdbbcbcdcdcbacacdbdcaddadbdabacaddcddbabbbbadbccbabadcacacbdabddbbdbbbbccaddabcacabccaddcbdbbbdccacbcbaddaccbcccbcdddaddbdbbcdaabcbdcddbccadabacabcaaaddcbccddabacabcaaacaabadbaacdddbbcbadccddbacdccccadabadacdbdacbbbdcdccdabdabacddacdbbabbbaccbdbbadcdcacdcccacabbbbdddddbcccddcbdbccbaadbacbbdbcdbdcbdcbacbadaddbcbcdadcdddcdaddaddbdccbbbdcdccaacbbcaabbadbdbcacadbbbbadcbcdcadbdbbdccadccdcdacdbabccbbcaaadabdabdcdbcbabdbcdbacaaaaabdaaddbbadaaadcdbbbdbbddcbbccaccbacdabcdbacabbbdadbaaaacabbabbacddbbcbadaadadcbbcbaaabbcacadcbbcdabaabdbadbccdbdcbabdccbccdacbbabacbddccabdadcddddadbacabacdacdbbbababcdcbccddaadbcaacbcdcadadcdcbdbddcccdadbbbbaacccdccadcdcbbacaaabbdacaabbbbcdbadabdaccbbaccacbcdccdcbcddaacbdadaabdcdadcdcbdbbbcabbacaadacbddcaabaacdbaacbbdaccddddacdbaccadbcbabbbdbacbdabccdaadbdaccaccbbaccaadaabcbdcddcbdccdaaccdddcbbbdadccccddadaadcacdaccddddcccadbbdcdcadcddcbdcdbdbcadbcaabaddbbdcbcacabcacdbbcabbabaccbcdbaabdbdccbbaabdcbdbdbababcacacddaccbbbabcdbcddbccadcddabdddbdccdccbcbbadbccbdbaacaaadbbcaabaccabdbcabbadbdcdbcbababacbdadbdaabaababddcdbbbcbbbdddcdbdcccbcbacaddbdababdcbaabddccdabccbddcdaaddddbbabbdaacacbadddddcbcbdbbbaddbdacabacadcbaaadabacabbabcadbdabcdbbdacddcdadbbccbcaadaccbbbacbaabcdcdcbcdcacdcddacdddadbbbaccbacbcbbacdacacbaaadacaccdaabdacbdadbadcddcccbaddcabcadbddcddabbaadabcddaddbdbddaacaaaacaacccaaddbdcabadcabcccdcbaaadbdbdbcaddcccabddbaaaaccccacbbabddaccaccdccddabcbabdabddaabacbcdcbccddcbdbbbacbdddacbddbaccccdcabbaaaacdacbaccdbccdbdbccdadadbddabbabcbdcdaabdbdbaddaddbbccdbdbcbbacabddadabcdcddccaddadcdbdabbbbbcdcbcaddcaddbaddbdbdcbdddacadcbbcbadcdcdadbbdadbdcccabbaabbcdddabacdaacbbaccbcbbdaaabcbcadaaddcdbbbccacdadcdbadbacabbbbcaadcbbdcbcdcdbbbacaaacddccdddcbbacbcbbbbcabdbcbadacdadcadccdbccdabbdadbcccaddccdaaaacdbcbcdcdbdddbddcaabbacdbbadcdadbbbcadbbbdabdbdbaaaadbaccbcddbccdacdaadabacdaaaabbbaabcdabccddbcadbadbcbabacbcbdcbbcbcdcddabbcbcadbdadaccaabbbdabdbdacbccbadabdbbabdcaaaaaadbcbdcabbccadddbbccabaacbdaacdbabcababbcddbbaccccbabcdddadaadcadcddbddccdccadaccbaddabdaadacdabababababdabacbcaadabddbdcbcbdadcacbabccaddaabacbccabbcbddbaccddcbccdbddadcaabbcdbadacdcaaaacbcdadccdddccbbbadbaaabddbbadcabadaacbcdbababccccbdbcadbbccdcabcccbcabbbccbdadcdabcaacdcbdbcbabadddadcddbbbadadddabdcbdbccacaacaaacaabdabdccdbbbcbbadcacaccbcbacdbbdbadbbcdbdcaaadabbbdccaacadcabddcdaccbcacabbdabbabbbababbbbbcdacdabacabbacbdabccccdbdcaadaccddadabcbadabddbcdbdadbbadabcadbdbabcabaaadbacaadaaccccdadabbcbddaadcadbcdabbadbbbdadcdabbcaaacbccdbcbbddbaabdaadadbabcdcaabaabaccccbbbcccdcbdcdacccbaacadccadcabadcbdbbbabddccdabbccdbacabdccdbaaabbdcbbbcdbacdbdabadabaabbccadbdbaaddbcdbcbadadcbdbaccaccadbcdcbbdcacadadacbdcdbdcbbbbbadcbdbddcdaccbabccaadabacabccdaadabadddcbcddadcccdcaabbddddccacadcccddaccbbbaccadccacbcccbdaadccdadbccbbbadcadcbbbdcccbbcbabcdddabbdabbaabddabcadcbabcddadabbbaadcbabdadaabcacbabaaccdabddbdabccbcacdcdccacacdadaccabadddacddbdaaacbbbddbcaddcbbaacdcdbcbdadddacdabcccbbdbdbaaccbccbabaddabcddcbdcabaddbdaacbabcaddcbddadcabccdabaccbbccdccaabcbbcbaccbcacbcacdcdcdbdadbaaddcaaaddadbabbbcdbddaddcbadcdbacbbaaabdcdbddbabbaddadacccdbcbbadbdcacadddaaabcbaccabdabcdbaadbdadacbbbcbbdcbccccdcbcbdacbdbbcddbbddcbdbdaaddbaacdaaacadccbbddbdbdbdabddcaddccccbcbdadabbaabcacaddbadcdbcaaacccbaacbccabaaabddaaabddadbaaddbbcdacbcabaadcbdadccaacbbbaaccdbadacaddcbddcbcccdabcbbbddbaabcbddabdbbddabcbadccdbbbddccdbcccdcacdabcdadacaabddddabdbdbdbabbdcdaabaaaaddadbadbccbdabdbdddcbccdbacadbcbcdacaadbcdaaaacbaaddcaabadddbddadababadcdacbadbbccbadabcddcadddaaabdadbcadcbddcdcccaaaabbcaadaadcdacabbbddadcadcababcbbbdaabdacacbacbabcabaddcbadbaddcdbbbdacabcaddcdbbbddccbbcdcbaacdbaabcdbbbcbcbddcddabccbcaadaaadbbabdcbdddddbbdbcacddbbbcbdddcdacdaacaabcbacccbdddabbadcacbdaddcabbbccdbdacdcadcacddaabcbcbacdbaaaaccdabccdacbcdddcbdabddabcabacdbdbcabaaacddacccdddcbacbaccdbcbaacccdbcdccbcbaaadaabdbccbabbddcccbbadaabbbcdaabcacadbabbbadabbdbdccadcbadbbbdababcdbaaaabbccbcbccaadcdcbcadbbddcacbcaaadcdbcdaddadabbddbddaddccdaddaddabacccababaccacaddccbccbadacaaabdcadadcdadadbabadcdaccaababbdcdacdcdcdbdbddadadddadbccdbbbabbbdccadccdacccdddddcddcaddcbbdbcdbdcacdabcbcababddbbddbbdadbdadadcaaaddcccccbcadadadcdabbadbcdcbbcbcdddcadbdadadbbacbbbbbcbabacbcacabcbbbdbccadbdadddadbacbbabbdbacadabacbadddddadcbabbcbccddabaddacccbdbcdcdcbbdaababaaaddadabbccbcbdacccadacbdccdabcdbadabbdccacaccdadaaadbddbcacbdbadacdaccccbbbaccdcbdbdccbdcabcabaabdccaadcddbbccadccdbbcaacccddcaddcddadccdcabdbbbbcbbdbaabdadbdaccddbbcdadcccdbdacadabbbbbbbaddbbdbadcccabcbbbaccbadcdcdabbacbababccabdadabacbbdbcddacdccabdccbdddadbbbbbcacaadaabbddcbabdadaccaabcaadbbcdabaccacaabcdbadbbabccdcdbaccbdabacbadaddbcdbdcdccbdaddaacdcbbbdcaccdaddbcacadadcbdcdbccbbaaaccdacdbabcbcbabcbdbbcbdcddbcbbcdabcbadcabbacaabadbcddaadddddbbbbbbdcbccdbccabddddbbdbdacbdccbadbdbbbacadaadcbdcddcbddbaccbabdadaccaaaaaddccdbcbabdcdbdacabbabacccbdbbccabcadababbacbcdcacacbabccbcacdbdddcacdcacabbdaccbdbcdaabcacccbccccaaaaabbbbbbcabbccaadcaddbdcadcddddcccbddadabbcdabddccbbcccbcdcdcbbadcddaabcdcdadccababadbbadbaacacbabbbcadadadabbbccadbdcddabddacabacddcaadbbdbbdccccddcaabdcdadddbdabacdbbabdbdcaccbdddabddacbabbdcccaadaddbdccdddbdcadcabbcdcbabaaadbdadbaabaddbdcaadbbcadcbdaacacbdbdddbabddcddaccabbcbcaacdcdbabcbbdacbaadbbbdbbcaabdcccacdddacdbdcdcdacbccdcbdadbbabdabbadaabbdbdcbbbdddbaccabbbbcacbcadbbcdacddaaacccbccbaaadcbbaabbccaabbbcddabaaaccacccabcccdcaabbaabdddbadadcabaadabbbadbbccadaabadaabdabcdbbadaaabadddbddacabadcdbbbccccadcaadccbdccbccbdddbcdccacacadcabacbdbccabbccccbaabababbadddcdcccddabcbcadddbacbcdcabadcabbacadcdccbdcddcccbdcdabcaccacacdbacbcbbadabbcaabbbacdbdddadcdcbcadbdcaacdcaabbdadcdcdbcbcddadbdbbcccbcbacaabbadbddbbcbcbbdcbdacdadcdbabdaccdddabcdbbaddbdbdbcdabaacbacbccbaaaacccbcbccaddcbaacbdcbacaaddbcaaacccadbadbcaabbadbcdacbbdaacdcccccddadddabbadadadabaccbdcdcbcbacacdabcdabbbbacccabcbcabbccabdcbbdbbadbaddcdbdabddacbadbcddcacabccbbadbbdbabcacadcbcbcbbddddcabccaddcddbaabbbcccbdbcacacdbdcddbddacbcdbbddddbbdbcddbabbbadccaadacabdaaccbaaddbdcdbbbdcddddbbabdcbbbdadadcbddccdcdbdccdddbdababbcbaddccbdddaacacbcbaccdcbbdbdbdaaadbbcadacaadbcadabcaacadadacbcdcacdaabadbabdacdcdbbdcbbdaacdaadbdcdbdaacabbbdbabbbddacbbcaacdbaacacaadcadacadcbdadbddbccbbcacabcadcabbababddcbdadbcdddbabdbbdbcdcaadaddddacbcbacadcdadbacadcbcbdadabdcbdadccadbcddddbbdcdcbdbcbbcaaadbabddddcdadabcdbcdabbcacaaaaaddcaaabddbbcdadddaabdadaaadabbacabaddaccaabbbdcbcdababbddbdcadaddbaabcdaccdabdacadbbdcdabdbbbbddaabdaacdccbdbadbddbdaaaaddbdcbacbcdabcddddbccacddbaabaaadcbbabaaabcacdbcabbdacdbcabcabcbcacbadadabdcbccacccddcddcdbacabababacaaddbacabbaacacbdcbcdacbbacbbcdabcaccbdacdbabacaacddabcaabdbabdbbbadadabdaaaabdabcabcbbbbaaabaacaadbdbdbccaabacadaadacbcccababcadadbdbbaccccaaaabcdbcacbdadbcabaabbbcbcaccdbcadcabbcdbbbaddacabcdcbddbaddaaddbddcdddaacdabdcacbccaccdaadbaadbbacbaabdaacaadcbdabcdddbcccbbdbcddbcccbcbbacaaadbcacaccbbbcddccccddabcdbadcdcabcabbdcddbdbcddabdabadbaadcddcadabaaccbbdbbcbabddbbadacaddaccbbbaccdcdbdacbaccbdcabacaabadddbcabcddbbaadddcdcccaaacadcdadcbdddcdcbaaacaabaabbdabaacadadaddcdadcaddabacbcddabaaabccacaaadacddbbcacccabcaacdaadbdaaaabcbadbbdccbacbdcdacadbccacbdaadadadccbdadcbdcadbcdccbcaaacaddaabdccdaccacddadacbccccbbcaddccaadadabdacbccbacbacdbadaaacdaabcbaabddabbcaddbbcacdadcdaccdbabdcdbcddcbbdadabbdadacbcacabcccdbdcbacbddcbdddddcabdcacabcdabdaabaadcddbaaaccdcdadcbccbdbcbcbdbdaccacbccacdbdacccaabacbbbdddcbadabdccdaaacbccadcdacccdadcababcbcdacddbdabdadadadbcbbdaabcadbdcbcbcdbbaccdcaacabcdccdbdbdcdcdcadbdbddbcaabbdaccbcaaadbcbaccabbacdbdcabddddbddbcdddbccacabcbabccabbadcccadbacbcabbaaadaddddbdaacbdcdbcbabcbabddadadbacbccdcbdadbaddacbacaabddbcbdbdcbabbaacbbdbdcaaadadacbadcabbcddccccbcddbaddadadbbaabaddcdadcddcddaababdacaccbbdcdbacaaddddcadadccbbdccdccaaaabacdddabdcbcccaadcbbdddbabcadaadccdcaadcbabdddccdbdccddaabbbcabccaccbbbacbadaccdbcbddbddddbbbbdaaabaddbdcccdddaacdabacabcbdabcadaddcbaccabbacbcccdcacbbacdcdacdccaacacdacbcbabbdbdcbdbdbcbbabacbaacdbdaaabcdabbabaccddcacbcdacdbdacaaadbbdbcdadacdbbaaadbbacdabcbcadbdbacdcdbcddbcababdcaaadccdaacaacdbdbabbacaddabbbbbadcbdadadbcbcbabdbbbddccbcdbacbdbaabcbadabcaabdcbdccddabbddbdbddabcadccddbbddaadaacabaaaddbdadaaddccbcddbdcdcbddaababaccadaacacbcdccbbdabdbdccbaddaacdbcabadaccdbddcacdbcbacddbadacccabaccabcaabdadacdaaccbbbdbbbbbccdcbdbaadcbcadacaaadbcbdcdadbbcdbcbccababaabccddacacdbaddaaaabcdcdddbadadaabbddcbadbcbcbbacaccbdbaacdbaddbcdbcbbcdcdcdbdddcbcacdbdbbdccddbdabdcaadadddccccdbaabdbaaabaabbbbcaacbdbcdcdbaacccbcbdacddabaadbcbdbaadbddbdcdacdacdadcacdddbbbbaababbcabdaadbcbcbbcacbcbbaddbcbbdcbacdcbadbdcbdbcdbcbabdabbcdacdbdbdbcacaacadcadbcccabdcbcccccbaaadbacdaaaabacbddbddbcbddaadddacbaabdcdaaccabbcdddadddbccadcbaddaacbcabcaccbdcbbdcbdcabdabddaaacabdabdbaaabcacdbddbabbdcabadcbccadbaddcaddcabacdacdadddddbcaaabaacdadcbbdcadcccababccdccddbbbdcacbaaacdcdcbdbadccadddcbddcbabbccbdaacbabaaaacccdbabacadcccbdbcdadacdbaadcbbbdcccccdaaddbdbcacacbbadbdbdbdccbacacbabdccdbdabbdcdaadadbbadacbacdabcccdbbaadbcaaccbcddccdaddbababcadaacdcbdabdcaadcbbcccddcdcccadcaadbaacbcbbcbcadccadabbadcbdaaacdaccbdddcacdddabcdabcbbdccacddccdaacbddcbabcbcddabbabdbbcddababdaddacadcdabdacadacacbdbcacbcacacaaadabcccddadcdcadbacbbcdacabbaadacbbbbcadaddacccbcaccadbbaadcbdbbbaababbaacaccadadbbddbbddbcdddaccbcbababcabddcdccbbdacbcccadcabccbaacabadcdacadcdbcbdabcbcacdabaadbcbbabdcaddbccbdbcacbbdcaaccadacadbdbacbbdbdcbccdddcdabbabcddbcabcbcacbcacabdcaabbadacaaccdabccdbbdcdbcbddcdccccbacddbabbaacabbbaaccbcacbcbabccbaabdbdddcbccdddccbdadcdabdcdbdbabbddaadbcbdbcacaacaaabdbccdddadbcadcaccddbbccabcbdcbdccacdddbdcaccbdaacbaabcddcdadbbbddcdaabdabdacbccbbaccdaaacaadccbadbbdbcacdaccaddbbbadbcbccbcdacbbcdaccbcbdaaccaccbdcacaddbaadbaaddadbdcbdcdbbadcccaccbcdccbcdbbdbaadabbdbabbdacdacdaddbdbdaddddbadabacdbcacdccbdabbbccabadbddaadccbcabbdbccbbcddccbdababbcdbbbcccbccbabcacbaddccaaccdcccddcdacaaaacccbadabcabaadaacadbccbdacadbcddbdcacabccadacacabcbdcbddabdbbcddcccccadccbbdccccabcdcbcbdddaaabdbacdbcbcdcacabbcdabaacaccbabaabbcbcbbadcbdaacbababdabaadcaaddcbaddcdaaaaacabdadcaccbabbddaaaadbadababdadcbcaabcbacdadbcdcbadcbddcdcadcbcacacdcbcbdbdacdaacddcccacaadabcbacaccaacbccccddbdccccbdccccaddbcdabcbacdbccbdabaddcbcabcbddbacccbaabbbbbcdcdcbcaccabdababadcdabdcdadbcbdaacbcddaccaadcadcddcbacababadbddcdbddbbdccadcbcdacbabcbbcbdddbadbddadcbdbadaaccbbcccbabdaadcabbbdabdbcccadcbdcbababcddbabaaacdbadacabccbcdcdbbcbbbacbcacdcaacaccbbbcaddacddbcbcbddaababdabcdccdacccccaacababcdbbdabccaacaccbcbadabbabbacdcccbccbaddabadacbdbadcdbdbaddddbddbdbaccbacaaaadbdbddbdbbbbdcccabbadaddcbbadcdaddcbdcacbdcabdaadcdadadaaddcbddccacccccdaaccdbaadabdbaadcddbaabbdbccbbccbdbdadccbdadcaacaddabcbacabbacaabddbdadcaabdddaaddadbdddacbbcbabaadaaaabaaddbdadddcdcadccdbbaaabcbbadaccbdcdadacaddbadcdbdaddbacccbccdabdaacabcccdcdbdaadacdccbabcacdccccbaabdcbbdabaaabdcdcacadadadcabaacccbddbacacbdbdadddcdccabaadcabbbaadbcadcdbbdbdadbdcbdcdbaabdabbdcadcdcdaacaccddddbcbbadabcbddbdaccaacacbcacbdadbddabaccbbbddcccdcbdaadadccbdcbbdbabbcaddacadcccbdcacdcaddccdcdaddcbdbdbccabaabbdacdcbadaacadbbaaccdabbcbcddbcdcdcdddbdaacabacbdabcabbbddbacdbddcabbccabcdcbadbaddaaccaadadaabcdabcccdcbdccbcbacdbcbdbcacaadcbacabadbddcabacaadbbaacaddacdbcdcbadcbcddbcadddadaaacdbbcccabcadccccdaccbcdbbdccbcdcaabcdcbbcbcccabaccabcbcdadacccddbacbcabbbabdacabaadcacccacadaadbbcddcdaccbcdacbcadbcaadcacdccaaacccbddaabdcbbabdddbabdbbbdbddacdcdadbbbbabacccdabdbbacabbcbcdadddcbbccabaadddabcabaaaccdbabbbdacaabdaabaacccdddbbbbccccaabacbaaabddcadbbddddbcdbcbbbcdbaaabaccaacacbacbbbbaabacbcbdbacbaacccdbccaadbdbcabdddabcbdbaaddbccdaccccbadccbbcdaaacababdbaacbdccbddbdcaabbdaadbcbaadadcaccbccbabdcbccabcaabbbdcacabacdccbaccdabcbcadbbcdbcadddabdcadbdcdbdbddcccddcabdddabdbddabcaadbccaaccaacbccbadacbaadaaddcdddbcddaaacdcbddddbdddadccbddcacdbdddabcbcddcdadaaddcaccddcabacadbdcbaacdccaadcbccddadabbadcdbcbacbbaddcbabcadccbbdddddcbddccaddcbabbbcdacdcdcdcbbbdacaabaccacccccbabcaccddbbdbdbdbdddbdbddbaabbadccdaccbbdbadcdcaccccdaadbaaacdbbdbbaaccabacccacbdbdbbdabadaacabdbbcdbccbbbdbcbccbccaadacbaaaddbabcacdcbaabcbccddaaddaabbaaddacdcccaadcadbdbbaabcacdcccabbcdaaacbbaadcadbdcddcbdcbacddcadbcddbaaddcdcdaddaddacabbaccadddbacadacddbabaaccacdddaadcdcdbdbbdcbccbabcbdbddacacbaacadabacbbabdbbbcccddbcacacadcccabcddddbccadacbdcdcaaccbcbabbbbccdaddcbadcacabbaacabccdcdabbcbbaacbbdcccdbcaadddadbcdcdbccaccaddacccdbbbbcdcbcaddbddabcaccacddacbbdcabdbadaddbbdccdcdcbdaaacccaccbbbbaababbdcacbbcbcbbbdacdbdbcbcbadadddadbcdcbdbbcadadcdcccdcabccdcacdbcacccaaaacbcbadbadbdddadaaddcccacdbbbadadcacbbaccdbcaaacaadcadbdababcbaaabcdaaaccccabddbddcdbdaababddacddbdccdcdbbaabacbcdabcbadbaadaabbcbdcadbabddacaaaabddadcabcdbadaabdacbacdcdaddbdcbccdabdaccadaacdddaabdcdaddcdbdcaccaabdbabddaaacabacdbbadbbdcacdccdacdbdababbdccabdbccacacaacaaccbcdacabacbbdbbacdacadcbababaccacaabddbcbabdbdaacaaacbabccbdaaccadcadcbbaadaacdababaaddacdbcbcadcdbdaddcdccdcadaacaacbddcabadcdbbadddcbdaabcbadadcabdbcaccdbadaddabbddacccdddbcbacaaccaadbdccccbbabbccabadbaabcadaccbabcdccdadbaadadcdaddcabaabcbbcbcaabcbcdacccccdaaaddbabadbddcaabcbabaacbabbadbbcddcbbadaaccaaddbbbaabdaddbdbcabbdbaacdcdbdacaccbcdcdcbdcabbcbbcdaaaccaadacbcadcdddbbacbccdbbbbcbbcbbdcccbcaaccacbcaacddaacddccdcadadbcadcaaadabddcdbdbcbccababccccabdbadaacaadbbcdadbdcdcddbbbbacdbbabdddddcbacabdaaadccdcacddaababccbadbdbcccccdccbcccccbaccaadadcdbddddbcdacacaabcacdbdbabadaabcdccadbbdddabdbaacdbcccacccbdbbddcabcdbbcaccddadbbcbdcddcbadcacbdddcadbcbabdabdacabdccacccbddadbaaabcdcdbdabacdcbbdcbaddddaacdbbcbcdbcccabcabdbcbcbdbbcbcdccbcdcaaabbbcccabbbbadcbcbdbddcacdbbbcbdbcdaddbcbddccbbbcdcadcaacacdaadcaacdcccbbcaabdccdabcaaaccbbdbbccccdbadccdbadcaccccdcbbaacbdabddbbccddbdcdcbdabbddbcddaccbbbdadabbaaaadccdddaaabcbcbabddacddcdaacddadcddcccbbabbbdbcbcddcccddbbaaaddccdddaccbdacbaccabcbcdadcbabcbbbbdcbbadbcdddcacbdcabadacabdbddaaccbdacbcdcaccbdcaabbbcdbbbdbddabdaaabdadacbcbdabbacddaaccdbaccacccaabaccabbccddabdcbcadddaadababcdacddcdaccabcdbbabbdbadacbdcbdabdadddbcdbadabdadbccddbacbacdadcabdaddacbadacabdcccbcacabcabdcabaddaababcaabcaccbcacdddadcccbabdcabdabaddbbcdbabcaccabcdabdccccacadcdcdcbdcacbaddbbabbacbdaabddbbccbccdbdcabddbbacdadabcbcbacccdddbcacbcbabdcdddacbadbddaabdacbdbbdddcbbadbbddcbdbdcabababadcbaaaccaabbddabaabaaadbaadbdaccbaddaabaadbaacdadbbacddcbcabbadccbddaaabaadccaaaaadcadbaacbddbddbbdbdcaccbcbdbbadccdbdbccadcbddcbbddcacbccddccadbbaacbaabdbaaabcddcccbbccbbcccababcbccbbcbaaddccabcbdccbacadbbdcabdbaabdbddbdcdabbbddadbcdbddadccdadbbdaaabcbdacbbaacbabaabbcccdddadccdbcaaadcabdcdaacabcccaddcaddccbbdcbddabccdbaacbdddcdcabdcbdbbdaadbdcbaaccdbcbcaacdbcaadbcccdabcdbcabcaadbbaacccbbabbabcabbbcacaddbacadbbbaacabbbcabbacacbacbccbdcdabcadacabdccaaacdddcdcdbdbcddccbdddcccccccdbbccbdddacbdcbdddaaddadcdcddbabdaabacbbaaccbbaccaadcbdccdaadccdbdacaaddbadccbabdbbccbbaaccabdcdcdddbcccbacacdabbddabcadcccbbbbbabdcbccbdccababadbbabbdddadaccbacccdcdddcbdcaaccdbbcccdbcaacbbaabbcbadcdcccdcbaaddcddcaccdaddabbddabcdbbcaadabccabaadadacacacddddabccacdadcdbddbbbcbccacbadacbcccadbcccbabacddacbadbdabccacccdcacdacbadbaadacccdabbacbbcdbbcbcdabadabbbcaacbbdabbbcccaaabbbcdbaabacabbadaccdddacbbbdabadbcbccabadcdccadbbccaabccacaaabbaddaddcadbdddaabcbbdacacccbbbbcdcacdcdbdbbbbbaacbbabdbcbcbdbdaddadddacdacdcbdccbbcdddccbacdbdddadbddcdbbaaadcbccdabddcdabcbbddbdbadcaddbaabaadadcdaccaabbbbdcbccdcccdcaadbcdcaadcadccadbcdcdbdadaacadccdaaabbbabcadbbdbddacbcadbcadddcbbacaadbccbdbbddbacdaabbabbadcacdcdbdcccabaabcddacdacbbddaaccaaacdbcbaaacadbaaacccddccccacabacdaddaccdabaabbcccccbacccdadbadadbbbaabccbcdcbabadbbbbbcddcbbccccbcabcdcabdbdaacdaadacbcddadbddadbacaabdaaccaabcdcabcdcbddaaddaddabdaccbbcddbbdcddcaacaddbcacbdaacdabdadaabbcaaaccccdcaddbdaddccbadcbbdbddbcbaabcdcbbcccadabaadcdcadadcccaabbcdaccbbbabacaabdbdcdadbdabddcccddddcdbbcbbbdaabdddbcaabacdbbbcdcddbdadddcabcdadbcccddcbcbbcabadacdcadbbaabccbccadddadababcbdcadcacbcbaaacbccccddbdadcaadbbdcadbadbccbbaacdaaccadabbcdbdadccbddbaadcadddcccdadabddaddaaadcdcbaabccdadcddddbbacbcbcbccbbaddddadaccbddaddbaaadcbcccdcdcdacdcddbbcadabdcdbcccaccadcccbdcdaabddcddcbbadadbcbdbccadcddcabcbcbbcdabdbbacbccccbdbabdabdcbdddcadacbdbcccccaaacbccdaaccbccdadddccbbcdbdacbddcabcccaccbbccacbccadadccdaccbdaacdaabbaadbccbcaaaaaaddcbddacdcdcdacabcabdbadabbdcddcddccccbcadbdddaabdabacdabaddcacadcabcaaaaaabdbdcdbbaccdccdbadbcbdacacccdcaccacbbabadadbadcbbacaccaadcaaccdddacccbcbcaacbabcaddcbcacdbcaadabdadbbabdbccbcacaaccdadcabbbddddacabdaccbadccddcababcaadcacadbacdcbacbdcbbcbdaaabdacbdbdcabbdaabaaadcdcaaadcddbbbcaadcbbdbccbcdacabcbbddcbbddadcbabdaaaddcbaaccdadaaabbadacbddddcbddadaccabaddbccddcacadcdbbbbcddabadcbdbababbbdacccbddacdbbaabcbbaabcbbbdaadcaddcabacaddbcccdbdbbcbacbabacbbbdcdbdbbcbbbbddccbdbcaddddcdcbcbcccadbcddccacabdaadbcdcabbbbdaabcdaacccacbbbaddcacdcbbdabbadbaadaacacaddcadaddabbabcacdabdacccaaccbbacddcddaaccaddddcdcacccdacddacddbbacbaccbdddcaaacdababdaaddcccccddadcccadddddadcbddacabababcadabccdbdabbcbbcbcadbcbabdaacbdccbdbccaccababbaddccadbabcdbcdcdcccbbccdaadbdcacacbccdbacaccbbdddadabaacbbadaddabdabaadabcaaaabdadbbbcdbadddabdadacdadaaabdbabacdcacdbbaacbacacbcbccdcacdacccbccaabbbcbbdcbcbddabacbbcadcdabcaaadcdddadaddcddcdcadabcccbbbdbbdcdabdcdddbabbcccdccdadcbadcdcaadbabbdcbcddcdadcaccdbbabdccaaadbababcddadcbabcdabbaccbcdddadbbbdbbbdacbabbaddaaabbbacccbcadcbaddddbbcbacaacadccdacdddbcbcaccbcdcdcdbaadcdbccbacbcccbabacbccabdbbcaabcddabbdacaacbdbacbddabcdabaadcbdacbadacdbcaabdbaccabcaadcdaadcccaaacdcdbacaddcdbbaaaabbacbababcbaacabbbbbdbdddcdbaacdbbbccadddadacbcacaccbcccdacabbdccdcdcdcadcabbdacabaadbdabcbbdaccccbadccbcacaabcdcadcdadbdbadcabcabbdcacdacdaacbabdaabacdcccbdbddbdabcdacacaadabbacabdbabdcbddbbdadacabdacbdcbadcbcbadbaaddccaacdaacdbddbdacaacaccbcbcbbadccaadccacdabcbbbdddabadaadbbacdcdacadcdabdddddbbcdbaabbabdccbbbddcaacaabaadacddddabdcddbdabbddcdbddbcdccacaccdddbdacbbcbcacaabbacdaccccccccacaabcabbcadcaabcaccaaabdaaabbdbdadcdbaabdddddadccadcbcbdaacdbcdcccbbaaccdbabbabdcadabbccadbacddcdbadcdcdbbccaabbcabcdbdabcdbacaaacdbdbacbacdcbbbdccaabcabcbdcbdaddaabcbccdbcdccdbbbacacdcadbbcbabddabbdddaddbcbacbbbbcbcdcdbacadbbdbccccacccaccbacaaaaabbbbcbbdddaddbbcadbcdbcdbddccccaddcaaaddaadacbbdbbdddccbccabbabdcbdddcadabcbacbdbcaddddcaacaccaadbdbbcbcdbaddadccdddabbbabcadadbabacbbbcddcbbacbddcababcdaadcaadacacbcbcbbdababdccccdbcccacadadcadccccbacdccacbabdccdbdcdabcdbdbcabbabdcdbdabdcacabbbbdbcdbabcbadddadbdacadcaadabadaabdabdddcadcdbcbcaacccdbacbbacccadbdabacdbccdcadccacdcacdabcbdcdacadbdbbbabbcccccdbabddadbacbbabcaaaabcbbbbdbacccdbbbbcbadacbdcbdddacbbaadbcacdacbcbbdadcabbdaabbcdcabccaabaacabbbaccaacaccadacaaaccdcccbddaacadadacccbcdaacadbbbccdbcbadcaaccbcccbdddcdcbacbacadbaccdbbcaddaddbdbbbddccbbadbbaddacaaadbddccdbaabcbabcadbbbccabcaaddcdcbdcabbaabccdcacccaacaddbcccacccdcbbdbcdaacdccabcdccbbbacbdbdbdabdbacdbbcdccdddabaabdcdbccccbdaaccdbcdabaccabadcabacdcdacbaacbadccbacbcdbdccdbbcbbbbbdabddddccbdadacdbbdbdcacbdaabddccdcbcbaaabdcccbdbcddabcaababdabdcdacbbccdcbadbdcbbddccbbcdcbcbadcaaaccddadbbbbcdadaaccbbcddacabbcbcdabdcdcabccbbabdcdbcbacabcbadadbccdddddcbbcddccbcaadbbddbbdacdcdccbbcabdaaaadacdcccacdddaccaaddbbcaadbdacaadabbbaddbacbcdaacdccbcdbccbadccdcaadcbbddaccaabbaaaaccacccddadacddbdcacdacaacdcbcbdbbccccacddadbcbabdbabcccbbcccabbbabdacbaddcdabacbcaccccdabaaccbaccdbaacabcabadcacccaaadbabadddaabababbbdabacbcbbabcdccdadaaaacbdbbdcdabbacbcdabaddcadaddcbcbdddbdabcaabbadccccaabbabcaaccbcccdacbccaaccbcbddddcaccaaabbbbadacadcccaccbcbddcdcccbcdcddbdaabaabddbdcdabaacadcadcaadaccdbcbccccaccaaabcabaabbbcbbbdbcaccbccbadadcadbaabbbcdbadcccacdbdbccdbbbdcbcbccbabbabdbccabddbdcdcdaadbbabdbbdacdaaacaacbbbaaaaaabbbbbdccbccddacaaccbcbcccdcbdccaadbcbbcbbccaccbddccccccdacabdcababbbbccacbddabcdabccadcbdbbdbcbddadbacdacbaaabcadabcadcaccbbaddabdadbdcbcbcaabaccaddacbacbabdaaacabdabcdbbabdabccdccbcdabddbcadcdbddbbcaadabbbdcabcccabcdbaaddabaccadcbcddcbdacabccaccadabcbabadbdbadcdccadaddabcaddcaaddbdbaccadacadbacbbadddbbabacadadcaaaacbbdcdcbbabaacabdbadbcaaacbbcadaadbcabbdcabdacddcbbcaaaabbacddbadcdcdaabbddadaddaabdcdbddaccbbcbadbbaaadccdbcccaadddbbaccbbabbadadcabaccbadaddaddbddcabcadabadddcdabdccbdbdbacbacaabdbaaacbbdbcdadbaddcdbcaaccdaaadcdcdccbdcbaccaddbacccbdbacacababcbbdddadabbdaaaaacdbdbdccbababaaaccdaddbddccdabcaddbacbcdccacadbcadaaabbdbaababcdabdbbcbaacbcbcacbaaccbcbccdcbabcdadddabadacbccabbadcabadbadcccaabaacbacdaaaccbccdbdadcddaabccabcacdabdcdacbaddbacadccccdaaccabccddcdcbdaadcbdcdbabcccbcaaccbadaacdcdbcbacbbbbcdcabbcbdaacaaacaacadcbccabcaccbbcbcabccddbbbacbcccddbddaacaabcacaaadcbbaabdccdaabbaabbcbbddddcadaacbddbcaccdbbdcbbaabcdcbacddcbabbdccbcbbcabcaadcbdcacbdcbdbacbbdcacbcbbddbaccdddbbbbacdacbbbcabcdabdcaabdcdcaadbaabbbbaddbcabaacbabcdabdacdbddcaabbdcacbdaaaabbadcddcbbabdababbabacccacaccbdcccdadbdacdbaaadcaaababddadcbcbadbcdccccdabcabbaadbdddcbacbccbbbdaccccbdbdcbbadbbcccddddbaccdcacccdddadabaadbbbadcaaadbdbdbbdbdbadccddadcaccbcaabcbabccdbcdcbbbaaaddaaccccacbdcadbbbbdadcdbcdbacbabcbbdbbabcaaaadbacddcbbbacbcbdcbbbabdddcdcababcbdcdaadbbcbbaacaadbbcaadccaacddbbcbbbbbddbbddaaccaabdbcbcbdccbdabbddddabcdddddbdaacdccdcdadaadabdddbadcdcddcadbaaccadbabbddcbdcdccdbccbacbdbccccabababdabcaccbbadacadbcaccacbddacbcddcbcbbaabbbaacadabcabbdccdabcdbcadcdacddbcadbaaadcbccabbbcddbbacbcccdacadacacaccccdbcddacacbabcbdbccdbbddbbacdbdcbaddcccbadaadaaccdbabbbccadcccccbcbbddbcdcacbccddcadccdbaccbcadadbcbcadbdadbabdccabcbbbdcddcadcbbdabcaaddcaadbdbaabccdcaaabbaddcdaacbabbcaaaddbdbacddadccbdabdbcaccddbbdabdcacddacbaadaacdadbbbcbdaaaccbcbbddbaccbaaaabdbdaabcddaaabdacabcadbbdbaacdddccbadbdbbbbbcdcddacacbbdccacddbadabdcdabdcadbadcbabcdddaacbbbdddbcbccadadbbbaddaddcbdcbaaaaacacbacaabadbbbacdbacbbccbabdcbadcccdcdbcbdcdcababdcccbaddbdbbdbaccacabbccdcabbbdcadabcabdbbadcadacbbadbdbcaadbbaccbacbddcacdcacdcdcddddaaddccdabcaddcccabbdbddacaabacdbcabdbadcbbcdbabdbcadaccdbdadaaaaccaaccccbdbbbbacbcaabcbaabaddcbacddcabcdacddbbdddcdaaacdabacdcdcbcdddabdccbabccdadaaabdcddbbddbbabacabdccabcabcabacddbbbaaabdccbddbdacccabdacbdcddacabbaabbddbbadabccbbbbddbabddaaddaaaccadaabbadcaddbcdbbadbcbcddddbccdabbbcccbdbdbdaddabbabaaccbcbbbdccdabaaddaccacdbdabdacbdbcddbacbcbdadcbdbddbbccabdddbcabaabccabccbdccdddadbcababcbaacbcdacccccacabccadacbbbaccaccbaaaccdbdcbbdabbdcadadbcccdacccdaccdcbdabdaacbbbdacabdabcdddababcabadaadcadaaddbcdbdcbcdddacbaaacdddadddacbacacdabbbbabdcdaddbdabddacdbaabbddddaadadbccbadbbddbcdcaddcaacdcabcdcdaacdaacbadcddababcdbbbaababddacbcacaddabbdcdcaadaabdcbcacdcdbdabdddbacabcbababaccaccdcdabacddcadbcccbcccddbbbcbadcacacabddadcdbdcbcddcacbddddaabbbdbccdbdbcabcaabddcbcbabcddbccbbbabaadadddbdccdadbbdddbadddbccadbbddcbadccabcddcdacaaddbbcacadbbacbbdbcbbbabcdcadadabdddcadaddcaabbdacbaaabdbdaabcbcdacbbbcbbbcdbbabacaadcbcadbabbadbcaccddaadbadbdcccddbaadacdcdbdbdabdbaacacdbaccdbcaaaadacbcabcadaabbacabbdaaddddbbbcbadcaacaaabbbccacdcadadabbdbddcaaddcdadadaddbbcbdadacdcbacbcaabaabaddddaabacdbabbcaaddbadbacaadabcdbcbbdbdbbbddcabddcddcabdcaadadbcadcdcabdcacaacdddaaddbcbaaadbccaababcdcddbbdccbadbadbbdcbaadacacaabdcccbbacdcbbbccccdbbbcbbdbacbaacccbdddadbacbdbcccbcdbabdddabcacbbcaccdcdcbbdbccaccddddacbbadcaccaccdacdbadadaadcddbaaaacaacabccbdabbdbccbdadaddcacdbbadbbadcbdcacdabbaacddcdcdbbbdbbdadabadccbddcddbabcdccbabdccddbdcadddcacbcdabcbcbadbbbacbbdbcbbdddccabdadbccaabbbbcccaadcacacccbdcaabdabcacacdcccbdabacbaabadaacadabcadccdbacdddbcaacbcadcddcaadddcdcbcbdbcccdccbacbabddcbdbabdbdbccbccaaccdadcbcacbbddbaaadadcbcabaddccddadcbaaaddcbabbcdcaacabdacbcccbccbbadacbabbcccdcabdbddacacacacbaadcddcbbbbcbacccbaabdabcabdcaaacaddcbacaacbcabdaabcadcdbcbacdcbbdbdacccaadbddbddbabaaacddbbacacbbbbabcddaadacbbcaabccbcbcbcccdddcddcadaadccdbddbbdcddbaadbbdbdadbdcbdcdabcaaddbbabaabcdacbdbbcaacabcbccadcacccbcbdabadabbddcaaaaaacaccddadccbdcabcbdccaacadbaabdadbcbcbbcabcacabbcdcdacadbdacbbcbdcbdadcdbadcbaaababbadbacbccbcacdcbabbccdabadbdbcdcbbbcbcddbaaddadbbdcdacacbccbdbbcbcdcadcddcadcbadcacaddaaabaddacadbabcbbbdccaadbabbdaacbbdacbcdacadddabcbaabcbbdcddbdadababdbbcbbdadbdabcbddbabadadcccadcdcdabcbdacddbdabcddbcbbaddcadcaaadbaadbdaadbdbbbaaaaabdcbaabdacdbabdcbddddccdacbcbdbaddaddaababaddbbbbbadbccddabbccdcbbcaaaccbaddcaabcbacaabdaaaabdddacdbdaddacaaddcaacddacabccacacddbbbbbcccbdcaadcaadaaccdaaccacddcbdccdbccddbbcbcbdbdcdbaaacdccdadadddabdadbdbbdbaddcaaadaadbbabbbadbbccacbbbbaabbacbaabbbcbacdcdcdcacacdbcddacdcdcbbaaaaddbdcbbcaccbaccdccadcccadabddcbdaacdbaaacbcabbcbbdbddaddcbbcbabdaaadbaacdbcbddbccabacbbdadbcbdaaacdbdcddadbbcdcbdbacabcbbdadaaaaacadcabacacdcbbaaadcdbbbadcccbbaaadbcacaabacdcbdbdabbacdbabbbbadacbbdcadbadaccbabbacbddcbddcaaaddacbcbcbcabcbbaddcdbdbdbbbcbdddbcabcbbacbcbabacbaabbacddbcaaadbcabdcbadadacadbcdbdaccbdabacdcadccbcbaabadcbcadcccbcbbaabccbbbacbbbdbdccadbccddbbccbddbdbacbccbcbbbcadbdabbbbcbbabbcbdbcbcbdacbadccabbaccacddcbbcacddbbddcbdbdaabdabadcadbdbbcdaadbbcbcdbaddcaaadbcdcdcbcddadbbdbddcbadcaccddccddacdaddcacabdaacdccaabbdbbbbbbbacbdbcacdacdbbadcdccdcdcbdbaccbcabbbcccadacaccdbbabcadddcdcddbdadacdbdcdbadddbcacadaccbaaabbbbabbcabcbbcbdbadaadbdddadbbababacddbcbdaddccbdddaadbbddbacccbcccbcbdcdbddbcbcabdbacccccdbcdaddbbddcaddaabcbddbcacdbabdbcdbccdabbcadddabcdbcbadcccbabcdabbdadcabbacdadcabcdccdbdadbbcdcbbcbdbacbcbccbdccadbcadaaddddadcdddadcaaababbbbadbbdbddaccdddabcbdbaabcacbbaccdacacbdcdddabcaccacbdcdcbaababbccccadadccdbbdabdcdcabbdcbcdcdabcddbccbbadcadcaadbabdcbcbdbdacbbaaacadbbcbacbbbdaaaccdbbadabacaccdbbbabbabcabdbccdbaadacacadbbbaccdbcbdddbaddcdbcbaaadcdbcbaabdbcadcbacbaadacddcadcbcdbcccbbdcbbbcddabcdbabdccbabdccccaaccbdaddbdbaddccddcbabddadbaacccbbacddbdcacabbddacacccabcabadbdccdbaaaacacbdacbaacbccacacdadadacdcccdacccabdadbdbabccbcdacdddadbdadbdadcbbabbddbdbdbcabcccdccaddbabdbdbaabcdddbcdbbabaaadcdbaddddbcadbcbbdddaabbacbaadbdcaacaadccadacaaacddcacbbbcabadbaaadcccdbabbddacbbdcddadcccacaacccaddddaacbcaadcccabaccdadaacccbacdaddbbddccadcdacaaaadddacdaddbacbdbaddaaaccbcbdbdbcabbabbcbacadaaaddbcbdaaadaabaaaaaadaccaddcdabcdccbbdaaadcaccdcdcdacbacccbdbaccdcccdadbbdbdcdadbadcdcaabcbdbcdbccdabcbccccddcdccbbabcaccbbbbdacdcdbddacaadddcccadbbbadbcbbdddaccbdbbaaaacccadbcbcccbacbabdcacddcabbbcddaacaccdbcdbacaccdccbddbcbdcbaadcccbccbaaadacdabbccbccddcbddcdbcccaabcbdaddbbcdbdccccccabbabcdcccbcddbdbbaacdbccdaddbdaacdcbcabbacbdbdaabaddccacdabbbdccdcddacbccbcdcdbdadbabaaaaadcacabdbbcbccadcccaccbdcddccddcdabdbadaccaccadcabcdbcdcddddadbbacdbbabcbdccccccaadbbcbdacdadbaaccbcdbadbbbdbccdbababdbdbbbaadababddcdcaabbbcbadacbdadbcdbbbaacdcddcabcccadbbacccdbbcccbaadcabddbbadaacdabacababaddbccbdcddaadddacccbaccdbcdbacadccddccbddbbdcccbaccadadddbdccbbadbaddcdbbdccadcbbbbbbadbaacaabcdcabaaabaacacbdacabcdbacdbaddbabdabadadaabcacddbcddabcbabcdbacbcaabbabacacbcacadcdcbcaccdddcacdddcdbabaabadadbaaaaddcaccbcdcbadcdaacdaadcbddacbcccaddbbcbdabbcaaaabadaddbccbdacaccdcaaaddcddaddcddcdddbadcbabbbbbacbbbbbdcbccbabaddbcddbaacabdddbdbdbbdbcccbaaddcddaacaabaccacadcbccabcbaabdaacaacdcbdccdcccddbbbcccbbbbbddadaddcbbbcbaadaacacdbcddabadbbbabdcabdbccabdacaaddbdbcaddacbbabadbbaaddabacddbccacbadaccbcdbbbbbcbdadddcbcbabbbccddcdbbcdcddaacdcdbddacdbbccbbacbacddbabdcbdacccabbadbbdcbdbbadbdadacdbadcdacbaacccbaaabaddaabbadababdcdaabbbaccaddbdbbcabadbdbbcccabaabaacbddcdcacbbacccdbbddaadabcaabddcbbddabacabdadbcaacbbcaccbacdcabaccaabcadcbbdbaccaccbbacccbbcbcaaddbabadadacbaaabcaaaddcddddcadadadccddbbbdabaaccccbdcddadaadbaaddcbcddccadbaddbdcdcccbcabdbabcdbdabccbcccacdddbdadadadaacdcccacbaaaaaaaacdabcaadaccdabcaabbbaacbdcccbabbcbbcadccdcbbacabbabccacaadbabbacccaaaadbcabddbcdcacbddbdcbdcdcdcddbacaaddbcdabdaabbbbdadcdabcdbddddcbdddcbaaaacdbbacaaacdccbabbaaddabacdabbadbddcaadacccbdbdcaaaadacabbbaadacadbaabdbbccbbaddbbbccaaababdcbdbccadbcacbcbadaccdcbacdcaabccccbabbbbabaaadbcbdabccacacdadccdcacbbcadcadbdbbcaaccbdbddcaaccdbdbdcaaabadaddadcbadccacbadbbcdcadaddbccaabdbcdbdbdabdccdaacabdadcabcbbcdccadadddcdbccaccaabacdbdcdbadbdbcadabdbdccccdacdacbaaadbcdadbaaaabdcaabdcbbdddcacbcdbdcacababbbdbacaacbdbdbddcdbbbabbcacbbadabadacdbcaabaaccdaddacbcdbdaabaadbaddacbadccacbcdcdcdbbabcdadbbdacddcdcbcadbbcddcdccdbaccacadbdddbdbcbccbbdaaddadbccddacdddcaccdcbacbbbbababcbacdcbbbabbddacadcdaadcccbaadbdbdcccbbcadbbddbaccdcbacdcbacddabcbdbdbdccbacbbbbaccdbcbcbabdcacabbabbcadbccccbbdbaccbdddcaaabdbabddbdbacdbaacddddaabcbdabddcabdcddbabdcbdccabcadbbbaacbccdcdaddcccbcbccddbbbadcaadbdbcbbcadccacadbcbcbbbdbbacdcdaadbbabdcbbdccdbcabcddcddbaccbacddabadabbbaababbaccabcdbbdabdbbbcbbacdbdbcaacdcddbdccccbabbccccbbdcdabbddcccaacdcdbadcadccbaabbdadbdddddbbcadcddbbcddcbbadddadaabcdbcadcdddbbbbdcbddccaaadbaddddddabdabdcdccdacbacaaccccabcccaddbddaddbbbbdbbcbdbaaaacbccbdacabcbabacbbadacbdbdadadacadaccbdbddbbaacccadbcbaabcbcdcdadaaddaadcdbbadbdabddabaaccccbcccbddaddbbbdbaccccbbadccadbcdbacbdcaadaddbababacaadbadaddccddbaadddbacccdbbaadccbcddcbaaaabbddcaccdadddaacbacabbdbbcabddacaabaacdbcacbaadbacbacaaacabadabbccbdcbbabdcbaabcdcccacaddcccaaabcdddbacbadacabadddbabcccadbcdadddddbabbadabacdbbbdbcdbddabaabbbcbbbbbbcaacddbcbdacabcabdccabcbdabdddcdaaadbbbaacdcbacabddabcccadabdabcbbbabdbdaaaccdddcdcbddaaacabadddacdcbabadbdacdbbccbadddccdabcbcacdabaadacdacaddbbdddaaaacccabbdcabcdbcdacacacadccdabcdaaaaddcccbadadbccaacccadcdcbcdabcdabcbbdcdcbadadbacddbadacaaabbccacdccddaabdbdbaaadcbdbabcaaddbddadbcdbadbdabbdbbcbdddccbdbdcdcccdabddccbaabdbbdcabdcbbaccccdbdcdcbddbacbcbbbbcbacbabaababadcdcbcdacbbbbaadbcbcacacbdaddacbccdcbaccbcbdabcccadabbcccbcaccaccaccabcbaabaacdaccadcaadcadbbcccccaacadcdcbdabbdbcbbdbbcdabbbcdbdaadddbddbaddbdcccadbadaccbccbccbdddcabadbbbdadaadbccbcdcababcdddabcdcbacdbcbdbcbbbdccbbacddcdcdddaacadcabdcdaacdabbadadbbbccabacacabdcdcacdcdabcccaaccbdccaaacaadbabbcdbaaaabbabccbbdacddcbabbbdbcbacccacaddacababcabddaabbcdbbacdcdadbcdccddcadaaaaabbaadabcccdcbcdaabbcddbacccbdbdddaccdadadddcacdaddadadcdccaababcbdaacbdbdadaaabcacdcddaacbcdadacbcaccdaabccbabaabcacabcbdcabcaabdadaaadaddcdbbcddccbbcddbccacacdabacddddcccbbcbbaddccbddabbbaddcdabccabdccbddaaccddcdaddabaadbddaaaabccbabcacdcadddccbcacabbadabbdababadabaaadbbbadcdadcbdbcacbcbddabdddaadacbddcbdcdbddccaadbdacbcbddcdbccbddaacdcaaddabadcaccdcbcdcbcbddcaaddabbdacdccadabcadcdcdddcbbacdccdaacdacadbbcdabaabcbcddcbdccbccdcdbddcdccbbdbbddddcccddcabbccdbdcbcbbddcdcabdadbdcbdabbdbdaddaacbacccaccbcacbbaadcdbdcbcacaccbcdabbbcadddababbabacbdddcbdcaacdbcbbdacccdcaaababaacccdcbabdbadccbbdbbcddacdcaabbdacdcbcacaccaacdcadbdbcbdbacbcddadabcbdcdabacaddadaddddddbcabbcabaadbacdbccaaccdcbcbdbacdcccdcddbbbbccabbcbdddbabddcdaacdadbdadccbdcbadaabcdcabaadbaabbdddbbaabadbcbdaabbddccbaaaaccdadcaaccbacddbdccadbdcddcbdaadcbbbabbcabaadcaaddaaacdacaacdcbcdacbabbddaddbcbbaadbddccbaddaccababccbbdbcdcbbcdddddccbcbadddcdcacbbaaccbdbddbbcdbcaccdcdaccadbacdabaabcadacbdabacbdddaabadacddcbcaccddbdcdabdaabbcdadcabccbcdcccadaadbbbbbcccdbbcdcbadadddbdcbcbaaaddcaacdbaddbdcaadbbdcaaabdadbdbbbcadbbacdbadccaadbccdacddcbbcdabbdcdabbbabdbddbdaaadaddabdaccdaddbabaddcddbdbaadcdddddbbbaacddcdcbacaababdccccbdccddcdbdadddabbabccacdbdcacccbbbcacdbacddaadbcaddcdccaabcbbaccbccadbdbdaacddcdcbcdbdbccccaaadcabdadbccbaacaabdcdbabddcdcddabdabdccacbadccdcddbdbcaddcbbcdbdbccadadbdadccaacaadcddccbabbbdbdddddddbacdbbabddbdbcdbccdcbacbcbcbaabbdbbbbcbbdbdcbcdcacaadacaddbbbbcbdccddaddcbabacbddcaabdadadaadddacdaadaccadddbbacddbdbaaaddacbbdcbbbddabacdcddbbbbcddababbbdaccabbdccabcabdacbcbacadcbdccaddacbcddbccadcbccbddabaadaaabcdbccacabcbabacaddbbcbaaabbbadabbdcccbcddcbadaabbbccaadadcddcdbaddbbcdcaaabcbcccbaaaabacdcbbdcbbaabbdccddcadcaaccabddadcdcdaadbcdcbdcacdadcabdcbdcaabdbccdadcbaacbbdddcbcacbadbcadbabbbcabacaaacbbaacbaccdbdaacbbccdbabccacbacbcdabdabccbcaacbaaccadbbdaadaddcbdcdbccabbbbccdcabbccabcdadadddccccdddcccdbddbcdcbabcbabcdcbdadbdacddcddbdccdddcdacacdaabdabcaadaaddbdcdbbacdddacaaaccaadcdddbcabcacbbaacaacbaccdacbcadacadacccccdadbbbadddacbcbcbacddbcbabaabbdcbcdccaabbddbccadadabbccbacdcbaddddbdbccbbccdadbbdbcabadbcadbacacabdcaaccbbaabacabdacbadabadcaccdcadcaddbacaacccdccadbadacdbdcbbdaddabdbbabcbadaaaaabdcacddbbabcbaabbbcbaadabbdaddacbcbaaddbdacaabbcadabccdbabccbdabbbccaacabbdbdbcddadbccabccdccccbadabadcbbbccbaaddbbacaacacdccccbaaccaacbadbbadcdbcbaacbbbbbcdaacbbdccbdcdcabccdbcddbcaccacccdcdadcadaaddbadbabccbacbdcadddbbbacbaaacbabdcaadddabaabbabcdbccaccdbcaacbbbdbcbacbddadccaaddcdcdabbbcadccccbccddbbadcccabdbcbacdcbddacaacbaddabbacdcccdcdcaabcdadcadbbaabddadadbaabaadcbbcdcddcdbbcaabaccbaddadbbaaacdadacbbbaaadaddcdcbbcdbbdabddcddcdccabcbbcbabbcabccacdccbbbacdbdabbdcbddcacbacdbabbaaacadcbacdbdacbaaddacdcbccabbacbadbcbdbbbbbacdbcbdbaccbabacddbadbdccacadacbcddaacbcabbbccdaccadcdbacbabcbcdccabcdadcccddcacdcaacbaabdbbbcabbaabbdcbbcacabcbdcaaacacaabdaabacdbbdbabcdaaddcddaabdbbaddccbcdddaadacbdccbdadccdaaabaccabcbcadbbccadbbbccdcbcabcbadcdabacdbcccbaabaacbbdaddbbacacbdcdabcaaddacdbcaccdbcdbcdbdbadcbbadcaacdbbaadcdadacdccabccaacddaddacccbbabdcaddbbddcdbabbccdcbdbbacbccdbdaababcbbdcccbbccdcbbccbdbbcabbcbaddccadcacbcbaaadccaccdadbbdabbdadadacaaaaacbccbbcdaabbdcdcbcdddabbcbcbbacacaddccadcaacabbcaacabcddbbbdcaaccdbdadacdabdbccdccadcabbdcbdbbacabaababdccdadadaadcacbbddbabbdbddbdacbbcacccbbddaaccbbadcabbcbdbdbbcddddbbdadbcbaddabaabababbdcccdcbbabaccbacdcdcbcbadccbdaaaabcbcadacbadccbdacbdcbddbbbacbdbcdacbacbaabaabdbcaacddcaddadcddbddacbabadbacabcddaacbcddabcbdabdadccaccbdcdddacdabdbbabbbbdabadabbdaddcbaccabddbcdcccabadddcaaaddcacdabcdbddacabbacaaabcdcdbddbadcddadabaacdcccabacbbcaccbaacbccbcdabdcdcccdaaccacbdbddbaabcdddbcdbdddcddbdbcdbddcdcabdabacbccdaabcbacdabacddcdacdccddcdcbcabacabdccbaddabbcaccdbcaddabdbdaabcaadddbcababbdcbbdcbaababbabcccadbadacabbacbbbadcabddcdccaccacddcccaadbdbccbddccdbdaadbdabdacddccdbdcddccabdccaccddbadacdcdcacbacdcbcabccdaddadddcdcddbaadabbadacddccadcbdabbdcadccaaaccacccaddabaacbbcdcabdbadcdcdcbdccdabdadcccddababbddcbcacbadaaccddaaaadadccaadbdbbacddbbddcdaacddbdaddabdacdabcddbdbbababadbcbdaddabbcbcadaacaabbddcdcdcabcabcdcdcdbdcbaabbbbdcbbbadaddddbdabdaccdbdcbcaaddcabaabbbadbbadaaaacabddcbdbadcaddccbabbcddbaddddcaaccddbacbdbabbaddbaccabbdbbddaabacaacaacaabcccaaabdadcdbccccbccaccbddcdccaadcbdaccbadccdbaddddcabbddbcadbdcdabbddddbaaaacabdccaadacbadacccdddaabdaaddabbcaccddacbcabcacacbddcdaaddcaabbbadcbdcabcadbacdbcadbbadabccdabaacbdccaaabcddbbdaabdacbcbadacbbbccbddccaaddacdbbdabcbcddaaadddadcdbdbdaabddbabdbaabbadbacacadddbcbbaacdbbadcabbbacdcbdabaddaddddddbdcabdccadbdbddcccabbaaacdbdccbacccabadabdaabacadbbabbbccbbadaaaddacbbadcdcdddcbcbaadcbddbcbabcbdccdcbccadcadaaddbdbcbcddabccdccbcdbccccdcdbdccbccdcdccabbadaddcdcdacbbccbbbacbaaabbadbdaadaddccbbabccaddccdcbbcbddcccbaddaaaaddbbbabadcbbdddacacbbcbbcccabbdaacbabdcddcbabccccddabdcadcdcaacacccddcbbbbdcbbdcddbbaccccddadadbcaabdccdbcbcadccbcabbcbbcdabdbacccccbacaadcdbbbbcaacabbbdbdacdbcadbcabdbcdbddaabbadabdcbcaaacddcacdcaccdbbabccaaccbbabbdabcdbadcbddcabadaacdcbcadabdbdcddbddbabdbdadabdcbbacadacabccdbcbbdcdccdcadcaaacadcbcbbcdbbaaacbcbcaaacbbcdbcacddaacadaccbcabcdcdcbccacbcbcbdbacdadbbcabccbdaaadcbbbcbcadacccdacbbdaddaddbdbdbddbcabbbcacaadadccbdcbbdcbabcccadcabcddcdcdbcbcbcbaacbbabbaaacdcaabcacbddcddcadccaabdbadabdccbaddaadacddcbdabcacdbdacadbbbccadcabbaaacbadbbddbabcabcbcbabbabccbabddddcdbdbdbcabdacdbabcbabddaaacbcabccacdcbadcdacbddccddbccbcdaccdcabbdbcbddababbbaadbddbdadacabdaabddbddbabadbccacadbbcadbabbbaddbbcbaaadddbaddcbaccadbdcbddbdbbbabdccddbcaacaadbdabadddadcddcccdcbbbacbbabacabbbbcdcdbddaddbddcbddbdabdcaccddbccddbbabbacbacddacdcbbddbacabaabcbdacbadbbdbdbccacadcbacccbaaaabbadbbcacabbcdbddccaabcaabccaaddaaacacbabcadaccaabcccbddccddaabdcaccdaacdcdadbdaabaacbbaaabcbcbdcbcdbadbcdccadaabdacdadcbbddbbdbabccdababccccacccdbdbdccabacdccddbccabbbbcbbbaaaaccdccdcdcacbbaababcdcbccddcaabccbbbdadbbcabadddbcbdadbbbdaaaddbdadbcdcadcbdabdabdacadaaadbbbbccabbcabccddacadbcbcdbcdabcbcbcabbccbabacbadbddccabdbacddaaadcacccbddaadccbddccdcabcbbcacaabccbcdabaaaccbdabdacdbdccbdcdaacbbdccdbcabbcbaabcbacbbddbadacdadcbdcaaddccdccddbcaacbcaccbbadbbdcdccbbbbcabacdbccbdbbdbcdadcadbdacdabddadaadbcaccaaaaddcbaadddadbbadbcaaacccaabdbddddcbccbbdbdbabdbbaaaccbcbbaddabbcddaabcabcdcdcbbdacbcbdbcbaddaabdbadcbbbacbcdbaccadacbccbdcbbdccbcaadcddddacbdbbadaadabbdadbaccbcacabbdabcdddcacaadcdbbbdaaccbdaaaabbbddcddbdaccbdddcaaaabaddabccbabacbacdbabaaababdcdcabdbddcacadacddbddccdacdbddadbcbdaaacdbdaabacdccdddccdaddcddcadaddbcabdadbdaababdbcbccbdcdbababdcabbdcaddcadcdadcaadcbbbdbcacbbdabaccbdcabbbcaabacbdacaddcbcbddadcaccbbaccbdddabaccacbabbaabbdbdcbcaccccddacababaadddbdcccaadcaccaadabccacbaaadabbcbddbaadbdaadbdadadbcbbacabbbbdbdbadbdcdccaccacbbdadaabccabcbccbcaacbccabbbabccbcccacaccabbdcbdbdaababaacababdcbaacbcdbaaadbddcdcdaaaddccaddbbdbadadbacbabcbadbadaddaddadadcdbbabddcdadbdbbbdcdcbbdbcccbbccabcdbbcaddbabadacbccbcdcacaddcccaaabbbadbabbcbbccbadcbbdccccabcbdcdcbbbdbbbadcdadaabbdbdbccabadcdbbdabcdddcdbbdbcbdbbccadcabcccadbcbbacdacccbdcddcbdbcacdcbbacabacdaadddbdcdcbbbdddbbdccadcaccbbabaaddddcbcabdcabcbcbbadcacccddbacaacadadaadacbbbcdaddcdbcdcabcccadacbbacbbdbbacdbbbddacdacdacdadcaaddaaccbaaaacbddcbdbbadddddcbccdadaaaddabaaccbcabddcbdbbaacccdbadbccaddcbaccdcaadcbadccacdbcdabaabbdcbacbdcdcbaddcbbbcdadcdccbadcaadbdacacaccbddbbbcaccddccccccbdaabccddcbcdcccaaddcdacbcbaacaacbdacddbdcabcddacbbddadbbcabaadbbadccbabdcaaddbcddaadbbaadadcddaccdbbcacddcabacdbaadcbdbdbbcbaadadbbbbdcbbcacdaccddccccabdbabcdbdacdabddbacbadbcbacbbaabadbcaddaaabcdabbbdbbbdcdaaaaacdacadbbabdccbbaacabaacbcaaaacaccabdaadadbbbcdcbdabbdccbacbbacbdbbdddbbadbbcccbbbccdcdbdbbcaadbadcdcdcdbbccacbdcabddabbbaaddddadbcaccdbcaccacbadcdbccccccaaccaaccaaadaccdbcdcadabbabbabadacddcdbbcaadbcdbbadbcacbadbdddccdbcdacbbaacbaaacbbaadaddbccaaaabbdaccaccbccddadcabddbabdaaccaabbbbbaaabcdaaabbdcdabadbddbcdabbbbbacdacabcdcdaabadaacbaaccaaccacbbbcacbadabdacaadabbdacaaabcccdacdadaddcdadcabbadbcddaacbcbdabdabdabbbdacbdcdabdccbbbcacdabaacddbbcbcbddbcadcdacbbcbadaabccbbbccbacaabccdbaaaacdacdbdcbbacbbaddddccbdabcdaccbbdbbcacdaacbcdbbddbabccbacdbacccbddbabdabcdabdbddadddddddbbbaacbbbadababbbcbbadbdddacadaaabbdcbdaababaccbadbdaccbacaabbbddbcbdcadddccaccbbaaccbabdcbbdadbcdabbcabaaddbbacbdbbdbabbcbbcacacddbccdadccbbaddcdbbcadcdbdaaaadbdbadadcadbaaddabcccbdccdbdaaadbbacbaaadbdabcacbabacbacacdabbbcccacabacccccbdccdbcdcdcbcbcddcdbabcbddbaabddadbbababbddcbcbbddbacadbdbbcdbababbbaddcbbdccdbdcccbbbacaadbccdbcdbcddbcdadcdbdccdbcbacbcacbdcdbbaccccdbdddcbaacadabaabccdaddbccabbbcbcabdccddccbcbddbcdcadddaadaccaccaacddaababacacababcdbddbabacadacdaccadccbccddabcbaaddacbdbaacbcaabbadabcddddddabccdabaadbdcddaacbcabdadadcdaabbdaaacccabcbabbacdbbabcbcbdadccccdcbbaaaadabcbdabbbbaccbddccdcddddcdbcbbbbdaddbbbbbbcdcccaaaaadcbaacdbadbbcaaadbbbadcdabddbdddddaccdcbbacdabddcdadabdcddacdcdccdabaaccacccdcaccbbdacbcddabaddbcbbabddbdcdacddaaddddbaadbabaaccddcacdbbbacddadbcbaacdbbdbabbbcdcaadadcdcddacdcbbccbdbccbbcdacdbcbdabbaadbbdccdcddcccdcbdbaacadbcaaddadacaccbadbabbabcdabacadbaccaabddbdbdbbcdcbbbdaddbadadacaacdcbcbbadbccdbddacddabbdbbdaccacacbacdbcdbcddacacaacbbbcaddcdbccabdbbdbcbbcbcbaddbdcacdbbdcaaabcdccababdbbbcabcdbdcccdadabddccabbbdccbcabbdabdbbbdadaadadbcccababbdadddccaccacabcdabdbbbccdadbabacbcabbadbdbcacbbcdabbadbaabbdadbcabcbadaabbbabadabdcccaaabcabdbadacddbccaaabaacbcadadcbbaddcabcccababccabbbcddaadacabccbacbcbbaddbdcbaccbdbccbbdbbbacacaccaccbaabbcbcabcdbadcddcbabbcbadcabddddcbbcaadadababcacbbbbaddbdccdaccdddbaabdbddbccbaabdbabadbdcdbdcdbbbdccbbdcabdcabaacdbbaadaddcddbdacbdabcaaccaabdacabcacccddbddabbadbbbadaddaaddddbababbcdabacbbcdbbdadaddccbacbdbbacadaccddddddadabcbccabcdacadcaadbcdccdcabbcaaacbbdcdacbdcdbadaddbccabccddaccdacccdddcaacdccabdadbdaabaaacdccdbcddcbbbcbdbadbcccadcbbdacdacccaddcaccacdcbbaabccbbcbbabdabcdaabcbcabaaddaddddbcaddddcdaadbbbbdadaadcbbdcbbbdabcdcccdbbcacccaddacabaadddbccbbbadddddcddaddbdcacdbcbdacbbabdcbbcadbbabadabdccdabaacabdadbbbcdabcdaaabbcaabacbbbcbcddbdccdbcaababcaddccbcdbdcbdabcdcbdabbcddaccaaabdbabaabddadcddbaabdadaccbbcbdbabacccacaadaaacabdcbdbcacaacbacdbbcdcdbaabdbcaabcdbbadccddcdaadbbdccabadcadddbdaaccdcdcccaabaaacaaadbcbabdabbcacaabadcccbdaacdcdbabccccbabdabdccbbddcaaaccabaaaacdbaadcaadaddacbaaacbdbdcdaadabadbddabcdaacadaacbddcaaacdcbbcdcbddacdcccccbbcbadcbcaccabacdcddcbdcdabadbbccccacbacbcccddbbaacdabdbbccddabbbccdddbaaaabbbbbbdbacbdccccbcbcacdabdddadccdddbddcabdccdabbabadbbdbcabadcabbacbbcdbcbbbacbdaccacddcdcbbddabdbdcddaccadbaabdbadbbdcbadbcddaababcbcadbcddcdbbbddbaadcdbacdccccdddaabcabbaaaaddbcccbcddbcbdabbbbcdbcbdababaaabcbdabddabcbbaaddcabcdbaddadbcaaabadddcbcabdadcbcadadbbdbccaacbacdadacbadcddcddaacabbbbccdbabcbcddcbaabbbdcabacababbcdcdcaadabcbdcaacadccaacbbcbbdacacabbbbcdcbbcacdadddbdadbdabdcbcacddaddbbbccbdccacaabacccbabaddabbaacabbbdcaabddddbcddbbadcdbacdadcbcbbdabacbbccdababcadbbdbcdbdcbadbacdbbcddcbbbbcdadbbcbdbbdbddbdbaadadaccaaccddcbcbbcdacaadcbaacbccccabadadcaabdacddadaabcccbbddaadbababcdbaddacdaadbcbcadcadbcdddabccddcabacbadabdddabbacdbadbbcdbdaaaccddcabbcccacddbdaacbdcaaaaddcddccbcdcbddddcccaaaabbdcababcdbacbccbacdcacbdbcbbbabadddbcdabcdbbdcaddbcdbacbbdcbbcddacadbcbddcccaddabaabdcccdabacaccdababdbcddccabadcbddcaddbadbdadcccaacbcbcdddbcbadbcddacdbbadaaddaadbcbccbddcdcadcbdcacbddcddcbacbbaacdaacadbbcbdddbccacbbcadadcaddddbbcaddccbabcdaaacdcdaaacdcabcbbdccdabaaabdbdbdcacbabcdaacaacbaabdaccbdbdbbbcccbabdbcabbabacccaabdddddabdbbbbabdaaddbcaaccccbdcabcbbabbbadbbdbcddaaddcaaddbcdaadcbbdbadacdbcbccaddabcbdcddcdcccdcdaadabadcbacdbacdbdccbbdbdabcbddababbaddabcdcdaadbcdbadaccadbcddbdacaccbcaadbbdbabcaaaacdbbddbbcccbddcdaccabcbbaddcdcccbcbdddcdaccddcbcbdcdddadcabcbacacbbdabbdaddccaadabdddabbbabdbadcddcabcbbbcbdbcbbdbacdbbbaccbbcbbddbcbdbdaabbbaacacbcdbcabbccbcabdbdbcddcdaaaddbddcabadcccbdbdbdacbbdbabbdabaadcccacaaddcdddadcbdbdaabdcdbdddcaddbbcacabacbdccadbcbcbcbbdbbbbbadcccdbabbbabbaacdbddcaadbdcdadcacbbccbdabcbcdabbcbbdcbbacaabacbabbdaabddabccdabbdbbbcbbbdddbbbcabbabcbdadbdbadbbdcacddbacaabcabccddbbbcbbbdbdbcdccbbbbcadbabaddabaaacadbcaaaacdbccbcaaaaabcabcddcbdaaabbabdadaaadaacdddadbacddcdbbcbaddaacadbcbcadbddcaddcdccbaddadadccbcabaacabbbdcabddaabdcdcbdbbccdaacabdbccbadccacccaacccdabaddbaaccadcbdbcddbabbcacbadbbccdadbdcbdbdabdbabdacbabbacacdaabcbbabcdacdcbcdbbbcabccaabbddcbcbbadbaaaaadaaadbccccddbbdaccddbdbcbbdaccaccccdacdadadaacaadddcbbdccddcabbbabaddcacbdccddbadccbabdccaccaabaccbcbdadbdcabdbccdaddadaadbddbcdbabcdabcbdbdbbcdaaadbbacbaaaabdcbbccddcbbaaccbcdcdcdbabaaadbbaadbcaacabbbcacbbbaccabadabdbbcbdcdadbadcbcbdadcbdddaddccccbbcabcdbbdbdcbdcdddabcccdadaaabbdcacbdbbbdccbdbdaaaadabcdcbdadaaadbcadcbaddbbcddbbcdbdbbddcbbdacbbdcababdcdccadbcbaccadddddbdddbbaddabdabacdaadddcddcbacdaabaadcaabdacaadcbcaacddaddcbabbbaacaadaabcdcdddbdbabccacadbacaaaabbdadcdacddbddbcbcaccbaaadcbcabbdbcadadbbbcbddbaacbabbcbabcabaabdcdbcccaacbbddababdbabcadcadbcbcadcacaabddadaaadbddddadbbdcbcaabadacccdbccacaaaaacbccdacbcaadbcbaaddacdbddcccbcccbcbcaaaabbaccdbbbdddcddbdaddccdcccdabbcccbbddcccacccdcacadcbbbdaabbcbaccdaabbbbcdbccccabdbbbcaaacaabcbdcdaaddbadbdcdbbcadccdbadddcbcacacacbcaccccabcdadcbcdadcaacacccabddadbacbddaadcacadbdaaacccbdadcddaaaabbdbddbaabcdbdcccbabababbababcadddaaabccdabaccbbcaccbcaacacadaabddcabadacadcdcdcaddbcdcdcdcccdcdccbdbabdcdbbdabcaccbdbcccbdadaaacdaadbbcbaadadadcbabaccdaccbcbaaacdabaabbdccddccddbdbcbacccdacccdccddabdaaadcdcbadcbbcaaadbcbadbbbddadbbdcacaccbbcadbdccdadabccaddccbbbccbcdbddaacccababdccaaacbacccccbdccadbbabcccabdabdadcdbdabdaccdbdcbcbbbaaaccbdcbcbbbcddbcaaadbbbbcabacdbcbadbdadbabccacdcdbbcabbacdbdddaacdcccadbadcbdbbdaadadcbaddbacbabbdbbddbccbdacbbbdbdacacbadccbdaabaadccbbdaabbacddacbbddbcdccbcdaaaaabacbddcbddbccbbcdcbdacbdcdddbbabdbddcaaddbdbccabdbadcadabbdaaadcbbbccbcbbaabbbbaacdbabbadddbaaccbcadaaaacbccacdaddadbbaacabdbbddcadcabddddcccbaabaacccaddccbdcdccacdbcabddabbdabccdcabcdaccbbabbbacaadadcbbcdacdbdabaacbabcaaaacccdaaddcdabbaaccdbacaabcabaabcabacddddcaccaabdaacadcadbcbbcbcdabcacddbcddaacbcdddabcdaaccddbcdaccbdbcdddaaaccacaacccbbbbabddbdabaadccdddcbbcaaccddbdcaabbddddddbcbddbbbbbdbbbcabbdabaaddcdbcbcbbcccacddbababcacbacbdaccdbbdccadddadbabbccdbcdabadbcccabacbadaccdbdcdccccccbddcaccbdacbcaaabbaddbbbcabcaaddcddbbcddbadbddacccabcbcdddabaaccbbdacccddadadcdacdacbdcbdbabaaaaaaddccccaccabadddbcbdaacdcaadcdbccbadacdacaacdbdbddbdbabaaadcabcaadddddcadbcdbdbcdaaadabbdaaabbcbbdcacaacbbabbcbcdbddaacdccccdcddbcdddacbccaaacdadbbacdbadabcdbcbdbdbdcdbddcacccbcadbaabdbbbbdcaaadccbccacdadddddaccadadacdacdbdcbbacdadbbbbbdddaadbcbaddbcacabbdadabdcdccbadccaddbddbaadacbdaccabbabdddcdcdccacccccdaabaaddcbdbcdbdacdddaacddcbccdcaaaaaddbabdbbdbcdacadadbaaadcddbcdcacbcbadbdcbbaccbdccccaadbbdcacbcacdcdacbddcbddcbccadacaccdbacdbdadabdbcdcddbcdaacadaaaccadcdbaddbaadaaddabcdabcadaabcbbcdbbcdcaacacaaadabdadcbabadcaaccabcbbbdcbbdaaddadacddacaadbabdbabdadbcccacdcaccadccccadbacbdcdccdacdbadcddacbddcaadcdcadbdbdddcdaaccadaddcaacabbadccabddcdbbddddcdcbabcbdcbacbdbcbdaababccbbcbcdabdadacaadddbdcdddadaadaddbdcbcbdcdbbcbaaccacabbbdccdadaadadcabcbdcccdcbaabdaddababbcbbbdcbabcabcbccacaadabadbbcccddacbacdbcbdaacabdbabddbdadbbabbdcdcbbbddbbcddcbcddcccdbcacabddaaaaaabcddbcdcdcbdbcadbcddbcabdcdadbacbacdddcbbcddabcdadabbaaddabdbccacbdaadcbbcddadbbdcddababbcbbcbcdcdaabdcdddcacdbbacdabdababacdaadcabdbdabadddddaacdcdbbbddaccaccaccbccddbadcbaadddbbbbbbddabdddaabbadcccaaacaccaaddbbdbacdbccaadccdbbcbcccbaaacddabcbaabdbacacbccadbdcbacaaabbbaadbaacbaccdbdbcdcadbabdacaabdabcbbacbdbacbccabdcadacadaaccddadbaadcabbbbaadccddbdcdaaadcbabaaddadcaabaddabdbcdacbbccccabaabcdbbbbdcdaccccbbdccdbaacbddaaddcaadaabdcadcaaaccddaabddbdbcccbccddcdbcbddaaddcdddabadabdcdccabaadbdcccbdcbccadbcbddbdcaaacbcddcdcbddddbabcbacccabbdccacacdaadddabacbcabdbbcccddaccdaadbcdbaacabccbbadadbccdcdadcdcdbbaaddaccbdddcbaabbcabddabddacbcdcabcabcccbaabbadaaccdcaadbbdaacacddadabaddbddabdcbdcbbadcadaaddacdacdabbdcbadbddcdccbdadcbdddcbddbbabddabadbcbacbcbdddabddbbaddcdbdddcabdccbdacccbabcdbabdaddbabcbaaddcddaacbabbddacaddbdbccdacbbacdcddcabdccbabdadbbbacdcbabdbaabcbdbacccaaddaaabdccaaaaccaadccaaddaddadcbddbacaccbcaabacdadabdadbbdbabbaadcddbdadabaddbbacbbbcdcaadbaaadadcadabddcccaccdcadcbcddaddbdadabccdacdccaaddcaddadbaaccaddabaddddcabacdbdaccabccabbcaacbdcadddbccacacbbdcdbbdacbddcadcabbddbbabbbadcadcbcbaabbcdcddcadadcdcbccadbaadacbaccbcdadbcddabbcaddbdaacaadcddaccdcbdcbabcbdaddbabbbdabdadddddadbacbdccaabdadddbddbdaaadddbadacbaabacabbbddcaadbdadaccbdbccddabbddcbcbacadccddbdbbbdbcccbbacdddcbadcbbdddccbccaddacdadbdaaaacccdabcdcbcbdbcabdaabcdaaadbcbbbcddbcabcacaddabdddbddabadabddbccddddbcddacdaaccbbccbaabaddbbdcccbcabdbbdbabbabaadaddaabcabbdddcdddcacdcadbbcbadbaadcaaaadbdabcabdcbaccbbbacddbaaccddbaaaccbadabcadbbbdddaacaccbbaadbcacaadaadbbddcadacbcaacddadababdaaccaaaaacbabbcdbaacdccbcaddbaccdaccaadbbabdcbbcdabcaccdcbdcdcdbccdcdcdccbdadcabdadaccbdccdddbdabcaccccbccbdcdddbdbccbddbdccccdbdccdaadbcacbadbccabaccccbbcccabddcabaabddaaccdaaabcddbabaaabadbaddcdcacaaabaddaabbdcdbbdcbbcdcbaadabcdbbccbccacbadbcbcacccabddbbbbaddcbbdacbadbacbdbddaaadddaaabbcabdacdcacabccbaadbddabbdccbdbcaccbaacbbbabbdcdcbdcbbcadbbadccdbcbadbbdadddabacdaccadddcdacabbcdaccadbabcadbdcbccccdbbcabddddaddbcbbdadbccabbdcddbdbbbcdabbbdbcdcaacacacccbcadbdcbbbddbcdbcaabcccaddacdbabcbaccaaddcbcccbcbdccdbaacaadddabbabbcddabdcabdbbbadcdbaaaaacbadadcdaabbdbabbdbdcbbcadcbacadcdbdcddcdadaddcccadbbdaddcccaabcdcdbdbbaaccbacaabbcdaccaddbbcabcaadbadbdbbabdbcadcadadacadadaaadbbdbccdcbdbacbadcddaacbbdccbabcaadbcacdabcbbcaabbcdbcdcccdbacdbabcdccbcadabdcbbdbabbacdacddababdcbcdacaacabdabddaabbaaaaccdbbaaaabdbacdcbccdcaddcabdadaacabadbdcadccbcadcacbddabcaaaaacbcaaddcdcbaccccddaaaaadcacaaaacabcccdddbaabbdcdbbcbcccbdbcdcbcaaaccdccabcdaccaacbcccadcaabccdaacddbbaaabccdcadddbddbcdadabdbbccccbccbddcbaacdabcdabddcccdcadadacaaaccbdbbcccbddbcccdaddabcaaabbccccbccdadbbbddadbaddabcbcbccabaddcccbcbbdbdbadbddbdddadbcdacabbcdacbabaccdcacaadcbdacadbcdabcaddcbdddbadabcdddcbabbdbccadccdacabdbbcaacdbdcddcbabdcdddbaaaabdaadbdacbdacddcacaabcbdaacabdabbaacaaabdaacbbdbbbdccccaaadaddbbbcaaadbccbcbbbabbcdcdaabcbbbddaccaadbdcababdccbdabcddbccdbccacacbadddacbdabdcbbddcdbcdbbccdbdcdabbbaaabbcabaaaccccddbdddcdaabdadcbbbaccabbdabdcbabcabaabbdccddcadcabdcbdabaccdddcbddacccbcbadbcdbcbbadcbadabcbbcdbbaccabaccbbdccbbcbdddaacbbcdcdcaddcaadacddaccadbcaaaadacbbaabbbabdacbabdbcdbdbdbbbbdcbcdccaccbcaddcdadbabcddbbbddbccadcbdcdaccaaacbccdbdbddcccdcbcbaaabbdbacbbabcccdcbcacaaabdbabadbccbbaaaccaaccabccdcbdacaccbbcdbcccabdaccbccdbcdddbbacaadcbcababdcbadabbdaddbcdcbdaccaacccacdcabccaadacbabadddaaccababcaadbadccaaccaadccccddcbdbbdcdcbcdcdbaaddcaccbcdbcddcbcacacdccbdbabddbbdbaabadbcaccbbabaaaadddcdbdcdcdbadcdabdcdcdddcbadabcbdbaacaacaabadaabddcddccabcdcdadbabcccdadbbcbbcbcddbccbcdccdadaacbbbabdcdbaabcccbccddccdaaccababcdbcdddcbadabbcccdcadcbbabadbacbddcdbbadcbbdbccbbaccbdddcabddadcdccdadacccdaddbcacdbdabcbcabbabdcddaacacabadadbbbcbbbbbbbbbddcaccaaddcbabdccbbaaadcbaccddbddabdccaadbbbacddccdbacbbbdbccccdcaabcaddacccbadcddccaccbcaccbabbbbaadddabbbbdbaaabaccadaacaccbaccdabaaddbcadcadccccddacbcbabcbadbdccadcdcdabaccabbdbaddbdcabdbaaddadccacadcabcacacccdadbccacdbdcbcdcadccdabaddbbcadaddbaaddddabccbbcacbaaabcddcbbbddcaccaddaccbdbbaccccddaddcbabbbbadaabcddddbdbdcdccacadcdcbcaacaabcadbcabbddaaacddcdcbbaabacacaacddbccdcbacccdadacdbdbcdbbcacddacabbbdbcbdabccaccdbccacbdcbdcdbbcbdacdddadcdddbcadcacdaadcbdddcadbbccbadbcbaaccbbcacccddadcbbddddbadabbbbcaabdbcaabbcbccdcdacdbbdddcbdbcabdccbcabdcbaddaadbbbbdacacbccdbbdbcadcabbdaddadabcaccccdcdadcacccaaabcadabbddbacbabbbdccdaccacdadcdcabdabdadccdacbccdbbacaaccbbdbbdbdbccadbcaadbbcdaaabcbcaadcdbacdddbbaacbbabcdbcadcbabaaacaaacbdcdcbcddcdbcbabbdcabcaccabbacddccdbadacdcbbcbcbabdccbbccdbdaaacacddabbcaddadadbbbdbaccddbcbbdcacbdbdabbcadbddabdcccadacdbbdabddbcbcbacabbcaabcdbadcdddbcbadabcbbdcccbacccbacbdbcdabaabdcdadacbadbdaaaabadcacdaaccdcaaddbddbdcbadbbcccaaddabdbbbdcdadaabdbbbcdadadcdcacdacbddbcacbcdabcbdbcbbcccddccaddccabdaddcbdccdabadddacbdbdbdcaccaabbbcdbdcbaadbddacbcbccbbccdcdbababaaabbbdabacdcbccdcccccdcbddcdbadadabcabbaaabccdccccdbdcadbddddaccadaddcdbbabddbadbdaabbdcddccacaacaacaadcbdcbbcbaacbdcaadcddcbbcadccbbcddcdcabdccdaababddaaabacaaccccbaaaadaaadcbbdacbbcabdcbdbcbcdddaacdadcaaaccabadacaacdddbccdccbabbbdaddbcbccbccadccaddabcabccadacadaddacbabccdddccddbcadbbdbcbbcaddaadccabdabcddcddbacbacbbabbacaddabddadadcadaaccdccdbaadadacddabacbbdcbdcacbcbbddcbdbdbcddcdddbdadddcddadbaccdabbdbdacdacbaaddcdaddddbdccbbdccbbbdcddadbdbcdcabdbdbcabbddbdadbbbadaacbdcbaddcdbabdacbdbaccbddbbcbddcbbacdcdadcadbdadcadcacdbccbdcacaabaabdcabaacacdbddcacacbdddbcbabbdcdabdddabacbbdadadcddbbaccbdcdcbabaccdcdcddbadacddbdcbbddddddccccbbccbcbdbcbdbbddacaaddccbcdaacbcdcbacbacbbdddcddcdcadbdbcacdcbcaaaaccddbcbdabbdcbababbadbacbbcadbbaaabcaadacabdcdbbacdcbbbddbccccbdddbaccbbbcccaadcdddcbbabadabdaccacaabcdbdcbaccaabccaddcadccdcbdabcadddbdaaabdcdadaadbbccdaacdbacabddbbbabbaaadbcddddabbbaaacdcdacacdcadbacbaacdaddbaacaddcaccdcdddabaddbdbabdabcbcbbaaabadaddabdcddaabdaaaccbaccddbbbdbdcbccadbdcbcbacdbaadbabcbadcbbdbdbdcbccabdcddccaddbddcbbcbababdbcacbdadbbcdabdaccdbaaaabddabcadccbdbaaaaddacbdddbacddcadcccaccdbcaddadcccdabadccbabdcacdbbddbbddbbdcdaacacdbbcadabcccdadbcadccbadaabbddbacccbddabbccccdbbacbdacbaacddbcdbcbabaaccbddabbbcdcdcdacdbbacbbacdcdbcaabcdbacadbacbdbbabbbdcbcddaddbadbabbbbdbdddcbcdacdadbdcbacddacdcccaacbcbdabcbababddddbbcbcabdbdcdccdbdbdcbddccbbbddcbababbccbacdacbdadbbaabbddbcdbadbadbbdbcbbcbdcabacccdabccaacddddbdabaacaabbaabaadacbdcccdcacbcacacdccdbaccbdddabddaadddccdcdbdadbadabaacbcaacadabbabbbcdbbbcbbdcccbdccddcbcdcaccbabcbcdcbcbbcdbbcbbadaddcdadcacdabbbddcbdcdbccdadaadadadddccdaababcbcdbcdcbbabbaaaadcadbcdaacbabbacabdaacadbcbddddaadccdcdaddbadcaaaabcabbcacacccbdddcccaddcabdddddcbdcdddcbaabacddbcdbadcbcdcddacabccdcddadaddcaadadacddadbbbadbaccdbcdacdadabacbaddacbdbabbcbbacdbadaabbbcccdadacbddcccddbddbaaccdbccdaaddbbdbcaacbdccbcbbcbdabadcacbdbccddaccadcbdbacdcaaabdcdacbaddbadcacdabaddabbdbbadcbbcdabbadbbcdadcabdaaaddbaddcabacccaabdaabddddbdabccaabbddbabbaabcdaabcdcacaccbcabacabdbcadbccdddddbddbcbaabcccbdbaddbddbcdaadbbabcdccadccbcbaabbccaacdbcdccdcabaaaadbabbdcabbabacdddbddadcdadcddccddadababbddccbddbdbbdaddcabadabaaacadaabbcbccbaaadabbbaaaddaddbbdbadcadcaaddddbcbbcadaccdddbaacdaccdcbdbadcbbaacaadcacdbcacaaddadbbbadcaaadcbcdcabddcdaaabbbdbcccdcbbbdadbddacdbbbcabcbdaacbbcaacaccbdbaaabcaaaadadaacbcbccbbcbcaacacdadadcabbacadcbadcbbaaabbbacbaaacacddcbdabacddaadbaadddcbbdcbbcdcaadcdaadaabbbdabbdccaaabccdaaccbbdcdbdbdbbdcddcdbbbdcdcdacddacabcacdccacabcdacbddbaaababaacaccbbbcccddcdcabcacdcddcabcdcdacaabacbadcbcbacaacddadadddbaccadcdaacdbcbcbdbacbcccbccddaacbdacbdbbcdccbbaddbcabcdcdbbdaabdcaaaabbbdaaaacabddcabacdaabcabaaadbadccaaaacdbcdacdadcbddbbbadddcdccacbbaabadaaabcbddbbdccccadbacdaacbaabddbadaabbccdccabdcbadabbddadcbdccbdbcccccbaabcdcdcdcdcaccbabcaccdbddbdadcbbdbbaacdcabbbcbdacccacdaadbacbbbbacdbbabadbaabcdcaaddbadbbdcccbdabcdccbdbdcdcdcbadcddcbdcbcccbdbdaabcbbcadbcccdcdbdcddacbbbacdcaabbdccccccaddabdcdbadbbcbadbbdaacbbccbddaacadadabbcbbdadbdaaccacdadcadabbacdacbadcdbcaddbbbbacbdccbbaaabdbdbddcdcdaddbbdbadbaccaadbccabcabdadbdbadccdddddcbdbaadaadcdcdacdacddaacacbadacccbabddabbdadacbaddacbbddcbaaacacbbbdccadddbabaabdadccdadbcdbddbdcdbadcacdddccaacdaaccadbddddaccbbdadaaacdddccabbccbbcabbcccccaabccacddcbbcbcbccaaaaacacdcbbccaaaccbaaabcdacccdcbbadccbdddadacddbcbdadcbbbbccdbcdadccaacbdcaabccaaaccacacaabaadaadddacadbdddccbaacdddccccaaadddccabdbbdcddacbbadbcbaccdbaabbdccaaccbacaaadcbabaaacdcbabbddcaaabbdddbccbbadccdcadcaadcdcdbcdcabcbdaaccabdcadddcdacdadcbabdbbbcbdcdcdbddcadbaaaaaccaccdabbbaccacbbcadbddaacdcaadbaabcbcdcbcbbdbcdaddacbaaaadddaddbdabcabddbbcbcbcaaccdacdacddbbaaaacababbdddbaddddbdbabadbabdbadcdbbdbccabcdadaacabcbadbbcacaabbbcaaadcaddbdbddaacdbabadcaccbbccbabacbacaaadcadadadbaccdcbbccadcddacbddcaaacddbbadcabbaddcabdcbaccccadddccbccbdddcbbdddddadddbdababcdccdacacdcbbabdccbbbadcbcbdbadbbdabadaccdbbcababaaabaaabdbcccbadcccbacaadcbcdbabcdbbadcacbadcadcdcdadadcbaddadacbbabbbcbccababccaddbbacdcbbdcddddaaddcacddaaabdadcdcbaadadaadcdcaabacdcbcdbdbadacdaccddcabbccabbccccdaababadcdbcbccdbcbacaabdbbaccabddaccbccbcdcbddbdbaacddcbcadcccadcbdbdcddddacbacccabdccdcddabdbcddbcdacdcddddaaabadccbaaadacdbddadccbdcdddaddacbbacdbcaabdbcdacddabbaabddcccbcbcacbadaadacbdcbcabadcaadadbbdbccbadaadaadcabccacaddacaadabacbbbabdbddcbddbccdcabdaaccbbddccacdbbddaaaadcbaadbaadbdbdcacdbbbcbbccddadadbaacbdbcbabcadccadcdcbabccccdcabbbdcdbdcddbcacaadbadcbdbababcbccbdbcacaccbdcbbcdcbccdbdbbbabadccbdbdcdcacbcbbdbbdbdadccaaacdcdcbbdbadaadbaddbcbbddaaaacdccdbaaabaaacaaacadbabacdddcabbabcddadbbabadcadcdaccdbdbddbcbdacddddbccbccbadaacbadbbbabcabdbdbacddcabdacbbacadddcacabdcccdaabbacdaadaccaacaaaadadbcabadbcdccadaaacdccdddbaadcaaababdcdcdcbddbabbdabdcddacdddddacadbaacaccbacabbcddddddccbaddadcabbadcacdbdabbdbacbbdbbadaddcbcdabaabbcaabdbdcaaacdbbddcaddacdbdcdabbbddbacddcadccadbbbdddcbbccccbdccaccbcdbdabbcdcbdacabdcacdbdabdcddccabbdaaacacbcadaadbacdadcbdcddbacbabdadacdaabaaccddbdaaabdcacdaddccbcacbdabdadccbccbdddacbbdbacbbbaccddcdcbdbcacbcddbbdbdadccbcdbaddcbdccddcbaaabaccaaacbbccdbacaacaabcdccbcdabbdbcabbabbbccdcbaabacbbbddddcbbabbabdadadababdcabdadbdbbbcabcabdbccabaabccadcdcdcadaccadadbdacadbbcdcbcdbcdabdbaadababadacccddcdbcadddccabdaadbcabbaacaaabdbbbcddadcdccccccadadcbbbcbddbbcddbcaaddaaacdcdaabdddaababcdbaccdcccdacdadbacddaacdadbbbbaaddabddaababbbbabbdbdaacaadbdabbddbddbbbaadbbdbbbccbaadcbbdddccdbdcaaccdabcbdadaacbbcbaacadcbcccdadaabcaabccdbddaacaccbaddadadcbabcddbcdcabcbadbdcaccbcbddcaacabddddcbcadbdacddcccbbbdaacdabdbcaaacbdcdbcccaccddaacabdcbdcadcbaaddcdaabacaddccdabaacbadbcbbcdaaacacbccbacbbbbdcadbdbcdaaacccdaacbdbdbbcbddccacdacdddaccaaccdcadadbbbcbbdababbdbbbccdbbbaacbbdbbadcbcdaddaddbcdcbcacdcdddbdabaadbbcaabacababbdacbdccbcbbaaccadcacbbbcddadbbccddbacaaaddccddadccadbccabdbbddbbdcadcabccdacbbadbbddcdcbaaacaacdccacdbabccdccdbcddabdcacbdcaddcdaadbcbadbbaaccddbbbadccbcdacdaabcdbaccbaccdbadadcabadbababbbccadbdddaaacbacbcadddcdbdaacacbccbdadcdccdbcdddccaabaaababadcacbabacbabdaccdcbcbabccdbacbacdbadcabddcddaaddcaccabdacabcddbdaccbddabbcdbdbbcbcdcddbddcaaddddbbadccdcbbaddcdcaacdcccacbbbbaadccaacbbcdccdacdcccccaadabccaababdccabcbddccbabbdadaadcdabbbddabccbbacaddaaddcabadccdbccbdaadcacdcdabaabcbcddadbbcbccdcbdbcacddabcadcbcccadadabcadabbbccddaabbbaadbbccacdbcdcbbdbcaabacbcdcaaddaddbbadcccadccacdbcdaccccacdbcaccdabbbbccccaccbccbdcadbcbdcababdbbadbacbbdbbccbaddacbabacacaaadbdaccadabbddcadcdadabaabccbabacccbccdddbdbabcdbddccdbbddbccbbabbcbdacadaacddbcaabbdbcbacbababcadbbaddcadadbacccbabaaaddacddcbacdadabdcacbbadadadcaaabdcbabcabcadadcaaacdbacacbaacabdbdccdbccdbdbbdddbccdbbaccdcaacdcadabadadcdadcabadbadddccabdbdbbaadadbdbddcdddbadcabdacadcbacdcdaacdccbaaaaaccdcdddaaabbaaddccbbaaddabcaadcabddabacdadbccacdbdacadcbcccbddbbbccadddbacdbccdcaacadcacacacaababcdbdccacacbddacdbdbabdbbcaaddadacaddcddddbbbadbacdbcabbabdacccddcbbbcaccddadbdbbdcddcbbdabbadadbdcadadbbccbdbddbbdcacbacdcaaddabbbdbcdaacccddabcacbcddadcbdcbcacbddabcaacddbcbdbbbddaccbcbbbcbcddccdcbcdbbadbaaddababbcaccabbcabccdbbbdcadacadadcdaaccaadabcdccacaccbdbcdbbaccccccdcdcddbccacdddbcaaaadaaaaaacaccbdacdcaaacbaaadbdbdcbaaccdbdabbbbddcaadabbcabdacddcbbbcbcacdcabcaabcbdaddcdbccacbdbdbdadbdbdccbbabacaaabcdcdaadabbaddaadddbabbbabbbddcadabcdcadcddcdcadcaaaccdacccdcbbcacaadacdaddabdabaabaddcddcddbdabadbbadcbbaadadaaddcdaadcdabbbbbdbabbccabdaddccabcbbcdcdbdbbccdcacbddaaabcbbadaaadbabdaacaabdbdcccabbabbbacbddbddcaddaaccbabbdbddabdadcbcaadcbcaccabbaadbaccbcdbcaaaaddcbdbdababababacaabdbaacaadbcabadabcbdbacbbbadbdbdcdaacdcacddacdbabaaaaabaccbaccabddababaacadcddbbccddbbdddbdacabdccccaccaadaacdcdaadddbbaaabababaaacdaacdabaadcabcaadccadadabcccbdddcddabbcaabacbabaaccbdcbbdbcdcbccaddbdbccaaddcddaadbadddaacccdabbbcdccbcddcacbcbcbdbacccbdadbbabddbdbddaadcaaccdbbadddcaddbadbddbbbccddaaaabaddabccbdcabdcbadcdacaabcdacbbcadaabadaaabcdbbddaddbcababadccddbcabacabdaadbccbacccdbabcadcbbdcaccdcbcbdabaddbbbbcadcadccaabbcacdbdbcbabcbacbdbddadcdabcdccbdbdbacabbaccbdabbccadcdbbcdadbbcdbcdbbcaacdcdaaababdacaadbcdbabcaadcbbacbcaaddccbbbcabdcbbdcccacdabadcabaaddccadbadababaddcbaccabbadacbbbcdbdaacbaacacddaaacdbdcabdccdcbcdabadbadddadadcdcdcacdbaadadacdbbdadbcbacdbacddabbddcdbbdbbbbadadabccacdcabaaadcbbddbacddbadcbabdacbccbbddaddabbdbaccdabdcaddbdbbbacdbcabbbcacddbacabdcbdadcaababaabbacdacdbadddacbaccddcbabdbadabddcdabbacdcbcccaaaddccbadcdabccdabddcdacaadbdabdbdbbabbddbaadacdaddbcdbcaaacacacdbabaadcdabbaadccababdabdbadbcccaccacaacbccbbcdcdaaccbbccccacddcbddcbaccbbdbccbddbcaadadbdcbbddbdcddcbbcdcddcdcadcabccbcdbdabcdaabbbdadbadcadadcadcdcbdcdcbcbdbdadbbcdbcddbbcdbbacddcbcdaddaacdbbbccdaccbbcdbbadacaabdbacccdaacdbdbacbadaabbdbadcaacccbbcdcadabcbcbcaddacdbcdbddadcdccbbaabcaabbbbbdcacadcdddddbcbdcabbdcdabdbacbabbaaabbcaadacccacacccbaccdddbdabadbaddcdacabbcdaabccbdcaaabccaabbdcdbdccacaabdcaadddddacbbabaaabcbbaccabbcadbdaddcaaccdddcbcadbddbcdadbbabbdddbabccacbbddccdabadbcddbcdcdbbddcbaaaadbcbcccbbcadddbbddabdaacdacaaacacddacabbdcdaadccdbccdabbcacdcccdabcddcccdbddccdddcccadbbcdaacdccdacdddcaddadbdacababcccbdadbcbccaddbabaacdbbcdcbdbcacdddbbacddcbdccdcdcddbcaabbaccbaaaadbbaacbabbabadacbabbbbababdbcdbcbddaaaabcdacdccdbddcaabccbaaadcbdcbaaaaccdcddbdcabbaabcbbacdbaddaaadadddabbdcdcdcbdddacbacdbdbadcbbdadaaaabbcbdabddbddabcddbccccdaccabccadcbabacdbaaadabbcbaabdbccccdadbcaabbadcbddbacddabddcadabbddbadadadcdadaababcbbbabddbbdabababddaaccabbcdbdbdbaabbdcdadcdabccdacbccacdcaabdbcbdcbbabaabaaacdbadcadcdbbdbddbdcccbbdabbcccdcdcbadbccaacdcdbcdbcaaacbccbacacaacbbbabcdbcbbcdddddbadccaccdbbbddbbaddabddabdcbdbbdcdaaaccbbdcccbccababbdcbdacadbbcccadcccbdcadccccddadadcbbabcaddddcaccdcabacbdbdcbdbabbcbddbdabbcdbbcbcddddcdcbbaacdcbcadaaaddbdbaadcbdbbbbddccdabbcbbbaaccbcccdacdddbcdbcabcacaabaaabacacadcddcaadcbcbbbdccddbbddccdbbabbbdaaccdbdccdaabbcbaccabcbbccaaccabaabdabaccdabadacdcbaccdcbddcbabcbcabcbbcdccddadacccccacccbccaabdccabcadbcbaabbbcaddbbadcdcaaddabbdabaaabcbdcdacbbaadcbbcaccdcdccbbdaccdcadacaadacddbcbadbccdccaaccaaaccadcdbaaabdcbbccaacaddcbcdaccdbbaddabccbbddadcaddcdbccbadaaadbbccddabacbccdbdbaabccacadbcdadaabcaaabdaabddaabccacaabbcababcbabbbbbdcaaccadbccaadbbaddbdabaddaadadabbbbcdbbbccddbbcaabcbaaaadadadcaccccdcaccbcdcdcdaadcbbcdbdaabbccbcbdcadbaaabdbdacaacabbaadcabdbbabdcdcbabacbdadadbcbdddaabcccaaacddaabaaabcbddddaadbacbcdbdaccaabbadbdbcdcdcdcbbccaddbddcacbccdbaabacbbbabddaddaacadccbdccbccdacbcadbaddcddabadaabcdcbdbaadcaaabddadcbcdaacdddccdaaaacaddcccbbcbddbaabcabccbdcbcacdcbdaaacccadbacdbcbddddddbdbbdbbbaadaaccdcbddbadaadcabccddcbaddaddcbccdadbacdcdbccbdbcccddaabcacbcadbcbdbddbcbddabacbdbcadcdbcbbcccbcdcaccaccabdacaaabdbdbbcaaacbdbaacadbcbbcabcbbbdbccbadbbabaccabcdbaaadcddbcacbcaadddbacbcacdcabcbbcadcabccddaddbcbdddddbdbbaadcbccccadcaddcacbcdccacbccdadcccbbcdbadaccabdcacdbadbdbcbdcacbcdbdddddbabccdccdcbbdabcdbbcdbdbccaaadcaaabdaccdbccdbbcdccdacddccabacdabdadadcaccadcdacabbcdcccdbddddabdbcdcdadcabaadbabcdabbcdbdaacababccadcaacaddbacacabddddcacdacccdbccbcdabddddabcaacccbbabddddcabddacdacbbcbdddcacbabacbaaccbbaddaadabbcdcabcdddbabadccbccbdcddcadcdbabdaaccddccdbbbaadbaabaaccbdccaaddadbbdcacaaabcdbacdccbdcccabcabbacbccbdbdbdaaddaabdddcbbddcdcadaddcbbcdaaddaacbabbdccbddabbbadccdabacdbcdddddadccdaadabdacbdddcbbddacbcbdcbbddbdcaccdbaadbaddcbcddbaabaaaadabcdaddaacdababbcacbaddabbbadbbbacddbdcabacdababbaabbbddabcddacccbbdadcabaaadbddcacbabdcdcaadcaabaaadabababbbaccdcbbcdcaaadcdadbabbdcadbbcbacaacccaabaababdbbbbdbacadcccbdaabcccdcacccabdbacadaaadcacbcdaaaacaaadabbbdbabdddbbcacadbddaccccdbcbdbaccacbabcdbbadbdadbccaddcaacddcacabacacbcaabadaabcaaadbcbccacbacbaadbabbbdaadcbdbdcdaccabdcaddcacbcdaccbdacbcbdabdbaabacdbcdbbdbacdbbdaaccacbccddddddcbabcabddacbccdadcdbbddbbcabcaacdacbdcaccdbaddabadbdadcbaadcbbdadbdaaaacccccdcbddabdcdbdcdbdccbaddcddcdbcadbcaabbaadbbabbdcaddaaadabdcababadaabcbbbadabcbaddddacdcddabcccaccccdadcadbabdabdacadcacaabbddbcbabbaaccaccaaacdbadddcaabbbbbdbbbaaaabacbdcdbcdbaccaacbbccabddaacaabbbacbbdbabccdccdccdbcdddbbbcddabaccbcaadaaaddadbbcbbcadccdbdddddabacadbdbcccdccadcbdcbccaabcdaabbcccbbdaadbabddccbcccdaacabcaabbdcaccdaadcdcadbcadcadcdbbbaaadbadacaddcbbbdcddabccbcccbadcbdacdccacadcbbcccacadcccccbdbdbcbacacdddcbcacddcadcccbaadbcbaccbcdcdadcdccbcbccdbadcccbdcbcdcbcdbbddbabcadabdadbadbdcdccdcdbaacbcabdadcbddaddddcadcbabaadcddaccdbbcababadcddadaaacbbcaaacbaacacbbaaaacbdaacbccaabbdbddcdcdcadcabcabcccacbdbcacbadcddbddcdbdaccdbabacbdaccaadcdccaccbcabdadababbaddacaccdadccdacaacddacbacbbcbbacadbbdacddcccbcddaaaabcdbadcccaacbbccddcbccdbdaadbbbacdbabcccdddddcbbdaabaadbdbddcadadababacdabbaddaaababbdbbbcdcccacbddbabcddcbccbabbacdddcbababccbccbbaaccadccbcbdbaadddbbcbbaabdaddaccbdacccdacacdcbacdbdcddbbaababccbbddcbbcbccbcbdcdccabacccbbddacadcaacdcddcabcadcbacbdbdbbabababcaccdabcbcabbdcbcccccddadaccdcdabbabaacaacdbadccbdaacadbadcddbbabccbbcdbabbcdbcdcddcbaadbbddaaddababbcdabdbbcaccacbadbcdcabaccbbbadcbcdbbdaabaabccabadababaaccacddabddddabddacabcbbddcdcacdbabbddcdbbacbcabdbccbdbabcbdddbdacdcaadccbbcddbdccdbbdbcdddcbbdacaaababacacacaddccbbbabaadacccdbdbadacbaadbcccddcaaaaccddaabacdbbbdcdccaddcdabbdbdadaaadcbbadadbabadbcccccdcccbaaadbaccbdcabaddadabbddddbdcdccabcbcadbabbcbbbcdbcaaadccadbdbbbaacdccddcbcdbdbcddabbdbbbcdbdaccbdbcdacdaaddcdaaacbdadaadacacbacdaccbcacaddaadcdadabaaaadaddacabddadbdbdbcbdcbbdcabaaaddddadababbaadbacdbbcdbacaabadadcadcaddbdbdaaadadadcaadcabcdabacddbbacdcccdadaddadabbccabbdacddbcbdbcdabcddbbbcccdadcbcbcdabcbdbddaddadabddabdbbbdabcbabcdaddacadbcdaaadbbdcbcabaacdbbbbddcddcdbbddddcabbbcdacddbacabbaaddaacddcbccabacdaddadbbdddbaacddcbdadacdcdcdbbcbdcaabdaadabaddccaaccbaadbdddbabccdcccabcdccddadccdcdcbcabddcccbbcddcdadabdacababacabdcdaadbbdacdbdbdabcadcbadaacabdbdcddbabbccaaaaabaabdababaddbccabdacbcdaabddcccbabbaacdbbcadcbadcccddabcbcaabacdabacdadcbaacaaacaddbbaababaddabccacacbaccdcbaccbdacaacdcddbddccaddcacabdacadcacddaacccccabcdacdcbabccabdbdddcbcaabbcacacaabadbddcadbabadacaccddddbdadbadbbaababaadbaadcbbbbddcddccacdcbcdacddbcbcbaabdddcaaacbaabcccbccbdcbbddcabbccabcdaaaacbadbdbcddcabbcbadcaacdacbdcaadaadbaccaadadabcccbacbaadadbabccaaadadabbdbdcdbdbccdacccccddbdbcbaacdbbcddaacaccdbddbaaaabbdaccccbbadaddcdacdcddddddbaabadaadbdbcdcddcadbcacadcbbacacabcdcbacdcdbaccccaccdccddbcbdccbbbdadbcaccbdddbccaaacdcddbaddbaabcbaccbbaaddabbcaadcaabbcbaaccbbccdbacdddadbcacbbbbbaccdccaddbccbadccdbcbaabbcaaacbcdacccbcbbabddaaccdcbaacdbbbadaddabbccbbdcdbdaabcdccadadaacadbdaacadabbdcddbaddaccbaddabdbddbaccdcadddbcbadbdcbcbcaabcddcaabacdbdcabdacdbbaacbccbadcddcbbadbbbdccabcddbdcadadabbdccbcadacadaacdddcbcdbcbbcccaaaacaacbbaaabcccccbcaddcaccbbddabcacadcccdcacbaccaaaccdcabbdbcaabbaabddaabbadadbacdccbcaccdabacdbcbdabaacabadabdcbcdcaadadbbdbdabbcccabcbcddaaccbdacacdacbccdaacdcbacbbbbababacbcacbcdbccbacbdcaddabadcccabbadcaddbabccadcbabcdccaacccacdaddddbbcdcabacbbdbbcbdaaddaccadbdaadaabbabbcdabbbbbccdadbcadcaaddddbbdbaacbcadbbdaaadacbdaddbdbbddcbdbababcccccaddccadcbbdbcdcdbacbacdbbdddabcbcaaccaadabcaaaaadddcdbabbcdcaccdadabddbcaccadcccacbdccdaabccdbcbababcdbddaadaddbbcbadcdcdddbdcbbccddddccacdbbacaccbbadcbdcaabadbbbdabccbdccdabcabaccddcbadadcdcabdabaddadaabdddbbabdcadbbccbbaccccbbbccbcdcdccacaccbcbaaaadcddacbdbacacdabdccacbcdabdccbdcdcdadbddaadbbcadbacddccddacdddcddadbcaadbbcaccbccacaccaadbadbbbbbaddaccabbdbdbacbcbaabbcadbdcacddabccacabbbdcadcababcabdaddbaadddddacbadddaaaabdbadaccbccbcdcdaadbbccdddccbacadcbdbbcddcbbdabacbaacdcdcbdbdbaddacddbbbccbcadbbbdddbdbadacaacaddaacccaabaddaabcaadcdaddbbaabdcccdcaccddbdbdbbcbdbbdbbdbcbdabacdbbdcbbbdbdaacacadddcaabbccddaaacadcccdbbddcccccdcaddabdabddbbdacbbaddadccabcabddacbacacadcdcdbdcacdcddbaacbcbbdaccddbbbccabdabaabdbddccdbabacbdbbbaaaacdabdbbdddcabadcdbcbcacadbdaabcbddcaadcbbcaadadbdbbcdcbcbadadcdcbaacdbabcbdcbbdcabbacbcacdbabdbdaccbadbabdbcadacabbcbcaadabdcbbcdacbbdacabbccadddcadcccdcdaddcccdddacbdbbbcddbcadbabdcbbaabbaacabcddbbbadbbcaaccdcabaaccaccaccabadbbbdcdddcdbcbcbdaabddacbabbaadaadbddbbaaadbbdcdadcbacabcbbddababbcababcddddacbcacbbdddbddddbbcadbcbdbcdaabaddcdaacbabdcddcbcdcccbccddaaddabcaabdbbdcdbbbcabddddbbcbaabdcabdaacbdaabcabbddbbbbbbbbacacdcacbcaacacadadbcbadaacbdcabddcccdaacbcdcddcdbdccacdaaadaaadbbabcdbbcbccccacdaddcbdcaccbcbbbcacccbcadbcaaddcabccdadbbbaadcbcacabcdcbbcddbdbdadaadbdbabbdcbddcccbbbacdacbadacbbcdcabdaddbadbdcbbaabdcdbadcadcadaadddbbadbaddbcadcddbdadbddccccdcaabdbbadbddbadcdddcdbabdbdaacdcdbdcabcaccbbaadcdadbaadbcddcaabbacbbaccacbaadcbacabddbcddcbbbadbbcdbdcdcdbabaabbdabbadaddaadddacddbdbccaadcdcbdbbdbdaacadccacadbabaaddcaaabcabbaddabddcaccdccbcbacdadcabcddbaddcacadcbbacbcddddcaabcababaadbbbddacdacaadbbbadcbbaccbcccaacddcacaccdcbadddaacaaddacbcdccadbdcaabddbdbbbaaacbdcbcacacbbaccbdcbabdddcddaacbacacbccbbaaaabdcdcaabadcbaadbddcdbbadbccacbcdcbccdbcdcddbbdbdabbbadddccccdbcaccbbcabbadbaadcdbcaccbbaaabdcdadddaabaccadbadcacccacdabaadaacdbacccdaaccbdccbcacbdbadcaaaacdbcbdddabbcccaaadcdbcadbabdcccaadbcbcccaadabaabbccadbddacbcdccbabcdbaddaabaaacdadacaabbbaabbaccdbcaccaccdbaacbabcdacbaadbdcaababbddaddaddddcadbccbabcccccbdcacacadbacbdddbdccadbaabbabaabbdbcbbcbbdbcacbdbaadbcbbbccbcabbadddbcddaaccbbddaccabbcacbbbdcccadccddacbdadacacbbcdcccaaabcbaadadcabdcbcbbabcddbacbacbcaaacbccddcacaabccdddcabcdbabacacbccbbdbdacbabaccbdadbadcadbdbccddaabdcbdcaabadcbaddbbccbbbcdcdabcaabbbacbccbbacddbcdbbbdccbdcacdcacacacdbabdbcdaabdabcbbdbabacbadabaccbcdadcbadbcacbbdcdbbaaabccaabacacbabacabaacbabbbddbcacaaacbcdddbcaaccbcacbabbcdbabddabbdcdbdbcbbbadddaabadbccabbabbaacccabdcbabdbbaadcdccdaaddbacbdbdcacaccccabdbcccadabaabaddabbcdaddcbcaaaabbdcdadacabccaaabadbddcbaabbacabadbbacaccacacdccdacccababddcdcddbaacadaaadccadbbdaabacaadadcacccacbcdcccbbdbcabcbcbaccbdacdbaaccccdbccbdddaadadadabacbbacccaaabddcccbbccababcbccdcaccdbcabddbbdbbaadbddcdbcbcbbadcdadcaaabddccccbdcbbcabcbcbaacbcabbdbdddcadbbcbacbddacbdbddbddccbbadcabcdcbabdacbdbccddcdbcaccadcdccdcddcbbbaccbacccddadbbdcdbacccdccbcddcababbdcdbcabaddacdaadbbbacbabbcdacacbccdccbaacbdcdbdaccdbbdaadcbacdddaadbacbbabdcbadccacddcbabdcbdbadcaabcbacccdabdcccacacbbddcddccaaabcaddbdccbbcbdbabcdbdcaaabacbbdabaabdcbaadadcbbaaccddbdbdabacaaddbbdcaaaaccdcaaadbababdaadcabdaacacadaabcbaccacacbadcaadaaaaabdcdacdbcacbabdabaccadadadbadcccbaacabaacacddbbadadaddacdddbbccbbaccacbbddadaadcaaccccacabdbcabdddaaabddaabdcacacdccdcabcddccaabbdacddcbcaabcbdcdccaabdcabddcabaadadbbddbbcbdbbcdcbdbabdacdddacadbcdcacbdaadaacdbdccdddcacbcdbdbacabcccbabdccaabdbbdbdabbbcccaccbbccdabdddadcbdbddaaabacccacabcabdddcbbaaabaadadbadbcdacdabcdaaccadacdabacbddcbbdbdcbdcacdccbaadcabbcadccbcdaddbcdaabbddacddcacbcdbdbbbaadcdbbbadcaabbdacbaabdabbbdccaacdcdcbddbadcdbddbdbbadaccdbcaabdabcbcadcaaacddcaaacbbdbabbaabbdcdbdbabbccadcabcccbabadcdbaadadbaacacdbccbbdbbcacadcdcaaccddcacdddbdddabbcaadaadccacadccdcadbbacabddcbbaddcbaabbddccaabddbbbcadccbbbccaccbcbddabdadbbbbbbabcacadccddddbdbdcbddbaadaadaccdbbddcadccddcdbbdbaaaccaabcbcdddcddbadbccddaddcbddadccddcacbabaacacabcaaadcdcdacdbdacbbadadcbaccaccadbbbaabdabcabddcacdbdaabddbcbadcaccadabdcbccbdbddcdbcccdcccabcbacadbdabaabdaaddababddddacadcbcaddcdbbcbdacabcbdbbbdacabddbbadcbbcabbccaaadcddcbbccbdcdadcccbadacdcccbddbcbabdbccdcdddcdabccccabddddcaccadbddadccacaaabcccaddbdcccdccdccaabccddbdbddddbadbbdccaccdaddaaaaaacacaccdbaabdadbdbddbbcaadadabccdbbbcccabdcdbdcabcabcbcdbdddcbbcdcbcdbbbdbbdaadbcabbbbcdccabdcddcaabdaabdaddaabaddacbaabacabcbdbadaaadacddddcccabaabbacccdddabcdddbcaaacbacabcdbcbbaabbaaaaddbbbccbccbadbcbbcdbcabccbcabcaacbcddbbaadaabaccdcdadcdbcbddbdcddbaaacdacbadbcccbdddaccdddadbbccdcbbccbabbbcbaaddcddbadddbdbcddbcccbcdacdbbcababccdcadbbddabbcdbdddccbbddaaccdcabcbbabcbcbdcacacbcaacddaaaadcbdccbcaacbdcdadabaaabddbdddabaadbccbacacdbcbaddcbcbbbbcccbadaaabbcdadcaadabbbadcdbcadaddbcbacabcdddccaccbbcdaaacdcddddbdcacbaddddccabdcdbbccbdddcabbbbacbdcdddaababacaccdacbddcdcaacadabcddcabacdcdaccbdadddadbdaccaddcabbdbabcbdddcabdababdbdcacccdbcaddbaaccdcddcbadddbacbdacacadbcbadddbdaababaccdacbaacabdcbabcdacdddababacbccabcbdbdacabaacabacaaabbbdadacabcbcbcdabacacabbdcabdddaaaadbadccccdbbdbddbbabdbcbbadddcdacbbbbbdcbcbbbcddcbbddbacddabdddddddadbdddabcbadbacbacaddcdbddbbcddbadacdcadacdaaaacabcbcaddbadcadbdacbaccccaaacabbbddccbbdbcbabacbdcdcacabbbcbabaaabcddddacadadbaccabcbacabbbccaddcacababdbbcabbdcadccdcacdabbcacbddddbbaadbdddbcbbcaabbabdddacdbccadbaaabababadadccadccbbdadacaadaccabdcbbabddcaaabbbddbcbacdcdbadccbbcaaddbdacaaacacacddcdddbacaacddcaacccadcabddcdddddbaddbabdacbbaccdbaaddabaccddbbdbaaaacdcbabcadbbdabbccaabccacdcdcbdcacdbabdcbcccdcccacbdabadbddaacddbaccacbcadaadcabbcadcadbabcccacdbdcabbcdadaccbbdbbacbadacbdbabdbbdaaaaccbdabdadaadadabbbcdaabcccccbdacbbcdbddabbbdacacdbcdacbacaabdcdabababadddacbbddabcacccbdbaadaadbdddadddbcbadababcabcbaacbccccadbadaacbbbddcaaaddccabaabdaabbacabcdcbbdabcddadaabacaddacadddcddcdaabdbbacaadcdcadcdbbabcbccdbdbdbcdbcabdddcbdccdabdaaadcaabcbdaabdddbdaaccddddbcbaccbdadabcaccbdcdbccabddcdaabcccccddbbddcabaadcbcaaabaabdabdccbbcdcdacaadaabbcbbadbaddbdaadbadabcbcbabdcbadbaddccccdbdcabdddacadbbbabbaacacdaccbdbccccbcbbbaaaadbadabaacadcaacccadbcddbaaabcaaabccbcaccccbadcabbadbbacbaadaccbddbbbcbacccacdbdcddcdcbbbcdccddaadacbdaaacadbccabcddbdacbbbbccbbbacbbcabbdcaacccdbaddddcdbabcbcddddacdbabbdaadaadbbcdabcbabbabbcaadccadbcbbadbddcbacddbbbbdabbdddcaddbabbaababdbaacddaddabadacdcaccdaabcccbdacddabdaabacadbaddbbcdbbaaacacaacaacaaaddcbcbdbacadcdcdaacbcdcbacdabbaccbbdaacaaccddbcbddabbbdabcdaddddabbcbccbdaabdbbbabbddacdadbadbddaacbaccddcdcdccacacbdabadadcddbacbcbbcdbabcabaacacccadbddbbcadaaaaadcaddbdabbbcdbcbccdbccaabcabddadacacaaadaaabbdcaaddaccdddbcabdbbaadcccdcadbadbbadcbacbdaadabcacacbcaaacdcacacddbddabacdcdacdaaadbbadddbcbbddaaccaadbbaadaaddbaacdaaabdbdcdccdcdddaabbdccaabcabbdaddcdbbdcbabbbabdaacddbddabcadcdaaacbacbdbbacbcabaccdadbbbcccadbaadbbbabaadbdcaadcdadadbadcdbcaaddcbbbbdcabbaababaacdcacbccdcbdcaacdddaaabcabcbdbbaddbbbaabcbacabdaaabacaddcabdccabcdcddccabdbaabcdbbdaadbbdcbddccddabcbabcababcdbdadbcbcdccdddcabdcbadbdcccbbaddddbaabdbbcdadaabbcbcddcbbbbbcccadbbcababdbdbaabbdcddbaabdbbcaadabcbacaaddbaddbbbcbdaaaccbbdbcdddacbaddcbdadacaccbaacdccbbcaaacbbdcbcccbccaadbbbcdccccbdbbbcabbbbbcbabbaaacbdcbdddccdcbcdbaadcbabbcbcabccbacddbaabdccadddabcacddbddadcccacbcdcaabbcbcdbbacdbddbbbacbbbadacacdbbcdcccdbbbccddabddbbcaccabbadcdbdbcbbcdccacbbabacbbcccbdcbdbacccdcccddacbabcaaccaababbcbbbdddbbacaacacdcdadacccbbabcbbdabdaadaabbdccdcdccbbdbdcccddcdbababddbabaddccbbcaccbaddcaccdaddacacaacbbbbdadabddadcdcacddbccdabcddabbccbadbadbccaabbabcbaabadddbdabbadaaaddaccbcbddccbcdaaaaccdaadbcdcbdcbaabdbddaddbddcacbcdcbdbccbabacacaaddcdababdabccbadccdbdabdbbbaaacabbaddbbbbbdccadcaaacdcbacddbdcabbdcccbddbcbbdccaccdcdbbdabbdadcbccbadadbaccadbcbcccdcbdbaadddddcaabccabdcabbcddcdcbbbcacddbabbcdcbdaccddcadcbbcaccaddacdadacbdadbdadadcabbbdbdaacbbcbdaddaccaaaccdadacbcadcbaccaccbaaccbcdbaaddddbcdabdccaabcbdcbbcdaadcdabbdcddbcacdcdcbbadddddcacbdcbcdaacddadcabbacbcddcaddddbabadcbdaadaacbabccadadcdbcaabaddadacdbcdabdcdccabcbcabacacacddadbbbcbdcccabaccbcadcacbccadaabdbdbabcbdcaaccacbbcaadcbcaacbbcbdbbddabbaacbacadbddbdadabadccccdacddacaddccabccbacddbabcbcddbdbdacbadcddaaacbaccccdabacabcacacbbbbdbacddbcbcbadbbacdabbaaddcabdabbaccbddcadbdbdcbbbbdbddaccacbaadbddcccacdccbddbcababcabaabdcbdaadacddccbacbdbbcdadbdaabdccdddddcacadacadcaaccbbbaabadbcdcacbcddccacadbbabbabbdadbabdddccacdbdcdcbbabbdacabbcdbacbadbbbdcccaddadbcacbcdcaadbbbaabaccbacabbaaccbdcdabcacabdabddbadadcadbbcdcccacbcbdaadcaccacadaccccabdcababbcaacccadbaabdaabbadabcbcadabccabdacabaacbbababdbddabaacdaacdabdcdaccccabbddbbadabaacacdbbbabbbdbbbcbdaabcacbbadabdddcbbdddbbddadadddacbabbdcaabbbbbdaacbcadcdbdbcdbabaccdcbdaaabdbcbddaddabdbbdccabccdacabcbbadbbcdccaaacdddbabadcaaabdbdbddaadadbdcdcbdabbdaadbdcddccddcaabcbcabdbddaabccaaacbcccbcbadbadcddabdbaaddaadccabbdaddbbbddcacabdbbadadccdacdaddddcbacbbbdcbacbbabaaacacbcabccbbbbcbcdbcdaadcbbbacabbcdbbcddadbdabbbacbcadcbadcbdaddcdcaddabaacdcbdcadbbdbdababdcccdbcddcacacdbabbcabdbcbdcddcadddbbaaabcbbbadacbdcadcacbbdadcadbaddbdbbbcdccdbbdacbabcbdbcadbcabdbacadacbdaccddadabbcaacddbdcdcbadacbdbbabbaccdddacadadcddababbcbdabcbccdaabbaddddccabcbadddabccbadbbcadccbcddaddcbcdcbcabcdaddcdcdccacdcdbccaddacbdadbaabdbbaaccbdcadccbdbbbbbcccabdccbbdacbbabbcbadaaddccbbaadbdbaccaabdcbcdcccdabbbacdbbcddacddcdcaaacadbabbacaacbcbcabdacbccdddacccbbccadaddacaacdcadcacaadbbbbbabdddccddabcddacdcacdcccacbcbaaddccddabdcccddccaddbcadbdddcacabacdcabcacbabdddaadddcabbadadbcbabacddcbabadbcdaabbadddcbbadbaddacbdadadcabcdbdbdcbabbaadcccddbdcadbcbabbbbabccbdaabcbcbbadbacdcdddbacbbcdacccbbbcbcbaddcddcdbcbabcbbaabbdacaadcbbdddadbdadbabccdaacabdcabcccabbaccbabdaacbcaaadcbbcaabddddddbabbbddcbaaaaccbdaacddaabbcbdddcddcbdbbcdddcaacdbdbcdbdcacabdbdddbcbcacdbbbacbdabdbbcbababbaddddbcaccaaccabacbbddabcdbacadcacbcbbaaccbadaccccccccddbddabdabcbdaaddcaccdaaacddcaaddabaabdcadcdacbbbddacbdabdadaabdadbabacbaacbbcabbababcddcbacacbbbbaabcaadbcdabdbabcadaabcbdcbbbbaaabaccabaaabddadaddacbabadabaaabcbdcdadddcdcbccbbccdaddacbdaddcddddacabdadadacbcbacdbabccbbbdbcbabdbbcaaddcaaddccbdabacbbdabcdbcccaabdbaaddcdadacadcbccdbabcaadacbcdabcdcdddcabbabcaabbdbddcdcbdbbbbcbbcdbaabdccbcbadaaacbbacdbadbcabcdbddbadcbcbddbabdddbbaabcaabadcbdcabaababdbacaacdaabbbaccaccadbbbddbdbcadcbdaadcbacbdcdcdbbacddaddcdbccbdcbdcdacdaabbcbddbddccdacbadcbaccbadaadcbaacbadacdbbcbaadcadbabbddabcabbdbdcaaaadacccddaddbaaacddbbcabdbcabcaddaaabcbddcdcbdbdbbcadcdbabdacabbbccaaacccbcacdcdbbbcddbdcaacaaaaabbaaabadbddbbaddaddcbddcacadbacaddbbcbdbcadbbcacdcadbbccdccdabdcccddbcdababdcbadcabdcdacacbddbadbdcbabdddcadcddbdccadbbadacdabccacabbcbaacdddaddbdacdccdcacbaabadabacadddaabadbdaaabacbdcbaccdaabaadbabbcbaadcdbbddcdbdabdadabdccdbcaacaccdcdacadccbcdbcadbdbabccbdadabcbbdcbbddbcddbaacbdadbbabddaaadcccacabaaaadaaadadbdbdbbdccbbdbbcbaaccddbdacdbbccbdabdcdbbdbccbccbbababbabddabcdccdcccbcbbcdcaccdabcccdccbacaabdacdbacbadcdbbabaacdadddcaabbdccdabaccaddbaaabccaaccdabbcbcbbbdcdbcccaadcadcdcbbbdabdcbddaacdcdbcbbcdcaacdcdabbccadbaacacdcdacaadddaadbccccacccadbcbabdcdcbdbaccabbbbbacdacdcdddacccccdbdbccccdabbbbbacddbcdabccaaadaacdcadadcbdbcbcaabdaaadacbbddcdadbdbcddcbbacacaaabadacacddadabdacbbddcbbddcbacddccababdbcbbddaabccdcccabcdbddbdbcadbbddcacdabbdbdcbcddabcbdababbcdcbcadaadaabdcddccbacacabacddddaccdaabdbadadcccbcaadcbadccacdaddbbaccdccbbbcaccbcddcacdcabddaadbadacbbcbbabdbcddabcdbdbaabccbbcbabcdcaabccaddadbaddacddcbbbdccbdbccdaddcdbdabbbdcbcacaabdbdccbabcabadcbadacacbbabcdacdbbaccbbbbabdbdacbbccabcbbdadcdbadbbdbcddbadacadabbdabcdcbdcbccdbcbbdbacdcbdbdcdbbcdaaaddabdcaabbcabdbdcccabddaadacccbadbabaabadddbbbaabccbbcdcaacaaadacadacaabbbaccadcacdbbcaddccdbbcaccaaabccdbcacaccbadcdbdbaabcbcbcdbccbcdbacddbcabcadcaccdbacabbadabdbabdcadbcadaacbbadaabcddabcbdddbcdcacaaccdadabccdaccddcdbbaacababdcaccbcbabdcbdbdabddbadaddddccaacaabaacdaaabbbdddccabdcbadacddaddacddcccbdaabaabdbccbdbdcccbaccbcdabdbbcddadcadcbcbbdbdcdaabbbcbcccddcddbdcababbdaaccabdbcabbbacddcbccccdbcadaacaddbdabccabcacbbcacaccbdaddcbdacdaacddacacbdcababbccadbdcdbaddaaccbbaabbadcacaaccbaabbcaccdcaccbccaacdbcbbacccddbbacabbaadacbcbdbbaaadbcccddcacbdcbccabcdbbcdbacdcdbbdbabbdabdacabbaadbbbccbadbbcdbabdccabdaacbdadcdaabccccabdcdcdaccbdbcbdcababaadccbcddcbccbcbdcdcaccbbccbdbcdbddbbadbddccabcbaaababcdabcdacaaabbabadbbdacbcadcdcadcdaddaaddbdbccbcdddcaddaddbcacbccdbbdbbbaabbccccadbccbcacadbcaadcdcbccdccaacbbbcddbdcddbcabddbdddbdbaccbaabcdaadcddabdaabaacdcadbbddaabdaddcdcccabdabddaddbabdadbcdacdbaccbbbbbbabdbcccddbbcacdccdccacadbbbcabadaaabadbdcdccdcdcbdccdcbaacbdabcdaccaddabccbaabdadbdcccdbdcdbccdddcabddbdadabbbbccbabbcccbababaccbcddddacbcbbbcadaababcbdbdabadccbcbaacdadcbaddcbcbbaddabddadbdabbccbadbbadccabbccbcaadacddaccccccdaadccadcccdbabdbdaaababaaddaccbcabdddccbaccabbadcbdabccabacaacaadcabccdddbbdcdbbdaccdbacbdacbaacbdbbcdacdcabbbcbddbcddddbcddcccaaacadccdacdadbdcaacacaddbdbaaadabbbbcadbdbdcddabbccadabbdbadccaabbaadaddcbcdbaadaddabbcaacadbbcaabadcacacccbaabcdddcbdbcbacadcdbdaabdddcdcccbdbadacdccbccbdccbbaacaaadddcddaacacaadbbaabbabdaadddcdddbadcbcbbaaaccdbaacbbbccbbadaaaccbaddbbdcdcabccdabaaaacdabbdcdbdccddccccbbcbdbcdbccbddabaaccdcbaadcaaaddabadabdbccdcdbbdcadacaabaaddccdbccdabadcdbbabbbdcdadccbccbacadccccddbcdbbcacdaccdbaabaaacbdaccccdbdabcccbaadcbcadcdbcaccbbaaccaccccbbddacbcbdcccaaabaaacbdbdaddababccccdabcadabcadaaddccacdccbadccdbadcbdbbcbbcddbddaaadcbccbcabbcddacabaccaabcbaacdbbcccbcbcccdccabdcbbcddcbdabcdacaacacbbcabcababdbcdabdabcabccbdbcdbbccbdcabddabcabccaacbcacbcadcdcdbbbaabdcaaabbaaaabbbaaabcbbacaacacbcacbdabbdbadbcccaabdccddccbcdcaaadcaaaadbdbabbabbdaabdabdbbbdaaaabbcbdcdbacabcadcdbbaaccbbbaccdcdbdcabadbaacbabdccaddbccdacbcdaaaccaddcbabcabaadaccbddcaacccbdccabcddcbbaadcbcaadbbbccbdabcbacdbdccbcdcdcbcbcdcbbacbcddadbcbccbddacdabacaaddbbbaabbabcbacdcbadbcbacccbbbcacdacbdbbcbcadcbcacbcadddaabccddcabadbaddaddcaacbbbcaddadaaadcccabcdabcadcabaabdcbdcccbbcddaddabbcbdacdabdabaccdcdadacacbbbdbcccbbddcacdcdcbcbbbacadbdccabbdadacdaacdbbcaadbacbbdadbaadbcbcbdddbbbbdcdacabdabbdccaddcdaabadbabddabaaadcdbccbdaddacdbdccbddcdcdcdbdbdbaddbaabccdabbbdbdbabcadbacbaacdacaaccacbaddaddbbbdbcbdadcacbdcaccbbacabaddcaacbddacbbdccdcdbabacadddbbabaddcdcccadbccadaccadbcbcddbbbcaaaaaaadcadbadbabadaaaadbdcbaddbcbadabbaccaabbdbaaddbbdcaabbddcadcdabababbcbabaddababcdadadacacbacbcaabacabcbacabdcabbccaaacbbcaaababacdcacdcbcbccaaccbabacbdaaaddcbaabdadaadbdbbdadcbcddbcddcccadcdadccbaddcabbacdbcadbccbbcadacaaabbbbaadadbccadabadddcbddcbcdcdbaabdacdbdddddacaddbccdaadbabcabcdcbbdddbbdcbbabbbababcbdacbcabadbddbddbdabcbadddddbaacdbbaaacdddbadccabdddbbddabcabdcbbcabcbbacadaddddddbbcbbccdbacadddacdddcbbddbddbcabbbcdcadacabacacabacdacaaadcacbbbdadbabcddcbaadcdadbcbcdacdcbdccbacacdadaabdcaaababadcdaaadbabaaaadcbdabadbdbacadcbabaaaacadadadccacabbccaabadbaabdcdbadadbdbbaabcbccbdbabdbbdcaddbcaadcaddcdbbbacdabcddadabcdccdadaaadbddcbaccbbbabbaddbbabadcbaaabcdaacadadccddcdacbadbcbbaccdbcbbbbaddcadaabcbddaabaacbacaddbabbcbcbbabcabdadbbdaabaddcddadaaadcadcaddddbccdbbdaadacbadcadaccaddbcacabaccddcccdcdcdcadbdcddddccbccaaacabcddbcacaadcadcacddccacddbdbddaadabcbccaabacaadddabbaaaadbcdaacabddbaccacabdacaabbbaddcacdaadadbdbbbbdadccbdcacbdbbcadccbbadcbbacbaddaaabbbdbabcddaabcbacacbbddbcdccbbadaacadbbbaccdadccaaabbbabdcccbacabbaaaabdbdbdbccacccabddadadcdaadbaaccdcadcaccdaadadabcdddbbaccdbccacacacbccacbbbbabacbacbaddddabcbcbbbcaabbcbdbbcdabddbbdbbdaaccdbaaaccccdbbbdcdacbcddbcabcbdacacccbcdccbabcbbabaddbdcdbaccdbdbaccdbabacadacaabdcaddccdbcdcbbdaadbbbbbabccdadabacbdbacdaddbabdbdbcbccbdaddbdacababbbcbcadcaaadaddddbccbdbabdabaabccdbdbdabccabacbabbacdacdcccadbabaaabbbcaccddcaacbabbdbcdadbdddbdcbcbddaacdabadcdbddbdccbddadddcdbbdacdcbccabaccddbaabbadbbcbbcdcdbcaacabcabccbababadbadbacdcbbaabcddbbbddabcdbadddbbaaaddddaacbacdadaaddcddddabadacabdccbdbbdddcaddcbadcaacabdbbdaadabaaacdabdaaacabbaaacadbcccddacadaadccdcbdbcadaaadbddbadbbbdbbdddacdcbbcbcdbabadcddccdaadabacbdddabbcadcaccbadbaaadcbbbccaaaccadcdacadccbbbcaddcccccabccbacdbbbdbbbdbbdccbdcddacbcabbadaabbacccabcbcbbadbaddcadcddbbcdbaccacdcdaacbcaabaadcbcdddbdcdbddadcaabdddaadbcdcadaacdbdabdcccdcdadbcbacbbcdbdacbccbaddaaabbcbccadccbdacaaabbaadbcbccbadabbdbcbdaddadbbdbbabcbbbccaaaacccbccbcdcbdcccbacddabadadbdaccbddacbacdbdcbdbaddbbbdbcbddddbdccdadcabbbddababbdadcadacadaadaaccacccbdbcbbacbddcdccbbbdabbabddaadbcdddabbacdadabdadcacbdcacdddabaadcbbddacdacdcdddcbacbcbacaabdcdcdaaabcaddaaabcccdbcdbdaaddbcaaadbbbdbdcadbadddccddcbcaaadcdcadccaabbaadcadcdadbacacbabccdababaacbcddddbbddcdcaacbbccdcbbcdbccabadbcbddaddaaaacaccbdcadaadcdddcaabdbacdcddbbbaccdcccdbdcbdbadcbdadcacdcbdaacaacbcacbbdbbccdabddadbbadadcdcccaadbbdbbdadcdacdbabaabacbcccdcdbdccddadddcddbcdcbcbbbbbbadcaadcacdaabaadbdcaaaaccbbddbbdbdbaaaaddbababbaccdddbaccddcdccaacabccadbaacaddacccacddabdcbadddbacbddbcbaadcbbacabcdaabcccbadddbacdcababcdbcbbcbdccddccddbdcacabaccbadabaadbcbcabaaaadbddcdbbbdddabcbdadadabacddcdabdbbdcccdbddcbbbbbcbccbbbccadacbddbbabaddbbbbbbbadbaabdcadbbabbdadcabcbbcccacaaccccddbcddadcdcdcdabbacadcbbddaddacacbcadccdaddbcdcbdbdacbdbdaadcdaabdcccdbaaccdadcabbccacabaacbcccdcdcdbcccddddbaccdddaaadcaacdabacabdababacabdadddcbdbbcbaccccaccbbccadbdaccabcdcbccaadddbacaddbbabdbdbcdaaabcdadaccdacadaddadcabdcdddabbdaaccbcadabccbdddcacbccbacbdadbdccadcbcacdbadddbbbdacddddddbcdccddaaccaabaddabcddbcdacdaccddbccdbbcccbbbcddbaabbbdcbcdccaabbacccbbddcddcbabacbdcacaaddaacddcdbaaccddcaabdcbbcbddaabacdbcadccacddaddadccacdacaabcdadabaaadbcbdcccccdcaaabaaabacbbdbbccccadcbccaadcaaadaddabbacabacadcaaccabdabddcbdcdbaddcbdbbadcabadbadbbbbaabdddbccaabacdbadcbddadbcadccadcdcbcacddccabdabbdddbbbcaccbdabbaadcbbadccabdbdcabaccdacdbdadddadcbccbbdabdacbaacaabdbccadddddbbaaadaddcdabcaaaccdcbaadbddddbaaaaadbaabcadbbbbdaacbadbbbcacbbbaccdabdbbcbcaabcdcbadbacddcbdddbdcccacacdcdaccbbdcddadabcbccbbccccbddbdaaccbdbbcdcccbbcbacadbccabbdccbdbdbaccddccbdabcbbddddbdccaddaccabcdaaccdbacabbcccaabbbcbdcbdcbcdaccccbabbdcacdddcbbddbbbcccadbdddccabcbaaccacadbadbbdbccadadbbbdbbbbbbddcbcdbaddcdbaabcbacaadbbccdbcabbbdababcbbacccbdbdbadcbadbddaccacabdbacbcdcdcdcadccbbbbddaddacbadccbdacccadacbcabbcbdbcbaaadacdcadbcdcbbcacdbbcbdacbdcdbcabadbadbbdaddccacacdacbdcdadccbdabadcacbddabbdbddcddbadccabcbdcadadcddccacacbdbaddbdbaaaccaaabaadaadaccccdabbadcaaddbbdcadadddcabddbaabbbddadbbbdadaaadaddcbbabacacaaadaaadcbcbdadcccadadbbbddcbadbbcadcbdbcdbcbacaccbaaadcbaddcbdabdbbcacbcaaaadbdcaaaacaadcbcdacabdcbccdcdcabdabaccdbcdcbbcdaabacbdbbdcdcadbaaaaabacdcccaccabdbbddadcacabbbdcccccbbdbdaabcbdadacbccdbdaaaadaacbaaaaaaabdabababccacbcadbdcbdcacdaacddcdacdcaadcbbbcaacaabadcbdadaacdacdabcabcbcaddcaaccbbddbadbdcddbbbcbdaddabcccacacbbcddccbcadabdcddccbadbbcccacaabcdddbbcdddaaccdddadbccbbccbbabadcdbbbaccadabbbaacbdbccbdbaadadbdcaaaccaccdaddaccadcbaacbbabacababddaaabbccddaccdcdaccdcddddbbcdabaabcccacbdbbbcbabbbbcbbaaadaccabbdbabbdabbcdadbabacddddabcbbdbcadcbcccdbdbbdbacbddadacdcadbaccdacbcaadbcadaadaacadababcdcacccbbcaacdcdddbcaabacbadbaaccacdcdccabccaaabdcadbdbaddddccddbcdbcdbcabdacbcdccdbdbbccaacaccccacdabadbcadbbadabcdadbcabddccabdbdbcdbaccbacbcacadadcccacdcdcbdadbddddacbadddacbcbbbddabcabdddcbbdaaabcdcaccdcacbbbbccacbbddbaaacccddabccbababccdbbbccddaaabbcbccdddaaabcaadaccdbccdabcccabcbbdccdccaaddacdaacdddbaddaaabccadaadbcdadabcbbbadddbacabdadcbcdcddaaacdcdcadbbdbacbcdbcabcbaadbbbbdbabdccdadaaadccdcccbbcbdbbccbaabcbbccbcacccdaccbcacdaaababaacadbcabdcdcdbcbabcaacadcacbacdbacccabdabaadddcbcbbbcbacacacbadbdddcdcaccbabdbccbcdbdacbacaabcdcdaccabcdacbdcbcbdbbcbbbacabcbcdcdbabdaaadcbdacbcdacbacabbacbdbcbbdaaabcccbadcbdbbbbaabcbbdaaacaaccbcaabcdbdbdbdcacbadbddcbaacacadccdabcbccbaddcdddabcaccaabdaacddccbdddabcdaaddbcdbdbcddadacacbdbdccdabccabcacaacdaadaadbbbcbdccdbabaaddddacacbcccdcbaababbbbbcadcbcddcdabdcbbccbabcbdcdabcbcacbccccdbadbbddcbbacbdaacabcbbabadcbabaadcbbaadbdbcacacaabddabbbcdabbcbbabcbabbbcabdbddbdcdcacbcbadbdbcacdcbacbccbabbadbabcbcabcbdbbbdbbbabadbdbbbaccccdcddbdcbddabaadbcaacacaabdbaddcbdcbdaccbacdccbbaaddbcdbdaabdbbcacbbcabddccdbbaccdcbdcdabdcdcdbcdbdbbbdadcadabdadccacbcbaccdccdbbcbccababdcdbaccdcaccabbccdccbcbccbdddcbabbcbcdaacccdaabcdacccdcacadccdcdddcaaacadabaaacddadbaadabdbaaddbcdccbddbdbdbbbadbbdacaacdbddbadcbbcabcaabbdacabcbacccbbcaaccabdcadbbaccddacabcacaacccbcaddaddabbdbadccaaaacaddbcdcacdbaacdcbcdddbaaaccdadababdcbaabcdabbaccbbbcbdacccccacbdaaddacccdcbabbabddbbbddacaabadbbdcabdddadabaadbdccbacdaaddbbccbddacbaddbdaddddacbcdaaccaddbcacddbaacddaacdabbcaabddcdddbcdcccdcccccdaaaddaaddbccddddbdacabbdcaabbdaddabbcbbbdbbbdaadbcabacbadaccccbcdacdbbabcccdcccbbdbcddcdaaadcabdccdcddbacacbbcdbddcdbaaccabdcddcdabddddbdacbbacbbbadbdbccccddbaaddbbaddabbacabdadcbadbcddaabbacadccbdcaadcbcabbbdbcbdbbdcdbdddacdaabdccbbadabbcadddcddbaababbadbdaabdcaacccbdaabbadaacbcdabdbcbadddacdccddabcdaccbdbbdbbadcdddbddccbcbcdcdbbccddbbcdadabbdaabaddcdbacddddddbbbabbaccbccaaadacddaaadbcdcacbdabbddabccdabbddbbccaddcacababcdacccdcbdbabdaabacccddbdddabbbbbdcbdabcadddcdccacaacbdcbdcaabccbdcddaabbcbabbaacaddababdbbacbaccdabcdadcbdbaddaabcdabbdcadbcbcccaccbcadcacbacdbbbcadbbcbdacacbbabaacadbcaddbbabbdacdbabdbbccacaacdbcaaccdbcabdddbdcdccccdcbabddadabacdacdbbacccaddacbaacbdccccdaaaaacaabdabcccdbabbaaadbdcadaaabdbcdcababaadccbcaacabacacabcbaddbacdbcaccbbcacdbddadadcbbddbbacbdcdbddbcabacadcccbacabccbbbdbbddaddbdbddcbadadddabcbddabaacabdbbaddcaabadcdacabcbcacaaacdcddbcddddccdaabcaadbbdaaddbcccbbdbbbdbaddbbbccaabdcdcaabdbcdacdbcbbddcaccbaddbacbbdcabcbabccabdcdcbaabccbcabacadccacdcdbacdcaaacacbabbdbdcaccaacaddcddbacccadaddaaaaccdcbabddaaacdacdaacdbdbdcaabdcbcddbabbbcddbbcbdbabbaaaacbccaaadbcbccccdcbadacaabbdbaabccbaddbbdabcccdaadbdddacbaccaaadbacddddaaaacacdbbcacbcdddddbbabcbcccaaaadccdcdcdbdcbcabadabcbaaabcabdddbbccdabcdcdaccdacdcbdcaccabbccabdcbabddaaacdbdabbadacddbbbabdcbddadbcdccddccdcdadbbaccaabbbbddcbabaaadcbbdbadacacddabbcababcabaabccaaadccdbabcabadaaacccdbdcddcacadbcbcdddbcbbbdaabdaadaacdbacbccabaabcbbacaabdcaddddbcdcacdabcacaddaddbdbdcccaabbdbdbaabbabacaddabbcdbdccadbbddaadcdbdabadbdddbadcdaadccdabacccdacbbaccadcbbdbdacaccdbddbccbcdbbdddbabccaacbddaacbaddaddbccddcdacbdddcabcdcdbadbbacbccbacacdcbbdccbcddcadbaadccbccdcbddcbbdddadcbadbbdbbddccbbbcacdadaccbbdcddcaabdbdaabacdabaddcbbccbddbdaaacdbbbabbaaddbdacdcbcbbbdabbbbadbacbcdaabbabbbdbdaccdcdcbaabbadcaacacbaabcabbccaacaaaccbdbcdaccaacddaddbdcccdbddabdaaadabdddccdabcacdacbdbdaabababcdcbaccbbcddbcaacaabdbaaaadcaadcddbabbcdbdbabcbcacdcbcdadbbdaaadbccbdcdacbaccbcabbdadddbddabaccdcccdccdbcadcdcbcbddbbdabaaadcbadbbacddbbcddbcdadcbbabcdaacabaccbbdbbaadcbdbcddacddcdbbbdbbddcddbbbaacddacddaaddbbcaadcbcdadaddababbbcbcbbcbcddbadcdaaaadabccbdddababcccdbbcdcadcbaddaddbacbcaddbdaddcddadcbaabbabddadabdbcbdbabdcaacacaacbbaddbdaabbbcccbacdbddbadcddbbaaacbbbbddaddbdaadacbdadaacabccccbdbaddcdacccabaccddccaddbcbddcbcbbcacddddaadcdadcbcddcacccabbddbcbbdababdcbcadbdccdcabaadddcbdbdbccdadaddadbdaccbdcabcabaccddaddacdcadbcbaaababaccaabaccbbddbbbdadcaaaadacadbddcccababbcbadcdcddbbdcdadccdbbadaaddadcddabbbadbcddabbabadddaaaadccbdadadbcaacbadacbdddcabdadabccbdaaaacadaacbabdadacbccbbbdacbcbaacbcbabcacaaddbbbacacbbbcbbbcadaabbddaccbcddbcbbccbcbdbabcadcabbbaadacbaacbcdadddabdadbdaabbdabddbddbcdcbddbcadbaacdccdabcdbbdaaddbababbcccddcbcbcabddbccacdbadadbbacddbcabaddbcbacdccaaadbbcccabacacdaadbdaaaddbaadcaddabbadaaaaaaddbaaaaaacdddbaacddbaccdbcacbbbbadaaaabbccdcbdddcdbacbcbcddbabdadbcbbcbbdcabbbddbbcaaaaaabcdacdadcdcbdabbcbdbcaacaadcbbcdabaadbcbddacbdaaababdabbadaabbddbccabbbdadacbaabcdcbdaacbbbbcaddcaddcdadcbadbbbcbcddccdbbdbbaddcddaaccddbbdbbdabdabababacbcaddabcaabbddcbbbcbbcaccbcbbbabdaddcaaccabbdabacbcccaccbcdacbdcbadacddcbdacdbbcbcbacaacababcbaadaaaddbcbbcadcdacacddddbbdcccbccccbcaadadcbdbcbabadcaddbaabcaddbccadaaccdbdcbdacbbcbbcdccdbbbcabdbacdbddbdbcbacbdbdbabdaaddaddaabdacbbdacadbcbbcdddadccbcadadadcbbadabdadbbcaccdbbdbaabbbbdcaadbbdbbbdbdadcbddabdcdccbacaabacacbccdcacccddcbbabddcaadabcbdddbcadabaabcbaabddcabdcbacbccddbadcbadbcdcacccddbddbdcbbdddcabbbbbdaaaaabbaccaaadddababcdbabdaacdaddbcaadabacacbabdccccbacdbcbacbacadccaadcbbcbadcabdcbddacbddbdcdbbdddcacbabccbddcbbabacccabddbdcadddbdccddcadbbbddbadccbacbcddbdcaccaaadcccccbbaabbdadacddacabcdadbbcaaaabdabbabcccababddacdaaaddabcacbdbacacaadbbbcbbddbaddadddddcadccabdcdbbbbabbbacbdccaaabaddadadccdddddaaaabacdabdacabadbbdbbcccbcbbbcabaddbcddbdacbcbbddaaccadbdbdacbbdbcdbdccbccbcccdabdaaacbddbccbbbbbadbbbcbaacddddbcdaaddccdcbdbadcbddcccdabcdcdacccaddaacaabdaaddacbccabddacdcdddbacabddbaddcdaadbadaaddcbdddcbacccabaabdbcadbbdddbcdaacaddddcabcbcbdcdaadddcdabbbdababdbbadbbabdcdbdadacdbdbbbcdabcabcacadcaaadbabbccbddccdaccaabdabbdadabaaacdbdaaccccbdbdadbcdddaadbccccababaacbbdacdcbcdbddbbbabdbaddbacdccbaaabbadbbadddbaccacdaaddcccdbcdaaabdbddbdddbbacbbcabdcbbdcabccbdadcabadbbcabbccbddabcddbddadcdbdbbddbdbdbcdcdddddcbccacadbabddbaccadabccdddbcabacbdbccddbcbadabaccdcadbcbcbdbadbcbcdbadbacddadbdacbcbaccbbbacccbcdbbdaaddccbcdbdbabbcdbcabddcbcbccacaadaabdbdcdadbbbcdaabbacaabdadbbbddddadbcbaddadddcbabdcdcaccdadcbcbbdadaadbabbcddbcbcccbadcdadadcbcabdabbdabdcbdadaacdabadcbcbccbbdbdaaccaabababbdbaaabadabcddbdcbdadabbbdbacaccbaccabbacabacddaabbdcadcdbbbbdabccbccccbcabdddbdccbdabccdddabbacadbbcddaadacbdcccabdbbbdbdaddbacaacdcbbabdbbbbddadbbdbcaadaccbaaccbdcbbcbcbdadcdcabadcdbccaaadbcacacaaadbcdbabccacaacababbbbcbabcbcaacdaadadacabbbdddaabadccbcdaaaccabacadbcaccacddbabbacbacdaababadddbbadbddcdacdcddaddbdbaaddbbcaaaadcbaacaacccbccadabbaddadcacacabbdbaabadcaabbdcccdaaaaaddcbabbdabddaccaddddccddcdcddadaaaccbdddcabddadbdadbcaaabacbdbdacdaaccabdddbbcdbddabadadbdbddcbddbcdccccdbbaabaadbaaaadbdbbdbbadacaaabbcdbbaababaacccaabcdabaccbacccaccdcbabbdcaddcdacbcaaaaaccbcaacbbbccacadaacdbdccaacbacbcdbbabcddaaddaddcdbdbacbdbdcadbacdcacacdaccadaabbadcbabbdcbcbccddcddbbacbbbcbdbacaaaabcaacdbcbbdabddabbbdcaaacabbcaddbcaadacbbabacbdcbbdbabdddbabdaadcbaacabadadbdabcacbabaaabbcccddcabbaadcdadcdcaccbbdcaccaccdbccdcbbbccdabadbadbbbadcdaccabacdddaaccbadcdaadbdacccbbbabdcddbccadbdcabbadadbbcaacbcbdbacbbaccdaacdccacbaddcaadcdccdbdacbbbbccdbbccaccdacccadbcbbdbadaababadcbbcdccaccbcaacbdaabcacadcdcaabbdcdaacccdabaccdadcccdcacbbdbbcdcacaaacaabddabbcbdadaabcdaabdacbdccaadaddbdadcadbcbbaaddbcddcbdcdcacdcaaaabaabadbcaaaddbcadadabdbdaabaaaaadadcaacbddaabddadaaaddbcdacbbdadabcccdbcccdbbabcdabadbabababaacddadddcbabdadddbbbccdbcbaadacaadacaaaabdaaacbcdcccdbcaaabccdacacbdcaaddbbbdaaacdbcadadcacaddbcdaacbadbbaacabadccccadadbbdaababaacbacaddadbabdacacdbddabaaadbbbdbdccccaadaacdabbbbcbdcbbccdadbbccdcbaaccadbcdcbcccbbbcdcbcabaabbbadccaadadcbddbcbacabccbbbbbcadbaaacaabddbccbdbbbdadddacdaabddccbddddcbbbbaddbadabbcbbbcbcbaadbaabddddbacbcaaabcdaccadabadbccaadabdcbddddaaabcacdbaaddabbdaccdbcdabadcdbccbaaadadbdabcbacabdcdcbbdaccabcbabaddabddaddbddaadabddcddaaaacaadaaaddacccadadcbcdcaddbbbcadbccdbbbacbdbdccbdcbaabcdcdbaacadddaadbadbcadcaaddaddbadbcdcaccccdcbbaddddddcadddbbacdababddacccdaccbbbddaadaacdcabcbbdddbcdbdaaccbbbabdaabbbcabbbdbbaaccccdcaadacabaabcbcbdbcacdcadcdaccbaabaabaaaabbabddbcaccbadacaddabdadaababaadbcdbadbcccadaddaacdaddcbbcdbccddddadbdadcdabcddcbdcbcddabbcdbaaadbbcadcbccbdaacabbbcbbdddbccabcdadabbcddadbdaacddcadbdaaabaddcdbcdcdbddccabcdaabcdcdddbcbcaabcacaadbccacbcabdbdcaccdbbcbdabdababbbaccccbddaaaadaccdbcababddcaabacddcddcbbddcdadbabcacdbddbbdddabcadbabbccddacaadcbcdbbcaabcddaabbdacdabbdbdabcddbdaaccabccbddbbcbdcadbbdcbdccaccabcabcbbdcbccaddcbbccdcaabbbabbdcabaddaccbadbadcdcbbdbabbbcccaabdccdccbccdbbccdbdcbbbabdbbbbcccbcabbaabdabcadbacdcbdadbcaccabacbaaccbccaabdabcbbdcccbadbcaccbbcbbcaacddcaadaaabdbcaaacdbacdbaaddcdbbcbcabbbcdbacbdbadadbcbbaddacddabbccdcacabbaacbcabbdbdbcbdbcbabacccddaadbbbdddcaaabdccabdbdaddcdadbcccdcacaaadadaaabaccbbbbbabbddaaacacbdacdacbbccabdbcaadacdcacbcdddacbbddccaadccdbababdabadabbdacdabddddddcccbaacacaddbddbabaaacaabdccbbcabacaacdccadccdbaaccadddcdbacbcbdabbccaabdcabbbbabaddcdaddaabdbbdcdccbcadaaaaadbcacdbcacdccacadccbcbcddcbccddaaadbbbddbabcbcadcbacadabdabbadbbaddcdaabaddbdcdbdcdddaabcccbbdccacdcaacddcddddddcaadadcbbccaaadddcbdbaaabaaccdcaabdbabaadbcccaacabacdbddadbaabdbcccbdcdcbbbccdacbcdaccbcccdcccddbcabddadadbddbaacdbbcddbcddccddaaabbacbbcabbdccadbaaabdcadbbcaadabdacdacadaacaabbbaaacabacaabcdcdcaaaadcabccbacbcccbcaaaabaabadbcdcabcabdcacbdbabadcbadbbbbbadadcdbbaadcbaccaccdbddbdcbbdccacdaccaccaaccabaacdcdcacdaacacadcddaabbbdacbdbbadccdabbccdcadaddcacbcacbadcdddbddbcadddabadbacadcbcdcaabcdcddbdccabdadddcacbadcbdbbbccbddbddbddabcdccdbdccbdbdbcbdabcabbadbadabddababacdadddbaaabdcabadbdbadaccaadbacadbbbccbbcbcbdbbdabdaadabacdcbadcaccbadcababaddcbacabbcbaadcbbcbddbcdcacbdddcdadcccdbbcabaacacdcbadaccbbbbdcbadddbcdbaaabaaabdcdaccbddccbccabcaacdbdabbdcbcddbbdcabbdaacdababcdcacccaaacbccbddaabdaacbaccadabdaabdccccacaccacdaaaaaddacdddbbacbaabbccddccdcaabcbbabaaaadaaccbbcddcdacdcabaaaabccabdadacacbcdcaacbddddbaccaaddabcacabcacadadacdabcddcdaabbdadcdadddccbadbbacacdaabcadcbbdacababaadcbbbbddcaacdacbbbaacbbcbcdbdbcccacacacdccaabbaacabbabcabcbbaddcadbdacacdbabdadddbdcdbaaccdddbbbbddbddbadadbcaabcdaacacdbdcddabdadbddbcccbccabadbbcbccdbddaadcabdaadbccaddaddbdbdddaadcccaaaddaabdadaaccbdadcbaddaacccbcbcaadcbaacdadcbbaccbcabadbaadbbdbbddcacacadbaabbababcdbbcbddadabdcbcbbdadadddacbbadbcdbbcacadbbcaadddbcddcacabdaaccbacadbcbdbdacadcacdadcacbbbadcbcbbacdcbdcddabaccacdbdabacabccdbcdadcaabaabbabcabcacdcdbddddcbdbbcbdacbcacaadbadacbbccabadddbacadbcabaacdddaddbdcddcbacadcddaddbbcbcdabbadcbdadccdcbbbdacbddcbaadbacbcdbdbacbcbabbdababababcccbccddcacabbbbddbaaaaddccbddccccdadccdadbcabcccbaabbbdbdbabaccdbbbbdaaacddaddcdbaadbcdaaccabaaadacabbaaaacadadbdabbbdbbcbbbcbddbabdacbdbddcacdaacbaccababcdbcabdbacbaacbadbcabaacadadddccbbaababbbdbbacdaaaadccbcdcbabaccabccdacabdadabcabbadbaabccbcbdcabccddbadcadaddccbbcadaaaabaacadadcadcbdbcbdbcaadaadbcbcbdccdabbbbbccbbccbdddccbbcbcbbcaccaaddbdababcbacbbbdccccaaaccbcaadcbacaccdbbcadbdaaadaaddcaaadaccadbcbcbbdbacbbaabccbdccadabcadbdadbdbcccbdccacbcdbabcaddbaaccdcdacddcbbdbaaaddccadcdbbaddccbdaaccdacdcadcdcaabdddbabccdacbcdbbcbcdabdadbdcaabdbaddbabbadbcaabbaaccbaddaacaacccbbccbbcbcdbbbbabaabcbcccbbbbcaccbccababbcacacacddaaddcdcadbcbddaccadacdadbacddaacdbbbaadcbbbcddcaadddcccbcbbdcadadbdacdcbccbcadccdbbdaccbcccaabddccdcabcccaccaaabbaacbcbaaccbbccddbbaacbdabdbcbdcacbacbabdbdbabbbdddadbabcaddcadcaacccdbdabbcbbdcdcccbabddacaaccbcdbddcadadbcbabdbcdbdaaabdcdacabddcaabdbccabccbbadbccbdabdcbbdcaaddbdabbccddcddaccdcbbababddcaacbdccacdacbbadbcdbcbbaddbaaabddcadcdabadbcbccdabcdcdacbccaccacbbccbadbcadddccadbacdcbdacabcbddccbcdaddaaaccddddaccbdbbbdadadbccdabbbacbaccaddcadccdadadaabbdcadcadcccacdcdacdbdabcdabbaaadabaaadbbbdcaacadbbcacbccdbababacdabdabcadbcdbbacacddcbccacddbaaccdbcbcbaccaadadddccddbbbdccdbccabdddbddcbdaddaacadbabdbdbdcdaacbbcacabaacadddabdcdcabaabaddaddcdbabbcaaacadbddbdbbbbbcaaabcbbdbbcbbaaadadccbcccadaccabdabbdddcbccbddabbaddcabdcccbcdcbdcdcdcdcacdcbcadcccddbdacdbcdcbddccadbbbaccaadbdcbabadbcdcdcabbdbaadbdbdacabadaaacbcacccaaabcbaddcabccbbbaddddbdcbccacdddadcdcbdabdcbabacbabdccacacbdbccadadcdcabbdccabaadddbdacddccdaacbbcacadbcabacdbcacddbbbbccadddcadcdbdcbdbbdcbcdbdbadabdabbbcaaaabdbbaddabacaabcdbaaacaacbdacbcadacbacbbbdccdacbbabdcacddddccadabbacbcccdbcbabbacbadbdddbcabdbdacccbcbdddcacaddadaadcaadbcbcacdabccccbdaacacbcdacaccbcbacdbacacabdbdcdadabbcdbcccbbbaddbaccdccdacbcbddccadabdaabbacabbdcdbaaaccddabaacabacbdcbddadbcdabcccccbbddbcacdbadcbbcdcccbadabcabcabdcaacacdcadabaacadddcaabbaacdbdabbabcbbdbbbadddccbdbcdaaaaadbbdaaadadbcddbcdbdbaaccbbcddcbbabcbadddbcbcbcddadddacbcdccaaabcbcbcacbbdacddbaabbadbabbbabbbddcbdabbcdbbccacaaadbbbddcdadbbbbcbbbcccbbaccdbccbadcbbabdabbadbacddbbcadaaaaaabaabcbcbbdbdccbbabbaadacccadddaacbddbadcbcacddacdabddadcccbcadaccccabbbbcddccdcccbdbbcccbcdcacdbacdacaaadccbcdacbcbbbbacdcdddbdcdccbdcbaddbdcdcdbcdddadcdbdbacdddcbadabbccbccccccadabdaccbabcbaccaddaaadadbcdcdccddaacdccbbcbaaaadbddacbabbbbccaaabcdacacdacbbabddbddbdcdadccacaddbabaabbacbcccbdacbacddcbbabcbbcabbbbdbdbdcacadaddaababcdbcbacdddbaddabcaccdbdbdadddbabcdbabcabadbcabdccadcbddbbaaddabadcbacccbcbaacddabacdbdbabacaddddbdbdccbdcccaaabacddbbdbadbddccddacacaadccccdcbccadcbdbcabcacccdcdcbacbbaccbaabababddbdcbacaacccbccbbcccbdbccdbcbcddddddabbcababdddcadcbbddacdaaaacdabcdcbaabdbcadcdcdbddcddacabdccccdacaabcdbdbbcaaccccaddbdcbcaddaadcbbddcaacbdabaaddddcadaccbcacbcbacbddadbbcbdbabbcadbbcdbbddccabddbddbccbdcdcadddbdcddacdadcbdaaccadbbbbccabbcacdaadadaabaacbaadaaccabbdbbcdbdddabccaccbadddbbadbbcdcbccdaadcbccbacbaacbadabacddcaabccbcaccddabbaadcddabccccdbaabbcbdddddcbdbabbdccdcbbbbdcdbabbdcadbcdadaddccdccbbaccbbdbaabaaadbdbaccbbccbabcdbcbcbbbcaadcacddbdbbdbacbbcbbbdaaabbcbdadddccdadaddbccbbacbbbacaadddbbdcdcdadddababbcccbbccabdccdacdaaabaccacbbbabbccdcbabadcadccdadddaaddcbbacdbacccbdacbaabcddadcbcdadbccabadbccaadbdaabcbbcdabbadaabdcaadcbbbcadaaccbdbdaccdccbababddbccadabcdcdcacbaddabcbcdabbacaadcababbaadcdcadbabcdcdabaddcdddccbcabbbbadabbabdaadacbcddacaaddabaccdddacaaaccdbbbddbdcbbcacbcdbdccdaaaccdbdacdbaacaadbbddddcadcbdbcccacddabaccdbbadcbdbbdabdbbdbcdbddbdddbddbabacacababddaabbbdacbadddbcddcbccbbabdbaaabdbcacdcadcbbdacacbdcbbbddabcdabdcaccadbacaabcbdcadcabcbdbaabcaaaccbbdbbbbdaacbbbbbcaaaacdbdcabdcaddbaddcabddacbbacacdcbbbccdbcbcdcddabcadabcbbadbbdbdaddadccabacbdacabbadcaccdababcbcabadbcbbabdacacdbbdacacdcdbbacdbdabbbabacdadccbdbdcdabcdaabbdcacbccbdbdabdcbadcccbabdddacddbabdadbcbcdddddbabbdabccaabaabdcdbbdaabccacabccabbbabbdbcbcadddcccdadbdbddcbacbbabbbbbbaadbccaaababacbbbbaabdaabcdcbbdadcabaacdadbbabdbbaacdccddddcabcdccddcbcbacdccdddddccccdcccbddbdacdacbdbaadbbcdddabccaccbcdbabcdcadadbddbddccadbcbbbdcbdcdcaabbbbaccddcadaaabaadbdddbbccaadbaccdbcbbbbccdaacdaabdacabbacaaddcacbbccaccbdacbbdcabdbdaacbbcaacccbcdabdcccbcddabbdbacaacaddbabdadcccdcacdddbbddaddaccbbdccadadccbbcddabbbdccddcbbddbaadaccabbbaccacadcbadcdbaddcdacbbcacddbcdbdcbbbddaccdbbbaacadaaadcdabcbdbbcaccaaadcbaabacaddcaadabaaaabbaacbacbcbddaacbbcaabdcbcdcdccadadadccddaabdcccbabadbabaacddddcdddbaccadddcaaabacbdbcaadaaaaddbadbbbcdacddaacccacddccdcbacddabcddbcddaaabbabadaaccadbdccacbaaccbccccbadaadbddbdbaacaddacaaccdabaadcddcaccaaccbbdbcdaccaacadccbbbdacbcccaaabdbddaaaacdcccdddbabdddbcdcbbaabddaacaabccbcbdcabdcdabbbbcabaccddccbacbbdadbdbadbaabdcdbbacdbbddbcacaaddcaacbdbcdbacdccbacccbdddacacbaacabaccabbcbdcacddbddccbcadbdcbbabadcaabbbabcdcddcdbbbcacdbbbccabdcdccaabdbaccaacdbbdbcdcbdddbcddaaaaddbabaadabdbdccbcabadaacbadbaddcdacccdadcabcdbabaddcbbcdbcacadacabcdaddaaacabcbdabddaccaadccccbbbdbbacabbcaccbcbacadadbccbacabcadddaccdbcdcdbbcaddbdcbbcadaccadbcdabbadbaadaadcdcbabaaadcaadaaaacacbbbcdcacbacbcdddbdadccdbadccddbbcdbbadbaabcabbbdccddbcabdbcbbccdbbcbbcdabbdddaabdbdbabbbcbabbdbcbcbbcabbccaccbdcabaacbcdccdabdddacbbdbacdbbdbbbdddbcbbdaacbdacabdbadbadcbbbccdabcddddbcdbacaaccdbcdaadccbababadadddaabccabbddccdbabcabbcbbddaaaddacbacbdaabcddbdcbcabddacbcacccbbaabccbdbabcdcadacbaadcccaacaabbcabdabaaacadcbacdbddbcaddbbdbdccdcbccddbbcabdbcbbacdcbacbcadadacacbdacccabdbdbddabbacdbcccabaacbabcdddcadaccbbdcdcacbaabcadcaacdaaacbbcbddabadbddaacccaddbdbccbcbdcacababdddacbcbabbbbaacbcbcddbaaadbcaccdcddaaabbabdaaabdaddccabbabcacbabdbbbdddadbddbbdabcdbbbdcdbbbaacabacbbcabdbdbaacabbcddabddcdddddacdbccaabbbdbdcccadaabbccdbbcaacccaccaacaaabddadadabddddbccbcdcbabcbcdcbcbddddcdddcbbcdabbbbcbdcacbacdadaadabddcdbadcdcabbbcdaaaccdcddbbabcaccdccadcdcddadbddcaaccabbccdbdbaadabcadccbdcababcdbabdbdbbbabcaacaabbbbadbdcdacbdabddcbabcbbbdaadbcaadadcadbcddcdddacdaddcdcacbcbacbddbcabdbdccdcdaacaabbababaadcbcdbadbabbdaaaaabcbacdbbbcbcbbcccdbddbcdcdddcdccccddaddacbcccabddbadbaacacbcdddddbacbcdddcbaadbdcabbdacdcadaaddddbacdcddabaccbbbadcddcdcdbcbacbdbdacdcccbcbaadbdbddbbabacdadddaabaccdddabbbbdcdbabcddaaaacdddaccbdabcbaaabbdaacdbbccaacbbaacabdbcaabdaddcdadbdccdbaccdacdddadaabcccdcaabaadbccdadddabbbcddacbaacaabccaabccadcdaaddcaddccbdbabdadbabaadcdababddddacacddbddbbcbddbdbacabcddcdcacababbdbdcbdadddcdddccdadaddcaccdccddbdcbacabcdcccdbcacccdbccdbdcaabbdbaaacbadadddaabbbacdcadcdcabaacbbddbbdadbcdbcdbcdabadbbbadabbdaadcdaddcaddbcdabcbddacdbbdacacdaabbcaabaaccccdacdacdadadacbdacdaaaccadbdddabcbdbaabbacbaacacddabbbbaabcbdccadcdcabbddcdcdddcbdcddbdddacbbbbcabcdcccddaccddcabadccdbccdbaccdcaddbacaabaaaacdadbdcccbbaddbbcbdbbbbcaadaccddddbdbbddcbdabbbddbcbdddcadbddacbddbbdcccdccccccddcddbadaddadbcbbcccacdbcbaddcabaddddbdbddabbddbbadadcaabdadabdaacaaaaacaacbabcaaaddaccbacdbcaabdcdbabdcbaadddadaadacdacbabadbabacaabbbbbacddcacacaccdcaabcaacaddaacccbdddaaabaaccbcaddbbbbbbaaabbbdaaabaacddabdbdaaddadbcabaccabbbbacbccbdabbdbcdcbbcddbbbdcbdbddadbdbdddbcddbcbbddcbdcadccacaabccddbbaccbcdadbbbaaacacbaadbbddaacdaccbbaaddabbbdcdcddcadadadbdabbbdbccbaaddccaadaddacabccbcddacdaacbdcbdccaaabdbddbbbbacdbcacaadaacdcbddbccdacacadabbddddcabbcbcadadcbbbbdccabdadcacbbdbbbbacdbdcdcbdcadcaccbcdaababdddcbbddbbabdddaddbdaccadacabdbdaabcbdccabcddaaddbdcbacdcbcdbccaadaacacbcdbbccddcddbdabbdddababcdaadddddcaccacdccccbcdadccdcadadbbacaadcbcbcbbbbddadacddaaacabcbcddaadacacabdbcaacccadabcbddcccbcabaaabadabbaaadbccddacbadccdcadbcdddddbdbaddcbaadccbbcabcbaaccacdccdaabdccabcacccaabacdcdbcccbdcbcbadcdcdbcaadbcdccbaccbdabaddbcccdcacbdabaadddadcadcdcbbcbddaaabbbcbacddcdabcbaaabcddbabacaacabbadcbcbddcdabddbddcacdacacabcbdddcabdddbcdacbaaabbdabbbcabcaadbcdcbabdbcbabbabddddbbdddbccaacaacbdbcabacbcdddaadcddcabdacbdcdbbbaacaaaabbbababccbbadccdabdcbcdbcbdddbdaacbcbccdbababdcacbddaadaadbbcadcaddabcdadbcacdcacbbaddddaaddadaacbcaacddddcabbabccadaabadddababddbababcabddbbcabbdcacddbdbddbadbababbaddbcacbacadacdddaddacaaccabbbacdbbdcabcdcbdcbdcabcbabdaddbbadbdccbbabbcbbcddacaadbbcdcaacddbbcdcddccbcaacdaaabccbaababdbcbcdcacbcdabcbcdcbbddcddbbcaaccaaadbacddbabdbdcadbbaadcbadbadbbaabadacddcacabacdabccbddacadcababdbbcdbccbcbadacdbdbcdcaadbbadaadcbadacaadddacddaaabbbadcdcdbcbacbcdbcdbdcdcdbadadbcadbbddddabbcababcbcbcbcbaddddccdddabababacbdcdcccabbcddbccbbbcabdcabacccbacaabbbccadbadbbddbbbddbbddacacccbccdbcbbdadbddaaadcbbbddbcaaddabcaabcdabacacabdacdbbdabdbdcabaabacabdaddcdcadbbaddacdccccabcddcbabddbbbdaabcdcddaadddabccbdcaaadadcdaddadcabdccccddaadcacacbccdaabbbbdbaccdcccbbacddaababccdaabaccaaddbbdddddcdaacaccccdacdbcbcbddddbbcbbddccaccccacacdcabbdaaabdbccccbabdadaadcadcdaccbcaccaaacdbaacccdcaabccccdcbbacabaccadabacacdaadaadddcbccabcccacbbbcaadbccdcdcbbbdbabacbddbbccbacddadcaacbcbacacccadbdaabdbacbaabaaabbcaadccdddbbdaabbdacacaacbacbbbbcdcdccdbaaacbdcbaccdcbacacbdbadacbbcdcddcdcbaacbaadaadbdcaadccbbdacccccbbbbcbcacccbcaabaddaacacbbdddbbdbcbdcdcabddbdabcadabdbadadcdddbdacdbdccacaaabcbccccaacdcbdcdbcddbccbbcbddaabccbbacdaccbbccacccaacbbdacbabdbcabbddaadbaacccbccbadbabdcbadacadaadaddbcaaaccbacaadababccbccadddcdacdacccadcaadabbdddadabbacacbcdbbddaabdcccbbcbbbcdabdabacccbcacacaaadbdddcdabcdaadcaaaaaadadddadbcddcdbadbdbacdccbdccadcddacabbddbcaccaadbaabbbdbdcbacadacabbdcaabdbcddbaabdabcbbdbddbddbdabcccabcddcaaaccacbddcdadaaadbdcababdacdcaccbdaddabddbadcacacbccaaaaacbbdcaaaddcddaadadcbdbdbcdaddbbdcacabbbbcdbcbcbcacbcaccbdcbaadabcacadadacbacddbaadcacbcbddaabcaacdcaadbdabbbddadbcbabdcbcbbaadcccddadcbbbbdcadcdcacacbdbcddcbcdbaadbbabdbacadbdacaacadbddaaddccdadcbdbcaccbbcddacbabcbabadbcbbccddacdbcadcbbbaccbcdbabcabadabaaadbdbbadcaacbbbddadacddbadaacbddccaabddddcdbbdcbcdcdddbbdcdcbbdbbdbdcdbdadbdcabddacddbabbdcddcbbbdacdbabcdabdcbcbadcabacbcabcaaabdbbbbadaadbbdaabcdbacdbbccacddbdbcddbcdcabbcdababadddbaacaccadbdbabdbcaadccddadddacdabcbcbdcccbccaaadcdcbdbbddcbaadcddcdadccbdadacacadbbaadccacddccddbbaababdaddbbacbadcacadccddbbddbacdacdddbccabdbabacaadbdcaaddabcdcccbcaccbccbbdbdacbbabcacaaddbadccbabcdcbaaccbbccdbaddbaabacdcbcdbcdcbbaacbbbdbbddccccbadbabbdbdaaabacacacaadcaabddbdbbbcdacbbcbbadbdccacbbddcabdabccabbadddadbdcbbbdadadaaacdabbbcbacaccccbbaccacbdddacdbddbbccbbcdbcaabdddbdadbacabdcadccabacccadbbaadacbdacdbcbbbcdbcccdcbaaacbdcbbddcccabcddbccdbaccabaacabcadbbadabcbdbbcdabdaaaccbcbcacdcbabbddbbccaddabcacadddacbccabbdaacdaaabbaaacdaddcbdbaddadbbcbdaadbccbdbddaaddcdcbbbcdcbaccddbccdccdddabbbcaaccadadaadabddbabbcacadaacbddcadaccdbbdcddacaddabacbcdabbbacdddacdcbadbcdabbbabddbddaddaccbdcacbacadccbbccbcbbddbdbabacbccdbdadbccacdcdcddddbdacdbddcbbbdcabddbcacdbacccbdcbaadabbbdadcabaadabccccabbbcbbcacaddddbbddcaabaccdbcbdcbbbdbacacccdbcdaacbbbcdcdabbbbabcbabcbccccbccbcabcbcccdcbcbabddaacaccbddbdbbadcdacdbaaaaccabdddbdbcdabcddacbcbbacbdbabbcacacddaccdddcacaaaabcbcaacccbdaddaccccdacbaacbcdacccaadaadbcbbddccacadbaadbbbaadbadaadbacacbdbbaaaacdcdcddcdbddabbccabdddbbcccdbcadabbbdddbaccbadababaadcbadcddbaddadbbabacdadbdadcddaddabbbbadbbcdaddbccbccdcaccadacabdadaacdabcbcbaccbdcabacdbbbbbddacbccdaccbbbadacdaacdadcbbabbbddbbcbcbcdddddccdadcaccaabcddadbdbcacdbcdcbbdadacdbadbcccccdaaacccdcbcbdbcadbadabaaabacbcacaddbacddddbbdabdcbdbbdabaaddbddddaadabcadbaddadbbabdaaaaabcabadcdcbaabcdbbdcbdaabadcdaccaccbaccbcadbdbbcbcadbddaadcadacccabdabbcabacdbcbabbccbcdbddacbbdabcaadbdbabdcdacdabaabaabbccdabbcddcbccaababcbcabaabaacddbcaddacdabcabbbccbacbbcdbbcbccdcbcbaddbccdaaddccdabcacddcabddaaccdcacaaaddabdabbcbabcccdadbaddcbbdcdbccbccacdbbdbcddcdddbadadbcdacddbaddbcbdabbdbcdbbaaccbdbaaacbbcdbabadcbdcdcadaacbbccacbaacdddabdcccbdacddbcacbbdabdccdcbaadcdddcadcbaadacccacbbdddcccadbbadcbcbaaababbbbbdcadbacdacdaadacabbccddccdbbcdabbbcbabdddcbaacccbddbbdbcacacbdabbcccbbbccaabddacacaabdcdcbccccbbacccabcdaccdbabdadcdccbcbdbbadcbdacdbcbcdadbbcadcabddddbacaccbbcdcbbbddaabdbbddacdacbcaddbdbdaadacdacaadabccdcccdbbbacdaddbaabbbadcccacaacbadabbbcdcbdbdbddadcaaacbacaabcbbccaaddccaccdbdddbbacbadcbaaacbbccbbdbbdddccbdcccbccaaadbaaaadcbdadbcdbdbcacadcccdddbbbbabdbdbaaddcacacccaaaabdbacccbddaacbccccddbadabcaababbdcdcbdbabbdccaddcddadddbabcababcddaddabadbaacbaabbabadddbcccbadaddddaaacabbbdcaabbbddacaabcdbdbcbbcdddaadcadadabccaddcaccbdcdcbadbdbcdbbacabccbdcddcaddaaacbdcbacadabacbbbccadcbacdbddbaccbbddbbabdbccdbbcaadbcccccdbbaaaabdccbabcbdbaadcccbcccbbadababcdccdcdbbddabbaabddabaadacbdadadbddddbcdcabddbcadbbacbddddbdbabdcbcdbcbcdacdcadcabacddcbbdcbdacadadbcabbadacaacccabbcddbcbdcbdaacadbcdaaadcccbbbacdcbbcacccabbdabbadddcaaacaccaddcadbcbcdbdacdcdbdbbdaaabdcaadbccabdbcbdcaaabcddaaaadbabadaabbcabbcdcdcbbadabaadabdcbcdbccdcdadadcdccacadabacdbacaabaabadaadbbddbadcabbcdaabcbcadcccacdacadbdadbacbaddcccdcddbddadbdcbbdcdbadabdcacccbccbabaaddadadccdbacacdbbddcddccaccbbaacbccabcddadabbddbbaaababcccdcbbaadaaddcbbddbdbacadacccbccdaacacddabbadbacaadbcdadaabadcccdabaacacdadaaaaabcabcabaacaddbccdabcabcbdbcdcadddabacddbaaaccccdcccbcccacabdbcccdcbdbadcdacbaddbcaccdbbdabbdcbbdbabdbdbdcadaadabaddcddabcadaabbbddcdbbcbdbdcddccddccbaccabcbccdddadababdcbcdabaccaaaacccdbbdbabdbccccadccbcbadacdacbdaabcddbacaacdcacabbcbabaabadaacbdacdbdccbdddadcaadccbbdbbabdababbbdcdbbbbadcbacbdacabddababccacbacabcdadcaddbacccdabbddacddcdadabcadbddabccabdbadacaabbdbccdaddcbaadabcdcadaadbbbcbdcacdabcbbccaaddaadbdccababaccdcdbddaccacababcbcbbddcadcdddbabcbbadadcdbaccbddcadbdcaadbdbbcbbacdddddaadcddddddbdabddbbccbaccbadcdccdadcaaddbdccccbbabcdbbcabadbadbcbddbcabcdbacddbcbbdcabdccbaaaaacbdacccccbcadabdbccabacccbadcaaabbcdabdacacccbaadcabccdcddbbbabbcaddadabacadadcaaadbbdbccdbadadadcadddbadcacaccdabaaadababcbabbccddacbbacbaabdaadbbacbbddcdbcababdbbdbbddaaaabccddbbdaccaaabaadcbbdbabbcbdddaaabbbadacbaadddbaddcbaacbccddadbccdcdbcbccccdacbdbaacadadbcddaacdadcccbaccdcdbabcdcddaddddbbcdcbaacddaccccbadbccbdcbcbdbbbbdcabcdbbcbcdadbbcbcbcaababbcddcbbbbdaadbdcddacdbacabbbabacbccaaacbbbcabcbadcbbbabcabadbcdcdcbdbdacadcbbaccbbdacbcdaacdbbdacbccbcbbbdbcacabcacdcbcadbacabccdddcbdaabbabadcdbabdcddcdbbcddadbaccaabbbadbdaabadbabbcbdadaaadaadbadcdbbadddddccbdabdadbadbbaddbcbcdcbaadbaabacabdabadbbbacccacabcacbadbbacccdbbcdbdbbdcbbbbbbcbddddbbbcbccccdcbcaccacbdcbcadaddadccabadddababcbbddaacbcadadcdadbdaaabbcababdcaaaddbddccabcdabcdabacacbbbcaabadbddcbdcaaccdbbcbbcdcccacaacdcaaddbdadddbacbddabcababcccdcbbddcbcdaaaacadddbbcdddcacddbcddcccbcbaddcacaacddbdddcadadbbbcabdaaaaadbdbbcdadcdcbbbbccacbaadaabddddbcddababddcaaddadaaaabcaacacaabdbccbcdcbdcdaacdcbabbdbadbacacdddaaddbcdccbabbdabacaadbbdbaaaaaadbaadaaadcbddcababdaaabcbddbdabacdadadbacccbadcdbbdbdaaccaaccdbadcdacbbaacddbdacbdbacbcacccdaadcdbbdddbcacbdbdbacbcbcccdcbacadbbaaacdaaaaacbbcccacdaadadccddadbdadccbaccbbcdaccdddbdaaacacbbadaaddcadbdccbaccbaabdacddcbaacdddddadddddabaabccbacaaaaadbbddacbbbbdadcbcdcbddaccbdcdccaaaacbdadbcbaccaaaadacddbadccdcdcbcbbddbabcbbbcabcdabcbccccddcddaaabbdacddcbadbaadbbcacbddacddbcdcadabcaacdaccccabdadcddbaabdaaacababaadcbdbcadcacbdbddbccaaaaacbaabaadcaddbcdcdaaacbabdabababababcbaaaccccaabbcaddaaaaaaaadbabadcccdabcccbbaabaaadcdbbcbcaccdccbbdbaaadddbaacccdcbdacdcbcdbaaaccaaccdcabcdacbaddccccadbccdddbcdbcbdbdcbbbccacacabbccdbdbddccaabdaaababcdccaaabadaababdadaabbbbadcdbccbbccbdccbcbcbaccabcabaccddccddbacdcbcdbbccadcdaccdaacdccbabbccbaacbabaaabaacdadbccacbccdddabadcdbcdbbddbdcccdbdcbbcadddcacbbdabccbaacaddaccdaaadbddcddaacdbdabacadcbccaccaacadbabbbcbaccadbabdbcbddacbdddbabcaccccbbdbbdbdbcaaadcccabaaabcbcaadabdaacbdbdacccdbddadcabdcacdbbbdcadaaabdcdcacaadabbdbcdcabdbbabaddbadbccdabacaaacbcabadccaadcddabdadbdbddccdccbdbaddbcccdbcbaaadabadcdccbabadddcbcbccdbbadacbbcadcadbaddaccdbdbbcaddaccdacadbbdcdabbdaabacabbbccdbdaaddadbdaaabccdbccdccdaaaadbbbcdadccbbdababbbcdcadcdbdbcdbbddbaaddcccabcbddaabdbbbaccabadbdbcaaddccbadbdbcdccbdbbbbbbbdcbbdccccacdcddacaadadacbcbdcccbcaccaaadacacdcdbbaadadbaaaacaaaabcccbbbccdddccbdddcccbbcbcbaaacadddbabdcbcbbbcbdabccbbcdababdbadddcaacbbdbacbadbbcaacbbbadddadcbbcbacaaddabccdbdcbdabdcbabdadacdbdadccadadaacccaaaaacacaaadcccbccbcddccbbadcbdbdababbacabdbbbabdbdbaaaddbbdddbcabdbbcadcbaaccbcdcbdcadaaadadbdcbbabbdcbbbbabbdaccbaccacbaccbcdbbdccccaddcbccdaadddbccccdacdccdcadadcbaaabddbddcabccccdbdcdacacccbbcbcaadcbbdcaacdcdcdcdaabcccacaadcdcacdcccabbabdcabdccbbddbdcdacaabaccaabcbddcacaccddccbccddaaaabddbccdabbcdacbaadcddbabbbabcdbdcaccaaacdddaaabddbaccbbbbacabacdccdaaabcdcadcbddbadbcdccccbbacadaababdbbdaaccaababdaddddcccabcbdddbbdcabbaacaacbcdbdadcddbaccbdcdaacaaaddcdcbccacbccdabacbabadadcdcdbdadcdabbaabaddcdddaaabaadacacadaccbabcacbaddddcdddaddcdbaaddcdbdbdbcaabaabdbcbbaacbdacbcabaacabbacbaccdbbaacabcdbbaacddcddbcacdccdcddbdbadddadcaddabdbdbbbdcbabababddbbcbadaabcacaccadccdcbadbaaadbcbbcabcbddbcddcaaccbbcabbbaadcacadddbaaaccddbccdcbdabbabbdcdbdaccaddadadbbbcdcaccabbdcbcbbcacdbcadcccdabacdbaccccddcdaabbacbcddacbdaadaadddcbbcdbbbddacbddaadcaabbcaddddcadbcbbbadbadcddaddccabbaacbcddcdddcdabdadcddbaabdcdacccbcadaaddddaacadcabbbaabcacccddccbacccbdadccbdaccaaddcaccbddccdbcaabaaddcddcdbcaddacdbbcadcdbabcbaabaddbabbbbdaaddcbddbacadcacdccdbcbdacbddbcdcacddcdbddbccdabdccaaccbdacccdbaacddbcdcbcbdcbabcdcbacbdacdccbbbccbabdbbcbadbcccdcddddbdacbbdddcccbddddaabaadaadaccaabbdcadadbdacccabbbcbacdbbaccaddaabddcbbccbadabdaaabcdbbcacdcaadbccbadcdcbaccdabaabadadbacdcadacbaaaddabadcdbaccadadadbdaccbdbddaabcaaaacacbdababbabadcbdcadbdcbdbbccbbacdcdadcacbbadadbbddcabbacdbabcdabddcddaabaabbbadadaacbdbdcacaabacacbbbcdbcddbbbabccbdabccdaddbcaacaadadbdcdcbbbcacddcabdaddccadcaacabdbccdcddddadcadbadbdbcdbbdabacbdbbbccaabcadbddaacabbdcccbbcccbcbbacacbdacbbbccbcacbadcacabaaaaabcccdccbbbaabddcbddbccdbbbcabddaaabdbddcbbabaabddcccaddbccdbcbcbaccddbbdbbbbbabccccdbbbbacbccdbaaaadcbadbdabdcaacadddcdabdaddcbdacacdbdabacdbacdccadbcaababdddcbbdbaacbababcccbadaccbbbdaadcbcbacccdaaabcacaabccbccbacdddbcccdcdcdcaadbcaacdaaabacddddccdbdbcbccbbdadcbcbcbdccbbbdbdadcabacabbccadbaaacdbdcaacbcdccdadababbacdbbadccdcccdbabdcdbbbdbabcbccaacabcabdaaaaabbdacbbaccbcbabacaadccadaacaaddccbdaadababccacbcabaabccdbcadddbdcbbbbabccccdadccadcbadaaababdcddddbbadddcbccabaaccbddcadbabccddcbddbadaabacaadbaccbadabcdcabbacaddbbadbcccbaccdbbdabddbdddccaaacacbbbcdaaaacaccdaacaaadccccadbdacaadcadcddabadacdcdccdbbcaaadacbcccbbdccdccaccbbbacdbddbabaddabcadabdadaacaccbaaaddbddbbcbadcdcddaddcabadcccabbaaacabdbdddddcbdacbbabdcdcdbccbaaddcbacdabaaccdcbccdcdcccbbdabaabaddccdaaabbcaaabcaccccddccabadddbaadcddbadbcddcbaadacbbadbacbdbabdcbbdadddacdddaacdadbbbcbcadbdaddcddcaddabddabaabbcbcdacadbcadcabaabdbaddbbdacdbdadadbdbdbbbccbddabddbcccbdbabbddaadaacaccdccadaaddadcadbdaabbbdbbaadcaababbbabcbbcabbadacabdbccdbbabadbdadabbadcbaaadbcddaacdccbdccadbaacdcdababacbaabadbacddabbcbddcddaaabdbdaddcdbadbdaccdccbdccddbaccadbaaddcadbbcabdcdbcbcdadacabdbaddddccbbdbdbbcdcacacadaaaddabbaabdbdaacabdadddcacbdcbcaacccccdbcbabcddcaaddbbbabbadcbbbacbcbddaacabbdcdccdbcccbcacadbcdbcbddcaadcbcbbdddbdaaacbbcbbadaacaaaabaabdaabbbcaddcdaabaadcbcbbcdabdcdacbcdddccbcbbaabbbbcacddbcbddadbbddcdadcacdbcaccdccddbcadcbdcadddbcdacacbabbcccdcccaacaaadabcdbccacbddbcbaacbaddddcbabdccbdcdaddcbcaacdabcddbbacdabcdcccbdcdcdaadcabdbcdacbbdaaabddcbabdbaabbbbcbbacdccdacbadbaabdbbdabbcbcdcdbadcbacdddbbdacabcccaacbdaaacdcbdadadcbaabaddabdbbccabaacabadadcacdbcbcaacdbacbabdcbbdbbacbaabdaddaabcacacbbdaacccdaadbaccbaacddacdddaccddccabcabbdcdababbabbadabccccabdbdadbdaccdabdcaccccdaadadabdcbabcdaaccdcadbbdaaacbdbadbddcdacdbbdcdbccbadcbcbdddddbcbcccbcadbdcbdbbcdbbbdaddaddddabaaabccabdcdaabbacbaabbbccbaddacccdbdacbdacbadcdbdcbdadcacbcddbcaadbaadddacadacbccdacdabcbacbbdbcccadaaaacaadaaccdcbaacdccdbbccacbcacddccbdddcccabdcdcdccddbcbabccbacddbcabcdacdadbacadadbacbcccbccabdcabaabacccbcabaabcdcbadbcdcccdcbcdaccacdcbbbbcdbdadbcdbdbcababdcdaddabddbbcaadababbdbbddccaaabbacabadbacccbadacaaddbcacaccadaadcaabdbdbaddbbddacddbbadcdacbacadacbbdadcdbbabcbcdcaddbdaabacabbbdcbaddccdacabdbdbdbaaacabacadbbbcdbbcdcbbbaccdaaacacddcbdadbddcddcdaaaabbdddbcaaadcbaadbcddadbcadaccaddcbbadccdbddacdcabdbcbbcbcabacdadbabaaaacadbabbaadbdadcbcccddbadbdcacadddcbcbabdcaccddcbcddcddcdacdbbccdabacbabccbbbacdabddcbabcacbdabcdcbcbaccccccbaadbdcdddbbccdbdcddabadbcdaabcdcbdcbdcacbadbcabbdbbabdbdaacdabdcadbbaadccaadcdacbdcadbcdaabcccbcbbdaccadcbccddccacbdadcddcbccbddcdbcddcdbddbaacbacabcacdabcaccaaadacaadddabbaddadaccbaaadaccbcdbdbcddcdadcccaaadccbadcbbcbcaddbacabbaccaaaccbaccccadbccbbbadacadcbbadbaaccddbccadcbbdddbaccdbbdbcbbaaabbacccaaadcdacccdaaccccaacddaaaaabcbadaccbcddbcadcdaaaddcbbcbbcdadaddbbccdcbabccaadddbccaadaaabccbadbcabaccadbaabadaddbbbdabcaddbdadaacbddbabcbabcaaccacbdccddadbacaaacaaacbaccaacccccbbacbcaabbaaabbadcbbdaccdbcdcbaaabdaabaccaacabccabcdbdacabdadddabcdbbbabdcabbcbcaccdbabbccacbcbbdcdddaabdbbabdadbdaabdbbbcabdbcccbbbdbbbaaccaaabcbddaabaacaabcabbcccacbbabbdcbadaacabcbdbadaadbddcbabdaacdbdbdadbdcdabdccdabaccddbcddbcacdbaadcbaccabbcbaadcdbbccaabbadcbbbcbddcadbaadabbcabddccbdddbdcdbbcacdbaddbbabbcdabccdcacbabbadbddddbadddcabcbbbdcaccbacccbbcdbcaccdbaadcbbccbdbdaaadaacddcdabacbaddaccdcbbabbdbbbaadbbaddabcdabddcddadaadddbbaadbbbabddaabcddcbadcdadbbddddadcddbdcaccbddbadbbbabacacbdbcbbdcabacbdacacdccccbbcddcaabcbdaaddaadcddaccdbcbabbcddddccdbabbcdaacaabdccadddddbbddaddacdccdcbddaaacdcaababbdddbbadaccbadbccdaacdcbccbbdadcbcdacdbccdabcadacbdbdabbabdddbaccbcdadcbbdbdbbccdbbbccbacccabacbcbdcbbadbbdadbdcbddbaccadccdadcbdbbbacadbbcdcdccabddabcbddbbabccddaddababdcaaacabccdddaddbdbcabdaacadccdbacacbadaacacbcabacdadbbdcbacadaacdbaabadbabbdabcbccadabbdbcacbabcbbcdbadcbbdcacadbbabbacddaaadadbbbdcdaaabdbbaaccccbbccacdaadacbaccdbbcddbacdbcbbbabccdaadbdcccccabdaabccadbacbbbbdbabdcbcbacaabbcdabaddbdcaadcdacdbadbcdcdbacddbdccccbaccdadadacbdbcbdbcacddbdcbcacabccdadddbaacadbdcbbbbadbbbbcdbdcaaaacbddccadcadadbccdcaaccadaddbacddcacababcaabadcbaaacacddaccbabcdccbaabdcccdccccbcbaabcdcddcbabbcbdbdabbdcbcbaddccadbdadadddaacaddaacbdcdabdbcadbbbdcdaadbbaacbdaaabdaadbbdbcacaccccdbcdabbcabcbbbbcaacddaadabcccccaddbcaaacddcacbddbbdcdccaaaadcbbbbcaaccaaccbdcabbabbcdccdcaddabbdcacbddbbbbcaaddabbdbadcbbcacababdaddabcacdbbaddacbadaadcbbdccbbddbdabcbccbadcddbadccbaadccbbccdddaabadccdaccddaadbdbcbdabddabcbddcbdbbddbadadbababbbbbcdbbdccdccaccabadadabaadaabacaadaaadccbdcbbdcbabbdcccabacdbcccadcddaabbcacdccbddbbaccdbbcdbdcbabadadbcdacddadccdadaddbcddababacdbdcbcbbaddbdbacccaddcdcaacbcbbabcbbcbaaabdccccaaccaacadcbcbcabdcbbbbdcbcacbbdcadccbaabccabbabdddbccadcdbbdbcbcbddaaadaabcadaaacdcbadadbddcdbbabdcbddcabccccccadacadbaadcbcadacacacddcdbbadcadacbdcdccbbcbacaaacbbcbaabaccccabcabbadbacbaddbabadacdccdbdbbadacdacababccddabaadcbcaaadccccbacbbaaddbdbbcdabbcdbbdacdaacaabcbcbcdbddbdcdaccddadbdcddaaaaccbbcaaabcaccbddddbdcaadcbdcabcabbbcabcdbbcadcdbdaaccccccaacbbbabcdccdbcbdcdbaddbaddcadddddcdbdbaaabcdacbbacaaabdddbadbddddaabdabacaddccccdcbabcaddcdaccbdcababdbdcdcbadcbabdacdddcddddaaabbaaabbaadcccbcddbccdbbdbcbcacbaccadcbbaaaaabadbacdabadbdcacabdaababdccbacbdbdbddaaccbcdbbadccadaabbbabbbdbcddbadcbdbcaabdccdddabaaccadabcccbdcabcdacdcddcbcabababdaabcacddccbcbbadbdccabdbbdcacbbbcbcdbdcbdbdadaccbadadcdaddccccbdcacabbaadcbbbacccaaddbcdccbdddccbbadbaadbabadabaadbcdcbbabcccbabccccbccacbadbadcdcaaaadaaaddbdacdbdabaccdbcadcddcccacbdcddbccccbddcadddcabdaaadddcdcdcaddbcdcbcccdccbaabbccbabdabbabbbacabbadcdbdacddcaadcbdddbdbdccbdbaabbddacdacbbcbdabdbddcbaaacdacddabadaccccacbdbcbcabbacabcacdcddccadbbccabbadccccacbdcbcacbccdbbbaacbdbcdccdaddaabcbadbabbbbdcacaadcadaabadabdbdccdabcdbdcdcbdbadcabbdccabdacdacdaaadaadbddbbcccbbcacdddbdbbdddadbbcbddcdccbcbcbbcaaccbdccbaabcbcbcadacadbcaadaacdabddccaddcaaddcccaccacdcccabddbcadbbcabcdabadbacbabbdcabaabcddcadbcaabddccadbddbcbcbbdadabdddbbaddacdcaaadbadadbdccdbbacdcccccacabcddcbddbdbddbbddcbadbadabdbaddaacadcacadadbbbcbaadcadbddcabbbabbadbcdbbabaccbbbdcaaadbbdacbddcbabdbaddcdabdbcbabaadbcbacbbbadcbacabadadcaabaabbdabcaaabadbcdacadddccacadccaadcdabdaadddcacaccdbbdddddadddaaccccdcbbbbaadcadadbdddbabcddbcacdccdcbcbabdaabdccdbabbdaaaabdaabaaddbdadccdcababbabbbbbcbcbaccbaabbccbdcdddbdbbcabbddaacacacaaacccddaacaadcacaabbabddbdaaccbccbccbaacbbabbccabdaaacdcbbabadddacbbadadbbdbccbbaaabbbadcacaaacbcacbdbbaaabbaacdcabababccbdcdbbcbdaacacbcdbcbbcabdbabddabaccbbaabbbdbcaaddbbcdbbdbcabcadcabddbcdbadcadbabdccabddbdabbccdcddaabdbbdbbbbabddddccaddbbbdcbddaaacbdbaadcaacacaaabcaacdacccacabadddcaabbdabadccbccbbcaaacddbbdbcadbccccaacadacdddcbcaabccdacdbbbcccabbccabccddaabbbddcbddbacbabaabbbbbacbcbaaacddbccdabbcbcbbcabdacacabadbcdbccbbddadcaccadcdabccaacadacbacacadbaabadbbdddaddbcccdcdcbbabdcdccdbcdcdcbdbaaabbcadcdbdabdacccabdcacaccbcaadcaabdbbbbcbccaaccbabdabddcdcbbdcdabbadbaddcaadaccaaabcaabcbddacacabcaaaabdbaabadbbbacaacccbcabcddacbcbbbcbdbbcddcbdadcbbdddbaabacbcadbacdbabbccbbbadacccdcccbacbcdaccdaacddcbdacdacbabdbcaabdbaadbadcadcaaacbadddcdccabccadaaddaddbaccbbbccbcdcadadacaacbdcacacadaabbabacdadccdccbdadabbddbdacbddacbadacdaaaaddbddccabddcdaadcbbccdbcbcdcadddbbbbabcbcabdabdcddcaaddbaddcabcacacbbbdddcbcccabdadcacdaadcbdbaddacacaaccbcadadacabcbabaaacdbcdcbacdcddccadbcacabccbbccabcaacbbdaddcdabacbbbdbdabacdcdccddcbdbbccdcdcaabddadccbadaaddaadcbdabdcccddcaacadddcaabdadcabadacdcccdcddcaabbcdcbaaacbacbdbaccadacadddadcaadaabaacbdccaacbdcacbdbdcddaadbccbbbcccbbdcdabcaddacbdddbaaabcabdcdbdaddcddccdadaadacacbaccbadddabbdadcdcddccccccabbabddcbacccddddddacabdbaacdbbcabcacaadcaababbddcdddaacdaadbbdcbdbbbdcbcbbcaccbaccaddbccbbbcbbdbcabbdaabcddcacddaaccbccaadccabcbcaccabbcbbbcbbbbabdddcddaadabddbcadcbacaacaccabbdbbaacdbcbbabaabdaddbbbbbaddcdbdadaadcccacacaaaaabcccbbddacbcbbbacccabdbaddbdbabaccbccdbcabdcbcbdcccbdaaabadccabcadbccbbdcdbbbaadacbbabaabbcbcccbacccddcbdbbadccdaccbddbdbadccaddacbbabdbbcadcbcbcabccdbabacbbbddadaddbdcdccdacbbdadaccdbdcbcccdbadbdcdcbddaacaddacdbdbccaaddddbbbcabcccdcdadbcbabcbddbdcbccacbddacbbcbccccbdcabbddaabacadcbdbbcbaaacbbaabbbcabcdcbbccaaddcbbbbddcadbbcbcbcbbcdbccdbdcaaddccdabbcbbaacddbaacbcccbbdadabcabdbddaacdabccbdbaaccdacdddabdaacdaaddadbaadcadbcbbbcadcddddccbdbbabdbbcbadaaddcbbabcdbbbabbcbbdbcdddbaabdaabbdbababdcdabbcdacddadbbbdaddbabbacaddadbaaacabababbadacdccbdbdacbaacacdacbabbbcaadbbdcbdbbdacbaaabbbdddbbddbcbdbbacbcdcddcccbdabbcbacdaacbdaabbbccaababddddcaacbaaaababdbdbdbacddcdbbdbabcaacbdcaabaaaabaacbbbadcddbcabbddbbbaccbabbbddccddbddbadddacdbcbaacabdcdaccbcaaacbdbdbbacdabaddadbbabbdddbbbbbdcacdbbdccdcaaabccbbaadbacddbbacaadddadccbaadbabcdbaacbdcbacaabbbbaaadddbaddcbbdbaadacddccdcacccabccbdabddcbadddcdbbdabcbcdbaddacabbdcccdbdcaabddbdccbbccddcbadcdcbddbacccaaaddbaaaacacdccddbdccaccbdccaddaacbdbbdbccbdaabcdbaabcdaddbdccbdccdaaddacdcabcdbdcdbdcdbcbcbbadddaadbdbbcbdaabdbdbddabcadcbdccddababadacaadbcacdaacbbbcbcdacaadddcbccbadcdbcddaacaccbabdbacbaabbcacdcbbdabbbcabccdbcaccdbaadabaacbacbaaccdbdaccbaaaccdbabaabadacccaacdbadaddbbacbadabcdddcdbdbcabbcdaccbbdcaccdccddadabaddcdadcccdbacdacdbabbaacaddaabaacdadababbcbccaaddcdcdbbadccbcbddadbabbcdabdbcacdcdadccabdcbdbcdccccaddaadcadbddaacbccbcdccdcbabaccddbbdcaaadadbcbcbbbbbadbbccddcddcdbdbbcbcdcacbdcbaaabacdadaadbdddcaccadbbadaccbbaadadbbcbdddabbbbcbccbbdbbcbcdbbcacdcbccdcbacbacaaabcdbabdcdadaddbbbdcdbadccaadccbdcccdabacdabbbdcacbadacbdbadbdccacccbbdcbbbcbdcadbcdbbcbadcdccbababdacabbaacaddbabbbacdbbcbcabbdddbbccbbcddabdcabbbddbabdbbabadbccabddddbbbbddabccdacbcbdccccabcaacbcdcbbcadbbcaabdcabcadbdbaccabccccbbbdadccbbcdcdbcddcabaaaaacdacbadcbbddbbaaaabddcadbbabcabccacaaadacabbaddadcdaddabdaddcbaabcaaccdcccdbdcbcaadacdcbccabddbbccbadddccddacbdbdbbdcacdddddbdbdcbdddddcdcbddaddbcbdcbaaaadddcdbdccdacadccadcabcbacdcdbbdbcacbbbcacccbdacbdadbabacccdbadbddabacbcabbddacbccdbaaacababbdbdccacaddbbaccbcaccabcaabcbacabdbdbbbccccacaacadadbcababcccddbcdaacbcbcacbaacddcddbccbdaadcadabbdbaaddcabbdcdadcbdcdbbadbacbbbbdccdaccdadaaddbdcabbaaddccbadacdaddccadbddaadbbadbdcbcbcbcdddbcbbdabcdbabbbababbdbcdcdcaacdcaabcadabadbbaddadcbdbcdbcaaabbababccdbbccddbcadbabadbcbbaadaaddcdbadbbbaaccaaddbadbcbcbdababcaabbbababadcccddbbdbbadadcabbabaacdadcddbacaaabaacaaddcbacbbcbdaabdbdbbcdaadaaacddcbabaccbdabdbdacdcbccbbccbdacbcbdbbdbaccddcdbbacddbdabccddbadbababddcbcbbdcbbdcbbdbaadbbdadddcbdbdcaabdacdddcdccccddacabbaababadddcadaabcdacdcaabbbcdddccddcdbacabadacbaaccaaaadabdcdbcaccbdcbdcbacdcddcabbbccdbbacdbdadcacdbddabadcbaccccdbdbdabbaccccabbadcbbbcbdcacacabacdcdcabbbbcabadabbaddcbcdbaaaabccbdaadaaddadabcadccbcdbdacbbcabdbcdbcbabbcbdcacaadddaadcabdaabadbdaabcdaddbbcadbbaadbbdddccaaaacadbbcdcddddaddcabdccaccbcbddacbdaddabccbacbccbadbcdbcbdcbabdbcbabdaaabbadcacccaacbdbbbcbadddacbaadbdcaaddababccddaaabbacaccdacbabdacadccabbccbdcdbccabccdaadaddababccdadddacacbbcdbccaaddcabacadcbcdbaccbbcbdbddbcbccbdcadabaaccabadcdabbcccbdbbacbcbcbdccbbddbbbdddcccadaabcbcbdddbdccdbddcdcbdbcaaaddbbacabadbdacdbccbacabaacaacddbdbdaacbcbbcbbccdbdbccbbdaabdbdbdcabdddcdaaabacdabcdbadbddcbdbcadacddacbcdadbbdccbdaddacbdccbbcccaadacccaabbccbbdbcdcababbddbdacacddddbaaccacacdddabbcdcdcacbdcccadabadbdddabdddbaaacbacacaaacbcdadaacbcacdabdabddcadddcddbbddcaccadcdabaccdabdcacabcddadddcbaaccbdacdcacbddababcabaacaddddccacdcdacadccccbcdadcacccccababddabbbcdaabbbcabcddddcdcddbcbabaabdbdcdaabcdaaacabdadaaccccacadcdaccdcdcccdaaadbbcccbbadaacababddccaaaccccdabdbbddabacadccadcdadbbacdbdadbbbbdbaacdbbbdabacbcaaacbbcaadadcbbabcbacacbddbcabbabbccbcbbbdabcbdababdbcadcabbabacdbbaccccaadacaccbbbdbcbcbdcadadababbababcadaabdacddbccddaddabbdbdcdcdcbaabcbbaccadbcbbbbccdabcddaabccacbbdaaabcdacddacdbaaddbabdcbcbcabacbddacbcbaacaacddaabbdddddaadacbccbdbdbaccbbabbcaadadcabcbcacaadbdccbdaadbcaccacadddaddcaaddccacdbcdbdbdcbbbbbcdbabbbcaaacddccccdbbacabaddaccccaacabbcaabaadadccddbbdadacbabaccdcccaaabccbaccbbbbcaaddaabbdccaaadcdaadaacaacdbbacccccddbabdcbcdabdbbabdcccaaccbbcabdacbbcdcabdadcbacbcdbbadcddcdbbabbaadbabbdcbbbdbadcbdcbcdbadbdcacbdbaccdabadaaccacaccbaabdadbcdcbbaccdcaacdbaabababdbcabccacaabcdbaacabbdbbcacaaacdbaacacbbadaacdddddccbdbccacccddabdacbcccaabaabcdddbadbcdcbabbbdabbdbbdaacdbacdcccdbaaadaabdbccadabcadaaddadacbbbaaacacdbdbdbbdbbddaaaddadbacabdbdccbdabcbdbacbabdddcabaadcccabbabdaccbaddbcadacbdccdcddbcdcdcaadbdaddadccbcabdbbbcdbbadbbaddaadcbbbccbdddbbbdaaacdbdddadccaccdcdcbddacaabbadcdcdbaddacaaddddcbadbbccadabccccbbaddbaabccaccdcaddddadbbacbbdbaabaabaacbdbcdbdbacbaccdddadbdbbaadaaadbbbcdadddbccdabbaccabccadbdabdcabaccbdbcbadaabbbcadbcbdddcaaccabddbcdcbccdadbddaaabcbabccbbcaabacbacabbbcaaacbbbabccdddbabadbbacddcbdcbbdadbaaadcbdddbccbacdcdcaccdbccdccbccbbcdcadbcdbbbbccdcabcbcaddcddbacdaadaddcaccdddaccdababccbabaabbdadbbcbaadadcccdcbdcdaacaabdacddcacdbbaaccdaaaaabcaabbabccdcddccddcbbcdcbdbcabddbbacdddcdbbaaadbdcdddcbbbdaadbabaccbdccdabbcacdbbbabccaabbcdcadaacddaabbacdaabaddbaadbabddcaaccabddbddaddbbacabbddabbacdddbdddcabbbbcbccdbbabcacbabbacbbddddccdbacbdcbacbadddbdccdadadaddccabaddacaacddadbddaaaacddbdddcbcccbbadccdcabccdaadbbcdccdcdbadaadcadcadaccdccdabdcaabbcbaacdcddaccbbdbbcbdacdacaaabacdbcdabccbaadbcbcddaadcaccacdbdcacbbbcbdcddabdddccaababddabacdacaaccbdbcadcbadcbdacabacbacbbcbdbaddcddcabbaabdbbdcbddbcaddbdadddbabacaccccbdcabddccbadcdcbbadbacdacaacccbdcdbdcadddbacdadbcdadbcbdcdacdcccdbaddbadddcbccdccdacbdadccddddcccccdadbacabdccdddacdbadbbcccbdcabaaadddcddacbbaddcdbccaadbdadaaadbbabaadcbdbddddabcaddbbdbdabaacccaabdbbaaccbbaaddbaacdacbcdabcbabbbcbbbaaadddabacdaaacadcbbbbbdcdddddddbacdbbdbdadcccbaccaacadaaadadddaabdadcadbaaddbdaacccbddcdaadabdcddcdadabdbbadbcdccaadcbaaabbdbdaadbdaaadabdbaaaabdbdbdccaabacdcbcbbaabdaccbdacddcbbdbdadbccacccbaddcbdadcacabbbbacbacadacacbbdcdcabccccdadadbbacadbadacaddcbccabdadadcbbccbaadbbddcbdbbbbdcadbaaacacddbbbbbbacdadbacdaacacddddadabccbacdabbaacbdadbadbdacdaacababcddaadabbbcbcaacbbdacddddcaaacaccdcadacdbcdcddccdabddabbcddcbbdbcccaaadaaccbbccdcaadaadbccbbcdcadabccccdbdaaacccadadbbdbacaccaacdabddaccbbacccbbdacbbbbbcaabdbabaddbdcdcaabcbdcacdbaccddcaabdcacbabcbadbcabdcabbbbacbcbddbaacbdcdbdbadaacbcbcddaacccacabbcdabdcddcbbcdcdccadddbcaddaadddccdbccdddabcadbabbdbcabaccdcdbcddcccddcaccabdcacabaddbaacaddacbcddabaabaddcbcaaabdbaacadacdaadcbaacadadbabdcdddbacbbdbbdcdddbdbaabdbcdbbbbbaadaaadaacbabcddbcdbabacccacccbababdddbcbbcbbdcbcadcbcddbdcadcabadcbabdaababbabcbbbabcadbbaabbcbadbdbbbcbdbacddcdaaddbdbcdddbabdbcdcdcbdbddcaadddbcdadabbbbacdcbdbadbacbbccdcddadccabcbaabddbdbbddcabcdbdbcacbdbabbddcdacaaabdcbabccadcadbccaadabdcdcadcdbbdabbdabbadbcbcdccaaaadbaabadcbadcdadbbcdcbacdcdbacaaaaadccdccaccaaacbcadadccabcddbbbbbdcdccdddcbccbbadabbabddccacbdbbdabbccbabdcbdabdbbaccbbbdbccadbbbabcaccbdcccaddcaabdcbcbcbcadbaabddabddddabadbbdacddddcdbbaabcadbbbbcaacabdbbbcabbacaacdcdcddddbbbcababdbcbddcabadcbccaaabacbbabbbdbdadccbbdbadabdcddccabdacbcccbaacbacdaaabcdcdbbbcaabcddcbaadcaaaacabaccadbcccddaabddbcaccccbbbacbdabacdbadcbacacbbacbdbdccabdbbacdacbacbbcdcbddadbdacacbdbaacbddadccbdababdabbccdcbbddbacbcaabddaaaabadbabbcadbbaaddbcccdabcbcadcccaababbaacbbadcddcbcbdbdbbbccbaccaccccdcddcaacccadbbcbdcbbdcdaabdabbaabdabdbdbbaabacababaabcccbcdaaadbadcddaaaddbdbbdcdbddaabbadcadbacdaabdbdabadddbdddbabbaabbbbdaacbcdcdcabcaaaddbbbcabdbdaabdcbabccddcdbdcddaacbabddbdcddcacdabadabddbcbacabbaaaabdbbbcbcbaaabbdcccadabcdccbccbadbcddbacbbbbdcacbcccbcccadbcbbdddbbdabcdbaaddbdabbcdcbadcdbdbccdddcdadaadaaaddccabcbaaddbadbcdbcacccddddabbcaadbcbdbbddbdcbacbbadacccdbccdbcabaccddbadaadbbbbabdabcdcdcdacbdddbcddbcbcdacdcacdccdcadbcabbbdbaadbbbdadcaadbcccaaaadccdbcdcddddabbbbcbbdbdcacdcaaadaabccaddadbaddccadbcbdddbbccaadcbaaccbcaaccbadcabaadaabbbadcdbdaddccacaccdddbabdadaaacaadadaadbbcaacaababdbcbaaacadcabcbcadcddddcaccbccbbdbdbdddcddcabcbcbdbcbadaaaadacabddcbcbbcdcbaadaaddbbbdbdaaabaccbcbdcbacabaaaaabbbbddaacbcccdabacbabadacbbabdcdcacabddaabaacdbcccabbacaabbddbcdcaccbcddcbdcadcdbbbcddddcbbabccccdaaacbdadcadaccaabbcacbadcabadbdbcdabacaddcdddbbcbbdabdddcdadbbcdcbcbdcaababcbdcbbcccdbdacbbdcdbdccabcdaaccdbaddbcdcaccbdbcbcaabdbaadcdaccdbcaabbbbbbddcbaaaabbaaccdadddadcbdcaacdbccdacbddcbdabbdbacdacacaccbcbbcacdbbdabbbccdbdbcadacdaadadacbbbaddacacacbcdaabaacccabaacbacdaddacbcbabcdcacaadacbbbcbcadadcaadcadcdbdbabdabdbdadbbccdaaaccbccdacbcdaddaccccdadbabbcabcccbbcddbcbcacacacbbcadaaccdbbdcaabbadcadbadaadbbcdbcddbbdadcdcbbcccabddabcdcddbcaddacaadabdbbacdadcdcaaaadaabbaaddccdccccdbbbccadcbdccddabccacbccdadcbabacbddbdcdadddcbadccaaabcccacbadcabcbacaadccdacdbaadaacbbdaaddcacdbbbbcbdaddaddddccccacaabbccadccbbdbdacbadaaddbcbbabdbbaddcdbcdcaacdabdddabbdbabbacdbacbbcabbcdbaacbccabaabbabdbcbdadbbaddbacadbdccdaadbbdadddddbbadbabccbdbbaaacdbbbbcbdddcbaacbbbaddcacaaacdcdabbccaadadacbacdbcddacadbbccbcbbaabcbbabdcddbacddbbccdcddabdbbacadcdcbacccdcaddcaaaacdacacdababaabbcdbccccabaacaadbdbdcacbcdbcadccdbaaaabddadccbdabdbddcdcdbbddcccdababcdbcbbbbacddcbdbcdccacddddaaacdbbdbaccaddddbdddaabacdacbdbacbcdddcddbcaccbdddddbacadbbdaabacddbabcacccbdbbcccccabbbdaacdddcabdacdbcbcacdaadcadddcbdaaccadadacbcbacbaaaadcbbbccaccdcaabddaaccdaadacacbdbddccadacaacbdbadcbbadbadcadddbdabcbcbdddbaadcdddabdbccdbcdbcdadacadabddadddcbacaadbbabadbaacbbadabccabddbadcbbdbcdcaddbbbbddbddcabaacaaacbadaacaacacacbdddccdbcabdadcbcddcadcaccaaddddcbddaadacbdbcabcaabbcaccbbbcdbbaddcadadcddccbcaadaabadcbdbddbacaddaacaccddddcadcdcaacaabaabdbaaaacdcdbcbdcbdbbbadacddbdcddaccaadbcdddbbcabcdcddaccdcaccdadaccbbadbddbacdccccaadcacbdcdbbbcdbccdaccbddaddacbcbadcadbdcbbbdaabcbcaaddcdcbaaaccadbddbccbdabdcbcadabcdabcbbaccdcdcbdaadaaacaacddcdcabbdbdaadddabcaaddbaaabbdaccdcddddadabadadccbcabbccbbacbddcdabcdabcccabcabadddabdaddbcaddbaacabdcabdddadccadddcbbdcbaabaacccbcacbcabdcdaaccaacbbdccaaabcbdaddddbbbdccbbdcccbcacbcbdbbabbcacadccdcbaaadbadccacaccabaddbabcbddcaacdbbdacdadcacdcbdcccbbbbbcbdacddddcadddabaddccccacbccbaaccdbcacddbcadaababcaabcaddadbddcaacacdacabcabdbbcdbbadaaddcaaacabcbdabcacbcbbabaccccdabccdaaabadcbddccbbabbbaddabbdabacccacdcacccccaacdbccccbcaabacbbdcdaaacababcdddcaaabccdcbccdadddddccbadcbdcdacbddaaaadcdcabcbcbbbddbbabcacdcbdbdbddddaadddccacbdccbadcadccabdcdadaddcdadcbbbddacacaabbbddcbbadbbadacdbabacccdccccdccbbcacacdccadacaddbaaaccdcdadcbdccaacbaaabaadacabaaabbdbbbbadbbbbddadbbbcbabaadcbcbbdaabdabacbaccdabdccacdaaacdcdbcadcabdbbabadcdcdacdcddbbbbcdbbaabcdcbdaacdcbaccadacbacbcdbcddddbcaccdbdbdcacccadbcdbabddbaadbbcccacdabcccdaddccadaadcccbccbcaaabbcdbdacbbbadcbacaccacbdabcddadccccaacddcbcddbdabbacdacbacdddabcdccdacddcbabdbcbadbcdbbdbcbdcdbcabdbbcbccabdbabbbdccbadbdadbcabcaacbaaadbdbadadabddbbcdccabcabdcccdcbbacdcbcaadbadccddaaabbcdcbdddccdcaacbdabbbddbcbccaaabcccacdbbdbadddbdbdcbdabbadbbadcdcaabbbacaadaadddaabddacddbabbccdbdadadaacccbbdcdcddbbbdccadcabbacbdbdcdcdaacaadcccddabccadabadacbbdbdbcbbbcbcbaabccbaabccbaddddddaccbdadacdccbbabdbcbacaabbdbcddccadbcdbbcaddacdcdcbcbabadaacddaccbdbbdaddcccbaabdaacddaddddccbdaaaacbcbdcddcccddbaaaccabadcabbbcddccdbaccbaadcaabdddcdbccdbbadbcabddbccbbaadaacaaabbbddaaabbddbcacccbbbcaabadbbbdaacbbbbabadbacbccadacdbdcbbdcaabcabbabbcaaccdcbabbbbdcbaddaabadbabbddaacadddbaabaaccadddacaabcdddacacdbaaccbbdbcbddcdadacaadddadbaaabdbaadddcdbbddaacbdbbcacabbcdbbccdadcacadcbdbaaccccbcadbcadaacccdadccbabcbdbabadddcbcaacbdcaacacbcbaddddddcaabbdbacdbcdcdccdcddbbbdabbbcdaabbdbcbadaaaddcdcacacdddbcabadacccadbdaccdaaaaadaacccaacaabbabbbababbdabaddbcdbdcdcabddacabaccddbadbddcbacbbdcacdadaddbccadacbdacbdaabdaacdbaccdbbddbabbbbdbbbbbbbccbcacaccbbacbdcdabadcadcbdcbbcbcddcabbcddaadacbbdbdcdbdcbaababbabbaccdaadbbcbbddadbdcbcbbcabadbaaadcacbbcbcaddabcbacccbdccacdbaaddabcddcbaadadaccddacabdbabcaabcddadcaaabccbcaadcbccacbdcbdccbababddbcaabccdcacabaabbbdaddaacbabddbbbaddabdbaadcaddbcbacdbbdbcaaddbbaabbbbccddbcbcadabcbbdcbddaacdbccaabaaddcdaaccbbcbbdaadcccacbddaccbbcbaabcbbadbaaabbabadbbddbcccaabbacaadaabbdaabdcbdcbcbdcccdbbcccbaacbaaabcccaabdadabadbccdbcbbcadaadadaabdabacabddaaabbcdbcdbabbdbcacbbdadbdabacbddabcbbaaabbdaccaaaaccbaaaddbbdbdbdccdddaaabbdadccabdaddbaddadadbaabbbdbaddadddcaacdbabdcacabddbcdcbbbcddadbadacadababdaaadcadaccbdbcbaabdccadacabbcdcbbbaadbadbaaccdbaacdddaabcadadacdcdadadbadadbdcabbdddcccabdaacbdbbdcbcbbbaddadcdcacaacbbbbacadbddabddbdcdcabbbbddadcadbdacbabddabacabddbdddbccabaddcbdbcdbcacbaddaddcccacbbbdabcdabbdaddcdddaccdbcddddcccbabbbacbdcadbdcdcddcdbcdacbaaabdadccddbdcdacbbdbdabdcbbbdcadcacbddcaccaadbadccccccbccdcbadcddbcdbadbdaddabdcbbccacbcaababdaddaaabdaabaccadacbabcaacdbcbcadbcddddcabccdcabdccababbacaacbcdcbddabdacbbbdbddcccbababdddcaaacdabaabcdcdcaadabcbacaabddccdaccdccdccbdcccdacbdddcadadbcbbbbcabacccbbbdccbcbabbdaaddbbbcbbadaccbccbabbdadbbcbbddcbcbbadbddcaadcbbddddbdccdcccdaccabaadabddbadcabccadbaacacacdbbdbbbdccbbcccccddddaaacaabbccbccdbdbddcdbcbadbcbcdadbbbacaabcaaabbbacdaadcacabbdcabdabbdaaaccadcbaacbacdbdbcdabdbbdcaddacadcdcabcaabddbdbcdbaabdcdaddaabcaddbdcabaaadbbadcaaacddabdcdbcababddabcaadcbcbdcadbadbaabcdddaabacdaaaccabcbacccbdcdababaaaaacbdcbbbddadaccaadaaadbdbabbbbaccdabcdaabaadcdcddabaccacdabdcbbccdacddccbaccaddaccaabdcddbdababdbcbaadcaaadbacacabbcbcccbcddaabacdbbbbadaccbadcaccacbbcadabdddcbcaabbdddbdcddbadabccdccddaabcababcccabcdbacaacdccbbabdcaaadbbbdadcbabcdaacbadcccbababaddaabcccbaabddbbababcacdcadabdbdcbabdddadbadcbcbbbbddbbbcddddcdccacdcadcbdddcadaacdabdbbcbbbabdccabadbdabdbdcddcdddacdccdcbdadbcccdddbbbbbdcacbabbbbcdbbccbdacccdbcadaadbcbcacaddadaaaddcddbbcabddabbdbbdbadbacbbabccccaddabadbadbacbdaadcacdaaadcadcbaabbadbadcaacdcdbdbcbdbbaabdadabbcacbcabacbcdacdcbbaacdcaaddcabbcadddabcccdacaacaaaabbbdccbccdbbcaaccddcaadbadaadcbaaacacdabdacaabbdaacbabccdbccdddbadaccddbcabdcaabcbcbccadcacabcbacbcadcdadbacdabacddadbbbbcbbbccddddcddaacaabddcbadbacbcccbdcbdcaaabdacdbddacaaacbcaacccbadcdcddadccdbdcadcacdcbbdabacaadbbcdddcdcccbbbcaaabbaaccacaacddddcaccbcdacaaaacdabbdcdadddbddbadaddaaaabdddaacdbdacdcaadcdacabcdbcababcbabbdaaabddbdddbccdcbdadacddcababbcdbbcccdccdaadddcdadcbdcbbadcdbbdbadabccccccbcbccbcadddaaabccbcacaddabaccccdbcabbcdadbbbcdbdcbdbcbacdcdbdadadcbcdcbabdcdacadaddddcdbaacdbaacaacdcacdabaacbdcbcddbddbaccaaccccdcddabdbccabbccbacabbddcbbddbabcaaacdaaabdacccacadcdcaaabccbdacabbdccdcdaccdabdbddcdabbbadcddbbacbbddbbdbcaabdaacddaddcaaacddcdcaabccabcddcbabaadcddadcbcccdcbbacacaabdbdddbcacbdcdbcdbdbcadcdcadddaacddcbbcacadcabbacabcddaabbabccddbdcdbbcaabcddccbaabcdbbdabdbaaccbababbaccbdcaabbddbcaddaaacaccbbbdcbabdbadbcabddbbdbccbccdaabaaabdbcaccdcbabbaadbcbddbbbdbaaacdaaaacababadabcaabaddccabcdbabdbbdcaaabdcabddcbaabcbbcbababdacbccbbbdccdcbcbbbadccdccacdbdacdcaddcabacaccaadacdaacacabbbcddabdcaddbacddaabacbbddccdabcbdabdbddbcdacbbbaadcbbbcbcdccabcddbcaaddbadcddaadcbcbadddcbacdbccdbdcbbbcabcdbadbdadbaabadcbcddbcabcadcadcacabcaaaddbbdbdcddcabaabacadbabacdaccddccccbbcdccaabdcccaaabccabdbdddddacbbaddccadccdbddacbcbcabddbacdaddabbcadabcdbdbadbbbabbbbcaaccabdaacbaaabbcbddadbcdadaddbbbadcbbacdddbddacaadbdbacccbccaddcaddbbcdabbbbabccabadcdbdaaaabbdcddbaacaacbabbbbbbcbbbcbdbbdccccacacccdababddabcbdbbbdaadadadabbdcaacddccbbdbdcccbadacdaddaddcdcacddabbaccbcaaddadaddcacaadbbadacbabddbaababcdcbabcdbdbbadcbcbdaabddddbcdacddbdacdbcbbdbabacbadcbddcabccaaaccadbcbccaaacdabaadbccdbabbbabbacababbdcdbddaabbbabbbdadaadbbaadcaaabadddccdadccabccadaddbcadcdaccacbbcddbadbdddbccacbbcbcaaacaaadbcabcccbcdacacbbcccccdcacdccadaaccadbdbddcabcbcdbbbbbddbbdadcddcdcaddccbdcaaaccdcccaaaabaccccbaddadaacabbbbaccdcbacacaccdcaabcacdaaaccddccddcccbdcbcdcdabcadbcdbdbdaabcddaaabddaddbaacdbcdaacabcdbdcccbaacdbcdcbcbdddacccacaadbdacbccccddadabadbadbadbcbcadbdbbaddcddabacadddbdacbdbcbdadadabbcdccaddacadaddbaaccadcbbaddbbdcacbddbabcdbacdacaacbdadcaadbadbdcacbabcdaacccbbbbaacdbaaabbcddacadddbcbbcdbccdbdcbcbccabccdbcbddcabcccdbacabcdbbcddbdaddcbadabdbddcbcdaabbbcdbacbccbbbcddccadbbbbbcaccbadcddbbdcaddcabbadaacbababccabdcdbdcabbabdcbbcdcadacdddddaaaaaddbacacdccbcadcaaadbbdbbdabdccadadacbddcddbdcddabadbdbdbbdacbbdbdacaddddaadbbadcbadbdbdaddbdbaabccccdaaaabbdcccdabbddbdbdaadbcddadacaaaccadaabddcccbcbacbaaddbbbcbdadcacdacbccdabdacadacbcaacbcbbddabcdbbccdcabccdcbbdcaacbbaaaaaadacbdacbbbbabdbbddabdbbbbcbdcacabbacdccdcdbadcbddbbdacbbacbdbddbdbcaccdbccadbdbcbbbdddcadbcbdbdbbabbdcaaacbdcddcadbacdbadadbcccadcbcabdbccdddcdcdcdcdccbddabbbbbdbcdacbbccacdcccbcccaccaddddadbbabcbbbdaccdccbdbadcbabccbbddbbaaaacbddbbbddbacddccdcbaddbddcaacbcababcdcdbcababcdabbcbccbbaabbabbdbbdbdaaccbcdaddddabbcadcaabbddababcdbdbdcbcdacccaccddacdcadbdadbdaadbacacdabcabdbaaccdcbaacdacddadadbaacccbacdcdccbadcddababdccdbdbccbccaaacdabdbacacbdbabaaaaddadbdbdabacacdabaaaaccbbbdbdadcbbbcdbacdaadacbdaabbaaddddcbabcadbccadddbaaaaabaabcbdcbadcccbccdbddcdccccbbaabcdbaabbdbabaacdcdccbbcddbdcbdacaccbbcdddacdbcbcbcbbdcbbcdaaccdcdadabcacbcdbaacaadbbbbccdbbdbadbabbbabdbcddadddbcbacdabacdbcabadcabcbcacbaaadbaacbccababdbcddcabdcdcaddcdacdbbcaaccdaaddabbddbaacaddcacdaaabdacaccdccacbbcccddcdbbcaabdcccacccccdbbcabccabbddaadcdbbbbabbddaacacbdabacbcadbbccabdacaaddcaadaccacbbcbdbdabcddcaacaccdddaabdcaaddacbabcdbdcdbdcacbcdbbdbddcccddcbdccddaadbaaddbcdddbbcdbbadacccdabccdbbaaabbcdcadcbbaaadabaaccaadbcdbbadbaccbdbdbacaaaacadbccdbcddbaacdcaacadadbdbbbbadbbacdcbcddcdabcdbdcadcbcdbdbaccbcbdcdcddabbadabcbbaacdcdaacadbadcdcdbccbdbddbbdcacdcccacdabcaacbcbbadcacccbabdcbcbbbdaacaddadcbadaabddcaaaabcdcbdbcdabdaacdcadadbcdcaabadcabcdbcbaaaccaaccbccdccbbcdbddabcbbbdbcddbcddbdcbdcbbdacacdcabdadbbbbdccdddbccadbcdbbbbabdbbbdcaaacdacdaaccccacdbddccabaaabcdabcacbadcbbdbdbbbbdccdcdabaacccbacbabdabddcbaccdabcbcbcaaabcdbcacacdabadabcbdcdabadbddcccaacccddbcccaccabaadaaaddddbdbddbcdadccbacbabcbdcbccbbddbbaadadacdcbcaccdbdddbbdddbabadccdaabbdcbbacadddccaccddbbabdbbacbbbbdbaddcccaddbbabbacbdacdcdddccadddcacbabcabbbdccacabdcaababdddaaaabbabbbbabaabaadcacbdddbbddaaabdbbbcdcadbcbbdcbddacabbdbbcabcabdcdacccbbcbdcacdcdadddaaaacddadaadbcbdbcbdddcdbabdcadababaaccccbddacbcaddddbadcdbaacdcbabaabdbddadcaacbacabacbbbabbbdcaacbaadbccbacddcbbddccdaaccbdcaababadabcabbaabadbaadccdcdbcaaabdcbcabdacbcaadadbbbbdaaaacbccdccacdabcbaabbcdcacadcdbbacdabcabacabacaabddbacadcdccbbbbcbdababbccbbadccdbcaaacbbcbbddcccdcabaabbabcadbdaddddbacdcdbcdddddaadbdcabbddbadacccdbccbdabdacacbbdbadabcacaadbdbaacddddccdccccddcdbbddbaaddccddacacccadcbdbcdacbddbcbcbcbdbdbcadcbbdcdddbcbcbcbdbccccccadacccacacabdacbdadabbabaddcbacddcccddbcbdcabacaabcdadcbbabdddcabccccddacacbdddababadbbbcbbbdacdbddddcbdbdbcccbaaabbaaddcabababbdacaabcaaabddaabadbbdbaabccbbbcbbcbaabdcacdacbcdbcdacbddabbacabbbbdcddcbbcaacbaccdcaccbccaccbdccabcdcdcbcccdabbbcbacdbbacdbddbacdaabaabacbbadabdaaaaadaaadabacbdbbbadabcadccdbbaadddacdcbcbacdcddbcddcbbbdcdddababcaddaabbcccdaadbabccccdadbdcacadbdaacadcdabdbdadaddadbdbdbccdccccabdccccdcdbbcbacbbaabcdcdbcbdacbaddcaddbcdcbdcbcdcabbdccadcabbaacbbddadcacbcddaabbcdaaddbdacaabaacdadbcdddadbcdcacdddadbacadcaacdbbaababcadcabaacacbcdbacbababdcbcbcaddaadcbddaaadaccbaddcacaccdcacccbacacacababddbbaddcccacbcdbdcbaabadbddaddcbcdbbbcdcbbaabccacdbadadccbbbaccacbccbaccabacddbcaadaacbaaadbdcabcbaccadcdaddacdacacabbadbbccdcddaddccccbbbacdddbdaaddbcbcbcbabbbdcbacbcdcbdbddccadccdaddcccadadddcbbcaccbcadbbcddaccdabacbcbbadccccadbbbbcdbdbbacdbcadbacbaddcadbcdbbcdccdcdaacdbcddddcaaaadddbaadbcabbabbaddddddcccaababccabdcdbdcdcacddabcbdccddbddbaaacacbabcbbadcadabaacddcddbbbbcbdcdacbcabaadabddadbbdcabacdddcabaaccdaaadacbdcccdcabcdabbccabbddbbbaacdabdaabbdbdbadcacbbbcdacbdbdcacbdcdbccbdbdddddbdacdbcbbadacbcddbadcbacbdababaabcdddabcadbdadcbabaddddbcaddaaaddbabccccdcbacaacddbcbadaadbabaaadadbaabbcaabcdabcccbcadbbdaaabcbabbacbbadcbccaccbbdbcbabcddcacbadddbadacabcdbcdbaacdcadbbcdcabadbddaccabbcbabdbacbcddaddbcaadbddddcbcbcbadbbbcacaddbcbdabddbcdabaccbbabdbdacadbaccbdbacbcadcadbdadbbcdacdaacadddbddcbbaddcddbddaaababdabaaaccabbcdaccddbaaabaddbcbacacaaddbaacaaabdbabdbcbdabdcdbcccbddcbdbddbbbacdadcdaadbbbbccbdadabbaddbaadcdbaaccbdcddbccdbaababdcabcacbbdbdbaccdbbcabdbabacbbcaadcadabdbbbadcbccbaaadaddaaabccbddcdcdabbaabdbacaaddcdddcdcbbacadbacacddcbbbbdbccadcadadbacbbbbcbaaabababbbdadabacbdcabcdabcdccccccdccabdaaaaccdacdddcaadbbcbdddadabaaabccdbbbdcbdcddaccbdccdccdacbdcaddacdcdbabcbaddbabdbbcbcbddcbacbbcacddbbdabbaaaabcdcdbbdacccbcbbcdcabddbcacdbddbdbdcacacddbdbadacacdbabccabaaaccbdadadcbdadcdcaacaaabcdcbbcdcddcaabbabcdddbddbcbdacaacdabdbbdabbcdccdccccadaddaccbabaddbbccccadcacacbdcccadbbbadccddabccbabcccaadaccbbdbaabdcadcdcaabdaaddbbdcdbbacbdcaadbbddabadddcabaddccbdbdaacacaddabadcacacddbbaddbddbbacaadbbabddccccbddbdddabdbdcadbcbbbccaacaaaabcabbaabadbacaabbcbcdccaaacabcddcdcbcbdadbcacbcccccdddcddabbabaabccabdbdcabcabccbddababbbbbbdcbbcbdcadaddbabddaabcaacaabacbaabddbbbdcccbddcdacccdbbcacaabccabbcabdddbcdcdabdaccdacadbadccacadabcbadccbcaaabbdacbcbdabbddcaddacbbccbddabdbdccadcabcddbdbdbbbdacdddbbbcadbddbccbbcbbaddcacccbdcbbcccaadcccbddadacbddcbcabaabbbddddcdabadddbdaacdddaaadaccbddbddcbcdbddbcdbbdbacdcdcacacbcdbacdccabbddddabddcccbdacbbdbaacacadadaadaaaaababdadbbacddbabddcbbcbbcdabbcacaabccdcabccdacbdddddcaaadddcbccacbdcdcadddddbbacacbbaabddbddccabcaacbbadabbdcdbacaaccabdbbaaacdbdcdababddcdcabccaddddcdbcacccccbacbdcbcbaacbcbbcaaabccddbbdbdddadbcadccdcacddcbdadcdabacaaccdbdccbaabadbbaddbdadbbcabdaccbddcddcacdddcbbaddbadbcddaccbccaaabbdaabbabdadcbacdccdabcaaacbacaacdadcbbbbaccdbbdbbcbbcbbcddcdcadbbbaabaabaaaddcaaaabaadbabbcdaccabcdcaaddbdcbbcadacbadabbbdaadcbbabbcadabcbcdbacbbcbdcaacaacaadcbcaaaccdabdbadabdacbacbddbbbdaadcbbcbadadabbdddacabbdbccacdbbaaccaabadcacacbcbbcdcbccbbcaccadaddcddaabdccbcaacaadbbcbacbacddcddbddcabbdbbcacccbcdbdccdcdbababaabbcbaadcbccbdacddbcbbbccacddabadcaacabbddcddabddbdcdcabdbddcdcdbaabbccabccbcbabdbabcccdcbbbadcaadccbdddacbabcabadabbbbddcbababccdbdcccabbbccadbbddaccadabdcbaabcaddddcbccdacaadaaabcdbacadacbabaaacdcdabdbacbccdaccccadbaaacbdaaddacdaacdadbdabcddcbcacdbbdcaddbabcadbcbdaadccdcadcbaadcabcbbcbcbaacbbcbcacdaacaabababacbcabddadbccbadaccdadcbaccddadbadddccdabcdddbddacccaacdbddcdcaccabcadddddabcdbcabdbacdaaaabacddbcdaccccbbaadbdbacddbdcabaabbaabdccbdbbacbbcbabcacaaaaddbabcdcddcacddcccabcdddcbbccaaaacdacaaadacaddacaaaabbdabdddbdccccbcddbadbcadddbdaacabdcbbcadaabadabaccddbbdcdaaddcccbaabcbbacdbabcdbcdbbdbdccbdcabddddcdbbacbbbdacbabbabaadbdbddbbcbcbdbaacdcbcadadaabbbcccaaabaabaddcababcdbdbaadbbccadacbddbacdaabaccaddcbdbabccdcacaddaaccdccadcbbdbaabdcddbbddbabbacbdbbccbabddcdddaaaadadbcbdacbaabdadacbcadcbdabbaaccabbddaccaccabdadcbcdbaaccaddbcadbbadabbcbdaacdaabcaaaaddabcadcabaaacaacacbcdddddddbaddcbccbbaadccacddadbaddccbbbdbbaacabadbdcddcccacdbccccadbabbbbbbbbadcddcccaadadbbddadcadddccddddacbacdbcccbcdcbdccbbaacababadcacadacdaccbdabbdcdcbdbddccccaaabdbcbccbcdadcddcaaabaddabccabbdbddcadaccabcbaddaccccacddcdcaddcbadbbdbbddcabcadaadbbdccaacbaccdacabaacaacdbadbadaddaddbdabdadccaadddbaadadaccaccabcacddbbdbadacbccdcbbdcbacddbcdadccaddaccdbdbcaaccbaacabadbbcdbdccaddbacacbdddddabccdbabbadcccdcaaccabcbaaddbcacabcccaacdddaaababbdddddcaaccbdbcbcbdbbddaddbbaadaaaddbdbbcccabadcbbbcdaaadbabdccdaacbdbcaccbddabcdaabbcdddacacbbaadddaadbacbbdabccbcbccbcbcbbbcbcdcdcccbcbdcbdadaaabbcabcbadaabdabcbbabdadcdbbadaacaaaaccbbbaaaacbabdbcbcabaaaaacbccbbbccdcbbcabdcbbbbddabdabacdbbcabdcdbdadacdbbbbaccdccdddcbabccdadbddcdccddbaccdcbbdadaaddbdcdbacdabdbdcddabbdcbabcacdadbdabbadaaaddbccbdadbcdccdbcaccbbdbacddcbaaaabbccaccbcaaacdddcacadccbaacaadaadbdccacbabadccdddccbbbdbbacbbdaadcbccddbbdcaaabbaccaadabadccdabbdbdbdccbbaccdddaadcbaddbdcbabbcdcbccdbcadbacaabbcacddbccdbcdaddbcdcadaddbcbbbcaabcccdadcabaacbaddaddbcdbdbddaddccddcaabadcacdccdbdaacbbbbcccbcbbadbdccdacaaababbccadaddacabdbbabbabdaddcaabcdcacbcadbcbadccbccbadacbaccbcacdbcccdbdddbdbdacaddbdcabcddbbaddcaccacaabdaabdccddcdddacaccadcdcadcbabcabaaabdcddddddcbccbcbbbddaabcdbbdccbbabacddacbbbbdbbaaaadcaabdbaaabdddddaacdcadcbbabcdbdcbcddccabadbdbddddddcdbbbdabbdcddacbdccbaddddcccbabccabdbcdbacadaadbadbccdbcbdabcbdddbabbddcbabcdcdadccaadabcabbdddcbbaaaddbcbdaadabbcaccbddbababcacdabbccbadbabaccadbaaaadccdccdadbaccccbbdadaccbbcbccbacccadbbcaddabbaaaacbadbbdbcdadcbaaccdbacdbcaadbcbbbaaaddaabbabbbaddabacadcadaacbbcdcbddabcbcbcadbaacbccbcbabbbabcdcaddaddaadcbdcbbbcaababaccaaaddaabddadbdbcdbdcbbcbbbaabadcacadaadabbabccdcddadbacabcdacbaccbbdcdbbcbcbcdbcddacbdacdaacabbcaddbacddcdacbacacabbcadaaccbdbcacbbdbbadcaadccbcbadbbccbaadbacbcdbbbbdddadbcdbcccddbbbabbdbacbdcaddbbbcbcddcacbadddbaddbddbbdabcbaaaabcdbbdaabcbacddbabccbadcabbccdbdadddcccdabcdcbccbbcdabcdcdaddababcabcdacadacaaaaababdacbdbddcabdabdbaacdaacdcbabddddcbbdadbddcdcadcabacddcabcddabbbcadacbaacccbddbbdadadcbbddcacadcacdcbcbccccdcbbabcbddbccacdbadbadbccdabdcbacbaadaadbbbbbabcccccbbababdaaacdcacdcdadabcbdbaddabcabdccdbcadcacbacccbbdcccdabacaabddabbbbdcaaddbcbbbbcadacddbcdddcbaadddcabbbcbcdcdacdbbbdcdbabbdbdccdbbbddbccbdacbbaacaaddaabadbccaacdcccddbaaadbaabbbdaaaaabbddabadbcddccbaaacbcaabdcaaccdcdaccccdbbdabddbcdbbdcbdbcaabcbdcddccabcccadaadaadacbcbaabbbbcdcacacdadcadaacdbdbabcbbdaacbbcbdcdcdccdcdaacbadcbdbcbddddabaadcccbbdaddaaddaddcdaabbcbacabdbbcaaaccccadccaacaadbababadabdcdbacdbabdabbacdabbbdcdbdbdaaccdbbacdabcacacbdbbbbcbddbbcdcdcdabaabaabaccbbadcaaacadacddcacadabdaacdcbbbaccbccbbabacddcdbdacddcabacbadabcbcadbcaccabcadbcbcdcdbbdbdaddcadcababbbdcadcddadbdbaddccadbaacbadadbcbccdadaccbbcbdbcbacbbbbbcbbddadaccddacddbbacbccdabaccddbdbdcbdabbdbbcdacccdcddddbbdabcdbbdaaaddccdddddcbcbdaccdbdcdbbacbabccdcacbbabacccbcbbbdabaaddddccababaabbabaccbacbcaddaabdbabbbbbbbdbcbddcdaacdddddbdacdcabbcdbcbbaaababcacbbbbacdbbbcdddbaabddddcaadbaccbbdddaadbacabbbcaddbbddddbccdbcbbbbbccdbdadcaadadbcdbdcbaabdbabccbdbbadacababdbaaccacdcddcdbdccdccaccadbdbbbdbdbdbddabcadddbbaaaabcdddaccccddcddcdcabbcacbdccabaddcdbbdabddbdbcaacccdabadbcbcbcbaabdabadbbacaadbbaacccbcddcbdbcaddacbadddbbcddabccbabdaaabbacbaabdababaddcbddadbcabaabadbdbbacbaaacdcbcbbbcdacbbadcaadadaddadbcbccbdcbdbcacacdbaadabcddbababcbdbbcbabddaaaaadcabcabaabacadbbcabbabbdacdcabbcdbccdbbbbadbcbcdacbdddbdadddddcddcbabcccbaacbcccacbbbcdacdbcdaaaddcbdcadaaadccaddccbdbccbcbbacadaabbcadbbbcdadbbcabbcabcccbabcadbbabcaadaabddccabdbdccbbaadbbccaaaadbbdcbacacabbadcbbbbaddbcbcdcbdcaddbabdbabbcacacddccbccdababacadaacddbddaaaaccbcdccbbadcbccbaccbdbacaaabbacdcddcdaaaccbcadacbbcbbbcdaccbcccabcbdcadadbdcbddbcdbddccadccbadaacabddbadbdcbdadbacabccbdcccababbccbcdaacadcccaaacbcdcadbdbabcacccabadccbcacdbaaacdbbbabbadddbbbabbccaaddadabddacbadaaadacaacddcbcbdddbacdaaddddabdadbacabbabbcaadcdccadabcabcdaaabadccdccbbdabbacbcaabccccdbdaabcccadcbdaabbbaacbdcabbbdcacbcbabbbcdacbcccbccacbaacdcbadabacdccccabccaddcdbbcacccdcbdcdcbaacbbcbbdadabdaabacbccdaacadbbaddcaacbddbcacbcbdbcbdbaccbaddadcadcdacbcdabadcbadbcccddbccbcbbdbaacaaddcbcdcaacdacbbcddbcadadaaccbcdbbabddabdacadccaccabaacbbdadcadabcbaabadadacabbabcbdddccaabdcbbbaadbacabddbdbbaabccddcadaddcabaadcccddcadcccddbddacccaccbcdbbadbcdaadddbcbcaaaccbcaacdbbdcdbaadacbdbdcaaaaadbabaddabaaadbbddcbbadccacdbcbbcbcbbaacaccddcbaaabbaaccdcadbbabccccdcabbabbdacbdaddcbbbbddcbaababbbdbcdbdcbbacadcccadddbaabaabcdbabcbdcdbdcbddbababbcdabddbbcdcbdbaadcabbadbddcdadcaaaacbddaccbddbddccdcbbbaaacbabbccbabbabaababdaabdbcbdbaacbabbcbbadbcdbdabadcacaabcadacbcaaababdabddaabdcdbabcacbddaadacbdcdcbcddabcbbcdaaabddccacdddbbdacdbcdddbbabddcbcabaaadbcdcaccdcbbddcacbbbdccbbbccabaddbacbbabddcbbcabbbcdcdcabdddcdcdadbccacdbbadcdaccdbbcabddadddccbccddaabdccddcccadabadcaaadccdacaccddcbbdaccaaabadddcbcdcccdcdcbabcccacabddddbdbbadabbaaddddcddacabbddcdbadcccdcdcacbabdcdbdbbcabadbbcbaabdcabbbdbadcbcdaabcccbccbddaabcdacdbcccdcbbbbcddbdcbbadcacadadbbdacbdbbddadbdddcaabdbccababaabbbcadcdcacbbcdddbbcbccaabcdadadbdccbadabbddabbdabadbbcadadbaaadcddbccbcaaabdbbadbacdaacaaabbdbbabdabccacccccaddddcbbbbbaaacbcabcdaaadcacacaaadacadacabaababccddbdaacbdbdbacaadcccdaddabcbabdbcaddcaadcbabdcabbbbdcdbbddacddbdadbdaccbabccbbbdaabdaddacbbcbccbdbdccbddabccadaccdacbddcacdccbcacadbdaabcbabdaadcccbbdbacccbccbcbbbcdbabdcbdcddccbddaabdbbdbccccbcadabcddbabdbdbdbaddddbbcccdababddbacbdbbccbdcaccdacbbddccddaadabadbbcdbdbbdccddacabcdcbbddadbbbccbbbbccccdcccbdbcbadddcbccbcbcbbdbbadacdbdbbbccccabbccdaacbcdcabacddbaaacccbbdddccdbccbccddcbdadbbcdaabbbabdcbbbccdcbbdcbacbadcabcbdcccdcacabaccdabcdaccaadbccddbadaaadbadbabaabdbddbdaccabaacaddbcdcddbddaaaaadacadcbacaaaaabdbabdccaddaadbabcadcbcbbaccacdabbbccbbddcdabbbbbcdcabbabaadbcbccbbbadbaacacccbdcdcbbdcbbccaddcbdbaabaccdccadddbabbaddcbbdbdaabdbaadbabcbdadcdbccadaaddaacacddaabdabbddcaccbbdcdabccaaaacdddacdcbdabaadacdbdcccdcccadaaacaaaddbdabbcbdcabcaacdddccadacdddccaabcbaccbccdcccbadcbddbcaccddaddaacbdaacdbaabbcaddbdbaacdbadcbbdbbdacbaaacdcacccddbccdbdcabbbbbbacaccadbadcaabbdddabbdbabcdbdbddaabbdbbbbabbccbbbcbbaccdddcdcabaabdbcacdcbdbbaaadaccadacdbbcbdbbaababbccdabbdbcaabbadddcbcdcacdcbaadacacaabcbabdcdbbdacbbaaacdcdbdabdaadacbccacadbabbbaadcadacabbccbdcccdcaabbdcccbaaccacabadbdbbbbdbbcbdadabacbdcababbdababbddaabcaabddcbabaddcabdbccabccccdcadadadcbccabcdcbbbaaddadaadcadcbbcaadcadbbcccacabdcdbacbdbccaccbbdcadccdddbabcaacacdccaddcbcdbcccbcdcacccacdbabdcaaccbcbbadbbcacdddbbbabacaacdbbcbcacaaaadbadccbaaaacbcabbbcbbbbbdddacadacbcccdabbcacdbbadccdbcbbbbdaadbdbaddccbbbbcadbbbcdcccbacadbbcbbcbcadbaccbaadcdcddcacacccdbabadacadccdbddcbbdbdddaaddabbbaadddaccdbbbccadddccacacdbaabadccaadddbbdcacacbdabaaabdcbaaaccdbabbcbdabbcaadacbdcadbacdbcdccabcddbbbdcabaddbcaabacbacbcbdacbdabcccabaaccaccdddaacdcddcabdbaccaadcababacbcacadbbccbababccbdacabbcdaaacbadddbbcbbaddadabdccdbdbaaacddbbbbccddadaaadbabddbbacbbdabbaccadcadcbcaaaddaaddbbcddaababbcdacaccabbacbbaccbacaabaccaccdbabacbcacbddcdabcabbdcbbaccbabbadaccbcaadcbcdbaabdaabbdaddcadbbcccbbaddbbbdcacbbcdcccdbdddadbcbcacdacdcbacbcadcababaaddaadbbadbccaacbbabddcacbbbddbdbacabaddabcbdbdacbdcbbdbbcbaccccccddcbbcdcbcdabdbacbbdadcbdcdacbaabcabcbdbacabcccbcbdadcabcadacbdcadbccdbbdbadacdcacaaccbacababbaccbaaaaccbaddccabcbbabadbaddbbbacaccabacacdacbbaadbddabaabaccdbddcbacacbdcbbbabcdabcbaadbbacdccbcddcacabddbacccabbcabdcdbbcbdcdbdcdbcbcdbaacacddcacccdddacdacaaadabbbbdabadacccadbdcbcbcabbaccddcdbaadaaccabaadadbcbacdaccbdbdddcbcdddbbdcabdcaadacddadbbdabbcbaaabaabbbdcbdbcabadbbbaacadcccccbabacddaadcbadcbddddcdcabbaabccadaadabaddcaaaadcaacbacdbddddaabbcccaddaccaaccdcdbcdbdacbbbccdcacdaaacbacbdacacaacdbcccacabbbbaccbabddbdcbdcabdbcdcbaaadbabcbccdacaadcddbdbbdaabbaacbabdbdbbaaacddcbdabbccacdcbcabdcbdacbcdccabbaaabaddbbaaadbcdacbcbbdccddbdbcdbccccdccddcddbdbdbdcadaacddddbccaabadaaacddacdacbacdacdcabbdabacdaccabdccacacdbcbbccccbdbacbbbcbcdcabbcdadccbcacbcaabdacbdcdabbacbdbcddabddcabbbaccbdcbbabbdbacdbdaadcdabdabbcbdcddabbadccbdabcbbcbccdcdbaacaaaabbadbaaaacbdabbdbbadadadbacdbdbbbabadddcacdcdabcbbbadadacccdcdabccdbdadbcbdbaddccdcdccaacabcbbbdaccbbdacbbbbcaadbbdbbccddbddbabdabadddacdbdcdcbbabbbaccadccbbdbddcbbccdcadacacbabdbccddbcdcdbaabcddddaaabdaaaaaadbccbdacccccadcdbddbcbccacdadaccddbcacbbbcddbdadadcccaccdcddbdddcaccdddbaadcaaaacdbaacbbabcccabaacadacbccacbcabbdcbaccabddcdddcbdadaacabcdabbcddbbbcdacabbadabcdbccaacaaabddddcddbdaacdabdabbcddabddbadcacaaadadaaddbcbcbabbaadddacdabddcbcaabadabcccdddccdaabddbbdcbbbdbbcdcbcaaaaaccdcbcbdddbbabbbacbaaaacbacdbbdbaabbdacaccbacadbabdaaccdbacccdadcabbbaddbdcccbacbdcbacdcabbaadcdacbdaaaacdbdcdaddcacabcaadcdcbbdbdadcbcbbdbdaddbdbbbcadcaddcbadabbccccacdbcadaababcddbdbdddbbddabbbdcccacbddacbcaababcdaaaabccdbcacdbdadaacccaddadccadbacdbadbbdcadaabbcdbaabbbdabaadbbbbbbbdabdaabbdbdbcdccbdbaddaabaaddabacdcbcbbdaabaaaaddaddddadcddbdbdcabbcbabaadcccadabadabcddcccacabaaddadaabbcadacbcaaccddcbcbdabadbdaaadbdbdccdcdabbcaddcbdaccdabbadcabcbadacdddaccccccabbbdacbabaabbadcaadabddcaadbdaaadadbdddadcaccbdbddadbbbcbcdbcdcdddccaaddcaabaddbbbbabcbbaaccdbaadbacaddcbbdaacacbaddbcacdcaacaaacddddbdbccdabbcddbabdaaadadcccccabccacabababcbbbdbbdadbcdabbdbbaddbaadcdbbcdbdaddacbbabbcaccbbdcacdcbccaacdbacddaacdaaadaacababcbdacdbbaaddabbaacccaddcbcabbdbcdadaadbcdbdbbabaabdddbadadbaaabccdccbcbbbbdadaacbabdccdcbbcabdaaacadddccabcddaaaabbdcbbacabbbbaccbdcbcadbcbbbaccbdcaacdbacccabdbbccbacacbabbccbccbbddbadaadbaabcdcabababbbccbaadccbcbcdcccbcbccddcbaabbcadabbaddaaabbadcbbdacdbdbbdaabadaabaaaaacddaccababdcabcadbbacdbdccabcdbababcccdcacacaacbdcdacdaacbaddacdcbcbabbadbadcddbbcddcbaccbaaddaabddbabababbdaadadcdbcdbdaabdcbbadaccadcaaabbabacdadcbbacbaacbaaaabcdbddcbaadcabdbcbadbaacbcacadddcdaccdcdcabaacbcccbddddbaddabcbbbdaddbcaadbccaadadbbabcdcbabadddacbaaccbbbaccaadcdccdcdacbbbbbadbbbbbaaccddaccabbcccbabadbbadabbaacbddbbbcdaabbdcccbadaccdbddbbbccdbaaabdbddcadcbbbaddcaaadbdcabcccbcacaddaadcbddababdaadcdaacadbcdcdaaddbaabdddbcaadbdcbbacbbacaaabdccaddddaaadabadaccbacabbbcdacbaaddbabcababbcaacadcadaabbccabbbdbacdccdabbabcdcdbcdcdbbabccbcdabbbbcabdabccaaccadbbaaadcdcacccdbcdbaddaacdcdaadbbccbcadaccabdbdcbacdbcdcccbbacaddabadaacccbaadcababdbccaabcdddbddacaaadcaddbdcbbccacdcdddcbbcaccaddacbbdcdbabacbbcbaabbdbbbbdbcdccdcdcaadbdbbbadcbadbbbaabbcaccbbddaaccacadcccacaddccbabcacbbbbabaabacbbbabbaabbaacdbbdbbacddaabdadaaddcbdaacabbddbdbcbddacddaadcccddbcaaabadbaabaaaacdabadcbdbdbdacbadcacdaacccbadbbdcdbbadcbcdabdbdbaacdccdbdcdabbcbbcacccbccdcddaccccacccdcbabbdcaadcaabbbbbaccbddcbbadcbccacdadcdcdcababcadbadbbbbcbbcbbcdaacabdbcbcdbdcdaadabdddcbdbbaadbdbdbddcbbcbdadcbdddaddacdadccabbbcaddcaccbaabaadaaaddbdcbbabbcacaddbaabbdaaadddcabdcabcadccaddbccbaacbdabbadbdcaacbadbbdbacbbcbcdabbcadccddabdabcdbbccadcdbbdbbabadbabdaddbbabdbddbcdabdaadcbcadccadcccbbbbddbdabbdbdbbaccdbadcddddaccdcbdabcdcdcdaadddabadacbdbcdbacccbdbaddddcddaaadabcdccdcabaddbbbdadbbccdabcabacbdcaaabbbbcbdadbccbddcdcadcddaabbdcbbcdcccdacbdbccbbbcadcdadbabccabaabdcadbaabbbccbbbccadabcbbdddcbccabdccddbdccadbacaccbbddcddcdcbaaddabacbbbbaacdaadabaacaadacaadbdaabbbaccdddccccaccaddacddcccdbccabdaacbdccbcaacdabcdabaadbadcbadadccaaadbadbdacbadbccbbaccdbcdbdbbcbccadaddadbddddbcddaabcccdbaccbcbbaaaacdabbaadabddbcacaddabdcdddcddccddacccbadccdbcacbbbadcaaabccdbbcacaccacadbccbaaacbcbdcdcdbaaadcddadbabcbcabcdcabcddcdacbdacdccaabddabcadadadddbbcaabcbbbcdcdacacddaddcaccbacdbdcbbcbcbbdbacdaddbaddcbabdaabcdcdcccdabacbccdadcbcaaabbbddcbbcacbcccddcbaacccdcbcbdbabbcacaadaccaddccdcadcabadbdccaaddbaaaccabbbcbcddcdacaddacaaaaddcbcaddbcddbadaadabadbbdddccaabccacacbdbcbacacbcaababcccddacccbbdddbcadabdbaccacdaabdcdccabdcaccacbddbabbcddaabcaabbbcbcccadddbaaddcbbcabdacdabdadbbdaccadcbbbccacccdcaabbdccdaaddaaccbbdadbadcdbbabacddbbaacdaabddcbadaaabdbbcaacbabcacbbbabbdccbddcbcdaabddddcdcdccdacaddabacdaaadabaadcbbaaaaaabababbaabdcdcabbcddacccbddadbaccaccdcaacbcdcadcacbbdaddbddaaddaacdcabbdbbababbbdddbabbcccbddddbdbbbddcacaabcabadaaaccbdddbaababdccabcbddbbcbccbacdcdabbcbcbaadddcddacddadbcabcabcbbaacdaddbacaddbcbdcacadbaacaddcdacacbcbccbcdadacbcbdbbbacbccbbbcddaaccdccdaadbdabdadaddbbccaaaabdcccbbdbabccccdadbbdbbdbabdccdcaaadbdbcdbbaaaaccbacddcdcabcdaabbbddbbcdcddaacbbadaaadbdddaacbacddccddcadddbbdcaabddddcdcbbaabaaadcddacbccdcccbdccbacadccbbdcdddbbaabccdbbcdbbbdaaadabcadbdccbbcacdbdbbaacdcbcbbdbbccbcdaaddadbbacdaddadcbdbdbdbcacbcbdacaccadbbbcdcdbcbbccaaaddcccaaacccdbcaadcdadbbcbacccabbadacbabcddbabcbcbcadbddcdcbabadbacbacbbaddcbdbccdacdbcddbcaabdabaabccdbbcabbaccbabddbbaacbbcccdddddbabbccbcdbcdbabbbddadabacadbacbbbdadaddaddcdbccbcdcdabaaaaddabcdbaccacddbacbddbcbbbdcacbadbdabcdcaddbbbddcbcccbcbabbcbadcaccbaacbaabdcdccaaabdaabbbcabbcbacbbacdcdbdcadaccbdaacbdaaabcbdcccdaacabcbbbcabbccabdcdadbbdacdadbdbdcaddaaaaaddddabbbbdabcddbcccaccaddcdbaccaadaabcadcdbdbbcaddcdadcaaacabdcdbbdbadcdbcbbdacccdbbdcacbbccdcbccbcccbdccacbcabadabdbacaddcbcdbdbcbdadbdcbddccdadaabcbcadbdbabadcbbdddccaccbbbabaaacccddccbcdcadbbaadcbbcbdbbdbacaaabbdcdcdbcdcdaabcbdbcdacbbcaccdbbbaccccbabacbdaccbdcdabdacccdacaabcbbbadcbddbccbcaacccbcdcbccbaabadbdacddcaccbccdcadbadaadcddaabbabcaccbdcbdcdcaaaddbdabcaddacbdbbccdcbaadcabdbccdddacabcacbbadbabbadbabaabddbadccacbdaabdbbaabbccccdcbdbbaaddddadbbababbdcdcacbddacbdbbddadacaacddcddcdccbaacbbcdbdaaabcacabbacaddaacdabcdddccdcdcbccdabdcbddabcabbaabbcbcbcdbbccbdaacadaccaaaccdadddadabbaddcacaabcdcdbbaddbbccbcccdcbaddbddcabdcdbbdcbdcddadcdccdbbaacbbdddcbdbccdcbccaddcbaaaabdcabcccdcccccddccaadbbbddaddcbccabacacadbdbabccbcdcabbdaabcacbbccaadcddbdddddcdcccaddacdaddbaaddcbccadcbdabdcbdcdadabbcdabdccdabbdccdbcaddbbbacbadcdcbccdddbdadbcadabbcddbcdbadaabccbbababbabadcccbdabcccaaabbabaddbbbbdcabdcddbbabdccbccaaabbbbccdcabbdacdbbdbdbababcbbdddaaccadcadcaaacbaaaccdccdbdcaddcdbdbcdaabdaaaccbccaaaddbcbcddbbbbddbbddacbadaacccadadbbbcbdcbbbcbaacbdddacddcdbdddabaaadabaadbcbdddccadcbbabddaddabdabadbdaadacdaadcbccbccdacdaaadcbcbbddadbbadbbdadcdbdadccddabaaacbcadccacabadaaccbdcbabdbbddbbdccaddadbacadabcacdbdcdacdabccdbccacacabcdabdcbdbaadaabacddaaddcabcddccbdcbacbccaaadadbcbaacdbcdabbdadbbbaadbbbdaccbbbacdcdbcacadbadcddcccdddddabbbacadbadbddcbcdbdbabbbbadcdcbcbabdbbcacbaadbbcdccdababbbbcabcbdcaddbbdadccbabdbbdcbadabdaadcbcbcccbccdddcdaabdadbdbdbbcdabdcacbdbdbbaddbbbabdaddcdaacaaabbbbacbbaaaacdabcbbddaddbcaababcddababadadbbbaaacbaacbcadcdcaadbadbbddcadbaabdccabcdbbbbbabdbaabaddbccddbcbbdbdadacaacbbdadcbbccbcaacbdcdaadccacbcaccababaacccbcaaddabbdbbccbbbacabcbbbcacdddaaddbddcbdbdabcbdaadcabdcbcdddbddccccaddacddcddcddcbccdbdadbbbccdcdcdccbdbbdcadaaacdaacdddddcddcccabccacdbdcabbaabccdccbccdccdbbdabaccaadbdbadbccdabccbcbcbcbabdaaddcdcccbdbcdaabbbaaacadabcabadaabdcdbbabbddbcadbbbaabcaaabbdcadadcaabcaccddcdcadaabbcdadcabccbabacbcdccadcabdabbcbcacbbbdabbbdbaaddcaadbaddcbbcddbdbcbdbbaababdcabbbddbbdaaadccbacdcaadccddcabadbcddcbddcccbcdbabcaabaadadacbddbadbdccdbbadbbbbbabcdbddacbddcaadbdcabdadaacbaadbcabdcdcabaadbbbddcbaddcaaaaaccacddbabdacdbcadcadcbcdadaabacadcbcabdabbbcbabdbdcbaacbacacddcdbcdabdaccdcbcabcdccabcbdcadabcdcadcadaaacbbcbccbbbabaaadaacacaabbcbcbbbaacacaaadcbaabacabddabaabacbabbbccdbaaabbccdcbbbabccbbcabbacacbdbbcbdcddbdabcdabddcdaddadaccaccddaccbcabadadcdcbabccdbcabaacdbbbbcbaaadadccaacadcdadcbcddadaacbdabdbcdadbdabadaaadbdabaddbbbddbdadbbacbcdabadacbcbdcddacbbadbccbddadbdcdbcccdaaabaadaadacaccdbbabdbabbadabbbdbacabcacddbdbddcdcbddaaabdcbccdcdbacddccdacbaaadcbcaabbadbcdadbbbabbcdbcddbbdadbaccbaddacbacdaccdddabbbaadddaadcaacbcbdaabababaabbdbacabbbdbaabcadcabaabdcbdddccdbcaaabcaadddcbcdbaaacccbdabccbcadbcbabbcbddcdcbccbddcabcabcabccbdbaadccadbbcdbdcccccbcaddbdddbcdbddbacbacabcbcdcbbdaccccacacacbcabadbcdddbbbbbacbbdbcadddcddbbbdadcdcaacddcadcbaadcacdacdabcbbabbbddadcbddddbabcbcababdaacdcdbcaacaccacbaabdbdaddabcdccdbacabcaddcabacdcddcacbdbabbbabbcabadabbcddaddadaddccbdabdbaabdadaabbcacbabbabddbaddbabdbbbadadabbacbdabcddacabadddcdaaddcbddcdbbabbbbaacdcacbaadccaadadcbacbbdaccbddacabccacaabdadaacddbbcaabacbccadabcbbdcadbaddccbbacdcdcbacadbadccdacccaadbcbbaacbdaadddaadcaadddbccbccbcacabcdbbdabdaaaabbbbadbabaadcaddadaacbdbdcabdcbbbdcabccdaddbbdaaadabccdaddabcdaadadcddbdcaacacccccbadcabbacdbccdddacbbbcbdadbdacbacbdcaacbdccacaadaddccdcbbbbddbdadccaaaacaadaabcdadcddadaaaccbcababcdccbbabbbaaacbdabdaccbbccabdcacdbdbcbcbabaacbbacbcbbadcbcdcbcadcacbcabcaabbcdacaddccbbabbbdacadcbdaabaababbcbcdaacaacadaccdacaaacadbbbbdbcaabcdcbbadcbdbdaccccbcbadddaaaacdddadbddbcddbbbcbaadbbccabcbcdbbbdcdbcacdcdabccccdacbaabdbcdbcbddabbcabcabaababbddabbbdadbdabacdaababcbcacbcdddbcbaddcbccdcacacbbddbabbabbadaddddcdbaaddccdbabbadbcdcaaddabbabcbbcbcdbbaccbbbaabdcdcdabbbaaddbaacbccccdcdbdabdcacbccaaacbadbaabdaddbcbcbabcbabbcdcabbcbbddddcacacbacabccccccbbdddadcbdbcdaaadabdcdadabdabbbbdddbcdbbcbcbbccbcbccdccdbcccacbbdccdddbbaddbdadaadbcaaddbbdaabbbaaacaacacdaadcadbdbbccdabacdccbcdbdbdabbbccbbbdddbbacbabbdcacbddaabacaaadbccbbbadbbcbacbadbbacdbdaabcbdbbbddabbccbbcdbcbbddcdacdccdcccbdcacaacccddcaabbabddcbddbacbcadddbcadbaddacbabdcabbcaaddabcabcadbdcacddbdccbcbdcadbbdaabcdaadcdbcaabbdbbcdbddcbdaaccdabbadbcbcdaacdbdccadccdaabcaacadbdbddabcdacbcbbabbadccabcbdcdbacaacdccbbcabbadcadcdbbbddcdacbabbadcccaaddcdacabacbcccdcdddbbbdcadccccbaccdaccabdbcbbabdbdbdcaaddaaaddbabaabdaaddcbbcacaccaccdbadbbdbbbcadbadaccddacbbbccaabbbccadddbbbacdabcccbbdbadcbcbbcacccadacabdbdcadaccbacbddacbcabdbabdcabdcdbdadddbadbcddbdcaccacbbaaccaadbcdcbddbdcdccacdbbbccbbccdccdbababcabcbccbbdcbcadbccabccdcddaacbbcaacccbdcdbadaccbcddccbbacadadbdbbbddbacacdcdbddbbdacbacbdddbabbabcbbccdcdadcccbdccccdacbaccbcbddadadbdadbbaaabbbbddcbdbcbbdbacbbaddaacbaccdcadcbcdddaccacadddadcbcbabdcaabadbabdbadcdbbaddbcbabbcdddcbdbdcbcbdacabdaacaacdaaddbabcbabbabbbbcbcbbbacbdbbccbddcabaaccaadacbadbcbaacbddddacacaccccdccddacdaddbcdcdbbbadcbdababddcadbdbcbdacbcabbbbcddcdacbacddcddcdacbbabcaaaabaddaaccaacabcbbccaacabacacccaddabbaadaddcbaddbbcdcacdcbacdbdaddaccdddddbbadbbcddcddddccbaaadccabccbacdaabcdcddcbabccddcdbbdaadbbabbdcbabcddddddbabdaaaddacbcbadadbdccccadabbbbddaaaccbadbcbdbabacacbabadbdbddcbcbacbabdbddbbadcccbbcbdadacbaaccddddaccdbdabdadddbadbacaddaacabbcbaadbdbcdbccbcdbacbbdbdabbdccddadbadbdbcdaddaaaaababbdbdbacbbdbddcddcadabccdbbcddccbabbdcccccabaadbdabdabaccacdaddcbaacbbacccadcbdccbacaddddacabaadccbddbbbdabaabcbccdacbcccddcdbcabadcddddbaadabcbdccabdbaaccdcdaccdcdcccddbbabadbacaabddabddbcaacdcacbdaaaaddbadcbbcbacbddbcaaccbcacdbacadbbadbabcdddbcbbaacdadccbbbabbdbcccdbacbdcddbabdacdcccdcddabcaaadcdddcddadabdacaabbdddccbaaddabacdaccbcadcadcccacacdaddaadbcdaaaaabbdcddaddaaabddbaacaacaaabadadadddccaacbcccdcdcaacbbabddcadabdadabbcbacdacbdadccdcccdadaaadcccdbbacdddccbddddcbbaabdcacabbaccbdbbcadbacabaaaccbdababbdbcdddadcaddcabccccccccdaddabbcddbaccaaabcadbcadccddddccdcacbcacbacbccccbbdabaaabacbaaaadacaaabbdaadaccbbdbccdacbddadddaddcbddababcdbbacdbcdbbcbabbbdcdcbadbdbbcbaabdaaaaaacddbdcbacbabacdaabdccdbcddbbcdddcdcddcbacdacbbbbbacacdaaacaabcbcabcbcdcdccdbcabdbddbcabcbadccbacaabdadbbabbbddacaabadbabcdadcdbcdbadddbacacdbbbdbdaaadbddadacaddaabadadbddbabadadcbadbdcadcaadbaadcaacbadaacbbacbdbcacccdcabacbbdccabadbabaacdacbaabddaddddbbccbadabccacaadbcadaaacabbbbccdbcdccbddbdbbacaabdaacadadaadbacaccddcabadbcbadbadccaaadbcddbccbdcaddabcdbacaadaaadacbdccdddbddadadadbdbcbdadbdcbcacbaacbbbdccbbcdcbbaacbdcddbdcdacccabdabcbbccaabccaaccdabdbcccabbdbdcdcadacbddccdccacaaddaacbcabbdbcbbacdaaddaddbccacdccbbcbadddcabdbbcaddadadddbcbaaddddcaaabbdbdcccabbdbdcdaabcaadbbddacbcbdccacbacddaccdcdacbaacadaccaaacbbbbbacccdaccbacbcaddcaccacaaaadcdddaaadbdccbbadabaadbbbbcdcdaacbddbdcabdcddaccbbbaacbccabababadbddbbaacddbbaabdaacccddcaadaadadacacbbdbcdccaacaaabcccbbcbbaabdcdadbdbaabcaadbadaacddabbcababcdcbccbcbcbcaacbabdaacaabccbcabbccacbdcdcaddddbcadccddbdaabbdccaabbaddbacbbddbccdacbcccacbadabbbbabcbcdbcddddcbbdcdacbccdbddadcaaaadbdbbcaddbdadcccaadabcdacaacadabccadbcccadcbccdbbcaacdadbadadabbccadbabddaaabdaaaccaacbdccddcdaccbabbacaccbabdabbbccbcbdcccbdcccdbaadabbdacdbcaccadadbdbdbbbbdacdcaccbcbccaacccaaabdacdadaadcdddbdbdddbbacdacacbbdcababccbbabdcaabadadcabdadacddddabcbddaadbbacbadddadbcccadcdbaadbcbabdcadcabcbdbdcdcdabacdbccaadddcabcababaabbabcdcbabadaccaccbcdbddcdaababdcaccbdddccdaacccdbcaaaddbdabbbdcbdabcabdccbcdbdbbaaabcbddcdbbabdccacadbdbddbbbcbdcdacacbacbdaccddbdbddcbccbbbbbcdbdccbbdbcdcccccadddbcdabcbacabdcdbbdababbddcadcddacccdabdaccadcddbabcdabdccccabbcdbccdadccdbccacaccbdbbacccdabbddbadbbdaccdbdaddcdacccbcdadcabacdcdcbbadadbbacdaaadcacaccdcbdacbacdbbddddaacdcaadabdbaaddcaccbaaacccabbbcddbbcddabbabbbdbaacbadccadcaacddcacacddbaabbaacdadaccaaddcadbbbcacdaaddacaddacadaadcabbbbcdbaccabbcabddbbddddaccadadbbaddbbcbabbacbaaaabdaacddcbdcdacccabbadbbddaabacadadacbcddccdcdbdaacabddcabcaaaabbcddabddddaccbdababbdccacbbdcbadddcdbcababdbdcdbcdcaadbdaabaabadbbcbcaadccaadcbaaaadbaaaadabbcccaccdbbacccbccaacbadbbadbaadccddbbaccabadccbccacbcacbadcabdabcbbddadcabddccddbbbcccddbadbddaddbabbbadbadbcdbadbcbbcddaaaacbaaaabcbbbbbdbabadcacaddbabbaadbcbaadcbcaddabdbddcabbaccaadaabddacabccdcdbdbdbbdabdbcbdbaddbcccdbbadbdbdaacaddaddbbadacbccccdadaacbdcacbdcaccacbcabdabdaaacbcbdcaadcdaddcaabcbcccaaccbabcbdbdbbacbdbadadbdaadbdaabccbcabbdbddbbaaacabbbbaadddabcadbccacaadaabaaccdacaadadbcdadddbbcccdaacbdadabbbdccaaaabdcccdbabddbccaddcbdcbaacdbcdbcdbcdbadabcbcbbbbccaddcabdadbdccbdabaccdcbdbaccacaacdcdcdabadbddcbabaaddddbbabbbabbacdddaacbccdbcbbdbdbcabcbbcbcadbcccadbabacadbdcdbcdaabdddcadbcbdccdaccdaacaadbbbbabcdaaccabadddbabadbbbddcbbccbcdbcadcaadccbbbacbcadadcbbaabadccdbbdbabcdcdacdddadbcbdacbabccbadbbadbbccdbcacdcdcabdcaabdbaaaabababdddbddaccaaccbcbacccccdcdbcbdbabbdcccacbdadabdcbcbdddadbdbbadcbbbdadacabcbaababbcdababcbddaaccacdacaacbcacbdcabaaccaadaaabdcbacaabadccbdbdddbdcbddcdbaabddbbabdbabbcddcbcbcbcdbbaacadddacdacacdddbbabbabdadccbdbddabcddadabcdddacdcabcdcabbdaabcbccdbdbddcdacbacbaabcbbaacddacccbdbbbbcbdcddabbaabadaaabbccddccdaadcddacbdccddabcbbbddbabcdabdbbdbcadbaabdcdcdabbaaabcbcbaccbcbbaacbbcadbaabdaaddabdacbbbdbbaccdcdccdccbcdcbbcbcabccccaddccaabdbbcacbbbabddccdbcbcdadbbcaadaaabaccaabbddddbbdabccaabbcaabaacdbcaccdcaacbcdabccaddddaaddaacddacddcdbcaaccbbcddddacbcbadaccdacacdccbcbaaccbddbadcbcbddcdadcddcdbbcdaabbdcdcdcbaddcbdbbcacbadcbcaacccaabcabccbcbbbaadcacbccbaacacdaddbdbbdcadcccadbcabcbccbbaccbcabacaaabdcddcdcddabbcbddababaacbcacdcaaaadcbbdbbbacabcdabbdcabccdcddadadacccaacacdaadababbabababdcabdbccdcdcaabdbabbcaaaaaaabdddcaccdabbabadcbdcabdbbaabaacdbabbaddbbddcdcadadadddaababbacdacdbcbbdddddabbcbbbbaacabbbaacccdccacadddddaddcabcbbccbddcabdacacdaddcabdbaacdbbdbdddcbcdabcaccbdadccdbdbbdbaadbdcdbddaaacbbdccdcbdcbdbdbacdbbaccdacccacbcdcdcbcaadbcdcdadbaadbacdaccbbdccaddbaacddadccdcdcacaccdcbbbdcdcccabbcaabcaacdbcbdcbadaabcdbddacdbdbcdbbbdcdddddcaabdcdbcaaaaadabcaaaabdacbcdacbdcddcabaaadddbbdbdbcbdcaaccacddddcdbbbabcddacacdabadaddcadacdbdbcdcdcdcaacdacbbdaacabbabacdbaaaaaadbadacbbabddaddcacbbabcbadbbdcbdaadbddbdccdddbdcacabbdaadbddcddcdcbbddbdccbcaaaddbbddadbccacdadabbbdcabbabcdbddaadcacccddcdbdabdcdbbbacdbcbdcabbadbacddabbbdbadccabbbbbdadddcadcbcdacdcdbadaabdadbcbabbcbdcbaddabadababccaddccdddbaccdbbabcdaaadddbacaccbcdddabbdbcdcaabccaccbcdcbcbdddcbbbbdbabbcacabccabdadcddcadacbddcdbbcdbaccdcccbcaaabcbadbbcdbbdbdddbdaadbaadbdcdcbbadbbdaabaaaadddbaccaddadacdbdaacdacbabaadddbcaddcdbbaaadacbbdbaabaacbacbacabcbabbdabddabaccbabbbccbdddaadaccadbddddacdabdcdcbbabdbbabdcbaaacadababbabcbbabcccdcdcdcbbaddadbdbbcacbdcbcabdabdddcabacbddbdaaaccabaddaabacdcdadcbcdbdcdadadbddcaabdaadcadcbdbdadccaccbaabdabbbdcabcaaddaacaaddadbddcddcbbcdaabdbcddabdaadbdaacccaccdcbacbcbabdcbccccbdbaaadbccdddadabdcacaddcddcdddbdbabcdcadcabadaaacbdddbbbdaaadacbbabddccdadbacbabcdcddbcddcbcbcacabbcaaddcddddccaddddaacbbbbddcdabacdbaabbacbddbddbdcdadcccdadddaddcbacaddbcddbbdbdcaaadadbdbcddddbcabdbabcabadadcbdcdddddbacdaacbbdacdbabdcbdcbacdbaaabbbdacbdddcdcabcaababcabadcabbdcdcdaacddcccccbbbcaadccbdadbcacdabccabcbcbadadabcadddbdcbbdaddbbaaaabdacacadcccbcddcddbddbcacdbaaaddcccbaaacbbdddccddacadbbbabaaccdbcbacbdcccccbbdcbccabddcaddadcbcadccbdaabcbaadcddddbcccccdacacbbacddcabaccdbdaabaccbbbbdccbddcaccaabacaccacaabcdcaacbcaacdaccbdacacbadacddcddbbabcdacadabcdabbcdcaadacbbddbbadabcdbbbddddddbbdccccbcdbbdddaddaabaabbcccdddcddadbcbaacccddcbadbadaabcabdcdbacddbadddcbdcabdabaadabbdaccbcccdbdcbcaaccccbcdccdadbdbaaddbddcbbddbbbddadbcccbdccbdcdcadabddacdabcccdcaaacdccbbddcccaccadcacadccdabbdaccdbcdbbacccaacccbccdaabbbacdaccaadaacdcbbbddbaabddddadbbabdacdcadaabdbcddabadbcdcbdcabdcbcccbaabaccddacbbcdddabdaaadaccdbbbcacaddbdabcaacaadacbacdcddacbcacdbcbbdccdcbbddaacacbddabdadcaccccbdadadbbbbccdcddbbaccbdbaabcdbbbddbccdabcbabacbacbbdbbcdddcaacdbccbccbdadabacbbabdaaddcdcdccdbddcdbadaddbcbccddacddcbddbdacdaddccccadddacbcbddbdaacaaabccacacadbaaacbccbbbcaaddcadadbdacabacbddbbdbdcccaacdaadbcdccbaacbddcdaacbbabdbabbdbbcabdbbcbbdabaddcdaadcaadabcacacacdcddadbbabbadbbdcaaaddabbaccdcddbbddcaaaaaabbaddabdbaabdaddacccabbbcaddbcddbdabbcbcbabaadbabbcaacddbacbbbccbabbbcabdabdaadaabdcadbdcccdcaabcdbdcacdcbbdcadcccdadbacabadbaddcbacbacaaabbacadccdccadacddcdbdccdbbadcdddcacdcabddacaaadbaacddbbccdbbdadddbaddadabcacadcababadbccbacbccccbddcbcdcbcbacbdcabaacdabdbbacddbbcbcbbbaccdccdcccccbacacaaaaaaabbdcabdcdddadcdbccbcaaddbdbddcabbabcbbcbbbdadddacadccbdcacbadcccbcdabaabdaddabadabdbaacaccaaacabbdacccdcbddacdbcabdbdaaabbbadbadaadcacbdcddbabaaadadcdbbcbaaaadcccdcdbcbacccddaddabdcbcddccdccbacabbdbbddcabadaddddbdbabdccbadabcbdbdccccbccadaabcbdbddddbadcbcadacabdabbcdaccbcacdbaccdcbbcbadddaacbcbbaabdabdccaacbdacdaadacbbdcdbacddaaabbbbbdabdbacdadbcbaaccbdddbadddcccbacdaadadbccdddaddcdbdadddbbdcdcbadbbbbcabcabbbbcbbdcccadbbccbbcdbbaabbddbacdaadacdacccdaddcacccbbddbccccadaabcccbdcdbcbbbdbadabccabbdaccbbbdddbdddbbdbbbddacadcccbcaccbccacdabadbbcbdccdaccccbcccdccaddbbbcbbcdcdbdbdbacbadccacdadaadabcddaabdbdcabacccdbcdbcbacbddbddaadbccdcdacbdaccadbbbbadccacbaabadbccaadcddccbdcbcabbdbcacabadaabbaaabadacaccbcdcbbcacaadabcdcdaddababaadcadacacbdababacbccaacbcdabdacbdccccbccbbbbdbcabdaaddabaadccbcabdaadaaccdcdbbdbaccbcadabaadccaabbaddabdcbdbbabcaaaddbcaadcddbabccdbdbbacaaaccabcadbbaabcdacabadcdbdbdddaaccdbcbcacbacddcccaccbdbdcbdabccdaaadaccadadbbdddbaccdcaacccabcdbabdbacaaadbbacbddabcddaaacbadbbdbbdadbbdadabcbddcdcdbcbababcbaabacddcddcdbacabdbbacddbbcaacbbcdbbcbadaadacccbcdcbbbaaabdcccddcaabbbbddbcbcbabcadcbcbddacccabccddabbadbcccbbbbbdaccbabbcdddbbadbdccabcdddabacabdddacbdbbbdcbddddccbdcdbbcbaabbaaadddabdddbddabdabbccbbacaadddaddaddbacdbdcbbcbaacabacadbaaaddbbabbdbcacdbdbbbadcdbcbdbaaaccbabdbabbbbacdbcdccaacaacccabccbddcbddbbbdaddbacaabdadbdcdbbaddabcbacaddadcdbddcdbbdcadbccdddcbaaddbbcabaccabddaadacdbacbdcdcadbabccbdaadbdbbddbbdacdbacccdaacdacbdccbacdbdaaaabacadbcccbaacbcaadbbcdbadcbcabcabdcadaadbdcbcaabbaadbbcbbbdccabbcbbbcccbccdacaacbbcdcbddddaddbbaddacbaacdabbadcbbadcbcaacabcaccbacaaaccaadbdcacdcdaabcabdcabcaabdbaabcbcccdaddcccbaaadcbbaaaddccbaaadacbdaaacabbbaccabdaadabacbbddbacadcbcabdcbcbcccddabccccabdadccabbccdadcdaababcbccadabbabdbbbcacddcddaaacddaaaabbbadadadbbdcdcbbbaacdacbdcbcccaaaacddcbabaacbaaacdacaaabaabdaabcbacbdddbbaacaaabcbbaadcdccadbabadcccabccbcbabacbaccbcacbbbcbbccbdcdcaabccdcdaabdaabaadacadddadadcbcabdacbcbbaccbdddacdbdcaddbaccacccbdacddaabcbaacadcbcaacbcbdbbbcadbcbccddadbcbbbcacccadcabcaabdbddbbaaaaabacbdbacbdbccacaacddcdaccabcaabdcbcbbddcbdcbcdabbbbacabccdbabbccaddbadbccbabacbdaddaabccacabadbcdbcadbdcdbbdaccadbaabaaddcaccadbaddbbccabdbabdadabcadabdcddbcaacaacadbdccbcabbdccabacdddacbbccabcaccdcdcaddbcddabccbadbbbccdddcbccbbabcadadaabdcacbdcbdccaddcaacbcdbcbbabdadadcbbdaddcddbaadcdcacccbaaabbbcbdacdabccabcdbcccccccbbaacdcdddccdddaddaacbdbdbdcdbccbaacdbcbbcdbbcabacabbcdadadcdcccdbdccccbadcaaccbacdbdaabcbaaaddcadcacbdddabdbdabacccccdacadbaaabcbcabadbdaacbccabaccbcbadacddcddbdbbaadddbdcacaddbbddbbabcdcbcdbadbcdbdcabdccaaaddcbccbbacaabcdaccabccacdbddcabdbdddbbdabdccbbcadccbaadbdbbdbcdcaccadcdbdbddccacdcddddbcdbbdababcadbadcacdbcbbddbcbacbcdcadcdbadddcacddbdccddaaaacccdccadcdacbadbbddabbdacbbddbcabdabcabaccabaabcddaabadbdcbccdadcddaaacbdbcccbadccbadacdbcabbbbabababcdabaccaddcadbccdbdaaddddaabdccdadbdbcddabdbbadcbdaaacacaddaadcdcddcaadddbbbbcacacdddbbccaccdbdcccabbccadbcdaaccaadddcabcdbabdcbaababcababccddcaaadddadbbcdbcbdadacdbccacbadbdbcdbcadadcaaabbbabadbdddbbbdcddacdcaaccbbbccaabbaccdcdbaccbcdcddccddccaddadabcbadddbaaabcaacaddcdcacbbbacabbdcbbdddacdcdabbddcbddacbbaacabcadadccdacbaabdacbcadaadbaacbadbcabbdaabdadabddcadcaacddccaacbdaabdbdbcadccbacbbbddaaabdcdcdadaadcbdabcdcccbadcbbcdddddcacabaddbcadbcaddaadcdabccbccbbabaaadcdbcbdcbadbdadaddddbcabdaaaaaaadcaaadbcdcdaacabbabdaabdacbbcbdbccdcdacadbbbcbaddadddcaabdcbbdabbcccdacbcaccbbbdcadcddabbbbacdcaabccacccbcddbcaaccdcbacadbbababcbabaaaabacabbadabbabacdbbdaaaabdbbbcbbacaacbbcccaabaaccabddddcaacacaaaacbacaccbccaddbbccaacabaaaacddbcdcbaababcaccadcbbaacaccdabbddbacccddacdbadbdbbdbabdbadcbdbaacbddadacccbbbcbdbdbdcbacdcbdbbaacdaaaadbbaacccaabcccaabdcbaacbbcdcddaacbacbccdbaaaabbdadaabbbccbcdbbdbcdcadbbbabababcbcaccddbcabdbabcbdadbdcccacbadbdbdccadacacacabddbdaaacbbcbabbddadcbcbdbacbabaacbdddaacbcabaacadcdccdbdadadccbcdacabdccadbcdacacccdadcdcccbccbbcaccbdbdbbdbaadddddacdcdbdabadacdbdbbcdaabbbbdaacbcabcacbdcbabdbbcbabdcdbabdcaaacabadcddddcabaabbacdbcbcadbdabdaabdacbcacbbbbdbcdadbcdbcdbaadddcbccaccadbbbdaacdcaaaacdabaaacdbabdddbadbbdddbbcddddbaccdbcccbcbbddbacacdccdcdbccbbabcaaababaccabbdcadbcacdaccabacdbcacdaddbaccadbbcdddacabdccdbdcacaadbbbcdcdccbccbdbcaccaccabcdbcaccdcbaacadbdcddadbacccbbddbbbdaccbabbaaadabddbccacccadbabdacdacabaddacddddacadcbddbcbaccaadaacacadaaddcabdcabacabaabcdbacaddcaccbacbccadaccdbabbcaadddcacbcddbacadcabbdcabacdabdcaaaacdccbadcabdbbbccdccbdbdbcacdddacdbbddadbccbdbcccdadbabcccaacadabdcbddccacbabbbcbdcddaddcdadddbaddabaaddbbdcddaabacdaccadadbcacdbcaaccacbbbdadbadaacccddccdacbdadacaddbdaaccaaaabcccadddbcccbcbdddaadccacaccaadcabcadcbadddcbdccbbbbbadcaddacdaccadcbadddcdaaaabccacbcaacccbcdddcdbdbbbabbdbbdadcbbdcdbaaadddcaaccadbbacaddcdbddcbcddccdddaadaddcacabddabddacabacbcbcaccdacbaabdcdacdcabcccaadbaccacdbcdbcccbdccaacbcccadbabccadbbcbbaabaadbcdbabbaccadbbcccabcdcabaccaadbcdaaadcbcaabbbcdcccadcbaccccabcdaccacadbabddbdbccdaabddbaddbcdabddcdcadddbcbddabcabcdbcbdaadacbcccbbbbcbabadcdcbcddbbcadccbddbbbaddadcdcacacdcbdccbcbbbdccdcacccadccbdabcacadabbbcddcaddaaaacdccbbbacccbacacbaccbdabcacccbcdbbcbbadcaccccdaaccbaddbabcdaadbdababcbccbcdabbbbaacadddcaaccdbbdcbaabccdddbbcaccccdabddcadadcabaddabbddbccadcaccddadcccccbbbbccdacccbcddcdbacacbacbbacadcbbcdcbcbbccdddbcaaadccacccacbdcbacdcabdaaabbcbacddccdaccbdbbabadbcaadadcabacaddabcababbbcbaccbddcaababbcdcdbddddddcbbcdbadbcdabcddaaacabbdddddbdacbbbdcdddaaadddcdcabddbdaabdcddacdcbddcbcaaacbbdbbbbbbbddcbacaccacaaadddaabaacccdadcadbbdadacaabdcddcddabbccddcababbcdcccbbcbaaaadbaccdaaaadadaddacdabcaacbacaacccdaacacbdbbaaaabdbcdddbbdbbcbcaccddddddccbaccdcacdccbdabbcaccacaacddcbdbaabcccbbbaabdddbacabaccbaabaadddcbabbaccaabcaabcbcaacadadbcdccbaacacccbbcaadcbcbdacbdacbbbacddddbbdbdbcabbddaccbbabdddcdacbccbcaaadaadcccacbcdbbdacaddaddbbbdadbbaadcadcbbacdaddddcdabbdccdbdcddbddcdbdbabdabbcbcbacabdddbabcdcddbbaaabaacdbaaaaacddcddbabdaaabdacaabdddacbdacdddcbddcabcbbcccbacadbacaabacbacbacddcbbbccbaadbbcbbbaadcbadcddccccaacddcbcbbcaacbbacdabcbadddbcbdcccbacbdbdcbbdaabcbbdacccadddcabbddbabcaadacbdbcaaaaddaaccbbbdaddadddcdcabdbacdabdaddcdaabdabdcbcabcdcdabcdbcdcadabbbdcaadbdbabddabaaacacacdccdcadbabbcbddbaaabdcbdadddcabbbdababaccbdcbbcbcaddaabbacccaaaddcaaccdcabcdaabddacddddbacaadcaaadbbcaaabdbcddaacaccdbbabbcccadacccaabacabcdcbbbccddcbbaddcacddcadbddbcbdddcbdbbcbaadbacdddbdcabaabcabcabacdcccaccdbdbbcbaddadbbbccacddddabdadbabbdddcabaddaddbabcadcacaacacddcabddbbddbbaaddaabdcbbabcbdaadaacccddccdacabbadadcdcdbccdcbabddcbdbbdaababcbccaddbbaaccbbdabcaabcbdabcabccdbbcdacdaacdacdbbdcccdabdadbcbcdbdabcbabacaabcaaaacddbcbccaaddadbacdcbcbabbaaddaadddcdcccdccddccbdaabccccbbccdcbddccadddababbcbbcbbccabaaaabccbcbdcdabdbabbdbdbabcdbbcaaddcadaadaaabbdbdccbdabddcbcbcaabaaaccccaaabbbcbdacbabcddcddbcbbabacadcbaadccbddbcccabdbadaacbddcdcccdacbbcabcdcaadcbcbabbbbcdcabcaabbaacabbddcadbadcabddbddaabbbdabdbdcbdadbdbdacbbbcaaaacddaddcddbddccaadcdbabdccabbabbbcccaabcbbcbbbbacabdcabdcaadbccaaabcbccdaccbbcbabaabbdccdababbcbcbbbbcdadbadccabccbcbdaddcaacddddbbabcddadabcddbaddddcabbcdcbddbdbbccdaacbdccadbdcabadabcbacddcdbcbcddabcaacdacaaacdcbaadcabdaabdddbabcbcdbdbaacbababbdadbacdaaccaacdbddacacbdabaaacdcccbcdcbbcdccacccdddacbbacadcbddccdddbcdaaaacdbdacdcabdccbdbdcababddcddabdaaddbcbddaadcccbabcacaccbbdcbcddbcadbbddadcbccbccbdcdddbdccacccdcabbbbbddbdacbbcdcdbddabcddabdaddcbadccdcbddaaaacbabccbdcdcdcdbccdddbdddcaadcadcabbbdabacbababbaabcdababcbccbbbacccbccdadacdacadcdbbddddabcacdadbbcdbccccdadbcbbcacbcbdbbbcaadbcbbcbccbbcacdbdabadabccbaaccbdadbbcacbbdbccccccdccccabcacdabadbabcdbdaaaccdaaabdcdcdaccaccdaddaddadcbaaabbbbcdbdaccaabddacccacdcdcbabdbaadbddcdadadacccdbaabddbadcbcdbcaabbccadbcdbabcadabbcaadabaabbbddddadcbdadcaaababbaaabaaacddddbbaadcdcaddcbcbacdaddbccbaacacbdbbdacbdaccaabcdcbcabbdcbddaaabddabdaadcdcadbcadabbddcdbabcdaadaabbdccccdbbdcacdadcabbcacadbddadbbbdcaaacbccbbcccaddaccdbbadccdabadddaadacbbcdbdcdbbdacbcaccbabbaacbddccbbdbdbcbcabcdcacdbdcdddbcccbbcbacaabccdaadbdaaabdabbdaccbdaddcacadddddcbddcbbbccdacddccdaaccdbcdbccadbdcdcbbdadcbdadacbadaadccddbaacdcdcbcaacccbbabacbcabdbccdbdbcbaccaadcaabbaddcabaacdaadacbdddacbbbaaccccddbdbaccbaccbbcdddbdcbdadaaadbdacdcabcddcdabaacdbbcabadacbaaacbccbbdcaacabcacdbcddaabaaaabdbadbddbcccccddbbdcbdaacacaacccacaaaaadadaddccaddddcaddaddcdddbbbaddbbaabcdccccbbbaaacbcbaabbdccaabccaaabbbdcabcdcbabbdddbbaaabaddbccccbbcabdabbabacaaadddddacabdaddbabccabababadaabdddcdaccddbdbaadcddcbacbacccaaadcccadbadaadadababdbadbcdbacdcdababaadbcdbbacbdcdaccdadaaadaccadabbbdcbacadbccbcdbdaddbdcaaaacbacddcaddadabbabbddddccccadddacabacdababcbcbacaadadcdbddacabaadcaccbbcaabcdaadacaddaadccaccaadcbbdaabadbbbadcabddbcdabbaddbbacaaabbdddadcbbccabdcabddbdcddbddbcbaacbcadcaaaacdcbdbbbadbdacadadcddabdadccdbddccdcdaddbacabacddadddbadcddacaabbcabadaadaadddbadaccadbcbcabadcdcdadbaaadbcbabacbbcaadbcacccdbcdbbdbbdcdbcaaadccacabdabdbdddddccaacacaadaccacaaacbabcccaadcaddabdbbadabaccbaacbbabacdbadaabaaddbdcaabcdbdbdadadbbbcdcdddcddcaaacdddbdbcadddcacdaacdcccabdbacbbcdcbdcaacdbdadacbdabcbdcacdabdcbcdddbbcabbacdbaaadabcadcddcadbacbacacabbdadacbaadacdcdabcaaaaadbcccadcbcdabdacbcbdddcdbddcdbdddbcacbcbadcabacccadccdbbcbbbdadabaacdcdaaccacdcddaacdbddcabddcbddbcddbdcabbdabddddcadddbcaccadbcabcbbaddddddbaccacbadabcbbcaabacabcdbdbacbdadcadaacbddbbbdacddaccccbadaddadadaabbcccbbadaabaccadbbbddcbddbbbacbbbbaabcadbdabadaacbacdccdbcadbbddcaccddacdbddccbacbcbbdcdccccdbddbddcacddabaadaaabcddcbcbbcabcbbcabaacaaddcaddcbdcaabbdcbababbdaabccbdadababaabbbbdcbaabaabdbacdcdaaadabdcacacbcdaccbbbabbcabddbaddcdddccacbdaacbbdcacaaddcdcacdaacdcdbdcbdcadaacccdcabbbdaddcbcdaccdcdcadccccaacdbadcddbbbadadccccdbcbacbcbacaacdcdbabcbdcabbabdadabcdbadacdcaabcdbbdbdbbcabadbbacbccdabcabaabbccdbcbbabaaaccbbbdbddaabadbbabadaacaccbaacbabbdaaabaadaadcadcacddbddbacadcababcabccdcbcbdcccaaddbccbdccaabbacabbadbdadcccacbacabcbdabdccbadadcdaddbadbaccbbbacabaacaccaccbcadbccbcdaaaabdbaaaccbbaddaccdddabbcbcbdadccbcbcbacadbcabadbabdcccdbbbbdbdbbbcadcadacbdbcdbdcdcbbdaccdbdbadbddacdbacdcbccbaacbcbcadaaabbddbcdcccabbddaaaaaccdcbccdcbdabacdaabcccccaacbbaccaaabdabccbaaaddccaabdcdcacaccaccbcbcddddaababadbadcdcbddadadddcbaadacccbacbdadbdbaadbdcdaaaaaaacaacaddcaadbbbdadcbbdcbcdcdccdabcdbdaaaaabbacddbacbaccaaacacccbddcabcdaacacabbacacdccbadbbabbaabcdcbbdccddabaadbbbdbdcabaaadbbcdddabbccdabbabdaddbaaadcdbdaacdbabddccadacbbbcbcadadddaddbaaaccccaccaddadacbdddccadbcbadbcccadaadabaaaccdbadbadbdcddbccdadcbbdcaacdacbcacadaabdadbccbcdcbdaaacbacbddccccbbadabbbabbbbabdaacbadcbdddcbcdbbdbbaccbdacbcbcaddcdcdacaacdccdbdbadaaacdcdcbdbabddbccaadcadcddbbdcbccadabcdbadbcdabccbaadcacccadbccadaaddaacbddddadaadcaccacabaabaaacdcbbcdbdaaccccabdcaadcadbccdbcbcbddabadcaddccabbccccbddadcbdcaccaacdcadcdbbbbacadabcbcabdbbccbbbbacacbcbacabbcbdbbdabdcadbdcdbaabcdcdbdccbdbdcadccdabadddacabccbdbcadcdccabdaabdbacacabacdcbcbcadccadaccbbcaadbcdacddacadcccaaacbcbdcdcdcddccbcddadbcbcdddabaabaccdacbadbcdaabaadcdaacbbcdcaddcddcdaaadbadccbbdaddbabcbddbadddcddaadbcbadcddbaacbacbbacabbbaaaadcaabaadbcdcdbadcbcbbcaabdcaddadcddcababdcbccccccbabdcbcacdabaabadcbbccdbbccacacdccdaaacadbadbddbdbcabcdbbccbcbbbaaadacdbadacbaaabbcdbbcbccbbbabbccdbcadccdbaaacbcaaaabacbabdabbdbaadccbdadccaccddbccabddcdbdcbbaabcccddcbacdbbdbcbaaacbbbaabadbdacaabbbcdacccbabcdadccccadddabbbbbadabcccdaaababdadaadddbccbddbcccddadbbcadcbcddbabdaddacdcaaadbdcabcbdbaadaabcadcdaabdddbcccddababbccdbccaadbdbddbbdabbcddacbccaabcbdcadbaacbdbdabbbacacaaddadabddbcabbbaabaddaacadbddaadaacaaadbcacbbacddaaccbdbbbdccdddbbdbdbcdcbdabbccbbbdbcbbbbbcccbaadabbbcdbbabaaabddbbbaddcdaddcbaccbbdbdaaadbbddcbcaabababbdcacddabbdbcbddbcadabadccdabbbadabcacabcbcdaddcdcabccabcddbcbacbdcacddcdcbaddaaaaccbdcbbbaadcbdbadaaccabdccdccdbaacddbaddacbddaabadcabbbdbcbcbcaacaaacbaabbabbcbbbacacbcaaabacbbabdaadcacabaabddcacbccdbacbbcbbdbdbcbcccbdabdabcbbcdcccbadbbdccdbabbdbbbdbdcadacbdbdccdccdbddacdcbdbaaccbaadaaababddbdbbabcbdbccdbdbcacddbcdabcbbdbccacabacbabcdcbcabdbaaaadbbccacbbddbbcbcdaabdacdbbbadcaacddacbaaabcaadaabdacbadcbbbaadcddbacddbcbadbaddaabaddbccdddbccbaddbdcaabdcccbbacdcdbadadadcadbcddadbddacbccdadabadcdacdbdbaaccbdbacabdccbcbdbdaddadbdcccdaabaccbdbbddbbdacdacdbcaccaacdaadaabbdbbbdbcbabdaadbcadcabddacdaadcacbddbcacabcbacccdcddacdbbaccbcaaccacccddcbadbcdabbddcaabaccaaddbabbdbcbdaabcdcccabcadbaababbadacaaddcbbcbcbcdacbbcbbdabbababbdbbcacbcadddbcccaabbabbbadcaaddbaaccbdcbacbaddbcbaddccaccbcacccaaccbabdbbdddbdddccadcacbcbcadcabacabaaddddaaaadaadbbdadbcdddcacbcaddaaadcbaddaaddaadaccbabadbadcddadacaddacadbaabaaaddcaddadbabdbbaadcdbcbcaacbaaaabbbcbccdddcbdcdbbabbacccdaacabbdbccbaadbbbbbaacabdddabccbbbdcddbdccccabccdccbacccdaaddbccbcbcbdbcbdcbaddacdbcdcbcbdcacadcdaaaaddadcdcdcaaddccccabbbaccbcdbccbbbbcbcdcbbdcbbabcaaabcddbbaccccadddacabbbdbdacddbaaddbbadaadbdbbaadcadcccaddddbddbcbdbacdcddacccddddaaaaabbbcbdcaccababaaadbcaccdabacbbcccbcabdaabccabddbacdbcdcabddacccccdcbcddbacadadabbbdcacddbccdaaabdaddbcbabaacbdbddcbaabdacabdabbdbcbbdaaadddbdbddbbabcbacacbadbbaaadbbdcdacbcadaabcdcddcddacacbdcbacbddcacaaabadbabddadaacbbdbdbcbccaddbddaacadaadbccbabbdacbcbcbbbdcabbdbcdbbccbabaadaababdbbacadadcaddcbbbdcdbcbabdcdaddcdaabdbcaccdddbabdbcbadcccdbadddabdabdadccbdaababaabbaadcdbdaddddbbaaccdbdbdcbbbdddddbbbacaacabadbbabbbcdaaacddcccadadadbdabbacbcabaacccbdcbcdbbbbdccaaddbccdbdbcbaadabbaaaabcbabdcacbabbacadbacdaadcaccbaaddaabddadabcdaababaacbdacbddacddbabddadbcbbdbcacbacbbdcccbddcacddcbddbdcddcbbccaccacaaadabbdcacdbbcbaddcbbbabcdabaaadcacccdaadcdddddbdbcbadcbbcaddbabaddbcddcabdbcbddaddbabdbacbaadcbaddbabaabbbbbbacccaaadacbbcdabbadabdbaccdcaaccabacabbacaabbbddcaccdbdccccbdadcabbdaddccabadcdbdaaabddbbacaaddcbcbcbadaacddadabbcbacacdbbacdcbbcbaccdccdaaccadbcadabcadddccdbcbacbccdddbcbccbbacbdadaacddbcbcdcdcbcacbcadbccadbdcacaabbdadbbddcbadacbabbbacaabaabcddcbddaacdabccacdcdcbaaccdbdadbaadabaaccccaacacbddbdbbddabccbacbddbcabacbbccdbdcacddbbbabccbdddbacaababaddbbcdccddcdccacccccdddabbcacbddaddcbaccbbdaadacccabbccababcadcbbdccbcbdabccabbcddbadabbcbbbbbbcddcbcbabcdbbaddaadbadbbbadabcaadadbabaacccbaaddacdacccbccbacbbccabdccbaddcabdabbbadddbacabddcbdaacaadabdaccacdadbacbdddbbcbdddbacddddddaabdaabacdaaaabbadbacacbcbbcbaddccaddcbbacbbcdccabbbaddddddcdcddaabdddabdbaddbcbccdcaaccabacbbadbbccbbccbdcbcadbccacbcdcdaaabbbbccdbdcdabaababbcdabadbccaacabbaaaacbcdbbabbdcdddccababbdacbdaabaaccdcacbaabdbbacccbccddadadaccdaaabbcaadabbaacbababcacaccdbdaabdbcaccbbbdbbbbaccdcbbcaabcdaddbdaccbdbcdbbdacbadcaacdbccbddaadcbadbdcacacccbbbbabbbbcabacaaddcdbaacacdbdaaadbcbabaaccdddbcdacbcdccacacdbabadcbdadbaddbdbccabaccdbcdcaaabccacabdaadaadbcadcacacddbadbcababadccdaaddaabddcabadbcdadacaaabaaccdcdcddbabdbddcacaccbdccdcdcdcbacdbddabbcdaddcdabaccdbdadcdcddaddabaacacacabbadcbcddadbddbddacacaabbccbcbbdccadbcbddbcbccadcccbbcdabababaaaaabddbaddbacccdddcbbaaacdddabbdbddabbbacabccdbdaadcccaaccabcbabcadbcacbbbccbbcacbddddccadddabbacdabbddcbbababadccdbcbdadacaccbddbdcabdcbcababbcccdbcdcdacacaccdccaaddcadcccdcdacabcccaccbaabddabaabcbacaccadbdcdabccbdddccadcbddccaacccdacbddcddaaadbaabcdabacadbaccdadcabbcccadccaaabcdccbcbdcdabbcdcabadadbcdbadadbcacdddaaababbaadadacbbdaacdccbccaacacddbabdabcabcbcaccccaddcbdddadabacadcdccaabcacdcbbddccccdacccbcacdccbddcabbacabdcddcdaadccdbababbccdbacbadaddbbadaacadcbccabdadbcbdacabcbdcbcabaadbcadacacdabcbdcccbcbcbdbaaacabdcabcaabbdbacbbccbbdbadddcabaacbbbdddbaddcdabbadbbbcdaadcbaabaaccacadcdcacbaccbaccbddcaacddbbcdcbabbdbdcdabcdcadbdaddcdaaabddaddbccbdaccaaacbadbaaaaddcbbdaddbddbcccdccbbbacdbdaacddacbaabadbaccacdcdcdacdadcdacbcbaacdaaddddcaacbcbddacbccbddaacaacacccadabbcadcbaddaddbcddbdcddcdbdbabdbcabbbdcbacbcdbdddbaddadbabbbaabbbdcacddbadbdbcadbdabdabbbcddbdacadddbacadbcbcdcdacbcdcbcccbacbbcaddabcaadacbaddaccbbdaccbcbabbdcadacdbaabcbcbcadccccbcbbdbbdccdddbaacacaababaaadbcdbcaddbcdbdacdacadbdcccaccbbdaababddbaccdcdddcbaabbacabadcdabcabbccdbbcbdcdbdcccdadbbbdcbcadaabbcdbadddcababdbbddabbddddbbcddacaadbbaccccddadcdacaabacbddaaabaacbbdcdaacacbdbcccdbccdacddbdcbbcddbbbaabcbacadbbdbcdaabadddacbaccadaabadaddaadcccbccdcddadaabdbadbadccdbcabbddbddccadaabaacabacabadacaacabacdacabbcbcabddbcaddcbdddcddcaaadbacacacaabcaccddaccbccbbcbacaccddbbccaaaaccbbdcbdccacbcbdaddaaadabbaddbcbccdaddbbccbaaadccbbcaddccabadddcbcdbdbdbadbcaabddaaaddcdcdbdabbbdaaabcaacbccaddcaaddcbbbcbddccaacadcbdaabbdaadadccdcddbdbadacdddaddaaccdcacabadacdbabbbccbbcbaadbacabdacbdbbcbbcabcbbcdbadbbacadddcabbacdddacdbabaaadcacbacadaaadcbccbccdccabaddccbaaadbaabcadadddddddbaacbaabccaccccacdccadaabdbcbbcdabcbcbacbacadccbbcadcabcbbdbcabdaaaabbdadcddacabdadacccabddcdddabacadbdbdacbabccccacdcbbaaccaccadbcabaddabadccacaddcaacacddcdcdaccaacbbdcdbdbbacdbbbdaaccabbdadcdbadabcbadbabcdabbcdbaddcabadaadabaacabcdacacccbbccbbbdacddcdaabdacbcdbdadbcdbbaddbadadcaddcdbbcdabcaaadaacdcdccacccbacaadabbdacbdbbacbcddbcbacabdcbdaacbbbbcdacbbacabbaddbacadbdbdbdbabbcdacdabbadbaacbddbcaacacdbbbbacabadaaacdabbdaaccddbcddcccbaadaacaccdbcadcabdaadcbcaaccbccaadccacdbabccdcaabdbcadcadddddabdbccbcdaabbbcdbdcacbbaacbbdddadcaadadbbddabaabddacccbaacaadddccbcbaddcabcbbcdbcacbcdcbcdbdccdbcbbdbdcaddaaadbaaacbdbccacbdddacadabacbdbcdcdbbdabbdbbdadabcaababcdddaadacbaabbbadcdcdaaacdcccbcacbbdccbddaddcccddbcdcbdadbbbdaadccddbbbdbaadddaadbdbdbacbacbdcdcdbaaccdbddddacbdcaacaaaaaccbaccbcabaaddbcaacadccababbcbbbcadddcdbbccbaddacaacadcaccbabcabbddabbdbddcddaaddaabcbbbacdabcbcadcbdcacbdcbccdadbddbdcbddbddcbddcdcabacbdaddbdaddbbbcccacbddcbcdabcdacaaababdaddaccddcbabaaadacbacadbcaabbdacaaadccdacdccaadcaddbadccaaccbbdcbbaaaacacaabaaadbdccabbdbaaaadacdbccbabaadadabcaaabccadbddbcccabddcdbabaacbbaaabbcbbcaccabbadadcaaddbdcdaadbcaabccbbcdddcdcdacbddbbabddacaabcdcddccacaaabbbbbbaabbcdbbbdccbccacdcddcbbcdbbacccbcbbababcbdddbaadddcddcbbdbcabcbcacdccbbacbadaaaaddcadbcccacadacacaacacaacbabdbdbbabbddbcaacbadbccdccdcaaaacddaaaaabbddccbbabaabbabdbaabadaddbcdbddccdbdacacdadbccdbcabcacbcbdcadbddcddddaddabbcacccbadabbcdadcdbdacddddadabbaacbcdbcaadacdbcacaddbccabddbccbddbbdcabbabcdadbadddbbbbaddbadcadbcbaccdadccbdbdcacdccadbadadadabccddbaaddabcaddcbadcacccabbdabcabbcbaacbbccabadcaddddbcabaacacdbcbcaadccddbcbdbbacdacddcbbbadccabddbbaccaaabbbaddacadaabcbcdabdacbaaccacdbcdbacacacdbcbccacaddacccbdcaaddccbcbcbcdcaadcdbdcaccdbbdbccbbcabccdbcbddadaacddadadbbababddbadcabccbddacadacccdabadddaccbaadadabbbbdcbbbdcbaabdacdbccddccdcbbbbaabdcbababdacddbcdcadddbabadbcbaaacadcbadbaadaadbbcabddcdcbbacaaadabcabdcbacadcaccaabdbddbadcccccddaacbddbcbdcaaaddcbcbabccaabcdcbbccaacadaaddaabccbdadcbdccbdaabbacbbcbbcbcbbaaacbacbcbbcaaabcdabbaadacdaaddacbcbdccabddbbbcbabbbdaaaacadbdabdddbdcacbdbccbcbbdcdbaabbcccbcdabaacdabdbadadcbdcabddccdcddbcabacaccbcbbabbdbadbdbdcbdbdddcbabbcbacbabdacabcdcbbaadddaaabbacacadacaacacaaddcccdadbddddbacaacadccbbababbadbdabacbaaacdacdddbccdcbcddcbdbcadccbdacdbddddddbcabdacaccbdbdaddcaaccaabddaadcdbbacadaaacdddbbcbaadcdaadbdbbdddbbbbdcaacbbcbabcacbcbaabaabcbcdaadddabdcbbddbcabdcbbdcabcbbcdbacbbaaabbadddabbcdcdbbccccccdaadadbadbcdadcdcdddabdbccaacabcbccdbacbcadadbcbddcbabbdcbcabcccbbdaacbaabccbbdddbdbcabdcbdbcacbcdaccbabbdcdcdbbccdbabcaabdbbbcbcbbbdbbcbbcdacbbcccbbbabbbcaccbcacbcbaadbacbbdcccabdccbcdcccaccabbbcdbdbdacbabbbadccdddccaadcacccbddcbbaacadbdadcdacabcdadbcbbdcddbbcababddaddbbdccdbbcabdbbbdadccbacabcccdbcabaabacacabaccdbaabbcaddddccdbbbadacddadbcababbbdcdcdaabbadddabdbdabdcdcacdcaccdbabdabcabbccabbdbadbdbccdaaddcdadcbabbbaabcabbacabdcaccabbcaadcbcddddadcdccbaacbdbaddabccadbddcbdcdaddcacbcdabaacbcdddbdbabaddcbadbcdacdaacbabacdbdbabcadcbdcbdabadddabdabddbdcdcccaabbcdbadbabdcaccccbccdaddbccaabdcdcddbacbdcbdbdabbbaaababaaaadaaddbdcacaabcabacacaddccabcccbdbdbacdddbbdbdaaaacbbbacddcdbcdcdcbccacaaadcdadacbcacdbbccbbccccadcddccbdbdcbdbbbaccddbcabbdcbbcacbaadcddadaadaaaccbbcaabdbabddddacbbbdbacaababccacacbadaacbadccdbbbacdcbbcdbdcacbdabdbacccdccccaadccbdcdcbacaaabdbbdcacabdccbdbbcccbdadbaaadbbadddacdadcbddddbcbadbbdbaaaddcddbaadbbbadcddacccdbdcbddbdbcbbcabbdbddccccaabdcbdaddaaababbdaabcbcccdccbdbcccbccadbcaaddabcadbacbaaaddddcacccdbbaaaadadbbcbbaaadddbadacdacbbdbdabcdacaabbbadaaacbbadbddbcdbbbddcaacddbacdabaccbbbcaabddbddabbaddddbdccabcabbaccdbadbaaacbccabbaaabbddccbdcbbdbcdaccadaaccacdbcbaddcaaacdcbdbaaacdacccabdaaccbacbcdaddccdaccbccabbcdadbbcdbabaabdbcaabdbdacbcaaddacdccbcadcccdcabccdbcabaababdcdbccabcbddcdcdcbbabbabbdaccacdddbbdcaaddbaddabdcdabcddddcbabacbcabbcabbabdcaaccdcbdbaaacbabcbdbdacdaddcbbbaaacbaaadcdcabcacbbacacbadaacbbddbdddbdbddadccadccdcbadbaabdbddcbaacbdadcdddacdcdaadcadcbdcdacdcabdddcdcacbbadccdbcccaabdbccbaabbaaacbacbdacccbccaabcabbdbcbdddbcbbdacaccaacccccddcdbdaaabdabdcbbabccbbaacacdabbaacacdcdddcaabacddadddbdbddaddaacacdbdaaaabacdbabacacdccbdacbdacbbdcabdccaaddbccaccbdbaccccddddbcdcaadaccdccabcdcacbcdcdbcabcdcccacdbbaadabbdbdbbbaacddbbdacaabbcadabbabcaaccdccadccbbabacddabbacccbbbbcacbddaabbaadcdaabacbcaadcacbcccccddbbbdccbccdbabdccbdbbbbabccddcadccababadcacbbbcbbcdabadadabdbdbbaddcadadabbcaadcdaaaaadbacdbbaabbadcbcabccbadacacdabbaabbdcadacacabbdcabdbdaacbbddddbbbdadbbadacddbdbdcbbbdaabadadbdaddcaaaddcdbabcbdaaaddbaadadabbcccadbbcaccbdaadbaabbcdcccbccacdbacccdcdcbaabdacacdaabbdbadcacddcaadcabcccdaabacabbcbbdbbdacdbddabbdddddbbddbaaacacacbacacabcbdbadbcacababbdbddcbcaaacccddbbadaadbdbddadbdcbdaccadcddacdcdabdcbbcbcdcabcababaabddbaaacababcdaabbadccdbbcbbbcacdccabcabccccabdbbbdbbcdaddbcabcabdbdbdcdaaaabdaddbacbddbbacdcbdbbcbccccbabdaabdcadcccacdcabbbadadadccacbdddcdacddbdabadcbcabbaacbbdcaddbbabbcaddbcdcbadbadbaacbbddcaccbddadcabaccbacbdcabcccdcbdcabdadaabbdcbddaaccccabbcbdcbbbbccadbadadbcadcdbdbcadcacdbdcbdbdcdcbcccbacddddaadabbaadaacdaddbadaacddbcdcaacaaccdcbacdbabbcdddaabbbcbacaacbaacbdacabbacaadccdbabdaabdcabdbadbcbdaaabccdbaaaabdbddcdadbbdabaccacbddbcccaabccbbadbcdaaddddddddddaaaacdaaddbccdaacaddcddadcbdacccdbbcabcccdbbcccadcdccabacdaabadaadcaaccaabaaaacccbcabbcbabacdddddabadbcdbaaaabaaccadddcddbbdbacddaaccaacadcadbdbbabcaacacbacaacbccaaaadccbddddcacbaababbdadbdcaaaabdbdababddccdcbcbcacbcdacbdccdbacbbbbcbdbbbbdaaddccdbcabcacdabbbadbabcbdadabacaccababcdbadadcbaddaacaadacacddacbaabcacbabaacdbcbbbdccbdbcccabbdbadcbdcadbaaaccdabcbcdaaaddddbcbdacdbdddbbaacbddcdcbaaabadddabcdbaddacbacbdcbcdacadbdbcbccadddddbadaaacaabcaccbcbcdaabbbdbcaccbdabaaadcaabbbcdacbdaaccadcccdadbacdcaabaaacddadbbccacbaddcbaacadcaacbdacddababaaacaadccccabddbcabdaabbacadbabdbacddadbaddabdccbdacddbbdcdcbbabdacbcdbaaabcdbcccbbbbdacdcbaadcaccdaddabcbaabdcbdbcaadbbbcbddccddccaccabcdcdbdadcadcddabbbcdadaaddcccccdcbbdcdaacbbcbccbddccbadaaddbdcacccbbbcbdbbdbbccdabdbbbbcbbbdbbcbcaacbcbcadbdccdabcccccaabdaddacbbaddabcbdbbadbbcdcdbcadcdbbcbccbbdcbcccaaacbbacaacbabcaacdcccccacbccbaccdcdadbbabacccbbbdaaccabcadccaccdcdbccbabdbadbbccddacdaaacaacbadddccababdcbaacacbcbcdbacbbddbddabddbcaddbcccbbbabbdacaaadcadaabbabdbbabbdaddbaaadaacacbdcabbccadddbbabbcdbbbbbdbdccaabdbddddaddabcccbccaaacbbcccddacaccccadbabababbddcddbdabbadbcddbadcaabcdacaadcaccdaccbcaacddbbadaaadabbdbadabacababdaabbaadacacdaaaadcdccdccacaadabdbcccdbcbaddcbcbbdccbccabdadbcddbaddbcadbcbacadddcccbcdadbddbaddacaccccccaaacdbcbbdbabbddaaaacdddddbcccabbaabbbdbacabbdbdabdaddcccadaddbbbabcddddcadbcddbcdcbbdadbcccbbbdcabcccdbacadddddccacaccadaabcbddabbbdddbabcabcdabdadcabbabcabbdbacabdacabcbcdbbbadaacddbbbadcbaddaaababcabbdddccddaccbcbbaabccdbbddaaddccaabcdbabadbdcdcbbadbaccdcbdcbbbcaaccddbbddcabbdddcadadbbbcaaaccddbdadbabacbaababadbcccbcbddbacbbcaccdcbaccadcbbccacaddbcdacaddcdcddcbbabbcdbbdacdccbcaccbcdcaaabaddccbbcbbcddbcdddbccdbacaacdcbbaaadabbaaaacdcacdccbadddabcbcbddcaccbcaacdadbaaaabbbbcabaccdcddcaaacadadcadbbdcdcbbabccadbcbabdaadacaadcccddbbcdbabadbaddbbacccbcdaaacadaabbbdcdabbababdddcbdabaacbdcacadcbbbacccdbcbbbbaabbbcacdccdbbcabcdbacbbcaadbbbcadababacccbdbcdcddcccbcbcadcdddddadadadbdacbbcadbabdcddbabccdbdadadccbcbbdcaabaaaadadcaccacdcbcbcbdaacdbcbbbccacbabaccbddadcbcbbbadddadacadbdbacddcddcabbdabdbadbabccbcbadabccbbacacccbbcabbbdbadabcdbbacbdbabccdaacadaaacdcaccdddaaacccadaacdddcbcccbabcbdcaccdddcaccdcadccdcdcdcbdbadaddcdacddbadcbcadccbdbdbdaddddacacaaadaabbbcdbabaabaadcdaaabdbdbccbbcbcadaccabdddbcddbbbabaaddacbbaccabbccddbacbddbacdbdacbaacabbdbdbbcbbacadbacbadcbaabcdabbbcacbbcccdbbdbdacbbbbaadcaabacccdcbbdbbacddaccbcdddaddbbacdbccbaddadbbaacaacbcaacdbaccadaccddcdcbacbbdabcacbbddddadbdcababbccabbaabddcbaadcbdccadccccccaaadabdaddaadddacbacaabbcdcccacbcbcccbdaacbbaabcabcdbcddaccabbccabacadbaadbbadcbcdcbacddcadbabccbdbcbbcbcbdbaacbbbcadccaddbacbaddaaacbccccbadcaaabcaddcabbdddadcdaaaccbcdaabdcaabccddadccbbabacbaacccbcdddbacdaadcddabcbdbcbaabcccbcbcbccdabcbacaacbadacdbacbdabcacdccacacbcdcaddaddadcabccdbcdaaaaadddddcdaddcabbdbdadacdbbcbabbdabdddacbcbdabcacacdddadabcccdcdddbcabccaccdbcbcaddbbbdbaaadbcabcdcdbdcdaababcacdbcaddbcdbacaccacddcdcadbcabaddaddcddcabdbbcaadbbdcbbbbbdaaccbcbbcbdcbadbbddbcdddbcdddaacbdaccdcbdcdbdabaddcbcddaccdcdbcccacbbbcddbdaaadbabbcacaddabcdbbbbcddbbcadcbccdbbcbcabdcacbaadabdcbbbadabdddbcbdcaaaabddbccbacaddccbdbcadcddaaccdddbbaadbabdcbbcadccadbddcbccccddcbccddbdddcaaacbdcaacbdcadcacbaccaacdbbdbbbacadcccababbcbbbabbbacddbaaaddcaacbcadcdbadaaddaccabcdabacdcacdddbdaaddddbccbadabdadcbdababbbcabadadacdaacbcbccdbdbaacbcadacbdbadddcabcbccbaacbbdcdbbdcbdabdaccacdcacbaddddcbadbaaadcabaadacaacdbaaabadddbbabdaccbcaadcdccdaadbdbacbbbcdbacccdbacdcacbccadaaaddcddbacdaccddbccbbdbdccbcacdcbbaddbaaaaddabccdbacabdbcdcabdcbbbdadbdcdacadbbdbadaabcbccdbdcdcbccddcacddddcaaabcadaaaacdddcbbdccdabaccdbdaccbdadcccaacaacbacbcbbdccbbddcddcdbcbadddbdbddbdadbacacbcdaccbcacbcabadddcbabcaacacbbacbbbacadcdbccdabbcacadddcdddbaacbdaaacddadbadbacdccaaccabacdcaaaaaaadddacdcdddacccdddabcccaadaddddadabbabddadccadaccccdcdcbcdaccbbbaaaabaaddaddcbcccabdacddcacacbbdbdbaccdadcbcbdcbcddaccbadadcaaccccdccbaccbcdacdaaddbcbddddbbcabbbabcaaadacbbcbadaccbcdcddccccabdbdcbdbdcbbdcdcbacabcdadaaaaaccbccbccbbbcbaccaabaadddddcbdbbcbcdbadbabaabdabddadadcaaccddbacabbdbcddbcdcbcdbcdababbdbcacabbcaabbaaabcbcadcdaaabacaabdcacadacdcaaacddbccbbbcdadccacccbadbdcaaaacbddbcddccadacccdbdbaccbdacdccdbdcbaabccaccbbaccdcdacbaccbcbdbbddcadcacdaccdbbdcbbcbbcbcadadccbbabaddabaaaabcabbcdcadcacacacbcadabacdbcbcbdbcddcbdabbbacbddbaabddcddbdaabdcdbccbcdcdbabcbcaababdaccadcaabacadccdddababdcaabcdcabcabbbbcacaccdccdabaddcabcbbcaaadddcabaddddccbcabcbaadbcdaadcbcacddbadacbcaadadddbdaccddbbdddcbadcdaadbcadbbbbadabdddccbcbdbdbcbdbddbbccbbbbcdbccbbccdbcacdbabbaabbdcddacaddbdaabcbcdccdbabcdbbdbcdaaaaadccbccdcacbdccbbdbbcadccbabdbdcddbbccaaaaabbcadbcdaacbabbbabdadadbcaadcbaadcddbcbabcdbbacacdaaccbaadcadabaddbdaccbccacadcbdcddcabcabaabdcbcddbdbcdbcdbbdccdbccdaaababcadcbdadaccdaccaccdaccaaaaaabbdbbcabddccaabbbbcbcadadddccccdcadccbcdadaabbbddabdbbcaabcdcddcddabbdaaccdbdbadbadbabaccddbdaadcdbdbdbddccdcaaddcaddaadddbdacdbdaddacdacbcababccdcabbdaababbadcabdcabbbcdadabbcaccbbbdcabdcacddcbaabbdbbbdcbabcddcccbacaccddcdaaaaaddccdaabdabadaadcbdacbcdaddaddbaccbdbaddacadacaaaadababaacdbabbdbaddadcbdcacdcbadcdaabbaddacdbdcddddabddbbdddcbdaadddcbdcadabbbcddabccddcbccadabbadddacbcababcacacdbbcccacbdcdcbbcbadbdadaccaabccccbcabddddbbabbcadaabbbdcdcdaaaaccabdddbadcbacbaddacaadbdbbbdbacabcbbbaaaccccadabdaabaccbdacaaaadddbdcdddbddbcabcdbacdccbcaabcbbbaccacbadcadbadaaaddccbaaadacbadcddacdbacbadbbdcbbdabddbdaaabbcdabcaaadddaadcaaaadbcdcddacaddadddabaacdbababdcbdbddadcbaccddcaacbacbbccdcabbbcbbbdaadddbabcccadccdbadbbbcadacdddbbabcbbbddccdadbbddbbcdbdccaaacabaccdddacbbdccdaccabababdcdacbccbcdbdabddaadbcbdddbbdbddabbbaddaaadbbdbaaabbbbacccdbacbdacaacbbdddcaddcdbbadddccbadadaacbbaababcbbaaacbbdccacdcadbbbdccdccbdcdbcbdaddbbbcdbcdacaaabddcbdababccbccaadccbcdbbabbddbdcbbdbaaacbacddcbacabccbbaabcddbccbbccbbcccbabadadaaccbcdadcaddaddadbabcdbbbdacabdcabadddbbcdabcbadbcbdbccabbdbbacdcababaccbdcacbacbabaacaddddbcbcbdddacdcadccbbaadbababaacbddbbccddcddbbaddabaccccadbcdcacdabaaaadabcdacaacadbdacccbadcacbcdadcbbbcaccbaadcbbdccdbcbddabbacbadcadcacaccacadadbbddcbbabccbbdddadaaaaddbbdbbacdbdcadacadacaaadbcacbbbacccbddacbdddabcbcbabbabdcccacbccdcccbaccaabbcbdabaacaccaccdbaddbaabdddabcdaddddcabdbadcdcaabddcaabbdbabdddbacaaacaabdacacddaadccadcdabdddabbdbcccdbdaabccccbacdcccdddaaddcbbdcaabcdbdbaccabdbbdcccbdadbdbcccdbddcdbdadcbbdbacdacacdacbdadccacdbcbadbcddcadbcacbbcabbddcadacbaabbbabacadbbdcadcdaacabcdbadadadcbbdbaacdabbbdccbdcdcadcbbbcbbcdbdcaabdbacabbcaaabbadbcbcbdccbcdcbbcabbcbcddaacdbdcbcbdbbbaadccbaadaaaacbbbcaabadbbbbdcbaaccadabbcbaacdbaadcdaabcbbbcacbdbaadcabacacdbdbacdaccaccabaaddadadcacbadcbdaabbccaacbdadaaadddaadacbaacdadbddcbbcababdcabbbbdbccddbacbbcacabdcbccbccdbacdcbaaaaccaccdccccbdbdcadddcccaaddabcbcbbabbcdccbabcccbddaadcbcaacbacaabadaddacdbbbddbdbbdabdddbcbdaacabcdbcabcbadcdabacdadbcbdbbdccccdccdadacaddadbadaacaddacabacaaacbdbbcdadadcdcdabaabdaacbaccdbaabadaadbabdabacaacadccacaaccdcabacccdbccacdaddaacdadbbadbddabbbbbcbcaddcdadddbaaaaaccbdadbbcccaaddadbbaaccadaccdcddbadbbccbdbabadcdcbddbccbdbdbaccdbbddcbbdabdacabddacdddaacbdbadabaabcdddacbacbcaacbbdcabcdcabbbaccacbdcdcddaacdccaabccccdcacaadcbcdcdaacccbbadabadcdcbccacbcabcacdcbbaccbaaddbabbcddddbbdddbbcdabbcdaccbbccbcbcadbadcbccacabadcdcadcdbcdcbddddaacbdaacaccdcbcdcbabdbacabcadcacbcbaacbcbccacabbadabbaaadaacaabbabacdabdbcdbddabadabdbadcddaabbccdbdaddaaabbacbaaaabcbbacaccbcbaaaddcacbbccccaacbbaaacbaaacdcbabdaddbcaddaacbdcbdccacbabbdaaaabacdccbbabbcaccccdbcaccdbdcaddcdbddbabbadadaadddbbccdccdaadcbdaddabddbaabcacacdcdaaacddabbadcadddbbacbccabaccbadadcbbdccadcadcbcddcacbccdaacbdbdaabacddaaccabdbaadacaadbacaadbadbbacabddddcbdcdaaaccdbbcbbcadbacadacbabbcacdbacbcadacbbbaaddbcdbdacddaccbadcbadbcbdcdbacbadcbcacdcddcacbacddddacadabdddcadccdabbdadadccaacdccadbdabaacabaacaddbdcdadaabbddddbbcaabdabadccccababbcdbdbbcadcbcacdcdbaabaaccbdcabbddbadcbcaacbacaabacddccbdaacaacaddadabdacbcdbdbcdcbbabdcdabbbbdcdbbdddacdccbdbdbabaabbaccadbddabdcaacacacabbabcacdddddcadcacdbbbbcaadaccdcdbbbdcaddcadbcaaddbcdacaaadcdcdbaaddaccabdbbbadbbbdacddacabcccdabacdccabacbabaabddbcddaaabccbadbbbbbbbbdabdbbaacdbddbbababcdbaacddaddbadbcdacacbbbdccbadcdbcabdcdacadbdcabcddcabddaaaddcbddadcdaadbbbdbcdccccbbadbadbcdbdddcdbaaacdaacaccbbabcdbbbadbaccdadadbbbabaaddccddbcacddcabcbbacbcabdaddcdcdccaccbdabdbbcbccaddccccdbadabddbaaddbadadcbcddcbcbbaadadadbabdbbaadacccbacbaaabbdcbacdadbbdbcdadbabadababbbbbdbaabddacdaabcadcaddabcccbcccdadbddacbabddddbbccbabacabbbaacbdbcdbaacbbdbdbaddcacbaadacbddbddaacbdaccbcbacbbcbcbddddaacbaadabdddabcbccbaddaabbabbbdddddaabbccadcababdcdbbdabdbddddaddccbbdacdbcaabdbbcdbcdccccabbadddccabcbbbbcacbcbaabcadacaabbaadddcaadddccdddbbbcaddcaadcdcdccdcddaccbdbcabccbaccdbacddaadbcbcdadacdbcbccbdadadcbcddbcdbaccaacccaabdbdcbccbcbbbcacaaaaddcbcdbcdaacbdbdcadcbabcdaaadabadacaaaaabcbddacbddbbadbcabddbbaabbdaadddaababdddbbdccbacdaccbaaabbcadcacacbabdabccabccdbcbcbbbdadacbcadbddcdddbcbddaaaccccdacbdcdbbccbdadccbdbbabccdadddabdaddadbbcaddcdbadddcddddababccadaaabadaddccdbacdaabccaadcbdaadabbdbcdacaaabcdddcdcbbcdaabaaaacbbccbcaddcacbdddbacddadbbbabacbbdbbbbdcddaccabdaaabcdacdcaadcddaacbaadcabdbaaadbcadbaccadbdbabdabddabdddddbdadbdadadddcccdddccdbbabbcdbbdbdbaadbaddddddbaccdbadcdbddaccbcaccccbcdddaacabaddccbadbaccbadddbccbabcbbbaababcdbbbacaddbccbbcabdcdbcdaaccdcabddddacabadccaaaccdcdcadcddaccccccaacaabdbadaaaddbcbacacabbadabbcdbcdaaabbadaccccbacadbabbddadcdacddbabcbadddbdcccdccdccbddbabbcbbdcdaccdaddbaadcacccbaacaaaacdbaacabaddacaacaacabccbdbbcbbbbaaccdccddcbbbddabcccdcbbdacbbaadbddcbcbbccaaaaabbbcdaacdaabcddabcdccdbcccbbcaaacdadbbbadcbcadaaccdadaddabdaddccacbdbdbcacbaadbaaaabdaaaabaabcaacdddbddccadccbcddcbddcdadddabdbbabbddbabbaddcaccaaabdbdaabddacababddbdbadddccdaaacbadcabdccbbdbcadacbcddbaadbcbdccdbcbbdbcdbcdaadacacdbdcbcccdcbcbabbddcddacccdaacbdbddacdcbbddadcdcabbddaabdcacbdcbcbcadbcbdabbcaacddbddadddcabddacbdcaadcbddbcdbddaacbcacbdcadaaadbbbdbdaaabddcdbcbbddbaaaddcbdcdccabbacdcccabdbdcbabdddaddbbcbdcabcbddcadcdbccdccbacacdccabbacdadacbbdcaaccbbabbbbccaaccdbbdcacccbdbdcbacaddccaddcddaabdddddbadcaddddabdadddcccabadcbcacccdadaddccacbcbcdabcbdcbabbcadbacdaabbbabbcccbbabdcaccbcbdadcdcbddabaaccddacccddcbababddbdcbaacacbdaabdadaadaacdacacbacadbaccaaccdbabbcccdbcacbbcbaacadadababdbbbccaaaadaabcbacdcadbddbacddcbbadbbcdcdbbdbbcbaabddabbbddbbbcbddaadddbbcddbadacbcadcadaaaabdcacccddbcadaaacbadaaddabdadcaabccdabbdadbddbdcbbacbdcaddaddabadcaccddcdcbcdbdddbacccaaccdacaddacbbadaaaadbbbacbdbcbbdbbdaaaaccadbadcdbadbcdcdcbddbaacbdccabccdddcabccbcacdcadcbdbacccadcaccbdbcdbccbdacbaacdcdddbccabccdaadcabaacbbcdadbddaabdabbcabcddddbbdbbdbddadccbccbdcabdbbadbabdadcbbcabcdcabacadaddbcdcacbabacbacccaabacabdcdcbcadcbcdcbabddcabbcbaabcdabcdacdbbddaabbaccaabdcddabdadddcbdbaababaccddadccdaadaacdadaabdbccdabbaddbaacabdaaadadaadcdccbddacddcdacaaacdbbbbdbbdcbaddbdcddcbbbbcaaabbdacbbbabdcdbadadbadddddcacccabbbdcacacaaaaddadbabdaddacccdacdadacadbcbadbcbddddccbbccddbcbbacdbbabbbcdacabacbbaaccaabbadcaabccccabdbdaddbcddddcccdccbbdbcccbbbcccddabdcccadaaddaaddaaaaccadbbbbbabbcdbcdaaddbdddacabacddcccbaacbaaccdcccdccabbcddbdacdbcbbcbcbabccababdcaaddadbcddcdbaadbbbaaadbcbcccbdcdcbabdacacdaddcdcbabdadaccabbddabdcacbccddadbbbbabbddbbaadadacbbcbbccdccccbdabdcadadbbaccbacbbaadbcacdabcddbacccbbcaddabcadaccbbdadccaadbcabcbacaacdbcdcadacabcababbabbabdcacadbacaadacbcacbcadddbcbadabaaaaabcadbadbddccbdaddaaabbabbbcaadbddccdbadbbbdabbddcbadbdabbbbaadabddcaaddcdbdccbbcacdbdbbdaaacbddddcdddadcbcdacddbaaccbdaccadcbabbcbbaaacbccbddbccbdccbdbbaccacdbbabcbbbadcacacdbcbbbbadccabbccdbcdbbbccbabdaacababbbbcbbdccacaaaccddacbabcadcdcbbbacbbaddabacdbabcdbccacbadcaadbbabdcbbabcbacdababbbcbaababbdbcaacbbdbacaabbdbacccbbaccdabadddaaacaddbacbddbdbddbbabcbbbdcbadcacdabbdabdabdcbdacacaaaabcadbddadccdbacbcdccbddbabbdbdddcbaddcbadbadccabdacabaadddadcaaacdadbddbbacbccacbcacbcadbbcbbadccabbcabbdbbddbabdaccdddaadacddbaabadcabacccbdadbaacdadbcbaccadabccbbaaadccdaaacdcadadcaacbacacbbaddccabbcdbbadcabbabcacaadadacbccdcbdbbdbccdbabbabbbacabcaadabbdcaddcbcdcdaabcdaacdbdadbcadbdbddcdcdabdaababcdaabaccddacdabcdaaacbbabdbcbbddacdaaaabdccbcabbbaddadddcbbcbdbbdbcdabbcccbdbdaacaccdbcdcddcabcadddabcbdcdaccaccbdbdaadddcdaaadcddacacbabcbcdbbacbabddadaacbdbacccccccdddabbaddcdcdbdbccccddbcbaadbcbddddbcccaacbcbacddabbbadccbbcccacdadbccaaaaccbadbcdbccbadcacdacabbacbdabbbcabcaaddbdbbdadbccbdadcbddcbabcabbdccbcccddabcaaccdadadcbbabaadaabcbadaacbbbdbbaacdaacbcbbbdbdbadddbccbabbbddcdddadbbaadddbaccdbbcbacdabcbcdcdbabdbcacdabcddbddbdaccabcacacdbbccbcaccaccdbcabdadadbadbacbcdbccdadddcdcaadddcccabdbcddaaccabaadbcccacadccdcbbcaaaddcaabbabddcccabbacbbdcdcacbcddcddcaddadbdacdbaabcacbbacbbbddacdccbbdcbbbcdbabbbccadbdbbbdddccbdcdcbcdabbccdcbaccacbcacdabbddcbaaccdcabbcbbdacdaaabbdcccbabcacdcbacbacdbcccdcadcdcabdbddcbddbcdabddccdbacdaabcacbbacdbbacbabdbbcbcaaadbcddccdcbcbdbbddadbcadcbcdbbbccdacbbdddbdcbdddccbddcddabbbdbdcacbaddbbdbbdacdbccadddacdabdbcaddbbddabbccbddcabbacadacacdbbccbdabbacccbdaccddddabcdcaddabbcabaacbabaadbbadbcddbdcbbcabdcabadbbbdacbabadbacadddcdcbccdbcabcddbdbcdbbdadbacbccbdcdacccacabcaaabccadacdaddbdddcdacdbdccbdaaaacaddacdabbacacddcbabdabbcbbddabcabbdcbbcbcadaaacadccdbbbcabbcacddcbddacbdabcdcbdcbadcdddcaccdccdccadcbdcddddddabccbbcbbdbdcdcacdbbacddccbbddcdcaadbbadadbbaccdcdbddaccacdadaddcdaacdbdcbcdbbbbaddbccdbacbcaabbddabcccccbbbcadaabccdbdbdabcdcbaadababbdbcbddbbdaabaaaaddbbdcdccccdadcbacdbbbdcacbddabcacdddccababdbabdcbadcbdbdcbcbcbbdbadccdbabbaababbaacbcaccbbccabdbbcdccaabdaabcdabcacccaaadcdbabadbcccbcdbcbddbdcbbadaaaadcaacaccabddcaddaccbdacabadcccabcbbddcdcbbbcacddcadccbbccccbdccdcabddccbbccdccccacdbacddbdcbcbdcdacbdacaaccdacccdcaaadcabdcacbccbdadaacbcddbcbaccdabaabbbbabcdcddcbabbacbabcddbbdcaddadbcbbbdcadaddbddcabaabbbdcbcabdbbcbabcbbaccaadbaccbdaacccdbacbabdcdbccddbcdadbbcbcdcccbbddcbaaccdcbbddcbabcbcaaadbadacacaaddbbdbaaaabbcbddaabccdadbadaacddccccddddabbbdddbcccdadbbaabbbcabdabccdcbdbdbabcabaacadccccadbbddbadbcbbdddcaaacaaaddbaaaabbcdcbdbbcbcddaaddadbdaddcccababcdbacdacadbbcdaacdaaccbacdccbcdbcccbdccabdbdbaccdbcabababdbdaaadcabcbaddadabddabccabbaabaabbbbdbcdbacbabbacacddcbddaaddcbabcbbcdcadbbabccbddbbcbabcdaaccbbcabacdcbabbcdbdaddabcddadabacbdbacddaddacbacaccdaacaabdbdbbbacbccccbbbdcacdbcadabbbcabcdaaabdaaaccaaaacadcadaaddbccddadcccabcdacabcbabccadcaadcdacbcbacaccbbadccdcbaadbacacbcdcbbdcdcadadcbbbbcaaabdabaabadadbbcadaddbccdcaabdddcdabcadbbddcdadcadbcaddddcadbbcdadbcdbdcdadcdabdabcddbadccadbdabbadaaddaaacadaadcabbabaaabdddccbaadbdddbddbaddbdaaabacdbdccdaaddbbcadcacbabcbccdbcdbbdaccdbabdcacaccaaddacadacbbcddbaaccbaacdddaaacdbbdadacbcbccdbbaddabacdaaadcdcddbabdaabbbdacdaddddccbbcaaaddadcadddcbcaacddbdcaabaadcdbbbdbbbcaccbadccccbbdabccdddccdabddacccaddabcadcbccabababdadddddcbacbaddaabbaadbaccbadccbbdcaaadcbcbdcccacbdabcbcadaaaddddaadcbbdbbdcdaaacdabaccdbbcbadacccdacdbbaaaccdaddddbcaaccbaadddbbdadbbbbbdabaacbccbadcdddabadbbccbdbcddadadadbabddacbddacaacbbdaccaaaabbcbbbbbdaaccbadbbcbadaddbdbdcbbadbcadbdcdbabddadbbcccdaaddcdcdaadabbcdcdbbcddadddabaddacdddcdaddccabccccadaadcdbbdccccccbacabaccdbcbdbdbcdbdbabdbcdccdbabbdbcdbbbcccbcabaadbdccbcdbdbbcabbaabaddcccaccbbccbabcaccdbdbddaabaddcbccbaabccbaaaddaadddbdbbcdcdbbabadacaacdbcbacadadbdcacbbcbbbaacccbdbacccaaadcadcbbaaacbdaadddcadbcbdaaddcdabbcaadaabddccbadacaccccadbbdbbbbbddbcbbbacddcaccbcadcdaddabcbdcaadbdaabdbbcddacdcddcccbacadbaadabaddddbababbacadadcaddddadddddddabbcbacacaddcabbcbadbdbadddaabaabcabcccddcdaadcabbbacdcabbdbcdcdbbccccdcadcacbadaaacdcbadbcdcbdaabbcbcddddccdddcbdbbdbdcdcdcabcbdadadbadbbbaadcdddacdbdaddcbcabdddbbcadbaddadbaadbcabbdcabddadaaababadbbdadbdaacccbbabdccdaacdabddcdcacccaaaccdbbbaadadaadbcdcbaadcddbabcdbaaabdaddabcbcabdcdcaabbcbdcdbdccdcdcdbadacdbcdcaaaccccbbcbbdaccbcbbbbcadadbabbadabdbdaadcccbaaadccaadbbcccabaccbddddababababdabbdccabbabbacccbcbbacaaacacdbaabaddccdcbcdacdcadcbcacababaccdacaaacbaddcdbcbbcbbcbcadbdcdbddddccabadbdccbadaabcbbacaddaccbbaaabdcddabadbccbccbaaabbcbdcccddcababacbcbdaacacaadcddbdababacabcbcaddcdcbaadccaacdccdcbcdaacabacddabcccbabcccbadaadaaadbabddbdbcddaaadadacadbbaaccbddadccddaababbbadabadcacccacddccbabadadadcaabaadcbdbaaacddcaddacbacccccadabbadaccbabcbdbcbdbdccbbccbcdcddbacdccabababdccaccbabccabbdadcacacccbcabcabcdbadbddcbddadacbcbbdcdbccbccbabcdadbcbdaccabbbaadcccbbdbdbdadbdcdabbbccccababdbacddbddadbbdcaacabcddacbabaadaaaddccbdcdbcacdcdbdabdacadacbdbbacbcacbbccbdbcdcbcccddbcbcdcdcdcaaaadcbbdbacbbcdddaaaaabbbbdcabdabcadccaabddaaababcbcabaddccababacbcabccbbcdbacdcbdbdadccbaacbbcdadcbcaacbcaccaadddbdabcccbdddacbcdbaaaaaaaacbbcdddcccddaaccbcabbbcbdbbdcbcbadabbccdabadbcabddacacbbbdaadcaddbccabccdaadbccbdcccbddcccabbccaccbddccbdadcbdbbbadbbaadbbaddcaddcddbcdcddbdabcbcadbbbcbcccdabacabcbbdcbcbabcccbabcabababaabcbbabcdcdbacbdcdccbcddcdacccbbddccbbdaddddbaabbcaacadcdacccacbdcbdcdcdaadddadccaacbbaddbbbbbcbcadddccdcbaacbccddbbadbdcddbcddcabbccccbadccbcddccabcdcdddcbdbabddacdcbbbbdddadadcaddbdabaabdaadccddaaccbcaabacbcbcbccbccabbccbcdbcbbdabcadcdcbbbcadcaadbdbacabcbcbdcadaacadcbdabacbdcacbcdaddabddddcccbcaddcddcdccbdbbacaccdcbaccccdadcaccacdaaaacaaabccccacaacdabdcbccccabcacddccdaabdcddcaaaaacdbdbbcabbddabbabcadcbdbcdadbcabbbaccbccbdbacbcccbdcdcdbbaabaaaaaaabcbcccddadaadaacbcadababccbbdbaadaaacbacbabababcbaddadbbbddbdbadbcdbabbdababcbddccbbcbdacaaabcdababaddcabaabddaacdbdbddcbdbaaddbcdcadbaaaddaaddcbbcdcacbaadabcabadbdadbacdbabbdaaddbddbbbacdadadbccdabdaabadcdbdbdbaadccbbddcaddaccbdbdbccbdcdbaacbdcbaacdbdbacbdccbaacaadbabcccccbcbbbadcccabdababcaabdadbcabbbdabdbdabdabddabcdbdacddccbcbbdcabacbdddddddbcbbacdbbdccdbddddaabbabcababcddbcdccdbdbcabbdacbcbbaacbbcbacaadcadbbaadaaadcadbdbacdcbdabccddcababddbcdabacbacaaacbaddbbcaaadbddabdddbcbaccdaaaccbcaccbcdddabcadbadaaccccdbbbbccacbcbbcdacdacbcdaaddaccbcbccacabcaaaddbbcaddbccbaadbbdabcdaaadbdbabdcabccdbddcacbaadcbccabddaabbdbddcadbbdbaccdbcaacbdabccccccdbbcdbabdacbdcddbacacadcbbbcbccbddbddacaabaaaddadcaddccabbbbdacacbcbbdbddaccbcababccdabdbabaacbccccdacbdacaabaacabcababaadbaacaccddbcbaabbbcdccacaddddcbddbbdaacccbbdaadbbcbbaccdcabbcdbbabcbdcbbabbaddaabddcbcaaaabcddbacbccbbcacaabbbdbaacacbbdcbadacdbacdddbcadbaacbdcbdbabbdaccdcccddabcacbdbadaadacaaababbadbdacaccbbbbcbdccdcbcabbcbbcdbdbbabaacadaccdadbdaabbaccbbddcabbbaabbdcbccdbbbabbaadcabaacdbaacbbaacabbbcdccadaaadbcacbadbbabaadcbadaababdbdcdbdcaacdbccdcdbaaadaabdbcbbddcdabcabdcbcdcacdccdbdbabcccbcaccbdcdabcabcacaadcaadcaaddcbdccdbaaaccabbcdcbcccddccbbbabcbabdcbabbababbccaacbabbbbdbcccaabcaddbbbabbbbbcdbbaadcabcbbbcbbcdacdcbacbbbddadaccbcbdcccabdcbbaddcabccabaabddbaaabdddddbdbacddcdaabbdcaaccdacaaddbcdddcaddcdddadbabdcacbcdcbacbacaadcdcaaadbccbbdddcaddacbdbcacabcaabbcddabcbcdcabdabddbacddcbbccaabcacddcccbbadaaaacddbaaacddadabdbdbbabccccccaaccbacdadbbcbcbabbbabcbabcddabcacadcbacbcdcbbbcaabcadbbcacdcccddacbcabddabbadddaaaaacdacaaccbbbbdabddaacbadababddbbabbdcdccbabdaaccdabbdaacbaadccdcdbcbaadacdbcabccbcdabcbbcbccddccaaabcbcdbddbbcddcaaacdbccdbbabbdbdadcdbcabacdbbcbbaadacdcabbdabbccadabcbbdadbadcbbdcccdddacaacbabcdcdacbdcbbcbbabbabadcdbdcabddddccaccccabacbdcbcbdbdadbccbadadbbaacdbdcababaabcaccacbcaaabacdccadcbccababbcbbbccaccdacbbddcbbbabaddccdddccadabddddcddaaaadddadcdadcaabdadbddadabdcabaadddbbcddcadcccccccadbdbbbdbabcadbccbcacbccbcdcaddccbcbdbcaadcbdacdddbbcdbccbaaaacddccdbbddccbdabaabbdbddbdbcbcbcabbcabdbbdddabacadbcdbdaccbcaaaaddabbbcdbbabcbacaacacccdcadaaccdbbabccddabbcdbaccdcbcbbaddcdaccbccbbdbcbbbcacaccdbdbacddcbcbdccdbdbbdbbcacdbbdcccdaadbcdaadcdddcdadabbcaaddbdcdcdbcccbbabdddccbbbcaaadadaaaabcbbdddababdcabcbcdddddbabddcddbadcaadaaadcbcccaccacadcbdabadcdbdbcbcddbaaabbabbccccdaccdcbadaaccdadaaddaacdaacdbbdbaabdcdadacadbccdaccbbcaabcdccbadddcbddbbbcbdcbadbbbbbdbbbabdccccbadbcdbbaaccadabdccaaadbbbdcadacbbdaabbacadadbdcccbdcaaccabbaacbbadaadcbddaccdbbbaacbcccddbdcadaabbdcadcdbbabccadbbddacbddbbcacadaacccadababcdcbbbdbabbaccacbbbadbbaddbadacccbdcbabcaddcbddabaccbddcacccbbdaccacccacacdddadddbbcaccabdaaccadccadabccbcddcabccdabdbbaaaaacbbcabcddcabcdcbacbdabddacbdaccaabbaccbdbbddccccacaaabccccbcbaadbabadcdaabaaabdcbbcacdcdbdcadacdaabdbaadcaabbdcbabdbabdaaacdbbdbdcaaabbacaddbcddbcbbddbcdcbabdadbbbdcbbcdbccabbcabaaaaaaadadcaadbbcbddcabdaadcbddbdddbabbcbacdabbcddcaccbababdbacbddcbbdadaddcbabaccddcdaaddcdbbddccdcdcadacadaadccaabbadcacdcccdacccdacdcbdbbabdadbcbcddbccdcdadcabdcdcdcbdabacacbbccdcbccdbbaddcacdadabacbaccccddbdbbbddbbddcddddabcadcdddbaaacdabccaaabcaaccdddcdddbdcaacbcdcbdbdaaabbdccdcdddcacbadbbdbcbccdbccbbbacdbcccacdcadcbcbddaaabdbcbabbababcddbaccbddcbbcdcdbcdbbaddddccdddabbdbadbbcacdbadcbaacbaadaaaadddadbcdcaaabaddbcabccbdbcabccdbdaccbaaacbdbcddcddbaccdbddbcdcdddccdbabdbdccbdcadcdcabadccdaacddcdbccbdbbabccccbdcacacaadcacbccbbdadbaadacddabbadcabbadbdccbbdadbddddcdbdcbabdddbaccbbbdbdcdbdccbacbabdcbbdaddaaaddbdcaccbacaaddbbbadaabdbdacadacccbccccaaadacaaaaacaccaaaacdcbbababbddcaaaababdbddabdccbabacbbdcbdcaddabacadaacbcdaaccbcabcbbaddbdbdcacbdabdadbaabacbcdadaaccdbbbdbbbccabadabddcddadcaaddcadcaddabdabdaaabcadaccccbdbbcbadcaaadcdbbbadaddbdddcbdadddcbbcdcccacbbdbadcbcbabdcadddcbdbdabbacacccadbcbadadbacaabbddcadbabacdcaaccdabcbababddccbdddbdddcdbaacdbbbdcddbaddddadaadacbbddddaacdbdbbcccacbbdbbbdcbdacdccdaadcbdcaaccccaaddadcbdbcaabddddacbcbcbdcabbbddbabdbbdaaabcdadacdbbcaddbbdbabdbddbbcabccbdccdcbcbdabbcaccadbcbabdbdbbbdabdabcdadcbcdbbcadcbbaaacaacbcddaadcdcadbabcbdbddcabdacdbcdbdcdcbaaccabdcbbcabbbadcdcdbddbcbadddaabadabbbacbdabdaccabadcdddbdbbabddcaadbabdbcdcbbdbdddbbcbaabbbbccccdaaaaacbddadbccbcdadabaddbdacbbacdcdbcbccbabcaabaddbaddccddbcddaccbcabcbbbcadbbaabddadcabbbabdcbdddbbdcabbbbabacbaacdcaaccaaaccbbdbaabadaaaddbbaabccabcaacbbdbcbbbccbcbdbdcabbddabdabadabbbbcadadcabbabacdbaaadaabccbadddcdccccbbbabaaadbabcdbcdbcbdcbcaaadadccbacddabdddacbdccaaabccddbdacdacddacaabacaaadbbdbadaadcdbccdddcdbdadadbddadadbddcdbaaddadbccbbbbccbcdcccccddbbcddaabdabdbcacdbdbdccadadcdccccdacaacadddcadbaddbdccbdbabacddaddaacabbacbdbcdcbacdacddcccaccacbbcdddddccdadddaccddddcbdacbdcdcdddacdbbbbdaadaddcaacaaababdcabcbbaaccccdbdbcaabbdadccdbbaabcddccacabdabcadbdccdabdddcbccadbcbbbadacdbacddcbbbddcdddadcbcabcccbbcabacdbaadacaacccaaabaccacaababcbbcccbcddbabddbdadccaacdbaddcdcdcbdcbcbaccdddbdcbacbcdbabbaaaacddbdbdacabbbdbaddcbdacbbbcbadddbbcccaddddcdaabcbbcabdaacbbcabbcbccbdacdbcdabacbddcacdbadcdcacaddbbbbcdcdbaddbddcadcbbbabbdbccbcdddbaaddbcdbcbdbabbcdbbcbcbbcbdaddacbcccbaadcabccbbbacdcbdcabddccccdbaaabddbccaababcbcabbbcdcacbbddcccdcbdbdaabbbaabcdccddccadbaaadacdcabcbddccadabbaadcaddaddcaaaacaadbdacadbdabdddcbaabcdcbabcdabcbabacdcdbcadddacbcbcbabdccacdddddabdbcbcdaadcabdbbcacdcdaccabacaacdddaaaadccbacabaddbdadacacccabcbcdaadbabaaacdcccddcbdbaccdbbcbbbbbadaabdbbdaadddadbdacccacdcadbaabdcbbacbaadbdbccabaddbbdcacdbcddacdbaaacdaccbcadbbbbaaddabacbbcbccaaaadccbdadaccdbcccabcacbcadccaadcdabcdcaaccdbcacbcabbcababaccadccccddbccadddbbdbcbdaacacdaacddddccdaaabbacaddabdbcbcdabcccdaababccddcdbdacdaacbdbabdbaabddddbbbabdabcaddddbcbaabbabdbbbacccdcddbdcbddbbacacacacbabdcabcaddcbacdadbbdcdaccdbbbabcdbdacbdddccdcabbcbaaadbdacadabadbccdaaddbbcbabbcdbacdcbbcbdcccdbbacbabbccdbbbbcbbdcbabcccccdcdddadbdccabdcccbdcdcdaacbacbdacabaabcdbbaacadcddcccdaddabdccbabdabbddabadcaccbddaccbabdcaaabbbadbdcaaccdaabdcabbaccdcaabddbcbbbddbadabbaccdbabdacdabdaccdcdcbadddccbabcbbbdcdbaabacdaabcccddaddbbacacdcdbbdccbbdcbadaaaddcabcdbcabddbddabcccadbadbaddcbdabadabaaccdbbaaadbbdbabaccddaadcbadcaccaaadccdddacbaabdadacbaccbdbdccaccbddbdbbaaabdbbcbacbcdbadcbabacbdccaddccbcccabbbdadadabadabaacabbadadaddaddbcacaacccaabddddacdaabcdcdaabdbababcbbbdabddbaabddbabbdaabdcaddaaadabdabbaccbabbadadaabddcccaccacdccdcacccbcccbadbcbdcbacdbadcddbdbabbcbbabbabcaacbbdacdaadddbaccaddcadddddddbccacdcccdbddabdcbdccbdbdabdaccacbddcacccaccacbddbddbbcdcdaabbabdcbdadabdbcdaaaaaacbabcccdddccddccbbcdaddbadbcbbcdcbabbbcdaadbdcababcadbddbdcbcdadaddbadacbdcbacabcbddaccddaddaddbaaccdbcaddadbadacadcdccbcddbadbbaaabcadcaabcadcdddadcdddbcbbdbccdabadbcbbddabcdcbaabbcdcacacaadaadaccdbdbcccbcadbdbabcbdbabbadacdcdbaccbdbbddbadacaaccaacaabcdbcbbdbcaaddabcbcadbcdcabbabbbddbcadcdbdbcacbbccabddabcaacbdddddbacdaaadadcbaccdbbdbaadabcdcacddbbcaaacbbbdbbadbacddcdbdacaaabcadaaabcbaabddcbbaacddcdddabcdadadddbdcadbabadcdcdcbcbbdbaccacbdcababcdcdbcdcccccdaaabcacddaacbcbdddccacbdbbbdbbbcbbcdacbdcdaabcbadcacbbdacabbccddcadbbaacbbbcacbdbdabcaadacbcabcabdacbcdcabbcbbaadbbaabbacbadbcdcaadddcabddbcabddccbabbbdbdadcbdbddccddccdcabbddcbaccbbbabdbbcaacdadbbbaabadbacabcacbcbcbaacddbaaccbabbcdbcabbcacccdcdaccbcbdaacbcdacbcdcbdcdaaccdbbbbbdcbacdaabdbbbbdcbdccccacbabbaabbccabdadcccabaabbaddbadcaabaacdadcbacdbbbacbabbddbdcbcbaddcbcaddcbbbdacdbcaadcadcdadcdcddccbbdcbbbacccabbdacdaaddcbbcccdcddbbcaccaaadbadbbdcacddbbbbdcaccacddadcccdcdacbcdcbcbbccbdccaabbdcbaabcbdbbbacdadacdabdbabcbddbbbdbdbccbacbccacdbcdbcddccaacdbbadccbcccaacbcccdbddaaacdacacccdccbcdcbadcaccadbdcaddddbcadadbaabccddbaccbcbbadbbddacccccadacdddcbddbabcdddbbcdcabaabddbacbbaccdbccabccdcbcacbabdcadcdbadaacddbccccddacdaabdbcbbcacbaddadbcdcccacbbbcdddbdaabddbcbcdcbbdadbbdbbccabcbbabcbbdaddcadcdccbacdddaadaadbdcdddacbadbaadabacccdcddcdccccdbadbabdacacddbacaccabddcbcabdbccadbbbbdbabddacacbccccddabcaabaabbaaccacbaadbdcccbacddccbadddbcccabdaddcaadbaaccadcabacaaabbbcadbdbbcaccbdbbabcdccbbadcddaccacbbaccdcbddbbcdbcbacbadccdbdcdaadcddbbbcbbbccbaaadcbdbaadadaaacbbbaabdbdbabdddbacdbbbdccbcccacacaaacbccacbcbbdbcddccabddbbbddadbcbdabdcbdcbbdbadbdcdbacaddaccbbbcbdcabdbabcbdddccaddacdddaadcbadddcdabdccbdbbcbacbbdddbbdbbbbabbdaabbcaccabbbcbcabcbbacdabdcaaacadbbacdccacbadbacaaddddbbabdbabccadcdcaaaaaddabcaddcaabcacacacaddbbaabdbdccddaaadacccccccdcbaabaadaccbcccaadcdabbabdcacacccbcadbbbddccddcabdcabdcabbbccdccdbcbccadaadbdddbdcbaccacadabaccadadbcdbdcbbddcddbadcadcdddcccabbcbdbbabdbdbabadbdcadcdbbdbbcadbdbccaacdadcbaadccccaccbddbacdddddadccccabaaaddbdbadbdabaadbdbbbdabcccdbdcbdbdddbabadbbdabdbcdccbbbbbaccccadbcaaadadcdbaaabddbdddadcabdabcaabddbdcaaaaaaadcbddababdbdabaddbcdbcddbaaadacbcdbcdabcddacaacdbcbbddaddacaabbbdabbddcdaddbccddabacbcbacccbcbcbcaadddcbcaabddbdcbbdbcaaccddaddbbdbcacbcbdcbabdbbbcdcbadaaddcbcbacbbcbbbcbaacccaddbacbcddbbdccccdaaddccbcdbbbaddcaacccbabbdbbbbdcdabcaaddcbdbacbbdbabdbadaaaaaaaccbdabcddcdacbddadbadccbccbcacddcccbabacdcbbcbddcbddddababaccbbacbbddcaddaddbcbbcbbbdccddcbbcaabcadaacadcdbccbbacbcacbbbbdddcbbabddbbbbdccbdbbcbbadcdadbcaacbdbadbdcccdcbcbcbdcccdbbbccdbbdbaadabdddcabbaabaaadbbaddaaaaddacbcccddcaccddcbdbdacdbdabddbddacdaacdcdcccdccabbdbcbbadabaadcabcdbddddabbbcdbacddcadacbcacbcbdaadcccbdbdcbbbacbccdbcadbdaabadcbabcddbdbdbddaabbbbbacbcccacddadbdbacacadadddadddcbcdbcdbbbabdaaccabdccbbcbcbdbdccbbaccbabddaaaadbdabbccdabdcaacbacdccaccbbbcccbabdaaccaaddbaaddadcaddbcbdadbbdacdbabcbbabbcbaadccdcbabbccaabababbdcbcbbadaadcaabcbbbacbdcadcadbabadccddacbbbcdccdbcdcadbaddbdbbdddbaaaddbbabcbadddccdcbdddddbbdaabcacccdcacdcdcdbabbcacbbcdbddbdaabdbbdbaccdabddaccabcaacdbaabbddccdaadbadbaddbdcbaaabdaccdaccdabaaacbdacbabcddbcdcabbbababacadbbcdbcdbccabbadacbcadcdacbaacbdbdcabcbcdcabadcddbcaaaaaccbddddbdbaddaabdaacabdadaababcdadcdabbdbdacaadbdbadbdccbdabadcadcdaabaaddbdbbaaaccacbadcbaaadcccaacacccbbdcbaaaaabcaaaacacdadbdcacadaaaaacbbccaaaaabbdabdacccbacadabaccbddbbcbabccccabddbccaababccaabbcabdbadbabbaadccacadbbcbaabbacdcdbdddbdccacaaadcdcacbddababdbbdbccbdccbcbccbbcdacdbcbcaaddbddadaddbdaadbdaaccacccdcdbbcdccbcdcbdabcacbdbbddcbcabbdddbccbadaaddbcaacaadcddbccdbabdcdbaddaccbadcddcdabdccdacaccddcdcdaaaddcdacdaccdaddcddcdacdacbbddabcbbabaccdccacddccdacaacdaddddcacadcaaabddacdbcdabaaacdcbdadccccccacddddaddbcbbaaddddabddbddccbdadccabbdcbbcaacbdbcbddccbaccddacbbdcdcdccacbacdccdbabaddcadabdcddadcaddccaaacacccdacdccacdcddbccccddbacbdabdbcabacccababdbbaddcaadbdaacadbddabbbbaadddcbcacadbdddcdacabddbdbccbdbbcaaddaccbacdbcbabcbadcbbccdaddaddcdcbdacbcddccacdcddddbbdcbcdaabacdddacdcacaaddccbbdcbcdbacccacdcccadcbcacabaddaacadbaadabbbdabdbadadccbbbcaacbaacaacadbaadcbabcbaacbbadccdbbbadddcaaacdacaadbbbbbabaabcbaaabcddccaaccddbbcaaababbcabaadbbabdcabdbddcbdabbcdbadcdaadbccddabcdccddcabddabdaacdbbdbdbadbbddabbadddddadbbddddabccbadabbabdbacccddaadbbaaccbccaadacccdaddddbdacbcbbdcadbccaaabdabaaabaadbddcbbbacabcdcbdadbbbacccdccabbbbcbaacddcaadbabcdddacadacdbdabbccbddbdcccaabadbdbcbcdccbdccadbdaaaaaccaccdbccdccadaaadddaadbbaaccccdbaaddacaabddbdddbbdcadbdbdcacbacbdaacddddacabbacdcacacaddcacaddcadcbdacabbdbacdcccdcbddccbabcccdbadccadddabdcacccbbddddcdabddbccddbcaaaabbbcacbddabcabcbccdbbcacaabacacdabbcabddaaaabdbcccdadacccbdcacacaabcaadbbdcadacccbbddaccbcbccababcbbcdadcadabccdbcacddcaaccddcddcdcbbabccbcbcbbbdcdcbaccbcadacbcbccacbaabbadddbbacdddcbcdabaccdbddbdacbcbbbcbcbcabdacacadbadaadcbadddbabbdcdbacabccdbddcdcdaccadbabbdadaddbaaadbabddbaddbdccabdaaaabccbaabcdacbdcdcbcbcacabacadcadbaadabbcdcdbadbbdaccaaddbccbacabacbacaabbdccaaccabbbabadcdababacabddacaadaddbbcdddbdabadbacbdcbdabbdddddbdcbcccbcadcdbbdaacacdbbcbbdbdaaabdbcdbadabacddacadabadaaabbccddaacbabccbbbbddbbcbdbbaccbccbadccdddcccabaddcacdabcdcdacadbacddaddbbacbbabaccdaaccddccaaabaacbbdabbcbaaadbaaabbbbccaadacdddddccbaccababaaaddaccabacbbcdcabcadabbcdbabcaaddddaccabbdcadcabdaabaabbaadccdaabaccabdabbccdcaccbadbbbdaabbdbbddbdcbdcacccbcabddcabcddadaacaccddaccdccaadbcdaccccdacdbcabdbbcbadbdbabbcacdddcdddbdbbcacadaadbcbaaddabdacadcaddbcddabacccbdacbccbdddcdcdcdacdaabcdcabdcddcbdbcbbcbdddbbdbcddacaccacacacabacbdddacbdddadabbbaabdcdccddacdbdbcdaaaaacdaacabcdddcdaabdadcbcaadabbdbabbacdcdcdcccbdadddddddadabcbddacddddaddaacccdbacccdaaabdbabcbcacbcbbadaaccdacbccbbccccadcdaddcacddcaaaabcbabbdaadccccadccbdabbcdbcdcddcacdbdbabbbbbbdababbacabacdadcaddbbcacbadbbdcddcadddadbcdbadcbabbcaaddcbabcbdcabbdaabaadddbbadcddbadcddccadaadbbabcbbaadbcabbddddcbcabdbacadcbcdccccbbacbaabdcbccbdaadddaabaaddbdbbddcaccccbdcaaccdaadadabbdaddcaacccaaccbdaababdcddbadacbcbbabaacdbcdbcabaddbbcabcababdddaadadcacbcabccbaaadccdbbbbacbdaacbaadcccdddcbbbcabdadcdbbabcabbbaababbaccbadcccbdcccdbbadcbccadababacdccdaccaababddaacabdbcabdbbaacbccbbccbbaadbcaccaacabcabddbbcbcccbdcacdabbbdbddaababdcbcaacbdaacccbcdaaabcccdcdddbaabdaadbcdcadcadcbdbacbaababbcbbdcddddcccaddabcdcacdbcaccbcabbcdabcbabddabdabcdacdcdbcacbdabbacbcaabddbcaccdcaddaabadccdaadbaadbbabbcccdadcdaabbdddcbbdccbcabcbbddabdcbccdbacbcbdddabadcbabbabbbdaaacbaabcbdbcbbdbbcadcdadaabddbccdddacbbdcaadddadbdaaaadcaaccdbbacbadacadbdbdbababaacadbccccdbbaacacbcbdbdabbbcacbdbcddccadbdbabdcbbdbcccbabbddbbdbbdbcabcccaaacbccabccdcccbabdaaddabddbaddddcbadcbacdbcccaabdccaddcbddaaddaabbdcddabccbcdbabdabdcabdababdbadaacdddbdcbadbaadbaddbccabcadbbbdccbcbbcaccabacdbcacacacbaddbddddcbcddacdacaccbaddccadbdadccaacbabcabaddadadccdcaaaddcbcaccdbdbbacdabbbbaaaddadddbcbaabdccdbdccbdaaaddccadcbbaddbdbcaddaccbcccdcacababcbbbcadbbddabdbcdbccabaaaadcbcabbbcdaddddadbbccaaaddadabbbccaccddbaccabccacdbdbabacabcbcbabdcddcdcacbcabcabbcbacdbbbdccdbdcbcadccacaccbbaddadbaadaacddbaadcdbcaaccbbbcccadcadcbcdcdccacdaabbacbbcbcddcbdbabadcabdcccccdbbdabbddcccbdacaacddbdacddbccaaddabcbdabdbccccbddaaacdbdccdaaacbbcbcbbddcbacbbabbaaaccadaaabdddbdddadadbccddacdcdbacbdaabaabadbaaddbbdcadaaccccbcbdbdbdbdbcbcdbcaabcdbbcabbbacacaaadcaabddcacabdadbbccbddbaacabadcbadbbbbcbdaddddaadcbaadcbaaaabdaadbdcdbcbdbbcccddbdadadcdaabaabdcdbddbadcacbacdccabcbcbccdbdbadbbbaadbddadcbcbcccdcbcbacdbdbbbcdadaddadcccacbdbdbbcbbcbcadcbcbdbbdcbdbdcaadaaaaaccdcbbacccddbaaccbbabbcaabaacbbcaddbbdcadcdbbaddbbbadbbabcdbcaddbbdababbcbccdcddddddabddcbbdbadcadcdbaccaadcdcaaadacdcdbcddbcaddbabacbabccbcbbadcbadbabcaccdaabaddadbbabbccdaabbdaccaabdcbabacdabacbacbaccbabdbcddaaaccacddcaabdddbbddadbddccadacabddbaacccdbbdcacccabccccaccccdddaaababbbdcaaacaccddcccabbdabbcccadadccdabadbbdcbdaccccccadadccbaccabcadddcbbbbdcddcadbacbaacacbbabcddddbdddabbabcdabbacbacdbbbbccdcdacbadabdcaabbaaaadbadcabcccddbcbddadbacbbbabbccdbabcbadaddadcacaaaabbbdbdbaccabdbbadabccbddbbdcddbbaacdddbddaccabcdccbbadaaabdbcddbccbbbcbadbcbaadbbacbadbbcddabbaccccbabdcbabbadbaddacdddcbbcbbcdbaadbdadddadcbdcaddbaabbbdccdaabaddaabadcbadacacdabccbabacaacaccbdcabddcbcadcdcccccdbbddacccdbccacdbdccabacbcdabbddccdaaaabdddbbdacabbabcbbbcdbdbbbabbacccabacdcccadbdbbacadaadbdbaadbacbaaadcabcdcaaaddabddbabdbccaddcbabbadadbabbbbdaacdcbaadcdcbddcdbcbcaaabddbdcdcdacbacddbcccbcbdbcabbdcbdadaddaabbdcdaadcabdabadadadbbdcabddbccacbdaaabcdbbcbaacbaccdacdbddaccdbdccadaaaaddcadddccbcbadadacbbacaabdaaccbccddcbcbcabaaaccdcbbbbbbdbcccdaccccbaadbaccabcabacaacaccdacbddaddcadadbaaabacddbcacddacadccdddadcabbbdadadbbdcdbddccbacdcaddcaaabbdadcadcdbabdcdadcdcbabdaabaddabababbbccabbbdcccaacbbcdadacbacadaddbcdcaddadccdddabccbabdbaadddbccaddaaccbacbdbdcbaadbaccbcbacbddabaadbbdcdbbddaccdbdacccacdbcabbbddaacaaacadcdaacdcbacadbaadbbdaacbbbdadbdbbcddbdaabbdacbccccbabcbddaacdbdbbabcccdaabddcbbcaaacaccbdabcdaaabbadbcbcccbdccddacbacbddcbdbcdcabdcabbbddddbdbbabbaacdcabbdcdbdaabcbdbbcccadccccddbccadddabbdbccdcaaddababcdabaabadbdcadbdbabcdbaacdabdcccdadbaaacdccadbaddadabbbbdacdcdcddbbccabadcadacbcdbabbbbbbdcbcccadbdabaccaddababccbadbbabacbbadcbbacbaabddbcaadcdcaabbccdcdacbadbadbaacbccaabcaabccbccbdcbddbdaccdaddaccabdcdaccdaaddaddacabdaaadadcaddcbcccaaaadcbadaaadbdcacaababadbadbbadaaccbdbdbbabbadadabcccbadabdbbbddbdcdbabccbbbabcbcaadcdcacddaaccdbcbdbbcaaabaadbccaccbdcabcaaadbaaaaacdacdacabbaddcdbaaccddadabccbabdacbbdcadbaaadbabcacdbacaacacdcdbcacbcdabcccadadcaadcdadddbcacbaabdddccddaacdbbabcbacbbbaadacbddabadbadcabccbbaabcbbcdddccaabdbdbccdccadbddcdddbbcaaacdaccabcbcbdadcaadcbddcdddbcaadbccaabaacaaddbcdbdabacbcbaaacddaddcddbaaddcdcabccadadcbcbcacacababdabacbcbbcbdbaadaccdcbaccccadbbbbcccdcdacacacbcabbcadabaadabdcbacdbacadbdacadadabcdabccadaaaccadbcbadaadccdbddddaddbbdbbbdcaaabcdacdbcdcbadabdadddcbcdbcbabdaabacadccdcddaddbcaccacdbbbddbcadddadbdbabbddaaddbcddacdabbbadccddddbaddcdcbbbaadaaabcdaccaacdcaaaaccbbcdabccdbacbddbdcdcacacddabdbbcadbcdccbdaaddadaccacbaacaacabbcbabcbdbacbdabddcbbddaabbddbadcadaadaabcdbdcccaaddabdccccddddaaaddcdbdbbaddcbdcdbabaaacaaacddcaacdaaaacdbdabcabaabcdcbaacaaadccbccacbcddcbcdcbaaadcbbbbacccbabadbdddacddaccccdbbbcadadbcaaaddcabbcddccdbaacbddaddddbcaaddabbdbcdddcadbdababcccbaddcabadadbbbcaadacbccbccdccdcabdddddddaabbbdadcabbccdadacabadbacdbaabcddccbdacbcdccbaabcccccdadbbccaccdadaccaacccbdcabdbdcbccaacdbdaabdabcbbbbcacacbccababbbdbabaadabbdbbbbaddabccdbdbbcaabaddcdabbbcbcdabbacccdadacbddddabaabdcbbcbdaaddadcacaadbacbdddadbbaccbaccbacabcddaadccaabcacaaaabcacdcaaabacbbcaacbacccbdbdccdaaadadccdacabbdccaddccccdbcaabddcbcadbccbbbcbdccacdbabaacdabcdaccdbaaccacdcdaddddccdadaacbbabacdaccaaccabbbbdaccadaccdcdccdddadacabaddadaaddbaacacdadcdccdaaacccaaabaccbaabbccabdcdaaccddcbbbdccdbddbcdccccaadbbbbaacbdacddacacdbccbcbaaaaaccdbbbbbacadccccdbabdccababbdcbcbdccadaaddcbbdddbacacdddcbddcdadaacbdcaabadacbaacadcabadccdddcbdbdddcccbadcadbaacdcaaaddaddbdbbdbaacdbddacdaacbdbdddaaccababbbbacdacbdaabbbacaacaddcaadabdccbbaabdbdcdbcbacbbccabbabdcbaddcbcdbbaddddabbdddcdcabccadddcaaabccabcddabdadccabcbabdcbcdcbdbdaaabacdabcdaddaccadccccacdbabdbcabcbbccbbaabaabdcdcddabcaddbaacbccccacbbbcdbabdddbbdbbacbcbabbbbbbcccddcabdccccdcadabddbdaadadbdbcbadbacaddcaadbdacccacdcbabddbdbdbbcbadddbccbbcadadaaabbddbcaaddaaadcadcbcbccacacccbdbabbbcadbcdadcaacadbaabadcadcbdbaabdabddcbbdbdacdcbcbbdabbddabbcdacdadaacbdadbbbdaaccbaddacabcddcaadabdaddbccdbabaabbdcbaccdcbbabdadaccdabcbdbcbbaaacdddbddbdaababcdbdccbabbbbacdcbdcbcdbabaccbdddcccadabaccbacbbaadbdbbcccadbcdbcddcadcaaabcddaaabaacaacdcdabdacacadcacdadbcbabbddccddbcaacbdddccadbbdbadcaabaabaddbabbacdbdacddadbbcbabcdcabccccacbcbcdbbabacbddadbcaccddcbbbacacccadcadbbcbdadacdaaaadddbdcccbbbaddacdbbabddbacadadcbdadddcdabcccbdddcbbcbccccbcdaadcabdbdccdccdbcacabdcacdbadbbddaabdbabcacbdabcbdbdaddcdcdcaababdbbcbdaaabbabdbbddbccabbbdccccaabbccdacbdbcbddacbddddccbadbcadbbaabddabbdbbddccdcbbdaaacbabccabcddadadadbcbabbabcbddcccaabdacccbdccbbabbccaaccaabddaccacdadcdddddacacbacdaddbddbbadcaacabcacadbcdbdbadddddabccadddcdabcbadcbdcdcdbcabccadcdaaddabbdabcadabcdbbcdcaabdadbacddababaabcddaacbccbdbdbcbcdbccbabbcdbaddbccdaabaadbdccabbbaccbbcbcdbdbbacaddababbcccbaadbdcbcbdaddcddaacbadbcbaabcaabcbaddbdbccbaaddcddcbdbbbdbddbdcccccddccbcdddbbdcbdaabadbadcddaadacbcbaacddccdabcbccacdddcbbdcabcddadccdcbcddccdaabaacaaaccdcaddbdbadaadaacaabdcdabadcaacaaadcaccadbcbabdbaaaddbadcbbaccbdaccddbdcabcadccdaaccbcacbbcbddbcbbdcdcdcbaabdacaccddcbbddcbcbcdaabcbccdcccbcdabdbccdccdbdaccaaacacaacddacdbadadaadcdadcdaacabdadbbcdacbbcaddbbaadaddbcabbdcdabbaadbababccdbbcacdbcbacdaccccbacbdcadddcabcbbaadddbcbbcadbadaacabcaacacabadddbcadadddcdbdcdaaacdbacdcaabbccaadaddcacaabacdcdcdabccbbcbbaadccdacdacbcdbadbbbbaddacdcbacccabddbcbddcacdcaaaabaccdabdcdabcbbcdacbacaaccddcccdddabccbdbacabbdcacaadaaaacccddcbbbacacdaabdbdcaabdabccbaddcdabcdaabdcddcbabdbcacaabdaadccddbcdcbcadabdccadbbbaaaacddabcaabadbdaddadadbbdcaaadaaccdaabcbccbdcadbbabcbccacaabbcaddbacabbbdcbdcbccbddadddacbccaaacccbacbbbdccabacacbaccbcdabbdcadabcdcabdbdbadccbcaabbbccdabaadcddabbababcabbadcdcdaadbadcbababaabadbdadbdbacacaabacdcaccdcbdbaadccdbbccadbdbbaaacbabadcbcbccabbbbaccddbbcacddcaddabdcacbbbcbabccbabaacaacabccbabacadacabbcddaacccbbaddcdbadcadccabdcbbcabaccccbcdccddcbdaabaacababbdadbcbcbbbdbcdaaacdabdaacabbbacdaabbcdaacccdaccbdacdcbcaaabbdbcbdaccaddbbbabbcaaadacdadaabdbcaccbcacdcadcdddbadcddadcbdacbcabdcbdbcbbcdabcacbdbaacaaadabcbbdabaddadcdacdaddcdadbacacbcccdcdbcdcdbdddacbaaccccbcabbdabcbdabccdabaddbbdcdacddccdaddaaadabcddacdadbdcabdcabdadccdcbabaadabcbacaaccaddcbcdbdadcccbdcaabcbadccabacabbbaaababaabccaaacddcbcbcadaababcaddcaccccbbcaabcdbbabcaddadbdccbacacbacbccbcdcaadbddacabdbddbbdaccaddcdddbacacbabcbbaaadbacadadadbabccbcdacccbacaabbbcdddacbcaddcabdaccdcbadaccacbaaacddbddbbdcabdaadbaddbcbbadaabbccaaabaadbaabacabdccabbacbdaaddddcabdaacdacabdcbdbccbbaaacddcccddbacaabaacbaaccccbadcaaadcaabccbcccacadaccabcacddaddadacccccadaaacadcaddbabddcdddddccaccadcbadbcaccccbcdabddcaadbcbbbdabdacddccbbaabbbcbccbaadddddbbdadabccbdbcbbcccadaddaacaddbccacaaaacddabcacadbdcabacabbaccddccbdaaccbddcadddacbbbaadcacbaccdccbdbbadbcabdbaddadbcccbdadbbdddbbddccbdbdaadcaddbdbabdadadbcbacdbcdcbddacdbccccccacaabaabcaadaaacbbcddacacdbbcbbaccbcadbbaabbbabccbbddbccacdaccbabdcaccdcdabdcbdcddddccabacaacbcbccbdbbdbbdcdaacabcdccdbabaccbbddccabdccbcdcbdbaadccadcbadbdbdacadbabddcacccbcccadcbbcacdbddddbacacaabbbdcbdabdbdcbcdccbcacababbcbbdbcabcbccbcacccdccabdbddbcacaccdaabaadbaadccdbbcdcbdbcdbaabcaccbdcdbaaccdddbbdaacaccadcbcaabbbacccdbdbcacdababadbbaadaadabaaddbaaddcacddddbabddaaacabadabadcdbcdbdaaaccacaadbadadbcdadbbbdbdcaabcacaccdbbbbddabaabbdbcabbaddcddaabcdbaaabbcadbccabdabcccaaaadbdbadcadbcbcbcbaacdbdaddcdcdbbdcddabbbdacdcabddccdcabcccbbcbcabadccaccaaaabbbdababbcdcbcdbabbbabbbbccddbddcdccbacbdbcdcdcbccdcccbdcdbaabcaaabadcacdbbdbaaaaddbcacacbadbdaaabcdcbadcacbbbdabdcadcdbbbcabdabdcdccbdabadcccbdcddccbcdddccdcdbbbabbbabccdccbdddaccdddcddcdcabbbcabbcadcdddddbbcdcbbaaccadbbbaaabddaadbadacddcbdccddcdcaaccacabbacbcccdcbbbadddadcccbcbbadccdbdbcdcbdaddacccccacabbccccddacddcadcaaddbabbbccdcbccbccaddbaddcdcbdcadbccbcaaddaababadaaccccdcbcdcdabaacbbbcbbdcadcacbbdcadabbddaacbcadcdcabddaccdadbacaccacacdbcbabcaabacadcbcaaaddbadcdbcaadaabbaaacdcbadadcdadaddcbcddbdbcabddcabdbbbcbcdabdaacbdacbcabacbcdcccdbddcaacaaccbdacaadcccacdcdacbadcbbbbdbcccabbcabbadadbdabdcadddbdddacccdccaddccabacadbaabdbcabadbacaacadacaabcbbaccddbbcadcbadcdbaddbdcdccbbcdccbaddccaabacdadcacdbbbddbddddabcbbdcaddbddddadbdcdacddbacadbcaaadcdcaccdcaabbacccbdaaddaaabdbadbdddbacdddabaaabccdbcdabacddcdbccacbbaaadaadbadcadbdadccdacdddcdaaccccacdcabdbadddabbcdcaccacdaccbabddacadaabadbdbadbcaaabdadcdaabcbccaadaabccbbcdcbbbbbdaccdacabccbdcadbbdabccabbddddcacaaaccccaacbcccbbddccdcdccbdbdabcaabccbcbdbacbddbabdcbbccadadacaabccadddcbaadcbabdcacacdbcaccddabcddbdbdcbadcaaaaaaaadbbdddabccbccdcacbadbadbdddaccabccbcdaaabacacbddcdcadacbcdcadbcbbdbaadacccbbccadbdaccabadcababbabbaacbdccccccccccacabcabddadcbcdbdbacabbcacddbdcccacdaddbabaacadbcdaadacdadbbdcbadcadcdbcbdbbddbcbdacbbacccadaaaddcdcdddaaabbacddbaacdcdddbcbcbaabccdcacaadaabdcbabaabdcddbabbbbbbdddaabadbbddcaabbbdbbdcdbabcbababbdccbaabbdcccdbaaabdbbcddcdaacadaaaaccdadccddabbbbbdbabcabcdbbadbacdbaacadbbdcabbabcadbccabddbcdbababbbccbabacabbabcbcdcbccdbdbddcbdccabcdbcbcbacdcadadbbdbbbdbbbabbdbdbddcddaabbbbbdbaadaaccbcadcabdaaadcbddacdaaacaacabccadadabbccddcaccaacdbddbccccccbabdadddcbdcabbccccddbadcccdccadbddbdbccaccddccdbdcaacbdbdbadaacaccdbabbaddbbbdcabcbdbddddacaacdaadbacccdccabccdbdabcacaaacaadccdaaabacabdbdbaccdccaacddbabdbddaccdabbcbabaabddddcacdabcadbbbbbadcbbadbabacbdbdaabcbbacbdcccacabcbdbadadcdddacbbbbddbbbdabaddbbbdaacbbcaabccdbdcaddcacbbdaacddbbaabbddddccdadccbdababbdacaabddccdabcdaadabadbcbbdbcccdcbccccdadcdccbdbbacdbddabcacccddbdabaccbaacabdcaaaaacacbcdbaccbbdaadcbbcabddbdadabcdabdbccccbdaabdacbbadbddcbabcacbaadddcdbcabbaacccaddbbbaaaabddbccadabdacccdadbbcdbcababbdcdbbbabcddccdbdbacabbbaacbbccddabccdbcdcbdcadabacbabbdcbcdacadcacacaadcbaddabdccdcadbcadcbcdcbcbccbdcaaacdcdcbdbdbdbabbaabcabdcacddacbbabccbadadbaacabcadcbcacbabcdcccccacccddbbcbdbcbccabadbacccccdbbaaccdabcbacbcdcdbcdbdcabdacacacacccababaddccadacdcaccdacbddcdcddcbbdbbacdabdaadbdabdabdcdaacdadcacabccaddcddbaaacaaccdaccdcdbddbacbaaddbdaccbbabacaddaacbbdcdcaddacdbcccdbbcdbbbacdaaabadbcacdbcbadddbabcdcadbbaaabcadaabacbcbcabdccbbccdcbdcbcabcdbbbaacadaddbdabbdcdcdbdcdbaabacccacaccdcbbcacbabccbabbaddadbcbcddabaabacadbcdcacdbcdbbabadbacbbbbdbdbadcdadbddbdabdbdcccabdacbbdabacbdaccbdaaaaaccacbdabbacbdbdadbbbcbbdcbbbdabbacabddcbccbbcbababaadabacbddacacdcbcabcdcdaadcccdbbbcacbccabbcdbddaadcccccbcaadadddddbcbabcdcbcdccabdcbdaaacccabbdaabaaacbbabaccbcbcbacccccaacdbdccbdcbabaacabbdbcccbdacbbcdbdcaaacadbbddccdbcacbdaacbbcdaaccaabbbacbaccadccddcbacccabdaaabbaacddcadbbabcbbaaccbcccbacbdcdabcabdaacccbaadabccadadbbbabdaaddbdbbbadacbccbcaaccaacaababccdddbdbcdccbadadcddccdddabdbbacdaaccbaacbcddcaadbadacadbcdabdbbbbdcabcbcacaccacacacadbcadbcbdcbacbabcbcbacddaaacbbadacccbaadcbdcdabbadadcacdcdbaaccdbbabaccbcccdbbbbabbccabbaabaabcdabdbacdbddbdcbbbbdadccaccaddcbacdaadddcacbcdabccabaabdcdcbdacccadbdcbcdbadaadaadbaaddbdbabdaaaaddcdcbbabcccbcddccacccdddcbcbdbdabbccbbabdbcdadacbbddbdccddabacabcdbaacddbccdbcbcacdaacbcdaddaadabcdabddbdcdcdcadddbcbcaaccbdaddccbdadbadaccdbaaabbbbacbadcdadbdccbcbcdadadddacccaadbaaaabaadaccdccacdccadbcccdabbbcaacbdacddbdbbbcabddaddbadbccddadcacaaacaacacdaddbbaaadbcaaccbbdbbdaadcddbddacdcdaaacdcbcabbdbacdddbcbbbabcbbbacbbcbdbbdddbdccdcadadcbdcdabbadaadcbbdaaadaddcababbbcbdcbaaaabdabcccdaaaabdbaaddbbbcdcdcdbbbacbccbcadbbcdacbadbdacddaabccaacdbddabdcdccbdcdddbcdaadbbdbaccdbabccaabaaaaabddccbcbacddaaddcdbccacbdddcaacddccaadbadabdabccccacccbbbcdcbdaabddaaabdbadbdcbbacabaabcbaaccbadbacbbcdcacacabadccabbadddddcadcabdacdcdadddacbabacacbbbcaddabddabbdbacdcbbdaaabdadacbacaabbcdbbacbadcddacbccccdddcacbbbcaacaadaadaacccbddccbabccabbccabbcccaddbdcccadadcccabccaababdacbbdcdddcccacadbcadaccbcbbbaadcdaaacdaabcdaccbabbbcdccdbdabbaccbdcacccbcbdabadcabbbadcdaccddbcccbcaaaacdcbaddddcabbabbcdbcadcabbacacbcbcdaddabddcadbadcbacaaadddabbbabacabbbdabcacbbbcadacdbcadbbdadbabdcbadcdbccbcddccbbccdcdbbddddacddcbacdbdbaaacccdadbbcdcaacbbdaabcccddcbbbcadbacccccdcbdbddccacbadbabadbdbbcdccbbaddbddcbcbadabccdbaccacbdcdabcddaabcbbbdddbccddcbcdbccadbdbdbcdbccbdabadbcdbcdabbbbbbaadccdddbadcbacccacabbbaddcbadacddcbadbcacacddacabdbcbdbadbbdddddabbaabbbacdaabdcdcbadddabcacbdcadabaabbacbaabacdddcacababdaacdbcddbdcdcdbbcbacbccdabdbbadbcbdbcdccabbbadacadddacdccdbbdddbcabccdbcdbcbbacadbacaabbaadbaddaababddcaaddbacdbccbbadcdcdbdcbacdacbdddbbcbbcaaacbbcccdabbcdacaddcccabcabdccadddcdbbbcdcbacbbbaccbdbabbbbadcabbbaacdbddddddccadcccabaddcbcbbdacdbdcaadbdbbcccbaccacaddbbdcdbaababdccaccbbdaacdbbbccaddddccbbbbbdcbdbccadaabddadabccdabdadaddabdbcbabbddcabdbacbaddbbbbdcccbcbbcdcbbdcddadacbaabbdadccbbbbcbcbddaadcababcbbaacdccaaddbbbbccbccdbdcaabbacdddbcbddadddabbaadccdcdcbcbaaccdcabcbcdabdabbcdbbcaddaddbdccacbddaabacbddcbabcdbddbbabdacbaaadabcccbdcddcaaaabccbbbbbadcdccdabcbcddcaddcabaabcbacbccbbdcdbadbacccbcdacbdaccdbaadcdbabcdbcdadabcbaaadaabddcbbdaabcccccadddadadaaadcbdacbbcddabbddadaabcbaacabcccaddabccdbdcaccdbabaadaaabcadbcbcddaaddcbccbabacbaacbdcbdccaddadcaacbdccbccbadddcacbcbdbaababddaaddcacbccbdaacdbcbddbdbbccbccbacccadcbcbcacbbbcbbdaacdccdbbcdabcbcbbbacddccaadbabdaabcabacbbbdcadcaaadcabbcdddddddaccdcbabbcdbadacbacacaddbbccbbabbdddbdcbddaabbadaddabadcaccdcaaaabbaddabcbdddaddacaabadcccbcdbacabcaabdaaabaaccdbbbdbacbadcbabaddbdabccaaabadbcbbadaccccadcaddaddbaadbacbccdbdacabdcdbddbaaccbcbbccaaabbdbdadcacaaacabcabbdaabcdaacacaabbccdbbddbabccddbaccbcdacacaacdcaaabacadaddddcbadddcbadaadbddaaababadbddbcabdabdccbcdcbdbddbabbcbbdcdbcdccbcbbccaddbaaddaabbbccbccdbbcddcabddcbcbdcadccbabacccbccabacacccdbcaddbcddccccaccccdbbdbbbdccdbcdccdbcbbbcaddbdddccacbaddacdbcaaabcdaaddbadcacccbadddbbccdbbbbaacbbcadaddacdccbdbacacbdaaadacbaacdbadabbdaabbbaacbdadababadcdccbbcdbbacacdabdddbaacdbdddbcaddbcddbbdcadbbcbcbdbcabdcbcdacbaddcddadbdaaaccddacadabcdbabcdabdbddbddcacdcaccaadddabdbdbdcdbadcbcbbbbbcadbabcdddbacdbbdccadcbacbccbdaacbcaacddabdcbacbdaadccabbdccaacccdbdbcbadabcbdbcdcdcadccacaddbcbadaaccbbdbcaacbcdbbabbdcbdbdabccbaacdadbdaaccbdabbbabadddcbaddcdbbcdcabaddcccbacbbcbddcbcccabdabcadcbbbcdbabbddbcccdbacbbddbcbdbdcdaaacbbabbdbcdbdbddaadbdddbadccaabdbbcbbbbbbabddcadbddacabadcacdbcbbbbabbadbcccbabbbbbbbdcabcbbcabbaaadacacadcbbbbaacdaabdcacbbddacbbaabbabdabcbbdbacaacddbdaaddddcdcbbdcbbccbdabdcdcbbacdacdacaabbcabcbdccdacacdccaadccbbacaaadbdbdabdcacaaabadbcadbcdddadbbdacdcdaddbaabaccbdbbdacccdbbcdcccdadacadcbcbadccdacbaddcbcccadbdbbbccbcabddacddddcdaccabbbbcbdcbccacccacddacabaacadadbdddabcccbaabdbbdbaacacdadaadacddcbabacaabadbaadbacbdcacaabacddccdaccbdcaddcadaaadadabcacbccbaccdcddcaacbbadabcdddcccddbdababbaabdcadacdbcdbdcbbbadabacbacaaaacdaddacbbababbdbdcaaddcddaadbbbbbbadadbddddddbbdcbdccdaddabaddccbcacadcababbcadbcbcdccdacbcbdbddbcdcacbcccacabaadbcabdacbdadaaadcddbabbcdaacbaaaaaadcdcaabdbcbcddcadacdcabadaddcdbbcbcabddbdcacbdbbcadabbddbcccddabacdcadaadaccdddaadbbcdacbadcaabadbdcaddbacabccacdcaadbbddcdacdccadadabbacbacbcbcaacccaadccbcbbdbccbabdbcbabcbcdcadaaadbdbacdabcbadadcbbdccbdbdacbddbbbdbdacbabdaabdcabcdaddccdbacccadcabaaacddabbcabaadbdccabbaddcadbcbcbddcaadcaccaabacdcbbcddbcddacdbadbbcbbdbddddccacbbcdcacdabccabdcbddbdbcabaacdcdadbadcbadacddcabaadcccddbbcdacdaabdbdabcbdaabdadbcbdadbddccadaabcaccaaccaddbccaadbadcabdbbcdcdbcdcbccaccaadbdbcbdbcdbacdabdadacbcdabaacbdcccdcbacddcdbbaadbccccdacaacbbaabbadbccaaacacaddbbaaaccccbaabbdaddaabadddbbacddaaadccaccdbaaaabddbbdcdadadddaccdbaaddbabbcaacbdcbcbcdbcacaacadcccddcdcaaddcbdcdbddbcddbadcdacadcbacaadcbabdbbccabddacbcaadcacddbddcbcbdcdbddbdbcbbbbdabbbabdaddbcdcdacbabcccdccaaacbacadcccbbbddccabdcbabccdbccacddaadbcbaccbabacbaccabbbddbbbabdcadacbadacddbbbaaccbbacccdadcabddbaaacadbacbcdacdcabcbdbbaddbdaddcabbcbacbbbaaaddccabdaadcdbacdbcbadddddcbdbbabbadacbdccdabadbcbbbbcdbaaaabccabcbddddacaadccaacaddcbcbbccabcadaccbbaadcabdbdcddbcaadcdacdadaccbadbcaadcaaccdaabdcddbaddbbdcbcbcadaacabcccbbdccdcbacbccaacbcdacaacbcadcdacbdbbbabdaabaccbbaadaacbdcdabbcababadbcaadcbdbbddcbddcdbccdddbdaadcdadabdbcdaaabbdbdcacadcbdccacaadbcaaddccdacddaddcdbcacaadacbabaccabacbaabccaccabadbdcbcbcbcdabbbadbdcddbdaaccabacadaaabbdcbbbbbdbacbadddbbadbbaabdddbbddbcaabdabbcaaacccbacadcdadcabaaaaccbacadaabcdcddcabaabaaaaaaccabababbbcbcdcddaccdbcadddbdadbddaaccdbdcabdcdaadaaddabdcdacacaadaaaacaacdbabaccdaccddcabdbccbdcdacbacddacabaadbddadbbdbcdacaaabbcccbbcdaccdbcabbcaccacdabbcabdbaabbcbdadbcdcadcbbdaacdccbbabbbdcadccbadbcbbbbcacabbabbbdccbacabcccdabcadadcabbaccbabcbdcaccddaacdbdabadabcabdccbbcacdaaacccbbcabaabdacbabdcbbcdbbdcabbcdbdccabaddaacbadbccbcadbcadccaaadcdbadbdbacdcbbdbaaccacbddcacdcddcbaacaacadadabdddacadbddcbbbbbaabddccccccdabcadadcddbaccbcaacccbdbbacbbbaacaddcccccbdccacadabdacddaacadaaaabdbccddcbadddcdababdaabdabccaacacdbcddbcddbdcadbadbcdddbaccadbadcaccbabccbdcbcbabdcdbccdcbdddbbdacadbbbdaccdbccccdddacacaaccbabaadaabccccabcdbbdbcacdcddaaddcaaadbacbccadbbccbdcbbdcadcccbdcddcddddbbdaadbdcaaabdccacacbabababdadadcdddbdabdcadbbbcdcacdbabbadbbacddcdbcdaddcbdddaaadabadaddbcdaaaacacdddbbddccadcddacbcdbbdbbababccdcabdadcdbabadbdbcdbaabaaacdbadaccbadddcdcdacccbbaddaddbbaabadacacadbbbcbbabddaaccaaadcbdcadddacccdbbddcadcddccccaccdaadcdbbbaaacdccacaadadbdcdaaadcdcbddbcdcabdccdbcddacbcddccbcdaddacacbbbbddbabbabdadbbbbdbdaabddccddccadbbaddbcbdccbddcaccbcbabcadabbacdbdacaaacbbccadcccdccdcbdaacbdcddaddacaababbacbdcaaacabdaadcadcbbcddaccabbbcdddcdcdcbbbbabcadcdbdccdabccddabcbbaadaddbdccbdabccbcbacbddcdbbacbcdbadacbaabaccaadbcbcacbbdcdcdaadbddadcddbbdabcccbaaaacaacdcbcbaabdbddcdcccdddabddddabbccddcbadbcdcabdbbcdbcbdacacbbccdddadcbbdcbccbbabadddabcddcdbcabbccbddbadcbdbaccaccdcdabadddccdcbdbccaadadcabdabdadadcababacdcbdcbabdcddabcddbadcbacdadcbddbbbdabcdaddaaacbcbbcadacbddbbcbcadddadbbbaabacdbabbdcaaaacdaaacdbdaabcaadabcdacdcdadaccbadadabdaabcbcbacbcdbdcbccdbcccbcbbddccaccbcbdaaabcabbcacdcdbbdbabacaddccbbbbbaaacdaabdcbacadbabbcdaacbbddbadcbbaacabbbaddddcaacbdacabbbddaacbbdcdacbbbdababaadddcacbaddcbbaccaadbabbcccdbdcadccdcdccbbbdaabdbdddbcccbbdbacdbacddbcccdcdcccabacdcadaddadadbcabbaabadbddcbacccccacacddbadbbaaddacadabdaabbadaabbccdaacbdbadbdaabccddbaadbbaacdddacbcabbccdabcabbcbddbcbdcbddacdbabcbcdcbdbbcdbcdaddccbacabdbcdcadddbbbcbadcbccbcdccbdccbabdccaababdbcbccaaaabbbdddccbababaabaccbacacaadcdbdabbdacabdbccaabdacabbababbbabcadddcbcbdcdcaaabddcbabcadaddbcccdcdcbbadacccdbbabcaaaaaadbddacaaaddbabcbdcccdcaaacdadddbdacacbccbdcacbbacdbdabccbdbbcbabdcdbdadbcadcabbddddddccbaccdadadcdaabbdbcabbcacdbbaaadcbadabcdbcaccbaabddaabaacabbccbcadcdbccdaccaaaadcccccdcaadcacbaabbacbdbccdbacbdacdaccdbaadddbbabbcdaabdcdaacbdcdabddbdcbadbaaaabcacbaccdacccbddaacadabdcaaaddbdbbcdbddbababbaddabcddaaacaabccccaddaddbbdcbaaacbdcaacccdbabcadbadccdadadcddcacccabacbbcccbbcabcddccbbdacddcbdcdcdacbadccaadbabdadadbbdbbddabdcacadbacaacbcabccaddcaabcbcddaaabbcdabdacdadcabdcbadbcddbcacdcbcaadadbdbcaacadccbadbbccababdbadaacbcabccdbbccbbaddadbabdbdbdcbdacdabdadcdabccaccdabbcabadbcbacbadcdccdddaddcaabdcddabbcdbbbabacadccaaaaabadabbacbadababbbdcadccbdbdabcaadacaabaccddddcbbbccaccabdbbbacbabccdcdbacbcbabadadbdcbcccbcdddcaadcacbcddddaaacabadadcacccaabbcbdcadbdcbadabbdcbcbdababacacacadcadbcddabbbbcdbbbdbdbdcbcaacdbcddbdcbaacbbcbcdccabdccacabcabdddcdbdccdcccdddaaacbddbbbdbcdccadcbadcacbadcddcabcbcacbbbaddacaadaadcdaccbcaacdaaaacbadcadacacbbabaaaccdbddcdcaddbcaddaccbcbcabccdbcacacbcdbcdccdaadbbcadcaddadbbbabbdaccaabadadbbaabbbaddcabbaabbbabcbbabccccddddacaddbabccddbdddcaabdbccaaccccacdabddbcaadbdbbdaddbdaddddaadccbdbabdbacbdccdbdabdcddcaabddbbbbbabcdaadcddbdaabadbdabcddadcdbdbbaddddabbbcbdabacaacbaccbadbdaabaabcdcbcdccaaaaaaaccbbbccabbbaaccccbdbcbccbadabdddcbbaabaccaccabaabdcadcaabacdbbbdaccadcbadcddbcbdbdcbcbdcbbbbdbbdbccbdacbaaacdaccacddcacdadcababdbabaaabbbbcdddbcddcaacaadabdcdabaadbadccadcbcccbbccdbcadadadbacccccdbadcbcccdbabadadbdbbacdbdbdcdccabbbccdadbccacaaccdcadcddcabdbbabdbcdaabcccaaacbdbcbbdcababaacdbaacbaabbdcbabdaddcabbaaadaadddaadbcbdbdcabdabbddbcccabdcadddcabacdbcaccacdccddabaaccbaacacdcbcdbdddbacbdccaadbdaacdccbaadaddabbcccacccdacabddcccdacddbccdabaacbdddcdbccdbccacadbdacbabdccddaccccddccbdcacbcabadbaaacbdbdcdccbdaacdabcadacccbdcdacabbdcaaadcbbaccdbdadbcabcabbbbdadbdacaabcaacbbdbbadccdcbddddcbacbdcadcccadacabdadbdbbdbabdadacdccabddbbdddcdbbbcddcaccdccbabbabbdabdacbdbddbddbacbdbadbddcabbcdbcccadabdbbdbacadaccdacccccdbacccbbccdcabdaddccbbadbcbdbcacdbaadacdcabdddacaaccbddaacddbbadaaabaaadddabdccacacdbbbacccdadcbcacdbbdcbabacbdbcbaacdbddadabbccbbdccddccccdbddabbdadadaccdabccacbabbbacaaccabbbdddddabbdbacbbbcbacacbcddcdccbcbcdbdcddcbddcbcbdcdcbdcacbcaabccccdbddcacbdddbdadbddddcacacdbbdcdcabdadbaababcabcbadacdddccccacdadcadccdabadbaadaddddcbbdcabcacdbdababacabacdadabcbdcbcabdcaadbbdddbbbcbbbdbdadacddbbcccbccdbbbacaaddcbbcccdadadcddacdcdcddcdadaaccdbddbacbdcbdcbbaabdabcbadbcdbaccaccccaadcbaddbabccdcbccbcaaabadbdcadacacbaadacacbaaddbdbcadcbacdabcdacaacbdadaacabdbcacddadabadacbabddbbbdbdabaacdcbdcddbcbacaaadccccdadddbaddcabccbabaaccbaacbbabbcabbbcdcddadaacbacbbadccccbacdcacdabcacbaabccadcadddbdadccdabaddbdcbbcacbccbbdcddcabcbacddaadcbdbbddcbadacaabdabcaaccacdddabacaaccbaadbccbbacadabbcaacaaabcabccadcccddadbbbdcdcadbcbdadcbcdaaddbabacdddcbbacadbdcacdddadbadbbcbbddabaccbbcbbaddaccdbdaaaaadbcdadbadacdbdcacccadddcdcdccdadcbdddabdacbabccbbbbdaaabaacaabbadcbcddccbbcbcbcaabcbddcddaddaddddbcdcabbdbcdcbacabbbbcbbaaadcbcdccabcdabcabacacbbcbdcdadacbddbcadbcdabbbaaaddcacdabbdbdbdacddbadaccbbabbdbcbdbcddcabccbbaabccdbabdacdcdacdccbdabddcbbbacdddacdcbbaabcddccabbaadcabcadcadcbcdcdacbccbdbabbabccbbdabcaacdbdcccacbdbcbabbbccacbacadabbacdcacabaaddbcbbcdcddcdbbaaaaabbcadbbdcdccdaadacbbcbddadcaaaddbbadaabcbccadadbcadadcbabcadbadcaadaacaabcbdccaddcbdcbadbdddacaccaaabbabccbacdccbccbabcdcdcddcbdbabaadcabdcddcbacccdcdbdbbaaddacbbaaddbbdbcccacccbccbaadadaadaaadccabcbacbbcddadacbabbdbbbcaabdbdaddbdccbddcdcdbbcabddbaadccbddaaddaddbcccbaccdcaddccaacdcccbbacddabdcbabbaabdbcaaddacbcbcadacabdccaabacabcbcdbddccadcccabbdadbacaddbcdbbcacbbcbcbacccdbdbbbbddaccbdcbaddcaaabcdbccbcdbadbabcbadccbabddcdbddabdaadabdbcaaaddbdbbcdabddddbdccdcbadcdabbbcabddcaaadbcbacacadaddbbdbddbcaaaacbbaababdbdabbacadaaccdcbbdbcdddbdccaaddbabbdbadacbbabbcadcccaacbaaaddccdccdaadcabbbacdabcbcbdbcdcbcbddababdaabddbdddbddbcddacdabacbbbcbabcbacaaddbaddcbddbdbbaddbdbabdddbdbddbcbbacbabcdccabadddbdacbbcababbbdbadbbcbccacbbadccaddbaabaacddcbadcaacbabddcdbdcacadabcbcadadacccaabdbaaabdbbdbbcaccccdcdbbdacbccaabdbabccddadcddbbacddbacbccdcaaaaacacaadcbdbbcbaabbddddaddbcccdbbaaabbaddbabbdcdaccacdbadcbbcaaccbbabcaadddbdbbabcbabdddbabbcbcbbbbadcadbbcbdabdbbdaadbcccbbbdbcccdccccbdcdaddaccacaaddcdddabdbbdcbadcaaabacccccbbdaaddcabdcdbadcaadcaaccadccddacbaccccbcdcbcdaaddcadcbcbaadcdacdcddcccabdaabaddaccacabcbddabbbadaccccaccbdbadccdadaaccaddadcdbcbbbcabdddacaabaaadcddddcccacdbaabcacdcaaacbdcaccabccacddcccaddccddddcddcadadadacbddacbdaabbaaacbbabbddabdbbdcabdabcbadacddcdcbaabacadacbaadddbbdbcccbcaacadbcbbbbddbddbadddcabbcabdabdbcbadaacaacccbcaaddcdcaddbbadadaccbdccacbdcccdacdbdcdddabaacdbbdccdbbccaccbbaacbdadbbaddcabcbcdabcccbadacdcaadabdacbbcbdbddbabbbdbaacdcadcaaabcabacbbdaccddaddbccbbacaacbdadcbbacbbabbbcdbdbcbbccbbdcdcdbdbcadaacddbbadccdcdaabadcdccdaddacadcacacccaabbcddadaddaddccdaabdcbdacddcdccbaabacbdaadaadaadaccdadbaccdcdbcdcdaddadaddbdcddcacdcaccdbbbbbbdddbcbbaabaabcbbbddbdaabdbbbdcccccbccddabbccbbdccccadddbdbdbacbacadabdadbcbccbcadccaccdbccdbcabbbabdcbbcaaaaacbaababccaabaaaabccbacacdddddbadcdbacbcbaaabdbbcdaaacbcbbacbddcdbdbdbdbdabadcdadbaccbccbaacbdbbaaccacdcbdabcccdcddcbbcbccbbabbdaddcccdcadadbdbddaaacaaddcbacabacdccacabaccabbadabdbccbbcaabdcabcbabaccadcddcaaccadbbbdabcdccdadcdbbbbbdadbacdbaaaacacbdaaabaccdccbdcdbbdaaabbbdcbaccdcdabccadbbacdcaaacacaaaadddbdcdacddcadababaaaaaadbbaddbbdcdbaaddadabacdbbadbcadbabaacadaddcbbcdcadabcdabdcddabcbcadccccddaadcbcdabcabddbddaadbccbbaaabcdccdccadbccbccacccbcbbadcdcbacbcaadccdddcbdbaaabbbabbbadabcdbcdaccbacababdbabbcbcabcbabdccdaddbacddabbddcdabcadadccdaccddbacaacadaadabaadbcabdcdcbccbbcaaddabcacacabdbbbcdbaccabddccdcabdbdabcacbdcaddddbcbbccaddacbbbcbcdabcdddbcbbbdcdadbdbaaadacabcaabaaaabbdcccbcacccbaabacaadbdbcbdbdcbbbcdbbcbcdadabccdabdadabbdcaaadaabddbabcabcbcdcaaaadccaaabdccacbccaabddbdcaabcdcbcbdccababaddbbcdbbabadbdaabccbbabaabddabdcaaaddaaacbbadbccaabacbdbacbddaaddbcaabbabcddccadaabdcbbcabdbbbaacdcaccbccbbcdcdbddcdbccbccadaccdababddbbabdcacddcbdbcbcabbddcacbbdadbdadbcdaabbdbccacbcacbaddabcaababbadbacbbccabbccdabddcabacbbaaadbccbcdcaabbbcbccdbabdcbdabcbabbdddbdaddcdabadbcabbbbacdccababcbbdcdddcadbacdcaaaaacadbabacbdacbcbdbacaddabacccbbdccbbbaaaacaaaabcaaaccddddddcacaddbabdadaacaadacaccbbadbbdbbaddbadcadddacbbddbbdbdcacbcbdcbaadbcbddbaacdbbdcbadddcbcacddaaadbcbaaadbdcabbcdccdacabcdbdbaddbdadbbacdcdbacababddddcdbcdaccdddacbbdcbadbaaaddadcaddacddcdbbddcdddbaaddabcdcadaadbbddadaccbccacdcdaabbcdccdaacbacdddacccdabbdbccdcacbcdaaccaabbbacbacdbabdcaabbcddddcbacabcbbdbccadcdcdcacbbcdacdccbbbdbdcbbababaddddaaacacbabdabdbabccbdbcaddaddbccccadacbccbdbaccbbadacaccdcabadabcbbccbbdcbcdbbacdaaabadbccddcdacaadabcabbbacbcbddccacdadbadcdacadcaadcadcaacacbdddddcddaaabacdadbbcdcacabbabbbaadbaaabdbacadaaccdbaaadccbbadacadbdbacaccaaabcaccbacadacdaabcaabaadbcbacbcaccaaaaaccbbcdbadcacbddbcdcabcabddcbcddabbacbcabbdcdbacbbcabbaaccbdcdbadbdccacddaaabbadccccdabadababacadcbacadcdbcdbacdbdcaaabddbcabcbadcdabdaddddbcbbdadcccddbbddacbbccdbcadacbddcacaaaddbcababdcbdbbcbababdddadccbbdcabaaccddbbdaddcbbdcadaaaabccaaddcccbbbdbbdbbcaccbbddcbabbddbbddcbddddacacadddabdaaadbbcabcaadcbddbdccdcaccbccdbabddccacdabcdbcccacaaabbacaddcdacadbaaabbdcadbadaddbcdcdcbcabccabdaacccdcaccccdbcacbabccdaadccbadabcdddccddddccdcacbababaddaddcdbbbbbdcadbcabcaacddbdbdcdabbdadbbcdabbccabcaccaadabbdddbccabaacdddbccdaacbbcdbcadbcdacadbbaabaaabcaabcbccbaadbbbadbcdbabbbdaabcdbacbabaacdaadccdaaabdddbcacaaabbbcaccbbcbbdbcacdbaadbcdbcdcdcacadbabcdccbacabcdcbcbddadbcdcbabcaccbadddcdccbbacbdbbccddbcbbacbcdddaadaaacaaccddbdccbbaccdbcaccbaccdadcbdabbababbcbcbbbacaadddaabbaaccaabbabdadabacaddbbcadaadbacbbcaabaacdadbdbdadaabcdacaacdbccbaacbabcdbcdcbdbadbcddbacbacadacadacdddcababcddabaabbbdcbacccbbbaacddbbcbaaddddcbbbcbdcbbccbdbabbcabccddacbccbadaadaabcdcbabdbdcccacbdabadacaacddaddbaaacdaacdcabbbbdbbcdbbcbcacabcddcadacbcabddbcadcdadddbbadadbacdababaddbbbaadcaccdbbcbacaaabcadcaccddddabdacdadcaacabcddcacdacbdadadcdaaaabcddcdcbcaccdddadaaaddcbcbddcbaabcaaacddccadbbadaabddbddaacbdacbddbbcddcccbdadacdcdacdaacbddcbbdacacbabbaadcddadccbbcdcacbcbaddbccacdabdbadcacacbbccbaacbbbbddbdcabbddcabddcaacdbbaadabadbdbbdaabbbaaacbacacababbabaacbccbbdcacdabdaababcaacaaabbcaddbaabdcdbaaddddbdbdaddcaacbdbacbcabdabdcddccaaccdcaddcdaccccacdadbbdbbdbadbddabbcacbadddaaccbaacaabcacaabaadccaccbdcabdcbcabdcabdbacccdddcbbacaddbdbcdadcdbbccaadadbcddadcdddbdbccabdcbbaccbdcbcdbadcbcbdcbbaccaaacbccabadaabbacdccdcdaaccbdacabcbbddaaadbdcaadccabaaccdbbacdcbcdaadcdbdbbcacababbacbdbababcddabdcddccbcabdcbaaadbdccbdcdcaabaadcaccbcdadcdbcacbaccabdbbcadbbcaacacbabaccdcccbadaccaadbaabbbdcdbaabcacadddaadaaaaadacbcdbccccadcbcbaddccbccbacabdbbcaddaddbddaaacaabdaaaaacbcbcdbaacadccbbbcbaacbdababcbdbdcbccadaaabcdcbacadbaccdccdbabacabdbdabcbccaddadcaddcdabccaaaaaadabdbacabdabaddacbbdbabbbcdbbacdbccacdcdcdcbccccbcddabbcadadcdcaadcaaabdaccbdaabacbacaabbcbccbdabdcccabbddbcacacbddbdaadaccbddbccbcaaadaaacaaadacbcdaddbcabddcbdabcdaadcbcadbccbbcdcbcdabacbacdbbcbccdddcbaddcabcbbdcbbcdcbbcdddadbdccbbdbaabcdcbcddccacabbbdcacbadcaadcbbaccbadbcdabaaadabbcbccbdabbbacaacbdabccadddbcbccbddadacacadacddcabbbbcbadbcdbdadacbccadcdbcaabdcaadbdaabdacabcbdaacbadbcabadbbaabdccbdddbdcccbadababdbddbadcddcadaddadbdcbbdbbabacccbacbddacacadbdcbdbddabbbbaadcdddcaadbbbcbbddccdaaddbccaabadcaabdcbabbbcdcabadaddcacadaacddcdcddbabcabdaccdadccaddbcddcbbbadccdcacabcdadbbbbbdbcbbdacbabacacbadcaabbddbccacbcababaadaacccccaacbacbdbbbccccbbcbaddbaabbacbacbcbcaadaaaaabaadcdadbcdbbdadadbbbbdacabcadcbabbbbbdddddccaadaabdadddcacdaacbaddcbacbccccadccdbadbcacababcddacccbabcdbbdcdcbbabaccaaaddccbbbaddabbaccbbdbbdbbdbcbcadbbdcdccbdacdcaaaababdbdaacdcccccdbccacabbbadbccbcbdcadadabbcbdbddacadbbbaccbcaabdcccbdccaabaaabcddadacddabaabaccaadbdaddccbadcaabdccbbdcdbacccacabcdbdbddacacddaabdbbbcbcbabcaaacacabddbacbdacbcbcaaddcdbbbddacaabcdaddaccdabcbccbddacaabdbddcbacbcbdabcbaadabddcbbcbcabddabddbaabccabcbbaadbbdcaadccacbcbbcacccaacdbbccacbacaaaccbcddccabbccdaacabcbdbcddccaadacaabbddccbbbadcbccbddddbcaabddcaadadbbcdacdbbdacbadbbcbbcbccdababdacbadadbcddbadddadaababbbdbdcbccbcacdadbbbbbaadcddacacdcadbddbaadbddbabaacdaadabcadbbaddacddbcadbadabdbbcadcccabbcddcdbcbdadccaddccabbabcdbbcadcbcdbdabacbdbcdddccbaababaaadbccdbadcbcaaacbdcdaabddaccbdcadccdccccaacdcaaddcdddcbadbcaaccddcbbabacadadcddbadacdbddabdcabbaddcbadbadacddcacabbbcdbccccadbbccdddccccddbcccaabdbdcabbabbbaccbcaacadaddaccddcaababbddadcdbadaaccdaddbacbdccddddabcdbbbaccbcdddababdccacbaaadccdcbdbcbbcbbabdbbcbbdddaaadbabdbbdaaddaddabbaccbaacaabcbacccbbacdcbccabbadabdacdbdcbdbdcccbabcccacdbabbddcabdddbbddbacbcdbdcacbbcdabbdaddadabbdaabcbbaddcbadccadabcdbabbacacbdccbdbabcccaaacddbadaddddaccbbaadcaadccbaaababcbdbbadacbbaaacccdacacbdcbbbabbaccdccaadacbbbabaaddbddcaabadcabbaaaddaaacbcccdcbbabbbdddbcbacbcdddcbdcbddccbaaaabbccbdabbbbdaabdacacdadabbcbdccdccabacbaabcbccbddcacabdaaacbddbcaaacdcabbbbbcbbcdccadcaddaccbccabdccdbaaccadcbaaabaacdcdaababdacabdaddcbdbdacbbacaacbacbddcadcdccbdaaaabbdccadbdacccdadddabdabacdbabddbdaacbdbdccaacddaccacadabbcccaaaaabbdbadcddbaaddadcbbabdbdadcbbababadcbdaaadbcbbaccbaabdcbdddcccbcddabaaaabbcadbcddbabbadccccdcdaccbbcbcdcbadcbdcdddcbbaacdbdbbdbccddadcdaacadbaabdacacccbbaabadcbcbcbcdaaadbcbdcadbbcaccccdbdbcabccccdcddbaabdcabcadddaabadabdbdadcaacdbcadabbcbacabbcbaaabcdaccadcbdaaaabcddaddbcbdcadbbaaddddbbbcdbdbdadddaacbcbccabccdabcbcdaabdaccabbcbadabdbcddabccbbbccacddaabbadabccdbdcdbdadcbcadcbadabdbdcaddcbdcbddaabbccbadccacacaababbcaccaaaaaabcdcccddddcdbaacddadccddbaccdbcbabdbbbdddbbdbadbbcddbddbddaadccddabbcacacddccabaabcadabcbdbbbccddabccbbddadbdaacddbaddaaadcbdcddaabdabcbcdadccbddcbbcbadcbabbadbbcadacdabacdbdcaadcaccdbcdcabcbcabdcbbaaadddadabddbbabdcddcccabdcabcbcdbcdddaaadabdbdcbccaababbcbbdcbaccbbaabacdcddaabbacabcbccdbcdadbdbabcdbddaabaaadcbacbdbdccaddbbcaaadcaadbdadbbbadbcbcbccbbccbacaadcabaaabbabdbaacaabbabcdcddccccdbadabdadddacbcbcabdbddbbdbadbbdcddaabccbccbdbaadadbdcbaaabdacdadbdacbabadadbcacabdaacddccbcadbbbbbdcccdcadbadabaabbcbcaaacabadbcdbcaddacddcbaddaccdbdbcacbcdabaaacbdbccacbbbdddabaacabdcbbddbcdcabccbdababdcdadbaaaddabdcbbbbdddaaccadadabbacdccabaaccacbbbdbadbdabcdcbddcdbddabbcdbadbcadadbcabbdcdbcacdaaddccccbbdcbcbccadcdbdbcddbdbdbaabbdbdcacadcdccccdbbacadcdacbbccaacdabcbcbbadbddcdcccdcaaaabcabdddbaddddacbabadaaddacabcdacaaccaadbccdbadadbabddbbaacddcadcbbbddddacaaddcddddbddbbddcdacaabbcaccbbbdadcdccbcdbbcacdddaacdbccccddccacbcdccbaacdaddabdbdabaadcbbbbbcccadddbcccacbcccbbacaabbcdbddccadbcbcbdaccabcaacbdccacbcdddccdccaaddbcdbdddacacaabdbdcadbdbddbabddbdccdcbbbabddcccbccaaddabbbaaccacdbabdabcabbcabacdccadcacccadabddccdacabdccdbbcacadbccacdccbdbbbacbabcddaccbabbddabaaddaaccdaabdddaacabbbadcccbcbaaabbbcddaddaabdbbdcbccbbcaddaabbaabcaccbdbccadbbacdcdddadcccdddaaabccaadabdadbdaaadbdaaaacdbdaadaaabdbaabdabdcbbbdcaadcbdddbbdbbadadcdabadccacacbddaabdbdbadccacddcabdbadccbaccabccdaccadddaccbbabcabbacdcacbcbdabdaadddabcbacabcbabdbcbcadbdbabdcdcbcbbddddddbdcdadbbbacaacacacbcbcdcabbbccbbcdbacccddcdbdbbddbcbababbadcabacccaaddbaccdcdacaccadaadaccbbdcadcbbdddabbabddbacabcddbddaaacbbaabccadbddacdccaacacaccabcbaccdbcddaadadcccadabbdddcbbcdaddbcdcbccbbcccdcbcccddcadddaaddabddcdcdbabcdcbcddaabcabcdbbbaacabcdaaadcacdbdaadbbdbcaacdbbccdadddbdacddcadbcaccacbdbccbaccbcadcbadbddadcccbbcdcbbacaacbabcaaddccadccbcbdbcdadcabcbcddacbabcabcddadbccbdaddaacbcbdaaccaddddbbbaaddcdaabadbdabdadcccadddbaccbdddccdccdacacbddccbddcaccdababadbcaaacdadcbbadbacbdabaabdcabcbbcdbcdddbbdadcbadbaacddcbbdacabdbaaacdddbdddacabadbbbbccddcdbadacaacabbabcadaddaaacbbddddcdadaabdddcbcaddbbbdbdadabaddacadaccccdadadcabcbbdcbbbbbcadcdadcbcdcbaadbbdbcabbadddcdbcddbdbadbaabbdacaabccddcddbaabcccddaddbccacdcbdcbbcdcbdddcacaaadcccbbacabbadcdacaaabcccddbddbaddcbdddaddccaabbaabcdddcaabbdbcaabcaccaabbbdaddbdadcbbbdcdadaadcacccbacacaddcdbaccdbbcbaaabbaacbdaaaabcddcdbddaccbbdcdbbbcabaccbccaccbdbbababddbacacddadcbbbccdabbabcbcbadcbacabbdcaddaccbcdacdabbccbdbabaddcadcadbcbcbbcabbbcadabcbbcacaabbccbaaacbbbdbdacdccbdadaccddcbdbdbbddcaabaabdcccdaacbbbdbbddbadaddbbadbbdbbddccabdddddbdacccbdddbabddcabdcadbaaabadbacddcadddaddbddbaacccdacbdacbbaacbbbbadcdbacdbabadaaabccdaacbadbabadcadbbaccddbbcdabddbaadacbddacdabbcaabdcadcdcaddbacddabddcaaadacaadbccbddaabbcaabdaaccddadcaccaadabcbaadabdabddcdddbbaacbdaabcaacdadbcbbcacccccabcdacacdbbbddaddbccaabacaaadbcdcabccaacbaddcaadcdbcdcdbcbacbdaadddacbcabdddabdccdbcbddadabcdddcbaccacbddbbbccddabcdcddcbdadbbcdcaadcdbdbddcccdacddcdaccbabadbdabcbadaabcbbcdacdbdaccdbcdccbdbbddacabbcdadacdbdcbbbbbddadbaabccabadcdbdcdcabdbbdccabcbccbbccdcccbbcaacaabbbadbdccabccbacaabbabbddabadaabbcacdcaadbdccccbacacdcdccdbbbbbabacbaaadddccdddacdcbaaddacdadbddccabcdccddbdadcbacbdbaccdcaadbabcbbaccbcaadddccdcadbdaaadaaabbdacaacabcbcdbddcccbddbdcdacddccdcccddddabbbaaadbadcaabddcbcdbaadcdaacdbdaabdaabdaddadbaaadcaddcabdddaadbacaddcbbaaaaccdabcabcadaacbccddaccdaadabaaabababaddaddbaaddbdbaddbabdcddaddbcddcbbcbbbadcdaddaccdcdbaabbcbddbccbdcdaaabbdccadcbdadaacdddddabadadcdbcccbdbabadbbbcdabdbccbbbacbdadbababdaacbdbddcdabaacabdcdbdabbdacbadaabddbcbbcddddababcdabadcdaacaddacbcddbdbaaccaabddaacbdaccbcbbacbbbadabbabacbaabcbdbcccaddbdaacaabdbcabcacddccaabadccdcadaaadddaacdcdaabbaabcbdcbdaaccbddbbbddadccdbdccccdddbadbcbcdbaacbabcddacaddddadbbbdadbdbddbadcabccacdcbbdcbbcaacccbcdabacddbacdbbabddbabbcdccdabccbcadaacbdcbcbbbacddbbadbbcdcabadaadddabcadcddbcbdcdcccabaacaaaddcaddccadcacacbcdbbcbccadabccbddccdbbaacbacdbdccdddddaadcbadcbdbdbaabbbccdcbbdbadaaadbdccdcccccddbdbddccaaaabaadbbdabdddbaabddaadabbabdcbdbbbabacddaabaaadbabdbaabdbbbacbbcacbdabddcbbadbcabaccbbcacbcccbbaaddbbbddcdcadbacdaaadcaabbadacbbdcbcddcadccaacacdabccabcddcdcdadcacbacddbcdbdccbcadaaaaadddbaabbdddaccbbdccababdcdaacccdcbadbbaabcacdddcbaccdaabacadcdbadbdbcababcdddbbbcadccbdcdadbadccdaadcaabcbcdcdbcbdccdccabcaddccbbadadbbbadccbbbdddbacbddaadbaacddcbacabdcbdcababcaccdacdcadadabcbddaddddaabcadacaddaabdadcbacacadacbbdddbabbcaccbbccccbddcbdcadaaadcccbdabdbadccddbadadddbbcbbbccabcaaccbaddcabbbacbccbddbacaaccdabdacccbabddadbbccacdcaddbcdadabaaddbcabcbabcabcadbcddcbdccbcddbdcccbdaddbbabcadcdbdbddbabbcaccbbddcbbdcbbbdccaacdbdcabcdabbaacbacbccddbcbabacbcdcbcccbdbdbaabcaccbadbbcbcbabbcdbaabccddbcaccbddcbcbdbabbcacaaaabddcddcccbaaadabdacdadbbaaaabdaabcccacadcbacddaccadacccddcccdcbaccbbaacdbdcaaadcabbabdcddcacdaabcccabbbcbabbaaddbdbadcbbbbccbacdbdcdbbbcbcddcbbdddadbabbbadbabcabdcddadbaadbdcbccbcdbaddaacadcacacbcaabbcbabbcddddcbdbcbdcdcdadbababcabdbaddaccbbadccbcdaabbbddaccbdbddabbbdabdadaadddccadbccccbabadddcaccabaaabdbaccabcdacdcbddbdacbddcbcaddcdbcacacbdccadbcacaaaccaaaababdacaddbdbddddadacdbdaaaacbadddaabcaaccbccdbbdaddcdbdbccaddabcbadacbcdadbcbabadddbcbccdcabdbabbcbccabbbadcbbadbaaadacdcbdcbaccaacdaccbdcddccddbacadbbccbcbbabdadcbdddacaccdbaaddcccadacadcccdcaccdabdaabbaacdbaaabadcdcdcbdccaabaccdccbdbcbcbcbdbccdadaaaaddbadabdabadddaaabaddaccdadaacdbbadbbccdbaabccdddbacbbabcbbbadcdbdacadbdacdacaadddcdbbcbdbdabdcbcaaccbaacddadbdaadbadcddaadacbbccaccbaaabcadcdadbacacaadabdbbaaaabbbacabaadbdadddaccadadbabbdcbbdbddcaddbcbaabbaaacdaddbbabcdbaaddddcddbdacdaadbcdbbacabaaaacdcbbcacdbacdbdadccbdcbbdccddcaacaababbcdcadadacdddaccacabaddacddddbabbacacdcadadbabbacaabbbcadcddcddbaccadbddddacccdadbbbabaacdddbdadccacdabdabdddbbadbbabcacbddbccabbadabaadccacbcdbccbbdbddcdbbdadbdbdbcabadcddbcacbadbcccaadddbddcacdacdcdaddaddcdbbdabbdacdaaacaadababcaacaaccccbaccaaabacddbbadaabbadbbbdbbaaaaabaaccccccadbdaaabaaccbdcaabdbbacbddacabccbccbcbdcddbbdbddbaadbbcadcccadbbcabcabaadbcccacccdccdcbcbaadcbdcdddcbdbcacaaaabbadadddbddacaacadaacbbadcbbdddadddccacdbcabcddcdabdacddcccdcabadccdddcdbaaacababccbcdccdccaadbaddbcdaabbdaabdcbdbccdcddadbcdaddcadcccdaccdccccabbbaaaacdbbaacbcbacccabbcabaabbabdcddabcdbaccaddbccccddbcbcccdabdadcaddaaaccdbcdaccaccddcadccaabbdddbdcccdaccacdabdaddaadcabdbabcbdbdcaadcdcdcdcabdbaadabbcaccdabacddcdabacdabddacbcbadccaacadbdbbcbbaccbaadcccccdcbaacbbbbbbcddaaccdaccabcddcadbbcadbbbddbdddcacdbaacabcbbbdbaddbadabddbccdcacaddcbbdadcabcbbdccdcdbcdcbbbcadddbaaabbadcacbcaacdbbadbbbcadcbbcdbbcddbdabbccbbcadadbddbdbbcbdbbcdabcbadcbaddcbcdcbbacbbadbccdacddbbddddbbcbacbbacbcbcdbccdbabadadcccdacbbbdaacdccaababcadccdaacdddbbdcbcbbacadbccdcdbcccabdcdadacabbbbbcbbdaaddbbbbbaaaaabaccbaacbbbccaacddbadbccddddaaabbccddbbcdccbbabdbadaadccccdbccaadddbabcdcadacccaddcccabccbddabbcbdbcbcaccbccbcbcbcdddaaccbabbacadabdaddaabddcbbcadbcdbdbabaaaaddbcacdcdcabbdadbbbddbbdcbacccccdddaabbbdddbbcabdcbcbcdaaddddabaddaaaacabacbdbadbaddccbdcaaadcdcccbcadcbbacddbbdaaddddbcbcbacdbdacdcccaaaaadabdabacdcbadcbbbdcbdbccaccdbcaaaddacadadccddcbdbcccddbbbdbcbcbbbcbcacdcbbbdcaddbaccbaabadabdbdabacbbadabcdbacaaadbabdbbcbaccdadacabaabdacbccdbdcacabbacacacabacacaaaadccbabbddbddcbadaaadabaaabdbaadaaccdcaaccdacbcdaabddadbacadcccdcdbbbabbadbcbdccddcdbcdaabadaaddadabdbacabccbbadadabdbcccddcacaccacaaadabddcbdabbccdbabdabaddcdaacbbbbabacbdaccddcdbbaacbbbcdbadbcdcbbcdddddbbbdaddcbbbbcdababadddbabaccbbbccadbcabdaddbaacacaadbddacbdacadcbbdbddbdcadbcdbcabdddbdbcbdacabcadcaddbaadbdbccacdadcccaccdaabcbbadbccabbccbddacbacacaadcadccbccbccdadcbdabdddbcbcbabdcbaacccaacaddcbbbdaaaaccaacaddbacddcbdabcacbbabdcdbdcadaabdccddbaaacacbaabcbccbdbbdbbcdbddbdddccadddbbaacaabaaaacddcababdaadadddddbcccabdcbccabdccbcbaabcbdaccaabdadddccaaacdcdababbacbcdaaaccadcbdabcbbccbddadbaaadaaddadabcbdcabdccccdacacddabbbdbdddbbabbaadbacdaccabcacbbbdcdabbcaaabbcddcbccdcbaaaaadbbdcddadbaccabaaacbcbbbdabcccbabadccacccbcbdcdcbadcbbbadbdabdbbcdcdddaddaaabcbbbccdbdacdcbdbdcccbbaacaccabbbcbadbcccccdabadcdaccbacbcbacdadbadccdabbcccaacabbacdbacaaddaacdddcadbacabbaaabdadbcacadddcadbccdccaddcdccbdddcbdddddbbddbbbcbdcccadadbdbddbaacacacbaddcabcaddadbbccdbcbdacdbcdaadddcddaddccaadcadcccbadccaabbadbbbadcbaaacaabbccdcacddbbccdaaadbccbacbaaacccadaccddbcbcbadbcdcdbccbaabaadbbbaacdbbdcccbcbcdbbcdcbddabdcccbdbdbccadbcdbdbacbcacddbaaabcbccbcdbbadcbccdbccbbadddaabddcdcaddcbcacdbacadadccadbcdcdadbbbacbbabcbcabaccbadbbcdabcbbbcbabdbdccccbabaacbbabcbadcbddcccabcdcabdbdcccdcbacaadabdcbbaaaadbabaabbaabdbcbcbbbaaaaacadaccbcadbdadcbccabbbaddcddadcacdbacabbdadbcdaddaaacbbcdbbaaacdabadbaadcdabddadccaaadbabcaaccbcccbbcccaccaddbbdbdbbcbbcdcdcbcaadcdddabdcbdaabadbccddacbcaabcbdcacdbddbabacdcdcaabbcbbaaddccdaaccdcadbdadccbcdbddccdcabadaaddddabbdaddbdbbadaccaddbddacadcababdadbcadaaaacacdbcdcabdddcccacacbcdbdbabbbbcbbdadbcccaccaacadddcbcaadcdccbdbddbcbadcdbcdaaabddaabccaddcdbdadddaacaabcdbaccbdbddcacbadacdcabacbdbbdabddbbdddbccbbacbbdcdcddaddccaacbacbcbcadbcaaaddabaaaccdaccacdbcccbaaacdbadbddadabcdacdddcacddccacdddacadacdbbaadacddcabbadbaadcbbbcbdaacadacbabdbaaabbbdaadbdcccaadbabdbbabbdbadcbababdbcdbbbbcbbaacaacdabbcaddbcddbddbbcbcddbbabbbbabababccadbdaabacaccbbabcdadbcdbdabcdbbddacdbdcabdccbbdaacbdaacdacaacbabdbdcbcaadcbbabacadabcdbddabdcaacadbadbadaddacbaabacabaabccadcccadcabbcbdbbacdbddccacbdbbcdcacabdbcdddcccbadaacccaaccabbddababccadddbccddddaccbddbcbadadcaddddcbbcdccbdbccbcacadcaabbdadaccabbdababcadccdaadcbacbaabacaccdcadcdcaabdacabbccbbdbaacddcbdbddbadaddccdaacbaaadcbddbadaadcbcabdacdbadbbacbdcdacacbaaddcadaadcbcdbbbaacdcbcbbdadbbabcbbccdcadbbabbcccaccacccddbbadbddbadabcadddcaaabbdabddcdccdbdcdbcbcbadaaabbadddccbbcacabadbbbddabbbddadabcbbcddcddadcbccabcbdaadaabdcbdacdcbbdbccdcaddbdbaaabadcbabbcaccbddddbbbaaadcbacdaddbdddabaabddcaccbdcdbdbdabbbcccbaccbcbaddbddabddcdcdbabadbbdacbdbcdcbababaccdabacabaacbacaddbaabdbcbdaddabaaacccddbbddaaadaababbbcdbcbabcdaaacaaaabaddbcbdaacdbcabdadbdadabcdcabddabcdddcccbadcabdadccdccdcacbcaacddabacaabdccbdabaddadbbcdabbddbacdddaadbbbabdaadabdacadabbbaabbdabbaabdbddcdcccdcaadaacacabdacdddcdddacdcbacdbbabcdbccbdcbddacbdaaadcddadacbadbcbbbbcaddbbbcdbadaadaababcdcbccaacdadddaaadbbcdddddccdcadccdcbbabadcacdabcdbdadbdadbdcbabbcccbdaadbddbaabacadcdaababaadbadabcaacabccbbdabddabadddbacbcdbcadbcbdbbbbdaaddccaaabbadbccdcdccdcccabcaabadadccaadccadbcdbaddcadbcdadcabcdbbcdccbdabcdcadbcccddcdcccdddabbdadbccbcdcbbcdacbcaadccdaddcadddbcaddadabdbaabcdbdacbbaaaccccaaadbcbbacabcdccaddcbcdaccabcdcdbdbaddcdcabcbacbccbdbacbcdaadbacaadadbdabaccccdacdbabbddcdbdbaddcadbaabadacacacdcdddbabbacdcddcbacbdbbadddacdadccccdbcacccdcbbacaccaccbabdcbdaaaadacddadcccbabcdcdaabaadaabdddcdcdbbbbbddcbbcccddbcabdcbbbdccabaddaccddccdbadaccaabddbcbdaaaaacbcbabcdcdbdbbdbbbbdcdbbcadaaccaaaaadcddabcacabccababaaccaabaccbdcdaababdcbdcdbcdacacacbbdaadbdddbbcbbdbacbdbbcdccbacbbdacbdabdbcacdbbccbcbacaccdbbcdbbabcaaccadbcddbaccabbbccaabadcbcbbdabcaddbbcaadabdbdddbddadcccbacbbdbdbbcdacabbcdddcdabbbacccddcaaccaddbabcbcdbacdadabbbdbdbdbcadbadabaabdccdcdbbccdcbdaadcaaaacdbdbdaccbdbaadbcbadabbdaccdccaddcaccacbabcbbbbbbcbbbbbddaccaacadbdcdcaaacaadbacddcbcbadcbdddbcdddabbacacbbadccbbccadabbadbcddabddabdddcdddddbbacddbdbbadccbbbacbdaacbdcbcdaacdcaddccbdcabcdccaabbbbccbadaaddcbdddabdcccdbcbadcadacdcdddddaaacdacdcdaadbdabbbbcbacaaabacccdcbdadacabbbbbcacaabbbbdbacabbbadbdadbdaccabccbacdcdacccdcddaddbdbaacbdcaacddddddbddaacdcacbaaaadddcbdaaadbbbdbcbccabaddcabdbadaccbdbdcddabbabdbacddbacddddadcaccdbcacadbabcbdbabbccadccadccddccbbaccbcaaadcbbabbcdccddbdccabdcdacbddbcacdddabbabddbaaddcbaaddbdaadddbcbcacdcbddbdbbcdaacdccaddcbaccaabaddcdccacaaccaabdcabbcadcadaaaacdbddbaccabcddacbbddbabcdbdbbbdbccbccaaaaadbcccbaacddcdddcabdddcacadbcaabcccaacdcbcdbaacccaabbcdbbcbadbabdbcaaaaaabbdcabbcaabbbdbcbadabdddaadcaaaabcdcdcbdcbcdbacbcabbcbaddccdacdaadbacdaddbbddbaaacdbcbbcbbabdaadadcbabbccbadaadbdcdacbdcbaaadbdcdcdbdacdbcdcdaccccaabdcbddcabbbcbcadddccaacdcadacadccbbbddacbbdabbbacadbabcbabbcccbbbdcbbcbacbbbdbbccdbbcacbcdbaaddcabbdddcacbdbbdcdcbaaccddcbdbcacdddaaacdabccadccbadaaadbccdddccbdacabaddbabcaaadadaddbdacbcbabdddbaabdacddbaddbabdbcbcbacdbcbbcbcbbccdbbbdddcaadaacbbabadcbabbacbccbdbbbdbddcdcdcbdbdbcabcbaacaabdabbbaddcddbbaadbaccbbbcbbdcabbdabcbcaacacddcabbdbacbbabdbdcacccbaadcadacbcadabadabbdcccbdaccbbacdbdbbbdabddbabdccbdddddacdbdcccdadaabbccdabcddacbabdbcadadcaddcadbbcdbbacbdcbbcabadaabdcbccabcaaddadaccdcbcddbcdbbababdababcccbdaaccaacbdabacacbccbaccacadaaaadcaacadddaabcaacaadbabdabdaddddbcbcacbabbbcaadbcbacdaaccdadddabbdcddcabcccbddbddaaabacccdaacaadcdabaabdcabaadbbbacabdaadabcaaaaccddccacdbdadaadbdbbcbcbbbdbdbdcbbdacdddbbabdcbddbccbddcbbaccbbcacbbababadadcadcacabbdadcabddabcdbdacacabbdabcdaddadbbdadbddadaacdcbbcddcccbcadabbbbababaaaabbcabddbdddbadbcbabbaaacadbaaccddbaccabaadcbcaddbcbccabcabaabbddabaabcccabaabacddaabccbcbdcadccdccdbcdcaddbdcaaaacbbbaabdbbaacddbccdbccdcdabaccadbbcdacbcabbccaaaabadabdaacbdcaaadacacbdcacadbdaaaabadadcbdaddcabbbaccacdadbbdbadccdbdacdcdcbbabacacadbddddcdddccdadccadacbcabacabccbbbbcbcdccdcccacdbdbabcddbbbcdddbcdaadcddccdcddadadcacbbdbbaddaaacbbabadbcdacbcddccdbaabababcdcaccbaadadcddccbcaaaaabaccacdbdcbdddcbababaabbdccdadaaabcdccdadbbdcbcabaaadbcbccbadacbbdcddbbdddccbbbddbddddacabadcccbdababbbbacdcbdbbcdccddabacdccbdacddcadcaabccbdbabbdcbcdbbabdccbccdccabbbcadddbccccaddabcbdcdadbbadaabcbbbdabcbabadacdaaadbcccabaabaabbbccbcddcdababbabcabaddbaccbcadbbccbacdaacbcccdadddccacbcdabdcadbdbcccdbdbacddccbcbbbbaccddbcdddcbabcacbbcdabdddcdcadbbbdabbcbadcaacadadaccaabcbddbcdbdbdacdccbbcabddddaddabdaadacddbcccacdddcbcbbbadcbcbbcaabdabacdbcbcdbbdbaccbacbaadadbabbccdabbbcdcabddbdbbbbcacadddddccdcdcbbabccdddbaabdccabbbacbabbdcdabbddbcbadcaacadabadbcdcddbbcdbcdccacccdbdadbccdcddaccbdbaacdbacbabbcbbdbcbcccbdabbbbddbaabdacbbcdacbdcdaddbbbdadabacbcbbbcbadbacbcabcadcacaaabbdddbdadbccbcdacbabababcabadbcaabdadaadcabbabcabbbaaddbbdccaaaabcccadcbccbaccbddadacdaacdbadcadcabcabcadbbdaddadccabbdacccaacddcabadcadadddcacdbbabcbadcaddcaacbcdabdcdcbbabdbcddcabbadcdbdcccdaddcaaccbacddbacbcbaccaabcbaddddabadcbbdcbccaadacbbabbdadaaaacabaddccdbdcbdcacabcdacbdddcabdbadbddadcbaabbccacdcdcbbcbbdcdccadcaaacadcaaacaddbacdadcbaabbdabbadbbddcdcccdbcbddabacddcbdbdacaabddaabaaabcaacadcacababbdadbcdadabccadcbbccdabbabdadddbaaccacabdaccdddddbccacbcbccdbadcaaddbbbccaddcadaaaabdccabbaacabcbddaddbbadbbbacaabdcaccddabcdbbbacabdbccacbcdaaabdcdbbbcdcccbdadccdcdbcbaabdcbabcbddacbccadacacacabbabdabbaabbbaabacccbdbcdacdacddcacddbcabcbbaaddbaccbdcbbbbaabdcbcaddabacdabdadbbbadcbcdddddbaabdabaaaddabbbddabacadabbaaabadbbdbcadbddcacbdbdacbaaabdaaabbabaabccabbbaabbcbcdacdbdbcbacccadccddabccdddbbcdbbcbbbdcaaabdccddaabbddbbbacacddacaabaaacbcadbdabddaabddcccdccbaadcadabbacbddbcacabdcbcccabcacabccbbbddbcbcdadbbcbadbaacadbaddcbcdbaaabcbaddbbaaabddddddcbaccdacaabbdbdbbbbbcaddcacddaadbaaacddccdcdbbdcccbbbcabdadcbdadadcbcdbdaddcacbbccbbbaacbbbabcdddadccbbcdadccbabcddccadbcadacccabdbcbbdccbbdcaadccdadddbbdbcbaaadbddaaadbbddabdacdcadbabddccddcdbbccdddbcabcccdccbbcadbabdacbaccaaadacacbdadcbddcccddabcdcabdddbddccdbcbbccadaccabbaacbdccaaddcbacdaccddaadcbbccbdbdcddcadbbbaadacbcbccccddbcacaacdcaaaabdcbbbdcbcbaabdabdbabadbdbbabacdbdbbadbbbcbaabcacdddaaacbcccbbdaabcaadaccaccbcbbbbcbadaadddabdddcbbcabaaadcdadcadcbbccbacaaabdbcdcadbcdcaaaabbabdadaaaaabcdcabbcbddccccbcdbabbbdbaaaadcaccbdabbcddbddbccabcbbddaadccccabadaadddbcacbabaddbabdbaacbbaabdcbbcdcbdadaaababbddcddbbdbdabaacdcccbadbaddabdbbcdbbddaadcaacddbdcbabbabaadcabadaababcbbdaabcbdddbddacbdacabbdacabddcbaaaccbaddbdadbddbbbaccdbbbbbaccaaabadadbacbdbbcacdcadbdddcacadcacbdabaccabaccccdbbbacbccacccdadcacbbcdbdacdaaaabbcbbcdcaccabcbdcaccdcaacacababcaaacbcccaaddacbdaabcdcbcabdcbbbaddacbacddacabcbcdbcdcacadccccbbcddabbbbddbdbdaddcbbcccaadcabcbcaabccbcaabaabaddadaddcdaabdaacdcdcaccbcdaddcabacdccdbcbbdbdbdcddbbabbcaacbabcddadbbbbadccdbccacbababcbbcabdddccabaddbaaccdcbccdaabddddbbcbdcdcbaaabccbcadaccccccbdbdccbbdbaccbcdbcccdcacadbbbdbdbadbccbccbaaabacbbbcbadcbdcbcccacaaacdbbccbacbcabacbdaadccdccdcbbacaaadaaacdaddadccbbaaadbcbccbbbacddabbadcdbdadabcbadbdabbcaaabdbbdddbadcbbbaabaddccabcdbaaabbdcabdcdbdcdaacbaadcacccbddbcdcdbddcbabaddabdbcdbcccabbbccdbdbdccbacbabdbabdbadbbddcdbbccabdbbabbbdbcaadadcbbcabddabcaabbacaccacbbdabdaccdbabdacbcacdbdadcabababbbcadaadcbbbadddcadcbbbddaadbadbddbbcdbddbadacbbcabdbbaaabbbcaccccdbcbbdbdbadbdcdccbcddcaccdbaccbacbccaccacbbddabaaddddbcbbbaacbcaadcabaddabcbddcacbcddacaadbcaacbabbbacadadbaacbddabacacbaaabdbcdccadbdaaaccbaadccddabdddababbbbddcdbaababaaccadbcbaadccdbccbbdbdbcaaaabbccdaacdcbdddbbadbdbcdabbddbadccdadbdcdbacbcaaccbdaabdcdbababcabbadadcacddcaaacaaaccdddaacadbcadccdbaccbbadccacbadbacabbdacaacdadbdaaadcaabdbbcbbddcabbbacccbabaacbcdbcbbdccbbccaddaddbabbccadbbdaadbbacabbdbdccbdabdbbcdadbccbdaacadcbbabaddccbacdabcaaadabdbcbdabdcddbccbcdaadbddcadccaacccbddabbccbdddadacbddacbcabccaddaacccacbddbabadacacbcddabaaacabcbbbcccaddcdddcbbaadadbcacabcdbccbdbadbcbababbdbacaadadcbccaaabdaadccccadbcbaaaccdcdacbdccaabcacacacacdcbbbbbbadbbaabcdccddaaccadccbbddbbcababdadbdaacccaabcdbdccccddddbddcdaaacbbbcabbabccadccbcbbdaaddbacbbccadcacababbcbaccdaccaadacdbbadabcddaccccaacbbcdcadcbaacccbaaaabaadacbbbdccdbdcabdaabbbadbacbccdbbbdcadbcaccadadabccdbaabdccadadcadcddcabdaaacbdacdcbbcaddcbadaaabacdddbadccadbbcaaabbbabcdacbddddabacddbaacabddcdaddaabdabadbacadadccbabacababbadcacccadbdadaddcbdbcccacacdccadabadabcaabadccdccaadbdbbbccbacabdbddbdbbacddaabbcccdcaadbcaabbabbacdaaacbcbcbaabcbcbbadccdadbabdcacdacbcbcbadcddbadaaaacacadddaddccbaadccccdbdddabacbdcbabcdbdbbbdcbcabaaddacccbcacdcbcdcdbbdbaacadbddcdcbdabbcadcbbcaccbdacbdcbcbcadbbdddabdbadbabcbbaadcdadbdcddaaabdcbdacccdbdaddaacdcdbbbcabbbdacbcdabccabcccbbdcabccccccadbaaaddaaaabbbdaccaaccdaadbbbbdcbadbdabdadcabddbaaddaadaadcddbacabcaaaadcdaaadcbcbdbbccbccbdacacaacdccdbbddbbadcabdcdbbcdabdbbcbbaabcccbdabdadccdcadabbbccbbddcbcadccbcdbaadacaacbdcbbaaaabbdadabdbdcdadcccbdbddaadcccadcacccdabbbbccddddbdacbaddbaacbbadcadccacaaabbacacabccbbabaadcccbbadcaacddabbbddcbdabcadddcbaacbbdbaabcabbbdbaacdbdabdddccbcadbadbdadaabcdcabdcabdcdccddbdccdcbcdaabbdddabcdbacacdbbaaabdbbacbcadbdddbabbbbbdccdcdbdcaddabaccbbcababcbdcabaccdacdacbddcbabcbdaadbbdabaaacbddbbbcabcdcbadcccbcbcddcdacacaaaabcdcabcadbabadcbbddcadbddcdaddcacaadddbdbbcdcaddccbbddccaddccdddacdcbcacabcadbdaadbbdabcaacaadacacadcbaddcbdbbbaabcddaaaabbbbdccbcddcacbbabcdcbcabaacccdbcdccbadacdcdcdbadacbadadaaabcbbaddbbadbdaaacabcbdacdddcaddaadadcddcbcaddcadaddbcbbccaddcacbbaadacbdccbdcadddcdbabbdccbcabdbbadcdddcacccbcdbbdabbaccdbbcdbadbacbdcbccaaaacccdbdcccbcdabacdcdaadbbbadaaccccaacbdaaaabcddadbccdababbcaadbacbaccddbcdacbbdbabddabbacdbdadcbbdbbaddddaadadbbdcbabadccbcbbdbdbcadbbdbdcbbbabadadabbbcacaabcdbbcababdcabbbdcdabcaadccabbabcdbaddbcbdccbddccccdbcaabbbdbaccddacdcaaaabbbadbabbdddbabadadaadbcabcbbcabbacbdaacbacbccbccbbadadcacdbacbdbbcadabadcbdddbccdcacbbcaadcabcabdaabdababbaacddbabbaaacacdabddddcccbcdccbdbaadbabdccdaaadcccdbabdbbcaaabacaacaabadacacdbbccdcadabbcbbdabbabbddbabdbacddcdcdbacacdbccdaacdabbadcbbcbbdbbddabbaabbcaadcbcccaadccadcacabccaabaabbacbcdbbddbbcadbcbcaabadcbabaaabaabbcddacbaaaccbdaacbaadbdabbccbdbddddaaadbbdcbcccbbdccaaadcadcdaacbbddabdbdacdbbcddccbdcccddbbbccadbaaddcbadccaddbddccbdcccbadbcdcbadcabdcaabaaaacdbaadbdbdaacdcbbbbcaacbbcacbbbbbabbacdbaaabcdacbddacdbdadabbcaadabbddbaadbcabccaccaccacdcbccdcbdcdddccddbccbbbbbbcbdbccdbdaccbadcbbadcabcdacdaaadddcbbbddaadcaaabcdcbabbdcdcbcbbbadcdcdaccabadcaabbddbcaabdbadaaccadcbaccccdbadcccbcabccbdcbaababcbdccdadacaddcdcbaddabdddbdaddddcdccabbaadddbdbccdbbbadddccbdcabcbabcbbcccccabdacdbbcccccacbcddcdbabcabddacbcdccaadcbbcbddcccdcddccdbddcdbbddbdcbbbcadadaadbdabdcdabbadabbccbaddcbacccbbbcccacbbdbccdbdabaabbaaddaadcbddbdbcddbdbdcbcabbbcbbbdaadddcbcddccaadabbdbaacabbdabaccbdbadbaacacabccccaadbabddacadbdbabddbacadbbbacddcadabdbdccccccbdabcabcaddddcddccbccbcaaaaaabcdbaabbcccabbaabccadcacddacdbccbaabacadabcaaccabddbbdbbaadbdabbcbbaaccbbcdccabdcdbaaccbcbaaccdcbccdbacdabcababccbdbcbccdcdbddcbcdcdcaabbdbdcabddddcabbabadbdbbcaadbcaadbbbadddbdcadbacabacbacdddbcacbbbdbaddcddacdbcdbabbccbcddaccddbcacaaaadbbacabdacacaddcbaccbaaadbbadbbbdbcbdbcbbbdccdcbabccbbdcdbdddccbaacaacadbdcbaccadccbadccccadcbddacbcbbddcaabaccaacbaacdcbadccccaaaadaacddaccadcddbacbddadcbcadccaadaadaadbcdccaabbcbdabdbdddccdaabcbdddaacaabadaabaabdccabdbacbababccdaccddbcbabaaddcbcabbbdcbbdccccdacccccdddadcdcdcdbababddcbcadbdcacabdbdbcddabcdccbcdcbbbaadbdaadbddccbddacbddcacbbbaabbccacddaaabcbaaabbbdabadbddcccabcdbcccbdabcabacdbacaacadcbdacdadcbacacdddbdccdabaccaadbdacdcbdddabbabdbbbdcbbbabcbddddcabdbbacdaddbdcbbbbdbbdddddddbaaaaabadbadabccadddcdccbbadbcdcbdaadccdadcbdcddacaababdddddcaddaacbdadddacddbabddabcaadcadabbadcaccbbddbbccbdcaaabccadcbdadccddccccbdcdbbbacbbaacdadccbdbdbcbcccbacccabdccaaaabcdadcdddbdadbabbbcacddccdbbdcabbdcccdcdbbccacabddddaadacaadcdabdbcadaacabdccbbaccaaaccdbcdcdcbdadaaadaaaabcbbbdbddadaacbcbbabcadbbcccabbadccacbbadcddbbaadaccbaddbddddbaccadddbbbbbaabcadbadcadbaadadcabddcacacdadbbdbcdcbccabcacccdcbcacaaddadcddbacaaccdcccadcacdacaabcddaabcccdadaccaadcacdbadbdacaabcbbddaccdbdbdcadddbdabddacccdcdcabacaadbcaababcbdaccaaccaccacabcacbaaadccddcacbacdbaabbbdbccaadcbdbadbaadcabcddccbabcbbdbbbcbcdbdbadacdcdccbadaddbabbadccbcacacacbacabaabbddddabdacbabcaaaccbaabcabdabbdbccaadaaccdcddadcbbabcbcbaabbcdcddbaaccadcbdcdabdcbadccdcbcdaccaaaacdaabccbacacabadbbddaccacadcbdcabccacbddbaccabbccabaacdbdddbdbaabdbdcbadccccbaddabcbadabddcdbdbcccbadbadbdbddcbabcaccacbddcacaabddcadcddaaccbadcdacdcdbaabcbbcbabccccdbdbccabdbbcdcdcbcccdcdcabacdcadcdbdbadddcbcbddcaabbbbdaacdaadddccddcabbcdcbbccaacbdcdcadadaaacacbbbcddbddaaaabdabbcdadbacddbbcccdaacccbcbbdacaacbddbbdddcaaabcccdddabbdbcccdcdbbbcdbdabcacccddbccddbdddabbcbbdcbcadcbbdbbcdbddabdacbbdbaccccabccdcdacddabcddbbacddadcadbdcddadbaccbcdcabbcabcabdaddcbacacddccbdbddccacbccacbadbdbccdcdbacbbcbbddbddaadbbadbabdddbadddbdadabddbdadcadbbbccaccdccdccabcdaaaacdcbccdcddcabdddadcbbdbddcdccdcbacbdcbcbbbcdddbdbacdcccdadcccddcaacaaccbdbbdbccbcabbbadcaaaaacdaaaacdadabcbadddaaddcdbadbbbabacacacbdcbacbddcbbdacbbacbacaadadaadddacbbdaabcbbdccdbabbddababdbbbccdbaccaccabcabcbcbacdabcabbcdabccbacdabdcdcddbddccadbcbabcdcaaddbabdbacdbacdccbabcddcdcbcabdcacdccddbbcbbdccabbadcbdbbbdccadcdabdacdcccbddabdccddbdacbcdbacadddbccabcddaddbabdcddacbbdbaacbbbcdcaadaabcccbcacbddbbdcdbcadddcabbddaddcaddbcaabaabacddabdddbccdcdddcbaacdbbcaabaaadbbbdccabcdabadcdcacabddddbcddccdacaadbcaaddaaadacdacabdddcaddddddcccdbacdbccbcacddddbbadaccdbbdbadacdbdbbbdadbcdabacdbddbadadcbbbcdbabcbacdccbabacdbadbbbaabbddddabcccadaaaaddabdbdcdadddccaacbbaccbdccdccbcacaacacacaaacbdddaaadccabbccdcbadacbbdbbbcdbaaaabcdccdbbaccacbddaaaadbddabaddbccdabccaaabdddcbdcababccacdcddbdddcddbddbddadbbddabbbabbdbdbbdadabbbddbccabcdacdbacaabdbacacdccccdbbdddbcccabbacbcbbccabccdbadadaabbccdaaadbdcdddcccbbcbbccbdcdcdcadaadddbdddcdbcacadadacbbcdddadddbcaaaabdddbbdacaaabdcccdddacadaaaccdcdabaaabcdaaaadaaddddddccddbdbadbabcdbbdcbacacbdbcbaabdadbcacdbababbcabddcabaacdcdccbcabbcabdccaddcadcdbdcdccddcdaaacdcabcbbaddbcbdbaadcacdbadbdccdacdaabdabaccaaddcabbccadaabdadaacdcdddbdbdbdddddacabddaadbdcdaccaacbaadabdabcaabcdbcacabbccbabbcbacaaaaabbadbcdaaacadbbdccbbdadddaabbcacdbbbdbddaadddbaaabdcdcacddabddbddccbbdbcaadcacbbdbacbdabcddddbaaabcbdbccdbdabaccbaadbaabacadaaaaadddadcbaddcacddbbbdbbaaaaaaaccddbaabdbcaadbcbdcbbdbaaacdbcaccccccabbbdcbabdbcdabdcbbaabaacdcbcddcccbbbdabcbbadaadccabddabccddbbbacdbdabaadbacdcabbdadbacadbddcdaaadbdcdcaaabddcbddbdacadacaabacdccbacaacccadccbdaccdcdaabcaccabcadcbbadaacbddcbdcbddbbcabcdbcccdbdcdccaabbbdadbaaddcaacadabcdcdbdaabdccadadabccabbbbbddcadcabbccaaadbbbcdcbbbaaaccaaadbcbbcbbdadabcddadadcdcaadababcbcdbcbccddbcaaacacbaacdabadbcbcabcdaadabbcbbcacbcbbabdabacaccccdccdadbdccbcbdbbcaabaaacbaabbdccabdbdabaadcbdcdddddabcabbcdbadabbdabbbbdcccdddbbdddadabbaddcaaaccaaaaadbbccabccbbbdbacdddbbaaadbdbadaadabddcbddbbbccbacbdcdaddbabababccccbbcbbddbadccbdcbcadbabccbddcbddbaabddbcddbddcdabbcaabccdaaabdcdbcbbacddabbbadaaaacacababcbcbbacdccbacabcadcaaacdabbbaabbdabcbacdcdcdddcabbddbbbccbccbcdabdbacacdcabbbbcccccdabbacaaabcbdccabbdacdbdbccaadaaabdcdaaadaaacbbabdcdcdaacadccacddcadabcadadbdbccdabbbddcadbbabcbccccdbbbcdcabdbacacdaaccababdcbbbdaabdadabbcdddddbdbdbdadbbabbcdabbcaddbdbaaabdddabbcddddacbaadadadcadddadccddddbbbccababdabbcccabbadcbbdddbabdccadaabcddbabadabaacddcaddbbbbdadbabbadabdcccaccbdcddbcabccdadabcccbadddbcbbdcdcaacadccbbcbdacddbdbbdbbccccacbdaacbbdcacaccbcbcbddabbacdbdcacdddccdaacacdcbbbbddbbdababcbdcddbadacdcaddadbdbcabcbbcbdcdcbcabadaaadbbdcdaacbdacbdcdaccddbadccabbccbcbcaccaabaccaaaccdbcbcabcaabcabcddcdbbbbdddbdabbadaccaacbdcacaacacdbccdaccdcbcbbacddbdbacdaadaddbabcdcbbbaddadbbbbdadabcdcbcccdbabcbcaaacbcaabdcaccbdcbadabcbacabdbbcacadcbbacacbddcaccdabdacbbcbdcbabdcdbdccddcadccaddacbdbcccccdabbacbddacdbcbabbbbbcccdcbdaddccadbdcdbcbbbdcdbddbcacaadcdccdababbbbdcdacdcddbcaddaaddbacdaadbcadababdbcbcdbdacabbabbccbbddccdcdbdbaaccdbddbccbdccaacaacdaaacbcdbbcccacabcacacbaacaadcabbdddcbadcbbbaaababccdadcbaadddddcdbadabdbcacbcbbdcbdbbccbdddcbabcddacacabdabdccabcacbbaaccaddbbcbcaadcaaaddcbdddcbbbcdbbbccdcbbaabbaddcbacabcadcaababcbdaaddaadbccacdcdacbdbbabcacdbaadbbacbbdbbbbbadabbdbabadcdcdabadccaabddabdbdbdcbcbbdcbcdcabbddabbcbddadabcdaccbbbcbcdbdbcadcdbbcaabddbcdbdddcddaabadddacaaccabbcabbdbaccbbbbddbbcdbabdccabbaadcddcdabbadbacbddacddbaacabadbaddacdbccbcdaacdcdbdcdcacbcacdccdbbdccdcdcdacbaacbdacbabccbbaadcdcacdddaadaabababdadbacbacccaaddcbdbcababdaabacbbdabbbadddcdbccbdbbddbbdcdcacbbaabccccaacbabacccdbbdbdbcaaacdabccabdcdadbbcdacddcdbbbadacccddbcddcbdadcbabdaccaccaabbdabbabbbabdcdcdbbadbbbccdacbbaacdccbdcbaabbbdadabaccacadcacccdaddcbdbadaabcadcaabdbcabacabadddcdcacbddbbcabdbdaababacabaadccdbbcbbaccbacccbbcddbdbdbdbdddacdbddcccadaccbadbadbbcccacabdddbcaadccccddbdbdaccacbddcadaacabaaabbbcacddcdddbbbdbacabbbcdaacbdcbdadcbbbcbcccaaaacbdddababbddddcbdbbbbbbaaddaaddcbcddbacdbddcbbabdbaaadddcccacbdaacbcbbaacbdaaabaaadbccbaacdbacdadbaacdcbccdcabbaadccbcbbdadbbaccacabdbccdbaacdbcdbacccbdadacbbabbacccccbabcadcbcacdadabbadaaacabcaabdadcbbcbdcadbcbdcabadbbbbccaaacaddddccbdddacacbbbccbdacdbcbcbbacadcccbabaccadabbcdccadaababcacddacacadcbdadddcdabbdbbcdcdddabdaaaddbccdadaabbcbabacbdbdccadcdccaaccacadadcbbbaaacddadddcbccdddadcddcacadddaacbbaacdbcbcbbcdddbcdbddcaddddbbbbddcaacdccdadcacadbddcdbcdcbcbbbdcacbabdbbccacadbddcacbaaddabdabddcaabbcdbbbbaacdcccdbddccbcadccaacaabaacabddcccaaadddaddbdbcacbbabaaccdccbbaaddbaddcacaadababaabcaccdaadbacdcadcadbcbaddabadcbcabccaddbccdcdccdcbbcccadcddddacabdbcacccdaaacccaccabbdbacabcdbbadcabaacacbccbdcadaccddccccabdaadddcccdddadbaadcbdcdcdcbdaddddaabbbacabccaadccdbcbbdbbacccabcabdacaacbbdabddbdcdaabacbaaadcdacacdcdaaaaabdcdacaacaddccbccdbbaacbdcacdaadbcdccdccbbbccaaaaabbadcccdbadbcdacbcbbdbdcaaabcdcbccbbbaabcdcbbacacaabddcdcddbdcaacdbacdadbccbdccabbacaabaabdcbbbbbddddcbabacaadabccdadbcacdbccababcbacbdbaccbcbaadbdabccdcdadbdabdcdddadbabcacdcabbadbddcacdacccddbbdaacaaabcbbdaabdadccbddcaccbdbaabadcddcabddacdbccccbbbabababaddbbabacaddcddbbddddadbaaacaddacaaacaaabdabaadabacaadddcbccbcaacdbccadbacbbaccdbadccddbcabbabddbdaaccdddbcadaddaabdacdddcaccdddacdbcacadbbdadcccaabdabaccbcdcbdcaccbcdacaadaadaaadccbadaadabbddaccbabdadcdadcdabcdcdcbbbaaaabbdddccbdcdcacabaabaaabbdaadaddcccacbcddbdbacbcaabababacaaddcbdcaaacadccbcadaabdbcdddadcaacbcdaaacadcddbbbabcbaddcaccdbbddbbaadabdcadbddabacaaabcbdabadaadaaacbccbbbccbbacababbcadbabdbddadcbdcaaabcbbacaacacbbccaacaddbabbbadbacaadabdbabccaadcbabcbbbcdbcdbcacdcddabaaaacdacaacdcaabcbadacbaddbdbabcdcacbabdcccaccdcbcacbbddccbaabadbbbddbdadadcabcccabdcabbcbacaacaadbbdbbaacbadbccdaccddacdcbaabdbacabdcabababaadcddaddcbddddbcacdabbaadcadaaabddaaccdcddaccaaacbaacddbdcbccadcbcabdabbdbddabbbaccdddacacdacbbcadadbcadcbdadcbcddcbbaccaabaabbbdbdadacddbdbbaaacacadbadcdbdaaddcccbaabacdaddaaadaadadabddcbdbacacddababaadbdddbbdbbabbdcabbbccadbbabbcbddcbabbaacbcbcaccbabadddccabaabbddbdbccdaaadcbbbbacaabbdaaacdaadbdaacddaccccdcbbbcdccdcbbbacccddabccddacdbcdddcadadaccbacadbacdbddcdbbbcdaaabcbbdcbcaacaaddbbdcdddcadbccdcdaddaacacacbcbccbadbcdbddccaaadadcabbacbaaadbbaabccbabdaababcbaaaadcbdddccbdcdcacacabcbcdaaacbabcdcdcacbbccddcdcbaccdaadabaddcacdababcacbcdbbcadcddbacccdcbbbdbccaabcbbacabaadcabcabcdadccaacddcdbdababaaadbcbdbaadbacdbcdacabcbbbaaacacdbcbdaabdcadbcbccadbbcccdbcadcdbcdccbcdbdcbaaabdacccbbcbccbacbaadcddbcbdcbacaacddadbddbcdadbbccbabcbcabbaabdcaaacadcdadaababaabbdcbbdababbdcdacbdddcaaccabddcadacaaddbdabccaaadbbdaacabacbaadbacdabcaadaaccadadcaadbdbbbdddcbccadbbdbacdbbccadabbbccaababccbacadbcaccddddbdcdcdcbccacbbabcadcdaacacdcbbbbbbdbcacddaddcbadbbbdbabcdadccdbbbcdabccdbabccbcadbdadadcdbddccccdcababdabbcbcdcaaacbbaadabccdcabcbddbdaaaccadbababcdaadcabbacbaaabadcaabdcbcdaacadbcbcdbacbadccdcccddccdbdddddbabbcacbadcdcbcdadbdddbbadaccccadabcdaddcdaccbadcddbbbbcbbcbcababcdbdbdcccddadcababbcddabcbcbbadcbcbcbdbccbaacbcbbacabccaccdbbabddcdccdcbacadbbbcbabbcbdaabdbacababaacddccacbadcbadcaabcbdbcccbbbcacaabcacdcddbcbacaccbbdaacdddccdabcddbddbdaadcabbbbdabbabbbdbbcdadaabdadabdbdbadbdadabcbacbabdccdcccdbaacbcddacbbbbdadddbbbcadcdccbcddaabdcddcdcacacccacdccbadcaabbcbdbdaacadaaadcabdcccbabcbabccbcdbabddbabcddbbadcdbcaacdcbccbcbabcabccaccdaacdbbacaddddcdcaaaabcbaababccbaddcbbdccabbdcabbaaccdacddabcaddbdbdbabbcbacbccbdbddbabbcaadabaccbcbdbdbcaccdaddcdadaddacaccbdddcbbbdbbbdcabcbdaadadddadcdbdbaaccadaddbcacdccbbbdbacbaaadcbbadbacbccdbbacccbbbadcaacabdcbdcbbddddcdbacaabdbcccbbbbaadadbcbbcaaacdcaadaaddacbbdbdccbbdacabcadcabdbdadaabaabdbccacacdacdbcdccadbbaaaaaaabdcbbababbbacaadcaccdaddddbbaccabcdcbbaadbacbdbbcaccacdbaabbaaacabddbaddcbadacddbbcddccdadcbddbaabbabbdbcbabadbbcadcdaacddbdabdbcbadbbbdbbcbdcbbacdbacaadddbbbabbbcdcbdcbadcccadbbcbbdddccbcbaddbadbdbbadabbbabbdddcbaaccbbdbccaabcbdcddcacddddcaabcbccbadcadadcccbbcddcacabcabddbadcaacdcadbaccaccdbccdddcadbadbcadcbdacacdacdddbbaadcccdaccaacdabbcdcccbdabcbbcabdabaacadaadbadadaabdbaabadbaaacadbacaadcccbdadddcaadccbacddcadcbadacccbdbddadbdabcadbcabcdaddddddcddcaabdcdcbdbbcdcadababadbabccdaacdbadbdcdbcbcddacdbbcbccdbddaadbaaaaddabababaaadbacdbbdacddbbadddaccdabadbacbddacbdbacbdccccbbcdbbdcabccaacadcaccaddaaaadaabdaacdbdaaadcbcdaddcaacdddabcbbabcccdadabbaabaaddadddabbcddcbbabbabbcbbabdddbcabacabaccdcbcdabcbdccdaabbdcaacccdbdcbccbdcacaacbbbcbacccccbacadadcbccddcbaaddbacddacbccadcacddacabadcbbccdaaaaccdabdaccbacbdbccdcddbdbbbbadcbaacbbaddccbacbccabacdbcdadcdbcbbabdcbbbdaaadcdcbdaddbdcdaddcadbbdababadccbccdbddaccddadbcdbbbbddaccaaaabababddddccacadccadcbcbbddabacadaacbaccbadacdbcabcbbadcabcbbbbbdbcbcacbaddabbcbdcbdcddaaadabcabbacaabcbacddaadadabbcbddccdcccbccccbdbdadddaccdcdccdadacabdbbdcbdbdabbbdbdbbdcaadbcdbcadbbdbabaaccbdacacdbdbbcdddacadbdadbdbcacbbadccabcbdabbbcdcdacabdcbcadabcbacccbdcbcbabccbbabbbbdddcabdbbcdaaaabbbddbbddadbdbacdbcbaacbcbabaaddcbbaaabdaadbbbcdccbdacddcbaabdbbbcccababaccddbcbbadbadcdbcddbaabbacddbacaadddcddcddbddadaaccbacacaaddadbddcdbdacacabdbddddbbaabdaddabaaacacaabdbdadacdbabcbdbcabcaaadaabddcbdadabacbbcbaacddcadaccbdbdbccbcbbcbabbabbbacdcccdbcbbacaaabdacddccbadabcaabbcdacdabbbcabdabbbadbadaaadbdabbaaacddadbdcacdbdbcccadbbcddccbcaabacddcaccbcdaacddbddddbbbcbccbccdbcbabbddaacbadbadabdccdbadccddcdddbadacdacdcbdbddbbcbdaddddabaddbbcbccdbbccadbadcadcbaddddbcbdcdbcaacbdcabcdabdcdbcdaaabaacddcbcddccdbbabccdcddabdbacacdbaddddcbdcabbdbaaacbadcdbcccbabbadbabddcbaabdaddbdaccdcacbdddadcacabcbcbdbacdcaddbdbcbaddbadbcdcccdcbadbdaadcacdbcdaabadbababdbddcddaddaacdacbbabcddaacababcabaddbaabcaabdacdaddccdcbddaccbdbaaaccdddcadcccbadabbbdcadccaaddcdcaddbddabdcabacacaddcaacdbcdbccabdccdbbacdddacababdddabbacbaabbacccccdacabdcdbbbcbdaadabdddcddabdaaaadcadccdddbcbbaadcadbcbdabdbcccbadbdacaacbdbcdaadbdaabacaabcbaccacddbccdabbdbcacbdcacadaabacddaddcbbacaddbdabcabacccaadbabdcaccbcbaaccbcccbbbcabcdcadcdcdbcddbdbabbbbbdacbcdcdabcdabbcadbbcccbacdbdcdabcbdaddbbbbdaaddbcbdddcdbcdbbadcbcadbcbbddbbdcadddaacbcdbdbdadcbddbadadbdadacaaacdccdaabcbcdcacbcbcabdadcacbbadaccdbabdbdbcacddacbdaabdcacbdbbdbdbdbbcaaccaaccbbddacdbaaccdcbcbbacbaacdccdcadbdcdbbacbdacbdaaddcadccbbabbddbdbccccacbdabdbaadabdbdcabacbddabbacdabacddabcbaacaccddaacddccbdcbccddbbbdbababdadbbaaccbcddabcdacabdbadadaccdbabcabccabbbbaabacaacadccacdaddaadadcccbddbdacacdbabbbbcdddcddadadbbccdbdbcdadbabdbacacdbcdbcbcdcddcccdacbbcbbaadabdacbaaddbbcdbdbadaacbabcadbdddddcccdadbcacbdddbacabdbcdbabcdaabcabaddccaccbbbdadacbddcbddabbbacdaaaabbaddccadbcdbddcbabaaabbddcdadbcbbddadccdcdcccbaabdddaadbbbdccdabbddacdabbbcabbdabccaacaddbdcabdbbcbbaddccdbbdbbaabcaabccaadbaddcbccbddacadadacadcddcdbbbbddbbaadccacabccddbccdadddbaaabacabdbdacbddbcdcdcdabccdbaacadaddbaabadcdddcbddadbcbacbbbddabcbbbbabacaadbdabbacdbaabdbdaccdcddcbbacdbccbbdbbabbdcdbcbdbddcdaddabbbcaadaccadbdddabddbcbcadadddbbabcbbbcabcbbdbddccacbdbbccdacaadabddadddbcbadadcbdcbbbcabcabbcddacaddddcdacaabcdbdacabadcdbdbcbaadabccdcccdbaadabacbdbcdbdbcccdbbbcdddcbcdaabdcaadbadadbdadbbdacdbabadbbbadadaabdcaaacacccababcbcdccadaacdbacbadcdcddaacbacddbcaccbdbcaddbbdabbcdcccccdbdbdcccbaaccddbbaddbbcdbddaabbbadcaccbdbaadaaccccabaacbdbaaacddbdbabaabaddccaabcdccdcaadabdbcbcbcabbacacaccacadacbdacdcaaaddbbcbdabdadbdbbadabacbccdbddbbcdcaabbdaccaaabbccbbdbacdccbbcdbcddcbcaababccadaaabacbacbabbaddcccdccddababdbbdccccddacccbacbdacadbbcbccbcabddcbdadcaadbdabdabbddcadbadbbddcdcccddadabcadaccbdcbacdbbbbbdccdccdaaaacddddddcdaabbbddbcddaaadcbcbcaddaabbacacaccbdbcadaccacccbbcdaadcbcbaddabdcbccdbbabaabccaacdbdddcbaadacbcddbaaccbaddcdbadbcdababbdbadadaacabdabbaacaacadbadaabbbcdccbbacdccaadcbbbdabaacdbadcabcbcaabadccbbadbcaacbdcdacbcdcdbddbacdbcbbabbbcddaabddcbcdbccbbacacaacbcdcaadbbadcbbacbbcbccadbdaaabbbddbaacdcadbdabcabaacddcbdbdadadaacaddacbccdbcdbacdabcbaacaabcbdcbdacdaaacbabcabdbabddcacddbabdcddabbbdacabcdcbbabbdcccaacbcacbbdabdbcbcbcabbaccbccabbdbdcdacaadcdbcbcbbdbabacddbbadaddcbbcccacddaaacabdbdcdcddcdccdbbbbbadabacdbcdbdacdcbbaccaadaccabdbdbadcbaccbcdbadcaacdcdacbadbadcaacaababcbcbadddcdddaacdaacabcdddabaccbbcbdcdcabccbdccccddbadabdcbabcdddabdccddbabdaaacdaabbabccaadcbcdabbabdadacddcadbcbbdcddbdadbdababdbcdbcadadadbdccbaccbbcaccaadadabcacadddadbaacddbabdaddaacccadaaaaaabcbbddabbcadabccaadbbaadcdbbdccadbabbabbbbdccaaabbdcadadddacccdcddcdacbbddccccdacbbaccddbddbdcbbcbdccdaddabbdadaaddbcccddbdacbbdbbcdcacccdccccacdbabacbbdbcbaccadaaadabbcdddbdacaaaaabdcacdadcdacdcbdddabacbdcdbdbcdbadadadccbbacbbcdbdaaddcaadabadabdaacbbcaddaaadadcbabaddbbaacdabcddbabaacddbabdcdcdbaccbadbbdaddaccccccdcbcacabccacbccbaaaddbdcbbcabbdbaccbbcbcdaadbdddccbcbaabcccaddbcadababbddacdcbcbabbbbcabdbdcddcddbbdbaccaabcdabaabbdababacdbbdcdbdaaabcdbcadbdbbaadcdaddcdcdcabdbdababbddddbdcadbaaadcacbddabbdabcaabbabddccdacdadddbcaacaacdadccabcacbdbaadbcbcbddadddbcccbdacbdcaaaaabbdcaaaaccaababdaaddcdccbccaadbbdbadacddacabbcdccaacbdcacbdbcacbcbbaaadcbdbacacbbcbbbddabdcccdacdaacccabbcbdaddbdcccbddaccbdbcbbaacadcaacaddbbccdbccbcbdbbdcacbacbcdaaaaaabddddbabcbdbcaadbbbdbbccbacccccbcddadbacbbddcddcdaadcbbbbbdaadaaccaaddbcaabddabbbddbabcddbadaddacabdaacbbcacdbdcbbabcbdadbcbddbcbbaadaacabcaaddaddcadaadbbaddbabccbcbbadbcdaacbabaacdddbddcdabccbdcdaddbbcbcdcaccbaacbdbdccdccacacaabdccbddccdccddddcaacdbcdbdddbbcacdcddabbdbbdbabcbdbbccaabababdaabbcbddaccdbbbbacdbacdcccbdcaacdcacadabcbbacdcbdddddccddccaccadbadcdaadccaaaaaaaccbbdcdacadbaadbcdbbdbccacbdbcadabcdabdaabcabbcbdcacdadadccdccabcdddaaccdabcadaaddbcabbdddccdbbddcdaaaaadaddbdcbccdcbbdbbdaadacbbabcadcabddabdaadbabbccccddcabddbdacaabcccaadcdccbbabddacbbaabbdcadcddcdddccabcdcbbaddaddbcacbddabccdbdbddaabcadaadabadcdcdaabbcaadccabaabdcdcaaaaabbdddaccdbbcbbadabbbcabbbaddbdcdbbcaabdabcadddcddacdbbacdaabbbdcaacaccbdddbdaddbaacdbcdbbbcbdcbbbcbacdacddabcddabaddcdbccadcaabababcbdbacaacbcadbdbdcbaccdcbabbbbcacccaabacbcadbbcbcabdcabbbdaddbdbbacbdacbadbccccacaacccbaacddcbdbdbdcbcbacbbadcaacdadcacbdaaacaccaadcddababaacbdbdaddcdbdcbddcabcccccddbdacbcbcbabaadcccaccbaaccabbabbdacdcaacadaadccbbcdbbbdcbbdbccdcaacbbdbccbbcbbcacaabdbccbcbbbdddcbbbcdbcdccdccaddbbaaacbbdbaaadbbccabdbbabdbdcbaabcbbcbddcbdcaaddccaacdcacbdcabdcdccacdbbbdcbdcdbcadadccbdadcbdcbcbadbdbdbddbdbaababbdbabbabaadbbabadcabdbddbaaabdbbbccddaaddcacddbadabcbccadcaccbbdacdadcbadbdddaacaaabcddabaddcaacabcccbaadcadbbadcacacacdbabdaaccbbcbacbbdadddbbcbdddabdaaaabaccbcbabdbadbbbdbabbdcbacbddbacabbdcaaaadccbccabadaaccdbaabaaabddacdbacdaaaabbcdbdacdbcaddabdcbbaaaadddabbadbabadcdbabaaddcbacdbbcbcdbbdacabbdbbbbabcabdbbbaaadcabccbdbddbbccaacacccdcabddcddbdacaabdbaabbbdabadccaddccdbdcdbccbababddbacbaccbdcaadbdabdcdacaabdaaaaddadaabdaadaadccbdacacbbcabdaccbccdccccbddcdadddbdaabbacdaddcaddbddadaddccaddadbacbddaadbbdaccbdbbdbddcbcbadabbcccbaadddbdbbdabdadaaaccbadbaccabbddadadbccaaccaacadadcdcccddcccadabadbbdcbaddcbddaabbdccacaadcabbcabbbbbaacccdcbbcbbddacadbcbbbdbddcdcabbbbcaaadbcaccdcadbcbcabbbacbacbcdadcbbababaadccacaccdbcddabdcdaaddcddbbbbaabbcdcacaadadacbaacacbcdcaccdaabbdbbaccdabdbbadaacbacaacaabbddabcadbaadabbacabcbaababdaaacccbbdcbdadddddcadbcbdaaacbdadbcaabccdaccabdaacaacbdbbabcdbddbbcdbaddbbcccdbdaadbbabcddcccbbddabcabddbcbbaccccaacadcbdaaabbaddbbcaadacbddddbdadaaabdcdbacddabcddbcccccaaaaacaadcbbddcacbdccdbbdaadddcadcdcdababccdaddcaccadcbccddacbbdaacccdaccbdadbaabcacdabbcccbbcabadcadcadacaddabcabcbbddccdadabcdabcbcbcaaaacccbdadabcddcbcdbadbbcabdadcbdaddcbabdcbccaaacaddcdcbbcbbcacabadbbadadbaabddaaddcbbacdbacaddaadbacabdddcadcbaadadcdacbbcbaacbdcdbcdbcccdcbcbbcbdadbcbdacdacccacdbbacaccccbbdbddacbccdabdcdcbaabdabbbadaacbbcdadcacdddccaabaabbccdbdbaaaabdbbbddddcdcbbccccbadddaaccabacdcdbacbdccbacdcbccdadabaacadabbcacbaaccbbabdbcacbddbbbdbdacabcaabcbdaccccdabcdbccccdcbbaccadbdcdcabdddadacaadcdadcbddadaacdcbbbbcbccbacaccddbbaccacccbdcadbadbadbcbbbadbddbabababbacdbdcaaddccacbbacacbaabbbacccccdacbbabaacdabbdaabadcbddabbcaaababadbbdbdacbbdbadaccddcacadabaadadddbcbddcddabadaabddbccbadacbbddadbcbbabdaaadbccaacadcdabcbabbdbbabacadbddccbcdbbacdbdbbacaaadddddcddccaaddcbddbddbcbbadbabbcdacaacbaadacdaabdcbdacbdbdddcccdcababbcdabbadcacdaabcdabbbdbcbddcbdcaaaaabccdabbacadbabbbcbdbdadadcbacdbabddaaaabdcdabddcddddabcccaccbcbaaadadcbbbdddccaccccbcddabaacbabdcccaaacdaddcaaabbababdacabadcbaaadbacbbcbbcabbddaaacbdbdacdcdbaaacaddcbaadbbabacddcdbcdbabaddacbadbdcabababcdcdcdabbcadbbcabdccbcdcdcadaacdbbaadbdacbbbabaccbadaacdbdbdbdbbcdcbbdacdbaabddabacdcbbaadabbbbbbdddaccdabddbadcbabddaaaccbbbddccdddbccaacaddbaaccdbaaacbdadabddbcdaabababbadcdaccaadccaabaddddbaaaddcccccbbdabccaaccbdbacdbbccddddaabccbdbdadbadbcdbbbcbdbacabbbacdbcbddcabdbcadadcbcdcddccadbdabadcdbaaadacaacdacaacbbddcbccdabcbdadddbbdbdbdbdacdbbdbdbddddaacdbddbacbdaacdbbadbcddacdcdcdacadbcccdddcacbccddbccbcbacdcacdbbcdaccdbbbbbdcbbaaaadcabcccbccbdcddbcdababdbabbcbbcababcbdbabcdcbaaadabcccacacabbdbabcadaccacadccddbadccccabdbccdcbdaaccbbaabdaaaacbaacabddbbdcbccabbcaabcadbbbacbcabacccadccddccbccdacdbbaddaaaddacababccdcbbdcddaababcbdcabcbdcbaccbcbacbcaaccbdbbabbadcddaaabbddcaaccabaccccbabbabbcbadcaacbcccacbdacaaddadbcdacbadabbbdcddcbbbbdbddcaabbdccdaacdcdcacaadbadcacabacddacdcabadbddddaadbcdccadbddabcccdccdcacacdbdabcddbbcdccadbcdadbdcbccdddabcdccdccdcbdacaadaddbbadaacadbdccbdbaacbbbccbdbbdddbbdcdddaccbdbccdaabdadadbcbbcccbdcbdacbabaaadcabaacdaddacdbdcdaabaaabbabcacbcbddcbbddbdbbdbacdddabdcbbbdbcddcbcccbcdcbabbcdabcbdcaddcdcbcdcaccadaabaccbbddddbdabdbadcdbcbabaabdddcccbbbbacbacaacdcbcbadcbdbcbadbdacdbcaaaccccacbdbcadbdabaadcacabaddcdbabadcbaddcacddaaddaccdcdbbbcdccbaadacbcdcabccdcabcacabccdbbaaaadabdabcaacdcadbaadcdcdddcabbcdcdcdcaacbabcacaaddadccabadaddbadadadaccdaaabccbdacccabbcdadccdadabaacdcbcdbcbccddaacbadaadacbadabccdaacbccabdccbbadbcdbadcdcbcadbaaccdccdddacadbdacddcdcabcdbdbabcbccaacbcabccddaababcbdadaccaaaccaabadcdbaacccdccccaacbcbdcccdccdddbdbcdbcccaabadbabbacaadcdabdccdbdaacdadcbdbbdccaddbccdccaabadadabcabdadbabbcacdcbabbcccbaabcbbacbbcdcbaabcbcbbadcddaabcaabbaacbaccdbcabbcccbcccddaaacbddbccddaabcabaaddcdaabcddcababcdbcdaaaaacabcbbcbcdabdcdbbbadaccccbacbdcbccdabccaccdbcacccccaccabbbccddccbadabbacadddbacdadabadddcddadcacadbaaacdcbaadcddddaaccbcaacdbccdcbbaddddaddbcbabbcddcbbcdbddcadbbdddaaabcabbbaddcbcddaacdcadacdcaddbbccbcbdbcbbaddbdcadbcbbbaaaadadccbbddcdaddbdbaaadbdacdcbdaddbadcdaaadadbaaadabadcddbbdddcddbaadacdddbbaccaadcddbbbdcaddbcdcdcdddcbbbbacacdabbabcdbaaccbabcadadcdccbddbadcbaccddabcacaddacdbdcaadbadccdacdbcccccbdccdccdcabcbccddcbacdcbadddbadbbdaaaacbccabdaadadcadcbbacbacdbaadbcdcdbabaaaacabcaddbdaddbabdadbcbdaccdcaabbaddaadccacbaabbadbdcacccadbcbcadddddabdbacadddabdbabbcaadccdbabadbbabcdacacdacadcabaacdbbadbdababbbcbcdbcbdcacadcbdcacabbbbbcdbabbacbbdaddbdacdccdcddcbcabcddcbdcbabcabbdaddccbddbccabdbbcaadadbabdcabbcbdcabcadccbcacbcdacadddabbbddbddbacbdacdaaddcaaacdddddbcbdcaccbccdcabbbddababadbcccdcdbccbbacbabddbddbcacbbcbabcaddcdbdbaacddabcdabbcdabdbadbbccaadabcbccbbabaadcabaccbbcbacbaaccdddbadbcaabbdadaaaabbadabaddaacbbbddaacbcdbbaadcdbcaaadbcadccbcbacbdbbcdbbdacdddacbacbabbcbabdbcacdbdaaacbcccdddacbbdbdddbcdabdbcaabddbddaddcaaabbbaabbccdabdcabdaaaadaadaaaabbcbcddcbbaccbddbcddcdcddabdcbaaaccccdaacaabaaabbbacacdabcabcbadcbbcabbabbbddccbaccbdabadaabbadacbcbdccabbbabbbbadccaaaddcbddabdbcbcabaaabacadadcaadddbdddbabacccdbacaacacbbdbbbadcadcbbabacbcdacabccadcbadbbaabacabcbdbbcdbdddbbaaadbadacdbcdcbccdadabaddbbbccadbbddacbbabbbdabccbabddbdacbccbaddaaadcddabaaacadcdcbdcddcaaccdbaaaaddbccdbaccbddacccccbccbccadaddadcdbcdaaadaadcbacadcadbbbaaabddbbbbcbdaddddbdccadbdccdacabcddacbcabdbccdbbbbbdcddddbbdcbcdddbaabdbcadabbbbaddbabccbddbabcdacbabbabdddadbdcacadcdcbcdcadcddbacdcaddaacbcadcadacddcbcbdcdddaacdabadacaccbbbbcdbccadddbdaddbcdabdabcccccbcaabaaddcbbcddcbdcacaaabadcabdbcaccbbabbadadaadadccbccbbbacbadcabaddadabbccbbdabadadbddabddcdaaccdbdddaadbcbbcaaaacaadcdbddcdddbccaaababcbabadbabaccdddbbbbbcdadccadcdcbbdbbddcaccabddbcbdcddbddbacddacbbdbadbabdcacdaaddbcdcdcaacdcdacbacababdaabcdbcbabcbdbaddadcdbdcadccabdbaaacbbabdcdbdabaddccacbccbaacbdabdbdcaccabadccbdbbaccdbadbaabcaabccdddbaadaaacbddbababbdbabdddddbcabbbdcabdcccacbbcbbccdaabbddbcbabdaacccbcdbcbaccccddbbcbcdcaabcbcbdcbadcacdbbcbdaaadbacadbabdcbccabbadaadbdabbdbabbaccdabdaddadcdcbbbccdbdaddcdcaddcdcbdadaacdacbdbdcdccbcdaabaddaddaaaacbdadcbacaadaddaabddcababaabaccdcdcbcbadccaaabdbdabdacbabbadcddbabcccbacccbcabcccbddccaabbcadacabbaacddcbbaadacdcabbbccbbaabccccdbddaadbccdabdbbcbcbcbcadbcacccbbbdcbddbbdaccbabadbddddbbbdcbaacddbabaabacbbbbdcbbacddcbbadbbbbbaaaabcacabbbcbbbbcbaadbaacadadcbcadabacacbddbcbdbddddaaddbacccbaaadacdccdddccadddccbcdbacccacbbdbcdddaaaccadbddaddbdcbdccdcbdabcbbdcabadaddcbdbabcdcdcddbdbdadabadabcdbddcdacbddaabcbacbbacbccbadbbdcddcabbdbbdccaddddbbacbaccaadcccccaaddbadccdacbdbaaabcbaddaccddcaccdadbbcaaababaadbcccbbcbbbbabdccabcacabdcddbcddcccddacbbcabbcabdacbabcacbcdbdcccddbccacdccbaddbdacaccdcbdccbccbaabbabadbbcacbadaccbabdccdccdaaaddbabbbcbadbabacdddacbaadbbaddcbbcdcbbddddbbadaadcbcdaacaacbddbaacbaacaccaaaacaacaacdacbbabadabbbdcabdccacadadaccbacddbadaacbdaaadddbcaadcbdabcbcbabaabcbdbbcbabdacdcbcbabadcaabcbadacabcabdbbaacdbaacbbcadcbbacbcbdddaadccdaddccbccbddbbdaadcdbbdbdddadbcddcdccbbbcaccddbcbcadccbdccbadccadcbbabbddbacccbcbddddabbaddbcadbdbaabdcabdcbccdbdbadabcbcaabdbbbbdaacbbddabadadadbbccbdbdbcbbcbabbaacbbbcdabddccaabcdbccbccabddbbbbbddcbbbcabbdbcbacaccabdacccbdadbaacccbcdaabacaccdcdbcccacaacaabcdbccababaaadacccadbcaccdbabcdbbbcbbdcbcbbdbbdcbdddcbacbdcdcacaabcdddaaaabdacbcbabdadcccdabcbadaacbaccddacdbaababddcdcdbbbadabaaddadbddcdaabbacbcbcbccbabbdadbccdccbbdccdbdcdbdcbbddcadccbabbabdaaacdbcabbcbaadabbaddcdbcbaabcbcabaddbacabacacaddadadcbbcddababcbdddbbbbbabbcbddcadbdbdaaabbbcdabbccdacabccbbccaabadcacdaaadbcdadbcabddcddddbdaddcdbabddbadadccbcdadbacaddadacadbcccbccbbbcaddbbbcbdaccabbdbcbacdbddbdcdcadaddaccacdccdbdacbabbbaaddbadcdbcbbdcdbabadbbbdcacccabddaccbdadabddacddaadadbabadbdccccadcaabdcaaadddbadcabcaccbddcaacdcabcccddacbbbacbcbadbbdcaccbbaaddbcdcadbabbdcabcdaaccdbcadacadcaddbbcbddbcabbcaacacbbdddcccdddabaaccbbbdadcaaacacdccccccaabbdccccbbddddabdbadaaaacbaccddbcbbddabaaaddcacddadcdaaacdcddabacccbdacddddddddbdadbacbbbcbbcdadacddbcacbdabcdbccdbcbaacacbbbdcbbcbadbacbbcaabddcdbcabdacaadbcadbaaaacbacabcbccaddddabcabcbdcdcdbdadbcdcabbbdcacdcbcbbcdddabacbcdaacddbabcccadbabbadaccadcacacacacddddacdbadadaabdacdcbddaabccdbcbabbaadbbbabdbaadddcdbacadabadbbdaaabcaaccdbbcbcabaabaabcbadabbcbaddbdcddaddbdcbbdabdabcbddbdadadaaddddadadacacdabdccaaadabccaaadaaadddbdbccaabddacdbaacbaabbadacbdbabdcccbbdaadadcbdbdbccbdbdbaaaadabdbdcccaaaaadcbddaaaaccddcbbaadaddcadcbaacaaccbbdbbdbccdddbbabcdadcdcbbcdcabdbaddaadaabbabcadaddddbcabdbacdbcdccdcacbabdbbcdaccdadacddaaacacdaccdcbaaabdcdccccbbbbabdcabbddcdbbbbbbbbccabacccdabdabbadbbbbbcdcbbbcabdbaaccabbcbdbbbbabdddcdbdbbbccbbcbcdcddadbccddacdbbbdbadcbdaddcddbabbdcccbccdcbabbbccccbbdbabbbbcbcadcadaccdaddcbadbbdacdddcdcabacbcadbddbbadadcccccbdacbaacacdccbdacccdadaadcbdacbdbddacbcdbaaddabaadaaacbdaabdaaabdacabccdadcdccbddabbaabbbaabadccccddcadbdbcabccadcbcbddbcbaccdaaddcbbbadabccabaadababcbaaadcdbaabadbcdadbbcddbabaccabdbcbacbddcbcccaadabcdbaaddbbbdbbbbddbbbadcdaabbcabadabddaadbbadbbcddadbaacaccdddadbacbbdccabdaddcadbdacbbadcbcdcdbcbcacbcdbdaadababcbdacddbdbdbaabccdbbaabdcdadadbcbbdaabdccdaaadcbdccdcaccbdaccaacdbdaaaaccccbdbadadbaaccccdbddbccaacdcdbacccdbccaaccbccbaddbddbbccccacdccccdbaadbadbaabbcdacaacdabdacbbabadcccdccddadcaacddbdaacadcccbabdbdcccdcadccdacabddcdabcaddcbcdddaccdcadcababdabbcdbdbdcddababdabbccadcdabddccdbbbbabdbbcdcdcdadbcbdbcdbabdaacbdbbdaabdbdaadddaacddbdbbdbaddcddbddbdadddcbbdbccabbaaabdbbdcbadaccddcdcbbbddadabbadcbdcaadbdddcdcdcacbbddbaccdadabdccdbdbaaadadbccabbddacbccbbdccbcadbdadabaddbdabdccacabbcaccbcdcadbadbbadaaccbcababddcccdbdccbbaadadaababaaaccbaaccddacbabdacadaabcbcdcabadaadcdadccdcaaabaabdcdbccdabbdabbdbcbdccddcdbddcacdcbdcbddcadcacabbdcbdcaddbbdcbdddbbbbbdccadddcadcbdbcadccaabdcbdcadabdbadbcaacdacbcbbcbacdbccbabdccbccbdabdbccdcaadcbcacddcbcdbccbcadcbabbdacacddddbbaddcdaccbcccbcbbcaddbbcacddaadbbcdcaccabdaaacdbbdadbcacbaabadaddbaccacbbcbcdccbddccbcdbbcbbbdcdaaccccbbcbbadccacdaddbaaabbadccbbaaaabadadaaaddbcdccabcbcdabaacbcadbdbdcbbbbadcadbabbcccacdddddcdbabcdbccbbacabbadadbdbdacbcbabbcabbaaddbcbcdadbdadbacbdbdbacddbcddbdbaccddaddddbbccacadccccddcbdccccbaadcbaccdccabcbdbddcacdadcbdccdbcbabdacddacabbcbdbbadbbcdacaddbccccdbbadbcacbcdacabbaabaabbadcbaccadbaccccdcdabcbccacdabbacdcaabccabccbaacccabaaadccaaadbdddacacddadaddcbcbaabaacdcabbdcaddbdadaaabcaccacadbaacabcaadabbdadadbdbdbdaccdabcabdabadcbbdddccbacacdbacccccabbcbcddcacaabaaddcddbabaddcbbddabbbabbaabbaacadaaaadacaaddabcbddadddbddadabdbdbbaaaddacadccbdbdcaadabccdacdcaabbadbadbcbbbddddadcdadaaacbccabacbddbcddbaaccaacbcadacaccacdcaccaacaddabaabcacadbaabbdbcdaaacddcdddacdcabcddbdbdddadcadadaccbaabcccccccacbdbdbbbaddccdcabbdcaaaaccdabadcdaccacddbcccbdddbdabbdaabcaacdbcdbabbcaccadbccbbbdbbaaccdbadbbaaacaccbcabaadcaaacbcbcaaccbbcbdcacbdcdaaadcbdcdadaaaaccacdabbcdcdbcaaabcaccbccabcdcdbdcbacbdbbbcddacbdadcbdcbbbbdcdbdabcbacadaabaabbdbdcdccdbddbcaaabddabbdabcbccdccaacaddabbabcbabccbdaddbdababbbbbbbdcaadbcbbcddbbbbddcababadddcdcabbccabaacccaabdbaacabbabcdcabadbaddadbddabbcbdcbbdcadbcaaccbdddaabbababdabbbcdcbdaacdbbcacccdddbdcadabbbcddbacbbcbbababbdbcdcdccdddadaccbcaddbabddadddacaacccadadacbcccaaccadadbbcbbcadcbcbbcbabaaabcbacaacbbddcddccbadbacbbbcbdaacccdabaccaaacbcbdacacadbdbdbdabacbccaabbbcbddccdccbbbdbdcbadbacdaaccdddbcaadbabdbacbbbddcaaacbcdaddbbbcbdaddbdbcbdabdcabdbcdccbbdccddaacddcbbccbdbbacbcccdcccbbbcacbabbbbbddabcdbcadbccbabdccbdbddbdccaacbbdddadcadaabcddcabaaccadcbaabcdcdddddabdcbbcbbadaccbdcbccdaabddaacbbcdcbddddbabdcadddabbadaabaaaddabbadcbcbbdbddbcdacdcacabdadadadacaabcbabbbddaabcaababcacadcadbacaddcadbccccadadaaaacbadaddcccabdbbcbaacbadddbcacdcdbcdcccaccdbaaaaadbcddbbccbcccdcdbbcaccbbcbdbadcdacdddbabacccdbddadddbcbddababbdbcadcbdaadadccacbbbaaaabdaddaacabdcccdcccddccbbdaaccdbaaacddbbbadaadbcaadddadacbaccdbacabcbacaddabcbccdcdbddbaccbcbdacdaadbddbbbacdadbcdabbbcddddabcbadcbbbcdbccddbcababadadccccdbbcbdbccbbcacdbdcbacdaddadaacdbddcaccddcbaabadccdddbbdabaadcadbabcacdabbbcbbbabbbcdcbdbbaccdadccbbbdcbbbcdabdaabadaabbdcbaddbcccbcdaadacabacaacbdcabcbbccbdcadccddabcddbbbadbddcbdbdcdabbdaacbaddaaaabdddaddabdcacadbccbcbcccdcdaaabbbbddcabcaadaacbbdddaddcaababbabaddcbccbdccabacbbcdcadbccabcddbabddcdbdadbaccadaadbaabdddacdbdaacccacbaadabddccdbbaaccaacaadcabcadaccaababdacbaadaaccbccabccbbbaaacddbdaaddaacaacbbbdaaaacacdbccdbdbadbbcdccaaabcacbdbdbbdbdbdabcbdcbababcaddaaccbcadcbbabbcbcdababccdbcbadbddadbccbabbbadbbbdabbaddadabbacbaaccbbbddcdaaccacaabbadbbbaabdcbbdcaddcabababdcdaabcccdccaddabbcdbcacdbcaabcddadccadaaddbababbacdcababccabdbbacccabcabdacdcdbdcccdaadacbacabbbdcbacadbaacbbcbbdbcdcaabcbaddcbdadddadcbacbdbcbbbbbbadabbbbdbabcbbdaabbbcacbabdcdbaadacadadcccbbccddaadcaaadbcbcdbbaaccbdbaacabcdbacaddbabbbacbdccbbaacbabaddbcdabdbbababdddbbccbdbcabacabaddcabcabbacabbcbdbabdcbcbbbddddbdcacdaacacaaddaadcbacacdadddcddbaaddcddabbdacddbbbbcdcbdcaadadccbaaabdadaddcabcddbddaddaababddbaacdaaacdccccbdadcbbdbdddbbabbdabdadaccaacbdcdcaadaacbcabaccbbdaddbddcbbdabdabcdbdbcdcacacabdabccbdbcbbdadadabacdcaccbcbcccbdbabacccdabcbbccbdbdcbadabadadcdbcddbdcabcadabcbcbddcdbbbaadacbcbbdabcbbbabbddbbcbddbaccbdcdcbdbababaaabdabdccdcccdacdabaccdaddbbdbbadaddbccbaaddcbbcabdaadbbcddbccdbdbbdbbabaaadacbddadccddcbddacacccadcdddcccbdcbbbbcdcdddccbabcbbaccbbbaccdbbccaabcdbaabcadabadcbcadbcacbddacaddddacaacbacccabbcbdccbddcdaacbbdcdbbdabadbcddaabddcbcadaabddcccbbabadbdddaabddcdcccccababbdcbcddbaadbabdaccbcdcbbaacabdccbdcacbdddaacabdbddaaacabcaaadcabcacbcdddadbdcdacadbbdbaccdaabdddababdaadabcbcccbbacbabcbdbacbbbabcdbdbdbabbdadddbbcbacdddddabdaababbadbbcbbaacbdcddbcdbabbacbcabcbdbbbadbbcaaadadbdccddddadaddddabccbabcccdcbcacdcacdddcacadcbdabbdcbcaabbcabdddcbcaaadccdbbcdcbaadccbaaddcadabbdbbadbbabaaaacdbcbcdadccbdbdabdbbbacdcdadcdcadbcbcacddcddabcabdcacdbcbacaacbcadbbbdcbaaaaddadccdbcbcbabdbddbadbcadbcadaccccdbcdbdbbddcabcbbabcaddabaadbbadcabcddbbdabbbbdadccabcddcdcbcacdbdcacbabbabbabadddacacccddaccabcaddaaddbdaabddcdacadcbcdbabbcbddddcdcbcdbbbcccbbaddbbcaadcbaadcbbaacbcaaaabccabbcacbdaccbddadbdccababcdbabddbaadaadddcccacdbbdadddccccaaccbdcdabcbcbcbcabdabaaadcbbdadcadbbdcabbaccacbcdcacaacdccadaadabdbbdcadcbddbabaaccbcaaacdbbaacbdcaaadbdbcaabaadddadaabbaabbabcddcdcdadaabaddabdbbaacacccabdbdbabaabbdacdaddadbacddaaddddcbaadbbbdaccadcccbbacabbaaabcbadccabdaabdaddaadadcbcddaadcbdadddddaddabacabccadabacccdadaadbccaaabcccbdbcbbbbdaadadbaabdcacbadddacaacdccacbcdacdcccddbcdbabcbdcacaabcacdcbdabdddaccddaccbaaaddabaaccbbdcabccadaaaaaacbccdcbdbcdbcaabdcbcdbcbadadbacdcadbccababbccbddbdbbdabdbdcdbbaabbaacabdcaddbdcaaacbaacdcdaaadbdccbcbcbdbdbbcdddbbcccdbacbbabbadccdcbbcbcabbbcbbbaadccbadcabaddbdaccbaccccdbccaaaddaadbcdbbabdcabbdbbaccabdcdadcaadbddddacdcbacdacabaaccadbccdbbabaabcbbabdaaddaacdabadccababdabbabcbcbdbbddbdbcddcadabdacdcbccbcbdcccdcabaaadaabaababbdcdbaacccbdadaadbbdabdabacccdabcdcbbcccdcaacdbcaccadbccabcdbbcdaaaaacbbbddbbcbbbbbaccbdbdcdabbbdbdbcbcbadddaadccdbbacdbbbccadbabbbcadbcacbdbdbdcbddbccbcbdcbadadcbdcbaccdadbdbcaaadbbadcaccbcbabbcdddbddcddbcaacacdccccdabcbbbabbddcbddaddabcaddcacccabbdcdbabddbcacadcbcbddbcacbdcdadcdaaaabbacdadbcdadcbadadbddaaabacbbaccbadabadbbaacbaddacdbbcdbcabadadaabdbddbccadcdaaccbabcacbbccdadadcadbccaaadaccabcccadaccdcabbadddadccccacccadcddacdbadacdbdbdbbaaccbbccaccbabdacaddddcaccababddbbbaabdbadccdbadddabaadcbbbdbbbbddcccdadacdbbabbaabcaadabdcddaacbbdcdccbcbbdcbdddcddabbbdabbacadadcbaaabbcaaabdadcdadcadbccabaccaaadbdabacdacadbacccbdcaaccdccdbcdabdacdacbbacbdcaaaddbaabccbdabccbcababbbcdbcbbddbdcbbbcacbbbabcdcabdacccdcbbcdbadacdcadcbccadcddabdddadccaabaddaacdababdbdbcbbccdccbdbbcbbabbbabbbbbdddbdcdacababbaccccddacdcccbbbdcaabdadbaadadccbbcdaacabadadcacbabbbcdcadbcaadcbabdcddaaacaadabcbbdaddbbdbdadbbcdccddcddcdbddbacabbcbaaaacbbdcaccabbbcdadbcbabddbaddadbadbabdabbadbbdcbaaabddacdcbcbdcbabbcbdaabbbbaadccccdcbdbdcdcaddbbadbadbcbcdbbcbbacdabacccdbacbccaccbcddaabaaccddbcadabcaacaabaaccdabaabdabaadbaabcbaabdcaaccbcaccddabdacccdacacbacbaacccbabdcaadcbcdbdddbdccadadccbdabbdcabdbddcddcdccbcbbcdababdccaddaadcdccccbbdcbcbdbcccdddbcbbddacadbbcacaaadccaadbdccadbaabccccbdaabaccdaddcdcdabadaacbbdadcbdcbabbadabcbadbccaddaabaacadaccadcbcdabadddbadcabcdccdbdcabdbdcabaaaacabcaaadbcabbcdadbcccdbbcbbabccbadabbcdcadddbcccaacadbdaabdabdbbdcdbdbdcbdbdbcacabdabcadcccabbcdddcccccbdddcbcdaadddddcccccccbaacccadbbcdcbddbbdbbddbdbcbcccccbcaaadbddbbcdddcdbabbcaddadcccbdbbdbabdddcdacbdacbbbaacaccddcbbcdcabdbcdaddddbbbcacaaaddddabddbcdbcbcbdbdadacadbaadddccddadabbcdcbacadbdacabbcadabcaccaaabacbacacbcbcaabdddbadbabcccbbaabddbbcbbdbdbaccabadaddbdabdbdabadccadcddabadccdacadccbccdbbbdbdaaddccacbbacdcbdbacdadccabadcabbbbcdbcdccdbdcddcbcdbaaabbbadadbcdbadbdabbcbadbaaccbbccddbbdcbcbcabadacabcdabbcaaaddbbbaddbdcddbcccdaaadaddadcccdcdacadcadaacbaacdccaacbbbdcbabacdbcabbdacdbabbbcadaadcacdadabbbbadaabbaccacbcbbaadddbdbbaabaddbacaabbabcacadacdbbbdabccdccacbdbbacbacadccddbcbbacadcaabdddbaacdcbbadabbcddbcaabcdbdbdcabacbabdbdddadbdcaabbaddabaccadaabdabccabdbabcbddccbdcadcdcbaccbbbaaccadbddaadcabcdbdaddabcdacacdccdbbbaccbddacbdabcbdadccaccbddddacdcaaacacdccbbcbdddbccbddcdbcccddccabbcdddabcbcaacccdcabcaadbdcacdacaaabaddbdcdbdbdbabbdaacbcacbcddbcbbbaadddcdcccbbcbdbbabdbdbcdcabbcadddbacbbacbcccacbddcbabaacdaaadabccdadaaaccccbcbbacccccddcdababddbbbcaccabcacaaccdbdbdaaaabbacdcbabaaabbadadbadadddcbbbccdbbcaaabdbdbdacbddccacacacbccddbcdadbadcbddbcdcbabcbdacaccdacaaddcdbcbdabbbadbcbaddbbcdddcdcbcbcacabcacdcdaaabbdbbcccbacbbddddcddcacaadabacccbaabccbcaaaccdccadcddccbbccabddcaabcbddbccbaabcbdbbacbbaabbaddcbdacabbccbdabdcddbbdbaaaccacdbcccabcacacabccbaccddacaddccadcbdbdbabbacdbcadaddabcbdcabcbcbdbdbdbccdbacbbcbdccdcbcbcdbbcbbcacbcbbdababcacdaacadabbddddaccdcbcabaacaacadcdbcbbabdcacdabccaaacbccadadacdccbbaacbabaadbdcaddaddcbcbabcdddbaaccdcbbcabcbdaabcbaabbbadcddaddbbcdbabdbccbddcadcbdcbadcbdbccddccbccddccbbadbcccdddadbbabbddcbaadbaddabdabaadbcaabcaccccdcccddcccbaaaccacbdbabcabbcbadabccacbabadccdacaddaadbbcbbccdccadbadbcbbdbcbddcccdadcbbacbbbdcbbdabdabbbdcaadababbdaaccabcdbcccaaabdbbcdcccbccdcddbadcddcbbcdbacdaaccaccbbbcabddabacacbccbabbcdcabcdbdbaccddacddbbcdadacddcdabadccbddbdccddcacdbddcdcdbbabbccdcaaacaacdabbcaaabcbadbdddacbcabccbbabadacbdaaadabbcbcacbcaacccbbbcccccadcadbbdacdbaaddcacbcdbadddcbbdaacbbcdbcbbbcdbaccdaacacadadabacbaccdabcdacccbbacacbbbaababccacccaaddccdbbbcccdcccdaccacdccdbaaacaddbadbbacbbdabaaaaaddabcabbcccabdccbabacccccabaccbdabddcabbaaabddbcbadbacccddbbdaacccbacbacbabdacbdcbbdccdacbadcdddbdabacdacdabccdbcaabddadabcdcacaadacacddadcaadbbbadbaaaacbbddbacbbdacbbbaaadaaddccbcaacbdbdcccaabdccdbdbabbaacdabccacdcccbbdadbcdcdccbbbbdbadaadcccccddacddadbbcddcbaccaadaccabcdcadbaaddbccabcdacdbadacbabcddaadadcacdabddccaddcdbddacaddcdcaabcbacdbbbdccdddaabaaccccddbacbcadbdbbaabcbcababccbdcacaadbaaaddccabbbbbaddbbabacdaddadcbadaadcbabdadaccbaccabcbaaacbdbddaaabcdcbcaaaaadbdddaabbcdbddabdaadccdcadbcbcadbcaaacbcbcadcacabadaadadacbbbccddcdcdacaabadabcabcaabbbbbbdbadcdccaabcadcbbdabdcbbabccdabbddbaddccbbddabaaadccdbcabadbacddadcadcacbcbacadcbcbcaabdbbabdcaccdcbccaccacbcbcabbabddadadabddcaaadaaaccabdadbbccbaaddaadbdcdadcdcaacdaadaadcdbaacccaadaadbdcddabdbabdbbbdbcacdcdcdbdacaccbdbbddadcdaccbaacacbbddcbacdadababdbdadcadcbcacabbdcaccabdcccbcabbacdbcdacbccabaccabbaadabaabdbcdbddcabdbbacaddccccbcacbcdbbcabcbbacdbdddbcdbbbcbdcccabacdbbdbacadbaaadccdcddbdcbdcaccadcadddcacaccaacadbbdbccdaaaaaaabacaaddacdaaaaaddaadbcbddddabcccccbbdddacabbccbcdcddcaacbccaabddacadcaaaaccccacddddaaadcbabddbdaccaacadbdcdbdddbdacbcbccddddbdbdbabaccabcaaaabccabcdddacacadbbabbdddcdabaacaabcbaadcdacaaabdcacdbddbcdcddbdbdddccabdbcddabbdcabbbcadddcbdcaabcbaabcacdcccbddcabcdbcaddaabadadcadadddaccbdaddaacbaabdbcddbadaacdbccbacbacabbbcbcbbbdbdbbacbcccaaddccabacaacbdbabbdabddaaabcdbbcacaacabbdcccbadddddcbccddbdddcabbcccccbcbcbababbadcbaacaccbbcabcbdddaaabacccadbaacbcadcddcccccdacbbabbccbdbcddddcbadacadbacbbbdaccbddbdcbaacbcdaabcadacaddbbadcbabbddbdddcdddcdaddcbbbadbaddbcccaaacbcdbdacbcaaddbcbddbdcccbccbbacdbccaaccabdcccdbbadaadbadbdaadcadaccabcaddacdacdbadbbadcdbbdaddabbbcdaccbbbacdddbabdddadacabbacddbacdcdbddbaabcadadbaabdccdbadbcdacdcdcaacdcaaacbcddbabbbdbddabcbabcccbbacdcddbdccaccddadaadaaddbdccdbcccadcacdcdbdadcdcaddcdbacdccdbddbbbcdbcdcadababddacbcababbacbcbdbbaabccdacaccbaddcbbccadccabcbccdbccacdcadcbbbcbbddaccaddcacabaaadabddcbbabdcccddabaacddbdcacacdbaaacbcbdaacdcbdbbdbdadaddabbddcddcabcddaddcbaddccdabdcbddcaaddcacdbadcccbdcacaadcbccbbccbaddbcabbdaaacbabcdacdbaabcadaccdabacbdcadabcbcadbacdbccbdbccdaaddaacbccbcacdcbcbddbcbaabaacadbdaddabaadadbccadabcabdbccdbadbadcbcdaadbadbccdadabdbaadbbabbaaddcccdacbaabdcdcbadcdabbccdddbaccbdaddbadabcaaadbbadacddaadcadddbccabbdcbbddadcbdbdcabdcbaaadccdabccdccdadcaddccbcdcaabacbacccdcdadccabacadaacbbbdacacddcabdadaadcbdadbbbbdbadddbddbcaabdcdbcdacdbbabcddabbabbcadcdabccdabdcdcccdccbcbbcacaddbbbcbccaccbcaadbcaddcadacdadcbabcdaabdddbadbdcabbacdbccccddabbabccdaaddcabdcdcdbadaccdaccaaccaaaddccaaaadbbddaadcccbdccbaaaaadccbbcdcbaddbbbdcdcabcbaaaccabcdabbcdabdcaddaccabcbabdcaadbbdaddccddcbdabccdbccaacabaacbbbccaacbdbadabdbcccdbbbdbbdadaaddbcdbabdbddcdbaddaadaddbbbdabbbdbbcaccaabaacbddcabbaadcadbaccbbaacbcccdadcbcabdccbaccabcbacaaadadbccbdcbbadadadcaaabbccdbaaccdcdbaddacbdababcabcbbddddcadababcdbbacacddadcaadcaabdabddcdcdccbccbaadcadaaadbdddccadabcaccabbbcbdbcbcdbbdacbbacacddbcaadaabbaddacacabccbcadbaaabbdaaccaacadccbbbbccaadcbaabdcadbbadddddcdaccbbcbcabacadbbabbacacabdddcacaaccabbcdcbcadcccbdbcddbdacadacdbacbdbabbcaabcbcaaacdcaaabcbbadcbbbcadbcbbdcdddadadcbdddbdbdcdccbdbdcadbddbaaccbdbabcddcaaccbbdcdadddadbacbacdcabaccdaccccccccbadcccddadadaddbcacdbccdacacddbaaadabdcacadbddadaaaadaabcccbdacbcadacaacdbdddcdacbabddcdcccaccaaaacbcdcddbcbcddbacbadcadcdacbaadacadcdcdddbaccbacdcacdbadcdbdccbbdcadcdcdddccaabccbbbacddcacbbbaabcbbccdaddbbabdbbcdbddbadbcadadcbaadaccbdcadbbcbcadccbabbdbaddabacacbccbdbccbddaacdabdcacdbcbdbdadbdaaddcbbdcbadccdbddddbbcbbdaabaccdcdccdbbacdbbcbaaccadccbabdbcabbcbcdaaddadacdbccdaabbdcdcddaaaaccbcaacbdacbdbdbbbadaabadccdabccdddbbcbbccacdababcabdccaddbbabcaacddabbcdaaaaaaaaccbbbdccababdcbbccbcbbdabcddaccbadcdbddcdddaccdbdaaacbbbbcbbaabdddcadacacddbdabaadaabaacddcccdbcdcbadbcacabddacabccddbcbaabbaadabdbdacbdcbcdddcbdbcbbcbbbbbacbbbdbddcdcbadadcccbdcbcbddbddddbbcddbbbcccdabdbdbcdbbacbcdbccbdccbadbacaddaaccbbaccabcbadcdaaddbdcdbdbaadacaaabbacddaabadacddbbbaddaddbabbdcdadddcdcadacdbcabadbcadbccdbbcbadbacbcbbbdabbabdbddaadbaadacabccdcbcccdacbcadbcacaccadbdddaddbcdccacbbadbcdbbdbdaabddaabdadbdaabddadaacbdabbbccbcdcdaacabdcdbdababccdadddbdcdaddabcaaabbaaccbaabbccaaaabbaaaccaaabadbadbaaadbddbdaacddadcaddddaaadcdccabbcccbabbcdddaddbccaacbbadbdcabdbbcabadaccccccadabdbcaacaadcdabacdbacdacdcadcdbcaabadcabacbbcbadbcdbbcdbccbbcbaddacbbdcaaacacbdbbaddbbaddbdbccbbcaacdcdcbddbaabbcdaadadbcbaccbcbaabbbadaadddabbcbaaacbcdccadbbdcbbdaadddbdaacacdbdcbbddcacaccaccdacdcabcbbdaabaccddcbdbcddadabdddbabcaabaddbacccadacdadaaddccdccbdcdaacccaccbaaabdcbdbbbbdaacdcdcbcbdcbbbaadbaadaadacbdaaadaacabadccbdccdcdcdbbabdcdcadbccbaaaadaaccadbaaadcdabcbdccabaacdddddcacbbbcdcacdbddbacbbbadcdcccccdddbbaadbbabadbcdbbdbdbbccaabcbabaaabdcbdabdbbaadacdacbdbbcadaaddaadabababbcddbabbcbbbaacbaddcccdcaabcbbabacbacdddbbdadbccbcdbaddbbaaabbdaadbaaadbabcbbcccccbcdbaccbddcdddbdadddbaaadcaabccdaadaddcabcbdccdccbbaddddcddcbcdbaadcdcccdbaacbbcdddbcccbaddbdddbbcbacdbcccdaadbccbccabdcdadccbaacdaaacddacbdddbbabbcddbcdbccddbcbcdaaddcabcadacaabbccbaacbcbadbdbadabbccbacacadcdcacabcbcabdbcbcbbdabdaaabdcdabdadbdcdbcabdbdddddacbbbdbababbcacaaccccbcdcdaccdbbcbcbddbbcdacbddbcabdbacccabaaacabcbccdcadaacdcccaccbcdddddbdaabbabcccdcdcdadbbaaadcbdbcddcabccdcbbbdaacdacbdbcaabadabcbabababdabcabccdcabdcddadcdcdaaaadbbbabcbcacbcccbcbcbdaadcaadbccabcdababbbaddcbddbccbbaaadaddbcdccddabbccacabbcdabcbaddcdcabbbcbbbabaccbdadbddabacccadbaaccddcbcabcdcbdbdbacabbdcdcacdbccdabbbadbccdaabbcacdbdddbcdbabbbdbacbbbabcddbcacdabcaabddaaccccddbccccacdbbdaadcbdabcbbdcbadacbbdbcdaaaaddbababcdaaddadcdcccbccbbdccdbadcaccdddacabcdbbbaddcccdcbbaccbacddcbdabdabdcdabcadcaaaaabbcaccadaaacccadddcdadcadadcaadaaacdbccdcdbcbdacaacdcdbacddcbdbdcadbdadbadbdbcbdaddcbabcaddbddaabddddbddcacbadcdadbbbdbbabcadcacdaccbdcbcbbbbcddccbdabcacaaccccccdcbbdccacbddcacaabbabbbacdadaabbdcaddcaadcbcbaccdcddabcdbcacbcaacacdddbddaacaddadbcbbcddaacdbbaadcbacdcdabadccbddabcbdbbdacbbddcdcdacbddaaaabadadcdcaaccdbdbadbaabdaddaaacdcabdbaabbcacdacdaacbacbddaaccdabbdbdbbbabbabdcabacabadcbcdddbbbbdcababadabacbacabbbbcbcdacaaccddcbbcbcabcbdcabaabccabacdbbacdcbbcdcaaaccbdacbcabdddbdccadcdcddababdcccbaacabacdabcaacbbadbaaaaaaadbbddcbacbdcccdccaabacddcbbbcdcdabdcddcdcadcddbcababcadbddabaccbababcdbddbacbcaacbccbbdabcadccbaabbadbdcadbbdabaaacaaacaddbaacddabacbddbcabbcadbbbaadabbbaacaaadbdadbabcbbbacbccbcbaabbbbbbbbaddcadcaabdcbacbddbdddbbbcadaaddcbcbcddcbbcdacddbcaababaadbbcabacdbcbaaccdddddadcdbdacaaddacbcaddcdcbddcaaaccbcbdacbbcccdbdccacacaccbaacccbcaaabccbdcbbcbaadacddabcccadbcadbaaadaddaacabcacdaddbcacabdabdddddaccbdaaadacbacabcbbcadbccaabcadbdcdacbbcdaabdabcbcdbaaccaaacdadcbbaaddacacccdbccabdadadbccbabacabccddabdddbdddacccdbacdcabcccbbababcbabaabcccccdcbbdcbaadadddbcbddadbdbccccacdcabacacddacaccbbbbabcddaccdaacddaaadbcaddbaaddaadddbccacaacbaaacaadbdcbcbbcdcaccdadcccbabadbadacccccccaabbbdacdbbbcdadddaaadcbbacadaccddcddbdbdabadabcacaabadddacacaaabbacaabcdcdadabaadbcdadcaaadbbcbdbdbdadaacabbdbadbcbbbdcccdabccbcacaabacbaaadaaccccaacbddaaaabdbddcdcbbbbcbccaaacacadabbccbacbcaaadadbbcabdcdccddccdcabaddcaaddbddcacadbcbbadabcacaacbadadaaaddaddbadbbddbadacdcddbbcaaabddbddbddbdababcadadabbbcddcbabbaaccdbcccbbbbaccdddabccacbacaccbbcdcddbbadcaccdadadaabbcdccabdcddcbcccdddadabaddcccbddbddbbaaadaababbdbdbcdbbcdbcaaccaddbdcbbcccbcdccaddcbcbdcacbcddbcabaddccadddcdabdbdbcdbcbabddbcbbdaddcccacaaabbbcbcbbccbbbabaaddaadccdcacbadddabcacadacabddcdbbbadbdbdbbbdadaaddadbbbaababbddcbbddcbdbbcdaabdabbdcdabdabbccdcccdbccaabcbcabaabdccaccbbdcabdabbdaadbacddbddacbbcdaabdddadaacdbdcdbbcbcbdbaaccbbdadbabbabbcdacbdcdcbdabacdcbbbbbbbcbaadcaccbdbcbacbcdbdadcdaccabadabbcaacdadaaaaccbddcbbabcadbbcacabdabbdcbabbabaacccadcadcbcaccdaaaddabdccbbcdabbbcdbcbaddadbbadddbdadbdadabdbbdbbccaaaaccbaabadcabbaadccabadcaaaaaddccacaaaddbcdabbcaddaacdccbbbabdddadbdbadccbdddccdbbdaccddcdbccadacbaabdacccbbbcbdcaabaabcdbbcdacbddbbccdbcddacaabdbaccabbbaababcaddbdddabcbbcaaabababcdadadbcbbababdbddadbccabdbabcbbdbbbcdbadbbccbbabbdacddacdabbcdcdddcbddccbaddbababccbdcbbabcdabadcddabbdccaccbdaccaaaabdcdbbccaddabcadbadaabbcbcabccdddcbdcaabccaccabcddcdcbddcaacbbabbcbababddbdddccccbbcbbabbaaacdbdbbcadacddbddddaccccdbdabadadaacdbbcdddbaadbbabbccacdababadadadddbacaacdcdadaadabddccdacbbcdcbcbadbddcacdacadcccbdcdbdcddabdbbacbcacdaacdddccbadcabcdacdccacccdbbcccbaadabcddadbdcdbbaabddcddacaccddabadcadbbcbacadadaabbdacabdbddccbbdaacbddddcabbccbbaabdcccaddddddccabaaacdbabbabbcbcbddbdbadccabaddbcbcaacbbbdbbcbbccbacccaabbaacbacadabcbcbbccadbdabcdcabcaacaccabaadabcbdadaaabcbcdadadcdbdbcbabdabaacabcadaddcabbacdbdbdcdcdbcdbcbbcaadbbbabacdcdbdadacbbacadcbdabbabbbbaabaacdcabdaaaccbbddadabcddcdcbbacaccabdcdbacbdbababddaccacccaddbccaccbabcdbddcccddccbccdadbabcadcccdccccabaacadabccddcaccbadbcccbbdbbbaabadcbcbcdbcccbbabdaacdbaccabbabbadadacdcbdaadddabacdbdaadbbcadccacdbcdbaddacdcaaaabdbbccbcacaabdabcacbcbbddcabddbdbbbdbdcdbabacdadabcabddadccbbbacbadbbcbcddaadcaccaabaccabccbaadcbcccddabcbaadcddabdcbbddbacdabbdabbabaaaaabdcbaacabcabbdbacabccbdadbcaabbaadbdaacbdaaccacdbadccccabbbadcddaadabcbdabadbacdddabbabaddddddcdbbbdbdcbcccccbdaaabaaddbaabdbcbbcccccbdcdbbbacadbcbdddadddcaabaaccccaadaadadaabcdbccbacadbdadababdbbbbddaabddabbdaacbdaabbbdbbcbbcacbdddbdcaadddbcacccdccbbccccaddddbdbcbdcbccdccabbddcdcaabcaaadbdbbdaadaddbbdccaccabddbbbcaaddadababccbcdccddababbbbabdaaacbbabcacaabbdabdacdcbaabacabadcccddcaabcccbbcabddcdbbcadaaacacbcdcabcacbbbbabbbcacdadabcbdddbbcdaaacddbcaccddbbadbdcbacabcbdcacdbabbcadbbaaacbaddcbbdacccaabcbaabdbcbacbbccdbaabcdabdadbdbddddaddbdaadadcbdddbdabbbcbcaaacabddabcbbaaadcbabdbacaaadccaacbddcbcdbbcaaccbddbbdbbacdaabbddbddcdaabcbbaacbddddacbbdcadbbcaddccbcddadacddbdcabbdddaddcbaaabcaabbacbcccccaddcdcadbbabdcdbaacacadabcaabdddaccbcaadddbcababccabcddcadcaadbdabadccbbbdccbaacbdbacccabdcdcccbcdabcaadcdadcaadcdddccddbcdbddadacdcaaabadbdadcacdadabadccacbbcbcdcccabcdacccdddcbcaddbcacdacacbdabcccabaddbbcababdbadbaadbdbdbbbbdcaaaaaaddccdcdbcabbdbdbbabbbcddbbadacbaddabaabdbbabdcdbcdcabbaddaccbcddcbbbcaddabacdcabcbabdaaadccaaaddbacdabdbabaaadadbdbdcdbddbddcdbcdcabddbcdccccdacdddadadbdbdcbcadcccddbadddbadccacdaccadbcdddbddcacdadbdbdddcabbabbccddcbdbdccdcadbdcabdaabbcdcbaaadbdbcbcaacbbacdbcaddddcdababdaadcabcbddabdcacbdcccccaddaddddacaddddabcdccdcaadbcacacbbcccccdbbabcaaababbddadddddbabdcbdccaccbdccbaacacccdabddcdbddcbbcdadbbccbdbaccbbdcadabddcbbacdabbbbabcadadcbccabdbbbabccacdcddcacddacdcdabcddaabadbbbdbcccdacacbababcddaabaadcabaccdaaccbccabadbacacaaaddbbababdcdaaadcabbdabbdbabccbdaaaabdcdbcddcbddccabbdddcdbcacbaadbdcccbaddbcaacdcddcdbccbcaaabdbbddcbaccaccabacdcacbbbdbbdabadbddbacbcacbcdaaaaddaacaddadcadbcccccdcdbaacddcccabccccacacadcbbbbbdbcbdbcadbdcaabcabddbbcbbccacdabccbbcbcdadddbdabbabacdbaccbaccdbbaacabcdaaabaacbbabcabdbbcbdcdbbaacbaccbbbcbabddbbbabddabdaaccadbbcdbdddabcaaccaadbaabdddbcccacabddcbddbbdbbbbdbddbdbbcacbaaaabdcddabcdcdadbabdccaaacabbccbddcdcdbbcaabcbdadccdcaaddbccbaaddcaddaadccbcddbbdccdabbdcdbcbddddaadadcdccacddcbbdccbbdaaabdacbccbccaacdbdbaddcdbdccdcbcacddbbddbcdcbadddbdcdccbbcdddbdcbcaadbadadbbcdbabcbdbccdbacccbccdbaabcadcbadacadacadcccbaddcbcdbdcccbbbabadacddadcaabacbdabdabcacaaddacdbabbdccbccdbaabcaabddbccdddaabdaabcdcddacbabddcbbccdbcbddbcbbbbcdbbddbacacaaaddccbbaaacdbbbcbcbcbccbccacbddaadbaaaadaaddcacaccdadaaadcdddabbccacbdbbadaabdccaccbacbbabdabbbddbbaaaccdcddabacabacaccbabccbcdccadcacaaaabbcbdbdbdabaacacbdacbddbadadcacaadbbcdccaadcaaccbabbcdabcdbcdbadacdacdbdcbbcdacdcabbaadaabbcdaabbadcbacbcadcdabbcddaaacaccbbcbddddabcacbbdadadcbaaadbccadadbcdccadcacdabcabcdddadabdabdbbcbcdbcadadaddcdcbaadabdadaacbacaabdbadcbadbcdbdcbabbddcdbaabbddaddaacbbddbccbcbcdcabcdabcadcdbbbdaadabdabadaabcadabaaadcdaccdcdababbcbbbcbdadbdcbcdadbacadbaadabccaacdaacdbbbadccbbbbaadbaddccabbacabbdbbaaadcdbadcddddbabbacdbabdbababddadcacdcddddacbbbcbcdcdcdcadabababdabddaaababcacdcbcbccbbaddbacadbbdbccaccdbdacadacdaabbcabdddcadaabbcbadddcccbbabaabdcbbdcabcabaddaddaccddcccaaccdaadccccbcccdcadcacccbaadbcdbdadacdabddcaaadaaabaccdccbdccbcdbdaaabcbacbbacbbbbadccddabdbadbdcdaddababcadcabbcacccbcbaaabaddaadddabacaccbbcdbcadcbccbcbcaaabbdbcadaccbacbbbdacccbacdbbccbbdcdcdbbbbaacdcdbdbaccbcbbbadbccacdccccadcabdcdcbabbdbbcbcdccdbdbcdccbacddbcabbcbbdcbccaacbcccccdcbbaacdbdbaddcabbcccbdaacadbcacbbccadbabdbccddbaadabbcdbcbdcbcaddbdccbcaacadaacdabacacdcdbacdbddddacbacdccddbacbadacdbbdcdacddbbcdbadcdbcbabacaaacdaabcbcccccdbbaddabdbdcbcaadabbacbcadcdacccbdabbbcdbbbcadcadacacccdcdcaddbcbacabdddabdcabdcdcddcbcbccdbddcadaadbdaabdcadacaababbcaabaaddbbbcabcbcdaaaddcabbddabbbbbcaadcbabbabadcdbbdabcdcbdcaadcaabbccddbbbddbdddcdcbdcdaccdabbbadaadddaabaddbdaacdcbabbbccdabacaadbbcbbbacaadcdcdcdaadbdbbdbaabbcacadbaddabdacccbcadbaddcdadaccdcbddbbcabadbcddccacababadbddbdbdacbdaaddbaaaadbdbdaacccccdddddcdcbbbcdbcdbcdcbbbdccbabadcdcdbcacadddbaaadcaacbadcbaccddcbdaacccbdcbaadcabaacbbddabdcbadbaddaaaddbdccbcdacbdbdaabdccddbccacbcaadbdcaddabddbbcadddcccdadcabccbdcddacbdbdaaadcdbddcdabcaadbadcdbacbddadbdcdabdccbccbcbccdadabacabacdcaaaadcbaabdbddacdcddcbadaabbccabbccccadbbacdbabcbcadddabcacdbdcaddacaccbdddaaaabccdccaadbddcddcaabcbddbbccababdbcabcdbbababbcaddacdabddddccbbdbddcbabcdcacbaacdcbcacadddbcdabbbcbadaccbadbbadaacbbcaddddbabaabbabcbdcadbdacdbcbabadddcadacbdcddbddcdbbdcdccabbacdacccbbdcbaddcdbbcdcbdaadcdbdcdadccadbbacdcbcaccccabdcbabdcbbccaaabaccbbadcbabcbdabdccbabcaccaaabacdacbbbadcbaabbdbdccaddbdcdbddbcabaaaaaaccabbdccdbaabdbcacddddbcbbdabbdcdcdbcddbcaacbccdccadbbbbcbdccdadddbccdbbbcaabaacabaccbdddaacacaabbddcbbbcaadddbbdcbacadbbddbcbcdcbdbcabdccbabadddaabcdcbdacdbbaccdacabcbcddcadbbabbaccbbdbbcbcdbdcdcdbdddabdcdabcbabdbdaaaabcbdaabdccccbddcdadbddddcdbaaccbbabcdaaacddbacdccbaccbbabbdddcaddbbcdaaadbcbdcadbccccddaacbdacaaabcddcccddabaaaddbcbbdbcdbcbcdcabccbadbcaaadabbdcdbcdaddbbacbabaacbaddacbcaadbbaadbdbbdcddabacbbbacbaddbdbadaacdadadadcbcbbcdabdacadddcaaddcaaaddccdbaacbabcacdcbbdbbaddbdcdcdbbdccaccdaaddcdbaaaaaabbabbadaadccabcacaaddabcddcaadcacbcdabddadadabbbaacdcabbbbdcbdbcddbaaccacdbabcaccbbdcbbaadabcbbadcaccdcabcdddcaccaddabdcdddacdccbabdbaacdadcbadcddbdbdcababacbabacaccaabbabddacbccdbdadddacbbcdcbbdbbcbddcbcdddcdacbbadcddadadbccbabbcdaabaadccbbbabaddbdcbaddcbbabbddbbdddccbabaccbddacaacbcdaacabdcdcbaabcadacdbcbabbccabdccdadbaccccacddccbdbbadabadbaacddbacdbddaddcdaaabbccbddcacabcabadcbdbbbdadbbacddcdcbcacbcddbcaaddbcdddaccdcddaabcadbacbbdcbdadddddbabdddcacbcbcbadbdcbaadadbddcbbadcdaddbaaabcaabbabbdbbabadadddbdbadcabccdaacaaddacbadadbdbababbcaadddabcdcbaadbacdccbbddbccbcddacdcadaababadbbaccaccdaacdbaccaadbbbadcdbcdacdacdacdcdcadbbbbcabdcccbaaddcaddbadddddaccdbbadcacabadbcccbcbbadaababaaadcccacadcbdcdaacaddaddbbbcdbdcabbacbcdadbdbaddadbcbccccdcccbacaabaaddacbbbaacdbbaacbadcbaabdcbacbddcddbbddabbdbccbbbdaababbcccbbdcadddcadbcadcdccddddcabdbcbbdaadbaccbdbdbcdcbdbcdbdabcadadbaacccacbaddcdaaddaccddabcbcdacbdcdccbbcabcaaadbdacbacbdcaacdbcbdabaaddbcacacddabdbacbcaacdabcdbdbcabcdaddcabdacbbcdcbddadcdbbabacbacdaadcdacaabaacbdacdaccddaddbbabadabcddaacddacbbbcaddcadcaddaacabaabbbacdbccccddacababddbcdbdbddacacacdabdaddbccacaacccbaaabaccacbadadabaddbaadabdbccdbbccbccbcddbbadbaccabdadbbbdaaadbdaccbccabddbcaaaadbaadaabccdbbabdadabdcdbcdcbaaaddcbdbaaacccdacdbddbddcccaddddadcdaaadacdabbaddbdaddddbacbcbbbbdbdcabdccacbccabdadddadabaddbcdbbbcdbbcdbbbacbccabbaddccacadccdcbacadccdccdcdcadabadbbadadbbcacdddbbcdcbabdbbbddcdbdbbcadbdcdcbacdaddaadbcbacaccbabdacbdbbabbbdbccdacaaabcadddcadcdbdbcaabdbdbabdaacbacbbdbbbbadaaccdbbcacbcabddcdbbbbbdaaaadaccadabaabbbabdabdbbcdabcbccdbaaccbcdaadabcaabdcaacdaddccbdacbddaddbdadadbacadbbababbccdaacbadbaaabbcdbadabadcdbdaabbbdcdaacdbdbabdabacdbcacadcbdadccabbcabdbbbdababbcdccddcbcaccdaccaccacaaaddcdabcadcbbbbbdadbbbbddcddbbdacbbaddccabdbdabdbacdabbddadcacbbccbdcbdbdabcddddacabcacabbbcdddcbbdccccdccbaddacaadbaacbdccbcddccabcdccabbcaaabcccbcbcaaacadacdbcabcccccdbbbbcdbacadcaababacbaadbadcbcaaacbabdacbaacbaabcaddddbdaacabdccbccbabadbdbdadacbbcdddbbdbccbabcacdcacbdcacdbddadabdcbbbbabacacddcaadccdadbbcccbdddbdcabcacbcbddbcccbcbcdbbbbacbcbbabadadcadcaadcbbdaddccbddadddacbdccdabdacaacddbcdbbcdbbbcabbdbacadaccbbddadacbdcddcbcbabddaacadcaacaacacbcadddabbaacbbaacabcbabddcadddaadbccbdddadcdcdaabddbddacbbbdbbbabdcbdcdaddddbccdababddaacdaabcdcdddbdbdbbabdbbdddadbaacbdbcddaabbadbaaacbbbbccdbaabacabddbbabaaccdbcbddcbdbadbcadcbcdccccbdcdbdcaaddcbddbcbdccddadbaadcccaccacaccbacaabcdaccbaaadabbccbdacccdbaaaccaabbaabddddbcadbdcbcbcaabdcaacddddadbcbdabcaaacbdbdcbcbdcdabddaacbadbcdaacdcdbcbabdaaabdbdcddbbbabcbdcaadbdabdcddcccadacdccdbbcacdccdaddaaaaacaabcdbbccbddbccdcbbdcdcdaaaddbdcbdcbbacbdbaccadabdadbcadabdccdbcdcdaaaddcdcadcdbbbbadbccacbdacadddcdcccddbcbdccadbabcbcbcdcaddabaadccdcaddddcccdcbabddccbcaabdbabdbbaabbcbcbdadcbdaacadcabcabcbcbaaadadcacaabbabbadbbbdcbcdacbbbccbcbddbdcccabddadcbdaddbdbcddcbbddbdcdcbcbbabaadabddbdadbddbcaaaadbcaddbddbdbaddaaadbdcbdadcdaddabbcaaccddccbcaadbacacbadaddbccbcaddcadbcabcbdadacbddbbddcaaccdcbcaaaccaabcababbaddacbbcbdadcbcdbcdbbbbbdcacbbbccbcadbdccddabdcacbdadcdbdccbbddddbbbadcbcaaaabdbadcabcdadcbbaacaadcdaadbbbacaccdddcccbbbcccccbacdcdaadadabdbccaabadbbabcdbccbbabacbddaacaacdcdbddacaaadcadcbbbdbbcdbdadbcdaaaabacdcabaaabcbcbaaadccbaccddacabdbdaaabcdcbaaacccaaabadabcdaaacddcbacbbbdadbaadabaaacdcbcccacbbddccbbcbddaabbcddccdaacacdacaabaddcbbabdacdbcdcbccdbaddabcabadccacaadcdbddaccdcadbadcbdacdaabbaadbaccdbdaaccccdbadcccdddcbccdcabdbacdbaddbbbadabbdbaddaaccacbddccadbbddaaadbdbcbdccccdbaddccdbdbdbddaacdcdaabaaacbcdddbaccdaaacdcabaababbbdcdcbdbdcabccbdcbdbbcadcccaddaabbbdcbbbadaabadbdaaadbddbcdbcdabadcaaabbddbcabcbbddcddacdaacdddcdddabcbabcbbbabacacbddaabcdbcdbcabbcdcbcdaaaabdacacbacaccdabdbcbbdadccabaacdabcabaababbdcdbbcdbdccddbaadcdcacccdaddbadbdddcadabcdbccddabaadddbcdbbbababddccbdbbccabbbabadcaaaddcacbcdbbabcabdabddadddaababaaadabcdcbdacbbccabcbbbaddabaccacabbadccccbdcdbbbaababdbdbcdcababcbccbaabccadacdcbcddacbaabdabcabbcdbdcccbcdbdaadddbbabdaabbaccbbdaadbdbcacbcccdacadbccabdbabaddcbbaabcacdadcbdabbababcdacbddaabaaddcdcccbcabdbaababcdccdbccbadacadbbaaabccbbcdccdccccaddcddbcbbdabbdbcdcbbddbbdbcadabbccddadabccbbcdaabacbbbdbabcabdddccdccdbdaabdaaaacbadaacbdaacabddababcddaddbdabdbcdabdadbadabbaccdadadaccacbbaaacccaabbadadaaaabadbcbddabbcddadbbdbbddcddcaadbcaaacddbaaabdaadcbdbbbcaccddbcdbbbccbaaabccbbadabbdabbaabdaaaacddbaccccdbbcbadcacdccadbdbbdcbaddabdcdbcabaacbacbbbbbdcabddcbcaadcdbabcbbccbbadacccabdabadcaacdaaabbdcacdadcbbddccdbdddaaacdaaaadcbacdbaddddabbbbacbccdbcadcddcacdcdadbaccbacaadbdcdcabcdbacadbaddbabbbcabbdcbbcdacddcddabcbbcacbcbbcbddbbbacbabbdbbacddcacbbababbcdbccccaadcacbdcbcacccdcaaacbabdacaaaadadbdacbcadbdaaaadbdbdcdcddaabbbbdbbcbddbcdcddbcdcdbcdcccdacdbcbbbaccbdaacddcddcbacabcdddabadbcdbbcaadbacbdcdcccbbbddccbdabddacdaaddcbdcbcbababdaabbdcccccccacbddddbdbbddacbbdbbcaaadbadcadbddbdbdccabdcbcaaccadcddbccdacaadbbbdbbadbdcbcbbabcbbbbcdcdbddbcabdbcccddccaadddcdbababdcabaabdcbcaccbaaacccbaabaddbcabdbddcdcadbbaccacddcdcdbdccdabddababdddddccdbbbdacdcaddcccaacabaabbbdbdaadddbbaddbcddaddbaadcdccdccdbcdadcddbbcbccabdabdcacbdbcadcdabacdcdbcbaadbbcadcaaccccadccbbcbcdadbacdccacbbdacdcbaddbadbcdbaabaaabaaddbdcdddccdbcdbbddacadcadccdacabbbccdcabbcbaaaaaccdccccacaaacaddabbbdacaaacdadbaccbccbcbddbddbcacdadcdbaacbcbaaacbaddbcacabcdccacaddacccdaadccaccbcddccadbdbccddbdbbbdaababcdbadcbbcdacdaacaccbdbaaadccaadadccbcabbcbcdcacbcbccdcadcdbbdddcdacdbaddbcdcabbabdddaccbdbbdbdaaadbcbacbacaddbcaaadaabbccbdadaacbcacaccdcabdbcbaaaaadbbcdadddbbccbacbdbbcbcaadbadcbaabdadbddaccccdaabddbadbbdaddbbdbdaddadaaaabdcccbdcdabbdddabcdcbacccdcbdbaaaddbcbdbabdbdccbaabdadbadbbcabaabbaddbdcaccdbaaabdcbbaacbccbdbbbbbcbddcabacbbcbdbddbccbcdddbaabdaadbbcbabbcdaaaddcadcdaaaaabdaccccbaaacbcacdababcbacabacccdbddcbabcbbddaaadbcdaccddcddaaabbccbacaaacdaddadbcbabdbbdcbcadbaccdbddcbddaadbaaccdbbbbccbcdbbdcacadabdbacbadcaccacaccabbcacbdabbaddababddcbcbdbcdddbbbbdcbdadaaacbbbdaddcdcdbcabcdbbdbbaaabcbadadcbdcabbcdaabbdcbabbaacdaabdaacaddcaddbabdadaadbaaccadaccacdccaccbbdabaaabaabdcdaadbddccacdbbbbaadbabcdacbabcbabccdccabbcdbdaabdddcacccacccbdbcbcbbbdcdcccdaaccdcaddccbbabccaddcbadbbacadcabbddcaccaaccbadbbdbabcabdadbcdbbccadacdaacabdcaabdacbcccdbabdbcdadacaaabadaddbdadaabaacaadcabdcbbccacdcadbddccaccbcbccccacdaccbbdadbaacaabadaaccdbbddadbbdcdaadcabdcadcdcbdbbccbadcacbaacaabbaabaadcbcbcdbcdcacadadddcdbdcdaabccdbbdcbacaddbcbbdcbcddaabdadadccdcadbcaabdbddbbdadcacdcbcdddbadcdabbdacaccaacbaadcccbbcccdcdbabdbcdddabbdbbdcabbbdccabbddacacbbaacddbadbacaaccdbddaaabbbcaabdbcdcbaccadbadbdbaadbabbcaaaacbadbbaaaacdabadaccbdacbddbaadbbbdbabdcabcbcbcddabdcdccdcacadcdcbcddccbacacbbbbcdcaacccbbcaddcccabdbcaccadcbcdcadcccdadccbdadbbbdcabddbacdaacbbdbcabdbdaacdabcbbaacbddacabccabbabddcdabaaaabbacccaabbabaddcacbdccabcccddbcdacaacbaacaadbcbabcababaddcbddcacdbaaaddcddaaddcbcddcbcacaadbbacabadcdbcccabdbdcbaadcaaacccacabbdcbbbadbdadabababdacdddcdbabbcbaaaaadabbdcaacbdccccbcdccdaaaabdbbaaacaccbadaabcabcbcaddccaddbdbcbbccdbadbcdcbcbabcbbbbbcdcddacdbacdacbaaabdccdabdaabdabbccdaacddcbcccbbdaaabdacdabaaacdddbccbcbcbbcbbdcabaadbbbdcdbacadbcbcaadcacbdcbcddbacacbbcbdadaabdabbaccaaaacadcdcaadaabdcdddabbbbabcadbcdadaadbdaabadcdabcdcaaccbcbcbacbbdbaddaccbddaaaaccaabbaddbdadacbcacdabbdbdaabaddacccdbcadccaddbbaccdbccbdacadbdcbbadacbbabcccccadadbadddcbdcccaddbaccbcaabbcdbbddcddbcdbbcdcabccdaabcccccdcaaabcbbabcacdbdabdaacddbabbdaacdcbdbcbcabaadabddccdcbadaacadbbccdbbccdddbacaadcbbccacccabadacaaababbaadbbdbbddccbbadbcabaababaddbddbacdbbddaacbdbddacbcbbdacabdabdddabddbcbabbdacddccdddacaaabdacdacadacccccadabccccacdbcaadccccccdadbdcbcdaccccaadbdcccdbadbbbbbcadcbddbdaacbdabddabdabddaddccdcbcabcaccbdbccbddacaadbbdbdbabcbbadccadcccbabaacdcdbcdcbadbacbccdbbdcacbbccccacabcdddbdacbcbddbccbababaadbaddabdbacbbacdccadaadbbbdddacdbabccbaaabbdccaabcdcbdbbbacdbcbabcabbbabddcdadcaddadabcbdbbbbdaccaabaadbdcbccadcdaabcddcddcdcaadccbbbdaddcaccdcbbcddcdbbadccdabadddbaadcadaccdccdcbdcabdcdbdaccbcaddccacdcacdcdccbdadbddcdbcadcddbdccdddaddcaadaabbdbabbcbcacaacddcdbacaddcabbbcddadaababbcddaacbddbdaddbdabddcddadddbdbddcacbbbcbcbbbdaaacdbbcdbdacdddbaaccaabdaabaaacdacaddcacbbdcbcbabdcbbbccbbdcdcabdddcdcdbdcabdaabacaccabbdacaaaccbbaabcacbdbbccccdbbdabacdaaddacbcdacaacdacbdddbdcaabccbdcbabddbdbcdcbaadccddcbbddaacdadcdbbcdbabddbbdbcdccdbcabbaaaaaaacddacabacbcdbbdbdbdaaacdbdcccdabacbbdcaccaccbdddddbdbaabaddcbabadadbbbddabdadabbcaaaaacdadbadacbccadddaaadaccadcaaaacccbabccbcccccadcdbbaaadbdcdddababdadbccacbbcccbdcdadcddbbdacacaadaaacdadddcddaaddbbadbdcadcccacadbbababbddbaccbbdbdccaaddaacacbcadcccdcdabbacbbdcbbaaadcadadcddddcbdacddaaaabbdccbbbdcdabccddabaaadddcbdabcbaaacdcccbdbbccdcdcaccbbdcdcbbacccbcbcaddcdcddcadabaabcacdddcaacaccccbddcdbabadacbddcadccddcdcdaadadbbbbccbcacdcacddbddacbdabbbdcdaaddbbaddcacbcbadaabacdbabadacbaabdbbcaabcbcbdaadbddcddbaddcbacabccadacccbdbccddbaaababbdcaadabdacbcbdabbdbcacbbcadabdacdcabaddbbbddbcabbccaadcdcddaadaddbbaaccbbacabaacdaacaabcacbabcdddcddaaccaadccdccacacdddbdacbddbabadcbbdadacdabdddcdaacccbadadddabadbddbcbccddcbacbcbabbadbdbaaaaadabbbcccacbcadabccbbccdaacbdddcccbbdcadbaadbddcbbcdddaccaacbbbcacabadbaacadcbbdcabdabdcdcadacabbdbddcaaabbddcbcacccaabcbdcabadbcbcdccddabbbcbbbcdadbcaccaabadcddbcdccdaacbdddaaacdbdaaaadccdadcaccbacbbcbbdbddbdbcaabddbaccabcdcdbabcadbaacdbbccabdcaddccddccbbbaadacaddbbaabdddcbdaadabcbaabcbdcdcdbdbabdbbabdddaabadcaaccacbaccddcddcdadcabdabcbddbcbdbdbccdccdcabccbabbdcdddccbddddbbcbddbaabacabbbbccbcddbbcdcddcbadccadcccaabacbcdbbddcbbadddaddbcbcacabaadbddccabdababbacbbdacddadacabaadbaadacbacadaccadcccdacbbdabcbbddbaabcabdcbbccccccbbdddddbbdbdbaabababbcdadccabdccdbadccdcacacacbbcadbbccabdbcdcdaccbbbccabdbacbbacccdddbcdbbbabdddccadbbabbdacaabbabdaddbcdaadbbcdddaacbbabaacdcaabbdcdccacbddadbabaabbccacddcacccbbaaabdbbdaabdcadacaccdcabccbcaacabbaaabbabbdbcbadcaccbaddcabbcdadcddbaaadacdabbccccaadbdadaaabdccbbbbbbbdcabbaccbacccbbcdbcababbcbcbddbddccdadbbcaccccbcbbddbdaacaacbacdaacbddacaacaabdccbcaddaaaccbdbcdacacdabbbacabcabdadadbcccdccbccddadbaabdbdbaabbdddcbabdcabcabbacbbaddadababdaabbaacddbccabddbbcdcbbbcbadddbdbcacdaddccbaacacdddadaacabcbacacacabcdbddbbbabbaaaccdbcddcdbdaababdadabcadbaddacdddcbcdabccbdbdbdddddddaabdcddacbcaacdadababdaabadcdadcccdcbaabacacacddadccacddcabaacddacbdbdbbddbddbbacacdbbdbacaadbadacaabbcddbdacccaccdadacaaaabbdcbcdddcbccbddbdcaccabccdabbdabccbdcccabababbbadccadbdccdbbaabddadcacdddacacbaabdcdbbaadbdbbaaadcbccbdcbaaccbabdadcaaadbbbadccdaccbbdbacbdbbcadacdacadbdbddcadbbbcbacdbdbabbdacbaadcdadacbbdbdaddabcccdbbacacdcdadccdddddbcbdccccdcdddaacbcbcdbacacabdabbbcadadddacbaabddbddcbddadbcbbdccbddbacadcbbabadcdabbadadbdcccdabaabadbbdddccacccdcddbababbbadbbadabbaabbbbcbdacabcbbdbddccbacdbacccdbaccdbacadbbbcdddcabacdbcabaabdcbabadcadcdbcbbcabcdcddbcdddcbbcbaaabcddabdababcbcbbccadccacdbbdabbdcaaddaadcbababcbbdadaabdcbcadabaccabacacbcadaabbcbdbbbdaabccdaccaccabbbadbcbccbbbddccdcdbcbdbddcdaacbbcabcccabdbdabccdaabaaddabaccbdcbbddaddcbdbcdbcddccacbabacaaacdabadcababddbdbaddcbcbccbdcadccbcdacababdbbccddacbcdaaadaabaaacdccdcaacbccdddcbaabdbadaabbbcccdcbadbcbbbabaadcccdbddcbaacbcadacdcaacdcccccdcbbbccbbcbdcdcadcaaddcdcaddcabbddcaadaaaddbadacdcbdbbcbaaccabdaadbccbcddddcadcabdbddcbdbaabddcaddadadababcabcbacabccbadbacdaadccccbadabbcbdbcdaddddaaabcdcddcbccbbacdaabbbadbbdcdcbbdbacbbabcaccabcbdadccdacdadbcccddaabdcaacabddbbdbcccdccabbdbbbcabaadddcdacacabbdbbddbadbdcdcaabdaadcabadacdabbabbdccdcdbabcccdaadbdccadcddcabdbdcabdbaaddccbaddcadcbadbaddacdadcabaaccdbabcbcbababaabdacbcdcaacddadbbccacabaabbbbbabcaccbcddbcdabadaadcdbbbdccdbbadbacabbcdcccbbaacdcadaddbacdbaacdbaabccaaabbcbcabadcabaccbbabcddababadbbbaddddacdbdaddacdbadbaaaaabbcdababcaacacbadcccccbbcdbbdddbbdccacdacabaddaacaaadaadbacddabbaaadbdabcdcadcbccadddadaacaaadcbabbabddcdbadbbcababdcdddbdcbdbdadaaaadadaadacaddbdbadbcbdddacaabbdaddbcccdbbdccdcdcdaabbadadcacdbdcacdacbbdaabdbdcacdabbacdbddadddcbbddabcacaadbbadcbbaabdcbadccdbbabbadaddcbdbcabdabbabacbcaddcdcbdbabdbaabadbdababdbbdbbabcccaaddcaaccdccdabccbdaddddadbacdbbbdbaabbdadddabcabbaacdbbdacdcccdacbdabccaccaccddcbbacbbbadaacbbaacccccdbdddccacacccbaaddbabadcaddcdccaaacbdadacacadbbadbcdcbacbdcccaabacacdbaaddabacdddbdadadabcacbccaadcaddcccacaacddaabbcbbcadbaadcaaaabcaacabdbacdcaacbddbcddacacbdaaabcbacabccdaccbacbababacbbbaadbadbddacdcabccabbdadacdddadcbcbbbcbabcbacabaddcaacbcccabcabbbcccbccdadbdccccbddaccaababadaccdcabcdbbccccadbaabbdabbbcbadbabcccdbcbdcbdddcdcbcdddaccaabadaddbababddabddbdddcbcdbddddbabbabcdcbaadbdaaacdcdbcbbdadaabcababdcddccabaaaddccddbbdcaaadbcdabaadbcacaadaccccacbcccbbbadacdbddaaaacabdadaaaaddcabaccaaddbdccdccccbbcddbabdbbccdcccabdadbcaddadabdcdcaadaddadbcbcccccbbaadaddbcdbbccbbacdcaacdddabdbbaabcaaabbbacdcdbccdadcaaaabbacdcabbdabcdabacbbabcbabdcbcabbaddbcbaacbcbaddddbbddddabaddbbaaadbbbdbcbaabccaaabcacbdddadbbccabddddadaabadccdcacadcddbdabbccbadaaadbacdbcdcaabbdbabdcdbacaaabcdccadbaabddaacdbbabbabaaacdcdadbcaddcdacbbaddcdcddabdddabadabcdcacbcdbabaadabadcdbcdabbbdbddbbcddbbdcdaacbdbabdcdadabbcdccbcdcdacaaaabcaccbdbdbdbdbbcbdcbbdccbccccbdbabadcdbddccdabaabaadbabbbadabcddbdccccacdcdddacccbbcbbcbbaadabbabbdcdbcdbdcbbcdcdabcdcaccccbdccbbbbcabcaccbbdcbcdacbcaddcbbaaacbbbdaadaddaacabcbbabbbdacadcccdcbccaacbabcccdbabbbdaadacdbbbcadbaccadbacdbabbccadadcdbdbbccbbbbcbccadddaabdbdcddbdbccabadaddadcabbbddddccdbcbabacbcaacdcccdaccbacacbddbaabbcccccbaacdbababacbccdbbccccdbbccbbcaaaacacbadabcdaabcbdbdabddbcdcabdacdcdccaababdbcaaccdccbabbddbbacbbadaccdabbaccadabcadddcbadbbacbbbacacccbbacbdbcdbcababbcdbcdadcbdadcbbbaddacbcccbbcccdcdcbbcdacdddcccbbaabddddcbdbaabacbcdbddcaddccccadccaaacdcccbaaddcddcbabbbabcbdabacdccccdabbdbdbdbdddaadadcbcbacbbbbabacccaacbbcddcaacbaabcbbcacbbcdbbbddaddcdcbadcadcccdbbaacaddabadbacddbdabacacdcbdbdcaddcccabcdcbbcbccdaabccbbccacbacdadcccabbbddadbbdcaddabbcacbbbacaacbdbbcdbadabddcaaabacddcacbcdbdbaabcdabbdadcaacccddbdaaaddabbbddaccbccdcccdcdbcdabbdabcdddbaacaadcbdbbbddddddaabbdcbdcdbbcbdadaaccacaaaddacccdccdacbbddddcddbcbbdcdacdbbdcdaacbbddcbaabaabaacbaadabddbacdcbddaabaddddbdaabdbccbcbaccadbbcddcadcbbcddcacbdaaacccbcdbbdcbdccabadacbdaacbaaddabbadbbddbbccbcdcadbbbcbcdcbadbbbdcbdaabcacacaabbbcccdcacdcddaaacadbbabdbbaacdddcacdbddadbbcadbbadcddacabaacbcdccbdddbaadcacbadcaddadabbababcccadadadaddcddbbaabcacacbdbccdacdccdbcddbccdcbbdccbaaaddbaddcdaacbbabddadadccacadddbbaaccccaabacbbadccabcaacccdaadacaccbabcdcddbdaaadbbcaadcdaacdadaadabacbcacbbbbbcbaadddbadbadaaabbcabdcbdacbbdbdbcdacbccdaccddaaccdbcbccdcbdacaaadaddcdcadadbdcacbbbcbbabdaccccbbabaddaaddcddccbbdaacacdbdaaabcdbadbdbbadbbccbdbcbdaacdcabdbccbbabddbcacdddbaccabcbcbbababadadcbbbcddadbbadcdbacbabacbbbaabbbbbabccccddbbbadabbbddcbbccadccbbbadbacabcccadcccdddbcbbcaddacbdaaccababdbbcaadbcbddcdcdadbbabcacdbbacbadcddabdbbdabaadbacacdcaaabcadbcccaabbaddadbccacabdbcdadbbdddbdbcccbcbcbcdbadcbbbbbaaddccdcbccdaaabcadbabbcdcadcdcdcbdcdbcabcccdcdcaaccbcccdbabcbcddadccddbaadbbacdddabaaabaccadaaaadcbccdcdabbaddabbbddadcdbdabbabddaabbddbcdddcbbaadbbcaccbadbaddcbcaaabcaabbabcdddabaacbacdbacaabbcbcbdbbaacbbbadcadcacacddabdcaabbacababadbcaadaabdbdbdaddabdaaacaacbcaacaddbbbbaacdbdadccdaddbddadacbabcccadbdabbbdaabbdbbbbaccbaddabadabbdcccdabbcddbccacccccabbdbacabababdcdcadcbdbcdacbbacabbacaccabaacbdbbaacbadaddabdaaddbdcaaacadcaaadadaddaaaadaaccabbadadbabccdcdabcabcbccbdcbccacadbcabbcbadbcadccbdadbdadaacdaadcccbccbbbacccdbbddcdbdbcbaaddbcbaabcbadabcdabcbcccbdbdbdabcacacdccbddbbacddbcdabbdbbbabdaddbbccadcabdcdbcbababcaacbbbddacccbabcdacdaaccccadcbdcdddccaaacddbbcdaaccbbddababbbdbcbaccbdbdddacdadadbcbbcccdadcadbcadbdacdadaaddbbcccddabadaabcbacdabdadaadbbbbdbbabbaddcbbadddddbababaabaccbcbdababbabdaaaaaddddbabdababdbcabdcdbbdabdcaacdbcadcdbdccabccadbbabdddbbddbcbdacbdddccadbcddabcacdbbacadddcadbcdacdaaccccccddacbcbdcdadcdaaaaaabaaaababbadcbdbbdacaaabbbbdbbdddacacdcdbaabbbccdabaadccacbdccdaabaacddcbdaabcdaaccacdbccbadaaccbaccadacddbcadddbbadbaccbcaaccaadbabbbdaddacbcaccdbaccbbabbbcdccddbdbaadcacdbbcaadcdbdcabbdbddcdbbdcdacaddcbacabcadaddabdddbddcdcadadddadbcbcdabcacadaccaaaaccccaabdabcccbbbadacbbcdbaaacbcbccddbcbdbdcaaddcadaabcbcdaabdcbcdcdcdbacbcdcdbbbbaadccdbdbacbdabacbabcddddcdabadddabcaaccdccbdbdcdacadcadbbbbdbcbcabccbadccbcacbadcbcdcdbbdbddaadbbdccccdbdabcbacccccddaccdaaacabdbcdbcccaadcdbdbacddcbababbadcbabaacbbcbdcbabccbbcadcaaaccdcbcccdbadbabaacaacadcaccdababacbcaadddccadaaccaccccdbadbdbdcccdbccdbcabacdbbadcbaabaabcabcbdddacddadbcdaabababdbddabdddcdababbcbbcccdbbbbacddbbaaddaabdabaddabbbdacbbaabcdaaabadcaaaabdbcdcdacdcdaaddcdcabcbcdacabcaddbadbbccaacbdabaabaabbbabcaacbcaaddbabbbddbddadaadacccadaddccacdddaaddcbcbccbddcbabbadbbcbddbbbcaacaabaaacaacbcaacdcadcbcaaacccbcadbcbdabadbcdabdccddaaaadbbaacbddbbaaacbbbddabdbcbbaaadcacaaaaddcdcabdbaaaadbbdabadbaccccaadcadccdcabddaacbddaadabdadcbdcbcbbbbacadbaabacddbbdbcacbdcccaaaadddcdbdddacdabdabdaadbdddaaccacddbadcacadbbdcadcccaabbcbcccddadcbadbadabbaabdbdaacdaccccadcbdbdcdcadccacbccddadbcdcbdbcaabdaaaaddaacbccdbcaacccbaabacbdbbbbabccbddcaccdadcdccadcdbbccbbddbdcdbbbadbdcbdbccbabcddcaaccdcaaaacbcddbdabdccbabdbaabbabbdbcacdbdadbbcdbdbdcbaaaaadddddbbbbcaddbcdaccdaacdcccbcbbdddabccaddacbddaddbdabcdabaddccbbcaccdcdcaacbbabcbdbcaaadcdcacddbcccbaddacacadbcbcbaabddaadbccadbdddaadbbbbccacacccadbabdcdcbbaaacdcccadbccaccaaadacabbcacaddcdadcadcabcadaaadbcadcddabdadccbdbdcbaacbdcdbccccaacddbbccbcbacdbdabdbcbbcabccaadaadbddbcaabddabccdcaddcdcadccdacbddbccadcabcadbbadaabdddabbabdcdaabadcddccdaabaaabacacbbbcdbccaabbaabcbbddcaadaabdbacadaaddcdccdadccabddcdaabbbcddcdbacccccdbdbbcababddcdbdcababcaadcdbabbbcccdaabacdcdcddcddbcddadaccacdbadddddcabbcdddadbcbcaccacccbcbdadbccccbddbdcbccaadbcbacabcdbadcaaacbbbbadabccbbabbcbdcdcbadaaabbadbbdbbaaaadabdcacbcdddbbcbdacbbdaaaadbabdaaabcdacdcacccccddabddbadbcabdacaabdadabcbababcababcbabacdaddacbaabcccdbbccacabbbbcbabadccbcbbbdbcabbabdbcdbbadcdaadacaccadcaaddbccddcbdadadcdcabcbdccacacbbaabdbbadccaacdbccccaabdbadbacdccdcababbcdbbbcdbbacacbcbddaccdbbcbadabbddcbabbdbcdcccdcbaaadaccadcdddcbdaacbbaacabadbcbadbbcddaacccddcdbddcaaaabbbadbddcbbacccdaadcacbbaccddcdcadcccdbabdacddacdbcaabdaaacdbaaaabbccabbddcdadadcaacabcdabaccadcbadccdcdacbbadddabccddacbcdcdbbcdacddbbcddaadaddacbdbddbdbcbcadddcaaddcabdcaadbacddbdaacacdaaacbdbdabaadcdcacbddbddbacaddbdaccdabadacddaccdacbdbbcaacdccdaaababbcbbbbacacacaadbcdcaddaaaaacbbccccabacdddcdaabbcdcabbdacbcbbcbcacadbdbabdcbdadddbadddccbbcabdbdbbbacccdbacbaabdccbdccbcccbabdaaaaabdcadcabbbdbadaaabdcaddbcbcddcbcddbabaabdabacddddbacbdcadccbacdacbdcdbbddaaaccdbaaadcccdcdbbbacaddacddbcacbaadabacdcaccbdbbacaadcabdaccbacaadbdabddbcdbdcbdddadabbaaaddbdccaabaabdccccccbcbbcdccbcadbbbaccbbddbdbbadaaddcdabdbdbdbcadbddbacdbacbbbbadbcbbacabadccbbdabccbdcdadabdbacccabaccacdaccbddbdbadbbdbacbcbaaaaabcabacadadcbdcbbbddaabccbbcbbbbaadabacdacadbbbdcaabbbbdbadcdbaaddcdadddacbaacadabbacdbdbdabbddcdbcdaadbabcdacaaadcccddabadadccabcaccacbcbbadbacdddbacdcbccbdaaddacaacdbbcbcabdcccdbbcaacbadbbcaaccadadcccbdadcbaabdbcdccaacbccddacaacaccabdaabdcadaadbadcbdbdcbdcdacbacdacccababcdbbabddbdacddddccdbccccacbbaddcdcaddaccbcbaddcccbdaddddbadcabddbbdabdcddcdcacdbcaabbbcacdbdcddaadaccadcabababaacbcccbcbccbacbabcaaccdbddcacdaaaacbbcddabddaabababdddaddaccbdadbbdbbcaaccddcadddddcbcabbadbabaaadddcdbbbaddcdbaabdcbbdbaaaaccdbbbbcdccbdbddabccbbcbcbddcdbdaddbbadadcccbbcacabbdddbccbbdaaaabbaccabaccdcdadbaddcdacbbbbacbadbbacadadcbccdccddcaaacbacabdabacdddbcbaccdaaabddaaabbcaddcaaaacdddcbabcabdcaddddabcdabddbbdacabdcdabdbcaccccbcbbdcacabddaabaabbddcdcadabbdabbcbdadcadccaabddbbaccabbdabbbaddddcdaabddcbcbcdaacdbddaddccdbbbdbdadaabaabcccacacbddbcdbaaacbbdbaaddabbbcdccbcacdaacddbcbcbbaadcdcbcaaabdadbaddadcacadbbadcabbbaddbddcaabcdcbddddbcaaabbaadacddacbcdacadcdadbddbbbacbcdadbbddaccbcbddbdbadadacdcacabdbdbaccdcadaacdadababdcddbbdadcbbabaabaacacdadddddbdbaddbbadcacbbdcabcaaacbbcbbcacabcabdbdbbadbdaacaaddbddabbdcbdbdaadbbcccbcadbbccbdbbaaadbbdbadaabaababdbcabaccdcddcdbdadbcdadacadbdbddbadbaaaccdcdaddaadacdaaccdbddacdccdcbcbdacdcbabdcbbdadbdcdcacbbcccddbbaddabddcdbaadcadbaccaddaadadbacbdcadccdbacaacdbdccadaaadcdbcddaadbdcadcdcbadabacacabcccbadbccadcbbabddddbadbdadcaadcdbddbacababdbdbbbbbdadaaccadaddbacbcdaacadcdddabbbaaabddabadccdcabbdabbadacaadbaabbcaddbdabcabcccaadcddbcdcbadbabbdacaacacbbbabbddbdbacacadabdbbcccbbaccbabddaadbbbcabdadaabbdddddbbddcddbddccddbacdcbdbddadccaadcdabbacbdbcdbddbdcadabddcbccaaacbbabdbacdaabcddccadddacdddabbcbabcccbacdacdcbaabdabcddcbbbddccdbcaacccadcbcabbbbccdcacacbbccccacaaadacbccadbadbdadcbdccaaaddbacaaaaccbadbacbcaaabadbbbbdbacabbabaaaccdbdbcbcddcdcdbacbddcdccdabaacacdbdcbcbddadcddbddcdcadddacabdbcbccbbdbbccbadacacdbdbaacbabcaddacdcacaccdaaaadacdbddbcadccdaabdbcacdaccccadaacdaadbaaabcbddbadabcabdccbacbbcbcadbbbddcaccbabaadcbadbcabcbacadcbabbddbcbbbbbaacdcacbbcdcbbadcaaaababbbdacaccbdaaaadbbdddbdcaccbbcbcdadadccdcdcabdcacbdbbdddacbababaaaaadaddabbccdaabcbdcdbdabbbbddcbddbddbabbdaddbcbbcbaccbaaaabbbdacbacabdbbddcbcddcaaabccdcacbcbabbbaddddcdcdabdadcbbdbadbdcadcdcbcababdaaabdacbabcaddccabbdcadbbadcaabaacbaccacdcddbddbcacbdaabacabdcbcabaaadcccdbddacaacdddbccbaaaccdaabcddcddbacdcbcdbccbdbdcbdabbbadccccacccbddbdabdcdabacbdbaddbcdaadacdcbbabbcdbbcacbaacaddacdababccadadadbaacadacaacaabadacabcbacabbcabdcbbddbacaaacdddbbacbccbdbbbadcaacddacbbbccccbacccdcbabdcbbdcdbbcbdbcbbacadcddadacbbcdabbdcaccdaddbaacadcbdbababbabdacdcdcbdbbcdcddbaabcaababbadcbaccaacabbdccdbbddccbdbaababddcbacdddcbdcccbbbcbbbadaaadaaabaddcbaccccbacdaccdbdaaacbaacdcdddbbbcabbbacdaabbcbcdbcbacaadaaacaddaccbdcddbacbdbbacbabddbcaabbccdccaaaaccadcccbcdacdabaaabcdcdddabbcddadadabdbabdbdbcacbbaccaccbcbcadcdcacadbdbaabbbdbacacacddcaaadcabaabdbbabcddbaacbddabadcdbbcacdcbdddabbdddadbacdbcdbbcdcaaaaddcdbcbddbbbaccbbbaadcdcabcccabcdcaadacccbbdacbbadcbacaacdddcbbbddcbdccbcdcacdbcabdbcbbabccabccdaadbccbdbcacaadbccdbcddbdadddbdddccacabbdbabaccaabbbcbaabdcdadddadbbddcddcccacbcccdcabddaaadacddbcdbcacdaababbabcadcbdbcaadbaadcbbbdadbbabcddcbbcadbdddddcbbaccbadadbabbdabbddaddbbccdcaddbccadaabdaacbaaadabdbdacdccaddcaadbbdcccdccbbbabdbddbddacacadaaaacbabaadcbdaadbaabbdaddaacacaadadcdddabaabacdaadcbbabdacbcdcddddcccdccabdaadddbdccbbabbdbdaabccdcaaacacddccaddcdadccaadbdbcbdbcabaddbdbddcbdbacbcbbadbbdbddcdacbdcdcccaaabcabcadabcdbdcbccbbccdbcddbcaacdabdbacbdaacdcdbcabcacbadbacbbbabacacadbcacabccbacbdbcdcbddcacabadbbbcacdaabddcdcccbcddcdddccbabaccadbddaaddacbabaaadabdbddcbcaadbdaabcbbcbddcdbbdadbbdbbbccdbdbacdcdabaaacdcdccdadaadbabcacbadbbdbcdcbabdbdadacdacddabcbadbacdaaadbdbccdbaaccbcdbcdccbbcbdcddadbcdbcbbdddbcbaababbbcadcbbccacdccacabdddaabcdccbaddadcddaaddcbcbdaddcadddaacadadaabcddabdccbbbcaadcbddbdabbcadcadabbcbdcdbdcaacdaabacdadbdadbbadddaacdbacbccaaadbcbcbcdadbdcccdaadadddacbbdabbddcbcbcbabacaaaaddbaddcdcbdcbbadbddcdbcddcbcddbccacdbabaabaacdddcabaaadbbbbddccccbdcadcaabcdaaadcdbdacccdacbdaccabbdbdcdabdbccccbdacdbaadbabdddcdcddcbbadbbdacbdadadaababbdbddccaabbbdacddbdabbccacacabacbaccccdaaccbddccaccdbaabdbdccbaaaddddadbbbbbaababbccbcbdbaababdacaccacccacabdcdcbccabacbbcccbbccccaacadbbdaaccabbabaacaacaaddadabbababddbcdddadcbcbbbbcadbddcacdcbbcbadddbdbabcccbadaaacbabbdaddabccdcabaaaccdbcdcccbcadcadabaacbbdaabbcbcadbbadddacaabbdcbdbadaabddabdbcccccbcabcacbbbbbddbadaadaacdacdbacddcdcbbccbcdabacadbcdaabbcbadabbdcbddaadbadacaccdaadbaaabcadbbaabdbdbdacdbbaddcdddadbdbababadbbbbcaccdaacabbadcacaccbcaccabddbadabdcddbbbdabdcbbcacdadbacdbaaacaacaccdcaabcadbdcabcdacbcabddbbaaaddadbdaabddcbddcbbbbcddcbcdabddbcabdbdcbadacacdadbdcdcaaadcaddbbaddabcbccdddbadadbbcabdabbbbcdaaabadddbdacdabaacdbbbabacbaadcbcaacccbaddbbbcbdbcadbcbcbaaabddcbaabddbbdddabbbcdabadbaddccadacbaabdbccbbabcdcabbdaaacddbbbababcaaabdcabcbdadbbaabadacadddcbdbbcbcacbcabcddaccabdaaacbacbacacadcbaddcacacabaabbcbbabcdcccddcaababcbccdbbacdcbcbcbcbbcddadbccacabddacdbbabdbdcaacdcbbdbadcabcddacdacccdcccccbbbbbdcadcbcdcbdcdcdaaaccccbdabbbbcdbddacaccbdcddbbcdbdbaabbaacdadccdadbaadbabddcabdcdccbbacdbdccbbcbbcabdacdacdbcaacacadcbbcbdcadabddababddaacacccccddaddaaaabbbcbbaaabdaaaddcaacaaccdccdababdaabcdcdacacdcbdccccbabddbdccaabcaaaaacdadcabaabadbaddbabdccabbadbbdcbcaadcacdbacdcbacbaddabdbddcadcdddaadddbcadccdaaaaabcdcddbadbddaabaddccbcdcbbcddaacadadbcadcbdbdddacccaadbcabcadcbabcbcaaacbdcadbccdbabdbcdacabbddbacaaadbabbbcbacbbacabbccbaccdcadcccbdddcbcdadacdccdbbabacadadccbbadccacaacddbacaabdcbdcbccbddddbdaababaccbbddbbcaddbcabbabcdbaadbcabcabcbadbccacbdbddbcccacdacdbbdddcbbacdaacdccbdaacbbddacbaaabaaacbbcdcabaaadcadbadbdcabdadcdbdbcdcbcbbdbcdcccabcabdaaabcbcdddcacbdbcdaacdabaadaaccacddabbaabbdbcddcbddbdbcbdaaabadaaaadbddbaadbaaabcdbcdadbadbccbaccbbbbdddacdcbddcdaadabdacdcabccbbacbcadaddcacdbcbbdaabdbcadadcabbcdbcabaacdbabbddaabbaaddbabcbabaaddacaaacbcbcccddaadcacbbcbadacdaddcddbdcdadabdcbcabbacbcaddbcadacbddcbbdaacdbbbabcaddccaaabadccacaabdbcabdcaccdabcabcdcabcbbbabcccaddbadaaaccddacadaadabbbcbbbbabbccdccdcbdcaacbbbdcbcdbbdcdbbbdbcadbbddbbadbbaabcaaaabbbadcaadacbbabdbbdcadacbbdadbcdbcbdccccddacdbbaadacccacdbcaabaaadcbcdbccabddbbdaaadcdcaadaaddabaabbdaaadabbcabdcddaacbbbabdbcbabcaaaabdcbcbbddbcaaddacabdaadcaacacadbbaacaaaabdcddbccacbcbabbdaddbdcacdadaddabbddbbbbcddbbdadaabaadddbdaacadccbcaaaccdaacbdaabcabdbbbbdaabaabacaaabbaddbbbdddbcacdbcdcbddbdcacdcdcbdcabababcdbababaccbccadcdabadccddcadaabadbbaaacdccbbcaabdcbadcbbbdcaaddadcaacbcbcddaccabdbaccdadbddbddcbdaadbcdbdaacaababccabacabcabbccdbccadccdacdcbbddacbdcbadbddabaacccaccdbbdbcadddbdadcdadababbbabdaaabbdaacabcaacdbdaccdcbdaacbbddbdcdcddcadbaabdcddddcabccbcbcadadcaadaadabbddcbbcbbbccdbaddacbcadddbacaaddcbadcaaaaccddbcdbcaaaccaadabbdbbbabbacccabaaabdccacccadbbaaccacacacadcaacbcbbcdacabddabacacbbbdabbbdbcbaaaacbbcdcaacbbabaacdcdcacdcbbcdbdbcbabcaddbccdccdbcddbabbbdbcacadcabddbbabdabbdcbbccbcaabbcbadaabcbbbbdbabaaaaccccadbacdbbbbdcacabcdcadaabdcacbaccacacdabccdabbcbbbddbccdccbccbdaadbdcbbbcdcbbcdbabcdbcacaadbddbdabbcdabbbccbbbbadbbdbcacccccdbcaacbbacbcaddaadbddcdcbddccadcdadadbbdbbabcdcbcbbbabbacacddbccddbabbccabaabaabbacbabdabbdaaaaaccdbaadddbdabacbdbcdcabbbcadadbbacbaccaabadbabbaaabacbacabcdcacbcdcaddaadcaadbadbacccbadabdbcdbbadcbbbaadddbaaccadbdcbabbdabcccbccbcdbbbacadbddcdcdcccaaadabdbbaccbddcbcabdacddbacadddcabaababcadccdcbaadbbacccbccbdbccaccaddaaababcabccdbdadcbdabdabdcdbbddbacacbdabcbdcacdbbcaddaccdccadcbdcbacbcbbaabddbabdaabdcbcaaddbddbdbccbdcadccdcddaaccbcbcdaabbacaaccaaddbddabcdcdcacbccdccddddbdddccbaacadbcdacdcadcbabcacddbadaabcbacddccdddbdbbdcccdaddbdbdccbdcccabddbbcaaaccdcbadaacbbdabbdcbbabbadabdcdabbdcddacdbbacddbbdbadcaabdbacbbbdcbaccdcbacdbccdbddccadaaccbbdbcadbdaacdbddddcddaaccaddbcbcbbdddbdbcdcacadabaadccaddaadcacbbbbabcbcacaaabdacbdaaddcbcbbbcbacdaabbdadbcadadaccbcbdaddcabdacababcbcaababaddaabcdbbaacbadbdbdaabbddabdacdacccacaaaadbdbbdcdbaabdbdbbccdadaaadabdadbaccbdadcbbdadaccdbadcbacababcadcdadcaadaccbccacdbcdbacaaaaacccddbadbdcacbbcbaabbcbddabadbaabdaabbdcbcdcbdcaaddbdcbdabaacbcacccdbcaaabadaccacccddcbdbbbacabacdabcdbbdccbbabcabdcdbccccabcbacbadbbacaaacacadaacababadaacacdcbbdaacdbbbaaccbdaccbadadaccaadadcccadabbbacbbbabbbdbbadbbbdcabcbbdabdaccdcaabbdbcdbabbadbdbbbacadacccabcbacaabacbaddbdcbbacabcbbabbabaddaddadbbbaaddbadbddcacddbdacbddbdbdabbbadcddacddccaaabdbccbcbbddcbbabbddbdcccbbcaacacaaaacdcdadaccdaddbababddccacacddbdbdcccbdddbcdcbaddcabadacddadccbdcacababacabccdacbcbcabcccaadccdabbaabdbacdccbbbdaccdcbddadcacddadbbbcabbccbbbddbbccdccbcabcdcabbdacabddddbcbbcddaaccadacadbbabbdadddbacdddddccaadaddaabacbacbcbdddadccacdcddabaadddadcaccddccbcddbccccdabcbbabdbacdcbdbdddacaddbcbcbcadbdcdbdcaadabcdddbbdacddabbbadbddcacaaacadadaaaccabdabbcbccbaaaacbcdabcdcbdbcabbaaddadabdcddcbdccbccdddbcdcddabcabbacacdaacdaaccabbadadadacadaabbbaadbdaccacabacadadcbcdbaddddadacbabddcbdddabacacacbadcabcbdcacdabdacdbaaaabcabdcaccadcbcccdaccbbcbcbaaacbadcbaddcdabdbcdcbaddcabbbaddbbccbacabdbcadbbddcadadabbccdddadcababaadadbcccbacbbcacbaadcbbbadcbcbcbcccbbccccbcccccbdbabdddaacccbbbaddcdacabcabadcbcadddccaddbddaadbddbbcbbbaccdbabccbccdcbcbbadbabdbdbbbcbadacadabbadadddcdcbbccabdadcaabcaccbbadaddbdcdababaaadcadabdbbcabcdcdddaaaccddddabacbadbcdbdaaccdccdbbbacadddbaadcccbacdcabdcabdcbdcaaadbabddbdabbadbaccacdcbbbcbdaabbdcbadbcbcbdddbbcabcdbccbbddbbdbaabbbbcdacdabbaacadddccdacadbbbadacddcdbacccbbbdccbbccdbadcbbccdabdaddacdbabcddddcddcccabdbcbbdaaddccdbdacbadbabbbdbdbddccaaadadbdadcabadddcdbcacdabacbdacabadccddcbaadcaccabbcaaabbabbacccdbbdabbcadbbacbdacbdbccabddadccbbaacdcdabcbdcbaaaddaddcabbccddbbbbbdbaaabbcdadbdcbdaacdbcacbcadcdacdcaaaadcaaccddaaccaabdbdabbbacdbadddbcbadadcaaadaddcdbbacbaacbaccabcddcccddbaabdcbcabbcaddddabcbacdbcaddadaaabdcbaabcbdbadddcdbcdbbcacacbcdaabbacdccddababcccdabdaddbdadddbbabacdcaddcbbbbdccbbddadbdaddbacbadcddabddddbccbacabcabdcdbcccdbaacdadcbaabacbaaccccbddacdcbcaabdabacdcccdacacdbbbbcaacccabccbdddcbbdacbabdbbbbaddcbabbbbbbddbbacbdddbacddabcbdabbcbdcbccdddacddababacddadabbdbcbbbcbcdbcbdcdbcaddbbdbdadcadccbbddadccddddababdabaddccabbaabcaadcabadccaadcdcdacddaaadccabdcaaacababccccccdcbbbddaddbbaddcbbcbdcbccbcbabbaaacdcdbadcddbadabddcaadbbcaaacbbccaadddbdabdbbbdcabddddbbdbddcbbadddbbbbabacdcacbcbbbdcababacbaaabdabcdaccdcbbcdbdaabcabcdadcccaabdbdbbcbaacbbcbdacabbdbbcdbddbcdabccbacacccbddaaaccadcaacbdadbdaaacbccdbaadbbadacccbdabadcaabcacddaadadacdccbbbbdcabdacdcdabcdaabdcccdcbbabaadabaccadabadbbbcabbcbaabaacbabaadcaacadbaadccaaacddbcacddbbacccbacaacdaacddbbccccbdcdddaddcbacbdbbcaadbdaadcdabbccdbddddaddaadaccbbdcddbddcbbdcccdbbadbcaaacdcbcbcbbddddbabbaabccdcababccbcdcabadabbdbacdccccdcdacddabbcbacdbbdaaaccdbccbcdadbbdbcbbcdcaddccacadcdcccacadacdcdbdbddaaaadcabacdbbbdddbaacdcacbadcccabbcdbcddacccabcbbcdbabadcaabbadbcccadcacaabbbddaaabbcacaacaabdbbddcdabbbcdaaaaddbcbccacdcbbdadbbabbddddcdabacadcdadcddcabbdbdadabdbdccdadbbbadbdcaabcbcdddaccccacccbddddacabcaddcacbdadbbdbbdbbdbbbbbbbcbdbacaddcadaddabdacbbdadaccdcbddbdacccadabbacbdcadcccccabadbdcdababdbbcbdbcacdddbbcdabacdaddbcccbdbcdddbdcacccacbadcccbdabbbdbdcabdbbacdcdcdcccbcccbcacdabbdccaacadbcbcbbdabbddbcacdcdcdbcaacaddacbddcaccdbacdadcdcddbdddcdddcbbacccaacaccaccbacddcbadbbababddcbcddcacdbdbadddabcbdccdbccbbacaaabacccbdcacddabcccaadaacdccdbcdbdacdbcbdbcdcdbbadbdcdaacbadcadcddcacccacbaabdccdbcccbcadcbcaccabdccbbbccbaababbccaacbdadcddaaddaaacdbdbcdbbbbabcaaadbcbabcddabbcccabccbcbdacdbbbadabbbadbdbddacdcdaaaabdadcdbcacaccdcdbaccbaccaacdcbccadabcbcadadadaadbaadcbcbccabaaacbccdbbddbcccdcdcadaaaaadabbaccabaaaacbcccdcbbabbdccdddabababaabdacacbbdacdbccabbbbcdcacabcabdbacaaccadddbccbccddbcddacaddaaabadbbdabaacbcaaaccbdaacaccdbbabddddbbcbcdbaaabcabdbdbbbcbadcbadabdadbaaaaabdbdbcbdbddccbbbcbbcadbcabdabcdabdadacbdbdcaddadcbcacaaabbabccdbdbdbaccaabbbbdbdccdcadcdcdccbaadcbbcbbabbccadaddaacdbcdaacddaadbbaabacccaaaaabdcbabcabbaadbaddbcccddbcbcaddabcaaaddbbbcaacdccdacbddbbdaacabdabadaaadaaaaddaadabbadddcbbbcccdcaabaabdbbcdaadcbccdbcbcaddbaddaacabcacadcbccbbabcabdbdbadbdcccadbcacaccbabbdacbcabcddbacdcbbaadacaabdddbdbbcbdbbabccaddcbdcdbcbaccbdcdcbbdbacbacadbacbdabbddccccbbddaccdbadacdaabdddbaabcdcccabddcaabbcbdacdddbaaaacdabdabbbbdcdaccdcadacbacdacdddccbcbcbcaadbddcbaddaadaaabcbbcdbabbcabbcdabddbddadaddbbadbaacbccbdcdbbbdccbbbccbabbddddddddbbbdbcdcadddaccbdbbdbdcddccabbbddcaabaddaaddddbbcadccbcaabddbcbbbbabacdddcdbbddddacbabadaddcdbddacabacbabdbacaacbddcdacabcdbcccdbbbbabaaaddbccadadbcacdbabdcadaddaaaaddddadbcacdcdbbbaacabcdadbbcbbcacabbdaccaacdbaadddcbcabddacadaaccadcaabbcdadcdcccbdcadaababbbacdcccaabaaacbbcbdbaacdcacddaadccbabadcdabadcccbbccadcdbdbcadbdcabdaadcaabcdaacdaacadbadbdbbdccacaccaaddadbbcdadbdaaabdbcccabbcbacdbaaadddbcbbcababdbdcbbbadcddadddcdabaaaacdabaabbbbbbcaddcdabaabdadbaccccbdbccacdcbcabdbaacaaacadbdaadbddbbdbaccbdcbdcbbacbcdddbadcaaccbbbbadbaccadababaabdbaacaabdbddcaabbaabdcdaaddabbdcbdbdbbddddddbaccbccdccaddbcdcaddccdaaaccaabcccdaaabcadbddcaacbddcbcdcadcababddcbbdabcbacadaccdabcbababdbbbdbadabbabbcbcddbcacaaabbdadcabdbcaccdbcaabbcadacddabbddccdddbbbcacaccdddbdbacddacacdcddacdbcccbadbaadaadcbbadadbcbdcbaadcddcdddcbbaacaaaaaadbcadbbbbbbadbcadccdadacabcabcdaaccbadcbbadcdbdabaddbcdaadddaccbbaaccabbdbbccdddbbbccdadaaaadbddcaadbacbcbccacdcccdaaacbacaadccddcccabddadaacbbbdbccdccccdabbaccccadacadbcabcdabaabaadabaaddddbbcdbcccccddcadabddaaccaccbbcdaaadcdcbddcadaccdbaadbcbbdbdabbcdbaabaaccdccbcadaacdadccbddbadbdabdbbbcddddcbaadcbaacccddcccdcaddbbbabccabcdacdadadabcccbdaaaddcabadcbcdcacacabdbccbccbcddaadbcdddbcdbadcdabddbdcddbaaabdcddccbcbabdaacbbabbcaabcdbdcaaccdbcbbcdcdbacdbcbbaacdcbbbbbbaadcdcbbabccacdbdacbbdbbaadbbacbbdaaabadadbdbadbdaddcdabaddbcdaaaadaaaddcbdbbcaadddbadabddcbddbabbabdabaaabdcaadcaccbabbcdbbbbabdabbdbdabdcadabcabcdaaacbbabbbbccbabaadccabcabcdaaabdbbdadababbadbbaddadcdddcabbcbdbbdacdcbaaddbdabdbcabaddbccbadcdadddcacabdccdaacaccaabbdadcbbcdbcacdbbaddcacbcadaacdbaacdbbdcbdcccacdddccbbcacacbcdabdbcaaccabdcabbccbadacdbcaddddbbaaaacaccbcdcbbdbbbbacacddccccbdcdabdadbabdadcacdbbcccbdbdabdcaccdcabbdcdabdcddddddbabcacbacbabbaaabbbbccdbbbdbcabdccbdabdbcdbadcacdcbacdcadcdbdcdadabccaadaacbadaddadacbaddbacacbdabbcdcbddbdbaddbccbaccccaccacadbbbaaadabaadaaaacdadcacccaacbcaacabccdbddbcbadbdcdcbcbddabdcddacacbccddccddcdccaacdccccaacdbabbdbdcbadcdbacdbdbaddcdddacabccdccbdabaabacbccaacdbdddccbabdabdbdaacddcbbccbacabaccaaddbbccabadcadabdcdaddbdbaccbddcaddabddccccabdbbbcccbbcddacacabdacababbdbdcdcaddaaaabaacbcbdbcdbbccccdbdaaccacddcdccadbabbcddcabcccdcbdbcaabccdbbdbdacdadddabdbadaabbadcadbaacccbbcdbabdaaddadbcdabacabbccdcdbdbdadbcadabcbbcccabaddbdbdcacaccbdbbddaadbccddcddbcdddabaabddcdbbdbcbacaabbdacdccbacaabdcbdaaccddbccbdbadabcacccdadacbacbbacdbdadccbdacddcbddaacaabcabbacaadabcbcddaabcbdbbcccdbaaddbcdabcddadbddabacddbbddadadabcaacbbddccbcbbcdbcadcddadcaaacddaadacdadbcbcdddaddacabaadadadabcddaddbacacddadaaaadadadbbbcdbcdcbacbaccaabbdbdadbdccaddabadabdcaaaadcabdcabdddddbddbdbcbdbcbbaddacacbcbccbbacabcbacbaacdbabdcbdaaabccaddcdadacadbbccdccbcbadcababcbcddcddcacbcdbaaddddaaabcbbcbacadbcabadbaccccacdcacbbbddabbdcbdbadbcccdcbcdccbdcbabbccbaccacabbcdbdccdbaadddcacdccaacabbaacabcddbdbadcadacbdabccbcbabcddbbcabacbddcaccdbdabdcadabadccaddcadcaadcdbcbbcdcabbdaccadbaadbadaacbacdaabdbdbabbababbbdbbdcdbbbabbbbadacddcbbddbccdaaaddadaabcbdbcdcdbdcbccdadcbabadbbbcabdbacbdcbbacccaadabcbdbbacdaccadbdcabaabddcdbaadcdadacbbdddbacccdddadadbbdadddabbcdddbadddbccbabbaddbcdbddabbcdabbdaccadbacacddbadbcbcdcbcacdbbbcccdbabaabdabdacabacdadbcdcbadabcacdcbacccdcbdbcbbbabbacbcaacdddbbaaadcadaabcacabcbcaabbaacdcddbabbccaabcabddccbacbdabdabadaadbbdacacdadcabacdabbbbbbdadadaabcaccacbdcbcabcbcdabaabcdbbdbccdcbabdccabcdbdccbdbcbacdcbdcdbbbccacabddccbcdcdbcdcbabdbbbccabababccddcddbcabdbbcdcbaddbdbcbbdbddaaacbbacbccbacbbcccababacbcddaabbcadbcbabdabcbbadbdaadbcbdcabbcacddbdddaacacddadbadbbdbaaddbdbdadddcabcdadcabcdacbacdcacadadcaabddbcacdcaaacabaaacacdbddccadcbdcadcdacadadaacddcdccadbabaabccddacbdbaadbabcbabacdbbdcabdddddbbcabaacbbdbccddabdbdcbcdcdbaddbabbdaacacbcdbadabcacaacdbbddaccbdbababdabddacdaabdadcbabaadcdccdbcaaddabcabadaaabbabbbccdbbcbccbccbdcbcdbaacccbabadadcbcccacbccccdccddddbcbdadcaadcbbaccdadbbbcabdcdbcccdcdcbbacacbbccbaccacaddbaaaabdadcdbdadbbcbccacbabdcbccbaccdccaccddcbbabbddcdacbadccacadcddccadaaacdadabccaabccaddbcbadadbbdbbdcbaaadbddddabaaccccdabbadbcacacbadbbbcdbdbcbadabccdbaabaaddacacbdcbaadbcabbbbbbabaaabddbdbbdcadbddbbacabaacbcdccaddcabcdadaadbdbcdbddabbdcccaabacdbbdbcdaabababacadaccbccaadccdcbbbabdbddbbdadaacdaaccdbdaadbddccccdcbdaabbbbabcdbbbbbdacdcdacdaabdacabcaacadcacccbbacbacdbdcbddbbacdadabbaabaabdbbccbdaaaddcaabbcbbaabcbbadacabdacacdbbcacdabaaaccadbbacadcddccbababdddcdbcbddaadabbdadabbcbbdbbacbccaacbdccaacadbadcccbabdacccbaccccbbccccdaaacabaaaccbbdbbdcbcbdadddcbdcdccacbcdcbbdbbacbdaccbbcdaabdabbbacadadddbaaadbaabdaadcccdcbacbddacbaadbddaaaadaaabdacdadbdadcbaccdbbdcbbaabbdddcbcacadacacacddabdabbdacdacdcbdacbdbadcadddabaccadaccbbbbabaccacddcbdbbbadaabbccddddbcbbacbbdcbbdcdaacdaddacaacaacddbabcccccddbcabadbcddcdcadcbbabaadabacccbdccbdaaacabdacbddadbdcdaabddaaaacbddcdadddaaabdbcdbcabbcbdbacdaccaabdbbbbbdddcacaabcccbabdbcaadcbbddbdbbbbdadbdbcdadccbdccbbbddcbbbbaddaadbdabbacadccacdbbabbdddcdacadabdabccbdbaabbabdbcdcadacaaccaacddbdbcbcbcaaabbbbaadadcbdaaaccdbdcadbddaacccdcdbacdbcacaccbdcbddbabdcacdabcddcbcbabdddcabcccdcddcdbbcdbacaabcccaabddcddddbbcddbabbaadcbdbaacbacccccdbbbdaaacacabacaabcacdabaaabcccddbabbdbbbbcdbbacccbcdcaddbdaddaaadaaaadabbacbcddbdcdcbcddbccaccbddaddacadcacbdadcdddcadbccdbbaddbbddcbccdacccbccadcbadbdabdacdbdcdbbbcddabdcaadcccdcacadaddabdacbccdbddcddbabbcbccadddcbcbbbccbbabdddbaddbbabccdbdbacccabdadabdcabcbacaaaccbacccdbacccbaacdacabbaddcbdddcacabcdcbbacdcadbabdcaccacdbbdaccdababcaabddabdbbbaabcddaabdddadbcbbcacabdbadabadbbaabbabddacdbcbadbdaacddcdacbacabaaacbadccabddccccbbddddabcdadaacdacaacbdcbacdacabbdcccdcdbadcdaccaccabbbcddabccdccddcbdcdccccadcaddadddacbdcadbcbdbadaacbdcabbaabddaadcbaabcaacabbbabcdbdccaacbdcacddcaacdddbabbcddccbdcaccbddadbdddabcdcbacbaacdaaabccdacbcddaadcacdccaaacddabacacdadbbdccdcadbdcbdbbdcbaaaaabaddababbdcbbccabdabbbabbcbcabccdddadadddbbbdcddaddbcdacbdcbdccdadccbcabdaccabadbbadcaccacacdabacaabcadacaabdacbdcbbadacdbbdbdcacdabcaddabbdbdcadaaabbadbcaaabaadddccbaaccdaadbbdcbcabccccbacdddddbbaabcccdcbddddcdbbdccacbadcadaccaddcbdbddbbdbdbdbccbabaacddcbddcdacbadadbbaddabbcaaddddcbbbbbcddaaacdbddadadacbacadbdaaadcdbbbbcdabacabacddbbbbccabdddcbabaccdcbacaababcabcabdcdbcaaddcaabcdbaadbaccdbcdbaccaacdcadddbaaabbcbbaadcdcdabaccbcdbbcabdacbbdbddaaabcddbdcabbdabcbbdbdbcbcacbdddbdbccacccccdbcdcdddbcbdcabaaabcdcbbddbdbdcbdaaccbbdcdcdadcdcaddadaadcaacbcaabadbcbabadacaabadaadbdadabbcbabbdabadabdadcdbbcdcdbbaaaabacdbaccbbabbdaabcabadadaddaabaadadaddabaaddbacacbaddcacccaaacddcccdcbdabadcabaabaddacdcddacbcabbdcbcaacbcbbcbaaccbaaaddcbdcadbadcdcbdabbddbdcddaddbccccaadadbbddcaddaccbdbbaddadbbbabbddaabdacacacabbacdcbabcadccdbddccdcbaadbcaaaaddadadcadccabcabacdcadadbadbccaaadbaabccbbadbdcccbbabcaaadbdbcdcadacbdbcacadbcdaacccdbacadaddbdabcdadbdbbcdbadadbdbbadddccdcdbbccbcbadbdbbabaaaaaabbcbbbdababbaabcabaabacaccdcbacaaacaccbcddbadabdccdcbccdcdcddbdddadcbddabdcbadccbdadbccbbbbbabbddabbdbcacbadbcccadbbadcddbddddcbbadbdbacaabdbccccbcdccbdabbcadaaccccbdcdcdbdcdddcadacadbcdaaddadbabdacaadcbaacddcbdcadcddacccabbaabbbaacadadcbdcccacaccdcdcbaccdadbcacbcdcabdacdbcdadadaadbbbbbbadcdaaccdcccbbdccabbcbbcbdccbddbdbaacbabacdddaabbcacaabbbbcbddbdacbcacaacacbbbacdabcadaacabbcbcbbaaddcbdccddbccccddccaddbadabacdacddbcbbddabbdbaaaccbddaadaddaadcacaddccccccbaadcdbdbcbbcacbccdaacbdcbdbcbbbcddaadbdaddcbadbbcdaaaaacdcdccaadcaabdcbcdccbbddaabbbbdacdcdccccaccbcbbdaccaabcabcbcaddbcaccbaabaabaabdbbbaadcccacbbdacdaccaaccbacbbbbdbcbaacabcbcaddddacccbcdbbadbbccbdabcbaadbcddbaadabcbabbccdcabaabcdaabbdbbccacadbdbadabadacbccbbacbaadaabcddacbbdadbaaaccdbacbdbbbaddadbdaaccdaaaabcabaacdddadacdabbbadabaabcaacdadcdcacdabbbbcbabbabdbaacadbdabbacccdbdbcddbbcdabccaaaaadccdcdaadaaadbdcdcbaaaddcccbddccbbaaaaacaabacbabcabcadaccbdbdccadcdcdacbabdcbccaadbcdcbddbdbbdbbadbabbbbaadadabddcbccdddaaaabdddbacabdcdbacdbacbbdbcabbdaccdabbccbdbdbbccaadacbcbcaacaaadacbadcabaaaacbbbdbdddaddacbaaccddcddaaddccacbbaaadbadbadadbccbbcddcbadcbcbdabdcbdbdaacacbcddadcabcddcaccbcacaddddacabacabccacddddacbddabdbbdbbdcbcaccdbabdbacbcccdbcaddbcaaacccdaabdbbccbccacabdcaacdacccdccccaacadaaacaccbcdcddabcbbbcaaababdccbbbbadcbbcbaccbabadccbdaacdadbadadcadcccbcccaacbbcdddcbcabddcddaabdacaadbbcdbabbdbccdddbbcdbdbacbcaacabaaaabbdcabaaccadcaaabbbdabcccbabdbadcddabbccbaacbcaaabbcdbccbddaccbcdadabacdacacdbcbdddacdccdababacccacabacbdacababcbbdaaaccaabbdbdbcdabbcbabbbadbbcabacadcddbcadcdaadbaabbbcbcaaadcaaacaaddccabcaabbcaacdadbddadbaddcdacabaadbabdcdcccbabaadacbdaddbaddbacaaababcccadcdbbcbbccaacacacddbadbdcccdcddacadcbabbabadacbdbaaadbdabaabaaacdacccdbbbbdcacbcbbdcccdaabddcccdbbdbdcabbddccadbdbacacccaadbbcbbcbadcbcccbddaadbccbbbcdadbdacdadbbdddccdcbbcdadabcdcaabbcbabaacbabcccaacdcdbbabbaccaccbcaadbccddabadddcdbcacbdbcccbcbcaabcdbbacdbabaccbcdadbbacacdcbcacddbdcddddadcbdbabbdcbdcaabadbcadabdbacdbababdddcbabdbdaadccaccdcdadacddbdaccadadaacddbcabddcddcabcdbcdbbdbdacdddbdadcccbddcadcabbcbabbbcabaddacadbdcddccacdbdaccabdddbdabaabdcddbdcbbbaaaabbddcaadaccccbbadaadcbaccaaccaaaaabadbddddcbadcabacadbacbdddaacaccacddcdcdcdcaaccabcabdcbabacddabbbadabaddbcabaacdbaabbcadaadbbcaccddbdacacdabddaaaaabcdabaaadaccbdcbabcbcdbdbcdaacdadbcccdadbccccacdddccaabdaaddcccaadcbdaaccacbbdcaccbdabdbaddbacddaccabbaaccdbcaabcddcadcacdcacbbbbacddbadbbccbaddcbccadcbabdaabdadbbdadccadabaddaaccaaccdbdadcdcdadaccbcddcdcaacddbacbdddcdbbccbdacccbdabdaaaccdbdbbcabdbdccccbccddddacabaabbabbcdaaccbbbaacbcddbdcdbbaccbbbdadbbaadabcaddbaabcdbbcabbcaaccabcdbaadcacbabbdcdcbbabdcaccdcacddbadcddaadabbdadbbdddbdadddbdbdbabddbabbdddbbcacdbaddaacdbbaabbaacccdbdadbcdbdabcbdbacdddabacbcbacdacbdcbbcaabdccbdbccdbabdbddcdcabacbcadabdbdbacccabbbbbddaddbbdddaadddadcaabccdacdabdcadcaabbbbcbdaaacaaabcbdbaccdcdadbdaacbcacccabcacdabcdadbdabdccccbbcccbbdadcdddadbbdaadcadacabdcbbcbdabcadacbdadcadddcbdbcdbbabdabadcdcadcddcacbddadbbbadbccdcacccacbbbbacdbcdbbddaadcbdcacbcdaddbbadddddddbcabccbbbbadddcaaaadbbcdbdbbcbaccbaacaddabcdcdbcccdbacccadbaabaaaababdcdcbcaacdacddbbcdbcdbcbaddacddcdbacacbbcdacbdbbbcabdcaddcaccbaccbadccaabcdacbaabcacdbcabbadcdbbdcdbbabbbabbcabdbcbccdbbbbcaddcbbdaccbbaadaabbadbdbcadcbbcbadccdbaacbddbaddbcadbccaccddccbdcacbdcdccdbddadcacbdadbdddbdabcbcacdbcddddadcabbaaddbdabacdddcadcdbbcabcdcaaccbbbcbdcabdaaacadccbccccbbcdcdbdabdbdabaabdadccbcdaabcdcddbacdbbbaccadcdddbaddbbaabdbcbdbabdabddabcbabdbbbdcacbbddacbcdcbcdbcabcdddbccbccccaabaaddadaaabbbccdbbddcabdcdababdadddadccccbdabccbbccbbcdbcaabbbccacbcabadabcbdcdbbcbbcaccbcdcadcacbcbcddbdccdcabbcbcbbaaddcaaddbabbdcabdaadcddaaddaccddcbbcadbdaabadabcdbaaaabacbcdabaabcabdcddaaaddbdddcddbbcdacbdacbbcbdbacbbadbacbacbaadcaacdcbbbbaaadcacacbbddbcbdcaaabcbdcbcabdcdaadddbbcbdbbbabbcaccdddaacababdcbbcdbcaccdcbdcacbacdcbddcbbdbccbccabbaacabaddddbdaddbdccbdbddbccaaccaadaccbcdadbbbbadadabbaddacacbcdcdccaaaaddacbacadcdacbcbdcbacdabcbdbcbaddaddcaccbdcbacbdcbdcdcaddbddbddbbaaaccbcccaaaabddbbdcaccaabbbddbdadaaacacaccaacabaddadcacdcccdbdcbaacbdcacccbcaccbadddcdadbabcdbdccdacbaaaacaaadcabbaccccbccadbcaccdbbdbcccdbdbbbbbaaabcbaaababdccbdbaacadacdabbccacbaababcadaacddddbdcddabddaddcbdbabbadcacdaadadccabacabadaadcccabcbdaaddccccadababadbdbcadaabbadbaadabcdbdcbdbaccbdccbddbdaaadcdcdacdcbbbbbcdddcbcacaddcccbaacabcddadacadcdbaaadcadcbdbaabdbadcbbdbddcadbccaabbacccdccbccbbbbabbaaaacdbaaaccaddbccbddcdcdddabbbbcabdabdcbbdccbbdacabcbddcbdbaccacaaddacdbaabddaabdaaabbbddcbdcacbaaaddbddcdacbbbdcbcdcdcbacdabdbbadcabababccadabddbdcadadbadcadbcdddcdddabbbbacdcaccdccaaaadcbdccdbdccdaabcccccccdabacbaccdccdaaddbbddcadcbddadacbaadaabadbbdadaaacccdacbadaabadbdabbcdbddddaccaadcabbacacaddaacabdacbaaadcdadcbbcbdabaddbdcccaacdcabcadacaadddbcabcacdcbaacbcacabddccabcaadbbbdbabaadaabcabcddcadbddcbadbdadabddacabdadcbadcddbabaaaabdbdbadcdabadabadcccdadcabddddabcbcbcaaacdabccadcdcaaddbcabbcdabccacccbaadaadadbcdcdbaaaaacaabbcaadadadccccccaaaabdccbdcbcddadbbdccbbdbbbdacbccdcababdcddabdbadcadadacbdacdbcdbcdcacbcddcdbcdaddadbaccadcaddcaaaadcacdbdcdbaccdccbdabcdbdcddabddbccccddbadcbbbcccbdbbbbaabacddbcacbbcdabaacadbaaddaddcdcbaccaacdcdbbabdddcddaaadcddbdddcbcaaabdbcaddacdacccdaddcbbbddccacbcdbadbbbdcbdaadddaacdcaddabcdbababbdcaadcacdccacabbdadcacccabbadaaabcbddbdadaccacdddacbcdabcabbcaddacabdadaddaacbaaddbdadcdddbbbcddbabadaadadcdcddbdbdcdbcacacbcdbdcadccacdccdbbabaddcacbcadbacdaaaacadcbccabcbccbdcbcabaddadccbbdcdbdbcccbcacbababbbcdbacacbbccacabccdbdcabddccdbcbbabdaabbbcabaccabcccaaabdcddbdaadbbdbacdbbacacbaadccccddbbadababaccacbbcaabadbddddabcadcdacdacbddcacdbdaddccdbbdbcdacaaababcbdcbbbbaaabddadbcbdbcbcccbadcaabcbcbacacadbcdcaacdababdcaabacbcbcaabcbbbbccccacddabdccddbadccbdccbacbabdbabdaccdbcdabdbcbadadddcdaabdbbaaccbcaabadaadbcdccaddccdcdcabbcacadbbbaaaccbbcddcdbbdbccbbabbccdacccbbdabaabadbcdabbadbdacacabbcacbbdcdaabadadaabaadadcbababdcbddcabacbaacdabddbdddbcddcaaccacadabababdbadbcbcaacbbdaddbacbacdccddabdbabbaadaddabacdcdbadcddcdcacccdcbcaababcbabdcbabbdacdbaacddddddbbdbbbcdbbbdcadacbaabaddcabdcddcaacbcbccacaacddbdbaddabbccadcdddcdcbccaacdcbbdbdccdabcdbdbabbbbbaaaadaacdbbdcbbcaabcaababbcabbbdbdbdcadcdbdbabaccdbbccacbdcbabddcddbcddbadccdadabadcbaacacbbbcdbbbcddcbcddddbdcddbdcdbbdbcccacabdacdcbdaaadaaabaccbddabcacdbcadbaaccbbbbcbdadbbbcdcabcbbccccdaaadabbcbdbadaadaabbabdbaccbdcbcadaaabdddbcbdcadaccdbbaabcbacccbccdcaabbbcdcbccbdaabbcbdacaabadcbbbbbbabbdbbbccdaadbcccaddabbcabccdacccddbbbabdbacadbdaadacccdbcabaaaadbbdcabcbbcbccdabcbdcdbaddcaaaacadccddccaaddababaadaaaadddcaabdaaabaddddabddddaabcacaabbcacbbcbabaaabdcbcacccabacbbdbacbacacccdaabddcddabbcbaccccdcdddbdbbaaccccdcabbbcbbabddbdadbaadbbbbbcbccdcdcadbdbcdaacbbabbbddcbbbbabdcbacbabddacccbdcccdbccacbcdaababccbdaccbabcbdcaddacddcbaabcdcbdcaaabbccdcbdddddbdcadccbabcdbdbbbbcadddbdcdbbdacdadddacaccbdbdcbcdadcbbdcbddbccdddcbbbcddabcabcddcabcdadbdacabcacbdbaaacabacacadabcdaabbbbcaadbccaabddcbbaadabdddabcdcddcddabbaabadcbbdbaadbbdddbcacaaddcacbabcccbdccabcdaaaadaadadcccadccdcbaadaaadbdcdcbcdcadbcaddbaadbbdaccdbccaccbabdcbdcaacbbadbcbabdaadaadbddbbadbbccbadbcccdadabcabcdcacdbbcbcdbcbababcbbbaacdccbdcbabaabcbbddaddddbaccdabdbdddbcccbccdccddcdccbdcccddccbdcbcaaccabdcbccdadbdcdcbcdcacddaaaadddacbbdbdbcabacacdbcaccaacbdbabdddbcdababdbbbbabadbbcdbddcdcdaabcdaacbbcaaccdaaabaacbacaacaadcdcdbadacabadcabdabdccabcadddcbccdbbccdacdcdabbbabbbcccbcdabdddabbdbbaacaaaacccbcbdabaabcabcbaacadaaccdbcbdcdcbcdabbcddabcbadccccdcbcaaccbcbdccadbacdabdaaaabbaadddcdbbddbdababbaacdcdbbbaabbbdadddaccdcacbcbadaddbcdbaadcadaaddccddbddadbadbcdbdbcabddadadadacbcacabadadaaddcdaddabddaddadcadaacdbcdcadcdbdbdbbaababdaddccdaadcbccaaabcdbcadbdbdcabbbadbcbdcbdaadcadadbbbdbcababcccacacbbcabbaadababbbabbcdaccbddccdbcdaadcbacbdbdaacaaabcdbbdcacdabbdcacbabddccdccdcdcdadcddcadadbabcacdccbaaabacaddaccabddcbaacbcbabcbcaabcdadbdccacbbacaccddcbdbcbbaaabdbddcacdcdbbdcdcbaadbadacaaacbabacbacabaaaacdbdddabddadcddcdabbadaacbbcbbbaddaddcaacdbcbbaaaddcadabbcacbcaacdcdbbabbbdabdbaabaabcbbbccdccaaddcacabddbcdacadbaadbacbbcbcbbdaabaadcdadbabcabadadddddcbabbabcadcbbccbdccccaadcddccbbcddaabbdbdbcbaadacdabcbccbabbbcddcaacbcacaaccbdaddbcacabdbacaaddddcbdbcadacadaacbcccbadadabaaacaaccdccdcadbddbabbbabdbccbcdbcadcddcacbaabcbbaddbcddbaddcbcabbcdcbbaddaacbdbcbbbbabdddaacdbaadcacaaacabaaacdacbaddbcaaabcaacddddbddbbdaddadbbaacbabacddacdddbdacbcbbdccadabadbaacdcbcdcaacabdccaaddcbbbdacdbbcbdddbbbcabcbcbbcbbdcdcdcddabcdccbbbbcdbcbacdcddaaccdbbccbdacaadddcdbccdbcbcabcbcabacbdbaddbdacadbccaabcbaddcbbabddaacdaddbddaacddccaabcdadddaadcbabdcaabdccbbdbbccaadadcbddbcaaacabccaacabdcabaadaabaabbccccdcbbcdbbabbadbadbabadddaaadbadaadacddbdcabccccbdadbdacacbdddddaadbdcddcbacbbcaacaaaabbdcccacadddbabdbcacdcaacabbcabbccacbbabbbdabbdabccddbbcacbdcbcdabbbacbbdcbababdcaacbbababcdacacccbdcdaddcbdacddcaaaabacbaccddbcdbcccacccbcccabbbdbdbdcddcabacbaaadccaaaccbbcddbbcccacadbadcbccdbaabbdcdbcababcacccaddaddcccdcaaaadabaacdbdbcacabbbaaaabccbbcddccddddacddbcccdaaacbbddcbcaaaabddddddcadadcabbcdcbbbbaccccadcacdccacbbadaddbaaaaddacbaddaadbdcdaadaaadbacbbcadcbbdadaadbacadacbbbcaacbcdabdcbcacaddabcbbbdaccadbdbaddacccabddabbbbaabcdbbabbcbccbccabbbadccbbcabbbccaadcbbacbbadcbadabaadddcacccdbddcbccacbadcaacccdccddcacddbdaddbcbcdaaadacbddbbcaaddccacdbdccdadbbbcdddbcbbdaadabdabbdbcacbbdaacacdcadcccbccbcdbccdadabbabadbcaacccccbbcabdbbbabddcdaadaddcdadbbbaaccdccccacbcbcbdaadacabbaadaaabdccdcbbdacaacdcaddccabdcbcabdbbaddbddbdccacdabdbadaccaaacbdbaadcddbacccdbaaacbdbaacadddacdcacadabaaacdaabbadbdcbdddbadccbdbcddacabdbddcabadadddbdcddcacccbadadbacbdaacacbcabbbacaaddcbcbaaccdcdbbdcacdbccbacaabccddbacdbdcdaccdbbbbcbaaddcddcddcaacbbacdbabdbdaaccadabcdcdcaaddbddbcbddaddbbcddcadcbcabcbaadacacdaacaabbcdaddaddabbddbbbdccdadbcdcadbdaccdddadacdbaccdccadccdddcccdcdcaadbaadaaaacdcbdacdbcdcdaccdddaabdbddbcaaaadadacbdadadbbccbacbbcdbccdcdadacccddcddabccbbcccbdadadbacabcbacbdadadbbcbdcbcbcdbcbddbddcadbdbacddcdddbdacbaaaccdbdadacadabaadacaaaaddcaaaddcdbccabbcccddbaddcabaaccdccdabacdddbbabccdddddcbacddadccbcabbabddccbddccadccddaacddbdaabadcbabbbdcdcdbabbddaacaccdcbdcdacdcabcdddacaaaaccadccccddabcaacdcbcddbaaacbadbdbdcbcdbddaaaccabbcabbacdccabdccbddadbcdbbdcbbccabcbbaacdaabbbaabddcabcddbbcbbcddbabaddbdbaaacadadabacaadadbcbacdbaabacdbddbdabadcbbadcdbbdbbbacbddbbbadccccbdaabbbcaaabcdbbddacbbbbcccaabccacbccbccbabbccbbaacbabddaccdadddccdbcdccdbcccaccabaababbdbbcdaaabcbbcdbdabcacdababdcdcadabbbbbcababdabcdaabbdcdcbbbccbaabcdcccdcdabcccadcacdcbbbbdadbdaccdaacacbccdbdbdadababbcbcabaadcadbcdacadbbcdcbddadabbcdadaacdcddcadcdbdcccaabcaadabccbacbdccbcbbbcccbabcbccabdcabccaabcbddcdaddbbbcbbadbabacdcbbdbdcbabbbccbddaacbcadaabbcbbbdabdddadbbacdcacabdaddcbbcdcbbbcbbacdaacbdddccbbddbbccadcdacdaddacddabadddcdddbbcddaaacbaabacadbacccbcdcbdacdbbbaddadacaacddccdcaacbdbcadddddbabcddccbbacbacbbcaccbaadddcdcbcbaacbdbadbaccdaddbdabdbbdadcadddbccadcdcbbadbaaabbbabcbdaaddcabadcabbbcabdcddaaacccccaadbdcbddcaddacacdbdcbdaabaaaddacbcbbbcddccddccbcadbaabcbacacadcbacdbccbdbcbbbadaaaaaddadabcbcbccbbadcbdcaabcdddacdbcadbbccdbdccaadaddaaadddabdccddcdcdddadbcdbaadaacaaddcdbabcababdacabacccdcdabdbbcdbcddcbbbbcbbcddcdbccdaadcbcbcacbdbbbacdddcbcaabbadbdabaddcbabbacdcdaccdcacabcacbadcbcddbabdbacddcbadcbbabacccbddbaabdbacbcadcbdabccdcddbddcbaddcbaaaacddcadaccacdabadcaadcdcbcaaddcabbdbaaccaccddcddccacaabadbbccbbdabdccdccddbccbccdcdcdbbdcccdabdaaaabbcddadccabcdccbaccbbbbaddbbcdccabbabadbcddadacadacabccdcbacbbaaacabbaaccacbcddbcdadabbcccdadaccbddddaabbdacbcadaddddadcbbbdddacbabccdadbcbbddbbdddcccbdacccbbdbcdbbbcbddbdacddbccdcccacacdbcbbdbcccbdbbddbababdabaaadddbddbdacbaadabbbbbaaccaccbdadbcbbbdccccdabbdaacdadabbccdbbdcaaaabbaacababddcbcaabdaadbdacdcaaabdaacdcacbbdbaaccaabddcdadbbdbababdcbbababdacadbbbbbbbbaabcbbacccadaaacbadccdddabccadddadaabbbbbdddadcbaabccbdccdcbabccbcbaadadcaaddacbcdaddccccdcdcbadcbabcaacacadbbcbdaacacbabbdabbcaacddccdbaadbdbdaddcabacaacadabbdcadbcbddbbabddacacddccadbaadaaabbddccdcbbccbabbcbaddbcddabacaccadbcbdaacdddaadcabdbcaaaacdbdbbdbcbccddaadaabddbbcccdcadbadbdcbadacccdbbbcbdccdabcadbccadacbccadaccaacdaddaabccadddcdcddaabccbaacdddadbcdcbdcaccacadccbcbacbbbcaddacdaadadbabccacdcaccacccabaaacbdaddbcabacbacccdbabbdbddbdddacbabddcdbdbbcdacbbdcbcacbcccabdcdacacbcbdacbdcdcddccbdbbbbdacadadaadbddabbcbcadcccdbababbaddcaadbaaaccaacdacaaaabdaddcaccccdbbcccddbcabbabbabbadcabcbdccccbddaddddbcbbdacbdacbcaaabaacbaacbdddadcaacbcabbbcbddcacbaacdabadaacadbdbcddcddaacbabbcbacadaacdbdbaadabccabbdbdadaaabaccbaddabdabaacbdcbdcbdddddaccabcdbcbddacbdbcbcaacbbdaaaadbdacdaacbcbdbbbcccdbacabbbbcdbbdcacddacbcddcabadbbdacdddabcbcbdadadcaccabbabcbdbddbbbbbcaacdcbaaacabacddbdbcbadcbdaabadcccddccddcddabcdcccdbadbbbcbadcacdababacbbdccbdccaccaabdaadbcaacdddcbadbaadcdccdcdddbbaacbbddcbbacdacbaddaaabbbbbdbddcbbcdccdacbcbcdabbadacbcaaaccdbdbbabccadaaadaccacbcdccadcbacbcccacbdcdbadcccadcaaccaabcaadacdddcacbabdaddbadccbbbaadcbcdcbdadcbcbbdddbacdddbdaaadddcbacdbcddddbcabdcdaacccacadccdbcccddddbcaacadccabcbcbaddcadbcaddbbdcbdcbabdadccbaaaaaacccbdcdbadabbccdacacbcbbbbcbbbadadccbcdbdbbccdddacadddabbccdbacaaaaaabbaddbddbbbabddcbdcdadbaabcababdbaddacddadbbbacdbdabcbccdabccddacdddbcbadcbadbdbcddcbadcabdddcacbacaabacadbbdddcdbdadddddbbcdbbdcbbcbbddbadbbcadabcdaacccbbcaadbbaddabadbababbbbdcbdcacdaccaccbdbabcacabbdbdbbbddbbbcdacacabcdcdbbddacdcdbdddabdabcdbccdcbbcbacdaddadabcbbccaccdccbdcadabbcdacaacacabcbcdbbddaabbbdacddaaaacbcabadbadadcadbadaccbabcacbbddadaadbadaadcdabadcaddbcdccaacddaacccbcdbdcabccbcdabdaabcabdcbbcaaddbccadabccbccdcaaabccaadadadbbacdadabbaacbcadabbbdadaadcdbcdddcbabaddbbcdbcadacaabbcbdcaaddddabbcdcbbbaabdcacdcbabdccdbaaaadccaccbbcbbaabdcadcaccddbcaabccbdddcdaabbaddbdaaaddcaaadbadccbcbaacaaaaaacdbdcadbadcbbccbcabddadcbbbdbdbacbabacaddacababdcaadbcadddddbdbbbcdbdccddabcbbaccadccdddccbcddcddccabbcbbaabdcbcdbdbbaaadabddbcacddccdaabadcbbadadbdccccaacaaaaabcdacbbdabacbcbbdacbacbcabcacdadacabdaaadbdbabdbbadabddddcacabdbaabcbccccdbcdbacadcabbdaaccbcbcabcddbbccabcacdbbdbabbbbaccabbccabbbbbddbcaccbaadabcabaaddabdbabaaddabaadbbdabcaadddaaabddbccbbadaddcadddcbcddbdcaaaddcbbacbbbdddcababadabaccbdcaaddadbbbaacaadbccbacddcdabbdddbdacdabbcadcdcdaabccddddadabaacaacbabdcdcabbdaacdccddbdaabdbdbadccdacbbaadacbbbbbdcaaabdaaddcaccbdddabccbcacccddaaddaadbcdcaccdbdabdcdcaadddcbadabbddccaaccadcdaababbbdcbabddbbdbaadcdcddaccdccabccbcddddaadabbabadbcaaacbbbbaacdacacddcbccaadcdaddbaaccabaddcbaababcadacdabcdcdbaacbcaaacabbddbdaadaadbcacdddacdcbaaaacdbabbdbbcaacbbacaabdbacbadbbdcdcddadbabbbaadaaabccdabadcacbbdaacdacbadaaacdccccdaadbbcdbdacdbbcadcbddcbabcacabcbddbccbdcbbbbdbcbbcbacaaddbacabcdabdbbacacaaabbbbabcaadcadacdabdaaccccbabbbccaccdbddacdcabbcddccbdcbcdadcdddabddbbbacbdcdddbdabcccdddacacbcdabaaddcabdbadbcbacbcdcaddaaacdcdadcdbabcbcbcbdccdcdbdcddbbbccaacbbdbcabdacccdccdcdbcabbdabacdadabaaccbdabbccadbcbdabaabbcabbbdbacccdaaddbbcacddbadcabbccccbaaccccadddabdddcbdaccbcaaaadabdddddbadcabbbbdcdcdcccabcaccaadadbbadbcdababbadcccaabcccbcbcbdadbbcbaabdcaadbbabacdaabdcaaabdbdaaaaaabcabdbcdbadcabbccbabbddccbabddcbdbcbdcbdabbdacdacbbcababadadbbcbdccbcdacbaabddacabaadcbdbbdcbadacccddcacacaddadadbbadcdcdbbcccbbcbdcbbcacddcbcdabddddcdcbbcabccccdcaadaabacbadbacacadbbaaacdbccbbdadbbdadbbcabdadadbbdabcaacbbaabdcaabbbbdadcacaacdcbccacbdacdddcbbaddcabdbdadbccbdbcabadcdcbabaabddccdacbbbbdcaaabdadcbdcddccdbdadabdccbdcdaddaaacadbccdadddadbbadbddccbdbbbbbbddbccbdacdbabadaabcdcbdcacaabbdcbaaaddabdccbbdacdbaaabdabccbdbccdacbcdcbaadacdcbcbbbbbcdccccaacacabacadbaddbbdbdccbcbaacdaadddbadaaabbddcccbdcdbbddaacbadcdcbbbcdadbabaddbccbbacaccbaddabcbacdbdaacadaabddbacabacbaccdacccbccabaccbdbdbabcdaccbcdbcaddadddaaaccbcbbaacdbcbabaddcbddccacaacbddaddabbdaacacadccdabbabddbadbdbdcadcacaacddabdbaddbbaccdcbbcdabdcbcacbccccdacbbbababacadaadcdbaabbdcbaddbbcbbadaaccabbddacbbabbacbdcbabdbbaaddacdddbddacbadcacccdcdbddbcbdddaadaabbabacdbdcbcbbcbbdaaaddcbbdcbdddbabbcabdcaacdcddaabbccdcabbbdcdddacbdaacbbbbbbcccdcaadaadddbbdbccababbababacabdcddacaadccccdbadacddbabbabdcbbbacdcaacbabdaaabdbddcaccdcdabbaadaaabaabcabccababdbdacacaabadaacdaadccbddbdaabdbdaaacdcacbdccdacddbcacdcaadcadbaabcdccacbadbabccdbbabdabbaccccacdcbacddbdcdacbaccbbabcdbdbdbbbbcadbdacdcabaaaadabccbacbabaddccdbadbcbdbdddcbacbaaddababadbddbcbacbdabdbcdacccabacdadacddccacccbcacbacbdaaababadabcbcccdbdcbdccdbcabbcbbdcdddccaaaaddbdcdbabdbccdadcbbddacccbabbdcccdbdaccbcdbdacbcaccacabcbabdcbbabdbaacddcbdbccbcababbbadcbcaabccdaacaccadddcddbdabcdacdcabdddbbccaddbdddaccadcbbdbadadbdbabbbccdadbabdadbcbbcbaacddaaaccdbdaadcdabbdaadabdabbcbcbcccbddccbabaabcddadadcdacbdcbdbcaddabcbcdabbadccaddcdcccbadddaadadcaaacccdcabbabcddbdcaabacccccdacacdbdddadddacdacdacddaccdcddadbcddcadcbaddbccddaabbbcabcadbadacbadaacdbcdbcabbcbdddbddadbccdbcadadcaacabcdacababbbcabdccdadbabacdabaaadbdcabdbddbdcdbcdcddbbdabbdabaddabbabcababadcacdddcddcdaacacdabcbbacbbdbaaacadaacadacaddbdadcacabccbccccbdacdcccaadbdaacaddaaabadabbccdacbbbabcbccbbcdabadacddbcbdddcababdadbbbacdbddcaaddacaaabaabacbadbbcbacccbbdbbaacaacbcaddadaaaaadcbdadcdddcadbacaccdccbbdabadadbdaaabdaacdcdbaabdcdadacbbdbacabbaaccadabaccabdbcdbdbabbcbadbcaaccabcbbacdacbdadbbbbbabcddbbcbbbacaacdaaadabaccdbcddcdcabaadaacaaaddaadccbcbabacacddbadcdbbdabdbddadbcdbbaaacabbbadaddcddcaacddabdbadcbbbbdacdaaddaacbbddbacaadaaacaadccaddadddcbbbbddacabdaabdadbdddacccabdbcdcaadbddabaaaccacdcacdccbccaacbbcccccdabaaaacbcbaabbbbcbdaaccbccbabdbdddadaabddddbaacddcdbbabcdbbdcbdadcddaaadcbdbcacdbcbcbbadcbddaaabccabcbdaaaaabdddbabdbdbdabddbaabdbcbbddbaddcdabbcddbbaccddacacdacdabbbacccadacdbbdbddaacbbbdcddbacbbcbbbdcdcdaccdabaaccaddddbaacddaabdbddaacdabbbcdaccdcdcdbcbccbbdccddcdadbdbdacccbdcdbdccadbcdacbcdadaccacdadacdabddddaacdbcdaabaabccbadaccdddbdccbcddbdcbdbcaabddcdbadacaddcdbdaadcdbcddbdbddaddaadabddcddccacbddcaccdabdbaabccccdcbbaabdabddacdacaaaccacccabdacddcbdbccdbcaacdddcccdadbbcdbdbabcadddcdabaacbddbbccacccadbadbcddbdbddcdcbcccdcddadcbbbadabaddbabadbaabcabdbddcbcdbadaadcdbbaaddddbadbdbcdcabbdabcbcbccadacaabddccbdbabcdbcddbddacdadaacaacbcdaddbddcdbababbcaabcbbcabdbdcbdabbdbbaaacbbcbcbbddbacdcdbccccacacdbacdcbcbbbbadbcbddcddddabbabababbddaadadadabaaacdccbccacbbadcdbdbcabbbbcdcaaacbcdbcbbcccbbadadaccdbbacdbcaccaaacacbacddbdaccddbcacddaabcabcccddaabbcdcacbacbbdacacdcdbcadbbddacbdddbddacdbcaacdaddabdadaaacbcbadcaabccbdbcbbdbbccdadbadbcbcddabadadcdcdacdbdbcadacdcacacdcddbdddbccdccdabacbacbabadadccdccabbdbdbcbbcacaaddcaaccbbcdacbabdacccccadabbadbdbccaadbdabdadbabadcabdaacbdddaabbaaaacbdcddcbbbcadaacaabddabcdddbddcdbdcacbdcbccdcbdbdbcbbacdcbbababadabbdbcbdaabdcdcadbdccaacaddabadcabacccbdcdabdddbababbbadbccbbcbccbabdabacdcdddabbdddbcdbcbbccadccabddcaaddbaaccabcaaadddccdbddadadcdaacbddbdbbbbbbdabcadcacbbbaccddbbcbcdccabbacccbccbddaaabaabbcacdcdcbabccbccbdcabbdbbabdbccacabccbbacbccaddcbcbacadcdcabbbadbabadacabcbabdbcaccccdaacbcbdbcacbbdabcdbcabcbadbcdcbaacdcccdaccaacbcbbadcdbaddcdcbbcdadadcccabcaccdbaaabcdbbbadadcbdbaddccbcbaaaaccaadcdaadbbddcdcbabaacbbbdbdabadaccbcddaacacdbadcdddbabaccbbdcbbcbcbccacccbdbaabbcabacccbdaaccccdcccaccdbbcaaacdcdccacacacacbaccdababbacaaaaabddaabcadacbdddaabbbadbdadacbcddaccbabaddcdcacdcbdbacccadbaaaaccdbccaddaabcddcbbacccaaadcaaaacabbcccdaacbbacbbdbbacadadbdccbddcbbddbdbcccbddaadcbdcdcbdadbcbaabdddbcccacdadaacabddcdbacccbdadcaccaddccbacadddcdabbacbbcbabccdccaccbacdbcacaadadcdcbbaacdcddaabaccaadddaccdbbbbdaaddbdcaaababdabddabcbabbcdacaabaaddbcbcbccaaacdbdcdddacacdacdcaadbdacadcacdddcbbddaddccbaaddbccbcbdcbbadcbbbdbccadbdddcddbbdcccaaadbccbababccaadaaababaddcbdcdcaccbaddcaabccbcabbcaaabbcbdaccbdbdaccdccadbcdcddcdaacbabcaaddaacabbaddbacddadaddbbbcccdbbdbacbaaccbccbbccabcaabadcbdbaadcacccbcabbcccbccbcbdabbcdcababdbcddbddbacadbddcbacbdacbcaaaabdbbcabcadacdcaaacadcadabcacddcdbbdabbbbaddbdcdaadababbbaadbacccacbccbaacacdbbcbcbddddaddacddcacddbacaaacbbdacacccadcdadacadccbbbbcddcbabacddbcbdababacaabbbcacddcbabbcbccbacccdadabcbbbaabccadbadbcacbcccbcbcaaddbaabbdbcbacacdbccbaadbbcabddbdaaacbaacbbadbcccbadbcaddbddcaaabdbaabbbacacdabdddadcddadcdcadcbdbcddbacccccdadbcdabadadbacadbadcaaacbcdcabdbdbdddadcdcadaacaccacbdcacbacdaadbdcbbadddcbdbadbdbaccccbbbdcbcadabcbdcccdddcaccadcbccbabcdcbdcdadcadcaccaddacdacadcbcaddbbdddacbcacabbacdddcbcddacccccaaccdaaaadccadcabccacaabcadddcdacdacbadacddbabadaaccabbdadcaddbabdcaccdadbbdabbccabbacbdccacdccdcdcbcddaaddabacacbddbddadbcbcabcdcacccbdbadbccbdadbcdbdacaddbabcbbbabaddcdddbdaadcacbdddbdccdcadcdbbbbbdbdaabdaaababacddcabadaccddadcdcadabbdcbdaacddbccbbcadcbadddddbbbdbaccbdcaacbcabaddababcaadccddabbbdbccdcbdcabbabccdbdcdbbcacdaddccaccadaabbadaabddacbaacbcabcdbbbbdcccdaaaadcdacaabaadcbccbadddbaccccacdacbccdabacccbacccbbdcdaacdabaaaddcaccdbacbdcddaacbcaddacaaabbacbadaddbacadaadcddcccdabaaccbdbabdabacbcdaacbbbdaadaabcccdbbbbacdbcdadcdcbbcaccdabbcbadcccaadcdadabcdccdddcabbdddddacbcdbbbcbdbdbdaaddacdcddabdcddcababddbdacbabdcaadbcbcacbbddaabdacdbdaccacbbbdcdabadadadcccbcddcdadbabdabacdaadaaccdbcbbcadcccaaacdcccdcbbacccbbdbdbcacbaabadbbbdaabaabddaacdabbbbababcccddddbbcacaabadddbddcbaccbaaadcbbdaadbaadbcdcaccbdbccccadcbacdbcdcbdaaaccadcaddacaadabbacacbbdddccbdaacdbadddddcabbcbcbcadcdbacdcbbcdcadacaabbbcddbabcaccdcddbacbcddcbadacbaacdcbdadbcabbbbdbabbdbccaccbadbacdbdcdacdbbbddaacadccdaddddcaaadddcbddcdbdacdabacddbcbcdbbddbbbbdacdbabdbbdbaaaadcabdbdabdbbacbcaaabcbcbcaaaacbcbcdaabadbcbcdaddcbadbcbbbdbccccaacccdcbabdabdcbddbccccbcacdacbacaccdcaccacdccdbbbdadbddbcdcbacbbccbdcabdcaccaccaacbbcadbbbddbabbddbabcccaadbbdaddabdabadcbbadcdaacbcbdaadbdbacdaabcbbdabdddcaccbadbaccbcbaadcaddccbcddcdcaabdabbabdacaabcbacdddabcbaadbcdbcabcdaaddcbbcdbbaacacbdaacdacdacdbacdbbabacbddbababdabbddaccbaaadbacadacccbbabdccbbccbdadbbccbcbacbbaccacbdcbacddbddbbabdadccbabacabcccdcbabbddcdaddbcbccaadcdbcdabdcacbacaadcdabbcaabacabcdabddbdbdcdaadbbddbabacbdadbbbbadacbdcacaaacbbdbdccbcbcdbcbbddacacccbaabcbadbddabbdaacbadbacaaabcbabbaacaaaadbadaacbcdcaabdbcadadabbacbadcdaaadcdaacbbddacabaddccdbdbabbadbcdbdaddccbcddcccdcddbdbcdbcabcabdadaadcadacdddcdabacadbbabbacdbddaddcabbdacdcbdbccdadbdaadbbaacabcaaacdaadccdbbccbbaaabbaccdccbbccbbadadcdbbdbcacdcbbcacdabbddbbdbbbdcdacaddaaaaabbbcdbcccbbcadadbadbccdabbacbbadacadabdcbcabdacddccbdcaaaaaacabbbaaaddadbadaaacbaabbbcabbbbadbdbdbaddbcacddacdadccabbabbbdbcddbcacabbdbbccbdcbddadacdadbccdcdcaacccbbbdabaabdadcdcddbbabbaacadadadaacddaaccdaacdcbaabccdaaadcdbcaabdaaaccadaadbacaccbdaddacdbdaadccbdcbcbdddabcdcddbbddacccdaaccbcaacadbadbadbbdcaabbddadcddcdbbbbdccadbbacbabddcbabadbdccabbabadbbdbcadbbcddbcdadcbcdadbabbcddadddbabaaaacadbbadbcdbbbbcaabcaababccbbccbadbbbddacdaabadadabdcccacbacaabbbdacbacbcdccaacbcaddaccccdadddbaaaadcbaadbddabacbdcddccdbbacdabadbddacbdcdabcdcaacabdaacacdcaadcccbadccaacdcdddadddbbacdabcdbdbaaabdccbbddbddbddbbcccabaabbdacdbbbcaabcdddacacbddddbccacddcdddcdcdcbabbadcdbabaabbbabbbbbabddcadbbabdabdcbcbcbbdddaabccdcccabbdbbaddbbbcabdbdbacbbcddaadbcdacaabadbbdbcdccdcaaacbccabdccababddbcddbcbcacacbbadaaabccaabacbaacddaabdbbabbaaaddcbdbcacdbbdbdaabbabcaddbdbabbdadddacadbcbadbadaaadcabcacdadbacacbdcdacbacddbbbdccccabbdaacaaadabaaadcdddbcdbaacdcdcdcadcbbcbccddbbddacaababcddabcddacaddccdacdcadbcabaaacaddcbddadcccaabbbcdbacddaadaacbbbaaabaddcbdaddacabbdaacccadaabccdbbacbddbdcaddccbaabdcdcadbcbbbadabdaadbbdaabbcabdbccccbaadcdabacdbaabbdacddacabbbababadadbbbbbaaaaaccdcddaaacdaddcbadcaccacbbbddaccbbdbdddcdaccddcbadddbadcddcbadbdbbcbadaaaabdcadcbdbaacbcbccdddadaaaadacadbaacdbcabdcbccaabddbabccccbadabdaaccdcaadbaccdbbacadbccccdadbcbbcccddcadadbbbddacacbcdbcaabbbaadbdcdcbbbbadcbbaccdcbdacbcbcdbabacbdadabbadadabbbacaccbcacbbdacbadcccabbcabbbccdbddcdcbaabcbcbddaaadaadcbaabacabbaddcbabbcacddcccaadcaccacbabddbddbccbbacddaaabdcbbddcdbdaaabaadacaacabcadbcbbdaccbabdccacacabbcdbddccbddadbdddaabadcbadbcdcdccaccbbadbbdcbcaadbdbaaaccaabdbbccdaacddaddddacbbdbcaddcccbabbabaddabccdaaabcbccbadbdaddaadcdcdccdaaaccdbcacbdcdcbcacadbccdcabbbadbbaaddaadcbaacccbaacbacdabcdacbcdddbcbdbccccbdccadadadccccdcbbcabacbaddaddacbcaacacaccabdcccbddbaadbabcadacdddbcdbccbbbabcccaaadcabaaaccdcbbbbddccaccbccdadcaacabdaddccaaacdabbbbcaadcbdbadaaacadabbdcdcccaaabcbdaacdadcdbbbacaacabdcbaaabcadcdabcdbbdcacdbcdbcdcdddaadacacbdccbdaacdadaddacbdccacddccbbcadbdcadbcdbbbaabbdbbbbdcabcddccdacadbcdcbcdadcababcbadcdacadbbccddaddaadbbdbdacbdcccbadbaddcdacdbddddaccdbdabcdcbdaacbdacddcbabdccdddcacbbbabbdbcdcdccbaabdbabddccdbacdbacddaabcbbababaaddbbdbcdcbdbddcadcaaabcddbbbcababbbaacbdcdaaacabccacacbbcbababcdccacccabdddabcacaadcadacdacbaadabcadcdbaaddacabdcbcadcaaabaaaadccadcadcdcadaacdabacddccbdcacaddaacbbbbcacabaccbcadccadbcbabaadaadbbbaadcbaadbdadabcacccdacccbcadcccbbdadbdcacdadadadaddcaaacdbbdcaadacababbdcccdaddccabbdadabdbcadadbcabadabdccbbbcabbbaccbbaaccdcaadccaacabbaaddaaacdbabcdacbaccbccccbaacaaabababdacbbcccabbbdcdbcbccaabcdbbcaadbabbacbcdddcbccbbbbcbaaabccccdcbdccbaccddcddabdbbcadccbadbcccbbcacccbddcaccaadbaaaaaacadccaacdcacabdcadbbcdadbdbbaabaccdacadadcdaaadcdbaaccadaacbbaacbaccabcabdcbddcacbcdcaaacccacabbbbadbbacabbaababcdbbabbdccaabacabdabbbcdbacdabbbbaddcacdcbdabdddabccaccbaadbbcdcaabddcbdbdaadacbabccaaaccdcbbbaccdcdbaddbddcabbcdaacaccdbbdcadacbbcbadbadbaccbbbadbcdbacabaddaaddbacbcbacadcbcbdbadbabcbbdbbbcdadcbdccbddbabbccacadbadcaabbabadbbbdabaadbbdaaaabbabddbaacabdbbbdbccaaabbcadbbacdaabbdcdaabbabcbccccababccbdcdbaccddccdcdaccaddbdddcaaddcdaaacbccdbbcadbaddadbdacbbcbddabdbbadbcacaadbbcbabddadbcdaddaccdbbadabbbcbababcdaaaadcabdbbadaabbabadccbccdabdbbaddadbaddcabcdabbbbcdccaddbadbbddaddaaaabcdbbddbadbcbcddbaaacdcbabccacbabdcbddbcbadcabbaaabdbbababbabdbbdbaababadddcaabaacdabaadaddbcadbabcdaccddaccabdaacbbbdbdaadbcabdbbaddacbbbcdbadddbcddadcabdcbbbbabdbddacccabcdacdaacdbbcacabbaddbadaaddcbcdddbbbdbddbcaddbbbdadccbcabaadacbcdbdccacbdddbbcdbabaacacdcabbdccbcbdbbaaddbbabbcbaadbdbbcdccbbbacbbbdbaacabacaacbccaccabaddaaadadbcbddabcddbcdcdacbaabbccacdcaaddccddadddadaaadacbdacdcaabdcabaaaaaadaaccadababdcaaaabcbdcbbabadadbcbabbcadcdccacdcbaddcbabbdaddabcdaacdcdaadacabcdaabcdaadabdabadadbbcbcabcaabbdbbdcddccdbccadddddadabbdccdaabcadaaaddddccadddacbbadbadcbddddcbabcaccdadabdcadbdccbbbdccdadddacdaaaacccdaadcccdbcccddbdabbcdcaabdaddabcbcddcddadabdadbbbbbbbdadcabbdcdaaabbbbabdddbdbbbaccdaadbbdabcdcacdacbabddbddcaabbcbcccdccacacdaacabddaacdbbabadabccbddbbabaacadcdaacbacbbabcdaadddabdcdaaabdcbbbbddacbcabbbbadcbcabbcccdbccadaacbaadadabdcbcbabcddbcddaccbbcdcabcbdaccaccaacdbcaccabcabbacaddccacbccdbacddbccbdbcaddccdadacaadcddacbadbbccbccbadaabacbdcccbacbbdbbcbabbcabdccddaaabdaddddcabcacabcacaaacdcccdcbcdddadcbbbcbababcaadddcbbbacdbaaaccdccbbdaddabcbdcaccbaaccabbcbcaabccdcdadaaabcadddbbcbaaaaaccdbdbdacaddaaacacacdbdaacabbacaabcbccaadadbcdbaccabcdaacadacdabdabaddbaaadaadadbadabdabcabccdabdcabccbaaaaabbcddabacacdcaaaacacabaacaabbabbacbccadbbbddbbccbadbddbccdbbdcbcccadaddbbddbcbbbccabbaaddccdbadaccdcdcadbbacaddaaabcbbaaccccaadbcbbdabbcbbdabcaadbadacbbbdaaadbdccbccbbccbaabbdcadbaddacdacbdcbbbacacbcdaacaccbaccddabbaabbcbcabcbbdbcddcdbcbaddacddbaccacbaccdbbadbaccdcbacddccddbcddccddcaababaaacbdacacdbaccdadcbdcbbbcacbcaadcacbdbbcccbadadbccdabbbcbcbacaaacaabcbdbabadbacbddadaaacacbcacadddbabbacaaadaddcbadcbcabaaaaaacbcdadcdcbaadddbbccabbbcaddcadccdcaccbabcbaccaacabacbadcdbbbabadcadcbadadbccadbdbbbcccbdcdcbcacdbbaadddcaddbdcadaadbadbdabcdcbcbcdabaccdddbaadadbbaddadbbddcddbbbaadccccbbdccbdcbadddcbdcdcddadccdbdaabcdabbdaacbbcdbaacdacbbacbbcadddcacbbcdabdacabdbcdbbdcbcdaabdcdbbaacbdcabaccddcadaaabcacdcdacdccaacdcadcdbbdbcabacccaaddbadddbabbdacdbbcddbdabccbccdcdadccadbabddccdbdabdcbcddccddacbdcadcdacacabcdabbdccbdbdcbbaddcbaadacdddcbcacabaccbcaacbabadaadaabddabbabbaacdbcbbaddcaadbbaabbcbcadbcccabbdacbddaddcddcbdbaaacbccddbaaabdcdabcbbbccadbddbbcbcdbacaccdddbbadaabcaacbdbddccbacbaaccdbcbdaccbdcadcadbcbcacacbddbcbaddaccbbcadccdcdccdbcbbbaaaaccbdbbbbccaddcccaacddcbacbdbacabccabcaacdabbacccdcabbbdaadbcccdaaccbdacaccdbabcccbabcdcdcbddabcdadbccaddbddbaddccaadbacddcbbbdadabaccdcccababddadabbdacbcbcdcbaadddcaaccddbdbdaddabbdaddabcdddbadbddddbbaaddbaccacccccabaddbdbbcaacbcacaddcccbbdbcdccbcbadabbcbabdbacbdbdaddbaacbacbbcdbbdbbdcacadbaadacdccadddabaaaddbaacabccabcacddcacacbaacadddbbdadaabccdbbbaadbbbbbbaaccdbccbaabbdbccbcdadbcaadaaaddbbdaabcacdbabdcbbcbadabbbccaaddbdbccacbaabcabbbdbabdbadbdaaabacacbadddbbccbcdacaacccacbcdbabcccbdbcacbdaaddaaaaddcdacbaddacabdbbbcbdbadcaadbcadbbbbdacabdaaabbdbdbcbaccbaccbadbbddccadbdcdcbccbacabbbdccbdcdbadcdcabacacaccabaaddadbbbbbcabcccdbddabdcacddaacddccccdaddcdbcbdbacbdbabccdacdaababdbcdadcbbddcdabdccacdcbaabbbdbdaacabbdadcbbaddbdadabbabaacdabcaccabbbcaaddbdbabbbabddabacdbaaadcbddbaadcccdacddbbdddcdbaccaddadcbbccbcccccacaacabadcaddddbbbdabcddccdacbdacbacdaaacbdbcadbadcadbbbbdddcddadbdbbacbaadbdadacbadcdaabdabdccadcabaccbdacdbacdbbabddbddacaaccaccbdddcaabaaaacbbccbccacdcdccacaabdaadddcabccacdcbbabddbdaddccbdabaacdbddabdabcbaacdccdbccaacaadaddacdbdaabacdaacbcdacabacccdbddbdaaccbcdcdbaacbabacdccabadbdadcdaccaabccccbadcaddabdbabdbdbcaccdcaaadcbabbadccccabccadbbbbbbadaccabcbbdbdbbddadcdaaadbadaaccabddcbaaddbbdabcddcabccbbdcbbdabaaddbadccabcbbadbdabadddcaccbbdbccabbdaacacbdbdbbbdbdcdcaddbabcbcbdcbaacbdbddcdaaaccdbabcdcdbdbaaabddddddcccaccaabcccdbccddabcadbddbbbdadcdddbaacacbccbaaaccaababdaddcddcdacacbcbacccaccabbdbbacddbbbbaabaabbabdabdabbccccbabbbdcdcdbdccbbcbbcbcddaccadadbdcbbdacaccbddcdcadbcddaccbdddcabaccbdcdbcacddbacabccdcaaaabddbdacdbddccdaddcccaaccdbdbcdcaaaaabadcdcdcacdcddcdaccdbabbcdcbdbdabbccbcdccdcccdcbaacaababbdccbacaaccdaabcbabdbbbaaddcddcacbabdabcbcbcbdbbabccdccbcdbacaacbdbddcbdcaaddaddbdccaaddbacdacdcdabbbdcacdcaaaadcabbbdadbacdddaabacbcccdcccbbbddcabadaccccbdcdbaddcddacddbbabdaaaddaddcadbaabcccaccdbcadcdbddbaddadadcbcdcaaabcaaddadcddbccabcaaddaddcdadcaadccaaddcccdacaacbbdcadacbddddcadacbdcdacbcbbbacadcccaaddcdbdcbcdcbbbcbdccdbdabcadbabdacdbcadcdbbdabbbcabddbbddddcbdbbacbcadadcabbccabaabdbbabbcabacccbcdcbacddbadabcdcadaaabdbcbcccccddabbcdbdcaddcacbdabbcacddcdabcbcabbcdabbcdacdbbbacbcbbadaabbbdddcccdacaccadcaaabdbccabdcdadacccccdddbcbbcbbccacbcdbadcdcbdbabccbbdbcbcbbbcbbaadaadaddcacccabcdccdcbaccdbdaaccacacdbaddcbbcdbddbdbacdcbcdcbacbadbacbbcbddbbbcdbacacbdcabacbcbcdccbccbdcbadbcbbdadabbbadadccbdcddbdaadccbaacacdcdabaddccaabbddaaaaddcdbbdbcbabccbdbabccacbcdabacacabaaddbbbcbacdccbbccabcbbcbbcabbcacaacdaacabddcbccbdbacdbbdcadbaccddddbbcbbcbacdbbbbbdcadddccdcabcadbcbccbcdaadaaadcbaccbdddbcaadcbbcddbcaddcabdddddacdbdbccbabdbdbbbbacdcddcaabdabdccdcbccdaacddaadbcdccabcbabdacabdbdbdcdbcacbbbcccdcaccaaaccccaddaaadcabacabbddabcbbacccbbdcbbbcadcadabaccccaadccdadbbbbaacdcbbccdcdcbdbaaadbaacdcdccdcbbacdbaddcccbbdcaddbadddbabacbbcdbacbaccacdbcadbadcbcccbcddacdacddbadccdadacccabbbdadbddadcabdbadddaacdcacbaccdcbddaabcacbdccabacdbbcdcdbadcadccdcaabccbddadccbbdcbbacdbaabbbdcdbccbcdbbaddcbdabccdaccdacbbbdcddabbaabccdbadccadbaaabbbccdccaddaaaababdcadccddaadcbaadbbaccbbddbaabdbabcacbddacacdddccbbdcbadddaaababdcacabbcadadbccdabbddbbdcdaadcdaccaaabcccbbbbdbcbaabccccbbacaccbacdddcaddcbddcdddcaccacdbbbaccaacbacddbacbbbdcacabcbaccacdadccbadadbddbbabbadbbcaddacacacdccadcbdabcaacdcbdbabcbbcdcacbbdbccbacccacdaacacaabaacabbbbccaddbaccbdbbccbbdbccdabbbddbdddadcdcacbbcdadbbdddbabcbacacbacbdbdaaadbdbabbdbaaddcdcbdccacabbdbccddcabcbbaacccdcabbcdaabbadbcbbccdaaadadacdbabcccbbdbbdddcaabacaddaddbcccccddccabcadcbdddbdadbaccdbdcdadbabddcdcddcdaacbbaaddabdbdcbccccaabadcdbcaacbbbdbaadccacaabccdcaadbbabacdccadccbbcccbaddcdbcadbaabcccdaddbdddddbdbbbaaccadcdbaddbadddccacacbbaaaacbccbcadddbddcaacdddbdaaccddabbbddcbcbccacdcddbabbccadcddcbaabbcbacabaaaacabddcacddccdbcaabcdbbaabdcabacccccbbbbdacbaaadacddaadacacbbadacabacdcdcbababaaccbbccbadcdbbcaabbdccbabcacbadccdcacdddcbdacbaacacdccbdaccaccdbbababbaaacccaabdddbbcbbbabadcacbabadaaccdccbbcbbabdbbabaabcaaddcbdcabcaabbadaaadccccddacbcbaabddbabbcdbdbbabaadbdbcaddbbccccdcddabbdaaabdcbbadcacbacbbabccadbcbcbcaccaabdaccbcbbababbbdcdacadcbaaaccbcbbcbbddbcaadbbdbbddacbbbadaadcbcabdabbacdbdbdcbabcbadbddddbdbdccbdbdcaddadbadbbbdccadbcddacbbacaddcbcadaadabdcacbaadabaadbbbdadccbdabaaccccddacbaabcadcadabdcbcbdbbdddadadaaabcacbbbcbbdbcdababbaabbaacdadacbdccaacaccdabbccacbcbccccdaccbdaaaabbcbbcbcaacabadabcadbadabdbbdbcddadabadaaddcccddbabdcbdabaddabdacacdadddcbcaadddcdabdbddabacaccddaaaddbdbbbaaacadbddddaacddacaabcaccadbdccdabdadbccaaabadbbcbabdadcbbadcddabbccdddadadacabbbdbdaacbadbadacabadacbadcbaccbbdbabaacdadbaddaacccdaddcddcdcbdbabcddddccaabdcdabdddaaadababbdcdcbbaadcbdcbbdbccbbcabccaadaaaacdcaabcaddaddcdccbdcbcddccacdbcaacbdcddbabcbabadccacccdaacbcaacdbcccccbabadcbdcddcbdbccbbddbcacdabadbdaacdddcccadcbacddbabbacaddcbddaccabbcbdbdadbddacacacddddcabdbbbbbdbbcdcddacbbdbcddcbbbddcbabbcdcbbbacababbaccdddbacaaadabbcaacbcddbbaccdaddbdbdbdaacabbcdcdcdaadccadbaaaaccdcacccbabadbaddabdacbbddaabaaabccaddabacabaddaabbaddacbacabbccaacdcdabddbbbccbbcbabaccdacdbcbdacacbbbcadadcbbdbbdbdcaadabcaddddbacbbbcababdbaadadbcbbdbcabdbbadccbdbcadbccdcdcbaababadaddccaccabbddccdaddcbdadbadbbddadbaccdbcdccbccbdcdadaabbaabdadcabcdcbacbcbcbacccabdbababdccadadabcbdbbbbcacdacaccbcadabbccdacccbdaabbdbcaabbbcbbbdbcbdcabdbabdbbcaacadbacdbdbcccaadcbbbbdbabacdacdccdbcacddadbbbdbaadbddbcadbddccbdababbadbcaccbbdddddabdbdacdddccbbdddbbabdbdadaacccdbbcbcacccdacdddabbbcabbacaccacaaabacbbabcdcdcdcbaadaabccbbbaddccdacbdcbbdbadacddcdaddcbdacbabbdddcabbcdcacaccdddacabaadcdabdccdcddcbbdccacabccbadabbdbbbccdcbbbdddbccdbaadbbbbaacaccbbcabdacccacacbbdacccbaaacbdbabbdddbcdbcbdbbbbacccbadbaddbbccabcdacaaadabbddaaaacbcdcbacddaababbabdabbacacbdabccaabddbcaadabcbdcccabdccbcaddcdcaacdbbaccccbbcaaabacbabdcbcdadacbbdbccccaaaaabdbcbbbbadddaabdcadccddacdcabcaacacabbaabbcadbbdadbacdddbadabaaacabccbabadcbdacaaccbcdbbbbdbbdabdddcbbcddabbadbdacbbdacdaabddadadccdacbacbacaaaccbbdddbdadbcddbcadabadaabdbcbcdaadacccdacadcbbbccdaadcaabacabbbdadaddddbcdabcbdbcdabbccbccaccdddccbbcbaabdcbbaaddccabdabcddaabbbbddaadaabccacdabbadbddacaccbbcadcaadabaaddbcabbcbbccbacccddacacbbccabaacaadbbabddbdaccabcccddcdbdadabbcbbdbbcccbbdddcaacdccaadcabddbbcbbbbcadbcdbddbcadcbbcbdcabddadabcaacdbccaaccaaddbaadbababaadbaccabdaadaadbcdcbcbccbcacacbaccbbabcbcbdbcdbbdbbacbdbdcabcccbddabcacdcdbacabbadbabcaddbcaaddbdabdbbdbbbdaabcdaaccdadacbacdddcaadcdbcddbaacaacdcadacdaacbabdcbdbabdbcbbbcdcaccaccdaaccbdbabcbadaccbcbaadcaadadaaccccadaababbaaadcabaabbdbbdddbadacdcddaacccaabddbbbddbcbccddbaabbdddccbaacadccccdbcdbcdaddaaacabccadaccbdcbaaaaaadaddbccbcdabbddbddaaabbbabbadbabdaccbddddcaaccaaadbaddcaabbbabbcdbaababccbbbadccdbcbcdccccbabcbababcbddacbcbbcabbdbaaabbddbdddaddcbbacdcabaddcdccdcacdaaaadbbaddadbbaacdbdbdbaccbbacddbcbdddddcbbaadbdacbbcbcddabbacadbdaadaccbdbadcabddcdcbaacabaccababbababbadadcacbdadacdcddbbacbabbabcbcaadccabccaaaaabbbdcdcabdddbcdbcaddccbbbadbbadbddddccacdaabbdbbcabccbcddadacaddacbaadbbacbdcddcacdbbddbcaddccddaadccaddabaaaabaadacbbcbcccaccdbbbacddcdadbddacaddacbddadbcaaacbcaccbacbdabccbcabbccbaabddabdabdcadbcbcddbcbcbbdbcaaaadddbabcbadacbdbbabaabbbdbbdccadbbcddddbcbbbababccabbdabcccdaddbbdaddddcccbacccbccadbbbaaaabaddccbccdacabdcdadbbdbbdcdbaadccbdcadbbaabcdbcaacbcdddcdbcabbcbcabbcbcddcdbbabbbddccaccacbdbbdbadddbaccddcbaddaaacabdacadbdddabbabbdddcbdcdcadcccaaadabcbacabdcbdccaaabddbcdabdcaadbbdcddaaaadccadadddcbcaddbdccbdcbacdbddccbdcccacbccacaddbcdcbacddabbbccbdcabbcacdaadcacabadcdcbacbddbbbacddcccabbdaababcaabbbbadbdbaacabddbbcacdaaddadabccdcaadcabbabcacddbcbabccddaabdbcababcdaabdadbacbccbbcabbdcccbddadbbcbdccadbadbbabbcbbbbbadaadaabbabcddcbbadbcdddddcabcdacaadcbacdcddbcdcdbabbdaaccbddaccabbbcaddbbdbdbddbdccbbacacaaadbbdacaacbaacbbcddcbccbcdddddbccdbcccaacddccadaddacbacadbcacdbadbacaddbddababcccdacdbdbcabdbdbbacccccaabacbdbdabacabbadcccbacacabcbccadadadaaccbcbaabadbcdacbcbdbbdddbbdababbdbadadddbcbcaaccaddbcdcdbacaabbbddbccaaabcdabaaddbcdadabcbcdcdcaccadbbbccbdddaabaaadaabbaccabbcccdadadcccabbaadcaaddacdcbdadbaaabddadbbbbadbcdbcccdaddcbdacbdcbdcdaddbdcadbacddddccbccadabbacdbbcbbccdadacbadadbccbcabadccbaccbbcacdccbabaccdddbcbaccddbdbbbddabcbaaabacdbaadbbbbbcdabdcabaabbcdadabdddbcabcabdcbccdbccacccddaabccacbbdcadbcdacbccbbcddadddbdbddbbddaaccacacacdbacbaaaaaddddabaddcaadcbccabbbbaabcbcbccadcdacbacbbabbcccbaabacdcccbabddbbcbbcbabadccadacadaadddbdcdaccaccabcadbcccbbbcbaabcdcabcbabbdacaacadccadcdbaaddcdbadbbbcbadbcbcdcbdccbbddabbbcbaacaaddaacdcbcdcbdcaccaacbcbdabaaabdbdcbadbddcbadbadbbaadcacddaabbccadaddacbbbdcabacbdadabaaadcbacccaabacdaddadbbbcabaaadcbdabccdabcbadaaabdaacbdccaadadccabdcacccccddaaadaddbabbbaabbadbabadbadbaddbaabacccadaccdbccccdaaabbcaaaacddaaddabdbdbbcbcdbbaacabdddcddcadbacddbdadcdccdabdbaadccdcddbdaadddbbbdabbbaddadbacdabacbacbddbacaaddcadbcdcdcaddadaabdcadbcacbabdaadbacddcddccdabdcaaaaccccbaddcaccdddadbbadbacdbcabbdcdcadddcbdcabacacdddddbacabdacadcdbccdcbcbddbaabdccbdbbcbcddddcacbcbbbbcdbbdabcccabbdbcdcddccbcbacdaabadddcabcabbccddddcdcbcdcbaccddaaabccdcdbcadddbabdbaaddcaccdcdcbddddbccbdacbdcacaabacddaabaccacccdcdacbdcdbcbcccaaccddbaacccbabbdddcbacaddddddccbdbbddcabdadbbbbcbaaccbccdaabcdbaaabcdbdbcccaaccacbbcdccccbdccdccabdacdbcbbcdbdadcdbbdadddbbacbaccbcdddacabcdacbaccbadcbadadccdcabacabcddaaadaccacdabddbbaaadcadacdddbcbbbdbbdddbccaacadaaaadaaccdadddbddacbcbabbdddbaddddbbdcaaadddbbddabddbdbbbcccaaaacdadddadaadacaacbbcaadddbccdaddcaabacbcdcbaddbcdabcacbdcaabbdbcacbbbdccacadabbcaacaaaaddbcbabababbbdbbabbbcbadcbbbbacaacdcdaddbdddbbbcbddadcdddbddaddadccbabaaccbcddbcbdbacabccacbbcacdbbdbcddcdacaadccddaabccdcacdbabdaadbcaabaaaabadcabcdbbcaaabdccacdcbcacbacbccbcaabdadbddabdddddbdcadbbcadabbadcbaadcacaccaaacaaccdbbcabacdbbbdbbcdccaabaaddcbdbdbccddabbabcbddbdadcabcbbbcadcaaccbbacbaccaddcccaacbbddcccdbccaccdbbbcacbacbcabccddddaadadcbccbdbdccddcdaaabdcbadcadaaabaccacdddcaaccbadbddabcddaddbacabcccccdabcccddaadcacdcddcaadadcbdbbabbcadcbcadadbaddbbcaccddccabddcaadbcdbbbccdbadcabcabccdcdadacadacabcccccccabcadabbbdaaadbccdcabbbcbddadbcadacdacccabaaadbdabbacadbbadaddaccdcadabcaaadbbadaacadbdadbadbdbaaadbccabcadabdcdacdababdcababcdcabcbddcbacacbacccbdbccbbcdddccacbbaacaaccdabbbcabccaccabccacbcdcacaacddadadbddbdbbdadaddcdacaacdacbdddddccadbacadadaddcabdbbcbcbdacdddbabaaabdbdcbdbcbacdbbacbbcccbcbccbdcbbdcccbaabbdaadccddbccdbdddcdbbcbbcddcccdaddadbcdcddccbbcccbdcdabbbacddbbbbabddadadcbcdaabbcabbcbaddcddacdbabbbcacbddbdadcbbadbcbcdaadabcaaccaddbdbcbcddbaccdaaddcdbbdcccddbccbabdabccdddaadbacaadadabcdccadbbdabacaabbadaaaaacbbbcaddccbabbcadddcaaabccbababaccaadcdcdaabdbbcaabdcddacdbcadcaaaabcccabbacaccdbadabccbabbdaadccdddadbabdbabbacadadddcabbdbccdbdcadbadcdcadbaacdbadccdcadcdcdcddbddddddbddcccabaccaacbacccdbdaaacccbbaadddddccaabdcaadabddbaadcbadbbcdcbdcdbaccdaacabbabbabbcccadddbabbabddccbcadacadbbcdaacabbabbaadbadabaadadbcdcadaacdaaddbdcaddaaabddddabaabdacdddcdbbdbabbbaacadabdabcccaccaacadbabcadccbbdbbacbacdbcaddcdadaaabcdaabdadbcaaacccbbcbacddabadbbaacdcacccbbcbdabcbdcdabaadddbcdbdcdbbdcbaaddcbddcdbadaaaccdbbcdabbbaaacaddaaddaacbcccbbcdbdcbdcbdccaccaccccdacaccacabaabdcdbcdabbabbbdcdbacddcabbccbdbaaddddbcddcbbabbcdccccbdbbcbdbbcadacacaadabadaaddccaadcbcaccbcaabbcbbacbcdaddaabbacbcacabdbbcdcdbdcadcccdcadddcbcbdcdcdcbddddbdbccadcdcadbdcacdcbddaaabcccbadaaabbdabcccddaacacabbaaabbbcddbccdcddabcabdcaaccabaaddabcdaaacacdbdbbcabcbcacdcacdabaddaacdbdaabcbabaadcdcbcbcccbddbdbabdacaaabccddbbaadccbdbdaadadbacbbcabbdacbbdccdbccbdcbbccdabbcbaadbabacddbabbdaacbdabbadabcccbbaababddadadaccbadadbadccddccaadbbcbbdccddacdcccbbddcdcabbcadddaaaaabaddbbbadcbbddcdababbabdcdbabdcaaabbabbcacacbccccaadacdbdadcddbcacadcacacacbdacddbdacaadcbbcdbcdabcbdaadcaddadcdcddbdddcbabacacadadaddbaccacdbcccadbacbdbbcbdadcbaadcaacddcaaaaccabaccddcadbdcbdabacacddddaaaaddbccacdbaddbcddaddbccaccbcdbcadbccdbcbaccccbbabccbaabaccadcdccdbabddaddaaccdadbaacdbaccaabcdaaaacddbbbcccabcbaadcdaccbacabdacadabddababbcadbbbdcccaaaddacbdbdaabbbcaabcbcaadcabacdacabdbcbbababcbccdccdccddcddaadccdcbcababbcaddaaddcdcabadbcbdacccddacbdbdcbcbbbaaabadddbaadcabdadcaabcdbbcadddcabcbdbbdcdcbcbcacacbdddcbdaaaaccbbcaadaacbbdadbcbbcbddccbdbaadaaadbccdaccdccdbbdcdccabcacabddbadbddcddbdbbdcacbacabbaabbbbdbaadccdcbdbacddaabdcdcbdcbbdbbdcddaccbdabbdcdcdabaaccdacacdccaddababddadadbddadccabadadaaaabdbacacbcdbbddcdcddadccbdabdcbdcabdadccbcbdbddbbcccbadbbdaadcdbdcaabadcbccccaddddbbbaddabbcbbadbbccacaabbabbddaaacddccacbabcbbdcbcacbdbdcdcacdcadabdcdaaacccaccccbcbacdaaadacbaaaccabbdadaddcbaaabbaddcbcbdbdcabbababccbbdadccbbbcbaaacbbaccccbbdaddbdddcbccbdbcbcbcbbbdbaabdcddabcbcdadabbabdbdbbcaaddcddcadbacbbdcbacbacccccdaccdadbdadcdddbabdccbadaacacbcaaacccabdcdbaddadadbabdcdacabddcdcbacbbdadddcbcdaccdbcccadbcadadadaabdbbccddbabbcbcbccacaacaccdcacddaadabddcaccacbcaaabdcaadbdbbbaadbdcbddcdbdbaadabaacddbcdacaacdadcadcdcaabdbabaccbddabddbbadccbcccbccbacbaddbcaddaccbdbabcccbbbdacbbadadacdcbadccddbddbdddcaccdddacdbcabdbaabacbaddadbcbbaddbbdcacaabbbabaaaccdabcdddbcacdaccdbddcaabcbddbaabbacbccddacddacdabacccbdccadacdaccccbadbbddadcdadbabddbcbabcdaabbdcccaccccbbaaaacacabbdabbbbdbadadbbbbacaaabbabbaddcaabbcbacadddcbadcdccadacdcdbdbdbaccdbacbdcbdbbdcbbcbcbbccbbdbdadcaabcbddaaccddabbaabbabacccdcbacddbdcbdcdcababbdcacdcbbdbdccccdbcbdadcdbdaccbaabbacbbaaadcbaddacaaadcabadbccdbcbcdbdcdccbbcddbaabaccbacacdacdbbbadccdcacdbcdcdcababdcdadcddccadaddbacdccbcadaddbccbdadbbaddadbdbdcbacaccaaccaadbbaccddbdcbcddbdcccacaaccdbaccbddaccadcbcadbcacbcddcdbbbbbbacbcdbcdbdbadbdbdccdbbdccbcbdbaadabbcbadccacccbbbadddbbbbcbcdadcdadaddaadabcdbbcbcdbdaaacbcddadbddcdbdacddbbdadcabacabccdadcbcccccdbaababdaaaccadcddadcbaabdaddacdcaaadcbbbadacbcbaadcdcdadbcdaabbcdccdcbdccadbbcbcbbbdccccbabbdadbacaabcadbdacabbcbacadbbdbcdacaaccababbbccdddcddccaccacccdddccadbdcbabcbdababdcddaddccdddbccddcaabcacdbbbcbabcadccdcbadbbdadacabcbcdddbaccadababddabaabbcaadbbbabdaabbcdbdadbbbdbdabbbaadaaddaaddcacdcdcbbcabcbbcdcbcbccbdaaacdaddbabddabdbaacdaaadbcaacddabccddcadccccbcdbbcdaacaccbaacdbcbdaadabadaabbbbcbbcdbcadcabbabacdcdbabbbdbdccccddcacbbbddaabdcbcaacacadcdddabdcaadbdabababcdabcbbbaccdbdaaacaccbbdbcbbcaccacabbcccdabccccbabbcabcdbdaaacdcbbbdbdcbadbccbcccccccdaadbaccaaddbdaacadcadaadbdcdbcdabdbcdcbaaddcadcbddbddaddcaabdccdcdaccaadbadccaadcdcacdadacdaacacccadadacadcdbbbadaaabadbbadbacaaacaddcdabcbddbdcdcccdbcabcdaddbbccdaabaabcaccdddcadbcddbdbbdddbbcccbaadbbdcddaacbabddccdcdccbddccaacbbdbccaabdbababcacaaccbcbbdbcadbcdbaddcdcddbcabcdacbcdacdacdbcddaacdccbbdcaccccdcaccbaaaacabcadbaadbaabddcbbdcdcccdcbdbdddadabccadadacaddbdcdcbbbddacbcadbdbaaadabacdbbadabbbddcabcbaadbbdabdadacddcbcbbadcabcababdcdcadddacabcddcbdabdadaddabadbbacbbbcbbcccdbbcacddabcdccbcbaadcdbbccdbcbcdbbcaabaabbbacbcacbbababdcdcabdacabdcaadaabbcacacdbcdbbdabacddcabddcbcddcbdbbdbcadabcbccaacdaccddadbadabbcbdbababcdbdbbadbcbdbacbaccabaabdbbbdbadbccbddabadbadcdcadccbcbcddcaadabaaaabcabdbbabdcdcbcdddbacabbdbdaabcdadddcbbbaddbaccaaaccaacddbdbbdccbddbadaabbcdcbcdbbcaaadcbcdcbcadbcabcdbdaccdcdcdddcbbccdacdbddbddddacbbbdddaaccdbdbddbadbacbcccadaaabdbbcbccaccdbdbdcaabcaccaccdaccbcbcaabbaccaadabdabddcbabccbbdcbbbdacbbacccabdadabdddbbbcadbcddbcadccbccaccaabdcddcbaacdaddacacdaadadcdaadadbcdacdbbcccdbdbbabcabadccbcdbbdcbddcdbcccadacccabdaabcccaadadcaccdbddbcbddabbbcadadbcdaadcaaccbabccbadccabbdcdbbbaacdabdbdabababbdddbabbbbddcaabcaabbacddabdaacccbbadddacdadddcddacdccacaabcabddaddabbdbdaadbbaddadacadadbabaaaabccbbaacabbdbadccbaaabdadcaddddbadddcacaaaaaddcadbddadadbcadbcaabbcdbbabcacddadbdbdacadcdbccbdccaabcbcbccbacbdbdadbdbaadabacaabacacacdcdccbcbabcbbbbadadbbcddbabcbdbdcbadcdbbdddbcddbddcddbacbcdabcdabcaabaaacddabbacdaabccbadbbbddbcabbabbcccdacbbbdcbcbbdaadbbbcbbdbadaabaddaccaabdcdbcdbcbbbbbcdabaacdbcdabadbabdadcbaacabcdadaabadcdcaaacccdbaabbdadaadabbdddcacdcbabaaabdbaddbbbdccbdbcddcccddacdaaccdddbdacbcbcbacbdbaaabaadadcbaaacbcdcdabdcdbcdcbabcbcbaadbcbcddddddbaaadcdbdbcbbbcbabdaddddcadbdcbbbcabbccdadccabaabbdabbabcdccadacadccddaadbcdadddcdabadabaaadccaacaacadabbacadaabbadadcaacdbcbbcadbcdacaaddaacddcbadabbdcaccbbaddaaadadcacacddacaccccaacbddbddbadbdadacdcbcdbcdcaaababacaccdadcacdbbcbbcabbbcdaadacdcdbbbbcdabbacbdbaddbacdbcbbdaaccaacaddbdbddcbabdddcdadcbdbabbccdacdcaaddcddccdbbddcbbcaaccdcadccbdcbdcccdabdaccadadbddaaaaababcbddadabdcabcbbcbcacababdcabcdcaccddcacdddcddaabddcdaadcaaccddbddcbdabcbdbddcacddcbccbbdcabdabcadcdaddcdcaaddcbdbcccabaadbcddacadbcbdaacbadcdcbddcbabbdabdbbabcbbabaadcbdcccaacdccdcaaccdddbdacbbcbcdbdadabdaaabccbdbadbbcabcadabcbdcbbbccbbcccabcbaddadbdbdddbcdcbbdadccbcdaaadbacbbcbbabcbadbabddbcdcadbdbcdccdaaaddbdbdacbcaababdbcbadcbbaabacacddbacddcbcdacdbabbaddcbadccbdbcbabbbacdddbdddbabcadbaaddbcbcdbabcbcbbaacacdcbbddacdbbddbcdccdddddbcbaabccddcdbdccaadbddaddcdcdbccbdcabcadaaabadbdbcccadbcabcbadbbcccccdcbdbcacbabaaaaccddabadbccdbcdddcabcddbadbcdcadbcddcdbaacbcaabababacbabcdacdcdadabcccbbaadbbdcccdcbbdabccabbbddbbbdccaacdbccacbcdbcacbcccdcacbddaccadaaccddcacdcaaadaacbbdbddaddadcdbcdaaaaacdbbbadbabcbdcdbdadababaaabbbacbbaaadadcdadbcccbcbcdbcadacdcadbcdabbcdbbadadcccadbcdbcbadbbdadaaacabcabbbabcdabccbbcabaaadcdbdadbbccbaacbadadabcaaacadacdddccccbbaacdadabbbbcdbaccaddabbcdcadabcdcdacdbabbdcbbddabccaccaaaacacbdadaadbcdbdcddccdacabbcabcadacbcbdcdcbcbbccdcdbbbbadcdbcaadccccdcadbabaccbaccaacaddddadbddcadbabaaacacbaadccdbdadcdabcdaddcddacacbadbbdccdcdbccbcaaabcdbdcaccbdcdacbcacacdbcabaadbcddbbaadcaddbbccccbacaccbbdacadbccbbddcdaddbcddacdcaacdccbccabbdccaacdcbdcddbcbbdbdacdcbbcbaccaabbacbbaabcbaadcccbacccacbbbbbddbadcbcacccbdcbdbcbbbabbabbabdcbcccacbdccdbddbbcdacbaddddbacbdbbccbabdaddcaabbcdddabcdbcaabcbdccdcdaadddcacbabcababccaaccbbdddcddddcabadcdbdcdabdabdbcaddbbabcccbcdaadcabbbadadcaaddbdaabaaccaadbbbdbacccbaccddbabbcaacabbdbcdddabcdccadcbdcbdbacadccbcbdabdbbcbdadbbbcddcdbdbbbaaaacbcbcdcadddcccbaccbbbaabbbbcbadadadacbadadbcccbccbddcbacdacddaaaccdaddcbaaddbdbbcdcadaacdcbdacbbdadcccaddddcdaacbbacbbbcbdacdcadbdcccaccbbabbccadacdbcdbcbbdbaaddcbccddcdadaacacacadabaacbdadcdacbaaaabacacadbdbadcabdcddabbcdcbdbacdcdbcddbddbcabadbbacdaddddbbccbdddcbacbdacccddacaaccddbbcacdbadcdadbcbaaabcabadaadddbcacbdacbdcbabaabbadbabddaccddddabbdadabddcabccbbacccabcadddccababcabbbbaddbbdcabaadcbbcbabcdccbcaaaccabddcdcddccdcadabbcdbdaddbdbdcbbddbcadbcacbcddaadcddcbccaabdcccdbaacccccaabbadbbbbdcbdccbcddadbaadddabbcdbbcaadbadbacbcdabcbcdbaacaabadcacaacdbdbddaacaacbacbcabcdaccdbabbcbbaaccabdadacbbddbadaabdccacbadbcaacdccaddccdbcabacdbcbddbacccbcabdcbaddaabadacadabaabbcdabccbdcdaadadcbdcababbaadbdcbcbdbaabdbcdaddbdbbccaddccaacdcabddddbcaabddddcdabbdcdcbdccbbcccbaccddcdcccdabbbddbbdccbdacabbabddbcadaabdbcaddcbcadbbbaadccabdbacbcddbbbabadcbbcbdccdbdbcababcacbbabccaacabadcadabdacaaccbbdbaadabcaabbdcdbabdacadbaadabccccdcdbbabaccdddacaabbcccadabbdbcbbcaccccacdddcddadddbccbbdcddbcccccdcaabaccbbbcdcdbcdabdadcdcbaadaaccccdbcbdbcadcaaabcbbbacaccdcdddabbcccdababdcbcdddbabccdccbadbdadbacdddaaabccadddcacdcbadbdcccddabbcadaabcbdbddadcbadbdcaacbcacacadcbcddaadabcdcbaaccadbacdccddcdadaaababcdcbdbdaccbbbdddacbdbcbccacbaaabbcadaababcadcaaabcbbdccdccabbcaabccabdcbcddcdaccdcdcaadcbbdcbcccdbcaabcadbbabadcaadcbbaadbaadbaaddbabacdcbaadcdbadabbcdcbdabacbbbccddcaadcaaaccaaccddadcaccbddbcbdddcaababcdadddadbadccbbbabacabddcacadaddcbabcabdcabaaacccacbaaccdacadbacabaccdaccdcadddcaacbcdadacccabaddddcadcbdbdacdddadccdbcbdcaabcadccbbdddbdabcbacdbaabddacbcdbbbaccbcbcabacdcdbdaddccdddcdcccddcdbbbcaddbbcdccbccabccccdcabcbcadbbccccdcdcbdabcabbbdcacdcabdacadbadbbdacabaaccabdaccaddabcddbdaccbabbabbdccaabcdaddbccbcbdbcccabcdbdabbbdabaacccabbacbabbccaaadbadcdbacbabdabcaccdbaadadbbcddbdddcadbbccbcabbcdccbddbdacbbadaabbccbdcdabcbcaabbdabcabaababcccadabdbcccdcaacabadabdcacbcacabbadbadddacbabaacbbaadacadadbacabbbcabbaadbdbddbbbbdbdbccaaddcddcdbbdacdadaadcbdccacccbddabddcbdddadcabddcbcdaacdbbccbcadccccddadcdbabddabbbacdccdaadbbddbdaacaddacaadcdbacdbccbbbccdcbddaaadacabbcadbdadaccddddababbddacdbaacdbcbdbcdddabcdccbbcbcccdcacdcbbbcbdacbdaaaccaabdbccaaabbbcadcdacccbcbdbacbcdccdabcccbdacabcccadcbaadaddcdcbbcaddcbabdbddddabcadddaaaabcaddbdaaaaacbcacbdbdadddbbcabbbbdaaaaadbbddabdcbbcbbbddbbaaabadbcdccbdbdbdaacdbdcbbacbaabdacaacaaccabaccdcdbacdbacdbdaabdbcddcdddaddadaaabcddbdcddabcdcccbddacdcbccddaaddbaabacdcccbbaccdccbcabcccdbadcbcdaaddacbadcccadccaaadaaacbaabdaabaaccbcdbaaccdbdbdabcbbaaadccadcdddcdccabdbcdaccccddabcbcccdbacacdcbacbaaadbbcacbdabacbaabdcaaacabacbdaacccccdbbdbbacadbaaadacddbbddabcccbbaabcbcdaabbbbcbcdbcbdcdacdacbddbbbaddacdcddbccbbdadbadcacdcadcbccccbcbdbabddabaaabdcacabbacadddbaacbbccbcbabbadacdacbdcbcbbbcdbcaaacddbcdbaaaccacbdddcdbaaabcdcbcbbadcdbccdcbaadacbbadcbaaadababaccadacdbaaccabbabcdbabadaabbbaaacbbbcacabaadaddbdadbcddcbbabbdaacdcbbcbaccbdcbbcdcacbbbaddaadadacaabbbbdcbcbadbbcbcaddbaabaddadbddabacdbdadbbccadcabbdbacdbcbbbcdcabddaaccdcbacccdcdaaaaaccbcdcbccdbdcaaccaaabadcccdccbdddcbdcadcdbddcdbcddcbbadbcdcdcddddacbcbacdbbdcdaacadddaabcbabdaddcbcbbaaccbccdcbdcdbbdcbdcaacaacdabcadccabdddbbabadbcdaadbcbbabdbdddbdaaabdadcdbaadbddcbdbdccaddbccabcadcadbaabbbcbbbbcacbdcbbbcbaccacaabbbaaccbacdabcabdadddabdbbbbdccadbadbdcaaaaccaddbcdbddbabdaccdcabdacaacaaacacbccccdbacbaacadacbbacababaccbcdcacbcadaadadcdccddabbcbdbaccaccabccdcccdcacbddccaadadccbdccbdddbacbdcbacbdcabdadabadddbbcddcdcbdaaccddcdcbcaddccacccbccbdabcbdbcccbbddadcdabbbcdbbacddcbabbbcbccddaabadadaacaabdacadbdbacabdabdcdccaabbbadbcaccccbbcddabbadbacadcddccbcbdbddcccccbadcbbcbbbccdaccbacbccacdddbddbadccaaaacadaccacbbaabdaabaccdcdcdbdddcdbbcdbcadcdbbcbbcbdacdbcdaaabbbbbacbddadbdccadbcdbccbdcbdddacacbccbcddcbadbcdbcacbbacbadbdcddcabbcdbccbaacbadbbdadabdcadadbbcbdbcbabddbbdcddaadbadabccbcadbccacbcbddaacdcddbdbacacbdddbaaabccccccbbdccbbbcdbdaccbbdcbdbbadbdccaabacbabdbcbbabacddddabcadbdaaacbcbaacaaccdadcccbdcddcbbddabbddacbdccbbddbcaabcbcdacbcdaabdbbdbcdbbcabcbbdaadabdbbcabaccdcdcabcababccbdabccdbbcbabcdcbbcabcaaacccbaacccbdaabcbadccdddbdcbddcdcaabdaadcccacccbddaacbdcbbdbcdcaacabadbdbdaddacddaaadcdaacacbdbddabcdabaddbbcccbbbbddbadcbbbbdcbbcccdcbdaacadaaaabcddbdcddabbbaddcabcdabaacbbbbaaadabaabccadccccacddacccadbcbacacbadcaabdbaaadadcdddbddabadcccddcdcbcddbacaadccdcbcdcbdbdaddbaacddbbdddbacdcbbccccacabcdddcababdbbbababdbbbccaadddadacdccbabddaabbbdcccdcdbbdccdcdcaaccaaaaddaddbccadbbbdabdcdcbcdcddabcdadabccbabaaaabbaacdabdddabdbbccadaaaadccccbcaadabadbacaaccdbaadbbdaddbcdccdaadbcdccddcbbdbbacaccdddabcdbbbddacabbdddbcaabbbacbccbbbabcbaaacbddbdacddddbaccddcccdddcabababddadbaccbbaadbcdbccccbbcdbccdaaabadbcbbadaabccabbbdbdbdcadbaabccccdbbcbdaaccdabaaabbcbdabcbccbddccbbcdccccbddddadcadcdbbcbddbbbadcabdddbdbddcdbdccadaabacdccaadadbddbcbacdcaddacdddcbcabdacddacbbabdbdbccddbccadaabbcacddcaabacbcacdcdbdcaabdbcbbabadaaadccbaaccadbcaabdaadadbbbdbabadcddbdcbcabadddcbcbdcbbdaccaddaccddacacbbdcbcaabdcaadadcaacadbdabbbdbbadbabccadddadaacaaadddddcdabcaccdaabdcddddabcddcabdbbbcadddbcadadcddbaadbabcaddaabcadadbdbcabdacbacaadcdcbcbcccbbaccaadcdcadddcaccbcdaabcccaadcacdcabdbdbddabcdccbbdbdcbbdbabdbbcbabbbcbbabcccdccacadbabacbbbacddbbaabcacbabcdbbbdbabdbddacddbbbbcdbdddcbdaaaaadbcaacabdcdcaaccbadcdaabacdddbcaadbabbdcabcbcddcabcabcbbcdabaaddbacdacdaccbaadaccabcadddbadaacdcadddccbbaddbddbbdbcdcddaacbbbbdabbbddacadcbdccbbcbdcccdcaadcabccacbbacbcbdbbdbcbabcdbcbcabbbdaadcbbdbadaabdcabdcacababadcbcbddcabddcbdcddbabdddccaddbdbcbdadcacadcdcabcbcabbdabbabbacbbdbbdbcdbdabcdaccbdacdabaabbcccbaddabdacaaaaccbcbbbdccddbbbcdccbaacacddacddabdacbcaadacabbdbaaabbdbcdddbbbcbbcaaadbdbbdbddcbadbdabadacccbdccdabbdbdcdbbbcacbabdabadabbbcddabadbccdcddadddaacccdddacbbbdacaaddacacdabdadbdaddaadddadcdbccdadcddbdcbdbdaaddcdaadaddacadbacdcbaddadaacccabccabcaacbacacabdcdcabaddcadddbbbbcbcccccbadbddddabcbabbcbbdbdcdbaaaccbbadddbdbadbdcbccaacdbdabaaaabadddccbbcddaadbcdcabcddbddaabcbbdbbaddcbbdcacdcdadcaabdacbcddabcaddacbaddbabadaabbdbcdbabdbddbacbddadccacbaaacdbbcbbcacaddcabcaabccdbcbcaaaadaaddbcbaabdcddccbdabaacacbacbbbdacdddccccdcddddbaccadadcdaccccbcdbdcbdddaaadcbbcacbcccccdbccbbcdccbcbdacbdadccbbabdbbdacacdabacbaacadbaddbbdbcdabbadaaaaabaaabadabbddabacabcaddcbbaadbbaaabbbcbabbbbcccdcbcdbcdcdbbacdbcaaacadddbbdadabcbbacaccaabdadccbaccabbadcbabdcabadbbbdabbbbcbccaaabadbbcacbbaadbacdbdddabbcbccdabbdbbbbcbadcbabddcaddaccbdadbcabcaccbcababbdabccabcbabbddababbcdddcdccdabbdcdbcdbaaaccbbbcdccadccacabcdbdccdbaaabbabcbdcdbcbbccbcbcdbabbccdcdcbcccdabccccacabbaabbabbdcbabcaccabcdbacdbddacbaaadbadcccdbbbbbdbaabcbbbccbdbacacdbbbdbdcbbcbbdddbcabadcacacdcddbdbbcccadcbcbdbbcdcdaabbbaabdaabccbaacadadbaaadbabbbcddbddaadbcdaabbbbacbdabccddbaddddadbaccbbbdbdaccbbcdbdcccacabcddaaacbcacdabdcabaaabadbbababbddaccadcdbbadaacbabaaccadcababbbbdbddadbcccadbbbbacdaaaddcdbcbcaaadaaadacbcbadaadadabbadbcadbdcabddbaddaababbaacbcdaaddbcbcdaacabadbdbabdbccbbdacbcadbacbcbdccddcdabdabbcabbaadbdcddbcadbbacabbbabbdbcaacabcddbcccbdcbadcdadabbccdbbdcccdddacdcddaabcbbcdbbdddccaddbbcdcbacbbacabcccdaaacacbbbdaacabcaaaccdbcdaadbcadbcccbcbcdbacbdbaccbcbddbcbcaddbaabbbdbdcabdaadabbcbacbdaacbbcddabddacdcdddcbdcdaabbbccdadadccaaccababdbaacbccaadcbcbabaddadadaabdaacbdcdcdbdbddbabaabdabbaccaacdaacbbaaadccbbdbaccddabdccdacddaaaaadddddcaabcabaabdbbbcaadddbbaaccabbcbdabbbcdaabacdaacacccdccaacabccbbccdbdbdbbbbbbadbdcbccdacabbbacdcacaabdcacdccaaadbccbbccdbcabbaaadaacdaccbdcbaddadbdcbbddacdcddabbabbdaddbaadbcbdbdcccdbcaddbbbbbaacaccacabcbcabaadcbdbabacbcccdcdacbcacdbdccbdbaccdbdacaaaaaaabdcdddbbccbbaacbbcccdacacabbdccdbbcdddbcacccbbabbcdcbcdbacabcbccdbbcdabaadadbcddbacddcdccdbacdbdabadbdcdbdaabdbcccdadbcaddbbbdcdaccdbaabccaddcbcaddacbadcccdacabbbbadacadbadcbadabaadccdbbcbbddbbcabbcddaddbbacbaadadddcbbdabcacdaccabbccdcbcbcbcacdadbddcadcccbbbaabddaaccdbcddcccbadcbbcadcacbdcdabbbbccccdadddcacbdbbaaacdddbcccdcbbbbbdbabbdcbcdadcdcdbccabbccaddbdbbaddadabddcdccacadccbaaddcddbdbbbacccdaabdbdadcbddbcdcacddadccdbddcdbdcbbbbabdcbdccdaaadcaacababdcbbcbabdcaadbdbdcadbdbccbdacaccccadddacaddbaaabcbcadadcbdccabbcdbcabacdaaaadacaddbabbcabbdbbbabdbbbddbbadbcabaddacdbcabbaddadbbdcbdcdccaabccabacbaacbdbdadbbbcbcbbbdcabcdddbccacdddbaabcddbbccaacccdcacdcabcadacabdbcdccbdbcacbddbcbacaababcddaabdddadcbacabaabddbddccddadbcbdcbacabacddacdcdabbbacabbcadbcabbadddbdbcbaddbdadbbcadccddaccbaadbcbbcbccaddbbcccccdadbdacadbcbdcbccdaabbcccbbbcbcadccbddcccccbcaacdabdacadbbdaacdabcccbbadbcaaaddbcaddacdbcccccbdbdddcaadacaddadcacdacaccbbdbddcadddadccabddbdadbabccbbbccbcbbbdadaaabddbbcdcabbbdddccbdbccaaaddcbcbbdbdadddaacbcbdcdaddcddbadcbdddddabdddbacbdbcadcadcccbddbdddaccaaddbbdbdaaaabdbbdabccbdcaaababbaaaaadddccabdcbdcbbbbccbccbcdcacbbadabbbddcadacacadbbabbbbaadabdcdccdaabcccaadbcbaaaddbbbacdccbbdddcbabcbdbabdadbdacbcccacddacbadbdababcddccadcbdbdadcdabdcdbbdcbbbddcccbbacdbdbcddbcdbcacbbdbaaacccbcbabbaabaddaddcbabacbdbdbcdadbabbbbdcccdabdddadbddbaaadcbbbdabcbabdbddabdbccbbacabcdbcabaabccbadcabacdbddcccacdbcabbcbccdaacdaabaaddbbbbcaddcdacddbbaddcbdbdadcddcdcdbddadcaddcbdcbccdbaacdacbbbcdcabdaaaaaabccddcddcddbadacdaaccaaaaaadbccaccdcaacdcabbacbdbcadbaadacdbbcbddcccbdccdaddddabcccbabbdabdbdadbbcacdcadcbdbddbaadccacbdcbbcbcbaadbacddcaddadadaaabadaaddbaabdcddddabcadccbaddcdbccdbaaabcadcacccdaadcacccaabcdcbdbdacddbdbaadbbcbddaddbdcbddcaabbabdcacacdbacdcddabbbbddcacabdbbcbbcacacdaadbacbadcabbbcddacbddbacbacdbbaddaddbdabccadddaccdaabcabbacbbccdcbccccddccaddbdbbbabbdbbbbbaadccadaaadbababddaaadbcbdadadaacbabdbabcdccbbaaccdabcbdcabcadaacabbccdcdacdbdccaacbdddcbcbdcbcbcaddcdabacdbbabaaadcdbbdbabadaddbcabadaabbaddbbaabbbccccccdaacbbcaacacabaaccaaacacbdbadcccdbdaaddbcbadaaabbbbadbacbbbbbcdcbbdacbbcbbbbbddbdbcadbdbadbabbaabddaabdccddddddaaccbaacddccababdcbbcdbbcbcccdbaacaddacddcbabbdcaccdaaccbcaddcddbbdcbbabcbbbddbbccdaacbabcddbadaacbabbacccacaccbacdababbadbcbadbaddbaacbababccdcbdabcbcadacdaabccddbddaadcddaadcbcddaaabdcbcdabcdabaaddababcaadaacbbacabcbadacccdbdcbbcdaddcdddcbaacadcbacbdaaddbdabcbcacccbdddcdaacbcacccabdbacbdbababdbcacdbbcaacadcdabcdcaabbababbdabadaccbacbbbdbcdcbdabadccadddcdcbdbacbdcaddaccddaacaadaaaadacdbcbcddaaadbbadbdbdbdaccacbdcadaabdacbadccdbadcddaadcbabdabaaadbddaccbbaacacccbabddbdccddbdbbddaacdbcbcdcaacbbbdcdccaacbbaadadcbbcaaddbaacbcbcbbcaadcacbdbdccdccaaaccddbcdaacbbcdcacbbddabcbadbdbabbdbcacadbdaaacdaddccbabdddbdcaacaaaddbcbdabbabbdaaadcabacdccbcbadacdadbdbbabdddacbdabdddadbcbbdcbdbcaccdddabdbaadacdcbbbcddccdbdddacdcdaccdccdccbcdcdbcdbbacacbdacbacddcabdadbadbaabbabbcacabddabbbdbabadbbdacabcbaddddbaabdacbbbbdcdbcadcdcccadcabdddbdabcacadaccdacccbdbccbdccdabcdbacaabdbaaaadcdbcdbbaccdcaccdbbddbccbbcbbbdbcccddddbbbdbccabcdaadacaccdbdbabaacdbddacdbaccbcdcaacdacdabbadbccccadacbdccaadaadbabbadbcbabbbacddbbcabdcaabcddcabddcdbbdbcddcabadadacbdbbccdbaaaadbbccacaccacbddbabddbbcbddcddcbcabbddbdccacadddbaacbcbabcdbbccbddaacabdabcbabddbbdcadbbcdccccdabccbbccaaaabbcaaddcaaadbbaacbadaaabaccadcadbaccccccbbadccddbcccbdbabaadcabcddadaaadbabaadbcaabddddcbbaacdbabcdcdbdadccbaddbdcbcabbdbbcbadddbdcccdabcdddabcbbacdcbdabdcdbbacbbcbadbabbbadbadcdabbbdccddcddbcabdbcbadcbdcbdcbcddcabdaccbbdcccbaabbbabdbccbbcbbaacaaacadaabdbdbabcbbaccdbaacddacaaacdcacdbbcbacbcaabadbbacdaccbadbaacbdacddabbbbabdaddaddcbdcddabbbbbaababccddcabcbbcddaddbbcacbcdbabbadcacbbcbaccdaabcdbbaadadaabcccdddccbbcadbadabdacaacddddcaadbccbbabcbbaacdccdacddcbacababcbbdcadbbdcdcbdcbbbcdbdadbdcacdcdaabbaaabcacbdabbbddadbdcadacdbaabbbcababcbcdbbcdaccbdbddcddcccabdbbbacaadddccccccabdaaddcdaddcdcaaabadcdccbacdddacbccabacdcabcbcbdbabbbadabcbccdacbddcbccbccacaccddbbddcccabdabaaccdabcdcddccddbabbddccaacabbdbddccccdaaddcbaabccbaddadcbcabdacdbbdbadcddcbcabdabdacbacdcdcdbacadddddcbdcabbdbcdabcadcdbaadaadadcccdbdacccdccbacaddbccdbdaacccbdddcaaacaacacccccaacadbcaddddadcbbaddabbdcddaaacbdaacdbcabdcabababcddcdcabbddcadccbcaabdaccbabddccddbbbaddbccaadabdccdbbcbbddbbabcaddbbadcbabdccbbcaaddbccbcbcdacdbdacaadbdaadbdcbbddccbbbddbdbddcadbddbdbccaddbbbbaadcdaacdcdaaadbbcacdbcababddcbcbababbaabbcdcabdbcadbbadcaccadadccbbddddccbaadbdddadbcdaaddddcbdaaddaabdaccacdacbbabaadacacdcdacbcbcbaadcbbdbbcabcddadcdcbcdabbbdadbdddacdcddccdaacbddcaddacccdbbababacdcadbdcaabdbaccbacdcadcaaccbdaaaddccbdcbbacbcddcbacbdaababaaaaddacdbaadaddbcdbdcbcaaddbcdacdbadbdabadbbdccbdbabbcadbcddbbdccdabcbadcbcdcbaaacdcbccacbadddbcdcdacbcdaddaccbcaacbabcbdcadbadddddcdbddbadbcccabddabdabbcbcbabbdbcccdbbaaccccccdccccbbcdbdbbcaddcdbcbcccaadcdbbaccdcbbbbcabcbdcbbdccbbcbbacdaacabdbdabcbbddcdaacbbcbdbbbdbbcddcdcdaccabdbccbacbbccdaaabdbabadddaddbaadcaacadcccdccdcabdbbbdccddadacbbabbddaaabaacccdacdbdccccdacdbbcdbdbdccbcdacacdcbbddacbcbccabccdadbacbcabbcbaaddbbaadadccaaadbdcccabcaacddcbdbdcbdaccabacbbabcbcdcdcbabbdacabdacccbdccacbbbcabdaadccbabaaacacbcbbdacbabdccdcbdbabbacaddcdddcabdcbbdcbdcabbaadbddaaacadcadcbdcabcdbbcbbdbacaacacbcdadddaddadbacadbcdcdddbbcdabbbccadbbbcbcbbadcabdadbbbbdccdddcaccbcddabbddabcbaccddadcabcbaccabcdaacbdbbcbbcdccdbdaabcccadbccacdccddcaabdbbadddddcdaabbcacbdbccccbddcaadbbdbdddcbddcacdbcadddcaadaddaaabccccdacadabccadbbdbccbddddddcbdabacbcccbaadcdbccbbddababbadacccdbbaadbaccaadccbadadcbbdaddacaacbcbbdbddddcadbbdacacbdccbaaccbacdaabbcadaccabaacdcccabdabdcbcabcdabbbbbcdddbddbbdadcaaaadaaabddbccabcddccaabddbacaacdaadadccaaaaabbaaaaadbaacbaccbdbbccdcbabaadabdbdbdacbaccadcccdaabbaaccbddcbcacdcbbacacaccdadcccbcdccbbadbabcdbacaccbdaddabccbadacbcbcaacabbbccdcaabcadaacabacbcdbdcadadbbbaaadadaacbddccabdccbcbbbbbcabcccbdaddaaadccacbbcbbacbdbabbdcddacaaabcbdbbbcbdacaaabddaaaabdbacbdaababdaababccabbbbcccdbbdcbcaddbbbddbccdcdbbbbadcacdcbbcadddadacdacabdccabdabbcbbaabbbddcabaacacccaaccdddadadcdcaadbcaaccccaadbacbdadddbbbdbaacacbadbbdbbddacbbddbcadddbacbccbadddcabcbaacbadadbdaccacabccabdcdccacbadbbaadcdbabddcccccbdabddacdaaccbdcdacbdbdbadbdabddbcbadbaababcbcdccdcdcbbabbdcbbcbaacabcbcdbabddcacddccbcbabaaaadbccddbbadcacdaccbcbdaabdccbdcabdbcbccaaddcbacdbcadbaddddbabddccbabacdbccbdbbbbdcdadbbaaababccdbdcdbaabdcddbdcbabcacbdadacbbbccabaabaccbabbdcbacaabddadaacccbdbcbcdcbbdbbaacbadcadbcdbddaadcacbbcabccadabccacdbcbcabbabdccdadbcbdccbcdccccccadacccdddbdbbccaacbcacababddbbcdbcacbbadcabdbdaaddabbcdccbcababcaddaaabadadacccdbdacbbcacbcadbabcdcdbdcdaaaabcbcdccccadbdcdddaadacbbdddacadccbcadbadaacbdbcdacdadbbaccabcddbcaabcddacdcddadbdbabbaddddcbdacdacdcabddbdbcdabaddcdacbccdbccacbdacdcbbdbdcadacdbdbdbcdabdcaabdcdacdbcdcadadbddadcbcdacbdacdcdacbdcdbdbabaddcabacacabccdbaacccbcbbccdaadcdbdacdcbcbdccbacabaacdbabaadcacdcdadaacdcbcabcadadccabdbdcbbddddabdcabccddbddaaacbcdadbdbcaaabcaacbbcbdbcbacaaabacdbcabbcabbdcabbdbcbddbacbbcddaddbabcbcbdbaaddcadaccdabbadacbccbcdbadacbcbcdaadaacddacdccdaddccccbddbdbdcbbcabbdbdbcadbbdbaacaaccbbcccbcdadddaccbbdbbdbbbaadabddcbcddacacaacdadbcdbcabadabaadabbccdcbadcbabbaddbacbacccabdbcdbbbccaaabdbbdabcbdbbcbdaaaabcbbcdbddbacdacbbbdbccdaadbbdaababaadcbdcdbbacccdddccbbbacdccaabbdbccccabbaccabdddaabbddccbcaccdcdbdbcdcbcdcdbabcacadcbddbddcbadccacdcbaaadbdabddcbccdcacccddabbaddcddaadcabbdadcaacbadcadcacccdddbbbcddddbbdbcbccaddadccbbbdabbcaabcdcddaadabbbdbddadadaabbbdaacdacbdcdcadbacacbaccccdadcaaadccaadadaaaddbabccbaababcbdcbcacababbcabadabbbcaccdaddabcaadccdbacaddcbcdbabccdbaaabcddbcadadbbacbbdcdababdabbccbaddbdacccaaccadcaabdddbcbddbabddddbdbccbbccbcaccabddbaabcdacaaddcdacdacbbddddbdacadcadbbbbcbbdbdacbbbbccbcddacdaaacadcdcdbcacbbccbabaaaddcbcdcadbbbaabbbacdadbccddbbaccbccbadcdabbcccddcbaadbbbdcaaddbcccabbdcdbadabadcbbddbbabdaacbdddcabdbbcdbdcccbbcbbcbdbbadcbdaaacaaadbabdbccaacbbaccdabaacaaadcbdacbcabacbcbddabaacdcbdbdcaabdccbbdbcdadbcdbccdaacaacddacbdbdddbaaaacbbcdcacdabcbadcbababbdcaadbccdccaaddbbdacbabcbdbaaabbccaabcbdaabdbaaccacaddddcbdcaacacbbcacdbddabddbdadbbdbbdaaaccadbbdaddcdacbcbbcdbdcbcaacaacccccbdaacadaacabcabaaddaaadbccbbcdbacccbaadaaddbdadcdccddadaaddddadacdcdacccbccdaaacdcadabbbdbadbcdbdbbbcbddbaadbdbddbabbaacbacaddaacbcacadabbaaadbaadadbaddbdccbaddaaccadabdbabccdadccaadcbdccdcdadcaacdcacccaadaacbcbcccababacbaacbcbabcbdcbddcbcddaddbddbccbcaddabacddacaacdaaccdddcbcdbccdddbcbadacacbaacdcbcbbbdaabdbbbcacddccbbcddbddbbdbccbcacacbbbbccabcacbdbabcddcbbbabbdacdbcdbddccacdaddabbbcaaadccadbaacacdccadcdacbbbadadadcccaaddbdbaabbcddaabbbdacabbcaddbdccabdcdcacdaaadbacacddbadccdbacdbbdadbcbcaabcaccdbbbaaabdbbdbccbcbdddababbaddcbcadcabadbddabaacccbdccadcadabbcddbbbcbacdacdcccddccacccbbdccadbcdabdddcdaabdbacbccbcbbddaabddaaabddbdcadccdadaccccbdbaacddcaaabcdaacacdcdbacdbcdbabccadccbcbbaadaacdcdbcdcadabbacdbabcbbabcdcccdccbbdbcbbccbdbadbdcccbbdbdcbaabdbbbcdbadabbaccadaacacbccbdaaadbccdcabbadacdbbdcddcdcadbccbccbbaabbcaddcbbabdadbaabaddcccddbdcdbcdcbbaadcaacbcaadcbabcaaddccdcbcbddbcbcaccabbbcbcadcaccabbabbbccdaadaaabcdbbdbddadbdddddadaababcdbaaacbbccaaaddbcacacccbbdcdabbadbdaadabdaddcbdadadabaacdcadbabaaacbbadadacadddaabbbcbdacacbddaaaddcdadadabacacdcdaddccabadbbcdccccdacacabacaababdaacadbdcbcdbddcbaaccdbabbdcccadaddadcbacaaaaddccabdabccddbbadcabbaabbccdbacaaddddccadbbcaccbbaaacddabdcabdbdcdbbbbdbbbaadbcdbcbddbdcdaccacaacdbcddbdcdbabdcdaacddaddcabccaddadbababccddccdacadbbacdaccaddaacddaddcabbccadbbccccdabdcacbaaabbcbbadccccbaccdaccbddbcadbadbbbbbbbbaccabccbaccccccbbdddabcaddcbbbabdacdbbaacdbbcbdbbddaccbccddcacbcdcbcbaccaaaabaaddabbaabcabddcaddbcdcdcccdbccbbcbaddccdcababadbbcacaabaabccccdbbdbaadcadabadcbccddddacbccdbbbdccbacbdacaabbdcbaaabadcdbaaabadabacbdabddbdbdadaadabaabacacabccbcbcbbcbbccdbcbbbacbbcaddbdcbaaccadccddbabbabbbacbbcabbddcadcacaaabcdaabbccddcbdadcdadbdaddcbcbacdddbbdadbdddbddbadcbddacdcdcdcdbabcbdddbadcddaabcbadcbbcdcbbcbbabbbcbcabdbdbdabbcccaccbbdacdcccccdaabacdbccbcddadcdbacccadbdaabacacdbcbadaccacdcacbcacccddadcddacaddbacaabddababddcbdcbbdadbcacbacabcdbddcbcccdbbabddccbcbbdcdbadcddccbbccbddddbaadcababdddbdccacadcbdbacabdbabdaabcddaadcbacaccdacbcdbdabbccdabacbdcdbdacaccbccacaaacaabaabababddcbdbdccbbccadabdddddabbbdacdbbbcbacacccbdcddcdadccddadbdaabdababbabcbadabacddcabddcbadcbdabaabaaabaaddcbdcdaaddaccaccacbaaacabcacbdcbbadadacbbabccabbadacbbaabdbdaadadddcbdbbcbbdacbacbbadcdcacbbcbdadbddacadcdbacdbcbbcaccbbddbcadbbcddbbdccdaabbbcbbcdaabdacaddcbdabdcbaacbdccbbddcdabdddadddabbcbdaabcdbaccddcdcacbbccaabbbcabbdcacbcbbddcccdabbacbcdcdbaaccadaadcadadddddbbabbacccbbcaadcaabbaabcadbccdacccabaccabccbdbdbbadadcacbdcddcaccbaccadccbbcaadabdcddbdaccccaccaababbdddbbdcacbadbadcabbdbdcddbbbddcacacabccaabbbccdbcbaadcadccdacdcbbbcabccbdadbcbdcadacabcadcccdcacccacdadcacdbdcbbdddcaaddcacacbdcaadcdaadcbccdaadadacbdabcaaccddbcdbccbdbddabdadcddaddbbbadbabdabadccabaacaabccbbbbabdbabddcacbdcbadadaaaacacdddbbbdaadccbaaaddbbcbbbaadcbcccddabdbcaabcddcdbbccddcddbbcdbbbbcaccdbdcbbbddbaadbaddabbbdcdddccccacaddabdcdbdcccdababacdadcbddcbdabcbdbddaaaabacbaacabaadbccdaadabdbcbdadcabadddaacbabcbccbaccddbccabbcabdabbdadddbdbcdadcdaddccddddcbacbdcccbbaadbbaccbbbbaadcabbdcdcbbaacabdbcabbdacbcadcbabaaddcddacdbcdabcbacdbdabbcbaadcdcadadbbdabdabbdabbdbbcbbcdcaabbccccbaacdddbbcbbbbbabcacabcdddabccdcbcabddcbcaabcaaaadabaacacdcdcdadbbcbdbbacdaddccddcddcdabbcacaadbdcadcddbacaaddadccacbdcdddccdbdbcabaddbbddbbcbbadbcbaccaabdacbbbabcbbddcacabadacbadcabcadcababccbadcbdbdcdcbdababaddcddcdccbabcdacacccadccdabdaccdbcacadbbaabdbdaabbdddbbdacdaddcdacbcccabddbcdcccbbdbbcdaadadaabbaacbbcddaaddaacadbcdcccbbdcddacaaddcabcacabcbaabdadaadcbacadddacdbbaadadbddbbbadbccabcccdbcdaaabadccbcbaadddcccdaacdcbadadaaaadcbbbddbaddbcbbdadccbcadcddaddcbdabaddddabaadbaddccaabdacbdbbadadabdbccbbadababccdaacadaaaacdaabadaadddddbdcddcccbcbbddcbadadccdaccbcdcdacbdcacacdacaaccdabdcacbccdabacabbdadcaddccbddbddcdbbdaacababbcacdadcddcadacbcddbddcacaccddcabbdbddcbacdcdadcbbbccaaadcbbcbbbbcaaabbadadbabacdbadccddaddacbbdcdbbbbdcabdabbbdbaaaabaaabaacccabcdcadbddbaaacaccdcacdcbdddabbdadcbcdddabaacbbdacabadcdcbbaacaddcdcccbbcacdcdacdcabbbacdbccdbdbabbdadabddddbddcdbaabbdadddcdcdcadbcadcaddbacccdcabccbbacbdbbdaaaccacdadaadabbccababbcbcccddbbcbdacbaddccbcbddcbbcccbccccabccacdbcddcdcabccdddbaacccddaaddadacccaddbdbaccbadacacabaccabacadddcdadadbbcdcccabbdaabcaacadaccdddaabcdbabcbbcababbcaadbababadcabbbabcacbdbdddbbbaccabddbbbdcdadacbdbabbaaaabcccbbcccdabcbabbbccaadaaddbddacbcabadbccabbdaabacccdcdddadcbdadddbbabddaabacbdbcccbbbcdbbddcbadcdcbcdbcdabbdccdcbabacbccddaacddacbbaadbadddccbdaabacbadabccbbcbdbcbaddbcccdbdbdaadcababdcbcdcbcabcbcdbdaaaddacbbadbcbdddccdcadbdacbdacaddddcbacbadbdbbaacbbacbcabbdaacbabdcaabacbcacabcccdccaaabcbcdddccaabaccaccacdaadcdbcadcdcbdbaadacdcbddbabbbaabadacbaddddcdabbbcccadbaccbdadcdbabdcdaacdcdcddaadbbcbddbaadbaccaccdcbbbcadcbadacccbbbcaccbacccababaaadcabccddbcadcdbaaacbccabbaddaaccbbbcabacacbcabcbaddabbbaaaaddacaabddbcccbbabbcbbcaaabadadbdadbcbbcbcbacbccbbdcabbadbaadcdcbcbdaddcbadaabccbcabacbddaadacbddbcbdbadcacaaabcdcbacdcddcdbcacbaacabbaabdcccbbbaaacdbdbdbcabbcacabbdbcbabacdaabccccababacadcbaaccbcbcdadabbabbbaacdcdacbdaadbaacaabbdcbaacaadbdcbabbcbbabdaccbbadcbbccbdbddbbbdcddbbabdabdabcddcbababaacbdbabcdbbbdbdbbddbadcdcabdcaccbcccacadaddcaabdcdcaaddadbbcaadbcababdaabdadbbacbbdcacdbbdccaabdabcadddabdbbcbbdddabcbacabbbdbcabadccadbbcbabbcaacbdcbbaadbadbdabbaddadacbaaadcacbdaacccdbcbbdcaaccabcddbdcbbdaccacdcccbacbaadadbbdcbbbcadccabddddacbbdcbddbdcbaacdcadaddcdacaabdcbbbaccbaabcccdaddbccbdacabdcddccbabbabdbddcddbbcabdcbbdabddbaddabddcacbbaddbddbbdcabcdbdccbbcdacccaabababbbddcdbcdabbddbcbaaaccddabaabbddcdbccbddcbcacccdcddbadbbdabbdcdddbdddaabbacacbcbaabcbdcbbccababddcbabacaacdbdaadddbbbdadadbcdababdddcadbdcccabaacaacbadcbccadcacdbaacbcbadcdacdbbadaabcbbbbdddaaaaacdaadbdcadbaccdcdabaaaadaadbbcccdcccdbabddcadabacbcadbadccaabdadcabcaaadcadaddacccdbcbaabbaacdadcddccbdcacbacbcababddbadcdbaababcbccccabdadadaddbacadcacdbbabacacdbcbcadbcabacccbcdbacdbcddabbbabdcccbaaadddadccacbabadacdbcaaacddbdccabdbdaddddbbddaabadadddacdabcdccadccaadadadddaccbaacaaaabddcdccababcbdacbacadaddacccaadcccbabbcdcaadbbcaddadcabacbaaccccdcdaddbacaacacadcadcdadcaacabdbccbabababaacdcbaddcabdabacadcacaabcdcbcbdbdaddcabbdccdddacabaccaaacabdcbacabdcaacccbdacddcdacdacbcdbbabccacccddbdbcccdbbacaabaaaaacadcbcbacbddbdcabbddbbdbacdbcccdaaaaacbcdcacadbacdcbbdacabccccaaddbaacaddcbcdabdcbddaabbddbbddddadbddabdcbdcabccacdddddadbbaacccdddcddcaabbaccdbbbbbddadbadcabbcdcdaabdabcbdadbcbacdacdabadcbbcdaabdbacadcdcdbdcabaacadcdbacdbcbcadccdcbcaaccaaddbdddbcddcabbdcccccdcdbdabdbcddcaaaaccbaadbcbbdbbacdbabccacddbddaccccababaaacdadcdbcaccacbcbacbabddcbcbbbcbdababddcdcdbdacbaacbbaddacaaadddababadcaabaabdacdddddbdcadaacdddcadcddacacdccbdbbcbacccaacaadadacadcdaccdadcdbbcabdcdbbddabdcbcbdadbccbdaaaaabcbdbcbdabdbbcadccbdcaababdddcadabddbabbcdbadcbcccbacabdabdbaddcdaddbdaddadbcadaccccdcddcbabcccbbadccadcdcdbbabcddcbcacccbbacddbbccdacaccabdccdaacaaabbabdbbbccdccccbdcadcdbccbbbcdbbcbcacaadcbbaabacdcbcccddbcacbbadbcbdccacaddcacbbacbbdcccadcdbbaacaddbbdabababddbbcccdbbbcbabccaddbbbcadbddbddcacaabaaccdddbdabbbbcddaccdaaabcdadabcbdbbdaaadbaabdcaccdcdcaadcbddbacbcadbcaccbdddbcabddbcbbababccacbddabcbacadbbcdbbdccbdddddacbbacadccdbbdcbbcbccdcaacdbbabccaccbadaadcbccabccdcadccbdcabdacbdcdbbdddddcdcaaccddcabbadcbbcbdaddbadcdbabbbacdccbaaadaacdaaccdcdbcdcaabbdaccadadcdbdaaacdccaabbacdabacaddaabcaddbbaccddaabbbdaadaabdbdbcccbdcdbdcdbdadcbbbbdaabdddcddbbabcaddacdcddaddbcdacaaaccbddcadcacaacdcbadabbdcbbdcacbbacabbcdcdcaabccbbadbabdbdcdabbcbabbcdcdcacadbadbcacdddddcadbcadddcccccccbcbccbcbbaddacacabdcacdacbbdaadadddccdbadabddbabdbadaccbbbdadbbddcbbbccbdbdcabbbaadbbcdbdcbccbbcbabaacdbadbadabacabccbaacadaaadbdbccdddacdddcbbcddaaddccaddacbbacdcbbdabbbdccdadbdabdcbbcaacdcabdabdaadcbbcbbdabdccadadacabcdbbddbbdcbadcaacccacdbdbbcdbbdccacbbabaacdcbabddbcdadacaacbdaacbddacabddaabcbaaaacdbcbddcacdccbdbadbcacaaddbcabbadbcdbcaddcbbdabcaadbcaadddabcdcabbddcbacaaabccbbdadaaabcaacdcaccbdcabdcbbddcabcaddabdabcadbbacccdbacdababcddbbacadccabccbcbbbaadadadaddbaaddbcdccbacdadcdacccacacadaabbcaadaaacbbcdacacdcaddacbbdcbdaccdccdbddbdabdabcbcadbbadcdaddccddbbadbccbccdbcbbdaddacacbbddcccadbbaccbdcabcdcacdbaddddcaccbdbbcbacdbbadcbcccccdaacaacacbbcbbadbdbcdcaababdacdbadbbababcbbabbcaddcaabccbaabadadcadcadddabbaabcdccaadccadaaadabbcbdaabdbdadcddddadccdbdbbcbddbcacdaddbaabccdcbbdcababacdddadaddaddbcbbccadbabcbabbddabdddbdbbbabdaabcabdabdbbcbdcadacdcbcbbbdbbdacbdaacdbbadababaaadccadccdbaacdccbdbcbbbdbcbaddddbcaddbbdcbdaccddacaabbccdadcbcbccbdacadadcbbcdacdaabadccdbcabcddbdccdbdcbdbaaabaaabdadcbbcbbacaccdbddcbcccabdbabcaccbbbaabdacaabcdadccdcaadbacaacaabdadbaccaaacabcaaabdabdaaccabbcaacbadcdddbdadaadaaadadabbccdbdcdcaabdccaaacdcccddccacccccdbcdcccddbbdddccdabcbdbdccabbabcaabaadacaababbddbabbdbbdadacdbdacdacbaadcbcdbcdabbcddbddccbbccbbadaccbbccbcccbaddddadacdccdacbaacaccccdcbcbddcabdbbcdbcbaabbadcbcabacbccabaacadbabcaabbababbbddcbcdbbcbdbbbcaaacccbaccbbdaccdcdaacccbabdacbbdbbbccbcdcbbbcdccbbcadaabcaadabadadabcdbbcaabdbccaaaddcdcddbbcabbbcabcdddcadaadcdaaadcbbccadbdaaaadbaadcacdbabdbacabdcbdbcadcdaaabcbdbcabcdbdaadbaccacaaaadbaaacbdcbaccabdcbbbdbcccdccbcaddddcbdcadacbcdbabcdbdabddcccacdccbcdaaacacabbcbbbccbacdbbddbaababbadcdbadbaadadcbcbabbacdcbddccccaaaadbbdbccaadaccdacdabdbcadadaabcacbdbdcdaddcbbccaaaccacbbccbabcdbdabaccaccaddcbbbcdaadadbdaaccababbbbaabcdadbbaaaaacbacaadcccbaaabaacddadcbcacbcbaccbaabccbbcddddcddccbbcbbaaaadacabdbcacbdabbdcacdcbcddacdaaabcdaaddaaadcdcacdcabccaadbcccbaacabddbaacaadcbacacbcaddadabbdddbaadacbacddccdbbdcbaaaccabbbbccabccacaaabbcabaaadbbaccbacaaabbbccabcbcbddacdcddaabdabcdcccbccadabddcbcabdbcbbaaaddccccaabccbccdbccabbcdadcdaabadcdbbdaadbdabbdcddbadcaaabbaabaabaadabdcbcaabadaadbdcbdabbdccbcbaccbdaabacbcbaaacbababaddcdbbacddbcacccaaddbbaccbbcdadbbdbdcacacdbcadcddddadaaabdabaddcddbcbdccaccccadccaabaaddbcbdbaaddddadabdbdcaaadccccbaddbcbacddbbbddcabcadabdbbbbadcababaddacbdbabcbbadbdacadcbddddcacacadababcddbcbbcaddadaabaacddabaaaccdbcdacdbacdcdcabcbddddabbabacabcacbbcdddadbbabacdaadadcbccbaddbadcdadbbbbdbbaccdaaabaacdbacdccaaacbaaccadbcdcbbadcccbbbdddbdbcdbbccababbdabbbbacaaadcdccdccbbbdbcdadcbdbbbcccbcdbdbbdacbcabdcadcbcbbdcbcbcdddccaddcaabdadbacdcbdcdbdbcaddbbccbabccddcbdccabadadddddcddbddacdbbacbdabacacbacdacbbccacdacdaccdacbbacbdaabcccccdaacdadaaccaadcbbadaccaccbaddcdbbcdcbddbadacabcbdbadbacabdbcdacddacbcccacdabacccdbbdbacbabcbbbadccbdabbbddcabcbdacaabcabadbcadabcbabcabaabdaabcbccbbaccaaaacaacaacdacaaadcaddabadddccddaabdabbcbcabcadccadbacadcdbbcadcddaabbadcdcccdddcbdcadddabddcccddadddcdddcbadcccbcdabdccbdaacbcdbaabcdcddadddabadaccaacabcdcabbdbddbbcccacabdacbadcddabcddacadabacbbbabcadbcbcabbabdbcaacccbbabbcabacabcbdaccaabaabadcdbdccbbdcaccbbacbdcdccadacacdaccabacdccadbdcbddbcaaddacacdcacbaccabdabaadbacacbccdacaabbccadbacccdaddadbbacaababcdbddbdacdbdddabbcbdaaaddbdcdabaaaddaaaadcdccbddbbdbbdbbaadbbcbacddccaccccadadcdcbaadcbacbdcabbddcacbacdbcddacccabddacdcbddccdbdcdbaadcbdbacbddacbcadadbcdaaadcbdbaddcbbbcabbbcdbabbbbdcbaacbbcaccaacadddccccdacbdaadbbbcacabbabddcdadbbdacbcaadabadbcdcaddcbbbdbacbaadbbdbdcdbdcdaacaacaabaadbdadbbdaacbbddabaabaccdaccdaaabacdcbbdddaacdbabdcabaabcabbdbcbccdaddbabaacbdbacdaaccabcadacadabbcdccccaaadbdadaaacaacbdbdabdcabddaabcabdbcbbcaabcbdaddbdcdabaddccabcddbdbadbbadaacbbbdacbacaaddbbddaadbcbbacdbdcbdcccbcabbbdabaaccaabdccbcddaddaddbddaadbbabbbbccdaccddcbcbdaadbbadcbcaccacdabdacaaadbacadbacbcadccadaadbbbabcbcaadaddcbcdddadadbcadbabcaaacabcadbcdbaacdcdadaddaadaaabcbbdcbccdbadcaacdbdddabcdcabbbccdadbccbaacddddbaaaddadccbbbbbaaaaddadbccbbbaacdabdcbdaabcbacbaabdabdcaccaaadcadcbabacdcbccbbdadacaddbcacababaacdaadddbddddacadddddbcbaaccbaaabcacbbaaacaaacbaacbadccadccaadababbbabddaabaddabdcabddadcdabdcbdaaddbbcaacdbbabaaccdbcbdcbbabbdbaccdcddbbdacccaaaabdbbdbdcbbcaddbadccacdddbbbbbbdbccbbcadabaaaaadbdabcccddadacabbaabadddddddbcdcdaadabaccdadddcddcadadccabacaacbcdcacbbdcacdcdbabbbbdbaacdcbcaccbcdcbaccabcdcadbccaccadabbdbcccacbabddabaaacddbababdcbcddbadcdacaabddddcabdcbacacdcbbccabcbaddbcabcadcaabacdbacdcdadcdcdccdaccdbbacdacbabbbadcacdcdacbadcdacddacddcacbadddaabdaaccdadbdbdbdbcbbbddacbabcdadccaaccccaccdcbbabcdcbacdacdabbcacdbdaacbdbdcbcbdbcbaabbacdbabccbdcabbadbbbabbcaddacaacacabaaabacaaacdbacbdaaabcbdacdadbddcdaccddddcbdbabdababaadbcbcdbcaaacdddcbccacadbcbbccddcbddccddabdccbbbddcbccbdbdaadcccdaaaaccacbacdcdbbdcbadbababcdacbccdcaacdbcbdabadcdabaccccbcabdaacbbacdccbaadcdadddbcdddbbbaaaddcaacbbcaacbcbcbbabbbddadcacdcbaadcabaaacaabcdccadbdcddcbadadbccbbcdcacbbdbcacbdacaabdbccbaadddacaddacbacbbadaaadaaaadaacaaacadcacacdadadcababbcdbcadbcabdabdbcabaacbdddbcdbcdacccacdbbccadccdacdbdddbcbcbdddbdccbbdccabccadbddcabadcddbacacdadbcbabddbbccaacdddabdadabbdcabdcdbaccabaccbcdaabbcdaadbaddacdbaddcbbccddaabcdadabababdccabcdaddcccabacccbccaddaaacdcdaccbbaadadbacadcbacbcdbbaaabadabbdaacdbbaddabadbabdbbbbaabdbacaccdcbdcacbbbacbbcbddbcabaabccdaabccdbbddabbbdcadddabcdddcbdaccabbdddabdcdaaaadddddcbccdcdbcdacacbbacddadcbbbdbbdabbccadcbbccaddbbaddcaacadcbdadcadbbccacdadabddbcdddaaabddaccdbcabdccdbabdcbbcabdabcbcadbababbacbaccbbccccdbdcdaccbdaccbcdadaacbdadcaaadaabcbaaadacbaccbcabbacacadbbcdadcacbaabdcbddcbcacaddbdcabcaacaabdabcdaadaabacddddbdddaddbcdbdaddabbdbadbcadccddccbdadcabcadbbcbbdadacdbbbaccbbbaddbaaabadbbbbccbaaaddacacbbdaabbcbdbbadccbdbdbabaccccabbbdabdabccbdcabdbdbcbabcccabbddaaddadcabbcddccdccdcdbcabbbbdcabcbdadddcbdcadbcbbacaaddababdbaaacdadbcdcddcdddccbddadadcdbdcdcbddabdbcabdcddbbbcbccdbbbbadacbdbbcdabcbddcacbccbdcdcbdbccdcbdbdcbaccabddabbadbcbbdacabbabcaaabbaabdadbaabcaddcbaddddbdabdaaddaacdcbdcbcccaadcbdcbbcabbaabcacbdcdaccdabaabacacabadcbbdadbdabdbadabadabdbdccbddbdcadcabaaabcdadbcabcadbcbbdabbbabbcadabadccaabacdadcbabcbcdbabcacbbdcabbdbadddcaadbccdbcbddacabdcdcabdaccdbbbacdbcacbdbaacdccaaaaddadbbccbcccabdbcbbcaddddbdbdcadadbbcddaabbcbadbbacbbbbcdcbdccdaddcdbddaacccbcbdaaadadbcccaabcbcdadabddccdcddcdabccabccbdbaccdaddcabcddabdddddbcacacadcbbdddaaabadbbdddaabadbbbccabdccacdcadcddadccbbbdaaabdcadacdcbabdacacadabccdcbacabddcccddcddcdacbdadccabcddddbaaaccccdccdbdadccbaddabdcdccbbdccaacbbdddcccdabcacaccadbbdbdadcbcadbdbadcadcbbddbdbccbbcbcbdbabcbdcdcbdabcdadbadabcbbdcdcadbbbaddcabaddbbcbbaaccbbbacacdacbadadbcbdcbbbaaabaacdcdabccabaabdaaabccdcbbadbdbacdccbcdbaabadddcbdabdddadbdbbcccbdbaaabbdabdbdcaabcaadaaabcdadabacccdaccbacbbdadacadcdbcdbbbdcabcdcadadcadbbadabcddbdbbbbaacaadccdbbbcdaadbabcacacbadbabcdcacdbdcccbbababdbbddcdabddbbccdaabbdccacbaabbbcccdbbddadadbcabddacbcccdbdaaabdbccaacbbbbabbdaacbaaddcccabaaaacddccbbddcadbbbdcacbaddbaabddbbdadcdcaacbbdbbbbcbdaddcbcdbcaddabadaddccbaacadccbbccaaacababbcabdaaccadabaccacacadbcdabccdccdbdcbbadddabacddcbddacacbcdaabadaddaacaacdbdababbcddbcdcdcbcddadbbadaabdccccaaadacdbcaadabcabbbabdadbcacaddbddaddabacdcaacbcdaaacaacdcbdbbabacddccddbdaadcaccdbbabbdcaddaaabaabddbacbdddbadccdcacbbdacdaadbbaccccdccbcdcadbbacdbabcadacacdbbbbdcbdaadcadcbabdcaadcbccbdacaaccdcbdddbcaddccbcbbadaacdabdbcbcbaacbaccbcabbabbacbacbabaddcdadcdcdccaddcbaacbabbbcadaabcaabddaaccabbaaabdabbccacdabbcaaaddaddcbadddcddaddcdcaadddaaaddbddaacabcdbbcadcbabaccbaaabdbacbabdbddadcdbccbccaadddccdacabcddddbcdbdcacabbdcadadbdbddacdbabdbabcbaccbdbcaadabbadbacadbaddadcbbbaabbcddcdbcbaddaaaabbaccbdaaabdcdcdadbcbddabcaacdccabdbcacaddbdcabdbcdababdbbcadcdacdcacdcdaaccbababcabbbdabadcbcadbddacdddcccbcbdbacdcdcacaacdacadbbbddadbbdacadaacdadcbaadaddbdbadbaccdaaabaccbccaaccccbaadccaadaabcdaadcbdcbbacbbbcabcbabdaaaaabdbdcbbcbbdcbadccbdbbbcabcacbadacdabddaaddddddcaacbadadabcbdcdddaccbacbddbbabbcdbbacdaaadbaccaaccabbbabbbacbdcdbdcaaacdadadabbdbaabddaadaadbbbbbcacabdccbddadbccdccbccbbadcacaaaaaacbabadcabdaaacabbcbcdbcccbabdbaaaabddccdccdaddadaadacbcbcdabbdbdbbacdbdddaadbacaadcbccaddabbcaaabcaddaacadcdabdccdbabbdacddccdbddaabbbbabddbbbcbcbbcdbccbabcbdbbbcbbdbaaadacdbccaadbdbbcabbacdbbdaccaccaadddadaccacaabdaacbcdcaccabddababdaddbadbaacbaabadbcacdccdcdacdccbbaadbdcabbbdddcddaadbbbcabbcadcaddddbaacabbabbadcacabbbbbcddaaaddabacbacababbcccddabccbddbaacaddcdccdbcdcddacdcdddaabcdabccccbacaabadabadabbbbbccaacccbbaaadbaddcdbadcdacaaabcaccbcdcbbacdbdbabadcbbddcbaccadcaadbddddccaaacbdaabcadbacabacbdcacdddbadbbbbcdbbbaddbcbccaacdbdabaccabddbbbadcabdacdbcaaacdcaccaadaddccdabbacbbbdddaaaccbcdaabdddddccccaabbbbdaaadbaabbadbaccdcaddadbaaadccccddbcacddbcccabcaaadbbddbcccbdaadcdaacbadbacdadadcdaadabcccddaaaccbaaacbdcacbaadccdaabbcdccddcbcccabdbbbddabdcccdaccabbadccacbcbcbcdbdddabbadcdaacababdaaddbdcacaaadbbdaacdbdadcadabdbcdaccdacccbbbdccdcaadbcccbddbbccbacabbbbcdabaddaaddcbabddcccaccccdddbdaadbbcacdabbcbcbabdadbdccbbaddaaabdcbabaaacdaabadbbbdbbbabcadbbbaaaddbcdbccabbbdaaabbacdaccbcbbcbcbdacadababcabaadababbdbaabbbbddccbcaabadadddddacdbbaccbcbcacccabbdbccbcbbdcbddbcbdccdddaaabbdbcacbaccbcdddddbdbbcbacaaadaddbcdcabccbcbaaaabdcddcdcdaadbacdbcbddaccccbcbdbcdbaddaadbacadcbbdcccadccdbbacccbcdaacbabaabccccdadbacdbbabcbbaaabddbabadcababccaabcbbbaaabbacdbcddcbcdbbbbaadcbcdaccdbacacbdbdddccbbabccacccadddddadcbbdaddddadbbaadbbdcbdccddcaaacbbadaaadcccbbcaddbccaaadddaabcaaccbabaddcabacdccdadbddbaaddaccbdcdcaadabbadadbddbbbccbaadcdcbbdbbcdcdcbdadbdcdbddbcdadbcbadbcddaabcdaddacaddddaccbaaabbccddcacbadddddacbddddaabddacbaaccdabbaddaabcdabbbcaadacbadccdaacdacdddbccaadbbcbcaababbdcccbbdcdbcadacbcabbdccbadbbbabcccbcdddbccacaaabcaadbbbaacdcacdadcadbaabbabcdddcbaaabbbabacbaadcaacabdaaaddbaacaddbccabdddcaaaababcddcdcbbcdaddbddcbaddcaabdcdbbaaaabaabdabbaabbacacbcbadbcaacdbcbcacccbdccdabacbcbdbdbddbadcbbddddbdbdbaccdddccadddaabacdabcacabcbcdcbcabdcdabbdaccdbbaacccbcdcdbdddbdbddcadbcaabddbdbdddcadcbcddacbcddcadababcbaacdcbccbabaaadaadacddbbcaccbbcbcdcbdbddadddcdbddbbcbcacadadaacdbbdccbadadddbcdabbabcbadacdaabddacbbacbabcbbddbaabbcbcbbdbbaabcaaacdacdcccbadcdbbcaccbacbbababccacacaaccdadbbaadbadccbbbabbbacacbbaddbaabbbccdcababcacaaacbbabacccadcaabadcbcaadabcababadaddbdabbbccacccacaacabcccdbabadcbdbdcbbdbbbcbcacbbcccbadbbbcaaabacbabdbccdbbaccddbbcdcbbaccddbdacadabdadbbcbcdbbbbaabbdbbdccdabdcbadcbcbacdcdcdadabbdcdcbdabacbadadcaddcddbadcbdccbadcbdbdacdccaaabbcccbdbccaccdabacaaddbaabcdddaaaaaacadbbccdbbacadddbddbbabdbbbbdadadcddccddcdaacaababbadbaaaadbbdbaddcaacdccdacccabdbdcccadbbbbdcdacbbccbbbddcaaccbdaccbddbaaadadbacbbdcccacaccabcbcdbbbccdabbdbbcacacaaacadcbabdaccacaacadbaabbacbccaccdcdcabdaadbbbaadcbbbabdcaddacbcdabacdabcbddcacbcbbdccaccddbbcbdbaacbddccabbcacdccdacabdcbcaaaaadbbbbdcaabdcabaaccdadacaababadcbaaabdadbcdcdbaacdbcbabdabccdaacbdbbadcdacacddcbcccbadacaccbcbaccbcccdbaacdacbbbadbddcbccdcaabaddbdddaadcdabdccaabbabdccabbaacadcabbaadadbdccddcdacadbdcdbbacbdabcbadbbccbbcbdbdacacabccacdbccdccabdaabbcaaaddcbbbaacadaaaccdaaaabcaadacddacdcabdbdcbcbaaadccddacbdaabdbdadabdaabdbddacacbabaadcacacbaaacaadbabbddacaddcbdcabcabcabcdbadcddabcabbaadcbabdabaddbaabccbabaacdccaacadcaddbacddcabdbcabdcacdcabcaaadbadcddcababcbdbdcdcbbaacdbccbaacaabbcbdadbcbaccabaadadaccbadadcdcdcadbcaaddbdbbabcacabcbccbdacbddddbcaaddcdddcacdddabcddbcadcdabcdccbbccbbcddbcabcdcbdcadcbbcdbbbddbdbdddbccaddaaabbbcbcadbdaabbddddabbcaabbacbaabacadccbaadbacadbaaaccabaccdbdcdabadcdaaddaaabbcdcbbcabbaccaccccdacadddccbbbdacdccdcbcaaccdbadacaacdcbddbdbcdccddadddbccbdacbccacbabcabaababcadbbadaccabcdccaaabaadcccbbbbccabddacbbcdccdbdcbadcccbdaadbcbaadcaccdbacddaccadacbcdadaabccdbbcadadcccaddcbcbdbdcdabadaacbccddaaccdcaddadbbccddbbcdcbabdcbcdbbdccbbaabcbbdddabddbadadbcddbdbaccaacbabcbcdbcbcdbdaaccacbbdacbcdaacaababcbcbaaabacbaacacbabdcbcaddcbbbdcadaabdaacaccbabbbdcbadbdbacbbdacabdaababcbddcbdaadbdcbaaaaddbdbbbbdbbcbcbbccdabacabdddbccbcddabacdabaaddbbdcbacaabadddacbdcbcadaccdddacccccbbcdabdccdaabdcbacbcadbcbbacbdddbbabdabacddcadaddcdbadaadddadaacadcaacadccabbdadbdbbadabbaadcbadcacdcccbdaddaabbbddabbcabaaadaadaabcacacdcdcacaacaddadadaadabdbbacacddcdadcbdbcbdcbcccbbdcbababbdaaadabacaabdaddbdbcaacbbcbbddcdbdaaaacadbbbbdddbbaccababbabdcdacccccccdbddbddccdcaabcdbbabcadacdbbbcadcaaadcbdccbaddccabcccbbbabbbcaddbcadbcabdcbcabdbddacbacdddddbcddcaddbcbacbacabdacabaddddcbbddaaaacacacacadcbaccdcdaaabbddbdaccdacdbcadaaaaaccaaacaccbaddddadabdadbbabdacdcdbaacaabdbacbcbbadcabbcacacccccddbdadccbabcbdcddbbcaaccbdcdbcacdacbaaabdbcacaddcccddcbbadcdcaadaccabaabdcaccaaadcaaddbabbacaabadaacbbcbabdacdbdcaacadacbcdbacdaabcdcbbddabcccbccabdcbacacacaaaddccadccacaadcdacbdcacddadacbcbcabcabccaddabdadcacdddadbcbaaacbccaaddbaddadaacbdcabcaccadacbdacbddcacaaabccaadbabbcdaadbdbabccddaddcdbcbbacbcaacccbccacbcbadabbacbacdccccadbdaaaabbacdabcbaadbabdcaddbcdcddbbdccacccdadcaaacbbcccdaabbadccadaacddcbacbdabbcdadabcacaacddbbbcabacdadbdcaadacddaccdaddddcdddbdbdacbdabbbaabbacdadbbdcdaacaaadcbcbbcaccdadbddcaccaacdddbdabcadaaaacabccadcadbcbdcbbdbdadbabdddcddbcaacdcbadaaaabaccaacacdcddcbcabdcbdccccddcdbbdbbabcbddbbcadabcbbdacadabadbcbbaabdcadbaccdcadbaaabadaaddcadcaadcbcccbaacbbbbcdbccdaccdaabcdbdcbacbcadcacccdcadadcdbbbadbaababbdabdbbabbcdcdcacabbcdadabadaddabbcdccacdbccdcdacbbcccbacacddccaddbccacbbdabdbcccdacbbccbbcadcabaaaacdaddcdacacbddabbccdbbbdbacadacbbabcbdacdcdcbcaccdabbcadcaaaabdbabdaaacbccccddcbbabdacbbbcbacacbadbbccacbcbaabbddcbcbccbbbaccabaaacacaccaadcbabcbaabaaccdadbcbdccbbcbadabdacccababdccaddccaabddbdaaabbbbacabdacdcabaacbadaddbdbcaccdcacdbddcccaccccdcabbddbdcacdcdcacacdbbbcaacbcbcbaabcdddabbcadbcaddccdbcbadbbbdbcdcdbdcbcbcacacbdbbacddacddabdddbabbbdbacaadddbcdaadaabbbbcdbddbdddcbbcbdbbbaaacaaaabcbdcdaacbaadcbaabdbacabadcacdddcdcddacdddadccadbdddbcccbaccbbcbbdabbdaabdcacccddadacbbaacaccbbaadaccaabbcbbacbabcaadcbdadbdcabaddbddbacabdcadbdaaaadbdddabbcdbaabccadacabdbdbcdbdababadcacdbcbbccbacdaacaacaaaaacbcbadcabcccdccccdaccbccadddcacacaccabcbabcaabdaaddadbaaddaaacbdcadcdacddababbcdcdcdcacabcabacccabacdcddcdacbcabbbacacaabbbacadcaabacadbacccdacacdabcadbbdbbcaaaabbacdcbaaadaaaaabcadbadbaccacddaacbbabababdccabbbbdddccbdbccbcadcdccbbabccbcadacabcbccadabddcbaadcdbaaabcdcdbcabccacbbaddacdcbdbadaccabcdbcaadcaaabbaccbcabccabcaadddadddddcbaaacdacdabcbbadaddbbccdbccbbacbcdcaddaababcabdabbbddcddcccccbccbcddcabcaabadaddadbddcaccadddcddacbabdddadbadbbbcacbdbdaacbaadbccacbcdbbcaccacbbdbcdbdbdbaacabddcbacabddaaababadcacdcaabcbcdbdbcbaaddcabcdaaacdaddcabcabdbacabbacabcdabcbbdbdcacabbdacbdcdacdbdbabbdccddddcddccbbccbcbbbcbcbcaaccacdbbcaccabacdbabacbbdccaababcddbadccbbbddcdbadabcaaadcbddccabcdaddddbcdbdccaadcdbadbcabdcaaaaadadcadbccdbdbbaabddcdbcaaccabbbdcbbdcdacdaabdbdbbaacbbbbacbadbcddbdaadaadbaabdccbcaccdcbdcbbdadbacdcbbbdaccaabdbccbaacbadcabadcbccdcccbcdcdabbccdcdccddcdccbbaaaccdabcaacbcadaadabbbcdbcbbcbdccabdacdcbbdadadcdabcadddbababbccdadcbdacccbcaabbacdbacbcddbdbcbacddcacddaabcdbabbabcbccbcbbbadddabdcdddbadbccabacbabacbaccbcbccaaadaadcadccdcdbadbcdacdbcaabbadbbadadbbbddbcccdccddbdcdacccabbbaddaadddaadcbcdadbccbdbcacdbcbdbbbddcbccbbbdabcbccabccaacaaabaccabcbdbdacddddccccaadccbcadbcbbcadaaabcbdbacacdbdabdcbadbbcbcbccacddbdbbbdbcccdbbcddaccabcaacddcacadadcabadcbabcdcdbabdbdadbdcacaadccabddbbbcbcbccbabdadbccdcabbadcddabacbdadaacabdadcbaccacbdcabdbccdbacabcbccdbddcdaccddddbaadddcbddcdbcadabacbccdbbdbddddddbcdbbdbdbdaaccaabacdcacdddcadbdcbcddbddcdbcbacaadabbccdacdcbbddbdbddbbddccbdbdaddaabdcdcdbcadcacccadcaacbccccabaccabadddaacdccdbabbbbcdacbdbcabcacccccdabcdacddbcdbabbacdcbbbcbabacbccadddbddbaabcddbbdabdcbbcaacdabbddbababccbdaadcbbcaadbdcaabdcbcddaaddcddcdbabbbddccaddccbdbccdaaccababbadddbbdcaaddbdbdbdcdbcccbabdabdbddcddabdbccddcaaccaadbdcdadbaacaabaaccadaabbbdaddcacddccbccdacaabcbdcddbdbbbabbcdcbdababcbacabbddddaaaccbcdddcbcdbbdbdcccadcbdababddbbabbcddbddddbabcdcadcdccccdaccbacbdadcacadabacccdaaadccaadbdabdbabacabbcccbdddacdcabadaadadcacdbcdadaaaccdacdccddbdbbcbbcdcccdaaababacaaacbcbbbcbdbabbabacacddbaaccaacbdccbbbddaacdaaabadbadbabaabcccacabaacbbbbbbaacddaccbbddcddcbaddccdacbaaabcccbcadcccaaabdddadbbaacbccddddabbbaaabbabdcaabddccdacaaddbbbdcdcbbcbbadcdacbdbbaabdcadddadcacdccaccbdaccabbbcbaabcbbcbbcacbaabdcabdcbcbbcabadadddaadccaadcbbaaacdcbdbdcaddbbbbadcdcadcbdcdcacbccadbccbbabadcbadadccadadbcccadbabcddaccdabadabacdbbacdbbdadacaabcbabbaaabccdadbbaaabccabcaaddaabcbaacdbacbbbbbbbbddacadbadcbbcbabdabdcbddbaaddcaddddcbabbdcacccaacaacbccbccbbccbacdcdbbccbbaaddcadbaaacbcbdabcccbbbdcbbbddbcabbdaadadcabbcbadbaaccbbadbcbbdbdcdbdcadbcacbdabcbbddccccbdcdabcbbdabacacacaccbaccbabcdbddcadcbcddcaadbdbdccacababcaacadddabaccacaadadbabbadabacbabccaacddbddccbbcdcdbdcddaabdaadccbcabbdbbcdbccabddacadbdaccddabcccdddaaddbbcdccacdaaddbcbcadacaabdccbacbcdcaacdbcddbacbccbbcaccaddbaadaccaddbbddbcbadcdbabadbcacbbdbcdcbbcbddcbdacdacdcaacbaddabddcddbbacadbabdcacdcbcbcbabcaacdabdadababccadcdaacbacbbdbcabbbcdacbccdbcaabbdcddddadaccdddabdbdcaadabcbcdbdbdbdaaacbaacacbdbdbdbaabbbcbbdacccdbdabaababaccdcdcbbcdcbabdbbcbbcbdadababcabaddbabbdddcbccaaaadabccbdbacadddddbdcdabdaabbdbcadcbddddabacabbdadddddcbbbacdcdcbdbcdadcdbddcbcccabadcbcbbdcdbbbdcbacccbbbbddacaadbacdacabadabdabaaaacbddacdccabccdbccacbdacdccabdbccdacdbcadbccdaaadbdadbabccddcadbcccbbbbcbccbccdaaabbcabaabdbabcbbcabcdadccbbcaccdbdaadacabcdbaddbcbdadbdcbaadaccccdddccbcacbdcdaaadaaabbcddccdbbdacbbaacabbabdbbbccdbddabadabcacdbdccccbadcdadbaccdaabbbaddcbbddddbaddacaccbacdbdbacdbdbacabaaccccccadbaabadabdbbbaabdcabacadccbabcddcdcbdbdabacacabcddadbbbbdcbbbdaabcacbadbbccbccdabdabacbbcdbdccdbbabcadacdcaacdbcccdadccabcbccbacdadacddccbcacbabcbcbacbbcabdcdaacdbbdbccaccadadbccdacacacabccdbbbcaccdcccabbabacdaddddcbcdbdcdadcdbacbbaccbccaadccccaacacaddbaacdcbabbaacbabcbacdbcbadabadcaadcacdadcbccbacbcaaacacbcdabaacdbdccbdaddcdcbcdabdbbbadccbccccdababbbbbaccacacaaaddbdcbbaabcabbaddaabcbdccadccbbacabbbadaabbabbdbbbbcddbabccbbdcbbbabbacbdaadddccabcbbcdadccadabccbbdacadddbaccbbacadbbdacbbabaabbadccdbbbaaadbbbbcbdddbbddacbacdbdadaccdcddabaabacaacdcccdbbacccdbbaacdbdcaacdadacbbddcbaaacdadabbdadbaaaadacdadccbddaccbcbdcbbdcddcacccbdddbdccbbadcbababcbddddbccbddabdadbdbacdccdaacaccdabcadabaabcbbdabddcaccbabaadabacdadcdbdcbdabbcacbdbababcbbcdcaddbcbbcacbadacacbcccacdddabcbcacadcaccdbdcbadcacbcbabaabcaadbaabddcababaddbcdcdbcacccbdbbbbacabdacabdcbbabbacdabdbcbaddccadbaddbbcbdbaddbcbddcccbcbadacccabcdcdccddcacbbaacbdcddddcdbdabdabaabdcccbccdadbdabdbddbcbbacdcdbcabdbabaccdccaccbbbcadaaddbbabddddaccaadddcddaaddcbabddccddccaacdbccadacabdcbacacdadabbbadddacbabccbcbccbccbbbbcdabdaababaacbabdcdcabcddcabcbccbdcacacddcdbdaddbaabcbaaddbacaabdaacaccaccbcacdcdcdbbbcaacaaddacbdcaacdabacbdccacadaaccccabacbacacbccdaacaddcbdacbacabadccddacadacaaaccdddcccadbbbdcadbcccbbcbcbaadbcccaccacbbdabaddadaccccdabdbdaabbbbccaadabdbdacadaddbccdabbccaacbdbcadabbabadacacdadcbadcbbabbccaaacabdcbdbbbdababdaadaccabcbaaacddaddcaadabaccdccaabbdadccbcbcbddddcbabdbcacaccaaaccbcbcbdadacacbccabcbacabdaabadbcdddddbdcbdbabdddcdabdcaaacbdaddcbabdbdcbbaddbdcbcaacbbcacdddddabdcacdcacababddcbccdabcbcbdbbcdcbdccacbcbbacbcdbbccabdbbcaabcbbdabcadccdbabcdccacabacbdcbddaddadbabbacbbbacabccadcacdadcbaacbaabdabcbdcddddccdabcaabdcaabcdacbcdbdbbaaacdadccdbccdbadbdabcccdabbcdaacaddbcdabccacdbabacbbbcccaacdbddccdadcabdbabbabaadacccacbaaabdabacababbcdcbbacaabaabbbaddbaacaccbcdbadddbcadbcdacaadcaaaccadcdddbdabbcbacacdcdbcabdacbdbbbabacdbdcaddbdacbccaaccdbdddaaddcbcabacbcbbdddcacccbaadddadddccaadbbbcdaddddadcbcdcadaaabbbacadcbddaaadcdadbacbacbacccaaccdbdbdcdbcacbcbbacabbacacbdbcdcaadbccabcdccbaabaaaaccaacdbbabddddabaddabdbcacbabacccccddacbabdaadcccbbdacaccaccdbcacabacbabbdcccccadbbabcacbdddacabbadaaddddcaacacadbabaaccbbabcbbddddaadadacdbdcdccdaddccabaaabcdbbcadbddabaacbdaadddadaadddaabdaabdacbbdcdcbaddaadbbabdaaaccbccbabdcdaccbccabdadabdadcabbacdccbacddabcaadcddccacddddbdbabbdbaacabdcadcddcbdcdbadcabaccdbacacbadbabdbcbcababdbcaacaadbabdccbccaaabbdabdbcabdcddddcccbbbbdbcbcbcaaaaddbaccacadbbdbaacbddddabdbdbccbcdcacbbdabbddadcabcacdcaccabcbddabcccccadcbdcbababcccadbabdcdadbdbbdcdddcacccdccdbbddccbbdbdbcbdcddccccbbdbcabacddbabcaaccbdaaddccbcbbabcaadacabdbdcbadccbadadbbcabbdaccccddcccccbdbbabddcacbbcbdcabbdcadbbbdddacaaddacccbbddbaabadbaddbdabacadadcdbcddacbacdcadabbbbadaddbcbbcbdbdbcdabcbacbbdcddadcdddabccdcdadcdbbdcaccbcdbdcbabdaabcadbadcdcbbdcbdabbcaccaaadccbdddaadbcbcabbbcadbccddaaddbbadadbadacdabccadabccacbbdbccbbbcccaaabbacdbcccacbbababaddcacabaddbabbbabaadbaddcdadbbcdbdbbbbacbbddbdccdcacbdbabaabcdbaaddccaaadcbddcbabcacacccbcaabdcaadacddbaccbbdcabcbddcdbddbbacbdbcdacacbcbaaddddbdacbdbbabdcabcacbacccabdbdcadbbcacaaaaacbabaadbbdcadbbcdabcadaabcddbdbbcbcbcdcadcbbaaaadadacbccacbdbbdadbcdbadbabaddadcbdcdbbbacbcbdcbbdadcbcdacccbaadadddcdabbacbdcadbcdcddbbbdadbacccbcbcccbadddbddbadbbacacddcabcdccadbacbacbbbbcddcabcbdadbdcccbdbadbaacbaacdbdbbabbbbaababcdbdadcccacccaccaabddacdcbaacbcabcadabdbcbaddacbdabdccaddbacddcadabdbccadbabbccdbbbcbaabbcbbccccbddababdadadccdccacccaababcbcdaaacdbcdcdaddcccddbacacacbadcacbbaacddcaaccbcdcbdbaabdbdccacbcaaccdabbabddbacbdaabadbbdcadadbdbdbbbcadabaccadacbaccdbbaabdcccddccdcaddacabcdbdcbcdddbdcbcbdcbcaaabaaaabdacdccccdddaacdbbdadccaaadddcdbbaacbdddaabaacccbbaccbcbabddcaaacaddddaacbbbadcaddbdaccdabbdcbccbbbaadacbdcdddabbcaacdcdccdaabcaccbbbddcdddcabcddcaaaadabddabdcbccbccccdcadadcbcddcabbccbddbdddacdcccbcaabaccabdcaddbcdadaacaaddbbcbbbbcaadbcbaddcddabcadbcacabbdbbddaccbdbbcabbdddddccaabcaccacbbcbadcdabcbadcabdacbaccdbdcbabcaaaabbadbacadbccdccbddbdcbadcdccdcdbacdbaadbacddaccbdabbbdadacaadacdbacddccabbbcaacddddbbcbdbcbaddaadbabcadcccabdcabccdadcccacbbcdbaddddacbccdccddccaadbdbcdcbcdbcabadcdacbcbbcbadabbbddaabacdcdbdaccdbdbddadcddcacbcbdcaddbbdaacabdcbcdaadbcbdcbdadacbacbbdcadbacbbcbcaaccdaaadaaacbdbdccdaadcbabaccdcbacabadbdacdccbbcbabddadcbccbadbcabacacbacabccaabdddcbdcaacacdadcccbcabacaaaadbcbadacbdddacccabacaabddacadccccabdbccbaadcadaadaaaccdaacadbdaccbdcbacbbabcdccabacdbddcdbbbbcbbababcabaabcdccbccbcccacaddaacaccccdacaccbddaadbcbacaadddbcbcddccbcaabbacaacbdbcbcbbbacddbbcbbcddacacbacbcabbcdababdadccbacabbbaaacccaabacbdbdccaccacddbdbbaabdabdbcdaaabdbddbdcadcdccdbbdbcbdbabdabdbcadadddccaccdcbbacdbdcbdaadacaccacdacadacabadbcdddacbdcccdbacdbdbcddddcdddbcdbcccdcadacdcacddcbabdbccbaaabbadbdcbdbadbbddbdcdbdabbbdbbcbbdacbccccddbbcabcdcbdaacccaadbdabdbdbcdbdbcdcbacbabbcadacccabcccdadccbbddbccdddcbccdcbcbcbbabacabaddddaaddddbadcbcdabbadddbddcabadcdcadcddcacdcdbbdbcacbacddcaadddadbdaabdaaacaabbcabaaadcdddcbbdabaddddbdcddaacababdcddcbbabacbdcaccaccacadccacacdcdbddcabacdbbbdaabadcacddabcbbbaccbabaaabbacbdaccdcbacaddbadaddcddccbddabaaaadcadcaacbdabacdbcacaaacdbcddbdbdaddbbbdbcdacdaaccaabbdcdabbabacdacddbcddbccccddbddddbddbaaadbcbaacdcbdbbaaaaaddccdbabacaaabadaadbccaccdbdbdbbdacbbacababccbcdbbbaabcdbcddbcdcbccbcdacdbbdddcbacbcacccadbdccadadcccddaddcabcdccadcadddbddddbaadbdbbbaadccabbdbaaaccddaccdabccddbdcddbdaddccdcaccacacdacbdacccabccabdcadcbaddbcaabdcbaaaccdbddcbdaacacdbbdaaadabbdbbbaddcbdcbaabbacdabdcbcdcacaacabcdababacdcdaddcccbbabdaaccbddadcadbabbaccbddcdcbcccaddabbcaacbabddadabdacbdcdadcbbaabddaccadadccabdbcbbbaacbabcdaaacddcabcbcadbcccaabdbcaadacdbaabdcbabbcbaddbbdaabccdbdcdccbcabbbbbdaabbdcdbccaacdabbdcdadabddabbbdbbaadddbbbbacbbddadcabaabddbadabbddcbbbccbdcddcadccdbbdadbbadbcbcccdaacaaddbacddcbacbcbaccadabadadcdbababaacadcadbdddaaacbaadadbcddacdaddcbdddbcacccbbccacdbcbadcdcdaadcdcdacdcacbaadabaddabdcbacadbacccddcadabcbbdbddcaaddbddbbcdcaadabddacbdaabacdbaacadccbbdcabdbbbbddddbaccdcbdccdddbdbaaaadabbaabbbadaadadaadadcddccaaabcbcaacccbabcadadbcaadbacababbdcbdccaccbcccddcdadcdaccbbdaabbcdddccacdbbbcdbdccdddbacdabcadbdcbbaccabdcdaaadbccaadcdbdbbaababdddcbdcabcdaccbcccabdababdaddccaaddcbdacacaaccbbadddbbbabddcccacacddcbbcaaccbadabbddcbbdcbdbabdcdcdabccbcbcccaacdaddcbdbcdddaabadcccbcbdacbcbdbabaadbbcaacdbdbbbcaccadbbcbdaabbabbdacbddbbdccdbaaacaaaadbabbccbddcdcbbdacbdacbdbacdabbabbaaaaacbddbdbddccbabaadaccababcdcadbdadddbbcaabcdadbdbcaacadacacbbcdabaaabdccbabccddacdbcdddddaaadbdacbbabcacccaabcdbbddadbddadabdcaaddcacddddaacdbaadcbccbbcbcddbcccdadbcdaddccddadbcdaaadcaadcdabaabbdaddcdcddcaabcbcccbdbbbaccdbacdacadaacdcbbdadbbdbbadcaccdddbabaabbbddadabddbadaadbbcdabccdabcacbbbbacbacdbbccbcdacdcccccacabcbacabbbccbbbcbcbbcaacbbdaaabdbcccdaabcdbbbdadacacaaccaddcdacbabdbcccaddccdbaccabdadcadbcacbbcadcbbbabdadacbcdaacdacdddcabbababddadbdadddccbcaddadbdcabcabacbdadcdaabaaacdabaccdabcccddbbadcadbddbdcdaaacabcddbaccbccabbacccbaadddabbcdcdcbbaddbadaabdbbbbaabadaccccdcbadadbbbcbacdaaaaaaacacabcccbccacbbbdddaadadabcaccdcbbcabcbccdccbbadacbbaadbaabbcbdbbacbbacabcaddddccbdcbdcabaacdaccdadaddccaacadacddadacdadaaaabaacccadaadcacbddcbabacacdadadccbaaacccbcbbdbcbdccccbcccbcdcdddbccaacccaccbabbabdabbdaabbbacbcccdcbccabbbbbbacbdabddccbddbcddbdabcccddcacbddbcbdcddbcbdddbdddbbaaaccacaddcbcdaaadccbbbcdaaabcddbdccbddcdcbbcbaadbbabbbaacdacababdbadddaabadabdadaabaabcbaccbbbbcdbadadcabbbcabaaaaabdbcbdbcaadaadabbcaacdabcdbccaaddcbcdcadcddbcddbabbbccabbdbdabcaaccacadcccbbddabcddaabaabadaddabaadddabdcbbdcdadcbbdcbbacdadcbcaabadcdcdddbdbabbbbabbbbabcabbccdcdaccdbdbaccabaccdccccddbdaaaaccbdcdccadacdddabdabbcbdacbbaacdddbacbbabbbabaacbbabddccabdcbdbdadacbbbaccacabcaccdaccdccbbacabbbaabccacbdabbbdbdddbbbdccacbddababbbaddcbdcabbccdccdaacbdabcacbaccbacbcacdcbcaaddbaccbabacbcaddddcbcaacbbdcdddbcdcdabcadcadcaacdbaaaacbbbbdcdcaabbbadcacdbcbcddabdcbbcacbbdaaabacbacddccdbdacdcddddaacbcbabdccbcbdddcadaaacbbacaadabbbcacadabdabdbbbacbbcbcaaadadcdbccaccacdbabcddabdbcddddbbcaccddcbababcadbcdbccccabcaddddcddbbcabccaaaaccbbaababbbcdadaddaddaaaaabadbbdbdaabbaabcbcccaacdadaaacbbbcdadbdccbcabddbbdddabcbddbcadacbaaddaacacbbaacdbcbbbcbbbbbdaddabacadcbbbdbdcdaabdadabdbacaaaaccaadbabaddbacbcccacdddccacabadaccabdaacdbadbadddabdcabbdbcbdaacacadababaccacccbdabbddabdacdabdacdadcdddccdbbbbdbaacacdcabbbcdbbbddaacdbbddbbdacccdbabcbdbaaaadcdabbcacacacdcccbdcdbbbbddabbcaddbbcccbcccdbcbbdcadcdaddbaacdddaddcdcbdaadabdaccbcccacaabbaadbbbbbdbacdccdcbbbbbbbbaaaccaccbabbbbcacbddcdccabcaaabaadaabaaadcdabaccacdbabbabbaacbcadbdcaddbbdccbcbbdcacdbbbdacaaacdaaddadbbbcbcdadbccddabcdbabccbcaabdbccdccdababcbaabccacdadccccddadcbdddabdcbcbddadcbcadcdbcbadcbbcaddddccdcbddcbbbaadaabdacadacababbdbcbdcdbdaadbddbdcabbdcddbbddbbaadbacdbcddddcbbabccabcacacababcbcdcdcddadaabdcaabbbacbcccbddccdcdcababddcdaddbdaacbcaccadacbcdadcdabcddbcccbabbcbacdbccddbdbaabaabdcdbdcbbbbdbdabbccaccbaccdbadccbdacaddacddbaccdbbdababaccddabaccaadccbccccaadbcbcdaacadccaadcdadbcbaaadccbcccabccabcbcdbbcccdcdabbacddbdbbabdcacdbbbbdbcdbabccddddcaadadbbbbadcacdacdadcdbcadaddcbddadaadcaacdddaccdbdbcabdcadbdcdaadcccdcdbcdddcbddadaabaccbcacadccbbbbdbcbbaddcdbcbcadcacdcdaccccddbdbbaddccadbdddbcabddabdccdddadbaaabbaacbcaabbbdddbbcacbcaccabacdaaddbbccbacbadadaddbacddbdacabbaadbdadcdcbcbbbcaddbbcaaccccbbdadaadabbacadabdbddbccadbadddbcbbdbcbbcccdbaabcaabbdcbcccdbbdabdbaabbbadbddcadabddbdbdbabacdaabbdccdcacaccabcdbdcbabadcbdcabddbbcbcbcbdabcdaccdcbcabaddcddbacbacddbaacdaabdbccadccbddddaabdcdbbbdbcaddccaaacaabdbcadaacccccacabaababbbaaacdaddcdbbcaabdaadadddadcabacdaaadcbbbaddcccdaabaacccaaadcdbaacbcccabdbbdbdbdabdaccbbcbddabbdabcbdbdbacbdadcccbcacdadaacacbcaadcdaacaabccccbcbddbbadcbbcbacdbcdabaccacadaadcdbdcddbacdababcddbccdaaaaccaccbbadaabddcbccaadcaaaadcbcaaabccbcadbdabccbcddcacccdcbadabbaddbbdddabbaddcbbddaddcacaabcdbaccaabddabbdcbddbccadcbaaddcaccddabbdaccaacccbcdabcdaccdaadaddcdbbcbcbaaaabccbddcadcccdccbccbaabddacaddacaadbcadaaddabcdabdaabdbdbbaaddbdccaacbbacdacbcdbacadcabbacbbdbbdcbaccdacbccabdacbabddadabdaacbdacabcdabdccddbcacabcacadbbbaddbdbaabaddaaadccdcbcbabcbaadbdddacaaaabadcbcaccaacaadaddccabbdbabcbcadacbddaddccbadacdcbacdbacadddbddcadaaccddbadadabacaadcdbcbdabdcbcdcaddddaaddbadcadabadbcaacabbbdaaddacaccadbbadadccbdbdbabacdaacaabddddbaaddbcaacaccbaabcbbadbdaccddadbacbadbababacdcdcabacddaccccacdaaccddbabaccbbbbdcabddccbcaabbdaacbbaadbccccdcbddcabdbdccdcdbdcbccbbadccaaaddccccacaabbddcabbbdadbdddddbbccdccbabbcbbbbadaaaabcbdabddbbdddccdbaaabcbbbcdbdbbbcaaadcaddbbbdccdcbacbcdbaabcdcdccbabddcaaadcdbddcabcccadbcdaacaabcabbbabadbcddabcbcbabbdbcacdaaacbcabdcacbccadaaccaaaaccbadbadcadccdcddddaaacbcdaaccbbcbdbdbcadbdbadccaaddccbccaabadaacdabcaadbcadbacbdddbaccadbbcccbbdcabbadcbdbdcdadaddbcbaabddcddcbbcbcbcdaabbbbcbaacbaadbadcbdcbdacddbaacabcdccaaaabcdcaabacabcdbbaaadabcbacbbaaccddcdabdcdcccbccabdcdacbcaadccaddccaadaabaadcddbcddbaacbbcbdcccaacdaadccccdcdbbcccadcdaabbbbabcddbabcbcdddcdabbdaaacbbbacbbaaabdaddcadbddbdbbbcaaccdbadcbabddaccbdbdccbccbbcdbadcdaadaccdbbdabdabacabcdbacddabacabdbdccbadbcbaabbacccbbccdcbabadcddadcdcdcbabbcaccaddcbacacbdbccccbbcddaaaaabcdcbcbcdbaaccababacaabacbbcabdbdbbbacbabbbddadddcacbbbcbddadabbccbacbbbaacadaabdcdbdcccaadbddabaccbbadabcadcaacddbcbbdabaadccbaacaadccaddadcddbccabccbbcbacbabddabbabcdbcabaccdaddccddcbcbbbabbbdcabdbcbcdbbabadabbadddcdddbdaccadccbadacdcaddabcadbdcadacbccccccbbbacbcccbcadbdcdcaadaacbbaccbdcbdcdaddcbdbcbbddcddcacadcabcabbbdbdacdbaacbddaabbbbccbbadbbbcaabbabcdbdadcabdbcdaadadacdddbadaacdcddabbbdbdcbcdacaabdbdacddbacdccaabdacbbdabdacccaddadccbaccbdcabaaddadccdccdddddcbaadabdacabaccaabcdacddbdbdccdaacdcccbddbccadcbbadabbcbccabddcabcaabcbbdccaccddadabdccaabdbbdccaabcacadccaccccadacabcaababaddcddbcddccdbadbccdbdbbbdbcddbbcdabacdbbccacdaadbaddcacabbbcacadaaadcacabbcababaddacdbdadbdabdcaddaacdcbbaaabcbdcbdcdbacabbadbddbaabdddbddcbbabccaacbcbabccccbacaaaabadddddccbdacdcbbbdaabdabcbbbddaccabcdadbcbdddbaccabbababdbcaddacccbccdababcadcdaadbabaabbccdbdbbbdadbcbbbbabcaaddbddaabbccbcabbbdcabbadacbcabbccdaaaadbbcbbdbdbccabdddbcbdbabaabadbabbbdbcbccdddccbcdddccbcbbddddabbaddbccccccbccbcdbbacaacabdcbaaabcddabdbcbddbbdadbdaaaadbaaccadbbdbbccaacdbdddcdcdcdcbbcbbacbababdadcbacddabdbabbcbabddbbdccdccdadabccddbacdbcdabacadbcabaacaadabacaabbccbadbdccbacdcbadbdcdbbcacccbdccdcacbacadbdaaabdcbdadaccacaabcaacbdcdbacbabacdcbabadadaabdacaccdadbccbdbdbbdcbcacccacbccddbaacacbbbdccaadcbbddabdabdaccdbbacbabacdcccccdbabbbaaadbbcbdabcdadccabcddaccacabbbdcabdaacccdbbdacaabbcadadcbdbcddcddcaccadbacdccdbbcabbbcddbaaabcacdcbddacddddcaccdbbaadbcdbbbcddbbbabdaabdacbabbbdcdcddbdabdacaabdabbbdacaaacbcaddacbddccaabbcacadabbdaddbbdaadadabcaaaabddadcadbcbaabdbdadbbccdaabacbaacbbdbbabdadcaddaccacddabadaabbbcdbaddcbadbabbaaaacbdccdbdbddaadbcbadaadbcbcccbcbaabadccddbcadddbabbdabcadabcabaaabaaabaaccbcbbbdccdbcbaaabadbdddbaaabdababcbbabdaaacabccacdadbdbbdbdbabcabbabbccbaaabbaabccdbcaadbabbddddcbbcadbcdbcdabbbaddaadcdadbddabacdcdbbdcbcadcddbccbadbcdbdbddcdbabcdabacacbcbbcbbccccddacdaabbaadababcaaaadabaacaaadcdbbcbcbcccdcbbcadbcbcdbbbdbccbaaaccbdabbcbccabaacaadbabccaacadddddbdccbbdabcabcacbbabaacadcdbbcddcacadddcbacdaaddabdcdabbbababbaabadddacabdbddcdcaccddbcdabadaadabbddbdddddaabaddadccbbcdaccdaabbacaadbbcbbabdccbdacccabbaaabacaacbaabdaccacccbddbccbacabcadabdbbcaaddbabacbcaaaacccadccadcbcdcdccdcbbdbcbbcacdbbabbacbbadacabbdaabbadbabbbbacbabdbcaabbbbcabbbdaaddaaaacccaccbabdaaaadaaababcdaacbacbbcadbdcbdaacdcccbddaacbabcdccdbdcccddacddbacbdddacdcaccdbacbaacabbdaadddddadaabbbddcdcaccbadccddaccccdcbbdbacbddccdadcbbadbbbbbbcccbbbdddcbcdcdaccdbbddacaddacacbcdbacbccbaacaabacaccbaddacaccbbbbbdadbddcbaadbcbadbcbbcaccadcbcabddbacdbbdabcaabddcdcdaababdbccdacacbcdddcccddcddadcdbadcabccbaabdaadacacdabddaccbdadacdcbccacacddcdaacadacaaabbaaabaaadaccbcdbaccacacabadabccdbddcdbcadcbdaaadacddcaccbabaddcabcbcbabdabcdcbbbaabbacbccabbabdaacdcbaaddbaaacbbaccccbbbacabbbccbabdcacdddddbdabccbbcbdcbddaccdaaaacdcddcdadbcdadcaadabdadacdbddbdbbbcddbbaabbabdcabdaccabadccadddabdadacbabcdbdaddacaddadaabcbdbbcbbdaadabdbdaadddacabdbbadaabbaaddaccdcadcdcabcbbaabaabbdadaddddbccbdcccbcbbabcbbaaaadbcadcbaacbbbaadabcdccacadbaaccaaacacacbdacdbbbddcddbdabbacdabcbcccaaaacddbbcabdaaaadcacdddbabbadcbdaaabaabcaadacdcdcbbaadabdaaadaaddabcbbbabdcadbaaddbbdcbccacbdbcbbddaacdabbcdacddbabddbdaccbcadbbadcadabaabadbbbcdbdaadacbcbbcdccabcdccdcdcacabccbddcabdabcccbdbbbdbcabbaadbbcbdaccdadcccabbbabbbaaaabdaacbbadabaabaaaadcbdbbcabdcddbbcabccdbcbdccbbbbabcdbbdbddcdadcaaabdbaddbdadbaaadbcabbdcddcbddcaadabbabaacddcaaccdccbccdcaababacadacabbbcabbbacbabdcbbcabaadcccbaccdbccbccaaddadaacabbacdcbbcbccbbabdcbbbdacbbdcaaabdaaabbdbcababacccbadbcbccdcccbdcaababdcbadbdcbccdbdababdcdbcccabdddddbdcacccacadcbdaababddbbddbdbcbdbcbaccbacbacdddaddadbabddaaaacdcbcddadcabaddbccdabadddbdbdbabdccadbacdccdcaadbdcccacbaccbbadbdbaaddcdbabcccaabcdbacacdbcaadcacabbdcacbacddbbbccbadcbaabdabdcaaadababccbbcaddacddcccacbababddbbcdaababbbacaadccabadcdcccbbacccababaaaccacdacbbcbcdcbaadcaabcaacdddcdccccabaaacdcdccddaacdabddcbdbabacbaddacddabcbddaadaacacaccdccacdcadbaaccaaaddbcccbaccdbcdabddabbadbdddaadadbddcadcabdbabaccbbccbdbddabadcbbdaabbacbddaddcaaababaaccdbcaacdddbacbabdbcadabbaadddabaaadaaccadcbcdaadaacddcacdcaccbbccdbcacbdacccccbccdcaaccabcbabdadcbddbaaabdacbbbcdddbdcdddbddcaacbddcbaddbcddbadbccabcabbbcabdcadcadabdbccdcabbabdcadcbaaacaabaddacbccadddacdcbcbdbdadadaadacbcdcccbdcccddcccaacadaacbbcaadbcdddcdcbaabbbabcbadbcbaddadcbccadbbcbdcbdaacbdaaadcaabcaaadabdbbaabbcbbaaccadabbbcaacbaacdbbacabddabcddabcdbdccadabacbcadddaccbbbddccadbdcdabbaadaaddbacbcadaaadaadbdbbbabbdaabbbbaabdababcccbaddcacabbcbadabcbdcdbcccdbdaaddbbbaadcdbddcdcaacaccadabdcaaccacdcacdddbaddbdcaabdcbcbdbacdcabdabdbbdbadacdaaddddcacdaddbdbdcbaadcbdccdcdcacdadccdcbcddbcaaccbaacbbaabcdaddadaaddcbbcabddbdaccdcaacccccaacabcbdbadccbcdbcccdacbccccacaccbcdaadddaddbbbbcdaddbdbbcdaabbbbbdccddaaccccadddcbdcdcccacaaacbdddcacaaaadbaabaccaadcbdaaabbaddadabbacbdcbcdcddccdbbaacaabdddadabcddcacadccccaadbadacbbaadccacbcccccbdaadaddcdabdacabacbddbccbcdddbbcabddadcdcdccbadabaaccdadcabddddcabccddabdccadaacdabcabdcaacadccabdacdbccadddbcdbcdbcccdcaccaddbaaabaacbadaabcccadaacabdabcdcdbddccadbacdcaabbcdbcbabccaaadabdaaaaddaabdcbcaacdccbaabbbbcdcdaddddbacabaabadddbdaadddabccdcdcabcaaadadbddcbcddbcdacacbcdadabdaabdacabcdadabcaabbdccdbbbcbdcbcbbdbcddbbcbddddcabdccdbccaadcbdabdacdcdcbcbdbccbdbbbadacdadacbbbcbdcbcbabababcdaaacadcbcbcddbadaabdddbdccddbccdddbdcdbaadadaacdacaaacdaadcbcdbcbdadbcbbcbaddaddcaaccbabadbbdadccccbadbbddabddaddbbabbaadccdbdacaabcbabacbcbcbbcaaaaccbbcabaabcbbdccacbbdbabbacbbbbaabbcbadacdaadcbbbaabdddacacacddaaabbdadacbdabbdbadbcbacbabdcbcadacdabdaaabddbadcaabadddbcbbccaaacddbdcbcdabaccbccdaaddccacabdbccadabcccdcdaadaaaacabbdaaaabadadbdaaacabcaaaaacbccadcdcaccdaaccadcdaacaadcbaddababcdcdbaaddddacddcddddbcddbdcccaccdbabbdcdacbccddacdcccacadbdbadadabaddbcccdddbdacbcabbbccdcabbcccadbcadbbaccbdbddadbbccbbadcbbbdbbbdddcdccaacadbccaaaaaaddababcbacaddcabbdcabbcbbacdcbaabcbddddccdbcddcaddabccbbacabaacbacbadacadcdaddccbdcabbbadcbacdbdcabbbbaacbcdaacdaadbadcacbdbbddbadbcbbdccadadbdbdbbddcabdbdcbdabdbdacdaacbbccbbccadbdcacbbcabbbdcdadbcdcbddbadabbdaddcdabdaaacccaabbadaadcccdcbdabaccbddcbbccabdadabbdcdabaccacacaadcbdbcdbbadaacaacacaabcbaccdccddbcdcdbbadabadccacddcccabacaacadcaaaaacdacdcbaabdabccbbbbcbcabbabcbaabcbbccabcbaddccbbabdbdabbdabbbbbdcddacbbbcbcabadcccddaddcadddcadcbdadcaacdcacbccaadabcaadbdddbcddccaaaacdddbccbcdaacbcdaccbdabbadcddccacbbbddcdcbaadccacabacadcbadddcdddcddcbcbcaaacbbddbcaadcdbbdcacbdadccdcaaabdaaacbadcdcadcaaabcbcacdbaadadcacbccdddbacdbbdbdcbbbdcdadabdabbbdadcadcaccbdadddccadbbabcadcbcdbcabcdbbcadbdbdabcccbccbcbadcadaacbbcccbcdccbcbcbbbdbdbbdacabbccbaabccbddcabbcddbadcdbacccdcadadacdcbbbcddddcddaddddccddbdaacacccccdbccabadadadbdcaabbbdacadadddcbaddccccdddddabbdcdbbcabaacddcddbbbaabadbadbcadaacccdaabbdccdcaaccddccbadbaccabacaddbdbcabcbddddbbacbdcbacabdcacaabbaacdabdadacddabccadcbdadaadbadcdacbcbaaddddcdbabacdbcdbccacdaddcbcddbbadcacaccddacddaacbdcabcbbbdcbcdbdcbcdabbdaadcbcacccddbccdcaabaabcdcacdacbbacdacccbcaadacdccdabbbccbccccccbbccbcdbdbcdddddaaabdbcbadaaaadcadcacdadabdbbdccccdccdbbcbabdadaadbbaccadccdbbabcbcddccaaccdaacaccccccddbdbccbaaacdcbbbccaadcadcbbabcccacadcadcdbddcdbccbcdcccabaddcdcacdddbabdccbdbcacaaacbadaadabbdcacbcbaadaadbaabbdbbacbbbdccadaddadacbdbabdabbababaccbbddaddcbbabddacdcdbbaadcdcbcdbcbadbddabcbccbdaccdaddaaabddbaaaaaaacdabdcdbcbaabbdbbbcabaaadbdddcadadaabdacabdacacaababdcdcdacbdccccdbacbddcdbaadbdccdcabaccaabcdbdbcccabbadadbaacadabcbdbdacabcdaaccdadbbcdaaadbcbabadbddbabcbbcababbaddcacaccbacdbaaaddcddbcdcadcbcbadabddaacccbaacbaaaacccaaabcccccbabdcdccbcdabdadacdaddddabcaaddbaadddcddadbdaadcbdcacdbbaabadcdbacdccdcacbaabdacadadaacdaccbabdabbbaacccdbdacdcbddbbadcccbdabbbdccdbbbdadcbdbaddbccaabbdbccbdbdbddccbdaaadcdddddadcdcddcddbbdbacbbdabcacadcbaccbdbbdcbcbacdcdacccbbccbacbadaaaadabbdaaddcdccabdaadabbbbcdaccdddbbcdabadcadcbbbcdbcabcdbcddaacaddcadcddddcabbdbbddacaaadddabddbdcbadcacacacadddccddbaaadbbcdddbaacadaadccbcaabcbabcbabaddbadcbbbcddaccbaaacddcbcdcccccdccabbcccbdcbaacacddddcccbdbdcbcaabcdaacbbdadcbabbbbcadacdadbbabacabbabddbdccbdacacabdcbcbccdadbadabacbacdbddbccdcddcabccddaacdacacdadbdcdbdaadcabcdddadddcadbbbaddcbbbddbbcaaccdabaaadababbbcaabbcbbbbcbbbcacbcaddbadcbabbacacbacdcddacbcdccbcdbbbbbdbbdccccbbccbcbbdbdcbdcbcdabcccbbcacbcabaaabdadababacabccbacbaaacdbcaddcadcdaccdccbbcdabcbcdcbaadcdabbaadcbbadbbdbdccbbcbccbddcddbbdbbcdbdadadbbdcabdadccdcacaddcdcbccabbdbbcdcddbdababdbccbcdbcbdaacadcdcdbdaabadaabbabcdbbdbdacdddbddcbabddabaddaacdcbcbbdcdbddddcdcbdaaccaaacbabcbbbdcccbbbaabaababdbbbcbccbabcbddacaccacdbccdcacbccdbcbbdaaadbddabadaccadcaaaaadddcdaadabaddcaddddacdbdcbbacbcbbadcbacbbcbaabbdbbcdcdabdadbbcbbbdccdcacdcbaaaabcacdbadbdbdcaddcbbaaadbccdadbdbcdddbaddaccbcaabbcddabaddbbbabbbdbbacccbabbaacdbddacdcbccaabddcaabdababbbcacdadadacbaaaacabcccaadcadddbaaaaadcbccddbcdbcbaaacaadbcdcddabbbaaacaaadbdacabcdcacddbccdccdadacaaaacaaaddbdababbcdbacdddbbdbbcbdddbcbaccdabadacadcbabdbababddabdddaabcdccccccbbabcdabbcdddacbabdbcccbbdbdaacccadcbccdcdcbccadddababbadbbadbcbbddacbcbdacabcacddccadaddadccbababbccbbcabccdacbaadddcaabbbbabacdcabbcccbbbdddbcacddbaaddbdbaadbcdabccbdbcaadcccbddbcaccbdbcdbcbbcaaabbccbadaabbcbaaaadbbdaaddbbddbdcbadaaacbabcddaacaaacdbadacbcabcddbbbabbcbdbadbdbbddbacddaacdadadaaabacccadbbdcbdbdddcddcbddccacdcbbccdcbaacbbdacccccaaabbdbdacabbcaacadaacdcacbdcaacdadcdadbbdbadbdcaaacadccccbbcbacdaddcdabbaccadbdbcbcbcadccaadacbadcadcdcabdaddcbbcdbbbcabdccabbadcdaabadcadcbcadcdcacacaaadabaccccabdaadcdacbbcbdbbbccdcdbcbdbbadadacabccdacabdabdbcbbbabdbcacaaacdabbaababbaadcacddcabaddabcdcacdbdaddbdacacdbbacbbbcdcbbdaccabcaddcbadcdadaaacdcabdbabccadcccdbabadaacdcaddbcbacabddaddbddddbbbcbbbbadacdaddaddbacdbbdbbddcadcdddcdcabdcacaaacabdaccdbcddadcadddbcdaadaddaccacbcdbabbbddbbdbbdcdcdcdbacddabbdbcdbdcdcdaddcdbadaccdaacacbccaacadabbdaabaaacbbdccbaadccdadacbcbcbbbbcadadbdbacccddbabcadcdacacadacabcabbbacdccdbbcdaadcaaadbddadbcabdcbbacdbabacbacacaaacbdcbdbbbdbcabdaababcddcccbbbdadcbbdcccdabdbababdacbdaabdcbbabcdcabaaabbcacbcdadaadbadbdcabacdddcacaaabaaaaaadcdadbbcccccbaacacdaadcaddadcbbbacabccaabdaabaddaacbadbdaccbcbdcddbdabcdddcbaccbbbbcbddacacbdddccbdaaabcaccbacbccbcaabdccbddbababbbcabdbbccbbaaadabadabcbcddcbabdbadcbcadbadbbaadcdbcadddbaccbcaddbadadcadaacccddacbddbcacbbaaabacccccddbdababddbdbbdacbdccdbdabcbbdbcddabaaabcccbcdabdcbbcdbadaddcadaaccdcabadddddadcabbdbccbadbdbbcddaabcbbdcbcdcabdabaabcdcabddddcaacadacdddbbadbcdacbadacddaddaabacacccaabbadbcbbbdbcbdbbccdddddcbcbbadcacdbabbaacbadbccabacbcdcdadcdababbbdcccbdddabdadbdabaadccbcaabddbdaaddabbacdbbbdcdacbcdaaaddbcbcababaadbcaabcddddbdcabcdabbcbddcdbdadacdadadcbbccccccbbddcddddcadabacaddaacadababbdbcaacadbdbbdbcaadadabbbccbbbdbbaaaaacbcdccdcdcbdaccacbdacaccddcbcbbaaaabcaabccacdcaacdbcdaabdbbdccaabbbbbcccddadcccdcacabbcccacacdacccccdaacacbccdddabddbdcabacbbdadcbaccaaacbbaccdddbdbbcaacdbadbddaadccbcbdcccdbdaabdaccdbccbbcbcaaabdbabcbdbcbdacdbbcccccdbadbbcbcbdaaccdcdcabbbcdadbcdbadddcddadccaacababccadbabadbbdbadddacdbdabddbcbacbbaabcbdccdccbbaacbcdcadaacdcdccdadcdbdcbdbbdadaaaddcbdababcdcddbccacddcdaaccbcabacbdbacdbcbacacaccbbbccadddcdcadcaadbbacccddbcddbdbcaadadbdcdaddcddddccaadbaddadcaddbcbccbabbbbbddddbbcbccbdbdacdbabcabaadacdaabbadddcabcdaccbadbacbacddcdcbadaadbcabbabaadccaaacbbbbdcaddcccdcbadcbbdbaccbacddcbdcacddaccbbddbbccdccdbcbbddccbdabcdcccdbbbcbdaaabccdcdaadbacbbcaadbbcbbdaaabdcdbdaddcabddabbdcbbaacdcbcdabaabaccbcbbadbdbaaaadcaabacadaadbccbbcddabbbbdddabccddccccccccbcddbdcabdaaabdcadbdcaacbccccbadcddaaabdcadabcbaaabcbbdbacabcccaaddccacadcadbcdaaadbbdcbbcdaaccbdccdcdcaaccbdcaaddbbbbbcbbcaaadddbcbadcddbcbcbcaacbbcadabccdbbdabbddbcccccbacbbbacbbcaccccbbabdaabddbdcababbbdcabdabbbdcdaddcbdbcacbdddcbdacabdabbcbcbcdcdcadbcdabcccdbacabcbacdababdacbabcacacadbdddcdbaddbadabbcdbbbcabbbadbbdbddabbbcbadccaccdbaaabddaaacacdaacacbbcdddacbabbaaacdaadbdcdacbdcdcdbbaaacdbaadcbdadabbaadbccaccdadddcbccbaadbcacabadadcbdcabccacdccccbcdbbbbabcaaadcccacdadcaadddbbbbdaaaaabdcccbdcdbbddcbbaaacbddaaddbcdcaacdccadababbaaaaabacdaacacbaadbdabcbbccbdddddbddadbbbddbccccdddccbaaddbadbdbcdbaaccbdbcbdbabadbaddbbbbaadddacdacdadcadacbddaabaaddbabadcabcbdcbcabbdbdaddabbcddadbcbbdcaabddaacacbaddcddbbbcabadbcccdbabccdadcbccddaabcdacdcbdadaccbacccccbbacbabcccabcdcbbccbdadcbcabccbcbccbbbcaabddddcadcdbacabacccbdddbcadadaaabdbabdcbdddddbbadbccdbbcaccacaaacabbcdaadaacacdcdbdcbccdcdaacbddcccdbdbcdbddbccaacabbbaadcddcdbbdcbabcdacccbdabdccbbbcddbddbadabaccbdbddaadaccdcbacadaacbaabaabadabcbcdadaacccbbbccaaaddddbcbbcbcdcaacbdccddabdaaddcdbdcadcbabcbabbabadbbadcacbbdacaddadcccabdaadadbaacabbccbcdabacdbaacacacaabcbcaabdbbddaabaacadbbaaaaacaddcbbbcbaacabddaacddcbbddacbbcdadcbbadddacccbbbdaadaacddbadbdbbbabbddccddabcdcdcaaddbbcdbabbbacaabcdbcdaccdddaabbacacccadbbcbabdbaaccdaabcaadbbddabbcddbcababdccbcbbaaddbacbcaccdbdaadddaabadddcaacadabbbbcbcdadaabcdbbdaababdbcdbcbcdbaccbabbcabacdbccbddaadbcadabbccaabbbbabdccabadaabdadbccbabdcdbbdadccaadacaabbbdbddcdccdcccaabacdddbadcadadabaadbabadaaaabdddaaddbaacbbbbcabbcaccdacbdaabdbcdabbadabaacdabdbababccadabdababbbabcacdccbdbbcbacbbdcdbaadaabccaabcbbacddccdbdddddccbaacdaabdadcbcdacbbaccbacbcddaddbccabbddbccdbdccdddabdbcdbcbaadddbabccbabcaddababaabcabbdabcadbaacdbcdaadadbcbabddbbbaddbdbadbaaacddbbbcbcbbbaddcddabacaaacbacccccbbadccadaaccaddadcdddccdabdacbbcbabccabaacbaccccbdddabdcbbbbaccdbdcdacbaabbcabbccccdddcabbcabbbacddacacdcadbacadbdbdbdddbbccddabdcbcabbacadcabcdcacbcbccbacadbaacadabacbabbbccbadccccddbaaacdcbcdccdddbdbdccccbbdcabbbdddbcaadbcccaddddddcdbaabddaaacabadadbadddbaadbbaacbcaadddcabbdaddbcccdbddbcddabbddacbcbcccdaddbdaccaabcddcbabcabbddccccdbcccbabbdbcacabaabbaccbcdcaadaabaadcbcbbcaaaacddcbbddccbdccbddabdacbccaaddbaadddcaddabbabaadbaacadbbdccdaddacbbdcaabddcacacdadaadbcacbbaddcbcbabdcbddacaadacacbadddacababdbcdbbbbbacabdbacdacabbdddbdaadacaadabddbbbbcbbdabbcbdadbbccdddcbacdccbbccbccdbbdaaabddbbdddaadbaadaadddcbdcacccccaddcbcdbcacccbccadbdcbabccccdcacccbadadddbacdabbacacccdacbccbddbbbbbbcccacbaadaabbdbbdabddcbdaddbbbcbacacaacabdabbccdabcdccdcabdddcdcdbdbdacdbcaabbcdaaaaccdcbdbddbbacbbbcccdabdccbbdddacbadacdcbcbccdbdddbbcacbddcdbcabdacbcdabddddddcbdcdcbcdcadbaabccdbbacdbababaacdadabcbdcaabbdacccbbabdcdaaaaabddaadabdcaaddaccdaabcaabaacbcaadbbbaddbadcbcdddbccbbbcbbcbbbacdbbacacbcccbbbacdbacbdcdacbdcabcccacdadcdbbcaabbddddbbbbcdbdcbbacaabcacaadaaacdddcacdcacdcacbcccbadcaacabdacbbcdccdccbdcaccccbadcabddbadadddcdabaccbddbcabdcbbcbacbdabdccbdddcbdcadcaaacdaccddbbdadcbcadcbacabbdcacdcbcbaaaabcaacbadcadbdaabdcbaaaabdabbaddabcaaccaadbadcacbbbadbbdddbbbcbdacbdaaccbaddaadcaacccaadcccbccddccdcadccaaaadcabbabadbaddbdbcaadcacbaddacbbdddccdadbdabbbbbacccbccbbcadbdbdaadabcbcddcbddabaccdbddaddccadbdbbdcddddccdbdbdbcdcccbbddabccbabacbabcabbdcabbcddaabacbbbaadccadacabadccdccbabccaadacadbcadcacbaccdaabdaccdccccccbbcabbcaabbbcbbcdcadabccbddadbcdbddadccbbadadaddcaabddcbabcdcbccbddcddaddbcccababbcaabbdabcabcababcdbbdaccddabadaabcaccdcdcdcdbbdcbbdacaadbbccdbdaacaacccaadbcdabcaddcaddadccadacdcdcadbaaabdbcaacbccccababbacbddccbcdadccdabbdbdbbbabacccdcbdccabbabbaadadaaabcbdcdcbbdddcabdccacbbdbbdbbcbcdbcbccccddbbcbaabaccbbdbcbbcabadddcbdaabdaabacbabbabaadbcddbccadaacbacbccadbddaddabaacacddbcabdadcdbcdadadabdcbdbdaddabadadadaabacddbddbdccadcbdbabbcaddabbabacabbabcbcdcddaaaadacbddabdbbcadabaaabccadbbcdbcdbbadccdcbcbbaddacdcbcdbdbbcadcdcddbabcbbbccdddabaaabcdbadbcadbcbddcbcbcaddcdbcadccadbbbdaccccadbbacddbdccdbdadccbcbabccacdbcbbcbcbcbacdaabbcbbcaddcdcadadacdbbcbcbdccaabccbaacdccbcdadadcdacdacbbddbbbcddacabaccbbdabdbdacbdbcdadadabccccbaaadbcbccddbaaaacdaddbadcddcbccbdcbbaaaabdbcbccbbcdccbadabaadadcabbbabbadcccdacbcacddcccacccbabdbdcdcabccdacbdadacadaacdbccccacbbcdcbcdadaccacaabadcadaacdabccdcdbacdacdbacadbbbcdadbbabbacbccdddabdbaddcaacdcbbabaaacbcacdcdaabcdddaacbcbcdcccdbbcaaddadccdaabbccabbbdcadbabacdbdacbbbbcbdbadcdcdddacabbacabbcddbddcdbdcabbaaccbbcbbaabcadcdaabdbbdddadcaaacabbbcdbcadabddccabdbddcaccdbaababddbbabbdcdcdddacccbdcadbbbdbcccbdaacdacbaccabbbbdccdbbbddbddcbcdbdbdccbaadcdcadadaadddadabddacbabdcadccdddcccdacdcdbddbacbddadadadddddddbbacbbcddacddccdddcdcddabaadaadcaccdcacaacbbcdbcacaccbdcadacddadaaabcaaacadcacbbcdacaacdbaababcbbaaabbbdacdcabddcbddbcbbbbcddcabcbadddaababbaaabbbdcbdcbacadababcbccdcacbbcbcdabcabbdbcdbacccddbcaccdcccdaabcbbaadcbaacdddabbcdbaadccdbbadbcaaccacbacdddaddabadadbdbaccadbadadadaadbaaadcaadccacddaddbcccccbdbbbdddbcabdaabaddddcbdbadbcccaddabdbabccaabcdcdcbadcddcccaaadcacdddcbccccdddcdbccdadbaaccaaacaaacbabddbbdbcabcbaadabdbddcabdaccabccddbdcbdaddbbbcbacadbbcaadcdcdcbdbaaddacbcaccabacacacbbddbbdaadbbcdbbcdacbcdbbdbccbacbbaddcbbdccbcdbcbcbbdccacdcddcdcacabddbdcbcbaaabddcdcdabaccabccbccbcdddbacacbbacdbddabcdacbbdaddccbbabccdcccdadcbdbbabacadddccbdadcbddbadbccabcdaabddaccbaacdacbbbcbadcbacdaabbddddccacaccbbcbdcbbddcabdabcadbdbddacbdabaddbcbcdabbccbddcdabaadbcdbcbbcbaabbacdabbaacbbdbadadddddcdcbcaaadadcaaddaadbbdbbbcbdbddbcbccaacbaddddadcdcdcddabbaddcdaaaaddcacaadbadcbbcbacbbdddcadbadddcaabcdbcaabdacdaaaaaddcbbcdcbbbaabacdcbdccddbcbabcadddcccbacbbdcaabadcabaccbaaabbcaddacddcdabdababadbcbaddccdacddbdbcadcdddccdaddaccbbdcadbddbdcaababadabdbcadcdddddbacacbdadbcdcbdcadaccbbbddccddddbdbdbcccdcbbaadbadcdcbcbddacbadccbaaaadbbdbddddbdbbddaaadcbaddbacbadabdbaaaaddbdadaddbccdbaddbcacbcbbdaabacdccdabaadcbcddadbdddaddbbccbadbdabcbabdacbdaaababaadabdaaaaaccdbdddccdbaddacddacdaddadddbcaacadaacdacbaaddaabaaadadbadbbdacdcdaddabdddadbdcacacbaacadbdcdccaccdbbddcbcbccdddbbdbdabadddddcccddcadddaadcaabcaddbbaccccdcaaacdadcbaccbbaadcadddcbcbbddbbaaddcadaccdadabcddcabbaaacabcbaabccbcddacdcbcaadabbaccaadbcbbccabaccdbacccbadcdbabdabddbacaccabdbddabdbadbbaacadbcaacbbddbcbbcccbdabcdaaaacdbddbdbbaadcdacbccdaaadaadadbaaabccdadcadabcdacdbdcdaadbccaddbbaabdaddddabdadbacccabbbdbdbbbdabaaadbdccccbdcaabdcadabaabbbccacdacbdacdbccbcccbccdcbcbdbaccacbcacaccddbadddcddbbbdbaaccaabadadddbacbaacbbcbbcccccddbdabaddddabdcccccabacabddaaaaaadbaaccdbdacbabdaaaabdaaaadddccdcbccddaccdcdbabaabacdbbccbadadaabccccbccdaddddacaabacadcacddcbadbbbacaccdbcbcddbdcdcccaacddbbacdcdcbbccdadababbdcbadbbacdcdbbcabdabbdcabdbbcdccbaaabaccaacadbcabbadaddccdddccdbcccabcadcbaacacbaacdbbabcccdabadadcadcdcdcbdcabbccdbcdbdaabcddddbcddbddacaadbadcaccadbcdbaacaccabcdaccbbbabcdabbadbcdbabaaabccbcbdcbdbdbadddbaadaaacbccdaddbacadbcdacbdddabdbadbcacaccdbdcdbbbcadbcbcbcdddbababbcadbdbbbcadbddccbbcaddcdaaaadacdbcaaddacdddcbdacabcabddcbdbabbaacadbbacdbbdccbdbbaddabacbabacbbbbddadacaabaabacbcabcabbadcbdbadbadbaddabbdaacdaddbcddbadbdcaaacabbccbacacbbdcbbbbaddcacbdadccbddbccaaabccacdaabbdbccbdaccaacabdadbcdacdcaacbaaabaaaaacabcaddcbdacacdacabddaddaccadbcacbcdcbcaabdacdbcbcdbcdacbcbdaacdacbcbcccbbbbdaabaddddcbadaddbdbabaddcabdcdbcdcccbbccadaadccdabbbabacbddbcccabbcacdddbbcdabccccaacbddaccdbaadccbcbdcddcaaccbcdbabbbbbbdaabdcdbddacbbcdbcabcccaddaccbddbdcdcadcaccdbabbbcddbcaddcaaadbcdbbdadcddbadbbadccbddabdbadcaabcbcdcaabcbbbdacbdcabaddcbbcacdcbdbcdcdbabcacabdaaabacbbcadbacadacccaccabdcddadabacadbcdabbcdbbabaccadaaabbacbccabbbddddbabdbbbabcaddccbbbcaacbbddacdccbbabcccadbdbdabcadddcbbcdccdccaaaaddcdbbcadadbccdabcadbdacbddccdacddacddcbaabacaaddbcdcbbddccaccddbadacaacdcbaddbcabdbbaddbcbcdbddcbbacbdbdaddbaaccdadadabbdcdbbcbcdabddbcaaacbcccddbaabcabbdbdcddcacdbcacbbcbbbdaacbadacccdbaccccadcdaaddcdbdbcbccbcbbabaddaabdbabcddccbcaccbdbcaaabcabdaccccaabdacbaacbdcdbcbbcdaadaadadcbadbdcbadadbcdaaacbdadbdbddcbdcabaddbadabbcbccdbbbacaacacadbcdcbadbdabccadabccaabacdaaabdabadcbccaccadabcbcbdccdaadbbdbaabbabcbdccbbdcdddbccbcbaabbbadadbdaaadbdbdabddadbdddaadacabcdaacaddbcdaadcbdabccdbccdbbaccccdcbbddddacadaabdbbdcadbcbcdddbbadcdabbcddababdacadbbcdaaaaabddacdbdadabaddbccbcadcddcabaadadcdbccbcbbbdbbbdbbdaacaacdaacbbaddccbabcacdbadbdacdcbadbbabcdbacccadcabbdcdabbdcccdcbacbaadcacbbddabbdcdcdddddccadabbbddbbadaaadcbddbccbbdbdbadcbccbcdbddccbcbaacbbcccabdaccbdbcbaccaaccaddcdcabcbabaaccdadaabcaacddbaddbabacbbddaacbcbbcbddbcbbdbabacbadaabbcbdcacdaaddabaaabcaadabddddaaadaacbcacbcaddcbacbdbdcadcbdbcccdaabdcabddbcbbccaabcbdcbbcdbdaadcdadadaaabbabcbacccbaccdcbdbbbadcbbadaababbdacccabdbbdcddbbaacabadbcacccbabdaadcbbcbaccabdcdabccbddabccbcbacaacabddbccacbababacbbbbcbacddaccabcaacddaadcddaddcdbcabcbadacccddbddaacdcdddddadadabbbdcaccdbddcdaccdccbadbccaaadbcaddcccadbadababbdaabcabcdbdadcbccddaccaccadbaabdaddbcacaccdcdcccbabdbbbdcbddbbbdbccccbdacdadcdbacbabddbbcbaaadddbcbcdcccabcabbacbbcdcadadbaabccbbbdcadbbbccccbbbdccbdacbbbacadbcdaadadcccaabdbcbadbcccaccdcddcaaaadaadddbdaadcccbdcbaaaacddbadbcbabacacbddddcddccaaabaaadbddbbbaabbaadabbddbadaddcbaddbadcbddaaacaaaadbadadcaadcbabbccaddaccbcbcbbacccdcddbdabdcbbbcacbacdcaabbbacccabcaddbdcbdbbadbcbbcbaacbbbbabbbbdbbcabdaccdabbacbbaacddddcaacddcadbcacccacaddacaabbaabcdcdacccdaccbbadadcabadcdccccdbabccdadaddbabcdbadddbcadaccdcadcdaaccadabdcddbdacbaccaaccadcdaadacabadcaaddabaaacadabacdbcbbcbcdaddbcadadcccbdbccbccacdaacddabcbbacccdadababbccbbadbcddddaccbddcaccbbdbacaaabdabcaabdbdcdddddbcbcbdbaabcccadadadbdbddbadadbaadabcabcdbcdccadacdbccdcbaadbcbcccdbababdbbaddaaacadaacadcdacccacdddcdbadbbbabbbdbaaccbcabccabccbddaaaddddbaddacbddbcabddaaabddacdabdcacbcadccbbbbcbcacbaaacdbbcaaaabcbbbcaababdcbaccbbbbbbccccadbbaadccdccadacacacaaabcbcbbbdcdcadccabcacaaabcbbdabdbbddcddbcddbadcdaabbaabcdcbcbaccadcbdcccbaacddbbdbbdacbbccddabbcaddcaadabcbaddbdbbaacddaacacaadaadbbacabdbbadddccbdbaabcadacbaddcddcdabbbcdcddcdbcbabaabdbdbbbbbcddbdcdccdbcacdbacdaadcacaabcadcdddaaaadbccdbacbbabcadacaaaabacdbcacbbacbaaacdaaabbaabbaccdacdbdbacbcaadddbaaabbcbcbbadcdabcdbcabbbcacaadadbddacabbddcdacaabcddabdaddacddcdbadcddcdcdaaadadddaabcdcbddcbcbcdabbccdbdacabcdcbdbbdcdadcddbdadadbcadddadcabcacbddbbbbbdddaddccacdddbcbbadbbdbcaadbcadddcdbbcdcddabdaddcabaccbcaaccacbcbdabbaadaabacadbabadabcadbddcbbccbabdccbbdadddadcbcaccbacbcbbbcaabcbbaddcbbcbbcccbbbbbdddbbbaabcbdbdbcbadadbaaaacaaabcbcabacbccddadbabcddaaabcaccccabcbbdacadbdddacbaacaabdcbbbaaccbaaabadcaabcdabaadbbdcccdbddbcacbdabcdaaddcbccbbcaddabaddbccbacaabcacaabbaaccbdbaadcbdacbdcbaacbbbbcddbdabcbdccdcbcddbdccadaacadbaabddccadcbacbbccbcacbadccaccacadbccadaaadbdddcacaddcdbcdcccdaccdaddabccabdcddbdcaacdbddaabddacabccbbccadbcdadaadadbcdadbaabcbababbbddbddddbbbdcbcadbaabacbaadaabadcacacdcacadddadbabcbbadbbbdaaabaacddbdacabbcdaaaddaacbbdcacbadacbacbdbbabbadcdcabcdbaccaaddaccabaaabcaaaadaadbdccbabbaadcccdcbdbadcccbbdddaddbaadcdcdbddcbcddccbadaaccdcccdaddbddaacaabdbddccdaabbaadcbbbbadabdbdcddccbddcaccdacddcabaccabaaddbaabcbadcabbdabacccbddcdacbddaccbddbbcabaacaabddcdbccdcddbdddabdcdbccabbacbbacbcbdacdbabcacadccacbadacbcaacbbdcdbbacbdbcabaccaabdacbadadddaabaaabadbdddbaadacbbdadcabcbbbbaabbddbbdbdbdbdcaabccbbdbacadadbbadacacbcdcbcaabcdabbbabdbaabaaadddbaabbcbcddcdbbdbbddcdccdadadbcbcaabbcabdbdaddbdadabadbcacdbacaaddbcbcbdabdcbcddcdbadaadaaadbbccccbcdcbbcccbbcbccccbbaabbdacdaccccbbabbbadbaccdcbbdcbddbdbcaaddddbddcdabbdbbdacddddacabbbcababdcbbaaadddbbbcacdacccccdcaaddabcabcaaabdbabdcdacbcbbabcdccdbcdccbacdcdaaadcbbdbbbcbacbbbddbbdbabcabddbbdcbabacaddbccabaddbdbcddddbacabdddbcdccccabbaabababdbaadacbddcdabbbbbaabdcadbacbadddbbabaaadcdaccdabdbdcaccdbbbaaaccabcaacabdabdccccaacabcabadabcdbdacdbacbccbabbcadbabcdcbaabdcdadaadccdabaddadaadaadaabdbdaabaccaccddabdadadbdcdddbcaccdcddbcabbaddbcadbadacadbbaabccdbadabdaddadacadbabdacbbabdbddbbdbabcddbbccdcdbdcaabadbdabddbbcddcdaacdababaddcccdacdcbbbcbaacbbdabccadccbbdbadbccbbcdbcdccbddcbcababbcbbccbbabdcdacbdabcdccddcbcbbadacdbbdabcbabacababdcddbdcdaabccbdbbbdbabbaadbacaabadbdacabacdbdbbdcdcadcacadcccbaaccaaacdcdcbcbbdccaccabaccdbdcabadcbcadcabacccbbbdccccaaaaadbbaacdcdabbbddbddaacabaacdcabaadcadcdddccccdddcaabdcbbacbbcbdccacdccabbdcbbbbcddbbccddadbcbbcacdcdbadcbcdacdccbbacadcdbdadccbddddcdcbacccadaadaacdcbabbdadddbdccacdcbacdabacbaddaaabdacdbdbaadbcbacaadcaabbcdcbcaccbdaacbcbbdddbdabdcdcaaaabaacccdcccddccddcbbadcbcdcbaadbcbddbcaaaadadcccddbbaacdcdbaadabccbddabbdcbacbbbaccbcddbccaabbabbdbdcccbdccddcdadaabacddabddddcbddcbcdbddadabcdddabaadaaccdbcadaaadaddcdaaccbdabadbdcdacccbbccbdcccbaddcdbaabdcaaccabadbbbbabaaddbbdabccabcdbaabbbaaccbaabaccadddcaabbcdaabbbdbbddbdbdadbbbddbabdcbbccddaddaccbabccbdbabbcadbbbcbcccbadbcbdaccacdaacbbabbdaabaabcdacdabaccdaddbcaadabccdbabccccbdbdacbbaaccaadacacacdbadacadccdbcddcdcabaaaacbcadacddabddadbadcbdddadccdbcaadaddacbadbddbcbdbcddcbcaaadbbbbbdccdcdbdcdccadadbdabdaaddcbdabdabcabdccbddbccdbadaaacbddaddadbcbabbddadacbacdccbaabdcdbaabccaaccdccdaabbdbadbcabbcaaccaaadddacadadddbbcccabdcdaaadaaaccdaaacccbdadcadcacbbaacbabdbdbdbabdcbbdcbadddbbacabbbbbdbadbddcccbbbcbbabdcdabcbdbcbaadadccbcbbaaaddbccdcbbdcbabaabdcdbddadcbadbccdbaabdabdaacacadaadddbbdcbdabdbbbcccbbcacdccbcbcbdabbdbcabaabdcaacadbdccbbacdabbddabbcbbccdbcbaaaadcadaaaaddacbaccaabcddcaacdcccaaabbccccdbacdacacdbcccbcdaabbadbccacbdcaaacbdbacdbbadabaacbbcadbcdbcdbdbbabdcacadcaaddcdaaacbcadbdcaccadadbaacdcccbadbccdddbbadaabbbcdcadcadadcabbdaaadbaddcbaccbcbdaccaaddadccaadaaccddcbdabacabdbadbaaccaaaccabbddcabaaacdddddadabccddaddaabcbcaabcbacdcadddcbccadbacadadcababbcaadacbcbbddcbbaacdbcaacadccddbbbccbdbbdcbbcacacbcbbddaabaadaccdbbdbbbadcadaacdbcaadcccdbacccbccbdbadbdbbacbcdddbcaacbbbaccccaaabbbacdbdadaabddbcdcadadbcccdbcdaacbbcbdabdbacbccdbaaadbcdddddbabdcaccaadcdbcdbdbdbdbadabdccabcddcbabacccbcabcbcdbaccdbdcdacacacbbbcacadcabbabcbdddabbcabcadbababdabbcbdcbdccaccccaccabadbbbadadbadaadbcdbbcadbdcddbaccbabbdcbabbbcdaddcbadaaddccacbdbdaacccbcdaccdccaabbcdbaaaaccdbcbddccdccbbacbaabbdddccdaadaabddcbdbaaacdcddddacacaacbbcccadadaccaaddabcabcdaadddabbbaacbccaccccabcacdbaccdbbaabbadcbdcacaacdbacaabcdddacbadbcbdaddbcbacadbaacbbbcbacddaacaabdcbababdcbdbcacbbdcbcbdccdcbbdcaabadbdabbcccbdacbbddbbbacabcdcddbcaacdbbdddcdddbadbacdbadcacddcdbaccbdcbbacadbbbcbadababbcabaaacbcbaddbacbcadbccdcbccabbabbacadbadacdbcacbaccddcdddcbddaaacdccbdaccbacacabdbaddddbadcbdcaddaaadabaadacbacdaaddcaddcdcbccbbaabccadcadcbabbbaadcabbbbbcabddaabcaccaadbdbacccaabcaadbcaadccabababbcabdccbdbabaaaaccbccbdabcadddadcbbacbdbddcbaacabdbdbdbadacdcbccddabcdccdcdbabbaadbcccabcdbccbcdaaaccdbbddcbbddacbabdbacccadbcbccbaabccccbdbdbadcadbbddacbdaaabddaddcadadcbbdabcbcbaaadccdcdabdcbcdbcbaabcadddacdaabdabcdbaaaddccdabdbdddcbadcccccaddadabbcccacbadabdcddccdbcbdbcbcddccacaabdaccbcbdabddbdcbaddbadbacabadddcbccaaadcaaaadacacdcbabdbaadbaddcacacdbddbddaabbdcaccdbbadabddcdbdcdcdcbaccccaddaacbbbadaccaaaabcaabadbddacbabdcddcaadabaacdccdddbbabcacabcaacddccddaccddcacddbcbbcbdbbbadbadddbaaabcccaacccbdaaacbcccabdccdbdaadbdbdbdabcaaaaaabcbbadcbadbabadabccbbbcadabccdcdadabbaabacacadbbbcaddbcdcdaacddcccccbabccbbaaadbdbbbabddbdadbccbadbbabcdaaaaccdbdadddbbaadcabaabacbbbdabaaabcacbabadadcddcbcaadaaaddcbcdcccabbcaabaddcacbdacdabadabbdbdbcaadbaacbbdccbabdbbdacdcdaccbaacbcacaccdabcabcaccdaaabadaccbadbdcaadbadbdcbdddcbabbbbcddbaadcaadbdaccbdacaccadcbbbbacbbdcacdbbaaadcdcdaabccddddbcabcaccabaabbabaabdabdcaaaaadcbdacbdccadcdbaacbcdaddbdaabababaccdbacbcdcabdbbcbbadaccdcabcbcabbdcbaaabdbdadaaabbadbabcccdccabadbbddbddbdcdaaabbbcbbccadcbdccaddbdabccdcbddcccbaadcdbbddcacadabbcdddcacbacaacaacdbccdcdaabbacabcbdadcddbdabcbbdabddcaadcdbaadabaadbcbbddcdabcaaabdcddaadcbcdbdaddadabbbacacabacbcbcbbbbddcdcbaacdccabcccbddabcbcbbdbcdddaaddccabbdaddaacadbbadabdccbdbbaabbaddcacddbbbcbbaddcbcccccdbdcdbcbbbdaadcdccdbadadacadcaacabbcacaaaacccdcaaddacdaadaacdadbbaddccdcddbdadbaabbdaabcabbaddcccbccbabadbcacddcbbddbabbdcbbadcdbcccaaaaaacbabdcadcaaadcccbbbcdbcbdadabadadabcbbbccdbbbddcabcbddcaadabcdabcaaabcbddbcbcdadacbcbccbbddababdddbabcddcacddaadbcdcdadabcbbaccbdddbccdcbaadccdaadcddbaabbcbbdccadbcadbdaacddcccabaadadbaabcababdacdabbcadadaabbdcdaadabadcadbaccbccabdbdadabcacaacaadddaadddacbddaabadbdadccacabdcccbbbabaabdbcdbdcdbabbbaddbccbaabbcaccacdccaabcccaaacbcbaccbbabcddabcdacccbacccddbccbdaaddcdcdddddcbdaaddcbaccbdcdbadbdddaddbdacbbccdcabbabcdbaabbacaabddaadccaccaccdcadbdbabacbabbbcabdbccbcaddcbccacbbbccbccbbbabdbabbacddaabcdacabbbdbabddbdccadabcaddaabbaabbbbaaadcbbbcbdccabbaddabcaadccdaaaadaadbdcaabbbdcbdbccbdbddbdccabcbcadbcdcadacddaaadbddcbbbcdcdabdabddadaddcddccbbbdaaabaadcdaacbcbadbbadcaaddacaacdacacbdbbabcadbddaacbbcdcbccabdaabdddbdbbacccbacacacbbcdababcdaddcdbccabbdbdaacbcdccadccacaabbdcadaacdddaaaadaabdaadacbdbbcbaacaddbbcaaddccabdbabdcdcaaaababbadaaddbaaadbdcdbbdddccadccbcbdbdacddaddcdaaacabcddcdbbdadaadcababacbdcabccbdccbdabcdcaaacbbadaaacdabdcbccdbcbbbbaccbbcddababaacbdcccaddbccbaabdccccabbbaaadbabcddbdcbdccaaccbaacccbdadcccbadbdcddbdabcbdbabcaaccabbabbdaaaccdbbbdddababbbccbbbabdadabcbdadbdcbdcccccdbbbcdddaccaaccdbcacbdacdbcaaacdbdddbdbbcddcdaababdabddcabaddacbcbcbacabcdddaccddccaddbccbabdbaabcbbdbddcbacabdacbadcacacbcddacdaaccbaddcbbcadcbdabdbbbcdbacdabcabccacdcdaddcdadacacddccbccaccbbbabbdbababacaaabbbcbcabcabdddbdabcabcbccddaabdbbadcddabddcbabccbdabddbdbddcabddbaabbdcdacbbabaacbbcdabadadacadbbbcbdadccdaaacaccdbbdadaababcbcacdbbadacacbcbbaabbbcabdabacdddcdadbbabdddcbbdabaaddbabbbcbddbabbbcddccbdbdbbdcdccdcbcdabdbdcbdcbcccbddadbcabadddbababacbdcabddabcbbcbadcacbcbaccdaaccdbdadcacbdaaddbccbdbdddcbddbccdddaddbbddbdddbaaabaadbcccccbbdaccbddaabdaddddccaacdabcddbaadadaaadbccbcbcdbbdbccaccabaccdadddddddabacddacbbadabddbdbbdbcbdcbdaacddcbbdbbccbabacbccaddcabdbbdabdcacdbccaaaadadbbbabdabdcdbabbaacacdbadcccdaddcacdbddcdabdbdacdcaabbccaababcdbdccacccbcdaabaccacacabbaaadacbabdbbbbbaaaacaabddbcacdbabdabdccddcdcbadbcbbcbbbbcdbaaccacbcabaaaddbbbbacdcbcacdacbcdbcadabdadcbcdbaabbdcccccaaabcaddcdddcdaadbadabacbccaacbaabcbacccccdccabbadddaadbbddcddbdbaabdbbcdcdccbdbabbdddcbcadbbabbdbcacbccaaabddcabcadbdabcdabcbbbddcdacabcbcdaacccbadbbbdaaacbdaabcaadbbacdbddbbbbdbabccabccacdabdaddbdddabcadbabdcbbabcdcdcbdbdcddcdaabcdacdbcbadbacccaabdcadccbdbcbaaccbcdcbbccabdbcabacdaabcbcbaadcbacdccbbdadacacccaacaabacaabddbbaccadbcbcaabaccdccbccdaaaabbcbaccccccbbbabcaddadbadacadaabaddbcbcababbcdbaccacbbaaccbabdccbabaabcbabdadaacaccbddaadccbcdbacbdbddbdcacbabbdbcaadadaabbddbbcdbdcaddabbccdcacccdadcdcbcacabaacdcdcccacaaaaabdddbacdbaccadccbcbccaccbcdbbaaaacbcdaabbccdaaabaabadacbaddadadccbadaddcaddabcccadabbacadcaacbabcdcdbabbcadcddcbcacbcabbbdbdccbdbbaadacbabbcadddaaaddacccbacbddabadbccddbababcccbaaaacdbbdadbdadaaabbadddccaccaadacccbddbcabcccaadddbbacdaaaacddcbbdabcabbcabbababadaccacacdabddcaaaaddcacdbadbdcccbbbddaddccbbaabcddddaaabacadbaadbabdcbcbbadacdabcbccabdbbdadddadcdabcddcddccdcabbdcddacabcabbadaabddacbababcacddbcaababdabccbadcaabbddbcddabccdcdbcdcbdbadcaccbcaadddadcbbaacdcbddcadabbccaacdcaccdadacadccddcdabccbacdbccaaacbaabcbccdadbcddbbdbcadddaddbbbccdcadbcaacbacbadbadabdddbdabddbcaaababcbcdbdcbcdbdcdaccbdcbbadbdccacccadcdcbdacbabddadabbbaccdddcdcdabcdcadbaaacdabcaadddbdbbacccbcbdadbbbcdbccaaabddcbbacbdccbcbbabcdccacbdbabaddcdbaddadddcbdcbcbaacacdcbbbabcababdbbdddbbbdcacccbbaaadbdaadaacbcadcaadccdadacbdabbdbddbdadcbadcccdaccbdacdcbdbbddbacbbacabdbdbcccbacbddcddbbbdaccabcdcaddcbdabdbdbdbdaadcddbaacaadbdbccddacabbcdacaaabdddcdaaaadaabcdddddbaddbbaababbacabbadbdacbaadabcdbbadccacbbbcccaccbaacaccbbadacbdbbdbcdabdcbbcbdddcbacdaaaddacdbadabadadadddcacbbcbdcbaacadccddcdcbbbaacbaabdaaacdaccbaacbaabcdddacaacdabcbacdacdcbbcacbbbdbadddabdcccdcdabdabbdcdbccbdbbaddccbabddbabadadaddbdbcaabdabaddbadcdcccacdaaabdacddbdcbcadaabcaacacdbdbdccdaabcaacbcbbabccacccdcbcacbcccaaababcacdcbcbddadcbaadabbcbadbdbdcdbcbacaadbbbbcbcdbdbaccabbcbccaacabdccccbbaacdcabbcbabdcaacbccbcbaadbadbaaabacccbabacdcbcbbdbcbabcadadcacddcaacabdadabdddbbccabadbbcbddbcdbbbdcbadacbcbddcdbcacaccdbdcbcbcbcacaabacccbacdaddacaacaacccbbaabdabcbcbdbacaaaacbdbbbcbadbbdadaaccddcdaadbdbcbdbcddbcabaadbbabdadcdaadcaababdbbdaaadbbccdaccadcaccadbbcdacaadddcbacdcabcabddddddaabbbdbcabbbadadbdcdcabcbccbcaabaabddbdbcccddbcccdbddcccabdadbdccbbddbcaaadbcdcabdbbdbcdddbcdddaabdbddbababccdcdcadcccabadddaddcbaadccccbaaaccabcaacaadcdbaabbabbbaccdcbdbdaaadaaaacbadbcabaabcbabbcaacacadbddcbbbcbcbcaadbacaaacccdacacacccbcdcddcaadbbaacccabdcddbabcbcbbbaccccbbccaddaddccdbadcbcaaaddaccdbdddabdabbacbdcadccbbadbddacabacbadcacddacdabdbcaddabccbddadabbcabddbdadbadbabbbbdacaccadacbdbabdbaccbdababcacbdccdbcbdbdbdbccdacdabccadadcabccdcbaaaadbcbdbddcaababacdddddaccacdbcccbcdccddadbbbdacdcdabcdcddddccabbdcdbcadacbbcbbbcaddbbddbcdcbabdbbdbddcbaaaadaddbddcdcbdcaaddbaadcbccbcadcdcbdbbadcbdadbbbbbbbdcbccddbddaccdaadbcbdcdacccabbbdababcabcdcacbacddadbababcbcaadddcaaadcddcbbabdcbabadacaccbbcbaacadccbbdbadadacacadbadbbabdbacabadbddadacbabbbabbacacddcaaabbdddddacaaaaababdbbaadbdcccdabcbccaccdccaaaaabdcdaacbdddddaabadbdbdbddbacbacdcdbcbadcaabbcbddbcdcbcbadcacccabbbabccdcaaaacdccbbdabccdbddcbcdacdcccbdcdbcabbbcacdbdcaaabbcacaabbcabcaacdddacccbcdaacbacdbbbadbadabacbdaabbdcbccbbddbbddaadbbcddacdabbbacbdaaabaabaacbacbaaccabdbabcabaddbbdbcdbdcdaacabddabbddadaaccabddbbbdcdabbccccacbadbacabbbdbdbccbcddaddddbbcbcbbdadcbbadcddacbabdbabadadadbadbcddacbcdcccbbabcbdcbcdcaaabbbadbacadaccbcbcbcdbccbadbdcbbcbadbccacdaadccdababbabcdbacbaddbdcadcaaadccdaaacdbcabccdaaabaaadbadbacacacadddcbcbcbbabdbccabcdddabbbcccbbdbbadcdccbcacbaddbdabacdadddcbbbbabccccaacdbbbabaccdbaaacabbadacbadcddabaacdcccdcbabdcadbaccaacbbbabbbdbabbbabcadbddbdbddbbaadcaccacbadbcbdcdbdccabdccccaacacccdaccaddbcacaadbbcacabdadcbbccbbdababbcbdcbddaaadbbdadadcdbcbcdabdaabdccdddadacbaaacbadbcdcbcbaabaacacdbdaabdcccbdccbbabccbaddbdbaadbcbacbbdbdddcdddbcbdaabbaccaacaccdaaabadacbcacbabdaacaddcddccababdababaccaddcbcbaadbbdaaddbbdaabdabbdbdaababdabdadbdbbcbdcbaaacabbcbdbbcbbccccabaababbcbbbdcbbdccabbcbbaccaabcbcdbcdcdbbaccddbacbddcdcddacadcddaabbbcbabaccdccaababaacabdaabcacbbabadcbdccaadbcccbdbdbdababbdcdccbacdbcdacdaaddccdccbadcabdbacdcbdcbcbbdaddaddcaacdcbabacaaacddabcabddababcbddaddaaddcbdacaaacbdacbbacdcaccbdddadbddadccabdcbbabcbaabdbdaabbabaabcbcdccabadcaddccddddbbcdcaddddcdabcdcdaacacddcbaccbcbcdabbcaccbadacbcadcdcaccdaaaabdddbbbcbdbccdabaccdacabccabcccbbbaacdcbdaabdcbdacacadddacadaabcacabbacdbdaddbbbbbbaccccdababbcbddccccbdabaddbaadccaddbaacdcabccbbcdbbcdbcbacdbcabaccdbaadbbdcdbcadcdacadddbddddadacacaccbdabdcdbcccabbacabcbbdacabbacbdabdcbbabbbabdaacaccdccacccaaacacacdccaddadcbdcaddcbcaacadddbddcaccbbabdddabaacdaddbdcacdaaaaabdcacdcadddaadbbaabadbdcbdadabcdbcaccddccbaabbcdacdbaaabdcbadcdbcbcdbdcbccddacbdddcdbbbbdbbabbccbcdcaacadabadbaaabcbbbbcbadbdbcbdcdabdcbaabcaaabcdbbccbccaadbdadaaaabbbbccbbdcbdbbbccdcdcaacbddadcdccdacdbbddacaabaabbacbcbadddbadcccbadcbabbadbbdcaadcaccbabacaacdbcdbcaadbbccbdbabcadaabacbdabbdcdacdadccccbccbdabbcddddadccacbacddbccabdbdbbbbbbdcabdddbbcadcdbcbcbdaaddcacbbbaaccaaabdcabdaaacabacbcbbcdddadcbacaaabbbcbcabddccbddbcbcddcdacccbbacadbbadcbcabbbccddcddbbadcdabbbdbacaccbccdbccaaccabaaddbbcccdadcccdaaddbcabcdccdcbadcdbabbaacdadcacabaadcacbcccdbddccdcdacdddbcdababaccdaaababcbbabcbdbacbacbcdaaaaddbccabcddcddcdabbdccabacbdddbbdaacacacddbddbbcccccaadadacdbbbdcabdabcdccaabadaabbcbcdbadbcbccdcbaddaadcccbbaaaabbddddccdacacbadabdbddcaccaabdbddaddaadcbbddacdbcbabadaadadcabdbbccccabccdaddbcaabdacccbddddcdbacababcddbddaddcacbcdbdcccaadaaaaadcacaddaadcdaabbccbcccdcadabcbaabcbdbaabcbadccacaabdacccdcbcddabacacbdbcbbccbccbcdbcbddccccbbdbbaddbbbdcbbccbcabaacaddadcabacabdddbabcbdbbacbaaaadddcbaabcdbddabdbdbdcdcbddccbaaabbaabaaabcdacbaadcccbcbdacdcabaccbdbaacbaaacccacbbdcacdaabbacaccddbabccdcbcdcddadcadbdbacdacabaccdbcdaccadbacadbbdcabbadbdcdbbcbbacdbdbdacbbdcadbacdbcdbaaadbdbabcbcbdcccadccdbaadacccaaaadcaabcacabaaaabccbabdacdabdaaacbbbcabaabacdaadddcaadaadabaccadaccaabbaaabcbdaacadddcdbaddcbdacbdbaaccbbddadadbabdbdabadccabaddcdaaadbdcaaaababcccadcdbdbadbdddcccccaadbcdacaacdacdabdcbdbdbddabdddcdccccbbddddcdabaadbbbcaacdddcbdacaabbadccdccadcbdadbddadadcbdccabcaddabdcbccdccbbacbbbbdcacdbcccdbdbaadadadbdddbcddbccdadcccccaaccbacaaccdccdbcadbbbdcbbababbbbabdbbadaddaacbbadbbbaaabbcbccdbcadabccdabcacdadcbbcdaaddbdbcdaadaaaccccadcbbacbaaddbbbbcacbddbadabaddbcccddccdccddddbcaadadbbbacbbdcabbbdaadadbabbacbbdcacccdccadccbdadcbaadcdbcbcabaccddbbcadddbaccdacabdbdcdabddaaaabcddbdabdbbbdaadccbbaddaaccdaadadbcbcaacdabdccaadcdadbacdbbabadaadcccbcdddcabddddacbadcdaaccaccdbcaccdbbcbccccddcadbcdbabbadadaaaaaaacdaaacdbbdcbcdbccdaabdbbcddbcaccaadccbcdacbacadcdacbdabccccabbadaacaabaaaccbacaacdcbbacdaabcdbbbdbcacaacbaccacccdaddbcacacadbcccccbdcbaaadabadadaccccdadacdbbcccbddbcdcccdccbdddbdcadadccaabaccbbdbcdcdbcbcaaadcabacbbcbdbdcddaacdadabadcbaddbddccbdbbbbcabdadcbdcaccdbacdbdcacbdddbcccacdacbcdbdcdadcbacabccaabdacbcdcbbcbdbbadcbabdadcdbbdccbdcdbbaaddcddcbcdbcaabadbdabdacbbcbbddddcdbadbcabadccbabbcadbabaabdabbadcaaacbdacdcbdcbbdcadacccdabdbaabaacddbadcddadaacddcaaadababcaacbbaaccbcbcbddaadbcbbdacddccbbddaadbdacadcdbabbbaaababcaabbdbddadcbaccdadbbacbbdbccccbdbbdabdaddabdbaaccbbbcccdbbddddacbbdcabdddadaccdddbcdcdbdcdbbaabacaaacdbbaccbadccaddccbcbccaaabaaacbcabdcdbaacbcacbcbaaaaddbbdccbabacdccdbdbdcdaaadbabdbcacbdabcdbaadddbbaacdddddbaddadadcdddbabdcadcccdaaaddacccabcabcccdcdadbdabbbacabcdabcdcdbadcbcbbadbdbbdccddacdcddbdbacabccabdaabcbacbabacbacabbadcbbdbaaddbbcbdbbcbbddcdcacbcddbddbcabddaccbcbcaaabdaacabaaddabadabcdcaaaaaadbbabbcbcadcbbcdbbbcadcaaaddadcadcabbbbbcdcacbaababbbacbacbcdabbadbacabcddddbcbdbbccccdcacacaacccabcabdaaddcbaadcbadaddcacaadbbccdacdbaddcbacacdacdbacdcdbbaadbcdabbdbdbbdbaddbacddccccdcddcdaacbcbdbaabaabaadacbaabbccaaadaabaacabadddbbcabaaaaadaddbbbdbbbadaacbadaddcbdbbaaadddacbcddacddbadabcacdbcdbbacbcbbdadadcdbcdbaacaacccbbccbdaaddadcddbbddaacadbbaaadaacddadaabbddcacabaddcaccdaabaddadaabaaddbbbaabaacacbbdcdcdddacbdbabdbddbbcadcdcbdbacabbacccdbdcabbdabcdcbccbdbcdcaaacbdaadbacacdaccbcdabcccbbdbcaaaadacadbabbcbbdbaaadaabbbcdddcadccaacccddbbacdcddbcdabccbbbbacbdbcbddbddaccaababaabadaacbbcaabcdcaaadccdabaabdaadcaaccabbabbbbdaaacbddabaadbdabaabadbddcbddaddaccaddaaaddccaabdccbdcbccabacdbcdbababbacddabbbacadacacbabdcabbaabadddbbcbcbdddbacbbbbbbaccadbcaacaadcbaddaabbbcbbdaddccdbbdcdcabcbdccacbaddbdcacdcbacccacdbadcaccbaacbbdabbcdccbddbacdcabbcddccbaacabbbacabdaadbabacabcbbaacdadcbdbbbaacaaacdbbbdaaccdabaabbbbacdbbcbddbaaddcbbbadbdcbabcdbdaddadacaacbaddcddcacaadcbaccababdcbcdadccdccaaaacaacbdabdadbcdaadcabdcabddabbddbdacdcdacabbdbdacdbbcaaabaabdadbcdabbddacbcabadbbaabadccbacdbabdadccdcbdcacababaddcddcabadcdccdadaddcddcdcdadcadcacabaabcabaacbadaaddabbadbbcdbcaabbaacadaacdabbadacdddbddcddbdaabdbdbbbadaabdbadabccacddddbabaccbdccbcaddddddadbdcbccdabdaaacbdacdbbbddddbdcbbadaabddbbbbdbcbdacacadcbcabadababaccdbbbabbbabaccccadbbababdadcccaddacabdbabbcdbadabcdcadabadcbbdbbcacaaacccdcccaaddcbadbabccbcbcdadccbbaaaadbabdddaababdcacacbcdbabdacdacdababbaddbacbccdaadbdcacdaababcaabcdaccbdabbcbcbcdabaddbbbcbacbbdcbbdccbddabacbbccbbbbdacdbddabbabdbacbacaaacacdbccabdcdaadadcacbbbaadaadbbacdbbadbdcadbdcbbbadbadbbcadaddcbadabadaaabbbaacbadcdbdcdcccdcbbddcaaadbbcacdcdcacacabcaddcdccdcdadcbbaaaccdaabaddabccbdcdabbdabaaaacbabbdaacddabdaddcddaabdcacdccccbbccbaccaccdcabbdcddcbddccbcaababdbbcabaaabdcadccccaaaacdccbcacccaaadabacdddbcdbcdabdacdbcdddadcaddabcacbcdccdbadbbaacacdbcadcbdacccbdbbdbaccdaadbddddbcddccdcaddcddabdddadcabcabcdaababddbdbdcbcabddcddbbbbccdbbadddddbaaadcadadccabcabcdddcbbdabcbbcdbdcbdbddaaabdcbdbcaddcbcdadbabbbbccaaabbdacdadbbcdacbddbdaadbaddbabdadcbbbccdddbbacaaccbbcbdaabadcbabbdaadaddbddbbbabdddbcacadbdcacbdbddbdbaadccacbabcaadcddbbbbdababdcdcdbaadacdbdcbbabdaadcadaabcaccdcbadbbbdbdabdddbbdccdddcacabbbdbccdddbbbaacaabbcdbbbcbcbcbcbcbcccddacaabcbbcdabdbcdbbdacdbdabcbaabcbbcbbbdadbdabdaddbcbcadabacaababccccbdccbaaadddcdcadbbabcdbacbdadbcacacdaaaacdcdabdbbbbbbdbdcddaabcadcbcacbcdbcbdcadaacbcbddabcbdabdadbbcccbacbbaaddaaccbcdcacdbabaddbbdcbbacadcddbbbaadcbaacabbddcbcbbcbdcbabbdacdbacabbbaaacccdaaddbcddcccbccccddbccacabddbdcdcddcadcdadcdbbcacbbcabbcbabaddabadddcaadbadbcadaddcacbcdadddccacbbbbcccaadcadcdaddbadadcdbaddcaabbdaccbadcdabbccadbaadcdbcadddcbabdbccbdcbddcababcdaaabbdbabaccbbbdbdacbabbdccabcbaaabddccdbaaaadcbbcbcbdadbdbccbdcdcbaaacdbacbaddbcdcacaccabddbaccbbccabbbdbbadacddadadbacbcdcadbddbcabbbabbcabbacdccadcdbdabdccccdacbabacdaacabbdadabcbabbacaadaaadacbccaadccdcdaddbbadddcbadacaababbbdbdbbcbccdbcacccdaadcbdaccbbaacdcdadabcbddcaccccacacbdbdbaddbaabcaaadcddabccbadbcddbacdacbdadccdaaddbdabccacbbcbcbdacbcadbaaabbadccaddcaabaadcbbdbcdbdccbbcdcadcbcbadacdcccabacaacbdbacbbbadadbbdbbcdcbcaacccbcbcbaccaaacaddcbddbdabbdbbaaadacaddbbdaaddabddbcacabcdbcbbcbdbbabcddabbcdccbcaddadaccddddcbcabccacaaaaddccabbbcdcabbbaadbdcccaaccababaaabdaabbbdabaababccdbdbbdbbadacbdddbadbbbadbdabcbaabddbabdcccdadabcdaababbcdbdbddcdabaacbcbaabcddbabcadacccbbbddacadcdadbcccacbaadaadbdababbbcbcdcabcbbcdcdcdbaddabddddbcadbacbccbcacbaadbddadcddddacddbbbdaabbbdbdcbbcabdcbdbbcdbdbcbacaabbddcaadbbbbcbacccdcaacaacccbdddbcabdbbcabacdadbbabbcaaaccdacbdbacddccdbbddcccccbcbddaaabbcccbdabddabbabaccacdbcbbdbacbbbddaacdcbccbcbdbcadaddbababacdbcababcadcdcbdbbaaabaaadaccdcaadcaadcdacdbaddabdcdadbcddcdaacbadcacbbabbbbdacbaadccaacbcdabcaabacbadbcccaadddccacbaaadcdcdbbcabacbcccdbdcabbdadbbddacadabacdabdadccbaddabdcdcdaabdbdbcadcdcaadbbbbcdcacbccbbbbaaddcdabcddcdbdbbdcabcbacabbadabcacdccccaaabdcaaacbaddacccdcddddcabdabbabadcdadddabddaabadadaddbcbbdabddcdbcbbbbcddcbadddbaccbdbbbcbaabcabcaddabcdaddbaccbcdadbbbdaddaabdabbcbbaadddaacccabbdadbaaaaaddbcaaaddcbbcdbbbbaabcbbabaaabdccbabbbadbbbbbdbbacbdbcdcccbbacbddccdcbccaddddbcabadccababdcaabccdbbddabdcdcaadcbbacbddbacdccabbcbdcbbcbdcbaaabbbcdbdabadccdabbbabccbdcdaabdadbcbaddcdccdcadcdbcdbddccddabdabbbbdadbaaabdddcdaacacbcdabacbadbabbbacabcbbcadccaaddcaddadacadddccccbbabdccbbdbabdbbbbcdbaacddaaddaadbbbaabbbcaadbccddddabdccbaccddaddbbadbabaaabcacacbcccdabbbdcbdbaddcbdccaccddcbccabaaccddcbaccdbbcdaaddddccacadacdadbbcbdbdccccddcbcccbbcdbbdbbacbbdbaadadcacbbcadaddbabdbacdbbbcaabcbaccabdbbdaaadcaaaaaacaaccadbdbadcbdbaabbccdbdddacaccccbccdbaacaacbbdaabadcbcbbcbdaaacccadbcdaadaabcadabadacddcbcbaabbbcacdbdbabdbcbbbaacdcdabdbbdbdbbdadccddbbdcbdadcbdcddaccdccdbaabdadccadadbcccddccbabbbbccdadcbabcabcbbaaccbcbdacabdacaddbdddccdbbddaaabccddcadbddbccaacdbbaccdcbabbbbddcacaccadbddabacbabbacbbcdaccbccadabacdddcbccddcdacbcdddbadbcddcbcaaaadadaaaddadbaadccbaadbcdaaccaddaaabdddddddbdddddbdccbdbbcdbbdbbcaadcdddbcccacdbdcdbbbccdbcddaddacabdcacbbbacdcbbdabcacdabaabdbccbadbcbdbacbacdbdccacdccacdacbadddcccacbbcccddacbdccbdccccbcbadaaaacdcdcacabccdaadbbabcdbaaddcdbbabcddbcbcbadbaccbbdabcabdaaccbbccbcacdbbaacadaabdcadcbdabbccccdcbcdddbcdbabddcdabddcbcdbcadcababbdaacaddcbddaabdaaacccdccabddcadadbbdddcacdccaabcbbdcbacacaaabaaabccbcadbadadccababbbadadccadccbddddbacabacacbbaddccbbbddcdbcabcacdacababdbcdbddbdccdabdddbacdcccdbdbcacccddbdacadcaddaaaabadbaaadcbbccdaabaadacdcacabddbaaddbddabbcdcbabbddcdcadbdbcddddcdababdbbcbdcdaabbcdbabccbcbdbaaacbbaadbdccacbbabcbccbcacabcaabadbaaaaabcddaccbdcddcdbcabadccacdacddbaabaaabdbbbdbbddbcacdbbdcacdbadadbccdbadaabcbbaabbbddbadccdcddddddcaccaddccdcabbcbaadbdbbcdabddabcacadcbcdcbbbdacdacccdaccbbadbacdaddccbbdcdcdcabdccbbcabbacbabbaacdcababababdcaabcccacaabaabbadadadbdabaabacccaadbbdcaaaadbcbdbcaaaadcaccbcddadbaabbbcbbadacabcacadbdbbbdbaddacccccaaadbabdbaabbaddaaddaaddbacccccdcbcbbcdabcbdadbbdcbaabbbdddbbcbadadbabcdacbccccabcadccadbcddadcaadaabbccbddbcacbdddcbdacdbaaaaacaadbadaccbcdcdbdccbdabddcdcabaddabbbdbbbdababbdbbbadcbabbabaacacabaddddbcbbbbdcbababacdcadabdbabbaabcddaacacbbcbbcdabdacccdbdacbcadbcabbadccbadbcadbabbcadddbbddadcdbbaaadadbabdbaacbdabbacabdacaaccccdbcdccadabbdbacababcccaadbbbdbadbbcaddbaacbbadadbdaacacbbbbddbdaadabbdbadbbacadaadccbadcacbcbbbdbadcbaccdcddaabbcaccccadadddbbcdbcdbadaaddddddcbbbacacdbbaccbdbcdcbbbbaacbcbbabbacdadbddcbccbbbddddacaacbcaaabddcdbadaccdcaccadacaacbabcdcacdccaccbbabbccaaabddbcbbdcdccabdabdcacadbdaaddabacdbcbaccaddbcaadbadaadaaaccdaabbacbabbddcbcaabaabddadacacbdbbdadbbccddbcbbbabbabdccabbdbddabccdbbcccdddcdabcaadcbdcadaacacaadbccaccdcaccacdbadacccdaaaabbcaabadadcddacccaadbdcdbdcdabcbcacccbdddcdcbcdbddcddaacbcacccadbdccbdbbdcccabdacabbabbdbcbaaaaaacaccccadbacacbdaadadbcccbbbaaddcbbcabdccdabddccabadaccbcdabbaadccbbabbbdcbddaddcbdbbacddbcdcdbcbddbcbbdabcbbaadbbdcdacaacabaaaddccaddccdbbabdcdccadbcdbcabbcbcaadbbdabbaddbcccddcbdbacbacaaacbddddabddddbbaddbbdabcddccbbabadbddbcdbdadbddadcbbcadddcddcabcabbcccbcaddcbaacbcdccccccdbccddcaddcbdcabdacdabbdbaccbcaccddabcdddcbdadcbccbadcbcddabababadcdbbbadbbabbababaddadaadccdbabccbdbbdcbdcaccddbbcaaccdbcadccaaacbbdbbaadcadabdbaaaadbcbdbcdaacbdcaccabcdcbadacccdaccadbdbbdcacadbaababbaddbdcbabaadccadaaadccacbccddcadccabbccaddddddaaaacddccabcadccabaacbbbdbcacbbabacdddaaadbdaadccdacbddbabbbbdcdbbbbbbcaacbbabadcdbbdbbdacdabdbdbddcadabaaddabcbadcdaccdbadabacccaacdacdbbabdaacdbdcdabaabbacadbacdbdacbcbcacbabbdaabdbacabbbcaccdabddccbdacaaaccddcbcabbcbbcadcdaabbbbbdbaadcbbaaabddaadadadccadbacbaadcddbcacccdcbacbcbbbadbaacbdbccddcdbddccacccbdcdbcabdbbbcadacbbbaadcbcddbdacdacabaabdbcccdddaadbdcacaccddacbcbbbdddabdadddcbbaaccdcabdccdbbcbdaccacacabdccacdddddbccdbcdcdadddbbdddacabacdcdaccdcddbddaccdcaacdbcdddbdadcdbadadacacaaadcbdabdbaccdbaabcadacdbccdddccbadccbabcbcdddbbdcadccababbccabcdaacaccbacbdbcdadddbdaccdccdacbbcbbcdbbcdcdbbacadbabadbacbbadcbbacacbdbaccdabcbcdaabcdbdbbdadcccdabbdbbcbdaadabbaddddbbdbbaddccdcadccddbbcdcaccbbdaddcaddaccbbdddcbbbcbcbcbcbcbabdaaccabaacaaabaadaaacadaabbbbbacbdcbbbdaacacabcbacdaddabcdabbddbccbcbcabddadcbdaddcadbcabcaabcdddbbcbbbaddcbbabdbddddabadbaadcddabbaaabddccaddabddbadcdccaacccdcdaccbcadadabbcbdccbbdbdcbdccabacdabbcdaadcdcdcdbadbdcabcacbcdcadbbccdbddbabbbbbdbdbbadaabacabbbbdaacbbacbcccabcadcccbdabadcdcdbbccaacbbaddbacccbbbdabbbaabcbaabadddbadcabcdddacaadbddcadccadbabacacbcbadbadabccbdacdabbbdaaadadcaddbacaaadcdbdddaccbdabcbddccaabcccbcdccdcdbcbcbbabdccaacacbabaabcddbccaaadbbcadbddaadbbabdadadcdcaccbcbcadcbdddcbacbbaddcdcbcdaabcbcddabbcbbbacabccbcdddacbbabdaaccbbccbcadbbaacdcbacdbcdccbbbdacadaccabccabdbccccdadadbbcabcaadacacaadbabdbacaaacbadadaabccaaabdbdcbadacbaadcddbabacddadbaaccbcaabbccccdcbbbadaaacbdcabbbbacbdabdbcdbccabdbcbabcdbbaadccadabcccccadcbbdcabdddbcbdbdcbddddbddacbcacbaaacdccbbaacccbdbcaaacbabcdcbdbdbbcdddccddcabdcbacacdcaadbaddbbdcdbdbdcaacbbbccbdbadbdcddaaaddcabcdadcbadcdccbbaabbabcadabddabdddcabcdabdcbdacbddcbbcccadddcadcbbbdcbaabbcdcdbacabbcacbdbdcddccaacdacabbbabaababaacccbdccbcbbbbdcabcbbadcabbddcdbdcdabdaccddddbcbdcadcbdbddbcbbdddcdcaddaaabbcaadcaacabaddbcbccdbbdaccadbaacadcbbbaccdbbcababbbbcaccbaadbcadccdbcbbadaabcbaabbdbbaacbbaaccdababcbbbadacacbdbcbbabadcdccacacadaccdbacccabdabbadccbcbaadbbcbccdbababacabcadbabbcacdcabdadbdabcdcdccabcdabbcbcdbdcbbacddabbdbacdcdbcdbdbbcddcaabcabbabbaaadbbabdcccaccdadcdbcdccaddabbbbdadaacacdbbaabbdcacccbaacbddddaabbdccdcdbabbcacdcdcdadcddcdcddadaaadacccdccbddaaccdaaccbacbacadbaddcabbdcaadadbbbbcdaaaccdbbcabcaddbabdabcddbcbcbcdcddbabdcbaacabbababccabacabdcbbadcdaddbacabbbadbdddddadabbdbbcabdadaabbabdbcdadcbcbcbbccdcadaadcbbcbcbdccaabdcdcbdccacdcacbcabadcdbabcdcbbabaaccadcdccaabaabadcdbdcdcbcbacadbabcaabdbccbadadcddddacacbacacdadbaddccddbabbdacbdaccbaddaaaacdabdaadddcbddbcbcbbaaaddabcbbbbdbddbcacdadacdaacdbbbcbbaadcabcbbaacabdaddadbcdccaaadbcdcadaadbddaaccdaaabbccdabdccccabbccbabbdddbdbdaabbbadaacdadadcaacdbdadcbbdacdbaacbaccbacdaccdbddbcdbbcabcaaaadcaccdcaccbcccacdaddcbddcaacabdcddbcabaaaccbaabdbcababbdcbddaddcbdadabbbbcbbabaababbaaacbadbccbdabbabbddcdcacccaccaadbccadddbcbcadddbbdbbccdbddabcaaabbcddbdaaacadbbcbccabbbaaaaacbdbdbbbdadcaddbaaaaccaccbbabacdbaddacbbacbdbacdddbcccccdcccdcdbabddabdbddbdbbddbdabbbbbcddcbdaabcbdbadbaacdcbcdcbcaacddacdccdabbdbcacabdcbdabbdcaabababcdcdbdaaaaaacddccbabdadacaaccdcccbbdccdbbdbcdababaadbabdabbbccbbdbbdbcdcbbcbbbbdbdaaaaaddbbcbdcbddcdabbbdbbcacbabdbbcdacdacbbddbdcbbdbcadbaadaddabadbdacbccbdcbaadcaaccdcaabdbbabdccadabcbbbcbbadddcbabbbacddcabbacdcccbbaaaabcbbaddcaacdbbddbdacddbdaabdcbcbbddbaababaaababbbbbdcbbcbdabbcbbdbaddbaacadabbaddbbbbccadacdcaabacdacbacacbdbabcbbdaacddadcbbcdbabbcddcddccbdadcddcdaacaccabddbdcaaadbcadcbccdcaadbdddbdbaccbbddadabcadcbcacaaadcdbbbadbdcaabacabadddabbddaacbbdbcadacccdbcddddbadddcbbacabaddcddaaadcadcbdbadccadacdcacaadccccbadadaacdbbddbabdacbbddcdcdcdbccabcbacbdacdccbbddcccdaaccdbacbbaaadaaabcdcaabcabbadbcccaaaaacbcaccdacdbddcbbbdccaaadaddbdbcadbaccbadaabddbdabdbadaccccababccccbcbbdcabbabddabbccdbbcbabaddcddbddbacdacbcabcbccbdcbbbaccaacdcbbdabcdddbbacaaaabacbcbcbbccdcbaaccddcabcbdbbcabadcdaadbccdcbbacdbdaccbbcbdaccbcdcaaabbdacaccdddabdbadacacabbbdccbdccabcbdabcaabcdbaaabcbbacabbddddbdcbccadcdcdcdabbccddabcdabcccccabcccbcacbbaaaddbcdbbaabcbcbacdcadcdbbadabddaacbddadcadcdabcbbbcbcdbcbbacadcaccaaadaacacdbacbdbacdddcbcdbbacccdbadcdbcdcdcaaabcbcadbbaabacadaabddabbcabaccabacbadadcccdcbdbbbabaadddcbdccccaabaabdcaaabbcdbbbdcdabaadcabdabcdadcaadccddcbcabdacdcbbcdcdbbbbdddbbdcbcbbaadbdbaadbbddccdbdaadabdbbbabbabddbdddbbbdcdbcdcdddcaaddddaddddbabbacbbddabbdadaaabbabcdcaabbcbdcbadbccddabbdbddcabdcbbdcadccbdadabbdbadccbcdccaccadaabbbbaabcbbbdcdacadbdbdadbdbbdacabcaaabadacbadcdabdcbaaccdbccdddbaaadbddbdacdbacbababcadcdddcbcbdcccddbcabaaaccaaacdcacabdaccbdbdcdbddacabbdaaabacabbacccacddcacadcdadabbcbcccdadcdbdbabcadbbadabcccdacbbccdbcdabcbbcdddcadadddcacbbbbbcabbabbbbbcbbbcdbccbbdcdadbadcbcabdcbbccddbdcdbadacadddbddbaadccaccccbcccacacbccbaadbdbbdcccacddbcbbaaacdcccbbcbdccbdcadddbddaabdadbdbbadbbbdcdcbdbbdacabccdcdabbddbdccdcaadacdcbdbaabdabbcbbcbdcdbdabbccbdddddbddaddbdcbaccdcdcdacddaaababbdcdabcbabbadcbabcdbbcbbaaabdcdbaacddcacaabadbbcbccaabacbcdddabccaabadddaaaccdcadaadbbdddcabaabddccabbdbacbdcbccdbaabcabdcbaacaabbdccddcabddadbcbcaababaadbbcacdbccadcddbdcdcbabcadccabcbadbbbcbbbaabcbabaaabcabbcdadcaadcbddbccabbccbcdaddbaababbbbdcbbdbbabacaccbbaadbbabbbddadcbccdacbaadcdcabbbbbcdbdaccbdaadccbdbdcdcbacbaaaaddbcbbdcdaccaacadcbdcbccabddbadadbccbbbbdcadbdcbddddddbdaacbdabdddbaacabdacccabbbacdacabccabddcbcbddbcbddabbdbcddddaaadcdabcacaccadbdbacbbdadbccdbbbabacddcaadbbaacabdbadabbcdcccbbdcdbaabcdcbdccdbbbadabcccaabbddcdcabcadbdabcdbdbcbdabaacbaacdaacbdbcddbbbacbacccbbcbacdbadadabdacdbaaadbabadddbbdacbbacbbdaabaacbdbbcbbbcabcdcbaccabdbcadaaababdbddcaacabbaacababbcbddadbaaabaabbddbbacbaccaddacadcccbcdbdabaabdbbacccddaabbaccdbbdcccbddcacbabcdbddddbbabcccbccadaacbaccdababcdbaaabadcdccdbbcbaddcdbdcbbcbcdcdcbbbdddddccbadbcbbbbcacbbbbbdadcaacbadaacadcccbacaaacbbcbaacccbddaabaadabcbcdccddcdabbbcccaadcdbbabddbbabdbbdcadabcccbcbacccddbcbdcbcaacaabbbbabdddbabcdcbabdbdaccadbcaadcbabcdddcdbbbaddcbdbdbabbacbcddcdcdbadacababcdcbdcbdaaacaacbcabddadaacaccccaccdccacadbaaabddbbaddbaadddbabbabdabbacaaccaadcabcabcdbbadcabdbadbadbbcbabdadcabbcddabdadcacdcabddacdbcbbdadbbcdccdddacacacbddbcccacbabacbacdbccccdcadacdcddcaddbdcacdbdadbbddccbacabbaabdcdaabbcabdaabdccaddabbdbacbdbaacddababacbbdaaacddaccccdcbdacbdabcdadababcaccabaabbcbbbbccbccdbcaccdbbbdcaabcbdacacabdaaccdcdbdccaaddbcaaadabaadbbabbcaabbabaacccbabcbbababccdbbbbaddbccbabcbbddcadbccadbaccadbbbbbdddaaaaaadbadcabdbbbadcdcbababdababcbbdddccacdaccccadbbcadadcbdbaacaccccbdbaaabcbcbcaccdaaabcbdbacaadaccabccaadcababadcacadbcacbbdadcbbccdcabddbddacddcdcaddcbbdddbacbdaadaccbcbdadbaddacddbddddaccacdbdaabccdbdbdabdcbbbaacdbbcadcaacabdcdacbbadadddcbbaacbaabbcacadcbadbbcdbaaccbcacbbddbddbbdbabcbacaadabbddbdbbcbbaadbcadbcbdaaccbbbbcbdacdaccddccddadcbbabddcbdccbaccbddbdadddbaaddbcdaabbddbbbbcdbdaabaaabcbdbcbcabbbddccbaabbacbadacbbaabadcdbdcbdbdbcddabcbacdbacbbccacbcbdaabccbcbdbaaacbdadaaccbadcbcdccccddbbddadaccdaaaaccaaddbbbdbdddacbccbaabbabdaccacbabdcabcbbccaccacdbdacabdabbcccaddbdbcdbcacddacbdbcabacbdcccadacbbbdacbbdacdabdcaabbccaddaacaaaaadcccacbbaaddbdabdadcbadbacbcbbbcdbcdacadcaabdabdcccccbdbbbacacbcdbadbcabcccabbacbbacddadabbcddabdabccabdcddadbaaadbaaddddaacabadcbcdaabccadabaccabcccbdcbbddbbbcccbccdacdcadcbbaadbaaaacaabcaacdbdabbbabbddccbcdaccbacbaccddddadadacdbbbbcacccbaadacdddcaccabbbadaddaaccdabccbbddadccdddbdcacbcbaaacccbbcbbbbccacccaddccaacdcbdbcbcbdababcdadcbbdbabcbddbaddbaaddbbdcbadddbadcbbbbcadbcbdadbddcbdabccdcbddbdadbdbaabaccdddaaccdbacaabaccdabdaacdccadbcdccadaababdcbbcddacdbdcbacadabcbabbbcadbddaabcdaddcdcabdadcdcdbbbdcbbbdabcadaadbbadcacacadcdbaacbabdccacadbbbaabcbcdaaabaabccbabccabaadcaacdcacbacbcdbbddbacbabbbcbbbdbdccbadaccccadcdcdcbcbcbacacbabbabdbacaddcacabdcaaadddddadbcccbaccddbddbbbadbabacddaadbabdbcdccbcaadbadacddcdcaaadbdcbbcbadacbabcaabbadaababadccacacdcdaddbabcdaacbbbcababdcaabacbabacadddbbdbcccbdbbbcccabcbbcbbadcaababbcccadaabcdddcbcabcdacccabdbbbcdcaddbbadacbbaadddbbadadadcdadcacdcbcadaddccccccdabcbbaaaaaadbcdbcbcdcbccaadddcbcbbccadadaadaaccdcabadcbcadadbcaaccaddbbbacbbbcaaaddbbdaccdcacdcbddcbabcbcdbbaacdbaaadcccbdacaadbcacabbbbddcccdabadbaabbbdbdbbacadbbbbabcccbddccabbcbddbcddcbcbaaabcdbdcdaabbabacdabacacddccccdcacbdcbcddbbdbcbcddabbcbccdbdcacbaccabdaacddcaddadbcdbabcccddccdbdccddccdcbaaabaddbdcccacabbcddccbcddddabababcaaadcdbdddbadaadcacdbdadbadbadcdbbaccbcadacccbcdddbdbdacbaccdaaadcbabaddcacdbcbdcbabbbacdcbcdacaacbdaccbadddbabaacdbcdcbadddacabcbbbbcabccbbaadcdcddcccaadccabcbcccaaacaabaccbbcbbdabddacddcdabbcdaababdbdcdcdbaaaaddcdbcbacdaadddabbacddbdaccbbcdbdadabcbdabdacbaaadcbabcbddbdbbddaddadacadcbccdaabbdcadcdccdadcabddabdbadccdcadbcddbabbcacaacadbcbcbcabadaadabddcabdddabbcaddbadcddacdddaacbcabbccbadcaaccaccabbbbcbbcbcaddbbbdadbbcdcbccacaaacccaabbbabddccccdcdccbadbcbaaadccdababbccaaddaadbdbacdbbccbcbdcdccdddcbbccdcbabccdbbbaababddbccccddaddadabacacaddcdcbbddaaaccccccdbdddadcdadcadbbbccabcbabaccaaacadccdccabcbcdcddddcdaabbccaddddaddabdbddabdabbacbcaaabdacdababaacbcbcdddbccdaaddcdadacadabccdaadacacbabccbaacdcbaaccabbbaccdacadabaaaabcdbdcaddbacabdcccadcbcaaaddacdbcacbabcdbddddcccabadcccdbcbdbbaddaddcaaddaaadbadcbbabccadbdcdbcdbbbbcdddcabbbaacadccacaadbadcbaadcadbcddaabccccbbbaccacacdcabdaaaaccdabdaaccbabcddbbbdabbcadccccdcdabaadbdabdadbcbbadbabdadaabdaaccaacccdcbbccdcdabbdbbccbdcbdcbcccdbbdadcbaccbcdaabbbbbaadccbdbcaabccbdbdbcdbadcdabcdddabcbadbccdcbadaddacdbcbbaababbdaadcbacbdbdbacadcbccaacbbdabbbabaacdbdbacdaddaababbcbcadcbadbcddddadcbbcabbabddaccdaadbbacacbdccbdabaaacdabcbaacaabbdbaddacddabdcccdcdbadabccabadcdacdabbcbbdaadabacacbabcbdbbccacbccdbaddaaccdddcbacacaabaacbbbddbbbdbaabbbabcbccccaaddbcdaadddaadbbadbabccaacbcabccccdcddbdbcddacadcdbabcbcddcbbdcaabcccddacaacabdacabcbbadcababdddabdbbdbdadcddbbbdbbddacbbaacbbbaabdababddbaccbcaaaccddbdcdbabbdcbdabadaaadabdbcbacdbbcbabadcabbaddcccccdbaccabaccdcaacaaaaadcbdbbcbccabddabbbdbdcbbdbcbbaabbacadbbddcbdccdacaacbcbbbbdacacadabadbdbadcdddcbcbbbaadccbabcabdbdadbcddccccbcbcdccbabbdddbaaacbdbaabbbbdcbcaccabadcbddcadbaabcdbcbdccabbbbdbcabdaddbbaabaccbccbdbdacadcabbdddccabaaccddddbcabacaaaccbcccdbbbddbdaabdcbadcaadcdbbddddccbbddbdbcbcccccdbbadbadaaadcdabdcbcadbddacbdccaabcaabcdbcdbabddbacbdbabcdaccacdbcadcacddcccdcacdbaacadadccdabdcddcabbcadadaccbcadacbadaabdddaabbbabcacacbdbacdabbbdcbbabcbbadbabcdbababdbdbbdaaddbbdbabbadaaabbbdcabcaccbacadaabcbaadabadddbbccbbbcdabddaacdaababbcbdbaaccccabdcacdadcbbdbbbdddbcbcbbabcacbdadbccaacdcacbcabbaabccdcdbaabddadcbdccccacabbadccccbcbacadcaadcccdccbccdbabccdadcddcdbcdddcdcaaadddbacdccdcacbaadcadacabdbdadbbbbcdabcccdbabddaadababdacdddaaadbaccddbddcbcddbbbbabcccdbccadaaacbcacacabaaaddcabaadbdaacddaabdaadccdaabdaaddacbddbbbacdacbaabbddaaacdcababacaacdcbbacbcbbbcadddcdbbbcdabcdcccaacddaddccddbddcaadcaadacbdcbccbbadccbdcccdbccacddcdcaaadadcbacdddcaddbcdbdcabaccdcdadbcacccbdccbbacdcbccbccabdaabdacdcbcbcadbccbbcacaabddabccbabdbbacdddacccaadbcdacaaddbdaadbdbdbabcddbbdccccbbcaaababcaddbbbbabbdbbdaddccbdbcdabbaabdcaabbbadaaaccbbaaaacbdacbbcbacadddcbcadbccbdaacacbbbaaabcbcaddbdcdadacdaababbaabcddcadcbdcbcaabcaaabcacdbbcbbaaaaaaadabbccdadaacabcbcbcababcdcdbcdbcdcbccacccccbcbddbadcabbddbbcadbdcacdabbdcbbbbbdabaabaabddbdadabbbcbbdbaaabadabbdbccddddbcccbcdbbdaddaaaddaccaaacbaabddaccccabcdccbabbcabbbddbbccccccbccbbdaaaaaadabdddddddbbccaaacdaadccdbdadcacddbbcaaddcdddcbcdcadbdadbcbdccaaacdbcaaadacccabdccdcaacbcbcddacbdddbbdbcbaadaacdadbcbdbadaaddbddcbbcadbdaaddacaacccacddccabdbdbdaacdaadbdcaddbdcabbbacccddbdadbbabdcbabadcddbbdcadacbdaadadaaabbdbadbcbaccbadcbabdabcbbadadbdbbbcaacbbcddbdaabdcdbcadbdbadaddcacbddaccaacddabaadbbcbcdbacacaacdddbbbaccbbabbabaabdddcbcadbcacbbcbbcddcabdbbaacccddcacbdacacdaabbbccadcdddbcacdaccdbcbddaacdabddccaadbaacabddaddbddbacdddcdcbddcbdacccdccbcaaccacdddcbabadbccbdcbdcaacdbdacbabcddbbdcadacaabacabcacbbcbbccbbbabacdcccbdbbcbcddadcccdbabdbaabaccdddadbadabaabadbccdbbccabaabbcddccbbbbabaadadbddddbccdadccabbbaacdabbdbdccdaacbacdcacbdccdabacdbbabcdbdbdddabdacaddaaaabccdcbadddadbcbdccbababbababccbdccacbadbaddddbbadddbcddbcbccdadccacdadbbdcdcdcccdcabaabaddcaadabcabadcbbabccccacbbbdbbdaddacdacdbadcacbcabadcbdbdcbdbdcdacbbcddccbaaabadbcadaadcbaabcacaadbbadaabdcccccaccddbdbbbacbddbbcdcbcbdddbacaabbddcdbccdacbcdbcdcdcadbbaaadabbdcabdbaadaabbccdbacdabaacbcdcababcdabcdacbddbaddacdadcdbbdabdcdcbcbddadcaaaaddadbdbcdbaddbabdbaaabbabccccbccaddabbabccbdaadabacdaacbbdadbccbabacdcbdbadbcacaaddcdbabcdddccdbddccbadabdcaddcbbddddaddaabbbddcdbcaddacaacaaddabbaaaabbdcacadbddcbddcbccaddaddaabcdbcaddcdacddabccdadabdcbbaaaaadcbaaaccacdaacbdbccdadcddcdcbacbcdcbdaadcbaccdccbabbddaccbbbddbccccccadccabaadaabababddacacaacbdbaddddbbbccbcbddcbcddbddbddcbdcdbddcdbacdcccaddacccccabbcbccbcbacacbcdccbddacbddaccdcbbabbccbbdddccbdadcbbbdbadacdbdddabbadadbcbdadcbadbbbacbdbbdcbbccabdabacdcacdcbbcdddbaaadacbcbdbabbabcaccabdcdddacacdbcdacbaaaabaacbadababbccaddcaabacdcaadbdabccddbbdaaaccabadabdcbacddbbbcddbbcadbbdabccabddddcabacbdacbccbdacbdccabcacbdaacddbbbdbabdddddaaaccbdcabbacdbcaccbdddbaabadcccabaddccbbcaabccadcaadcccdaaacbbbcbcbbaadcdccbbbcccabdacbbbbdcabbbacbdcbdbcccdcbbdbcbbaadbbaaadbaaddbbaacadbaddddbaabdaaabaacaddaddcdabaccacccbdcabacadaababcdadcadcabcbbdbaaabadadccbadadaccabacbcaadadbccdbbdbdbcabcababaacbababbbaabbdbaaacadbadcddabadacddcadddbbddcdbbcabdbccaddbcdaabaabcabbaacacadbdddccacadaabcdbbbcadabcacdabcabbcaccbbdacdccbaabcadbbcdbbaabacbbbadacbabbcadbbbddaadddbaaadddccbaababcdcaaccdbcbcddddaaddcdabddcdaddcdbdabdccbabcccdaadbbdccdcddcadddbbaccabbabbdbadcadcccdcaacddbdccbbbddacabcdcbdcabbaadddbccacdbdacbaacccdaaabbccacddddbadbddcdbbdcdddbaacbdcdccadddabaabccbdababdcddddbacaabdcccddcacaadddbdaabcdadabcdcccdbabddaabcbbdbbdcaabdacacabccbacbbadbbcbcbcccddcadcaaacdadccbdaccaacbadbccbacabcbbcadadbabaabdaabcdaaccccabdaacdcbccbbaabccabdcdddadcdcccdcbddbbbdabcadaddbaaccbaabddcbcdcdcdddbcdddbbcbadabbcdadacdddbcccdcaddaccdcdadbabdcabdcacdbababbbbbaabbcbbbbdccaabdbbdbcdcadadaacdcdbbdddbaabacbdaabbadcabdbdcbddccbdaacdcdcdaadbaabdbabadbcccacacbbcababbbabccbbbdddcaccdbabacdcdaaabadbbadbbbcabcabcbbbddabbaaadacaacababdcdcacabaccdaacadbbadcbdcccbdcabbcaadccbacadaccbdabccccacdaddcddadadcbcbadbbbcbbdcabbbabccdbaabcccbbcaabbccbdcbcdccdabdcddcbccaccbbacaadadbdbbadacacccbdaccdbadaacadcccbbdadbbcdaacaaabbbbdaabbddacbcddbaaacdcbbddbaacdacbadabacbbdacdbcddbdadbcddbbcddabdddacccaddcbcdabdacbccdbcbddacaddcddddbacadcccccccbbbcacacccdcdaaccacacbbacbbacdadcdbbcbcccdabbdadcdcdbadadabccbbacbddaacccbddddcaaacbdcdcbbbbcabaaadddcbacbadabadbdbdabababacacbdcbdacbacddbaadaabdacbbdabbaaadbabdaacdcbccdbdbbcbaabddbdbadaacdaaadbaacbabbcacaacadcaaadaacdbaaddbdaaccbcbbbdcccdbaadbcbacccdaaccabccbabdcdccbadbcbbcadccaaccdbcacddaadcccdbdcccdbdbcdadabdbbbaadbbabacacdbdaabadddabdcdcadaacaabccbcadbaabdbbbaadaacadaacacaaaacdacadcabbaaaabdbcdbacdadaabcdbaacbcdccacacadbaababcddbbddabcccaabaddadbaaaccdaccdaddcacdbaabccbdcacaaadbacbdbadcdbaaabdbbbbdbacbbddbcaddcbdbacadabbbbbbdbaacdccaaaaadddbccdccacabdcacdcabaacabdabdaabccaaddcbcbdbbdccaddacdbdbdddbaccbcdddcadccdcdcdbcbadbadacdbccdccccdaaacbddbbcaaaadaccbccdacaadccbbbcaccdbaabaabccdabacbabcaabcacadbbdddadadabacccaacccacbabdbbaaaddcadbbacccccdabccbbdcbbaabaaaabbccbabcaaacabadaddbbaadcccdbdccadbbccbcdcdcaacdabacacddcdbcadbcacccaabadcbcabaccbdbbbdcbdadaddccddbdaadacadbbddbdacddccdaadccccbdcacdcbacbbbbadbaabdaccbccadcddaacdcbccbadacccadbababcbbdddadbdbcacddbaadbdddcaaabcccbccdcdcbbabbaaadccaaaccbcabcbddddccacaababdcbcbbbacaacbcddbdcbaddbcabbbbbadcbbcdddcccdccbdcdbbadacbbbaddabaaaadadcdbcdbbaacaaddbadcaccaacdbbabcdbaabdadbdadbcdcdbadaabacaddddbdddadcdbddcbdbcbddccddbdaababcdbcdcbbbdbddcdacbadabbccdbddddcdacbdccdddbcddaddaccdcaabaaaabdccabbddaddbcddadbccdabbdcdcbcbccdcbbdcddacbdaccbadbacccacaccddbabadcbaddbabcddddbcbabaddbcbbcdddbdadcdccbbdbcbdacdaaacbadbbcbbcbbdcaccbcccbacbbacbdddccdcbdbcdddadddadacdbbdabdcdbaadbdbacbadaaccabcacdcbdabacbcdbccaadcbbabbdddadbbcdaabcdbcddaddcabcbbbcccbababbdbabbddbaccbadbacabdcaddcababbbadacadcabbdccdabcddbcbbaadcccaaadcdbccbcccabbbdddcbdcdddbbddbcbacbbdbcdcadbcbcacdcddccbbaddbcabaaadadddacadabdadcbacdacbcddbacbbbbcacccbcbbaddbccaaaccabddcbcdadcbaacbdbabadbbbabdcccdabcabdcbcdbabacbabcadbdcdbbdbccbdaabacbdcbcabadbaaadacbdabdbbbcbcbaacbbdaaddabadbcabbddbcaccacabcdcadadbbddcddbacdcbabaccdbaacbccaaacdcdabaccacbaaacdabcabbcdbadcaddbbdddabbcdbccbbddabaabdcaadadccccbbcdacadbbdbbbacdbcbcbabbcbcbccaaacacaccddcbacddcadcdaaddcdcbcdcddacacadcadddcabbddbcabcadbadadaddbcdcacbbdccbbdabbbcdaadccbabcccabcdcbcddbdaccaccccbcbaadbdbbdacdacddaccabbaccbadabdadcabccdacaccbbabdcdbbdacdddacbbadddababdbaadccacaaabbcadcccddddacddccbbbddbadababbbbcddbadbcabbcdbabbdaaacaabbadddbdacbbbaccbcaabbdddaddaaabdabdabacbdadcacbddbdbddcbbbbabbdccdaddbddbdbddddaabcaadadbacdaabcabdccabdadcbaabcbdadababbbaaacaaddbacbcbcdaabcbdcdbbdbcacaadaacbaadcabbcaacbadcdabbbababccddbcccaabcdbbdbcbdaaabcabaddccddabababaabccacdacabadaabbbddcaaccdacdaaacadccaadcdacccbcadcbbdaaccddbaaaddcacdcbdcdcbbbdadaaabcdaaddabddcaabcbbacaacaabaabbcbbcdacadccadcddcbccdbcaaccaccddaccabbdcbaacddadbabadbbbbbadccdcacdbcbabcdbacddcaacbbaaccbdacabadcbcddbdacdddacadbdbbcbaccddabcabbdbbcaabbcbadddacbbaabcaabaadaacdabcababddcbdabcadadbbbabcaadcbcaadcaaaccaccaadacacdcdccbbcabdccdaaaccabcadcbcbcdcbdacabcadccbbaaaccaacbbdccdbabbaabdbcaccbdbdbbcdadcadbddaccadcdcabacbcaacbaaddcbcdbcaddacbdbbaabddbadacadcaaadabdacbacbaadaacaaddbcadbcabbdbcadbaccadccbddbcccddccaacacbcdcbaaddabbabccacccadddbcbddbaccbdbcadaadaadddaaddbdddcbddabcdbddacadbddbdacabccabccaacbcddccadddbcdccbccbcadaddbddcdbdcdacdbdbdbacadcbaaaabbdbacdbcaddbcdbbbbaddccbbaaacbacbadcbcadcdacdacdcbbdbbaabcdadaadbbbadbbbdcadcbdbddcaaccabadccbaabaacacdcbbdcaaacddbdaccabadcabcadcccddbacbdcbbacdddccaddcdaabdabcbbdababacddcbbdadbbaddcaddbbdcacbdddbcddddcacaadadddadabcadaaabcaddcddcbabbcbbadbdacbbdbbcbdbbdaacdadddccddcbbcdcccabcabbcbabacbbbadcdabcddccbdadcdbcbddbdacdbdaaccabcbdaccbdcbccddbbbdadcabaacaccbcaddcbccbacdabadccacccbcabddaadcbacbcddbbabbbbbaacdbccbdcbdadaccaccbddccaccdabddcdbaddbbbdcacadcabdccabdbcacccbabbdbcddbcdcaacbbccbdabbcbabbccaabbaaddccabbdbbdbbdcdaacbbaaaadcbadabcabbbcaaadadddaacbcddccacaaddbdccbbbadaccdbbdbbddcdcbccaadbccdcbddcadbadabbadddbbbbcdbbbbabddacbcbbccadddbcaabacabacacbdbdabbbcabcbbcabdbcaaacbadddbbcccbadcbbabcbadbacadbcbabdbddaddaacabbdaabbcabbacbbdacdabcacdccccadbbdaacccdbabbcdbdaccadbcacaadcadddbdaccdacaacddabadcadaadabcaaaabdddcbdbccbccaadabbdddcccbbdabacbbcadcbdbaabdcdcbacddadcdbddbccbcbddccaacdcbdcbbbaadcdbaaacddcbddbddbcccaadaacdabbddccbbbbccddabbddbbdbacbcccbdadbbbddacbdabbdbdadabbdccaababccbbcbbdbbbbbbaaababbadaddacbdbaaaaddaccddccbabacbdcddbbccabbbadbaababcababdddcccdaadaabacdabdaadaaabdbaadbdaabcddbaddccdbbcdcbbbdabdadcabcabdcbdcdabccbadacabdcbacabccbdbdcdddaabcccbddbccdddaccddaddcdaddbacccbdabdccddaabcacabbdddcaabbcbccacabcaabbaadcdbdadcbddcaccbddccdcbddccbccbdbbcadadbbaccbdbbdabbacbcadbccbbddcadacdcccacbcdabcbbadacaacabaaadddddcbbcdaaacdabcbacdbbbbdaaacaaadcacdcccdcbcddcbacdddabbcacbcbccdacabdbbacbdacdbbabaababbadcbddcdddbbcaabbcbdaddcabadabdbacbbbddbaacabcbbbdbaacccbabbbdbacbcabcaabbaacadbaccddcdacccccbdcdadbdccaabacababaddacbbacabccdcbabcbdaabaadcdaabdbcddcaabbadabdbbbbcabcacbccacdbcbbcdbbaabaacddbabcccbcbbccddbbcabbaadcaadbabbcdacabaccbbbdddccbbadabccaaadccccbbdcdcaacdbcdbccadcbdccbadcdaabcbcdbabdabaabcbababdbcabadddabccddadcacccddcddcdddcacbaccccdaddcadccbbacdbcbbabbdcbbdababcbcbcabcbdbcaaabaadacababaaddbbcccbadbbbdabcabcdcadbdccdacaccccacabdbadbaccbdbbddcadacbcdbccbdcdbbdbabcddbccdcccbdccbdacaabbdcccddabcbbcaaabadddadbbadbdbcbbacbabdabccacddbbbdcdaaddcaddabdcddabdcbbbdbabadbbddcabaaddbabddaaabbdaadbcdaaccbcddcbcbbcdbdccdcadacbbaddbabbbdbdaacddaaadaaccddcabcbbdadbcdbbdbdbdcadcbbaadbbddacbddbbbdacaacacabdbaabbdadddadbdbcabbcaddcaacbcdaaaaddbbdaabbbcbcbddccdaabaabdadccbdbaabcbacbacdbabcbbacdadcbdadaabbbbdabbaadbdbdaababdddbcbaccadbdcbbdcbcbbddbaaaaacbddddabcdcbbbbcaacabcadcdaccbadacdbcaadbaabddcacddacccbdabaaaaadcdddacdbdadcdbdcccbddccbbabcdaabacbdccaccbdcacdcdbcdabcdddbdcbbaaccabcddcbddbcbcaabbdbaadbccbbabcabcbccaacccbdcbdccbabcbcddcdccddddadadddbbaacabbbbdaacabdaacbcdadaaaaabadbdccababbcacddbdcbbcadbcdbbbbcddbabcacbadabbacabdaaaadcdbbdbbacddacaaaabbacbcdadcdbdabcdcbdbcdcacbbcdcbcbacdcddaccdacdbabbdddccbdbacbaabadbabbadccbaabacdadcdcccdbdddbdbcbabbcaacdadacbdaddaccddadaccbaabaddbcddbdcbbbcbddbbcacbaacdbdadcbbdddccdaabaacbcbabcabbcaddcbdaddaddbaacdbadaabaabdaccbcdcbccbdacbdabacacabaadabaacddcaabbbbaacdabcccadddcddbcaccbcbacbbadadadbaaabadcddbdbccaaadacabbabbacaaabccadbabaddbccbcbdccaccdbbbdcaaccbdaddbdbaccacbaababdaddabcdbcdcdbcdcbccdaaccbacddcdcdabddbaabbacccaacacddcaaaacbbbcabdaabdcddcababbcbcccbbdbbdacbcbcadddbdaabbbbacbbdaacbccadccccbddacddbddbcacdacababacdacaaaddadaaaccdbcaadcbaadadcdbdddccccaabddcbaccabbdbadddabdcbabaadaadabcdbcbdccacabacadcaccddcaaacadacacddabbadddddaadccdadccdccdadacbbabdabcbadddacadbbccccabcbaadbbbccdadbcabaaabbdcbabcccccacbcddddabdbcdcacccaadbdbadcbaabcaddbbdcbdcccbbcabdabadccacdacadbccadbbacdcdbbdaccbdacbabcdbcbcbcadccadddbddcacbbabcacdcadddccbcabcaddaaaadacaaddbcbddbcaccbaaacbccacdbbaadaadadbbbabdaccdbbcabdcdaddacbadbdbadadcdbcadadcddddcbbadadaddddcbddaabacdbcccbdbcdbddcdcdcacbcddaaadadaaadabbadccbbaabddbbcaabacdddccabcadccaddaacabacbaaabbcdcacdbcddadcaabdcabbbabdadaacdcdadbbdacdcdddcdbaadaacbacbcdbcdcdbadacadaaaaaacbbddbcaddadbdcddbcbcdbdcadcabbcbbacabbbccbcbcdcacaaaacddcdbbbcbadbdccdadadcadcddacaddddddabdbccaabccdcdbaabcaccabbbbabcbacbdaabdabdbcdaccbabdbabaabdacdbacbdbbdabaacbbbbbaadbbaadcdcaaadcdadcdbdbdccacdbccddbcaadaaddaaabacddcaaadaabcabadbbaddcdabbcdcdbdbbddbacabbabadcaddadcadbaacaadacdbcbdcdddcabdbaddbbacbaabdabcabbbccdcdddabbabdbaabacbbadaccbcbbdbdadccdbbcbddccbbabcacaaabccdabbbdabcbdbacbdaabdbacbcaacbbcaaddbdadcbcabdaaccaababbadbdbccbcdacbcbbbadbddbbddadbaabaccabbbdbcdccccdddababaabddddadcbadbccdadbbcdacbccbdccddcbaababdbabdccddccccaaaabbcabbcabdcbabbbacbcccbdadbacdacccababbccacccabcbcdddccacccdcbbcbbddccbccddbccdddbaddaadabacbdcadbdbbaacdcdadacbdcdbcaacacacbddaccbdbbddabbccbbbccbbcdddbdccdacbcdaddadcbdadbccdabccbbacdbcabaabdddbbadbdccddadbaaadcacbccbacdaaadcadabaadbdcbbcbbbbbadcbdddddcdbdddbbadbddbcadccadbbcbbadacbcdccdbbacdbddaacdcccaacbacaadbaadcccabcbbcaabdcbdacbadaadcaccaabcbdbcbcdbabdaddcdbabddcbcbbdbabaacacabdaddbdbbdccdbcbbddbaccccbcccaaddcbdadadbadabdddacdbdbbcdaccdbdbdacdabcabcdbcddbdcaadcdccbdbadcdaabbdbaaaacdaaacaccdbdcbacdbcbdcacabcbdacadccabbccababddbcdbcdddcbddabcacabdddcdacdaccbcaaadcddcbcbaaadaadacdaaccadbdbcccbbdbadcabadbddbccdddccddbcddcbbbdbdabccadcbdaabdccdddaddddbcabddbddaabadacdddababcabbabcaaacabbbdbdbbdbbcaaadcccbacbabacbbabadcacccbadbddabcbabdccbbbbbaaacdcbdbaccbcdcabbbbbaabcbadcccbdcbdbcdcddcdbbbbccacbaaccccbdcddcaaabbbacacaacdcccbaddcdaabccdcddcdabadbbccbcaacbbaadaaaaccdbacabcbdcdbdabcdbaababddbddccabdddcaadccacbbdcacadadaddddadbdcaacbbccdcadacadcddacabacacaaaccaadabcbababadcdbbbccbdacadacacdcacacadabbcacadaaadccdacdabaaaabadccdcccacbabccbaccccdbcacbdcdabcbbbabbbdcbacccbabbaabdcacbbaacbbabdadbcccabccdcdaaadabacddddbcdddadbbdcddaddbdddddcdcdbbbcbcabbdacbacccbddbddbcbdbbadcccbcbddccbbcdbddbbabbcdcddcdabdddcbbdcbaddcadcddbcbbcbdadaddbacccdcabadbdcdccdacbaddaaadddcaccdaccddcbdadbccdaddbddbaaaaababadcaccabdabadbaadaacbbdaaaacdbcbcdbcabadbcbabbbaaabcbadbcccdbbddcdbabddcbdbbcbcabbacdbcadacaaccdacdcbcaddbbbcbdacbbdccbdaabddaddcdbbccadbdaddbdacdcaabddbdaddddaaaaaaaaabdacbdacbadcccaddcadacaddcdcdabcdbbbcdaacbdbaacdbcccbbabaaccdabcbdaddbcbbaaabcaabcbabababaadbbaccddbdcdcaacaadcabbbcccadbcdbacaacbacbcbdddbccacaaaaaadcbacaaabdcdadbadabdcbccdaacabbcddcadbdbdddacbbdccbcdccdddbbdbacadccbbbcabccddbdcccacadbbcbcddacbbacccccbaacbabdbddbabdbacbdcadbcdbbaccaabccadcbabbcaabaccdddcacacdddccdccbaadbabaacacddbdccbcbabbddcdccbccababddddaaabbacccabcdcbddabbbddccadacdaadacdcabaddacaabccddcacdaaadaccabcabcaacdcaddaacdccaccdcbabcabaababccccacacdaddbbbcacababacddaadccadcacbaaccdddbbabbbdadbcdbbdbcdbacbdabcdacdcdcdcaaadcbacabdbbadddccdcbbdaadbcacbddabbcacbccaccdbbbcdabbbaacacabddcaccaddacccadaccacbabbbccccaddccacbbcddcacbaababaacddadcbddabbaccdccbbadcddcadcbdaadcbdacabbdbacbaacbdaccaccdcdabbabdddddcbcbdcdaababbcbbbdbbacabcaadddccdacbdcdccdcaabcddaaadbcbcbbddcaabcacacdacaacbbdaadcaddadcdccaacccddaaaadaabbbaabcbcabbcbdabadbcaccacabaaddacaadbdcaccbacacbdaaddacbdcabcabccdbdcaabdbdccdaddcaaadbdaabbcdcdddadaccadadaaccaadccbbdddccccacaabdccbaaabdbdddbbcbadcacabcdcbdbacdddddcadbdbdabaadcadcdccacdcccaccdabbccdaccddbdabddcdcdadbdbdacdccbbcacdbddabcbbbcaacdccbdcbdcdbcbcdabbdcdacdccaacdcbabaaaabcccadbacabbddddcabcbdbaacbddcbcbacdbccdbddbbaadbaccdddcabbacaaaababbcaaccddabcbabbacdbddaddcbcdccdabbaabbcbbddcaccdbadddddaccaaabdcaabdbddbccdbddbabddbdbaccbcacbaadcbdaacddcaadaabcdbbbbbbddbdcbdbacbbcababccaddbaaaaadccacbdcddacbdcbdabacbcadacacdddadbdcadcacbaaccdbaabcdcdcadddcabbddadaadbbdaaabbddbbbbcadddabbbabcddabdacdadcacbccbbcdbabaddcdbbccaaaddbcddbbcdcdbacdaacbcdcbacdbaddcbbbbdcdcabdadccbaaaddadbbdaaaacccdbbabccbaccdbcbacdccaaaabccbadaabadddaaabaccdccaabcacdcabdbbcacbcabadacbdcdadcabbabaabcabbadbcbbbccaccabbddabccdbdcbccbcddcdccadcbbacdadbddcdacadcdbaccaddccbadacbcdcdcaacacaddadaadcaabaddddcbcacadcbabcbbbbdccacdddcaacbababcdaddaaadcbcdcaddcbccbacbdbcbabdabbcbaccdaabcbbcdaacabacbdaaddcaaacbdbadaccdbcddbcdacbddcccacccbcbaddaaabddbdcadddbdbdadcaccacdaaccdbccdcaacddcdbbbadccbbbcadccdcdaaccbbbccabacbccaabacdcbaacdbbacbbcdbababdacaaaadbabddccbbacacbadccabcbccadbadbcdcbccacbbbbaaacabacdcdcddbcaacadbbcddcabdacdcdcbbbbddcddaaddcdbacbaaddbdbabacddaccdddcbbdbbabcabcdbaabcacaacadaabcdbcbbcccabdbadcaddacbcdcadaaaacbbbdaabddabadbcbdbdcdaacbcbacadadcabcccbadadabdbcabcbddadbbdccacbadbdaddbbcadaacbccddadbabccbadcbbbcaddbabaccbabbbdbacdcaabacabadddddaacabdadbddaaadaaccbadaabcadabadddadadbccdacccaaccdbcdbbbbdbbbcaaacdddbaddbdccccbdcbaccaccdcccacaccbcbcbcdacaacaccbcccbcabbdacaabdddabaabbaaacccdbbbcacdaccacccadcbaaccadcdcabcaaaaacacbaabaacccbddccdbdccbdccddbcdbbcbdbccdbcbccdaadbbbbcdcabdccaadcbcbdbcdbbccbcdadbbdbacbdbcdcdcadaddacdbcadcdcdbcbaadccccacbcbadabdccabdacbaadbdcddbadaabcdbbccbbaddbabcbaacbcabbdccdbddcccbcaacdaddcaacaddcbdbddadccdcbaddbdabdcddbaccadbbdacdbdbbbdacbccdccbbbbaabbdcbddbbdbdacaabcacacdcbbccadabadbdabbcadccdcabbbabaaaccbbdaaccbbdcacbdcccaaadcbdaacbdacdbdabdccdddbaabdccadabcaaabadaadddccacaadddcdacdadcbdddadbdcdcccbabaaacaacaabcdbaccbcabbdcbbdbdbbdcdaacdcbddcdbabbadbbaabbdbbcacbdbcacbacbbaccaaabdcaabdbaddabcadbccdbcaaddbddbdddcadadcdddbcbdacbcdabcaaabadbdcacaddcbdabdaddcbcdbbacccbaddbbbdbbcbaaaabbabdbcbddadaaabcbccaaaddddadbcabbbbccdccdddbcbdacbaccbdbcccbccbbacdabacdcbcaacddbdbdbddbbaacbbdccccdaddcbdbabcaadbcdbdccddccaadadacbbcddcbdddaadbbdcdcaacdbccbddddaaadacacdddacaccbdadaacdbbbbbdaddbbddabcddcabacccccbdbabddacadcabbcdbdcddbdccdbdcbbcddcdbbcbccabbbbaaaccacddbdabcdbdddbcdcbacababbdbabddabadddcddaaacdddcbacdadbbadddcbcbcdbddcdbbcaccddabdbbbbacddccabbbbccaacddcadaccccaadadcddcccbcababdadabcbbbdadbddabadaadccaadccdbdbdaadbcddbacadbdacbdbbdbbddbcddbcdaabadaccccddccbbcccabccdadcaadcdaaacaacdcabcbaddacabcbbacbacbcaadcddbddadaabdcdbdcddbdacbcbcaddcbadbaabccbdcbdccaabaaacccbbcddcddccabccdccccbcbadcdaabadaadcaccbcbcdabbdbcbcbccddacbcbdbcdadabbaabdacdbbbccacadbacccacbacdadddacdccadbccdcbcacbbabdbdabdbcadabaaadabccaabcccadadababbbdbdcacddccaacbacaadbbbacbddbadbbddcbdcddabccdbdddcadddaddacdbadabcccabacdcaacbadaccddabcbadbbaaaadbacacbcdddcbcdcdaadbdacdccabaaaadddcaabddbbcbabcccddaadcccaccdacacbddbcbccdcaacddacbbcdadadcdbccabbaacacbbaddcdadbdccabacdbaacaabbbaacaaddacdabcbbdbdbabcccdcdbaddadbdbbabbbadbadbaaddddddcbabdadaacdacdaaddbabcbddabcbacacacaacccacccbdcbbcddbbcbbbbcdddbbadacdadddacddccdcdcadcdcdaccbadccbbdacacccccaccaabacdbbcccbcdcdaccbacadacadacbdadaadcaaddacdadaabbdcddcbacaccccadbdccdacdacbacccababddbaccbddacbbdcacaaadbbaabaaabacabbbdaaddaddbbccdcdcdcbdabacbacaabddaacdaccbbdcabcadbccccdabccbcdacdcdacbcacdbaadccabddbdccccacccaaaabccdcbddaccdadadaadbcccabbccbababdbbaabcaccdbdacbddbcbacbabbccdaccacadaaddadbcbbabdaccabdbddddbaaadcbccdddacbabaabccacbcabaaabdbaadadacdbccaadddcacaadadbdbcbcbcdcbdcbaddcdccaccdbaacbabcdcdccdcddadcdadbdddbcdbadcacccabbabdacbbcddcdabbaadbdbbadcbabaaccdbbaababaccbaddddddcbddadaacaadadcddccabcbcdabcacbaccacaaadccaacccbccbbbddcdbabcbcddadbcbdddcaabccadbbadacdbcdbdcdbbadcabddbcccbbcdbcdabbbcdcaacaadadadacacdcccdbbadaadcacaaadcbdccabbbdcabbdacdcbbdcacaadbccacbcdadbabcbbacbdcbadbbaadcbdbabbcdbbbcddbbdbdababdacababbdbaacccddbadcadabcdcaddabadbdbdcddbbaaaadaccccbcbddcccdbbbbabbabacdabbdcacabcbdbaaacdacadbccabdaabcaadbaaaaabaccacabdcadaaacddcaacbbcacbbadabbbcadbacabcdaccadbdaadbdccadbdaabbaaccdbdddcbbadbcdcdacbaddcbbcaddabdcbbccbdadacabdbcadddcbccbdcdbdacbbacaddbccdbdaccadabddcadabddaacbacbcabccbaddabbacbcaabacccbdcaaccaccbaccddccdcbdbdbcddbbdacdbcdabdcccbbddccaacadbbdacdadbddbbaabddbccccaabaacddadadccdcbabbdaacbcdcadbdddcdbdddcaabddaccbcdddaddbcbacabcbdbabbcdbccdcdcabbbacddbddcacdcacbdbdcadbcbbbbddaccddcaadbaaccbddcaacbcaacbcbbbbcabadabccbcbcabadacbacbcbcbacdbabcaaacddcacbbaaccbcadadcdbacadbcbbbdddaaaabadabbbcdccadaaddcdaababbcaaaabdcbbadbdbbdadcbaccadababaaaadadadbadaaaadabddcddcdbcacaddccabadaabaaaabbcbbddaabadcabdddacdcbacbccdddaaadcdbacadbabccababcdacdacbccbabccdccbbbddaddbbddacbddcdddbddabdadabcdadaccbbbcccddbabbcabcddaddabacdcbcccaaaabbddbdcacbbcbccddccddddbdbadddbadbabdbdcbabdcddadaddabcaadbbcadabddabaabcbcabddbdcbacbbacadaadaacbacccdbcacdadccdbadadacabbaddccbddaaabbdcbadaaaabbcdabbdadaccbaddacabdccddbdaabdcdcbdcdcdaadababdcaacdcdcaabbcdbccbdcbddcbabcdabcbcdbaaaadcabcddaddaacaabcaabcbdbbcaacdaacbbdbddadabcbabadaddadcaccdcdaddacdaccabbabdacdaddabdddaddccccbbddddcdbacabdcddddbdaccbcdcdccdabcccaaacbddbbadbbccccaddadcccbcdbbcacdaacbccacbcdbbaacbaadaaaacccaccbdcddadaaacbdcdcbccadcabbccddccadcbbddbcdbcacbaaaaddbcdbbbbccdadbccddcddcdddaaaadaddcadadaccabcacbaddcccccacadacbddcdbdcabbdadabbdcbddaabccbcdaacbadddbddbcbddaaaadadddddcdacdcacaadaddabaaabcbacaacabbdccadaccaaddadbcbdadbcdaddcbbaacdbccccdacaababddadaddcdcbbcdbdbbabcabccddabdbbdaabaddadbbdacdccabdbcaadbdaadcaadcabaadbcbcdabcaabdababbdabbbabacaaaaadcbcabbdbddcaabaababcadabcabacaccdadbbadddaaddaaccddcbdcbdacdcdbdcdababcdbddacbabbdbdaaaaccbabbcaddccaabbdccdaaaddbdbadbccbacdcbbbbccaccbdbaddbbaadcbcacddbcadcbcbaaddcdcadbabbbbcbdabcaddaacbbacdccbdccbaddcaabacbabbaacdacaccabcabccbcdabbcadddaadbaaccccbbcbbdcadbdcbccdacdcbccbabadbdaddbcabaaadcdbcbcddbdbdddcaccbacbcadcacddcdddcdabaddbbbbcaabddacccadacabccbbadccbcaadbbabbdbdbaccdbadbbbadddcaabcbcabdccdcbddccbadddbcdabaccbadcbbcbbbbbcbcadddbbadbaababcbbddbdcbdacbdabdccbcbcccabcbcbdadacccaddadadcdbdcdcbaddcdbbcdabbcbdbbcdbcaabdcbdddbbccddabcddbccbdccdcbbcdcacdaaaadbcdadbaddabcdcbcabcdacaacaccbddbabcbbccbadcbabcbacbdbdadbdbdadbacadbacaacdcacadddacadbadddcbcaadadbbbbdcaaaaaacdcdbcabdacacbacabcadaadcadbdbbbdcbbbddcbcadcacbbaababdadbcaaccbadcbacddcddcdcbadddbbabdabadbccbdbaaaacdbdcbcdabacadddadbaaddaccdcbbcbabccddbdcaacccabbadaddbbaaaddccccaabdabccadbacbddbcccbdcdbbbdbbcaadddadcaacdcbcaadbadcadcaccbddaabcbcdbccababccbbbbcaaadadbbacbdbccccbbcccdbcbaddbbababdadadacdbccddcddcdddddbccbabcaaabbcdcdbcddcddadccbcacacbcaadbbdbaadaaaacccbabcdddcbdbdcabdaccadbdbbadadddcdcdcacddbcdaaaaddabdaaadaacccababdccbdddcdabbdcabbcbbaaaadacbadbbbddccddbddbcacbbcdddcccdacbbddcddbdbdaccdacababbcdccabccabdbbbdbbadbddaaddbdacbcdddbccadcbbdcbabbdddbddaacadcdccbbbcbcbbbddbbbaccdbbccbcbddbbddaadbbacbdcddcdcdabcadddccbbcdabcbaadcdddbcbaaccbdddbbcadbddbacabbdddccaaaabadcadbaadddbcdbbabdbaaacaccccabcbbaadddbcdcdaacddadcdcadaaabdbbccccaadbaddbdaadbdcdddcdccdacccaaabbaabccddddddcccacadbcaddcadadbbcaabccdabbcabdcdabdacabccaabcbaddbbbdcacaabaadaccdccaadcadbabccbbcabdcaccbacbcbbacabbbbdbadcbcdbaacbdabdacddbccccdbcacdcccadaacbcaaacdbccdccacbcccbddacacbcbadacbaccacbcbaacbcdcbbadcbcdcddabbbcdaacababdbdbdabcacbadcbdadcabaddcbccbcbbccccadcdcbbdbaddcadabacaccdadcacacbddcbddbddddbbbcbcddccaadcdcbacdcdabaccacabbbcdbaccbddddaccbbdcdcddadcdbbbaadbcbaadabbcbdcbdadccbacddcdbadddabcbbcbddcdcdcbdaadcdcbabccdbdaddcaaaaaddccaabccccbccbbbdcdaadcdabcccdbbddcacbdabadccabdbabdacdbadcbcabadaadddbdbcddbbbbacdbcbddcacddbacdcaccbbabcbadbcbbbcaaaccaccdadcaacadccdccdcacdaabcbbbddabddcdcbdabbaabdcdddaddbbaacadddbcaaadbcddcddaaaadbdacbdddbcdadadcaccaabdcaadacaddbdbddaaccacbdcdbcabdaaaaadddabcadacdaadadccdabddaccbbbbcdcdabcdbbcbbdabdcdbaabbcaddaccbcbcdccccccacbddddcadbadacdcdbaadbaaccccddddacdaaddaddacdcaadcacabbdbcbbabddbaaacdbabdcddadbdabbaadabcbacdbbbaaaaccbcdccddddadcdcdcbbacbacabbdbabcdabcaabbdadbdbaccbcbadaabaadabcaadcacacdbcabaaabdcbacbccdddacaadacbddaaccabacbccbaaddadabdadbdbbdacdbbabaccabdddbccbddadcbaddabbaaabcaaacacdcacbaabcaccbadaaabbbddccbacccdbdaadddabacadadcddaddabdacbbdadbaddbdabcdbccccaacdcaadccccccccbabccdbcdcddcdbcdcdadbcacaadaabcddccdcdbdbbcabadddccacbcdcaadabaaabccacccddcbbdaccdabcccbacbabdaadcaddbcddacbcabcdbccbbacaabccdbdccdbdaabaaddaccdadccccabdaabbcbbbdccbdbcdcdbdacbccadbcabdbcdadbaabddcdcdccaaaccbbdadddbcbababbadcbababcbcdbcbdbcdbbbacddaabbbaaccbddbbbdaabaaabcdbaacbbcacddacbdccacbcdadabbbbbcddcaacabcacbcbcbbddbdbadbcbabddccacdabdabdacbadcadcdcbcbaccadcacababbdaaaacbbdddacbdbcbdccdadcbdadbaacabdddccdcbbcccdcdcbccbadacbabcbadbddcadbcbabcdbbbcababbbcddcbdbbdcbcbaabbdbbbddcccdcadadbcdabcddddacbbaaaddccbbadbbccbaaddaabaaadbddccbcbcaaacbdbaddbbadbadadcadcbbccdacbccacbbadabdcdaadbcbabdbcbcbdaacbddcdbadbbdbbcadcdadcaddabbdbdcdbcadcbabdccccabacacbddbccdddaaadbdddcdbadcddbbbdaaddbdabdabcabcbdadbabbaaddbcccaddcccddabbabdcbbdadccbaabbbbcdcdbbaabaccdadadbabccadcbacccacdacbccbbdbdabdabdacbdacdadcbcdbbbccacdccbbbcbcddaabbdbbcaaabdbacbcbbcbddcdbacbcdadcdbacabadbbacdbaccdcdddaabdcbdbcddbdadabdddbdcacaacaacbadaaaaccadbdccbbcdcdbacdddacdcdbdcaabcddcdcbbccacacdaadadacadcbbaabdbabdbbadbadbdbbdaacccdcdbcacdbcdaabcbbdaadabbaacbdcccbcacdbbbdbbbdddbdddccbcdccddbadbcdcdabbadadadbacccddcabbabbadaadbdcdacaaadadaccbdbadcdbabdbbadcabbbbadccccccabbdbbaaabcbabdaaacbddbbdadddcabdbdabdbbaabcaabdacdcdbdacbdcdacabcabddadcabacdcbccdcbcddcdcdbcdaaaadabcbaaaaadaabaaaabbddbaaaccacadbdadbdcbcbdbbdacdbabcddaadcaccabbabcababaaaadddabdbdabcdcbcadccddddddbaccababadbabbdcaadabdbddaadcdddcdbbdaaddcdddccbbbdbcaddcccacdcbcbadadcdcdddbdadbddcadabbbadacacbbddabbaabcdbdbaadbcdbdbdaacdbbcdaddbdcacadacdbbddcddbcbcbabcccdbdaddaabbacbcbdacbddcbdadbcaabaabccbcacdbdabcdcbabbddbaaabdacadcdabbbbacdcacdccbadbbcdbbcbaddcddadaddddaacbacadcbccddcbdcadbbbcbacaabdabccadccddbcdbadaadacdbabadbdcabadabadcaddbcdbdbabbdcbbbdaaadaaacbcddacdccddaccbcbaaadbaddccdcbaaacbadbcadadcddcccdacbcdccaaacdcccdacacdaabccabbdaabbacdbddbaccdabacbadbbbadccadabaadbacdbbbcdcdcbcabcacdbccbccdababcdbcdcdcdcbbaabacaaddbcaadbddcabbccdaadaadcbbcabbcbcbbaccddbbbcacacbcbabddadbadbdccdbababdbdccabadddbbaddabbabaccbdccbaaacdadbddccbadcacddbacdadaccbbcacbacabbdddaaacbddcacadaabcaaacbadbabdacbbdabdcbcdcbbbbddaccdcbbcabdabbdddcbcaddcbddbdbcdabcbdbccdcaaabcaaacbadabbaadcbabccdbdaadccdbdadcbcccdbbdbccadacbcbbbdaadccdddaacabccdddbcdaadbaabcccdaadbcadaaadcaaaccbcddcdbbddbcaabbaadababddcbcabacdbbbcaadcbdddaadbadbdcddaaacbcabbacbdcbbdaadbdddbaabadcbbacbcdbcdcdabddccabbdcdabbcbdbcdacbcdaddcbbbcacadbacccabdcdbadcbbdbadacadcadbbdadadcacdbacccabacabbbabcabbaddaccdadbdbbbdccddadaadadcadbbabbcdaababddddbbabcbccdaacdaacddacabdbbbdaadadbbbdccdbcbbcdbbbbbdbcccacbabdbbbadcaacdbcbcbddddbbcbdbdddddcadaadaaaaaddcdbabaccbaabbbcabbdddacddadaddadcadcbcdbabaaadddabcaddaddbdcbbbdccdabbbacabbdbccdadbcadadbbaaddcdabddddcbdbdbbaadcacabdbaccccadadccddbadcaacddaabbbddbdbcbddddcccddcbcabcddbbcbcacacbadbabdacdaabbbccbccdbcdbddaddddbacaacdaccbbcdbccbbacaabbabdbdadcbdbbaccdaccbcdadacddccaccddcacccdbbabdccacdddbadbaccbabbadaddaadadcbbdacadbbcabbabcbcacdcacbdacbbcabcdbdaaadccdbdcccaacdcacabcccbbddbbacddcbbddbbacccbdcbbabababbcccbbbacadcdcdbdaccdcccdcbcbcbddabaabdbcbababbcdccadbcdbddcbabcdabcaacdcacbbdcbacbdddadbcbbbbcccdadabdabbacbdcadaddaaacddaaccbdddcbcccbbacaabcabbdbcadcdbdcacccdcaabdacbbaacadcbbaacadbdcccbadbdaabddaddaadccaccbbcadbcbdbabbacdbccdbcbadcbcabdbcdcacdacaacbbadcbbbbdbcaacddbdcdbddcdddddaccdabdbbcaccbbacddcbcadabddcadbabbdcacadcadbbaacabcdaadaddbadbddddbbddbabcccddbddddacaaddaccacbbddbbddbcdabddddddcbabccaabcccabbddcbdcbcabcbdbbbacbccdadbadbabbbcdbddcccadabbdcbaacddbbadcacbccbadabcbaabdbcabdcccdbabcabccdbcdabccccaaaddccabbacbaaccdccbadaacbbaacabccdcaacaccaacabadbcdcbbaccabbaadcaabdcdaacbddcdcddacabbbcbdabbcdcddbbbdaccddadaacdadaabbadbddaaacddbddcbcbacadcdaabbbaaddbbdcaccbdcbbbbccbabdcacaadbcccddbcdbcaaaddaacaccabcdabadcdcadbbaaadacbcdcdccbbbcbddaaccadaadcadcacdbbabdcdacacbadddddcabbbbaacbbcdbdaabcaccbdbddabdbccdbacccbbcbbacccbcccccbccddabcbbcdbbbacdcacdcdabadcbdddcabbaabbdddddaddddcdddbbcdcdabcdbcadbbddbbccdcadcadddcadaddcaacacaadbbdaadcababcacadaadbabddcdbbdbbbddbcdddabacddddccacabbadacabbcacbcbdaaacdcadaaabbdadbcbddddacbdaaaabdcdabdcdbdbcaccbaaccbbacddbacdcddbdabdbbadbbacbcdccbbabbcabacabadabadcadadbadcabbcaddacbdacbabadcccbbdccabdaabcadcdbdbaccccaabacdbcbdabaacdcaddcaaaaabaddaacbbbacdcdbcaddbdbadabbcabadbdbcbaabaccbcadccbdcabbcbabdbccdaabdbdddcacbcdadbcacccddddccbacdbbcabdcbbcdbcddbcddadcdadaabdacbccdcdcccaadbcbbdcdcacadbdbbaabaaaabbabbdccabcaaccbdabadccbdbdbcadcbdaacabadbbccbabadaaaabcdabbcaaaababbdcacccabdaaaacbdcdabaaadddaccbaaccdccdccdcccbaccdcdbaadbdcbdbabdbdbaadbbaabbcbabdbcabdcdccdbadaaaacabadabdcacdbbcadacddccbbabacacaadcbdbccbbadcbacabadbbcccdbdbdbbabbbdaadacbbdbbccabcddbdbccdbcabaccbabccdabccdbabacaccbbacdccdbdbdacabacaadcbbcddcbbaaacadddbbcbdaaccdbbaaabacbbdcccacbdbbdbabbcdcbdbbaaaccababccbdbccccccbddadbccdcbbdacbccababacbadacddbadbdcdbabcdcabbbbdccdcbacccbcadaabbbadbdcdaabdbdcdaddcabbaadddbbcbababdaddcbcddbbbabdccaddbdadcddaaaaabccbbccaaacdadadabcacaacabaaaaabbabccbdddccdcbdacababddcbabdccddbadadabdbcadddbadbbdbcdcadcdbacadababaaabbddbcaabcdbbbdbcdcddadadacbbddaddccacdbcbddbacdcaadcbbbcdacbdccbbcccbbcbbdcdbcdbbacccaddbbaabdbcdbbcaddaccdddabcddadbaacddbcdbdcdcdddcdbdcbdbcadcdaddddcabacbaaabadccdbaaacbccccdcccabacdccaadaabdbbcbddaacbabbcacaddcababbdddacbdabcccdcadcdcddcaabdbbdabdddbacbcaacdbddbdaccbdddccdacdaacbcccdbcbbcadddcccccaacbdadbaddccbcadaddaabadccdcdcbadcabbacaddadaabdbaadddbaaadcabbbccdcacddcdccababbbcbcbcdddacbabcabcdcabbacccadbcabbdcdacadbaaaaabacbcabdcaaacdcdcacccdddbcdbdbaacbddadaaadcbcadcbdcabcbcbbadddddcacbbbacddaadaabddadcbabddabcdababdabcabbbdbcadaaacdccbbabaaddbbdaccabadbdadbacabadaababbbdcaccbcacccddaccbcbbaccdcbdcbbdbddddbdadaccacabcbbbcaacbcccaccacabcaccaacccdbaccddacccbdcaabbddddacbcbbdbaadadccbccadbdbddadcccbcdddccdaccbbaddcacbabcddddcdcabdbdcbbadcdadabbccabdaaaaccadddcdaadaaabbadcaaababbbbacccaabcccbbbbcdbadccbdcbdbcbbdadaaacccbbcbacddacccbccbbdadbdddbdcddabadbcbddddddcbdacddaadbaddcbddcdcbadcaadcdcbdcdaabbdbcdbbadbdababcdccdbaacbbbbbcbdcaabccacbaddbcbabbbbcabcaccddcbdcbcbddadbdcbabacadbadaddccccaadbbdcbabdbdcdacaadaaccbaaacccbbacdcacbbdbbabdccbdacdbdaacdcabccbcdbbdcbdbdacccacddcacccbdacdddabdabbababdbdaabbacadccbabaccbbcabdbabaacdbcadddbabdaaddbcaccdbcbcdbabbabbbdcabacadbdbdbdbbabaaabddcaabbbcabbdbdbdacdcacddabdbccaddcbaabdcbbcadcabbdccbdcdccddaadcbaaabaabdcdbdccacbadbcadaaacdbbadcaaccbacabcaabaaacbcaddaacdbdabdbacccaaabcdadcabdcbadaddabadcddccababadcddddbdaccaddbbacccddbddbcabbabddbcccdcbbbccaddacbaddcbdccdbadacbacabbbadcdbddcacaacabaabccdaddcdabbaadabbdcaaadbccadabbbbcabccaaaabdaabbadbaccadbdbabbabccaabcdbdababdbbaadaadabacaabcdbabcacdabddbccbcddbbdbdcbddccadcdddbaddcbacdbbccbbccdadadddabbdbbccccddcbbdadccbdbbdbbcbccaaaadddcaabdbbbaccabbddcaacdaaaaadaccaccaccadaddcadbacacabcbaddacacabcaccbdbbccddcdabcbdacbddccaaaadbdcbcdabdbaccabacbdcaabdbcacaaaddbdbaabddbdacacabdddacdabaaccbacaccbdbadacdbbdccdccdadbbcaaddbcccaababcdddbcdbacbdadcabbdcadcdcbdbbadabddbbadacaddcbdababdcdbcabbaaddabcabbcbdabccabdbcadaacbbbcdbccbacaaabddbdcbdddcbbbddcdddccaddbaaabbcdcdaadddbadbddbdbbbbbacaadacccdbadaaabbdbcaadcdbcdbacaacbcdcccaddbbcddaaaacacabacddcbcdaddaccbcadcadaabaabbdbcacbccbbbdbdcbdbbacbaabbbaabccbdbcaabbbabacabdddbbddbdbaaacbacabdbadabaaccdadccdddbabcdddcbdcccacbbbcddaccbaabdbadbabdcbcdacaddbbcdbddddcdacbdcbbccdaabdadbadddacaacbbddacbcaacdcabcdcddbdddcccbbddcccabcaaddcbbaacadbccadcdbbbaacbacabdcccbadacdcacacbddddcadababaccdbcaacbdbcdbbdabacbbcbcdadbadddcdbdcddcdababdbadadccdbbdabccaaabcccccbbdaabbdbcbbbdddbbccdabcaacbdddcdaaaacdcccdbdaabccddcaaadcacdbbadaaabbcbbbddacaaacdbccacccbbabcaaabbabbbaccaaabbbacaaaaadabacccacbcbbabcaccdababbdbbcdcaadcbbdbcdddcdacadbadccbaaddbcadcdacdbddddbdabdcbbbbbaacdcbcdccbbddbadcbbcdcaabaadcaadbdabaadcbdccbadccbcbcbdccaddbdbbbaccbbddbbadbdcbdcadbaababcaadbbcabbddcabdbcbaabddacdcdaaacccbdabcbccadcacdabacbccdbcadddabaccabcbbccbabdbddcdbdaaacbbaadbdbabbdcdbccaccabdaabbcdbdddbdddbdacccbbcaddabadabdddbddcbbdbaacadcdabbbdccdddaacdcbbdadacdcbdbdacbdbadbdbccadcdacdadcccdcadacddaddcbcccdacdcdccabaccacdcaacccdcaabbccaddcacbddcdacbabdcccbcabcdcaacdbcdccbdbdddddbbbbcacbdccababbbabdcbaabcadbacdbbdbadccacdccbabaaaabdacdbdcbacdcbdcbdadbdddbacbacacdddbdacccccdaadcbabbcddccdcacddddadacddddbdacddcdadaabcbcabbacadcababcadddcdbaddccbcdadddcddddacdabdbbadadcccadbdaadcadbdacdaabccdbcbacdccbdcddabbcaddbacccdcbbdccdbacbacaccbdccdaddaaaabbababaaacbbcabcdadadacdaadaaaacabcaadacdcacdcbcbbdcdcccdbadabbabdbbaddbcccdbbbdbcacabccbaabcadcaaaadcddbbccdbcdabbaddcdabdcadabccbacdbdacadaccbdccdcbbcdbcddaadccaccaadaaacadabcbadadacabbcdbcabcdccbcaadbddcdcaacdbacccddcadccbbccadbbbcbabdccacadabbbdbcbcaaacbcdbbabcabdbcdbcaccdbdbbaaadacddcdbadaacbadcdddacbacdbcbbbbcabbbddcbaccddbabbbdaccccbbbacbaabbbddbcdbbaabacdcacabacabdaccdacdccbaaabcaadbcdbcdbadccdbcbddadcaaddaacbadbbcaabcbcdccaccacacbabdababbbcbcacbadbdcddddacdabdcbdbbbaaaddbcaccacaaaaccbcadbaaacbaabadbadaabddcacaabacdacdcacdbccacbacacbabbbabcdccddcdddccabadcccbacbdcbdbaabaaacbadbbbacbcbdbbddaadcaddcdcadcbbccdaacbaacdababcdcbdbbbabccdaacdbabababbbdcaabdbcbcbbbbabbcccdddddabbbbdcbccbdaaabdaadababadabbcbadbccbaabadbddbcacacbdacaaabbdccdabcbbccbdbcababccdccdcdbdaabdacbdadccabbdadddaccabdbbdcbacbbcbababdccdaddbbbccaddaccdcacabbbbabdcdabddababdaacadacbababaddbabbdccbcdbbddaaabbcaccbdcbabacdcdbdcaabdbddaccdbccbdcbacbabadbacbdcaaaadbcababbadddcabbbdddaaabdccbaaabbcdbdccddbaddabdacbadcdcbaccbbcadaddcccdddcdcccccccbdbabcbbccccccadcbdbabdbcaadacdbcaddcdaaabcdccbcdbaaaddaacacdcbbbdbaddaadacbccdccaaabdaccaccaccccacbdcadacccaccccbbacbccaabccbddadcddacaccaacbaacabcaaabdcabaaaaaaccbdbabaaddddcbbbdcdbcbbdcaccdcbcbdbdcbbbccdbdabbddccbdaaadcacdbbcadacdcbbaaaaaaacaddbabadcdcddacabcaaaadcbcaabcdbdcbbaaabbabbacbdbddbdaabdabddbbaaddbaaabaddbcbadbcdcacdacabcccbaacbadcddcaabdbccbdcaddbdcdbbddbcaccdbdcbacadddcadaadccbacdbacadadaaadccabcddccacacbbdbccabbdcccacbdddcacaaaaacdcabacbdabbadcabdacddbcaabdabbcabddbcddacbcabcbaddcdccdcdddbdaaaccabbdbcdbbccaacaadbbaccacadbdccbbacccbdacacacccacaddcabcbbbddddbcccaadbccbabcddcccbdcadddcbadbabccbdccdcaddadccabbaaaaddacbbbdcaabadcadacccaccdcadabacbccdbccaaccdbdcdbcaccddcccbbbabbccadaccdbbbbccbdbacadccdadbdcabbbaadbdabbadaaaabdadbbababaadbdacbbcdbabddccbccacdaadaadbaccccddbbcddbdaadadaaddddcdaababacdcdcddcbabbbccadbbbaddccaccbaadaadbcacccacbbccccdccddddbaccdabcbbabdddabccaabacdddcbabdbcacdaccbbdbabddabacbcbcdcbbabacdccddcbacdcdbcabdbabaccbbcbdacaaacaacadabdddcabbcaaadcbabccaadbabbbaddcaabdcbdbbdadbddaaacabdcacbcbdaadaaddaadccdcbbbcabdcdbaccabcbbabdbbdcaccbdcadbbaaccadbccbcbbdacbbbaddbdcbdcacbbcdcdaadbdcaabdcbdadaabbdacacbcdbaaacccadccccabdbcbadcbabadbbbaabbddbcaddcaddcaadacbbcdacadcdcbacaddcaaddcbbdcbbddaaacdcbcabbaabacbddcbcbbdddbcabcdabcddcabaacdbcdcbaaaabdbcabdaabcccbcdbcaabaadabddbdbcdbdbabadbbbddaabadaadddcbccdbacabdcdbbbaaddcbdcdbaabbabcdacbcbbbcbbccdcddddbdaadcccadabccabccdaadbcddcadcddabbcccdacacbcabaccdbccbadbabbcdddccbbbabcacaccbabdabdbabcbadacbcbabcadabcdaccbdcbbdccdccdaddcabaaaaaddbcacdbabdaccadbddddccabaabdbadcabccbcbcdccccaaccbbcacdccadcacabbbaaadaabacbacdabadcccaccdbbbacdcbcacacbbdaddbccadbbaabcbbcaaaabbdbcdcdccaddabcbbcbcacadbcadaddaccabacddbaabbbbdbcddcccbdbbccddadddbbaacadddabaadcdaadcdbababacacccdbddbbadcbcdbbabcdddcbbdbbbbdbddaddcacbabcccacaadcaddbcdbbcbddabcbacabcbaadaacbcbaaabdcacdaacdadbabcddbadbdadbcccabcdddddadbbbbbbddcabccbcadadacabbccbccddaadacbcdadaaacacbdbadbabdaccdbbccacbdaaccbbadbdacbbbbdababdbbaaccbbacdccccdcadcacdbcdddaabbbddcdcdaadcdaacacabaacdbbddbdcbcabbbbdbaabccdcacbbbbbabddbdcddccdcabdcbdcbccdbcbcbcadcabbacababdcacdbbadadcbcddbdabdccbaccdbdcaabaccbddbaccabdaabbdddddabaddaaaddacabdcaddbcadaabddaadadbcbabbccdacabacadbaccbbbacddbcbdddbacbbabbadccdbccdcdcbdbaadadadbdcdccbbdbadadcbbadabdadadacabddadbdbacccbabdcaaabcdcddacbccbaddcaacbbcbdcaadacadccacadcbbdcccbbdddbacacdbbccbbdcbbccbccaacbabcccdddbcbdcbaaaaddacbadbcccacdccbbabdcaacddbbcdbccacadbbabaacaabdbcbacabbbddadccbcacdaddadbacaacaccabbacaacbdbcdbdcbdbbdddbcaccbcdaabdcbdcbbddbdbdaddcdaaacbbdcaccadccdbcdbdcadaaaabbbdbbbbbacbbbadddadabdddcccbabbaaacbcbdddaaaaccaaaadbdbdbdbcccacdccccbaacadcdcbbbacacbaddcaacdccccdccbcdcddbddbcbaabddaabccbbdaaaaaaadbcaccaaccbbdacbbcacabdbaabacadacacaacdbcabadbccaccbcaddbdaabdccbccbdabcbdccdadbccdcdccdcbcadbccbbcaabaadddbdababadaaddcadcabacbaaabcaccdacbaccdbacbddadbbccacbacdcbddacaabaaddccacdcbbaddccbdcbbdaadbdccddadadddbccbbadbaccbbabbacdccdbabbacbbdbaadcdaccbaabdcacaacbcabcdbabaddbdbbbadabcdabdcacdbcdadcdbcbaaacbdbbacdbdcbcaacbadbadbdcbcabcdbacabbcdbbdcaaacccddaaacaccdcacddabbbadbabbaabaaacbbcbddabddbdddcddbaabddccabccdbdbdacddddcccdadabaaacbbcccbccdadccddcddaabdbbdaaadbbbccdaccbdddbdcbacdcdadbbbbdcdaaacbbacbcdcdbdddbccdcbbacdcabdaaaccbccdcdbcabcbcbccdaccaddaddbbccacacbbcccbaaacdadacbadaabacddcdbcaacdcaccbaacabdacbccbbababdbacccccbbddcadccaabcdcdbadcdbbcbbbdbcaccaabcbdaddacadbcbbbcdbbadadcaddbbbbccacaaddabadbadadabbbdcdddadccaadaccbcabbbaadbcdadabacaabcbcbdbcdacbcbaccadbcbddadccbdaaabaabdbbbcbaabbbadcbbccbdbcccdbadaabcbdbcdcaabdbdadbaadaadcdcdbbcdbddbcbcaaaaacadbabbacddbdacccacdcadbbbbdaacdacbbccaacbcbacbcbddddddaacabdbdbdaadadbbbdcaabcaccdaccccabcdabdacacaacabdaaabcabbdbbcbbaacbdbddabdddbcaadccabcccddadcabbbdbaadbcddbbdcdbcddcbbbdacaccdcaaabcabdacccdcccdbbdbcdcccadcddaaacaaaaaabbadcdabadbcdbdbddbbcdbbbabdabaabbaadbaabbabcccdbaccabcbaaaaadadbcbcbbdcacbbcdcadaaaccdccbadbbdadbabdbcbbddbdabdbcabccddddcdabacdaaaadcccadadcbbbacddaaabccbaaadcbbbbdabbdcdaabaababadadaddabdaadabbbaacccdbadbaadbdabccbcddbccbaddbcbbabbabadabadddadbcddbbacdaccbddadbcbdbbcccddcdbabddbcadcadabaaccdaaacbcdadddadadabbacccdbcccabccddccbdccdaacadacbddcdabcdacaacaadcaacabadccbdacbcbcbbdabbabddacdaddbcdbaccbbcabbcbcdcdabdaacbcbbdbdbaaaddabcbbcdcbdcdcddbdaabbccddddcabcbbcccccdbbabcbbcddacdababdbccdacccdcdcacdddddabbdbdbccbbbadabdddacdbbcabadababacbcacbabbbdcbbdccabcbadbbdacddbaadcbadacaaccacdcdbaccdbdccaaabcbcabbdccbcbbddadaddadababadbcacaabaccddacacbddbdbbaaadbaaacaccdbbdbdbabdbdcbdbcdadbadacdababdabddcacdcabdadcdbaadadbaacbbccacabdbaabbaaddacbbbdbacacddbacadadacdcdaddabacaccdbdadaaaccdabccddcadbadbbdabaadbaaaaaaddccbaadadabcbadcddbcdadbbabbcbbadaabaddddcbcbddabbabbdabbcbccddcbcbaddcbcadbbdcbaddbcacbbcaaacdbcababaabcdbdbdbcaababcddcdcbcaabdaabbdbccdaddadbbdaddddaabbccacdccdbdccbbdcccbdcbdcddccbbbcabdadacbdddbcdcdaddacdacccacdcdcccadadbacadcabacbbbddcacdcabddbddcbccccdbbaaddccaddabcdccbdcbccbddacddbbdbaaddbbdbacddcdbdccdbcbabcdcddcabdcacabbadabadacbcdbbdaadbcbadcbacababcdacadaaabbdbccdacacacbbbbbbdbdababaabdcbccbadbdbdddabdabdabccbacddddacadaacadbdabbccbaccddddadbbadbabaddccabccbbdaadabddbaaaaacabbacacadddcabaddadddbddbbdaacdaadcbaacdcdadcbaddbbcbdccdbddbcbdddbcbaabbabdddcdccdabccbbcacacadabcabdcbaadaccddaaacdcccdcaddbcddcbcbbdacddbbbdbbdccdbccaccbcdabdcaabaaddaddbdaaadbccbcadddaaddbacbbdbcdbddacacccbdbbaadcaacdbdbdbacacbcbaddcabcadcbdababadabcdcadccaacbdacbbbbbdcddbaddcacbdcbdabadbaacbddcbacdbcddddacadbadadcdbdcacdababdcdbadbbbaccababbdaadabbbbcdbdbbcabbabbaaaababdaacadccabdddaabacadbcdabdaaaacadacddacbdadcadbcdcaabbcaaacbadaccbacdbbccbbaccbabacdaabdadadcbdadaadcdcabadbbcbcbbbbaacbabccddabcdbdadcdabdbbaacdccbbcaadbcdabcaabbaababdbcdbccdddcaaadacdacbdadabdbacaccdacbcccdcdccbdbcbaaccbbbbbcdabdcbdabaabcdcadcbdcadabadadbdbdccdcbabdacccadadacaacdcaaddadccddddbabaadbacdcacaadcdabdbacdcabcdddcdbcbddddcabdbdddccaaaadacbbabdddbaaacbbdabacadadcbdaaccbabaddcbadacccacdbbbdcccbdacacbbcdcabacdbbdaacbcbdabcbcbacaccddbadaacdababacbdbdbcabbbdacbbadcaaabadbbcdcdddccddddccdbdbdacbcbdcdbcaccdccaccddaabccccdabbbcccdcdcbbddbcacdcccdadbacaadcdaacaccddcddadbcabccdaddacbabdcdaddcddbabcdadaaacdccdaacbbcccdcabdbbaacdbbcddbdadcacccdbcbdddacadabbddcadadcbdbcacbdcccdaccbdcbabbddcdcdbcbdccdddabacbbaaadbdcbdbdcbccbbbcadbdaacabdcdaddaddddbdbcabacaacdcdcadadabcadcccbccbddcaadbbbdbcdbcbbaccbdbcbcabdcabdcbcacacddcdbdccbddbccaaabccbddacdcadadbbbbbacabccbcbdadadbbbdbddbdacaabdaacdcbccbddcacaccdacabddccadbdcacbabacddccccaabdaddadbaddbdccadcbacdaadbbbccddaaacacbcaabcbaababccbcabcccbdcccddbacaaddcddacbcaddaaaddccccddadcdacbdddbdabbddabdbcbbbcddddcadbaaacdbadacaacbaccbddbbbbcaacabddaaacdacdcdccaabcaddbdacbdddbbaadcabaacbddbabdcabddbabadddcbcabcbbbbccddcabcddccbcaccadcbbbdccdccbabadbcadcdbcdabcdbaadcacaadacbabdacadbcacadcbacbcdadacdabbaaadcbaaddabbdcdadbddacbcddccabaaaddabddcbdabadbbadbddacdbdabbdacbabcadbcbcdcbbbabcdcbadaccdccbdabbacbdacadcabddaabaadabcbabdabcddcdbabccdbadbbcbdcaddbcdcadaaabdbabaaccacdbbcdadbcbdccadbdcccbadccbacaaadddcbbcabbaabcabdaddadcaabddbbccaacadaabaaaccbcbbcaddacabbcbddbbadbacdbbcccdddcccbcabdbcbcdcdadacacdbdcbcbdddabadbbbdcdaadcbbbdccdcbcacdbacadcbdccbaabdadbdcddcdbcdcccdccbcababdbabbdcbccdbadabababadcadbdccaacddbaacdacdcbbbabbdabdbbcadddcbcddaccdcbdabaccbcdbccddcddcdbddcaadbdcbbddabbddbccbdbdabaaabacbccbdcbacacdcacaddcaccbacaadaaccddadbdbdacabadcbdcabcbccbdcaabdbabbdabaccaabcaccaaacaadabbabbbbdccabccbaadccbdccaabdbacddbabaababcbacaaabccbaabcabaadadbccaabcbbdacabbbbadbbadcbacdbdabacdcaccbdcbcaccabdbbdcabcbccccdcacabdcdbbbdcaacbcdbdcbcbbcccbabdaccaabbdacccddcaacccddbcdbccacdbdcbbcbbbaddbdbccdcdcaadacbacadbdbdadadaddcbcbacaaabccababbcbbbbaccadadadacadabdbababddcdcbdcabcbcacdabddbabbcbaabcacaaaddddddbbbdaccbddaaccdbcacacacaabaadbdcdccccddaadaaddadbcdcccdcbbcbcabdbbcaadabcbdaacdcdacddadabbaaddadcbabbabdddbdbbcadcbcbdcabdcdacadadbadcdccdcacacddaddaabcaddbccaaddbdabbdddcbcdaaabaacabdcbaaaccadddcbbdddacbcccdcadaadacaabdadccacaacbacabcccbbdabbadbbdabcdcccddacdddabdbdbbcccacabbacdcacbbcbcdcbcacdbcccabbbdcbbbdbabbcaccadbcbbcddacddcbdaadababdacadbcbccabbaacababbdccdaadddbbbbacccdbdddacdaacadbcaaccdaaababccccdbdbdcbdaccdcbcccbcaddbccdcbadbaabbadaccbcabbcabbbbaddcbdaadbcacdddddaacdcbddacdcdbbabaaddcbbbdabddacccbddcdcadbddbaaaabbadcacccbcccadcdadaccbdacdcdccabadcccacacabdcdcbcacabddbaadacddddaadaccdadcddddcdcdaddbadcddcabcabbbaadbbccbccbdbaddbbcaaccacbaacdabdadabcdcacdbcaacbaabccadcacababcbbcdadbdcbbdbbbaccaabccbaaddadcdaadadcabadbbbacadbadbacadadcddbdbcbadaddcbdaaaadaadccaaadcbbdbddbaadbcddddbadacbcaccaadaddcbbcbdccaaaccabdccdbbadccdaddaaaabcbddbdddadadcadabcaacdbdaaabdddaddaaaacbaadadababdbbdbcbaaadaddaacdbaadddbadddccdadcdadbccccbaaacbdaadaccbcdabacdbccabdccaddcaaabdccadabdcbcdbbabdadaccdacbbdbabadbdbccbddcaccccadbaadcbbcacccaccacabaddaaddcacbdcbdbcbcacdadcdabbdaacdcbcdcaadbdbacdccadbcccddbdcddbccddcdaaaabbabaaabbcbcbccddbbddbbadccddacdaabadcabdccabccdaabddabababbddacdbcbbdaacbbdabccbbaddddbddbddbbdacaabdddabbbbcddabbadababaaaadcdbdbdacbdccbbbddbdacbabaabddcabbccbabdcbcdabaacabcbbabaadbbbccbaacabbcbbadddbaababbccbddacdbacdcbaaabdaabacccabbdbcabaaccdbbabdcaaaccadccadbbcccaacaabcacbaadbccbdbddcaadbcbacaadcaacbccadcaaaadbdbaaaaadcaacaabacdaadbdaaadbdbbdbacaadcbcdcbbadaacabddabbadcccbbcacccacabaccbadbccaaddbbaadccdcddabddcbbcdcbabdadcdadcbbabcbddcaabcddbccaaabddadbadacdddbbbdbdbbbbbccbcdadcccadccddacbcdcbddcdbdaddbaacaccaadbddaaacbdbbcabbaabababddccadadbbddcdbacbadcadabcdccccbbadcccacadbbdbacabdbaacadcbbadbcccbcadabaabdbbacbbddababacaabaddabadccbddabadcdbdbdddbdadbdababddaabcadbccaabdbaaddaacaabdabdcdcacaddadacaaadcddadbdcabdcccadbbccdddadbcabbbddcabbcbadbdbdddbcaaddbbdbbdbdbacababbbcbbddaddabbcababddcdacabbcbcccadccabcbbccaadabaadbdccdbdaddbccddabacacabbcccbcbcaadcacdcdabddcacbaabbbcdcdcabcbdccddaadccbabdbacbadcadbdacbcdabbaabdcbdccbdabddabdbabcbaabccdbbababdddcbaccbcdaadbadbadadccbabdddddcdcdaadaacbcdddbdbadabcaabababdddcddadbadcccacaccacdcbcbcabddabaaabaacccccbabaaccaccbabdcabbdbbbbdbcbbbdddadcbbbddadbccdcbbbdabcacbaddccddccbbdbcccdcdcabcddbdbddbdcbbbddbcbcbacdbcaccaddddcadcbcadccabadcabccdaaabaabcadbcbcacdadcdacbacccaccdacadabbdbccacbbcbdacaaaddccddbdacddabcaadbabdbabdcaaaabaaadccccbbccaabdbcbaabccdddbdadacbdbbabaadabbcdcadaabaacbbddcdbbcdcabdaadabcaacadadabcbabdbdcdabacdcabbcdccdacaaabdbaddcdbaddbccdddacdadddacbbccdacbbcbaacacdccacdcccacabccaabaadadaaddbbcddbbbdcbcdbddabdbcddacadbaaccdccaddadcaadacaccbbccadacbabbaddabbdbdaaadaacaaaabaabdabaacdaddbadacdacdbbdbbabddcbacdcbbdbcbabcbdbdcddbacccddcadcadcdbadbaadadcacdadadbabcacabcbbaccbbcaaaabddcbacacbbdcaccbcccbbabadbcaadacbbccbddbbbddcabbcdcacbbacbabbbddbbdacadbdbcbddcccbbccdabbdbbdabdccbbacaaadcacbddadbbddccaccaaccbbdddbdbbdabdabdbacdabcdbdadacdbccbdcabaacdbcbdabbcaadaddbdbbbbbbdccbaddbcacddcbcdbbbdcbdcbaacdcacbadaccdaabcaadbcbdbaccbcccdbdaddbbacbdcbdbacababdbacddadbdbdbbabcaadadcbacaadbbdbdddaddacbabbbbdcccaddcdadabccaabdccccbaabaaadbacbacbbbcbcaacdcbcababbbdbcdccbaaddabbadbbddbabcbadcdaadbdbaaaaccaadbaccbbdaadababcbbaabaddbbbcaabdbaadbbbbaabacadacdbbdaabbdbcddddbcbbdcadacaddbcddcccbcdbabdbdacdbcccabdabbadaaadcdcacddacaabacdcdbbaccccdbadbaadddbccbbabdcabbcdbddaadbccbdcdabcbdcbcddddcbbbaaadadcbcdbbdbbbdcbadbadcdcaabcbcaacbbcbddcabcabcddbcbaaaabcbdcaddadcbddbbdbaabacbbdcaaccdcababccdbadcaadabbbdccacaacdcddacdaacbcaadccacadabccbbcababaaddbccbdcacabbbdacbadacadddbcccddbcccccdcabacaddbbcbadccccbbdbbddbbcabbbbababdbbbbbdadcaddcddccbaabcbdbbbadbddcdacddbbdbaaccbaacacccbccaacdcbdddbcbcdadaacbbdbdddcdcabdaabddddaadbaadcccbabbbadbccccdcbcaadbcbccababadcaababbdcbcdbcbcbcddcadcbadcbdaddccdadcbdbabbdbdccbbaadcbaacbdccdbbaccccccaccacabcddbdcaaacdbbacccbcbadbccabcdcabbdadadcdcdababccddcccbcccbbadcbdbccaabcccaacbcadadbdbbdcacabbaacbadcdbdabadaddcabbaadcbdcaacaccbdadccdccabaadbcddcbcccadcabdbdbababbaccdbddcdabdddacaababbbccbbacdababddbbccdbacacdbabbcdcddabbaccdbdcaaaaadbbbbccbaacdcadacdabacaddadcdccadbcbdbadddcacabbdccbbdccbddadabbcaaabacacddadbbcaabaacbabccbaadddccabaabaccadccacaabbcacbbcaabcdcccdbbdcccddcbbcbcddadddbbcdccdcaaaabbaddcdcadadbbcbddcaabadbbdcbbbbabccbddbadcaadcddddcddcdcddcdddbdaccaadcaddcadddbdaaaddbbbcdcacccbbbbdbaaabdadcaddcbdbcbcabcccaccbcdcdacdcdabccdbdcddbcadaccdbcccbaabddabacccbbdddccdabbbddacaacadaabbacbaaacdaaabaadbddbbcdbdcbaddcaddcaadcababcccdaccabcaddccdcbaacdddbddddadcbaadaabdaacaabcbabdcdcdadaabadbcbacdabbaadbdcacdddabdbabdcbbbaaabdddccaabadbcabaddcddaaacaaaddaadacdadcdbacbcacadccbbdbacaabcbbadcddddadcdbacbadbcaacabaaccbcbbdbcbbacdbbcdaacacbdbcacbbaaadbaaccbddbbbddcaabcbdacacadcaaabcdacddbdbbbaddcacdcaacdbcbadbcbdaddabacbbabcbbdbcdbdaddddadbcdcbbacdabddbbbcbcdacabccccadcbbaaaadbbabcadbabbabadaddbbbbdbbabbacdcabacacbccbadaaaadcbabdbcabcadcbcbadcacaaadcabbbcdbabbcaddaaacbbbbbcdbcddbbdadcdccdcbbbdadcacabbdabddadbbcccaddbaabbdabcaddcdbdbcdcddddccdabcdcadadcddbddaaabccccdddddadbcbbdabccbaddcbdacddbdddbbacccddcdbacddcdbacabbabbbddbdccdbdcabdadbcbadccabbdaacbcabbcdcbcacdbbdacadababcbcaabdccabbdbacbacbbaadbddbbbcadacbbdcdaccacccacdbadbaadabcdbcdbcddabbdcccaadbadacbbacddacbdbbcdddaacdaddccccdacaccabdcaccbcdcaabdcbbcacbbadcbadacdbccabcdbadbcdacadbcdbbdbdbacddbbaddadcacddacacccbcdbbbdcbddbdddbbaccaccdabdadacbcbcdbcccdcacbacdbccdaaaadcbcbcbcbdbadaabbbdadbdacaadbadcdacabccccbcdaaddaabdcadcbcbcbcacbcdbabacbdcdcdbcdbacccccdacdacdbdcdcccabdcbabcdacabcdadddacbdcdcccbbcbcdaaabcdaddcadcddaccaaccdabcbcdbbdaabddddccdaadacccbbbacdbcdcdbbccbcddbdbbabcdacddbadbdbbbbdaaccbababcccdddddccaabaaddccbabadbddbcdbcdcdaacbaaccbcadcdabdcdbbbdaacbcdcdbdaddcdddadcbabbcdadcbcdbcbcaaabcccdaaabbacbccacdadcdbbabbbbccddacdcccaabbcbbacdadaabdabdbccddaaaddcdddadbadcdddaccdbcacbcdaacaaddabbbcddcbcaacacbbcaddccbacbccbcadbbccccdabcadcdcdaaadaaddddccdacddcddddbbbaacccccbddbddadcddbcbbbcdddacdaadbaddabdcdbccccccaadabbdadbdaadcaaaadadbdbaabbbddcbbdaccdaacabddddabadabcbabccdcccabdbccadacababdccaabcabbcdadcccdcbaabdbaacbacdbababcdaabcabccadccababdbcddbbacabacabcbcaaadbbcdcadbbacdacbbdabbadadbaabbbadddddddcdaddcdccacaaabccaaabdbabcacababadbaadbdaddbcccaaccddababcbdababbbbcabbbddbdcdacbdcabdadaaacbbcdddaccdbadcdabbdbadaddbcbbbaaccdbddaabbabbcdcdadbdccccbbabbbcdbcbddcadbadcddcdccdddddcadbaddacaabbdacdaacdaadadaaaaddabcacaddcabccdcbcddacdadcadccccaaaddbaadcdcbbbdacdcbbcdabbcaccccaabbdbbbbcadbddbcdcdcaacdbaacacaddbcddccabadacdaccbccdbbddaccadbabaaaacadccbcdddbaddcbddaadcddaccabadccdaacbbcaabbabbdbadbccbcdbcbdababcaccdbcacccbdaccccdcdbdcddcacbdabdacaabdcdcddcdbbccabbbbbcadbccacddcddaddbbdccaaccbcdbabcdbacbdacadbbbccbacdbababdabddbbacdacdddbbaadbadacdbdbcddbbdbabbddcadbbbaabcdacaaacaddccadddbcabbbddbdbbcbbabbadaddcdabccccdbacaaccddccbaacccacbdcdbdacadadccdaddcbcdabbaaddacbddaccddbcdbadaacadccadabcabcdcabcaabbdbdabcdbddbbccacdbdcdddadcdacdaadddadbccacddcabcccabdbdcbadbaadcccdbcdadcbaddadcbdbcdbdccabadddbdbbbdddddabcddbbdddbabbacddabdbbabccbaabdbcadbcdbccdadbcddaabacbbbcbabcbbabbabdcbccbdbbccadaabcdbddadcddabacbdccdbaadbcdabcbcbdadcaabbddcbcdcbaccbabdbccbcccbacacaababdacdcddabacaddccccabbabccbccaddabdcbbabdcddcbdbdaadcdabcdacdabcdbdbbbbdbcbdcaaabccdcacaaacbcdcddbadcccaabacaabcdbdcdcbcddddcbaadbdcbababbdcdcbdbbdccddabacaddadacacacbadbcbbacdcbdcacabccaccbadacadaccdbdbacbbcdccdacbaaabccbacdcabaacccacbdcdcccaaabdbbaabadaccbdacdcdbadccbddaccccbccbbbdaadcaaabdacacdadbabdaccddbadcdcdaacbbcddcbdacababababacaacbcbdcaadbcbbdbcddabccdcdadcaaaaddbdddcaacddbdabaddbcddccadaabcdbabbabccacbbcbdabddaacbbbacccbbdadacdacaaddcdcbbcbbbbadcbbabdbadbdababddbdbbbadcaaabbcacabbdbcadbdaaacbadabbcbccccddacdadadaadbcbbddcbddaaabccdadcccdcadababcbbcacadaccabadbdabddaaadaaddcaaaacdcdbacbbcccbbccdbaaccacacaadddabcadcdbbdacabdcbdbcadbcabbcadaadabaabbadcabcbdddcccadaacbccbdaddaadacaabcaaaadacbbcddacbccacdadcbbbcdacbaacccbacacbdbbadadacbcbddbbbbdbdadbbbbbcaaabdabadcacbabccabcbaabdbbaccbadacadcddbcadbcdadbaaccbbbbccaabddccaadaacdbccdaccdcbbccbbadbcdbbcbdabccdbbdddbadccbbaacdadadbcbdabccbbadaaddbccbdcdaaccdaaadcdcaaacbabadbbaacacdddbaabccbccccadbdaddaabcadbdabbcdaccabbcdcacbadccbcddacbcbacaabdbbbabaddbdccdddbbddacadddcbdbabdbbacccbbdaadbccacdbdaaaddaccbcdadcdbbdadbbbadddcaacbbbaccdbadcbcdbcbbcbccacbcdbcadcbbbcbcacdccbbdaadddbcbaccdbdbdcbdcccdbcdcbccdcabbdadaccdcabdcacbababbdbdcaacbccddbbddabbabddcbddbadababdccaacbcddbcadddabaaaaccdddbdccdbdacdcddacaadddbbbccdacadddaacdabdbdbdcdbbcabbaacadccccacccdbccadacbbabadcbadcdcabdacccbddbdddacbacadcabcddccdaabdcdbdddbaabbbcbccbccadccacdbbdcbbcbaaaabaacacacccccbacacaccdddcbbcbadaddbddababacbdccabbbdccccabaaccabcbdbdcdccbcabbbccbdcabacccacaabaacaadddcbbccbdcdabcbdddadbcabdbdbdbcdcabddcdddcacacbdbccabdababacccbccaaccbcddcdacabdbacbdcccabcbdabbbcacbaabdabaabaccbbcbccbbacdbbbdbcccabbdbdccaabdadcadcbaababbdbdaacabbddcaddbaacccbddccdbdbbcbcbccbcbaddacbcdddadbaacadacbabccabacbbdbddbadacabcadcbccddcddcdbcacbcbddacdcadadaabbcddbcacdabddabcccadbabbcdbcccbabdccadbdaddbacadcabcabcdbdbcddadbadcaabacdccdbbdccdcbabbbbdadacabacddacaddcdbbabbabccdbbbaddcacacbcadcacabadbaaabcbcaacccbdcdabdacdbabbdcccabcacdbcbcdbbcdaaaacccdacccaccbccbcbddbccbcdacaccbbbdccaacdddbddcacdbaabbabacdcccccbcabaabddbaaddcbbaadacbdbddcaabadbbcdadabbacdaaccaaaccbcbbadcbabbdddaabdbdacaabaaacdddccdbccbbbcbaaccadaaabaacacadacdccdaaacdbaaacabbdabbdadbbabdbaccbcbcaddaadcbddbdbdbdcbdacbcbbdbccbabadabccbcccaccadcbadbcaacdabbcdccbbbdadabccccbacbacbcdccdddcabadcdbdadcbcdcddbbbabccbacacbdbbcacabaacddaaaddcbdbbabdabdbaacdccbcbaacbacbdadcbbbabcdcacdadaaccdaadcbbabdddaacdbaccbbabbdadadabdbbdbbbcdbabdbadaccccadbbdbbdacbadbccddcbadadcdcbaadcababccdadacabadbcaadadbdcaabcccbdbbcaddddcccacbcdacdcbacbacabdadbdadaadbcccbacdbdbbdcbbacaabdcabddccccaddbcdbdcbbdabdcdbcbdbbbcdcddcbcbbabdabbdaccdabcadcccdddaabcababddccaddbbbccccbcbdababccabcdbcadbddadabcddabbbaaddbddccccaabbccbbddbcadabccbadbbccababadddadcbaabcdcbbaacaddccdadccbcdcdacddbcdcdcabdcabdbbbcdbbadbbdaabcbcaadaaddadccbbddddbdcbaaadbaabaabdddbcaaadaaccdbdcadcbcbccbbdaaacaccbadddbddcdbaaaacdcabbbbdacdbdaaabcbcaaccaddbddbbcadddaaccbdccabadcacdcaccadacacdbbdbbaabacdabdcdaadbbaaccddadbcddabacccaadbdabcabbbdaadbcbaabdbbcabcdbababddcbdbdacddaadcdddacdadbbcccadbbdaaaaabdbbaabbacbddacaacdbdcaabbabcadabbadaacacadbccccbaddbabcacccbbacdaddbbddcbdaddacddddcddcaaddbddcbadaaaabcdaadddccccaacdaaddbcdabcbcccbbcaddddbbdcccaadbbdbadaaabdbdabbadacccaabaadaacddccacdcbadcbacddacbadcccdabcdcbabaccbccdaddccbdbaababcdadbaacdcaacdaabdacddaaaacdcbbdbaabbbaabbaddcdbbabacdddbacacabbdbcbcdabdcabdcbdacdacbcccdcdcddcccddaccbdcbdabdaaaacbaaddababdbbababcabdbacbddcddccbabaccdbdbdbabdcbdbbbdcacadcddbbccbaadabcdbcabaddacabaddbcdbaccaabddbbcdbdccaacabacddacacccdddadbbcbddbacdbcbbbdbccadbbdccdbdccbaccdcdbdddaaccdbcbbcabbbdadaabbddcdaddbbabdbccadcdcbbdaddcbabdabbcdcacddcbadddcacaddcbcccdbcbcabbcbcaddaaccbbbdaadaadacbcbaadaaccacacdaaadabaaacbbcabccccacaddddadcacacabcbbdacdaacabbdadbaacdbccdbaadcadbabdabaabdbdcdabbccacdbdacababccadbcbbababcddcacdbccacccddbccaccddbbcacbbaddbcadcccaadabddcdbdcdacdbcdbcabbaaccdccbcaacddccdcddbcbcddbcbcacdacaadaccccaddaccdbbdcacbddcbabcabcbbbbcbbbcabbddbaadcabadcbcbcbbccdccaacccdcadcdbdaacaacccacaccdddccabdbabbcaadddbccabbbddaacccacccdbbbbbbbbaaccdbbabbcddcaaabbdbbcdaaccbbccdbacbddcdcabcababcabdbdacaacabddbccddaacbabdccacbbabdccadadcadcbdbdcccdbbccccdaddbdbdabaddadcddabdbdcdbaadccbacadbdbbbbacbbcccdbcdcabdcdcabccaccacbbabbbacdcccdababbabddcadaaadadbbabdddddcbccadbcbddddaccdababcaccbdaddbdbccbadcddbacdcbdacaadbcaacbdcadaabacdccbbbcabbbdabbbcadccddbcacacbbddbabbbcbaaccadcbbcaccaaccbdcdbcdbddbabbcaddcbcbbcdcdbbcbcbdabcdccccaddddcbbcdbbaacbcdaaccddadacadccdcbabbccaabbbcbbbcdddbdddcbabaacccbdadadadadcaccacbbaaaacccadcdbcdacbcbaadddabddccadbcbaaadadcbbbbdccadccacaaaddcacaabdddbaccbdaaacaadccdcbbdbccbbccadcacdbddccbbccccdccbccbcbbbabcdbbdbbbadbbcccaacdadcbadbbaddbabbcccccdbbdaadbbdcbdbcbbcaccaaabbcaabadbaddcdbdbcbddddaaadbbdadcbcdcabdcbbabbacaacacbdccbdcbbdacbdcbbaaabababdaaabacdbcdbaababbbcdabcacbcacaaddbbcbcbdcbaabaccbcbbcccaaacdaaccbadbcdadbdaadcdaaccccbaaccbabaacabaaacddacaadadcacbdaaacdcbadaaaadadcccbbcddbbccacbbbcbbcbacdcbcacbabdbddddcbbabbbccdaccaadccbabbbccddacbdcacaadaadbcdaccdbddccdccadddabdcacabcbddcdacadbdabaabaddaabdadaadcdcdaacdaacdacdbacbbabdcdaacdbcacdbdbcacadcacbbaabcdcdabadbccdddccabadccddcbdbdbbbbabdaaabdccaddbcaddbbdbbacabbcdbcadbbbdcbbbcdabcbaadbbdddbbcddcaabdaddaabbbabbcbbabbcbbbdacbacbbccdddaddcdadbbdcabadbdaadbbddadabbcbababbbbbadcacabbdbdcccaccacbacbcaaccabdacadcbbaccbddbcbdbddaccaacacbbccbbdcdcbaaacbdaddaadbcaadcbcaadbddaaddbcabadbbdcdbabcbcddbdbaabacbadbbacaddaacaccabadcbdddbcccacbbddbccccccaccdcbabdcdcbaddadbdabbbcaabaddaadaaddaaaacdacaddddccddcaccaadccdaaabccdbacddaccbacbdbddbadbabdacddbdcbdacaaabaacaadcbabaacaabbadcbdbbcadbbabcdabccaddcbadbdcdaabdaadcbbbdccddbadcccbcdcbaacabdbdbaaaddaccddbadadaadacaaadacaacdadcbcdccacaacbaacccccdcaaddbadcdaddbbbbdcddcdbabbbacdbaaababbccdacbabcccdbdbbadbcccdadaccbaabcbcaaadacbacbcadcbcdbbaddaddabddadbacbdbbcccddbcdbcdbcbbddbdbbbcccbdccbaaabcccccaddcbcddbccdbdcdacdbaacdadacabbccdcaacdacadcbdcbbdbabcbaddcdcccbadaaddbdcdbcaccbdabbbbdccccbaddbdbdbcdcbaccabcaacbdcdbdddcbcdcabbccdcaccdbaabddcdadbbbcaddbcaacbbdaacbcadbcbdaacbaccdcdbcdbccccabddbdcbadcbcacdbcadcaabdbdabadbcadbacaaadaacadabbacdbdaadddccdaacbbaccbcbabaacacbdccccacddbccdbaddbdbbccabbcdaddbadaaadbabcbaddcabdbcbdccbcccdbabcbabadacddccdaddbdcdcbabdadbddabddbbdcbbaccbdbccabbaabcbdcaadddadbdbdabadccdaccdabcdbbdcabbaaddbdaddcdbaccdbbdbaabdaaccbdcacbcccadbdabadcbcbbcdacbbacbacbcdaaaaddbdcdddacadddcbabcbcbcbaaaacabdbccdcccddaabcccadbacacdadccdacdaacdcdddcdcbbbbccbccccbacaadadabbdabdadcbaaaaacdddadaddbbacaacdbaabcbccbbacdbdaddaaaccaabbbbbcbddbbbacbcbdcabbbadbabcbbcddcbdcabbaaadacdcabbdccaddbbababddbbdbaabbbcacbdcacdcacbacabacbdcaaacdddbcdabddadbdacdbcaacbbddabdccddccdaabaabbaccbadbcacdacaccacabdadaadcddbbadbcbdcbcbbdccddcdcabdccdbddddbaaddddacbbcbdacabdaadbbbbbaadbbddccdacdadbbcdbbacbdadcbabbabccbccbaccaabcbbbabacbadbdcdcacddabddcaaaabdaabbbccacdddbbbbbddacdaccdcadddbdadcabdcbbbbdaaacbdcddaacaabacbcbaababadaccdbccabdccdcbdbcabbbbdabdcacdccdcdbdddcdbbabcbacabbbdaabddddaccacdaaaabdcddcadbddbccdbdadcddcccaabdddbddacbbadbdcdcdabcbaadaddabcacacdacaccbdadbcaabbbbdacbabdcdddcbdcabcbbdccddadabdcdbdcabbbabdacdacbcbcabcbdbccaadcacbbbaadcacdabccaabcbbbcbcbaaacdaabbbbbaacdbbcbdbccddabbaababbcbdadbcdccaabbabbdbbcccbbaccbcadcaadbbbbbbbdaacbbdccccacdbcdccbbddaccccccbaaadbdcccddcdaadcbbdbcbddabbacccdacbcdbabbdbddcacabdcccdcbbddcccacadbcbacccdccddbaccbdbcdaccaddadcadcabbbdacaacdccdcdbaabcdbadaccbbdcbdbaddbacddccbacbbaacddccbbdcbabbaadbbcccbdcbaabddacbaacdbddacabbcadccdbbbacdbdaadddccccbdbadadcbbbabadcabcdbbbdcbaccbaacaddcbacbccbacdbaccddcccdaccccdccdbbabacdccdbcacbadddccddaccdcaabacababdabdccbbabdcdbdbdabdbbccbbbdbcacbaacaacbcacbdaddadaddabcdacbacabcdacdbbadbdcabbadadcbcdbddadaddbddbbdcabacbbaaabdcbdbbacabbcbcdaaadbdcdaaccbacbbadcccdadabdaccdbcdabccbadabcdddcadabbacccddacddbbbadbaaacadcbbbabcabadabdbccbacabcdcdacaaaabcccbbadbdddcadbcadcdbaabbbcdcadccadbdbaabbbdaabbcdadcbcccdaaadcbdacdbbbdcaabdcdbaabcbcccddbccbabdccaaddcbaababdadbdbbddabcaddabacadcbaaccdcdcdbcdbaddbaccdbabdaadaabbacdccabbccddadccaddbbaaccbadbcccabdbdaaddddabdbbadcdababbbccdbdaabdcaabbdabdcdcddaadababbcdcbbabbcdbbbabbbbbdbcadbcbadaadadadaddadaabdbdabdbcabcbadbaaccdbbdbbdacccbcddacdadcacdbbddbaaabaabacbcaaaacccdcddbadabccdcddcccacddaaaccddcdcbcbdabacccaabbbdbcbdcdbbcabdaadcccadbddbbccbdddcdccabddbdbbdabaabbaaccbbbcccacbcacaddddabbdcacaddadccdabdcaabacbcdbdaadcbccaabdcacdbaacaadadddbdbbbaaaddbcdbaaacbcbbdbdcabcabbbaacadadacacdbbdbaadaaaaddcbbdaabcaaacdaabdbdabcbbbcccdaccbbcacbcdccbcbdbbaccbdccadddbdddabbcacacdbcdcbbbbdcbdaccbdcbabddbcabcbdcdbdadaacbaacbcdbadacdcadcddccaddddcdccdadacbabdcacdddaddcbcdabbcbbbaacaabcccdabaadbdacbcbbaaccddaddccddbdccdcacbcbddbdacaabbbdbdbabaccbddcccbabdcbadbbcabcbbcabacabbdacaabacbcbddcbacbcdbaabdddadcaaaaabdcdcadacbbadddaacadacdaacbcdacbdddbccaddcbcbdbcbcbbacbdacdabdbdacdccdcabbcdcccbcbadabcdbdbbbaddadbacbadcaadcbbcbccaccdbddbacdbcbcddcddabddbbdbcbcaccbcdccccbacdccbbabcabdaaaccbbbdbccddacdbcdccbdccdabdbcababdabcaaaadccacbddaadacbdcbcbcaadcbbacbabbbaadcabdddcacbcbaaaccbddaaadbacbbcbcaaccddbabdbacdabdbcabcaabcbcccbcaddadbababacabacbccbadcdbcdacbbdbabcdabdaccddbacabdcddcbdbbcbbaaabdbdcbdaabccaacbccdcbbbccbdbccabaddddbcacbdddaccbbccddabccabacacddacaaadccdcadabcaabbdbabbabbdabaccadcdddbbbccdddcdaabcbabbaccbcbcdcbdddacaacbcacdadbababcccbdaabdacdabddcacbabcdadcbababdccbaddcbdbbcbbbcadadcaddaadbbcbdaadaadaccdccddcbbdabccbbacdbcdbdbbcacacbabdcbabcabcccaddbcacbadadaabdacbbbbdadacabdbbadcddbbdcbcadcccbbabcdbaccaddbddcdabdacccacadbcacadbbbadabdadddadddbbacbcadbabbaaaadbcdddabbccababbcbbbabbaaacbdbdccdbdcbcdcdacdabbacdddaccddbabbdccacacdccabddaddabcbdbdddaacbdaccbcdacbbbddcabbadabccbccbacbdbbdcccdccbdcbbbabdcddddadaddbcdbadbadcbbdbdddbaadaddadcbcbadcadcddcdcdcdbbbdbbcbabbcaaccdbacaabbdbcadcbdbccaacdbadaddbabbdacdabddabacadbcdcbaabbabdaccbadbacddbadbadbdbddaadbbaadbaabdcdabddbdbcbddbbabaabcdbcdccdcdadcabdbcbdabbabdcddaccddadbbbccddabcabadcaabbabdaacaccabbccbccaacabcbaaccccbdbcdbbddacadbabbaddcdccaabdbadcbcbbcbbabcbaacbaabbcaacdacacabbadcdcbbdbabcacdabdcbddbdcdabbdddabddcadababaccacdcbabcaaacddacabccaabbcbcabcaddbdcbccccdcdabdbacbaaaabaddcabccaddcbabacdcabdaaadaaaacacdadccdbddcabadbdaabdcbcbdcadbddbcdcddbcddcbcccadaabdadbccbcdaddddbdabbdccddadaadbcdacddcdddacabcadadbcddabdcbcbbccdabcbdadcdcaabbdadbbbcaabdcaacbbbcbcdcddbaccabcccacbbcdbcbbaabbaaaccbdacdddbcccdbabacacccddcdacbbbcdcbabdacccccdcabdcccaaaddaaadbcabddacdccbbacddbccdabababbbcdbdbbbddadddacbbdbdabbcdbaaaddacdadbabbadbdddcadbddbcdbbadbdaaccaabdcaddabbccabddacadbacadcddbccccdaacddccddcdbcdaccacbdcdddbacbcbdaadbdcbbccbadbdddaadadacdcdbdacdbcaccddabcbcddbbddadcbdcaddbccdaaadcaadcdddcbbabdcabbbacaadbdccdabcccbbdcaadccabcadaaabaadccacddaaccccaacbaabcabbacdbccdddccbcdcdcacbbbcddcccadccbcabcdcbabdcbadddaccbbdbbadadbbbcadcabccabddcacbacbcadcadbcbabdbadbcbadbddcadadccababbcaaadddacdababaaccdcccdccdccdccbadabcadccdadabcbcbbabdacbdccccadbccbdccdadcacbdddcacbbacdddaccadbbdadabdbbcbddcdbdadaccbdadacdadbdbbcdacaaacdaddbcdbbddbcbbdaadbbbdccbbadcbcabbacabcbdcbcbdbdbbcccdddaddadcabacabaacbccaaccbdbcbbccabbdbdabdccabbdababccacdbaabdbbcdcacbbccadbadddcccdccdbaadaacadcdbacdbbbdbccdbcaacdcdadacbadbacabbbcdcaccdcabbbacadcbabbccabdcdbabaaabbacbbaddcbbaabdaddbcccbcdbcccdbaccdaacdbcdacddcadbcddcccbccbaccbddadadcddbaacaabdccbadacdccddcbdbadbdccdddaaaaabadbbcadadcdcdbbadddcabbaaadddbdbdabcbbccabdabbabddbcbcacadbdccbdaddadabdcabccdabcbbdaabaadbcbacbbcbacadbddcbacbdaadbadbbbbcdbcbbbbcaccbabacdcdcbcadbbbdbadbccbdcadccdcaacbadcbabccaaccbdddbdcaaddbaabcdcbcbacbcbdcddbbccccadadbdbbddbccaddbdcbaaabbacccabacaaddbbcbbdcaccdbbacabdacacbaccdacadacbbdbbcbbcddbbcbcdbbcabddbcdddaabccdcbcdcddbcdabadbdadacbdbabdbcbabaacbbbacdbbbcdacbabaccbcaccadcabaabdccaaadbcdbbbbddcbaadacbaacdadaddbaacbadcbcdaacabacbdadcacaacdbababbaddcacbbadcaaaccbcbdbcbadbbdadaccaccbccdbbdbccbdabcadddbdaadacdbbaaacddbbadaccacdcadcaddcdcadcbcbbdadbdbccbdbcacaadacbdbacdbacacbcadbbdbcaccbaccbbadaaabddbdadaaddbabdcbdadcccccbccdccabcbacabdcabbdadccdbcdbcbbaabdcaaababaabdccccbdcbabdadcdadabcddbabacdddcdddbccbdaacdbbbcbccabbdbccabddaccbdcaaddddadddabbbdcabddbaddccdcddddbdbababdcaddacccdbbcbdbdcbbddbdcdbbccdacccbccdcccdabcabacadbcaddcabaacbdccbccccbcadbcadbadddccbaabccbcaccadaacdddbcbddbdcaabddccadddbdbcdabccaaaaabcddaadacabadcddddcccaacdabccbcaaddbcbaacadccccacbbbcbdccddcdadcbdadcbdbabaabcccdbcacccabaccddadbadcacdbaaabccbbdbcadbcbcacccbddcdcaaaddccbdabcdccacddbbcabbddcbaccabcccdcaabbbcacdccadaabaadacbddaccadbcdadcdddddabdcbbbadbbbdddbdcdaaabcaccaaaabacaaccdadaaacdddaadaccacabbcaadcacdaaaaabacbadbadadccbdadcbacdaacdbbbdadbddbcbdbdbbbcbabcdddbbcadacaccccadbcadcabdcabccabaabaddbcbcdcbbddccbabdadadbcaddadddbcccdcbadcacddaabacccaddddcccadaacabcadcaabcddbbdbdcacdaadcabbbabaaababdadaaabbdcbccadcbbaddcabdbaaccdadcdadccdbcdabcbbacbdcbaadbbbddcacdbccdddcdddadccbabbdaccbdabdbdbbdcabdcdaadbdbddcddbbbddaddccbdcacdcbdcadcbdabbbddbdbacbadbccdbadabdaaacaacabcaaabcaaccdbadacbccacabcdadabadbcdacbccaabbbbddbcddbbdbbbbaccdcbbacbbabdabbddddabddabbcccabadbbbbadcbbbcddbdbdccdacdcbcbaddbcbaaccbdddcabdabdddacaaaddcbbadaacdbdcccbdccbbcccdacadbdabadccdbdbdddbacacccbdbaaacddcacbbcaaadacbdbbbbaadaccbcbabdbbddabdcdcadaadcbacbcaaddcbdcddcbdaacdbdbdcadcddcaadcbaaadcdacdaaaccaddbcbdccacabadccbbbdabdadbccccaccacaacdacdbddbdacbacdccdccccaadbbdaaabcbcdcdacbcccbbcbcaaacabbaccbdacccabbaacdccbbbadaddddbdaaaddabacbabdacdcbbcbbbbccbdacdcbbddbccddbdccbdcbbadadbbdbaadbddbddcabccadddccbdadcabdacdcdabccaccbbadccdbbadcaacdcbddbbbbcddddcacddccbdbbdbbbadddcabbbddbddcadcadcbaabcaacacacbbbbdaaacbddccbaccdadcadacccadbdbdaacbcdadbbdcadccacdcddadcaddcabdbaddbaadaadbaddbbdcaacdccabcbcaaddabaaddbcbccccadcdbbcacbcdcbcdcccdbdbdadbabadbcdadddadcccbbbdacddddbccbaabdabddcbdddcdaaacdbbbccdcacaadcbcaaaabadaabdcdbdadddacababddcbdddaccaaadacbcccccdacababacbdbccaccddaadaaddddcbcabacdbdcacbcbaaacbdccdaddadacacddbdadbbabacddcadacbdbbaabccaabacadbdacdccdaccabdacbcdbbcbbbbdbadcabbbbddbbabddaabbdcdabcbbbdcddddddadcbbdccbadbccadaaaaabaaacbaacdddbdaabcbbcbacabccdacadacbbbabbaadbcadacbdcbbaaabbaadacbaaaadcbacdccccaddddbbcaacaaddbadabbaccdcbcccccdabdddaabadcdccaadbbbdabdddaacadbbaabdaaaccadbccabacbcdcbabdbacccabdbbacccbdbbaaacccbabddbcbbacdcaacddcaddccdcbacbbbddabaccddbcdcdbdcdabaacdcbacddcbcccdbbbcbcbcbdcaddcbbcacbdcddbdddbcdcbcdbdaabbadcabdcbdcadabcbbabcdbbddadadbaabcabbbbcacdaccaadcaabdcddbcacbbaacaacbcadacddbbdccdabddcbaccacabcbacacddcadddbdbcaaabdcbdaadcaacbcabbabdccdbcbddcccccadbbbccccbddcdbaddaddbcdbccdbaabdcdadbdcbcdccccccdcacaddddbadbacbcdacadadaacacacddcddabbcbcccdddcabbcabdbbbcacbccaabbddbabdddbaababcccddcccddacbaccbabbddcbcabacdbcbdbaabccacdbddadcbaaaaacbaaadddcdadaddabdbaccddadbdcbabcaccaccdbbcaaadbcacdacbbacaadddcaacaadcbdcddcddbdcdbacabcbcaaddcabddbcabddbbcadcabaabcbadbabadbdaaaadadbcdbbdddabdaddbadbacdccdcbccddddadbadacdcbdbddcabababbdaddadcacacadcbddcabdbcdbcadcddaccbaddbdacdcbacdcdbdaacddbdbdbaadddaabdcbacbcdccdbcbbbcbdacabbcdddcdddcdbbdadaddcddcbacbdbacacbaccaacdbcdaaacabdcddccadbacaabbabdaabcadccbaddabacabbadcdbaddddcbbbccadbdadabcacaabbcbdbcbcdcdbcbddbaadccbdddddbdadabbcbacaccdcbcddcbacabcaadaadcabdddcbadbdacadacbacbdddaaccdbdbccccacbacdbcddbdddadcdbbccddddacbdcccccbdbcaccaacdcdaddddaaaacbccdaadccdddcaaadaacaabacabacacacccdddbabcdbadaddacdaaccdbcdddabcabcabcbdaadcddccaabbcdaabacbaddbbbdddabaadcccaadddaaccadbabbdccbadaacdcbacbbdbadbdcccacccaacdabcbabccbbccdbcddaaacbbbacaadbbbbacbaadccdbbdcabadbaaadccabacabcbbdabadbadcabdbbbaddcadddcdaddacbbcccbbbdbbccbdddcdcaddccaababaddacddcbdabadcaaabbadacaaabaabadabddbddcbdacbbbdbcdccadbabadcabbbdccaacbcbadbcbbcacdcbabadbbdbbcdbacddcdccbdcabcbacdcbcdbccbccdcbccbcccbbbacbbcaacadcdadadacdaaabdadccabbbbcddddadbabcaabaccdadbbcbdbaddbbaadbcaabcbbcaaccbcbacdbbdbabcdbcbabaaaddbbdbbdccacddbbadbcabcbdcbccccbcbbcbbdbacaddabbdbcabbdadbabbadcdaaacdadadabdabbdcaabddddbdcbcbdcacdcbabcbdacaccbbdbacbbdbabdbdacdccdbdadcabacbabcadadaababdcbdbdddcadcabcbbccadcabdbadbbcbddabacbcabdcdadccbccdbdaabdaabcaadadddbdcbbadbccbdbbdaacbbbcdacbbaaaaaaddccdaddacdbcadccdbddcdcabbcaaadddaadddddcbabcbdcddbbaabacdadbacaadbdaabbccddaaccbbcbaabacaaccdcccacbcdbacbacdcdddcdcbaaaddabcdddcabbbcaacdaabcdcbaadbcaabdbcdabbadabdcbacdcabadbacbcbbbdadcaacbaabbcdabcaccdcbdbbcbdcabcddabaabdbbbdbadadaaabbaadaaadadcdaaaaddcbdbcbacdbacacdacddaababcdcbdacabbbcaccdbbcdadabdbcdabccbbcbccadbcaadbdaacbaacacbbbacdcbadbadaacbcbdacbccbbcdddaadbbbdcbaaaabcdaaabbcccbbcbbcabcbdbbdbbcdaddbadbccddbcdacccbadccadbbbccadcadcbbccddbbcbdbdbbcdbccdbabaabcaadcdcdaabddbdcbbcaddbabacacdbcddbadadaadaddbddcbdbbdcacabacbabddacadadcadcabdbcaabdddcabccdbdabcddacaaabccaccdadbcadcacddddabcdbccbaadaababacdbbbccdaacddcccabdcaaaabccbcddbcbdadbbbdcbbcaaadcddcccdccabdbaaccabdadbaabaadddbabccbcbbadddcdadadcaacacaaddbbccaddabdadcccabdddacacbdacaccbbddbacbcdbdadaccacaddadbcdaabbcadcacbadddcaaabadcbadaabaacdcdbaddccccacbdbcdbbcbbcadbcccbcdddcdaddaccccaadcddcabbbccccacabddcbadacbbbbdddcbbacbadaadaddabaaabbaabcbbcaacdcbdabcdcadcbbcabcabdaddaccdacadacabcdcaacabbbccbbadbdcbcbccccbcbadcbcbbbbdcabcbbccaaddaabcdacbabccacdcaaddcccbbddabacbccaaaaaacbccdddbdbdabcaadbacbcacacaaadcadbdcaaccadccbacbdbdcdccaaaaaccaadcbaacbacabcbddccbccadabdbbbcbdbcdaacbdbcdabcabaaabcbdcabdccdcdbbddbbcbcbdcdddddcdaddcabadccacadacadcddcacbbcbabaccbccccbcbabddacdddbbbccadbdcddbadbddcacddbbdcadcbbbaaadabcabddbdacdccaabcadbccdabbddacbdbcbabadbbccbddbddabbcbabaaadbcacbccabacbabccaaddadccadabababdbaaddaabcaccbcbacaacbbbbbbabaccadabbdacddcbcbbbdddbccbbcdbdadcccacccdbcadcdbdaabcdcbddaadaaabcacdbaacacdddbbbddadcdccdbaaddaacaccbacbdcacccdacaaacbbdcbdccaccdabbddadcadbdabbdadddbaacaddaabbabdaacccccaacbdbbbdbdcbddabaccbdcbabcdbcbbacbbdcddcbbadccddccdcacdcabadcbacabcbaadbbcadaacbbccbbccdcccaccbdccbabcdadcaaadcbbabadccbbcbaaabbaabbbcdacddbdacbdcbddbacddacddaaccbcdbdcabdcdbbadcbccdbcaccaadcaadccaacbddcddcddbaacdbdaacdddbbdddadaccbdcccbcaadbbbacaacbbbdacbbcddaaadcdddacadcadcacbdbbcabacabaaabbbcbabaaadcbccabaadcdcadccbcbacaddbbddabdbcdcbcbacabcdabbdaadbbadaabbbcbdcdbbadabdaddcbdbbcdbcaabdaadacdbaabbbcbdabddabaddbcabaaacaccadbbdbaadacbcddadccbccddaaccbcdabacccccabcbbdbbcdddcddadcabcdddcdccabccbbbcabbcdbacbbacbadabdddcccaacadddacccbdabbbbcdddbaacabbabbadddbdbddddcbaabaaddcdcacbdcbbabbccdcdbabdccaabaaabbdadbccdccccacbbacacbdcbdacabbdadacacbcbbcdcbddddcdcbdacdabadbabbacbcacddaccdbcdaababddadcaaaddaccabaccddbbdbbbddbbadabdcddabcbdcbcbdcddadccbbabaccadaaadccadacdcabcbcbdbcbcddabcdaccaaaccbdbaddacdbbdcaccabddbcccbbbccddcbdbcdcdcbadbbdadddbcddbcaabbdaddccdddabdaaacdbcabbbdadcdaaabccdbcdaaadcaddadabbbdcaadacbccabcbdaccbbcdabaacdcbcccbdadabbdccabcaaadadddacdbbddbdacadcdaddcddaaaaabadaaadbacdbdbddccdaadcaacdcccabcabaadddbabbbcbbdacaccaaaacadbacbaaccadaabacddbcdbcbbdcdcbbaacaacbaabdccadcbdccdacdbacdcaaabccabdacccdbcbbcccbcaaacacdccacadccaaabbdadadadabbbcccadbadaddcdbccddaacccdaaacdcadadacacdcaccabdadcabadddaaacbbccccacacbaaaddadadacddcdaaaadccdaacdbdabdcaddaabcccccdcdcbbcacbccaaaaabacacdacacabaacddcbcdddcaccadaccaacaddbbcbadbddddbbdabcbbaaabccdccbbcddddcdcdababcaaadccbabacadbabadbbaabbdbdacaabbababddcbacdcadcdcdaabbcbbaaddcbccdaaaaabaadcacbbbaaadcccbccccdbdaccbdbabddbbdababbbdadddccdccbdbdbdabcbcddaccbbadadadbabbbddbcacccbbbcbddcdcbbdbdacdabaabcaadcbdbdbccaaadbdcdbbcdbadcdcdbdbdbadaabbaddcdadbdbccbbdddccdabadbcdcacadcbccbddbbbcadbacadbcbbbacadadadaccaaaabacdaaaddcdcabcadcbaabdbcddacbdbcabcbbbdabcbacbccbaabdadcadcabccbcbbcbbbcbbbcbabaddddadccbccddadcaabccacbdcdbcaabbcdabbbabacccbbaaadbaddbbbdaaaaccbaadcbcabadbadababdbabbdacabacdcddbbbbdccacdbbcbabaddabcdaacccbdaaddbbcbaadbaaaacdaaabcdadbcadcccadabaacacdbbdaaaacaaadcdbcababaabadcbabadccdcacabcacdacbabcaabcddadcddacbccbdaaacddbdbbdbaccbcadbbcbbcbdacddbcbbddcddaacdddbaacacddacbdcdadabcdabbcacbaddbdadbabbbbccabcbdacbdbadabdaacaabcdddacdbdcbddddbabcbbacbccaddddbbddcaddbbdcbabadcadabdbdadbdbdaacaddadbbabbdcbcddbcbbcbcbccabbddbcbddacacaabbaddabdcbabbdbdacddacbdbadcacadaabccbcbcbcdcdbdcadbbcbdbbabbdbaddccadbbdbaacbaddaadbccabbbcaacccddabcdbaccbdcdabbbcccccbbbcbdcbdccacbbccaaddabaabcbbaaadaadabdcccdabbcaddcdaacbccbaabaaadaacdcdacbcbddcdaadddbddccaaabbaccbdcabdbdccbaddbdcddbcdbdddbdbcadbaaacdcabbdaddcaadccbbbcaabcdadbbcdacdcdbbaaccbcbdbcdccaaabaadbaadacbcbccbccddbdbaacdcabbacdadaacdcadddcbccdbdbddabdcdcacddbabcabcadddaadadaccbbaccbbbdcaaacabcacbdabcbcaabdbcdddcaccdabacdbdbadbbaaaaddcbadacbbcabddacacacabadbdaadcbccddcdbaccbbaacababcbadcadadddabbbcabcdbabdaaacadbbcdbcddabcbdcbcacabaadcbbaddaacbdbcdcbdbbaddccbacbbaaadddcdcccccabcaadcdcdadddccadbcadcaddccabddbcabadbbdbabadcccbababadbbdcdadaabdcddbdcaacdadcbaadcbdadacdbcadddbacbcbabcbcdbaaacbccdcbabdbcbbccacdbbddabddccaacdccccaaadbdacdcccabddabddcdbdcabbdaaabdbaadcdbddaacbcdbbdccabdcbbbdbaccdbdbbbcdddacbdcaaabcdcbadbabcadaaddbdcbccbadbabcddacdaaddcaabbdcabbdcbcbaacaadaddaacaacbdacbdabbdadcbcbdddbbccbcbbdcabbdacaaabdcaabbabbdbccaccdadcdabdbcbabacbcabaddbacbbddcccdcadbbacacadbbddcdcdbbbcdabacbacdabbadbcadcadbbbadcbbbbadcbaddabdcadbdcddcbcbccdbcdbacddbbabbcbdbdadcddbadabbddbbbbcaddccdcbdaddabbaacdbcccdccdcdbabbdadbbccbcdcaacdbacbbacadadcbcdbdddcdcddbcadaaaaaaabbabbdcdddcbbdbabdabcdbcdabdbcaabddbdcdbccacdacbadcdbcddbbbddabbcbddccbbdcbccbcdbdbbadcadcabcaacddbbaabadccaddadcddddbaddacdabadaddacbdddaaabbcababbcbbaadaabdcabcccbaacabbaadcabddcddddcdccbcdcbcbabaacacacdddaddbaccdbabcaadbccaabcadadcacacbaaabbbddcabadadcadadccbcdacbacbcdbccbbabbcadcbadcdbbcabdcdacbbcdddbcaadaacbbacccbdddbccddcdaabcdacdabaccbcabcdddcddbacdcbdbddacdcdabcbaaaababdcbbbdcabbcbbbadddbccbdacdcbaaccddbddddaadbdcbcbadbbbadadaddddaddacbbabcbadabbaddddacbddbdcdacddaaabddbdadcacabccbdbbcacaacadbadcabddbdddadbaabbccbcccbdcaacadacaddcdbccdddbbcbdcaccbdcaabadabbcdccdbbaadbbcbbaabcaccdbccbddcaadcdbacadcabcddaabcbabbbccbbbcdaaadcdcdaccbbbadbdabcdcaacdbdcabcdcdaacbdddccdabbdbbbdcdcbcbaaabadacaabacaabdbdbbaddbbddbbdaccccdddabdacdaadcbabdddbabdcbadacdbdbdacbcdcbcbbdcaaabdbbacaaccdcaaaabacabbcdcccccbbbbcabcdbcdcadbdacaacaaaadbdaaddabdcadadbbdbdcbcbaaabcaaabbabadccdadbdadaadaaabbbdbacabddbdccdaaabbbabaddaaacbcdbbadbbaacccbbacadddcaadbbaaaaaaddcbddadccbdbbcabdadadcddcbabdacaabdcddcdadcdbddabdccdcdbcacbdbcbdbbbdcbacabcdbcdcadcddcbcbbdbbcccdabbdacabccdacaaddddcbadcccbbdbcdacacdabadabcadabddaabcdbcababaddcabcdabcbaccacbabcdccabbbbcbdaadcabdbcbdaadaddbcdbdbadadddccddbcabddbddbcbcbdddbaaaabbdbdbbcadabadbcddcbabdadaccdbadcbdcddccddcbcbcdaccaccaadabbddcabbdcdcaaabdbadbcadaabadacbddccadaabcaccbababcaadcbdcacaacbaccacdccbcaabdbaaabdadabcabdcccbdbbccacbaaaadcadaabaabccbacbcbdacdabbaabbadcbbaaabbcdbbdbbaddbbcccddcdbaabcdabddbacbababbacdbdcddaccdccbccbcddbadddcadaacdbddcadadccbcababaacbbcdaddcdcdbbbacdddddbccbabbcadddccadbbacbcddcbddcadadabdddbdaaccbbaddccdbbcabddbaddcbadccabacbabdaadddcdabccdcbcacdcdccddccbddbaaababdbbabcacdabdbaccbcbbcddaaddabaaccbbdcbdcdaabaddcabcbdbbcaabcddcacdcdcabccbccccdbccbadaadbabbbcbaacbbbabcaadbadacdadcbadbcbdbbdddcacbbabcbacbddbababaabdabdaccdcabbddbadcccdabbdcdbaddabbcdbccdbcbbabbabcccddbaacddaadadacbdcddcacaaaaababaccdbcbddbbbbbdadabcdabcddccbbccabbdabcacbbccbbcbadadcbdaabaabbaacccdcbcbcdbdacbbdabdabbcbaadccccacdcabdccaccbbbdadcddccadacaccaabdacdbbcdadbddcdcbcbadcddcdaadbbdcddaaabadbdcadbcbdbcacababcbcbadadccbdddcaaabcacddadbdaacddabbbdcdcaadacacaaadbdaaddbacddabcbdccbcabcaaaacddababdcccbdcdbdddadcbadbabdddcbbbdcddabcbddccbbbabaddbdbaccbbccbaadcdaccdbdcdabadababbbcadacabaacbbbbbcbddabaddcaadbabcccdacadadbcacabbccaadadbdcbdccddababadccbacdabbccadcbddbcbdbabaccbddcabacbacdcaaddaaacdcdadbbbbdccdacbbaabbbddcabdbdbdbbbacbbabbaacbdacabcbcaaaabacbccaccbcdadbcbdbdaddabdbcadaadacadbbaabdadbddabbcccaaabbabcbccdbbccadaacadbbaacaddaaabddacbcbabbddddcacddccdbdcacabaccbcdbcadcdddcccdaddddbdcacbcbdabbabbcacacaaaddcabdaaaccadbcbdacbbdccbcabbcaaabddcdabcddacdadadbbcaccbddadcdbcbbcdcdacdbbbcbddccbcbbadacbccbbbadcccccacacabcddcbbbdaabbbcadadcdaddaabbddbaadddadcbbbdbcbbdaddbddbaacccacbaadbdddacbaacbbdbcddcdbadcabdbdccabacdabcabbdbacdacdcbaaaabadcbcabccccdacdcdbbadacbbbdddcaaabacacadbccaadcbbcacadaacbaaccadcdbdcbddacdcbcdddadcbabccabdaaaadbbbdbbdcacaddcbbabbdddbcdddbaccbdbcabbaadcccaadaacdbbcbcacddacabaddccacccaaabbbbacaadadcaacdabcdcabbcabdcacbdabdcabacadcaccacadcabbbdbaabddbccbdcbaddadccdabbbdaccdbddaababdbaabdaccdbcbcdbbdaabdbacbbdacccaabddabbbbbabcaddabcdaababadbbaadcbdddabcddaadacbdcdbdbbdddcdaabddaacbccbababbddcaaddabcaaabddbacaadacdaaadabaddacbbadabbbdbaddabbbddacccbbddbcbcbcccdbdbcdadabcabbbaaddbaaadcccdccdccbcdddbabddadccaccdaaddcdacaccbbbdcdaaabcdcdbacacacdabdbdcbdcdcbdbcbdaccdaabcdbcabdaaabbdadacdcaddaaddbdabcaacdaddcabbabcacadbdbbbccaddaabbccbdbddbcccadcccdbdcacacbcdadabaaccbadbadadadadccdaacabbaabacabbaaaaacbaddbdcbbcbdaaadbcacdaadcbbddcbbaccabbaacadddabcadadadccbcdbbabdaccaacadcdacccdddcbccabbaabbbcdbdcbcddcdabdddabbddaddcbabacabacaddaadcbaccddbbbdbccbaacbbdbcdacaadbadccbcabbdbabdcdccaacbbaaaacdcdbbbadcdbdbaaabaadccaabddbcdcbbbcdbddbddaabbbbdbbaaccdbdabacdadabcdbdabadccbadabcbcccbbcdaddcdbbbdddcdbbbbdcddbccbbbbbbdbacbadbaaaddccccbdcdccdacdcccddabbaaadcabdabaaaccbdcababccbdcddbbabdcbbbccadcadcaadbaaadbcdcbbabccbbdbddccabbaadabcddbbbbaaaccaaabcbcdcaaccddcabddaacacdddbbaddbcdcabbaacdbddddcaccdddacabacdabcaacdabbbcdabadcdadbaaddccadabdaccdbdacaacddddbaaddcbdccdacadabbcabcdbbdcabbacadccbdacbcccddacbcbaddaccdbdcaabcaddadddbdaddabdbdccbcacdabdacdcadacddccaaddcccdbcbadadbdcabcdadddbaabcbcbcddcadcaaadbbdcddcaddcdcacaddaabcaadbddaacbbaaaabcaccabbcaaabbababcaacbccddabaabcbcccccdcbdbdaabadbdbabddacddcbcdaabcadbdcbdaacddcaaaabccabccabaabdadadcbacdcbbaacdacdaadababccbbabddcccdddcbababbacdaabaddcadbbcbadacdcbbadcbadbdbabcaccdabbaacdcbcdacbbcadaccddcdcbdabaadbcabcbbacdcccbcbccdbbcadcbadcbcccddaababacabddaadabcdcbacbcaaaddbbcdcdcacdbbbbbbbdaadcbbaacadbbdcdddcdcccccbdacbdadccaabababbcaccbcdbdaddccbcdccaadcbbdbbbadcababadadaadcadccddadaadabbbbacababdcaacbdabddbcbaaaabbbbacccdcdddadccdcdbdaadbdbbaabdabdcadacccbabddddcabdbacaddbcbdcadcaacbccdadaadaacddcaaabaabadadbbaacbabdbbbacbccccdbdbdadcccdbcaacdadabbdccbaabbccbbddaabbacadcbbabcaaaabcabcbbbcbcbdcaadcbdadcacbabcabaadaadcddddadcbadbcddbdcddbbbccdcccbddcbdcbdccdcaaacbbcadaccabbbcacaabcaccbcdabcccaddadbabadabcdcbbcabcdaccbcacbcdbcccaddbacacbadaacdacbbbbcddacabcccaadbbadaabaccbaccbadbaaaacdabacddbcababacccabbbccdcbadccaacbcacddddadaacbbdcbbdaabbaccdcdddcadabbccbbddcbddabddbdbacdcabbdaddcbacaacdbadccdbcdadbbdabbccdbdddaccaabbddabccddacbadaadabdcbdbcbabcdccccacbddcbbcadaddcdccdacdcdcccaacbbbadcadbbcddaaaddbbccdbcacccdcdddbddbaabacabbcaaadacbabcadcabbaadadbdbddabdaccdcdadaaacbabbdddbaaadbddcaaaccdbadcbdcabaaadbbbbddadddcdadabdcaabcacabbabacdbdbaaacdcabcbdccbadbbddabbaacbdbdddbbdadabdbbbcddcabcbddccadbccccbbdadaabdbaabcdadbdaccaabccababacbdbdadbcdddcdabdcdabccbcddabbcbacdbacaaccdadbacacdaadcdbdbcbaccabcdaaabacadababbdaaadbadaabdcbcaadbcbacadcdadbddcbddbcdaadcbdcdbddddbcddaddcacdacbbcbdabbdbadabadbdaadacacdcdbaadabdcbdaccccdcdbaaaaccbcddbccaaccbdcdcbccdcccddcbadcbdbcbbabbcbbacdbcbcdbaddcdcdaddaabcaabcddbacdccbaabdbdbacdacdccbdbdcaadcbbbddcbdccacbaddbadccdabaaacddbdacdccdbcabcaabbdcddbbddbacddacbadbabcbcdbbcdaabdaaccadcddcbabbbdcbddcbabadbaddcadacaaaadaacbddccdcccccbdbdddbdbbddaabbbdaaaadcbcdccdcbcccabcdadadabaabacacbcbadbcbddcadbdaacabbdbcaddbccacbaabaacadaaaaabbcdcaccddbcdacdbabcabcacccaadbacaaccaaacbbadaddbcbdadbcaabcabbbaabacbcabbbcaaacdadabcbcdabcbaadcbbbacabdcccccdddacbabcdbccddcdddacacaddabdbacccdbcadccabadcabccdabaabdcdcababbbbaacbdbddbacaaccbbdcabccccccacbcacbaccdabcdcaddddbdddcdcbcddddccdbbdccccbbccddddacbbdaacddaacccbddbbcbabccbbcbaacbaccbcbbcddbbbbbcacbdccdccdababdddcdadcddbbbcadacdcccbaacbaabbdbcadacdcbccdadcddccadacccdccddacdddadacdcccdcdccaaaacdadddaaacaaccbddadbcdbabbacbcdabddabdccadaaabcacdbaaabcbdddcccbcddacccaaccbaadbccbbacbabacccdcbdcbdcbccddcbdcadcdcdddabbbccccabaacbaaaddaccadbacbadbcadccdabbacbbbbdcdaacbacddcbcbbcbbdbaabdccccbbdacdccdcbccdddbdcacdbdcacaddbaadbabcbbdcbbcccbbbcddcccbabdacdbddadaacabdcbbdbbaadcccbcdaacbbcbdabcbcddbbdbbbcabcaabaababbacddcccdcacabcbcdcdcccccabdabaaacddacddcadabccacddbcabcacadcadadabbdddbdddacababadcdbbabcdaaccacdbacaabcbbcbbdbbdddddcbaddbabbbbcdaaaadcadbaacbbcbdcdabddbdcbabbababccdcdcacdbadabcbdaacbcacbcadbcdcdbbbcabbcadcabacdccbdccbabbabcbabcaccccaddcaacbdbcbcbbacabbcaaaaacdbbabdcbbbbbaabbcaddbacdabbcddbabdbbdccadabaadcccddabcdbacbaabbdccaccbcdaddaaddbddddaacaddbbcadddbbabcadcbdccabdacbdbbadbacbbadacaabccddcadbcdbdcbababbcacabdaccdcacccadcddccaddcdcddcbcbacabdabcdcacbdbddadcdbbcbdcdababacbcdadaccccbdbcdadcabbbdcbbaacccabddcbcdddcbbdcdcabaaadbbdccccabbabbcbbcabdacbdacababcdabacdcabbddcdacadaaccccacadadaaddddccabcbabaacaaadcaadbadbcbdddbbccabdabbcbacccacdcccddcadaacdaaadbaccbdcdcacdcabbbbdccdcacacbbdadaaabbcbbccbaabbabbcccdcbabadacaabcdcdabcadcbabdbbdacaadadabdaddaadcccdcdbccccaadcbacddbcccddbcabbabacdbcdbdddddbdaaacdaaadacdcbdcbdbbbbddbcdadcbccacbdababddbdadcbadcbaacabccbddabcadaddbdcdaccdbbccaadbbcdcddbccaccdcdcacccbdbcddddbbdbbacccbdacbbbdcadabccbcddbabacccdbcbbddaaccccbccdaabbdccdbacaaddadabcbaaadbbdacdcbcdccdcbcdaabdcccbbccccbcddcaacbbbccdcccddaaccccabdcbcacaabcccccbbbadaadaccbbdcadacddcbbbbddcbacdcaccaddbbdacbaaabbcbbdadccccbbaacbccaabadabbcdccbdbbcdbddddadcabbbadabdcaccabdcbcdcbdbcccbbadbdcbaacbbbadccccddaaddabacaacacadbcccbdbbcaddbcdcaadbddbcdacdcbacbccabbdccbdcccacdddcbdcadcdccacbbaadbbabcddddadadccccdcabdbdbbcccbcddbdcadcdaacacadbaaaaaaccdcddacaaadacccbadabbcacabcbdacccabbddcaadbdbcabbdabacabaccdaacbdacadbddaaabbbabcadaacabadadabaabdbcdaacdcbacbacbabcddaacbdbababdacdaddaabbdbbdbbabcdcacdcddbbdadccbccdbbabaacabdccacabbbdbdbdabbcccaabdbccacadabbcbaababcbacbadbdadcdcabccddbcaaadbbddbacbadaccbdadbbbbbddabdadababacbaadababbcbbdcaaccccdbddcddbbcdcccdddacacadcbdacdbcdcabaddcbbcbcdadcbbabadabaacbcaddbbabbabdaacabadccaccdabbdbccdaacdabbdabbdcbcddcabdacbdabbbcabdabadccbbadacdbbaaccbbbabcdcddddcacdddabadadccbaddaccdaaacaacccacbcccdaacdccaaacabdddbddddacadadccbcadbbbddbbaacddbdadcbbdabbbacdabbcaacabdcbccbbcbccbccbadcbdaacabcadccccbdadbadccbbabdacdbcdacddcdddaadcdbcbcbbaadcababbcbdbbaaaadadbaaaadddaddccdbbadaababdbcbdaccbacbdddccccddcbadccbddaaddaacbbcacadcdaabdabcacddacdcdaaddcaacbddaaaaadbaacaaaacccbbbdcdbcdbddddbccadbbcacbbbaaacccdcabdbaadccbccaacbadabcdbadbcbadacaadadcbadbabadadbabbddcbadaadddaacdccbdddbdabdccdaccdaccddcdbdbccdccaccbbbbbddadcdacbbbabbdbabccbbbbddbadddbddabbadaddbbdacdbbadbbbbbcdcacaccbaadadabbbcdcbdabcdbadbccadadddadadaadcbbbbaaadcacacdccaddabcabdddbdadaadcbaccbbadaaddcbcadcdbdcadddaadadbaddacbaaccbaaddcbbaabbdbdcadbcadcbadbaaadcaaccdbbbaadadcdadabdccccccddcccbacbcacccbbdacbdbaddcdacbbadcddbbbacbdbcccdabcddaaacdcdaabcabbabbbddcbabbbdcddcdcbdcddabdacabcaaacccabababcbddccbbcaababdadbdadcbaccbdbdcdadadbdacadcdcdcacdddadaaddbdddaadadadaabbdacaadabcacabbacacbdcabddadcdccdbddbcbaadcbbcbaddccbabaabddcccdbdbabdccbaacacddcbccabbbbaacaccddadddcdbacccadadcaddcadacbdcaccddbbaddcbcadbdbbccabacbdbabbcdccbbdabacacccbbdcbacddcdcaccdbbdcdccbdbdabcbdacbcacdbabdaddbdaadcbcccaabcdccbadbbcbadaadcbbbbadbcbaddccbbabcdabcaacddbcaabdadccdadddcddadbcbdbccacdbbcaabccaddddbbdddddabdabadbbbabbbbcddcbadbbcaadbcdccdaacdddbdbdaaaccbdabbdcdadbbbdbcdcaaabdaccaabbbdadcacdbbcbcdbdbacccbaddadcbcbadbbdccddabcbbaccabdadddaddacddacbcdcbdcbbabddccbbdbdadbccabcbabbccaadddcdbdcbdcddababbadcccacabdcdcbcabbbccdbbcaaccbaabaadbababdaaabcabdabdbbbcbdbadadbbdcdcdcdbabcbbccccdccacabbbbdcbacbdaacacbbbabbdaaababdbbcaaccccdaaaddacbcbcaddbcaaadbacdbbaccbcdcdaacbbbabccbadbbbcdcbdcbadbaddcadaacccacddccdccdcabbadcccabcaaddcabbacdcdaaaddaddbdddcadcbabcabcadbcacbadbdabdabbcacaadbadddcaddcbcbbdbdcbababaddaccbaabdabdaadabcbaaccbccbccccbbbbbdadbbaabbadbbccddcddacaabbaabbbcabcbbacbdcacdcbabddccccaaddbdbcacabadcdcdbcadccccbaabdcbabacddacdaccdcdcaacdbdababbaddcdcbdbacddbaadabdbdadddadacacabbcbbdadacddcadbaadaccbddbcbcbbcabcbddacddadbcbdbbbdacdaacaaaddabcbbdcacdabddddbabcdbddbcdaabbcdddadbcdbcaacadccdbbbaddddddaaabacbcddcdacbcadaaaabadcbbadbaaaaacbbbbdaaccbdbddbbabddbaaddbcacbcccbddcacdaddaacaddbbcdccbcaadaccdbddacaabdabdcdacbabaadacbdccdddadcccacbdabbddbbcbcdccabccddadcbaaadbbcbacddcdaaababcababbccadcdaaddabdcbcbadccacabdbabddcdacacbacdbaabdbadbcbadacbadddddaaccdbbabccabacbadaaabababdbbbbbaadabababaaaaaaddcabaaaccbdadbcbbaaadaddacacdbaddaaabaadcdcddddcbdbabcaccdbaabcdcdddcbdadbcdbdddaaacdcacbcbdcbdbdcddbbdadbdccdbddcbdaadabddaddaaddbcadacbabdbabdadcadaccddadcaacaabcdbacacdccbbaacbbadddbacacdacbcaabbcabbdabaacacbacbcabaaabbbbccbccacacaacbdbddaaddddcbacbacdaabababdbbbabbbbaadcbcdadacbcaaaddbccacdcacdccbddddcbbbaaddbddbbadbacbdcbcabbaddccbccbdccbdcbdbdbdcbdabadaddddbdcaacbdadcddaacbabdbddabdcdcdcbaddbdccdaadbcaddcacdbcacbabdacdccaabddbacbcbcdabadbdabacdadabcdaaaabcccdcddccacbccdcbdcaabddbdbcabadbacdabdccadbbddcadabbddabdcacbaabccdbcbdacaccaabccaacdbbdaaccacccabcabbdddacabcdcaabacccbbbccdddbababacacddcbbcccbcdbaddccdcadbdacdcacbccaabddcdbbbadabbbbddcaabbdaccccacdbbbcaacdadbacaaabcdabbbdabccadbdccbdccbbaababbccdbbdbadbbcaadadcbcabcbcbdbdbdcabccdbbcddccaddccdcbdabddbabcbcabccdcccddddcccbbdbccdcbdcdaacdcbccdbcadcdbacdddacadabaaabcdadbdbbdbdbbaddbbbaacacdcaddcabdbadcaabbcbdbcaacddacbdbaaacacdaabaacaadccaabdbcddcacacadbabdbbaadcddaabaabddabbbaddcbcaddccbbcacdbbcdaadacadadbbbddbbbacccaddbdbbdcddbabadbaddbddcbdcdbcbacbbcdcccacadaccdaccaddabaadccdddadccabcddddacbbddaaabdbcacacddbddacbaadbbdbbbaadbacbbbadccabdcddcadaabbcaccaaddbabcdacabacbaaadaabcddbdcbaaadcadbccbaadaaccaacbabdbacddbabdddcdbcdabcbabdaaaccaadacdacbdbadccbcbacabadccddacbdccdabbcccdabdaaddcbbcbdbbbccdcadaacdbbbdaddaddcabdbdbdcdadbabddbdaacccdcbcbcaacdbaabadcabcbdcbccabadbadadacbcabbbddbbcddddaacbabcdacdadbacccccdcdbdadcacbdabcccabbbaacdbbdbbdcdbaacabbaaabaabcabadacacccaddacacbcbacdcccacdaddcbdbadabacccbcbcaabdbdddaccacdbcddbadcdabdaccdcaddbbabaccacdcdcddddccbaabcaababccabcadacabcdcaadaaaddbccbcadddbadbacdbababdaddabadbacacdadadbacacbccbcbbdcbdbdbabbdbcbbbbbbaabdcbbccabbcdacadaddbcbaabddbdcccdcbddbadbacbddadbbadcadabbdccadabbbaabadccabdadddbbacabcbcccbdadaadbdcadcacadbcdbaddcaddacdabdbccbaaadbbbbdddccaadcacaacdadacddcdacabccbdddbcccccbccbdaabadcbabaabadbcbbcbbdaabdabbcdadadcbbbdcddbdccaccbbcdacbbbbaabbbaacabadcccbdccdccdcdccccacdcaaadaadcababbcbacababcaddcdadcbccdcdabccdcacbacddaabbcbcbaababcacdcccbdbaacaabccacacbbcdccabdcdabaabcacbdacdbdcbbcdbccdacaabbbdabcdcbaacddaaddbcbddbbabdbacacaadcacdbbcbcbcaddddddaaddbcadcccaddbbacdacdbadbcaaccdaaccbccdbbdcadadccbbaabcacacccbcadabcbcbdbaacacbdbbaacaaaacbccdccddaaaaaccdbbadcaacadadcaabdccccbcbbccaadbabddbdbabaabcdabdbbcacddaabcbbdacdacdcaadddcadbbcdbbcbacbcabddddbabcdcabaababdcdaabbcdbcbccdbccbdddcdcccadbdcbcabcdcccccdbacacdabcabbcabdcbbddadbdabcabcabbcddbbccdccbcdbcddbddddaadacbcabbdabadcabbbacbdbacaacaccbcdbbcccdcadbbcacbaabbddcdbddaccbabccbdacaccdabcddadbadbdccadcbbdbbdbbbdddcabddaaccadaadccdaabccdadaabbbacdbdbacbdbbbbdcbdcacddbcbbaaabaaaaabbbabcccadadbcaccbacbdcbdbcadaaddccbaacbdaaacbcaaccbacaaadddbaacdcadcdcbaaacccbdaaacbcadadccdcddabddbbbcdadbbcaacdcbcaddcacbdadbdccbdaacbcdccbacacdaddaddbaabdbdaddaaadcdccaabadbdccacdbbbdcacbbbdaccbdbddddddcbaddcdcabbcbacbddacdcbccbccbcabbdbaadabcbdcacddabdbbcbadcbcacdcbccaddbadadaddcccdcbdbbdadaacacabdbbdbaacdcbabaddbaaacadaabcdaddcabaacbacbabcbcadabbbaacdabbadbdacdabaaadbcacbcbbadabacaacdbbcbcbdadadcddbbcbdaaaccbaddcccacbadcdcccadddbcadcaaaaaccaddbacaccbbbccddbdcaddaadbdccabbddcbcaaacaaddbabccbbccaabcccadaddcbddbadcdcdbdbcbbdcabcbadcadadcabcdbcbbadcddaadaaaaacacaddaaaacbdbabacdaaadadabbabcadacaacabcddadaaaaccabdadcdcbdccccbaabacdbcdccdabaabbcaddccdbaddcdccadbdadcdbacdbcddadabbbbcacccaddcddcddacacdccacabbadcbcadaabcaacbabdccdbbcbbdaccacdcddbdacdcacdcdddcccccdbbdccdadabaccdbdcdcbcddcdcdaaadccdcbbbcbcdadbbdcdaabbacdbcbdcbdcdccabccdccbaddccaccccabcdccccddbbbabdacdccdcdbcccbbbdcbddcdabdbbbccaadcdbbdcbbddaacdaaccdbdbadcacbadcadbbaaacbbdcdbdcbcdaccddcadaddbaadbddaabadcdbbdababadddadcaadacaddbbddadabbadccbddbbcbacddcbdaadacdcdcdcbccbddadcdcbdaaadbcbdabbcabcbdbadabbbbbbbcdcdcbadbaccdcaaadbcbbdabddcbbdcbdbbbcaddddcadabbccdabaabdbabdddabbabccbddadbddacdbbcdabaadddcaacdccabccadbbadcabdbdcaacbcdacbbdcbdabbccbccdabbbcbcdbdbcacddbbdddddadbcdcdaaaadcdddccdcbcdabaccaabbcdaaddbabdbadddbdadaaaddbcaadcaabacadcbadcaccbdcdcbacabbbbcdddacddbbdbcacbbaadccdddaabdaddddcababdcaddccaaacdacaabbbbbbadbaabacadcbaaabdbbccdbcdbccbabcdcccacdbdacbdcbdbaadabddcaaddddcdacdbadacdcdcabadddbdadabddcbcbcddaaabbbcbbdaddacdabcaabadbcbacaabbdbdcbcdaccdaaccdacabbcdaaddacaabaacadbdccacadbcdbacbbcadccbbcbdacdbcabccbaacacdcddbdadcbcaddcdaabddacccbadbadabbabccdbbbbdcbbaacdbbbddbcccdccacdbdadcddcdabdaadadcbadaadbdbbcbaddbddadcdbddacbbdbcbdabdcdabcbcdbaacdcaacabacccbcbbccaaadbdaabadbaadbacbaadcbdbacdaadcdddacabcbabcaddaadbabdaccacbcbaaaabadacabccdccccdabacddbdcdcdcdbabdcddaabccccdbaccaaddaaadbcbdbcdccccacbccaacccaddadcddaccdcaadaaadbcdbcdaadbcabbbcabacaadadaadbcdbdacabdbdacbbbbaabdadddcdacbcdcaccaabcdccabbbbddcdacdabbbaabacbcdaabcbaddadccbcbabdcadadbadccaabcdcaadadbdcbdaaacdbaababcdbaacaaddddcdaacadadbcddbbdddccdcdddaabbdcbdcbacadcddcdcbbacabcabaaadddcdbcbbacbddbbbdbbaddbcababaddcbcbbdbaadacdbabdadbdddddbabccdbdbcdcbdacbacddadcaaccbdbdbdbcaaddddcabbcdbcaddbdaaacdcadbacadacacdddaabdcbacdadddcaccbbbcdccacdabdbbbbdbbbbbaccdcdcbacdcacaccbaccdcabcdaacbbcdaaccacaacaccdcbcadaadaddcbcdcbddacbdaadcbcccaacaacbaadddbccaccbababcaaddabdbcddbcdadbadcdcabdaacdcdbaaacabbdbcabdaabbacacdddbaabadcacdbadadadcaaddaaaccbacabbcdcabbbcbcdbbaaaaacbdbdcdccabcdaaaabbbdbcccabcdbcacdacbbbbccdadabddadadbacbadbcdacadcdacdadbcdbcbddccbbcacadaddaaccdcdbacaaacccbcdbcdbcddcbaabdadcccddbdccdbbcaadbdbccdbaddbabcbadaacacaabdadabaabacbbaccbbbddbadbddcabababbccdaaaddccabacadcaccbccaabaaabaccdbbbccccdaabbdabcabbbbaabcadadddbcbacabbdaddaddbdcdacbdabaaadaaddcbdabddcadaabadbbccddcadacdcadbadccaaddccacbbbdbdbcbbdbacbccdbdabbcaccadddbcbddddaadbcdcbacacaacbdbabbababacbdcbaddbdbbdadbbddbbbcbdbcbddbbadddabadcdbccbcaddbdabcbbbaddcacdbbdadabccbdcbbacbadcaaaaacbbbdadbcdcccabdcdbaacbdddbbdbbbccaacbdcadcdbcdddacdaacadabbbdaadadaaccdcbbaaacbbdabaacadcaaacbabcaaaccbaadaccacdbbabcccaabacabccadaacbcbaddbbabbaadcbccbbddcbbabaadbdaadabbdccaadadccbdadddacbbacbdbdbbadcaddadddbcdbdcbadbdbbcaabdbbaadaadabcbbcdacbcaabccbcabbabadcbccdacaacaacccabcccccdabdcdbbbcabbcbdaacadcdabcdabdbdcdcabaadbacdadacbbcdadcbcadaccccddabdddbcadccaaabbbaccbcbbbdcbccbbacbccbccadacabbcabccccabddcacdcdbcbcacdcdcdbdbaaabdbbbaccbabbbadcbaccaacbadaadbaababcbcacddcbaddbbbacbbabdcdddcbaccdababccaaadaaadadbdcadddbbdabcabdddcbcbdabcbbcdbcddccabaddddddcbaddbbadcbbdcaacddabadbdddabcaaaaabdcdabaabdbdccbcadacddbddbaacddcacadacccabaddcabbadabaddbcbbcdaaadbcbdabbcdaddcdbdbacacbabacaadccddaaacdbcdaadcbbccccacdcddcbddacdcbacbbaaccacdbabdbbaabcbacdbbdadbbcddaabdcdabdcbcddccaabbbdccdabaadcbbccaadcaaddbabdadacddbabbdabdbdcbcaddabbbbcddbabcddabccbaccbababdccadaacdabdaadcdadbbbcbadbccddaacacbaaabbaadbadbabcbbccaccaaaadbddcbcbdaaabaccdcaaadcdaccdbccaaaabddaabadacaccbddbcdadbbddaaacabdcddaacddabcaabdaaddbddccbbbbdcbbcaabbcabbadcaacacdaabaaaaaddadcacdddadbdcabaadcbccccaaddaaaacacbbabcccaacbbcaabbcbbaddbadcdcabbabbadcbbccabcacddcbaaddcccbbcabcbbccdbbacbdaadcddbbacadcddbadccbadaaabdbcabdbcabddccaccbbcbcbdcaccbdbbaaaabccbaacdbcaacdabacbcaddaccddacdddbdddabadcbcadcadcbacadaabdcdadaaadcbcdbbdacabbbcbbdaaddabdaabdbcbcddbdbcbaaadddbaddbdbddabbabaadddadddcaaabadaababaadabaaacbddbacacadaaaadcdddddbabababddacbcbbdaccabcbabdbbdabaadccabacdbacdbbbadcdbbaaababacaddbdabdbcaccddabcbbcdacbcbdaddabcddaacaaacadacabcbadbacabbdaaacbcadbddbbbaaccccadccabdbacaabccbadddbabccbddcbbddcaadcbacccccdadbdbaddbadcdcabadcdcababaaddabcdaddcaadcbdaddaddadadabbcdbadccbcbabbcdbcccddcaaccaacbaadbacacaaaaadabbabdaaabbdbccaadaddccdbabcadadbcbacdcdcbaaadbbbdbbdabbabdbbcbddccddcacabacddcadbcdcabddbbacbabccbacadabdddaddbadbbcbbdadacdbbaabccdabcbcdbbbddbbbcabdcacabadcaaadbacadbdccbbadddbdacbbdcdcddadbadabacdbacdbbcccbbdacccbcabbcbbcbaaadcdcaddcdcbadbaabcbbbacaaaacdbccdccbbdbbdbccbadacddbdcaddcddbddbbbbdccdcbcdbaabcddbaccccdaabcbddaddcbbcccacbcdadbdbdabcbddcdcbbcadcabdabdbacbccbcaadbdccbdcdbaaabcbcbccaacbdbcadbcadbcbcbcaccaaddbcbdbbccadcacaabddbadadaadcacdbdcbddbbcddbabaccdcbdcbbadcbddccbabcbbcadbddbbddddcbaccaddacbaabcbcabcdabcaaabcaacbddbabacbcccdbbbdaaadbdaaccccdbbbacacbabaabcaccdbbcacdaacbbdbadcdababbcbbcacccdcbccbccbcbcaadadddccccbaadaaabcbdddcdbaaddcbbaaddadbcbcabacbabdaabcdbdccbccaaadadcdaaabcdbddacdddbdbacddcbaadbdcabcaabaadaacdddcbbdddcbbabccbaadaadbcbadaadbddabcccdccadddcbcabaddcdcbcbccccdbbdccadcdcdabbdcdcabaabddadcaadacadccbbdddbdcbccaaddbbbbbccdddbbbaabaddcadbdadababbdacbbbcabaddcbdddabddaadcacccabbdbbcaddcaadddcddbcaadcdccdbbabbcbaabdbbdbaaccbbdcdacdbadbdbabbddbabbdacdaaabddcbcaabdacbccaaacabcabbdabddccbccaadadbcbbcdadadcdacdbcadadcbaabdcccdacadcbbdcabcdadcbdbcaccabdbbccadbbacbaccddabcabadbbddddbaadbaddadbccddbacddddaaacbdbbbccbbdcacbbbbadcbddcabcaabdbbbdadcbbaacbabcbdcbacaaddbabcacbbacdaddcddbaaaacaddacbabbbdbccdcdbaccbcbdaddcbabcaccadaaabcbaaddabbccaadbaaabcdccbadddddbcdadbccdcabcdabcdddddcdcdacdcacdadcdbcbabbdccddcbbddcbabccbabcbbcbacbabbcddddabbdabdbccaadaddcdcdaacbabbbadbcabbcccbaddcbcbbcbcabbbdabcdbdccbabcaccabbddccaddccdbbbdabcbbccacdadbababbbdbbcdbdbabbbacadbbcaabbaabddacabccbadaabcbdccdbcaadadaaaaaccbadddaaacbdbcdabadaacdccdcaaddccddaadddcddbaccdaaacaadcdddbcdccbaddababcdbddbcdcbaddaddcdbaacbbdacdaadddbcaccbacacdccbdbccaabddcaabcaaabdcdadacddbadcddbbcdaabdcddbcdbbbbbbadcacaddabacdadbbabaabbcdadbdbcccdcdddcabcccdadaaabcccbcacdaaadcbbacdbaddbdbdbbaaaacddadbddadcaaddcbbbcbcbaadcbadcdcddcccabcddcaccccabbcdbabdcacbcccbbdddcbacccbccadadbcabcbcacadaccdbbdbbccbdaacdcbaabadbbadcacbaaaaadacbabcddaddacbbadcabdacbcaabacbdbdcdadccdabcbabdbdbaaacdbdddbdbdacbdadcddadbbbaabcdbcbcbcccccabdbdabcadcbcdcbacbacdcbdbddaabcabddbbaaadbdbdccddddbbbccbdbdcadaacbacbadaadddabdddccaacddbaaccdacccadbddcbcaccaadcadbcbcaadbbdbaaccbcdbcdabdaadaababbcacacbddbbaccaaabcbaacdbaaddbcdccabcdadaadabccaccdcdaacabbddaabdbbabbcabbbcdbdabadccdcadbcbbbbdcdcbbbaccbdccacabbdddbbddccabbcaacbdbbabdabcddacdabdbbdccdddddababaddbcdabadcccbcacdbadbdababbccadccaadbabdbcacadbacddcaadcdabbcdabdccddabcdcbcaaadaccbbabaddccababcdcaacccbabcadcacdabaadacacaabccaadabacbabbdbdadbcaaaacdbdacccbddabaabdbcdbbbabaadaabcbacabcdadcabcdbacbbddbbcccddbbccbabdddcccdabcaaaddddbabadabcbccbacdbddbddaccbbcccaabdcbbbccaaaacaacdcdddcabacbbbdcbbadcdbacbbbdcadabbbbbbdccdaacdaabcdccabadadcabbcbdacdaccbbdddcdbccdccaacaabbbbaaaadaddbddbbdbbddbcbbbcbbbbcbccddcaaabdcaabbdcaadccaadddcaacdcbbcbbbdbcacdcbccdbabbbdcdbbacaadaacdcbabddddbcacbcaaadddbcbaaacabdabbcaacdbdbaddaccbdddbbccaabaadcbcabcababacbdddbbabbddbccccbbcdddaacaaadabacbaabacbbacddcaccdacbdabacccbcacbdbcddbddcbaacabacdcbdbadcaaddbbdcccbcdcbcbaaabaacdaadcdcdbdbddccaccbbcbcdddcadabcacbcdddddccacbadbbdabccdadcdabdbccaddbcbdccadacdbcacbcdcddbcdbcddcddbaaacbdabbaadbaaaaccdbdcddcacadcbdddabadcbbaaaabbdbbcbadadaadaddacbcddacbaaddbdadbbbadaddbaadbbddaacacabdababacbadcabaaadddbcaaacababdbddbdccbacccbcdabdcddbaacccccbacbcadbdacaadaccdaabcddaddacddadbcccddabbdbdadccddbbddbcdcabdabbbbddabdcdaaaabadaacbbbdbbbaccdddcdacbbdccbbaccdcaddcaacdaccdbbddadbbdbbbbdddddacdacacbcbcabbdacaddccbcbddcdcaccaabbbadbabdddddaddcadcdcdaaabaacabaccddcdddbdccdcccccadbbbaccabcbcdadcdcbadabcdadadddacdacddaadcaabbbcaccbadbaaccdbcdabcbbdabbccdccbbcadcaccbdbadddbaddccbbdbbddadbdddadadbbbaadbdddcdadbadacdccdadbdcacabaddbcadaaddcdacccacaddbdbabbddabbadbbaadddbbaadccccacabbbcbabacbdccbdcbcbcbcbddbabccbaccacaacababddddbbdabcdcddbcdbabbabccaaaccddbcdacdcbdbdacccddbbbdbbdcacddcccacddcddcbdbadaabdbdbcbbcbcaabcbdcdcbddbbbaaaadbccaacbdddcccbbacaabdabbabdbacacdbbcaadbaabcaacbcddcccdbaadbdbbdbbbbaccbcadabbcdadbbbdaccdcbdcbbcaabdcdddaabcdaacbbcaacbbbaacbcbacbdbcddaaddbcccdbdacdcacbdaadadddbdcbbbaaadbaabcaadcadcdacbcbcdbdaaccdaaabcadaacabcdbbdbcaadcbccdcdbccbbdbaacdacccdcccdcabacdadacaaabbabccacdddcddadaaaaacbdaaddadbdbdbdbcbcaabbabbdbbadabacadaddcdcbbabccbddcaadccadccdadddcbdabcaaadcccbabadbbbdcadbdcdbbdddaaaacccdaaacbcbabdcdaddbcddcdacacdabacbddbdaddcccbbdbacbcadcbcdadcaaaccbdcbddacabcbbbaaaaddcabacdbabcddacabbbcabadddabbabccdabadbcaaacccaccadddbbcdabaaaadabdbdadacbcaaccdccdacdababdcdcccbbdaadcdbacdbbdbbdcdaabbabbbdaabadbcddcacaaccdbdbaabadcbbdbacaacddbcbcdaaacbaadcbbaadaacdbcbcddccdabcccbdcdaccbcadbcabcbdbaaccaabbbbbccaadaddcbbacccbbabddccaaadabdbdcabbcaadadbadcadccbcccabdaadcddbdccbcbabbadbcbdbcadaccdccabbddcacdabbbbcdaaaabdbbccaacccbbaaacabbcabaacccabbdbbccadbdbbbdddacbcbaddabaaacdcaccdbbdcadcddbcbccdbccbcadcacbddbaababdddcbadacacbdbaacbbaabdcddcccdbbdaacacabaccbddbbbadacbbdccbbbccbdbcdabbabcccbddadbaddcaabcabdaaccbaadbbcbbcddababbaaddcbcdbccdadbdccbccbbbdaabbbdbabcadaacbaadadadaaaacbacacbaacdcddbaadbbacbccdcccbbdbaadbdddabccccaaccacbbccabbacbddbcbcaddaaabddcbccbbcccbbbcdaabbaccdadcdcadaabadbaccccbbdbbdbdcadccddadbbaaddaddaccabdabaabbcbdcabdccdccdbbaabbcddbadbbdcbcabacaccddbbdbabbcacabdbcacbcccddbccabbcbadaaddbbbdaaaacbccbdbbdbaabddbbcaaddcaacaacddadcacbddaccbbaddadcabddaccaccbcbccdabbddbaaadcdbbaccbcddbcbaabbabdbadaccbcaddbcdcacadcbcdadbadabcaaabaddaabbacdddbbbccddcccaaacdaacddccdddadddbcdcbabacddcdcdccdccbbadddaadbcbbadaacddddddccdbbbccdcdbcacabcadacdbbbadcdcbbbbadacacbabbaaadbbbadcbbaaacdbaaadbaaabccbdadbbdbbdaddadaddbccaddabaddbbcaaccabadccbacbdbdcbadcddadabbddadabacacaacbdaadbcabdbcadbcaaddcadbdcbdcddabcbdcaccccbcaadccdcbdddbdabbdcccabdcbcabcdbcadbbddabaddbcaadadbdbaabcdcabbbbdbbdbbbbbadadabccdbdbaddcbcdbdcccabdaddcbbccacaacdbcdcdcdcccdcbcddbbdcdadddcaaaabdbbcdbaccdcabdbdbddbcddccbdabcaadacdadccbbabababdcbaacbddacbddacadbddbdddcdacbdadabdddcaabdbdccdbaaddcbdadbbabbbababcadcaaabcabbaaacabbcaabcabadabbdbdcdabaabbbccdabadbbacadbacbdbabcbadcdadccdbccabcbdcbdbcbddaccaacaaddbaadbcbadcbcabacdcbbcaadaaccadaabdaccaaccacdcbbdbbbaacdbcadabbbccbddbbcbcccccdbabbcbbaacbabbbcdcadcbdadacaabcccbacbcadcaaacdcbbdccdcaccdbbadbccbabcaaabacaadbcccaddaabdaacbddacbbdabbaacdbdcddbbdcccbdddabcabbbbbcdcabccdabacccbbcbaccccbaddabbabbaacabdcaabacbcbbccdacaacadbdacabcdcdadbbccbdbccadbcbbcddabccddcbbacccbddcadacddaabcdaaccdbbcbcadcdccbdbdbdcdababaaddccddbcccdcdabdbbbadbdbdaabacdbdcdbabbbbbdadbadaacbccdccdcdadbdbbcadbcdacaddbaaccabbdcdadcdbbdbcdacddcdcbddaccbbbbddddabccadcbcdbcddddccbcdcdabaddbbbcdcccaddabbcdaaabccdbbbaaaccbbbbcabdadaadaacdaababaadcbabcbbbadcabbdcbbabdbacbcbabcbccaadddabdddabcbddddcadbacabdaabccbabaacbddccabbbbacbcaaadadcbddddbbcbbddacbddbdaaddddcadccaaaaacbabddcacaccabcbddddcacdcbdbccdbadcdadddbdccadacacddaacbcbddbabcacadcaddbdaccbccaaaabddddaabddbddbbcbabaacbdcabdbcabccadaccdbabdabaaaadabaabbacabaaccbbcabccbabddaabadddcddbccccccabdbccadbddcabdddabcbadabdaacabadcbcbadbbcbbbabddbccdddaaddabddbdbdcddcdaaadaaadcabcccdacbaadddcbaaadcddbcdababcddccadbcdbcdaddadacdcaacdccadbcddbbcdcdbcbacbcdabbbcccbacbbccabdabdcbccaacccccdcbbcddaaabcdabbcdcdabccbdcacdabdbdbdbddbdcdbcaccbbcdbcaccadbbabdcddbbbdbddaddccbdcccbcbaaddcaaaabcdacbccdcbcadabaaacaccabaacbacdbbdbdcaaaccabbbddabcbdbababacbddaddbcdddabcabdaddadadabdccdcbbcaacadabddadabccbdcdacaacbbbadcbdcbacdaaaadbcccacdaabdcacbabcccbbaaaacbacdbacbbacdcbbdadabddcdcdbbddbdacbbbdadbabadcdbcaccbddaddcadbdbbdddccccacccdcabdbbbbcbaaccbbbbcdadadbadabbcbdbbdbabdabccdbcdadbacccccdaddaabcabdddbaadcdcabcdbadbcccbddbbddbccbabdacccbabbbabbcccbdcacbbcbadbcbcbcadbddacacccbadbadddaabdacaccbadccdacbcbdbaacbcaabcaaabdabccdaaaaacacbccabaacbbdbaaccadcbabcbccddccabbdccdbacbacadaadbccadbaaabacbcadadacdbbbacadbabcbdcbbdacdacbccccdbabdccdacbabdcddbbdbdccdcadabcacbdacccacdcdaadaadcbbdbcccdaddadbbacdbcbbcababadaabccdbbcddaccdaccdbbdbbcaaddbbcbdcaccbbcdccaabcabbaacbcbcabcbcadbaabcbdaccbdcddaacdadbccdcaaddbccddabcacbdddcddaaddacbadcadadaadcdadbdcbcabdaadcddbdcdbdcbdbdaaabbcbaddadbdabaaccbbcdacadbbdbcadcaddadbbacaaadccaabaccccaacacdabdbdbdabaaaddcaadacdbdcddbadbddccacdcaaaabcbacdbdbcabadcdaddddcccbaccddbbdbdbcdcaddadddbdccbddbccbdcdddaabbdbadddccadaacabbcdcbddbccbcbadaadbccdadbdaacbbaabadcdcccddbbbcbbbdbccadcbdadbbbbddabbbcdcbcdbcddacddaabdadbbcabadadddbbcbaccdabaaddaabcbadbdcacbddbdacbbcdddcbdbdbcdcdbbcaddccdccdcdcdacbbbdccdcccadacbabacacaaaacdabcdabbcccdcddcbbcbdaaaadabadcaccbcccdbaaadaddbbdccdcbaaaaacdaaacccabcbddbaaccdbbdddcbddadbbddddcccbddabbbdcadcabcbcbdaabdccbbddababacccbbcccaccccddddacbdaaacccbcdadacadacabbcaccabdacbacaddbabbacabcbddcacccdaacbcababdcddcbccbbccddddcccbabccddbbabaacbddbcdadaabbacadddcbbadaabbddaaabdddadabcdbcdbdaadaddbddcaabadacadbcccacadaabccccabcabbdcaddddcbcaacadbcabddccbdbbadcbbdacbadbbcccbcacbbaaddacccbacaabbcbbccdaddabacadcbcccbdcccdabccbabbabbccabbddbaaaaabbcccbbabccccdaaccbddddcccdccadcbcbddabdadbccabcddddddccdacdabcdbbbacabbaaaaddabacdacdaddccdaddcacdbbdbdaacaccbbdadadbccadccccadccbbcdddbcdddbaacdabddadabcdbcccdcbacdbaabbcaccdbcabddaaacbbaddbdbcababdccabdacaccdababaccbbcdacbcabccaaacdcbdadccbdbdaddcaaaddcadadcaddddaccabccbcbbcacdadddcabcdbabbabddcccacbccadcdbdaaaccdaadbcbaaddacdbdcbabdccababbabcccaccbdbbdbbdddcddbbaabbbabdbcabdabbabcacacbcdcaadacabbbbddbcdacbbcbbbcaacadcddcbaadadbbacdadcbbbbdcadcccddadaadadaccabddaaabdcdacdcbdcbbdacdadbcabbdbacadaaaccdccdbdacaabbccdaddadbaaacbcccbcbbdacaccadbadacdcaadccaccaccaddacaddccadccbdcbaaaacbbdabdaacddaddbcabccacabadbaccabbbddcbdaacdbadcccbdddddbdcaddbbbbbcbbdcddbcacaacbcdbbbbacaadbbcddbbacbccbcbbdacbacabaaccdacacddbadbcddadacaaadbbacddbbcacccabbcbdbabcaddacbabbbdacadbdccdccaacdbacadbddbbccacabcabddcabcdaaaadabcacddcdcbbaaacbbaddcabcabbbdcbdccbdaacddcbbdbcbcdbdbddbcbbabbddadabbcbddcadbdccbccdcbddaabcabcacbcbdbcbbbbcacdbaabacadccaaabaadcbddabcdccbaacdabddbbaacccbdcdbdbcadddbbaabbaaddacdcdaadaaacbccbccddacabbaddcbbbddddcdacacdbbdbdcacbbaabdcdcdcccacdadcdccdcacdcbaddccbbdacccbbdbadabaddccadbacadcababcaacbcabcbdcddccaaccddaddcbcacdddbcbcbcacbcdbbcadacdbcbaaccdcaadacdadbaddcdddcaddcdbadbbbdbbaccddacaddcddcbacbdbddadcadbbbdaaacbdbdddbabcdbdcdbadaabbcacbaabadddcdcbaadcbabdcddcddcdcbdccdcadadccccdddacbcbadddacbaadadcbddbdddbdacdcaabcdbdcabdddcddaadcaabdcabacabdddbcdaadcbabbadaaadccaacbbdcdabbbacbacccccbdaabcabdcccdadddbbdbabbcccbcdaadbabaabbccbcbabcdadcdabaabdcbacccacdcbdcadadcdbaddcdbaaacbdcbcddddacbcabadababcabbbcaccabcbbddcdaadbdbcacdddcacabdbbadbbacadbdccabacbccbddcdaaacbccbdaccacabaadcdaaabccbddbabccdcdddddbadabccbbaadddabccabdbbbcadcdcccaacccacacbbbaaabacdaabcddcacddcbcbbbdbadcacdcaacabcdddcdcaacaadcadcdabbccccacddaddabbddaaccacbaaacaccacdcdbdababacacbcbbcaccdcdbdccbbddacdbacacbbbbdbabcbcbcdbcdccccbdaadbdcbccabdaddbaddbdbbdaacbbbdabdccdabbcddcdbdcdbcccdcccbbaaaadadadccbcbbabcbbbcddaacabbdcbaabdaaddadbbcbbbcdbdbbccbacddddaccaddcbabacaaacbddbbbabbabdcbbabaadabcadadcdddabcadcbbdddbbcabddcabdbddcbcdcdadaaadbddbccaacabbbaadcbdcdcadcdcdccccbdacaadaaddbdccaccabdbbcaddbaabbbdcaaddbbdcbcabdbabbddccbccdbcbbbacacadacccbbdbbdadbdbcaddcccddbcbdaddabbbacdbcbadbabbcaaabdcabbcbbbcccdcbccbcdbbbbacccadbadbddbdccaacdaccbacbcccacccaddcbbaacacacbabcdddbbabccbdaddcbbbaacbaddcbdcccbbbcdbddcbacdcdbacadbadabbbbbbcdcadbbacccccabbddacbaaabcabbcbdcbaabdccbadcadcdcdacddaabdbdadacaddddbbdaabcdabdabcbdcadaaadbbcbbdaaccabcaadcacbdabdaacaacabbbdabddbaccbcbddabdbcbacbbddaabdcbcbbbdaccaccdcdbadbdbcbcabbcacbdddcdaccabadabcddbbabdddbccadccacaacddbacababcdaadadcbbdcbbbaabdcbbbcdcbcdcdcbacbaddadcdcacccdbbadacbcddddbcabcbdcaabbccbccbcaaadcacabdcbdbbbacbbadabbdbccbcaaabbddbadbcacadbbacccbbccdacddbbababbbbaabbcadcbccadaadbaadbdcbcdabbaccaadaaddddcdcccdbcbcdcdbdbdcaaadabbbbcbcabcadaabaacdaccccdbcdcadddcabcdbcbcaaccccdcddbbdcabccaaadcbccbbddadbabacbbcccddcbaacdacddaaaacacacdcaddcdaddabaaddacdcbdbbaddcaacccdbbbcbaabadbbaabcaaadddadccbcbbdaabdbdcccdcdddbabcbaccabbbcbabcacdbbcabcccbddadbccbbacaabccaabbcdbbbbdddcccdabbabbbbadabbbccadbacdddacbdccbbcdbbabbadcbababdddaadaaacdcadabadcabbdddbaaabaccacaadbbdbcadaadadabcdbddaadccdabbacaaabbcbbadaacddcbacacbddbabbdbbbdbdcbbdcbdbdccbabddbbccaabaddccbaddcadcadddbaadcabddaccccccababbbddbdbbbdcaabddcdaaccbbbccdcbbcaabadaaadadcdcccaabdddadcdabbaaccbcababbcabcddadcaaabdbbbdaddadbabddddbcacdcccabadaacccdaabdaddacaccdcbbddadbcaadbaabdbbcabcdadacccdcddcbacdaabbdcddadcabcdbdacbdbbcadcddddacddbbcddccadbdcadbbddbcbbdacbadbdccccacbdcadcdcdaacabaaacdcabdcacbacaaaaaadbabdcbddcbcbaaaadcbcadddaddabcdcdcdddbcbdcccaccdccadabacbbacaacdadaaaacccbbdaacbbdacbdbcdabcdabdaacbabbbadbcdaabadcbcaadcdcaababbabadcaccabacdaacaddacbccbcbdcdccbcaabddddabcbdaccdaaadbccabadbabcbbccadcabbdabcbdbadbbbacdadacbbbbddddbaabaacddadadcccdbcabbdaaadaabdadcabbbbbccdcbaacbadadcbabadbbcdcbacddcaadccbbbadddcdddabcccddddadabbbdcaccadccabbcbabdccacddcbbcacddcbbbbddcbbcddddddbdccadcccdbccadaadaddabdbadcbcdcdddadcacdddaacbaacabddadadadbacdacbcbcabadaadbbaaacaaaabdbddbbdddbcaaddbbcacacadbcaacdaadaaaababcdaddabacbcdbccbdaabcbadabdabadbcdbaaccbcacbdbaaaabbabcddcbaccbddabdcdbdbbbaddbcccaacddabdcbcbbdbacdbcdbdcdadbbcadabaacccccbccddacacabbbccaadbbaddbbbcacccadabdbaabadadbbdbacdddcbacdadbabbccdabcabdcadabccdcbdbbcccaaadabadaacccadbbaddbdcabadbaadbacdbcabacddbcacbbcbbadbbbaccbcdadbcaadcccabcdbacbcdbbabbacbddbcaddadddcabddcbdcdcacaddcdddcabbcbccaacabadbabaacbcddccbbbaaddbadabbbdddccaddbcccadccadabcbdddccabdbddaadcacadbacdbadcbdcbdaabbbcacdbabbbdbacbadccabaddbbdbadaaadbbacadacabcbbcdabadbdcbcccacdadbddbadbcdbccacdbbcbadbcbaacbdadbcaabadbbddbbdcccabbaacbddddabcaaadbbcbabaaadadcaaccacddaddadaabacadccdbbdddcaccbacdcbdbadcdddbbdadcdacdccbdbaacaaadcddcbacdbadaadcacbacbbddddaaaaaddaddbadbcccbcbbbaddcdadaaadaccdbabdddbcddccccbcbddbdcbbabbddcdadcaaabcdabddcbbdcbcaddbbddaccbadbdcbcadcdcdabdcabbdcbcdaaadcadccccddaabdbabbddcadcbcbccddacdacdbdbbccdbcababccdcabcaaacbadbddbaaabdddacdbbdcacbbabbcbbdaccbbbcdccbabcdcbbddadcabbdabcdcabcdcaababbcdccdddddbadaaccabbdbbaaadbcdcdbcaccabbadababdbddcbbbcdbddadcaddbbbdadcccacdbbbcdccabdbcbaaaddbdbbdaaddacaabdaaacaacadcadddcdddaddaacdcccbdacdbadcacaacbbbccdcabccbdcabdaadacdbddadbadcdddcbdccbabcaababbcdabbcadadcaadddddddacbabbbccdbbabdcbabaabcbacacdadabccabacaddbaaacbddcdcaadbbcadbabacbdaccbdacadbbdbaddadbcbdbbdaaabdccdddbbaadccdcdcbdabccacddbdbdbcbdcbadbabdcccadacabcccbdacbcaccaaaccabbccaabdbddaccadcabcdcbaacaabbdbabdabcbaabbabcbdaddbcddbccddddbcabbdbaaabbabccaacacaddbabddbadcbadcdddabaadbbdcacadccabbcabcabdcadabaccbbacbbbadcacbadbccbadbbdadadabbdabbdcbdcadddccccccbccddccadcaacccbddbbacbbaaadadddaacddbccdbdbcdaacadadbcbaabbccacdcbadaddaacccddaacaadadcdbabaabdabaabbcbbabbdaadddcacadcbaabcaadddabddbdbcdcddbaccbbacabbadbbadcadacdabbbcabacdcdaccdcacbbccbbddbcacbbdcabcbcdadacdcdbcabcabdacabccdcaaccabadabcacaacaabbdaddcadcdabaaaacbadadcddaddcddcaabcacccbcdbdcbdadddcddbcbccccbbcdaddadabdbcbdccacbccadaaadabcddbadabababacdcdcbdddaddcdbbbbaccbdcbabbdcabbaddbadaccdccbcddbbbcccdcbaaacaacadbaddbabcabdaddcbdddbcccddccaaddbddadcadadbbbaddbdddbadbaacccdbcadcbabbdddacaaaccbbbbccddbdbbcaadacdcdcdbccbdacacabbbdaabcbcdddddcacbcdaccadddaadacdbcaaababdbcbdbbbdabdbcdbbaabcbcbcdddbcdcddbccbbcbabcbcdabdbddbcbacbadcdbdacddcbaaabddcdaabcdaabacabdbdccbbdbcbccadcdbbdbaadbdacbaccbaddcdbbcbbddcaaddbabdbccbbcdbadbcbaacbabcacadabdcaacdbddbacbbaacbcbabbbbcbcadddadcbcdaadacabdcbdaaccbcaacbbbdcbddacaabdaccdacabdaacdbcbccddcdcbdbddccdbcdaacdcbbdcaabdccccdbccdbddcccaaddcbcdcbcbbbbcaccacdcdcbabadddccbcadacbaaddbacaabcacabbcddbdcbbadbbabbccbbbdabdcadccdcadaddddcbcbdbdabdcdbccdcbcccadcbdaabdaccbbbbaddbdbaabaaabaaddcddaabacddabcadbcabaaddcdbcadddaacbbcbccccdabacbdcbbcddcddcabbbbacdacdbcadabaadcbbaccbbadaaacdddddaaaacddbdcaadabdbbaacaacacdaccbabcccbabaccaacddbaaadaccbbcccadabbbcdccdabbbdbbcddbddcdccadcdcbaaadbcdbbcabcdcccdabbbdbbddbcabacabdcddbbbdcccdabadacabbdcaabdbdbddddcdccaaabdaddabbabcddadbaccdcddcdcbdcaacdbbcacddcbaccdaabccacabdcbdcdaabcbdadbbbdbaccbbcbddadabdccadadbdbcbdbbaccaabbaccabcddababaddcadbccdbbaddcaadaadabdcaadacbbabacbccbbadaddadbcaabcaadddddcabdcaaacbaccaabdbcdacacbbbcdcbcdbdbccbccddbcdccbbaabbbcdadacabadbbbbaddabbabcbcdbbbcaacbaadbabccabdddacbddcdaddbdbbadddbbbdacbcccaaccbbcaddccacdbdddbadddadcaddadccbbcbaacdbddacbdadcdcbcdacacddccaacabdcacbdbbabcdbbcccadbabbbbabbbdbcbcdccacbccbbaabcabcdbacbabbcdadcdacacddcdabaacdaacadddcbadaccddbdbdaaddccacdbcbadcaabadcbcbbbbbcbacbaadbcaadbddacdcacacdabadabcabddadacddcaddcdabddcccdbbcbcbdaccaddccbdbabccdbaccccccccbcdcdbadcaccddcdabcaaddcdcadcdbaadccddcacdddbabcbaadcabcbabdbadacbcdcacaadccaabbdbbccadcbdbbbbabadbdabcbcddaddbabcbdaaabacdacaccacccdabbbccbcaaccdaccaaccdbccdbccabdabccdccbbcbbbadbacdcbddcbaabdbaaccbcbddbaabcaaabbbcdacbcaadadccccbcdbbacbdbdddadaddbbcbabaadacadddadbcbbaaacdacccbdccdcbacadbcaccabbbadccdbbaacabccdbbbdcbcdccbcbadacdcddccadabcbdcdbdccbabbbcabadbbabbbdbdadddaadaccbdbbbabdacddaaddbbbcadcbccbabcbddcdcacababcdbccdbababacbdddcaabdbccbddcacccabcdcabcacddcacaabbdacbaaaccbcbbcdbdabadacbcacbadccdddbcabaaacdaabdcbbdadbdabcbccdbabbcdbaaacdcdcddbdaabaacaccaabadcbbcdddabbaaababbdcbbcbabccacddddacdacdabbdbdabcbcbaacbacbbabddadbaaaacdbddababddbbcadddbadadaccbddcbacbddcbbcdbcaccaccddcaccbcbdbcbacaaababcaaddadadbbbbdccdcbdddddcbadcbadcbcddbbbdbababbbbbdcdbababdddcabacdbbbbdbcaacbaaadaaaccbdbaacbadadbdcbcadabdadbbcdcbccdbbddcabbdadabbbcbcdaddcacdbccadcaddcdcbbbbaadcaadbcbbadccdaddaaccddabbccdddbbaadcccadccbcdbddddbaabcaccadacadddccbcbacdacabdcccbcaabbdddaaaaccbccbddadbccacccbadacaaabdadcbcdcaddbbbccabbcaacaccddacadcbacacbcdcccdcabdbabccaababccadbbcbddccbddccdaddcdcdacacbbadcaabbbbdcaabdcbadaddcabcadaacddccbacacccadddcdcdabbaddcdbccabbcbcbbaabcbbadbdbabdacbbbddcdccbbcadbadacdbbacccccbbcbaaaddcbdbccacddacbbdccdbdadcbaaaabcbacacadbbacddacadcdddbcbabadcdcdaaccaadccdbcccdbaacaaccaccbbabcbdacacacdbdaacabbcdbcbdbaadadcbcccdbdcdaaaacacbbccbccddbbdadbbaabddcbccddbdadcacbcddcccdccadacbbacbaabcbccadbbcdadacbcbaabaadcdddbaadcabdccbcbdbaccabcbbcbbacbcbaddccbbaadbdabacccbaabcccaabcbdabbcdabacbbcbccccaacbbaaddddbdcadcaadcddbbbcdaddccdbcdbcbbdccadacaaccbcbadbbddaacdddcbccdadcbccbdaabdbcbdabbdccdbcddaaabcdaddbcbcaabaadcdacdddacbcabadaacdaadddcbbccbdbadaabbbdddbccbbcbddcbabbbbbccbcdddbaacdaacbcaabbcbdcbdbbbaabacaacaabcdbababbbbdaccddaacabcddcaddcdbccbacbcadaacbbbababbbdababdcdadbdbdbababaaadadbaadbcaccdcdaadbacadaaacbddaccbcacdbbdadbcaacbaabcbcddddbcaacabbbdabaadcdbbaabadcdcdccabbcaaddabadbdccaaadccaccbdcaadbdcdacbbdaaadaddaaadcbbaadcdcbacddacbabbddbcacbcbdcbcaccdacaacaacbcadacccabcbbbccbcaadcacaccdbcdbaadcbbacaccacbabbccbcaacadbacacbdcdadbababacaabccaaadbabccbccbbddccbdbacdadaabddbbdcbcdbccabbbcbddacbbccbcadddbabbdcdbbdababacddbdbbbcbccbdbcabdbbdcbcaccdddbbaddbcaaccabaaddbaddabdcaabdaddadddbcadadcaacdbbdadbacacddabdbabdaabcabcccccaaaacbbcacbbdaabdcaccddbadacacbacdaadbbdcdddcadadbdababaadadcdcacbcadbccdabbbbbcbacadcabbdcdbcabddddadabcdddbbbcaddcddbddccadcacdddacbaacbcadbcbcabdbdabdabadabccbadcdcdbcabadccbddbdaccdcddcaaadccacdbcdcaaddbacabaacbbadcadbdcbdaaddbbdaacadaabdcbdbabbadaabdbaacaacacdabdbcdcabdbcadacdbaaaaaccddcabadadacdbbbcadabdccadaaccdbbddbddaccbdabbdddacbcdccdcbacdccabcabacdadaaccaddbccdddcbcdbabacddbbdcaaddcacbdbaccbcbcbabcbbccabcddbbbcddadabcaabcdabccdbdcabacbbdacddbbdcccdbacaabcdcbaadbbdcbbccdcbdaabbcacdabddacbbbbcaddbacbdacbcccabbdcabbabacabdadccdcaadddcaaadaabadabdccbacaacaaacbacddcdcaacbdacbbbacccabaaabdcdcbcacadbbcabdabcddadabccaadddadabbbcacccbcccdcddcdbbdbdddabddaccbdbbdadccdaabccdaadcabccbbbabadacccadaadbbcabdaaccdaabacdbccbdabccdcccbcdadcabbacacccabbbccbdadbaabdbbbadbddddabcdcaadbdaccddbdaccbacdbaababdaccbbddccbcbcbbdcadcacbacaadacbbdbdaddbcdcbdbbdabdaadbdcadcacaabbcddacabcbbbcdaabacabcabbdccaadcdbcdccacadbcadbdcdbcbdacaaccddcddaddbbcdbbbbbcabaccdadbbdbcadabbbaadaadddcbbccaccaaddbdddaccadbddadbacadaddddcbdababacbbdccabaccadcbccdaddbccbacdbacdcabacbccbbcbcaaaccbabadaddccddaddadcdacdadcadacacdaabaacccbdacdbdbcaadbbdccddaacacabdcabbdddadcccdccbababaacddbabadcaadcdccabcaddbaadcacbaaadcbcaccbcdcbddcdcdcdbcabbdcaddccdddbbddcbdddbbcbbcbcccababdaacbdcdababdbcaabbcacbcaccdbcbdabcdbcabccccbbbadddcaabbacbbcddcbdaddaccbcadbdacdacdccddbbdbcbbdcacddacddbcaadbcdacbdaddbcaabaabacddcbabbdcacacbdabdacbbcaaddbacaadbdbdcbbbbcaacabdcdaddabdaabcacbbcbabcbaadbdcdccccabacdcadadaddaabccdbbbdcbcdcbbccabbddcadcadbbcadbdacacdcccaaccbdcaccaadcbcbbaaaaaddccdcaaadadaccabacbccdcbabcdabaabacbbcdddbdbccddbcdadcbbcbbcabbbbcbacbccbdacddbbcacbcbaaadbdccaddaabdcbdcbbbadaacbaacddcbcbdbadadabcbdbcaddcdadacddccacbbaabdddcadcbbabccddbacbcccbdcbbbbddbbdabaddaacaacbabdadddcbddaabbaccadbbbdaadaccadcddbdccdadcabacbaacabdaacdcbaacaaabaadbdcabbdabbbaccabababddddcbcdbadbbdddcaddbdaccdadaacacadbabbdcbbacdbacbaabbabcbddacdcacacccacadbaccccadbddcadbdaadbdabbdcbcbdbbabaacdccdadcddddccaccbccdbcdadababbcabcaaabbccdbddbbabbcbadcbaccdcbccccadcaadaadbaccbbcbbadcbcbdcaadcdabdadcdbcadbcdabcdbcccaadcddbbdbbbaccabbcbcdaabacaaadbacbbbababcadbdbccdbbadaabaddbddbdddcddbdcaacdbaadbadbcaaaaddbcadcbaabdcacabdbcddcdcbdcbabdacbdbabadbcbddaccaabacadccdacbcdcbbcdccdcaaadacccaddcaddcccadcabcdbdabbcbaaccaddcdcdcbcbdcabccbdbaddddadacbcdddbbcaabadcaabadccaacbdccdbacdaddbdbbcacbbdbcdcddacaacaccbaaddadacbcdbcccbbcacbdacbcbcccbcdcbccdbadccabdabdabcbbacddcbcaabbdabacbbcabaadcdccabcbcddcbbbdcdacaaabdadababaddadccbacbccdcacdddadaaadcdcbcbadbcaabdacbddccdbdbacdbdddcbaccdddaccdcccbaaabcdddddcbabddccacbbdcbabadabacbdacdbbbbcdbddbcbddddddadcbabdddcadcacdbddbaaaccccdcbdddcdbccacaacccaadbdacdabdadabcdacdacddbcccadbccccbdcddcddcdcdddcdbbdabdcbbdccdbbacaabdcaddbcaccabbcddadbdbaccdbbaabcabcacbcbadacdbaccddbaacadabcbcdbdadbadaaccccdbacddbbccbcdbcbccacdbcacdaabcabcaadbadbbadaacbddccbcbbacbdccbcdbadddcddcdadbbaaabbdddccbddabcaddaadbacccacdcbbbbdacabcdbbaacaacdbabbcadbbacabcacacbdcbaadadcabaababaccacbccacbabbcacbddcdaadbdccbdccbbbbbcadddabcbccbbcacdbabddaccccdaddbbbcdbddacaacdbadcddbdaadaccdbcadbddbdddaaadccbdabbccbcbddabdaabccbccbadbdbccabbbddacdaaabcabdaccabcdcacbbdbbacabacbddcbcacabdadccbbbddcaadbbabacdcdabbcadabbcadabbccdaaacacbddbabbcaaccbdbaacccbbacdcbabcbcdbaaacccddcabbabddcdbcbddccbadcdcabbcbddbabdcbcbdbbdbcabaabbdbbbcbddabaadabcdadcbdacadbdcbdccbcbddbdcacaadadbddbccccdcabdcbdddadddcdddbdbdbdabcdabaddbbdadcccbbdcccccbdabdccdadbaacbdbdacabacaabacdabbbababbacbaaccadaddbacadbbdcaabadcaacbbcbbccbcbacadcdabaaaabaabdcccabbcaadbdcaabddadadbcdadbadbcddbdacdacbbdbcaadadabccadbcccddbbbbcbbbabbdcadcddccdacbabadddabdaddcbadaddccadbaabacbabbababcaaddacddddcccacbabcdacddcbdbccdbcaabcdddcbcadcbdbbcdaabcccddbbcdbabbdaaadaacddaccbacdacddacbcdbadccddbdbdbbaddcbaaabaaacdacaacaaadcababddbabbdddaadcbadbdcaccaaadcaabccdabddbabdaacdcbabacbabaadbbcacbccddbcbacabdbdacddaddbabbcbcbadaddddcabddbbacaddddbcadabcdaacbbbdcbbcbbdddcdacacbbaaccbbdddbbacdaabddaaadacacbaabdabdacabcdcccdcddabbacccddbadadcdccccbdbabaacacaacabdcbdcdcadabdcbacccacbbbbdaaaacaaddaabdbcbdbacbcbcbaccaadcdcccdbaccddbbdaabcadcbdcddbaadcbdadabacdcddcbdaaabdbdbddbbddcadcbdcbcbdcabdbccadaddbdbbbdaabbcddddcaaacdaccbbbacaaddccbbaadabadbddbacaabbaaccacdcdccdbbacadccdcabdccdaabbddabcaabcdbddaaaccbbbbbaccaadbcbacbcbdcaddbbbadcdacdbcabdabbddbdccdbccabdabaabaccddaacaddcadcabbddcdaccdabdcaccdbacdabdabdbdadbcaacccacdacbdadabccdaabacbaabbbcbbbaaaababdbaacddcdacbdcdacbccabbcdcbaabcaacdbbdcbbbccadabdddaccadcaacddadaacccbddbbcdbcabadababcdcbadbadddcdaaadabdadadccdbcbaaddbddadbddbdaddbacddbaaabbcbacbaadabaababcbcbacdddcbcccabccddccccdaacddcdaadbcadcbdbabdcccbcbacadcbddbddcbbbcbcdaabbadbcabcabdcbbddddcdbdcdcbbcbcbbabbbaabaabdbbbbadccbcaadccabdcccbbacdacacdaaccaadabdcacbbdbaadaacbcacdcacaccdbcddbcddadbcadbbadccbcbccdcddaccdccaadabdddcaadccdddbddacaccbbdaadcdcbadbaadbdcaabdcbdcbaabcccccbabaadddadccdbdbdadbbaddccccaddacbbcdccbdacbbcacdcdcddbdbdbdcabacabbbadcbdaaadbcdaababbbacbbdbdadccabcddccbcbaaadbaabcbdacaaccdbcadaabbdddbdaaadbddaadcbaddcccbccadbdbccbadabbbbdccddcdadadaddcbadbdddaabadcccbbabdcacccdbbbcabcbacaabbacaacacabcabdcbdcaddbabcacdbbdcdbddbbabdccabbdccbbcbdcdbcddabbddaaddabbaccccbabdbdadcdcdbbcabccbbbddcabdcaaadcdabacaacabbbacddaacbbacccadacddaabcddcdadddbddbdabcdcddacadaadaacabdbacdaacbcdbdbcdabddddaccbcabcdacbcbcbacbdddddbadcdbadaddadcabbadadaadaadacdacbdbbadbbcdcddbdcddcdcabaddbdaacaadabbbcbcccbccbbdacddccccbacbdbbdcddbcdccacadbdcddbbbcdbccdaaaaadaddccdaabbcccdaccdccdccccaddbdccadbdcdcbdcdabaccdacabbacacdccdbbaacbcaabaccdbabccbbbdbcacbbabaccadbcbcbadacdacbaddddcacabbdccdbadcaabcbcddacacdadcadaadcbddddbbdcbcdaddddaccdaaaccaaaabadacadddbaaadccacdbabcbabcddbadbaaccadadbddbdbacbabbbadccbccdacdddbdcccbddbbccadccbbadcdadbcddcbddcbcdbbabdbabbaabdbccdccdcdccbbabbccbdbbdacbccbdbccbcbbbcbbaddabdbcadcdbadaccdddbdbadbdbcacbdbcaaadaacbadbcdaaacaaacddcdbdbadbdbbccadbacabaddaacaddbcaddbcddbcadaabccddbcbadddbcdbabbabbabbacdbabbbbacccdccbbacaccaabccbcacabaccbcdcaddbdaaabdccdbdaacbdccbcaadbaadbdaabaaadacdcabababcddbddbccdacdbccaddaaacadbdabbadbbddcaddbaddaccccbaaacaaddbdcadaabdadbdcabdbbacdddddadbabbbdcbcccacacddcbcdacdbccacddbccccabaaadaaccbbccccdbccdbbddadaabbaccccbcdcbabbacbdabdcdcacdbbadccabdadbbccbacbdbccdbbaadccacabccdbacccddddcccdcbbccbadbaddadaaaacadcacbbcaaaabbcbbacdcdcbdccdaacdcaabbacdccaddbcdbadadbcdbadcdbdcaccaaccbbddddcabddddcdcbccbadccaabadcbbbaabbdbdcbaaabbcdcdacbddddcdccddadaddcbdcdbcbccacbbcdddbcddbdbbacccaabcaadbabadcddbbdadcbcdcbadaacdbbbbcdbabbbbacdcaaadabcbccdcabdabcdbbbadbbacabbbcdadcccbbcdababdcdbbaadadaadadbdaaacccaacdbdbadbabadabccacbbcbcacdaccddacddbbdacccabbaccbacddbdbbbababcbaddadcadddddddddabacdbacacacaadcadaaabbdbbccadcabcdaacbbbdbccbccdaacabaacdbbcbbacdbabcaabcdbbaadbddcabdbacbcdccbdadcddbacacacddccbacdcadbdbccccddbbbdcbcbbcbcbccdccabadabacaadcccdccbcdbdcddabbbcaccdcbdbcbcccbdbaabbcaabdcdaacbdcacdcabdbdcaacabdaccccbddabddbbddcccdcccccabaaddacbddbbdabadaddadcbabacbadababbcbdbabaadbdccddcbbaaadbdddabdabbcabadbdabcddacdbadccbbbaacacaacbdccdacabacddcdadbbccacadabccdbccaddcabdbcbcdcbabcbaadcccdccdbdddcabacbbccdacdddcdcdbdcddbcddbdbdccbaabbbcccdbdcdadaabbdbbbcbbbacbccbcbaaabdbdcacadcdcbccccbddadbacdadaccdcbdbaccdddbdbccdadccbaaddbadcbaaacccddcddabacdcddcbdbccdbdddcdbbcbcdabcdbbccccddbcacdadcbdaadbdbdabacaddadcbbbdcabbcbcbbdcdbddaccaacddcddbdccdcaccaaaaacdbdbdbabdaaabbadbbddccaddbdbdaadbdbdcbbabbdcdcbcdccddbabacbbbaacbaaabcaaadddacabdcdabbaccacaaccdabaaddddbaadcacbcbadbbcbaaaddbdaaccdbcdbbdccadbddcabbcbccccddacbacadcccaacabadcdadabdabcbcccdabbbdcdbaabdadabadccbbbaddbdaacdbabbcbaadabbaacbdabadcbccbdabcccbccbbdaaccbdcdcbbccbbcabdaacbdaddaabbacdadbadbcbbbdaacbadddcabdbacbacbacccdbcacbdbddacdabcabcbaaacbdcbdcacdababdddddabcdccdaabdabbdccabbbcbcaaacdbacabbaababcbaaadbcbcdcbaabdddbbdadbdccadbbcacdbadbcbddcdaaaaadbbaccdddcaabdcbabbddbbdabbdaccbbdacddbcaaabdabcbbabbcbaaddcaccacdcdccdcbdaccbdcbacabcacdaacbcbacacacadaaaaacccaadacbbcaccdcdbbdcadcabdacbabdaccdaccdbabcdcaabddcdbacbaccabccaaabcacadaacccdccadacbccbaddbcccddccacbbabbdbabcbcdcacccbcdbaaadcdcdbcdbaabddbcabbbcbcccdbaddabddcbabdcdaabcbbccdabdbdcbddacacddcaabadaaddabbabadbabaadcacbbcdcccccaccbabacbabbbcddaccdbcccdbccbcddbddccbadcababcbdaacbadaaddbbcccdccaacadbbcadabadcacccbbbcccbbabadcaaabbdbbbbbcdcaabaadcbdccabbbcbdcdadaccaacdabbbacbaccabacdcdbcdcbdddbdabadbaccdaddcbaacbabdcddacddccccddadddcaacdbdbcbabbbdccdbbaacdabadcacbadbaaacbdddbadcdbcdcaaaabdabadcccaccbacdcccdccbcaadbaadbaddccdaaddbdabddacbbbddcbcdaabddbdbcbdddaaacabbdccbacaddcbbccbdcacddbaabacdccdaccaabbcbdbccdcbcaadbcabccaacddadadbdcbdbbbbadbcdadcbcadaddadddacbabdbaaccdacbaacabdabcaccbabcbdbbdbccdcdabdccbcadbccdaacaabcacbcbadabbbdaacdcbabbdaabacbdacdddbbacabddcbcbddaddccadcdbccddbaabaacbadacaabcabccccdbacbbbabcbaccbcdcbbbdaadcadbdcabcddcdbcdbccdcccddcabbadccaccabcabdaacbabdbddabcaabcabccababbcaabcbcbacdbdaabbaadcdadbdbbdadbbbddcabbdccabbbdbabdaacbccdacacaadaacaabdadaaaabbbcccbbbbdbcdacbdbdcdcdabaaabbaabdcabbbcabdbacacdbbbbdbbaccabdacbacdcaabdacbcccbaaaaaaddbcabdbababcabdbaacbcadcddcababccdbdcbcaccdccbdaacbbbbbcaacdcbaaaddccbadbbdabcbdbbbcdccbcbbbacacbddadbccdccadaadbdbbdcbaaabddaacaabaccadacadcbacbccddcccaaddccbcadcaaaccbdacacbbddcbcaacbbacdbabdbadadbcbcdccabdaaaaddabddbcaaaaabbbadccdcaabbadcbbcdacdcaddcccbdbdcbbcadccbdbacabbcbbacdadcaccbcdbddbbcdabddabdbbdbdddbdaabcadbcbdcbadccadacdcaacbacbbcbbacaabddcbbcdccddcddcbcaacbbbabdbacddcabacadbadbcacadaccbddddadcdbcaaaaddddacdcacbccaadacacdabbdabcdbcbcbadaadaabdacbcbcdbccabcdcbadabaaabaabcbbaddccdccdddadbbadcbacdcbbcddcdadbddbabdcdadbcacadadbcaccdcaccaabaccacdcdabdbbbddbcbbcaadbdadabcaacbabbbcbccccbbdcbdabbcadadbbbbbabdbcdcaccadcccdbddaadabdcbaaadbcccdccdddacccdddcccddcdcdccabcaadbdbcacadbbdbaccdbbcadcadaacdcdabdbbdcbdaddcadabdbdcdccbbacbdbabacdabbadbbdbbbbacacbbadadadabbbadcdcdccdbaadaaadcaccdcdacabbaacdddcdcadcaaacacadacccaacabbbcbacccddcadbcbcaddcdcabaaaacbdddbbadbddcdbcdbdbbaacaaadacbbacabcbbccbaccabcdcddbbdbbcccccabadaadddcadbbaddcbbdbadbdbbcdadcdccdddccbcdabccdbcadcdacacdabbbdcadcbdcdbbcbccaddcdbbcabdaddabadaadcadabcacbddbbcccddcabadcbabbcdbaddcaabbaccdabbbccaaaddcbdcacbcdacbcacdacaadaaacccbdcdacbadddacdbcbddbabdadabcacacababcbbaabddbabddbaddadcabcabdbcbcaabcdcacdbaadccdcccbbbcbcdccdcabcbaabbbbdadcbcdcccccbacadddcabdcadaddcacdccabcacdccbcaaabbacdabaaccacacdcdcdcbbdaaaddccadabadcdcdbdacbaccbddaacacaddcacaddbcddddaaaabdddbbdacacccbbcdcacadccadbcddadbddabcccdcaaaaacbcaadacbcbbddaccdbcabbaadccdcbcbbccaaabdcbabbabcdabaadbbbbdbadbdcbdaccabbacbbbbdabdbbaddaddcadacaddaaabcbcdaadacbcdccbacdbbddbdadabaadabadacababdcbbccbacbaccaabbdcddddbccadadabddacbacbddccbbcababbbadcdddabdadbbadacadabccdcbaaaadbcacabadcddabcbaaadadabbabdbabcbbbbabddcbccbccdcbadcaaacbdadbcdaddaabdbcdaccbcbadacabadddbdaacbaaacbcccbaabaaabbbbcdbdcbbdabcdcbdbbdcdcdcdcccddbbbdabbdcabcdacdbdcbcbabdaaabdbbcadbcacbbbdccacdbcbbadacddaacadbadabcbbdbcdcabcbdaaaaacdbabdacaaacbbdcddddacbacdbaadadacdaaddbabacaadcbacccbbcdbccbcbbcbbabccbdabcddadababccaddccaadbccdacccbcdadcbadabbbaddaaddbaadcddacaacddaddccdcdbdddacacbadcbbadabbabbcbcccbcbdccdbcdcdbccddaddbbdbcacdcbbcaddaacbaaaacaadaaadabdaaadacadabcdabaacdaabdbddcdbbdbcdbdabdaddbbdabbcadbddbcbbcaadbdbcdabdadccaaabdaabbddcaccdbaddbcabcabddcbaacbcccaacbabccacaadcaabcbbcbabcaaababbdabcabdbcccdcaaacaddaaababcabddcaaaccdbdabddbcdbbdbdcddcadabccaddbcdbadbcbabbddcbdcdabcbbdcaabbbdabcadcabadaccacdcabcbbcbbaacadabdabdabdbcbccbacdcbccabadbdcdccdabbdadcdabddadddbbbdbbabcadabadadcaaacdbccabcabbcbbcdccdabbbdcaadcbccdabdbdacbccccadacbaccdadbdbbbcdbadbdadcabbcdcaadbdaabdadbdbadacacbaabcdcddbcdabacbbddcdcccacbddcbbacbdcaddcbcbacabaacddcbbddcaadcdcddcbbbcccbbcbdacdcddcdcbdbaacabdaababbdcbcdccddadcaacaddcbabdabcabcbcadadcddaccccabcdcbbcdaddbdacdddbcbcbcbddcbdacdcbcbabdcadcbbbaaccbadcccbdddaccbadbbcadcaadbcdabbaaaacabcbaadcdabbcaaddacaaaabbdcabdbbdabbdcdbabdabbccdcaccddacdabdaaabcdccdbcbdcacdbdbaadbbbaadacddacdcaabdcadacddbcacbbaabdaccaccabaaccabcdbadaccdbabaaccbaacabdbabbbbaabcbbcbabbacdcacbaccddcbcadccbcdaabdabbaddddabccccccddabdbcddaabcadbcbbdaabcbbdddadacdbaaddacaabdaaadbbdddcaabaabdaddbaabbcccadbdcadcbcbbadbaadccdbbaabbbbabbbdbaaacaabbbccbacbddccddbabdbdcacdddcbddbbcbdcdacbcabcabbccbdbdddaabbbaccbdbaacabcdcabcbbacdcbadcbcbacbbbdcdabcdbcdbadbcdbadcbbdcddccccbddbcdddbdbbdbaccbcdccaccccadabdbdaccadcdbdbdcbcacddbbbbddaadacbaaccccdcbdabcdcdadbcbcddcaddccbdccbcdcddbbaccdbddbadbdaaaccdbdadbcccabcdccbbdcacaacdbcdbacbacdbcccaaaaddddaabaddbcacabaabbbcccccabbbbcababbddaccdcbaddcacdaddbacadacadcaaadadcbcaaaacdbdccccbccbabadbbaccacaddcdadaaaccabcdcccdccbcbddbdaaccbcccdbcabccabaadaaaadbccccdacdacbcadbcddabbcaabcbddbacdbccbbbccbbcbaccacaabaddabdccddaacdccabbacbdbabddbadbddadcbabddcaaddbdbcbddcacbbbaccabddccbbdbaccdcaadabbabdcacaabbacaddbccacacaaaadbddbddaadbdcabddcadcbaaddacccbddbbbdbdaacdcdbacdadabcdaadadcdbccacabdccbddaacabdbdcdccaabbbadbabaadccaccbbdbdaacdcacbddbacacacadcbcdadcbccdddcacacddcacccadaacacaabbaddacaababdcaabccccddcacacddacbaaddaccddaddabbbccdbbbbdcdbddbaabaabdbdadcababddccbdadabcdccabadbdadbccaabcabbbddbbcabcbadadaadddaccadacbbabdadbdbdaacbcadddbccaddadccbcaaccbcbadadbccdcdddabddcaabcadbbcbadacaccdabcababcbbdaadcdcabaccdbdadbbadcccadbabaabbbacbbbcccdaddaddbddbddcdcbbcddccddcccbbddbbacbabdaaaadaababbbbadddbbacaaccdbcabaccccbbbddaddddbcbcdbacddbbdaaddccdababbcabdcdbacddbbacabccaaacbacbadcaabcabacbadcdcddbaadabaadbdacacdacbccdbadccbaabcbdcdbddcacbaadaccaaccbacddaadaacadbccccabaabcbabacbacdabbabbaabccbdbbdabdcddbacbcaadaccbdddabdabddaadbababbaccccadddccadddcbbbababacadaddbaabdcdbaabdaddccacdbdacabcdbacdbbabbabbdcdbcacccdabcaaaaccdcabdcccdbaabdcdcbaaddbbcdcccacacdbbaaccaabbdbbadccbcdabdbaacccbcdcbadcccadbdabbddbbcdacdadbdbaaccbcdabcdddcbbadbabbcdcaacabbadadbcddacbbacacbdcbdcbcabdbcbdadcdadabdcbbabbcccaccadababbcbaadccacabcbcacbaadcbbbaddccccdbcabddabcaadbddbaaabcbddccdacccaadcdddaaaaadadccbcccdbccabadcadbbdcbddbdddaadbaaaddbcdddbbbababacadcadbabcbbccacbadddbaaccadcccaddabbacbabddacaadcdbbabdcbcaabadabbadcbdcccacbdbabdaccbadcdbaabbcadcaddccabbbbadbaaddcabccdcbaaadccdcccddbcbdccbdbdbaabbacbdbabbddadacbadadccbdddddaacccaaacacdbccdbaccadabddaacbacbadabcddaccdbcdcacacbbcdaddadadaccaccbcbcddbccbabdbadadabbbdacabddccccaaadbdcaabaddcadbcadcacdbcaccdbabdcbbbaaddaabadccbcdcdbdcdbdbabccaaccbbcdccbbabbddbadcaadbaabcbcdccbdaabbbbbdcbadabcadcddccacabbdbabbdccdbabbbcbdbadbdaccbdcbccacadbcdcacadddccadbbbcbcaacbcbcdddbdadcdacbdaccdcbbcaacbbccdbadcdbdaddbdcadcdbdadbdbdddccbbdacacbcdbbabcabadaadadcbcdbcbcddadbbccbcaaabdacccdddabccdbdaaadddcbadabacdccbacacbdbcbbbdacaddbcbccdbccabadaaadbbadccadbcdccbbcbaacacddddbbbaacdbbdadcddbaadcdabadbccabbcbcbdcabacadcbbcbdbccabbdddbacabdcdbaddaddababcacaacabdddcdcadabbacbabddcaacddbbbdcdacaddadbbdbdbdbaccabacdbddbbadcddaaadccccabdadbbbbacddbdbadcdbcdbddbdcbdaaabbdccdacbcabbbdabccadddcdacdacddadcdddcdaabdaabdbcbddcadccbddabdddcddbbacaddadccdaadddcbcabcbbccadaccdbdabddabacdbbdaccddaccbaacaaadaaadadccdccaccaddaacbdcbadbdacaaaacdccdcbacccddaadcadddacbcbdbdbaadddabdbbbcdccdacdabddccdbbdcdacdcbbdddbdccdcacdabcdabacaabaadcdadaacbdbcaabcadccdcdcbdccdadcccaaaadabdbccaccbdaaaabbaaccacbccacdddbdbcadabdacabbcdcdcdcbbacdbadcbdacdcbcdabbbacbacccbaabccdcccadbcdabdbcaddabcbddddcaabbdaccbbbbabacbaacbdbbbdcdabdbdcbdacbbadbaaccccaadacaccbdbdcccbbaacaabadbbcbabdbdccadbcdabbacabddadaabcdadbbcbbadadbcacddbdbcddaaabdbadbaccbabbcabdccabdabcacbababdbdaadbabbaadddcdbbbdbaaaadcdadbcdcbdcaaabcbbdabdcabcacadbacadaadbbacdccdddcdadccdddadccbbdbbacdccccabdabddcacbddccadccccdbdaaadcdddddccbabdabbaabddbabdcbccacdcdbadaacbddaccbbabcdbbcbcbaaccaccdcccababcdccabbddcdddcbdadcbdbcccbbcdbdbacdcdabcdabacaaabadadbdabbaacabcaccadcaabbbbaccdccbdadaabbbcacaaaddcdbdbbcdcbcaadadadbadbaadadcddccdbcbaacccbdbbadbbdcdbcbaadabacbacabadadaaaccadbabdbaacabcdaabbccbcccbccadacdcbabbcbccccadbaabdccdaddacbbcbbcdcdcbabdbbbbbdbadccccabccbbcdddababdbddddbbdadbbdcaddcdcbcbdcaaaabaaaacbccbdabbdacbcccdcadbaadbbcdbbdbaabbbbbadaaddcaadadbdaccaccbbcaaadabbadcddcbbacdbaddcbcacccbcabdcbbabdbcbdcbcbbacbacbacbbaabbaddabdddddbaacbaabdcaaddadaadbacbdbaacbdccbaacccaadabddbaacadcbabdacdbdabdcdbdbbaadacbccdbddcdcdbccdabbbcdcdadbdacabbddacbdaadbdadcbbdccbaccdcadcadcaaccbcaaddbbdacbaaacddcdbbadbacbbaaabacaabdbcdaadcaaacabbbcadddcdacbcbaddddbbbbddabbadacbcdddcccddabccabbccbccbadcdcabcccbdddacbadadbbcabccdaabdacbcabbdcdcdddbdbbbabbbddcadbbaadbdccccabcdbaaaabccbdcdccbbdcbbcccdbaccdbdbcaacabaadcadacdbdacabbbcbdcdcdcaddbdccabaddaabbbdaccbdabaabdbbdbacaaaaacacdddadbaadccddbdaaadddbacdbdcbbcaaaddddccaadabcadcadcdbdbdabcabbdcabddcacaaccbaabaddacaacabdbcdcdadddbaabdbccdaadcbbbacbaccdadccbabcbbaadcaabddbdbcdcbcadcabdcdacacddddbdbdcadcbacacaaddbadabbccdbcbbdbadcaacdcdadddbddacabcbcccabdcdadccdbdcbabdcddcabbdcbaadddcbbbdcdddaddbbaadbaaabcdcabacbdbcdbdabbddabcbacddacbabaadbccbbacbbaaacadcdcbcddbbabcdddbdcacbcbcdcccdaaccbccdbcdccadbbcadddadcacaccbcdbbddcddcdcbbdcaaccbdabbadadbbcabddbdbccabbbacbcbaddddaacbcbbaddbbdbcacaaadbdadcbadbabbcdabcbcadadabbbabbadccacdbcaddcbbbdacaabccddcdadbccbbaccbcddabbadacbdaaabbaaddadbacbbcadbbacdacabbacdccccbbdbddddbcbbcbcdcabacbbbdbadaabbccbcbadaadaabdddbbcabdbbdbbacdacccadaddcaddbddccaddaaddbaddcdaababadcbaccbdcdabacdcbdbaaabcdabbabdadcbacdacbdacabdbccdbddbccbcbbdbccccddcbccdcdacdacabbbbddaadbbadbbbdaabdcacbbdadaadcdbbbcaabadcdabccbadabbddadcbdbcacbdcbcabbcdacdccddaaabbdcddbbcbddbddbdbcababccccadcbbaaaacbbbbaddcbdcaacabcbddcddbaabccacbdabbdabccacabcbddabbcdadddacbcbdadbddbcdcbdabcbadbdcddabaccacdccddaaccacdcadbdbcdbcbdbaccbacdacccaddbcddbcadbbccaacdcaaabacacbabcdbccaaddabbbadbbdacddacaacabbadbabdcdaadadcddcbadbbcbbbbaacaadcadadddabbcdabbacaccdbccdbabcbddbcccabcabddddadbccddbdadcdacccdcabadbbacbbcacdbcccccdadabaaaddacdabbabbcbbccdbadbdaaabcbcaadaacdbcbdaddaaccdbabbabadbbadcdcbccccdbdddbcddccdcddbdadcaaacbdbadbdcdbadbcbdddccbcdbcadabdaaccaaddbaabcaddddccbaadcdbbdadcaadacbdcdbaccdccdabaaababbabcabcbacdcacdadacadccacbddbaabbdbcbadccdbccaddacbcddaaabadbdddadcadccdaddbbddbaddbdccccaaaacdaaccabcdddbbbacdcadbababcaadcbdddbadccbcaaaadacdbbcbadcbbdacddddabccbcdbaddddaaaacdbaadaccaacaacbdadcbcabbdccadcbddddacabbacadbbcdaaabadcdaabccbddbaccabcdcabcddacbdccbbbddbdbaaccdddbaaddaaccdcddbdaaacdbccbbabbcadabdbcbddcacbdcbdcbdacaabaabbcabcbaddcbdbdcaccdcbbdababddcbbababbbacdadcdabdbadaadabdbdabbcbccaabbdccaacddcbcccccdbbbbacbacbdaaccadaabbacdadbbbbadbbbdbdcbadaddcbccbccdbadddddacbdadbbabcbacdbbcdcaddabcbbdddbbaacbcdbdbbbbbbddcccbabbcacccbdbdcdaccdccbbbbbabdaabdabbdbabbadadcdbdbddcccdaadacbdacaadbbadaabdccbbabdcddaadbccdacababccdbcdbbaacaccabbdbbbababcacdababcadbbdcbdadbccaaddbabdabcababcbddccddbcadabcaccbccabbddcadcbaacddddcbdcbcdbbdcbdbbacdbadacbddbddabbbcbdabbabcbccdcacadadaabbddbacdbadacdccddcccccbbdbbaabadbdbdabbabdccaacddbdbaccabddbacaadbdddcaddcdbcbdbdaadcbaccdabcbdbacccadadddddaccdaababbbccccbdabacddcbdcdaadcccddacaabcdaccbcbbabbdabbddcaaaaaddbdddbcbddaddbaacaddbcddcadcbbdbcdaabcdddbacbddaacbbbbbabcaadabadbdcdbcbdadddbcdbccdbddcdcacdcaddaccabaaaccdcabddacabcccacbdbabcbddbdcbbacbdbabaabbbbddadddbadabcbbdadaabcbcbcabdacaabcccbcabdcdaaaccdaabdcadbbadbbddaadaaddccccbbbacdadddaddabbaadbadadcbbaadbabdcccbdcacccaacbdaddccdadbabdbbbdddabaddaabaddcabbcabdaddadddcacaccdcadbdbabdbddaadabbddbccbbacacabdbbdabbcabcdcaaddcacccbbdcdacbdccddadbddadabdacbcddbadddcbcdbabdcbddaadacbbabcbbbdcdcdabdacacdabddbcabbccdcdccacccaccbddadddbabbbadcbddbcdbbbdcaabccddcacadcabdaacccdbcaacacddcbacbcdddacbddacddcccaddbcbcbbdbbaccdbcaadadadcdababadcdcdccabdcaccdabdaddbcaaaaccdbdccbdaadacdbcdccddbdadbacaabcacbadcdbacadabbbababdbcdaccbbcddddadcddbaadacacbccdaadbcccbbcacabccddaccaacdbcbccbdbaadacaddaaabccbadaadadcdbadabcaaabaccdcdccaccccdcdbddbbdbacccdaadbbdbacadbacbaccbbadaddcabdadbcbadcacddbcdcdadbcadcdababcccdcbcdacabdadccdcadbbcccdacddddccbcbaaacaaaaccbaadcdaadcbbdccdbaacacbccabdaabcdbabcddbadbbbbdbddbabacbabcadcaccdacdcddaccbcbbbbcacaccaddbcbaccdcabbdacddaaccdbbadbacdcadadbbbacacadbaacaddddcbaddadcacaacacdcacabbaacbabbbcddadaadcddccccaddabdcdbbbdacbdccbcdcadacacdadcbcadbaabbbcdcabbdbbabaaabbdcacbccabccdacacccdccdadbaacdaccccadbacacbcacaddbddaacbbaaadcaacbacdacaddccdbadacbbaddaabbabcabbcaabdbbcbaaadbbbbacabdaabacdccbddcacadbbbdcbabaccdcdbcddcbcadcdbbcdacbdbdbdabbccdbbbcadbbabcaadabadbaaadbbadaaadbbbdadbaacdcdcdbccaabdcacaccdaabadaadbbcacaabdcacbaccabdbdacdbcdaababadaacccbdaabcdcdbbdbcacbdadaacddccddaccadbbbcaddcbbcdbddccababcaaddcddacccddabcdbacdcbcdddcdcdacadbcbddbbbadadaacdcabdacbcddbbacccdbaaabcabbaddabddddacbddbaddddadbcdaabdddcbcbacaabddcdbacbdbabaddacdbddcacacadbbcbdddbddacdbbdaccdcbabbbbcdbcdddbabbddacbbcaadcaaaaabacddadbcdcacdbbdacdadcacaadababddbabbadbccbbdaadbcbabdddbbddacdbadcdbddcdbcbdaabcaacdcdbccdcccdbacbcabbcaccadcdaccabbbaadcbcbcdcbcadddcdbbaadddabcccbcbbacaaadbddaccdacbcccaaacabaabdacbdbabadbbcddababbccdccabdcddbbcabacbadbbbbaaabbccabacbadbcdccbabcddabdabaaadbaddccdbdcdcccddcaaabdbadaaddccccdddbcadaccacddcabacccbbaadbcdaaddaaacccddcbbaacbbadadccacabaaccadbbdabaccbbdccbdcdbacabccdcbccccdaddaacacbacdbcdcdbccadcccaccaccdccabdbdacbadbcbccacabcbabdadccaabcadabcbcccbddaccaddcbabadadabcdaccbdaaaabacbdbaccbcbbaaccdcbcadbdcddadaccacabdcbcacdbcdcbbcbcbcbbdadabcadacadbcbaabacdaccbcccbbcadddccbdbbaccacdcbbaccbaabadccccdaacddadbbaaacddabccbabcccbdcadbbcdcdcaaaaddabbbadcaddcbdaabbcddbbcaccdcdddbadbcdcaaaadccbbbaddbbdbdaccdbccccbaacabccbabbcdddbddcbabaddcdacbadaababcbdadcbdbddddacdccdbbacaabacdabcbcadcbbddcadbbcbdaddabcbcbacbbacdcadacacbbbbcaddccbdbbcaabadcdcbbdbbccacbdddcdabbcccbcabbbabdcaccacdbbadddccbcbdadaacadddbbcbcddbacdbcabbbdcaabacdacdacbaccabcddccbddbccaacbbabaccbccadbcbadbabacdacadababccccdabccbaccdccdcacbacadbacaddbadabbcccbcacdbdacbaddccacccbbabdadccabdcbadccbabcbbadaccdabadbddcabcccaaadadacccccbbcddbcdbbaacbacdcdcbcdcaadcaadcadccbdacdbabaaacacbdcdcddabdadaccabcbdcbbccabcabbddbdadacccbcbacaddbdbccbcdbbbdaddcdcadbcacbacaaacadadcbdaadacbccbddbadbcddbdccabbdbdbbcadbacbbabacddbbccaaadaddacbdbdddbbbcbdcbcaadccddabccccbdcbbbddabbcdbdcbbbaadacdaaacbdccbadcdbbabccababaddbaabbdaddaaacdacaaacbddbdaabcaccccdadcbcaaacddadaaabdbccdcddadabbabcddbbacbcbdcadbdbbcbbdabcddaccdbbcbaabdcdddabacbbbaddadbcbdbacbbcddbacdacdbdadcdbcdaadaadbcadbbcddadcddcabbacbccadacdbcabcbbabacbcdccdbaadccdccdaadadbccdbaacaabbbdbbcdabdabcccbccdabaadcbccbdcbddcbdcabcadbcdcaddccbbcccacabbabcbcbdaaacccbcabccdcabadddcbcbcdcadadbbacaaddaacbbcdccaccdababbdbbcabacadbabbaaddabbacdcabaabcaabddcbacccabdaabdacdcccbbaccdbdcabbdccaaaadcbbbccabbabadbbaabddcdcadabaccacaddbabbccbdbbcccdaddcbcaaaaddcaadccaacdaccaaadbdbcddabadaaacacaaabcabaacccacabbcddbdbcadcbddbcaccdabbdbbccabaccbcbcbdddacdaddcdcccbabccabcddcdcbcdccccadabadccdacbbadbdbcdccbccccacbbadbddbadcbacabacbaaacaabbcaaddbcbdbcdcdbbabbacbccabdbdccabddadcaaaabdcccbabcdabdcbdddcabadbccaacaddccabbdadbcbccbcccdabccccadacbcbaccacdbbbacbddccacacbdccabdbdaadabcadaddbddbbaabdccdccbcddabdddacdcdababddcacbbcbdbddbdcadaddbdccacdabcadbcdbdaadbccdccaddcaabacbbbbcdadbdacdbdbcaadabacccdadccaaddcdaddcaaacbccbabdaccabccbacabbbaddaacaaddbbbcadcadcbcdabcabacdbbbddcdaacaaddbaccddccdbcaddbccabacbcdabdaddacdacaadaddbcccacadabcbcaabbaaccddcccbcaaabdbabddbdabcabbaaddaddbdcbdbbccabdaabddddcbbdbcaabadbadabddcccbdbbaaacacaaacbccdabdcadcabcbbadcbbbabdabdccdabcddbabddadcabbdbccbcdbbaacccbcbbbdbabdadbdbdbccccabaacdbbdcdbdcbbbdabccbccdbccccdaadadcacbabcbcdbacbcbdbbdcbbdcaabdcabdbbacabcddadcaaabaccbcbaabdccaacbaacbdbbdbacccbcdbbbcdbbbbdacaabccaaadbbbcbcddddaddcdccadbcbdcccdbdcdacbcababdbbcccadcacccaccabbcbaadbbcdccdddbabcdabcdacdacbbccccaccccccdabbbbbacbdabbdbaabddabbbcdcaabcdaddaaadaabcdcbcdcdcdcddbccbbdaaccbcbccbaabaddcbbbacabccadbdcdbaaccacaaddcdcbabcadaabdbccbdacbacccabbbbbcabdbbdbbaadabcbccadddabdbbabacdbddbabcdbbaaacacdabdacadddabccbbbdbbcaaddabcdadcdbadabdddcaacdcbcbbabbcabaaadacbccdbdcabcccaadaababccdcbcdaabddbaaacbdbbbacabddbbccbcdcdcddcbdcdbbacbbbabbccccadcbbcbacdbccbdadcabacdaddaccaabcdddcbdbddbaabcdabadcdbbdbcacaccddbcdaccbcdbabacbbabccbdccdbacbcacccabdbbadabccaabacadcacddddbddabaddadcdcabdcbbadcdbabaddcaaabaaccdabdabbdcddcaacacdbdadbdbcbdbcdcacaadbdbddbacddbbadcabbdaddabcbcdcbabadbccbbadcaadaacbdadbdaabbdccbacaaabbbcdacbadbdbbcabbbbdcdabcdaddccabcdcadcddabdabadcdcddacdbabbdccacabdacaaadbdcabcbacbaabbcdaaacdaaacabaadbaddacddcaacaabdbcdaaccadccdbddbbaddbdbadbbcdddbaccbdadadabcdaacadcdcbaccaaaddbddcdcbdbcaadddddbaabbcacaaabbccabdcbbbcdccdcdcbbbcabadbdbaadaaabcbcacccccdccaddbadaaadabacbbaccadcbbbcabadbdbaadbadabcaddadbacbbadddcdaacbccdadbdacdbcdadcdbdbdcbccbaabcbbdbabadbdccdccbbdbdaaadbccdccbbcdbbdadcadbdcaaadccddbaddbbcadbcbcccbccbaabadacabcabdbdbaaadbcadccdbddbccabcadbdbbbccbccabdbcddbcabadccdaaacdcdaaaaabdbcaaabcdbaaccabaabbacacdcddaadcdcaabccdbddbcdccabcbbabbacccbacbbcbabbaddccdadbcccdaabdcaabbabadbcbbcddcacabdaaabcbabdabdaadbacdbcccdddcccbbbcdcddadbbbbabaacddcacdadbbdcaddddcaabaadddbdddbbbadcabaddccadbcadbcbcabadddadabdcaacbaadabadbcadcaabbcacbabcccaabadccbadddbcdaddacdccaabcbbacaddacbcabcabcbbaccbadcadbaabdacbabbcdabccddbcddabaaddaacdcbaabcbdcbccbdcabbbdaddcccaaabacbacabbcbabbdadaadaaccdbcacdccadcccadbbcbdabbccaadbacdbbbbcbddcbdbabddddaddbdddddcadbddaccaddbbdcacddcbbbddaaabbaccdccbdccdbcccdbddddcddacbcabdcdabcdddcbdbadcbacbbddddddcddadabadabdccdbacbcdbccabbbaaacaddcdbcbbcdabaaacbbcbcaabbcdabbdacddbabcdccbaddbdddcbccabbccdbdadbddbdbcabacdaddcbbbcaacbccccababbbcbccaadbccbacaadbabbddaccddbacdcbbadcccdabcdadbadbcacadcbddaaadaacadabcbadcbbcbdbbaabdcadbdcabbcacabbacbacababccbdccbabbbcabcdbbdaaadacbadaacdaadadcaacdcdcbbcdabcdaacbdacbcdbacdadddcaacacdaabadddbdbaadbbddbdaabbacbcdcdaddbbaacaddacddadacbaaaaadddbcdccaadaacbadacdacdbaaadaaabcdbadcddccbdccdaddcaccaacbbcdcccbdabdbdaacdcbcdbaddcbabbbddccaaaaadcabbbadaddcddadccbaaacddcbaababdcdbddbccacbcdaadacbadbbcbbdddbadacadcaacdbdcbacddcdacabacbaccdddacbdcbdbbcbddacbbcaaadbcbabadbabbbdaadddbbcaabbbaabcdabaaccdcdbdccdcbdbdadbdbdaabcaaaacddbbbababcaaccbbcbadcbddabddabdcbdabbacaccddadbabbcabaabccbaaccbdbaadadddaabdccadccaabdccdcddcdbcbabcdbacbcbcbcbababcdccdadcbdbbbdbdcdbbaddddcbcbdaaccddcabcccdbbbabdcbdadccdbbbbbddacccdbcdacdabbccacdacdbbddddbdccdaadabcbcbdadbbccacdabdacbcdccadbabcabbbcbccbacacccccdccbbdbbbdbbdbbacddcdbdbdadcaadccadccdadccabadcbcdcbddabcccbdcbcadbbcabacdadabacacbcdcdaacbcbbabdbbcbccdbbcaabdddddabacbccabcaddbdaacadbabbcbccbccbbcabadbaacccddacddcabaccbdacdabcaaaddadabcdcdaddcdbacbcdaacbcacacdbabababdaddacddbccdcddcbcccbbbccdddccabcaaccdcdcaabdbbdddababdabadbcbaacddbdbcacadddbcddacbddabdaacdddbaacdbccbdaddcacbbabcbccdcbdabcbadbaadcadaacadbdbdcacbaddcdcabcbdcadaddbabbbdacaabddbcdabbcacbaddacbadbcdcdcacadabddcbdbdbadcabbbddbcbaabbbbdcbccddabcacbcddaddadbcbdaabbcbbacdcbccdadbaccbdbcbcdcdabbaaabcdbabadcbcacbdadbbabbcacdbcdddaaddbabbdcddbcadcdbabddcccdccbcdcdbdcdbdbbaaadcddccaddbbbdacccccdaadbdddddaacadbadcdacbcdabddacaaaaacaaddadbbcccacddacbababdcabcdbdadacaabaddcbcdacbdaabdabddbbabaabbbaddaaacadbbdcdacadadcabadbbdccacbbddaabdbccbdaaddaabcccbacaaadabbcaabcdbadbcacbacddbdddbdadddcbbacbbaaccbddabadcdabbbacdacbbabaddadcdcaccbcdbddbdcacaadadcbbbaddddbcaaacadabccadbadcbdaabaddcabddbbdddacbcbbadadabbcccbdbbddadbadbaddaadadbbddbbbdcdacbaaaaabaddbbcadcbacabcdbbcbcaadcdccbdcdbadaabcaababbcacddddbbdccacdbbccaaaccccaadcdcaacbccbacbbbdccabadcbabdbcaccadabaacccdaccdcdbaddcabbbcdbdbbdcccbcadadabacbcbdabbbbaccbddaabddcbdabbcacaddbccddacddbaddbaacdcabdcdbbcadbbccccacccdbdbdbbcdcbdaaabcdbdcdcacaabdabaaaccbabadbbbdcdcccabdbcbabaabbabdbbaddbdccdacbbbabcbdaaadbccbaaaadddadcbdcacdaaccdcbdcccabbaabcaabdcacabbddbdabcddbbcdbbadcabccaabaacdcbbbadcddddadbbdaccdabdbacccacbcaacdadacddbcddcbaaccccdbcaaadcddacdddbbcccdddaccabbcabcdaacadbaabadbdcbdcddcdbbcbcbadcccadbabbddadbdddbaabbbdacdbbdacaddaacbaddbcbaacdbcbccbdbaaaacaaccdabacacbbddababaababacbcbdcdaacbcaaddadacdadbddcdacaadabdcaabbccdcdbddcdabcacaacbbcbdbdabaacbdbacacaacdcbabccdabdaddbbcdadabaadccbaabbbbccccbbcbcdccabbdcbbcdddcaabdbdbdbadaadaaabcbcdcccaaadccaadddabbbdbaacababdbdcdcadadbacbaabdcaaccddbddcdcaadabcbbbbdabcbcdadaadccdacdabbdbacaabbcdcaaadaddbbcabcdcddabbacdaaccaadcccddcacadcacabccacabbabddcdaddcabcbbababbccbdccdbcadacdabbaccdddbcdbbddccadbadcaadadaadccddabcdadcdadddcaacccdddccacaadbaaacddccbdbbbdaaacbcaaccccbbcacdacacbbccccbbabacabbadbdcababbaddddcacbccdbadcdbcdacacabcdadbaccdabaddddcbbbdaabacbbdaccbacaadbdbbccbbccbccbdcddbdddcbdcdcccadbdcbbddcbcccddaddadadabbbcbdddccddadcbbcdcbdcdbdccbbabbbbdddaddadddacccddadcbaaabaccabaaadbcbabdaccdbaaccbdacbadcacdbaccababdadbdbcbdbadbccbaadbccccdcdcbcaacdaccdcadabacdccabdadbbbadccbacdacbdbacadbdbbaaabdcdabcccbaadbacbdbccddbcbdaacdbbacacccdcbaaaccbcadaaadbddbcbbbdcddccadcaabdbcccadcabdacaaacadabbddcdadadaccaacdcbaddccaaadbdddaaccccdcabbcdbddddbdcddcabcdbbabaaabddbccdbdadabcaccababcdbbddddcbcbddbbdbddbdcccbbcdbdddaadabdbaaaacdadadccbaccccccacccdbdccdaddcdcadbdabbbcccdaddbbbacccbaddbcababdbdddcaccabdcbdacccadbabbdccbabcbddabcddbabbbbbaadbbabcaabcbdabbaddbcacbdacbcbaabbcdcbcaaabcaaaccdaacccbddaaabaabbbbcddabadadbdaddabbbaadcddcabccaabcbdcaabbddaadabcdbcdacbddaacaddcddacddacadbdabaaaabadcbbcdbddbadbdccccdbbaadbaddbabbaacbdbbaddcaccdbadbdcdadabbddbaabadbdbddddccbbbbaadabaabcabacddcacbbbdddadbdcabcdcaadcbbaaccabcbdccbbdccdbadbdabbddaacdcbdcdcbbacacbcdadcddbdcabdcabdcaaaabaaabcacbcacadcbdcbccbbccbbbcaaabcdcbbdbbdcadcbdbccbbdaddbbdcbdadadaddaacadcacbaddbdaaabbddddadbdbbaabcccccaaacccacccbcbcabcbcbabdbcdbdcdddbdcbcddcccacaacddbaabbcbdcddaaabaddcaddddacbabacaacdcbdaabcdadacaadabcaadbdbdbcdaaabcdbacbcaabcaccacdcadcdcbcdabbadbdcabbddaccccbabddacdabbcbacdbccdcabcacddcabdbacabaaabaacaababaccdadbbdaaacadbcbadcaaaabdababdaacdddcbbaccccdbabdcdcbcddcdbdccbdccdbccbcbabcdadbcdbccabcbbacdbcabbccadcbdabadbbbcbdacacdddadbabaccdddcbacdabdaccaccccdabddddbdcdaccadbdadddbdacadbbababbccdacdbdcbbddcbaccddcbbdabbccabbabbdddcdcadaadabbcccbbcdcaadaccabdaccbcddcdbcdbcccccbacdddaacadbbcaccdaaaaacdddbacadccabbdbbbabdddddbccabcbaddadbbbbddabbdadbbaaddcbccbdccbdbcdcaadccbcbbbbcdddadacbbcdccaabdacbacbbaccbacaacacaabaabddacccdaaacaadcdbbdccbabbbcddbabdabdcbccdbbaacbcaaaddbabcbcabbcabcabdcbacaaaddbaddcdcddbcdbcdcdcadadbabbadbcabdccbbbbdbcacbcaaadcdbcddcbcdadaddacbcccbcadddaaaddadbabbbddacbdcdbcbbdaccbcbddcbbabdadcbbaabbbddcbaaaaadcbbdacdbddcacdcaabcaacdabbdadabbadbdbbddaabdaacacabadccbcabbabdccbbddaababbdbbadaddaadbaabdcdbbbcaabcbdddddbcbcdabcabbcdcaaddbadabdcdaccadaddcacacacbabbbdbcccdabbdacadbacdccaadcbcddadbcaacaadbdbbdaabbddabcdadbcacaabdddbbbbdddaaaabccabcaaccababccbaacbbaaacaadbcccbddacdcbabdccbacbacbdcacacbcbcbccacbdabbcbbbcdabcbdcdcbdabbbaabbbaddbdcbdaddcabcaaccccbbcabcbbcaaccbcdcbadabdbaddbddbddaaabcccdbbbdbbbbdcdadaddbdaacdcbcdabddccabaabccbbbbaccbbcbbaabbcdcbdbbacbababbcddbbdbccddabbacaaabbdaddacacadadbacbaacbababbbddacadbdacdcdbdacbababdcbdcccaccacacacccbcdcdcaabcdddddadccdccdbccdbaddbbcaddaddbccbcbbacadbbbaaadabdbacacacbbacaabcacbadcbddabcadadbabcbccbadcaaaadaacbcbcdcdcddcbddbdcabaaaccaddbabcbdaaabbbbccadbdcdadbccadacbbccccdcccdabbbccdbcccbdaaccaddcdcdcaaabadcbacadcdbbbcccbadcbcdcbcabdaccdcbdcccddcdbdccbabccdbcbadbacdabcbbbbcdddbddbaaccccdadbdabbcacddbbadbccdbaaadcbbcabadbdcabdadbddcacacbbddacabbabdaadacadcdddcdadbbbccababadacdddcdabcaddabbabcbdbbbaacadbbbdacaddbcbddccddacddaacadaacdbbdbcdaabacbdcbbcbcccdaacdddabbddddccbcbcccbcdcdbacadbdaabdbcbdabbccdbddbbacadccdcdadcbdbcaabbddbbbaabdacabacdbaaccacdaacddcbcdbabbcbdcbbabdcdcdbadbcdcddddaaaaccdccaacbcdbbbcbabdccdcadacbcadcacaddbcadcabcdaaacabbacddbdaddbbddabdaabdccacbcdbbbdcbdababcbcccccaadddccbbbdbdbdcdbbccabbbaaadbddbddbbaaacdaddcbbbdbadaaccbacbcbdcbbabdbdcddaabcbadbcabdbabadbdcacabdbcddabadcccaabacacacdddbcbcababdbcadbacaabdacccdacbdacbaadaacbbccbcbadadbacbaacacdcccabbadcacaacdcdcdbccbbaadaadacabdacdabacacadcdddddcbcbadbddccacababddababcabcdcbcbdcdbcbabadbbccdacaababbcbddadacbabdccccbcccadcbadcdacddaabdaddddccabacbdabdcdbcacaccdaacddcdbccdaccdbcbcccbacbabbbcadacdadacadabacbdbdacbbbadbbbaacadacbdbcbdccbdbcdbddadddbbbdbdddcccabacbacddbdaacacbcaddbbacaadbcbabcbbcdddcbdabdcbaccdccabbcaaddddbdabcbdddbddcabacbcaacdcdbcdddbbbaaabbdcabbdbcdcacddbbcdaababdbbaabcbbcadbdddacddbacaacdccdddadaaaadadbbacacccaccbbbbaabaacdacaddabddaddacbabcaccdbccdadadcccdcdddaadaadcbaadbcabbabdacdcbdacacdcdcacbaaadacbaacaabbbadcddadcbcaaaabcccdaadcbabbbacacacabccdbcbbadcbaabbabdcbaccdadabaaacccabddbdcccdcaacdddbbcdaabddacabadbadccbddbacbabacbaccaccbcbababaaacacbdbdbbacbbaaacadcbccabdddadbcddddcbabdcddcaadcabddbcbbcadccdcdbcdabcdaabbcbdbbccdbbbadbcbcbabdbbaadbbdcbdabcdababbcadcdbcddabcdccaddcdaadcbbcdbcbadabacbbbbabccdcbccacbabdcaccababdcdcbcbbbaccaacbbddaadbbcbdaabbcdbabdbcaacbdbbbbbbdcddbbbdadcdcacadaaaabdaadcacaadadacbcbbcabbccbdacdbdbbbdbdaccbdbddddadadadbaadabdbbabcdbadcaccddacaabbccdbacccabbccddddadaacccadaddbddbadbdadcbdcbabcacadacaadacddaadbddabaacbcdabbdbabcaccdaaaadabaccdccaabdaadbcbadbcdcdcadbdbadbabdbcabcbacdabcdbdcbaacbccbcaddccaacdcdaaadcbdbaccbcbdadabdadbbdbbccbdbccbcbccbadadacdabddbadccbbdcadcaccacaaabcddcabbabbacbbdacdddbbaddadcdaccdbbbdbabdcaaabcbadbaaaadbcbabcbccaaacdbcaabdcaabbabcbcccdabcdacbccdacacaaddaddbadcbadddaddcbdabdddabcccbcadbcddadbadbdcdabcdbcaabcccbadcbcbcbbaabcbacdcccababbcabdbddaacaadaddccbdbbddbdcabddadcbdcaadbacdcbbcabdcaccadcadbbabcabacbbcabacccabadbdcaaacdbababbabcbcbaccbbcabcaddaaacdcdbccbcacaddcaadbabdaadbbadabcaacddcbabcacbbaabbaadbdaadabbbcbcccadbcccbcbccbcdbcabbbcabbdddbacbaadcbcccccbccabbadbbbdbbcdabaaddcadaababccdbcabcababcddbccdcbdbbacbadaccbabbdcddccdbbcaacdacddadcaaacdcddcddcbcbdccadcddbacddadaadcbbabcdadbdcbadccabdddcdbabbbbcaacadddabddacbcbcccbaaabbbabbcdabadaacaaddcbcdcbbcadbbdbacddaccbbcacadcbdddaaddabbdbdaabdbbcabddccbabaccbdbbbbaabdcddbdbcdacdabaccbccabbaacacdccdaddcbaacbdcdaddcbabcbbddaaabbdcdacadabdabadbcbddbcbcccdcbdabaccdabaaacdaabbbcadcadbbbdcbaacaadaacbddbbbbdccbdcbbcdcbddddbcbbccdcabbbcdbabaddadbdacdddbdbcdccdaaacadcacccbbcccdaacbcabbabaabcbadaadadcaacbadcabaacbdcdddcbbbabbbdabbabdbcdcdccdcdcacdbdddaabaacdcaadababcaccadcccdbbaabcacddabcaabdcbddcdabaacccddbcbcadcccaabccdbdbbacadacbabaaaadcbbddbdadddbcbadadddcddaabaccbbdbacadbdaabdbaacadcdbcbcbacddadcadbacababbacddbcdabdabdcbccdacddadcadcccbbadaabbabadacbbadcdaabacddcdbabaaddacadacacdacdccccababbadcaaacbbbdcdbaccdbbbcdabddbccbbadbccacbbbbadbdacbabdadcdbdddacccbbdccccabdcadadaacaaaaddbcdcbaddddbcacaaaadacabcdbaadcddbdbbcacdbdaabbcdbbabbcabcbcccbabbccbdadcbaddcadacadbcdcbdadbcbcdbaacbbdadccacdabdabccabbccaacabddbcbaabcadccadcabdaacaadcbabccbbdcbacbbcbcacdcabaaabcdbdbcadddaabaccddbbbddddbdcbdbbbcbdcababdcbbcaaddcdbbbcacbbaacadbcdccdacdcbbbbcdbbdbcbbabaaacbdadbddacddbdddbbbbdbbcbbcabaacacdacccbdcaaacaaddadddbddcaaacdbcabdbcabcbdbaabdbbcaadbacdcadabaaabbbcbbbcabddddacdaaccbdbaccdbabaddacbdddbccabcabccadabbdccbcacbccaaccadaacbbacbadcaaacddbbbcdacdbaabcccbacccbbbcaacbabcbddadabccabdbbdbaddadabdbddaaaadcbdbcdaabdcbbcddcacacdadaaddbdabaaddacbcabdcacaaccbcaabdbdbcacdacccbcdcbadcbcccabbccbcaaccaadbdaabacdaaaabbdcabdcadcdcbbddbccdcbbbdbdacdbdadabcaaccddcbadacddcabbaadbbcacbbbdaacdaabdcbbbbaaaadbadcddcdabcaaccccddaccddcdcddccadbcadbbdabcdbbcdbacbbaaadbbdcddbbdbbdddaddbbaadadbcdaadaaaaacbabacdbcbbcdaadcacdabddbcdbcacaabcbbbcbaccccadaababbcabbbcbcbdacacdcdaadbccccabadcdccaadcabaadccdbabdbdcabbddbaaaadcbaccccccdabbdcbdadcbdadaabdaaadbbabbdaddcdbddcacdbbacdaacaabacdcacdbbdcdaabacbcdbbaacdbdcddbdbcbcaabdddcdbbacbcbdabaadcbacdcbdaacdcdcbcbababbaadbadcbcbdcccaddbbddadbcdaccdabcbdbabdacaaccabcdccdbbcdbcabdaacdaaadbcccbcabbbadcbbacccdbdcddadbcdaabdcddcbdbdadcdaaaabbbcbbcacdcdddbbccbbdabdaaabbaccdacbbaabcccaaddaaadabacbbdbacccacaabcdcabbadbbbcbcdaaddcabbbabdddbbbbbcabccbcacaaadbbbacdcabbddccccdccdccbcddcbadadbababbdbbdadbaacaddaddccabcbddadbccabdddaadbcacbcabdbbcddcddddbccdcbbbcddcbcdabacdcaaacacbadbcdadabbbbaabcdbbcbcdabbcaabdacaddbdccbdcddcbdacbdcbbcdcabaaddbdbcabbbdbadbdcaaddcbbbccabcdcabbadbacbdcdcdcccdcdcbcaaadbacabaadccdacbcdbcdbbcaabbbcacabcdccadabcdccaabaaddaddcccbaccbbdaddadaacdcadcbdbdccabbaccbbdddcbdadaccabdabdacacdbcdcccddbcdbbbccccabcbabaacddcdbbbdaadcdacabbadacdbaabccdcbadddabdcabcbcbaddcadbbddcdddbcbccbbdcacbcbbccbcbdbcdbdbbbcdabdcaacdddcbbbbddabbbabadabaabbabdcacdcdaadababdcdbcacbcdaddcdddbbdbacdaaaddbaabcaddccacdcbbadacccdaadddccabccadaadcaaddaacbbbacdcabddacaddadbcacdddabbaaddabdbcbadbbbacdabaacaaccbcccdcaaaddccbcccaddaaaabadbbcddbdbcdcabbbbdbcdacacdbbabbcaacbabccbcddcbdbbabaaadacddbaacdbdccabddbdbadbabcdacdbccabcdbdccddbcddabdddcddcadaabdddccaacadcbcaacbadbdadbddddabdbdcbbdadddddadbaddbbdcdcddccdccdbabaaaacacbbaabbbccbacdbdacdacbdbdacacabdacbcddccdcacababbcdaabbcdababddbddcbdccacaddbcabaacacbbccdacaacbababcdbabdbddddbcaabadddbaaaacaacbcbadcdbbabcabcbdadccddbbccaddabdabcbddbadcdaddbdbbdcdacccababdbdbdbccbbcccccacacbdcbdadcbcdccacdcabcaacacbcdbbaddccadacdadbcadbbdacdbadbddbcdcccdaddbaccbbbcadddddcdbacddcbabadbdabdcdabbabbcdbbbcadccbbdcbaadbadbbccdddacbcacacbacbaccabcbbccdccaadbdcbbdbddccbabcabacccdccdabbdabcdccadddabcdccdaaccadddddcbdcabcabbdcdddcadbcacadddcaaaaaaadbaadaabbcddaddcaacabbcabddbcabaaadbdbbbdbaccdbacdcbcbbaaaaabcdcccbbdbbcaadcbbcabccabbaccaaadbcddbbdddddddcccaccadbdaacadaccdcaabacabddabcbadbcbbcaadbbcdcadbbdcbcbbcbbccaaadddaacdabdadcacbadaddaccdcaaadbacadbbddcbacdccbddcacccaddcaabbaddcbabdbaccbbbbdaccaaabbbbacbddaaacdcdbddccbbccbbbabddbdcacdaccccbcaaddbddbccacbbadbdcdabbbdccadbdddadacbbaccbddcbdccbadbaaabdbbcacadadbdababdbdcdbbbaaadbabcbbbcaacdccbbcadcabcddcdacbaccadccadcddabdbbaadadbbcdadcbcbbabcdabaacdabadddccdccacbcbaabdacaccdddacaddddabbdddcbcbdbcacacbaaddcdbbdcabcdabadcdbaadddbdacdcbbadbacdacdabbabcaddcadbcbaacbcbbdbbbbaadddbbaadcdccbdbacdddddbdacbcadabcccbdabdbdaabdcadadaabaadaacacacccabbbbcaccbccccbacdaacadabbadbbcbbacccdcacabbccbabacdaaaabadcbbcbacabaddaccbaabdcadabbabbcabddbaaadacdcbbaccbbbabcaabbbacdadaaccbbabcaadadcadcaabdbbabcdacaaaabaddaccdbabcbbaaadddbacacccddcdaddddcbabacbbcccabdddbccdcbaadcbbbbbabdbccbabbccddbdacbbbdcabcbbddcacddaddacccbbdbcbbdadccbaaccddccbbdbbdaacaacbccccbabcaadadbabbaddbcdacacdaacbdabaacacdcdacdbdddaaaabcabcccbcdbbdacccaadbdbddcabbbcdbdccacdbcbadcbcdaddabddccbdbcbdacdacccbabdabbcdaccbabdcabcdcbacdcdbcbdbdcdabcddadcabddddbcddbacddaaaaddcccabccaadccadaddadacbccccddbccdcbbccbbadabcaccccacddbdcadcaccdcdbdcdbdaabaabcdaddbbccccaadabddbcdaaddcbdadadaccaccadccddcddbddcbbbbdbdbbbdcdddbbcbcbdabbbaccdabbbdddcdaaaadddbcbcbbcbadbaaaabcbabbbdacadcabbadcaddcdbaddbcbddbdcdaabadaabababbdabdadcaaaaadaacbabacdacdbbdbbddcadbbbbddddaaddabdbcdaccdcddcbcbadabbcabdadddccccddaddaccababdcdbddcbadcaadccbddcddcccdbbdaaddbdacdcbcaccbadabcbbbabbcababdcdaabbbacaacddcdbddcbddcacaacddbdddadbdbacdbadbabbacbddaabdaccbbdabaccdbdacbcadbcadbacabcdcacbcaababbacddccbaaaabbacdadbacccdabaaaddadbbaabcddcdbbbbcdcadbcddcdddaccaadacdccadbcaadadbcadcaccbddddaaaccbdcabbbdccadbaddbcaccdadbbdcbbadacbbbbcdbdacbadadcbccabadcbdbabbabadcacdbacacdbcabdbbbcdacdbddadbbcbaaaacdcdaccccaddccadbdadbccbdbccaabcadbdbcccddbbbccbcacaaabbabcacbcccabcbddcbabccdbdccaccdcdaadbcdabbabbaabdadabccaabdadcbdcbddbbdbacdbcaacbbacdadddcacdbaacbaaadddbabcbdcccccacaddddabcbdddcbbadbbcdaddccbbcbdcbaaddcddbbbdbddcbbcadcbabccdacbcdaadbbccbbcaaccadacabdcdabcaccbbbadcdbdaaccbbaadcaabbbcbacacdbabdcadccadcbbcddccbdcabaddccdcbbcbaccdacdbaadabdbaacbadcdaaddabaaacbcdabbadbdacadadaacabacabbccddccbdcbcdcdadbbdbbdcdbcbbbcacacbbdabaacacbaacbdbdadcdcdbbccabcbccacdbbabcdcbdccdacadbbbaaadccbdcaaccadbbdbbccddbdbacbddbbdcadcbdcddddcabdcacabbaacddababaacdbbcddccbccacbcacdbbddddadaacbbbdbcbdcbaccacdcddadaccadacadcbdaaccbacaaabbbbddadcddcacaddcabacadccabdbddaacbaccaabcdddadbcbcaacdbbbddbacabcdacacacadbbccdcbdddacacbcbccabaadbcbcdaaaadbaaacccbaccccdacaadbdabaadbcdadacbcddbbcacdcadabcbbadabdcdbcccbabbbbacaaadcbcbbaacddabcabaadccbcbdacbcdcdcaccbddaababdcbcbddbadaaacadbdbabbdccadadabbdaabaddcbbcdabdcbcbdcdbddabbcbbbbdbdbabdcbcdaaccacdabbacaadabbbaccaddbadadbdadcdacdbdacdbdaaaacbcdddaacbdabaccdaacaaabadadddbbdcddbcbcacababbbcbbccbdadcbdacdadadbaaadaccbabbcabcccabbacbccacdccadaaaadaacddbaacccbdadbcaadadbcdcdacaabccbabcbbcdcdbdcdbddbdbaabccacdccdaccddcdadcaacaddbabdcbaddaccabcadacdcadabdbdaaddccbbbcaacabdcdbbcdabcdcabcaadbbbaabccbadddbcccdcbbabbaabccbabdbbcadadaaadccdbaacdbbabababbbbdddbcdbdbbbbadcbaaccaaacdcbccdbdaadaacddcacbcbcbdcaccdbaccadbaacaacdadbdcdbabaabbbbbdadadabbcbdcacddddcddcdcdabbddaddadccaacadcdcdbccaaabbdddbabbcaacaacacabccccdbcdcaacaccdcadbdaaccccaaadaaaaccbbacdadcbdbbdcbdccdbcbacbabbdbaabadbacaacaadcbbcbccdbadaddbacdaddcabdacadaadbbcabdabcadcbcdabbcaacbdddccabbcbabdddaddcccddaadbcbddacdccdcbbbbabdbbdbbbcabbbcbbdbcacbdabadbdbccdcbcdbacdbadbbbbcbbbddcadbdaaddbacdcdbdccabcdacadcaabaaddabbacdbbcacdacacbdbbdbddbbadddbdbaddbcacdbcabbcdddbcdababbaadadbcccbbacbbccdacbcaabdaccbacdccbcabbcbabccbbbadbadaddcbdccbabdaaadabbdaddcadbcaadacbadbbcddacbcacacccaccbaababdbbdacdbcdadcdcbacdbdabcbaaccbaccdbabcdbbbbcaacdcadbcddabccbcdbdcbbcababcaaaadddbbcabcbaacdcdcdbdbcaaccaccdacbbabdabcadbcdbbadbbdadbbbaccbcdadadcbacdbbdbdcccccbcadbcdadaddcbbadbdacacbcbddcbabcbabcbaccadacdbcccdabdacbdadaadcadbbacdbdccddcdaaadcabaabbbcbababaacacdaaaacbddddadadcccaaabcdcccadbddbbdcaacbbbabbbaabcaadabddcacabbdadbccbacacbbadbdaaadabdcacaabcaacddbcbdddbdccacadabcbddababcdaccbddbcdacacbdaacbbacacbcabacbdaabbacaabcdcbbadbcabbbddacdaaacacbbaaacdacbdaccdbabbbcaadbbaacbbcadacbadababacbcbdaaccdabbabddadbcdbabddaaaadabdaacbabbaddcadcbaabdcbccbdcdacbcbbcabdbbcdacadddcdbcddcdccbdaaadbbbdcaacbdbbdccbcbdbdcadcbdcdcdaadaabbabcdabadcacadaddddbadccccbcacdabbcaddaaadbccbdbaaddddccabcdcbbcdabacbbddbcabbcdabbddcadccdaccbdbaabcccdcbbccaadcadcabbdbbaabbabbaadbbddddaacacbcbbcdacdaabcababbddcdaaccadaacbccdbbcbccbbadcbcdbaadddbcacadbacbdbdbdadbbdbaaddaddcbcdacbcbdbacabcccddccdcbbdaadabdaddcabbcdcaaabcddbccbabdaabdbdbdaadbabbacaabaccddaaddbabdbbabcbdbdddaaaddccbbdaacdcbcacadbccdabcbbbbddaacabdaaacaabadaddddccaadcaccccbdcccdbccacaccbddaccbabadbbcaabccacddcccdbaadcbdbccbacdabacbbbcccaaabcaaccbadcdbdcbdccbbccadbccbadaddadaadaadacbcabcdcdcccacdbbcddcbbccddbdabdabcdddddccacbaabadacbcaaacbadbcabbdcacdcdbdcdbbdcacdbcdbcccbaddbcddadadddaddbcdcddbdccdbbcabbbadabddddabdaabdcbbbddadcaccadcbdaaadaabbcadabdbdaabbbadbbbccbdbdcdadbadaadbbaabaccccbbaabaabbaabddadddaccccbddbadbcabbabbdcbdabbccdbdcaadaaacddbbbcacbddbbcddcdabbcbcdbdbdaccdbcdbadbbcccccbbbdcdaabcaaddadddccabdcacdccbbdaddccabcdacbbaddbcdccdadbbddaddaaaadcdbddcadddcadddccabdbaabcdddcbdcbaabcbadaaddacbddcbbdaccadacbababddabdacddcdcddcdbcccbcabbcddddbacacdbddcbadcbaaddbdcddaadbbadcadabcbbaccabadbacddcabbcacadbcddddcbbdddccdcbbaadcabccddddbbcccadccacdbadbcbccaddddddbabaaccabbabccabaccaddcdabccbabdaabdadbdbcacaaabacabcbaaaabddbbcdcbcbdbbcaccddcbbccbdadcaabdbaddabdcbadbbaacbbbcccabdaaddadbdababacdbdadadaabddacdcdcabbababcdadddcadbabcbadddcbdbdcccddbcbdddaddddcddabcacdabcccdcaaccbcabaacbbdbdcbbcdadcaddbcbbdacbbcbcdcadbbdcbccddbbabaccbbcbadbddcdcddcaacbdaaaadbccddcbcaaadbdbddbabcdbbaacaccabaccdacdacabcacccddbaccdbacaabdbdcbdabcdbadcabadabcbcccbbcbddccbadabbbbaaacbcaccbbabdbbcdbbdbdbaaaadbcaccbcdadcbcbaabaadcbccddbdaaadabbbcabacdbbabcbadadbaadcacccbbdcadadbdbbdbabacdaddccddabbdbbdcbbbbacaccdbbdaccacddddcbbaacbcabbdbabcddbabaaaabdcbbbbcccdbcdcbaaaddaddbcdbaaabdbcccdabbdadabbaccabacacabdacaddbddbcbdccadcddbbcbbcaabbacbdcdbbabbadbccbbbdbdbdabbadcacadbbaaacabbdddabcddcbbdbaddccddaaccaaadcddbabdbccaabdadbdabbbabdcabcbabdcbdcdbcdccbcabccaabdcbccdddabdbbdaadbacbdcddddbcabbabadbcbdcddacdbcabbaddbcdcbacbbdcacddadcdabcaddddbcddbddbabaaddddabdbbcbabcdacbbbdcbacabdbcbddadabcaddcddaddaabcccaadcbaccabdcaabadddbdabccaaccaacdbccbabaaaddccbcacbcdbabddcddbbcbabacbaaabacacccdccbbcdbccaddbacabccbcadddbdcbdbbacacacacdacbbacbbdadcdaaddcbdcbddcddbcaccccdadabaddcadcacacaadcaacacabdaaadcdacabaddabacddcdbdcdbaabccdcaacdabddaacdccccdcbabdbdaccacdddccabcdcbaacabcadbbabaacbdbbabaacdabcabddbcbcbddcdabbdccabbccabdcdccbbaaacbddbddbdaabcaabdccbcbcbabdddccdbdbbadddaacdabbcacdbdcdbbabccbbaaacacdaddbcbccdadaaabcdbbcbadcdddcadccdbbbcbadbccbcccbaddaaacbbdadcddccdadadacaacdaccaadbacddabccaddabaabacaddadbbcaadcbacaaaddbacacddacdcadacddbdcddbbdadbabcbbdbccbadbabcacbbdacdbcabbbacdaccaddabacbbbcbbaaacbcabacabaaccdbbaadbdbaaadbdddcdcbaaabaddbbadbdcdacacdbacadcaadaddaadacccadaddddaacaccadcabddaddbdcbdcccbacccacabbbbbcbcdcdaaabbdcbdccddccddadcaddddbdacdcccbbdbbadddcbbbbcdddddaccbbbdaccdcbdaabcadaaadabcaccbdbcbdcadcbbdcacccaaaccbdabdbdccadbbbdabdbddbbcbcaadccdaababdbcddbcaaacbacababdaccccdddaadbaccdbabbdadaabbabbccaadddbddbcdcbcababaddbadbdacccbdcbcbbdcadbcbabbabaadddbdbdcccabaadbdacacdddccadaadbaccbdcbbacbbdabdcbacabddbbbaadbaabbbabaccadabcdabddccabcabaadbbcbdcabacbbbbccadcaabdbacdbadbbdcbdcabacddbbadddcdbaadbadcbadcbaabacbdadbbbcdcadadbccbbabbbadbdbbbdadcadabcddbccdadbabacadaaadddbbdbaaabdccbbcbdbabdcdddabbbcdccadccddbdccabadbbbbacadacdbbcacbacbacadcabccddcaababbabaaccabcdbcccbacdbadabcaabdbdcbddccdadbadbcbcbcccaadacacaaaabadbdcccdaacddcabdbbccaacbadcadcabbacbdabddbadbcbcaccbdcbaaacbababcbddcaacdcdadbabcbbbdbaaadcdccdbdcdcbacbbbbbadbdabbcbbbcbbaababbadaabdaaddbdccaaccbdddccccdbabcabbdbddccbacddaccaddbbcbcadddccdcaaabbbdddbbdcddddabcbdbdadbdabdadcbdbbcbdcbaadbdcddcaaccdacdcddcadcaabbddaacadbcabbdcccddbbaaabdbcdabaacaaccdbaabacddababdddbadddbccbcdabacabddcabacdbbdbddbcbbdbcdacbccaaadacaabdcaabddbcababaadaacdddababddbdcbaacdadabcbcdbbaadcbbbadcadadddcddababbabccdacdabccdacaaddcacababccbaadbabcaadcadbaaccbdbccabdcddcddcacaddbcddaddddbbcddbaabbbabbbbbabdcaccdbcacddaadaadaacdaabdadabaddaddaadaddcbcabbcbbbdcbbcbddbccdbabccaaacadbaddbdabcaaddaadcbcdaacbcdaabbabaadcadbaaddccaabacbdddabdccbaaccbabccdaabbdabdaabaddaabccaaccccaddcbacbdcabdbbcbcbdbcdbccccdadcddaacabbcadbdacdacbbdcabbccaccdcdbbabaccacdabdabadadbdabbdbabcbbdbcccbdcdadbadcbdccdccdcaddbcddcdaaabadbbabbdaabdaacbddcbacabaabddbbacdcbbdabaaddcdaaadcadbdbbabacbadbabbccaadbdcdbaabbdbcadbcbbcaabdbdcdbbabdadbbcbcdcdddbdababbacbcbbbadabdaccbbbdcaddbdbcacadddcdacbccbaddbdbadbacacaadcabbcbcbcdcddbdbcaadbdbcdcaabbaddcccbbbcddadcdcdbababdacaacdccdcbbbcaaacacbadddbbbdaadbccabccdaaadbbdabbbcacaaaadcbdcabddbbbddaaabbbdddbdbbdbaacddbaccccbacabbaabdabaddbdaaccdbabddabdcaabacbccadccbbccabbbccddaddbdbabadcbdabcbabdacddcddadabccdddabcaaadacabababbadccacadcddbddcaddcdcacdcdcaccababdcddbacbccdbacdbbaabbadbacccaddbdcdbcaaabaadaddcdbbabadaadddacaaadccdbdcdcdbbdadabacdaccbdcbcadcbddcbccaccacbabbdcbddabcbddcddcadddcbccbcbacaadcbabcadbcccccddacadbdcbbacacdcabbaababdbbbcbcbaaadcddaaacbddcddcadaccbdcdaadbacdcadcaacbbdaccddacdbadcadbadbbcbbdbdccabacabacaacbccbbdaddbbabddaaaddaaacbcdcdaddcccdbbbdccdbaaadaaacbdacacdaabbacacddcbaaddccddadabddbbadaaaddaddcdaaaccdcccabacdbabcaacccbddbadccbbdadbbacbaaadbaadaddbbcdcbcabcaaaaccbcacdbdbdcbabcddddbbcdbcdbaddaccacddcccdacdbadabbcaabbcbddbcaadcdbdaddaabacaccdddcbacaaacccdbabccccbacacbbadaacbdbcdbccbbbaaccbdbdbcadacdcaadddbcacadbcadbdcadbbdcdbcaabadcabdbadccabdadbbbcdccaabbcaacdadbabacadbadadbdbbbdabccaddacdcaddaacdbacddbabdcacccbcdddbcdabccbaadcacacacccddddbcabdaadbbddbaacdddcacbaabbcdccbdcbbbcbabadbdcbccddcbdadbdcbacbacbaabddcbbabcccddbdbdbacccdbbadadbdadabdbbdccaddbcadcaadadbdbdcdbaadcdcaaabbcdccaccdccbbaadabdbdbbdcabdacbbdbcbbbbdaddcbbcadbbdaaacabdddadcddadababcbbcaccbacdabccaddbccdbcbdcddbdabbabccabcdbdabadaddbaabcabdbaaddddbcddbbcacadabcaddaacdccdbcbdcdadbbcaadcccbbbbccbddadadbddaadcbdddaddbddbaddbdabbcaabcbbddacbccdddbdacbaccbdabccccbadcdcacabbbacdbaaddccacaaccacadccaddcbdcbaaabcaacaadadaadbdcbddacddabbabdccbaadddcddbadbabaccdcbadbaccbdcaacbbacbcdcabbdbbcccdccbccadaddbcccdaadaadcbcacdaaaacdabddcbbcaaadcaacabcbbdbaaccbdababcdbdbcadbccabbdbcccccdbdbdbbcbacbbdbbbbdbaccbdcbccbbaabbbcdbdbdcdaddcbadccaccddbdbdccbdbacababbcbddabcbbcaddadaddaadabccbcbcdddbcdabaacbcbbcaccbbdbbdccbaccdcddbadabaaabdcaacdccdcbadaabcdccbbaabcddcbabbdcaaadccaaccadbadddccdcabbbbdbcdacdadacabbdaacbbacdcabdacbccdadaaaaccccddbddadcbcbdcdcddccdcccacbdbdcdcdcbbbdadddcbccacdbacabcacadadaaacddbbaddcbbbccbcddbbabcdcbaccddaacdcadcbbdddcacbabcbbdcddacbacbdbacdbccababddaccadcbabddbacaccbaccaaabaaabdddcdcdabcaddddbadccdbdaaddccbbccdbcaccaadccdbabaaadcbacbabaadddaabdacddcbbadadcdddabaabdadababcdddccbadadcadddcdbbcbbaccccbdcaddaacacbaaccabccadacbbcdbccbdabbbbdaccdabdabdbcbbdccacbcbabdcaddcdaaadccddadcdccbdccabdbbbbdbaabddbcbaaabcdcbdccbaadddbcdbacaacaccccabcddaaaadbddaccadcdcdadadbcccbccccaaacbbdacdabcccbbbbdbdccdbcdbbcdcabdabbabbcadbdbbdbbdaaccbccaccacaaacaccdadcdacdbcccdbcdaaabbacbbcdababdcccaaabbbccccbdcddbdbdcabadcccabbdccdbacdaabbbaddbdbaabbdaacbcbaabcadddadcbccabddaddadabacddbdacbbcccbcdddadacbbbddcaadaaccccdbbbddddbbbdcaacdaccbcdcdbddbbaadcbdddbbadddbcbccbaadabbadcbacbdbbdbabbbbbaccabbbcacbadaddccbdcadcbdbddcaadcabbcdbbacdaaaccababdbdcacdccbdcbadabdacabbcaadbbcaddaaacdcabbbcddbdbbaddbbdddcaccdddaaabbcadddbcdccabdcdcabcabadbdadcbdcacccccacdabaabaadcdbbaacbdbaabcdaaccdbccdaadcaaccabbcccbdddabbbbbcaddbdcbddbdddabdcaadbcdabcabdcdadaabdbbcdbcddadabcdddaaaccacbdcadbcaaadabcdaacaadcdcaddddcbcaddcdadabcadcbbccdbcdbcdaaccbcadabaadcdcabaaaadccdadbacbcbbccccadcbcbccbbdbbdddaddbdbdaabbdbdbdbccadcdbcdbdacdbbbaaabddcbbddcadbbdcccccaaddddcbcddddcdbdbaddddbcbdbbbaacddcccbcbdabcadddcdaccbadcaadccadcdaadcbdccdcdcbbaaabdaddababdccdadbdddadcbcbabaccbaaaababdccabaacbdadadcbaaccabaabaaabbadabbbbdddadbaccabcbcacdbcbadabbdbbaaacccbccccdbcbddbdcdcddcdccdcbbaccdbabacbabcbaccabbbcabcbaabbbcccbadcbcaccbbdababcbdbccacbcbbcddbabcccacaabbbdbcadcdabcddacdbccdaadcbabadccaadcacaccadbcbadccccdacadcaadbadccdbdcadcdaacabadbdbbcddaddabaabadcdabdabdbcccdcbbdcaaadbcdbddacccbcdabcdabbacdadbadaaabaddadcdbcabcbbcdcabdabcaaacbaddcbdcbdbdadaccdbcacadaaabcdccbcdabaaaadbaccbacdbaabcdccbddcccaadacdbaddbacbaadbacbbbdbcdcccbaabcccabdabdcbdcbbacabcbdbcbbcadcdccbabddddbbcabccadcaaacbcacabadacaccddacaacbacadbddbddadaccadadadabcdccbbdbacacaacbaccdaadbdadbbacdcbcccccabddadcaaadadabadbcccbdaabddbbbbbcdcbcbcbaccacdabdadaacbbabbccdcdcaacdbbbacbbdbabcdcaadaadcccbcdcbbbcdacdbdbbbbcbddcdadadbcdcdbbccbbcbdadddccbaaccbbdddbcaadadaaabacacaacddadacacabcabbdadcdbdaccaccabacbbaaabdacdcccbdadddddabcbaacadaabbabbddcbbabbadddcdcbdaababcbdcdadbaacbcdcdccbbabdcbabdbaabdddbbcbdbbddbacadaabcaaddacdbcdadccbbaccdcdbdadccaabadbbbcdacaabddabbabdacccdcdabdcbcbaccabccbbabcbddcacdadbddcadcbabbdbabbcdaabdcddddcbbabaabcddbddbdaccbcbdbccabbabdaccddccddcddddaddacbddddbddddcadcaadccdbdaccdaaaabbdcdccbaacabbaadbcdcabccdadbbbadbbdcdababacdbaadddccbddcccbdddacaadddaaddbabdbddccddacbabbcbabdccabacbabdccdcbcaabbbddbbbdabbbdabdbbcddbbcdabcdbcbabababaccadcaddabaaabbcdcaaddccdcccdbbcddbcaadaaddaaababbaaaadcddaadcaadbdbabcbdaddbbadcbdbbaccadacdbcbbbcccdaaaddccdbabddcbcbbacaadadddbdbabdbabbcbcabbcddccaaddaaaadadaccadcdaadddddcdcbbdcdabacbbbdbcdcababbacdcbdaabbaddaabcdaabcdbbccbacbbbcbdbbdaadbabcbddbaddacdaaaabcdccbbdaccbcdbaddbdddbabccbadabbdbcdadaabdbdcbbdacbddababacbdbdbdddcbcccddcbcddaccdbdbcbddacdbdbdbadcdcaacccbaadbddacbcbddccabccdcacbcbcdddbaddaadabdbdbacabcdcabbcabbabbacccaacbbcaccacccaabbdcabbcbbdbccaabddacbacdbaaadcacbccbadadcbbbcbcabaddaaadacaaccaabbbdbabddbbbcaabdadacacdadacddbaddcbbabcbcdabbbddabadaacbcbbddbadbdbbaadbacbaaaacccbbdaadbadbbddcbccdccdbcdcabaadddccdbadadccabbbcdccabbababdcdbadacadbabddcdcbbabbbcdabaaabdcdadcabbcbdadbddcbdbcacbcbccacdddcccaddbbacbdbdaccbcdaacadcdbbbabcaadbaccdcbcccdaadbbadcdbbcbadbccbcdccbaaadaaabaaacdacddbbbbabdaccbabcacbcbcddabadbcdaadddcddbccdbcadabcbbbcbdaccbcbbdabdcdbabacbbdabbddcacbdcdcdabaaccacddcccbbbdabadadaaaddccddabdabbacacaaabddbbbabcacbaaadcdbddddcbdaaaabacaaaddcdcabbcabbbcbbacbdaddbabbdaadcbacabaaddbcbdbcbddbcccbabddddcdbdcdccbcdbdccaaddabcacbadccaaaaacabadbabbacddcdbcbbbcbaaaaaadadbbcbdacbccadadddbdabdddbbbbdaaaddbabddabddabdcbbadddaabadcdabbdaabdababaddbbdadcaacadccabccdcabadbadcccadacbbaaadbdcacbccadbadbbababaccacdbabdcdccccbbcadabadcaaccdacadbbcdabdcdcbcabbbccadccdddadaabdabadacdddbbbadacaaabaddabbadadacccabacccdbccdadbaddcadadacdccadacabbbdaabbbcabbdddbacddacaaaaacababcbbaabcbcabdaccabcbaaccbcbaccadaabbadcacccbaccbbacababccacbdccbadbabddccabcddddbddbccabdbaddaabbbcabcbcbdbdabacccacbacdbaacbcaccccbcdbbddcaccdabddabdbbbbbbddbcbcdadcacddabdccdbcdbbdaccadbccdaddbcbbbdaabaaabaabdcccbcbacbbadddcabdbccdbcdcddbadcaaadcddbdbccccaabbabcaabdccddacdbbdcabcbcdadbcdcaadcdcbddbbaaadaabbadbbbbccdcbabbcddbadacbdccbdaddcdbadadcdacbdabdddcdcdcdadabcddddcbbcbbcacbccbcadaabadcabacddacbdabadadaadbcdccadacdbbdbcbcbacbbcaaadddbbddcaabaababcbdacaaccdbcadaabbdbcdabbaaaaccbddabcbcbdddbbdbbccbbdabbbabaccbcdbbdbacacbadcaaaacabbcbcccadddacbbbddcbadaddbdcbdadbaddbbcccabaabcbadcbdcbcbdbacccddbbbdbabdadacbcbcadbcdacacdadbbcacdbdabdabaaadcbadbadddbcddccbdacbdaadacddccaddaddcbdabdbaababacccdbcdaacccdcdaccccdbddcbccaaabbadacaadcdcaadaaadabddcacbdaabddccbccacddabdaddbcadddbacdcbddcdbcdaabdaacadadbacaaaababacaaddadcdbdaaccaccbdadbcdaaccbdcabacbbbdcdabdaadacdadcdbdbbbbbabbcbacdacaabcbacdabdaabbbaaaaccddbbbaacbddadacdcbadacdccaabadddbcddcbdaacdbbaccbabdbabdbdbbdbdcbcbbccbdabccdbdadacbbcbddcbaccdcabcbdbbcadccadcacadadcbccdcdcbbcbbbdadaaccddcbbdbacbdaddccabbbdbcbbacccabcbabcdbdbcaabddbdccccadccdbcbdbcbbabddbdbdcdbdbbabaabdddaccbdbddcaacbbdbbcaadcdaaaacabddbcddccadbdbadcbcaabcaabaaabcdabddddddddcbbadcdbcbcacaacbcabbcadcccaaccbacdcadaadacbadadbbbdcdabaaddadddacdaadcbdbdcbacadacbccdaabbadbcbbcdbbaaabcbbbadcdaaadaaadcbccaccbcbbddbcbdabbbbdbadbcbacccaabaacdbadcdddadcaddaadcdaacaaadcdadadcacbdacacbcdaaaccacaacbcdcbdbcbddbaddcacaccbddbaacbccbdaaddddcbdccccaddacabbaadddabdccdcbdbcccdabdaadddbacdbaaddcbdbdbddaadadadaccdbabcdababacbccdadcccaabcbccbabccbcdccbaabbdcdadaabbdcbbbbdccdcaaacccbdddbbcaabccaacdccbbabacbbdddbdddaddcababbcacdbcdcdadbdcccacacbdacbabaaaccdaaacdbcddcacacbdadabbdabbcdccbababbbbdbbdcaadccddccbdaabddbacbcccbdcbbacdcadbacbdcbaaccbabaacbaaddccdadbaccdbcdcdbbadacdcccdbaabacccddcdccddacacbddaadbcdcbcadaddcacdcccadcbbcdddcddaaabbdabcbdccabaccaccbdaaccbddccdcadcddbcbcddbbadaacadcddcaaacccdbdcdaaabacdbdcdadbddbdcaacacbccddbacdddcaddbaccabaabdbcbaacddaacadbbdcacddbabcdadcdacbacdbabaabbcdadacabcbbaccacaadbadabccacabaddaacbdabcbcabbaaddbabbcbdbbcdcadabccadcabdadabbdbacaccdcdddccddbcaccbacbabcdabddbacadcaaddcdbcddbadddabcdcabbdbdbddcabddacaccacacbbbdcdddcbddaaccdaaacbcacbdcddbbbcbcccbdacabdccaaadcdabdbccadaaadcbabccbddbadccadaaadbadabdbcdbacbddbdccccadcdbcddcacabcaabaddcbcadccdcbcabdcbbcaacddabddbabdcadcacababbbdbacdabcbadadbddcdadcacadbcccbadaccddacddddaacdcbaddcddcbadaadbdccdcdbdbcbaacabaaabcdbbbdbbccbbddaacdcbadacadddbbacacbadacabcbccaacacdacbbddcbdadadbadddddbddaaaddabccacdaacbabdacaabaacacddabadcdcbcadbbdbcdacdcaabdacdcabcdcacddddabacabcadaccdccddadabcdbdacdccbaaadabadcbcaccdcddcadcbbdbadddbcccabaccdcaacbdacbabdbacdaadbadbccddcadcbbaccabdbadbdddacdbbbbcbbadaabaccbccbabdacdaccacdaabdbbabadbaacdbdcbbacabdbdbbdbaabbdddadbcbccddbacbcacaaacbaacaccacdbdbcbbbcadadaddbdbcbbbaadbbbbbcbbcbabbdcaccddaccdbbbacdddaabdcccaccccbdbddbbcbbccbaadaacdaddddcdabcbddabddcbddccbcbdcddbadcbadbccacadaacadcbbcbcbdabdcbabccbdbccbadbdbabcccdcddcccccdbdcbadcdacddbdbdddacababbdbdaadaddcddcacadccccbbbadcbadbcdaaabbdddaddcbbcabaabdcccacbcdabcdbbcdcdcaadacbabcbccbcbdacbbabcbbcaddcabddacbddaabdbbdddcbbacaabcbaabbcdbdddbbbddbbabcdbadccbcbddcdadcaaaddaacbaccccaacacdddbacbbabdadcdccabaadacadbbdbdcaddadcadbabbabcbcabdbababdddabbbcbadbdbabccadaaccdbdcbbdddabbdaadbbbcccabdcdcccbbacbadcbdddadcddcdbdadadbaaabacaacddbbdaaacdcacbbbccdbaaaacacadcdbabbddbccdaccdaadacacbacddcbcbcdabaadddadcbacbaacbcbbcbdadcabbcbbbbabccaadddbbabcdbcbbcaabdccbadacdbbdaddbcbcaacccbbdaccaabccccaaabdcdbadbdcdddbabcaadacccaaacbdacbadcbbabddbdadbabcbdbcaacbdddbacabccccdcaddbcdcccdbcccbbdccbdbdbbdabcadccddaabdbbcaccbbdbdabdcbbbdabdabbadaacaadccadbabdaddbccacddcdcaccbcabacaddabdcbcabdabadacccbdbcabaabcdabcdcdaadadacabddabdbddcacbaddbdadabddadccdaaaddbdcdcdaccddcdabcdaccddccabbacdcdcbadccbdbdacdabcabcacadacacbadbacacdadadcabcabbbcbdbabbbcbdaabbdcacaacdbcdcbbbabdddbbdddcdcacdbdcdaabccdcaddcacdccabadddbcdbccbcaabddbdbbdaadcdbccbbcccdcbabcccaacacdcacbbcbdcaddddddadbacacddbcddbbbdadabdaabadacadacbadcacacdadcadbcbbdacbdbbacaacbccddacddcacabadbdabddbcbbaabccbcdcdddcbccbcdcbbacbbcabcaadabcadcbdaacababbbbaaabcbbdbdbcacbaaccdcbadcdbdaccbdbccddbdabaadbbddbcdbdadbdabdcbbbbdcaadcccadaadacbcabbbdabbabaddddddabaaabcacacabaabbcaacccaabdcaccdacdbcbdbdabdddbbdbdabbcdbcbbbbaaddcdbddcdcddadbdacbcbacbccdcaccbcbbcacabadccdbdbcdbddccbcdcadcdcdbadacbadcadbcbbcdbbadacabcadddacccbcdccabbbbcbbdbbaddacdcdbdbdadadbaaadbaacdadaaacdcadbcacadbcdddbadcccacaddcdadcabbccadbcaddcbddcacddaabaddccbcdddaaddaabcaaaacbabbcaaabbbdcddabcabacacaaaaadcbbaddcadadababcdccacabbcdbbcccaddccabcbdccbdcaaaaadcbbdbddccbcbdaadabadadcdbaacadbdbbdabbaddcadcdbbbbadcddccacddbbaacaaabbbcadbdcaaabcdbdadcccbbcdababbccbdadaabadbddbacbaaacddcbbddddbccbabacdcdbacdaacabdabaadbcbddcdddddaccddbbaabcccdbbdcdcadaaaaaacbbdcdccccdbdabbadbbcbbadcacdcbbbbbbddaddbcddddaabbbdbdaadadcdcbdbbbcddbdcdbbdbcbabcbdbbddcccadcccacddaaaaabacdbabbdbaaabbcdcddcdbcccdbcdccadbaddbcccbccdcccdccacbdbcccddcbcbdaaaaaadbbddaddbaccdcccbdddcbbccbbabbdcdadccddcdccaddacaddbcabdbcdbbbadcadccdadabbcacadacabddbaadbbdddbbcddcdadcdabcbdbacbdcdbcbccccbabbcacababcbdbdbaacccdbcacabcccddcaadabbdbbdbcdabdbdcdccaabaabadbcadbcbcdbbcbbadccccdbbadccccccabcddaddccdadddddcdddaacbaddabacbacbdddbbabdbbbcacddcccccaadcadcabaabaacbcbcacabdcdbcdadcabdcbaacdcbadaddadccdccdabdbbcdbcddacacacbccacbcbdbdadabcdcadaddbddbcdbdddccadccaadacddbbbdcdadbadbdbdccdbbadcbbcdbbdbcdabdaadcdadabcaabdcaaadbcaaddcccbcdbdbabaaaaadbbbaadddacbdddbdccdaadaaabaaaaddbcdccdbbdbacdcbdcadcbaaacbbdbacbbbbbcbaacaddaacaadccdccaadacadabaccbacccdacddcdcabddddccbccdcdbbabcccbbadacdcaccdcbccdabbaccddbaadddabcaaccddbdaccaaccaacbacdbdcccddcdbcdbadabcbbdcdbdbcaddbaccaaabbcbaccbbadaccacdaadcbdcbcdcbacadbcacaddbacdacbcabaaabadaacbddaabcbdadbaaccbbbddcdcdcadcbadbabdaadbadcdadddcbdaaadadddddabbacdadaabbcbbaaabbacaaaabccdbddcabcacadcbacacacaadbacccddbddccbddaddbabccaddcbccbbdcacacbddadcdcbdbacccdbabaacdcaadccbddddaddbcccdbacacddcadddccccccbbadadacddabbaccdccdaadbccdcaabbbaacdbdbbcbccadcdacdcbddccbbddbdbacaadaabaabcbdadcbbdcbdaadacaacbcabdabddddcbdcadbdbdabadcbbbcbdcdacaddacbacacacdabbbadbddcbdbaacadbcacbacacaadcadcddbabadbacdbdaadaaaadacadbcadcadbbacabcccabcbcabdcbcbccadadbbbcaabdbbcbadcdadcabbdaaccaaddaadadabddcccccdacbcbcdacbcadacbccbbccdbaaacdaaadbabcbbbccaacbcdcacababcccabcdcdbbbcdbcdadcabcaddcdbdaadbaccadcdcacbbdcccacdcababbccaddcbccacbaccdcbbbdbcdcabadabbbddccdcdcbabbcbadadaabdcddcdbcbaddcdccacdaacbaaccccdabcccbbbcbcdaadcdcddadaccacbdabbaadddcdbbbbdabdbcccbcddddcbdcccdcddbabdccbbbddbbaabccbbacddbdcacacacaacacddaabdcbbcabadabaabbdcccbabcbbcbcbcbcbdcbbaacbdccddbdacdaddbcddaacbdbcaadbbcaddbadbcbdcaddaabaacdcdcabdddddbcdadccdbcaddacbdcabbbbaabdbdcbbccdbadacbbdcdcdabccdabaababaabdcdcbdacacdabccaccbcabcdbaadacacabccaccaabacddaabcadaacaaaacdccabbbaddbcdbddbcdcaadcdcabaccadccccbadbbbddbabdaabdadbacaaabbcadabaccdddbdadcddbadcbddbbdbbaabdcabadbbddbacdacacabbbbcaddabbcbcbabaadbdcabdbdcdbdadddbdcdbdacacacbcadcddcbddbbcccddacbccdcbdabbbaabaabaddcaddcbccbbcaaddaaadaabacccadccbaadccbddccacbabacddbdbbdddbcccbbbbdabddabbbdddcdadbacbbdadcbbdacddabcbdbdadcdbdbcdcabaabdabbbcccdddbabbbaaaadcadcbdbdcdddbcbcdccbcdbbdadcdcbcabbcbabbdbbbddbcbabbbadbbcaccbbbadddcdabdbdbccdaabcacaadcbaadacbbaaadcadaccaaadddcbadccbdcaabbcdbbbddddbcccbdadbbadbcbadadcaabbccdaaabbdbadacaddcbbdbabbbdcaabbdccadcadabcdcbabbacbdadbdbadbaadddbccbbbcdaadcbaabacaddcabdbdbdbcdcabddccddcacbcddabdcdabcacccddabaddaadabacdcddadabbaaccaaaddbdcdddcadabcbdcdcbdbdbadaddadbbadcbbaccaababbbdacbdcbdbdabcdbcbbccdadddcdbcadaabdcdcacbdbddbbdbccddaabadadcdcdbdbaddccccadddccbdaabaddcadccbdccdbdddbbddaaacccbcbaddcbcddcaacddbcbbacddcdcbadaabdabdcbccbdccaabcdcbacaddbabcbbdaddcdaadbccdbbcaaaacbacbdddacaaaadadbcbacbadcbcccaaddcaabcdacdccbccbbaaacbdcbaabddbbdaddbbabdddbcbbdccdabbcbdcadadcbbcbabacacbadcdcaacdaaddabbbcacdccdcbadcadbadbbacacadadbddccdcabccbcadabaabcadadaddaadaccddbdccaddcbdbcaddddbabadbdddbdcbabccaccadcbdcaaaddbaadbbdbddacacacdadccacaadadaddadbabdccbdbbadacccbcccccdabdadbcdddabdcaababcaadaacacbacbcbbccbcbddacbcbcbbcdccadabccdcddbbcddbcdccbccccdcabdcdbadbacbdccdbbadbcdbbdccdddcbdcadcdaadcabbdbdacddcabdaaaadcdacaddbbdcdbbaacbdcabdadcdaccbadcaadbacbcdaacdbbaaabaaddabbbaadddcccacadddacddacccdadbdbccbdbbaccddabbaaacacdbdadadcaadccbaabcaaccdbabdbbcdadbbbcabdabbbdcdaadadabbaacbdbaacdddbcdcadccbadcacccbbabdcbbcbdcbcababcdadbdabbbcaacabccdacbadcdcadacaacacbaccaadcccacaacdddbaccbbcaaaacccbbbacbcbdbabbbddcbccdbdcacaacbbcbaadaddaacdcbabcddacabcbacbbadabdadbadadabbcbadbacdadcdadbbdbacaaddcbcdcdaaccdcabcbabccbbddcbcacbcdaacbddbdbdbbddcacddcdcbcdaabcbbaabacaabaccaadcadadabdcadbcbcbcaabcbdadacbadbbcdcdadabdcdabcaddaaccddadabbddbcbcccbbbccdadbdbdbbdcdbcbcbdcbbbaddabcddcdbbbbbbdaaaccdbbdcddababcccbdddbcbdbdacadbddccaacdbdcbaaacabdaabcdaddbaababdaccbcddacadbdbdbaaaddcdbbaabcddddcbdccccadccdabdcaaaaaacbcdcabadaddacdddcdcdbabbbdcccbaaacabdcadcbbcbadddcadaabccacddaabcccacccbcbacbccabacacccbcddbdcccddacdaaacbdddbccaacabcbbbdbddccabcacaddbcddbdcbccdaaddabbacabbabbcdabadbbcaddaadacabbbcdaadccbabdcacadbccdbacdbcacddaabacddddadcadbadbbdaacccabcccaccaaabcdadcabdaabacdaddcadbdbdacddddaadaaddbcaccbadaacbaabdbcbbccbaddbbcbcbddbcbdaabcddcadbcdcaabbdabaaabbdddbdbcaddacdbccaadababcaacaaaacbbdadaadbdccccaabdbddbccaaaaacbbbbbadbdcbcabcabbccccdbcbbdbabddabcdcddbcabadbdacaccabacabadadccaddcdcbbddaddabbdabddbbbdbaabbacdccaccbbdabcbcdaaddbccadacddbaccaaabacbdcbbcbdacaabbcbacaddbccccddddcbccaacdbbcdbcaabdbccbcabdcbcadcddacdabbadbaabccacccaabccabdbbdacadadadbdcdcddacbdccbddbcdccbabbcddcbccbdcaaacdcabddacbabccbacdcacccbdccbdabccccadccadbadcccdbdaabaabadbccbdabadbdaaabbccbcdbcbbcbdcccbccdcbacbcacbccaacdbcbbdadadbdbdbbbccbadbdaabcabdaadbcbacadcadcaabdaacddcacaabcabbdbcdddacaadabadadccbcbadddadbbbcbaadadbccbdddcadcadcbdaadadbabbadccbadadbaaabdabadacacddbacddcabdbcbbacbbccbdabcaadcbacdddcbadcbbacbdccabccdddabdcbaacbbdbcdbcbdbaccbbabbccbcdabadaaacbadcdabdabcbababbacacdbcccabbdabacbcdddacadcdabaaaadacbacbcbcbdbbdadddbaddcbcdcacbbcbbacadbdbbdbbadadadcacbddbabdbabcadddbdcabdbbbdcaadbaaaacbbcadcddbdcbdbdddadacdabbcbdacdbbadccbcdabcadbacacccccbdcdcbdcccadbcadcccdcbcccbadaccccbaaccbdcddcabbcacbcadccbdbaaacbbbdbbbabdadcacdaabcccaaddaadbaadccbababdcdbbcbdcddbdbcdadabaadddbadaadcbbaacbbcdddacdcbdddacaaaacbcdbabcbddacbaaabaacccbdadbacadbcdccbddacaccccccddcdabaccbbdddcccdbcddacbccbbbbbbccbbbbaaabaddacdacaabdadcbcadddccccdaccacadcbaadbcddabadabdbadcccabccbcdcbaadddacabdacabccccddadbddbddbcbbadbbdcdabaabaddadabdacbbacbbacbabaccdbbbdbcbcadcabcccaacdcbbbdcdcbddcddcdcdbdccbacbbddcacccccbcacacdcddbabacbbbddbabccbbabadcaadbcadacdbdcaaaccdaacacbbdcbaacddbccdcccddbcaddcadabcdaadbaaacbddaadcbdbcacbbcbdbddccabbbcdaccbddbbbddbdbaccaaddacbdbccabccbacbdbbdccaaabcabcbbdadadbadaddddcacadbcadacbcabdbadaaaadddccdcdadccdbaabdddbababccaadcaabdcdcadadcbcdbbbbaadadcacabbadbccaaabbccccbaadbccbcaabbdaaddbdbdbdcbbadbacacadccdcdacacdbbccabaadabbdaddbcaacdadcdabacbbabaccbbbdbdaabaddacccdacdbdadbccbaaacbacbdbbbacdcbaccadadbccbccbaccbbdddcdcbacabbcdadadabcaccbcacabbdccabcccbbdaadbacbabcddaddadbbbbbdddabcdbadcdcbddbdbabcdacdabdadbbcaabddbcdbbadddbbcdbbdadcbbddbdbbaabbbbbddbaaccbbcaacddababaaabdddcacacdddaaddaadcbccdddaabcdbcdbbccbbbddccdbcdcccacabdcbaadbcddbadbacddbdaccdbdddcdacddabacbdccbbdabbdbbacadaadabbaccbcccbadcbabbbbcddcdbabbadbcdadcdccccbcabcbcabacaabbcdaabcbcadbaaadccddbaddccaaddcdaacccbacadacddacaaabdbbcadabcbacabaccccadaaaccdadacbbabcddcddadbbbcbcbbacabbbdcbbdddcaacbdaaddbbacbbacbdcbddbccadcdccadaaaadccacccdbbaccddacabcdbadadcddadcdbbbacbdbaacdddabbccdddaabddccbcbdbbadbdbbabbaaabdabdaacbbbbcdbdcdcbcadccdbaddcabcddabcbbcaddaacdbccaaacaadddcbdbadadccdccdcddcaaabdcccadbbbcaaabbabbadddbbadcaccbcbbacbccbdccdaddacdcdccbbabaddcdaadbacdaadddbcdbbdbcdabbdcdcdbaaccdddcbbdaadacdcaaccbdccbbbacaddcdcddcbcbcbccccdddddccaaaabbdcbdaabdcbbadacdbcbcaccbddcddaaabcaccbccabaabaabaadcdacaabadadbcdbadabdbbdacaabcddcabbbdbbdacbabdcdddaabbadccddacaaacacaabadcbcadbcbacddcaaccacdccbbadcadadaadbdcbbdaaabcadabcccaabbbdcddcdcaddbcabaddbcddcccaaaccadacbabddaaccbbbccbadccbdddccdbbbbdbccccbabddbbbdccbabbbdbacbcddddacccdcbccdddbcabccbdcbddbdaccdddadaabcdbccdbaaabadabacabababbdbcaddcdacdaabbabdcabcbbaddacbcadcacacdbbaaaaaacadccdccbcccaabbcbddaaabddaadacdbdbaadcbdbcaaaadaccdcdddbcbbcddbbadcdbabdddccbadcabbcdadbbcaccaaddbaadbbabacccdadbbdcaadbdacdbacccaccbccbddccbadabcababcbdabddabbbbbdbbccbddacbaddbabcccbbcdcabddbbbcdccacdcadcbbcacdadcbbaadcdcbdbccccbddbcdaaacacccbcacbbbcbcaaabaaaaacccbdbddaaddaacbcdddbbbadbddcdcbbcabaaddacbdbcabcdaaccccabcacbaacbcbddbacccacbaacbdcacdabddbcbccbbcdaddbacaaccbacbbacbbcbdabccadddcbdaacadbbadaabdddadaccdabcdccacaaadacdbabbcddccccabbdcabdbcbacbacbcdaadcbaacddaddbbacbaaaacbcbababdaccdcaaaaadadaabccdadcadcbcadbadbcccddbcbcdcdaddbaabcbbabdcbcbbbbcddcdcabddacbccdbbbaccbdcdaaccacbcbadbaddbcbaaaabccbcaaaaccaacaddbabdcbbcbcdcbdcacadaadaabcabbdccdcdcdaadadbabdadabddaaabdbcdadaccabcaadcbdaccbbabbabdbaacdcdaadbbadbaaabadddbacbdaccdaccabbadaadcdddbcacaabdbdadcaaaaabdbdccdbdbbbcccbdbcacabbbddddcbbadbdabdcaadcbabcdacbcbcdaadadaabcacccdadbdbbdaacdcacdaabdaabbcdcbacbdadcbcddbdbabaaddcdcddbbdacddadbdbbcdddcddcacaaccbddaaadbbbdacacdcacdadcbcaaaccbabbcacaacdaaabacabcbdcbccbdbabacccaaaaadacdccbaddbbdadcdccabbbbbbdbdcdbbabaadcdacabcadcdcbbbabaacccaabccccabaadbaabdaacbcdcbdbbbcbcabbcbdcdbbbacbdcdacdcabcbdbdabddaddcddbccacddabbababccbbcccaccabcccacaacacbabdbcdcacddabadaabcbddadcdcdaaccbaadcacaacadcddaadcacbabcaadbdadccbbbbcdcacccbdabbdbdcabadcdcdcaacadaacdbadcbcdcbcdaacadadcddcddaaabadbdcccddbbdcbdbcabbccdcadacdbdbcdbacdbaacbacbdadbbdbcccaadcbcddcbddcdadcaacccbcbcbdcbacbcdaaaadadabdbccdcbacddbcacdabaccbaaccbcdcbaabbccdccccccbadccdcdbaacadccccdccdbdadbaabdcbbcdbcdcbadabdadcadcaadacdbbaaccccdbdcacccddcbcdbbabbadadcabcbcddaddbbbbdadbabcdaadbdbcabbcdbabadabccaadbaabccbdbbdcdbcbaaaccadcabddcdcbabbcbdbbadacabacbcbbacbbbacaddadccbadddcadcadcbadaddabadbdddcaddcbbaabbddbababdbbbbdcaaccccbadbcbccdabdacdbdabdbcabbdccbdcabbacabbccccbbbadcaaacbdccadcdaabdbcbadbabdddcaccbdadbabdccaaccadadadaabcaaadcdadcadccdaddbcaacacdcddbdadaababbaacdbbddbdddbdbddacadcadaddabcabbcdddabcdcdbacbcbdddddcaccacdcabbddababbcaabcbcdbbaccbacbdadbbcbacdcbccccbbbdabcdabadcbdcddcbdbaadccbcbbdbbabadcabdccaaaabbbccacdbbbcdccbdccccbbdaabcacddaadbdddcabcdcbcdbdaadabcddbdbcbbaadabcbccdcccbbddcbadadbbdcdadcbcdbcdbabcbbbcaacabdbbdbcdcdcbacaaadbccbacdbdccddabaccaccadbcbccbbadacabdbbadbbacdadaabdbdccbcbaacdbdcacaaaaaaddbbbbacbaadbcddbbacbbbdcbbbaccdcbdacbbbbcdcacdadacbcdccddccdcdaabccbabcbdcbaaaadbbdbbbbabcbaaccaadacbbcacabcbbcbdcdbbcabccbcdbbbbacadaaabccbcdadaacbdccadcaabbdcababacdcbaacdcabccccabcdbdbbadbcbdbaadbbdaaaccdadaddbcccbbaadccdaacdcdbaddbdcaaddacacbabadaaacadadcbaadbcdabbcdadaadcdbcddaddcabbddbbdbbbdacbccadddcddbdadaccacacddddabccbcadbddccacdacbdcdbcbbccdcbbbcbbcccdddddaabcdbbdcbcdbccccbbbbbbbbcbcadbabcaacbcbcdcbbdcacbddcabddbdccbdaaddcaacdabcbbaaaaabacbccbcccdabbbbcadddaacdbcaabdbcaccaacdbbacbcadaabdabbbadbbdcdaabbaabacacdccccccccbccabaabbddddaddacdcbccddaaccddbacdbdcdddcbbbbcdbbccabbadbdddbcabdcbdccadccdbbabcbdaadcacccabbabcabccbcdddacabaaabbcacbcadcbbcbddaddbcbadadabbaadbacabbdbcbacabcaddccbddbddabdccdcddcbabadacbcaabababdcadcbdcddccddcbcaacdcbdbbccbcdabddcddaadcdbcacacbaaaccdcadbdbabaccdbbaccbcdadadabdbdbadcadccdbcddcbcddccbddccdbcdcbdaabbccbcdadcdbcddabcddccdacbbdcdccbdabadcaddacdaaaccaabcacbabbaaacbcdabddbcaabbcbabcabbccdbbdadddadcaaacabddbacacbddccbdbacabdaccbdcdccbabccbccddacbdddaabbccbccacadbcbdacbdacbabacaccadbacbbccbadadcbbdddcbbddcbcddaababdcbcccdccbdcdbcbddadbaccddbbbbddcaacdaccdbdbbcdacdccdcacbdcabdabacbabbccbbcccbbccacbbcbcccbccbabccbdbcaacacacddcabcdcdcccbddddbdaabadccadaaaaaccccbcacbbaadbbaacdabaaccdbccdcabbcbccabcbcacdbcdacdabcccbaddbbacccadddcdababdcaaaaddcdcbddadddaddcbcaadbbcbdccbcacabbccbcdbacdcbdaadcccadcdcccddddadbdcbcacbccbbbcbaccccdabdcbbbcbccccaabaabbddcdcabbddddadddabcdcdabababbaccdaddaddaddccbbaccdcbcdadcddadbcbdcbbabbaaaaaabbdcdccbabccaabaabacaabbdddadccdbcacabcacacccddccbcaaabbdddacbabadccdcbaacbdccabacdcbddcbdccaacbdddabacacbccbbadccdbcadadcbaddbabbbbcccacbcbaaccabdabcdbcbddcdbbdaaaaadbbcbadccdbdbddccbcccababdcdadacadaddcaacbbcaccbbcbabbbdccddcbcadabbcbddbbdbabccdbccaadbddaaddadccaabbbabaacbccdcdbbddaddcacbccbaaaacccbbbcddacdcccaadacacacdbbdabbabdbadcdbccbaaddcbccdabcdcbccbbbbdbcacbcccacacaaaacddcbadabcdbcccaabccccdcdacccacdcbcccbbcabadcacabadbccacadabaddbbdcddcadbdbabcabaccaabcddabadaabaacdbaccadbbcaaadddcaabbdbbdbdbdcdabacdadbbaccbcdbadbbaccaddabadcadbdacccbcccacabbdcbabdccdcabdabdbcaddbbbcbbacadbaddbaaabcaccccbcaadbcbadddbadddccadcdcdcdbabddacbbdcadddcabbbacbccdbcdddabadacddcaaddcbabcddabcdbbccdbcbdddcdbbbdbcaabbdbccbddadadcbbadcbcbbdadbdacbbabbacdbabdccadaccacbabbaadccbbacbdccabaaadabcbdcaaadadbacbccdbdadbaaddbbbdcbdbbadbabcdbbabdcddcabbdbbccaaddbdccababacbacbbdadabadcbabcbccdcdbaabbdadbbdcbabccdaadaddcdcdbdabcabaaacdcccbaacdcabcacddbaddbaadbadcaababdadbcacdccdbcdddadacaacdcaabdccdbdbdaaaadbdaabbcdccbdadbadbdcaaccdcccabccdbaddccddaacdcabdabccddcdccbadbbcbbbcccbbabcdbbbdabddaddccbdbacccbaaadcccacbbdbdbdbcdabddbdddabcabdabcadadbbbcbabcdbcbbcccababbcacbdbbdbcbbccaacdcaadbdcabcccccaaddaacbdddacbaadababbcbbaacdcadcccdbdcccbacdaccacaccccaabdcccbacbcdcdbaaaacaabadaabcccabdbadcabccaadbadcdabaccaccccdcacbcdbacdcacdddcabbcddbbaaccbcbabddddacbdbdcaaacaacaaddcadacababbddaccdadbcacccbcddcbbdbcbccbbacaabbbdddaaabbcadcaddcbcdacbbbddbcadbdadcccdaabccdbcacdcbcadcdcbbdabbbcabbaddbababdddacdcdbaadbcabbbcbaaccdddbbbacbcacccdcbacbbcacdccdbaddddddcaaaadcabacbbdbadaaadadadbaaadabbbcacdabaadbddbcadbadcccadaaaaadcccdccccbadaccaccadaccdbbbabcdbcdbbbdabbdccbdcdcdbbbdaddcbdcaadbdbdabbbbaabbaaabbaccadccddcdbbdbbaccdbdcbcbdabaacacbaccccdabacccdaddddabdadcaacaaacdbdcccaadccaaccddaacbdaccbadadcaacaaadcbdabdadcbabbccddddadbdbbacdaccbccdbbdbbcaaabadcdcddccadbccadbdbacadcbbdddbcbadbacdbdccacbcbbddbccaadbadcdbbdbbbaacddccdbabdbabaaaddccbacacddccdaaaccdbccbcddbadadbcaccbcdddddadcdbacccbbdabacbccdcdcccbabacabcdaccccdbadbcccbdddbdbbbcbaaacaaacbdcccccdbdbbccccdbccbaacabbcaccdcadccbdacbcadbcaadbbdcbbddcdcccaddcddcddbdbabcadbbbadcaaabbbabbadbadbcaaccbbcbdbdcaaadbbccdabbcadabaaaccccbbbdcbbdaadadaddbadaaaabcdccccdacbaabccdbbdbaacaddaabacccccbbbddccabbacdcdcddcbbadcadacddcdaadcabbabbcdddaaddcabcbbcdadacdbaacaaacbbbabbcbcabccadddcaabbdacadbdbcbaccdbcbcbbcbaabbccccbcbadbdddcdbabcbbcbbbbacbacccdbadacbaccdbdcbdacbbccacabdbcabddbdabadddacdcdaabccacaadddcdcdbdcdcdabaabddddaabbdbabbdbdaaccccaccbdaabbbbaadccbbdcadabcdbbbbdbccacddbddacbacdabadabdddccdcdbbcababdcbbdabcdbddcacdaddddccacaacadbbdabcdacaacbdababddaabdbcdadacabdcaacddbbaacbbdcabadaacabcdddcacbbadcbaacbccccbccddbddcaadcddabcadddbbabcdbcdbbaadbcbdabdbbdbdccadaadaadcbaadbddbcabdcacccaccaabdcdcaacdcbbcacaabdbaacddccdcabcaadddccaadbbaccadcdddbccadabdbdacdaabbbdbcabcabcdbbdcdbcaacaccbddbddcbdbcaddaadcaadbdbadbcdcccabbbddabaddddaadcadaabbdbcccbddcdbbcddddddcbaadacaabbcddaacbccbadbabaccaabaabcddcddcddbbccccabbdbbdaccabdcdbbadabbcbddaddadcacdadbbcddbbccbbbcccbcbdbbcdcbbbadadcdccdbbbdcdcabcdcddbbddbcaaabddddbabbbdccacbbddbdabaccddbaddcccdbadbbcaaccbaaddbcbacbdabccbbcbbbbabdaababddadbccbbddbcadbcabddaadccdcabbaddabccabcbadbaadcbaaabdadacdcddadcadbdbdccdabcccaaadcbdbacababcacbaabacbddcdcdccccbadbddcbbcddaddadbaccdbbdbadcdcadcbbbcbabcbbdcabdabaabdacacacdaadbbdcdbbdcbdbacadbbadbddbbdddbbdaabaadadabbddaabcdbddbcdcabddcbabdcbcdbacbaadcddadccbdddccabdccddadccccdaddbaaccbbacbadcacadbdcbdaccacacbdabbccabddabbccbabdcddabadadddbaccccdddcabccddcdaddcccdaccccddbcdabdccadbaadabddabadaccdddbccababababcdaaddacddadbddbabdbbabdacdaabcabadbaadcbcbbadbacabadddababcabbdddcbaababcdcccaabbbdbbcdacbcbcacabaccbccabdbdbddddddcdaaccbdbbdbcdbdbddaddcabcdbacccbcaacbbacacbcbbdccddcccadaaadbbbcbdaccbbabcbcbbddcbcbccbdabbadccbdacdbadcdbdddacbdcdaaddbdbcbcdbcdadadcadddcbdddcadaddccdbcbbddacbcaddbbcbaacddbaadbdcbadbdbdbdabcdabcdddbcbbbcbbdcdcdcaaabbabccbdccddccccccdccbbcbbcddabddbccaadbaccbdddddacaacbbabacadddbaccbcbcacdbdcacbddaacdabbddccddcaddadcaabbdbaacacbccacadcabdcdcbbbaabbabababbcbbcddcacdbdcabddddbdadababaadaabdaabadcddacabbabdaabddcdaccbbbacaddbbcbdcdabccdcbaccbdcdbccdcadcdcbbcaaacabacdddaccdbddbdbdaacbbadacbdadaabbbddddaabcbacdbaadaabbdaabdacacbbcccccbbbcbcbdbcaaccacadcccbbccbababcdcbaaacbdbdcdccccddabcacdbbccaadddadaadbbddcdcbaadcccdddcdacaccaaaabccaacbddacbdcbdaaadbabdcbbccdcaabcdcdcbdbcbdcbccdbbcddcdbacdbddacaabcacddbccacddbdabdbdcbbabcaddccbbcadabdbcacabcaddddaacabaadbddcbccdbccccdaaacbdcdccbccacabbcbdddccdbaabcacdadbbdabaaacaadccbcccbcbbacbbcdabbacbdbbacdccdadbadbbccbdddbbbcacaabaccddcdccbbbbbaaabbdbaccbaabdccbdadbdacaaacbbcaacddbadbcaccdbdbdaadcbadcdcacdccaccabbcccbcacaacabdbbbaddabbbdccddcaacacdbcbcdbcbbdcbacbbadbbaccbdbcadbdaaccccddccabaddaacaacdabbbdcbcadbbddbdddaabababaacababbddddbdbbadddacbaabaadccdbcbaaacccdcbbcdbbaabccdbdbcbdbdccabadabbadcabcabdcbcdcbbccadcabdcbbabddcacababacaaaccadacabbacacabcdcabccacadbcccddddabadcdbaabbbbaabdaadacdbcdccbdbacdbabbdcacdbadddbaccbbcdabaaacddcccbadcabcbbadbdabacdcdadbabbadccbbdaacaadcaddaaaabbabcbabaaddbbbcaddbdddbcbdacacaadddadbdbdbbccccdbdadbdbcbbacbadccbdacbacdddbbcbaacaadbacdabcbccbbadbbcaddcdccacaaddbbaadccdabbcacdbdaabcadbadbcdbaabcccaaacadabbabbbdaabcbabbdaaccbddbaaadbbadcdcdbaadadddadbcaababaddadbcccddccbcddcdacdaaacdcccbaaacbabcbdcdaabaadaaccbbbaabdaacbbacbadbadabcaccbacadcbbdcdbabcbadddaacaccabddabadcbdbbdbbdbdaadacddcbcdbbadbcbaaadbdaccbddbcaccabdcaacaabcdabbacdbdcbdccbdddddcccbabbadbddabbbbdbccabbbbcbacddbbabacaccdaadcadadacdcdcbdcdbdcbabdcbcccbcdaaaddcaacdbccadadcbaadcccdbadbdbbcdccbcdddbbaccdddabbdbcbbbbadbbbbbddaabdccadbddbbbcadbcdddbdadccccbccadcddbdcdbabaadccaddadbadcdddddabbbbacbaadbacaabbdcaadddbccdbacbabbbbccddaabdabbccbcbbabbbbbcbcccdbdddaadaddbacbcbbdaaadadaacdababcbdbdcbabaddccaabddcdaaaadccaaaccdbaaaddbbbcbcbbcccbdcadddbdccbbcdcbcdcddcbdadaabadcacadcbdcbbcabdddadbbcaabbdbcdccaadaadbbccabccbcbddcdbdddccaaaaadaccabacdcbdaaadaaacadadbbaaccaadacbbaddcdadaccacbacabacadccacbdcdddabaccabbadbdbcbaddadacadcacacdcaacacadbddcbdbdccbdcddabaaaddccbaddcbbbcbaddcacadbcdcaacddbacacabdbdbcabcdaacabcccbdcacbacbcdbdabdaaadcddaacadaddbbcbadcbcdbcbadbccadababadddbbdcaacadaacaabaddcdbabccddcacbcdcdcbbbbcbbbbddbdbbacdbdbcababcdcccdacbccaacabcaadcbbcdaadaadacbbdcacdbacddddabdcaabbdaaabcabadabddddbbcdadbbcdbbaabcbadccdcabdbbcbbacabbbbbcaaacacccdcddbabbaabdbcbdabcacdddcddbdabddccddcbcbdcbcbdadacbdcdcadccbacadabbaaacccbdddcaddcadcdaccbacbbccdaccdbbadaaaadccaabdacbcdcbdbcbcbadabaccabaabdbbadacbcacaaddabdbddbdbdbbdababbdcdddbadbabdbccadaabbbddcdadadacccdbcdacdbcaabbbcddaccdddcadcadddccbbdbcdacdbcacdabbccbdaaddcacadcacbabacdaaccbaccabbbddccadddaccdbbbbbcdadabccdbadcaaabcbcbdcbaddddbbcadbbcdbadccdbddcbbbbbdadacbdacbdcacadcdcaabddaccacccacdacbdcaadcabadcccadbddaccdbbbbabcddacaddbcdcacddcdbdacdadcdadbcddbbadbdbdcddbcaaaababbdaabbcbacdadddbcbcdcadccbdddacccdcbcbbddbabcbcbaabcccdddddbbbaacdccbcccadcbbadacddacadabdbbdacacccbaabdcdcbbaaccbcaabbabacdabdbaadbccbdabdbbdcadcddcadadadbbadaacbddcabdcacabbbdcdbdcbbadcdbcaacbdddbdcbbddcdbdcccdbdcbdaacbbbcbbaadacddabccadacbcdcbcccadaabdaacacacccbadacbdcadbbbaadaddacacadadbbacdddabbbacbbbaadddacacbdaccddadbdbdcacbbabcbacbccdccbbaacdbabdabaabdddabcacbccddbabbaadbdbcccadcdcabdbabddddccbbaacacccadcdadaaacabcccabbabcdaccdbcbcddbdbaddbbdcbaadbbbaddbdacababccdbdcdabacacaacdccbabaccbdccaccadcbcdabccaaadacbdaddbbbdabddacaabbabdacacdbacdadcdcdcaacddabbdcdccdcaacdaacbbccdcddacbddbaacbadcbdcbabbbacdacbdcdadaabbdaacbcbbbbbaddbccbcbbacaabbaacabddcabaccabadabdbcabadaaabbdadaacabcacdadabbbbaacbbdcaaadabccabcacadaddbbbdccbbcabadaddddcaccdbbdabadcbcadaccdbdcdcdcdadcdcbcaaacbaababaccdcabccdbcbddaddbccdbcbabaddcbcbaccbbacdadddbaccaaddbbadabbbacbabbbcacbaaccdddcadccacbcbdbacbbddccbccddbbbbbacddccbbcacacdbbbdddddaadcccbbdcaacddbcbacccddabcbbaaccdabaccbaddacadabbadaaacdbcacbdbcdbcaaabdbddcaccbcbbdabaacbbaabcccbdccbccbdadacaacadaadcacabbbccacdaabdbccabbddbadabdabccbbdbaabaddddcdcbadcaddcadcaacbdcbdaadcacaccaccadbcbcbbaacbdccdcabdcdbabdacbcacaadccdbdabddbbcacadababccdadccdbcdabadacabccaddacbccaabacdabbdadccaccdabaadddcbdcbcbbdcbbaccaadcdbcbbbdbbdaaccbddaadabdbbcacabdaabcddbdaaddacbacbcbbaccadadcdaabaaadbbcdccadbdacccccaadbabbabcbdcbcaddaccbbcabcbcbcabbaacbcbbcddccadbdaddadcbadcbaddbccaabddabaabbacbcabccbabdaacbcadcbaaddacaabbbbbddbbbadcacbadbbbcbdaccaaacaaccbabcccddbbacadccdbadbbddcacacbbadccbccadacdddbbbcddacdacbabccdabdcabbcbdbcdbaddaacbccbbdbadbaaaabbacccdcddacabbdbbdaaacacadacbcbbbacacbcabaddacacdaddadbdaabacaacdcbabcbccabbdacaadbbbcdcdadabacccbbcccbcabccbcbadbbdddcaccbcaadccbbbcbcbddbddaddbcbdaaccbcabdccbcdabcabbacbadaaccbaabccdaaadbdbacbdbbddabbcaaccadbadbdcdabcdcaccddaccaabbddcbcabddadddaacccbbaabbbacbbbbcdddaacdcaaabadbddaddbaddcdaaabbccbbdbabadabddabbcdbcbbdbbcbaccabdcadbdcaaccdaaccaaccbccbacbabcbbcdabcdaccbcdcacadbbbdbadbbcbcaddbdcbbcabdccdadbddabddcbcdbaaaddcdacccadaccbaacbbccaccbbccbaadccadccbbdadddbccacadcdcdcdbacaccdaadbdabddbbbdbcdbadabbcddaacdddbcdbcbbdcabbdacabbbcabdbdccbbdcacaadacabbddacaacaddcbbdbcdbccabdabbcdccadaadcaabcdadcacdbcababcabccaabbbbdbbdadcdbabaddcdcbdcbabcbacbaabcbcbbaccccbbdacdadddaabdabbdcccababbdddacbccabbaccccdaacdaddabaabdbddbabbaddbadacdacbcbdbddddaaaabdbcbabbacccbdcbdabaacdcbadabcdcccdcddcbabdabcadaacccbbbdbcbbbacacdadcdaddcabaaaadabdbabcacddccaaadaadbbdabbabbccaddabaccddcbdccbcdbdabcbdccaaaccbcacdaaccabadbccdbddcbcdaacdadcdbbdbdacaaddbbaaabbdaadbabcaddcbdccdbbababdbaaddddbdbaddacbdabbbacdcdabccbadbdddacbaacdbbcaadccbddbdaacdddbabddcadcaccaddcbdbdbcabaaccbcdbbbadccdbdcdcaaadbdaadcdbdbbdadbadccbacbbcbddbbdbdbccabaaccbcadbdabbcddaababdabaabcbddbbccdcaacccaaabdcbaadbbcbadcdcbcbcccdcaabdccaaddbbdbcccbabdcbdbbbabcbdacdaddacdaaabcccdadddcdbdaddaccaaddbbddacddcacbbcbbbcbcaaabdbaaccbcadaacaacbcbbddacadaccadbbdcbcdbcddbabbbdbadcddcadddbddbbbddacbbccccadbdacddbbcbacbddaadacdabdacbbdacabacdccdddbdccdccaaabdcbdbbccaadbbbdaddbcdcbadbdcbdcddbbbacbcbaadabbdbaddbadbdbadbdddaacbbcdcbdbccbdcbdbcbcabdabcacccdddabdacbbabddcdbadcacacccadddbabbbbcabdaadbdadbbbabcddaaddbdcdbaacadbcbcdaaacadbddbbddaddbdbccbdbccaabdccdbaadadcdbbccdcdbaddbdabdbbdcbbbdbaacdaadcbccbacdadcaadcccbdcaddaaaacddacbcaaaddbcbadbddbaabcaaadcddbbcaddbccbbdbccbabdbddaabaadbdcbbaddaaadddccaababdcaacdbdacadcddbccdaaacbcabaadadcaacdcbbdbaacccdaabcdadddbcbccdcacdabbcabadaddaccbcababdbbccdbbcbdbaaadaacdcbdaccdccabbbdaabcaabaadcaabccdacccccbacdcabaababdbddcdabdcbcdbabcacbdabcccdaaadabddccdcaadbbadddccbdaabbcbaccbcccacabcaaadddbcdbbcdabcbdbddcbdaabbdbcbdacddcddbacaaccdcbbbdbdbbdcbbddccbcdccbaddcaaadddbcddcbdabdbadbddbbdddcddbbcbdcdbddadcbdcabdbccdaadcdabbabbbcbdbbbcdcabaaddddaadbbbbbabbcbcdcaddddbbbbbbdaaadbdacdaadcbdcdaaaabcbaddbbdbabddabcbbddbbbbabbcbdbdcbbdbabccaadabaabcbddbcddcbaacadbacbaccddcacacbbaabdbabdccaccacbdbcadbcbadddbbacbddbbadcdbbbdbbabdbdddbcadcacbbbaacddcadadabcdbaaabddddcdddacaaaabdacbcdabccdacccbddadacbacdbdcacccddbaaabaddadcdcdcabcbaddabbbdacccbdbcadcbbcadadcdccdbaddbaddbccbdabccdabccbacbaaccabaacdcdbddddbbcdbbccadbabcaabacbdddbbaadbaacbabcadabbaadccabdbdcdadcbdbadbcbbdadbacbaadababddaaaaddcccbacbbccacccacdddccacabcddaaccdadacbdbabbbacabaaccdcabacdaabbdbbcccbddaabbacbbbcbbbadddacbddaaaadccbccbbacaacdbabadccccddbdcdabdacccaaaaccacadbbdcdbdcddcdbcacacabcdadcdcbbcbdccbddbdadbcacbaccdacbcbdcbcdbdccccdaaaabaddaaccbabcddbddbbbbabaaddcccbabdcadbcdddbbbaddcbbbcbaaadbbcabcaabddddadabbcbcaaddbcddcaaaacbbcdbbdbcabccdadbbdcaddbdbdcdccbbbdcbcdacaaacbbbbcbcbcddbccbdbbdbbaadbdbadbdccbaddccbdcddadbbbdcbabbdcbacadccbdbcdcbbdccdbbacadacddabdccaaacbabbdbbaccaabbcbcababddbcdbdcacdbacacacabdaddbbbbdcaccdbddabccdbdbdcbcdbbbbbdbccdbddbbcbaacdbdbaaadbabdacaddcdcbdcdbdbabbaaaacdadddbaaabaddbbcbaabbdacbbdbadddbaaadbdcbdbdbadcadcbcccaddabcbdbccbdbadddcdcabbcdcabadbdcdcdcdbabbacaaadddabbbdbcbbbadbaabbaddccdcbcbdaadbdbcbcdccbbadcdbbccbbadbbdccccdabacdddddaacbbbaabbadacabccaadaaacacbaadadbcacdbbddcddddddcbdaddbbdbdadadbdaaaadadadddcdadabcabbddcccbcddacdbabdacbdccbbabcabaabaadcabaabbadccbbdaacdcbaaddaacbbccdddbbdcadbdbdbcaccadddbcdcbdbadabbaccbaaadaaabacdcdaadccdcbbcdacddacadadbccdaadaddbdddcccdadcdccbdbbacbbcacbabcdcacaabccaddbabdbbaaabddcadbddcabddcdadbaccbdcccadaabbdaabdbcbacaabdccbccaacabcbccbccbacabbccdcbbdbadabaddbaadbcaccdabddcabcbbababcacaaabbbcddabcacdccabdacdbcadbcddaadabbdacadaabbddadcddbbcabdabcbdbdaaacccbadcbccabdbcadddbcddcadbacaddccaabacdaacdadadaadbadbccaaddbdadcbbdacbdcadcadbcaccbbcddbaddabbbcdadcdccdbdcdaabcadbbabbbddcbbbddcdbcdaddddcbacabbcaadbabdcaaacbbdcccdcccabcbacaccdbabadbbdbccbbdccbdccbccdcbaaddadaddaddbcbdbadaacdcaaccbcbbddbbaaaabababbddccbddccbcdcaabbbcbbadadcbcabdcdbacabcdbbbcbbaddbcdaccaadabbbdabbacbdacacacbadddcddddbcddccaddaccabbaddcbaabdccaccdccbcadadbdcdbbdaacbaacabbdabbacdacaadaddbdcbdacbdcaaddccdbdbbdcbaababddcaabdbabbabcaaadcdaacbbbabacdbbbcaadbaacaccdcdaaacaabcdbabcbcbdababcbccbddddbacdccdadadaabcdcadcadabbbdaadcdcddbcbdcccabadadcaadaaadbabbabbcabddcacdcabccbbddddadaabadddaccaccbcbccbaccadcdcdcdddbaabaacaccabdbbcbbbcccadbccbdbcdbbabbdcbacccbddccdaccbaddcdacbbbddddcdaabacaaabdbddbadacccdcddaacbbcdabddcdadcaccaddaadcccbdacdcdddaadbccaddddaabaacabdccdbabacbaacaacabcaaadcccabdabacacadbbcddcaabcbadbadccaadccdbcdbbcccbaddcdbbbbbdacdddcbbbcdadccabcabddacccdccbbdccdacbbdddbbaadaccdbcccdcbdbcbbacabbacabbdcdbabbbdabaababcadbaaadcbcbbcbcdbbccdcaddddcbdabdbcaadcbccdabcbabdaccbdabdbbdbbbacacbaacdbdbcbddcbcbcdbbccbcbacdbdabbabbabbdacdddaacdccbbdadadbbcbadddccbbddaaddabdadaccdcbdbdacadabdcaaacdaddccbaaacadcdcabddcbabcddacddacbbddcabcbbcaacdbbbcbacdbbaabdccccbbcbcbabcaaaabbcdcdacbbbcdadcdccbbbbdbcdbdbcbbaaacaaccadaacacbccabcadaddaabbcdaadadabbcadabdbdcbdcaddbabcccacddbdadaccaddaabdacccacccdbccbdbadcbccbcbaccbadbdccbcadacdaddccacaccbacbddaabaadcbacabdbbabcdccddddcaadbbbddddacdaddaabadabdcbccaabbaaadabacacbcbbcbdadcbbabdadbcacdccbcbaacadaabcbddbacdddddbbbbcbbdacaabbaacbdddcbcddcaddcdaabadbbdbacbdacdaacdcaababcddcbccbaacdcbbcbdcdcabbdcaadddbdbbbcbbdbaadccddcbbdccbadbacbaabcdbcbdcdbbbcaddddddddcaccacbcbdbdddbddddaaccbcacdacaddcbbcbccbdababcbbcacbaddccacaaaccbdadabadabbbabbbcccbdbbdabcabacacacdabdbcccbacbcbbdbdbabddcdbaddabddcbddcbaabcccbdbddcabcbabcadbccdcdddaaabdbaaaacadccbddbcbabdcbbdcaccdaadbaacbbcbaabbbcbcdadacdbdcdcacaabdbaaaccdbdbcacacdcbdddcdacddbabcbacacbaaaabbbbbcbadddcdcdabbddabcdbacdbbbadaaabdcbbbadaddacadbdbcacadaacbbcacddbdcccbcbaabccadabbcccbbdcdbdabdaadbbbadcacbabbcbcccdadcdbabdbcdacbbddccbbbddbcabccbcbadddabaabcbcaadcaaddbaacdccdddcabcaddbcaddcaabaadddccdaaabaabbdcadddbbcacabccdcbacaaaacabcbbbdadcdabdadbbabbabcaabcdcadaabccaccbcbaabddcdcaadbccbbdccdacccadbcbdcbadccbaaabcdcacadcbbddabdaadcddbaacacdababaadabbadaadbdbbbddbaccdcbaddcbbbccadbadbacddacdabbbdccbdbbcdaccbccdddbadbbddbdbaabaccdcccadacdcaacdcddbaacccabcbcdbbbacbcdbcbadcbaacdbadddadbbdbacdcadaaaadabdcddddacdddbdcbacbacadcddcbbbccbcdbaccdbadcddbbdbbcbbaaacabaccacadbcadbccdabdbbdccccccbaddcdbbdcccbbcbabcabccbabcadabdcacadacbccababbbaaabbdcadcadddbdbdbcabccabbbdaddccacddbcdabbcccbcaaaaaacdcdcaccabbdbdabadabdaadcccacbddbcbadbaaaababdbadabaadccbabdadaacbcaadadabdadbbdbdddbcaddbbabdddbabdddadddbbbdaccddcababbdaadadabcaddacbcabbcbaacdbcaabccccccbddcaaadacabbaddddddacbddcadddaccdddaaaccbacdabbaccadacdcaacaabbbcccddabdaadcdaadaacdcddcdbacbbcdcacbcacaacdaabdadaadccacbdadcaadabccaccbcbbadadccaddddacadcdbdcbcccbbdbbaddadaccdcabbbcacdcddacdaaabadaccdbcddddbcdccdcbaaadbdadacddaddcdcaadbcbcaaccbacbbbbdaadbcbadcbdcdcacabbbadcdbddbadabcabccccbaabbcbbbacabaddcbadddcacccbbaabbbdbbdaabaaddabadcdaddadbbcbdabacccbcbbcacadbbbcabbcbdacdaacbbbdbbadddcbbabddddcdcddadddbdbcadcbbacddccdbaacdcdccccdbaccacaaddcdddbcbbaadaccadbbbbbcdbaaabdabbdbcdacdbcdbdcabdbccacccbadadaabaccaaaadbbbccdcdacbcdddcbcadccbcaaaccbdbdbbadccbbaaccdaadaaccaddaddcaaddabcdbcbbcdbbdacacbcaacccdbaacaabdccacadbbbababadcabdabbdccaabbadbbcadcdcbccbcaddadacdcccbaaacacadabbbaaadbcaccbbcaadabbdacbaccbdcbdddcbaabdbccdcbadcdcddbddcaabdabcacaacbabddbabbcccabbcaccdbdddcddcaaaddbbbdbbdadbcbdbcdabddcbdbcadacbcabdadadddbbaadcdbcbccbcabddacdbcaccadbabacdbbcbdcabbabaadccccdcacbbccdcacbdbcdcaddaaddcccbbadacdbcccdccaaaadbddbabbaddbddddbcbbacdccacaadbadadabdaadcdaddaddabaabbdbcdaabccaacbddabdaaaadabddaabccbdaddddbdbdaddcacabbdbbaddbcbbaaaacaddccbdbdddcabbccbdccaacaccaacbddbadabaaaacacdcbcbacaaababcbbcbdcccbbbdcadcaaaccdcadbaddaabdcbbdabbccacabccbbbddccaddddcdcccdcacdbcadadadadddcaaabcbdacbdaacbaddbcdbdcbdbbabbdcaddcadaaacccdbadabccbddbacadbdcbadabcbbbbbccbddbaaabcbacacdabbbbaddabdbbaddcdbbbbcbddacddacbbabdcbccaaabcdcbbdababcabbbbabdbcdbcbacbcaabdbaaacabcabccacdabbcacbabcaacacbdcdabacadcababadbbbddbbbbcaddaccbcdcddaadbadadadcbdbcadbaddcdccabbdcaddbdddaccbabacaabdbbddbdcccdaddbcbbdcaacbcabbbbcbbbaaaaddccbdbdbcadabcdcadadbcdcbdbcbdbcccdddcbaddbcaaccbacdababccbaddcaccbcddaddbbbaabbcdddcdacdaddaddbcbaaccdbccadddadcbcbaababcdbbabdbddbcaababbcbbcccdcdbcadcdcdbaacccdcccabcbadcccdddbadbcdacdadaaabaadabacbdbcbbbdadbdcdbacdabccdcbadcaacbbdcbcbddacadcbccaaccbdcbadabaabadcdacdcadbacccacbaccccbdadccbdaacbccabbbdbdadabcdbbbccbddbacbdccbddadbcaddadbcaddddddbbcdcbcadbabcacdcccbababdcddcbdaacabbbccdabbaaaacddbcdbbbdddcdccdbdaccdbcbdaabbdacacacdcbaaaabdbabcbcdcdddbcbbbaddacdcdcbddbbdcaddacbcddcdcdbbbddcaddcacbdacbcaddbbcacbbacbbcdacdaaddbbcccdbcadbdababddbadadccacbabbabadcdcbabccbbccdbaddbbccbdabcbabddbcdbdcbcdbcacaabbdaaabaaacabbbcdcbaaaddadaddcbaacdddbdabcacbbabdbccccbdbbbadbccabbdbadbdcaaddaddcbbacadaccacbdaabcbbccccdbaaadccadcdcbaacdbbabacabadbdccaadaadacacccacabaabcabdabbbabddabbdacbabbaaaccdbcdbabacddabbccccddcacbcdaaabbacbbaaacbdabdbcddcacacbcadbcbacaaadaccdcdbabbdccbdadcbcbbadbbbbbdabbbbcbacddabdccbcbadcbbccdcdadaddbcdcbcbbcabaadccabacbaacbbcaabcabadbaacadddabcabaaacbacdaadbcdcadcbcbcaccddcbcbcbcdaaccbacddcadadccdcbbabdaaaacacaabbddddbcdddcdcaddcbabaaaacbbcbadadcdbdbdddbbcdadcdcadccbbcbcddbdccbccaabcaaaddaabbcaabaaadcddaccbacdcbaaccdbbbcaccacddacadbccbabcddbbccdabbdadcbdbbadbcbccdbababdddaaccbabdbcdbcdbcbcccabddaaddbcdcdccdcdcacdaaccccaccacbaddcbbdacdcaabcdabdcbbdbdaadbdcbdcadccdaacdacbbbdbccdbaadddadacbbbcacbdcbaabdcacbbbbaddbababaadcaabdbbabdcadaaabccdbdababcaddaaaabbcacbcccbbabbcbbaaadbcdddadbbdcabccddadaacbccaaadcbbaabacadbdbaaaacacbdddbdadbbbcaadbdcabddbaacdaabbaacccbcaabdbbdabcdcdbcdabdcdbdbcdcdcadadccadddacbabbbbabdbccaadcaaacccccbabbbcbaccbcbaaaccaadaabacbaacdddbcabddbbaaaaadcaabccbcbccbcbabbdcadccdcccdcbbcadadaabcaadaabcbdbbdaadbbbaddbadcdadabbcaddbccacdbcdbaadccbadcadcccbcacadbabacbcccacdaaabccccdcacaabbbcacacaacbdbdabddcaadadcdcbddabbaabdaabaacababadcacddcdcdbabbcddccbaababaadacdabcdaabcdbacdadbdbdbbbdacdbdcbbaabcddddccddbbbdbbcacbcccbbbbbcbbcbcbcddbccbdbcbdbbbbbcabbbddcadbbbbdadacbdcdcaddbbddadbababdddacdbccdddabdcdaacaddcaabcaadcdcbbccaccdabbbbccbcabcbbdcabacaabccbdcabddbbccbcaabaadbdbaabdcccabaddacacabdbcdacabccdddbbcdcbcdbcccbdcccadcbaaccdcbbddbbdccbdcbaadbcdcacacbcaddacdbdcbddaabdbaddadcacdadcabdadacbdcacacabdacbddabacdabcabcddcbddcccaddacbbaacddbdccccdcadbbbbbbcbcbcbcabdaacaddbadbbbcdbdcbbccabbbbdbdaadaabdadbdacdabddddbbddaacdbccdcbbbcdaacaadcdbaacbdbdaddcacabdbbdbadabbddddcbcdbcdcabbddbdbdcdbacabbccdabbcdcbbaabdbbcdcbaabcbacbcdaacbdbcddacacccdadcddbcabaddcdadbaadbbcdbcdcdabddbccbcabbbdccaddccbbaaabcabcbcdddbdcddcdcdabbbbcdaccacbccacbbbaacadcacbacccadcaabcbcabcbbdabbabaabcccbcdccaadcbdbbacccabbdaabbdaacbcccdbcabddbcbdbdadbbbdbbbaddbddbaabadadaccdddacabacdcbaccdddadbddcdadaabbcbcdddacabbbddaddcbcdacadcdaabbbbacaccbccacaddcddccaaddcaccbbdacbadbbbddabbadbddbcdabadbbadcdbdabdbaadaabdbbbbdacbcbcdcdcaaaabdbadabcdadcddadcccbbbdcaacccabaaccdbbaccbaabdbaccbdddbbcdcbccbdacacbbacbbcdcbcddccbcbdcabadcdacdbdcacaaaccbabbdbbccadbbabcbaadacabbacdadddcbccdbbadabadaacbbccadbbdadddadacabdbcbdaddbddcbdddcdddaadbbabbdcbcdcabbbacbcbccbacdccccbdabbbdbabcbcbdbacbddbdbdaadcccbdbdbcbaadcccbbcccdacbbcbbbbadcddccbcbcddbccacdaddcdccaccadbaabbccabcdacbbbcdbcbdbcdbbdbcbaccdaabdbbcdccdcacdaaacadbccabcaadcdccabbcaabaccbccaaddcabbadaaccabadcbcbacdabbddaadacaabaaaadddcadbdabdadccdacccadcadbcbddaccdcbcccababdadccbbbccbaccccbbbacadabbbbcacddcdacabdbbccadbcdabddcacabdabccbccabddabdcbbcccbbcdadccadbcaaadcadabcacaccaabbbbbddccbbcdbadacdaabdcccbbdcddddbaccaacdcadddcaacacdcaccbbaacbdabbcdcaaaccaacdcddccbabbbacadccacbaadddabdadcbddacbadacdbcdbdddbacacbaddddbbddccddaccdbcabcbdaadaccbcabbbdbadaaadaabcacabbdabcddabbbadbabbbdbdacacaadcbabbbaccdddaadbdbbaacbbcccbdcbbdbbdbcbdcccadaaddbcbdcbdadcabdaccccadccdbbbcbddadbdcdaacabddcdaacaabccacbdadaabbcbbdacbddacbbbabdaabbadbbbcdadcabcbcbcacabcabadccccdcbcddddbbdcdbbdaaaaadadddcdcaababbdcaabadcaddbdbddddbcdddbddbcbabbcdcacbdcdabccccbabddbcdcddabbbdabacddddacabcccadddaaccbccacbbcbababcaaddbcccbddcbbdcdbadbccdacdbcdcbdbcabadccddbcadccbccbbabddaccaaccacbcadcbdacaacbbcaddaacabdabcdbbddbddbcddcbacadcbbcdbbcadbadccaaadbbbabbccbccdaddabdacabadcdddbccdbdaadddadbbddddcdbbccabadbdbdcdccbacbdadabdccacaabccbabababcdabdcdbbaccdbabcaddaabbacbbbcaddcbbdccacaadaaaadcabcdadabdccaccaabccccdbabdbcaabbcbbacdddcbcdcccdadaadcdccbcbccababddaccddacadbabdcaacddcadcdaadacbcbdabbbcbdaacccdabdabaccddaacdccddcdbabbcdccababbcadbddcdcdabddcbddcdbdaabbabdcadccdddbdbdcdcaacccbbbbccdcbabddbabbdabacdccbdcccacbadaadaacaacddabdaaababbcbdbdbddbdcbadadbadaabdadcbaccdcbccdbbacddccaadbadacacbbbdcdcbdcdbabdacaadadadcbacccdddbcdcbdabbbbbcdcbcdddcccacdabacaaddcbccdacbdaadcbcacaaacbddcaaabcaccbbacadccdcaabbbaddbbdcbaabbbcababcbddccdcbccbcabcaccbcacbaaccadccbaacbccbdddbadabccdaddcbccdccabddcbdbcbdaabacdaccbdccbdddcdccbadbabadddacbcdccbbabaadadabbbdddbadcdbbadbbaacbdcaddddbaacadadccacddcccdcbdbbdabdaaccbdddbaacccdaabdaaccbaabcdbbccacabbdccbbbcacdaabacdabbaaadaaaccccabbbddcdcbaacadcbbcacdbdbaddbdcaacbadbcbaaccbcadbcacdacddcabcadbbbbbdcbcdcbcaabadabcddbbaaadcbadcccbcbaaaabdcbbdcadbadaabadddabacbaccbaaddcddbccbcacbccbbadacacdbabddbdbdcccbccccbddcdbcdddaaabacaaaaabcdbbddbcaddccbdcdddccbacdacaadbbabadddaabaaaaddccdabcabdadbaaddbdacddbcadbaccdadabcaababadbdbacdbddbbbcbdcadcdcbbadadaacdaaddddbbcddccdcbcbabacadaacaadbaadcadbcdddbcbcaccdadcdcabbcdbbbacacadddaaaacbbadbccbbdccbcdddabbadcbccbccdcbbdbcdcaaccdadddabcbdbddbdadaacbddbdacdbbdcacaddaacacadcbdbbcbcdaaacbabbdbbcbadbaabddccccccbacabdaaabbbdaaaabadcbacbbbabdcbdccdaacbdbcaabddccddcaddaacacddbcbadddcddcadcdddadcbdcdcaccccbcccccabbcccdacaddccccacbadcdbccaabcaaacccdcbdcbdcabdacbaddbdcdbaabbbcbaabdbcbbbaddbadbbbcaadbdbcbacadbaacbdbcdcabdbadbbccbddcdbdaaababaddccadcbdacdbabaacaadbbcaddaabdaadcbaabdbbbaababcdcacdcbdadabccdcabccadccdcddcabaabadadbadacabaabaaaaddbcacacbbccbbdabcbbcbcbbddcbabbacddaaaccccdadcdbbabaccaccbaabbabbacdcdaadcddcdabbcdddcbdbcddaaacccbabdcbaccbddcbbadabbaccbbabbdbdacdadbbdbdccdabccbddcdbcccaadccaccabbbdcdabdcdbbccdbabacddbccbbdcabccdbcbdbcaddccddbbacbbdbadbdbcbbcdaabccadabbbcbadacadcbbcaacccddadadbdbbaabbabbacacbbbdaddacabacbacadbbaaadadcacbcaacdadcbcbcccbaaaacdddbddccdacdcbcdabccbacdabdcabadccabadaaaabddacaaabdacdbcddacdccadbdbaabdddacdddcbaccacbbdcbcaacbdbaddadbadabccaccdabcddddabbabbaadbbbabddcaddaabbbaddabadcacbcacdbabdaddcbdcbbaccbdbbbadddcaadddbbacddcccabccacbdacabdbbcbcadcbbdbaccbbcacdcddbcabadbaddcbbbcaddbdabcaadcadadddadccddbbdbaabbddabbccccdacbbaadabddbcaadbacaadaabddbccdabcabcdabaacddcdddabaddacdacbbaaabdcbddadddcadbdbccbdadbadbcbbdcbacdbadcaccdabddcaaddcacabddcbbaabdadbabddcdcdbdaadbaddbdbbcccadcadddbbdbdaccdcaabddacabbcbcaddaaccabbcaacbcdacbdaccadbdddcbbdbbabadbcacbdbcdbdcaacacccbcdcadddddbddbdadddbbbbdcbbdcbccdbdbadaaabdacbbdadadaadadcddbbcbcddbbaccbbcccbbddddcbabcadaaccbbcababdbbbccddacabccccbdccbabdddcadddcaaaddabcabaaadcacdccadadbdbdddbbddadbdcdcddadbcbbabbacbcaddcbabccddaacddccdccbadabbbcbabadbbdcccacdcdcaddbbdbcdcaacabddcbbdbacbdccabcacacacddcddddddabdaccabbcdbdadddbaaddcbacacccadbabdbbbccccadadbabdcacccbacdbaadabdacdddabbbcbadcdcbbacdcaccdbbacbddddcdcdcaabacabaadcccbbdbadabadbdabbbccbcbacabdbbaddcdadddadccbdcbdddbcadaabbdadbbbabdaadbbacdbdcbbdbbdcabcaaddbadacddbdaabcddbccdabcacbbbbbcdccadadcaccbdcadaadccdccbaddaaccbcacbbdaadbbdcbadaaabcbbbacbdcccaaacccbcbbabacdadddcbdbdadbcbdbdcacdbdbbbbdaaddddaaccbbdaadacaddbcaabbbccdabbcbbbcdabbbcaaacdbabbcadacbcdbcbbabbbcdaccdadcbaccaaddaacddaaaadcdabccdacabcaddbadcccbabaadacadcccbbddbddcadabacdbdddacaaaadcbdbdbddbccbbdbddccadabdbdcbaacbcbcadaabcdbbaaaaacbaacabadbaabbbcbdcbbbdbadadddaddabdadbdbbacdacaddbcbacbcbaccddaaaccbaccaadbbdddbbdadacaadbddbdbbbbdcbbcabcddacacabdddddbbbdddbbaddcbdccbacdacdbbbbdddabbaaccbaadcddcbbbcdcdadbdadccbbdcdaabdddddbbccbbaccbacddccbadbbbcbccdcabdcbdcdaaccacccddcbdcadbdcdbdacbacdbbcdababaaadcaabacdbcbdacbaaabcccbdcdbbabadddcdcdaaddbbadcdcdbbdbddcdbaaddaaacdcbdabaabdcbacdcccbcaabaacddbaadaaccdbcbddacbbbaabcdcaabacbdacbcbaabdccdbcaacdabbbcacdabdbdaabcbbacdadaaddaddaccaaaaddcaacbabdaabddcbbddbbdcaccacbcbccdddacbbcdbdddaddcbaddddddcbbcbccbcbaccbbcdbcddcaacbacdabbcdbadaaaaadbbadbdddddacdadcaccaacabdbcaadbcddcacbcdbcbdddcacabadaabcdbdcbddbaaccbbdbbdaadcabcadaccbabdacddbdbdcacdcbaaddaacdddbbdbbaaadccabbbbbdbacabadaadbaaccadbabdababdddccbccbaaaddcaccccbcaadbbdacacdbddcacdcbbcaabadacbdabbadccdbdcaababbaacdcbaacbdbadaabbdddcdbbcbbbaddcbababcaaaabddacabdcbbdaccccbcdcdabacdcdddcbdbbcdcccaaabdbcaccccaabadacbbbbbddadcabbbcdcccdcaddaadaacdcadccabcacbcbaaabcddcaaaadcabdaddbbadaccdaccdaccaddcdbbcbbadddbacababdadbadaaadaabaacdabcdbaaadcbbcbdcccbaacdccdadabcccabaacbcdabcadbcdbdddcbadbbbccbcacdcabbdcdbddadbcbadbcabdddabcadbddccbbddcdbdacdcacacadddddddaaaddddbbacbdbdcdccdbabbcaddadadbcacabbcddddaadcddbaddbdcabbcbbcaadcbbcddccbcbacddaddddbbcccabaacdcdaccccadadbdcccacaaaabbbccdbaccadcddbaacbabdadabbbabaadbbdbbdadcaaabcaccbaaccabaabadcbabdacabcbdbcabcababccdacacbcdadabbbbbbbdccbaadcacdccccbcdcdbacddbdcbdcdddbdcdcdbaadbcdbaacbbcadcdbbbacccbcabcccadbdbddbacbbbcaabdacdaddabccacdbacdddbdcbcddcdbdbcabcbabadcbaccaababddacbdaddccdcddaadbdbdaaababbdaabdcdcbbadcdabcaabdcabcdbdcbdadadcddaacaddbbbccadbbdbdcabcadddaadccddacbdcbcbdbcbcacddbdbbccccccdaaadcaadddbbaacddadbcaaaabddbbdbcdabddcdbbbcccbaabadcdaacddddcaccddbdddcdbaccbdcadddccababacdaaaacdaababccbbcbdcacacaccbaadcccaacadacccdccadbaddcacccddbdbdcaadcdcacbdcdbbcdadcabacabdcacdadbcccbdaabbccccdbaacbcabdbadbacaadbaccaacdabcbcdbaabcdaabcdaacadcbababcacbdadccdbdccacccddcdabbccabcabbbbddabdabbbbaabdccbcacbaabcbcbacbadbdbbdaddcbbabbadabadcdcddcbcbacbdddbaacacbcbaacabbcccadcbaaddbbcbaacadcdbdaababbcacbdadbadaadddbcdbaaaadcabaccdcbbdcdcbcdabcbbbabdaaddaacbdcaabbddcdbadadababdacccbdadcddaddadccddccaaabdbdaaddadabcbdcacddbaacdcddbdcdccdddacabdbbddddbabbcbabbdbcbdacccaccaadababccddbbddbdbbbbbbbcbcccbdcdbcbdcbcadbdbcdbdaccddaddccdbadccbcbbdaccbddddcccdddadbdccdcdcbabacbaabdccdbddabbdaacadabacabdbacccaabcdbddacbdabdddbbcbdbcbbbbcbdcbdccadcbbdaaaaddaaababacddabccbdccaccbacbbadabbcdcabcccaabcdbadaccabcaabdaabbdabcdbadbbaaaccacdcccdccbdbcdbaddacdbabccbcbdacdbbacaacdacacbaadccbddcdbcacdbbbadbcccdacacdaddcacacbdacadbdacbbbaaadcbabccaadcccbccaaabababadcadbdabbdaaddddcaabbccdacbcbabbdadabccabcdaddadbdbcbdbccdccadbdbbaadbccdcbdabbbbcadaadadcbdcaacbbaaacbbdabdcbbaabbbdadcdccdbcbccdcaaaacabcdacddccbcddddabdcccaddbdcabdbddbddbbbcdbdacddbdbdcdcbdccbadbaddaacdcdaccdccbddccacdcbdbdabcbadddabccdcbdacacbdaddbbaaabbaaccbabbccaddcaddbcbcdaaabdadcddcbaabddddcdadddcddaabadbaddadaacbaaadabbadcacabddabadadacdababbbbcacdacddbcccababcdadbdacbcddcbbdccccabbcdacaaaadccbaaacaadccadbdcdcbbbdacaddddcdcbbabacdcacbadaabaadadcdcbcaddcddaaabaacbcbbcdbbaaddccddaabdbbacbccdaaaacdcbbabadaaacbbdacdadbbcbcbbdcbaacdaaabbacaaddaacacdddbddcaadadddbddacabbadddddddddcdccddccdccbcabbcddbbdcacccbcdccadaaadbcccddcaaaaaddabbacadabdabdcbcdbcdbbdbdbcdbcdddabdbabcbdbdaadccadbcadcddddaabbaddadccbacacdbaddbdbbbddccdccdbdbddacccdcccdadacbcbbdddabbcccddbcdaaacccadabcbcccbadababaacdcbacdbacddbcaadacdcddcaadbcadcacccbdbbbdaaabcbaacacbcbcdbabbdcadacabdddadccdccaabdddbbbbcababbccaddcbbbbcaaccadddaddaaddacbdcbcbcaaaaddabbbacdcdcacdcdcbdcabbdbdcabddbabcaaadacdaabcbcdbcbbbccbbcbdcbddddcdacbbaccbadabccddbaadcdacacdbcdabcaadcadccddacdcdddbdabbbaacbddcbddbcdadbbdbccabcdbcdbddaacbabaacccdabacbbadccdadadbdabddaabbaddaacabcacddcdcbaddaaddadbbcbdcabccdcbdcacaacdbcdcacdaaddbbbdddbdbcdcbaabbbcbadcacdcaacabdcbbdbbcbabaadabbcbbdbaadbcabcbbabaadacaddcdbaaaccdacbaadcdcaaadadabaddddbcccddcddbdccbcdddadbbdccaacaacbbdbbbdacbddabdbbabdabadcabcbdbadbacdcadccadbacbcbccadacaaacdddabdddbccccdbbdaccacbcdbabbccbbcabdcbdabdaccbcbdbbccabbaadbdcdccbdababdaabddcaccdacdaacdcaabcbddcbaccbdddcbdacdcdbcdadbddabddbbbbacdccdddcdcdcbacacdcaabccddccbcbdddbcbcdcabddcccddcdbaccbaabaadbacbcdbcbcacadbdbccdabdabbaabcbdbaacddbbcaddbcadbccdbcdacacbabbabcdcbdaabadcccccdaabbddbbacaaaacacdccbdaaacadadccacbcabacdbdbdcccababbbddcddaacbdbbaaabccadddcdcacbcacacabcbccccbacbbccdbbbdcbcdaabbbbbccabdabdccbbcdbbbcbadacdabddcbcddddadbbdccbbbdddbabcababcacacaaaabaddddbdbbbcabbacbbabdabacddbccbcadccabbdcadbdadcaadabcdacbbcdbaadadabdcbbdcabaddcdacdbddadcdcbbcbabddbcdddbaccacdbdbccacabadacbccdccdaddccddbbdcccadaaabdaabdccbbcbbdcbbcacaacaaadddacddccabddaacdcddbadacacbdbabcabdcaadbbcbbdcbccccadcaaadabcbcaabcbaddbbcddbbbaababacbdcccdcccdcdadbdadbbcccdaaadbcbbcdcdbdaddadadaaaacdaaacbaababcddcbbbddcabcddcdbcbbbaccdbdbdabbbadaabaaacdbccbccdccabdbabcddbdbdcadcaaabacccdbaddabcdabaabaddbdccaabaacabddccddbcbdbdcdabddabaabdacaabdbdccdbbbcbbbbbadaabacaadabdaccababddbcacaccbcacbdcacdaacbbbdcbcbdcabdaadcabdcbbdbaacdbccdcdaadcababccbbaaacdadaaabddaacbdadbbaddabcbbdbddacdcdcababbbdbbddbbdacacddbdbbdcdddddccdadcacacdcddddacabacabdadbbabcbdddcdaaccadabddadbbaadbcdccbcddbbbadbccdcdbdcdaaaadcdabddbdcdabbadabaabaddaaaabaacdadaacbcccbbcbbcccdbcdccaabacdcacadddadbcabbdcdadabbbcddabaadaddabcbadbcbcacbbcdbbbaabdccaabbdbabcdcaadbdbaacbdcccbccbacbddccadcbbccaaaaaacddbccaccadbadccbccbbcacabdcbcdaddabcacacbcdadadabcacccdcbccbabcadbabaaabdababbdacabbcdadcbddacdadaacbcabcdadabbaabbcaccbcdbcdaaccdcbbadbcddacdcbcdcbdacbbacbaddccabdadbcbcaaabcbbaabaaadbbdbaccddaadcabcdccbaabbaccdabcaccbadddcbbdddbbaacbcbbdcbbaaabacdcdbdbcadaaacdcadaaaadacdaabbbdbcaaddaaccaddacbbacbbbbabbdcbddacadcadaddaabddacbdbadcaabdccddcdbbddbcdaddcabddcbbbbdaacccdcdbbaabbccdcaabbcbcacbbdaddabdbdcbabbabcabdccddabcdaadbccabdccaaacadabdadbbdbcbaddbdcaaabcaccdccddcabbdccadbdcadbdaccabbdaddaadacdbccbdadadccbdcdcdbdbcbbbdddcbbcabcbaadcadabcddbdbdbdaddbbbbcaccddbbbbbccdaabbbcdadcbcaaddbccdbadbdcbacdaaccaacaadbaaccadabbaabddaccbaabdbacaacbdbdcdaaaacbbddadcdcacbccbdaddbabcaddcaababbdadabcabbcaadddbdcdaddbcddabdbddbacdbddaabbddadccdbcbccdaaadabcdaababcadadabccccddcadbcbbdabdabbbbddbcbddacbbcccacdbaadbdcacaacdaccabaadcbadbaadcacddaaadaadddadddcbbdbcddadbabddccadadcdaddaabacddacddbdcccacbdcbdbdadacabacabbbbdcaadaddaccddcbbcdbcdbabbcbbcabccaaddbbcbcdcabcadcdadbcccbaabbcdbddbaddcccacbcccdacddbbdcaccccbdccbcdacbabcdcbcddcdaccccccacccbccadaaddabddadbdacbaaacbbbccbcbdadbaabccadbacddbacabdddabddcbdccdbcbaadaddbcadbbbdacdaccbbbbdccbabdaaaacbadccbbcacdbdabdbcaaaddabdaccdcdaccbbdaccbccaacdbcbcdcbccdccdacadcdadabaddbccbaacabbdbcabccdadddabddcabababbdbabcbcdbccbdabaddacaadaddaadcccabdadbddabacddbcdcdbdaacbddabcbbccccaacbabbcdaaadaacabdabbbcacdcdcdaaaaddcccabdaacddbcacabbabbcbdcacdcddcadddcdaddcacddacbcdbcddaacbabbdbacdbbacadaadabcddabcababacddaddbaabccbcdacacdaacdbdcaccaadaaddbcbddddbdaddabdddbabcabdccbbccdcadbaccabbdbacacddabbdbdccadccbaabbdbdababbaacdbbcdbbdaadacdaadbaadcbabcadaaccdbadaccacdcaabaaaacadabcbacbcdcddaddacdccdcacbabdadcdadccaddabdccbacadbbaacbcbacbadbaaabdbdcdcdbaccddbdbbcdaadaccdabbacaddddcbbadadddabdacabdccaddbaddabcaaacdbbdddaddaabdddbdcaddcbcdadcbababbadccbcbabcacabdacabacbbbcbddcbbbdcabcdcdcddadaabbacdcbbdddbaddbcbabdccbadcbbbcdcbddbcadcaacccdcdbcbdbcdbadddccbcdacacbccdcbdbaadcddcddddcbdaaddbbbddadccbacddcbdddcaaccbdcdcdbaaddbaaccbddabddccddccaccbaadadbaaabccabdcacadadccccbcdaaccbdcbbdccbdaadababacdaddabacabcabbacacdabacaaaaccbcbacacbdddabdcdaabdbdccdaabaadacbbaddddbdcdbdcbcbbcaccbcadacbabcbccdcabcdcdbcdbcccdadbcaababcdacbbbddddbabbddacbabdaaabcddcbdcddadacddbbcbdadcaaccbdccabdcccacddabcdbaddaadbabcbdbccdacdcabdccbcbbcbbdbcdbddbababaaaaccabdcabaadbaccbabacaddabdbbcbcadcbcdaccccaaaddcabcdacacdccdcabcdbacbadbdcbddddbabdcccdcabdbcdcdbbbbcddbddbbbbccdcdcddcacaaabdbcddadccbcacdbabcbcadbbbbbacdbbbbdcadabcddadcdcbdccccddcbbcdcdcbabcbdaccdccbcadcdacbdaacaddcbdcbbcdaaaaadddccdcadaabdddbbabadccadaddccbaacdcdabdcacbddadbccdadaddbcaadabdcbadcbddcccdddababdccdbdadabbcdacbcbdcbccccaabaacacaababcaaabbcdbaaddcdcbacaaacadcbdacdacccdaabaccabcaaadbacdacaacabcccbadabababcbadcbccaaaadcaacbcdacbbdcadcccbaddcdccdccdaaaddbacbcbacddddcdacaddcddbccdcddabbdcdabddcacbcadcabdcdcdcabacbddbdcbabbdbdcdbaacbaadbdccdacddbcababbdabbaaaaacbaacdcddccadbccccbccaabbabcabbcccaaacdcbccabdbbdbcadcbcccbbdacbacaaababdbccabcbcbaacdcbdbbdbbdabcbbbcbcbbcaaaabdbbdbbdbdadacccbacbccaadadcbbcabbdcbadcdaabccbcaadcbbcaddbbaccbcaacacaabbaaacaabcbdcadddcabdbdabdacaabdddbbcbbcdcadcbaacdaccabcbbadcdcccdbbddadccddbabccaaabcdcdbdacbabbadccbbcdccaccddbabcbabcabaddbbbcbcababcbccbcbccacbaddaaaaabacddbdadbcaddccdabadddbdadaddccdbdcbdbbccadddacddcacabcddaacadbddcacdbbbdccbcbabaaacacbccdcdcadaacbbbdcdabbcabacacaababadbabdbaacadabcacdddbccabcadbdacddadcaadadcaddbcdbccabaabacaddcadddbadcadaaadadcbcccbaaabcacaabbbbaccdaccbccdabdabdbdabdcbaaddcbcbdadbdccabaaaaacbacccabccabddccababbccbbbacdbbdbaacdabadadadaabcddbdbcabddbbdccabddddcdacdbbbdaabacbcbaccdbdaaabbabcbcababcabaabbcacbbcbbadcdbbadbcaddbbaabbbababddbabdbdccaaaddbadddddcccdacbacbcacbcadaabdbcacbaaaacccddcacaabbcdacbccbdabbccdddbdabbbccdbbdacdcdccadddbbcbcbcbacdadcdadabdcadacabaaddbdcbaddaacaabbadaadbbaabacdbbadbbaabdaacdddbcdbbbdacaadddccbdcabbabcdbabddcbcdacbdbddccdccabaaddbdbabbbbdcbdababdbacbccbcbcddbddaabbaccaaccdaccdadaccbbadbdddbbbadabdaabcddbdcadaccbddacabbbdbcacccbabbddcbbbbdbdccbccaaddadadcaadbdcdbcccabaaccadbbdabbbbbddaccadbbabcabdbccbbdbddbaabbbadcbaacbbcdbbbddabbdadcdbbbbbabadbcdadbabdcbabacbaaddbccadddddabcddaccadbcbcabdaacdadcadddcdaaccaabbdbcbacdbccdabbbcbddaaddbbbcdacbbcdcbdccbcbaddcdbaaadcbaadcaaabcddcdadcaaaccbbddbcacdbaabcacbabcbbddccbdbccddaddbdbadbdcdaabdabbbdcbacdcbccdacbabcdacddbacaccbcddacddacbadaacadbccaddbcbacddadcdaaaccbdaaccbbdcaacbdadcdbaccadcbbdaccdcccadaccccabdbcaddcaddaadcbbabdddbccaccbddbdcbdabdaacadcbdacdcbbbcccacbbcbcbbcadaabcabaacacabdaacbabacaadbbbcdacababbdadbaacaccadcbccabaabaabdabbdacadbabdcadbcbbacdbbcadabdbacaabddcbddcbdbbcadbbcbdadacabbccaccaaccbabacdadacbcbaaadccccdbbddddadcdcadacccdadcbccccacaaadabbbdabbbdcacbadcaacdaacbcbdcdccbcdacbccacdccdcdbcabaacabcccabcbbadddbdcbadaadbcbbaacbbcaccbbdadadbbbdabaddccdcabdcaccabdcbadbcadcadadcdbbdbcbdcdcdabccddccadcddadadcadbdaaccdacdadbabaadbacbcacccbbdcdcbdcadcaaddbadaccbaabccaabbcdbbabcddcacdbaacabaaacccdacddaabdacababcacabdbacdabcdbddcaaabadbaddbdaadcbacddaaccdbdbbbdbcccccaccdabcadabadaabcdacbcdcbdacaaacddbacadadaabcccdbbdcbcdbdbaabddbbdbdbdaadccadcccacacadccbcbccbcadcaaaccbcacbbcccdacacbabbbdddcbbbbabbabaccdcbbccbbdddddcacccbabcbbaaaccabdacddaadaacbcbddabadcbdcaaabaaadbaabdcddcbbbaaadbdacdabbbccabbccbbbaabcdabdccacbccdcdaccbcbcdaaadcadbddcccaddbaccbcdbacaabbbcbdbdaaccababcdaababaccdabbddccaccbabacaabddddcbbbacaabaacbdbcdbcbbdabdcdddbdaadbdabcccdcbaabbbdaadccbcbbbacbdabdaaccbbbddadcabdcddcddadaaabcddacbccbdbacbbbadbccbbcadcabdabccaddcdcbdaadacadbabadaacdabcabbcaccdcbdbdcbaccbabcdcdaabbbaddcaacbbbcdadabacdacbcccccbabaddbdcadaccabadaabbbacaaadccdcabaaaacbababddaabbcdaadaadbddbbabaacbdacbccdcddcacbbdbdaadddadcddbdddcbdbcdadbbccabdcbcdabdddbdabacaaabbccdbdbbddacadbaaadccdcbdbadcbdcdbaaccacabbdccbaddacbbadcbabadbbdcacabcbacbdbbcaabaadaacdabcaddcddddbccbdbddbdcaccabacbabccbdaabbaabdacaaccbcdbcddacddccadabdbcabbdacdaadbdacaacacccbadccbccddcccdbadccbccccddabacabccddcdaaccabdcbcdcbccbadbadbbcbbdccdbbacdbcdddcbacaaadcbbcccccabbbdcdaacaadadabaccbabacbdcddcabbcbdcdaabcbddbccabdccbdbaaccbaccddbcadbbdabbddacbcadabaddcdbacbabacbdbbaabbdacbadabcddbdabaaaaaadbdabdacaabdbbaadbcdacbadcbabcdabbbcbbbadbabdbcbabccbdacacaadbbdbdaacbbdccacdbadbbadcacdaacbcbacadbdacaacaacadcbdbbcabdcdcdddacddbcabcdcccabcaadcadcbdadabdccaccbddcdbcabaacaacdcbdbcadacaadadddaacdacbccbaccdcabddbdcccbcdcdddbcccdcdbacabcdbcacdcbaadbdcdabcbbabbaacabdaabddbccadbdaabacdcdbbdcdcccbdcacadacccbddbcbdddcdddcababbbcdcccdcabbccdcddbcdadbbbbcbaaabccdcdaadbdadbbcbbcbaacadadcbadbccacdabccadaabdcbadcbabccadabadbabdbbdcabcbcbcaadccddbccbbbcdadaabbaddcbabaaccacaacacccaccccaaddbbdabbcdbdbddcadacadcaadddacbcacabcadadbddaacabccabdcccbbddcddbbcaabbdadcbcccdddccbbcbdbbdcccbbadbabdbdbdaaddcbcbcbadacbdbaaaddadbabdcacdbbddbaababbadcaccccccdaaacdbaadbdccbdbbabadcbaadcdbabdcbccdadccadbbbbdbbaabbabddacbcbdcbaccaaaaaddcbaacdccaccbbbbdbdbaadddccdabcbadbdbcbdccabdaacbccdbbcdacaddcdccdbdbddbaabbbbdadabccccdbcbaddadbcbcdbdbdcdbbcbabadbdaacacadcddcccccadcadabcabbccdacdabbbacbcdccadcbaccdabcabcccdcddaccdddcbacdccdbdbaddadadbcaaaaacadccaacdabbdaccdcbddcabacadaacbabdbdacbdbdddbbbdcaaddbcbbdbdabbdcabadcddadaabcccdcdabbccbbdbdababddaccddbbddabbaddcaddcaaabddadcbbcdbcccbdaccbbaaddadbbdbaaadaadcbadaabbdabacbcdbdcccbcbdbacaaabdcbccdccaccbadacdaaadabaadadbbabdbacdadbbdddadcbbdbbbaaabaddcdcacacadccabdbcbbbdabadbdbadacbbbabccbcabdbcddcadaacdaaacadabcdbbccbdadcaacbbabacdbbcbcccdadacddabaaaccacdcbbababbcbcbabdcbddbadadddacbadcbcbadcbabcbadbccacccdcdbcdabcbbaccabdacaadcdacdabaacbdaacaacbaadacacbccccddccdddcccccdbdbccadbadbacdabadadbacccbbbcddddacccbaadaacabadabbabbcbaadbccbddcdbddccccdddaacbdadbcdbbbbcaaddcabccbaabcaadccaddaacaaababcbabbabacbdcdacbdbcbcacbabcbbcabdacacbaacbaaaabbaaacaabbabddcdadadbadbbbbbbccdccabcabbbadacaadcbbbddcdbcacddcaadddbccbccdbbbcababdaabadccbcaaccacdaaabdcaaabcaddcdbbcbbddbdcacababddadddbdcaccbcadbabdddccbddacabddcbcdddcbabcbcddcadddaabddbabcdadcaaccbdbadddcacbcaaccacccbcdbccaddcdabcbbdbbccbbdcdccadbccbbdbdbdcbcacbcbadabacdaccdbdaacdaacdbcccdcadbdaaabdccdbcccaaacbdbcaacabdcbabddabbbcddbcdccacacccccaaacdbabdbbdcdaccacdcbbcababdaadbbbdcdcacabdbbddadcabbacbbdcbcccdcdabbcadabaabcdaaccbccbacadddadccabcbdcbddbadacdcbbabdaaaadbadacdaccdbabdaabbacbbcbdacdbadbdcdbbdadacaccbbbacdcccbdaaabccaaccadabbcacaadddaddcdcaabadcccbaaadaadbadddbaaddabadadbbadaccacdbabdabccabaaddadaccdcaabccbcdcdabcbcaacaaadabbccdabdbdccbbbbbdcadcbdaacaddcddadbaaaadaaacdcdccdbccdcacddbaacbccccccddbdabdccbcdbcbbdcabbbabaadbabdacddaacacdccbbaddbbaccaabdddbacabababdcdbbdbacabddcdddaadaaaaaabddabccddacddbabcdbbcadacbabaabcdacaaadbcdabbdbdabbbbbabdbdbdcdddcacdcabdcbccbdbbdcabccaadaaddddcacbdbaaabcbbadababddccbbddabaaabdaddcccccbdadccdbaaadcbbabccdaaabacdbcdcacdacabaddbacacaaacaddcacaabbcdbccdbabbbccddbdcaadccbbdaacbcdcadcddccdcacaddaddcbccbbcccaadbadcdbbddbcabbcddcddaabbdcbbbcbbdacabbdbddaddddacdcaabbdbdcabbbccdadbacaddccbcbdcbacbdbccccdccbcaaacbbaacaddabcbcccadadbdcdcacbbcdbcdcabdcdaacacdcbabcbbbddabbdaaacaadcaccadbcadcaddbdbbacccbdaaacccbdcdcaabdbcdaaabacdbbdacdadadbacaccdadccbadbdacababacabdcaddabaadbadccbadbdcbbbbadbdbacbbdabddaccacdadabacbcccdcdbadbcadacbacdbcbdbddbacccdbbcdbaabdcccccdbdbaddaabaaaabbbcdcccdadddbbbabbabacabcdadcbdbddabaaccbcdbadbbbcabdbbccbabddbcbacdadbdbabbcbcdbdcbcddbabcadbbbbbdabaadcdbddbccdbbbcacbbbdbbbababcdaabcabddcbbdbaddddabaabacbccddbcacaadaaaaddadcbdcbdbcdadaddacaabcdadcbdaacaccacbdacacdbbcdabdccababbbabdbdabadcccbddcddbcadabddcdabadcbbbddcdcaccadabcacbddccadbcbdcdddcdbcbddadabaaaccdacddcddaadbbdacdcaaccabdcabcdbcadccddbcbdadbadcbacaddcaabbdadacdcaadcbdcdcbccdbaabbbdacddaaddcbaddacabccbaadaccccdcdcbabdbacbcaaabbcdccdabaacbccababcdbdccacccacaccbaaaabdcbbabcddbacdcacccdbaabdddbccdbaaaacddadbdccdbddcdbaddccbaadcddbaacdddbabaaaaddccabbbbaddaaaaddbddabbddabcaadcbbbcabcddaacbccaccacbabbcdacbbcaacdcdaccbadbdcdcdddbcccddcadcdbbdcbdabbccccdbccdaddcbaddabdadbdbddabbbadaacbddbcaaadbacacccdacbbbdaabdcbacbbbcabbcdbccdcabdabcbabaaddaababccaacaabdcaddaddbccaadacccdbabcbacacccdcdbbdabacbbdbcabdcadcdcacacacdcdcdcabdacdaacdaccddaadbbadacbadaaacabacbadccdadbcdddcabbbacadaddcdbacaaddbddcdbdbcbacadbabdadbaddbdbbddcddacaadcbbaacdcadcabbdccbaacbcbabdbbbbbcbddbdcdaadcdbccbbcddadaadcdbaabbcdcabcdabadbccbcaccbddccbdcddccddcbcbcaabaaccaddadadcbcbadbabcdadacddadddccadbccbacddacdbcbbaaddacaacdcadcdaadcdbadcbdcddacabadcddcccbcdbccccdabdcdaadaddabcdcaddbabcdcbadabcbccdabaaadacaddcdbddadbcccacaadaaaadcdaddadacdccbbabbababbcadbcadbaddaaddaddabcdadabdccacaddaaaccabbddcaccdcbaaaaabbacaacabdddadcccacbbdadbcdcbbacbbabdbdadcdbdaaccdbabadcababbdbcdaaddbdccccdbaaccbcaaabbbcddcddadcaddcacadcacacaadabcdcdccaabbbbbcaadabadbcbbadbcaccacbbbbddcaccccbbcdcbdbbacdbbbdbdcddbddbccccaddccaddaddbaccdcbcdadbaacccdaccdcdabbcdbbbbdddcabcacdccdbbadacbabbdbabcbbddcadaddbcdaabcbacbbdcabdadbbabdcbdabacbacdbaabacdbaabcdbdbbababadadbdbaadaadbacbccacdcdbdbbccdaccddcaabbbbbabdaaccadbcaccabccddadabbbdabbbcbdcddccbccabaabdcdacaaabddbdbbbccaccbabdabcdcaaccbdabdbcbbbcdccaccdcaddbbcabdccaddcdbccbcadddccdbacacabacbccccbbbcbccacbcdddcbadcabdbbdaddacddbbabaaddadadddbaaaaddcbacadbaccaccbbbcbabddcababbdcdbacdcaadcaaaacbabcddacbbcbabbccbdacadddacbdcdcdcdccdcbacbbddbbdbcaccdabbdbacccdbbadcabaacdbdacadabcddbbaddacdccccbddbdccacabdaadadaacbbadaddbcddbbdbcbdacaddaddddacbdbcbcdadacdccdbbcdbccbcadccdbdcdbbbdbadadccbbaacadbdacacdddadabdbabbdadddbabcacacadcdcaddcccbbccdcbdababcaddbcbdbaccbcdabdcaaacabbcdddcaabcdbbbaccacbadbccabacacbbcbcbbdccbbbaaabbabcdbbabaadcaaabdaaacabddadbdbaacadadbcbdddcbacaadddcdbabdadbbadddcbdcaddaadccbcadbadccabcbaadbcddcdbdadddcdcadddddcdbddcbdbbccaacdababcdccddbdcbcdacbcddaaccdbacabbbdaddacdbcbbabcbccbcdaaaacabacdbdbdccccdabccbaadccbcdcabbacccdaddcacccabdaaddadbbadbdbdaacdbcabdddbdaabdcbdabcbbdcbcdddbacadcacbdbbbdccadabacdddcabadcbabdacddddbbcddddadbbbcacdbdadccdadcabbaccbdcbcdcacabdddbadaddcbcdcdabaabdcabdcdbcbcdbbbcacbcadcddbdbdcbabddbbcdcabbcddbccdcdbacbbccaabbaadcaddbdaabcacbdbadcadabdbdbadcacbcdbaadaaadcadbdabcdccbbcabdbbbaabbaaccdabbaacdcdccbbcccdbbbbcdaddaadbabbaacbcbadbbcdadacabdabddddcbcbbdcccbbbddcabbbabacbabcbcbdabbddacbbababccabbadadadcdcbdbacddddcdacdbcbaaddaabaccacdabcabdcdacaacaccbcddcdabdaccbaccbbbcbcdbcbbdcdaddbdcdcaccdacaacdddcaadabacdabcbcbbddbcadbdbcaabdcbdacbbdbbbabdcacdacacbdcddbcccddaaabcbaaacdabbccdabddaacdcbbcbbcdbacbaacdabadaaaddaabbaaacaaacabcbadbddadcaacdddbccabacadcadbdbbaaadccddbabadccaccbcbabcbaacdcdbdadcbdccbbdcbbcdbdbbacaadccccbdcaccababdccaacaddaaddbbddadddacaddaccaccccaaccbbabdaaccaaccbcbdbdbdbbcbbdbabdabdbbdcccdbccacddbacbacacabdccccdccadbcbddbbcbacddcccadbbadbdababcdaacabacdcaccaccaddbbabbcbbbcabbcabbbdcdddbcbaacbadbdbbcbccabbbcbabccbdadcddbacdbdbdbbdabcabbbccaabadbbaadabbbcbcddbbbbacccaadcabdbcbbddccbbcdcdddacadbbcccdabbbacaadadccbcdcbdaaccaadcadcdccaaacabbacbdaadccdcaabdcabdcaccbabdadbbadcdddaccabbaccaccaddbdaacaadabddaddbabbcccdcccadcdadaadadacccabbaacccdcadcdcbcadbabccbdcbcdabaaabbaaadadcdcaaadbdbdccdadcdcbddabbccadddbabaaddccdbccdabdccdaadaadbbcdbbbbdadddaadbccdddabdcddaccbccbbcbabdcddbdaaaaabadcdbbaaaddddbbbcdbcdcccadcdddbdbacaacacababdbcadbaccdcadcdbabddbbbdcbaadccaaadacaaccddaacbadcaadcbaccadabbababcccbcaaaccbaabbabadbbaabaaacbbcccbddacddaabcbbccccccbdaccbdabcdbbbdccadbbbbadbcbdcdcaaaadcaaddaccddddbaddcdcadbaddccbacbbcaaacacccabaacbbbacbccbcbcbcccbbaababcadbcbdcbabdabaacabdcddabaaccbadbdacdcadaacaacbbaaabccacaaadabddbcabdcdbbbbddaaabcaacdbbacbcadacdaccddbdbbddabbaccbbbbabdbbdbdadacbddbadcaaaadadcabcddcccbacbcacddbdaadaaadddcacbccacdaadabcbadbadddbcddcbcbbababcdbacadabccdcbbcacadbcadcbaaaaaaabbcdacddabbdcaaccccdddadbddadcabccabdbaadbadacacadabbdbdcbddcabdcdacbbbbcbdcaabadcbdaabaddcabacbabbacbcdaacdccbdcbbdadadbbcbddabdddbdacaccdabbccdaddbbccadbcbdabcdaadcabcacccdcbdcabcbcadbcacbccbaadacccdadbcacbddacdaabcdbbbacdbccbdbabccabcccacaaabdbaccdabdccbdaacbcabcbdbbcdccacbdbcabcadcbbabcbabcabacbdaadcabcbcadbabdabbaaddbbddbddbadabbcbbbbdaccddccddaacaadcaaacccbccabadcbcdadbbadaabbdacddccbcacdaaadadcdbaaacbcacddbddbbdcaabdccbacbacdbbccddcaacaccabbcbcdcdbcbbbdbbcddddbaacbabcdacdcbddaddaccaddbddcbdcbbdadcddacaccbadcbbbbaacacdbcbcbddadbbabdacdbbaadbcacaacccdcbdbbcaababcddbbbddcddcbcdddadbcacdaaccccdbaabccdbbabbbcaaccdacadbcadadbbacadbdcaabdcddccdabddbdcbbdddcabbcbcdbadcdbcbdacbaddbcbbbabdccbcccbccbdbaabaadcddcbdaabbdcbdddadaacbccacbdadddabcadddcacbbcbaabcbaaabdaddcdbbdcdacccccdbdcdbacbbdccadaadddbcbacbddcdacdddaacdbbbacbbacbbbcccabbdaabbddabddacadbbdbbbcadaddcabddbbbbabcdcdcadadcbdbaabbbabcbcccdddabbacabccbbbdbabcbdddbaaaaaccdbadacaccadcddadcdccdaabacbdbdbacbbbbdcbccadadabbdabacdacacabbdbdddbdbacdccbddcabdcbbbaaabaadddbadccaabcbbccbcbbcbabdacdbbccbadaabadddabdbaaadbdcdaaaaccdcdccbdbcaccaaaaabaabbdccbdbdbaacdbbaabdadddbcaaaacbcadbbacdacccbdbdcddbdadbabadbacadbacccaacddbbbadadaacdabdcccdadacddbacaacababbabadbccaabddbbadbbbacacdccdccbdcdbbbcbcabaadcbcaacddaaadccbacbabadaaaaccacbbddddcbabbcabbbdaddddbbbadabbcaacacbccaddcadbcbacccdcbbadcbccbdccaddacdbdcaccaddaddbabbaacbcacdadbabbcccdcacbcdbcdccacdddbdcccdadcdaadcadcbabccdabddaacadcbabcadddcdacadcddbccaabdcadadcaaacbdcaababcbdabcbaadddbadbabbcababdbadcdddcbcdcccabddccbcddbdddacdbccccbbcdaaacdbcdbcaacbdcbabbcaddbbdcdbccdbcbbdccacbbbdbbaaacdbadcdbbcbddbcddaddaaadbccbcccadcadddcdadbdbcdaabddbbdcaaaccbcdbbdcbcdcbbbabcbcadccaaccbbbbddaaddbdcabdaadcbdaacbadabdcadaddbbbabaccaddcadbacadbbacaadcdcbdabbdddcaaabccacbabbdddcccadababbaacbdcdccdbccbcbdcabcbbacdbcbbbbbabbbbaaaaacbcbbcdabbadaccbccbcbcbcbadbdccadddcbcdbcdcababbbdaacdcbaddccbbbdcabcbbbdcbdcddadbbddacabbbaacbbaaddcccccacdaddcacabddbdcbcbbabddbcaacbbdbdaadddacbabbbbbbdbcabdbbcbacdbdaabdbabaacdddaddcbbbdadcdcdbdccdcaadbbaadbddadcdadccacccdaaccbaaabcdcadaabccabcbabbbcbcbcdcbaccdcbbbaabdbddcacbcdadaacabcbadaababbcabddbcbcadcdccadcddddabdbcbacbadadbcadaadaabdbcbadcbcbcbcbbcdbcdadddabbccaaabaccbdddcabdbdbcdbdccdadcdbaaccddacbbddccaadbdcabadaadbdbddbadacbbbacacabaddabccacbbbcdccabdbcdbdaadccbabdddddabbadbcdbbdbcababcdacccacdadabbcccabacacdabcaababcacbbbadccacdbdbdadbcdabddcbcdccbbbbddadbabbcaddbbcbadbacaccaaaacdbdbbbdbcbdabadabcadcaddabdbbdaabadbababdbadbbcbcddbbcacbdbcdbabdbaabcadbdacabbbcbabbbcccdbbbcbadcaccbdbdcabcbdcaaccbaadadcbcddcbaaadaaccaabbbbaabdcbaadcadababcccbcdbbaccbbcacbcbddaacdcbbcdcdcacddcdababdbdcdcbdabdbddadaadcbadacababdacbdcaadaaacadcbdaabdbadcddbabaaddbbadcabadcaadcbabaabaacbabadacdbadbdbbaadcbbaabbdddcbccddcbabcddbaabcdbdabdbcdadcbcbdddcaabdbcabcccadcbbacacdbdccbcbbadbdcbaabadddaacccbbaacbcdaababdacabcacaaaacdddbaacbdcbcbdddcabdcabdcddddaddddbadcdaddadcdbbbdddcbbdaddcabbdbdbcadaabbdbcaaddabbcbdabcbbbdadadacbaccbbbadadcbddbaabccabbdcabadaabdcccaacaacdaddbdabddaaddcaadddbcdcaccdcccaddabdbbccbbcbbbbbbccacbdaddccdccbdbbdbabaacadcadccbdbbcbdbbbcabaacbbdaddacccdbaabcaddbbbccdadccbcbbadcbddabababcbbcaaabbbaaddbdbabdcdadbdbdccbaabbcaadacbbcbddcaadacacbabcbacadbaabbbabcabaccaddaddbdcbbbabaabdadbdadacdcabadccbadacdabcdaddcdcbaabcbcbdaddcaababdacbcdcdbaaabcbcddbababadbbaddacdbddabaddcbaddbbacbabbbabcddaadddcdccacdaddcabcbaaaabbaaaaccddcbdcbaabcacccabadccdcaabadcaaabdbabddcbbcabadbaacccdddcddbbbadacdadbdbacbcdbadbbbcdccbccdcbbdcbbdcdbbbddbbcadcadcbcddabdbdddddcdcddaaabbcdbbcbbdbcabbcabcdccbaaacdbccbaaaadbbbaccbbddbabaaadabdaacdbbaaabadadcabbabdbcbddcacbbbcddbcdbbcdabcdcbbcaadcdcdadadcabbdddbaacabccabcdddcaabadcdabdacccabdddccbcddcccbaacdaabbadabbdbccbbbccabcdcbcdcbcdaabbcabadadbdbbbcbbabaaccdbabcbcabddcacdccaacdddacdcacdcabaaadbbbacbbcaaacabbdbaacccaadcadadbccadccbbcddcadcbbdbcaacabbccaabdcaaadacbdcddaaacbbdbddbdbcbaddbccadbacdaacdcbcccccdbddbdabccbbcbaacadbdabdcbbbbbdbccdbdcbabbcaddcbbcbdbcadacabcbcaacdbabcaddbbcbcdaddcbabcccababbcabcaccbccacacaacbaabbbcccbbbdbcaaacddbabccbccdddcaddadbcbdbccbcabadbacbdddacdbcdcadbacbbadacbbcccdcbdcdcaaacadcbdaacdbbbcbcaccddccadcadcdbccddadbbdcaabbcbcbbbdacadccadcdcaccaadbdddcdabdcdaddcbccacbccdabbacdccaabaccadbccabacdadcbccabaabbdddcabcccbcbcccdadadcabdbaadbdcababbdabcccccccccdabdccbacdcacadbccabbacdcbdddcbdadaabccdbacdbadadacaadcdadccdbccdccdaabbdaabccdaabccdcddcabaddbccdbbddccbaabdabbcadcbcccabadacccbaacccddababaddbadcaddcbdcadacbcccbdabaddcaabcbbcbbbcbadddbdbbaadaadbdcddcbccabaaccacbddabcbbdbabbcbacbdbddbbcabbaccabcadcbabdcabcbddadaacacddbdcddaabcbacbadbcdabaaddcaadbdbdddbbadcaacccacacbaddabbbdadbcdacdabcdaadddcddbcccdbdbcbbdbbcdbcdbdbbbbdcbcadadbcbdbdbbabbdbcaddadccacbacadadcaaabacccababdccdaaabdcacdddacdbbbaccdddddcacaabdadbcbdbadcabbbddcbabacacbcbababdbbccadbcbdbaaddddbdcbcadbbaacaaacaadbbdbaadbbccbaadaacababbacbacccbdcddcdbdcdcbcbdaddbbacbddacbdcdcdddcdccabbcccddaabcbcccbcbaadaccdabcabbcbbcdaadacbbabddabcacacbdabdccddcbdcbccadbaddcbcbcaaabbadcacdccaaabcdbaaabdccbbaabcadcbbcbdcbcbabddccddbadcbccdaacaabbbacdcbbdbacbdadabdabdcdadbcadcbadddcadacacdbdadadcaabdbcbcaccbdcdbaaddcbdadcbabbbdccbaaacaabaccabdcbcddcbddbbaddacbcabccbdcccaaadbabddbdcdbaabdcccddabbbaabdbaccbadddabacbabacdcccbbdccaabbbbbbadabcddbdbcbdadcbacbddaaaccdadcdaaadcabacdcbacdcddaabcdddbbaaddbdabddbdbddacbdbaacdadabbdcbadcbabcdadbcbbcbbccccccdadaacbcbcaabbaadccdbabbcbabcabdbcbcacabbbbcabbabbbaddadabdaadacccaacadabddbcbabccadbacdaabacababdcabbddbabdbacdcadbabcaaddcccacdadccddbdcdcadbdabacdbdbbcabddbdcbccadbdadbbbbaabbbabaaacaaacbddccadcbdcacdccccccbbbbdbdaabbbaabddbdccabbbdbbdbdcaacbaacdbbbcacacdcadbbbccacbbbabcbabbacbabbcbacbaabdcdabcdaabcddabadabbaaacbadacddaddadccdcbaacdccbdbacccdaaadadcaaabbadbaaadcadcabcacaaacacbaccbdddcdbdbaadaccabdcbacdbdbddbdabddabbaadacdbbdbbdccaabcbccdbdcabbbcacaabddcbcddddcabbabbacacbcccdddcccbaccbbccabbadbbadbbaaddadaddcdacdccabadbabadcadbbbadbabcddabdcbbbadcbaccabddbdbaaabcadbcbcaacbacacbacccdcabbdacdadcbbbaddbdabcbadcbbaadbabbabcadddaaccbcaddbbdbddbacdcbdaabcbccabdcbdacbadcdbbddddbbbdabcaacadbacdbcdcbbbbddcbbccabddabbabcbaacdcdbbbbcdabcdcaadcdbbadccbaacadacbbdabdabdaadbdbdcdbcdbaddabdadbcccccbbabcaaddccddbadcdaddbbbdcaadcabcdcbbaabacbcabaddcdcbbbdadddcbdaddbdddcbadabcdcdccddbbcddbabbdcbcbbbaddbccbacdaddcbcbcbdcbddaacdaabbccbbcbccabacdccaddaccdbcdcaccbcabcbdcaddaacbbabbdcaccccdbcdaadddbbdacddbdbdbdabdcbcbcbbdaabadbcabdcdbdbcccccaaddcdbdbcdadbcbaaabddaaadcaaacbcddbcdcdaacaabcaaaccacbbddacdcbbbdabacbcddcdaddadcabbdbccddcabcbcaadbcbbbdbbdcccdccddbcdabbbacbaacdabcbcadbcdccccabacacccddbcbdbbddddbccccccdbcbdbbcdcdcadbbbabcbbbcbdccbccaccbdbbcacdbddadbababbbaaabbccacbdddcabbcccabcbabaaccdddccddabbcabccabddbbbacaccddbabadddabcbdcbbdaacbbbdcbbbcbaacabdcbcabcbcacdaaacaacdabaccaacbbbabbadccacdcdbaacdddaabaccaaabddbccbabdddcdddbcbbaddcaaccaaacaaccdbdbbddbbabbdbaacbbbdbaacbabadbcccabbbabcaaacdcccbbacbbccbdaacdccbdbdcdcbcdabcbacababbbbabbdcbccccbdacdbdbcacaabdbdaabbdbcdddabdccaaadbdabcdcbbadcbbbbdbdacdacadcdbbbcddbacabaadaaabdaabbaabddabacabbccbbdbddbddbcdbbabcdaabacbaabcddadcddbdddcccdcacddbbdddcdbbaddccbbcdccbbccacdccbdcbbacacabadcacadddddaabaccbbbcdbbbcdbdbcaacbcdccdbbbdaddcccdcdddccabdbdbbdcbabdaaddbbdcbddcbbbbcbacdbdbcaaadcbcacbcbdcdabbdcbadabbacaccabbcbabbdabbbaddcbbadccdbcaabcbbcdddbdbcccccddacabbcbacdabbacdababdcaadcccdbdcdbdbbaacbbaccbbadcacaaacbadcacbddbcdabdbdcdaabcaccbddacbdcbbaadaabaadcccbcbaccdcdacbacccdcbdcdbdbdbdabacadcdcbcacdcaddcaabcabbcaccbcbaacbcbaccabdcdbaccdbadabadabbbdcbbbbddddadddddcddadbdbcabaaabdcddaabbacbbbadcbcddddcadddaabdbcddbcadcadaaccbcbcccacbbabbbbcadbaadcbdcdcdbbcbabadcbcdbbaaacacdbbdacddbbccabdabdccaabaacddbdacdbacaccbbacbccbbddacbacacdccaadddcbbbdbaacdacdbcaaabdbaaaacddabacbabcdcbbbadbbbddccdabddaccbbaaacdbbadbdacadccdbabbdcadccccbaabdbdaababcdadabcaabbadddabddbbaddabbadddccaaaccabacdcccacddacbaabcbdabdbcbdbaabadadbccbbbabacccbdbacddccbadaaacccbbbbacccdadacccccdccccdbddcaaccbdaaccbadbbcdbaaabadbdbdcdabcabaacaabaadbbdbadadcaabcddadccaddaacbbddcddabbbcaacbbddccdddabccdaadbdbbcadcdccbddacaacdaacbbaadabaccdbcccbdcadbbdaaadaddacbbcbccaaaadbbbddacdacddacdddaacbabacccdcbddbdaabbbacdcaccbabcdadbbdccacabbbbaddbbbddacbdcdaaaadcaadcbcddaabacbcccccaadbbbbbcdacdbbbadbbdddadabacabadcdbbbdbabcddbbadbaccbbabdcacbbadababcdcabbabbabdcabadbcacbdbbaaddcdbabdbbcbdbcdacbcbcaaddcdbaddaadabdacbcddcccbcbdadadadddaccdadcbdcdddbdbdabdbcacbcdcdabbdaadaadbbdbdcccbbaacddabcddddbbdbaabcabcbdcdcdbccabdbdcdbddbcacbaaaacbacacdbabcaabdcbacaddacabdbcaccaddbccbcbaacadcadbcdabcdacdbcbabbcdcdabbdabcaadddacbbadacbdbdbaabdcbcbdacdadbbcdddccdbdddaddcaacaddbbcdbbdbbdbddcdaaaaadadabcbddddcdabcbcacaacdbacadcacbadcbdbacbbbddccdccdcccbbbcabbccdbcadcaccbdcbaddbccbcacaccbbdbababcccbdcddcaaaddbacaaacdccdbbaccdacbbbcdcbcdbdcddaaabadaaacdbccbdccaaaadcccccaaadccdaaaaacabcbdbbabadccbbaabadddcccccadddbdacbdaacbccaaacdbdcbdcdcddadaddbbadcdccadbacaabbcbadabcccbcdcdaacddadcaabcabbbbdcaaabdadbacadcadcdcaacddacadccbcdbdbddbabadabbacabcbccccdadbabdabbdbbaadbbdabbcbdbdabbbaaddacdbbddbdbabcdaacdddaabbadddbdcdbabdcaaaabbcbbbacdcdddcdabaaabbacabccabcddbbaccaadbbddbbccacbcabbcdccccbbaccbdaadddabdbbbaaaddbdaccbbbccbdaaadaccbbacbbababdcdccaacddacbaaaaddcbadadcbcbcacdbbdddacbcbcacaddbcdbacadccabaddcddbacaaccdacdcabbaddcccdccdbdacbddbbcaddadcdabaadaddbcacacacaddacbacbbaddbdbabaadaaacbacdbccbacbdbdbacdcbacbdaaddcaccdcccaccbdccdaadaacbdacbcdcbbdacddaccadcddcbabccdbdcdbbdcaadddcdcdbbcbccabbbdcbadcbadcbabccdcdcabdaaacbbcdcbddacdccadbabddbdbadadcdbdccadcacdbadddcdccdacbccbaddddbccdcaacddcbabdbdddbbabaadabbcadabdacaddcbddacdcdaabbcbcaacbdacbccdbacbcabbbbdadbbaaabdbdcbdcbacadabdadbcabbacccdbbddcdbcacdacdadcacadcccaadddcbcdbcdcddddaabdcdbabbacbbdbacbdddccddcabcbddbacbcacdcdcbcbdbdcbcbccabacacdcbabbbadbaabaabcdccddacdacccdcdabcaacdbaabccbaabbdbcadaacccccdcaacbadccdbbabccbddddaadabbadcdbccbbbcdbbddbacccadbdaabcbcbbaabacdcdcddababccadcdbcccddcbcbbcadabdadbccbccadcbacdccdccdbbaddbaddccdaaabddbadccbbbddaccabbbacccddacadaadbcbcdbdbdadbbccbacabdccddadccaddadcbdadbbaaaabaccccddccccdbbdadbcbbcbaadbcbaaccbbbbbbabbdccabbcabdcabdbbbcdbdccbabcdbdcbdcabdabdbbcacbdabbdbdbaadbbdbaddaadacbbbcadbbbbdbdbdccbbbaddadcbcbdbccdaddbccbaaaadddabdcbacaaccdcbcabdcdbdaccbabddbbacabcdbcdbaabbcddbaababbbcdddabdacbdccdcdbbaadbccdacadadbbdccacadbbcbbabccdcdbcabdaaabbdcdddbcddadddbaabbaabaabccdabdaadacdaddcadadccdbbcabbaacabaadbabdabdccdabbccccbdcddddcbccccbbccabcddadbadddccdaaddbdcdbaacabaddaabcacddcaaddbaabddbddadbbdbcbaabddbcbdcbcbcccbcbbcaaaccbddccdbadcccadbdacabbbaabcaaadacadcccaaadadbddcadcadcbabcabdbdcdcdadbdaacbdaaaacdcdbaccbcccdaaaabacaabbcbaaccadbcccbcdaabbccacccddabdddddbbdddaccaabdcacababcdbdcbdaabcccabcabaacbbbacbbbabacbcbdaddadcddbaddacdaacbddbcbbacbbbbacacaaccdbaacabdacacccddcadabcccccadaccbdcbddbcbabbdddcdcbcdccacbbcaabcaabaddbaabbccadacbcbccbdcdacdbcdacbaacdadcdabdbcbbdcccddcdbbdabcdbccdcccbdcabacaabbacbbaababcbdbcdbdbcbcaabcacabcbadcbdaababacdddbcaaddbcbcbcaaaadbdcdbaddadddddcbbdabdcdbbaaddcabbcddbaccadcdbdaddbddaacdadccaadcbcdbacacdcacdcdbbbdddabbaccdcbabbabcbcbcabcdcbaccacdcaacbcbabcddbcdadccadadcbabbbddbcabdbabbddbdadcbbbabdcdbacbcdbaaacdabcdbbbdadaabccadbbcacccabdbaddbaddbdcbcdbdbddcccbcbbabcaddbaadacbddcdaababaabaadaccabaacacbabdbcccacaacaadaacccaadadbabdcddcbbcaddabbcbbbaaacbcbbbcbdbdcdadabcadcacbbbcdbbababbcaabdbbaabcacbbaccdabaddaadaccadaacdccbabadacbabbacaaccbbaacadbcdcbbdaaaadbbcdbcdbadadbccdccbabddbabddaaabbdbbcbacdcaacdbdbbbcadcaacacdadcbdcbbbbbaacadcddcbaacdacadaabaddbdbaabbdadcccbcdccacbdabaaabadbacbddbcdcdcdbddcccdaacddccbadccaabcdbdacdadcdcbdccdadbbaaccaadcbabcbdadccdadacabdadabbbabbcbcbbabacddadaabcacbacbcaaccdccbddddcdadbadcdcdcccdcaccbbbbababaaabcadcabbccbdbcbcaaacdbccdaaabbcdcddaccdddaaaaacbbdbbaddadaddcbdbdccdabacbdaddbaccdcbacdcdcbabdabccaaccbcdacbabaccccccbaabbbcbacababcdbdabacbaabddaaaaabbcdcbbbdcacadabccbbdcccdcbadaccadbddddabdaacbbaaddbddcabccbcccacaabcaabcddbcacccdcdabadbbbdddcdbaacbcadcbcadacbccbccddacdcdababccbdadadcbbacdcbcaddccbaacdcdaddacccacddcdaccbdccaadbbaacabddbcddddacaaabddaadabaddaadddadacccabacacadbbdccbcbadccaadacddbbabbdcbdcbbbbbbccdddddadbbcacdadacababbaacabcdcaabbabcaabadaccbccbbbbcacabdbbadccaddddbbbdadddddabbbcbdbaabbdbaadcbcdbaccbdccdbbcbdabcbdbdbaaacacdccbbccdaddbbcccaadbbbbdbcaaaadbddbcbabccbabcdcbadadddcadddbaddddbdaccdacccadbdcbbbabaacdacdabddcdaabaaaabcadbbaccdaaaaabaaacccaddaabcbababdaacbaaabacaabbacbbbcababbccaddbacaadaadccbbdcbdcaadccbddbaddacbcbbadcdcddccdaccccbaccacbddadccadbddcacadaccddddacaaccadcabbbbcaabbcdacdccdddcdabdbbaccdbdbcdaddbbccdcabadbaaccdaababaaddcbbdaddadbaddabacdcaccbbbbdbdaddbaddcdcadbcdaaaaacbccddadddaacabbcddccbcabdcabbbdaccbdcdbbaaddadcbccabadbdccbbbdbadaadaabbdbcdddabbbdbcbdbdaaaabcbbdccbaabbaaddabcdbbcbcabaddabbdcbcbbbbacdabccdcabcbcadacccddcbdbdccabacabababcacbcbaacadcdccccddddcaccbcdbabcbdabccaaadaccddcbbdcccdbbdcbcbcbbcddbbaabbadcadddccadcabbbacdabcabddcdbcccdcddddbcdcaadcdbadcacdaababdcccaacacdbbbdbddcdbdcacbadbabbcbcacacbdcabcbdbcacddbbbdcddbbdcbcabbccaaaaadaaccacadcaccbdadddaccdcabbcbdbbdbcacabddcbddaacdaaddbdddcabcbcdcdcdbcddaacbbcddcdbaabcabdcdcdcaabcdaaccddcbbddaccbbacdcacccbcdcccdadaaddbaccbbbbabadaddaaabdabbcbcbbcadcddabccaadadadbabcacacbadbbadabaacbabcdcdbbbabdbddddcbadddbcaaadadabcdbcbdcdbacccabcadcbbcbbbdbdaacdbdabaacbbbdcaaaccdcaacdcdcbbcdadcaaadabdcccaddbbcdccdbdaaadbacabdadcadbabdaaabdcbadbabaacccdadcccddbadacbbadcdbbcacbdbadcabdaacadcbcccbdacdcdadaddcaacccdccacdbcdabacaabdcbbadddcabdadadaacbccaacadaabbaacccbbccdbbdacabcbcdcdaaadcadabdbbdadacdbadbbdaddcacacbadadabacbdcdbaacdaaadabdbbdaccddbdbddbcdcbbbcbadcdddbdcbddacadbcdacbddbccabbcbadcbbadaaabbcacccddabbdacbcdcadcdbcdbaabaaacaadadbddcddcdccdaccdbaddabacabbdcaadbddbbbbdbdcabbbaabaaaadddcdadccabbdbccaacdccbcdabadadcadbacbacbbadabbbbabdcdacdbaaacccdaadbacbdaccaddccaccaabbacbdbdbddcdcdacabcdbadacbcbdacdccbcaccabbcadaccbccddacbbbcabcdddcaaabdddaaddbbcaacdacacabbbadbaccdadbdbbdbdccbcaddcadadbbaabaaacbaabbaacbaadcbcccadcdcdddbcabddcdbccaddbdaadcdbaadbdcbabcbbbbbdbdbbcaadbbdbadcdacbbbbdabbaabbbadbcddcaaccddacacabdbdcbdaacdcbadacbcaacaabdaddcabbadbdacdbcdaddbbcbbdacddbbcccdcaccccacdbcababcbadbcdddabaadaaaddccbbaabdcccbbbcddadcbcadbaccdabdbdcacadbcabccaaadbacbacdabdccbabacbbbadbdbccbbaccacaacaacbcadbdbcabcbbbbcdbabaacdcbdcbbdcbcacaabacddcddabdcdabbdbcdbddccbabcbbaacdaaddcdcadcdadbbaacaadcbddacddcddaabdccdcabaccdddccbdcabdccbbcabbccaccacccaacababdaabccabbdddcbcbbabbaaacdcdbbbbbcaabacbcdcddcbbddcccdcdbaaababbbcacddbbaadcacbccddddcdaccadcbaadbbbdbbabbababddddbccaacabdbcacdcccdacbcdcaccbcadbccaaabaacbcaaddabcabacacadccdccbccacbacbbadddaccbcbbdddacdbacaaabbdadcdbccacbacdacaadbaddbccdcbbbacabdccbadadcdddbccdbdbcdbcbdacdccdadaaabddccbbbaccbcccddcadcdbaabbcdcacaacabacadbacbcbbddacddbccacdbdcdbdcacbcdbadadbdccddbcabcbbcacdbbbcdaccbcdcaaaacadaaaabacddbadacbdcbcddaabdbbbcabdabbdbbbacbcddacadcaadddacbcbdccdcbddcddaddbccdbcddbadaaddcbcacbaddadcaaacbacbdacddbbdbbaccbadbcdabcdbbacaabbbadabbabcaddbadabdaabccbcaaabdbcccabbaadabacadbcadcdbbddddacaccadabaadcabbdbdcaacdcdaabaadcaadaaacddccdcaabcdaabbdcdccdaaccadbaccaaacaddbdccbadbcdadccbccaacaadaaccbcabcbdacddcadadbdbdddacabacdcdbddaacdabbbcabadbbaddadcdbaacaabaddaccccbdddabadaacdccadccaadcbddbdcdcdadccbbdaadbcbbddddbaabccbdcacbcbdccbaddcacccbbdddbbadbaccadbaaccadddabaaabadabdabcdabdcdbbadccdbdaccdbaaacdcccbaaddbcdbaccadabcbcaaadacbdcccabbdcddbbabaccabadcdccbcabbdaddabdbcbacddabcabdaaccaacbcdbacdccdadccbbbbdacbbcacdcddccbaacaadbdabdaddabdbabdcbcddacdddcadcdacabadaaaddaddbacbdabbaaadcbaadbcdddbaabdcbbaacbcdcaabbadabbccbdcaacbdbbdcbaddbdbccdddbdbaaadacdacdbccacbabaddcdcadcbaaacddaaaccddadcdcdcdbcbdcdcdaacbcaddccdabdaddcdccccbddcdcaccddccddccdbbdddababacacabddacabddcabbabbabbdcdabbaddbdcbbababddadbabbbcdbbabacdbabcbccdcabbaacacaaabadddcdcbdbdacbbbadadddaaaabaccaaddaababddcdbddaacbdddaaacdbdccaddcabadcdbcdbdcddcbacaabbdbabbadadbdccacdccbaaadaaabdabbbaabdcabbdbbbddbbdabcbaddbbcacabacbbdacdabdbbadadbaccaaabccbccabdaaadcdaacbaabcbaadacaaccbdacddaacadcaabaaacabdcccddbadbbcddbababbddcbabdcbabbdbbcadaabdcccdddbcdcbbdcdcdddbbacdbdabddbacddcbcaabccaaccbbadbbbdacddbbbcdacbbdaacacdabcacabbabacddbadbadbbdadadccbdadacbbdaabbbbacdcaaaccdaaaddabdaaabddcbdcbacdcadbcbabdacdbbaabbcaababadadcdbdacabcbbbbcddccbbbbccbbdbdacdccccabdbdacddaccadadbcbbdbacddbbdcbabcabbdddcbbdaabcdcaddabbdbbdddcdccbbdacabbccaaabcdcbdabcdabbbbdbcdcccccdbcaacbbcddcdcbcbaddddabbacadcaaabcbabcabbddddacddadcabacdadacccddcaaaaccbcbadccbbbbcbbbbcdbddccaadddddcadadddccdbcdadcbddacdddacbbbdcdabcddaccbabcaddababbacccbcaadcccbcbbdabadcacdacccbaaaadccccbadbadddcadddcccadaacabcbbcaaaddcbbacaadcbcbbbddddabcdddcdadcabbaabaadccbaaaacaccdddabbbbddbcddbbbbdaadddadbbdadccacacdaddcdbbddcacccbaaaadddcdbccaaaddabbaaddbdcdcacbcdbdbbcdbbacabababddbabbcdbaddcbcabbadcbbbadcdbddcccabddddbaddddbbbbccbbbadbacbbcbbbcdadbadcabcbdabdbccabcbddadbaaccdcabdcdddcbddbbbacdcabdbddadccbadcabcbccadacddadadccdbdcbdaccacaaadcaaadbcacbbabcabaadbcdcdbbcacdccabdddbbcbcbabababacabadddaaacacbaddcadcdbbcaabaaacacdbdcdbcdcabcccaacbbddbbcacdbccabdabdaababaaabbacabbadcbabbacbdcdadcbbaccbdcdbaadaadbbdcbbabbdbcbadddccccdcdbbbccdcbccbdddbdbbcddacdabcbdbdadccbdbaacdadacaddcaaaadbdcaccdadddbbccadacacdabbbaccbbacdbbdaaddaabbbbaddbaddccbdbabbbacdadbdcbcdabaaacdabbaddcbddcbdbccdbbbdacccbdbdbcbcbcabcaacadaadcbbbcdbbbbbbdccaaadcaddcdddcbbadbbcabbbcabdbdbbbaccdcacbabdbaadaaccabbdbdaacababacbabdbbcbbcbbcbdbcccbbbaabcddbdababcdbccddcbadcaaddabbaabdbbbadcdcdacaacdaacaaddddaacbabcdbcaaddabcabcdbbcaaacdaaacdbbadbdcaccbdccbbaacccdbbabcccdabdcadcaaabaddacacdaacbcccbcabcdbabdadaacccdbdabacdbcccdacdacacadcbbbddadcabcddaadaacbbbaccbddbbadbcaccadbbdccbbaddbdbaabaaadaacdbabcdadcdddbabcabaabacbaaadaabcbbbaddbabcbdabcddbdbbcabbcdcdadbdcaaabbcdddabddccbadccddbcdddacadcacbdddacaadadcbdbcbcaccbcadaddabcacddcbaaaadabddaacbbcaabdddbddccbcbdcaadbbabdcacccbdabbbbbbdabbbdaabaaadcbaddaabcccccbccacabccdbcacdcdcbacacbabacbcabaabdaddcccbccaccbdabbcbacacbcbaaaaccbadbbbdccaaadbccbcadcbbabdbdaacbadcbaadacadbccacacccbbabacadcbdaccbbadaddbabcccdbabddbaddbdaacbbabbcabdacbaabdbcaddcabdbcaabbadaddadbddbddcaaadadaababbdcabcaadcadaaadadadcdbdcbabdadbcabcdadabddcbdccdbdbaaabcbcbabcbcbaadacdddccbabcbacaadaddbbccbbaabdaaababcbddabddbaddcbcacbbbccaaacdcccdcadabdbbbbadbadddbbadacbdcbabaacbbaadaaabdbdbcaaacbcbaacddcccacaddabcadaabacdbcbbaddcaadbacaadbddcaddccdbbdcaabcbbaadccccbadcdaccddcaaccaddbabcbdcbaacdcdaddbcddacbdabcbacdabdddcbabdccbbaddcccdcdbdababddbabcddbbccdcdadddbadbdaccabacbadcacdcabdcacdcdbcdacbacbcabcbcadabdbbccaacdadaddbacccccadadddacaabbdcbcaadaadbbccacbdaabbbacdbbbaabaabccbcbdbcaadacdcbcbdacaaacadabbcddadbdcbacdabadaadaabcabbbadbcdacdaaccccbacdbcdabbdbabdccdabcbcdbbcdacbbaabbcacdbcaaaaaabaabbcbcdbcbdbbcbdbdddccaaccdbdaddaaccbaacbdcbddccddbdadcbdcadcdadcabacdaddacdaacacaababbdadbddbccadbddbadaddadbdadbbbaacbcbadababbdbabddccbadbccabbccacbcbadadaccddcbbbaacbdbcbccacacddadacaddadaadbaaddbabcdaadacabdddbdaddcdbdbdbaadabbbadacbdcbcbaddbcbbbcdcdbacadcdacabbdbadaaacbcabbcadacdcbdcdabbccaabacaccbcdcaabdcbcaacbbdbbabcbdaddccbdddabdccbdbbabbbaaaadbadbddababcbaccbbccdcdcaaacbaaddcabdbaaddbbbcbbbaccabadbccadadbcbdbcdaccbdabbdbdcadbccbcbbaadbbbdaadbbadacacbbcdcaabdbbcdbdddcdccaadbabbadbccccacdadaababcabacdaddbbbccabbabbaddacbacdababcaaadcdccdbaddaddabdbdcbbbabdcabbdcdbbdbbdcbacbbcbabaddbbbbdcabcddbacbbbcdadacbcccdaaddddcaadbcadabcbbcdaadbbdadabdbdaaacdabdaaccbbcbabbcdabbaaacbcdcdabacddbacabcbababddaabbccdbabbcbbabaccbaaabbcabddbbaacbabcbdbbdbcabcaaacbaddbdccddadbdbdabcbbaccbbcaccaaaccddbbbbbadbcaddacbccdacdaaabccdbcabbabdcabbdabaaaabadddcdcdcbabdabdaddcdbbcacbccbccbbbccbccadccbbdcdddbddcdcaccbdcbcacdddacdbddaadaabbacadcdddddbdcddbcaaccacadcaaccadbcdbacaadaabaddbdadcaabdaacbaddcabddcdcbcdbdaabccbbbcccdcbccbdddbdbbbdcadacdcadcabcbaacbcabbddcdacaddcddbbccabddcbcbacbcadcbcbbadaacdaccadcdaaabbbbaaaaccdddcbcccbdbdaaddabbbcbbbacbadbdbbcabacaacbcccbddbccdaadbaadcdbacacabaccbdacadbaabcbacbadcbbccdcddbbacdabdcccdaaddbacacdbadbcbdadaccbbbdcddacbbacbdcdaadccaddcccdccacdadccccabaabbaaacbcdbbbdcacbacaadaddcdcaabcbdccabadbcbbadbccaaccadbcddbabaabaccbcaabadbbbdbbabdbddddbcdccdcaadcdbdcabadadabababdcbcdcadbcdaccddbdccbadaacddccdbbcaccaabdbdcacbbcababdababcabbbbbcbaadbdadabdbbabdbdcbabaaaabbabcdddcaccaadddcaabcadbcbaccbddcacbaabbabcadcaacddacddbaaccbdbadddabcccbcccabddbdcbdaccaaabacdccbdaadccadcbcbdacbccddacbdadbddddddcddcaccaccbbdbcdbccdabbacdcadcbddadaadaccbcaccccddbcdaddbbccadbbddbbcbacddaaadcabbdbaccabccabcdbaccddcddaacacaabadadbbacdabbbadbbcdbdddbcadcbcaacbbdbbcdbcbabcdadadcadcadbacbddcdaadbdacddbbccdcbbdddaddddcbddcbbaacdadccadcbacbacbbdbbcacdddaaddaaaadbacbcadcbdcdcdabdddbcabddbbcbccdaaaccbbbbddbddbadcadabddbbdbdcadddacabdadcbcadacdbdcaadbcacccddaabbddbacaccadddacbdaddabccadbbbadbccbdcdcccacdbbdddcbddcadccdabcbbccdbdbbdadcacdbbaacdcabdbbcddcabdcddadaddbcccabccdacdcadbcbaccdbcbbcaacdcbdaacaacadcccdcaacaccbbdbbbabbbdaabbdbbadbcdadcbdcadbaddcbdddabcabdadcaccaacbaddcadbbaabcabccabbacccdabbddddbdbcbcbacaacaaaacadabadcbaddadacdaadcbaabdcbaaadbdaaddaddbbcdbaaaddbddcdcdaddbadcacdaaacdcdbacacdbaccbbcdaccacbabdacbdddaccacbcacdcaddbddbbdaccaddccbabcaddbcacdbbacbaaccdaacdbacbcbbcacbabcaaddbbbbdcabbdbaadcacbdbaacddbcaacaadcbabdaaaacaccbbbbdabbbadaddbcddaaccacacddbcbaadacaddaacadbbdbdabdabcbadbabcbddbadcadaaabbbaccbadcccccbabaacdcdabbaccbbbdccbabcbbdbbcaccbdacaddbacabbaacadcaccaaddacbabcadcbcaadddaabbacdcaaabdaadbbbdcaacabdacccabbbadbcddcdccbabacadaaadccaccddacadbdddccacdcaaaddbabdacbcddabbabacccaddcabadacccadcccacaccbadbacbacadbdcaaddbacdcdabbdaadcccbbbbaadcabcddccaccbbadabadcdacbdadbdbcacaabcdabdddcdbacdcbbdcbdabbdbdcacabcbbdbcbcaaacdaccdaaadbbdddbbbbbbbdccacccaacdbaabdadadacbbbdabcbdddcbaacbbdabdddaddabadabdabcddbccccbaccddbacbcbddbddbadccbaaadacdccdabadbcbbbadbabaadcdaccdbbbdcabdacdbadcbbdaaabbbadbcacdcaccccaabddcdddbdbcacabbdcadddbdbdbaaddccccaaaabdaddbdcabcdbbabdcacaaadbcdbabbdddcaacbbccdccaccbbbbdccacbcddbbcabdcccaadbddbabbdadbdcddadacaaabccccaacacaddaddcbbccbbcdcccdbdadbaababadabbddcdbdacddbbbaabdabcddbadadbdbdaaccbacabddbbbaacababbdddbcbbaddbacbabaddbaccacadbabcaddabdabcbadcdbdbdbabaabaadbcdbdcabcbadaabaccaadcacbaddccadbddbcaadaabdcbaddbdabcdbcacbabddaabccabcdaabbbdbccdacbcbacbbcbcadbcaabddabbacacdcddbccccccbcaccadbaacddccabaaabadcbabaadbcdaaadabdaadacbcbcacabdbbccdcdcdccdddccccaccbccdcacabbbbbabdccbbbcaababcbabdadcdacbabbcbbdadcaccdbdadadddacacbaaccdbadddcbcadabcacaadbadabdabddadbcacbccddbdbcbacabddcabbbccbcdbbcabdcdcadccbcbcaaabacbbbdacabcdcbcccbbcdabddbcaadcdbccdaacadcdccbaddbcabcbcaaabcdcadccdccdbbcdcdbccdccabaadbaccbbabbdbbddbcaaabcacbcdbbcabdddcdbdddcadcdcddcaabacdadbacacbbdbcbcdaacbbbcadaabdaddacbbcdcbcdbdadcbaabccabddbcccdcaabaaddcdccdccbadcacddcdcbcddbbabacccdbadacdcacbdcdbbdabbcdbacbcdacadccdabaacadcdcdbacdbaadbdbbbcbbddcdccabcdacacdcbcbddbbddabdcbaddbaccbbacbbadccaaccdccabcbdaaddcbabdcbabbbaddddcbbdcaddbdcbaabdbcccdacdcaccabbdacbdbadddaadacbbdacbaaddbcbaabdbdccdbdbcaaabbcddccbacddabcbdbaccdcbaddcadbdaaddcbaabacadccbdababcbaacbadcabcdbdcdcaaaabcbbabadbbacdacabdccccdcdbdccacbbcbdcdcbbbaadaccaacaadddcdbacaadbddddaadcaadddbaadcacbccdccbadcdddcaaddbdddabbbbccbcaabbcaadcbdabbbcbbcccddabbdbdbadcbbcbacabdacdbdbabcaccbaaadbadddaacdccadcaaaddbdddbccdddbbbbbbbdcbbcadbccaccadccbcaabcddcdaddabbdacdccddbcabadadcbdabdabbdbbacadddcddacbcaabbbcddabaaaadddacbdacabcaccaccbacaddcbadbacddcdcdbcbdbcacccccdacabdbccbbdbcaacdbabaddadddbdccdacdcabacaabadadccdacdcabcabacaaadcdcccbdbacdddcadaaacdbcdbdaacccdbcbdbaddababdbcbddddcadacbdbcdbdbcaccbaabcbdbdabbbdbdacadacdaccbabccdcadccccddadbbdbdbdccdbdadbcdabacacabccddacacadabadbcbbabdcaddcaaaabccbcbcdaabdddcacaccbcdddaabdaddccdddddbcdbcbbadbbdaadbccabddaacbbbbdaddabccbdcdadabcbcadacbbccddcddadabcbcbbdcaaadacbddbbacbabbdbbccbdbcdaccaabdcccdbcdababdbadacbdbcdaddddbdcdaacbcaccaadcccaaacdcaaaacccdacababbdbbddabaadbcacaadbdaccacaddaaabcdddcccaabcaccbcbbbddaadadccddbabacbdcbbcadbbaadacbaabaabaccaaadbddcbccabacbbcbcbbcaddcdaccdabaababdbbbcaaddadadbacbddccbabbbcdcccdaabbcbcdadbabbdaabdbccbacbccaaabdcccdbdbaccbaadabbaaabdacacbabaacdcdcbaaadbbacaabcabdddacacccddcadbdcacabbaddbcbacbbaaadbcbdcdccccccbbcadacabdaabbbbaccabdcdbbdcaccadabbbcbabbbdbbdcbccdbcdbccdacccbbddcbcddbabcabbabcccbacadcbadcbdccbcbcbbbcdcabaccaacbdcdacbcdadbccadbabcbaadadcbbddbddcddcdbdbdacaccdbcbccbadcddaddbcdddcbdbbabbcbadadbdcbdddabaddaccabaccbbaddadddaadcdadcabddccbcbbabcdccbadcadcadadabbabbccdacacbdbbdbbabbcaabbddabdbdccbcacdbbaabaabbbadcdaddabdaaabdcdddadddbbcbacacaacdbbdbbcbcdaaddcacdbaaaaaccaabcdbcaaadccccdcdaadccdddaccdcdbccaaabbdbbaadcadcbdadbaadcacdcdbbbccdcbccabddcbabdcdaabdbacddacdcdbabcbabcbabdbdabdcddaddaaababbacdcdddcadcbdbaddbadcbcddaabcdabdccbccccbaabadcdacbcddbabbddabcdbabcacbcbaccaacaacccaadccdddabcbcadddbbacdabdabdcacbbbbcbacacdabaadcaccdddcdbadccbaaabdabcbadcdabcdaaadaacbbbacabdaddbaabbdbbabaadcdbbbdadaacacaddacbadaabdaccccdbcaccbaabdddcddcddabacbcddaaddcacabcdccacdbcacbbbabdbcaccdadaddbdddacacdadddcaacbaddcddbddacccaacaccbaacdcdcccaaccbbacdbdbcdbcdcaacccccaaabdbabaaaddbbccacaaddaadacabcabcbbdddaccdddadcbbcdaccbbcacbbadaadcdcdcaabdcacababbbdbdbbdccbbdddadaaadbdcdccccbbabcbccadabacbdccdcddacdccacbbdbccdbdbacbbdbdcbbacdadcdbadbaadbdcaadbccdaddaaadabaddcbbdcadcccdbcccddbbdbdbbaccadcaacbdadbadbbbbcacbcdbcdadccdaacadcddcaabcabdbaaabaadccdaadcbbabdccababcaacbbdcddacbdaccddbbbbdbbbdaacccbbcabdccbaabaddcdabcdbacbaacdabacacccdddbdcbcadaddddcdbdaacccabbcbbdabcdaaaaadcacadabdcccdccdabacacbcacbdccbadcccbdbcaddacddbdddcaccbdccdacbcadaadcbdabbacdddbbadbcabbaabcaacbbdcacbbbacbbbddabcdadbaccbcaabcadcaadcadbbaabacdcbabcdcbddbacddbbdacacbdbbcbadbbabddddcdaabbcbacdcbccadbcbbdbcacacccabbabbbcaacabbcbabadbdbaabdbdcdbcccbabaadaddbbcddaadccdddadcacdacaaddaadcabaabddbcdccacddbcaabacabcbcabbadbaabbbccaaacbccaddbaaacaacdadadaddacacacbabbbcabaaacacbbbbbaadabbbacbdaccadadaabdcbbbdaaddddcaaddabdddcddcdcbadbcbdcbcacccbddbdacbdabdcaadccddcdcadbbabcbadaadddcacadcbdbadccccdaadbbbddcdcadddcbcdbbdccdadadadaaacbbacbdaccdbccbdbdccabdbaaadbdacdcacdccadadcadbbbcbacdbdaccabcadacdbadddaabcccbccbbabaadadbdcbbcdbbdcacdacdcbaadcacbbbcdbdbcdababccdccdaaabbdaaaaddcabbaabbcbbcaacbdcababccdbbcbdbacbadacdbdbbbdaabdadacacabcccdcdcdcccacbabbaadabddbbadbbdaddbdcdbcdccabccacbbdbadbccdcdaacbdccbdaccacbabbcacbcdcbcbcaddcdbbdaabacbcdbacadaaccdbbddacdbabcaaccaabcbdabcddcccbcaaacabdcdabcbbacbadccdbbdcbbcdccbddbbabddcdcadbcbbddaabdcbacaaccdbbddddacbabdcdcabccaddaaddaadacccbdaabacdadadbdabccdbbbadaabcabadddbdccbcdcbdbbcccdcbdbbdcaabcadaddcccccbcacccaaaccdacdcbbbabbdcaaccacaadbcaabacdbaacacbdddacacccaabccbcbccbcbaababddadcadbcaaacccbddbcccbdcaacadacbacabbabaaadcadcdbbabaacacddccddcbadbacddaddbcbcabddacacbaacddbabddbbadcddababccdababbdcdccccdabddacbacbcabdddcdddbcbddbbdcbabaccbbacabdcaddccbacaaddcacdabdddccbbdaabcdadadacdacacdddbbcabdabbccbadbacbdbddcccaaacabacaadcdcbccdadddcdabacaddcbbbcbcbbcdccdddbcccdddbaabcbddcbbbbacaccdbcbcbccacbddddcddabdbdccabbadadacaadabaaccbcacabbaadbdddccccccdcabaccaccbdaadcbccbbdacbadcadcdbbcaabbcdbddcccdadddabacdcadcaadcccaacdbdccbbddbacbabccaababccbacdbdddcddccbabbbcaabddadccdaadacdcdcbcbcacbdbcbdcbbcadadaabddcdbddacabdabaaccabdbbcbddacccdccbbdaacdacddccbbccbdcaaadaacabdbaaccdbbadabaccdcbdcbcbaabdaaaaacaacaacaaaabbbdcbccddacddadcabcabccbbabbbcbccccadccdbccabaadabdacdadbbbdaadcaaccaddaacaaddacaadcbadcabcbdaaabbcacbabddbbcaaccaacaaacbddbdbdcabcabbcdbacaadbabaacacaaccaacddbccabcbdadacddcaddbcdbabacadcbbdaaadbdacaddadbaadbcdddaacbdacdaacdadcbdddabaadaaaadbbccadcdbcaacbddabbcabcbcbdcbbddddbbacbbddabbddbbdbadcccbbbadaabcbdbcdbcbbcccbbbcbddaaacbbdcacbdbbbbcdbbabacbaccbcaddadcddbcdacadacaaadaacbdddbdbdbacdbcbccaaaddcccaaabcacdbaccbacbaccdaabdcbcbabbbdbabbdcabadcbabdacaccdddacabbbbbdbdbbbdccdbaabbccabcbcdcdcadadcabdcbdacdbaaccdcaabbbcccabcddbabcabaacbbcdbcbabcdddcbdcadcdbcdddbcadbabdaabbadadbcadbabcddabadcbbbabdcbbbaddbbcdbbbacadaacdadbaacdacacccaaabaaddbbcdddbacacacccadbadaabadaaabcbcbcaacabcabcdabccdcdcbbadaddbadabbcbdbaabaadacdcddcabcdddcadaccdbbcbdaadbbbabadcacaaabcbddcaaccbbbdcacbabdbaccdaacbdddacacbcbdcaacbabdbcdddbdabbaacdacdaabdacbbdbbdbbcacdacbccdddbacbabccdcabdcddbbaabcdcddbbaccccdbbbaacabccdaadacbdbcccdbcaaabcccbbbacdbbaabdbaadcdcbbbaacadadcbabbaaadbacbadaccaaacaddbadcdcbddbccddacccccacbaaaababaabdbddbcdddddadcbacdabcaaaadbcbddabcdcbdccdddbbbbcccdcbbabcabcddbdcbcadcdacbdadbcadcbdbadbcaccacaadaaacbcdbadddbbddadcbcbbbcdadcadcbccddccdbdccbaaacccadcabbbcbbcadacacdaabccddaaddbcbbcdddddcddbbccdacddbdaccbadadaccbccaabdbbcdbdaaacdbaabbaadddddddbdaabccbbacaccaccacdcabcddccdcbdaccbcaaaadccaadccdabbbdabcbbdbdcbdccbdadbcbcbbddcadbbdabadcdcaabccdcbadcbcbdabbbcdbcdbdccbadadbbccaacabdabccbdcdbbbacaadcbdddcdddbbbbdddcdbdabcabbddbdcbdacacbbdbcabddcbcaccdbdbdabadaaddbbcddddaccbddadbabdbcabaacbcbbbadbdabcdbbacdaddddabbbbbcbcbbadbdbabbbaddaadbdccaadcaddcdadbccbacccadaccadbbddbdcdaacaabcdbdaacbaabadacbbacabccababadbcbabcdabbcdaddbbbbbccaadbacdbbbbbddcbbbadaaacaddccbabadbccaadcabcbcadadbcaaccbaddcaacabbccbaddadbccbbbdcaddbaccccabdcbccbadbcaacbbbddddbbbadaabacacabddcbbbdddbbddcbaacabaacbdbbddadbdcddbbcbabacbaacdabcadcabbbbcdcbccbbadccbabdccacaccaabacdaabbbcbbbdbabbcbccaddadccbbdaabdabcbbbabdbbdabacabacaddcbdccabcbaacbdbabdcbbddccaabaccaccdcddaccbacbbbccbcbccccacaaaadabbcdcdddadbadbcabbabdbaacadacacdaaacdabbccbdcdbbaccaaaacdaccbcdaacbdcbcbbcbabcabbcbddcbaddbcbccdaacabacaddbcdbacdabbbcdaddadbbabccbcccabdabbcadbcdbcaddbaddaadcacabdcdacbdddddcacdadaaaadbdcbbbadcbddbcbdcbbdaaadbdbbdbbddccbacaabbbabadcabdadbbdbdcdcbbbdccbaddcccbbbcbdbabdbcbdccbcaabdddaccadbcaabcabbadcbdccdbcdbdabbdccbacdcdddbcdadbbabddbacbabcbbabbcaacdccbabcaabdbcdccaabcdaabbdbaabbbdacbdbcdbdcddcaabdbbdcabbbccaacabaaccbdaadcbaaaddcbdbbbcddbbccbaabcbcdbabdbccbdcbdbabbcaccdcddbbcabccabcdbcccdabdddadbbccddbaaabccadbcabcbcdcbbddbccbdacdcdccbbdaddcaccddaadbadabaabbdbcadbdacaddbbacbacbbcaaddcbbaccdbbbcadaacdccccacdcbbcbdbdcdcddbabdacdabacdddacacbdabcbbbdbcddaddccacbccbadccbcddabacacabadddcabdaccacddaabcaacbcabccaaabdbccabcdaddabadcbbdcbcaabbbaddaaadacdddabbbaddbabcbbbacaacbccacdabddcacbbdadcddaaddcccdddabaccaccdbcabccbcbcddabacabcdbdadcbdcdadbbbcacccbbabbdaadbbccabbcdadadadccbddbcccddcdacbacdbadddbdadbccacabbbaaaccdbbaadddccdbccdbcbcacbcdbddcbccacadddbacdadadbabcaddbcbaadbacdadcadcadabcacdbabaacadbdcdadcdbaacbdcaadcddccaccaacaccadbaacbcabbcbabbbcadccacbbcdcdbccaaaabcddbabdbcdcdcaacacbbbccaaddacabcabbabbccbaddabddacccadaaddbdbbdcbdcbbcdaacdaabcddaddcdccbaacabbacdaddbdacabdbabbddaccbddcbacbbcabdaddababbcbadbbccbaddcccabacddccbbdcbabcadddaacddcdcbaabaccaaccddacdddddadcddbababddabadaadabcbbabccbabdadccddaddbcaacacababbaaadaababddabaccbcdacaccadcbcccabccaaaccdbabbbaaacddadbcacccccccbdcbaacdbbcabadacbcdbdbbcbabbaccdcaccadbdbcbaadaccaaaabdadaacdadcaacdddbaddccdbadbbaccaababdbcdcacadacdbddacdbdabaadddbdbdbccccbbcbccdacbcadadbddbabdcdbcacbacadaccdbaabcacbacabdbdcbcdccbcbcdddabcdbddbccabbadbcababbabbbcddcaadccdaadbadcccabcbcdadbbdccdcbadabaadbbcdbaacdccbbcdddcdbaaaabddbcabadccddabbabbabdaaaaabaaaabdcbbdbaccdcaacbaddddbcbdddcbaabddddabdcbdcddaabbdbacacadbcdadabccaaabddaabbaddaadbaddddbdddacccbccacdcacaadcabdbdbacbdcdabcdaabadbdababcdcdddccbabcbcccdcbdcaabacdbbdcccdcdbbcdcbccbcaacbaddccbadcbadbbcdcdadbacaabababaddcadddcabddbcdcadbdcdacacabbbcdbbcccabdbcacacaabcaccaacddcbacdbbbbbbbcabbddcdddbcdcaabacaaacadccbbdbddbaccbbdcdddadbccccdacdbacacbcbaadbbdccaabaaacbbdbbbcccadaddcaaabcadaabcbccdbdcbadaabbcbacbccabcadbaaaacdababbcaababccadbaaccdabdbbabcdddaaddccccabadbcbbcddbbaddbcabdaacacbbbcddcbabadadaadcbdcddddcdabdddccbacdcccddbbaadcadbadadddbaabbaabdbdcdcadbbcdbbccaabdbacadacbcaaccccadccbbddbcacdabcccbaccbcdccdcdcdbbbbaaccacdacdcaadabccabdacdbcabaaabcabdcbaacabccccbacdbdadccaddcaabcbddabaabccaadadbadcababcabacbcabcadcdddacddcddccbadbdacddcaaaddbcdadacdbbbcdcadbaaadbacbaddbacaaaddcbcacbdbdaccbcdabbaabdcdbadcccdcccabbbdbabbaddadcadcdaacacaacbdacdcccaaaccccbaddccdcdadacadcddbccbddbacaaabcdbacccdcbddadbbabbddaddccbcabddcbcabbcdcaabdccdaddbadccbdcdcbdadcacabaddcccbdcdcdaddbaabbabccdabdbabcadbcbcdaddaabcacacddbbcbbaddbdbbbdddbddbabbdbacbadbacdaadcdababdaacbcdbadaccaaadcdaabbdabacbcbcacbaabdbdabddcacbddcbbababcabdcbcbacaabacaadcdaddabdacbbcbbbcacdcbcabbcacabddddbbbbdbcaccabaaadaadcdcabdccacccdacdddbdbaddcccbbabddbccbdddbdbcdbacaddadbbddcccdabddbbbbdddabaaddadcdbcdadbdbbacbdaabccdcbdccbaccadcadbdbddcaaaaccdcddbccdbacdddabcbcdacccabcbbbcbacdbcdddbdabbdaabccdabaaadcdbbcdbadcaabbddbbbcadbdbbcddcbaacbdbcddccdddccdadadbdbdccbcadacbbbcbcacbbacaacbcdcbbcdbcacdacbbddddccaabacbabbbaddadcabaccdbbbdcbbabdbbaccabccbccabccddbbcaddccdddacbdcdbbdbadcacacbccbcccababbcaddadbcdaadbdaaaaaacbbacdccacdcbaaaddcdaaccdbdaddbabdbdadcddacacbbddbcbcdaaaadcdcddabadbbdacbcabbdabccddbcbcbbccdadcdcbdccdcdaccccaddabccbccccbcdbccdabcbabaabccdcdadddbcbccdcaabcaabdabddcbbbddcbdcdbbaccdababbaadacccadadbddacacbacdcadddabadbacbcacbcbcbbbdabbbbcaabdaadcdabbccbbdddadbbbcbcdacabccccabcadcbddaabbcabdcbabdbdcddbcbabcdccbdacbdcbbdcaddadaabcdbddcaabdabcccbacdccdacaaaacbacacdadadcabdacbbbbababadbbbaacbcdddcbcdbcdcbcbcbcbabcbabbcbdcdddbbadbcbbdcbadaadbadbabbddbbccacadadbccabdbcdadddacddddcdadcddabbabaaadcdaddaccbcadbadacbaadadaacbaddbadccbaadaadbbdaadcdbbabaacabdcacacadadadcdacaaaadaacadacbcdabbdbaaabcdddabcdcabbdbaabcccdaddaacbadddadccccbbbaccacbcbcdbbbbaacabbdabdcbbbbbbccbbbbadcdbcaaababdbbdbdaadcbdacbbdabbccdbccdacbbaadbadbbdcadabaaacbcabdcbcadbdaacaacbbabcccdbccabddbbbabbbdabbaddddcdcdbbbbacdaabdcaccccaacbbbcdcabbabdabbaabbbcbcaadbbabdddabacddcaabdbaaacdbdadabcababcdacadacbdbcadbbbddbbcdddccdddcbbbcdbbccbdbddcacabbccbdccaacabdddcccdabcdcbcdcbcbdbddbbadcdbdcdbbabccaaacabdbaddbcaccdabdcbbbadbcdadcadcccddbccacdbacccbdbccaaacadbabddcdadbbaaaacacdbddbddcdcabaddaadabbdaadddabbcbcabcdbaabcddcbacbaaabadbadbbcbddddabdcccbdcadaccbdcdacadbdbcbbbbdccbaddbdaaaabbbabbadcadbcdccdcbcdaabcdacdadcdabbdaaccdbbadcaacdabadaaadaaccdadbabaaddaaacbddbcbcdaadddcdbbbbdcdbcbabaadadccdbdadcbcbadabacbdabacbdcccbabdbbaadadaccabcddcdcadcdcccbabcadbabbbdbdbdadddcdbabcccacdabcbccaddddadbddacaabdacdddabdbccdaabbdbddbaddcbdbbaacddcbabcddddabbacddbbabcdabadcdabbcbcdaaaacdbadcdbaaacadddadddddcdbdddcacacaccdbdadcdbbdbacbbadabcbaccdcbabdbdbbccacdcddadababaadbdaabdcbacddccabddaabdddbbaabcbadcccaacddaddadcaacaccbacbcaabcabdddbdcbbbadcdbcaabacddcddbdcbadaacbcbaaddddddacbbadaaccacaadccacacabcccbcabdcaccbbcdabbacccadbcdabcddabbdcbdcaccdaddcddcacbadaaaadacdbbbbccabccdcadcdbdbdbbbabadbaadcabdbacddaabbaadbbcbbdcdbcadcdcabbabbdddccbbbcddbbbdbaabbaadaccdccbaccbdcacaddbbcddabcaacddcddbbaabbadaacbbadbacccacaaccacbbabaddaadabdcdbcaacabcddacbccccccccccdadadbdabbaacccadcdccacdacadbcdbbcabbbbadbbbabacacbbacbadcdddcdccdaadbaaabacbacbacbbaccdacaaccdadccdbdccdaaabcabdbacbcdbdddaccdaaacbcdadbcdbbabacaddccdcbdbcccbadbacccdbdbaddbabadcacddbbccddcbccbdadcbaacbabddddccdaabbdbadcbaabaacbbcadaccbdddcddacdcdccabcbcabaacdccbdadcdcccacdaddccccdcbbaaaccbacbbabacdacabcaddbaaadacabcdcdcadbddcdccdcacbcacbbbbdbbcbadaacbbcddbabcdcbddaabbbcbccddacbbadcbbcbdbaadaabbbbcccdadcabccbbbccabadacacacaccbcbdddcabccddbbadadccdcccbcdadcdbcdcbccddddcddaadbbaadacdaadcdaaaacadbaaacaabbdbabbcaabaababbdbddabbaadacdccabbdadbababccaacbdddbbcaaaddbcbadcbcccdbbbbacaaababdcdcaccdbcaddaaaccabbadcbcaadcbabdacddddcccbadabcdcddaddcbcbbbcbcddbdcadcdbacddbbabbaadbcdadbbbabddbccddadccaccbbdacabbbbbdcddbcdcbacdabbddbdadaabbacdcdabcccdbdccbccdddcbcccaadbadcbbcbdaddaccaaddadbbcddbabcbcbdabccccbbcacccdbbdcdcdcccbabbcaaabdbccdcddbbbcccdcdadbcdacbdcacadbccdbdcdcbbaaccbaabbcadbcdabddabaaacbcbacaccbacdaadccbdcdddcbadbbdcdcccdbabcbbcaaccbdbbbadbcaaaabccaccdbbbaccadacaabcdadbcdbdcbcdaccacbaaacccbcbadcaacdcdcbabcdbbcdcdadabbacadccdbcababbabbdcaaaaaaadaccaabcdaacaaaddadaacdccdddddabbabcacbbccccbdacbddaabddbddddcaccbdacbaacdbbcccdbadaabdcacddcbacabbdcabdbadaacbddadcdcddcdddadbcbabcdcdbabdcbdbbddcbbaabacbdcdbccdddbbbbacdddaaabacadbabcadcbdcdcbdccaaacbaddcbdcdcadbcbddbddbbcadcadcadabbabcdcaabdaabacdbadcbbacbabacbbcbbdacdccccacaadabcccdcdbcbbcdcadcddcaddbacbdddbaadaabacbccddddbacdadcdbbcbbacdcbbaabcdacacdcdaabccaccbdadacbadddabcbcbcbadcdbaadbbccbadaaabaccaccbccbcdadcdccdcdbbdadaabddcdadacacbabbacaaccdbaaccccdabcacdabcabaacabbbabbcdbbbccdcdcbccdbadaacbadacccbcadbbdccbdadaadabdccdadbbdccaddbcababbcbdcbcdcdabbbbcaabbbbcadbccccbdaaaddbcaacdcdddabddbacaaddbcabadbcdcabcdbadcdbacbcdccaccbabdabaacdcadbaaaadcdcaabbdbdddbabdbbdbcacaccaaccbcbccadbcccbaabadcbbdaccddbdbbbdabacdccbabaacdcbcdcdbbadbbbbadddbabbdbdcaacaabddbdbdcccaddbdccdddcdccdcdbadbacdbbdbaaccadbcaccbddaddcdbdbddacabaaabcbbaaadaadacdcaabaddcadbbbbdadbadbadacbccaccbcddcdcbdbbbadccddcabbaacbdcdbbdababacabcdabddbdcbcacbdcababacaadbcccbaaaccadcccdbbacabbccadacdbbcdadadccaadabcbabdcbbabdadcdbcdbbcaddcdbaacaaacddcdcbdacbbdacdbaadcabaddccddabcbcdbdbdbacddcadbcddaccddabcbcdbbdddbcbddaabcabcdcaccbbdabcacddcaabaccacacddbbcbcbaabbcddacaddcccbbcddcaddcabaacbdbacdbbbdcbdbddbadbcdccadcaabbbbccaacbdbccbdddbbcadccdacacabcaccadddadcdbddbddbdcccbcdcabccbbbbccbbacdbcaccddddbbabaadadcdcdacccabdadcbdbdadbbdabaabbccbadccdabadddbbdaaaabcccddcbaabbdabbcccbacaccabbabcbacbbcbbacdadddbbbacadaaacbacabccddbcaaacdbacbabaaccdacbacdbcbcddbbaacaadcabddbcddbbbcbcbcdccbabaddabddbddadaddbcbcbccaacacaabbadadbbdcddcdbcbcbdddccbdccdabcdaaacbdcbddbbbcbcbcbbbcddbacacaccdadddaacddbcaddcddddcaaabdabccdbdaaaddacabcbcddccbccaabdbbaccadbdbacaccadbadaddcaababcacbcbaaacdaaadadaacdcbccdbdbdacdbbbbbadabcaddabdcdaadbdbbdacddbcdcaabccdbcbacbbbcaacdaabbdcaacaabaddacdaddcbbadaaadaadddacddcbccbcbbdbdcdaaaadbbbbdbbdbbdabcccdbaadacbaccddcdcbababcbcbbbdbcbdabcaddbdadbcbcdadcaadddcaacdcbdaadadcbadaaacdbccbbababddabcaccbcdacadabdcbdaaadbabbcccabcbbaddaabaacdbdadabdcaccbabcdaabbaadaacdddadbdcaddcaacbbabbbcadbcdcccaaaadaabbdabbabdccdcccbccacbaacababcdadcaabdbcdabaacdaccbcdbccdcadcadadcaabdccabccacabadaacaaaacaabbcaddabacbacdbcccbdbbbdbbccbbcacabcadcdadaabbbcabaacbcbdadcdcccaabddaaabacbccdbbccbdadadaaaacaccdbaabcdcccacbacdbbbdadddbcbbacabacbbccbdcacaadaddbccdcbdcaaadcabcaaaadcacacaacddadbcadaabddbdddcddccbcdcabaccaacbdddddaaacaaaaccabccabccbacdccbbdcbdbbdccdbaabbbbbcbacbbadcaabbacdadaaaabaccabcbbdacccdcddddcddaacbdaadacaacbcdadcbabacdbbabbacddbccdacbbdbadbdacbadcccaadadaddacbcadcbcbddbbaaacabccacaaaabcbbbadbdacdbccccdadbadddcbcadadbdadbccdbabbabbdccbcbbddddbbacadbdddbdbbbdcdbcbacbcccddcbbcccabddadccadbaccabddcbbdabddacbabbadadcabddcabbcbadcdbdbcdabaacabbaabdbacccbdaccccdcdacdabcbabadaddbbcacdbbacdcdacbbcddaddbdcabcababbbcddbbdacbccabddbbcaabdbaaadcbcbabcbadddbbcbbcbbacbbdbbdadbcbabdbacacaabbababcabdaabdacddabbbcdbbdbbacbbcacbaddbacadabaddacaadcdacabdccbdadcbcacacdcdddbabcbcdcdbacddbcccbabacbdaacbbaacbbabdcbacadccaaccbbdcabaaccccddbcaccabdbcbdcaabacbdbcdcabdcbdbacbcdaacccacaddddcccdbccbcdbdbcdadbcadbdbbcdbaababcbbdbcabdabbcadddcbbbadbdabaccacdcdaabbccbdcddcdccadbdbdbcbcacacddaaaadaacbbbcacacbaaddbcdccacdddbdadadddadbbdaadacbcbdbdcbdbddccbddcaacababdbacdaadddacbaccdbccabadcdcddbdddaacaabadcadbbbbabbbbcadcdadcdadcdbdccbdadccababbdabadcbbccabaabacdacbcbabbddaadbbcbbdcabbcabbbaaabdddcacbdababadabbabccadaccccccccabbbdaabbbcacbadaacaddbdbcacaabaaaccbacdddbbcbcbcabcbbadbccbbbbcbdbcbccdcabddcabacdbdbccbcabcccdcacaaaabbbaadbcdbdbcbdabdbdcbabcadbadaaddbbadaaacbadcacadaabbbbcaddbcbbbdbbbcddaaddadcbccaaaaaabccddabaadabbbaadadbdcdababbaaabcdabcddbddddbcbbadbcbcbadccdbbcdabdadacaabaaaacdcdbcdbadbababcbbccddaaccbacabdacbbcddbabcacacdacbadacbaabdbaabcabdccccabaabcdaabcbccabddabcdacacababccacaaccacddbaccdbcdbabaddadbababbccabacbccbdacdbdcccdbccccdacbccadcdcbabcababdcbdbcdaadcddbaacbbbaacddbacbdbdabdccbcdccbadacbbcbcbcbbddcbdbcbabacccbcbcbcdaaaddbdcddadcbabcbadbdcdddbbdabbacbcdcbbdadbcddadcdcaddbcbddbacbdadabadccaabaacbdbbcbaddcdbadbabaacaddacabdacdbbcbadaaaaadadabcdbdcccddaccaabcabadbbdbbacadddccdbabccadacacabbbcacdbcadcadccdadaaabdadaddddbdabbbdaddbcabcbadbbccadcddabdbdaadcadbbdbcccadccadaacddcdacaddaccbddcbcabbbcdcccbbadbcccaaadbabdbabacabcbcabbddcbcbddddacdaabdaadcaacabdcddcbccddcbaccadbabddabdbadccddcbbdaccccabcdbbaccbbdbdbabacdcbabcbabbcbacddbcbdcabbcbdcccacdcdcaabcdcbdbbbbccabcbaccaaabadaddcccdabacbaabcaccabcdccaaddacabaddcddbbabdbbbbadccdbabdcdccdaadaaaaacccdacddadadcbbbaaabbacadccbccbcabdbcabcdbcbcdabcbbbacccbddddbccbdbacbdacdcaabaaacbcacdcbdaccbcbdcaacabcdaddbadbbbacdcbcaaddaadbcdaccdbacbcdbabbdcabdbbcadabdbcbadbcdaaccadaaadbddbcbcabccdbddcdaccbbddddbadacbbaabbcddbacdacdbacabcdbdabbdbaaaabbcbbcbcdccdddabbcabbdbcabdcacbcdbdbaaadcccdcaccbadbcbdccbcbddccbdccaadbcdbcbadcbdddbbadacbcacdbdbcacaacacbadacabccbaaaadaabbbbbdcdaabcdbcbaadbacacabcabbadddabddcacbdcbdaccacabbcdbabddcdbaababaacbbdbaadadbdbacbacbbbcbdddbcddbddcbaacbadcdadcaaaddbacddbacaaaadbcbbdaadddbcadaaababcbdcaddbaddbbdcbccdbbddaabcbbcbaddcbcdabbdcbddadcbaabbdcbacdbbbadddacacabbccbcbcdcbcacbacdbdddbaacdbcaacbdcbdddbaaacbdcccbdcdccdadccabcddadccbdcddbbdcaccdbcdccdcbaccbbbcdacdadcdbcbdddaddaaadccdbdabcbbabcacdbbcadcdcdbddaccdbdbbadccbcbcadddaccbdaaabaacbcabcdaabbbcdadddbddcabacadbbaccaacbccbddabacccdcdcaccbbbabaaaccddabbbbaabbcbcbbdadadcaacdbcbbbcbacccbbcaabacbdbdabbbccadcddadbbabddddaccdccacaddcdccbacadbbdccbcadadbcadaacacaccabcdbdccdaadbbccdddbababbdcdcbcabacbadbadadabaadbcaadcadaccdddccdbcaaabaaddaaabbbcaadaccadccaacdaabbaabcdcccdadccacbadcadcbbcbadccbcbcccacbbaadbdbdbadcddaabdadabadbdabdaadadadbcccacdacacdcdcacccdabadddcaddcdadabbdabdcddcdbbdbddbcbdcdbbcbdcdbcbdbaacdcabadabcbbcbbcbdabadcbaacacabccddcaddabaacaabacbddbdadbabbacbadaaacccddbdccdbacdbaabbbcbcabcbdbddaaacbbaaacadbadcadbbaddbbaabadcdcbdaccbddbdbbaabcbdcaabccbaacbccbaacdbbccacbbbcccdabcaadcababcbbdadbdcaccbdddbcdcbbbabddcdddbcbccdbabbbbbcbbcccbbbdcddbcbdbcabbbabadcbddaaabbadbbacddbaccbdcabcacdabdbaccbdcabcdbbacddbccbaddbadbdccdbcccbdacdddbbdabddcabcdbddaccabccaacaadbccdcddbadcacaddacadbcccdbccbaccbddbdbdddbdadbaabacdbcddbbdddcdaacacddaddcccaadcabbcdaccbdccadbbcdbcdbbccabbdcadadcbdbdabdacbccbbbbaccaadcddddcdccbddaabbbdcbcacddbcddcddaaacbcbacddadcbadabbcdacbcadbaddbddacbdcbabaaccaabadababdbbdabdacbabaccaaccdbccacbcbabbdcbcabdaabdaddacaadbadabcccbbdadabcacccbbacdacacabdcdaabbaadcdcdccadbcadddddbdabacdaddacbccadccccabaaccdbabbccacccbbbbdbcccadcaadcdccabacdcdbcdddcddbbdcbbacdaddcdbdddbbbccbdaacdaddcbabbdcdaaccbbcbaccdbabacdbdcdcccbacbccbcbbbcbcbcabaacdcdbcbbccddadabcdcbacaccbcddadaaccbdcadccbcbdcdbddbadbaabddadbbaabdadaccabdabdcbbaacbdbcdcdcbbccabddbdaaddcacdccbbcbacabcbaadcaacbabcccdbcdcbcccbdbdcbaaaacbbcbcccabbcaccbdcdbddddcdadbdaddabbddddbcccdddcdcdcddaabddadcddaadbcbadacbcdcabadadcbaddccdbaabaabcdcdabbadadacdaccddaaaadccabcabacaabddabadbdbabcaacdbddabaacabbdddddabbbddcabbacdcbdbbdccaccccbcbdadcabdbcaddbcaccbacddcbbbcaacadbabbcaccddcbaaacdaccacdcbcbbabcaadbaacddbcbdcdabdacdcabcbaddaccbcabcdcabcdaccadbdcbbbdcdabbbabccccbdcbbabbbbdaccdbccbcbcbddcaaaadccbdcdcddccdbdcbcbbabdabdadddabadaadddbbbdbacadbdccdbddbdcccddcadcbdaccbbbcbaccddbcbdabcbccbabababcdadccddbdbacbdcdcdcbadccbcbacdcadabdacdbcdcbdddddddcbcdaddbaacdadbacaadccabccccabccbabbabbbadccbaabdbababddcbdcaddbcddcddccccbdbcabbbbcbadcbdacddddbcabbcdadcbbdbdcdbccbddbbcabcabcdaaaacdcacbcabacbabacaabccbcddbbaabdbdccccaaabcdbdacaadbdabdcbcddcdccbdaacdcbadacdbacbbddbdaabbbcbabdbcadacddbabaabdbadaddcddbaaadddddcccccbacbabcadcbddbcdcdbbbbadcbbbadabcabdccbddbcaddcadccaabcaccbbabdcabdcaccadabdccbdcbbadcdcbdabaabdacdabddcccdcbabbddcbcccabccabddddcdcddcddbdccdccaadababbabcaaacdaddbcddaadbdaacabcaaadbaccddcbbabcadbdddaabcacddadaabbacdcdadacaaabccbddacbddbbcabaddcdbadbdaacdcddbbabdcaadbbbabbbcabbaabdcbcadcbaadbcbcbbddaaaccddbccaaabdbbaaddbdbbbbddbabbbbaaacdadccbcdbaccababdbdddabbbcdacdbabadbdcacdcbbcbabbcdaaabdcbbcccbbcbccdaaddcccaddaaccaccaddacddaacddaadbbdbccdaabcddcbcaadbabbacacbdddadacdcbadbcddcddbddaaadbdaccaddaacadaccddbadcbdaabaadccddbcbcccbabbccadbbdabddadacbccbaabbccadcdabbbdcaacddabadcccbabbddadadcababadccbbacdcabdcdcdbcaaadaabbbacbababcbabccddddbcccbdccaabadabccdbbcbadbadbcccbcabddcaabbccdcdababddcccadabbbabcbbdadddccaadccdbacaabacbccdadcacdbdadcccccccbdadbaaddaacdbcadadbadbcbdddacadcabdbdddcdcacabdcabdbdccbdacccddcbdcdddababcabdacdaaabcacccadcccbbbdbccbaccbddcbdadccabadcdcbaaaccbdacabdddcacbdcdcdccdadaaadcadcbdbcddcacddadbcdacddacacbdbabaaaaabbdbcddaadbcbdcdaadcddaacadbadaaccbbbccdaddaacdaddadbabbccacbdbcbaccbbaacbbacbbccddabdbaddbcabcdaacacbadddaabcadadadcdaacbaacbccdaaddccddddbbaccadacaabbdabdabddcabcddbbacbacdacacbbddbddcdbbaacdbccddadddbdccbbbbbcbaddbcccadddbbcabacbaabaabaacddacaabccdbbdadabaacbcbdcabaadcdacadcaddcaaabaacbddddbdbcbbcaacccdccdbcbbaddcbbacbdadacbbcbabbdbdcacddaadcddaadcbadbdabbcdddccbdcdcabaabbbaabbccdbbaabdcdbdcaccccaacdbaabddbbbddabbcacdbdaddaddbdacdccbbacbbbdcaadacacbccabcdcaabbacbbbdabaccdddacdaddaacdcbbdccdabcdbdbbacbbdcbcaccacdbdccdbdbbddbdcdcbdadbaddbbbcddbbacbcaadadbabcaaccacdbcdabacdcadabaabcdccdddcabdcbdbdbbdbacacbdbccbadcaacbdaaddcbaccdacbabdcbaccdcdcbbcabbccbbcdaadacacbacbacdababcadbbcaadabddddcbcdbddaddddcaabdcbddbcabdacdccaacacbdbbbdacccccabcbdbadbaddcdadcdbcdabdbcacddcddabbbbbacdddbadaddbbcbabddbaacdcdbcbbbabbbdcbbbdcbbbcccaaaadbcbacddbcbacccabdadcbdcdbdaaacaddcddbadbbcbbaaaaddadcaabbcbaddddcdbbddaacabadccbabdaccbbbbcbbbcadddbacdaddbbdccaddadcbdbdadaadcadddbdbcabacabcbbadbaaddddddcadbdbcacabbbccbdacbdacaaaadbdbdbacdccbbdaabcabcaabcbdaabcddbbaabdbdcadcddacddbabcdcbacabcddadbbbbababbdcbcaacabcababaacbaaacbccdadbccaadabbbbaddacaadbbdabaaadcdabcbbbcdddbdbbbbcaaabbdccbdbabddcadcbaccadcaacadadbadccaadbdcdbcbddcbcbaaaccadadabdbddcacbcaacdaccbaadaacdcaadbcbbcacbdbbcbcbcbacbbcaccddaccdcbcadbbdcabcaccbaaadccaccddcdcddbbccbcbcbddbccccbaddcccddacaccadcdaababccdbcbcbdbcdddbaabcdbdabbdaacdadcacaddbaabacaadcabaadadaacdbcdcddcbcabcccdbabdddbadbddbdbadcbcbbdbbdcaaabdadbbbabdcbbabdcccdadacadbaadaccaccbaddccbdcbaaadddabaaddcddcccdbdcacbcbcabaaacabbddaddcacabcabadabcdaddabaacbcccaddcddcdcdbabccdcdacdadbdacaacbcaaacaddcaabdadbbbaadaccddcbbadcdbacabcdbaadcddadbcaaabdccbabdcbccddbacccdbbcdcdccbcabadcbbdaaaabbccbaaacdaddccbabbdbbacacbadaaacdcabcbaadaadadbcbaadbbdbaacdbdcdacddcbccbbdcdddbbdbdcbdcdbdbadabacddbcbcddbdddbcaabbcbccbbdbadddbdcdaccacddccdbddabbccdcacbdbcaadbadccbcacadaacaaaaadcdcadddbdadcddcdccadabaaabcdbacaadaccccbbaaadadbcdbadaabadcddbbdbddaabbbcdacddbbcabcacbdbcbdaabdbbcacdabdddbcbcdbbabdadddcabddbdaddcaccaddccdbaaadccadcacaddccdbadcaacaccacccbcbaabdcdcaadaddcbdbcaaaadcdbadccbcabacddbaaccadcaaaccdcdaacdbbcabcdbbcbddbbadaadaabcddababbabdbbcbbddabbdbdbbdbcaaabaadbbdaacaadadaacbddaddabbbdabdbbcbccbbdaddaacacabcaadbdbbacdabccbaadbdcbdcdbdbbbcaabdcddcbddcbddcdccabdcabdccdcdbbabbabaccdadcaccabaaaddbccbcaadddbadabcacbaadadadadabcbaacbcdaaababdbbbcbcaadccccbdacacdcadcbabdbcddabbbcbdbdddabdbbbaaaadbcabcddddbbbdddbbbbdccbbbbcbaaccbbcbcabbaaacaccbbbacccabadbdbbdbadcdcbdbdabdacbcbbdbdacabbcdcbcbdbcccdcacaccbadbbcadbdbadbccbdabadaddcbdbadaabcccbdcaaacbbabadbdbcdcdbcdbddbaccbdaddbaadaacdddabadbbbbbaadbbccbaabcccdddabbcdbadccacacbaaaadaaddadabcbdacbdacbdccaadacbbdcadccbabcacbaccbcdaaabbabccddaabaaddcaddcbaaacaabcbbdabddddcbcddcadaabdabccdacdabcdaddcdbcbcabcccabbdddcabbdadbcaccadbcabbdcddadbadccacddbbadaccbbccbabcbadddcdbddaddacbbdacdabddbdbbbcbabaacacaddaababbacdbabbccaacddabcddcccabaddbbcacbdcabaddadaabdaaaccdbcdddacbbacababddccbdaabbbadbadcdbbbddbdbadccdbdbdcdbabaaadccdaaadaaacbaddbbdbdcdcdcbadbcbdabaadbdbbccadbbbbacddccdbcbaabccaabccbacddbabbbcacdcbdcadaddbacbbabbbaaddacacddaadcdcadcddcccbcbaddacacbbbddbccbaabdcdcdcdaccbbbcbadbbccbdccdadabaabdccbbadcbcdcbcdbbadbbbdaabcaaccbbadcdccbbdacadbbdcddacadcdcdadaacbdcdbddaacaadcccadbdcabacdbcaddcccaadcdbbdddddbcaadddcdbbbdbadcadddacbcccabbababbdabdcccccdcaabdbbaadabadaccbacddbbdddcaaaddcbcabccddcaabbdddddadcbdbbcddaacdbacdaadbdcdaccdbcbbcbbcadcbcddbbadccdccbacddccadcdabadacadabbbadaacbacabdccccbbbbbbdabcbcbdbbbcdcaabdcdcdabccbbcbaadabddcaaacbabadaddbaaacbcdccdadcabccbcabdacdcdcaadaaccbacaabbdbddccdbcddcaadacddbdcdbcbbccdbcbbaaddccacbacdadccabbcabccacdabbccdbcadaaabbdcacbbaccaddabddadbadadbdbccdaabcdaacbbdcadcbbbaacbdcaccdcabccdbccbbaabdaacabbddabbbdbadcdabacabcdbcbabccdcdccdddaababaadacdbaabcdccaddaadbacbdacbccccbcdabbaaaddccccbbbbdabaabbabcdbbadddbaddabbaccbdcdcbdcbcbbaddaaadccbbdbadcbdacabccccbcaaadbdcadddadcdbbadbbabbdcccdcdbdbddbcadadccbaddbdcdabdabbadabbbbacbbbbdbcbdaaddaccbdabaabcdcdcbccadcacbbcacbabdadacadbccacdadcacbadddccacdddbcccbdccadaaaaabaadadccdcdddbabdaccdbccabccccaccdcbddbcddcdaacccbcddbcdabbdaabbcbabaacbcabcdbddadbbccbcbcbbabcddcacadcbbcdacabcdccabbcaabdcddbbbababcadbabcbccbccadbabdcbaaddddcdaaabadabbbcdabbbccacdcdbbdcddcacaaabdcdccbdddccdbabbaddadbdbbadcadcdbcbddddbccaaabdbdcaacbdcbbcdbdccaccadababdbbbbbbacababdaccbaddbacadddbdcaaadbdaacaabcbdcadddbbabbdcbbcdcbccbdbdddcabdabdaadadddadbdbbdbdbcdcbbcbbcdbbaaaabbbdaacdddcbadbaaabaaabbccbaacbbcaaacddcccccabddaaacdcdbbdbdbbabdbdbcabdacbddaacbcacccdddbabcacaacdbdcdddabdadbbbcadddaaabdcabdaadbcdbcbacbccdaabdbbadabbcddadaadaddddbaaababdbdbdccbcaaddbacababacadbabbbcccddbaacccddbcbdaabcdccddcdccbbcdbcddabcdadbbbdaabcaddabcdaacabcbcbaadbddcbdcbccaabbcacbbcbdddcdbbcaacccbacdbccabcaaabcaaabbabcdbdbcdcdadcbbbbdccbacadcccbbddccabbbbaacdcdbdadbdaabbdaaccabbdcdddabcbdaddbddbccdacdcdbbcadacddddaadbabcddbbcadcabcdaabbabbdbbcabccbdcdabaabacaddbbbcaccabcbcdbadbcabdcadcbbcbbbcaabcdadbcaabaddcbabbdcbcacbabaaabcabadcbdddccbcbccbdcdcddbbbcacbccbbdddbaaacddbbcaaccaaaddbcbcaacbbddcbabbcbbbdadaaddbccacbcdbacddbbdcabbadaabdabbacbdbdbabaddaccbcdddbbdadbcddababbcbdbddcdbadbdbccacbcbdbaccddcddbacacbdcbccadcbabbcdaabcaaadddbbbcadbadaaabacaaddadbdadcdbcdcdcdccdcabbbdadadbdcddcdaabbcababccdbbddabdbcbcbacbbaaabaaccaadcaababbcadbcaadbbaabdbcbcbadcbbbacdbadcbbcccaccbbbadbbacbabdbcabbcacdddacdaaacaaaaddcdbbaaadddcdbdbddbdcbdaaabaabacaadaacaddaddcddcdccdbbabddbdbbdbcbacdabbccddbabccddddabcdddbcadbcadaddccacabbadddcddaccabdabddddbbddadbdbacbadddbbbddbdaddabbdbadbbddcbcdadbdccccdcdbbbccbdccdbbaacaabcbbbabddacdbaabcbaabaaccbcabaaacadbacadddcbbcdadbbcdabaaddcccaddddcaaddcbbadbdcdbacacadcabdddadbacaaabcddcbaaaccbccbcbcaaddabccaacadddbcccbcdbbcdaadcccdcdbaaababcbbbabacdbccccdaabccaabbcbbbaadcbacdabaaccbbdadabaabdbbcadadddbadcdbdcbddcdbbdaacddabcbacdabbaaaccccddacccaadbbcbcaacabcbbbbcdabdcbbbabcdbacadbcdadbdbadcacaabbcadacccbbbccbaabdadcaacadbaacdaccbcaabcaaadacaabcadcbbabcdbaadadcabddbadbddbdabacccdbbdbcbcaddadbdaacaadbbcbdabaabdbbadbbdddbbbbbbbcbbcadbacdcbdadddbbdcbaabaadbccabcccddbdaddbadadddcdccbabdaccdcbdccccbcdbaaddbadcddcbbbcbaadcbddacbdbadacaadccdcaccaccaacbbbbbdcdaddddcddbadcacbcabaadabaccaabcdbaddbbabbbabbcdbdabacdbdaccbcccbadcabdabccabdacacbdbcddaaadcadbabbdbbbbcaddbddbcbbbcdbdcaddccbdbadbcabbdbaaacaaadddbbcabbbbbccdbadacbdcaadbcccdcddadcccabbacbbbdccadaaaccabcbacbcbcbdacbacbadaadcdbbbacdaabacdbcbbbbcabbaadabdbaddbbdabaaaddacabaadbadccdcaaaabdddcaaddbdbabdabbacadadcbabdcbabaccbadddcabddddddbcbaaddbdcacabbcbaaaccbabbdbcabdacabdadbadaadcaccddbabdacbaabcadcdbddabacbdbbcbbbcadcacddaddacaccddcabadcbdabcbccabbbddcaacdcdbdddcbdacccddadabaadcbcbcbbbdaaccbdbcdcadadbaaaaadabbaddcbdcdbbbddcbdcbcacabacdcdcbadadadccccddaabcdaadcabdabdccdacbccdabcabbdbaccaaaabcdbaddabdccaacacdaaaabadccdccabbcddabadbcdaacbccacdbddcccdbaaccacadcbdacbaddcaacabbbddccbabdcbbdbcdbdddbbdbaadcccbdcdbbddccdddbaddabbaadcccccbcbbadaaabbccacbcaccaddbdbccdcdaddbcddbbbccaacbacabddbcddbcbadcbaabadbbacadbaddcadcdccdcdbadddadadaabdddccdcbadcddaadcbdbbccabbaabcaddacbbccbacddccdcdaacdacbbaadaacbadcbdcbadaaadbbbcbcbaccabddcbdbccbabdaccdbaaacdcddacaaadccabcbbdccabccacaccdaabdcaaabbabbcccadbabcaaddbcacaabacbdadbcddbbbddabcbcacdccddbabadadbbbabcaaacbcdabddcbaabccaadacdaabdbddbbcdaacbbdababbdbadaccbbcabdbaddbbacadcbddaabbadcbcbdacdddbdadccacccaabbccdbaccccaccdaadcadcacdbcbcabbabacbbbcbdcadaccaaacccaabbbbbabbabcdaadabdadbaaddbccdbcbcaadcadbacbcadadacadaccabccdbbcdddabaaaccbbdddacdaccdbbcccbdaaaadcdbddccbcadcddccddbccaaadcbcddddaadbbccbbabbdabdcdbccddccdbbacccabacddbbbdabddacadcbdcdcdadbbdcdcccadbdcadcacbaddadddadcbcbddcddaaacddccdcbbcadacaacaabaaaaadccdccbcadcdbabdccccaacacbdddcdcabcbaccccaadcbdbaabbdcdcaadabadcacdabbbcacbabcaabadddacccaccdcabbcbdcdbbaacbdbcdadbabdcbcddcbacbaaccbbaddcadcabcabdcaddadcdcbabcdddbcdcdbccaabbaaababcbbcbbacddaddacddcdaacbbdbcadbaadbdcdbadcbaabababdabadbdbbaaadaabcaccdcbbabdabdbbcdcdbdbddbadacbbcdbdcbabaabbdddaccbddcbcdbdcccdadabaacddddcaacbddccbacdabbccdcbaddaddaabcacabbcadbadcdbbadbdccddcbabbdddbdbbbbaabcabdccacbdbaaccdbcbbdbdddabccdacacdbbcccccaccccbadccbcdccddabbabbcddaddcddaabdbdabcbbaccbbccaacabcddcdbbbbddbdacacdcdcbacaccbaddcbccadcaadbbbbcadbcbbcaaddacccdadbcaabccaaadaddadbbddbbbacdabaccdbacabdabcbcbbabbcadcdadacbcdcccaaaaabbdbddddadadbcbacaddddbabbbacbdbddbdbdabcbbbaacdcddabcdcbacbabbacabcbddbcdacabaaccccbbacdbacbbabaccbddaccacbabbaabcbdbbaaabcaccaacdcccdcadcdcaabbcabaddcbdcaadabadbcdbccbacabbbddabbcbaaabddbcabdddbabdadbacbdddcbcaabdadbccaaccccdcadcbdcdaccdabaabaadaaaaadbdcacabcdabaabbcdcdbdacbbbccaccdddaaddacddbaddaaabaabbcdbcdbdcdacddaccdcbccdcdcacadadddcdcdbabaacadbbabdcadadabdbcdbbbddddbddaccbdcacdccadbcaddbdabbaddbccbccbbabadacbbccbcaddabddbcbacdacbaabcadaacccbccbcbbbccdacbbccadbccbadcaaddcdbdbdbccdbbadcaccbdcdaadacdaaadddbacdccaaaadbddcdbbcbbcacbabcdaaacadbcaabcacacbaccbdddaccdbdbaaabcdadcacbaabdcabacbcabbabaadabadbdbcccacbbbaaccddaccdbbbcbcbddcdccbbadbbdcbdcdcdccbbcacacbcbdbccbbdaabcddabcdbaccdbdabdbadccdabcacbdaaaaadbbdadbcacacbadcbcabcbcbbdbddadcddcdadcbcaabcbbcaabcdbbbbbcaaadbbbddcaacddaaaaccbacccadcadcaababaaccdcdcaadddcdbcccaaaaacaacadadabcdadcdaaaadddcbcadbdbbbbbcccbcadacdcaabddbdacbdbbbdacbbdbcbabcbbabcdbcbdbcbaabcbcddadbddcaddcabbbdbbbdbcabcdbcdcdbaacabadcaaccaddbbacaaaaaccdaddadcbdacdacbcabdcdcadaabcaabbcdaaddbbdbcbddabbcddcddbbdcbcaddacdcbdcdcbdbcaddacdcaccadbabcbdbccbcaacbcdcacbaddbdcbdbbdacbccabdabcdbbaacdadbaaccaabcbacdcccdabaadbdbddbcddadadddcbcdadcabbcacbaaadbaaabdccccbbaccddcdcdabbbaacbdaabcabddbbbbabadddcbcdacbcdbadbbbdcdabcbdbabadcdabdadcaddaabadcddacbaaabbbdbacbcbcaabdbdcdccabdcbadaaddbcbcaccccccbbaddadadbbcbbbcbacabcbaaacbbdcbdaacdbbaadbdbaabbaaaddbcbdadcadbccdcbcbddbcdccbbcadbbacadbacadaacdabdccbcdcabbabadddacbdddbdacdccbbabcbcdbbabddbbcaacbcbbdaddacddcbadccaaabbabbdcbdacbaccacdcaacbacccdadabbcadbccadaaabddcdcacdaaabcadabdbabcbdcaabddcbdbdaddbcbcdcbdabdadbbcbddcdabdabbbabdbaadccbdbdcbbddacbcdcbddbdaddadadcaababdcdbbdbcbdadbacadcbcaddbcdaaddcccdadddbcdcccadcabbdcbdaadbcacbadabcabcabaabdbdbbdcacdacdcaaddcbcdbbbcbbacdddadccddaadddbacdccacaabddddcdccbcabcaabacaaadabcdddadbcaddbddbbabaaacaabdcbccaccadbdcdcdcbcdbcabaccbddbccddcbabddbbbdddaadcdcdbacdddddaddcaaddacdccbdcaadbbaddacbbddbaccbabadaaabdbdcaacadccdbccdabdacdbbbdaacbbdabccbabdcbacdbbdcdcddbabababaacbbcbdcccdbdabadbdbbcabdbbaccaacbdaaadabdddbbdcbbcdcbcaaaabbdacdbbccacddbcadcabcdaadbdbbacbdadcbcccbbbbbdaadaaddcdabbadacbcbcacdbdbbacbccbbdaaadcbbcccbabbcbcdccdcbbcadcbabbdaacbbdbbbdcbbcabcabacddaabaaadbabaccbcbaaabbacdbbcdccdabbcdbbabbddbdbdadcbcbcbddaacddabaccbaadbcbdacbccabadbabacddcbcdccaacddadcbadcabaabdcddcbbcbdbacdddbabaabdbbdcdbcaaadbcbadccdacdcccadaabbddcbbcaacacccbaddbbaddacacadabaabcbcabacbbbbddbbaaaddbbaaaacaccbaaaaccbdbcdaddddadacacacbacaaabbcdaaacddbccbcbddbddbcdacbacdcccadcdcddbdcdadaadadccddaadcccccaccacbacdadcacbcbabbdabcaccddcaabdacaccbcbacaaaaddddbabdadabddccccdaacbdbcdbaadcbdbcdaacabcbdbabdcdaadbadbdddadbabccaddbaacbcdadccaaaadbcdbcaaaabbdbccbacdcacaabbabcaababdccadabccbacbcabdccabcdccbcdabbdabadbbdbacbadbbddacbadcabbdcbdcbdddcdaaccadcbcbacbddacbcbaccccdddbdacccabdbaabdcabbdbdbcbdbaaccdcbdaaaaaaacdaacadcdadbbccabcaacaadcaadabdbaddbabcbdcaacaaadadacdababacaadccbbbbbacbcadcbcbacadddbbbcbddacbacbcddaadccacbdacbabbbcbcaabccbdbbdaaddcbdcddddcdccccdbacccaacccaddaaccdbbbbcdacdcddaccacacccddbcbdababdcbadddddbbbbbdddcbcbcaabdbcadaacabbbacccacdbdcdbbcacddaabadcadcacbabcdabadcadbcdaaddaccbbcbccbcdacbcabbbcacddcbadbcabcbadccddcbaddaaacdbddabbacdacdbababcddcbdccccaadbcddbbdcddaacaabcabdadcbaaccaddcbdcdbdacbdbcaabacdbccaccbcbbdacbdbdaabbbdcdabbbdbbbddbdcadbdaabdacbbaccadbccdbcbbcbacbbdaacddbbbaddacbbbbddcbbcbbcddadddbbdbcccccdaaababccdaabbdbdabbdddcdbddabacbcddbcccdaaccaccaabccdabbabdacaacbcdddadbbadadcbdccbadbbcdccabbddcdaddaadbabcaaaadbcbacaaadabdbcabcddbcccdcdcbadabbcbcabdabddbaacaacbdabcbcaccbbddcaabbcabcadcbcadddabaddadccbcbddadcbccacacacdaabcacbcdcaaaddaccbaccbdcadddbcdadbcbabbabacbdbaaaddbdccdbddbbaddbddbbddbcbadabdabddbddaaccabbcdbcbbdadadacccccbbdcacccdcbcbbccacccadcaabdbabacbadcdcbaddbccbabaccdbcbaabcbadbadbddcdaadccddcaabbcbaccccabcacacdbacbdabadcdabccbddaddbbabcccaddbbbbbbaacbbbdbabcddcbbcccdddcccaccabbbcdaddccdbcacadaaaacabcbbdcadccbadccabcbbddbaabcaabccbcacbddbacabacddabacdbcdcdadccccbdbabbdabdbbaccbbcabaabcdcabaabccdcddccdcaddccabcadddbbacbcacdbadccbacdbdccbdaddbbcaaccdcbadcadcddbaacdbbcabadbccdabbbddadacbaccadbccdcbadbdccabdcacdadbbcbcacdcdcdcdadcbcdcbaabadabcccbabcacdbcaddcbdcbdbcddccaaacdaaacaaddabdcacaddbdcbadbdcaadaabddbdcbdadcbabddcdaaccdcacdbacaddbadcbdbcbdddcabcdbacddcabcdbcaacacabcdbdadbaddadddcacccbccabbabdaddbaaadcbcaababbbbdaabcbaccacddcacbbacbcacbccaacbcccaabbdbacbbaadbacadbadddbaaccdadbadaacaddcadbbcdadddaccacbbbcbbbdbaacdcaaddbccbdbbabbdcbaabddbababdcaddbbacabbcacbcbcccbddacbccdcccccdcdbbabdbdbcaccbdabcdcccbacbcccdcaabcccbaccabacddbcbccdabbcabddaddcddbabbbdcccbcdabbaabdddbbadaaccdabddddddbacbaabaacbaccababacddaccacbbdbdbbcbaacabbcacdccabdacdbddcdadcbabccacdbcbdbdadcdaddacbabbdbdaddbddcdbabaacacdcadbcbacadbbaabbaadddcabbbaaaaddabccdadadbabdcbbacabcccdbacaadcccdbabccbabdadcdbacaabcbabbdaaddcbcdbddcdbdaabaadccbbdcdaddcdbbacdbdcabcdbacdcddacacdbbaacabccbcabbdcbaaabcadcabdbcdbddbbbababbcacdabaacdaaabbcdbaadcccccccbcbbaabbddacdcdccbadaadbccadcadcddbddaadaaadbcbdabadddbabbacdcabcccbcbdaaadadcbccdbbdadbdabccadcdacccdabbdcadaacbdcbbbdddaabdbbbaaadadaccdddbaddbdabdcbacbcbabbbbbdbbaadacabacbbdcadadccbccbbaaacdcddacaacacbbaaadbabbcadddbacdcddacaaabccdbbbabdbdacdaaaababddbbcccddcabcddbabddcbdcccccadbdbdcabcdabbbaacaccdbadddbabdacbdbcdcbdbdbadabcdcddacdbcbbcbdbaccbaabadadcadacdcacddabbcacccaabcadbcdcbccbabcddabdacbdadabcddcbdababdcbacaaddbacbbccbcdcacddbbdcbbcacbbcabacbabdcbdabcaadddbbbcddabbababcbbbdacddbbbbcbcadcccbccbabaaabacdadacddbaabccddcbbaccccbaabcccdbcbddaaaaadacbacabdbacbbcabbdaccaccabadcccbabaabbddcbcdbbaabbcbaaaabccdcaddbaacacdcdabbbcdacbcaadaddddbccbabbdbbcdbbaddadcabcdbadacddabdaacdabbaaacbcaaaccdbbaddbbaddbbccaabdcbaddbbdabcdadbbacccbbbdbcdcbccbcddacbdadbdbdbabcbdacacdabcdbbdcdcbcadabbdbaccbdcddcdcadccaaabaccaaaabdbcaabdaaadbcadcdcaabdccdaddccddaddcaccdabcbcbdaddaaccbbddacdbaaddbdbaabadbacadaaaccadacddaacbacdddcbabaacacdadbbbbddcdccbacaccdbcdadbdaacacabdbbddcacccdaabcabccdaabddcacdbdabbabcbcbdcdcccbbccadbacdadababdadbbccdabdaccbdacaababcaddccbbdbadccdbcacbaaddbabaacddcaddbddbdadbaabdaaaacabdbbdcdddbdbaddddcdcabbccbdaaaadcbcacbdbadbdadbbbcbcdcccbbadbbbdaadbddbdcddcaddcbadcacbbdcbdccdcbaabadbdcabcaaadddbacaabbacbccadadbabcdcbbbbcacbdddbbbccaadbbbaadcbccdbadcbbaddaacbdddbbcbabbcadbacdaaaadacbbbbaadbccbcddbaddbacddbddabdccddbdbcabbadccbbbdcacbadababbdccaacbadcddbbacbdbdbdbdcaccabadcbadccbbabdbadbbbadbcbadcbaabadbabdabccbabaccdabccbbddbcbbbabacccbadbacccbabbbabcaaacdcbcaabbcbdaababcbaddadccbbdaaacddcbdcbdbbcbacdccaaadabdabbbcbdbddcacabbbcddbbdbbadadaaaacaddaddbccbdadbccabddcacddcccdbbdcbbbadbbaaabaddbacccacdbadcababbbbacaccbcccbbbdbaacdbdcbbaaabddacbcdabdacabbdcbdcadccdcdbbbbacdbabaadaddaacdaddaccaddcdabbaacacbbccacaaacddacbddaaaacbcacaabbacabcdbbddaabbbbbdaddaddbabdbbdadbcbadadbddcbacbbbdaacacaddadcddbbbadccaaaadcbacacaababcbdbcbabdabdaacdcaabbdddbdaacdcbbcbcadbababddaccdcbbdadacddbadadadbdcadcccdcadbbaccadadbacaddaabdbbbcbcababdccbdaabbdcadacbcbbbdbbcacbcccccbaaabdcbbdcdababbadaacbdaaacccbcbcbcdddbccccdbdcbbabcadccbadcaaacbbababdabcadbaccaacddcbcacabbbcadbadbbccbaabddcbdaaabbabadddadaccbadaaacaccacbacaacbdadaacaabcdabacaccacddadadbaabbcbaddbdacdbdaadcaccaddddcbbccdbaaaaabcdbbdacbbdadcadccbcdddadbccacacabdbdbbadbddcabbacdcddddcadbbddbbabccaddbddbcddcbcadbaabdbbdbccadbdacbcdcdcdcbcacdccbccbddddddabaacaaddadbcabadadaabbbaadbbabbcacaccbaaacabcccbadcaddccddddcdcdbbcddaaaaadaacaddaabddbccdcdaaabacdcbcabbacbbcdcabddcbbdbcdccbbccdccbacdabcccbdbaccbbcbcbbdddcabddccbcccbddabdbacdcbbaabcadabdbbbbdbcbcabddaccbddbccdacadacacdbdbadbbabccdbcccddadcabcdabbcbbdcdccdacadcdcbaaccdabcaacaacacabbcaaaccccaadaaddcbcdcbcaccaaccabddabcaaacbbcabdbdcbbddddadbdcdcbaabcaabbbcabbbbbbbaccadbbcabcbbacdaadaddbcbccddbbabdbbddcacbbbaddadbbdbccaaacddaddddbacddbdcbddcbaaaadbadbdbdaccabbccdddaddbcdcbbcdacacbdbccdadbdddbccbacbbcbccbcaacbccbbcabaacabbbdadbbaaabdbbccbabddbbcdcdbbcadbbbdacbbcabdabaadbacacaccbacacdbdadbcbaccadcdbaaacbbdddccbcccabaccadaadcadcbabbcdddcdacacdccbbcdbacaacbadadabacbbaabdbabbdaacabccacaccabbddccbbadbbccdbacdacadacddcbabcbbccadbccaaaccbcdbcbacacddadbacabcbdcabaccccbcddcdccbcabcdadccadcbdbcbaaaaaccbacdcadaccbbcbacadadccdcbdcbcbbaacbbdaccbdacaacadbdbcaabaaacadbbddbdacddbacaddbdcbddbdbbbdccabacddccdcadaababdbdbbbcdcdcaddcbbabaddbdccaabbdcbdaaaccdcbccddaadacaabdcaacacdaabaaddabdacbaddddbddcddcdbabcbcadabaaddbdbadbbacadccbdbbcadcadcdaadbdaabdcaacabcbabbbcdbaadadddaabcaccbadbabadbbccddbdcbcbbbaadaaddbcdcdadadbabcdbacabbcabcacdcacdaacccbabcdcaacbdccaabcbaabccdbcacbbcabcddbdaadacccadacdbcbdcccdacdcdddbbbaacbdcdaddaadbbcbddccdabadadacccabbadbdabbacbcbabaabdabcadccadbcccddaaabaadddccdbcaabccbcdcdabacbddbdabcdbdadadddadbccdbdcbbacddbdaadcccacdacacadbdbcddacdacbcabbaabadadbadcabbaacaadacccabaacddabdbbbdccdbbcdacabcbbdbccdbacacaccacbdcbacacbdcaaadaabbcabbaabcccbacbdabbdccbbbcbbcbacbbacdaabbbabcdbadcddbaacbbdadaadacdaaadbbacaabddaadbabdabbcbacaccabccdcdaacdbddbbdbcdcabcdbbcaaacaaddcadbdccdcddacaadacdabdcbbcbddaaaddcdbadbdbaaabbaabcbbdadbbaaacbbdccdcbcbadcdacacaddddbacddacdaaccbddbabdaccbdcdcbbbbcbcaccdbbadaccccdbaddcaabadddbbcabccccdaddbdcddabddadbcabddcccadadacdacddaaddacdcdabaccdbbaddbdcbcaabcdcaadaabcacacdadbcdaddcadbcccbbccccadcdbcadabddaacabcacccdddccacdcaccaabaddcdcaabaddacabadabaaabbacdcddcadbcccacdbbbccccdbddcaaacbcdcbbcddbbacccdccdabbdcadcdabacbbddbcaccbababbdabacdbbbaccabadcbbadddbbdaccdadaabacaccddbbdaabaacdacdaaccabbdaacdddcbbcacbdabcbbcdbbccacabacccccaccdcdcaacddbbdcddbbcddbccabdaadcadbadabaacabdbcccadacccadccdcbdccabccdacacaaabbcddbccbaddbcdabdcadbdbaadbbddcbbbbddcbbcdabadabacbdcccdcddcadcabaaadbaaddbaadbccbbbacbbcbaddbcdcdbccacbabddbddbdbbcdcbbcbbbacdcbcdabaccbcadcaabccaaacbdccddddadccdaaabcdacdbadacaaadacaaccdcbbbaabddabccdbcadaacbbbaacbbcbddcbcabbacadaacccadadcababdacadcaaccdbccbbbaccbababcddccbbcbcccbbaddaccaddabdcacdbbbccadacddaadaccabaddabcaabcdabadcdbddcaccacbdddccccdddcdbbccbdcbdcbbabcbcabdaacaacadcbbcbabbddcabbadccbdcbcaadddaaabbbaadcbadcccabdcdccaddbaccadbabcdbbacbcaddcddabcabccbaacaacbabcadaddcaaaaabdcaaaccaacbabbadddbaabdcbcddcbabdbdbcaadaacaaccbbddcbacacdababcccabdcacbacbabcacdcbbbbcbbccdcdaaabddcdccbdbadbdadacdabdabaabbdbcbaacdccbbbbbaccabbcabcdbbdcbbacbcaacbabbbbbabdbdbaabdbadaaaababbcbdcaababdcaaabdabbbddbadadacbadddaaaabddcbbbcccbdddcdbdbdcbbbbacbadbaaabcddadbcabababcdacadadabccdcddaddabbadadbbccadaacacabaddabccbcbaabbaabbacadadcdadddaabdcacbbacccdacdaadaacbddcacbbdcacabdcdcccdcbcaadcbbddbbbbbcdcaababdbbbdcbbdcbdacbdcabdacabbcdaacabdcbbabdabbabbcabcbabbbbcadbcccddbdcbaadcadcccbdbbbdaccdbdcababcaacbdbcbcdbadcdcdcaacdddbcbcaabdcbabcdacadbcddcccdcdcdacbdacddccdbbdbaddbdabcaabcddadcdcaabdbdadaccbbcaadbbcabcabcdbcbabbbcaccddbbbabdddaaabaddbddaddadacdcaddaaabcccaabdbaccbcdccdbcccaadbccbaddacdbbddcabdcddcbababcbcdadbdbcadbbbcaaccdcbadbbbbdadbaccbddbdadaacddbdbbaccdbcaaaaaaadbdccbbdcdbcbcbcdcbdcbbcbcbcbbadbabbcaccaaddccbdcdabbcacaacbbbacbcbdabdbaabbbccadbdadabcabccbdadcadadcddcddccbbaaaadadcbbcbacccdccdbbacadddabbaccaabccdcbccbbbddacbcbbdbcdccbdddbccccddcbabcaddcabbcdccbbcdacacacddcbcdaadcdcdddcbdbcbcaccdbbabbcbacaacbcaddcbdbbcbaaadbcaaabccaaaaadccbbdbcdbbabbcddcbadccddadbabbccdbbccaaabcbadccdababbcabaaacbcaabcacbbbaabbdddaacaacabacbdababbbcabbadacbaccbaddacadcacddbbccccbdcbcbcbcaadaacadabbbdcbccabdbbadcccaacbbbbbccadbcccdaacaacbdccdcddcbdabbcccadabcaadbcdadaabccdabcaddadadaabbbbcbdacbddbaabbbcaadbbdbcacaacccdccbdcacbbbcbadbbbdbadccbbbccabbaaababcdadabdabbbabcbcadddbadcdcdbdcdcaaccbbddcddbdccbccbbbacadcdabddbcabcbdbddaadbcddcbcadabcccacbbdaaacbccadcaaacbbbddcbccdcbbbbcdcacbdbaadcbbcdacdaabbcaccbbaacdbcaadcdabcdbbabcbcddbabbabbbcbbcaaddaddcccbbbbccbcbddbdbadcdcbadacbcdbaadbcdbbdcabdbbcbbbdddcbddcbaacdcbacbcdcdbbbabaddbacabdbbcbcaabccbccdcabdabddacbaabaddcbdcadcdbdcabcdcdcbdccadcacdbacbbaccbbbbcccdabadacbbdbaccdbbbabdcadaabbabadabdbcdbabababbaddabbbbdccaacbaaadccccdbacbdbacbccccbdaddbbddaaacbbdcbdbbbbcdbcdbaccdbddddcacccacbaabbcdbbdaccbbbccccddbccccaadaccbbaaacdbbacaccdbabddcbdaaadcabaacdaabddccdbbacaabdabcaaddbdcacbabcacabccdcadaabddbdcbcdbbcacacacabbccbbdaaaddcbcbacacbcdbbadbccbcbdcacbbacbadbbbaacadbbdbbcbbddcdcbabbbcadaaabdaadbdbacaabdcabcadbddababadcdbdaadabbaddbcaabacbdbbddbacdaabbabccdccbacdccdbbbcbddaccdbdaccbcbddbacdcadcbacaaacbbcbbabcccbbdabdabbdabaabcccacbcdbbdcddcbaacbacbdacccdcadccabdbbdcaccabaacbddacbaabacdbabbaddbcdbaaadddcdbdaaabcacdbcbabcbbcdbbbdadaddcaabdcdcbaabbbcacaacaccbccaaadbaacaddabcacdababddabacaaacadddababccbababbdbdbaddddadcacbccdcbaccacacbcacccaaabaccacacdcccbbbcaddaaacdaacdbdddbcbbbccdbdaddbdcadcabdccadcbabcbcdccaaadcbbdabbdcaaacbbbdaadcadcbcabbcdcaaacdddccbcbbbadbdadbadcaacabcacadddadbadabcdbbbcbdbbadadadbbcbcacbaccbdcddabbbbbcdcdbacbdbabbbbaccdbcaaaabaddcbdabdabacabdacbacbdcdccccabddcdaadcdcdcacaaccadbaadbbcadbcabdcacdadaaaabadcaddbacbadcdbcbdacabcabadcbcdbbbbbaabdadbabadbaccacddabbacdddbbcabcacccaabdccccccabcbaccdacbdadccbccdbbcdddaadbaaadaaddbdacdccccdccbbbcbdbdaaacdacacaccdccbbaaddcdbdadcabbddddcacddaccbbaccaabdcaacbacbbaabcddcdddddcaccaddcadabcabccaddcbdbaaaabcbccccdbacdadbbadcddaabccdbbabdababdaaabdbccdcbbdadcdacdbdabbcbbbccabdbabbdcbbccadadadbdbbbaabccadcbdbcccddbabcdabddbcaddbbdcadbabbbabddbbdaacddabadbcddcacdababcdaabbcbacabaddadddddbccabcbccaacaabdcacabdcbdddccddadbdbdcccbccdacdbaabddbdbaabcdadcbdabaabcccababaadacdbbaabddcadbadcbbcaaddabadbcbcbacaacbbadccacaabaaccdaabdabbbbdcaacbbcddbdacbdcbbcadadacbbcbbcdadbbdbdbddacacbdacbbcabaadbdacabcbadbbbadabdbbddbcbbdbbddcbaabcbdabcccaabaddddcbbccbdadcbabbbbcdcaaddadcaacdcdcaddcdbcbcdcadcaadddabdaabbacaacbbccdacacabcbabcaadcabbacdbcdccdaabdabaadccbccdbdaccadcbcbbaddbbdabcddadadcbbbcaabdcdbdddbccbacaccadbabdddadaaaacbccbaadbcdacacdbbbcdacccaaadcdbdcacaaadddcacdcbddbccdddbabbbbbaddcbbabbbbdababccaabbccaaadcddcadbcaadcccdbccacdacbbaccbddabbacbbddaadbcbaccdbcbadcaccabcababaddbbaadccabadaaabcaabbdcabddddacadbccdbcabacddbcdadcbacddccbcbababbdadbcbccbaaacaccacdaaadaabadcdccdbaacadddacaabcadbabcbdaadcacdaddbdddbaacadabbadccccaddacadccadbbacaaabbadabddbabdaabcaddcadbcacdcadccabddcbdcdacccbcaddaddbccdbdddcdadadcdaaddadadbcabbbdabdcbdddbddbbbdbdaccdddbdddbdcadaccddcbbcacddbdabaacaddcbcbbddbaddbbadcacdddacbcbbacbcbabcababbaaaabdbaadcbbdacddcabdadccaddbdaabdbabbbdcdbaabbdabdabddbbbccdbaadbbdbbddaaaaabcddcbdabdabcdaadcdccabadcbbbccbdaccacbcdcdaacbbbbcbdcdbbbbbcaabbdbbabccacdbcddcabccaddcbadccbcbdaaadcadcbdbdccacaadcadcddbabacccdcbabccbcacbacabcacbabcdccddacccddbaaddaadadbcddcbcdcdaacdbdbdaacccaddbccdabddbbbaaadcdacdcabddadaadcdcccddbbddbacccacaacabcbdcbbccdababadccdbbcdccddacdbbccdadcccbcddbcadbbabddacabcdccabababdbdcddacdadbcdccccddaadacdadbbcbccbbcdccaddbcbdacccabbcccbddacadcaaaaacbcaddabddaccdaccbabbdbcbacbcddbdcbddaaaacabcacccdbadaacccbdcbacdbcbaabccadccabbacacdddabadcbbcacdadccbbaadbddacddbcaadccdcdbaaccadaddacabddbbcbbdadbddcabcbbacbdccabacbdabdacababbbdccaabdaabadcbbdbbbaacdaaabccabdddbabbccccddbbadcbdaccaaddccdaaacacdaadacabadddabacddcdbabbaaadcddacccabdcccadcdbdbccbbbdbabbcbccbbadabaaaaaaaabcddddcbbdcacabbcaddabcbcdabdbaacdcaaaabbcbcdaadaaccbcbdcdcbbdbbdaacabddabaabcaacbddcbbaaabdacbccdadaaacbbbdbadaccbabdbdbdcddddccbcabbddaabcaddbdabbaabdbcbbadcdacddbdbadddacddcccbbdadabdcdcbbadaadaccabbcdbcdcbbacdbbbdccdcbadbbbaadcbaadaacababacacbbdcbdbcaaaadabacbbabcdbddbdbbdaacacdbddcaabddbaaddcdaababbdccdcabdcdcddccddccdddccaacbaccccadaccadcbbcbddcabdaacbdcdaddccddacdaacbaadddbabcbdbccabaaccacbadcbddbddccbdcbdcaacddddaaadddcaccbccacdacaadbcaadcabdaadbbdbdadbdaadddadddcbdcddccbdccbcaddacababcacbbcbcbbbcaadaabdbdbdbadabacbbccdbdadacdbcdcaababaabdbadcbaddccddbccaadcdbbaaacadcaaabccccabcabbadadbbbcccabcddcccabdcabccccacadbdbadacbbdbabaacccacbbbabbababdacddcababdaaaadcbcdabbdbdabdbdcbcdacbaddcbdcbadccaddcdabbcdaccdbdadbdbbababadddacbabdaddcccdaabaabbddaccbbcdcbbccaacdbccabdadccdadcdcaaacaaaacbaabdabdddadbcbcbbcdcbbcbbdacaddacbcadbaddabcddbaaaaadbcaadabadaadbccacdccbdbcbaabaacadabdbabcddcccccdadcdaddcacbbdcddcbdbacadaccbddbdcccbccccdaabddcbbbbabdbcdccccbaaccaaabaccbddbcdbbdaddccadbbabbbcacacadddabadcabccbbbcddbcdabadcabcbaccbbbdbccbadcbcbbddaadddaccabcacadbdbabdddbbadccddbbcdacadbdcacccddaaabdbcadaccaaaddbdabbdbcbcbcdbcacacbbabbaccccdddcdbbbcdabbddcbabddbcbacaaaccbbdbdaadbcbccddabcadcadabaaacbaabcaaadaacadacdcbaaacdcdddbaaddacdbcbbbdddddadbdccbabbabcdbdbaabacdccacbaabcbddbacdddcbddddbadabaabdbddbcabacbcbddcbcdbbbababbdccbcdabdcbacddcaaccddcabaddbacaccbdcccdcadcdccbdcdaccdbabdcdcdccaadabccbaabcbacaccaaaaacabbcbbadccdcaabaaccccdddadacdcdcabdbbbadbaacddbbdcdbbbbbddbbccabcddaddcadacbbcccabdbbaccccdacdcdabaabbaadbcbccbadbcbdccdabcdcacdbcbaacacbbbdbaacaddadbcbbaabdacbdadddddddcdadcbaccdcdbbdcbdbacadabcccadcadcacbcbcadbccdddcdbadcbcddadbbcccacabdbabcdddddbbacaadaaadbaacabbaabdabcaabdadabacbbbdcaabababcacbcccdabbdadabadadbcbdcabdcbcdbbdcdaabcbadaaadbccacacbcdcccbddcdbacdbbbbbdcabcbccddccbdcdcadbbbdcddbababbbacbccbdaccadacaddbcdbddaacbdcddbcddcaababadcbdbcadbcbacdbbcacaabddcacdbddaadaccdbcadacabdcbcbbbbbdaacdcacbadcdbabcccbcaabadbcdacdccacbdabbacbdcadadbcaddabadaaadbadcccbdcbbccbdaddabbbacbababadaddaadacaaabdaabbabcbacbdcbabcdbbdbcabaadbcdbdabbbdccbabcbcbdddaaddabdcddacaadadddccacccaacbdaacaddddacacacbccccaadbdddadcbccabccbbaddcccdabaaacbbbacddcbcadbbdbbabcccadabadadaaadbbaabadcccacdaaaacbdcdbbadcbbcbdbbbbddadbbcbbccbbcdcabdbdabcbbbabbcacdbddabdabdaabbddddcbcadccbaabaccdabbddbccbbaacdbdaadbbadcaaadbdaccdacacddcbaaddacabbbcaccdacadcaddbbadddaaccdabcbbacdcabbabbbcdcbdcdadaacccbacabddaacbbaaacbbdaaaaccacbdbbcbcbabacccdcaccbcbadaacacbdccacaabbcaccdcdadcbaabcaaadbcacaddcbdbacbabadbaacbcaaacbbaaabcccdadaddcdcbbcdcacadaacabaadccdbadbdbcdcddcbbcbbcacbcbcaccbadcdbbcbbbabdaadcdacdbdacadaccbacdbdacbdddacbccbcddbbaabaacdddadccbabdbadcbabbabcdabbdcccdbdaabadaadccccbacdadccbccabbdbcdcccaaabadbdcdadcdbdbcdcdbcdadbdaacdbcbcbcbbcacabbcdaaabcbcdacdbacbcbcaaaaaaaabbdcbcdadcaabdbbcddbbbdbdadbcbdbcdaacadacddbacaccadacdbdbaddcacbcbbacdacacbbaccbdccdcacbabbbdbcbbdcddacdbddacccbdbddbacbacbacbbabddbcaddadbcabadababcadbbdccbdcbddaacdcbcbdaccbbadabcccdddcdadcccbdcdacdabbcdadccccbccacaabdbacbcddbaadbdccdddaaadcacdaaddacabbddabccbccccadcacababdbccddddabdcaacddbbacdbcadbccadbcdababbbacdbbdabcabacbdcdaadbccccdbaabcbdcdbcbdaccabaaabbabadacabcdabacacccadbdbdacdbddddbdcbbcadadaddacacdddcbabcaccdcbccabbdbadcbdcdbabadacbbacbabccdaabdcddbacdacccaabbaddbbadddcadcabbbbadccbbaacadbcdaacdbbaaccccaadcbdaaaddbddccccaccabcccaacdccbabbbbccccdcccccdaabdddbbadccacbbccbacdbbabbcdcbdadbddddbdbbabdccabacdacbabbcbbbdaabdbddcbadcbaabcbabacdadacaadcddbadabbacccbacddbcbbdcdadcbadcabbcbdcacdcaadbdccddcbaacaccdbbcaadcdccbbcbcadbcaadddacbcbcdccbbcdcbcdcdaabbaaaadaacddcbccbccadcaddabbbcbbaddbcdbaabbbcbadbbbccbabbddcbcbdbabcbbbbccaabdabcccaaacaaabddbbbdbbbcbadcdcdbacbbcbcddaaadbaaacbaccadbaabacdbcbdccbbbcccdcccdddabdcddadcdacabbdddaadcbccccaccdbdddcdcdccaabbccabadbabbcdacbcddcbdacdddbdcdbdacbbdacadacbccdcbadccbacdacbddaadcbcbcadcbcdbaccdcccbcabcbbcbabdbcdccbbdcccdccddbbcdcadbbccaadbbbdcccbcdbddbabcbabaddadabddcacbbdbdbccadbbdbcbabcdbccacdccdcdcbdbaabdbabddbaacdcdacbabbbabbbddcdcbcbcacdabdccdccabcdbacbddacddccdbaadbbbbddcdbadbccabdabdacccadbcddccaadaadbaddccabcaaccacbdbcdadbacbcccacccdbaadabaccaabccdbabbccccdccbabacdabaddbcadbadbdbacddddabbbadabbabccbbadcbabbdbccaddbcbacadabbbcadaadaadacdccaacdcccccbcdcccaaaaaababbbacbbabdbbdbadabacdbdabbdbaddaaddcbdcddaddcdadadddbbcacadbdcbcbabadbacbbbcdcaccadddbbbabddbdbdddbcadbccdbdadaaddacbabaddcbaabcaaacabdccbbcdaacbddbdbdabadccdcdbbbbccddbacddaccdabcacdbddadacdbdcacbaadcbdcdccbbdddccbaaddcbaddddabdbdabaccbdddccdcacdccbaadbbabbaccdaadbaaabcdcddabdbbdccdabcdbbaccddbdabbddbaabdadaccdddbccaddbacaadbaadcdaacbbabaaacdbacbdabacabbcbacbcadabbdaddacdacacbbaaccccaabaddcacdcaacbadbadbcdddbaaddbacaacbcbacabbabbacaddcacddcbcbbccaddacacdbddbcbdccddbcddabcddcacbbcdbccddacbcbacaaacaadcaabacaadbcdabddbacdccbaddbddbdcbadbcaddcdadccadddacaccabbcbaccdcdbcdbdccaacccaaccabacccabdcbaabdabdadbbdbcbcdcdbcdbaadcdadcacbbacadcaddcdbdcababcacbbddcbbccdbacbcbbbddbadabdbdbdbddbdcdbbbdbbddbcdadbcdbdabdcbaaadaddadcdacadddabadcdacbdbaabbbbbadbcddbbdcbcddcccbbddbcacbcbcbbcbbadbcbdddcabcdadadbdcaaabcacdcbbbaacacadbbacaaadddcddaadbbdbdcdaaabaacbdacadbddadacdccadbdcadcdaaacdcdddbbbddabbcabddbbaabaacacdcbbdbddccabdcdcdabadaaddbccaacbbdbcbcdcabdaaababcabbbdaaadccdddbdacdddddbbbdccccbbccaacaacabbddccadccacbdacbccddcbdacadcabbcababbccaddbaacdcbabbabdbdcddcdaccbbbcdacbadddccdbbdbdbbbcdbdbcdabaadbabbbbabbdbbabacadbdbbbcccabdacddcbdacbaccddbcdcbccdcddaabdcbbcccaccbbccdbddbcbbccdccacbdcdaaabbacdcbcbabbcdcbddbadcccbdbcaabaaccbbaacabbdbcbdccabdbaccbbcabbcccacaaacbcabbbdadbccdcbddbdacbbdbbdacbbbdbdbabacbcbdbbbcabdacdbbbccbcbbdcbaccacaacddcacbaadbaaaabdcdcccdcacbddbacdcaadbbccbbcbcbbdadacbbbcdcaccdcabbccdbabdcdccdcbcdcaaabcbccadddbcbdadaaadcacbbcbcbbcadccaacaccbcaddabbacaacadccdadabddabaaabaaddcabaacadaddaabbbbaccabdbbdddccacbbdcabdcdcadbdaddbbcabadaaddcadddbcaadacadbcbccbadcddbdddbabcabadcbaddccdcbaaccbdbbbabaccccabaadcdbacaaaddddcdbbbdbcddaccdbdcadccdcddbacabdcbcdcdcbdaccbaddcdadcdcbbcacdbccbdaacccdaaaaacbdbbdcaadaadadbcccacaacdcbaaddbaadacaaabcdabcbdbbcbbbbdddbadaacbbcadcbdbdaaddaacbcabcbdcbbddbbccacabbbbdccaacabbcccbbdbcdacbdbdadbbbbdacaabcdaacbbabaddbdbabdacacddbdbcdbbabddcdbdbadcbcccbddbbddadcabccdcdadbdaadaabdcbcdcccccdadbadadccdcabdbbbcbccddbdcabbddacbccadaadaabcdacbadbcdabadcbcbbddbaacacbcdbdbccaacabddabbdbadcacdaaadbaabbddbbddaaaaabcbbddcdbbbccbbcbbcacaabadcadbbabcdcdacaaaadacccbbabaabdadaaadbbdacdaccbcdabdccdccccddbabbabaacddccadcadcadcdbbaddaacdbdbdaccddbabdcabadacddacaddadaddcbbacbdabcdbcabdbabbbcdabcadadaadaadbcddccaddbdbccdacccadbdcbaaaccdadbcdbddcacdacdadacddbcaadcdcddabcccbaaddbdadbbdbabcbbabddadcabddbbdadccbbbdbacbbbcdbdbdbbbbcbadcdacabdbbdcbbbbdaaabbaababdcdbddcaccdddabdababcbdcbbdbbabddacbcadadbdcaadbdcadbaadcdcddbabcddadacaabaacbadbbcbacbbccdccabadcdbdbdbcccccbccbbdddcbbbbaacbaaabaabdcdcbddccadaccdbbbacadddabdddddcbbcddbbaccabadacbcdbcdbbddddddbabbcabdadbbadcdbcccdabbacaacdbabcbccaadaabcacacbddcdabdbbabcabcddbaddccadbdcbbbaadcddcabbacccddbbccadcbacbcbdbcdbcacadbaaddddcbcadcbdacdcdbacabacbcdcbbaddddbbccabaddaccabbdacbccdacadacbcabcaddaabadcaccabdddadaabacccbcaacadcaadbbdddccacbbbccacbddddbdadcbbbcbbccaacdbbbbdaaadcbdddbacbcbbdbbbcacabbabdbadccacbbcddbaaaadbbbccbabacddbdaabadcadadddadbdadbbababaadddabbcbbcaccdabdacddbcacbdddacaadabdaabcaadaaaccddcdabbdcbabbdbddbddcbaccbadcaadadddccdaccbccddcbccddaaabbcacdbdacbddbddcabbbcaabcdadbcbdcaaaccddcbabcddacacddbcadcddcbabacacaaabaccccacaccccdccbccdbcccbbacadaaacadcdbbdcddccbbbadcaabcbbdcbbabbcaadcbcbdadbccaaaabbcbcdddcbcdbbbaddaccbbbdaabaaadbdcbaccbbcddddadcdaacdadadbccccbbdbaddcadbcbaabcabbabdccabddbadcbdcbcddbccbacddaacbaacdaadacdabbadadcaacacdbccdaadbacbcaabddbaccbcacabacbbcccddbcbdcdcacbdabaabbcbacabddabadddbccdcadcdbddbacbacadcbcbbccaadbaabcdadadcbdaaabccccbbbbcabcacbadaaccbdcaddbbbcbcdadaabacdacbdbdddcdbdddbddabdcbddbbdcbdccccdacbcbcdadbbcabbdadcddddadcbccddadabadcdbdadccdadbdbcbcbbccacdacbbdcbcdaaacabcaadccdbadcdadabdbccbbbdcccdcdabcddabdbaaacadcacbaaaabdaadbddadcdadabacdabdcddbaaacadcbbdbbdacbaaacbcacdaabdacbcbdcdadddacacbdabccccacdbdddbabcbcbbdaacdbdaabdddadddabbcabbacdddbaadcaddcdcadbdcddccbaddcbadcdacdadbdcddbadddabdbcddacbadadaacabaccbababadcbcabbcadcddcacabccbccbcbabbabbdadcbccbaabcdaabcdddacbbbcadcccbbbbabbdcaadcbbadaddacaacbbabbbdbbbacddddadccbdabacbdbcabdacdbbcbcabdacbddcdccbadbdaadabaabcddaaaaddbbccdadcaadcabcabaccbdbadbaabccdcbadadbbbacbdccaaaacddccaaddabbbadbdbdcaddacbdcabdcaacccdbbadadacbbaabdbaddaadcbabbacbddabacbdbbbccdacbbcbcdcdbcdabddacdcdaacacacbabccbdbddacdbbbaddcbcddbccccbcacbdbabcaacadadccabbdbaadbddabbcbabadaadbcabaaccdccbacacdccbdadbaabaacadababddbadcaabaacdcaacbbbdcbccadcdcbdbbaaadbdacbaddcabacaddcbdbddcdcdcaadbcdadaabaabdbcddbdbddbbddaccaccacaadbcbdbcddaabddbabaadbadabddaccdadbaacdbadbcbccdacaabbbdbbddadbbcadabddddabccdacadbdadcadccdccdaccaaccbcacbdcbcbcdcbcabbbcddcddcabbcabcaddadbcacbdddacacccaddcbabddacdbbbbacbddadaabcdbcdaadaadbbcddbbacaacbadccdbcadcbbacdbbbbabadbadacddbaaaccdcadcdbaaabaadacbccabdcdcdaddacacacdabaaccccbdcbaccaaadcdbbabbbccdadadbbbcabdcdbacacbbdcbacaccbccdbcdabbcbaaabcbccacbcccbcbdddcabbcbdbcaadbbabbbaabadaccaccaadbbabdaaabadabbdbcaadacadbdbbbbadaabddccaadcddccbbddbbdbcdcdadaadcaacacddcbddbbbcbabbddcabacbddadabcccabddaacacdcddddabbdccbbbadaabdcdbcaaccbaabccaadacddaadacdbabaacdbcdabdabcdcdddcaaababcadcadbbbadaddaabcacdcadbadbddcbbdccccbddcaabdabcccaabcdabcbcaacbdcabdadcdbacdaacaadaabbdbcdabbcadcccdcadbcccdccbdbcdbcabccdaddadbdddbbbbcdcbaccbcadbbccbdbbcabaccddcabccbacbddcccdacbcadbbaadccabbbbadcaaaadcdcbaaadcaadbbbdacbaaaadbdaaccabcdacabbaaacdbbdcccdcddcbdbacadaabadcccbcabbcacdacdbcabbdcaacabbdcabdbbcdcbdbdaabacbdbddaadcacdababaaadbdcacbaadbcddbabbbadcacdadadcccadddaacdaabddbcdbabcbbabccdbbcdbdababccbaddbacdacacbdbbcddbbaccdadbaaddcccbbdcacbabccbcbcbaaabdbbadabbbddacabcbbadddcdcddbddddadbabbcadbdabddadbdbddaddddcdbbdbaabbbcdadadbcdcccddaabbcadcbcabccbbcdaadbdcadaaaccabcdabcaadbaccccbaabcdbcacbccdcbbccbddabddccaabcccbddccdbcddbdaccddcbbabcddddcacccbacaadcdbcbacbcbcabbbbdbadcdcaabacdaabaddbcdbadddddbabdaacaaabdbdcddadccaacccccbbbdcdddbdccabddbbbabccbabcabaaddadbddadcabadbcdadabbcddddadcbcbaaaaababbbbcdacacaacbdacdbaacbaaadccacdccdbaaccbacbaaabcdacddcdabbcaccbbacdaaaadadddcbaddbacbdbcabbcdcbdaddbbcccbaabbccaaccccbddbaaaaddaaccaadccbddbdbbbcbbbacaadadbacccabcdbabbcadbbbddddcccbaabadcaddbdacccccabdcbcddcadaabbadbdcbaabdbbcbacbabbcbadcabbcdaacdacacbabbcddcbbbdabaddabbabcacacadcbdaaacdbddacbcabddddadbcdccbcaaacdcdbabbbbbcdbbbbadadbcbadbcbdcccaacbaddcbbbcbbabdabddabbcdcbbdaabacccaacadbaddcdccacbbbdcdacdabbccdbdadacbadddbddabaabdcdbcbcbaacbdacccbcabaabadaccadbbcdaddcbdacbacbdbbbadacbadaadaabcbaddccbbdbbdadacccaaaadbccadbabddbaacabdaacdadabcdcbbccccbdacbabcbdcdacbbdaddacaddcbadcdcbdbcabbaadcbcccbbdbcbdbadcddaacdadaaaaabcacdbcdbdcdabbccddcdacbbdddaddbdacbbaaacddddadcbcccbabacdcacaabbaadaadcbacacadacdbadcdcabdbddaaabaddcdabaabbbccbcacbcdcbbbcadbaccbabadccaadbaadadaacbacbbddbbacbbbabadaabccccadbacdbdaaabadbdbadcbcacdbaddabdaddcabbadadabcdcbdbacdacbccdbdbdcabaabacacbccbbbaaaccdaccabdbadabadaadaadcdbdbdbacdbcbbcadabcaacddcabddbdbddcdbdcbaccadcdcbbddbccdcbbbccaacacaaddcdbcbbaabcadabcbbbadaaaaacdccbcccdcbddbccddbdacaccbcacbacababdbdbadbdbcddcdddaadcbccdccccdabccbcddbcbbadadbabdbcdbdacdddadcdcdddcdcdcdaaacbadababbadacacdbdddabddbbbaaacccadbadabbccbaadadbdadaaacddbabbbdbaacbcbcdcacccdcbaacaaadaadbcacbaacbcabdddacbdccbcbbcaabddabcdccdcccbcdcabdcbadbccbcbbacbdadbbddabdabbadddadbbcbadaccacbaacdaacbdcbaaabcccbcdacddcaccddbcbbaddacdcbccddbabdbdbbdbbabccbcdadacabbbddadccbbacbdcddccdcccabacabdaaacadddbaadaccdbdaacbcbddbcbbadaccbdcbdaacaacacbaaaccdbaaaadcaabacbcbcdabdadacddadcabbcabadaccbcaadbabbdcccdbcdaacbbbcddbcddcdacdcaccaaddcdbcdbdaddbaaccbadabdcaaabdcbcabcddacddaccbbcdbacbddbdddbbaadbcbabddccacdbacacddbdbdddcacbbaababbdabbbdcdbbbbacaaddabcdcabbbabcdddddddbacdacadcdcddbdaadbaddadabaaaabbdcddaacbcdbbbccddcacbacbacdbccabdccdccdcbabaccacaddaaacbcccaccbbbabcaccdbacbacbbadbadbacdaaacacacbbcdcdadaddddacbcdaccddcbbdcbadcabbbddaabcdabaccdcbaaaadcaaccaaccdccaaaadbabbbccdabcacdabaabccdabacbccbabbabbccdcccaaaacbadcaddbddbdbbbcaaadcdcdaddddbacdbcadbcccabdbddbdacddcdabbcbdbdabadcdacaabaaccbbddbccdabbadadddaabdcccbadbbaddbbbdbddaacaaabaccddadbacbbcbaaacddcddacbbdcaaaacaacabacdaadcbabdaadbddbdcccbddbcabaacddbaacdccadccdadbaccbdddcadaddbdbcaabdbcddbdaaaacbbddaabbdacccabadcaccaabadbdcdaaadadcadadcaaadbaadadbcbbaaccdcacccaddabdaadcacdadabaaddaccdabbcbacdcaaddcddbdaabcccdddcaddcbcddabdaccdacdcbbacabdadddcbdbaaccdacbaddcbdcaacaadabcbbbddacadcbabbbbddbcbabccaabcdddbdcbbadadbaaaddcdcbbdbcabbcdbbdcacabbabccccacaabddcbadcaaacaadbbadcadddbbacbddbbbdaacaccddcbdabbadbcdcdcaddcdcabbdbacdadabbcdbcdacbaababbaaaaabdcdacbdbcaacadadddbcacbaabbbaaaadcdcdabdddaddaadaccbddacdabcdcbbabcaacabaadbabbdacbdabbbcaabaddacbccadabdaaabdaabcbbdadacdacbcdbdccddbbbdbbddcabbdacabbbdaacbdacadadabadcbbcdbaddabbaccbdabbcccbbcbcbcaaadaaadcbcababccdddabcadccddadbdcbcdaaccbcbbbcbcdabbdddbbcdabbadccacdcbbbacccbadddaccccdcbccdbccccdaacacdcbbbdcaacdbcddddabacdcddbaaddababdabccccddbabdaccdcdbdaacabacadbbcbbdaadbaaadadccddddccabcdcdbaddbaaadddabcbcbccadbbcabbcdaabbbaaadcacbacaabcaccdddccbcbbdcaadbdaadcabddadbcaddbbbabddbbccaaccdacdbcaccdaacdccbcbddaacdadbddbdaacdcbabadadacdcccaaccdcccdccbadbddbbdbdbdbdddbbbddddabcaacbbbbdadccabaccdaaccccdadbcaddbdadcbdacababdabddacbabdbccbcaacdbcbccbaaccdbccddcdbadbbcdbcbdbabbdbbccdbbadcdacadadcabbcdcadbcbaddadabddcadadbabddbccaacbcdddbbadaddbacadcbaddbabcabcbbbabdddaacbbdaaddcdabcbbbcaaacdbbbabdddadacbbbddaaddcaacaabbaacadabcabcacdbdcacbcadddcdcdddddbcbcbdcbdacbadcacdcbbbcbcdcbabbbbbcddabbacacacdddbdaadcbacdccbbabdabcbcccbbdbbdaccbbcbddacadbaababbbccbddcdababbdddacaababdacabcaaccdabbdbccbaccadaddccacdadacadcacabbdabdbbaabccaabdacdccaabddbccadbbbdcabdbdbbbbdbcdbaabdaccbabcabadddadabbcaccdaabcacbdccabcdaadbbabcdcddcbabdbacddccaabacbdbadadadadcbbddbbcdbdbaababaadabcddaacbcbddddacabacaacacdadadbabdbdccbbdbbbbbddddbddbdbdcabdadbbdbcdbdbcccdbddbdabcccbdbcccaacdaaccbccbbddccddddcdabccbddbdaacaccabadbbdbabddcbdaacbbdabadacbaccbbcbcbdbcccdabdcbaddddcdbdaabcdababddcdbcbbadcddbdbabbcabbcdbabdcaaccadbcccaddccbcadcdaddbcddcbaaabccbdbbbdaddbbbbcaadcaddabbbaddcccbccaaccdddbadcbbcbcccdbbddacdcccdabaadbdaabbddcddbabbbdccbacbbdbbabacadbccdbccbcaccaadccacdbbcabbbccabaaccbacbddcdacbddacaabbadadaadbbbbbacdbccdbbaadbaaddcbaddccdcdabdbdbbbdcabdbcdbcddabccbdcabbdaaaccabbadbabdcbacbbaabddaaaccabcaaaaccababdcddacaccaadcaccadcccacabbbcbaaadaacdacbbbcbaabdbbaacaaadcabdacbbcdaccdcdaaccdcbdbbdbbcccadbccbacbaccaccbadbbadacbdacbdbadbabbbcabbabacaccddbcadcbbcadacadcbaadcdbbdadcaadacaadcdbdccddbcbdabdbbaadbdbaadabacaccdcdaadbdcadcbcdaabbbaccdbacccdabcbacbccddbddacbadaccddbdbbccbabdcbccccabdcddacabddaabbabaadaccababdbdaccdddccccdbccadadaababaddbacacccbaacdbccdbaacabbddbcadcbbbadbcadbdbbdbabccdbaadbcacccadcacacdbcdaadcabccacbbbbbccacbbabadbdaddccaaaaccbdbabbbdddaccabbbdbcdddaacddbdcccccaccdcadbbbadbdababbaddabbadbbbcacdccccbbccaddbbbbcbcdcbddcabbdbbbdbaddbcccbccbaaabcbddcddbddaaacacaddacacbadaabaadadcabbbbbabbadcadabcbcbaaadcdbbdbcbcddababbaaccbdbcdaccdcdcdaacabcabdccccdabdbdbaabddaddaacadbdddcbcbbbbcaacccaacbddcdcdacacbadacaacaaddcaaddcbadabccaabdcbbabbbddcdbabbadddcadcaacaddbbaadcdcddbbacaaacbabccbbbdbdcccbdbacdaccbabdddcbdcccbcaadddbcdddddcbddbdbcbcabadbdddbbadaacbbacadddadaddcbddbdaddadadcbcbbbaacccabcccbdbbbbabbcbacdbdcaccbbbcddcbbacdbbbbbdaaaabaabdaabcccbcabdbcdabcacaacdbbaccdcadbbdbdbaabcdabbdacbabcdaadbacacdacbcddbbcdcbdbccacdcacaadaddacdcaaacabdbabddcbcaadbdbcdbbdabdbcabdadbbbcabddcaacccdaadbcbdddbacdacabddbdcdbbcaaddabcbbdccdbbaccabaabbddacbdccdcbcdbcdbbacbdaabdacbbccdcdbbbbdcaabcbababbcadbbcbacabadccabbdbabdcdacacdacdcbdddddaadcbcbbcbbcdbbbdbcbaabcaccdbcadabddaddabaddddbcbbbcadacabbdcdacdcbbbaabcbdbbcdbaaacbaadaccbdddcadaddbddaacabcdcdccdbcbaadcaaaddacbadcaadbddcbabdddbbaaaadbdbbdabdbccbacdddabbcacbbdbddcdcabbaccdacccdbcbbaaadcddbbbcbaaccababdbcbcdbcddccadbdbccaddacbcbbaddcabbcdadabbbdadbcddccaadcaacbaabdbadcccbccdcaaaddadcdcbdbbcbcaabdaadaaddacbaacaccccdbcbccabbcdbadabababdcacbbcdbccbbacacdababbbbcbbbdcaaccaababbcdaaccdccabcdcdbaaddabcdddccaaddbdbdbbcababdabadddbddbaacbcbacbdbabccdcbdbdacbadcdaabcccacacddcadcadcdcbcdaaabbdccddddabbcadcbcdcbaaddcbcdcdccdcaaaddcbdbaddacabacacdbbcbdddbbbbdccdbcbadacdcddabbcbbcacacabdbcababbdddddaccadaabbdbcabccacdacbbdcaddddabddabcdabdadbdcadcaaaacdacbabdbbcdcababcadaacbcadbdcccdddcbdacdddacadcdcddbdabadbbdcdcadabadcabdcdaaabccdabcacbabdcbadcdccbabacadcbdbbdacdbbcaaabcbdccddbdaabcddaddaadabadbbdaabcbdddbabdbcdbbcdddbadadcdccddbbbbaacdbcbdabaaaaacccbddcbdcbccaababccbccaabbdaabcbbacdcaddbcbcadcbdbccbdbbbdddbbbcbbcccaddcdccadadddabdbdbaccbbabdddaacbbabccbdbabdddcddbccbdddbbaadcbdacaaacbcaacbacaadbdbdaaaddbbbbdaadbdbdaadddbbccabbbbbddadbddaccccdbdcdcdcadbdbbbdadcacdcdcdaccdbdccadbbdccaaacbadabacadcbcdaccbdacbdbacacaccdbcccadacdcaaaabdacdabacbcbbdbcdbbdabcdcccabaccacdcdcbcadcdaabcbabcdadbbcacbdbdccccbdcdcdcdbddddbbdcccdbcddbabccddacddcbccabacdcddcbddbabacaadcddaaccdbabccdcbbadbbaaaadacadddbbcdacacbdcdbcdddbbcdacadbaddddadcdadbbadababdccbdbcacdcbbbadacdaccacdbddbaabacddbcdbdacdbdabadbdabddaaccabbbbdbbabbcdabbbdcbbdcbcbabaddbcdcbdbacbcbcdbbcbadccabddbcaacdcadbaaaabacccdbcaabcbcbdddccbcbcdbcaccacbcadacdbbacdadddbdcbdcdcdccdbcbcdbdabcccdbdcadccbaacdabbbbaadbbbadbbaadbbbbcccccaaaaaaaabccacaadadabbcbdbacdcdacacbdadbdbdcbcdcbacaadbabcbbdbcdacdadcccbcbaccccadbbdbbcdccdcadadaabcaabccacbbbcbbaadabbdcbccadabdcabddbcbbcacddbaacdbccdddabbbdbbcabbdabddddcbaaccddadbbcdacaccdcbcdbdcadbadcbbcbdddbdbccaddbadcddacdcbdbbacbdbdbdbccbdcabadaabacbaaadbaabdadababcabddadaaadbccadccdcacdabcdacbadbbbcdcdbdcbadbcbcabcbdcccdbcadcaadbcadcbcbdbbbbdbcccdabacddabbbabdcdabccdbcaacddbcabcaacdcbcbcadbadbcbbcbcadaabdbccdbccabaababdbacdbbdccaaddbbdcdacdbdbdcccbcbcddcacbbcbbcadddbbdbdddabaddddbbaaabbdcbbaadcdaccddaacacbccdcadacdcbdacccdcdbdcabbacaddaacbcdbdbbdbadadccbbbbcdccbcaabacacaaccccccadcbcbcddcdddaadbbbdbbcccbbbadbcccbdbdbdbbbccbdcdddbcaabccbbadaabddbbadacaaddccbdcddcccaabbacbdddbcabadccacdbcadddbacaabadcdbddcccabcababdabddcaccccdbdcdcadadaabbaabdadadccdacdadabdddadcddacdcaabddcccabacaabdbabaadccaadbbbdbcacbcbdcabdcaabacdcdcdcccdbacaabbdabdcadbacbbbaadbbdaacabacccbbdacaacbcdbcaddddbcdabdddcabbbcdcdbdccdcddaabcbbdcaababddcdccaabdabdcdcabaaacdaacdacadddccaacbbadcbdbdbbdbbdcddadbcdacacbabcbaabcbdcaaabbbbcadcabcaddaabacdabbacccbcdadbddcbbccbbcabcbaadbdbddcddbaadbcdcdabcbdbbbddbdcaaddcbbdbadbbbdcbcbbbadadbddcbaaaccddddcabbddbabdbbbabdbaaaaaabbcdddddbbddcbbbaabcdbbacadbcbdcccbcdacbdddcbddbcdbccadbbddcddadbdbccbdcbaadadcadbdaddcabbbbbdadcbdcacaddbdbacbabcdaacbbbaadabcaadccadcdbacdadabbdaddbcbdcdccbddcbacbbddbaccaddbbbacbabababcaababbdcdbddbbbcadacbbbbcdacdbdbdddacdbdddcdabdabccbdbcaabcabdbbbabcacdbaadccddcabbccccbbbbbcadbbacbaddabbdbbdbbbacbbabbddabccbddddcababbdccccababddcdaaababbadbaadbacbacdbaaabbabdbdbbdacddacaaddaaaccdbabdadbaabaddbcdccbcdaaaabaddcdcadadbccdddcbbcdcadacadbadcbadbadccdcabacccabccbcbcabdbadaacbcdbbddcdabcbcbdaaaabcbaccbcbcbbacabaabaaddbaabcdbdbaaabdcabacbacbaaccacacbdbbacdccdcbacaabbaaddbbcdaabddccbbaccbcbabbcbdcdccccdaadbccacdcabcbddcaaaaaacacddacadbdcaadbbcddbbcdcaddbcdaacbcdbbabadaddccdbbabdcddcdaaacacbcdcadbccbbddbdabcbdcbddaaacadacbbaddcbabbcabdcacbaacadbababaaccdacbbdddacacdacacdbcccabdabddcccbaacbcdbabacacdbdadaccdccdadbadbdabccaacbcdbcababbbbadbbdadddbbaacabcdcbdaaacbdcdadbdcccabcbbccddcbddabacdadbadcdabadbaababcaabaccbbcdbbdadcbcadbbbadbdadabcdabccaccacbabcabcbccdaddccbcdbcdacdcbdccdbdcaacccbbadddadabcbcbaadbacccdbbcddaadcddcdaabaaadaabbcaaabdbadbbddbcdadcbadbbbdbddbcacddaacbcdabbbabdcbdbddadacdadacbcadbbcdbacdbacaabacdbaccdcaabadcdcadcadbcaababcbbbbbcadaddccdbdacaabcdbcbbabaacbcacbbbacbcccccbcacbadccbaaccbbdabadcdbbddbabdcdadadcbdbbadbcaaddaadcbabddcddaaccbbdddabbabdddcccdbdabadabaabdaadbbdabbdaacdaaaabcbabdbacbaacbcaaacdaabbdcdcaadbdadccbbbacaadccbddadbcbaddbcdbbcaabdcbacdccccdbbbccbcacbdbbdbdbcccbdcacabbabdbcaaacdcadabcbababcbdaaccadbddcbaaaaadbbbdccbaccdbcbaaccbdcaadacabcdabadbdaccabccaacababbaacddacacaacdbcdcdabccabddbaaabdcbaddcddbccdcccbdbbbdbcdcdddddaaaacbdccdadbbdcddbdbaabbcbddcabbcbcdaadadcddcbddbaaabacbcdcbcbdcbdcbbcdcbadbadbaabdacbddcdcbdbcbbaddddcbbacbabcadbcddbbccccccdabdabbcaabdbbacaaddbbdadcccbdaccdcdcbcbadddcbdacbcbdacdabcddbcdbbbadbadccdbcdbbcdbbdbbcccaaddcbaadcdccdbadcbccbabbbbbdaccdadbcdadaabadadcdbbccbccbcbbabbbcdddaddbcbddbcbcdcbdaddccbacddcddcbabaacbcabaabbdaccaaccacacbddaabcaacbcbaabdadbbcdcbbdccbadcaabaccbccadcacbddbbcdcddbbdbcbdbadbdaaddbbadccdbddbbaacaaacabcdbcacabcbadcbbcacccdabcccabcdadaccbbbdcaaabcdabdaacdaccaddcddacdacbdcdccacabacdbbbdaabdcbcbcdcbaadacddcbaabdbabcbddaaacdcaabcddacbcbcdaaabcbcacaabdcdaabcbaaadcbaccacadcbdadcaddbcaaddacabacbcaddcbcdacdbddbdddaacacbdacabbabcccdbddcdaccdcdddcddaabdbcbbabbddbcbdaaddcdcabdcadddcdcabdbddabcdbaaddaaacaaddadaddbaaacbcaabdbacbcbbabcdbbcacbbbdcabddbddadbabdaacaccbcbaaaaabaaddadaaaadcabdadaddcdcdcbcbdbbbaddcdbaabcdddccaaacdaadbadbaaddbcabbaabdbcabaaadadaadcaadbabcadacbbadbbabddbbbddbcadadcadacadbbdbccbdaabadaacbaccbdacddbbdcacdadbcdddbdabbbaddbbccbdcdbadabcabbaadacdcbbacbcbbcacabbdacbdbccababcacbbdbbbdbaaadcbbdbadaaddcaacbcbbbbaaddbbbabccddacddaacaacddaabadddbaacbacbcbadbaddadbaccacbbdabdbbbcbcddacaadcabacbcbbaadbcacbcbcdcbaccddadabdababcadaccaadbdcacbaccccdbcdabcdddbcbdcbabadacccbdcadcbcbddaabbaaabbaadbcababadccdcdcbadbbbdddccacaaadaacdabdaaccacbbdcdadaabaccaaccdbdadbbacbaaabdbcdccdcacabccbacdbaccdadccdaddcabbcbbddaddacdbdccabccbdcdbadadbdbccdcdacbadbcbcbcbdcaaababcbacbbbcbcacbccdacdbbcaabcaadcccdbcccbdacbbcbddcaadccacdbadbacaccabccaabdacbdaaacbcccbbaabcbabadcaacdccdbadcbadccdaadcdaadabbaccdcaabaacccdcacbbcccccbaadaddbcabdccdaaadbaaccdddcbbadbaccadccaacdaddbccadcabaacdbdccccaccccaccdadbbdbdadddddabdadbcdcbcbabbccaccccaadbcaaadabccccccbcbdbddabdacbbcbcbbdacbbcbdccdccbddadcdbcacaaccdadcddccbdbabbcbbbdcaccacbcddccdacdacddaadcddaadbdadbdbddcccccbadcddcdcacbabbdcdddbbbdabbdcddcabddcaacacddccdcbdbdbcadbbbccdcbdcbbabbabbcaccabcdccdabacaadabddddbbcbbdbcbccbabbcabaaaccbacbcdbdacddbcdcbaaadccaddadaabcdbabbaacdbaacababaabcdddabdcccdccddccabbbcbdcacbcdcacbcbcdabbdabdbacdcacaccbbcaadaabdbcddacabbbabccabccacddbbacddaabbcbbdababbadbdacdcccdbbbbacbbbdbadaccdcdacbcacadbbacccddabddbdadccbcbdbdbaaacbadcacdabdbddaadaaacbddbadddacdbadaccaacacddcabccacddadccbadcdccacbdcdcaddbdcaadbabccbbbddbcbaadcdddcdccccbdacdacdaabdbdddabdccaabdcdaacbbcdcddbbbabccdbaaadbadcadbccbdabcdacbbacdbaacccaaadacdbadabccccccddbdcdbcdbaccbccbabadbaccbbadcdaacaddabbaabbbccabaabdabaccdadbbbdbbadcdadcbabcdabaccbaadbddddcbbddaadbddcccdaabdaaaabcbbddddddcdcabaabbcdcbcadaddacbdbacacdabacacdddbadcccbbabaccacbcbaaabbdabcccbcbbbdbcddbbbdacbdbdbccddaddcbbcddbccbcbcacbacdadaacbdccbbcaddadaddbcbdccccccbddacbdaccbbadbaadacbddccaabbbaaddbbaabdbbcddaaadccdddddcbdbbbbdacbddcddcbbbbcbaacddadccbcabbbcadcbcacccadaaaaddbdaabccdcbbcabdbacdccaacccacabcdcccdcbcacbacabadddcbbddaaadabdccccdabdadccbacaabacacbbcadcababddaddbbdcdddabdcdaddbbaaccdaaacbcaadcddcbdaabcadcdacddaaaacbdbdadbaaaadbaacbbbaadbbbdcbbabbbcaabcbddcaddbcdcbccdabccbbcbdaadadbcdbacdcdcbbdadcbdbbddcbabadaaacabddcbdaababcbccaabdccbbbacbdcddadaacddcdcaccbdbddcaddbadbcccbcabcbcaaabddadcacbbacbaddcbcabdadcbcababdcadaccdacbbbababaaaaabdccbccbadcbbdbccdcadcbabadbbbcadcbababcdcbaaabdbbcbbcdcccaacdabacadcabaddbbddccacdcaabbccabdccabcbacaadcdadcaaaabdabddadadbbbbaaddaaccadcddabbbbcdacaabbcccbcbddbbacdaacdbddcababdacbbaadbbcdcacbccadadbcaaadbcadaacadcdcadbbcdaddbbbddbbddcdcdbbddccbbcabacccbbbcbddaddbcbaaddacddccbddbbdddaddabaccaaabdbdcdbabccabbdbcbcdabdbbcbdababcbbddbccbdcdcacccbbababaadacddcacabdcdaccaadddddcbdccdbbadaaacadaccdaccbaaaaaabddbddcdcddcdcaacacacaaccabccaccdbdcbcacdccdccdabacadabcbbaaddcbacacdadccccccadcbccbcdaaacddacbdadccbdcbcaccabacccacccbdcbaadbcddbadbbccdcbcbaaacdcabdadcadbbbddbcbaadddbccdcbdadbcccddbadabcbdbdadaacaccbbacadacddaadcccadacdadacccadaabacbacbdacdacdbdcdaddbbccdbbdbcbacdbddcabaadbcddadcbcddabadadcacdaccdcbcabadaadcbaacbbddaddbdcbdcccaccddadabcbbdbdddbadcaadcaccdbabcabdacabddacaddbabdacdabddcbccadbdbdbcdbddbacabbdccbaddcbbddcdaddadaadaadcbdccbcddbadabdbabbccabccaabbacbdaddcbdcbbcbabaacccdbcbbcabadbdbabddbacaabcbbcdbbdcabbabdcddcbacaddadddbbdbaadacbbccdccbbadaabadcabaddcbadcaccbdbccddadabdcbdddbabbbbcbddabddacdaabddddddaccdddaabccdaaaabcacddcabdbbcaddadaabcbddabaabadacaabdcdaadcddbdbcbcaadcacbcbccdbbaccccacdbaccacccabdbdcdbbdaadcbdcbabcbcacddaaaaddbdbcbddaadbbacadbcaccdacaabdcbcbbbddababbcabdaabdcabaaababbcaabbbcaccdccbdccdabaacacabacdcccbabcabaaabbbbaacbacddadabdaabdbdbcccbcbccbdcdacdaaaaabcaabddddcbcacdcbbbabbdabdcdcbcdbbaacdaabadadbcaccbdcddabbdbaaccdbbbbdbcacdcaabcdcabacdcbdddcdbdcccdcbdadcadcbadbdcaccaddacdbdacdabaccddbdaaadacdcaacccadddddabbabddccdaababcbbbccccdbbcababbdccbaadcadadaaacacdddddaadbabcabaabcccadacabcccadaacadcbcadcbdbbaacdadbddcabdbabbccbcbbaadaddabdcbbcaccabcddcddbddbadaccdccdadbddabaabacdbccbadadddcaabdbcdbbdabcadbdcabcaddbccdbaddbadbbdcabacddadbdadcadabdadaddbbcacaabdaadbccbaaabcdbddbabbbbbdbdddccabcaaddcabadbbaddbaccdddcdacdbbcbdcdbcdbdbcdacbdcdaccccaddbdddbdacaaaabdccbbacdabdadcdadacdabbcbdaadaacdaabbacdaddddbadddaadacdacdcdaaabadbbbcccbaccccccaacdaadacdabaccdadcbaccbcccccaababaccbdbaaabbbaacbdbddccdcabbbcbbbcdaacaabcbcdadcbccaacabcaacbbdccadadddaddacddbcbbddadbcabcbbdcaacdbadbcacacdaacbadcdcbbaabbcbcdaddbcbbcaaabddbcbcdcdccbbababaaccdbcccabddddcaaddcacccbbdabadcaacdcbbcddacaabbdbaccadbdacbcaacbadcbdbccaddcabcaddbdaccbcbaadacaabcddbacbdbbbacbdaaccdacdaacabdbbbdccddaaddbdadbdaccaacdbccbccbcacbbbadbbbbaacdcabdadcadbacbcbdddabababccdadcdacdcddcabcbaaddaccddbbdaadccaaadbbcaaabcabacbacabcccdddbdddcccdcbaadcdaccdacbbbadbddcddbcdacdaacbdcacdcdccbcacbbddcdbaadcacdcbcdddcbbaccbdbbbaddddcdcbaabdcbdcdbbccbbabcaabbaabbdddacacacdadbbdacadccddccbadaccdbacccdaaddcdccadbaddcbcaccaaddcdadcaadcacdcdacacddcbdaddaaddadcadbbbcbbbcbadcbdccbdaabdabacdcbcdabcbcbdcbcadbababbaaccacdbddbcdabadadbcbadacbdbcdcbdcccabaacbdbacdccabcdcdacbaddcccaaccdbadbbaabbdabaddcaabababbadcaccacddccbddbcdddddacacdcbdabcbcbbdddccdcbadcabdabdccccbdbdaadcbabaabdccdacaccbdddcacaadbbcbcccbadadbbddacdcbddcdddbbdaccccccadababbaabbdbaacaddbdabddddabbadbcbccdcdcbadabcaaddabbcbbdbdddadcaacacbcdccabbadabcddadbcaddacacadbbbccadcbbaccbabddcbabbdbdbcbccbddabdadcddcdabbaaacaabddcbcbdabaccbaadaadcdcbcadcdbaabaadbaacabbbaabbaadabadbbabadbadddcbdcbbbcbdcdcacadaddcabaaccccdccadbaaacbaccababdbbadacbdacabdddcbbbdbcddbaadabbbbdccaadacccbdcbdbcdabbabdbcbbdbcccbcdbabbabacccbacbddcdbaacbcbbadaabdbcbbbacabaccacdddddaddabbbcabddcdbcbaddabbbcaccbdddbdcabbccbccdaccadaacbcdadaddbbadddcdddbcabbdaddbdacaabaaddbabaaacaabbbcbacbcbabddbaacabcacbcdbddbbbdcaabdadcbbaddcbbaabcbadcaadbabcdcdcccbaadcdabdcdbdaccacdaaadadadcadcdddbbabccdadddabaacbcbcdaddccbbcbaddcdadadbcdaddbdbbccbadaccdbbaaaccccdabcbbbaacdccdbaacdccbaaadbbccddcddcabccddccacacdacdbccdaacaddaadcddcbbaadabddbcaccadacaaccaababccbaabbbcacbcaaddcaccbcadacbacadaddabddcbbcbcdabbdadbbbbaccdacbcbcbadbacccddacdbcccbcabccbdccaadccabddabcaaadabccdacbacdbaccbaaccdddccbdbcccbdcccacdcccbadcbddbcbddcaadabbbcbbdbcacaccadcccdbcccacacdcdaadddcacdabcbdbaddcadadaccadcdcdaaaacdddcabaaabacbcabdbdbcadaadbbabcbbaddbcaaaabddaaaadbcabbcaabaaabcbabcadabadcabdccbaacdbbcccacabbbdbbbddacbcccacccdddbadadbcbccbdbdadcdacdacabbadbbbddbabccdbccdcbcdabbdbbcbccdbbdcadcbcaabddaadbbbbdaabaccbdcbdabdbbbcadcabaaadddabccdbaadcabdbbdbbbbcbddcbddabdccccabbdcdbcacddbbadbacbdbcccadbdbcacbdcabadadbaadadbcabbcbbcbacdacaabccdccccaddadbcccbddcdacbdacdaacaaadcbadddbcbcdaaaabadaaadbbdaddaddadcdbdcbbbbabccbbcadddbcaddbbbbddbabdbcbaadcaababbdaccccbbbaddcccdcdcacbaacbbddabaacdcaacdcaaaaaabcbaaabdcdcbbcddddcccdcbcbbaccaddcabccacdaacacacdcaddbcccacacccdaaabdbacdabcaadccdbcddaadcdcaacbcababcdbaadabbcdcbdbabdbbcbcdcdcbdbcdcadbbccabacdbccdcccdccbaacccdcdcabcbbdbcdbccbdcdbbdcadddbcddbdacdbbdcadddbbadcbcaaaaaaabcadbacdddbaaaaddacbcbabcaacbdcdadbbdacbbdcdcbadbcbbbcbcacacbbccdadcdddbcbbcaadcddaabcbbdbacaacdabdabdbdcdadccdbaaaaccbbbabcddabdacccddcdaacbdcccadaaabbcbaadaddaacaccbccccccbcbabbbddbdbbcdcbdcddccadacccaddcddadddbcacababcbcbacdabacccabbacbddcbbbddcbcdaabddcdcbaddddabbccbbaddaaadbbcbadaadbbdabbbccdababdccababbbbbdddcaadbdcbabcbbbbbadcacabdacdbccdabdccccacaccdbddcbbaaddabadbabdadccdaaacbcdbbcbacbacbbabcddddacddcacccaacdbdbcbcdccbdbccdcdccabcaacbabbdcaddcaacaaddcacbbddbaddcbddbbdcaccdbcddbdccbcacaaaaabbaccabadbaccbacbaccadcdddbbabbabacadacbcacacddbacccaaabbcdadbccdcdaccbadcacacdcdddcbdcdabcaababacadaccabdcbadbbbcacaccabbccddccdccdaddcadcdcddcacdcddaabbbcccacccacbdcdabbcccbdcacccdddbcdabbbdbabdadbcdcbacccdddbbbdcdcbacadcdbbacadacbbdaacdccaccdcbccbcbbbadbbaaaacbcdcdbcdbcdbaaaacdccbabbbccaacadddcbdbadcbacddbbaddaaccbadaabdbbbaddbcaabcacddbadbbdabdcacaabddaccdcccddadcdabadbdadbbcddddaabcbdbcdddacbaaaccabbbadadbaddcacbbbcaaacbccabcababacaddabadddbbdbdddadcdcacbcbcbcdcaadcdacdddaadbbdcbaabbadbbbdabbacbccddbcddaabbacdddbbbcabddcbbcbbdddddcacaacdcbbdccddabddacdbacbcdaaabdcabcbdcccbbacaabaaddbadadabdddbccdbdbdbcccabbbdcdaacabcccbcdcaaaddcbcbddadabaaddabacadabdbaadadcacdacaacdbbbcdbdadccdacaacdbcacabadabdcddaaabcabcaabbadcccaaadcbabbaaaadacaacbddbdbccacabdbadaccddcdadcbcbadcdaabcdcdbbdbdababbbcddadccdabcdbcbccabbaddadadbccdbbcbaabaadccbcbbdcbcacaaacdbddcabaccdbcddbadccadaaddadabbcccbddacddcdaccbcadbbdbbbacacaaacbbcababcacddabcbbddacdacdddbcccaccdaabdbccbcaddbbabbacdcaacbdcabcddbbddccaaadbddbaacaccadbccbbaacdbbbbcaababadddabcaabaaabaabddbaddcabacaccbaddcbddcbccdbaabcadbacadbaaadcdcdbddbadbdbadbaadbaccdbdabdaabacaccbaaabccddccdbbdadcccaabcacaaaadcabcdcdacbacbbaabadacabbabacbbdbddcbaddcbbddaccdbdacbabaddbdccbadaaabcccdddbdcbbddaacccbabdcbdbbacacaadcdadccbcdcbbbabbcbbbbddbcdbcaddccbbdbdcccccddcdbadbcccdadccdbbcacacbdadaabbcaaadcbaacbbdaaddccabaacdacabbadbcbcdcddabbbacbdcbbdabbdadabbbabddcadbaddcdcaacaadcaccdbbbadacadddadcdaadccabcaabdbddbabaabcdccdccdabbdaaccbbcddacbccdbdaacabdbbaadaabadcdabbcbcadaadcacadcaadccabbaacacacdabbbccbcaacdaccdabddaabbdaaabacdcdccdaabcdacadabacabbabaddadddacdcccbdadcacddddaadbaaacbcdcdcacaaabaaacaaccaabdaaadbaabdbaadbbcaddbacbaddddbbcdaaaabddddcdbcccacbcadbdacbbbabaadbcdacadddabaccdcacbdbcdcaacccdcaadbacadbabccabbbbccabccbacdccbbddbadcadddcaccacadaaddaabcbcdcbbadaaacbcaadbdcbdcbcddaddcaddacadbcdaaaadbbddcbddcbabcdbaaabddbdabaaabaadaddcdacbdaabcadcbdcbbddbdcbdbaddbdcacddcccdcadbddccabcbbabadadadbdbdacabdccccdcccabcdbaddacadddcdbbbdcbddaddbadabacdacbdddcbdacccacccbdcbdbaacdaccbaacdabdccbadbbdcbbbaddbabcbddbacbacadbcadcccabcbbadaddddcbccdbabaabbbbdaddcdaaabdcabadcbabccccbcbbaacdadabdbdbabdbcabadbccccdddadddcdbccbbdaccccadbbdccdccadbaadbdccdcabccbabdddadabcbcabdaaccdcbaabbbbadbabcdbabdabadbcaddabccdcaccdabcbddcbabcccbcacacdcbadaabdcbccbcdaabdddddadbabdccddbccacdbcabdacdacadbbabaaccbbccbadbcbaadcbabcdccdccbdacddbadaacdaabdbccdcdcccbdabaddbbadabcdcbddbdcbccddcacccdaaaabcaacdbdbccdbcbabcbaccaaabbacbbdbcbdabdbabbccdbbabbcdaacbbaddbbdcccbbcdadadbdccdcdbaadcacddaddcccaaacacbbdcbbdacccacabaddacdbdbcdcacbacddcbbdbadaabccbccaccbaccdcaaaccdababacccaadabbcdadcaabcbadbbabbbababdccabbbbbbadabdbbaabcbdbadcbcbacabdcaccbddabddcaaaadcadddcabbaaaaabbcabbadcccccbbdbcdbcabdaabdbaabdaacbbccbbadacbbcaacadcddbdccdcdccbabccdbcabbcdbcaacabdabbcccdaaddbdbbccdcaaacaacbaaaccdbabdbbcdabaadacbadbcdaaabacacdccccbcdddbccaacaccbdacbbccddddbacacdbaabacbcdaccdbacddaaabbdabbcacccacbacbdbaabcbdabcaabccbbdabaccddccbbbbacbbddcddabbdddbabacdadbaaabdcddccbbbdcdaadbbdbdaacdbbcaabcbacbbaabacdabcaccbcadadddbcacdcdccdcadacabcaddbbdadcbaabbccccdbdbdadacaaaabbccdddddccdabccbcacbccaccccbddbadcbccaabdbcaaabacbdacdbdddddcbbabaabaaadaaaacacddcdbddcdddadcadbcabbbacbdabbccabbacdcadbbbdaabbdcdacabbabdaddadbdbccdcabbdcdadabdbcaccddddccabbcdabadddcacdaadcbccdadbcdadaaadbcbcbbbbbacbcccbdacdbabbbdaacdadbbcbaddaabdacdadcdadcbccccdbbbbabbabbcadbdbbbacbacbcbadaadacdcccabdbacaddbdabaddbaddbdcbabccdbbacbbaacbcccbabbdbaaaccbcbcccaadcacddddbacdaabddadbdbadcbabcadbbbbacbbccabccabddbaccaddbcddbbaadddbbdbccccbadabcccaccddcaccccbcddddbdabbaadadbbcddaaabdacbcdcddbdacbbaccddcaadcbbccbabddacabbbbaacbababbbdbbdadbabdbcdadcbccacbcbbdaddbabccacadabbccddccdabbbaacddacdbddbbcdbdcbcdddbadbbadabbbbaacaddddcabdcdbabcbacaacccacadbddcaacdcadadacdbabcdccadbcbbadabacbbbacdcbbacadcbcdddbcadcbabbadbaacddcbcbbccddaccdcddcbdcbddaccaccdabcbdaacabcbadccccdadadadcbcaccdacacccadcabcddccbdcbcbdacbbdaadcbdbaadcaabcbbdccbdbcbdabcabaccaacddbbbcdccacbbbcabbcaaaacbbcbdacbadbdcdcacdbccddcccddcdacbadbbdababddbaadaaddbbabaccdaaddbdccdccbbccdcccbacbcbcbddddcddbbccbdcbabaadcdcbcdcabcccdadcbbcacabcbccaddbcabdaccbdbadbdacbaccbacbaacdabcaddcbbbcabaaadaccdacaccdbbdcaaccdddccadbdcbabadbabbccbacdbcaccabcacddbadcdbcabadabaadaaaadbbbccdcbcaacacccadadbddabcdcaacaabaaddbbdcacbbdabbcbcbdddaabbbdbbbddcaabbdbaaadddbdcdadcddbbabcaccdcdcacbaabbcacdddccdbbcbabdcbbbaacbabdbccccdbbbbabbdaaadbdcabbbadabdaccabadddcdbcddbcaabbccbcabadcdcbadadacaccbccbabddbdcdaacdacaddacbdabcbbdddbcaadaacdaabccacbcdaabcaaadcdcddbcbbabdbdddcbbbdabcadcdbbdcdcbbbadcbdbbbbabccbdcdcbdcaccacccbbccdbadcddbacaaabccdccddbddcccadcddbddaccaaaabaacabdcddcaabdbadcdcbdbbdccddabbaacacacbdcbabbacbdaababddacbcdbdbbcddacddcdbdcdcaabaabbbcacdbaabbdcacbadddcdcadcdcccaaacccccbcaddbdbdbadadadbbbbddbddbcabcacdbcdbccacdabababbadcdaadbcbdacbbbbadbccdaddaadcabdcbdddcbcccadbaadaccabdabdccbacabdbddbdabadabacbadbcddbbbdaabadacbbbacacbddaabcabbcdacaabdadbdccacdaadadabbbdbaaaabacacbbadacbbdacbcdbcacdcacadacaaddbdbbbbcabcbaadcddbbcbadccbaacdbbacddcccdbbbcaababaaadcabbbbbabbcbbdcacaaadcdacdccbacabbdbcabcdaddccbbcbabddcdbbaacdcbadaaaabacddcaaddcababcbbabcababbcadccbacbccdabcbddcaacacdacdcccacccaabddbadbadbddccaaacbdcaaacdbbdbcbcaadacdbabadabcdbbdbbdabdcccbcadbbabbaccdbdbcdcbdbbbcdcaacabacccbbdbdcadadbbabddabbbcddababcadcaddcdccdcadbcacaccabbddbbbddbbcacaaabcdadabcacabdcbddabcbcdbcaaaabbdcccbabdcdbadcaaddabaabacbbaddaacdbabdcdddcddcaabbddaaacdaacacadbbbaadacdcbbcababbcddbbacbdaddccdcbbddcdabbcbbdbdacdbdbadbabbcababcaabacdbabcaabdccbaccacacdadbbcaadbabbbcdbbcddddcdbaddcaccddddbcacbabcdbccacacdabbacaddacdbaaacacbdaaaacaabbdbaddbdcbdbbadacaccdaadaabbcbddadbcccaddbbccadadacacbdddcadbccbbcddbbbdcdcabdacadcadccabbcddcabaacaadacdbbbdacadaacabccaaccdbacdcdaadccbdaacdbbcbadbaccbdbbcbdacdcdabbdcbcaabbaadbcdaaccbacbdcdbbbccaaadacbcbcacdabbadaddbddbbbabcaacadabccaddcdddbdabbccdaacabdddbaaacacaacddcbccbabdcdcccadcccdddcbdddaddaadadcdcabdbbccaccdcadbbacadccaaccbdacbacddcbbcdccbadaacaacddadbcbbcbaddcddbccccaaacabdbaacccdddcacbbacbbabbccbbbdddccacadddbcbcdbccbdcacdbdbbdddcdbdaaaaccccdaacddabdbccabbdbaadbbabdacdcdaccccdcabdabbaadccddbbcbccbcccdaacbdccabcbcbadcbbddbabbcbaaaaddaacaacddddadbbabbcccacadacbcdadcdddbddcbbdbcbadacddcabcbcabdaaacdcbcbbabbaddccbcaacdabccabddaccbdbbcaadaddbaabbdadbbabdcdbcddccaddcbccbccbbdcdcdbadbacbcabccdaddbcadbddcadddcaccbdccabaabccbbbbaaaabbcdbbccabcadacdcbadbaccaaaabacdadbadbbbaddcacaccdaaabbaccdcabbaaacadaddccbddddaabcdbbdccadcaacdaddcdabcbcdbdccddbdddcaccaadccbbadaacacbbaccdddbbbdcccacacaacaadccbbaadddbcadacdcbadcbacbbabdbadcdbbadaadabdddabbadcbcccddcdcbdbbcbcaadcaacadacdccddabcdddacddcdcacccddcaababdbddcbdcaaaddabdacbabddbdabbabaabdabcaddbcddacdaacbabcbbdcabaddcdadbddcdcbdcabcbcdabadaaadbbaaaabdaccbddabddabbcdcdaabcaabdaacaabacbacdcdbcccaacabacddcbdddacbccbbbcacbcdaadbdcdcbdbabcaadbcbdabaccabdcdcbbdbbbdbccbddbdccbcabdbbccaabcaabbcdacccaabcccbdbaadddbdbccccaadcdbcaaaaadaadbbdaabadaaddcdcaabcabcccddaadacbdcaadbddcbdabcaadbbcaccbccbabdbbbcccaaadcbcbdaccacddddbcabdabbcddddcacbcadadbddabcdcabadcdaacabccaccbadacdacbaaacdcabbbcccdddadcdcabbdbbbbdbcccbbaabbabbccddbcacbabdbbcddccaabbcccdbcdabdbddcddadacacbbacdadbdbaaadbbaaacdaadaacacaaabcbdababccccaaadbaccdbabbddaabdcccbbabccdbbbaadacdbdbcbadbbddbdddaadaacbcaddadcabddbadabddacdadbdddabadbddaabbbbccdabdbcbdbbdccbbcbdbbdcbaccbdccbcaddcbdcdddcadbdbacabcaacbbadbbbdcccbcddaadddcdaadabdbaddbaccacbcddadcbdadbccaacabddcdddbccbcabcadcbdcaacbbddcdacbdbdbdbadddabbcbbacadcddcccddacddadddcbdaabcadbbcbbadcaacbcaabbcddbdbbbacbaddabbbcbbdbbaaabaaacbcbabddaabadbaacddcbdbcbbcdbbccbdbacbdcdcdbcadabccdcdbbdaadaabbdccabbbccdbddcccacaacbccddbaccbbbaccdbbbaccaabbdabdaadbcddccddbaaacbbdcdaddaabcdabcccaabbdbaababcdcadcadcccbcbbadccacdbbdcbbaacbabcbbcccbbccdbdbdaadacdccbcccdcbddbddaabcbbcdcbbbaaacbbcdaadaaddccbcddcdaaadddbbbacdbbabccaacbdbdbcdacbcbcbaccbadbbabdaabcadcdbdacbbdbdabacddddbacaacabcdcbadddacbacccaacaabaadbccdccdcacaaddcaddabaabbdbbadccdccdcdcbcadaaabdbcbdaabdcacbbcdbacbacadcbcbaabccadaabbdcdbccdcdbaadabdcddddbbdddcbdacacbdadbdbdbcabbccdbbcbbadbddbdbcabacbbcacbdbdbbdbbabcbbdadbcdaccdacacadbcbdacdcdaccddadbaaddacdcdaaccababaacbdadbbcbcbcdcbbdbdabaccbcddcbddbdcdbdcaaddcbbabbddabcbddbabaaababdcbbaddbbdaaacbcdcbbacdbbabccaaabdcbbacabdccbddcccbdcbbaabcdbdabcdccbbaaaaaacaacadcdbddacacbbcaabccaaccabbbcacbcddaadbcdbdadbbabdabccdcabdaaccacbacdcbdcabbcdadbddddbdbadbccababccabacbbacdaaddacadcbaabdccccdbcdddbddcacbdddcdddccaadbcccddcdbbbcdaacbcdbcacbabbabccddbaddccdbabbcacdbbcbcddbcbaacbadcbcdbdacdaadbadaabbabdaaacbdcaaabccabddddbcbcbcaddaacbabdababbcacbdcaddaabbbbaaddccdcabdddbabaaddccbbcabcbacababddcadbacdcdddbadcdcdcbcbaadbdcdcabcabdcddabacccdadadcaaabbdabbabdbaaddcbbcbaacdbdadcbcbdadcbdadbbddcacdcdabbccaadcdabcabcbbbbdaadbdaaaabbdcdadbccdaabbbcabbbcccbabccadcabddcccbccadabcbddbbacbaadbacaccdbdbbcbdadcccbdaccbcaddddacbaddbddabbdbcbddabdddaaddacaccaadbbacdbbcdadacaaacadbbacbdddacdddcbacbacccacdcdadacdcaabbccbddbcbcaaabdcbcddbaccddaddcabcabcdababcddcdadaddaabcdadacaacadaddcbcadcaccccddadbccadbcddbbbcddcbdbbbbdbbcddacbbdacbbcacbbbbccdbcabdabcddcaddbaaddadcbcdadacddaccaabacdccdaddcabcadbbcbacdccbacbdcdaddbcbbcdcbaaabcbcbbdcacdbdabcbbddaaaccaccdaadbbbaccdcadadbabadcaacccdcdacaddccccaadddddbaadabcaabdbdbcbdbbacaacacccabcacbcccdcaacbbcdaaaddcacabdbdbdacabcddbdcaadcdaccdabbaadadbdddbdbcaccbbcbaadacbabbaddcbcaddaccbacdabdbcaccccdacaccbdababbbbcbcadbddbcbdacdccccbbcacdaccdbababcabadbacbcacadcaccbdabcbbacaccdccdbdbbdcaaaddaaadbaaddbddbddbadcacdbbdbddacbcaddcaacdbabaacbdbdacabcbdccbaadbdaddbbbccdcddcacbbaabcccbaabcbcddbccbdbdbacdadbbcdbadaaddbcaddcaccaaabbddbdacbacbaddcacabddcadbdcdcdcdaccbbbaaccbbacdbaaddabacbabaaddbacbccbcacbbbdddadaccbacbbbbabbbadddcdbddcccadbdbdaddabcbcbdaddbcdabbbcaddabaddadabcbaaabbaadaccdbbbcbcaabdbadabccbbbadddccaddcdbaadabaacbdbbbaadcbacbacbddaabdcccdcdcdcdcabcdcadddaddcadddbacbadbbbddccdbdcdabdccadcdbcbcbdbacabbbdcbbcdbdaacbbccbaabbbadacbddabadddcdadacbbbabcdbbccdbacbadacdddacdcdbdabbcabadaccbcddcabbcabbbcdbbdbbbdbcdbccabcdaacdbcbacccbdabcdcdccdcbccbdabacbbbabaccdaddddbbacadddddddbbccdcacadbdaddacacabbacbaaaadcacacdcbacdadddacdccdaccbcbaacdcadcccaadccaabccacbadbdcdacdcbabdabcbcdbabccbdddcdacaacbacbcdbaddadccaadcbcaaaaddcbaaabbcabbacbcbbcccabcccbbaccbccbcdaddcccccabccbaacdabddadcbdbddcbacbbddbacaacaadcaabdacbaccaddbbccaabdbdcddcacbdbaabbdddbcbaccbaddaddacdcdccddbccddbccbbacdddcdbcabaaaaabadbabdcbabdcdaabcdbddbbaabaaabbbbabbabadbbcbdbacbacccbcacccdaddadcbdcbdddbdaadbbcbcadcddcacdbacabbddadaaadaacacdbccaaabaacbdaabbacddaacacbdbbdcabdaddcdcaabdbbbaabcbdbaccbdadbcdabddbcbadbbcbbcbdbcdaaaadccbcdadbacdccabbadbaddabaddabbbdacdccdabcbbdabacdcaaaaaaabdddabadaccacabaccaccbbbcbabaaccbcbdbbdcdbdbdcaabdcbdaacdacccdcbcbdbbdbcdbdcbcbcaabaadddbbcdcbbaddddbaabaadacaabdabadcccdadcdcbdcaadcbdbcadabdabcdcdddddaacabcabdbbadbcbcdacaccbcbcbcbadadacbdaadadcbcdbdabcbbadccdaccdcdbbdcccdcbadacccadbbddacbbcacbbabaaacbdacdbcabbbcabbdbdcaacbdbbbbcbadaacddccdaaadcdbabdbaccbcaddcbbdbdcabcddcadcccccdbcaabcaadbbbbdcdabcadcacbbdcbdcacacbadadaccaacddccacaccdcccddbdccdcbcccaabcaaaccbadccaabdbadbdcbdcabbcbccdabdbdccbdaccbdbccdaddabdbcbcccdaaaccdccadddcdcbaadbddbcbbdcdbbadbbcddcaaaaaadbadcbbdcaddbbcbcccbccdcdbaaabdabdcaadcddacabcabbcbdcaccbcbaccaadddbdcacabdccacccdadbddaabcadaacaabaacdcbdacabccabdcdddbdabdacaacbdcacadcdbbdabcbaddcddcaaabbadacbaddaaaccdccdbdcdbadcbbccbccacbdcaadaccdccaddbbacaccbdaaabcdcddbdaabacdcddcdaadcdcbccaacaaccadabadcadbbbdbaddcbccabacaddbdbadccadbccbdacdabcaabcddbacdcddcabcddcbacbbadaadbcbccabbcbdcabacdcadbdacadcbcdbddbdbccdcbdcbcbcbbddabdddabadaacbbbcabdacbccaadcdacbbcbbadbabcdddadbacbbcbcbcacbadadccdbcdccccbdbaccdcdaaccdabdcbbcdcddaccbcdadbdacddbaabdbdaddaddbddccccabcdcacacddbdbacabdbbddaddbccaddccbbbbaccbdacaaababaddabadacbcbbaccaaabbdaaadaaccdbdadcabcadaacaacdacadadcadcdaacaacddccbbbabbdacbdbdcdadcadadbbabddabccaaddcbadabadbbcdcccbdbacdacdabdbcddaacaaccddaaacdaaacbcdcbbabcbaacbddbaddcdbdacbbcaaadabbdbdcbdcddbabacadddbadcddbaacdbbaccdcabdbaabacbcdcddbdcccdbbabbabccdaabbddcaaadbccbbdcacccbbaadbbbbaccbddcacdcaacbddaddbcbcbccbabdaadbaabbccdbdacbaacdabdabbbdbbcdbbbbaddacbacccbcaaaccddddcdbdbcbccadddcdbddaadcbbcdbadbbaadacadccccdcbcadccdbbdbcaadbadbacbbdabddacacdddbbbdbbdbadababbdaaadbdcbbdbbbccabbdaaccbdbdcbcddaabcbccdbdcabbadcabddacaddabddbddadababadbbbcbdaccddccbdcaccdabdcccccdabdbbaabbddcddddccccabbbdbcabbcaccacbbccddbdaaacaadcbadadddcbdbadcdadbdcabdcdcdcadccdaccdbcababdbabbbbddddcaadabbbdcbdddacaadcdbacbbaacbacdabddaacacaaaddcddddcadadaddbddcaaabacaacabbcccddaacaccddbcdaaaddcacaadaaaaaabdbbacacbbdddbddbbdcccccaaccdbaabcddcccbbabadccdcdacaabacdaddbcdaccdbbbddbcbaaaabaacbddcacdaacccadcadacdcccddcbbbcbdccddcdddcabbadcbcabddbacadcbcabdcccccdabdbdcabdbbdcdacaacbccbbbcadbdaabacdbbcadbcdbabaddacbbbadcbcbbadadaabccddbaabddabacacddaccddadcdcccbcbcccddaaddbdbadbbddbbacabbacdbcddcacbcdcbdabadcdcaababddddbbaccbbcbdacdddacdddccbadaabaccdbccccdacdcaadbdacdaadcbcdbacdccaaabdbddbaaaabbdccddddcabaaaddaaaccbccdbabaaabadabbbaabcadccabbadbacccbbaabdcabaaccdcdccbbcacdbadccdadacbcabaaadaadbbcbdbaaabbacccaadddcabdacbcaacbaadaaaabbccabcaacbdbabbdabdbcddbaabccbaddbbdadcbbdcaadbcbdaddabbdadcdcbdacababbcacdacbddcbbdccabdbcaaddddbbbcdbcdcabacaddacdaabdcacbcdccaddbbbbccccacabdbbbcccabdadbabcbaccbbacabaaaccacddcdacbccbddabaaadbbcbcdcabdbbbbddbbbaacbaadaddaaaccdcdbbdbcdbdbbcaccddbbcacbdaccbaaadcdbddbbbadbdacdcaaddcdbcddaccbdbcdbdacdaccbbbcdaccabbacdcaddddcaccdacddcabbaccdbacbbdbabbcabaddccacdaccbababdbcaccdbcbacabcadddaaabddccadabbabbbccabcaaccaadbbbcabbdcdaccbddcccbcccdccaacbddabbccacddabdbcbcaadccbdcdcaadccccdddacdbbaacbadacbbadbcdcaaaacacbbadbcadadccbbdcddbddadababdcacbaaabbaadbcaabccaabcbaaadaccccbbddacaddcccbbacbaddacaacdbcaccccaaadddccaaadcbdccadbbcabcacaadaddadaaddacadbdddabbccbabbaaccdcdcbdbcdaaabddabdbbdadbdaccdddbaccccadcabcdddbcadcdacbcdccddcbacbcdabdccdabdbbccccdaddcdcadbcbbddccccbbcbddbbbabddadcdccacaadbcdbbcaadccbaacbbacdccbbdddcbababadacacabcddbabcbadacbbcdadcdadcdddcbcbdddadcdcccbdadbbddaabadbacbcbbabdacadacccabbaaddcdbadaaabcccacadcdbdabdaaadbddaccbbdacadadaacbbdcabbcbcccaaaaabababdcaccbbbacbdadcdadaaacbacabcdcadccaaddaaddcaadaaccbaabaabaacabaabcacabcadacdadbcdddcccabccdcadaacdddadaadadabdabaabbdbababbacbdbddbacbbdcdcbabbbdccccbdccbbcabddadacddadccdcddbaabacdbcbbdbdcbdabdadbdddcdaccabcbccccbbdbdbccdbdaabdabbccabddacadaabbadddccddcbbbccdbbbcdcdcaadbabdcadcbdbaaabdbabbccbacdbaabcbaaadabdacdddcbdaabacabadaadabaaaaacdcccaacbaccdcaadcadcdcdbacddbcabacaacdabddcbaaabcdbccbccdaaacacbdbccbdccdadabbacdaaaadcdddcdbcddcdacdcddabddbaaabbcbacacadbacadcadccdbbdbacdbdbdcaacccbadaacccbcbabcbbdbcccbaabbddcbcaddbbaddacadacaaabdccbbbacadabbabcaacadbbaadaadadacdddbdacbabdbcddbcaadababcdabbadbbdaddcdcabdcddcadbdcbccdcadcccddbacdcbacbacdbdadcbaadbcaaaadccdaacbacaddcccdcbbdbccddbbabadcadbcdbbadcdbbabaaddadbddaacddcaadadabcadaadabcaabadaadcccbaaccaabbacccdadbbccbbabcdabdcbaadbbbbcccddbabbdadabaaabdddbacbbaddddbbcbcabbdadbbcaccddacdaddacadcddacbaaacddbbadbacddadbccbcacddacaddbcdcbdcbccbcdddcbdcbccacbdcbcdcdbbdbccdcaadaccdcccacdacabcaddadbabbacbcbbddbaabcacccbddcbdbdcadabdabdbdcbabdaccaadacdccaabcadccdacaaabcbacdddaacbbdcbcbaaddbbadccadaddcdddabddabddcdcccadabbdcaaaacbbccdadaaadadbdbbccabccbdbcaaaddcdbcbaacdadccacdacadcdddaaabdbaddbddcacbaababcdbccbaaaabcacabdacddbcababababbdbccdbaababacbcadbdbbabaccabbdbbacbadcabcabbdbbbdabbaccaabdabacbadbbcccdbcbbdaabbaddbcccbcccaacadabdcadadaccdadbadadabacccbcdacdaaccaacdcbbbabdbcdbacadadddaddbdbccdddcdcaddcbccacddddbbbbcdbdccabddbbdabdbcadaddcddcaabdbccbddcbbbccdcaaccbdcddbddaaacdadddddcbcccadbbacadabdccccdbbddbbdcccbabaaacdaabccacdcaadccbcdbbddbcbacbaccabaddccbccdbdcdabbbcdbddcadacbcbbabdbddabcbddcdbdbdacaacabddbabacadcccbdcddbbcabbddcbbbdbaaddcbdacbcacbcdabdbaaabdbabbccdacdacbaadbcadcdccbdcbbdbcccbabcaaddadbaaaaacccddbdccabcabaabaacaaacbbaaaabbaccbdbddbcbdccbdbccbbbdbdcabccdbdabcbcdbddaadcbadccbdccdaadddbadcddbadcaaabacabbadaabbdcbbadccbcbdacbabdbcdabbababcadddddadccdacdcbbabbdcdcbbaacccbbbacaadcbbdcbacaaaccababbacdcabdcdcdbbdddaababcccdbdddaadaabbdbddbdcddbcabbbbacccadbaabacacbaaabdcbbbdccbbacbcccbadbdbbcaaabbbadcbdcbaaccdaaddcadbdccdabaabddbbbcdacaadabbacbbacaacdbacaabcacacbabbaccbcdbbbcbbccaddbabbbaadaabdddcadbdaccaacabdcdabdccddaadcbaabbccddbcddbcbbbcabbccdaadabdbccadddacbcbbccbbcbbdddcccacacacdcaaaabbdbcccbcddcdcccadbcbbacbacbbbbabdacdcccacdcddabdadbadacabacabbaaaccbccadbcddcdaacccacaddacdbcdacabcddbddbbadcdabcdcdbcadcbcacaacdcdadaaaacdcdccccacbbdbdbbdaddccbdcbddcaabbbdcdabbdbddcbcacdabcadacbdcaabdcaabdbbbacabdcadbacdaabdacbbdddcdcddbaccddabdaaadbdcdddbabdbdcacccadbabbabbbdcdcdcbcabbabdbdadbbbbbacaacdbdaaccdccadcdaadbccacbdaddacbcaaaadbcadadcdbbaaddaacbaccaddbcacbadccdaaabaccbbabdbbbaccbccabcccabaaaadaaaddaaccadbbdcddbbaaddadbaaaaacbdcabbcaabcbcacabbdbdbcabbadbbccbbdbbddddadadbcacbdbdabbadcadbcbabcdddabcdbdccdbacdacbdcdaadbcccacdbaccdcadaadbdbbdcbcddbacddcadadcbdbcdcdbacabcaaaddadcbbbcdccbbbdbbdbbadaddbaacbaacbaabdddadcaadcbacbbbbddacdbcdaaabbadaabdcdcadcaddbaccadddcaabdbbcdbaccacdcaacbddcabcbdabdcbddddbabaccbaadddbdaccadcacabbbdbdcaabaddabcdcbabbddabaccbaaaddaadadaadcbbdcccdccbdcdddbbaddadbdbddbcabbbdcdbbaddbdbbadddbdaadbcabadabbbdabbdbaadddcacddadcbaccabacbbdcdaddccccbbbacaacdbacabcddbddccdabbcabccaaadcadddcccadbabdccbcacaaadbcaadbcddddbacccdaadaccdbbdadccacddaadccabbccadbadaddccaacbaaadcaccdbdcdbbccadbbcbdaaababbdbcdaddcadbbabcbbbcbdbabdabbadcbcdabacbcacdbababbbcccbdcccdaaccbdddbbcdbdaaadccabaabacabdbcdbcadadccadcacdbbaaadbcdbccdddcdbaababbcabbaccadbadaabddccacaaabcaaadddcdccddabdbbbadcaddcbbcbaacdbbdcabbdccbcbdcbbbbbcdddbaabbcddccabbacacacccccadadabbcacabcaadacdabccccaabccbcaddbcaaacdabbdbbbdccbadbcabdcbdcdacdbcbdbaabdccdacabcaaabbcbcabdbcbbbdabbccbaabdcdcddcadcaaacabbbcbadcddacacddddddbddcabbbccddcbcbbbcdaadabadabacdccbbbbbbabccddbdcbbbaddbddaaccabccabaaddbacdcabaccdbdbbadddaaddbbdcccddcaadabbabdcdcbdddbccdcadcccaddddabdcccdadbbbbcbacbdaacadcaacccddbbaddaabcbddbbddbbddaaabdbacbdbdcaabdbcdbabbaaabadadcbababbbbcaddbcdbabbbcbcddbdcddadbabdcbbccdacdbbcdcbaccabbdbaaddddcccdbcbcdcddccbccdabdadcbcaabbabaddbcaadaaaadcdddbaaddbcdbdcdbdbadaacaadcaabcdabadccdbabdbccdadbbadbbcbdddaacacddccddcbdbadabddbdbcaacdbbaddbbcccabddcdabbccdbcdaacadcdbdcabdcabbbadcbaddbdbaaaabadcbaabcddcdaddabbdbccadadaacacdccdcaddbbddaadaaddbdcddcbccddccacdacabdcababddbcacbccdacdabbbbccbdbdadacdaabbbabccdababbbaddbbbaadabaaabbdcbbddcbdbbaaabcdbcaddcccbdddbbbdccccdadcdccbbacaabadcbaadaacbacabadbaccacbbdbdcdacadbccacdddbadbdaddbccbbdbbdadccccbaadddaadbabdcabbdcbcccdadbcaaabadcaabbadbbdbacbadabdddadbcbaadabdddadbcccddbdccdabdadccdccbbdccbbcacbcccbbabbbccdbcccccdbbdaacddcbacbbcbcacbacdcbddbbbcaacdbcdbdcbaaddabcabdacbaccdaabadbcbddaadadbbbbcbddacabcacaddbdacbdbdccbacddbbddaaabdbdccbdadcacadcadbbbacdcccddbdbdacdddddaddcbacaccdacdacadabbddadcbbaaddcdbddbbaaaddaabadadbccdaabbaaabbbcddaddabbaaacdaaabacccadddadbccbddbddaacaccabacdacdaabdbdbaaccbdcdbbadcaddaaadcdaabbaaaccdcddacdabacabbccbcbcbbdcbddccbabdbbcbddcbacdbcdabcdbdbccbbdcadbdaaadaddbcadadcddcaddadbcaacbacadcdadcbddaabdadcdaabdcaccadbcabbdccdadcbdcacbbabdbaacacdbbaabbddbdbbcdccabadacbabadabcdaacaacdcdddbbcbcacdbdcddddbaadddcdbdbdcbddaacaabacbbdbcdbdcaacbccdbacacbbbdadbabbdcadacadbcbdccabdabcdddbadbabcbcbacaccbbdcccccbddcabbacbcdbbbbccdacddbcbdbbadbaabdbccbbaccccdaddccbadabdcdacbbaacabdccdbcbdaadbadabbcbcbdaccbcdabaccaaababbbbcccbdaacabdcaccbcabcaccdacdcdadbbaaddadbadcdcdddbdacdcbdbcdbadccbcddabdddccbbbdcdbacaddadbcddbcadadaadbcbadacbabdcbdbcdadbccadbcabbccbcbcaaacddbcddddccdbabbcdbdbcbcdaabaaccccbcaaaddacabddaadccadcbcaccccacddbbaacdbaaacddacacccbcababbbdacdddbdacdcdbbabcabaadcaccddccbccdcdccdcbbabcbbdbdbcdacdbacaccadabaabbdbdaadabcdbacbdcadbadbaabaacabdcbaabbdcddcaaadcdbdacaddcdcbcaabddcddcaacccbcaaaabcccdbcdcacbdabddccdcdbccdddaaabcabdcdcaccddccabacbacbbadabdbcbcbbadcbaabdccaaacbccbdabcdcbcbacccdbcdcbdbacabdcababccbdbbbadcddbdcababdcbbdccdbbdddadbabaaaddacbbabbacddbbcbdcccccabdbadcddbadaabdbbbbdccbbaccccbabcdcbcbcdacccccbbddddbabadcbddbccdadbabadcadabcacbbdabbddbcccadccbdcadcbcbbcbbbaacddaadbaacacbadcccbbcccdbbaccabbcbabbccbccdcbcabddbcaccaabbcabdcdbbcddbaaababbacdbcbdacbbccbaabbadabdbcacdccdabbadbabdbdddbbabdccccddbbbadaadaddbbbcdbcabdcabcadaacdadbbadacbcabbabdaddbcacdcbadccacbbacabbaccbcaaccaaaababcacbaddcdcadaddbabacacccbcaccdcdbbccbddacbdcccbdcadcccadcbabacadabcacdabdaacaadcaacbadbadbdccccacdbdcdbbbdbabcbbddcbabbaddadacdcdcbcbaabdcdddbcbbbccababccbbbcbaccaddbaaddbaaacabacdcadadbccbadcaabdabaddddbbdabcbdcabbacdadadaacbbdabdbabdbdcdacccbbdccccddabaaabccccccdcccdbdaadcccaadcddacbbaabcadcadbabdccadbbcdbacbccabbcdabacccbddddbbdaacbcadbdbcddabbbabddbdaccbdbabdacdcdbbabdadbaaddbbbddbdcccdababdbccaccabaacdbdadabddccaddadbdaaacacdbacdcbbacbddbdcaadcbdadbddbdbccdbbdadccccdacdbabcdcbddabaddbdcddadccadadbbbcdadbaacabbddbccaccbbbcadcadcdddadbdddcbcccdcbbaacdccbccbcccaaadddbdabbbcbcadcdbababdadbcabbabaadbadacdabdcddbacdabadaaddccabbcacbaccccbdaaccbddbdcbaccdbbbdcccddbcbddccbbbbdcdddbbdcbadbdbddbbabbdbbbccbddcddadadcddccdbbddacbbbcaccdcddadccdcbaacadabcbcdaccbbdabacaacbbbdddbdbdddccabddaaccaccdabdcdcabbbcabcdccccbdbdcccacdbaacdcabbddabdcdabcaaddbcdbadcbddcaadddadbabbdbdbdcadbaddbcdbcddabaacacdddbcbcdcdbbacdadbbbbaabbbbdacaacaaacadbbacdbbabadacbbbcdadddbbcbdaadbbbabcbadcddbbbbccbcdcaddabcadddbcdbbabcddddccdbcddbaddddcbccbdacaacdcddbaaabaabddacdcbcbacccdaacdcacbcaaaaaacbbbaddcbdbbbaacbddcdcdcdcdccbbdabbcdbadacccbbcaadddbbaccbccbdccbadaddadbabcacadccbccdbddaabdadabcaadbdcaabdcdabdbaddadddaddbcdbddbbbccbbcdacdcbdacdbaacaabbbacccdbccbdbdbdaacdadccdddcdcabdcdbdcbaddadbdacadddacacbcbbadabcdaaadbdadabbacaabdabddbcadabbaaacabdaddcacdbbacbdcddadbaaddbaabdcdbdabcdaadddaccdbdddbabdbcadccabdcaacbabdcbcbcbcdcdccacddbdabcaaddbcbbdbdaccbdbbdcbccbbcddadbbdbcbaacdacccaacadddddacbabdacdaacdddbbcdadaacccbbbdcbddaadddacccdbabcbddabdaabdddbaccbdbabadadccccaadcdddacbbddbacababccdbccacbbddcadbbdcbabbcccadaadabacdacaddcaabbcbabbadadbbcbaaacbcdbdadcaacaabaaabacaccdbbddccbbcbdaddcbbbbdadbbbabddcbacdbddccaddcbaadccccddcdbcddbbbcbaccbabdcdbadcbabacdcdccaabdaabcbcdbdacdabdabcbdbddbbbddbddbbddabdbdcddaddcdadbaaacdbcbadbdcccbddadbccdcdbaaabddaaadabbcacacaaccbaaadabdccddddcddbccdabbaadacbcdaadcbcddacadcdacbaaaaaacaaccbcccddaaaacbbcbdacbdddaacbcabdcccccdddbbbccabdababdacdbbcaadcdbddbcdabcbcddcbdabdbcbdbbbcacccbdccccacbdbabddcadaadcbaadabacbcbccbdcdcdacbcadbdadcbbbadaaadbbbdababccdabdbdacdaccdddcdbdbadbcdabacbabaadbcdbbdcbabdcdbbbbbddbcdaaaaccdaddaaddaccdbdbbdbabdbbcbbbbdabcabdddccbacadddabcbdcbdcdacaddbcacccbcccbbcadbbcdddaadbacbcbdcdbccdddccdddabbdbbcdbaadbcbcdbbbbcdcdcaadbddcdcccccdabcaccbcbdccbabadbbdccabaacdcbccddadcbddbdcdcbbcdaccacdcdbdbaaaaaccaddcbcdccccdabacabdacdabcabbdccdcdaabbcaccbaadcddaaadabaabbbdbacddbbcbbddababcdcbdcadcbbbcdccaaaddacbcdccadcbabdbccdccabbbdadcdcadcaaddbbccccccbbdabbbbbddbadcaadcacdccabcbcaccbdcdcacabaccbdaacabdccdbadddaabacccabadbcddbdcbdcdddadbbdbbdccccbbdbabccdacbbcdcabdddbbcabaaadcacacacdddbaddcdbbbbdcababbadbdbbcadadddbaaabbcaacaabbbdbdaabdabcadbaddadddcbbbacadcacabccbdcdaadddbdcbdabacdbbbcdddacdaacacccaabbaadacacdcdbdadddcbccababbabaaaddddacabdbcdcbcbabbbaacbddbadbdacdbbbdcabadcbabbbdcaabaababcbdababadbccbacdccbcdcadddbbddcbcbacdcabbdadbbbbddacdccbdcadcccdbbbaadcaccdbdcdcdbdcbaaabbbbcdbbbcaadbbdacadacbbbcacccdcddabdccabcdddaaaabaacadcdaaacacaaadabddacdbddccccddbabcaacacbccdbdbdabcdccdabcdaadbaddacdbbadaddbcccbbdbbabadddcccdabcdcacadbdddadcaaccdacdccbbccbaddccdbacccacaccbaaabbbbdaabcabbbbaacacacdbadbabbbcdadbdbdcdbdbcdacabaabbcbbbdbdccabddadcbcaadaabbddcadbbacccdaccdcbddabccaddacbbdabacccadbbbcadbbabddacccddcacdddbbadcadabaabdcadbacabcbaaaacaccbabbaabdbaaccddbbaadbcabadbdcdbaadcdcbdbbcadbadbdddabdcabaadccdaadbcdabacabcdacaacdddccdcbdccaabacdabbccdbdbcbaddbdcaacabaccddbadcadabbcbacdcdbccdaabbabbddbcaadbadbccacdacbaccbcbcbcdcacdcdcdbabcdaabadddcabcdddbadccbbbcddcbbddbbadadaacbbcdbcdbdacacacdbacdabdddcbdacdacccaaddacacaacdbdbbabacbadcdcdcbcabddddcdbdddbddbbccdcdcaccddcaacbccdbcdaabdbbbddcbbadadbaccbdcadabbbaccabbbdadccbdadadaaaabbcacbbbabdadabbdbdbbbabacbccabbcccadbddcadcdcbdacbbcddbcbdcdddcabcdddaaaccabbaaccadddabbcaacbcacdbabbdcaabdbadcccdcdabbaacdbbabadccbdcdbcadbcdaddabbbdaacbdcadadaadddaccadadddbbbbccbbcbdaacccacccccabcdddaaabbbccbcaddbaaadcbbdcabaabdbcbaddccaacbdbbdbcdcddaaddddaccdbaccabcacbcadccacabcbdbacbaababbcacbbaaccdbdcdacbdbcadabacabbabbbcbcaddbbabbcadcbbbdbcdacbabbbdbadcbbcbbdbdcabcaccdbbdbcacddabbabaabbadbdcbdcddbbdbbbcabdcddcdbcdcaadaddabdaabbbabbdadabdaacdcdcbdaddddddddbcbbaaaadbdabddcbaadadadcdccbadbacabdbcccadbdaadcbdbbabbabbcbcabbcbbdcdbbcbabddddaabcbccaadbcacbbdabbbbdbcacadbbdaacdaabcddbdcdddbdcadadadcdcacabdcbdabccadcddcdbabdacdabcbdadbabcdadadbddbbaccbbbbabadcdabbaddcadbabaabcadacbaaddcdbddbdaacddcbbccacdaabcabdbdacadcdabcbccdcbddbdbaacdcaaddddddccbddcdbabcdccbddbdcbdaaabbcdcbbddcbadacabaddbdbbdddadaabaaaacaacbbcddbdacbcdddcadccbdbcdbbdbcdbdccbbcbbbdbbcacaabdaadacdbccadbdbdaaaabdbabccadabbcbbaaadcacccdbdbbdadadbbbddbdabdcacbdbbabbddadaddabaaddbbdacdcdcaacddaadcdbacabacbdccdbbbabaabcbbdabaddacaddbbcaaddaadbcbaabbadbabaddddbcaddacadabbdaadddabbadaddbbddcabaccdacccddddcbcaacacacacaaccdcbcbcabbcdbccbcbdcdaadbcdadabdaacdddbbbccdcadbaaaababdcadbdcdaaabaadcdbadbcbbaabadaaccdccbbbabdbbdbcbaadcdccabccbacabbbddccdacddcbcacdabcccacaaaadddcaabdbcbdbbcddbdcccdbbcacbaaccbabdbdcaadbcdccdccaddbbcaacababcaaabbbaadabbadcdaadcbccdcadacacddbaccbdccbacdbdcdcaacadaabdddccaddbddbccdcdbccbdaaaadbadaddadaaddbbcddcbadcbdaacdaccddaaccacacabbdccddababaabbccbbcdbcabddadcbccdbadabbbddabaadcaaacaaabbddacacaabadbbcdcadadcabdcacddadabbdbaadbdcbbaaacbdccacaaabcbcbccadaabbccaddaabccaccbdbaddcaddbdbcdcabbcccdcadabadbddbccacacbccddacddcbbbcbbdacbaadcccdcaabaccdbaacaaddcbaacbabdbcdbdbabaaacdabaabddadbbaddabadddbdbcbcadbdaaaacadbadabbbadddabdbbabccacabcccdcdcadcbbadbabccbbccdacbbbabaaccccacdbdabdbdabcaadacdbcbaaadcdadcdaddabdccdbabcbccabacbbbababbbbddddcbcbdaccccaddcbbddbdcdcaacdadddabaadaaabadcdcdbcdddacabcddcbbcaccdbdbcbccbcadddaacaacdccabbaababccdaaddabddbadbbbdbcdbcadcadacacacaaadccbcbbadaabaacbdbcccabbbacbcdbccccabcbdcbaddbadbacdbcccacbbccadcbacadcadcaadccacadadcddcaccdadabbadacdcbbbbbbbccbbdaddcaacbacadaadabcabacadcbbbdbbbaccdadcadccaacbbcacaccbddbccccbcadbbdbccadbbcdcbdadbddbddbdacabddacccdcdcdcaaaaabcbbbdaabdbdbcddbbcdddccbccaacbccababbbddccdbdaabdbbcbaddaabcdddccccaccdabcabcabbddbaddddcacbacadaaddadbbacaaaabacabdccdbcccdcadcabbcaaaddddaacbddcadccdadbdabadbbdcabcaddcadccdddcbdcccccbabccdadadbbccbdccbbacbccdabdabadcbbccadcacbacddbdbdcdabbdccdbaacadcacbdadadbccdddacbccacabbdcddddadcccabadccaaddcaaadabdccddabddbccacbdbacdaddadadcccdbbcdaaccdabdacbccaacdbbdccccdccdbdbabdacbadcbdbccbcbbdcaaaddbababdccddddcadacbacaaacccadbaddbcbcdbabbdaccddbccacddccccabdcdadcddabaddbaabbddddaacadaaccaaaadcdddbdcdddbcaddccbcabddccbbacaabaddccbbcadddadcaacbbbdaaddcbcabcdaccabaccddddaacbccdbcdaddaabddcdaadcabaaadaccdadccbcadcabcdcabbaadbabbbbdcbdbdadbbbbcbcbdaddcccaaaabcbbcdbddbbabdbaaaccbadcdbdccbdbcdaaaacdbcddbabaccbcaadadbbddcbdcacddbdadadcbaaddacdcbbdbcbddbcccbadabdabcbcbaccdbabddbacbaaccdddcbbbaddcbcccadbbadadddcddbbcbdccbbddcacbbbacdcdbcabaadcbbccbdbbdbddcdabadcadcdbbacdbcbacccacbcbaabcbcbccbdaddbbbcdbddaadbabaccbddaabadddadbabaccdacddbbdbdcbabcdcbaddcadddbaabcaadacabdbcbbbccdabbacbbdaabadcccadbcbbddadabddbdcdcaaddabcdadbbdbaacacacaadbaddbdccdadbbccabacccddabdaaabbbdbdacddcadcddbcccdbdbcdacbbdcdaabcdcdaaadcddbabdabaabaccadcdccdcbadcdbaaabaaccbbcadaabaacbaddabdddbbbabccabdadcaacdcdbacbcbdaabacddddcbcaaabbcbdbdcbcaabaadadadabaddcdbdddaddabcbbdbcadcaacadaaccdcabcbdcacbdaacabbbabccaaabbdccacbaddcbaddddbdbbccacdbcccddbbdadcdaddcdaacdccdacaddaabdcdccabacdddcbcbdcaccbcabddaabbbdcbddabdcbacdaddaaaaaacdabbbabaddbaadacddbbabcbdddbbdbbacdddcbadbaccbbacaaaaababbaadbdbcccacaadddbcdaabcaacdaccabdacbcadddccacccbbaddacacadbadcbbdcadbacabcdbcdbdbdaadcaacdbcbbbbbcdbabbbaabddcaddcdacddbcbacabcacbaaddddcadddbccbdcdbcbcccbaccacddbababdcdaadcbccccadcadccaaacabddccaabaabcdccaccccbbbccdadaaadabdccbcacdbabbccdccdacadccdadcbaddcbbcabdcbacddbcbdcababdcbcbdabababdbbabbcdaabccbcbdbdacdcccadddabcadaacbcabccbccdbccdcdabaaabcabcddcaaccaadbccbddbbadbbdbaaacadcddccbdadabccacdcadcddaacabcbbdbcccaabccaaaabcbaaaccbdabbdbdbddbdccacabbaacdaaaddcbcdddbcccaacbaddcdbbacbdbacaddccbaacaacacbdaacaaabdbcdabacdcabcbddbacabcadbadaadaadcacaacbacbcabdbcddabdcbbbdbdcbbbddadcbcddbabdabbbadcbabbadaacbcacaacaacdcccbdcbbbbcbbabcdbddbbcccbdadddcbddbddcaddadbdcaddadadbacbaddabccacabacacacbbacdabbbdbabaccadcbadbbdccdadbbdacdccbcccddbcbdacbaadbdbadaabbcabdaacbdbbdcdcccacacabdbdccbabbacccddcaaddbddccdcabddbcdabbaadcbdaaddcadabbbbdbababcbcabcdaacaacabbbcbddbcdbadbccadccccdacbacaacacddadaadcaaddccbcacdbbcddbdaabbdaacadcbadacdcadcdcbadcaacbbdcaacbaaabcdcdcbddcaddbaabcbcddadbbdabacaabbdabbbdddddcbbadabcacdcdddaddcccaaacdaddbaaadbcddbccccddddacdbdbbdbacaabbacdcdbaaddcbccdbbcbbaabddcdaccaacdcbbcdbdcaadcbbcaadadccdaacbadbbbadaddcddcabccddcbcccbacacddbbbcacaaabbacbdbccbbbabdbacbacdbcddadccbbaddcbcddbdcdbccbcaabbdabacacdccabbdbccdabcaacacadbdabababbaadabacdadddccacbadbabaaabcddabdccddbdcdbbbdbabdcadaccabaaccdabcdcbbdcccddcabdbcccccdbadcbabcacaacdaccddbcacdacdcdbddadabdddbacaacacabdbbbddbaadbacdbcadadadbaaaadccbdabbdbcdbaaabcdbaddcabcacbcaacbbccbdbdcbdaaabbcadadddddabbbcadddbcdbcdaaaacabbdcbdbbbccbbbacaabbadcbaaaccacbbdbcacdccdccdcdbbabdcbccbccadddbccbbcdacaaddcdadadbbccdadcbbbcaabdcbccacbcdcdadbbcbcabdcabdccdbcdabaddddaabbcdbbcbcddaddbcdadcabdabcbacbdadaddaccbccbdddcbbbdacaacccabdaccccdbdcadbdcbcaacbcbbabaaabdcabbadbaccddcdbbdccdcadddcddaaaaadabcbadabdcacccaddcacabaccdbdadacacdacadacabbcadccabdbddbcadddbbacaaccbdcbbbddabdccddcdbcdbbbbdcaccbddbbbbbadcbabcbabcddbbbacadddbdbbcdabdcdadbddcbbccbdadbbacbcdbcbbcdaaccacaabaadbdadabdbccbdcaabddbbcbabcbdaddcbbcbbaccbabdacaabbdbaacddccbcdccacbcddadddcdadcbcadddacacabcddbccdbabdacdbcdccaacadabcbcadaacaccdcadbdadaaccdbbadbaccbcdbcbbaaabbcaaacaccbccabcbdbdbccbddaabaaabdabdcdcbadbbcbacbacbaaabaccbabdcaadbdcadaddacadcadadbdacbdbdacbdbadadccdaacabdacabdbaaabaabcbdcbddcaadccdcadbbdcaddbccdbacdbdaddaadabccaadbabbddadacababbbdddcccaacbdadaccaacdaddbbbbddbdccccabaaddcabbcdbaddccaccabbdcbdbcbbbcbcaabbbbaaaddddcdabadcabdbbdbccbadcacaaadbcacddbdbccaaabaabdbdcabcccbcbdadcdddcaadaacdbdaaadacbdaabdcddcbdabbadddbacaddabbbcbcadacdabbdbcabaaddaaddccabacbbbcbcdaaacddadcdaadabcdcbddccbaadddcbadacbcabbabbcdaddbcbdababcccbbdcdbcdcaadbaccdddcdddaabaccdddaddcacdcdacadcdaadcbdcaabaadbbcbacbdcbaadcbdcabcddccccaaaccbbbdccdbadcdcccbcccbadbacabdbdbcbadbbdccbccbadbbaaaaaaccaddaadabdccbbccbdaabadadbaaabadcdaabbdccddcbbcbabaacbaaaaaaacabddbddcdbababccabbdbbcaddbbbcdbdadcbadcdbadbadaccbbbccbdbddbdcbcbadddbddbadbaacadcdbbbadcccadbbaacdbaaaaddacbbdbdddbdbadbddaccadcaabaacccdccadbcdddaaddcdaacaaabdaacaadcaaccccbdcabdbaabcdcabbdbbbcdbbbbadadadcdaacdbdcabbddbbaabccdddaadacdaaaddaaacccccabcbaaabaacddacccdcbadccdaddcaacdaaddcdaacaaacbddccdcacdaaccdddaaddaccaabcaadbbbbbccadbbaaaadcccdcbaabbacacdaccbcbadcadbabddadccdcbcadabccabbcaccbbaadabcdbcbdacabcbabdcddbacbdcaaccadaadccbccabbcbbbabaaacadacbababdddddabbadbdbdcccabccbabbaabcbbadccabdadbdacbdacdbbcabaacaddaaddabccaabaccdcabbabaacdabdcbabbadacccacdabbbadcabadcabccbddbbbbbaccbadadcadbaabadcbabbbdacbaddcccdbdbbcddcdacdacaadbdcdcbcbcdbcbdbbcbddadbccddcdadbaacbcdcbcdbaadcacbaccdabdbbabdcbabbdddaaadacbcccccacdaabdbbddddcbddbdcbaabdccaadaabbddbacabdcadbcbcbbbddadaddadbbbbcababdddbadabacbcabcbcbdcabaacdddacdbabdadbcbcbaaaabaaaaaaddccdcbcbdbccdabccdbdcbabddbcbdbccccbddcbcddbbdaaacadbbdbcdccbdcdacbbacbaaccbdcdcccddbbbcadacccacaaaacccbaccbdabbbabdcdbadacabdccccbbaacabdcbdabaaddbcdbdbdbadbbbbddabbcbcbdcabcddadadaccdaabcbbcabdcabbaadaddaccccbdbccdcbcbccbdbdcaccadccdadaacbbcbccdbdccbabbdddbcadddacbadbbdadbdcdababcdcacacaaaaccbbccdbcbcacaccdaddaabcabdbcaaddabbdbccdcbadbccbdaaadbddcaacaacaacddaddbbddbcdadcddcaadaccbabbcbaaacdcccacdaacbbaddabbadcddddcccdcdbddadaacbbaaaacbdbdbcadccaaababcdabaccbdabaaadcbaabdbdbbbdcbdbcbabaacabcacbdbbbabbcddbddbcdcaabbcacaddabcbaccdcbcbbdaabaaccabdaaccacadddddbcdcdadccbcaddaabcbdcccdaccdccdcaadabdaabbaaaacccbcbdbabcacbcadbbcbdadacdaccbabcadccccbacdbdccdaaddacbcccdadacaabadbbbaadbcdcabcabccbacdcbacdcdabbcbadbdacdabbdadcadcdcbcabbbaabbacdbcdbcabaadacddcbbacaccbcacbdbbaacdadbcccbabbbacdbababbdaccbcadcaaccdcaaddcadcdaccaaaccadaaabadbcdaadbdaaddbcaabdccbccadcaabbcdbccdabcaccdccdbcacbccbcdddaadcaaddbccbcdaabdacdbddbddbbccadcbabadaabbbdbdbcdacdadbdaacbaacbdaccbdaacadaadddbbbbabdcdababcbccdabbbabcbaabdcadcbcaabdcabadbdbddbcabddaccbabcabdbaccbbcbcabcddcbbccdbcddbdcbdbdcbadcdbaacddabccbabacbbcdddcacbdacbcbbbaddbcdaaadccbcaddacbcdbaacdaaccdcaaacaccadbdbbcbcccbbbadadcccbbacbdccbddbdaaacdcacdadaacccacacccccbaaadadccbbdcdacccadcbdaaddbcaaacaaaacaacbcacddcadadcbdbcdddcdddaddbdbcdddbaabdadacccbcccadaaacbddbcddadacdbabacdbbadacccddaacdaabacbcaaddcadcdcbdbcadabbabbdcbcacacadbcddbcbdddccddbdbbbdaabaaaaaabbabcabcdaabaaccabacccbbcdbcadaabaaddacadccabdddccbdccabcddcbacddbbcdbcbbbdbcbabadabddcabbabbbbccadcddcdcaabcbbcccbcadaadabdcbadaabcddabadbabdcdddbadbbadcaccaddacaabaddbbcbcbcccdaccdabcabdbcbbcbbdbbbdbcbabdaaadcadcabacbdaacdbccdcbaaddbdddbcabcbbdcdacbcaccdbabaaccaabcaadadbabdbcacaccccddcccadabdbdcbbcaacbacbaccdcbcdcccdbbdddccbdabddbcdccdcabddadcbbdacdaddcddbccabaaabcacdccbaaadabdadacbcdabbdbbbacbcccddacdacadbbdadddbcaccadbccbdbdabdcbbbbbccdddbcacabcbbaddbdcddadcbdcaaaabcbbdacbadbcbbdddaccbaadaddccdbbcdbcbdacbcaccccbadaabdcadbdcdadacadccaccddcccdbcacdababccdbcbcabdccddbbdcbadaddaabccaabcaaaccccdbaddbcabddddcbbadacadabcbaaadddababcadcccbaaadabcdcabdaadadaaabbdaabadddccdaabbcabdbdcdbaccdcbcccbdbaddbaccaccccddcccbacaccdadbdacabdcadabcaaaddcdbccddcaacaadacaacbcbdabdaddbbccdbdccbcccdababadbabdabcaccbbdbabdcccabcbdababaabccdddcdbcdbbdcadbacadabaddacccaabccadcccdddcabcdbcdaccabcddbaabdddadadccdbdbbcdbbddbcbdaaabbcdcaadcccbadbcbbdbdaabbcccdcdbbbcbaddadbcbbacbabdbcdccabdbbbcaddccabbdabbacdcddbddacdccccdbcdabbadabbbdbbdddbbcdbaccddbbaabdacddacbbcaabaacbcddaddddcaaccadadbbbdcacbacccdccbddacaddcbdabcbdcbabaacdacbbabcacdbcdbbadcbdddcbcacdbaadcadcbadcdbcddcbacdaacddccbdbdddabdcdcabcbdbbcaaddbcadcdcdcbbdabddddccadcdbdabddbaccdcdbbdcddddbcadbcbccbcbbbcdbaccccdcabdbcacabdcbabaacdcdcadacdccdddaacabdbbbbcaabdccddaadabbdacdbbcbccdcadddaabadccdcdbdcdbdcacacaadaddaacaaddbcdcdaccbdccdbcccdbbbaccbddcadcdcddadbddbdbdbcaddddccddabdcbcbbabcaaccacacdbcdabaacaabababccadbbddddcbbcdabddbdcadacccdbbccabcdbddaaddaadbccdbaabcacbcdadaccbaccabcdaacbdcdbccbacdcdabcbbddbbbabbdcacbadbdabdaabdacdacccdabbcbdcddaababccdaadadbadbccdaaacbadddacbddaacbabdbaaabdbcccdbccdcbadaaacdaabdaddcbabcaabdadbddaaabccccabdacdbabcddadcdabcaabcdaabbcbabcbaaacdbaddacbaacbdcabbaccbabbcdaacdccbadbdbabcadcbcaabaadacabdadabccaabadccdddbdbbbadccdcbaacacccadccbabcccacdcdbcabdbadccbccccbcaacdaaddbccdabddbbaddccaabadcddcbbabcdabcdababdccabcabdddbcccbabaaacbaddbbcdabbcdddbabddcabdaaccaaddcbacbbbcabcaabdadcbbababcccbbaabdadbabbdddbcddbbdacaacbcabdaabbcdacddbbacdbaaaaabcabadddacdbbcdbacbbacbdbdcdbdcccccabccbadabbbcacbbaaabddcdbacdcabbcadacacdbbdcdacdbcbdcbaacdadbababddbdaabaacaaadacacdbcbabcaacdcadababbadabaccacbadddcdadaacbacbddccabdcccadaddacadddddaddbdddaacdbbbcbbabbabdaddddaaacdddaabbdccadddcbbbcabdbcdaccdbccacaaacaacbcacabdccdbbddddaaaacddabbacccdbddcbcbabcdcbdacdbdbcdaacbadbcdcdbdbbbacbdbcbbaddcbaaadcbaddbbaabdcaccbbcbbcdbdbcdcabbcbdbbabbadbddaacacdcbaaacadcadcbaddbcbacbaddccbddbcdaabcdabdcbadcacdacdaccbaddabcbdbabdacacacddcbdbbbbacbdcdccacddcccacbadccabbcadcaabcaacbdadabcdbcaaddbacdbcdcdccdbadbbcccababdaacadbbdcdbddccddcddadaabaabcdabaaccbcacdbcdaddcabcacabdcacddccbccddbdccdbdcdcbddbadcdcdddabdbbcacddbbbccbccccbbcaacaadcadccadaccadcddccbcdaaadcccddcabaccdddacccaddbcadcddcdadabcccadcbdddcabbabdbbcababcbaadaabacbddbabcbcadbabdbdcbcbbbadcbcdcbcddcaddbbcbabbdbaadcdadccccbcdcabdcaadbadacdadcbdaacdcadbdabadcaddbcacbabdccdcdddcaadaccadddccaaddadcaaacabcaddacacaabbcacadbdcabbddaccdcacdaddbaaddbaabccabcdbaccbdacdddaaaadbcdcccbbbbbaadbcbbbbbcdcadadadccbdcdddbdacaacaadcbddcdadcbcccbaabdddadbdbcbadcddacbdabaabcacbaddccdaddcbbcbccadaacdcccacaabdaacadbacaccccacddccdcdddbcdaabbbaadcacdccadbccabaaddacabadabdaddadabcaacbabbadaddddbdadbabcbccccdbdcbccccdadbbddcccdabcdcbcbcbbbbbdaababddacbbdabdbacdddccccacaabadacaddaadcdcdbdbddabaadbbddaacccaaabbdbaacadaabaabadaddabdbadddccdabaccbbdabddacaadbcddcbcbdbccadbbaaadbdbaabcaccaabddaabbaaccddbdacbaabbdbbacaadaadbaddacbbacacaadcbbcdbacbccccaddbbbccaddadbbcabbbdaccdbdaaadcbbcaabdadbbaddbabbbbadcddbbbdbabcbbdbbdddadbccbabdcdbdbdbcccabbbbdaadbcbaaacbccacabbacccacdaabdcbacbabdbcddaaadcadbacbcdbbdcddcdaaaabbacddbcdbadddbaaddcacdabbbaabddcbcaaadbddcccababddddbbabadbbcdbbcbcadcdcbbcddacbdddcddacddabcaaadcdccccbacadddbadcbbdcdddbddcadaadcbdacdbddcaccddacdbcbbcccdaaccdbabcadbbbbddccdaaccdabcabdccbdccacdacdbccaccabcaaacdbdabbdcaaadbdbbadbddccbcddcdbbcbbddabacaddadccddabddcdaaabdccadaaaabdcadbccaabddacdddbcdcababadcccbcbcabcacdbbadcbbdccadabbcacdcbddbcadcaccdcccadbdadaaabadcdbacdbabdadddcadcabbdbbbdababdbaabdccdcaacacaaaaaccdcacdcddcdcdbcaaaadcdccbdbadbddaadbbddbdbbdadcabaadbbdcddbdcadccadcdbabaaabbcbacbaabcccdbaccdbaaddcdccccdaaddaccbcbddbccacabddbbddbaaaddcbdcddcddcbdaabaccbdabdabcdbacabaddcbcdcdddcdcdabddcbdadaccababbacbbdbadddabacbbdababdacdcbbcbbdabcbcabbdadcabbbbdbcdbcdadcaddbacaabdadcdddaddbcdbddbddbcdccbbdacbcbbbadaabaabdabcabbbbabbbdaaabcacacbbacdaababdbacdbbcbacbdcbddbaaabbadabacbddbcadcddadcddddcacdbbcbdddcbdcaadadadbcbcbaadadddcbddadcdddcbdddbbcdcabdcddcdaabbcbdaccabcadacaaddbbaadbdbbcbddddcddadadbdcbcccaacdbbbbaaadadaddabbbbbcdbbbabccacddcabdbdbdacddbccdcddbcccbadacbdbacbbcccdcacdaccbdadcaacdadcdcddcdbabdbabdbaabdccacbddadbababadcaabcbbbdcacabcaccddabbadcaadacdbdcccbddbadcdbdabaabbabadddbdacbbbabcbaacdddccbbcddacdbdbcadadabaddddacdcbabcdaacbbadaadcdcbccccacddbaddccddbbbdbbbdbdbaddaabaadbccadcdadadddbdbaadabccdaccabbbacdcbdadbabbcadaacddcddccbcadbbadaabbbaaabbccddacbbacacbdaacbadccdacccbcdccddabdabacdadcbbaaaaaadcaabbccbbbbdcadbabbdaadbcbaadaaaaadcbbdcaacadababacaddbabaccbdcbccdbcdabbdacbacbdabccdadabcbdcdacbadbadabcbabdcadccaabbdcbccbcdaddbccdaabdacdcbaddbbdddadccaadbbdbdccacaabbacbdbaccddcdcdcbabbcddadcacbdddbcbdcdabccaaddddcabbcdadbcbdabaddabccbbdbbdabcacabbddcbcdbdcdbdddbccbcabbacaddbcacddddcaaaadaabdcbddcaaaacaaacbcdaacbaacaaccaabbcaaaaccdcacdbbcddcaddabbcdbaacbbdcbdabdaabbbbaababbacabaabdddabadbaccddcddbbccbcadbcbdcbabcdcbabcbbdabddaaababbbadccdbdaddddaadbcdacdcabcaaccacaabcdcadabadcdcaaccacbabbbdcbbcbacaacabccabdbaaaaabcadcddddcadccdadbbbccccabcdbbdaccabbabcccbbdacadcaddadcbbaddbaacbadbacabacbadbbbdddcccacccbcaacbaababbbbdabcddcaacbdacbcaadabcbabbcbdacccdbbccbabcddcdcdcdadbdbacbadcabdcdcaabdccbaabbccacbdcabbaacdacbbbaaccadcabdaacbbabdcdadccacbbabddccababddcbcadbddbbdaaacadcbadacbccbacbdbabbdabddbaaaddbccddcdaacacabcacbccbbcccdabbddddcbbbbcacadaddbddcaacbdddccdbcccbbabababcbcadabaaadcbadaadacbccbbbccacadadaaaaaadbcdcadbbbbbdbdaccbcadacacdbadbacbdbdacccdaacdbdacdcccdabdcabbaccabcadbbbadadcdbdbaabccdddacaacdcddddabbdbccbdaacdcbdabddacdcaacacadcaaabcbacddcdddacbabcdcabcbaabdcaddabddabaccdbccababdbaaadcaaddcbcacacdcdcbaddcbbccdddbdbbdabbbcbdaabdbdddcacbabcaccbdddbcabadbcabdcccdccbccadcabdbdcdadbbdccbaabbabbbdcacbbcbacacbccddcbbcbacbbcbaababcaacdcdccaabdabbbbbdbcbabddcbadbacdadddaccabbacbaddccadccddddadddbddbdcdbbdbbbaccbacaacbbacacdadccccdacbbacccaaaddbadbababccbdaabbadbadbbaddbacdcbaaadabccdaabcbacbdbbccccbcaabadaaadadcbdbcbcbabdddccddccabcabddcacbdaaccaddadabbbabbaabbdadbcbcccabbabdddacabbbcdbacbbbaadaddccddddadbccadbacccaccccaabbdcdcbcdddcdadaacdddacbcccabbcacddbdacbcdadccaccdbcbaaabcbbadcccbdadccccadcdacbabcbadcbaddaaadcbbadcbcbadcbbcdddabbdabccbccdaababdabcbbacdcadcabcadcdcbadacdaddabdddcbcbcbdadcbdbdbccddbaacdddddaacbaaabbbcababdabbaacbdadccbddadcdcdcbabacadababdacbaaabcbaadabcaabbaccccbadbdddadcbaaadbadcbdcccddabdaaaabbcacdaccdbddcbccdacaadcaabbadbbabbcabbaaacbbbdaddcbccccddbbddaadbabcbbcbcbcabdccdcddcbcdddadbbdbcdaaadbdaaddababdcdbbbbbcbadacddaaccbabadccadddaacbddabaababaddbdddaddabcbdbcbaaabbbacadbdadbcaacabacbddabacaadcdcbdababacabdbaabaabbccbadcaaaacababbabdbaacacaaabddbbabcdcdcbccaccbdbccdcbdcccbcabccabdcbdbbddabacdbabdabddcacbdaaccdbadbbaaabbacbcbcbcabbdaddaaaddbccdcdddaabbbbdbcbabaaaadcbacadddbbababaccaacdddcdbbcadcccdddcabbaddcadbdaccdadbdbdccaaddcbdbaaabababbccccdcdbbcadbdcbaaaadbabcadbaddcacdadabbbdabbbbaadbbbabdccbacbdcadccacdbaccbbadcbdbccbcaddbadbcaabbccbdcbadcbbcdadadcdacacdbcdbcbdabcacdaccbacdaaaddbbbbabcbaabcaccbadbddabdadcabbcabbabbbcdadcccbdbdbacabbacabdbccbbcdddbaabbbcddbdcbacbcbbbadddddbdacaabbaacbabdbcbacacbbbbcbcdaacabacbccaacadbacdcddccbdbcdcccdddcddbcadaacaaaabaddabbdaaaaaacabaddcccccccabbaaabcddcadadbbdcbdaaacadbbadbcaccbdadcbdccdbaabaccabbdcddddbddaaddbcdccbbadcabaccbbddcccbaadcbcacbddcaacccdddbcdbbdddbdcbccbbbcaccadddacbbdbdabaaabdabbdcbcbbbdccadbbacdacaccaadbcdabdcbaabcabbaaabdbcddaaddadbcacbcddbbaadddbdaadddccbabdbdccbccadabdacddcbbddbcaaccabdbddacbdbadbccdbcbacddacbdcddacacdbcaacdbdcbcaaccaadcdcbdbadaadddcbcddabdccdcdcddddbcccdbccaacbaadcbcdabccadbaabadddaaacddaadbdbccaadddbdbddbbbadbdccdcbbcdcadadddbdccdbcdcadccbcaabaccadbcbcbdcdcbadbdddcbdacdbbbabbaddacbdbdcbbdbbcbadddbcaddbdcaabaccdbccdddacdacdcbbbdaabddcadbacbdcaaaccddccbcbabbadaddcdcbacdaabbccbdbbdacbcbdaaabbcdaacdcbccdaddcdbddbdcdcabcdcbbddaaadbabacdbdcdcaccccbdabcdbcccaddabadacdbbbacadaabcbdcddabbdbdabbbbcbbaacdbbdcdbacbcabdabacbbbacbdddcdcaacadabbbdacabcabdaabcabbacddcbcbdbadccdacdcbcccccaaabdbcaacaaddccdbaccdcadcbccdbdabcbbdcadaccddacabccdbaadbcdcdcdabdbaaddccbacbddbadbcadcabbdcabcbadabcbdacaccacdccbddbbadadcbdcaabbaaacdcdcbacdbcadaaaaabcdbbccccccdadbcbddcdcdacaabdaacdcaaabbddcaabacccdcbcacbaabaadcddbdcdbdddadcacadbbbbddbcdcdcddcbbcbdadbdacdacacdcdddbabdccbdcabccdbddadaccaaddddcccaddddbdcabcdcaaabbdbdabdacaaaadbadcadabbbccabdbdccbdaaaddabbdbacdaabadbbadaddbcaddcccacbbbacdddcbbabadabbbababbadbbcdbcbcddbacdccacddaabdabddcadacaaddbcbcdabaadaadcddcbdbccddbcdbaadbdccadbdccdbacdcadbcaadcbacdbdbbccaccdcacbbbaadbcbdabbabdabdaadaccdaddbdaababbbabddbcbbdddddddbbcbcadccbadbcddcadbbabddcdcdcbaabaaddcbacdbbdcbccdaddbbadaacbbcbadcbadbccdcddbaabdcccbdbbcbdbadcbdabdccbcddbddcabacabbcaddccdbdbabcdcaaabaddadcddcaaddcadbbbcabdbcccdabdccddbbbaddcbaacbbdbcbadcddcbccbbbadbcbbcdbbaaaddcadcdbbcddbbcbdaddccdabcbcccddcbccbccccaaaabbcbadccabdbbccbccccdcabcdbcabddaaabcbcadbbaabbadacdccbabbcdcbacadbabbdcdbcbdaaaccddacaaaacacbbdacdcadcbdbadccbdaddbbcaaacbccabdbdcbcdacddbddbacdbcbabaccdaadcbcdbbbcdbaacccacadbacdcbcabcadcabdddbddadcbaaacaaabcddcdbaaaaabcbcddcbccdbaababcdabbdbbadabaddcdbacacbddbaccaccbcbbbabdddacbcbbcaacabacdccabcccccabacdaaadccbaabbaddabcdcbddaaabbaadbcbabcabcabbccbbaacbccbdbddbcbbadbcadbddbdddbcaaaababbbbddbbbddabbacbcacabcdbbccbdcacbcbbaddcadbbcbccacbdbabbaddcbdcaacaaaddabaccbaaccabdcabdbcbacdccdccaadbacddaadacadcccbdacbaaaaabdaddcabcbdcdbdbdacdddcdaddbdcaacabadcbdaabbabcbadcacbbacacbcacdddddadbaabccdcdbadbbcaaddadbcddbdabcbcdcdabdadacdadcbababcbabcddaadbccdacbdaacaaddadbbadaacaaadadaacdcbcbaddabbcdadacaaacdbdcccacdcdbdacbdbcdabaacacbbcdccdccbccdbabbddccdabcdcababcdccadbddcaadcdcbdacdbcacbabbbcbbbbcabbdccbcacccccababbabcaacccdacdbccccdbabddcbbaabddbdacabdbaaccdabcdbadabbcdabbddcacbccddbbbdbbbcbbacdacdaabccbaadbaccdabdacbcdcccdaccbddcababbdddaabacaadbcacbbbddcbdcacabdcbdccacdccacaddbbcdbdacbcacbdddbadbcbdacbdaaddacacaabdadcdadcabdbbbcaddcbbadcdabbddcadbabbabdcdddbbbbdacdabdcacdacdbccaadcacdccbdbbcbbbdaccddcbbdadbbdbcccdadbdbaccaaabccdadadddbbcbabbadbadccbaaacacdbbaadbbadccadaadcdbcbadcdbdbcabbabcabaddbcdbbccddcabdacbadcaacabdbbbcbcbcdcdddbacbadabdacacdcbcddaacccbccbaabcbcdaddbcaacadadadabddbbdcbcdcccdabbadadadbacccacaaacabccbcacaadbabdddaacdadbdddbbadaabaaddbdadadadcaacbdddbddcabcbaababaddcbbcdddbbcadcdccaacdaaccaadabdbdcddbacdadcbddaadbccccbcdaaadacdadbaabbbbddcbdbbbdbdbbcacbadddbbbbdcdabcddbcbaaabdbbcaaacacabadcdbaaadbaabcbccdbddadbccadadcccbbdbdddadcddcbdcdcbaacbbaacaabccadccdbbcabbdadccaadabbaccbdddcdbbcaccdcbdbaccabadcbddbcbabcdcbabcaabdddccbaacadacdbaccaccaccadacdcabaabddcabdbbbdccdaccadaabdcdbccdcdcadacdabbccaabcddddbddbdcdadaaaadabacacaacccbacaddbadaaabcdddcddcaacabccdbacbacadccabbdddbbddddcaabbdadcccdbacdacbaadbdbdbdaadadabdddbbdaacdcabcadabccaabcacdabbadbccabdaaabdbcadcaaadcdcbbcdbcadcddbdddcbdbcbabbddddaddcaaaadabaaabbaabdaaaccbadcddbbaacaaadddbadcdaaaaadabbcbbacdababddcccaaddbdcdbcdacddbcdadbbdacdcbddcbacdbbbddaacbdcccddcbdbdbcbacbcccbdbdcddadbcbccbbaaddacddaacdbbbcacccddcddcaadacaadabddadccbdbbbadaccbbcbdddaddbcacbdcabdddccbdcddbcccbbdacbbcaabcbadcabadacbacdccacacbdbddcacddbcadaaddadadddbcbddbbacbbbcaaddabbaccbbbbdabddadabaacbdaadcababaddaddcacbaadabcbdacaaabbaaabaaddcaddbdddbcbabadabcbbbdcdbcdbacabbbdabcadbbbbaacaaaccccdccdcaaaabdccbddbbcadddcadbbdabbdddbadcaabbadacbbababcddcdabcbacbcacbbabdcccaacdcdadcdaadbaacccccdbababbbabdbaaccacdadababddcabbabaacdbddbadbcabacadaaccacdbaccabaadcdccdccdabdbbbabcbbcbacdabcdaadcbadcdbaabcadcabbccdbabdaacbddbccdbbdbadddacacabadaaddadbdbdcbbabcaaddbacdacccbadccdacacdbbcdacccbbbccdabbabcabadbdcbcddcbbcbbbbcddddadaadcacddccacabdabdddbaddddbccaddabcacacbcdbdacaccddabcabcdcacabcdcabcababdcdcadaacddcaddbcdcdbbabadccbcadcacababadbdcdbacddccccbbaacbdaaaacdadaddbddbccdbaccbdccbbbcadddacccccbbbcdbcabdadddbabacdbdcddadcbabcddbddcacaabbcbacbdaccccbcccdcaacadddcabbccddaadabaddaacdcdbdabaaabdcdaadcbaabadaddcaccccdbdbabaacaaabcbdbdabbdccbdccbbdaacdbadcbadbcacbdcbcabcabcacbdabccbbdadadbcbdbdbbcddcccbabcbcccdaabaddcadacaaabbdabdaabbbaacaaadbcbacbbdddaabdcbddbaabbacccaccbdaccbdcaddaccbabdbccbccddcdbabddababdddaaacaaabcabdcbddaacabadcbbabccdcabbcdcbabdadbddccddcdbdccbbdddbdcccbacaccacbdbaddccbaacdcbdcdcacbacbbaaadddabcbabbdddaabcdcabbcbaccbdabababbcdbdbdadccbdcdcccdcdccbadabcdcdbdcaabcbdaacdbddcacdadacdbaccaaddbbcbbdbdbbdbadddcdbcaaacbbadbcdcdcccbaaaadddbcbadcbdcaacccbdacccabbbacdbadcdbccbabadddaaabacddacbadbdabcdacabcadaabbdaacdbcaabaadabadcbcbbbaddcdbcdbaaabcabbbadadbcdcbdbcabcaaadadddbcacaddcddddbadcdaaccbabbdabdcdcdcabbcabbabcbadabdbbbccbbadbaadadabaabdabaacdbddcddcabddcbccabdccbccaacbbcabcdbaadcadddcabbcdadadddbdddcdaacdadcacabbcaacacbaadabacaddbdccbdabdadccdbbdadbcacacabcaacbacabaddaddcdcabdbadbdbccdcdbcacdbbdbcaddbdddcaaabaccbbbbbcdcccccdcbacdcaadcdbbaacdbdbdadbbcabbbdadbcccbddaabbbbddabcdacdcbdacccbdbcaaccdbadcacddcccdbaaaacbddcbbcabdaccabaadabcbaacadabaacdccdcbbadcbbbdacbabbdddacbccbcbaaacbbcdbbcdbddbdcabdbdadbbbdcadaaaaadccdbddaabbcabacababaacdbaaaabdabbdbdbcdddbdaabaaaacccaacbbcdcdcabcdaabdadadabbcbcaddcabccbabccdcbdcccdcbdcaabbcabacdcadadbcbcaccbdcaddacccaaaacbadddcabacaadbbcabaacadadcdcabbdcdcbaddcbaacacbbdcbadbccdcdbbcbbbdcdccbdbabaabdbbdccdacdcbacbcdcbadcdababcdbbdcaaaadabbbacdccdcaaacbaddababaddaacabbddccdacbaabcdccdbccaacdcdcdcabacdaaddaaacddacadcadbbcabcccaabbccdcccbdacdcbaddbdabdbdbdccadcbcdcccabdcdbacbaaccdbddacbcaabbcdabbaaabbddcdacabaaadccdcdaacdccdccdacacbcdbcbadaccdcbacbdcbadabdccadcbbbbaddbdaabbaddaabaaaaacdadadadadccbcccddcacabaabbbccdcbbdbdbdacbcbcadbcddaabdbaccddbbdbccadbbdaccdacaccbcaddaaccccabbdbcbcdabccabcdbabbbcaaddabcacbbdcabbdcdabccdbbcacddacadcaadcbacbdbddddbdababdcdacbccaaaddabaccacbbddaadcbbdacacccbbcaabdabbcccdcadabdbbbbbddcaacbcabcdaacbbccdbacddbdcbcbccccdadadbaacdbabbaacdbbbadcadccacbcbdcacacbaaadddbabbdaccdcdcacdabcaddcadcaadbadcbcaaaaabbacbdbbccacdbbacacabacdccaaccaccdcabcbcdcbcdabaddacccaadbcccbcbdccaabaacccaaddaadcbbccdbabdaaaaddaccdbdcdcadbaacdbdacdcbcdcdaddccdccdbccddbccabadaaacadbadbadcbaaacabbaabdaabccdbdcaaccbdccabcacaacccabdddcbddacdbacacadbbbcbbbadabbcabdbccdcbddcccddaacadadcaaaaadcccdaacabbcabbaabbbadcdbacaacbacdcbcabadbbbabdbbccbdddcdacdbaabbdacdcdbdbcdccaddabcbcbaaaccddcaaababaaababbacdcbadcaaddbbdaabdaaabddacbcdcdbdaabcdacbacabaccbdcbdbcaabdabaadddcbbcddaddcddcbcbdcbcdbacdaaccccbdaadcaccdbbcdabddcabdacbddbddcbbccddbbadbcabababcaabcdbccdabaadbcbaadcdbbabcbcdcadbadddccababcaabbddabaabcabbbadbcbdadbaaadadbcdcacaacadcbcacaadcddadbccabccaaacabadbcbddadabddddcdcaddddccdbbcdccddcaaddddacaccadcadaaacbaccbdabcdcbabcccdaacbabdaccacdcbabbcccaacaccdcaabcaddbcabccbbdddadbdbcabacadcbaddcabadaabadaaddabddaacbbcadbbcdaccbdcbaaaccbdcccdabbbbbdbbaacbbcaccdcdabbacccabbcddcbccdbcabcbdcaabaddbcaaddbadadbcacabddcbaddbaabcdaccaadbacacbabcbabdbcdcddbabdcdddbbcabdabdcbbbddaacabacddcaccbaddcabdabccbabaaacbcddbbdbddddabdaabcbdacbbdacbaabdcbbcbccaabbdcaaccbabbabcdbccbbcbaacdccaaccdacdddcaadccdcbddcacbabaabbddbcbcccbaaacbacccdbdddcbaddddccddbababbddbdbaccbbaccdcadcdbacccaccddcddaacbbbaacbaadabcbdddcacbbcaddaddadabdcacaaabdbbccdcbbddbbabaccacbcccdabbbbcdcaddcddddcaabdaabdabacddbacddaccccacbaaacaacbcbcbbddadbdbdddddcdacdbabcadbaadbdbaabbccadaababbcbcbcdbcddddbabddcaacbdbdacabaacddcadcadabcdddccaadaadbcadbbaddcdadbcadccbdacaddbaaaaaddcbaadadcadcbbaacddcbdbcdcddbbacdcacddbccacacdcdaabacdadcdccbadcacbdbcaaddddccadabaddbbccdddcaddbabdacaaabbcbaadcbaaaddbdddbaadddacbcdcccdbcdaadacadcaabaaaaabaaaadddddcdabddabddabadabbaacdbcdacdbddbadcccaadbbdbaaababaddccababbdacdadabccabaddbccbccbdcdbabcdbabbadadadcacdbccbdcacbdccdddcbdbaaddbccbbdcdcacabdcccbdbadcdabbbaaaaacbadbbaddcbbabcbccaacdcbccabbdabadadbbbbccaacccbdbabcdadbbdcbbddabaabccdaccdcdbbaaccdbadacddbdbabadcdcadddddbddaabbcbaccdcadcabdddbaaddcdadabdcdadacdccadbacbcbdbdbbdabcbddcbdbaddacdbabdcbdbbbcbdaababdbbbabcbbdadbaacabdbcaccddddddcbbaacbbdacacdcaacbabbbabbcdbcacbaadbccadbadadccccdaabaaabcabcbdcacbaabbdcccabcaacbccddbcaaacacadbbdbdcdddddadcdccaccbbdacbdcdcdbadbdadcbbcbbcdadaddbccbbccbdddbacbcaacbbccaccaabbaadcadcacadabddbcaccacbcdaaacdadbacbbbadbaabbdaaabcdcaccacaaaccdaadbcbbcaadbbaaacbcabcbcdbdcaabcaadaabbbcddccaacbcdccacbccdbabababddacdcadbcbcbdacbdcccbdaaddbbbcadaacbacbdcbdddcbbabaaddcccdbdcdacaaacadbcbcacadddacabcacabdcacabaddbbbacadaccbacdcacacaabdacddabddbcbbabbabdcddccdbcdbdadcaddccbbcadcddbbaadbccadacdacccdabaabccbdcdbdcdbbbabcbdddddaadaacbaaaadacaddbddbbacaaccabdaaaaccadccbddbbcacbdbdbdbdababdbdcccaadabacbdbbacccccdbaacadcaadabbcbacdaccdabbcbdabbadcbaccbdbcabbcaababadbbbcccccdadcbdaadbabcacbbbcdddbbacbbddacabbdcacbdbddcccadddcdacdbdadbbbdabcdbabdbaddddacbcadadbacaccacacdaccaacdccacabcbdbbcabdbdcaabddaccbdadbcaabccdadbabdbaaadaacbcccbbbcddbcbbaddcbcbccbddddcbdbdbdbcdabcabcbccacdddcbbbaabadbbddcaabcccccacdadcacacacbaabdcccbccadbddacdbbbdabddccccddcbbabbbabdabaacaacdcaccccbbbacbdacaccaccdabcbccabaaccdcbbbaaaadcadbdcabdcbddbcbbbcdcaacabccaadcacddddbcdbbddcbbdbadabdcbbadabbdcccabccdddaaaadbababbdaacbddbcbcaaddbdaacbacbcdcddbbdbcadcaddcbbaabdccaabaabddbddbaacabdbaaacdbdbaaabbacadbbdacacadbddcbbbdbdadadddcadadbccdcadbdbbbbdbcacccacbddbcadbabcccdbacdbdacdcbbcbdcbaadcccdcdbadabaddadaaacdaabcbdcaccdddcdcaaacaaaccdbaddadcbbaaacacacadbbcdcdcdaabbcdcbcccdcbbabcacddacbaabcbbbcbbadcdaaabdaacdddcabcdabcbacaacbbdbcdbadaacbcdadddcdccdddaaaaabbdabddcdacdcaabdbcabbbaccbbcaadcabbccdbcaddcccaddacdadadabdcbdbcabadbddcbabadaacddaabdcbbdcddbacdcdabdacdbcdddcdabadaacaabcbdaadacdcdbaadbcddbbcadadabbdaccbddacbdabbbaadbcaaaddcdadccbcddccccddabcccaaccbddaabbbaadddcbadabaddccccdaadbcddcddbacddaadaabdaacabdadaaabbaddbcbabaabaacdbdabbdbdbbaaddddbbbbcdbbabdabadcdabdbcbbccacbcbacbadbbccabcbaacdbbacddbcdddcaacdbacbddcdcacdbbcbcccbbaadbdbdddaaabcbdaacdccdcddbbcbdcdccadaddaaccdcbbdbcccbcacaaabbbccbaccabcbdbacababaccbacabdadcaddaabbbdaabbaacaddbbaddabcbadacdbaabbcbdaaabbaabdbcadaacacbaccdadbcacbcddbccbccadaadbabadcccddcbabdabacbdbdaaadacdbddbbdcccdaabcaacabcdadcdadadcaadaabaddcbaaaadbbadccddadaaaccabadddadacccaacbdcbcadbbadcdbbbddaabcccdaadbabaacbaabcabcbcbadddaaaacadaddbcadcdddccdabddddaddbabddccbdbabdabbccbabccbbcdaacaacbadbcddcdabacabbbacbbccbdccbcadadbbddcdabdaaddbbbadacaabaabaccbabcadcadcababaaaaccdacbacbadddcbbadbbcbdcdabacdcdbbdacacabdabbdabdcccbcbcbbcddacbabcabacbdacbadbddbbcbbbbbbbbbabdcaddbbdabdddacbadaaacabaacbaccccaabbdbaaaabcdadcbdbdcabdaccbdcdbaccdcdabbbbadcbbaddcdbbdaddaaacadccacadabaaadddbabbcddacdcadcaabccbccadbacbbcababbacbcadbdacdaacccbccddabbdccdbbdbacddbacdcdcdcbbcacdccdbcacdddadbccabbabddaacbdaaccdbddcaccbddabdcaccbcdbddcccacdbbddbdbbabbaadaaaaddcaaacdbbbcadccbadbaccadaddbbabcaaadcddccaacdbcaddbaacdcdababdabccbddabaaacabbccddccbaaaaadcdddacbbcbabdcdcbdcccdadabddbacbbcdbdcacdbbacaacdcbbdacbaaacacdccbcdddaadddbbdaacabdacdddbdbdadcabbdcdcabcbcbccdcbddcaababadbcadcbcbdabbcabbdaaccbdccdbddbbaaaccaaaabaabbdaabacdccdbdbacbaadbccbbdbbcdbdaaccadacdbdbdaaabaabdbcbbbadbbaddcacacddbddcaadccbbbbddacadbbdbaaabbcdccccababcbbadaabbdcddbccbbdbbcadcbcdaaccaacbdacdabbcabbddbccddacccdcdabcbccdacbdcccdadbccaddccccdcbdbacbbcadbacdddaabbbdbdcbdabcdaacdabdcbaacaccadabcbacdbbdcccdcdaacdcadcbacbbdabaacdcdbbbabccadcadcabcddbabaccdacdadabccabbdbaccccaaacbdddbadcaccdcbbabcbccabaaabcbbaacdacacdacddcdabbaadcdabcabbdaddbbadcbcccaddcbacdcdbdbdbbbddcddbbbccaadbabddbbbddaacaadacdabbdabdbcabccdabbcacaacababcbacbbcadccabbadcadbbcbacadcaccdadddadcaaddbdddccdcccaabbacdbbaacdadbcacbabaccbcdaaaaacacdabbbdbbbdbcdaccbbbbddcdbdbccbacaccbabdadabbccccbccaddbbbbbabbbadccbdacdabbdcddacbabadbdacbadaabbddabacdccbccddddbaadbcbabbabccadaccbaabbcddadcbdabdbcdcabaddcdcadbdababcbccaddaacccacabbdbcdadcbccddcbdadcbddbcbbabcccdbdccbddccbbbcabcdbaccccdbcbdbcbcdcbccdacccbccbaabcaabaacddacacdbbddbbbdabacbdacbbddadbcaddbacbcddbdbccababcacddcaadadaaabccccdcbcbbddacdbdccacdacbcadadaaabcbdcbcdcdbabdcaaddbcaddcbdacdcbbacccbaadddbabbdbcdabaddaadaaaadbcbaabbcddaccdcacddadcbbcaccdabacdaabcbabbbbdbcbcdcdbcacdcacadadcaccdacbacbbbaaaaaaacaacbdbcbdabdbdadccadddabcaabcadbcabdbcbdbddaabaabbabcacbabddbdbbbcbadcccadcbadcdaaabbcdddbaaaaabacbadabddbcacacdbbbccdaacddbdabbdacabbdacabdcbcacbadbbdacadcacbddabccaccaaaddcdccdccbbacdadcadacbaacaacbaddacdbcaacbabaddaabcdcdcbadbdbbcdbaaddbacaabccabcdcbdbaccbbbbcabacdacbdcbdbabbcabaacaccabddbbcdbadbdcacccbbbccbbbccddcdcbaccdccdcabcabdddccddacbadbacdbdbcbaaddcbbbaddbccbbacdbaabcbcccbbcbdcdbaabaaccdacaadaabacccdbbacdbbcdabdbbbbacbdddcaabcdaabaabdcddcababcaacdbcdbbdabcdcbdadcababbdacddcddbddaacaccadacddbccbbacdabdabbbbadbdddabbbbddddddccabcacdcbbcdccdacaccbcdbaaabacdbabcddaccdcccdacbaaacbbadbabcbcdadbdbcacdcaabddcbadaddcbacdcbcdadbdbddbbbbbbbbcddcccbcaccbdcbddbadbbbcdbadcabacdccccccaccddddccbdcbacdbddacadbdcdcbbbdcbaaccacdbbdcccccdcbbcdcbbbcccbddabadcbdcdbaaacccacddcaacdbaacccbbdbddcaadadacdbcdabcdbddaaadabbdacccacbdbabcbbdcbdbdacbdccbccdcdaaacacacabbbdcccacddcbdcdddabcdcaadaaaddaacacbadcbcbcdccabcbddddadbbccbacbbdbababbdcdabadccacbacbcbcdcbdcaaccdcaacaccaacdcbccabbccacabdbbcbccadbaabaadbcdcbdcaccbaaddcadadbccabdbdaddcbbccdbabdcbcccadccdaaabdcbcaccdcdbaacccadbddacbbcdcabdcacabddabbcdcacadaadccdcdadcccccdaabdaacabddadcaabaccabadaddbbacbcbdbbacbadabbaaccacbadbccddcdcadccccbdacbaccadadcbddcddbacbdcababddcbcbdbadaadbcdddcdbddddaaaabcccabdddbcbbdcdcdaaabbbadacddbdddcddaadaadcadbccadcbbcaaddaccddbdabdaddacbcaacdaacdcbadccabbacbdaccabcdbbacacadacdccbcdcababaabaaccdcbcdbaddbacdcababddbbabadbcbacbdbcbccdacdccadddabdbbdcdaddaddaabbcbdbdbdbbddabbdccbbdbbbacdcdcccaabbbdacdbcbabdccdadddbababcbadadabbddccadcdbbcabababdaacdcbdbdcccdaabddcabcddaacbcccaabbacbcddbdbabaaddabbcbaaaabbdacabdadcbcbacadbdcccccaabbcccbadbdcbdbaabbcddaacddbcbccdddccdbdacddbdadccdcacacdcdcbdacddaddccadbaabbdccbcdcdbdbbaddababbbdbdcbaadbaccacacbdbabcabccadddcbbbcacdbacbbacbacccbacbbdaaddddbcdbcaddcadbacdabadabbddabbaababcddacaaadacaacbddcdccaacdccbddcdbcbadbdadcaaaabcadbbbbbbddaaabccaadacacbcbaddacdcbdccccdadddbcadbbbcadabddcaacbcaaaadccabdbbddabcdaccadcbabacbccacdaabdbcccaaddbdccdadcbadabbcccccbbccbbddbdbabdabddacdbbbbadcbbbbccdddcaadcccbbadbadcbcabadbadabddacdbaddccbbbcdbabddccacbdacddbadaabddcbacddadbaaabcddacbaacdbbbacdcbabbcadcdcbdbacdcadcbabcbccdcdcadcabbddddbaddcaaccbcacddcddabbdddaacabbabccccccaacabdcaccbbcbdbcabbcabdbdacddaacbcaabaddbdcdbabdddadccddabbccdaaabcbdbccddcabbdcaabcadabbcbdcbddbbbacdcadcadbddcccdcdadbddcaabbacbbadbbaccbaadbdaadbdcaddcdadbbcacdcabcccbcbcabbcabdabadbbadbdbccaadabddddddacabbccbaabbcbdbdddbddbcdddbbadcdbcbcddadbcaacabddbccbcbadbdbdbcddbaaaccdcdcdbdaacbcbadbccabbcabbaaccbdcabcccdbacdaaddbaaccbbdacaaadddbbddcdbacbabcacccabdddacdcaadbbcbbccccddacbcdbccadbadbbbcbdbccabdddbcddcabacdcabaabcacbdadbbaccdbbdabdaacaddbbcbcdcdcdcdabacaccaaddadbabddbadaddabddcbcadcaababbdcadacdaaddaacabcdaccbcadaabaadcaabdcdaaadbdcdbaacadbbbadabbccaccaddadcdbaddcdccdbcbddcbbacccadbcbcccbdaadbdcdbdcacdddcadadddabbdbaddbabcbababdcaabbaaadcbbddaadadacbbbdbadbabbddbcccdcdcabcdbaabcadcadbaaacabcdbcaabdabdbdccdccabddacaadbaddcabaacdccdcbacdbbbaaaddacbaddadddcdbbcacabbaabcbaaadcbccacabaccababaccdcdbabdcbabacddbbddabdaabbaaaaadaddbcddaaadadaaabacddacbbcdaabdaabccacaadabbcadabbcbbaddaddabccabbbcdccbdcbaabcbcdbccdbabbcaaacabcacadbcdaccbbadcbddcaddcdcbdaacccdbdbcadcdcdbdbcadaccbccbddddacababbdacdcdcbccdadacbdbccdaadddacacdabdbabbddccddbdcdddbacbbadcacdbbbdaadccaadddacaddacbacdbaadcbcdddbbbabcdbcbadcadbbccbbadaddaacacbccabdbaabdcdaccddcbbcdbcdbdadcbdbbadadabbcbdbcbdcabcdabcacdbacdccddcdbbdbcbbbcddbcbcccaaddcbabbbcccbdddbcaadcbdaaaadbaccbbcabcacddbcdcaaabdbbdbacabbddaaaaadddabcbdcdbcbdcdabddbbbccadbcbdccabccabccbcdacccaadcadcabdacaccccbaabdcbaaccabdaadcdcdccccbccadcbdbaacccadddabacabccdbccdaadbbaabbdcddadaaacdadbccbcdcccbdaaadcaddddbbbabbbdbcbaaaacabcbaabbcdccbbacbddaabbcdcaadccaadbadcdbcaacdcbcccdbacaddadabacaaddbbaccdacbdbdccaabdacddbabdcaadccdbcaadbbbbadccdcdbaddaababdcdddacbbdddaacccdaddbdddcdcbcaccddcddaabbcbaaaccccbbbabadaabcaaaacbabbdbdcbbcddbcabdacbdddcbcaccdbdacabcbbdccdcacabacaccbcadccdcaaddaddcbdacabadddcadcacadcbbdddddaabacaaaadabdabaaaddabbbddddaccdcddbcbbcddbdbcdcbbaaaaadbaadabbacacdcdadddabbbdaccbaabaabadbddabbcdaaacabdbbcbcdaacacbcddbdcdddddabdccdacabbcaacbccabbbacaaaddaacadbbacdcacacdbbbbcdbdaaaabdaccadbdccaabacdbcccbdcadaccacaaabddadbdbacbdabdadbdcbabaacccadcbdabbcbccbcabdabcaababcabdcbbcabaacbbcccadbccabdaabdcbaadabcacadacacbdaaddcdbacaacdaccdcaddcbdbcbcddcbaddcccabbabcaaddacaacccdddbbdadccbacbabdcdcababbccdaadabddabcabbdbdacbaccdbccbbcbdadadbdcbcabbddbacaddcdbcaacaabdacbdacbbcaabadcaddcaadacaddcbbbbcddabadbbbdbcdabbdddbcbdddcdcbcddcdccacdbaaacbbbbbbadadccbddabbcbaaabddbdbdccabaacccabaddcacbddcddbcbbdbbbcaaaacaacabccacbbbcdbdddcbdddddaabdcabccccbbddcbcadbbdacbbdbdaaadcaccccacdadbdcaabbaddbcaadbababddbaadbbadbacdddccbcbaabdabdccbdaabacadadabccdbdaaaaabdabccaccaaabaadbdcddcaacdcbdadadddadbdcdcccacbdabbdccabbaacbdbdbdbacdcdcbadbbabaacbdbddddcbaccdbbdccabacdcabcdcaddbadbcadcaacaacbabaabccdabcbcddadbadccdaddbbaddcabdacbbdbdcbcbbcacbbddbcaabdccdccadbbbaaadabaddbbcccccbbddaabdccbabbacddcbbadbdccbcabaacbcdbbbcaddcabccdabcadbcabdaabcdacddddbcbddddccaddabbccddccddacccacdccccbbabbddadbcadcbcbbddbbbdaabdbbcbdabdaaaacbaacbcdbcabbdcaccabdcbadcdcbabcbbaddadabbbcccdabadccccdcaabdaabcddcabdabdccaadbbcadbdcabdbcdddddaddbdcdadadccabaaabdcababcddaacbdbadaadaaadbdbdcdddadaccaadacdbdbdbcacddcdaadbaadadccccdbabddbcbaaadaaaccdcbacdcabdacabdadabbcddddbabdabdbaaaabbcdbcbabaccdddabdadcdcdcdbbbcbddaccccddadbddbbbdbbdacdacddccdabacaaabbcdcbdbbbbabacbabdcddbcbcdacbcacdabaabbabdabbddbcdcddbdcdcdbbdacaccddcacbbadbccaadaaadabaacbcaaddabbadaaddbdacdabaaadabdddaaadbbcbabdccbdbcccbcaacbacacdbaabdccccbdbaccccbababbdbcbacdaadcaddcbacdbbabcadabbdaccbdcbdcdcadbcacbdbaaabbbaacabcdbaabdcddcddcddbbbadbacacaadbdabcdaacacddbcbcdcaadcacdacacbdadbacbbcbdbaadddbcabbaabbdbbbdcaacabcaccbaadcacadbacaaaddaadadcdaabddcdcdcbdbbdaccadbddbcaabaabcbbbddcbddbcdcddbddaacabcbacbdbbcbbccaccabbddcbbddcccbacadcdcbbbcbabdaaadababcabbdcbadddbcdcbddddcbcadcddccbbacdcbdabbacdaadbadbadcdbdaabcbbadacacbccccaaacbbdbcabdbadaadcbbddabaccaaadbdbdbbbbcbdabbadaabbcbbdcdcacadccbcaaacbdbdbccdcbdcadbcdbadbabdcdddadcabadabcbdadccabacacaadbbbbadadcddabbaaaccdcadbabcbbbdcadccccacaacdcacbaccbdcacbdcacdbaadcabccbcdddadbacdbadabadcbcbcadbbcddcbbadcaabbccacacadadbdbacbcbadbabbccacbddaadcbdbacbabbaaacbbadbdcaacbdbabcbaccccbabcabbaaddcbcbcaccdabaaaacbbcacbdddbdcaabdbcdbdbacadbddbdbaddabbccdadaabacdbadcabcdbcbdddcacddccaadbccbbdccdaacbdbbcdabacdadcaaacdcbaadbdcaacacabddbaaccabddcbabaadbbbcaaabadcbbdcdcbbdcccaaddacabcbbbabbcdcacbddbbbddaaccacabaadcaadbcdcbbcbaccaccabddaacdbdbccaabbbababadcabdacdcaabddabddababbbdddbabdbbaacacdbcabaaccbcbbddadadabcdbbdcbccddbaaccacdabdddadcddbdbdbcbdbadacdcbbbbddadbcccbdbbcdcbdbbabcadddbcaababdcbddaddaaccdbdaaddbabaddcaacccbbdaaacbdcdccbbbcaddbbbbacbbaaddccabbbcdbacbaddabbcaccbcbdcbacddbdcddccaaaddadabddddcbcbcadaabadcccddcddbabddbcacdaacddaccddabcdaddaacabcccddccbdadccccacadbaddbaccbcabdddabbcbdddcdadbacbbabbbccbabacbadcabcdaddbdbdabadbbcadadcadadcbabcbdadcddababcaacbbcaccdcbaacdaaccdabddbbcadcaaccacdbadcdcbccdccccdcbdaddbddcabcaddcddacdadacbdaacaadbccdbcaddcbddbbdaaacacbbcdcacabacbaaddaacbbcadbdaddabbdbaddddcacbdacdbdcacaddcacaddccaaaabaaabcbdcacbcbdbcabdccbaadadcdaacdaadbbbadbcabcbabbbdccbdddbccababbadaabbbdbddcdadabcbcacccbddcacacbcdcabaddbcccdddadcabbbbabbbaaaaaaabbbcbbbabdccabaabcdaacdadaaaaadaabccadcbddcabddcccdbaaabadabdabbaccbcbbdccadaddcbbaaaadaadccbccdadacdbaabdadaacbdcdccadbcbaadadbccdbbdcdbccbbdbbadbbaabddccabdabccccdcdddbacacabcaacadbcaacbabdcddddcdcdbaabaadacbbbadabbbbaacdacadbadddbdccdcabcdbcdbddcacaaccbbbdcdaaacccdbddacbadcabadadbdadbdbdcbcabaddbcdbbaccbbdabbcccdbaabadddadbcdcaddbdcbadcbddadcbbbbbadaadcddacbbdcabdbbaacccdacaccbbdaacddbdddbbddadcabadaadcddccabbababcacabccbbdabdbcabadbbddaaddcdcaaacbadbdadaabaacbcddcbbbdbacacdbbcaacadbadbbbdabdbadadcdcabadbbcbbdacacabdabacacbbacdbadccbbaccdcabbccbbaccdddddcacbcacacabaddbaddbdbadcdbacdcdccccabaadabacadadcadbbdadcdadabbdcbbcdacdcbbaababdcaccdddaacdbacacbbccdcdccbbabddbdabaadcccccdcbaabaadaacaaaadacddbadbcbcbadbdbcbdbcbadaacdbdaabbabbcddbddbaccaacddbbcacbbaaadbccaaadbddaddcbcbaddbaacbaaadccbbdcbcaaaaadbbdccddabddbbcadccddcbcdbbbdaddbdbcabcdcaabaadcddbbaabdacddbddadacdccddccbdadabcbbabaabbbcabdbabdacabdadbdbbcccbdcaddbcbcdcbaddaacbbbbcaaadcddbbaacdbcdbbbaacdcbccabababdbdcbbcccdddacacaccbabdaabbddbbadaabdcdbdacabbcbbcddddcaacaadddbbaaaadadbccdbdbaacdadbdcbbcbabdbacbcaccdacbaddaccdcccabccadccbdaadbacdccdccbabbdcbbacddbdbbdcbbddcdddabdbddccaadcacdbbcadbccdbdbcbdadddbccddaacddcbaaaccccaccbbcaacdcbddacddbdccaadcdadabcdadbcdabaabbaccbadcdbdadcbcddbdbcbdaddaddddccacbccbbccbcdcdbaabcbbaacaaaadbcdacbdbcaddbcddbdadabbabdacaddbbacadbaaabbcaccbbdcdabdacbacddcdbbaabdaadcccacbcacbdabaccdcabcbacacaadcadddabcbbccdaaadaabbdadacbaddadcdaacdbbdddbdbbcbaabbccbabbaacabbabddaabcaddcadcbcadcccaabdddcaaaddbbdccacbaacbdddcbdbbcdcbccabadadadbabcddcccddaababbacdccacdcdcdcadbacacdbdabaacacadddcccabddbbcacbccdacbccbdbacabbdacadabbadbdababbddadbcdbbddcbbcdddbbddcdddbacbbddcbaccacdabacbaccdacddbdadbbbaccbaacbcacdabcadddbaddbdaddadbcadddacdcbbbccbabbdbbccdddaaabcddaabccaabcabdbdaacabcbdbbbacaadcacbcbabaddcadadddcadcbbdabcdccbbdacbaaaccdadbccbacacccabcbbbbbccadbcabdcddabbddbcaccdcacbbaddbcddbcdcbaccbacabbabcbdbaccacdbbaadbddacdbbbdaccddcdbcaabbbbbaccacbaabcbbaccaacdabcaababbccacccdaccdccdcdccadaadcabbddabccaadbdcbcbdcabdcabcbbabcccdbabcaddddbbdcbbcdacbbdadcadbdaaccabbccccaccbadaabcbacbcbbbaadbadcddddbdbdcdddddacbabcdddababcbddacdadaabdbaabcdcabaddadbacdcadbbadcccddaadcddbbbbbbcddbbcadccdbdadcabdbdcaccbbabaadaddccabbbdbcaadbcadccdcdaccaaacccccbbccdaddcdbbdccbcbbabbbcacdaaabbaaadcaddbddbadcbbddbacccaaabddbabadacdaabcdbaabcabcadbbcadbbcddcdabaadadcabbbddcbcdddddabcbdabacbdddcdacdcabcaacdaacbbbdccddaabbcbddcacdbdbdaccddabdbbcbabbdcbbcabcdacdcccdbadbacaccdccadddbcdababcddddcbccddcadbcbbcaabbababbddbddbabaabdbddaaddcadacdcbadcdcddbbadcbadacdbddbddbdcdabccadbccdbaadbdbdadddcccabccadbcdbddaaaaaabaadbdbcabcabbdbbccacabddccaddccddcdbbadcccabacbcccdcdbacbaccbbaddddcdcdbcdacddbcacbcbabcaacdccdcaaccabddccdadbabbbbbadcaaaaddacaadaadbbcddccacdccccadddaabbbaabddbdaabbcdbdddccaadadbcaddbdbddaacddadbdbacbabcbbbaccaaccbacdbbbabcaddcdaaadccbdcdbdaacddaaaabbbdaacdccbcacbaacbcbbbcdabcaddbdabaabbbddbdacbdbdddaacbcbacdacdbacbdddaacaddcbcacbaacbdcadcdbccacadabbdcbcdacdbbdbbbbbacddcdcbabdddaccdaabdddbdbcadadcbbcdbacbabcddddacbabdbaaddcdccbbaadbcdcbacdcbdccbdcbdbbbcaacdbccacdacbbaacbccccccadacbadaabadbcdcccabcbadadaacadcaaacbccadccbbdbdcdabbdbbabaabbadabaccdbaaababcbbacbcdccccaabbdbcbbaccbaacccadadcaaabdddcababbcbaddbdbacccbdaccacbdcdaacccbaddaadbacdaadcdabccbccdccadccbddabbaaacabaadbdbbcbddcaadbabbddcbbdddcccdcacacbbdbdcccaacbbadabddccadbcbabdcdbabcddddaaabdcaadbdcacdadbadabbcbcdbddcadccbadcdadadabbaccbccadddbbccdcbdadabcaadaadadabdddadcbdcaabddacbbcadcaaababdcaabacdbaadccdcaccacddcacbdbaacdacadbbdcaacaabcaabbdbbbaccbcbacbdadabbdbabcbaadbabcacbacabccbccdcdaddbbbcccbdadaabcabbdcdaaaacacbddddddddccbbabcadbcadacddcbcaddacdcbddcbbacacdbbacdbadcbccbcbdaadadbbbbbbdbaaabcbdbaaacdcddaadbbabcbcaaaabdbbcabaacaacaadcddadbbbacbccdcaaabbadbddacbbcccbbacabcddaaacbacacbccacddccdababdcbabddcbdddadbadadbdcaadabcbbaadadddbdcbdcdadbbcabbdbcdcaaccdadbbccbabadabcdbbdabadacbbdbaacddbcbabbaccaadabacdcccdbdbabaacbcbcdadbabbccddabdbdcdcddbbddacbcabdccdacacdaaabbabbcbcdbdcadabdacacddcbcacdbaabbbcbadbcaccdddcadbadbcdbcbdcaccaadacadcadbdbabacbdcabdbbcdcbcacacbbadaccdccdccabdadbbbcbcbadcaacccabcdadbcbaaaacbaccddcaadbcdcaadaaadcdccdbbddccacabcdaacbddaadbccdaadaaccbbacdabacddccccabaaaaccacacbdababaddcbbaaaddcbdaaadbdacabdbadccbbbbccadbacabbaacbcdbdddcaabdcccdbdbbcdbaadbcbacbadbbcadbabdcbdababbabbdccaddbbaddddddcadbaacacaaddcbbaaccbbbadcadadccaacdcaadbbbbdaccbcbdaacdadbbddacacabcabbcdbdbbacbadabddbadabbbcbbacaacdcababdcaaaabaabdbbbdddbbcdcdaddadacacdabbddacaddbdcdcbbccbddbcdbaabbcabccaccabacacbdddbdddbdcbbaddacddacddcbaddadbcddabcbcabadbaccabccbdcdccaadddbbcabdabdacbbababbcbbdcacddbcbcadbbbcacdddbbcccdcbabdccbdbbdbccbcdccddccaaddcddadcdbbbcdaabcdababadaacbbacbdddaacbcddddcccbaddbbaabdbddbcadddcabcddcbacbdadbccacddcddbbddabcbbcadcbcddbabacbacccaaaadaaaacacaadbddcbcdddaadcdbabbcbdbacbbbabadbdabddccaacacbcabccdbdcbacdbdabbcabcccbbbbabacaaabcaaadabcdcacbbbdcbccdcbacadbdcbbccddcdaddccaacbbbccabadcdbcdddadadcaaadbcdaababacbaddcddcbdbcacabccdbbddccbbcabbbbbddbbcadcdbcadddcbccbdddcdacddabdbcddcdccbaddadbbaacdcabcccbddbdbbcccccccabaacadbcbaddadccaddbacaaadccaacbdcabaacdccbaadaabcdbccaddadbadddbabdbdabcacbddbdadabbbcbbcbbbcdcbcdaccbccbbcdbdbbcbaccdcbcddacdccddbdabacccdabcaabcdbcbccacddbaabaaccbbadadcadcdbaaaacdaaacbcbcbbabcaaabbaababcbbcadcabbcbbacdcbdbddaccaddbacbdbabdbcdabbaabcdddcacddbccbaadadccddddcbaacaabbbdbabbcdaccababdaabdbdacbbdcbbdcbdcdcadbbdcdcdaddddbdbdcccacdadccdbdcbacbcccbcddadcccccabbbccbabccaacaaacdcbdcabaacabbcddbabcbbddadcbdbacadacbdaadcaadbabcbbbcdabdadbbdbcacaaaabbcdbcbababcabaaacbccccddcbacbbdbcdabaaccdaacacbdbbaaaabbabccdcbcacbbbbbdadcccdaddddcbaabcbdcddabcadbccacdddcbacdccbdddcbdbbbcaabcacaacdaadcbabacdbdcbcdcdbacaccbbbcbcacbabacddddbabddaacadddcbccadcbdccaadccacbccadbdbadbabbcbacddbadcdccababcbaddabcccadbbaaabaacbbcaabdadddcbbcabaaadbdadcaaaabacbdcbbddcbcadaccbdcaabcbbcdcaabbccbaabccddbabbdddbccadacabdaddcbcabbbddccdcdadbccdbcbddcbbadbabdbabdadbbadadaabdcccdcbacaddcbbbbcccdcccdbdbbcddaababdcddabddbbcddcadadaadabbadbacdaabbaccbcbddcccadabcdddbbaaddaaadaadcddbdbadababcaadbccbcccbabacabaacbaccaddbbbdbcbadbbcccccddddbacdcddcdabdcacdbbaaacbbdbbdbaadbbbddbbdbdcbdccbcaaacdcdbadabbddabdcaadadabccbaabdadbacaddabdbadbddabcdaaccaaddaaacddbddaadcadbdadaccaccbbccdaabadcadaaddcbbaabdacbddddcddaddadcdcdcccdbaccbbcacaabbddbdaccacabcaabdbacacacbdbbbbcaacbcbbddbbaabbadbbdccbdaccdcdcbadcdbadccdbcabaaaccbbdddaadccdbbabdabdcbbcbddadccdbcbcaaabddbbdaaddbcdcccdccaadddbaabcdadcdcbdbdacabbccdcadbdbdbdbdadbacdbcaddcdccdccabdabccbadbdbaaddcadcbbadabcdadccbdaddaacbddddbacbbbdabaadacdadbbcdddbcaddcdabdbbbbcacacaabbcadabdabbcaddacdabacdcabbcddabadbcbcbbacbadacbcabcadcdabbadcdaddbaabccaaaddcbdddccbddcabbbbdabbbcdbdcdcdcdaacacdcababcbddadabbdbdbdbcaabaadcddabadbabcdbaddcccbadbcdabcdadbbbcadacddbaacabcaabdcbaddcdcabdbaadcdbbdabcbaababbdabddcdacccddacbcaddcdadcbaabacbbbcbaddcbdcbcdcddddcacaccdcacbaccccdccccacbcabbaaabdbcdccddccdccdbdcaccbababbaaaaccbbdbdddbdccaaccabccdddddddaabdaadadccdbbcdbcbcdcbbaaaddbaccddcacacbabccddddbbccadbccbdbbcccacbadcbbabdacdacddacaddbabaadcdddcbdbabddcaddaaabccdcdcbddbbbdcacdcabadcbbbdcabcabdcbddaccbddadaabdcbcbcdabdaccbbbccbbadcacbaaaabdcdadbbcbbdcbbcacabccbdbbcdadadbdadaaacccbdbcbcddacdcbcacccbbdcbcabccbcbccbbabcadbacabcccabbdcdccadddcdbaccdcdbaadddbdacbbcdddbcabaccdadadbcaddbbabddccaadabaaddaddcbbbabaa