dbccadbbacddbaadadabbdddcbadacabcbbabbdacbadddcabcccdacbbddcbbaadccdbddadcaadbdbcccbcbddadcbbcaabaddcdababbaabbaaababcbcbdaaacadddddddbadaaccdaaddccaabccccddccaadcbacdcdcabccaacbbbcbccbddacbdaaaaccbddbcababcbccabcdabcddaadabcbccbccbacbbacbdbdcdaabbdbabbbdcbacadddabcabdbaccabdabcacccabccdbcaddaabadcbbdaacbdaadbabcdbbbbaccdacadaabccbbbdbdbaadcccdcdbcbbacbddcadbcccdcadcddcabbcabbbdbdacddababacdbdaabdbbbcdbaccddcadadbbdababdaabcbdcddcabcabbbcadccdbabbbcadcadbaacadcdddcbbbabacddacdcbbdbabbbcadadaaabbadcadddbadbbbcaddbbbbaddcaddcbdadcdabcccbaabbdbadabcdabdaaabbccaadadadcdbbdadaabcbbbaccadcdbcbbcbcbdabdbbdccdbabcbbdcabbbacaaccaaacddcbcadbdababcacdbacacddabdbbdbaddddbdddbacbddcbaddcddbabddbdbaaadcbaddcdbdacadaddcaabbbbdbabddcbaabaabdcbabbadaccdccbcabdcadcaadadadbbaaaccddddacccbdbdcbbbabcbdbcbacdddddabdbcaaabbbdbddabdbcbbbcadabaddcbccaadcddcbabadbadaaddacaadaddadbdddcbacccbbcdccbcccbdbbdcadabaddcaaacbaddbcaacdcdabccddacbdbdbccbdbbcadaddaccdadddaabcdbcbabcacddccabacababbaccdbaadacdcdcabdbcacaaddaddbcddbcadcbcddcbcaadccbdcbbddcbdcddcbcdaaaadbabbbbcccddcddbbbaabbdcdbcdcccdcaabacaaabcacddacdbbcddccaadbccbcbcbdcbdcbbdcabacbccbabadccbadaaabcabcdccabacccdadbcaddadaccaacdbdccaaabbbbdbccbbaccdbdccabdccbaaaddccddacdcddccacbbbcbcdacaadbdbccdacbcdacbccbaaadddcbadbcdbcddcaaaabcbbbcacbdacccddddaddbddcddbbbadcaacbcddbbaccdbcddcaacdaaadcdddcbccbaddcbbabcaadbaddabbcadbbacabddaddcbdbdcabbcacdcbdcdddcdcdaadbaadbdddcdcbddabdaabaaacbdbabddacbaabdcdbdcccbddcaccccdbdcdadbabbcccdadaccccbdccaababcdadbbcbccadcbcdbbdddadccdddacdddddcbdddadbaaabdbacdbbddcbcddaaadccadadcddccbbdcacabcddcdacbaacadbcbccbadaabbbdcbaadcbadccccdadabdccdcbabbadbcacdaabbbcddccdcbaabdacabacdcddccbbddddbdadcddcdadccdcdbbbccbdacbbbacbcababdcbbdaabbbadaaccabddbcaacddbcadcdcaaadaccbdbcadaaadbdcddabbabbccdcbcdccdcdbdbcbcdbbbacbdbbbdcddaacdcdbbbcccbddaadacaadcdbaaddbaabbbbbdcddabcbcadddabbcdabbcadbbdbbacbbdbabdacddbdccaaadbababaaddbbaddacadbaadadbbaddcbaadccdababbcdbaaabcacdbacbcdbaddccacdcbdaacbabcaacdcacdbcdcacaaccabbdcddaddbcbaadcabbbbcbaacadccdaccbcdbbbccddadcbaacabbabdaddcdbaacabcdadcadbdddbccccbbbbdadccabbcbadabbbbaabacdcdabbcbdbcdbdaddcbdccbaaaddbdbbaaacadaadbaaddcbccbdbdddddcdadcabcdaaccdaadabbcbccddbbcabbdaaaccddaaccaadbcdddabddbddbdbdadaadbccbbcccbddddbbcabbdcdbdbadabadaadbaddddaccbacaadcdcdbaabbcdbdddccbdcbbdbdabdaaaddddacaaccdaacadcbacabdcadcdacadbddbcbabdbbbbbbdaccdaacaddddadbccdabbbaacacdcbacbabdbdcbdbdbcdaadcaaaadcdcadbabdccbdaaaaadbaacdaaabbdcbcbdacaaddabbadcdbdcccaccbcaaadacaddbbddcaabdbbbadabdcdbdbdcdcbddccadbdddbcdcdcaacaadaacdddbdbbbccaddcbcdbdaabddccabdcbabcbacbbadacbababddcdcbccacbdcaaabcabbdadbaacabccbacbadccbdcdacbbaabddddbcccadaaccaaccabdbcbcaddaddbbbcddbacaaddcbdbbbcbddabbcccccdccacadccdbbaccabaadabdbcadbcadbbaccabddcbbbadbccbbcabdbbcbdaadcaccbaabdcdaabadadbcdbaddabccdcbdbcdcbdcabbddacbdaabbaacdadadcabdcdcaabaaabacbaadbadbbddabaaaacbdddcacaaaabcbdcadabcbcabcaabdccbbdbbdbbdaaacbccaccdacbbdadbcbbbbcbbabdbcbaddaaadabbacababbdbdbdcdbdabdaccaaabcccddacddacbbaacdccbbcdbadcddbbdaabcadddadbbddadcaddabcaaacabbbaabcbaaccdbabbbbcaaaccaaaadbbcbbbcccacbaadbbbcabaccadabccccccccddddacbdaadbcaddaaddbdcaccadbdddaabdcbccbbcccbdcacdbadbadbbdacdbbabcdbdcbcadcabadbadadcdbddcbccabddabcaadcbcaccbadbaabacdbcabacccdcabbaacbccbabadbabbbdabacadbdbbcdabccdbdbdabcabcdcdcaadcdcbbccddccabcddcbdddbcbbdacaacbdcddcadccbcbcadcabbdaadadbcdcbcccbcaadadacdbaaaaddacbabadbadccadbcaddccdbbadaacbbbcabbccdbbbbdcaabbbcddcbbbcaccadcddadbaaaacaacdacdbcbddbbaabdbcbdcbcbbcdbadbddbbcbbcccdcbcaaaddabbaaaabadaadcdacdadcdbbdbddabcbdcadbadabdaabdaadbbdbabdaaaacabcbadccbdacbbdcccccddcbccdadddbcabacdbaaaacdacabbbbccaacadbaabadcdaabbaccbccaddbbabbaccaabbddadbddcbdcaccadbdaaacbaddbcccbcdcabdaccdbdaacadbcccbbcdaadddadbadbadcdddaacaadabbdbcddddddbcdcabddaadbdccabcbdcdaacbdacbdbcbcdbccacabdcadaddcdcdabbbcbabcdaddddbbbdbadbbdaccdbbbdbdbdadaacabcadccacccaacddbdbbcbbccddacdbaaacadbacdbcdbadcadbcaccddbaaacbdcccbbdcbbdaaabdbcdbcdcacadbddbdcbcdddbddccdbaccdbdbbdddcbbbadcadaaccddcccabddcdcdcbdadadbcababbbbacddddcbcccacdadcdbabcdaadabdabdadccabacdabbbbcbdaaddbbabcbdcacadbaadbbddcbcdacabacbbccccdbdcddbaaddaddccabbadabbccbacdacaacaaaaadddacacdbbcbadbaabaaaccacdccadbdddbcdabbdacdccdbbabbdcbcacdadaddcadcdbacaddcaabdbdbabdcbbaddcbcccdaadbccaacbbbddddbccddddaaaacccbbbccdacabcdbcadccbabcdbddcdaccabbbaccdccbdcbdaddbbddbadcacdabacabcdcbdadcccadbcddaabddcbcdccbbdcaacbdbbdadadcbcbbaccbbbdbcacadcaddddbbcbabcbdcdddddccdaaaabdadcdcbbdccacdbcbdabbccaacdccaaaadadbdacbbdaabcbacbdcabbbdbdaddbaddbdbbbdcdbdadbcacacdacaccbaaddcbadababadadcaacadccabbabacbcdcadcdbbacdbcdbaabdddcbddcadbbbcbacadddbdbbddabcbbdaddcadabaabbbcbcacacadaccbcbbdaabcababcbbadcaddbacbdacbccdcaaadccaccabbcddbdacbbccbdbacdcabdababbacbcdcadbdcbcdbaaadbbaadcdcdaddcccbcddccbbabddadacacbabbdbbadcaabcbbaabccdaabdcaacccdacddddddbbddaabbcddbacdabbaabcddbaaaacbcaacccabddbcabbccdadbdaabbddddbdddcadddbdbbdbacdbcaaadbadcaabdbdbdddacaabbdababdaacccabdddcdbdbacbabacdccbbbbcdcccccbbbacccadbcbadbdddaaaabccabcadcabcaddbcccaaaddbcbcbabababcbabaaaccbdbcbbdcabdcddcdcaadbdccaaacdddacbacdbaacaabdacdbdbcabbabccdccddcadbbaaacbdaadadaccacbbcdbcadbdaadadbccbcaabddbbdbddcadccaddaacccccbbbccdbddcccdddddbaaaccdbabadcdbaddabbbdbcaadcbddcbbcadcdaabcccaaaadbcabccbaacdbadbcaacbbbdbccaabcbaaccbabdcdaccbdaadaadadaaaddadcadbcbdcbadddcdccbdccbbcdccbcbdbcbaabacabacadcccadaabbddacbbdcbbccbbaabccdaddddbaacbcdddadccbaaaccacdaccccbcdcbddbdcbcccaaabadddabacbcdcbbadcdcaddbddbbaadcaadccacdcbabdcbcabacbdbdbaaaddcddabbbbbcdbdbabbbcbcccbdadcababccbdaaaddbacbdaccdbdcaccdddcddcccdadbaacabdacbbaaaadcabdabcbdbbdbaaababbaadbadcbddcccacbcdbcabadabbddacdcdacdaadacdadcbabddddcbcabcdadcdacadadadccbaabbcdbbdcaacdcbdcbdbaaabacdbddbaccbbaddbcdcadcbcddbacacdaacddbddadbbddbaccdddacbabdaacbbbcacbddbccbbcbcabdcaddbdbcbbaccdbbcbdabacacdcabcaadddddabbddbbadcbdbdcbdabddcdcbadadbcbdabacbbcbcdacaadcbcdcdbddaababacbbddaadcaaaddbbddadcaddaccaadadccaabbbcadcdacaacadcddccdcbababcddbdccbccdcdbcdcacdbabbbabacccddccdaaacdbbbbbbdcacabdbbccabcbbcaacaacadcdbabddaaadaccdddbadbbcadaddbccbcabcabdcaaaccdcdbbcbbccabbbaadaccddacdbcdbaabccbaadddcaaaaabaadbcccaacacccabaddbccaaaacabdbcddadddbacdbaaaaabdcbccaaacccbbbdbcdcadcabaabbacbaaddcabacbaacdcbabacdabbbbcbcadddbaacabddcdcdcaadaddcaacddaccbbbccdddabaacdbaabaaaabcbacbaaaaabbcabdcbdcaababcaaabbddccbabccbabacccabcadadcadaaabcacaaaddddbcaaddcabdddddcbdddaccbdcabdacaacbcdbaabbcbaaaabbddabcbdaaaccaaccdcbbcabcddacccccbdcadabbccdddabcccdcacbdabbaddaaaacacabdaabbdbaddbccccdbabaacadcdcdbbbdccbacccdddaadadcaddaaadadcddabcadbabcdccadabcdcbabdbcdbbaabbadddbcccdbccdddbdaabddabbddcddbdbdaddcbbcbbcddadcbcbcbcdcadcacdadbccbbdccdabbabbaacdcacbcccadcababbadaaababbbddabdabacadcdcbdbbcdacbacdccacdaccaaaaccaaaadbbddbddadaccadbaaadbdbaacacbbdcbbcaccabbbbccacbddbcadccdaddabccaddbcccccbabbdadbbacccdacabbcddabadcdaaccdabbdcdaadadcbdbadacbbdcdbaabdcccaaabdababaddadcdccaddbbbabadcccdbaaacdcaccbbabaddcbbaddababdacdccdbddbcdbdabccbcdddcadccacacccadadcdbbbbdadabbabbcbabdbaddccacbcbdbdcddaccbaddcdcadbacbaddabaadadccbaaddbcdbabcbdabddbbbaacbbcdbacdcddccdcdadbcbbadaadbbacbdacbdcbcaccbdbbbdbcddcbbcabcccccacbaaaacaddcdcabdbbbdbacbbbbccabdbbbbdadacdddddcbcdadabccbcbadccdcbbadddddddbdcdaadacababcbadaacaadcdabbbcacbaadcabdadcdacbadcadbadcddbbbdbddccdaddcbbdccaabdbdddababcbdaacbbccdadcdcbbbabbdddcdcdbcbbbdddcbbdbcbddbabbbbcbaacdcbccaccabaabadaacddcdcdcddbbdccdcbdabdccbcdcbdbccbdbcaacacdcbabbdbaacabbbbbbabaddabdddbccdabbbadbbcbdbccacccdcbddcddcddbdbaddbbaaaadbdcdaacadadabbbabdaabddbcdbcbddbcbdacddadbcdddadaacbabdbadabdaccdacaacaaadbbdbabbdadbdacddadbcbabadddcdacddddbacaabdcdaaddbdcadaddcdaaadbbdcdbddcabdacaacaaaccdabbdadcbdcbccbdbbcadaadaccaddcccbcdcdcaddadccaddbccbbccddabbaabbaadddccddbcbdccaddcbaccaddccbadaadcdcaabdcbcdacbbccddaccabaadbbcabaaaacdbdcbabdaaddbdddabcddacbbadcabccccbbcacddcadbcbbcacddadbdacbbbcdbadbdacaaccdddbcbcddacaaabbaaabaddccddbdacccdcbcdacaadbdcdaccdddddcbdcccdddbbdacaadcacabbaabdbcbcdabcaccdccaaaaacdcabbdbbdbcddbdcababccddccaacadaddababddcbacddcbabcddbbbdadadcdbabbdddacbbdabbdbbbddaaccdabccdcaaccdbcabdcaddaabcdadbddabcdbbdcccccbaacbacbdbddddcbbccdbdabacdaddccdaacbdadabcabddabbdbdbcabbddcddbbcdbbcacdacbcbcbcbbdabdacadccdadbcbabbbcbcaaabadcbccdabaccdabbcbdbbdbcadcadaddaddabbbcddddacacaccadccbadaaaddabbcddacaacbdbcbdbcbcddadbccdadcaddaaababdbdcccdbcadabdbddbaaacdbdbacbdaaaddabcaaaccbaaadbaccabbdbabcbdabdbabcabcaababccaccadacabcabcabcdbcdccbccccacbabbcabdaadbcdaddddbddbdccccbdaadddcdddbdacaacddcabaddcdacbbababbccaabbcdaabdbbcddaccabacccbcabccbdaadacadbcbaacdbdbbcdadbcacacdbaacbcdabdaaabcadbdbbacbdcdcabccbbacaddabbdaabccacccbccdddbacdabacddacacdcbadadbadadbcadccabbcbdbbbbdddaaabadadbbaabaabcadbbcbdddbbdcdbdbcabcabcdcdadddcdadbdbcadcacabdaadacadccdcacabccbbaccaabdddbdadbdbdcadbbcbccdddaabbdaddbbbcddcccdaacdadbcbdbdccdacabadbcaadcaadbacbbdcbbcabcddbcdcdaacadcabbabadbcadddadbcdbdbbbababcdbadabcccaabbabdacdccccbaacacdbaabacdaaadbbabdbdadadbbdcabbdcbbaababbccbdcccdaababddccbaccbdbbbddcdcaadaccddbdbabbabcbccdddbabddcdaadbaddaaaadcbdbadbddbbbcbbbacbbaadddcabcbbdaaccaadbddbddbcbcaadcbdcdacdcbbcaddaaacdddbbabaaddadbbbadbaacdbdcaabcbbaacadbddabaaddcaddbccadcdbdccccbddcdbacdddaccbdbbcaaadddddcdaddcbcbbaacbddaaacdcbaaadddbcbddcbbacdcddbbabcadbbacaabdabcdddbabbaccddacbbdaabadbbcaaacdbabaaadcacbdbbadddbbcbdaabcbdbaabddacaddcdbadcdabdbabdaddcbcddadaccddaaaccdbaccbdccdbbdbbdccaccaacabbbcaddcabcdaadcacacdccbcdbadacaaadabbddaaddcbcddcdbdcaaccddddcaaccbbdbbdbcdddddddbbaacddcdaddabcbddbadabacbabdbdcbddbbbbbbcdccacbcdcaaccaabdcdcdabaacdcbdcabddadddcdbbbaacdcccbcabcadbaccdbcdadddcdbcccacdabaabaddcddccbcaacbbcbdaaabccacaaddcacdaaacccbcbbdabbcdbabaabdbbcdbcdbdcbadcbdabccadcbdabcaabcdbdaadbabcbaadaacccaccddddacbbdbbdabadabccdcdbccbccadbbccbbdbaaabdacddccaadbacddbcdcbaaacaaadbcdadcdbacadaacadaccbbccbbbaddcacacdaadaddbdabacbadaaddaabcdbabcabbcadcbcacdbacdacbaaadccdcadbbcdbabbacdcabcddaabddcbdbdaaddbccadcabdccbdcabdadcabbcddccbaacdaaabdcbaccabdacdaddcbddacbddaadcbbdaddabcdddcbbabddcadaaaddabdababcbdadbccddbcdbbabacddbcdccdcbbaacdbcbddadcacaadbbbaabcbacabadaabadabadbcdcaddbcacdacccdbcccacdcbdadbccaadcbccbcccabcbddbbabcccbababcdcdadadaacdacdcdabadacbaadaadadcaddbbaddddabdcabddccdddaabdaabddaddbbbccaaaaaaaacccabddcdcdbdbadcbbacacddbbccacbbdbbbdabbbaaaadcbcbabdbadbaadddcacbaadddbaccacbacabacdcacaabdbabaddccddaaacacacccbbcdbdcbcbdcadbaacaddabdbcbabdaadbcacdbbbabdbbabcdcccadbcddcbdcbadbddabbacbbbbacabbdcaccdabbbbccabcccadaabbcabddddcbbcddddcacdccdbddacdbdbbbdddcbdabdccddcccadbacaaddddaabdbccbdcbacabaddcacbaadbabcbadadbdbadabadbbcdbdcaddbcabdadabdacdbaadbcddcdaadbdcdddaaaaabdaccdbbdabccddbdcacbdbdbaaddadcddacbadcababbcbdbababbadaddccbdbcdbacabcccdacabbcbaccadadcccbaaadcbadbbdbddcdcabcadddbabacabaaabadcacdabdbdadddcacadadabadabccbaaddccccdcddaaacdbcccbcabdbbaadbcadabccdccacdabbbdddcdbadccacabbaabcbcdbcaacaabcbcaddabdadbaabaddcbdaccdaacccbdbbbaadcaadacbabcacdddcbaaddcaacdabadadcccdaccdabbddddbdcbddaaabdacadbbcdcbdbbacdbaddabdcacadcaddbdcababddddbbdaadcbcabaaabaacaaadabdaaacdcbacbabdaccadaccccdcdacdbacaccadbabadababaccdbccbaaabaadabdcccbcdbbbabdcaacbdaacbbddbbadabdcbcadbadacbbdbddcdcddccbacccddaaadabdcdddbbddbabbbbbbaabccbbdbcababcdabacccdcacdbddacbbacdabdcdcaaacbabadbcbbccbbbbbdbddbbdbbdcbaadacdbcbadaacdabcaadcddbacabcdbbdadcdaacbcbacbabdadbdadcbbcaaaacacdabacbcbaaabdacddccccadaabdabbbadcbcccabbdbcabcbbbacadabbcdbbdbbbbaadcbbadaccbdbaacdaaddbcdadbbaadaaaaaaccacadcacdcdcdccccbdacbacdbacccbcbcacccacabdbcdadcbabaaadaadacbaaabdcdababbacbcddbddbcacccccbaadbddcdcdabcacadcddacadbccdbdcdccaadaaaadabadabacdccbdbabbccccbaadcacaddcdbcddbdabaacadadaadacbdbcddccdcbcdadbcdcacbabacbccdbcbdcbddbdaaacbcddddacdcdacdbdcccbbbbbdbbabacaabbcbbadcddacbacabcbccbaccbacaccbaabcddbdbbaaddcbdbadcddcdadbddbccdcacabcdbbbadccaddcadacdccaadbbadbcaccdadbbbddacabdbddcdcaddacbbabccbabdaddcaaccccadbaacabdcbdccadbbccbcdabdbacdcbddcdbcdbcdcacdaddbdacbcacaadbacaaadbcdbadadbdabccaccabcacbababcaddaaabbaaabdabbbbaacadacbddaacdadaccdcdddbbbdacdddcadcdacaccadbcbbbddacabdcabbaacbcabccbccbdbacaabdcdaddbdadbacaccbbdcbcaacbddabcdbadbccccbabaacabcdcadcbbbbbdcaaaadacbdacbddbcadcabccbddabbcddbbcccadbcbbddbdbbcacdbbdcdaddabaadbcbcbcdaddcddccbbcdbaaaaabdddbbdcdcdccdbdcababacadabababaacdaabbaddcdbdcbdbdcbabbadbbcacaaabbdcaddbdbbdbacdcdbcbbdbaacccccdbaccbbbddababcbcdccdaabbcdddadcadccdcaadadadbcbcbcddadacabdbbcddcacacbbbdbdaacbbabdbcccccadcadaccbcbcdabcaabaadabdacbbbbbdaadbddbdbcaaacccdadcacdbaaadddbdcddacacadbabbbadbdbcddacbdcacadacdcbdaacbbddacbcabdbcaddaccddddcdbcbaacddaaaaabbcadbbdcbbbddddadbdbcacabadacccccbabdcdbbbbdcdbdbaaadcdbcbddaacdabccdaacbabccbddccddccbadcddbdabcbbdbdacdddabcbcdccccadbabdbbaabaaacababdbbabccdcddabbaaabcbccddcccdcdcbbbdccdabbcbabcdadcaaadcabcbbbdddcdcccdabbbddbbcdbbdcbcabbacbaaabddaaacbadcddbdbdacadccdcdbdabaaacabdadbaddacaddbbcccbabddabababcdcababbcabbbbdcabbccbbbbacbcccaccdddbcbccdabababaaaadbddbdcdbbaabcccaacddcabdcddadadcaccabbddbdadbcbbccadccdcadbdcbadbdcdbdadcbcaddabcacccadcdcbacccdcbbcbaddbbccbdcdbaddcadabdddddcddddcbbbaabbbbcaacbbaaddbccadcabdaacaacacdbaacadaaadcccddaddbcdcdbbdbcaacabaacacdbdaccbdbbcbddcdcdacbaacadcdacabcacbbcdddcaadcadaaabcbcdbbaadbbadaaadaadabdabdbccbabddbdbaccddabdcaabddbcacabdaadacdbdadabdbccadddbacbcddabcdaadcaaaddabaddcadaaadbacaabcabcdbaccacadbcabccdddcddabadbdbcdaaaaabaadbbcabddcdaaccccdabcdadbcaaaabcddcacbbcbbbcaaacbbacabcdcadddcabbcacdbabdbcbcccdcaacacdcacacccbabdddbdacbbbbdadcacddbccdbcaccddcabbdccbbaadaabbdccbacbcccbdbcdacdadccbbdacbddcbcadaadcadcddddbadcdaacabbabccdabbabccaaadcdbddbadadbbbdacbcdadcdbcddbcbdcdcbaccadabaaadccadabbbdadbdaabbcdacbaadcabcbdddcacbbbbbbbaabddcdccaabdacaccdacbcdcdcabaacdbadbbdabbddcdddadaaacdddabacadddcdaccddbaadbcdbbdddadbadddbdcbabdaaadcdcccbbdabacbdbbccdaccdababcaccbdaabbaaabcabbbbbdddbddbddbcbbbcdcacdcddacbccaadabcbbaacaadaabdcadabcbcbdcaabcbcaaaddbabbbaccabccacbaaacdaaacdccdbadccbdbdbccbddcbcacbcbdbcddaaaaadbccccaabbbacacaddcbdbccbdbcdbcbcdcddddadaaddbaaccdcbacabadbdbaaaddadcdcddbdbacdbcaadbbccdababccacadcddaccdaadadaaadcddccabcadbadaccdaabaddaaacbcbbabaacbcbabcbdcabdaadacdcbcacadccbcadbbbadbcdacdabbbcdaaabaaadbaaddcdadbaabdccbadcdacdddabbddddacbcacbddabbbaabbcbbdbcbbbaadaadbcdccdbccacbcbdabcbabdaacbaaabadaccccbcdcacbcccbdbacadbcbbdadcbbdaccbdbcdccdccdaadaaddbbbcdbdcdaacabbabaddcbcabbcdbaacabadbcdbabcccabacdddacacaccacdcaccbacaabddadadbabbccdcabbbacbacdccabacaabcadbbccccdcdddddcadacadbdddacaacbddadcabbcbabcdcacbbccaabbccddbdddaddbabadddbabdbddbbdcbadcbadbcccbbdbadccbbcdaacbcbdbadaabdddbdbabadccdaccbbbddbbcdbbacabdbdaacdadccdadbabddbabdcbddbaaacabdbddbbbbcbdadbaabadabcbacdaadcbcdbbdaacadbcddadaadddbacbcddaacaacdbdddcacbbcaccadcaabbcaacdaddaaaadbbcdcddabaaccdcabdbbccdcbaddbcddccaccaacbaddbbcdabacccaaadadbbacbdbbbacddaacbaadacaddabababdabbcadcbbddbaadccdcdadababcdbdbaddbccaaadcbbdddacbddcddcdacaaabacccbdbaabcdbadaabaccbdbcdcaadcbaccccdadbaddadbacabccaccaabdacabdadcbacbdadcdcbacdbccdacbcbcaadbaacdacccddcccdcaacdcbabdabababdbddddaabdcdccdbccdbbcaddaccadbccabdcaabcbacabcccdaaccadccbcdadadacacdbdbaabadddbacaaaabadcddddddbcdcdbddcababdaaccdaabacbaabbcacdadbcacbcbabcbbbbcddaccddbbbdddccccddcbcbcbbdbcdbcddabbbcdbbbdccabbccdcacdcabdacaacdacdccbaddccbcdacdcacbabdadbabcdbaddadacbbbaccbdcdadcbdadcacbbbbaabbddbaacbcbcbcaddaacacbbccadabcdcccbbdaaaaadcdaddabbcccacacbadcddcbaddabcccbcdddddcaacdbdcdadbcdbccbdaadbaaadbddacbdcbaabaadbbbdcdbbdbdbbaaacbbbcbbdddcdabbdcaccdbddbbccbaadbabbdadcdaccdcacdcbabcaddbadaaabddacbcbdcdbcaccabcdbbacbddcdddbcbccccccabaababdbdbaacdacabbdadabccaacbbadaadadadcaddcddbbdacddbddcbcbddcbadbdddbdabbbbccbaadbbdaabbddbdaacbdbcdcdcdbbcdacdcbbddcabaadddacdbdacaabddbabcbbbbcbadaacbccbdccaaddacadcaacdcadbbdcdabadbacbdbaadbcdaabbaabcadabdbddcacbdacbaccddabdababdccaddbaccbdcccacddccdabbcdabbbcbacdbaaadbadddbdabaddbbcdbccccccadacadcbbacacabaddbbaccabbadbacbbbdaadaaadcabdbcaaaddccbdcaadbdabacacdaaacdbcbadcbddddccbcbbbdbdbadbbbbaadbbbcccccdbccdcdbcaddabcdaadadaadabdadbadbbadabacdbcbbbaacbbcbacbddbcccbdbcddddacddbdbacdadadbdbaccadbccabaadbbccdccddbcddddcacdbbbacbdbbccdcacbddddadddabdbdbbacbababaadbccacddcadacccdbcdbabbccbcccabcccaacababaadacdaccdcbdcdbcadbddabbacbdcddadbcbddadbaabccdccaaaaccbbccbacdcbdbdbbacbddcccddcdddcbabccdccbdaaaddddddcbcdbdabdacabbcaaaaccdbabadcbcccbdcabdcbacdbbdcadcdcacdbddacddbacdabdcaddcbdcaddccdbdcccaabccbccacbbadddadcdcbadacadaabcbbdaabbccbacddacdcdbabccaccaaabdcccbacabbcdbdabdaacbbccdccdacabadacdbadabddcdbccaabaabadabbabdbbdcbdacdabaabadbcdabaacdbddcdcdbdcabacacabbacdacdaacadcdabdadbbaaabcddacbaacaacbddaabaddadcdcaacdccaccaccdabaccddbbdabddbcbbdbddaccdccdabdadccbacdbdccdadbadcccbcdddbabcadadcbcbbbddcbdaddccdddbcbcccabbbdccacbdcdddcaddaccbabbadacadacbbdbdaacccaabcbbcdadbbbccacdcdbbbccbcddaabcaccbcaacaadbabcbccdddbdbaccaabcbcdbbdbcddbcabdbbdcabcbaaabacdaadbdccdcbdddaabdcaddaabddbdabacabaddcabadbddddabcabdcadcbccabdbcccaaabdcaccdccacdddbdbabbbcabddcbadcbcdcdbbababddaabacbbbabddccccbdcabdbcbcccbcdcacbcbacabadaadbaccbdaddcbbbcbabbcbaacacddbdaadbcdcbccdcbdacdbdcbacbaadcdacacdcabbdbadbadacdccbacbadaccbcdbdacbaaadcccbbbdcddddddbbdcaadabdbbbdaddacadcbbacadaadbcdbbcbddabbaddcaabaccacbdcdabbddbccdbccaccbbadaddbcddabccacbbbadbdacaddbaabdbcdbaaddacabbcddadaddadabbcacbdcaabccddccdadcbccbcccaabaadccccbbdcdbbdcbdaadbcbacbabadaadaaadbaacbdbadaddcccaddacccddaccbbcacadbacbcdbbdabbbadaababdcdbcdadccdbdaadbcbbdaaacdbaabbcaacdcbaaddadcbbcabddabcbddbbbcccdabccbdadacacadadbabdcbabadbdaddcbddaabaadcaddcacbacaaddabbccdddaadbccddcccbddcbadabbcccddbbbdbacdcababcbdbabdccadcaabacaaadddccbcbcccacbdacbdccdabbcdadacabbddddddcccabcdcaadbaaaccbadaaaaacacbbcccccdbbadcdacccddccbbbbdbbcdbddddadbadbabdbcabaaaddccacbccabdbadadaccddddbaacdbaaddadacbdabcdbacaaacbbbdacbccdcadbcdacdcdccacdcddacbacccaccbcdcbadadbcdbddbadcacbadcddbcacdcbcdccdddbdbaddcbdabcbbaddaccacdaccaabdadcadadbbcdaaaaaddaabbaaacdbbcaaddabcbddddbdbbabcccbbcdcdcccdbacbadbbbaabbdacbcdacaaddbbdddcbabdcccaadbcbccababccbacaadacdbbdadcaadbacdbacdbcdcdcaacbababcbaccabdabbbbdabbcddaaccbbababcddcaddaabdacdabcbabdaabdabccabbddaacaccdcaddabcbbbadacbadcbcbbbddbaccaccddadbdaadbdcaabadabccaaabbcacbbddabbcbbcdaddcbdbcbdbcdbbbbcacbcbccdaadbbabbbcaaaaabbdbacbdadcaadbcabdbcadaaabddaaaddadadadbadbcdcdacdadaddabdabbdadaabdabbdaddcabacdbbdbccabbdbadacdcbbcbcbdbdbbbddaccdacabaabacdddacaaaaabddcbcccbaccaddbccadddccbbdadbbdadaddcddaccaddadbaadadacbdcacbccdddbbcbbaacacdcbbccbbbddaaddbcbcccbbdaadcbadbaabcbbdabbadadcccbbbbddcacadbdcaccccaabccdcdaacccabccadbcbacddcaacacddcccabbcdcbbddbcccacbbcbddbcdbcaaaabdadccccddcaabdbbccbcaabddbcccacacaacbdbadcbbacbccbcdddbacacbccdddabccdbbcdbbbdcbaccabaacdabddcdadbdbabcdcdbbddaacbaddaddbbdbccbccdbbbaddcccdcdddbdabddcdcbcababadacdaabbbcddddcadcbbccaacdacddbdbbcbbdabaccbdcbbbabdcbccbbdbddcddacdcaccabccbacaddccaadcbbadacbdbbbdabdadbdcbbbaaccaccbacaabaddbccbbdddcdbcaaabdaadbaccabcccbdaaadbcadccdacbbcccaadaacabacaddcabaacaddccbccacccbcbdaaddbbbabacdcbdddcbdccdcbdaabaddcacccdcdcdbadbbadcabcdcccabccbccddcbacbbabdadabaadccbdcdcbbcbcdbaadcdacdabccccbcaaabbbadbcbcdbdcabcbabddbcdcbabdcacbabbbabcaacabdbcabcacdcbbdacccccaabadccbbaccddcbdbcbabcadcaadbaaacbadbcbacbbdbacadbbddcdcbddaadabbbccabbcdcdbbcdbccbaadaabbaabdaabdbdadbdacaaabdddbacbcabbccccbcabacbbbddbbacdbdcccabcccabbacadcbbbccdddaacbbdbabddcddbaccbabcdaddbdccbddddcaadccbacabdcbdbcacdabcddccbbacaddbccdbbabcdbcddadcadacdabbbcdcadbacbbacbdbdaadbadddbabbbacccdcbccbdcabddaddadabdccbdcacdbcaaadbdddabaaaddcbcaadbbdbadadddadaaddbbbdbbbbbcbbacbacddbddabbdbdabdcccbdabacbadbdaddcddcdbcbacdcabbaaaacabdcdcadbbcdbcccddcacacbdadaabcadddacdababbbcccdbdbbacacdbadbdbbcbacabbcacdacaddabbdacadcccddaccaacbddbacadbdccbddbacbaaacaacdbabbbacaadcdcddcbcacadddddcbdcabaccbddbdbcdacabaabaadccdbabaacdbbcbccdbbcbcabcbdcacdbadcdddcbaacbbbdbbbabbddcbdaabacacabaacdacbadcdcabadcaacdddacddccacbbadadccdbbacacbaccdccadcbcdaabcdcbadbdbdbcdcbcadacdbdcabcbcdbbdbadaccdbaddabdabbcddddddaaabaacdabbddadbacaaddbcadadccccacbcdbbdaddbbbcdaacdbdbdadbcdbabbccdbddcbddcabdacabdbcbbbbcccbbdbdddbcbaddbaabbbdababccccdadadcdccbbcbccaddbadddcdcddacabadacbbccaadbddbbcbdbcbcadcbbbcacdbdbcbbbdadaacacacdcccbdbaacabaddadcdcbaacadadcaacbccbcadaccdcdbbcadbcbddadbadbccdadbcbdcdbbdacbcddbdabccbbbccdbabcccacaaaabacdaaadaaacdabcaadabbbcbdbdccdabccbbbacdcbaabacccdbbdcccdcabcccdaacdcbaadadadabdbcbbdcbbadcbaabaaaaccbaaaccdaaaadacbadaadcdcbcaaccdacdddacddabcdaacaaadaaacadbdddccdddabcdacbbcdbdbcaacacdabadabadaaddadacadbcdbbaadbdbdbcbcaacaadcaaddaaaaadbdbccaadcbcbbdddbbbcadccadccccabbdbcaddadbdddacddadcabbdccbdcccccbcdbaaccccabbdbaabcbdacbbadcdccdbacbabbdcdaacbaaacabdaacbcdbadaaacaaddaabadcadccddaaddbddaaaabbbbdabbadcdbbdbbccacbabbacadbadbacbadadadddadcacbaadbaaadcbdbaacabdcdcdbcccdcccdaaabbcdcaacccbacadccaabcacaabdcbaddbadadacdbaacabbcacbdacacabdcbacaaacdbbaaaccbbbdbbbdddddbcbaacccabbaadabbbcbbdbabbcadbbbbadcbbadbbddbbbbcadbcdcdaccdaaaccbbcbddbcddadbaacaccbbccbadcabbbacbcbcdadadbddacdcddacbdcddacddcccbcbbbbbccaaccadcbccbddcbddaaadbaabaaaabbabcbddacabddbdaacdaddbdaaacdbacdbcddadbadabcdcbadbadbcddbcdbabccdddaadcaaddbbbabdbdcbaabbabbbdbbcddddcadbbabbbaaaaabdaaaacdacbbacbbccaabbaadbddabddbbbabbccacdadabcaaabbaaaaaaaaccbbbcbdbcbcbdadaccaabddadabddcdaabaccdbbaaadbdcdbdcccdcdbaacdadbacbcbaccaabcadbdbddaaabddacddccbcdabccabcdabcdadadacaadbbbcaadcabaadcbccdddccbbdbbacbccbcdaccccdddaaddbdbbdacbaccacbdbdaacabdbcbbbbccdcccccabaaabbbdaccbcadbbcdccbacdcaaddbbcbbabcdaccbcbbbbdcaabbdcadbbaadbbdcbdddbbbabdbdadbaaddbaabcdcabbdaccbdaaabaadcadaddbbacdcaaccbccabbaadbacbdaddadcdcccacdcdaadbcabccacdcacdabddbdabacbbdccacdccaaadacbbcbddadacbbcbdcabcccbbabcabadddbadddbbaacbbdbbabbcabcdaddcbbcdacaccdbccadbadbddbabdbcdbbbddbadadddddbacbabaabcadbcdbaabcbadbcccbbbaadcbdcbdbbdbdaadbcabdddcdcbbdabdcaccccaabcdcbbcbddbcacaadabcaddcbdbccbcbddbbbcbcccaacdbbabadacacbbbbbaabadadddaacdbcabbdadcabcdcbdabdccbaccadbaccdacbbabdcadcabbaaacbcaaadaadbdcdddccbacccadabcbaddbccbaacaaadacddbadabadadccdadcaacadacdcadcbaaadabbdabdddabcdcdbcaadddaaabcbbbcbaacbccaabcbcabaddcabbdbbbbbadaddcdcdadcaabbcbcddccdaccbaadbdcdabbcadcbaabcdcbdaabbbaddbadbdcbbaaadbbdbaaddabaadcdaccbadcdacbadccbbdbdcdbdabccaabdbcaadccdbbcacdddcbabdcdcdccacbccabacabccaccaabdbccbbdbdcadabdacbabcacdddabcadcdcacbcadcaaadacacbbccbbbbddbadcadbbaacbcdbdabdccdabbcbaabcacdacabadcbdacccbcadddadcaccaacbcaacacddabcdccbddadaadbddccbdabdbbbdadaadbdcdbbdadbcbddcacdacdbaadcdabdcadcdcccbccabddddaabcaacadadaccdbbbcdaaddaddddbaabbbddbbcacaaccbcddccdbaccbdaccccabcabaaccaddccccdbcaaabccbccddbbbadbcacddddcbddbaabdaababbbaacacacadcbccaaccccddabcdbcccbbcbbccbacacdbbdcdaacbcddccdcdcdadaacacdabbccbbacbbaccadacccdadabccbdbadbacbbdaacacacabcdccadbccdabcddddadcdaccddcbdbbbdbbbccddcdcaaccbbadcdabaddadaacbddabcdabacbddadcdacdaddccdabbaabacbcbabacbabaaaccadaabaccbcaabddbbdbdddbddabcbdbdbbadbcdadbcdcabbdaaadadbccdcaccbddcbababdbcacddaacaaaccaaddacbbaddcbbbabcdababcaacacdaaccabdbbddaccbbaddaadbbddbcdaaadbbaacaabdcdccbdaddbaddbadabbbaddbcdbbddbdbdabbcadaaacadbbccbddbabcccdbadadddbdcdbcdbadabbabdcaccddccaddbdccaabaabdcaccdccabddddcddacacdbaadbbcdcbbbadcddaabcbaccdcdbaadabcbcabdbbcabbacbccbbccccadbbadbadbddcbacbcdcdbacdccbdabdbccdaacacbdbbbcdcdabadabdbaaddaabbaabaaccdccadcdbdcccdaccbdaabdaabcdadaccbcbdaaacabdbcaaaabaccdccdbdcbdcbccabdbaadcdbcbabbadbdbdbabcaabbcbddacaaaadaddbcbbabadcabddadabcaddcdadccbcdbbacdaaacdcacddbddddbbbbcacbacbdbbbaaacbddddbdbbbabddcdddababbadcddaacdccdcabacadbdcccdcddbcbadcbdddddbadaaabccbdabbdaccababcbbdbcabbddcbcbbabbcbacddcdaccbbcbadbbcbacbddbaadabadbdabcccacdbdccbabacaadbadbbccddabbbddddaabbbdbabdcddcddcdaadabacadbdbcdaddadccccbdbccccacabddaacccabaddccdbadacccadbbbdcacbacdcaccacccbddbcccaaacaacaddbabccaabdcbaacccacdbdbcdddcddbaccacccddcccaaadccdaacbacdabaabdcacbdaaadbbacdadbccaabdcadbddbdabbdcbbaaabadacbbacdbddddccccaadcdadbdaacaadccbcbcadacadbabdccabccacabcaadbcdccddaadbabaaadbbccadbbbadbdacddbcbcdcbdcdabcdbcddcacdbdadabdbbdbcccacdadaccadcbdbdcccbbccbcdbaccdaadacbdcdbbccbadbbaaababbdaacdcaadbabaaddbddddacdbddbddcbcadbaabaaacbcbddccabdaacacddddaabbccbdacbbdcbdacdbbbaccbadbbcdcddacadacdbadcdbbdbacdbccacdcadabaddcddacddbdaddacadbabddcbdbddbdbcbacaddbbabcbcbbaabaadabbdbacadbcbaacadcbbbaddbcbdcaccadaadbadbdbdaccccccbddabaccbabcdbabcccdbcdbbdbbaacbbbaddcbdaabdabbdcddddcddbbbabccadcabddcadaababcbaaddbdaaaadcbdcdaacbdcbaccaaccbdcdacaabdadccadaabdddcabbaddacdccbadaadcdcadbbdbdaaadcdcadbdcbaccdcbcaacbccdabdabccccdcdcddbbbbbdbcbcdbaadbadaaccbdbcdaaccbdbbdabbdabbaacbcbabbabcacdacdddcbcbcbaaccbcbcdcbcdccaabbddcaadcbaabdbaabdcdabbbddbddcbcbdcbdccacbbbbcccbbbdcaaccacccbbbabcbdadccabbadadbdcbddcaccaddbbacddbcbacabdbdbcbadadddbacabddcaddabdbcbabddcaabbdacabbddcdabccaababbbbdaabdcdbbbbcbadbabdcddacadadcdabdbbdbcbccddbccdccbaadcaadccddacddaaaabcbadbbadaadbdddcccdbaadacdbaccccddaadbcdbccdacdbccdddddabadccccbadabdadabccbaccdadbdcdbdbcbdabbcbaaccccdcabdcdadbabcdcaaaabccbacbabdabccaadbbaccdabccdbbcdcaaadcbcdbcddacbdbccddcbbbcbbbbbbcdbbcbacdbcbcbaddaaccbbadcbdcccdcdabaaabbcaaddbcddcadcccbddbdcbdabddaddccdaaddddccbbcdababdbdaadbddbddbacadadaddddabaaddaccadaadaabcbcbbcaacdadddcacbcccacccdbaccccbdcaabbacdbcdbbbcbdbdbbbbcddbaddadabcdbcdbbdabddadacabbbacdabadcbcabddabccdbcadbadbcbdbdbcbaadbadddaabdcaacadcadbadbaaacdaaccbbbacdabcdcadccbbaddbbdddbaadabbaddcabcdddacbdaabaadbabdcacdbcdabdaccdbcdbadaacdcbbdbbccaabcaaccadbdddbbaddddbdadbbdaacbacccbababbadcaababacbcbbadcbbdbbbcdabbbaadbcbcacddcbcbdbcbcaaaaccbcdcbcdccdbbddcacaaacdbbdaabcdbbcddcdbcaaddadcdacbbdcabaacbdddbdcadcbaccacaccbaccacbccadcccdcaaacabbccaaadadaacbadddccaddbcdcbaaccabcaadaccbcbbdaababacdbaaccdacadacdcaabcdcbdcabbaabdccaaabdcbbcaaaacdacddddcccbcabbbbdcdddbabbbccdcddcbacaadbacabddbddcaddaccbcbadadddaddacdbcadacdaaccbddadbabcdabdcbaaccbdbbadacacabcbcbacbddaadcadcbaabaabcdbdccbdcdacbaacbbaabbdbdcadbbcadcddddcaadcbdcbbacbcbcdaccaadddabaddccbbcbdcbddaadbcdabcbacdcaaddcabaacdadcdabcbbadaacdccddbccbbcdaacdccadaccddabccabbdbdddccdbaddabdadababbdabaacabbbdcadcadcbadaacbddbacbadbcddaabacbaabdccbdadbdcaabbddabbbcaaddabbdacbdcacccdabbbdaacbdacccbbbcdaddccbdbccdbcdacacacbbddcacdcbaabcdadbcaaaddbaccbbbbcdcadcddcdbbbbccacbcbdcbcbdcccacabddaaccabaacaaadabababbaacbdaadcbdccacaddcdbabdcbbdbabddcbbcacbaddcccacbdbbbaabadacaccdcacddabbabcdadaadcdadabbabdddccbcbdaddbdacadcaadccaaabaaacabdcddabdadbadcdddbbbbdcdccabbcabbdccdaaabcbcbaacddcadaaabcbadaadcbdcadddbadcbbdacacbabbacdcbcdcdcbbbdbdccbbdbacbcbaabdbccdbbbdbdbdbadbbdcbbdbbbdbcbbbdddbbbbdbdbddadddaddbadcddaccacbccaccccbbbbbcbbdddcdaddcbcadacbaddcbbcbaaadccccdaccbaadacacbbcacdccbdabdacdadbdcdccdaccbddddadaacacabccbbbbdcddaccddcaacbdaaadacbccaaaabcdbccadabcadacbddbddadaadcaadadadccbdaaacdccdccaabcccdcacbadaccbdcdaacaddaadabaccbbdcacdcacbacaaccdabbdcbdccddcdccabadcbacbcbcdcbcbcccadacdcddbdadabbaccabcdbbdabccabddacdcccbabdddaddccdbacbbbcdbccdabaccacddabbcdddcaaabaddddcabbdaacadadbbdccdabddcbabbbdadadbddcbbcadbbdadbacdaadcdbcdbbddadcaadadadbcbdbcdbdcbbacbcadbdacaaddbacbbabdadccbbbaddcdacdbbbbabccbaaccaaacdbacdccbbbdbdbbcdcacdbdcbdaaaabbdcdaddabdddbdcabbcabcdccdaabdaaaccbbaabbabdbcdcdddadadddabcbacccddcccddbbbaccbdddacbabddaabdcabcaacccbacdcdbbccbbbdaaddcacbbbabbbcbadabaacbbbdadbbcabbacccbaacdaadddbbacbadabadabaccdbcdacbabddbacadcbdbcacbcbaadccaddcbbcaaddcbcacdccbdbbbabaadbacbadccacbbdacbcaccabaaabddaddcdbcbdacdabaadadcdcaacabdacdcbacbbcdbbdcadccdaccdbadddbcdccbdccccbcdadccbbacbccaabbbbbbdababdcccddddbdcdadcbdabdcdaaabbcdacdabbdcbcdbdddacbbacbccaacbaaccccbbccbccdacaabcccabdbcddbaccacabacbdcacccbcbdbadbccccbbabdacadcbdaaabcbcadcabcbdbaddbcdbbccddbcaddcacbdcccdddacdaaabdbcdcaccbabbaadddacdddbbdaccababacbdbadcdaaaadababaccdbbccbbddccbddcdbddadadbaaaabccdddacacbbadaaacabcbadbdcaddbdbcdcaccdaababbabcdbbdaaacbaabbbdbddcbccbdcbaccdbbcaddabdbccbbbadbbccbbcbbaaabaddaddccadcdadbdcbbbacdbaadaddbbdbcabacbdadaacccbccbdcbaaddbdbabddbddcabcadcdacbbccdacaadcaaadbaddbddcbbdcbcdacccdbacbbcccbdaadcbccbdddacacbbadcdbcaabdcaaadbacccbadbddcdbbcbbcbdbbaacccaadbabadbabbadddccaaddccbaacbdccaddcccddcbbddaddadcabababcdcbaacbdcbbabcdadbaddadddadbcdbbaadbbdaaaabaccaaaabdaccdbdadbaadadbbdcadcddddbaaacddbaabcddaaaaaadababcabbaabddcabacdcddbcdabdddacaaccbdbdbdababbdcaccbaaaaaadcaadbbccdbbdbbaadaabcaccdacbbadbdcaababdacbdbadcdaabdabababacddcabcdddcabcbcbbdaddabcccbcadbcaaddcacbbcadbcbbdaacdcddcabaabbdbdcbdabccbdbacaacbbadbbccbdddabccbcdcadaaddcddbcbabcdacccaaccdabaccbacaadbbdcaacdcddabacdbbbcbabcadabacaaabdbbddabbcbbdbbbbbdaacbcbadcbbbdbabdcdadadbddacbacdabbacaaabcaadadadcccdbdcacaadcbdabcacbdaccdadcdbadabcdcdbdddbacaaabdadabddaaabdbcbbadbddabbcdacbbdddaccdaaacaacbcbacabbbcbdbaaaadbbddcababacabccadddabdddbadaabadccadcaabbccccacdaadcdcacccddabaaddaaaacbbbabbddbdadcddddadadbcdddaccdccdccadbdcbaaabddcababcccddcaadddbdaabaaabdbddbabddadcddcdbaacddddbcdcbbaccbccbadaacbadcbbdabdbcadcabdadbddcdddbdccaccccbcdabbdcdacabaabbaabdccccadaadbbdadcdaccadcdacdacbbcbbdccacdbcdbbdbcdbddccadabdcccdcbcdadccacccdbbaccdabccccaabacbabbbccaadabbaaddddbcdbaddabdcaacdcaddbdcbbdaddcbaabccdabaabbdbbadcaabcbbdccaabcbdbacbbccdbccdabdaccbdbaabcdacaddaccaacdacaaddcadcacbdacdadcaacbbdddbbdadcaabdcbccbddbaacddcdbacddcbdddddabcdbacbadddbcdcababcbadbccdcbdbcadadbdcbddcbcbdbaaabcbcaaccacbcbaddaadabdcbbadabcbcdbdabdcccbbbdbbcacbcddbadadacadcdaabcabcccaaaccdabbcbdcbadcaaacccdbaabdadbcccdccdddaccbdcdbbbcdbbaabbcdaacacccddbbbbcccddaddaaabbabccbdcacbbbabbdcbabddcbbbbbbabbaadadabaacbadccabacaaabddcbdbacdbdbccbacabdbdbdcadcdccbcbaacacabcccbdccbddcbbdabddadbddadbbaacadbcdacadcadbbcbabbdacabdbadbbadacbddddccdaccccadcbdbbddadaadbdaaaaaaddbabbcdcddbacddcddccaccbbaacdbadbcddcacaabaaadbbadadbdcccaaaacaacadbcdbcacdaadadcdcbdcdadcaaccbccabbddbdbdddadcbdbbdaabdcdaabbaddcddacbaaaaaddbbbabdbdbaacbabacdcbdbabbbcabdadbccdcdbaabcdbacbdccbbdcabaccddcbdaccacdcdbaaaddddbbaccbdcbdcbbdbcbdbaadbbaccacadcbbbbdcabaddcaddcaaabcadbaddbdbdbbbcaccddcdaccbdacbdbdbdaaabaaaacddabacbadcbdddabbccbcbdddbdbdabcccccaadbadbcbbcdbccbdbcacacaddddacbacabcbdbcaccdbdabdacdbddcddcacddabdbdddccbcbdcacaccabadbbaadcddbbddbdcdcdbbbddacdddaccbbddabddcdbdbbcccaccadaabcccdcaccdddaaabddbddadbbcacccdbcdbdcabaacdcabbcbabbbacabcdbbcabcbdadcacbaaacadbaaacbbadaccdcbabadccbbdbdbacadbbddbadbadabbadcadbdabccadbadcbabdccacadcdbdbdacababbcdabbdbddbdcbbdddbbcccaddcdadcdaddcbbbccbaadbadcbccacbadadcbccbbaabaabcabdbcdadaacccaaccdbbbddcbccbadcabbbdbbddcdbdbbdcbaacacdccccabdaddaacbbcbcbaaadaadccadddaccabbdacbacdbcbadcdaacbdadbdbcbbbbbbbddbaaddabadcabcdcabbaabdbdbddccadccaaacdcabbddadabcaaccdabdacdcbdbdccccaadccaaccbaabbdbabddabacabcddcdcbaaadaadcacdccdbdbbbbbbdabbdbdbacbbdcdcabacacbacdaddbdcadbdacbadccbccaadaaaacaddaabbdcdccacbcdcdcadaccddcbccdcbccacbdcbbcbbddbcbcaadbdcbcdcbdbbdbbaccccbdbaccbaadacadcbcdaaadaabadddcadcdcbcaacbabcadddbdcaadaaccbdaddbaddaacccccccadcaadcdcdbdccabaddabcdcbbdacdbbaaabbbdaabcadbaaadadabcaabbdcadbaccbdabccbbdacaacaaadbcbacadbaacaddbdbdcccbaabaaabdacddabbdaccdcbccbabdbbcddcdbdddddcbdcbbbababbbabaccacabaddcadadcccacddaaaadbacccbdaadbdaabdcadcacaacadaaacadaccbaccdbbaccaadabdcbcdadaaddcdbabcdcabbaaaaccccbcabbdbbddcdcbabcbcbcbccdccaddcccadddacacadccbaabbcadcacabccbcbacbdaccbdddbdacabdaadcdcbdddababcbbaddaddadabcdccdcbadbdcadabddbbaadabdcbdcdcdbcddbaadabdbcbdbdadbcbabadaddabbbabbcacbbaabcdcacbdaadcdaaaddbdadcabbbcdddbccdbbcabcacdcccdbcbcbbbbcbadbcabbcbdacadaaccdbbaccabbcdadbbccaddadbabacccacaaadbdadababbaabbcdbadadacacddbabcdbdbaadcabaadacddcdcdaaddbcdbccbbcadaaabadbccadaadabbbbbcbcabbdbbdaaccbabbbcaabbbdbbccdbdbbbddaddabdabdcabbddbcacdbacccbadaaaacbbdabbdbdcddddddadcdcbacbacdbbadbdbbccddaaadabaabaadccdabbbacdaacbbccbdcaabcbdcadbabdacabdcaaabdbaacbbbbabadcdabccbbcbbbcdbbbbdcdcbdacdaaaccabcbcbdacacbadbadcaabdbcbbdbccdaabdacaabccdcaadadadcdbccacdaadaabddccbcdadcbacabdadcccddcacdacbccaabdaabbacbddcbcddbadbcaadabddddababddadcadbbadbdaccacbaaabaccadadacbdcdabcbcabdccacdcbdbadccbbacbbdaccbaabbcdcddabababadbdbdbaccbbaaabbdcadddbbacabdbaddcbbadaadcbcabaacadbdbbbcdccdcdbdadccaaddccaacdbcabbcaaddaaadddbcdbdadcadbbbdbaccbcbbbadbaabacdbacacdadcaadbbccccaccaaabcbaaacabcddcccadcddaaacadaddddcbaccacacddccabaddbdbdcbbccbbdbcdcaacdadbcdcdccadcbbdbcabdcccccbcaccbacacaaadcbcddbddbddbacbcbaadcdabaacdabaadccbbccabdadaaabdadcbbdabacaccdbbaccbbdcadbcdbbcbaddbadbccacadcbdababdabdddaabdddaaaacddcdddaabadaccaccdbddddadccccdaacacadbbabcabbddbcbaabbcaacbaccabaadaadadabcbddbaaabbadbccccbdaddbbdcbcaddcadabcdcbddccbcaaaacbcabbbccaacaddbbaccadaacdcdabbabadbbddbdbcbcbccccdccadcdaddbcacbcacabadcdadaaacddccbadbadcaabcccabdcddcadcdcdbbcddcbbcdbccabccacbcdbbcdbdcaadddccadaaddbdccdbbadbbccdacddccbbdbabccaaadabbcddbdbaccdbcbcccbbdaddcbdabcbcddbdabbadddaacdadcadcdaacbdddcabdacbddcbcdbabaccadbacabaaaddccabacbcdbaabccdbdaabcbdacacbaaabbacbadabdcacccbacbcacccdbbcbccccdacdbcdcccbbadbadaaccacabcaaabcdacbbccbaabaabdadacdaddbbabacdcddcbbbadbddacdabdcdcabbadcacdbcacabdabddccacdcabcbadbadbdcaaccaaddcddccacadbadaddbbaacdbcbcdaabadbcacbcbdbbdcaacbbbadcadddcdddacbacbbadbcadcacddcccccdbabbaccabbdddabcbddaadcbdbbdbddaddadcdddacabcbabbcbadcdccacbadcaabcbacddcdbdaaddcadcadcabcacacabdbabcdcbdbbbdabbabadbbbcccdaaccdbdcacdacdadbcbcbdbddbddccdaddaabdabaadbbccdaabbbacdbdbababcbacddbcbadcccbdbdccdccabcaddabdaaadbbadcdadacaacddaddaccadcddaddaaaacaccbcaabadcdddcddcabbacdbbdadacbccdaadadbdabbdbabdddddcdabdcccccbcabccadbabccddaccdabccbaddaccddaddddcabbccbcccdacbcdcdadbbddbbdbddbdaabbabbacaabadaaadabccddaaaddbdbbbaadbbabadabbdaaadacbcbdaacccadddcdacdbcbadddaacadbdbdbbaabddababcabacddcbddbbbcdbaaabdaaddbdbabccdccdbbdbcccaaacdbdcdbbcadcdadaacaabdccccabadddadcabaadcdccdabdcbbdbcbcdabdaaaaacaaabcccdcdabbcadaacacdddbbdbdbdbdaacccccdbcbccbabbcbddddccbaddaccdbbccbdccddaddbbabdbbbcacdbcaaaddaadadbacdadbadcdabdcbacacdadccdbacdabbdbddacaddadbdbdbddccddbadaadbbdddabdcdaacbdcabbbbdcdbbbddbdbbccbddbbaaabaabdcaaaabcccabdbcbdbddacdccaacadbadcadddcadadacdccbadbabbdaddcacadbabcabdddababddbbbbabcbabddcdcbadcbddadacdacbbcacacbaaacbbbddacdaabbadcadadacbaccadaddbaaabcaadcacabccdaacdbacccdccdbbbdbbbabcaaabaacddbcdbbdcdddbdacdcdabdaaaccaccddbabcaccdbaabbbcbdddaddcabbdabcdbbadadbbcabbaadcaccadbbbcddbcdacdacabbacadadaaabbcadddcaadbaabacdbcdcddacddccadbddaabccbacaccaaccabacadddbdbaadcddcbcdcdbadbbdbbcadaacbababbdcddbcadcdabaaaababbadabacbdbabbdaaddabcddaadcbbdabccbdbaccaddabdabbbdddcbbabdadabaddbdcaadbcadcddacaabdabddcadcacdadabcbaadcdccccbaddbcaaadcddcddaccbdccaabdabcabdaadadacabbcbbaacddadacaacbbcacddbbadbdbbdcbbacabcaadcabcdaddabdadddabbdbdcadbadddcbbbcbcababddaccccdddcdddabbbacdbadadadcbdddcccdbcccccaaacbdbcccdcbacaddbcbdbbdccadccdddbddccbdddbccbdbdabccaacbabacbabbdabdabccddcddcbdabdbaccacbbadcababbcbccbbbddbcbbbcccbdcbbccbabaacbccbbbcbbdcddbddbbbbaadaddbaababcbdbcdadccbcabdaaddadcbcccabadbaddbbbcbdbcadaabcadccdaabaccbdbaaccbadbdbbaaadccccadabcdcddaaabdcbdadabdacbabcabdadbbdbadbacbdadaddabcbdadcbbacdaddadccaadaacccbcbdcaaddacdbddbbabdbdccaccbcadaaccbdadabdccdddbdabdcaaadaaaaacbaabcbccacaaaabacbbbcdbabbcbdadcaabacacbbdbcaddbcabacabdbadbacbddccbbbbacdacbdabdbdcacbabaacabaccbdabccabccaddcdbddaddccbbbbabbdccbadbbbdcbaadccdccabaadcccbabdcccddacbbadcacabcdddbdcbaabadadabbdacbcbcddcbdbcbdbdbacbddabbbbccbbcacccbccbadddaaabbbadcbbdaabdbbdbaadcbcaccabbabdccdcdbdcabdcabcdddacabdcadbdacaaddbbbbcddcbddabdacdcabbccbbbadcdabacdcbdaabcdcadaddbbcccbbcdddbddcbbabcddacdacdcadbcdcdddcbbbbabdbcdcdcaadccdbdcbccdcabbbabcdadadbbbadcbdabbdbbabbadaabcddbddcbaccabdadaacbaccaacbdabacdddbcabcadbbcacbadcdaaacabdccccbccadadccbbdacddcabbbbcdcdabccaaaaccacdcdbbddaddbdccddaaabccdccbdccbddbbbabbaadccbddddbbadbaaaacdbdaaaaccbbdadaadadabdabdbcacdcacabbdabcdaddbbccadadbbadbdcacdabcbbcadcacdacadddbacbcbcccdacaaaabdccddddcacbbdcacbdccabdbaadbcbaadadbbacdccccbcabbcbccdcbbbddaaadcbcbddbcabbbcbcbddccacbbdadadbbdbccdabcadbbaacbbdcbbabddbddcbabccaabaadccdbbccdcdbabcbcabaaaabdbcdddadcbdbbdabacbdcdccdcdddccdabbcbbacbacccdacdbddbbadbbdbbbbdcadcbbdbcabaaccbddbaabcadcacdabadabaaaddadaadddddcbdaddabdbcddbdccadbbdcacdcbddaababdaccababddcbabaacacbcbdcbdddacbadcacaadcdbcbdddcbcabacacabaacdadcaddaabadaaaadbabccacbdaddddcbaacdccaadcccbcdbbcbcbacaacadabaccbdcacaaddbcaacadbbacacacbacbdbccacbabbabdcdccdadbdddbcbacbababababdbcbcbdacdbacadabbaababbaabcbacaccacabbbbdcdacbcbadbaabcbcbccbcaacdaaacdcbaaabdcbcbdbdbadadbbdcacbdaccaaadcbbbddbccddacbdcacbddadccabbacddcbddcaaccbcbacccccdcbaabdaddbcacdcadcaaacdbbbccddbacabdccdcacaadcadbcaadcbdbcdcbdbcaaaababadcaacdbdddadbabddbdbdbdcbccdcabdbbbadddacdddbaabcaadadbbcaddcdabbacaaaddacbbbcdbdacdbcaaabaadacdccdcbdbbcacdddddccccdbdbcbaabbcbaacdaccbcdccddabcababddccabbbdbaccabacdbadcbbdbcdccbacbccbdaccacbdaadcbdbdabccaddaccaddaddbcccbddadadadddadadddddabccbaabdbcaccdabdababcaccabbccadbdbbbaabbccccdbcbbadacccdcdddcacbdaccabdcbbaabacbdaacaabaabbacdcdcaabccdabbbdababbbbdaadaabcbcbbddccbcbcbcbbbbccaadabddcdccdaacbbccdddabdcadadddbdaaaaccbddbadacbdabdbbadbadccdaacbcacabcccbcdbdccaaaabdddaadbbcadccadbbaacabdadbdbbabbbbaacddcccbdacbbcccdcbbccadaadbacdaabcaacdbacacaacdbcdbdddadcbadddcdcbdbdcacdbbacddaadbddbdacdcdddbdddabdccbbcacbacccdccbbcddcacabbbcddabcdadbcadacccdacbabdaccdbadadcbdddccbdbdcbccadddbddddaddbdcbaabbdcdccadbdddccbaaccbcbbcaadaabcbcdacbdabdacdbdbdbdbbcabaddcbdddbccccbbcdbbddaaadbccbbccdcbadadaadcdadaaccacacaacaadbcbcdbdcddcdabddddcddadbcabcbadaaabbdbabbabccbadbabbadbbccaaaacbccaadadcbdcdcbcdadbbdbdadccadcaaabdbdcaaabcabdddbbddadbaaaaacdcdcccdacdbadcbcaabcccbaddbcbbdbadadddddbbdacabcacdbacbacdbbbbbaaabbcdabbcdccdcabcddcbcdcadcbcbaacaaabcdbcbbbcacdcbabcdaadbcdbacbaacbccbcdbadcddabcaaadcbbcbcddcdbbcbacccdcdadcadcbddacabdbacbaccabcabacbbdadccbcdcabdbbcccbddacbdcbabacadbddbbdaaddccaabdacaacbbbabbaaaadcdbdbaadaadcbcbccbabacacadbacaabcbaadabcdaaddbcbcdacbbabcabbbccbbbddadbbbacbdddddddadcacccaaaabaadacdaaadbdbcbbcdddcdcdaddaccdadbcccbdacacdabcdbdddaacbaadabccdddcaddaccdcbbbbbacdadbdbbacccdaddbdbabbddddccccbabcabbcdaacbdaaacbcdcddddbcadbbcbbaaadaaaacaabbcdbbaacdcadbccdbbaccbcbaaaaadbaabacddbbddaddbababdccdbbccdacbbcddcbaaaaacdccacbadddadbddbabacbcaaadccddcaaaddcccdaccbdbdabdcabaabaccdddcaddacdddcabaacbdcaccaabccaacaacaccbbacdcabbcdbdadcbddcdbbcbbbacdbadbccccbbaaaaaadadcccddbbcdabccacdadcbcddddaadbcdcdcddcdaabcccbcbdadbabaadccbddbccdccdcbcccbdddaddbbaacccbcabccabdababbabccaccbdbbccbcccabaaaabadbadcaaabdaabdaaaaabcbbdacadbbabcdddddcaaaaabdbdadddbcbacabdbccadaddddcdcabbddcdcbcccccbccabdcbbabbcacccdcddabbadaacdadbabcadcdbcccababbbccaccdbcbbcbccbccadacadaaadaacacbcacaacbdbaacdaccdacdbabaacadcbaadabaacbadbbdaacbbddabccbdbdddaabdabadbdcbaccaaccbccdacbcddadddacacacccddcaacadbabbbbdabbdabcaddbbcdcabcacbcccccabcbacbcbdbdadbddbdbcabbbddbadbddcbdacabdddbcaddbddccbcbcdddabcaaddbcaadbdcbaaddadcaacbbcadbcbdddbcdcdadbbcaddabadacaacdaabdaccacdcdabcdbadcccabdaaadcacacadcabadaaddcbadbadabcccbccaabaacaadbacdcaaacdbbbbdbbbbadccccacbbbababcccacbcbddcadccccbcaadcccdaaabaadddaacabbcbddadbbbadabcdbdccdbdbaaaacbcbabccadbccdbcdcbdccccbaadaabdccabcdddacaabbdcbcbadacbdbacdadabadcccddabcaadaaacbbdaaaadabbcacdbabddccdadcbdddcdbdaaaccaadaabaacdadbddcbdaddbaabadacbcbaddbacbcbdddabbdacbdbacdaabbbdbaccaaccdbdabcbbabadcdbcbdabcccbccaababbccacbbbdbadccadbaadabbcadaccbacabbaaccdbabccdabbcaccccbddacbccbcababdbcddacbbccbdcccddcaaddcabcdbaadcaabdddabbbbadcbcbbdcbabdcdaabbcddcbdbcabacbdddbdacddaacbddcbbbadddababcacdddacdcdbcbbbcbaddaaaaccccccdccacbbdaaacaacacadbbccadabcdcbbcabbadcdbbcababdcbbbbdcaadbbcddccbdabcaaadabdddabddadbbaaaddbddbbdccacbdadabddcaccbadbdababcbcdbaaddddcbdaabcdbacdccabbadaababacdcacccaccdcdcbddcadcaccccbbbaccddaaaaabdcadcaabdccbbcaabccbaacadbccaddcacbdbbddccdcadbdacabbacccbabbaddacabaaccccadccaaaccdcddabbcbbbbadcbdbadacddbdcabccaaacadbbbbccdadbbbddbccdabddaaaddddacdacbcddbbccabbbdbbcdbdaabbcbcdcacdaabaabdaddaddccbddadabdbacdccaddadabcaadcaacadcaddddbbddbaccbbcbccbdbdbdbdbcadbddccdbacccdacccccacdcdaadcaddacdadabbaaabcaaaacacdbbaadadcbadbbdccdadacdcdcddbdabdadbaadbcdccacddbdddadccadcbacbbcddcdccbdacdbdbbcbccddadaacddbdccabbddcbcbacdbdacddadbddccbbacddbddbbbadccbbcbadcadbcdccdacbbcdcccadaddccccaacabcabacacdddbdcbdbdcbbbabaacaaaadcbacababccccbcabaddbbcdcdaddacddddcdadddccbaddaaaacaadbcacbdcacccbadbacccaacbacdcabbbcdcdabdaabbdadbcbccbddabbdbbdccadbaccaabccbabdacdcdaadabcbcaabccbccbbcbddddcbbbcabbcdbabcadccdadddaacbbccaabcadcdbccaccbdccadbbcbacbccbbabbddbddadccabadbabdacacabbdaadbbcddcdbdadaabdbdacbddaddadbdbbaadbcabaacdcaddacbcaabbdccdcbbacaaadcadddbacccbddabacbbababaccbcccdcacaccddcbdaccbdccdbaabacccdbbcbcbdaaabddaabacadcbdcdbbcbadddddaacabbbdcdcdcbbdbbddccdbadbaabcddadbaacbdaccbdccddbbaadadacabdabdbacbbbadababbcbcacbbcdabddacbababcbacdcbcbcacadadacaadddcacddbdbbbadcbbbadadbadabbdaddabadcaccccaacadaaccbdbcabcadbddccacbdbdadadbcbbcbabbbcdbcddbbddabaabacabcbabccacdddcdbacadbcabccdabacbbabacbdabddadabddcdcdddddbdcbadcbddddbcbdcddcdcbdbcbadaacacbcdacbacccacadcabbbbccdcbdcdddcacadddbdcbbbbdadabadacccadbdababacaadbbccbadbaaacdaddcabccadbabcbcbaaddacadbabaadacbbcaabcddcdddbadcaacbbdccdcdcaaabacbdddabddacdcdbdbabdcbbdccbcdddaabbdddacdbacaddddaaddadcbabddcddddadbbacccadcbbcaacdbbadcccbbaddbdbbbaadbccccbddaaadabdcaccbdbabddabadacdaaccaaddcacbadcdbcaaddcaddacbddadadbcacdbcddcabcddcdbddacdbaaacddddddcbbbcbccbabcbdccabbbbdcbddbbdbcadacbbcacbaaccdccbabbbbdcdccddadbaddaacabbbbabdaadabcacbcccbdacbabbbaacdcccdccdcaabcbbdcadcacbbdbdccbbbdbdcacbcdddacabadbaacbaadbdbccdcaaadcccdbacabacacbcccabbdccdcdbddaabdaaadaabcdcbcdabcdcdccadbcdbbccccacdaaaadbaadccbabcadcabdaabadcabcacdabddddcddccabcbcdcbacbbbadcadbdcaabdcabdbbaaabddbdcdbdcdacccdaabaccdcbbbccbabbbbaccaabaabcabcbbddbbadacaacbacacbabcdacddcccadbacadbacabbadaacacddddccbacdbccacbdcadcadcdbaacbdadaaacccccadbcccbacacbcdccddbbdaaacbddbaddcadadaaadccadbddcbabcbcbbcdddbacdccacbcdbcdbaadbbaddadaccccdbdacbdbcbdbbacabccccabbcbbdabdaacbabacaabadccbacabddaaaddaaacdaddaaacbaabcdabbbdccacbcdaaaaadbadcccbcbcccabcaaadcbbcadbddddccabddcccaddddbdaaaaabcdbddcdaadaadaccabbbbdbbdccdabcabbbccccabdcbacddbdcabdccdadddbbadcddbddbcdcabaaccadddbacdbaabddcabddbbbbbbaabcabaddbdacdaabadaccdcdaabbbbabaadaacbaddbdcbacaccbaacbccaaddbbaddacabdccbcaaacabcddcbbcbdcdcdacddbdcbccabaaadabcbdbbcaccabdcbabbaccdacaaacdcccccbdacacdbcbcbccbdbddaddaaacabadccacabdabccbdddbccbcdaadcaabbbdbaaddcccbabcccbbaacbabdbabddacbcbcaadddbccaccadbdcacbbddacbbcbcbadadbcaacdcbabaadbacbdcbcdabbbbbadddabdccbaadccbcdadbbcabcccbdbcddaaddcbabcabaabdabaddbbdbbcccaacadabbcbaaddbdcacbdabbaccbaadcdbdadadcddbbaabddcccbacaadcbcacdddadabdacadbbbbabbdcdbcacbaabaabcbcacbcddcdadcadadaadabcaccaccabbdacddcdadbadcbcdcbcabcbbdacacaccdddbacbcadcbcdbbdaddcbddaccbcaadcbbacdddbadadbadaccabccbbcdbdabbbddcbddadcaccbcbccdaaaacaccdcddccdbbadbbdcadcadadcbcaabaabdacaacbcbadcddddcaababcddcabdcdbbcaabdbdddbaaabcdabddbacbbacbbcdabcddbaabcdababccddcbdbdcaadcadccbabbdcabcaddcdcabdcccccbdcdbcabdcbadcbbdacbbcdddcbbddcacbacddbaccabbabcbccbccdcdaddaaabacbaaccccdcadaadadbaabbcdbcccccaccaaaadbcccddbcaabdbaabcbbdbaabaccdbbaabbbccdadbdacbcacccbccdcdadbbddcdaadadbbcababcddbdabcddddddaacaacadcccadbdadcbdcbbddadccbabadabdbcdccabcddbaacbddbbcbcccddcbbccadddaaccadcccabcdabdbcdccbabdaddbabbbbabdbdadacbbcdaaadcbbddbadccccddaccadbcbcaabcbbcbbbcdaacbdbcdbbbaccacacaddbcdbbcddcadbbbcadccaaaddbacacddbacbadbdbbaddaacabacdcbdccdccbcaadacbacaaadbcadcacadaacababcabddbdcbdabbdbacacaabbcbacdbdccbcaccaadcccccdaabdcdcbaccdcdddacbaaabdaabacabcccdacaaabdbcdbaddcdcaaadadbacbdbcdbbdcdbabbbcacbaabdddadabbbbdcaccbacbccdabdabdbdccdacdbbdadadacabbbadddcacbbdacbdcbaccbcadcbbaccbddaabccbbabbdbcdadaaadcccdcbbbacdbdccabdcdbccabdacddabcbbbaddaaccccdcbabcdacbcaddcddddbabbbcadddcabcbcadaacbddbabcacdbacddabbbbabababcdcbccdbbcbcdbdacbddbddccccbbbcdbcaddabdcadadccbbcadcdabaababaddccabcdccbcdcabaaaabcdddbdadacdbcdacbbcccccbadcaadcaabaacaacdacaadcdacddaddcabcdbcddacaabddcdbdabcbacbaacdbbaddbbabbbabddacbccccadabbbcadaccaccaaadcdabaaabcaddacaddabdaccdadbdcdbddadaccbacbdccdacacadbcdadbbddadabaabccdbbabbdbdadacadbabbaddadcddaacdbddbdbcdbdccbbcbacdcdccdadbdbcadbdbcbbbdccabaadadcbbdbabaadcdcbbcadbabbbadbabdbaabbaabcbaabadabbbdbdaabdcaadbbccadbbabbcccdbddbddddcacaaacbbddbaadccbbbbdcbdabaddabadadcbbbddbdccdccbdcbaacccacbacdcacbbdddcddaadaccaccaadddbacdadbcccaabacbcbadcdcadcabdbacddcbdbdaacacabdadbabbddadacbabdbcdbadadccabdacadbbdbbaccaddbdabacdcabbccdbbcacdddadaadaccbaabbcdaccbcabcbdddbbbbabbcdccbcbccbcdcdbbddcdadcdcdacdddcaadbaacabcddcadadacaddacababcbcaddbaaaccbabcacccdbdbabadcbcdcdbcdbcbccbddaccddbbdbbabadccccdcccdbcbcaadddadbbcacdbcccdbabacabcbccabdcdcbcbadcddadaadddcbaaccdcbcbdcacaadcbcdacaabbcdccddbabacddbdbadbddaddcaabaccaaddbccddcaadcacabdcbbcdbcbcaadddccdcacdbbddbadddbabbbdbabadbadcccbdbadaddccdcbbbaaddacbcadaddcacacacdbcdaaddcdbabbdaadadadaddcaaacbadaabcdbaccbcdbdcacdbbdbcbdbdbccacdbaddaddacaaacbbbbdccaccdacdacdacdbcdbdcdcccddcbdbabaccbcabbcbcdcdaddaccdccbddbccdadbcbadcbbdababcaddaddaaccaabdbdcbbdbacabadbbcbdacacbbcadcdabadbdaccbbdacdbabdaccdddbcddbbccaaaaacdcdaababbbdddbbadacbdabdcaaabacaaacdaaacaccdbacdbbaaccaabdcbdbbadbdccadacbcbaaababaaccabacabcacbdbcbaabcdadbdacdaabdddbaabdddcbabdabacbcdbbacbadacdcacccddcbaacaaaaadccdcccbcabdbbabadcbddadddcacaaaabaccbddacbcddaccbcbacadbdccadacaabddcdbcabccdbbabccbadccbaadcaadaaddbcddacaadccadabcdacccccbcbcaddbcdbcacdbcabccccacbdaabdacbcddcadcaacddabcbadcdcbccbdccbacababacbbbdbcddbaacabdbccbdacdadddddccbaadcadbabdccdddbcddadaddaddcdccabcdababcbdbccdcaccdbdabdbaaabacacdccddabbcbddddbadbacbdbddcdbcbbccadabadcdadbddaababcbcddccbdaaddbcabacbacabadbcdbdcaadbbaddadbdccadcddaacadacadccdbccacaaaabaadbdbdbbcbccccaccbcbcdbbbdbabdcbcbdcccdcabadcbcacbdcbaacbacddcadcdddbadcddbccdcbadbabddabdddbacbadcccbcccdbbabcacdcbbdbdacbddaaddaaaaccacdacdccabbbacbcdbcacccdbdcaacabbbbadacdbcbcdaccacacadabadddccaccbddccaddcbbbbbaaadbbaabbbcddcdbbdcbaccdaadddbcbdbbbabaaadbadcadbabbccadcbcaacdcaddaabadcbcccacdaaaaccacaccaaaadccbcccdacdbdcdaaadcbdccadcdcbcbdddabababbbbcbbdcabdbaaddbddbbaaacbdbccbbcccdccacaadbbcacdbabaabbacbacddbcaccbcdadccacbcdaddcccbbbaabcbbcbcdcdacaabdaadadccaddcbabbddacaddcdbbbbacbbbbadbcdaadbbcaddadbaaabcbdbabccdcbdcddcaccdabaaaccccbccccacddcadadacdbddbdaaaadbcbbdaccaaccccaabcdcdadbacbdcaccaacbbbaccdaacccacadbbdaaacddacdcbbdddbadabdcbbddacddbbbcadbaccacbabdcbaaaaaacdccdcccdddddbcbacbdbbdbcbbdbcdddbabcbccdccacdaabddcbddbcdbcaaacabdcdcdcadcdaaaacbbcbbbacdcbbabddddbdaaadcddcdcddddbddcdcaaabcdbbdbcdadcdbaadddbccaadbccbabcccbcdbaaccbbcbbbbddbdbddcabdabbadddddbadaccabdcbdddacbcbbcaacddacbcddbadbdcbbddbcbaaccaddabbabbbbacdcaacbccbabacbcbbacacdbbdcaaddcccbbbcacdcbacccbdacaccbddbaabbadaaddabbadbaddabadddabbaababccacbccdabcdccbacddcbabdbbaddbdcabcdbdbbcbbcdcbdccabcbacbcbbbabcbddbbccacbbcccbbaddacdcbaccdbcbacaccaddbdccacbbddcddccbaacaccbddccabdbdadbbddadaddcddcabdcdcdaaadcadaabbaccabbccdadabadadcdbabaacbabbdcbcdacbbcbbdcbbabdddcbdbcdcbbdddbbbbdcbccdaddacacaacbbcbabadddbadbababccbacacdbdbddcacbcaddcdbdaacabddaaaaaacdbdacbaadabdbbcaadaccdcaacdadbccddbacacabdbacacdcbbacabdbbbccadcccbacacbadbbbcdaacbbdddbbcabdadcaacbbcccadaccdaabcdcdabbbddddabdcacabdddaabcbbcccaddaabacaaddbdcdadbccbdadbaacdcdcbbcdddcaddaacbbbacddabbcbaaadaabdcbabccbcabdddbadabbdbcdbbddcbacccddcbaabcbacaacbadcddadbccabaccccaaadcabadbadccdbcdcabdabcdcbadcccbaddcaadbbadbbcabdbbaadacbcdbabcaabcdacbbdbdcaaaaccdddabddbbdbcddcdcdadcbcadcbccbbcbcdbcbbddbadadcdababcdcdbbbccacddbbdadacccdbcadcbaddcbbcaacbbacaadbabbdccaccaacdddbabdbdbcabbcdddcabbbdddaaddcabdbccdcaaddadcddcaccdadaabbbddbbdcbaccdabbbadacacdbdadbbdcabbaabddcaabcdccddcaadbaaadbaacdcbabdcbbbabdbccaccbcbbcbdbabcaccaddbbacbcacbdcbbbbcdcaccaaadaadcdadabddbcaacdabdacccddddcdadaaacacbcbbcaaddbabacccabababbbcacadcabcacaccacccaddccacdaaadccdcdddabbdbbbccbdacdbaacdbbbdcaccdccbcbbdcdbdbcdbdbcccabdbadbdbcdccdbacaddddccadacaadccbbdcdcdbabcabcbbdbdcabbbdbadddaacccdbcadccabbdaaddaadcaddaacbbccbcddbcbcaabddcacbbdddcccdcddacdadcbcbcacdbbaadbddbccbccabbbaadcbddcaaabcabbdababdacadddaccaaabccabbdddddadcdadabcadcdabdddbaabdbddbccdcbaacdaaadbadddbbabbadddbababccaacabdaacbcbbbcbaaccadbdcdbcdcbbbdbabccdcbbcbbcdadcddbddbdccccdcabcdaddacadadbaaadcaadcadaadcdcdcbacbadccddcaaaadacaababaacabddadaacccddcdddabdadaaccdacbbbdccbdddcaaaacdacadcdbbdcabdcaadadaaacabbcbaaddbadbcddaadbcbaabaadbadcabbaadcaaacacbbaaadcaccbcbbcadccccbdbcabaadcdcbbdbccacabdabbcbbbacdcccadccadcaaddddccbbbcaccaadddacccdcdacacacbccacdbdddddcbadadcdadbbabbcbdbabcdbcadcdadaddccdaadcaddbbacabdcddaccbbbabaaabccdcbddaaacccbcaabaacbcdababddcccbaaaddbacdccabcbadcabdccdcdcbcbcdbbdcabaaddddaadccababbbaaddadbbbbaaabdbbdbdaabadcbccabddcabbddcabaddccacbcdaabbacdbacbaacbccdabdadcccaddabcddbddcccbcadbccbbccdcdbdadbaabdcddcabddacbacbccaddababccbcdaaacbcbcbcabadbcdcbbadccdbdbabdaadbdbcddadcabddcbddcccdacdccadcbaabaacbbdcbdbbbbbdacbabacddcccdcdadcbaabcdacadaddcbcabbbcddaababbbadbaccbabbcdcbdcccbbdbdbdcaabcdaddbbbaddddcadccddaccaacdddcabacdabbbbddacaaccbdacdbbaaacdbbadcdccdadaddcadbdbbacdcccdadbdbcdadaacadddbcbdbbababdcaaaccacaacdbacbacabbbdbadbbdababbaccbbabdadddbabccacddadacadbbdbcacddaabdababbbcbabcdcbdabcdbcddacadccbdcacdbdddbcaaabbdbccabdddbddcdcdcbdddabbcbdbdbbaddcabdbccddbbbdbbbdadaddcccaddcbcbbdababdbcdbdcddbcbbbdbcaadcabcaabcabbccdddccdabbbabcabacbdbbbcbdcbddacdbbdabcdccdbdbbacbdabadacabcdabbbddbbccbcabcccadbaaaaaaaddbbbabacddccdcbcadacacbbcbaadcbdcdcabbaadcccaaaacacababacadbdcdbdbdabdcabdbcbadcdcbdbddcaacdcaadaabbccacaaaddddcccadacadccbadddabdbdaaccbdaaaabddcbcadcacadddbaacbaadaccdcbdddcdccaaaacabaadabaabcdabdbbabbccbacabbdbbaaaddaccdbbbbdcbccccbdcccbabccbadcbdbccbdbdbddaccbcbdcabccbcccacccdbadcbcababbabacabdcbcbdddabadbcbccbaacbbacaddcdccbdcbabddcbccaccadaddbbadbabddbacdbcdaccdaaadcdbaaacabdcadabbdcdadacbaaaaacddbcbabaacacdcbadadcbadacaababcbdacbcdaccacdaaaabcdbbaaacbddacbabcdaacaccccdcaddaddddacbaddccdbadabacbacaddbcbdbcbddacadbaccbcbdbdbcabdcabdadcbacabbbabccbdddabdaccdbcccaddcdbcddabadcdaccabacaadabbdbaadcabdcabadcddaddbddddacaaabbcbadccdcbdbdacadacdcccbcabdbcbdaddbbdacccacccbdcddbbdbdaacacbccbdbdcdcacbddbcdbcddbcabbcacdddbdbdbdcbcccdaaabcaacbccbcbcbcacaacbdcbccbaabcddadccdddcdbaabbadacbbbacdbdacdaadbcdddbcadbacbdaabaddcdccbddcabccbdbdbabdcdabbcadaabbbcacaaccbddcbdcccacddadabbaacddbdbaccbbdabcdbabbddacbadaacdacbadacbaadaabacddacaaadbcccbdbdadcacacbbcabcdadbbbbbcdbcbbadcccbdaddddcdcdaaccacddcacabddcbcbbdbdccadbabcdaccaaddccbbdbdbbaccbcbdbcabcbbccdcbcdbdcabbabaaacbaadaaddcadacbbbbccdcdcddcaccbabbddabaacddbbdcccadddddbdaabbadaacabbaddddaaabdabddcacbbddcbaadccdbbabadaabbcaaaacbcadabdccaccdbbbcadbcbdddddbbbbcdbbaabccbbbdaabbbcaacdcdacdbcbbbdcbdccdbabaddacddccbacacbdbcccabaddcdbacbddccdcdbbbaacacbadabbbcbcabaadabbbacdaabddbdbdbdcabcdabcbaaaadcadbdaabdabacacbdcadaabbddacbcbdcbabadadabbcaabcbdbdbacbcdcbaaddddadaadddbcbbcabbaadbddbbbadbdacdaadbcbddaccadadbbbcbbcaccddddaabdcadaadacdacabdcadcdcbdcacdacacdbbaccbbbdadcdbaaccddbacbcbdaadabccdbdadacbacadbaaccbbbbbbacbdbcdbcdabbcbddaaacdcddddcaadccdbbacdccdabcbdcbbddbccbdaadcdcadacabbdaccbdaccbbcbcacadaabdaabaadcbcddabdcbcadadbadbaaacdcaabacbccabbcadabdcbdcaacbddcccccbadcaacddacbbdaddccbbdddbbdcbacddcccddbbdcbaabaccccbcddbbccccbbabbbabacaadabcdcccdbbabcdcabcaccdccbbcbddcbacdcbaabacdcccccadaaacbbaabbcbadccdbbcdcadbdbbbcabaddbabccccaacdcccdbbaccbdbbcaabddccddbccbaccbcadddabdcbbcddacbabddccbaabbdbdaababacbbcbaaacdddbcdbabaacdacdddacadddcacccbddbdcaaaacccdcabbacaccbcacbbbaadbaccabadadcbbbdaddbdacaccbccbcbaddbcbcbacbbabcbbcccabbcabdcbcbcadbccbcaabcdaddcbccaabccabbcdaadcddcdcdcabbbcddccddbcdacdbcabaadbbbddbcabaddccbdddbbbdcddacbbacadbbdbdddccbabbadcbcaabcdbaadcabbcacbabbcabcaadacbccbcaddabccbdaddacbdbbcbbbcdcbdabbaddcaadabadddadbbccdacdcadcabccbacbccabcacaabbdccdcdbaaaaccabdccbabbaccccabcbbcbabbdaabcbaadcddaacdbdddababaacbcbabdbdaccdaacbabdaacaadcabcdaaddaadccbdcbbbbcacdbbddddcbabccddabaccabddbaabdbacdabbcadbdabddbcabbaacbbccaccddabbacdbcbdcccbbdcaabbddbcaaccadacddccbbabbccdbdcbbaddaaacbdcbcabbbdcabcbcddcbcabdadcdadbcacadddaababacdddcbdddcbdcabbaaabdbbdadcbdbacbccdbbcccdaadcddbdcaacddbbaaadbcdbdbddcbbbdddbbaaacbadddbbddbabdbdacdadbdccddbcbcbbcdddcbcbbaddcabccaccbadaccbabaddacaccadbbbaddacbbbdbbdcbdbadcdaabbadccdadabadaabcbdcbbaadcccccacacbaadaaacabccacdadccbcabbbaadcaadcccbcaabacccccddcddadbadcbdaaabbbcaadacacabacbdabddadcdcbaacaabbacbdabdbabdaccdbadabbaaacbdcaddbdccdaaaaabadbccbcccabbbbcbcababddcbadddabbbbbdacbbccaacbddcdacabbbbabbbddababaaccbabdadadabbbbaaccaaadbabdacddcaccacdbbbddcdcdacdcabbaabbbdcbbbbddbaadbddacaddacdcdbabdbaccddaabadabccaacabacbbbcbadbcbbaadaaadabbdabbcaabcbcbabbabccbbacdaccdbbacaaadbdaaaaacdbdccadddcbdaadddbaccbbaddbcbbdbacccaccbdbcdaadcdbbabbabcabbaabcaaaccdcaccdddbcbbcccbcddcccbbcdacbabbddadcddbcbbdaadacbccbddacbaccdbbbbcadcbadbbacacacdccdaaddacddcdacbbdbbdbbdabbaadabcaacccddacbddacbcbccacaadcabcccbbacbcddbcbacabaaccaacaaaddaaadadcabcbabdcdbcdcaccbcdcaddacbabaacbbcdbbcccbadbccbddbacddbcdabbacdbddaabcdccabaaacaadaaaaabbabdcccdccdbadacbdcbcdbcbdcbcabaaacadacabdddbacbcdacccbaddaabbddcdcacdbcadbabcaccdbcbdcdaadcdabdabcadbaaadcacaddbacdacdacaaadcaaaddbbaddbbcccdcdbdabdddcbcdbcacdaaadddacaccbdbccadbbaabbcbcdadaadcdacdccdbcddadcddaadddcccddbdbdcacdbbccaaaabdbcbaacccdacacbabcacdbbcaddbcdcaabdccaccdacbdcbaaccaccbcbabcbdcaaaaaccddbdcbbcccbddabccccbbcbbbdbdbaabdaccbaabaaccbacdcabaccbdaccbcdacaddccddbbdabbbcabbcdcacbbadaabadcdbbcdadbdababaabdbccdcdaddccddccccacadcababcdddcbaacbddabbabdbbdbcabbaadbbddbbccadadaadaabdbabbadabacccbbdddcbdcdabbabcadcccaaadbbbabadcdacbdbdacaddacbabbacbacbddddbababbbdaaccaaaabacadcadbddabddccbdcdcccadccaadbdbdcdbdbaddaabcbddcdddcadcdcbcccbacbdaadabbbbcbdddbaddbdcbcacbbcbcdbdaaacdcaadbbaaaacbabbdcccbddccaacadaacbadaaaacbcddcbdabacaaacbcbbbdbacacbccaccccccccdcdccabbcbcbcdbaaaadcdaabdcdbabccbdabcddddabbbccccadacabcbadbbcdbbbdaadabacabadccdcccbcadccdcabcabbadbcbcbdbbcbaccddadccbdbcbcbddacbbbbdcbcdccbaacdddbcbabddcaacdbcdcbbcccddcdcdddbabdbddccaabbddaabddcbdcbaadcdddcbaabdcdcacaabaddddbcaadcbabbcadbddaadcbcdbcaddacdcabdabbaaadcdbdbdcbadbbcaddcdcbabaccbccddbbcabdbaddaadcdddaccdccddaccbbbaddddbdbcccccaadccdacadcccddccddbaacdbdabacddadcccacdaccbbcadabdacdbaddbccaccccbaaddadccabadbdcabccacdbddcbbbcdbbdabacacbddbaddccddcdbcababacddacbbadabcbaabbadcacaacbccaaacbdabcddddadaaddabdbddbdcddbdddcabaacdcaacddbcddbcbdadabcdccadcaadadabacddabddbbdccdaaddbbcdaddccbdaccbcdadabddadcadddacddbdbcbdbdcababaadbbcccacdbcbdccbaddcaccbaaadabcdacadddbdadaacdaabaaccbdadbaabbabcbaaabcbbcbcadbbbbabcadabcadcdacbdabccbaabbbcdacacdccacdccddddaacbacdcbcbcadbccbddaddcbddddbbabddbbbaacbadbdddcdcbacddbabadbaabcbbdcdbbabcbaaddbbbbacdcabadbdcbddddbbbcbbbbabdadcdcabbdbdbdabbacbdacccaccdbbaccdcdcbdcbbdbdbcdccdcadacddcbccaddcacdcdbbbdcadcdbbadbccdcddcbbaabcddbcdbabcdcaabddbcddacbcccdbddabcabacccadabdcbbbdcdccbaaabacbdadadacdadcdbaabaddabadbbdcadcdccdaaadbdcbcbbbadcbddcabdabddbbacddcbacbccddbaaacbdacbaccabdbddaacbcdcccbdadcabcaabdbdbdaaccbbdbaaacbcbaaabbbbaabbabddbbdccbdcdacdcaccbdddbbbbbbcdcdddaadbaabaabaddcbbbabdcbadcacaadcabbcdbacbcbabcbcadacbabdcacacbbdbabdaaddaaabcbbcaabddadbccdadbcdadabcbccbaabcadacbcdddcbaacbacbbaaadabccdbaaddbacbcdaabdcdddbbccaaddbdacccacacddacccabcddccdabacabdaaabbcbcbdabdccbaddbacccacbbabcaadccbbddbdacbcabcbbbdcbdccbbcbdccdbdaddcadddcbcacbaabcbcbaabbdcabcbddddddbdbbaccbbcbccdbbacdbaccccbdbddadaaddabdacacaddcbabbdadaacddccbccbcaadccadddabadadbabcaabcaacdacdccabccccdcadddccacddbdaddaacaccacbacadddcdaacbacbdddcdbdcdbcbbadcdbababdbbacaccabcabdbdbdacbdadaddcbdcbbaddbcbacaadacdaaabacadacdbbdcdabdadcccdacaddadcccdcdbdadbcbcbaacdadbddadbbdadcddccdaccaadadbbcbabdaaadcbbdcdcabbbabbdbcabddbaabbbbdbccdbabcdaaadcdcaadbddccadcccadaccbdaacadbbcbbddcdbaaccacbddddddddcbccdcbabcccbcacacdcdcbdabdccbcbbaabbbdddacbdabbaadbcdabddacdacdabacaabcccddddcacbbaaaddbbcbcdabdcbdbccbbdbdacdcdbdaacbbaacdbcdacdcabaaacbddcaacdcbbcccbccdbcabaacdcdadbdabbcbadcdcabbadcadcadbdcabcdbadcbcbaddbddbdcbbcadcccbabbadcdbccdcbaaabbdaabaacbabdadbbdbbcdbabccbdccccbbdcddccbadbcaddcdcdacdbbcadddcbbaaaabdbbddbaddaaccdcdbbcdbcdadccdaadcaddccaabbbadbabbbbcdadaababccbdccaacdabccacbaaabbadcdadcbabacdbdcccaacdddddcadbabadbdccbdcbbaadcaabadccbcddaddbccddccdcdbbadbbbbdbddaadcbdcaadcbcaaabdabbcddddcdaadcbacdacdacbdaddcccaaddcadcdccdacacdaddabbdcbadabcdcbcaadbababcbbbbdccbbaccdadbcccabcaaadcbcdcabdcdcacaddaadcbcbbaacaddbaadcadbadabcbcaaaaabddcdbcdaabbaacadcbcabdaddcccccbdbddcbbdadbaccdbbbadccaaaabaccbadccbdadaaddabddadbcbdbcddcdabadbdbbaadabbbcaaabbacabcabbcbdcadaabbbacbacdbbcbbbcbdaadcbcbaccdcdaacadadddbbdaabaadacbcaabcdaddcabdaccdccddbaccbbdbbcddbcabdddddccdadbbddbdbdccbbbbacccccaababadacdbbbcacdccdddcbccddbbbccbcbdbdbbdbcdbbbddabdddcdccdbabbbbdbdbbbccdddaaacadacbdaaacadcddcdbcaaacdadbbbdbcbadbbdbbaaccdbddccbdbadadddacbaabbcabdbcabccadbaaddddabbbcccdbcadadbcdacabdaddaccbadabaaacdcabdacddcdccacbbbbabbdccbacddadbcccdcdddcbbcdbacddccccccccdaacdcbdbaaccdddcddadcbdcbbaacdacbddcccdbbaaddbcbbbacbcadbbdaadaabbdcaadcacddbdbcaccbbdabdbcbdaabaaaadcbaaabcbdbcddaccdcdadbdadcccbbaddbccaacdaabcdddcbabcdabbdbdaaabcbbdcbaadcaadbbcccbdadaaabbdcaccabcbadcadbcabbcddbcabadbdaabcbaabbadccaaccbcccbdccdbdcdbcdcadabdcdbcbbacccdcccccbacaadabccbcbaabbcdccbcadabacbdbabacbabcaaabcbbabdcdcbababacabddbbbabbbddbddddcccadcdabcbaaadbddbccccdcbbcbdcddcbbbacdabbbddcacacaadccbbddaacbbcbbcdcdcaaccbdaabddcccabddcdcacadcddcaacbacdccbaddccadbdcaccdcabbdabbcaccbadacdccadcbaadbbabbbccdacaabdbdbdabdbdcbdbccbbddbcabcdadadaccdcdcacdddacbbabaddcdaadabcdaddcbcbcbddbdcdcaaccdddbaadbbcbcdddccbdadaaacdbbdacadcabcdbddccdcdddcdaaabddaadbdabacbddbacbcdaacbccddbbdbcbdcbbadaacdcaaabbcdbbbcbaaddcbbdbaabdcaaddaacbcdcadbdabadbdbddaddbdbaddbddaacdabbddcacddddaddbdcadbaabcbcdcabbaaacdbdcccadabcadaadccbdbaaabaacbcaabbccacbbaccbddbbcdcaddcbddccacdabbccdcbcbaaddbbcacccbbdcdcaadadcbbbbdabcddbbcdcbdcabaddccdadcbaddcaabadcccddcddcabdcbbcabcddbcdbcdcbcccdcdddcdbcadabbdbcbbdddbbdacbaaddbacababaacdbdbcbdaddccdcdcdaabbcacdccaaccaadcddaddcdaacccbababbabadaaddbcbadbdcbbabbaabbcacbcaadbcabcdbbbdbbdcdcacabdadcddddacddcdddcacbbdadcdbbcdabbaddbacdcabbcddabdcbbcdacdbddbbcbacccdbbdbbddbbbaadccccdaabdbdcdabdbdcdcdadabcaadccdbcabcabdbccbcaaccbdaabbdcacddcadbcddbcaadcacbdcdccbadddadbcacabbaaddbcccbbcabcdacabcacddbcbdbdaccdbbdbdcddadbcaddcaabddbbadccadddcdadbccbacdcccbbdccadcbbbaabbdabcdaadccadcbccbabbadabccbdbadbcbdbbabadadbdcdbcdcacbaacbdabddccbcddccbcdaddcbddcbdbdbdbdcbadacababbddaadccbcabddddbdadbdacabdbddccdaabdacbdccddbcdbdadbcdccccdcaaaabbbabbcdbbabbaabdddbcccdddababcbddaaabcabbdcbbcaacdcbdddaacadbdcdddababbcdbbcbaababbaaacadcadcdaaabcabdbcdcbbacbbdbaccccabdbabccababbccccbbacaabcdbbbbabbaadbadcacacddcdcbdbabbacaaadcbbcccadddbcaabdbbdcacbbbdbbbcdbdcadcddcadcdcdbbcbcbabccaccaddddddabbaaadcbcbdaabddbbccacccabacaadaaccbcddbaabbdcddddbcdcbbcadcbdbcccaadacdaaabbdbccacacbadabbdadcdcbbdbbccddbadbadccbdadbbcccccadcbbcdcdddbddaccdaddcdbaacdbcaccdcababdacbbaaaaddddddbbdcadcccbccadcdbbcdadbbccddcddadcadddcacacdacccddbbddbdcbbddbcbdadddabbcdbdbbccbcdbcbcacaccbaaacccbdadbbacbaacacadaabccbbadabbccdacbdccadbacdddbbbdbcabdcbaccbcdcdbbcdbcbcadadabcadbddcabcbaddadddcacbcbbabdccdbcdcbaacadbddaddaabacbdabbbbddbadababcbaabbabaabbaddddaaababbbdcaaabdbadcddbcbabaddadddbadacbabaaabaacadadacdaddbdaddcacddaccacdcaadbcaaadabbdbdbadcaacacdbcbdacbbbdadaddddaacddbdaddacbbdcbcbaaabdbbdbbbdbdbabcddcabaabbaadbcaadcdbbdbadaaadcadcdabbaddbddadddccccddbbaaaaabdbbcbcabbcacacbdaaaadbdabcacacadbbbcdaaabbabbccdbccaadcdcddabdcddabcdbbcdaaabcadccbdbcbacadcddccdacddbdbadcbdacbbacaddcaabcdacdcbcdccdbdcddbdbcbaacbadcbccbbbacaabaddcdccdbbabdbbcdddcdcdbcbbabcbcbddbbddbdaabddadaabddbccbddcbacccdadccdbccdbaccacbdbcadbbcdbabdcabcbddabbbadcacdadadabdbbdcddcabcabcbbbccadcacdaadcbdddaaaaaaacdadbccacbabdcddadabcadacdcacdadbaddbaabcdddadabbddaaabacbddcaddbdccdadccdccdddacaaadcbbbacddcddababaabaadbadaacdbadcabdacdbdcacdcabcbbccdbdbbadcdbaaccdbabaacdbddabadcaadbcacdcbabdbbccabcdccddcabdbdbcadbcbaccabdbdacabbadbdaacbacdddadacdaddcabaadddabdabccdacdcccaaabbbabdabadabbdaaadbabaddbdcccdbbaacbacdabadbbcbacadadddacdbbaaacaabbdccbcadbdccdddbbccabcdabaadbdbbbcadbaccdacccbdbbcdcadcabbadbdbcbdcabdabadaadbbabdacbbdcbadbbbbdbdcdadbcabccdbcaadbabaadbaaabbddadcbacabacabdccdcbcdcdabbbbddcdbdcdcdbcbabacdcbacaccdddcabdacabdddccbdddbadbdbbcddcbaccddbccbdbcddbbdcbadacbadbbdddcdaaabdbadcaadccccdccccacababbcabccdcacdcaaadbbadcabbddabccbaaabbdaacacdbcbbcadbdcbadbdaaddcdbcccaaccabbcabcaccdcddbaacbcddabbdcbbaccbdaaddaadadbdddbdcddbdbcbdaacadbaaadaabbadadbcbbabbbcdcdadaabdcdddbdddbcbbbacbbddcdddcaaccdacadbdddadacccacbdbbbcdabbddcbcdadbccdbdadbbbabacbbccaaccacaddacdabcabcabbddacaddbcdccdcddcbcccbdcbdaaacdbbabbbbadbaccbdaaccdddadcbdbdcadddbabadbdadddacbadaadcdacddcddacacdadbcacdcdbdcdcdadabdabdcdaabadbaaaadcbcdadbdacbadbcdbcadbdcacbadddaccccbacdaadbbbacddcddbdabbbabbadddddcaaccaadbcaaddabcbccaadcdcdaaabdabbbacbddccacbadcbdabcbbdbcaadcbacaaccdcabbadbadbdbbaabcddbabbccabdbcdbcaddccdcabcaadcdadddbddaddbcbbbacccddbdadcacbcdcaaadacdbbbdcdabbbccdacbbabdbccacadaaabddcabbadbcdbbaacbcacbcdbcdaaabddcadbabcdabdcccacaaabdddcbabbabdacbcaaabddddbabadcbcdbdcbbdabdbdabdaddbdbbbcdbcddcbcddaadabccacadbdbcabcbbbacaadbcbdccdbdbadaacadcabbcdbdcbaccbdbaccbabdabaaccabcbdcaacbbbabaabaaaadbdcabacabccbcaabddddacadcbbcdbdbbbbcccacbbdadabddddcacbbbacbbbcacdbaabbdbcddacdadcddccbdaabaddadccbcaaaccbccdaddadbdabdcddbabccddacdcbcccccacababadabccddbbdabdacadbcacddadbabcbdacaaccdddadbdcdbcaadadaabbbdadccccdabcbccddcdcbaabbbbdbdadcdabdacbddaabcccaabcabddbdcbcbabbabdbdbbabbcbdbacaadabcdaccccaaaacacccbadcbcacdbbccaacdbaabdaddabbdaccccbbbdbcbbbbaadcabbaadacdabccbcdaaaccccbbbdcadbaaaaadcaabccbaccdadbbbddbbcddaccaaccbcadcadbdbadbbcaccaddcbabbdccbbabbdbbbdabcabdbbbabaaddadbbbabcbabdbcdccccddcdbdacadcdcaabaadabcdaadbbdacddbdbdaabccbdbbccbdbbabbbabcabacdadccacaddabbaabbcacbdabbcdbdbabaccacbbdbabbbacbcadcdabdbaccdacdabdabdaacddcddbddcdbbcbddabcdcabaabadbcdabadcabdadcadadccdddcbaacabaaddaddcaacadcddacadccbcadbcabbdbdbaacdacbbcabdcddbcacdacdcccddddbccdacbcaaacacbcdcdaadbbbbdaccbcbdabcdcbbbbddcabadcbdabdbadccaddbaacdcbccddaddacdbaabdcdcacabaddabcdabdabddabadadbabbadcdcacdcbbbdbcaaadcbbabadacccaddabdbacbacbcabcdabbbcddacbcbbcacdbbbbbdabadbadbabaabcdbdbadbccbacaadbaddabccacbdcaaabbabcdcadbcdbddcbaaccccdadbaccacbabacaaabbaaccdcddcacaabdbcadcdddccccdccaacaadccaaadabcabccadbcdbbcadddbadcccdbaddcdaaaacbcdccccbcacbabdbdaaadcdabbcdbabaababaaccbbddcccadabccbccdacabadadaadccbdbbddcccbacaacacbccdcdacddbcddddccacdacacdbdcbcccbbdabaabbbdcdabbacbdcbbaaddcbcdbbdbcacabaacbdbbbcdbdabbaabbbddddbbdabcdddbabaabbcabddcbaabdcbcaaccbaddbbdddccdbbcbddcaacaabdcbaacbcdcadcdccabccaccaabbccdabdbbacdccdcbaabdababcbbaaaacdcabcabcadcbcbcddcdcbaabdccbbddddbcbbbdabbadaddadacccadbcccbbbcabaaaaaddabdacbabdaccabdbdbddbcaccbccccdbaaaadabbbbcabdbbcbdccadcacbddddadadaccabcdadbcbdabbcabdadadcbbbcbaacbbcdadbababcdacabdbcccddbcbaadaabccaacacddcbadbcbcadacbbcddcbdacbbccdcaacdcacabdccbbccbcbdbdaccdccdcbbdbcbaadabdbcbddbdabbbbbbddacdccddbacbdbcaacabbaaabbdbdccbdabcccdabbdbacaccccdcbaaddabacbcdddbabdcccdbccbcdbbcbacbabdacaadcadcbdccbcabacadcbaabbbdadcbdaddcaddadbbcbaaccdbcdaabdbcbcddccdcbcaaaabbccbbdbbbbaababbacbaaddcdbbbcbbabadaadcaaaaddbadbdbabdadbbcdcbabcdacadbacacadbcddcccdccdcaadacbcaacdcdddccdddabcaacbacbcbadbbacaccbbdcddcabcaddcbdacaaddabcddbbdcabcabbbdbcdddadbabcdbbdbbaabaccdccaababddcaaccdbcadccadaaddccaacdbbbadcdbdacbbdbbabbccdbbcaaabdddcbbcdacbaadaaabbdcbcaddabdbcadcbdddabbdbbacabccbbdadbacddcadbbbcdcdbbdbdbaaddcccdcbaadccbcccdacbdaddcbbdbcdacbcaabcabbbbbcbaddaccacdcccacaddbbadacbcadacbbacabacccdaabbcacaddacdadacaacabdcacbcddbdccdbdbabbdaaccbbabbaccdddadbbdaaacdadcddaaaccacbcbacabdbcbaddaabcbccbcbcbcdcadcccddabbaccacdccbbcbccdddadbddabbdcdcadcddccadadbaddcbaaababaadcbdbbccaadadccaccbcdccbcbdabdaacbdaacabaaacdbcbcddacdacdabaaacdbcccdabbcddcdcbccaadddccbdabddcbccacadcdccacbaacdbcdbacadbbcadbcdbbcccbbbadddbacdcdaccbcbadcbabdaacbdadaacbcbaacdcdacccaacdbdcddddcbaddadcdbaadbdcdbdbdaabbbdbbadcaabcbcaaaaacbcacacadaaaddbabddbabdcadbcbdbabcbbddbacbadbccbbaadcabdcbacdcabbabaabcacdbbbaadbcbcacacabacaaacaabcdacadbacddddcbcabbddaacadcbddbcbbdddbcadadadbacccbbaccbaddbcdbbccbccdcabaacbcabccdbaaabdacabdddddcdddcdbadcaababcabdbbaadacadcadddbadbdaddbdadccbbababbbddbccabbbbcbdabddcbddccadabbbddacccccaabadccabaaacccbacaaddaacaabacbbcdbdcaaacaccbbbbcacddccddadaabbcacccaddcdcddbabdcbaccbaaacdadbbbbcbcdbdabcccaadbbcdcdcbddadacbbbcccadcbddbdbbcdcacbaacccadbaadacacbbbbbdcbabcdccbddadcdbaabbcdabdbcbdcddabdcdcadbaacdbdacbbacaababbcabdbdbacbbacbaccacdbbdadbbddcbacbaabbdbbcabcbddaddccccabbccdccdabdbbdacdddacddcbcddbccaacdbadcadbcabababcccabcbcccbbcdddacccbdabcdcbccbabaaccaaccdbcddcabdbacdababbbcddcdbbbdabaddbdccbddaccbacaaccdcbdbdcdcbaabbcbadadbabcbdbcbaabacabdcbccdbbcaabbccbadadabdcddcbdbbdacdbccdabcbcccbdccbbabaaadaccbcbddbabdadbbcbcdacaddccacbcdcccbacabdcdcddbabdcbadcdcbcddbadaabbacdbdaaabcaacbcdbabdbdaccdbdbaccaabacdbcadababbcdcbccadabdbdddabccbcaccabdcdbbacaccbdccdcdcbdbabbabbdaddadbbbbbadadcaacabbdccddacbaddbddbabbcadbcccadbdabaabcddadbbdabaabcacccddccaadadcbcccbadabddbcbaabcdbcccabdadcaabdbcbaacbbbdabcdcbdbaacbabacbddcdcabdacabaabcddbcdaacadbdcddccbdadcaaadaddbdadbbabaddaacdcddabddddaacbdaddbcdaabcdabccdcbddbbcdcdcadccaccbaccdaddbcdcaddbbbbbcabbdaccaaccacdbdbaacdbbdbadaacaccbabccdbccacccbcbdddaadddccadbbaabdcccaacbdccdbbdccbaacbbadabcdadabbddaabcadccbcaadbdacabadbaabdbbccdbbabddabdbacadadaccbabdacadcbabaacdcdcccbbabcdbbcabdadccabbaadbccadccbccadbbbddcacadaccadcbdddadaabbcccbbdcbbabdcddbacdbcbcabdbcdbaadcababadbdabdbaababbcccbdabcabbabadadaddbdbcaadbbbdbbadaddbacabbcbbdcbdaccddabbabdbdcbacaababdaddccdccaccbbddacbbaccdaaccbcacdcbdadabbbaaaaabdbcdadbadccdcabbdabdabdbbcddbacbacddabdadcdddcbccbcadccbcbacddacddabbbacdadadbcdaaadaaddaacadacbaaaacdacbacbabbabdaacdcdcdcabadbdabbbaabcdbdcdacdaaabbbabcbcdcacadcabdacbbcabdadbdbaabbddaadbbababadcabbaadbddbcddbbbdadcbbacdadadaadbddddabccddbbccbadabbaacdabdaadbbbdacacbaabcacdcaacabbaaabddddcddcabcdcdcabaabdbbacbbaadcbdcdbcbdaabcdddddcdacbcaccdcdbadbddbbbacbcdabdadadaadbcabbdcddbbdcaccdbdadadabbabcacddabbddddddaaabaddbdacaaacadaacddbdcadddaaabcdcaddbdbdbbbddcadbaadbbcbccdaddcacaacbddccbdabcacccabddadcbbabbbcaaddabcaccdbadcbbdddcbcdcbbbbbbcddbddbaabaaabadddbccaabaaadcacdddbcbdcacaccabbdadcbddddbccaccbbcbadccbbcaabbabacaacdbccdbdacddcccbacacdbabbbbcbccaccbaccccdccdccdabbdcabcdcbcbcbabbdbbaabadbaacdbdccdbbddaadabadccbdcdbbacdbccdaaccbdcdcbcabddbdacbdcaddccdccacccadadbdabaaabbcaadcddaaaababcdddbadbdcaabaacdbdcdddcdabaddcbcdbacadcbbdddddcbcdddbaacdadcbbcadabdccaccdaabcadbcbaddcaabccddccdaccaadadbccadaabcdbbadabaddcabadcbaaabcaaaaddbcaddadcaccddaababbcbbddddbbaaddbbdabccbdaabacbccdcabaadbdaddcdabcddbabbcbcccaabcabccdbbccdcabcaabaadaccabbbccbadacabdbddaaacacadddbbccdacabdbcabbbbacdabcabddbcdbadcacadcdaabddcdcaaccdcbdbdabddcbdaadcdbcaccdbbbcabbabaacbcaabdbccdddddaaadcdaabccabacadacbccdbaaccddbacaaccbaccbccbdbcddddddaaadbbdadddacbdaabacbbcbadbddddcddcdcbbbcacbbdaaadccdaaabcdcaabbabcadddddaddbacddabdabbcdacbbcdcaccdbcbbcbbdbdddaadcddacddadadaaabdbbbbabcdcacbbaaccacdabdddcbbdaadccdddbcbccdbbbcabddbcaaaacaacaacdaddbdacdcabababadcdabdccdbabdbccccaaaccacbddabccdddcacbacbdccbdbbdddabadacbaddacbddbccccbddcbcddcacdccbdbaddbbdbdacbdbbdbdbadcbbdacdadbccbcbbbdcddabaaddabcaaadadaddcaaacbbcdcdddabaadaaadbbabdabbbcbbdcddabaccddbdacbaaddabddcdbdbdbdcaddbdcdcccbbbcdbdadaaabccdabcdaaaacdbdbddbbdcaddbdcdbbdbacbabaababadcabdaabcddcadbbdcaacbbbdacadbcdbddbcbbdcabcadbadcbccacaadbbbcdbcbbcbbdbbbabddccaaabbbbddccbccbdddacbdadacbcabbaadcdacddaadbdabccacdadabbbcdbaddbccaadbacdbcadabadcdbdaabbddcabdccacadbabdaabcdadddcdaddddddaadcaccdbcbddcadbdacbdbbcbccbcaadddbccacdcddcdcbcdbaccdccaabdabbbabcbdcccadaabcdbadbcdbdabcdcaacaacacbbcbcdbdbbbacccabdbccbaddbdadbdddcadbcdcbbbbbccacbbadccadddaccabcbdccaacaccdaddacbdcdddcdaccaadbcbdccbcddcaaccbaaadccccacccbbabcddcbaddcacbcacbadaddddbcadbcdabbcacacbbbaaaabbcadaddbaaddbdbbbaadcdbddaaddcbdacdbcaddbbadddbbcaacacbcdbacbbbbdbacaadddbcccbdbcadaacdacdbccacbdcaaaadacddabcaacbbcdccbbdcbaabbddbabbbadbaaaacadbbddddbabcccaaccacbcaccabadaaabdbabdaacbbdcaccdacacacdcddcbddbbacaddcdacbbaabadccdcacbabdcbadcbdaabdcaabbcaacdbbabacccbcdbacbdddadcadaacddbccbabbcbbaadaadcdbabcabdcbdbadcdbbcccabbbcdbaabdbdabdcadccbddbadcdacdabdaaddbdbdbccdaadaadadacabcbabbbaabcdbbaacdccbdbbcddbcbbdbcdbdcabbddcbccabdaaccdbdddcababddcccababcbbadabdcdcbcdcbbdbaaaadbdaaddabbcbabbbccbacbcadcabbdaabbbadccdcbadbcbaaaabaabdbcccbcbbddbbbbbbbbccbbcbddbbaccccdcacdbcbbbcbaacdaabaaddbacadadccdcaddccacdaacccbbdcbacccbcdccdddccdadddddadcccaccddaabaacbbcdcdacbdadcaaddabaabacbbcddbdbcbdabbbdccbababacabbbdadcacaddbcdabddbacddccdcdadbdacababadacdcadccbcccdacaddcaababaccdcbdbaddaadbcabadbadddccdaddbddcccacdbdbadddbbcaadaabaaacddadccbaaacccbbacadbabbbbbbcbddccbbbdaddccddaacacdbadddcddaaccdbbdabbdddacbcdddabdcadbcbbacabccbddcbacbacdbccaaddadacaaabbbadbdcdcbdbacbbdacadacababcdadcdadbbbbbacbbcbbadabdbcbbcbdbdcdacadabddadccccacabcacadcdcbaaadbccbbcbaaacbbdbccababbcddabddcabbcacbabaabbbbcbbadbaadcddcccacacdcaaccaadddcbcccdabcdbcbdbaaaaacbcaadaaddbadcdcccdadbdbcdbddccdbccdadaddbdacdadcdbcaacddcaccacdbbcdddaaadaacdccabacbddcaddccbadccdaabcaacccbbcdcbaaabaaadadccdabdbcbdccbbadbbbcdabdbbcdadacabddccabcbddcdcbcdddcabaddacbbbdaacbbccbddaadbbccbdbacbcacaacabdacbcbaacccbdbacabcdccbddbbdddbbddcaaccdbcdddabadabdbcaadbbddbacaabdcdaadccaadaacababdabccabbbdbbddcdadcabcdccccaabababdbaddaadadcdbadbbbccadbdbbacddddabbccaaabdcaacbabccbdabbaabcbbbbcddaabbaabccddbccadbabbdadcadbabcddadababcaddabbaaabdaccdbaacbcdbbdaaaadddccacaadbdcdaabbadacbbdadbdbcabababcaabacadcdbabdbbbabbcbddacadccacadacbaddadcbdacacbcddbcdcdabbddbcdbacdcdbbdbcccabcdbacbdcddccbbdadbadcbdcbdbbbccbbaadaadacaacacdaccbbabbbacbbcacbaaaccdcddbbacaadbdddaaadaddaccacdadbaaddcccbdbbddcddcbadaaabddcbdcdaadcacdbdbdcccdaddbdaccbacadaabdbdcacaacbcacaddacbcccaabcabddacbdbaccabccacccbacdaaccdbccdcdbacadbbcddabdbaabdcdadddbbbccaacbbaacadbcccbbabcabcdabaccacbabbadcaaacbbbcccaabdcaccbcddcadaabbabdacdccaaadcbdacbbadbccccacaadbaddaacdabbddccddacacaccccaabcabdcddbaabaddccabdbadddcbbdadabbddddbabdcacccaccdccadaadcbaddbacdbacbddbdcbdbadcdbcabaaccbacdabdbdcddddbbabbbaacccddccaacbaaadbccbbdcdcddcddddbadbbbbccdabdbcdabbbcbcdbbdbaddddcacbabccddaabdcbdaadaccdbcbabcdcadbaacadcdacddcdbacdbccabcbcdbcadbabacabaccccdcabbdabdbddaabcddadbdaacaabcbbabbacbabcaddbacddcdbbbdcdbabddcaaadaddbabaadaababdddaaddcdacababadbbcaddccccddbccacabaaacdaccccdaddddbbacaadddddcdcdcbbbbdbaddcdccdcacabadbcaccacdadabcccbdcdbdbbdcadacaddcbdcdcdacddddbdaabdcbdccaaaaaadcabaaacdbdabbaacdbccbbdccbddbccbbdacdaacdaccdcccccbbbbaccaabdbdccddacaaadcdcabdbbdbbaadcdaddacbbaccbbcadddcbdadcadcadddaccdaadbccdcabbdbbbbaccccbdadbcacaccdabaadccbcbccbbcdbaddcdbabbaacaccdaaaccacddcdcdaacccbabdccddacaadaabadacccaadadadaddbdccbbadbadccbcacdcaaccaddcbbadbaccacccdbbcbddabdacdaabdbbcbbcbaadccdccadcabadabaadbbdcaacbbbacbdcddcacbacbccccababadcaadabaccaaacccbdbddacaababdabbbcbcdacbcbadbaabbbbaaddabcbcdabdbaabddccaccadcabddbabddacdbbacddadcccdccbadbddddabbcdaadbabbdccabbccaadabccabadbcdbadacbabcdcccdbabdaadddbaacdbaddcbaacdadbbabcbbbadacbccdcccabbdbdacbbabaaabbdbcacdaadbddbacdaaabaabbdbdcdaaddbdaacaaccddcadadbcacaadaddcdaadbcbcbdcbaacbaaddaaaccdbabdbcabbbbbabdbaccdabbbaaadcacddadcabccbcbcadbabbbcccbcaaabacbdbacdcbcccbdbdabbbcadbabdbbcadbacbddaacdbbccbdcbdbdcacccaacaddadbbbcbddbddacabbbabbbdaacdbabbadccdddabcbabdcaaccdadcdadccbbcdaccddbbaccaddbcdccabdababbbdbddadabdbdabdbdabcccbadcdbacadcaaaabcdccccbaaaaabbcddccdabccacbdadbacbadddbabbcabbdaacbdabcccadbdabacbacabcbdbddaabcbaacacbdaddbabddcbddddcaadbabdadbcacbdbcccdbacaaddcdbabacacdbdacbaadbcbabbbacddcaddaaaccaabcccbaadcddbcbdcdcdacacaadcbddabcacaacadadbbdcadabdddaaabcbdacaabadddaddabddcadbddacdcbabbcdbbabbbadacadbacdadcdcacaccbaadbacbddccacccadccbcddcbbdcadadccbbbadbdcdcdbbdbaddcbcdbababbccdcbdccdbccbbbdabaaacadbdccdbdabbbaaaadadbbbcbacaacbadbdccbabadcaccdacabcdadbbdbdcbbadbcacddaccdcbcbbbbcadcadcbdcbdbbbabacadbacbbdaaadaadbbddadbabdddaacddddccbacacbcbccadbcacacbcbcdcadbcbcbaddcabbbbaaaacbaccccdaccacbbccbdcabdccddacddbaabddcaddadbbcddacdcbdcacbacbdabbbcbccbbcaadaadacabaccaccdadabcadcdddabcbccdbababcdacdccbacbabcaddbabbabcadddbabcadcaaababacdcdadcbcacbdcddbadaababdacadcbdcccadbbdadadaacccbdbaacccdcacddcacdbdbdabbcaccbddacddaaadcacdaaaacbbcdaaccacbdbdacbcabacccabbdcdbbaccabdbcbdcabbdddcbcbdbcaabbaabcbcadbcabcbabdacddddabacbabbbdabdcdbaaaaadbddcabdcbbcbbbccdcbcbabacdcbacbacacbdacdddccdbcbbadacbbcbaaddcbdcbbabdbbbdbcaabcdadbaddaddbbddacdbbaabbbdaddbbbbcdddaccdcbacbacdccaccdacddcadadcbddbcdaccdcccabcdadbcababcdcabcccddbbbdbcbcdbcdbcaaabbacddadbacadabdacabdaaaccdcacbbbabcdcaabcddabcaddbdaccaacadbaaacbaaaccbdcacacccaadcbcabccbabcdabbbbddbdaabbabcacacaabdccdbbbddddcabcabbdadabacdaddacbcabdcaacdcdcacaccacdaabcdbdddbddbcabbaccbccaddcaadabccdadbccadbacadbcbbabbcdadcaccabbababacbcdadadbbddacbaadcdbbbdadcbaddcbcacbdcbcdbcbcbdaaaaacbbbdbcbdaaadccacaaddddccbcdcbbbbaaddbcabdcbdbacdabdcdbcddddcabadcacbadadcdcadcaacdbbbcccbdaaacbdcaabadbcdddbcabdcbadcbaccadaccdbcbdaaacaaabddaadcaccbcbacdcbcdcbdaacbbcbddacdbcaabbacaaaaddbdbbbdadabadbcababdacdcdbcbcbbcbbccbabddcaddccdababacdbcbaacabdacacaddccaaaacbcdaacdcddcbbccbadddddbacbadcddacbbcaccbbbdacabcabbccadccbbdbcdbccbbdacdcbababcccaacbcddddcacadcccdcddcdbbdcbcabdaadabdbaccaadaadddbdbbdcdacdcbabbadccbbcbddaabbbabcabdcadcbdcdacabdbaccddbdacccaaaabbbacaddbaaccbcadcacadbbcadacbdadacdbdbadadadcaccdbbabaacbccbcccbdbbacabdbdaaacbccabdadaacdcdcacaddbacccbadacbcdcbcbaccbdcadbbccbdccbbabadaddacdddacccadcbadcadacbbccbabbbbaaadbcbdaaddccbcabcabdbcaabcbcccdccdccbddbaabbbcddabccdcdcbbadaccbcbcddcbddddbdbabbdbcdaccdbaabacbcbcdbaacdbbcaddccdddabbdadbcccdcdccbbcbbbddbdbabbdabaadaaadbdacbdaaabbbcbddababbaaadbaddccdddcaadcacacbccacadddcdbdcadcbaabdacaddbcdbabbadbbdbabadbdadbdabdbbccbccbcbaadbdbabccaccdbdbacabbbdabdbdbdcaddddadcbbbbbbbadcbcdabadcacdbbacdddabcacaddcdccbabcdbcaabbbacdacbbbcbbabcccbdbbdadadabcccacccaabbcbabaddbdcccddbabacbddcbadcacabbbdddcaadacccbcdaccccdbadcccbcaaddbccbababacdaadadbbbdadbbdaaddbacabccccbcccdaccdbdbdaadbbdcacdddbabddcbaacdcabacccaacdcaccbaaddacbbcdaabcddcdabbcadcadccadaacbbcaccbcaaaaadcdaadcbcdcddbcadcdcccbcabcabbadccaabbddccdbaccabcdbbabdbabbacdcdabbddbddbdcdccbbadddcbccaccadabacabaacddddcddbcabdcddddadaadbcdbcdbbaabacacadacbacdabdcbccdacccacadcbaaabcbabacbcbcdaadbbaacacdddbaabaccdcdbcaaadaabcbbcdccbbabdbaaadddbdbdbccdbbdbccadadabddabaaacdcabacbccaaccbbdabddadddcaabcbbbccbabbaabdacdcbabbccdbbbcdabccaaadcddbcaaabbcddcbacccbddddbaabaabbdcdcbcdcdcddaacabddbddabccdbcbddcdddbabaadbabadadcdaaddcdccabbaadccababccbcddabcaddacdaadadcacbcbcddcddcdbacaaaabccdbdcbabdadbdadbacccdcbacbccbbcaaacbdadabbddcdccbcbcabbddbbbdacaaabdacbddcbaddcbdbbadacbaadadddcbcbaaaadacdbbaaacabdaddcbbdbdabccdbadbbbbbbbaccccddccbaccbabdbdabbbddbababcabbcddccbddcdaacbdccdbccddbcaaacbadcddbdcbacddcbddcdccdcaddbdcabadadbbdaddddaabacbaddbccdbbbdbcadabcacdbaddcbbcabdddcccccacaaaddacbbdcadcbdacdaadcbdcbcbdbdbdadbdcaacdacaababaabbddbdcacddaaccacddcacbacbcdccadbcccbddcdcbbccbaadbcadbadadcddcdcdbdaacaddcbcbaaadbaaacccbcddabcaabcadcbaacaddcaaacbadbbbbaaacbabdbcbdbcaabaaacabacbbbcbbccdabddcacbcdabdddcdaccdcbbddabbcadcbabdddcddadcddaadbbacaddddbaadadccdaccccbcadaacabdcbbbddcaacccccbbdddcbdccddccabbadcaadbcddbccddaadcbcdcaabccdccacdcdccdcdaacddacddbcddcaabddadabbbbaaaaabacccbaadddbcaaaadbbadcdababcdbddacbabcbbdccadcdcabccadcdadbdccabadcbbcacdddaccbbbbbdabacdbaabaaccabccdadacbccaccbdbcdacabdddcbadcdcaddadaacdcdbccddacdcaabacccdbddbbcbaabcaacaaabcbccbabaadcdddaddcadcdbbcbbcbcddbdcdabaddadbabdacabbccbdabbbaacbdccbbdacdbbbbbddbdbcacdacdcbcbbdcdddbacbbabbbadddaacbcbcacbabcaacbadbaacdcdbbababbdddcabcdcdddcccbaddadbacbbacbbbbcdadadbacacadbdbacabaccabbdbccccbadcbdadcacbcdcccccdbdbcadccbbcdcbcaadacdaacdbcaadcaddcdbdabbdcdaccaadbaabbbdbbadccdccbbbababbabcdadbddddcdbdbbcdaddccdcbbddddcacccccadabadbbbcbadbbaddcccabbadaddbdbbadcddbabddcbacbaaadcabdadbaaccbaacbbcacacdaabcbddddacbddddaacdaacaccadcbbcccddaccbabdcccbaadcdccacbacccdcacbbbddaacdbdcabcdacaddcabacbacdcbcaaaabcadbccadccdadcdbcadbabaacacdbacaadcbcabbccbacaacaabdbabbbddcaabdddbbdccabaacccdbacabcccdbdacadaaabdadcabbccaabccdbabbaacabbacadcdadaddbccdcaabcacbbaabcbadcabbbdcdcbbabbdccbbdbbcacacabccbbdabdadddadddbbdbadcdacacabddaccadddaaacabbaaadadbcdcdbddbddabcadbccbadccacccacacdabcabbbdcddddcbbcbbaccbbdbcadcaabdaddacabcdbbdccacdcacbabcdcddaccbbbdadacbcdbbaabbabadabbdddcacdabcdccbabbcbbcbcdcacbbcbbbbcaacbacbadabdbbdddcacdadadbadcaddddcbdbbaabccacbddcdacabcbcabadaddcaaadbadddaacabdbaabdacaaacdddcddccabdcabbbbadcdcabbdddcccdcadccdcdccbdbabccbadccaddabacdabcdbacaabcabdccddcdcbbcddbcccabbcdbbcbbabcabadbcabbaadacbbcddccaacbcccaccbaacdbcdaaadccbbadcdbacbaadbcbcddcdcccabababbbbacabcdccaddaabaadadddadbccdcadcbccaabcdcabbbbcabdbcabbbbdcabaacbdddbcababdaaaabbacbddbcacbdabaacdabbdacaacadbbcabdcbdcbcdcabccaaadddcaadaaaaacbcacbaabcdcdcddbcbddaababaddbbaacbaabcdabdcbbbdcdcdcdbbaaaabaaddccdbdaaacdacadddbabdacaccadcccccadcabababbbabcdbadddbdbcdbdccbcbcdcaadddadaacbaddacdccadcdaadadbbcbacdccbbdcbabadbdadcadbddacabcbbcaccaaacccbbbcbacbdcabcdbdcddccacacadbbabdcaaadbdcbcaabacdaabcbbcacddbadddabadcadbcadabababcccbdbaaabcdcdddcbbacacbbcdccbbccbdcbccbdadbabcdabdcdacccacbbbcbccabaacddabcdddabdabdcdbcbdabdcadbbbcacdabaddaacaddcdccbaadaccdbabbacbddaaabaabccbbbddbacdbacbbbabdcdbacbdccbbadabbdabbdcbdcdacbcbbcadbbbddbdccababbbacbacbbdbdcccadcdddcdbbacbcdcbdaaddccbaaabbababddbabcbddaadbbcdccabdcbdcbbbdabcdbcadbcdcbbabccacbbdacdadcccbdaccacdabddbdbcbbbaacbbaccbddccbdadcdabaaaabbccabdbdbdbadbdbaabbbbbddbabdbbbdddaabddababbddbabdcdcdccbbacbabadbabcdddcabdcdcdbacaacbcbacbcacccdccadccadacacbaddcbdccdabcabbcccdadcdbbacacbcdacbccdabbadcbadbdbdcdccccbbdcdbadddbcbccbcbddbbbcdabbccccbdcbbaabdcabcdcabdbbcbcbddbdaadcbdccbcdaadbdacdccbcdbadbacadcdcbdccccbbbbbdcaacddaabaaaadaccabdbcbabbbbbdbbdabbacbdbcccadbdaaaacbddbacbbddbdbbdbaddabcaddcbdbbbaadababdcbccbcacdadccabdcccddbbbdacbbadadabbacdbbadaaccbbadcbadcccbcbdbdcbdaabadcddbbccddbdbacaabcdaacdabcaabbacbbccacbaadaddbadbabddbdbcaaadccaadbacbabdbbcdbbcdbccadbbaaaaacbccdbdaccaaadbacbdcdacacbacbacbbddacdccbbdbadbbbcaadbbbdbabbacadccaadabdddacbabadbadcbbaadabaacacadcaacaccbaabbbabccacbbdabccbdcbacddddaadbccbbadbacbacacbdadbcddbaaabdbccbaabcbabaacdacddddadcccaadddccacbbacdabadcadaccdccccacabbdccdddcbdadddadaddbdcacabcbdbcbbcddabbcbdaacbdbacdadabacdcbccdddbcdcdbdcdbaadbddbbcdaacacdcadcbbddcbcdbddacabbaaabcbabbbbcadbadbdddaabdcddddcbadbccdaaabcbbabddbbdcbbdddababccbdcdaadacabdbdaddabaacbddbabcdbccdcabaabccdccdcddadabaddaccbbbcdaacbcbbbcdacbabdcbdaadadabcccabcbacdcdcdbcadddcaacbabcddbcdaacbaaabcacbadcdbbdcaacccaccdaaacbccaabbdbdabdaddcdcadddadaabaabbbbaacdacdabacabdbadaaacbaacbdcdbaaaddddbbcbbabbababcdccddacbdbdcddcccdccccbbcbdadbcbdcccdaabcaccaaaaaddbdadaaaabbddabddbddddadbaacbadadaabaddddabacdcdbddcdbbdacdaaabcccbbadbcbbcbbdabddcdcdcdddcbdddbcdddbdabbbbadbbbcaddbdccbcbcabcbbcbdcddadadaaddacadcbbabdaabbdbbbdcbbabddcaccdbcaddddaacacddbcacabdbabdaddddcadadaadaabbaadbddcdccdcacdcbbcdbdcaaaabdabbacbcacaccbcdcaabcacdddabaddabaadccbcbcdbccbdcabdabddcbdaccbdaacbacaccaacaddcddcbdadcaaabadaabdccbadadacaadcdaacdbbbaaaaabcddbbdddbbccacddbcbcbbadcaacddbccbddbbabcaaadabbddcaadbbadabcacdbbddccaccdabbcdbabdaacaadaabadbcbaabcdbddcaacbadbaccbcbcdbdbaadccccdbdabcabbbdacaabccddacbcaaadcbbccacdbcababdbdbbadbaabacbadcabbcbaacccbdababcdbacbcbcabbcaaabaabaccccadbcdcaaabbbccdbaaacbbbaacbcdabddbdacabbbcbabdbdaacbdcabbddacabadbaacbcbbccaabcacdadccbdcabcdcdddabbabcbadcdcbaacdacbbbabcbdadcdaadabccbccadcddabadbdbdbddddccdddbbbccadcddbbcdbddcbbdbaaaaabdacacdadaaaadabbbdabbadbbabdcddacadadddaaacbcbadbdabbbdbcdacbbababbcbbbbddbccbbdddcdcadabbdacdbdbadbdacdcbcaacdccacccaadacadabbaccbadbddbcabbacacadcdcdcbbbaabbdcadbabcbaabdcdaccddbbabcdcabbcddbbaaadacdcaddbdcccabcaadbacbdbaacacbaacdbcdbddbbdadbadcaaddadadacdbdcaacdabdabccdbcdcbaddcccbcddbaddabbacbdcccaaabddddaaaabcddbcbbcbcdbaacabbacbabbacbcddaabacbaccabbcccabbcdaccbcdddabbbdbaacbdaabadbccdabccabdcdcaaabdcacdccddbbcbbcdbbcabccbdabaccdbdcdcdaaacaccbbabbacaaabbccbcbdcddcbdddbadbabbbddccabacbcaccdccdadaaadcdabcdacbddcbbaadacbcabcdabbbcddaacdaacccdbaddbabdabdabcdabadabbdbdbaacccbdaabbddbccbdabcdcadbaadbbbbbbbdccdcdabdaadddccdbadaabaaadbdbcaadddbabbcaabbabccdbdcdcbbcadcdcddcdbdcbaadcbcbababbbdbdbbcbbcbacbbbdcdbabbaaaddcdabadacacbbaaddbbbcddacabbbabdddbcdadcaadcbdcdcdaacbadadabccabaddabbaccccacddcbacddcddccbacdabccdbbbbcccccaacccadbcccaabbcbbbdacadcbccbccbdcaddabcbbdcbbaacadbbccaacddaaaddcacdbbadadadacdbbcbcacaaabbacdaaaddcacbbdbbdbabdddddadababdabcbddacbcbbacdbbcbaacccdadaaddaccacadcaddbbcabddcabdbcbbaccabcbbcbbddccacccbbcdbcdbcbadddaadbcdcddbbaabcddbacbbdbbcdbbdcadadadcbbdcacbcccabcabcbccabbabbdcbdbcccadaccbaaadddabcbcabbcacccbacdddddadccabacacababbdadbaddbddadcdabdbccadbcdddbddbdcbabdccdcabaacacbbdbbdaddccccbdcddaddabdbcadbbdadabddadcbdbddcdacbcaddcddccabbbcccaddaadddcaacbdcddbacaaaddadbcbbacbccddcbabcccaabccadbbcabcddaacaaacaadabaaabaddbdaabcaacadbaaadddcadccbcaaddcacdaaadabdbcaadaccaadccdaacbacdadbbdddaaabdbcbcbaababcaadaddaababbdccacadbbcdcbbcaddbcbaddbbaaabdbaadbacadcbdbadbcdbabbabaaabdcbdcbdcabbbadabbbddaaddbccbadbbbbdddaabacddbadcccbacdbdbccaaacbbaabadacbbacdaadbcadadbdabdcacbdabddabdacbadcadcaadbddcdcccaadcdcccbdacddadabaddadcaadacaababccdacddccbdadacbbabaababaccacacacdaacacdaacdadbcaddacdacabdadcdcadddcbbdcdcdadbbbbccbcccbacabaacddbbdcbcbbbdbcdaccdbacbcdbbdacacccabddacacddabcddaadbddbdbcabbdcacbaddacadbddbabdadcacbdbcdbcdddcbcadddaccdabbbddbaadbdddbcbdbdabdbcdadaacbddbaacddbbbdbcbbdcaadccacbccdddbdaaadcccdcaaaddacdcbdbcacdbbdaacddadaacacbbaacdcadccaddccdbdacccaaabcccadcdabacabcbaaaabcbbaacdaddcddbcddadaabaaddcbdcaccbdaddbabcbdccbbbdaacbabaadabcbbcadbaccbddbbcaabcaacbbdbcccbdabcadbccbcacbbcbccbaacacbcaccbccbcbbbbacbaccbaccdddbbdaacddbbbcbdabaccbcadcbdaddbdbddaddbaabaaaaaccbcccdbdbcbcdbcbabddbdbdbabbddcdddacaacacacdbdababcddadbabccdcacbcabcbccbdcdbbbaaacbbbadccaccccddddcbabadabbaddbababacadcaaddddabbabccabacbbadaccacbcbacdbabdcaccdbcdbddcccbbbbadccaaacdaaccaabdbccccccbcdbaadcaaadcccbdbabcbbbbdaabacbacbddaaadadbcacdcdcacadadddbbadbddabbcbbbadabaadbdbcabdbddccaadcbcabaccabdcdbccbdadbddabcdaadccdbbdadbadaaabbbabaaabaddbacacadcbdcadbddacbacbdbaadcccbccbabbcbadabdcaccdadccadacabbbaacddbdabdaadcbacacdaabddaaddaaaabbbdddbdcdbbaaddabddcbbaaacbadcdcbbacdadabaccbccabaccbaacccdaaaccccbbaadcdaaadabaaccaaaaaadbdccaacdcdaaadbcdbaaaddccddbbccaacccabaccadbdbbcbddbbddccbdddaacadcdcdbbaacbdbaabbbbcbbcadbcadcabbcdbabccddcdaaabccbadbaccaaabbdadacbbbbdccddcccbddcdadcccbbbbacdcccccbcaddbadbdddddabcddbddbddacdbcdccdadcbacaddbdbdbccbccacabcdcbbadbababdabaccabbbadadaaaadcacccabddbadababdaadabaccabbdaaddcabbbadbcdabcdbccbbaaababdccabcdddcccccaadaaabacadacdabcadcddaaaadcbdacbacbbcbcdcbabbdccaaddaccbcdbdacddcabbcddabccbbabacdadacbaacbdcacdcbabacbccbcadacbddddcabadadbaaddbdcbbdccaadcbdadcccacdcdccdaacbdddcacdcabdcdabdcabaadabddcbccadcaacadbcdcddcbbdccbbddcbdbbaddbabdbbdbbcbcdcbaacccdabdbadcaddadcbccdaacabaababddadbdbbdcaaccadddaadadabdcdbdcdccbdcaadaccabdddacacadbddbcaadabddbddbabcaddbcddcdbddadccbcadcdcaddaccdcdacbaddbcbcaaabbaddcbbdacdaaaddcbbacbacdbcadaabcbccbbbbccabbbacddcdbadbbbbbccdabbcbadaddccccbbdabcaaacddbaabbdaacdbbddbacaacddbacbdaaabcabbcbcdbddabdaaccadbcbdcbdbcdadaaabcbdbdccbabbcbaaabbcdbdaaabadacdcdbcdaaadabbdbbaadaccaccdcdccdadcaddbdddbbaddcadcbacbddcddacdcccbdccdddaccaddaaaddadcdbadbbcadbdbdabacbaddaccdcbbaddbdaddccbcdbabcddccddcbddcbccabdababddbcdaabdbbaadcacccabbcbbacbdbbacacddabcdbaaabacbccabdcdadccaaddabdbaddaacccdddcccaabcabbbaabaabaacabccaddbdaacdaaaaadaddcbadbdabbdabbcaaaddcbbdbdbbaacdddbdbadadadaabcbccbbadaddbddbacdadaadccbcbdbbccacaacacbdcdcdbbdcabdadacbbdbdcbdbcacdbdccbadddbbcbaabcddccdccbccaadacbccbbabadbbddcdbcadadbdacacacadcbcaccdbbbbabadbccccbcbccbaaaabdbdddbaccbcbacdccbacbbbdcbbaadacacabddbbadcdadabddccbbbadaabbbbcabadddacabdbcccbbaccdccbdbdacbcddbacdadbcdcbdbdbacdcddbcbdaabcbaccbacaccdcabbcabadbbacaadacbcaabdaabadccbbdacbddadabadcadaacbccdbbaccdcbcbcddabacdbbdcacaaaaccabdacbdabcabddcacdcbcbcaccbdddbdaabddbbbaaccddccababacddbbcbddacddaabdadcbcacbcdcccadcbdabaacbdddaacdcbdaaddcbaacbaacadbbaccbcbdcbcdbaadcaaddbbdabdcacdccdbabbccabdcccbaababdccdbcababbadbdcbbcdcbcbaacdadcaacdabbdccbabcdacdbdbdcbadbccbbbdcbbbcaacbabbacaadadabdcbdbdcbbbcdbcbccaaccccacbcbcaacaaabdadcdabcdbcadcabccddcacaccabbcbbbdbdcdadaabaddadbcdbdaabbabaadacbdaccdcaadbddaaaabccccccccaabcacadddaaaaddbacdcbdbddcaaddcdaadaadbadbcababdcbdbdcbaaadbbaaabdaddbccdddddbdbdddddacaddcabbdabdababacddddbacdcacdbccacaaddbaabbccccdadbdacbddbaabddbbaaccbabdaaacaacbcbbcbbbdbadabdcadbdcbddcbddcccbcccbabdcbcbbdacbcaabaabbdbcaabadcddbdcbabdbcacdbbdadbadccdaccbdabcbaabbdccccbbbdbadcbcbcabdacbbdccacacabaadbcdabdadccdbdadddbdbdcdcbdbccbdcbcbdcdcccbbcdbbaccbdaabadcabdcbcbcdcdaadcbccdbcaccdccddcbcdbddddacacbaccdbccbbabbaaacdabaadccbbbddddbbdbbcadbdcbacadcdbddbcdbaccacadddccdbdbdcabdbacaabbcdbabbcbbaabdbaddccbdcbdcdddadabcbbadbbaddadcaaabbdccadcadbaccabccaabacabdbacbacdabccacbadacadbdcdadaacabbbdbdcdabccbdbaabaaadcbddaccaaaaabcadbaaadccbdcbbaaacbdbdadadccadbccdcbbdacdacdaaabacbccaaabccadddaacbcdabccdbbaaacdabcbdcdcbbdccccbacdaaaabccaadbccabccdadccdacadbdabcbddadbddccbbdabdbcabcdacdbbabbabaddabcbdaccddbaddcdcddccadaccacdcaabddacaaaabbaacbccaccbacacbbddadabccdcaabbbdadbbddcdcacbbccaababbdbaadaddbabaddbababcaccbcbdacdbcdacaddbcddabddadbbcccdcbcdbaddcddcbabcbbddaaabddaacababbdadaabcbbaaccdacabcacbdacbdbbcdbdaccdbbdabcacbacdaaadacbaaabcdddcbbddcdabaddabcddcdbcbbcddbcbbccbbcdadcccbbacbbcddccabddbabdacbcacadabbacbdabbadccbbbaccdacdadabbacaddbaccacabcdbcababaacdcabdcaadbabaddadbadabcdcbbdbbbcbcdcdbdacadcdcacdbcdddbdbcdacbcbaddbcdadbcdabaacccaadbbbbcadbadbbbdbbbdcdacbbcdbdbcdcbacabcdccdcacddbcddcdcbccdacbbbbdcbabbcbadcbcacadbdbaaccabaaabcddbcdcdbbbddbbbbbcbadadbacbbdabcdaaddcdacbbcbdcbbabddbcdaacacbdcabaacdbaddbbabacbaacadbaabacabcabcddbbcaadaccaabdbdaaabcbdbaadcbcdbccccdcadbcccacdacbcacabbdcabccaccababddbcadaccadddbdacaddabbcccbbccdabbdaabcbaadbbddaabbdbbdcbdaabadacdaadcadaddcbcdabacbacdacdbabbccabcabbaadadabcddbbbbbcdcaaacbabbddbdaadddadabaaaabcacccdbbabccccbacdabdcccbadcdddaadcaacdaabccaadacdbdbaccbadaaabbdbaddababbcbbacdbaddaddadddabccaccbcdabccbaacaaacaabddbdaadbbcaacdbcccbaddaadaccdbcacbcbccacdbbddccbabcddaaaccdcaccabcdaddbbbdcabdddcccbbabbcddcbdabcdbacabadbdbabbddcbabaabacdcaaacbcaabcabbbacddbdbcdcababdcdbbddddbccdcddcbbcabacdbdbbcbacacaacdcdcccbdbabaacadcccacddbaaaddbbaaabddcbbbbccbdcddaacaccbabcbdcaaddbcdbddaaddaabaaddcbdbaacabbbacababdcbaddcaabcaacbbccaccbdbabbaacbddaacdabcbdbccbccacbacddcacadddccdddbdccbbdbdadcaadcacddbbbcaaacddcbcdaccacccbadbcaccacbcbbabdbbbcbcdbadbdacdccdcadbadaccadbcbbccbdbcddacababbcabdabbabbcbcabbaccbababdaddaccbbcacdcdbddcddccaadbcabdcdbdcdcddccdadcadadcbbacaccacabacadccadccbadcbcbadbacaadddcaddaaddbdaacdcaaccccacaacdbbbdbaabdadcadcabbbadbccbccccdabcdacdcbaaddcdcbaacbcacbbcdddcdcbccabcaccccadbacbacabdaabaadddcbcbcdcccaabbccadaacaaaccbdccdaadbcbdbbcccddabdbacbbacdacdbdbccbadddbdbadbbaadabbcdcbcaccbddaaabaddbcdbbccaadacaddaaaaadcbccbabcccacbcdcbaabbccddbbdcbacdbdbaccbcdccdddaccccadcbddbccabdcbcacadabdbdddacdcdccabaabdcbbbddcdabaaccaacaabccbaddacdbacadbddabacddadabccbbbccbaddaabbccacadaaacdddacdcacaacdacbddaabbdbbbdacaabbbdaccddacbbcaacbdccbcbcabcbddadadcbccbadcdcdabcccaadbddbddaddcbbdcaadbbbdacccbbbacdbbadcdbcabddcbdcdacdbcacdbaddacdbdcacadcbcaabcbadaabdacaddbbbbbbbabbcabdadcdcaddaabbdacabacdbbaacadadbdcabbaabcbaddbddbbbccbbdddbdbaabccaadcaddabcbaabbdbaacabdabccdbbbbccbdcdbdbcdabcbabbccacabacaacddbabadddccdbabcbbdbaacabbdbdbdccadcbaadbabcaacdddadaaddcaabcdaaaadcaddcadababccaddbadbccadddbabaabdbcacdbadbbbabbacdbacbcdaaccddabaccbacbdcaabaacaadadcabbdbabcaccacddbadbbadadcaacbadabcbdcbcabbaacbcbaadccbccbcabdcadcccbdddcaaadccabddadcbaacbddbdcdddbbdbbbbdbacddbabccdbdadabbdabdddcdbacdabddcddcabccdabddbaabacaacaaccddaaddbdbaaacaaaacdcbcddcddabcddddcabccbdbddabcbdbdacadbabccddcbbdbadddbcddcddaabcccbcccabbaabaaacbbacdddcccccdaacbbdbaccccbaaaccbddbdcbcdcbcddcbbdcaaabcaabcaddacddaacbbbacababacaaabdaccbbbcabcbbacacccadbdcbbcacdcbaabbabdaadbdcaaadbacacabacaaaaadaddaabbbbaababdcbbdaacbaacadbaabbbcccadcbbdbadcdabbbaadaaadbbacdbcdabdcdbdadabbbddcdaddcdcaabaccbcabbdacddcccdbbdabbccbddcbccdcabccdbabdbbdaaaadcbbddcdacbababbcadcaddddbadbcddcaddababbadbbdcccbcdccadcdbcbacbacdccbbbaaabdcabcddbabbbdddcabbcdcdbabbcddcbdabbbcccbacbdacbdddbddcabcadcdabcdacdddcabadcadbddcddbaaadbbcabcdbcdabaaddbddbdddcbdcbbacbcdbdbadddbbdbcbcdcdabccabaabbdacdccdaacadbcaccbdcdbadcbbcddcbcdcabbcbaddccdaddcbadaaaaaabdbcbdbdcccbabdbdacbbbaaadbdaabcaccbbdaabddbbaadcbaabacbbacbdbcddcbacacdbacbbacbacdadadbbcdcdbddcbcabddbabddabbbaaadbaccdcbbadcbddbcbaacdabcaaaabbbaaacaacaccbdbadcbddcaadaddbdcbddaaabcacccbcbababcababcdcbacacdaabdbdccddbbddbbaadcbbdbbbddbabbcdbdadcacabadaaaaaddbdadcdabbdabcbdacccdddddadbcccbbbdacdaaccbaabaccbbdddbcbdcdaacbacddacaacbdcbacabcddbbacdaabbdddacbdcababcabdaaaddbacabcdbaadaddaddccccabcbbadabbbacddbcbadacdcadddbcadaaadcabacabdccddddbbcabdbbbabdbdbacbbdabbcdddadcadcaccacbdccdcbdaddbbdadacbadbcddadcbcaabcbccaddddbabcadabcdabcdaaacdbdcbbcbccaaababddcbdbbcaaadbdabdaddaabcdaddcacddbaabbbbbabddcaacddbaddcabcdbababaaabaacbaacdaaadbbdbbcdcabccdbbccadcbadaabacbccdaddbbcbdacdaccdccbcdbdaccbbcccbddbddbcbdacdadcccddacabbaddbdbdaaddbbcdaabcdddbbabdcdcdbddcddbbadbbababaddbacacbacadcbabcaccccdbcabdcddccddbdcabdcdaaabccabbdaacabaabaabbacadcbdcbabdbbccdcabaaddcaacddccdbaccadabcdabcddaacdcbdbdccbbbdbdbddbddccbacccadccdcabcacccbdbaddbdacdcadcdadbabcbaccdbcabbababadbcbdcdabcdaadddbbccabcacbaccbcaadcdbddcadcbaaaaacddcbbaddbaddcdbbcadacaaccacacaacadadcabddcabcbbbcdabdbccdadaaaabbdbccdbbdabcbcbacacdaaaadbbdbbbadaaddccaacdcdbaccacbaabbcabdcccbabbabbacdcbddaddddabacdaacbbbadadcacddcbcaaadcadcddcdadacbdcacddacbcbdbcacbcaccaabcdabbaadbdccaaadbbcddcdacbdddbbacaacbcdddbcbdacaabcddadbddacdcdcdbbadcdcacacadabbdddbdcabacacbbccadbdbcdcabbabbcaaacbbdddbdddadcbddbccacdacddaaaddddacdcaacbabaccccdaabacadcbccaabacccadbbccbaccbcbbcccacaababbabdcaabbabbaadbdadbdccabcdabaacbdacdadbdbbcbcddcaabdcbcbcbdcaacdbaaadadcaabacacbdaccccacbcdcdddcbdbcbdabdacaaadddacacbdbaadacaabadacadaacabdcddadbbcabacdacaabddbcacbcccaadccbcadabcbbbdbacbadacaacccbbdacdaabbccdcccdcdcccdddbbbaabdcccaccbcbacddbbccdaddbbbacccbdbcaaaaaabbaaaabbdacbcaccbadbacbddbabbcaddbcdaabdbbbdcabdbbdcabbbdbadcbdadaccccaabaccbbdadabbbdbdcabcbaadadabcbacbcbacabcadcdaaaaddcbddaaacaddbabadbddabdddacccaddaaaaccdbaabbdbcbacacadacccccdddcabbdabdcbbccdacacdbcdccaaabcaaadddadcdabaaacdccbaaadbbcaaadbcbcbadbccbddcaabdddcbcaabbbaccacacbabbaddcccaabccbaadbbcbaabcbadaccdacdbbdcdbabbddccdbddbccdcaddabadabddaaaddbcbadcadddbbcbdbbcbdacddadabcdbddcabbbbbacaacdbccbbcbddaacdabdcdaccaccacbbcbbbadbaacddcdbcccdbabacddbdbccdadcbcddbabdbbbddddbdccadccacddddbabaddaaacdbcdcdbcaddbabccaabdbcdaadacabadbdcbcacdadbacaabcddcadaaacaacaabdbbadddadcadabdacdadaccdbacddaddbabcabccdbdbbbcdbbdbdabcaabdbbcaaabadaaabaddbbbdaabcdbadacaaadbcdddbdbcbddbdcbddbaaaaaddbadaddbccbcddaaadcddbccadbcdabacddcdadddcbabbbcbdcdacacbcccaaadadcacddaddacddaaadcabdaabcdabbacdccbdcddcbdddccbbcacbaddcaabbccdcabdacacaabdadcdcabacbcbcbabbdccaabcacbdcdbccabdccadcdbaabdcaaacaccabcabccbcdabcbbbcaaabdbaccabbbbddaacbddccdadbabdcbadbcbdabcbabbdcbdabdaabcdddbbdadacadbabcaaacbddcacadcbabbbbcbdbcdddaabdbcbaabdcabdadbacdbbbbbbacbbccccaababdbcaadadacdcdcbaacdbbbadbacabcbadbccababcdbbbacbadcbaaadbcbddcacbdbddbcadbdabbdabccbacddbaadcbabdabbaccbcbcbadbbabaaccbcddbbdacbacccdccdddabbddbaddbaaacbadcabbabadacdabcddacdacccdddacdddbdbbcadbaddccabadcbcdcababccccaddccddcdbddbdbbdaaaabadbdddabadcbcdbbbbdaadbaccbcbcbbabbabcacabbbbabbadddccabacbbadadadaccdabcbbabbccdcbcbacdabacbabcbbaaacbccadbbcccbaccbdaaaaacbccabbcbacbcbdcdbbcadadbcdbaadbcbbdabacccaccdacbabcbabdaccaddcbabaabcadabbddadccababaadadbbbccabaccbabcdabadaabadadbddbacddbddbabdabdbdacadbdacdccbcaaaacacabacdccadacdabadaabddacdcccbcccaacdaaadbbbcdddabbbcccaccabdbabacdbdbccccaadabccdacacbabccdccbbacccabbbccabbddaabadbdabcbdbcaddcbabaccbbbcdccabbcbbddabcbcdababbbabcdbcaccacdcacabdccaddacdccabdcababbcdbbddbbdbbdbdcccbadddaacbadbbcbabadcccdbcbdabaabcdcdbdddbbcccddddccbbbbcacaadbbddaabdadaadcbdbccacccabbacadddbbdbdbabcabbcdbadbcbdcaacaadddbdaadcdcaabcccddcbbdbbdbaaadaaabaabaadcdbccbcaccaaccddbbdddccbbabaadabcbcabaddabccbcddcdbbcabcbacccccbadaddbddcdaacbcaadababaacdadcaacccbcbadbadcccdaabbaaacadbcdaccddbcbdabbadabdddaacabcdccdbacbbabcdcbccdbcdcbadcdccccbabacbadcbaacbadddbbdbdacaabcdcbacbabcccbacbcbcbdcaadaaababcaddbcdaaccbbbcbaabccddbbaaabcacadcbcbaaccaabdabaabdadbbcbbcbdbacbbbacbcdbbdcaadddcbbdaababcacacadbcbdacadaadcadccbbdbbcddbdcbcaaacccacdabcabcdacdbbaccdccddbbcdadaaddbcddccbbdbadbadcdaabddddcaaaddcbcdabdcacbbdbbbdadadadadddaacccdaddbaadccadbbaddbdbbddadcbdbbacbadabcdcbdcacabddccbcdbabdcdccccccddaddddbbacbccdcdccdabaadcbbbbdadaadabdccbbacaacbbddbacbddcdccbdadacadcacadaaaaacbcddbbcbdbbbccbcdaddbbbbcdbbcadadadbddbcddcddbbdadcccbdcbaccaababbbdcadbddcdadcccdcbcbabcbcddcbdcbabddaadbbcbdcdbaabddabcbaabaadadaabcccbccaaccdcbbaacbcbbacacabdacdccaacddabbadadaadaaaddcddbcdbdbbcbcbcaddadcaabbdddaacaadbcbdaabbddcdabacbdacaaddbbcdaccadbbdcdccaabcacdabbacbddbdcbbbbdcdaadbddcccdacbcdccadabbaabbabbcdcbdbababdacabaddadaacaaaacbdbbcabcdcdcddcbdcdaabbadbcbdddaddbababbcacdaddaddcaacddbcacdbbbbddbcabbadcdcaddbcdadbabdcdabdbcaddbbaaccdbbbcadcabdcacbcaaadcdccacdbddabbcccccbdacabcbcbcdcddaadaadcbdbabbbdcdbdbababcbdaadccabbcccaddcdbbbadddaaaddbbddbbbdbddadccccaaaccdbccddaccdacddacddaacbbdaddabbabcbbbdbbdcacdaabbdcaaaabbcabcdbadbaaacbcabacbbdddbcbcaaabaddbddadcacddcbdadaabbcaabdaabcbbabbcccddabaccdacdcaacccdabcdbbdcabbdabccbcbbabcacbbaadbbbdaddcbbcabaccadbacaabadcdcdaabbccdcbabbdccccabdabdbaccbbdbadaadbaadccacabccbdababbcbbbddababdcbddadcadbaadbddbdbaddddcddbbaccaaabbbbcccaddaadacbbdaabbcbbcdddbbbdcbbacbaddadbbbdbaacaacadbcccabcaaddcadaacdcddadbaadcccbdddcaaabcababcbbddcccddbdbcadabababbcccbbdbbbacdacdbbcbcabdcdcaaabdcdcaaddbcccaacacbbadacdcadbbddbcbdccddcaaadcaccccddbacccdcadcdcddbdcbaaadddaabcdbabadbadadcacbaacabdabaccadbdabbaaabcbdddddcbaddbdaaabcbcdaacacaabdddddbacdbdbadcabbaddbaaacbacadcdacdbdaadabaadcccddccbbbabccabbbadaccbaaadbabcbcddabcabcaabcbbcbbcdcdddadadaccbcbdbbccabbaccbcdaacabccddbaacdddacbacdcddbaddbbcbbaacccbaabcccadbcbcbadbcaddccdadbccbaabbdbabacbbdadacbacddbadcaadacbbbcbcccdaabcacbbccbcabcacddccdcdbbacddbcbccbaddaaadaaabcdacbbdacadadddcdcdccabaaabaabcddbddcadbbbaadcbcbbbbbdbdacdbbbdcdbcbaacbadacabbdcabbccbcabbdcaacabddababbcdacdbbadacdcaabadaaaadbdcdacdccaddccbdabbdbcdcdabccdaaaddddabbbcddcdabadcbbbbbacddbbdbabadbacbcbadcbbabdbbbcaacdbdabdcbcdacdaaabdcacaacdadbaaacbcdbcdacccccdabaccadcddbdcdbbbdccaacaaabbdaabdbccdbbcaadabcddbadbdabacaddbcadabcadcacadddbdbaccbddaccdcbbdadadaaadbddbacbccdcbdadbccbacdaccbccdaabbbcacbdccaddabbddbdbbcddacbddbbcbdcbbdbbbddadbdabdaabcbacdddbbccbcdaacbbbacdaddadddaaacabbcdbabcbddccabdadacbbdcdcccbcdccbdbcdcdcdadddcbcbaccdcadbccdcccdadbdaddcabdcacaabbcbcdbcbcbbcbdccbddbbbccdcbdacdacdbbcacbaddbbbabddbadcbccddacdbbccdacaddccacbbdcaaaabcababbdabbaccdddcbcabbabadcbdbbabadcaacadaccdddcbcacbccbcbcdaadadacdadacacdccccbcdbadadbadcacbdccdadaaccacbaabbaaacdbdddbadcdcbbcbdcbdbaccabddbcabbbddacbddddbacccbcdcacacbacdccccbbbadcbbaabddacabbadcbbbbcbaacdaaccdccdbabcabbbbdbcbaaaccaccdbbccabadccabbccdcccacaaadaabdcbdabdadddccdaaaccbccacbdddaddbdbdcadcbbabdbcdbdcdadaabcaccdaaaadcdadddccccdaabcabddbbacbdaabbaacadcdcbbbabbbbadcdabadaddbaddaabacaabcdaabbdabbcddcacbaabcacddbababdbdaacdacbadacaabbcbbdbbdccbcbaccbaadaaacbbbcacbabdadbaacbbcddbdbbdaacdbaccdbbdcdcaabbbbabdbdacabbcddcadcaaccbababbcbacdccddccbbccdddccdaacbccdaadddcdbaabadcddbbcbcbadaaadccbcddbbbbadcbaacadababbbacbccbcccbccbadbdccbdccacaddbcaabadcacbbcdbdbabdcddababdddcaccadcadbdcbbaadcdbbbcacabacbbcdabbddadcabccddbbaabcdabdadbbdcacdbadbdaccddbaddadcaddaabaacdcdcddbadbcbcdacbadddcbacdacdddcdaadaddbbabdabaaddbddcddadbbccbacbdcddccabcdbbdccbbdaadbcadcdcbbaadaccdbabaabccaadcabccbaaabaacacbbbdabaaadaabdccbdabdbdababcbadbbbbcadbdcbdbacacdbaabcabcbdbbdcbbdaaadcdbaacbcbcdbacbcacbcddddccacacdabcadcacdacaddcbccabacccccbdcbdddbcaccaacdacaabcbdbaadacaddaaaccbcbcbcbbaadbcaacbbcbbadbbaadddbbabaddddcdaddaaaadacdbdcacccdbcccdbaaacbbbabcdcdbcbbdaacadbcbdcdcaddddabadbbbbbaabcdccdddaaddaadadcdabdacdaaccbbbabbccadacdabcbcacdbcadadbdacbabdcccbcddacbacabccbaabbdbdaacddbbaaacccaadaccbaabaaabaddcadcaddbcaabcbadbacdccbaaacdbcddadbbccdbdbbaabccbcdddabbbdacbcbcadccdaaddbadcdbbcbccabcddabcbcbdacdadccccaabbcbbcddabccacccaabdcdabccbaacbbccbabdbdbacdadcbbcdabdaacddbcbbccddcadcabddcabdbcddcbacbaabccdcbcdccacdacabdddadbcabbaacdbaacacdcdaabdbdbacbcbbadbdabdbccbbaccaabcdaadaabaacccccdcbcacadbbbdaacbacbabbbcabccbaabccccdccbabaaacbaabbccdbcaaddddcddbcbacbdcccbbcddcacbbbaababbbbdcbdacbbbabaaaacadaccbdabadadaacddbbccadcbbddacbcddddacabbdcbdccdbbabdccbccbcaacabdadbdaaddcabdbaadbaddabaaacacccddcbaabdabcabcaacababbdcbcaabadbcddcdcbbcaabcbacacddccbcbdacdaccddadbcbcbbdccddacabadcaaaaabcbddacbadacbbbcdbacccdcdbbcbbdcbabccddaddccacadbcbbbacdbdcdabbadcadddbaaaddcdabbaccabacbcdcadabadcadcbbcaaaabdaddbaadabdbcbcadbbbabaadadaadadbbacabadacbcbdbcabbaaaabadaaadadcbdddacadadabdadccbcbccddbabbbabcbadbadbdbdcccddcacbcdacadabdcaabdbcccbdddaacbcdbaaaabccabbdbddadccbbabcdcbcabbcadadadccdacadaadacddcabcbacdbbccdcdccabaddacabacbbcddcaaadddcaddacdccacabadbbacddbbcdbbabacccddabbaaacdccdbccdababccbbcdcddadbadbcdcbcbdaabdcccbdccbdadcaaabcaccadcdcbddbadbdccacbccacbdaabcaddccadbbaabdcdbabbcadcdcbccdcbbddbadbddbadcacabccccdbcaddcbddaccccddadbbdbcddbbdcabcbabcdccbadbaddcaacdcbcacabaacdbbcaccadaaddaadbbcbbcdbbadaddcccbdcacadabbcdcaddacadadabbcdddcadddcccbdbccbbaabcaabccdcbccabbdcddbdcbdacbcbdcccabaacacadddcdcdcabdcccacabdaddabbaabbcbccaacccbabbcdbbaabdcbacbdcacbdbacdabcaabdcdacdaaabdabadacddbcbbdbacaacbbdbcdddaccdddabcbadcddbdcaaadccccccbaccbdcbaacdccccaadbbdabccdabbcbbddcacbdccbadbabaccacacdcdcbabbbacadadaacacbbbdbdbbcaadcddddcdaabbadbaddaddabaccccbbbdcbadadababcadaaacbdbdcbbdbdcccbcddccdddacbddcabbaadabaacadabbccbbcccbcbdbcdaccaabccbdadccddbccabbdcabbaddcbdacdcabdcbbdccdcdddcbdcbaaccabbadaabadcadabbadbdbbaccababccabcdbabdaaabcbcccacaadadcddacacdcbdbacbdcbcdbbcdbabbadcbbbadacdcbabbacaaccdbaacbaaddccbdabbaaaccddddabcbdcabaddbaaccbaaaacdaabcdcdcaaaaddabddbbcbabdbcdadbcadbacdabaaccbbbdcbabcbacbacbdabadbcbdbbbadabccbbdacdcccaccccaddabaababadcdcdbabdbdcbbadcabbdcbddddbcaadbcbabbddccaacbaccabcdbdaddacbddcdbcbccabadacdbdccaccadbbadbccdaccbaccaabadbbccbddbcddbaddacddcbdcdbddddabcbbabbddadbddcaaadcaabacddcbdbbdcacbcdbbbdddcadccbdbdbcbcddbbbcbadcacbbabdbbadaadabadadbdbccadabbbbaddddddcbbaacaaccbdcbcbdbdcababbdcbadbbdaccabcbbcbdababadccaddbbacacadaababbbbadacaaadaadbbacdaaaadbbcdccbccdcaccdadbcbbcaacadbdcccdcccdcdddacbbabcbacacdabdcbdcdbbcaaccadcbbddbaabcbaaabdcdadbbaadcaaddbdbbbbdccbbcadbacbabccdccabddcbaabbdadaacdcabcbadbbaaaaaaaabdbcaaabacaddabadbabcddcaccdcbdbcdddcdbdcacdddcdaaabccacacbbddbdddadabbcdbddcbbbacadbcbccbbdcadaabddaaacdccbbdbacdcdbaadaabaacbcdbdbabccadcbcbccbbbadbcdcbccbabdbdccdccddaacaadbaddcdcdabdbabdcdbbbbccbccbdcacabdaddbcdabcaccabccaaccbddaacaacadadcdabcdbdcdcabadcaacbabbbcabcaddcdcababbccbbdcdcdcddccbcbbdacadcaabacadabcacddcbdbcdcccaacadcacacaaacabaabcbcabbbbacaacbdacbcdacccacdbcbddabbababcaaabdbaccbbbdadcbcaaaacbabadcbcbddbbdcaccbadacbcbccbbbdaacaadbccdbddbddaabcccbaccbdbddcadadadccabaccacadcbbcbaddddbbbcbaadcbabbdbdbdaabddabcaddbdbddadacbdbdadcbcddacbbaadaccbadadacadcccbbdbadbcdbadcbbacdacccdabbdadbadbbddbdbdbcaddadccbdddbcdcddadbdbabcdddaccdcacdaacdcbdccacbcbacdadcdababcdbaabadcccabcddcbbbdbcddcddbbbbabcbabdacbbdcbacccdbdccaaababcadadbbbddcdcbccacbbcbccaddadccadcaddcacaaaddcbbbdcadcbdcbcbadbccbbabacaddcaddccacabcbccddcacaccbacbdacadbcdadabbdacdcdcacabacddaabdaacbbccbdaacdaadaacddcbddacdbbcababddbddddbcabbddcabdddcdccdbbcbccdadcbaabbabdcccacddcbdcdaccaacddcadadcccbacdadccbbbdcbdcbaacbacbadabcbbdbadccaddddbbdbadadcdaabddbaaabcdadbdcddbacccccabcbdadbcdcdbabbacadbdcaaabbdddcacadacbdabacbabdbcdaccadbddacaccdddacaddaaccadbdabddcbdbcdbaddddcbcabdbbbdaadacacababdcbabdbadbacccdcbbdcaababccadcabcbbcdaddddcbccccabddadbbcabdccddccabdbbdaadbdbbaccabcbadcbcacadbccbdddcabccacbdbdbdcdcbaacbabbaccccabbbccdbbcddcddcdcbacdaababdcdadddddcdcccabbdcbcaadadccbdcbcaccabaabadaacdddddabdaddababacacdbaabccbcbdadcbbadacaabccbdddbabccadaaacbbcadadacdadabdcbaababcadbaccbaddcacbbbbcbddadbddcdbddcbcaaacabcbdbbcbdabcdbdabccbadbbcbbddcbcbcaadddbddacdcdbcaddcdccacbbbbadbdbadcddacbccdbbadcddcddcaccaaabbbbbabcbaaaabccdccabdbcdcaddaaddccdcbacadadcbbddcadbaddcdbadbdcdbdcccdcbbcaabbcadacacadbbcddcddcabbaababbcaadacaaddbddbabccbababbdbbbcccbaabbaccdcccaaaaaabddaddcdcccdacbdbacbcdcdcabccaacbdbccddbbcacdabdadbcadacbabdddcdcdcdbdbabdbcbcdbbacbcdccddaaadbdcbdccbbcbacdcaababdabadcccbcbbaabcddadcacadcdbcdbbacbbcdcaaaabcddaabaacbadcbbbcdddabdaaacaaccacdababcbbbdbbddccdbdcaabcddaababaabcdcbdaadadadadbbbbddcddabcaabdaadbabbcdadbbbabdadabcccaccdcaabdcccccabaadcdbddbbaabbacddbbccbbaddcdabacabbbdccdbadcaabcbdddbcbaddcbabddddbacabdabbdddcdbbcbcdcdccccbcadacccababdbccddcccdcddacdbbbaabcaaabcaababbabdbdbcdcbbdabbdadbbdbadbbbbaadbabbabdcddccccbdbbcbaddddbcccabadabccabaacbdbbbbbbabaddaadcddcadcdadcadccdcababacdaabaccbcabdcaabdacaabdaaaaaddcaaadbdaabbdbbbdbbadbaccadcbbbadadbbdcaccdaaabbbbaacbcddbdbabbbdbcdcbbbdbacddbdbbdabaacbbbabbcbddddddbbdadddbcdbacdacdbcdbbcdabcdbababcaadddacacbcbbbacacbcbddacbdabaabdbbddababaadddabaccabdaabcaabbdcbcdabcccdacdbbddaccabdccadbadbcacdcdcabcacdadcdcdacbddbaabbbbcdbaaacabbdabbbbdbdcdaaaadcdadbbdbaacbdaddcacccadbcdabddbbbbdcabcdadabbabbdcabcccdbbdacccbabbccdbcbdbaaadbbcddbbabddaadabbbadbdddbbcdcbdcbdbdcdccddcabbdaaabcabcbbadaccdcaddacdbddacdccccdabbddaaabbcdbdbcababcabbbbbbdbdaabddabcdbbcbdbbabbabdadcdcccadbdcbccbdcbcdbdcabdaacaacdaaabbadacbccaaacbbcdbcaacbbdddddacdcbdddcdcccdbbcdddbcbccdbcdabdcaacdbbaabcbddadcaaabdccdbacbbcbdddaabbbdabdcaabaaadadacbbdcddadddcaacacbdcaabcacdcbbbcdaadcadbbdbabbdbaaabcabcccbbddabbccddcccdcccadacddbbbcaddccddcacddddbdbaacacbbdadcadaacdadbbdbbacdcbdacadbcbdbbdbddbbcdbdbadcdcbaccbdaaacbdbdcaaccdbaddadabbaccbdacacdccccbdddbbdbdccbbcaddbbbddccdddabccdcbdabccdaddcdbbbccdbcdcacbcaaaabccacbcddcbddacaabaccbccdcbdaacccdbccdcaadadbdccabbbdabbbbcdaacdbddacadddccbdacccbcdbdcacbdadacdbabdaaadddaaaaccabdcdbdddcacbcddbdaacbcacccdcbabbbacdabdcdadcbbbacddbdbcababcbcddcdbbacdcdbbdbaaccadcbccbcbcaaccbacbabbcccdddaddbccaaccdababddccaddcacacddbaabdbdcbaddbabddcaaddadadcaaddaccbcbdddcadddacdabbdbbbdbbbadbbaccadadccaaaabcccbcbbbacabccaaacacdccabbaaadbacadcbbdaaddbdcbdbaabbaccdbcabaabbaaddcacdbbccbbcdcbddccccaadbcbbcddabdbccabaadccddcdabdcdaccaccbbbbbbbdcdbdbccabbacdadddbacbdccccacbbdbdbabbcbbddbbdaaacbdabcaccdadabbdacccaaacaaddaccccbaddcbdacbdcacabcaccdcdcbcaacbcabbcdadcdbcccdaadbabdbdacdbabbaacbcabcddbcdadaabbaccbcbaccccadbdbaccdccbdbdddbdaadacccccadccbcaaccbddbaaabcccbcacdaaaaccccbdcbdaadacdbbdcdccbcdcbccbabdbbbcabbbaaacabacbdbdabddccddacbdaadaadadacabbcdccaccdddacdbaadccdadddbbcaddbbbacbcddaccaadbbbaabaadddcacccdadaacccaaabccdcdcdbcdcdcacdcaacdcdbbbdcaabadbadadabdbbbabaababacdddadaabaadacbcbcabdabdcdaaaacbdbcaadabcbcdaacddabbcbbcbcbbddacaaacaaabaacdbcdcbbdabbccccbccbadcacbbcbdacadcdbabcacacdbcdbdcdcbddabaaaccaccdcaddddbaabdabbaabaccbbcbcbdbdbabababbbcccddbcadabbabcbbcaadbadbadaaaabdbbddcabbdbbbaaadcbcccaabccaacaaccdaadcaccacddbdaaaabcddadcaccbacdacbdbdbacabadbaaaccccbaddaaaddbaabdcdaadadccbbbdacdcdcaaadcabbdaddaddbacdcdcacdcacdbcbccbcacbdacbcacdaaadcbbbaddcabbcaacbcabcbabddcacbacadacbaaadabbdccdbbaacbdcddbdbadccbcbbdcaaabdbddacdcabaabbdadbbabdaaaacbcbdabacdbbaccdbbaddbddabadadaacadbbbabbcbbabcdcabccbcdcbabbaccdacabcdcbbacbbdadccdcbbbcbaabcabcaccbcdabdacccdcccdddaaccacdabcaddcbabaabbccbadbacbbbaccbacbddcdaaccaddcbdacdccddccdabbbabdddcddabbdaadbbcccdbaacacaadabadaabdbcddccddccdacbbddaadcacdbddcabcccdcdcdbacbacccdddccddccddbaddcdccabcdbacbadaaddbaabadbaacadaacbabcbcaabbccabaddccaaddababadcabccbccdccaddbbbabacdbddacbbdacacddadbcacdaadbbbcacadcddbbabbbbacabacdcbddacbcddacaadbcdcccdbcdccabacaabaadaddbbbdaacbaadabdaccabcabccaabdbadddbacdacbadadacaccddabbaccbadacbabdacadabbdadcabacdacdaacccdadacbdaddcdbabaacaddbcdcbbaaddbcbbbaabbacddabbdaddaadddbcddabdacdbdddaadaabbdccadabcaaababdabbdcdaacbcbddbbcbabcabcbdbdbaddaaaacbdddcaaadbbdbbabdccaacbdaccabddddbbccbcbcbaaacbddaabaddbdcaccbacbcccaadbbcbdbaadababadbdcadababbbbcbabbbccbbcdcddddacabdbcabdbacbdcddcdbbbbdaadbdcdcaabdadcdbbcdcbacbdbcadbaadacdacbdababdbbccaadddabbddcbbbdacbaadbaaaddcbdaddaabbabaacadaadbbccacccbadbcacabcbcbabaadabaccbdbacaaddcaaadbabccabcaddacdbaacadadbdadccbdbccccdadcdbcdadabcabbbdddbababbbbddabcabccdcbbcbddadccccbadaaabcbbdbcdadadbaacaacaddbbdddaccccdbdcabacaaccababddcdbbdcdbcbddbbdacaccaacbaabcbbbadaadbadadbcbccbabadbbaadcddbcddaaabadadbdbbbbdaaabbdacbaacadaacccbacbccccdcddabbbdbcbdcbdddbcdddaaddbcbddaaccaabddcbbbcbdacabacacadccacdccdddacbadccdccacbbdcdbaaadcababdaccdbabdaddbddbdbadababacaaabdbbaabddbbadbdcacdcdaadaaaccccadbdcdaccdccbcdcbaacbcbdcaddabbddaaddacadadcbcdccdbbacabcaacbaaaadabbccbbaadcdbcbdbacccdbcdddbdacabdababacdadbddabddadbabcdaaacabcdcacacbcdacbaaccabacdbcacbdaaacdacaddaaccaaabcdaddabbcccdcacdacaadcbaaaddccbbcadcabbaddbbdcbbcacbcbaddcbcddddddadcababdccabaaaccdcbacaabccaaacbbcaadbcaddaaadddabbbcccbbccbdabbbcdcdbaacacbacbaaabcbcbddaabababdacacdabaacbccbddaacddbdcabcdaddbcdbbbddbbdacbabadddbbcbbcbcbacbbbcadabbabcabbbadadbbbdbbbacabadddacbcadcbaadbdcbddbadbbbcdaaaacbcabcaacccbccbacaacddbdbadcbcdcbaacdbbdbcababcdbdacbabbddaabcbdbccbaabbbdcdbccabcaacdabbaccdabdbbbcacbbbaadcbcdbcbdddaaddcdbaccdaacbbdbaadcbbdaacddadccccbbdbdacadbcacbcadbadaabbdbbcdbdadcbbadaadbcccbcbddcdadacabdbdadaadccbbababacbbdbbcacbdcbcddccdbabddbdadbaababdbdcacbdccacccabbddddabddbacbdbdccdabddddabdaaccbddbbacddbbdbdaaacbbbdcaabccbadbbcbccbabbacbbddbadabdbcdbdccababdabcaaaddababdbcdcadaabccdbbbcdcaccbacacccbbababcacdacbaccbddcaaccccdbcdcbacadcdbcbdcdccaaaddaacaadcdccdadaabcdcdadacbccdcddcdccdcdacaabdabbcddabbcbbccdccbcdbdacacbdaaabaacbacaaaaacbdacabdbdaddcabaacdabacdccacdabccddacbacdcabaacaddadcdcacadabacbaabaacdadbddcabcadabcdddaaadccccccbcdaaadccddddadabadccbccbabcccbdbbdbcdabaadbabcbaabdbccadbccdbcbaadaaadcbaddcbcbdbbacddadbccbccdaacdbdaccacadaddcbabccacdadbadddbacbbbaddbabaddadddbcbadddbacbcbbccddbddcbaccadbbbacddadcccbdadbaddcdcbdbdddcabbbcdccdbabbdddbcdcadaacbcabdbcacbbddbcabbacbbdacdccdabcbdaaaaddaccaaadbacdcbbaacddbdbbabaccbacbcddacddcccdcabdcddcbdaadbdabcbdbbabcaccabababbcadbaacbdcacabddcaabbcdacdadcadbbcdcddbcaddadbbabcdcbccbbcbabbababdabaacdddbadaabcadcbdbccdabdacbacabbaadcbbcdabcabdddbadcdcdcccbbcabbcbbcddbbbadccbdbbcdaadaaadccbbccccbdddbadbacdccacbdbcabbdcddbdcbcbbddcbacadaddbccdacdcddbaabbcdcadccddddbdddbaccdbdddddadbdcdaadaadccaddadcbbaacdcddbddcaddadbddabcddcdcbdacddbaccbcccaaadbcbdccbdbddcabcccddacdcbcdaaaadbddbabcccbcbadbbdbbccdcadabddccabcdddaaaccacadcddbbdbcaacacddcdbabccddbaadbbcaadcbaacbcbddabcadcdccaacbadddbcdbcbccddbcdcdabcccddacdbcabcddbcaacdbaabacbcbcdcdbcbcbaaabdddddbccaadbccabcaadaabcbcadbbbdcadbbaacbadbbbdbbdbbadbccddcabbcdadabdbcbdcbbcccccbabadacbdbcbcdcbbbadcdcccacbbabddaaacdaabcbcbaacbcaccbdabcddcaaddcaacbbdadcbbbdbcdddacdbabadbabcbdccacacdabbbadbacbadbbaccaaaadbacdcadcbddacabdbcbcbdabddacadbaddbaadbdcddbabaaccbdbabdbbcadaabaaabaacdccbcdacaddaddbaaddcdcbbcaccccabdcccdddbbcacbcbabdcccdcbcadccccbddcddcbcbcadaddddbddbcdcaadabccbaadacbadbbddadcadcdbbddbacabcccdaabbbcabdbabadadabadbbaddadabcdccdaadadbcabbabaadaaddbabdccaccbbaddcdddbdbccccaaddcddaddbdbbddcdcbbabaaaadbcdbdbdacaabdcbdbddadbadbcdbabdcdccdadddcaccbbdbdaaabbcddbabcaacadbcababcabcdbacacabcbddaaadcbcbacbdbddddccddcbdcbdbccacdcccdabaaddcbbdbadbddccdadcacacaacaccddbccdaadbcaaabcddaabdcdacbabaabcbbcadddabccadcabbcacadbabbbddbbbbcbcabcbaccdbccbacddbcaacdaaadcddbbadddacabdaacacadbcadaccdccbbbbcdacaacadbcdacccddbdbbbdcbbdcbbcbbaaddbdbbacaacbddabdbddbbcddacaccdddaadcabcabadccdbdcdabadcdcaacbadbccacbddbaadacbcadccacabcacdccbaaccbaddcbcbdadbccdbdababdbabbdacbbacabaadcaabacbbddadadbbcdcbadacddcdaabaaccbacdabacbabdbcbdadcbabdddabbcbcacdbacdbccddbbbbbbdaacbabbaddddaaaaadcbbdcbcdcaaddcabcabcccbcccaabacdccbbbbbbbacccbcdaadbccdcaacbadccaabbaddabddcddcacdbabbdacaacabcddcbaabbaaacdbaabdcadcccaacbccadaaddbbbcbbcacdbccdbadabdabdcaaacabbaabcddcbbcbbddbddbacbdcbccbbcadadddccbdbccdadbccbddaabccbdbcbbadbadcbbdccacbcbdbabcdaaaaaababcdbcbcadbdcdaaccdadbcbcbcccccabccdbcacaaddabdbcbccabaacdaaccbacdbbacaddbbbaccdccdcddbcaabbcdcbbaccbadbdbcdabaacadddbcaabdadbccbbcadddcdacaaabaccbacdcbcdcdcabdcdacdaccdccbaabbadcaddbcdaaccddccdacdabbcdaccdccbaaaabddcccadcbbcacaabadadbcbbbdccddddddabbcbdaccddcacbdbcdbaacccbdddaccbabcddaacbddcbbdadadcdaabdacccdaacbcbbbbbccdbaabdcaccaccbcaacbdbcdcbacccdbccacbacdaacabbcdacdabccdaadbccbddcbcaaccbabcadbcbddbaddcadcaabdaccbaabcaccdacdbcccabbdcbbcdbcadaccacbcbaccdcdddbbdcbccabadccacbdbabcbdbaddaaadbbaadccdcaaaddabbbabbddadccaaadbcdbadbccacdbdcddbcccacaacbacbdaddbddccddabacacdccbbdbbcaaccdddbdaddddaddcadaccdccacdaadcddbaaaccdcbcbbacdcacadaabcbdadbcabddccbddcbcababbcbaacbcaaccbcdbbacaaddbccacbbddcccdbbbdcaadaadcacbccbaccadaadcaccbcabaacadcaadabcccbabdcccdbcdbcddddbbdccbcdccdcbdcdaddbddcddaaaccbdbadbbaccadbabdabbcdacbacabdbcdccbbdbddbddcdaaaabccabbcdbbdddbaaadcbbbbcaacdaabbdcbababdcccdaddaacdcbadcbbcbdddbcccbddddacaadbbbcadbdbdbdbdcacacaaacdadacabdbcabaaabbcdccadccbaddbbbdccccbcdcaddddccdadbdddcabccdddacbbcddbddbdcdddcadbdbcbacccbbcbbcabcdaaacdadbbdbacddcbadbddbbccdbbcaabbccbadcbddabaaadadcadddbcacbbcbdddbaddcaacbccaddaadbdabaccbcaabcdaccacdcdbcaaccbbaabbacbaccbbbabcbbcbcdacbabacdadccabbaccdaddaaccacbdacdadbbbcbbaddadaaccbbcbbcdddabcdabddddccdbcacdbacbbcdbcddcbddcaaddddccbbadccaddacaaadcdcbabbbccdddcdabdcbbdacbacadcdadacbbabdbccaababbaccdadbbbaadaaaaaaaaaccdaddadaabddcdadabcdbddcdcadcdbbcababdcccccdbdbbacadcbdabadbbacadbbdaaacbbbacbcdaddaccccaaabdacabdaabdadaccbbccccadbcacddabbddbabbdaabcccdbbbacadcaccbdcaadadcbccadcdbccbdaddbcbdbadbbadbacdaddbcddabbcddddabcdbbbcdbbcdcccbbbacaababccbbdcabcbababaacadaaacbbdbbcdcacbacbaabdaaabaacdabbbdbabbcbbadbddbbdbcaadadcbbaccdcdcbbaabdcdbabbdacdadbbcccbcdadddabbbcdbbacddbddabaccbdadccdcacaaaaabcbabbcddcaddaacbdbbabbddaabddaaacddcaccadcabcbaaddaadaadacdddcababbdcdbcdabbcdaabbdddadabbaaddbbacbbbbabbadadaccadbcbadcadbbbcbbabcacbacbcaaadbcbabccdbbacabbcdcdcbcabdcdcddbccbbcbabbbbdacbaadbacbcbbacacaadaccdacacdcbcaccadbacbdaccddcaabbddbcdacbabbddcaacddbacccdbaddbdddcccabbdbcdbddbbabcccddacadacacccadcadcbabbccbdbacacabccacacbccdcbccaacddcabaccbaabadaabadcdabcbbcbbacbaddadabcacaadababbdcaadddcbcaaabbacdbdbbbcaccabdcacadccbabcbaccaccacdacdbddaacaaccbabdaacbddaaabcbbddccbcacdaababcacddacccaddcccacccbcbaacadacbabccdaabcbcaabbbbabbdcccbcdbdadabccccddbbcabdccdbabccbdcdaaccbddabacdbdddccaadddadbccbacacbdbddcabbbccadabcdaacadbcbbbdbdccccabbcdbadbbabdbcaadadbdaabdadcbbcdbdcbccdbcbbbadbbbcccccbdccbcbdbabaddcabdccdbabdcddbadcaaabcddcdbbbcaddccdcbbcaccbaabccdddabbbdbbabddadbdcdbdaabbcdbacccaaacbdabcaadabccbabdbadcaabbdadcbbccababaaabcbdacdbadcccadcacbcbdcdcaaaddcadbcddcabacdacdbdcabbcbbacaacbddccbbdbbadcdababddadccbbdbdddadcbbadaddadaacccaaddaacbcbccadaddacbadbaacbaaaabdaaabbddddaaabcddaacccbcbaadcdaadbddcccbcddbccdbddcdbcccabcccaccbabcbddcbbadccdddbbddabdbdbdcdcaadbabcdcbbcccdddbbdaabdccbdccdddcacbdaddaddddccdbdaaabacccbabaaabbabcbcdcaabbcaddbabaaaabcadcccacdcadbabcabbaacbbadbdbbdcbcbddadccacaccabadadccdccdbdaddddbcadacdaabacdbbdcbcbdaaccbdabadbbdacbbddddbbccaacdccbccabaddaabcbdadbcacaddcbdabacdccadbcbddddbbcddcabcadbbccbcabdbccdcbbdcccdadaddcaccccbacdcbbcbaacadcbacddbdaabcabaccccbddbacbbdbabdbcbbdabdcabdbcadbcaddcdcbaadaacaacdacabcdcbdcbabaabdbcbaaccbdbddbcaacbcbdaabaccabdbdabacddacdabcdbddcdcbabcaaddbbababdcbaddcaadadcaccaccbcaccbcddcdcdaabbadaabaacdcbbbadbbcddaccacdbbcbcddcaddbadbdcbbcaddaaaacaddacbddccaabcbcccccaacadbdbbbcbccdcbacddabbaabdcbddbcdbbbccbbddbdcdabdccabccbdccacaadadddbdcdccbbaddcdcccabdcdcddbadababaddcccdcbbdddcbacccadacdabcbdcbabbccdaabbdbabdbdbbddacbcaadbacbcdabdcababdabddbdcdaadabdcbccddaababccabadaabdabcaadadcaadadbccbddaaadadccaccdcababdbdcdcddbcdbadcacabadcdcdbdcbbacbacbbcabaaadabbccbadadacbaddaacddbdcababddccaccddbdaccdaacddbadbdcbdccddbaacacabbcacbdcabcdbabdaadbccdcadabbbcaccacbcbdbacbdbcbabcbdbcbcdbcdaccbabdaacbdabcbbcbccacabdacdadcdcadccaaabdaaddcbabcbabadadaaaaabdbaccdabdcdbacdcdaacdabdbbbbbbdcdbacabddacdcaacccabddcdacacbadaadccdadbcadbdbadcdbbbbbbdadabccdacbbbccaccdbddbbaccaccaccbcaaacbdadcaddacccccbbcdddabcbcdcdcbccabbdbadbcccccdacdbcdcccccadbababcaabdcdbadddcdbcdaababddbcddacdbabcbcaacbdcabcccbccdbbbabadddbbcddcdacdadadbdcacbbdcdabcbbbddbcdcbcabbacccbabdacbaacbbacdaacdaaabcdbccadabcadccdbadcabbadcabbcaaadbadcdcbbabbadcadaabaadadaaddddadcccabbadbddcddcabcbbdcdabccbbbcabddcaadaccdbdbdacaddcdbdaaaadcaabccbbccdacbdbbdbcddadcdddbbababcaadcaaaacaacdbaabdcdcccacbcbcaabcadbadbcbacdccadacaaddbdccabbdcbadbcdabbbabcdccaabcccdddadbabbabdcbabdbddaaaadcadcbaadadabcabccdbbdbaadaadbddcddcabddababdccbcdaabddbcdccabacbaacddabbacbcbcaaaaaddadabbdacdaadadaadaddbcbcbdbcdddadcdadcbcdcdcaddadcaadcbcacccdcbbdcaadddddabaaabaaabccaddabcddacbbcddbcaacccbabddcaddaadddddbdacadaaabaccdcaabacdabcaaaccccddcbdacdbcdbbbcdbbcdadcadccdadaadbabddcccbccbbdccbddbabbdcdabddddadadbaddabbbdbddacbacdadadabbbccbcbadbbcdbbdacbacbcaabcddacaabacbddbcdabbbdcbadabaadcbddaddcacdbbcddbaaabddcabbacdbdcdbbdcdccadbadddddcaacbdbcbbaacbdcdcdaccdaaccacabcaaaaacbaddadbbaabdacdbddcacdcbaaabacbcacdbdbdcabbacaacbbbaddccccdaccdcbcacdcadadbcbadaaacdbdacccacbcddcddabbcccdbdcccdbbbbaacdcadaaaacccaaaabddbbddabccbacadcddabcbddddbcccdbbdcbcaddabddbacacabbbbbbdbacccababbdadddaccadddaadababaadabbcbaabbbdacaacbdccaaddbbaddbabdbcbababcdcbbbacbbbccdcdcccdaacbadaddbdcdaabadbcacabbbcccbcaadbdacddcabadadacaccdddcdcbbddaacadadbababbddbbcdbddabdbcbcbcbbbdbccacbbdcabaddcbcdaddadaadabbdbbddadccccaddcbdddcacadacdbcbdcdabaaaadaacbdcabcabadcddbddbbaaaadccbccccddaabbadcbcbdacdcbdbbbcbcadbacadbaadbddcddadbabbbacabbaadcdcababcdabdcabddcdddcdadcaacaabcdbbadcadddcabbddbdcdaccdbdbddcabdbdbccdabcbacbadcccbaddaacdaaabbdbcbcaaaabaddcabbdadacbdbabbbaccddabccdabcaadbcbbddcdbdccdaaaaacddcbbdaddbbcdadddbabadbabdabccbcdacbababbbdbadddbbbcbddcaabbddbbbaaccdddddddabadcbbddaccbbdabacdbbbccbacbdbdcccdcbdccbdabadbcbccddaabaacabdadcbcdaabbbbdadabdccacbddccacdcabbdcbdbcaacabdddbbbbabccddcbbabaabdcbbbbacaabdcdbacddacadabdbccdcccadcacdbddacdcadbbaadbcdcaabdcaaacdbbdcddbbcddabcaacdbccdabccccdaababbddadccbabbbacacbdbdaabddacbbcaadaccbddacdcacadbbdcdddabccdcacacbbbbbdbbbccabaddcbcdcaccbbacbdbdccbcdaadbbabcdaadadccdcdcbaabcacdadbcadddaacbcacbadbdbaccacbcdabcbadaddaaabccadbdabbdaaddbabcbabadcadddaccaabbbbbacbbaabdbbbcaaadddacdacdcbcbbbdbccbaccacbdaabdaddccacaabccbbdbcabababbabdabdbbbbaddadbcdccbdacbdbccadbbddddaaddadccbaaddccababdacbcbdddbcaaacbccdaabcadddacbacbaababadddcbaddbbaddaaccbddcdcbddcdbbacaadbccbbddadabcdbacccbdcbdcaacacdcbabdddadacbbccbcaabcdbdbccdabcbddccacdbbbddbbbbcaabdadbcdaccaabaadbdcbcbacdbdcacbbabbdabbdddabbddcbdbcdcccaccaddaaadbcbcacbacadccccbcbbdaddbdbbbcdcdabbdcdaacaaabadcaccacbaabadaddccdacdbddbbbadaabdacdaaabbcbaadabdcbbbbcccdcccacbdcbdbbddcdcccacddcacdcddcabcdadcdccdbccddacdcaddbaabcbcdadbcaacdcdbbdbcabdaadccacbdbbadaddcdcacddbabacdbbddbaadabddbdabaacccbbdbcdadcbddabccbaacacadbdacaabcbcdbbbdddacbbbbaacccbccabcdadbdddbbadbdabdcadacabdccbaaaaacccdddbaadaabadcabddadbdbddbdcaaaadbaabdcaaababdadbcdbbcdadbcadacbdbddddbbccccccbbbcccddbcabacabcdccaabdbdbbdbdbddbdaacacccaacccbcdaaaccbdcacdbacabaacccaacabaabccacccbccacddabacaabacdbccaddcdddaabcacdcbbddabadbcdaaabdaacccdadaaccdbcadbccadababdacdcbaadbcbacaaababcccdcabdbaaabcabaddacacabbdbdbdaaacbbcbaccddddccdbacaaacdabcabbadaaccaaabadcbddcccadbddacadddbaacbdcbdacccbbacdbcddadadcdcbbacabbcdcbaaddcacbadadbccadddcddcbaaddcabcaccbdadbcabbbbdcccaabcdcbcaddadacdacbcaacabacbdabcabbaadbddbcbdcbacbaddadbbadadbbbbddbabcdcdbabcbccbddcdbbaaadadaacaabdacdadddbcddccdddbbbdcaaccabdcaddcaabdcdccadbdbbdbdcbbcaabcdacbdbccabaddcababdacadadaddcccbbddcabbbbacadcbabdcaddbbdcadbaddabdacbccadddcddddddbcbaccdadcadadddbcddbdcacdcbbdbcaaacbadadcbcbcddaaabddccadacbabcbdabacccaddcccabcdcbaabacbbadbaadaacadbddaddaaabbcdcbbcbbbbaccdcdbcbcababacdbbabdbccabcdbdacaccdaadadacabbddccadccdbababbcbcbcbcdcbccbbdcbcbccabcccabbcddbaababcabbbcdcabcacdddcabcdcddbdcadbbadacbddcdbbdaaddbdcbcdadadcdacdadbccbbdddaaaabacdbdbadbbdadaabbbcadcdadacdababbcbdcaacddbbbcdcabbbababacbbdcadcabbdaadaadbcdbadbbcdabddddccbcbdccdddddddcbbbbdaadcabadbccacbdcabddaaacacaaaaacababdacbbddaccdcaaacbbddcdabcaccacdbdcdadcdbabbacbbaabbddadbddadcacbcaaddbbcaaabddbdaaabdacbdbabdcbdabbcbdbabdbcbabbdaadccacaddccabdadcaababdacdcddbabdcbdddbcdcddbbcadcbaadabaddbdbacbbaacabbccaddadddcabdaabcadbbcdbbdcacdbdcbcbdbdaaddaabcaaabaadbbbdbdbbacbcacbdaabcddbdaacacccbbaacaaddaadadcddcbccdbccdcacccdbabcacdcccaddabaaadcabdadbcdbdbbabbcdaabbbcbbbcdabaaadbacaaddddbbbbcdabbaaacbdbaccbbcaabbcabdabbabadadaddaaabcbcdbdadcaddcbdbdaaccbdcbadcbdcbaabadaddbacabdaabababbaaaaaaabbddbbaacacabddccdabbccdcddbaadddcdddcbcadddacbadadcbacccdacabbcdddbaacacadbabbdbacbdadcacababcbacacccbdbabaaacbadddaaaaababccddabaabbbabbdacbdcdcbdaadbabcbcdcacdabdaaaabddddcbcddcaaccaaccddddabbabdbabdccacdddbbcdadbabcbcbbbdbddccbcbdbbadbdaacddaabdcdadddadbbbbbabdcbaddabddabbbbbcccccbddddcccbdddcbcaddbdacaacccacbaabbcdacadddcddbcbbcbaacacdaabaabcacabcbbcadbdbbccbdbdcacbcadbabbbbabbdbcccbdaacbbacdccbdabdaabbabdddddddccabccdbadbcbbaaabdaddbdcbccadcacbdbccdcdacaddbdbacacbbdabdcdcaaddabaccbadddaacadbdcacbcacbabcbaccbcaacbcddaaabdcacacbccdaccbadabdcbdddccbdcccbcdbaabcccaabbabcabdcaabcbacdbdaaddabaabcdddbcdabdcbdccbadbbbcadcbdddbdacabbdaccadacbbadbbaaaddbadcabbababcabccbadbabbcadaddddbbbcadaadccadbbdcbabbbadbdbdbcdcdcdaacaddcabbcdadcacaacdcdacdbbcabcbdaaccbdbababcdbdacdabcbcdbaaabdadcdadcddbdccbaabdbdcacabcbcbbcdbddbabbaaacbddbbccacdabbddddbbdbcdbaacddddcabaaaabadcabbccadbadbacddbcbbddbcbcabdbbacddcabcbaabbcdcacadcaccacbadbaccaaaaaaadbbbbbaacabdbdadddccbcddaacaccbbcdbbdaccdacaccaddddaaacbccccaddcbcdaaaacdcccbabdbcaaccaabbcbbdabdaaaaaadddcbabccdbbaddcdaddcabaacbdbdadcbcccdccbbccdaadbdababbbcdddcbbababaababcabcaddcabacbddcacabacccdbbbbadbcaacdacdcdaccaadcadcddaacabcdcbccaccacacadacccbbbaabdcbdcdabcdddbcdccbacbacdcbbbaaadddcdadaaadabaabbdbdcccdadcabbcbaddcaaadbcacbadbcdadbaccddddccabcaacbdabdacdcbdccacddbdcdbdabdbabcddcdcdddcdadcaaaadcbbbcddbbbccbdaddabdadbbcbbdccdacbaadaccaacacbbcbbdadcccabbdcbdbdddcaddcacbbbaacdbadbbcbbacdbcbdcbabbaadbcccddadbdcabcaccaadcadcddabcdaacbaaaaacabababcaddababbccbccbcdbddbbbaabaacdbcbbbbacbcddcbdddbbdbcdddabadaacbacadabacabadcbcbdadacbdbbbcaaacadbbdaabbacdbaabbabcacaaddaadadbdbbabcddccbaabadbdcacdbabccbcaccbaabbabacdadcbcbbcddbbbccdacbaddbdacbdbbabccddbabbccaabacccbacbddadbbabadbdbbbcbdddcabadcbbabbdcdcbcdccccabcdacddabbcadbacadabacacabcbaccaacdababacdbadcbcddbacbbcaaabbdadcdddadababcdbcddadcabdbacdaacccdcadacdddbcadacaddbdcccbddaddddbbbabdabbdcdcbcacdaccabbddbaccccaadabbbbcabdcbcdbdbdaacccbbabadccabbcaaddbbacccddccbabadccdacccabdbadbdddbabccacacabddbdddacbadbbccccddacbdbdcccaacbdabadbbcadcbbcdbbdaddcccddabbcdcaadcdabcabbaabdcadbcddcbdbadbdcdcbccadbdaaabacadbdbbadaccdacccadcacbaabddaaaacbddbbdddacbdbcacdddacdbacbdbccdbaddaacddcdbabdcaccaabbbdcbcbdabccadcdcdbadddbcccaaadbaacacabbddccadbdcacbcdacbdabbccdadcbbbdbccaccbacdaccadbcdddbacdddadbaacaddcccccbbdacbdaabcccaaaabaabccbdcbcddbaaadabdcccbdaabbbbcacdabbcbdacdbccacacaadbcabcdbdbacaccabbdcccbdbdaadccbadbcdddacdbccbabbdaddbbbabbadbcbccdadbccbbbaadccbabacddcbcbcbddadbadbacdacbabacdbddaaabcabdaccdbbddcbbdacbbdabcdaaaaccbacbacadbdbbcbdaabbccbaabacdccbaaabdadabcaccaaadbabadcacbbdccbcbbcccbcaabccccaadacdcdadcdccddbbbcdbaadcbadacddccacdbcddaaaccddbccdbdcbbbdacbbacbccaaabdddcadbacaacadaaddcdcbacdabbadbddadddacccacbccccabcccdbadaacddddbccacadadbcbaccbccbbcccacabdcadcdbdbbcabdccdadbcdadbdbbcdabbaaacaddaacccadbaadcbcaccbddbaaacbcdbadbaccabcccdabdbabcaddddcbcabdbbcdddddbabadabdcdbabcdacaccbcddabcdbcddaaadaaadbacdbbaacdcdccdcaadaacbcaaddaddcbbcabccabdbbbcacdbbaddcbcbaaddbcdbddccbacdabacacadddccbbaddbdcdabddadbcdacabbdccbadacadbbdbaaacadaddabaaacadbdcdcabbbaaacccdcabacaaaccaabddcabaadbabdcdadbaaaaadcdabdbaadccbadcacbbcbcacaadcaaadccdbdccaaddaacbcdcbddbbaabdddcccdabddbbddaadbadbddcbcdccbdacdbadacabdabddacaadcdabccbcdcacaadbbdcbdcadcccadbadbbcacdddcbcddccaadcaaaacdbdbddddddddcbcdccdbccbbaadbbacdcdbaaadccbdaadaadcbbacbbbabddcadabbcbdbbbcddbabbadcddbbbbbbbbacbcbacaacbcdbdddddbabdabccdcbbabbbcbdcabcddbddcabaaadacdcdaaabbaddadbddababbaacdadbdaabbbadbababbbbabaddadbbcbbbadaacccdbcddaddadbbabcaccbbbdbcbcbcaabdcbcdabcacbdaaabdcddbcddadbbbbaadbcacdcbccbdaaddaadbacccabddaaaccabcacbddcabbbcdccabadcbacdadabdaddbacadbccddabdbbaacbbdbcccdaadcadcddcdcbccdbcbdddbcdbaadcbbbbcdcdbdbdacdadcdddcabcbccaadadbacdabdcdcbaccdbcbcdabcddddcdcbbacaabbcbbaadabacacccacccbbcbddbabcadbcacdcdacdbbcbbddccdbadbababbacdbdccdaddabacaacdcddccdbbbbddacbddcacdadabbaadadacdcacddcaadbcacddabcadcdbbbccbbabddaadbccabdcadcdcbdccbadcaaaadbabbaadcbacbbaccdaacdbcabdbadbbdddbdcaaabcbcaaccddcacddadcdccdadacbabcaaadacabdcaddccbbbccadddadbacaccdbabbababbaadbcadbbccbcdcdccabdabadddbdcdacbbbbbbbadbbddbdbbbcabcadbdbcbdbcbdcbdddccbacbabcaaccdbaddbcacdabdcaabcdabcabbadcbdbdaccdcaaddcaacadcbacaadbacdcabdbacababadbbabbcdcdabdcddbaaddabaaabacbdbaddcbaaacdbbdccaabcdccaaccabdacdddcbbabadaccddcacdcbcdbccdbccadaaadccaabcdbcaccaaaabacadbcdcbaccaaddccaabccbcbbcdbcaadccdabbdbcaccababdacdbddbbbbadbbbcacddbccdcbdacaacbcbddaacdabccbdbdacccacdccdcbcccccddadbadcbdddcdabbadbbacbadabaabdbacbdbcabddbddbdaabbbcdbdabdaadabbcaccadcbccdbcacaacdabaadbbccccbbcbcabaabcbbdbaacdddddaccaacaccaadcbbaabbbbdcdcbcaddbbcdadbdbacbbcccbabcbabacccdcbdbbacdcacabaccccddccaddbcaabadbbbdbbbdabbcbadacbadacdbbadadbbaaacbdcdaabcbdbcbdbdbbadcdddcdbdbddacbacbaaabdcbccccaadabcaadbdcdbdccbccbddbcdddaabdbaadddabbbadcdcbcdcbabaacbbaaaaacbdbbacadbdddadaccadaadbdcaaddbacaabdabccdaddddbbdbcbdcbcdcbcadadadadbdacbabdcadbbabdcbccbbcbbabdcbabbcabacdcddbcdccadbdcaccacaddbcccbacabcddacbbaaccccbbadcdcbcadcdbbacaccbdaacabbcababddbadbaddbacadcdbbdaccbdadaccbdcbdadcacdbdbbababaddcdbbdbcadacabbbbacacbdaccabdcdaccdbdacdcbadadadbdacabcbdbbdadabbabbdbadbababacbccbbccbadddadddbabbdbbccabdbdcabcabcbdbaacdcbabcbaadacbacabaccbdcabcdabadcbacaaaadbddcbbcadbcaddbbdacddbddcbdaaddcacbcaacbdababadcddcbaadabddbabaacacbabdddbbcaacccacdcadcdddadddcaaddabcdacddbbaaccacbbaaacdbdcbaccbbbdbdbcbddaadccbcabddccdabcdacaadbbddccdaccbdbddcacabadbbbcaabcdaaabaaaaaaccdaabcdbdabdacadccabccccaccbdccdbbaccdacdbbadbcbbbaabccbdbccacdbdbcbabbbcaabcbcacababddbdcddaabccaccccdbabaddbddccaaaabbbbcccacccbcadbdadaababbbdbabaabdadadbccdbcbbdcbcddaacadabccaabcbcdcdcccabdcddcdaadbbcbacbabaacbdcacbaddadabccadacacdcdbcacaaacbddbacdacaabcaccaddbbcbaddaaaddacababcdbbcddabcdbcaadbbdadabbcddbdbbcdddbbcbcddcdbdbdadacbdaacdbbbcabababccdbcccbdcbdaccdbccdbdadcaadbddbdcbdacdadacabaccaabddbbcacdbdddddccacbddbccbbcaacbacabacccbbbaacdbacababcbcbddbccdcdbbdccbbabaaaadabdccacbcbccacdcdbdccbbcbdacdbbadcbdacbadbcabdcadcacababbddcbbaaabcbcadaacbbcabbdcabbcaddbababdbdbabdcaadcddbcccadbadadcccacddbccabcaadbaacbcddbdbaaaacaacdabadbdbbcaaabdbbbcaacbaddcaaabaccaacdbdcbcdcddacadcbcacabbbabddcccacaadcaddbbacbcbdcbdccbbdccddadcabbaaabbabddacadaadddccbcbbadbdcbaaadcbcdddddaadaadbabcbdacbbcabbcaacbdabddcaddddbadbaabbbddcddaaabccbcabadbddbcabbdcddbbabddbccdaabcbcacbbbadcdcacddaababbcabcadbbabccbacddbdbdddcdbbcacdadccabdbcdacabcbadabcdcbcbcaaccddcaacccadbccbaaddadaacdbdcddbacdcaaacdbbdbdacbbbdbdaadbdcacacabcbdcbbbdadbddaccdacbcaccbcbcabccdbcbdcadbabcddbbdbcbbabbadaabaaacbbcdcbaabcabdccdaaabaacabcaaaabdddaacdbaadbdbcaddbccbbdcbdaddbcbcdbadabbbccbcaddddbccdcaccdcdaccddbdacaabcdbcdbdccaacacadabbcbcabcacbdabacddbcaacddbaababdbacdcbaccdccdaacddadddbbdbcacabadcaaacdacbabbadabacababccdadbccaccbccddaddaabcbcdccdccbabdaaaaadbcdcdcacacbadaabdbdadcaabcbcccddbbacbaaddccdcaacdabdaabbaddaabdacdddbadadbcaaaaadbaaabdcaddacabacbacdbaaaacbcaabccacaabdccccbbbcadbbddbaacdaaccbdbccdabbbbdaabadcdaadbcbaabcccbaadaadbadbaacccacadbadcacacbcdaadddbbaabcbdddcaaddcddbabdcbbcdcaaadbbdcbcdaddbaabccaabcdcdbbccbcdabbabdccaddbcccdabbcbbcbbcbcadddbcbdacdcaaaabaacbccdccbcadbaaabbccccbcabbabadacdcbdcbdaadcdbddacbbbdbadadbaccbbccdaddaadaacbaaabbdabcbcbabbcdbabdcaaaacbcaadadcdbabdcddbcacbbdadcddaddbcaccbadbcbbbbdddcabcddadbbddbcababdcbaaababacbddaacdccbaccccdaccaadcaadbabbddacdccacddabadbddcdbccdabadadbdaddacdccbcdbdcdbacdaccabbadbdadbdaabcaabbdabacabbaddaabdacddbabaacddcdcbdaddbcdcdbbacbaabdbbbaaddbccdaababdbbaababaccdcdddbaabdbbdddadbdbcabbabadcaadaccaccddabbbbbabdbdaddadbbbcacdbccbcacadcccbdcabddbcbabbcccdbbdcbbaaadcbbbbdbcbdcdbdacddaccaabbddcabaadbdaccbacbaabcbabbcdaaacdbbbbadadcccbadbcaddbaabbbcdcbaccbbcaabdcaacbaacacdbabcbaadaacaacaaccdbbbacacbbdbdcacbddcbdcdbcacdbdaadcdbacbacabcdbdccdaaaddddccdbbaccddbbaccddadacdcababbddcbabdcbcadbacdbaadbbaddcddadcbbbbdddcdbadcaabdbccabcaccdbdaaabaabcddaaabccdcaddabdacdbdbccabaabbbbcbdbdcdbadaadbdcdcdbbabbddadaacadcbcbcdbccdcdcdbdbdcdddbabcdbabaddbacbdcababacccbbbdadadacbbddadbddddddbdadccadcadadccaaccdaddcccdbdaaabbddadabdbacaaabddaaaccabaacdbccddbccddbbbadadaabcabcdbdddbacacdbbbdbcccdbadbbbbacbddabaacdaabcdabadabacdaaddbdccbcbbdcdbbbbddadccdaccaaccbbcbcbaacdabadabcdccbdbcdadbbbdbdbacbbbacdbacdbccbcacbdcdabbbdbdcabaabaccbabcacddbbaacacccbbcddabdcaaacaccdbdcdcacbaddcacdccbbbbacdadddcadbbabaddaababccbcdaabadddbdadbbcdcadadccccdccbacbdbadadbbadcddbadcbcddaddadcddccabaddccabadadaacacbcbbabcabcbbdacbacdaadbadbddbbababcaccadacadbccdcacadccbbddabdccaababbbaccdaadbdacacaddccdbabddccdcaabcaacacbdcccacdddaddbbacabdcddbbccdbbddcbbbabccdacdaccddadbddaabcacaddcccbaddccbccbacbbdaacadddcccbaacbcbadbaccdbaacaadcacadbcbbcacbbaaacbdbaabdcabdddbbbbdabadbccadaadbcbdbdabdcbaacadbddccdabddabccbaddaaccbddddbbcadabaccddddbabbbccaccddcacabbbddaabbdadcabccbdbdacadabbadddbcaccaacaccccbbddbbdadddddcbabbaabccbcaabcbaaabddcbaacabbcdcccbabcacaaaaccccbabdbaabababddabbcddbbcdaadcacccbcacdcaabddaabbcddbddbcdaaddbaacbcbdcccacadcacbbabaccaccbcbdcadbadcccabdcaccdbabddcdbbadcadddaaacdcadcccaaccdbbdcbddbbdccaccbabcaddcbdabadbcdcadbcdbabdbdcddabbabcccadaabcdbcbbbaaddbdbcccadcacbddbaaddccdbdabcaaddccdbccbadbadbdacaccaaaabaabcbdaadccbacbbacaddadccdbbcbbabccbddddcdcacadccbcbacbbadccbdbbbcdcdaabbdacabdbabbabbdaabddbbcbcdddcccacdbadcdbcbdaabcbbdbdabbdcddbaccbdadcdaaddaabbacbabcaddacbccaababcbcbdcadccabddbdaacdabcbbcbcbdacdbacbcdcadabdadbddbbbcdccdabdcdadbbbbcdcccbddadcbacbdabadbdddcacbbdcdcdbdcbbdccabcddcaabbcaacdbaacddddbbacbcaabaaccaabcbdccaaddbaacdbccacbbadbacacaadbdccdddcbbbdaddaccaccdcdddaddbdddbccdaaacccabcccacdbbadbcbccadbdbdbcbabadbcacadcdadcdbbadabdaacdbdbaddacacadacabacbcbccdbccbbccdadacbdbabcdadddcccbacbdbddcbbdddbbadabcacabcccacacddabbcdadaccdaacccaccabadadbdbccbcaddcabbdbcbabccadbabdccadadccabbdaccbdbcbcbbbcbabcdbadcccacacdbcacabbcabcaabaabcadccaaccbdaddaabdaabdbcbdcdbaadabbcbcddbcaddbdcacdbcbdbbbcdccbacadcbabbbaacacacdcdcaddabbadccaadbccbddaaaadcdaaabaabddccbbddbabacbcacabccacbadcaadadaadacbbbccbcddaccdccccbacccbabdccadabcccaaccdadbdbbabcbdbcabbdbabaccdbcdbbbcdbcbadacadbbdbdaccbadcadccccbccbddbbcadddadcadbdcccbaaacbbdbabcadbbcabdcbcdbabcdcbadcddadccaaaddacbcccdbcabdabbcacdabbcddcbcabadcdddacdbcdbbdbbadacddabaaccadbddddcbccbaaacbadccacdcaabdcadcdddaabbabdbdcddbbadccddaddccadaccbbbdbadaddccaddccacacddbbdbadcdcbbaacbbccaaabddcaaadaadbabacddcdabacaacacabcccacadacdcbacdaddcbcbcacadacaccaccdcdcbbccaccbccdcbdbbdabdaacddcabdacddaaaaabdcdabaabdacbcbdacccbbdacabdaabbbdbcaabcacaaacabdbdabdcabdbcdcadadbacaccbbaccbaccdddccbdcdbddabcaabcadbdabadcabccabdccbbadcbcaddcadbcdbadadccadbcadcddbcbabdcddcdabccddcdccccadcdbbddcdadddcadcdadbaddacdabdcbdcbccdddcabbadcabacccdaabcbaddbcadbdaacbdadaabcbaddbcdcdaadaacbbdbbdcbbdacccccaaadcdaacdbdccadabcbcbdccccaaadaaabbcaccbbbcbbacbcbaddbabcbdcbbbcaccaadbbbbdcaaddddabdbcddddcdbcbcdcbadcbadaaccddbbccbcbaccbbbccbacaacccdcbbbcbbabdaccbbcdbbcababdabaadddbbadacbbaabbabbbabadadcdadcadcdabcbacdbadcacbadbcccbbdbcabcccdacaccdddadcbbbccbddadbcacabcddbbcddbcdcabcbdcbdbddbdcbccabcbdacbcbcbacaccdaddacccbadbdcdabaaabdaaaddabcdaccaddbdddccbbaadcadbcbabdcbdbddcdadacdbcbbbbbbcbdaaacaccdabdcbbabbbcbbaaabaddcbbddccdadabaabdcabacbabdbcdbabbcddabdbbdbdcddbaaadccaacbabbabcdbcabdbdbadcacbbaadcdcdcbadabcccacabdcbbcacdacaabdadbbbdacadcaccabcacddcbddcabdcdddcbbcacbccdbdaccbcccbdbbbbdcaddbdcddabcaacaddcbadbddcbbcaacaccbdcbdcadadddaccbaadccadddcbdbadcbcbaddcbdcdaccdcbcbbbbccaaccdcbabbbbdbacabbbadacccdbcabbddbcbcbcccaacabdabddbcdccbbcbcddaacbccadbdabdaacaabcaadacbbbdadcdbadaccbbdcddaadbbbbcdbbdccbbcddbbcbdddaddbcddbbcbccbdbdcdadddaadbbdbabadaadacbabcaaccbdabcaadcacdaabbbbacaaccabbaaaacccabacccddcdbaaddbbddbbdadbaaccbdabcdaacbabaaadcabddccaadacdbcbcdddcdbdbbdbaadcdaccbbccadddbddcabdcbaaccaabbdacacbddbbbcaaaababdcddbdcdbdcbccdcdcdcdcbadaaccaaddbbbdabdadcabdacddbacdadbadbcbadbdbcabddbbcdbbacbcbddaabdddcbcdbaccbdcbbcaaaadaccdbbcabcdbabbdddbbbcdaacdabbbbaccdbcbabdcdaacaabcacccbbbcdbcbccdcacbcdadbbadbdccdacbbccccadacddcbbdcbcadccadbbbacdaacbacaccaddabbadbadcbdaabbaddaabaabdaaacadcacacaacdbcdabbccbdcbabaabcbaaccabcbcacdbaadcacbacaacabbaacdadaacbdacadddbabccbccdccacbdbadbaccccabdcadcdcdcdaabacbaacdaabcabdaaadbacdacbddbdbacdbcbdabacacaccababbccbabbadbbacaabccdbccdbcbaabbcbcbabdcacdabcccdbcdcbdcacaadaddbadadacbbababbcdbdbbbababcaaddcdadbdcacaadcabbcdcbdaabdbcacbcbdbbbabaccadacbcbcdabdbabddbcbbabccabdcbbcdaaaccdddcbbdadcabddbcaaacbcddccaabcdabcdddbababbcabcaccdabbdaaabbdacacbbccbbdaccddddddabcbcdacadbdadbcbbbbadbbcabbdddabcccccaccbaaaddabcbadddcbdaabbcdadabbababdabbbaadbbbbdacbbccbadbbadbcabdaadbadaddaccdbbaacdacccababdbcddaddbccdccbcddcbddcadcadacbdccbcdcadadbbcadddbdbcdaaabcacbcaaababbbbdcbcbcbbcddbdbbdcacaacddcbbdbcbddabdaddcbaababadacaccbbabadacdcbdcdccbbdbdcdcabcacbcdccddbdddcababadcccacbbdadccdabccadcabdddbdcccccbdadadbbbbdbaddcdaabcabbbbcbdbbabacdcababbacbdbbdccaadcdaacdacadbddddbacdacbaadbacadadcbacdddcaabdaccccbcadcbdadcbcaadbaabddabbcbbbbaabadadbdaaaacdbcddcbabcaaadacbbbdacaadbbadbbaccdbccbddaaaabcccacaddcdbbdacadbadbccbadaddcadacdadadbcdacdbbddabbccbcccbaadabcbbdbbcdcdacbbbcbbdcaaabaddddaccbcbbdbbbdbbdbdadadbccaddbdaaabadabadcaacbbbbadbcdbbabcbddaacabbabccacaaccdcdaabddaabdbddbadcaddcabddcbdcaadbacbdacdbadbacadcaabbbddbdaacbaddcadcccddddbdadbddcacdabcdccddabdbbacbdaccbdacbbdbabdbddbbdcadbcabbcddadbdcadbddcccbacdacbddabcdabdbbbcccdcbbcbbdcadcbbcadcacdbccbdadcdccbbabcabadaabcbacdbadbabbcbcbbbbdbcadaacbdcddaaacaccbbddaccdccabdaccddabbdcddbabbaaaadcacdbabbdbacaddadcabcdaabbcdbaccbcbdabcccbbaacbacccbbccadabcdbbddcdcdbdccdcdddacdcdcadaaccbbcbbbccaaaacccaadaacaddabbcdabcbbbdcacbbcdddcbdacaabbaabbbaacadabddbcddcbcdaabcacbbdacbaaddbccadcaddcaacdadabaadddacbddaabbbccccdcdcddcdacaaadcbcaabcbaadddacacdddabaccaabcbaadbcccdaadbacdddbacbccabccbdbadacbbcbadbccaacabaacbddbacdcaaadbcbabcbabcdcdbccbbbcabdccadbdcdcaaccaababdbbbddddcccacdcbbbdbbccddabddcdaacccccbbbcccdcbcadacddddadabdacbbbcbbacdadbcacdcccaadaadbbaccaabbaacdcdbabdcbcbbacbdcddccdcddacbddcbacdccbdadcddacbdbdadbabccaabbbcadddaaddbdbadddcdbbbddadacadabcdaacbadbcdcabbbadaabccccbbbbadcbcbbaacdabcabdccadabadbbbacbbdabcadabcabdcaabccdadbabccacbcacdacaccbdcbccdbbadcbacbcbcbcabcdccbbacadddbabccaaaacbccdbbccaaaddabbddcbcbadbbcbbccdbddbddcdaadbddcabcadddccdaccbcccdcbabbdccbadcbabaddacbddabcaacabccabcdcaabacabadcacbdadccacadbbaccbcaccdcdbccaddaaacaacbbbbbbbddbbabbcbcbbcbacccbcaccdccaddaabdcbbbcbadaadbdcbbcbacccaadbbdcdcadaabbaaccddacbacdadacbadabdbdcdccdbccdcdddddbbccdaccaccacbaaadaadccacccdbdbadddcacbbacdcabdccadbaabddacacbbaaacbabaaabaadbaaccbdbbcabccaddcabcacaacabdbaadabdbaddbadadcacbbbbaabdaddaaaabcacbaccacbaccbdcdddacdaddbbaaccacdccbdadccdacbcbbcdbadbcadadccadbabcbacabbbcdaadacbdadbabdaacbcaacbcaaadbcdccacaabbdddbacabacdabdddabdabcdccabadbbaadbbcbaccdbbaccaaddbbbdbccbcbddacbdadcaaabacabdcbabdbdbcbcddcbcaddcdbabaabacbbdcdadaccacdcbdcadabaccacccdbdcbbbcadcdaddddcbbbbbbcbcccdcdbaabadacacbddcbadaadbbbcddadbdbbdccdacbbabcbabdbdcaabccbcbaacbbaacacdccbccadcdbaacaaccdcbbdabbadbabacaaacdabbadcaccdbccbadbccadcacddbdbacdadddbdaadbbbacadabcabccbbaaaabcbcdcacdabcabccaaabaaadacdbdcacaabadadcbcbccbcaabadddcdbbadcbcbcbdbadbcdcaabcacabbaabadabbdcdcbbbdaadadbdcacdbdaaadcabcdbdbbbddcdaadccadacacacacadddabbbdcaddadbcdccbbddbcdbdbddbaacabddcadcabaacaaadacddaacdaddbbbaddbaddbabccabddabdaddcdacadcaccaabdacbbdabdbdbdccaabcbcccabdabbbaadccbabcdcaadbdbcccaacacdbbdbabaaaabdbcdaaacdbbdcaaccccccdaccacdddcaadaacbcccabcadbbbbdddcbcdcdacbdddddbbbbaaadbaaadcadacdbbbcdcddaadabbbcdadaaaddddbdacabdcccbacbcbccdacbdbbbcdbccccbadccbdbbdcdcdcdadbbabbcadbdcbaabacbbdcabbcdbccdccdaadbbbadcdaccaccabdbacadcdacdbdabbcdaaddaabcbcdcaababacbdacaddcbdcbcccdacdababaaaddbddaacdddcaabccadcaaccdadaddcddddbcbadaadddccaabacdbbccdadddccdbbdbcddbdabdadaccccddaadadccdcdcabacddacabbcbbdaabbdccbcbbdcaaccbaacbacddcddabadcbbbaddcabcdbcbdabdddbcabbaabbbccdadcbabbaddbccdbddcbaacbdcbdabcadccdcddbddccaaacadcdbbdbcbbcabddbcdcbcbadccbccdddacaadbbcbacabccadadbccccacdabdacdabadbdccacbbbcabcadabccaabcadaacacabddaacdaabbbbababbcaabbdcaaadaddaadbcbcadcccadbadccdbadbacbbdbbaaacabbdbabdcddcbbcadbaaabddbdccbadbcdbcacdccbadcadbccbbccaaacdccbdabddbdaaadbaaccbbaaccadbccdbacadaacbacbcdacdccbddabbcbacbaacbbabcaccaaadcccbdbacdaddcabbccadadaccadddcdaabdcacddbdabadcbccbbddcdabbcddbdacccacdbbbdcccddabcbdacaadbaccbbacdadcabaccaaabcdddbdaabdaacacdadccdbccbadacbcdcbaadbcabaacccbccdcaaacacddbbbdacaabdcbcbbabadbabbadccbcbaaaabcadcdaccddaacadbbaddcdadbddbaadddccadabbbbccaabdcbddcbcabcbbaaccaaabcaaccadadddbdacbccbccbacaddadddbadcabdaccadacddcdcadbddbcaaddbacaadaddddaacbddbbabaadccdddbdaacbcadcccadcbdddbcdcaadddccbdaadbdcaccdcadadadbcabbbbaddccaacdbddbbaadadcacbcdccdcbbbbcabcdbbbcdcabdbcadcbcccacaaccccdaabbbccadadcaccdccbccdabbadacbdcbdbdcbdabdcbadbcaddcabadccdadbdddddabcdbddcaabcdcabbacdaaabcdaddabbccbcababaccacbbacccaddcabcacadccbadabbacbbbdbddbbccabaabdccdcdcddccacaadccbdcabadbdadbabacadadbddddcdcdccbbbcabcdddbbccaabdbabacdcccdcdaccadcacbdbacaabcaabaacbaccdacdddbdaabbdcdbcacdbbdbddbcaacbacaaaacccdccaabcdabdccbbbbdddcddabadbcbbcdaccdbbbcaccadbccdcadddccbcbbdbddcabccaaadbabaadaacaddddcbbaccdbddcddcdaaacbdbabadabccdaddabbbbaadcdcbaabdacbbcdddbbcbbccccbcdbddadbabbdcaaaddcdbbabccabcdbbcabcccbaaaaadbcbcabdbccbaccdbddcddbcdcdbbbdbaaddaacacbcbaacaabcbcccbbacabbabbdbcaadadccacccaaccccbdacbcaabcadcdababdbaaddddaadadcbdabdcbbbdbdbddbadcbaaabdcbdcbcbdadbadbcdabadbabbcddccdbbabcddadcacdbaccabcdbcccadbdcbaacdabbccdabccacbddcdbababdccaaccbbccbbccaaabbccdcdaaaadcbdadabdabdcadbdacaddadaacccacccdcbcaababcdbcccdabdccdddcbccdabcaacaacbddcbcaaadbadaaccdacdcbddcababdaabacbaababbcaaadadadbbaccacdbdcdcadacaadabcdadcaccbcdcbaaccdaadcdabbbbbddbacacddcbdcdcaacddabcadababadacbdabadbbcdbdbccbdbccacddccbdbcdabcbbaccacddadbacccdbcdcbcaaabbdccdacdaddbbcaababcdcbbacabbabdbdccacabcdbcddcddbdacbbadbaddcbabbacdcccdabccababdabdacbccdcbdbacdcbaadcbdabbaaabacbcacabbbbabadacbdacdcadadcaabcacbcacabbcdcbddddcaccdccdbcdbbbaacddcadacdcbbbbcadadaabbcabdddcbadcdcdbcbcabacacdcadbdbdbacdaddacabadbdadabccdadbcaadbadbbdaddcbabbbadaaabacdbbcbccdbabaaaacaabbadbbcdddcdabaacbcacdbcdccddacccadbbbabacabbcdbdccacbcabcdaaaabacacdddcbcdcabddcdacdaadabacdbcdbdccaacddbbbdbabbadacdadbccbbaacbabcbdccbaacdaaacabdccbddbdcbbbdddacbaddbbbacbbcbaabcbaabccdcbabacccbbccadcbcddcbabcacbbcdbdaccbadddccbccaaacccbcdaaddbabcdcdacbbbdcaaccbddacaccbcacbcbbaabcbdcbccacbcdbbabcbcbbacbdddabadaacdbdaddacbbaabbcdcdcbbccbbbdcaaaadacadccadacdabbccdbaacdadaaabccbbbcadbcabadccacdaccccbdaccadbcbdcdcddcabbdaaadadbbdbcdcdbbcaaaccbccbbaccacbcccbdccdbadabaaadddcdbbdcccbcbbadbbcadabbcaabaaddaddaaabdbdbcdacccadcccccaabbaddbbcaddbcbaacddbcdbcbcaadabaaadacddbddccacdacbcabbcbdadaacabcddccaddbcdcbbcbbcdbddbbdbaadcbabccdcccccdcdddbdcdaccdaacbbaaacdbacdacdcadcacaaacdacbccacabdcaacbaddaddbcddbbaaabccdbcbccdcddccbdbdcdcbccbcccdacbbabcdbcaadabaadadcbdccdacbabbbbcbabaaccddddbcacbbadbbbbcdbdadaccadbbcdcbcddccbaddaacbddbdbdbacbcdaacccdcabacbbbcccdaccbaddbabbcbaaccdbbccdbdacabccbdbdcccaadbbcddaddcccadccdadacccdcbbbcbdddcccbacbddaccbbbdcdbcabccddabdbdcddccacdcbcccbbccabcbabaaaabddbadcdcdccaacabbddabaabdbcdcadbaaacadbadbabdcbdbbadbdccdbabccbaacdacbbbdcddcaadabbdbccbadbddbcbbbabcbcaadadaccadbdbcdcbccabadbabbbbbbdadbcdddddcabdbbadacdadadbdadcbdabdbaabbaacbadccbaddbbabdddaabcdbdbbadbababddcaccadbcddcbcdabcbbadbbddcccaabcbdccaaacabbccbadcaaaaadddcadcddaabdcdabbbcdcdaabcdbabccdcccccacdcdbcbdacdaabbdbaddcabddbccdacaabbbbccadbcabcadbdaccdbacddaccaddcdccadbbdadaccbcaacacddbbbaccdbccacbbcdbcdbbbdaabaabddcbcdddacabdccacbadbaacadaaddbbaacabaaddacdcdbbddddcdbcadcacbabcacbacddcacbbbbbdcabadccdadbdacdcdacbdaaddabdbcbdddddbbccdadcccdacbaccbbdabacdcdaaccaddcdadaccabbcccbccccaabcaabccaddabdaadacddbcbcaaddbbbaabddbbabaadcbabcaccaaaabccdadcaccbbaddbbbabdddababaabdcabdbbbcbbbbdacbdcdbddcaadbadcacddbccabacdbbbacbcbacddcdbabdacdaaaddabadaabacdbbdaaadbbdacaddcbdbcadbacdbbabbdcdadbbddaddbdadaddbdbaccbdadcdcaabdcbccbdbbaddaaddcddbaababaaccabcabbabbddabacacacbbaaababcbbacacccdbbdadcbbaccaadadcccdccccbcbcddacdcdaadadbbbdbbdcdbaadcdacddbddacabcadccccbabbcddcdbdabbdbdacbacbaddaaabcbddbaddaaadccaaaaccaaadabbcbbbddaddcdbbbddccbbcaacadadbddccdaacbcaadabbaadcdbabbdccdabcdcbabccaaacbcdcbdaadbbadbcbdbaaaabbaaabbabbaaaabdbcacdadddbcddbddddbaaccccccdbddbabbdcbbaabaaddaaadbdaadccdcacdcabbdabddcabcdbcbbccbdbcaaccaadbdcaaadcdbacdddddadacbcdabbccdbadbdcbbccbdacbaabdaadbaadaadccabcbabccdbcdacadadbbcbccacdcddbbabbcdcbdddbbdddbadbccccbcacbdcddaaddbadbaabddddbaaddccbabaadcacdadcbbaacbccbcdabcaddaccdbcabddccdbccbabbcdcdacdcaaaabcddaaaddcbbcadddaaacbdabcbcddcbbcadccccdbdababcdaacdacadccaabcdcddccdacaccaabbaccdadbdcaabbdcbbcccddadccbbaddbaadbdadacccadadcaaacccbbccbcccdbaabaaaddcabaadbbcdaacadcacaadacdacbbdbdccdabdabadaddbadbaccbcaadabbcdaddddaacbbbcbdaddbdacabdddaaccacaadaddcaccabcccbabcadbabadbabdbcdddabcbcbdcaabbbbaccacddacdaadaabbabdccdbcdccbaacbcabcccabdccabadcbdabcaabaaabbacbbbadaddddadabbdcadabbdabcaacdccdbcbcaccbdadddbabdcbbbcccbacabbccdaddcbaacabdbbdccdbbdbbadacdabbbccdabababcdcddcddaccacacbaaabcbccdaccddcccdccdbaaabaccddbbacdadcacdcdbbadddabbdcabbbbdabcbbbdabbcdcaacabddcdacdcbbbcbbadadabcbadbddcaddacaadcbcbccaadcbbccbaadadcbbaadbddbcbddadddabbdbbcbbaadabcccccadadaccbbccadacbbbaaaabaaccbddcbdabcadbacccaaadcbbdddaaadbdacdcdacdbdabdbbbaadadcdacbbadddcdcdaaccddbccbacadacddabcacabaaadcbbbdacbacccbaaadbcdacbadbdddadddcdcbacbabbbadaaddbccdadcacbbaddcdaaccaddbbddbbcddccbbcddccddcbaddcbdabcddddcaaddbdababcbcacdabbdabbaddacdcabcadbbdbbddbbcdcbdbcaccdaddccabdccdbdbbdbbdcdaaabdcddadadaadaaddaabcabddacacdbabbddadabcdadcbdbaaddcacbcbcbbdbbabdbdbddbbcbbdacbdbcbacbbdbccbadacacddcaadacbcccdcaabdbdbcaadbbccdbbaaddabadccccadccbbddcdbcbbccabbadbdaccbdacddcdbbcabacbcbdcacbccdccbbbbbcdacbcadcdcccaacacaabcabcbdcabdcbcabadcdbccdacdddaadbabbbbaccadbbacadcacbaadaccaddddacdcabcddadbcdacdcadadcccbadbcbcddcdcccdaccccabadcdbbcdbccdcbacccaabaccaabbbbccabacccacbdaaccccbadabcccdacacddabadaadddaabdbadbdddcbabccbaadddbdabdaddabcbbcbbacabbbdacbaabccbbdcabacaccabbacacccdaddadbcdbdddbbdbbdbbabddcabdaccbcaddddbbacaccddbbcdcdcdabccdbcdbcdbccdbbdcbbadbdcbadaabcbddccadcacbdccadcaddabdbcbbadaacaadbcbaabacbbcccccbdcadccdacaccbbbbbdcaadaddaccbcabaacabbdbdccbcbdaabaccadcdccbcdbcabcbcdcccddcddccbabbbdbaaadcbdbacdddadadbbdadaacabdddacdccbcbadbabadddcdbaabaadadbbbbccdcbacdaabcaaadabbcccccaaabdddacdbdacdbdacddddaadabcbbcdcbcccabaccdbaacccbdacbaaabacddbdbcaadcbbdabcbddbcbbadaddbdaabbbdabaacccdabddbddbbacbbadddccdadababdbdbcadabaddddbdaaadbdbdbadbabbbdabbcbcbccacbacddccddadbcbdacbbbbccbbbbcbbabddcbdcbabddddbbbbdcabadddabddbdcdcdccaccccbdddddcaadabbcdbbbadabdcacbdaaabbabcdabbddabbcdaddcdddadbddaddcadacccadccdacaadddcdcababcbaddbdccabdadcbdababbabbbabdaacbacbabcaabcbdaabbabcdcabbdaabbdabdaadbdbbdbadddcaabadbbdbacddddcdacbdcababbccdbbcdccdbddcbadbabcdbabaccaaabcbdabbbacaadbcacabdcabcccbbcdcaddddcbaaadddbdccbbbcbadabdbdbaaddadbacdabdabadbddcbbddadcabbcadbcdabaabddbbbbcabdbccdcddcdddabdcbbdabadcdccadcaccbbcadbbcbcbaaabbddcbcbdddacabbbcbcdabbadaccacaaabcdaccdcddaabbaadbcbaabddbbcddcbcabbbcbcbaacbbdbccbbdbddacdcdacdbabbbdaaabbdbcbcbaacdabdbdbcbaccbdcadaabbaccbadddadbaddaabcbadcbbbcbddaaabcabaddaccccabddadcabdccbccdaddacaabaabbacacabbabcdadcdbdcbbdcaaaadddadbcbaddbabccccaacaccaadabbdaacbdbddcaaccdcccadddacddcaadaadaabcacbcaccddadccbdbbbccbabacdbbbcabcbcdaccdccaddbaddbcacaadbcaccbababdccbdbddaccdbaaddbabbadacdbbbcadcdabaddbdbbbacabbbbdcacbdbdbadccbcaccadccbbabcbcdbbdaacdbbbabaaacbbbbacbcddcddccccbcddbadbcddadddacbcccbaadcddaacccccbcabadcddcababacbbcdcdbdcdbdccbdababdadacddcbdcabcbccccabddbadaacabdaadbcbbbaacdbdcdbbdaadcdbdabcdcadcccdcbbddbadddcacdcdcacadbcddbbdbdadbaddabbaacdbaaaccabcbaacacdaccbbdbcdacbdcacbabddbcbcbabaababaadbaababcadcdcbabdbdaacbdcadcbabbcacaccabbccbbabadabdaadccbaacccbacabacbabaccdddadcbdadccdcbadcdabacdddcdabcbdccbbccdbccccaddccccdbadcadacbcdcdbbbddaabdadbaaadddcdcddadaacaadacdbabbaaddcddddddcbbadaacacaaccddbddccdbbddbdadcdabcaadbabddbdbaddabaabcdaacccdaabadddabbdaaddddcaaadbddcabddddbbdbdddacabdacdddcabbcbadcaacadadbaaabddacdbcddbddaacadabaabacbbdadadcaabbbbcbcadabddcbbaacbcaabbccbcccacadbbdddcccbccbcadacabcddddcadcabacbadacaabcacbdcababadcccbadbaccacccdbccdbddcadcbddcccaacbcddccadcabcaacdccdddabccbbacdbbbacabcdbcccbaddbabccbdaadddaacabddbcdcacbbdddaaddcdbccacadbabaaaccaabdbddabcccadaadabdacabdbdbbbaabcdabadaddbdddbdbcaccbbbaaccbcaacbbabddcacdbbbdcabdabcbcddcdcbcbccacccdadcccaccacdcadaacacccbcbccacdacdcaadccaaccacaaabbaadddddcbbdbadbadacdabaacdcacacdaddaabaddbaadcdabadcdbbabdadaddbbaaabbdbdbaacdadabdbabcddddaaddcacbaabdbabbaacacdbabbccabacbdcadabdddccdbaddadbcdabadddbcdbdddabbbdacbabbaaddaaacdcbdcddabbdacabdcaadbabdbaaccacacbcaaccaabdcbdccbbbcaadbdaddbbadbbbaadabdccdbacdbddcabddadbaadabcccbdacddcacccadaaacbaccabdddadcdddbcacdbccaccdaddbaacbcaacdccadbbbbcabbccbcacddcabccdcabcbbdcdccbbcdcbcbdabdccadaaacccadbcbdccaabcabbbddbaadabddacabacddacbadbcacbcaccacdcddcbcddacdacdadcbcbdbbdbdbbbbdacaacadbcaaccbdaccbadacabdcbdacdadadddabcaacdcadccabaacbdbacccbbcbdbcccdbbabadadbbcaacadbbaaadddbbabcddacadadbaadacacbdadcdbaadbbbdcbabcdabcdccacbcadabdcddbadcdccddcdabaaabbccababcccacaaabdcbddbdadbadbcddbbabccccbbaccdaddaaabbbaaccccbdbacdbaabcdccdacbacdcdaabdbbbbccbdbccbccadabcaaccdaddcabcdcbdbbcbbadaadccabdcddacdbcbadbacacdbadcdacdcabacddcbacaaaaaabbbbdbbcaccaadcbccbaccbdcaababdaaabddabdcbdbaccbacbcdbcadabaddcaacdadbbbadaabbcccdcbdbcbddcddddaddddcabdddbacbbdaadabcabbcbcccdbddbccabdacadcaaacbaabbbadcdcbccbddcaccbdabddabadcdaccacacdccbbabccadacbabdabbbdbaaddcaabdacdadadbdcaaacccbcddbccaadccbaddcbbaaaadbccdcddbcbbcccdbdaacacccaccdabdddcdcdbaaaabaacdacaaacbdccdbbcbcdababbdbccabbbbdcaacaaadcdbdcdcacbaaacabbaacddcbcdabcbdccdccccadbdaadbccbadacddbbcddbcbcacbadcabcbababbddcacddaadbacacdacdbddcddabaadcbbcaddbaaaacccdadcadcdcbcadadbdbddaabdbcccddadacdbaacbbdabcacbdaaaddddbcdacbbaccdcbbdbcacbcaaddaccccccadbabdcadcaacccabcabcdcdcbaacbcaaccbdcdacacbabdcaaabddbdcdcdacccbdacaaaacdcacaccccacbaacdddadaacdcddcbaabcbdabbdcacbabdbababdacdbddbbdabaabababcaaabadcacacdcddbbacbbbddbcacdabcaacababdaadcacaccdcacbcdadcdaadadadbbaabdbacbbbbcdbaddccaabddaccdbacdabcddcaddaccdcdcdbdabdaaccddadbcdbacabcdadccccbbbdddbcbddcdddcccbdaadcacdbbccadbbcadbdbaabcdadcbdaacccabdbddcdaddbcdbdacbccdbcbcaccbdddbbdbccdbbaccbcbbacbbacadbcdacccacdbcdbdabcbbcaddccdcabdcdbacbcdcadbbabaaadcbdddcadabbdbbbbbabaacdcdcbddcdccdcaabbbcdbbcacadabacccaccbcadcadccdccdddbccdaccabddaadcbdcbcccbccccabcaacccadcaabacbbaadbbacbbdcdaabcaaaccbbcbdadaccbadbbbadadbddacadcbcaabacddbbbaaacadbaadcdbdacabbbcdbdcabbbcddaabcdabbabaaddadadadcacdcbadbbbcdbcccabbcdccdabadabbcdabdadbbdadcbaacbdbdcbdbbaacdabcaadddbbcbdccaaadbabacabadaadbabbcdbadaabaadcbdbbcabdddbacddbdcbbadabacbaabccddbbcabcdbbbacabacbbaadaaacdccadbcadbcacbbacbbaabddcdbaabbcdcddaaadbdbbddbaaaaddbaddaaccdccaddacadcdddcbbdaddcddbbbbbadddaaddbbbdbbdccaaadbdbccbbacbdcadcabbdcdcabdadbbbddccdaacadccadcbddacdaccbabccdabbbbbbbcddaacddadaaadacaabccabccdbadbcabadddcabbbdbbddcbbbcdcdacbdabdacaadabbabdadbccdcbdbcdcabbccbcdaddacbaacaadddbbaacdbcddbdccaadaaaacabcaccbcbbcdddaddcdadcabcdddccacddcacbaccaddcbbbadbdcadababacbcdbbabccbbabacdaaaacaabadccaabddbddcaaabdacbccbbcbdcdacaacbababdacccbbababdaacbbdbcbbbcdadcdcbcdabbbccbcaababcddbbccbcaaddcccabcdcddaccdbcbbdddabcadbcddcccbbbadcdaddcdacddadbbbacaadadcbabddbcadaabbbcbabddcccbacbacbbdcbddcdaccccdccadbacacdacccddcadcbbadbcbadababacbcbbdacbcaadbacbbddbcabcccdddacadbcdabdddababaccbabcaccaabbbdaabacdbaccbddabcdadacadcddcaccdacdadcccdabbcbdbbdcdbadbcbaabdbccaabddcdacdcaadabddaabbdbcaadbddcaccddbcccdddacbbbcdbdbabaacaddbadabdbaaccaaacadaacbbdabcdbcbdbdbaddaadcaacaaddabbbbcacdaacaabddbcbccaaaaccaacdcacacabcadabcdaaaabbddbbddccbadcdddbdbbcdbcdddbdccddcdaabadadbdacbcabdbdadcccaaddaacddbccbabcdaacadbbabaccdcaadcbcbaccbbccdbbdbcabcdaddcdcacbdcbaccbabccbdcdbdcaccdbbddbaaccdbadcbabcaccdcdccdbdbddababcadcacadaccdadacdddbcccacddbbbdddacbacbcdcbaabccbaccdbdbbdbcdabaaaabbdcccaaacbdbcabaadabdabbadbbbadabbcdccbabbbdcddacdccbdbcadbbbaaababbdbbdddcbacbaaddccaaabddabacaddbccaacbdacaccccacacccacddaadacacccdacabcbcdbcdbbdcbddccabbdaaddaddabbccdccbdcaadcaaccdcacdabdaccbbdccddcbdadbdabaaadadcdabcbbbccbbcbbbdbbcdbbdababbcaacccdbcabbcbcbbccacacbcabcabbbaccacdbbdbbbcbbbaaccbccdadbdbabbdadaabcdcbdbaccabbdbbdccbcbbddcabcddccbcaacabdbabcacccddaabcbabbbcbaaabddbdcbadcccbabbbadabbdacdddddcdcbbbdbdbccbabacabbaaabcaccbadbdadbdddabdddabbcdddcccacaaabbdddcdbdbdcbbaddccbbaaabcccdcbbadbbadacdbdbbadbdabdadbbacddadbdacbdadabdcbdbcdcacaacddabccbcbbcdbdacaddadabddbcacbddacadababdbdcaaabbbabcbdbaadcdadabbcbdcccdbcadcacddddbdcdacccbacccccdbbaddabcababbcadcbccbbbcccacdaaabcbcccadabcdabbaaddcaacdcbaaadbccbcbcacabbabaacadcacddcabccbbaddbbcabcacacdbcbabaabbdadaaaadbbbbaccbbcbcacdddaddacbcdbcaadcdacbddccaadbcacdcdabcbaabbbbaaadcdcaadcdabaaddcdadbdcabbddabaaacdbadbdcaccdacbbbaadddbacccdbaadddbadaddcaaaddccdaaabdababdbddacabdbcaaacbcabcdbbacabcccadabcabcbabdcdcccbbabbccbacdbbcacabdddaddacccdabcdbbdcddddbbacaaabdccacadbdbbbaabbadbdadbdcabdaacdbaaacdcbbadcbbdbcdcaddddcacdcbcbbabccdccabcaacbadadaddbadabdadaddababddbadbcbabaabbbabbacadaaccdadabaddcbaaabcabdcaabbcadbcabbbdcbbdbdddadaababaddbcddacbbacbddbcabbccccdaddbbaccbccccdbbbabbcbcdcadddaddccacbabaaababbbdbbcbadbacabbcbbbadbadbdccdccbdadabdabadddbabaaacdbcacddccabaaddbdabaabbacadadacccbacbdacdddabdcbababdbcaddacbaadcdccbacacdabcdcabbaaaabbdbcddabcacbabcacddbbbbcccbaaaddacacdaaddbdbabdcabbcccaddbbaaabbdaddbbaaabaabcbdddbbbaacdaadaaadddbcbdccccdcaacdccdaacdbcacdbbaabddbaacbcadacdbdbbbcddbaacbdaccacabaadadaadcccddbacaddbbdcabbaccddcabbbdabddcaddbbcbadbacdaaaadbdbcbccdbcddcbcdabaaaacbcbdacbdbcbcabaccadabaacdaaddadbbddddbbbddbbccdabbdbbacddcaabacbbccbcdcaacbcaaddaadabcaacdddbabcccacdabacdbdddcdbacbcaddbbaaddababdbaabbdcbdaddccdadddddbbcbcdaacddddccbdabbabcacdcbdddcaaabcdddcbaadcbbadbacdbcbbadbadadddabbaccadbabaaadbaabcbbdbccdaaacdcdacbdbaadccbaaaccdbcdcadbbbaddcdadbcaddcbbdcdabbbdbaddacbdbacdbadbdcdcdbddabdddacdbabbabdddddcdabddddcbcbacdbacaaadbbcdddbdccacacdcdabcbaacaaabccdcaddbdbccbcccdadccbccadabaacbbddbbdabdadadacbacadaddccadcbbdbcaadabbdccadaaddaadadcacccddbbcdcbcdbdbbbbcaaabdcbadcabdbcdadacccababdccddcbccaabbcbdaabddcdabccbcdaabababdadbaacaababdabbddbaacaababcbaccaaaccbdbabacbcacddaacddbdbcbbdacadbbbdbadbaacdddccbadbababcddbbcbaddbbcabddcbaaccbdccdbbadcddcbcdbdbbbdcdbaabcdbbccdaddccabdccdccdcacbdcdcdbadadcdadccbdddcddbbbcaabcaccbaadbcdaaccdbbacdadbdbcdccdbaacabbabacbccddbacbabccdabbcaccbddbccddbabcbadbcbbcadaaacbcdcccdadcadbbdbbcaadcdabbbccabaaaacbccdbdccbabccaadcabbcdbcabdabcddbcabdbcacabcdaaaddddbaacddacccddacbbbdddcddabccdabbdcabbadcabadcadbbccacbadaacabcdcbcabccddbbcccdddadabbcbadbdcdbddbdbdccbcaaddcadacabddaddbccaaaddcdabccccbacaadcdcdcadbcbcbdddcacbbaccabdbddcbabacabccdddcabccdaacbbabaabaadbbabccdcbbaaacdaddccccdacdacdcccbadbcbdcdaccbbdacaabcaaaddbbbabcacadbccdabbdcdccdadccbbbacdcdaddbbcddcccbbacaccdacbdddccdcabbdbbcbaadaacbcdcacaaddbbbcbcbbbbadbbbcaddacdbaccbcdddbdbbaddacdbbbabdadbbacadbcdaaadbdbabacdddabdccacbdabdccacdabbcaacbbcaaddcbaabacdacacaacbdcdcaaccdbacaacbabcccbdaadcaccbccbdddbbbacacdcdbcabcacdcddcbdbcabcbbbaaddacbcccadaacdaddaadcbaacddccdcdbcaddadcacbbabddaaabacdccaabbcddcbddccacacbcdaaddbdaabdcabbcdbabcddccbdbdbabbabcccbdaabbcddcdddcababcbbdddcaacaabaabaadbcbaaabcbdaccbcabbcbbadddcaddccbbccddaadbdbcdddabbdaddacadccaccdcdddaabaccbdccadbcdcadbddccadabcbccacdbcbbdaccccadccccabdbdbdccdcccdacddcaadadcbcccaadbcaacabddabdbaabccdbaacdabccbbaccabccdbbacbabcdaacddddcacccadbbccdabbdccddbdbddadccadccdabacccadbdbaaacadbbabcdcbddaddadcdbadbcccdbabbcdbacbbdddabaaacaccadbcaacadcbbadcdadcdbbbadbccdcbbbdbbddddccdabaabddcaadaadbacabdddccdaddbcdbaddaccbabdddbacbcbaacdbdbccdcddcaababbbabaaabacdabcdabacaccbdbaccbcaabbdddcabbabcabcabcdbcacaaccdccccbccbadbbdbabdbccdacaddbadaadcbabdadbdadbaadaabbaccddcbdaaddcaaacadbaabaccadabbaadbcdbdbabcbadadcababddcccadcbcddbbabdacbbbcaccdcddcadbbadcbadcdcacdabbbbadcbdabbbacbdbbdabaaabacacaccdccccdabcddcbdcddcccaadddbdcbdbcdcabaacaadcdcacbbdaccadaaabccdcadabddbcbddaadcabacadbadcddbccbcabbaabaddddcdbdbdddcccdadadbcbaaaabacababcdcaaabcbbbbbdaacadcbcaabaaabccdddaaabbdcbcaddbabcbdccbdadbcbbcabadcbbaabacdaadcbaddddacbdbbbdccdbadcadbcabcbaddbcabcddabbdbcdddabcdcabbaaccabddbbddcdadbcddacbabcadcccacccadddbbcdbbdacbdcadbbdaaabbcbaaccdcdcdcddddbaaaadbcbbbadabbbdbdddcabccadcbabadbbbdbdabababaacdaabbbdcbbbcdbbdaabbdacdcaacddadbccaabcbcccabaccbacbdabacaadacbcbadbabccabdacabbaaccdcaaabdaacaaabbddcaaaaacacaaabadbccbcdcbdcabacdadaccbbacbaddbbcabdbccbbabadcbbacabcdcdccdcddbbcccabbcccbdddbbadcadcdcdabddadcacdbaccaabddbcdcddcbddbdddabbbaacdadadccdbabbcdcdaabadacdacabbbabcabcacdcbdccddbadbabddbaccdbdabadccdbccdcddacadaccccdadbdacbaddcdcdbcbdcbaadbcdcacbbcdcbbdabbdcbaddbbaacddcccbcdbcccddbdbbabccabaccdbccdcdddabbbabacdabcbcbcbddcdddccdabddbddddacbcbaadbcadcabdbcccaddbbbcabbcaddbacaadadabbbbbdcddddadccddbcadcddcccdcaabadadacdabddacbddcbdbcabdcbdabbdacddbcaccdabbddbbdadadcbaabdcddacbabbdddadbdcbbcacbcccaccbcacddccddaadbcddbadcbcccdbdbcbdbcbabcacbccacbbabddadadabddacbbdcacbbbbaaaaaacababbbabbdcdddcbbacbdacbaadcddbdbadcbccbaabacdadbbbbdccbadbcbbabadaaacacbabcacdcdcdbcbdcdcbaabaccdbbdaaddacbdbaddaddbddacbabacadddbacbcbadbdcbdbcabcbdbcccaddcaadcaaccacabdadacbcdacadbbbabaadbacdbdaacbbbaaabdabcabbcddbadcbcbddbbbbbccacccaabbdccaddbcccdaccaabbdabbdcbbbbacdbdccdacddbcdccdccdadacccbddbcacbbabdcaabbbbdbddaacacdabdbaddbbaddaabbbddbdaacdbcacbcdbbcdbcabbbcaccadcdabcccddbbabddccccdbdddbbdacbadaadbcdcabddacadccbdaadaacacccabbaccccddddacccaccdcddbacbcaddcacbdaaaadbddbddbadbbabbbdadcccabacbaaadaaadbbdaaddcbcaccacbbbdcaadaaaddaabbcabdbbadbcbddbdabddbcddcbaacbaaddaccaabbccdadabcacbcdcbdbccbbbddccabaaadbacbbbbdccbdbcbdabdddcadacbcaabaccbdcbbcccdddbcbbadadabaadaddbaacdbcccbbadbabacbcaccdbacdabcabcccddabcacabdbacaddddbbbcdcdddbbddddcaacbdcbabaaadbcccdbaccabdbbdccdbcccbdccdbcbcabddbddcddcbcbadbdacdbcbbaabbacdcccbbdddbbbcacacabcddadbcacdcabacbdccbbbbcdacdabdadbabcdaadcaacadcbbdbcaadbbbcdcacdaddbcacaccbaaaccadbdcbabaabcbdcbabbdddccbdbaabbbcbbdbddbbbbbbbbcdbcdcbdaccaddbbbdbdccccbbacbcbcaaaadbadbcbbdadbcbadaacdccbcdaccdccabcbdcddddaaacbadadbdbbbdcddbbcdacabccddbaabbaabcaaddddcdccbddccdcabddbbbacbadcccddbcdcdddabbdbacbbbbdbaacdcdcddadbaddbccadcacbbdacbbbbbbddadaaacccdabdddccadcbacbcbdacacacddcaaadccdcccdccaddbbdccacdcadccabcbcabbccccddccdcddaaabbdcabbbdabccbabacdddabadddaccddaabbbdaaaabcbaabcbcabcbdadbdcdcccdcdaacbbadcbcacadbdbcdaabbccaaacacbdbccddbdcdddcbacbadbbcdbaabacacbbdaddbbaaababadbcbaccbacccdabbbdadabadbcdaaaacbadcbddccdbccdbadbacaaddccbccbdccdbcacaccadbddcbcdcbcdacaaadcacbbcdadbabdbabdddabdcdbacbddcaddacbdabacbadadadcbdaddacadadcbcdbcdcbcddaadbaaccdbddcdaababddbcacbabddcaddcbbdabcbbbbaabdcddcaaccbdaacaababdadddaacacdabadccabbbbcddcadbdaadadacbabbbbadddadabcdcacaacbbdccbdcdbaabcdccacdbdcaccccbbcbaabbbbababababbcaaacbbbcccaabdcdcbdbdacdbaacdcdccacdadabbcddacdbabcaacdacbabdbdcdacddbaacadcdccdbcbddabcbbdababdbddcdaddbcbddcccbccbabbacacaacbcdacddbbaaabbcdcbccdbcdcdccbbabcdaccacabcdcccbbbcdaaddbdcabddadddccccadacbbaaabdbdbdbbdbcacdcbabcbddcdbcddbddbcbbabdcdacacbbddbddbddbbddbccaadabcbbaaadaaddaabadaaaccbdababcdaccaaacaaddbdcaacdcaacaacdbbddbdadacadcdbcaaaccddbcbbbabaaccccabcdaabccadbacbdadbcbabaabbddbdbdbabddcaacdbcabababddbcdadcbaaaccbbcdaccbcdbbccabadabccaabdbcbdccdaaddbcbcaccdbbdddacbddccbaacbaabcbbbbadbcdacddccccdbbdaaaaadabdacdcdadacdcbbabcadcaabacabcadcacdaaccbbcabddcccbbcccdcabccddcabadbacabaddacbbbdcbbabadcbbcbccabbbacbacaabccccdbcbbbddadddbcbccccacadbdacbdabdbadbaaddccbadcbacacbbacadbbdadbdbcadbacdcdddbcdaaccbcbabbccadbbbaccbaabbdcadcadcdcdddcbcbaadcbaccaacbcbaaaabcdbbbcdadaaccccdacccbbbccbcbadccdcabaaaddbaddcaaabdbdbddddcdaadccabbddbcbccddacdaddbacabcaadcbabcbaaabcdcdaddcbdddbcaaacabbdbabbabcccbabccdaacaacbcbcddacabaccbaaacbdddbcaabbaaabcdccbbcbadcadccbaabccbbcccaadcadcadbaaadbcaabbabdcdbabdddbdbdcdbcbcacdbcacdacbaaababdccbabbadadbdbadbdcacaddccdaabbbdaabcdaaccccabcdbbbaadaddbcbbcadcacabbacdbadcddbcdbabddcccbdcabccbbdcaaadaaaaaacdcabdaddccdadddabcabdcdadbccbdcdccadaddaccdbdddcabcdabdcabbdcbadbdcbabbdbcadbacdcaabadbdacbdadabadcaaaadcbbbcccabbcaddaaddbddddaaaddcdacbbbdaaadbddcdddbdbdaabbcacccdbcdddcbddcbabcabdababcbaacadcaaccdabcbdacddccbcadacdbdcddbddadccabacbdbcadbaaadadbbcbdbbadddcbdbaccbdbdcadcddcdbadbdabcbcaacdbcabccbabdacccaddccaabbddbdccdaccabcddcbdbadcdcabbdaaadddbacaddcdcbacbcbbbbbcddbaadccbaabadabbabdbacaccbbaaadbdaddabcdbbcadcacdcacdcbababbbcbdcbbbcacccddbccddcaabccbbbbddccaabacddacbabbadbbdbdacbcdccadcbbcbabaccdcaadddbaaaaadacbadadcccbbdabcbcdabbbaddabcdbbbdacddaaccadcbaddaddaaccaaabddcdcbaabcccbbabdaabdaaccaabddaadccbadcbadbdddacbdcaddddbccadacbdbbaacbcbadabcbbddababadcbddccbdaddaaabadacbabdcdbadcadacccacddcaccbadbcabcdbdbcbcddaaabcddbbdaccaddcdbbcddddbbbcbccadaaadbbcaaabddcdbcbbdccdaaaacbacbbadbabcdbbbbddddcdadcdacaabaadacadbbcddbabdcbabbbbbccacdddabcadccacccdaccacdbcccbddbcaaddccbaadbbbdddbacccabaccbbdaaccdbccdbbbabacdacaabcabaaaccbabbcdcaabcccccdbccdaadabcbbdddcdabdaaabcaaaaadcddabdaacadbcbddacdbcacadbcaabbcadbdddbbccbdacdaabaadbbbbacbdbdbbbdaaccbcababbbdcadbcbaaaacdaacbdbacaacadcdccdadbbcabcbcdbcadbdacddbdcddcaaacbcadcdbbabcdbbdbabccbaabbbabbdbdcacacbccaaacddadccdcdaaaddcdbbcccbdabcbdabadcdaacbbcadbcadccabccbccbdabdbbacbdbbdaacacbbbcbbbababcbdbdabbabcdddcdcaccbcddadacdaaddbbbdccbbbaaaabdcbbcbcaadccbaddddcdaddbcdacbaabdababbdccccccbcbcadaccccbdcdbadabdbddcbcccabcbdbccdcbcaddaaadaadbabcabaaacacbdccbaacbdaccabcdbcddbbdbbacbaacbcbdabbabbacbcbcdcdcbadadaaadbddccbcababdddcbacaacccdadbaadbabcadabcaddabbcdabdcbbdbdcdaabbaaccaacccdddcdbccbacadacacaaddaadccadbbadbbaaccbbddbdbaccacbadaccabccaaccdabcddbadbbaccacccbbdbbdbbccbcbbcccbadbcbaadcbcacacbcbbbabcddddaaccbcddabbcabcbccbddaacdddbaddabddddccaaccbdcbbcdbacdbdacdbaccdacaaadbbccaabcbbcbabbbcabdbcdbabddcdccacbddbbdbcdabaacbdadabdaabddbadddccbbbbaddabacabcdababadccddbdbbddcadccdddcbdddaaadddcadaaddbcbababaaccbbddaacdcdcbcdbbcabacacbbdbdacbbbadadddbddaabcbdddcbdbcbbccddcabadcdcccaddbbbacdcdadddbcaddcacadabaabadcbdaccddcbcbbacadbdadaddbdbbbacbadbabacbaccbaddbdaddddcccbcdbdcbbbcdadcbbbcbadaaacbcbbacacbdccbcdadccdbadabdbacbdbdcbcddcbbaaacbdbbbbaabcbdcadccadabddaacdaaabbaacbbabaadcccbdcbcddaddbbaaaaaacabcadbccbadcccccbdddcabcccaabacbabbaabaabddbddbaccbdddcbccbcbadaccddcbacadbbbabbadcbabaabdabbdacadbababcccbbbbbaddbdccbcdbcbdcdabcdcaaabdabbbaadbdccdbdbdcccddacbddcccbccacdbccabdcaaacbbbddcdacabaaabccdddbcddcdaddcbddccddadbdacddcacdbacbabbccaadddcdadcdaaadadacccbadbdbcaaacadcccdabbccabccacdbccbcdbbdbadbbdadbcabcbbccadabbbacdadadaaacacddbdbdcbbcabbcdaddcbabdbcadaccaddabbababdabdbbcbdddccdbcdbbddbdbcbccacbdcdabccaadacdbacdabdccdccdddbbadabbbadbbaacddacdaabcbbacbcdbcbacccdabadccdbbddbdcdcaabaadccddbacbcaccdcbdabacccbcbaabddcdcddcbddbccdcbdabbccccdcccbcaadcccbbdcddcabbcacbbcabcbddddaaaddadbdadbcbcdbadddababddbdbbcadbbdaadcbbdacbdddcaccdbabbcbbcbdbadbbbcccaccbabbbddcaddccaacbddbacbbbcddbabbdddaaadaadbcbacdddccddbbcdbdbdcadabaccdbbbcadbabdccbbbaccbabbdcaccaabbbddacabddcaabbddddbadabddcbbbcbdbdacdcadcbadaacdcbcdbddbdbbbadbbbdaabacaadbcbbaddcddaadaaddddcdcbcbaadcdbbbdacdaccbddccdcccabaaacadddbcbccbccdcdabcbccbbddbcdcccabcaacdbbabddcbcabacdcdadbcbbcdadccdadcdaabbddbcbcddaadcbabccccbdbdbdddccbdadacccdccbdbdadaaacbaddbbbbbacbcacadbcbccaabdaaccddcabbbddbbbacadababbdbcabbbbcdcddddccbddccacdcdccdcccccaccbccdbdababadadacccbaacaccbabbbaaccbcaccccbbbccdbcbacaaddddbdddcacbaabaccbacbdcdbabaacccdadcbbaabbdadcbacacccacdaadccddbaddbbaccaaccdddddbddcdaccdddcacabcdacbbadbaabddcccbdccddbbbdcdcacddddabddcdddbbbddccbbaadcacaddbbccdacbaacadacdacbdbbbdbdbdcbaacdaaaddcdabbbaaccbbdabacccacabbdaacacddcdcdbdcacdcdabaaddbdababdbdadaccaaddbcdbdcbaddadadcbdccabbaabcabcdadbabdbdddaabbddacadbddbadadddbdbcadacdbaaccbbabaddcbdcbdabbdadbcbccbbacdbacabddadaacdbcbdaadbcbbabdbadddaadbcadbadccbbbdbaddbbaddcbddbbcdbadacccddbcadadbcbabcdaccdbddbdaadcabacaabddbcababdcbacdcddcddabadbdccabccacadaaadcbddbddbcdadbabddaacaccbdddbbcdbaacddccdbbbadbcabccacbadcbbbcdabbbadabbadccacaabbbacadbcddcccccbbbdbadcbdaabddcabccbaaacbacdcaabbcdccbcbaddbbddcadabbcdaacaabdcccaaddaacbaaaadbdacbadaccdbbdddcdcaddbcaddcacccdbabbbcbcdaacacacdcccccdcdabacbacbbddbcbbcbdddacaabbccbdbdabaacbacabdbacbacbbaccdbbacbbacbcbcadbaadaccacdbbbcbbddcddbcaacaaddcdbbddaaccbcabdcdbbbdbcddaabbcddaaacdaddaababccccddbcdcdababdcdbaaddbabbbccddccbcaccccabcccbddcadcbdbdcdddcbdabacacbdabdbaaddaaacddbdcbcaaadcbccaadaadccbcdacabcbcaabcccbcacabdbacbcabcbcdaadbccadadccbbbccdcdbadaacaacdacaccdbadcabbcdaaccabadacdcaaabababbaabaabddcdbacddbcaddbdcbadcacbbabcbbbccbcdcacbabaaadaddaaccdbadbcadbdabdcadcccacaabbcaadacdabdbaaabbdcbbbbdbcbacdabccdcabaabdaacbbbabdbcddcdcacdadccaddbabccdbaabadcbcbbaccdaddccdccccbddbccdacdcdabcadccabaadccabadbabaaabcddbbcccdccddbbadcbcabbabadaaabdaacbbdcbccbaabddddbdcaadbcdbcacacbaabadddbbdccdbddacddbdbbbdabcccbbcbcbdbbbcdccbbbbbabdbadadcabbaadcbdbdcbbcbcaaadbaccdcbcacbdcddaccadaccbdacbccbdcbabadbadbcdbbdadccbaacccdacccabddddacacbdddaaccccccabdbaaaacdcccdbcabdadddccbbdbaaddadcbdbccbacdbabcdbdbddcadcdaadbdcabddcdbdcddabcdaabcadacdcdbaacbadbbacdabcdacdabacabdbccbdbbadccbaaccadbdcccaabbcddacdcaaacddacdbacaccdddbaaccaadcccbcdbbddabcbcbddbdcdcbbcbcdcbbcbabbcabddaababcbbbbbbdacbcbdcaddbbacdacacacccbbbdacaccccddccabddddccdaddddbdadbbcbbdacadbbbcdbdbbabbbbdbbdcdbaddccaabbdbdabbddadaddacbcadcaddbdcaacddbddbabaccbdadcdadcadbabbbadabadddcadbdbcbbdcccdaadbbadcacdbaccacbcbdddbbbdcbdbdcaaacbdccbbbaccacadcddbacdbaadddddbacabbdcdbaccdadcdacadbbbdccbaacddbacdabcbbddbdcacbdddccdbabcbbacdaddbddaadcbaaacaaaccdcdbbdbdcacacadbcdcacccdaddbcbbacdababcdbccdbdabbddbcdcdabccbdbcaaabbbcccdabbacccaddaabcdbdbacccaadcbddaaacabbcbcbdbcabadcdbcadcdddadbbdbacbbdbcabccadddbdaccddcadcbdaacabbbdadcbcddbcdaadaaaacaddabcacadbacdcdbdbccdbcacbcddcbacbbdabbbcaabcacdabacbdababcbaadaaacbcaaddbcdbbadabdabcbdbdcdbdcadabbccbabacdddcabcabdcaddbddcadbbbaccccdabdcaaacdababcaabaacccbaaaadabcbcccdacccbcaaccacbddadbacbdaabbbacccbdcbbcadcdabbcaacaacccaddaacdbcabbadbadcdacabaabaccccdacdacbbabccdcdacacbdcbdcdcdccacadcdbccbcdadbccdbddbbbbaacbbddcaccbdbccdacaccacbbdccdcccbcbcbbdcdbdbdcddccaccadcdbdabcbaaccdabababcbabbcdbcacccabdacdadcadbdcbaacddbcbacddbdbbababcbbdaccdaacccacbbbacacaadbbcabacaccbabdbccdbbccddccaccbcaccbaababbcdbcabdccadbbbcbbdaccdbbdcdadddadabcbccbabdbadddddaddcccabddadbadbadbdbddbdbdabdccdcdccddbabbbbbcbacbcbbdbaababdaaddbcbacdabbadccdcdaabdbdcdcaacdddcaaccdbbadcdcacbababdccdccdabaddcbbdacabdbdbdbaddccdabaadcaaabddcbbcdadcdccccaaabcaddadaccdcaaadabbddaaadaddcaadcbdabacccddbdbccacdadaccaadaabcdccadbcacbbabaaaaadbbdbaabacbdcadbbbbadbaccacabadddbcaabdcbbddccbddbdbabaacabcdbbbcdacdcdacabdcbccbacbaccbdcdacbbcabcabacdcaccbabddddaacbaacbddabbdbbbadbaabababbadcbdacccbbcccbdabadbacddcdabacdaccaddaaacbdbbaaabcaacdcccacbdcdadacaddadabccacbdbcbbdcacacddccacaaadaccbbcbccbdcabbdaacdbcbdccbbacbcaccdcadcdaaacbddcbacaadacddadcacadcabacbccacdacacbdbccdbdccddaccdcabaaaacacccdabdbcbadddcbbabccabaddaaaaaaabcbdacdddccabacbdcddbbbbcdbccadbccbddabcadcabbdbbddddbbbcbdbdabccadddadbcdbbbdcdccdabcabbbbcdddcacddbaacdccdbccbddbaccbbbddcdccccdadcddccaaddacdaccaccbcccbcdcaacaacdcaadbcaabbcdabaacdaadadddbabdbacdcddabdbbcaaccacbbadccabddbbbdbbcadcaccdacbbddddadcbcbadbabcbbcdbccabbdcdbabaaadccaabcabcbdcdaadcdbcbdcbcadaaacbdaacbadabcdbbdbbcdaaabdbbcbdcbcbbaaabccbabadcacbbaabadcccbacddcbbacdbdcadbacddbbbdacdbdccaddbddcdccdcccadabbccddcdabdbaabbacdaccdcabcadacabcdbbabbbcdabcadcbbddbdbbdcacbabbddaadbdbdddccbadbbbcacddddaaabddddbdcdccabdddbbdbbdbabcdddabcccbdbddcccccadbccdcbbdccdbabcdcabdcaabbaaddcacacabadccbabccdcbdcabadcbdacdadbbdaacacddbbbadcbccabababbcbddcdbababdbbaadccbaacacbcdadcabbbcbddbccccbadadaddacddcaacbbadcdddbacbcbddcacdbdcacdacdbbdacbccaadcddcabaadbacacdbdadabadacabccbcabcdcaccbddbbdabadbbbccaccccdadccdaccdccacbaacccdaacbaaccadabcbaaadcadbbadccaaaabccccbadcbcaaadadcbbcdddabaadccdcbbaabcdbcddbbdcdddcbdccbaddacabbabacccdcaacdbacddbdddaaadbbcaccaacaaadbabacdddbdabcddacbcbdacbadadbaaabcaacdadcbdaacbabaabcaddbdbbcadcaccacaadcbdaaaaabcacaaaadddaabccccadbdccbdddbcadababbcdabbdbdadbbaadcdcadbabbbbabadaacccdccddaccdbdbddababcadbbccbcdccacbdcadbbaccddccacbabdaddcbbabcadaccaddcdaccadddcddbaaccdaabaddccabcdabddbdadbbbcdadaaadcddcbccacbaabccdbaadcddccdbbcacabcdacddaaddaccbaadacaccdaacaadaddaacdcddbabdbcbaccadbbddbbccdccdbbdadcbccbddacbbcacaccaacbcccaabcdbbdbbadadbbbabdcddbbddbbbbbaccadccabbdbdbbccbccddbbdbbacdddbcbadaabacadacdacbcbadcbacdaaabbdacccbacbbadccabbadbcadbccaccdbbaccbddcbcabdcaccaddadbbbdaccbbbbdaccadadaccccbaddbabbaaccdacadadaccbdcbcaaddcabddddcbcccdcddbcabaadbdbaacccbaddaadbdbddaaacbcbccdcdabdcbcdacdabcabbddaacadabdbcbadaccadbcccdadbccbaaddbdbabdaddcdabacaaaadacbbacbcdbccacccabacdbbdcaddadcdcaabbdbbcabcbdbdccacdacddcaacddcbddcbadccbccdaadaadbcbbccabdbccbcbbbcdaacadcdcdcdbcddcdbaddbbcbdbbdaabdabcdcacdacccaaacabdddbabbcabacdaaccdbabcbdaadbbbabddcbcabbabadccbcbaddbabdbbdccdbddbccddaaccddaabcdbcaabbbabacdbccdcaaddbabdaacbcbacdbaaadbbbcbbbdcdccdcdcdbbadbbdadbcdbadcbcbdbdbbdbabaadcccaadabbbabcbdbcadbdaaacbdcbcbcaabbcddcabcddcadddabcbaacdcadabcaabcdcaadaabcabbdbaabdcdaadaadcccaddddddcacdaadcdabdbbccddbddacadadbdbdbdccabacbbcbdcbaadaccacddacccbbdacaacacbdcddabdbaaacabdacbcbcbcbdaabbcbbaadbaaccaaadcaabcbaaaadddaadadbdbdadadbacbcdbcbccacbcbadaabbdbddadabdadcbacababbbddbdaacdbaacacccabddbacdcabdacbadbdaaadabdcbcadaaccbbcdbbbddccccacadbddabbcbbdbcddcabcaaabddcbddcdabcbbcabbaddabdddaaddcdcbccdccabdaaaccbdabddcbddacbbbabdacdacdadbbacccbcacbddcdbdcccdcacaadbbaadaddaacadbaadabddabbaabccaccdabcacccaddaacadbbadaadacbadcbbcdadcccbacbcdbbbccabaabdadccadaadbbbdbaaccdcccdbbcaadcbddcaacbbadcbaabbaaaaacdbccbccdcabbbbccdbdcabdddbbabbadbacacdbacbcdcdbaccdccabddcdaccdcadcdbbacaadddbddbaaacacacdccacbbbaacbadabdaacbddbcdadcdaaccbdabbcdcdcddaabacdcaddcdbdbdbbddcddabccadbabadbcbacacbcddbddbbdccccaddcaddbdacccadbbbdcbabbccdabdabdbcdbadaaaadddacbcccbaddbbdbacccdbdcbaddccbdadabdcaddbddaaabcdcadaccdadbbaccbddbdbbddabddbaaaadddcbddbdddabaddbdccbaaddddacccaacbacaabbccadddbddcbbcaaacadcbbabcbabbbbbacabbaaccdcdccacbbbbbaabcacdabbcbaaacddbacdcdddaabdcacadccaabcbcdcbccadadacbccbddddbddcdbaddcddcacccdddcbcdabcacdaaccbcaaadaadcabcaaabaccbccabbbbaabdaccdbbddccbacbacabcbddacdcbaabbadbdbccbbabadbddbbbbabdbbadcbabcddaccbcbdcaababadbddbdcccacdbdcbbaabdbcdddcbcddbaadbaabddcdcbacbacbaacacbddddccdbdcdbdaddacacadccacabacaaaacacddabadaadbcbabbcddcbcdbdbadabccabdcbcbdaaabcadbddcddaccdbcdbbbcbdabcdddcbcdaaabbbabdbcbdcaabcadacdabccdcccbbbcaacccbabbbbaddaddacbaddbbcdaabdcbdcbacdcaadaaddcaabacadababcbacdbddbadbdbbbddadacdcdcddaabbcdacbacddccaacaababcababcacddcabcabbcbdaccbdbcbabcaddcbbbbdbadddcabdcbdcabbacccbbaacbbddabdbbcbcadbdbdddcbcdcdbdcaaaadaaadbcaabbdccdaaabcbaacbaaadbdabdbbcdcbcabcaacbccdaccaddbaccabbcbdaddbdbaacdadacdaacddccbcddbaaabccdcbaaacbddbdadbcddaccbcaabdbacaddbbbbaaaccbaccdabcabcccaccddadacbcacaccacccadaaacdadabddbadbabacccdabbcddadacbacdaabdaddbaaadddbabadbbdbbddcccbbccacaacaaadcdcbacdbcdadadcddadcbabdbdcaaadbabdbdbcacbddbacbbdbabbcadccddddcacdacdcbcaabcddcbabbabbbbbabdabaacacdaabddbccbadbaadabddbbdaabdadbdcbcdcabccabcbdbdddacbcbacbbccacddccccdcdaddcccbcaccdcdcbbcabdccddbdacdbccaacbccbcbbbcabadaaddbdaaaaacbddbcadbcbaacadcccddaacadbbbcbacbcdbdaadadbbcaadbcdadbcbbcddcabaacadcdccabcadcaaabaacdccdcadbbbdbddbccbcbcaaabdbdcadccabcbbbcbaddbbadccbdacdddaadcdcaabaabbcdbadcbbacbccbbaabdddacbcbbbdaabbcabdccdacddbcaacdddcbabacadaccdcbbbddadacababdaacbcdddddabbabacaabdcbabcaadacbadcacdbdbcbcacbbbacddcbdbdbdcddccbddcabdaaaacdbddbbacddbddccdaddbaabcdcdddbbdbadbdbaabacaabdcadcbccadcaacbcbabcdcdbbdddddcbdbcabddcddbddbbbbbcaababacddbdbdacadbdadddaccbddbdcdddaccccdbccbcdcccccaccdabcaacdbbccccabccdacdadccddbccddddcacdcbddccbbddadbccabbccabccadabdadbaabacaabcdadaaacbdaadbcbdbcbabcdadabcabbbaadddadadcbdbbaabdcbdacbaadabaabcabdbdcacbbdcabbcbcbadbcbddacbcadbdbaacbbaadbbcbcadcdacbaaaccabacdbdbcabdcabdccccadabbcbcaabaadccababddddbadcaaabccbacbaabdbcacdbbbabbbaacccbbaabcaabcaccddccadadadbbacbbadabbcccadbabbbacbcabcbbaacbbdccdbacaaabcadabadcdacaacadcdbadabbabadbabdaddcadbacabadbcacddcaccaccbccbdadccdccdabbddcbacadabcaddaabbbaaaddabcabbdbbcddbddcbcbcaddcdbdabdaaaccddabcccbaacdaaccacaabcdaadacabacbdacbcccdabdaabdccccaaddacccabbdcdaaabcdcbbcbabbccacddacaaadbdcdddcdacabadacaabcabababdddcabacbaaacaabdacbdabaacbadcbdadccaccacdccaaddaaabcabcbcdcbadcaddabacadcdaabddcaccabcbdadcdbbdcacabdccbdddcacabddaaaabcdcddabcaccdcbddadbabbcaccabbcadaadcabbdbaadccdbbbabdbdcbcdcaddbacdbabcddacbcaaddadcbdabaaaadbbdcdaddadbbacacabacdabcbbbbccbcdabbdacbdccdcadaabcccabcbbddddddcaabcbbdabbddbbddccddbdabbdcdccabbdcaacaaddaacabbdcddcbdccbbaccddcbdbdcbcdcaaadbbcacbacddaddddadabccdcaacdaddccbdccacabbdcddcbdccaddbdacdbdcbbadabdbbbabdccabcbbbbbdcbcaaddabdadcaadcbbcdaaccdabccdadaabdacaccdccadbdadcdbddcbaabcdaddbbdccbacdcadbdbcbcbbcdcbdbaccbabbcacbacdabbbbbbdcbcccddabaaaaaaccacbcabcccbbddaabbddabcadbbcaacbaabdbbcaaddabadccbdcabbbbbadbbddbdbbadcddcbdddbdaacbcaabcbacaacdbdaddcddbadadbcacbcbcdaadcdabddaddccbabcdddcabbadabdacdadbbdbadabababcdbaabaddbdbdacbcbcaaccccaddcdaaadaacadbadddbcacbdaadabdcdadbdbabbabccbabbcaaacdcdcbadccaaccccabababbacdcbacaabacddcccabadbbaddaacddcadaccdcdbdbbdbdbbcbadbcdddcacdcbdcdddddcdbbdadadcbbccabadbcbaabcadaddacacaaadabdcaaddbcadbbbbbadadcaabdbbcdcdaabaaaddbcbccbdbcabdbddaccdcabcdaadbbbdcadbaabadcdabcbabaddaddaaaacdccaaaddcbacbcbcbbbdacbbdbdbcbabaabaacdacabbaccacddbdcddacbddaabdbbcabbbaadcdddabcadacdbacadabadddccaabbbdaccbcdcacdbdbdacdbabbacaddabcabdcacdaaaddbddcbaddbbccbbcbbdaabbcdcccccdacbbabbddddabddddddcbdacacbaccaabbcbabddcdcbdcaadadabdcbccbacaabdadcabbdddbadcdcbdccddbbbccadcbaddadcbacdbcccbbbcacdcbdabadaadbdbcdccdccbcbdccbcbaacadacccdcccacacbadddabddcaabdbcbbbabcbbcccbddaadacbdaacdcccbdcdbabccdbbbbddbbbbcbbdabacbaccddabdabddbcadbdacdbacdbdcbdbbdcdadcbadbcbadbbcaaaacbadcccccdcdabccdbdaacddadccbdccdddaccadcddcacbdadbcabcaddcbdabaaaaaddcabcbabadacdacabbcdbbccdbdbbbdabbbcadddbadbbdadcdbaacaddbbacabcababcbdbdbacadbadbdcabddcdbccabaaccdcdcbadbbbaaacddaddacbdbdccdcddccbddcbdcdddacbddadacbcacaaaaccbaaddbaccabdcbbbdcdbccaaccdcddacdbddaaaacdadadcbabacbbbabcbdacabcddbbcaabcbcbbcddbdbadbbdbcdcaaacccddbbabaabdbdbbddcccbcaddbdbaacbaccbbcdbadbbbcdbbdddddaadaacbbbccdacabcbdadababccabdaaccddbbbbcbbdddcdcadddbcbdbbaaacdcbdabadbddcacdadbdabdbabddbbbadbaddbaaacbcdbcbadbcbadcadabdbaabaaccbddcbcabcbdabdcbaaabcaacdabaadbdacccdabdcbbdbbbbaabcbdbababbdcbcabdbbaacdcdbadbbdadddbdbddcdabcaaaaabbdcccdcabbbadcdccdbbbbccdbaadacadbdbbdbabccdabddbbabaacdbcaaabaabdbabdcdbaaacbadccbcdaddcdbadcaccbdccccdcbcbccbcaabadcaaadbcbbbcdbaaabcbabaaabdcbabcbcadcabdbdddaaabccaddbcddbcbbacdbcdcadcbadbccbbdcbbcabbadccdaadccbbdbbdbbcbbddabcbbcbcbbbdbccacbdaddbbddcddacadcccacbcaadcabbbaadddbaadbbadbdaabadbccadcaabccccbbacbaddbccaabbdaccbcaadacabaabdaaccdabacdcaababbbdbcbbccbaabbacdcaabcbabcdbdaadbcddcbdcbbcabadaccaadddabaaaabaddaaaacdacaddbaddcbccccccdddccabbbccdbccbadbabdbbadabaacaddbaabccabdcdddadacabbaabaacaadcbadadcbdaccabdbbbbcacabcacbcaacbdbadabcdaabdabccbbbcbcbbadddddcbbddcdbaadaabacaabdcabaabcddcdcadcbcdaccaddcdbbdcbcbddaadcbaadbbbccbdcccbcabdabadaabbbdbdaccabbdacbacadbbccbdbacaaddbabbadbabacdaabdcbccbbabbadcdabbcabccbbdadcbadddddbcabcccdddacddccadadccbabbbbdaabbcdbcaabdabdadcacdcdacdabbdabdcabcacbcdbccbbbbbcbdabbbacbccdcddadccbdccccdbbabbdddaaadbdadbbcaddacccaccbabacdbbcaddaabadcdddcbbbcabacdddbcdddbcdccbdbcbcddcabcaabdacbdccdbbdbaaaccbdcddbcdcdbaacbcabdbdbbddbaabcaccaabbbbdcbdbabcaacddbbdcdbbcbccdccccdaccbbacdaddcdbadacbcbdaaccddbcdbcaadabbacadbccbcbccbabccbdddcbacadccdaccbdcaadbaacaaaabbbdbbcbccbcddcbbbadcadddaacbcdcbdadccaddddadcbacbdcacddcccbbcbddadbaccadbaaaadcccdcabbcbdbbcccdabbdcadaacbacdbacbadddaddacacdbbbbbbdcbbbaacaccbdaacdccddaaacdbbcbdddabbcbabdaaaabbdaaaddaadacdcdacbbdbddadabdaadabbaabcaabadbbacbdabaabcdadcddcdbbcdccccbcacddbaabacaddacacdbbabdabacaaccbdcbcbdcdccdbadbdcbbbaccdaddcacabbcbcaadacbbcbbaddadbadbbcaccadcaaaddbabcaddcddcbcaaaccbabbbcccddcbbacaacbbcddccbaadccbdadabdbdaaccbdbbdaababaadaaddcbccdddddaccbaddcabbcdacdabddbadacccdacdccbcbaaacbddabdddcdcbcbadbcbaadcdbcabbdbcaddbbcabbbbdcacccbabacbaaaccccdaacbbbaacdcdbccbccccaccddbcddcdcadbcdadacdcaccaddbbabcbccbadcdbdbacbbcbbbdacabcacabcbbddaabbdbbccbccccdbaadaacdcddbbcccaccacdabcacadbddcbbacabaabdbcdbabccbbabccbcbcacdccccbcabcaaaabacaaacdbccbbccddabdcacddbddaabcbcabcaaccbdbbccdabdbccbaacbcccacabbadddbdccacccacadcacacbbdbaaaaacbcbccabbdbabcaabbcbaccdadaadaacadbcdcbbcabadcbbbabcdbaaaaaabcabadbaabaadcabcbaaddabbddbccbcccaccbdbbdaabddacaaabdcabadccabdbbacdbcdcddcccbabddbcadddddcdbadcabbaabbaaaacbcccacdbbcccabcdddcdadbdaabddbdaacaabbdcdcddcbdabdcbaaccaddddbcbbcaaddacbcdcddcdddbaabdbdccdabaaaddabdadcdbacaabcacddadabadcdaacccbdaabccdadbddbbdbbbbbabbacbcbabcabcdcccadbcababbbdcdabdabddcccbcacbadabababcaabdcdacaaadacccabccddbabcbdadaacdbadccdadbdddbaacdccbdccdababccabdbdcbdaababdaadccdcbbdcdcccabcabbdcaadcdbdadbbdaccabaabdcbcbbcdacaccaddcacbbdbcccaaadcadcdcdabddaababacaacaaadcbcbbcaabdbdcbabacdddbcaacdcdadbccbcdacaacabdccabcdaddabadcaccbcbcbcabbabbdcdaddcccadababccabdaacbccdcabcaadaabcaacabaadacabbacdabaadabbabadbadbdbdacdcccaccbbabbbabdccacabaddcbddcdabcdacbcabdbbbbdacaadbdbcdcdbddcddabadcbbbccaccbddbabbadbcabddbcccccdbdaddccbdcdccccdbbbabdbdacdddbaabaccbcbbdaabbcbcbadcdcabbaccbcdacadbacdcdabbadcbbdcdddcacbadddcbcdddcdcabbdaccabccbaadcbddaccadcbacdaaccbcbadcacddbdccccdcdcdabdaddadcbbdacddcdbabadccdaccbadcbcaacaabdbcabacacacdcacaadddadccdbadcbcbdcdabbdcccababbbccbacabaddbbbdcbddaabdbcdcaccbcbabaccbabcabbabdbcacadcbcbbadcddccdbbcbdbdcccdbbbcddddaacddacdcdbadbbdabadbdcdbadaddaabbdbcddbadcaacdddaadcadbcdccccacaaadaddcdbcdadadbdcbbdbcdbcbcbcabdaabdddacacaacbbbbdcbaccbbbcaddadadccdbacabdbdaaccaacadcbacaadbbcadadcbbbabacbadccbdaadbaddbdcdbcdaccaadcccbdbababbbbcadbbdcbcbddcdcddbdbcbcbbbddbcdbbadbddbcdaadabdcbabbbbbbabccacdcacdadddaaaaabddbcddccddabacddbdcbbdcbaadcdddbaabdaadccddbcbcabdbababdcbbbbabacdbccbdddbbbaaacaaccaadcdcbdcaccbaabdbbcccdcccbdddcadcbacbdbcacaddbbdcaacdacbbabaadcddcaccbcbcdbacabbddaabadaccdcbcbadcaabadbaccdabbbcbaaddbacbdcadcbcdcbbccdcdacbaaabddcadbacdcdadadcaccbbccadbbbaaabbdcccaaddbbaacdaadcadadbddcdaadadadcbcdaaaacddcccdcbdbbbddbabdadcaadbbbdbcbcbbbdccdbcdcdabaaddbacbcabbdbddbaddccdacbdcdddacbcbaadacababdddbdcdccbdcaddbcddddbddccddabccabbdbdbcccdbadacccabbdaabaaccdddabdbabcbdcbcbddadaacaddaabbddcdddbadacaaacadcdbaddddddaddccccbaaacaddbbbadababdcaccacbacbbccdbbbbabaddabbabbbcabdddddcbbdddddadddaabbbdbcbcddacbcbbbaacaacbaccbcaccadcbdacaddbbbbddadcccbcdbcdbdabdccaccdabacddbcdadaaadbacdcaccbbbaddbdabcdacdddcacccdccbcaadbbdabaababadaddcaccaaaaadacababbdabbcbacabbaccbbabcbdbaacdccdaccbabdbaccaccccdccaaccddacabacacddcdaaadbdabadbadcaaabdcacacaadcbaddbaddddddbbcddddbcbdadbdbadbaadcbacdadcaaaabbabbabaabdccdaaabbdaccabdcddaaaadbbcaacaaddaadbdddbccacdabcbaaadcdddabbbaabdacabbccdcddabdbacddabbbcdadcdddcdabcaddbccbbdacdccaabbbabacbacadccccbadaaabcaaddccbbaaadaadbabbccbccadcbdbcaaacacaabdcbdacabbcdaadbbbcacaaabdcabbbdcdcbbbddbddaccdcbcdbcabbbdbdcacbbcadcdbcbbaacbabaacddccbaccbacabacbbaabdbbbabdccdbccdbcbddacbbbbdacbacdcaacadcbcadbcbadccdaaaddaabbcadccacaaacabcdcddabcabdbdcddbbadaacacbacaabdbbacdbbdccabcaabbcdaddaaaddacdcbabbbdbbdcbacdddcbbdbcbbdacddcabcaddbbbbcadbcadaababbbbcbbbabaccadcbacbababdacbbadbaacadbabcccddcadcabdbcdddcadacadcdacccdbcbbdaabcaaadbdddcbbacbccdabcddbbbcadbabadcaddcabbadccdaaadccdddabdbabbbddbbcbcbadbabddaabbddabbccaaabcacdabccacccdddaadbaccddbbdddcddddaacacdcbccacbabbccdbbddbaddbadabcadacacbbbccbdccaccdbcbdbdcbacaacbcbbaaaddcdcabcadabbcadbaabababdbaaaccddcdbbcbdaaacbccdcacccdccdacdadcaaabccbaccaaacabddacadbaacdcdbcadcdcdbcdbdabdcaacaadcbddbbaadcdbdcbadccbbbadccaabbdbaaaddaadbabbadddbdcddbbbaddadddacdbbbadbdcacdabdcdddcaacddccadcaccaadddbcaacabddbdacbbccdbccddaddadbababdabcdbcabcddabcbddddbabdcadbbcdacdacdaddbbccbbdcdaaabcdacbbccdcbacbaadaacacaaccccddcdacddcdccaddacbabdcbabbbaaddaabccaabddcdcaaadaacbbbccbbdcdcddbcccccabdcdcacdadbadbabdddccadbddbcabbabdddccdacacddbbdaddbddadbaacadacbaaacbdaccbdbcabdabbbabacbcbcbaccbcdcddcaccbbacbcadcaacadacdcbbccdcacbabdbbccdcdccbcbbadbdbbabbacdbacbccdcbcaddddddaccadbbaaacddccdccacbdbbacdacdbbbcccbadaacbddcbbbcaabcdbbddddaabaadacbaabbbccaabdcbcabadcdbdbabcbcdcdbccdbbbcdadcbbbddbcdbaddccccacaddadacabaddcbddbdccdccaaadddadcadccbccbcdaacdadbcaddddccbbcbbcdadcdccabdacabcadcbccdcbacacdabbbaccadacaddaccaabdcdbdbaacbaabddabcbbbabbbcabbbcaabadbbdbbbcbcacdbaabcdbbbcccaadddccddacccabdadddccaaacccaadbcdaacadaadcbbdacbdbcbbcabdccbadbbccbabbddddaadaadcacabccdccacbdddcacaadbdddcbbdbdbbdaadcddcdabbddbdaddaccbbabdcbbdadbacddacddcdbbabadbbbaddbbaabadaddadbaadcddaaaabdbdadbcaacbbcbccbcbbaadcbdcdbacccccbaaacbaacabcacbccbbdbdcbbdddddddcdcbbdcbccbddcdacdddbdadabbabdccadadadcbdbacdcaadbdaacbcccddabdccbcbdbcbabcdcbbccdcacbcacdabbbcabbddddbcbbaaccbcccaddaccccacbdacbcdbbaccdbccacadacbbbbbadcabccddabdcbdbccaccdaaddcdcaadcaabdabdbbaaadbcccbdcbaabcabaacdbdccbdabaccbdacbcbbadadcbcaabbdcbabbbbcacadddbcccdcaaacdadbdccbcaddbdcdcbdddbaadbcbadaacacddddbbccdacbacbdbaabacbaaabcacbccbbbadbabaacdbbaccbcbabdacacccabacaddddbbbddbddccbbababdcadbdcdbdcdbcbcbbbbdaccdcbcadbccaaddbcbbcbabddaddbbbadacdacdbacadbbbbdbbadcadacdbcabbdaddaadaaddacbacababcacabbacdccbadaadddaaddcddacaccabdaadbaacadbcdbdcaacbdcbbdcbdadbadaccaaaaaacdcbadabbccbcbcbbcaadbcbccddcbbbbcdbdcbadcbadadbccdacccadcdbcdabcdbaaacaacdacbdaabdcddaadbaadacbdaadcbdddcacadbabadbcbcacbdddcadbabaacabdaabbbdacbcdcabbadcdacdbdcdbacacbbccaadcaacbdbdadbccaacdcbbcddbbbcaabaabdccbbcdbbbadcdcddccdbcdddabddbadaddcacccdbdbbcbcaaabbdbdbaabacbddddbdcccdaadccdcabcacaccddbbadccdcaddcbaadacbcdcaddcdbcccaadcdbcdaccacacdcbbbdcacadcddbcdbcbabbdcccdacdaaacadbdacbccdcdabbbdbabcbadbcbcddaccbdddddbbccacdbddabdacacccccdaadddcdbabadadcabdacbdcaccbcbccadccbbcdacbcabbcbdcdaccddcacddccbabbaadcdbbbdabbabccbbcacbabbdbadadbddcdbccabbabababbdcadcbcdbadddcabcccbddacacbcdacbdbbaaacccdbaaaaccaacbbcacadadbacabccabdaddcddcbaddbabcbabadbdddcadccadbdccbbbdcdcbadacdcdcbbccddbbccdaabddaadaadcbaabcaaabadbacaaabdcccbaccbacbadcacadddcaacabcbcabdddaacaddbacaddbdbcdaabccddbaaccabaadadbbaabdbddbbdcaccddcacdaacbbbdcadccbacacdcdaadbccbbadacddccbccbabbccbbbbccbdbadbdbddbcaabdcbabcbccadadacdaacadabddadddadabdadbbdbbbddabdcdbccdabdbbacdcdaccacbddbcdacabbcdbcccacbcdbcabddbbbcacabaacddabbccaccbdaacccddbbcbcbadbdbbdcaccbccddbadddbdbcbacbcddcbcbacbcdbbadcbddcadcdbbcbdddabcbdcbabbaaddddacccbaabcbdabbdcaadabdacbdcdbacbaaccdabdabbdccbbccaadacdcabcabbadddcccdbbdcaddacaaaadbdabcadacbdabcbbadcdddbcbbbcaaabdbccacddacbbddbadacdadabbdcbdabdddacddcaccaccdbdcdbdbacaaabdbababdbabbddcaadabdbcccadcabcdccadbdbabdbacdbadddbdbccacbbacccadcccdadabbccbaacdaaabbdaacdcdcbdacaacdbcacdcaaccdcadbbddcdcaddbddaaddabcccddcbddbaabddcaccaadddaacdcdcdacaabaadcdbdddabcaddbbbbbcaabbbbcdccacdbdcaddacaadbaadcdbdaddaddadaaddbaabddbacdbdbabcdbbccccdbddadbcbbbccabbbacdcabcddabdbbaacbdcacdbddbbdcccdcbcdbbabbccdabbbcdabcbdabdabcbaacdaadbbdcaacbbbaabdaabbadccdacdadcacdbacabbbdbddcdbaacccccbdbdbaadaabcbcbbbcaddacadcbadcadcbcdcddaacdcddcdaacabcdcbcbcadcbbdcbabccacdaaadcccdcbdabbacbacdcdbdcbadcacabcacbaadbcadcbaddcadbdaddbddbbacbcbbcbcccdaaaccacdbbacaccaabbadadbaddcccddbbabbabaacaaaddcaccccacabcdbddcbdbbddabddcccdbdccccadabadacadaabcabcabcbdacaaccbddcabddccdabbbcbbdcbdbbabbaaaaacacccdcdbbbacdbccdcbdbaacbdccdcbaaabdcbaaacacadbacddcdddcdccacdbccacabbbabaadcccdcabbdaacdcbcadccacbaccacddddadbcccdaddcccdbcadccaacabacaaacbdaccdaccdabddaccbdbcaadbadccccccbbbadccabbcaddadcccaddcccabaabdcdbbbbdbdaaadccdaddcdcaccabadaccadccdbcbbbdddddbbdddbddabdaacbdcccaaaacdabadcbbdcbbadaccbdddddccaadaabddacacdadcbaabcdaadbddbbdbadbcbaddcbbadbadddbabacdacdcdccadbcabdccadabbbbbabcdaaababbdacbcaddcbadcccbbbdddadbabbcbccccdadaddbbbddccddabdbccbddbdcbabbccdcdabacddbddccbbaccdabdddcadaccccdbbdcdbcccbbaabcadbdbcdcdbabdbbacddacbcaaabcadbacdddccbcbcbadbbcdacbabddbcdcbaabcbdccaccdabaabdaabdccbadbcabadcaccbdaacbddacdbbcbdcbdbdaccdccaadbacddadabbbdcbddacbacbabbdadabbdddbcadabccbcaabacdadabcdadbcabbbcdcccdcccdbcadabcdbabbcdbbabbbacbabdadbdaddbcccdaccdadbcbbcadaccbcacccdaccbabdaaabbbadcdbbdaccadbcadcbcadcaaacdcccacddabdbbbdabadabccbacaaddcbdacddacadaaaaaadcadaddbabdcaddbacddbcadbcabbbbbddaaadcccbdcbccddcbabbcbaccdacaaaaabdbabccadadcacabcaddddabddaacacdcbacdcbacacddaaaacacbbdbaacddbdbacabbacabcacbaacbdcdcccdbbddbbcacddaadcddadabbbbaabcabdcdbbaabcbcbabddbcdaccbccadcbacdaddcbccdbccdbccccadbaddcdabacdcbcdcbdbccbaddbbbacdbbabcdddacbcbadcbcbaacbdacabccacaabcdccbccddbaadacaddadcadcbbcdacadcdbdacaccbadbacacddacdabadccbcacaddadaccccdcacdadaaabcdbbcdcdbcbadbcdbdbcbdabbabadaacccddbddcabcbcccbbdbcacbaaacabcaccabddcdacaddddbbbabbcdcabddacabaaddadbdbdadccbcdbabaaadbbbcdddcdbcbbaddabdbccbcbbcdcbadbddcabaaddaccccadbbdcbaddbddacdbcddabccbaaabcdabcacdccaaadabcadcdcbbabbcadbdacbabbcccbccbbdcabbcdaccaccbccbaaccaaacacdcbabcdbdacbbbbdbcbccbcbcbdaaccbbaadcdbbaccbbddbaccddaacbdbabadbdbdcaaccbbbcbcbccdbcdbbcdbadcdddababbcddcddccacddcaddcaddacbcbcbacabbbbadbddccbcaadddadcacdcdbabaaccdbcbcbdcdabdcabcdacbdccacdcbabbdacddaacaacbddadadbaaaddacbcbccbacbbbbcabdbbacabadccadbdcddaaadddcaaddcdddaaaababdcbbcdddbdbdbadcdacddacdbbdbacbcdccaabdaaaacaadacbbccccadaabbddbccaddddbccabbbacbdcabcdbdadbddabcacdbddbadabddbdcbadaabadabbcababbddcabcccbbdcddcddcadcbadaadcbdacddcabcacdaaccccbdcabcabbbacabbdabcbcddcadacccdaccbbacaacadddbdacdadddaacdcbbbadcdbbcabbaacdaccdcabbccabaaaadbcaabcbcccdccbcabdbdaaaabbadcdbabdadaaacaadbdbcddcdccddbcdabaccdbbcdccdbcddddcccccaccdcccbdbdbadbdddbacdccaaddddbacaaadacdcdaabbdaccaabdccddcdbccaddcbbbacababacdaaacbcdbdbbadddcdcdcddbbadddaabcdacdadddabdbdbbbbcdbbdddbccbbabbcbadcabbcbacbadacbbacbbaacabdcbadbbaacdddcdcababcadbdcaacddbababcbaadbacbdbaaadbbbaacbaaccaaacbabaababbbdbbbcbadababaacbaacdbddcadbcbcdcabaadbdaaaabbbbbcabdcdcabbdcbbabbcbddabdbadbacbabaacbbadbabdcdacbabbbdacdadbbacdbcdcccddbddabadcaccddbaccbdccabdbabbcacaacbcacdbdbccbcdbcbcbbabbcbcacadbcbcdbacaddabbddaabaaddadbacaaacddcdbaacdbaacddcdaddaaccdabddbaabcacbddacdcabadbadddccbcacddbbbcabdbdbbbcacdaadcdabcaaacbbbddacaccbcbbacacbcdbbadadacacbbddbadbcccadddccaacbdabbacccadddabbbcccacdaacaccaaddcaacdcdcdcadddbdddbcabdbbcbaabcabcdbaababdcacccbaabacdabadbcbabccabddccdcacccabaddbbcacbaccdcbddccdbcbbcbacccbdcaacdbbbbcdbcadbddbcdbabacccddcbddcdcbaaccacabdcbacbaabcdcaccbbbcbbbdacbabdadbbcabaabdcdbcabcabddabcdccdddbbbbaddacdbcadccccaaabcacacabcacabcdddccccacddddbadccaaadccddddabcbdbcdbbbdcdbadacacbcacacbdddcdacacddadbcdccbcbabbcbbbddbdaaacbadcddcccddbacabaabbadbaccbaccaccdcdabbcacadbcaddaccadccbdbabcbabdbbabdaaaaccaabbcdcdcdbbbabaccdbcdcbdaccbaaadbbacdababccdabdbbdaadbaaaadbbdabcabaadcacaccadcdbdadabcabbdbccdddbbbccccaadcdbbacaaadcbdcccdadbacbbbabdabccabaacbaadbcddadcccbacbbaadbbdcacaacabadcdadadcaacaacbdbdaaaacbdcaadacabbbaacadcccbacdabbcdbadadcbdabababbbbcabdbccaaccababbabaaccaaaacbcccbadcdcbbcbacaccadbdbccadccaadddcacdacbdbcacdccbdbdbdbcbaaccbdccddcacdabccccabdbadadabdabbcbbabdbaaadcccbbacbadadcacbcccbbdcbbbdbdaccdacbddbccaaddaadccacaaaaaddacacbdacbbdabbcdbbbabaacccbccccbddbabaaccdbddddcadaaabccacbbacdcdccbdaabdddddcdbcadcbdbbaccbcdcddaaaabdbbcbcbbbdccacccaccbbadccbcaaabbbbbcbcaddbaabdcabdaacddcabbccddacddbadbcddadddbcadbccbdddbbcbdcaaddadbaacdbabcdcaddbbbbdcbcabbcabdcdcacacddabcdddccccbdcbdabcacadaadabababcabaabdbdccacbaadacbcaadbdababcbbdbabdabbddcacbabdccbcdcddabbccbabbaabcbdaaababcbccacdbdbdadbadcdbdddbcaadaccadbdcacbabcbbdadaccdbbcaddabcbcacbbdcbbcaadbbdaacbbabbcacaaacacbdaaccabaadabaabdaacbabcaabcddbdabcaaddabbbbdccbdaccddaddacbbbdadcdcdcaabccaabadcaadbacdbbbaccaabbcdabbbbddcacddabddaabdaccdacbbadcdaabadabaaacdbaddaccbbcdbbadddbdccbbaadababdadbabacdadddcacabbcbaabaadbaaacadbdbaadddacbaabcacacabbbdacdabadbcbbaabaacaaadcabcbcaacbadcabaddabcabbdbadcbcbcaddbcdcbacadaaccbabacccaabdcccabdacabcacbaaccbdcadcbdbdbcdbddadaadccdacdadbbbcccbdcdcdaddbbbbbdacbcdddcabcaacaaaaaacccacbaaacadbbcaababdbbacbaaccbdabcacbdaddbccccdaaacaabcaaccacacbcacbbdbdbccccbbcdbadccbaadcaccccbbdcbcdadcacdadcdbdcdbcdcbbccadcccdbcbbdcddbddcccccabcbbdacdbbcdcabacbdbbccbabcabcdabcbbbdbabadadbababcbaadababddcdbbdacbbbdadaabbbcbcacddabbdcadaabaabdaddccbcdcadcacdccdddadaaacabaacacccbdbcdcbddcbaaccdbbbbbdccdadacccbcbabdabadabddaabaacaccadddbaadacbcbadccbbdddddbccadaaaadbbbaacbbccacacadcbadacabbccabaacbaddbcbbbcdcadaabaddacadbacddbbcaabbcadbbdbbbbbdbbdbcaaabcddbcadbbbccdcabbbbcbdcdaddbbaabbacbdcacdbddbbbdaabdddcddaacacbaabddcabaccadccdcdbdbbbbbdbabaababdcaadbaddbabcacbcbbbddbbdbdcaacdaacdacacddcbcbacbadbbbbadbdbbdbacccdcdcdcddaaaabcbddacbbadcbacbbdacadddadaacdadacdaaccbcccbcabcadcacddabaaacdbadccbaabdcdcacdabadaaacdccdcbdddcdcabbdbabadddbacccdaabbccccbbdcacaabbacbcbdbacdccaaddabacccddbabaaabccdbbbbcdccadcabddbccddbccbaaaaacdabdcdccccbdabdbcbdaadbbbcccccabcbbcccaccbadcbbbbddbbbdbdbcadbbcdacbcdbcacadbbccddacbcdbbcbabdcaccbcbabddcdadcdacdcbaddccdcbbbcbadddadddbbdcbbcbabcbbaccbaacaaaacccdbccdabbbadbddbdaabbbbabcdcaacdccbadcadddcabaaddddacdaaabdcbdcddcbaccbcdbbaabadcaccbcccbbbaaaaabcccacabaabdbabaaddbcbaccaaaaaaacdaccacbcbdccdddcccbbcbbabdcccabdddbcbdcdaddddddddcccbbdbddabaacbadbdabdbbaccddcbddbcdbcbacbbccbabcaabdcccadbccdcddadaabbdaaabaaccbdbdcbddbcabbcbcccbbaaaababbdacbbccbbbbcbddacbbccdbbaabbbabcdddcccabacdcdccbbadcbdbbabbababcaadaddbaddbcbcdaabcdbbbacadcdcbbcbbaddccabbdbaaddabcabadccadddaabccbadabddccadbdbbccdddaccdcdbccdddbcacacabaaacbbdbbbdbcaddccddbddabbddbccbbacacaddcdaabadbaacdddbccababcdcabdcdbdbddabdabdcccccccadbdcddaabdaccdccacacbdbdbabbccccbbaaabccdccbbacdabcbdbdbaadacbacdacddaadccbacddcddbdabccbcacacbbbbbaaccdbcbdbacbddbbdbcccbadaacbbacacadcaadbcbddccdcdaddbdccdcdacacbcdabacdbbbabccdcaaddcbaaccddbbbacbbcccbabbaabbcddcdaacdddacbaddcccbbadcdddaccdacddbddbaddcdaccccdcaadcbcdcabdbabdaacbbacbcdddaacdcdcacaaccbbbcdaabdbdccbdcdbcaababacbcccdabbadbbbacbdbadaccaaaabcaddddddadaabcccbbdcbabaadcabcdbaacdbbccdccaaccddadbdaddcccbbbbdddcdbbacdcabbdcaccdddcdcdcabdaaabbcaaaddcddcabbaabcaabddaacbcabcacbbabdbdabaccdcccbcdaacaaddadabbccabcdcbcabbcdaadbbccbcadbadabbaadbdcacddddbdbbbdcdddacdabaacdccdcbdaddcccabaddbcabdabdbcbccbdccacabccaaadabcdcababcdcbabcccdcaacdacabacdaaacacdbbdabdcbacadacabadcbabdbdadddcabcabcddbbddcbdccabdaadddddccdacbbbadbbcdcdcabddddbcddadaddbddbdbdbcaadaacdabdbddbcbcaabcdaaaddaabbdcdbcbbcbcadacaccdaabadaddadbaabcdadabcdbbadbaaaacabdcbaddaaccddcddbcccdcaacccbadabdaaacbbacabbcaccbaaddcabdbddadcbdcbcacbabcadcccccbbaaaccbaaccbadadaacccaacbabdabcbbdaadcbbdcacdbccaabaabbaadaaabddaccbadbcdbcacddcbcaadccadcdbddccdacabbaccddaaadddbdbdbcbbddaaaddbbccdabbabddbaaabbddcabacbddbbcbbbbdacddbbcdbaccccdaabadacdbcdacddadbcbdbadabccdaccdadbabbbcaabddaccddbcadbdacbddccdddbaabddcdaabdaaabdbcdccaadbdbddacddcbdbacbdaadccdbbddccddbccdcccdbbbcbdccbdadcacaadcacccacacbadcaddbdabcdabbcdbddcabdbaabaacbbdcbcbaacbaadbbdcdcdbcbabaabcdabbaadbccbdbddcbdcdacadbcdaccadbdcdcdbbaabaabdcdabaabbbccaddbbacddcaabbcacacccbddbabadbdddabacdadcdcadbcccaccbdadcbacccadbcbdcbccbcbadaaccbccccccdbbccbddcacdaacccbbdbddbbacbdcccadbbabddcdbbcbdcbbcddccdbbcabaabdbaddcbbbacdbaacdbcadccddcbdcdbcdbdcaadccbbddadcabbdacaaddccbddddbddaacadbdcabbcdbbabdabdaacadabaadbdbcdbaabbacdaaddcaabbcadbdbabcacddccbdabbaddaadabbabcbccadadaacccabbbbbddbcaccadccadaadccbabaaadcdaabbdcbcddbadbaaadbcaaaacbcdacbbacddacaaadcccbbbbaccbcadcacbcdadcacabacbdcaaccacbccddabcdcdabdadbaaacbbbaabccdbaadcdcccdacbcbdbcddabdccbaacbbbdacbbbacdbcdbbdccccbbbcddddcdcbbdddaddbbabcbaaaabdddaaabaccaddbbadadbaccdbabaaacaacbdaddaccdbcdcbaadabaaccdccbbddbcddccbbabcaddabcacbabaccadcdaaaaddcaacdabdcaaabacacacbbbcdbdbdbcbdcadadbcdcbcadbbaadcbabccccbdaabddbccdbdadaccbcdbdabbdadddaabcaddcdcbacadbcadbbdcdbbcbcaabcadbacccccabdddcaccaccabcdccdbbacaddbddabcacaccbbdaddabddacacacaaaaadbcacdadadaddbbaadbaddbcadcadcbcdbbcaaaaabccdddcbcaabcdbaaccbaacdcbbbcadbddcbacacbdbdbaaccdcbacadacacbdbbbaaadcbddacdacdbabcacdddbbcacacddaccbabbadcbdcddaacbbcdddacdaadcbcabcbdadbcacbbacddaabcdcccacabcabdbacaabddadbbbdbdcccddccdccccbacdabaababcbccdccacdcdcabdddbadaddaabdbcddbcbcdbacdbcadabaacdbdcdbdcccacaababdcadacadbcadcadcbacaddbcaabdadcccdacdbdbdddddbacddbacdcdacaaadddbacacadcccbbbacbacabcaccdbadadbdbbbbcdcadddbcbcaabbcccbbaabdacbacccadcdbbbcabdccbddbcbbbdbbdbcbbdbddcaddcbdbbdadbccbcabbdaadbdcaccbdcaccaddbcdbaababddccbbabcbcaabdaddddbbaabbadaacddabcddacbcbabcdabcbdcbbdbadaabcbcdbaccddabdacbccbbcabddcaddbacdbddabbacdcaddbcaccbacbcadcbbcddbdaccaabdabaaacccbaabcadbbbdbdbbccbbaddadbcccabdccabcdddacbacbabdbbccdbacdabdccbcacaababdbdabcdcdbdcdbacdaacbcddcadabdabdcabdcccabbadbdacaacddcccaaacacddaaabcbbccccdadbdbccccacdbcacccddaaadbcadcddacbcdccdcdcaaabbadadaabadbacacabbcadcdaabbdccddcdaacbbabddbbcdcbddadbcabbcdaccdbccddbdabcbbbaacaacbabcaabdbccbcbcdbaadacaaaabdccaaaabadccadcbabcabdccddbbccccbbbaacdacabbccdcbdbdacddbbbabadabaccbccccdaddadacadadbaacbaacddacabaacadaaabacccabdbccacbdcadacdcdcdcadaadabccdcdaaabcccdcdcdbdbbdbbbaacdaacbabddddbaabbdbbdacacdbdaacbadbdbdbacaabbddacbdcadaccdaccabccabdcabdcdcaacacdcabdaddbbbcabdcccdadbcdbcdaaaddbcdbcbacbdccdbacdaddbadbdbbdcdcbbccadaccbcaacadaabdcdadccabddcbcabcdaaddcabdcbbbbabbccdacaaabbbcbabbccdbbdddbadadbcbadcaaacabbacddbdbbbbdbdcdcbcabcbcdbbcabccdbbbbbdddacddbcacdaaacbbcdadadacbcbcdcdacccadbaabcadbbacbbbacbdcdcbacbcbbcdacdbdbacbbaccabbdacbbccdabcbbbaacdddaaadbaaaabacbbdacdaadddaabcadbacdadbaabdadccaadcdcdbcbbbbcaadcdcaaabbbbacddbabbcaadbaadddcbdbacbabaccbabcbaddbdcabacdcdaddbdacbcddddbaacacabaaccccaabdbdbbdccdcbbbadcbacdbcbababcdbbacdaacddcbcbdabccaaaadbacccadbbdccbbcccaaddcabbdbbcaaccbdcabcbabcaccbbbcadaddbddbbcaadbabddcbcdcdcddbcdbdbdbacaadbacdacdcaadcabdcccaabcbccaaacdaccdddcaadbbdbcbddaabbcabcbcdbcbdbdaccccacabdbacddcdadadaadbcdabacccdaadadbdccdbdacbaccadabacdcbbcbdcccbcdcacddbabbcbbbbddabcccaaaccccbdccccbbbddacbddccadbabbdadabdcdccaababdbdbaaddccdbdcdbdabaaaabaaaabdbcabadbcbcbbcacadcbcbbdcaabadccbdaaaddbdacddbbabdbdadbbddccddcccbcbaaccbbdbdabdcddbcacadabadbdacdaccdbcacacacbaadcdddcdbbccdcabcbabbdadcabddcdcabdbabdabccdcdcbaaabcaaabcdabdcbbdddbddacaccdababbcdaaddccdbdcaacbdcbbbccdddccadbbcaccccbadcaabcdbdcadadabdccbadbcdaddacaaadbadcbcaaaadcabaddaaababaadbdbabaadbcbccacbaaadabcaaccddadbabcdccdaabaacbdbadbcdacdadcddabddcadaabdcdacacaaacbbddcaabdacbdacdbbcaabbadbdbabdbcbddbcabadadaddabcbccbbcdccccdabbaabbdcbdadcbbdcacbaddcabaacbdbccaabaadacbccdcbcabddabaabcaddbadacbcddabbdbbacdccaaacbdcbcbdaabaaacdcdbacdacdbcdcadabcdcadbbbbcdcacdaaaabcaadccdddbabdcadadbccabdbbdaabbdadabbdbcccbbbcaabaddbbddbbdddcdccaadccabdccbccdbacaadadddacdcccccbdbbcbcbacbddacababcaacacccaaddbbaabbdcacbcbdaacabccdabbbcabadcaabaadcdbcacbbdaabddccaacadccadadbbaacabdbadbccbddaabbadccacdcbaaacaacaadbdadcddcdbadcbadbdcdccbddcbbdbbaccadcabadccacaabdacccaaccaacadaaacabddcddaccbccdadcdcddabadbcaabaabdadbaaababdcdaddadacbcdbccaabaadbbddabaaddbdbbaaaaaaaadbabbbddadbbaacacbcccdacdcaaddabccdadaabbabddadaccabdabdbbdccddbababbcbbdddaccdaccdabdacbbbbcabbbadcdbddccbacdbabbdcdbadcadadbabaaddacbdaabbcdddcccbdccbdaaddaacccabdbbcaaabddaddcdbdabdadddacbbdacacddcbabadcadcddcbcabbbccaaaddbaadaccbcbcdbdcaaccdcaacabdadaddbbbaaadbaaabdcccadcddbccdccadababccccdabcdaaabcbdcaabacbcabdccbadcbbcbbcdbacccaaccbcabbbaacabacadcccdbdbccbbbabdbccadbbbabcacaccabbdddcddcdbccbbdbcacccbcdbccbdbbabdaabdcbdccadcbbacaddaadadacabdcbaacaabdcacbabbbccbcabdabbdbccacbcbcdabbbbcacdbadbaadccbbcdbadbbbccbaaaaabbcbbabcabcdcccaacaacdcadcbdadcddbacbcaccccaaccdacdaaabcaddcacabdcdbbaadabdbcbddbddddaccccbbbdcdbbbcacddadaaddbaadbbbbcbddacbcaadcaacacbadcacacaccbacadccdcaddcdcaccdabcdbbacbdcbcbbbbabccbabcbbdcabcdccbdcaaaabddbaadaccdbbbcacdadcbaaadcaadbdccacddcdcadcbbddacaddbbaaabacbaabacdbbdaabddabccacacaddbbbccbcadddcbcdabccbccaaccbbbdcbcbcdadbbdbbddbbddcacbabdacadacaccaaddaccdbbabacdadacbbddacddaddcadabaadccdcdbdaabbcdbbdcdaddbbaadabcaacdbcbcbcaddaddcdbacbcbcdccabccbbbaabacdbbbabdbdbcdddcaccdaadcbcbddbccbcdcbccddaacbbacbaababbaabaccbbabcbdbdcadcdbdcccabaddadcabcdbcddccbdbcbabccbadccbdadabdabcabcbdccdddabcaacbcacdccccabcbabcadbdbcccadcbadabcaabaabacdaddaaaaabdabcdacbccbbcdbbbccadcbbbabccaddbbcdcccddacbdddcccabbcadddbcdbabcdbaadddaadbcccccadbdbaaaadabdcbcccdbabcbcccacbcdccdabacbcadcdcdcaaacadbcabbdabcadbdcdcdcddcababdabdbccacadbcdbaababdbcccdcacbaabddcdcacdccdbdcdbcaaadbcaaaddbadaadcdbdaaaabcdbcdccdccbdbcdbbdbdbaadcdabdaaccdadabcbaddddaacbacdcdccaadaacadbbadcbabbdbdaccdbbccbbbccdddadabcbccacaadcbbbacdcbbacdabdcdcdbdadcbadddbccadadbbabaaacbccbadcddabdbaabadcaaaacccbbcbbcdcdaaccabdddcaaabaaadbbdcdacbabbdcbaddaccdbbccbccacaaadbddcdccccdadbabcdcadbcdababcaadcbabacbcacdaddadbcbddcdddcbacadcddcaaabacdabaabdcbadbbabbccaacccdcdbbaddcadbadddcabcacabbaadbcaddbbbddaccdbbcdbbaadaacbddcabbcabdddbcdbabcdaacccacacacdacdabcddcbadddbcbaccccadbcaccabcccbdcabccccadabbbddabdbcababacddbbbccbbcadcadcbabadabccddbdabbdaacbadcaccdaabbdcbdabdcbcbdcdcadadabccacbbacabccccddddcddbdddddbdbccadbabadacabcccbdbccbcbbcdacbbcaccabddbabaacacbcdbadaddbdbdacbcbbacacdacdaacdadaadbacdbccabadbabccabacbacbddbaabbcabadccddddbacabdbaacdabcadbabcbccddabadadcbccdbcbcacbaccadbbabddababbdadbcaddbaabcdaaacbbdaaaaddbcbbccdbacbbdadcabddcacbcdaaadddbabcaababcdcdcabacccbdacccbdcaabadaccdcdbdccbbccdbbaadadccdcabccabacdbddbbadcdbadccaabacabbcdaaccdacbcbccddabbadccccbcdbcadaaccbabaaadcaccbbbbaadbcdddccdbccaabcbacbbdabdbdcababdbacbdaaccddbcdcadbabcddccbbdcddbbcbadccdcdbcdbdbdcbdbdaccbbcacabcddbdcbbadaadabdcabcabaccaadccabccdaabcddacbdbbbdcbddbcdacacdcaacbbcdcaacabdbabdadcaacabbabcbcccbadbdddcbbcddbdbdbdaabaadacdbcdadcacccababcadacbdaacdcacbbbbddcbcdaababcbdadbbdbbbdcdcadbdaddcbbdbbbbabacdaadbbdacadcbaacacacaccbabaccabdbddaaadbbcacabcddcdcbaabbabcaaacccddbccabaaccdddbdabbaacccdabcdcabdacbaacbcddbadababadcddbbccabdcbcbbdcbbbcdbadadddcbadbcccbbadccbabdadcccddadcccaaccbccacbabddbcaaadcbcabbcabdacbadabcbddadcddaacadccccddccdcdbdaacdddbcaabcbcbbacbcaacdbababbdcbdcdcbdbbccbdadcbbcabcbaacadbddabddcbbdadcccaaacdaccbcdbbbcdaaddadbcaacbcacccabdaadabdbddacddcbcaccbdcdcddbdccaaabacbaddcdbdcdbcbccacaacabcdcdbddcdcacbccaddadadacacddcbaccaaadbaaabcacbdaddabbdcbdddcaadccaabcabaaabbcadadacbabcacbdddddcddcbdcccddadcaaccbcbabddcdcbdaabaccdacababddcbcadbdbbadabbdddbbbcacbadcabbcabcdbbaadddbbdadabddacabcdcbcddbbbabdaaccacaacddacaddbddbbcaabcdbbdbbddbbddddacbcbcacdbacccdcddccdaabbbdbcbbabccdccaddcbabcabbbcbccbbbbcdddaabcaddbacacaabaabaadbacbcabdccaaabdbcabbddcbbaccabdcbbbbdbcadbbddbbadaaaabdcbabbbcbcddaacdbcacddbdaacdbadbbabcdcbaaadcaabcacbaaaaadcbcacacbddaaaadaaabdcacccaccabdaadbddaaddaabdacdabacdddaccbcbdacdcdbacccdbccadabdacbbcddaddaaabdaccbdcbddddcddcdabdadabacdcdabcbdccdddaadaccacadcbcdddccdbbdadabaadccddcdddbaccaaadddbcacbbddcbbdbccbaabcbbabdacbbbdccbadacabcbdbcdddcddcdaadaccacaabaccdccdcacbbcccccbddaccdddddabdcbdcacacaacbbddabadbdcaadbbabcddddcdcbabdbcaddacccabccaabacbcdbabcbabdabdcbbdaabccaccdaaccbadaadddadbdbbbaadaacabbddbbaddccdcbccbdcbabbacabadbbaadbddcccccdcdaabdbcbcdadaaabdcbbcbcddddadbdccdcdbcbbadaaaaabaacccaabbccaddaacacdacacabaabbbadaabacbcaccabdabaddbccdbbcdaccabdccbcbadaaccdabcabcaaccbbacccaaadcacccdcbaaadddbcdcdbcbcbcbccbbdccababbcaccaadaacacbdcbdccccbdbabbcaaaaacddadaacaabddccacbdcdacdcacccbacdcabaacdddbadabbccddacdaaabbababaabcccabcdbabcbabbbbcacbacddcdbabacbcccabaddadddbcdcbbadadcacdddccbaadccddabbbcdbddddbabccadbabdcbcdbddadaddbaddcacbbababadcdddbdadabaaacbdccccacadaaddabbccddcdcadcbcbccbabaaccbdbcabdacbbbcaabccbcbbccbaaadbcdcabcdcdabbdbaabcddccbbabbbccbcbbdacccbacbadcabddddaadddbdccabcddbaccdcbbcccbabccacabaabcdddccbabcadabacacaacbabababdbaaccdcaabbbacdadbaadbcbabcacbbaaabadbaaccbaaaabdbbadbdccaadabbcccaddcdcdddcaacadaacccdaddaccacbbaccabdbbacdbccdccdabbdddbcbabccddbaacbbdcdaadbabadabccaabdbbcadbcaaaababbbcbdaabadbacdbbbccdcbdcbdabaaadcdaacbbbabdcaababaacadaddabcabacbbddcdbacadaaabbbcabdcaaacccacdddcdababcaabddcabbdadcdccbbdddabacbcdcdababcbcbabdadabccbcccbcacdadccadabbbcacabcbaddadbacbcddddddcdbacbabddcbbdbcddacaadccbddacacccdadabbbcabcabbcdabdcaaccdabdbbadacadadbbaabdcaaadabbbadbbdcadbcddbabcdcddbabddaacdadadcdbbabddcddcaaabcbcddababdadaccdbccbcdbdababcbdabcccadcbdcacaaaacacaddabadccadddcadccaacaabadcbadbbdacabbbcabdabbddadcabbbacbbcadaccdadcdbbdadbabbdcbcaabbcdaccddddbacadddddcbbcccabacbaadadcccbbddabaaaadbbaaababdaadccbdabadaccacabbdcadaacccbdbbdacacdaccabdbdbbabdbccbcbacccabdaaadcddbdadbadaacdcbcdadaaddbcadaabdccaacbccbdabbbdcbbaaccbbadccdbadadbccdbaacdbdbdbccbacadaaadddabbcbbbcdaadbdccaaaddbbbdaacaaddbadbabcdabbcbbcadccdcaadbddbbccdbddbcdbabbcdbbccccbdbacdbccdacabcaccacabbadbacbbddacadadbccabdddcbcdadcdacdcdbacacddbcdcdcdcddacdacdacdcdccbdaccabdbbadcacdbbbaccadcadbacdbddacddaabbccbcacabdbbbbcaabdcbbbacacddccabcdbabdcdccdcaaccdadcbaadacdabdddbdbbbdddcbbddbddabbaccdabcbcabddacaacaaaddaddaccbacdacdabbdcbaaaacdcbabddaccaaaddbccaadcabbcccbadccacbccacddccdddddadddbcdadbddcadcdcabbbcddcaccbaddccdaaabcbaadbcdbcabaacbdbbdbdcccabaabdddabcdcbdbddcadbbaccacddcbcaabdabbbcacdbbacbdabaabadbbdaaacdcccdbabaabcdbcacbbaacccbaacddabddbabbaaaccbdbcddbdccddbdccdccdabccbaddcdbdaabccdcadbaccbcbdcddcdccadbacbbaaaddcbadbcbddaccdcbabddbacbbcdcacddaadadacdadaddcaacdbbbcdaccaddcddcbdacbccacbaccdcbdaaaccdbdcaacbbddccbbcbdacaaabbdcdbdbbbccddcaadbababababddaaccccbcaaddaccbdcdadaccbaaacabbbaadbbddabddcdacdbdccbdddadbddaddbbbacdcacdaabacdcbbacddddcaddaaaccbccbbcbddbacbaabbadcdccadbccaccbbbdccbbdccddcacbbcdaaacaaccaacbcbbacacddbcbcccbacaccdacbbccacdcdddadacbbbccddccbadcacacdbddaababbbccdbcdcbdcbbdabaaddbdcbdccdcaddcbabbadcdcaacbcadcdcabbabadabdcddabdccadbcabcabacdbcddaabacbdcbbaddddbccdaccbddddadbcbaddbccdbcdccbbadadcdbcccaaadcaacaacdacbccacdbbdaacdcdaccdccccaabbcdadddddcaddbdadccacaabdddbaccdcabcacddacdadacbddadbdcbaddcaddadaddbbbadbccbccabacddbbcbaacabddaacdbabbdcdadbdabadabdadacabcbdbbcdbabcbcccdcccbccbabbccddbcbdcbcbdcdcadbbcdadcaaccabdbcbbddcaabbadbdcabbcbdacdadcabdbdbccbbadcddbdabcddcddbcdbdaaccbbbccdbcaadcccccbcabcdccbabbddcbaadcccabbabccdacaddcabbddccbaaaccdbaaaddacabbcdbcabbdccdcdcbbbacadddcaadcccdaddbbbdccaadaccbbbacbcbbadabcbbabaccbbcdcddacdcdccdbbbccaaabdadaccbddbddbdcaacdccddbddcdabdacddabbaaabacccbdbcaccdcdaadbaadabcacbdbbabbbbbabdddbbcbadaacdcabdcdddbabaddabbabbdbaadacbdbbdccdcabccaabddbbaabdcaaacbbaabadcdcbcbabbabdcbbcacabdbdacccdaabacdccacccadcabadcabcabccaccdddbddcdbccbaaacdbcbcddbaadaabdaacdbcdcbdcdcabacddabadbccaadcaccbcadcabddcdddaccbcacdbdaacaaaacccbadabbcddcddcbcddaabdcdabaddddaccaccbbaabcabcbdadccdcddccccaadbacbdcccacdabcddbaacbccbaaaaabaacccbdcabdaabbdadabcddccdddcabadccdccacacacdccdbcbddbacacbcbdabbcdcacdacdbcbadcddabcbdbbbcaadcccbdbdcbbcdbadddcdccdbccbcdccdcbbaabdbbddbdbdcdbabdccacbaaaddadaacbbcabaaacabdcadabababadbbcccccccaabadadccdaacacaaacbbdbbaccdcbabbabbddcaadccddabacbccadbdacababdccbabcadadabbaaabbcaacbbdcbccbacdabdabcaaadddbcacaccccdbaddbcacccddbbadcaadbdacbdcbacdcbbdbccdcbdaccaaacadadaacdabbadddddcbcacdbaddaabcbdabccacbadccbbbddbdbbbdaaddbbadabddcbcadbaaadadababdadddcbdabbdaddbaccbcddbbcadbbbccbbcbdcbdbacbbcacccaadcbacdadddcdadddbccbacacddabbdcadbdbdbbabcbdddadaddadaddccaddacdabbdcaccbbbbaddbddddbacbaccbcbaadbcccbabdcbccadccadcbdacbbdccbcaabddaaacbddbaddcabadcbddbadabdabcaccddabbadaaacadbbabbcacbaadcbabddabbabadbbaadadbdcbcddcccdbccdbccdadcdccdbbbcdacccabbaabbbadbaaabdddaabdbabbbcbddcaacabdacdbbbdddcdcdbacbabbbcaadacdbddddbbdcccbdbaddbdbbbbbacdbdbacddadddbadccabcbcbdbcdabcabbcddabccabcdbbabacddacbcbaccddcddccdabdddadddacccaabbbdbaabdddadbccdaacbdcdbaaabacccbdaacbddcaaabbaaaadbaabbdaddbdbdddaacaaaabcbaccbcdbbbcdcddbadbabcddadcaccbcdacabcaadaabcdddabcccdcabaaaabadadadbdabacabaccddbdabdaaabbbcadcabdaacdaaccdadadbadaabbacaabddbabdcacbadddbacdbacbdccabdbadabddbdbbcaadddaaccdcdcbbcbbabadbdcdadbbcddbddaabacacbbbddadbdcddacdbacdcccddcaaccabcddccadccbddccbadddadcbddbaacbbdaccdcbbbcbcbcacccbaddccbbcbbadbabdbadbbdaccddabdabdabcdbdaaccbdbdcbbdbaadcacacccbcbbacdcbbadaddccbbcacbabaccdadadddccaabdacabadcdbaccdccbbabacdcddbddcaadacbdaacdbdabdcdddadacdcabcbcdbaccccbcbbadddbcdacbadbaabdaaddbacadbbbdddabbadabbaddaccacdbbaacbbbdaadbbddaadaddcbcbdaadbbdacadccaabcbdcbacbdaddbaaccadbcdddddcbcddbdaaddacbbbcaaaddccaaadaccbabcdbddbbbaabaaaddadadccbadacdbcabdbddcddbdccacdbdadacacdaabdcacbaaacccbbcdadabdbbcbbaadcbdbbdcaababcacddaacdccddbccabcaaccdaabcbbacdaabacccccbbdbcbcabdbcaabbccabcadacbdbdaddcdbaccbbdbccaabcacabccabdddcadbccbacaddbbcbcabbbadbdbdbcbcbbbbccdbbdbbcbacddbdbccbadcbdabcadbabbcacadadcadbadbdddcbdddcacbcaaacabdaccbabcdabccdcbdbcdaabbdadcdddbdbbaddcdadcdadacddbcdbccaabcccdabacdaccddbcbdcdcacbbaadbccbbdacabcbdbaabdaaaaacbcbacdbbcddabaaaaabdbbadccbdcddabcdaadcbcadccadabbdaddbbdbcacddcacbddacdcadbdabccbababbbabddaabbdccdcadccbbcaaaaacacadddaccabcacbdaddcddcbbbbcbbbaacbdadbbaaccbdcbaadaabddadbcbdbadacbbbadabcacbadcbcbcccbbbdcacaaaadcccdbbccabadbbbabddccccdccbcaabddaaccabddaddbbcaabbcbcacbbccccadacbbcbbacaccddbdadbbaccddbcadccbdcccdcbdbbddcacddbbbcdaddbaddaacbdaadadcbdaababbdbddcaaccdcbdbbbcbbdbbdbccdabcabcdccacdcadbdbdcbadadabcdcbdbaccbddccbccadccdcbabaaaccddddcdbdbbcadcaddcbdaddcccaaabdbdcddddcadcbcbccbcbdaacacbddbbabacabbcddaddaddadbcbcaacacdcdccddbaddbccccddcadbddccdcbdcdacabcabbbcdcadcaaaabccbccbcdcbcacbdccdcdcacccadaadbdbcbdccbdacbcadacaccddbdabacdaadaaaddbcbbcbacadcddccbbdaaacdadabdcdcbacabdddbbacccbbdacabbabccbdccdacabaacccdbaaddbaaddaccabbaacdccdcbbbacbabbdcbcdccaddddcdccbbcbcccdcbabdadcddabaabdaacabbacbababcdccdbdacccdadcabcabdcbabdacbcaccccaacccacbbadbaabacccccbddcbdddddbbdbadccacbbdcddacccbcaadbbcaadddabadbabdbdaddbdcabdbadcadbccdcdcdbbdcbdcabacadadbccaadbbbcadcdbccbcddccababdabdcdddbcbaaaadddccbdadaaabdcdcadaaddaacaddbcccccabcbbacbaccdabacbdadbbdcddaaaacabdaaabcdabbaaaadadbcbdabadcdccdddaadbcaddabdbaacddbdbbcaacaaabdbbdcdadbbaddacdaddcbdddccbcdabdabacdccbbcdcbbdabcabaccccdcabbaddaadbbaaadbbbccacdacdbacddcbbcccbbdcaccaabadbaccdcacbdbadaacddabbdcdcbadbcbadaaaccdaabdabcaccdabddbaabcbddcbdddccabdcdadacccbaacabccdbdbbabaacdabbdccaaaccdaccbbcdbbdabbadacccaadcbcadcbbdaaabcacadddbdbcbcbbbbcccbbcbbdbbdbdcadcbadcadadbcdcbdbbcdcdbbdddcbdbbcbbacacaabcdacbcadddbbcabbbddbdbaddcbcbcdbdcaadccbacabacdbbbbacddccabcccbadbbccbaaddababadacdaccdabdddcacdddacdddaacddcbddaabccbddabbdaaccddcbdacdbbaabddbcddcdcacaadcbbacaadddddccbdacadaaddbaadadcbbabbabaaccaadbddabccabdadadbbddcaaabbdaaccdccdabdadccbcbabbccbbaddabcacbadbcabccccabcdaaddadaabcabbcadcddbdcdadccdacabadabcaccddbabbabdacabdaadbdcaacbddaddcdbdddaaaadbbbacadddcbcdbcabccaabcbcacacbcdaccbaaccdbdcbadadcdababdddcbcaadcdadbbabdcadcbcaaabbccbdbcdcccbbdccabccdcdbbabacbddcabddcbddacdbbcbbbbcddcdacbdcaddcbbbaaadddbdaacdddcddbdabdcdacdbaabdbdaadccdbdaadcbbdbbbcdbdcabacbdcbdaaaccacdbddbbabdccccbadaacdcccacbcabcbbccbbabcbcbaabbdabddcaadcdcdbacabcbbcdacdbbccbbbbcdbbcdbccdbdccaddcccabbabacaaccbacdaccddaaaccdcbdbddabdddddbcaaadaaabcdabacaddbddbbdabbbabbdbddbbdcaddcbabcbcaacacddcaddbdbaadacbadbabbbcbccbaccabbccbcdabccdcaddbbdabdabbcabdcdccdbcdcacadbcbcbbadaaccdbacacbababbcbaddaccacbccddbcdbcaadcbbcdcbccbbacacbdcacaddabdbabcbbccccccbadcaaabacddbdaaaddcaccadbdbcaabbdacadabddcadbcacdcabcdcacdabdcacbddcdcdbbccdcbcbbcaadddcadcdbbdbabccddacdabdbbddcbdbddcbccdccbdaccdacaaaaaabdcdbdddcbadaaacacbdbddbdbdcdddbdcbbcabbdbabdcaacaacccacdbdababdcccababddbddbadbccbdbbccadacaadacccddbdadbbdaabcccccacdddbdaadccddbddacdddaaccdaababacadadbcbdadcbbcaabaddacadacaadddcacbaddbcdbbdabcbcadadbadadcabcadddbddaabcabbcdaadadadadccaababcbbadbbabccdcacabababacabcdcbcdabadacdbcabddbaadcbcaacbbddccaaacccddadadddbdcccbdadccdbdacbcabdadabddabdadcccdcbcbdbbdbcbaabbddcaccccddccbbcacccacdbbdaddcccadccbdcddbabddcbddacacccaddabcbaddbabbaacdacaddaaaacddbacbbcbdacdbaabcddbbbabccadabbbbbbbcbbdcdadbbcadcabbaaaaacbabdaabcabaadcaadbabbdaadaadcaadaddddbabdbaadcaccacdbccdcacbbdbbdcdcbdacdadacbabbbcdddaaccbaaacdadbabcacacccbbacabbcbdabcdacbbdcabdcccbdcdbdbadadcdbdcbccbdbdbadacccadddbdacddadcabddadccbcddbdccbdcbcbdbaaccabcbbcadccaaabdbabcdbdbadbabccaaddaacaabadbbdcbccadcdbcaacdcbcbbdbdabbcbabdcbabacbcddcabdccbbbdaddbdcaaabdaacddbbccbdbcbadbcbdacbbacabcdadabdacddcdcbcbadaaabdabacabcddbcdbbddccdcaacdbadadaabadcadcdaddbbacbbcbacdbadddabaabcbcccabccbcbadbcdabbbaccdabccaaadabacacccdaaabcbbcdbacababccbddddcbcbccabbbbbacdcddcdbbaccdbaccccddcababcbcbcadaccabddbbbdbdadbbddadcdcaacdadacbaadadcaabbcbacabcbdadbcbddadaaccaddddbbbadbbadbbabdabccddddbbdabcbcbabccddcdccdccccccbcaacbcbcccccacadaaaabcdbadbaaabababdcbdbbccddccaadccaadaaddcbbdadabbabbcacbbdbdbdcdbdcbaabccbcdbbdccdccdccdbcacaaadcdbaaaccacbdcabdaccbdabcbccdddabbccaabbddaabbcdddbddadabdbbddabbcddadcdbbbcbbdbdcdbbbcdaaadadcbdbadcdbddcacbdcabcbccaaddbbcabacbdaabcadabaacbcacabddaabbbccdcabdbbcabbccdcabbccdccdcbcdbaabddaadbadacabdabacbddbcccdcddbbdbccaaaddaacbbccabbabadacabaaacdbccddcbacdbbaccbcdbcbbccbbdbbbcdbcaadddcccbadbdbbabccacbaaddcddbbdcdcadbabbadadcacdabaccbadacacbabbbbacbadddddacadaaaaacccbddadbbdabbbbddbabcdbacbabccabdbcbbdddaddcdababdbbccdcdcdcbbadabcddcaaadcdbbabacaabaaaadccdbbaabbcabcbdbdcadadccbcdabcddcaadcabddcddccdbacdccdbadabdbcdbcddbabaacdbbbcbabdbababcccdbcccbabbccdddaccbdcddddddbcabdaddbccaaddcaacabdadcdcabacabaaadbccaaddcaadccccdaaddadbabbdacbabcaccbbdbbaaadbcaaabdbccdbbdaabaabbadcbbcadabcaadcdcacaccaacbabcdcdccbbcbbcaccdbabbbdbaaabdcadacadbcbdbaadaadaacaabcdbcaadbbbadcabcdabdcdaaacdcbbddccaccbbaccdbcdcbabdbabcdaccbbbbcaddacdddcdccaaaaaaaacbcacccdbbbabbdbccaacbdbcacbcdaaaccbaadccdbaaaabbbdcdacccbddbbbdddadabbcddccdabbdcaacbaccdabbabaababcbdacaaacaadccdcddddcadcdacbbadddddddcbcadcdbccdacaabcbbaddcbdcaddcdcaaaacdbdddbaacdbdddabbacbabaddbcbaaadbaccbaaacbbaaaadcadcdcacccdacadacdaccaccbdbdddbbdabdcabbdcbbccbccbccbdbacdbbaacccadbbdddbbbccabbbadaccdbbaadacabadccaaaadddaaadccdbbacdcbcbbcbaabbdcdcabdbabacbbbbccbcdabaababdbbdbaabaccdabacbdaabcdbbbcadbdbabbdacadbacbccdaaaaccdccdbbbabdacccbbbbdadbdaaadccbbddbbbbcddddcdbdddccbdcbcbcadaacdcadacdadaaaccdcdbdbbadcbcdcabdbdacbdcbdcbdcadbadddcdabcadccabbaaddddbabbcabdacddcdbbdaccaabbdaddcdcaaaddacdbdadcdaddaabbcaccabdcbbccbccbccbddcddaddaacbbcbddaacbadddbdbacccbdccbbabcaacccbbadcbddadcccacdbbbcaaabacacaadcdbbdbbbdabccbccabbcbdaacdacacddcbcbdbcdcdbacdaaddaacadbacaabbcacaaabdcadcdcdbacdccbcbcddcdbcdbcadbaadbcacbbcddddaababbaabcabdaaabdbcacdacdddacabbaccabcbcaabbccbaddccacbdbacbcccbddbcdaccdbcddccdbcadaaccaabbacbcdcbacbbbadcacddaacbdcbcdcacdcdcaccabbcacdbabaaadbadaaddccaddabbacdccaccbcbbcbdddddcbacbabbccdcaddbbdbdbddbadbbcdccdacdcabcdcbadacccbcbcccddbcbabcdabbbadbbbbdbadaddadbbcababdbabcccadadbcdbbbccdaddbddbcbadbaacababddbacbaadaddbcdddadccacbacacacbadbddddbdcabddbdcdddababcadaacaccaccddddccdadcabbddbbaabcdacabdbdcaddbdaaabacabbcdcbadbbdbadcbcbcdacbcdcbccaaaaccababcadacacbddaddababccddbabdabcacdaaacbcabadbcacdabbcbabdbcaabadadabcbbddbcbbdaacbbddbcdaabcdbdbdacbcdddacddccdbbcbcddcdbbdcccbcdcdbbccbadbcccbbaabdcdcdbbbbadcdbaddcbcdbabacaabdcabbbcddcabbbaaddbadbdcaaabcbbacbcbbcddccccdbbadbddaadddaccdcbcdcccaadadabbacdcdbababdcabbccbacbacadcdadcdcacccaacccbcbcbdabccdaacdddcbcbcabdcbadcbdddaadbdcacaaaaaddacddbbadaaaddcccdccdbbccddcddacaaabadababcccacdbbdcbaabaddcdaccccaccbbdaabddddaadccaaacabbacabaddbdccdccaabddccaddbbabcdadabbadcddacbddcbadaddaadbddbdbcbcadbcdcccacdddaadaadbcaaccbbacaccababdcdccddabdbddcabdcbbaacbcbadbdadcbbbabcadabdbdbdbddacaabdddaaacbbbacbabbacdbdcadccbbbaaacadcaddcddbbbaadcbbbaaccbcdaacaacadddadadbcabbddcddbabadcdcddcaddcdabdcacaabdddcdbbbdcddbcccbbcdadddbabddcccdccabbcacccaddbabadadcdbbadcaabbbdadadcbcbbdbdbababbccbaabbbbdacdacacbdccdcbacaadcbaccadcabbbbcbddadaacbadbdabccadccbabcdbacddacbadbbcdabcccbcdddbbcdbbccbcdacabdbdbbacadbbdddaaacbaabdddcbbbcbadadbbcbbdaadacbcaadddddbddacbaaaabaabbddabdccabdbcbcbdacddadccddbcccbdbabcbdaddadcbaabcbbdcabbadcabddcccccccdaaccaddcbadbdacbababccbcdccaababaadccbddbbaaccddcdacabdcbcbaccbabddabbcbcdabbbcabaaadddaccdaaabbbcdcbcbcddcbbdbbbacddbcdcaabcdccddcbabdaacbdadabdcaabcabadbcbcadcddccbcdddbaccaccddacddaccababbbabaabdaadbbbdbaabbaadddaddcddddbbcabadbbddcbbdccbbdddabdcabcdcdcbabbacbddbbbaaabacbcdddccccbdadbccccadbddaaddababadccddacacaabaabacbdccbacdccbdcadcccbcddcabcbdbbddbdbdaaacdcddacadccdaadddccdbccbddccdbacabbcabadbbbacdadabddbbbcabdbbddbdccaccadbbdacbabacbcdcdccbaddbbdacdabdccbddcacdbddcbdabbacabcaabcccabdbcdaaabccdaddcccbcacbcacdbaabccacccbbcbddbcdbdddcddacdbacbbdadcccdabcdcaadacaabcaabbcddcdabadcdbcabdbdbcabcbcdbbdaaabbddbcdbadddabdbbcdaddbdabcdddccadaaadddbbbabcaddcbcccabdcbbdabdcbddabdddaabcccadaccdabdddbcddaabcddacbbccdbcaccddabddcaddbccadadddcacbbcbbbcdadcababccabbcdcbdccbadacacacdcacddcbcacdadcbaddbbaddcdbbcdbacbdccdaabdacabcccdabbbbddaabddddcadddbbcbbbccbcacacbacdbbddddcccadabdbbcbadbaaabaaadacacddcbcdbdcddbbbdcddcbadcccbaadcadcbaacacaaacbdcbcccbcacaacadadbaddcbdabddaaddccbbbdccbbdbbbcacbbdbdaaacccacdcaccaaadadcdddadbcdbabbcdabbaabdddbbbaacdbccccccccdbcddadcdcbdabbaabacabcccacacdbacbaababdaddcdcbccbbddcbdababdabddbdacadabacddbbcbcadcbaddccbbcadbacddbadadadccdbbdcddcadacdddacddcbdcbbbaadabbdbcbabbbcdcdadcdbcbbdccbddbadbdddbbadacccbbdbadcddddcdcbbbbccdcbdbcabbbaadccacdccbdbabadcacdbabaabcacbbdccacdaaaccacdcbcbaabaccbacaccbacadbaaadaacabdbbcacdbaaccaaccccaddcbdbdcbdaacdacbbbcadbcccdcacbddcaadbbdbdbdaccabbcdbadcdadacdcbadbacdcbdbccaadcbdccdaddcdcdcddbdcdabddacccabacabadbabdadccdbdcdddbabbdadcbcbbcbaadbcacbdbbabbbdcccbbbdcccdcdcbbbcdaabababdcdabcdccddbcacdaabcbdcbddaadbacccdddbbadacbbdacccdcbaaabcddddddadcbcdcbbaaccbdbbabbacbddabccbbccdaaaaddbccbdbcabcccbaacdbbababbaabadbccaddaddddddbdbbaabdbaccbccdbcadabbcdaadadaacacbaabddbacbcccabdbcadacdddcaaccddbadbcacbbacdddcaaaddaaabaaabcaccddbadbcdbbbcbabacadadcbccccadabcadbaacabcacdacbccadccbbbcdccacadadacdcacbacbcadcadbaadccaadbaadacdacccdbbdcdddddaabbacbbdadbcbddcdbccacabccabadadcdbabbbbdbacbdacbdbddbcaabdcabacdcdcdcddcabdadabcadbdddbbbaaabbcadaadbbddbcdacddbdbacaddcdaddaaadbcdcdccbbcbcaaccccabaadccbcbabdcdccdbdbddbddcbcbdadaadddacabbdcdadcbbcdbbbbdbccabbdcbcbababcdacadccabbcbbcccbababacaabbbaacddadadbaabdccbbdcbacbdccdddabbabbcaadbdadabcbaddccadbadcabaddabadbbbbaadcdcadcdbadacadbcbaabaaadbdacdcddbddcaccabbcbbdabcccdcaacddabdbbaccbbabccddccbbcaabdbacacdacdccadabacaaacbbbdaccdbacdbbcdadbabbaddcdbdabcabacbcbbbabbbcdbbbbcbaaaabdcbbcdbaccbbbabdbaaacabbaabdbaaddbdcdcdabbabdccccdbaccbbccdbcaaadbdcadbbabcdddbcbccdabbcbccddcaadbcaddbbdabdadaaadabadabadbbdbbabddbaccadccadabbdcbbbbadabcaacbbcabcbddccddccbacdaaacaabcabcddbaadacddaabdadddadbaacacacdcaccbabcbcbdacaababccccdaccacadbdbcdbbbabbcbabdddaadaacdbbccacbdddacdaacbccccdcddccaddabcdcbdbccbdcdccbabdcdbccbacbddbdacacdddcaccbccbaddaaacddbaacdabdaaabbdacdacadcbabbddaaabcbdbbcbadcadccaccccdbacadbacbcaaabbcaacbdacdacdadaaacccabdaddddabdaacbbdaccadacbacbbbbdbcbdadcacabbbcadbabdbdadbdababadbabdbbddddcbadccacdabcacadccdcccbaadaacbcbbdadcdaabbdacbaccdbdddbccbcbddcbdaacadddbdbbcbbdbbaabcdddaacacdddcdcbaadaadadbaaadcbddaaaaaddadbaccabccadcacabbbddacccbcacbdacaacbccdadbdabcacdadccacbbcbbdccdbabbdaaadcddbaccbbdccacbcaabcbacddadadcabacaaddbbdbcbbcbdcccdcdaabdbabbabcdcdbccdadcbdbbcbcacaaabaadaddcccdbbbaccddaddccdbdaacbddbaaadabacacbccdbbcdcbcbcbcabaaadbbcdadbccadbbcacbcddbdbccbdadcddbcbddbdbdacacbcbbdadabaaaadabdcddacccccbaddbdddcbabbadbcdcaadbacbddacddcdbdcdadaddbddcbcdcbaccdcadabcbcddadabdacbaddcbcabaaacabbaccddcdbcddabcdcabddbcaababcdcdbabadccbdbddaaaaccdddccdaadaaadcbdbbbacdacbddcbbdcacbcdddcdbbcabccbccaacbdbcdcddcbadabcaddadbcddabdaadaaaacbbcbcbbcddcbdbbdbbcabbcbcadaacaaadcbbbbddcddbdacabdcdbcdbcdcbbdabbabddcdddaabcadbacadbbbaacdcbaaddbabdddaacabcbaadddcabccdbaadadabaddadcdbcaacacdbacddaacadcacddadacabdcccbdabdcdbddcbadbcaabcaabacbabdacbdddcaccadcadccccabacadcddaacbbdbadbabaddadbbadbbcccabbadbccbaccddaddacddcaaccccaacdcbaaaaaadabdaadadadbbccdaadacccabccacdbdcccbbddaadadaaabbbdaabaabcbdbbaacbdcddacccbcbcbabdcbdaccccaacdccacdbdabbbcccaacadbddbacadaacccabacbbadbbcccbacbdccbdbabcbcbcabaaaccbbdbabacacbcbcadccbabbcaabdbaaaacccabdbbdaddcbacddbdcadbdccbadabdaccbabdaaaacddcabacdabddbcddaadbddbbcbacbddbcbddbcababaacacdddbdcdabacccdbbbbcaabddababaadadcaabbabdbccccdcdbdaacdbddcabddbcbbbabcbabcbadbdbddcbccbdcbccaaccabcddcadabdccacaadbbdaddbcccddcdddabaccbadbacaddcaabdcacbddbbbbdaaacbadaaabddcabbbdaccababbabbcdbdbddacdbbcdbcccdbaddbdbdcbcbcdddcbcbbbacddcaacaadcddacbacdccdaabcdacdbababdbbdbcdcdcabddbddacacacddcdcaaaabdadbacaccccdabaaccaaaaaabdadcdadabdbbadcdddbbcadbabaadbcacbbccbcdaaacddcdaabbbbdcaabbcaccdddacddcaabcaaaadcdcdadacdbcaddaaaabdbbaabdacdcbbbddacaacbabbbadbabdbaabbbcbbdcabdbbadcbcbacdbdabdddacdcddadcbadbddcaddcdcbadbdbcdacaacbaadbaddbadbadcadabddadacbccbcdabddacbcabbcccaaadcbdccccdbdcbacdcbaabacadbbabcdadddcdbcabcccbddddcdbbbccbbbaccacabbbabcabacacddbdadbbdaccbbdcadabdbaaacdbadbcbddcdbbccaccabcaddaadbdcadddccaabcaabdbabbaaccaccaddaddabbcacbdcdacbbccbcdaacbacbadccdcbbadbbababcadabbbddabddbdabcdbccdcbadcabbddacccbacabcbcbadadcbcccbcadccccdcbbcccbbadddbabbcbdacbcdbdcbabadabcacaccdddbdcdcadbaaaadddadbddbadbdaaddbbbaddddcbacbaccacccabcbdacbbdbccddbcadbbcdbcbbdbaadacdccabdccbbbdcdbddbdbadbdcbadccdbcddaaaacbabdadacaccdbbcbabcbddddddcaaddccddcacbcaaaaabcbddadddacababbdaadcbacbdbcacaaadccaacdddadbccbbbabcacbcbdaaaabbbddacaaaccddaaccbabcdcdccddcdcddcaabddbabddcbabcbdbdabbdadacacbdacbcdcdaabbaadbbccacbcaaabbbbaacbacdacadcaaabaaaddaaddbacbbacbaccacaddadcabdcaaddaaaccbcdaddccaadbaddabcbdadaadcdaaabdddcccbbadaababbbdbdbbbacccbbccadccbbbcccdcdcccacddababcabcaacccbdddbbdddcdacdabbcdcaccabadbbadcdddcbcdabcdcdacbabdcdccbdaaaaaddbcdcbcbbccbbcadacdcadabcbbbcabadbbcaccbaccddbacbaadadaaadddddacdadaadccddbadbcccaaadbabdcaddccacdddadbdaacdadbaaacaaccaacacaccdcdadddbbdccdadaddccbadcbbacabbbbdadcdcdaddcdacadbdbdadabddacdaddabadcbcdbccaadabdddcaacdbbdbcadcadabbadbbccbddadccaacacbbacbaabacccbcabddcbbaaccacccbabdccadccaddcbddbabbbcacadcbbbdbdbabaaccbaadaadacccacbabbcaadcbbdacccdcccaabbcddcbcbcaccadcbcbdcbddbcdabacccdacbcccccbcdaacaadbabaabcdcadcbcbabdaabadadbdbcbbabcadadadabbcbddaadddacadbbbbbbdccdbdcdbbccabbdbdbaaabddccbcacaabcbbdbaaacabadacacbbdddcbdabddcbdbcdaccbaccdaaaaacbbccbcbccbdabdabcbaaaadcbdbaddbdcdbcbcabccdcaddaaaabbbbabdccabaabdadccdcaccdcadcbdcadadbbdbbccccddcddaddcaaccdaacccbccdadbddbcbabdbccbcbbbbacbbbadabdbdddbbacbadadaacaaabcbaccbccdcdbccaaaabbdabaaddbbdcddaccccdbdcbbdbbddbccabccbbdbcccddccbbbacdddaccbabcaacaabcccabbdbcacdcaddaddacbbaccdbadbcacddbabdcaaacdbdacdabbdadddbacadacababbddbbdbddbbccbdbabccaaaadadcbacabbbddbddddbabacbbbdabddadaadddcddadccddbbdcdbdcdddabaccdcbdbbccbaacacdbaabccbbaabdbcbadddabcdccadacbbddcacccdcaabcaacddaaadcaabcbddbbcdbbcbcaacdbbadbabaaadaacacdacdccdbdbccdbdbcbdcbccabaacdcacdaadbbcabccadddacdbdbbadcabadadbaccabcddbaacbdbcbcbbaabdadacbcdcbcaadccdccbdddcccabcdccddacadcbdccadbaaccdbbcaddcadcbaabbaadaccabcabadccdcbaabbcdccaacdadabcabbaacabddcbcccdabbcaaddbdbcbcbddacbdacbadcdbcadddabbadbbdbcaabbddddbdbcbcaccacbbaaccbcaaabdaabddccaccccadbccbdcbdbccacdddddbcccacbcbcdbdbbcdbabcbcadcddccbbbcacddbbdadbcadbdadbdacbdbadcaacddcddccbcdadbdbdcccbbbbadbadadcbdcdcccbdadbdbbdccadcdbddabaaccbadcbdcdaabbabdcdbcdaacddbbcbbdacaacdbadadbdaaccabbcdbabdcbbcbcaacdcbdaccbcbdbbadcdbacbaabddadccccdbdcccbdcacdadddabcdbadcccbbaacdddbdcdadacdbdcdcdbbbbcbddbcdaddaddbbbdcababcbdabacaacccbabccaadddcacbbcdacacababbbddcbdcdbadbdbbacdadbdbccbbadccababadbbdabadbcddbcddaddcdbdddbadcaddddddbabbdbcddaababbacaaaacaadadaabdabacbbdbacbcacdddbbadbdcabdadcdcabadddcdbbbaaadcdaababcdcacdacacbdabadcbdddcdadabaadcababbacdbbcddacbbcccdccdbadadbbcddbccbcabcbaaabccbbbbbacdbbbcaccbcdddbbacbcadcddbbabbaacabaabbddccdcabcbbdbdaaaaddbbdacaccddbacdcadcccbabcadcbaddcdacbbcbccbbbcbbabbccddbbadddcbcbddaacccbcddbdddcbadcbbdcaaabccababacaacbaabdccccbdcdbdaabdaabccdcbaddddaddccabacdcdcadacdaaaabccccdcdcbdddcbbbcaadacacbbabcaccacadaacbbadddaadbcdcbbbcacadadcddadaddbcaddcbabacdcddbaddcaadcabcdcbbdaabacabaadccccbacaabdccdbcbccabaadbabcabdabcaddbaccbddcaadcdabadadccccdadccccbacaddacccbddcccadadcccabaccbaacbcabbcbadcbdbdbbabaddaabcddcbcaaacdacbbcccbabaaadbdacbbdcbbdbcbcdbddaddadcaaaaccadacbcbaacaabcadddaddaaaddaaddbdabbadabcacddbdcdaaaccaaadccaacadacacdccaabcbaccbaccccddaacbdabdbdcadadbbbcdcadabdbcbdbdcabcccaaaabdbdcdadbabbbddcdaaccabbbbdaacbbdbddacbccadaabbdbdbaacaddacbdcdacbabbccccadcccccbddccacbbabddabcdaaadcdbcdaaadccdaaaccdabbdbbbdbbddcbdcbbaacacddadbadaaacdcaacdbaaacabbddcbbcbdcbddbacdcddbddaaabcdaabcccbcdaddccbbbcabcaaabcbcbddcddbdbddccdbaacbdcbbcddaaadbcbdbbdccbadbbcabcdababdbadcdbbadaabccdbcbbacacbcbbbcbbbadbabbadcdbaaababddddcddbddcdbbccadabadbccdacbdbbacddcbcbabcccdcbcdbdacdaccbcadadaabdcbcbdbdadbaddcbbcdcadacdabcaddcdddbaadbdbdddaabadadaacabaccbcdaadacacadcdabdcccbdcbaaadacbabcaacbadadcadaabcaacccbdccdbabacacaadaabadbbadddbcddbaadbbaabacabccbdccdbaaadabdcccacbcbbcbddbabaabccbbacbdbbddbdadcddddbbabdbcadabbadccdadbccccbbacddddacaccdcbacdabdabccabbacdddcaddbdbcadacbbbacdcbbcdddbbbcdaadbbdbbbccbabadcbcdbdabdcbbdcadaadbbacbcdcddacbcbacdcadbccbadbddbbcbaacbdcbbcbacbacdadbaabacbdcdccbdbbdcdbabcbdccabbddcbdbcdcbdccaaccdaccddaddabcbbcbcadcdbdaaaabddcbbddaadabdaacaacdddbddadbaccbbdabbabcaaacbcdddacbdbdadccadbbbdadddcabdadbccbbaabdcdcdbdbbcdcaddaccdbbbcabacbbadccdbdabbbccbabbcdcccbacbcdddadaabaaacbabaaddbccbcadbdbadcbacabdcbbcdcbcaabdbccacbdaabcdcdcacdcbbaccbcdabdcbbbaabcdbddbbdadabcabccabdcadaacdcadadcbccbcacddbadcadcdddbbadaabcaacbcbdccaadaddababbcacacabbcddaaddccbbbbbabbcaadbbbdccabbcadbdcdcdbadccbbdadcbaddcacabbbacbccaaccbdcaadbbccddcacaacbababadcbdcbbdbbbadbcbcccadacabcaaddaaacaabbbbdaabcadbdcabcbcacbddcbbadcbcdbdbcbddccadaccbabbabbadaabbdaacbdbacbabaaadabcabdaadbaadbddaabddbdcbdabddaabdbbbccadadabddbadacadabdbcdbbcbacaddaabddcddabcbbaddcaacdaabacccbbbbbcabaabbbababcabaacbaddbbaaaaaddbddccccddbbabaabccddcbbddcccabcdbbabbbbbcaacbdadadccdaadddbabbddccdadbcddbaadaddccadacbcbcddacdbbddabbabdacaacdaaccdadbbadcadcbccbdbbabbbccbcabacbcadbcbccdcbacacccadddcccacdbcaddbcdcbbbabdabcdccddddabbbadcabadbcdccddbcbadacbbcdddcbdbbbcbbbcbccaaddcdababcbdbacabdabdcacbadcaddcddddcbaaacbaccdbbbaadcbadccaddddccbcdcaacabdbdacdcccdcbadbbbddccabcdabdcdcdbbddcadbccababdaccccdcbbbccadcbaaacaddddbadccddccabdbabaadbbcdcdabdccaaaddccdccbaddabbdbaabcbbccbaadcbbdacddcacbcddcbcbbcabacdabaddcadcbcaaccbbbbdbbabbddcddbacadcbabbadddacaabaabadbdacabadccbabcaddcabbabaaadcabdcbbbbabadccdabacbcaaabcdccadbddbdcbdbabbbaababcabdcccdbabdccabacdadccccbcbcddbdccbcddbbbbdccbabcadadbcbdbcbdbadadabbbdadbcdcabcabbcddcabbcccadbdcbbdcbdacdbddacbaabaacadbaccaabdcbbbbbbcddddcddadaaddacbaccdbbcbadbaacdbdbdadacbbacdcabdaccbccdbcbdadaabaaabbdbcaccbcddaddabdbbcbcbbdbbddccbbcdcabbcbbdbdabbdbdcbadcabdacccaaccacabddcddbdddccadcaaddcddcdcbcccdcbccabacdbcaddbccbcdabacbaccdddcbbdddaddccacbcdbdcaabddaabdcaabcbdbdacbacacaacccbbccbcdccdacbdbaaccaccbacdcccbbbbbadabbbccdbcbcdddcddcbdacddcacccbbabacbbaddcdccdaaaaaadbdcacbbdbbacddbdaddaadbdbdccbaadddddcdabdbbcdcaddaccaacadaccbccaacdccccbaaccdabdacccaaababdaabaadcbcdbadbcbcadaadcccdbabaaacbddcbdbbbccbbdcccdacdbdaabcacbddcadcbadccbcabacacdacabadbbdaacbabcadcadbcacbdbdcbdbdbaccaaabdbaaccdccbacbacaccbbadabdcabacdaccbcddacacbccacbdbbdaccccdddabcddacdbbadcababcbbbbbbcdaabacaaccbbdaadcdbdbccdacccabdaccaaacbababcccdcaccabbaadbcbdbcdccbacaaaaadccabdbbbbabdcbbbbcdadcaadcbdbbbcdbdcbdbccaccddbadcbbbdcddabcabddaacdcdcacadadccaddacaddbdbddabcddadbbacacaacacdadbbacdbddbdaacacbbddaaddcbdddaacbddabaacacbccabcaabbcacdbcccbadcbbacbcddbbadacbabdbbbdacaccaabdadacddbabbbccdcbcaacdabacbdaccdcbcddbaacdcbcbccbbcdadddcddccccbdbbccdcbccccaddadddccdcabbacdcdbdacdabcbbacbcbddaacbccdbacabdcbbccbaacaadccbbdcdcbaaddadbdadcadccbcaddacbccbbcbbbdbccadcdcbdaaaadcabadcbaadddabddbaaaadbcdcccaaccabcdbdbddddccccabbdddadcdbbdcccdaddcadbcbbbbbdcdaabcddacddcdbbbdcbbaddbdcacdbdccdacacdabcbdbaddbdacadddadacbdbcbadbaaddbdaaccdcdaadbbabadcabadabbcccbbccbbbccadaaaccccbcbcbbdaacabcdacbbadbadbdbccdadddcbbdabbbbddadbcacbcccaacdbaabbcdcddababbdddbbdcddaadbdaaaabdbbadcccbddcdbabbadccaabcbaadbbbaadbbdacdcaadababacccccbccdacdbdacabcddcbcadddababdaddcadabacbbcbccdccdbabadaadababddbcabddbacccddccacbaabbdcbabbcbbddbbdbdbcccaddaacbbcbcacdadcabdcdddabadbaaaadaabbacdbbdaababdcbbabbbdcccabbbbaabaccbcbcbababacacbcdbdabcdadbdacbccdbddbacbddbdadcaadccdbdcacaabcbbbddccdabdbdbcdbdddddcbdbcbacdcdbadabccdaddcadccddbadadcacdcabaacddabacaccabcdddbdbcdbadadacbdcdbbcddabdaaaccaccadbadaabbdaaaadbcadddaadadcbdbcdbbacbdcbddbbacababbccbadcabadacdbacbdcbacbbabcdadabadcadcacdcaddabadbdadccdddcbcbbccbbdccacbbdbbadcccdaadcaadcabadcbdcacbccdcdbbbbcdccbcbadaacdddbccdaddbdadccadbdbdaabcacccaabcbcdbbcddbbbdddbababaabdcbadcccaccaabdbaabcbbccbcbdcacadabadcdcbbdcdcdccdbababbbadabdadbdcddcbaacbdcaddaadbaddcdccdddcaacabbdbbabbbaacbdccdaaadcbabbbcdcddabddbabaccacadabaddcbcbbbbaabcaccbcddadbadddcdbaaccbabbbdbdaaaccbbccdcdcadcddaddcabccaddbdadbacdadaacbdcdbbadbdbbddbdcbcbcbcabacaccaadaaadccdadbacdddaadccaacdabbabadccdbadacbdbabadbcdccdadcbcaccbabbdadaadcacaaacadcbaacaddcabacbcdcaacdcaadcabbcababacddbcbcdddbddbcabbcbdabcaadbcdaacacdbbbcbcabdddbaddcaaabcdadcabdbdbdbcbbdcacdadbcbbdddcabcccacdadaddabcdcccbbdaacbbbbdcdbaaddbdcbbdaaabbaabdbbaaaddadccdddccbabdaaaadccaccbcdacbcdcbcbdadcbdbbdccacbddcbbdbcccccaaabbcdcaacabaabcdcbaaabdddddcbcbaabcadaddcbbbabcbcbdddcdadbbcdbdcbbcacccaacbcbadaabbcbcaabccacccccbbdabccdcbdbdadddbadbccabadbacaadabdcbcabdcddcabddcbabbabaccbdaccdcddcccccabbdddcdabbdbbacccdacdcacbacbbbcbcddcdddbcccbdaacbbacdacaddcabcdbbcbbccbcacdadbbdabdbdbdccddbcdbabcbacdbbbddadbbadbaddadbbdcbabccdacbabbadcaadaabacddcabdcdcaacabbdbccdaadbabacdabbdabadccadcabbcbadcdbdcbbdddbbdcbcacccbaabbdadcabbdddcbcbccbaccbdbaadadaccaacbdbcabcddcddaadddbacabbdcbbcabbadadccacadbacbccaacabddbaaddaccbadcdaaaaaccdcbbaccbdccbababbbdababdbdcccbaaddacdbcbcbcddcbcbacbddbdabccaccbcbcdacbbcaaadaabbbcdbcabbdcabddbdbcaaccadcdacaacaacbabbddcddaaaaadbdcbbbacdadbcabdaabbcccdcddcbabcdccadddabdbccdabaddbbddbbdabcbcaacadddadaaaccdaadacaccddadcbacccaaaadaaacadcadcbacbcdabcdaadccbcbcdbabacbcdacbcacddbbacbcbccbbcabdbccadbbddbbadcadcdabdcdddbccadbddbcbddadcaaddcddcddcacdbcabbcdcabcabbdcdbabadddbcddbcabcccbbbccaccdbcddaddbbbbccbcbbddcbabaaaabaaadcbcaaddcbbacbcddaaacbaaadaccbacaabcadabdacaadabaadbcbadcaddcbcddccadaaacaddacbbbcbaaddabbbcdadbcdcdbddcdbbdddbdaaadbacbbdaacbccbadddcdddbcbdcbabdabbbbadbcadddcbbbbdccaccdcbcbaccccddadaadcacdacaaaadaadaddcaabbbabaaaccccdcacaccaacacacbabcbadabadadadaabdcdbdddacdbadbacbdcccdcdcbaacddbdbaaabddcbcdbbacabddabdccccaccccdbadbbcbdbddbcbabdcddcdbcdcbbaaacddcdbbbbacabbdbbccacabcbbcadaaadadcacadccddaaabaddcacbadbaaacdddbddbacdbadbdcbabdadaacadababdacccdcaaabcdbadcabcbcabdbbdbabaabcdbdcdbdcccbbdccaabbcaacadbddbabdbbbdbacbcabdbccbdbdaadccbbcccaccabaabbddccccbaadbdccaabcacaacabcddaddbdcbdaddbaadcabbdababdcbaacabbbccaadababbabbadadbccaadbcdcbabcadaacaddaaadbacdbcdccadccbcccaababaacdbaddcbabaccbdbdccabadadccdccbaaabdbbcacdddcabdbaabdbcaaacdbaadbaddacdcbaddcbbbaccddbcaaccdadaaddbabdabbdabcabbbaadaadaaaaccbdbcccbadbdcaaaddadadbcdbddbdcaabdbdabddcdaabbbdabdbcccdbbcdaddacdcaacddcacadddbacadcbdaddaaadaadaadccadcdabadccabaabbabcbbbacbdadaabdccddcddbcaddabdcbabbcabaccaccacdcbdabaaccbdcbbccacaabbdcacabdcdcddddcadbcbbadaaacdaacaddcbbbcdcabadccccbbccdacacdcbdddadaaaaaddcbaaacbaaabbdcdbcabcacbccdaaddaabaacadbcaaabcddbadcddbbcbacbcbaccacbbdbccbccdddbaccadbdccdaadcbbbbadabdaccbaddcacbddccdaddadbbdbcddbdcdcacaacdcdcbaadbcddaaccaacdaddbbbbaabadccdcdbbbacccdabcbdbbbbdbccbbdabbcddcbabdddddbddbdadbdadbdabbcaacdaaabbacaaaccabcdaaaadcaddbbcadbabdaabcdccdbbcddbbbabdddcacaaccbbdddcddcbbdcaddadcbcbccbcabaacdcaaabcadbbbdddabdabbaaaadbcdcabddbcdbaabdbcaccadabbcddbcadbcacdaccdbdcbbaddddaabdbdbcbddabcdcccbbbbaabadddccdddbcddcadbabdbcdbdcacaabacbddddacdbdcacccbcdabcaaadddbacbaadcddcbcccadabadddbcacaabaccccbbcdbcbdcdcaddaacbdaaacdbababcbadcbbabdabcdbabaddbbbbadddccbbacbcaabdbaddadddcbbccabcccaacdddaacbabbbaccacadcaabacaaabaccdbdbadbaacdadaaaabdbbcaabcacaabdcbaccdaddacbcabdcdaabdacaddbddabadcdbcaadaacbbcabcbdbadbcbccdbbccddcdabddabdcdadbbaabcbbacbbaaadcddcdabadcdbadcdddbacacccdabadcaddbaabcdabcaddcddddbbabbccacbcdaadabbadaadadbaaadaabdcbcbcabcadaaadcccdbaacabdbbbabaabbcaacaccdadbddaabdddbcaddabcadcbacdacaabbabbddacbcdbcbabccccabdcbdbcddcaaadcddbbdcababdaaaababbacddbdabbdbdcddadaabdcacdcbddccdcccbaadbddbdcdacbcabbaaddbddddddcaccadaccababbbdcbccdcadcdbcabbcacbdcdabdbcbcbaababaabaddcbdbdacdbbbdbdaadabaababccaadacbddbddbbdbdcaadaacbbbbbbbcddcabacadcccdddcddacdcacaacaddbbdcaaddcbccdbadbcbcacbacacdacdbddbdcddbcddbbdddcdccbcabcadbcaaddacbaaadacdccbdbacccdadbccbacddadbacdacabcdbdbbabacacabacabcddbdacbcaacbadaacdcccacdbabcddcccccbabbcddacdadbcadcbcdbcacbccabdacdacaccccbccacaabdccaaabcbccadbaccbcabdbacccbdcabdbbcbcbdbcdbdbcacadacdddcdbbcbbadabbccddccabcdabcbcccbddcabccbabcddccaaaaccbbdbdbccdaabbdaddccdaacdccdcbddbccddddcadcaaadccdbdbccacaddacdababadacbdbccddddaacaddcbbccdccabcacddbadacccccbaddcdaadcccccacbcddbdddabcdadbbccbbdccbdabdcadadbbcabaadacddddaddabdccdacdbbbdbbcccdacdbbbbdcbacdddcacbadbdddcbaaabadabcbadbbdbaacbdacbdbbcabcccaddaccaabbddbcbbcdbbababbaabddcadcadcdccdabccabcbabcabbbddbdccbbcccbbcbabaadcacaddbbcbccbdbccbcacabdaccaaccdcbdadbbabaabbdabdbbcdcdbdbdcacdddacbbbaabacbaddcbcdaddacdaadbacabbdbbccdcdcaccaadcdcbbdcdadabdcbbaabdadcadbccbbcbcccabbcadddcbadadccbcabdcabaabacbddcadbdddbcadadcdcacbccbbacaabcbcadaabdccbacabccdaaabdccbacbccbabccbdddcdcbcddacabccddbbacbdbdbcbacdaccaccababcccbddbcddddaccaccccbababbbcbaabbdaaabdbbdccbacabdbdcdcadccdccddaddcaccababbccbdbabddddbcdbadbccabaacdacaaccaabadcdbcbcadaacdaddbdcbabbdcbabddacbbadbbccbcbaaaaccbabddccdbdadbacaaaabbcbaaabcbddcbccbddcacbadaaddbdcbbdcdbdcdbaaabacdbaddbccadcdaddccbabcadaabcbcaabcbbabcccccdadacaadacbdbabacbcdddacdcbadadaaadbadddcabdacabacdcddbbbbcbdbdbacdbddadacbbcdcdaacdaaabbdcabaacadbddadcacdadaadadbdaccabaabccbcaabcbacbbbdabbbcbbbbadddcdaccbbbbaaacdacdaccbadadbdcbabbaacdacccbccbdbdbdbabcbaabcbdcaacacdddcdaccbacacbcbacddbdcdddbdbcbcdbacabbbabccacccbcaabaabdcbbdbbdaadcacadbbccadadbddccbdcdbbbdbbdbcdbdddddbaddbadcbcbbdcccbccdbcdccabadbddaabbdadbabababdaacbcbccbacbcccbaabaaccabcdaaddacadcccdadabddccaccdcdcbbccddbbbbcbcdcccbdbdccacbabacdddaaaccdcdaacbcdddacaccaaddbcaabdbdbbddaacccbdbcdccbaaabbcaaddddabdcbadbcccdabdadacbdbbcddcdacbdacccdaccbcbbbadddcbacadbaddaccbadcadccbbbcaaaacacaccdaaabbdbdcbaaabbccaabccbcdacbbbaadbaadbadbadcddcdcbbbabacaabdaabcdcbbbdcaddccbbccacdddddbdcbbacaadaaaabdbcaacbdccccdadcdbbdcdcadcdbcbaaaaaadbdabccccabdbbccbddabaabadddcdcdaadbbdcbdbaadabcabdabccadbccaacaddddddaadddacdcdabdbbadabdabdddbcdcacbbaabbddcbcbdadabdaacbcaddddcbcddacbadcbadacbbbacacabdcbabcbbaccdaadccbdddcddbacdcabbddcddcabaabccacbadbcddaabcdaddcadcdcaaacddacbadadbabdbdcabdabbccbaddbbaabccccacadacdcdcdacadcabaacddcacbcdacdaaaaccdcaddbadadaacdcbccadaddbbdcaadbaacabcabccddcbccddddbcddcabadcbbcdcbbdcbbcbabbbcaacaddcadcdcbdcbdaababccaccdaccbcdddddcdaddcbcccbdbabdbaddbadaadbbbaabbaabdabcbccaddbdbbdbbcbccdacddbbcabcdacbbddacbdbdaabdbbacdbdaccdcdddaddbdcacadaacaccbacbacbbbbbbdccdadcaabcbdbaddccdadbbadcccadcbbdddcacadbbacbcdadccacbabacdbcdadaccdadcacbcdcdcaddbcbdbdbcdbbcabcacbbddbcbcadaaaaabdabadccacaacddbcacabaabbcddddadbaadaabdacaaadccccbbdaaacddcdccbbbcdaabcbdcaaabdbccaaccbddadaadcaddbabcbddcaaadcabbbcdbdadcaddcbacabcbaccadcdadaababdcddcabddadbbacdbbacbdbacbdaccbbdbbaccbccabdcacabacdacccaacdbdadbdcacadacdbcdabbdaadbaaacabacacdcabbaacbdcdadcdbbcddadcbadaacccbdddacbcdddadaddbdcacabdbccbbaaccaabbdbcdadcabbabcdaabcdddcdddabcaccaccaccbdcbdcddbadcdddbcadbddccdaaccbcacbadbadbaabaabaccacdcdbabbcdacbddbddabacccaabcdcacacddddcbbbcddbccdbbdcdbbacaaacdacbbccbbbaadbadcbdabbdbacbaaacaccdccadbcbdcadcabbacdbdabdbcdbbabbddaacdaddadadbbabbbaccccacbbdcbccdacabbddccdabdabdbdcdbdaddcbddcdccdadcaacaaadacddadcddddbbdddabccabdcdddabaacccdcbaccccdcabbcdadcadcbcbadbadddddbbdadddadcdbadcbdcbbadaabbadcdbaacccaaabcbddcadabacdbdaacaabccbcaacdcaadaddbaccbdbcadacbadbdbacbaddcacddccadadcbaabdbddaccbbbbcbdbbdbdbdabaabacdbdbcaabcdaaacadacddacbaaacabaadbaacbacddbbbbdcaadbdcbcbabdddacadddddbcaadcabbdbaaabadabaccaddcccaccdbccbacbacbacddaabcbaddbcbddaaacdcaccbbadbdaccbcdcdaccabdabaabcacbaaddabdbabcccdbadccdaaaccababbbaddadadcbcdacaacdccbdacaadbcdcdccbbabbaababbadbbdbcbdcaabcddabddddbaddadaabcdcaacacacabbcbbcbbcdbccbdadadbbbabcaccbccbabdbdcaccdcdcacdbdcdddbcbbdcadcdbbbccabcabdccbddccadccddccaaacbddaabadccacbdbbadaabdaacddbccdcacaaddbaddabdbdddbabadddadadaacddcabacaadcaaadbcdcaadbdaadddbdaddbdbaddcacdadcddcbbaacbaaaadcddcababbdcabdabbaacabccbdccbcccaacdabcdbbbcabdbdbdbbaaccbdcdaaaaccabaacddcacccbbaaaacdddcacbbdcbbbcadbabaabdbacaaadcdcbdacdbcbbbdcddbababdbcaccbcbddccdbababcadbdbacbbbbddcbbbcdaabbdbcacaacbcadabadbdcbaaddcccbdadbcbaaccdaddbadabbbbbddcdcaacaddbddadccaacabaacabadbbcddbdbbcaacaadabadcbcabdcdaddbbbcbaadcbdbacbbcccabdcacaabbbadbaaacadcacccdabbbabcbdbdcbbcababcbbadccddabcbbdcbcddacaaaadddbbccbccbaccabbdbccdbabbbaaacaacadadabbaabaadddbdcccddbabadbaaabdbbaddbddbaccadcdbdcdbbdcdddaaabddaabdadbcaabdcbddbacbcaccdabdbbdcdcdaaadaaaaaddbbbbacdcbaaddddcddbbddabcddbcdcdbdcaacdbbbbaccaccbbcadadbddaccaaaabbdadacdcbddcbacbccaacdadddaacdcbddccddbcabadbddbcdadadacbdaadccdcbbbcdabcdcdbbabacabbaddadbabcccdaadabbadbaccabdadbaacbddacdaddcbdbaccabdbccdccccddcdcbcbaddadcccdcadbdcabccabcaacdbababbbdcbbaacdbdbdbcdccaabdddbbaabaaadbabcacadabbcdbbbcbacbdacabdaabbcaaabdbabddcbbcddaadaaadcabdaddadcdaaabbaccddbadbcaaddccbbacdcbbbbcdccccacdadacabdbbbbcdbbdabbbdbabddcddadcbabdaaabdccdaacdaccbccdbccadaacdbcbacabacccccbccaadcbcacbccabcdcdadcaabcacdbaaaccddcccdbcabdcaadacbabdbddadbbbbcddccbcdcabcccdaabadcccddabadbaddcabcccacdcdbdbabdddbbcabccbabccdbcccbbdabddcbbdddccbddbaccbabacddcbadaddcaacabbababadcdadbacbdbbccbbabcbbabdbaddcccddcacdbcdaddccbbbbcccaabbcdbadcaccdadbaaaadabbcddbcdcdcdbcaadbaacdcaddcdcccdbcabbaaccccbbcacdcbdcccbbccccaabccbbcdcadbdcdadbdacdabbcaccbaabaddadcbdbcaddbcdaacbcbbccdaadbbbbbcbbdabdabacaabcdcbccbdacccdaddcaadabdbabbccbccdbdcaccbdacbcacdcccbacccbbdccaccbcadcdbacabcbdcccdbaccbaddbacddaabcacabbbbdddacabccdcbbdbbcdcabcbbbcccccbcadbccaabadadccdbdbdddccabbbdbadddbaaabbdbbababbdaabaaaadbdacdbaddbcdabbdbbdccccaddabcabacbbaacbbbbabcacdadccabdcdaddccacabdcccdcccacbacbaadcaddbdbbcbaaccdadbaadddbaddccccaaacddaacaacbccdacbadbaacabdbbdacabaaaacdbcccddcdccddccaccaabacccaadcacbccbbaacdddaccbcbbdbacbbdcbcbccbbaaadccadcdaaabcacaacabdccbcadbcbcddbacccbaabcbbcdccbabbdacccdaabdacbbaddaadcaaddcbcbabbdcdbabaacbccabdbccbcbbbddbadbbcddbbbdbacbbdcdbdccabdcdaadcaaabcdbbadbbaabcadaacbacbaddcddbaadaddabddbaacbcacdadbdddcacdbadabcddbabdbbabadcccacdacdaaacddaaadadbccdccbcccbbdadccdddabbbcbcbdbddaabaaddcbacbbdccddcbcbdacacbdacacaccabddcdbbddaadbdbdaacabcaaabdbbddaabbaccccdbabbabbbcadbbdbcdcabbaadddbbcbccbcdcbacbadbcdddabdcacccccadcadacdacabccccacccacaadbdadccabbbcacdcadcddbdabcdcaabddbbadabaccdbbccddbaaacbcdadbdadddbcaadcdccdddbdabbbabdccdccbbdadcbbbdddbddcdccbbcddddccbbaddbbacbbacdbacccbddbdbaccbcdbcbabdbccccbacdbdbdddaadddbdbccbaacaabdaddacbdcbdbaddcdabcbddcbdbdcbbadbcacbcbccabcdbdbbdaaaaababbadcdadbccabbbabdbdabbabddacccdcdabacdbcddbaccabbdadbcbccdddaabcadbdaddabcdcbbaabcbbbcaddcaaaacaccaabcaddcdbdcbddadcbbadddadbcaaabdababacdbaacdcdbccdbcddddcaddaccccddacbcadbbbaadddaabcbabbabaadaccaaaadacdbdaaccbdcadbcaabccdacccddddbbdcbbdadabaabbbcadbadabdcaddbbdbacbbcacacabdabaabaadbccdcbbdddcdbadbddaaaccbadadbdbdbcdcdbbcadcabaddcaaacdacaadabbdddaabacdadcdcaabcdcbbaabaabdbbbaaabbcaacddaadddaabdddabcbaaadaccbccdccdadbdbcccdaaacdbdadbbdcabddcbacdcdbbccbcbaaabadcccddacdbbcbcabaadcddabcbddaddaacddccbaddbbadbdabdaccccaabbadbbbcbddbadbccbabbadaabbaabbabacadbaadbcdddbbdcabdacabcabcccdabbacaaddacbabdbcacbadacdacaaabcabdddbacbaadddbbbcaaadbbbabaacdcacbbaacddbbaabbbdbbdadaddcdabccbbbdbdaadccadcacbcbcababadbdaddaacbbcbbbbdadaaccdccbcbcaadcccbaccbacddcccdcacdabadadadabdbabacccccdccbbbadddcaadaaaddadaadcbccbccddcccbcddcdacddcaabadddbcbbcbadbaadcdbbbccdcbdaaacdbcbbbabbabdcaddddbddaaadaaadcbbcaccbaacdabdbcadbbddabcdccdabbbdbbaabcdbbadbcadabcbdabcdbcdcddbaadcaddccdacbcccddcccbbaadabbbbaaaddddddbdddcbababbdcbaadcccdcaccaadddcdbbccdacdcdcbcbbbcdddcbbbacdaaacadbbdccaacbacdcbbdadaccdcacbabbbccbcdbcaaabbdcbccdbdaaaccabdcbbbabbddbabcbbcdccabaaaabacaccdbdaaddbbcacdaddaddbaaacbdddabadcdcabcacdbcacdbcdaccdcdacabaabbdaaadbadbcacdcdadcadbacddadabbabdadbbabcdbccadcaacbaabbabaadbcbdbcabdadabbbdccabababaadcdbbabdbaddbccccacdbbdccdbacccbbbbbaabbcacdacabdacbbaabbabcbbbacdbcacbaaccbabaadddbadadbababbcbacbbaaccccddaaadcdcddacccbadabbccaabbccacdcbdcaaacbbcacdbbcbabaadbbbdadddbababdbbcdabddcdabaddbabddaacabbcdbdbddaddcdcccdbcabbcdcacdbccbccaaadbccbbbacbdbcaccacbdcdbaadcbbadacbaadadddaabcadccbaabbcccaccbadabdadabdbbcddbbcccddbdabaccbcadabdbdcbccccbcbdacbcbdcadacdaaacdbbbcaddcdddbbcacaaadcbadcbbbddadbbdddaccaadbcadabddcddabaaacaacdabaacdbbcbdddccacacbcdcddccdaccadcdbdcbabdddccacdbcdaaccdddbcaababbcdcdbdddaddbbbaddcbcacdbcccdbabaaddcdcbccaababbadddccabbacacadadababdaccbdacaaacdaddaacadccabbbadaabacacbddabbdacbdddabddccccdadcacdcdbdccacaaacdcbbcdddabdbdccabccbcccbaaddacbccaacdcabdcdcbdcabcbbdcadcbcdabcbaabdcbabcdaddadabcbcddcacdbbcaaadcdddbcdbccbcddbdcdabaabbdbdadccaaacdbcdbcbbbabccadccdbacccabaccbabbdabdbcdbdcbcabdabcdbabdcdaaacadbcbcccddbdacddbcaccaacabdccbaadabdcdcccaaddcdaaaaadaaadcbabdabccdbcbbadbbbbdadbcddccbcddbadbaadbdbbbcaaaaacdabcadadccabaadcdcadccbbbaabacbbcabdccdacaabcaccbddbccaaddaddbdadcccccabbdcadcadaddcccadabdbdcadaabbdccccdccacbdbcdbacadabaaabbcdacbccbcbadaaacbbaacdbacadbddcaadadcbdcaadbbdbdcbbcacaddcaddacbdbdcbbccacacdbaadaccadbbddcabaddacccaacdddbababacdbdbcaacacbcdabcdcbdcadcdcdbacabbbccbbabbaaabaabbacddcbcababcddcadcddbdabcdacccbcbaacacddbbbcbabdaaccadccbabbbaabcadccadcacdcdddcbcadbcbdbbccdadbbaadcabdabbabadccdabdbddcadacdcbdbdadcbbdbcbcdcaadaadbbcaaacbaabdcbabbcccdabdadaaacaacaacababaabacbccdcbbdbbddacbadcadadbcabbcacacbbdddbbdcbddccacbddaabdacbdbaabddcdcabcabadcbadadabcdbbadabddbaccdddcccccdadadaadacaddacbbbcdcbcabccddcbaadbaccaccdaadcbadbbaaddcdabcccabaacaddbdbdcbddccdbcccdaccbabddaaaccdbbabaaababbbacbcbabcaacdbcdbcaaaaddccbabbcaabbdadbdcaadccadcbdcbdbbabacdcbbcbadbadaaaabbccbcbaacbccddaaddbbdcdcadabdacdbadddcdcddadbbaaaadcddcddadbbdbdacacbddcbddbbddcacbddaabbcdacbacdbadcabacabaabbdbabcabadabdccacccbdaaabcbadbbddabcdacdddbcbcbbabbbbcdaccabcaddddcbdabbcaacacbaaccabbdbddbcacdbbcdaddacccdacdcdcdbbadcbbcbabcaaccbbbbabbbcbcbdcbcbcabbcbdbaabdadbccddbabbaacadddcbbdbbbadccbbadbbcbbabdbcbdccdcccaadccdddcbbccacadadcbccabacabdcdcbdccdadaddcddddddbadbcddaadcbacccaadbbdaaacadcddddbadadaaccdcbdbbcbaaaadbbbcbaddbdbaadabadaaacbbcaabcccdbaacdaaadaaaabbbddddaccdbdbdbacdabcbdcbccadcccbcccbdcbabbaddcbcdcaddbbbbccddabbcabaaddcccacccbbadbacdcdcbbbbccccbadadcbdaddccabcdaadbdbcccbadacaadcccccadbddabaacabccabbcabacdcdadabbcacbabbbaacaddcaddbacacbcbbcbdcaddccbcbbdcccaadbcdbbbaabcdadccccddadaaaacaadaddcddaacbbadadabbadacaadadddbdabcbbdbdcadaadcdcdabcddaddcdabbbddbdddcadadacabbbbdccbdbabadcbbbabbadbddbcdadbcaddbadcbcbaaaabccddbbadaacbdacccdbacdacbdacaadcdaddbadbbddbddcaccccbdbaadcbdbacddabddcababdbccdcdacdccaacbdadcbbcddcadcbbabcbdcdbdbcdaadaacdbdaadacabdbaabcadcdcddcaccaddccddadabacbacbdaaabbacbadddbbaabdbbdbabccacdcacaadbdabaddccdacdbcabccbbcccbcbadbccbaddabcddbabcbaaacdadcabaacddbccddbabaadbbdabaabcaaddddacaddbcdaaacccdbababcacaadbbaabbccbdcacddbadbbabccdaaccabccaddccbddabddbdbabcaccacbcababaadbbbdadcddadabaddbbccbdcccbccbdbbcabcbaccbbbbbaaaddbdccaddcdaddbddbbdbaabdcadbaadcadbdaadbdcbacabcbcddbbddccbcbbadddabdddcccbddcbaaabcaddadcaadbabcacddddabdbcacadbdcaabbcbbccbdbaddcdbadbbcadbbddaabbcdbccacbcaabdccdcdaccaabcccdddbbcdaddcdaacbccaabaccbbcccbbbdbadcbaaacbbbcbbdcaacadbabababcdcbbadccdcabbcadcdacbbbbcadbadbcbccbbacdcbcccabbddbcbaadadbbacbcdcbdadbdccabbcddbbcdbaaabadbbacacdaddccabbccccabdcabddaadddddbbaccdbcbdbdacdbdbbaabbdbbbcdabcccdcbdcaadcbbacdcabadabcccbdbbcdacdcbdccbbacababadaadcaddcbdcdabcadbacdabacbbbadbcdaaaacdbbcacdabcadacdbdbabcbcbdcbbbbcadabbbcaadcbbbccacbccbacbdcdacdadbadbbabbbddcbbbbbcddcdadcdcbbabbccdbbcddaacaaddddbabdacaddabddbabaacbdcdcbcbaddaacadadadbddcbbbcaccddaadcddddabcabbcbbcbcdbdabcdbcadccbbdbbdabbdbdbdaabaadabacbdcdbdabcaabbcabbdcaabddbcbcadabbcdbdabbddaddabcadacabbadbddbcbcdccacbcaaccacddbcbdbbcdccacdbcccdbbbabdcbddbaddbdbbdbdacdddadccbbdbdcbdabcadaddbacbcbcdcbdddacaabcaabaadacbcbdcdbddcbabdcdbbbaddcccadbaccabbdadbbccacbaacbdbcccccbaadbcdbababcadcddcdbbdabccabbdbdbabacbccacababcbdbdaaaabaacccdaacdaaccbbcdacadccbcccbccdcddbadddddddcacdcadddbbaaabcbbdddbdcdbabacabcaaaabddcbdcddcbcdaadbbcbddcbacdadddaabacadbbcdcadccbddbddbcacaabdddbbdcbdacbacddaddbacbadcbcccbaadccbaddcacddcbdccbbbcbbbddacddbccdadaddbaadcaabcdbbaabdbddbbcacbbdaaccddcbddcdabcdcdbaacadcbcbabcdbbaccdababcdcdcbcccdddbddbadcbccabacdbdabddacdbdcdbaadacbddccaabdbbbabaaddcbdcaccdddddacbcbbaccacdccbabaccdcdadbdacbdddaabddddbacbcddbcbcadbdabddcbddbdcaabcbaacbaabbddddaddacdcbaabdbbadcddbcabbbbdcdacbdcdcaabbbcbcbcaadabaddbbbcbddaacdbaabcbcdbaddbccdbcbcdcbbddaccadbbddaacabaabccacaacddcdcbbadcdacbbcacbaadbdaddbbcaacacaddbaccbaaacbdcdaaddcbdccdccadbbdddacdbbcccdadccddbccbcbddadcdaacbadccaddacacabbdbbdabdccbbddabccadbabbcdbaddaadadbbdbccbcdaaabdaacbabcbaabdcddbacacddaccabdcabbddadaaddbcbbaabbbabccdaababdaccbacdaabbcbdccbbcacacddbdbddbadbbaacbbcabcccbaaddadcabdbcaccdcbdaabccadbdcdccbddaabbaaaacccdacbddabaccdadbcccdcdbdbdaabaacdccaccbccbaccacddccaaaabacccaabccaddacabaccabbbbccacddaccbdddbdbabdcdddbacccabddcabcabbddadcbbdcbbbbcadaabbbddddbcaacaddbaaabacbbaddabcdddcadcabddabaddcbdbadabcaccdbccdbaacdaababbadaaccdaacaacacdcaccaadabcbcdbbdbcdbdbdcdaccbbaaacbcddaabaabdbdccbdddcabcaccddaabdadacaddcadbcdabbcbbbbcdcaabcacdbaabbcdcdabbcddcbcabababcbdaacbcdabbdbcbcacabccdcadbbababbcacdcdabbaccacbcdbbbaabadabcabbccddaadcdcaccccdaabcdbdbcccccacbabdadbdcacbbdbabbcbcadbcbdbdabadacabbdbbcccacdaabbbdbdaccbdacacddaccbdabbbadccacdcacacbdaaadaddccbcabcaddcbddaccdcbaaaccddcabdcdaaabbdbbdcbcddcdccdbaddadabaaacaddddcbabbcabacbbdccdbdddaabdcdbadabcacadaddcbbbaacdcdbbdacaabcadddbdcdbdbcbbadcbdabbcbbbcbbacdbbdcdbbadcadabddbcbcddbadcacadaadbcabadbdabcdbbbbccdaacabdabadcbabcabbaaaacdaaadaabaaabcdaabcaaabbcdbcdaabddcacacacdabdcbbcdbabcccaccaabbcbcabddddbdacdabcbbccbdbddacddcdcdbddcbaddbcdddbabdbcacdaaacccaaccdaddbcbbaabadbabddcacaaacdcbcbcadaaabdbcadadcadbbbdaadcbcdabdacabbbbbcbddaccacacaddadbcaacdbcccacbdadccadacacdcbcccbbcaadadaaabadbccdaabbdddcabbbcaddabccbbcdaadcbabbcbdcbcbdbcccddaddbdbbbbaccbcdbcdcaacbddcaccbcdbcbdcabdbddcbabdccbddbabbbbbaacdcdababbddddcadaacbcacbabaddaccbbcacdadadbcaccaadaaaccabdcdadbdbbaddadaadbdbbadabadcdbcbbaababadccdccacaacbaddcddddbbdccdccbcadadacacaaacbcdccaccbcddcddcbcbdbdcadbaabbaacaaaadcacabcbcdcbaddcddadbdcbabaadaabcdcdbdcabdccbdbbdcabaccadbcbcabcccddcddcabdbdabadaaabbdcccbdaddcbbacdcddcdddbddbbaacdaacbbdddcaccacaaaccbccaadaabbcaabdbaaaccacdcaabbcdacbabccbcadbbadbbdbbbbcdaabccaabaddbdaaacabccdcccacbdcaddbdbabbbdcccbccdcbacbcaabdadcaacbdaaaacbcdaadcacbcddcbbcaadcabbcbdcbbaadbdbcddadbddbbbbcbabaacaccabcbadccbbcabdcaacbaaadaacdadacaaabdddbbaadbacadcdcbbbaddbcbdccadcdcabbbcaaaabbbabaccacaacbdbbdbacdcabacbacbadaabccbbbbbcabbcabadaddcaabdbacabdaabddbbbacdaaccbbadbacabcdbdaababbbbcdbabdddaadbacdacdbbbaccbdbabaddddbdddadbcbbacaadddddbaccddababcdcadcbdacbcaabcdbdbacdccbbbcdbddcacdddcbaaabcdbaddadddadcbdabdacbadbbbbcbcdadcdacdaabdabdbacaacaccacbaabacaccabdddbcdcacbccabbdadcccabbaaddadbacdbdcddbcabdbbababbdacbabbdaabbcbabdadbcbcabbbaaccbaadaccdadccbbbbcbcabbacaacdcbaaadcacccabaacbcdbdbacdcaaadacaddcbbbdddacbacbcaaaccabaccddadcbabaddacbbcbcdbbbddbadccdcccacdaabcaadacbcabccdaaabadcabacccdacbdaddbcdddcacaccdcddcdbddacbacdbddaabacdbababaabaccadbcdbacdaaacbcaaccbcbadacbcaaddbbacdacacacdccddbbdddbaddbdbdccadbcaaacdcbdacaadcdbaddbacbbccbbabdcdbbdbabdadadaacccadcbdbcbdababbddbbcbcbcbabaacbccbdabcbbcbcdaacadbddaadbaabdabddaaabdbdaabbcacdddacbbbcdaadccbcbdadcacdcbadbaccbabcbccdbdcccdabcccbaccdcddbbbdaaddbbcbbccbadcbccdddbbdadbbaaaabddcdcaadbcbcbcbbabdddcdadaacccacbcdacabcdbdbcacaaaccccacabacabccacbbadbdcbccdbaaccbbacbcdbbbdaddadbdbcaabcbbaadabbacdbcdbacadbbadbcacdaabbadbdddbbdbcbccbdaadcdcadaabaabcbdaadbbcadcddbcbdadacabdcddbcacbbddbcdcabcdcdbccdccddcdcaaacaadddddabacaabbbacddcdabddababcddbcdcabdccadccadccdbadaddddcdaddadbaccbadbcaccccddabdcbaaddacabadcacbbcbdcdcaacaddccacbaccbdcbabdbbcdddacdddddcababacbdbaabadbccddbadbbdbbbdbabddabccacabdcaccadddcaadbcbcdbaabcadadaaccbddbacbdaabadadbadbccbcbdcabdadcacdabdaabccbcdbbbacdaacbdcdcccbaddabddaadcddaaabccdbcddcddbcddcadcbacbbdbbdbbcabacddbaacabdbbadaaacadccccbbcaccddccadbaabccdcbdbadbcdbcaadaaddcdbbaaacdabaabdcadbcbccdcaacdacbccbccdacadcdddacdaccbcbbccacacdcabdccdcbbdbdaccbdbcaccddaacabadcddabaacacacbacdccaaabbdcbacddddabdaddbadaadaaccabbaccdabbdadddbdbcbaccdbdbdccddccbdaddcbbabacbbaaaadbcabddacabcaabcccbccbadacbddbcadcdacaccdcdcbbbbbddacabccbbccbacbdcdbbadcaadadbdabdbbbcccdcdbbdddddbbbacdacccdadddacaccdbbcbadacdccbaacabccacdadcaadbabcdbcbcacabbbbcdddacaccdcdaadcbdcdabdabdbddccdcacccadccddccabdaccabcbbabdbabddcadacbcdbcdbaadacaaacdcbaadbcbbacacbaddccdaadbaccdbccacaddcbaddadbacabdabbdcabbdddcdbdbbdcabbdbdddcbabbcbddddbbbaddaaadacbcdccbccacbabddadbaabdddbddacbabbbadbacbaaaacdaadadcadbbcccdadcacbbcccabcdbacccabdcbacccbacadadddbbaacbbcbcdacbadbaacacbdbbaabadcdbccadcbdcdadccacdaddbddbdccbdbbaaddaccdcdcdcccabaaddcddbabdbbbcaabaddccbaaaabbcaaabddaacbbbadbbdabccaccdbaccbbbabdcddbbccdbcdcacaacbcdabcbccbbcaccbaaccccdcbadabbccccabbbcabadabcbddccaadbdcbbcbdcabaddaadccaccdbcadcdcdaccbdaddcdacbcbdabdabacbabcdaaaacccdcbcbacddbbdcbbbaabbbcbabdbdbbcdccdbccddcaabdbcdbdbabbbcbcacaddabdbbaabdcddacbaacaabacaaccdabacaabbaddaadacbbcbbbccdcbacbccaddddcbbbbaacdcacabacababbadbaabbcacbccabccdcaddcbddbaadbdcbcdbdcdacddddccddbccdaccbddbcdadbbacddddcdadbcabdcacadddbabddbbccddcdaabadcacdabcbadaadbbbadabdcdabdcdccbdbddcdbacdadbcdbcbbdbcbdcbcbcadcbbaccdbadacccaccdabcbbdcaadcdbaaabadadabaabccdacacddabccbdbabbbaadcaabbbbcbddbdabcabaaadbdaccccdcdbdcddbdacadacdcdabdcbddabbabcdaaaadbadbcbaadcacbacbdccdadccbaacabdadbbadaaabdacaabcddcbaccacbbadabdccadcbdcabccbbacdbbdadbcabbcdcdddddcbaabdbddcabdbcbccbbdcbbdcdcbcdadddccaabdbcccadccabbbcbdadacaddcbbabcbcaaccbcdcbdbddddbaabbcacddbdbaabbbaaaabcbddbbcbadabaaaccadcbaccaababcbdaabbadcaadadcadabccbacacbbbaacbacdadddabcbbbdacadddaabacdadbbabdadadacbcaacdcccbbacbcdbadcddaaccddccaadabdababaaabaccadacccacdbcdcadcdaddcddcbbddccbccaacddbaddbbcdacbdadbdbdcbdbdabbddcabdccbccdccdacacacccddcabaccacadbcccddbaacdddacbcbbddcabaacbcdbcbaddddbdbbacaddababbdaaccbbcaabdbddadabbaadadacbcccabcccdbcddaacbbcabddaccdabadabddacdcbadaddcbabbbabadcbdacacdbdcbcbdbcacacacdbbdbaaabddddcabbdcbacbbdddacaccaccaabcbdbacdbddacdadbcaadbdbabccadcacaaaadbdccdcbcdbcdbadacdcacdaccddbcbacdbbaabbbbcdabcdcdaaaabcdabdcdcdbadcbdaacdabcbccaaaaaacabdbcbdaccacacdbacccacbbddcbacbbbbaaadaacddacdacbbbadabadbbbcdaadbbcddbccbcbabdaabaaccbdbbcbcdabdbdbaccdaabdadbccadcbaacccdabbbbbbcaabbdabcddaababcdcacadbdabaddbddadbaccdcaadbbdbdccdbddccabcaccdbcbdadabddcdbbdddacbbdbdadabccbdadaccddcbcabccbacadcbaacccddcbcaccacdcbcacbdbdabadcdddbcbcaabbdbcbccbabbdccadddbdcacbaacdcadadbadbabbddadcdccaaabbbbdcccabdbdaccacbbcdcdacadbcdbcbcbadccdbdbcddaadacbababddacccadcdaabadccaadddabadabcbaddcaabccdbdbdabbbdbddaccaabcaddaadadcacbacacddaacdadddabcbdaaadbcccdbdbadbadddbabcadcbabaddcdcccaccbcbbcbcdabccdacbcccccddddcccddccddbcaabadaacbbbcdcbcbdbbdcbadccbdccdcccbadabacabacdabacdbdbcbabbdadbdadcabccbbcdaadaccadaadbdbdcdabbdaaabaaddaabaacbadcbcaabccacadcdbcbdbcaccbdbdbbbddcdaaacacbabccaddbccacdabbbdbccaddbadccacadcbdadccccdccbadacdbddadcbcbbbcdbbbcdbbcbbadbaaacaabbabddbbabbacbabbcbabdddccbaacdaaadbbbcddccdddbaabadbcccacbccacbcadbaacadbdbdacddcbcbaadbaacbdbabddaababcdddbbbcdbaaccabcadbdacabcaaccddbababacabacdbbaabcadcaacdbbcbccbddababbdccbbcbcbbdadaddaaaadaaaadbbcabbbccabdbddaaacaacdacbcaccdbbdacccaadabdcccbaaacbcbcdbbcdbaacaaaaabacbabbbbadaaabbbbcdadaadbbbdbacababcaaaaccddaabcccbdcdaacbccdbdacbababcdadcdcbaabdcaacdbabdacabdbdaddcbcbbcbdbbcdcabbddbaabbbbcbddbbaabaaabadbbdcddcdbacdabcadcdabaccabdbcdababaccccadcdbdbdcaddbbabbaacdbaadbdbabdcdddbcbcbdccaaddcaadcaadaccadadaadcabcddbcccddddcdcdbbcbbbbaabccbdadacddbbbccdcbbadcbdccaccdcaabbbdbbbcdbcdadccbaccbcdadbdbdcddacbbbdcaacaabccbcacbacbbcbccabbabdcbdbcbbbbcdcddbbbacddbacbbacaddbbadcbaaaabbddcbbcbbadbabcbbabbabccaaadcacccadcdbccdbbbcadbddbbdbadadcddaadccadadabaccacabadddcbbadbdbdcabdcdccadbbaaadacabcddcadcddcaabdacbcdacdababdbcaaacbcbabdabbabdadcbcddaaaabadcaccadbddcbabbdbbbabddccadbddbbabdaaddccdcbbdacabaabddcbcaababdcbbcaddadabbaabcabccdabdcbadcadbdaabbabdbdddababaccdaddadcabdbdcdaaaaccbadcadabaaadccadddbaaadcbdcbbdaddacabcacabaabdbcdaddcadcbbdbbcddabddcacbbcbbdbdabddaaacabcdacddcbdcbacccbdbbaaaadabadbaacdbcbadabdbbdccadcbbadcdcbcadbccbbbdbccbcccbddaabdaaaadccdabbcccccdbabbcabbadaadaabbaccbacadabbdadaaddddcabdccbdacdacbbbabcbccdbdabbdccabbbadbbaabadcbddbaddcccbbbdcdccccadddcddcdccbdbacddadcaacddabbcadaddacbaaabacacccddcbccdbdccacdccaddcaadddcacacdcddabcddabcbcbcdccdadbbcaacadacaddcdadbaabacdabddabcdcdccbcdaaadccdbabdcdbcccacaccdaccbbbcabcbaaacadadddacabcbdbcdcbcbdcabbdadbcdaabbdcdddcbcddaacdbbbcabccccaaccdcaccdbbdbdabccbcbcbcddaccdabdddbdaacdbcdcaddbacbadacdaccdadabcaabcadbadbccadaabdcbdccdaccbabadacaabddbbddcddcbaadddbcbbcdddcbaacabbccaaddacacdaacbadccbacbbababcbaacacdacabcabdcadaaacbadbcdbdbcdaddbbbcddabaccaacaacdcacaaacacadbaaacdcbbabaccdbbddacadbacbadaadccabccabaababdbdabcbdacaccdaaabcabcbcbcbbabcccabdaadbaacbdaacdccbcdaadddbdacddccdcabbcdabcabcaabbdbabcbdacbdaaccdcacacbaaccdcbcdbcaccaaccbccadccabdbcdcaabadcacbbababaacbdcabddccdcdadcbddddadccaabbabbcdccabbbdbcdaaaccabbcabbcbabdbccbcbcbcbadacbbbcadabbaabcadcdcdacdbdaaaddddddccaaabbcdadbcbdcaacaabcbdddcbaccadddbdbbbabdcabaadbaddaaccbbddbbacbbdabdcdbcabcdcccccabadacbacacbbabcbbcbaaacccbbdddbdddccaccdbddcdabdbcbcdbddbdcabddabbcdabdbbdccccadbdaccbaaddbdadaaaacdcbcddbdbaacaadacbabdaacaabddddacbbcdcdddaabcacbbbacbbcdbdabaadbdcdbbabacbacdadbdcbbdaaaadaadbbccbbdcccbbcdbcbbdaabbaaccbdbcbababbccaadabbbccdabddbcccabdccabbbdcaabcdbdccbddccbcbbdcaddbddddbababbcccababdcbccbcbaccabbbabbbaccbddddccdddabbdbdadbbdbcdbcdacdaddccbabbadbbbbaadadddabcacaddccacacddadcdcbaacbddbdaabbbbacabdddddacdbdbbabcbdbbbcaabadbdacdaabaababaddbaabddbcddcbdacadcaccbddccdcaacdabadcaadcadadbbbdaabbdddabdcadabbbbbbcbdcbcbcccadbcbcbdbadacbadcbcbbcdadddddbdbcdddbacbccbabdbdcdabbbbdcbabbcdabbdcddcbabccaacbadbbbbacbbcadbcccbddbcccdbbbcbcdddcbccbcaddbaadbcabdbddababddddbcdbccdcabdaaacbbdacbbbdcababcaaaaccabcdcaaabcbccdacdabddcbaddbaabbacadbaabddcacbbbcdcacbcbbdcdbbaabaabbbbbbaacaaaccdcdacdddaaaacdabaaddcdaadcdadacccacbdbacaacbdcbbaacddddcdcdcbdbccdccbaabbbbccdbbbabcdbdabcacdadaccddccccbbccaabacdbcbcdabdbccdbaddddbcabbddbcbdaccacaaacaaabdacabdcabdaadccaabdaadacccbababbdacbaacdcccddbcbbbbdbcbccdcdadbbbddcdcabdcaacbddbbdcabdcdbcabbbcdcdcbadadbdccbcddbbddbbaaacacbbdbdabaccdcdaabcacdabdbbdaccccabdbccbcdbacdcabbbacdadbccddcaababbbbbaaddbdababddcccddcdcbadaabdcbdccdcadbdaabbaccdbdbbddabbccbacbdacddcbdcacaaadbccdcdbabbdbbbddccaccccdaaaaddcdddbcccbccbacacbbdacdcbbdcbbaabbbbcdbdccdcabbcdbdbbdadadcbadacababbcadadaddadcaacbbdbdbbadcdcdadabadddbdbbdadabdaadcbcccddbbabbcadcabbdbacdacccbdbdaaaddbcbccbcaabcdaaddacadabcdaacdadbbadccccccaadcbddacbcccbcaccdcadbcddbaabadbacbdbabaaaaabacbcbdadacdabdadbcdaadcaacdddcaacdcaacaadabcdddcaddccbbdccadcbabdddaaaddbddbddcdadaccccadccddcdbaccabbccddaadaaabbcacdbdabddadbacbddbdaababccccabcdbdcccdacbdabbdcdbddacaadddacdcdccbadcadcabcbddbbcbdbdccadcaddaadadcacbaddbdcbbabadcbdbdacdacababababacbddcddcbaabadbcadbaddbddbddacdadadbddaccdbccbbcdcaacbcadcaadbccbdacadacddadccddaccbddbcdddaacabbddcbaddabbabaaddddaacabdcacbaaddcaccdaacdaaabacabacdcabbdbaddbacbbdacdbabaadcbbaabdbbdbddadccbbacdcdcbaaaaacaddcddcddbbbdcdccbdacbaacbdbacddccbdbcabcddbdddbdcddaacdcbccbdbdabcdcbbcdbbcbbbaabcacacbcddacaaaadbcdaadcacdbaccbadbccabdbdbccccdbcbbbbbdbbccabaabdacbdcddcadaadbaddaabdabcaacccbbacbcdbaaaaaddddabdcaccdadbcacadbcdabacabcdcaaacccbdadccbbdbcccbdbaadddcbcccdddaddcbaaadcabcbccdaccadddabbcaadadcccbddaaaaabaabaccaadabdbdccacdaabddbdbaaccccdacddcddacdcadbbacddaadcdddcacacacbcdccbcbaddadababadcbdbcbaabcbdccadbbcbbaadcabdcbcddacbadcaaaabcccdadabdbcaddbccbdbbdcadbaabbddadcbcbcadacabadbdbacaaaaaacddddbdabdbbadaacbdbbbdabcdaaccdaaccaadbcccbbcdbacbcabdabcaadcccadbdabdcdadbcbcbdaaabddabaadaabdaabddbabbbadccccadaaddccddbcadcacaaaccababdbbaaccccccdaddbaacbadbcaddacacdaadadccbcdddaacbcbdbccdcdbadaddabaaabddbcdaddbdaddbdaabdadcdbccacabdacbcdaaccbcbddbbbdcacbcbcacdbbbbadbabbcccccacaadaaadbcccdcabcddacdccbcbdcbbcbbbdcbcdccbcaaddbdbdbbcaaacaacbcaabdcacdaababbdadaaccacaddcbcbcbbadcacbcacbcccabbcabbddadcbaddcbddbbaaabaacdccbabcdbdaccaabbcdbcdbcccbbaabdcacbbbcbdcaabbbdadcbadadadbbbbcbacddbacdbaaababdcacbacbaabbdcbacaaddabdaddcdcadbabbcabaabbccccdbccddadaabccdacbbacbbdddaadddabbdbabcaabbddcbdaccbdadcabbdacccbbbddbdcdadccdddaaadcabbddcbdddacbcdabaadbdbdbdbbdaaccabbdccdadaadbabdcdcabbadbcbdadbbccddddaabcdbccbcdabacadbbbadaacdcdddddcccdcaacbbbbacdbbdbcbcccbbabbdadabcdbbdacaadbadcdcdddddcdadadddabddcdccbdcdbabadbcccccaabcccdcdabaabbddddbbbadabcdbccdaacadbbcbbcaaacaaccbbbaabacccdadaadacbaadbbdabddabaddadcbabcddcadcbadaabcabbaabaacbccdaccbcadcbaaccabbbadaabdddaaaaacaaccbccabcdabadccadbaacbcaabbabcccdbaaadaaddbacadbbbabbaaaacddbddaacddcabdcdbcbdccdbccdcbbcddccbdddddcbbdbccacdbdbbadcbdcbacdbcdcbdcadbddaccbdadbdccdaddbacccadacbbbbcababaaacacbccdcacbcbcddcaabbcabbdbbdbcddcaadccbaccaddabcbaacbdabcdbcabcaaddbabbcdaaddbbcadcdaccabcbdaacdccccccbaadcdcbdbdbacbbbaacbcabbcabacbacbdacbbcccacdaccbadadbaacdcacbbdbacbcdcaadcacbbddbdbaaddbdbcdacccbbbccdcdacbccacabacbacbdcdbcacaaabcadcdcbdcbacbbbcddbbbabdaddbcabddcabdccdbaccdaaaaddccbccddacdbdddaaabaccdadaacacadadbabaaddddcccdbbcdbabdcddcababdddbdaacacdabccadcdadcaddbdbbcadaaccdaacdabbadcccacdaabccddadbcbdaacaddcabcbdbaaddcabbbdcdabdadadcbcaabadaaaabddaadbdddbbbabdabadbddabbcdbdbddacbacdbddbbacddddacbdaadbdcacabdccaacacdcbdadbcbaadbdaadddcbccbdcbdcadaaddcbddaccbdbdbcdadcbbdbaddadcadbcbacbabcdacbbddbadbaacabcbcadabdbbbcacadcdacdbbccbabccdcacdcadbaddbbcdbdcabbdadcbaccccbdadcbbdcdacabaaaddadbddaddcbbbaacabddadbbadcdbdadcaaadcabdaabdddcacbcbbadcaadbdcababcbadbddddaadacccdaaadcdbdabddddaddbccdccbcbdacaabababbadbacdacdadddcacdaabaaabdacdbbcbcdbbabcbccacdacccccaaaadccbcdbcbcbbbdbdccbdabcdcccdacdcaaccdddcddbbaddbccadddccbbdaccabbdabbbcbccbcccacadcabdbdbacadcdcccccdcbabadccbdcdcaacdaaadaaaadbacccacbccaaadddabccbccddbdcaabbabadcbabdaaabbcdcabadadcdcbdbbdbbbacdbacdbcaacacbacddbcbcdacabaccdcdddaacbcbabbaabbbaaacabbbadaaadbcddbadbadadabcaabddaccaddcdabdcabdbbabddadcabbbcabdaadbccdcdaabdbdacbabccbcccccbaddccbcccabbaccabdbbabbbdbbcabaacdbcccbcdabbbddddbacbbbbbacdbbaadbccdcbcdcdcbbccaccdbddbadabcabbabcdcbbcacccccbaabbbbbbacbcbbcccbcdbdcabacddaaaccdbdcddbbacbcbcbcdddcaddbddccaccacdaabdbddabbcbbdacdbdddbdacbabcadadccddbadbbadbbaaddbddaaacbdbcccaacdbbacbccaddbccbbabbcdcbdcbacbdddbcacddcddbdbcaccacabbdaaabcdcccbbadaacbcddcadbcdcdabaabbcdbdddcbdcbdbacbdadaacbaadaadabbadcddcaacbbacdbaabcdcadabadcddaddacbdcbcddaaddccbdbdaaccdddbaababcddaaaacdbbaaacadbdaadcbcdbdbabbdbbaaddccbbbdbbcdaacbdccbcddabcaadadbaacccacaccbbbdbddadaaadbaccdbbcbcbddaddcbddcdbdacbdbbadbdadcaadcbacbabbdaabdbbaddadbcdaaabdbdaacdcbcaadccccaddcaabbcdcbadcacaaababcabbdcdddadabdbcdcbdabdbcddcbdcabdbcdabcadccdcccacaddbbbcacdbdcdaabbbaacdbababbcbbcaaddaaadaabacbaabcdacdacdcdcabdddcbcccbacddcdadbaddcbbccaadacbddbbdddaabccbbccbabaadcbdacaaadabbccbbddbadbbdabbddacaccddbaadaccabdbbaddcbddacacbadcbbcddcacdddcbaaddcbcabdcbbcacacdbddacbccddcbadababcadabaddddddabbdbdaddbccaaacaacbabccdadbbcbaaabbcacbbdbbbbbcadcacadcadaccddaddacdadbbadbcadabbcddddabcabbdcbdcdadaddcabddabcbddcbcdadbcbcbcdabdddcacbbbdaaaadbdadababdcdcdcababccbacddcabdcdadccdbcabdaabdcaaaabbaaacddacdaacbdaacddcabddaaaadccacaaadcabcabdaaabbbbcccbcbcccbdaccccdbdcdcdddcadddabbccadcddcacabddddbccadbddcbabcddccabacaaaabdbcccdacbbcccddbbacabdbcbdddbcbcacbbbdbcabccdbcccacdacbaaadccdcacdbdbcdccaddaacbdcabbddcadcaccbaacbddaaaaccddbbcccddbdbbddcbbcbadbcaabacdacabcadbbaababbdcadcdadabcabaccbccbcacadbbacbdccaaaccabaaaadacdcdcbdbcdcbacbdabbcaabaccabccdcdbdabcdddcdaadcaddbdbacaacbdbadaababccabccabbdaddbbcccabcabdcaddddbaacaddcdbaabbccdbbdadcaabadbccaacbcdbcbcabbacbaacadddbbdccacdbbbdcdbadbdddaacdcaabbcdadacdcadbdaaaddcbcbbbcbdabccabaccadccbbddababbcbaddcacddcbdcbcadccbbbdaabbbbdccaddcdcbaaabcbcdcaddbcaadbcccbabbcaccbacdcdaabcdaddcdbcbbaccaacbbbcddaaacdccbdbddaadcbaacbcacdabadaababcdadabaddacbdddcdcccbdaadcdaabdacacadcbddabcdcbadcabcbbccdbaaabccdbbdacdbbdcdaabbccbbdadccdccbcbabcddacddbbbcdbcbabaaacbbbcdabdadadacddbdccbaabaaadbdccdaaacadbdcbbababdcadcddddcdcbddccdacdbbcdbbdcbdcaadadddddccdbadacccbcacadbcdbdcbaadcdcadddbbbbbbbbddabdcadbdbddababaabcddccbacabaccdabbbcccbdbbbaabbaddaaaccbacabacbcbbaddccbddbbabbacaddabddccbcbdbbbcdcddbcdcbdbdddbbcdbcbbacacdbbdbdbaacddacbaaadababdccbddaccdbdabaddbdccbdccadddbddaaabaccddbcccbbabbdaacbdcbbbbcccddcacccccabbbabdaacbdcacbbabacddbcdcdadbddaacaacbdabdabcacbcaccbdcdbcadbbcdcdabbdbabadaaaaddcbccadacacdaabbdcdddbadadabcdcabadccaccabbabacccdbdcbdccabcddaaccccbbdadddabbaaadbbcbacdadaaaabcadbbaabbcacccdbccdbbdcdaccdaabaabbcadaddbdbbaddaaccdbadbadacadbdbcccabbaacacadbbaadabdbaadbdddacbdbaadabbbbaddcdadbbddabdbbbbbbcbddaabbdacbdcbdabddacdcdcaadadaddbdbcaabbacdcbbcdacbaabadabcdabcdcbbccbcdaabdacacbbdbdcdcdbcdccbaabbcccacdbabaabbddcddbbcdacadacbaddcdcdcdadcdaacdddbdcdcdbdcbaababbacdddabadbabbabcdbabadacdccaaddcdcbcbcadadbcabbcadddbadddbbbccaddaddaccdbbbcdcbdccbdcddaacaaaabdacababbdaabbbcdccaadaddcdcacdabbcdcdcdabbaadbdbbadaadbabaaadbcacadaddaabbadadbcbdcbbbdbaabadaabbcdcbcadacccddbcddaccabacaadacccbacdcdcccbddbcbdbdabccdacabdcbddccdcbdbcacaadaccdbaaddaddaddaadcdadbbbdbcdccccbbaacabdaadaabbcbcccdbaabaaaddadbcddcdddcaadcdabccaccacccaccadcbdababcdababdbaadbdbdababcbddcacabbbaccadbccbcaabadbaccbccbcbddacaddcdbccbcbcbcccbacadadddcbcdbbddbbdccdaacaddcdbbccacdbadcdadcdaaabadabdcabddadbccddbaabdddcbcbabbcabdbbabcbdcaaddccdacbddadaadcabababacabddcbcdcaddbadcdbbbcccbadacdbdbacabcabaabcabcccadadadbbbbabdbdacdbbbbcbbacccbbacadadabcdcdaccbbccbccbbabdccbacddbbddbdccddadcbbddababbdacadacdacbbccdbcdacabbacacaabcabbbcbadbcacbdbdaddcbdbdaacdaccccaddaccadbbdbcbbdbcbdadbbacbdccabcaccddccccbcbadcdbbcbcbdcddbadbdbbdbdcbdbacabcbdcadbddbcabaccddacaaadbacdbdbdabdbdcbcccbcaaabbdccacdcabbdcccdccacdbdababccccbcabbddbaadcaabbccaddbbbababbcbdcbddbabdaddabaccdaaacabacbcbabdcaabcadcaacdbddcaddbcbddccbdbdcdbadbdcdbbadacdcbdbbacbbbbdabadbbadddbccdabaddccaccadccacabadcacabacacdbdadaddacbdacadcddbbbaacbcacbdbcbaacaddbbcabddbcbadadbcbcdaaaadcdaabcddbbbacaccddbdbdaadbcaabaababbdaccbbbddbdcabbbcbbaaccbcdbbaababbdaababddcabccbddcdccbcacdbacbddcbcacbdcbbbcdadabadcabaaacaaadacadacddbdddaaadabdadabbddccbccaacdaacaabdabaaddadacdadacaddbabbddcbbccddbdacbaddcbdcadabdbdaaaabdddccdcabdacdabdcaccddcccdacdcbaccdbadaddcccddbdbdabccddddacdaacccbbdadbbcbdbdbbaddccdbbadabdbcaccdddbdabcbabccababbcbdddaabcdbbcbcacacabbccbbabdcbacbcabbbcbdbcabdbcdbaaabbabbaddcdbacdccbcbccadbabddddcabbabdadccabababbbccbdcdbdcdababdcbdddcccdcbdcdccacaaaabcbcacabcbdcbdbcbbbdcbbddccbcaacddccbcbdccbdcaadcbdadaccdabcdccacdcbadadbdbbbadbdbdbcccaacccccadabdacdbcccacbacdccccdcbbabcbdccddcaaddcadcccccadcadbcdabdababbbcdbbdcbaaadbcdcababaabbbdcccacbabcdcacaacababbadbaaddacacaccbaadaabbadcbccaabaaddbaaddddadaaacadabccbdaacbbbacbddadcaabadacadacccadbadcacdcdbbacbaaaddbcbcbbabcdcbdacabcbcdbdbccdcdaddcacbdbcaccdbccbbcdcacbaddcbcdadaaacccadadbbdbbacaabcdcbcbdbdaddbbdcdcddacacbcdbcadbccdaabbcbdddccbcadabcccbbadbabdbbabcaacdadbcdcccabddccbcddccbddbbdadabdccdcbbbabccccabbddbdacbaccbdacabadcacaddcccaaccbcadacacdcaccdcdaadddadbaccccccbaaccbadcacdbdbdabacadbbbcdbcdbcabbbbbadbaabcbcbdbdbddbdcdddbbbbddaaddbdddcaadaacdaaadaaddabccdabbaddcdcdddbadcdadbaddddcddddaaaddabacaacacbbadccbcdabcbbdabcabbdbdbddbabcdccbaccdbbddaadbcdabadbdbacdbccdbcdcbddbabcacababbcbcbbbccdbccbadddcbabbcbbadcabbdcbbdcdcddddaacbdbcdbddabbbbbacddadccbcdacdacbaaaabcbcaccabbbbbcddbbdaaaccbacabaddacdcdabdcbbbabddbabbbabaccabbdddbaddccdbcddacabadaddbdacaadbdbdcbbccaccbcaccbcdccacbabbcbcaabcaaadbcbaadcabaaccaaadbcdbcccbabadabbadaabacacdaabdbcadadddacaabddacbbddbbcddbbdcdabcadcaadbccdccdabbdcadaadadcdcbbaddbabbccadcaabbadbbacaacdacbbadacadcccbabacbcdaadcdddcdadbbbcabbdbbbcaaccdddaabdccbacbdcabdbadaaccbdcaadaabcccccacbdcabbbbbccbbabddcddbddcbbddbdddacccbdacbbadbddcdccdcacbbcbbbdccadaccacdaaadcacdbaddbcbcdabcbcadbabdaddacabbbbddbbabddacddbabbacbadbcdbadccbaddcbdcabadcdbddcdbabdbcbbcacbddabaccdddacdadacbcdaccdccbddcbcdbcbbdcdcddabbcdbcbacadcaddbcccddcbabccadbcddcdddbbbabddbcabdcbbabddcaabbcdaacabacbacbcbbaccbdcbabdbdbdbcaaaaabdccbdbcdcbbdddbccbdbbcdbcbcdcddadcdbacddbbbbacddbdddcdddcaccbdadbaababdcdddbbdacbaccccabbbcdcdadaddbcbddaddbdbddbcaacaadcacdcddadadbdcdccadcbbcbacdabbbdadcdaadccdacbabbdcbbcbddccacaadabdbcdaacccadaccadacbcdcbbbabbbabacbacbaaabcbbcdabdbaddacadcbbcdacabcbcadbcbabdaccaabdaddbcccbabbbcbbdbccabcdbaadcbbdbccdbbdcacbbccadcacadcacdcaaaacaddcddcbbcbacadcddccdddabadaabbbdbaabaabbabaaddabbccdcadcbccbdccccdbcbbacaddabdcbacaccbaaccbbcdcabaaddcacdacaaabababdccabdcdaddbaabdaadcbddaadbdacbdabaadaccacbcbdcadbcdbdaccdbacdcbbdadbdaaacccdcccdbbcabdcbaccdcbcdacdcdcdadacacdcbcbcacbddbaadcdccddadbdcccadbdbcbdccbcddbcadcacbbcbcacdbcbdaabacabcbdacaccbadcacddacdacbdccbacdacbaddbdbadaaabddadaadabdbddccbdadaccaaabbbabbdcddabcdabdacddabdbbabbaabcdccbdcbdccabccbaadaadddbabcbddcbdadccbbddadcdcdbaaaadbdccacaaaabbdcbbdddbcabbcdbdddaaaccbcbaccbbbbbaddccbabaadcbaaccbadccabbbaabbccbbddbaccabacaacdbbbabdacbadbaaddcddbbdccabdcaabaaacbdadacadcddcbabdbcabcdccaabcbacdcdabdcaddacaacdbaabdcbbaccabdaadbdabdbcbcbdbadabaccbacbbccaccacadddbbcacbacaaccdbbbbdbccaccdbabbbdbccabbbdaaabadcadddbbbbdbdaacbbbacdbacddbcbcdcccdadcabcbdacbdacababdbcacdacdbcccbccacaabdcdbbbbcbccacddaddcaabaadabcadbdadbddcdbbdccbbdacaccccbcadccdcdadabcdabdccdcacbcbbbdaacaabccacbbcbbbbdcbaccdbccdcdcbabcacdadbcdacbbcaacbaaacccdbcabcdabdadacaddacabcbbadaaadadaacadbacdcdddccbbcdcadababbbaccccddddcaacdcdbacbbbabbdcbbaddcccdcbcbdddbccccabbddabcbbddcbcccdbdddccdaddbabcdabbabdbbbcbaccbdabdbbcbacbdbbadcdbbdcadbbabacacdadddddcbaabcdbcaaadbcccdaadadbdaaadaaaddccccbbbaaabadccabdbbaabbadcabddbccbabadcdbcbbddbbcbbabcbdcddadccbabdcdacdbaaacdacbccddadcdccbcadbadcbbcbdacabdabdcbccdbdbcbdcbddcdddbcbbaaaaccbdbbbbaabcadaddbdbdacddabbdaccbcddbacbdacdcadaddadadcdabacbaddabbbdcaddcccadcabbcbdcdbdbdcacababdabdbbdabdadabdadcdcdbaaacccbcaacdcdcbddddabaaccaccddcbccdccccddcbbbbdbbdadbcdcdbabdcccabcdccdadcabacbacdbadaadbbcbacbdabdbbdadcabdacbbbddadbacdcbcbcdaaaaddcbddddbbaaccaccddaaadddadddabdaccdccacccadbccdbacddadbacdcbabbdbdbcbbdcbbbcacaaadcbbbbbdcbbcabbbbcaabcdadbcbdcdbcbbdbadcbbadbbdcdaacbaaaabaabcadbaccbaaddaaccdbcadcadcadbcadabdbacadaccdbddbbcddcdaddccccababcbbbaaccbcdaaabcaaabbcdacdbadcbbdaacdbbaaacdaaddbaaddbcdbddbccdadbadcdadacbbadacdacacdcabdddbdcbbdbcdacddacddababacbcbadaababcbdadcbabaaccadccabaabdcccabaddcbacddaacbcdcccabddbaacbdadbbabccccadbbbbbacbbbdaabadbaaacaacdcdcaabcaaaadabcaacaccabaaccadcbbacbdccaadcdccbbdcabbabdbbaabacbdbdddbadaacbcdbaadbbbadbcacbddaadaabdcbdccaacabadddcdbddbbcdaaabdabababdbbdbbcbacabddcacabdadccdacccaabdccbcdcddbdadddddbcdaaaabdbbbadaccdccdbadbbbaaacddbbbcbdbdbbbaccddcbbcbdbcbcdaaadacdccdbabdacccaaccacacdbdbbcbbdcdbbabacbaccabacdcbdbacbabdbbccdbcabbbcabdddcacaabbdcbaaabcaaacadbbaaddbaaddaaaaabacbbcabbdadbabcadaabbbccababbcadbcbbbbbcddbabdbdccbcbcbcbcdaabdbadabaabbcbcabbddbadbcaaacbabcadacdacdbadabdaccbddbbbcdabaadddacdcaacbdacbbcdcacaccbdbacdddcdbabddbcaddabacaadcabaddbcbbcdcacdcbabbcbbbadbdabdaabcacacabbbaddcadbbbaccdccbacaabacdaddbddbbcacddadaddadcbabcaabcbcabbcbacbbcbadaabdadbcbbbbdacccadbcbcdbbabaccdcbdcbddaadabcacadbcdbabacbbaaabbbbdacdcdcccbdadbdbacdbdacbdcdccadcddbdddbaccdcbdbbdbccaabccabddbdcdddbdbbaabaadadadbddbcddbdaddabdbacdcbabbabcabbddaccadddadaabbdbaabadbbdbccbabcaddcdaddaadbbbacccdcadcadacabbdbaaddcacadadbdadaacdbdaaadddabacbaaadccacaacacdabcddcbcdadbaaaaadabdacbbbdbcbacccddaaaaabbdbacbabbcdbcdcaabbbaacdbdbddbdbbcdacddccdabbcdcbbcdadcbaddbcbcaadbbcadacbaabbcdaddbcdcbaacbdbdbcaaaabcdcbbdabccbaacbcbbcaadcaaadddbacdccbcbbdaabaaaaacdcbdaadadadadadbdbcccbcabbbdbbacdddaaaabcdbbdcacabddacdbaabddbcadbcdbaddcddcdcbcbbcbabddcaccacdbdaaabcdcaadcbdddbbdcaccddaadabcbbaddabbbdccbccabbbacccddbbccbbadcabbbbdbabadddcbadbcacacdbbcccaadbdacddcddcbbbbbcdacbdcaccabaddbbdaaaaacabdacbabbacccccbadcbaadcdbaddddbdcddddacbaaddcbaddbccabccccaaaadcdbdbdaaadacdbaddbcaacdcdddbcbcdddaddabdccdccabcaaacaddbcbbccdcdabdaadddadddbbbcabbcbcbabdacccabdadbdccbdadddadacdccbdddbdcdcbbdcaabddbdcbddcadbbdcadbdadbbaccaaadbdbdacacaaddacabcadcdbacdaacdbddddbbabaddcccbcdbddcbddccdadcdccacbbbbdaaaabdbcbadbbdacacbacbababcaaccbbbccdddccbacdbbbaacbacabcccabdccddcaacadacdbadbbcaababacbdbcabddccdbbbdcbbccaadcbbbccbacddccdcacddabcadadabaddbdccbcdbbcdbcabbcdadbbdddddbadabbdcbcdbdabbacbdabadacaaccbccbdbccbddccacbdbabcdbbbddbbadbbbddbabcbddcacbdddcbcbcdacacbcbcbcababcbbcbbdabbdddbacdabddddcbaaaacdcdabccbdaacbbcccacaddaacabdcccdaabddbccaccacbadbabcbdbdcccbdacbbcdbbddccacbcdccacdbbcdcaabbdbddddcbcbcbbbdbbabddcbbabccbbbbbaaadcdcbccaabcdddadcaacaccddcdcabccccbdbdcabddabacbaaddbdbabaadbdcaadabbbabdbdadcabaadbbbbcaaacdbbcbacbcabcaaddcccdacaadbddabbbcbaabdaccbbbcadbaccbcbcbcadabadadaacadcbacbcacadcdcbbdaadddaccacdccdaccaabcaaabacbdcbcdcdacdaaacbadddadddaabdcbdaabdbdbcdcdcbcabbcdcabcaccbaaadddadbccccbaccaddababdaadbddabbcccbcbbdabbcadbadacbdcaadcaadbdabdcbacadbdccbdaccabdccadaddcddadadacddddaccbaddcabdbbaccaaccdddbaccddccacdadacbbaddbdadbdbcdbbdabdbccdbbabbcbdaabbaccbbadcdabacbccabbbbccacdbbbaddabbacddabaadaababbcbcbcddadbccaddbbaabbdadbdbabccabcdddaadccccacaaaadacacbacccbcaccdcbdcacdacaddbacababdcaadccbdcddbdabccdadabbadcaacabddbdbaddacdacdaaadbbbdcadcabcaadbdbccdabaadbabdddddaaadaabcabdcbabdcbdcccabcccdddbcccbbbddbcadbbadaaddcbbabddcdcdadaddbdaabadbbcddcbcdaadadbbbcaaabbcacacadaadbcbcbddacaacddabbbbcacccbacabddccccdddbdbbaaadacababbadabcdadddaadcdadccdbdaccccbcaabacdcdbbadabdacddcdcbbddddbddbacdbcdcdcbcccbabdabdbcbcccbaaddbadacccbbaadcbcdccbdbccbacdcccbbdccacabdaaaddbdacabbcdcadcdacbadbbbadaddcccacdbaadddbbdbacadbdbacdccdbabdcadddddbddcadbbccadaabababdbdccbadcadcbccacbdadbcdcbcacdcdabacbcabbdaaadadbdcdcaadbdacaadbddcccabbddddcdbcccddbbdcbccbdabbacabdcbacabbdccdbbacacdcddadcacbccaadcdababbacddcbccadaacdddbccdaabaccabcbaccaacdcdbdbcaacbbacccdbdabcbbbddcdabadbabaccaccbcabddbbbcacddbcdcadccbadaccbcdbccdbcdaabcbddabdaddacbdbabdccbcdcbacbbabbbbbdabacadcdbccabbbadbaaaabbdabbccadadddacdbddddabcabbadddccbadccadababcbcbabdcadaddbddbcdddbccbdaadabcaabaaaaaaacddaadaabdbcdaababdaddcddabbcccdcadbabaabccbdadadcaaaccdbdaccdadbdbcbbdcdcdcbbdddccabbacbddaaabcaadbddddcbddaaaaacbaaddaacdcbbddacddbadbbadbbbccccdcacadacabbcacccdbadaacbbbadbbbdcacdbcadbbaacddadbbdbbbcdaccabbaddadaddbcddcacbaddcbdcddbbcdcabadabbdcdcaacdbcbcddbcbcdccdabcddadcdbccabcbbdcbccacdaacbbdaabbbddbaaadbcabaccbaadacdadcadcdbcbcacdaddabcddbdbcddbdbbbabcadbcbddabcdacdabdcbbddaadcbadcddaadbbcacccabcbdaddadbcaddbcdaadcddccbbdcdcdabccddabadcdadcbbabcaccbaaacadbbcccaacbcbdcdaadbddcdbabdababadbbdcadbdcbdabcadbdbabcbdacacbbdbdbbabcbddaacbdcbcdababdbbabddcaccbdabcbadaccbdaddbbabaacdaabcabccdbaacbabdabbdbabdacddcbbdbccdbaadccddcdccdcccdbdaaabcddacadbcaaacaabddbcaccbbabcadcdaabbacbabbadcaacbbcbccacadcbddcadccdbcadbcdddacdcaddddcddcdcbdbcdadabcdcdddcbadbadcddcccaacaaddbcabcbaccadcddbcacdaaacbacaddbccdadbcdcddcacccbaaababacdccaddcccdccbdabbdababbcababaadabbdcaadacbaabdcacdcdcadbbdcdadbbcbacdbbccdbdcdadacbadbaabdbbbacccabbacdcabdacddacbabbdcbcbcbdddcacdabbbbcccbccbcbbacadbdbdbcbbbaccaddbaddbdbacbddbcbbadbbaabcabcdcbccaddbbdbbabdacaadcbbaadccdcbabbdbcddaddcdabbdacdadbbcdadcdaadcdccdacdcdbcddcbddbacdacdcdaddaaaaabddadccbdcaddababbabbaacbdbbbacacaababcbabbabddacadcaddacabaccdadadcabbddcaddaabdabcabaabdacabadbdacabcdadbcaabbbbbdcbbacaddcababaaabcbbdaaccddbdbbdbcabadbcbaacdbdadadbbdadabdabbdadacdadaccddcdbababdbabadcdbdcbaccbdbdaacadacabbbcbdadbcacbbccdcdabddabddcbbdadaacbbbcdcaaccbdbabdacbdabbdcdbbbaabbadbdadcbabccabbbbcdcccaddbdcddcddbaddbbdcdbacbabcbcababaccacacbcbcbcdaaabcaccddadcabbaacdcbddadcbbcccdaddcdaabdaddcdacaadaacbccabbdbdacddcdbbcbddcacbbacdbbcdbdaaacddacbdabbdcdcddaabbacbaddddbdbabddcdcddacbcdacaabbadcddcdcaabcdccdadcccbcbcababdaaadaddbbabadabbabbabbdaadddbcbbacabddcdcabccacbdbcdbbbdcaddadcbadbadcccbcbcbaacccdbabdadccbbbacddabbaabcdaaabdbbbbbdabcbcdadbccaacdbabcdcdddabcadcbdbadabadabbdbabdbadcdacabdcdadcdbdccccbbbcdbcbcaaddbdaadddcadabddaccccbabdbdbcbabbccccdacbdcdcbdacbbcaddccbbaadbddcccbcdbcaacacacccbbdaadaaabacdbdbcbadacbbcadabadabaabdbaccaadabbbdaacddcdcacaacabdaaabadbdcddddddbcbadcddddbcdddabdcddbdcbbcbbddcbadcaaccbccadaabdccbdabbacbcddacabddacaddbbaaaaabdccddddadabcadcdaddcacaabbabcadbbbdcbadbbdabacddcbddcbaabdbbbaadaddbbacbcbccdbdcbdcdddddcbdacdccbcbcdcabbbdaccddcddcddabddcccbddadbcbdbcbaaddcaaacdbbadbdbcdaaddadaabddadbacabaacbdcdabbacadcbaaabdaadcbbcdbdaddabbdcaabdccadddababdabcabaddccdbbacddcbaabaaadbadddcddbdddbbbdcddddcddadcabbbcabaddddcddcbcbacdbccbcacdbabadddcbdbaacabdacbdccabdaacbdcadbdbcdbdddccddcbbcbdbdbbdcbcbbbbaacddcbcdcdbbbaddcdbaaccddbaabcacddbabaacbadabcccdbadccdaaacbdddbdccbdbabdcbccdbcaabaddcdcbadbadddaacabcaaadcaadadaacddcccacadbcdadacdbbaadbdbcacaabaabbadcdcbdadbbdbadccccccccbcbcadacccacccdbcbcbabadaccbdccacabbdccadacdccbbdcaabbbccdaddcabaacbababadbdccdbaacbbdbaabddbcabcbbcbddddbdddacacddbbbdabbcbcacabdaabacdddbacccccadbaacaddaacdcbadabadaccabaadbaaaddacacadddbacccacdcdbaddcdabacacddccbababcddccdadadaaabbdccbccacccdccbbaaccdcbddaadabadbacdddcacccdcdbccbccdcddbbdcbbdbbcbdccadcbbabbddbaacbdbdbdbddccdbbbbabaaddadabacccabdddadaabbaadcbcbcdadaccbbdbddabaaaaaacacbbbbacbaccacdbdbdcacbdcccdccbcdcdaababadbcabdbdcdcdabbacbdcababbadaabcccbcbabddcacdbcabccbbdcbcbdaacbcabbccdbcccbcaaabadaddbcdddbdddbadcbccbcddddacdbdacabdcdacabbdbabbddaacdcadbcbaadaabcdbaabaccaccaacdbbabaadcaacbddbabbbdddabdcaddadbcdcdaaacaacdbaabdbbcaabddadbbadadbbaccbaadaacddadcbaabcdacbbdacdccbcdbacdddcbccdbabcbdbbdabbdcbbddbbacbdcacbdadddadbcddbaaabaccbaacbddaccaacddaccbbdcadabdcdccabbcbcabdccadaddddcdcbbdcbdddbaabbcaccdabbcbcccccadbbbbddaacabbbbbdbaccbaaddcacccddcbbbaabdcdccabccccbbacacbdacdddbadabdbbaccacbdabccaddcaccdaabdadbcbbacbbbacdacaaddbaacddddccbdcdcccabaaaccaabdccddadbcdadccbbadbcbdbabcbbdadbcbacaadabcabaadbabbaacddaaddcdcacdadadbbbabdcaddbadddddcbcbddbbbbbcadccbdabccabddbbbaaddbbcadddcbbababbddbabcabdbbabbacdcaadbaddacadcbdbadacacaabcdcacccbaadcbaddbdacadadabdccabdadbcbdbcdccabadcbabbdaaadbbbaabbdcaacbcbacdcdaadbdcdbaaaccacdcbabaccdcacabbaabcacacaaabcdcbaaccaccbdadcdbacdbbbccdbdbaabaadbbdcddbcdcbaabccaccabddbcaaabcdaadbaaccbcaabddadaddcdbcbbadbdcdcccdbccaadacadcabbcadbddbaabadaadbcbadcdddcabccdcbbcabcadaaaaacaddbddbcaaddcacaddbadddbddbcaaabaacbaacacccdacdbcaacbacaccdadcaabcccbccbbbbdbbbccbcaabddbdadcadbbcbdcddbcacdbaaccababdabbcadbabccbddddccadacabbaccbcdaacacdbddcddddadddcbddaabccacadcdaacdbcbbbccbbcbbdadcbdbbbdcdccdcbddbbdccabccacccdbadadbaadddaaaadadaadbbbadacbdddcabbdcccbbbbbbcdcbaccabcddaadbcbacbcacbadbacddaccdaacdadacdbcaababbbcabacbdcdcccbdbcdaccdcbddcbabdaacccaadacccdacacaddcadabacaadcadcaccdccabbaaccabcddbccddcbbdbcabbbdbdaadccdaaaacabacbcaaaaacdcaaacccbdacbbcbbcbdcdbddaccbaddabcaaccccbdbcbccbabacbdcaadcdccdaaadbbbacbadddbabadcdcaadbbdcccacddbdbcbccacaabaabdbbdbabddaacdcabaddccbddadadbaaaabbbcdccbdaddabdbbcaacdacadaaadaadcbbabccbbdacdcdabaccacdaaaddcadddababdbacbbbbcddcbdcababaadaababbbaadaddbaadacbdcbbcaacabacabacdbddbbbadaadbdbbdaadcdbbadcdaccdcadbdddccabddddacddbccbcbabddaabdbddcbcbddaadbcbdadcdadbbcdbdbdacdaadaccdbccdcabddabadbdbdccdddbcabacacdbadcdcccccbabdaabcaadcccaabcbdabccbcccbcadcdadcadbbddcdabdbcdcdddcbadbcadccaaccccdababacaddbcacbdadddacccbdddacdaabadccdaddaccbcabcdabdcbbdcacbdadcdccbaadaaacaddddbcaddbccaadcccddaadbabccbaacddbdcbcbbcccadacacbbaabcaacdcdbabddcaacbcaaadbabdcdcddbadccccbdcabbadbccdbabacbbcccbcdcbcdbadcdadddccdccddbdcbabdaddddcbcadbbcadccaabadcabbcabcbbaaabccdddaaacdddaaddababbabdddddaccdaacbcdcaccddbadddbbbdabccbdcdcbdcddacaabdababdcdccacdcbbdcdcdcdbaadbadabcabdcbbabdadabaddccbcccdcdddbccbbccdddaccdaccddbcccabcadcccacccdccdbcacbbabaabbbbaaacdacdbdcdcddbcadabaddbbadcdccbbbcbaadbddcbcbdaadabcccbdccbdadcdaadadccdbadbacbaabaacbdaadbdddbaccbbbdaaddcdbabbaabaacdcdbddcbacdacaadcddcdadcdbaccaaababcdacbcbbaadbaaddbbbbbbdcccabdbdcdcbccbcdbdbcacbcddabaccbacacbcbababcacaccacbbcdaccacccdaddbbacdbaccaadaddbccccadbcccccbbcbaaccbcbacbcdbcbacbabacccadcaabdbcdacddbcbbddbacdbbadbccbabacbcbdbcddadbbcbababddbdcabdaccadbbcabbbddbdabccdcbdabbadaacaababcaabcddbbaadcdbdccccdbdbdbdabaacdbadbccacbbcdacbacbccddadaccdddccddaaabcdadbbdbdacbccaabbdddacaaddccadbbbccbabadbdacabbacdbcddcbcbcbacdbcdabbcbdcddbbbbcdabbcadaaacaacbcdbaccabddbaaadaabcbdcdaaadacbdcbdaabcbbcdbbdadbabcaaabaabcdbaabbddacabdadbcbcbaadabbbdacdadcdbdbbbaaadbcaacabadaacbabbbdbbadcadbabcaacbdbdbdcddbadaddcbbcbabcbcbdbcacbdcaabcbccbadcdaaddbaaadabccabcbbabaaddddcbabbbbbbbcbabcadadaabbdbcadbddcbcccddacabcabdcaabdcbacdacadaabbbaabdcaabcaabaabccaaacbadbcbcadcdaacdccbddbdbccdbabaccdccaadcbbdbadbbbcdbdbbbbddbaabccabdbcdcdbccabbbbcabacdccdcabaabdbabaaddbdbbabddbccacbbacdccbaccabdaacacdcbaddddaadadaabdabaabadddbcacadcddddbbdabccbaccadbcacbddcbccbbdaddbcaadacaddcacccdaddcbccbdbcbdadbaccdaacddbdbcacccbabcdbcdccdaacbcddbabbdadddabbcdabcaaccabdacacccaadcdababcdddcadbccdcadccbbabddccdcddacaabcddcccbbdbcbdbadbaabbaccbcaddcbacbbcbbadbddbccaaabbbcccccccbbacdbccacbdaadabaaddbdcabdddcbdddccaccdcadbccaacdabcbcbbcbadbddadbdbaadbbacccbbcaccddcaadcbbbbaadbcddcaddbbbdcdddadbacbcacbabacababbcaaabacccbddbdcabbdbaccaacbdbaacadabbbbaadcbdabccdbdabdadbccddcaddbadcabcbddccbccdbccccdccaaddacdacdbbaabbacaddabaacabadcabbacddacbabaacbccbbdcadbaadbcbacacbdcdcacdbcdbccbbaaaabbbaccabdbabdacabccbddcdabddacbbcccdacbbbddbcaccdcacdcccddcacddddacbcdadbbcacbbaadccacacabbbacaacbaaccdadabcccdcccbdcbcaabdaabcabcdbabcbdaaaccbdddabdcadbacadddbbadcbabbdabbddbddddcbcabbdbddaccdcdbdcaaacbbbcccadaddbccbaaadcdccbdaadaaaddbdbddbcdcadcabdbbadddabdbddbcbbbadccdddadccbbddbdccbbbbdadbddcdadbbccddcacbcbbdbaaaddbcbdacaaddbbdbbccdaaadccabadadabbabbbdbcadaabadcaccabbcbdcaacdddaccabcbdabadcbbddaaaddabacaccbbcacabcadadcdddbadbaaadaabccddababcdddaabcdccdcbbadcbbaaccdccdbacacdcdaabcbaacbdabadbcacadbacdbbdcacccaccdabcddcadaaddbccddcdccdadccccdbddcdddacdbbdccdaadabbabddddabbcbabdaabcbdcbbcaabccadacbdcddcadddaabbaaccddcaddbaaccdaddbabbddaccabdcdcbddbccadccbdcbbdbcccbcbdadcccdccdcabdbadcadbdcacabaccaaddbbcddccbdbbccabbdcaacadbaadddcabaddabcdcbbacbdabbbdbbddbbcbbacaaccccabcbadcabcdacccbccbaccbabbcacaddaabcdbabdbddacbddbcbabbdcdcbdacdbcabdbcdabbabaddabbcddccdcadbcccdccdbbbcaaaabcdddacccbcbbadabcbdcdccdbdadacaacccacdcadacbccdbddcabcdccbabbdbbabadccacbacbaaccaaabcdcbdabcaaccaccabbadacdbdcadadbddabcbabbdbcbdcadcbcaacbbbdcadabcbabcdbbabacbbdaacdcbcaaacbaabacbbdabbddcbadbacadadddbaccbbccdbbacabdbaacabbddbcddbdbcaccbcccadaabbadcccaccbdbaaaabdddbdbcbbabacdcbbccbbaaacacdbbdbaccbbdccbbbbabcbcccbbcddabacbbdccabbddbdaccabdacaadbbbadbaddcacbadbbdcbbaacdaabbaacbbcbdaabcaacaccdccabbdcadddaccdccbbcadcabacbdbcbbaddcbbbabbaccbbcacccbbabccdabbabacaabadadabadcccdcdbcdbddccbcdbbcbccacbaaacabdbbcdddccddbdcbbdcaabaaabaabababbdacdddabbaaaabbabdabbbcbcadddddacddcbcababbaacabdcbaabbcabbaadcaacdbdbbacbdabbbabbabccdadcaacdbcddcbbddcdbddcabadcaabcbcabacdcbaaddcaaadbbccdaaddbbaadccabcbdacddbddcbbbdbccccdadaaabdcbaacccddbbccbcbabbbbcbabcbadbaaadddcdbdacbddaadabbdacabacaddbacaaacacbabcddbcdbcbcdbcabbcaabcdbaabcacccacbabcadddbcbaacaacdacdcddabcdcdacdddbbbdacbdcacbbdbaacacdacbbcbdaaaabdabcbacbdddbcbdbcabacaddaabccdacbaaaaddaaadaacbabadcadacddbacddabdababdbbddccccdbbccdadbcabbdbaadbaacddbdaddbdbbcccdadddcbaddabadcbdabcbbbbdcabadccadbacacdcbdccadbacbbcabaacddccabdcabdaaadcdddaccbacdadcbbcbdcdbbdbbddddadcdcccccabddcccbabcdddcbcccaacadaddbdbcbacbcdccaabbdbabdaabbcccbbcaccddaabbbabdcadbacabdabbccbbaaadcccdbdbacbbbadaadcadcdbaddcbccabddbcaddcbdadcbddadccdacbbadbabaadbbbbbcbddbcbbbdadcbdccdbcaacdaccdbacdaabcddcddaabbdadcbdcdcdcabcbbaabddabcddcbcbcaabbaccdaacdaaacbbdcccabccbaabdabcaccdcdcbdcbbcbdbccbadcbdadbcbbcacccadadcbacacabadbaabccbdcacccdccabdaacdadacdaadbbabdacdadbadabddcbdadcdccababccacbcbcdbabbcccdbbcaacdbddcacbadcbbbadbcdcadbabaadcdabccbdabaddacdaacdcbadcbcacaacbccbbdaadbcacaddddcdbaddddcbdaccabccadbcbcdbcbcbcbdaadcaaacbaccddacabdbbbabddcbabdcabcbdbbaaabaadbbaabdadadccdbaccdcccbbbaacabbbcbaddbdaccbadbbdabcadbccdbaadaababadbdcbbbdcdaabadaabcccbdbcdbbddccaccacbbadcbadbabddddcbbcadbddbdaaddbdaccdbbbcdcabbaadddbbabadbbbbbdbbbbadabdacbdbacccccaadbcdcadcbcdddcacaabdaccdccbdaadcadbaddaadcacccdadbdbdacbdcdbbaddacccbbbdccadcaaaabbcbccdcbbadbabcdbbaddaacabbbccbdccdbaadcacacaacbdccddcbbaabcaddcdbddbdccbccbbcccbddaacccdaacdabccbaddcbabdbbacdcbaadbcbbdabdcaadbdcdbbaaacbcdacddbcddcddacddddddadadbbaddaaacaababbbabbcbbcdcacabdbbcaaacabdcbcaaadcdbbdaaccacaacacaadbccacbccdacabaddbcadadccdcaadddbcbabdbaacdcabbabacbcdaadcadcdddccacccdabcbacaadcaacbcdbdadcddadddbaaddcbadaaabbdbdcacabccccbbddbdadccaabdaccccccbccddbadbdbacbddbbddadadadbcddcdddbdadadbaccadddcadbbbddaddcbabcddbdbadacdbcadcccaabbbabdbacdbabcaadbbbdcbbaabbacdbbcdcdbadcccaabcccbdbcdaadcadcdbcddcaaaccbaacadddcbaccbbbdabdabadabaaddaacaaccaadbccbacdbdbdcadbcdbdaaaaacccbcdccbdacbdabcaadabaddcccbacbacaccacabadbdbddbddccdbadbbdadadabaddcdaabbcadcabcadbaabaadcabbdabdbbbbaaaddddcccbddcacdbacdbacbdbbdabadabcadbaadccdaabddccaacacbcbdacdbcacbdaacbbacbbbbddcaacaaccddcbdddbcaabdccdacdccdaaadaadbdadaabaccdaaddcaaacccaadcadadbacdbababcbbcdccacddabddaadddaddcdccadcacdcacdaaabcdadcdcbdbdbbbbdacadbbdccdaaaacaacbaaadccddcdaddbbcbbcdadddabaacbdadadcddcbbbbccccdbdcbdddbabcbbbdbaadadccbdaddcabcbdddbaadacdaabdcabbccddbadaccaddacdadcdabdaadbdabbccccdbcccdadcadaacdddccbddcbbdbcdddbdbdcdcbbcacdcacacddbccdcbbadbcccaccdadbabcdcdbcbdbabdbabccadccacbacdbcbacbabbcbdaaadbacaadbdddacabddccbdcaaccaaddbcbdaabcbcdcdbabababdaaacabcddcbddccdcbdcabadcacbcddcacddaabdbadcccdcccacabcdaadbcadadbdbadbcaccadaccbbcbacaccbdbdadcddadadacbcbbaaaacbabbadacdabbddabaabdbadbbdcdbaddbdaaddcaddbabdcdcabdaacbcccccbcabcdaddaadccdacbbdacaabadbdbcbccccbccbaaabbbbbbabdbdcdacaaddbcbcddcdcabcdadadabbcdcccaabdadbdadabacdddbcabdcdbdcdbbbabccddaacadbbdaabbaaddbadaadcadbdcabcccdbcdaacdbcdaddbadadabdacdbbddbccdcdddbcaccdabbacadcccaaaadcaadbbaacaccdacccbbbddacdadcddbdacabdadbcaaaabbdbcacddabbbddccdacdadccaaabdaabdcdadddbdccacbbdbcdcaaadacacbbddaaabdacccacdddabdddaccdddcabddbcaababbddcdbabcbddbaabcdbbbabbbbccdcdcbdccdcbdabbbaabacdcabcdcaddbdabcabbabccbbadabadbccbccacbbaadbbcccbdcccbdacacccbdcdbbdccacdbddbdaccbdbaccadbbbbbbaadbbbacbbadbbccdddbbccddcbbdacaaddabddddcbadaacdbaadbbaacbcaabaadddbddcdcddddcdbdacabdaacbbabdbbdcdbdddccdbdbcddccccbbdbbbbbacacdaaacaabbbdcababbdbadccdcaaaabbaaadbacabaabddaaaddacaabdabddcaaddaadbdddbbdbddccdaaddadddcccbccbbcbadabcdabaccabaabdddbaddbadddddbddbcdbadbdcbbcadccbdbdaddababaabaabdadabbcabbbccaaccdacaadbbcbcdcddbdaadbbdddddbbcaddbddbcadcbaaabaabbcbcbbcddadabddabddccdbcdcdddbcdcdcbcadbcbdbabbcddaddcabbdbccddbacdbabddccdccdabcbbbdcadbacbabaabaccdaadcabddcbcbddaddaccaabaacadaaacdbbbaabcdbaaaabaaaccacadbadabccdadaadacbbbbaacbcccacdbdbcdabcccaababaddcadacdcabdadadccaabbcdaabbddcccdbbbcccbcccadbccdcaacccdaabbcaccdccbddbccddcadacbbbadacbcadaadccbcadbaddabbccadadabcbadbbcccbcddccaccdcdcdccabdbcaabcadbadbcacbddddbdccdbddadbbddbcccbdbbacbcbcadbaabdcabdadcddadbdcdbbdcccccacbbdacdbaddcbadaaddacddcbadccabcbcdaabbacccbdbadcdbcadaccddddbbcaababacccadbbbbacbcdacdcacccaaadbcbcbdaddacbcdbcaaccaaacbccdcbabdbcbbcddccdacadccadcadcacaabddadaacccddbcbccabdabadbbdcbcacaccddaabadccadbdbbcbaacbbaaadbdabdadadbaabdaddccbccdcbbdbaacadabbbdaaababbdaccaacdbcdcacaaccdacccdbdbadbdcaadbcccccacddababaccdcbcaddddbaadadddbdcacdcbdcbbccacabdaaabbbcddccdcddaacacabccbcbabaaccaabacbbddabdabdbbaabccbcdddcaaacaacdbbaccbbacdcdadccbcbaabbbaabbdbcadaadadbcdbcdcdcdcaaacbcbcdbcdcbbabcbdbaddaadbdcaaadbcdcdaccbdaddcdcbdbcccaadadddcdbbbdbdbadcddbdaabccaabbccbccbbcccdcbcadbbccbdbcdbabdcdcccaddccdbcbaacdaccbabbabddcabccababcbbccdaacabacdbdacbbdcdbbbdcbbbabdbdabadbdabccabcccabdcbcaabaacbbbcbccbadcdbdaccaadcacdacaccaaadbcbbbcdaadbddaccabbdcacbcabadadbaaacbcaaaadcdacdbdaaacaaabbcadabcbbdcdacdaacacaaddaaaddaaccaccbadcadababcaccbbdbccccbdbdaabdccadbcdabcbdcbbdbbaccbaddddbbdccdcdbccbbcdabcbdbadabdaabbbdbaadabbbdabadaddaacacadbcbaddbbdacaccababbbcccdabbddcdcabcaabbcccbbddaabbdaacbdabbbbbaabbacadcdaddadaacaccaadaabdadcdddddbdacaabaabbdabaccddcabaabcbacbbccbcabcdbbbccadcbbbdaddccccaabadcbbaaabbbcbbbdbdaaaaabdabccbaabddcabaccbacbccdabdabcbbbbbddcdbddccbadaabddabbdbbbbccbcbbacaacdaaccacbdaaaddcddadcbbccddcbdbdbacabbdaaacadbabcbbddbbbdddacbbddbbcbdbbdcccbccddcbaaabacbacbddcbbbccbaadbcbadcaacdbbdacaabdbcdbdabdbadcbcacadcaaccabdcddddabbbccdaccbcdabadcaaaacdcddcbabccddddcbcacbdbabcbdcbcddbaabaccabdbdbdbadcdbbacadddcabaadcadbadbcddcccabcabbdcdbdcaabdabcdbadaddaaccdcadcdddcbdcabbdcbacacdcbdcbbadcdcacbabcacacdcabaabcbbaadaacbddacadbcadcdbaccdcbbcadcdaacddbddbccdccddbaccbabcddbddcabddddccbacbdcadbbccddcddaaaddbcccacbcacbcaacdcaaaabbbacacdbcbabbbaddddacdcddcddbccddaacacdbcdbbaaddabdcbdcccbabddcadccddacddbaddbcbaacdcdbccabcbcddbaacbcdabacbccddaccacdaabcccdacdcbcdadaadcadbbdbacaddbdccbccaacddcacdcadacaaaddaabaccdddcbbccbbaaadddbbccddbbaaacbabdddbbcdbdcddcabcacbbbaadadbdaddcdaaaaaccdaabadbbbdbdcbbaddadabcdccdbaadbbdbcbdbdbdadcababadccdbacddcbbcddbaaadddcdcadaaaabbbcbacddccbcdbcbbbabdcadadcbacdaabcccdacdbacbbacdadbabbaaaccdbdbaadcdcddbaddabdccbccddcbdcadcacdbacbbcadbaabaaddbdcbdbddbcadadddabbbbadbbbcadcadabbbbbacbbdaddbcdbdbccdbdbdcbdcdbadddcacabadbdcdadabcbdddccaacadcbcabcbbabcacdadadbbadaacabbbacaccbbabcbacdaaabadcbacadcddcbbadddddcbcadbbdbabcdcddabaaabccccaaaddabdcbbdcbdbccbabaaabdaabbdacccaadbddabacadaabbcdbbcbddccadcdbcaccbdbbcddbacbcbcdadaadaccbbcdcdacbbcbacdccbcbacbabcbbcaabbaddbacdadabacaabbccdaacacbadacababdbbadacaacabcaadaccdcbbbdabdcaaaadcabbadadbabccdbabbbbdbbccddddadacbcbcdcdbbcddabdbccaaacbadcadcdccdbcbaddadbdbcbbdacdcdccabaabaddacbdbacaaccddaddadbdabdddcddbddbaabbbcdacbccbcbbaacbdacccdbdbbbaaddcbddbbbdbcaabcbcccbcbdccabbdacadccdbbcbdcdcacdabcbbadbbdabcacccdbbcbaabddbbcdbcaddbddabbdcdadaddccabacbbaccdaddbdacbddbbdaabcaacadadbaaaabbddbddbcdaaadcabcbcaaacabdaddbabacabacbbabbaccbbdaabbbbcadaccbaacccabdcacdabccdbbdbaaadacaddabbacdcabadaacddacdaccaccdbdbadccaacaaababbdaccdaabcadaaddcbdbcbbcbccaddadcdcdaccbacaaababddaccdcaddcbbbbbcbadadbdaabdaabbdaaaabbbbaadbcdbbbbacdbcbcbdcbaabccbaaaaaabdadbacaadacdacaabcdbcaaadddabbddbacddbccddacdacbbbdbccdaaaddcabaccbbcbbbcbbbdcacdbcadbdcaddcdbcbdbdadbddcbbbabadcaabcdbcbacccbcababbdbdbcbcbabbcdababddcbdacddbcdbbabdcbacaabaaabcdbdcacaabaabccbacdbcbcbdacbcbdbdbbbaacdbaaacadacdcdbbdddacabababcbbacbcccbdddacbdaaccadaaddaadadbbdbbddcbdabddadbdaccadcdcdccbabaabacccbacbabccadabbddbdababaabbcaabddbdbcbbdddbabdcddaacbbcaccacdaabddbbbbccdacddddccacabcdbddddbcdccabdcbcbdbdcabbcbcdaabdbbbdcccacbcbbdaaaaacadabbdcdacabcbacccaddcccaacdaadbdcaaacbdcacdcadababbdcacaaabcbbbdbdbdaaacaacbacbadbaacdcabdddbaabbdbadaaaddacaaccdbaccbadabdbdccdaacaabbbdadcdabcdacacbaabbaabcbdcdacdbaddadbbbbaddddbdddaaacbacddbadddddcbacaccbbbccbdcbaccdbbbbcdcdcdadaadcbaaccdbabcaadccacacaccdabdcaaadbacddcabccdbbcdcdcbdcaaddcdcaaccdbabacdacccabdabdbddbabbadbbbadcbaababcdabdbdbbcbcbcccccdbbacbcdbacbdbddbbbabdaaaddcdccccccccbacbbcaadbadabadbadadadcbcddcbaacdccbcdabdcbaabaabcdcddacdaadbaaaababbbbcddcdccbaadabadbdbddaabcdbcddcbccdbccaccacdbdbdaacabaabcccbbdadddcbcdddbbcddcabbcadcddacbcbcabdcdacbacaddbdbabddbbdbbaddbadacbabdcaddaabcbacccabbccbabbdaccbbadcaddadcbcbcbcbaaadccaddbadbacaadcaadcacbdddcddacdcbcadccbadaccccccdadabaabbbbdddbadcdbbcddbcacaccacaaabbdbbdabacabdadacaaabadabadbadcdccddcddacccaadbcdbddcaaacdddcccbadaaddaddddbacaacbbbdcddaaabbaabaacdcbdbdcbbddcddcaaccbdccdadbcbabdcdaababacbcaaababbbcaccbbbbaacdbbcbaccaddcaabddcabbbdbaaccbdbcacabcbbcaabdbbadccccaabbdaabaaddcaaadddabcccbacdbbacbabaacabdddcadbccbcbdcddddabcccbccdbddacccdddbadccaadaddbcccdbbddbaadcbacdaadaabdabdacbcabbddbbdadcdbcddbccdadccacdadadcdaadbcbdccdbdcdabbcdaacbbdbcbbaccbdddbdddcbdbbccdbacdbaccababbcccaaaccdcacaabbcbcdbbbacadbcabccbacbcdadbcadccdbcbbdbcbbbbbbbdbddcabbcddccaccbbcddbcccccdaaacbcbadcaacadaacdaaabdcddddaccccbddcdbcdddbcadcbbcadddbacadbdcbddcbaacaaababcaadcbbadaccbdcccccbdcdcbaaadcbaddddcbccabddcdcaabadcaabbcadcbdddccddbdbbccaabdaddabcccaabbabdaaddcdacabdcadaaabdbcaddabccdaccdcdbbddcbdbaadcbbbabdcaabacbbabdcabaabddcaadaadcdcbdcabcaaabbadacbdbbdcabddcbbdabdbcbabcbcbdadacdbcdbaccbddccabbbcbdaaddbdaaabdbcdcbddadcbaadddccdbbbacbabcaaacaaabcaaccbadaddcdaadbacaacdbaabcccbccacaabcbdccadcddadabddcdcabaabacbbcbbdbdacbaccdcacddaaaabcdddcabdcdacdccabbccdcaccbcabdcacdbdaadabdadaddbccacaaabdbbdcbdbdbbbaacacddbccccccccccddbabdaabccccbadaaacdcdbcbbddadbcddbaccccddccdcdccccbadabaacbbccbcdcdcabddcdcadbcabaabdcdaaddcdcadbabadcaababbdbacacadbabdbdabdcdbcbbdacdabdcbccddaabaaacbcdbcdbbadacbbdbaaabacbbdbadbbabdbacbcdacbdcccbbddbbcdbcabaadcbccbabcdcadccabdbcabacacadbdbdddaaddcaaaaabaabbcbbadccbdbdddcbababaabdddcbdaaabdddbabbdaacdddaabddbddbaddbaccaacdbaabbbdcbddddcbdbadaccabbdabbaadddbdccacbbddaadddbcadccbbbdddcbccdacccbcbbbbaaacacdcdbcbaaacbbdaadddccababacaabcbcbdbbddaadbdabdabcbaccacbaadacadcdcbcdcdbaccdcbbddcdbabaddbdccdcbcbaccdabdacdcacdadbdbdcccbddababdddaddbddcdcdddbddcbdddbcdcaabacabcaddcabaccbddcacdbabcaccadacacabbadbdbcbbadadbabccdbabaddacdcbaacadcacbdddcddbcdddaccdddbbbaabbcbdbbbcdbdbbdbddbbdcbccbbaadadbbcaccadcbcbaadcbaaadaccdbacacbaadbcddbcaaaaccbababbacddbbdbcacbdcbdcacacccbadcbbcaccdbdacbdaaaddbdbbabababbbdbabccabacddcccbaacbcbacbaaddcabcdbaadbabdcdcddccabcddbdaabbcdbdcabcdccddddcdbabbdcbccbcbbbcacdacadccbbbcbcbdbacabdbbabddccaadcadaabcadcacabaacdaabaadacacbddabdabcdaaabaccccddddbcdddcddaccbbdbacccdbdbcdbcccabdbacccbcabdabcaacdaaacdbadbdacddcbdbdabcadbcccabdccaccabbabbdbdbbdaacbcdacccdadbbaccddcabbbbcbcbbbccacbabbdddcbbdbcddacbcbcaddacdcacdddcbbdcbddccadbadbbccacdddddccccaddadbbdacbcddbcccbbcbcbcdabbdccbbbbaaddabcabdddcbbcddbbbaaadcaacadbdddabcdadcaadbcadbbddabaccdbacdbaaabaaaaabddabcabcccbcdaacaaccadbcddcbcacdddbbcdbcdcbbddcbbdcaaabcccccaccdcaacaccdbdaaacaacaadcacbbbdabccbaabddbdbddcddbcaadcbcadcdacdbccbbcbcddbcbbaccdbcdbcbccdccbddaaaaaadcdcddbaddadccaccabcbcdaaabccaadadddbaaacbababbcdcdcbddbcbbcddcadbcaaaaccbaaaaabbdcacaabaadabacdbcddaadabbdbadcdccddcadbabcbacddcadacbbaadbcdbadccdbababbdcbbaadadbdacbcbabadadbdcdadcaabdbaaaddcadcbdcabadcdbcbcdcbabaabbbabacdcabdcaddcddbbadcbcdccdbbadccadbbaccbcdaacadbccbccabaddbdcdbadadcbacdaaddcaaacdabbaaadbacbbadcdabdbacaabdbcabaadbcbcadacabbbabdcccabaabaabcccbdccdaabbcccdbccadadcabccdcbaccbadabddcbabbaccabdaccdbadddbcabbabdabdaacbcdbabdbdaadbdadbcbaaddbddbdcabcaacabdbbdccbcdbdaaccabdcaddcadbddcaadadcbabcadddcdcabcbcbaaccadacdbcaddabcdccddbdadbcbadbdcbbcbcbddacbbccaaaacadcdbbbcbcdacdaaacdaaddbddbccadcbacaabccaacdaadbbbcbbcbddadaabdadacbbdadaddaaccadcdacaccadcacbcabdbdcddaacdaacbccaaabcbaacdbdcccccbbcdccddabcacddadbdbadabaadbaacccacbdbccdcaacdbcaadbcbbbdadadaadbddcbadcbdacabaccdbcabccadaadbdcbcdddbcdbaacadaccbbbccacdcdccbcababcdcacdbbaadacdbadcdccbdbcdabcbcdcbddbbabbabccbbcdccbbcccaabbbbaacdabdcbbcbccabdadbcbdccdddadcdbadacabcdddabbdaabdddadddadadcbcaabaabadccababcbdbdddbacaaabcbdddddbcacbdabadacaacababdcbbabbcddbdcbbcdccdcdcaabcabcbaacadbbacadacbbacbcacacdbcaabccabbbcbdcbdbddcbbdbbbcacdacdadcadbcabdaacbcbbacacbbaaabbdacbbdcdcccabaabdadbbbdababdcddadbbabbdadbcabcbcdaadadcccdddbbaccaabcaaccdabbcddcdcaacddccbaabacabacdaccaabacbbdcdbbbcccccbabcdabbccbbdbdbcbdbbabcdbbbabbddbcbbadddbddccbabdcacbccadaacdcbdadcdddabbaacaaccaaaddddccdbbcdacdaaabbbcccdaacdcaccaaaadcaacadacacddcbaacabaccbcaddccdccdabaccaabaaadcdadbcabccbdcddddcbaadbcdddaabbcccacbcdcdcaaccabcdbddbaddbdcccdbdaadbacadcddccbbadbababbbbcbddcddbabcaabadaccabacbdbacaabcadcacacbadcacadcddcbabcaaaadaacdbddcadddddbdaddddacaccbdccdbaababacadaccadcabadbdbcdadadbabdaddbdabbcacddbcccbdadadbbcbbbdaccbccbbcbacddadbcababaccbdaaccdcbcacbabdaddadadabcdadabdaaadbcdcddddcdbdcddcaddddcddccbdaacbacbbadcdbcaddcdccbccbbaddaaabbcccdddccabcbacbcbdbcbbbbbbacaaaabacbdbbbccdcbdbbbcbacacbdaaddbbdbabaadcbdddbddabaddcddddccdbbcababcdbaacbbbccccaacdcdddaabcacaccdacdadabccddcdbaabdbcbacadcbadcbbbdadbdaaabaddcabbddcdbcbcdadbcdddcddaaacbababdacaaabccdcaddbacbbcdddcbadbbaadabbdaadacbccaaddcccbadddcdddbbccdaaacbabdacaababdaccbdabbdcbbaacbabadcbdcccbccacdaabdabbcadaadddbbdaddcdadccdcaacccaadbdbaadcbdccddccdccbbcbdacbddddddaaccbdaadcdcabddbbdadabaacddbbcddbdbcdcccdacaaccbcbcaaabababbcbcdbdbdcdbdacdabcbbdcaacaacdaccdbabcaddbabaddccdcbaabacaadcddbacddcbddbbcbcacbbaaddaabcdabbccdcddcaccdddbaadbdcbdcacccbbcaccdbaddcdbabcdbbcacdbddcdbadadddcdadbcdacbdadbcadaadaadddcccddcbaadccadacaccdbaccccbbdbcddbccbbcdbccabcbbcdaaadadbabbbcdddbddaabccdcaddaccacbbadbacdbbdbbbadbabbaddccdbcdbcacccaccadadadcddcccdbcccbbdddbaadcdadbacbbbcbabdbbccaaccccabbaddcabddaaaabcadddbabaaaabdbadacbbbcbdcbbadbcacbadccdacdadbdabaddbaacbbcdaabcaccbaaccccbabbdcbdabacddcbdacaaaddaccbccabccddccacdcbadbcdbaadccccbadccdccdbcbaacacbadacaadccddbaacaaadaaccbadcdcaacbcddbdbadaacbababaccccdbacbdcbadbbdcbbabcdcacdabdabbacbbacddcaacddcbddbbbaacadaaabacdaaddadccadbdbcbbbdcdaddacddddccbdbcadbdbccaaabbcadbcbacbdadbddbcdabdabaddcababdbcabcccbacdbbdcdbcadbadbbbadcaaadbcdccdbcbcaccbbcbdbbcaabacdcccadcaadddaaddbccbacbadcabbadacbbbcdadddaadccbcacddbabcbbddbddabcacdbcdabbbbbdabcdbbcbbcbcdcaacdcadddabcdbbaabbddabdabccaabcbcbacbcbbbdabbbbccacdcddccdbcadadbdcdaadacbdbaddbdadabaaacdddcabacbabcaaddcaddcdbccbbdbaaaddabbbadddcbbdbacacdddbbabacddcbabdccbdadbcbdadcdcbcccaddbcccadcbcdacbdbdbbbabcbaabdbcadaadaacbacbdcabddadcddabdacbddddccdcaabccccaadcbaccdadbcdcbabaacccccdcdbaabbbdabcabdbacccbbcdcbcddbbdaacbabaddababccbbbbacbcbaabdacbbcababbbcccaabbddcdbcadbcdadcacacbbabadcbccdbdbccdccbacccabdaaaddbaccddcccbbcbdbadacdaababbdcdacabcdaacbdbbcabdbadccbccbcccacbbadbaabbbbabcabacaabddacadbbdcadcddbdcdadcdadadddaaacbaaccdcccacdcccddcdabacbcdcdddcbcdbadbcdaddccddcbbdcaccdadbaaaaaaaacdbacabaabcaddbbdabbadacabcaccdbcabadbbbdbaadcabbdcdabcdbdbbabdcabbbdcdccbadddacddbaacacbddabbbacdaddccbbaadadbcdbaadabaacbbaaccbdaaddccdabcbddcdadaddbbbabddaaadabababdcdcdddcbacdcabccadbcbdbcdbaaabdaddabcaddbbbbbdbacbaaccbbabccabbdcacacdadbaabcdacbcbccdcbdcccaacdbbdbabadbaaacbacbdcacaaadcdccbbcbbcdccdcabdddcabdadbacdacdaaadcbcdddbdadbcbabadbaacdcaddbcaabbbabbcbdbcaccbaddbaadacbbaccacacdbbbbabdbacbabcbcdccaddadccbbcbacccaadbacbcccbbcabbcadacdacadccbcbbdacbccddabdcabaccabaddcbbcbcaacbdcdaaacddddbbbacacbbdabbabdbdbaababacaadababaacbacadbdadbdadbbaaacdbaccddadadbaadaacaaaccbaaccdcaacbacddbbccabcaccaaaacacadddbbddbdbaadcabbbdddbdaaadddbdbadcbbacccaabccbdcbbaccadaabadaacbbacadaaaccbdaabccacbddcdadabdcdbacdbabcaaccbdabbdbbdaabcacccccdcbbaddbbbbbabacbdadadcbddcdacaddaaddbcdbbbadcccadccbbbaaadcdcbcdbaabdacadacccddabcbbddaabbddcabacccdaacabbdcaddbccdbadcabdaccbabbabacbcbaacaccdccbadaddabbcdcccdbcdabbbbbbdabdcbdccbaaaabcaccccbdbbbdadaaadbcacbadacddccadaacbdaaabcbddcaabcaccdaddaabdccddcccbabcdcbdaacdaacdbbaaaacacacdcbcaccabdcbaddaadaacabddddaadbbdbdabbadbdddddcbaccbabaabbdaddcadabcddcccabccbddaabbcdcdabadbddaaaadddabdadccaacabaccddcdbabbdbdbdaddaaacdcdcbddbbbbcbaccccaccddddccdcdcaaadbbbcbbcdcbacbaaacdddabbdcccbbdbaccaaaaadbaccadddcbabbcddbcdabadcddbbdbcdcbdbbbbcdccccbaabacdbbddbdbbbcaabbcabdbdcdcacbbabdabcccdcdcbbbcdacdbddadacbdadcdadddadbbbadbcabbbddbaabaabbabccaddddcacadcaaabacccaabcdaabbcccbbcbcaadcbaaabccdcbddbcdcdcabbadabcadbbdaadadbbbacdadcbbdbbcdcaddddadcdacbadcbbccbaddaadcaccacdadbdbbcbcbdbacaacabdabbcdccaacabbbcdccadadbcadcadabbdcdbcddacadabddddbbbbbdcaccccbbbabddccdabbbbaadddddbbbcbbcbcdbbacbacbccdddcadabcadabbdaabdcadbdbacbbadadaadbbbabcbbcddbacadddddcbadadacbadbdbabdadaabacabbbdacdccddbddaddddbbbcdddbcabaacaabacdcbacaadbacddadabdcbaababacdaabacdcccccbacaadbacaacadbccacbcadbbcdaacdaddcbdcaaaaabdabdcbbacddcdabaacdbcbdbccbacbabccabcddcdcddbcadcbdbdacddbbbcdaadacadbacdacbaccadaccacabbaaacddbcdcaabcadaccdbaccbadcbccaddbcaacbbddbadcbddbbaadbdbbadbbcaaddabcbaaabaadcddadcaadbbbbcbdaaaddcdaaaabcbcaadccdaddcdabaddbbdabddbcbccbdadbbabbbcdddacdcadbaddbadcdabdcdacdbaccadbbdcabdbddabcddbdcbacbbbadaadbcdcbaaabddcaccccadcbdacbcaadcccadbabdcbaabcbbcabaadadcbbccbaacccabdbbbddcabddabacbbadcbbbdccababcbcacbbdbbdcababaacdbabdccbabdacdddcbdbacaacbbdacdbbcbcbbcadbdcccbdaaabbadaaaccbcdaabaccdbcdcbcbdbacbcccdacaaaccdaadbbdcbdcbbaacabbcbaaaabccabddbcaadaaabddbbabdccacddbbcdccdbdccabdbabbddbddcccaaacbcadcdcaaddcadcadbaabcccbddbbaaaddbdacbabcccbacddbacdcbbbaabcabcbdbdadbbdddcbabddddbcabdcdbabccbccbbdbabcabddccdcaddbdacbaadccabdbbacadadbdbdbdaacbbdbbdcccacadbdabbbabcbcadcabcbbabdaacdbbacbbdcdbcdbdabaacbdaaccbabcadddadcdbaccadabdccbddddcabcdabbcbddabddaadacadaaaabcadcccbdbbcbacbdddbaccbabbdabbacccdbdabbacaabbdadbcacbcadcbabcccaddddbcddddbbbacaccbacccccdadabdbadacaadacccacbcccddccbcbacdaccacdadcbdbccdcddaaabbdcabbaacdaccccabdccaaabcaabcbddacabddbaacccabdcbcccbccbcdccbdaabbcdbdadbadcaacabdadbadaadbdadddcacdcadaabcccbadcbcdccadcdbacbddddbaadadadaadacaacdadcacacddccbbaccacdcbcdcdcbdccbbdbdbdaacbadbdbbbcbbdbccaaccdcaabcddbddbabcabcaabccbacdbbddcddccaaaabcbadbbdbcbcccbdccabcdbdbadbdbaabbcbacccbcdcccdccbdaaccccaccdcdcddbdaccdccddbcaadbdbcadbcbdbaccabdabcdcdcbbadbabcaadbbbcabccbddaaadbbcbcccdbbcdcadbadccdcbbaccbccabcbcddbcccacbaabcbcadadcaadaaadddbdaabccdbdacadacdbabbdccddadbdbddddcdabcadaddddcbddcabdaccdaadcdbddaaacacbcbcdbcadadcbaacbcabcadbdabbabccabbadacbaacbbccbaadbabdbcadcaadccdbccdbcabaabcdbcaccccbbddccaaaabdbbbccbaaaddddbcdcbcbbbcabddcbacadbbddbccdcadabbbcdbcbdbbdadbbabbdcdbcdaadaadccabccbdddddccadbbdbaaabdaadcbaccacdabaabbbdaaddaccddcdadcdabdccdcdcaabbcbddddbddccabcacdaaadcbdcbbbbadcdbabdbabdadcdabadadcbaddbdbbdacbbcaabcdbadaacdcaacdddabdaccbbdadabbcbdcdaccadbcccbcadaacccadacbaddcbaccccdcbacdcdcdddcbcccbbcadbcccabdbddaadabccacddcddddadacaddbbbdabdcbcbcdbdbdaaccbddcdbadcbdcaaddddbadbcaaababdddcbbcdbbccaccbdddbddbdcbacbbcbbccccccadccaddababcddcbcdacbaabbcabdbbcaddadcdacbdbacbcccdddabccaabcadddcabdcbbdddcbdcacdcbcababbacacdbbbcccdabbbddcbbcbdabaacddaccdaaaacdbaddcdcacbccddbcccdbbadcbbaaddcdbdddcbaadacadcbaadcaccabcdcccdcbdadabdaccdbadbdcbaccacddcaadddacaadaabaabbbbbbbddbbcdaaccadabcbdbdbadcbabcbcdccdbcadadccaaaacaadacbbcdcddcacdbdcaaacdaccaababcddabdddbadcdcbbdadbbadadabdaddaacadbcbadbdbcabbbaddadadcbdcaabdcddbdbccdaaacbcadbabdacbadabbcbccdcbdaaacbacdcdcabdbcbbdadacbaabbdcabbabbbcccddadcdabcaaddcdaccacabccdbddcdabcbacbbaabdaccbdacdaaacbaadddbadaadcaaadcacdcabdbbbdacbbbdbdbddcdcaadaaaddcddaaaddabbcaccbbbccaaaaadcacaddcadccbdcaabcaddbbbdddaccbcdcdacbccbbddadcbbccdaddadbccacadbddbacabaaaccaccddacaaccacacbbacbcdacdaddbbbdbbcdbdbcabbbbdcdbacbdcdaddabbaaddabdbbdddbbcbcddbdacaddccbdcbdaadadcddadacbacbadcddcdcdcacdaccbcacdddacdbbaccbbbcdbdcacdcbbbddbbdabacccdabccacdbddabbaddaccbbaadbacccccddbacbcccdcacdbadccbcbadadcbcdaddcacbcabcdaabcdccdbddbcbcabcbbdabbacacdbbdbacaabbddcccdabdaacadababddabaddadbaabbaacacddadddaacbdabbcdaabbaaabdbcccccaacadcdabdbdbbacabcbabbddaaabddaccabcbcbdbcdaadcdaadabcdcbcadbccaccbdaadcacdbdccdddbbbacaccadaaacaaabadadabccadcabcbcdbcacacdccbacdadcdacdbccbcbcbacbdaacbbdcadbaccddaadbacadaabaacabbdcddbcddabaccddcbdcaabcdbccdcbadbcdaddcdbccaaaccdcbacbdddadbcccccaddadcababcabbddcddccbbcabcadabcbcaacbdbbcaaacacbbbcdacccdadaaadcaadaacdbcccbddadddcbadaaaddcddbacadadbbdaaaddaccabbbacbaccddbbcddabcadacbbdabcdaddcdccddcaddbdcbbbabaadaaccbdbcadbbadaadbcacbbcaaacdcbbabbabaabbbabbcdcccddccabbdadbcbdcdccababccaddbbddaddddbbddcbdbbdcbdbabcacadcbacbbdbbbaaccdccbadbbddacccbdbaacdcadddddbdddbdcaccabdbaaaddbdcdbcdcbbadddbbaadbccdcbacaccccadaddcaddcdaadccbabcccbcdcbcdacdbbccaddcbadacaacdcaaadaabdaaadbdcdacdacbdabcdcbdccabbbcbaccadbdbaddaaabcabacdbbbdcaadcdcbcbbbabbdcdbabdaacccdabcbccbaddabacadbdacaabdcdacdabacbbbabadbcaccaddbccaaacbcdadbbccbdadaaaddbccabadabcdacddcabaddbcabbdadaadcacbacacbacdcbbdcaddacbbcacddcbabcbaaabacbbcaadaacbabdbcbcadccdcdacbcacbacccaadcbbaadaabdbadcbcdadaabcaadbdabcbccdcbbbdbddaabccdccaaaabdcccbdbdddbcbccabadcabccdcbabcbdbccbaabcaacbacdcdabcdcadccbcdadcabbcabcddaddabaccdaaabcddbcdacddccbcdcabbdcbdadbdaddacccabcccabbbbbdccbadbcadbcbdadabdcabcaadabdccbbddccaadabcacdacdccbcdccbbdabadcaababbdbaccbdcadcbcabbcccccdcbabdadbaabdcabbcbbbaddccdaabdbadadadaaabcdcdcdbdaddcacaadbabddacbbaacabdbbdcbbabcaadbdbdcdcbdddaddccdccbddaadcacdacaabbdbdcddbccababbaaaadbcddaacaacbbbcbadcdaaadbdaadccadcbbbccbdbabccbbbcdddbbadabddcbccdcdcbddccacbaabacdacaacdcabdabccdbdcabcbbcdcccdddbcabacadbccbbdbdaccdbbacdddcaabccbdbacaddccdcccbbccbdbbdbabbccbddbddabbdcccbaaccaaccbbacdcbbbbccdaadbbcacdbdabacbabbdaadbddcadbdaabdbccbacbaccabacccdbdccacdbbaacdcdcbabbacdcdaadcdbacabadacdabdbdcbacbccadcacadcabdcbdddddccbddaadbccdcdcbaacadcadaddbddccdddacadadbccdccccccadcaddcdaabdabbddbcaddccacbdcdbacabcbabdbcdbbbacdaaaacbaccadacbdadbbcdcdabcabdcdbdbacbadcbcdbbaabbdbdacacbbbdaadddccaabbdadabdabbbcbabbccaaacdabdaadddcddddcabdccccdacdccbdccdddbbcaccdcadbdbbbdabbbcdadbcbcbcdccdbcaadcacdddcddabcadcaddddabbaccacacdabcadacddcabadacbcddbabbdbadbddccbdbdbbabaacacbbdbaddbcaadccccdbccbdccbcdbdababadabbcdddacccabcabbacaaaddaaaadddbadbbdacbababbcbadacdccadbbbcccbbbdabacbcbbccadcdabdabbdccbbbccbdbaddddbacbccbbbbcbbcaaaaaddcbadbdbdaadaaddcddaddbadcbdcacbacacbddbadacddbbbabdacdbcabcaadddcccccaccdadcaaaadcabcacccaccdbccaccccacabdccbccdcadbaabcbbcbddcacbccbdddcdbaadbcccbddbadddbcddabdcdbacabbaacccdadadbcabadbdcacdddadbbbdccccaaccdccbccacadccadbcdaccabdadcdabbccdbabcccdbbcdcaaddcccbcddbbdcccdcbabcdaccddcaaacacccbcabaabcaddabcacabdcacdadbcaaadcabdababaaaadabcaaacccccccccbdbbccabcdaadbdaadcacacbacaaacbaacccddcddbbdaccaddabbcdbdcadaadadabdcbbddbbbcaaaccabdcaaccbbadaddbadadccdbdccbdabcbcbcbbaacccdadddcadacddbacdbaabcdbdbacaabcadadcabbbabadbcbcbdaddccaacaddddcaccdddabaacccbbbdbdabaabbddadbddcddabbaaddddbddbcbbdbcdcdcabbcacccbcabcdadddbdcbadbbadbaccdbdaaddddbbcaacbccbcababdcacbadadbbbcadacdcbddbccbaddadaddaabddadcbcaaccdaacadaabdaaacdaacbdcccdccccbadaacbaadbaccbbdbcdddbddcabaddccbddcbabaaadadaabaacdbbadadbcdaacabbdcbacdaccdbbbccacbaaaadbcdccbbbbcbbadddbdbcbabdbacbbacbadbcbcabbdccaabdbcccdbadbcbbaadadacdddccdddacbcdbababdcccacbcdabaadabadcacbbcdacaccbbbaaadacbccbbaaabddabbdddbabacdcaccbcbacddbcbcbbbccbbcadddcdcadbcadbacdaabcbdbbbadadacdbbdcbbcadaabbdcbdabbbdaabdbbdabbcbaadcdbcbccddadacadbcdaaabaabcabddcadaabadcbcdbadadccccbcbcdcbdcdbbdcdcdcababdaadcdadcacabccadddcaadbbabbbdddcbabddaccbcabcccaabaaaaddbaacdddbadbbadacbccdacdbcbaddcaabbbdddaaaacadddcbacaccaccabcccbddaacdacacbcdcacbcccbccadbcaddcdabdbccccbbaddddaacabcbcddbacdaadabbadcccdbdabcdbaababcbcdadadabbbaaadacccdabbcddbccdacddacccaaccaddbbcccacbbacabddbbdabcbbbbdccaccabaabbcddbbbcaccdbdcaaddcdadaacbdddadbadbddacdddcbadcaccddcaccdbccabaacbbbccbacdbdccadaacccbdaaacdadacaccababaacabbbbcadadcadacbdbbbaaaaacbbaaabdacdbbccadcbbacbaaacaaaaaabaacabdaaabcdccbaadddbcbaddabaadcbaaaddcdbbabcbccdcbbddcabacbdcccadddcbadbbdbccaccadabbcbaccabadcabcbbbcdcdabdbadbdaaddaccddbbdcbbbacdcdabccdbdcbbdcbaddbcbbbbabbaaadddddddaadbcbccddddabcaddccbbbddbdddabdaabbbdaabcdcdacadbabdcdcbdccdaabcacddaacbccddcaabcbaabccbaddcaaddbdcaccccddbbddbdbcdbadcbdbdadadaacbcbbbabdddccbcabddddacbadbacbcdbcaacdabddcbacbdadabdbcdddcddacdbdcbaadaaaddddacbbaaabdccdbaadadcbaccadcbaaacdcaabdbbccdadddbcaabcccaabcdbacbbdbadabdbcabadaccacaadbdbdacdccabddabacddbdbcbacadbdbdcacbbbcadadcbbccbdbdcaacabddcacbacccdcbcabdddaddaacbccbddcdacdbdaccabccadbdbcacabddaaadbadabcacacdbdacaacbabcbbcdaadccacbdddbacdcdccdccaccaccbdabdbcbcabaaccdbdadbbacddaccbbbbdccccdcdbcddcbcbddabaabdddccdcdcbbcdddbdbbbcbcacadccdbcdaabcddcccbadacdabbabdcabccbbdcddddcabbadcbbaccbdbdaacaaccbdbacdaddbdacddbdbacdadcabacdbbbbdcbdcbdbbaccbdadcdabbcdbbcddccdbdaadbddcabaddbdccaaaccdbdabacaddcaaadccbababcadccadabacadbacdbdacbbddbbaaabbabadcacddcbdbbdacadbdbdbbacbcddbaaabbadacbcacbddababaadddabdbcbcccadcddcbdbbdcccadbacddcbbcadbdaccbcaccccccdaddcabaabacaabcbcbddccabddccdcccbdadbddabccdcddbcaccdcbbacacccdbdacbaadcabdadaddbaccabdccbbdadaaabdcccaabbbbadbaddacaccaaccabcdcbdcaaacadbccaaddacdbcbcadabbdaadcbbbbdbaaddcabddddcdbdcdbdbadbbddaaccbcbbdaadbddbbddbcbbabddacddcbacccacbdbadbbdddaaddddccbaddcabdacaacacccbabdcddcdcbadadcbbcbaabadbaacaaadabbbadbbbddaddaadddcdadbacbadabaacdcababbbccbdcdbaadbcccbccdadaabbddcccbcbcbbbccaccdaadcabcaabaaddccbcbcbcaccdcccaacdaacacbdbacddabcbcbccbdccccbaadbacbdaddcbbddccddcabbacbaadaacccbbaabdddbddbddbdabbbaddcbddddaacdbbabcdacccbcacadccabacdacbbdbdacaaaddaacacdddcdaacabdbbdbbacaacaccbbdaabbcaaabdabcbbdccbdacddacbcdabaacbdddcdbbbcacacddddcdccbcaaadacbaaddcbccbdaadbbbbcbabdcdbabdddcdbaabcabddaaaddadaabcbabdbdadbddcbddcacdbdaabdddccabacdbbacacabbabaadbdadaabdbbacaabddcddaaddccbacccbadabacabbacbaccbbabbdbabbbcaabdaaaabbabddccdcabbadaacdcdbabcbbaaddbdabbacbbacdcdbdddbbccbcacdcaccbadaaaaacbaccabdbbdbcbbdddacaaaabdbbdabaaccbcdddbadacbabaddbcadbdbdacddcaacccabccdcadbbabdacbdbaadbddcbaaabccacdbdbcdadadbacaaacbbaaadadaccdbdbdccdbbaaaddbbcdaabbabdaadbdabcccdbbdbbdabdddbadcbbdcdbbcbabdacadcdbdddcbbdacdccadbbdbbbadbabdddbbdbbcbcbadbacadddbadacdbaaacacddbbbcabacadbdcbdbaacaacdaaccdbacabcaadacacdccdccccdcccdaddcbcccbcccdcccdcbabcaadbaacddbdddabcadbacacdabbabcabbbdadadbbdaddbddbcbdbadabcbdbddabcbbaadcadcdbcbddbacbcacccdaddbadcdcddaadaabdaabcbcabbcddbcbaaacccdddbdbaabaddcbccaddcacacbabbadabacacdcdaaddcbcdabadaccaabcacaacacdbddadcacbaababccbcaabadaddadbbbabccabbbbbddaadbdacdccadcbbbbbdccbdaddabacadddabcacdcacabbacaccccbabbccbacbccbaccabaaababdababddacbabcabdbbabcaacbaccabbbbddbbccdcddadcbcaddccbccdbcccadcccbccdbbccdbdccbacbbaaddabcbaadaabbadaabdaacbddcdcddbccadcaabadadabdacdcdabcdadaabadccddbdbacacbcbdcdbbbdcccdabdabdacbcbddbcbddbbdaccadbabadbaaacaadbaddbcdcdbbcdbcadabdbabbbcbccddcabccbbaadddccdaaccaacbaaccabaabdaabdbadcbdacaaabcbabacdbadaadbbcdcdbaadacacbdbbcbbcbabbdbbddadbdcacbdbadccdbddaabccdbacccaabddbcdbaaaaacddbcdaddbbbbbcbbcdaccdbdaadcdcddcccddcabcdccdaddcabbbbbbcabddcdbcbccccaadbbabbbdbabadaccdabbaccccbaddbddbbbbddabaaddccbcaabdaccabcdacdcaabdcddcddcddcbccdcabcabdbbccbabbcaadbbabbacdbbcbbcabcbdadccbbbaaaadddcddcadcdabdbcdddcadcddabacbabaccddcdadabadcccdcacccbcadbaddcadaddcddccbcbabddaacacaacbdbdabadddaabdbcaadcbcadbcbacdbdcccacaabacbddbbdcbdaacbdcadabbdbabbcdbdbcbddddcabddbdacaaddbbccbbadadabbbadddababdcaadbcdcabddadcadbadbabddcdbdcdddbcaaaccbaadabbaacbaabbacbdddbcbccdccbaaaabcaadcbcbdbdbccccbcacdccddabacacabbdaaacdaacbccabdcbbdccadacbcabcdcbadccccbabbbadcaddddbbbdcdaccbccadbcccadbadcbdbdcadccdccacabdddbddadbcbacbdbbadddcadacdcacddbbcbcdddbaccbccbbcbbadadadcdddadbcabcabdaacabddbbbdbacaccddaaabacadaaabbdcbdbcadbcdcbcbdcbccdbcbaccbbdbadacabddacabdcddabcdcdcdabcdababaccddddbbcdaaabdcaadbdbacadbbcddaaacccdcddabcabddbddaccdcadcddaaadcbdbacbcdccacaaacaaaadbcdcbbadaabccbccaacabcccdbdbbbbbdbdadcabdcdbdbbccbacdbabcbacdcbbcdbcdacbdddbbbdcccadadcadbbaddabdccdbbdadccbcdbbbabbcccaadbbbcccddcdbacccdbcbcacccbddaacccaacdabbadccbcdacaaddcdabcdbdcaddaccaacdbccbaabbadacbccaacccaabbcdacdbadaadcbdbddcbcbabbdddbdcbdddcccbccdabdcddaaccbdcdadccbaabdbaacdbcccbacdbbddccbbccbaacabbdbaacccddbbbcbcadddcddbbbacdbbadbadbdabcbabdbabdcabccdbaddbbdddadbbdbaddaaddcdadabbaabccadcbdacadaaaadacbcadbababddbcaddacdbbccdabccacddcbddbcbacaddcbcddddbcacdbbbddbaccbacaddabbacadddaabcdaaddbdabdcbdccbadbcdaadbdbaacbbbaacaadcaacccabdadcbdbbddadcbdddcccbdcbbdcbddbdaddacccdbaddcbacdcdccaccdcddddaaddaccbdccadadadcabddbbbababadbbdcdadcdabcdbdbbbdaccbcbbabdcdccaaadbcdadbaabccddbcacaccddcdaadabcbcaadacaddaabdacbaaacdbabaaadacbcabdcdbabdbbbaaccaccbdbdaabbdcbbdabbdcabaabbbccbdacbccccbbcbbadccdcccabbbbadbdadbbacdadcadacbcdcadacbbdadddabdbcbabadbbbdabddbcaccbbddcdcabbcddbcbabbbccdddcbccbbaaddbaaccbbadddaaccbcacabbcbcdbbcccacadcdbdbbacaaacbcadadcbddcadcaadabbbbcadaddbdcaddbabbbdabacdadbdbbddccbddbcadaadacdcdaaddadccbaacbdbbdcdacdabdaabdddaddbccdadccdadadaabbcdadadddaddcdcdabdaabacabcacabccadadcbbdbbcdddcbbbdbdcbcddcdadccdbbcbdcccdbdcccbcbccbdbcaccabaacdccbbcacdaddbcbbababcadacdbaabdccbabaddbbbcdbdbdabdcbadbabcdcdcbdbdcdcaacbbdaacbaaabacccdcdbbdbcbabbbcdbcacacbacabdbbddbadbbcdadddacdaddcbadbddcbcadbacadcbccdbabcdcdbbacccabadadbbcabddbcacaaadbbbbdbcdabcbbbadcacbcbcddbaabbdcbaaccdccdcacddacbadbcbabbdbabcddabcbabacdaccbadbcbacaacbabdbbadcacadcbbdbacdbacddbcbcccacadaaabacaaacaddaadbddcaabbaccbbdbdacabdacbdbbbdbbccdcababaacbbcddbbdcdbdcbcddcaaddcbdcacaccabcdbacddadbddcacacadbabadaddbabadabdbbbddddbaabdddddbcadaacbbabcdbadbdbbddbdcaabaadbccbdadcababadaaadabbdacbbdcadbbbaadcdcabbabccbbdacacbbaacbacdadcccacbcdbcaaacbddaddbdacdbbaaaadcaddbbddbccdaddcbdbcbcdbacbbaadcabdaadbbacacabbcabcbcacdcdadddbcadacaacabdcdbdbdbdbdaabdcdabadcaabdbcccbbcccbbcabccdbaadcdcaadaadcdaacdcadbcabccccbbdcdacbbadabcdcbcbddbbcbccdbcdaacddddbdbdaadbccdbbadbccdacdbcaaacabbdabbcbcbdaacdabbcccdcdcdcdbdadddbadcbcbbdaabcacdccdbacbbcccbacbdcccaaabcdddbcaacdbbaccabdacaccaaaacadaaddaccccacbaaadcdbbccacccabcaacdcbbbdbcbcdcdcbccccadcacadcddccbdcdbbbbbbbcddddabbccdacdbddadccbdccaaabbdcdbcacabbddcaccdbadbcbabddbccccadbadccabbacdcabaabbcbbdbbbdbaccdbabdcbbbdacadbabccbbcccacdaddcdacdbcdadbabaadaabddbdcdbbbddcdbbabccdaaacababdaccdaacbdcdccdcddcacdaabcacbcdcdbbcbbbdbddbbdadaaddcaaabbaaababdbaadbaddddbcbabaabbdbdcaacbddbdbbacbcaadcacadbccdbbdacdcbabbbaccabaadabddbcdabcacabbadcbbdbabaccccbcaabaaabccdbbddacbaadbababccadccaaaddbaaadccbcbcacabacbbacdaacbcccababbbccadcdddaddbadaacbccdbaccaaccdaabbaaccbaddcddcbdbbbbcabddcabbadaadcdadbcdbbcaababbddbbdabcccabcbcbcdcbacdbbadcdbbdbcaadbcaaadadbabacdccdbddddcdccdddddcbbcdadbbbcaaadbbbcdacbadcadbbcdccdbccdaccddddcabbdbcbcbaddbabcbdabacbcabdaacdbdbdabaddbddbacdcdbdddbdcdcdbaccacababccdaddbdcacadbcdbbbbabcdaaadaaabcdcbacbcccbcccbcabbaccaaabbdccbdcaddcdabdcdaaacdddbbabaabbdbccbbbbabcddacccababbcdbabcccbcbdbcbbbbcaacbbcdbccccabadcccbadcacbababdadddbabbdcdbbbadaadbbdddccbdcbbcdbdacdbabddcccbcdcdaadcacacacbdbacdbcabddadddcbdbdaabacbbcdccbdcadccdbcbcbbdddcbbcaabaababdadbbacacdadcababcbcbcbddcdcbbbcaaadddbcbaccdadaabaaaabacddadcbcddabbcbabaacddadbcdccaadbaadbcabdcdcddccdbcacdbccccbacccabccbcabdcaabacbddaaabbccdaaadbdabbbbcabacabddabacbddbacbddbacabaccbaabddacdbadcdacabddbcabcbcbbbcddbaccdaaacdcacbdcaadcccacdcbdbcaddacbdacacdabcdacaccaacdbbcadddbacaadbdaadadacccadcbaabbaaccbadabcddbbbbdbbaddcacdababcdbbbcbbdcbcbcbcbdddcddaddabccbbccbacabdabcdcbbccdccbcdbdabdbabdbcdaddcccccdadbcbdcbaaccbaaaabcbdbccdabdbbadbbddcddcbdbdaccabcbbbbadbccabbbbdcbbbbbbbbaddddbcdbccdaccddbadabddabdabcdbcaddbcdccaabacccccabbacbdcacbdcabcabbadbddaccccddbacddcbbdbabaadbbaacaadcbdbabccabccdbcacadaaacadccacadbbdbadddcccbcdcdbddadbccdcddbbacbdcaadadcbdcaddadbbaaaabdaadbbbbcaccbbadadabdcbddccbdcdabbcaaabababadacacdbccdccadcadacadcddcbacddcdbbcbbbcbcbdcaadabadcdccadcacbbcadcccabacbacbaabbbccbaabbccacadbbbbcbacdacbbbaaabacdadcbdbbcccccdbbcbdccbbbcdaaaccdbdaaddcdbdcbddcabddcbcbadbddcdcaaaaabcbbdddddcbabcbbcdabdaccdbdddbdbacaccbdbaccccabaacadbacbccdcbdabacdacbabcaaddbbdaabcdddcbacdacdbaaadddbcbcdcddaddcdccbaddbdaccabbadbdacccbdcbddcbbddccbcbdadabadcdbbdccbcacdcbaddcdbcdbcbdbbabcdbcbbadadbabbbaccbaadddacdcdbacbdbdaaacacbcdddcdbbbddacbacbadcdcccadbccddaacbcdabbbdcacbccdcbaaaabacdbbbccaacbcdcddabdaacadcbadabddacccddabaaccbcadaddbbcbabacbaddcbcdadadaddcadccadcbabbbdcdbadcadbacbaadaabdaaabbaaacbbcbcadccdcbccabbbdcbddacaadaaccaabdbaccababaddbaaaadccbbcbdadbdddbdadcdbddbcbbcbabcdbdbdbbdbdacbabbbbacaadacbacbdadacdaadbddcabaabccbdadcbaabaaaaccdaccadabbdabdabdcbbcbaddcaadbcccaaccdcdddbdabdaabaaddccdddcbbadbdaacbcdbddbadaabaaacdcccdcbaabdcaabccddddbcdabbddbaddabdacbddaaabbdadaaaadabcbbdddcdacbcacacabdabbaabacabbaaaaaadbcacaacdabaacbdcabadacdbbcabdbcaddabbbcddbaccdbcacccdabbadbbbadbcadbdabadbdbadaddbccadaabcdbcbacdcdddacdbddbcdbaabacdaaabdbcccdcdbdaccdcbbbbababddbaacdcaabcabdcadaaaacdccbdacadacbaaddccdabcbccaacdcccccdadcabccabacbbdddaccccccbcbbadaadacbbbcccdcadcbdbaccccacdbccadacbcbcbddacdaaddcbccdabacbadbaaddaacdcabcbcadbaadcacccbcbcadbacadbbbdbbbcddacbbbddabaaabbcadcaabcbbdcdbbdadcabacddbabddadcbbcbaacbdbbaaabddbbbdbdbdadddbdbccccabbcacbabdcdbbccabacddabcdbbbcdbbcddbcabcacbbadcdabdcbbcbdacaacbacabbacbdcdaadaddcdacaccbbcddddbcbadcbdbadbcababbbadbddbcdabacbdcddbcabaaabdacbabcdbbcacdaccbcdddbacabbcddccdcbcbacbaaccabcdccbdbbaadbbcbadbccbadadbadaabdbcbdadddbdcdbaaadbbccdddbbcaadcdbacdabcbdaddcccbccbbaddaadbbddcddbdadbcbaabcbabcabbbdaabbaadadcdadaacbaaaddcddbbcacabccadbdacdaaaddcadcdbcccbadcaabddbdccaaabbccaabbdbccbcabdcacadbadabbcdcddabacbabadbcdbdbbdbcaadcdbddcddaddbabbacaaadcdcdaacbcccdbbdddcaccaccdbdbddbdbdcadcaababacdbbdabcaacbdaaadacccccadbbcdbacddbbaabcdcacadbbbdbdcabddabdcaaddbcbdbcabaaabbdcadabbaadcdddaacbaacbccacdbabbaddbdcbaaacdcdccacabbabcbdbdaddadababdbccadadaadbabcccdbbbcadcbcbabadcbcacbbccbbadaaabccdddccdcddaaacaabdbacddaadcbdababdcabbadbbaaacacadbacadbcddabaabcabdccbabadbcaadaaccdaccbbccaacbccabadbbdaaaaccdbdcabcdddcbdcbdacccbbcdcbdbdbdddcadaacaadadcbdaddbdccbdbdacbaaaccbccbdbbdcadaddabbdaabbaaabdadabbbbdbadcbdbabbdaabcbaaddaccbcbaacbaaadcddbdacabcdbcddbccdcacbddadacdaabccbaabcddcccccabbadadaacdbdbacaabccabacacdaddaabadbcdcadccdbbaadddaadcdbdccdbabccbcbddaaacbbacbbcbbbadbddbdbbdcaddccdcacadaddcdadddaacddcbdcccbababddbbaccdaddddbbadabcbdabadcdddcabcabbdabdbbaabcaddcbbbcbcdccbaddcbdbdbcadbabccaccaabbadabddcdcbaccadcbbbddbbccbdbcdcbbdaacabaabbbbdbdbcddbbddbaaccdbbacbbadcdddcaadbdcdbcbadccdcbbdabdaddaadabbbcbcccacbaabaabbaaabadaadcdddccbbaaaadacacbbdadbcdbddbdddbdabcccbacddccaaacccadcaddcdbaabdcacbcaccaacdddbcbddaddaaabbbdacacdababbdbccbdcccdccbcbcabaaabcacccbaccccaccdddacccacaddaaaccbbcbddaacdcdcaacadcdcabacaadbcadcbadcbdbdaadcddbacdaddbcdddbbabcbcdadbadcdcbdcaddbbdbabcabdddacdadaaacbbdadbadcddaabdcbcbbdaccdcbaddcdbacbbadaaacaabbcaccabbbbacbbcdcbdadbbddabdcdcbdabababacbbbdaddadadbbddbbbadcccacbaadbdacadccccaaabacdddcdccaccbbbaadaddcdbaddcddbbabcdabccbaacbcccbaccbbaaabbaadaaaabdaacaabbabbaadbcdbcabcaaddbcadcdbddadcadcacccdabbdbbdaddcadcbcbdcdacdcaadaaaaaccccbaabacddbddddadccacdcabcbbbdddcdbabcdcabdcacbbabdbbdccabaabdabbcbcbdbbdabdaadbababbddddbbcaadcdacaadabbdbadabaaacbdddbadbddacddaadbaccdccdcaadbdbaababbbcdbdbbacdcccdadbcacbdbacabacbacacbdbbdbcaddcccdbcccbdaabaccccccbaadabdcbabcacacacbbabbadbabaccadadacdcacdccacacdaccddbacabdbddbdccabdcdcbadddbcaadaaacbadacacaabacdcbdbdacabccacbaddaddbcbabbcadaaabaccddbbdbdcbabcaacbaddccbdbdbdacbbbadcccadbaabcbdddbbddccabbcbdcdddddcbacdbcadcaaccabacdccccacaddbcdbbddacccdacacacdddcadacdddcadabdcddcacabadacaaacaddddcacaaabcccbcccbaccbccddddddddcbcbdacdbadddbbdabcbdbcbadaddbaabababbbbbddcdabacccacdddacabbadcbddaaccbdcaaaacadbabbdbbaacbbcacbdbcbdcbbcbdbbbaabadbbcaabdddcbcbcbadcbdacaddacaabcabbbadccacaadcdddabcabcbadcdabadbabcddcdddabbccaadabbbdddacbaadddcacdaabcccbddbbbcddcccbdacddbabdcdacbbccaaccbbcdbcdddaaabdcdddcaddbbdaaabbbcdcadcbdaccddcdcbbddcadaccbdcbbcaaddbbaaadadaaacdaccaabcbbdcbdcddbbddadddbbbbcbdaabbbdccbcbdadbdbddacadcdcdaddadadcacaddbacbcccabadbacdbbcadabaaddabacbaadccadbbbdcddddcadaddbbbdabadcaaaccdaadddbdaabbbcccbcdaacbbdcccabdcbbaabbdbbcacbbbcadadbdcacdaaabacdcaadadccdbdcbaaadcccccccaacabbcdadaaaadbabdcdbbdaccddbdabcbccaaacbaddccadcbabdaccbacdacdabbdacddaaadbaadaaaddacabadaaacadccadcbcabbcdacdaaabbbcacddbaddbababcccaddbaacdaacbcbcdbaaddbadadddacadacbdcdcadbdadadcbbddacdaacdababbdcaaddcdcbdadcdcbdccdadacddbcddccacccddccdcdadcabaadccbccacabbaacaadbcdcbbcdacabadcbbbaaccaabccddccbdcdcdcbdccbaddcbddcdaccaaccdcbddaabdcacadadccbdadadaaaddcdaaacddcbabcdacdabacbbcabbcdbddcabadbbbacccaccaddbadcdccadaddcaaadabdccbcbaccabbdcdcbabbaabdbbdccdabadbcccdcbbdcbbaaacbaadbdcbdcdddacbcaaddbaabcadbccdcbdddcbdbcbadbabbdddbbcddacddababcdbacabcdcaccbabacbbdbcaaadbabcbacdaaabcddddbacdbdcddddcddccdaaccdababacccddbbdcccdaaddbbaaccdcbbcababdabacccadddadaaddacdcaccbcdcbacaccbaaadcbabadbddcabaacabcdcadcddddcaddccaabaabcbbbccccdabcccbcbdbbcabbacdacbabcddadccdabbddbdbdacdadbcbdccbccbddbaabcbbdbabccbbaadcadbdbcdaaccccabbdddbddcbbacaacacdcaadccbcabcadbdccadcccadadddbbadddbbacaabbdbbbdabbdacaccdaddbcddcbccbbbddcddbaacabaacbdadaaddbaaadaccabcbddcddaaddccbbdbcbacaddabcadcaaccdacbddcbdcbdbdaaddcadccbddcdbcacdcccdbcbccdbdcbbddddacadbcbbdcabcccadbabcbbbababbacdabddaaababddcacabdbbaabbcacaddbbcbbacacdbbbcacbababbcabdcdacccdbbaaccbbaddcaccaadbbadaaccdbccabcccddaaabddacaddccdabddadbbbadacbbadabbbaaccdcacdcbaddcdbdbdbbadcdcacadccdbcdabcababdbaacccbdaaacdccdacbcdacacabbacccdddbaccddbccaacbcddabaaadddcaacbbbdccddaacdccbddaccbbacbbcdbbaacaadbcdddaaaadacdbacddcbaaacaabbcaddcbbacbbcabbccaddcadcababcbbccdaaccabccabbdaadaaadbbddbadddbcaaadbccadcbbdacbdbcacdcdcaaabbaabaccabbdcdbacbbddcabbddbaddccdbdbbbcbaccdccaddcaddbababbdddbccaaacbdcbdabcbbdbbadddbccdcdbdcbdccadacccdadcccddccdbadccdddddcbddcabdbbbacccdbddccdacabbccdacabdcbccccdddaccaccdcaaccdaaaaddbaaabadccdbaaacccbbbbbabddabcddbcabcdcaacbccbdcdabbdccdaddbaaaadbccbdabdbdabdbbaaaabababbdcdbabbbdcbbcadcaadbddacbaacdbaddbaaabcbdbbbdbbdcadddcacbbbccdabdbcbcdaadbdccbcdadabbbcadbbaaabdaadcccbaacbdccaacadbbcdaadddbdddbbaabcdbddbabbadadaabcdccbaaabbdcabccccddcaccddccdaadacbabbdccdbcacdbcddddacdacabcbccccccacccdcdcbcbadcbcabcbababcdcdbcbcddbcaabcbcdacbdbcdaddcdcbababbcbdcdabadaddcdcdbcdbbdacbddaaacbaadbcbcdcaabcdacdcadacdcdadbbcabbdbcdcdbbbcaddddccbabcaaaabdcbbadbadccdbdbaabbccbabcabbbddabaaacbcddacccaabacbddddbdaccdbaaacccbddadddbabbadcddbdbbdbadbabacbaaadbcaababaddabbbacadbcadccadcacbdbaddbabcccabadababdaacaaccaaaaddcddbcacbcdaabdcabbdbaacbdbdacadbdcbccaaccabbadbcdacacaaacdbbbacbbaabcbdcbaadabdadcddbabbacddaaadbdbaadadccabdbadbababcdcabddddcadbdabbabddbdcdbddddbcdcbdbcdccdaacccdbacadabdbbbcabaadcadbdbbaaaadcbbdbdacaaaabdadabccaabaaadacabcacbbbbbacaabdbcbaaabcdbdbbddadaacbaabbadddacababccddbccbdaccadaacccacbdcdbcabbbcabddbbbdbcbcdbddbadcadccadddbccbbcadccbcdcdbccadabdadcaababbacbdbabbbabcadcbcccbcdbaddaaadcabcdddcdcdcccbabbbcdababdbabacdddcbbaddcabbdcdcbaaacacdbbcbccbabdccdbdbcdbbacbcdcbbcacbbacccbcbcbaaaaadadbadcccababbdbdbdcaabcaacadddcbcdaabadbcbaacbbaaaddcdcdcaccddcbbdbaddabbcdabdcdbddaccdcacbabacdddddcccdbcbbdcdadacabbabcddbadbacbcdadbabdbcddcddbdaacbaaabdacabdbdbdbdbadabdcabddaaccdbcbabdbaabbcddbcdacbaccbacdbddadbacaaabdadaacabdacbcbcdacacdccacdbacaacdadabbccabdabdbabadaaddbacddcacddcbbbcbdbcaaacacbbaaddcbabdabdabcddbdadcbbdbabbcddadbdaddbbccddadaabcddbbbabbcccbaddddaadcddcabcccdcddccaaacbdbadbdabdacbdaccbcddcbdadbdadbdabdbbdbbbadcdcdbbbacdbaacadbabdcdddccdacbccddbdaabacabdbbbdcadccadcdcacccadcaadbdacbcddaaddbcdbbbacbacdbcbbabcdbdcbaabbddbacdbcdadcddddbbbdacadbdbcbbaaaaccdccbadbbdddbdbbddabdacaacaacccaabcacbcbcaccbbadcbbdbddccbbccadbaccacbdadbbddadbdaccaacdacdaddccbadbddcdbdbacbbdbbddbcabbcbdaaadddbcbdcabdabdaabbcbbacadcddcdcccbadbbccaacbbacdaadddbacdbcbabbccacddbbcbbbadcbcbaabbacddcdcaacdbcdcdbadadcddaaacaabbabdacdbdbcacdddcddccbcddbcccdbcccacaaaddccbddadaadcbccddddbdaaadcdcdcadbbadccddababadbbadbbcabacdbbddcabcdaadacaabdbbaaaaaaaacdaccdbccbccaaaadddadbaaabdcaabdcbcccbbbbdbbadcbadddbcdaaababbbcbadbdacbabdbddddacabbbdbccbcbbdddcabdcdaaacddbbbbabdabaacdacbbabbaaabaddcadcadcacbbaaaccbabccabbadacccbccdaabaacabaccaccbdbdccbdcbcdaacbcacdcbbbacabbadcbbbbababacbcbbcbddccabbbcdccddadabdccdcdabbaabbcccadcbcbcddbacdbdadbacabaabbadaaccaadbdcaaccbccbdacbdccdccadcbaccccccbbdbacbdbcdacacdaabdbccccdcdabdbaabccccbdabddbccdaaacbbbbbacabacabacbacaaccbcdddadcccacbbacadbccacbabcddcacbcadcbddabdddddacdbcadababccbcaaaaaaacddcadcbbadcdcaddccdaabddcadadccadbbdbbbbadacbcdddbbcbbcabdcaccdcdabdcbdbacaaadbddcadaaacbcddbbdccacdcddabccbccadcbbbcababbbbaddbddabaacddcabacbccdcabcaabbcbbacccbccbabddbaacbcccbbdbdabcccbbbdcaddbadababccbcccbbbcdadcbbbccabadddbacccbcbbaaccbbabbaabcbdacbacaddcbdbdbadbacabbadbdaadabbbdddcddacdcddddabaabdacbaadacdbbbcbdcdcbabccbaadbaabccbbccdbcaaacdbdaccbcaabdabaccbbbaaaccccacaabbddbdacadbadddaccdccabacbdadbcbddbabdbbbabcaadbdcdbcddabbcadcdaacdddcccaaabbacbabbabadbacdcbdddcdaacaaaaabcacadacaabcacbaccccabbbbccabcadddcbadddaaddddbbdbcdcaacdcddabcdadcbdbbcbabdabadadbbbaaaaccdddddaaaccacaabbbcadcbdadcdccdbdccddaabddaadccdcabaacbcbbbccddcbabbcbdcbcbdbdcabdacaadabdbdbdacbbbbddddcaccddcbaabbbdddbcdbabbacbaadabaddabaaccacddababcacdbccdbaaaadaabcadcabcbcbaccadccbbcaabdacbbbdbbcdccdddcaddccdcbaadbbbdbdccdaabacbdabacbabddabbdacabbabadbccacacdbbaadbccbcbbaabbadccaddbddbdbbcccdbabcaabcdaaababccccbdbcdbdddccaccaabdbcddcabddbccadddbcdacbcdaadcaaadacccaddcddcacadacbdbccbcbcadbccbcdadcbcbbadcddaabbadbbabcbbdbacdacdbcddabdcdcbaacdacbbbcaccaccddddbcbccdbddadcbcbddbaccdcdcaadcabcaaacccdaabddaabcbbbdaccbccccbbadbbdccaaaabdadddbbdcddaaacbcbcccbabcdbccbadbdbbaccbcbcdabaddbabcbabdbddcaadacabaadaaccdddcdcbdccccdbddbaccdacbbcdcadddcdaccbcacbbbcdaacdbdccccbaddacbbdacdcdabdbddadbacdcccbbccaacdacbbadcabacdbddbdcccadaacbcdadbaaaddddbdacccbcdacbcadbaadacabdadcccaacddcddccabcbbbcacdabbaadcccabcabbdababcddcbdaabbadcbabbbcdbbababdbcbccbaddbccbadbaaaaabbcbacaacabcaacbabaacadcadbdbbadbcaadbcccdbcbdddcbadbcadccdbdaacbacabccaacacbbccabcbdaadcacaccbbdbaacdbcbcddcdccdaddcdbaadcbcaddabbddbbaaadcabdaadbabddbdddcbcaacbccdcacbacdadcaabccaaaababdcddbbbbdcbabaaacdcacdbaaaaaddadaaaddaabbbcdccbadcdabbdabacbabbbaacbaaababdbccabbccbdabbdbdccbdcbdbbdbdcbdcbbddccabdacadbbcbaddbbdcabacadabcabdbaacbbabdccbadcabbdaaadbcbbcacabbcacccdcbbaaccdbaabbdcbbbadbbbaacbbaabdbbadaacbbbcbadabacabcdcbbcbbaadbdaaaadadabaadccadaaabacaacabbbccaddddcccaaabbbdcbcbaaadcdddbbcaccbbacdabaabacbbacacdacdcabacbaadcdbaddbddabdbadcddcaccabccadbccddbbcdbdcbcbaddccdabbbabbbcacbbddacdcacdcbaaabcdcaabbdbacbaabbbbbcacbccccdbdbccdacddcccbadbdcddaccbbaaabacabadcbdddabcdabaacdcbcabbadccaddccbbccddaccdcdaabbdcaaddabbcdbbcdadbcdcdbbabcdacdcaadaccacccbdaccdbbbbaadaabcdcccbcadbcdbdadbcadbbbcddbadbbbddabbddabdbbbdaadbbdcdcbabdaacbbddcaaadcddabbbcbcaabbbddacdbacbbccbaccdcbcbbbbbcaadccaddccaabaacdcadabdddbcabbcaacaccbaddbbccbdcbdbbdcdbbbdcdbdcabbababdcbadbcbcccccbbcacbabcdddbbbdcadadaabbccccbccccdabbdbbaadccdccbcdcbdbcccacdbdbbbbabcdaccabddabdbacdacdbaadabcdcbadaddcbadcbcdbdcdacbadccdddbabbbacddbddaaaadcdaddbdddcdbddcbcbcbaccaadadadacabdbacbdcaddcaccaaadddacbbcdbbadbabbcbaddbbcbaacdcaadaccdcadbcbbbababdaddccdabadcaabcbdbaccbdcabaabadbbbddacacababccbbacacbdbabbaddcabaccbcabcbadbdbdbcbacccaaaadbbbddaacbdaaaddcadaaccbcbdbadcddbacabcbcbdbadbcddbdbcdbaadddcdcbbddcadacadcaabbadaacacbbddcbabbadddccaabadbdbbbabbdbaabbcddbbaccbabadcabbabddcdcdbdbdbdcbabccaabcbbbbabcabddddcdaacbdbdacbadbdbccdbcbddbabdbdacdbaddaaccadcdaccddaaabcacbdbcacabbcdbacddbccaadacdbbbddddabaadcbbcabbbdbdabdcbddabbacdcdccbaabcdbbcdddccbccbdbaacdcabdadbcbadbcdddabaaaadbbbbaaacbadbadbbcbdacabaddabbbadcdbccdcdccdddaadbbdcacdadcccbaaaaadacacadaddddcbbbdabbbbacadbdddcbdcdabdbbbbccbbddccacbbbddaacddabdaababdadbacbcaaadbccddcdaaddacbbbcdabddacabbbabbcbaacdccdcaaacddcbddcbbdcdccdccbacadbaacdbddaaadbadadcdcaacbcdaabbbabdccddccbbacadcbbabcdbabcbaabbabaaccccdaabdccabbdddddadadbadacdabbaadaaadaaddabdbadbbcadcdadbacaaaccdccccbdddbbadbdcadaaccbdcaccbabadcccaadbaacabbdbcbdabddddbadadccdbcacdbcdddabdbbbdcadddadabcbdabaaccdcaacdacadadcbaddbcbdbcbddcbcdbacdcbddbdcacddcacccdacbbbdababdcabaccbbcacadccdcddcbcbadccdbcaaadcaabbdcdbcdcadbaccaadcdbbdddbbbdddbbadcbdadcbdbdbabddaaadcbbbdadcabddddbcaddaababdaadacacbcdcadbdcabaadcbabcaccabccccbbddbaadaaabbdcbadbaddcbabcddaccaaaddbcdcdadbcacbcdcdadcbccddbabddbbbccdddccabbbbbaabcbbaabccccddcbddabadcbcbdbdacadbabcadacadddcbcbcbabcccaaabbcccccbddaddccbabdaaacddbccabcdcdacdaaabbabababcdbccdacaadcbccdaccddacbcbdccabaaadacbcadbdccabdcaabaddcdbdacbbbabdacbaaddcdbbbcdcbcdaaadcdcabadccccdbcaabbbddbcdacacdbdacacbdacbadccababadbdcabbaadbcadbccdcbacaddddcdccdabbadaaccabdbbbcdaadabaaadddcdaccdadcddcbdaddcacccdbdabddbacdadcbdcbccdcadbacacabdabaccbdbcaddbcbbabaacabacacdbbabbcccabcbbddbdabddcbddbccdacbcbcaddcbaadaabdbdadddcbdbaccdaabaccbadccdcbcbadaabcacabdcddaabcbcbadcabbcccabbdbcdbdcbabdadbcddacaabadbccbbbabcbacaccacddbbdbdddaaddbccbddadaacdbbcaaadadcaababcccbcdbadcbdcbcbcdcbccddccbbccccbcdddccabccbddbadaddbbddddddccbcbbcdabddcddddbdadbabcbcddbcadcdcbcddbcaadcaabbcabdcabadabddbdacacbdbbdcabccccdadcdcdddbadbbadaacacdbcbbacddcdbbcaddcbacdcbbbdcaccddaccacadaaacaadccdbdabacbbbbcccbcccbdcdbaabdaaaabaddcbbbcdbbaddcabcbbbdcaabdbcacbbdcbcdccbcbdadbabbabbabaddbdbcdbaccdbddaaaaadbadaacaddcacabdbbdadacccbdaadbbbaabbdbabdadbbaacacbabbaaddbacacdbccbdbddaabddabacccbabaaadbadacddbbabadcacaabbccabcddbdbcccbbdbbbcdccccacdbdbddccbacbdcccddbaaccaaccdadcacbcbdbbabccbcbadbcdaccabcacabcdccbbabaabbbdbdadababadbdcccacdcaccdbbaadbbbabacbacbbabcbadadbaabdbcbdadbabaacbabaadcdcccdbbadcabcabccdbdddadabcdcadbbcaadcccabaadabbddcdadcbddaabbdabdacbbcdddcdcccccdcabbcdcdbabdddacdcbcadbcdbcacdacdcadabdbccabacadbabcbbbbadddabdaadccaaddddaacbdadcabdbbabdacdbadbabdbbdaddbcddaabbdccbcdcaddccabcadcadbdbcdbbbabbabaabcdbacaadccbbbcdacadbdbcdcdbdbbdddbbddcbbaccdaabdcdcdacabbccdabacdadbacdcbbcbdbadcbcbdaccdbddddcddbcbacbbdcbcabbbccbabaddabaadddcbbbdacaacaacbbdbdcbccbacccacbbbdbcbcbdbdccbdccbccccbbbccdaaacbdacdddddaaabcacccdcdcdbdddacdacbcacacddcccbbabdaadacbacdcaadbbbbbdcdcdadccccddcabbbdcaaabccacdadbbacadcbdddbbbccaddddaadcabbdbdabdcddbcdbcbcabbabcccacacbdabaacaadabbdcdccacdcdacdcdadabbbbcaacdadbabadcdaabddbcbcbdbdcdacbccdaaacabaaccbcacbddbdabcbbbaaabababbabaadabcdbcccabccdbbbcaadcdbbacacabaadacaadccaabacbdddcadacbbccbadbbccadcacabadddcddccadaabbabbbadcabdadcbaacaacbbcdbcbbccdbacadddacdccdababadaabbdcaadaabbaabcdcdbbddcacbddcdbbdadbaadacddacaadcccadddaaadcbbaddbaabcaddddddabccdccdabdcccabbdcddddcaaaaaccdbaddbacbddcccdaabdbbbcccccadbdcdddbacddbccdaddbacddcdbbdadccbbcddbbccbbacdadbdababdacaaddcbdacddadacccbabcddcccadacbdccdacabadcdcabcbaddbbacdbdbcdbbbddabdccdbdadbdbcdacaacadaadcdbadddbccbdcadbaadadaaabdbcbadddbdcbaabccbccbaccabcaccacadbdbbddccaabcbabdacaddcdbddddcacccdcbcbacdcdabcdadadcdcdbadddcbadbabaddccbbdbcbaabcdabddcadcdaaadddabcacdcdabcbdccdbbcccaddcdaccbddabcdadadbddbbbcaddddbcacddaddabbbaccacccbadbbaadadabdadcdacbbcabaadabacdaacdbbcaddbccaddbddbbcdbaddcdcacdbcccbaddadadbdddcadacddabacbcdcdbcacabbababdacdabadddcccdcdcadaaaccdbabbaaabbccddcaccdbabaacdcdbdcdccabcbdcddabbdcadbcbccbcbdbddaddabbabaaaccaabaadbbddaacbaabdacaacacbbcdcdcdbacbccdaadabdddbacbaccbdcacdadacdcadcbabadbbbcbcadcddbdcdbdaabadddcdabcbdccadbcbbdaccccbbbcaadbdabdbdbbcbdcdbbdbbdcaddabcdbccdaabdadcbaacababbbaacbabbcddbcacaabacddbcccbbbdcdabadacddbbdbcbaacacddbcdcdadadcccaaddbcccbcdccbdadbccdadbbbcbdbbbbbbcabaabdcccacbdacdacdccccabcccbbcdcaccdadbbbbbadaccaabccabaabdbcaddabbbcbacdbdadbcddbbcbacbaaacaaabcadbbbdcbcbbcbbdabbcdbdbdaaaddadaadbbacbbcdabdddddddbcbdddabdccadbaabaddaaaacccbcaacbdbadbccbbcababaadcabacdaaddcbacddcdbdbcadaccabcdbacccbcbabcbdbdbdabaacbadcaabaabdaccacdbbdabddcbcbdbdbcddcabdabcdbccdabccbacbabdcddabdbbaabbcbadaadbdcbcabadcbcdddcaabcdbddbadccbdbbbbabbcbbcaabbabbcaccdacdcdbaacadbdbcdbabbdbaacaddbbbddaabacdbdddccadbbaccacaabcbabdacaaabdcacddcdadacbcbdbaddadcbdcaadabdccddddadcabbbcdaaadcaaaadddddbdccccbabdabacabbbcbbcbbcbcaaddcbaadbdcbcbcddcacacdbccacccbdabbbaacbcdbbadaaacdccbdbccdadbdbdbccddbdbbbbacdcdbbcaddadbbdacbddadbbbdcdbbdacbdccdbcdaabaccbcadcbcbacdabddbbcdcddcadadabcbbabcccbbbdbcbbdaacbbdbcdacbbbddcacbbcbddbdbdaaaadcaaccddacbbcdbaccacdddccdcbcbaadcddcdddaacccbbbbbacdcdbdcdbddcaccddcaadaabcdaadacbbabbbcccdbaadcabaacbdcbadcbcbbcbcaddddcbddcbbaddacabbbabadbabbbbbbcadcbbababdabbbbbdacbcddbbdacaabdcabbaabaabbcddcabadcbcbacbcbbdcbbbadababbbcdaacbbbcdccdbdaadaabbabccabbdaaaaccdbbcacdbaccbaabdcbcbdcdcbdccbbbcadadccaabddccdaacacadccadaaccadcadbabccacdaddddcbbdbdabbaaaaabbdadcabbadadaabccacaaddadcbacddaccabadbaabaacdadddaccacdcacaabcccbdcdaccabdaaaddcacbbcccbacdcccdbbcbaacbcbadcabcdbccacdcdcdbbbcdadadcddacaccddbdcadcaccdaaadbdaddcaaacbcbdcdddacbcdadababbbbababddbcdaccacbdbdcbcbbadccdbacdccdabdcdccbadcabacdddbaaadaabcbcaabbcabaadddadbbccdacbdcbccdbcbbdadaabcadabdbadcbdbbddadcadccbacdacccdcdacacdbcccdcccdababccbabbdccaacaaccdaccdbbdbbbcaaabbadcbdcdcbabbdccbccbbdbdddbdadbbcbcaccbbbadbcabdbcacaddbccdbcacbbcadabddbaabdbabdbbbcdaccbacacbccdcddbbcdbacdcdaaabbabdbdbcbcacaaadcbdcccddbddadddbcacdddadbacdaaddbcdadbadadadbdaddbbcbadadcabcabcdabdbbccdadcbacacbdbdabdcdcdcccacbcddbadbcbcdbaacdaaaabbcdcbbcaacbbbbcbabacbbbacbdddacbbabdbdbbacddccbaaacdbdbcbcbddcdcadbdbaacdbbadddcbbbdddabdadccbdacdcccabcacdddbcdbcdddcdcaabcadabdcccadadcbdabcabbccdcadbbddddadababbdcdbcabddbccdccadaadaacdbdbccadcaddbdacabacbbadacacabdbdbacabbacdbcbaabaddbaacdadbddccbaaadabcbbdabcdddcbddbbcbabbcbbdaadabcaaddabaadcbcbacabccdbdcbdabbadcaabbcbcbddccbbaaaaccdbdaaadadbbdbcddaabadacccbbcdccdbdcbddcbdddbddddabcddbaadcadacaabacdacbacaacbbbacaccaaabdcbcddcdabcadacdcacbdbbcdabcbccabdddabcbadbdcbbdadcbcdbbbdcbcbdcadbbbcbccbcabdbabcdadcadaaaabdbadccdabcacaaabadbabacaabaddcadabacaabdbdabdaccaaaabdaaaacbbacdbbaaaadcbdccacaabadaccdbddbaadccbaabbaaacabcdcbbdaabdadbdcadaabbaddadcdbaaacbcdbcddcddadcbbaddacddccadaddccdcadacabaacaaadcbbcbdbbcdbbadbbdbbcdaaadbaadcaacccaccaababccabcdbaaadbdccabddaacdcccdacccbcbacaccbaabddbdbcbaaaabdbacddbccbcaddaaacaacabaaccbcdacadaaacdababaabadcbdddbdbacccdcacccbddbaddaadddacdcdabdcbbaaccadbcdccddbdddabdcbbbcdacacdbbbdabdbbbcacbdabccacdcdcaabbbabbaabadcbdaddddbaacddadcdadbbdbcbaadccddcccddabbddbdccddaabaccbbaaddaaacaabcbbbaacabcddacdaaadcdbbcbbaacdbbcbacddbcbbabdcaccddbccddadcdbdcdcddadcaaccbaaacbdccdaadccbdcbaabcbcdaddaaddbcbacbbccbbbbbdcacbbcdccbcbcdbaabaccbcbddcbbcdcbaadcdcbdcacbbbdaddddcadbaddbddaadbaccbdacbbbcdaddcaabaabcdbdbcbabaddddcdbcdabdcdbdbccdcdcdcaccdddccbddaacddabadabbcdadbcccbacbcacccadccaacabdaccaacadacaabdaacdabcddbcbacaddddbadabcbdbdbabaaadadacbbbdbcdbbbacaccaaabababcdcbcbdbbacdacbcabaadcacbbbbabbacbbcdbbadccaadadcaadbaabcbaccabadcdbbbddbcdadaaacddbdcbccdbdabdacacddccadcacdddcabbbbacadcaacdbcbccadabcdacacdddbccaacbcccdcadddbcbcaadddcbcaadbccdabbaacbabdcaaacdaaadcbbadcbabdadaadaccbdcacccdbbbdacacbccabccacdacdbbddcdaacdbdaababcacaabbdabccccdadbbadccadcabcccbabaababcacdaadbacbddacabaacbaabcacdcdaaadddbddbdabbcabbdbddbdaaabddbbabddcbbacadcabbdadccaddacacbddccdccabacbbdadcadaacbbccbdbccacbaddbadaaaaabcdcbacdccabbaabacbcddcacaabccdaacdbaabccacbcbaadabbdbcbddbbaddacbbdcdcaddadbbabdcbababbcdabacadadbddbdbaddcdabccddadaadbbbbdcbcbaadbcacbadcbaadbbdabcdbddbdabbdddbccabbdccdbdbabbcabaadbcddcaaaccdccccadaccacdcbbbacbcbbcbccaaaaabcdddcaabdabaccbbdcdbcdddcbdcbbbbbddabdcbadcdabaabdbbccdabaacbdbccdaccbdcaaddbadbcbadbbaaacbdccbbcccbcddccdccaabbbbadcbdcdddabbaccacdbacacdcbacbbadbccacdadbccdcddcabdcdbdccbcabddddaddbbdacbdbacbbdcbaaddcddadabcbbcccbddcbaaacdbcbadcdbcdbabcdbcbabbddabdddbdcbcbacdcbadbabadcaacaabbbbccadbadaacdaaabbbaacdaabccbcddcadcdcbbcddcccbdbbdabdbdacccdcacdacadcdccaaacccacbcabbccdbacbbbcdbbadddaddcbdcbdccababadcdbaccbdbbdcbddddcacddbaadcbaaaacccdaddaabccbdadbaadbacabcbacddcbadacbdcabacbdcbdbabbaabbabbbbcccabadcadaaadcacdddbbdbaddbbdacacdbdbbcbdcddacbaddccbdbbcddcdabccddcabbadaccbdbcdbcccbadcadcbbcddcbbcaddbdaddbcbcdadcbbacccaddcddbddabbbaabcadaadcacbaabdccccabaaabadbcabaabadacabcaaccacdcdddcbadabbdbbaadcabcbadcdcbbccdadcabcacdabddddabcabcabaaddbaccbddbbdabcbddabbbdaacaddbccdbbacbdbacbddaccabccabdadcddcabdcbbabdccabcbdcabccdadbacccbcaccadcacabbcbadaccbbdaabacdacdddabcbabbaabacdbaddbadcadbacacdcacaaaaabdcdbbcacababadcdadbdddcaadcccabcacdbbdabdadadacdbdcdacadcaaaccddbdcbbcdcdababcdccdcdcaacaaccbdaaadacdccabdadccbbbbabddbcdddbbccccadddcbaccccbdcbdccabcaccabdbdccacbbabcdababdcddbbbddbadcdabaabccbcadaabcccacdcbcbbdcbabadadbbdbdcdacbadddbbacbcdcacadcabdccabbccbcabbcbaacbdddacbcddacaccddaabcdcabdcbabdbccbbaabcbccacaccadcddccbadabababccbdacbdacccddcdccddbccbcddcadbaddccbdccdcbcaaccabcabbccadabbbbdbbbdcbddaccaadbccbbacabadabcdaabbccbddababbdbdaaccccdbbbcaddabcbadcbdbacabddbdaadabcdacabcaabaddabbcdcdddbbdddccccdacbdbacbddacddabacbbadacddcccabbdcaadacddaaababbabdabdccaacdbcdbbbcbbacabcaacccadbaccbccddbcbbcdcdaaaaabbbddcdbacaadbaabaaaadbccbdcbbacbbabbcddacaadcbcbddbdadabcadcbadacbddaaddbdaadaccccbbadbabcbadcaadbaaacdbdcbddbbdadbdcdaacbaaaadbbcbdcdabcdbbcabdaaadccbbacdbdadcdabccadccdacbddacadabbbddacacbcbdccadadaccadcadbbaabdbddcaddacdccdcdbdddcddbdbdccdbcbdaadcdbcdccdcdbccdabdaacaccbabaddccdabccbdaaadbdbcaacdbabadcbbaabdccbdacdaabcdacadbdadddadcddcbbccadcabcadcdcddcbdbcabcbddbbbdbcaacdbbdaddbadcccacbabcdbbccbcadabccadbaadcaddadadccbdcbabcbacdcadcddbaddacbbaabaacdbbacdbbabbdaadabcaacccbcbcbdccdaccbddbbbbcddaaabbcadbcadabbccaaacdcbdcaacaddabcccbdababbadadacdddcaaadcddbcbadabaacddcadcdcccddcdddcdacbcaccabbabcadbaabcccabbacdcbdaccabbbbdabadbcdbcddacacddddabaccdcabdabcabcdddadcbdbdddbabdccdddaccadadabbdcabddcadaaabaaddabcbccbdbdcabbadadcabadcbccbdaaabaabcdabcaddcccdaaadbbadcacdcacccdadbaddadbbaadadddacddaabcbbdcabccdabdcbbbabaaddbdacdbaaabababaacccbdacbbccdbbcdccacabcccbadaaacaccccccdddabadadbcbcddbabddbdddcacacadaacbbaccbaccbcbbdcaacadccabcdadadcdbbdcdbdadcbadbcbbdbdcdbcccaacddcadcccaaadcdcdaddcdbbdcbcdaaaccbbdadacaccadadbacbdaccaadacbbdbcdbccdbdbcbdbabacbcacacaabccadbcbbbdacaaabbbacbaaabaabcdaddbccbbcbbcbabbbdcaaaadaabbccadcdaabbcdbaaccbbcbdcaaabcdbccbdbacbdcaabdaacdcddcbcddddaccbbababbbaadcabacbaaccddbbabcbcbabbacadbaccccdadddcbadbdabacadcbcabdabcccdcabcadbcabbcdadcadcbcadcacbabacdcdddbdbdbacbbdabbdcdaacccbdcacacdaabbddccacccbcbdaddbccddddbcdddaaadcbbdcbbbcbcacbbccdbcccdadacbaabcabbddcdcacbcbcdadbdcaababcababcacbdcccaacabbbcdcadcbbdccdbbdcaabaaacbcbccddcacadabacbbcdaabacbcaddbabbbcdccddbabbaabbdcbcabcbdcabdddbbdcacbbdaccbacbdbbacbcaccbbbcabbbbdbabccbdcbcbcaccdadbdbcbdcdabddcdbdacddbbbbcdcaaddccbdaadcbcbaaccabbbbcbcdcccabdacdbbbbadccbcaaaacbdabcabccadbbbabaabccacdbbcbaddaaaabdcbadadddbbbaaccbbcdcadcdadcddbdcdbdcbdddccdbadccdcbdcbacdcbdbabdbdabcddbcddcadddaccbacdbbdaacccabcdbcaabacbbdabccccadaddccadadcdbbdacbbbdabbddaaccbcdacdaadddaacacccbdbcdddbaaddcccaabbddacbaadccddabacaacddbdadccdccbacbdabcbdbcacbbdbddaaacbcacaccbbdddcaacadbddcacaabcbabbddbccaadabbaccdbcbdacaddbaaccaabacdcbdbddadcdcdbbcdcdbbadbbdaabcbbbdaacbdaddaddddccbcbcdcaabcacdabaadabcdddddbdbdaccbcabbddabcbdaddacccbcacadbdbaccddaccddaaacaaaabcacacdcaacdcdacbdbddbbabddbbaccbdbadcbadbbaddadbbbccdcdaacadacbccdcacddcbbdaacdbbaacbdcacacbbadaacaabadcddcabbababdabdddadaaabccbaabdababdabcccabcdbbaacbbbcabdbabdbbdadbbacdbcdabbaadbcdadcdcccdbcbaabbcdacbdaabdcbaccadbdbadcbccbcdaabcbabddbcdaaacdadccbabbcabacbccddcabcdcaddbbadacdaddbbcbbdbccaddbbaddbabbcababddacacaaddbddacaddbcbbaadacbccdcddcdbbaaabbcacdbcacddccbccbbacccaabcadcadbcdacabdcaddacbdcbdbcdcaddbbbacdabcbddaacbbdddbcbadcaadccbacacadbaadaadaccabccbcbbdcabddcaacaabacaddadabacaccbbaadcdbccdbbbdaccbcbcdaaabdbddcadabdadcddddccbccdddcadddbddddccbdabbbadccdbbbaaaadbbacababdadccacdbbdbbcacabbbddabcaabadbccaddcbdcadaccccbddaadabcadbacadaaadacdccbbcdcbbbcbbdbdccdbbdacccdddcabcddbcaababcbdbbacadccccdaabbcadcacbabaacaaaabcbcbcdcddcdaabdcbabcbdcaddcdabbacccbacabdababbbaaaccdbaddadcbaacadbaaacbaddadbcdcbcaabddadadbaabcaccdacbbacabadacdbbaadbbabcbcdaaabadaddabcdbddccbbccadbbcabbbcbabdccccbadcacadadbacadbdaabcbcabadbdadcaabadbaccccbcbddbbccaacbbcbbacbdbdacacbdacdcccdacbcbbbbdbcbbdabcdcccdadacdcabdbadbacbcbdbdccdcacdcabbbacddaaaccabddacacbdbbccdaddcdbbbdccdcddcdbbcbcbcdccdcbccbbcadbcaaccdabcbdbbcbcabadbbcadacdcdddaadcccaccbababadbacbabbdcbdbddadcdbcabbcdcaaabbabbabdaaadabcdbdbdcddbabddaaabbbcbadadcdbbbdccbddddbadacdcabdbabadcbdcddaccbbbcbdbdbbbccabadcdccbbcbaabbdacabbddbcbddaadcacadaadbcdbbbabcdaaaaccdbbabdddacdcacaaabdabdaaacbaccdbdcadcdbbcdbcdaaadacadabbdadddadaccacbbaccbdccacdacbbaccdcccdacbbbbcbdcdacddabdaddbbdadbaabbbcaccdbbdaaadcbbcccaacdbaddbdbabdacbcdbbcbcacdaabddbcdbdabdbcbdbaacbbabdcadcbcabadcccccbcccadabaaacbccddcacbddbdabadcbaacacbbaabadbabbadbcaccbadaadcaabcadbdccccaaccabcdcaaacbdbcacaadabdadcabababadacacaaddbbbdacacaccbccddacaabaacddcbbdadccbdbbdadcccadbdbbaabaadcbcbcaaadabdacdbdacbcbabdcdbbaadcaabbcdbbaaaaacadcadccacdaacabccddcaccddaabcdcbcdacabdcccddcddabaababadabacddbccdadcabcdbdabbdbdcdbabddbdcbdcaddacdcddbcbdaaaacaabcabdccbcdccddcabcdbcaaadddaccbdaabaddababdcaddddcdccadddddaccdacaabbdbdbdccdcddacdddcbbbbdddacabcdcddcbaaabacdacccabdaccaacccaddbacadaaacabcbacccabcacadabcacaaadcbcaabaddbcaaddacbbbdcdbcdadcbbdcabcbbcdddcdadcacacdddadcdbacdbcbbabcbccdcbadacbcabdcaabbdadbdcacaabcdbaddacadbcabdcdabcababccaaccbbcdadaadddaaccdccdddccdbbdacdbcbcbadccbdbdbdabdbbcddcbbabadbbdccaabaddabbdbdbbbcbccdcddabcaaaddacaabddbbcddbdcbddadbcacdaddbbbdcdadbaddaaccddbacccbbabbacbbdcdccdbaadadddbcadaddddabddcbcbccbcbdadccbacdcdadbcbbccadddcbcdacdbbccbdbacbabdbdabbacabdabadabadadccaaacadbbbabdcaabbadaaddcdddbbbaaccbcccbdddcabbdcccdcddbcdacabdcdaabadbdbdbdaacbbbdbdbcbcdaaccbaddadadbdacadbcdbdacabbbaddcbacdbcbbccacabacaddcacdadbcccdbbbcdaacdcbabaaaadacdccacddaccbdcccbaaaadbdbbbacacdabbbcbbdcacccdbbadcdcdcdadabddccacadcdccbbacdadacbaadabacdccbbdcdddcacbcaaccbdbaaddcddadcddbbbaddcabbabaaddccbdcbdddccdbbdbbddbbabacbcccabbbbabacbcbbccddcdabcaadcdbcdadbbccadccacbbcdddbbbcbcbbcdacbbbacabcbcdbbcbdbccacabaadacababdddaddcbbdabcbddabcbacbcccabcbcdbdadbbcdacbaababbcbcdcadbabdcbbbabadabdaddcdadacaaacacdccacacbbbbbbaaacaacadccbbbcdbabaababbcbdacabcbcbddcdaadaababdaabacaccacbcdadbdbabcadacdabdddbbaaccbcccddbaacdabdcadaabbbcbbaaacabbcdcdadccdacbabacaaccdbdbdcbddcbbcabdbbbdcaccabdcaadabdcacabbadaacccadaadccdbcbacbdcbccdbcdcbaabddaacbcbdcadddbacbbbdbbddcabcaaaaadbacbacdddaabcdbcadcaabcbbcabaacdabdacbaabbdccdcacccbbcdadcdcdbcccabcbbaacdccbbbdcccbcbdbaabacbbbdbadabddccbcababadcccbcdbbaaabadaacbcbadddacaaccabbbabaacbaabdcdadddcbdcbbbaaccdbaadbadcdbdbbbbdaaccdabadaddabcabadcbcbabdbbbadbbccbbcbdbbbdacdbcacbcaabaaadbcaccdcbbcabcaaddbdabdddbcddcadacccdbdccbccabdddabacdbbcbabcbbbccadcdccadcbadcccccbbdabcdaaabdbaacdcdbdbacccbdcdcdabbbbbaaaddcdadcbbcbcdadacaccadcabcadbcbaaddaccbdbddcbddabdcbccabdaaacdababbdbcccbbccbcdbbacccbcddbcccbcbaddbddcbbaddcdbcabbddacaccbabbabddbdabdabdbdacabadcdddbaccbdbccddcdcbddddcabbddaccbcbdabdabdadcaddaddcdccbaadaadbdbcbcacdcbccabcdadadadaddbbdbcccbdcdabcadbbbbccadcdabacbabaddcaabcdadacaaddcacadbcddadbaacdcbdbacbbaadbaacbacdbabacdcdcabaacacadbdaababbcccabacaadbadbbccbbacbbcbacbaccadccdbcacadcaadacbabbddcaababbcdabcadabbacbaacaddcbbcaaddcdbcadbcdabbbcdbaddcabaacacddadcdabbdccbcddaccbbaaccbadaadbbaaacacddadabbcdcdcadabcddaddadbcdcdadbadbbcabbaddabbaabcadbabcbbbcdcbacaadbaabddcdbddbccabadcabadababacbbddbcbcbcccaadcbbbdccdbdacbbbaadbdbdbdbdaacbcaacadabaacabddcadbbccdadbcbbcccdadbadbbaddbdabdabddbbccddcdbbbbbcdbdaabccdcadacbbbdcadddbdaaadcaaabdbcadbabbcbbbccabacdbcbdabcaadddddcdacbbbcadbbdddccdddcadaddacbaaabaaabbadbddddcbbdbbbcdbcbcacdadcaababaaababadcbdcccadccccdbadbddacaacccbcdccbbddacaaddcccbbdccdbdbaaaaddbbdcbcbdbdccdccbadacdcdbcbacbcdbdacdcbdbdbccddacbbdbaadccdbbaddaccadcccadddbcbadbcddbadabdaabcdaaccacdbbdcccbddbccbdacaddacadbcacdbcccbadaaddbbbadccddcbcdcbcdccbaaaaaaddbdddadccacbbdbcddabdacccccdcbcdcdcaabbbcccdbabdcabaaddbddaabccbbbabdcbddccccbdadbbabbbdcdccdccbaacaacbcccbcddbbbddaaabcccddbcadccbacbadbabdcbaacadacadaadddbbbddbdcaaabdcaacccabcddabbaddcdacbdcadabdbdadddaabacabadcddcadabddbaadbdcdddcbcdccdabadcabadcbcbbacbcacbcbdacbbbbccddcacdabbdcbdbcdbbcdabbaaaabdddbbddccbacdaddbbdaadcaaddbcbcdaacaddcdabdbbdcddcccdccbaccbdbdbbccadababbdbdcbdcdcaabcbcdbdabdbcdbccadddcdbcbdcddaacccdbaadbcdcbdddbcdccbacdccabacdddacadcddcabdcdabcbbaaccdcbdcbccdbdcddaaadcabdddacdbcdbcccaadcddcabbcccaaaacbadbbccadbcdcccdbbccbcdacbccddccccbaadbbddccddbacdabaadaabbadbbbccbddadccbcccdbcabdacdabbabacdacdadabcccadaddbcdcdbaadacbacacccadbbbadadbcbdbaaaaacbbbdabbbcdccbcadcdbcbacaccddcdbccaccdcaabacabbabcabcabcaaddcbaaccccbaddaadccaccbaadaadbbbcbcbabdcbccbbcdcccdaccdddcbbbdddbbccbadcddbcbbcccdbcabacdcdbcdbddcaccdcbdadcddaccbdbbddbacacdcbbbcdaaadbcbdcbdaaabcbcccabbbdaabaaccbadaddbcbcbcacccabbcacaccdddbddabbbdacccbabcbcbdcaccddaddabdacbddbbcdcabccbcbbdbbcccbabbbaddccbdcbbcccdcadabdaaadccbcacbabcabbccccaaaacdbacdadaaaaddbdccddabbaaabddaabaabccbadbaadaacacbcccaaddaaacdcdbacabadadbcacccaabbaaabccdccccddbaabdbccccdccbccbadddacadbbabcbcadaddcbdbdadddbdcdaabdcaabacccacccdbcadbbaadcbbccaddcbcabaaaaabcbbbbbaacaabdbbddcacdcbcbcbcdabbbdddcbadacabdcccadcabccacdccbdbdadbcbdcdbbababcdacbaddddcdbcacabababdaababbdcbabbacaadaacbcabbbbdbddaddcbbbadcabccdbccddaddaadbaaacabbcdcdacabccbbdbcdbccaaaddccdbbcbabdbcdacccbdddcaabbdcbbaabbcabdcbccccadbbabadacbcbcadadbabcdcdbcbbbabdcddaacdcaaddcdcbaaadababddbcdcadbadadccbdbaaaaaddcdccaabdabdadacddbcdcdcaadaccbdccacbddbbbdcabdccbabcbacbbbacccdcbabbbdddbbbddddbadaddacacbaadbcbcaabddcbbdcddccbbabbadbcadccbcddaddbaccbdddbbcbdadbbdcdababccbdccdbdbbccddaabaacabbabadbdacbcbaccbcadcbcbcbabbcacaddcdddcdbbddbddcbacdabdacdbbcddcbdddabbccbabdcaabcdacbacdadcdabaadbdbdabdacaabdcdbaacdbacacdcdadacaacaadbdcacabddccdcbababcddabacacaaacdccbdccaacccadabccadbcaddbbddcadacddcbdbdbdacbccaacdcacbadbcdcdaaadcaadbdbcccbccddacacdbccdddcbdabddabcaddaccbcbdcbacacddcbdbdaaababcdabccbadddcaaaddbbaacadabcacbddbdbaadaacadcacbbccabcabcdcbdbadbcddcabbcddbcdbccbccdbbadcabcdbdaabbabcaccddbbbcbbdcdabbaddcaddcddddaaabccbabcaddcabcdaaadddddabadcaccdddadcaacddbbcbabbabdcabbabacabdabdccccaaccaacdacbdcdddabcbbbacabdacddadbabcbcddccdbcdaabcbcaabdcddabcdbcbbdabcababbabaacbcbaacadbcddccdbbcadadddaaabcbdddaccadcaaaadbcbaabcadbbcdbabbdcabcdccaccabaaabbbcaaacbcdbadaabcbccbacccabbacdbbabccbcdddcddabaadabbbcaddcbaabbacdcdaadcbcddbccbcadcccaacdbabaaacdcddbcddddacbbbddbaaadaaabdbbabdcbabccddcabadaccdabcbdccbdbbccbcbcaccbddccbdaadaabbcabadbdaccdacbabbdbbccadbcdaabcddbdcadcbcdbacbbabdaadcaacbdbccbdababbdacbbdcbcbdabcbdcacabdcabaaaabdaadcaababbbbaaacdacbdacacacbcccdbbcabbdaacddadacccbbdbdbabbddbacdccaaddbddadbbddcdbaccdadacadcbbccbddabbbdccaadbddadaddacdbddbabdaaabcaccaddbcbadccbcbabbbabcabcdbbadbacdcdcbcaaacbbbabcdccbdbdccbdbadaabddcaddabdacdccaddcccacbaddbccaadcabdbdbdbaaddaacbcbcbdadaddcaacadbcaddbbccbdbbcabdbdadaaaddccdcccccbbcabdccaacbaadcdcbbcccacdaacaacbcbcdcbdddbbbccbdacdcacdcdadbbbcbddbaadabccaadbadcdaaccaddcaccddabbcaadacabcbbabcbacabbcdbdbacccbacddacccdddcacacabaaadcabaddacdaddbcbbddcddaccddbbcaddbdcbacacbbdcaddaaadbccddddaaddacccbcbdcbabbaaddcdbacaaacbabbccacdbccdaabbaaddccbdacaddddcbdcadabcdbaacdbcddcabdcdadbadacddaddbacbdabccdcbbccbababdbcbadabcbbbccdacdccdaddcbacacadabbccdcdbaabadbaddddadccbaddcddcbdaddcdbcdacdacdccbadbdadcbddabcbbbbcbabdabccddabbbabccdccbcbdacdddabcabccbccdbcdcaaacddaaacdcbcbddaddcdadcacbcadcbdccccdbacccdcdddbdababcdbddbbdcbabdaccdddaaacdcbdadcbbdbbccccbdcddddabcaabbccdbdbbbbcabacdcddaccccdcadabcdabcddaccbdccbdbbdbcbbcbaabbddbaabcbdbbddbbddbabaabcbbdabaddbcadabdabcbcbbdccdaacdacbaacacbbdbadaadabccadbcdaabcacacbdbbaacabaddbbddcbacbdcacaacbcaadbacbbaaacbdddabcdbcadccbddbddbddcaadbcaccadabcccaccadacdadacdacddadccaccbaaddddcbdcccbaadbdabbddadcbbdaaacbddaccababddadcddbbccdadbcbaadccdaabadcabcbcabadcacdddcdddcadadcbddbdcbddccaaabbcdccacacbacaddabcabcbbbbaacccbadadbddbbdcbacabddcbcaadcbbbcdacbdbdbadcacdbadcadaaabadbbbbbcbbabbadcbbaccabcddbcdcbddcbadbbcbbbbcbabdbcacacabaabdbccadbbdcbbaadddccadccbbcbdcdcdadabadbadabbbabaabcddabbdcbcddadcdbdaabbdcadacacdcbacbcdbbbadcbdcccbccdbbbccbbddcadcbbdaccacdaadccabacdacbacdddddacaaaababbdcdcdbabdaccbbbddaaccdbaacdbabacbbcbbaccbcdaabddacbdcacadaacacdbadaadcddaccaaddddbdbcbcbabccddbbdbadbbccbcdbccdbdcabacabaabbbcbacdcbdcdcdbbbaaabdbbdbabdbbbaacdbaadbdbcbcbacdabcdaccbcaabbaadacbcddbcadadcbdaabdaaadadbbdbbdcaccbddbaccccdcabaaddbdbbdddcdccdadaaaccccadabdabbcdbbdccacddacdccccbcdcbdacbccdbcccabbbbbcccccadaddcabbbcbacdcbcdadcdcbdddcbadaddbcdbcacaaadaccddabaaaddaddbdcddaaaacabddabdcddbadbdaccbabadcccaccadccdcdaaabbacddcbbbbabdabaccdbdcabddadabaccdadabcadcaaccabccbcccaacdbacbbddadbacacccccbddadccadddbdadcbbdcbddbdccacdcdacbabdbbdaaccabbddcbbaaacddcbddbaccddadcbcdbbbbdcccaaabcaccddbdcdadccdbddaababcadaadbadacbaaccacdbdaacddbbcbadcdaacbbacdbbacbbbbdbdddaabbddbbcababcaaadbbcadbacccbdbaabacccbdcddcaacbbbcabadbdcacdadcdabacdbacbddacaadcdacaccabccddbaaddbcadadbaccddadbadccbacbbdddccadcddddbadbaadadcadaacdbacdadbaaabdcbbcdcdbdcdabbcadccacbadccaccbcccbadddccabcbaccadbcdddadacdaacdbaabbdcdadbadbadccdcbabbdcccdacbbbcdbaccddcaabcddbacadadbdcaacaadbccabbdabbadadcccccabbaadcbdbdabdcbadbdbbdcbadababbbccdcdccbddbbabaaacaaabccdbccbdbcadcadccbacdbdacdddbdcbbcccadccabacdbacaadbbdbdccdddbdcaddcbacdcdbacaddaadadadbaccdadcdcddbccbdbaabcbdbaaccbccbcbabdcaccbbcacddbddcadaadcbadaadbbcabcccaabcacccbabdbcdaacabaaddcbddddcacaaababaddacabcaadbbdbdcdbcababdbbbabadacacdcbaabdabdadbddbdcccdaadadcababdbccbdcdbdbbbaacbdadacabbacabdbccbcdbabbccaacaaaccaaacdcbabbcbbcbcaabdbbdbdcdcdacccacdcddcaadbbabbbcdccaabcbbdbbdccdbdddbbbadbcdcbddaddabacabdbccabbbdccacbcdcadaadbaccbcaadbbdaadbdcbcaaccdcaaabbdccddbcccccbaababddabdbdbdacadbcbdadcccdaabdbcabbccdacbbcbbbabddaabbdbdccbbbcacdaddbdcbdaccbdccbbcbaaaabccbddbbabaabcddddaccaccccacbbbaadcdddbcdccbcdbadccbdccdddbaaacaddacdacaaacdbbdaaddaaddbacacdcddbababbcdbddbbdcadbddccabacdbdcaddcddadbbacbabbbddacddccdbabdbdabddabadcccbcabaaaabbdadcabcdbccdbbccccbadbbabbcbabdaddacdaccaadadadcdabbccdadbdaddaacbbcdcdcabbdddcdcdbbccaaacbcdadadabcaaddddadacbbccdadabcdaccadababdcbcdcbcacaacbdaaccabacdcaccaaabaabbddabcacbcddbbcdabbccbbdbdbcddbbccbdbdbdacadcccabddbacdabaadbcdcdccacbbdacbdadcdaabbcadbacbddabbbdacaacdbabbaaddcabcbcadadbcabccadcbadabcadcbdddabdadcddacddacdccacaaddbcbacddbaacbabbbddcaccaaaabcbdbcabadbcabcbaacaccbabdabbccabbdcdcccdcccdcdbcdbbacbccbcbddbbdcdcbbbbcabbddbbdccddcbcacdacbdacdadcbdadccadaadbacbddadbbabdcdbdadbdbdababcdaadbcbadcdaccdbdaddacbdcbcdacbadddbabcbdbdbbcddbddbbdaddbacabbcaaccadcadbcdacbadbaadacdbdbabbbadaccaaaabbbbbaaadcacbcccacdaadbbccdbaacdaaacbcdbababdcdbcdcaabbcddbadaccaacbadabbdbaaccbacbcadadbbbdcaacbaadacddccddbdbccbdddacddbababaaacadbaddacccaccdbdddbdcadadbadccacdcccbabdabbdbacdbaadcccccdadacddbdaddbdaccaaccbdaadadabdcccbddbcabbcdbbcbabbcacbaacdbdbbdaacccccddccdcbccbaabacbcdbbcadabacadacdbcdcccacabdbcbdddababdbdbbdaabbccbacdcbdcdcbbabdadbdbccbacdccadcadadadacbcbcdcbcabbcdcdaadcadcadbaadcdbdaacbabbbddbdcbcbcabaaadbacbcccbcabcabbaadbdcbccabdcaccdbddacdcdbaccaccccdcbdbdaddbccadaaadadddacdbbacdddddacadcbcabdaaddbdccccddacaaaccbbbbacdddcbcadbcbbcccadbdbcddcadadaababdbddddabbcdabaacaaadcdaaaddbaddadbdabaaddcdbddaabaabbaccadcbacbdbccbcccdbacbcdaadaaabdadbacbababddcdaaabbbddbbbdddccddbaacbbbbdcccabdabbabcbccddcccabcabdcdcadabbaaabbcbcdabadcadaacadcabdbcadabcbbdbbddabbdbcbabbcbaaabbdacdabdcbddccbbcaddcdcbbacabddaccbbaadaacacdaddddbcccbdadcccdcbdbacbabbbbbbcaabcdbaadbdcabcbdaccbbbbdcadccbdaaccdacdbacbbdbabbacddcaccacbbddbddcadcccdacdadbccdaccaadcbcdacadaddabacbcabacdaacadaacddaabbbabbcbdccddbccdcaddccbdcbbbccdbadabdbcbcdbcbacabacabddbcaadddccdcccddacbdbbcacadcbcaabababadbcabdbbcdadcdbaccbadcdadddcadbcaadbdcdbdadadcababbdbabbcabdcdbadddbccabccbaadbbabadacdcaadaabbdbbdcaabcacdbcdadcadbcaaadaadcabdbdabdbcaadcadaccdabcccddcbabcbabaadadbdabcdcdbabdbdbbabadddbdbccacacadbcccabcccacaabbabdccbbbcbdaccbdccdaccccdcbdacddcbaddcaddbabddbaaacccaaccdcbdcabbccabbadddcddacdcdaaaddbdadadbcaddcadcacbcdccdaccababccadacdbccdbbaaddddcbabacaccdcbbdbaabadccdaacbaaabbbabcbbadbcdcacaabcbccaabcadabbdcdaabccbbbbabbccddccadcbcbdcaccacbddcdcaacdbcbcdddddbdbdabdbadcadcbbabccbcdbbaacbddaacdbcdbcbdabbabaadbaadabadabadacaccbcacaddadcbbdbaacadcddbbdbcabddabcabdbdbcdcbbbdccdadbabccccaaddcccbbcbbbddbdbaacddcbdbacbbadbcacbaaacddbbbbbaabacaadacddabaccacbabaddacbdcabcdbadcdbcccabddbdbbbbdbddabaaccaababcdacaacbcccbbdaaddbcabcbabdbbbdacaddbbabdcaacdcdacdabaaadcabbddabdaddbbcacdddcccadbcdacbbccdccadcbbbaddbaacdbddcaadabacdadddbdaadcdccaacbbddbdacdbbbaaccdbaaccdaadadbaddaacaacddbaacbbadbbcdddcdaacacdbdcaadddacdcddbbcdbbacbdbcddadabcdcabccbcacddbcbddabdaddddcaddaccbbcbcbbcbdbcdddaacdddcccadabbdcdbaccaaabccdbddcbccacbbbdddacdabadcabaccddaccbaddcdabbacdcaacbddbbcbbdcabdcbccbdbcbcbcadcdbddbbacddaaaaaddbabdbccaddbcdcabaadbaabaabdcabcddaddcaddaabaaddbccacdaccbadaacbddbabddadbcdcaaaddaaabbddbaadbcdaadaadcbadbaadaaabaabbcdbbadcdcdaddcadbbdadcbcacaaacaabacacccacadcbcdcabbdaababdaabcabccccddbbccbbdadabddcbbbcaddcdbccadadbbbabcccadadcdcddacbdcccbdbdbdbdbbcaadcdccdddbaadcaccbaadbcddcbbbbdcbdbbbbdaccabbcaadacbaabdaabcddbdcdadcdccaadbbcccaaaccbcabacbcacbdcbadddcbbbcdbcdacabaddcadabcbaabadbcccdaababdddcdccaaddbabdcdcabcbadbcabdaabbbabbbbaccabdccbbbcdcdcacbabacadddadadacdaacabacbbcbccabaabddbbabdbacabcdaabcddddcadddcaaadabadcbccaaabdcabdbaacabbcccddbcabdbdadaadaaddadcbccddcbacabaabacddbbccdbcbaccaacaabccbcaddbbaabaacdadcabbbcccbcbabbbadbababdcdcadccacbbbddcaacadcbdcadbadbbaadadcccbbcccdcbbbbaccdcabcaadabaababcdbcbbbdbabaccbbcadaaacaabdbadcabaabbbaadccdcbccabccbdccbadcbbdcbabcacadbcadaccabbddcdaccdbbbbdbbcaaabadaadbbdabdcaabaabbacbcdabdbbbaaadabcdaabbdccddcdcdcaadbddcbaccbbbddbaabbaabcdbcdaccdccdabaaddbdadcacdbccdbadbdbcdabdcadbdbadcbdabcadcadbaaaddcdbbbbbdcdddccccdbbcccbdbaabcbddadbaacccabaaacbbbccbbaccaabbacaacdacbbcdbcabadbcddaabbbacdabcdcabcccbbaaddcbadcacbbcdcacbbbddbbabdadddddcddbbdaaabcbadbacbdacccddbcaacccbddacdaaddabaabaddabcbcaacadaabbcbccadbdbcdddbdcaaaccdcccddbbcacbccbbbcbabbaaabccabbcdcccabdccbddcdbacadccdaabcdcdabddbbbdccbbdcbddccbcbcdadccbdacabaabdcaacaddaddcbdbcbcabdddccadaacbdcdcaabddddddcdaabccbbbdbccaabddabbbcaddddcadaaacbdcaddcadccddcbaaabcbaacadbabbbabaddbadaaadacabcaacbbcbdabacbbadacacbccbcbbbababacabbcdacbddaacadabbcdabcddadbaddaadbabdacacbbbccaccdcadbddbbbbcaddbdddbcdbbdccbddbccccccbabdbbcdcabccddaaddccbabcdddbdccabbabcddcdbbaadbdbbbbdbababbbabcdacdbcbbcbdbadbabdbcdbcddabbbadcdaabcabdabdadbabbadcddbabcbabaabdadcbbbacdbbbaaddadbcaddcbdcadabaddbccaadddcadacdabcabbcbdcbcbbbcdbadbdcdbcadaddaaaacbcdcbbcbcaacadbcaadbcdddbaadbdcaaaabbdcbddddacccadaccbbdabcbadcaaabcbdddaacccaccacbbdabadbabaabddaabcdadabddabdbadcabcccaaccadbcbacaccdaccddbdbdaacabdcccbdadbddcbadcbddcaddbddcdbcacbdcabddcabbdaaaaabacadaacacaddcbcbaddaccbaadcaacdbddcbbaabddbabdabadadcdbcdcbadadbabbbcabcdcbdcbabccbcacbbabbbcbddddbbdcadbcadbcbbbdddacdabcdadbcbddabddaaaddccdbaaadddbccdaaccbdbacadbccbaacddbbaddadadbcbacbabcadccdcdacdddabbdcccddcdcbdbadcacddbdcacbdcdcabddbaacbcabbacbacabaaddddabcaaccaadcbdaccaddbddbdbdbddacdddbcccbdddbcdaaccbdababdabbcbdaddcacccbbaacbacbdaabdbaacbadcabcadaabccdcacabddabccbaaabcacdaddccccdbbbcccbccabbadacaabbbdbddcdbccbbbaabbbcaccbcdbdcdacbbcbbbdbdddbccadbaccacdccadcccbdbddcbaccccacbbddbacbacabccdccbcacbdbcbdccdcdcbdbbbcddaadbbbcaaadcabbacdaddadaaaaacaddadaccdcababdabbcbccbdabdccddaabbbbcbdcaadcdadbcbcbacccccdcaabbdcdadacdbcdcaaabbbabcaccadbbcabbbbddaabbabacabcddccbdbabcdbcdddbcdbdbbbaabababcabdaacdddacdcccdbcddbcadbbddbddaccbbbcbdbaabcacdacaabccdabcacdbccdddaccdbddbdabcacddababddcbdaaaaacddcbddbadcdaaaaaaabbdadbddccddbdadadddcbdaadabccdabdababdbccdcaabbaacbcdbcaccadacabbccbcbdbdbacabbdbabadbbcadbdcaccbbbdbacddcbbdadcbbaddbdbbabbdcdaaddbacaabaaccdadcddbaaddadaaaaabaaccbaabbddcdcbdbddcababccdcbaccdcbdcacccacbdcdadaabcddbbabcdcdbcbacdddbcacdbcbcbdadbacbdcabdcbccaccaddddadabddcacdcbcdddcbbabaacbcaddabacbddcaadacabdabdbdadddcccdaddabdaabcdbcdddababacadccabbabadbaaacaabbababbdacaabdbbdcdcabaaadbaabaccbaaabdcbaabdaddcbadccdcdbaadaacbdcabbbadcadbdcdbcdddabbaccdddcdaadcbcdcdccacbbadccbcccacdcaadaddddddadbdaabccbdddabcccbcccbdaaccdaadbaccddbcabccbaacabddadddbcbcdcacabcbdabbbbaabbdcadbcaadcbcdaadcddbddcdbddaacaddcaacbaaabdbadddbababddcdbdcdcbbaadaccabbbcdbdabdcddddaabbccccaaddaccbcccaadbcabbbdddcbcdbcbccadcdbbacddbcddadbaadaabbdbdcccbdddbbbbdbbcacddacdaadccbadbdadbbbaabbcdadcdcdbacdbaadbadadddaaaddcacacbaabddabcaabbaabbcddbdacabaaadbaddccbadadbdacbcdcbdabbdccbdabccabcdbcccbbaccaabccdccaaddddbacadcaabcdcacbccabcccacdbcaadaacdcdadbadbdaaacbdccdbdccdbdadccacbddbdcadacaadaacccacdbadbdbbaddabddcabbcbacdcacddcabacdbabdcbcdbbddacbbbcccbadcbcdbcbdddabbcdbadaadbaaadaabaaaabbaddcadbcdcddacdcbdcabaabcabadcddcbbcacaccaadbcdbcabdaadbdbdababdcdcdcaddccdbbbcbcbcbadbbaacadbddacccbcbdbacccdaabadacbdbbcdabdcccbcaaaccbdabbaadadddbcccbcbdcdcadcabddadaadaabcaccbacbccdddaadbdddbddbcbaaacacbcccacadcbbaacbacbbbcbcbbdabcdccbcdccccabadbaccdbadcbdcbaddbaabdccdadadddbbdcddbacdbbddbbbcaaddaccddbabdbbabaddaaacbaaaadcaaabbbddddacddbaadbaacacaadcabdcadcdbdddabbbddbdadadcdbcdaccaaadcdabbdadbdbcaaacadaaacadbbdccaabdcbaabaccdacbacbabcdaacccabbbbabccbbcdbdbacacdadcbcdabdaacbdbbdcadabbacbbabcbddcbccbaadcdddaabbdbccddcbcaaaaaccbcdccaabbcbbddbaacabccaccdcbdacdbbbdadcbacadadaadcacbacdacdbbddbabccdbddbbacbdacacddcbcccbababcbcacdcdcacdbbbcbccbbcaaadbcdaabdcacaabdabaccbadcbdbcadccddccaddbcadcaddcbdacbbccbccdbccbaacaadcbddccabbbaccabbcccddbcddddabdadbddaabdcabaddabbaaddbadcbaccadcacabdcdccacbcaadcdbdddbbbbadabcbdcbccdcdaaadabcdcadaccddccbbcabccbdbdacacdddaaddadddbdbbabdaabbcaaaacbddabddddccdbcabcdcbaabcbbdcbccabcccdcaabdbcdbbbaabbdaaccaccdbacadbcccbbaccbbabcaaadddadcadbdabbdaabbdbbddadbabaddddabbddbadccbaaccdcdbadabddcadcbbbadcdabdddcaadabdbadbbcabcbccbbaacbbcccaacaccabacdbbcdcdccbdbccdadbacacbbdcdcbcddccaabcccbcbdbaabddaabddcbaaddacdcbaacbdcaaadcaaddcacbdddbacacaccccaaaadbdbadbcbabadcbdbbddadadbcbcbbccbbbaadabcbbadcdddbdacdcdcacacbbddaadcbcddcdcbaccacdbccbcbadacdaaadaacbcdbcdcadcdcaabbbcddcdcacddddcdaabbcccbabcdadbbcddadaaaccbabbbcacaaadbacbddddccdabdadadcabbdcbadbdadabbdddcbcdbaddbbbdadbccbaabbcbdbccbdadbbbddbaacbcbdaddabaaaadbccbdddabddaabdcbabddbcacbcaddabaacbdcacdccbcadaacaabdbbbbaaacaaaadcadbbbdcbdcabdcbcaddbaccbcbccbacaadbccbaddaccdabbaddadbdaadcdddacaddbbdccadbbcdcccbbcaccbabbcbaaddabcdadccbdbdcacccdccbacdbaaccbdbadbaaccbdbddadcaabddadbcdccdddaccadbbddccbacbbccabccdcdabcdabdcdbcdddbdacdaccbabdbbadcdacbdacdabcaabbbddcacaccaaacdbadbaacbbacacadcbddadbbaaabdddaccccbcaaabbdbcbdbccadaccacbbdaaadcdbabbbdcdccdaccbcaabbbddcdbabdaddaccbcaaadacdcddddbcddaccacadcbbbcbcdbbcacdcabcbaddabdaccdddbdabcdababdabbacddbbadccbdcabccdcdbaaccccbcddabaccadbaaaacbcbbacbbcbaacbcbccacddcdacbbcacddbaadbdcccbbbacabdcdcaccacabcbddaccbcbcbdcaccbdccaabbaccabdbbacacbbaddacdacdadababbaacacbddcbcabbbaccbbacadddcadbaccadaadbbbdbabbacdaaddaadbbcaaaacadaadadaccdbdcacabaabbcbcacadcbcadcabdccaabcadbcbaccccdbcccbacbcbcadaaccdaabbdcdcaacbbacbbdcabbaaabcadacacddbbabbbacdcddbdddacaacdacbabcbaaddadcabdabdddadbdcbdcddcbbabdadbaacbadbdcadbddadbdabdbbbcaaababbacdbbabadcdbbdacdccdbadadcccaccdabaccdddacaccbcbdcbaaccaccabadabdccccdaddabbadcbcdccbabacbadcaababbdabaccdcbbadbcacddbaadddddaccabcadabbccdaabccaccdbbcddcaccdcccaabcccddddbcbcaccddccdbdddacaabaadddddccbabcdbbccdbabbabcadacadccccccaacddacbbabacdaaddcaccaabbccbadadbcdddadadcbadccaccbddcaccbdcaacacbcddbddaddadccddbbadbcabdcbaacbacdbddbccbadbcbbadbcadbcdbcbcbbadcbccaaccaacbcaabbacacbccabcaacdaccabcdabcdbdddaacaccdcaadbbbccddbdbacbbcaddbabbbdbabdbbbbcadbccbdabdcccbbbdddadadbadcadcbaabbaabaabbbbbcdcbaccdaaaccacaadcbabddbbcddbbbdcaddaaabaddccbddabcddcabbcbadaacdabadaacdddbbbabcadbcbaaacddacbcbbdddcbbabdcbbdddaadaadddccacaaacabaccaaccdabbbccdccdbbccdaccbbcbabdbabaaadadddddababdcbcddbddddbcdddacdcadddaaabaaaadbcddbdacccdcbccdacdbdcbbaabadababdddccbdacaccadadddcdcbaccbaacccabddacaaddcabcaddbdabdcadbddbbdacdbdacbccabaccdabccddaacbcbaadaacbabcabdcbdcadadbbcdadbaccbaccdbbacaaccabbdbdccdbbaacdddcccdbddcaddcaacbaadbcabbadbcdbacdadcdbdddadbdbccbbadddbcdbacaadddcdcacdccbcabbaacdcbddcbaadcbccacadbcdadadbbdaaccbdabadbacdbabdddcaccbdddbcadbaccdacdaaddccdccbadcbdbddbacbddbcccdcdcbaaaddadaaddabcdaadbccdaadddccbdccbadbdadacccacaabbaabbabbcdbddadabdaadccdbacdaabacbaddddddacddbacbbcddddcdabdbadbacdcdcadbcccdcbbcdaacacdcbcddaababddbcadaacdcacdcabbcbdcdaacadbccabacbdbdccabccbacccdbbcbddcdadddaaccbcbcaabdbaabcaaddbbdacddcbaababdcdbbdbddaddcdcaacdbdbbcddcabccaabaadbbcbcdccccccbadadbcadcabdbdacbccdcacbbbddbbbaaccaaabdcdccaadcdbcdcaadaaacddadaaaaddcbbabacaaabbacbcbddabccaddbbbaacdcccccadabdbdcbcadacacccaaacbabcdabcacbabcbcdbdadcabacbdcabcabacdbbcbaacbbbdbccdcacddbbbdbbacddcccbcbcbbccadccccdcbcdaaddaadbbbacabcaddaabbacdccbbbbcbddbdcddcdcdacbcaacbcacbddbacdaacadacabaccabdbaaddbaccabdadbdbcbcbdcbbacacdcdadadbcaacbbacbbdcacbaacabdaadcadcbcdaccbcacdddcdacdcbdaddbaadadddbacddcdcccbbabccdbbcdcddcdcabdacbcdcaddbaacdacdaacccccccabadbdaddddabccbadadbcadaadabcbcddbaccadabacccabadbdbabcbddbbadadcacdcbaacbadcccbddbccbdcdacbcabccbdbddcccadbaaadabcdcbbdcdcacaccacbbacabacacbccacdcdcaccbcbabccbaabcbabddadbbacccdacababdaadcdabcbbdbbbaccdbaadacddbcbcaaaadacdbdccabbddbaadbbccdabbbbbadaddcacccacdcaccbdacbbabadaabacdccccbcbdddabdbdaaacbaaadbaddcccbbdbaacbabddccbbdbcdbdabaadddadbabccadddaacddbcddaccaddbdcbbacbdabbbbbdaacadbbcbacdbdcbcdcdababcaddaabcadbbdbbcdbdbaadcdacddccccacccbaaaaaabbcccacaddaadabdcacaadddddacbaacaccbcdaacbdbbcdbbcdcdaadcabaababcbcccbbbdcdabdaadcbbcdcaadabdbcacbaabbbacdccdbbaccacadbbddcddbcccdaaaaaddadbcdcbabdbcabbbbdcbdabdddbbccdbacccddcaadbbaaacdcddabbccdccdadadcdabadacaddccbacaddbadbbbabccbdaacbabbddcbabccabaadcabaaadadadbcccabbbbbdcdcabcdccbacacccbabcabbbbdcdcdbccdddadabdcccadcddbadcdaccadbbbbdacacbabdbaaabaddcdbacdbccaacabbdacaadcadcbaabbdacacddaadbcbcdddddabdcdbadcadbcaaaaccbddcbaabcbbabaacdccbbbbbdaaddcabdcadcdbaabcbcccdcacbccbdaddbbddcbdaaacccdaccddadbdacbabdaccdbbcdadcbcacdcbbbddbdccbcaddbbaadaadbaddbabaddacbdcddabccdcadbcdacdaaddacdadababdaacabdcbbdddccdcbdddaabccbcacdbdbbdccdcadadabacccaadacadacadaaacadadacbabbbccaabbdbcbaacbadcbdacdacbdcdcdbcdbdddabaddadbaaacbbaabcaaddaddadaccbddbbaacaabdcbbccdbcddcabdcbccbabbbaddbadabdbadaddcadbbbdbcaadbcdbdcddcbccccdbbdaccaadbcbacaabacaccabdcdbdcbdabccdaccddbbbbbbadcccabbcdaaddcaaababdabaddadcbccaadcdabbddadadcacadbdbddccbbdbbcbbababdcbdbaadbcbcccbacdbaddcbababaadbadccbacbcdbddaaabdddacdbcbbcadccdddbcabbbdadcbaddccddcbcbbbadcbbaccacdbbdcadbdbdbbbdbcdcaadcadbbacbbcdaaabaccadabbaccccdcdcaadaabcbcbdbbddcbdcddabcdbbbccabbdbbcdbddbadbccdacbcacaadabdadcacbdabbbbacadddaccacadabbbcaccbdbbccabdacdbdaabadaaccbaabcddbcaaacacbaabbbbdbccbbaccbddddcabbdabacbdddcdaabdbabbadddbabddcbccdbcddbdccbdcaaabbbbdadccdbbbacaabdacabcddddaabbdccdaabdaacabbbbdaaacbcdbdbccabcbabcbdcdadaacbdbdcbbcadabadddaacdbacdddbcccdadadabcbdaacbaabddaabaabdbcadcdddccacbbbccabbaabcdcadbaadcabdcccabbcdbdcacbbcdcddbbbdbadbadacbdcdcdccabbcbaadbdcdbcddbdcbdcbddbbdcaabcabaaabdadadaddbbbabaaabddcbdbacbaaccabcdabacaabbdbbabcabcacbbcccaacdcbdacdcdbcdcaccdcdbaabbcacaddabddaddaadcbdbddaccbaacdcacdacbcaddacdbabbcdddacddcbdbdcbccadcacacabadadbddcaccddbbbbcbccdcdcaaaadcdacdcaabcdabdcadacdbccacddbadcdcaccdaaabdbbcbdcbbabcacbdcbcabddcbdcbcbcdbabbcbbcccadbbbabdaacccaaaabdcbadaccadcdacbbbdddaccccabccdaabbacdcbdadbbcbdcabcadccdaacababcacbdcbbaaabaccdaddaddbdbcdabadbdbadbacadaacaddacdddddaacadbccbabdabbbdadcacdccdccdddadddbcdcbbbcabcbbaabaadcddddacacadbcbaacdbbbbccabdaccbabbcdbddccadbcdaaadbcaaddbbaabdadadcccbdabdadacbdabaabdaaaddcbcadbacdcddbaddbccadbaccccbdccabbcccccaadbbacdadadcabbabaacbccddccaabdabccbdccccbaacbadadcdaccdccddabcddadcbbcdcdadbacabcdcddcbbdcbccccdbcacacacccdcbbcdcdbaababcddcadabcbbcccdbcbababcbacadacabbdacccdaabcaaddcdcbbcbaacdcbdadcddddabbdadbddbadbacacabbbdadbdbadddaddaaddcacbcccdbbaaabdcaacdacccaabdcddcabdccdccccbcbdcbaabdcddbabddbcddbbcadcacdbaaaabdcdddbbbbacbdbcdbcabcaccddabdaccdddabcdccadaddababcbadcbaaadccbabacdadcabddbbdccccddabcadcdcadcacadbadcbddabddbbababcbaccdbbbdbdaacbdcbcddcbdbbdacbdbacaabcdaabdcdccbdbcdbbdabadcbaabcdbbccacacaddcaadaaddbadbadbdbbcbbdaccaacbdddddbdbcaaacdadddaaccdcbddccbbadaadddbccccdabcaaaaadddadcaabacdbaddbabdacbdcccaabcbdcbcacbbabdcddabaaddadbacbadbcbcbdcaabaccccddaccabbaadbcbddcdccdadccbdcabcdcbcdcbaddacdaacaccbbbcdbacdbbcbbbadbabbdbdddcabcaddaddaadbcdacbaabcbaccdadaabdbacbacdccacadacbcdabdbdaadccaaacadbdccbdadabdabaaddcbbdcccaacadaabdddcbbdbcbdccddabdcaacaaabbacdbddabddbbdddbddbaddbddbddbcaadaabcbacdbbdcabdbccccbdcddabacbdccacabcacdcbdbbdddbacabdbbccdaabaabaadbdcbbcbdbcbbcbbabdabddbdbdcabdbcbdcacddccbcdabbacbbcadddddcabbbcadacaaccdbbcdcaaccabaaddabcbbbddbbabbdbdcaacaacaddacabddacdcacbabcdbccbbbdcabcbbbdbcbdbdcccdaacbdadddaccbaaabcbababbacdbbacdabbcbddcbdcdddcacacddbcbcddacdbabbaadddbdddbbbbaaabaacabcadcaccbddbdcbadacaacdbadcacadcbdbdbcacbbaddbbbccdcbbdbcdcbaacdcadbdcdaaaadcddbbbdbaaddbddddddacbdbabcdcddabddcaccabacccbbbabddcbdabdcddbdadddbcaabaddcadddbbbabbadabdbcaddddccbbbccdaddcbdbdabbddcbdddbcdddcbcddadcdcaaddbdaaaabadcdcadccabdaabaccaaddacddcabdccbcdbbdbcbbcbdbcdcdabcabcdbdadacddbbcdaaadacccdbdbbdabdcdaaacdadadccbbdcdcadddacbaabdbbbbbabcdcacabdbdcddacdbcdabbdbadbbdbbbbbaddadbdbbcababaddbbcbdbabcbadbbaabddccdcdbcadbdbddacaababaaacbcbabaadacadabbdbddcadacadabdccadbcdddcdacbddbabacccbbddcbcacbaadaacaabacdcaddbccbbaaabdccbcadbccccbbbacacaccdbcbadbbccabbcdabadcbdbcabdaaadccbdbcdadbcdaaacbdbbaddabbcbcccdacabbdcccaddaccdbbbabcdbccbcabaccbadccdaccbdcabbabcbbcccbcbccabcdccbcccdccdbcabbdbadbadabcaabaaadcbbccdbdcbbbaddcbacdcabdcdcbdbddbbcdcccdacbbbdcbadcdccddbacacacdcbbbdaaadcddaddbababbdacdadbcdcccbbdbadacdabccdcbacddbccbdcccdcdacbbcdbbdabcbaccdaaaaddabbadcbabdcddbbaccabbbdbcdaacdabdaadddababdcbbacddadcdaccacbdbddcaadacdcddccacddddcabbccdcadddbbcbdccccacbadbcbddbbbcdbcbbabbbdbbbddddddacaddaacdacbbcbbdbcbddbbadccddcbacaccdcaabdccabdbcccadcdbcbbcaabbbbcbbddaabcaadcbcddbdbbaaddadbbacadabacbabdadbbbcaaabbbbdcccddabbbbcacdacaaadacaaabdbbbbbdaddddadcabcbcbadadcbbbbabbcdaabbcbdddbabaddcaaaacbbacddbabbdcccdbcabadbabcdcadaabcbadccbdabcabbcdaaabcabbbbbbaaabadaacccdcdcbbcddadaaacabbaaccbbcddaccadcddadbdaacdaacdabadaabddbacadbabdacdcddacddcddaacdabcbccbcbcaddbcadbadbbcdcbadacbbbccdaccbadbcccddbacdccdaabcbdcdcacbdbabaccdbcadbacaaabdadaabdcbbbccdcdddaaaacccdbbddccbccdcadbccbdcbccdbacbdbdcbcdcddacaababadbbacadaddcbbadcbdbacbcaacdaaabdbcaaabbdbbacaccaaabcdaabdcabdbdbdcddcdbaccbcdabdcbdbbacccdbbddbccacccaaaacbcacabcdcdbaacaaddcccddadbccdcaccddcaccdcacdcadbddbabdbbcbccbccdbbbccbadbabcdcbaabccbbbbaddddcbbbddbdabadcddccaadbbaaabbaaddaacdaaabcbacaddcaababcccbaaddcdcddddaaacaccaacdccabcdabcbacbabaaccaabbddbbadaadbaabddcacdbccaacbbdcdabcaddbbcdacaddcccdbccabcacdadbccdbdbdcdbccbaadbdcddcabdbcbacbddacdaadcbadbccdbbaacbaaaabbccdacdcbadccbdaaacddaacbbcdcdbacbddbabaabbbbbaababcdbdcdbabdccdcbdbcadabcabcadcddacaabadddcacbcdadadccaccdbcdabbaadbbadbdbbdddbccdcbbbaadccdabdbccdbdadbdbbddbcabcacbbdabcdabadbdadbbdadbbcdabddcddbcddcdcdabbaadcabbdaaaacacaccdcbbcaadadbdddcdddadcddcdcbadaccdabdbcddbbcabcaaacdadacdadaabbdbddcdcdcdbbbccadaabadabbcbbaaccaaccabcacccbcccaaccacacbbbbaacabccdaaadcddcdbbdbabbabdccbaaabcdadbbccbaacddabcbdbdaaabdcbacddcaccbccbdacaccdaadcddcdbbbbcacddaaacdcdcabcdaabacccbbcabdaacaaadbaccbcbcacabdcbabddcbcbccaacdbdbddcacbabcddccbbdddbcdabaadbbcabaccacaadbccdccddacddcddcccbdccdcacdcddaccbddccabdadbdcbabbbaaccadcaccacddbbdaccbadbdcdccbdbddcaabaccabccbccadabbbddacbaccaadcbdbccbbddcacdcaddacbadadaaaccdcbabbcabacbacdbbcddcdadccdabaddbabbccbdaacbadbbabdaaacbdddbbcaababccadccabacdccaadabdbabaabbbabcadcbddddbcabcabacbcaabddcbabbabcaccdaaaadcdbaddcabbcdbdcaddcbdbdbbcbdddbbabaadabdbdadaabcaadbdbadbddcddcbdadccddbcaabccadccadbdaaacdddbcbbbcacbbccdcadccdaddaaabcbacacaddabbabacabbcbcccbbacabacabbbccacdcbdcabbacccdcdccdcbbdacbbcbbabbabddaadcdadccddabcbcdccadcadadaacbdcbacbddababdbbbbcbcbdbcdacacadbdacccdacddadccacbbaaaccbadcabacbaaaaaabdcdaaddcdacbcdcdaddcdbbdddcbdccaacaaacaaaccdcbcadcacdbddddaacabbacdcbccbbbdcacaaacdccbcdcabccdcdaadcabcbadcdcaaadcaabaacccabcdccddddaadbabcaccbaaacbcbbbbccbcadccdcbaadbdbcadcdcdcdcdcbbabcbbabacacaadddadabdbcbbcbbbdccadcadadcbcbacdbbbcdaaaacdbdddabdcdaabdabbdcccdbabbcbabcbbcdbdcdabccdaabcbcbdabaacbcbddaddbadacbbbcaaaacccbddbbdbdccbcccacbabcababccdbcccbcbdcbabadaacbddbadbaaaddaacdccbbdabbdbdcbdbdbaadabaccbaabccadcacaaddbabbdadadbbcaadcdbdcdcdacbaaaaabadaddbcdbbdaabdcbbddddddddbcbaadaaacaaacdbdbcbabbdcaaaacdcbadaadcdccbddddbcdcdaddbdbababdabbdcbcdddcddccaaddacbacdddabbccdbbccbcbcbddbadbacbdcacdaaacbdbbaccccbadaacddadbdccaacbccbccaacdacbbddbcbcddccddbbabdbcdcbddbbbdaacdbaabbcbcbcbbacbbadaccdbaadbbbabbddadcbbdccbbdbaadddbcadaabdabbcdbacbbcbcadcbdcbddddcdbacccdcddaabdccacbbdbaddbbaaacabbddbccbaadbcdccbcdadbbbdcdbaacdadbddcdcdbcbaaabbdaabaaabdccaadbcacddddbdcbbabdbdbdcabaddabdacbccaaacccabcdbbccddccbabacabbcbbccadaccbbaaabdcbcbdccabdacacabcaacacdcbcbcabdbcaaaaccaaababbdacbabccdadcddadbcbbabcbbdcbcdadacbabaabbccacdcbcdbacadabdcdbcaaacbaddabcacaccdabbacdcdaacababdbddadbdcddabdaaccbddbaccbbcbcbabbaabcdcbadadacbabadbbcbbadabdbaacddabaabadcdbccdacadbdcaacacdcdcacdaddbdcabcbbcaaadadcdddabccbbabbddcdcbdcccadbacdcbdbbcbcaaabbdcabcbcacbbbaccdcdadcadcddacccdcbdbbacbcdddbbbdbdbbbadcdbccbadbabbababbdacaddacaadcbdbbabadaddcaadcaabacacbbddcbcbcbdbcaddaadacdaaabbbbaadacbccdcbbadabadccdcbddcaaadccbbcadbbdacdcbcbbbccbbddbdcdcddbabbbcabbbddabdddadadddcacdcdabbaddbdcaccbdadadaacdaddaadcccdaacbcabbbcbdabbcacbaadcaacbbbbdcccabbacbdbabccaabddaacbaabbbddbbcaabcabbcbddaccdcadcadcabccaabddacbcaadabcddbbddbaccabbdcbbcaacdcdcbddcadadcddddadcbdbddddadbcadccbcaadcdcadbacbbbbcdcaadbaababcccbcddcbbddccddbaabcbdcccdddbbbcbbadabdccdbdcbcddbcaccabbaccbddcbdbdbcaccccbddaabbccaddccbcddddbbdbcdbdaadcabcbdccbadabcdbabacbcddacbcbbcdccbddcdacdaabdacaaabbcdbcccdacaacddbccadabddcdbdddccaaccdbaabbaabcddabbadadccccddddacbdaaacddbcbadbabbcdabcabcbdadabaccccbbdacdbbddbbbccbabdddcacaacbdcddbabaccabacbdadbdbccdbaaaddccbcadacabbddbbddcadabcaacdbbdcbbadddccbaabcdccaacdcccbabbddddcbbdbdadbadbcddbccdabbacddabdcccaddbdccaddbccadacdcccbdacaddacbdbdcdaabacdcbaddacabbccaacdcbdaddccdbabbdbddcdcdcbbbaabdddbbdcbccbabcccadddaacdcdaddbabcacbcadcacaaadabadcaabacdccabddcdcbaaadcacadadacacacbddacadbcdadaccbcdababbbabaadcdccddcdaccccbbdcdbcbcaaddadbdbdbdcbdacdcbbcbdbabcacabaaaabbccbdbadabacdcbacbccbaaacaabdccbabdcacdbbbaacdcadadddadbdddadbbcaaacdbabdbacddcdddcdbbadddadabbdabdacbdacbbacadacdaabbddabcccadcdcadcdccaabdadacbaabacbdabbdbdcaadbdbddacdabbbadddbcccbccdccaddaacaadabbddabaaccadcadddbadbdbcbaaacbbcdccbdacdccaabbccdcaaccaacaddcddccdddaabbdbacabbddbabbdbaccdabaaaaadbcdbdaacabdcdbdaabbcddddbcddacdccaddbbabacababdaacbbcdbcaadddcddabdcbabbdcdabdbdcaaaadccadbbdadabaddadabbdbcbcadccbdabddbacdcdacdaddccbabacdccbdbcdadbdcdbcaddcaadddcbcccdddbbbbddacbdcddaadccaadaddbcbaaaadbcbbbacaccadcaababdccdccdcdbcdcdbccccbaccbaddabacbbbccadccabdaabaccacabbabcdbcbabdcabdbbdbaacbccdbaddcbbbcbbccddbdbadcadacabdaaccbdcabbaabdadaadabaaddcbacaccaddabcacbdcbaadcbabbabaddbddaaddbadadadbdcadacddddacbabdaaabbddcccbbadbdaabddccabaaacdcbaccdbcbbadddbbababddbbdadbabcadaaddcdbbdbdadacdaabcdadabaccccdacdbdcdbababcddbcabadacbabbacbcabccbbadabcadadbaabadbccccbcacadcadcdcacccbabbdcbadacbddbdccbbacbbddbcaaccadaddcaaddcdccccaadbacacaddcdbdcbbdbadcabdadaadbaadabcdddbdabdbbcadaadbbbdddaaabcdbdcdcdabbabdbdbdcacdccbccadabccddcdbcdaacbaccacaccabdbbdbaaacaabacbdbccdabaaacaaacddccdababdbbababdccbdddbbbcccbabcdbadccbccddcadccdbcdbdcacddccaabbdcbcaadbabcccdaaabccadadbaabccdcccabddddaccddacacccbacadadbccadcdbcacacabccbbbdcccdccdccdacdcbcdddadaaacbbacaaabbaaaabadbacabbdbbdbdacabbdbbadccbdcbabababccddcadbcaddcacadbaddaadcacbcbbaddccccdcbabdccdcdbaaccabdbdadcbabadcdbbbccbaddaabadacbbcbabacdbadcacbbadcddcdabadbccbabccdcdbaabbdaddaadbcbcdadbcdbaabddaaaaddbdaaaccddbdcbadaaabdcbccaaacababbadabddbdadabcbabaccbdaccaacccbcbcaccaadaadcbcddadbcdccbbacadbabbccaadacbbacaacddacaadcaccbdadbbdcddbccdbaccaaccdaccddbcbaabddacdbcdadbbdbdadbbdacbdcbcdcdaabdcdcadcaabaabccbddcadddcdbacdccacadddbddadaacdbdcaadddcaaabacaacacdabbcddaababdddddbacdcabbcdabdcdcaaacbccaadbdbbcddaacabcbcacdcaacbaadcbccabbddbbaacdbcadbdbaaccacdaaddbdabcdbdbbadbcabddaaaaaddbddaddddadaadcdcbddbdbcbaddcbcdcbdaacbcbaccccdcbccdbbdcaddbbccacbbaacdcbabaabadabcdbbabbccdbdbbcdadaddbbbbddbdbacaccaabdddcabbbcbcbbaddabaccdabccbabacbdccbbaadbcdbaaccddadaabdbabadcdadcdbbabdaadddbbbcccabcdabcaaddbabddbbadaacacdcaddadbaabbdcabbdbabccccabbcdcccacbdbbdcbadbdccccccbcaabbdcbadabababcccdddbacaabcacddacdbbaacbadddababccaacaaccccacdacbbabddbddbadbbadadcccbdacdbaaacccbbdadccadcacadabcbacbdbaaddaabbcbdaabcaaadbbaabccadbaaaaaaaadbddadcacddcdccbbcacddddddcbdddaabbcdbcdadcdaadbaaccdaddaaadcccbbbaacdbbaabdbabdcbacbccdccdcbcacdcddadccdcddabbbacaaabcdccdacdddaacbabbabbaaaabaadcbaacdaabcbbadaccbbaddcacccaadadaaabcdcbbcccddacaaaaadbcadccbbbdadbaacccacabdaadbddcccddcdaabcbcbcdbcaccccdadddccbacccbbdcbcddcbdbcdcbcdadabaadbcbdccbaaddabadddbbccadbbabccbaacbdadcabbdcdbacaccaddadabcccbaaaccdbbbacccaabbbcacabdcadbbcdbdadbddbdbdbaacdcbaabbaacddaccaccaddcbdabdccdbadcdbbabcadcdbbccdacababddbcaadadadcdadacbdcbcdabdbbaccccabacdbcabcdbadcdcababaaabcdbbccbbccbdbdabdbcaaacabcadadbacdcbaacbabbaddcddddbdacaadaddccadaacacabaaaadcbcacabbdcadacdbbcabababbddcacaabcbbaaaadddcacdabbaabdaaddbcbaccabaadbdaacdacccadabaddbbdbcdbdcadcadbccbcadbaccaabdddbbbdccddacccdccccacababdccadacbbdaccddbdaaabbdaadcbcdadccdabcdcadabcbbdacadbdccaddbabcacbdadbcdddddbbccbacddbadababaabcaddbbbddbbadaabbcdcbacdaadddbaaddabaaadabacadbcdaaadbddcbdaaacabcddabaaccabbcdbdcdabdddddbcdccadbacbaacdcadddbccdacdbdbcacdbdbdddabbdbaddcaaadcacacbbbabbbaccbbddaccaacdbcabdbdacbcbabbacdcbdcbabdbdcdbaaaabbabdcbcabcacbdaacbabbbbcbaabcbdbdbbcacdabdcdccadabcbaabadccaccbbcadddbbccabacacbabccaabcbbadbacdbdababbbbcaabbbcdcdbbdabcdbbcdcddacdcccdadccdabcbbdddbdaacaaabbddacbdbbcacaccdbadddbdbadccacabbabcddbbadabbaaadaabccccabdcdbacbcdaacdbacbbbacccccabcccbcdcdadcdabdacabdddbdcaabaaadbdcbcabddbcddddbccbcbbabcabaddbbcaacddcccbabcdabbaccadabdcbaddbaacacbdcccacdadbbabaaabacbdbadabdbdcdddbaacddbbacddcccbccbbcabcdabaacdddaacbddbaabdcadcdaddaacbdcbaacbbdbdaacaabadcbdaaadababaacbdaabbacdbacdccbaaccdabdcadbdbbabddbabbaddbbcbaddcbaaacccaddcbcbacdcbcddcdcadddcbbcdcbdaadcdbdbcabadccddbbcdcaaccbbbccabaccbbbddbccccddbcbcccbcdbaacccaadddbcbdacabaddaccacdaaadbdaaacbbabbcddccacdcabcbbcabdbbbbcaacaccbcdaadbcbbccbcccdcaddbaccdcdbaabbacbbaccbbdaabbbdcabaccdbbabcadbddaddbbaadaadacaabbbcabddadbaabdacdabdcdbdbbcbababbacbaabadcbdbbbcaccaccaaddcadacdabbccbaddbbcdcdccabddabcdbdbbbbcdddaacabcccabdddbbacbaccacbdcbddbaacacdddbdcbbdcaacbacccddcbbdbdbcbcdcdbdcaabbdbdbdbccdbbddbadcaabdbdaddddbccbdadbbcbacdaccddcbbadcbcaadddcaccbaddabbbcaccccdbabbacbdccbcdcabcbaadcdcbaabdbbbbbdccbcdbaabdcbbaccbccddbaadbdbbcccbdaacaacbcdcdbcccaaddbacbccdaacddccdcbacaabaaacbbdaabcbcccaadbcccaaacdcbddbabcaaaabddcaabadbcabddcdccdabdcdcaaabcdbdbbdabbdbcbdcddcdbbadcddabbcabcdbaacdcbabcadadaaabccaadadccddbcccaacbbcdccddccdaccaadcdadcaddcdbcacbcadddbdacbddcbaacabddbbcdcdaaabdadddccdddcbbbdbccbabdaabbccbdbacbdbaadcaadcaaacdddbbbdabdbabcabdcbdcbbcbacdaacdabbacabddaccdbcacadccbccbadaadadbcbbabdaddadadcacdbabdddbddcdbcccacdabddaadcbcbabbcababcbcacbcaddcabbbdccdddddbcbaacbccdbbdbcabbbbbdcbbacaaacddcdcbabbcabaadcdacacdaccadcadbbadcaccbcbdcccaacaddbabdcbabcbacbcdbdabccbaadbdcbadbabdbdabdcabbabcadcaabbbcbbaddaccdacabadbaaabaaacacbcbabbdbdbcbdcdcdccddaaaccdcbcdabdbcbbdadbcdcdddbcddccacdcbbddaabbccdbddcaccdbbcbabadcbcbcddabccdcadabcbddcdaabdacdadbbadaabcbbddcbdcabddbddddbccaacdadbcabbabdccaccacdabbdaccaababdacaabdbaccbdadbdbdbdaacdccccdbccaaabdaabaccabdabcbccbbcdadacaadaccaaccdbcbadbddbcaabdddcadcadbbababdbddcccacddbcccbccdaadacadcabdacccddddbdadccdcbddacccbcbdaabacddbdcdcccbbabbcbaccdccaddbddabcdbadddbcabcaabbaccbacbddabdabbddcacaaaabdadbbccadcbdabdaacadbacaaccbbadbbbbccbcdabadbaccbdbaccadadcdbacbccbdccabddbbadacbcbaabbddcbcacdcbacbcbcdbdccaddcbddcbabcdcaaadadaddbaacbbdabcccdbaccdbbcabcddbabcadaacaddbcacbcabdabccbbcbdcdbcbbbcadddcaccdbdbccbbcacbdcbabaadbbccacdcbcaaaddddabadccccbcbcdabcbdcaddbbbdaabcacdccabcccdadabdcdaacaadcaadbdbdcccbabbcacaccccdaccbdddcbbcbabcbcaddabbdccbaccdccabccbacabdadaccaacadcbcddbcddccacbbcaccabdddaddabcacbabcbcbaaaccaabadaaadbbcdccaacccadbbcddcdcbbbdabcaddbaddbddbbcacdccabdaabdbbbadddccdaddcdcbcdccbbacbbadcdddccbbabdbcccbdbcdababdcacbaaccccaaaddbcdcacadaacbbdabbbbbcbcbccbbacdadbdcaddcbbbccdaaadcabcdaccaaddcaaacbdcbbbbbccadddcabddaaddcddbbcdaadbcdcaabdacaccadbbadcbadbaabbddaaccbbaaabcacbbbdcaccdccadcabcbbaadbcbbdcacddbdcadbcccdbbdacaddcbccaaaadcddbdbdacacababdcddbbcccdacbacbddabdcdcbbbddcbccbdcbacdcbbddadbbabdacbcbbdcbccabdbcbbbaaadadcacbbaabbadaccdaddcbadcdbcccdbcaddaaccaabbaabbbcdcdaccacbbbaadccdacdbdacbbcaadaaabababcccbbaadccaacdcbbbabcadbdadcbcacadaaddadbbbcbcaadacccabadbcadcbbdcccbaabbdcbcccdbabaadcabcbbdccbcbdaabaccdcbbbccbaccbcaccbccdaacabcbdacbdbdacdcddaddcaddaaadcdcbaacbcddbccaababdacdbbdcdcaddaadbbcaaaaaabcacaacbcdacdaabcdbcdcdaaacbbbdddccdcadacdbbbdcaabaccbbcdabbaddbbcdcabbabcccacabbcbcdacacddbaddcbbcbbabcdcadabbdaabbcddbabdacccaddddaccaddcbdccdcaccababbdcddbadcaadacbbabcbdacabaaaddddbbdcaccdddacbcdcbddadaacabbacdddacdbadcdcddbdcccabcbbbbccbdacbbbacaddccdbbccddcbdbcdbbbacdcabbbabdbabdbcbcdcdbbdbaabccbbdadbbcaacbcadbdbadaabcadacccabbbacdcbdbcddbaabadaadccacadcaacdbbcbbbabaccbabaacbadbadaadaaabcaddcadcabccbcabdacbbbbcabbabbcbbaaababcdcbdaaadabbabaababacdddaaaacdcaddabcacbacacdbacadadbccdcabbbabacabdbdacccdacbbbcaaaacdbcbbddbbbbcccaccbdaaacbabadbdbbddcdcadcdaaabaccaaccddbacabbcaadbbdccbbdcdbcddccbacdaccacbdbbcbbbcdbccddcadabcbbdbaadddddddbaabddaabdadaadabcbbccbddadbaccabacbdcacbcdddbbdbabadbdabdcdbddcccabdaabacbcdabddcadabcdbababbbbbdbdcaacacabbccbbcccdaadccbdacdbbcdcbabadbacabcaddddcccddadcdbbabcadcabaaacdaddddbacdacddbbbaddbdcaaacbdbcbdbcabbcaaadaadcaacccbdbabbcacabdddccadbdaaadacdadabddbdbacaaadcadcdbdaadddbdcdaadabcdabacbbaddbbbbaaaaccabaacdcbdabbabdcadcaaaccaadbcdabbbcbcccdbaddacacbabdcbbbdcabbbbbdcababbdcacadcbaacbcdaadbaacabccdddadddccabdcacacdcabdbbbddadccdabcdaadcccaaccabbbcabdaaadaaacdacbdcdaadbaccaaddacbbbcdbbadbdbdacdaadcbcbcddcabbadbcaddabcbccbcdbbabbdcdcbadbcaaddcbabdbbcbdbacbdaabbcadcabacdaabbcdabdcddddaadddbacabacdcaabcddaabbddbbbcddbdcdadbbacdbbcbacccaabdbbbddbcabddabbccdaddbdddbdcabaccbcdacaadbadccbcbcacbcccabbaddadbacbacabaccbddccaababdbadbcbddaacacabbbcdabcbdbbaaacaaacbbcbabbaddbadbbdcbbaddcdadadabdabddbdaaccbbdcddaaadcdbcdcacccdadcabcadbccabcbacbdcbcdcdbdbcbcaddaaabbabcacccccabacbcbbbbddddaaaadadbabbbbaacbbababaadabbbbbbaadabcdcdcdbdbcbdaaadcbaaacbccbbdccbbadaddbadddcddaaaadbccccadcbcdcddcbaabbdaabdbbdbcbaabddacabdacadaaaddbacddbbcdbdaabdcccabcbcbaccbcadbddcacdcadadbcabaaccbacbcddcbbadcbddaddbddcdcdadbaaaaddaacabcadbcbaaccadadbcabaddbabdabaacaaabaaadadaadacabadbaadbacdccbbcccaddbcacbddbdcacabdcaaabaabbaadbdbaacdcdabbdadccaaadcccaddddadadbabddbaabaccdddadbadbacbbcddbdbdbabcbddddcbcaacdadacdddaabbbcccbbcaaaacdaccccddaaacbdcbcbddbbabacbdcdbadabadabbbcaddaddcbaacbcddaddbdccabbacadbdadbcaccaaaacbdbabacbcacabdcddaabcddcabdbbbddcccddcbdadcddbdcdbbbcccadabcbabadcbbabcbcaaacadcddcbabaabdbbaddbacdccddbbaddddabddaccbbbbddadbdcbcacbdcddaacdbbdcdcdaaacadbbcdbbbcdbddccccaaabbcdbbcccdbdcdcababbdbcaddcbaadbdddaabdbbdaddcdacacdcbdbdcccdbccbccdddbabdbacabcdcccccdccccaacccacdbbdaddbabcdbdabacdcccddbcbadacadcaccbcbdccdbadbbdbdccbacbcacbacdbdbacbbccabddbbaccbbcdaadbcddcddbbcbcbbbdabadbddbcabbcbabdcabacbbddbbcadabaddbcdccdbaacadabbcdddbcadaddbcbbbaccdddbbccbdaccdabddbdcbdbbbcddcdcacbbbacccccccbacaacddaaaacdbbdddabcccabbbcabaddbbcaaadbdccabdbabacacddcbbaacdcadcdaacdbabdcadcdbcdbdcacccaadcbcaacbcaccbbcadadabdbabbdcabbdadabbcddbcaddccbabccbddbaddabdbacbacaacdcccdbbbaacaadbcdabcacbccacccccddcacbcdaddbbdcccdcdbdadbccccccdcdcbbaabdaaabccaadbdcbadccdbdbddcddcddcacccdabdacbabbddccbcabccddadbbddbbbcabacaccbcaddbaacccbbcaacacdccaaacadacadddbcbaadbaccdcaccaddcdcdabaddddcadcccabdbdaccbadbcbbabadbccddaacacbbcbabcdbdccbbdacbaacccddcddbdddbcddabbdbbdaabcacbdcabdbbcccdabaadbbcaabacabcdbdcdcbacabbadcdbdbdaaaacbabaacaaddbadbbaddbcdcbcbbccbdccbcdccaabcdcbaccdacaaccdbccbbbddbadacbbadadbbcdccbbbabcbcacaabadbcdaabcdccccabcdbaaadaaacdabbdaaabbdcddbbddcbbbdddddbbcdccdabaaaaadabbdcbcdbdbdbccbbdbccacacdbcbccacbcaababbccbcddaadcdcbdaaabbcbdcdcdcdbbddddcbdadcadcbbdabaaddacdaaaddaccadbdaaccbcaadabacccadadbcddcbccdaacbbccbdacbccacccccbcaaaaadabdcbccabaadcbddcdbbabdcbbddddabcdbbdadaacbbcacbbdbdddcabbbbacadccddbbaccddddbcbdbacddaddaacbdacbabcaaaadbcdbcadbbbaccabcbdcdbadbcaadbddacdbcdadddcbbacaccacdcbdcdbbabdccbdbdabaccdbadcacdccdbacccdabbabbcacdbcabaaabcbbaddbcbbbbaadbabccbccbcddbdccadcaaadddaabbcccccdaccaccddbdbddabbbdcbddcdbbbcdbbbcacccbcddbacdbaddcccdcabacccacadbcbbcbcbcbadbcdcadabdbddbabbddddcaaadabadccaccbdaddabdcabdabadcabbcbddbdabcddaaacaaabbbacadadddcabacccbbccccbdbcdbdddadbabccbbaacaaddbacaadbaddccabbbaddbabccccaabcbdbcbbcccbacacbacbcabacbdacbdddbbaaaccbdaaaadbcacbdadcdbaddcaadbbdbadadbdcabddbbddbacdabacabbadddbbcbcbccdabbddbadccbbaadababacbaddddacdcabbaaccdbcddcbbcbcaddaccbccbbdaddabddcdcbcbdcccaabacbdabbcaadaaaccacacccadbabadacadbdbdabbdaddbdddcddcddccadcbddabdbdadbdaccbcdbbbcddaabbcbbcbabaabaccaadbcacdabacdacadddcbadddbdcbcbdbdccbbdbacdaaadbddcaddbaabccaccdcbdbddcbabdbabdadcbbdcacacacaadacadcbcbbcdbdbdbcdcdaadccaaabbcbdacabcbaabdcdcccaacacaadbbbcabdcdacbabacbcabacbcaacaaadcabdabbabcadddadacadacacdbaabddbacadbaacddcdccabcdbcddadaabddbaddabcbddddcaabcbdcdbadcabbbbcbcacabddadbccbbbabacabcabcbbabccacddabaddabaacaabcddadbdddcadddabddcddcaccabbdacdbdcadadcbacdcbcdcdaaddbaadddcdbccdcdbcdccbdddbacbccbcbbdaadddcaabddcbdbcdcaaaddcccccabacdbddcacdcbcacccaacdcdaccaabacbcaddaabcbdbadcbddabcdabccacbdcbdabccdbacdcabdbbbccbcaaabadadacaccaddbcdaacaacabbdbccccaacccbaaaccaadaccdacddbddcbadaacdaaabcdabadcbbbccccbdbacabaacddcbacddaccacaadadababbdcdabdbabcbbbdcdbabdbabaaddcdbdbacdccdadcdbbcacddbbddbcdcdbbdbcbcbdcacbdacbadcaabbdaabbddbccadabcdcbbaadaabbcddcbdaddcdadabadcbadddabdbccdaadcaaadcacbcbcabdbdcabadcbcdbbdadccdacbdacacdcadbcbbbaddccdcbabcbbcdbabdddbcdcdaacadcadaaddacbcccdaadccbdcbbadcdbccadcddbbaccabbbbbdcadbabdadbdcdcbdcdbabcbdbaccbaaabddbabbadcaacdaaddccbbdacaadadcddccbacbbbabcabcaadcabcbaccbddbacaadbbbbcddbaddccdcacbcddccacaaabacdcbadddccccadcacdcdaadcbcccdccbdadbdccbaabdbbdcdcaabdabcbddadbbcbbdacbaddaadbdabcdbddcaccbccaabcbabcaaaaadccddbbbcbdacddccdbdbabbdbccdbdadabcbdcbcaddbbbdbdbdacbbcaaaddabcbccabbcbadabdbbbcdddbadacbcacddaadbdabdbbdbacdbaaabcccddabdccaabcacdaccbdbabcbbccbcdcbcbcacacbdddaccbdbabbaadcddadbdcaacbabbadbadcdcaaacbbcabcabadaddddaabcbcdcdbdcaabbdccddbccbcccadcdbdabcbbddbaabcadcdddbddadcdbbadabbbdbcbcabcbcaadbcadcbaadbabcbdddcbccbabdbbdabccadaadaadaabdcaabddddccccbcbaaacdcddbcdcbdadbdaabbbcbacbacdcbaaccdacddcacbddaaddbdbbdbacdcbbaaddddacdbadcbbacbabccdbdadaababdaabcdacbbaccbbadadacdbbcbacbdcdacdaabdccccccdacbbcaadbdacddbabbaddbabddcacbcaddaabacbddddabacacbdbcccdabdbcbdacaabbbdacddacdbcdbcaccdaadaaaadcabddaddadacadabddddbdccdaabbadcdbcbdabdbcacbadccabacacbadbdcccabcaaaddabddbbcddabccadcbdabbcbcdbbbaabddcbcddaccbadabccdadcdbbdbacbcadbbcbababacaabbbcbdadddcacbdbadbaccbabbcbcdbbbdabcdbbaabaddadaaddadacccccbaabadbaddacbbdadcbcabadbbbaaaccaaabccaabdbdacaaacddadadcbccabdadbcdbbcadabbadcaabbadbaabbbccbbdbcacabacdadcdddbdbbadacabcabcaacbbbcbabbbabbcdcbaaadddccdcacdaaabadddacddabcdbabbcbdbaccbcbabcadcacadacdbacdbbccdddcacdccbdaacbabacadbbdbdcabacbcccbbaababdcccccdabcabdbbccadbadcbaddbacdcbbddaacabbabbdccbbbaacabcdbcbbacbabdbaababdbbbdacadddbdccacdcadabbadacdbbddbcbaadbbadcdddadabcdabcaacaabbbbaacbcaacdddcbabadcadbddbbdbacbcdcdabbdacbbaadbbaccddbcdbadaacdaacbdbcbddaaaadbabccbcbcbbacbaabccadccddccaacdbaabbdbbcabdccabdacddaacacccddbaaacabddcbadddadadbaacbddcbbdadcadaddcaabddbdbdcbacbbccbdadbbacacdcbaabddabbabbdbadcaddbddcdbaadcdbbbdabdcacacdccbacdcbadbbbcbdcdaddbcabdbbccbdcacddddabadcbcccadcddbccbadbdcdabbadcaadddcdcaccdcbbbdcadaaddcbbacabadaabbabcaacbcdddcaacbacdbccdcadaaccbacbaaadcdcadcaabcbcbdacaddbdabcdacddbdabccadbdccdcbbbbdcdbbcacdbdbbaacabccdaddabdccbbcadcdaaabcbdddddbbbbcbacbbcbddcacbbbdbadaddbccaaacabbbcdcdbccaccabdcddbdbaacbddaaadadbbddddaccdbadadbdbaccddcaaccabdccdcbcbdcdacabbdcadabcaddcaddadcbcaccccbbdddbcbbaccccbaccaabccccbcccbbbcbaaddcdcacbddddaaadbadbaadbbcabacbcabcbabdcaccbacbddccaaabcdcaaabdcdcdcabbdcbaaacdabccdddbcadacadbccabdbcbcddacdccdddcccdbdcccbdbbbcabcdbabacdadccaccbbbadadcaaaaaddbadadcccadabcddcacabdadbcbddabadcbbddbacbbbbadabadcdccbadddadbcabdacbbcabddcbabbadccaaacbdacddcadacbccdcbacdcdbbdbbdadcdcacbcbcbbddcdcbcdaaaabbdaabdcccccaddabcdcddcacdccdbcdaccbbbdacdadbdbccddbdbcdcbdbccadbaccdaadaccccbbacbcaadadbdcdacbaaadcaaddbbdcbabaabcaacdaaaabdcccadaaddddccdbadacadacccadabcbbdcaabcacaccaddddbaaaacdabbcdaaabbaadbdcadabbcdbadaadbbdadadadccabaccbbcbbbacadcdddbaaababbdbdabdacddbacaccdaadbadbacbabbbdaaddbccadabdcbdcdbbababdddadcccaaaacbcaccadcdddadcbdcddcacddbacaccdcaacadcbaadabaabbbabbccadcdcbcadcacdacaaabcbbbcdccacdadccbbddaccdddbabcacdcabbddbcbadacdbbcaadaddbaacbdccbadbccbaabccabdcadbddaabdbdaaddabbdacccacaaabacaaddbacdccbdbbbcaaddabccccdaabbcaababaabbbbbcacdbbbbbbddadabdbbbddbcabbacddbbcbcbdbcadcabcbacaabbbbabcbaaabcdbbdbadbbbdbdabcaccdbcbbcccbcddcdcbacccbddadccaabaaaaadbbabcccacbdddbcabbaccabdcccadccdbaaccdddbdbadaddddbcccabdddccddaabadcbddadacaaaacdcabdbaabbcaaaccdccbdbabddacacbdaabadabcbaadadcaadcbdccdabcdcdbabddbcdadcabdbcacddcdcdcabbbcdabbbbaddbacadbbbdadbcdcbcbdadcccdabadbcdababdabbcbacbacadbabbaddaddbbaadccbabcdabcdaacbcdcdbacabdccabbacbbadbcbddccbbabddabcbcbbbbdcaccaabbabdbddbcbccabddbaaccdcbdddbbccccdacbaddbdcdadadbabbcadacbdaccaccdbbbbabbbcdbcddabcccdacabcdcdabbccccdddcadbabadcdacbdbabccdddbabcccbddbdabcdccbcaacadbaacbacababbbdcadbbaabdbacbbabdaddbaabacacdacaddcbdbcdcddcddbbbdbcdddabddbdbacbbdabbddaaccccbbaacbdbaadbcbbccbddaaabacdadbddaabcbbadcbaddadcadaabaccbccdcdbbbabbcaadbdbdcbbbbcdcbcdcbbdcbacadcbdbbadccbcaccbdbabbacaddddcdbccdccdddabccccdbdbbababdbcdabbbbbbcbacacabbbbdaccdccdcdbcadaaccbbadbbadabbdcddcabdcccbabadbbbacbccabadbbddbabcaacddbaccdccbdbbcddadbaabbddaabdacaaabcaaddccbbdddaaccccadcabdcbadaddcdbbcbddbbabdadaaacacbaacabadaacdbddddbdcdddaadddadaccababaadcadacaadadcabdaabcacdccbcacccaadbdccadbdcccbbbdaaabcbbadcbbaabacacaaddcabcdaaabababaacbdbcaadcaadbcdabbdcacaaadbbdddcadcccbaabbbdddccaabbccdbabddabaccdccacbcdaabaabdcaabcadcabbbdcbbdbdaccbcaacccdcaaaabdbdccddbcaddcacdbcdddbccddbbcbabbbcaccadaabcccdbcabccbcdbdccbbbccaabbbcbbcdabddbdddcabbccccccadcacacbdbabdcabddabbcdadcbcbbbaadaadbbadccdbdbdbbbddadbabcbcbbacdacdabacadbcaddadbacacccdddcdbabcaddabbabbcadacdabbbbacccadccaabddbdbbbcaaadbbbaddabbdcbabbcacbbcadcccbabdbbbccaaaaaabcaabcabdcabddcadcdababcbcddcddaababcacccacbbdbaaacdabcbabbdbcacdbaaccdcabddabaabbccaddadaccabaccdcaccbcacadabdabcbdddccccbcadbdbdcdcbcbccacdabcddbcbabdbcabbccadddbcdacacbbcbacacbbdcadbacabcdbcaadccabbdabbcbddcabadcbacccaadbcdbbadcddccddccbdaacbbbcaddbddbaadccdddcacaccaaacaccaadaadbcccaccddcdbbbcdaadbacbdbdadbcadbdadbdddbbbbdbcdaacabbbbbbccdcdcdccaccabdbadaababccbcdabaabcabdabcbdcacaacdbcbdcdddcbdcbcaaabddcddabddbcdabdbadcbcbdcbcadbccdacabcacdddbdabacbaabcdccbbcbcaabacdcbadacadbddadcbcaddbdbdbaaddaababaddccddbabbccdddabcdbccdcdbdbcaccdbdbaacbacdbbdddabbccbacabddcaadabaadddbdddbdabbaacbcdcdbdbccdbaacabdaddcccaaccdaddbcddbbdcddaacdcdcddddcbcccbbbccbdabddacdbdddcdccdcdbcccccbadbddbccdcabacbcdcbcadcddbbdddadadcccacadaacbbdbbabcbacbbdbccbacdabbbcaabddcadcaccdadddabaaccdbbddcdcaddcbdabbdaadacccadbaaabdbbdbbcdddaacdcccaccbccdbadcccbddbcbccbdaddabcdccbdabcabcaaaaababcccdaadcadaaababcdbddacddccdadacadbacbdaccddabcabdaccccaacccabdccabadaccbbbcbadbacdaabcacdddaacccbbcaddbcdbaabacccdadadcabcdccccbabcdbbcacdadadadccdddadbbabdccdbdabcbcddbdcbcabdacddcddabbbadaacbdadbdbdcadadbbaaadcabcbabdaababdbddababbbadaaddbdcdbcaacdddadcddbdabcaadbbcaabbdccadbccacabcbccbbcdcabbcccddbacadddccbbcdabaccadcbaadbaabccabaadbabdcacabbabacaaabaaaacbabacdcababdcbdcbabaccdbcbabbcdccaccacddabcccdadaddcdaaddbbccdacddbabadcaccbdbbccbbddacdcbdddcdacadcdbacbabddbdaabcbbdaabcdbdadcacbcbcabcaaddbacbbcaacbdccdbccaddbbdcbddbaaaccddbddbdccdbcadcbacdaaaabccdabddccdcdacabcbdbbccccdcbcbdadaadcacdbdbddacdacdccccbbbdcaaccaadcaaaaadcaccbbcbabababaccccdddaaacabaadabacabbcbaadbcaabacadaacabbbdbaacabcbbcbbbbdbbdcdccdaaaabbdccadbcadaddacaacddbbddbaabbcabababacdacadcacabadabcbdddbdcabbcbdaadadbaacbddcdadbcdbcbabaadaccbadcdccaaabdbbaaddcabdbadcaadcbddbdbdabaacadbacbbcaabacbdaddaacbdababacdddcbadacdccdcbbbcbaabaddaddadcbbbbbbaaccddbdcaddbaddabddbdddcdababacbdbddccdabbaaaadcccabcdcdcbabdcbbaadbdcdddcccccccccadddadbdaacabccccdddabcbcccbaaaaadadcdbdadabaacaadbcaacccadbacccadcdcacdadcbacabadacdcdcbddcbdddaddccbacdbdbbacdccaaadcdbddcbccadacbccaaadabccaaadadaddbccccaccabcadbabddbbbccccbaadcadcccddadadbcdcabddbaaaacdbdcbcabaacbbabdadbbccbcbbdbcbccccacccdbbcccdcbcdcbddaaacdddcccaccaabccddcabcadacdbdcdbdbadacddddcdaddbbaadcddcddacaccdbdcbadbbdbcadbdacdbccaadbdcbbbcdabbddcacccbaddacadbcabcaccaabdddccababbcaccddaaadbbbcbbadaabbbdbbdbcadbbbbcdbcaaddccbbbbbacdaadbabaabbdadbbdacaaaaddacababcbcbbbacbacaaccaaaaadbcbbadcdddcdbbccbdabaccbaddcbcdbdcbbccabdbdbcddbcacbaccaddaaccbaabccdcdcdcbbcadadcdddbdbcababdddddadabbbdcdaddadcdadbcddbdaaccbcbaacabcdcabaaabadbadbabdbaddbbabbcbaabddbaddaaabaacdcaddddccdbcdbdccbdaacbdbadcdbdcaabddbacdcdbbddabdbdbaacdcadbcadcdcdcaccccacdcdbbabbcccabbcaddbbcaaacaacdbdcacabaaaaadadccdbdbaadcdbacbbacaabcaadddaacabcabaddccadbacbdbccccadbabaaabcdacccadcbdbcccbcccbcacdbbaacbccbbcaacaabaacadcddadacbcbdcbbdbabbbcabbbbddbccbdbaddbdcabadcddbddaccbdddcacddaacabbccddaccbaabaaccaaaaddabdccabacbddbaaaaabddcaaaabdbadccbdbbcccabccbaabbdbadabacdaabbbdbddddcdcdadccaadabbdbacabdddcdbbdddadbdcbcaddadccbadbdcdbddbcddbccbbddbdcbcbcdabcdbaacaaaddbaddaaaaddadbccaaaadcdbaacdadbaacabdbcaaccdadbcaabbccabadbcddcdadabcaddaccddcacdadadbddbdadbcaabcabaccacdadbcbdcbbcbdaababaabdbacddadbaddaccbcaaccdcababbddbacdcbbbcccbabcabacbabdabcaaabcccdbabcccbdbcbaadccaacdababbabddabbbcdccabcaccbcbcabbcdcabcdccbccddbbcdcaaaacdbdbabcbadddcacadbccbbdabbdadbadbccbcbbadcdacaadcdbcaaadacddcdcbbcbccbbcddcbbcadbaccccaddcdacdcdccdcaababcbaccadacabbcdcadaaadacaaabbcccccdccbdcbdcdcaadbbcbbdbbbcdddccdcabcbbabdabcabadcccacdcbabccadddcbdcabddcdccdbbbdabcdbcbbbbbcacbdaabdbdddaddcaabbcdcdbdaddabdbbdaaaaaddbdadaccbcbcadbbcbacddcabbabbbbdbabbabbddabcdaadbdcbdaaddacdbadcbdaaaabcdadcaacdccabbabccacdcdddcaaccacaacaacabcadaaaadcabddbcdcacadcccacabbdbdbaabbabdcdacbacabcadbacdaaaaacddddbddbdabbdcacbddadcdcdacbdcbbdbdabdbbdcacdcadbbdddcacbababbdbacbaccbbcaaaadbccbcbcaabddbbbbcaacaaaccabbcccaccddabccdcdccacdaabdbbaadcbcbdbcacacbabdccbdaccbaaadaacdcbccbaddcddccaabbabaaaabddddddabbddaddbddaadacbdcbbadadddcadbbbcacbbbcaacdabcaccbdbbcaccdcababccdacdccaaddbccddcaadaaddabbbdadacbacdbacdabaabaddacdbccdaccbbacdacdbacdddbaadabadcccaadabbcdcaabcadbdbccacccaacbbcdbcccdaacbbbacabaadcabacdabdccaadddbcadcdcccaaacaadabcdddcdccddbccdcdabbccadcdddbdbabcbbadcccbdcadcbddbcbabccdccdccbbbaabcddacbbddcdcdbaaabadaabcacbacddbcdbdddadbbbcdbcbcccabaacdbdcccddddaacdacbabbcbccbccdccadcdabadbcacbbabadbacaddccdbbbbbcdcddbdabdcadaaadcdbabaddbdbacdabbadababdcddcabaabbbbddbdcabbabbddccaabcbdbdccabdbdbdbacacdcbdaccadadadbcdbadaaadbbcdcdcdbbabdbcdadccdbcacddabdabbcbdbbbdaaaabadccbbddbadcdbdacdbabddacabaccbcdaddbdddccbdbcddaadcacdcdadabcacbacbdabdbbbbdadacddabcbcbabadbbadcdaababdcbdaaaaccbcccadcabdbacdcdadaaadabddddbbaaabcbaaadcccdbaccbdaddccbdbccabbbabdddcbdaadacccaadababbbaabbbadaadbcbcaccaabbbabacaddadddaccccbacdbadcdadadcdcbaabdaaaaddaabcddabcaadcbbcdadcddadccaaacaabcddacaaadadbbadcacacdbdcddcbdddadcaaacdbbbcddcbaabddacbddddabbbcbaaabcddadcbbdccdacdcdbadcccacacaccdddbbcdddacabaabbdbcbbbbdbabcddacbdaadccacadacaaaccbbabaaadbdacdddaccdcdcaadcaadcccacdcadbbaabdddccbbabbadacbdbcadbcabdbdbcddcccadcddbcbcabbdbddabacdacadbbaddcbacbbbdcbdcbaaadcddcdbdccbbcadacacacabdbaddbcacdacaaabbabbcbcbadddbbcdbdadbcacaaaaaddcdbadbcaddaddacdabdccddaaacacacbaddacabaaddaacbcabbadbdbaaddcdbcaaaadddcdcadaaaddaccabdcacbabaabdcdbdacaabacbacdaddcbabcbacbabdcddcbdaacdddaddbbbaaababcdbdaccbbcadcbbbaddbaadddbcbdaacabaddcddcacdcccdcbadcddcdccbcdadcdcbdbddcbcabacbadccbdabacdaadbdcbdccbaccdadddabbdadacbabcbcabcadcababbcadabbcbbabddcddcadcddcadccacbcbabbabbbaacbacbdcbcddadaadadbddccbaabbcddcadcbbdbbdcdbbaaadccdbabdcacbadcabdadcacdaddaabdadbcdcbbadaadcbbcbadbcbbcdccbbccbdbcbddccbaccaadcacbcbadcbbcbcaabdddbcdbcabacaccbcdadcadbadacdcbaadcddbcccccddaddcacbbadcadcdaddccbcdcdadbcdadcbdabbbcbdcddabcdccbdbcdcbcacbaabcdaabacddbcdabbaabccaccdbdbcbccbadbcdcbcbcaaabbdcdcacddabdaaabdbadcddadddccaaccdcadbbcbcbaaccbddadcaaccdddcddacbabbacddddbdbaabcadbcbbcbdcacabbccbdbdcccdacabcbdcbcddccaacccdaaabbdcaaccabbcccccdaaddabaddcbdbccaadcabcbdcaccdccbbdbbcbbdccadcbdcdcbccdaddacbaaacddcccdadaccadbbccaaadadabadddddddbcaaaddaacabbdbddcbbabacddaadbcdccdbcbcdaabcccdaccadccdcccbcbbcdaccbbaaadcaaaacaabdbacabcdddadccddcaadaaddcbdabbccdcbdbcdbddcbcdabdccbbbdccbbcbcbbdacbbccbdcacddbbbdbccadbdcbadbddacdbbadcdddbaaaaacdadbddbbddadddcdaccddbdacddadbccdcdaadcddcbccbdcbbdcbbadccbbdcaacaabadadbbbaadbbcdcdcdaddbabdbadbdababdcdddbadadcbaacbccbaaadcdbcbbbcddbdabbadbbcbcadcccddbdddcdccdaaabcbdbadaccbcdacbcbbcabddacacbaadabacacddcccbdbababdcccdaaddabdccdbbcbbdaabdddadddcabcbbbccdccbbbabbabbbabacacddbccdbcbccdcacaaaabacdddcaabdabbadcdccbbaababbbbcbdbaddcdcabccdcccdcbaadadbbbacbbabcddbccccaaaadaadcaabddddcadbacbbbdcacbadccccadbdcdbaaddccabadbbcbccdbbccdcccaddddabdcbdadbacccbdbaddcdacdadabdbcdcaccaabbcdbadbcdcbdccbcdbbdddccdbbddabbbbbaaddbcadadbdabdbddcbbacaccddbaccdbccaadcdacbcbacaccdcbcbddccbdddadbbbdbbddbccbacbcbdabbdbdabdabacddadbdadaacbbbbabccbbbcabdccaaadbcaabcbacdcdbdadacaccbbcbabbdcdbdbaadbaabbabdcccddabcbbbcabbcabbcbaadcbbbcadcddddbabdcdbaabddbabcadddcdddcbaabdbddaccdcbaadcdaadbaacbcaadcbcdddcacccdbabbdcdbaddbcbdaccbdbabddbbdadcdadcbaddcdabcaddcaaccdddbbdacccdbbbaaadbdcbabcabadaccabbaadadabcccabcabaddddbcbbaccabdcacbbdabcdcbbbadcacbcbadbbbdacccbdacacdaaabcabcbdbabcdacaddaabcbacadcbcddbacbcdaaabbaaacadaadbdcabcbdbbdbbacabcbdcdbccaababbccaacadacdbbabbbcddbdbbddddbabbaabccbcabaaacdbacdbdcbbababcadccaccaddacabadbcaabcddcaaaaabcadcadbdabddadaacdacdbcbdaadacdaabccaabdbdddbdbdbdaacaababaacbaadcaabdbbabcdcaabaadadbbacadaabdcddbdccacabbccdcdcdccbbabdccadacbcdadaadacbcaccdaabdaadddaadbdbcbbbaaddbdaabbccbdcbbaaadcabcaccccbabacbbbbaacbaabcddcbcdabacabaabcabcccbcdbacbdccaaadadabddbabdcbbcdadbcbcbcdccbddbabdbcbbccdbbccacbbdbdaadbdccddbcbcdccaaacdccddbbacdbcadbabdaabbdbcddcacdadddaabddcbabbcbdcdabcdbcbdbadcadbccbcaccdcdbacdbcbbccbacbcbdbaabdbbcadaacbcddaddddbbabbdcdcacbbcdabaaabdbdbccababbbddbdbcbdccdacaaabaacbbcbdccdaadcabbdbbbdaadbcbbdcacdcacbaabbdcddaccbabcbbabcaddbdbcabdddacbbcddbddddbabaddcddabbdbdcacacdbdababbbaaadcdbacaddddacddbabbabbbaaaacabaaaabcacaadcadbbbcbdbcabcbcccbcddcbbdcabcabdddcbbbcbbbcbdccbaabdcdbacddadcbbdcabbcbcbabbcaabdbdbbcdccbbbbdbcdbabcbddbadcabcbcadcaacaccaabccadcbcbadbdacdccbcbbdccbabbcbcccbbcbdcadbcaccbcbcdabccabbdbaddacabbdabbbccbcbcddacdadbbdaaccabcabcaaccbaddbddbcabcadcadadabdcdcdbaccacabcccccdbbdcbcdccbddddcbcdbbaadabbdadcbaccbdaaddbbabaddbabaadbdadbbbbabccdadddadbddddcbbacbaadbdbdddaadcaabdbacacddcbadbbabbcaadcabbccddbddaccbdabdaacaadaccdabbcccbadbdbaddbbdadddcbbabcbcabbadcbcaccdbbabaaabdbdcaadccdadbcdacdccbbadcacbaacdccabbcaabddbccdcbcccddbcbcdbabcdabdbcbdaacdabcddcbbdacbcdaabbabbaaaabcdccddcacdadadcddaddbabcacdacbbbabdadbcababcdcbccabbcadcbaabdbcdbddcdbadadbacaccaaddabdacddaaaacddaccacdcabcbcabcbccacdcddcaabbaddcdcdcbdbacbacddcabaacadadabcddddaababbbbcccbcacbdcaaadcbcdacbddbacdcbaacbadbccaddbbbbbcdcdacbaaddabadbbcdbbabccbddbbababdbdadddacabacccdcdabbdcaacaaccbdcccdaccabdddcaabbbbdcbdabaccccaaacaabaddcdbcdcacaccbacbbbdaaacaadbaadccbadcdddaacbcabbdccdbcacbddaddbadacbccaccabdacdbacbbbcbcdbcdcdbdadaccdcddabbccaacbadcdcddadcbdcdcadbdcdccbbdbcdadbadabbbacdbcabdbcddcbaacdbdacdbcbbcaccbbadbdddabdbacbdcccddbcdcdaddddbcdaccdcdbbbcbddacdadbcdcbcbdaaddbdaabdaaabdadbabcdbbdbbdccaaabbcadadadadbbdcdaadcbbcaadcdabaaabcabccaabbbdabdddadbadabcaadcbabadbaabbabaadcdadbacbbbbbcbccaddbaddcdacaabaabccdccbcdcdccbccdccaabccdbdbadbbdccacdbbcbabccaadaddccabcddacddabdacdcbaddcdaddabbbaccaaaadadcbcabdddadaacbcadadcdaddddccbdddcbaddbdcddaaddbbaaaaadcaacdbcdbadbcbbdbbccaaacacdadbbcccdccdaccbccdbcbcdbcabaddbcacddcdbbaccdddccbddadbcdaaadacdacccabacbbadcbcdcadbcadbdcdbcadcbddcabaabbbbbcbdddcccbbaaabdaddbdddcbddadbacaaddcbddacaaabadccbaadbacdbdaacbccdbccddcdbcdbbdcdddabcbddbbdcadccbddaaccdbcaabcaddbdcabcdccdacbbaabadccbdcccbbcbdddddcadccdadabbdaabacbcbaaaacdabacaaaaabcbabaabcdbcaaacbbbbcbbaaabcccacbcadbcdcbcccbbcbcbcbcabdaacdcdbccccddcbbcbacaccacabbbccbdcdddabddcadaccaaaddbbcadcdaadaadbdaccacaaddbcbddcddbbcbcbaddbcbadcdbacbdabacbbacdbccadabdaccacccdcbaadbbdcadbdcaabbdcbbdbccccdaddabcbabbbbcbbcddbdaabacadcacadddcdadbbdddcadbacbddcbcbddcbbaaccbbacaacddbaaaddbabcabcbcdbcaacbdcacdcbaabccbbbdadddadbbbaadddccbadbddcdabdbadaccbcdbdadccabaacdcaaccbadcdbdcddaabbdaccccdcbbbbcabbbdacaddbaabbaadbcbccdbadabccbbdcbdbbbadbacbcdacabdaaacccbbacacbbbcdacbccbbcaccabcbccacbdcdacdbbbcbcbaababdadaacaccacadabbbbaddcbaacbbdddbbcaaddbdadcadbdbbacddabcaaaddaadaddaaccbbcabcdbdaddbddadbbddbcdccbcddbbddadabdbaddbacdddbbcaadcacabcddbaadabbdbbbbddbbaaccdcccadaadcaaacaadbbcabdcbbacdbbadabbaabcdbbcbccbcccdbacddbbbabcdabdacaabbadccabcbcccbbacbccaacbdcbcdbdbdacacaaadbbdcdaddacaddcccacdddccadbdcdacbddbdbaddbdbdbbcdaacdbcbacdabbaccdabcdbabdddabcdddaabdccaddcbcabdcacdbdcbcbcdcdbbbaabbbbcbcdcbabcbbabcbdabbaacbbbdabcaaaccccbcaaabbdcddbbbaaababcbddbdadcabbabaaababcabaaadbdccdaddcabbbaadcbdadcdbaabbaccdddbabccbabaadaaabcbcdbcbbbbcddddccdbadbcdcccabcbacbacacbbabcbdacbbbbcababcbdabbadacdcbdaddbbbccccbcddccacaaadbdcbdbcbdcabacbcbbccbbaccdaaabadddbdabbcdaccbbbcadccabdbcbcacdbbbabdabdaacaaaccaacadcabdadbdabdcaaaaccdadddacaadcbdccdddacbcdbbcabdcdbddaaabbddcbddcabddabcccdcbddccdababcdacabdacacaddbbbdddacdbabcbbbbbbabaaabbbbddacccbaadcbcaabdaaacdcdabdabaccbddabcbbaaacdacbdabddcabaadcbaacddccbabcdacbadcccbccbbbbadbdacdcccdaaabbbbdabcaddadbbdddcccdbddbabccdcbccddbbbacdddcdcddbabddccabbdabdaccabdacddbbbdddbdbcdcdddbdcabcacaabcabbdbcaaaaadabbcbbcabdabbabbadabbacabddbddbbdcbbcbdbbcaadddabcbadddaacccdccdacabacbddbaccddaaabaccbcaddbadcacbbdcbcbbdabddcaddbdcbabcacdabcaabcaadcbadaaddabadccddbcddababccdbbcdadaadcbcaccbbabdcdadabcdadacadccccabacacacbcabcadcbbdabcadcccdddaacadbdcdaaacbbabbcadbbcbdbdaccacbddbacadacaddacbcbcbcaacdabbcccbddacddabbbaccabdbcbcaaaacdbbaddaaacddabbbcbbabadbbdbdacabdabcddaddabcadbdadcaaddcbcabbdddddbccaabdbdccabdbdbcabbcbccbadcdcaddbcbdcaadaaabcdbdbadcabaabbdbadcdaabdaabbdccabbbbaaaaaacbbdccbbaaddbbcabaadaaccccbcaabdcbdbacdbcabaabcbcadbcaaadcdbbdbacdacccaaaaacbaccdddaaabcbcbaddcdcacbdcddcdacddbbabaddcbadddcaccdbdbcbaccdbcccabcabbabddacadadcdbbcaddcadaccbccdbacdacbdacddcabdadbaacdcbadcaadcadbdcaadbcdadcbdbabbbaadacdbdbacbdbbbbdadabdcabcdbbcacddcbdaaccaadadbcaadabbadcdaddcdabcadcdcbadddbcccbdaccdaacdabbcacbdaacabcbaddbaccdaabbdbcccbaadabcddaababcbadaaccadcbabacddbaaacabdcacbcacbbdaccacddcddbbbaaddcbbcabdaabdcdcdacbbddcacdaabbabdbdaddaacaabbbddcaadcccbdddadadabddcbbbdaacbcddccddbdacdbddadadbbcdcbbcbbbbbbaadabbdbbbcabbccacbbccbccaabcbcbdcbcbbadadcaabbabcbadabbabbaabdccbacacccdccadccbcdcbdbdbcbdbacaccabbbddcdbbbcdaccabdaaaadaaaabbbbcddcdcdbbbdaccdcdacadcdccccbabccbbcbcbddccbcccbcaccbcadbbccddadcbacccacccadcabaaadaaadbcbddcbbcdaabcdabaabdaccaaadddbdabbacbdccbaabdbabdadabdddbacacdddbdaaaaabdcccdcabbabbcbdbadccbbcdcabbdcacbadbcbdcddddbccadcbadbcdbdabbdacbcdcdbdadcccbcacacddbbdbbcdacacbbdbbcabcdabcbdbbdacdbaaddaabaaccabaaaacbdbcdbbcbdccbddbdcaacaccdaaaccaddcbcbbdcabbcabcccdddccabcaddcadbaaacdddacdcddbdcdacadcbbbcaacaddcdcdddbdcadcabadcacaadabcbbdbcadcbdadbaabdadbaaaadacdaabdacccacadcdbdccccadcbdbadadbadbaaddcbdaadbccdaaaccdcdbcbaacbaabacbdacdbbaacbdcddaaccccdcbcacdbdbacccdbbdbbbaadbddabddddbbbaabdcbaaabcdadcacadbbadabdbbaacbbbbbdbbbddcadacccaabaacccbabcaccbaabaaccbcbbbcdcdbbdbbddadbbddaabcdabdcdbccdcabdccbadccbabaaabbccbaddbaabaacccdbadaddbdcbdbccbaccaddacddbbcdcabcdcaabaabbcadbcdcaacdbbdbbadbabdcadccaaddbcbbbdacdbdbcbbddcbcadddcacadbabadccaddaabcbabdadadbcbcbbabbdaddccabdbcbcbbdcabdcbddcaddccdbacbcabccdddccdbccacaababadabcdadbddcbdbaaaabccbadaadadabcbdbabcdbdacccdccdabbdbdbaccbbdaaaacbdadbbabcdcacbbbbbbaadbacacdcacdbaacdcbbdcacaacbbacdacddddaabadcbdbcddabdbbbcbddbcbababbdabddcaddccbccdaabdababcbbbabcbabdcddbabcaccaacdababccacbadbdcaacbcdbcababbbcdddcbbabaabbbbbdcbddacbabadbcdddcbbacccbdddccabcabbacbcddbcdddcadcadcaabacacadcaadcdccccbaddadacbdcbdabddccbcadbbadadadcadccacbcaccabbabaccabbbbdddcddcacabdcbcddcdaadcdddbcddcbabcadadcaabacdddabdbcdababccbcacdcdacbadcdcbaaaaccdaacccacacdadadabbcabbdbbacddbdaabcdddbbbbdbdbacaccddacbabdadbcacddcabdaadcccacaaadaddddaabaaaabdadbabaadcdbdcaccbdccccaaabdbdddaabcbaddbbbdacdaacdadbdabcccddadaaaccbddcdcdadacdbacbdaaadacdcaabcbddbdacbcaacabdcdccdddcaabaaabaadbbbcdccaabcaddadadcaddbacccccbbcbdddbbababaaccbcccaaccdcbbcdcccdaadcbcbacddbbbaacdbadbdbbbacbcacdcbdbadccccddcadbadccdadcddccacbbdbabdbbbcdadaacaaddbbcabcbdabbabdcbacddaaadddcdaacddcbacaaacbabdbdaacaccdbbacdbbcdbdcbcdbdbabababdadcadbaccaadbcacbaabcdcbadcbbccddbdaabdabdbadabbdaccbabdabbbdcbabdddddabbcdbacaddaadcdcdcadcadcacbbabbbbbdadbacccddccdbcaaadcddcbabadacadaabbcbddbadaaddaaaccadcccbddcbbdbbddcdabbbdcdcabbcdcccabdcbddddbcdbbdaddbbddcdbdcaccdccbcdcadccbdbcccdcbdcdadaabddadcbabacccdddbdbccadccadaccbabadacaaaccddcbddabccdaaccbcbadaccbdbbccabacdbdacabcadbbdccbcbddcbcaaddaabbcbccbccbabdcddcaabdacbdcbcadcccdccccaadaddcacdbcddbccbabacadddbaabcdbddcbddccbbbcadbdcdbcaacbdbadcbbabadbbdbccdcccddbcaaccacdbabacadbbdccbabcdabbaacbdccbbabdbaabcaddaccacdbbbbacbadddccddbaddbadbcdbbcbbddccabbaaaadbadbddbbbbcaddbabaccbcddbdbcaabbbcabadccdcabbdaddbacccaaaabbadbccdbdaadcbadcacabaddddbbbbbbccbabcbddcacacacabccbcaabcdbadcacbbcccdcaadbabdaddbabddcbbdabaaccbbcadabdbabcdbdabcacbccdabdcbdbaaccdbadcdcacbcbbcbdadaaccdaddaaddaabaadabdbcdcabdabdbaddcbdcdddaaddbadcaadddbdddbadcddacaabadbcaabdcdaaadddbaabaacaccdbaaacdabcccaaddabdacdbadbabbcbdcadcadcabbdcdcdbdadabbadcadadcbdbbbbaddadcabccbaccbbbadcccaacbdcbdddbdabbabbbabcdabdbabbaacddabddadaacaccacdbccbabdabdcbdaccdacdacdacdcacddaccadcabbdcbdbcbdcbaccacbcddcbdcacacbdcdabbaadcdacadcbabbbddcbdabbabbdcbdbbadcaaaadbaabcdaaabdbdcacccddadcdcdcccdddadbbbccccbcadcdbbacdcbbccbabbcccddabbcdadbbcccbdcabcddcbddccacacaabcacbcabadddadcbbaacbdbccccabaacaabcbabcbaabcdaaaccbcbbdddaddabacbdaddcddcbaaddbdadbaacabcddaccddabcdabbdcddcbbccccbacdaaacadbbcadcaccdccbbdabbdbabacbadcbdcbdcdaaaacbcabddbaaacaabcabcaacacddccabbacadcdbddacdbbaccdbdabbdbbbbbddbbbaccbccbcabaaaddcddcdbdbdaccdabcdddccccbadddccaddaddbbabacccdbddccccbbcdbaaccddcbccbcccbabcadbaabddcccbadbcadacddaaadcccccaabcaabdcdabcdadbcbdabddcdbacdaaccbcaaacbaddcccddabddbbdcbcadddacabacbcaababacaacdcabbaacbaddadbbdbdcadbcbbdccccbabcaadcccbbddccbbaaabccccacabccaccdabbabaccbbbaabbbdbbacacbcaccdbcbbadbbdcccddacdcbcbcacbbccdccccaddbccbdcdcadccadbacdabdddddadcaacccadbdcddbcaadbbaccbaaaaadbbddaaaaacbdcbbcadaadbdaadbcddaccbbacaacbcdbccddbdadcaadcccabaacadddccdcbcbbcadabcaabccdaadacdadcdbccdbcbcadabacdcabcdadababadbaabbbacabdabcbdbbddbacdabccabdbdcabdadabcbccddcdbbbbcdcdbbabdacadcdacabbbaaccdadbdbcdacdabcbcdaaabbadcabbacdcbadbdbddbbaddbbbcbdabdaaccbadaddaaaacdbcbadccdbabdabaccbaababaacaabbadddcabcbbaccdadaacddbadcaddbdbdbbccaabcadacdbddaadbcbaccbcbccbaaaabbccadcbdddcaccbbbdacacdacdaaacbbacbdddddaddccbdcabbdbbbacbcbcbdbbbbddadabbcabdcdabcbbacaaccdababdcbdabacdcabccadcccdbbbbcaadcdddbcdddddbcbdcccdcdabbdddacbccaccdadacacacdcbacaaacbccccaabdbdcdacbbcccccdacabccddcddbdbbbacdaadbddbcbdbacabaddddcdaaabcaddadcbcbcaacaaaabbdaddaabbaccdadabaddaaaadaadbbdabcdbcdbdacdbbbdccdccabdcbbacdcaaadcabbacdcdaaacbbacddddbdacdacacadadbadcbdcabbababaaacaabadaddddccccacbcdabacccdcdcdbbbcbaabadcddacbaadddabadccbcbadacdabadadccbcabdbbbdbdccaabcadddbbdabddbbcacbdacbddacadbdaabadbbadbbadaccadadccbbccbbadabdcbcabcabdddaabdcdaadddacdbcbcdcccbabadadcdbbbdcdbacbdbcacdacbcdcbdaababadadabcdbadaabdcaddcbdbabbbabcdcbdbabdbaccbcabdadcbbaacbadbcbddbdaabcaddcaccccbddbadbbbccccdcbadbaccadbdcadbcddbaddbbbacddcbdbbacbcdddbcbdbccbdbcaacbbbccacaaddcadcbcbabdbdaabbdbcbdddbbcbbdcccbaccabddcaabbbbcabbadddcccbbccdbbacbababaabbabaabdbdccaadcccadcdaaddbdaadadbacdbbcccdbadabbcccdcadcccdaacaadbacbcccaaddadbccbcdcdbcbbddbaddabccbabbccddbaccdbdcdacbababcaddadadaaaddbbdcaaadcddadaacaadddbadbbabcacaddbacdbcaaaccdcbddbabcdadbacddddcdddccdbbcbcdbcbbdcabaabdabbbacbaddddadabdacadcaaaccaddbddcddcbaccbcdcbdadbabbaabcadcbcadaaccacdcabbbccabcdccdbcbaadcbbbcaddadadadcabcabadbabcdcdbabbabaaccaddcbcbdbacbcbbdcccabdbbbbdbbcadbbbdbcddabdbadbaddaaacbbcacccbabaccabacabdcdcddabbdbdddadddcadadccbdbadbddcddabbbabbddbdaacacadbbbbadacddbddbcabbdddccdadabdbbacabbaababdbadccccaaaacdcabcbddbcdcdbcaacdadadaadabccccbddbcdacbbbcddccacdcddabcdcabdcdccbcdacadadcaddcccdabbddadcbcbbddadbccdcababcadcbcbaabcacdacbacddaacabacbbdabcdcdabaddbcddcddcaaabcccadabbdbccacadbadbabcdadbacbbcadbddadaaacababbccdbcacbbaccdaabdabaacaadcbaabbdadcdbbcccccdbccadcdddcbbdbaaadadbcabccdbaccbaabbcbbbbacacadcaccdcabadbcadbacbbcabacccacddabbcdadddbaaaabaaaccbdccdaabacbbbbdaacdbbddddbcacddaabcbdacadbababddbaabbcabddddbbbbcaaaacbacbbadddcacbdcdbcacaacdbbbadbbdbdbdddddcdaaaaabacbbabadcadcccadccbddacdddcadcccdacdbcdabccaabacdcbabcadccccacbdabbcaabcbcbadbcadbaccbbacdaaadcacdaaccdcccccccddbababdcbccaacbcacddcccccaaaacacbdbbbdaadddcaabaaacadcccdcdcaadcbbbaabdabdcccacbcdbdbcaacabbdcdaacccddacddbbbbcaddcacacdadcabacbbacdadabbbcdbbcacdbcadaccccdbcddbdacaacdadcaaadccbdcddbbdbaacdccdbcdbdadcbbbdabbbcdbbccacbcadccbcacbaccdbdbaadcccdddbacddcdabcbdddccbbaadddacdabcbdacaacdcdaddbaadadacacccbbbdcdadddbacbcdbdbacaabcaaabcdabdccccaacdabcdbacdcbcadacbccadccdcaccbcbcbadabadbbacbdbaacbbcbbcadacccbabaaaababacaaadaddbbabaadcaabcadaaaddbddbcdaabddaabcccdbdcdabdbababcccabbcbabacacbbbdbacbdbdacdbcdcccbddccadccdacbbabdccaabcbacacdcccabbabadbabbdbcddacbbddbbcbacdaddbbcadaccbbadcbbcaaabdabaaccdcbbdbacdbbbbaadbcadabacbabcdaaabbaacaccdadacdccacbcabaacdbbbadbddadbcacaaddbddabacaddbddcdabbcabcaabddaacddbaacbdbadbdabdacbacccaccabcbaaadcdbaadbccaddbbddacbbbdacbcbdcbbcbbcbbcbaacdacbadccccdacbdadccabdcccdbbcaabcdbaddcbcdaaaaccaddadaabcbcaddcaadabacccbbddabbcadbbcdbccdccbcddcbdcbdbbdacccdacbdbaddacbdaccabbabacbadcbbccdbcdcdadcddcacbbbabdcbdccbacdadcacbdbaacbbcbcccadbacdbabdaacbadcbbcdbcaaaaacdaabadaacaacdacddbdabcabdadbcbbcabdcaadcdaabaaadbaddabacacdbadcdbbccccaddddaaccbcdccddadbadcaccadddccdbcaabcbbaddbabcbddbdacbbcddabaacbbaacbdbdadccdcbbdacbabbadaaadddcbbcbbadbcaaaadbbcddaadbbdaccbbbadacacdbcdbdadccacdbcdaacaadccbddbbdbbaadadcacdbbcdaaabbbabcaccddcbdcdaadbdabdcdaadadbdbadcaaaacaaaabcaccdacbadddccdacbcccaddbbccdaabdccbdacdaaabdbadcdabaacdaadacdcaccbdadcabcacbbcdaadcbdbdacbcdacccbababbaabccbbdacaaabdccaacccccbcdcbddadccadacbabcddcbcaadaabdddbbdabdacdcadcbcbdddddcabddaacbaadbdbdbbdccbaabcaacbadbbbdbdacbbbdbbbccccbadbdcabdcdcabadbdbacbabbaccddcbaaccaaddaccabbbcadabadcaabdcccabbdccdddbdabddbacdcdccadbddccbcaadbdcaddcabadabbbabcacaabdcadadcababdbdcaccbaaddccaaadccdbbbaabccddbddbbbbbbbbbadabdbcbdddaacddbbcaaabaadbcdbddadbbdbcbbdacdaaabadbbdabbdbbcbdbddcbcabaaccaabcdbbbbbbbccaddadcbdadaaaacbdddcddcbddbaadcbdaddcbcabcccddddadcbcbbccdbaaccdabdcbccdddcdcdcbaadbbabccbdcadadabdacaacdabcbbbacdadacdddcaacbdcdcbbbbddcdbccaddcddbadadcbdacacaabdcddcdccaacbbdcdbaaacadcbbbcaacddccbdcbacccdcaaccdbbabbcddddccdcacacbbaadacbdacbcaadcbdcccbdcdbdddbcadadadccbdacddddcadbcbccadadccddaddddaaacdaabcacddcdbcbaabcbcdcbadcdcadaaddbbabcacbbcacbaadcacddbacdbdadbcaddcdbdabdbbaddccadacbddccadadcdcccabbcacbcbbcbccaaaabddcbbabcacaddccddddbaabadbcdbabcdddcdadbbacccccbdddbdbdadcaaababdcdcaddcacabcdbbabdbaaadaacabaababccdbdcbadcdcccbaabcbdaadbcbbcdadbaccbabdadcbbbacddacddcacbcdddaaaaaddcdcbcbaaacaaddbabcbdaaddbbabaacdbdcdaddcacabbcbbccdccdbadaccabcddaabcacbddcdbdaacadbabcbddcadcacaccbcaaacbacdbbcdcccaacdccbbccacbabbbbcdcbabbadcdccabbbdcaacbbbccdaaadabababbbbadbdddbddaacaacacadbaabdcacdbcabbdacabbdaaabaccdabdbbdadbadabcbdcbcbdaaaacabcabadccdcadabcdabababdcadaaccccbdaddadbdddddddbadadbdbcbcbadadddcbbaccdabdcdcdbabbcdcdccbbcccacacabacacacbbabcbbbbbbaabddddcbbdadbcacddcadaddcdcbdbcccddcaabdacacadcddbbddcbcadaacdbddddcbbdbccaaabdbbabbdbbdabcbacdcaacacdcdbcbdaabddbdcbaccababcbdbadddcdbdabbcbcacabdccbcdddccccdacdccbaddbaccccbacdadddabcddbabdadbaccbccbabaacbbbacadccdbcbadbbbcbdabccdbdddaddccaacbbdadbdadbdadaabacacababaabdbbaacbbdcacbcdabbabadbbbbddbabadddccbdbcddabbbaadbbcbbbdabdabcccabadccdadbaaabcdababbbccddcacddcdabbddcabacacabcdcbbaacdaadbbcccddacadbdbbdcbdbcadbdabcbccbadbbbbadddadbddbdccbcdabccabdadaaddadacaaddbdcbaddcacdcdadadbccbaddaabcdadddcaddbaadcbbbadddaaddbcadadbcbddaaaccbcddbccbaaadcadddcbabbbadadabcddababadabbaabbddaddbacccacabdaddcdbadacbadcbbddabcbcabcdddcccabcaabacddcbcdadbccdcbdddbbabcdcdbbbdcabbbdbbbbbcbaddcadcdcbcdabacaadbaadddbbcadddcbaddaaadbcbcdcccbbcbdaadbdcabdaadbcddcdaccaadbdbcbabdccbddbbdcdbcdbdbacdbaaadcddaddacbbbcccabadcbbabaadbbcdbdbacdcadabaddacbdddaadaccddcdadcacdaaaccadacdabccabcccbddaccbccdbadbbdcaadaccbddcbddbccdbdccaccbbdddaccdcabbcdbcbbcbcdadcabaabccbcadcccbcddacaddbcdcabaabbdabdbdbcadabacddccbcdabdccdcabcdaadbacbacdcdccaabacccdcdcaadaacaaabdbaaccdaaacddbccabacdbadcdaaacbabbbbbcacdadacabcdbacadcdcbacbbdcabbbbdccdcdcbdcababacacacddbadbdaaddabcbbccccaddccbdaadccbbcbbaaddbabddacacabcdcacdcacadaaccbadaacbbdadddcbcabbaacaabbaccdcbacdacbdccbaccadbdacadcbcaabbacdbacbddccadbbbbbabdbccdcabcabdbddabdacbcacaccaacaacaadbacbcaadabdccbadcddbcbabadcadbdbbcacbccccaccbdcdadbabddbdccdcbbcdbccbacaddbbaabadabcbccaaddcbaddaccdacdacdbadacabababbabaabbccdbbcaabaaddacccacbdaccabdbbadaaaacadcadacdcbcaabacbddcbadbdacacbaabaaddccbacdddcccdccbaadbdabdcbacdacbccdddbdbcdabaddabbadcadcddbcaabaaabcbacbdbcadacbadbddbcbabbbdddcdbbdacaababaddadbddcddbabdaabdbccacacccaaacaddabcbabbcdaaddacddbdbddaababdbdddadcbcadbccddbddabdddcccccaadbacbadbacdadcdaabcdbbadcdcdaaadcdcbbddbcdaaaabbdcdbbadbbabdbddbbcbcbbaccbbddaddcdcaadddcbbaaacbbcbddcdcbccdcacccbbadadcdddddbabbccbddacccaaaabbadaaddcadcbbbcdcadbadcadacdddbcacbcdbbccdcbbddabcdbcbcbcdaacbdcadcadaaacabaadbaddaabadbcdbdcddababdddadabdbdabacdcdacbabcbaabcbbbdbdbdaddabdbbaabdababbdbccacbbdbddbbaabbcabcccdabcadaadddccdaacdcbaadddbcdcbdacadbdcccdbbbbccbbddbacbbdaababcadbdcdddcabaacabbcbabbccacdacabaabcbaacaadddbabbcbaadbcbaababbdccccbbbcbcabdddbbaaaaadcaadcddcbdabdabcacccbabbcbccdcabcadbcdcdcdacdcdccddaddbabdaadacbcabadbdacdcdcdbcaabbbcdaaadbdcbdaddbbadabbcadadcdcddcbdcccdbcabbdcdadcbccbadaadcbabdcdddcdabbdabdcdcbbbdaddabbcaabadbbdddaddcdaddaccbbadaabccdcbdccdadbcbdbcccabaaddcbccaacccbcacaaaacbadbaaaaadbabadcacabbbddbdcbcddacadbaacddcdcbbccbcdcbbbbbcbcbcdcabadccdccccaabdcbdcaddbcdcabdbbbbabdbaabdddbbabdabaaabddddaabdbbdabcabccdddcbbbdaabcabcabacacadccdcabacacbdacccaacabdbdcdcdcccbbbbabbdcbbabdcbbaccbadabdccccdadadaccccccbdccabcbccbbdbbbbdacbdddcddcccdacccaccacabaadcccbcdbbcddcbdcaacbcbbddbbbadcbbdbdadcbbbccbdbacadacacbbcbaacbcabacacdabadbdddbbbdbacdbbddddbcdbaddabbbcdddbbbcddaaabadbcccbabcbacbaaccbcddadccacbcdccbdbacddabbcbabaaadabdbbcccadcbcbccacababbcdcbaacaabddcccdadbbbaccabcdabbdbbacdcdacbccaddaadadacbabbacaaabacdadbbbbabbadddbddcabaccddbbcdcaabcabaadaddccbababaaacadaaabcaabadcccababbddddbdcccbaadcdbccabbdaabadcaabaaacabdbacacbbbbbccbbdcbbbdbdacadadbdbccacdccddaaaadbcdbbacaaacabacbcbcdbbddcbdbcaccacccabcadbdacdbacacbbdadccacacbbabadcbcbabdbcddaddcbadbbbccaadbaaaadccacabdccadcbbabccdbacbaaacbcdbabaaddddadcbdbabaadccabcbdccaadacccbdcddaaaccaadddaccaacdbacbbababbaccdcbbdbbcdddbabbbcdabacbbdcccdccabdbababccbdcadabcaddacbdbdadbadcadcaddcdcabbccdcddcdbcdbbbbcbacbbdcdadadbadcdcacddacbcbcabdbcbaabbcbcabdcbaacacdddabcdbdddccacbbdaddaaddbddabbddddbabcaacdbbdbabbaabacccddcbbcabdacbcabdabbdbdddccbbbdbcdddcadbcaacdbccbbddadadcabbcbaaabacdccbaabbacdabdacbbaabadcbdbdabccccccdbbaabcbaaccabcbbbaaacddcdcacadddcdbaabcdabbdddcbbcccdabaaabdbcddccddccaaacccabccaacddaccadbdbcabadcbbaaaddbbaacadaababbadadbadaaccadbbdbbacbacbdbbdbcaabbadaadadadcadccdbaadadaaccdbdcabbcdcadacbabcdbccdbdcdabdabddacdccdbbdccccdcabcddacadabaccdbdaacadcddadbacbcdcdaccdbbcddaccdbdbacbccbddbbaccbbbbcdaccbbabccbbdbdbbdaccbdabcdaccddcddcdadbbbaddadbbdbcccddbaaadaaddacabadadabbcdacddcbadaabddbaccaadcdabaddcacbcddadcbadcbdcddadbabbcaaabcbaadbbaabbbdddcbbabcbaabacadacbbacaddaadacdbdaacadaadbcccbbbcbccbaccaaacbcddcbbdabdbbdbbccdcccbaadcdbdacdaccbdddccbcabcbbbadcbdbdcbaabadacaaacabbcacaabacbbbadaaadccbdacdaadddaddbdcdbabddadccbdcbcdaaaaaddacbcdbaacddbcdabbdcabdabdabacddbcacccbdbbaaccccbbcddccabdbabcaddcdbbadbccacbcadabcbcbabaadbcadddaacccccbddddbacdacdcdcddacaddcaccccadcdbabbdbdacddbbdadbdbdcdadddabbcccacdbcbcabcdbcaaaddbdddbdcdbdaddcbcadbcbabdadacbdcaaaadbcaaccddbaabcdbbaacdcdcadcbcaaaadbdacccbcaaacdadabadcbbaaaabcccccbaaaaacaacdbdddaadbadacadaddcbdcdbabadadaddbabdaaddddbcddbdacdbcabdccdadabbdddbbdbbcbaacbcbccaddadcacddaabadddaddcdcacacccdabddcddcababdbbbadbdbabcadbacadbabdbbacadbacdcaadbbddcadbcdbddacacadbaccdbbbbdbbcacadcabccbbcbcbcaaddccdbbbacccbdaaacdddddaccdbcdbbaddcacddbccbbbcababdaabbabccabcdaaabcaddbdcdccccdaaabdddcdadbcbaddbbaddbcbdcbdaabcddcbdbadddcdbdbbabcddabdcddbbddcdcdbcccadbccabcdbbdcadacabacaabdbdbdbccbdbbbbbccacddcacccddccbaccacddabcabaddcbdacdacaaabbbccccbdacaacbbaccaadaccbcbaaaaadaacabcaddddacdccadbcadadbcdbbabbddaadbbcabdddbaaddbacbccbcdbdddaabbccdaaccdbdccbdbcaacddbbcdbbdddccdacccabddaaddcdbccababdaccbaaddaadcadccabadbdbbacaccdabacabadcacbbddacdbddadaabadcacbddadcddacbcacdcbaacbcddbbaddababbdbccacaaacacbbdddbbcdbbdabbdadbdcaddaddbcbdbacbaaddcccbcaababdbccbdcadccbacbbbbaadbbcbdadcdaabdddadaaadcdacbbdacdadacacccbdbdbaacaacbabacccaaddccdccaabadaddddcdbbdbcccddbcabdcdbcdccdbdabcbccbdaaaaadddcabaabaccacaadccdbcbbacabccbaadcbaabdbdccddccdbadbaabbdddddccbbabbdbccadadacbcacaabbdbbcbaccaddadbcdaddbdbcabcbaabbacdaaaaabccdaacddadadabbdcadbcadbbabaabdbbbcaddacacdadddbcabadcacacacdcddccbddcbdbabdbddbbdadbbbadddddbcaccaacadcacaacbbacbbdaacbcbcabbbcdcacccacdddacdacccbdaacdbdabdbacadbdccaadbccdaabdcdcdcbbdacdcabbcdacdadbabaaabbabddaaccacbbdcbddabcbdccdbbbbbbdbcabaadbadcaabcadddcdbccacdcddacdddbcaaddbaddcccdbccdacccacbbcddcdcbcbccbcabbbdabadcabbabcdbdaddbcdbabaccddabdadddacbbcbcccbbdaaaaabaacdabddacadcccbcbdcaaaacbaccbcaddabccccddabdaacbaaadddcaccaaaaccdbdacaabcbcbddcccdbcdaabadacbcabaacdbdccbcddabbaaacbcbacadddcdbbbcadcdbdbdbbbbdcdbcbcccadccdbaabccdbbbcaccacabbbdbdcbbccdcadaaabdbccdbcaddbdcdadcabaccddbbdcdabccdadbbddbcdcbddcdaadbbcddddcaadbabccddababdaadabcccbabbcaabaccccccbabacccccddcdacbbaaabbbcdcabccdbcbbcbadaabbadaabbcddaddaaccddddaaabbbaadbbbccbadaccbbcdccbadadacdbcdabdbbaadbacabaacdbbabdcbbcabccbbcadbcdadabadcbdbbcbcbaaadbacacacccccccdadbacdbaaacbadddbccccaacdbcbcdbddccdabaadccbaadcacbbddabcbdaddccbcdbcdaccacbddcdbbbaddbabcbcbabdddacaacaadcbddaacdcdaabccbbbabccdacddccdcbabbccbcbccdbacccccadbdaaccdadbbbddcadacccbcbccaacbadcdcabcabacbbcabcbcdcadcaabccbabbbcabbcacabbdddbdddcbcbddabdacdccddabdbdcdbcacaddccdcccaadbdabbbdbadadababdaccddcbbbaddcadcdbacdaacaabbaabbccccbbabbcacbbcdcaaacbdcbbbabcabacdabddadccdaaddacaacbadadbbbbbadabdacbacdabdbcdddaccaccdabddbdbadaddccccbbdadabbacaddddcdaddaacccadaadcccaacbabcbacbddabcbbdbabbadcabccacadddacabdcbddbdabbddcdbddadbacbcacbbbdbaabaccaddabccdaaaabaabdcacbdacdaacdccdbbcdbbbcbdcaccbbbabaaabdbacbbabcbaabadaccdabddacbaadbcbccbccaaaaadcaabcdbccdadcabbcbcbbacdbacdbcbbdbcbdbdaadccbbbdbcdaacacdaccabbdadddccbccdddbdcbddcdcbaccdbcabaaabcdcbdccaddcabdcbabdbadcccadccbdabbaddcbddcdbddccbcbadcabbadbdadcdbbbadbcbacdbcdbbcbddaaabaadcdcbdaaddddaaaacaccccddbaacbccabdcccbabdccbbdccaaccdbacbaddcbaabbacbabbbabcccbdccbbccbadadcaadddcddbccbbbbbbbdcdabdabdbadbcdcadaadcaccbcddaabddabcddaacbabdcdcacabcdcddcdbcbdabaabdadabccaddbbddccdbbbcdaaddacbbadbdadacbcaacbadadddcbadcaddbdcaaacdabddcdcbbabcaaaaddaccbdbcbaadadcbccdabbdcdccacbdcbcdddcacbbbdcdacadacccdadbbabbdcddacdcdaaadcbbcaadadacddbacadaddbbababcbbaaabcccddababaaabdbdbcaddbbbdadcbdcaadcbbadbacdcdcabbacaacbacbcddbaacbadabdcadddbabadcdcbbbdcbcabbddcbaccaacbdccddccadddbccbcbcbcaacbacddbbbddcacdcbcbdbdbbcadcaaaaddbdabcddadbcaadacccadcdacbcaadccbcbcbcacbacccccbbdbcacbcdbcbadcdadccbcadcaccbdadccbacccdaacdcccbdbccabacbccbbabddcacdddbccbccbdcdcadaddcdcbccbdcadaddcaabaaacbcaccdcdacbabcbdcadddabcbddcdcdbddaaccccadacadbdbaddbddccdddbdccbbabdddaaccccaadcbcbcabdcbaaacdabccdbaabcbccbdbdddcaabbbaaacdbcbadaacacccbbabcdbcbcbaccdcdaaaccaddcdbdcddacddbcbcadadabaaddababbabbcadacbaddcadbabaddaadbdcbccdbbccdcacacccdacabddabdaabacdcbcbcaccccadcdddaaabaacaabdacaababdacbbdcdabcdddbccadcaacbddcdbbddcbbbabdadaaccbbabbaddcaddcdcbbbcabccacadabbdcdbaacdddddaddcabdadadcaacaaccacbdaacdaaaadddabbbbdbaccdaabbacadaaacbcccabacaaacbccdbadadabdbdadccacbbbbadcadaaddabaabcccaddacddaddbccccbcdcdcabcbdacbcdabbddcbaadbdcccbadaaadadbabccbcccabbcaddcdccacacabcaaddaaaabbacaabbaccbabdbddcdcbdaabdbadbdbdcbcbcadbbcabbdddacbdacbabadddddacccbcabaccabacacbadabadcbaababaaabccdbbdbdbcadbcdbadddbddacbaacbdbccdbadcddabddaaddaaabaaaaabadbbdabbdbadacdcaccbcdddbbaddbbbccdcdbaaccbcdbadadaccbabcdbdacccabadcadbdadadbdacbcbacaabdabaacbbaabdccbdaddccddddcbbcdbbadbdacaabcdcaacaabdcbbdabcccbcddbbdbaadcbacadcdacbbdccacbabbdbbacaabdacdbdcdbaddababcabdbddbdbcdacccdbbbdbbbbcacbdcbccbdcdbaabdbcddcadaadcaacbddcbaacaacacabdcacddbbddbaddbaabcdbaccbacdbcbddaaddbcddadbcaddaadadadcdbbccdbcddcacdcdccdcdbcacccabccbacbbddbddbbbabbbcdbcacaabbbabcbdbbddccabdbbdcbbdbabbcbdcbccdcccbdbbcaccaaaabaaabcdcabbadabddbbbdabcacbccddcbaaabddcccdccdacbdcdbccacdaccaddbddcbdcadddcbabcbaddddcdbacabbdccddadccacbabddbaddbddaaccadaacadacdbdcdddcbbddbdddaaccdbccdcdcbadcbdcaadcabbdddbbcddbcadcaaddacbacbdaaabddbcdcdccaadacdbddbccaddbaadadaaaaadcaaacacadabacbcdccdabdcddddbdcccbbaaabaacddcbdccadacbdddddaabcabaadcccdbacacaabcdaadadabaabdaaabaacbdbaabcdcddabccaabbcabbdccdcadbbadacbdddacadcccbaadacaaaadcddabcddadcbbbcdcadbaccbcdcdadadabaddbcacbdaddadddcccbabcbbbdbbcdbbbabbaacbbcdadadabbabbbababccdadbbbbcdbaababcbabaaadcddddabbcbacadadddabcaababcaccabccdbacbaacddccddaaacabcbbcdbcdbdadddddacdcdccbbbdaabacbbbdbaccdcdabddbbdcdbbdcabccadcccdccdaddbaadbaacbdaacbadcaaccddbcbdcacccdbcbabbabadaaabbcbbcbacdbcdabdabcaabdbdcdacaacbbbaabdbbdacbabccaacdcadbacbabcccaabccdcdcaccbabbccdbcddcbabdaaadacdbdddddcabddadbcabaacbcccbdadbadbcbdcbdccaaddcdbbcddddcbbdcdadcbdddcccdaadbdbbcbbbdbdcdaaaacbacaadbadcbdddaabaddbabdbcacadadccccddaddbbcbccaadcdbdcddbccdbcbbcdacbadaaaddbadbdddbadccaacacabbabdaaabdccabdbcdbdcbadcbbacccbbddddbcabdcdcdadadcadabacbacbcacbdbcbdcabacaddacbcbacaaabddcacaadbdddacbcdbccbbdadacabdabcbaaadccaadadbbadababaccbddcdabcdccdadaadadbbddabaadbdbbabcaaacdbcbccdcbdcdbdcccdccaaccaabdbabbbccbcaacadddadcbdabaabaacddadabdbbbbcdbccbadcabbbaaacadbddbddbdbdcabcdbddbbdbdbcdcbabaccadadcdcaaadcdddddccbadbddccbacacbbdcabbbbccabccabaaabdddaadcdcaacaaacaabdacaaadacddcbbaddabbbacdbdbbddaabacdaccbcadcaadbdcaccdcbadbbdccccdacbcbddacaabcddccdcddccdddbdcaddaabbbbcbdabbbaabdaaccdadcaaaaddddbcbccbcbcabbabadcbaccabadbdbacbacacddcadcbaacdbaacddbdaabaaddadcabbbdccbaaacbadabadabcbbccddaddcaddbdacdadacadacabcbbbdadccabadcbaaabacadddccababcccddbadbbddbbbdacabdbadbbbdcbcabdccccdcbccaaccaccdaaaaacbabadbbbdbacaabbcdcadccddacbdcddbdccadaabdcccbbcadccdbbdbbaacaccdbaaaabacdbddacccdbbabadaccaccbababadbbacacaacbbaddcdbdbaccaddcacacbcccccadbbdadbaccbdadddcdababbbacbdacaacdcdbdccaaccdcbacbbacaabcbcacaaddaccddbcbcbabdbdacbcdbdcddadaaabccdddcdcdcddacdccdddcbbacabadcaabcabcccabdabcdbdababcbdccccaaddadcdadcaaddaabbcccbddbbdaadbcacdbcbbcacdbdcdbdccdddcbadcaacadcdabbddabdacbdacccabbdcacdaacdccdaccacacbbcbabcaabbdbaaadbccdadbdcbdbabcaccacbdaddacbbdadcdbbcbbdaaaaddbccbdabdbacbddccdcbdbbcdaddcddbbdabacaacadadcbbbcdbbcabbbcadacabdcbdbbaaaddbadcaddaadacaaabbddcdddacaaccdcabaaddbdddbcabcbcdcaaccabdaccbbdcbdbadbacdcabccaacdbaabbccdcdaddbdbaccaacacdbddddddcdccbcbddcdacaccbbcbadbccdbddacbdcacdcbccbdaddcacaddcbbbbbddcdabdabdcdbcacdbbcbacbaaddcdcdddcaaacdcbbbcbcbbdabaaacbdabacbdbddbbaadabcddadcccbbdbbbacadabacadddcbbddaadddddbbdaacbcbcdcaadbabbbbaadccaddabcbddccccabcdadacbcdaddacccdacddbbcbcbcdccabcaadcbbdbaacbdddcddcadadcabadacabcbbbdcacdcacddaaabdcadaaddbcbdabacbcbabcddddddbccdadadddaaaaadbcdabbdbcddbbacaaacacabdbcdccddddbabacadabbcadaccddaddbccdbcbdbcdccacdbbbcbbdcdcacdabacbacddcddaaacbdcbbcabbadabddcdbdccaacdadbabadaccabcbcbcacabdbbdbbbbdbdcbbcbaccdacdccbbbbbdcdcbbabbdccacbbbdbdbacbcdcaacabaabacbdacdbcdabbdbdbdbcbbccacaadabbbbcacdabbccaaccbcbbcbccaddacccbaddaadaddabbdaadcacbcaaadbcbbdcadbacbaadbbaabaccbcddcbabdbdaaddaaccadbadbadcabddabbccddadccdccdbadbccdccdbdcbdaadacdbaadddadddbcbadccdbbcacccdcabddcdcaadabbbddbbbbaddaabbbdbbcbbaacdaadbcbdadcbbadaabacddcabdabcccadabdbbdddbadbcccdcbbbaabcbaabddcacddbbdcdccaaccddcdcbcdcbcdaadcbcbbbcdaacccbdccbbcbbddcccabbcbbacdacccccacdcacaccbbbccaadaabbabbbaaadddbbacadadbacbadddcbdadabbcbaccdcacacbddbabacbaddcadaccbadadcdaccabaacdaddcababdabdcdabbadbabdbbdbdabcbabcbcdbabbabcbbacacacdbdacaaddabcacbbcaacacadcbddcbabcbcccbacbacdbdabdacdccdddbabbbadcbaaaacbaaccccadabbcbdddcabaacccdcdabacaadbcbadcaadbdacbaabababdddcdbaaadaacbcbcbccacbacbccbaaadadadacaacdbbdaadddbaddbcadddbacbcacbaadabbdcdaadbccddbacaabbccdbdaacdddadadddcddbcbdcbbaacacaabbabbdccdddaaccacaddbacbbcdccbbabcadcbcdccbbadcbdbcbcbdbcdbcaabdbccccabcccdbdbddcacaabdcdbcdbdcddabdcdcdcadbaccbacdcbaddcdacbbdbcddcaadccdabdcdbacbaddaabcabdbbaccddbccbbacabdbaccacdbadaddaaddcdccbacbdaadcaddcdaadaabcaacbccdabdcbbbdcdcbababdabbcadabdabdbbcaaadaccbdbcddabaacbabcbdaccadacadbddacdbabccbbacbadaaddcdaccaccadcdcbcbdabcdbdddaadcdcadbbbbbcbabacaccabddddbacddabbababccbbabdcdbabcdabbcbbabaccbaacabccdcaacabbbaddcadadddcaaccaaadacdddadcbccdaccdccdbcccdcdddbddcdbcbdbddbabaabaacbabbdbcacadbbdaabbaacabdacdadcdacdbaadacabadcbdcaabdbcdbdcbbbbccbdaccbacccdabdccbddacddbdadcccaacbdcbacdcbcbbbabcddadabbbacdabcbbcbabbbbcaccbdcacaaadabaddaadbcbabcbcbdddcbabcbaaacabdccdddccccccbbdabcbbadacabaabdbddbcccdacccdccaabadaabacabddcbaadcabacadcbcbdbdaaaabcbcdadbbdaadccbabdcdadbadcbaadcbdbcadcccdbbabcbbadacdbdddaccccadbaaaaabbcdbbbcbdacbadaacdbbbcdbccacabacdccbcbacddcacbcbadaddadacdbcacabaaabbdccbdacccdbadbbddbddddbcbbdcbcbaaaabdddbdcdbdcacdddddcdbccadcbbabaaabcdccbdaabcbabaacdbdaccacaaaaacdaaacccbcadbdbdbcdcccbcbbdbadcabdadbdbdadbdbdcdbdbdcdbbbbdcabcccdcabbaadcdcdbabddddcccdacdacdacddcdaacbbbdabbbbbcdbcaadccbdbbbaccacdadbdcabbcbbbbccbccacdbbcbbdaaabbbaaaabbcdbbabcddbccabadbaaabdabbbcdccacbcbabcaabcbbaddbddbaabcccababdbabcaacdbccacddcabcdddbddbacaabcababacaddddcbcacddbabadababacbaabccdcacbacacaaacbccdcdbcddddddadacdacadbbbdcdacaacdaaabcddbbacddbdabdbcaadadbaadbbcbbababdcbddcddaddbcdbbbaccdadbadcddcdaddbacddabaccdccdcbddbddcbdcbdaccbdbbdabcbcbabbbdbdbcbcbddbbbadcaccacbcababcccadbcbcdacdaaababadbbaaadccacbaddcdddbbcadacdaabbacacdbbbaadcbbcaaacaabcddcdcdababcbdacdccacbcccbbacdadbbdacdabacdbaacbccdadcadabcbbccdcdddabbabccccccaadbbcdcaaacbbddbbaabaacccacadcbcadbbcabcaadbcdddacbdbabbcacbbcacbccacccdcdabbdcbbbdcbcbbcaddccdadcbbcbabdbbcbcbaabdcccacbdadbbaabcbdbcbaadcadbdccaaadbbbcadbbcacbcabaadbbacdbcaadbabdaccbbabddbabddcdbdbabddacdbacbadabdabaddbbbbaaabbabcababbaabddcddbcccadcabacbcddabacababcaabbcabbddcdcbbddddaabbababddacdacacbacccbccadcbacaddbdbbbbbaccaacdaaccdcbabcdaccaacbcdacacbaaddbadabbdabbabdbbcbadbbcbabcbbdbbbdcdbbddcdaddddcbaadcaddcabcaddbdcabdaabcbaddacbcbbbddaacbbcbddcaccdcdddcbdbcddbccddabcacddddcabacdadadaadbaddcacacccaacaaabdbcbaddbccabcaadacacbbaaaadddadadbdabbdbacccdaadbdbdbaadccdddbbdacabcadbdddbdbddaadcddddaccdbddabdbbdccabababdccdadbbcddadcdccadcadadadccabaacddcbbccaccbcdbcccaabbddaccaaacdbbcaabbddcacabddaaacacdadadcbbcadccdbccbaabdddbbbcbcaacaadcbdbbabcdaacbddaccdccdabdbbadccaabdccbacdacdabdcdcabacadbcbbccaabcdadcddabcdbbdadcddcdaaadadcbaabbaddddbddbdcdbcbabccbcaccbcbbccbdccdabdcaabbdcbcbdccdbcdbcdcacababcbdbbacaacdbacbbdbbbcdacaaaaacddbadaadcdacabdbdcbbdcbaacabadcbcdcdacbcddbcccaccbccaaddddddcccadddbdaddcdadbdbacdbcbccccdaadbabdacadccbcbabaabcdbabdccdcbcbcaabaaaccccaacacaccdddbbbdbaaabcaacbbdabcbdbccbdacdcacbaacccdbdcabbdbbbccbaacbdbdbcacabbddddabcbccbddabcdddccaacbaaabcdacbabcbbdbcaccbcccdabcdcaccaacbbacccacabddabcbdabaacbabdbbcdddbbcdbccbacbddcdcbadddbbbacbcbccddabdccaaabacbbdbacaccbbcbaadddbbbbbcdbacdccdadcacabbabaaaccbbbdcddddbbacbccdddcbdabdcbbdcdbababdbcacdbdccbcdddaaddabcadaddbcbacabdcdbadbccaadbdbcddbbaccadabcaadcbacabadaadcabcbabdbdbdcbacbbbbbcbabaaddbabdbacbdcaacacdadabcacadddadcaddadcaacbbdddbbbbacacdddabccaaabcddacdccabcdabbdaccbdccbbcdbdcdaddbcbbdbdcabcaacddabdbdbbcddabcaddabcbccdcdcddbdbabcdbdbdccdbccdcaacdcadcdacbbabacbababcdcbbccbbcdddbabdbccbcaddcbbbcadbcaccddabcaaadabcdacdbdabacddcbaadcdacbdbccaaaabbbccbaddbababcbddccaabacbdccbbbdbacdcacbadddbdcccadaddbbbaabbbcadbbccacdbababaaacabcbddbacacaddbaaaddabbcacdbbacdbadddddaacaaacbdcccccaccabbdbccaaadaadcbbcdbbbdaccdddcbccbddbcbcaaaabccbadcaccdabaaabcdcbaabbabcccaccdbdabccddbabadadcbcdadbbbcabbdccacdccddbcaadabcbbbcbcddccabadccccaabdbcadabbacbaababdbcddacbdccaabbcdacaccdcbdcdadadbdddddddcadcbcbdaaaccbdccadbcdacaddcaacdccbddbdaacadcacddbaabdadddacbdabdbabacbaacbcaacaccdaddbdadcabdaabcbcabddabdaadabdadabaacdbbbbbdcdccccabaadbdabbbdaccaabaacdaddabbdcacbaabdbadaaacabadcacabdbacbadaacbadbaaabdabacbdbcaddcadcaccdcdadabddbdaddbdcdbbadccddccaaabcaadbccabaadcdacdabcbbcbbabbdcacacacbdcbccaaabbdddbbacbbaaabccacbdaddccbbbdaadcccbcccccadadabcacaabdbddbbddacbcadabaacabddaacdcadddbbcaabdbcabacbdcaddcddddaaaccbbcbacdabccddadabaaadbddbdbcdcdabccdcadcadaddbdbabbdacbccaaccdbabbabdcdaaccbbccbdbdcabbbcdbcdccdcbccaababaaacabacdbbaabcbbcbdbaabddcdbbcbddcbbaabccaabbcaadcdccbdbbbaaadbaaadcadbcddaabcddbbbcdccdaaccadabddbaaaadbaccabaabaccbabbabbcabcccbcaabddcadbbcdddbddacdbdbdacabcdcdaddccaadccbddabbbaadddbcdcacaadadaaccaadbdbbccbdadcbaadcddddbbdbcacbabdadabbdaaccaabaadbddbcdcdabaacaabbbacccddbacacccaacbbcdbbabbbadacbdcdbbacdaaaadadcdbccadcdbccdddbacbdcadcdccdccdabcbaadcabbcabdcdcbddabdaaabbccbadbbdabcdadbacbcadcabccdbacbdcdbadabacbacdbdadaaaabdccababbcbbcbabcbcdaccdcabcacabbdbbdcabacdadacddaabdccbcbbbcbdbcdcacccaadddbabddaabbbcbdacbdabbcaccbbbccdccbbcbbbbcacadbaaacbccdbddddbbdbcdbacaadabbabaacccabbcabbcdbacbdccaaaccabbdaabacbdcadbdcaadcadbadcbdbccccdbaadaaccbbdccdaacacdcbcaddccbacddbcbdabbcbaadcdccbbaccadabcadbacaddbbbdabacaaddbdacabcbadaaabccbdbccaaababadcdacbdaaabbdbbbdadcacbbbbbbdadacabcbdccaccbacdababcdacddbaaccddcababbaaabddaabbcbbbbdcdccabbddadbdbbbbcababddacddbacabacdacdbbcadbabccdcdbddcadbbbabcaaabcddcacabadaadcdbacdddbdccaabdbaccaacbcababadbdccbacbabccdadbcaadacdbbababccdcccdaaddaaddcaddacbadccabccaacbcdaccbdabccaacbcaccdbadcbbbbbccddcdcbddbbdbcbaaaaaccbadbddddbbadabddadddadadbaacaaddadbbbdaaccbccbddcabbaaaccdacdbabbccabdcacddacaccccabbdcacdaccdaadccdcdaaadadbdbaabadadbcbbadddacaacdaadbcbdcdaddadccddaadbacdccaccbccccaddbcabccabaacabacacdddcddaaadbabbbaabbbaadbabcaaadaddbbaaabbaaabcadcbdcccabbadbdaaabaadcaabccacabcacdcbadbdcbcabbbcdcbccbbaccacabdadbdcdacbcbdabaadcadcaccbadababcbcabccdbdbbcbcddddadbdbccccbadddabddbcbaaaabdbaddbcbaccadddccdbdbbcbcacabbcbdccdacbccddcbbaccddbcccadcbaaadcbdacbdbbcabcdcbdcdcbcddaccbdbcbddddbbdbdddcdadcdbacaccbcaccbbaccadabdcdabbcaccbcacaaabcaaadbdbcbbccdcbbdbabccbaaacccacdcdadbcbdbcbaaadbaddbbcccbcccacddcabdcaaccaadababbdbdcdaaabaabccbbaddabdaabbbacbdabbadcbbbdbabadacbabdcbcdcabbdabcccddcacbcdcdcacbcddbbcbbdddddbbaabcdaaabcbaaabbbddabaadacbabdbccbbccbacabdacdbccdabcbcbddbdacacdcbacbbaaabacbcdadbabdcbdaccdbcadcbbcadcacbcddacaccdababcaacacdbbccdcadcdcbdbbcbcbdbacbbdbaaddbcbbdccacdaadacdccbddccdadcdbbacbbdaaababaabbbddbbcaddabcdcbbdbbbccbbbcbadbbaadbddcaababbdcbadccdccbacdbcbbcbdbcdaaabcdbdccaaacaabadbcbbdddabdcbdaccaabdabdcbbadddbcadddccccaacdbcbcddaacddbadacbdcddabacdaaddbbbbbcbbcbbdcbbbcdaddbbaacabbbbaabbaddcadaaabddabbbaabadccbabcdacccbcdccdabdbcddcbdbadacbacbcdababbccacabcacbdbcdabababbdcddddcdcdbddaacbbbbbcacdbbbdabbdababdcadccccccacdacbbccdcdbbcbabddccaddccdcbbcbaadcadacacaadcdddcadabadbcaccaddabadddcdbadcdcbacbabdcccbacbbbdaddacabaccbcdcaaacadaacccacbadaccdbaddcadaccddccaabdaadcabadacccdccdcdcabbbbdaabcacbaabcbbadabbaccdabdbbbcccdaababdcdbbbacbbdcdcbcdcdbaaddddddbaaabacbbbcdbcddabbccdacbbdcbabcdabcbcddabdbdcbaaaadcaadacccbbdcbdcbdbdabbcacacabcbddcdabcbbbcdacaddacddcabbbaadbbacdaabbcabacdcbcbdcbabaaadacaabcadacbadbbdcbcdcbabaccddbbcaabbcaccaccdcbacaadaacdbdabcdcdcaabdddaacdbdcdbdccaacdbbdbbcbbcbcaaacddbdabcdbdcbbabcdaadbbdadddacdbdbddaaddbcbdcacabddbbbacdbddcaabcbdbdaacdabcddcdbdbaccdabaacdabaadadbdacbadbdacadbbdabdbbadbabadbcaabcddddcccaaabacdcabbcbaacdddadadcdacacadacdbbdbdacbacdcdabaccbcdadbbabaadcdaacaadacabaccacdcdadbbaaaabbdbaaabacdcbacdbcbbdcacadaaadacbcabdadbcdbaaccaacdcddccbabbcaaabcddcaabbcdccdcabaccaacdcbdccdbbbcdccacdcccadcccbaaabadcdccddacabadbbcadaddbbbbdaaacdacaddadaccbadbbcaabaabdbcbbddcbbcccacbcadbbdaddacabdbbdcacbcabbbbababbbadcbccbadbdbcaacbaabccadaadcaadbbdbdcacbaadcababbbcbbccbdbadbadcaddbdadddbcadacccbcdbaddcadacbdabbaaaacbbccbbaaabddacbadcbdaaacddbcaddabcbdaacccddabcbaccbbcccdcdabbccbdcaadcdabcbcdddaddacaabcdabdacbacbadcabadcaddaccaabccbdcbbacabdccbcddcddbaabbabcbdbcaccdbbdbcdcbabcdaccaacdddadaccacbabdadbabacbddadcdbaacbabacdacdcabbccabbacbacddcdcbaaaaacdcaaaccbcdddcadcabaccbbaabaabdcababccadcbccbbddbcdbacaaadabdbadbcccadabdccdaaaabcbadaccdbadabccadcddcacadbacbdccccdddbaaabcadbbcbadabacbcdbddbbbdddcdcbbabacaacbadaddbdbdcdcabacdbdcdbbabddcababaadadaaddcbdacbbcbcddddbbacabdbddcaaacaccdbacbcbcccbabddddbabaccbdddcbcdbbcdbacdbbddbddccdbcbadcdccdcbdccaaadbdacbccddbcbcbddbcbdccbdadababadbdcaddabbdadcbdcadadadabddccdabbaaacbbadbdcaddbcccaaccbccdcdbbacdcaacacbcacabdababaaddccccccdddcbdbabdcacacaddddbcbbdccdcaacbcbbacbaddadcaaadcdbddccadbbaccbcdbdbddbabdbcabcdbaaacddddcdddacbacdadaaddaacadbadcccaaabdcacdcacbcdaadadbbccdaadaabbabdbcdcabdaabbddcbcaddaadbadcabacaadaadadcadacbaaacbacbbbdadcaccbabbbbddbbdaaadacbadaddcbddabdbdabcccccccccadcaddaddcadbdbdcdbdcdcdddadabbddccadddaadcaccbbdbbacdacbbcdabdaadcdbbddaadbacdcaadddbddabbbaacaaadaacabcccaddacbadbbdbdadbcbbdaddcbaadadcccabbdacbdabaccdcbcabbabcdbacdbcdcdbbdabcbcddbbcaabccbbbccbbddbabbbadbcacaacccbbdaaabaccbcbaadbdcbaadccdccddacabbcbabbcbccdddcdadbcadaadacbdaccbbdabacabdabcaadababbaadddcaabcdbcddcccbbbdbbddcaccbdadaaddccaabccbddbdddbddbddabcdacaaccbadabcaaabbaadcacccdaddcbcdbbbddacdddbbbbdddbbcdcdcaadacabdabdaccbbcdccdbcbcacdddaabbdcaaddbccdbdaaadccabddcabbbdabadcbbaccbbbbdacaabacbbdbbcaccadbcdcbaadbcdcccbadbdddddacbbdcddbccdcddabaaabadaabdcabdbbcaabacbabbdbbababddcdaddbdbaabccccbcbcbaaabccbbbcccdabcbbdddccadaccbccdcbbcbabbdbcbdddddbdbcadacbcbadbdabaaaddbdddcccdbdbbabbbcbacbdbdbbaddcbabaabbabbaccdbbcddbabbcdaaabddadbdbccacaccacaaadbccccdbbcbccddbaccdbaddbaddddabdaacddabbbbbddbabccbddbbbdaacdcababdadbacdcdabcccdbaddaccbcaaabcbdacddbabbabbbcdcddacddbdadcadbbcaacdbbbccaccdabdabcadabadcbcbbddacaccbcddbbcbbcbdcaddcbbcadcdbbaabdcabadcbdbcadaddbaabddbbdadcddacbbabdcddaddacdddbadbddcbabdcdbbbacdcccddddabadcbdabdbcbdbbabacbdbbcdadbdaabaaaabcadbddbbcdabcddaacabbcdbadcccabacabdcdddcdbbcadbdadabbacbdaccddabddcadbcabbccabdaadbcdccbacccdbbabbcdcdaccaddacacdaaaaacabddbaccbabdaacbbcacaaabbbabdabaadbbbbbdddbdacaabacbbdcabddbdccbbcaacacbcddbbdbaacccdcadbdccdcaddbdcdaddbbcdddbdbccbaddcdccaccacaaadaddbcdacacdaadabcaadcabbacabbddabbaadbbdbcddbbbaaaadaacbcaaaccdaccaadcbcbaabcacaadadaabdabdddabcacbaadcbaddbabccbcabbadccadaacccccbbcccaaadcbbbabbabbbbdcaadccaccabdacdabacbaacdcbbcdaadcccdaacbdbadddcdccddaadcadacaaacbdcbaccdaabadcabaacddbdacbdbadbbaacaccdbdbbacaacdcbcbcbdcaacddcbccdaabddddbaccaccabbcbaabccabbcdddddbadbcbdcbdcaaadcdcdaddccbbdabdacddacadddcddaabbcadbcbcbdcaddadacbbbcbbcaaccdbbddccbcccdccccadcdcbbadaabccacabcddadabccdacbcdaaabdbacdbcccbbdbdabaacbcddadbccbdccdabdaadaadddddcbdcdbcabaacbbbbbcaacdbabbadabcbcbabaddcabacccdbddabbddccbdccadabacbcbacaccaccacdddcdaadababdaadbabcaadbbcdddadaadcacabcccddbcddcacbbbcbadbdcaaddddccaadadbddabcbccbcdcaccaccccbbbdbcbabcbddcccbcdddccadabdcddcbcabbabdbccbbddaacabaacdbbababbcccaabaaaabbddcbaaddcbbddcdabcbdddcbcdacdcbcdbaacabbbcdabdbcaddcdacbbacabadbcabbacccddbabdbdddbbdbbaaddadbcdcdbadbccbbdddcadbbbbdbbaccbdacaaaacdcbdbacdbcdbabcbcddbbbbbbdbbaabdaaddcddaccbcaabcabacbacacccbbcacaddbbabddbbabbbababbdbbcbaabdbddbcccdcadcccacbdcababddccbbababcddbcdaacbdddadcaadabbcdaacadcdaddcdcaddcacbdcadbccddaaacdbabadaddbabadcbdadbacabcabcadaaacdadbbdbddcdcaccaadbcddbbdaaaddddcdabcabadcbbaabcadacabcbbbabbcabbadcdcddddbcabcdabadbddbbdabdcdddcdbdacdcbcaaddddbccccaaadcaacdaaadbdddbdbdadaaccabddbbcaacbabbbadaccbabddcbadadbddaabbbdccccadccbdbdcabbbcbdcbabddbcdddaacbabcdddbbcbcbabdbbbcbcbdbaadbdacadabdddabdbabcdaaabbbcbabcbbbabdaaaddcbdbcadaaaacccbbabdabcacbacdbdcbaccdbcdddcaadddcbbbdbbbdacbdbabccadbccabccadbddbbbbacacabcacbdbdbcdacbbcabcdbcbccdabaadddbcccccaaccaccadcbabcdcbcdcdbbcacacbadddccdcaaadaaabcbbabdcadcaadbdbaabdabddcaadddccdbbdcbccacaabbdbdbadacbbcdadacdcdbcacbdcccdcccccddbbbddbdcdbdccacbacccdbbabdbcbadcccaddbbacacdabdaccdddbcabbdcaccdbdacbaaddadaddacbacccdbbbddabbaddbaaabbadcbdcbdbcdcaadbacacccddbadbcaddbbacbdadbdbbbdaacdcacadbbcaccdddbdbadbaaabddcbcdcbdbcacdbadbdadabbbdbbcdccbbadacabadadcacacabdccbcdbcabdaadcadaccdacababcccabdacaacbdabdcccbbcdacbdcbabcacdacacadaacaadbcdaacdacdabaccadccdddbaacbcbdbbaaabdbadbbcdcbaadcdaabbbadbbccdcddabbcccddadbaaacdcbcadbacaadbccddaadddabcbabbdaddbacbbccbcbcdadbcbcadacbaaabcbdabdbbabacdadacccabcdcabacbbdddaacdadcddabccbbbcbdcdcadddbacbadcbbdacbbbaabdbadccbdcacacaabaadcdcbbacbcdbdcddaacbdbdddadacabcdaabdcbdbcbcdcacbbaaaabbadddbbaaacdcdbbbabdcdcdccaabdbcdccdbdcddcabbbddadacdcadddaddccdddddbacdddcbcbdcbaacaccadacdbadacaaccccbbdaadbaccdcdcbbaacdddcdabbcbdbcaacbcddabdacadccabcccccbacdbdcaadbacbaddbcbbdddccacbbcdcdbadadaadabbbaaadcdacbbaaddbaccaddbbcbdabdbadcbbabadbadbcacbcbdacbdadadacaabcdddcaaaccdbdbccdcbbbddaabbbbccbbcbbcdbcccadbdcacdaababccacaccbacabbddcbcbaacddbacbbdbdabbbdadcadbacdccddbbabcbcdbdaaabdbbadcdcdcbaadabbacabdaadddbdddbdccacdaacbbadacbadbabdcadbbaacaacabbbcdacbcdbbdacaccbdccaccdcddbaaddbabaddbdcdccbbcbadcccabbdcbdbabaaaacaadacbaadbdbaadbddbabbabacbadbbdbddaabdabbcdcaccccbadbddbcbbcccbddbdcccacbdbcadadddabbbbbdaacdabccbabddbabbdbbdabcaabacaddadbbabadbccdaabcadbcaaaabbbadaddcccbdcbbaaacbcbbadcbcbbaacdacdbabbcabbccadbbcbcddaadbbaacbaacbaabccdccbcbabbddacbbbcaadacacdcababdaaccbcacdcaaabadbadbddabbbadbbbdddbdbcbacdbaacbaadcadaddbccacbabdaababbacdacbdccabddcacacccbababbcbabaaaaababcbcdaccbccabdcbcdbbbdcccdbdabbbbddcccddddbacabbcbcbdbcadacacdadcaddccabccadbcbbbaddbcaddabcacbdbcbbaacbcbaababcdacabdbacccbcaabaddcccacccdcbcccabddadbbcdbdccccccadaaacacadccdcacddbcbddabdadddbbacbbbbbcbacdabddadacbadcabbbdcaabbcbbdcdaadccddcccacbbccdabcabdccbbabadbcdbbcdcdcabbbddaaaadccaaabdcdbdddccaaabaccaabbbdbbaddbcaabcbbccadbbcbbdacdcabdcabdbddaabdacddcacadbaaabcddbbacabbbdcbcbcbddcdddbbcacabcbcdbbbcddaddacacdbdcdadacbcbdcabaaabdacbacbbdadaccccdcccdbabdcdbddaacdadcbaaadbbdaadcccdccbabbbbcbbaadadddcadbddbbbaddcbcbcbdbcdcdcdbcddaadcaabacccdbcaaabcdaadabddacbcacdccdbdacabdabadccccbabdcbbbbdbacabdaabddaccabcbccbdbbcdcabcdaacabcddbabbcbdcbbddcbccacbbccbcbbabbbdaccabcabbdabdaabadccadbbbcaaacadaabcdacaadbcdcdbabcbcabdbdccdccddcaccabcbcbcacdbbbdbdccbcdbdcabccdcdcdbccdbdcbdcaddacddcccbbbaabcddcdcbbbddacdacbcabacadbcbddcabacadbacaddbaacddacaacdccddadbcbaabcaacdccbbacbdcacdbdccdcdcaaacdaadbdcbaabcabddbddbcbcbdadcdbdababbcbadcaacaaacadbdbcacacacdbcbcbacccbbaacddcbabbbcccdbaabdcdbccacbccddbbcacabbbaacccaccabddbdbdadacabddddccbdccacccacdcbacbabccddcadbbddbbaababadcbccbccadcbcababcaccacdabcbbbbdcdccbdaddddacacdaabddbcdabcadbcdcdddbaccbcbdccbbbbdcdcbcdabacdbbbbabbaadcabbbbabaaacdcabcbddbcccbbabacadcbbccddbacdadccadddddcacbbabddacddcaacdccdabdccccbaabdcadabbbbaaddbabaaccadaccddcaaadcbdccccabbbccbccdacadccabdcbbbadccddaacddaadcbbadaccabadcdcdacbdbcdcaddababdddcbbbbcaadcdcbdbdbbcabcaabcbddbdbdcabacabcdcaaadcdddbadcadadaccddcadbdbabbccdabdbcbbcbbacdcbdddccccdbbabacbcbcababcddcdcbacaddaabadabccbacdccaacdacbddabdbdadaabdcbccbaadddadaccdcccdaaccdcaabaccdadacaddcaabadabcdcdacbbbcadaddbbdacddcccdbcaaddcddbdbbbcbacbabaaaccdcdcadcacbbabbbbcdbcbbabdddbdcbacbabadcabccbcabbacbaaabacadccbaccbdabcdcaccacadbadaaadacccddcddadabbbbbcacdbacdcccdbacadcddadcabcadcdcdcdbabadbcaacddbccddaabaacaccbdabadaccdbcdbdbabcaaabdacbcbbcbacbdcaaccaabccdcadadcaadcacddbccababacadbbbddcacccacbadbacdbbbdadcdbbbcdbaaacacaabdcadaccbcbaabcdcbddacccbbaddaabbcdbbdacdbccbcddadabccdcbddbbadddacddbbbaababccbaabbbcdbbbbdaadcccdabddccbaacbbcbbacbbcabacddbabcdadadbcdddbababdadadbcbccaacdadbabbabadaaacabcbbcdcabbbbcddccaabadcddbaaacbccadcbababbabcbccbbdbcaacdcbbdcbacdcdbbddbacbbddacbdbdbababaacbcadcbbdcbcdbbcccbadccbababdbbbacbbbacbbbadabcacbdbabaadaacdcbbbadadcbaacaacdddbcadbbdacaabacdcbddbadcddbbbbadaadaabddcdadadddbabbccaabcdabddbbccabcabacaacddabbddaadcaccccdddcaacaaacbdadcababdcbaabccbdbccabddcddabbbbaabbcbacdabaaddabdaaabddbacdadccbadbdcbdcabcbbabdaccbcadbbcbbcbcdcbcdbabbabdbcddcbbcbacacdccbdccdbcccacbdbdacabdbdbbdddcbccdcdadbacdcddcddacddcbacbdcdcccbaabacbccbbadabbaabaabcccabaccdaccdddcbbcbcbadabbbcbbcbdcbbadaddddccaccdcdaaaaaaddacaabadddaadcabccabbbaadbcacabddbbcaaddabaccbbdaabcbbabbadddadbabddcbcabcbadbbcdbcacbcddbdcaaadddadbcdaddbbcbdbabbacacaaaccdcddcdcbcdccadbaadddabcbbdddcbadabdcbabcbbccbdcacaccccccbaaadbccccdbcddbbaddaddddadbcbcbdaadacbdabcccbadabdddbbbdbddbbaabbdccdadbdadbadcacaabdcbbacdbdbccaabdbcbcccababdbbaadbbdabcbbadadcccdabbadbdbcbbcdbdaddcddddacbacdbbcdbbdbdadbccadbababdabdcabcabbaacccacaaadbdcacbddaaccbbddaabccbabddacacdbaccdcabcaacddcacadabbbdbabdabadabdcbdabdbccabdcdbddbbdbcbddbcccabcdcdbaaaabbdbddacdccababdacbcdcbcaacbbbdddbccdaccbadcdadcabddbdbcdcdddbcabdccdacbcddaacdaabaccbcbacdabcbacacdbabaccbdcbcadaacbbacaaddcaabbbdcabcbcbccdcbdccadcdabdbdcdbbdcaddcbabdbbbacdcccbbddaddcbdbdaacaaabddbabdaabcdaacbcdcbbbbddccaddbddaababbbbbcbccacdbcdcbdbaacdbcdcdcaaaddbdbcbdccdaadddbccdcaadbbabcdcaadbdbbbddddcaccabcbbaabbabcddbdbabbccbbdabdccbabbaabdcdcaccdccaacadbdcccbcadcdcbcbddbcdaccccccdccbbcacbcbbdcbddccbcabdbcaaabddaaabbcdbaacacccaadcddccbabaddcabbbdddadcdcdccadbcccdcadbabdadbaabbcdcbdddcacdbcbccaabcbbbbccaabaddbdadbabdaaaacdbdbdacddbbdbddadbcddbdadcdabbbbccdabdadabbbabacaadcccddcbaabdbccdcbcdccabcaaacbdbdbcddcdcbabcbccbaddcbbdcabcaadccaadbcbcddacabbddbbbbddccabadcdcbcdcbdacabdbbadadacbccbacaabadcacacadadcddccddddaccdabddbcdcbaadbaaddaddababdaddbadbbbabadcbdadcbbddddbccccddcdcacabbabdbbadbaaabbaaabdbcabaabdadadcadcabadcababcacacaadabadcacdcbdbaccababccdcdacadaacdabcddbcbcbbdbcbddccadaccbdbcabdbaabbbcddacdbbcbcaddbddaabadacaddccbbcdddbacbbccabcccbbddddcbcbccbccdcacbbcdbcbbdadcbcaabadcaacaddbabcbcbaaddbddcccdabdbbdcaccdbabcbbbdabdaacbbbbabbcbabaacadbdbccddcbbbbdcaccdadabaddbacacadcddadbacbddcccdccaadabadcbdabaddcddaaccdcdacdbbbcabaacaacdddccbacacadddbadacdaaadcddadaacdbbbabcbbaccdbdccddccbaddaaccabddcabcddcbdabadcbdbcbadbdbaccbcbcadaacacbabcbbbcadcbcacdbadcabdddabbdcdabdabccdbdbcbdbdbcdacdacdcddbcccdcbbcddacacbddbbbadbcdaddadcbdbdacbcbcbbcbbcababcabaabacbccabdddadccbbabbdcabcacddadabcdbddcacacadadbbbbadadaccdccdcccdcaccdcbcdcabcacadbbaacbcbabcdaddbadaacaaabbccaddbbcbabbccdcbaaabdadcdcaaadbbdbcdcbaacccaccaddbbdccacbbabadbbbbddbcccadbadadacdbcaccdcdaaccacddbdaccdbdaaaddcbcacdddadbabadcddcbadadabbcbcdbcaabccabdbadbcacacbbdcddddadbddadbccaaccbbaacbabcdcaddcaabacddacdbadbabcaccddabacdaadcaabcdbddcadbbcccddaabaabccddccaddabadbbaacaabbdacccaaddcccbddcdacdddccabbcbdbcdccacdacbabbbbacacbccbacccaccbcabccadadddbdbaccacdaabccaaadadacbcdcadcaddbccaaabaadddbdadcccaabccbcccaacdbcbbdaabccaacdcdcbccccbcbaaccdddbdabdbadadbcabbcaadcdcadcacadabdcabdabccaccadcdcaaabbddcadcddcdbccbcbbddbccbbacababddbdbbaabbbbcbbdbddcbcccbcddcdbdaabdbcaddadadccabcdcdddccabcccbdccbcccdcdaddbbdacabcaaacbcbccccbacdbadcddddaababadcababcdcbdabcaaaddbdccdcdcbaddabcaaadaaaaacaaacddabcaccdbccccacccdacdacccdbcccdcabdbbdcccdcacbbdacdacdcaccdccdcacdddbcaccacdccdbbadbbbccaadccccbbadacdccddccbaacabacbddbdaccadcbdcdabcabadcadddabbcaabacbbbabcaabddccadcdcacbabdbbcdcdbaaabcacabdcbdacdadcbbaddbddaacadcbdaccbcbdcadaadddbcbabacacadccbcbbdcccadbabddddbcababcddbccdbaccdbaadcacccdbddabbbdbbdbcccacaaacdbbbbadaccaaabaadcdbbdbbcbadbaddaacadccccdbddddadcaadbcdaddacbabbacdcdcacaacbbccbdcdbaadbcbcaddbaaccaaaacddcbbadbcaccacabaacbbdccbcbdcbcccaadbcddcbcabbccdacbcdbcccbabadcdbabddccbbccdccbadbdcadabccacbaaadcbdbdcdcddcacddabaabcdcddcacdbaaadccadacabbdcbbacdacccbddcbcabadbbdabdaaccdcdcbcacdcdbaddbddcbbccaccdaddacccadbbaabaabddcbdcdcbbbccbcaaddacdcdaabcaddcddccbbdadcacdcbdcdbabbcacadbdbccccdbacdcdbccbbddbdbcbdcbddbdcbccdadbddcdcaccdcdcaacbbdccddadacbdcdbcbbacadcddacabdaddaaccadcbcbcacbbaaaabccbcabdabadcdcddacabdbcdadacabcccaccccccddcbdaaacdddbbbbdcacabbcbbcadbcdbbbacbbdacdcacbbdbacbbbadddabaabccccadaccdaacadbdcbddcccbccaddcdaadbdaaaadacccdcacccccabddbcaddcbacbabdacdaddadcbabbbddbcbcbcabccbacdaaaabbaaadcadacbacaddccdacdbdcababcbcbcacdadabcbdacbbcbabbabdadbaddcccdcadacbcbbbdddbacdddacabdbbcadaddccbbaddbdbbadcbcdcabadcacbddaccbaccbabbdcdbaacabbdadcbabbbdddcddbddbadbabcacaacdcabbcbbcabbcddbdcbdbabcadcdbcccacbcadddbcaabcacccdcababbcacaacaacaacdabaddcdbbdabdccdccdcadcdaacddaccdbabcddbaaddaaaadccabbbdaddaaacbddaccabbbcbaccaaccddcacbaabbbddcccbaadadadccdcbcdaadbdbdabbbccadadcdcacacadadaabcbdbacbbdccaddbaabbacaccdbcdbabcdbdadddbacabcbdddbabddacdadbdccdbadcbaadbcccbabbcbcbaaacbbddabdacaabbbddbcdcadacdcbcccbbaabdacdbdbccdccdaaccadbbcbcbacbdbdbddbbabbaacdddcbdbcbbcbcdcdaccdbadbbbbdbdcdddbaadcbbdccddcbbdaaadcadacbbddabcdcacabbdabaaaabbabbdbacdaadcdcbacadabbdabcbcaacdaacbacbdadbccddbaccbcddbcbdaaddcdccbddaadcaabdcaabdcaacadaacbbdbbdbbccbacdacadabadcbcbbacbcdcdbaadbcbcabcbdddaaabcbcddccaccdaabadadaccdcddddddcaddacbdcabccadcaaabadabbcdaccdadbdbbdacacbdaaaabdbdddcdaacdccbcbcdcaabcacccbddddbcdbccadddbbcbabccabdccbcddadacbcaaabbaabababccbbbdbacaaaabdaacbccaddccddbacdcadbbbbadabcbdccbbadbcaabcabdcddccbdccacadcdcadbaadabcabdcaacdcbdacacdcdbaabddcdccdbacbcabbcddbbacbbdacabdbdbadabbbdaaacbdbcabcacbbccabbdddcaaaacaacdcabdadbccacdbddabdbbbcddacabbacddccaacddbbbdbcbadccbccbcbbccaccddbddabccbdadbbdbdddabdabcccdababbbddcaacbcbacaabaaacaadcdacaddccbbdddbadbcaaaacdbddacdccdabadbdcbcaaacaddbabaddbddcbccbbdbbbbbbbbdcaaddbdabddbdaadabdbaaabcbdbbcdaddbacbcadbdddbcacdacacaaddcbcabccbddaddbbadbbdadbbbbdaddbdddbacccaabcabdccdbaacccdbcaddaddabacdcadccdaaaaccddcbcddcdbccbcbcdabaabdbccbbcdbbadbdcdcccaccdcadacdccddbadbbaaaaabbabbaaabcccacbcdbbdbddcabcccdcbdaaadabbdacbbbbccbdcbdcbccdcbcbaabaaacacaccbcbdcdaabdbbbaacbabdbddbddcdbbbcbbacaccdcbbdbaabdaadbcbcbdbcccadcdaaabbabbdbcabbcdaadbbdddbccaadbbacabbcacbabadbacbbabdaddacacadccdaacdcbddcbdcddbbcdccdbadadbcacacacaaaaacadbddcaaacdacdadbabbacaababaacaadddbdbbbbdbcaaabacccbabdaccbbcaaccbdadcaaaaabadbccdaabccccbcdcaadbaaddacbcabddbcdbdbdaddccbdcacddcabbddbbcdcddccacbabbbccbadadaababbcaccbaddcdcbadabbabadcbcbcccccdcaabaacbbcddcbbdcdcdbbcbacbaddcdcabcdccaccaccbadaacaabdcaddbadadaadaadbbcdcacdbcbadbddaacaadaacddaccccdaadbbccabcbadaccdbbadadcaadbdccdadbabcadccbadddabbacddbadaddcacaddaabaacccbadcadbdadbcbdaddccbcaaacbbabddccabbcccaaccdccccbbaabdcaddbabcccbcaddcccddcaabaacdcdcacaadaaaccdababcbaaabddacdaadbbdddcaddcadcccccbdbcaaadaacadbacbdacbddbcdbdddbdbbabbddbbdaddbabcdaacdaddcadaccdcdadcbabdcaabadacddcdacdcaaddacbcdcdadbbbdcdccdbdcdcccbabaaaccbcbdbacbacbdabbddcdaaccdbbdbbabdddaacacddcccbabbbdbaaccdcaddccbcacccdcaacdddcdadbbcdccdcbbdacbabaccaddaababdadbadbbaaaadacaaddbbbccdbaccddbacadbcadddadaaabaaddccbcccaddddcacdcaccdaacbccacccdcdbbabacdbbbadacdacdabcbaabcabaaccaccbdddadbbdbccdddabbbddccdddcbadbbbcdbadabcdcbaadcadbccdadccaddacbddbbacabcdbacaccaabccaadbcacadaabddbcdaacaaddbddadbcbbdbccdabcbadaadcabccbcaabcbbcdccabbbbccbdbcbacbcbbdddadbcadaadadcabcdbacaddadbaabbdcbdbbdcdddcbbbdaddcaacbabadabbcdcdbcabaacaddcbbaadabddddabbabaabcdaaaabaaaccddcdbaccddbdccdcacabcabaadddcdadcbabdbbcadabadaacbadadbaccadcdbadaabaaaabcaacaadabbbbaadbdbbadadaaaabdbbdbbbdbadacdbddbbaacbbcabacaaddcdaaddbbcbccbbadddcbcaabbbacbbaadbadaabddaccadbbdcbdbadbcaaadbdcaaacaacbabdbcccacbcbbaccdabddacacdacabcbdacabbcbadcabbbaababdaccbaaaaadcdaddadcabaddbdbbcacadcabccbcabaabbcbbbdbddababbcdccaaacabccbcbadabcdaccbaaabbccdbbdbdddcaadbcacbcdabdbdadcbadbbaaacadbcbaadccbdaadabaddacacaacdcdaabddbaabaaabbbdbdbadaabbbacaaaabacbccbdbdcbaaacccacbacbadcddccaccccccdabbacddbdddcdcdcbbbaccbdbbdbabdacdacbbddccbdddbbdcaccadccddbcabcddbcacdaadbbcabdccdababddabcbbbbccccdddcbabddcadcbababcdacdabcaadadbcbddcdbacacdcdbabdbabcdaddbbdbaabadbdccacaabaaaacdcabadaddaddddcacbbbcbbadbdcbdccddacbbdaaccacadadcbbbaabbabbbdcdddabcaaaddbaccaccbcdcadaaacbcadbabaadadcdacbddbddaaccbdccbbdbacdcdbaaadaabddbddccbcbddcbbadbcdcdcabdacbbbdcaadcacbcaddaaccbcdbbdabacbacddaabaaccbbdddbadacbabdabbbbdddaccccabaabdabaacdbdbdaccdbcbdbdabbcadcabdbcddbcabaccaabbaccabacabdbcddbcbbcbcdcacabcbcbacdbdbbabbaaadbadbbdbbbcccadddbcdbdcbccdbabbdcbbbadacadcbdacabbaadcbcdbbcabbddbbdbbcacbaacaadaccadcadbbabbddbbaadacccbcdbaadadbaaccddbcaddbcaddcacadadcdcddabcacdddadacaddadaccbdcccccdcadbdddcdcadbacabdbcabbcbbcdcddbdcbdabcdccdadbbbcadbcddcacadddabbddcadccddcabaadbdadbbdaadbccabdadcaabcaddbadadbbbabacabcdbcabaacccdbccabcdbccabcdbacddaababdcaacacbcbdcadcabcacddaddcabaccaddcddbdaadbbacadbbbddcdcaaabadcccabddccaacdccdcaabcacdbdcbbdbaddcbdbbddbcbdddbabdcaababdbbabcbdaddcabaddcabddccccdadaccbddabbbcccdbdbaddabadacbaccdadabccbdaacdbadbddcbbbbdbcdcbcacaaacccaadbcccbadddcbbbabdcdcacdbddcccaddabddbacacbdddadcadaaaaccdbbadabbcacaacccbddbdcccacbdabcdcbbbaaabdaddcbdbccbadbddcccadcaccbcdaccaddadccbcdcddddaccbcacccbdddbbbaaaccaaaaacddaacaaacacbcdbacccaaabbbaacccdacaccbcacbcbaabcaaaddcbdbdcdbdaaabaccbcbcaabadcbbbcacbabaaadbcbcccaaadbabddabccbadacbbdbbccbdbcdcbacdbaabdaadcadaaabaddaacddbccbbcaccbadbdabbbdcaccdddbdadbbddabdcbddaabdaacaacdcdcadacbcabbaaccdbaaacdabcdbacaabbbdadcdacccadcdabaacbbacdcdcbcddaddcadacbcaccacaabcdccbcbdacbcbbdcbaadacdcdddacabdabaccdccacabbbdacaaaccccacabbbadabbaaadddaccbcbddbdadacaaddabadacabbbcdaaacaaccbacacadcccadaaacbccdabbcbdadcbdbbbbdbbbdbbcacdaabbabccbadccbdcbdcbbdbdcacabdbddcadbacabbacdddcbacbaddaadabdabcaaddbddcadbcdacccdbabccadcbbbbaccbcdaccbaddddadadbdcabdbaabacdbacbdacbaaaabaddbdbdcdadaaaaccaccacbdadcbaacacccadaacddbdcaaabcdadddaadadcbbbcbbcdbadbbccbbbadbcaaabaacadcbbdccaddaddbcddcacbaaabbaacadaabdaaadbbdbddcdbdbdbbcbcbaaacbdabbcaddbbaccdabdcbdaaacacabbdabcacdcabcaaccbabdbcbacacbdcbbddccccadcaddacabbbcbbadbbdbbcdcdddabcbccdbabdbbbdcbcabdbdcccbcddbbacdaabcabdccaabcddcdbadbcbbbdbcddccaacdccdccabdaccbacabbbddddadbdcdbcaadbdbadbaaadccabcbabcbbddaaabdcdcbaaacdbcdacbdbdaacbcacdccdbbbbbbcbcaadcadcdacdadacbbadbaaccadcbdcdcdabdcddbddcbdbccccbaadbcaadccacaabbadcbcaaaadccdcdbacbabcdbaabdcbcddbaddbbaabbaadbabcabccdcdbbbabbaabbcccadaadbbacabddddcbbaaacbccdbabccbcabbbaaadbaadbbbccccdcbcbbacacbdaaccbdaccdacbabbbbbabbacbbaaacdbbcdaadbadacddabcbdcdcaadbaadaacbdadadbdccbabaaddabbccacabcbdcbabaddaabdccaaaacbccbcccbddbabadacacaacbdadcdadbbacccddccbdaacbcaaababadddabacdbddadcbbbabcabdaadacaddacbbbbbdbdbbdbdcbcacddaabacbbbddadbbadbacaabdaaacabbdcaaddabccadacdcadcccbcabbdaddaacbbddadcbbcaaacadcccabbbcbacbbcccabcdacbcbdbadbdacbcdcdacacadcccaddabadbdbcbbccbbbdddcabcdbdabdddcdddbabaaacbbdcbbaaccadcaadabcccbcdbcdaabbabccbadbbbbddaadabbbdaaaddcabbbadccddbbbbdcccbccadcabbbbaddcdbcdcbdbaacddcdaadcbbbdaddbddbdaaccdbbadbaccbbbacdaadacaaddbcdaccbddbdadcadbdccddcacacadcacbaacddabdcbbbcbcdaddaabdcbadcdaacacdbcbdcbadbdaaddbaaadadcaaaacddbcdbdaadcabcbbbddddcabdacaaabcbdacdadbdddcabcdaddacdabdcdbaddbcadaacdddcdacacdbabdddbbccacdccddacacddcaacbaabccadcaaccdbddaaaccaddcddbcacaabdbaaabbaacdbdbacdcdabadbbabdabcdcdbabccdaaabcdcabbabcdabbddbdaddcddadaabbcabcbabdcdabccdcadbcccaccddbabacdbcddabdaabcbacdbbbbaadaaaddcccbcdbdbadbcccabcacbccbacbdbdaabbddcdcdbadbcbacccccbdccaabaadbdbacadadadcabdddcbbbcbbbcadabacdcbbdbcbadbcdcdbaccadbbabbbdaabbbaccbacbddddbccdccbabddccacaadcccbdbbabbcbdbaddddaaccbdbdbacddaacbbbccbcadaacdbacacabcdccacccbddcdbdddaaaddbcabacaadadcdaacdabbaaaacaaadbbcaadcdadbdcbddcbadacacdbbbaaadbacdbbdbdbabbbdccbaddccadddcddbbcbbcabbabdabdbaccddbdcaaabdcccbbabacdccddddddbcaccdcbdddaaaccacbdbdabccadccdbcbabdbadccbaadaaadccddbcbddacdaccadbbacbddbddbddddcbddbcaabadbccacdbaccdabccbaccbdbdbadbacbcccaaabccbccabaaacdaabaccbbbabdcaccbddcbcabbbdabcacadaabaccbcddbbddcbcdcdabcdddcdcdaccabdcccbdbbbabadbccaaadaadcbaaacbaccbdcaabbacadcbcdcddbbaaaddbdcaadabcacdbbbcbdaadcdaccddaaadcabddbadddbdbbbccabcbcbdccbdaddaccdcbbabbbbacdddacddcdadcbaaadddccaaddbdcddddbaaabadacaccbccdaaacbcdcdddcacbbbdcbbdaaabbdcccdddbbcadbcdbdbcbaddbcbddbcccbcadbdaababbadcaccbcadddbbbadbdbadadcabadddbdaddcdcbaacbbbaaccabacbaddbdaaabbcadcbdddbcddcdadbabbabacbcadbacbacddcbbcacaabdbdcdbabddacdacaaaddabaaacdbabccbdbbadbcacdcdbbaddcbbbcaaaacbbcdbcdabaaacccbdcbacbcbacabbbcdcaadaacadadcbaaaadcdbbcdbdcaaacbacaadbdddcdcaacdcbbaccaaddbacbbbacdaaabbcdadcadaadadadcdccbccddbbdcbcbdddadddcdacdcadbbaabddddadacbbcaaaabbdabaaadaaacbcdbdddcbdccbbdbabbcdbdcacabdbdbabbabaadccabbddbbcbdbdbbbcadbdaddacbadbadaabcdbbabbcdccbdcbabaabddaaddaddccbaadbdbdcdcaadadbddabdbbabdbaabaddabbccdaadbabaabcdabaaaadbdccbdaddaacabcabcbcababddbaddaaaaabaabacbcddcbddbdbadabcbbadadadbdaddcbacbddbcaaccababdccbabaacaacbcaabcdcdaddacbdbccddcdcbababbadcadbbddacaabdcbadbaababaaadccaaacbbddcdbbadbcaaddbcccbdacbadaabcdddbabddbbcdbbbcddabcbcbacbaaddbcaddbaacbadddcbcbdcbbbdbbabcdccbccddcdacdbdbdcdbdbdacdcdcdaabdcbaaaacbbcdadbcccbcbbcbddccbcbddcccddacdddbadbddcabcdaaadddbdbabbdaccaacdcaadbbbddaddcbbddbddaaadcbdacdbcaadacdcdacaddcbbcbbddcaacaccbbbcddbdadcdcabadacdadbcdcabbaddabaaabaaaaababdddaaaadcaaaadbbcaabdbcabdaaddaaaddacdccbbabadcdcbacbaaadcdddbdbbaccddaaabcadcbddbbdbabcbaadbabaacccbadddbddabdbacddabcdadddaadbccbcbbdcbbaccdbacabaabbdbdddcddbaddabdcccbdbabcbbacaddbccaccbacccdaaabcbacaabcbacbbdbcdbbbcddcbbbbadddcbbcddccdcacdcbaaccbaccccbbbbacaabdcbcbcbcadcbbcabccbabccbadacabdcdbadbdabaddccdbdcabdcabdabadbabcdcdacdaddacadaabbbbacacbbdcaaaacbdbcaccccadacdadcabcbddbdccbdaddcbbdbcaabbcadcbabbdbabdccdadbddbdadadbadbcbbdbddabadadbadbabdaccdccbddbabbabcdaddaabdbbaacacddcdadbccaaadcddcdaccabbcccbbdbadaacdbbacbcbaaadbbddbacacaadccdbadbdbccacabadbabcadaddadcdcdbcadbbcbbdbcababacdbbbcdadcaaaaabbdbddbbddccbdaccbbadabbadbabbaabaaccbbcdaccdbadbabadaaddbdaabbacbdcbbbddddacddacdadbcdcaccbbccbcabdcdbccccaadbcaadaabadcccbdccbbbbbdbdbacbcdbdcccbdcababbbbbaacaccaacbbabadddcbabcddabdbbdddcdddddbabdcdccdbabcbcdbbdaddbadcabbccacabacccaaadcdddcadacbcabdbaabcdbcaddacddbcccbbabcccacdbccacbcdadbbaabdcccdddaddbcccccdcbcccbadcadacddaaabdbbdaababacbabcbcbccaaddbccbccaacbcabcccdccaadaddcadabddadadabacbcbcbddaccdcdccbcacacabdbcdbaccdbdbdcaddacddcbbdddaaddbadcaddcbccbccdbdacbcddbaddaccdbbdabcccdddbaaabddaaacddcbcbcdcdcdcddbcccbaacaccccccaadbcbbcbdabbcabcaaacccbcbccaaddbcacccbcdccbbcbdbbaddcbddbbccabdbdabcddabaaaddbdabdaaadbadccdcacdddabdbabacacbadaaaddcdcdddacddccbbaaacacbaadabbabbdbddccbcdabbadccbbccccdaaabbdcdcdbabdccbadccaaaccbbcbdabbccabcbaabbcbdaacdddcdcbbbababdbaadccdbdbaddddbddaccabddadcadbccccbadaddaccccbbcbdaddccbbddddbbccacdbacbdcbbdabcabcadabaaadbabbaabddacdcbbcbaccccdcdcadbcdaadbaccacbdaababaaaaaadbbcdcbbcabdbbdbccdbcaacdbacddbbbdadddddbccdbbdbdddbccabaabdbacdccbdbccbabbbcadbaadacdddcbdaaccccabcdcabcbdcbbbbcbababbcdabaaabcabbaaaaadddcbacdbabcbbcaaaadbcbccabcabaaabbbadccdbabaaabbacdccaccaaaacdaabdcbcadbdadbcaadaabcaacbaabbdbacdddacacacdbbddaddadbcaabaccdcbccdbabbabddbabcdbcdcdcdccaabdbdbdcbbbdbdcabbddbdabdbbaaaaabbdbbcdabdbadcdaaadcabdbacdddbcababcbaabdcddcdaaaabbccdcccdddbbacaccdcbbdcdabdcabaabaabbaddccabbcabddaaaaddcabddccdddaababbdbabcbbddcccdaaaadabbbabdcadbcaabacbdbbbdbcdadddbbacacdcccaaabdadddabccdaccaaddcacdaddacadcadaaadbbaddcccbacbbaacccdccccadbaaadcbdcadbdaaccabaaabcbacbccbbbdbddcccbdcaacacbccddddbabcdcbabcdcacbaaaaadddbdbccccadcaaaccabadaddddddcddbacdbccddcaccbdabbddabaacccbbcabccddaabcdaabaaabdaadaaddbbbbabddcaaacbbccbcdacdbaaccacbabbcbabbdaabcdcdbaadcddcdcbccbcdccccadbacacdbcadacdcdaadcdddbbbddbdbddbcbcbcdccccbdbbbbacabcdbcbdaccdcdbaddbccddbcbabbadbbdadcbbccbcdcdcaddcabbbddcaadcbdabbdadadaaaabacddbccadbdbdbcaaacababccaccbcbaabadbbacbdbaabbbbdaddbdbcdaccbdbccaddbbacccddcacdcdacdaaaccdaabaacacbdabcccccabdbbaaaaddcdcddbbdaabccdbccdbaaabdbbcaacdcdbbcbccbdccbadabcacccbbbdddcbcdbaaadbabdbacdbdbdaaddcddccbdbcbaaaccccbabbdcadaaabdcdaacacdccaaddcaacccdcadbcbcdabaccdbcdddacdddddaabccbddacdcaddabbbddcdcdcbddcbbadaacbbcabacdadaddaccacabaabcbddadccbbdcbcabaddadbcadbdddbcacdabdaaadadabacddcdadadcdcdcadddbadaaabaaacccdbacdbccacdaadaaaadcabbbbcbacdcabaadcadcbcacbadabacddbbadcccabbdddbccbcdddaabadbbbbcabbbbabdadabdbbcbccdbabbcbdcbbaadbbbbaadabbbacacbaadcadcdaabbaddaccadddabcbcbbbcbddcdbddababbbabdaadbbadcddcbbbbbbabaacdbcacccbccddcababbaabdddadcdabdccabcabbddcdbabccbcdbdbcbbcbdbacabbddddccdabcdacacabbcadddaacacaccccacaacadababddacadddddaadbdbcaaccbbbdbabcddaaadbaaabbaaddbcabaabaaaddcaabbccdabdaaaddbdcacbcbbaaddaaaabbbcdadabbdbcbcaabdcbdbabcdbbcbbbccaaaacbadcbdbcaddddcbccabccaadabacccdddabdabcbaabdbdcdddabdbbadadccddbcaccdacccdaaabbadcdcbcadcdbcdaabcabcbdddbccccdcdddbbddacacbdbbabdbccadabaadbadbcdaabacbdcbdadddcbccddaaabacdaabacaaaddacadcaabdbcbcbaabcdcdcadbdaabbaaddcbdddaaaacadacbddabcbcccddcdacaaacbacddcbbbabdaddccbdadcbcdbadddbbddcbcacacbbdaaaadcbaacdababbacabbcdbcdabcbcacbcdcaaabdddcbbcccccdbaacbbbccccadcbdcdcbbdadabbdabacdcbcddccdaccbccbccbbabbbdaaaaccccdadaddcadacacdcbacdadcdcbabcdbaaacdabadcadbcddcbdcacbcbddadcabbcdadddbdacdacaccdbbbccddbdadaaadbacbbbaddabcdcbcbaadddcaacacdbadaddaadddbcdbbbddacdacccdcdaddadcabbdacbdabcdccbdacdbdaabdcbabaccabcdccaabddccacabadbbbabcbadbbccbccbacccaccdabaabbcdcaadadcdabcbbdbaadddbbcddabdadabacbcdbdacadcabacbabaaaaccaccdacdcbaaddcadcbcccdabccdabbdcbdbaabdcabbcabbcabddddabbcdbbbcddbabbaaddddaabbcbbbadadbaccbbcaadbacdcdbbcbaabccbbacaccdcbbacabaadbbcabbcbacbddcaadabadcbbbbbcaddbadbdaccadbadaaacdbcaabcaabdcbdbcccbcaddbcbcacdcdadcacaacdbbcabacabbbdadabcccbabcacbddbbbaaadbdcdadbcbdcaabddbcaaacbdccadbcbadccaacabbdadabacddbbbacdcaddcaccadbcdcdabcdcdadaabadaacadbdadbbdabcbbadabbbbddccbbdcadcbdbdbccbbcddcddaddbcbacacbccddddacaacaabdbcbcbabdbbbccaaaccdaabbccbdbbcdbdaddbbdbdaadbbcccadddaabbcbbcdbaabdadacadccbcbaabdcdbbdcdadadacadbccbabbadaccbddcabdbbcbbadcdbbdaacbbbdabddcbddaabdaacccccadbdaddadaccbabbcadcbdccadaacabaccbbbcbadaacacadaacbccabcddbccdcdcdbcddbdbcdbaddbaadbbcdcbbbadbbbabcdcbaacbaccbbbddccaacadaaaddcdbbbdacddbbddaddabcdbddbcbcaabdcbaabadbddbdcbccbdcddabaadbddcddcccaaaadaacbacaddddbaaadabcbbaaabbcbcabbbcddddcdbccbdbadaacaccaadcbdcdcbdcabdddaacdaddadcdcccadadccdcbaaabddbbcbabdadcabccbabcbaaacdcaadcdbbbacadcacdaaaacadddbabcacabbadcccadbdbdababaabdbdcaadbddccbcacbadaaccbdddcdabcabbaddccaadbdcdacbcadaccabaababbccadcbacaadcdcbcacddbcccababdcddccdbaaddacbbcbacabababbaabcdaaababcadcbcbbaddabbbcacddaaaddcbaabdaacddabdccaaacbacdadaabdadcadddcaabbcdbdbbcaaababbadcaadcaddcdcbcaccbbcabcbcacdddacadcdddcdadabccccbdadbabacabddcbbdddddaaadacaadacdcbcdbaacbdbddddababdbcdddabdbdccddcadbacbaddcaaacdabbdcbabbcddcbcbdadbaadaccdcbdaadcdcdcbcaabbabdddbcbbcbdddbcddcacbcdaaabcbaccabccadaadddccbbdccdcadcddacabcdcbdcbcddaadadadbcdddccdddacdcdddabbacadbbbcbbcbcbdbcbaccaccdbbdadbdaacadaacdadcaabcdcbccbbadcccaacbacbddabbddabbcabdbcdbadccbccadcbddddbcabbbdccbcaddcacbdcbacbaacddcdbbdbacddadcdcdddadcbaacbadbcbbabdabcccacbbbdaadbbddbabbcdcccdbaaaccadcaacccbbbcacccbbdaacbcbbcbdacadaabadbdbdbaddbbbdbdabbbcaddcabaadaacdbbdbcacdaacdacdcabcbcdadadaaaacbabdbbaaaacaccdbadaccbbbbdcdcbbbbacbdbdcdbbacabaccaccbbaddbaccacdbacbbbdbaabacddcccbaabdabbdcaacaddbcaaacacdacdbaacaaadcadbbbaabdbaaabdccaaabcbdddabcdcccdcbcaaaabdacdcdcbaaddaddacadcbbdabbbaddbbdcdaadabdbacdadcdaaadcdabcaacacabdbadcbbcdccccbdccbcaadcdbbcdccddaacaadabdaabcabdabdaadbcadabdabbbcdbdbaacadcbaddcdadacdccbaddddcbbdadcaaabdaacccdbcddbdaabaaacacdaabdbbdcbbaadcadabcbadcdadcddaacdbbdcadbcdddaadccdabadcdccbccdcccbdcdbdcabaccbdcdcaacbbdcabbdacacadadddabaccddcddccadababcadcdabbabdcacbcdcbcdcabcbbdbdadcbdbcaddaabbbdbaccdbbadababdacadcbbbaccbdabccbccbcbcdacacacdbccdcaacacdddcbcdbdbcadcacdcbabdccbacdccbcdcbddadccabacccddbccacddcccbbbdbabbdabddabbcbdaadacbabdaabacbbdbbcacdcddcbacadbcacaadcdabdcccbcacadacadaddddabbdabcbaabbccadacbddccbabbbacaddabcdcaababbdbbbaabadacaabddbbccacdcbdccdaabbbbcdddddbdcbcddabccaadbcdddbababaacbdddcaadcdacbcbdaaccbadbaadbbadacadddbabdcabacbcbdacdcdaadacccdddcdbadbaadcaccccabacbcbcaabcddbadaddabdbabaccbccdbbdabbdbbcadaadbcbdaacbdcbacbbabbbbbbacaadddacacbaddaaddddcbdacacbcbbdbaacbaacdcdbadcdbdadcddabcbdcaabdcccacddbddbccbacaacdcacbacdbaccbccbacabcdbabbcaccdcbccacdaacbaacaaabcdaacababadcdacbdadabdbbddabdbdcaabacadacaabaddaacdaacbbababbcdddccddccdbbbcbdcabdaddcbcadbacbadbabadccaccccdbacdcbccbcadcbcacdcbcdcbbcbbadcdadbacaadcaccbbdddcdcdbbaaacbbaabbbbdaddcbcdbabcbadaccabbcbbadadaccacabbacdabdcbadcadcbbbcacbcbcddbbcacdbbbbbbddcacbdbbdacdcabdcbbabdbaabdaadaaabaaccbacccaccbbbadadbcdadaddcddababcabdcadbdcbdbddaabaccacddbcbababaaabcbbcacbcdbdaacdcababbacbcdbbdcacdaddbaaacdadbbbdacddaacdadbadbccdbdadbbbacdddcadccddcdadacdcaaabacbbcccbcacaddcdcbcdbbadcabcadccccddcbcdadbbdaccddccaabbddbcaaacabaabddaabbddddccbdacacdaddbdadbacccbcdbcbcabacaadcacacaacbdcaabaccacbcdcdbcdcddddbabbddbcabcccadbcacacaaaadbdcbcbcadcdcaddcdddbcccddaadbccdbbacaabdbcbababdcddadbdbbbdcaaacdbadbaadbcdacdaabdcaabbcacbcacadaabddddaddacabddbbcddbacddadbcbbbcbabcddbbaacbccabdaddadcccdbcadaccdadcaddccadbccabaaaddbbdbdcbbabddabbcbbabadaccbcabbdbcdaccdcabadadccaddbbbbbbadddbdadabddcbaadadbbddcadbcacddcbbccccbacabbddabadbcbbddbbabccdbbbadccacaabcabcddababbcccbdbadabdddbdbcbbcbbbaabdbbacbacccabccbbccddcabccadcabddbdbdbcccaadadacabbacdabbaaaadbcacccbcabcdccbcdcacadcdbbdcddcaaccacaddacdcddaadaccccdcdcadacccbadddccadadbbbdbacabcaccbcbcacaadccdbdcbbdcddcbacbabcaadbbbaabdccacadabbdccbbbdcdadcbbabadccabacdcbbcdacddddbbbcbacdcdbdabccbdabbcdcadccdbabbcaaaabbacadbbadaadcdcacabdbdaabdbccdcdbbbaabaaadddddcabcdcaddacbccaaababbaddcdccbcbcaccdcbacdaadaabcccddcbcaabadbbadbadddcdadcbbadccabdbcdccbaddacdbddcbbaacaddbbacabaaccddacdcbbdabacdbdccadaadbdacadaccbddaccbcdacdadcddcbcdccdcbcdbadbbcbbdabbacacbacabccbcdbcabcbddbbcbacacdcddbddbcadccccdbacddbbbdacbdcaacaabddcbcacdbdbbacbbcbcccabcbacdcccdbdddaccddbcdaddcacbabbddbcadcbddddbbdabdcacaddaadcdcadbccbcabdcaacabbacbcdbbdbaaddabbabbacdcccccaccabccdbccbbabddadcaddbdacbaacbdbcdadbabadbbdacbacccdbddcddcddcdabcddddbdbcccdcabdcddbabdcadacbcbcaaaacbdcdacbbcdcdbdbcaccddaadcbbcdcbaddcdabdccddccabaaabaabbbababbccdccabacbdccddcbbbbbddadadadbbaaaaabbccdcdbbcaaaaabadcdcbdacabdcbdadbcdbacabbbbcdbbdcccaacdcacccacaacabcbadddcbcbccdcbccdaabcccdcbbbccabdadacbdbaccdddabdcddcbccbadbbdbbaabbdbabbcadccdcbbcadbccccccbacbadbcaaddacdabbbdabdbacabddcbcbbdbdbadbdacdcdbdabaddbcbcdbcabbabbacdcbdbbabdddcddabdaacbadcadbccddadddcddddadbbbbcbdccacaccbacbadccdcddccbcbacabbbdbaacbbbbdababbbbcacdcdddddaadddcddcbcdbadacbcdbdccdcdbcdcadaaaaacabcccdadbabdbcadddcbdddbbbadcaaacdadbaadcbabcbcbabdbccccddbcbbacbacccbbddaddaaddcbcdaaddabdbbbabaabdabcdbccbbacdcbacacbcbdcdaddadcaddcdadbddacbccdccbdabdababbaacadccaddabbbacbacccaaddccccccbcdbcdbaacbacbdcbcdbaaacbbadccdaadbdcbbaadbddcbaadbdcdddabbaacacacadcaacddbbdaababccddddddddcbcadabcaadbdabcababbddbcbacdadbcddadbbdbcbacaddbdbdddcaaaaaacbdbadababadabbbbbabdabddadbaaabbdccdbdabbcdcccbabaaabdbbaabbcccadaccbdabcbcaccadcabdbbdddcaacbabbbacccbbcbcdacdabccdacdaaabccdbdbaaacdaadabacdaabbdcddbbbbcbabcaaadbbcabaacaaaaccdbdbdccdcdcdbadcccdbcccdbbbbcdbcbcbbabdacdccbbddbaaccbbcbddcaddadadaacccbbddbbbaddbdcdabcddccddcddbcdadcddaccddbbabbcdbbbadaaadcaccbabdbbadbbddcdbcbbaccadcccacccadbadaacbdabcccbdcbcbaacdcbbcaddaabadadbddaabbbacbaccccdacdabbadabdabacccccaaabaadaddcaabcddadcbdbdbcaaddbbabcdaccddbcaccaaaadbdcddacbccbcacbaacdbcaadbbcdacdabccbdcaccaabcbaadacbacdacddaabddaddbadacccadbbbaddbbcaaddbcaabdccacdaabcdcacddabadbacdccccaacdcabadcabcabdbaaccbbaacbacccbaaabaddcbdadaadccaaacaabbaddbbadcadbddddcaacabaabddcadccacdbcacbcdcabadcdbddccbbdddddaadaccabbccdacddddbddcaaadcdcbbddcbdcdaadbacdaabaccadaabbbabcbcabadacdbaddbdbbbaaacbabdadadbbabbdabbabcbdaddccbacdbbbaddacdbdbcaadccbdbbbaddbabaddacdaabbbbdbacbdddcbcccbdbcdbdddcbdcbdadcacdccbcacbbccbaddcadacbdbcbaabcacaddbbbdbdddbbbacdaaabcaaccdcddaabaaabcdbacccdaaaaddcababbbacdbbacbabbcdbbdcadddcaacddaaaccbbddacddabccaaadbcbcbcabbcddbcddaccaacbdbbacbdcdabaabbcbbaccbacabaaabbccbbbbcdcacadabdadabcdacacdbdabbcdbdbcdabdbcbdacdbbdbaabaccbccccacbdcaabbbacadcdaadddcacabdcbadddaadbbbcdccadbcddccaddbbccaabccbdacccdbaabcdababbdcdbbacbabdcdabbaabadacbbabcabbbcddcabdcdddbbddbbdddcdcdabbcabcbcaacbcadabacbbccddacccbddcbcaadbcdaccccbdaaaaabcaaacabbaaacddbdbdcbdacbaabadaabcccaabaacadacaacddababacddcaddacdcdccabcdcabdacdbaaadcaabccbddbbdbcccbadcdcdddbdcacaccacbddcddddccbbdccdbcaacbcabcabdabdaddbbadbbcbdaaaabaaccbadccbddccbddcdccbcccaaccdbbcabcabaddddbdbdddcaabddcababaddcdcdacadbcbbbacadcbccaadcaadacaadcbbccadbdbdcbcdbcdacdbbdbaddaaddbbcdadcbccbabbababcadcbadbcaadbccaccbbabadbcbadabbcbaacaadaaabbccbcabadddcdcadaccdcccabbaddcbbcaabcdcdcabcdcacddcbcdbbcbcaddaaabddddbbabdcccdbbdbcaacdcbdcbbdacacbbacdabcbaddbcdadaddccaaddbcbcaabbadcbadbbbcdbbcacabddbdcacaadbcadcbbdabdcddcababaadbadccbacbdccdbbabcdccddcadaaddbcbcdbaaddcbaacdbabdcccaddaacdbcaacccdddacbcbacbcbaaccdcbdabcacabddacaaacdbadbadcacbdbbdaacdcadcbbdcdbdbdadcabdcdabccbccdbdaaacbdcdbbbacbdccbcaacdcbcbbbacbaacbbadabbacababddcbdbdacbbbddbcddbdbdbabcdbdbbacacbadaadadacabacaadaddbbccadcdabdbcdadbadbddadcdbadabbbdaaacabdcdddcaadcdbacbcdadcbbddaaccaabdcaccadcdbabbadbdbadbaacddacaaddcbdcccdbdbddcbacaccbcbdcacdaacadcddcbdcdcdbbdbabccacbcadbbbddcdbbabaabbabbdccdcaacbaaccabccacbcdddcbaacadcabcacdaaabcabdbaabdaccbbaabdddadacadcaabdacbdbdacadacdadcdbcbbdbdccdbcdcabadcaacccbddacaacbacdbbddbdbdccccbcccbccbddaccdccdcdbacaacdaddcbdadddcadadaadcdcccddaaaacdcbbbcbbacbcbaccdcbdbccdcacccaabcaadcccbacbaaaccbcabccabcaccbacbdbdbccccbddbcbddbaabdaccbcdaacbddbaadbaadacdcccbbddbadbcbdbabddbaacdadbddadcadaababbdacccabcadcdbdddcdcbbbcdddabdabbcbccabdddbdddaacddcbbaccadbcabbbcacacbdbaccadcbbadacadbcacadcbcbbddcdcbdbcbbbcdabdccbaccacdbdacbabdccdaacadacdccbccccadbacbdacbbaddaddbbacbababccbdbbacbccddaadbbababdbdadcacbcbbdcadbbcbcdccdbcadcadcdaacccbdbcccbdadbdcdaaaabaadaacabdcddddadaaccabcaadcbbbbcbccdbabbabdbbadccaadbdaabadccabdaccbdbaaddadbcaaabddabbdcbbadabdbcccdbadacdbbbcadccdaaaaddadccaabdbabdacadaadcadccdacdaaccaddddbdcbcdacacbddbadbabbccddaacbbabdccbcbccdcaaacccababcadadacccbcbcdabcacaddbddaacdbdabaabdcaabcdcdbdcdcdbdcbdbdccbccbaababacacabababbbadbaddbcbcabbcddaaddcbaccdbdddabcdbbcbbaacdbdbddcdcadadabbacdbcadbadddbacadaaddbbdbcaaddbcaacbddadbdacdaabdcdccbcadbacabbbbbccaabacdacdaccddbcccbabdcccbacabcdccdccdabadbccadcabcbabccccaabcdaacdcbbdbadccadbaaabcddbdcbdbaacadbdabbadbdacdcaabaaaaabaacdcdcbabddccddcbccdcbbddbabdcdbbdbbbddbdccbbdcdaacadcaacacbdbbbcdaddccbddacdbbddcdabaacdbdaaadddbaaacbcabacbdabbcadcacaddcbacdbdaabbabbbcdbbbabaabaaabdbbcbdcbacdcccdabdbbdabdaabccaadccbcbcadabacbcacaaaaacadaacbccbbccbaddcacdbdbacdccccbcabdabbbacdacdbabadbddbbbbccbbbacbaaddadbddcccbcadddcbcbddddcadcadddbccdabbcbbadacbcdcbddddcadbddccbcadbccbcdcbbbabaaccbccdbcdbdccabbadcbbcaababbbabbcdcacabdacacdabaabaabdddaccdadabcacbcdabbcdddbacccbbcbacadddaaacdbbbcabdaadbbdcbcbdaccaacabdbbcdabdbcdcbddccdacbadccdbaccbdabddccbddacdcdccdccddabacddcdcbacaaaadbbbcbdaddcbdbccdacaaabdbaccaaacadbdcbbdcadadbbdbcaabbadadadcabbbcdaccadacdaaabcddddadadbddacbabccbaaacabaddbaaacddbcdbbcaccabaccdbccbaaacdacaccadccbbabcbabdcdbcdadaacbdadccdaaccccbdaaccdaaabdccabadbadcaccdcbbdbabdacaacddcabcbcdbaaddcccbcbbbbcacdcacadcbcaadddddbbbacdcabdbbaabcccacbccdaabbdaacccaaaddcbbcadbabcccdabbdcdddcccbdcddcabbcdccbdcbbdbcbacabdcabacaccbaacddcdbcaabcdcaadcbcccabdbdcdaddddcdadaaddbbaabdbbaccbbccddbccbdccabbadcdbabbaddacbabbccdaabbddcccbcadccccdddccbcdbcccbdcdbdacccbbdbdacdcdbcdbbaacbaabbabcdbccccbdbbcdbccabbbcbddbdbaacddbbbbdddbdcbdcbbccacacdabbccbdcbddcbdcccdacdcbccdbddcaabbbbdabadbdcbbbdbacddbacdcacacabcaaddddcccdbcaddddcabbcbbaccbcdcbbaabbbddcbaabbcddaccacdaabaabdbaadaadabaacaacbacdabaccccadccdcaccdadcacabbcaacdcabacdbadacbbaddcdabddbbddbdaccacbdddaadabcdcbcddbadababcdcadcdbdabbcbcdaacdbbbdbbbdddadccaacabcaccbdcbcdcbcbabbbacbaacaababdabdbdbdcdbddacdddacdccdbddccacacabbbcacadabcbcddbbdacbdcdaadccbbbcdabdcddddbdaccddddbcaacaddbdabcbbdabddcddadcbbacddbcbbbccadcddddabcdbbaccadddcabddabcbabaccbcdddcaadcddacaddbcbbaddbdabbaababbcdcddcabcddacbdddaaadbbaabaccdcdadabbcdcccbbacccbdcbbacacdabadddcaadbdaaddccddcadcbabbbbdcbdbaacdaadcadabccbcbabddccbcaadabcadbacdadcaddccabbcdccaabbcbddabdcccbcccccbcbadbbadabcdbcbbdcdbdacbbddbcaaddccdbbaddbdabdccbdcabbabcbacaadccaadadddccaddcaabdcbdcbbdcbcbdcdbdbaddddbddcddcaacdabaaacdcdadaadcbddadbccdaddbbcdcacdccccbdbbcdabcdacdabbcdbdbbdaadbddbdbcbcababbbaddcbaaaababdbccdaabaccdccbcbcdddcbbadbaacdaabbabdcdacdabbbdbbddaadbbcccbbbaadabbcaadcccdcdbdacdaabaddcadacacdccdbbaccbccddccacabadaccaaabadbcdbacbadabaddbbccbcdaacacccaccabbddddcacaacdcdaacacddbcabcdcabbdbcbaaaaacbdcacdbabcaabcbacbddacdacdbaddbcacabcbdcbcbacdbcdabcdcbddbddcbaaadcdbdadcbdcbbcacdaccdbacaacabadcadcccabdcabcaaccdbadadcaaaacbcaadbacacddcbcabdabacdadbacadbaacdbdabcadddccbbccbacaacbadababbbcbcbadadbaacadbcabcdddcccabccdbaabcbccdaccaddcacbbdacccabaacaaabaababddccacbbcbbccadcdcbcabcdabacdbcbadbcdccdaacdddbcbaadddbbddadadcccadddbddbdcbccabdadbcaababacdccdddddadcdaacbcbaacbdcdbabdbaddbdbdccdcddacbdabbbdbbccddaacacacbccbdadadbbaaacdbcddbacbaacccbbbacbaabcaaadcdbcdddccbadacabacbadacacddcbbcbadccbbdacccaaabbaccddcbddddaadbbdabdacdadcccaaaadaccaadddcaacdbcaccbcdbabacdbdaabdcdcccbadacdabddcddcbdacacddcbaadbdacddbabdddabccacdbbaabacacadabbbadbaadbccdadcbbcaddbddacdcbbccbddbadcbabbbcacabbadcbbbdddabcacabccbbbbcdbcbccdcadabbccbbdddbccddddccbcddaacbbcbdbadaaccbccccccdcdbdbacddccaaaaccabadbaacdcdbcbcbbcccaaacddabccbbddddabaaddacacdbbbdadbbbcbccaababbccbbabdaaccacadcdadddbababbcdcdcdaabcaaaadbadbbcaaaddddbbccdccddbdcdbbaccadbababbadcaaadacbadbbdabbaacdbcacbacadcccdabaddabbcbabcadbbdaddcaccaccabcaadabbabcddbdcbbbdadabdccdbbacdcbaabddacadbbcaadbccbdcdabaacbdbdbdbabddcbdbdbabbbdabccacadaabcadcbacabbaaabaddcbbacacbdbbadcbccacacdacdcbbadcccdcbabbddccdbcbbcdacdadabcaaddbddddacddccbdcbbdcaddbadacdadcbdadbdbbcbcbddabadbbabdbcccbcbbbbacacaabaacccabadbdbdcdbbcbbddaadaabdcaaaadccbadadcdcdaccabbdaabcaddbcbabaabbcabcacaddacccbacdccdcaabdacddcbbdddccdddcdaaabaccbadbbdaabddbdbbaaadabbcccdbbdcdaaddcccbaddccabcbabdabbaababdadadcdcbdaacdcacdbdacdbbbadaabcadcabdbdcbbbdbcadaadacabcbcbabdcbdbdabdcbbaacabaadbbabcbaccccbcabbcddabbcbcabbddacbbaddbddaacaddbdcaddddcddbadcdcadbbdadcabbbdbdbdababbabbdbcacdbacaacbcaacdadbcbdcabddbdadabbdbcaadbaabbcddbccaaadacdbadbdaccadbaaadaccbdcacdbdcaadacbcddddabddcbdbdddcbcbbadbbbbaddbcacaabdaddcaacbccddcbaddaddcbdcbaadbdbdbcabdcdcadbabaacbadadbdddcccbbddcdadbcacbbbaabadcacddcbdcbaaaddddaabadbbcbddbcaddbbccddbddcadcabbcbbbcabadbdacacbbbddbabadaccddddcdddbcaddaabbcbcbbccdadcbabaaaaddaccbbdccbbaabdbbcbdbdaddcdbbcabdbcbcbdacdabcccaaccacadacdcbaaddabdbdbbbdabbacbccdadddababbdcdaadddbadbaccbdcbddacbcbcbdaaacdbadbcabaaddddaacadbbbaabdcddcbadccadccdacbadabacdacbcbdbbcabbcddbbcaadbabbdaabdacbcdccccdadddbbccabddabadcddccaddbdabbbadcdbcbbcddbcdcdccdcbbcabbcdabbdbbcacabccddaacbaadbcdbacabcddcddbdbbddcbbccadbacdcddcdacdabcbbbcadbddcbdabddddccdadcccbbcdcadcbccadccaadbbdcdcdcabccaccacaabadcdbcaadbdaccdaddbacbccbcbaccdbdbbddbbcacdcccddcdcbdaaddadadcbcbdcadcabbbcaaacbcdbddadddbdcaabadbbbabccdbadaaccddbaaaabccaaddadcdadaababdbbabccbcbcbbcabdddbdcccacdabaaabdccbcacdcdbbdabbdcccddcbdacdbaadbadcdadaadddcaabcaabccdbddbdbdcdabbaaaadbadcbdddcacbcabbaaccddcbbcaaabcabcbdcbacddcdcacdbacddaacacccdcacbddcbbddbbbdcbcccdbacdabadbbbbcacadddabbdcdcdabbccbbabcabddaabbabbdcbcdaccacbddaadbddbbacbacabdcdcdbbdbacabaadbadadbaadabbcbabccccdaabddcdccccabdbbdddbdaacddccdacbbbbcdbdddddbddacadcacccdbcdaabaacdaabcaddddbabcdcdacdadcbadaacdaccdcddaccaaddaccbbbabacbdbcdddacacdaaabcbabaacbcdbbdbbcbdccadbdbddcddbbaacaadbdcadccdaddcaaccdcbcbaddbadadaacadccdcddcdaccdbdbbdbcacddbddacaccdaddadcbacaadcbbcbadbddddbcaaddaacacdbdcbbcbaadbacadcaaabcddacbbddcadacacdaaaccccdcddbaccbbaadbdaccdccdccbbcbcdbdcacaacbacbddcdcccaddacbaccabdabadbdbdbaacbcbadbaacbcbbddbdcaccdbdbdbcdbdadcadddbdaabdcbdddadabcdcdbdbbacbbadbcbadcbaacabbdccddbbadcbdababbbacaacbddbdaaababacabdcdcdcacbccaaadaadadbdcaacdbaccababcbdbccaddbabadadbabdaacdabcccbcabbbcddacbdaadcdacaddbcdcdcccbadddddbddccababdbcdbcdbbaccbdbbdccaaccaddabacbdcbcbaddcacddadcdcabbccacdbcadbaababbcbabbccdbdddacbcdbdcbacbddbcdaabbdcabaadbababbdcabbcbbdcbbbabdadaacbbcabaadacbcbbccadcbcabdcabbacbacaaaadcdaccdabdddddaabddcccdaadaadcbbbbbdabcaacddcbddddcdddcbadddccbddaabccdadcacaadacadacacbabdbabbbbacccaaccbdacbcbdabacbdcbddaddadaccbccaabbaacbcaaacddcbdbdadbaaccdadcabcadddbdbbadccbdbbdcaadabbbcdcdacccdbaacaacaabdaadddcaadaaddacaadacabddcddcadadadcbdcdddbddacdbcdadcccdccbcaaaacabdcbabadddcbaadbbaddcbbacbdbadccacadaacdddbbacddddcddcdcdbccacbbdcabdcbdaabadabadbdcadbddaaccdccbbcadacbadcadbbcadaddadccbccbdaadaacddacbccbcbdbdbaddbcadbcaaaabcdaabacbccbdabbbacdacbbcabccdbadbdccdddddcbddddadabdaacacbddccadaaaaabbadbcdaacabaacddbcbabcdbdddbbabdbdbbaaacbaaccbcdbdacbcacddddacbcacdccbdbdaddacbddbdcdaaabbcbdaacacaabaccababcddcccbbcdbbdbbbdababdcbcddbddadabdacadaabcbabbcacbbadcddcdadbcaabdbddddddcaaccdcabbbadacacaccbadbcacdaacbcbcaaacbdaadaacdcddaddbabadddaacdcdcdccabbbcadbabdbdacacacabcdcbcacbbdcdccccadabccbdbbdcaabacadaadddddabbcacbcdddcbbadcccaaddacbcdccdcacdacdbaaccdaadcbcacdaddabdbdbcdaddbdcadacadbbaadbcabbdbcacbddcbaabddbccdcbabdddddbddccabdadcdbcdabdbccacabaabcaacacdaccbbbbabbcaddbbcaadbcdcbbdcbcacdcabcdbbbdddbabcbcccbddddcadacbcabbbdbcbcdcdaccbdbddaccbcaddbcbbcdddabcdccddacbbbddcddbcabbbccaddcddbacbaabcbdbcbbbbbbbacccdddbaccbddadaccdbbdbdadbdcabdccdddcadcbcabbaccdbccbbdbcaaadaddcbaaaabddcabcabdddacdabdddddbbbbacaaaabcdacbccbadddbaaddbaddcbdcddcaadcbcaadbccbcccbddcbdaccadbcdbdcdcbaddcbadbddbcaccacbcbcaccbdacadcadcbdcdbcbaaddaabcddabdaaaabbbacadabbcccdaddaadcbbdadddbbcbaaabacbaddbaabccabbcccbcbbbdbaadaaaccaaabcbbcbbacdbddbaabbabdccaadbddacaabdcacbddadddaadaccbcbcaabdccbbadcaabcabbdadcaabbdbcdbababbbdacbddaaddcadbbcaccabdabdbdccaacaadbcabdabadacbbcadcbbdbaabcdccddcbbbdaabcaadacddcadcdbbbcaabcbbdadbdacdcddbbdcacacabcaddbbadcaccbbcccbacccccadacabacbbdcaccdcabababcddccbadbdddacdcbbdbcbccabaaccaaddbcbddacadbddcbadbdcadbbdbbdbaabbbccacbbddaddabdccabadbadaaccdcadbccbddbdddbbddabccadbcababaabbbdadaaddddadddabaacbbddadbacbdbdcabadbaadacccacccdcbdadadbabbbadbdbcdcaabccccbddcbcbcdbcccaabaaccdbdbbabbabaaaadaddcdcadcbacdaacaddbbadcddaaaddabaddbbaccabaaacbdcdddbadcddacbbdddddbdacaddcabbdbbabcabdcacbadbddadccdbbdadcccbbbbcdcbcaaabadddddbddaadcbacbabdccbdabbcaabcccadcddbadcacbddbddcbdbddacbaccaabcdccbddcadcbbbbddbddccadaacacacccaabcacacbabacdaaaadbcadacccabddaadacabaccdcdaaabacbacdcccdabdaccacbdccbcbdacccbcbbcabadbabcbbaccacccdaddccbbbdbbdaccacaabcddbbcbcababcbcbababdbbdbccaccdcacdabaabcbbdcbcbcbaddcdaccbddacccbcdaadcbbbaccbcdcabcbdabbcbbbccdcddbcddabdcabccbddaaabcbbccdbdadbbdbcbdbddadbbbcdaccabdcddadbadbdbabbbbadcbdbcdbaaaccccddbdacbbaadacbacacacbddbbabacaadaddcbcbabcaababbdbbbdcabadbadbcbaabaabcbbdaccbcddddbadacabbddddbbbbbbcbccabaabacdabaaabbcddcdbdbbbcbdbbacacdcbabdcdcddbcbddcdbabcbccccccdcdaaadbbdbcaaaaacbabbadabbaccccddaacaadaccbbadbddbaaddccbdaccbbdabcbacbaabcdadadbadadbdcadbdbcacdadacbbdbabdacbaddaadccddcdcddcccdaacbbcdcbbacdcabdbbaaabccadacdbbaabddbbadbcccbbbacacacdcbddcdbcdcdbcdbaaababddcddcbcdbaabccddbddbccbaccdbdbacdcbbacbcddadadcdccddaaacadcacbdcaddccdbcbbbdcbdabacadbcabcabbcdddabcbbbadcdcbccdbadaabacdbdacdaadddcbdcdccabbbdbabcadaacaabdabaccbacadbbadbcdbdccabcadaacdaadadbcdcbdcbdcdccacbdbbdabcaaacdadcadcabcddcbadbcbcbaacbcabccccddbaaccdacbddddbbccddbbcdddbccaadaaabcbaacbcdadbabbbbaacaadbbadaccbcddacaaabdccccbaddabdaddbacbaaabbbacbcccbbcacdaaadaaccdbcbcacbcaadcacdccbdbbddbdcddcdbaaabbbadbaaddbbdbaadcabdcdcdaabddbbdcdaadcaabcadbdbcbadcdcdccdcbaccaacccaddbccbbacacdacbdcbbbbaaaacdabaacababdaaaaaddbadbbcabbcddcbacddacbcbadabcbacdaccdcbaacbadddbcddccadbdcbcdcbcbacdcdccbdbbbadbaddddddabddbdcdaacbbdabdbbdbdcabcabcacbddaabbcacdbdbaaaacccaadcbdbccdbbbddcacdbcdccdbabacddbabdddaccbcabcbaddcdacdbbaabadcacdcbaddaaddaccdcbdddcbbabdddabdddaddadbbcadaccaadcdcadbdabdaaccaadadbbcbddaabaccbacabdccdbdbabacbaaaadbacccacadcbbcbdbccbcdabcbbacdacdccbabdabdaaaabdccccdcaabcdcbdcbaaaabcdbbaadaddabddadcadcbcaabdbcddcdabcdabcddcbbccbbdacdcacdcdcaadcccbdbaccbbdaddbcbcacadbcadbddadcddcdcaaaccbdadaaacadbdcddaacdbbddcabdcabcdbabddbccbdaaddccbabdaaabcbccbabdadabbacadbbadcdbbbcddccbbddbcdccdbbabadcccaacaaddadcadaacccaaaaaddacbbbcabcccbaabdaacddacadabbdacdabaaccdaadbbbbcbabdabdbcaddbaabcabddbbbbdcaccadcddcdcdcdabcbbbabdadcdbdbccabbccbaacbbcdabdadcddcdabcbadacbdcccccdbabcbcaddbdbddbbdcbcdbaabcbccabbdbaacaaacdbbbacbbcdcadacaabbdcaadaacacdabbadcbbaabaababcbaababcbabadaadaabbcbccaadddbcadbcbcdccbcdbcaddbdddcdcdcbccdcdcbbacdcbdbddabcbcaddbcaacaadbcbbcccccdcbaabddcbabdbbbadcdcdbbcbacddccdbabbabdabbcaddcccbabdadbaccaccccdbdaadcabbcccabacddaccabbcdacdcbbcaddadbdbabaaddaabdbadacaccdddcdbaacbdadbbbabadcbabcdaaacbdababaadbaddcbcbbdbdadcddcabccbcaddbcbbccccdbccdaddaccbbcdbaaccacaaaccbbdcbbbbbacdcbdbbadcdadcdbdbaacbdbbcddcddcaddbddbadacbbdbdbacbacaacdacbdcccbadcccaaacadcbadcddacdabcdaccbbdcddbcaacddbbdcbcabcbdbabdbbbcbddabdabadbbdbbbacddddcdadbaabdacdbbdbbbacaccadddadabbbcdbdadbbbbbabbacddcdaccbccddaacbcaacaacdadccbabbabccbacadcaadccdbccacbadccbacdbccdbdcbdaaddcbcbdcabdbbddaadbdacbcabdaddbbacbdddacddbccbcbdbcacacabdccdabbaaaabcabadbbdbbbaddaddcbaadaadaabbadbabdddbbbaddabcccdadacbbcbbabbcbababbbbbabdcbabacacabdbadbdbadbaabdbcaaacbbcdcaaddbdbbdcbadaabccbaaccadbddccaccdacbdbbabcbbdcadaddaabcddaddcabbcacdbadbaacdcbcdabcdbdcdcbdabccdbddaaabdbdbabbdcbdcddccdbdaaacadabcabccbbcdcdcbcdaaddacbaacdaaacbaddcbabdccbaddaacdcabdcabcdcabadadccaadacdbcbdbcabddbbbcbcdadaddbbaabcbdbcdbabdaabacbccddbaaaccddbbdabbdbdaaacdacbaccdbbbddddbaabbddbccdbadddccaddcbacddaaddcacadcaacbcdddabccbaadbbbaabcacbcabccacccbbccdcadbcadccdbcdbaacdcbcdbdcdadbdccabadbdbacdbdabddccabaddacabaabcaddcacaaadabbbaccdccbbacbcaadcabaabdaaaacacacccbdcbadddcbbbcdbadcbbaddccbbabddaccaaccbbbbacdcdaaadadbbbcbddcdcadaaaddccabdbccbddcbcacdcdcdcddacdbbdcbcdcabdababddcddcdddcdcabccddccbbccbbbbcbbcdbcbacbcbcbcdabdbdbdbcddcdacbdadaddccbdbcdaabaabdcabddcabaadabccdadbcbaacdcdcccbddaccddbcdddbbdcbbacbcaddabaadabbdbcdaaabadcbbcdabaddddbdbccadadababcbcbbcdababddcbdbaaabaaacaddddbaaacdcabdbdbbdbddccabbbacdbabccbcccddbdcbcdcdabcddbcbcbcadacdaddcbabcbdcadcbbcabbccdbcddccddcddccadaccdabdbbbdabbbacbbbdbaadbbadcabbababbbbadbccdbadcdbabccddbaaaaddacbdbccabbaddadabbabcdabcaadbbdcbabcccaaaabaaacbbbcbbbbcbcccddccbbaadcadbdbbdccbcbdcacadadcacbcbcdcdabcdbabdbdbccbbbdcbaccbbdddaccddccbcaabbdcbbbbdcbbdbcddacbadbbadbbcabdacbbdddacbddabcbcaacddbddbabbbbabbdcdcbbaaacbabcbddcadabadcadbdabcdbaccacaccccbbddddbcaddcddbacdabaaadaabdabbbadaaddcacbabacbcaacddddbbdbbdcbbaaabdbcabdbcdcbbdadabbbdccccdcccbaaadbbabdcadccaabbccdcdaabbbaacaddaddbdbbcaadbcbaabbdcbcbacaccbcbcadcababdbadaacdbbbaadbbdccdbdaacbacaadacacbacbddcbacabdbbbbaaddddcaaaaaadcdbcbacbccaddccbcbddbaaadbababdbcaabbabbbdcbabcdccacdabcbdbbcaacddabdcaacadbbabaadbaaddcabddbbdaadadcdcbbcdacdddbdcbcbadcccdcccddbddcdbaacdcabaacbdcacbabddcaddbddbbabccccdccddcddaabcddaccabadbcddddadbbccacbaacddcabcdcababaacdddddaabcccddcaabadbdccadcabbabbdbbcddccdadcabbaaabdcbbbbbacbbbdcbababdbdabcbcdadbddabcdaddbaaccaabdcdcccabbbcacddbcbbcbcdcbcaadacabcabbccaacbdbcdcbaaacdcacbdaacdddbcbccdbaabddaddcadaddbaabbcddccabdbcdbbaabcacbdbdacddacaabaababcbaadadacdabbbcdddadacdbcccbaaabdacabccbbdcaadcbcdbcacbdbabbddbacaaadaabcdabacdbabddcdcddcdabadddddbbadcccbdcdbbbacbddabdddacddccbddadcbdcadcdbacdcbcbcbaabcaabccdcccabdacaadbdbbddcaaabdccdcadddcadcddcdbabcdcacbaabbcadddbcdbaccababbaaccccbbdcaadacacdacdadddbcdbcbacbcdaabbadccabdbddcbbabbdbaddbcabdddadcdacbabcdddddcbbbcdabaccdddcadbcadbcdacaccddddcbccaadcacccadbbcdabdbdaddadacacbbbcbcaacccbbdccaddaabdbdcdadadacacdcbdaddbdcbbdaddbacdaadaccaccbcabcabcacacacaaabacdccbcdccbcdccaddbcadcadbadcdabdbcbbccccbadcacddddbddccaadccbbabcaddadbaaacddabaacdcaadbdddacadbcdbddacddaacdbcacbdacbaaaaacabbcaccbdaaabdbcdaddbbdbddcdcddaacdddcacdaacddabdbadadddccadcbdcdbaacadcbcbaadddcbccbabdddacabdbbacdcbdaccdcccbcdcdddadadaabaacabbdaacacdbcdcaacdbaabcddddcdadbdaccabbcababdcaddccdcdbcacbcbcabcadbcaacbddbcbbbbcdbddcbcdbbbdaccaacadbddaaccdcbacdcdbbabacaacddcbdccbdcccccacbcdadabcabdcbbcbccdcddbdaaabdcbccdabbabccaadabbabdcbddcdcbabdcaabcadadabbbcabacddcddbcacdabcabbcabdadbbddcadbacbcabdcacaacacdddbddbacbbdbdabaaaadbacabbababbccbdbabdaabbccabbacccabaacdaaddcddddaccacdbcadcbaccadbddacaadcbdbcdacacabcccaddcabadbbcbabccdbdcdccbcdbdabdaccdaaccdcacbbabcbabccbdbdacbbbccaaaaddbbbdaddcddbbacddbacdccdaaacabbcbcccdabaddaabaabcadacabbadbadacdbdaabcdccadaccabbcdcaaccaccbbaaadabbbbbbaacbdcaacdcbccabadcabaccadbcbcbdbdadccbcddacdcddcbcdcabdddbaddccacbabbddbbbaacdcbccdabdacbcacdcdabbdbdabdbaaabdbadccdccbbdccbcddccacabbbbaccbdaaaabbdbddbdaadbdcdcdabcaccbacaaddbbababbcdacbbdaacbcddbcddabbaddddbccaddddbcbbbbdacdbcdbbabcbcdcbbadddbdcabbbbdbccdcccacdadbcdbccdddabcaccbcbdbcdccddbbcbacdbaabbbdaaacbbccdacddadbbbbccabadddadbabcabbbdbcbababacbaaaaccddadadaaadbdcccddabcdbdcbabbddabcbccbddbadabcacaddadbbacdbcdcdbaddbadcbbbcaadccabbaabbdddbccbcbbacdabbaddaaabaccccdadcdbccccddbdabdcbbcabcbbddcabdbdbadcbbbccaccaddcbaccdcdaabbabaabaddcbbcbcabaabdbaacadbccabbdabcdcdcbbccccaacdddaccacbcdcbdbadbacacccddbccdbcdccccdbdbabdbbdddaacdabdcccbccbbadcbadbdcbbcbddcaaccccbccaccdaddadacbdcdabaddcdccabbccaccdacadacadcaacbcaddbccdaccdccbdabdcbdadadddbbdddcaacaaacbdacaaaddbbdadbabaaabcddbadacbbcdaadcbabacaaadacdacbccddbbccbbccbabbacaabacbacccbbbcaadcbcdaacaadbdaaabccbbbacdaadbcbbabaadbcdbcabdaaaabcdbcabcbdcacdccadbdabcabdbbcababcdcdacacabacbcdbdcbadadadbccddbcbababdcbdcaadcadcccbbbbbabcabbbdcadaabcdcadbabbdadcacadcbdbbaababcbadaccdccdaaadbbadbdacbddbddbbcbdbddbcccaccabcbbadccbcacdccbaccdcbbbccadbddddbdcdcbddcdadcdbddabcbacaadccccadcbbbadcbadbdbabdbcbacdaadddddccaacaccbadbabdccbddccddcbcadbcdbbacbcddaabaadaadabddabadcddacbdadbabbcdbcbcaaddbbbbcbbdabdbaadaccdbbdacbbddacbccbbbcadcbcbdaaddababbcdaabcaaaaacdaddddddabccbbbaadcadcbabdbbadacbdadbddaadcddccadaccadcdccacdadcbdccbaadcbbdbbbadcacdbddaccbcbaddbabbaaadbdaaadaaaddadaacbdabbddcaabadbdccacccdcbddccdcbccbaababbdbdccbbcbbbddddcabcddbddddabccbcdcdaaabdadbbaaddbdaaaacaacadcdacbccbbaccacbbadbdbbccacccadddadabcabdcdddcdbbbccbbcabdacabbcaabacadacbbbabcccbdaacaabccdbadadcbacadddccdacaadbcaddabaadcdccdbadbacdbbcaabbaddaccaaaccdaccdaabadcbbacbdaaabbcabcdccddcadacdddcacdccddaadbdcbcdbadccaddbdaaacbbacadbabbbbbcdaddcddddbaccbdcabbbdccdbabcdadbabdacbaacaabcccaaddaacbbbdcaacbbbbbbcccccaabacbcbdcbdcdbbaccaabaccabbbcbaadbaaacdaaaaabccabcacacacdabadcccadaaaddbbdbdcaddbccaaaadddbcaabdbabcabcccbbcacabcacbacccbdbbaccdddaacdadaaaacdadbdcbcbccadabccdbcbdcdcbccaadcacadcabdccddaaaacbadcccaddddbadaaabaccbadabbbdaccccbdbcdadddabcbcddabdcbacdccdabbacadbdbccadaabdbaaabbdbcacdcdbbacdcbbcbaaaaaadabcacbaacdcddbcdaccdddbccabdbccdcdcdcaddbacacbcabcddccdaddabcbbdaaccccdabdbaccdcbcabacbaabcbacacadaabcabdbbaccbbdcdccbdcdcdadccdbabbcbbcaccacacdadadcabbcacccdbcbcdddccdbddcbdaccddbabadddbaaaccbcbbcdccadacdcdbabbaaacdaadccdccddbaacddaadcdcdbdacaacdbbcdbcddcdcdadbdabdbbcabdaaaddcdcadddbbdbcaadcdabccdcdddccdbbdbcdccdcacaaaaadddabbbabbbdbadbadcbbadbabdcddcabdccabacddcdbbcccdcdcccaadaddbcbddcbdddbdadbbdbdbbbdcdbcabaddcbbdacbdcbdaaabaabbacaccadaadcbbdcbcdacdbcaaacaccdcdccdbddaacdbaadadddbabbadcadbadbcdbaddaacaadcdccdbbaccaccdbbbdaabdcaacaabdaccacbbaaddaadcccabcdcadcbbadbbaaaccbcdcabacaaaaddbbbdbdddddbadbbcaacbbdabbaadcaabbbdbacaadabdbbcccbdcbaacaccdbcabcccdcaacdaaabcdcbaabdbabcddbdbaabbaaaabcacdabcddddcbabdcdabbcbabcdbdbacadacacccdcacabcaacbdbbaccabdbcbcaaaaadbababbadbbbacddcbccddddacccccdbadbddcbbdaaadaccdadacbcacacbdddcaaaaccddbbdcbddcbcdbbbcdaddabdbbdbdbcbaddbddddcbddbacbaabddadbbcbdcbcdbdcbadbabcdbcdaadcbacdadbaaadaadbdddbadbaadcacddadbbdcbdcaddadcacbabbcacdbccbbaadbbabdbcdcbcaabdbadbdcddbdbcbcddcabddccdbbaaddbcbddccacbaddddcbcdabdbccccbabddacdcbccbdddaccacadcddabacbbddcddbcabcabddcbcccacdddcaacabaabacbbaacdcadbdaacbcdcbcdcdaabacabacabababccaaccbbaadbaccaccbabacbdbdccdacadcdababccaacdabcdcaadadccbabdacdabccdacdaaadbbdcaddddaabdcccabdbddcaabcbdcbdcabadaddbadbabdbcacbaaaadbdccacddacacbbdcbccbbbccbabbbcaaaddbbcddbacbabbcacaabadbcdbabbddcdbcaadadaccbabbddccbccccccddabddcdcdbacbaccaadaaabcabaccbabbdbdcaccadddacabbbdcdbaaaabacaaddcbbdbdccbdcbbddccbdbabbccbdabdaacadccdbcbdaacbdabccacbabbbadabcbadcbbacadcdbadcaccbcddbbaccdaaadadaddcabccbdcacdddddcdcaccbdadcaccabaaacccbbcbdacabbcadbdbdcabbbaacabcccbdcdccadcacddacadbbcdbdcbaacccabdbabadcaadccbdccabbbaccbcddcaddbaabccbaddadbcdccccbbccacbbccbcabbcacdcccaccadcdabdbbbacbcadbdbcccabadcdbadadddddcbdbacacdbddbbbdadccabdccbacdccdccbdbbcabcabdcccbbbaacbcdaabcbdbbaadcadbcaddabbadcbbcabcdadcbccbddbaadbaccbccddbbcdcaccdddcbddccdddaadbccacacdaddccacccdabcabaccbbcdcbcbcaadcdbabbbcaadbbcaddcdcbbbddaaadaaacbabadadccacbbdacbaacbdacbbbbadcaacccdbadaabcddaccacbcbccadacddcdcbcccbdbbaadbbbaababdccabadbacbdbbddaaacddcbcdbbdaabbddcacbccdcaacacbbcbbdbbbdbbadddbdaacdbaaaaacabaabbbdcdacabdcccbabcaadccdbdaaacdddabdbdbbadcabccadbbcaddcabbcdbcdacdcaabdbaddadcbbdcbcdccadcbccbcbdcadbdacaaadaddccbcaabaacbbabaaadcdcbcdcbcbcbcbdcbccaccbcccdbdcdbccacbbcdbdcbcbabdbbacbabacadbabbcabccdcbbdcbbcbcdcbbbacbbbcaaadacbaccdcdbcddbbdcdbccdbbdcdabdbbdccddbdbcdabacccdbccdcaabbaadddadcbacdadabdddcbabaabdcccccbcddaacdddacdddcaadbdbcbbdaadbdabbadcdaabaaadbabdadcccbddbbbbadbbadcadbbacdbbbccacddabdabcacadaaaccbdcdcddccbbdcbacdaaadbaaccdaabacddcdaacbaddbaaaaacddcbcdbcdbddddaaccdcbadbdcabcdbcbbdacacbbadcabababddaadbcaddddbbacbabdcccbaccbcdaaccdbcadbbabbdbdccaaaacdcaddacacaabdcabdacdbababaccaacdaabcbcaadbbdabaaaadbcbabccdaddbbdcdbbccadbbbdddbcaddbabcdcbccccbcbbcacadcbcabcdacacbbacdbdadbbaddbaadcdcdacbbcbaccdbddbdcbcbaaddcccddbdbbddabdccbabbdabdbbdcddaabaabdcdacbdccbdcabaddddbbabadcbbadaaccdacddacdcddbbcdcdbbccbbdccdbccdccbadddcacacddccaccacbdbaaddcddcdbcadaaddcbdcddcaddacbbbadbbbadbacccadabbdabacacbcabdbbcbadaaadbbaabdadacdccdccdabbdadacbccddcbdadacdbcdbabdacbacaadcadabbcbdadabbaaaabccdcdccaacaabcccdbcdadadcacaabacddbdcbddacbcbcbbcbccadbddadbbdbdddccccaadddcbbbcdbdcacdaadbacdabccadbcdbacbdcccbbcdadacadacdaaccdacbaaabddacbcdbdcaddaabcccabcaacbcdbbddaabbbcdaabbabbdddcdbabcbbcbabdadababaddbbbcbcadcbdaaccbddbabbabdbbadabdbbbccbdcaccadcbbabdacdbbadbdbdccbddbddadbadacbbccbddbaacddddcacddbdcaccaabbccccbbbbcaccabcdbbcabcbdbccbadacbcdabccddcddbbccbbdacdcaacababbaadcbbabdbcadcbbbcbbbbcbadbacaaaacbbcccbbdabadcbdaadaadccddabcdcbccbcadbdcaacdabcaabaccbadddbbccbadbdaccddbbabcbcbcddbbcabdccadacdbadbcaacbccdcabdcdbddacbbadcddcbbcbcdbbdcddcaabcdbcacdccddbaababadaaaabbdbcbddcadadcaadbadbcbccbbccacbbccccdbdbdbcadbcacddbddcabccaddccccacdaaaddcacacddbacbdbaaadadbaabaabacccdcdcdadcbdabbbbadaacdcbcacdadcdbbacdadcdbcdbbacadcacaaacbdcbcbdcddbabbabbabacacdcbbdddcacdbccbaaccccadaacdccddcbdcdbcadcbdbabccbccddaddddcadaaabbdabdcbbabadabdadbdddaabbcdddbcacdcadbadaaccabcbcbbdbdcbbadbdbbbcabbacbddacbdccbbbdbcaabbdacbdccccdcadbcbbbbbadaadccdddccdbdcbbacbaaccacdacbcdcccacbbadbdcbddbcdbcacbcbcaddbbbadcabcacacabdcaaadcddcbaaabcbbcabbbadcabadaacbbbdbbbadadcddaccccadaabacbcaccaccaabcddaacbbddbcadacaacddaacdcadcbdbcdcbcdbadddcaccbbbcbbcdbabbbcbdbbbdbdcbbcacaddccadcdcdbcbcbbdbaaaaabbdddcaddaacdbcbbcbcbaadccbdbdcadbaaaabcaadabcdbbbbaadacdadbcbadddbddcbddddccddcadacdbcacdcbabcbabbaccdbbcdbbadbbaaabbdbbcdaadcbcbaacdbaadadbaacdaadbdadacbdbdaaddcadbdabdcddddcbcdaaaccabdabcbbdacbaaadadbadccbcbadabacbdacccacbdbaaadadacbdaccbdacbdbdabdbcbbdcbbadbaaabadbcdbcbcadddbcbdddddbbcacabcbcacdccadbcbbbcabdbdabcbdacdccaabbbadacbaadaaddbacdbdddbdbabdbbaddddbacaccdbdccdadcddddddbaadbbcbcbccaadccdcbadcccabbcbccadacabcacdbdccbcdabbadbcbcacdadbddcbbacccbcacccabdcbbcbbababbaaddcdccbddbacddacbbcccbabccccabacbccbcbdcabcdbbbddcdcaabadddacdcddaccadcbbdaaddaddbdccabaaacbdcaacccbccbccbcdabcbcdbababccbabbddbbcbacdbbddbdbbdccbbccbbaccddbbcaddcbcdadadaacdbcaabbdddbccbcdcddadcbdabdbbbdabdbdcbacdcddbcdbbcdcabbbdccacabcdccacacaaadaadddcccadcaaccdadcdabcaabddacbacdccacdacddacabdbbbddadcccaaacacacdacbddcacdaaadadacbbaabaacbbdccbbbbcbbccdcaaddaaabababcbdddaadcbbadbdacacdbacbaabcacaacadccccccbdadbccbdacddadccbbdcdccbdbcaddcdabbcacccbcddcbaaacddcbcaddcbdbabadddcddccdccbbabdddacabaabbaaadabadadabbcabbbdaddaaddccdaccbbcdbacdaacaaddadbcbbcdbdcbcacbdddbbbdbcdcbcdcdcacbcbcdcacababacccdacaacbcbaccccbdaadbbaadcbaabaadaacbadbadcdacaabcbbbdbbcdabbdbadcccaaaabababcddbacabbaabaadabddbabcbacacbbcbcabadbaaacdccddcbbbcababbabaddcdabaadcbabcacbbdbcdbbdbdaccccddbdddccaabbdbcbdcadaacaadbccdccaacacbbbdcbaadddbdbadccbdccbcadadadaabcdcbabcbdadccdbabcdccaccbddbbaddcdbbdccacbacbcbcbaacccbbcbabacbdaccdcdcbdcbbcacbacbdbbdaacbddacbbcbadbdcbdbbbdbbbddcdadababaabcbdcddccdcabdbcddcabbabaddcbadbadaaadcdbdbbcaddaabdacddcacbbaacadcdadacaddcaacdbddbcadcaacabdadcdabccbcccbcddadccbbaccdadccabbdbabddbadcdbbacdaabdbadbcacabbccccbacabcdbccbcdbdcabddbccbaadcddaccbdabccaacabacadabccbadabbcabbbaddcccdcdcdcddddbadcddbbabdddddbbdcbbcbcdbbcbabccccacdaadacdcddacbddddcbcaaadcdcbcbcadadadaadbbdaaadbcdcabacbcaabbbcdcaaadacadbccbdaaabcaabbdadabbabdccbdbabcabacbaabdccaadbcadcddddcdaadbdadbdcddcaaccbbadcadbcbbcdaacdbdadbdaacbcdbcccbbbbcbcdbaadaddddaccccbadccdccbcaadbaaddaddccddbdcdbdddbbadddbbccbddbdcbbddcdcbdcdacbcddbbcdabcbaddddccdaddcbbabdcddaacccabbdcabcbddddbbccdcbbccddbcbcdbcdaccdccbaaacddadbbbcdddcdaacbcabacddabcdcacacbccdabaccacccabcbcadcabbaaddcbdbdbabadbdddaabcbbcadaababcbcaaccaabaaddbbbcaadaaadcacdddcabdadaddaaacdbbacccbdbcbaaacdccaaaccccdbbabcdbdabdacadbdddbbddabaacdbbdabcbbbdacbdaccababcbbcacdbdbadcbdcbacadaaccbccabddaaadbdacacbbbadaadbdddaddbdcabbabcddaccddbbcbcdbabcbcbabbabdccbadadacaacbdaaacdadbbdccdbbcadababbdbbdbbbcaadabbbaadababccbcabddbacadbbdabbdbbbaadbdccbabddcddcadbddcacbdbaaccccbabbdcbbcdbcabccdbbabccaabbaacdddacaccbcdcbccaacaaadabcdadccdbabcdabddbccbcbbddabaccdbbadadabbccddccaccadcccbacbcdaaccdabbbccdcabcddbccbdbabbcbbcccddddaaccdaabaddcaacacaccabcdccdbccbccbcbacdbcdcacdadddcadcaaaaadcdccbcbadcabdbaddacbadddaadadddbcbaacacdcbdababadbaaaabbccbcbccaaccbccdcdcacdbcbdaddcadcbcdbbaadbcddaacbcdcbddbdccccadacdabdbddcbbbdcadcbcbbcdabbdbacbaaadcbcabadbcacaadcabcdbaccdddaabbcbccbbbcdbcdcbaaabaabaaababaaaddbabdaaaabaabbdaaaaaabadbcdbbcdddacdcdcccdacdcdbbacabbccbaccccdaadbdddbbbdbdbdcbacaacaabbaaddaacabdcbddaaddddbcbbabaddccbcbcacbdddccddbadcdddadbdbbdcabcaaadcacdbbbcbccccbddbcdbdcadddcbbbbbbdccbcbdaaaaadaaacbcbacbbccbcaddbaaaabdbcabcbaabccabcdccdccddcacbbadbdcabacabbcbcacacaddaacaadccabddddbccddabcddddccadadcacbacadacdcacbacbbacccaabacdcadabcdcbcacbddddacbddadbbccaddacbccdbccdcadcaacdddcbbddadddcdbbbdbccbdbcbcdacadbbcdadbbdddbacdbddbcacaabdbbbddbcacdbbbdddabbccbdcbcdddacbdadbbbcbcccbdadbbbdcadcccaaadccadaacdbbdcbdaddcbdabcbbbdbdbccbcabddbcdcbcccabbcaaccaacadabacbbdcdccbbcacbcabdbaabaddaccadabbaabcccacdcddaacbbbbbabdcabbdbdbdadcdcbcccdaccaabacbbabcddabcccacddacdcacdddcabbdaccaadbbdaadacdabdbcdddadacbdaadaaabdcdbcacdcbcdbbbdaadcccbdcabcaaaaababbcaaacdbcccdaabdbcabaadcddbaacccdbdbaacccdadcdaadcdccccdaaddacbdabcbadacbaddcacadacdbcbabaccdccacddcdccdbcdbaccbaacbbbdbbcbaaabaadccdcbcadbaaaacdbbbadabcaabaddcbbacaadcbcdccadacdabdbcddcbcbbcdbccccbdaabcaccbdbababadacabccbadadddabaabcaabbcccbbcbaaddadbbbaaabdcbaaaccdcddabababccaccbabddbcaaaaabbcacdcbbabaabcbadadacbcbcaabcbaddbabcddddcdcdabcdbcaadbabbbbbccdccbcbbdcddddbbabbcdadbddabdccdbbdccadddbddbccdbabddbbcdacacccbadbababbbacdcaccadccacabbaadddaadbcbbacdddaacccbcbaadddcbadbcdddbbadbdbcbdaabccccbcbdcbcbadbcacdbdaabbcdaccadcbbbddbcbbacccbdbcbcbabbbdadddaadaadaabbdabbbabcacbabddbbacddcdaadbcaacbdbbaddbddcdbcdabbacaaccaddcbdaaadbdbadcdcacbbcccdbdbdcddaddcdaabadbbadbddadcbdaacbbddddcacaabadbcdabdbbdcacbccbaaadbbaccadbcbddbdabccaabcbbdbcacbdcdcdaabdbacbaaabdbbdccdaacbacaaabadbbdccdabaadccacddbcaacbdcabacaccdcdcddabbbcdcababdbabdbdddcddbbdabbbcaaaddaabbbddbcadacdaadabcbaccdbbcdbbcabbbabaccbcbaaaddbdcccdcddcacbbccbcdcabdbbabccccdddccdcadbdcaadadaadcdccabbcdcbbadadadcacacabcadabdcbbacaacadcabddabdbbbddccbbacbbcbadadccccaacaddaabbccdcacbdbbcdadcbbcbadbbacddbbcdabacbddddabcadacddcabbbccdbacbabcccadcbacbdccacdddcdcdbbadcacabaaadcadadacbcdbcbacaccddacdaadaaaabcccdabaacdcdcbcadcccccbabbbcbdbcacacbdbaabacabbaadadcccddabccbaabdbabdadadcbcacbcaaacabadadaaacadabddbccbbdacccbbdcaaacddcababcdbccaaacbbaaabcadcdcbcaccddbadcdcadaaaabcddbcbabacdaabbadddbdcaccdbbaaabcbadcabdabbaabcadabdababdcbddcdababbabcdbdddbdabadcbdbaaadbdbaccbcddbcddabbcaccadbdaaabccddbcbabdbcddbbbcbdaabcaaacdccbcbbbcabbbbbccabbcadcddbccbaacbcbdacdccddcaddddccaacbcaddcaadbbcdbaadcacacdaccbdbacddabadacabdaccacadcdddbaaaabadbacccbcbcaddaccadbcbdabcabdacacbaacbaddabbcbdbaadcdbbacbbdabdcacaabbddbdcbbaccbddbccbbcabdbdababdaccdacddcaabcbccddacbbcaaacacbccdaacabaaabddbcadbdbaaaddddabdaaaccbdaaaadbdcbadbdbdabddcacabdbcbbdcbdaabbaccddcabdcbcabccdbaadbaccbdaddccabcabccdccbbaadcbbdcaccbabddccaabbcdaacdbbddbacbbbabcbddacdcdccccacbdabbdabbbdcdbddcbdacccbddcdbdabbbcbcdaacaddabdaaadbdbbadacddbccdccbdccbcbaccbbabcdcdddbcadbddddaddccdcdcacaacdbccbcdbcbdaadaaddaacaaacaaabaaccacbcaabbdbcbddaaaabbdadbccaccbcdbdaaacdbdaaccdccaaaadaacdaddbbaacbdcdccbacdcadadcbbccaacdaabddbadabbdacbbbbccbdbbaabbdbdaddcdabcdcabaaabddcdacaccaaabcdbcaadbadcacbcdddcabdabcdadcccaacaaabcabcabccdddaaddcbbaaccbaccbdbdbaabccdbdbdabbcdcdcdcabadaabbadacabcaaacccbbcdbbcbbacdabaabbacdcbbabacdcadacabaaaabbbbdbdbadbdadcabbccbdcacbdcbdaccbcbbcdabcdabcbbdcacbdddbcbdcadabcaaadacbddcbcbabbdbccabcbbadadacaaabbabbadcdabbdbcbabcdabaadcabaddadadacdbcacaddddccbdbcadcaacabdabcbbdcdbbcbbdcdcdadacdadcddccbacadadcbdacbcdcdcacacabdbbcdccbcddbbaaacbbaccbbbcbcaaadbacbcaaacacabccbadcbcdacccaabbdbddaccadabbbbbbcdaaccddcdcadddabbbcdacddddadbadaaaabccdbbcbddcddcbbcaadcadccdcacdccdcbcdddcadcbcbdcadddbadaccddddbaddadaccabacaacdaaaddbdcadccbcabccacdbbdaaaacdacbddbabbbbbddcdaabbcadbbcbcabaccddabddbddcacadacdddcabbdcddbcaacdcbdcbcdbdcbdccaabbcdcdaddcdcbacbcccdaacbcacbbabdcddddadbbbcbccdcabdddcdbddbabcabdaccabdbabbcbabbbdacccacaacbbcbcbbbaaacbadbdcbdcdcbccabbabbaaaadddbdbcbbdbdadcbaacacdbaadaccadabbaaadcdcdbddbbbaaadbdaabddcaabcbbcbddcccaadbdddddabbacdddcbdcdcdcaaaabccbdbacbcabcbcdcdbccddbbcbcdabadcbaadbdbdbabbabccddaccaaddbaadbabcabaccbccabbadcdccdbbdbdacacdccdabdabcdacccaddbbbacbdbbdccacaacdaacadbaaaaaddbbbaadbbdbcddadbdbacadcaddadbddacccadacdcbcaaaacaddcbaaddddddbbaacadbddbbbdabbbddadaaaabaaddbcbcaadbbdbaaaabbdabbacccacdbbdbcbdabbbbbacbdcacabbdcbadcbaabbbcaddadadbbbcbcbdbacdcabdccdbcadcbbdbabcadaccacaaaabccdcdbcbdcadabdacaccabbbccdccdbacbdcaccacbcbccccbdabbcdddddaacbccbcddcaabcdddbcabbdaadadcdddcacdbaddaaccdcdcdccdaddaddccbaddbdabdbdcdddbcdcbdbcdadbcbaadacaaadbbbaadbdcdbccddadadaabcdcddacdacddcdbcbcaccdcddbbcbaadbadacccdbacbbccbdbdbacdcdbadccddbdacbbaadbbdccdcddaaddadabbbddcadababddbcbadcdbdaddbdccaddbcabdcdbbccbcdccacbdaaadcdacddcbcacaadcdcccbaabbcadddbdacdbbdabdbccbcbbcdcdddbdaacdddccacadbabadbaccaadddaaddccbabaacdbbdcccbbaadcbacdcdcddadacaddcbcdadacaaddbdabdcdbcabddacdbddbbdbcbdabdcacbacdbcababbddabcdaabcdacbdbacacdbabadbacdbadabccadacbcdacadcbbababbdddaddccddacccaabbacddbcbbabdababaaabcbcdabcacccadabdbdbbdadddbaaddbdadccbadaaaacccddccdcadbdaaadbbddadadcccabdabbcccbabaacbadcdbcccaaddaddaadabcdacbbdaaddabbbcabaddccdcdbbadbdccaadbccbbdddcadcbacdaaadcaddcadcbabadbdbacddadcdbbbcbddaabcbdcccbbabbabaaaaaacccdccccbbcdadbdddadcdcabcacbcdaadabaccbabbddbcadcbabbddaacddbcccabcdcaaaabaccbacbbcdddcabacccacdbdbbcbdcdccdbddcbbbccbbccaadacdbacaddbbbbdccbadaabbacbbacadbaadccdbbcbbdadadadcbddbbdbabdccabbbcbcdaacbabcabbcbdcbabdcadddcabdbbcdbdbcacdabcababcdaaabbdabcabbdcdbcccabdadbbabababbcbbdbdddadcbdcbbcddadddbdcdddbdddbacaaadddbaaddcbbdadaabcdbcaccdaddddcddbdabdcadacdbdcadcdccdcddccbdbcabbbaabbcbaccbcbbcdbdddbcbbabdacbacdabdcddacbdacdbbbcaacdbaacadcacacbdbcbbaddaacbaacbadacccbacdadccadddbcaacccacaaddacbadcbbdabbaaababbdcbaaaadabbcdabcabcbbbdaccdccdcbabdcdbdabdabbacbcbddbcbbcdbbcabccabdcbcccbbcbcbbacaddcbdacccdadcccccddccacdadccdadbdacabcbcaccbdddbcacdddaccbacddbadabbccbdbaaddbbdccccbdaccadccdabbcabcbacabcacaaabacababaccacccacddbdbccaccbccdbcabaabbabbbbdcacabcdcabaabbdcccabcbbbbbddbbdaccdcacbaddcbaccbcbcbddbcbadadcddaadbccbbdcaacbcbcccbddcacaabbabdcaacdbdddcaaadbddbbdabaddddbdbacbacaabadbdaabdbbdccdcbdbbaddabddcbabbbcddabdbaaaadadcdccccdcddbaabbabccccbdbaaccccbcaabaabadaadcbdcbdadddccdddbaaccbcacdccaaaaabbccdbabadcacacccacaaacdabccbaaaddcbaddacbacdacbabbdaaaabcabbbacccadbddaddddddcadabaaaadaaddadddbbdbabbacbdbabdcdcbbdcbbdddcacacdbbbddcabaabccbbabdcabaccaadcbcddccdccccaaddababcaaabbdaaababdacadccaaaabbbdcbdadcdddcbbdacbbabbbbbbbcdccdccacbddaccbbdabdadcdbbddddbcabaacddbabdbbcccadbdcbbacaacccdcdabacabdddcaccddacbadbdbbcccccabcabcbaaccccbdcdadbdccbacaabbcaabcbcdbcacabcacddaccdabcdabcacdacbdbdaacadbbaacacbaccdbdbbcabbadbcccccdcbbcabdbdaaccacccadadbbbccdcbadcbccababaabbcbccdcbdbcababadbcdbacccaacddacdbaaabbcccdcbdadadccadcbaacdbddcbdcaadacacbccbcbcbddbbbddabbcddacbbbaaccbcadccbbcbbcacdbdcdbadacadcbdbabacbdcabbabcaaadddaabaabbcdcdcaadccacaaaacddaacbbdacacdcdabdaaccadaaabaddcccdcacacbbbcbaaabbdbaacbbbdadddcadbccbbbbddccbdabbdcdcaccdddabcdbacdbdaaccbdbbabcbcabbacbbcddadcbacbbdcbacbcdabcacddcbadadcadbbacaaddaacacbdaaddcdbdaaadccbbcddddaaaccaaabdcacccbaddbccaacbbbadadacbcbccdcadadabccdcdcaccdbdaddabadbacbabdaacadcadcdcaadbcbaadbbadbbabcabdbbaaaccacdaacaddcdccbaaaadbdbadccbcdadbddccbcdcddcacbbacdcddbbbbaddaaaddccdbdabcddadcdbaadcdccabacdbdabacadbdcdddcbabcddcaabcccdaaddbccdddccacbacadddbcbbcbadadabbbdaabddaabcadadabadbddddcbbaaddcadcbdcdcddaaccddcbabcacaccbdcdbabbbcbdadacbadaddbabbaccaabbdcacccbcaccaccbaacacacaadbdadabcbacbdabadacabbadabdddcaacdcbcadcbcccbbcdbcadcaadbadabbdbacdbbabbcccaadbccddbcaabaddbdcdddadcadbbadbbaacddabbdbcadbccbbadacdddcdbbacdcdbbddbddcdaccddbddcbaaaccbabcbcdbabdddadbcdabbbbdbbacaacadcbcccdabaabdbadacbbacacabbbcaccbcccaaccaadacdcaccdcddabcbdccdcbacbdddbbadadcbcccadcbbcaaadcacccbbabbbdbcccbbacddccdaccabacabcdcdcbaaaddbbdbcdadadbadabdcacddbcaabdbdaadacbaccddcddbbabbddbdbbcdccdbdcdcccddcdadaddacbaadaccbcdbccacbacdccbbadbccadbbbabaaaabbbccdbdaddabdcaacaabcbbabdcddcdcdcbdcbbaacdabcabdcdddcdccccacabadcccabaccaaacbdbbbaadbddbacdccaaaadcdabaadbacabddbbddcbacabcdabcaccbdaccbaddbbcdaadccdddadadacaadabcacabaaaadcccbbaacbddbbcacabdadccadccdbabdbacbbbabadccccdccccdacdcdabddbdaddcacdbcacabacccbababadacbdadbbdabbcbbacdcacddbdbabbcbddbadddcddbbdcbbccbcabcdddccbbbbdbdbdabaaaabcbdbcdadaacdbcdccbdbbbdcabccbdbccddddcaddbabdcbccddddbbcccbbaccbcdcdbccbadbbdabaabbbbbabcaadaaaacbbcdcdcaddcccabcdaacbabcccbbabaccccddbacadbcdaddacadcbdbdcacadacbccacbbaabddcaabbbbbbdddadcdbbdccdadcadccdbcbcbdbbcaccccbcbdcbbdbddacdacdcbcaddcaacddddcacdddacbdcddbdcbcbacadbcacdabddaadddcdcaabcbabbdcaadadabbcbbddcddabbadaacabcaacbbdaaabbdabbbbcccbaabbbbcbdbacacabbdaabadbabbcbcaccbaacacdbbcddbabaaabdbbdccaddabcddcabccaccdcabacacbcaaaddbbbbaddabdabdacadbcadbaadccdacbdcbdcbcaabcddbbdbabbbdddbacaddadaabddccdbaacacccdccdcbadcdabbcdacccaddaccbccddadabacaccaccbddcbcaacddddaaaabdddbdaddaabdccdbcababcdbbcbbdccdcddbacbabbbdabdabaaaabadbbdaabcbcadadcbbbdcaadacdaaacdcbdccdaaadbcbcbdcdabcbbacdabcbaaaadbbddacdcabdcbddcdcbcbbbccdbaaabaccdcadcbdaaabbcdbdccbcabdcbaaacddcccaddbcdccddbbabdacbdbddcbadbdcaccdabadadccdccaabadcdacacacdaddcaadbbadcabcaaddbacbbdabcbcbbdddbdadacbbdadaadbaadcbadcacbadbcbcddbccacbbbddbadbbdddbbbbcdccdadadaadcdccddaabaddbcbacdccbcadadcdcddccdaaacacaccbcadbbddddcddadddddaadcbddaaadcaaacdaacabccdccdbcdacdbbcababdbdacbcdbadcabadababacdadadcddbdacbdddcbcacacdabcccddbadbcbababcaddacdddddbbbbaaccdaccdabcddbbdaadaccdbabbdabdbcddbdbdbcaacdcabcbddcadadccabbadbbcbdcddcdaddbddbbbccdbcccbcacbdbdbcbdaaadccabdbcbcaabccacbbabdcacdbdcaaaaddbccccbdcacacabbaaacbcacbbccddcbccbccccdbbcdddaaabddadddcccccbddbbbbccabcaabadddaccaadadcbddddabbcadcbacbbbbbdcccbcbdddadaaabdcdabbadadacdcccdcbabdaaddccabccabcacadcbdbadbdbaddbbccaacaaadcaacacdcbabcdabbdadcddaccbcaccdbcdbadcbbcaaaaaabcadacbdcdabdddbccdccbcbaabddddddbdccadbbaadbddbbddddabdccbdcdaaacdaccbcaacaabdcbbdacaabbcbbdcdaabadccdabaccdddccdcbccabacbbadabccccbddabcbcaabbbababbabbbdbaddcbccdbdbdddddcdccdcbacddbbaaadadadbccbcdcdcadcbbcbdbdbcdaaacbaaaacbdcaaabaabdbcdcadcbbdacabbacbadabbadccbcbdbacaadadcdbbbacadbccbdcbcdcaddadaccdddcbaabddbaccbcccdbaacdcbaacacabaaabbbadccbabcaadadbcabaddbdbdccacbbabdadbaadaabbbadaddaddcdaaaadbdcbcdcadabbaabbccbadcaccbbbddccccdbcbdcddcdccbcaccbadacbdbadabdbdacbbacaaabadcacbaddcaadcbdcccdcdabbcabaaadbbccbdaadbcbaddbadaacbcadaabddcadbdbbabcdbccaaccaadddbaccccdabbcabdacaabdbddbacccddaddddabcabbabacaaadddccdaadadbbcbddddccdbccbaabddcdddacbbdaddcbddadbadbbbccdabddaccdbbbccddcbcaaaabcddaabcdcaddbaccababadbcabccddddadbbdbdcbcddcddcacdabdadcbababdcddbacadddbaadcaccbbdcabdaabbbccaddbbadabcabdccababdcdccbdacccbbbabdccdaddcbcbdcbaadabaabbdddbbaacdbabdcaadbbaddbbcbbdadccbcadabcadbdbbdbcbcdccbcdbbadaadbbccbbbbccbcbdddcacaaaddadbaacccdadbdbcaaadacdbadcaccadadcdaadabcaaaccccbccabbdaadbcadacacbcbdaddbddacaddddacdbccbdcbbdabadabacbcdbbcbdbabcbcdbaacdacabddcbcdaabcdadbddbdabaabbbaadcdbdcadaabbddcbdaaabaacadcbcdbaccbcddadaccaaccbbccabbcdcdbaaddaddcacbaaaddaccdbacccbdabaadbaabaddabddbdcadadadbcbbadcabddbacadcabbbacdcbbdadddbdaabcbcbbddaccbcddcacdbcbdcaaabcbcaddaddcaacbaacbdcaddbbbbaccbabddccadbbbdaddadbddbdbbdbbcdcadbbdbbdcabdddbbbaadbccbcdcccddbcabccdbcdccbddbabddaccaadbaddacaaabdbddbcdbddbddbbddddaddcbababdddbbadbababcdadcbdddcccbacdaacbcaccdcacaaccababbbdaabccbdbabdcdbacbdbaccddadddcbcbadaaabddabaaacddbcbcdabdaddaabbacbbdabaddcddcbbbabccdbbbccdbdcbbbaaaddadaaaaabaccadcccbdbbbbdadcccbcdcdcbdaadcabcadccaccbbaabbdbaaabdbacabcaadbbdabadbaadbabdadabbcabdbabbdcccdccadaabbdbaacbdbaabbdbcdcadabdcacdbbdabcaddaccdddddadacbaacdcbacddcccbaddcbaadcacddabbdccabbbdcacccbddacabcdbbdaadbcdcbdbbdbadbbddcacbccaacbdbadcdccaadadddddcaadccadacdabcabcdadaccbcbccadabbabcdbdcadbcaabdbabbcccbdcaaacaadabdbabcaaacdabddccddbbcadddbdadbacaabbaaaabcaddddbcaadabbacaaccbbdaabaccbbabdadbdbadbccbdccabdcabbaadccdaadddddbdbcbcbaabacbcababaaacdaddbbbdbbdbacbbaacdbcbbbbcabdcccabcddcbcbcdaacabdbaccacddadcadababdbddbabcbccbbdacccdbbaccccaddcaabdbcbcbccbbabcdcbdacbbbbadccbbcadbaabaabcacccaabaadcdbbbbadbbadabcddbacbbcdcadacccacdbbbdbbabdaaddcdbdabdaccacdbdcbccbacccbcaaddbccbadbaaadcbbbaaabdadaacdcddbddccbaccadadccbbdabacacddaddbbcdaadcbbbacdcdbbdadcccadcdddddaccddbbbddcdcdbdcdccddaaddbdbabbccdccddcbbdcbbccbbacabcdccabcdccbcbbdaabbcdbddddbaadddddbbdcbbbcbabbdcabbaccabcddbddcdcbbcacbadbcbdcabadbacdbaaaccdabcbabccabaabbadcaaacdaaadabbcacccbacbcdadccbbabcdbdbbcccdcddccdabcdccbddccbbcccbdabcbadabaaadbcacccaabdcbcdccdbcbbccbacbaabbbbddbaacdbbdcdacdbdacddcbcaacbcbddbdccadbcbccacdaadacacddbaacabbcababbddabdcabdbacaadaacdcdacdcdaabcccbdbbbbbbcbccaacbaaddaacbdbacddaabdbaadacbaabcdabcdcdcbbdcdaccdcababbaacbaadaddaaadaadabdbadcaaacabdcbddddbbcadddaabbdbdabacbccaabdababadcbbabaabdbdbcbdbdcaddabbacdaddabcadbccbcadbadbacbcabcbbcdccbddcaddacbccbdacdbdaadbaddcbabdabdaddacccbcacbabccaaabcdadbbadcadcdaababbcbaddcbdbadccabcbbbbdcddbbbbcacdbbacacbccadadccdbcaaaabcbbdbaabdcddccdddaccaddbddcdcbacadacbccddccdcdaccbadadcdbcbacacaabdabadcbddbaccbdadbadbbcdbadbacdbbccabbdccbdbabbbadadaccdcdbdaadbbcaaaadddcbdcbacadcddaacbdadabcacdbdcdbbddbcbddddacacdbadcbbacddaacdcccbccdabcbadcababacbabdccbcdbcbaddbaddccbaacacabcbbacacdaddadbabbbaddbbccbbadbdcdbbcbacacaddbdbacdcbcbacdcaaaacbdabbadbbabcddacdbdaccbabdbcacdcccbbcaadadacdbacdbbdadccaaaccdabcbcbabadcddaadaddbbdaaddccdadbdccbcdbbdacadadadcbccccabbadbcbbadbabbbccddbacaddaadacddcacccddaaaddadaacbdcbcaaccabcaadadabbcacdababcdccccabbddbdabadabcadbbaaabbcbaddcdacdcdaadbdcbcdbaddbcdbdbadcdcbccaabbcccbcdddaacdaacabddddbdbdbacadaddbdcbacbabbbbbbaccddccbcabcbacddcdacdbaaaccadbbcbcaccbbdacccdbbbdccbbbbacbbdbbacadcdadcddcdbaaabbababadddbcdbaabaadaddbcddabbdacabdddbdccdbbbddcbabbadcdccbadabaacabbdaadbacbdcdaadabbdacabcccddadcddacdadcdbdbadabcdcdbaccbcabcbddccbbbacdccddccdaaadcaccdaacdcbdbcaacbaddcbabdcaabbbdccdbaadcdcdcbcbdcdababccbadcbccbccaccdaadcaadcaadabbdcaacbabdcbacacbdcbabdabbaadcdadcbdadbadcadcdcabcddbadbbbcdabcdacdcdaddbbcaadbccdcaadcadbdaccdcdbbccaadaaadaadbdaaddacccbddaabcbdabcddbaaaadcccaaabcdbbdabccabdddbbacdbcbbaadbddbdbabbbdbabbdccdbddbbaabbcbdacdcbcacacbdbdadbbabcccaabacacdcdddabbbdbcdadabbccbacccbbbbbccbbcccacccbbccbaccbaadbdaadacbdcaaadacdcccdcbcbcacbdbabacbdabdcabcbbacaabbbbbccddcdbbbabbcaccddddacaddaccbccddaaddcbcdcddcaacacdbabdacddcabbbdabbcbccabbddabbbbdaddacbdbaccababbbdbababcdccaaacbdbccbbddbdccadabbdbdbcdcbdcabdbcadcbabbacdbcccccbccbdcddcbbaabdbddcdcabaabcaaacadabcbcaaabcbbdccbaccdcabdbacdcadccdcbadcabbaccaaaadbdddacbdbdcbcbaadcbbcaccaaadccbdaddccbbcdcdbbddbbcabbabddbbbbbdcdddddccababbbdadddaaabadabbddbdccdbdaddabbcbdcbbaddddcbbcbdcababbccabdbbdcdbabbadbcbdccdddbabdbcdacacdbbbbbbdabbcacdcbdbabbdcdcdcdddbcdcbdcaacadababcacbcbcaabcddcbabcccaccaadbadabdcdabbdbbdddbdcbcbccbbaccaccbabbcbcacdccaacaacbbdabdcdcabbdccdddbacadcdcddbddaabcdacbabcdcccbadbaccaabaccaacbbcdbbddadcdbaadbaccbdcacccdbbcacdbacbcbcbbbdcddadcdabdbdbdcadccbdddcbbdaadbcbcdbbdcaaadbaacabacadcbabdcbcdacbbcdbdbbdaabbcaaaabbdcacaaaddaccaabddacbdccbddadbccccbdcbaaccccaadcbadadbdcdbccabadccabacadabcadddbbccccccbbccadbdcdccdaddacbaddbcbcccbcbcdbbdccbcabbcaabdacaadbdcbaacbcdbbdcdbbaddcaddabccdbbddbcdcadaadababdbadcabbdcbdddddcbaabbacccacadbddaabbacaaabcaadbbbcbddbbbbdacccabccdbbbcbacdcbbcbdbaadadbdbadbaccabcccdcaaaaacbcdcdbaccabdaadcacadccdacccacbbbddbdadaacddaddabaabddcbbaddaadaaacbbdadabccdcabcbbbcbddcdacbcdaacdbaaaddddbadbdddcabcdacdddcccdabadabadabdbcbaaaacdbbdddabcbdaaddabcdcadccbbbbbddbdcacbdbcaababcbbcdbbacaabaacccacdbdcccbdddabdaaccadccdabacddaddadbbbdbbcdccaacccbdddddcbdaaabddcdbacbddaadaaabcddcbacdcaabcddcabddccdcaaadadbadcabacaacdbbbccdacabbbdcdcabdbccdccdbbcbdbbcaaaadadcccbccdacbccabadaddaadaccbcacadcbdacbaaaaadcacbacdacbbaadabcddcdddcddacacbbccadaddabdbccdbbcacbddadddbcbccadcbcddabdcbcdbbdcccadadcacccbbadcdcdddaddbdcabdcdcbdbdcdbdaadadaababcdbaabdbcbcadbaaaacdabdbddcacdbbdbdcaccbbdddbbbabcddccdbabaaccbacdbdbadbdbdbdaacaabbacdbbdbbacbabbadabdcddcabcaccbdcbcbbabccadddcadddadbbadaccacbcbdbbcbacdbdcadaacadddbaacaaaacdbbbddaaadaadbcbdcaccdbcdacabdacbabdabbadbccbddccdccdbbdbbaabacabcbdcddbaabdacaccbbacbdddbadbcbabbdabbcbcacaadbccacbaaacacdaaabacbcdccadabdacdadacbbdccdaddcadcddbacbaaaaaaaabcdadccbccbbadccddbcbaddddccabbdbaaddcadacadaabdcacdacaaaadabccbbcddabbcbbbbcdcccabbacabaccbaddbcacaaabaaaccabbabaabbddaacaadcacbcacbbccddcaddcbbdadabacacbbbddabbbcbdabcacaddaacbbaabdcccdcddacbdccdbcdacabcdcbacadabcdbbabddcdbadaaabcacbbdbbbddadbcdcbacbcbdaccbbbbcaccbbcdddbbddacaccddcbccbcbdcccbbcddbadabbbbdbaadbdcbdbccdcbbacbabacdcadbddbbbadabccdddbabcdbcadcdbcdccaacdaccbbddaabcbcadcdbaaaaccccadbacbcaadacbdadcdadbbddcabadaaabacaddacdbcabaaaacdaaadaacacadbcadccabaaabcbdacddaadbddcdcbcdccdaaabddadcddbabbbcaabadcdcbdcddbdacddcbdcbcadaccaccdbcbaaaaadbdbcccdacdcbaacaacddaadacdaaababdbcdddbabbaadacdacbabcbaadabacccccacaccacdabdccbaaaaadcabbdabbccadacbdbcadddababaaacadaddbbaaabbdaaabadadbcadbaaababbbadababbacadacadddbadddacbbbcbdadadacbcbaaaacbbadacadaddcdbbdacadddadccdbacacadaadbdbdabbdcdcdaacbdbbacbcadaccbdccacbdcdadaabacdbbbcdaccbbcbcbbaadcdcdaadaccaadcccdcaddaccccbdbccdbbbbbddcbabcabcddacabcbdcabcaabacbbdacdbddacadbbbbbbaddbdaaddbabdbbdaaddbdabdccacabaddadacdbdaadbadbdcabccbdadbdabccdaddcdababcdcdbbdddbbbcadbbacbbbbcacaaabdcaaaaaaddaaabbabdbcdacabdbdbbaddbbdbbaccaaddabbcbccdbacaddadccaccadbcaadcbaaadbcbaadbbbcbcbdbcabcbacbababdacbbaabaddcdbdddaadbadcdccadbadbccccbaaddaddabccccbdcdadcaaaacbcbcbddaaaddabcbcaabcbbaabcccaddcbcdacbcdababababdabcdacabcccbbddaccacdcbaddcbdcacbaaaccbcbaaadaaabcacabcccbacaddcbdaaadccccbddddbcdbcccdacbacdaccdaddaadabacacaaadcabacaaabaadcdbadbdccdcddbacbacbcaaaaadbcccbdbbdacadadbdaaaababdccacccccacacbabadbccdadbadbcbaaadacdcccbdababaddaabdcbccdacabbbaaddbcdabaaadabdaacbcccbadbbbdaddbabbcacacbabacdcddcaacababbbdcbbcaaddaaddbabdbabaddcddaadcdaaabacbbcaadabacbabdacaccacbdbcdccddbdaccdaabdcaababcaccbadbbabaadcbaababdbbddaaaddcddcaabcadbdbccbbbddcbadccadbccadddccdacabbddddbdcbbbdabdacbbbbacaabdcdaddbddccdbccaaadbdadadbbdaaddbcbbdabaacacacaaddcaaddcdddbdddabbcabaadccdcddcdababbbccbcbbaadbdcdbbcaccbbcbdaabdabdabccbbdccdaabbbadcddcdaadadbddadddcccacdadcccabdabcdcbacbbcadbadcdcdbaacdbaaacbcbcdbbcadabcdbbbcbbdadacdadabbaddbdbcdbabbadbcbcdddcbcddddcbcdcddbadbbcbdcccbbbadcabadbbacdadabadacdcbbdaccaacaaaccbaaacbccaddaddcbcdbcbdbabddbbbcabacbaacccabbcadacdabccbacbacdbdadcbcabbdbbbdbcbacacdddcabbacbbdccbdbcaaaddddcdbbabababaabcbccccbdcbadbaaabaccacccdccbcccdabdabcadcdcacdcacaabbbbaaaaabacabdbbbcababbdcbddabcdcccabdaccdadbbbcddcbadbcadbbadbbcdcdcbdcacadcabaacddcdacdcbacccacaaaaaddcbdcddcddcbdaabccccbacadbcdbbbdbcbccadcacbbdbbbcbddbdaacaaccddddcdccacaacadcbbadcaccacccbcacadcddbadcababacccbaddabcbbdbbdccccbdcbdddbcbcbcadccdacbbadaaaccbdaaaadcbbdbdabdabaabdcababbcdacaddccdbbbabbbccababacdbcbcabbcdcadbbdbbdbdcacbabdaccbadaabbaadcbdbadcacaaacadbbbbddbdbccdaabbdbadcadabdcaccadcbbdadbcccccbcbadcabdbbbaabdbadabadabdbbdcdcdabdaddcabbbacdacccaddbddcbabacbdadcbdcaacccdcbcabaaaabbbddabaacacdaadcdadababadbacadbdbcbdccabdaadabbcaccbcccacabcaccaccccbaabbbcacabaddabdbcbccaccbacddbddbcdbbabbccbbdadddbbabbdcacacdacbacccddddacccdbbddcbccdacaadbbdcacdcbcdddaacabaadbacbacccdabbcccbdabccbdddbcbdcbdbbaccaacadcbdbacddccaacaadbcabbbbbbcdccdbbbcbbbbbaddbdbbdaddbacdadcbaddcdbadaabcbbbacbbcadcbabbcdddcdddbbdbababbbddcccbbddcdccbbccbaadabcbcbababcbaadaaabcddbdabacccbddccbcadcbcaccabbbccdccacdccdbbcbcdabdcbadbcabacdbaacddaddcaaaaadabcaabcbcbadbcdadcaacadbdabadbddbbbbadbccabddaacccbbacddacccdcddbcddabbdcdacbcbbccccbdcdacadadcbbadcadccaddaabaadcdabcdaacabcaabbcdaabdcddccbbbbcbdadbcaaddcabdacaabbabcabdddddcdbcbdbbaccadaddccaadcddbbdbddbcaadacbcacbccbcacdccbbcddacbcabdcdbbbcbbbabbcbddcbdcaadabbdabbaddbdadccbacbaddaadbddbcbccaabcaacbbaadacbaccaddddcdbbaddcacdabcbbbcaccdcabcdbbccabadbacdabadccdbdbcbbcbacdaaaaddbaadaacbacdaaddadadbaaccbdabcbbaadcacadbbdccbdcaacaabadcbdcaaabbcbdabcbddbdabaddcdbdaccaddcabcadccabbbcdbbacdcbccacdddbcbbabadcdddcbbadabaaadbbacabdddabbaaccbcaaadadcbbbccadadccbabdbabbbadbaacaadaabcdacdbbaaadcaabbcadbdcdbbcbcadcbddacadddcabdbcdacbcbbbdddcbabdbdcbadcddbbbbccbdbbddcaadcbcdbadcbacabacaaddbdcabdcabdaabbdddbdbcccabdcacdababdaaccccbbbbaaaaacaabdbbbbbdbbdcadbcbcbacccbbacdbadcaadcdbabbdddcaddbdccaadccdbcbbdaddbbbaaccbbbacdabccaddbdaacdcccbdacccbbbdcaaaaccbccdbddbacabcaddddaacbbcaaacaacdcdbdcccdcbdccdcbacacbdacddcbabbbcacacacbcdadcadbcabcbbbdcbbddacabacbbdacadbdbdaaabbbcdcbaaddbadbbadbdbacadadadbbcadcdccdaabccabadbbacbdbaddcccbabdbcdadbddacdbccdaddaabccddcccacdbbdbbbdababbddadaacaaabbcbcdcdcdbaabbabbddcaaacbabddaadcdbacaddbaabddbacbbcccabdaccddbccccbaabbccaadaacbbcccccbabbddbcddbacaadcadaacacbdaccaadbdcbcdcdddcdcbabccdcdaabdaabdbaaddbacccbcbdbacbdacbbbabbcbdbbcbaaababbbaddddcadbbcdcdccdaddbaabbcbccabddcacbcadbdaccaadacbdbcccdbcaaadabddbcabccbcdbdaabdaaacddaddbadcaaabddbacdbdbddcbbacbbbdcbddadacbabbdcdbccdcbbadccbbccacdababcbbbbcaababbabdbcdabbddabcaaccdbcbacaddbdbbcdbbcdcaaabdcaccabccbadacdbdaadcdbcdbccadbdcdcdadacbbcaaaddcdaadadcbbadbdccadaccaaabacbccddccadbbcccaaabcacddcabaddcadbbadcbdadccaadcacbbcdcbacdcdcdbdcbadacbacdbacaacdcbbbcaabdccacacbbbcdaacdaadadcdaadaabdcddacdcbdccdacdbabacbcbcccaaadbccbcadddcacdaababddcacbbaacaadccbcadbabbbddcccddaacddaabdadccbcdaadaddacdcacbbcbccbccdcadddbabccadacababacccbcdcbcbbddaaccaddddbddbabdaabbddcddbacccaccccbbbddbaacbddcaabbbadacdcbabbacdbaccadbbdccadbdbaccccdcabaaaabacdbdcbcbcbbdacbbcbdcabacdadbddabbbdadcbdbbacacdbcbbaddcaaddbcdaacbdadbbdcccaabdbacbdbbadaacdbcdbddbcbadbddbbdaaabaadcdacbbadddacababbacbcbbcbbddbacbbddcdbdbcbabcabaddabbcdbadccdbccadbdacaadbbbbdccdaabbcabaaccbbbbbdbbbacadabbbcccabdaaccaaccaaaacdabbddcacbcabdccadbdcaacdabddcbbabcdcdbaddaccacccccabaccbaaabcbdaccababcdbdcbcccaacabadaddddcbbccabdbaaddcdaaacadcdcdaabaaddbddbdabdbbbabbabaccadcaddcdddbacbbaadbcdadcbbdcbbaddcaccccbcbddbaccddaaacacaccaabaaabcccaaddbdddcbccbacbcadbdaaaacdaabcbccbcccccadbcdacbbdbcdabccbccccbadacacdcadddadbcccbcbacaadbbcbcbbbbaaaaacbcbbccdbcddcbaabdcbacccaccaddbdadcbbccdbaddcccccbcaabacbabacdaacbaccbdaaacbcbbbaacaacdabdcccbbcbdabbabdccbdcaddbdddcbbddbdbbdccadbbbcadcdbcbacaccaabacddaddcdabdcbdddaacabbcbdcabbcaccdcddbdcadbbdbcdcbacabacadcbaabbabddcaddccaadbadcbcdbbaacaaadcadbbbadbdddbbcacdadbcdbcadbabcacdcabaaacaacbbacddcacbdccdadbcadabaababbdccbcbddadbdbcbbcacbcabccadbabcdcadaddcdbcaccdbdbcdbbadbdaacdaaacccabaccccbabddccbddaccdadbcbadabcddaddcbaadadabbddcdddbadadcaddcbadaddccacdaacabdccbbacaabdbcdbbacdbcaadcbadccabacdbdacccbbbacddbcacacccabacdcddcccadddbbcacdaabddbdadcdadcadacddaaaddcadacadbdddcdaadbadbaccbabbbdddccbabbcbdcbabaaccabdbddadbccacdcacdbadbaacccaadccdaaabdccaccccdbadbbbbddabdadaabdcbbbdbddbbbbdbbabaaccbadcccdaaccdddcbbaaccaaaacadbcdabdcabdcbbaccbccdacdadabbadadbcababcacabddbddadadcabddabcabddcbbdcdcadccbcbdbabccccbababddbdbabbaadcdaabdcbdcbcabbaddbcacccbcdabbdcbdbdadaabbdcadbcbbdbbdabdddccdccdddadbdbbbabddddcccdabaabbaccaccaabadcdbadcddbaaccbcbbbbabbbbbacaadabcabbbddbabdbcbbdbbdbabdabcabbcacccbdbadbdbbddcabdbdcbdccccbddbcbdbabcdcdacccbbdcaaddabcaadacaaabbbdbbdcbbbabbacbddccdddcddbccbcbdbbddcdbdcbcddababbcdbdabcabacdbccbbbbbcccdcdadbcbcdbdbcadbbbcdaacdbdbddaddcaadbacbdbdbcddabdcaacdabdaacacaddddabadabbcabadccacbcbaaabacabbabbaadcababcdcacadabcbdcdacdbacbdbdccddaabbacacadabbbddbdbbdbcaaddabacabbcbdccddabacabcddacbbacdcdcdcccabcbacacdaddbdbcbdabdbacadcacdbabadacbcbaccaacabdccdccbabbadddccccdabccadaccbadddbdddcacbbdbdddddcccadaadadcbdbaaddcddcbdcadcbcacadbdcbaccbccbaabdcdaddcdabdbcbdbacddddbbcddcaadcaabccaaccdcdcddaaacaabadbdcdcabddbbadcabaaaadcdbababaadcdcdbadcdbccabdcbdbaddbaaadbdadcdacacbabcdbcdbbdcbaaccccaaadbaabbabcdbbcbcdaaacdddbcaaabadcdcdaddcbccbabadbbbabbacddabaadbccaabdadbbcabbccdcbcbbbcadacacdacbdaadcdbcddddcbadcdbbbddacbaadaccdcaadbdbbbbdaddadcbbaccacccccabcccaddccbadbddcaacdaacbbddbadaaddcdbddadcbdcdbabcdabccbcaacdbdbdbdcdaadcababbabbcddcbccbdbcdabaccddcbaacdacbbcdcbaadbccbdacbadbbdddbbdccccabdbbaaababdbaccaddabbbcbddcacabcbaabdcddbaddbaddaccdadcbaaddcbbcbdabaadcabdbccacdcaacddcbdcaacccbbcdbadcdadcdbdbbbcbbdcbadccadbdaadbcbbcdcdbcadcbdcacdcdbaaaadaaadcbdbdddbabdccadcabbbacdddcbcdbccdbbbbacdcdcbdcdadacdcbaadbdbbcccacacdacacdbcbbaddccbddacbdbdbaadcdcbdadbdbbaccabadbdadcabcccdcdcaacbcadccbbccacaabdcaddbacbddcdabdbbbdddcabcbaaccbcbcabccabcbcadbaccdcaccabcabdbddadbdccbcbcdadbacabaccadacacbbbbccbaabdcbcdbaddadbbdddbacbbadbddadaacaccbadcadcadbbabdbdbadbbbadbdbaaacdcddcbadbdcadbdacdcdddbccdaddcbccabcaadaabcdabaabdaaaacddaaabbdacbdbdbdccacdcabcaaaddbcbccdbdcbcadadadcdacdcadbcdbbdddabcacabcbadbbadbabadacadababcccdbadbdabcdacbccbccdbadcbaaabddbabdcbcccdcbadcaabbcdabdacdbdccdcaabbddcbdabccdaabaadcdbdabbadbbacadaaccaddabccdbadcdadabddcdaaaddabdacbbdcdabbcabdbaabababadbdaacacbbacabcbcbbcbcccdaabdcccdcbaaddccdbdcccbabacdbdabcaacbcaaacbbacaaaabadadabdddacaabbddddaddcdccabadbacbaadbdadbbcccccbcbdbaaadbcbadbabddaabbbbddcbbdabdadbaaadbbbcbdcbbacccdaadabdccdcdbadadacbdcddbccaabdaccccccbdbddcbdbbabdcdbcabaddddacadadcbcdbcbacaddcdacabdccbbcbbccbdcbccacdababadccbdddbddacdbdcbcbdbbcaaabbbaaacdbcccdaaabaababdcdbdbdcaaaaccddccdbdacacbccadaaacdaaacdbdccdddbbacbdabcabdadbccdabdbdbbcdbbcdaaadadcbdbdaaacbcbcacbadbabbbdccbbbccccbabbcadbadabdbaacdabbcacdabccbbcccbbabcbacbaacaddbbcbbdacbaacbadabadbdacdbadbcddbbbcbaddccdbbcbdcacbbaacbdabaadabdbcdddbdbbddcdbbccaacdcaddddaaadbbbadbbacabdbdcdaccaaacaddbbdbdabdbbaabaabbbbcccdcddcabcbcdcacddadabdaccbabacabaaabdaadcdddcdbcacbacdbaccaabdaabbcccbccbaddaadcdccccccdabddcaddddbdabcdddabbaaddbbccdcdbcaaaabbcbbdabbabdbbadcadacdaaadadaddbcadabddbadbbcdcddacbbdadaacbcdadbdacadcddaddcccaabddabbcccbcdcbdccddcabbdadcaddabacbbbddcbdccbdccadabaaaadcbcdbbbbccaaabdcdabbbdcdccbabdbbcbabbacbcccaadabbbdcdddaccadccdcaabbddcccbccaacbaacbcbcddbaccaabcdbabdbbcbdddcbbbdcaacbdcadadadbbccbdcdaaacaaacadbcccabdadcdcccdbacbbbadcddbabcccacabcadbacacabcadacbbdbdbacdcdccddcdaabdbcbdcdcdaacbaaddacbbabbccaaabbdabaabcccdabacbbcbcdbcdbcadaaddcdccadcdbaccdadacdbcadbbccbaabaccbdcaaabbbabaaddcbbcabaddcaaccadbddaaadcbcacbbbadbdbacbdcacbaaabcaabdccdcadadcacddccbabdbcbbbcbcaabbccadbaacbadbcdddbbcaaaaacbdadccccadccbbcaabdaacccdbdabaadbaabcdcdacdccdbbbcdcabccadcccbbbddcabdcbbcaccbbdbacbdacdddcacaabadbbbdacbbddcdabbbcdbaacdacbcdbbdbdcbcdacbdcabbbbaaabdccabcbbdacaabbcdaadacbbbcbdbcacabaaacddcddacbaabdccdcaccbbbdbdbccbddabacacccdacddadbabccbdbbdaaccacdccccbccadccbadaacaddbddbdbbdbbdacbbaabbabadbddcddbadacbabadcdddbddadcddaaabdbbabbddbcadddcdcaccbaaddbbcbcabdbbadbcabcaaddbbbaadcaaccaddadccddcbdaccccccddbcdaabcdccdcdabdbdabaadcddbcabaadadbaababdadaddcdaadcdabdaabcdbcbabddcccccabaabdbcadabcacaadbdabadddbcaccdddbbdaabcbbcbbcadabaaacbbcdcaccccddaddbdcbddcdcdcacbbccccdbddababdaddbdbcaabaccaaacacaadacbbacabdbbbcdadabdddcdabadbcadcdcbcbdcabdaaadccbbacdcbdbadbbbcdbabddcbccbbacbbbbcaababadabccaddddabcccabcdbdaabbdcabdabcbdcccdabdaccdabddbabaacadcbcccaccbadabadbbdbbccddbaabbaddccdbccbbcdcdbbbccadcbddbaababcbcddbdccddacacacdcddbaacbcddcbaadbdcdcdaaaadcbbbdabdabccbbdabdaadcbabdcaddcbbadcaaaabbbaaacdcbcaabbdaacabdcdbbbdbcccadcddbdbadadcdaaadcaacadacaaabaccccccabcacabbdbbaaadbcacadcbdcaccdaadaacccbabbcbacacccacacaccdbbddbdcdbbabadccbbcaabdcbcdbabddcdadaabcbbdbabdaabbdcacddcabbcdacdccccdbacacacbdddcbaddabbcdaabbacbccddaaaccbdcbcdcddaacbdaaadddcaadbdbccadbccbbdcbacaaaddbddcccacabddbaacddcbbdccdadabdbbddbcdbdccddcccccbdcbdcaaaacaaccccabbbababdcacbdbabadacbbdcadadaaacccaaadacabbaccbbbddbdddcaaabababdddabdbacbbaddcbdcdbbbddbdbabcbcccaabaadaddbdddbbdbacccddbdbccccbdbdbccddbcbaccccbbabdcbacddabccbdacabccdddcabbacaccdaacddacacbddaabacacacbdcbadcbcaaabdadaadaadabdccbbbabcbdabcdcddaaadbccccadabbcabbcdabbaddabddacdbcabbdcdacbdadddbbbdccbbdaadddadcacdaadacdccacdaabccbcccccabbbccaaacbbcdbcccabbbbcbdcdcbbdccbbdaccadddadddcdbacbdbbaaaddacaababcadadacaccbdabcbccdadbcdadcdabdaacaaddcacbcabccccccdcddcaacbadadcddababacdccaacdadcbbaddaccabaccbbbbdaddcbccbcaccddddccadccaabdbbacbccbdcdacadadbbdabcbaddabadaaabadacdcdbddbcccaaddbddcdddbbdcccaabaabbcccaddbdadccaaabaccacbdddacbadcaadabaddaabddaddabbddddcbdbabaabccdcbcddbcdcbcbbbadaddacdcdaaacdcdcccaaddbcacbadbdaddcacbaccbdddabdbcaddbbcdccaaacbdbdddbabcaddcddbdacccaccdbccaadccadcbbdbabbadadccabbddcbdbddacddbdbcaaccdbccaabcddbaadccabccacbbdddcbcbcaddbbacbcaddccccaabdcacbbbdbddadacccbcddcdcacaacbcbcaaaabbbdccbdaacdbbbbddaacadbababcdcbcabaacbdcccbddaaabdadabacccbaccbdbdacbacbaddccacbddbbbcbdbddaaaabaaacbabbaabbdbaaadbccabdbdccaadbcbcdcdbcabdccdcaddaaacdcbdabaaadabddcdcccacdacaaccccbabcaadacbdddaacdbdbbbacdbaacbcababcdadbbbbaacdababaabdbabcbcababaadabcacaadcbbadcbdbbddcacdbbbcdadddabbbadcddcccccbdacadbaabdbcbacccacbcccbcdbddbcdbcdacddabdcacddaacacdcbdadccccaabcdcadaaabaddbccadbcccdabdcabaadabcaabcdddbadbccbaccdcccbadadadadacddabdcbbadbdcabadcadacbddbacccccdabdbdadbbcdbbcadbcbabddddcbdacdaabacdbbccdbcdadbaadbcbbdabadabcabbadbddacdadabdbabbbcccddcbdadbdaddcacdabdccabaababbacbbbddcdcacbdddcdcaddcabaabbbdbbcdbadadbbcbdbdaabdbbdddccdacacbbabbcabadccbbdbbabdaabbbbbaaaaacabcdcadabcbaadcadaadbdcdaccaddaccdbabbddcadabdabbbdaabcdbacbcdcaadbadddbcbcbdabdbadcdacbabcacbabdbddcacacbcbccbdccadabcbbaadadcdabdbccbdbdbadabbabbbccaaacaabaacbacabcbbdbcbdaddbbadbaadaacbaabaccbddcacdcadbbbdaadbabacdbaaaaccbdbbdadbbbddcacbacdaccddaaacdcbbdcabbabaaabaacdbdababbacbbbdbbbbdaddcddbcaacbbbabcbcbcdbbdcbaccbdacacaaddbadaddcdaabaddccdcbbbabbcaddacbadcbadaddcdbabcdddabdbdbbdcdddbccbbaddddbbbdddddabcdccccbcdddcdbbaddccdccabcadabbdcccbbcadddddccaaadcaddacbcccbbbddbbcbcddcababcacabdbbadcdacbcdadbdaadcaabbabcdacacdabaddddcabbdabbdadbdaccadbacccabdbdcabbaabaaddcabcdcccacbcbbbdbddcdbdacdadcaaabbbacddbbbdbbbbdddbadcbdbddacdcaabcdcddaacbcdadabacbdccdcbcbbacdddaabcccdbacacbaaaacaabcadcddcddacabbabbbbabcdddbdcbbbbbddaddccaddcbcbacaaaaddcdcbdbadaaacaadccbccbcadbccaadabadcacccccaaccabddcdaaadcdbdcdbcabbbbaddccdcbdbbdcbabcbdcababadcacbdbbadbacddadcccaaddabbdaddbabaabcaaaaaacacbcdaadcccaccdbdaccdabdccadcacbdbdcacabbdddacadbcbbcbdcaabccccabcdcdbbbdaccddcaababccaaabbaadbbcddddaaaacbbabbbbadccdadabddbabccacaabbbbdddcacbaddcbdddbdcddbcaccabdddabbbcaccdabccadabccdbbaacabcddbbcdcaaaadbbbcccbdcdcccabcabaabcbcbcacaaadcbdadcdacdbbdbccdacabcbccacaccccbcbdcacccccdbcbcbcdcdacaaacdcaddccbdcdddcbbcdcadaddaddbaabddaadddabaaacdaaabbdadacbccaccadaaadadacbbbcccababcacabbbccbaabdacacddabaccdcccdcaadadcbddcdbccccddaaddbabcddabdbbdbacabcabadccbccbcdddcbcdbbcdacbddbdaaacccddcbbcaddbabdaaadbaababadbbccabcacdddbadcddccddbbbdbbadabbbdbabddbabddcacdccccabbbaccadcababcaadcccbcbbbccbaddbadbacabbbcbaacddbdcadcaacdcdddaaabdaabcabcdcadcacadbbbdbacabbdbddbabacdbaaccabdabcbbdbccacadddabbbcadcbdbddbcbbabaccbcdbabbbaddcdabdddcadccbddacdcdbbbcacddcbdacdbacdbbbccabccadbdaacacddcbabccbcaccadddaabbacabcaccddbacbbacccccbabdbaadbcaccabbdcccddcbccdcbddbbbadacdbaacccddbaaabddbacbadccbbdbdaaacadacbdbccbbcaccbbdddbaaaabddbdacabdbaabdbacddbaddbaccacbbdcbbabcdbcacdacdcadcaaadabadabdaaacdddbcaabbabaaaaaadcbacbacccadbbdcbccbabdabdadacdbcbccbccdcadcaccdcbcbacaaababababbdcdbdabacdbdbadcbaccbbcccaccbbadddbbbcbaddbbbccddbacabaaaaadadbcaccdbdbbdaabbbdbbbcaabbaacbbcaacbaacdbbadaacddcddaadcabcbaaaaddababaadacdbddaacdccaaddddbddabccdadcacccbaabbcaaacdcbacccbddcdbdaddaadccabdddbbbdcbcbcdbabaaabbdaadaacaadccdccacadcddbdbcaadbadbdcdbbbddaccaddddbcdccacccbabcbdcbdbaccaabcbabddcdcadbbccabbdaabadbdccccabbccddabcadbbbbdcdabbcbcabbbcbbdacacdbacdadcacccdabbcdbaabcdbaadbabbcabbdcbacddacadbdbddbbaabbadabdbccddddddbacddbdbadbbbacaacabcddcaddccbaddccdbaaacbccdcdcccbcbcddcdabcccccddcacbcdaccdacccdabacdcdadaaddacacabbdaddcdddacbbdacbacacaadbdbdbcdbcdbddbaaaadbbddbcccaadbababaaacaaabacdddcbcccacdcaccadbddbbacadbadacdcdbbcbcabddbbccbacbcbcbaabadddaddaadcddbdabbcdbcddbacaabdbbaacacdbaaadbdadcacdabcacadcdcdccadadaccdabaacddbcbadcaadbbdbcccbbdcabbbaddbcdabcdbbadbadabbabadcdcabcdbacdbacaabbacadcbdadcadadccbdcddccabccdababbbbabadbcdccdaaabcbdcabddbbcbcabbcabdacbbaaadaabcacacaaabcabbadbbccbbabccaacaabbcbbbbddddcdccbaacbddaccdcbabdabdcdaacabcbcdccbbcbcbccccabababadacacaccdbacbddadccbcbbbbaabdcacbabaadcdaabccabcabcbcbbcabcbabbbdcccbbcacbabddabdbaadacaadaccbddbadbddbcccbccaacdbaccadacdaacdccadbbcbbcbcbbbabaadbdcaacadbdbbbdabdcbbbddacaaccaaacadbabababdbccdabdcabdacbdccbdcdabddcaabcccbaccadddbcdbddbbbadcbabbbdcbdbacadbcaaccaabbaadbbbacacdccadbaaaaddcdabcacacaddaddacbcdaabbdbbaacccbdcabacccaabbddaaabdbdbbddbaddaacbcbacbccdadbaadddbbaaabacaccadbadbdabacddcdacdbabbadabbbcdacacdaddccbbaaabdbdbbbdaaaabacbcadcdadddbbccbbdaabccacdaddabdbccbbbbaabcaacaabdabbbbaabcdccccadabcbddbdcbaadbdabbbcbbdccbcddccacdadabadbacaaccdbadddabbbdadacabbcbccdccccabbdcabccddddbdaaddbbbbabbbbcdccdaccccbbaababaadbdbcbbcdacabaddabccbcddadabbbcbadcabddcababacdcdcdcddadbadbbdadcadbbbacaddadcbaaabbabdccbcadcbacbacadbbcbcbdcdbbabcddaabbdacbadabdcbbcdabaadabdddbddccacaabadcbbaddbacccbbcadbdbdadccabacdccdaccabcdababcdbacaabcabadcbbcbbdbddcccdbbdabcccdadbdbaccabdcccdaacababbbbaccbddcbccdcdbdccadcdaadbadabdccccaadcbadcbdcadaadaaabbabcacabadbbaddbadabdaabddaddabbbcdcbdccaadabcdacbbddccbcabcacdaccaabbadabccdcbaddabcdbbdaaccbacabdadbcdacabdbbaabccaadddbbadabdccbcbbddadccbdabbddadacadbaaabaaaadcbcccddadccdadcccaaabddbbdbcbbdbbbdcacccbbbbdbdcdabdadadbcabcdcdadbccbdbcbcbaadddddacabdaadbccacacbccdddcbbddacaadccbbbcdbdacbbcdbcbdabcdbabcbacacdddbcaacacdccbaabcaabbdadcaadccddbadaadcdbbbdbbacdabddcdbbaccdcbccbdadcbcadccdabbabbcbbaabbbcccaabddcbdbbabaaaddadcbcdddbbbbcccacadaaaabbabbbcadbadbbdcaaddbccbbadabccabbdbbabdcdadbbcbdbaadddadacbbbbdbadadddadbacadcaaababdabacaabcabcdaabccacabacbdcdbbddbbdacadbdccbaaccccbaabdabbcaaaadacbbabbadddbbdccdccaaabdcbcbbcabdbddabcbdbaadccdbbbdddcddaaadbbbbdcccaadcbaaaabccbdabaccadcddabacddbabcbcdcbcdbcdcddadbacdcbbdacddddbaacbcbcbcbdbaaddbccddacbddbbccabcacadccabbaadddabaadbbbbdcbadaddddbbcadbbababdcbbdcccbcbddcadbbdccbcacccaaacaccdbccbddbcbccdadacaccadaddccdcddccbcbdcabadbbbcdcdbdcacdcaddddbcadbabcccaacbcacaabcbcbaacdcbabcccdbcabdbddadcbababcbaccbabadbbabbcdddadaaadbcdcbdbbacbaddbabdbabdbdbbcdbcbadacbabdcbdcdabcadcabadabaccabdbbdddbdaadcdcacbacdbbddbcdcadddacddbbbcabdbbaadbcacbcadacaaddadbddaabbccbcbdcbdabcccbdaabacdbbdddbaadcabcbadaccacaababcdddbabacdbabbdbcbbaccccbbabcbddacccdddbaccbbcaddadbacdccaabaabbdbdaadacaddccadadacabdcbbcdddbbdcacadccdbccbbcddacddcbdddadbbcdbaaccddcdacccadadccbbbdcacbcccaddaaabdcdabcacddcaddddbacddcbdcdacbabbbaaddcddcdcbdacbbcadaaacdddaccacdbabaadcaaadadaadcadaccdaacbcbcdacdaabbccaacbabbddbabbaabdbccbbaaaabcbadddbbdadcdcbbbbbaddbdcabddbadbadabdccbabbdcbbdaabbdbbcabaccadcbccbdddcdbdddccbacdbbacdadabdbcdcbcaaccaddaabcdbadcddbdcdccbdabadaccbbacdbbccaddddbdcdaacaacadccccadbbccaaaccabcaaccdcbbdbbbbababcddacadcbadccaabbbdcaacaadaabddadccadcadbbdaadccbaaabbaaddddcacbbaacaacdbcdcdcaacbbbabbacdabcbdcdabdaaaddcddbdcccdccabbbabdbcccddbbbbcabdaccacadaabdcabaadbbdaadccacccbdaaaddcaadcbbadacabbaacacaadbaddabcbccabcadcabccaacddbdbadddaabbccaaacdbaabcaaabbbbbaddbaabdabbbdbbdadbdabbaccdddcaabdbdadbcbcbabcddbaaaaabbcaabdcabcbbcdcaacdacbbabbbbcdcbadabdbabbcccccdbddcdbdcabddbaabcacbccdccaadaddaadbbadcbdbbaabacbaaaadacaacdbcddbbdaddbbccadbcaccdacbbadbbaddbaabddadaaddabdbabaaccbcaabacccdadbcbaddacacdbbbcacadabbcacababcdcaaccdcacdcbacacdbcccdcaaccbacbaccabacdadcdddccadbdcdbbdababbabbcddabaaaadddaaddaddbdaddabbcdbbbaadbabddcadcdcddcbaaadbcddbcbbddccbbaacdaacbbddabbccddcdbcabdbcdaaabcabaddbabacccbcbbbcaccdddcbbabbacdcdcdddcadccacbdcdbadacbdacbacaddaacdbccaacbdabbcbabccaccaaddbcdbaaacddbbdccdcddbcaddbcccdbbadaddbbddbbaadbbcbcaabbdacdabacdccbdadccaddbadaaadaadddaaccdbaccbddcbaaabbcbbdccdabaabdbcbdddadddddbadaaccbbdadbcababcdbcdddcaddddacbccdcbaddcbdabdcacdbdabdccadbacbaccbdaabdaccabcddaaddadbcbbccdababbcccaabccabbcaddcbadabdadbcacdaabcbdcbdcbaadcdbddbccbccbddcbadbccaaacbccbdbaddcbddaccaccaacbbbddcaddbddbacaacbcaabacccbbdbbababbbcddccbacabbcdbacdcccdacbdabaadadcbbbabbcddbadaaccaccdddcabcccadaaacabbbcaaacdbcaadacbbaccbbdadacdcadbddbabdbddccbaddadddaccdaaacccdbbdbbccddadcddcaaddbbdaadbccddadccbaddaadadaddbaddabaccbaaaddabcabbcdaddbcbccddaddabccaacdaaaaabcdabaaabbbbcdccbbacbdacdbcbaddbaccdddbaadbcdccccdabacbbcaaadbdcccbccbbbdbcaacbdbbcccbbbcabcaadcdbadaccbcbadbbddbcaaaabbcbcdbabbaabcacccdccdacdcacbcadacbaccdbdcdabcacbbcabbbcdcbbccbabbacaaddddcddacbaccbcadbbcdabcbcdcbbcbdadbacbbddadbaadadddbcddbbbbcadcabcdacdaaabaddcddcdcdaabcdccbcaacbaddabbcbadccdadadababacbcadcdcbbdbadaccbdadacaadccabbcdbdabacdbabaaaccdcdbbbccacacbbbddabdbacdcdadadbbcddcccabbcdabdabadadcccbaabacbccbabacacbdbabdaadacaaacdbcddbdcdaadbbdbaaabbdbadbdccdcbbacdabacabadbbadcbcaccddbaddbcdbdcaacaabcbdbdcddaaaabbdadddabccadbacdcdadbacbabcccbbabadccbcbababddabdabddbaabddddcaddadcbabbbcbcacabcaaddcdadacbbadddddacbdbcdabdbbbcabcbcddacdadcaccbbbbddacdddbdddcadaadcbcbdcbcacccdbcbcadbacddbaabdbacbddbbcdbbdabdcccbddddbdccdacbbdacbababacdcadacdbbbdcbacbcacdcbcbaacbabaacdbddaccbabcdccddacadccdadadbcacdaddcdabcdcbbcccdbbcbdabcdadbddabaaaabdbccdaadcacdccdabbdccbddcacbbcccdddcbbcacbdacacdcaabdacdbcddcbadbadddacddbdbddabdbaacaddbacbddaccdcacbdcbcbadccaabcdcbadababcaaacbccbccddbcddababbdcddbcbdabdbbbacaddbcdbcdddbdaccdbcabcbadbcdabbabbcdcdadcbbcadbadbcaccccbabbbdcdbdbbdabadbbbddcadacbbddcbbdcdabcadbbaddddabcabdabaabcaacbbccdabdababcadbacbabccbbacdbacdbbddbacccccacdbaacaabdddbbaaddabaddbbdaddadbbdabbaabccddcbdbaccabaacbccbdbddddabcbbadadcddbcbddadcddcadbbbccaaaaacbbcdddcaddddccbccbdcdacaccadcdccaccdcbabddbaadbaccacdbaaadaacdacbdabdcccaacbaacbdabcbccaaabdccbabdabcdbaddbaadcccaccadbbbbccbcbbbacbbdadcadbadccddbdddadddabaaaddabdadaabaccdcccacbbccdcbaabcabbcbacdddcdbcdadcabdcabdbcdacaadbcccaadbcccabcdbcbabbdcaadadcbdcaacaababbacabbabbccaadaddaddadabbaddcdbcbaddcddcbcbdaabbbddbcabdabcdadabcdacbacdddacaabbdaaaacddbaacbcabbcbbbcaaddaadcdabaddccdaccbdabdbcbbbcdbabcbdbcacacbbcdcbcccbbcbadcbdaccdcbbdababbbbdcdbdcbdcbabdcaddaddcbbddcdacbddcdbbccbdbdddcccbdccbcccdbcbdbdcacadcacdbaaddadbbcbabdbacddbadcacbbcbabadcbbdabbdbbbabababaaddadabcbbdbadcddacccacbacbcbdcdbbcdcdbbbadbbddddbdcdcbbddaabdbcbbcbbdcdaadababdccacadbabbdaabdaacadbddcdbabcddccbddcccdaacdaccbdbabbbdbbaabdacadacbbdbcabdbbaadddddcbdcdccabcbcccdccdcbdcbdddcbddbbbbbbabccbcdcdbdababcccddacaabddaddcbbbdabacaadccacdbdbdabbcbcbdccacdccdaccbdcdbdcbabccbdabcbabbdcacdcaacddaccddbddccdaddbadababacbdbcadacabacdacaacaccbddaacacbcbbbcbcacbbaaccccbadcabdcdadadbddaacbdbcacccbaadbdadababaabdbcdcabaacdabbaacaccbaddabdbbdcaaacbccbdcbbbaadbcbaacbbddcaccaddcbbdadaabcbbabacbbcdbcabcccacdcbbddddcdcdddbbadbcbdadddccaccdababcddbcabaadcacccadbadbcbaabadcdababbdccbdbbaccaaccbbaadaaccaacdcacdcacbacaabcbcbcdaacdaaaacadbabdabdadddadbdbdbdbddabaaabcdbaaaaababdbbaadbdccacbdabccdabadaabcccbcacadbbbbaaddbdabacccbdddacbaabcdcbccacabcaccbadcdccaddbadbcdccaadddccddcacbdcbbdddcacadacdadaddcbbcdaddcabaabbbbcaddbaaadababaaabdccdacdbabdbbbdbdacacbbababbdbdaccdddbabbacaccadacbdcdddbbdaccbdcdadaadcbdbadabcbacddaaadddaccbdcacacdcdcdddbbcddcabaaabcddadaaacbdaddbdabacbcbabcdccbdaaccbdbadcbbdcddcdcbaabadbddddbbddccbdcbdadcdbbbacabbbdbabacddbbadbbbdddcddccacbaddbcbcdbcaaadbbcdbcbbadccadacdcdcdaacbccacbaabbbaccbdbabbdacdadacdadbcccdabdaaabcccaabcbddbbaababcbbaabcdcbacabdbcbcdadddcdabcbabdbcbdbacdbabbdadaadacdccadaadcdcddbdbcacabaaaaaddcadbcabdbcbcaaaabacdcbbbbcbdbbadddabdadbcadaddabaccbcbcbadacbbdadcccdaadbccbdadcddbabadcbacbddaabbddcbcabcbcccabddadbbbdabbbdacbdabbadcbdbdbdddcbcddbbdaccdcababababbddbccacddbbacccbbcbbdbdcccbbabbbaddaaaacccbccaabbdbbdbabbaababadabbccacddadcbacbddababbaaadadacadbbacddbcaddbdbbacbdbccabdbbcbbababccbaabaaddbbcabcbacadadcaaaabdacdccddbcdbcdbcdccabaaaddbcbadcbaadbdccbaadccdddbdcdaabaadacccabdadabdabaacadbdaccdbbddbaaaddcdddbaacdddbacaacabaccbabdaabdabdbaacccaacdccbaacadaddabcccdbbabbbbababacacdbadbbccbbdcbdddadbdbaddbdccbccacbbbbadbdbbbabccbdcabbabbddcadcdccaddcaabcabcbbddabaacdabdbaddacdcadcabccdacabacaabcacbdbaacadbbaabdbabcacbbccddbbdcbbacacadcbabdabacddcaaaacaddaadaccbadaddbcdbbbdccbdcadabbbabcbcacbddbaaaaccbcbaabbdcaaabddabccddbabaddcaccdbbdadbadccaadabdadacbbcdaaaddbcabddcacccddbadaadaccdbbcdcdbcabbccbdcdccdccababbdadddaccaccccccdcbbccdddbbdbdababaabbddcdbbbdbdadcadcacadbbaaacbbdbbcccbdbdcabddcbbabdbcdddbdaccacacccddacabdcbabbcadcbacaccaadcbbdcbcaadcdccbaccbaddbddacccdaccbcccaddcbbbdbbcddcbbbdbacbdbaabdcaccadaccadadcbbbdacbacdbaabdcbcbddcddbaadcaacddbaddbaadccdddbaccbcdcadabbdcbdcdacdaacdababdcdabdacdaadaabdaddabdbbabbadbdabcddccbcbaccdbcacabcbcaacacbaddbbadcdbacbbcccabbabcccaabaddbabddcbacbadadcbbbddacadbcdaabbcdcbbcddbcccaacbbccabdbdacbccbadabddaadbabbbbadbcbcdbbdacabddddcbdacdccdcaacddacbcacdcacbdacbabcbacbaadaddaddaccddbdcacccbdbaacaadacdadaddbaddaaabcbddbcadaaddbcbdbacbdbbcdbadabaaccbaaddbbadbaaabbbcbcdcdcbabacdabddbbdcdddccbcbccccabbcbbbbbddcbbbbdabddbaddbaacdbdcacaaacdddbbcadaccadaddbddbcbabdacdbdacbbdaadabaaaacabbaaadcbcbaaccacbcddccdbaabbbacbbdacdabcbbaabccccdaabcddcbbabcdcddabcdbbbbacdbacdbcdaabdbccbcaadaddbdcaddcbbdabcbbdacddaaccddbbdccaabdcdddaadccbccdacacaaddddbbccbddaacccbccdbcbabdaddbddcbcdaddbddbdcadcbacbbadbbdcadacabccacadbdbdacabbbbbbacabaccddccbabccaacbdcbbbdcdbdbdbdabddbcbdaadcddcbdbcaadadabbabdddbaddddddccbddaabcdcddaacabbbaabdbccccadaacbbaaddabcadabbcddcacccdcabcbaacadcdbdbccacabdcdadbbdbbacacbdbcddbabaddccbdcdcbabdbbbbbcabbddbacdbadcabcbadacacdabccdacddadadcabdabdabdcbdccdddbbdccccdbccccaababbbbbcacbaccbacdbdabbdbdbbdbabcbcadbbacbbdadcaabdbbbabcbccdbbcbdbdcdbddacddaccccddaccccbcdbbbddccbcbcdaaacdbdbcddbdddbddbabaaacdcaabccadbcadcbdcddccacadcaadcbbbdadbabbcaabdcbbadbabcdbbcdcbcabbaccdccbbabbccacacbdbcddcdbbdcdacabddbddbbbbcbbccbbdbdaacbcaddcdbaaaacadcbddbcdcbcaccbabccccccbacdbdbdcdcdcbcddabbbbbcbbccdcbcbbcbddaaabbbdbdcaacbbaaaccdbabaaabaccacadcccdacadaccdaabdbbcdccdbbcbbadcacabcccaabdabacababadaadcdddbccaddbacaacdcbacdcbcdbabcabbdcdadacbdadaccddccccaaadbacadcdbbaacadcbcccaddccccdddbbaccbacabcabbbdaccdbaacaadaacabbbdccadbabacaddbcddcbcacdadcabcababbabcbbbdbbdcddddaccbaacdabbbaaacccddbddadcdbddcaccaddcadbaacbbcacdbadcddbcdddbbadabdabdccdcdccdddccdaccdacddcbbcadcabddaddcbddabdaabcbacbdbdadbccbabdbabbcbcbcabcdddccbcabdbbadbdbdcadcabdabcddabcddbdbaaddbaabcdacacbdbacccaddcddcaabaabcccaaccbaaadbccbbddbdbabcddddddbdabcbabcbddabaaaabcaabdabcdbcdbacbdccbdbbdcddcccbcabdbcbdaacbadbbbbcdcdadbadcdccabbaddddadbcdcdadccaaaabaadacddcbbdbccbdcbddcababbddabdbbccaabdabcbcdabaaccdabdccddbbcbdddddbdcabbdcdadbdabacdddbddbabdadbdabacdbcacaacbdbaccddddadacddcabbcdbdcbccbabcbdccbadccacacbcdadbadcdaaadaacdbaadbcbcddbcdcaaabcabdccbdbacbdaacdcacbcadcabbcabcdabdbdabdaabcbddcbcacaadbddbbcdabcbdcbdbcadacccdababbcdbabdbbddbbbdaabbdbbbdddabaacaaccbdcacacacdbcbcbdcdbcccdaaaaccdcbbbaabdbddcbddbbcbcacacbcdbbdbdcbdabcdbdabddacccaabccaacabdabcdddadbabacaacbabdbdcbbbadaccdccddadbccdbbbcadababbdcbcbabdadabaccbcacabbaddaabdbdacaacadaabcbccbaacdcdcadcbcddbdcbacdaadccdacadddaabbcabdcbacadaccbddccbaddacabbdbacddacddcaabaddbcddddabacddbbcbaaaacadbccddcadcbcadbdcbbcadcbdcdaadbabdaadbddbbbdbcdaaddcddddcbcbdbdbddcdcacdbdbadaaddabaadacabbcadbdabaccbdadaadabcdbcacbadcdcdadcacadbbbdbdccccabdcaabcaddbadababdbbabddbcbbabadacabcadcbbdacabdbdcaadbddccacdccabcabcbbaacaaaaddabdcaaccbbbcbddadbcdbbdcdbcdacbdcdddaabdadbadcbadaacdbbccccccddcdbbccdcaccbcdccdaccccaaadcdabbcbbaddacaaaaddacadddbbbdbdaabbdadbdbddaabadbddcbbdcbbbaaaadaadcdcadacbaccaababccddacaabbbadbbbaddacbddddadbdccbbcddababdccbcccdcadaacacabbccacbdbbbadcbaaccbdccccadbaaabbadbcacbaaddbbadccbdcbacdadacabcbcbdacaaccabbbbcbcaaddadcccacdccadcaabaaacacddbabbbccccaaccbdcaabaabcbaabdaabdbaccdcdbddbbcdccaaadabcbadbcabccacacdcbddaaddaccaabadaccddacbbaaabaddddccccdbccdcdcbaacbcbdddcabddcdccccddbacdcdacccbaacbbccddcdcadabcccdadacdbdddbccbccdaabbaadcbbdaccdcbbcaadacacbcbbadcbbababbaadacadababaabcdcdddaadabdaabcabadccaccdbcbbcaacdcdbcaacdabcccdaacbaddcbdddacbacaacabcacabaadbbcdddbaaaddcddcdcbbbcbbbbdcdbacabaadbddbdbbcbadbcabddacddabdbdacaaabbccadaccababdbdabdaabadcccadccccbacaccaadacccbbdaacacdaadabdbaadcdbacbddccbadcbcdccbbaabacbaadbdcdaacbcccbddaadbcdcdbbbcaccdcacbdbbdcccdcaaaabacabcbbdaaaadcaaadbcdcdbaabaccdaabcadbccdbdcdadcacbcbdcacdccdcbbcccadbdbbcdcbbadabcbdaccabbabcdaaacdaacaaddccbbdbcdcaaadaabdaabadbbabbbbcbdcaacbacaacdccccabaddbcbdaadacdccbacbadaacabdcadccabdababbdacdbdaabcacdbabbcadbdaadbbcbcaadaadbcadadaacddcaccaacacdbdacdacdbdcacccdbbcbdcddbdcaacacddaababcccbaabcbccbaccbbacdcabbaaacdaadccaccaadbdddadbaacadcababbaaadcdbcdcdcbdcbbddbabbcbddddaaacadbabadabbcbdadcaabccdddadcdacdbcbacddccddabccbbabccadabbddddaabddcccddcaccbbdccaccbcabddcdddcaacdbdccbbbcdcccdccbbbcbadbdaabcccdcdbbaabaabadabccacbdaaaabdacabdaacdbcdbcacdacabacbaadaaddaaabcdbbacccdadcbcbaacdababdabababcbdcdaaaabcdaaaaaabdaccdcbdcddbbbdcbbadadadaaacadbaaabacbccabccdaccdcbadaabbcabdbaddbdbdbabadbcdccdcdaadbabaadbcbadbcccdcbbdaabcacddbcdbdcabddcbdcabdcdbdaabbabaccacdbbbaddddabdcbccdccbdcadbcbadcabdccdabbdddbdbcabaddbcbcbbddddddabcbccabdcdacaacbcbddbdcdadcbcabccdacdcacadcdbdbbcbaadaacbcbbcaaddcdbaabdcdcbcadddabdbabaccdaccbacdbacdacaabbaacbbddcadcabbdbcadcadddaadbaaadbdcabcdbbbabdcdccbdadabbddcddbdcdcadbbabbcdbaadaabdbdabacaaccacddcdabdcbaaabdbaaccbcbbbddccdbdcccdabaadcdcdbdabcdcbcbcaccabbbdcbacadaaccdcdcddbcdabbddddbacbcbdbddbbabcdbcadabdbabbddbcddabadabcddcabbcbbbadbbbcaacacaabccaddbadbacbdabcdddcccbccdddaabccdbcaabacdaaabbcbabadcbdbddabdddbbcadaddbaaaaddddbbcadccabdcdcccabdccabbaadcbaaabcbddddbadcbcadbcbbbcdbbadbdcccbcddcccbbcabbbbacbccaabcbddbdaccadcdcbbaccccdacaddbcccbabbabbbcaabbcbcbddbbdacdcaddaadddadabddddbbdccaccddcbcabdabcbabbcbaaadcccadaacdcdbcbacbacadadaadbaababbccccabbabcdbdabdbcdabccbbaabcdacccaabdbcbdadadbbbcacabddaacbabbdcaddbdcabacacdcaacbacababbaaadadbababaddccdbdacaddcdbbcabdccbabdbbcbddccabacdacbcdacaccbcbbbadbbacadcbcaabadddddcddbcdcadaacaacbacacbcddbadcbcbadaadbbaacbbcddadbdbcbccdddbddaabdbaccbcdbcaccccbcdccbadaaacdcbbcaaacbddbbacdbcddabbdabcdcacaddccdbcbcbabcdadccaababddcbabcdabbccccdabbaabdcdcabdacbaaddbbcbcdcdbdbbbdcbdadcbdadbbacabdbaacdcbccadabcacadcadabdababdbacbcbddddcccbcccbbbabadbcdcdddbbaadcbaaccdbbacdcbbcdddbacdcbcbcabdccccbcdbaaaccadbcbabdabbbabdddbdcdbcbadcdccbdaccbabaacdcbbddadddcaaacdbbcbcadadcdaccddcdbbdcdbbdbdddaaaabbbddbbcdbdaabadccaaacbaaabddddbddbcbbddaddbbbacbbadcccddaadccadaadddacbbadbaaadcdccbcdcbacbaabbadacbbadbdcbacbbddaadddadacaddaacdbdcdbadcdbaaacccbadcdaadcdcdcdcaacbccbdbcbddcbdcdaabcbdcdddbcbdcdabcbcadbdcdaaabcdcdbacdbccdaccabcabababcaadbdbbadbbbbadbbdbdaaacabccbcbbbcabdccbbadadcbbdcbbaaccddddcbbcbabadbabaabcdbbddbdaaccdbdcbdbbcabadbbdcdddabdabcabcbcccaaaabcccbddcdabbdaabaccbbdbbaaccdddbdccddbccbabcacbbccdbadbcbcabbdbdabcabcabbdbbbdccabaadabcaadabddbaddacdbcacbacadaadabbacabccbbbacccaccbabacccbdcbcdccdccdcacaddaadababaccbaadbcdaabbbadaacbabdbbddaadbcdaaaadbcdcbabadbbdbccbbbbcbccbdaddcdddcbcdbdbbbbcddabcaaacabacaadddccdbbbdddcdcaacdcbadbaaacaabbcadbaaddcbabaccacdddbbdadbadcccbbabaaaabadccabadadaadcdcdcbadbaccbcdcaddacabdacaaccabcadbbddbdbdcbccdbababbacdaddcdddddbbcbaacaacbccbbacacacbcadbccadcabdccbddabaddacaccdbbddbcdbacdbdccbaddbadcaaacccccbaabcaaacbddcadacddacbdccbadbbdaccabddabcdbbbbccbaddddcddccccaddadcccabcbdccbbbddbcddcdcdaacbdbdbcdaababadddbadcbabdddbdddadcddabcdadaadbddabbccabbdbbaacdaacabdbdacdbadbbbbbacbabddcdccbbdcdcdacbcbdcccddcddcbaddaccdcabdcdcbaabccbdaaacabacdaacbdcaabaacdbaacaadccaaaaaccaabbdccdadadadcbadacaabdacdbabbdcdddcccbcbbaacacdcbbacadccdcbddddcbbabadadaacbaaaaaaddccccbcabbdbcbdcabdacbdccaabcdabbcadaaabbdbbdcaddbbcacbbabdbcdbbabaadaadaaccbabdddbbcdbbbabadbdadadddccaaacacccbcddbabcdadcccacdbcaddaddbaccccaabcadadbbcdccbbcbbcdcccdbcdbbddcccdababaabbdaadcbbdcbccccdccbcddabbbcbbdbadabdcbbaadbddcaabacbdbbccacdcdbdccbaccacdbbaaadcbbdbbabdbcaadccaaaccaddddbbdbabdbbadcbdcabadaababdbbcdcdaabcbdcaadabbaabaccabbdbcadddacbdabbcbcdcccabcacbcddbccadcabacdadccaaacadaabddbbbcacaadcacbaddccbddccabdcadcdacabadcabcaadbcadbaadabaababacdcaaddaadbbcadaacbcbdcaaadbabcddaaabaaabdcbdbbacdcabbabcbcaacddacacadbdbbddaacdaadbcccbcccdbcabaddbaabcccaacddcdbbbccdbbcbaadddbdaabacacdbcddacbababacacdbacdacddbaacccddbcaabbacddcbabcadaaacdcccddbcbdbbccbccdadbbcdabdccdbcddbdcdbbaabbcdbcddcbddaaaacddbbcacdbababbaabbcacdaadadcabcdccbbbddcbabbbdbdabbbcdcabcabbabcdcabdcbdccdacbacbbddacbbcbbabdcabadbacdaabadbbddcdacdcbdbbbacadcdaaabdbdaddaadbcdbacaccbabbccbcbacdccdbdacacaadaaabcadabbaccddddddcbcddddadbcdbddabcccacccdbacacadcabcccacdadcbaabcadadcbaacdabbbddadadcbcaadacbaaddcaccabdaccaaaadbbbbbcacdabbcddbcabddccbcabbabbaccbadbcadbbabdaaadbdbacacbdadbbdbbccabdcacbaadcaaadabbddacaadbaabdcbbaaacaabbdcabbdccdddaaccdadababcbbacabbddcdcbbcdacbadbbabdbaaaddacccdaadbdbbbddcdcababbdaddaadcaaabacacbcacbcdcdaabaaddbdaddbbcaacbcbaabbabbbadbcaadcbcddbdccdadcdbadcddbdcdacaabaccbdddcdcbccbbbdadaaabacbbabdcbabdabaddabbcdaaaddadabaaccccaacccdbaadacdbccdcdcbcdbdaabccacacdbddccdaccacbbdadacdcababcbccaccbbcabcabbdbaacdbdaadabbddadcaddbdabdcbdacaacabcddadaaacaddacccbabcacaadabbadaccccadccabcdabadbcdddbdcadcccbbbabcbabdaaaddbccdaaacbbadcbbdccdbaabcaccacddabcbbcbdbbbccbcbdcabcddabcaacabaccddccdccbcdbbbcdbcadcbcbacbaababcacbbaddaaadadacaadcabacbddcabdcbbdadbabcdbaddadacbbcbaaabcaadcabbcbddacaabbcaddbcdccbddccdadcdbbabbbaabbbadaaacdbbcbdaaaccaadbbabcdccbddbabdaabbcabdbaaccdaababddcabbdaaccbbdbcbaaadbdccadabcaaddadaaccdaddcabaddbcdbcadaacaaccddbadbdbcbbbacbccbdcddbacaccdcdbcbadbbdadbdccdcbbdddbcadcdacccbcbdbbcccdbbdcbdbbbcabbbabcbabaaabccbbaadbadbdacddcccacddaddcccacbcdacabbcdadbbadcadaadaaaadcbaadbabaddddbbbdddcdbacaadcccbcbaacbbbbdadcdbdcbbbcbdaaadccdbaacacadaccbcaabcacdcccdccaababdcabbcacccbddaacaabddabdcbdcbcdbacaaaddbaddccabddaccbbaaabdabbaaaaddcbdcacccadccdaaabdaacdadccbaacbcdcabbbbcddabdabddadbccaaccbbacbdccbccbcadbbdbbdccccdbbdbaaddccadbdbdbdcbdcbbccbbdabbbcddcdaabccbabacaacbbabdbbabdbaadcbadaddbadccaddbdacccbdbaddaaacaddadadbdcbdbdcadccccbdbcabababdadccdacdacbdacbdaabddcbddbbcdcbcccbacbabbbbaacbaababddbbccabadaccbddaaacabdbbcbbadcdabbdbababcbabbccdbdadacbcbccdabcdbaabdccaadccabddabcbccbbddaaaddaaabbcacbababbbccaddddcbacdbbabdaaabacbbbcacbaaaadcccacbbabbabbdbcbddbacddcdacdcdccadddbbcdcdbadbbaabccaacdbbbdbbccbdcacdacdcdadaabcbcbacdcbcbdabbbdbdcddacbabddbddaddcbdcdddcaadcbbbaabbbcbbabbccdbabcabdadbabdaaccacaacbacdbaadcacdcdbdbcdbaacddccacadbacbbbdacddccdabddccccdaaabbbdaaabccccbbbbadacabcadbacdddcabaacddccabbacbaadbdddbddbccbbabdbdaacddbdaaaadbcbaabcacacabacabaabcddcdbdcdaabbcdcdcdabacaddcbadbcbacaccbbcacbbdddbbccbdcaccccdbcdbabcdbaaabddccacabbdcaadcdbacaaabaccdcccdaccdddaccacbbabcccbccdbddccbdbcbabaaaacaacadadabdcdabcbdaccbdccacbabddcdacddacacbbdcbbbbcbaccdaaccaabacddbdccaabddccdadaccbdadbbcdcdcbaddbbdbbdcadbbcabcbddbbdcbdacccadcaaadcacdddcbccdddaacbbcccdcaacdabaabccabcccdccdadacaaaaadcdbcdccbaabadcdbabddbddbcdcdccadccabadbbbcabdabcbcaacdbdadacddaabcbcbdbdddddaaaccdbaacaabacababddaccdcacbcbbadbbbbdaaccaccaddcddaacbdddcddccdbcaddbddcacccdacadabadcccdcacdabcbbaaababbcdbddcccdaacdcbcdacadabcbdcccadddcdcdadccacddabadaaccbddaadabcabcbdadbdcbbcbbbacaabdbdcbbabbdcaddaaaabcaccbbdadabacbbcbccdcbaccacadccccbcacdccadacaadaabcaddddbdadaadadbcdcacbababbbbbaabbdbacddbcdcddbdaccdcdbdacbcdbbbdbdaccccaadbcccbbacbabcdbddaaadcbdbddbdaddcbbcddcdbcabdbabaccacddaaacacaccdbadcbacacacbbadbbccccacabdbdaaadbadcdbadbcdaccddbbcaadbdbcdcccbabcdbbdccaadbcacbdaadccabdcaddacaabbccbdbadddcccadcddbaadbcdabccbdddabbcacbcdcadcdcbdabaabacbbddadccdacdaaaddbcaabbcaaaabcddaaaddacababdbbbdbaaabdbabadcbaccdbcaadcbdacadaaddabacccbbdadcbccdccdccdccabbcabbbaddbcbbdccacddababcadaadacdcdabbbadabdcdcdaadcdabcacddbdaabcbbbbadbdbcdaddaabdacdbaddbbbdcbbcbbcaacbadbbdcbdbbbcdbadcccabddcbcabbdadbbcbbcccbbcdcaaabacdccbbcabbaadbddcccbaaabbadccbddcadcbdaadbadcadaadcbdbdaccabcdcbabbdaabacaadaddadadcaccccccccdcdaddbdbcbaadcbddbcabacdadccbcccccbadcadacdabbdadbccbddbdcddcacbabbbdbaabdcbbbaddbcccbcddddddbccabcdbbaadbbdacbcabcdccaddcdbacdaadabbcadbacbcccaacbacadcbbbdcdbbacddbbcbcccadbccdcacdcbcbdabdcccccddbbabadbdacaaacadaaccbcddaabdcdccabdbaccdadaacbbabcbbcdacccaabcdbaddaadcccbabbcbccccbcdcacacdcdbaabcacdcccddabdccdaadcdbdccbadadcbbbbbcadddadbcddbdaccdbddabaaddbacabcbcbdacadbddabddddcdabccbccaaadccbaacccbbbcacbccaccaccbaabdcadcbddccccabccbcabccccbdccabccbcaaabbacbbbdcdbaccadaddbaddccdaddccbbbcababaddcaacbadaacccaaadaacbabbdcaaadddccacdaadacbbcaccbbbaccbbdadccdbbbcdbddacccacdacbcccaccaaccdbbaabdabbbdcdccbcbcccbccddcaccdcdacaaaccbacaaaadabbcbdabcadacabbaaabbbbcaaadaccbaaabadbbdcdbcaabadbbacdbdbadbddabcbabcbbddbbbdcabdccbaababbacddacbbcaacbcbccbbcbcdcdcdadccbaccbdbabcabdbddcaccacdbbdbcdddacdcaddbbaadcdabbadcadbdacbccdadabbdddcbdbdabbcdcdcacbbcbcbcbbcddbabccdbbacadbcccdcbadbdadadaadccdcccccbbbccbdbaddbbdddaaacbbacdacaacbbdbabdacabdaabcdbabdcbdbadaabacdacacdabcdaaccddbdcbbcddbdabaadcadcadcccccbadadcddcbdbbbbbcaadcbcbbddcbdbacdaabaacccaacbdcddadbbaaababaccdcdabdaccbacdbbaccdcdddbbbddcbbaddadbdacadccadbaddacbacbababbbadcdacabcbcadaaabccccddaabaabbcccadacadcadbdcdccbbcbdbaddabdcbcccccadbacccaccabadbbbddbabddcbbcccababacababaabacdbcddabddbbbdcacbabddbadadabaacbdaabdbcbbbcdbcbacaaacdbdbcccacabcccddbdacbadccdaabaddcaddcacbddcccacdcbdbaabbabadaabdcdbacadaadccdbcdddabbacdbadcdaacacaabdccbaccddcddcddcdbbcbaadbdcdaddbacdcabbdccaabccadbaabcacbaccdcddadaabbaccbaaabaabbdaddadccdaccdcdaaacccdbacbdaddaaacbdaaaaabdcdadaabbbacabbccdcaccbaccabaddabaaccabbacaacaabacbaacacacabbbbdbddbbddddabadbabaccdcbdcacacbaacdcdabcbbddbabbacdcbabadabdadbddbbdbbaabacbdadbacdabddbbcddcbcccabadaabdbcdaccacddcacacbabddccabbaacbccaddadddcdabdcdbcabdbbcdcddccacdacbcddbabbbcadadcaaadbacddbacdcadcccddbbddcdbdcadbbbaabccbdcddbbdcdbbabaabdcacaaccacbbccacbccdaddccaabacaaddabbababacddcaccaddabacdaddbbccdabacddbcbdcccdaadcabdcacbcbbcdccadadabdaabbadabbbcdccaddacdbddbdddcacdbabdbbccadbbbdaabadabdbaacadbadcdcdcbcddbdddadcbddaabbbcbabbacdcccbaabdbadccbccdbaaddcbbcaaabccbdcdabdcacdcadbaabcdbcdddccbcbccaaaadbdbdccddbdbbbacdbbddbbbadbacbbdcbccabdcbdacddaccacbcdcabcbbcbbbcdabbbdccbcccadbcdcbbcdbddcaabdddadccabacddcddccbacabacdbccbacacadcbccdaacbdcdacbcddaddddcdbddcbacbdbbdadddbaacccdcdaacaaaadadcdddadbccaacdcbacaddaddcdbdddbbaaddccbbaddadbdbacdaccacacababdccaaaccdccdabadbbccbcbcaccbddbdbcdbcdbdaabbbccabbbbacacadcaddadbbaddcbdabbbcdcdcdaccdaddbddabbbacbcbaabbaabcdcacbdcdbddadddcbdbcbdbbdaaaabdabacadbddcbacddaccacdbbbbdddaddbacddbddbacccddcabbcccdbccdbadbbcbbcacdcdabaacaaccbdabcbccddcabcddadabdbadddddabccabcdbccaacdcacdbacbcabdccadddcbbadadbaaaadddddccadcbccadbdbabbabadbcdbcdcadaccccdadccacdbcabcdbbaddcaacaaddbcacadbcbaaabbdabacbacdabadcbaabadcdabadccbdcddbdbcdadacbadcadbdcdcdcbdccacdcacacbadcbdacccddcdaabdbabcbcadddddbaabbaabbbbcdadabadccbdaaacbdbbcacbdacbcbbccdcbdbababdcdacdbcabbccbcdadbabbdaccadbacabcdcccddcbcbabbaaaddbcabbcadcdddcabaabbabbccccddccabcdccadaacacbddbdcbcaabdaaabddabdaabddbdcbdcbdabdbcbdbccbaadccaddbccddabcabdcaabcbcbcddaabaacddcacddcdcbdbcadadaaaaadcdcdbadbddcbdbaccbccbadcdbdabcadadadddaddcaddcadbabcacdbbbcaccaddbcbdddbdabcdabcbdbcaacdcbaabadbacaacabbbcacbdbbbbadabcddbadaacccdccadabccbbbdcabadbbacdbaabacaddbdcbabdadbdadacccacaabcadaabcaadadbcdadcddcacbbaaacdbcaabcbaaabaaddcbbaadccbabcaccbdacbdbadacccbccabcdbaadbdacdbccbbddbccaabbdbadcaaddddadccdccbadcaacdcccddabddaabcbaddcbbbdcaabbbddaaacabdadacbcbdddbcbbbabbcbaccaadadabdcaccdccddacdcddcddcdbcacbadcdccccbdbaabcdabcdbdbcddddbabcbbacacaaadcddabccabddabdddaadcabbdbdcaccbbcdbcdcaaaaccabbadbbaddbcdcdbdbadbaccdadcabcbcbabaabdabbcaadaadbbdacbddbaddccdadaadaababaccaddbdcddabcbdcbbcddcbddacbccbabbcbcdbacabcbaaadbccbdcacaadabbbddcabbbbabbabbacdcbddbbcacbaaadbbacdddbdadbadbaaaabaabaaacdcdcdadacdcdcbbcdababacdcbbbabcdaaabddcbdbaabdcaccdcdaadabacbccccdaaacccdccbbdcbdadcddbadcdbddbbbacbbadabcbaadaadabdbdcddcaacbbbccbcbadaaabcbcbddaddcbacbabcbcbdbbbdbaccbdcbabcaacccacdbbdbadcdcdabddcaaaabdcbbbddbdbbaadbdbdddcbddccadaabdbcdaaccabddabbaaaddbabdbdcacbadacbdbadabaaacabdcadbabbdcbccabddcadcadaccaaaccbbcbdcbddacabacdddbdddcdddcbadbdcbdacbaccdbccbdbaccccadcdcbdcddacbadcaabadbbdddabbccbbdcaccdccccabbbbbdaadbadbcaadabbdddbdacbbdcdacaacddcbcbcbccaabcbbddcadbccdbcdbaddbbaaaadaaacdccbbdcccadccdbadcbdaaddacacbdabbadaabadacdcaccbdcdcdadadacdadbabcbaaaacdcaaccdaddaaccadddddadcbabaabdcdcadcaaaaccdcbdbccabbdbcacdbacdcbadccdaadcdacbdaccacbdacbacdcabcaaabbdaccdcacaabbdcddaaccbadccadddaccbdabcaabccddbcaddcbddcbcccbdccadacadcddacabcababddbadabbcabacdccabacbdadbcaaccbcbcdbdbabbabacadacbdcbbcbbcddcdcdabddbadbadadddcbacbcdbadbbdacadcadccbdaacbbbccdcaadccbddabacdabcdabdadaddadacdabbcaadbcacbcdbdaaadacbcaccbdcaadacdcbacccdbaaaabdcaaacdddabbddabacddaddcccaccdccdadacadadacbdbcacbcaddaccabcbdbdacbdadbacdbcbddccddcbacdcbaccabbdbdccddcabaacdabaddacacbdabcdacacaccccccbdcabdddabcabbccdadabdbbddcacadaaacdbabbaccacdacbbcdbacacdbcadcbdddcccbdbacbabddabaaadddbddbaddaacbaabcaabacbadcdacbdccabcaabbacccbaccdabdccddabaabbdcadacbadbadbbbdbababaaadacccddcaccaacadcdaadbddadabbaacbcbbdcbaadacccbcabbcaadcdacadcabbacdabdabcabddcbaacbbcbabadbcdadcbadbaddabcdddbbdadacadddcbacaabdccadccaccabbdcadccdbaacdbbaccadaaabaddcaadbdabcbccdbbaabdcddccaabacadacdbacacdddcbdbaaabaabadccababaaadacdcadadbaacccdcddaadcbccdddacbadaacbacdccddaacbaadabdadbddbabcaadbdddacddcccbbbbbaaabaababdcccabdcaaddcbbacccaabdbbdcbabddbbcbbddcccbadcbbdbacabbabacbcbacaddbccbadabacaaddcaccbabcbbbabaaabaabdddbabbcabbcbddabcbbdbbbbddabccacbadaccbbddcbbccbbdddacbacccacbddbdddabaaccbaadadcdcdcbcaddbcadddcddcddcdddaacacbbcbcbdbabddcdaaddabaacccadaacccddadbacdababacbaaaaaaaacccddddabaccbbdcabcddadacdadadccabbcaabdbdaabadbdacacacdddcdacbdcbadabdbbcaabcdbcadcddcdabaccdaaccaccdcabdacbdbabdacddcdcdbaabccdccdccdcaccddabaddadaccbcdbbcdbbbdbdbabcabcccdbdccbdcacccaadddacddcadaaccabbdbcdbadbdacbdcbbbdabadddaccadbbcabddcbcbbbabcbcadaaddbbcddcacdcbdbcbacaabcdddddacdababbdccbacddabdcbdbaaaacbaaabdbdadbadbcdaadbaacbdbddbdcdcaddaddbbdaccbbcddcbbddbbbcabbcacbbbddbbabcacaccddcadcdbdadbbdbddaddcaaacbaaccadcdacdcbcbaccaabbcacdabdabdacbaacbcdadccdcabdcaabcaabacbaaccacdbdbdcdbbdcdacdbbccbcbccbdbbcbacbbbcdccbddcadbcdadddbddaacbcddcddcccbcddaccacbbcbbbcbccacadcacadacbcadacbddcaaabbdbddbbdbcbadccacbbcdadabccdcadcadcddabbbbbbdabcbbbcccdcdcbbbbcdaadbcbccbdddcdbdbdccbdccbadaacbbdabbaaddcddcbdabcbdcbadccacdbcadbacadccccbcbdabcbbdadcdcdcabdbccccccddcccadcddcbbdbbbabdabbcddbdbbbacdbaccbdddaacbadabdddcbacdcadbcaaaacacaabddbdcdaababcacbbaadbbcacbccdbaabbcddaaccaaaccaaacaddaaacdcbbcdddabdabbbadcdccbbcacbaadbdaaacabadddbdcbbbbadadabbcdaacdccdddacbccdbabaabddbdadcbaacddaaadcddbddbabccdddadccaadcbdaaadaccdcddaccdcdcdcccdabdbdbddabcdaadbacbcbbbdbcabcadddaddabdbccdcdccbdcccaadcdabcbaacbbccbcbcabdcddabaccdcdaaaabbadaccbaabcbdacccaddcbccdddbccdbdbbcbbcaabbdccbccbaababcddabacadabaacadbcccadcccccddbbaabccbdcbcbcccaacaabbddddddbdbadccdacaddababacabbdcccbabacddcdbaaadabccadccbcbcbbcaadbbcbbccbcdbcbdcabaadccacccaadabcdadbacddcbdcabbbbbacdbdccdbbbdbdadcbbdabbaabbabddbaddbdbddcddcacbbdbcbcddadabcdabbabcdacabaaddbadcdadabcdadcbacaacbcbbabbdcbbcddddcbcbbcacdbaaccaadbbacbbbbaacddcadbbbacbcadcaaccbbbacdcddadcbdbbdbadbbdddbdacbbaccacdabadacadbbdadababadcdaadbbaabbcdbabcbcbaabbadacdbdcbabdcbcacbdacdccbcdcabbaaccaadaacdcbcbbccbadaabbbabacccabaccdabbacabaacbadbbacabbdbaabbaccabbbacbcacbaccbdccaaccbaacabccacdadcadddcddaccbacdbaabbaabbdcdcadadadaaabadbcbcbcbbbaaaacddbbbaccbcadaabcaabbccbcdcbaaacccbbdacccacacbcbcbdbbadaabaccdcaabbcaccadccbcbacdbbbbdacdaccccbacacbbcbadaaaccbdbccbdbcbcdcaccabadcbbdcdbabcccbccacbdacddbcaddbdbcccacdaacddadddacbbcdadbcbadbaccbdabacaadacdcdacbcdccdddbbabdaaacccccdbaadadbbddadaddbcdadbcabdbbcbabbaadbcbadcddaaddcddcaabbaaacdbacacaabdcddaacbcbbbccacacbacadaabdbbaddcddcdcbcadacdabadaaacccbabdacbbaddbbbacddbdddbaaccbdcdcdcbacccbddcbbdddabbdaccbcdababcacabbbbaabddcddadbccbcaccaaacdbdddaccbaabbaaccdaadcdcabbababccadbbabcccacbdadbabdcdacbbdcbabdabdbabccddabdbbcbcdcddaaddbbabcabbadbdbadbabccdcbacbacaabbabacdbddabdabdddbbccdabadbbcabcbbbcacbabaddcccbbdcdcddabcdcadcaadbdddaccbabdbbaacddbdbdbdbadbaccabdacbdddcdadaabbcacbdbabadbbbaabbbbadadbdddadaabdbcdddcaadbdcaaaddaccddcdaaccdaaaaadbabaabdcbdacbddaddbbddbdbcbbcbabacababcabdbcdccbcdbbcadaccbdcccccbbdcdcadbaababacbbadddcabbcdbaaacbbdccbdcbbadaabbbccaddabbaabcbabbacacbbaacccccdbbaaadacccdcaccabbdbaacdbcbcadcdbdabdddadcabcaddbcbabcddcabcabcccadcdabcadbdcababdcdbbddddadcccbabacccacccbaacaddbbbddcdadcacdcdbddaaddcbcdacabdbbbabbbaabddbccbdbcaabddcbbaddcdbdacddabdabbbbdcbddcbdbbdcdadcacccabbaccabbabaabcaaccddcbcdabcbdaaabdaadddbbbabbcbabbcdabdbddbacaadddcdcaacdaabbccbdcddcadcdaabbbbbcaacccbddcacccacbbaddadadbdccadcdaccddbacddbbaccddccbacadccbadaacdbcdbbcbdcabcbbabbbababcdbdaadbdcbabdcdcbddaacaaccbbcdccbbcccdbaddccccdbbaabaaabbbacaccddbadbadddbbacdcbdbabbacacbaddcabbcaddcbbabdcccaabdcbcbddbdaaddddbadadbddbcbbcccabbddcbdbaccaddbabdcbcdbaccabbddcbaccdbaaddcdbcabcbaaadccbbdcabbccbcdddbadacdbdadcbadccdcbcbcdcbadabbcacbdcbabaadabacddbcacdcacacbcdbdbbdbcaaacccaacdbbcacddccbdbbbaaaadcacbcabadadbbbbccbdabbcbddaacadcacacccdbcdbdacbbdbccbcbcaacddccbacbcbbbacdacbbbcadabadaadccdcbbdabddbddabbdbabdddaaddaabadbbadcbdbacaabbaadbbcbdccdbddbccdccbaabbaccacbcdaaddaaabbdadcbadaadcacbabbbadbaaddcadbccdacccccbcaadbcadbbaaaacddadcabddbdcbbcdabdcccbcbbcccdbdcdcaadcdcdcaaacdddaddcdddacabadaadadaddacdaababaddabbcacacdcbacaadccdaaabccddcabaadcabcddaacdbaabbbaacdacddcacabdbccaacacbababddcccddacbbaacacbccbaaddccccbdbdbcbccdcdccaadacacbccbbcadabdccaddabcdbdddcbaaabbdbccdcacabbbabbcadbddbbbadddccbbddddbcacddaddbdbbcdaacddabacacbaacbdddbdbabbdbaddababddcdcbaabdcdbcaabbcadddcaaadaaaddbdddaabccacccccdabbabcccccabddacbcccbcdaaddabdbddadddddcdaadcbbbbacdcdaaaccbdbadacaabbddbbaaacdabcaacbcbdcbbdaadbbabcadbccaaccaacbbdcdbacdcccbbacbacbdcdbbaacbbbabadcbacabbcdabcbaabcddadcbcacdcdccadcdcaaabacdcbccbbaadabdaddbdadcdcbbbbdabbbccdcaaaabacbbacdddaddbbddbabbbbcacaabdccaadaabbdaccdabdbccdabacbddbdcacddbdabcbbcccdccdbdbacdbbdaaabbabddaccdaacbaacbccdcdcbdabdbdcdddbaaaabcadcaddabbdbbdabccaaacdcdcabdcadbcbdcdbabbadcbaacabacdadccdcaaababcdbdccbbcbacacbdadbcbbadacbddadcaaaaddaabdaccbbbbcacbabccbbdbabdbdadcbcdadcaacbacdadcdbbbddacadadcacbcbadbbadaaabcbaaddcdacabcdaccdbadcbdbddcdbaacabdbcdbccddcbbbacdacdbcdaaadbbbaaaabbcbcacabcaadddcabdcdacdddcdbdacdaddadbcdbaadbcbbbbacdacabdccbdbdcbdbadccbadcbddcccababcacddcbbccddcccaadcbcbbacdcbdabaaccdbbcdddbbacdccadccdcdaadcadccdbdddaabdadcbddbcddbbacbaacbcbbcacdbdbcccdadabddbdbccdadcccbbacccddcdaaabcdcdddabbbcdcababbadcdccddaddaaadaccccacbadcbbdcdbdaaadbbaddabbadbcdbdcbdbcbbbaabdcdddccddaddcbddbbbdacdbddbacbbacdbbbadadccabcdbdcdabcbbabcaabcbacbaaddaadacbbdbdbcccbcadaaacbdccbadadbbdbcbdbdbabadddccccbaaaaddbdabcaddddcdacbbcdcadcaaccbdadabdaabcbbdbdcdcbabdacabbadcadcdacdaadadcdaabdadaabcbdbbdcdaadccccccabdacbabacbbdaacabcdbbddbbbaadacadbcacabaccbdcbdcbbabbddabcaacdcadcbcddbabccdcbdccaaddaacbadddbbbdddabacdbadcaddcbaccccdcbaabdddaddaaccdcabadcdabbcdbcaabbcbaaadbddbbbaddcbcccdadcdccaaadaabdddadabdabaaabccddabcbbacbcabcadabacabcaacddaadcdacaacabddbcdcbaaadddcabcabbddadbbdbbbcaddcadcbadaccadaacbdabdabacccaccabadabcdcccabbcccabbcacadbdbadcdacbadbbabbbbdbcdbcdcacacbcacdcbddccadcbdabcbdbabacdbdacddbacdbcaddaccbaddbdaaadddccbbbabdbcddabbacaaccccaddabbcbacdcdaaabcbadcddcdddbbdacbcccacdbadacacdaabbddbbabcdbcccccdcacbbbbaccddcdacbabcdbbcaabcbbdbdaddcaadbaccabdaabccdbdddbcbddbdcdbbcdabaaacbaacccccccaaabcadccdabdbbbddcadbaadbaadbcaccdbdcdbabcadcaccacdacaccbcbbcdbbccbcaaccdbbdbcbbabbabcbbdbaacdacabcdbdcabdabbbbbdbbbdbcdacdcdaccdabcddbccbdaacaacccddbbcdcbbcaababbdcacadbcacbbdacdcbbcbcbbcbddaddbbcacddcddbdadccbdccbbdbaddbdbdabddbcabcdccdbbbdadccdccdaacccbdbccccdcdbbbaccaabbbbabddadbbdcbdcaaabcbcbdcaaaabbabbacccacaaabbbadbbbadaaadbddcadbabbddaacabcddcbcccaaccaadcbaddbcabdadaabbbabddbbccacccddabcdbaddacdcdacbcabaabdcddcbcaabdbccdacaacacaadabcabcdcbcbcdabbdccccacdccccacdddbabbbbddabaaadbbcbacbcbdacacaaccdcdbcaacdbcdbdddbbabbbdbdcbcbdcadbabdcabadadcdbabbbbdbcdacdaabbaadcbbcdbcdddbaddcabbbabcacdbbdcdbdaadddbbbacddbdaddbcacaadaadcacaabcbadbcdccbbcacccddbadddaaabaccbdabbccaababbabbccbcdbadcdccdbabddcdcdabacdbbcdbbcacdcbcccbacacadbcbbbcaabaabbaaadabdddaaccddcaddbcbadadabcdbaccadccdbcbcddbabbcbaabacacdbaaddcddbdbadaccacddcdbadbadbbdcbababbcabcabcbcacacbdcddcccacddaddbadabdaabbdcddbddacdbbdbccdadccaabbcdddbacdbbbbdbadcbaabdcadbccbddcaaccbcaababdccddaacdbacdbaacdbdbddddbbabcdcccaabcacaacadcbbdbbcbdbdbddbdcbabcbddacabacbbaaddccbabaccbdaaaacacccdccdccadacddcddabaccaabcdddbcbcbbdccbabcbdadaddcabacddaabdaaaabdcacbcbbaababbcaacbaddcdbacddddbdababdbbbcabacdddcbcccdcdcabdbbcaadddcbddbacbabcccdcbbdbabbdccccaddcdbdcdbbabbbdbdbddaacbdaaacacaaadcbbccbcbbccaabbdababaaaaccddddbbcabbbcabcbcdcbdddbcabbbcabbadcdccbbdcdaadabaabbbccbcdacdcddddaaaabdcbaddababdbaaabcbbadcabbdbaaaaaaaadcabcbdbbddabcabbbbbcbbcbcbdccbddbddbcbdacaacbdcaacdccdaaadcbccababcdcabdcaadaddaabacdbcbbdcbaaddcacccdcdaccadbdcbbcdabccadbcbcaacabcbccddacdbcaaddaaaccdcbbcccccdbdbaaaaadbddddacdcabbdcdadabddaddadddbbcacddcaaacbaacbcdbacccdabdcbabbadabccdbcabbacbcacddddcdadaacccddabbdbacadabacadaabcbdbcabbdbdbbcaaabcabcdccbddbbadcbcaadccadccdadddbcabbcbacbdddcdcdcaabdadcbaaaaacccbbccdaacbcccacbdbabbbbdcbddbadcddcaadcbcccddccbdabcabdadcbbcadbbadccabccaddbdcabbbadacacddddacdbaaaaccbcadcacadadbabdcbbbbbcdbacdaccbaadbbcabadaabbcddccaddccdddcddddabbdddcabdccabccdbdbcdcddcdbddccabdaccdadacbbdacddcacdcbaabdccbddadbbddbaabadccdcccbaccbbcbdbaabbabadbdcadcdcbccdbccbcadabdbddacdaccdccdbbdbdbabccacabbbbaddbddcbbcbbcdcbadcbdadbaadbaaddddabadcaabcddbbacadbbabbdacbaaadcdccaddddbccddddccbcccaccdbccbaccbdcadbbddccaacbcaaaaaadabbabccadbdcdbdccdabbddabdddbbbccdadbddacabcaaabcdbcbbdccaccdbaadbaabcddaabbbbbcdddccaddcabbdbaccbcbdbcbdcddbbbbcccbddcdbccbbbababbbbbbbdbcdacbcbcbdaaadabbdcdcdcccdbdccdcacccacdaabacaccddbbacbadaacbcbdccaddcadaacbdbcabbdcadadbadbdacdbdcaddacacccbdaabbdadccadcabdcdcacadacacadaddbccababcbcabbbccccddcbcacadbdacacdaccccddbbddbdacccaccbbcdddbdccaabcccdaabbdcddbdccdbcdabdcbccadabdbacabdbcdcdddaccacdddbcaadcdbbdcabbbccbbcbabacbabadacbbcccbbbdacbabdcdbcacaadbaacbcacaccddbcbdcbbbccdccbcbdbbdadaddaccabbcabdbcbccabacdacdadacacddcbbddcaadcaacdbaabddcdbdccabddbcaaddcbcbadbabdbcacddbdbadccabcabaddcdabbcbdcbcdcaadbcadbdcddadacbddbdcbcbaadaabcbdbbabcacbddbabdaddaacdadccdcaaccddabbacdcbabdccadbbddbaddbdcacbadbabdbbacbbdccbbcaaaaabbcbbadadbccbcdbacdcaaaddcdaccabbddcbddbacaaadccdabaabbbacaabcaabbbadcdbbbddbbddcdaadddcbaadccaccdcddcdbaccabbaccdabadaccaadadccabadaaaadccaccccbdaaabbbadddadbcbacabadacbdddabbdaabdbbbccbaccbcbadbcacbdbaaadadadbabdcdcabbcbaabbadbdcbdcbcadccccbbdbcbacdacacccdacdcdbbbdadbadcdbcbbdacdcddbddcbbadccabcaadbabdcadbbbadaabbacadaadddbccccdadbccadbacadbcabbaaddbadbaacadcbaccbddbacaaacbaaabdaddaccaaabddbbcdddabbcaccacabccbddccaaaaddbccdbbcdccbadcadbdbdbdddacdabcbcacbddddcaadddcacacbcbdcdaccaacbcccabcbcaacababdadbdbcbadaabbaadbbacddacbadbbcdcaacdadadbdcbdcdccbdbabaaadbddbcabaabaadcbabcadbaabbcbcacaccdcacbdbcdbddcdbbaabbaaccadcacadcabccbadabcdbdcdbdbbbbcbbddadbbcdbcaacdbcbdbaadddbacdabbdddbadbaaccbcdccaacbdacbcbcdcacacadbdddbaabbdddddabadaaadccbacabbbdabdbcccbccbaacbbcabbaaacbbaccdbbdccdcddaabbadbdcdbbdbabcdbdcacbacaaaacdcadcbabaabcaacdacccadccbcddddddadaadabdcdcbccbaabcbddcabcabadcdcabcbbccbacdbadcbadabcbcaadaaacbacbabaadacbcdcbccdabcacdcadbbbaaacacdcdaabdabaaccbbdabdabbcdaaadccbccaccdbdcccadaadaadcdabbcacbddabdbccbaacddccbccdabdbbabbaabbbcbdadacdbbaadbacddaabadcccbacbbcadababdddddaaaacaccddadbcdcdbbacccacbbbdaadabaccdbcdaadcddbaccddcbbddccbbdccaccaadabacabbbadddbccddcdddadcddddadbadaacdabadddcbaccdbbdddcbdcadbdadbddaaacbcdbdcdcbbcdacccdadddaaaddadcccddaadbaabbaadbddacbaaddbaabcadaddcdcabdbaabdadbcbbabdbaabcbbabababbabbddccaadadaadddcbbabbdaddcaadbbacdaccbccdaabcbcdccbabaaacdbcbcbbbdbcdaacabdcdddbdacbbaaadcbaacddbbbdcbddcdccbabcdcdcddacadcccdadccddacadddaabdaaacabdcacccaadcdadddacadabbbbabbdacbbaabbdcbcabccbbaabdacadaddccaadadcbcdbdcdccaacdccdbcdcbdbdbdadaabbabdbbadccbcdbcacaabcdaadccacdddcdbbabdabaddbdbcabcadabadbcbaaaccaabaadbbdcbbbadcbdbdbdddabcbbabdddbcadcdbadcdcabdbdababdcbbdccddcbcbcdddddcbcddbdbadaabaacbccbcaddcdbabadccacadabbadbaddbccdddbabacaccccdbbcbbbdabcccbcbcaaadcaabdacbacabcdadcaadcdcdddddbabdbacdcabbdbbacbcddcaaddacabcdaabdadabbacdaaabbdaccdccdbadccacadaadacdaaaccccdbdcdcdbcabaaadbaccdcadaaaadddbcdacaadcdcaaaabdadaacaadcaabddcddcbbcdabcbdabddadbcdcabccbcaaaabdcabaaaddbbbcbccdccbadbabbbbbbbbbaabdccdabacbddbdadcdaacbcdabcabccccdaabddacadadbdcaaadbacbddbaadcdbbbabdcdabddbcbabdabbabcdcabdddcabdcbabcbabbaaaaacbabbdbcbddbabdddcbabbbdccccaddadabacaddbcbabcdcaaccadbcabbadadcbbacbdbaabcbabccacbbadccaaaaaacbbbcbcccdbccbbccddccdcbbbadcdbbaaccbcaccdddcdbacdcbdcccacbcbdcaabdddbdaacbcadddcaddbbdaabddbdbdcabadcdadcabbddbbbddcdabaddabdadbacdccbdcabccabdbaabcdbadacdbbaccbcbcdbdaadcadbbcdbcadccdacaadccdaddacadaabcabcddaabbaaaaabaacaccdbddbdabdcbbadaaddcddadbbdbdddbdcbadbdddcdacdadabbdbcddacbcbcdbddddabddbcdcaabbcccbcdccabcbbbadddccccdcadcacadcaaacabbdadbcbbacacdbcacdbdadbdbcdddbaccdadddcdccbaaadacddadadacacbdddbdddbbdacdaabbdadaadccaaccbcbbaabcbcdadadbdbcbcccaadacdccabdbaccbcdcdcaacdcdcdbcbaaaabbabaccdbbbdddbbdcbdadadcbdcaabadaaccadbcbbbbcabcdbddbddaadadaaccaaaabcacadaadddaabdcacacdaddacacbcdcddcbddbbbcdaacbabadcbbbcbcbccccbcbdcdcdabbddadbdbacbdcabaccabbcadbdaabbbbdbabbcdadadbdaccbdbcbbcadcbbdbccbbbacdaaaabcbcbbddbcdbbdaddcccccdbdabcbcaddddabdccacbbbcadabdaaacddcadddaaabcdaabdbdcdbbbabacacbbabbadbacbbbaccabbaadaddacdbbbbdbdbabaabcabdcadbacbbddcaddcbabcbdabdcaadbaaabccdababdaadccddadbbbbcccbcbcacdbbacdbdddbbbabdccbaadcdbccdbdcdbabbcacccdbcbdbacdcbdccccababdaaaabdcadbbabcdbaacdbcbaadbabdabcccaddbcdcbaaaabbbbcdbcaabbaaacdacabacdcdccbbccaaacbadbaccccaadcdcabaaabdcaadadcbcbddbdadccbaddbaabbbdcdcbdcacadadcadacbddadddccccdbdbddccdbcbbdbbbbadaddaadcaacdccbcbdcbabadadabbbaddccacadccbcddccdbdcdaabacaaaadbbdccdacbdacaccccdabbabdbaaacdcdccdbbccbccbcbcdabaaadbbcbbbdcaaccaaacbbbdbdbbbddbcddabdbccddbbbcbadcabacdbcacbdbdddbaccdcdadabadddaadcccbdcbadcdbbaadacaddaaabdddacccacbddccbcbbaacbacaccabcbbdadaccbacbcdcdaadccdcbddadddbaccdabdcadbaadcdbcccaabddaadcaccaaabdaabadddaabacdbaaddbdcadbdcacbcdaddbcbabcacacdcccaddcccbaabbcbbbbdccbcacdbcdacacbcbbdaadccddbdcaaadabdaadbbcbcbcabcadcdabacddadcbcbdcadddccbbddacbbbbccddacabcaaabdbdbacaaabdacccbdaaaaabbbdddcaaadacacddadbadbbaaabbcdaddcbcdbddbbbbbccddcdcccddcbddbaaabdcbcadbbbdcdadadaddadcdadbbbdbccbbddabbdcbdbcccbccbabdcddbccbdbcdacbddadbdaaabdbbacdddcdabadcbcbdccbbdccbdcbbdacacbaacadbacdcdbbbdbcdcabbbabbdcdcbcbaacabdbdddabbcdbdacbacdabcaddabadaaaaabdaaddccabbabddbaddadabadbbdaadacdadcbdcdcadbdbbccdcbadbbddcccdbdbdbcbaccdcdcadbdddddcccbdacaabaaddbdababcdcbcdbdbddadddbabbcaabccacbaaccacbcdbcabcdabcbdbdcdababadcbbdbadcbbdddcabacdcbcdaadcbdcbbbcbaabcbdcadbadadbabdbbddbdddbcadccabddbbbaacdcdbcbbdabbaaabbcabcaddabbbbacbacaacbdccadaabdcbcdcbccdadbbcdbcbcbdbdbacdbdcbcaccdcdcbdaacaabbbdccabadbdcddcbdabddabccccddcdcddbbdddaddbbdbdbdcddbdcacddcbdbcaadbdbbdbaabbbcdacbcbddbaacdcdbbcbddbccabcaadbbdbbdcdddaccbcadccacadcbaadbcdbcbdbddcbadcaaacacababadacdddccbdbdabddbbacddddadbcaabccacddcbddbabdabacacabcdadddbdcbdadbbcbdbcbddcdcbacbdacccbddadddabdbadabcbabcdcaabbadbaccdddccdbcacacdbdbbacbbcbdcaddbccbabccadcbadbadabaabadcaaaaadcbbabcccdbadbcaabacadcabababadcabacabcadabcdccacdabbddaaddcaccddcabacccccbadadabbddcabddcaabadadbdbcbccdcabbcdddbcaadcabbaddddbdcbabaabdcbbbaabddcacddcdccbbbbacacdacbbdcaaadcadbbdcaddbbcbbddcdbbdbabacadbdabdabbbbccccaddbcbbbdddcbbdbdcbbacdcbbaaadbdbcbbcbbcbcdacdbbadcadaaacbbdcccabddcbccbadacbbddadcacadcabbcbcdcddadacbdbcbcbbdcdcabaadcddacdadababccbbcaddabbcacabddaacadddbdaabacabcdddcadaaddcabbbddbbbbccaddcbccbcabdbabaadaaccdbdcdaaadbcdbbcbaccdbcaabdcdcbcddbbcbcbaacbdcdccddabadaabaaaaccaadcacdbbadcaabadcaabdcbbcaaadcbbccdbbddbccadacabadaadbdabccaabcdcacadabdddcadbbabacdbcdbcbccdcaabcdaacaacdcacadcccbdaacbcaabccbaaddcaabaacbdbaacbabdcccdabddccccdbabcbbacdcaadbbadbacdbbbbcbddbccadacacaacdcaaccbbaabbaabbbdaddbccdabcacccccbaaadcbbbbaaddcddacccbdaaadcddcabcaddbcbcadbcbdcbbdcabaaacaabbdacdaccddcddccbcbdccbbbccdbcbbccbbcaaadadcdcaabcbadbadbcdacccdcbcdcdbbbbddbcdcaacabdadadbaccbdcbcbbbccadaacacdcabbbabdababdbcdcddaadabbdcccddaabbcbbbdacdbddbdbdbcabbcaddbacdaddcdbcdccbabbcabcacdbbcaabaacbbdabdcbacbdadbccaababadaccabbbcbcccbbbdbaaddddccdbccbbacdadddaaaccdbababddcbdabdcdbbdabdcdbbcacdbbdbcbccdbabdacadcbbccdccccdcdbdcabbaacdacbbcbdacdbbddbbacdbbaccbdbabcdcaddaccadacadcbabcdbadbccbdbcdaadadbcdbbdbddcdccddcddcadbacabcccdacaadcaabdcbbdcdbcbdbbddaabcadaddccdbdbcadbadcbddabadbcabdccbabdcbcccccbcddbdcadcabdcacacaddaabaaccdcabccaadbbabadcdaaddcccacaccdcadcddbdccaddaaadcaadcddbcaddddaccaacaadcdbbcdccabbbcaadccabbcaddccddddddbdadcccdcdbddbaadbcacacaddbddbcacbbaabbdbababbbdacabdaddadcaaabdabcdacbcdddacdbbcabbbdaacacbadaacccbbaacaccddddccccdcacddccddabacccaabbabdabccadacaddcbaadbbbaacccabaddddccddbbaacaaacaabdabdacbbccddbcddbbccccaaadaacaadadccacbcdcddabaccaaddbcaaacabaccddabdbaaaccddbaddcaddaacabcbbbabccadbcbbdacccddddcbadcbcddacadddbacdcbadacaddcacbccdacbccddbcbbdaadbcccaddcdbdcabccabadbcdbcadddadadbcdcacbbdcaabbacddcaababdcbdbbaabccaccccdaddbcaabcbcbdcadcaaabaaabacaaaadbbdabaadbbaaaaaddccddddabccadcdadadbcdaaaacaacbdddabaacddaadddacaadcabddcacbcaccbdadbbdadccdacbcdacbcbbabdbbcccdbbbabdddabdccbdbbbaadbcdcbabccbacdbcdccaddcabaddddbcbbcbbbbaddaccbbcacbdcdccaadadadaccccbdaddbcadaaddadacadcaadaccdaabccbbbdcbaabcbadcbcdbbcadbbccdcaadadabddaabacddccdacbbdaccacadadcccdbbabcbcdcdcdbbdaddaacbcaaadbccdcbbabbacccaaabaadabbbacadacbabcdcbccabccabaadadbcababdddadacbcdbdcdabbbbbdcbbcdcbadabdbbbddcaaadbddccddcacaacdddcaaaddbadaccddbaddbdbadbbddacdbadbaadcbaaddcaaabcbbcbabdccacbbaadadcbcbdaacbbdcdadbbbadacbbdbadddacbdbadbdbccbcdadddcbbccaacbcddcbbbdccbdbbdaddadbdcbdaaacdbcaaaacdabdcacabbacabacccbcbaccddabbccabddcaddacaacadaaaabbaaaabcadcaadbdacbbdaabbaccccdaaabadcadbaaaaddddddbdaccbbadabdaabdabcbaccbcddadaabdadddadbcdbdbbcabaddabbddcbadaadbdadbccbbbdcbccdcacaacbdcbdacbcabccbbcadbcaabcaabbcaaddddcccccddcbdaaaaadddcdaacadccabcdaddbabccdabcbababccdabbcbbbcdbdadadbcbddbabbddcbbcaadacdbbccadcddcdabacaabbdbadcddbacadacdacbacabbabdaaabbcacbcddcacbdadbcbdbdddbbcbcdaaaddababbcbaaabcbabcaadddacdacbcdabadbddccbbaaacaaaaadccbccacdbacabaddcddbdcbbcbbadbabcdbabdddcaccdccbcbbaccadaccddbacbccbaacbdccbabdccbcdcbcacacbacaabcaadcadcabcbbbaccdcbaccbdabbcabbbacccacdccdcaadbaaddbdcddbabacbdbcbbbaccadbbdddadadaddcdcccaacccaddacadaadadcdcbcdccacaacabadcadcddaaadaccbadacbcabbcabaacdaabbddccaacccdddaaadbadaddcdacacbdacbbcddabccacdbcabbabdcbaabcddaabdacadacbbddddbbbbccdabdadacaadccadcabbdcdddcaccdbcdacbddbcabbdadccabdcbabdbacbdcbabddddcacdbbdbccacacdcaddbdddababadbdcadbaadbdbdacbddbbdabbcdbcbbbaadcbbdccdaacbcddddadadabaccaacadaaddbadcbaaabdaacdcccddddbdacaacbaaabbdaaabbdaaadbadaaabcbadbadbcbcaddcabcdcdaccaacdccabdabacccdaaccdccbcbacbddbdabdcddddbdcbbbdcaadcacdcaccbaccdcadaaaabdabcababdaccacacdcdbccdbbbcbabaadacbcddbcbbccbabddbddccccdcdbcdddccddcdccbbbacdcdaacdcdacaaacbbccdcabbcadbaaadbdaaccbbdcdccdadabcdcdadaaacdadccbcacccdcbbacddbdcdbcdbbccaccdcbddadddccbabaaadcbdaccbcabacbdabacdbacadcdaddbdbbcaaadaaccbcacacddddcddbbaaadbccbdcacdbabacbdccbabaddadcdcadddcabcdacbbacadcdbbadcdabbcdbcabaabbacdcbdbabadacacbdcacadabbbbdddbccbddbdcdcdcdcdcbcaacababaadabaacbdabccbdacdabbccbdcdcabcdbcccddddabadcdddadbdadabbcccccdbcccaccacdcdcadcbddccacabaddcdddabdbbcccaacaccbbcaababaddcbbccbbbbccbbcbcacdcbcddbacadaccaccdcdadbcccbdddcbbcbaabadadcccabbddcbbbadadbbdcbbcbdcaddbabcacacbcbccccbacdcdcabddbaadbcacbdaaccacbdbcbadaaddbccdcabbbdadcadacdbbdabbdbdbacbdbccaaadbcccdddbadbdcabcbdbbacdbbcdddcdcababdbdbccadbcbbcaaaaddbccacabccbdcbcacabcadddbbaacbaababdaabdaddbacbaaaddacaddcbbbccddaacacddccaaadddacdbadddbcdadbdabbbbaccaaccabbdcdbbbbadbcbabacbdacdcdcccdcddadccaaddbccdacabdcbdabacdabcbbbcbcdbdadddcadabdbbdcacabcdbaddddaacaaaabbccdcabcacbbbdaacbcbadcddcddcadcddaccdabddbcdcdbacdcacccdaaaadcccddccabaadccdabddbcdbdcddddbbabddcdcadbbacadcabdabcddbadbdabaddaaacbadbabacddcbbaaccaddcbaacadacdccacddbbbbaadbdadbdddbdabccacbdacdaccadcccdbdbabcdbaacbbcccadcbdcbadcdcabaabbdabdacbcabcdddbabbcaccbcbcaaacbbcdbdddcbddbbadcdabacbcbccdbbcddbcbadaaabbadcbbbbbdbdcdcbabcccbbcbcddbcdadadadbbdbcbadccbaaccbcdbadbcaccbaaccdbaadacccbbaabdbabbddcbbccacdbddbccbdcacdbbabdadadabcbabcacaadbaadcaabbbcbbabcbcbcddabcddaabcbcacbddbadbabadacbbddaccdcccaababccdacbacccbbdbdbdaaacbdcccbbcccdadcbcbbbbaaadabccacababdcdcdabdabacdaaacbbdccabdacdcccdccbdabdadbdbacbdcaaccdbbcbdcddddaddcbdbcdbdabcabacdbcbbbadcaabdcccddcdcdcdddabcabcbcbcbbbaccbacabccdccbaadcbcbabcaacbdccbccbcabadabbcaccaaabadbdaabbccacdcdbccbddbaccdbdbcaaddaacbdbdadddacbacbbaaacaaaaaadacbacbbccddbaaccbacdaacdcbccbcbadbcbccddbacddaadddabcababcabbdbcabbbbacbbbadaacadbaaaccadccdbbbdabbabcacdcbdaddbacbaacbcadddcddbbddabdccaccacbadddcabcaddbddddcbacdabaababbbcccbdbabadcacbbdbabbacbaacdacdcbaabbddbdacdaddadddccdccaccadbbbdaddbdcabdcccaadccacbdacaaaaaadbbbbcccabcbcccbbcbadcadcbdadbaaabcdbdaadcccbabbbcbccdcbacbcddbbaddacddbcabbcdbbdddcbaccaaaacadadbbbdbbabbaabbdcddadabbabcdcdbabbcdacddbcabcabcdbcabbbdddddccabddcadcbacdabacaaaaabbacbcbadacddbadbdbcbdabdbddcdbbbcaadbddbbbccccbadcddbbdcaccdaadaaadbbdccdcabacadaccabadbbdcdabccadcacbbccddddabcdcaddaaddcddabdbcccbbddcdabbabdaabdcbadbddadabcdcbcbcabbbaacdcdcccccaddacacbdbdcccddddadadabbbccabadacbbcadcbacdacaababbdaddcdaaddbbdbcbbccadbdbbdabdcdcdbcaadadcbddadcdbdddddbbcbdbbbccccbdddacdcdcdccbbcdccbcbabcbcbcacbbdbadadadadbabdbacdbcddccdabdcbcbadcdcbcdaadadcbacabdcaacdcabdabbcadabbcbcdddcabcbdbdadcbcddbbbacbdcacdbdcdcbbdbacbabdbbcacacbdcccbdccbdcaabcccbbbccddbadcbcddabbacaacaabcacbcbdbaaaddbbcdbcddcbaabacabbbaacdaccbdaabdbcdddbcdddbcbacaabacccdcacbbacaabbdccdaaacbcdccddaddcdbcaccbdcadcccbdcddcdccdacdccdaaabacadccbcdbbadbbadbbaccddbcdbaabaccdadcbdcdaaabdacdbacbaacaadaaaddabbccbcadbdbcadbccbadcaaaacdaadbbaadcdbacdcccadbaddddcadbdbdbbddccdadbabcacdaaaaccdacdbdbbbaddbadbcbddbabbccbbabaccdbabbbdbadadbbadddabaaddbbcaaddbcddbdddacbcdcbdadccaacdccadcccdcdccdaacabcbbcbdcbabccabcdbabaccadbbaabdccdacbacdacacddbbbadbbbabcdbdcdaaccccbdccacabdcbdbdcbbcbaabdaddbcaaadcdaadbccccbbbbbdbdbcaabadccacbdbbbcacaacdcaaacaabaaaaabaccaaaddbbaaacbabdcbdaaabddcabbcdcbdddacbdabacdcdacadbcbbaddabcbaabbcccbaabdccaacdadabadcddbbdcacdcdadadccbadddaadaddaaacacaaddbbbcdccbcabacaabdcdbcbdadcbbdacccdbacacaabdadccccbbcbbbbddcbddcabbdcbbdcbaccabcabaadbadadabddacbbcbbadaddacdacbdddacdcadbdcacccdbdcdddbbdabcbdccbabbcccaadcdddaaadabcaaaaadcbcbccdcaadbcbbbdddcbababacdabadacacaaccabadbcdadbababcddbdcbababbdbabccdcbbcaddbcccaaadadbcaadaaddcadcabccbaddcddcbadabaadbadacdccabaadcadbbdbadcbddacbcabdcbbdaaaabccaaccabadabbdcbadbcacbdccdcaacdcbcbabbcbacbbccccdddadbdbbbdaabbbdbdacdcbaddbcaadcaccbdcbadcdbdcaddbbbcdddacdccaccbbacabdcbaddcbbaaabbddbacdcddbadbbdbcdbcbdacdbccbddcbbdddcbdadaacdcacddcbacaacccbcbdcdccabdcdccbbccdcaccacbccddbddbccddaababbbacdbadbcdaaacabdcbbcbcbbabbccaabadabdcddabaaddcadbdbdbabbadbbdbabcdbbbabbcabdcbcbaabadbdcbdcadaaddbadaaadbcaacaabbcacadaadcbdbadcddaccadacbbccaaaadcdcbcbbcbbbaccaaacccddbbdbaadbcabadbcdcdbabdbaabddccdcdddcbcabdbdbacabbcacacdcdccabdadbacddcbdbbcdcbccabdcacbcbbdbbabdbadbcdadacdbdcdabbcdcaadaaabbdcacadbbcbababbddababdadaabdadddaccccabcadaacdacbddcaababcccacccdbacccddbbadcdadbdbacabbccdaadbbbbdcbabdbdaabbdccaaaadbbdbbddcaabccdcbcbcbdadbaccadcccbcadbaacdadcbabbcdacadcdacccabccacbdaacaddaaabccdccabbcaccbbccdddcabcaddcbacbccacbbcdaccdaaccccdcbadccccbcdacabdcaccbdbddbcaddabababbcdbcdcacddadabdacdbbddcadddaaacdbbbaccccbadadcaaccbbdbcacbcddaabdbadbacdbaaaddbcacaaccbbabbaccabdaadcbbaaadcaaddbdaccbaabbacddbbaaaadcccaacddacbaaaaadaacbdcdcdbdaaabccdddcccccdbababaaabdabcbacacababdaccbbaaddacaaddcddadcbadadbdaddbcbddccbbadacbadcbadadcabadcddddaaacccbdcdbbdbcbcbbadbaccaccdadcdcccdaaccaaacbcddbdbddbacbaaccacdbdbbcabcdcbdbcaacaabacadccaccaaaacaabdcdbdcadddbcbcdaadcadbcdddcadcabcaddcabbdabbaddbabbbcddbddbabaaccbaaacaacdabccdcdccdadcacababaaabcddccadcaaaadbddcaacdbdabdbdaabccdadbcdadaaccaaaaadaaccccbcbaddbbdaacdaabbabbdddddcbbdddbccbbdadaddadbcacacdbabbbbbabdabaddbabdccbcaadcccaaaaddcbaccdccddbccacdabbdbcbdcccdaaaabadcdaaccacdbcacbddcacccadbdcdbabadbddccacddcbacbdbbcaaacdcdccaadddabdddcacbdbcbbabbdabccdbddaabbacdcababbcdbcadcaacabddbcbbaadbbccabcdcdadcbcddccbcbbabadcadddcabdbadccdccddadbddbdbbbcccbbbabdbacdbcabacbbdaccaacbadcabbddcaaddcbbcdcbaccbcbdadbaddcbbcdccbbddbcdcacdcdacdaaabababcddbccdddaddbddbdabcbaddbbcabcdcababacaabbcacddcaddabaccaabbaacaacbcbdaccddcbccbcbccccddcccdcbdabaabcddbaddacacdcdcdcccdddabacdbccacaaaacdcacaaabdbdbcbacddbaddbbbabcbcaacacbbadddbcdbbaacdcdbadadcccdcccddbaccdbbccbdbaaabadcdacadaabbbaabdabdbaddbabadcdbdaacccacdabadadbacccbabbcadcdcdccabdcccbadacbaabdaccccdcacdbbbaccbbcacbabbadcbadcaacbabddacdbdbbdbacbabcabaadcddddcadbaacbcdaddcbccdccabaaddaccdacdcddbdcabdacbccbcbddabadbddbbbdacbacbdaabdabbdbcccadbcdbadccccdbcbbdcbabaabbcbcdcdbcaabbacadddbbddaacadbdbdbdcbabcabcddcaaadacddcaaabbddccdaaaddcdadacadbacadaabadbcabcacaacbacabbccbcdabccbacacbbabbbbcdaaadcddbaadbcdaddbddaabbacbadcbbddacadcdddccdcdbdcdcdcaddddcdcdcddaaaacdbdaddcddbccdcbbbbbadbcadabbdccbdacadaadbacbdbbbadabcaacbadabdcacabbbcbccaaabbbdbabdbdbbcbccdcbdcbbbdabccdabbdcbdadacabcbbabacaccdcbacacbbaccddaddacdbaacbdccbdcbcadbabcbabacbbcacbbdacbddadcccdcdaaddadbacaadbdabcbdcadabddacadcbbdcdabcabbcdbccdadbdacacbbbacbcaccbaacdcdcadbbabbbadbcadcdccdccbaacdccbbcaaaaccabaacbbbcadbddcdbadddabbadccacdcdbccbbabacccadbdaaadcaaaabacbadaaccacbccabbcdabadcabaaacaaaaaacabcbdbaddccacaabddaababcbbbdcabcaababcccbddbcdbddcbbddbbcccdabdaccaabcddccabbadacabdbcadaadcaacaadadbbcdaccbbdbaddacdddbbcadbaccaacabacaabcdbccadcdbdcbadccabbcabcdbdcbaaaaabddbbddaaddbbdaadadacbdcbacdacbbcbcabacacddbadadcdcdabdcdbdccbbbabaaccddcbacdabcbbccbabcaddacdaccadbadacddcccaabaaacddacbbbaabcabaabbaadbadcdbcdbcbadccdccdadddcaadcacbcccddaadbddccadcabdbddcacdbcadbacdabdacdadccddbbcaacbaddbbddcabddddddaadadccbccabaabbbddbdbcaabccabacdaccaabcadbcabccddaccacaacadbacdcdcdbcbdcccacabbcadadaadbaaaabccbabbcdabccbccaddaaaaaabcdbadcbcacccbadacaaddbbabbbaadbdadcdcbbcadcbbcdacbdbbabcaddadbdcccbdcbaacabbdacdcccdabadaadcdbbcaadcabcddbcdcabdbbdcccadabbcabdcbadbdbccdcbccbccdccbbcabbbcacdddabbcbdaabdcadadaddbccddcdcabdacdbccaadaadacdbbacddacbdcdbddadacddddcccbccbbbbdcbcbbccbaaadadbbadaacdbdbaadbbddcdcdddcdcddcbbabbdbbdbbccbbcaaaadddcacbaacddcaaadaacabcadddaaabadbcccdcbaadabaccdddbdadcadbaccadccddcaaccdaddccdaaacacaabddcabddaadbdacbdcbadddcabcaacdcabbcbaadaddcdcbcbccbbaadcbbbdccdadadbabdcadbbababddcabdbbaccabcdabdcaadabadababbcdbbadcadacdcbcdcadcbbbacbbccccdacbbadbaccaccbdddbbdcdacbdcdbacbcdacdbdbbbbccbaaaabbcddacaababaddcdbbdbaabcbcdbdcbacadcdcbcbbaaacdacddbbcabaddbbdddbcbddcbaddccabcdbbdcdccdcaacabcbccabdacaadacbaabbdbbadcbcabadacaddcbddbbcdaacaabdaccbcacddbacacdabbabbaaccaaabcaaaabcdcabbbbbdabccbaacaabbbdadabdddacabbcdcdccccabcadcddcbcbcbccaccbcadcdcddabddcddccbdcdbabbddabcabbcbcacaaabaddaddccdbddadcacdcccbcccbdadbddddddbbbbddbacacacaadadcdcbcddaaccccbbadacccaaaaddbbcddcbdaaadaabcabbbaabcdcdbcbcadddabaabdaaadadabddabdcccacdaaaacacbddcacdcaccdadbaadccdccabdcddabddbabcbccadcdcbcdcbbcddacabccabdabbdbaddababacadbcbacabbcdbcbcaccdcdbabaaabadbddcddcabbbcdbdcbcbbccddccbadbddbcdbcadcabacbdbbbcabadabcdccdbdbaabbdadbabdacdadbbbacbdadbbaddaccbdabddcbbabcaccacbababcbadadcabcadcbcdabcddabbdccbcdbccaddcadabddadacacdaabbcddadcbacddcccdbbadbacbaaccdbacbcbcdaaabbbddccabaddababbcaccddbadcaaccdcbbdadcdcbddabcddadbbdcbabadcaabdaacaacdaaabbadbadcddbaddbddaddcbadbbcddbccbacbbacbccbbdbabddabaddbdddaddbbacdabcbabbadccbdbddabccddcbcccdcdabcbbbcaaabbddddaaabbbccadcdcabbdacdaaadcdbbaaccacbbbbccbababcabbaacabdddccadddbddaccdadcccacbbadcbaccbbcbacdccddacbdadcacbcbbbacaabccdcadcdadcdddcdbcbadcbdbcdabcacbbcaaaadabbbccadcdbddabddaadaddcbadddcbaabcaadbdddabcdccdcabadccccbcbddaaabccabdcabbdaabdccabaabcdaadcbddbddbdbccbcdcdabdbaadbabdcdbcaabdbbcddcacdbccdcadbdbcbddcdadcababcccaacdbadcbcbbbbbdaadadaddcddbbccdbabaccdbddcacbcdacdcbdbabacaabadbcdddbaababababaaabaabdabcbbbccbdadcaadcaaccdcacdcacabccdaaddbddcddbaabcbdbabcdaccbabacccadacccdccabbacbddccbdacdbcadabdbcbcaaabaabadbcccabcbabdadbacabcbcbbdacacdcaadcbddacaddbcbadcdcadacaaaadbcbaabddaabaccbacdaddabdbabbaadbcdbccdddbcadcadbdddbddabdcddaabbbaabadbcbbabcbddccadbabbcdbbcaabadbadaacddcdcadbaccdaccaacdbabbddccabccddadcdbdabddabbadabaacdccbbaaadbbbbccbdaaddcddacbbddadccdabbadbbaaaadabdcbaddcbcddabadaadacaacbbcaaacadabcbabccaaddcaabcabdabdcccadabddbbcaaabcababdcdbbbcaabaacbccaadcbdddccdbaacbdcadaaacabcdbcdacbaabcddaacabaccaccbbbbcabbaddaadabbcdcddabcdabbcaccabdbdaddcdddadccaaadacbadccaabbdcbaacabbbbbdadbaddabacadabccbccddddbdbadcdabddbcadaaddcabadddcbddcadadcaabcbcadccbdcabaaddcadcadbabbddacddddaddababdbdbadbbdcdbbbdabcdaacddcdbdcbcadcbacdddbdacbdababdcacccabbdccdcadaabbdcbbcdaacbdcdadbcbccbabcbcbdccbcacddcaccabadccdbcacdaccadbabcdbadbcdaabbbbbabbbaacaddbacbcddabcbbaaddbcbcadbcbabcdccaacaaacbcdacdbcccdbcacbadddcaacdccbdccbddabacbaddcababbccbbddbcbdabcabaaccbbcdcabadcbccbaadbddbbbcadbcaabbacacdadacccbdcadcbdbaaacbaddadcbcbdcaabbcdaaabbbdcbaddbaaddaaabccadbdbbadcbbdcaddcadacccbdcbbacccbdbdcaadccabdccaacccbaacccbaaaabcdcbccdbcbbdbbcdabcdbcdcbdddbabbaadcdacbadddcccbdaacbbccadaadabdabaccbcddbbdcdbaddcbcbaddaaabbcaaddabbcbdaccbbdcbaccdbdbdbdadcbbdddabccdddaabbdbaccadcdbacadcbdbbabdcbdcdcadcbabbcdbbbdbacddddaadbccbbbbcdabcddaddaaaddbdbbcdcabdcddbabdddcdbcacbdcddbabacbabcaddabbaacaacdacdddccdadbdcdbcbadbdbadbbcaaaaaabcccacdacadccbdbddbbdcdaacdaccccccddcbbaacccbcbaaadcaacbadbdaabddadaccdbdadcdddcacaddbbbcbabcacbcccaabbcaacaabbabadbaacdbdbdcbbbadbddddcdcddacbcadaabadcabbdcbaadacbccabbdcadcdabaadadacbdaddaadccbddcdbbddacccddabccaccdddbbbdcbabacdcddcaddbdbadccdcbcacabdbaccdaadcdbcaabdbbdaddcbbadcdbaabacaddabcaddbcdbdccbbbaccabdccdddcccbabdbbabbccabccdcaccbddddbabcbdbcdadbaaaabcbacbddaaddccdacddcabccaccbabcccacdbbcdcdbabadbdcacacccccccbcbcccdbabadddaadbcdadbadcccbbbbdbcdbbdddcccdacadcdddbbabaaddbccdaaccdddccbcdaabbacbdbcbbcddccacacbcaaadbcbcdaaabcdbbcadabbaadbcdcaacbdddddaababacaadadadcbcbaaddadabbcddcbcdcdbbddadcacabcccbcdbddcbbbabbbdadabbccbbadaaddadbcadcddbcaabdbaccadabaaaadaadadabbbbacbbbaacadadbaddbbdcacabbbbbddddadbdadcbbbbdcbbdbabccbbcadcacddbbcbadbbddcdadacabdaacbbaabadbbaaccbddccaaaadbbdccabcabcbcabadabdbbcdaabbccdabdbbbbbdaadcadaadbdddccddaaddabdbadcaadbbbbacccbccacdccddbcccbadcabbdadcddabbbdabcdbbcabcdadadcddddabdbcddbcbdabadaaabaabccbbaddccaacbbdabbdcbadbabdbdbaaddaacaaaccbbdcbbaadcbbaddbdbbaabcabdadcccacdaacccccdccbaadaccbdbbbaaabcbdbdbcbacdaaaaccbaacbcdbcdcbbbddcbacaacaddcddbcdacbdccdabaababccacaddbbdacddaadcaaacdabcddddacbaccbdabbbcabaddcdbdaddbddadaccaacddbadadadcdddaaaabbccdabbcdadbacddcacdbddcdbbbbdcdcbaaadacdbcabbdbbaddcacbdbacaabbaddabdbddcccdcbbcddddbdcbcddcdbbbbabbddbadbbadcbabadcdacbbdbabaadbaccbcaaaddbddbdbcabaabddddccdbbcadcbdbdbcbdccbacbabdcabaaadadbdcbbbdaacccbcdccadaccbcadacbdddcaccccbadcacccdbbbccabdbbdbcccbbcaccbbcbccbaacdcccbaccbdabdbcccdcdcdcbabdcbccdadbdddcaadabdcabaabaddacbbbbacccdcbcdcbabddbcbcbabcdcddbcddadbdacdbbddacbadcaaadadbbcbbacaadbddcbabcdddccbcabdbbcdcacbcdcddccddbbcddbabacacbcbcdaabddccabdddbcaacdacbbcdabbbcaccbcdccadbaddcabcacdcbcaaaddccaddbbddcaaadddddacdddbdcacccdbdbadbdcbdadbbbdbbbcdadbaddcbdddaaaabdabdcdddcbbcadbaadcdadddacddbacdbbcbadacdaddbcbbbcdcbbabdabcdaccdcbbdbdacbcbbacbddabcbaccacaabcbddabbcbdadbdbdadddddbdaadcddddaddcaccccddadabccbcabaabbcccdabdbccdacbdabadabbbdccbcdaabbbcbcbabbcccabbcdacdbcbdbddbcddacbcaddbddacacbaadcbcadacbddacbdacbbdbaaacbddabbadbdbacbddddddddbababbdccbdcadbdcaacaabbaadbbabbcdbbbbacccbadbbccdddbbadacbabcbcbdccddcbcbbcaddabdbbdbcbdbcbbaddccddbaacccacacaacdcbabdadcbccbbacacdbcccbbcbdabaaaccbacbcbcbaadbbdcdbadaaccdddbcdddcddccdbdacadbadabccbcabcabcacdbcdddadcbddabddccbadbccaddbaadbbbbcbaadbdbddddacabaccdbcdaaccabbdbbcaaadbcbaaabcccaadcdddcdcddbccbcbdbdbcbaadbbbaccaddacccaadcaadccadabdddcdaaaacddcadbdadbcabccdcacadbbcadddabcddcdddccbcdaacabdddabbaddcddacacbccdcddbabbacbbbcccbdbabaaccdddcabdbdaddaabcdccbaaccbbbbdbaddbadacccadbbbcababcaaaaaddbadccbacbadcacbaabbcdcbdcdccbdbccbcbaccababbccccbaccaaaabcacadccbcbccccabdaacaaccaccbbbddcdcdaaccbbacccabbabdadcbabcabaaadccababccacdbabbdabbcbbaadcbccaababbaababbbcadcdcccaadbbdbcddcaadddcccddbdadacdadadbbbadaacdabbdcdcbaacabbadbbcbdddccdccaaadbaccdaacdcadbcdaabdadacaadbaadcdbdadcaacadacdbaacbbbcadbdcdadabcdadbaacddccddbbbbcdadbaddddcbdddcbbcdcccbadbaababcdcdbaaccacbbdcbbbdacabcdcbdacacbcdabacddcadadbccccccbabbdccdcaadbaccaacaddcbdcbbcbcbaacddbcdcdbcadaadaabdddccabcabaadcbdbddadcababdaabdbdadadbcdbdcaacdadcdcabddababdcdbbcdcabbbccddaabdcdcccdaaaabdcdcdbbadaccaabbcdcabadbabaccbbcdddacdabdbbbbadaadcaabcadcccababdaabdcbacddadbcaabdacaabccababbbcbcccadcbacbbccdaababcdcdcadbcbadbbacacbccbabccacabddcdaddcbacdaacbbcccddaadcdbccadddabbdadcacabcadbddadcadcbdccdbdddcdacccdadabcbdbbdcddabcddabcbcadbabdcbdabbabcdbabbcbdcdacccaaacacacbdddabdadbbdaaaccbccdabcacadacdaacdcbcdabaacbcbbccbccddbbcddbdaaaabbdbdaaababddcdacdaacccdcacbcdcddacdaaddbcaaadabddacddaadcbddddbaabbaccdadadacaaccbcaccadccaccdcbbcdacbbcccbaabaacdcaacbabddcabdcbacdcdabbbdadadaadccbdbacaadabacdbbaacbcdcdaaddbbcabadbccadddccccdbdadbbbccdddcccbaccacdbdcabdaacabdcbbabaddccddaacddddacdaabbdabaaaadaddcddcbdcccdcbcbdbadabbacbadaccdcbadbbcbbddcbdacdbdddddcccdcbadbabddabcacdbaccbdccccbcacbdbdcbdcdbddaccabbdadcbcbcbcdcbdcccccadababcbcbbccbbddbbcabcaadcccbaabbdacbcdbccaadbabcacabbcdaaabbcaaccacdaddbaacdcbacdbccaddcacacdaabbadccaddbdcacbaabbbbdacbcaadccbcbaccbddbaaacdbbacbcddcdaaadddcadbdbbbabbabcadbdbdadabcbdacacbcabaccccabbdaaadbcbdbdcdaacacbcdddadadcbbdbddcabdcbacadcdaababcccaddbcaccdadbadbbcddadccddadacbcbcdcbbdadadcdcdcbacdadbbccdbdccdbbddcadbaacbabaacabbaadabccbaaaadccbddcababbcadbbadccdbbababcdadcbabcadcbbcbbdcaaccccccdaadacdbbbabdbbcabcabcbabacdbbdabddaacccbdbbcaaacdaabbbcacabaccbdbbcadcadbbcbcacbbdcbccbaaadadacbbbaccbdddacdcbcbdbddabbcdacbcbacccbdcbbdacbbadabcbcbddadccaabbbabbcddaadadadacaaabdcddbddabaddadabadabdbdbdddddaabadbcdadbdacadcccccbdddcdbaabaaacccdaaaacadcacbadbcddcbcaadcbaacabbdcabbcdcadacaabcccbbcccbcbbcadbdbcbcbdbbbcdaccdddcddaabdddadbbabdcccbcbcbacdabcaaccdbcbbbccadacabddadacadbcddcaabbdabbddaddaaccbdaacbcdbcbbbdbcccdaacccbbbdcbbbdcaadabdaaabbbdaacacacdbcbabddddbdaacaccbaabccdccbcbcbbddccdaaadacbbcbcdccaababcaaccbccaccbbabadbdccbaacdbbdccadbcadbacadbdccbddaccdabbaacacbcabbbbabbdaaaccddaacadcddbdacdacabaaccdbdadbbacdadbccabdabacdbdbbdabdbabccacbdcdccaddcccdabbcabbdcdaaaabccccbdcbacbbdababaacbabdcccaaadababaabadbaaccacbadacaaddbbcdaacdaddaccacdaddaccdabaacddbbdccacccccacadacbaddcadacccdbbbdbbcdabbbcbacbacbbbacabbccccacbbaaaacccacddcdddbcabbddaaccddcccabddbbdcaccbdcbdadabcdcbdbaaacddacabdcdcaddcacdbdddbdadadbdaaacaccdccaabbbbcdabcdcaddcbddabbbcccadbbcbcbbbdacabbbbaccdbbdbbdbaaaabdcccdccbbbabcadabccbdabaacbdcdbccdccdcdaaabcdcdbcadabdaadcdcdbdccdcaabdacbababccdbcdacdcdbcbbcddbabdaaaabcbbcacbdaabcdabdddbaababaacabccddcbdbcdbabacdbdccbcbacdbbcaaadcdacbaddbbaadacbabdabdbacccbdabbdcadcbbababbbcabcdbaacabaabdddbcddbccbcbadacacaaabaccdcaacbcddbdbacdaddabcbbbabbcdcbcabccabaaadabdccadbbdbbaaccbcacddbaaadaccbbcabddbcbadbdaccbdccdddbbdbdabadcccbabdabdbccbdbbdccacabdcaaddabdddcdbbcbacdbccadaddbbacdcbcdcbabcdcadacadbbcbbcabdbbddcddacbcccbadaacbbddcdaacdadadbabbdbaddbcdaddcdbaccccadcddadbcdbcccbdccbddaaabbcccbbccdcbcddbacabdcacbcabdaaaabdaaabdabacadcdbbacdbcddabdbbcdbbdbbabacabbdbdacaacadacaacdcdcacbcaabbaaaacbccddbbbcdcbcaabccdbddbccadbbddbddacbccbdbdbaadaacbdbbdacddcabbdbddacdcbbddcaadacabbddcdaacddcdadaaaaaacbacdaabcabbdadbcacaadbcdcbbcdcdcbdcdaccbcccbdaaacdbddaabcaabddcbdacadbddbbbbabacabdbdbabcdbdddabaaacbadccaacccbbcddaaccbbddaaacbbbdccaaccaaadadccbcaccaaacabccaaadbccdcacdabbdabcdcaddbcaabbabaaddbbdabdcacdacbaacddbacaadccbadccaabbadaddbdabddbdcbabbbabccabdddbcccacbdddbcbbdabdcdddcccaacbbcaaccdadbcbadddbbacaccdcbadcacbbcdaadcdddacbbdcbaddcaadccacbcdacbccbbadcabccadcbbdcaadbadcbaccaacbdcaabbcaaddbbcdbddcbabbbcccbaaaabdbddaccdcabdbcadcccbdaabacaadacdcabbbaabaaadcbdcbcdaabbbaabcaabacddccdbcbacdaadaddadaaddabaccabbaaccddcaddddddadacbadccbdabdadadcabaabaaccbccacaccbddbccbaccabddcccacababddbaaaccacabccdaddccddadacdcadaadbdbccbaacbddccddbcddacbbbaadbbaaabdbbcbbdccbdbbcababbadaadddaddbcdacccbcbacbcddbccccabcacaccaacacddcbbdadddcbadabcbbabddbbabcdcabaadacbccdababddcbbccababbdbbcccaababcbdbaabcdabbabbddacacdacdbabdcdcddacbdaadacabcaddcbbacbcbbcaacadacbdabbaaabcdcdbbbbcaadcddcdcccdadaaddaccccdcdcaabbadcdbbccabcccbddabdadbdccdcaacdbddddbdbdcbdcaddbadbcbcbdcadbcadcabbacdccaccacdadadabbaabcddddacdcbcaacdcbaccdaddcbcabccbcddcccabbacbccbcddcbabbdacacbcdccbcbdbcbcdccbddbdccaabdcdadbbdbcbadbbbbcbacbccdcacacaadcabadaddcccabacdbbbaccbaabcbaccabccddcdbddcaacbaddbddbbcdadcacdcdadddcdbacddbcbcaccabaccddbbadcacdabcbdacacaabcabddbabbdccaaaddaccbcbcccbcbbbcdaacaabcadabbabaacabdddcddacddaaddadcdccaddddccbdacbaaaddcbdbbbaacbdabaadcdcacdabadbbacdbabdacacacbacdbabadaaaccdabadcccbbdaccaabcabdcbbacbdcbbdddccbcbccaadadcaadbcdbbaabaddbadbaabbdadacbbbcaacbdbdaccadddbbbdbbabcaddacbacbabacadabaacadddaaaaaabddbddcaacadacddcabcadaaadcdabccbaaabacccbaccbddaaaabadcdabdbbabbccbadaabdadccaccbcbabacdbddcacdacabbcccbdcbbcaadbbddcccaccbccbaadcdadbccadaaabaadbbbaddcadabddbcdbcdbadccdbadadbbaadbbdaadaaaddbcacdbdcdddaadcbacdbacabddcaddbdabacdacdbbcdacabddababdaaabacdccaaaddcddcaaaccbabbbadabcdbdabdaccadcaacbddbacbcbbbdccdcacdcaacbbaadccccbbadbcdcddaaaaacdbcdbbddcaaaaadaddaccaacdbabdabbdddbbadcbaaccbccddcddcbaadcaadbdbcacddcbbabadabcabcaadbbbaddbdcabdcabbcbbbdbadabddddcbddaaacdaacbabadabccdcdbddbddbaccadacddadccaccbacaccbbcbdcdddbdccdcabadaaaaccabddbcacdbacccdcdaacdbaccbdbdddbcbbaacaccdcdabacdacabdbdcdcbcbbacacabbcdcbacdbbcadddcdccbdcddacdbdbcadaccdacdbaaccbccbbacaaddaddaadcadabccbdbccbbdccadbdbadbdbdacadadccdbdbbbdcdbabacaaabdcabdaabcaccbaaccddbaaabacabdcbccadacddadcbbaadabcdbabbdacdacdbaacbacdccadabdbbbaccdcadddbdbbaacaacadbcdcbcdabdabcabaadcddcbdaadbbaaddcbbdaddccadddbcacdbbabdabddcbaacbadddddccbcabbbbcbadddbacbcaadabcabacbadcaddadbbdacbaaccbadbddbbadbccabacaadbadcabcddbdbdadbddaddaddcdbcbdbbbdbacaddcbcbbdcdbdbbdcbdcccccdbdaaaccdaaacdcdddcccdbbcdaabacacbdbbddddabdacababaaaacbaacccbdbdcbaacacdbbcdacbcaddbdddcbcacdbccaabaccaacdbabcbbbadadddacacdaddddcadcbbbdcabacdbddddbbbccdcbbddadabacbcdbabddaaaddbcabddccadabcbdbccbcaddbbaaccaddddadcdbbdadbbdbdacbabccabaacbabcabddbbaacdadbcadccdcbcdaacadbbabcbcdacacadddbddbdbccaacbddaaabbbbccccbaacadbdcbcbcabbccbdccbbddbdccabbcbdbbbcbcdddbadccdcdbdccadcbcbbacccdddacbdbcadaaddabbaaddbbcdcbcabdacbabdbbccabdaabcaaddcbbddcbbbdcdcaccdbdbaaadcabadbcadbadadaaacaccaadbadaaacdccddaabddadbddabcdbabddbcddaccaadbccdbdabddcbddaabcabbacccddcccaddaadbcacbcabdbddccbbabdbbcacdcbdaadbccbbccdbbcddcbaccbbadcccadbdbbbddcadddcbcbdcbaaabcaaccabcbbadadcaaccbaadabdccccadccbbcdadbabddadaabbaddadbcacabdbbdbdcccabbdbbaaaaaadbaadbdadbbdbacbbbacbaadddcccbabbcbcbccbdbadddaccdadcbbdabcddbcddcbcbcbddccaddabddccaddcadcccdadadccbcdadbccbcdbbdabccdabcacaacbbbcdcadbaacaababcaabbdccddabaacddcaadcbbdcdaaaddccdcccabccbccaddacadbadcbdbbaabbcabaccbbadcaaadcbdbdccdddaabdbbababcbcabbcdbbdccdabaabbdaddddcbcbcdcabbadadadabdabacdbdadbbaddccaabdadcdccababddddccdcddcddbdcbbcdcbdaaaccbdcabbabaaaacacbbdddcacbabdbabaabdccbacaccacdaccdcbbcbaccbcadbbacdddbabadbdabadcccccbbbabcccccdabacadcbaaddcccbacbabddcaacbbcbdadbadbbdcdbccbdcaabbdbbcabdaaadccddabccaadcdbdddbdcabccccbbdcccadccbbdcaabdbddbdabdcacbadcdadbaabbbdcdaacbbccccaabcccbaacdabbbcbbddadcdacbdbcccacdbacdaadbadcccadabbbdbbbccbadbcdccbaddacbbbaddcbdcbcddadcdcbabbbaabcddbbbccdbbacddcccbddcddddbabdabcbacbdbcaaddbabadbdcdccccdaaddcacadbdbdbaabddabdccddcdadcdbbdbbdcacdbaabdadacaddacaaaaccbdccddbdbddabbcaddddcacadacadccdabacabadaaabdabaacbcbacdbbcadbdcaacbbabdacdcbaabbcdddbdbdcabaddcbaddaadcdbdcdadccaddccabbdadcccaaacadccccbdccdabddaaadbaccbdbaaaaadcabcbddaccddcadbdaddbadcbddcdabcdbaaaddbdcbcdcbbadddadcbdbddcdbdababacbdcbbacabaddbcdadacbaacbcdacacabdacacbddbcdaadbaadaabdaadcbbdacbdccdbabbdcdcbcbcddccdbcbdbbcadbddccdbdbbbbbdddbabadcdabcdbaadadbcabbdabcdddccbacdddabdcbcbcabaddcadaacadabbcababdacbbadabdacccbdadacabbcbdbbbcbdcbdabbadcbdcacacabbbaabcbdbcdaaccabccabbdaabaddabbdddccaaabdbcbcbadabccbabaababcadcadccadbcdaccbdabacccddaaadacbadaaacdadaaadbbdbdcbcbcacadddddaacbcdccaabadbcdcacdacdccabbcdbbabacbcabdddddbacacdcdbcaabdcddbbddccbddbcabacadccbcdccddabbdbdcacdbdbdcccabaaabcadbbaabacadcddddcccabbddacbdcccdbbcccbdaaaadacccabdbbcaacdcdbcbadacaabacbddaadbaaaadccbacacdcaadddcdbbaccbabdadadddbdaacdaadbbdbcbdaacbbbbddabbdddbcadcacdbbbdacdaaaacdcdcbaddbbadcbdccbbadbcdccccdbbcacdbccbdabcbbcaadbcaacbcdadcbabbbddbbbacdaabdcaadcacacadbbcdbcaabaadbadddcacdacbcabdbcababbbdacaacbbcbadadcdabbcadadcabbbcabcacbcbdaabbbddaadcaadacbdcddadbbacabcbaddbbaccbdaddadadddbaacbbadbcaccddcbacdcdbbcdaacdabdbdaaddcaadbbacbaadcdcddacbbddbdbdbbdcddcacccbbabdadbbccabdcadaabcaabacbaccbbcdddcaddababdbdcbdaacabcbcdcbcddadbdadcbccaadbbaddddacdbbbbcccbadabdbccaacacacbaadcbcdcabaacbbbadaccabdcbcabdbcddbdcdcacaabdcaadccccbabcdbabddccaabacddcbccdcbdabacadcbcdddcccdaadbccdddddcaddcbbabbbacaaddaddddcbdccccbcddbdcacadaacccacbcadbddbbccbcccddbadccdbbccdcadcdbdddbcdbdadabdbadbaccddbadbbcddadacabccaabcaadbcccddaaadacdacdabacbadbbbddbcddbbbacbabacbbcccccabddabdadacadbcbcbcdccccbbdbdadbbbcdcdabdacbbadadbabdbdcdbcbdccabdaadacddbdacdbcdadaadacdddabbcbcaabadddaaddacacdbdabbdcdabaddbacbdaabacacccdabdccdabccabddaddadddbadcddcbbdbbbabdaaacdbbabbcdbaccbdaaacadbcacdbcaabccbacacabcdabbcdbaacbbbaaddacdccbcdaadbbbaacabbcdcbacbdcabdcacccadacccabcdddabaddcbbdbccdbacadacabcccccaaaabdaadccdaabcdbbcbcadabbbcddaacdcdcbabdbdcabddaddabddcbcdcadbadbbacbcacacbbbdbdbbdddddcdacacacaabbaacbdccbaacbabbcbdcbdcbadadddbbadbbbcbaddcbdddaacadcbcadacccdaddbccdddbabddacabcacbdddcadbdbbbccacdccdbcccbdcdbcabddadddcdadadbdddaabcbdabaaddcbbdaadbdcbcdbdcaabbabcdcccddcbdcddbccbcddccaacbcbcdbcbcaaaacbbabddacbcaabbaacaccaabbaacdaaabadcabccbcadbccbacbbbdadcdbdcdaabddaabcacbdacdcaccdcbcaaddddadcdbbdaadbadccabbdbddabdcbdacadbbdacbbadadaddbbddccbbccacdaabbabacbccdacccccabcbcaadbbabddcbdbbcbbaabdcdaabacbbcabdabdbdadbaaacdacdccddaaccdaccabddadabbcaddcabacaabddbcdbdcdadccdacadcdaababbacbcbccbdbdacacabbcdddbdcdbdadbddbcdabdddcabbbbcabcccacdcacbbbbbbbcbdabbcbdadaaccccdaaabdcbdaadaddcadcdaaacdcbbccdabcddbaacaadbbbdacdabdbbbabbcddbabbddddbdddbbcbbbdaacabcabbcbdacbcbcbadaaccbddabddbacaacdcccaadabadabccabaabbdaaadbadddcdcbaadaadcacacdbcaacbdabdabcadccddabddaaacbbaacbcdcadcbadcdcddbdabaddcbcccbaabbcaaacdbcabbdaddbacbccdbcabbaaccbbdcdbabbdcdbcdbccbadccadcdddbdabaabbcadcdbdacdbcbdabcddbbccbbbacaadcadddbdaaccdcacdaccbaccabddabdbaadbdbdaaacabccbddabaaaaaabdaddcbcdcddddaaacbdccccbbaccaaaddaaabcadbbbdaaddadadbdaccacbdbacbaccbaabcbabddbcacacbdabbcccdbbccabadbabcaadbcabbdccccbcddccddbdcdbbbdcdccddddcaadadcdabbdbccdaacccaacbcdcbdbcbcaabbdbddcbdadcdcadbabcaabdbbccbaccaaabaacdbcbddcbddddbcbdcbacdbadcdadddcbdcadcbcbcbabdcdacddaacabbbbbccbcaaadcabaaaddabbaaddbdddbbddbdcdadacababbcdbbbabababdddbccdccabbdabdcacaababaaacbbdabcddcbadacbdaddabbcdddadbabbdadabaddbbcdcdcdabaddcdcacadabbadadcddddcaccadacdbaabcbccbdadcbaccbaddccbdabaadbdcaacddcabbbbababdcbdbabbabacccbbadcbbdcdcbadbcbddcacabccabacadaabcbabbcdaabcbbcbacacaacaadbbbdbcbddbbcadadacccdabcdacdccaabcbccbcdbccaccbbbdddcdccacdadacdcdddabdbbaaaccccacbcacdcdcdcabdbcdccacaaaccbaacddbdacdcbbcdaacadcdccbaacccacbdcbdcccbcbdcbdbcbccacbbdddaddbaadcdcacbaccbdbadacddcdbdbccdcaabcbddabbabdbbbbbabadacdcacdcbaabcacdbbbbddaddbbcbbabbabdbcbbcbccbadcdacbbddbcdcbdbdaabcdbbddccdacbdcbbccdaaabbbababdaacdcbdbcdadadccdcbabcbdbcdaabdbdbabdccacbddbccaaccbaadcbddabbabdaacbdcaaaddbaddaccbccbababbcbcdbaaaabbabcbaacbbaabdccbacdcbaacbcaabacbadabbbacdcbdcccbdcdddacaadcdcddddadcdabdaadcaabbdcaccabdbdabbccbcadcdacbbccadbdcbdbdadaacaaaddcababbbbcdbaddddbcdcbbddccdbbadcdbdbcbadcbaababddcadcaccaccdaaabbddcccdddababaaccadacabdbacabbdccdcadaccaacabbdcaabdcdaccddbabbcddddbdbacaaddcbabdbcdbcdacbcacabbdacabcbddcccaadaaccdcdcaadaacabcbcbbadbccbccbcbaabcddcdcbcbccbcddaabaacdadcdbbdcaadccbaccdcdbbcccbddaccaaaacbddcbdacbdbdadbbccabbaacdccdcadccabbabcaacdaaddbbbbadbabbdcacddbaabbababdbccccacbdaabaacbadabbdaacdcdcbdcacdcbbaabddbdcbbabbcdddaaccbaddcdbabcbacccdaddcddcaabcabdcaadaaabdbbcdcbbacadcbbdbcbacbcdaccbdcdccdabcaccbdbcaccdccadbcdccaacddbdcbbcbacacbcaadbbcaccbbddcbbaadcccbccabbccbdccdacdbacbdbbabbaabdcdbbdcacbaabacbdbcddabcacabddadbbdbdabdbccadcabcadbbadccacddadacabcdccccdcdcdcacddaddcbbdabdbbcadbcdabbbacccdcbbcdbaadbcdbdbdbcaaccddcccaaaadacabccddcbddccbcadaacbcddcbcbdddabbbcabbcadabbbbcdcacbcbbaaacabbdcaaccababcbbcadcacaabddbcbacdacbcbabdbadcdabbaacbdccbcccaacaaadccabbcdbcbcbacabcabdcacddbccdccddcdcbadadacdbadcdccaccdbbccbdacbbcbdbcbbcaacdcaacdbcdcadaaadbacacbdbddbaadbcbbbdcccacabbdbbddbccaddbcbaabadbcadacccdbbdcbbcadbdadabdbabcdccbdbaabbdcbcdccbbabacbdaaddcadbddabdcabcacacacadddbccaddcbacabdcbcadbcdddbddbadbdddcccbbaccbcbcbdddccbcdacbadccdbadabadbaadddcccdbddbaacabacbaaadbbdcaccdbabdaacbabbbccdcdcaddddbaaccccbcddcaccbcaaccddcbcaaacbabaadcbdbbbacccdcacacaaabcdcdaccadacacadccccbadabbacbdddababadcccabdcbacddacabbcadcbccbbcdbbbbdbaaabacbbdbcdcdadabccbcbbcbaabddcdcabdbccaaaacbdbabdbbdddaccccadbbcadbbaabaacadccacdbbdbadadbbbcdbacbcdbbcbbbdbbcdcacddcddbbbdbdbbdacabcdaddbdcacbbcdddacbdaabdadcbacccbcddddbdabbbaaaababdbdaccdaaadbcdbdbddddbdcadcabdcbdbbbcbcdcddbbacbdccbbaccdddadacccacabcbdbcbbccddddabdadaadabcbcccbcdcddccdcddadcbabaabdbcdbcdcccbaaaaddbbccbadabcdbbdcdcbbcbcaabadbdccdccbcbbddddacaddbbaadbbbdcddcbadacccccdabaaaacbdadacabcddcadbcddccdbdbdcabcaabbcabbbcbacbabccabdbdbabbbaacadcdcbdadbbacdaadcadacbbbdadabaccacaaacbdbcdabdaadaabacabcacbaacaaabdccbccabcdddcddcdddacbacbcbcabbabaababcadcacababaadcbbcbcbcdbcbacbcbbaddbdbaaacccbbbacbbbaccddabdcbbbaacbccadcbbadbbcbabcccbbabccadbdccbccbadccdababadbdddccdabccabbccadcdbddcbbdaddbbddaacbabdbcbacdadadbcadcdbbddaccbbdbcaccacdbcccaaadbcabababdababaacbabaccddabdbcbbadbcaababbcbadadabdaddbccbdcdaaabacacccdadaccdbbadabbcdabccaddbdbbaaddbbbbccbbaaddadadcdabacadbadbccccabaaacaaaabcdbdcbdddbbaaabccddcbcbdbbcddbcccbadaadbacccddbaaabdcdbacdcaabdbdaaaabddabdcbbbadbcbaaabdbbccadbdaaddcccadccdddabacbcbbbdbdadddcccbdbaaabdadbddadbacabbabcaaddbdddbcabbbdcccadacdabddabccdababdbcddbdcacccddabdabbabbcccabdcacdbccbadadaacabcccbadacccabdaabadabdbaccaaccbacdccbcdbcaaadcdabdabacaccbccbaddababacdbcccbcdbdcdcccabacabbdaaddaaccbbaaddaadbcbdccacdaaabcacdacdcbdcdcabdbcabccbbbdccdbbdcadacadcbbcdaccabcacdaacccdacdcaadbbdacabbcddaacdacdabbdcdcddbbbdcaadbbbdaadcadcaabccbabdcccccbaddbaacdacbddcbbdddbacaaadadbdaccbacbccbaaccbdbbcdcbbcdccaabacdbdaaaaadcadcdbbabadbcacddcdcbccddaacabdbccabcbdbcddcaabbcdbbadabcbbbacbccacbddaddbaddcdcccacbdcbcacdcdcabbbaadaaddccddaabddbcccbadcaccaddbcdadddcccabddacddccbaccdcacbaaacbacaabcaacdcdccdbacbbccbbccabadccbcbaccccadaadcbccacbabbacbcacccdbbcdbccbdaddcdcbcdbadacdbddbabdacacccbbaadadddabbbadcdbcccbaccacdddcbaaabbacadcccabdabdbababdcdddaaaddbbccdbabadbdddbadabcddbacccaccdacaabadadacabbabdbaccdbbbbcbbcbbdbcdaadcdbdabaaabcdcbbddcccaddcdaddddddddccbcabadaabbcaadaaaacaacadaaaaacbbbbdbcdbbaadddacacaacbcdcacaadbbdacacccacdddcbdaacabcbabaddbaadcaccdadcdccddaaacdaaacdbabacabccbbdabbdbabadcbaabbcbaddbcabccbabbdabdddccbdcddaddbdcaabdcdcaadddbbdacaccbbbaacdddadcbcdddbddbaddbcccdaaddcccbbdcabdbabbadaadbcadccccddacacdbdadbdbabacaadacacbbcaaaddcabcdddccacbbccadabacdcdcdcbcbcdbacadbdcccbbbdabcbcccaacbcdcbcbbdccabbdaadcaccaabcdddaaddabcacbddbdcddaadddcaacdadcadabccccdaadbbcdacdbabcbccaabddcddcaccbadcadbbbabbaddcbabcadddcbabbbdbccbcbaadcbbdddcadddabcbddcccacdbadbbdbcabbccdcccdcdabdddbbdccadbcaaaaadddbdddbaccababdacbbacadcbccdbddaacbddcbcbcabdaabbcdabdcbabddacaabdbaddadbabaabdacbcddabdaadcaccdbcdbddcdacdbcbbabbbbbbcddcacbbcabcacaacabaacbacdbabdbacacbdbabdabcaaaabadcbbdabacbaddbacabaddccdbcaaadcbcacbcdcdccabdabcbabacddcdbdabdcabcaaacabbdbcccdcadbdccdcdcdcdadbcadaaaadbdbacdbdcdabddbaadaacadaabacaccdcddbbdbdacdbdaddbdddabaacadadccbddcaacbabbbaccabcdcaddacbdcdbbabbdcbaadbadadadcabcbaccadbbbbcbcbaadcbbcdbdcbbbbabbabdabdccddcaaabbdbbbcdddaacbaabaacddcaababadabdddacbbccbaadaaccbcbcbbccdbbdbcaaacaabadbacabadccbdaabbddcdcccddbccabaaadcdddabadaccaaaccbabbaaadbbdcbaddbbadbcbcbcbdbcbbdbbbbbdcaadcbdbbdcaadcddbcdbbcaaaaacadcabbcdbdbcadadbbabbdcdbbaaaadcbdcacabbdadaacbcbadaaacbacbabccaabbababacabadcdcdaadbacdabcbddaaaccbbcccaacacaaccacddbbbbdcdaabddbdddaabadcccdababcccbaaccbabbdbdadcddbdaccaaaacaacbcabbbccdbcdababcddbcabbbdbdddacddacbcabcadcbdcddacdabddcabcdacababbcbdabdbaccdcdbddddccbaccdbbcaabcbdbaacdcddabdcbcbccbbdccbabaccbaacbdccdacacacdcacabcabcdabcddbcacdadcadcccddabbcaaaabdaaaddcacbbbabacddcaadbbbacabdadbdcddccaabaadcbaddcbabaadbdddddbccadacacbadbabddbdcddcbadcdcbcbdaaacdaccdbcdddddabddcdaadbbbacbaabbcaabdbcabaabbabdaadbcbbdcadddddccacdaadabdbbdbabaabcbcdcdacbdcaaaaaabbbbcdbcdbbbbcacbcddcdbcbdddcddbddcbacbaaacbdcdddcabcdddacabacbdcbcacdbbbdcadcaaadabccababcbabccdcccaaddcaaccdadbcdccbbacdbabbdbcaabcdacbbdbcbbcbadcaabbadacdcdbbaaadcadcdadcdcaddbbddbbcddbacbaddddbacbdccbdcabaabbbbbadabcacbdbcdaddcbcdcdcabaacbccccdacdabacdacadcaddcdbadcadcdaacbdbddadcbaddcdbdacbccbcabbaabaabacabacdcbddbacabdcbaccbdaabcdddabbdcacbcabacacaaabccbdabbddbbbdddcaabcccddbcaacbcdbbdaddcaddcbcddccadbcdbadaacadbbcbbccaabccabccacccbcacaddbcddddadaccacdbdadaabbaaabbacbdcdccadbccbbddacbcadbddbabbabacbacbbbbacdcddcdcabdccbbdcaccccaadaaabdccdbdadaaabcacdbaccabcbacccbaccadcacaccdacbdadcbacbbddbabdadcbbddadcaacbcbbcdbabcddbdacabacbccaaccbdddccabccdacaadbbcbbbdadacacdaabaaaccbaacbadadccbdcdcccdcaacddcdccaabbacccbbdcbbabaabacbcbdddaccabbcccaaddbdabddbabbbbbcddcbccdaccccdcdccacbdcabdaacadbdbcbbddddcdabcdddcddccbacccbbaaaddaacccbabdabadbabadbdcadcddbdcdccbdacbaaaccbbbbadaaabbcdcbdcbdbddbdcabdcddcbccaacbbdabcbdaacbddbbddbbacdaacaabbabcadbbccaaaddacbabbdcdaaadcdbaacbabbddacaccdccbdddbbaddccbcbbabccacadadcdbdbcdaccaccddddccdcbccdabcdacabbbabcbadbbdbcdabcdacbaddbabccabdabdcbbaabdaacaabacdadbbccbdbdbbabbdbddccabbcbadabbcaddaddbbadbddadadbcbcabbdcbacaddcbddcaccbbdbcabbabcababaccbdacacbddaddbacdcaadacbccbbbabacddabbbddbabdbadbdababcddccaaacabbcaaabcddcadccadacbbdbcdacadddcdccbcbdbbdadabaaacdddacaccaaabaaadddcbddbaaccaacbcccccbdbdcaadacdccbacacbbbddaaaaadacddcabcddbacacdcbbabbbcbaddbdabdccbcdcacabbacdbdcabbccbbdadcaaadbcabaccadcadbacccdabbacdbbcccaaacadbabcaaddcacaabccdcbadccadbccbcccabbaadbcaaadcbcababdabacbbcdcaaabcabddabdcdccddbcdbaaacacadaadcabcadabbbaadbadcdcbbdcdadbbadcabdacbddbaacdccdaaddbdcbbbdadadacacddbadabadbdccbcdddbbbdacdbbdcbddadcdcdddadacacdacbdddcbdcbababacdccbdcddbaacaacacadbcaddadabdbdccdabcccadcdaddcbdcbbaababccaaacacbbbcadbbcacbbcdbaccaaadccdcaaadcadbdccaadccdaaddbddcacbacbabdbadddcbbccdadcabcaacdccbbbbabaacaddabbbdcdaaccddaadabbdbdadcddcdcadcdabdabbcddbbdacdaabbdddbadddabcdabdacbadbcbbcbbddadbacbbabcdcbbabccdcaacadccdcaacbdcdabacbbabcacadaaabaadccbacdacabdabddabddcaadbcbccdccacbbdbcdabadcaadaccdddbcacddabdccabababdcdccadbcddddbdcbacabdddadbcdcabdacbabdbcdaabddadcdadcadbcadacdcaaaadcccaaabbdbaaccabbabbbddabccabdcdbdacbcbdbacdbdabbccddadcdadbbdbddbcdbcadcabcadbbabadbbabaccacbaddadacadabaaaaabaacaccdbcacdbdacbaccdaadadaacababcccacdacbdbbaaddaadbacccabcbcaadbcbacbcccaabddbbadbbbaddacbbddccabbcaacddbdaabadddbbdaacdccdaaddbbcdabccdcbacadbbcacddcbccbdbcacaacacababdddcbccdbacdddcbadcadadcdadcdcaacdabcbbcdccbcaddcabdacacaadcbcbbdacabccdbcdccdabcacbacaaaaddddbabccababadcabdacacdbdcbbbaacdacddaabbbbadacbbdaabcdabdbbddaaddadadcdaabddbbbcddcaadbbabbccaabaacdacbcacddadcdcbdcbbdbcdcdaacaacddcddbbcabbbcccccadaddccbaaddadaddacbcbadbddadbbdbadccabccadabcbbcaddccbbbbdbcbddcbbcbdcbdcaaaabcbcbacaaacaaccabbacdaaddcccbdcbccbaaaadbdbbdcadcacacbddcabbdddbccabcddcdaabdcacdccacbaadadacdcdbcdddcdbbdbdbcdaccdbbdbbbdbabbbccaabcbdbabbaaaaabacdcbbbcabbbbdcadabcdadbcaadbddabaabcdbdacaadbbccbabcdcaabbaaadaaaabdadbcbcbddbbbdcabcdbbcabaacabacddbddadbbaddbdddcdcacabadaacdaddddbdaaabbaccaabbcabaaaddcdddcbdaddcbaababdabccbbadddbadcdbccadccdacddcbddcaacdddcacdbadbdccdcdddabcbbcacdabbdbccabacbbccbacbbaaddddddddbddcdaacaabbaaccaddbbddbbdbdabbcdddabbbddcbbdbdbbabaaaaaaccbcdbadcbacdbadcbdadacdbbdadbcaabdcbbcaaccbdbcbbddbcddcbccbbddcadabcbbbadbcdddddcbdccbbabcbbbbdadaddcdcbbbcaaacddcdcbbaacbccbacaaacdddcdcabbbddadcaaaacdddadbdccaddcbcabbaadbaaacbcaacadccbacdcadcddcbccbbaccbbbdbcdabaadddcaadddbcaabbdcbcbcabbbddbddbcdaadabbbdcdcdcdbbccaccdacadadbbabcdaadcdadcaccabadcdcbacccdadbbdcadaacdacdacbaaadababbbcabdbadbaccddcccabddcddadadbcdadacdcbaddcaacbcddcdabacddbbcdbbdacababadbdccbbbacddabbbdccaaabacacbdddcdcbaaabbaddbacdadbdcadbbbadabcdaaadccdbdbcddcabbacdbcacaabcbdbbbdddaadbddabcacaabacadddcacabcbcbadcbcadacbdbbbdaaadbdbdbaddbbbdadccbcdbaddccdbdbbbdaacadaadbbabdcabadacdacccbabacdaccdcddcdbadddcacaadabcdacbdcaaaaddddccdbabbabbadcdaddcdaadbddbaabdddabcadbadabddaaaddbbadbacdddddabcdcbcdcdadcdacabadabbcacdaacdabcdaacbaddbaadabbcbddaaacdacddbdbaacaacdcddcdcdbabaabdbdbaccbbacbbbacaacccabbcbadbcdbbabdbbcddacdbabbaadcdadcccdbccccbbadbdacaccadabbddabacbdcbbbabdacaacdddbbbbbacbabaabdabdadabcccacbddcddcbdbbccdabccaaccccacadadcbcdccabdabacddbcdcbbbbdaccdcadacadadacbaabcbacbadacbdcbbabadcabddbbccccaccbcbadbcddacdaabbbcaadbddabddbbadcccdbaababbccccdddcbbacbdbdcadddcddabdbacdbcbddbdddccaaadaaacdabbacdbaaddabdbddaddcbbaabbacdcbbbaddbcbdadcaaddacdbccdbdcbdcdddaaacccbccbcdccdabcdccbcbaacbbbadcccbbdddcadddcdbbadadcbcbbdadaddaccbbbbadbbcbaccabdbccbbbdadccddddbcbdbdcccbbcadddacdcaccacdacdddabcbbcbcacadbbbaddddaccbccadaabdabbdbcddcdcaaadbccddcddbddbaccddcbabacbbaacaccadbababcdaabbdcdbaacdddbcadcaaaadcaadbdadbcdcbbcccdbaacdbabaddbbcabdacaddcdaacdddcbaaccdbadaadcdbbccacbabdbddabcdcaacdabbbdbdaaadccadacacbddddbdbbbbccacccdabacdddbabbbdddabbdaccddbabacccacdabbadaabccacabcdbcddadcbbaabacdbbdabaabcbdbbcbbbbabcdbdaccbabacdbbbcabdcabbddcbbdbabbbbcbbdcdabdbcdddbaababddacdbdccdcbddcbdabccdcccaabcbbbddacadbaabbdaccbdddcdcdbadbaacadddacadbddbaaaccbccddaddcccbdaaabbbdbccdcccbadddbcdadcacccdcbabbdbabdbbaabbaabddcdabccaccbdaccbcdacbcdaadddacdacbaadddcdcbbbabdccbacbccaddaadbaccdbdaaadccbabbbbddbccddccdabbdbdaccabbacbabcbcbbadcdaddbcbbadacacbcccbaccbbabcbdcaaaccdabdbabbcdbdaaddbbdbbcdcbcabbdacabcacdbdacbcbaccacbacdaabbcacbaabcccbcdddacbcbdbcdadabccbbdcadcccbdbddadcaaacdadacacbccbccbacadcddaabdbaccabaaccccdbabdaabcaacdbdaacdbccbcccdbdbbdacccbcbbbcdcadadabacdcdddaccccddcadbdbbdbbddaadadacbcbbaacaccdcabdabbccaabbdcadcddccaacacdbbdcacbcbacacdacbdbbadcaadbdbcabbbdbcbbcbdcdaabaabbddcbcdccadaadaddadbbabcdbcadbcbdaaacbdbdacabddddadadbbcbacbacadacaccdccabdabbdacaacbdbaddbcadbbbdbcbbabcacbbbdcdbdbdcbddbdbaccdcbbcadddcbbbacadabababbdabcbdbdddbccbbdaccbdadcaaadbcabcdbaabdadcaaaaacaacddaadcdbdaabcdcbdbacdcddcbdcaadccbacdddccbdabbcadddbcadbccdcadaddaaddddbcccccbdadabcabccaaccdcbdbaabbbacbbabdadbdcddabdaccccbdaadcdbbdaaaabdbacabddadacabbcaadbaddccbcacdcdbacbabacddcbbabbadbaacdacbdaabcbaddacbacdcabbbdccddbcdcbbaabddadcbcccadaabaadddcbabcdbbccbccadccdccdbbbcdcabbadbcddaacacbcbbdadddccaaccbccccdaddcdadcaabdadbbdbcabaddadaabdcbddaddbddcacdcbcadaaacdbddaadbaadcacccbacabccbadaadcdbcdaabbbbdbcdcdddddbbdaddaacbcddbbdabdadadbbbccbbcaaddbaadcaadbadbbbadaadbaadbbcdbccdcadcaccccdbaacddaadcaabdbbdcdbabdadccbbbcdbbbcadcaabbbababbdadbddbcdbbbcdcbadddbbcdbbacaacbbdcbbbbdcadddbddcbbbacdbccddaaacbcadacadbbddddbdadbcbbdbcaaaabddcdaddadacdaaddaaddbdadadddcdddbcdddbbbaccbadaacacdbabdadbdababbdbcccbbdacabbacabcbbdcbdabbaabadcccabbcbdcbadbcbdcbdccdccbccddddccccdaccccacabcaddcbcabddaabcbbadbbadcbbaccbbabdccbdbbcddadbcbdddaccccabcbacdbbdcbdddadaccdacbacdbcdccdaddccadbdccdabbaacbddaaabbbdddadcabddcbaaccdccbcdcabadccaacbdbbababbdcdadbddddcadacbccbbbdbcadccacacdbbbcdbbdabcaaaadabcbcbdbcabdadddccdbcccabdbcdbccaacccdcaadcdddcbcaabdcddbcadbbcccdbcabbbdbdacacbcbaaadadaaddddadcbbcdcaababddbcbddbadbdadacdbaacbaccaacccddbaadaaccdadadcddbcadccddbadaddddcbdaccdabbadabddbaaacccdddcadbccbadcbbcccbddccbadacdcacbbabbcbdbaccacdcacdbdabcdcdbcbaadacccccdddaddcbcbbadacbdbdadadbbdaaaabccbaabaacaccbaaddccabdbcabcdcaaddddbdcadcbadbabaadaaacabaddbaccdbaabdbabbdadbcbbdcaadacdadacadcbaabbdabdcacdbdcbdadbcaadddaabbcadccbabddbabdbabaacbbddcdcdcdbaabaabbccdcabddbcbbbacbdaaaacbdddccddbacabcdcbcabbcdcbcacbcdcaaacbdbdbdcacbbdadaadbbcacdddcbdccbbaaabddacbdcccddbcdaccdccdadbdcdbdcdabddababcbdcadadcbdbbbcadacdddccdacdadacccacccdcacbbbadababbbaabaaabacdcddcdbcbaabdabaadbdddbddbacdabbdaaaabddddaccbababdbddadcdbbccaadbaaacbccabaabdcbdacacbaacaaacddadcbbccaaabcdddbaddcadaddcdadcbbdacbcbbdcadacabddabdabdddcacbabbacadaaaaacabcdbbdccacbdcdacbbcaccabdbdbbaadccabdccabbcbccdabadcadbbcbdbcbddbaacbcabdbaacdcdacabdccaadcdaaccdbcbcadcacddcdabcacdacdbcddbdcadbcadcdbdcacbcabacdbdabcbddaadacadaacaacacbaadcddddcabdadbbbbcaabbbcbddcbcbadaaacacabbddccbcddacdaaadbbaacadaddaabadbaaddaddcccdbddcbaccacbadaddacbabdccadcccadaaadbdaadcacccccccabddcdcdddbacdabddcbaaabbbbbdcdcbbbcbaabbabadcbbccadcbdbdddcadcaddbabdacaccbdaacbcaccddddcbddaabbbbadbdaacabaddcbbcbdadbcdabbbaccdabdbaacadddcaddadccabcdbbacaadabcdabacccaddcdcdbccbcaabdcddbbbcbdcdcdbdcdadbcddccbadaccbaabcbdcdbddadbcaccdacabccadadbaabbcdcaabdcbbdcccabaadbddcccbcacbaaddadcbddacbcdbdcbccbaabcdabcaaaadbcbcdcabddcbaadcbabcbdaacaabadcaadabdcbbadcabadadccbaadaaddcbdabdbdcadadcaabcdaabbdadadddaabdaababdddcaccbdcbbdbcadcddacbabbaccadddadacddaadacddababbdbaccaacdbcdcdabddcddcccdbccdcbbcdcdcadbbdddbadcdadbaabbcaaddcadcdcabddaadcaabacaddccbdcdadadacabddcddaacccdcbdacaddddbcddbcaddbaacdbdcadaaccadbaaaabccdbcbacdbccbbcabcaccdabdabbbbcbbdbcdcbcbddabddaaabbadabccdbdcbdbdaccbddadbcdbacdadddabbbddaabacdbccdbdbbbcacadbdbdadaadcbbddbbadacbbbbddbaccdacbcdbbcbccabdcadcbcdccadcadaaddcbcccdddccabbcccbaaaccbdbdbcaccdcdcdcbdaabbbcdbcadabdbdcabbaccacbbaabcdcbbbddcbcbbbdacbdbabbbcdcadabcddbddbcacacadabcbbacbcbdddaaadbbbccccacdbbdbcadccaddbccdacabcddbdbabccadcbbadbcdbcbddccbcabddaddadacdbaadccbadaccddddbdcddcbdaccbbddaaaddabaddacbaadbbbcbadcbadababbbcacdcbddbcadbbacbcbddcbbcacdbdddccccbdabcddbaaadbbbacdbcbcaaddaaabbdcbccaaccaccdddacddbacacdaacabbbcabacadadcdbdacdacdccadcbbbaaacdacccdcbadbacaddbdcdcdbdcddabcaccbcdbbdccaabbdabadabadbadbacccbbadcbadbbcdaaaddbbacdbcddbbadacacdbbacccbacbaaddcbdcbbcdcbaaddacacdcaabdcabbbccccbcdbcdaacbcadbbccdcdadbbdbcadcbcdbbccbbadccbbadcababaababddddaaabccdcdcaadbdcdabcacacbacabaadbccbddadabddbbcccdcbdddaabbbccccacaccbbdaddcabacbccdcbabbaaaabbbbbbadbcdadbdbdbcdddbbaccdadbccabacbaacabdccbcbbddcaddccddbdabbcbacdcbbcdbaddacddcdcdbcbcdadbcbbdbdddcbcccdcbdbabdbcbdbbbdcbccaadbacddbcdaaddbaddababdcbbacdabbccdbdcddbcdcabbcdbdbaabcbdbcdcdbaaaabdaadabcccdaaccccabbcdaaaacbddbbccbadcdcbdbcdadbadabbcabacacbaaadccbaccdddabaacddabdbbcdabbdbdbdbddcbbaddacabdcbaabacdbdaabdcdccddbdaaacadbcddcddabdcadaadccbbbbcdddcddbacacbdbcddbcdaacbbbddababacbbbaabbddbaacabccbcbbcbbbdbaabbacdbabddaccacaadabdcbbbaababacdcaaccbdbdadaddbacabaddbccdcccbadbbbcabcaadcdbacdadcbcbaccbbacbacccabbcaababdbdbdaddabaddcaabdbcaacddabbaddcdddddaaccaabbbaccccadbbbdddadbbbadabbadcbbdbccdadacddcadddaacaaacdababcdbcdabbbdddabbaabdcaaabdddddaacbbabbcbdaabdcbddadcbbcdcadbcacbdcdaabdbccbbbddadccaaddddccadcdaabdaaadcbdcbbbdabaaaddaccbaccaaddccadcdcacbcdbbabccbcacbabdbbdadbcdcbdbbbbcaddddcccbdadbddcaacabdbdcbaaaccaddabaaaaabbbccacbbdcdbcbababbccaacbcdcbbccaadbccbcaadbccaadcbaddddaccccdaadcdddabadbbdbdbaacbaadcbaaaccaadcbbcbaabccdadcacadddcdcbdbcabaddbddadbaccdabdcccbadcdbaddddaabcbdaadbddaaccdbccacaddacaadabadbbbddabaddaababdcdbdbddddcbbddbbdcbdaacddcbdbbdacdcddcbcccaabbabaadbddbbcdcbbdcbbabbddcdbcddaddbacacadcabcaadbbbbabdcbcbbcbdbaadaabadbbbdcabbbbcbbaacdcbcaddbbbddccacbcbdddbcbccbbcbaccacdadbcacbabddcbcacdaabddaacacaabbdaadacbcbcadbbbabdaaadacaaaabcbbabcdbabaacbbcbdaddcabbbdbdcbccccaddcbcbdcdccaaccaddbccdbabcacdcacdcabbccccadacaaaacbbddbdadcababaaabaacbacdadadbaacacbacdcddacbaacbacbaccbadbcbaadccaacadbcccddcadbaccdcdabacacbbbdbdbccdbcabaccacbbdabbabaaacbaddbcaacddbcbccbcbdcdcbadddcadddbccccdbcbadccabababcabcddaabbdadcaddbdcddddbcbcbdaaacbdcdbacbacccbbcbdbbbadadcdadcdbdcbccbcbdadcdcaaabbdabdadacddbcbdaadabbdbcbdabdbccabaadcddcdcabbddbaadaabababadcbbbbddccdcbdbcdccccbacbabbbacbacacaadccaabadccbcbbacbaaaacccdbcbadaddbcacdbcbacdbddcdacadcbbcbccbadccdadcbaddbadcacbccbccababaccdbbdacbbccdccdaabdbccdbacccdcabdddbbccdccabababcbcbbadbdbcdadcacdcacabaababdbbabcccaccacccaacaaaaccdcbcdadddccdabcdacddccdbabdcbabbbccdbdcbadcaabacabcdbdaccdbacccdbddcddbcbcdacdcdcdaddabbbadaacdadbdcdadacaccbccdddadbdcccddccaddbcccbadadbcbccaaddbdbadaaadbdcbccaabcbadbbaccbbdcdbaccdabdaccaabadbcbbababaaccdbbcbdbdbdaaabaacadababaaabccbbcdcbcddaabdbababddbdbabbddbdabdcdbcdabdcdcaabcbcbdbaaacacdcacabdbccabbcccbdbdddcddcdcbabcadbdbdbddbcccbabbbbabcdccbacbaaddabdcbadbbcbdacacbbddccadaddaddcbcbdaaadbbcdcdccaccddbbddbbdcdbcbbadcbababbadddbcabcbdaaadcbbaaddabccbdacdcdacabbacdadaccacadbcccdbcccdaccdbbacaadbdcbccaadddddbbabbabbcbcbccdabdbaacacdbbadcbdbaaacabbbcbcdddaddddcaadabcdcdccbbcddbdbcbaaabcbcabacbdacbbcbcdbaadbccdbddbcaabbdacdcbdaacabaddacabaaaccbdaaabbdbbbacbbdbccddaadabcadcbcbddbaadabcacdaadbbaaaddbaabaaacdaabdabbdacdcddabacbdaccacddbaddabdcdbbbccdccdababddbddbaccabdccbbddbcbbdaacbaddbdddbabddcabdcddbacbdaddbddcddacdcbcdbdcdbdadddbaddbbadcdaaddcbcccdbcbbcadbdbccaaddcbcbacddbaacadbdbacbaaabbaaccdcdcabdccaacbadbcdddabbbcbbbccbabdbbdadcddabdacabddccccbccaccbaabadabaddbaddacbaddbabaaabddacabdacddcdcbcddcdbbdddbdbaabdccaabbacabcbbabccbcbbdcbcccdbdcaadaacdaabcddbccadaaaadcaaacdddbddcdddbdccbcacdbbddcddccacaacdacdadddbdddbacbbcdbccabcdaaabbcccdaaabcadaacabacdcddcbccccbbddccbcaaadccbdcbdbbbcccbdacbcadddaccaaccabbcaabddcbcbccbbcbdccdccbcdaabcabadaccbbaddcabbaddaaadccaddbddbcaaacbcbcaccbbbbaccbbddcccbaabaadccbdbadbaabcdacdaadddbadddcacccbdbcacdccbaccbcbbccdbabcacadaabadddaccdabbdbdabdddaabacabcbaabbbcdabbcadabdaccdbdddbccdbabcdbcddbdcccadbcbdbcaabbbabcccaccbacaaadcdaccbbcbabdbbacabbbaccacadadbadadaaabdddaaacbdddbccbadddcabcbdadbabdbbdbdaabcacbbbadaaadcbabbaaaddaadcaddccbbbccaaacacdabcdbddabdbaabcbbaddbaadbddadbaaccabadacbdbdacdddccbacbbbcccbdaacbbcabcacdcdadbbcbbbbddbbcdaccadadbbabdbabdbbaacbbdbbcdbdaccaaabdadbdbbdddcabbadbbbaadbdacaabcbcbccacddadbcadcdabadbbaddadcbdabaaccbaddcccdbcaaddbdcbbdccdadcbbcbcdabaadaacaadaccdaccbabdbdacbbdbcabababbdbdcddbaddbbdcccbdddcdbabdbdddbdddcddccadbadcadadbacaccbddabcacdcbbdcbcabdabcccbddbaadaaaaccacaadcbaadcadddccabbdbadddbbbaaddadccacdaccaccdbdccdadadabcabbaaadddccaaaadddaddadaacbcbdccbadacbcaababacbbbabbacacccbcacbabbaadbaacdaccdaccbbbaabcdacaddcadadcdddacddbcababbbddaadcabdcaddcabbbadacbccacbddcadcabcabacaccdbaaddbbbbdbccdbdccddbbaaaaddcccbdcaadcdbdcadcbbbcaacabddccaacdadabdbbcbbcbaaadbabbbadbacdaaabdbdadbdbcacdbccadacabdbdcaccaabbcbbdbbabdbccadbbdbaccaaadaaadaccddddadcbbbdcaabbaaabdbdadbbadddccbdabacbaddddacacbddadcbacdbbaabcaaaadbaadddbabccbbadddbbbbdcbddaddaadcbcaabbccaaadabbcddbccbbaacccccdcbacbadcadadbacbaddcdadacbacaaadacaaadbcbadaadbabbabaacbbbbddcabcdabcccdcccdccdccadccadccaabddaacaadabababcbdacdcccabbcaccdbdaddacabdccccacddabcdcaccbabdbdbaddbaaadddbbcdabdabaaadccadbabbccaacbbcddbbbacacdbaabdcdddcaccaacbbcbadcbadbabbaccabcbdbdaabadccccdbaaddbabbdcbabcbdaddbbdcbcdbadcdadbcdbbbbdbddbdaccddcdadabbbadcdaabbccdcbadbaacdaadbdcccccbacbaaacddbdaccabddbaacdabcccddabdcadbbbcacbbaacaaababcadcbababaddbbccdaadadbacacaaddbcadbbacbbbacadcadababaabbaabbcbdbcadcbdaccbacbaddabbcdcddadbaadbdcaadcbacdcaacccbccbddadadbccbbdbdccccbcadddcaaadabaaddacaabcbaadacbbbacbbdadcabdcbadbbbbccadbacdaccddcdbdbcbaccbacdadcaabbccdcbaaadbcbcdaadbcbddaadadddacbbdbdcbbddccaaddccbadccaacbadccabaccbabcaaccabccbbbcbadcabcddbacaccabacbbddabcddbbbdaccacdadbdbdbabbbbddcdccadcababcdbabccbcbaacdbacbdadcbcccadbbbcaccabccbdaddacddadbdcbdadbbdabbaaddbcddabbdabcdbaabacadacdabbbbbbdacabacdcbddbbcaabdccaabdabdcaaacaadbdbdcdbbcabccbadacccdadbdadabddccccddabbacabaabbbdcdddbdbccbcdcbbcabcbbbbacbcddbbccaccaaddddadcbbaadcacdcdabbdacdccbcdabccbdbbdbccbbacccdcabcccbcbadaaaabbdbdbccbbaccbcbbaccdddbabccdadcbdcabccdcbacabdbbacbababbabcacdcdadccccabdacbdcbacacbddcaddbbcaaaaddcacddbcbabdddbbbbdbdabaacddbccacaccaabcbbcdadcbcbdbdddbbdcdbdbdadddcacdbaccdcacbdaccacdddaadbdbaabdadbcdbabcabcdbaabdbadabacbbbbdcdbaaaacbcbcabbbbbadbcaabddccdacbdacabcbbabdbbdbadcaabcddbdcdbaddaaaaacacdaacacbabbcabbaddbccdcaabdcdddcaaacdbaddcabadbadadbcaccaaaadabcbaacaacbaabadccdacacadaddbbabaaabaaacaacdccdbbaacbaacabdbddabcdddacbadcbccccacddadcbdbdaccbaacdadaccdacbdbacaaacdcdcdbaddbbadddcccbdbbbaacbbabdbdadcadddaccbdbacdddacdcbbcabbbcabcabcbdcacbbabcbbadddcddaabaaddbcadadbaaadbadbcdadbaccbdbaadbaddbcabddbdcacaaaadccacacbadcccdbcccbabddaacaacacdddacbcdacdcacbacdcdaccbbcdbacbbabdcdaccabaddccaaacdadaaadccbbbbaadccabcccbcdbcbdbbaccddbbdaaabdbbabdacaacbcdadcbddbcbbccbcccccbaccdbbbbbadcbbacbdabcacbbbaacbabddccabddaaaaccdbccbacbdbaacccdaadbcabdccbdbccacdabadadcbbdcadacacbcbbddbbcdcdbccddcabbadbbcccdcabddacabccacbcbdbbadddcddacaabadbbccccdabababcddabaabcdababddcdacdcbcddaababcdcacacdbbabdbabcadbddbaccdcbaccbadddccbdbcbdddbbcccdabcbaabdccbacbcdbacabbaddaaacbaccccabdcaadbcdadaacddbdacdbaccccaddcaacbbbaddadcddaddcbdbacccbcabbdadaaccbabcbdbdccbdcaccccbabadbadbcdbcbaccbccbbacccbcbabbccccddabadadbbadbcabadcadbbaacbcacdcbcdbbcbabbbdddbabbbdacccabbcabbbabcbddbaacbbabcabcdadbcbdaabacadbbcaccdcdbccccadbbbcadcdaaccabbcbccbdacbdcbcccbdabdbbbbddccbabadbdcdadbabdacaabdcdabaabccbdbaacdadacbdcbcdcadcdacccdabdddcaddaddadcacccdcbbacdccdddbcdacbdbbddcbbcadbcadacdccacddaccbcdcacccdabbaababcdbcccabcaadcdbcddcdbcdddabccddcddadaaadccddcddabdaaddbdddadbdcbbcaabcadacabddbcdcbcadcabbcbddccbdbcadadbccbbbcbdaddaaaacdadabbbdcbdcdbaadabacbbdbddcdbcbcccbbddadcaadbdadcddcbbcdaccdbbcaddddcbaacaadadaccdbdccbacabdbabadabbcbcdacdaacacdaabbacdbbabbcdbdabbcbacccdcdabdcbacddadcacdaaacbdbcaccdadcdbabadaabababdbbabbcbdddaccbcdcaaaabdcdbdcbacddcbabddababdabacacacbbcddbdbbbcbaacaddccdcaacddbddabdbccccbabbbcccdbccdaddabdcbaaacbddcdcdddadcacbccabdbbddaadbdbccbbaaabbccacbdbdbaaacabadaaadabcbcaacabcbdaadbccccdcddaacbdcabbcabbabbbabccdddcdcddaabaccbcbacbaacabcadcbcdbdddddcccdbbbdbcbaacaacdcdacbbdcadcaabcdaadbbdbdbdbcdbbbdabbccdabdaaadbcaabcaddaaadbcadaaaccccdbccdcdcbaacbbbcdaccbddadcbdcdcdbbccbcdbbcbbcdadbdcbadcbdaadaabbdbdacacbcdbacccbdcbcbaaccabaccdaabdaaaadcccacdcabacdcbbbacbacadadcabaddbcadddacbbdababbadabddaabcaaaddcdbdddddaabbbacbcbbdbbdcdcccadcbcbdcabaacbccdbcaaaadaddbdbddcdcddbadbabbdbcadabbacccaacccbcabaabbdbddbcdddbadacaaacbcacdbacdcabbdccbaccacbabdcdbdbbddacbcbcdaddabccabddbdaddcaddabbdbdbdacccaaabbbcdabbbccaaaccdbccdbdbadbddcccdddacbcbdcaabaacacddcbcaacdaabdabaabcbcbdadbdabccdacadbaabcbbdcabbbddbdcddcdbacacbcbcbdddbccabcdacacadcabccdaaacbbccdcdabdabccccbcaabbaacabccadbdaaaabaaadbbbccabcaddcaacdccaaccacddcdbbcbaadccbabadbbcaacbcaddcacdcaadbdbabcbacbdccbcdbdcdbdadadcbaacbaddabbbbbacccdbbccbacbcdcccabdddaacaccdbddabcbbadccddbcbcaadabdabdcbcbacbaddaacbacbbacccdcbadabbdcdbccbaccbcbbccbcccdadcabdcccbdacaddcddcaaaadacdbcacbcdcabbcbcaabababccdccbaddbdacdccddbcaaadcbabaaaccabbdcaabccbbcabcaaaacaddaadaadaacbbaabbddbadbaadaaddcddbdbcccccdacadbcbbcbccacbdcbbbaabdbadaaaddbbcbabbbddccdbaacbccadcbbcccbbdacbabaacbcccbddccdbdbadbbbbbcdcacdccdbbcaaccddbbababccdbccaacacbcabdbcbcdcbcddaaddabdbcdacddadbddbdccaaddaacadccbaadbaaabbccaaabccbbabcacddababbcadadabddadaacbbddcaaddaacccadcdcbdbdbaabdaacdddccdbbaccbdccaabdbdadaaaadcbdcbdddababababcdaccbcccdcccaaacaaaccacccaaadadcdbcdcdbadcacbdbcbcdacbbcdcbdacaaaaacbdadacbddddbaccbdbaaadbcadbccaccbbdaabababccaadbbbcdcdacbaabdcacbabdbbccbcccddacbcbbbaddcdadcdacacbaababccbadbabdbbdcacadbcbbacabcbcacccadaabddacdcacddadcbabccdcbddaddcbadbcdbcbabcddacccbddbbdddacabcadadabdabccccddddadccbcadaddddbaaabaabddbdbccdbadbdacadaabcdbccbcabbdbdccaacbcaaadbdbaacbcacbbdcdcdccaadaddabddacccccabcaaaadcdddcbdadcdabdbcbcdbddaaabadcdbaccdabdbabadabcddbaddbbcddaaaddcaabdaacbabddacbbadcabacadaacddbdcdcbddbdbacbbadabdbbaaababdbbcddbdcdadbbabbdbbcdbaadbaadaacabbdbbdaabdbdaadcddabcdcbddcbccbcccccdaaaabdcbbccdcacdbbdcbdcacdcbdccabbcabcdacadabcbcabccabcbaadcbcccaccdacacbdcbbacbbbdabbbcdbccbbddabdddbcadadaaaaabccacbbcdaadbdbdbdbdcaaadbbacaccccbcbbcadbcbaacaabbcadbcadbdbdabccbdabaadcaacabccdbcdbdaabadcadaabdcdddabadaccaccddadaaddccadacdcdbadbdbdaaabadbbababcabdabddddaabbababbaccbddabbbbbadcccbcbbbacaccdadbdbadddadccdbbcacdcacdbbbbdbcacdddabcacdcdaccbcaaacbacdcadccdacdadababaabbdadbccddbbdacdcabbdaaaccabcaababdcccbbbbdbabddcbddbcdcbadbdbbcddbcaddaaaacdcabdbccacdcaadbbbabcdcaaaaaabcccccaadacdacaddcacabaaddbaaaabbdaaabcbcadddabcbccacadbabdbcbabdaaaddbcaccbcacabdacadbaabdbdaacdcdabccbadbccdacaadbdaddcbccbaddaadddacaadcddbbabbcdcbaadccddabacbcccdbddcbdccccacbcddcdbdbbddbcdddcaaccbacadbccdabcacddcaddacbadadcaacabdbdddcdcdaabdbaacdbacbbcccbaaacadabaadabacabbbacbddbcbcabcacbabdcbcccbbbcacabdbcbaddcbccdcbdddaaadcbdbadbcbbddbcbabcadbaccdacbcdccbddabbbddccaadacaadcabbddcabcdabadcacbcbdcabacbcbccdaaadcbdbbbdadacdaababddcdcbcadcdbbccddddbdbcdbabbaaabdadcadbdbdcbbcdbaccccabaadcdadccbccaacaabdacbbbcadabaddbabcbccbdddccbbcbdbbcadaddabbabcbdabdcabdaaacbaccdccccbbdaaadaacccbcbcaccbcacacdcaaaaacacbbaddbbcabaabddbccacbabdacdaddbcbdddddabbcdaaacaadacbccbabdddcdcdddbadbababadcadacbbdcbaabcdbadabbaaaacaabcdbbbbbbbdcdbadcccabcaadcaabbdbdaddcdbbbbdbdcbcdaaacbaddcbbacdddbddabbcbadbbcaaabcbaccbdcacadbbdaadbdccadbcccbddaaabddacacdabbdcbdacabadcdaabdbbdccccddbbdcdadccaabacccadbcabaadabcadccbaddbdbabbbaabbbcabcaddabbbdbccdcbadbbbcdcdaaadacbcaddbbbddcdaadadbcabacadbbabadbaabcdaccaddcdbdaccddcbddbbbdaaaddadabbbaccbcbadabcdaccdadabdabcaabbbacdccaabdbddacdcdaacbcaccacabdaccacdadcdbbaadcdddadcdbaabadbccabbaccdddadcbbddcadacbdaddcdbbdbcbacdbdbabbbabcabbdcbdacadcdddaaccacbcdcadbbaadccabdabbabbadddacaabdacbcaacbdcaddcabcbadacdddddbdaaabdaabbbaaddcdcadacdbbddacabacccdcdbbdccacdaccaaadbadaaacdcacdadddddbbacacbdaaaacabdaccbcccadbdbaacacbcdcdbaacbdccaacadaccdbbcadbcaabccabddcaddcacddabbbcdcbbccdbdbabacccdbdcdbbabbddbbdccabdbcaadddbcdddbdacdcccddadbdaddccdabdcbabcaadadcbcadbbabcbbbdadddadcaccaaccbaddcbdaabcdacadbbbddbddddacbdbcacacbccabbcdbcabbcccacdabdddcdcacdacdbcaccbaacdbcdbbabadddbdaadbcbabaacabdccdccaaabbcdbabbbdbabcbaacadcbccadcbcdbaadbaabbacacaacdcaddaacaccdabcbacccaccaacabcbcddbcdaabacdbabaabddcccadccbacdccbabaacbccabdcdaacbabcdbacaaaadcdcbbdcccacbbdbddcbaadcabbaaccabdcdbdaabdbcbcdcccbcabdacacaabaddacaaccabdbaddadcbdbabbdcdbadacaadbbcdbdbdabcaacacdbcbcddadcadcaddbaacdacbcbdbdadbbbdcabdaaadbddddbdbabacdbcbbacdddcaaadbdbabddccdadcbcbacbcbadcbddcccbaacdccdccadcddcdbbdabbbaababcacdaaacbbdcdadcccbbbcccbcccaadcadbbabacbddadaddacdbbbbbdaacbadddcbcbcbbbbdaacbbbdacdadcacadcabbacccaaacaacdbbdccccdcbdacbdcaaaadcdabbbbadccabbcdacbdacabcddbccbbbbccdbdcaaacbccabdacdcdccdaabdaadcdbbddacccbbdbdadabadcaabcadadaadbaddbdadadaabcbdacddddabaabbbacbbbadbadddcbdacbdcdcddcdbacaadcadacbcdbadcabccdcdcccbdaccabcacdacccddbabadddcbbddbbbaddbbaaccbbccabddaaaadaadcddcaacadbcabbccddcbbcdaabdaaadaaadaacbccaaaaabcbdaabbdacbacadbddabdbacddbcdbcbdacbbbbcddcdcacdacbdaaccdaadcdcbcbbbbccbbddaaddaddadbbcbadcadbbbabaabacbdababcbcabdaadcddaaaabcbaabbcaacddacacaaabccbbdacdbabcdbbbcdaadccdddcdadacaabddaaadbcdbcccdaabdcbabbdcdcdbbacbccccbbccbaacbccbacddcdbaddbcdbcdbbbaadcbaaccdaadccdbbbbdbbabbddadccbcaaaaccadbccddbcddbbdbddabbdcdaddbadbacabcababbacdabaacaccccdadcadcaaccaaccbaccbdbcddacacbabddcabdbdaabcaabccadbcdcababbdadaccdbbbbadaccbddacaaddbaadcdcbbcddcdcdcaccaadbddbdaaddadbcabddbbaabcaabaddbabababdbbddbccdbabbdccdbcadaccadbcabadcbcbbbcdddbcacadaabcbcabdadbdabdabadbcdacadbbcabbdabcdacbcbacbbcacadbdbcbcdbbdccababdbdbabcdabbaadddbcacdcbbdadcaabcbdddabbdadabcddadccddbacccbdbbcbdcadaadbbdaacabcaacbdcdacbdabccccbbcbacbcbdccaddcddaaacaaddbdacbcbdbaaadbbabcbdddcbabbbaccbbdddbccabaabcbbbabcbbbcccbbadccdcdabbcddbcaddddbadcdabdaccadacabbaacdaaaddbbdbcbccacbacdabccdbcacadcaddccdcdddbcaaabaaaddbdddbbdddcadacadaddcbbabdbdaddcdabdadddccabdcbcbbdaabdcdcadabbbbdbcbabacaaaaadbccabbcdaacaacdcdbccddcdadaaaaccdbcadacbcdaabaaadbdbdaacbbdcdacdcbbcbabbdbcbcdcacdbcabbccddcbbccaabcbbacbabacdacadabdbadabddddbbdbbbcbdcbcadcdbbcccaddbdcbadaccbcabcacacccbcdbdbcaadbdcabcbbaaccdbbbcdbcbabdcccdbddadbbacaadbccabbccdcaccdadaacbcadccbaaccaabcdbbbacaccdcdbabaaaddbbacbaabbddabdabaaacdccaadacccdbcadbbddddbdadacbadabcaacbadcbdddccbbcaaddcabbdbdbcdabdddacaadcdbddabaaabdbabadbcbdabddbbdaadcabbdadabdadddbddccdbcacaadbaabcadbadacbcabbdddbbbabcbbcbaaabccdbccdaadcabadbaacdaddabcdacbcbbcbadabcaadbcdcbbdcabdcbabaadddacbacadccdbcbcdcdaabacacbaacaacdbaaacbddbddbcbaddadcbdcbbbbbddbbbdaccccccadcbbbddddddcdccddbdbaddbaccbcbdccbbddddaaaaccabadcddadbbbbbdbcbdbadadbbcbbdcaaacabccbaacacbccaaddabbdcaadaabbdbabbcccccdccadcabdccbaabcaadbdacacccaddbadbaacacbcacbbcbdbbdabacaacabccccbbdcdbabaccaccdbdcdabccdddbaddadaaddadcddbbacdccdcbccabbbbaacccccbccbbcbcbadbdbcccadbabcbaabdcbbdbbadacddcdcbbddabacdaccabddaddcccbdaaacabaabcdcddadaacddcaddddcdbbdabbcbacadcccdbddccbaacbaacccabadbabddbadbbdbaacdddcdbcbdbbccdbbdbaadcbbdbcdaccdddcdabaadaddabbcbabbadccbdaddcbbbbacddbcdcdbbdaadabddbcddccaddcabdbbbabcbbdcdadcbaacddbbaabadaaddcacacabaadbdcbccccdaacaadaaaaaaccbcbbdaccaddabdadccdcccbdbabdbbaaccdddbcabbcddcdcbcabbadbadbbaccbdbdcacbbddbbbbadbcccdbbbccbcbcaaabbabbdccabdcbacabcdaccaabbcbcbacaacdaddbaadddcdbdacbadcddddbbabacaaccddacdddccaaaaaabccaccabbccdcbbdccbddbddacdcbdbbabcbcdddaccaacbdbcddcdaaabaabccaadadadbabaaabbabbdcdacdbabaddbabccbdbcacadcdacadbcbabbadcbdacdadccddbbbdccadcadcbbabadcddbabbbbabddadbbabccdaaabdccabbbbadacabadcadabaddadcaaaddbdcaaadabadbbabbacdcccbbbddadbbcabdcccbbdddcacdbcbcaacddacdbdbcbaccaadaaaccadcabccbcddddcbabacbccddbbcbacccbacdbacdddcaccadddcaaddacdbacadababcdddbdabaacabcbdccbabdacbdbbcabbabddccabbcdbddcadadbdcabcddcbbdddcabcaadccdbdacbabcdbdbcddccaadabcddababbbacbbaacddacdbccbbcdacabdbbdcdbdccbbdbccccdabdbabbbdbbbcbdacddbcdaaddbdcaacccaaabdcaaabcddcbdbcbabacadddcaacbaaabcccdcccccbaabcaabcddcaabdaccbdbdadcbacabdccacacadacbcbbadbbcbcbddcbdacccbadbcdcabbcbddcccadbbbccdaccbadcaccddaaaaddbaddaadaadacbbdddddbdcacbabacccaaacaadcdaacaabbabddccababcaabdcbddbabbccabcadbcbbcdcaabcdccdaacddbaccabbacdbcdcbacbcacbdddcbaddaddcbbbccdacddccaabacccaacbbcaddcaacdabaaabddbccaaabbcaddbdddbbdbaacbbaabbacadbdadbabdbdcbabadbccccdbcaabdccbadccbabbaaaaacddbbaccbbdadbbdcbcdabdcadcbacdbccbddaaaacdbbcabcbbddcddcdcbbbbbaddbdbabbbdbacdcababbbabcdcbabcddbaddbbabbcddbdbdadbaaccbacbbcaaaaabcdbaddbccbabcacacdaadadccbcacaacbcbccccbbcbbbddcaccaacdaabddbadbadbdaacaadaabbccbcbadcddcbadabaaddcddcccbaaaccccdacacbdcbdddacacccaadabadabdbaccacddacdbcabdcbbdbbbccbbaacbcbdddbacaadbbcbbaaacadccadaccbabcdadcacdcbdbdccdacbbcabdccdcbcbcdadbabaaddccbcabbccdbdcdabccbcadaacbbaabcbbdcdbcbcccccdbcbabdbbddabbaccdabaddbbadbaacbdbcbcbdbdaababddbcddabddbbcbcdabbbcbaadcadbbcdbbcabbbcddcacdcbbdbdadcdcaddcccddccbcbccbdbdabcbccbddaddbccdbbdccaaccabcbabddadcbdbbbdbadaacdbacbaacadacccbbdbabaaaaabdddbcbdaacbdbcabacdccbbcbbcdbbbadccdabcccbbacbabaadadcbdaaccbdbbcaaabadabbccbcdcdaadccabbcbcbddbdcccccdddbddadbbdbbdcdadababbbddacabccbdaaddbcdcdbccdacdacbddabbdbaddaaacaccbaaadabbdaabdacaacccccacbcadacaaaaddcabacacddbbaacdcdcadbbaadabdccdcdbacbacacdbbddbbbdcdaaddacabdbbdccbcdddacabddbaacbdaadaadcccdbbadcdcbdcdcabdbdbcaddaacbbdaadcbdaadcccbbadaccaadabdababbbdcbacbbbabddbbaccddacaabcddabacbbdbbcacbdaddadcaddababadbbdccabcbcdbdacdbaadddccdcdbbcdacadddbdcacabcdaadddcdcbcbaddccabaddbccbcdadddbdabbcaacdadacadadbddbabcccacaacaadbcacbaacddcbdaadbbbdcacccaaaadaddacaacdacbcabcdcdcddaacadadcdccddbcaadccaadddacacabaaabbcaacaaadbcadabadcdbdabbcccccdabcaacababbbccbcccbcadabbcdadaabadcbacaacbacabacaacccbbcddaccdaaabdddabdbaddabbcdcdbcaddcaabccdcbcbbdaccbacdcdacabaacbdcbcaacaaabcbadcbaaccaccbcbadadcddbddbaacacdaccdcddbaaababcaccbcaaaaabbaabbcbabaabbdbbadadacdaaaaabbadddabcbdbdbdcccdacacbcadabadababdacbbcddabdddccbbdcdcdddbaccbbdacbbdbdcaccbcbddcbadaaadbcdbcabbcadccbdbbacbbdccabdbccdcbcaccbdccdcdbbdbabcacdccabdbccacbdaacbcacdbdcbbcaacbabbaaadaadaddddadcddbccdbadacbbbbacaadadacbdccaaddacbcbacbbbadadbbabccccdcdbccbaccacabcaadbbddcccdcccbccbbdaaacbbcdcdbdccddaccbbddcadabdddbbacadcdcbbbacdbcaaadaabadaadddbbaabaddcdcbccccaaabadbccacaddbadcbcccaaaacacbaadbcdcaddbdbdcbaabbbcaadbdbccbddcadacdcbbcbccabbcaccaacaabadcaabccadcacaacaadddbdbdcbaddadaaabaccdcdbdaacccbdbcacbccccdccccdcdadcddadaadbadcbbbcccdbaccbcbdbbcbbdabcbbadddacaaaabcbbcbbbdbbdcbbddbaaddaaacbbaccbcadcccaaadacbdcacabccdddccbbdddcdcbaccdccaaadccbccbcaddbcdcdccbbbddbbdabadbdccaadabdabbcbdbcabdddcdcbacdbdbcbdadcbabbbdababcdcdcabcadcaaabddbbbabcabcacdcbdbddcadbdadabdacadbaacdcaacbcccbddcbcbccaabbbaacaaddddbbbbbaddcbcbcaccdbacbcbbcccadbcccacacbdbdcbcbaacdbacadddbdaacbadadcacdcbddbbcacbbccbaadabacdadcdbadcdbcbbdcbbdcaabadaabaaccdabbcadbdcababccbdbdbbcbdbdbddddbdbcadacacbdadbbabbcacbacbaabbdabbcbddbbcabaabddaadacbdbcabdabbdbabbbbbcaccaaabbbcbdbbdcbabbcacbddaaddcbbdcdccaacbddadcacccaddacdbadccdabdcabacccccabdddcaabcddcdbaddcdaccdbdbbdbaacbadbdbbbddadddcacccabdaacbbacaaaadcadcaadacdaaabdcdbdbcdcbcadbbcbadbaaabdaacacabddabdabccbbbdadccbbaababcbaabcabcadddacabcadbdbdbbdbcdbdbdabdcbbccbdaabbcbdacaccdcdbdcaddadbddacdbbcdcdcbcadaccbdbdabcacbcacdcadccaddcbcddccacbcdccaabadabddbbdaacdcbdaaabbaabdacadbdcadbaacdbbacaabadccdbdcbdcbacccccabccabcdcbcdcdbbdbbacccbcadababbaacddadcdbacdddbdabbbccadabbacddbcbbccdaaaddaacacbccdcddddbdbbcccdcbcadcddcdbdddacabadcdbaddbaaabcaacdbadbbcbbbdcccabadbdadacddbcdbbdbdbacabadaaaccdadbcbbababdbadbacdbbbdaaacdaacaaccddaccccdcadcadbddddbcccadcaccaadadddbdadcabcbbadbcbcbbbdacbbdcacbabbabadddccadcdcdacacbbbcbccdbcbdaaabbdabdbacbbcbbcacdbacbcccacbcbbaadbdbcddcdaadcddddccbdcabbccbcbabacbdbbcadbaabaccbbcbcaadbcdabbaccddaacbcccddcccadcdcddcbbddacbbabbbcccddbdccbbdbaadbdbaaaaccadacbbbbcacadcdcddbbccbdbbcabddbdbbaacddabcbacaaaaadcbbccdbdbbaaabdbdacbadaaadbdcddbddbcdabdadadbbdcacaadcdbdbbccaadccbcbbbbdcbcbaccdddcdccccaacddbddddabccbbdadcbdbddaacccbbcbabbdaddababadbcbcdbcaabbbcbdcbdbabbcdbdbbbcdcccbaabcbdcccaadabaacbacaabaaccccbcccacbcbcadccddabbdbccbbbdabcadbbcaccbbbbaccccdbdadaabcdbddbbaaccddbcdbddababcacbcadbadadcacaacaabdcababdaabbddcacdbadbdbcbabbbbccaddcbbcaadbbdabbbbdccbacbddabcdadcaacdabdaaaacadaaabbbadadbaddadbddbccbddaccababccbbdadccbacdbdaabcdbbbabddcccbcbbadcccababccdacadadabbccbdcadccbabbbacdbddbddacbdaadbbddbdbbadaaadabbbabacaadbcdcdccbaaccdbbbbbdbbaacbcdbdddadcaabbbbbdbcdcccddacdabaabbdcdababcadaacabbabdbbaddddbdccdcadccadaaacdcdadccaaabdcdbddcbccbabbcddcdbdccccaccddbbaadcadacbadcddcccacddbdbcadaabcddbbbbdcdadadabbdccdadbbacaccdcacaaccbbaabddcaaabdbaabaccdbbddadcabadcbdabdcadbacdcbcbbdaaabcdcaaabbdaababcddcabcbcababdcbcdddcbcdbdacabccdacddbdbcdddacccacbcccbbcbbcaaabbbdbbadaaacadccadddbccccdcbddaabbacbcdbcdbadbadcadcbabadacbdbdbcbdaaaadddbcbddaabdacbddaccbaabacbcdaccbbabacabbbacbbcaccdccadcaacbaacbcbcdabaddbaddcaacdbdcbcabbddcacdabbbcaaabdcddadbcdbcbaddbdbddccdccdbbdbadbaaaddddadcabbdadaacbbbacbbcbcdbabbaddcccaccdbadacabcabcdabdbacdcaacbabdaacbdadacacddbdcbadbbadcabbbdadabccdbabbabbbabacddcbaabbdbbdabcaddddcaaaacdcbaadbcbbccbbbbcddadbdbdbabbbadacabcbcdbddadaddcbaabaccacddbcaccadcabdcbacacbadacabdabcaadddbabbbdbbaababaabcbcbcabacbdcbccbcdbcbdacccddbbdadabbbcadcccaaccdbdaabbcbcdcdbdbdaacdacabbcdabaddabcdbacccbbdaabbccbcadaabddababacbaadaddbcddcadacabababbcdbbbbdbdadcccdddacbccacacdaabbaddcbbacadddbdaccadcadddbbccddbcddcacdddadbbcccbaddcacbacaccdaabbbdcdcaadbccadcdcdddabbdbdddbaadcddcdbccdabcbbdcccdbadcccbaaddbdcaddddbccdbbacadcaacdddcaaabbcbacabcbbdabcbabcabaabdbcacdbddbcacdccddcabccbdcbacdaadcccadaccadcdacdacbcbbdbcddacdcdccabcbbdbabcbcdbbabcdabdabdaabdababcadaabdcdcdacadbccadacababcdbdcccaaacacbcbdcbcabbababbbabbadddbbbacdabccdadaadcbdaaaddadadaaccacbbaaccbaabbadbdadacdbbbacaabddbbadadaadacdbcdcaccbbcbcbcbbadddcdbcdccbbddaaaacbabaabcccddbdacaadccdadcadaadccbccdcdccdbaccbcbddaddbcbdddaacbabccbacdaddadbabccbddadcccbcbaaccdabbbbabdbcbbccbcbaadacbdabadbbdccabcdaddbdccdbbbcaccdcacddbdaabdcdbccbdbbbccbaabadbdaabbccadbccaaaadbcdccdcbaccdaccccdcdabdaacdccdccbcbbdccbdaadbbbaaadddbdddbaaaacbdcdcdcadbacbdabcaabbbacdadbabbbdaccdcbaabcccdcbbacbbbdbabcacccbdcabdbbdabcbcdbabcabbdbbdccaaccbddcbaadacddcbccccaccbddaaccbbbbcbcaaddbaacdaadddabbdabdcabdddabaddbabbaadcddbacbdaccbbddaabcccabbbaddcbabadcbdbabcaaadcaaadbadaddcdcacddbbdaaaddccbbaabbadcdcaacbbadcdadcadabadabdaddababbcdacacdccccbaacdbbcdbaaadccbcbcccabacabbbddbbacdcbcbbdcacdbaaabbccabaaaacabadacabcdbcbdbabbbccbcbcacdddbcdbabcbdbabcdccdbcbadccccdbdbdcbabdbcaddadcdbcbaaaaaccbaddadbbdabdccbbdbcccabbcaaadaacdcabccabbdcabbbaabbadbbddabaacdacadcbaacbbbdddccbbcccaccaacbcabadcdadddcabbadcbcdcdcdbccbbaacdddcbbaddaaacaccbadaacdbcdbabacdbaacccccacddabbbbabbbbdcccadddcddcdcccdccabbccdbcccadbcbcbbddacdadbdaacabbbddaddbadacddbacabbbccbdbcdadaccccdcccdbcdaabbdcacdbbbadddbbbcadaabcdbbbdddbdbadccbbabcdcdaadcdbbdadcadcbdbbdbbcddaabdbaadacadaacccbcbbdbaaccbaabcbbddabadcddbcabccbbaacababcdcaaabbacabcabaaddbbdcdabadccccaadacccccbbdddadddbcaddccdadcccdbdbadbbacabdabbaacccaaadbbcccacaaccaaabcdabbccbdcaadcbabbbbbdcdcaddcbbadaddacbabcbbdddbccccaadbdcaaadaaaccdacbdddbcabbbadbcbacdbbcbdaaacdacddacaaadcdadbabaddcbdcbdcdbcabdcdcbbbdcacbcbbbcdcacdacbddabacadcbcbddcbdbbbcacacbcdcabccadacccdbbcabbcbcdacbabadcbccbbdaddcddcbdbbbaccbdadcdbadcdcdbcaabbbdbacacbadcdbbddbbcaddbbbdaabcadccbbacdbbbbcdddabcbcdcadaddcccbacdcbccabbbdcabdabccdbdbdbbccbdccccbddcabdaadbcbaaadccbcdcadccaccbccdccbdbcdadccababcbcbabcaabcacbcbcbcaacbdcbdcdbddddcccdbbbcbdcbdddabdacddbbaccabdcbddadbcadbbbddccdccadbddadabcdcbaabadccaabadbcacdbdcddacaabbacbdcbcddacdadbcadcddcbbdbdbcbcacbabddbacbbdcbddbdabbbcddabcadbcbdbcdccdcccbdccdbbadbcbbcdbadcdbcbdbacabbdcabacaadaadaaadabdbddbcbbdbaaabccaacaacaddcddabccacacbadcdccbccbbcbcdccdcacbaaabaccccabcbddbcccbbcabbcdbaabccbbdbcdaccacdbcabcbbabaabcdddadbaabccdbddccbcbdabbcaaccbbcbcaaddcbccdbdcadbdddcbdcccbdccbdddbcdcbbccaabdcdbdddcccdabcccaaabcdacadadbdcaccacbaaadacabacbccbbccdccdbadbbcadcadaddddbcbbccaaddbcbaaacaccddcbdabbdacaccbcbbdabccbbcbbbdcdadcbacdcaaddbadccadbababadadabbcddbccabbdcbbdbbcdcddbdacccdddbbaaacabacdaacabbcabbbcddcababdaddbdabbddaadbddcabbbadaddbcabbcbbcbdadabbbddaabaccbcdddbaacccddbbbdcdaddddaacbbcbdabaaaccdbdbdaabcddaabddacccabadcdbacadccbcaadcbaaaaacbcbdbadcacbacdcacdccabaabccbdaccabcadcdccbaadcccddbaccccacbadacbcbcdbbccbcccadccbbbdbcacacbcbdaaacbbccaccdcbcdabdbbdaccdbccbabdbaacdccbbccbcbdacdcbccabaddcaadcccdadcdaabaabbaaaabbbcbbcccacaabbcbdccbbddbdbdaaccaccbcccadcbadcacdcaaacbacadcdccdbcbdadadacaacbadcbcabccbabccbcbabdbaddbbabcbacdcdbdbaadbabacdbcdcbdbdccacadabaaccddbbacbccbbadbaabdcdddcdbcccdcbbabcdbadddbccdacbdbdbbdccdcdcccaaabbaacdbacdadadbdbbdaaccdbdadcdccdcdbabdbbbccbadaddddbbdadddbcbcadaccbbbcbacddacbdbddbaaaadacbaaabdcbadbdcadbcbdccbdbadbcdadbaddabdcdcbcdccabacbdadbcddccddaaaaccaaadbdddaaaabbdbdbcddaaacbdddbddabcbacdccaddcabbddccaacbddddcbadabcbcdbcadbdadbcdbacbdcadddaadbcabcdbcbabcdcdcbdcaaacaddacaccbcacccaacccdabbacccdcaddadbccddbcbaaaaadbbbcbadaaacbdaccacaddddcaadabcbcabcccbbbcaccadababaabddddddcbddabdbbacdbcacbbcaabdaacaaaabbbccdaacaccbaaaaabbdcaddbbadcdbbcbadcdabcccbabbdbdcbbadbbaadcdcbabdccccbabddaacbcdbbabbddabbadbaddabdbcadccdadcadabbccdccdcbdaabbcddbdabcdabcadcbcccdcaddcddadcadbaaaaddcbdaacabddbcbddabdbabcaadcacabcdacddbaddadabaacdcbdcadbbdccadbdbccdbccbaadccbacbaabcdcaddcacabbbdbacdcddbaabcbcdaadcdbccbddabbbdbcaabcabcabdbccacdccbbbaabdaadbcbcdbdccacbdadacdaddbdccccbaaadbccbbbbcaaacbbdbadbabdbccaadacbdbbbbddcccadbbcabaadbabcdbbbbadcabccbcbbbcddcdcbdabadbcadacaadaaccccacbdddcadcdcbbbaddcadabddbcbcbbadccbabaccbbbadbcbcdbccbdbbcaadcbbbabbbbdccdcdddaababdcbbadddcabdcddcadbcadabdddbbdabbabdaacbccaadccdaacadbbbcaaadcbbdabcaababdcabdbccacbaadabaaadaaabbcbdcbadababcbbadccbcaccaabcdbdccbddbdacbbaaadddabbcbcbbcbaabcdbbadbccbaccbbdcaddaacabdbbbbcdbcddcdcbccabcaddadddbbbbdcdddbdadaabcddababaaaccbcdbdabcdadabdbadadcbbddcbcdddbbdadabbabbcdbacaabcddcdacdbcdbaccdacdcbadbbbdbabcabcaccbbacdbacccdbadcdaddacbaaacbcbbbaabbabdcccdbbddddacddaaabcdabbbddcccdbbbacdddbcdccbbcdabccbadbdaccdbdbabdddacabcbbdadbaacccddbaadbbdbbccdcbadbaaabbadbcddbcddbbdaacddcbacbccdacbabbdaaaaabacbdaacddcaccbddabbdadabbabdabacaadcadbcdcaccabdccdcdbccbbbbcacccdbccacdcbbcccbaaacbcdcaaadbaddcbadabababcbaadacdaadbbaddbdaadbcdadaaabccacdbbbdccaaacacccbdcbaadadabdbadbbcdadcabbdddcdbcbbdadbdaabbaaaaabdcabbbddacdbddcdbadadaababdbdabbdacccaaddcbcabccdbbcdbadccaccababbddadbddbbbccbcdabdaadcbcbabcacdcaacbdcbccdbdcaaacddcaabcbbdcbbcccccdccaabddcaadaccbbccddbabcadccabbcccbdcabadbbadadddbabbadadbcbbcdbcbadcadcacdddddcbdbcccaccabcddcdbbdccdaacaacdddddaadcbbaccadccbddcacaacbbdccbdbaadaacbadaabaabccccbdbdbcdccbdcabccdaacadccbbcbadbbcbacadbbdcdcdcacbacdbccddacacaadcdbaadabbdddbdaddbabaabdbbababacbbcccbbadcdcaaccdbccbcdaaacaccccaddbcbdbaabdacbbbbaacbcdacabdcccccabccdbcccdcabadccccbcadaccaccadbcbcadcdccbcbcdbbadcbcddddbababbccbcbaabbcbcdbcaddbabdbbdcbcacdcaabcdccddcaddababcbbcccdadcccacabdacbbccdacbcdabccdcdacaccbcdacadadbbbcbddbdbaddadadcaabdadbddccabdbbdcbacadbaabdaacaccccbcbadaadccaaccdddcacbbdcdbbdaddbbacbdbdbcccaacdabbdccaabbcddabdaccccccaabddbbcbdcccccbadbbaadcccbdbcbbbbaabdbbddacbcdddadcbabdbbbadcabbdcaccacbddbddaddbdccaadabcdbcdbddadcdbcabaabdbdbaacdaccbbdcaccbdbaddbbabdcccadabbacdaaaccadbdbbcabbcbbcccaaaacdbadcadddadabdcdbccbbadcaaacccbbadbbbbdbacddddcbddbbccadccaadabbaabcddddddbabacbadaabbadcdcaacdbacacabdaccbadcbcdadaaadbbaddbdbcbacccddbcbbddbaccdaddbbcbcccccdaaadbacacbabacadcbaaccbdcbddbacbcaabcddbbddbadbbbadcbcdcdcbaddddacbbddccccbacabdccbbdbadbdacaabaadddbaddccaddcabbbcdccaaabdbaadbcddcdccddabcdcadaaadababdacbabbcccddadbcaaddddddaccdccabbddacdcabdcccdaadbcdabccbcaaddcdddabadbddbccccbcbcccdbbcbcdbcdabcdcbadbdaaccdccbcbaaadddadcdacbbcbbbbdcbabbcaaadadcabbcdbaabdaccaaabdccbbccdbbabbddccbacbaacaddbdacbdddabbaabcacbdcadcbcccbddccbdabcbcadcbccddadacdcaaadcdbbdbcdbddaacabacadacbddcbaccbbdbbdccacdbcbabdcacccccbdcbadbbbdbdcdbbdccaabaaaccbaaaaaaccbcadccdbdabdacbadaabcaadddadbcbdbbaabbccbdcbbdcbdbadccdacbddadcacbccbbcdbddcacaddcbacdcdcadabbdcaaacdcacaacbdaabdaccaddcaacaacdbddaccaacbcaabbcdcadbcbababbccddabaaabbacbbacbcbbaddccdccacddbdababdcdabbbbdabbacddccdaaaacabdcddcdddaaacbddaabbbbaddadcdbabdaadcabaacdaddaaadbbbcccdcdabcbbcaabbcdccbaddbbdadbcbbcdddcbddcddadbaadadaddddacbacbdabacaacddbaddbbabbcbdadddccaacbcaabbbacccdcdcaabcddbcdcbadaccddcadcaaaabdcbcccadcaddbbcdcabcaacaddbbaccbcbcacbcaabaacdcaacacdacdccbddabbdabbbcdacdaddaaabdcbdacabbadbdadaddcacdbaabdaacaddbadcddccabadacdaaddcadaabcdddaccdaaaccbcbabdddcbbdbaacabbcdbcdbddabcdbabbccaaaaacbbbdbabbdbdbcdaadacdbacdbacdaaacddbbddabcbddabcadcacbdbcababaabddbcbacbbbbaddadcadcadcbdaadccbddaacadddcbacbbbdbcacdcdabdcccaccacccbbcbababdbdaabddbabdbacdcbbabbccaadbdabbdabcadcbdaadcbbbacdcbdabbbadddbdddbdccacbcaaabcddbaacadbaaacccbaadcdacaaabbaacacaabdbccdccbadcdcdababcbacdaabcdababdddbcdaacabbdaabccabadaddbdbbcddbadadddcaccccccdadccaabbdaddadbcacdbbccccccbddbdddcdaacbdaaaaddcdddcccaaacbaadddaccbabdccddcccbcacccaadcbaabbbcaacdbccbcdadbdcacdccaabacadaccdcbacbccabacdbcacbddaacdbadcaadcaacadbcdbadadddbaadbadacbcdbbddccacdcbbccccbcabaacdcadccdaacbabcbaddcdbcbdddcbbaabacccaccbacacacabbacacccbbbdadcdccaababdcdbddacdabbacddaadddbdcbccabbaadaaaccadbbdabcaddbaabaddddbcbabaacdccbdccdbbbbbdccccacabcabdbbacabddddbadbaaddbccbdabbababddadbdbadbabdaabcaaadbbdbcdddaadcbcccbabcaaabbabdbadbbcaacaacadabadcdabaabacdccbccadccdbbaddaadcccbbdaabccacbbdabbacacacbddddddcadbbbaacddabacbbacdbdabadacdcdccdcbcbadddbaccbcdadbdbcadcaaccccadaaacdbbdccadadccababdcbdbdaadcbadadbbccbccbccbbabaabdcddabaaababcdacddadcdabdcdcbaadbadddcbdacbacaacbcdcdbccaaaddacddcddabcddbdbdcadabdcbbcdaabcadccaabdddccdabdbccdddddabdbabdbbdccbaacddaadabbddccddbddabbcbddbaaadcddcbacdadabccbabbbabaacccdbabcbaaaccdbbdbbbacdaaacacacbcabdabcacddaddacbdcdbcdaadacdcabccadbcbabcabcabbdcabaccadadcdadbddbabbaddccbcaabbdbbcbddadadcccaaacbaddbbdacbadcbdadabbdbabcaccbcccbabdbcacaddddcacbbadabbabccababaaccbcacaccadbdcbabacbabcbbbdaadcbbcdbbbdcdddccadaadaaaccbdacccadddaadcbbbababbccdbcddccabcddbcaabcabcdcbaaaccccbddbbcccacababdcbcabccbabbcabbbbcabddbbcccbdacadbdbbccbbcdbdbcbdabdadbaddbacbcacdadacabdcaccbbdddbbcaaaacdbdcdcaaaddadbddddaaaabacddcccdacdadbddcbdaaccbdbcbbaabcdabbdcbbdabcbaacaacbcdacdcccddcccbdabcaccdcbbabdabcabbcbcaaaaababdbdaabdcdcdccdcbbcbbbadbcccdbcaacbaadcaaaaddbabacaccbabaadcbacbacadbdcccacddccbadaddcbacacabbdbbadcdababcaddbadadcdcacaccccccbbdbcadddccaaaadcccbadbbdcabbabdddbadcbadcccddbcbacdcdccbcadbdbdcdaaadacdadababddacbcbaccdadcadbddacbcdcaadbccccccdababdbdcbadcbbacdaacbdaabaacddabdcacdabbddaccdcdcddacacbddbccabbbddcbbabdaaadcdbabadbccabbbadbbcadcaabbaaccbbbbbddaabdddacbcaacbcbdcdcbdcbbaccbcacbdcaddbbdaabcadbdcbdabbcccbbbdbccacaccddaadcdbccbdbcdbcbbbbdadaabdbacbcbdcbcbabbdddbcbcbadddbaccbacdbccbdadbacdbcbccaaacbacccddaadbdcaacdddccbababdcdccbadcbacbaddbaddcbbdcacdddaabadccabbcbdcdccaabbbacdaaaaddbadddacadbbbdbaaddacbcaddbdacbcdbadbddcbccdbdbbacbaabdccaaabcdbabddcdbdaabcdaadbcccbbabbcaaccddbcbbdcacccdddcdabccddcacbccbdaacdddbddcbaccdccaadddaabbccbacccdcbcdbbbaadbacbbdacadccdbcbcbddbabaacdacbabbdcbdbcbdadbdabaabacabadaddbbaaccbcbdccbadcbbdaddcbddaaadddbbbcdbacbbddbcadbdcddcbaaadcdadcacdabaaccbbaadcdaddccdadbbcddbbaacdddacdadddbcbbbbdcbbcdccdacbdccbbaaacccddcdbddcbbcacdcddcdbadcbbdbbdddbccaddbbcddccbbadcaccaabddabbbbcababacabbbdcbbddbccdacbdcadbadcaaacdcabcbdcbaaddcaadbcaabdcaabbdbcbdbadbcaadacbacbdcbbadaacdbcadccbbccbbdddabbcdadadddaddbbddbccdbbadbddbdaacdadadbaacdccdddcbbbcccccadabaabccdbddabbcdbdccdcdbbbccaaddddaacbaaddddcbbcaadabaddacdbddbdbcdaaaddbbbbdaaccbacbaadccaabadbccdbdcabbbbdccdadbdbdaabaacddaaaaaaaacadcaccbcdccbcabcccccbbccabaaaabaddccdaaadbcccbbbbcdbdcaacabbadcdaabbcdacaadadcccbadccddcdabbcdacddbaaccdacbaaadbddddddacabdaacbabbdbcabbdbccdbbcabadcbbababacbbcbdadddcacdbcdccadcaddcdacdddbccdacabacaaddadaadaadaccabcaabbacbccdbbddbbabcaacbacdaacbcdddccadaccddaaddcccdcddbbbdbcdcabbaadcbaabbbcacbaccbacbcddabbbddbadbdcbaaaadbabdadaadbbcaabdcbdcaddccaadcaabdaabaddcbccbdbaddbcbcadccacddbbdacdbdbabacaadbcadbcaacddbdbcbdadcbbbacbbadcbaaaaaabaacacbcabbaaaadbdcaaadcddaddbacabdcadbbccbdcdabbcadbdaccdbdcccdabddaaadabaadbcdcbdbbabaaadadbccddacdddddccaadbdbbacbadbccdbcbbdddadadaababacbdaaddaccccaadacdcdcdcaccdcddbbccacccbcbbdbdbcdcdcdadcccbbbbbcdadaaaaabbbcddcccbdaaddcccadbacabcacccddcbdaddddccabacacacaaadbddcddacaaacdddadbadbaaabcbddacddbcaabbbbcaaccccdbdaacccadcddaacbcbaddacdabdcbadbddccddaaadaabcadaaaaabaccdbdaddbcbacadbdccadcbbabcddabdacaaddcccbcbacdccbadbaabbbcddaddbdaccdaaabdcdacadddbaabdbcdaadddddccdababcbaacadcdbcbaacacbbadddcaccdbbdbdcbcdbadbbcabdcbcdccdadbdaaacbcddcbabdbbcdcabdcdbbabcbaadabcdddcaaaacbacbbdacdbcadbaababcdabacaddaaacdaaacdaadaccbadacdadadcccdbaadcdbacbccbbcbdcbaacdcdadcaaaacdaabcaadddbcaacccbdcdcddcadcbacbcdcdcdbaacbcbacdbccbcdccbdaacbbbaacbcacddbcccdddabaabacdbbbbcdabbaaacbabcdcacdcbcaacdbdacbccaacddadbdcbddaadbcbaabcddacbdacabbdbcdaccdccabcbaccacccbbabcbdccaadabcccbcdccccadababcdbadabaabbbcbadacbbdaabcddcdbbacdbcaddbdbadbcaabbcddbabbcdaccadbccabdbbcbcaadbccbbdcaacddaaacaadadaaccbbadadacccacbdbdacbdabcdadbddbcddbdbbadacdcbcadccbdccacabdcbbacccbdaddcddccdbaadadadddcacddcddddcbcacbabbabaacbdcbcbbddabcccddaddcadcdcbbccacdacddcdcbacdabcbadacaaccccbcabbddbdcabaacbabcbbcbcaaadccdcdddcdaadabcddacacdbbdcacbdaddabdacaccdccaaaccacabacbdcdbacccdcddadddcdacdcdacdbbcdbcddbbbbaddcdccbadcdcbcdbdcbcadabdddbabdcaccdcccdcdbccbbdbdaacbcdadbabccdcddbbdabbcccdccaadbbaadcbcbaddddaaaacbbbcdcddaacddaacddbdddbdccddbdcdadbaacdbbbacddbabbdaabdbbcbbdadaddabddccabaaaabbdbacabbaacbccbcbccccbcbbbdbccbadacaaaccbbdccbaacdcccdbbaddbaddbabdcbddaadbaddddcdbacacdbaadbcccabacdbaacbaaabacbbddcdaccdbbbdbcdcbcccbaddbcaccbdcbbdabcbbcbbcdccaacbbcabccdddaadbdcccbabbbaccabbaabacadcdbadccbcdabbdbcdcdbccbcbddacabbbbdddadbcaacddbdccdadbccdccbbcacdcddccaccaababaddabcdacabdcccbbdcddaabaddbaaacbacabcbdabdcabdddaacdcbdcdabbabdcdbbbdadabdbaabbbddddcbbbbccacdabbbcabbbbacdbadabccbcbccccbacbaacdaabdacbbbaacddcbdbcacccbbaabdcacdadabaddaccbbccdcbdaaadbbabbcdabbadbadddbcacbaddbdadbbcbbdcaacaddcadddababacddcacadddaddadbbbccbccccbbccacdbcbbdadacabcbcbadadccbaacbbddbaccbcabcddccbbbbbddbadcacbddaccdbddcdbcbabddcbbccabbcabbbbadabdcaaabccbaddbdcbbabadcbabbabbdccdcdddcdddcbccbcabbbbbadbccddaaacaacacdcbcbacdccdddbcccbcdacdbacccdacbbccabbaaaacdbdccccbaddbdaaddbacadbaaabdaadcdbdcbcbbacdacbcbadcccabdbadbddbbaddadcaaaccdcaacdbbacbcccabdacbdddbcbbaabcbddbccbddcbcdbaadabcadbccdabbddadaccbdabbdadbdccadaabbcbabcbcdbadcbaacaabcbbcbaddaddcbbadddbcbbdadddcacaaacabbdadcccbbdabcaaabccbbcaddcdbcbdbcadbdacbddabaccdaccdddbdaacddcbadabcdddaddaadaccbbabdccaadcbdacacccdcadabdacaaddacbaccddccaabbacbdacdbbbabbdadbcbddbbddcbabdacbcbaacaadacaadbbccbdaadccaacbccacabaacbcabbbacadbadbdbabccdcddacddaaabacadabaddaaacbccbbadadbdadddaaabccdbddbbdcddadaadabcdcbaacbdbcccaaabbbbacabdaddcdacdbacaccdaadadbcacaddaadcdabbdbcabcdacbdcaacddcdabccdcbaacaadaacabcbdabcbcaaccccbaacbbacaaaabcccdbdaacbccabcaacacdcaabdacbbadacddbcddcdadacacdbdaadabcadbbadadddbacdbbabadcdccdbdadabcbbdcbacbcbbadbaabaccbddcabaabcadbbdbbcdacdbbbaaadbdaddaccadcbcababdbabcabbcbbacbdabcbcdcdbccccdaddaaaddaddbabcaacdaabcbccbddbbccdbdcbbddbcbdbcacdbaacabacacbdabcabbcaddbbcaddcadcbccacbcdbaaddcabaddcccaddddaccdbdbcbccdddacadcdcdbbcaddaabbaadbbaaadbacbcbbcddacacdadabcddaddcacbdcaadbaddddcdadaddabbcbcbbbdbdadcdbacddacdacdcaaacddbdccddcaacabbaacbcddadabaadabcddccdaaadbdcbcbddddbcddaddcabcaadbcaabadbddcbcbacadbbdbcbaaabddccdddddabbddacbcdbcaacacbabbcaabccaddabbcbbcddabcbabcacbcdcbdacadaabdbbadcbadddadbcccddadbcbccacdaaddbaaabcadaabdddbdbdbdaddbbccbcbbbdacbcdccccddbcdadbabbcadabdacacbbabbadcbbcabbbcadaababdacabdcdccccdaabbdbbbcadacdcbdbacacdadcbbdbbcbaddabaadcdcbddacabcbdbcbbbcbacdbdddccbabdcdcabcacacddbaccbddccbccbdababccabccaaacbadcbbcdbacdabcbcbcbcbddcaacccddbccbabaaabddabdddaacbcbdbbcacadddddbdbddbdbcadabdcccabddcddbadcdbcdabbaadccacdadbbaabdabddcbcbdaddadabccacbbcdbddcadadadbbbcacadbddbcabacddaacabbadacdbbaccddbdddccdadbcdaddbddbdaccdbccaabbddbacdcbadaaadaaadadcddababccdaccddaaabbcaabcbdbacabdaccabaabcdadaabbbdcdbaaaabaaadabbbbacaaaccdaaacdbbabdabcacbcdbababcdccaabcdaadbadcbbaadabcaacbdddbcabaaadcadcdccbdcddbcbddaddbcbdddccdddabdbabcdabdabcaacbddadbdcccbabcdcacddbcccbcdaabdabaddabbcdadaaccaabbbaacabcaabbacdbbabadcdcddaccdabadbdbdcdaaacabaadcabdbbbcdbcadcdbdcadababdbbabacbababaaaddabccdcbdabbdcaadabacccaabbcacbcbdcbacabbbabddaadcbdacccbcaacdbaacaadbdbbaacccadaaadcccbbbbdcbdabcccaddaadccabacaabcbbdbddcbbacdbbbcadbdccabdcabadbdbbcbcadbcbccbadbdbabdddabcdbabcaacdcbdcbcbcdadbaabcbcbadddbdacbacadddcbdacadcbadcdcbcccccddcbbbcdccadaaaadbddccbdbbbddbaabcbbacadcdacabcccdbbdacddcbbbcbcdbdbdcacbbddbacdabadaabbbcdbcaaabaabdcabccaadbadaacdbbbdcddccbbbbdcdcdbcabacbacddbbcbabcddabbacbadcacbccdadacaddbdbcdbbadcaacacddddcabcdadabdccaabddacacbabaabbbacdbccbabadacbdbddcbddbcddcccdabbbdbccbdadcaabbdbcbcdcddbadbaaccbaabccbdddcaadbcddbadbaacbbccababdcbbcbbccabdcdcadaaaaaabdcdcbdbbcbbaddacbcacbdbddbbcadbddcdbbacccdaaaabbbccacbabcaddddccdbabcbbaadcabcdccadccbcdaddcbdcabdbddaccaabaacdabbabcadcbdcdddbcdcaaccbdaaaddccbbcadcdbadddbacadabdcbcbacadbcccbbccdbacbaacbbbbcdbbddbdcdcabbabbdabaddcdadaaddbdbaacbadadbbcccacbcabbcdbbbdadcbccacdcaacdaaaaabbbbbacdbcadbbaaabdaadaaddccdabccbabbdacaddcaaccdbdcdccbdbadaaaadabaddbcbdcbadbdcddbdcabadadbcbaacbdacbcbadcacabaabadaaabbdcdaadcbbccbadcdddaaccddbbacbcddaadabdabbabcbbbcacddddbbbdcdababddcbbddbcdbaabbccadcdcadddbadcdbccbabbdcbdabbabaababbdbbbabbdbbbabaadbdadbdcadadbdaddbdbabcdcabbdbbddcddcbbcbdddddddddacdabacaddccdcabdbccdabddcacacaccdbacccbacaabddbbaccaadbaadcdaccdccdaadccacdbcddddcabcdabadccaaaaacbccbaacaababccaabdadacbaadadaddaadadbbbdbabadbcddbbcdccbbbbbbdccaacababadbadaadcbdcbacabcbaabdcdabdadccccdadddadcccacadbddcaacdbdbbbbdacdabacaadbabadbcbccdbcbbcabcdbcbadcababbaccacccbbcbcbbbccdcbbbaaacdbbbdbacbbccdbcddddbdcccddcdcdccddadbbbacbcdcacccddbaacdbcbccbabadcbabdacacbabbdadbaddcbdaacabbbcabacaabcaabcabdbccdbcaddccbdcccacaccbbbabaadcdcddaadaabbbcaccabaccddcdcdabadddddbdbcbcbcaacadbbdccbabacccaaababcdbcbbcdaddadcddbcccdddcaabbbbddaabbaadadcaaabdbcdadcdbdcdadcacabbcdbcdbdcabacadacbbababcaacbdacdddaddcbdbbabddadabbddddbadbddaacdacdadbabccacbdabcaaddaccabaddbaacdccacdaaadccbcabbccccdabbcbdcdabadbcbbdcadaabcdddadccdccadbdccdbdbddbddaddcbabbbddcdbcadbdcbccbdcddcdabcddcabdabacabbabbbbcaacdbadacacabcbddccbdddbccbabbacaaacdaccabadccbabccdacdcccabcacbdabbabcacdabdcabaabacccdbcbbdbbaddaaadddcbdccbcbbcddddaddcccddcdacdabcbdbabbbacccbcacdbbdcbdddaaabbcddcbbaadbbdddadabbbbbaadadacbbdacacdacdabcbcadaacbdccbcbaabcdacaadbaabdcbdaddbdaadadddbdbdcabdbadadddadddbcdcbabcdbcbbabaadaabadaadbbaabacacaacbbcadcdbddaabdacdcacbabacacbbcdbcccccbbaaabacbabdacbdbabdaacacababdcdaaabbcbadaadbcacabadbcaabdbcdccaacdbccbdbaaddcbbacdadddbbcbabaadcbdbbcdbdbbbadcbdaacbbbdaacbdaacbabbaaadbaaabbcbbbdacdaabdbbbcdcbbbbdbcbacaddddccbacccadbcdaddcacaadcdbbbcdbcdccbbdbbdacbcbcbcdbbdabcbacddbbdcbacaccdadddabbaaaabbbdcccdacbdddddcabcdcddddcdccddcbbddbbaacccbdccdcadacacacdaabbacccaacdabccdbdcdbdabdabbbccddadaccbabcddbcbbbacbddcbaccdaabcacdddadbdabacccdcbdadbcacddbbbccccbcaccdaccbcabdcbcaacabbcaabdbacbbcdadaddbddbacbbcccabbcbabbabaaabbdbadadcdadaddbabbdabcbccdcaccadcdbdadacbdbaaadddaabbdacbacbacdabbbdccbdbabddddadabdbcdbaccdbddcabaccaaaccbbcabaacddcdccdbcbcabcbcdbdaabaacaddadcababadbabcaabaddddaadaadcabaddbbcdccdbabbaaddacbcabbbacddcccccdcbdccabbdddabccdaaabaacdccadaabcabdccbccddccabcbdbabbacabccdaadddccdababbdbbdaabdcbabcbaadadbdccddccbdcdbadbdbdddaaacddbcabbbdbdbaabbacadcdddabaadcbaadddcaaabcbaacbabccadcaababacaadaaccddcdabdbdbbbdbcbcdabcccccbabcbbcbacbcacdabcaccbbacdbbbbadcbdabbbbdbaabbcddbbbadbbdacbddbcbcadddccacddbbdacbcbacabdcbabdcbaabbacdadaacabacdbdacdbdabdcccbdddbcdbbddcdbbbbcaabaddbdacccbcbddabcadbabbcadabacbcaaabaaacbadacaccdccaddcdbdcabbdacccacccaaabadbcdbdbbcacdccbdccaddaccbccadcbcdabdabadddbbddaaabdaddbabaaabbbddaddbaadcccdccadbbadbcadbddaaadcbbdadbbbbdabcccbbcadddccbabbabaaacdbbdddbcacaacacddbbdcbbcbcbadabcdaaacaabcbbcccbadbcdcdbcaabbddbaaddabadadadccdaaccbdbdbbcccdbbcacbcbacdcbdaacabdbadacdbaabaacababdcdbbcaacdaabcdcdcaccddaaddbcdbdddbaaddbdbdccddddacadddccabbabdcdddcabadacccdadbbabbddaadccabbddacdcbccaddbdaaccccadcdcaaccdaabbccdccdabbccccbbbbaababbacaaaabccddccdbdcacdbdccbbacaddbcbcbcdcdacdabbbddbcccddcdccddadbcbababbbcadaaacdbdaaabbbbbadcdaadaaababdaabbbabadcbdcaacacddccbcabcababcdadcbbaddcdcdaaabbdbbbdbbdaadbdbccaccdbdcdcabcdcdcccddbaaaabdbccbacdadaabbdadacdaabdcdcaadcdcddbcbdbcdbabcdaccddadabbcbbbbdaadabbdcbdccbdabbdbcabccbacddcbbaabcaabdbbdcbbacdbcdcbadccccbccbabaacbbbdcbcdcbaaaadcbcdcacaacdbbcdbabbcabdcabbbcdadcbdcbbabcaaaddddacbdbbdbcdbcbdcaccaddddbbdbdabdddbddabbaaddadaccabccbadbdcaaadabbbcbbdccbdbabcaacccaddaacdcdcdabcabcdacbcacacbdcabdbbaaabdaadddddbcabcbadcabcddbbcaadbdaddcbbcabbbbdbbdabddccabadcdabdcbbbddacaabbaabdbddbdcdcaddccdacbccdbbcbbdacdddddccdbbccddacbcdcdaacacbbabcdadaaaddabcacbadccbbcdcdabbacddabdbdbaddcadbbbbcdccaccccadcadcbaddcdbaabddcdccccdccbdacacbaaacacccccbccacbcabcaabddcccccaaacccadadbbcacdcbdddadabddcabdbbbcaccabdbdbdbaccaddcddcbdbcbdcdaddadaacccbdddbdbabbabccccdccbcdcdacdbacbccababcabdacbdcadddadddadcadddcdcbccdcbdbbbcacdaacbbaabcdbcbdbbcbabdababcaadccdbbdbcbdadddbbaacabbdadbbadadbbddaadbabaaaddddadbdcdcddcadadcbdadbbcaabdbdcbcabcdbbdabddabcabdcdbbacadcbdacccdbadaccdcccdcbbcababbaaacaaacbcbbcadacadddaddbdaddaaadacbcdaddbbbadcdabdaaabbcdcbdbcbccbcccabbccdbcdcdacccddbabdacaccabaabbdcaaaaccabdbcbcdccdaddcccacabbddccccadaabbcabacabdccbccdcbcddbabdcaacadcaabbcbdadaabcdaabbadcdbaacbbcbddaaddbdbcbcbbcbabbaabdbaacdcdbadcadbcdcdcadbccbdabdaaabdcbddaddccdaccbdadacabddcacababdcdbddcacadadcaadbcadbddddccddababdbadcdacadddcbacbcaacbacaacbcaaabdaccabbcadccdbdccddacdacdbbbbddccbcddcaacaaadadbbdaacacadacbcdccadcdaaccadcddbcabdbccddcbcabcbbbcddaddabbbdacbbccbbcdaddaacbbddccbcbccbabddacababacbdabbcbdbcccdbbcbbbcbdcccaacbddacdbdcdbbbdcabbcbaacddacabdabcdcdbdccdaacdadbabaabacccbaaccadbabcdddbcbabbcaadcbbbabcdcddadbcbcdbbbbcadadbaaadbdbdcabbbabaadddbddaccbcbaccdbacdbaadacdccabdabdacbabbbadcbbccddcdadacbcbbbabaddaadbdbcbadcabdaccadddbdabaddcacbcbdbbcbcdcbcdadbbcadbcabbadcdccacccccbdbbccaacdaacaaabddbdaabbbccabcbdacacbdabbadbdaccccabacdbbddbbaddaaacdabddcbcaaddabbbdabcbbdddbbcadacdbdaddbcbbcadcdbdbcddddbcbcdbbccaccdbdabbbabdcdccbddbdcacdbbadbabddcaacdccaaadadacbdbccbaacaccabaadadbabcdbbddcddccbbbccbbaadbaabacccbbdcacaccbbbddbaddcaacbaadccddbbdcbcaaadababcbaadccccbabbcbadbccdcddadccacaccddcabcdacdbadcaddcbddabadddbddcaadcddcaccccacaaabdddcadccddcbabbbdacacacddacbbcaaccdbabdaabbbdccadcadccdbadcdbccdbacccaabbccccacbbbcbcbacdbabbdbaddbaabbabddbbdddacadabbdcccdcccccbabbacadabacbbadacbacdcaaabcdbdccbcbdccacabacdadcaddcdccdccbccddcacbaddadbddbcbbcabaabacdaacbdaddbdbbccbaaccaddadadddcabadbabaacacbbacdcccdbbdcbdcbcbdcbadaaadbccacacbddaaaadbbcbdacddaddcadadadbbcbadbdccbbccbcaaadabddcbaaabddbbaabbabdaaaccadbacaddcdcdbcadbcaabcbdbdbdbadaddcddcdbbaaccacbadbacdaccbaabbcdbdadccbaadccbabbdcdcdbadcbbdddabbaabacacdccaabcbabdacbdddbaaccdbdaacdcdbabcbccaaadabcabcdaacbadaccbadadcadabacdcaccbddcdaadbcddbdbcacdadbbabddddaaacaadbcaccdbcbddacbaadabcbaaadbdbccdbbbabbadcbbbaddbaddcdccddbabdccacdbbabdabcacbadbcacabaadbbdddacadadcaddbdbaddbdaabdbdabcabacbbbcabcccbdcdcaacbcaaccdaadbaccdbbddcacaddcbacabbdcbcadcbcaacadaacbcdaabacadcaaddcdcbadaaacbdcbdabbdbdaadaddadabaabdbbbcabdcbdaaadabdbccacaaadbcbcdccabdabbdbaadcbdddaddcdadababaaddaaadaabdccbbababbaacdbaddaaaddddbaacbcaabaadbbbacbbcaacadaacbbcbccdbdcccdadbddcadddbaaccbdcacbddadadbadcdaabddcbbcdbdadcabaadaaabadccdaacdaaccbaccaddbcbcbdbbbdabbaabdbcdddacabdcdbcbcbbababcaabdccabadddbabddbccccbcdcddbaaadaabaacddccaadcbcbdbadbbcbaabaccbddbbdcbbadbdbabbbddcdddadbbbbababcacbacddadbbcaadadbbbdbddaacbddbcaaddccbdddbddcdbbdcbddbcbcabdacaccaddabccdaccdacadbbbaabcccbcdcbacbacbcddbcbaadadddcbdbdadccbacadacaadbbbcbcaabacdbcbbaabdcbabdabbbdcbaacadcbcadcbdbbbcdddccccaabcdbddadabcbbdbaabdccadadbccbdcadcbdabcbcabcbdaaccdabbacbddccbdabdaadbdaddabcccbbdbabccccbcacbbbaaaacdbdccddadddabbcbbacdccbcabadcacccdddadcdbbbccaaccacdccdccbdcacdaabbdabaadaadacbdadacdbacabbbdcbaacbdcbcadacacaabcddcdbaaaaabaccdbacacdbaddaabbadbabacaaabbcacdcdaacbbcacadcaaccddcbbabaacbcacdddddcddbaacddaacbddcbcccdbbadadadcdacbdcdababdaabccbbdcdddbadbabacadcddaddcdccbabdcaaabadbcdcddbddaabadacadcddbddaddacbabdbcbaaddabcccabccdaaadbbdbcaaabaccdadaabbdacbddcdccacadaabddbdddcddddbdababdcaddbcbbbaaccbbddccabbdbbdbaaaddbcdaaacbccccdccabdcbdcdacccbdcdcacabbccadbbbcccbaddcadbcbcddbabbacdcddadcacadadacdddbaacbcccabaaabcbcbbdaaddcaadbcaaacccbbabdbdddabcaacdbcdbcaaacdcadbdbdcabbdaaddbbabcdacaacdbccaaacadaddbddcaccbcdaababbccdbdcddbcccbbbccababacddadcbddddbdcbcddcdbbcacbbcadcadbdabcdcddaaddccddcaabbccaabcdbbbdddccbccbaccbadaaacdcbabbbbacdcccabdacabdbcbcadaababddcbcbcdcbcdddbcbccccdbddadbacbbbabccadabbdbdbbcacdabbdaabdddddabccbaddbbbdcaddabacaddadddaaadaaacbbacadcadacdbbbbcaaabcccddddbcbcdadbbcbadcdabcbccadabaabddcabacdaaaccbaabacacdccbcadcacbbbcadcbcabadbaddbaabbdacbbddcbbddbcccacdbacbbaacdcdcbbabdddabccdbcdcbbbbbbcddbaaccdcbabdababcaccbbaadccbacaabbcddbdcbbabbcbccbccdacbcdcdabcbbcdccaacbdbbabacdacabbadaaddccabcabdcacbdbbbaddacacacbdcbaaabcbcddddcadbaacbdddaabccbdbacbaddbbcbbaaacaaabbacddaaadbacabbcdbbdbbdacaacdabdbbbccbbddbddbaabababacddccccbaaabbdbdbcadababcdccacacaacbbdcacccdcacbbacdbccccadcdacdbdbcbbdabaabcccbdbdbdcbdbbdbdbdabccbdabcabacadabadbdcccacababdbccababadcdabadbbddbbacabddcabbdadbbcddbabbbcadaaadcdcdcaadddbabcaabcabcbbbdddbacddadaccbccdcccaadcbcdbcacccaccbbddbdabbbcaabdbcbddbdbccbdaaacacabdadadbcdcdbaddcbcaaacbbbababcabaadcbadacccdabadadcbcbdccaaabacbbcdcacddcacccddabbcdabadccaaccdddbaacdaadbdabaddcadaaaaadccbaaaaabcadacdacdcdadbdcdaabdbdcccbbcdcaaacacbbbdbbcaabbbccbcbaaaccdcccdbbcdabbbaadbadadaaabdccacccbdcccdcbdcddccccbdaaacbcdaaacdbcabccbbcbabcaddddaacdcabdbcabbadcbbccaccadbcdbcabbcadacccaaacddadbadccacaacdabdcbcaacbbbacbcdabbbdcaccdcdabcddddabcaddbdccbabdcbcadbbcccabacabdabbadbbdcccaccacddcdcdbbbacdddcdabaaabcbacdcccabbccbadaaddccbbdddabccdaadadcccbaddccbbaabbddaadcdbdccddbbbcabdacabdcdbbddccabccdcaaaadbccddcacdbaabbdabbbcadaccbddaaccadbcdacaabacaacbbcdcdabccbacdbbdcabbccaadacdcabddcababacdadcccddcccdbbcabdccccaabdbacadccbadaacbacaaadabbbdadbbbbbbdcacccddbadbdcaddbddacaccdcadbccbacacddbddacaacbadcaadcaadcbaacdddacdbcaccdbdaababbcbcbbdbddcaaadccdcacaddcadbdcdcbcaacabbcaccaccddcaddbbbbacdbcadadbbcbcadbbbbaadbaadbbdbabbbdcbbdcacddabbdcbaadbbcacdbcacdcddababbaacbccccddbcabbccadbbbababbbdccaaaaacddbccbbccacdcacbacddcaddaadababacddadbacbadcbbbbabccbdabcccbbbaacdcbcacdbdabdbbabbcbbccadaadccaaccccdbabdcdcdaaddabcdabadcadcabcbbbcaaaccadbddcbddcabdcbbaabdbacbbdddcbbcbccbdcbbcaacbdababdccbddcccacdbdaddcbbabacbabbcccdaacbbadbbcdccaadcdbaabacbcdcbcdcacddcccabdaccccbabdddbbcdaddcababbbdbbadcacbdbdbddcaccbdbbabcbdbbbbacabbcdbbdcaacddcdcbbcccbabadbcdacdbccccbabbcacbdbacbbcddabadbdbbabcdbdbdbbcdacbdbbdacddcacadcababccaddbddbddaaaddcadabaccbaddcdcdacdcbcddbcbcadddcbdbcdccabdcdbaddcdcdbabaacbdbcdcdddbcdbaaabacbadbdcddbaddbcabbaccdadcbdbdabccdadddbabaccddccbcabbcdadbaacdbbdadbaadcaaaadbbdbacadacadbabdddbdcbbcadadcdddbbdcbdbdbacbabadddacdbbbcadbdacbdbbdabcaabbadccbdacdcbdcbaadadbdcdaaaddbccbbabdbaaaccddbdcdcaaaccbbdddaabdcdcdbdbdbcabaaacaddbbbbbcbaabdaaabcacdbcabcbbacdadcddddcbcadcccbdcbbcddcbabaadddcdaaacbbaacaacacbbdccdacabdcaddbcabdbdabaacddbcacaaadbbdcbbcdaddcddcdcacddcadcacbacbbcbaaadadbbbdcabdbacacdaccbbddbaaabaabdacacbcdcdddabccadcdbdbdbdababacbcadddddddcaaabadbaddaaddacbaccbddccddbabdbcdcdcaaaaacddcabcbdcddbacccbaddbdddbbacddacadcbbbddbcacdadbbbccaaabacbbbcabcadaabbbbdcaacaabacdabddbacdadadacacadbaddaadcddcbdcddbbbbacaccabbaaacdcbddcdacacddcdbddcccbdbccdabcaaacadadcdcacabbdcdbaababdbcbdabcbdbdcdabbacaacbacdbadadacacabaacdbdccdcddabbacbbbcabccbddcaabaaabcabccadacaacbcabccacccbbaccddabaddbcadbbcbdbbaadddadbacdabdbbcdcdbdaccacbbddcabdadaaaabbddbcdcabddccacdacccbcbaddabdbcdacbbdbcdabaacbbbdaddabdcadcbacdadaaabddbaddcabcbabddbdacbddbbbddadbccbcbadccbabddbdadcbadbbadadabddadcdbcbbcabcaadcabddbaccbadcbabcacabcccbccdcbbacdadbdcbdbcbaabccacbbbbbddcacaabaaabbbdaadbbdaadcdcbabddadbdababccbadabababcacdbbbdcacccdadccddadadbdccabcccabbacadccaaabbcbdbacddbdcdcbdaaaccdbaadaadbcbdbacdddacddddbcbbbbddbaddcabcdcbaaabdcbccaabdbbbbabbacdbdaacadcadaacacdadcbcacdadaaaaabaaaccbacbbaabdaabbcbbacacccacdbdbddddadabdacccbdbbbadcdcdacabbcdddacbcbabadbbccdcadccaadcadaabbbbbcdadcbbddbacbccbbdadbbadaccccaababcdcacbaaaabaabbbaacabbbadbcbdcbbadddbdbdbbbbdbcdadacadabadcaddcaadadcdcdcbcbcdaddccdacdacabadddabdbcbbcbbbacacdbadbcbbdaacbabdbcacbddbcccbbdcbbdbdcdddcbbdaabacdcadaabcaaacdaacdaabdccddabbbddbdbccacadbacaddddcaaddcacacadabacbcbddabccbaaaacccabdacbbaadadccddbabcdaaddbacdadbbccabcbdddbbcbaabdaccabdbcdadcaabcbbabcdbdaaacbbaacbacbcbcdbabddddcaaaaadbcacabdccccaadbdabccaabccaacbcaabbccdcbdaaacaccbbbdbddcabaaccbddaccbadddbcbacbdcdbdcaddbdabdbbadadcbacadbdddbdbacacdbacdbcdbbdaabdaadccbadbbbddddddabcbdcdccbaabcbdbcadbdaacdbaddddaabdbccdcbbbdcddddaabadbcbaacbbbcdcdbdcbdcccdcdddcaadabbaaabdbbcbacaaaaaaccbadbbabbdabdccbbbccadbccdddadcdccaccddaddbacaabaaaddccccdacccadbbbcbbcdccbddadbddcacadbbcbbabbbaabccbbabdbaddcaabddccbcbbcbcacdbbabbbcabbcdcbbbaadbdddccaabdbbbbbcbcbadabbdbdcdaadbddddaaabaadaadcdcadcdcdcdbadadaccadaadddbbbdcbbcbabaaccbddabcdcccdccbbacdbdabddadabccbacadcacabadcdadbcadabccdbcacbbdaddaaddaabcdabdcabdacadcbadadddbbccbabacbdabbcabccbbaadadbdbcdddaabdacacabbabadaaddbadcbbbbbdabbdacdaabaaacbcdbcbbdbbbadbaccccdbcdaabbbaddccbbacdcadcbacbaacdbbbbacdddbbbcacaddddabcaaadcababbcddbdadcabdaaacabaabbcacaabbcddacaddaadbadacbbbcdcabadccdddbadaddcbddbdbaacdddbdbddacbccdbabdadcbaadcdbaaadbaaccbcaccbbbcccadbacbdbadbcbadccddcccbacdabbadaadddadbcbccbcabdbabbabdacadcdacdddbcdcbabcaddcdcdccaccccccbcdddaabcbacdaababcbadaccacbcabcbabdddbdbadcbccdacdaaddbbbcadadbbaabbbddacabacbdccdbbcccaaadcbdbcbabcdbcbabdcbadcdacccaacabbbbbadcaccbbdbdacdcdddaacadacdbcdbdbccdcbbbbdcaabdcdaaadacdbbadabacdbcabbdaaaacbdbaabacdcddaccadbabddbccccdccacdbccacababdbddaddcadbcadaadcaaaacadbbaacdccddaccaddbabbcbcababddcdaddbabdcabdbbddcbbacdabadbcdbadddaadcbcacddbabaacacbcaadcaccdabdacccdbabcccabbdbccdbbbbadacbdacbbddbdcadaccdaabadcbaccadacbcdbcdcdbdabbdcbcccdbdaaacdbcdcacdcdccbbaaccdcacadabcbbdcbcbdcacbddbdbcabcdaabbdabcacbdaddabaadccdadddddddacadcadaddbcabdbabbaaaaabbaddcddcddcccbaddbbddcbbddabbcdbddaadadacaccadcdddadbdabbbadbbcbcaacbcbcdccddabdccbbbacacbdbccaaddbabbdabcccddbbabddccdaccdccbbccdcacabacdacbaddaacddddacabaabbdddbcddadadabdcabbdaddcbabdacbadbcddddddabdbbbbaadddbdcdbdcbbacccaadaadcccbddbbbdbcaabddadadaddddadddbacdbbaabbbdbbdddcadadcabcbbabdbbdabacbdcbadaaadaacccaddacadbdbbccbdbcbadcbcaacdcbacadcdcddabbddaabaabaaaccabbbdabdccacbbdabbaccabdbcdddacdbdbbaacbabadaccbcbabdcdddbbdcdacccbddcccccdababbcbdbacaddaccaabdcdccadbccabcbdcdbabcaadbbadaacdabacddadcaacadcdadcabbdccadcdaabcbdcabddcbcbccbbabdddcbaddbdccdbbbbdcabbdabbdaccdcaaacccbdbccaabdacdbdbddbabaacadccbbccdcabcaacbbcbacdcccbaadaaadbcbbcbaacdbcddbacbacbdcddbddacddbccdddacabdbbabcdcdaabddcacdcbadcaabccadbadabdcdadbbaadaadabcccacacadcbdaacabddacbdadcdbbaaabcbabbdacaaddaaccbadaaddbadccccdaaccbbddbcbdaabddddaadcbcbccacccdccdcabadcbabacdbbcbacbddcabcbadcbacbadcdcaadcbbacbcbbbcbababdbaccbcccccdddabacaddddbccdbbaaabcbdcdbadddcaadccdcdbcacbacabddbabdcaadadbccaddabadacdbbadcdbbbbdccdcdadddcbccadccaadaacbdbabccadbbbdbdbdabdbabbcaabacbcdaabcaaccbadcbbcddcabbbcdadbaaacbddabdcacabdadcddddbccddaabccbcacccaaaabaacdabbcbaccbdabbacbbbcdbbcbcdbbdbccadabccccbbdbcaaaabaaaaabbcaaccaaadcabcbabbbabcacdacaabbcbacabbcdadaacccbdddcbddcabcabbcdcabaccacadaaaacdabcdbdbcadbcacccadcbccbcdbbcdcbbccbdcbcdabdadcbcdadcaadbccaabadadbbcdcbcccddccaacdcdbdbacaadbbdbabdbdbcbbdadabaabcbbacdababdabaccbbdbdadadabbdcccdbbbbcaccdcbcbddccaaadcaabcbcdbdbcbcbdaddacbddbbbccadaaaccdbbcddbccacccdbadaaacaccddabbbddabbccbcabbcdcddcbcbdaabcaacddbaddddcbbbddadadcbdbabaccbbccbbacddcbbaddcbdabdbcdbdbcaaddbacaabbcdaacbccddccbaaddbaabcaadbbdadbbcadbbbcddccbacadbaddbbdadadcadcddddbcacccddccddbcbacbdbdacddadcdbdbccacabbccdaccaacbbbaccaaaabcdaaaddcdccdbcbddaacdbccdcaabbcccadadccdccadbcaddaccbbccdbdcabdcccbbcddddcdbbbcaddbbcabbbbcaccaabcdddccbcdccbbcabccbbbcdbdcccacbcdadadddabdcadbdaccabccdddbdbbdabadcadaccdbcdaaacdbccbadcadddbcbdcadcdbdcacbdbadcadcdcabcbdccdaadbcddddddcbbcbdddbcadcdbdddadccdcdbdddcbcdaccbccaccaaacbadcbdaddbbabbacadaaaabccccbbccbdcddcdddacaccdcddaadbddabcabccbaddcbdcbbccbadbdcdcbcdcddcdbbdbccbddccbbabcddbbaddaacabbdbbbcbdddbdcadaccddbdcbccbcbbcbdabbbcbbbbabababcabdaadcbcccacccabcbbbaaddcdcabddcdadcdbdaddacccbabaacbcdcabdbaaaddbcccabddaddbdadabaacdaaabbdaabaacdcdaccdaccacadbadbbcacbccbcaaaadcabdaabbcadaabbadaabaabaacacabacdbccadacbccaadaabcadbbdcadcbdbaabaabdcaababadddccdbbddddacdcdddbbadacabbcaaccbcdddbccabcbdddcbcddcbaaacdbbadbcbbcbacacadcbcdbaacbcdcdccdbdbabcaaabaaddacabaabbbbdadadcadcdcaccdadbaabbbabbbacccbabbdcbdcdaccbaaddbbacacabbaddbabcbbbdccbaaacdaddccbbbdabaadbbaadcdacccbdaccbcddcbddddbddacbdcdacaabaaadadbdabacbddbdbbbcaccbacabddbccdddccbbbbbabdccdddaccbbbadbabbbdaacaabddbaddddabddbbaabdcbcabcdabdaadabacbbcababbabcbacabbcdaddcadbccddcbabcacacbbcbbcaababbdaabacbbaaaccccadddbdaacdabbcbddcccbabcaaabaadcabbcadcabdbddbcdabbabcacdcababdaabadbaabccccbbdadcbacaccdabcaddaadbadabdccabbbcabcddacdcaadddccddccaacdddddcacabbcdabacddbcaccababbbdbabcbbaaddbccccbaccadaaadcdaaababdbcbcddbbdaabbdcdaabbcacababccaabccabbcddabadccdbdddccadbcbdbacbccacbcbbbcddabcdbbccddadcdddbdacdddbdcacacbbdcaaaababcdbacddddacddcbddccaacacacaabccadadbcdabdcdbdcbddbdbbdadcbdacadaccbbadcadddcdbcdccbbbbbdabddbcabdadddabaacbbdacbcbdbdddccddccbaaccbcaadcddddccbdddbbcaabbbccddadcabaaccbcbcacacdbdacbaddcdcaddddccdcbabacbaabdcbcbbcaacbdadcdbcdbcbcbdccdcdcaccdcbcacabdcaaaacbbaadcdacaaaadbabcbaaabcdbdddcbccbcdbdccaddddbadcbcdcccbaaccddaacacdcbdbcaddaadabcdacbccbdcaddaaaaaddddcddcacdabccddabadacadbaabdcbabaacbdbabcbabbbaaccdababadadcaabddacadcbcbccdbddbddacdacaddcccbcaddabaacccdcdcacaaccaccabaaccbbccaacbbcacbbdccccddcadacbbdddaacdddbbccdddbcddddbccdbcdbdcccabddbbcabcbcdcdacccbadcbbaccaccbabdcacdcbadbccbcbccccbaadcccdccbbcabcbcdcbccbdcccbcbbdbcabbdaacbcacbabbacbbdbdbbaacdbdbbaadaaacccdaadccaaabbcabbcdcddbdccaaadbdabdadadabaaabbdbadaaaabbcaabbcccaabccaddaddbaaadcadbdbdaddcddbdaddaabddbdbcabdcbaabdbddcbaccdacadababdcaabbadcbcaaabcaadaddbcaadbcdcdabaccccacdacdadddaabdbccdbbdbbabdacccdabadbdcddbddbcadbaadccccdacbabcbcbbadaccccbcbccbddbddaacbacbbacbaccadabaddbccaabbdddaccbdcbdaabdcddaacabddabaabdbdbcdaaabcbcbadbbabddcdcbcdbabdbaabdddbcbabbaddabbaaccabdbaabcaddddddccbdaaacacabcbbacabaadadaacdcbacbcccaddaabcdaddacadbcdbbaccdaadddabdbaaaadbcabbddbabddbccbcaccdcdbdcdbcbaccbadccddddbdcbdabcddccacaccddadbabdcddacaadbbabdacdddbddaadaccaaadcdacdadbcdcbdbacdccddaddbdcdcabacdcddddbbbadacaabdaccbacaaaadadccabcdbdcaddcdacacbadaacccddabcdcadbabaaccdcbbbdbccdbccadbbcaadbcddaacbcbbdddcaadcccdccbbaccacbacbdcabdcabcaabadaddbacdadccadacaaacddcccbbbcbcbcddbdbacddcbcbaaaaddcbaaaacacbcccdddadbcbcbccacbcacadbdcdcabddacadbaabcbabaabbabaaaddbcadccbbbdcbcbbadccbbbaacacbdddacbacaacbddaadddcdabbcccdbabacdadcbbabcccdacddcbbdadaabbacdbccadbcbbbccddcabdcbccbbddcbaccddaccbadbccaccabcccccdcaadbdccdcdadcdbcacddbdbcaadaaabdcddbbcadbbdbbccaaadbdbdbdcccaccbbdcadcbaaddbacdccdacabbaccdbcadbbadbcddcaabbcbcbacadaacbaaabacdccadccbddddcacdbbdcbdaaaacdabaadadbbddcdcadacdbbddddaddbbaddcadcdcddbccbdbddadddcadabdadbacbacaddbbcbacbacdacadbcbbdbbcbbdcabdbcdcdaabacaaaadcbaadcddaaadbbadadbaddcadcaacbccbcbdbdcadcbcbbbbaabcbcbdaccdcbbbdbbcadcabaddbddbababcdddccdbbbccaabcdbcdcdcbccaaabbdbbcbcbddbcdddccbbbbccbccbbdbadbadbadcbbbcbccbddabcabcdaccacadababddcccacdacddbbcaaccbabaccbbadaccababdcdacddaacadcbdcccaacbdcdadbbbadbcbdaccbddbbdcbaddccbddadddbbabaaacdbcbdbadaaddcdbcacccdabacbaacabbcbccadcbddbaabacbaddcbacbdcdcacabcaaccdacdbabddbbdcbbccbbacadbdccccabdbbccbdbadccdcbbbcdaacdabcbadaadaabccccdccaddbadaddcabbabbdcccccdabdddaaddccbcdbbdabdbdbcbbddadcbbbccdbabcabdbdbacaaddcbacdcdcadacadaddddcbdaddbddabcdaaccaccbacdbbccdccbadcaaaccbaadaccacacbddccadbbbdbdbbcacbdabdccdbddcbabaaaaddadbacaccdccdccbaadadbaaacadabbddabdcbcbcaadccdadacbcabbacdcbcaaaababddcadcbadcabdbabbdadbbcbcdbaacaabcdcabcccdcddcdacbdbacdaddbccbddbbbbcbdbdcccdadcdcdaacdbabbcbdbdaccadbddaacaaabdbadbdbdaaacabdadbdabcbdbcbbcddbcbcbacccbaadcbdacdcbdaaadadbcddcaddccbaddcdaccbbbdbdbcabbadbcdbabbddcadddccdccbdbbcaccacbccccbacbacdcbaaaadbabddadccdabaaadbcddaacdcdcbcbaaaacbabadcbbcaadbbcaaccdbbbdaddbdacbbbddacdabbaabaaccddccbdabdacacbccacdccbdbaddabccbacbbbbbddabbacbdbbbcaccaaddcabaaddcbbdaccdcacdacbcacdbbbbbdcbbdbaabdbbbbdcaaaabaccaddabcdabbdacabccdabddbbaadcaacabcbcaaddccbdbbccbdddcaccbabdccdccaddbccbcdbdddbcddbcbbadbbcabaadacccbacbbbabddddabbcacdcccbaadbcbcbdcadbcbdccbadadcaaaacadbbadddbccaacbccbdbababdadbbcaaacccdbcabcbacbccddcdababddccdbadaddcbcbadabdaddbdbdbdbadcabdddaabaddaadbdacacccddcdaaccccaaacbddbaabddbcdbbdbccbcdbdbcccabcbbbbaadbccdbcbbbabbcdcdaaacabccdcadaabcbbddcdadccbcbcbbacbadadbbbcdcaddbcbcddbaddaaabccbdbdcbdbbabddabbacccabdacaccbccaacdbcdcdcbadcbaaacdbdacdbacadcbbdcdadbbacaaadcaaadabbaababcdcaaabccdbcabacadbbddcdadbccbacdbabcddcaabdddbcbccdcdbbdcdcddcaaabdccccccccdadcdcbddcdddcdbabdabcdcdbbaccbddcbbbcdbabaabdbdbbdadccbcdbaaacbdccacbdcccaacdcdadbdccaccbbdadddddcaadbddbbbbadcadcbcbbbbdbdcbabbdbacbccaaddadbcabdbcccadcddacacccbbddabcbacaadbddbbccabadaadbcabacdddbdadbaacbbbacbccdccabacbccccddcbbcaccdbccabdadbccbaabccbcbdcbacabcbaccbaabacdadddcadcbcbacbcbdcdcacbdacacdadaaaddacbbbdcbbccddbdbcbcdcddabdabcdcadadbadccabdcdbdaaabccadaccaadadabadaadabdabdcaaddbbcdaccccbdbddabccbabacdbdddbdaaddcaccdabcdacadcbdaabdabcccdcaacbcbcdcbaabaadabbcadcadddacdddbbaaabaaccdcdcbacdacdcdcbaaacacbaccdccabcbcbcbdddbddcadcbccaabcadcaadcadddabdcbbcabaadbbcacbddaccbadcdaadcbbbccdcbadaadbccbdcdbacaddbabcbcbcbacadccdcdadacacabaabdddcaadacaaabbdaadaaadadbabdacdaabcaaaddcbddcaadddabcdaaccbbbdbdcdabcbcdaddddabdaccbcaccbacacacdcaadaaccbaaaabcabdbbdaacbcdbcdbababdccbddcababadcaacabdddacdcdadbbdbcbcacbbbccdaaacdddccdadadabdcbabcddcbcadaacdbaaadaaddacaaacdabdcdaaddadccadcbbbbccbbbbcbddcbdcbccbaadbacbcadbaccbbdacabacdabbadcdcbcaccaadcdaaddadddbccabbbabdcbabbbacadddcdbcbacabcbacaacdcaabdbadacbbdacabacabccabbaccbcacaaccddbaccbddaccbdcdadbacadabbacdccabaaabaabaadcdcdccadccacdabdbbcaacbdaaabccadcdabcacbcaacbcdbadbbcacdadaabbacbdbbcabccddbccbcbdcadaaadbaaadabdbabdadcacadccbdcddcdbabdddacadcbddddbcaddacdabdbabddddaabbbabccbcddaddcccdabbadccdbabccababacbddcdbdcddcdcababccaadbaccbcbbddccbdcdaccbbddccdbbcbaaaaccdcccccdcdddbcbbabcabcaaddabdcbbadccbadbcadaaabcaadbbdddabacbabacaaaddaadadabbbcdcdcdbbaabcabaaadbdacacbdbbabbabcdcaadcaabcbcaacbcbbabbbaacabddaaccbacddccadbbbadddcddbcaaddabadbcdbdcbbadddbbdcccddbaaaddaadaadcdbdddbddcacddbccbdaccdcaaaabaaaddaabddaccccaabcdcbbbadcadbdaaddabbcdcddccabaddbaccdadbabcadbdaadacbadadadddbbbdccdbaacacdacaadabaabaaabdaaacdcaaddccadccccabddabbbcacbadabcbcdbdbdccabdadcdaacaadaabbadaaccbaadbcadcdacbbadcbbdbdabdaacabdbaabcbdcaccdcdaaadbadcdadacdadbbccabdcbadddabcdcabbaacaaaadccacbcdcbaccccacbdddddabadcaddcadababcbdcddabccbbcadcacbbdbbbcccdacbadaaabcabaaaadadadaaaccadccbbacacddcdadbabccaabcaaadaccbbbbdaacbbabbcabbabccddacabcabdbacccabbababbdbccbbcadaddbbacaccdcbdbbacbbbaabdbbacbddbdddbbabcbacbcacccbbacaabdbaadddbaaccaabcbbcddbcccaccbabbcabacccdbdbbbcdddbbdbaaccbddbbdaacbbdcbaaabaddcdbbdbbaadcacccdaabbadcadbaaccadaaaacbaadadbadbdcbabccdaaabcadbbdacdcbbaaaaaccdddabbcabccacacddbbbcdcbdbdccbdaadaaaccadbbbbbdddbcdbcdcbbcbccbdbbccabbcbadbacddaddcacaddddabadcabdbbabbcadbcbdcbadddadadbcadaaabccaccdcacbddadabddbddbdbcaacabcdbcbdcccaabaadcdccdcdcbcacdbcdccdbdbaaccdcdcccbbdbaabcdccccdccbbaddbbabbacbdcbcabdccdaacccaadddcadbabcabdaabbbdddddacbbdbaaccbcbaccaadcbcccccbaadcccdbdadaccaacdaacacbaadbaddadcdbcbcddacacadbcadadabaacdaddaadbccddbbadcbbddcabdbbcacbccdbddccdcaabaaadcbaadccddaaddaacccddcbbcddbaaacbdddaaadbdaccbaddadaacacababccdbdccdaababcdaccdaaaacadaccbadbdbbabaaacbbcaacbdbdcacabddbdababadcaddabbbbdddbbccdbcabccaacbabdcccacaabbacbcdddddbacacacccccddbaacabcddddabcabaadcadabbcbccabaccbdcdbdbbaddadbbcabbdcacababcabbaacaadacdaadccaccaccdbccdacddbcdddcbdbbbcdcdddccbaadabdcbdbbacbabbddbaaaadbadcaccbddacdcaabaaaaaaaacdcbddabadadcdacdccbcddbaccabacaccbdbabcccacbdacbddcaaddbcbabbbbccdcccdcddbcbbcccbcbbcdbabbcbbdbdcacdcdbacbcccbbbcbccadabbcbadbdbacdadabdcccdcadddaddddcbdaacadbdbbaaababbbbabdaabbcbabacbdbddbbdabddccccbbdcccdcabccddcbccacbcaddabdaccdcaacdcadcaaddacccaaacabaaccaaadaccdcaaaacbacdabdcccbdbbbccbadacadaccdacbcadcaccacababdcaaaabadcbaaddadaabcdbccbababdacaccdadcbcdddccddccdbcbabbcdcbcdddbbbabcbcdcacbdcbdcacccacbdacbbdcacbadabbaccabccbbdcbbcbaabbbadcbbdadcbdbbabbddccadabacbdbdbadccdbccdbbbbbabbdccbcabcaaddcdbbdddbaacbccaabdccadadcccbcccbddadccaccdabdbbbcbbcadbbccddabaaccccbacdcbdbdabbdaacbcdcdbadcacbdbadacdaacdadabaccadaadbbdacccbdccddbcbccacaddcdcdbbbbabddaabcbbacaddaaadaaacdadbdaaabdbababcdadcbcdddcacaddbaaddbbdbcbdabcdddddbdcbbbbdadaabadadaaadbdddbaadccbdaabbaadcdddbcbdbadadcbdbcdccbbbcbddadadaabdabbdccbbcdbcbbaaabacaadadcbcddbabbcdccccdddabcccadbbacadbcababbdcdadabadbccabcccdcacbbaabccbdcdbdbddcbbdbcdaccdbbacbacabbdaaabacbacbaaddcccccbaabaacdbbaabdabdcdcacdcdacabcdbacdbbcbbbcababadccbabcccccbcbccbcdcbbaacadcacbcbbbdbddcbbcbddcccccacabdbcbdcabcccdccbccbacbbababacbaacccddabaccbdbdaddcabbbadbbcdcacabbbaaaccabbbccadbdacccaabbccdcacacdbcadacabcdcbbdbbdaaddaaacaaabcdbcdabcaccdadbbacdddacdcacdacbcbbacbadbcaabddbcbbcbcaacbabdacccbaadbdbdacbbbabdaddaabadbddcccdaaddbabbbddbdaccacbbbbddddddcdacadbcadaddaddbadcbcaadcbcaacbaccbabdbdaadcdcbddbbdbacaadcdaacdaddaaaabbcdbdcaccbbcddacdbadbddcdccadccbadaadbaabcdbabbabbbdccabbdaccccbcbaaddbadddccaccddaabbaccdbcddcbbaccabcdbaddaccacddcbbbdaabcbdacbcdabdcaabcdadbbbcabacbcbcdadcbdaadcccbbacacbdabadccaaccbbbddbaccdadbbdaacaaaccdaacbcdccdcdcdbaaddacbcaadbadcddbadbaddddbbbacbacdbacdcdaadbdadccddaabbbbcdbbddcdbbcdaccdbddbbdbdcaacadaaabdacdddddcdbcabdbdaadcabcdcccccbaaaccabbddabccdcbabbbdbadbbaacacdbcabbcaabcbcdcdadccbadbdbbdcbcdcdccdababdddddcccbcaaaabbddaacbbbcaabbbdcbbdbddddcdcbadcbccbcccabacdbacaabcdcacadbadcbcdcaccacdaaabbccdaaadacbdbbbacacbccdbbbaddabbaadcbcdadcdabcacbdbadbadabddbdabaadacdcdbcaacdcbbdccaaacdcadbaacdbbaddabbadbdbcbabdccaabdccddbcadcaabacbbbccaadaccdabccbadcdccbbcbbccacdacacbabaacaaabdbddccdcbdddacdcacddcdbdacaadacbbdddcadabdabbdabaccccdbbdadcbbacbacdaacdcccadadcadacaaadddaddaccdbcaabdcbaddcddddcdbcdadbbddabcbbdbabdbcdcdcbcccbddbdacbbbbddccdcbcabaadbabacdcbabaabaacdcccbbabbabdabadcbcacddacbcdbdcdcacbbdddaadcbdcadbdcacbcbcabaacdbbadddaccbabdcdcadccbabcdcbddabbbaaadbdbbaabdacdcaacadacbddbabbabbcbdddbdacaddbcbbccdbadddcdbadbadbccbbbcacabbcdcadadbacacabbddacaaddbbdcbbddbadcdcdabdbaccdbdbdcbddcabababdcacbbccddddcdcdacdabcabcddcadcbaabbbbdddaabbaaccaddbcdcbbdcbcdddbabdbabccabaccddbbddbadbdbdbcbabaddadcdbacddbabdabbdabaabcbcabbdbcaddbcbbcbcbbbaadbbbcaacaacbaaaaababbabbcdbdcbcddcabdbcbaacbbacdacacaabcaadbdbadaadcbabddbcdcdaacbacbbbaabddbddbbdcdccbdccaabcccababaccacccabdaabbdddcacddacaddaadbdcdddcadadbdabaaacbbbcabcbbbbccadddaaaadbdadcbadacccaccdbddbadcaaccabccbcdacbdcadbacbddbbdbcdaabdabcbdccccaaaabbcdaaddcddbdcbdcdadbdcccdadaaabbddbabdcabbbcdbcbdacbcdacadcdbbbdabdcdacaabcdcbaacccddbbcdbbaccbdddcbacccdcdbaddcbabdaddabdaacaccdcddccbbdacbbbaaaddabcdcabacdcccabdbdbdcbaabbbddabacbdbaccaadccdcbbccbacddbcdbaacabcbbdbacbdbcccdccbaacbcabbccdaaadbdbdacccdacbddcacbcbcdcccbddcddaababacbbabddacdabddacbdadabadcbadccddbbddcccdacbabdcacdcdacddabaaccbcdddaabcbbbcccddbcabccccdddbcaadaddcaadaccaddcdbdadabcbbcbaaccadcabcbadadcacdcaaaabdadcdaccddccadaacccbdbbccadbcbbadadcacccddbccbbddabdbabbbbbbcdadbcacaaacddcbcacbdcbccabccaaaccbabaccacaddadabdccdaacccbaaccbadbcababbaaacadacbbbcbbbcbccaaaabadabaabbacbcaacccbcdaaacaacdddbcaabaadcbdcddacdbadcbdbcacbbcbcccbcaacbdaadbdaabbdbccdcccbcbddbccbabcadaacaacbadcccdcccbbbaaddbcbccdbcddaacbaddbadbaaddbaacdcdddbadbcaadddbbdbddaddbbdabbacbabccbbbacaccbdcccdcdcabbccdbdcdcaddbbdcdaddbdcbdabbcaabbbbadbacacaacdcabdbdabdbcbdcccbccacdbcbaaacdbcdbddcbaaccadcbbbcbbbbbddabbdabdcacaacbdcbcddaacbbacabdbcbabcbadbbadcbbcabaccccabbcbdcdccbcabdabcbdcbbbdccaaddaddccaabcdaccabccadabbbcaaaacdccaaddcbbdbccbbcbbadcaaabadadcbcdbcbdbddddabcdadcbacdbbaddbabdddbddabcdaaccccabbdbbcdacbbabdddbbbdddbdbbcbdbababbcbdcdabbdacaaccddaabdaadbbddacbbababdabbdcacbbccddaaaadcbcbbcbbdcbabcbcadcaaaccabcbbbbdbbbcbdccddcbbaaabccbbbddcbaddbbacddacbccbdcaabadbbaddbbdddcdbabccddbbdccddaaadbaaddbbdababbdcdcdcddcaabaccdbddcaaabdbbbcbcabcbdcabccdacddcdbccdadbdabbaaddadaccbbcbcbcddccdccdcccbaacabcbcbdddddaabcbdddabbaddcddcbadaadabbdcabcbdbdacccbabbdbbddbcbbcddabcddadaadcdbabcabaddccaaadcdbcaaabccbdbbccaabababaadaacbdaccbbddbadadcddddddbdadcacbdabdacdbddcbbbcdacbbbadcdcacdadbaaddccadacdbadaccbccadcdabbdcbacbbdbcbccacbccabdadcbbcbaccaabbccadaccacdaabbcacccdacbcaabaaaabacbbbbdacabccbbddaaaaacdbdbbcdaaaaadcdcbbcdcdddabdaadadccbbdbbdbbbdcbcdababbbcabbabdbacdbccadabddacabacccccadbcacbdacadadbddabdacadcaabadacbcbbbadcdabbdcbaabdacadbbabddddcacbcdcababbbdadabcbababcbccacbdabaaadbcddadcbaabcdadccddaabbdbadbccaccbcadaadaaadbbbcdbbdabaabdbccbcabadbdabbdccaadcbdadcdbaadabcabcabadddaadadcabbddcdcacbdbbbccabbcdacbbccbcbcbadacdaacbaadcccdddddbbcdccbccddbdaabcbbbdabcdadccaacabdccbccbdbdbacdbcdcacbdcbbdbbcbcaddacdcdaddbbddbcaadacaacdcddaddaaaddccccbbacdcdbcbabdccdccaabacadbcdcdbcddbaccddacaabbdcaaaaabcbbdccacbdbdacbbddddaddbcaccbbdadddbdadacaaaabcbdcabddcbdbcbababadbbbbaaaacabbddcabddbaabcbbdacbcbdbacdacddcdbaaaabccddadbbbbcadabdbabdbbcdbabbabccdaacbdaabddbbccdbccdaaabcbbcaccaccadcdcbabbabbcadbdbcbaacbdbcaaccccacdddabdbaabbadbdabaaabbbdcdbbdbcdadcadcadcbbbdcaadcdaccbbaabbdcdcacbbbacbabbadcabaccbcbdcaacdaadbabdacacbdbbadbcabbcaabbadadabaaacccadcccadcdcaabacbcbbccccdcdacadcdadbabcbbcbccacbdcbaacabccbcbcccccbddaababaacbadcaaaccadcbabcdbaaccdabcbbcbdbddaaaaadcdbcabadcbbdcbadbdadddcddadddbbcadccbbabdddddcbadcbcdacbbcccccbccacbbcdccaddbacdacccccccbdabdadcccdaccaacbbccdbaadccddbcbddbdaaddaaabcdcaabadbababbabacbabbaddcadcdcabdccddcbaabcbcbabcbccaabbbaaddcaadabdaadaacbdcccccacadadaaabbadaaadbcbaccbcdadaabacbcbacbbbbdddddcbbdaacbaabdaadbcbbcdacabcbccabdacacdbaadabaabdcacadacbddcbbdbbddbbbadddcaacbacdcbadcacaddbddcadcccacbcdcaaadbcdbacbdadacaaaddcbdabbccaacbaaabbbabbbbacbadcdcbbdbccabcacabdbcbacbcccabbabdaaadcabdbaabadadaacbbbbacdaabadbaccabbadcaacdadcddcdabccacbcaddccbdacdbcbdcdbabcadaadbbddcccccdccdcdaccdabcbbccadabccdbdcbdbaaaabcabbabcadcdccdbadbacbaabccaddbadbacaababcccabccccdddbbacaaaabccadaabdcdacbbcdcdcbacccacadbddbaabbcbacacbddbbbbadbddbdbcbabadaabaccdcddaaacabcbbbbccdacdbcbbbabdcbcaaddabdbacbaccbddcdbbcdacbdbcddabadabadadaddcacddcacddbbccdcbcabcdcdddddabddcccbbabbbccdadcabaadcaaacabadacbadddcbcabbacacbcbbadacccccdbbdaaacaaacacbdddddacdaacaaddccacddbbcdccacbadccabbdddddbdabacacaaacbdcadacccdabcdcdaccbbadcbacddcccacdaaaabcbbbdddcabbbbcccbcbccaadccaaddbabbbadadacdcdcadabbdcccbdbcccbcbaccbdcdbaccdaddcadbcaaaadbbdddabcadbabcddbdbacbcacccdacabccbdcdbddcddadbcaddaabbdcacbddcabdabdcbcbddddddddaddcccdcddbdaccadddaddcbabdadababaaaacbddbbdcbcdadcbbdcaaccdcaacbabcddcbdabcccbbabcabccdcbacadaccadccdbccbcdaadbbabcccddacabaaadaaaaaddbbabccadaccaadaacbdcbbbcdbbaabdadbbbdabdadcdaacbbaccbacaaddabdcbaddbbccaabddacdcacdbbdcdabcdabaacaabdbcdbcccbabbadacaaacbcddabbbcaadacbbcdadabaddbabcabbdacbbbbbbacaccbdbbabaadadbdaabcdcbccbaacacbdbacddaaacbdaabdadcbdaddbacdddcbbddacdcaacdaaaabaccadabdacbdbddcabbdcdccadccdccaadbaddbaabbcbdacddadcbbccdcacbbbccabcaddcddadcbcaacaadcbbabdbdbbcabaadccabcbccddcacdaddcdcaddcddcddddccaacadabbdcbcabcadacadbcbaadccbdabdcaabcdaabcacacdbadaddcbbbaddcacadbbadababbabaabadacbbadaaddadbcdcaaddcbdbdccacddbbbaaabaddccbbabadbcbcabccadcbcdcbbcdbcbababdcbccacbaddadabdaababcadcdcadababccadcdabaddcdbabcbcacacdaadaacaaacbaacccbdcabcddbdbacdbaddcdbdbdbacbbddacbcabdbcccaaadacdcadabcdaaacbaddbbbcacbcadbcdabacddaaddddccdcacaccddcaddcacacbdbadaccadbcabaacadbadbdaadaccbaabadabbcacadccbcbbadddabbdaccbaccabcddddddbbccabcbadcadaccdcabbbcbcbacdcaccdadddbcabdabdbcddddbcabcbddacaababdadcccdbdcdcacdadcaaabaabdbccbbdbaaddbbbcaaaccddbccabbddacdaccaaabcbdcdddacbaaacbacaabdaacddacaaaddbbbbcaacbacdcaabbacccaccdcddcaacbadbbdacbaddbdabaddbabcddcdbcdcababdadbdaabccdcdcddcccbcbddcbbccabbdcdadbacacbcbabbaaadaadbadbdabbbadaddaaccccdaadccdadaabbbaaddcddcaababcbbcaccbdabdbbcddbdccdbcabdaabadbdabdaabcbcaaddcdbddbbdacddbcababaadaaabacdbcbdaaaabacddcabbbdcccadbaabbdabacbcdadacbddabdacdaaddccbbdaccadadbbbbbbaccbadabdddcbaaddccacadabdcdcbdcbaaadbdbddcbabdbbcadabababdcbddbaaaddcadbcaaadcbddcccbccbbdbbcabddaadcddaadcdccbdabbacaddbadaadabababddddbcdcdabbdddadbcadbabddacdaaaadcdbcbdacbccaaadaddcababdbadaabbbbadcdcaacddabcccdddbddddacbbbbcabdccabdbdccddaaccabadbdbabbbcbaadacccdbaabcccbdddabdcbbaccdccbdcaaadaddccdababdbdbdbbbddacabbbcadabdbcbbacccbdbbdddddcbabcdbbaabbbdbcaabbddadbdbdaaacdaaacddddccdccccccadcdcbcbccabdaaadcadddbaacbbbabcbccbdcdcbcaccbcacdcbdcddacbbbddbbcdcbadabddcbddacdcacdbcabdcbcbbbddddbacccdcbbcacaaccbabacaacdddcdbcddacdddbbcaabdbabadbddbcdaddcacbcdbdccccddadcdcdacbddaaacadcdcadcacadababdabdcbbcadbcaabbaddbacdbbbdbaaabdbcddabdaaadadbcdbdddbbbcaabddaaaaabbaadcddbbdaaababdcaaacadcbbdabaabaacbbbcdaacbbccadaabdaaabbdaababdccddbdddbdbdbdaccadaaacdbacdddbdccbaaddcdddcddccdcdbcdadccbaaabaddcabbddacbbaddadaabcdbadaccccbacccbcaabaabbdacaadaabbaabbdbdaababcdbdddbcdcabbdcbddadabcadbbcadcbcaddabbabbbdcbdcccbcadcaadbbadbbcdaabdddaacadbabaaabcccadcbcddaacbbdbccbccdccbabdddcabbaadabddcadacaabcdadcbcbcdbdbdbbddcdaaacaadabdbacabddcabcaaacdbdacdccdadbdacabdcdadbdcacaacdcbdcaaabdaaaddbbdddbdbddbbabbadbcabaabbdaaabcbadacbcccaababbdcaadcbabbcbbcabdbaddbcdcacbbcabdbbccdbbdaacabdbacbadccdbcbacdbdacbcbbacddadddabbddbdabadababcccdabbdbaababcbbcadbacccdcabbdbbcbbbcbddaacacaabaaddadddcbcbdcaadaabaadcaabdbaaddcccaabbccadcbcbbddaaabababaabcadcccdddbcbcdaaddbcbacddcaacbdacddacdddcabdadacbdaaacaaabdccacbcaaaaaacdbcaadcdbbbccbcdbcbcdddbacaadaaccbcbacdcacacbabaccaccdababcacbcdcabbadcdabaddadccbdbadcbcbccbcacdbddaaabbdaabdcbbaddcddbcbdbaccdcccddcacdbadaabaddadbccccaabdcdacabcaadacdbcadbcbddddcddbbdadbabdaabcdcaacbbbadbaadabaaccadcbdbddcbdcbdadabdbadcddbdbddcdbcdacbcbaaccdadacbdcbabcdcacbacbaaabdcacacaddaddacababdcaacacddabcdaadbbcbbdcabbacaddadcbdccdbadcbcacbbdddcbdcddabacbacdacbdbabdbbdbbabccacccadcacbbdccabdddbacddbccaccacaccadbccccbcbdaaaacdbcaadcdcbdccadddabaabbacdbadcdddbadaaaccbacdbdabbabcdddcdadcddadbccbbcbbdbacadabbdbcbbcbcadadccccdabcabdbddddbbacaadadccdabbdaccacdcdabcbabdcaabacaddbdcbdcabdacbccdcbabbadabccaddcbaddcaadddbdbdcadadaabccaabdbadbdacbacdbdbccddbbcdbdbabcaddbccabcacbdcddaadccccbccbcdccbcccdabbcbbcadadbacbababbaccbaaccabaddaabdabcddcbccacabdabcbcbddabcdcaddccaacdccdbabacdadaddacacbccdcdcbabddcaaddbcddcddbacbdaddccaabcccdbcabdbabcccadaaccdcbadbacbdacabbabbcdbcbabaddacdcadadaaccaccbdccdccbdbadccbadaaabdbbaabcbdabcdaacdacdbcbccadbddbdbbbbdadacababbbbbbdbacdcaccadbcdadabddbbbcbcabacabdadcbbcabacddbdaddabcdbcdbdaaacabcddabdbbddbcbcadaddbdaadcaadbaacacbbddbacaccacacccbccdbabddbcccccbddbabaddbddbdadccadbbddcabcacabacddacdabbcabccbbabbbabccbdbcabcdabcbdbabbabdcdccababcadcababddccdabdbdaaabdcadaddcabacbdbabdabddddabdcbccbbccbdcabdbdbbaaabaacccddddabccaaacbacbabbcaddbccbdbdddbbdbddaaccbaccaacaabaadbaaadbaacccdbdbcdaddaccaddabaccdbadabbcabcacbabcabdabadabcdcbddcaadabbaabdabaacaddbacbacbddddbcabcbaabacbdacbdcccbcbbcbaddbacaaacbcbbdcbdadbdaabccbdbaaaaaddaadbdddadabdccacabbbbbbcacdbdbacccaadcbdadbaccbbcdbbcdbcbaacccbadccddcaabdbaccbaaaabbacdcdcbddbcdcacbbdcbaabbadbcbbaabbaabccbabdabdcddacbdcaaacbcaabaabccdccbdcbddcddddddbabbcdddadacacaddbdddbdadbddbbabaaacdadcabaadccaaaabbbdbadbcdacccdddbbacddbdcddbbbbccaddcdabdccddacabdbdcbbcadccccdbbbabbddabcbdcdacddbbadabbaacbabbaacaadcdabccbdcababccaccacbaaacaababdcaccaaabdccccbdbdbadcbcddababbabcbbbcdcdbbbaadcbabdabaabcacdccccdabcddbbbcbdddcdbadbddccabddddadaababbbdbacbbbabbabccbabbaacdbcadddbcdbdddacbabcdbaaacacddaacadcbabadbabbcbabbcdcdaaccbabccbbdcdabcddcdacccaddadcadcacacdccdbccababbddbcdaadabdccccdcbcbdbbbadaaabbdbcabccabcbdccdbaacdabaaabdaabcddccbdccacbccddabccdcbccaaacbbcabbbbaacbcdcbaccbcacadcacbaacaacbabccddcddaaddcbbbaddabdcbdbbcbacbcbcccdccacbcbbbbddadabaacdcbabccddbccccbaadddbdbcabbbbbabcddcccdaacbabddabcadddacddabcbdbbbcaadbabbaccbcccccbabdbbcdbcdadbabbdadcccdacacabdcadcaacccccdcccccdcadcbbacbcadaccabcbdbacbdccabbbbabccbdabdabbcdcbddabcddcdccaabcabcdccbcbdcacbbdadbcaaadccdbcdadbcbcdbbbbcbdabdbdacdcdcbdcddbcabbabcdcacccdbcbadccbcdbcbdddbaadcbaabbadddbdbcbdabcdbbdbbbbcbdcbcdadcccadacccbdadbcdccbbaacbdabbdcdcdaddbaabaccabacccccbcdbcddbcbbaabacbcdbddcddddadcabccbbccbdabcadcdcbdcddbdcdcbaaadaddcaadccdddcbdddccadaddadcacdbbddcbdabdbadcdcddcbbdbaaabdbcdcaaabdccadaddacdabdccabcadabbdcdacbcaabadcdaacbcbddbbdddaaddadbaabbdabddbbbcccabcaacbcdbabacdcacccdbcdabbccdcbbbdbaaadcbccddbbccdaccaaccbcabaaacaacbacdccacdbcbdcbdddabaaccdbccadccbdaabaabdacabdcbadadbabcbbbbbdabdbcdaaadcacabcaadcccbdcadcdbaadccaddabddbbacdacbcbcdcbdbbcabbdbbbcacdddcdcacdcbbccacbabaddbddaadbcaabbbcbdcccaaabaaabcdbccbcbcbddaacdadcddbaaaddcdaccdccdabbdccadbccaccaacdcdbcdadcdabaabacccaacbcbcdabbddabbcdddabadadadccccaabbacbbababcbddbacbbdccdbdbdcbccacdcccbbcbbdadcadacbacacbccacdcacdbcddabcbacdacadcdabbcccbbacbbadabbabdbaccaadadccbcaacbbdadbaccbccabacddcaabacbdcbadcdddbaaabbddbdacbabaababdccdddcdcbbddcaaaaacabdaadbcdcbcbccabbcdaaaccdcdaaccbacacaadcaccddaadbaddbdbaabbddadbddbabacccaccddababdadbbdacadaaacbabbbabdbdbcacdbcbbbbbdccbaaabbddbbcbbbbabdbadcaacbbadbaccaddacacaaddbacccdbccacbbdbadddbccaddcccddaabbccbababdbdabcaacdadaccdbcabdacbddbaaadcbddbbaadaacadaaabbcbcbdbbdcdbdbccabcbcabdbdbccdadbbbdddbadcaadbcddaacabbdbdacadcdbabcbaaacaacddaaaacbbcdccdbabdacbdcdddcbdbbababdbdaaabbddadcbddbcaddabddbabdcdaaacaadaadbdcbdaccadcddcaaccdbcadbddddbacccbcccdababdacbdbbacdabcddbaccdbcacdaacaadbcddcbaccdaaccaccdccdadaddcadbdaccacabacbdbccdcccccabccabcccddcbcbbacbbabbcccbdcdbddddacbdbddbbcbbbbcbccbbcddadbbdcadbddaabccbccccbadddcabbddbcabbdcadbdadcddabcddcdaadabdbabdbaccdcdbcddddddbcbadbdcadadaabdccdabcbdcdacbbbcdbaccbbdbdbdbaaacababdabadccccdacbbdcdbccddabcbacbacdbadbadcccabcbbadbcadbddcdbbbbcbacdcabbbcbbdbcbbbacacacabdadbccdcaacaadbabdacdbbcabccadccccadcdddccacdddaadccacbcaabbdbabdbcdbdaddddddddaaddabddabdcbacbcacdbadbddddbcdadbdaacddbacdccccbddccacddddbcadddcbdcdccbccdcaadadbdccddabdbbaaaaaaadbababccacbddaccaccabccacabbbbcddbadcbccaccdcbbcbdbddcadaccddcabdccbdadadabdcaababcacbbddcccaabcbdcbbcaabbaacbdddbacadccccdaccbaacdbbdbbabbcbbadbcbaacdcbdcdcccacbbdbcacdadcbdaabaddbaaabcbaabdabbddabbacdbabbccbddaddaccddcccbabacccdcabccacdcaaaaccdbbddccadcddccdababadcdbddbdbadacbdbddacccbcacdcdbdcabbadaabdbadddcdbcbbbcabcabcabcabbaacdbcddbbbaadcabcadbddcbdbbaddbaabbcaccbdccadbbdbddbcbdccbcadcadbdcddbadbaccbbbbbddcbbccdddbbbadbdaabcbcbddbcabadcdbbdddbdbdbdbadaadcbccdbcdacbcdaaddabdccacccbcabadcbccbcbbbbccdacdcbcccbbcdaccaccaddbbdbdcbadbdadbbaadcdaacbabccaadbacdabdddadbacbbdcdbbddccbadcbbdbadbaabcbdadcdcabbaabcaadbcacaccbdbbabcdcdddadbacdacbbcacbbaccaaadcbbddaccdcdcbcadccabbcabbccadddcccdabccaaadbcabbbddcbaacadabacabadaccdbaaddacaccaacbdbcbdbcadbcadcdcbcbcbbbacbcabbcabccadbccabdcbddacabaacdadbdbcdddbdddcabaaadcddaaccacdcdaacbddcaabcbadbcbdddbcbcabddbadbdcbdbcdcadddbbaadaccdabdcacbbabacadaddcabdddcdadaaaccadbacbbbcbbabdbadbcdacbdbcbddbcbdbcccdbcadacbadabbdbbcbdcaddbbdcaacabaacbcdabcbbbcadbdcacbbcabcabadaaccaacdbaababdddbbccabddcdbdcdcacaaccdddacbdbdbbdbbcbbaadcbdddadbacabcbccadbdabcbdddbbdababbadbbbccacccabdbaabaadaabbdbccaabbccbdcbabdbcbddbcdbcdbaaacdadadbaccdbdbacadbbdacdddcbdddcbcdcbbadbcdbcdccdadcbdadddbbaadcbbddaabcddaabacbddadddbbcdbbdabbcbacadcaaacbdbbaaddaadbadabbbddbcddddbccabcddcdcaacbadcadcbbabcacbbadbaaacdabddbcbacdaaccdbbbcadaabadccddaddddcaadcbbbaabbabdaaabbddbbdadcdcdccddcbcddbbcdacbddcdcdcbcacadddccbdcbccdaacbcdddddbcddcabbbaaabbbdadcdbacbabaddadaadacdcadcbdaaaacabcadddcbddbdcaadccdcabcddddabaabaacaddddddbcdadbddacbbabbbbbacdacdcbdccbdbaddbabaadbcccacbbddaddbcacdacbdaacdacbabdabcacbabdadaacdbcbbdadbcbaaabcccccaadcaccdcbbcbcdbbdbccdccddaadcccaacaabbddcacdbccbcdadcaccddadaacadbaaabcdbdbadbbddacbdddcddaddacdbadbdbbadadcdaadabadaabcbcbabdaddcccacaadcbbdcccdcbbddccaddabdbbccabdadcddbadccdcddccbbaaccbdbddabdabcaacdbdcccacacbbbbdccadacaaccaadcdcacaabbdcaabcdadbbcbddddbdbabcdbcadabbbdcdbcddccbdbcadaccaddcabbdadacbdcaacaaccaddcdccddbcdcadbdcdaddbcacbccbadbaccadccabcbbacaccadcaacacbbabdccdcbdbadadadcaacaaddcccbbbbdccbbcddcadadaaaaccbddaccadaadddbccddabdacbcabcaababdabcabacbcaacccadccabaccddaabccdcbcbadbbadaaacbbcdbadadcaadddcccdcddbacdaccdcdbcdaddbaddbadacadacabadcbbddaaacccccdacbccbbbcdbdadbccddbbcaddabbdbcbcaaccbdddbacdabdcaaabbbacadcbcbcdaddaccdbccbdbcbdaccbbaddaccbcabadadcbbbcbdbabbcddaccdbbabbbcdcbacdbcaaabccaabaacccbcbcdddbabcacbaccaadaddaaaaaddcaabdcbdaabdbcccccbbccacabadbcabbcbccbbbabccdaccbabcccbdbdaccaddcbbadaabcccdbcadbbcbddccaacaadabdcbbccdaacacdaabcbbbabcabcadcbbccdbcacdbcbddbcbaacccbccccdbaccacdacbbcaaddccbaacbabcbacccadbabdcabcdbcadcdbdcbcadacccddaccdbbcbbddadcabdcccdbcddbbabdbcbcddacbcbcbdabaabddccbadbccadbbdbcdbabdacbdadccdaaacccbaacdadbaacababddbadddbacaddabcaabccddcdcadaabbcbddcdddaddcadcbbdbdacdcbbcaccccdabdaacacccbdbbbcdcacbcdbdbbcacbbbbdabaccaccacdaadaabdcaadacabdcacacbbadcbcbbcaabacbacbbabcddddbcbbbbcbccdbbdddcdccdbcdddabcbbadbdbcbacdbacbacbdbdcacdabbdcbcaadbbbbdccbbaacccbadbdbdaaccbcdbaaaccdbaacddccabdadbbdbdaabadaaccdbbabcbaabcdabdbacdbcdcccdddddccbbdbbbddaabaabbaccccbdadbbadadbdacabcacaaaddcdbaacaabdabbacaacaddacaaaaadaaddccdbabdbcabcaaaaabbbccdccdddaabadbcccccadcacdbacbbcaaabcadaaabbbdaaaacccadaabbcdacdaacbaabbcdabaddabbccbcdbadacbccbbcacddccacbbccbbbbdabaadcdcbdacdaccdbacbbdcaaadbbcddbdccaccbaaccdddaddacaddadbabacbcdabcadccbdbcbacaaddcbbccadddaddddadaacacacdcccbddcabbcacdbcdabdadbaadccacbddabbbdbcdaabbacabbcdbbbdadccaaccbccbcbbbdacaaccbbbacacabcdcbcaabbadbbaccabdacccacadadcbbcacbbcaaaadccdbdbabbddcdaaddadaccbcbcddcaccabadadaabaacabbdddacdabdacbbadcacccaccdcbccdbcbcddbccaadcacabadaacdcbaacbacaddddcbadbdacdbbcbdaccccdabdabcbacadddacbcbabcdadbbdcdbbbbcbcddbcdaadbbcaaddaccdbdaaabcabdccbdbcdacbccbcdadcdbbcbcacdcadadbccacacacabcbcbbaccbacadbdabdcbaaccbddcabcdbabaccdbccdaabacdabcdddcbbabccdcdbadbddbbbaadadddbdbbadaacadcbabbccbacbcbdbbbdacdaccacaccbabdabacbcdcadbbabaabacbbbdacbdaddaaabcddccdaddbdacddcbcbdbdbccbcdacaabaadcddbaccadbcccccdcdcddddbabbaddccbabcabddbcabaccddbabbcddbacdaadbdbadcdbcbacaadcacdbaabaaccacacccbddacaabacddbcbaddcbaddabadbbbabaaabadacccbdaddaadacbdbccdcbbcbaaabbdccbacdcbdabaaacacbccdddcacbbcbcbdcacdbcbbacbbdacbdcabcccdaddcabbdbcdccbabcaddbaaabaaccaacbdcbbaadddcddbbdcaabbbdabdcdaddccbbacdddcbcadabdcacbdddabdbcdbddcaddaadaadcacbddaadbcacbacaaadcbababcaaadccddcbdcdddddbacddcbcbcbcddaadbbdcddacabcdcabbadadcbdbbaccdbbaaabbcddcabbccaacabaaaddadbcabddbadddcabaaaadccccbbbbadcbbbadbcbcbaaddacdcaaaccdbccddaaaddbcabbbbcbdabbacdabcaadabbabdcadddadadcddadcabcbdcacbbaabcbadbbbcbdbaacddaccabcbcdcdbcbbdbcddacaaabccbaabbabdccddccdadaddbcaacbdacadbddcadccbbbcabbdabbadacddcbdddaccaadcbaaccddbcbbbdddcbccbdcdadcacbddddcbbaabaaaacccadddaadacddcdcdbdacbaccdbbacbdabdddacdbcdccabdbacbdbbaccddcdbbadddaaadbdccacdbbcabbcabacddbcbcbccacddbcdbccbbabdbcacccadaabcbccadbbdcddcdadbaddccacbbaadbdbaacdadddbbcccbcddbdaacdcddaadbbaacadbabdbccbdbadcdbababcdbaaacbbcbbbcaaacaccbcbaccaaddcabaccbadaddccdaddacadaaadacbacdcbbaadcbdccdcbbbabaacbcdbbcccbcdaababdcdcdbdbbadadabbdcaacabbaaaaabbacbaaccccbbcabaadadcddbdbdbdbcdcaaaaaaacdbccaabdaabbabaddcccaabddcbcdcacbcdbacdbbcabcddbacabcccabdabacbdcadcdadbabacddacacccaccbcddabccbabdaaacbdddbdabdbaabaddaccbacabcbdaaccbcacdabdbbacdccbbcbabdbdacaaaccddcddbbbbadcbbdcacabdcdbccababbadccbbbadadbaacdccdadbdbdddacdbdcddacdabaabadacbaccdaddabcaccbaccdadacbdcadbaacbbbacbccdbcccbbddbbddacbabcabdddcadcbbcccccadacccdaacbccbdbddbddbbbdacddadcdbbccadcadaacbbcacccbbabadabdbcdcddcdcdbdcaaabcdacbdbadddcdbacddaadcadddccabdbabacaddccaacbbaabdadaaaadbaacdbdcbcdddcdcbcbdabadbadccccbdccbbaadabcdbdaddabbaaaaaaabdbabcbbbacbaaabbaababcabdcaccaddcbbcbcdacdaccddbccacbdcaacdacdabbadcbddbabcadbaacccbbdbbbbdaaddbaabcccdbdcdccdcdacdaaaaabaaddaddddabccbcdcbcaddbbaababdacdcbccacbabbabaaccbbacdadabbbaacaaabcdcdccdbccbdacbcdaadbadcaddabbcadcacbccacbabbcaadbccdadcabdaaabddccaaddbdaaababbdbbbcaaddccbacbbbaadddbdabdaccaabcdacaacdabbcbcdddadcddbbbbdbcadabcbdbcbbcbdcdcbadddcaacbbdcccaccdbddaabaabacdadbddccbdadccdddbccbacdbabaabaddccbcbddccbdcbbaadccdccbaadabdcccccbddcadcbadcbcacbbbdaaabaacaabcbabbacaacbdcaddbcaacdbdbbbaccddadcbacbddadcbcabadbdbcabaacbbbdbddabdcbcdaddcddbaabddbcaacccabbcddaaaacbcdaddabbadccadcddcaddabddabbacbbaadbadadcdccaaaacbdaaccaccbaabdcbcbabcaacbaabacdaabbaccccdbcadaccadacdacabcdcddbddbcccdcdbadbcacbaaddcbcacaccadbccbbbbcdaacdddbbaaadbcccabcbbadacacacdcbbcabacaaaacbacbcdacccaabacacdbdcaabccaacaddacdccacdaddbbbacaddccbddcdddababdddccabcabdbcdbdbbdddbcbcbbbbbdbdbdacaddbbbdacdbacddcbbaacdcabacdcbcacabbadccdcabdadbdbcacddbdacdcadabacdbcdbdabccccbaacbcadacbbcdbadacbdbbcaacccabbdccccadcdbbdacaabbbccbdcdbaaccabacaaccaabcdbcccbcbdcbbaacbdbabcabdbcaaacaaaccbadaddacbbcdbadbbccbcdbaaddbdcbabbbabcabccaaabdddcadbcabacdaddcbdbaccbcddabdbdabaddadabacdbaabdbaaaccbadcaddbdacadbbadcbcdabcdabbbbbccdcadcddcccbbcbbbbabbddcbcaddcbdbdddacacbcccdbdddabcdcaadcbdadcdcabbcacbdbcbabbcbbcdddadaadbbabaabddaabbbdaccdccabaccababbaadacdacbbccdabddaacaaaccadadbabaddaddcdabacddbbddbbadbcdcbabcbcbdcdbbbbadbbbbdacabccdcacbccdddabdcadbcccbbdccaabbbbacddadbaabdaccddaccadcacadcdbbbadaababaddaddcbdbbacbabdcbdacbbacadccbbaaacccdbbddbacdcdcabddbdcccdabbcccbadabdacbbadadbddaabbdbadcadcdbdaabdbbcdcbbcbcdcdbddccbdbdbcdaaacddcbcacbcbaacdddcadadcdcdccdcbdadbdcbcbaadccababccaaaabababcdbabbcbacdabcdadddcbbbdacdbcdcbbbabbaddadbdcbdaaaddaaccdbbbdcbbdbbdcabbbdccddcddccbdccddbbbddacbdcabadcbacaabddaaacddacbbaacdcdcadbbdcddacccacaaacaccbbabcbddaabadcacbcdbddaddabacbddbbadccbdaadbaddabdcbdcbacaadaacdbbaaccabdbcccbaccdcabbddddbdddaacddcbdcbdacdcbabbcbcadaaabdacacabdbccadabadaacccacacddbaadabccdaabdaacddbdbaaacbaddcdddccabaabddcbddbcbacddbbbbabbccacacbddbaacccbcacdbddcdbcdddcdacaaaaddaacbbbcddbdabaabbabcccacaadcbacaccbdbdabcabbdaacaddcdacddcaadaaabcaacdcdadddccaccccddcddddbdddbabdabbabcccaacbdcbdaabcdaaaabdbdccccaacadaccdcdcbdcddddbddcdaacbcaaacddbdcabbdcbbcbdaadbbddbabcddcacabaacdcbbdcbbacabbdbbbaacabbbbbbadaabddbbbcadcaaadaaacbccdccdddccacdddabaddcdcbdaabddbccddbdbdccdbddacddbaaaacbcaacacddccbdbdaaddcacadbcbdbaccaadaadabcdddbaabcdddbcbbccdabbbcbbadcdcddaaddababbdcdddcccacbccacbbabaacbbbaddbcddbdbabcddcccdbaaabbbbdccadcbbacccbbadbcadcabaccbaadadacaabababdcbbcdddbddcdccccbaccabbcdaddbbcddbcdadddbbdbbddbddaadaadcdadcbdbadccdacccdbbabbdcbaddbaaabacdcaaccdbbcadcdabdabdccabaabdcdcbcdcccdbadccccdcbdddbcbdcaaabcdbcdacddcdaddbdcbcdbbadccccccbddbaaddccacbcadaddabdabcbcccbabbcadddacbdaadaccbcadaccbabdbdcbddcddccccdcbadcdaddbabbdddaddadcabddddbabadaacbbaacadadaadccccdacdcdacbacbbacbddbdcdbacadcbaacdcdaacbbdcabdbdacbbcdacaccbbdbacdddadbbbbddabcdbcadccdcbacccabbcacdbdacccaaadbbaddbcdadbdbdbaabdddbaabbabaccdacabababbbcdaccdcbcbaababbabbdcdbaccbbaacdbdbbcbabcbcbddaabbcdabdaadddbbbbbcbaccabdbdcadbcaaaccbdbdabdaccacadababcccadcabdcbdabacaacbbbbdaabbdbcdaaddbdbcadacbacccadddbbbbbacbababbdcadbbddaaccdabdbcbcdadbbabacdccadbbbdcbccbdacbbbdcccaabcdbbddbcaaccdaccbbaddccbbbcccabbdcbdbbadabcdbacdbdadccbcababdbacdbdcbbdadbbdbddadcdcccbddabdbbcbbbdbccdccbbdcddadadbdbcbdaabaaadabbcdabcaaccdbcdbddcdaccdcbccbccdcdadcacacddacdbabbdbaddbcccccdaaabddccbcccdaddbcababbddcdcaaababbcaabaaacddbcaacccadbcacbdbdbdabaaadacbbcaacaddbbbcbdcaccdccccdcdabddacbcdcbbcaccaaadaaadabcaabbaabbaaabdacdbdbdbbdcbbddcbcdbdacbacbdaabacbcbbdabcadaaddabababbadadaaabbdbcdacbaccbbcabaaabdbddaadcabaadbdbdbacaacacdbdcaaadbdbcaccadcabcbabaabdaadbdbbddcaabcbaabdbcaaabaaadcbbadddcdaadaacbccdcdabdddcbdbbdcbbaabdccadacaaddddadccdaabcccdaccdcdcadcaabaabaaadbacabdcbadbcabcaacdbbbaabdcdcadadccdbbdaccaccdababbbddbabccacdddbacadcdadddadcddbadbaacacddbdabadbcbbcccbcacaaaadacaabaccdadcdcadabbdadcacacbabcaabbaddacbdddcbcddcdcdadbaadabcacccccaccdabdbcacbdacaccaabddbdbbbcdabccadcabcbccbbcbcdcabaacacddbcbcdadbbaccbacaccdabcabdaddccbbabbadbbbadaabcbdbcbcbcaccabbcdddabcccddddbacbbdccccddcacddbbcdbacbbcbaccbcbaaaadaaabbadabaaaddabacbccddaabdcdbabbdaaaadacbacbadbadbcababbbcadcccddbddcdaabcadabaccdcaaacbbccbabbdabbbcbaabacabcadaddbdaaaccbddaadccccabdbbdabdbcaadddccbaabdaabbbdcbaaddabdacbcddbcbddddcabdbaccdbaabacaddaddadddbcdccadcddcbbdaddccccbdbbacbdbbbbbdabbbacdcabbcdabbaddaccbaaaddbdbddabdbaddabdbbcbccacbaaccaaadcccdaabcaadaabbccdabacaaddaacabadcdccbdaddbcbbbbbbabddbadaadababdbabdbdbabddabddabbbacabadcbbabcabcccadccccbaabcdadadacaccbbbbdcabbbaaaaddbadaaaccdbbdadbaabdaabcbbcbbbccdabcacccacbadbabaaadbacaacbdcabbccabbcbccccaacbacaadcaddacbbcaaaaaadcbbdadadbdccadacbacabadaabbcdbaadcadbcdddcbdcccabbdbadcacdbbcdbadbdadacbbaabbccdcaacbddbcbabdcccccbcdaaacbdbbcaadccddbcbddbbabcddccdcbbdbcdbcdccdcbdcabdadbbcacbbbadccbdacccadbccaaccbddaddcbbcaacdaccddbbcdbdbacdccdcdbccccdaccbabaadbddbcdcbbddddbdacabcddcdbaaadcacbcbdbbbcabcdaddacacdccdaccbddaaadadbadadbaabbaabbbbbdccdcbdccadccbbdaacddacddaddbbdcbbddbccbcbcbbbddcdaabcacbbdbdcccdddbbdcdbddddbacdaabdccdadabbcdaddcbabbaabcdcdadacdcdbdaaddbaadcdaadadbaaadadcdaddcadddcdcaacdadbbaaddcaaaaaccccacccbdadcccbacabbdcdcbddcaaadcadaabcacdddccdbcdccbadadccbdacbabbadabadbdbdbdcdbadbcacbdabbdccbbbaccaaccbaabcbddbbabdcaaabbddabbdabcdcdabacbbadccacccbbaacbbddbbccbddddcadbbbabcabdbbdcadbccdcaadcdcacccabbabcdbcddcaadcaccdcabcdbcacdaccaaddabcbcccbaacacacacddbbdbdcbbadddddaabbbddabbdbacdccccdddaabdacdacbcbbabbaddbbccbacdbaccadabbcacdbacdadddcbaddabcaddcacdabaababaccbcbadbdcabbadbcaccabaddcbadadccabacbdaddccadcddbdadcccacccdacbcddccbbaababccbbdcbcaadcbadcccbccbcbabbbaccaadaabcdbcbcbddbabddbacabadbacdacccbdbdadbacadcadddccdcbcdcccbcdddbababdbbddbbaacbcdcdbbaacddbcdaabbacdccdcdddbbabddbbcdadbdbacacbdacdbcbdadbbcbdbdacdaabbbaccbacddabcbdccacaaabcaacbccdbbbdabdddbdcdcdbaacaaabcadbacbbdaacbbcccbcccababbcccbccbbdbaccbdddbbccaccbcbcdbcbabdcbccdaacbbbacacacdbadabadcddbdbdbacbabcbcccdcddcadaacbcaaaacbbadcbadacadadbdbabdadbbbcbaaacdbdddccbacabacccbacbaaaabbadcdccccadbabdbcccabdabadddaccbabcbbaaabcaabbbdcbaaccacdaccaddbaddbcbcadaadcdddbbadcdbdbcbcccaaabcccdcccdaadacddcacdbcddbadbbdacabdabcbaacdcbddbcbbdcadcbacaaaacddabadaccacaddbccbbdccabbdcbcdabcdddbcccccadacccccabcdddabbddbcacdacdccdddbaaaacdbcabadacadcbbcbcbdcbadbcdbcbcbacabcbbcbdabbaaacccdbabcdbcbbbcabcabcbdacaccbddccbcacccadccbddddadaabcbcacdccabcddaacbddcaadddcbcdbadbcccbcdcdadbcadadbbcaadadcdbbbabddaccbdddbbdadbddcaddddabbadcccabbdbbaddcacabcbddadaabcaccbdbabddbacccaaacbcbccaabacdbddcbabacdacdabbdabaddccacbcdcdddbddccdbdabccbbdcacbddcbabaaadcabcacbdbaacbbaabcadadadbbaabdaacdabddbbdcadadcdcbbcdcaaddcabdddacacaabcbdddcadddaadcddbacdcdcdddcdcccadadaccacabdcdbbdbddbbddccabcabdcccbbddcbddbababbbbbcbdcbcbccbcbcbbabcadcdbaaacbccdbabccbadacbadcdcbabcddbdbdaddadaddcacbddacdabadaabccbabbabdacabdccabcccacccccdddacdbabdccdddabbdcbddcdcdcdcbcddbbacabdaacbadcddccbdadcdcdadcbbcddcadbccbacbdbccbcdddacdaaaddadabdbccaaddbabbadcabccaaddccadddcdbaaabbaccbdbcbdcadcabdcdacbbbcdabdadddadacaacdaaadbccbabaaaaabdccdbacbbdcacdbcabbaddcccacddacadacaabaaaabbccdbaaabcbcbddccbabcbdddcbcbadbbbbbcbbbcbbbaabadccaacbdabadadadbdbcbcdbbacdbbcbbcbccadbbaddcdbbbbcccdcbbabbbcbbdcdacdddbbbdaddaabadcbdadbcdabcbccbbccadabccdaabaddbbcadbbabdabdbbaaadcadccacbacbdaccdbcddcbcbbbadcdcbbdaccbdcbdabaacaacccbbccddabbbaadcbdbdcaaabdaacdbbcbdcbabdcabccbdcaddacabddacaaddbbabadcadccacbaaabadbcacbbbcddbbadaccbaacbccdcdbcababddcabcbcbcbddddddbbdcbabaabccdadbcddaddaccaddbdcabbbacadbddadbbbdddaccdcadbbbaabcdbdaccaabadcbcdbdabaccbbbdddddcdacdcdcaaaaccaccbcbcabbbbaabdaacaccbcababcdcdddabbbabaabbdcaccdaabbabdbdcbcbbddcbccccdaabddbabaababdacdddbcddbaaabddddddaccccdcbbbbaacbbadabdaccbaaddacaccbccacaaccdadbdbccacabccbbdddccaadbbbdaddbbbcbbdcccdadacdccbdaaaaddadcdbdcabcddaaddadadadbcbadcdacbcaddcdcaacddbabbbcddbbabcbdcbbbdbcdaddabddddddacbbacbdbdaadaaddcaacbbddaccdbccacbdbacadddbcddddccccdbccacdbcacbcbcaabdbcdabdbdcdcdaccbabaddabdccbadcdbdcabcadacbdcdcccaadacaabacacdcbdcddbdaabbbdcdddadccdcbbcccdddbbdcbccabcbdcdcddcdbbadaadabbacdcdabbcabaaabdbdcadbcdbdabbaaccdcbbcadddbadcbcddccbcbabbbaabbabbdaadaddadadbdaddbadbadddbdbcccdcbbdaacdbdcbaabcacccabacccbaaacbaabacdcbaccaccbbdaaacabcabcbccdadbddddbcbcbababbccaacbcbdbdaadbdbcdbcddaaacddcdacadadacddcdcdcbdbadbdcbcccbdbdddccbccdaaacdcdbdcaddddbbdbcdccbdcdbcbbdcaadcdacbaccdbacccdacdcacabdcddbdddcdbacbbadccbddaabcddacbabdbabaccaddabbadaadcbbdacbccabdabaaacbbbdbdadacbcccdaadbbbdcadaabdbbbdbacddbbbdddaacadddacbbaadabccabdcdbcdaabdbdaaadbcbddbcacdadabcaacdadbdccccaddacdcabbdadababaadaacbadabbdccbdddbbacbabcbccbdacdaddacdcdddadbddadaddddbdacdabdacbaacbdcbaccccbcccbadcdbabbacbcbcbcacccbdcbacbaaaabdadaadadbcaaddacaadacbcaaccacbdcaaadbbbdaddbaddaaddcdbbdbbbcadccdbdccdbdbabdcbcbbabadddbaabbccaaccadaaaadabcadcbbbcddcbccdcabdccdcadbdbbcabaaabcaccbabbcdbcbcaacabcdbbbbcccaabdbccbbadcabcdcacaddccadbbbbccbbabbdacaccbbcdcbdbcdaadadaabaadacdccaaaabcdaadacacdabdcddbdadaaadbcdacbbcacbbabbacbabaddadabcddcddddabadbddccbbacccbaaaccbcbbdbdbbabaaccabccddbccbbabadcdaacbcdddbabbdabbaaacbaccacadbaabcdaacdcbacccaabcbbbdacabccddaaabdaccdccbbdabcabbcbccdbdcdacbddbcccdaddabbdadaabdddbaadcbadabdbcbacddbdbbbcbcccbbcaabaccabcbbaccadadbdddbdabdaaabbcdcbadbccaaddbccbdccdadbdaccccababacadaadccabccddbcbcbbaddcbdbbdcaddbaabddacbcdadbcdacaaddbbbadbccacdabdcdbabacabdadbcdddaddcdbcbaccadddcddcaabcaadcadccbacddacdbacaabacdaaaddbcabbacccdaacbaaaacdcadccbdddbcdacdbccdcdcbdabaddcdabadbcacbbabbcdcdcbdabcacdcdcdcbabacababcbdbccbdccbcdadcbbbdacddadcddbaaccbbbccabaadbababdcbccbcacdcddcaacabbcdbcdddcddcbbdbcdbcadbcdddcdbddcdbdcddbddaaabacaadcbadccdbbaaaaddccaccdbdbcdcdccadadabaacdcaddcaabcbadcccaadccaadbbbdbbbdcadaaabcdcbbbbccbaacbdcbaccabcbabdbbabdddddccacabbabccabaabbadbcdcccabbbbccdbdddadacaaabbbdbdccadbdcccacdccbbbbcadbcadacabdbccdaddbcdaadabccaababbbdacabbbdddbcbbaacabcbcbaaccabadadcaabaacbbcabdbdadbdcdbcadacccdcdaccdbaaccaabdcadbacabcaddcacdbdabbbddccaaacbdbaabddcdbacdaccdacbcacbbcbcabddaddabddbddccbbacddbdcbadbddbdddcccddacbacdaaacbcabcabcadacdcaccbbcabccaaadcbccbadadababbaaccbacdccbbcabccacaaacbadbcdadbacddbcaaadbcdcbaaddddaaacdcbdacbbbadddaacbdddddbaaabcdcbcacdcddcccdccaccbbaaacabaadadbbcbbadcabddaaddcbbbccddbcabacddcdbbbcdcadaaaacabadadbdbcacbbdaadbbaaacccdccdcdbcbbbababccbddbacdcdacdddbcaacabdbbabddbacbaacbccccdacbacdaccdaacdacadbdbcdbdbacdbaddbbbaccdcddbacbbdabbcdcbcbcaadbaaaabccaacbcaaaccabcacadcaaacaabaabddcaaaaadcdaaaadbabdccbdababbaadddacbdbbbdaadcbcddacbadcdcaaaadbdbbdadacdbbbbccaaddcaddccbabaadccbacbadbbcbdcdabaacbaccdccaaddacaaabbbddcddcccacaacaacbdbddcbcacdbacbcdcbacaaadbbdbccddcadbacbddcbddbaddddacbbdbddddcbdaacabcdadbbaccbbcabcddbdcdcbdcacacdbaadbabaabcbbadadabcddbdbadacabbdbccccbbacbcdbbadbccccdcccdbbccbdcccbcdddaccddcabddcaaadcdcdbcdaaacccdbaabddbdbcbdbadbdcbabbbdcdcbacddcbbddcddcddacbcdabdacbbcbdbdddcbbabbdacaacadbacdbbdbbcdabaabccacbcdbbaaacdbdccaabcaaadabdaddcdaabadabbbbbabbbcaccacadadbbcabaabacdddcdabaabaccbbdabddaadcbbcdbbbdaaabdbcaddbcdbdbddcabddbaabdcdbaadaabdabaaadbacacbdbbaadadadadbdabdabdabbbcbbbbbdbcbbaccdaddcdccbaabcadbadbcbcdacbdcadbaabbbabcabaadcdaabcddcccacbcaadcbdacaddcbcdcaddcddbaacadaaddcdabbcccdcbaacdbabdbbaacadbccdcdbcbdccaacbddcccbdccbbbcdbbbcddcdcdddcccdcacbbbbacbdacbadcaccddaacdbadcadccaabdadadaacbccdccccccdcbdcdbcadacdabdbbaaaaaddcccdbcbdbabcdccdabbccabcbcadccdbadcdbbbadadbdccbcdabcacdcdbaccdddaabcacaddcdccaadbbdaaacdbaaaddddbaaddbbdbdbdbaadcbdcadddcbddcbaababbdccbdcbccaddddacaadcbaababcccbaaddcacbdcabbacdaaddabbaabadabdabacdcbaadacbbddcadbbcacdcddbdbbabdadaaddccccbccadaccdbcbadcaaabbbcbcbcaaccbbdbbcbcaddadacdbbadddaddccdccdaaaccaccadccaaadbadbcddaddccbbabcbbbbcaccdabdccdbabcbbccaddadcacbcccbacbbabbadadcbbaabcdacaabdbbcdcdabacdbdaacddadaabbbcccadbbbbadbaddbbdddbdaaacadabcabbbddbbddbdbbadbdacdcdcbbadadcdacddcbcbbcabbbcaddbdabcdddabbbcacbddcbbbbabcacacbddbacaaaaaabaddddddadcbbabbbbbbdccdddbbabaddadadacdccdabcdcabdccacacaaadaaaaaaccadabddbdcddbaddacdcccbbcbbdcdddacdbcabbaaccabdadcdccdbdbcdadaacbdcbcddbcaddddaddbabaacaddcddbaaacbdabdbbbdaccdacccadccdaadbdbccaaddbadcacaddcbaadacbcccacbabddbaaadcbacddbbcccaacccccaccaaddcabbabccbcbcaddcddccbabcbcdadccdadbbcbaabdaccbbcbaaaadbdbcabccbccccacdcdccbabcbccabbdaacccaddbacbcbcbcdacdcbddaabadadaacbbcccccdabbdbcabccdcababaaadcacbbcdbababbdcaabadabcaadcccadccdaacbdbddcdaabdbcdaaaddcdddbdabbdbcccddcbdcabdcbaababbbdbdbbbddacbbacadcaaaaccccabcbccacaddbbdcdacacdbdaabcbcabbdaccbaccaddcccbbbdccbbdaadddadaddabddccadbdcacacdbdbaccaacccddabcdcbdaadcbbbdcdaabcdcbbbcaaddccdcbdbdcaaaabdcbadabddabbdacaaacdbabdbaaaabadbdddddcaccaacbbaccdbbcacdbcdbbccbabcbdbaddbdabbdccbccbaddbdaddcbddbbaccdccddcadabadabcabcaaddadcbdbaacdcdbbbcbabcccbbaadbadacacdbbdcddbbadccbddbdaacdcdccbaccdcacbaabccbabdbcdadababdacbaaaaacccbbdcbbbadbcbcdadadcdcdbcdccaacbbcdccbadacdacbcdabacbbacdcccbddbbcdabacabbbadcabcdcdbcacdbdcaddadbddbbdcddbcbdaccccdcdacbdabdccababcdbcdddaacaddadabbaddacacdcddddcbdddaabadcabcbcdddccaddcdbacdbcdacabdaaddbccbbcddddcaaadcababadacadabddabcbcbdcadbaadadcbcbddadbacaadabcdcdbcacbcbbbaacddcaaaaccccadaadcbdddbbdbacabcdcbaacbcbadcbdbbadbbcaabdbabdbcabdaadbacadbdadddaacdcccacabdbbccbbcabacacdddabcbcdaaccdaaadaabbccbdcbacbdbbbcbdcdadcbdbdddccccbdccdbcbdcbbdccbacacbabdbcaaccdbdaacadccddbdbbbadcdabdbdadcbccaddccdababcbcddabbdcdbccdbbadbacbdaabbccbcbbcdbcbcdcbdbbaaababadacccdadaddaabcbbbbbbaccdabccbbbdaddcacdcddaaadadcadbdccdcacbcdddcbaaacbdaddcbbaacbcbaaddcbbcbadbcabbacbdbdcbcaabcadddaddabbaabdabacbcaabdadccadaabccbdbcdccbcaaabcbdaaabdccbcacddcabbbbacbbcbdccabbabadbaacbabbaadacacbbdcddcbddcaadaccbbbccdcaacadadaabbccbaabcdbcabcabccdadaacdaddbbcbcbbdbcddbbdcacbaaddbbdabcdacdbadadbcdcbbcabddacdddabababaabdacdcadccacdcaaaabadcadadbbadddbddaadabbcdabcdccbabcaacacddccadaaaaaaaabbcbbaccccbccadaaacacbcbacadaccddddcbbccdbddddacacdcdaadbccddbcdcaacddbabdabbcdcbdadadacbdbdcadcaaabbdbddbacddbccaadabbadadaaddadcdaccccdccdbbacadabdbbacdcbbccdadcdcacbbddadbcdadccbaababaacbabddadcbcbbdbdddbbbabddcbbbcabaaddabbcadddbbdcbccbbcbdbdbddaaaabdbccaacaabdadcaccadcabbcbabdbaaaacacabcaadccabcaadbcccbacbbbcbccadccbddabbbbbbbbcaccaaadbabcaadaabddbdcdbbbacdbddaaaaabaadadddaccddcbbaddbbbbabcbbddabdddcbadccabaabacacbcbcbddddcbbdbdbadaacbbdabaacdddabdadcbbadcdbadbbdccdaadbbacccdcaddbdbddcddcdddccaaabdddddaaccdccbcdadddabadabbdabaadbcabcadcddbcdaadbabcabdcccdcaaccacacaadabddcadbabbcdddaacdbbaccbdbbabaccbacababdaccbaaaaddbadababacdbbaddccbddddddcacdcbabacabbcbaddddaaabacbacbcbccabddbacaaacabaacbdbdabcaaabcdacccaccbccdadbbbdabdcbabcddddbacacbacabbcdadcbcacabdabdadcbacddadccadaaadabcdbacbcbadaaababbbdadcbbadbdbcccadabbccbaabacdbcaaadcabcadcbacdbddbddacbddbbcacbccbdbccabbbbabcaabadbdadbddcbaaadbdabcdddadcbbcdbbccbbbacdcbcdbadcbdbaacbddaccdabdccdadcdadcbbacadccddaadbcabdcdbdaabcdccabcccaabadcccbdabddbccddaadadbcacadbdccbacacdaddbccaccdcabaadbccdbbdabbccaadacbcbddacddbcccaddccdbdcaadbabcaccdaadbdaaddbcbccdcaaadcdbbbcdbbaacadcbabdddabbbdacdbccdbcdaadabcdbcdababdaadabbbdabddcabbcbcdabcbabcdabdddbdadbbdcdbabdbddadcbbccbdabbbadaabcabdcbbcdcabcbbdbcaabacdaabccddcadcadccdacacccddbdddcdadacbccbaadbcbcaaddabacdacaaabdaabaabcdacaccbcbdbcbdacddadbbcabadcbdaccddbbbadbabcddcbbbcbcbdbbadbcbbdaaadbbdddcbaadddbccaccabbbdddaccdcbacdbcabcdcaacbdbccbcabcbbadaaccbcdbadcdaacabcdcacbcacddcabbaaddbbdbbccadcbcdbabcbacbbdcdccdddaadbcdabcbdcbbdadaabbdaccdbcccbbbccbdccbdaabdcdadacbcacdcdbcaadcccbccdcaccbacbcabccbbadccadaddccdaadaabcbabacabacbbbcacdcdccdccbbbdacaadccdacbbbcadabadbaaabbccdbccacccacabcddcacbcabcadaccbbdaabccbdcdbcbcbcdcadadabbcacacaaaabbacdabaccaddccabbaadbaabdabdddddbbbacdabbaacadbcbdcdcbbbdbababaddadcccbdaccabbcaadbdabacddbccabbcccbbacacdddabaaacbdcadcadddbcdacdcdaabccccbcbaccabcacdcccabbaccaccbcbaabbcdcaacaacabcaacabcdcccadabcdddcbbaadabcacddacabbcacbbdadcadadcacdcabaaddaacacbbcaabdbaccacbdacdcaadbcaabbdadbccdcbdbadacdadccbacaddacaccbcdadbbccdbccbbaccbdadcbaacaccccccbadbadaacaaddaaccbaadbdacbcddabcadaaabccbaabcbacccbabacbdbbbaddcbbcdbbacaacacbcdbcdbaaddacccbbdbcbbdcbbaadacbaddcdbbbcabacaadcbdcddddacacaddcdbbbccbbbdaddabdcdabaacaddaccbcbbbabdbaddbcaadadcdaacbabcbdddbddcbdddbdbadccbdaabbddbdcbaccacabcccaacadcadaacacbddabadacbbdcdcdacbadacbaaccbdcbacbcabdadbbbcbcdcadddcdbadaccccdaabcbccadddccbabcddcdcadcaacbacbbdacacadadccabadaccabaaadccabdabaacadddbbcacaaaaadbabcadadbdabccccdacdabbdbdaadadababbbabcddabccddcbcdddbbcdbaaadddbaddbddcacdbdaddcbacbcddbdabcddcbadbcadbdbcddbadbabdbabdcacdcddabbcacadaacccccacbbbacbdbdbdccccbbddcacbdbdabacccbaaddbddbdaccddaaadbaaaaadacdaabbdadbbdccdccadbdacbdccabddcdbbcabadbcbbdbbbbcaddcababccccddcdccaacbaaacbadddadcadbcdccacabbaccdcdbadcadbccadaaddbaccbdbdccbbbabbdbbabdcbacdccccbaccdbdabaaadddcdbcadccaadbacaadabbccacacabbacdaadcbdaaacbdaaacbbcbbcaddbddbcdbcadbacbabddbccdaadcbbcdcadcdcbaaabdacdcbccccbbddadabdacadbdabaddabdcacacdaadcacbbdabbcaaddbccddcaadddaacccbbdcbdcacbcadaddadacbccdaabbbdaabcadacbaadcdaacbbadadaaddaccabdcdbcbbbdcadccdaacdbaaaddbdaadbdbbabdcbbddbabbdddbaacabdbdadddcdbbadcabcabdcdbacbcacddaadcdabbdaddcbaadadbbbabacddaccadbccdbdabddabbcbaadccccccbdddbbbcdcdbdaddcdacccdcbbabccbcaabbcdcccbdbaabadcddbddccadbaadcabbbddaddacababbdddadcbccacabaacddddcbccadbbcdacaaccdddaccccdabddcadccbdccdacabbdabcdbabaaadbbacdaadcccbadcddbcbacaacddbaadcddcdaadbccbbccacbcbccdadabdcbcdaabccaacbddcbaccacddbdbcdcdcaaaccbbbddbddadbbddabddadadbcbbcbaacababdaabbdaabcaddacaaacabddddaacacabdbddcaddcdadcdbabbcbabadddbbdbcdbdababdddacabbbdcbdadaaabcddbabcacbcabcdabadadccbccdcdbadbadbcccbabdacaadadacaadaaccbbdaabdcdbddbdaccacdcadbdadcbbbcdcdcddcacaddaabaadbaadbcdadbbadbbccadcbbacadbcabdaaadddddcbbdccdccdcdaacbabcacdaacccbacbbbacdbbcdbddcdcacdcdcdbaaadcdddcdcdcaddaddaacbdcccabdabdcdacadbabbaaadcbacbadcadcaddddadaddbbaaabcbacbcddcabbdadbccccdaacabaaabdbabbbbdabdcccadbbcbbadaacabaacbcaabaaaadcdaddbacbdbcdaadccdbbdcdddbbbccadbbbcbdacccbbbadcdadbccdccdaadaabadccbbaaacbbdcaddaddaabbcccbcddbdbbbaddacdcddcbdbabadbbbcbdcddbdbdadcacddcdaaacdbacbbdddddaadcdbaadbbbaddcbcdbcccbadabababdcdcbbcacaabacdccdbbacdbcccacdcdbccaacbbcacaabdbbdcbadcacabaaddacaddacabdbdbdadbadddadadbbdaacbacaddbbccadbbdcbbcacadbdacccaccabaacaaabdaababaacbaadddbcbddacdacbbabbadbaacaddccacbcbbbcadddcabbdbacacbddccbddbccbacbbddaccddadaaddadadbaabbaacdbdbcbbcbacddddadddacdabdaaacdbbcaddbccccbdbbadbcbbdddccddcacbbdacdabbbdbdcdbabadaacbadaabdccacacdacaadbaaccbabbbdacacddbcccbdadcdcbaacabbdcddcdddcadcadddcadcdabccdbcaccccaabaacdabbbcacccbcbcccbaabdbbdbdcbdababcabddbccbbdabcbdcadcacaddbddadbadcaadcaabacaacaadacaadddcbdbcdadccbabacaddbaacddcdcdaddcbddcbbdccabcadcbccdccaabcddcadbbdcadccaaccaabaabbccbdbcdcadadbdabddccaccabcdaccababbdbbbaccacabdadabaababbdbacaccbacbacbcbcccbabdaaccaabddbcdbbbdbcbacdacadccbcaddcddacdaccdbddbbddabbcaadadcabbbdabddcaacccaabbccccbbdadbcbdbaabdcaacbbbdcacdbbaabccbddbbbbdcbcdcaaaabacdabaccacdadcaccadacdaddbcaadadbdadbbaabcbbbcdbdacdcbabcbbadbabaccdabcbbbddbccadccababddcdaccadbdccbccdbcaddbdacbdccacbbbabacbdcdadcddbcdaabdabccaadbbabbdbaddacbaccbaaadddabcbbdaabcbaabaaaddcbbddacdbabadcaacddcccadbbaaddcbdcbaaadbdabddbdcabaaacabbbaddaadcaddbbcadabcdcadbaadccadcddddccccacbbaacdcdaaabcdbcadaadabcddaaddcbbbccbbcbbbbdcbadcdcddcdcaacababddddcccbabbdabadabddddadcddacacdaddbaadaadbaabcccccdacdbbbbbbbaaaadbdaabbacadadbbdacdabdadbbacadabacabbbbacbdbcadbdcddabcbbccbdbdacabbdcaaadcdaddcdaadbbddabdbccbcadcbcbbbbadcddbacaddabdacacabdcdacdcbbcaddcaaccbbdbacabcdcaadaadbccdaabcadbbcaaaadabbccadbabacaadbbdaaaddcabdaaddbadbcdcdcdbacaadaadcdacbdcbbcddbdbcbaacdaaddccdadaadacdcdddabbaacbcdcaddddaabdcccdbccbcaaadabdbadcdacaabcdacaabcaacdcbadacddbaacdbaaaddbbcaabbaaacbadbddcdbababcdaddabbcbacaacdcaddbbcdddbddbadabaaabcdccbdbdaddcccdaaddcacdcdccacbaccacdbdddbcbcccdbbcabcadbabcbcbaacbcdbbdbddcadcccdbbdcaddccbbbdacbbcadaabbbabcaabccdadcabdcbdbaacccccaacaacddabcbcddcdaddbabababacdbabbbacbcbbdbccadcdbaaccbccddabcbdcbcdbccbbbccdbdaabdadcdacdcdaaabcbbaadbddbddcbbbdcccacacaddadbacdcabdbcbacbddabddccdbbcaaccaaabdcdbabdbccdadcdbdddddbadbbccacbadccddcdcabadcdbcaabcbbddbcacbdbddcacdddbaabcbbcdbbdaabddbccbbdbcabaacbddbcabdbccbadbbcabaacbdacabbccdcaccbbcaadaadadbcbaaccacddbdacaaaadbddbabcdddcbddabaadadadadbbccccadadadccdddbbccbdadbdabaacaacdcdaddadbdcbacdbbccbdbbbbbadcdddbccbabcccbccaabbdbbcdbaccadadacacdaacbadcbbbbddddcacabdbadcdcbbaadbbbcbcacbbaaccbacabbdaaaaacbabacdbdbbdcdcbbacaacaabcdaaadcbcbacbbaadaddcdabdbadcbcbbbabaccccaacddccaadbbbacddcddbbbabbcaaddcccccbbaddcdbcdddabbcbcbbbaabbcaacabccbbbabcdaaabdadbccacacbacbdbbbdacbdadccdcababccbbbabcdadbdccadcbbbdbdcadbddacabbcbbbdbdcbadcdccabcbbbdacadbcabbcddccbddabdabbbbaaabbbadaaadbadccccbcbcbdbcaddcdbcddbcccadadcdaacccdbbadbcabddcacdaabcdacddbbabdcdddcababbcadbcadbdcbcdcadbbdbdaacbdccacdadaaacddccababbdbbbdaadacddccbbadbdbbbddcbcdacdbaddccaabcdbcadaabcddbadccbacbddbbdbdbbdaadcadddcddbddcddbbddbacbadbabbcadadacbdacddbadaddccbaadbabdaaacccdabcddcbdbdcabdacdcdaabccadcbccbdddbaaaadbbaabcaadcacadcacabbadddabddaadbccacabbacabbbbcbdbaaabddadcdaacdbdaddcaaaabaddaccccccacccdcbcaaaaddbcbdacabaacbcbabddbcddcbcdcbdbbaababcbbbdddbbbbdbdacdaccabacbddbadcbbabbcdaddcacbaacccdcdbdabadbdbcbbcadbdbddabcbabdcccdccdbccaabbccbaabadaabaadaccacdacadbbabdcadccabcacabcdbadddbcbcdaabbbbccacabddbaacadcaccbbbcbddbddcbdbabadadcaacdcdbcdabaabaaacbadcadbbadcabaddacdbdddacbcccdabbdcaabbdbdadbabbdcaaaacdbaadcadcadccddccadaadadcacdbacbababcadbaddbbddcaababdabaadddcddacadcdbccbcbbabadbbbccbadcbcacddbbddadcacdabdbdaaccbbaaaabddaabacdcbcdbcddccccaaaaaaaabdaccdadabdabdaddacbabdabdbacbbaabbcadbcaccdddadbdbcacbccbdcddabaabacbdbdcbabaddaaaaaababbbdbbcaccacbcddbddabbdadcacccbbdbdabccbbbddacbcbacdabdbccdcdddcbdbbaaaacdcbcbcbacdbbacddadbbbdcacddaddccabcccdacacdccacbcaacbcaccaccbdbbdcdbabbbdbcdddabadacccacdcbaabacbcabaabdaaabdccddcabcddcdaaaacdccddabdddbdcbcdadbadbdabadcddbbdaaccccacbadbabbbdadacadaadacbbabaacdacadbddbdbbacdaacaabcabcbbaccdcbabcacbadaccccaccdcaacabcbbbbdccccacbaadbdbbbdccacbcbbcaabbbcdddcbcbacbacccdcbbbbbbdcbdbaabaccadcbbcaddaacbcbabbdbcdbcccddaabaddddacaddacbabbbcacccaddcbcadaaacbaabdaacbdacbbcabdcddcaaaadabdadbbcdcaadccbdacdbcabcaacbcbbddcbbcbadadbdadcdabbcabcdbcacccbddcbbbcbdaaacbbaadbbdcbccdbaaacdcddbadacbbabaacdcabaacacadabcdbdcadcaadbbadbdbbacdaccdbadbbbdaabbcbcbcbabcacdcadbccdabaaddbadbcbbbccddbcaacdbdccacadbdbabadbabadbcdaaadccacccdbcdabadcdcaccabacdadcbbdabbbcaabaaddabdddaadaacaddbbbcbdcbadbabaddbcdaaddcadcbcddacdbadbacdcdbbcacbdadbaabcdaaccadbacdcbbacaabcdabbbdbddddccbddabbcaaacaccbbabcdbcbdadaacddddcabcaadbadabaadaaabdaacaaadbcdbdacaacccdadacdbddccbdcabcbbdbdabccbbacabbbdcabdacddcdbbabdaccacacacbddadcdbbbbcbcabdadaacabcbdadcdbbcabdaabacaaaaadcbcdbabddcdccdbabdcbdcaddbaaabdcdbdbadadcabaccaaadbbbcbaadbabadccaadcbcbabdadccadbdadabcdaddcbdaacbbcbacaabcaacddbdaaabaccaacaddcdcbbdbadbbbcddaacadcccaacabbdbdbdcdaaaccabbaabbcbdcbdaaabcadcacdccdadacbaaaccabcabcdbbdaccaacbdbcdbaccbcaaccbababcaddabacdaadcddbaaacdcabdcaadbccdbaabddccdbdadbbdcbadbacbababddbbbcdcacaaddadbbbdacdbabdccabcaaaadadadddbcadbaabdacdddaabdacaabbdbbbadbcbdcbdcbcddccbcabcdacbdababdbdccaabbcacabdddccbdacababbcdbadbadcddcaacadcdbacccaacadabcaacadabcddcbcdadcbbdabaddadbaaddcbcccbacbbdcacdcadccaacabbacaccbbbcbbccdccbcdcacbbdadccaccaccacdadaadbbdaacadbacdbddcbadddaadbddadabdbbdadcadbcbdcccddbcbbbdcbdcdaabdacdbcccaaddccacddbcddaabcaabbcbbdcdbbbadddaccdcaabbcbdaccccacdadcbcddabddbbcdcbccdabcbdbcbdcaccacdbcdaccdcdddbccbcaacdaabcaaabdccbbaaabbccdaacbadcdbcbddaacccababbcaabcdddcccadaacddbddcbaabcaabddaabbbcadacdbcdabbabcbdcadadcacadbccbdcdbcdbddbbacbbaddcdaacddbbcbababaddbacaaabdddaccbbcbadcaccabaaacdbaacdcbddbbdcabcdbdbabbddaababdbdabaaadacbcdcaaaadcbadbaaacbdbddcbadcdcbccccdabbccbbcbcdbdadcdcabbdaabbaaacdbdabcbbbccbbcbbdabbcdaccdcccdddbcaddbbcaaacbbabadaddbbddcdbbdadddbbacdabdacaddbaacdbaaacbaababbcccabbccccccababdaabbcbcaacddaaabbcbdcbaaaddcadabdcdcbaaadabaaddadbcdbcacdcdcbbbbcbcacbbccaaaaacbaaddabbcbacddcadccbcbadbdabcccbabaaacccabcabbabdacccdbdbdaadbacbdccddaccccccadccbcdccadaddcbcbdbacabbbdcbddbabcddccccbccbbadbabdcdbdabbabddbaacdadabcbaccddbdaddcadabbadaddbcbbaabdbdcbdadadcdbcbdcacabcbcdbbbbbaccabddacdbcdacccadacaadaadadabdabdcabddbcccdbacbdbacacccababcdcddabcddddacdbdbabccadddccbdabbadabdbaabddbdcabadbabadbdacdcdddabccacacadbcccdabcccdabbdddbbdbbbbaabbadbbdccddddaaaaddababddcddaaaaadbcaacbddacbbcdaaadadcadbdabdadabdcccbddbabcbdadbaccdabbbcbacacbbbcbdbabcabdaaacabcbbabcdcaadbddbdbbdbadbcdddcabddddbcbdcddcdadcbdbddcaccdddccdcaaadbacaacdddbbcbbbbcaadddacabbdcbcabadbaccacccbcbbadabdddcdbccddcbacabccabcbadcddacaddadadacccbcdbcdcaddaaccddacdbcaacbddadadddadcbacdcabdadcccabdccacdcbadbbddbcdbaddabdccbbcccddacddadadcacdcaacdaabacdcddccdbdddabbbcbaacccbcddcdabadaabcdcbbccaabaccccadcbacccddabdcbbddbabbabbcbbccbdcdbbccdbdcbcbdbdacbbcadaabdcccabbbacbccaaacbabaaacdbbcbcddccbbbdcdacddcdacdddcbcccdaddcdbbbcaaccbcbbdbdbbbbdbbbdbbaacabbaaadacddccdcaacdcdcbcbbcabddaaabdcbaaadbbdcdbaccadbdcbbdbabbacbdadccacbcadddccbadabbcbadabdaccbcddbacdabdcdcbdaddcaccbbbbdaabdcdddcdcdddbcbacabcbcdcbabbacbcbbddaabddbcdabbabdbcdbcbdbabccadcbcccaadcdbdbbcadbdadbdacabbdbbdcdbdcadaccababddddbcacccbaabcaddcabbcadbdacdcbbccbcbdacbcaccdbacadcbbbdbbdcadbcabcdbaacabdbdcdaaaaabcdbbbadbcbaddcacbdbdbdadbcadababbbabddababacbadabcdadbbcbbddaabcbbcdadaccdcddabacabcbddabbbbbbadcdcdbabbcbccadaadaaaddcdddbabbaaaabddaddbcbcbdacdaaabdcddbddbbaaddababccaaddacdcabbddddadababdcdbdaddbbcccbaddbcccdcababcacdabdddcdbdadbbcaabdcccbdbcccbdbdcdbaadbadcbcdbaaddcbbbccdaccccadacccadcadddaabcaabccdddabcbcdbaccdcbbdbcbccacabbabbbadacdabcbadddbaaacbbadbcbbcbddccbdacaadadbcdaccbbabddaacdbdddacdcbdbcbdcdcaccdaacadabaacaaddacbdcaaaacddbbaadaadbcaacbdaadbbcddccaaddddcbcccbcaaddbadcbddddbcabbbddcccbddbabbdcdbabcbcdbbcbdbadddbacccccacbccdbdbdbabcdddacdacddbdccabacdccccbbcccabcbababbbbbbdcaabcdccbbacbcbdaaaccacaaacbcddbcacbbbabddbddbdbbbabcbbbadddbaaaccccaabbadbabcdadbdbbacbcbcbacacacccacdbdaaaacccadbcbbcbcbdddcbcdbdbadcadcadadbdcbbbddbabcdbabbadccccaacccdbdacddabbbaadddbbdbcaabadcadadcaaaddadbcadcadccaacbabdbcbabcbdcabcaacdacaccaabbbbadadabccadabaacbcbbcbcbaacdddcbadaaacccbbbaccddaacbbbcbbdaaabcbdbbabadcdddcdcbccddadbaccbdbddbbdccbddacddcabcaacaccbcadcbbcddacbaccdadbbdaaaacddadccaacadcabbbcbcdddbbaadccdbcadacdcdddbbccbbabaaccbbbabbdbdbcccdadcdbacabdbbcbbaccabcccaaabadcaacacabbbdaccccadbdbabbbdabcdbddbcacccbadbdccacbddcbdcdbcdabbcacbdcdddcabadcacacccbdaccdbbbddbbaacbbccbbbdcbdbbbadadcdaabbdabaccbabdabdcdcabbcbabbadaaaacdcbcacdadcaddbcbbcdadabcbabcbabbacbaaacaabaadadaddaabccbdacdccbbbadcbbdbddacccaabcdcdccbdddabbccccabbaacbcdaaddacbbcbdddbdccbbaacdddcbdccabaababcadcdbcbcbbbacabcbacacacaadcdcccdabddbbaabcbcaadcababdbbcacaacdbcdccbdaadbbcaaacbbbacbadaabaaabaabcbaaaaccabcbbadbddcabdcccccdccdccaabadbdaadcaaacaaaccbbcdacabbbcdabcbbadaacdcbdaacadbacadcbabbaaabaabbbdadccbcaddcdcbacbbacbbddcdbbacdcaccacdabdcbaddcacadbcbcdcbdbcacdbbbcaaddddaadcbcdbdcaaccbcdbbaaddbdcacdbaaabccddabbdabdabcbbbbabbacdaccccddbcccddbdcdbdcbddbdbdbdbaabacadbdccadcbbaddbcdddcacbbacaadcdddddcbcbbbabdcbcddadbbadccccbbcdbcbcbcbbbaaacacdbacadcbbbbdcaaccddcdaacabbbdcaabaaabbcddaabcccdaabcdcdccccbcbbdbabcdcacbadacccbdcacdbddbbdaaccdcdaccdcbbdbcddabadcdadcbcddbcddbadbcbbacddbcabaaadaccbabdcbbbcabdaadcbaaabdcbbbabbdaccbbaaababacdabdbcbdccddbcbddcbdacddbcccbbccddddccdcbacddaacadbbadcaccbbdbdabcbaacdbbccdcddbaccaabbaccbbbcbcbbdabaaddcbdacbdcddababadadcddcccadabbdcacdcbbcddcbadbddcbcbdcaacbddbccdccbdabbbdbbcbcbccdabbcaddcdcccdcccaddcabdbabbddcabbbabbdadbcadcdccbcbcdaddadacddaaaaccbdbaaaaccdbacbacbdccdddaddabdccdbaddbaabdcdddbbcbbbbabdadddadcbbbadbabacdacbdbbacddadcbbdbadbacdabaadddbdbbaccadabaadcabddbadbaaadabacccdbdbcbaaaddbcbbbbabcbbadaaaaaddaddbdaabbcccbdaabccbcabdadddcacbaabaadbbbccddacabaccbbbacabcbbacacbbcdcbacadbcbdadbcbabaddccccdbbbbaaabcbabbdbddddbcccbbccbddcadaabdaabccbcdbcaccbabbabadabbbdcbadabadcdcbcbccbbbcddaaacdacbacacaabbdcaabbccaadcadadcbbdbaabdcdacdadccdbacbdacaaddcabbaddabcabcdbabcdacaabdbdaabcddcdccaaddabcbcdacaacbdcadadadbcbddaacccdcdaaacbadabbdcabbcadcabcccbaaababbadcacbbcdcadbccdbdacbbccadbddabaddabdbddcdccabbadbdadddbbbcdbccadcdcdbbacbdcabaccadddabcdbccddacaacccaccddacdacbddcaccabbcacabaccabbbadbdcbcaabbcaaacbaddbbaabccbabaaaccddbcdabbbbcbbbdbcddcdaccbbadadacdbaaaaabcabcabcbaacbdcddbdacaddbcacdacbbdbbbccabdcabdcbccabccbbdadbcbcdddcdccaccaaaadbcdacaccbacbcbdcdddbbaddbccbbabcacbdbaadccddacaaacdaababddddbccaccdbbcdaababbbabdadadddbabbbbdbaddddbddbbbbcdcdadbdcabbacbddbdaacabcdcaccaccddbcdbdcabbddccdbaadbdcdbbbcbabbcdadabbabaaadbdaababcdbcbacbdabdacacbdcddddbbbabcdbdbbccadaabaddabacbbbccbdddcddbdbddbbbdbabadddacccacddbbaadbcaadddacdccbddccddcaaaabcacbdcabccccaddbbddacddcddccdaadbbddbbabdddadaddacbdbaccaddcbcbcacbcdadbcabddadbbdacdacbcbaacdbbacdacccbcabbbabbbddaaabbaccbdadcbaadbadbaaccbadbcddcdababaaccbbdaacadbdaadbbcdcbaacdcdbacacbbbadcabcdcacdabccaaadbdcacbcbcaadaacacdaaabacdadbbddaacaadacbaadccadbcacacbaabddccccacbacccdadacacddcadcdacccabbcadbdacadddddacabcdaaccddaaadaacaabbbcdbcdadcdbadddbbcdcccbabaaddbdbbccdcdddbbcccbcaaadcbbccbbaabadccbbdaabbcdbbbdcbcbccbcacaadddbaacadcdbbcddcbdbcadbbcbbaaacddcacbdacbcabcdcccbcdbbdddcabcadccddbacdaabacadbcdbcdcdddbaaabbcbdddbabbccdcdbacabacadbacccbacabdcacbdcdbcbadbcabcaadaabaccbbbbcaccccdbbcbcabcbddbacbadcbabacbdaacabcbacccacddbddbbcdcaddddaddabbdbbadaacbadbacbdbaacbcadbcdaccbdbdabcacdddbccdacacddbacbbdbdbbacbaadbabcdaabbaaaccdadaddbacabaaabdabdcdabcaadbdcdacaababcdbddcdcbbdabdbaccddbadaabcdacabbddddbbadccbdaabcbbbdaccbaccdabcddbbbaadaabbaaabdbaddccaabbdbaadcabcbadcdbdbaaccbcbbdcbbdbadadacdaaabdcaddaccbcbdaccaddccbdaaaddccbbbcccbcdddccbbbbabcabdbcdddccdcbbddababdbcbacbccadbccccdaacaacdccdbccbadaddaababddcdabccadcdadccbabbaababcaddaaddadcdabbadbcbabbdbbadaadcddcdbbcdcbdcccbdbadcbbcbaddadaabbaabdbdcbaccdadddddabbcdabdcbadbaaadcbadcdbacbbbcdacadaaacdbdacddaabdccccadbbaaddbcdadcccdaccbdcdacacadcadabaaddbcacdbabdcaddddddaaadbbcbcbdbbabcabdadacdabcaaacbddccbacadaddbaaddacccddcadbaddddacbbdbddaccbcbccaaaadcabbcddcccbccaacbdcbacddabdcccabdadddbacacbddaccaacabbbccdcbaccaabccbdadcbaadbcacdcdcbbacdacdcadccbdddbdaccaabbbbdbccbacddcdaacddcabcbadabcdbbcabbbddccbdbcbdcbbdbddabbabbbdcbbaccaacaabddcacadccbcacdabbbadddcbbdcadcacdaddbdabdacbbbddbadbbbacaccdacdabccdadcdcadbccaccbbddcbbddaaccdcbcdaccbbddbaacabacdcaadcccaadacbbdaadaaddcdadababacaccabcbddbddbacdbddcbdabcbcbbdbdbbabccbadcdddacdabacdabdcccdacccbcccbbdddcdadcddacdacdbcdcadacaaaabbdabdcdabcdadccccccabbbbbcbdbbdadcddaccaccbdcdabdcbcddbccbccdadaabbacccbbbaacdcdabccdaddbdbadabcadddcbcbbcdbaccddcadabbbdbabcdbbdadbcdacadabaccadbcbddcdabbddbdddccbbdacaacacbabadaacabbcbdaaabdbadaaaacddacabbabcacadddabdcdcbbabbabbcbcadcdcbadccbacaacdddbabaddabbdbddcdabdddadbcbbaacadccdbcddddadaccadcbcbdbbaabacddcddcdcdbcdbdbbddcabcadabadbabcdbabdaadaddaaacaccadbcdbdcdcabcbbbccbbbcccbadbaabacdbdbbcdbbcaddbadbdacdcaaacbdaaaccbbacdaabdcdaadbadccccadabbcddcbbbbdabbadadcabcbbabdabbacbbcabbdbababdabacbcadadddbbbaabbdcdaabdbcbdbacbcdbbddccabaabbaaacababcaabbaccaccdacaaacbdbcbbbcdbccadadadccbcbbbbbaaabbaaaadbdcdadabaacbadddacaabcdacdaddabbbcaddddaacabadacbdbdbbcbbabbadcadabddbcadadcdbacadbabddaabacadaccbdacadabdddbccabaadbdcaddadbdacbabdddcbaabbbadbacabacbbdccaaccabcccbbdbdbdaadbdacccaabdbadadbcababadbaaacabcbcdacccabdccddcbaaccbdabbdabbddcaabbabccbdaadadcbacaababdbacddcccbdbbddccbdddbbaabbbcabcbdacacaacbabaaddcacabaddbccccddaadadabcbcbcdbbbbbadddabdcabcbacdbdaccdacbbaacccabbdbbacaaccccacaabcbddacdcaacddcbcbcbbcabccdbbaaabcccacdcabadddbbbddacdabbdaddcbdbbbbcdcdbadadaacbbddbabadcdaddaadcacdbccbbccbcbbaccbcbcaccaadabbbdcaaaabbdddadcababbbacaaadbaccbadcddddcadadabdaaabcabbbcbdcbdbcdbaaabdbcdbdbbadccdabcadaaccbcdcbbabccbacbdcddbcacacaaabdbdcdddabbadaddbabcdbaddacddadbdccbbdcbadabdccdbacabadcbabbdcbddacdaacbaddcaaaadcabdbcbacadcbdccdacabddbddbbccadbcddbccbacddbbcdbbcbcbcddacdbcdcbbdbacbcbabccbdaadbccacbbcdbdbbcdbaadbbdbadbdcaacddaaddbabdcacdccdacdababbadacadaddabcdacacccccaacbbaddabdacacadacccdacbcbbccaaccadddbddcbcdddbdcddacbdaabdacbcaaacadbabccaacccaddcdadbddadaaaccdbdcbcddbabdcdddabcbbbdaadcdbdcdccbcdacbccbacabadbbadcdabccddbcdcbadcabbdbaddcdcbdababcadbcbcaacccaccbdbbddbbcdbddbbcaccbcacdbbccdbbdddbaaabcbaccbdbbcbcaaabacddccbcbcccdbbbacacbdddbdcaacbccbacbcbabcddbabdcacabadbcbaccdbdbabadcccbbadaaddadbcccdacbbddcbbabcdbaabbdbababdaabcbbbcbdaababcadbbbacaddbcccddbbbdcabdcabacadddccdccddabdbddddadabdaddbdbdddaabbabbaabababbbbbcddcabcacbacdaaabcabbbcaaabacbdabdadadcaccacdacddbadbcabbdcdccdddbaddddcbdbdadccdcdbbbcdddddcdcaacbdbaaadabcbcddacbadcdddbcbddcacdabcdddcabdabdddcacadcaddcadbdcbddccbdabdaccaabbdbdddaccbaaccbacdbbbbabdbcddaabbcabbccdcbddadabadbaabddcddbddbaaadbacbbdbacdbadddbadbcdcadcccbcaaddaccccdcbbacccacdabaabdddddbcacaaaadaddbbbcabacaadccdcdacccdcacadbdbccdbcacaddbddcdcdcccbaddcaabdbdcadccdbbaacdbbcaddbccaabaabbdaaaaccbcdacdadddcdcbccccabccbbacdbbbbbcbdbccacbdbdcbbacabacbcadabbcbdaabbddcdbacddbacdccbdbaacccddccaddacabaacadabccdbddababdccbdbadcdacadabcdadbdbcbacbdbaccacdaaabbaadaabcaacaaabbbababaddcbadbdcdcbbaabdadbbcbddddccccbaddccbadbdbccbbcadabcdbaabcccdcaadaabacbdbaadaddbbdbbaabccddcbdaacddbaabbaaadddadacacaddbcbaadbdcbbdadbccddcdccaaabadbabddabaddbcbbcaddcadbbaadcbcaaddccaadabccaadbcbcbcaddadbbdcdcdbccadadbbdbbbccbabcacdbcdbbbbbdaadcacdbbdbcddbbcbaaadbcbbcdbbcccccbbaddccbcaadacdbdbdbcbdadcddadcaacdaabdcaabbabbbddadaabcccdbdadaacababbabcadccbabdbdbdbddcacbcadacacddaaccddaaccabccdbadddcacaddcddaacbaaaddddbaccdaadaadbacbacabdbadccdcdccbbdbaddbdcdbaacbbbbbbbacbbadcbccacdcdccbbdbccdbacabbdaaacadcbcccaddcdcccbabadadcccddaaccaabbdcaccaaabdbbbdadaacdcadaababccacbbabdbbcdddaaacdabbdbcbcbdbcdaaccdbbabccdaccadcccbadadadabdaddbacdccadabcbbcdaddcbcadcdcaababcdcbdcdadbccccaadcaaccabcbcdddbbaaccdbadbcdabaccabdcdbccddbadabdacaabbbcbbdcdbcadcddaadbacbccbbbababdbcdadccadbcbdddadccacdbcdaabddbadaacbacbadbbccaaccdcacddbaacddcbdcacdbdcdcddbcaacdcaabadbcadcbdbdaaddcddabbbacbacabbabadcaabadbdbabbcadabcacdbccdbadcababddbcdbacbadadadacdaaadcddaabbaaabacbbcadbadcabcdbbcdabccbbdcabcadcccdcadbdbcbccdadcabbdbcadaddcdcaabdcabbcdcbadbadcdaabcbcaaacbddcbbbbababdbcbabcbdcbbadcdbabcaddccbadbabadcdaabccaabdccdadcddcaacaddddccccbdbbabacdbbcbcdcbbbaddcaaabbdbddccaadccddcdabcddbccacddacbbbcadacbaddbbbaadacacaacdcaababdaccaacbabcadaadccdaaacbdbaadbbadcadbbbcbabbccabacdcadacdcdaaaaccdadcdcabbbdbacdcdbaddcabcdcaaddbdabbdacccccbbcdddcdcdccbbdaabdbbcacbcdbabacddbbcdaaaddacaaddcbcbabdcdcaccbabbcdabaaadaddbccdaadddcccccbbcccbbabadaccbadccbcadcddacbbcdbcdcccccdaaddbdcbbacaddadaadbcccadcbbdcbabccbaacaccadbaccacabaabdccddccbadbddddacbddcddacdbddcadbacdbcdccbaadbaaacacdabccdadbaaaabdbabcdaabcdcadbabbadddcbcccbabdcabdadddbbcbabababccaadbacbcddabccababcaacdcdbbbaabcdabbcbbdcdcadcbbaaaadbbadbabdcccbabbbdbddaddbbdbbcbcddacbdacabcddbdcbccbbdbbbacbcccddbbdbadabccacdbcaccdabcdbabdbadccdcdbcdcbdacbabacddbacaaadcdabcabadcbcbcdcabbbdbdbaacdabaabbcdcbddadbdbdcabdccccbabddddcbddaababbbaccbbcbbccbbbaddadaadcabddbcddbadbcbbdccbdcdbaaabcdccdbbbacaddbdcaadbcabdbbcacdbbbaacadbbccadaddcaabcadbcbaadcadcaabdcbdcdcbaaaabbbdcababccbccccbbbccaaabddcabdbdbccaddcbaaacccdddbcabccbbddcccdadabdcabbbdaddcabdaadcdabbdccbcdbcaadaacbabaabdaacdaccbaaccbddbcdcdcadccbbbcbdddaaacdbcbbadddbccdabbccbacdcbbcabadbcdbacbaaadacdcddcaadbdaddbdaddbbdbcadadcaccccdabdcbabacbccbaabaabcbabbcdbdbbdadcdbaaacccccabbdccbaadcdbacccbaabacaaacdbababadabcadaaaacadcdacdddbcddaccbadbacbabdbccddadaaccadacabbccccaadcdcacbdcadbbbcaddbdcadbcbcdaacdcbdaaaabdadbcbbdcdcbaccaccccbdccbdabbaaddbbacacddddadacaddaaaacabcbacabccabbcddcbdaabdadbbacdddacdcddbdddbbcdadcdcdbcdccbaacdbcadccacbdbccdaaccdcaddbcbbccdaaddabddaaabaaccaccbbbddcaadbccbcabbbbccaabccccabbbbbdbdcabdcdbcdadbdcbcabbcbbbadcbdaabaddbadadaaaadccdaadcdddaabdbbabacbadacbaccdabacdcdccbaaaaabcddaccacdabacdaacbdcdbccdaacbbcdbdbbbadcbbddbdacdcbbdddacddaadccbbbbaaacabadbaaaddbbadadcdaacccbadbadbdabccdaacbddcadababcabbdacbcadcbacbdadcdabcbccaaadbcaabddcdcdbcccadcaacdabdbcccaddacbcaaaaccdcbaddcbdcadabdcdbaabcadccccdacaabbbbbcbadbcaaacdacacabcddacdadbcddbbbbcdcbbacdaabcaddadccacdcccbdbbbccbbcdbbcdaabdadcccbacadaddbdbccabdaccdcbcddcdaabbabaadaaddaddacacbddabadcdbacaabbbadcccbcacabbbcdbccbbdaddabcacbbddcbdddbabdccdaabcdaddacaaddbdccbaadbdbbbaddabbabdabadabccabcbccbdbcbbbcbcabadacacaacababacbaadbbdcdadcdcdbabddbacdccadacbaacddccababbaaadacdaaccbdcccbdbacbbcbbabbadabdccdcdaadbaabbddbacadbdbdbabdbdacbcbdcdbadbacabcdcaccaaccdacccbacbdaacddcdaacacaacbcbabdbcaabbbbbcaacdbbbdbdcdbacddcaaaacdddaabdadbaaadccdabdbdbbacddcddbcddbdacacaaabdbdddabbdcbcabbcaaaccabbaabcabcccdcbdbdbbbbbbadcbbcabccccbbdabccabccddddbcdcdccbdccdcadabccacaccddbbbbacdbbdcbacbdbcbdcbcdabadcbbbcabcccbccbdbabcccbbacddcaacaccaabacbbbbdcabbddbbddcbaabaadbdcabcabadaddaadbaabbbbbbadaaaddcccddaddabdbccdbbabcbabbbcaddbbdcadabbbbcbddcdaccbdaadaccadaccccacabdacdddccbbacabbdbbbcbcddbbdcdcabcbcaacbbcacaddcbcbccdbbdaacbbbbdabbabcadbbacbcbacaabbcaabddacabcaddcdcabadbdbdbababdbbaadbdcbbbddccccdacdadbdbdddacaacddbabcdaadbdcddbbbbbdcacccddcbbabbbdaaaacabdaadcdaadcdadcdddaaadabaadbbbbdccbcdaddddababccbcdccbbbcccddaabbdbaddacabbbccadadcbacadbacbdbdccdcadadcbdcadaadcbbcdaacbbbcacbcbcbcdacbcddccacdddccdbaccdcdaddabcadbaacbcbcccacaccacaadaaaccbdcbbbabadbdcacbdbcbdbccadcdbcdaadadbddcacdbaddababbcdaddcabacccabbbddbdbdcddbbdbdcaccdcbbdadcababdadbadddddacdcdccacbccddbcbcddbcdddacdcbcdcdcbbbbccbcdadadadddbcdcbadaabcbabdcbddbdbaacabdbacaddaabbabbddaabccccbbccbabdacbdcbaacbbbcddbcacaaadccccddcdabdcdbadcdbddcdddbbbabbdabcbdbbcbcddadcdbbabbddaaacabdadccbcaaadacadbaadbbbbadcbdaaadbbdbdacddbadabbdbdcccacddcdcbcaadadcdbdcdccddbdacbbccacabcbbddacbcabbbccdadccadadbdbbbbdcdacccdacabaacdabbcaddcddaadcacbbccdadacbacbcbbaacbadbabcbbbdcabadabcdbaabadabaadadbbcdaacdcadadbdcdcdadbbbabbdcccaabddbabbccbbabbbbccaabaabbacaaaadccbbbbdabcacdaadbbdcccdcbaaddbccdacccbbbbdbbacbdcdcbbddacaadadadcadcabaddbdbdbaabbabcddbcdcbcdbaabbbcdacabdbddbabbabbbcaccabdbbdcdabadcdaacbadcdccadbbabcdacacaacbbaaaadadacdaccbddbbdcdcddbcbcbaacbacbacbcbbabaaadacbdcbaabbcabcaddbddcbbdbaccbabadcbcddbccbaabbdbbbdcbcdbdbddcabcdcdbacdcadcaababcbcabcccdccababacddcaaabcdcaabdcbcbaaddadaabadddbbbdbcdbbcdbbcddabbbcabbaddcbcabddbacdadacdcdbabcadbcacddbcddbacadaaacdcaabdabcdddbabacbacdccaababcbcdbcaddbbdbaabaddccdccbbcaaaccddaccdbdbadbcdcacbbbcbdbbccdaaaabacacadadcabcccbddbacabbbccaaabddbccbabcdabaddcbcdbdadccacbccaccdddbddbbdcabbddcadcdcdcddccadcbdabacbccadbdabcdccabbabccccccabccbbbaacccccaadbaacbacdcdbaacdbacddcdaaddddcaccabacbdcacbbacabdcdbadcbccbbbbccaabbdbcbacbbdbaacbddadadcbabbdcadbddcbcdcbccdcaabcdabbbbcacadaccaacccdbbaddbdcdddbdabcbcbcdabaadbcaaccabdcbdbcddccdcddaaaaaaabbdbdcaddaaacaacaabddcaadddabdbcddddcccabbdbbddccabdabdcddaaccbbbcdbbaacaccbdcdccbccaacbadaaabddddbaddadcbbaadcbacbcbdddcadbacddbdacbbccbadaccadadcaaadadbdcadacbbcbdddacdadbdddbdddaaaacbcddcbadaccdcbdbcaaadacbdcacdbbabaadccacbdcabcccbaabacbababdcbabbbbcdaaacdaaabdadacbbbadbbddcddccbacaabdccdbbcadddabbcabdccbabccabaabdcccdbccdbbbbaaaccdaddacbccdccbbdadbdccddacacabdcacadabbbacdbbddadbaabdcdccabbcbdaccbcccbdacdcbcdacbdbbbcabcaaabbbaaabbbbcbccdcdcbabcbadbabdccdabbdabadcadbdabdbcdabbadbdddcadbadadbbcabaacabcacdcacbcccabaccdcaaacdbbddaaddbdcdccbacdcdcdbbdccdababbccdddbcdabbaabadbdbdbbaacdadcdadddbacaccbdccbbdbbaaacbcadaababbbabacdaddacbadbcabacbcabbcbcbbcabcadbaaddcbabaaabddccacadddaccbaddbbadccbdccbcdbbcbaadabdbbbcbcdcddbaacccdacddbddaaddccddcaabdadcdbabbaddcdabbdbbcdaadacdaacdbddaadcdadadccbddcabbaacccbdccbcbbddcdbaddadbcbdbabcdcaddadbdacaddbcbaababbacbacdadbcdccbbdaacbddadaddcccbacddadaaccbcccdabaacbdbbddaabacbbcccaacacbaabccbccadbcdaacacacacaaadccbcbaddcbdcabcbbdacbcccddbbacbdadcaadbcadabadbdbadacdacdadcdcbbdcdcbbacaccbaaccdcbbdabcdddddabccddccaabddbbbdabccadabcabddbbcaabadacaaddaaddcbdbacbcccbabaaccaaabaccdbddaacbdbaddccbbdabbcdcddbcabbdbccabdacbaadcdbdabbdcddcdcaaaddcdcdacadacaadccdcbacdbbccbacdddacbcbcaccddadbabccddbcaabdabcdbcccdcacccbbbbaaadddcabbadabcaccdcadadbdacdbaacddccbcbdcabbbbdbcccabbddadcaadbdbbbdaddcbdbdaaddaddbbadbdabcaaacbbaadadadcdcddacccbcddcbbcbacbcaabbccbcaaccacbdcaddabbaabaaaaaccddcbcddbcbcdddacdacddabbabdbaacdbdbbbaddcdacdbbdacaccdbabcbcddddabbccbacccbcbbdcbccdaccbabbcabbcdbdadbdbcaaddbcacdaabababbcbbacadbbdcabbbdaacbdabbabaadccdcdcbdaddcbcddbbaaacdcaaddaaccccccacdadcdbbabddaadbaaacadbcacaadbabcaacacccabbbbbccdaddcaccabddaaaddcacbbbacdccadbacacccbcbdccccadccabdacdbbcbbaababdcccbaacdccdcbcdacdbcaabdababdbcdddcbbaacabddbaabbbbaaacaabaaabacdcdabaabccadcdddaadacdabccccbbdddbcaaaadcadcacacdbdcdaaddddccdbacdcbacdcdabdacdbcddcccdadacdadaadaddbdbcbcdadbabdcbacdacaadcbbaacbdbbdcdcbdcacbdbabdccdacabdbbcddcdbadabaadcabdaccbdcbbddcbcbdbbbaddacdcdacddcacccabbabacbcccdaadcccdbdabbaabdcdbacdcbabcaaaaabdbcbdaccaaddabaadcbabddadacabbaacccabdddbcacbdaadbbdacccadbacbddbcaaaaccabcdddccaaacaabcbcccacddddccdbabbdbbbbbbddacbdbdcddcbcbddbcddbbaaadbcabbdabddcbcbccadaacdcdcbdcbcbbddbacbbbbbaddbbabccdacdbcbcddbacdbdccabadbadbabddddbbcbbadabdadbabdcdcbdcdacaadacabdadbbbdbadccacabdcddcbbddcdcbbbaacbbcaacbdabbddacacbbcbdcadbddcacbdaccbbdddabccdcacaaacaddcaaaddadacddccdbacddcdcadabddbbcccabbadbaacbdaadaccbbabcdbabbabbdbadbababbdbaaddccaaacdcdbdcacabdbabcbcbcdccabcaadcadaadcbcdccccbcdcabadbadcabcabadaabddbacdcccbbaabbdcaaabccddccbdccdaabdaccccdadbddbdcaacdcdabbbaabddaaddcdddddabdcaadabdbcdbcadacccaaabaccbbdaaaacacdbccbadbcbbcbcccacacccdbcbdbccccbdaadbdddaaaaaaabcacadccbdcddaaabddacdbdbcbdbcdadddbccdaaaaabadaadbccddccdbdcccaadaccabcadddaacacccdcdabbcababbabacbddbcbaaccaccbabcdcccbbbccbcdcacbcbaacbdbcaaaabdbaccdddabcddbbbdbcabacccdcbaddaaadcccdccdadbddcadabccccdaabbbbcaaabbaaacabbdcbbbdbbdcaaacaabdaaacbdaabaaddacbdbdacddadabdcdcbcdbacdaddbbbdbdcadcadaabaaaadcddbccddcabddccdcdddddcdcdcbdadddbabbbcddcadaacbcdcddbdbcbabcadbbbddacabccdacaddbdadbdbdcbaaaaacbccaabacdaabadbaacacddcbcadabddcdaadacccdbdacbacdccdbadbcbdaaaddabadcccbbaaaaaabdaaadacdaacccbabccadccddaadadcbbaddcabbcadabdbdacbabaccacbbacbdadbaccdaccbddcbaccbaccabdbdccdcabbbbccaaadacacacadcaacdcabbbadaacbccaccbdabaccddbaabacdaaadcbcadbbaaccdbbcadabcaaabdbbdcccdcabcbcaadaabcdadabddcbdabdbdcaddcdbdbaabddcaabcacccdcbcbdccaddaddbaaccdcbbddccacacdbaccbcbcacababddcacdbccdaadddaccbdadcbcdcbccccbccbbdcacbdabbbcdaabbcdbbbbcadadaccdbacadbacbccadbdbdabdacbadaaacdaadccdbdbcdabbaccccdcaabbbbaadcdadbdcbbdaccbabdaaaccacbbdbcbbaacabcdabcccadbcaddbabdabbdbaadaacdcdbbbbccdacaccdbccacbdadddbbbbdbacbbbccaaacdccabbacdcbdccadacaabaddbbaaababcacddcccbaababbbdcaabbdaabcccadbacbadcbdddbaaacbacdbddaddbdcbbdaabcdcdaddcbcbddddabbcacbadaabcdccbdacddccccaaccadcbbbbcadddbcadbccdcabddaccddbdadacccabcbabaabcddbbdccabcdcbabacbdcadcdaaddaacdbabaadbdcabacaadbbcacacbacdbbaaddbcbdbbccacacccaaddcdacbbddacdadcdddcdbdbbdacdbdcadccbaddaccaaddbbbccbbadaddacdddcccdbcbcbcdcdbbbcadbddacadbddbbabbbcdbddcabaaacdcbccaacabddbbbcccdcdaddbccbdadccbbbbdbadccbcdddadabbdbcccbacbdcbddbdbdcdbbdaadacbcbccaaabccacabaabcccadcbddaaadcabbcadcabcddbcccccbbbadabaddcadbdabbbbdabacccacbbcacbdbddccaaadadbdaaaaadbcbaccccbdadbbbacddcadddabccbaacddaacdabbaaacbcccabcaddaadcdcdadcabdaaccacacdddcadbaccabbddacabcbcbbddadabccbdbcdaaddabcbcbbabadbdaaaccdddddddabaddabddabacaddccdbccacbddadbccbaaacabbacabbdcbccaacdddcdccdddcbdcacabbccbdbcdbbbcbcabbcabddaabbabbbacbbadbcabacbdbdbbcaaaacbadccbdaabbdaaaabbbddbddcbbdaadabbbdcacdcaaaccdbbdcdbcdbcdcbaccbcddcdbaaabdcddacdbdacccacdccbdacbbddacacdacabbdacdadbaaacabdababcdbbdddcdcddbaabdcaacdccbdbadccbdbabcbcdcbbbdbccbdacdacadcacdbddacbdddcbcaccbabacbdcacddbdacabbdabacdbabaddaadcacadbdbbdddbbcaacdbaadbcbdacbadabaabbadaccdadbabbadddcdcaadccaadaddacacdbbcddbaabddbdabdcbbcccdaaadbddcbcbcdddcdacbbbbbbbacbbdabdaaaaddccccddaccccadccbabbcbccccccbcdcdbccbdcbccdaadddaabdccdbacdddabdbdaacadcbacbaacacabdadaadadbbddbdbabddddaadacacdaacdcadbaadddbbabdcabbbadcacbcbdaacbcdccaddabdbdccadbadaacabcaadacccbbddddbaccdadccaacadbbbccdaddaccbccdbddbccddcbcabdbacdbbdabbccccbcbdaddbabbabadddcccddccbcdabacadacabaabcccadcbbcddccadbbaddcbcadaaadbcacbadcbddddbcabbcbbdccbdbcbbabdbdbcbcccabccccbcdbaacaacdabadddbcccbddbdcbbdadcbabbbcbdbccdabdaacdcbdabbbddbbdcccabaddddbccbcbcdbabbcdbcdddcaaababadcadabadcacdccdcdcccbacacdacadbcbacacccacccccbaaddacddbdbdabcaabadaddbddddaccdbabaccbdcccdccbccdbcabdabbaabbbcdddaddccbcddbccbbcaabadaaadcaccdddbbdbdbdaccbacdcbdbbadccaabbcbcbbcdcdcacadcdadddddcadbddaaccddacdccbcdabcabcdacdbdabaccbccdbbaddbbddbcadaddcaddadccabcdcddcbbabccabbadcbbdadacbddacdabbdbabbcaacabbcdccccabbdddccaccabbcbbaddbcbbacbdddadbddcadbaaadcaddcabadcaadbbcbccbddccbdabbcaadcbadcddbcdbdbcadbdccddaaabacdbdcbbccbabbabdcdbacacbacacbcbbdacaaacaadccdccccdcdbccbbbdaacddaadbcbaadadbbadaddaabccacccacaaccaaadbccbbcabaabacdbdbaccdbdcbadabbbbaacddbdcdcacdccdbbcdacdcdcadadbccbdcdcbbcbdaacdcccadaaabbdbabccdddaadcccbacacbdcbdbbbcdaaaacccaddbcbccadcbbbcacbaaaaabbbbbcbadcbbbddccdacabdcbbabadcdcdbbbcabdcccddcadacdbcaaaacdacaacbadddcccaccddcadbbdcacbcdbaaabbccacaadcbcdacbdacbddaabdbbdcadbcbbbaddacdcbcbcaabdcaacadbbbdcddccaabaccbdbccaddbcbaaabcccdadccddcaadccccccaaacdcccbddbbdbaaddaddbabaaabdccdcccddbdaadbadddbbbbbccdcbbdbbccdcadaacddccbcabcddadbbcbacdbaccdcbcacdcbaacadbcccaabcddbbcadcadacbcdccddaccacbdcdcdaababcdbbadbaccbdbcbabccdadaaddaccabdccbaaaaadaacaadbcbbbcabdccdbaaddccdcddbbaadbdabddddbbdbadcdbabacaaadbacbdbaaadccacdbbdabcabbbcccbcddbdbbacbcaadaabddacdacabadabadbaaacacabcbdababacbacccdcaaccdbdcbacdaadaaddcdbddaccadccbcadbdaadaddaaabbbbcadabddbbdbacbbabbacaaddbcabbcdabdaadabbdcbccdbcabbabacdadcabacbdbabaadccadacbacadbdccbbdadcdcabcadcadcaadaaddddbabcbabadacdbdbaddbcccdacdcdcadccacccdddacdcbaddbbcddaabbcddbdddaadabdcbacdbdbdcdcdaabdccadaadddcdbbaaacdaddcbacdbdccdcadbddcdabbdcabbbadabaabddbdbdabccbcbabacbddabbadcdcbdcadcdbbdaaccdbdcbcdacdcaddbaabcccaccbcabddbdacccdabccbdcaabdabbcacddbbbacbbbdaabcdbbadbbaddadacdbbcbabbaddbbbbcaadcbcbdcbdaddcdddacccdddacbccdcbcaccaabacdbaabaabccdbcbdccbcbbaabadcccdbcddabbddadbaaacdddacddabbcccbdccabaaaabdacdaabdabbacbdaaaabdbbccdccaacadbddbbbdadaccccdbcacbbacdcdbcbcaddbabbcbdbbacdcdaaaaccbccbaabdacbabcabadbadadddbddcddaaaadcacaadbdbbdcddadcbacabdbdacdacdcdcddddcbaddcaacacaaabbddbdcccdbbbdcbbdcdcdccbcabcccbdcdcbdbbabaaababcccaacdcdbddbccbbbaabbadbcdccadbdbbbbcdaadbddcbadcaccccccdbdabbaccddabbbcbccbbbddccdabccbbbdbbddcbdbabbaacbbddddcaabbbcaaacbaddadbccbcdabddadacabcacdcdccdbbbcacbbbbcdbaabdbccdabdccdcccaadddacbbcbcabadababcbdcdbdbccbaddbcdbccacbbabdcbdbabcccbaadcabaabaadccbccccbdcdbcbadaddacddcdaccdbdbcccbbccbcdcadabdabacddddbacbbdcdbdadadbbddacdddadbdaddaabaddbcaaaccbadabbdbcdadbbacbbaacaadccaadbdaaacadadbccbdcdbadadacbdbddbabaccccddadbacaacabcaadaccbbdcbacacaabdbddccadadddddaacbdbdcacbdbbbcabddbdabaabbbddbdbdddbacabcbabddbcbddbdabbabdcccdadaabcabbccadcaadbabcbbdacadbaacadcacbcdadcacacccaccabbdcbabaccadccbdbdcbbddbdcdabdadaddbdabadcbbdabaacadccbdbdbcaabadadcbaccbcabbbabadcaccdaddabcdaabdbacbabcbdccadbdbdabdcdbacdbabbdcdadbbaaaadabbbcacdcacdbabaddcbabbcbdbaabbddaccbcaacbadbabbbcdbdacccdadaccbcbdccaadbdcdccddaabcaadbccbddccacdccbccaccddcccbbccdcccabbbbbcaaddabbccbbcbbbbcbbbdcdcdcdcbcdbacadaaddbccbccdcbcbbaadbdccdcdcbbdbdcdaacdbbcacccbcdbbbcacacddadbcbccacdbbbacbaaddbdbcccdbcdcbacbbccdcadacbbcdcdcabcabbabaacddbbabadbadcbaabcabbcadbdbdbabbdddaccbaaabbcddcbdcddacdccddacdadccdaadcbaaacdbbaabaababcdddadacbbaacacddaabadcaaccacdabcdbadbbdcbbcabbacdcaaddacddcaccddbbcddddbbdaadbaddbadaddbbacbddaaadbcccacabbaabadaddbbcaadccbabbbaccbddbabbbcddcccacbccdaddadcaacbdaddcdcbcbdcddbbcacadddbccabccdbdcacbaccdddcccdbacbddaadbbacbccbabbdacccabbdbbcbcdabacabbbcdacdbdbccdbddaccbbdadbdbddaccbcabcacccbbadaaabdaddbbadccbaccdccdddacacadddddcdcbdbdacacbabcbacbbbcacccbbcdbadbdabdadcddbdaccacdcdcbdbbbdbccdadbbcdcdaabacccdabdbabacaabdbcdaabcaccbcddcbccdaacdacdcbbcbbcacaaadccbaaacadddababcdccaacbaadbabbabdcdaddadbaadabcbacaadbddbbabcbdaacccadcabdcacbbdddcddabcaaabbccdbbccdcbcacdcccadcbbcadcddbdcabbabbbcddbcbbaccacdbabcbcdbdbaddcbacadddabdccacdbddcdbdbbabddbcccbcbdabadaaccaacdddcddcdcbabdadcdbdccdbdddbbbbcacdcbbddbdcabccbcbcdbdabccdacacbbdaaabaccaadcadbdbdbdabddabdcbdbbcabbdcdccdaaaadcdabbcddabbccbadbacaadaaaabcddcabdabacbacbbcddadbbdcacddddcbdaddcbbabaccdaadbddbaccbddccbacbbcccdbabbdacbcdabccaccbaaccaaccbcdbaaacbcbadaaadcddabcbbcdbdacabcbacabaadbbdabaaaaacabccacadcbacadacdadbdbcdaacbbdacbbbdadacbbbcdbcbbacccabccbddabcddadadbcbbdacdbbdbaabdcdcccddbcacccdcbaadddcddbcaadabbccaddbbadcdccbccdccdabbcbbcbddabccbdcdbcccbaccadaacbcbbbbabbdcabcbbaaddabadcddccddaccaabacdbaaacadddcadcdcaccbbadabcbcddbdabbabdacddcbabaababdcbabcacacabcadcddcabddabddcadbcadacdacddbcdabcccbddbdacdacddbbcdacdbccaacbcdaadaacbbacadaaacdabccdbcdccdbaaacdbdbccabcbadabddbadbbaadcacaaccdbcdbbccabcabddabdbbadbcabbacabaaddddcccddadbacdaacacbbdaaddcaaccdcdbbbbbaaaddbcbcbcacabbccbbdbbadabbacbccdbdaddabacdcbbbcbdabbcaddbcaabcaccbdbbaddcbdddcabdccbccbdadacbacdcaccdacdaaddcabdaddaacdcbbaddcacdbbdbbbbdbcbcacaddcbddddbbacbddacabcccaaaadbccabacabcaddcbddcdcdaccbddbaacdbaadbaddcccdbcaabbaddbdbcccaadadbcccacabccccccaabcabaccacdcddbabdbddbbbdbaaabdadabbdbdcdaacdcbadbbaacbddddabdbabdaadacbcadcddccccdaaadddacbdadcaabbcbddbbdadddadbcbbccacccacbdaabbdaccdbcdbdabbcddcbdddcdbbdddbbddacaaacdadddacbabbdccdccdbdaccabbccccbdcccccccbadcbdabcddadadbccdbbacbbdcaaaabcdaccddacdbcaabbbcbddbdabbdcbdacbaaddaccdbcdbcbdacdadcabdbddaaddacddcbbdbcbcbaaacbbbbdcbddabacaadcdbdbdcacdddbacbdbbdacbdccddbbaabbaabaadacddbcbcbbadcbbdddacddcadbcccbdabcdbdcdbadcabcbdabbcabaccdadadaabdcadcadcddcccbadcbccaccbcdbaadcabdbdbcddcdbaacbbbbbadbbbadbbbbacaaccdabaaaccaccbdcbdabcadcdddbdbcdddacdcbabaaaaacdcbcccbdcdbadbbdabbddcccbaddaabbdbccddadcdbbcccdaaabdcbadcadaddcabdbbdbaadddcccadbdcacdddccddcacacdcdcdadaadabdcbbaadaccbbcdbcadbacccadcdcaadadcacccabcddadcadccdddbdbdadcaddcdacdabcdcadcabbaadcadbaaccbadaabbcddbabbbcbcdccccdccadabadbbdacbbacbccabcbddacbcbaddadddccaabddbbcabdaabdccabccccddccaacabcbadbbbadbabdcdcbcbacbabcccdcdbdabddacddcacabbcbcdddcabdcddccbdbcdddcabacacadaddcaacccbbbabddddcaccdcbbbbbabbcbbdabbbcddabbabbbcdbcdbcdbbdbaabbaaaaadbbadddadadbacdbabdccbcbabadacbaccadbbcccbdbbaaadabdabbcabcdddcbabcdcdabcddbbacabddbccccdcddcabcbdadadadcdacadcaddccaadbadbcabaabdcacdabcddbcdabbdbbabbbbcddbddaabdddabbcabadcdccbdcddbcaacbbbbdcdadaadcdaacaddadbccaaaabdbccbccbdcacccbadcabbcadcaacddccadaaabbbcdcbacadbbddcdcccabdcbadccdbcbdadaadccbccaaacaabdbdbbacadadabbcdbddccabccccccdcbaccbacbdaaaddbabbcccdabdadcabdcbbbacbbcbabaacdddabbadcadbaaccacddcbbbabadbdacdcbbdcdccadcdadcdacdadaabcaacdbdabdcbcabaaabaaacadcbbabbabdadcbaabaddccdbababcaabddbbbcdacbdaaadddacbdddbbcaccaddacbdcdacbacbababacdacdabdcdbcdccaabbadadcdbcbccddaacccdbcdcbdacbccaacddcdccbacdabbdcbadddacddaaccbdbbcdaadccccbdbdbddbaabcbccbaaaaabbdbabbdacdadbbabaddbcaaacadbacacabbcdbacccbddddbaaccdadcbddbcbbcbdbbabdacdbcaddadddcaadbcabcdddcadccbdadcdccaacdbdadcccdacbdcbcaaabbdabddccdbbacdbbdccbdabadcbddadccacbbaadadadacdadabbccabacdaccadcabbdcbccaabcdaabcddadccaaccccabbcdcddadcbababacbaabddbdccbbaacbdddccdabcdaaadaabbaabdacdaddabdcbbccdcbaaddacddbdcbbcabcbddddbbcdcdcbdcdaabadbaadaaddddbddcdaccdaaadbddcdccadbdababdacaabdbcabbdccaadbadcabdbbbccbbbdcaacdcddcbdcdddcbdcdadbdbbabdabbdbbcbdcaabdabaabacaaaadabdaabaabcdbbdabdcdbbabaaacbbabaaacbbddabadbdadadcbdadadacadcbacaacdbabbbdaadbadbdabcdcccbbacaabbddacbcbdcbddccaddcaaaaabdcdcccaccddcacdaaabcaacaccaabaabcaabddabccdbcadcabadaaddabddbdcbadabddbadbcacccdabcabdbdadcdabadcadbaabcaddcbdaabbadcbdabdaaacbdbdbbcbcbbcbddaddbcabbbdaaccdbccbaaaadcdcbcbdbddbbbbcccccaabaadcadabbadccbbdcbdcbacabacaccbdaddddbcbdddbccaddddacaadbbdbdacacaacacbcaadcccccccddccbadabaccabcdbbccdcaadadbbcdccccccacddcbbcdcaddbdadddddacbcbbdadaccdcaacbdcadccaabadcabccaddaabdacadbabbbbcacbdbccccadccaaacbdadbddaaadcacbddcddcbdbdcaabcbdacddddcddadbcdabdccabdbdacdabbabbbdaacbbddbcddabbcdcbbaabbccdaccdabbbacdbcadaaccbddaadccbbdbcbccaacbacacbcdcddcadacabdabcbaaadabcdbdadcaaddcbcddddbacddacabadaaadbaacacadcddcaabccbdccddbaddcadbaadcccacccbdccbdacddbbccdaccabbdccbcdbdabcdbbcadccddadaacdbacaddcadbbabcaaadccbbcdbdcbdabdbaaddbabdcbbddacbdaaabdaadcccdccddbbbacabaddcbaadcadcaabcbdacaddbbddaaddaabbdbdacdadabaadbbdcadbcccccaccabdcdadbdbbabcabcaadababaddddaadccabdddbcbccbbaabbddccdacdacaaabbabbacacabcbcbbbdbcbcddbadbcaaabacbabaaaaacdddaadcdcdaddadbbacbdcdccaacdcadcbdbbadccabbdcadcacccbccddbabcadbddcaaabacaddacbabddddacdbcddadbababcbcbbcbbcaabdcdbcbddddcbddcbcaaacbdbadcbccbbdcdadddacdbadabdccabaaddaaacdbdaddcbdacbcacaabaabbabdccbabaccdbcdbcccddbcbddcaadcabdacbdabbaadaabbdbbdababdbaccdbbbcddbbcbcdddabdcacddaaccadbabdccccccdbbbbacbbcbdcccdaabbbaadcaacaccaadbcbacabacddcccaddcbabbdbbbbbadacaadacbcbdbcbacbbdadbadddbdacdcbddabbddccaadababdbadabdddadbabaddbbcabaaddcaacccabcdcbbaccbdaabcacbdbbddcbaddaaadabaacdbdcccdcbbacbbdbcdcabcdbadcdabbcababcbdadbabbdbcddddbdcbcddbbdbcadbdabadadaadaacbaadaadacbbcbacbcadbdbabbddacdbcccbacaacadabbabaadbaaadbaccaddaccabbcbbdbabbcbbabbcbcbaccaadabdcaaccddabdacdbcdabbbbccdabbbbccabcccdbaaddcccacadaadaadacdcbcbbbcbcacbdbbddcccaabddbcbcabbbacbdcdcdbdacbbccbbabdbcadacbdaabdaabddccacabaddcccadcdbabdaddadaccadaabadcbcacabbddcbbbaadcabcccbcaccadddccaabbcbaaababcaacddbdaaabdcacdacccddabcaacacaaabacaadbadbdbccdabaadccddbbbbacdbdccddbbdbaddaccaacbbbbcbacdacaaccdabdbdaadaabcbabdbbbabdbcbacdcddadbdccaadcbcddbcabacabbccdcddbddabdabbdbddbbabccddacaddbdabbdacccccbbdbddabdbbddddaabbacddccbadadaaabcdddbcabcdcacdcbcdaaaccccacacdcccddaabbbbcbcdbabdaccaddbccddaabbcdccabbabbdcbbabadacdcdbcddbcbcbdadadadadcadcddbcbadadddddcacdcbadddcddcaabdbccdbabbcabbcadbacdadcbadbcacaddcddcddccbcaddcaababadbacabbabccabcccbcbbacdacccacbcaacabcdbdaacbdaadadaaabcabdcdbcbaddbcbddddacabcbbbaadcaadadbabddacbdbcdacdbcbdcaabaacdabdaabbadbbaacabbdcbbbdcadbaacbddbbbabddcdcbddacabcbbdaaccbbdaaacacbcaabdcdbccabbcddcdaaaccadaadaaadcbbbbadadcbccdcdbdcdbddbcbdaabbdcaacabcabbacadcaabbdcbbdcbdadbbdabaadadaacabadcacbaabbdaccabcbdadccaaadbdcdaacdbbabbcbbcbdaaacadccbbbbdcdcacbbbdcccaadccdaadaccdccdcddaadcccccbbcaaaacdcdaddadacdaadaacdadbadacbcdbbdabbdbdcdccddabadaadccdcbdbdbddcdacabdccdadcaadaabbaacbbaccdacaaaaaaddacabddbdadbddcbddbbddccdcdcbbbcbcbbcbbdaabdacabdcbdabcbbbcdcbadcdbcbcdcbbcdcacbaacdaadbddbaaabdddcddddbbbacccaadadddbccbadccdabdddcbbadbbaddaddaadbbddcbbdcabaddddabbadaaccdcacdaabcbcdbabdacacadbdacbaccacaabcadaacacadcaadcabdcccbbcbacdbdbbcccbcacddccbdbddabcbdabddccccbcadbbdbcaabbbaccbabacabacbbbaddbadacdabccdaadacdcaccadddcaacbccdadbcbcdddddbbbbdbbcacccdcadadbddcdcddacbcacdaccabaacbdaddccddbaccdaaaaadbcdabcbcbdcbaadcaaacababccbabdcddccadcaadbddaaaacdabacccaaaddabdacbadadaacadccacdbcbbddabcdbcdbbaaddcdadccbbbdbdbcabcbbbaddaadadcccddcdabacabccaaacacadabbaacbbbcbbddaaddccadadbaabdbcdcbccadbbddcbdbcccdcbbdaacccabdbbdcaddcbdaabcacbdcdcdbbccdccdaaabbcaddcbdadbbbaacdddaacccbdbdbadbcaaacabacababbadcaaaccbbdabbaabdbacadadabbbdbbbdbbbbdbbdabcccdcbacbadccdaccdcdbdcdbdcdabbdccabddbbaadddcccddcbaadadcdbdadbadabcdbdcabdccaaacbbbadbacdcbbadadbbddadaccbbbccaaddaddaadbadadbcadadcdbcbbabbadbdbcadacaacabbbcbaccdadddbcadbacbcddddcbaccbabacaaddccdcabcbaabadcccabdcddaabcabdcbdccddcdcbcdbbddcbdbbdadacdbaaddababcdcdcddbdaabccaabdcdbadacbbbabdadcadaacaccbbcddcadbccaccaacabbdbcdcddcdcddacbabcbbbbcbcbccddbabbdacdccabbadddccaccabacabbbbbcdaddccdddabaaabdabdbbbbbaaadcdcbbddaaccbacbdaacaabdbccbbdaccddbdbbaccdcbbabdaaddcccdccbabcabcaaaacbbdabcdacacadddabadcaddabccbccabdcbcadccddaabbbdabcaabdcabbcbdacdbcccbcbdddcdbccbdabdadacbdccaadaaaababdbdaddbdcddadbdaabddacbcaddbacacdadbcacadadbbaddbbdccdccdaaadadcadccdaabdccccbaddcabbcdddaadabacbdcadcdbacddacbaacbcdbbbccbcaddbbdaaabbccacacabddcdacdadadcaacbcdbabcbdaababdcdbbacadcbdcacbcdadcdbcddcbccbbcacaabbcacdadaddcabdcadcbcaddcbddaddaababddbaacdcaadabacdabaaddabdcbbabaadabcaddbadbacbddcabccbcadbaaddbacaacbbcaabbdcdbddaacbdacdddcdbaacaadaaaadccacaabadbdcbbdabcabbacadadcabdaadcacdcccadaaddcacadcdbabbaaacbcdabdcbcaaccabcccbababcdbdbdbcbabaabbadcaacddddbcacccbdcdbcadbbddccdccacddcbccabaacdcdabdbdbdabadcbdaabcccdbddaddabacababdcbbaaddddddbcaabbbcdbadcddbadddcdbdbcdbdadcacbbcbbcadacdccadaabbaccababdcbacbdabccdccbbcdcccccdaababbcdaccddcbdabaadacbcbadbdabdbbadcbdbcaacccaacbdbbddadbadbbcaaddaaacdbdbacccadbbddaacbacbcbccbddccdadcddaabcdbadbcbbaaddbacbcacddbaaaadbddaadbdccabdbddaaaabdbcbaacadddbbcbbaddbcdcbbdacdbacdccbbbcbabaccdbcacccacbbdadcacdccdddbdacbbdadcdaddcdbabbcaddaacaaaadddabdbcadccddbcbacddabbbccaddcbacaadabdbabbdabdabcdadbbcabccdbadcadbcdcbbbacbddcacbcbbcacdbdcabddcbbabcaddbccabcbadcbcdccbbdcabadcaddbcbdbdacbbdcdbacbadadbdcabcdbacabadaacbadacbdbbadcbbaaaddbcabaddadcccddbcdbdcabdcabbbacccbdcddcaabbcbbaccaadbcabbbbaccbcccaacacdcacddccbacbdbdaaddcbcdacbbdccbdbcdabacbdbdacbbcdaacdcccabaabbbcccbdbbadbbdbcbddcbbcddcccccddcdbdcaabbbaabacadbbcabcabcbdbbcabddaaaccadbcabcdbcbcdbddabadaaadbaabdabbdcbacdddbbbdbbddbccdbdcacccddddbcadddabadccdbcbacdcbbddcdcbcbcabbacaddbcdbcaddacadcaadcddbdddacbddbdbdcacbadbacbdcbabdacccabcacbadabbadbdcdabdababbcbbaaaccbbdadaacbbacdcbbdbbacbacbbaabcadcabcaaaaabcbdbbdacaadddcbacccbccabacdbcbdabdddbcabbacdacdaddbddaddcadcbaabdacacddcdcdbdbdaccabacdddbcdcbcadabdacdbdabbdcadabbbbcdddbcbcdbcbdadcddabbcaabacaabbbcccddccbcababdcadbdaabdaaabadacdadaadaddacbdbacabcdcdbacaaadacccddcadacbbbbbdcacbddbaabdccabaacddbcbcdcdcdccbcdcabddaacabbbababbadbacbcdadcbaabdcacacbdbcbcdbdddbdbdacacadccddcdccabbadadabbdabddadaadabbcbadacccccadaddbdadabbacbcdccbbcbdddacabaaadbdbbbdcacacadbbccbdbdadaaccbabcadbdcdbbcabbcbcbdaddaadbdcddddacdbddabdbadaaabaadcbccdbbcbcdadbaadcdaccacbaadbadbbbcacdadadbbdbbccacabcbdbdccbcaaadaaabdadabccaadaccbdaaddbcaadbcbdcababccdbcabbadbdbaccabaacabbcccbcaacadbbdacddacdabbbcdacdbbccdadcdadabccbddbbddbcdbbbabbccacbbcccaadcdabdaccadbacdaabacdabdbcddbbcbbddbbacbbbaaadaacdabaaacbccdabdcbbbcdadaddddaddbcdabbccdcabaaddccabbaabbdcbadbbbbbcadabaacdbbabcbddbbdddcaadbbccbdadadbdbccaabbbacabdbacbbcdacdbadddaacbdbcddbccbacdbbaadcaadcdbdadacddccabbbddadcdbacacccabdaabccadccbcbbccaddccbaccbbdcbacadbcdacaccacacbbcccccbdaaccbdccabacbdadddcabaacbacccbbdbaaadbcbacdcbdcaacbacbbadbaddcbaaddacccbbcbbaabbacaaaaaadbbaddadcbacbaacbddbaaaddcbbdbbcabacadcddaddaddbbbddcabbcbbdbaccccacbccccdbcccdccacbdccbabccdadcabbbbcbaabadcbdccadcdccdcdabdabbbbdccadbdaacdccaadbcbbbaaccabbacddbccadbaaacddbdbabaddbdacbdbaacdbadabdbdbdccdcdaaadcbcbbcaadddcbddccadcbddccddcbddbcbbbcbabacaacbbdacababcaddbbccbbabadbaccbaddbbcbaadaddcdadbddabaacbcddabbaacaccbadbcbcdbbdbabacccbacaaddbababcadcadcdaddcdcacaacccbcbddcbcccdcdcadbcdbdddbcbdabcddbbcbcdbabcbcabaacccadabdbdbcbdcbdbabbdaaccbddcdbbcdcdbdcdcbbbccacbcccddccdabcacacaccaacdbbbcadbacddddaabaacaddccbacbdaadbdbbcbbadcbcbbbccdcdabccbbbacbacdaacdbaabdabbbacbcababbadddaaaadcbddaccddaaccdacdccabbaaabccbcdcbbbcbdccacdccadcaacacaddddbaaabaccababcadbacdabdcdabdbcbaccaadddbacbdbdddddadbbcbacdadcdaabaacdacadccddbccddbbdcbcdacaadcbacddacabccbadbdcbddddacbaaddaaaddbdbbaaddbbcaaccabdbbdbbdaaccaacbacbcccabdbcdcbcdcbcdacbabacdcacaabbbcbabcbbcccdcabcbccbabccaaacacabccaadbadadabcbccabacaddcdbccccadcddbcaaaabbdcccaabbdcdcbbcbbdadddccdbaaababbddbddcbdbbadabbbdcacbdddcbdbddbdacbdbadabcabcdddabcdbdacadcbbbcababacbbcddbacbdccaddddacccaabccabccdbbbdbbbbdabbbaadbabcbdcdcbbbadbcadbdbcaabdbdbddddbccbdbacbdccddccacddccadabadbabccdbdddbdcaadadcdaccdbaddbcbacaabcbcbdcdbdddccccdcbdbddcdbbbdbadaacdacbcbddadbbcbbadccdbbbbaacbdaddcbccadddbacabbbcbacdacdccbcdbbddbcddcbabcaaaaabcabdbdbbaccadbcdabdcaaacddccbbbccdbacadcabbcbbcabdbcacccddabadaccbcadbbadadadacabbcbbcbdbcadaddddcadcbabacdaaaacddcccbcbbabcaaaaacbddaadbadadbacbbabbbcbbcccaccabdadcbbcbccdbddbabcbdcbcbdcbabaccaaabaabcbdbbdadbbccdcbabacccaaaabbbcdbbcadabababdbbccdccdccddabbbdabcaccbbcbbbdbdccbadddaccababcdddacaabdbcdbddbaabbbdbcabbcdbaabccbadccdbaaddcaabcbddccdccdccbaccddcddadbcbacccacbcbadabaddbdcccbcddabdcdbdacaabbddbcabdbadadcdcddbbadddbbbcccbadddadadabddadcbaacaabccacdcdadabcacabbdaadbbbaadcacddaaddabbcbcddadddcadbababcaccddacaababbdddaacabcdaccaabaddcdabbbbddcdababbcbdcccadcaabccdacbdbcccdaababacdcbbdacddbcbcbdbabbbcdadcacaadabdcbdccdbddddddccbcabbcacddddddcdcbacbcdbbbddacbdabacdcaaccdccbdcabaabaacabbbddcdbdabcdabddbacaabddcabacabccacbadaccbbbcadbbccbbdbdbbcdcdbddbdabdbbbacddbdcdbbabbbaaaabbdcacabccdabbddcdcbadbaccacccadbaabcbdbdddbbaccaabcbadacadccbcaabddbcbabbadcadcbaacdcdcaaddddddaaccdaadcbddababbdcdbbabccbdacddcbddbdcaccabaccaadbbccacbdcccdbaccbdcaaaddcacaddacbbdbbbbaabaadcaccaaabcdabaadaaccacdaadcaaddcdcbdbbbdbaadbcacbccbbadcaaddadbdbcababbaacacbacbbaccccadbddbbbdbadabdccaaabcbcbcdbdccacdbdcbaabbbcaadbbbcaadddbdadcccdccacdadababdcbbddbdcadcbbbbddccbbcbdbbbbcdcdabbddbbaaacaaabbcabcdcdbaccbbcdcdaabbcadcbcbaaccabddbacdadcccbcddbcccabdbabcaaabbcccabdaadaccaaacaddbaabdacdaadaccdbccaadacbacabaaccccdbaadbddbcccddcccaddbaadcaaccddcbaadbccdbbbccbdcbabbbabdcbbbacababdaabacdbbdcddcadaaabbcdcacccaccbcdbbcabaccddbccbcccdcdbaddadbbddadaccadccdabdabdabcdacbaddcbddbadcbaddacdacddcdaddcdabddbbbbbbdcdddaabadcbabcdcbaadcdbadbbbcaaadabdddbcababbcadbccacaabcabccccbbbcacaaabcddacbbadbbbabbdcbabbadaacccacdcbadabcdaaabbbcadaaaabdaccdcadcbdbaabbcdacadcdccccdbbbabbcdacbdabcacadccdccbdaabcaacbcccbcadccbbbcbabdaaaaabdbdacbacdadccaddacabbdcacbdabcbcbbbbaabaadaccbccdbabccdccccbdaabbadaabccbcaabdbdbccbaccbbbbcdaaaacccbabdadcddcbdaaacbdddadbacaddcadbadaccaabdcabcabbcbaadbdbdadcadbaabaadcadccbadbbcacdcdddcddaaaadcdccdbddcbcdaccddcaccabcdcddbadcaadadadcbccaaccacdbcaadcbbbbdcacabdacadaacbbddadabbaacbbdcddaacbdccdabdcadacdbcaabbbdaacaaadcacddabdacbacdcccacdabcdaadabaacaadadcdbbaadadaacabdacacdcdcabdcddaddbcadcbbcbcbddbdddacadcacbbdcddaabdaaaaddddbcbacddcddcdbcdbdcbacccabcbcbcabcdabcbdaddaccaadbaaadcacacbdacddddbbbbbbcbcbdabbabcdbdbccdccacdbbdabbccdcbddcbacbdaaadaaadbabcabddadcbccdcbcdcadccbabbbcdbacabddabaacbaaadcdacbadbddcdacddddcabbbddaaadcaabacbcccdbbaccbdbabcaabdaadcbcbaccacacaccbadbaacbcbaabcdbdacccbadbccaabbbdbbcadddcbbdbaaccacadaabaddaabaaccabdcdcbaaadbaacdaaadacbcbbdcbccdcdccddaccabcbdaadcdccbbbdabadcabaaaacdddbdabaaadcbaaaccbdbcdbbaacbbcaaccdcbdadaaaccdacadbaccddabdddbadbabaacacbccbdcadccadbdbbaabadbdbbcabbabbcccbcbbdcbbbbabaaddbaacbbdadcacbdbcabdcabdbacddcccaacdcdbcccbccdadcbddbddddcddaccddcadaddacadaaccdaaddaadbbbaccbddababdcabbbadcbcaacbaccbdcddddcaddbacccbdaaadacbdbdcbdacabadadaabbadabccdcbcaabcddcbaabccccccacdcdadbdbdababbdcdaacdbbaaaadcccdcdccddcbdaaccddaabddddccbcdadbccabdcbcbdcadacdbbccdcdaadccaccbdadacbcbdcdcbaacacdcbbbbbacabcaccdbdaabdbaacbacadddaccbbccdcdcccccbbdacdaddcbcbacacdbaadcabbbcaaccdbbdbaaccddaddbbddddbccacdcdbbcdcdccccdadbbcdccaaadabcdbddcdbdaccaacdbdbadbddbadcbabbabdbdabbdcbbbaacbdbbcdabbccaccddddabaccdcadabdddaabcdccbaabbdbbaccddbacacdddccddbdbddbacadcbadbddabddcdccadbddcdbddcadbdcbbbcdacbcacdddbbbaabbdcccaabbdcabbcbbaccdcccdcdbbdbcaaddacadcbdcadcabdacacdbacbbdcbcdbadccbaddbbcaccaacdbcbcabadcbaaabcdcddcdbcbddabdcddddcacddadbdddaaabadabaccdbcadaccadcbaddbdbdcabbacadbbcabbaabbddbcbbcbcddbaddbcabbadddbabadababcbcbddbbcaddddaacabbacbbbbabbabdacdcabbddccbcbddcdcdbddcdadcacacddcadacbcdcdccaddadbaaabadacdabadcdaacaddcadddcbbcbbbadabdcabbccbbcaabbcbdcdbadbdbdcdddbbbaaddacaddbcaabcdaccaacacaacaaaabdcaaddcbcadbdbbdbbcadbbddadbcdcdddbbabacadaaddbcababcacbdabdcbabdbabdabbcdadcdccaddaacbddadbbdabaacaccacdbacdaaddcbbbdbacbdadabaccdbcbcacbdcacccdbddcbbcdddddbaccbdbabdadaacaabcbdddbbdcbdbaacabbbdbaccbbababadbacdcbccadaaacbabaabdaadabcddaccccadadbdaabcadaaadcbbbbbbbaccdbadcccddbaadbacddbcdbcccacdddabcbabdbbccbbdcdbadbdddacdabdddddcbabcbddccddddcbddadbcddaabcbbbdadadaacdbcddcbcadbcbddcccbcbddbbcbaadbdabcbabcbbbacdcadcddacdaddbaccaddaadaaaadccddacacdbbabaaaadbdaddcaabcbacdcbcaacdaaddcbaababaaaccdbadaadbdddabaabddcabadcdbadddadbcdadcdcdaddcbabaaaddbaddcacaaadbaccdcbddaadcadbbdabbddabbdbcbbbacbabaabbadbdabdabcddbbcbdadcbbbdbaaaccacbccaaddcdcadbdabadaacbdddcacbccbddbcdcbbbacbcdbbdcacdacdcacdadaaabdbcadcbcadcbaddabbaadbbbccadbadcbcbddccbaadabbadcccddadadabdadaaacccdcaaacaadbcbaabadaaddbccacbbaadabddadbdcbaacadcdbdcabadbaacddaaacdaacdcaacbbbacdcdddbdbdabbbadcabbcbdbdcdcaccaadcccdcbbdddacdbcdbccbdbdabbbbbcdccbdbaaacbddbdcbddcdacadbccabdbaccdcaadbbababbbccacabcbaadbdbbbdaabacdbaddbabdbacbacabccdbdbcacbacddabdddcaaababbabdbcdaaabdcacdccdadcbabadbdbbaaabcbadbbaadadcabbccaabcaaccddddadcdccbadbdcdbaaacbdcbcbdacaacbaacdabcabaccbccabbaaddbdadbabacaccdccbaadcbabddcabddadbcbabdabaccdbbdbcbaabdcddcbacadcdcdcbccddbdaddcbcbdbbbabdcaccbdbdbddcabddcaacadddaaccdabbdcddacbacdadccccdbbcadabccdaadadbbdcacaababddbccddbbcadcaccdbcdddaaddcbcbdccccddbadcdccddbabcaacdbbaadcccbbcbddcbaccbdabccdbacabbbadcbbbdcbdaaacaaabccbdcccbbaccdbcadbaacbcbccadccdcccbabdcabdaddbcaacddaabbcbbcacddcdaabddabdbccabdadbcadccabcdcaacacdbcbcacbbcababcbabddbaaddccccaacddcdabddbddabcdabdbbdcdaaabcdbddcccccccdddaabbdadaacbdacdaadadaddbbbccbaacdccacdbadbadabcaddbccbdcabbadbabdbadbcbadcddbddbccdbdbbddbadcaccbcbdbdbaabbacdcbcbdaacbcdadbbdadadabaaacaccdadcdaacbaaccdabcbcdcadaaadabcacdcaacbabdabcdbcdbbcbacdaaccdabbaaccbabbcddadcaddbaccddadbdbddccbbcdbcaaacdacbcddddbddacdbcbbbaccadcbabaccccdaadbaccddcbdcdbddcacabdadbcdbdcdadcdaddcdbcdaabadaddbcddaccadbdbcaccbadcbaaacacddadabcbcbcbccdcdaabccbbbcadcbadcabdddbabcccaccbcadbcbababbbdabdbcdacbdbbabaaadaaabcdcbacbbcadbbdadcabcacdcdcbbcadbdbdadaaccdbaccbbccdcdaabbbddacacadaabbaaadbdabdcccbadaabbcaccdcdccbddddbcdbccaadadadcaacdcbaabcbdbbdcabbacbaadbbcbdbbbddabdddbacbcbabccccbcccccdbcddacdcbbdaaccbabbdbddbccddcdcdcabcababcbddcbabbcaaacbbaaacdabdacdcdccbbccaabbccccdcacaacbdcaacacaaddbcddabdaddbcdaabbcdbddbbcbbccdbadcadcbcdbacccaccbacddcddddbbadacabbdadccaaccbaadadabaaaacabcbdaabddacdcbcbbcdddbadbcaabacadbdcdaacadcbbacdcacbbbbabbbbbbcbbcddbcabaccdbabdabcdcbbbccbddcdaabbcacbbddbbacddacdaccaccddcaccacabadccbbadaadcadcaddcaacdaddbcbcdbbabdaacbadbdaccadbacadbbaccbddcaddacddbbaaadcccbcdabddbcdadabbadbcbacbbabcdaaddcbbcdaadccaadbaddcbcdbbbaabdbddaacabbacbdcbdadbcacacadcdabbdabadacdddcdadabccdbdbbaddbadabddbdbcbababacaacbdbdabaddaadaadbdabbacccdadadcccabdbaddcaaacaacdcaccbcdacacadcccbdcbdbdcaabbcabadabadbbdaadaabaccbacbacbcdacbcaacbcaaddcbcbcddbcacdcbabddcddddadabbaaabdcbbcbccbacdbcdcabccdddaadbbbcdddddbdbdccdadcdacaadbbbcbacddcdaddbbcbcdadadddccdbdbbcbdbbcabbbbcabaaacabcaabbccbbaadcaacddbbaaddcabcdcbcaabadabcdbbbccbbbdadddabaacdabdcaabdccbdbbbdbbcbdccbbcbddadaaaccddcbdcbcadcadddbdadddcadbabcdabbdbdccbcbbaadccbbaadcadaaacccacacccbabcbacdbdaccddcccbaddaccabdbbdabdddcadbaddbdbbcadbabababbbdaaadaaaabddaabcaadcabbbbadcaaacbccbcccccccdcaabbdcdcbdbcabddcadcadcddcddddbabcbddbdbcdabaabbaadcddcbcbcacdcdbdddcadbaaddcdbbaaaacadbdbddacadcadabacbccbcdcbacbdbaaaabcbacacbbbcbdadadddaaaacdadbcbcacaadcdbcbadbbababbcbcaaabccdabbacddcdddcbbbaddcbbabaacddbcaddcabdbbbcddcdabddbacaabaaabddaaacdbdddcdbcadaadcdcbccbbbadbadbdaaadbdbdbbbdcdcabdbaaacbabdcdacabdbcbcdbacaaacaadacadabdccccdcbadbabdccdcdbdacbdcbacdbbdbaacadbcbbbdaccdbcddaabdcaabacbbbbabacdcdbccdaccaadadacdcadbacadbdcbcadaadcdcbaabbbabdabddbddcbbbabdaccbcbcbdcdddbdbdccbdccbacbcddadabaadaaaabbdbdbabccbcaccbdcccadabcdacbddaaacbccdbabdcacabddabddcadacacbcacccccbbaccbadaabdbacdbddcacbcbbabaaccdbbacddaaacbddbcbadcacbcbbbddbcdddcacccccdcccacbdcaddadabbcdcbcbabcaaaaddabdaaddacaddabcbaaabadcccbddddcccccdadcabddabdbcdccdbccccdaccdbdcbcbdbcbcbdbdbbcbcccdbbbbaccaadabddddaccdcaaaadbaddacadbccdbddcbacaadccbcccbdcdbcadcbddccdcbbacbaabbcdabbbdacacdaadddabdbbadcacaababacddadcccbadbcaccdaddbcbdccbddcacbcbbcddbbcccacbbacbbdacdadccbdbaddabcaacbadacdadaaddbbdbcbdccbddabaacbcdcbaddabcbdcdaacccdcdcbdcacbadcdbdacaacadbccdbdcaccdccadbccddbbbbbddcdabbabadbbcbaabcdcdbbdcccabbdbbbdbaaacdabcdbccbcddaadabbcdadacdbbbbbccbcdddabcabbbcbaaadbccaddcadbacbcddddabddacdcabcdbadaaccdaaabbbdacbadaabcadacbcaaacddcdddadcdacbbdbcbaadbbcdaddabbbcabcddabdbcbaababbbabdbdcddcdadcddbbbaadccbdcccbdcaaadadbcadaaabbdcbaaccdccdbdccaadccdacaadcbbdccdaaccdbdccdddadcdbcbadabccddadddaccbcbbcddbabacbacccbdcbdadccdabdcdbbbcaabcabcbdbbdacbacadadbdbbbcbcbbdbccdcbdcbdbbcbcbdabdaabbcdcabdcadbddbaacbaaacacadababcbddabbdccdcacbabcdccabdabbcdbdbadacbccacdbaacddbcadcbbccdbcbbcdabccbcbddcbdcbaccdcbdacbadbbadcabbbccbdaabcdadbcaccaacabccacbacdbbaaacadbdddddaadcbddbcccccdbbcccdaabbccdbbdbbddaacbaccddacaccdcddccdcccacdacccdacdbcbddbaadbdcbaaaacdcabbdccadccbabcdcbdbaabdadbdaabcdcdbbdabadcbacacbdbabddbcacdbabbcdcbdabbababdcccdddcaaccdabdbdbdcccdacddcadbbbbccbbdbadcdadcbdddbbabbbbcdadbabacbcadbbadddcbbdcabccbbacddbababbbddcddacbacddadacbbdaadbdaacccdbadddaddbabaadcdcacaadcdbbbcdcddccdcdadacdcbdbbcddaabbccdabacacdadacdbdabdababbccaacadaccbbbcabbcaacdcaabdaddaddbbdcdabcdbccadaaccbcdddcadadacbdbaabdaaaccdcacabbcbdccdbbdccbbdacbaabacacdbbbacbcaddccbacadbddadaadcbbdaccbbbbadbdabcadbcccdcacdabacbacacbdabddbadabbbdcadaacbbbdcdbaadadadcaccdcbddddcbcdaaddddadbcbdabdcbaacdcdadcadabdbabcabcdbbdcaabdddcadbdaabbadaccdcbdbbbbcdaadccacabbacccbadaccbbbcddaaadbdaadbbdbbacbcaccbbdddcccabbbabdaadacbdabaadbccccabcacacaddccbdaaaddcdcdccbbaabadbadabcaacacadcbaccaadaaaabdcbdadadabcacacaddaddbacdacbaccccbdaddbcbdbadddddabbdacadcabaddbabdbbbccdbdddbbcdaadcacabcbdacbaabcbdabdcdbdaabcabdaddcccdacbbbbabccdddcdcaaabdbdabdacbdddbaaabccacaaabcbababdddaaaadbcbbddababaabccbbddbbabdbdcdbccdcabccbccdcdbddccabcbdbadccaaadacadaaabacdbaacabcbdcbbcbabbaaaccabdddbdadcddbdabcdcadaaaabcdaabdbcbcacbdabdcacccabacabababbdccbcdbcacaccaccbcccccccaacdccbbaabcbcdccabdbcddacbacccdbbcccadaaaadaaadacccdddadbdbbddbbdcccdbdddaaabacbcabbbbdaacddadddddbcccccacdbddcacadcaddcdabcdcaccdcbdadadddcbacdaddbdbbccdbbdbbcabddbaabaadbabbbbcdbcadaabaadbdcabacadcaabdcbbbbbaaccdcacacbdccddbbdcdcdddaaddaddbabdccaddbcacddcabcbdaaccbaadddcdbccaadaccabacbddcabcaaacaaabcdddcacbadbaacabbabcaabdbbbdccbdcdabdadacbcdccdddcacacbdddbccbbddddaacdddadcdacbdbbccbababbddcacddbdabdbccabdbadbabadddcacdbaddbbaacdbdabbcdbbcaaadbcdbcbabbdadcbddbbcbdcacabcccbadccdaaddccdbdcdbdcdcbbcdcadadbddbbdddaccdbcabddcbdbbcaaaaddbdbadbbccbcadbcabcbbacdcdaccbaadabbbccbadcbbbadbabdcabbccacbbddcacacbaadbdcadbacccbcdddabdbcdcddabaabbbcddbdbabaaccbccbccdadbabbaaadaccbcdcbbcaddacabcccdddccdaadccdbacbaaacaccdbaadccbbcaabbaadbcbbbbddaddacdaabdcddacaaccddddcddddccbdbcadcdcaacaaaccacbdabbacdbdcacdadddcbaadcdacbcccdbdaadcabdcdbadccbaddacabdaaccddbbacccaaddddbcbcdaabbcacdaccddabddacbcbccdadbccbacaabcadacddcadbcddcadcbcbddcaadcbdabdaadadbbdcccaacdddacbaddbdbdccccdabdbbccabddabdcbabccbaccbcbadcdbbabcbcbcdbadbabadbbbabddabccabcadcdcbbdbcbccababbadcdbaadcacdacddbcddabbacbdcbabbbdbcccdcddddcaaccbddbdbbcdacadaacbaacaacdccbdcdccbbdacbabcbccaaddaadbdbadabdcbbbddadddcddadcdcbcbccabdadbbcddbddddccdcacccccbccabcaabddcddbcaaaccdabccbbadcbbbbdcadaccaaacbdbcddbadadbbbaabcabdccddbaccbdbbcadccdadaabbbcbccabacaadcdbcbdacaaabccaccbdabdadcaacdacbdcbddaaaaccabcdbdcdddbbcbdbbcacbcbcdaadcdaccadacbaddabccbbabbacbcbccbacbacadbbcbbacdbbdadbbbcdacddaaadaadcdbcccbaadabadabdcaddcdcdaadacbbdbdacabacdbbadddcabbbbadcddbbabbbcbadcdcaddabdccaabaddccddcbdaabdddacdcdacadaccdbdaccdcaadbbacddcdabcdcbccaababdacaabaacbaabaadbdcdadbabcaacacabdcddacdccddcaabdcccdbaadbaadbdacdcbcccccabacccdabbabccdbcacaaddaddcdadddadacdcacdbbdcdcadcccbdbaaacccacbdcddcdaadbdaacbaadaccbcadcbcbbabddbbdcbaaacbbcbcddbadbbcdaabccaccdbcadacdbdcaacddcaddbcbabbdcdbbdbcaccaccaadbbbbcbaddcbcabcabccdcccaaddcccabbdcdcdddabbbcbadbccadcbbabacdadabaacdcdabcbaddcbacbbdccccbbaaccbabbdccbdaddcabbdbcabacccadacbadaacbcddacdcbaacdcdacccabbbdcabdadaacddcdaabbccacacddbabaddaacbabcdbccaaabaccddabbabaabadaaaaddbcbbdabdbdbbabdcaacccdccdbbddbccaabcaddaaaddddabcdddccccddcdbccbdadabaddadccbaaaddbabdbacbdbccbaddbbaacbddcbadbdbcbdbdccacddbbabddabbcbadcdcdbbcadbccdbadcaabcccadbddcddcbaabddcddbabdbcaaaadcbdbcadbbcdbdcdcddcdcddbbacbddbcdbdbabcbdaacbcbabbaddbaaadcacbdabddabcacdacbababccddddcbbbbdcacabdaadbdbcaadadbddcabdaadcaabccbcaabbdbbcabadadcdcdaccdacdbbaacabcdbdcccdbdcbadcbaddadbbddbccadadabbcbcdbcbbabbabcddcabadbddcdaaaadabcaaabcbabcacbabcddacaadcadaddaacdccbdcddcdcbccddabbadbbcdacdaabdacdadadddaadbbdaabaaaadadcbbabbcdcaaadbaacacdadabbcdcbdcbccbbaadcbccbbbbaccbbabdadbbcbdaaabcbbaadacbcbddbdadcdbddadcddbbdccdbcabadcccddcadabddaaaaabdddbdbbccdcbbbddbdacbddcadbacaabdbacaddaddddadaaaaccbbaadacacabdbdaccddddcbccacddbcaacbabbbcbcacabcbbccabacabbcbbcaddbcddcdbcaaddaddcbbababcdbbaacdbacccdaccdabcbbbbbcbcaabbdcdddbbbccababddccbdcaabddabcaddccbdcbbcbbdaadddddaadadaddaabbdcacccccaabacbabcccdaabdbcdbaababbadbbabaabdbbcddbbabccbcddbaaadbaddccabbbaaadababdbaabaaaacddddcabbbcaabbbcdadcaccdcdccaabbbcbbdbcdddbadddacbbcccaaaabbaabcdaaadabcbaabdbddccccbcadacdabbcddbcaddacaccdbbababdbbdababadccbcaaaadabbdbadaacdcdbaddbdcbdddacdcacbccaaaaddbccbddbbbcccaacdcabbccacccadddbcdcbccccdddbddaaabddabdaadaabdcdbcbbdaaacaaccdcbcbbbadbdccaabbbcabbdaccbbacdbcbcccdabbacacddadbddaadbbcccdbacacbcbdaddcbcbcdbdcabbdbcbdcabacdadaaaadacbacddacdcbcccccddbdcbbbbcacaabaadbdaacacbabdbbcaccccaadcbadabaadacddbcbbcdccbddaddbcccbdbdbbbcdacaccbdaacbaacbdddaadbdbacdcdaabdbaccabdbaadbbbbabbdbdcacdacbccbbaaadbababcacccdadacbcdadccddacddabdaadabbabaccbcbddcdabacbaadccaddaaadbdbdaabbaaabcbcdcbcddbaabcbcbbbcccbdadcacddaaabbbaadbbbbdddbdcbcdabdcdcbdbdaadaddcbaccdddbcabbdcacacabddaabbdacbcdbcbccdbacacbccabdabadbcbacbdabbcadaabbbdbdabcdddbcddadbccbcdbdddcbcabadccadbcbdadbbbbbacccdadbcdbdccbcacaaddadbaabcdadabddadcbaccbadbcdcddddcbadbadabdbdbdabbddbdbbdcbdcbcbccbbdcbccdacdbdccdcacccddcdccbdcadbcacabcbabbbcabcaacaadcdabcabcabdbbbcaaadcadcadadbabbbddbcbbabbccbabcaaddddddaacdbaabdbcbdbabbacdcdaabcbdaadabcabbaabaaaaadaadaabbbbbbdcaacdabdcddddabaaadbbcdddbcbabbcaadbbadccddbbcbbaddbaccabcdbabbdadccadbabbabdabdaaabcddcbbdaabaacbabbddbdabdbdbcdbbabdcbdadabcbddccdcabadbdcbbbaaddaddbbbbbdbaadddadabdcacaddadccbdbdaabdbbabcbdabbcadbbbcbacdbcdbbbbdbbaaccdaabdadaadbbddaddccbcdcadcccdbacddadcbbabdaadcabdaadbbcbddadccadabadddbdbaddcbbdcbcdadcbbbaccaccddbddadcaaddaacbbdaccadabcbbadabcadcddcbacdacbcacaadddbbbcadcdddbcadacdaabbaadbacbcdbabbdbcaaddbdcccdddaaddbadaacacccbcdabdabdbdbdacacaaaaccbddbaaddadbdaccbdcbcadcbacbdbbbdacaaacaacadacaddcabdbaadaccddacddcaabdbababbbaadbcbaaabcddaddccdbcabcddbdcdbdaccaddcbdaaccbadacddbccbabccaaabdcbbddcbdababdabbcbdcbbabdbdbdaabbaacbdcbddbabdaacabbdbdbdacacdddabcbbdabbddadbcccaddaccadbbcaacccacadcbcbcbddddbbdbcbdacbcbbdacbadbbcbbdcdadabddcababacddbbbbbdcbabcacbcabcadcbbdcacdcbadbbbabacccccaacdacaadaacdcadcbdbbcbcbbadcabacbdbaaaabaabcddbadaddbaadaccccaddcbbacacbbbdaaabbcdcccdbdccacadddcbbdcbaabbbcacaababbaacddaaaadbbcdddcacbbdaabaabdcdacbaadcbaadacacaddababadabccbcbbddadbdadcdaaabddccbadaabcbdaccdbccdadacbdddbcccacbdadcbbbcbccbcbcaccabbdbdcbddadcaccdcaddbcbbdbdbbdbcdabbbcacaabdcbbabaaaaccdddabcbbcaaacadbacbadccadcadabbcadcdbcddbcaccadadcccdadbaadacbdbcdddcadabccaadccbcccadaaacacdaacbadadbbcddbcdbdaddcdadbdcaadcdbaccddadbcadccbccaabdbbccddadaccbdbbabbccccaabccbcdcdaabacbacabadcadabadbcbcaccdcddcbbbdcbdddacbabbdbabbadbababbaddcbdadccacbddaaacdbdbdbcacccaccaacddabbbdaabacbdaaccbdbacacddbaacddcbbbdcbdccaccbbaccdcbcbdaddaccddabaddbdbdababacbaabbbabbacddadbdbdbbaadccaabccacaacbaadcccbdaccbddacbadcabbacdcaddaaddacbbcaacaacaccbcbdbbaaadcbabcdadcbaaccddccaacbcaddaacdadccabacbdbcacacadbbcbddcadbbbbddbabcabbdbabbabdbccaddadcdcbcbbaacadbbadccabcddbccccadbcacacdbacbbccaaaaacbbcdcaddcdcbcbbddadbabbcadbdbbacaaacdacdddcaccccaaacbdbabbdcbbcddcbbddcdcdbcbbdcccdaadacacddbddbddacbbcdddcdbaaabccbdcdaacdabbbaaabbaacdddbabbbdbdaadcdccaacadbaddbbacddababcdacdbadbaabacadcccddadddcbdbccdcbcdcbccbbaccacbddbdbacacacaadbdbdaddccadcdabddcacdabddbbddadaaabbccbcdcbbbaaadbcabbbaaabababcdccdcbdccbccbbccddcddadaabdabacabbadabcabacbccabdacacbdbccabcdddbbacadddbbdbcbdcbcacccaacdbcadbddaabacdbbabbbaadadcdccadbcbbadacbababaaaadbdcdbaabccbbdcabbbbadbbdbabadbdabdaacabaccbdaaacbbacdcbdaaabaacaadcccbacbbaaccdaddbbbdaaccbcadabadcccbddaccdabdbddcdddcbdacabbccaadbdbbacdacaaaabadbcbbcdaaddcbcdbbbbbbccbbcbabadbadcdbacaccdddccbadccbcccbadddcabbbccbbccabdccdaabcbaccccddcdcacdcabaacccacaabbbbbcddadbcacbcdaaabbbacddbdcdabdadbcdcaabbdacacdadcbcbddbbccdcabcabbcdaabcbcaddacdbbbabccadddbcabacbabcbdabcaaabdccabbcbdcbbdbcaaccccaabdbddbadaccbaadbdadbdabbdbddbbbccdcaacdabbdaabccccddcabccdccbbabcdddaacaacdcccabdbbbdccdddccbbbabacbcdcdbbdcbcdbaacdccdbcaaadaadcbbbddcaaaccabaaaabdcaaccddcdcccacbabaacabcabcadabdbabdbcabdbcadbbdbadacdddccdabbdbcadaaadbdbdbdcbacdcbcabcbcabcadbddacaabbdacbdacdaaaadccdababbcbdcadcddcaadabddbacdadcadbbcddacbdacdcbdbcaadaacbbabbabbcccbbabdaddddadbcdccdccacadaaaaacbcaabbbdaacbbaaacadbbacbddaddbbdadbbddadbaaadccccbadaaadbbbbbbcbdcabaaacdaddddaaabacaddbcdacbbaaddaccdcdaadbcbcbadcbacadcbbadbbccacbdccbdaabcbccccaacbacdbccdaaddbcacccdccbadcadabcddaddcbbdddccdccabacaacbadcdaadaccbcbccdcababccbbbadabdabcbadabbcaabadaadddddaacbdcbccaacdaacbabccabdbaccacdaabcaddadbbdbccacaaccabbcdaadddcaddbcccdaadbcdaadabcbacdcaacacbacbbbddaddddcbabbbcbcbabdbbbcadcdccaddaaaddcaadbbaaacaaabacbcaadddabbbcaacacdbdadcbdaddcbaaaadaddbcaaadabaabdbbbacaaccdbacdddddcbacdadbdaddaabbdcdcabcdbcaabdbdbadabbcabbadcdcbcbddbcadacadabaadbacdcbbadccccbcbcadcbcddadddcbadacddddaaddddccbdddccaacdadcacbcdddabaccadbabbddaabddcdbbcaacabcccbbadbdadbdcdccadabbacaddbacddbcaadbaabaaaabbbdaacabcbcbcbdbdbbaabdcbbccaddbacbdabcddababcbdddbdcdcbaadcbdbdbaacbacbbdadbddcbbdadccccaadcdaadbccdcbaacadabcacdacabcdabaacbbdbdaabcbcbccaadbacbacacbabcacdccdcddcddadbdaddcaddbbbadaaccbaabaabbabcbadbdddddaaadaaddbdbbccddddbbbaddabaccabaccdabadabbcaacbaccdcdaadddabaccaaaaaddacdcaaccacdadbdbcaacdaaabadbccccdbcddcdbbaccacacddbcbaddabbbcbcdbccccdcadcdbdccddababbcccadaabcdbcbcadddbcdcdbbaaabcbadaaababccaabadcaadcbbcadcdbbbcbccddadbbbdadabbddaddbccbbababdbabbdacacbabbccdbddaacbaaacaaaacdbcbabdbbbcdbabcbaabcaacdddadbdabdbcbdbbbbbabcacddaababdbbaaccccbbbaccdcaccacbddabddaddcbdcbbcddcbcabacaacdbdaccaaddbccdbbddcbddcbabcddbcbcadcccbcbbbcdbdaacadabbbaabaadcddcdbdabccdcadbabbdbdbaaaccacbdbbcddadcacbddaabdcddcbdadbccbdcdbabbccacaaaddcbabcdaaddacbbbaabbccdbdddabccbcaabdcccaacaddcbadabadcabbcaccbdcdacbccaadaabccdddcdabdbcacbcabcbbacbdacabadbcdccadbdbaadcbcbbdcacbbbcabdcbbbddbbbcadaabdcbbbdadbaddadabbdcbabaddbcbccbabcdadbccbbdbbbbdacaaabbbdbccbdcacbdaaaadadaaadbbcabadadbadaaacbccdcdabbbcacbcdaaaccabddcbbcbccbbaacbcbbbbcbbbabcababcbdcbcacdcdbdacaddacbbcabcdadacacccabaadadcaddbdbaccbcdbbaaddbbaccbbaaadcbaaacbcbdabaddddcbcdcdbcdabdcaacccbaccddcccaacbacacaacbaaacbbdcbbbbbccdaaaaadaacdccacacbadbcadddabaaddddabdbbcabbacbbddacaaadccadcacbddaaacbbaadddbdadbaccdadcbdbdccddbdacddcbbacddccccbaaaadcddbcdbdacbbcbdbabcccbccaaddbacbddcddddbbdaaacccacbabcbaaabadaabadcbbbaacdccbdbdbdddbbcacdacabccbadabbabccbaaddddcbcddcbabadcadabbdacccccccbadcababbbddbdcbddcabadccbbcbcdabcacbbbdbacbbadbbbbbaabbdbaacbcabdcdaaccadcacabdcbdadccbadbadabbadabdacbbbdbadccdadbcdbcbdddcbbbccdadcdccbabcbcbdcbbcbbcbaacccdcbaddacdaadddbadbddadbdacbbddabbbdbadaabccdbdddadaaacbbccaacdccdbddcbddbacaaacacbdcbcbbbaadbddabdcbcdbdaaddddbaabdcadabdbdadabdbcddbcccacbdcaccbdcbdcdbbcdcdbdddbacdabcbbcbcdcaaabcbdddbccbdcbdadbbdbcbcacddddadadadbaacbcdcdcdbccaacbbcdaabcccacdbbbbddbdbdbacdbdddadaaddbbcaacdadcddcbdbadcccaddbadabdbdaaaccdadcadbcbbcdbcbabcdaccabdbadcdabcbdbbcbbbaaadbadcadbcdbadcbbabbccbccbdbaaabcddbcdbabacaabbaabccbcdaadbcacbbbcbbbbccadbadbbabddcacbaaaabaadabaccddcbcdddcbddaddbcaaadcacacdabcbaddacbddaadbdddcaccbcbcadbabddabdbdcbaccbbaadcbccadbadcaacbdccdabbdaaadbadbcdabdababbcbccadbddbabcbdcaddacbdbdcbccccdccbaaddbdbdaacbdcacddcabddddabcccdcdcccdbcdacabaddbaaaabadccabaccacabdabcabcdbcacacbaccadbccbadacaacccdcdabdcbdabbbbcaadabbccbdadacccdbcaaabaaddacabcccacbcadbbbdacacacaadabaacbcdcdddacbbdaadbadbdbdabaabccbcbdcababdccddaccccdaccaccacccaccaaaacbbacddadbddcbacbdbdbcdabccbbcbbdcadacadbacbdcbccdcacabbbdbdbbcbaabcccbcadbddcccdbacdbbdcdcbccadaddbadaabcccddaddbdbbacbdaabccbadaabdadabddcdadcbaddbadddddddabdabbdddcbaaddbbccbdcabcdacababdbaaccbdddbdadccdcdbcdbabcabcaaaddaacbadaacddcdbdadcabbddbcbbbccbcdadcabacbddcdbbaddbdcddbccbddabbcccabcdabcdacadadcabcccabadcabbadbdabcbbacdcccdabbbbdcdbabcadacccbbdccddadcbdabadcaccbbcdaccccabcccbcddcbdbaaadabcadacdcddacacbdaddbbdbdbabbddddbaacddcadbdaddbcdaacabcaccabdcbbcaddabdcbacbddadbbcbcdbacbddcaddaabbcacdbaacaaabccbbbbaadccaabcbcabbdbbbdadbabdcaaddbbdccdcccdbccbccddbccababdcdbbabbadadbcdacbcbcbdacababdccbaabcdacbcbcdbaadaabccaabcddadccbcdcacacaaabcbcadccdadcbdbcddabacbddbabbbadddbbbdacadbddabbbcccdcdcadaabccdbadbbabdabcaaabdcdccccdcbdcbcababcaadaaccdcbbcbcbaaaaaacadacacbbbcbcdbcdcdbbbaabcbcbaccacdccacbaadabdccbcbcbcdadbbdbddccdbcddbcdbbbaddadacbaacbababcccacaabcdcaadacddadcbbbcccdbccbbdadbdadaabccbbccbcbccadcccdbccbabbcbbbcbaacdcbdacacbbcdcdbacacdcaacccdbcadcbbabcaacaadcdaaadcdcbbbcacccdadcdbcdaaccaabaacadbcdacdbbcbcbbaccdbbbccaaaaaadabadcbdcabdbaaadcbdbccabadbcddabcadacdcdacdacadbabbbccdabccaabbaadaacbacdbdcbdbdddcdddcacabbdcaabbdbadbdaabbbacbacddaabcbdbcddccadbcdddbaacabbddcadbabdabbcccbaabaacddcdadcaaaacaaabdbdcacbcdcddcaacccabddaadabbaabbdacbdbccbbbbcbdadadadcabaabaaaacccdaadbddcdbddabdadbdaaaadcddccabdccdabddbccbdbacbadbabdadcdaaabbcbbbbabababcbdcdabadcdbbccbacdccabacbcbcacaadccbbbddcdcadbbdbcabbabbddadcdcbdabddaddccadacbabddcbababdaddbbbdbbcbaddcbddddcddadaaaaaaadacccbcbacdbaadbbdbcdcadbaadcbbbaabcaadddaabbccbadbdaddadddaddcbcaaadbcbbddabbdadccdccadcaaadbdacdbdbddcabccdbcbdcabddddbabbabbcbdcdcddabdcbdacacccbdadabbacacdabdcaacaacdcdbddbdccdbaabdbbcacadcadbbacaacdddadbdaacccadcbbababdcbdbdcbbccbccbacaccaadbaccdddddbcacbbbdacddcaabdbdbddabcabaccabbbacaacbcdbcabccdbdaabccdacdababaaaccacbaccdcbddacdddabdccdcbcbbbbaacdacadcddaccbccdaddcadccdbaacbcadcdaaacbdccddbabbabdcadcdcadbdbabcdcdcaacaaccdddacacadbdbdcdcccdadcaddabadbacdacadaadcbcdddbacdddabdddcbdccababaccddddddbdaacdccdcdcaddbdcacacaaaddcacabadccabbaacabdcabddddaabcdcddaabdabdbbddccdbccdabbbccdadaaaaaacabcdbcbacbccaccccddaacbddaddaaaaacaddaddadaaaabdbbdcdcdadddddaaccdbacccacdcadbbdacdcbcbadbcaacbacbdcacdcbaacccadbdbdcbcddddccaadcbbcacbadbbdcbabddcdcabbaababaabaacbbcdcacaadbbadbdcababbaabadbadccbdaabbcbbaccacbdcacccbabbaaacdcadbbaaaccadaadabcbcdbdbcadcadbbddacdbcacbaacaddbdbccadbbbaaabdbcbacadbddbdbdccbadcdcbdcbdadbddacbcadddccdcdadbdadccaddacccbbdaabccddddadabcddcdadcdabdaabadbddbbacacbcdcbcabacbabadccdbaacdbcadabbbccacaccabccbaadcbbdccbdbabcbcdbabbaaabcadcdbacbdcdddbaabcbabaacbbccacdddddcdcbbaacdbbcbabbccbdadaadbcdaabbbddadbcdbddabcbaddaacacddcacdcbbccabacbaaaabdbccdccadbadccbacaddacbabdbaacabccccdbbaadacbccddcacccdcdaddccdabbddaacbaaccdacdcbdbabadabdccadcdbbaccbdaaccbadccacadcdaabdadbdbadacabbaaabcdacbdccbbabdacadccaddbddddaccaabaacdaddcbbcdbdadadabddcbaaddacadcbccdcbcdbdcabdbacccdabdaaddaadcbbdacbbbbbccdbaccddbbddcbdbcbaaaaacbccbabdbcdacdabccdcbacabaddabaadcbdaadbaacabdbaddabcbbaadbbcdacadaccdcbcadccacccbadacabcbbdacbbaaddcabdacccbbdbddaabdcbaadadcacdbbcaababcaabbbaabbbccaadddddcddbadccbbbadddbadbdaaddddddaddbcacdcbbbadbdddbccdacccbcbbaadddddbbaacadddbbbbbccacdadaccccbddbdabbdabdbcacdccbbadacbadabbcdababbbcaabcddacdaaccadabadbccaacaadcaccdbadbdbbccdbaccbacadadbbdbaddbaaacdadcbcdaacdbddcdddcccccdbaaababbcdbdcadcaccbaabacccaacdbbccdaaddbaddaddbdbbcdbbdbadbdbcacdbcabacccccdbdccadccbcbccbccddacbdabbdaddbbabdccdccbacdcdadbadbdabccbbcbbcabbdccaabcbdacdbadbcadacabdadbccacdaaddbaabadabdcdbabdddcbddcbbbdddaaaaacdccccabdabaccdaddcabcabddbddbbdaaaabaccbacadcdcadadccdacabbbbcbaddadaadacacdadbdddddbdadccacddadddaccbbdabdbbaabcdacacddbcacdcbaaabdcbadaaabaaadcaadacaddcaccaabadacaacbcccdbccbddabbbaacccccabdaaadbddabddaddcdbccaccccdaccdacbddddcbcdbbdcabaddccdddbaacaadbcbddaaacbabbdbddabbddaabcdadbccdbcdcccddbcdcdadbdcbbabadccaddacaddbacbacacbdacbdddcdcbddabcbbbcdbcbdddccccbabbbbbbcbcbbbcbdadcdcddbdddaabcacdccdacbbbbadcdadcaddbbcbacdacaacbbaabdbdcddbadadbabababddbbcdaddbdcdbdccdabdbddddddadcbcdbdbaaddbbaadbdcabdcddbdcdbabdaacaaabdbddcdcbdccdaddbacbccbcdadccbbcadddbdcbbbdabcbdbbacabcaaddaccabccaaababaaaaddcdbdcdaadbdcadcbccacddadddbadccdbcdbdcdabbadcdcdabbcdcdaacadbbbccaccbabcdbcddbbbadccbddadaabcabaaaaccbbbaacaddadbcbcdbadccdcdcddddddadddaddcabcbacccddbdddccbcdcddbaacbdaacbaccdaabbcbcacabcabbadbabbdbacbdbbacacbbdcccbaccaddaccbdccbaccccbbcddbdbdccaccccccccabcadbcadcbddabbbacdadbcaddadcadbcbadabcbbabacaaadcaabbcccdacccaccbbdcccaaadaabdbdcdcdccdadcbacaadbdbdcddddcbadccbddddddaadacabccbcccbbaabcbdabacabcdabacbadddbaacdbcaadbbdbbcaddacadbbabaaadcadccdbcdbdcadcbbabbdcaadababbdaabdbdbdacadbaddaddacbadcdcbaacbbbcddcccdcccbbaadbbaabdddabbacbacdaaddbadbdacccbbcdccadaddcdcddbcdcadbaaacdabcdbdbdcadcbadcbdbadbbaadbdaabbbabcdabacbbdcbbacbbdaddadbbcddbddbcadbaaaabacdaaaacabdcbbacaaddcadacacaadbbacccaadcaddaabbddabdcdaacbdcadabbaccbbddbcbaddbaaabbcdcbcacbdcdccbbbddaadbcaacbacaadbcddaabcbccacdbabbabcaabacbbccacdcdacbbddcabbbbddbbdbaadbbcaacaabbbbaccacdbbacabdcbbcabbdbabbadcadabaacddaddbdcbcdcadbaddabbbdbdabbbdcddddddbddbbabbdcdaadcbbbdbcbccbdcdddaaccbdcaacdcdcddacdbabbdabdaaaadbaacbbbababadabbacdcaabccadbcdcabaabcaddbaaadabbcdbbaacdaabdbdcabbccadcaddabdcaccacdbacbadddcdadcccaabddcddabdbddcccbbadbddddacaccddcddadacabaadcbabbcdcacccaadcbdacdcbcabaaabbcabbdcbdbacddacbddabadbbbcacccccabbabddadcabcdabcabccdbaabdbbdcdccaacdcdcbadaaadddcabdcababddbaaaddabadcbacdacccaacacccbdbbcdbcacaabbbacdbacbbabbcdbdccbdccadacccbcadaddbccbaacaacadadbcacbacdccadbacadabdccadbbdababbddbcbbcdcbddbccacababbbbadbabddbdbcccddacbcaaacabcbcccdabacbcbccdabcccbbcbbbcccdabddaacadbbccdccbdbaaacacdabdaddaaacccdbccdaccaadccdcbbbcbdabcddccddcabbbacabcccdcbbabdababcdacbbbcaaaacbcdbabcccacdbdcddcacacbddcccacaadaadaabdaccadbcadadbcdacdcbdbccacdbabdacacaabccdaabcbabdadabcdddcbcdaacabbdccdaaadaddbaaabdabcddbbcbcdcdcbbddcaddbbcddbcbbabdadaabbddddacbbadaabbcadcdabaaccdaccadbcbdcbbccbdabdcabccbccbcddacdbcbdaadbddbbcdacacabdbbdacabcbcaccbadbbbdaadccbacdccacbccddaddbbaadacddbaccddcaadabcdadbcddccddbcddbddbaaddcaaccdcbdcacdcccbdadaddddbbccdbbaabbdbbbbdbbcadbcabbaccbaaaaacacddaadddbccaaabcaaddcadccddadaabbcdbbdcadcccdbcdacabaaadbbbaaadccbbdbbddcabcdacdddcbaabbdbdbccbcdddadcbbaabdcbaccbcccaacdcccccbdddcababcddbdbadcbcabcacddacaddabaadbddbddbbdaaaabcdcddccbbdadbbbccdcadbbdbbcbdbccddaaaabdbdcabcdaabcbdcbbdbcbabcbddbaabcadbccbdcddbdadcabbbdcbabbbabcddddcaaacdaccabdbbabcababacaadbcddbadddccdbbbacdacbbaaabaccadbcdbdaccdcbcdcccdcabcdacbaaacddddaaacdaddadabbabbacbcabdcbcaacacadacbdadbbdcdcccdddbaddbccaddababddbaacdddacdcabdacaaccbbdadccaabdabaccaccbdaddbccdbdbabdbadbabaacdbdabbbcdddaaabddcdcacadcdaccbacdaaacdddabaccccaadabcbadbacbdccbbdadddaacddadcbccabddaacbcbdbbdbabddcbdabddadbccccbdabaaadbbabaadbcddbcdbddcbcccaddadcdcddbbbdaccbaccabbbcbdbbccdbbaabbcdbcbaacacadbdababdaadcaacbcaacabdabdbabdcbdccbdbacaccbacadbcdbdacadabbaabbbaddcacabddbabccccbbabacabdccadacadcabbcaaadacccdddccdaabbaddaaabbcdddacacbcbcccbbbbdbbddbbcdcdccddbbbdcccacacdaabdbaabbbddbbbcbcdabbdddbaadabadcaaabddcbcccdbaccdccacacbacaaaaddbabdbbbbdbbaddbbaadaacdcdaabacaabdcbbaddbdcccbdcacbacdaddaabdcbadbabaaccaacbaadaaabaacdabbdabdabaabadbcbcaaccdbbabcdbbabbbaabbdbabddabcdccddccdcaaacdcdcdacbbcbdcabcbabcbddadadbdccccbccdaabddcccabdbddbdadbbabbdcabbcbbdaadabcabcadcbbdbaadddbabacadbbcbaccdaaacccdadddcaabbdcbadcbdcdaacbddadddacbbcdccdaccacadadcdddadadacccbabccbdcadcbdcbdbbdabdbcbcacbacadabdccaaaddbcaaaaddaddabddbcbcccdabacbaabdbbbdccddacdbaacddbbddaaccabccbdcdddbdbcdbbcbdddbcacddcdbcdbacbcddbcadbcacbcdabcadadcdcabdcbbbbbddcacacdddcbaadabadaadcbdbcadaadbbaabdbabddcddaaacbddbcdccabcbabcccdcabdcbdbcacbdbbbbcaaaacaadbcacadbacdbcdddcdccbaadaadbbdaaccdadaacddaddbbdcccdaacbcdccdbcdbdaadacccbdabacababdcbdbabbaacaabcdccaaddcdacabbccdabcaddaabbacbdabcbbdbbdccabcaaabbbacbcacabcaaddcadddbccbadcaabaaadbaabbdbdddddadcadccccacddadadabbdbdbcadbaaadcdcdcaddcaadcdccdaccccdacaacaccbbccdcbbabcbbccabbcaacccdcdababbacdbacabcddbbacacaddadcddabccddcbdaabcbaabacbbcbdbaccaddabddbddbcdbccacddccbdbcacaabbbbbcddadbbbabdccaaadabcbdaacbddbcbccdbcadadccddbbdaccbabacbbccdddcbacbccbbabddadddbcbabdadbbaddcbdaacadadcdccdadcbadcaacccbdcbadbaabcdcbcabadaaabbdcccccabcdaabadadbcbcdbaacadbacbbccbbcbccdacaabdcbdbbdddcbcdbcacdcbbbdacccaccdbdcbdabbadccdbcccccabadaabbacacbaacdaaacbcccbacadddacaabcbadbcccdbdccdacccdaacaacbdbaabadcdcdbbcddbccabcacdbdbbbccbbdccadbbbcdaabcddbcbbdbdaacbcddddcbdabbabadddaddbbddacdcbdbdacbcdcaccbbbadaacbcbddccdadbacddacdbcccbbdcbdccbcdabcdbcbcdbacbcaaababacddddaddddaadccddcabdcaadccbddaabaddddbdcbccdbadcabacacdbbcaaacdcadbbcdaadadabcdaaccabcdccbabccdcddadaabdadccdcabdcbdbcdbbabdcacdcbbcaddddbccdbbbbdbcaccaadcddddaaadadbaccddaaaadcbaabdbbbbaacbbcbaccdadaccdbaacdcbadbdabccdddcadaadaadbddccacaacdddacabdbcaddbdadccddbbcccbcccacdbdbbdbbccbbcccdabbbcdbbaabbcbacbbccdbbbbcbdcbdcbdabbaadbdaabdbddbacbbccaadbdccdacdacaaaddcdabcbbbdbbbacabdacdcbcbcdbdaaaaddbacadadbbaabadaabcbcadbaaccccabbabbbaccddcbcbdcbacaacdbaabcdcdadbdcbbcdbcbbddabbbcbbdcddcbcacdbbbcdabadddcbdbccddbcdadcbbdbacbbddcccdbcbaabcbccaabcdaaccbdbaacabdbcdbcbbaabbacaddcdbdbdcdbdadddadccbbcbcaacddcaccdcbadcbbcbbdccccccddbbabbaccbaccbcacbcadaacaaabdadbccbacbaddcaabbdabdabcadccaddbbcadcbbdcabbaaaabbaadaaacdbacdcacbddbdaadcbabaadadbbcbaccabcabacadbdacaabccbbdcbdccdbbdccbdababcdcbbcddbbcbddabdbdccddbaccabcabcbdaddabacabbcbbcadbacaddacdbbacbadcacbbacbabcccccbcbbccaaaadbbadcadcccbbaacbbdadbbbddcbcbbacabdabdbaacbcababdbbaadccbbacabcdaacccdaddcbaacbcaddcabdcdabddbdacdcacdcaccaabddcadbabbcadcabbbcddaaabadbacdbbccaadbcdcbccccdbbcccabcdbddaccdddddabdcaaddbdddabbdbaaabdcdcddadbabcaddddaccaaacabccbadadddcadabdbddcbdabbcbaabacdaacabcbbdacbabbdabdaddcbcccaacaacdccabddccacdabcbdaaccbbbcbbaaccbbadccacabbcdbcbadcbdbcacdcdbcdccddbabcddbcdcbbcbdccdcacddbbacddacdccbdbcacbddadababaacaccadabddabbbabadabdcdcabcaabcccbbbbadbbbbaccbbdbadacccbadcbadaddddaaddbbcdbaaaaaadbacdcdccaacdacdacbcadacaadacabcaadcbccacbcbbbbdccacadcabadccdcdbcdbbbccacacdcaaddcbdcaaddaaacddcaabccdcdcdddabcbbdadaddaccdbdcdbddaadabcbbbacbadcdaabbbaddbbbcbacddcbbbbacbdacbdabbbdaccbacacabcbdcdbdcbbdccdacccbddbacabcccdaacabdddabadaccbabbcaddcbdbabcdbacadbbdacdddbddcbdcdccccbabbbacdcbdcacddcbadbacbacadbdbcbabbacbcabbacaccacbbdbabaccdbcaacaccccbdccccbccbdddcccccdcbcaadcddacbbcdaccbdcaacdbadbcacbaddaaccbbbaabacbddcdabdcacdaabbbcadbcccdbdaaabdaadddddcabccadcaabdadcaccbbbccdadddacabdbdbabdacdcbbbaadbbacbdcdcbabbbadbbdaadabdbaabbdacdcbdccdbdcbdadbccabadbbbccadaadcaadadadbadbaaadabbddadaadaadbaabacbbbcadcdcbcabdbbccabbddddbbbcddcacddcdadcccccccdaacaaccbbcbdcdbbddbdbbdcacbcddbdcddbadaacdbaccabbccbacbcdccdacabddbacdbdbcdabcadcccddaccddbdcaaabcabdbcaccdccdabdddcabbababbdadabbaaaabbdbcccccabbdcbdadbacadadaccababdbbbcbbcdbbddcdddbaacbbcaadbcaacdcdaaaadadaccabcccbdabccdbbacdadcbbdccababbaddabbccacbadadddcddbaaaadaddadacbacaabcabbadbababdcdcbadcadbcdccdadbccaddcccbdabbccccdabbbabdccaccddaacbdbadaddcccddaacabbdddcbccdabbddcdbabccddccddcabcdccacdbbaacbbddddbbabddabbadaacdbdacabddbdcbbacbdaaaacdbbacdaacddaaadabdadccaaccbabbcacabacccaacdbacdbccaddabaacaaabadaacbaaacabadadacdccbcbcbaccdddacdcbaaacbadcbcacbddddadbbbbaacaacadaadcababdadccdcbbbabccddccdddcdbcbddcaccbdbdbbabcdaddcbdcadadcccbdaaaaabdbabdcbcbcbdbaacbbadbcdbddbbaadbcbbcbcdbdcdcddbaddadbaccabcaaccbdcdccdbaddcaaaadcaaaccadcbaaacdabacdcaacbcaabaaaaddadaacaaacbccaabddccadacbdbbbbcabddaaaabadddbcbdcdcabdbcbaadcdccbdbccbddaccbbbbdbcdacbbaadbadcdcccbaacddbcacdcbaccadbcccdcabbbbadbdaccbbabccaddbcacdddbbababdbaccbdbdaddbcdacbbdddadbbbbdabaacbcddcbcbbcdabcabcdacccbcdcadcabbcccbdabacdadcdbacadccbbaadadaabbaaaadccdababbdccabababbbdbbbdabacdcacacacdacaddbbcdddaadbbadbddcbdaacaabbdbcabddadaaacbabdbdcddcaadabacdbbbaadabccddbcddcdbaacdacdccaccbcdbdaccbcbababccccccbdcdbbaddddaccaacbbabdccdddbbaabacabbbbdbcdbaaacadabbbacdaaaddabbacabbcdcdaabcabaabcaccadaacbdadaadbbccdacaddbcaadacbacccbdabcaacdbddcabbcccbcabaaabdcadbcacaacdbadddacabadaabcaabdbbaccccdaadccbbdacddaacbcacadcdadbbabbdabdacdbccbbadadbdbbcdccacdadaaadddbddabbcacbddcdadbdbdadbaaaacacdccaaaddabdcaabdbcccbbacacaadccdccdbcdbdccabddbccddddacbabababbcddbcbddcddadddadcbdbdacbddcaabdbcbdadcabaababbddcddacdbacdcbcbabbddaadaacacdccadbabdbbcdcccdaadcbcddabcdbababcaacdbbbbcdcaabcbbdaaacdccbabcbccdabdaadbcddabbdacddcbaabdbabbabaaaacabccbcbaaaabdadcdbbcbcdcdadaacdbdcbabcdaccddadddcaabccabcbdaabcbbbabacbbbdbadbcbcabdbbcdccbdbcbccacdabdbbaaadabcadddacaadbcadabdababccdacbbbbbcddbbddaabbaccabbcdcacabaabbabcbbbcabbbcadddcadbadcbabdccbabaadadabddcbaaccabdacacabbadbcccddcdbbddddddaddcbcbcdbbacaadccbddcbcccbcadadacabaaadcddbbbcdaddbadaaaadcdcdacacbaddbcabcacaacadbbdbcabaacaabacacdadddbacadccbccabbcbcdadcabcdbccccaddddaccddcdaaccbddabdbcbcaaaadbcbbbcbbdbdbbdcbccdabcccdacabcddabcbcbdabacadadbbabbddaaadcbaaccdccdbcaccadadabcdbbabacbabbdbabddaccdadabdabbcdadccacabacdabbcbcabaabacacbdddbddbabaababccddabdddabbdcabaadccbcaacccdadbddcabaabadccadbddbadcaccdcadabcdabdaaacccabadaaaddabbbacddbcacbdacdcdcbacdabbcadabcccdcbbdccbdcaadcadbcaaabdaacbaaccdabadddcaddccacbbcdaccbbcadabbbabbbacacbcbacbbaddbacabdcddbaabbbbaabbaabccabcccbdaabbddbcaccabbbcaccddaaaaccbbaccaacaddabcbadcdacdbaaccadcbdbddbcaddccaaddddaaaadbabbabbccbdcdbbadbacdabdcbdaddbbbcaabddbaabacbbdccbcdbbdbabbcdccccaababdbddaacddbbdbdcbaabcddbbcdbddcaaabdcabdbabbcbcdbadbdcaaddbbcdcdbbdccbabccaadbddcabdbcbddcaccbadbdaaaabacdacbbdaddccdcdcbbdbcdabacbbdcaccccbbbabacbcaddbdcdcacbbcacbaaccacbddbbbcdaddbdcbbcdcddadbcdbaaaadaabcdbaaadbcddcdbdcacbaabadaccddbacdcbcadabddddababccbcdbadabcacbccbabcaacaabcdddaccdddddaaddbcbbdcdcdcccadcbcddbaadccbbccabbdbdaadadacddcaddbddbbaadaaddcaacdacbaddbdcaacadddbdbadbccdcccabcabcbabbbdabbbacccddddcccaaddbaacaaccaacaccaaaacbcaddacbcdacadbcbddbaddaccbdcbbcbddccddaacbdacbadbdbdbdbaddababadcbbdbcacdcbcbdcdacdacccbabcabbbbaabdaadbddbcbdbbccdcccbbaabbdabbcaadcddbacbcaabaccbdccbbaacdbaccadabddabadbbabdaabacbdbaabaddabacacbbacbaaabcaaabddcdcdbdccdababbbbcdcccbcdcddabdbdadbdcbcddacbbdbdddccbadbaaaabaacabaadddbbddbbababdddacdcacbadbaddcbadddbbbabdbcbabcccacaabacbaccacdbdadddbbabdccacbacabbadcaacabccbaadbbbbdabdcbdaccbaaaacaacabbcaacdcadbdaacdbbcddbbaaaaaddadadddbdabbaabacdccbdbddacbbcacabcaaaacbaddbccbcdadbbdaddcabdabcdaabccbccbbbdccbcdbacbdcddccccbdaaadcbbdcdcbdabadbbddbcbaabcdbadcdadcaababcbadcbbdaccbdcccaacdbaaccbddccbbbcbacbbadbbccbdacbdbbbbbccaaabcaabbddddccbdaddbccbbccaadcadbabcdbbadacdccddcbcdbbaacbcbddaccbaddccabccdaabacdacdddacccaababcbadddabdababcddbadcdbcacdcddcabcbcddbbbccacbbcadcccdbabcaabcdbdcddbbaadcdddacbabacaaaddaacabdaddaabadacacbbcdddbdbcaaaadaaaddaddadccdbaaaddabdabaaddbbdbcdbbbbcbcacbcbabddcdacabaddaabcdccbbdabcabdcccdbccbbbbaaaababcbbcbbcbabadbdaadccdbadcdbababcbacddddcbbdcbaacdbcadcabdccdbbababaacdcbbabbddbadbcdaababdcdccbabbaaadaadcdaddaddccbdbbabbbbabbadcbdbbaacddaaddacaacacaaaabdbaacbdddcbbbcdacadccaacbdcdaacadbcdacbbcddcbbddaddabbbdadadbccbcccbacbcbbcbcddaaddddcbdbcbbcddbacdabdddaabcdaabbccdccbbccdadbcdcccacbacbbdbccadddcdadbcdbcbadccbdcabdcbaabdaccdadaadbbabdddccaccccadccaabcdbccdcacabddaaabdbdccbacbccdcdbaddbdabacbcaadaccbaabadadacabdbcbcdbdbddcddbbacdccbdadcbdbacbaabbccdaddbdbcddbcaaccbbccaccddcabdbdddacddcddbdabaabbdbadcbadccdcabdacadbdbbbadacadbdbbbcbadaccaccdcbccaaaabaacbabdbbdaadbbcbcdadcdbdabbaacbbbacbcbacdabaabddadacdaaddbbcbbaadbccccaadacdcbbdcaadcbcdacadbddacbcbbacccdcadccdaddbccabddaaacddadbbacdbcaabadcadddabbadbdbaccddddcaabccdddbbdabbbccbbbdaaaabababbdbdbcbdadaaaaccaacaabcccdabdacbcbadbadddddcbdbdcbadddbbcaccbbcbdbbdcbddaaddcacccdabccdcdbacdaacabaacdcbacccddabbdbcbbabbbdabcccaccacbddcabbaddcbccbcabddccacbadcadbbdbccdabacacacbdcabbbaaccbdcdcbbaacdcddaabbbabdbcccbbbabdcabcbdbbddbabbcaaccbcabdbbcadaccbdbaddcadaabcdbacdabadbcdadacaccdbcbcacddcaccdacadabbbcadcbdcbacdccabbbaccccbcbcbcccbbdaacaacdbcdbdccacabaabaadabcbccbcbdadccacbcaccdadbbcacbcbacadbabbddccbbaabaadbddbbacaadbbaadaccbbabbbbdacabaaddbcabacccccbcbadbbbcdbdccbaccbdcbdbcdbbcabdadcbbdbdcaacaadbdbcdcdabcbcdcccbbcbaabacdabbccdbadabbabddcddbddbcaabbccdacccdbbccabdaccbacabaaaacadaaacccaaddbcbadaddbadbdcdcbbaacbccbadccdacaabcbbbbbacadaaadcbbaadbbdbcbaabadabdbcacdccbddcbdddcbacaaaaadbbbbdacbdaddbdbcccadaabdddacbabaaacacbdaacbbcdaacabcbbadabdbbacdcdcacddbdbcdbbccbbaddacbcacadabccadcbdcaaaddaacbcacbabbabccdaacccccdadcbadbadbcbbdacabccaadcdbdbcccdcbabaccacddcaaacbccacbabaabcdadaddcdbbbbaddccbcbacaaddbdccdaddabbdcddacdbbdddccbbadcccadbbcacddbcdbcbcdbbbbadabadbaababacbcbdbbabdabbdcbcaabacdbcbdbddcdadacdaacddaabcadaacdbaacccdcabaddacadbbdacbacccadcdcacbbcadcdaaacabdcadabcdbdcdadcdbcaababccbadacdbccadbccaddccabdaaccddbabccbcdaadbaacadcdadcacaabacabbacaaddabcdcbbdacccaacacdacdccbbdccdbdcbdbcdcccddbaaaddacbbcbaabbaaabadabcbbddddacbacbbccdbadaaabdbcabcdcadbbbbbbbaaccbddabbcaddaadcdbdabdbcaaabcdccdcaacddadaabaddaacbcbddcbaabdbdacbdddaacdbabbbcdccacbaadabadadacdcbadabacbbccdccccccbacacdbadacacdccaaaccaccacaababcddcbdcbdcabaddbbcadcbbbdaabaccabdadaacbccdbcdcdbaaccaabdddbdaaccdacddaccbcacaabaacdbaccaddbcccbbbdcabbbacccdccbcbbdacdddcaabbdacbbccddadbbbccbddcaaadaacbdaaddbbccccacbbdbaddccabdcbbcbacbcbdcdadcdbcddcbdaadddabaaaaadcabbcddcadbbabaaaaabccdcbdaccddbadacbbccdadabaccddaccabcbabcacdcbacdbaabbcccaddccababaaadabbdddcdaadadcbaacdcbccadbbbbaaaaaccdccadcdabdacddbcdabcaacacaaddddcbdcbcddbbcccbadbbdbaccddcaacdbdcabcdcdcbcdcbdacdcdbcbddbdaddadcddaabcababbcacbddcdacddcdbbabbdcccacdbdcccccaabdccdabcadacdacdcababbdadaaccccaabbdaccdccbabaadbaaabdcbcdbcccdcccdacabbddaabcbdcdabdbacbbacddbdcadaacaddbbdbddcbdcdccbcbcbaacabacadbdadbdabdababaddbcbadadbdcaacbbacdabbadcabbbadbbdddcdabbdacbccbcdbbdcdcaabdbddcadaacdcabcdaddacdbacaddddddddaaacdcbdcbbdacdcbdbdaddabdabaabcacbcbabaddabcaddcaaaddbbadabacaacdadaadbabbdbdbddddcbcabdcbdabbdccbbcccbbacbcaabacbaababaccdbbbaacbaaaadccdbdcbdccbdcdacabbaddbbbcdaddadbaabdcabbdccbcdaaacdbcbcdabcacdabbcccbdbdbddddcbdcabdaccaddcbddbcccbdababdbbadcacbccbacdbbaacdacbbdacadcdaddbaadcbbdbdbdaaacddacccccadcacbcbdbddabcaabdabaacabababddaabdabbbacbdaddbaddbaadddbcadcaaccdcacabbdbbaddddbcdabacbbbdbacddbadbbcddcaabbdbabbbbcdbcccaaaacdaaadabdccdbccbdacaacabbdddbcbabcaccdcdddbdbcddabdccccbdbbdbbdaccdadabdaadcbcbabacabacacccbacdccbabddabbcddcbbccbaddcaaacdbabaacbcadddbbccccdabdcbacbccbcaccacadbdbcdddcddbaaadabdadaabbddcabaaccadbaaadadbbdccddbbabbadadadcdbdddcbcbbcaaddaaddbcdaadbdbcaabadcaacdaabdacbbcacdbcacacabddddadcbccaddbacaacabbcbabccabbabdadbdabbbbbdbcadbaaaaccbbabdbbabdcccdbdbabaaaaacdbabbbadbcadbdadbaccadcdbbdbdddcabcaacdcdbbdcbddabbbacdbbcdacdacbbbaddcadbcdcdccbdbbdaccaccdadbbbddddabaccbdaddcbcbcdacabdabadcaadbbabdadacacaabcdddbaaaacdbdbcaabcbbbacdaddccacbcaacdcaaabaaabdbadbadbbcaccbaababddbbacacacdacbddccbbdcbccdcadacbcdadbacabbbbadbcaabbcabadaccbcbdaaddcdadcbbcaacccaccadccbbacdcbcdcdcbcdbccdacbaccaaaaaadccacccddcadcadadddbcdcadabbcbdcabcbaababaddcccccbcbbbbdaabaddabdadcabddcaaddbbadcdcbbdcaccacadadbddbcbdddcacaabdabadbcabadbbadadacbcdacbcabababcabcabbadcbdadddcadacccbcabadbbcabdcbbcbdddbdabbbaaddbacadbacbcbabcdbdcdabdbcbacccbcbbddaacdbcdadaccacdddbcacacbcaccaaabcddcabccabccadadddccacbdadacbadadcbbdcdcacbaaaabadddaddddbcbababcdcbadcabaacaccacdacbcbaabaacacdcaaabbbcabaadcbbbdccddccddaaccabdccbdadbdddaadbdbbbcbcaaabdddabbcacdbcbaaaabbdbaadbbcacbaacaaadddaaccbcadaccbbcacdacccbbcacdcbbaccabcdacdcbdcabccdacabbdcccbadbabddbbdaadbddcbabddccbddcdabddbbacaaadbddcabaadcddbdadbdddadcdbcabadddbaddbddcacacddcabadcadadaacaabdcdbdadbdaddaaadbbcbbaccaddacdbccadcbdcbababcacaccacbabcabbbccbcaaacdabacbcbbacadbbcabdacabdaadcaccdcadabbdbcddccaabcbbccbaabdcdaccbdcaaccdaacabbccccaabbcdccccdbcdbaaacaadabbaacbdacbbaacabcdbcdaaccdadaabadddbdabaaccadacaabacaadaccabbabdcbbcbadacbbaaaadaabbbbabddbcabaccbdbcacdcccadacacbbcabdaadcabddaaabcccbdabccbbcbcbccdcadddaaaaddcdbbdaadaabbddcbcabaddbcddbcbdbdcccadbaaacbcbcbdccbcdacabcccadddccdcddbbbdcadcaacbbdbdacadbaabdaacbaaddbccdcaaacabdabcddaadcdbdbacccbbbacdddaaaabcacdcabbcbdabcddcddaababaabbadbacacbdccdadbccabdacdbacadadabdccdaccccacdddaccdaabdccdabbccbccdaacacddddbdbbcdadccbaadddccccbcdbbcdbcadcdababbbaaaadbadccacaccbbadccaadadcdcaacabdbaddccbdabacbdddacddbddaddddccbcccaddccdcababbddbcadcddbcbccbbdadacbdacaddbdbbdacccbbaabdbcbcabdaacacbcdbadcccbcdbdacdbcdaacaaaacbcaababcdaacabddacddbbcbcadcccddbbcbcbaaabcddadaccdababdccccdbdcbabaddcadbccbcddaddcaccddadcbdddacdddcadcbcbaabbcbbababbdddcbacccacbdbcadbbdaaddbaddbdcdaaabdccdacdcddbcdcbacbabbcadbccddacccdbdbaddbdccaddddbbcbbddbdadbcdcccabcbaabbcbcabbacacdcdadabacbcbdcbbbcbdcaaadcadaaccbaccbdabccdccdccdcbccddbbbbdbbcdaccbddccdcbacdabdadbddabbabccadaaacdbbdbdacabbaabcaaccddbdbaaaacbdbcabdadbaccaaadabcddbacdbbadbbdabccddddacdddcdcdccacaddabcddaacdabdbbdcbddbdcadbbdcaddadcadccacadccccadadabbaaaabbacccddaaccbcaacbbbcabaabdadbccadaaddbaaaccdbcabddbbaaaddcbaadabdacbbdaaaababadaccbabdcaddccbdcddbaccdcdddddcddcbccaadcdaaadbaaabdbcbacdaadababbdabadabaabbdaabdccbbcdddcabcbbdbdacdcaadcaaadbcbbbcdbcaccbcbabdbcadddcdbdcddadcdcaabadaccabcabbcbcbbdccbddbabbcaddabdbcdacacdabcabadabcbdaabcabcbabddbcabbacdbcdbbadadcabdcbbdabaccbcdabcababaaabbacddcaabcdcbbbacccacadcbdbbadcbdabddbdccadbddbbcdacbbaaddddcccdaadbdbbdccdcddcaaaaccddbdcbbdccbcdaabcdddbcbddabbacddbaccdbbadbbdbabcdacababdddabcbaabbcdabcccabaddcacbdabbcbbabddacdaacbcdadacaccbbbbadcdadacbbbaaddacbcddaadadbdacaaaaadcbcaacadabacdabacabdabacaadcbbbaddbdddadcdbabcabdacdaabdcadcdaaaaaacabbacddbdaadaddaaaaaabbaccabcbdcbbbacccbbacadbcddbcabcdcabdcbddbcccabacbaacdddcbcabaadccdcacbddcacadaddbbcbacdcbaadcaabbddbbbddbbcabdbdacbaddabbbdbacbbaccbcbccdbdbaaaadacdbabdcababbddadadaaaddbabdcdcdcaccabaacbcccdccbabacbbbaccddddbdaabbddaddcccabcccdacbdbbcaccbabbcbbbabccbcaacdaaaacaaabcddcbacbcbdaabdadcdacdbcbdbabcacaadcbdccacacbdddaacdcccdbcbccdadcdadaaccaddbadddadbccdbadbacdabcdcbbcadddcbdbcbbcbaacccbbcaaccdbcacbddcdaabcdcdddcddddccabddddcdbabccacdaccdaabcaadbaaaccccbdaacacdadbbbbaadaccdbabbadaaabbddbcdddbdcadcadabadaadbabdccbaababdbcbbabacbdcbbdcacbbbdaccdadadbdcccdcdccdcddaadacccbdabdabddabbdccbcdcdbbacbdcbbbddacadaadaddcaddbaaabbbbaccdaacaaacdccabbcabbbddbcabbdbaaabddcaccaccbdadbaaabbabbccdbbddbbccadaccbbbadaaccaadcbabccaacbbacccddabacdbadacaddcbcbaddbcbcbadddaaaacbabdccccccadbadddbcdbdddddbdadabbccbbdaddaddbddcacbcbdacdabdddcbbcbcbadccdbcaacdcacbadcbddadbbcccbdcdadcbbbbdbddaabbbabadbbdacdcbccadbcbcabaacccddcbcaddaacbbadcacdddabbadbaddddbbacccdcdcbbdbdabdbbadcaaababbcbcbacdcdcacbaaacabcacbdaabbbdaccabbbdbbcdaababbcccaaaacbdddcdaccdcbdcdbacbaaddbcccbbaababbbabaababcdabacababddabacadabcddcccbdcaddcdbccdcbaabbbbcaddaaddadadacccbcddabbccadbdcdcbbdcaadabcdaadbdcaccaacdbcdbcddbacdbdbaaabdcabbbbbababacdbccdaadadadddbaadaadaaacddadccbdadbbcddcaaddaabccddaadbbcaddcdadabbddadddbdcddbbdbacdbdcaacadcaabdcddbdcdbcacadbdacaddbaccdbaaacbcddcbddcccddcaddbdccaadcbacccadbdcdabbadbcbbdadbacbaadcbdcdaaccaabdbbdbaaccbccbadbcbaaacccccaddbbbaabdbcbaabddbcaaabcbbbcbaaabaccdbddcababdbaabcaaabcaadabacddddcaacadbbbdadcabdcacabdbaccbcaccdadddbabcaacddcaabcdacbaacbabbccccbdbbcaababccbbbddaabaddacbabdbdddcabcbabbddddabdaadccaddcadcdcdacccabbddabacbdbadcccdcadbaaccccbddbdbbbbbdcbbaaadbcadcbabdddddcdbbbdadadcdbadacdaaadcaabdcacaadbaccdbabbabbcaaacbdabcdbcadadaccaadcbbcbcaddbcabdbccdcddccddbaccadbaacabbddacccbbdaccdabaaccabbccaabaabacacbbaddcbcdcaacaddcaacccacbcbcccaadabaabcacdcddcadaabbdcddaaaacacbaaaaacbccbbabcaabbddbbccbbadcdacaadbcccccabdcaacabababddacbcdcaaddbccccddabdabcdccacbdbccbacaaabbbbcbcccdbbccbddcddcbbbabbdccacbdcbdbcccbbcadbacbbacbaaabddaabdabaddabcbddcbbabbdddaacbdabddadbdbabcdaadddcaddbadaacbcbcbccaabcdbacdcbcbaabacdaabbbcabccdacacbdbdcacacbdccbddabbacdadabcbcdbdddbddbccadbdacddccddbdcdddaaddaabdccdabddadabcccbdcbadcabacadbaddcbcbdaacaacbddcabdbcbcbbaddbbcdcabdccccadabbbabaababbbdadabcdbabcdacdacadddcaadbadbccbdaabcbbdbdcbcbadabbcaccdaaccccacaddaccabcbcabdbdcdabbbdadaccabbbadbdbddccccaccbaccbcaadccbabcbdbabdcaadcadaaaccbddbbbbadbcbaaabcacaacdabdcccdbbccacbbaddcadddbaddaabcdcbdaaddadcdabcaddbdbadcdaacabcbbdcacbacccdcadadcabbabddccddacccacbaabcdababccbcabdaaadbdccdcaabacaaccccbdccbadcabcdbccabcdbcaaddacbdcbadbccdbcdbdcbddcdadbcdccbbacaabdcbcdddadbdcacbdbcbbcbbbabbacbdcbbcbdacdacdbadddabcdabddccadcacadbbbadaabccdccaacadcdaacacbcdbcababbacadbbbadaacddadbadcddcaddbabcbdadbcddababcdabacacbaccabcbadabdaaadcdadbcacbbbdccddaccddbdbcccaacdcdaabdcadbccacadaccdbbcabcdabddadbdbddddbcacbaccbddbbaadaddbaccdcbdaadcabbbbdaabbdcaddbabaaabacddadbdadcccccdcccacaaadcbcbdabdbabcabdbcbcdadcdddbdbbcaacdacabddcbcdacabadaccccbbdadbaccaaaaaaacaabdbcccbcaaccabaddcaccabaaddaadadbcabcbadbdcbabccdcabdbcbdbbaddddbcdbbabadcdabacacbdacaadcdddcdcdccdcdbcdaabadbbccbdbabddcdbbcbdbcbcacbcbbacacddaadabbcbdacaadccadbccbbbbdabbadccdbbdccbadbcdcbacadcacadcdabcabbcdcaacbbcccccbdcbdabadbcabaacbaddcacbddccbdacdaccbbbbbddbbdbbbdbccddcaddbcdcddddcdbbcbddbdbcbbcddcaabcadcdcaddaaabbdbddacdbacbabcbbddcdadbcbacdadbddabbcddaacaddbadcadcbbbbcdbbacabbddcddbcabadcacabcbdabbbadaacaaddddbbccacaccbdcabdbbcacdadbacdcacddccbcbcaccbaadabaddbaacaaacbcdaddbcaddbcbdbccabaadbbadbbdbcaadddccdbaaccadabcdbbdbccabbbdaccddcbcdcacadacdadbbbbdbabcccbaccbbcdbabacaabaadabdaadacaaddbdcaacdcbaaaaacdbbbdacccaaacdaaddccaacdddabddbaabacadcccdcccdbcbcadcaacadcdbbadaaaccaaaabcabbacccdbccddddcdcdbcdcdcabbaccddabbcaccaddddbcddccaddacddbbcbbadabcaabcbcaadcaccbbdcacbaccddaddbcacbdaddbcbaabdacdcbbbbccdcddcaadaabcddabdaacdaaabcbccaaddbccdadaabcdccacdccdadbbdabcdcabaabaddccccbbdcaddcacbbddbabbaccdbdbabcdcdbbaacadcbccddccaccaccabaabdbdcacdcbbaddcbbddacaccdadbcdadccdbcbadcdbdccbbccabbcdbdcaadccdaddbddbcbbcdbdddcacaacdbccbdcbbdcdbcbdcbbbbddbdddaadabaabadadaacaabcddadddcddcbcbdddaabadddbccabbbbcaddacbbaaabacbadcddccbccdacdcccdaaccbbccccbadbbcacbccbcabcadaacacbcbbbbbabbbcbdddbaabdbacabbcbacdccddbbcbabddadddcbbdaacacadacbcbbdcdcdaacadababbacbddddaadcbbbdbacbcadddbdaaaadbcacbdaadabcaabbbccabaccbadbddcdbddbabcbccdacdadaacbcdacbaacdadcddcbacadbabdababacbacdacdababcdadcbbdcbddbacdccaccbdcbccadcdcadbbcdbddbacbbdcacbbabcdaaaccbcdcddbdbdbccbdcbaacdcacbddadbdaccdbcaacdbbdcbdaccbaaabccbcbbdbbbaaaadcbabacddbbbbbadbabbadaccddcdccaadbaaadbddbbacadcdbdbcadccbdcbaabacbbcababbccbcaabdbcbbdbabcbcacbdcdbcddbdbadacddbabbbddabdccdacaddcbddbcddccdcaddcbcabcaaabcdbacbcadbccddbacbdcbacaadcdbdcbaadbbdbabcbbaadaddaddacdcdddcabababdbddbdcaacddbbcdccadcdcdacabcbdbaddaadabbdaaabdacabdbbbadadccbaacccadbcccbdbcdcadccdcdaccdccdddcaabddcccbcddaacbdccdcbccbbabcaaccdcdcbcdadbabcbacbaddcbccdbdacccbccbcbcbaaabccbbadcabdbdccbacbcbdadacadbbaaaccdbcdcabbdababbdbacaaaaccacbababacacdbdbbaaacbbccbbaaabccaadbabbadbababaabacccaddbdbbbdbabbdcbccabbcdbdaacdaaddadaccdcbdaabdaadbcbaadaacbdbadddcadbdbdacddabbbccccbcaccbcccaadbddcbabcaadbcabcacdbcddbccabbbaadabdbcbdabaacabbadcadcaadbbdcdcdcabbdddaabaacbcbbdadbdbdcbbadcbcaccdddcbcbbdcdbbaacabcdaddddbcccbacbabdabdabaadacbccbcbacccadabbccdbbdaaacdcaaccdabcaabcbcbdcbdacbddacdabdcabbbadbcabdcbadbdcccdcdccdbdcaabaacbdbdacdccadbbaabdddccbddabbdddcaaabdccacbbcdcbcacddbcdccbbdaacddaccbbbbddaabbcbbaccbadcdcdaabdcaddddbdcbbcbcccbbcdaadbdbcdacabdcddcbacadbdaddbacccadbcbdddbadbdbbbbdcaadddcdcbabaabaaaaccaccaddddbbbcdddaacbbbccbacddcdbcabaacabbbddadadbdbacccdcabdadcdababbaaddcbbdaaabdcaccdadbddbcacbbccccabaaabaacaadbabdbddddbbadbaaaccadcaccaadacbcdadabccaaadccabaaccdabccacdbcbccdccbddaccdbcccccdbdcbccadddbdacabbaaabdbabcdbdbcaaacccbacabbccbabaddbaacbbddcbdcbabcaabdcbacbbacdcbbbcadbdcacabcbabdaacbbdbcdcabaacdacdcbbdcdcadcacdbcbcaabbcacacdbccdbdcbcbccbacdcdccadaaaabbacaabbdbbcdcbbddaacbdcbdaacbababbbbddaacacadcbccaddbbbcabddccdadbbccdbbacabcddbdbdaddadcdcabbbcdbbaacadcaadcacccabdddadcdbcaabddbdbccdcbcaccdcbcbbdacccbcddddbaacbdacbacabbcdccacdadddbcccacbadbabdbdccbaacbddabbacdcbdacadcaacbabccbaacbcbdcbcdbdddaddcdacdabcdaaaaccbaaaabbbdbcdadccbccddcaaabccccddddacbadaaabdcbdaaaaaabcbbcbbaacaabaccdaaacdbbbdccbcbbdcdadaabaacbccccbdcdabdddabbadbbcbbdbaabcbcddbbdbcdddbdabbcadcbcbcbbdccaaddbdbcddabaacacbabccbaacadaabcbdabbbddccbcbbbccabbcbaaddbdaaabccddbcbddcdbdaddbcccbcdabbcddbcdddacdcababcbdbbbbddcdabaabcacbbbabcbdbccddbbadbddcadcaabdadcbccacbbdaddadbaaccadcabbcdbbbaaaddabcddcabdcabcaaaacbccbdbddcabcdbbcbcbcdabbbdddaccbdbabddabbddbddbabaccdacbbabcabbdcddaccddcdabdccadaccccdabcaddadacacabcabcacccdbabbbbaadcaadabcadaaddbacddcbacdacaadbaddcdcadcaabddbcacdabccacbddcdabcdcbdccdddbcabcdddadcbacddbaacbabacbbbbcdcdcbdbacaacbdcddacabccdbaddacacaccbaabaaaddbcbbbbbdcddadcdddbcbcabacbdcdcbccadccaadbccdbcbbacabbbbaaacdddaaccbabbdddcbabdbaaadadbdadcaabacbccddcddbdadddaaccadcdaccbdcbacbbddbcccbacbcaaccbabccdbcdaddcbcdaccaacacadccbdacddcccdbccdbcbddcaaacadbcaaabaadcdbbdddcabcbdbdcbcdccbcdcadbbbbbaaccdaacbdcdcadbabdddcddbacacaddaddbaaccdabdccdabbcbadbbadbabacdcdcabbbcbbdcababbaaabddcddbabdcbadcddcacaabacccdbadccabaacccbbbbccdabdacddaaaacadbabacbbbcaaacabbbbbcbadadbcdbaadbcdcbaaabaacdbabddccccdccbabbdbbadadabdbcccdaaaaabccaaddbadddbbbbdcccccbdddddaaaaacbbbcaadabadddcbdbdddacabdcadbcaccbbdaacaaadccaadddcbddaddadcabcbcbabbcbbcdbcadcdacbccaaddbcbcaaaccdbbadbdbddabbccabbabdbacacaddbdcdccdbdabcabbdabbbbdacabdcadbaabbaaabcdabdcbabdbdbaddbccabbcbdadcacdaaacbdbaabbcdddbaccbacbabccdbbcddbacdadddbaddabcdcdbcbaddcaccabcababaacdadbdabbbdddbbbacdaddcdbbacdabdbdccbcabdadaccacddabdcccdcdbdbbdbcdcaacabdacbccaadbabdbbccbdbcbdaabbddcabcdbbcadcdddbcdccabdcdbcccaaddbbdcabcababccacbdbbaccdabcabbcbabddccbbaaddaddbccbbbbbabbdbddabdbbbaccadbabddadaabacdcaaaababaddccdabadddcbaccadccdccacdbcaadadbcabddbdabbcaddcdaddacdbdabcbbdadacbabddbcddbbcbbddadaaddccbddabbcccccadccadbdccacbabdbadaadcacdcbccacaccccddbaddbdcbcbbbdcdcbbbccbaabccacbdccaabbbddddcddcdddbcaadadaabcbaddbbbbdbdbbddcaadcdacbcdbbaddbdadddbccbadabcdbacdadaccccbdabdbbdcabaadadacacbdcbbbbabdaccaaddacbccdcabcdcddbaaadaabaabbaaaabdabbddbcaddaadcbddadabddcabcdbddcdaccbcacaacddcccabadbbdaadcabddcbcbabdbbaaaaadabdbcccdbadbcdadbaccdaadbdabcbcccccaadcbbaabbbaabcaddadacdadcaccbdababcbdbdccbcbaddcccbdccdbcbcccddcbbbdaddccaaccadcbdcddbbacdcbadbdcbddadddcaaabadbdcbdcaccbddddbdcdbcbdbcdddddddcdbdcdbbdbdadccabbbbdddbbbcccddcbcaddbabadadabaccdccccbdbcddcaacccabcbaccacddbacdccdcbabccdbbadcccabaacbacdbdabbdbaaaabcbcdddccacbcbbbacacccdcbcbdabddbcaddcddbbaadcddccdbbdcbadbccadcbcdcccbbddbbcadbccaacbcacbbacbdbaaacadcbacbbcdacacbadcaabbbadbadccabcbdbdcdababbcbadcdadacabdcccaaaddbddadadaabaadbdcdabccbcabaccababaabdabbdadcabbaddacddababccbbbaccabcbccddabbbadcacadbdabaddabcbdccdaacdadacadbadccbdcbadcadcaddccbcabacdcdaadadbbbacdccbcdbacaddadbcaacbcdabdbbbcaabccabcaddcbdabdabadabbdcdbbbcccacdbbadcddccadbcdbbabcbdacbbcaabddddddbbdababaadaacdcadacaacabbdbbddabccddbbcbaadcdacdddcaacdcddddbcbbdccddcdaaabcabcaacdccaadbbdadcaaaaddcccccdbbdbbbddbccccbdaccaacaacbbcbdadbddbcbadbdaccdadaadacddbcccdcbaaabbdbabdadadddbdbccabaadcddcabddaddadbcabaabaaabccbbbbbddcccdadaccbccddcbadddbdccbccaadadddcbccadbacdbabbdbadbccddcbdbaacddcabbbcdcccadbaacdbbbbbddddacddaadabaacdadcddbabdbcadcaddcabdddddaddabbcdddccadccaaccbcbbdbcbcdbdccbdccdbaabddddbbacbcbcaaacdbadbdcacacbcbbdcbaabcacabccbcdaadabccdbadadccddcdbacadcdddccacbdabdcbabccaadadaacacbbddaabdabacbcdddabbcddcbcbaadcbddadcaacbaddbaabcbcdabdbcabbccbddbcacaacdbdcaabbdbbdbdadbacdbdcacbcbadbaabbcdbdcddbdadadcacbaaacabcbbbcacbaababdacbcdbadbaacddcadcccaddcbbabbabbccadbcdabbabbacbbadcbabccdbbbbcbcaadacdbbabbdbadbadcdccdbccadabcdcdddaccdcddbccacbbbabacabcdccabdbabcbadbbccdbabaadaaaaadbcdaadabbddacccbacbbbaaddbabcdcbbcacbcbaddaacbdbdcdaacdbacadabbdabcdcdccdbcdbbadabcdddcbbabdccadaadbabdcdaacaaccababaddcacbbbcaacabccbcccdbbaaddcccbbdcaaccddbcbbaccbdabbacaabddabcabcbbdbaaaaccabaadbcdaddcbdaccacdacbbbaaaacabdabbdbbbaabbdacbdbdaacdcdbdabcbaabaaddddabbabdbdaaaadddcaacbdbdbbcaadacbcacccbdcdddadadbdaccacdcbbaaababccddcacdbbcdacdabbdcccddaadcdaadbdcacddbdbdcdcadabadcadbbdbdbbdcdacdcbaacbbbcbabcbcbdabdabadbddcdadadacbdacbccbaddaaacacccadbaaabaaaabcaadddbddabacbdaaadbbcdabdddcbbbcaadcccdacbdacbbdaacbbbaabacbcbbdaaadddccdcdaddadacadbcdaddbdcbdbbadacbbdcabbabdbdbdabdcacaabcadddbdacbcdcaacabddbddacadaabddbcbcdacadcbbbadcaadbdacdadccbbaadbdccdcabbcacbacbbabcbdadcdcaabccbcddddaacccadcccabacdaadbcaddcacaabbabcdcdbcacdaaadabbcddbddbbdaabaaccbcccbdcccdadaaadddcdbdaadbccdabddbdbaabdaddbbbccdaddadaadccaabacbdcccccaccdacccbbdaabadbbdbbabbbcbabbddaccbadbbadbabdccbbddcabdadadcdcdbdcdbabbbcaddbdacaccbacdcbdcbacdddaaadadddabdaabadbdaaddcadabadcdbddbbbcbaaabadcaaaacacabcdaaaacddbacbbbaaadcbbcabdadbadbbbbccdcaadcacbdadccbccabdacacaccdddabaaadbbdcbaddcdacbccaddcbdbadbcdabbadccabbdcdcaddbddddcbdcaacbabcaabdcdabccbadbdcbcbdacbabcacaacabdaacdabbbbcbacdccbddcdbabdcbdddbbacdddcaabbdbccaabaaadccabbbaacdccbdddcbdadcabcdccbcadbbbbcabdcbdcabbbbabbdbccdcbdcbbdcdbcddbaccdadcbbdcaadbccdaddcbdacababbddacdaadbbacdbdadcaacaadbcaadcbbcbdabcbdaccacabbbabaadaaaababadadbcbcabaacbabbccaaaccdcabcdcccdddbaacbcbddaaccadbccbbacddaababaccbdccadcdbbcddaabbaababbcdcacacabacddcaccbbdccdbccbdacddcbcacabdadccdbbdcddaddaacadcdbbcadbcaccabbaccbcccccbacadbaddbadddcaadcdbaccababdbaabcdcbcdacdcbbbbadadbcccacbbbabacdabddcacbcddbdabccacdccbbccbadaaaccabddacacabdcdaccbccacccacdaaadbcbabababcadcccacabbacbbcdabdddbccaacbbabbcdbddaabacadbbcabcbdbaccdbbdaacdddccbbababcbcbaacdbbcbbbbbcabaaaacbdbbcabdacbdbdbbdbbbbbabdabdbacdcbbcccaabccdbbadaabacacacaadccbdbabcdbacaadbbadacbcbbaddcdbbddadabdbcddbcdaccdddccdcbdaadcbcccdccabacdcdcaacccccaacbbaccddcadbbdbcddbdadddcbdacabcacbadbddcacbccbbacdcabcaabbcabdbacbdadddbccbcaddaaaaddcbbcdbadcddbdcaddbaaabbdcacabaabcdadacddabadadbbccbddaaadcdcdbdadbcaabbcdbcbabbbadaccabdabbbaadddbddbbcacaddbccbcbdcbacbcacbdabbcbddddbdbcaccaacdbbcabcacaddcddcaacbbabadccbcadcbbbaccabaabbbadcaaadadbdadadbcbaabdcbdcadadaccccbbbaadcdbbccaddaabacaaddaaacbddabbdbadcabbaadadbaadabdaabdcacaaabcccbcddcddabbaccdabcdbbcacdabdbdcbcabcbcbcdacdaabdabcccdcbaaabbbaccdcccadadcbdaddaaadccbdbddaaacdcbadabadabbaacddbbdcabddcdabcbadddbcdddcdadccdbccbacabacadcdacaacdbbaaacaccccdabbbbbcacdbbcabdaacbcaabbddacddacdacbccaadbbcaadacbabcdddcdcbcdcaddbbacbbaaccdacababccdbbddcdaccacdbddabddbccaaaadcdcbbdaadcbbcccabcbcadcbbdacddacbbbdabdbdddcdacaccbcdadbbdbbaaabbccbabbcddcbcdddcabadbdadbdcdcbaacbbadbccdbdcbbdddbdabaadcbaaadacabaccaadabccccdcbdbbcdcaccaacabbddcabaacdcdcaacdbcdcdabbadbaaaabdbcdcbdaabaadcbbccadbbbddddbbcdcadacbbcdbcabcadaadbccadbbcccccacdbaadccaaabbdabaddcbcbcbdcdbabcabccbbabcaaaaccabadcadcadabdaccdcddacccaccbabcbccdadcbdaabcadbdbaacccdbbacbcaabbdaadacddaddbbacbbaccacbcbddadaddcbbcdcacdaaabdccabcbadbbbbdbcbaddbccacacdbccbbccdccaccacdaabacaaabcadacaaaabddadadbbaabdacdadbacbdbcabacdaacaadccbadacbaaabcbbadcabdbcccadacadccbaabdcabaadcccddbbbbadbbdacabbcdbbddbcccabaddcddcaccdabbccbcddacadcbabcadadcccbbcdbaacadbbddaaddaabaaaacaacbabacaaacbbdcddabccdcaadabcccbddabbcbdbcbbabddcbdaddaaaabbacadcdadadccddbccbadbdcdbbdbdbbdbdaccbdabbbabcbdbcaabbccdddccbcbccbdcddaabaadcbbddbdcabdcddbdcaadaacddaaadbbaabdadbabdaabdadadccbddbdaabdbadcbcbaccdbdabbcdddbcddccddcddbbbbbdddbacdadabdbaabaadbbaaaccccccabdbbcaaacbdaaaabbccdacdbdbadbcadaaddccacdcdabcdbbbacadbdcdabccacdacdcbadbadaddddcadacbcaadbaacaaacccacdddcdbadbacdaabdbdcaadcabbaabdbddabadacabccbadacccabcaccdbbddbadbabbcadbaacaabcddcdcdcdbcccbabadaddcadcbbdaacbdadcaccdcbdcacdcbcbbabaddaaddddaadacdcddbbacaadbcdddadabbbdacbaabbabccddadbbbcadbbadaaadcbbbdaacdbddaddaddbcaabaaabacacadbbacbaabcdbacbabaacdadbaacdabadbbabbadccbdcdaccdcdbaccbbddcdadbdbdbcbaaadbddccacdacacadbdcadcaadacaabcbcdddaaadbaaadadcbabdaababbaaccadcadccaacccdbbdabcbdbababdcddaaabdcadcdacdbcacbaacccdbcbadcdadaccdcbacbccacdccbdbdcdaaccacadaaabaabdddbabcadcbbcaccddbabbbbdcddbdbaccbccdbbcbdddadcbbdbbbbadaaadccdbcaccbcbbcabdaccccaccccdaaddcdcddbdbcdddabcccbddbabacbaadcabadcadcacddcabaaabcbdccdacaacddbabbbbdadbbadbccabbaadababaaaaccabccbdbaadaddacddaaadbdadcadbcacbccdcacdbdacddbbbbdcdddbddbccbbcabcaacddddabcadcadaddcabbdacbcaaadcdbcdacaacaacbdcdddbdcdbdcaddbcbabcbaabcbcdddccdccbdacbbcbbbdcddaadbdcccbdbdaaccddacadddcacaacbbccdbdccdddaabdbcaaabbbdcbabdaabbcbaadabcbcbdbbcdabcacabadddcddbbadaddaccdaccabbcbacaaaaadbbccdabcbcbaaaabddbcadacadabddbdcbbddccdcdcadbbdbbaddddbaddccddacbcbbcabbaadadabcdbccdddacdccbbaadbdcadabacddcbcdddcbbbacaccddcdacccdabdaadcadcdddbadbaadcacadbdadbbaaaacacabbcdbdadabcbacabaddddbdbadbcbbdaddccccdabbdcbcacdcbbbcabdcaabddbcdcabbaccaccaddacacbcdcbcabdacdadbabbabbccdaabcdcbbcbbcbbabccbdcacbbbdbacdaabccdaddaaadbcdccaddcbdccadbdcbbcbccbddbddccccddaadbbaadbcdccddccccadabaadcaddddacdcbccccdbbbccaddccdacdbbcdcdcdccabdbbdbbaaccdbadaabadbdacbbbabaadbabccbacdcdacadacbcdddadabcdbcbacbdaddbdadcaadccacdaaacacbcdbaddcbdadacbadddcadabaaddabcccbbabcdddacbcdaaddbbcaaaaccbbcababbcaacbbcbcbdbbccdadaccbadaaddaaabdbcbcbbdbaccadaadbbcaaddaadaacacddadacddccbabbdddbcaddcabcdacbbddaaddccadadcdbacbdcdcbcabddabadacbdacdaadbbbadcadbdbcdbddabbacacddbbaabcdccdddcccbadcbaabdaccddadcbcbcdbaddaddcbaacdbbacdcbcdccdaaddcaababbdacbdbbcbccddbddbacccbdbdaacabbbcccbccbcacbbaabcbacdbdbacacbabbbccbdcbbaadaddccccaacbddaaccbcbacccccbddadbacabacbabbdbadbaaaaccdadcbcbdbdcbcdababcccadaccaabdaaababdbcddcccabddadbcbdbdcbadaaacdbdbdcbbbbbddcbabcaadcbacdadccbbdbdbbdcaadbdadaaacbaaccdaccbdcbcabbdccdcacdcddbbcaadcacbcbabdbbaaacbddcbcbdbaababdadddbacdcbbcbacacaabddabccccbacdcdbdaadbbbbdbadbaacdcacdbccdbbdababdbdcdaaacbbcacddcccdbadadcbacacabdcdcaaadabbdbabcdbcacabacbbdcdbcadcbdacaacadcbdbbabbadaccaadbdadabdddbbadaadadabdaddadaadcacccdcbbbbbbdcbddddbbdcadcacbddbcadcaaabbbcdbccbdbabbaaddbdbbabadbcaadaaaabbbcdbdaaaddcaddcacaacbdaabcdddcbbddbdadcbabbdcdcabcccdbbcaacabbadbbdddbaccdadbdabaabcadadcccacabbcaaabaaadcacddbaacdaaacacccbdaddcadacdccbacadbabcaddaddbdbcbccddabcaaacbaddcdddbbbcbbbdbcdacbdbdacbbcbdcaadcbcabccbcdcdaaabcabdaccbccaaacbabaabaccdddcdaddbbdacbabcbdbcbbcccbccaccdaacbbabbcbccacdbdcacbcaaaaacbbacacacdddbcdcaadbdcddadacbacaadbbbaddbbcddabcabdbcdbddddcddcccabaccabdadbcbbbacadbdbdbabdaddacadaccddbbaccbbdabaadacdcdaacdbcacccabccaaaadccccccbaccddaaaadddbdddcdccadacabccccbbbcbccccccaadadbbdabcbbadcbaccaacccaadbcccbcbbadacaddddddcaccabbddcabdbdbdcddcbaaaaacccbcadcbcbcadadcccdadccddadacbacbdadcbdcbbccdcdccbbcacdacbacbaabbbadaabbaccbdabbcdcaccadbddbadddbbcdbcbbcbdccdbccbbcbbcadabddabcbaaabaadcdacdadbcaacdcdddccddaacaabdbbcdacddbaacdcbddbacaadbbaadaabbbabcadbabaaaaaadcadcbaaaccadadbbbbcadabbdacadcaabccdbadabcdbcbddbbdbccccadadaadcaccdacabccaabbcadcbcacdcbbbcdccbddbccabcbbbcabbccabdacbababcdacabdabaadcabcadccbdcdabdacabbaaccadbcddaabbcddbbddcddaddbdaaddcdbcadaadcdbdccdabccaaacacbdbdbbbdddbdcccbaaddbcadcbcdacdbbdabaacabacdadbddbbdcacbcdaabdaaccccbddbddbdcadcdcbbccdadddbdbaaccdcabccbacccccaaddbcbccbbcccbbdddbdccbbaacddcaacacbcacdbaaadbabddaddcaddcccadbcdbbdbbbcccdbaacadaadbcdcacdabcccbcbaddddaccbcdaabddccbabbbddadcabbabcdcdcababdcbddaacbadacddadcbbdcbddabdbddacadcacdabadbabcccbbbcaaaadabdddbbbcbccbbcccdbaddcdcbcbddddabaacaababddabbcdcddabadcdbcadcbabbadadaaacadcdbabbdbdbcaddbddcbdadcbdbaaddcdcdbccdacbdcaadddaacdcabaaadbbdaccbaabcdcadcacccacacddacbbdcdbaddaaddadddabbdcdcccadbbcbacbbabcdadcbdbcdbcadcbcdabbabbddcdbddbdbadbbccdbccdddbbbbadaabdabcaaabdbaacadadbdbadcbcabcabacccbdadabbdabbdbaaccdcbdbabccbabdddbbdcbcaacadadbdbccccabacacacbddaddccdbbbcacddaabdadadbdbadacbddddabaacbcbbdddbaaaacbabcbdcdcbbdcabdbcbaabdbadaddccadbbbdbdcadbacbbbaadcaaabbcdbdbddcbabbabbacccdbaaccccadcdbdacbbadcddbcaccabdaccdcdcacbcbdccdadbaccabacdcbbdddadabaccbadbdcdcaacbbcaabdddaacbccbaccbaddacaabcabdbdbabdadccaabbddccbccddaabdaabadabdcdadabdcabcabcdbddbbcddbcbdccbdddcbabbcadbcddbaaaccacdbbaadabdccaaddddaaacbbdccddabbbdbdcabcaddabbdabbbabaddbadcadaaabacadadcbddcccbaacdcacacbdacddccbaadcdccabdadaadbbdbccbcdabdccdaacbaddaaaacbacdacddcccadacbdabbccbbdacbdaddcdbcbbaaadbdababadcddaababbdadabddaddbdcadbaabaccbdadbdcabbbbdddadaacbaadcddadacaaaccdbdbcccdcdaddbacabbbaabadbadddaccbaaccddbbdaacacbaaddccacbdaabbbbdcccbdccaaddbabbdbcdbdbdccddbccdadcabaadbbddcbcadaaaaddbbaaaadbaccbaaddabbdddcaacccdabddaadacdaacadaacadadacbddacbbaabacbdacbbaaccdbbcabbbacbadbddbbccbbdbbccddbadabcddcacbdacbaddcbddbcabcdadacacddaacbcbdadbacddcccbdaddcaaaacddacdccaddbdaaddabdcabadbdaaacaacccdbdcbdbcccddabaacccbddddabbadcddddddcbbaddcdbbabaddbdaaaabdaaabcbdbadabaddbbbdadcdbacdbabcbbccabccaaabcbdcdacabbbbdaccdacbacacbddcdbaaabbacbccdccbbdaaccddbacbddcccbaddbddbccccbdccbbbaccddccdcacbaacdbbccabadbaaaccbbbbbccacadaacadacdbcaadddaccdcbcbacaaadabadcabbcbccadbbcccbcbdcaddbdcccccbdbdcddabcccddbcbdcadbdccdbbcaaabadcdaacbcbccdddcbddbcbdadcacdbdbdcbcbbaddddaddaccbaccbdacaacabbcdccabbabccdaacbcabbdaddcbddcbcbcdcdbbcbcbcbccbcbbddaccaaadbaccbcaccbbdabdddabbdcdddadabcdcbabcbacbabdbcdacbcadcddcbcdcadbcddccbddacbacddbabcaccbbcddccddcccadbcccabccaddacbcacccccddabadcbdcbaabddcddbddcbccccbdaccacdaacaccaaabbbbbabbadbbdbdddbbcabbddcbacbbaacacacaddbdccddaaacdddbbcccccdcdbddccadbdabbcdabdcbbdccadbccadcaddbaccdcbcaaddcbcbbcdbbaacbdcbcddadabbadaabbdcdadacdabdabbbcbbabccdcbbdaadbdabddcbababcacaccdddddaacacdddcbcbadadcabdbbcbbdadaabcdbaacbbbdcabdbdaaddacaccdacabadaaaadcbabbbcbabcdadbbccbdacacdcdbddcdaacacbaabccadcccbbaaacadcaacabdbbdbbabddcbbdbdaabaadaabaacdbaadabbdbaddaaaadabddcdcabdbbadcbbddaddcdccacabccdabdabdcddadbccddbaaccacabddacbbbcbbcbdbcdcaaacabacbbdddabdacdddbaddababdddbdbbcbbaaddbccabcbdbbcbbdadadaacadcacaacabcccddcbaaadbcbccbdabbbccddaaabadccacaacbddaadaccbbaccacbdacabbccbcdacdccdacdcdbadbdcddbacbcddcdaacbbcbaaccdbbbdbadbccddbadbbcbbdabdbbacdadbcdaaccbabbaadaaadcaaccdbadcdccdaccbcabcdddbbadddbdacbcabbadacadddbcaacaabcbbbadbbabcaadacbbddcacdcaccdcaccabdcbdababaddacddbbbabcdccbcccccabbdcbdabcaadabaadabbbddccccaddaccacbbbcbdcacbdbadabddabaacdccabcaccabaaabdcaaaacdcbdabaccacaddcbaaaadddcdbccaadbdcdaadcabdbccdbabddabaddccaacccddabadbcccbacdaccdbabbabaadbbbdcccbcabdbcabddcbabaacbdcbabaaabdaddcbdabacbbbcddaddbdcdcdcbddcbdbcabadccbcdbcbadcaccbdaaccdbcdadbbcddbbcbcbacaaadabaabaabdcaddbbcabaadbcdabcbbbdacbbddacdbacdaddbbbbabcacbdbbdbbdcbcacdbdbccabdadcddbaababbdcbdbbdbdcdbcacbbbbdcaadccddcbddadbbcbcacaadbcbbdcdaadadabccbbdabbbddbcbdabdbcababdacbabbdcaadabdcacbdccadcdbdaacdcbaaccbcadaacbdddcdaccacaaababbdbcaccbbcaadbccdacbccabdacdbbcabdcaabcbbbbaacadccdcbadbaaddacbbacccbdcaacaddbabaadaaabdbadabccadaaaababbdabbabaadabbdbbbdaacbbdcddcbdddbabdbaabdbaacadbccdababdddbbbdcbaadccaaddcbdccacdcbbabbdbbbbbcadabccacbbdbddcccbcbcdcbcbbdaccabaabddcabbbbcacdacddbdbcaccbadabddbbdcabcabbaaccaaddddacdcbcaddbadbdbbcaaadbdcbadaddddaadababcdabccccabdaccbdbdaabcdcbddcccbdbcccaabbabddddacabddbcdbbddbcdbdcadcabccbdcdadadaadbdadcddcaaacccbdabbbabbcacdcabaaacccdabdccbcddddcbabddcccdaabcacdcaadabaaacadaabcdaccbddcbbcccdcabbbadadddabdcaaabdbaaaadcadcadcdaccbbadcbcbaddcddbcdccaacabddcbabcaacbabbdadddbcacadddbbddbcdbaaabbddcdbbccbddbbbbcdbbbdabddaaadddacbbabaccbddcbdbdccbabaccbadcbbbadadbadddaaddbacbddbadbccbcdaabddadbabaadcdbbaccbbbbacdcaccadbbdbbcbdacdaddcdaabbabdddbccdbbdadabaccaabaddbcccbbcccdaabcddbadaacaadbbcbddbbadabbcbabadbbdbbbcccacdaabccdcdadabbdaddbddcbcabadaccabbbadcabdbbadbcccbcaaabbdaccdadcaaadcddaacdccacaadbdaacaadddacddbadbbabaabdaacddcdcbacdaadabbbdccacbdbcaaaddcccbabbaaddccdabaacadccaabbaabacdadbbaadbccddbdcabccdaccdaccddbaababacddacdbcbbdbaababcabbbadaccdacbbcabcaabccaacabcdddaccbdbbccdacdabdccbdcddbdbacabcdbcbcdacbccddbdbcdbbcadabadabcacdcabbdaadcdabdddbadcdbbdabccbaaababbdabcadbdaaaaaabdccaadacaabdbddccbcddbacaddacdaccbccddccccdcaddaaaacdbdccbbcbaacdcccdcadbbbabddcdddacccbbadacbdbbbaabdabccdaaacbdaacccccdcdacabbcdbbddcdbcdbccdddbbbdbbcbabccdbaaccddabbccaabdabaacabcdadacdcbddbbbdabcccdcccbacacaacdaacbacbbcaaddaddbdbccbbcdbdcdcccdbdacdaaaacdadbabaccbbbabccddcbbccdbcacddabcdacbbccdcdbcdddbacbccdccdabbddccabbaadadbadcadcddcacbcdccbaacddbcddacaddbbadabcdcbbcadcbcaacbbcddadcaabbdccacbbbcdaacbdaacaaccdcbdbabacadabccabccacdcbaaabcadbdbacdbdaccabaadcbbadccbcdacddabddcdaaacdcdabdbccbabadddddcdcbbdcabbbbbddacadcacdaaaddcdbbddbdbabdacccdabbadcbbcdaddcdcccdcabdcadbbabadbbbaacadadcdbccadcdcaaddcaacbaccabcbdadacdcbddbbabaccbbbddbccabbbddbcdcbcaabdcbabbdddccdaabddbcacbaabcaccccbcaadbbbadaacaddbadbbdbcbadaaccacdcabcbbccaccbbddabaadbaaabdbddbabbbdcdcccdacbdcbadccbabbbdacbccbdbcdabdbbdbdcbbcdcbacadbdabdaaccadddbbccbdadcbbdbcadcadcbdaccdbaaacaadacbabbaccdbcdbdbbbcdcaddccbddbbacdacccccaaababdbdaacaaadccbcacbdadaacddccbacbbbddaadccbdcccccaacdcdcbaacbcbccbbabcadaabbdabdabadabccbadcdcccbdababdcdbdbacaacdbdcabbcadbccdbbabbadacaadabaccaaabbaaaccadbdaccdccbdcaabdabbcdbcbdddcbdcadbdccdcccbabbbbaacaddcdbcaaabdbbcdabbcbababbacbbccabcdacbacadbaddbbacaacbbcdbcdbcabcabadaadabaaabcbcdbbaaacccabbbdddbacaaccacadccaadcbcaabbbdabacdbbdccbbdacbabbdbbcccbbbcbbddbacaccacacbabdabaaddcabddcdbcccbbcdbccddccacbbcbbddcdaacdcacbcddaadcdadcddadcdcdbaaacbcbaabbcddbacbdccccbbddcdccdccacacadcbacdadbadaadbaabbbacbabababcdbabaaabbccaabadbacdcacddbadbcaddacaacbadcdabbaaaddacdcbbdcccdadcabcbacacccbcaabcbbcadcdabacbacdcccbdcadbcbbbdbcdbcabdabccbababdddddbdaaccbcbbdadddacbbdcbbbadcddbadcababddcdcbbbbcaadadcabcaaddaddddabcbddddcadbaaaadcdadbcaddcbbacbbccbacbbcdabbcdacaaaadabdaaabaadbcaadbbddacbbcddcddabadbcdaacabbbadbadacdcbabbddccbdadabdddabbadbbccabbccabababdcbabdcdbabcacdbccdaaacbbbcdbdbcbbbbaacadcadcbdadabaabdacbbbadbaaaacdaacbacaaadadbcacbcabddddcbcabdbcaaaacbbbddbbbabadbbddcaaaacadaaccbcdaacbcaccbcaddccbdabacddabbdabacbbbaadacaabdaabbbcdaddadbadccbcbbcddabddaccacbaacdacdddaaddabcddddccdbbaddcdcbcadddcbaaddcadadadcddbbaadbcdbbbbabbcbdacbabdbcdbddbcaccbbabccddbdbddddddbcddadcaddccbdbdbcbdaaccadcbcaaaacddcaccbdbcdcbaaabaacbabbcdbdddccdbbdbcddbadbbdcbcdcbcbacdbbadabbdccbbdcacdcccbdddcbbcaddbdbccabddbbacbdcdbddbcdddcdacbadccccccbbcbbbdbbcdaaaadacbbccdccbaaabbbbcbaadcbaaaabdaacdcbdabadaaccdcbabbbbbabadccdbbbbbdabbccbcbdcccadbcdbbccbcdcacbcddbdadccabbaaabcddbabddabcbccacdcddcdbccccbcabcdcabcbabbdcabcbbcdbcaddbacdcacbcabdbabaaacdbdbccbdaddbcbaabdcaabcaacbadacbcbaacadbcaabdadabddcabbbddcdbdcacadaacacbaacddcacbbbdcbbbdbbaaddbdbdabcadcaacdbbbccccccdcaddcabbdbdabbdaddadbccbaadabcabcaadaabaabaaacdbabbdcbcabcccdacacaaaddbbdacbacbaabcbaabadadbaddcaadccbcabcdadbbabcbbcbcaccadbbcddddaccabdbdbdbcaabbcadddaabbaaabcdcdadbccaaaccdaabbadcdbadabacaddaddabdcaadbaaaabdadcaabbdabdbccccacaaaddaacbbcdaacdbbcdddbaaaadcbabddbbaadbdcacaccbcaccaccbbbcdcabbcdbdbdabcaaccddababbccbabbadcccbbcdbcccadadbbbccacdcbaddcbddacacadadaaacdbbacaabbcdaaabadbcccbcdbddadabcbcaacbcdabdaccdcaaaccbbdabdcdbbccabdbacabbabaddcdbbdccccacdbdaadabdcabbcbccccccbcbcdbcaddacacdaacbdbdcaacbadbbdccacaabbbabbdcdbaacccdccdbdadcbddbdccccacaacdaccdabadadddaccbcbabadddccabbbcdbabbacbbbabdabcdcdaaabaaddbbcbcbbabbcacacdcbbcccccdbccabcacaacbcbdbbbacbdabbbabbccdabcdaaaaacccadbadccadddaccbccccdcbbcacacbcbddbcdbbdccaadcdbddadbcaddcbcdbdacbdaadbccabbcbbdcbcabcbbbddbddcdbddbdcdbacdbdcddcadcdbcadcddaccdcdcdabccdbbbcbcccdadccdcbdbaabcdbdccadcbabdbcabaadddcdbdaccddbdcbbbcbdcbbdcccddadcbabbabddadbbbcddcdbdacddbbaabbddcbdaaccbadaaaabdcabccbbbbccdbacaddccdbcbddcdacdcbdcddbdaadadcdcdccdcbdbbbddbbbbaadadbacccddcdcbbdcacbcddddacdbdabbdbaddcddbbddcddccbcdcbbbbbcbbdbdbcddaaabaacdbddaabbcbaabdadcdaaababacbccbacabadbaabcadcbbdbdccbadbdbabbacddbdbabdcaadadbbccbbddabdbaddbdddacbddadacdccdabbabcacbbddbbddbbdddcccdaddacbaaabbbadccadddbbadbbbbabdabdbdbbcdcbcbbbcbdcacdadcabbddbdcacddbcbaaaddcdbabdcabcbccdbabcbdaabdacaabdbdcabbadccabdacabaadbacccabbcbdbbccdbdccaacdbbdcdbabbbbbbdddabcabbddcaccbcdccacabbddadbaacbbcabcacbdadcddcaadabcdabdbdbddddcacdcdaaddbbcaccbbbddcddcbaaabdbbaaadbbcddcbbdacccbaacabccbccddcbbddcabdbdccbbdbcabdcabdbbbdadcbcbbbcadacddcacaacababadbbdbabadbddbccbcaddadbcabdcddacbbcbdcbdacbabcddcbacdcaabbdbbccdbaabddcbdbccbcddcdcacaabbabddbbbdccdcdadaddabdaabccaddccdbcdbaadddadbdcbdcdcbadbbcdbcddbbabcccbcacacbbaaaabdaabcacccdbaadbaccdaccbdabcdbbdbbccbbddccdcacaddcdcacbbacbcaabdbcdabddbbdddcadacddadbaabaadaabdbcddccbdadcabadbabcdaabdbcababbcadddcbddcaccbbdcbcdbbddcddddbaabdcdbbbbbbccbbdbcccdacccdccbaddcdddbaacaabaabccacabdadcacbaadacbddbccddbacaadccbcbccabdcadbbdadbdcacbccdcbcaacbadbdcaccdcadadabadbbadcccbdacaaaadbaabddddbdccccbabcbbdadaddccaaaabccdadcdaccacacacbdaadadcadddadddbdbdadabccacccccccacdaacdbdbbacdddabdccbaccdddacbddcaddcbacbdabbdcccacbcabbddcaababcaacdaccaaddddbdcdbbbcacddadbdcddadaaabdabdcbadbcdabbacbaabbcadcdacbadadacadcbcdbabcdbadaddcabbdccdabadaddcaccbdccaacdddacadacdccdadcccaaddbddadbadbcdbbccdbacbbdddabdcabbaabbddbdbaddddabdcdcbccbcbccdbcdbbbabbbdccdcadadbaccaddcbbbcddcdacabacacaddbdaabbbcbdddaaabbdddaacbacdbddabbdcdbdcdddbdddbdabccddadcbbdbbbcddbbbccccaaabbaccbcacddcdcbaaadccddddcdcbbdbdcdcadddcddbddacbbadbadadbaaaaabbdadadcccdcbddaccbbbbdccdabbbacdabcbbcaaccdbccbaadbadddabaacdcbdcbdaddcbcabdbabcaadddbddbdddcaaadbdbbcaaaabbbabcdcabbcaccbabbddbccdcddbcdaabcbddbcdcbcddadcdbbacaabcbcbdadddadbcabbcbddcbdddddcbabdbacaadbdacddddbcddbbdcdcccdabcadcdccbbacdbbdbccaddbccaabbaaccaacbccbdababaacadaacccdcbddabbddababccdacddbcaabbdbccccddabdbbddbdbddaaacadaaccbddbbbdbdddbccdaadbabbdbdacbbadcbccdcaaddcbbbbccdbdcadaccccbcddcbabcdadabdabcbdadcbcdbbdcacabdcbbdddabccdbcacbcbadbcdbddbdbbbcadabcaacbdbdddcddccbbddaabbadaacbabbdbcbcbdcadcbabcbdbcddcbbbdaddaccccaadbbcaccddccacdcbbadcbcdbccdddcdddacbbddabcbbddabdcbdcdbaabddbbdccdbabcbacadaccdcacbdccadcdcddabdbadbdcbdbadcacdadbdddbbacabbcaadaaaadaaaabbdbcacccbcddbdaadbdcaacbdbabbacbaddabacddadcadababddbbbdcacacababcbbbaaadcdddddcdabdcadabcacccccdabddbcbbaabbacaccbaadbdcacababaaacbddaabcacdbabcaaaaacbddacdbcaaddcacbdcdccdbccbcdabcccddcaddbdccddbcddcbdaaaaccbbcabacbadcbaabbabacdbbadbdacdbabdaaadbcccabdbcdabcbbdbadddbddbddcdcccdcabdcaabccdcacddcddcbbddadabcbcdbaabbacddbacbbcaccacccaadddadcdbcddcccbcbdabdcdaccacbbacbdaadcbacdddcaadcadbcaadaccaaacdabbcbddbcccdadbccadbabbbadaaacdddbcbbbdbcdacdaabcadcacaaaaabbcabbaaaadbccbdbdbcaadbdadabacbccbadcdccadcddccdadcaadabaadbbaaadcbbdbdaabadcbbbdbcdddbbcacabbcbbcbddadccbccadbbcbbdcacaccdaacbadbdbccdbbaabaaaacddcbbbbbbccccccbdcaaaaacdbdcaccdabbaccbcdbcacddcabddcdadddbdabccabccdcadcbdcdbbadbbbccdcdadcdabdccdabdcacababaadbbcbdcaaadbbaadaacdaaacccaadbddbadcbaddbbacdacdacdadbdcdbacddabdbacbaaadbacdcdcdbccdcdcbaaacaadbcbcbacddabbcdabbadcdbadcaacabdbaacdcacbbccddaddcbadbcdaaacbbbdbdddcadbacdcaaababacbcddcbbdbbdcdddcadbbbadbcbcabbbbcaddcdcdcbcdcbcaacdcbdabbcaaabdacaabbbccddbcccddaacadacadadcddbbaadacabcddadcdddadbadccbadabaadbdbcdaaadcdddbbdaacdddbabdcbdacccdaaaadcddcdbdbccaaadccdccbabaccdcaabddcbbbddababaddabcacdbbaabbcbbbabcaadccabbcadcabacddcbbbdbcdcdccdcbbcdcdcddacacbaccccddadcbcdbbbdcbcbbabacdadcbcbccdcddbbcdadbaadbaaadbbddbcdcaabaaddccccadddaaababbcacdbacabcccbcadacbcbcccadcabccdbbdccadadbdcdacadaaccaadccbdcddacdcabdccbdcbdcdcdcdababdbcdadbbddabddcccaaaadacacccdbbcdcdabacdaaacaaacbbbabaabcdcaaccdadcdadccabddbbaabccbacdcbbccccbaabcaadccdabccdcdbccbcdbdbaaabbcdddabcbacbdbadbbacacccacadababbdbdcacbdbdbaadcdcdcacdcacbabaabdbcdacabbbbdbdcbdcddbcbadddcdddbdbddbabcccbdcdddadbcbddbbdbccdadbbdccdadbccbbcdbbadaaacadcccddabadbbabdaccbbabaadcdddcbbcaaabaaaabcbbcaabbcdbbcaddbadbacaaccbaacdcabccacadaadaddaadbbdccbdbcdcdddcdbcacaabddbbbacbdbaabbcbddcaddddaabddaabcccbcddbddadcdababaaacbbcbbaaccadbbcabbbdadbbbabadccdcbacbaddaaadccaaaccdbdaaadbcddccdadbdddbacabadcbdccbbdbabdbdbbabcadcbcadcbcdcdbdadbcaaccacaccdabdaabddcbbcdbdababbbddaaabbbdcaacdabbaadcabbccbbadaddacdddadccbaaababdbccdaadacdabdbcbbadddbbababbaacdbccbddbacacaadabdddabacabaacbcccbabbdaccdcbbbbdadababdaddbddcbcbbcbccadcbbacdbbbdcbbddbdacdadcccacdbbbadcbcabaadcdcbcddbddddcbacbcbbabcbdadbacadadcbdbbabdaaacaadabbdaacbaaacbbabacbddabbddddddcdbdcacbbdbbbacabdbabdcbdccdbaabdcdbbacccbbaaacdddaabbadbcccaaddacddadbdcccaccccbcdabbaaddcadaabdadbdccdcacccbbadccabdabcbbabdcbbcbadadddbddacabdbbdcbcdbaddccadcdaddadddabbdbacdbcbcdccccdccbcaaadcbbcadddaddcaacadabaddcbbdaccddccdcdbdabdbacdbaaacadbbadbbdadcacbbbcddbcdcadacbacccbcdcacadccddddabbbbabacdbcbabadbbbbcaaaabbbbbdcaaccdcdbbaaacbbcdbcdcbbccacccaadddabdccaadddcabcbdadcdaacaadbbabdaaccdaddcacddddadadabcdcbdadcacdaddddccddcbdacadcbccddbaddbdadbccccbcbcbcdaabdbabbdbabcacddbdcbaabbbdbabccadbaacdabddabacabaccacdadbbbdbabbcdddabbbbddccdbcabcccbaadbdcaabdaddcddcbcadaabddaaaccbaaaabbdbbdacbccbdcbcadbacadbabccbcdbcbdbbbdbdbcbbdaadccabdddcbdadccabcbbcdbbabdccabcaaaaabcaaddadcdbcdcdbddbbbccbcbabdbccabadadcacabaccdddadadaabbcabadccacddacbadbbdddbabdccacdddbbcdabbcaaaaaccbdcaabdbdcdccaabdacacdbcdddbadcacaabadcabdbbccccdaddabccdddbcbcbccbcdabaaddddcabbbcaabdacbcddcbaddbaaabdaabdcdccacbcaadccddbcbbcdbacacaaaaacaddbdaabadcdcacdbddaddaacbdaacaccbbadbcadbddacbadbbcdcabbcbaccbadabdbcacadaccbccdccdccaaadbdbadccabcbaabacdacaaddcbcdbdaaacabaddcccbadddacbddacdadbdbcbbbbadbbcdabbddcdcdccaabcddddbbbcacbcdbbabdcadaacbbaaadbdbbaccdabdbbcbcccababaddcaadcaacddccbdccabbddadddbabaddddadcaadbadcbcbaacbaadabddaacccaadddbbacddbdbbcbdadbbbbadbacdcbbabccddcabcabbcdbbdabccbbddbabcacbabcadcaaadaaddddbdcbdababcacdadbddbdbbdcaddddababccaabcaaacbbcababaddbdbdabbddbdcadbaaddddadcdaadcbadaacaccaacbaabaccabdaadabddcadbdaabccabddbddbcdcccbcdabdbcbdbbadbacdbadbadcdccacbcbaababccddabdacbbaacccbabbdcbcbccbcaccccaacdaacbdadabdbbdccbcdadcccacbcddccadcccaabbbcdcabdbcbbbbbabbabbdcdbcaadadbabcabcdbddbccaccdddbcbbcdacccdccdaacacbbcacadcbdbdcaadbdbcbcaddbaabbbabadaaccbdaacbbcadbbabbdccdabbadcbbbbaaaadbbcdabaccbbbabcbdabaabdbaacbbbdcbcdbdbdcbaccdcbaddacadbcbdcccdbdcaadadcaddccdaaddabadabadbcbabaabdcdabaacabcdbbdaacdbccbccbbabddcdbbbabdbdcadaccbdcadadbcabdcbbddabbbaddcddcaabcbabbbdcadadbabbdddcbaacccdbddbcccabdaacdabcaccddddbdaadcdddadcdbbdaabddabddbaccddbdcdabdabddbdcaadabdcbdcdbaaaddaddcbdaaccbbbbaabdcdadcaaabaabacabadddcbaadbbdcbaacddcaaadbbdabbadbbdcacbabaddcbdddaccaccdcccdbddabccacccdddaacaacaabbacbccddbdcccbcacddcdadcabdabdcabcabaddabdcaddbadbdabaabbdacbcbdcdddcdaccaadbbddbcccacadabccdadcdabdbbadbbabbccdaacabdbdbcdcdaaadcdbcbdabbbcbbdcccbcccadccdabcdcddbbacddaadbdccbbabbddabbbbbaccdabcacbcdacabbbdaacdadbdabcabcaadadccbbbbdbddbbabdacbadbadddaadcaddcdabccbcccadaadbabaaacadbcadccbadcbccbdddbcbcadabcaaaccdabadacadcbdabdabdacbacbcccabadadaaaabdaccaddbdacaccdddadcdaaccabcacbccbbcdaccadbccdbbbbbbacbcadcbbadbcdaababcbbaacaaccdcdbbdbdcbaccccacabbdddccdaddbacaadbdcacdacabbcbaaabaababcaabdcdccccdcddcdccbdabcdbcadaddbbbcaadccdbcccccaaabddcbbcadcbbcdbcaadabbbbdaddaadaabdadabdbdadbadabbdadadacdbbcdbcaaccbbcaabdddcccbdabababddddbccbbabdaaddddbdcbcbddaacbbbaddbdabdbdbbbadcbbaaaddcabcdbbcbadddcdcadddadbcababbaabccbbbaccdbcbddadabddacdbaaddcabacabbbaacabbdcbacacbaabcbdddbacdacbcbccbbcbaadadbbaddaaadaaadccaadbaaaccabcbdaabbbbdadacdbcbdcbadbbbcbdababbabbacbbccbdcaabacaaaddcacaabcaaccbbbbcbbcaaabbdcadacccddcbdabbbbcdaddddacdcaabddcdcbabbdaddddbbbcccbaccdddbbbcaadbbbddccacaacbabaccdadabddacbbaccbaaccbabaabdbdcddaccbbcccbbaacbcbabcdcaccaddbdabadcacdbbdadcacbbcccadbcaccbaabaabbbddaabcbbaaacdaddccbddcbbabbbddadcbcdadbbbdbaadabcacdabcdacdabdaddaabaabcdcabcdcdbccadcbabbdaacbaddadaadaacabdbdcacdacdcdbbacbccdcdbbbdcbdaacccbccbbdcaddbbcacddcbcadabdcdbaacdbccabdcadbdddddccdcdbddbadadbaaaabcdcbbabacbcdcdbcbabccbdacbbdcaadaaddcccbdbaaacacaaadddddadddcbbdbcdddacaaacdbdacabccbaadcdacccabbdccbbbcbaaaccdcbabacdcbcccacabacbcbcadbabaadbadbdbcaadbbcacdaaabadababdabddbacadaababbacbaccbcbaacdacccacabababcadaabdbccdcbaadacbdaddcccbbaadccbcbdddbadbdbcccaabdbbcaadccbccbaccbabbdccbbddaabbcbccdcdacdbdabdccccaaacbbabbdcbaaacdbdaaadcbacdadbaccbbdbaddbdaaabadadcddbababbcbbcdacdcbbcadcdccbdbcaaadcdddbccdbcbacdbadbdcdddcbcbdabccadddacdddbbdbcbacdcaaadaaddcdbddbbcdcacccbaacadbbcdcdaccaaaacdddddddcdaabbdbdddacabbabddaddbdaaaaabacadbcdccbabbcabdcaddddddbbcaadcbaccbacddaadbbaccbadddacabaabbdcaabbcbdccddbbaccabaccccdcddccccccaabaacbaddbaadbcbdccbcbdbbbddcaaaacbdcbbcbbddbdabcacbbcdcccbacbcbdbcbcbddaabdaacccdaaddcdbddddbcaddabdaacbadbcbaddccacabcaddccbbdaaabacadaddbcbcabbbaadbcdbdaddbbcacdadbdcdbdadabbbbddcdaabadcbdcadbdcdadddccaadccbaddddcdaaadaaacaabacaccbdaddcabcbcbaaabadbbcabaabacbabadabbdbaabdccbccdcdbdaccbadcdbdacbdbdcbcddacbcbbdbdcabacdbbcabacdcadaabccbbdadcccbdbdbbbdbdbaababbadbaddbbabadccbdcccdcacdabddaaaabacccbbdacdbccdaabadbdcadacadbcbddcddaaddbbaabacbbccbccbcaddaabadbaacbbdcdaacdacbdcdacbacccdbacdaccabacbadacbabbcbbcbdbaacccbbdbdccbacdbbbbddbaabddbdccacdcdacbbaabbcabdbdddbccddbcbaccaddbdbbdaadaaaaadddbacdbddbaaccdaaacdcdabacaacbacdaddbddbadcccdddccdadcadbbdaadaacadcddaaccabccccbddbcbaccaaaabbabcadcdbcbcbdcadcbddacccddaaaddcdadbbccddcbabcaccadcaadadbbbbaccdacadacacbcbdbdbabadaabbcaddcbcdacdacbbbadccacdbaddaabdcbdbaadbdcbdbbbaacdcaabdbbbcbcccbadccddaacaaaadaccacdccbcdbdabbabdccdbddabcdaadbdadbcdcdadabbaacbccabcbadccadcaddbdcbbcbcacbddcdbddbcdbcbdcddaabadbaccacbbacbaadddabdbabaaddabbccccdddadcdbbbbbbcaacbacbbabbcdbdbadbbbddddbbcdadbbbccbcadcaabadcddbdddbbabbacbacbadccbcccacbbaccbbaabaadaabbdcccbbbbacbadcabcbadcdcadcadbcacdcddaaddbddbadbbcdddcaaccadcbacbdbbbacdbabdcbdbdcbcdddbbbdabacddaabcccaddbbaabdaadaccbbbbdbabaccccdcbbaadbcddccdadbdcacaaabccbbabbdaccaaaabbabdcadcdcddbbbdbaadbabcdbcdccabdaaaabdbbacbdacddbacbbccadbbbcbdbbbbacdacadddbbddcccdcbabaaadcbcdbbabccdcbbbcacbdccbccdcacbbaccbabdadcaaccadbcddcacddcddadddccadbddcadbdcdadbccabdcccdbcccabdbacacaabdadbdacabcaaadadcabbccadcaaadbbcaccdcadbadacbaddbadadcdadbddaddddaccbacdcdbbabbaacbadcaaadbadadcbabbddbccbbacbdaaacdbcdaaccccddcbddabdcdcacbdcbdbcaabbbcdddbabaadbbbacadacaaaaaaacabaccdccabddbcddbddcbcbcbcdddabaaddbdcdcadcbadaccdbabdcbdddccbdcddcbdbdcbdccdaadacabdbcabadacdbcdbbdccbdbaccbbabacdbaccdbdacaadbdcccaaadacadbbdcdaacaadbdcbacbbdbdabdbbabbbddaaabcbdaababbcddbbddcbacbdababcbaccdbbadcabcbcbacdbbdccadaaabbddbbcdadbbabdaabaadbaaaaccbcbcccbddabbcdabcdbdccddaccbcddaababccdacbdbccadddabbaccbbbccdbaabbdabddbbaddacbdbcbbbbcdacdbcabcbbcabaacacacacadaaabcbddbbbbbccddbcadaabdccdcdbcabdaddababacbbbcadccabcdbcdabccbbddcadbdcaabdccbcadacccbcbdccbbacdbdabdbbaacbbaadccddbbaabacbadbdbbbaacddadddccabcaddaacbddbaacdacacbcdadbbacdcacabbaacddabccbdccbbacaaacdabadaacacaacbacacdcddbbadadbbdccbccaadbdbcabccddbcbadadccdcdaccddcaadccabbcaacbadaddaddbdbaddadacdbdaddbaddddbbdabdbbbadabbbbdcbbcabddaddcdbdadbacaaccbaabcbbdccabdadbacaaacacdbddbbcabcaccacddaaabbaaabcbbcaaaaaaabaccacbbdbadbabcadcbddbbcccdcbbadcbbccbcdddcbccdbdaccacaaadaadbccabbbbdbcdbcddcadacacbcbccddcbcbcacccddacbcacacbddabbddbcbddcbbbccccbcabbadbcaccdaacddccaaaaacddacaaababbbcbaaddbcdaacbbccdccdccaadccbcddacdaabaccdacdcdbcbabddacccdaababbddccaaabcbabbaaadddbdbdddabbacdcbdbdcadcbbadbaadcccaddbcccdacaddbbccaccddbbccccacbabbdcbbbbbdbabdadcbdcdddabadcbcaddbaadacbcbdcdbbddcaaacbcbdbcddbbbaacadbacdabacbbaacdadadbabcbdacbdbdbdaddcbccdbbbbcacbddadcbacddabccbbdaaaccdcacabddcdaabcbcaacccbabbbdabdbcabbbcbdadccacddccdbaccdbacbbdcbdccaaccdcbcbabdccabdccaaccccddccdcccccaaabbacdbdacacacdabddbabdbacabdabbdcbcbdbdbcbbbcabacacdbdccbacbabbbdbbbbbcadadbbddadcdcbadcbcacbbdbdbaccdcabbabbcccaaccdbaaabbbadddcdccccadbbcbcdbcaaddbdbcccccdccadccbcbbcdbbaadbcddabacadabaaabdbdaacccdbcdcdcdbdbbbcbdbbddcaacdbcccadabcccaaaacbdddbadcabcadbaabcdaaccbbcdacabadbbbabccdcbbdcaccbcdbaaccddcddaadcccbcccbaccaabdbabdaddcddaadbaadbbacdbcbbbacaaddabcaddbbacbcbccacbabcccabbacacdbbcaaddadbbdabdabdccbabadaaadddbcbbabcbdcbcddaadcadaadcbdbbaccbcadccabcdbccbbdddbcbadadbaadbadcdaaacabbdcddccdacadbcbbbdadbcaccbcbdccbcddbcaadabbdbbacddabcdcbdacdaabbabdccbdacaaccdddddabcbcbbdaccbcbddadddaddbbbcddcaaccbdcacdbddbdcacdddcdccddcaaacbccccddaccaaaddaaaaabdacacaabadcacaaaadcbdcbcacccabdccabcddcbdadbadbadbbcabcaccdbcadabddbadcaacbdddcbcbcbacbacadddcadcbcbccadacdbaadbacacabaaaaaadbabdcdddacbdaacabdccccabcabcabdccdaacbbdadcbdaacacabaddcbdcdcdbadbabaaabaaaddbadcccababcaabdcaacaaabddaddcbdccbacdadddcdbacbbadbbbbcbdbdcadcccaaaabbcbdcdcadcaacbdacacbabcdbcabdcbbccbddbadadbdcdcbdbbacabcacbdadbaabadabbdbcddcadbdccdaacdaacadccbcdbaacaadccacaaabdbadbaadadddaadbdbcdbbcdccbccbaaaddccabbdccdbabdbbbddcddaccbccabddcbccbddddbadcbacdbbddbccbbbbdaabdbcbcaccacdcbcbdcadbdbdbbcbadabcccbaacaadbabbdddcadcbcdcbcdbadcbacbadaaacaaabcaadaaabdbccacbccdcabcaccbabdddcbdabbcaccdbdcabdabacacaaaabcbacbccbcdadcacbbcdbacddcdbbcdbbddbdadbaccbcdbadacadbbcbcaaadcbadacaacabbaaadbcaacdbcabadbbadacbaddacdbaadabbddacaaccddbdccbbaccddddacaabadbbcaccbabaabbaabcaabdaddacbbabbabddccdaadbbabbbdcbdddcacacbdcccbbcabdaddcacdddcdacbadabbddddabdaccadcbacabaabbdbbcabbcaabacdcabdcdaaccbbdabadbcabbcbdabbabbcbabacbabdabbbddbacccddcdbbaaccdddbcaaddbbdadbbddaddacacbcbcbbdbdaddddaddbcbcdddcbbbdcdddbbbdbdadaadaccccddcadbcddaacadcdacadcadcbbcbcbddbacbacabaccbdccadccabdbabaddcbcddcdadadcdaabcbacabdcbbdcdccdabbbbbdccacabacbddccdadabddcaacaabcbbbaadabcccccadcbadacadbaaacadbdddccdcdccccdbbbcccaaddbadcbbbbcadbadcbddcccdaaaacbbdcbbdacddcbcdbbcacdcaadccccbaabbddcdaddddbdbaaadcadcdbaabaaabdbbbcabaccbdabdbaacdaaabcbbacadbcaddbcacadccbacbcccddbcbcacccacbbddddacdbcbadaaadbcbabadbabaadcddddadcacbaabbacdadccbbdabadabcadbbaacaaabbddaaaccdcccaaadccbbabaabbbccbacabddaaadbbdbcccdbadbabaaababccdbbaabbaccbabcaacccbdcdccddbdcbbbdccacaaaadcadbabccddaadadacdcdcdcbcaacdcbaabaabadadcdababacabccdcbbdbadadabbbdcadbcbbccabadcdbbaaaacadbccbaaaacdbcacadabacaddadbaadbdbbcbbdadcbdcdbabbabadbccccdccdddabccbccdaddbbdacaacaacbcdbdaadadcdcbccaaabcdbdacbddcddbdccadacabacadcaadbabdcadaccaadbddbbbdaccadaccbcbbdadcabadccbdccabbadadacbbcacbacbcccbbdcaadddcdbdcaadcbaccbaabddddaadbacdbcdacbbdaddaacbdcbadadcadabbababcbaaabacadcccdadbaaaddcddcaacbcbccdadaccdccaabbddcabbabdbbadcbdddaccdddbcbbcdbdacdbcbdccdbcddbbcddaaacaabcbddacadddbcadbcbcbadcdbcacaabbddccddacddcaccbcdcdddccdbdbaaaaaccbaccbadaddabcabadcdbcacacdaacbddbaddcddacabadaccbbbdddbadccdcbcaadacbcaabbccccadabdbcaabbabacbbaaabdaccacdcbdccadbbabddcccaadcbcbbbccacdaaadbbdacdaacabadbcaabdcbbaaaabbaaccabacdbdccdbbaacacdabcdcadcccdacacbabdacbdccdbbabbbdcccccbdaaaabdacdcdaaddacdcacbcbcbbcdbdcacdcaccaccbbcbaaaccabbbacccaacaacaccadccaacbcdbdadccbdbbbacdadacdccadbdccccbabbdcbcdabadabbacbbbbdcadbbabcacbaadacbcdaccccdcaddacccdcdaaabadadbcccdcbdcbbbcababaabcacccbbbbcbbcabcdabbdabcadcbcbbccbccbdccdacaaddbaddcccdcbababccbabadddbdaabcdcbcbdbcdbcccadaabcbacdbdaabcbddccbcdadaaaabcdbbbabbbbcddbbdccddbddbbadcddbcaabbacdcbccadbcabdddcbaaabababdccbccabbdbcbdbbaaadbacabcaaccccccabacadbdccccabbacbbbbddcaabddabcbbcadbcbadddccaddccbcaadbdcbcddccdcbccbdddbbccdaaddaabacbadddbacbdcabbadcdddbcabadcbbcdbbbbbcdddddcabaadbadadcbbcddbcdbacbdbbcbddacaabdddadaaadccdacbcabbbcbacaaaaccbacdddaacbddbcdcbcaddaabdccbddaabcaacdadcbabccabddcdbcabbbaccbccbbdbbbadccacbcadcaacbdcaaacabccaacbccdccccccbdbcbdbbbcbbcccbadddadbdabbacacaccbcdcaacadacbcaadadbaccaaaadccaacdcbcdbdabaccaaacddddaacabacabdcccbdbbdaabacccbdbbabdcbbbbcddabdaabdaaccaabdccccbabdaaddcbbcababdbddddabbaadccbadcdcbbaabddadadabadadbabaadbbadbacabbaadcbcbcbabadabababaabcbadbcbbdbbdbcdadbacdddbcdadcddcbbddddcdbbccabcadcabdbdababbaaaaadccbadbcacdddbcacaaccaabcdcbdbdababacadabdaddbdddcbabdcacdbadbdbbadacdcddccaabcababbbdbccacaadcaaaccdacbbaabaadaabcdadccadcabbccaccddababdcacdaddbaacbbaaadbcaaadadbbaddacccbcaabcddaadaacbdaaabbbcacdcdbdabaabdadcadbadbacadccdbadccacbdbdcddcbcddcbbbbadaccccdaddbaddcdccbdcbabadaddddaacadacaadcdcaddbbadbdbccccbbadaccdddbcabbdddadddadadaacddacbdcbacbcacddddacacacaadadadcbabacaabdbdbccaababcbcbdacdcdbadddbcadbbcbccbddbacaadcccdccabcaabbabacdacadadbaaacadcddcaaccbbbadcabacbcdcdcbdbbdbdbddcdccacccbdcbdbddcbbbbdcdddaddbddadbbaacccdddadcadaaaaabcddbaacbabdcdabbccadcbaabacbcdadbcbddabbbbaadabdcdbaccadbbcabcbdaaccaaaccdadbcddcaabadbcbadbdaaaccdbabbdbaacbbabbccbaaacdacbabcbcccacacbcdabcdccbadddddaadcbbdaabdcdccddbbbcabcabdcddbcaccbdbddbcdbcadbbbadabddcbcbcbaabdadaacbdbcdacdccadddaadaccdcbbddcaaccbacadccddbbacdcabbdadaddadcbaccddaaddcabcdbabccaddcacbbacccbbbdbcaaaddbadaccbcdadbaabdcbbbddcbadacbdbabccaadcacadacbccacaacbdcbcabacbbcaacabacccabbaabddacddbcbcacdaaaabbaddccdccdcaccbbdaabcbacaadbcabbaaddbbabbbabadbadddadaddbdccdddbbdaddddadaddacccbcdbdcdddaaacbacbbbbadddbddbddabbdaadaddacdaaaaabaaddbacdcdcbcbccddacdcccdbabbaddccbcdbdaccbbdaacaaaadacaadbaabdadcaacbbaccacbddccdacdbddbbcbcdabcacdbdcdcaddddabcabbcbdaaacddbadbddcaaaacbcbcbbacacbcdabbdccaadccdcdacaabbbcdacbbdcbbbacaaadcdbdbbaddbbcacbcaabddcadaddccdcbcbadbdbbdacaccdaaadabcbcadbaabdccbabdaddbaaddccddddbcccbddadbdcbbbcbabbdcadbadaacbcddbaaaabdabddbdcddabcbbaadababcddaaacbdbdcdbacacbccccbbcdccadacaacbabadccadaacdcddaaccbcddaaaccacaacdadbbddcbcdbaccacdbcdbcabcbdadbabcacbbcbaddabcdddbbccdccaccbddadcbadadabbdaccacacabddbbaabbcabadaadcccbaacdcdcdcbcadbdbbddbbbbbcdaaacacbdbbddddbbdbdcdcccaaababadcbbbddadbacabcabdcacaddcdddacadcacbddadbadccdaacbbcccbbaddcacbbddccccdbbbadcaabcccbabaddacaacccbdcbcaaacdcccdbdccaacdabdcbacbdcdbcbcbcbdcdbccbddabacdcdcaadcaaaadaadbcabaaadbcbcbbdbacbbbadccadcbcbabbdabdddbdcbccbcccadabbbdcaacbbaccbadbcdadbcaddaddacabbdaabddcdcacbcadaaccddaddabbacdbbcadcabadcaccdaccabccaaaccdadbdaadccccabdcdcddabacdcbabdcbaabcaddcabcbbdbbbdadadcadbbdcdadbbdddbaaaabdcaabcaaddccacdabdbcbcbbbbaabcdcdcbaabbbadbcbadcdaadcadddadbadadddcbbbbacddcdadccddcbdbcdbdaddcaabbacdabcbaabaaabacdbababbadcdadbabbaccacababaabcacabacdadbdaaddccdbaadbacdcaadddcbbbdcadcdbbdbdaadabdddabaaccaacdbaddcbddcbcdcabddaaaccbdbbcaccbacdadbbabcbadbcaabadaccacccbaabdabbaacbbcbdabaadadbbdccbbaacacbcccadaddbbdadcbadcdaabbdbdcdcdaabccadbcaabccbdabddbdaadabcbadbcbdaccccdcdddbaaacaddabddadbccdbcacacdacacdbddbcbaacabbdcbaadbbbbcbdcdbabbcabbddcbdbbaccdcdcaddcbabcbdabddbcabcbbdbaacbabbcbdbbbabcdcbdcbdbabbaaaabbaababbcbaaaccddaccbdaaaabbdbbbbabaddcdbccdaacbcccdbdadadbbabdcacabdcddbbccdbadaadaccdbcccbcbbcababbcababcbdcabccbbcadadabdcabdbbadcdabaadbbbcbcdddacaaabadabdbdcdaabaddccbabddadcabacccabbccbacacaaadbccbcbabcaaadaddadaacbcbccbbdacdbbbabaddabacadbccbccbbcadbdccbacdbacdbaddbacdcadbbbdccbcbbccddddcdbbbbbdcacabadddcbdccdacbbbaccddaadddbddbbdcbcadcdadbbcadaaabbacadddaadaccdbbcbdcabdcabbcadbbbccdaacdbcbbcaccbbbbacbbaadccbadcbabcaabacbacadccaddcdbbdabbaaabbdbacdaadacbabdcddbccbbdcbdbabbdcdccbccddabacbdbdbdccccaddbdcbadaacdddcaabadcacadbdcbdddcaccbaabbcbaadcadaaacdbcabaabbdadabcaaabacbbadaccbbdbbcbccaaaadbadadddcadddddddbaccbadbbcbcadbdddababdbadcabbabdcdddbbdaaabaccbbcabaacdaddccadcdabadcabcacabccacadbbdacbdcddaacacdaabcbdcbadadddcdabcaabcaadbabdddcbdbabcdbbdbdabadaddadaccbbbbadbabaccbbdbcbbdccccdadbccabdabdbbbddabbdcccaadadbdbcbbaddaccbdababdcacddabbccaabbdbbacdadbabaabbdcdaabccccbabbccbaddbacdaaaccadbacbbbadcddddaaccdbbadcabdccbbbdabdcdaddcbbadacabcaaaccddaccabcbcaadaaaadcbdbaadaaacccdacadaacacdacdbccdaadabccabcdccaddcddcbacdcdaaaabdaaccbccbcbdcadacacadaacbcbdaccbcdacdcdbdbdccbcadbcaacbbcaaadbacbdcaacbaddaaacbacacbdaccbddcbabdccddddcddbcbadbbbdbacdaadaadaacdccacddbadaabbbbaddbaaddadbdbdabbaadbcccacbabdcaabcccadccaddaaadcdddcccdcbcadbbadcbdcaadbbcacbbaabcacbcbcbbdddacaaccbbdccdadacbcaaacdcbbccdcbdaaaaddacbcbdbbbcadcdaaccbbaccccbdcdadcaccbdcccaccaccdacbacaddcccaddccaaaaacbadccacacbcaacccdbdcaccbaadcdbddabcdcddacdbcccaddacccadbcaacaaaaaabcbdbdbcacddccdaadbadccbdccbccddccdacdddadacabcabdcadbbbdbbbdcdadbbcabcadbddabcaccaabaadcdcdbbbaadccabbbdbcabadbdcbdcddbdccadadbabbbbcbbabccadcdaddabababbcbadbccbbccabbddaacdbaadbaaabdccdbbbacabccbbcdbadaaadadcbdaaabdabccacbabccadaadcadacbbabccddccbddadcdbbacaaacaddadacddbccacabccbdabaaaabacbdbaacabcbdccccdcdcbdbcdbcbdcdbbcdaccbcacbdaabdddbbcdcdbaccdddadddbddbbcbcacbdacccdabcbbbcbcdcbbbcdcbabbcdbbaaddcaddaddbcdccaaacadddacbbdccadadcadcccdaabcdbbccdcdbacbbacccccbbaabaadbaccbcaababcddabbddabcbbbddbaacbccdbddddbdcdcdbaccbbabddcaddcadacabbbabccaddbacdacdaabddbccacdddddbcadddacddbdcbbaddaddaccbdacbdccacbbbabbccbbbddabbbbccbcbdaabdcdccbaacccadbdbcacabacccbacddbcabbbddcbdcaddbacaaaadabaddcadbaaabbadcbbacbbcbadadddcdbdccadddacacbacaddddaaccbbacbbaacddcdbaddababdcdcdbbccaabbcabbbddcacbbbdcbddcadcaddbaabacbbbaabcadccabaacbdbadaddadadbabaacabbcaaaaacaadcbaadbbadcaacdcdccacabadaadabbacbdabbacabaaaaaadcccbdacbbbbdabccadcadabccbbcdbdcdadbdbbdabdacabdaddbadddacccaacbbdbdaadccabbabacabdcbdcdcbabbdbdbbbbbaadcbbacbccbaaaddbaccccbcdabddacdcdbddbbbbcbbaddccaabcbcccdcbdbacbdbdcdacadabbaccdbbdbbbabadccccaaadbacdadbcbabdaabbadcbbdbbbbaccaccbcaddcaadbbdacdccbcddbaaadabcbcaddacdcadabcdabdacacbdabcaacdddabcbbabdbcdabbbdccbdbdadbbbddcccdcbdbbacccdaacdcbbaaaddaacccbdbadccbcdcdccbbdcabddbdcbbccdcdcdcddaabcabacaccabbaabababccdbaddacdaadaabaddadcbcdddcacccddacbcabbaadcdaddcdcbabadddbcdccdabbbcdacaaaaccbbdadddacdddbadddbcbdcccddbacbdcddddbababdabdbbabddaddddbcbcacaddcbdacadccbabbbadbdbdaadccabbabddadaabadcbdabdacccbbcacacdddadcdcbdaabadbdacdbbbbdddaddcccbacddcbbadcbdddcabadacbdcbddcbcadddabdccdcabaabbcbbdaaabdbbcabdaaaccbabdabdcbaadcccbcbcdacbccccccbccdadacacbacdabdcadbddcbccdcbadadaddddbdacaaabaddcabdcadbbcacbbdaccdddcdbaacbcccbdadabccbdbbaaaaadcbabcdcbcbbdcacacdabdaaababbcbddbbcccbabddbacacbbadbadbbaaaadcbbbddcaddabcdbcdccaaabcbbaabaaddcbbacdcdaaddbaabdbbcbabacadbabbbcbabddaddcabccacbbaacaabcbcbbacabdcbacbcddbdcbcddbadcddbdcdadaccdbbcabbcbbbdaddaddbccdbdadabbcadabacbcccdcdcdddbbaddadcaccadcbbbddcdcbbdacaabcdbcaabddcbdcbdbbcbcbccdcdaabccdcdcbadbbdbddacaaacbddcbcddbccdbcdcabcbbcababacdccccdbbadbaabdbdacbcadccdddbaccbbccdccdbbdcbdadcdbbaddbbaaddddccbacdbbcdaccbdaddabbdaaddadbbcaacdacdabaaddbbdcaddccddbdcbdaacddaccccabbdcababadabbcacbdbdbcbddacbbacbbdbdddadbabbccdbaccbccaddcabbaddaaacbadddccacacabcbbdadbaacdacaacddbcdabdacadccaccaddbdcdbbdbadcbbcdbcacadbdabcacaccadabacdbbbccabbbacdabbccdcdabbcdcaacbcabbacaaadbccacabcdbdabdaadadddabbccacabcbcbcabcbcadabcadabbbdacbabdbadccdccddacdbcbabcdbbcdaadbdadbbbaddcdbabaacbacaaaabcddabccbdbdadcadabdbacdddbabbcabcaccdccbdabaadddbaacaacbacdbbaacdbcbddacabddccbaacadcdccacadbcdcdaaaadddacadbbdadbaadbbdbbcadadacbddabcbdbcbccbbdabdcdbcaadabdcbdbbdabccabbbccbbcbbcdaddbcdcccbdaaddcbdccdbbcbdcdccbacaccdabdcddcaccaaddaaccdabccbcdcbbdbbdbaaaaadadcddcdccaabaadbbcbadacdcadacdcbdbbdacdadbacccdcacbdccdcdddbcacaddcaaadacbbbbcbdadcaabbcbdabcabaabbdbbadbcaccaabbccaacbaabadadccbacabaadaacbdcbbdabbdbdddaddcdccbcadbdcbddadcacdacbbbdbcdcbbdbaaacdcaaaaaddcadbbaaaccccbddccdaacdcdcbdcccbcabbbcaaddaabddccaadadabaacacaadcbaadabdcbacadaaddadbacadcddbaaddcbbcbcbddbcbbbcbbaabcacdadcadcbadabcacdcdddaabdddcbcabaadbbaadaaaababddddddbbbbacdcacbbbbacabbdbcdbdbddbacdcbacccbabbdccabbbbcddadbbbcabcdcdaccdbccbccbbcddccddaacdabadbababcbdaacbdaabcbbbddcacadbaacacddadacdddbbdbdaccddcdcbcadcdcbdaddaccdadcadaaabbbabaaaccbdbdacdcdcbddddbadadcaccddcdcdcacdbadabaabcabcbcccddcdaabaabadbacdaddcddbbdaadcdbdddbdbcddaadaadddabbcbcacbdaabdcbdbaccdbdcbcaccdabaabbdcabddbadcadbdbdbcdddbbdacbabadcdbcdbbbcdddcdabaddbdbadabacabbaacdaacbdbaddbdccbdacbacbcdcdcacccabdbcaadabccaabbcdadbbcaddaacbdacbcaabddbbbcabbadcdcddbbdcddbcabadddcabcacbabaaadccddcabadaabcbcabdbcddccabbbcbbbcbdcdbadacddacbccabcacbddbdcdadcbbadacabbabbbbaadadbbbdccccdcbdbbbbaadcadacadaadbcbdbacdddcaadaaaadacababcaddbcbcbdbcccaacddcddabdbdbacacdddddcbdccbdcdbbbabddbdbdcddbacbbddaabdabbdbccaccdbbcbddabdbaccaacbcbbddcbbbaddaabaaddbcaadcbdbbbbbcdaaddbcaadabaadbbacabbdcaaaaabdcdbadaddbdbbabcabadaddcabbdbcdcccbcdadcbdacacdbcbdadabddacbcadcddbacbcbdaaabbbbbdccaabaaabdbbccbcabcdcadcbadcabcabaaabaaaddccbbabbdbacccdcdcdcacabdbcabcbbadccdbabccdcbccbccbcadabdddcccddcbdcadcbacabdacaccbbccbbbdabacadccaacabddbcacbaddaddadddaaaabbbabbbabcdcddbdaddadacbcdbdddcccdaaddcbcbaabcbbccbccbcdaccaaaabccccadbcdaabaacadbdcacbbbbbcbcbbbcbdacadbabbadddadabdcdccdbadcdcabcaacbbaddadcadbcdcdccaaaccdcadbaddddabcaadcaacbacbbadcdcbcdddaacdcddbcabbcdbcadabddabbacbcabcccaacacccbbcbdbabbcdbcacbdbdddddaabddbdadadbccadcabcbadcddbbabdddcbdddbbccdabadccaaadaaddcdbacccbcabcdcdbdcacbacabcdbbdcaddcdccbcccbcccdcabcdbdababbdccbcbadcbcdbbccababaccdbcddcbccdcdaddddbcabbdddabccbdbccacaadccdadaadddcababcdaaabbcbdbbacbcdcdcdabbdbbbabdacdadccddbddabcabcddcaccbdadbdddcbaaacbcbdbcbadaacbddaacdbbdcbdcbbacdcdaababacaddcabbcdadcbaccdcdcddaaacdaacacadbdabbdaacdbbbbdcbddabcdccdccbadbbbabccbaacbdbaadaaacaabaccbadbbacbbdcbadddcacbbddaaccbdbbbaadbcbbcadbdaddadcacdcbabbabaccadbbbdbdccdaacdcddabbbcddcacbdcddacbadbbbacbabacdadcbcccbbbbcacccbdadcaaacdbdbbaaadbccaddaccbcdbdbabcbaadddbbcdaccaddcadcdcdadccabddbbbccbcbbcdccdbacabbacaadccadddaaabbaaadccccdadcdadacabdbbbccdaaabacaccadccbdabddbaabaccaaaacddcaadaccccaaadccdbdddbbbabbbbcbbabadcadaccccbacccdabdadacadccabaaddcbaacaddaccadcccbbdabcabaaaadabcbccadbcbdbccacbacdbdbabbdbabbcbdbbbadaacadbaabdaaddadbabdbccdcdcdbadbddbdabdabddbddccdbbdddcbbdbbcbdcabdccdaccdbbaccbccbcbacdbcbaadcbbaddbbabacccdcdaaaadcacdbbaddbdccccbdddacdbbbcabacdbbcadbcbbaabbdbdaddacccbbadaaadcdaccdddabbabcdbbdbdabdababbddaacbaabaccaddcadacbccdbbadcabcabcacdcdbcbddbbcccdabcdbccbdbaadcddbdddbcabcccdcbcbdaababbbbdacdabababdbcacbadaccbaddcaccabbadcdbbaaacbabbccaaacddcdcadbbcbddaacbabadccdbdabddbbacccbdacddcbcacacbabcbaaadcdcbaacddbaaaacdbabbddaabcddbacdcbcacddaadbbadbaddbacbbbcdacccbbacbcacbbbbcddbcddbadbcbbaadccbbdcbdccbbccddcbccdbcaadcadcaccdddabcadccdadbaadbdacbcacaddcdbbdaccbbbbaaddbcdbadbdbaadcaddbdbbccccbbddcdbddddddbcbcddbbdbcabcdbcabccccbadbddcdadabadcbdbcaabcbcbbbaaacbabaccabbdbcbcadabcaaacdbbbbabcddacdbbbbdbbbaaacadabbdccacbbbadabddddaabdabdacccadcabbadaddacdbbadcacdbacabdadaaacabbbadacdcdddcbadacbdccdbbdababcabcaacdadccddcbdcacdcbccbdcabdcdadbaccadadcadddddccbabcdabaddddccbabbacbbaccddcddaddbaadaaaccdbdddccbcbcacccbbaaddbdbacadaabbccdcbbdcbccddbabbcdadaddbdacbcccdacadccbaacdcbbcadcccdccbbbcccbdcbdbcddcbbdcbaabdbdbaaddadcacdcdbbcacacacdadaabdcbccaabcdabbbacaacbbaccabcadcdbbdbbaccaaacabdcbbacadbbcccccdcbbaadbaabdbaacaaadaababdddcadcbadadacddcbcbcacadaababbcbbadcdddbaccccdcdcadabcdddbcddddacadccacacddbadbcdadcdddabadcbadcbcdabbabcaadddbaddbdaaabcbaccbbdbbbadccddcccbaaabbccdcbcccbaccbdbaccbcdbcddcabdacabbaaabdbcccbdabcbaadacccadacabdabbcdccbdcbadccdcbbaabcaaddaadcabbabccbaacbdbdbdbdcdcdcbbcbcdaaacdddbbaacddbadddbbadadaddbbadccabdcdbbcdcbdcabcaabbddccbcbdcaddbdcddaacdccdacdccbdabdacbbdadabccabcababbddbcaccdcabcccabdcbcbaaabaccdadbadbcbbadbddcdddbaaaaacbbabbbdabcaabdddcbbdaadabbbdddcbdcbaaabdcdbcdbabacaaacdaacdbbadcbbdcacdbbcaababdcbaaaccaaadcabcbcccbadbdbdaabbcdddadbbaadabdddcddcdcadabbcadaccbccdaaaccaccccdddbcbdcbdacbaadbdabcaabcdbdacacacbaccacdbddccacbbccbccdaabaccbdbacbdddacabcdcccacccbabaddbdadcbddcbabcdadddacaadaadababddcaccadaccabddddccdbbbcdaadcaddccbdacdbcbaddcaccaddaabadcdbcadbcacbcdaddccababdcadaccbbdcabccdcadbbbbcccbaddabbacbdddccbbcccdbdbddddbadaabcaccbaabdaaacacbacddadcacccabdbacbbcabaaadbbbaabcdabbddbbdbbdccadcabaaacccdbdbcbcadccbabcaddaaadbbcbbcddbdacddcbbdbadaacccacbbbadadbcbbadcdacdccdccabaaaddcbbdbadadbcddbcddcbbbbccacbadddcbbcbaacabaabcbbacabccdcbbaabbbacdccbdaacaabacaacccdccccababbddbbdaacbcccaabddbbacbbdcdabcdcabdacbbccbdaabbbbcccdbbaaadbaacbaaaacacabcaabacbaccccbccdcccabdbdbabbaacaacbcbcaadaacbbcdcacaabdbbbdacbbbdbdcadcbacbcadcacbdbbaabbabaaabcbcaadbddabcacbcbbadaaacdabcaabcbabcdabdddbadacbcccadbbcdbabdbadbbcccbbbabdcaddbdddbbbcddadcdcadacccbcdbabaddadbbdccabaddccdababacacdabcbdacacaabcddbdcdabbabccaadcddcccbdbadcccaaaccaaabacabbdadadbcabaabdcbdbcbacaabbbccadcbacaacdcaaccadcdcccddabdccdccabccdadbbccdbcddbddcabacbabddcbdabcdcdbbbdabdabcdddddcddcdccacaadadacabbbbdacdcacbbcbbabcabadabdcdaccadbbdcbcaaabaddbdabaacdccccdacbabcdbddadadabbcccddbdccdcdacbaaaaadbddaadbdccdccaaabcbbcdcdabaabbbaadccbbbdbbaddbcaacbcacbadbccdcbadddaacabacaccacacbadbbbcaadbbbdbdbbabaabbcbacccacbdbdabbbcdaccababadbbdadddbbcabacbcacadbcabbaaccdbcbacadcabddbbbbcbaabcadadcdaabccdccacadddbddcdbcabacdcbbdaddbcbccbcadccdbcddcaadbdcbaadaaaccbaddadabaccacddddbabbcdcbcaadddccdbcaddbdcabbdcabbabccbaabbbbdbdabbcdcbbbbabdaabcdaacbbbdaadbbadcdccbbaacacdacdcbcccbdccdcdcbcbcbbaaddabccbadbccbbdabbcdcadbabbadddcccddddbbdddccbadccdbcaaadadddbacccbbddbbdbabbdbcccbadcddbdaacbbcbaadcbcbbcbdcbcaaacdbcccdcddabcbddbdcaacaadaadcadbccbbccdabbaadcaabbbdcdbbabdbcdbcdbcdabaacaabacbbdbaabdababaddcbbbcadddcddcdbdaabcbbccaccadbdcdacdabcadabbdcabccdcddaabdcbdbbdbdbbacddcaabaaacbdacacdacaccdcaadababcdabbdbbbdaacbcccbdacdbccbbacbcacaaabdacacbabacabddbacbdbdaacacadddbadadadcaccdbcabcbadbaabbcdabcabacbdabcbbbbaacddccbdbabbbbcccbbcbbdbdbddcbacddccacabcadcacabdcbdcbbcaaacddcdcbaacccbdbaccbcbaddbadcdddcdabbdcddddbcbbbabaacdaacbadbaabddaccbadbaaaaddacbbabacbdbbcbaaccbaccdbdaacaddcdabcdbbbbbdbdacabbbabbdbbbdccdcdcdcaaadbcbacaaccdbcadcabcddccabcbabdabacbaddacbccbdaccabdddbdaabcbcbddabbcbbcabcdcdbddddbacacacadcccbaadacccadbdbdbcccddccbabababcddabbddbcdbbdcbadacdabddbabacdbbabbbdbcacaccaabcabaaaccdbbdcadacbadbcdbbcbbddbdbbcadcabdddadbbaabadbcabbabdbdabdbcddbbdccccdcadbabdbbcdcbbcabcaddddbbaccaaccabbcdbcabcabdbdccbaaabdbabcaccabddddadcccbcdddcccaddbcdbcbabccbdbbcbdaaacaccaddaadbbcaabaddadccbaaabaaacbbdcdcdcbdaabccbbbbaacacbdcacacdacdddcbcbabadbcaaccdacdbaaddcaadcbabdbccbcbaacbaccddaaaaadbcabdbabdcbbbbcbdbacdabcbbdbccbacabcccdbcacbbddaadacaacccdbddcdbaaddaacadaacdabbcddcccbbadbaabbdbabcaacdbcccdbdddcdddabcbdddacacadccbbdcbdcdcdaccabcdaacbbabdccbbadbddaaddbdcccacbdbddcccbdabdddcdbbbbbddacbbaaacccccbaccdccabcddbbbaccbddaadddbcaabbdbacbaaabbcdabcbcabdddacbdabbcdcccaddcccbaaaddcddcacddaabcbcbaccacbaadbabddbdddccbccbbdbabdcdaabcbbbdbabaddadcddcdcabacaaddaabdabadcddaddacaadabbbacdaabbdaccabdddcdabdccdcccbbdbbcdbbcaabbdccdacacabcaccaabcaabdddbdcccdddbadabadaabbcaabccbdcadcacdcbabbdadbaddbdcdcbccadbbbcbcbdcdcbbccbaacdaacabcacbcdadcaadcddbcddbcbbabcaadccbddcddaaadbcaadcbbcabaccdadcdbcdaaaabadddcabcbaabdbbaccbcbabcacddcadbacdabbbaddacacddddbdccdacabccbdcabdcdabdacbadacccbbcabbadcbdadbcaacdccccbbdbaadcdbbddcaddcacdbbbdbbdaaddcdacbadccacabacddaaacadacdadbacddccdadcdcbadaacbaccccbaabbdacddcbbcbadacaacacdbdcddbcbbabcaacaaaccadccdbcdbacaaababcbcaadddacbdabddcdbbdbdccdddcdddababbabadccabbccaacabccacabadccaaabcaaacaccdcdbbaacbdcabbcccbabbdacdbbccaacdbaddacbbcaaddacabdacadabbbbabbddccacbdddbbbcadddcadcbcdbccabbbcbacddcdddabbabcbcbbcbddabbcddbcdcdabbcddabbaadbacbcacdaaadbbdadcddadbddcaccaacdabdddabccddbcdbbbbddbaddccaaabaadaabbacaabaacdbcabaddbdcbcaabcacbadbcdabadccacbbdacdaaabccdadcaacdcdcddaaacabcddbbddbdadabcabcbdcabbcbddabaacbbbbcddcdcbbadcbbcccbaaddcbadbbaadddbcccadacdbcabbddbbcbabcccbcadaacbdaddcdaaadaddccacbbacbbccdcaccaaddbaccbbcadabbadacccbcaaacbacababdbdbacbccabbaaccbcdbdcbbbcabcbcbbbdaacccccbbadcbadababccaddbbbdacadbccdaadaaadabbcddcabbcbdddaabbbabddcbbbaaccbcdcdbbcdcbbaacacbbaacbaadbcaccdabababccbbbbacccdcacbddbddadbbcdacbdcbabbaadbccaccacbcccddddccdabadadcbccbccaabdabcaabbdadaddbacdcddadbcacadbccbbaadcbdbabbdbddacacabbabdddacbccddabaadbdacacdcbcbddbabcbdaccaddaabddddbaaaadbdbabaaaabaccdbabcdabcbbdccdccdbdbbcdcbacaddcabcacaddbbddddadadccccabdccddddcdcbaadbcdbddbdbdcdaaabbcdaabbdadcddadcadcbdbaabbdcbdcddacdddcabdaabcacdbdbbadcdddcbdaadcbdbbaaadadaaadcccadcbacabbbdcabddccaaaaadabbacbaabcbcdbbabddbccdacacbdabadcdbcbddaabdaacaaddccbbbaabadbabacbdbbccacdcadbbbadabadaddbdbddddaaddabbccccabccaaddabddcbddcbaadadcbaddbccacbbcbbccdaaadabacbabdadcaacbccdcbabacabdccddaadacdabddcddcccdcddcadbaaacbbddcabbaddddbadacddadacaaccccdaabacdcaaacbddacbdcdabdcbdaddbcabaaaadadbdbccabbadddadbddccbdccdbdbcdcbabccccabcddabdbbdaccacaaddcdbccdacdccabcdbcbcbdcbcccbaccacddcaababdbaccdcdbdaadcdcdbcdcbacdadaccaabccdacbacbaabbcdadcaacdcadabdadadcdabdadabacacdaadabbccbaddbdaababcbcbbaabdddbdbbaabacaaddaabbdccbaacbbbdadbaaabdcccdcdaaadbadcaabdabdbdbabcdadacbdbddababccbbcdccddbdcdcacdcddcdadcacbcdbddddccbddddcdacbdadaccbabcadadbcdaadcdcbaadacbddaabddadaaddbaabbcaacabcbabccdcbbbaacdcbdbabdcccaabbdcddacadadacbbdbbabaabdcaddacdadccbdbadbcbabbcadcdabdcbdbcdccbdbbadcdcdcadadbabaabcbcdaadacbabcdabdccdcbbaaaccdbabdadcbabaddadbbddaabcaadcbccdbadcdcdcbcaccdaccbdabdaccdbdadbbcdabcccbbcdcbdcabdcbcdabcacadbaccaddbdbbadcadaabaadabacbbcaddadbdbbabcacdababbcccaccbaacdccbccdaabdbbdaabadbcadcbcbdcddcadadbdbbddacabccdadbaddabccddbcdbadcddacdcacacacbcadaabaaadcbbbbdcaddabcabdbcdabcbbcddbcadcddccacdacdddaadbbacaababcdbcdadbddcdcabdccbbcdbdababaaaddbaddccdabbbaadadbcdbbbacaadcdbcabdbbbaaabbaadbbadbdbdbcdbdddcdaaaccccbccdbaacadddbaddbdabadadacddcddaccaccbbddddabccaaabdbcdbdbacdadbbababdabdcbacbacdacbcabdbbacaaadccccbababcdadadaccddbcaadbbdbddbdacabbcccdaabdaccadbbddaadadcacabbcccaccabbcaacdbabbacbbbcadcaacdadbaaddacbcacdccaccbdcdbddbddbcabaddbdddacbdadbaaacbdbcaacabcccaaadcabcbcdabbdcabcadcdbddcddcdbddcaacadccbdabaddccacabacdabbaaddccbbbdbbbadccaddccbdbcccbcddcddbdbccdcdadcdddbdcdbdacaaabdbdcadbccaccabacdabbdcbadbdbacbdbccdcdababbdcababbbbaadacaabbcbbdddbadbdacccbaacaadacacccbcccbcbdaaddaddbdbcacadaaabdccdaadadcbbbaacdabdbdbaaaaaadddcacbcbbddcddbdacbddabacbacaccacbacaadbbdadcdacdacbbcddacaabaacbcdcdccacdaaddcbcdabddabdcbcdbacbadacdabdbbddaacbccadbccaddcdacaabdadbdbbabcdcbccdcbcbdbcccbaaabcdbdabccabcdadabdcaccdcbcacbaaddcbccdbdacacddccaddbbaabcbbaddbbbdabdcabbcbdbdaaabdbcbbaabaaaaaccbaddcbbadddadbcdacdbcacdbdbdbcdcabdbbbcaaacdbccbbacdbddcacbcddcadddcadddacaccacbbbacbdbcdcdacbdbadddbaddacabbdccbdacaacabbccdaadcbdbdbabcaccabdcbbcdbcdbcdabbbdcdccbacdbabbbaabcabcbadbadaacababcdccccaadbbdcddaaddadacdabbccaacbdaaacaccdabcdbacbacbaabcbbdbdddaababdadcbbbcbadcdabaddabacbccacbbbabaddaacdadcadbacdbcaadcbcddacaabbcbcbabdddbbbadbcaabcbbbbddaccdaadbdaaaacbbbacabdbcaadabacdbdaacaddcacbaaabcdacdbcacbcaaadabababaadcbbbbbbbcdbacddddcbaacbbbbbbabbbdddcacdaccccbbdbcadcdcdacbbabacacbcbbbdacacbcdccdcaacdbacdaadcdabcbaadacddabadbcdaadccccdddadaabbbaddaaaabbbddcacaddadbabadaddbcccdcadddabbbbddcbbcaaaadbdccdccacdcaaaadcdcadabadadbcccdbcdcddcbdddcacbbcdddddcdddbbcdbcdaacccbcadccccaaaacaadccbbdbdccabcbdaabdabdddbddbdabbdadcbdbdaacbbabdbabbdcdabbcbbbadbacdbcbccbcaadcddcbbdcbbcddcbddbdccadbcdcacaadabacadccddcbbbcdbccccdddaadddabadcdbaccacaadcbacddcdbbadcdadbcbccaccbdaadcdddbabbdcccdadbaacdcbbcbaabbacdbdcbdcaabadbbadadcdadcadbddbccaacbaddadcdaadbdaadbcaabdbadcaaccabacadadbcdbaabacadcacabcacacaccabddcadbadcbbddddbbacbbaacccaaaaadaccadcaadaadacdddaacaaadbdbabdabdcbabbabadcbbacddbcabbbadadcadcbcacdbcadaabbdcbcaacbddddbdcbcbdcaadbabbdcbbdacaddcbadbcccddbdddabbcccddddababbabaccdcddcdbccbcbaddbbddbdbdabdcdacacdadccadddbbbaacdcbbbbbddadadddccbaadacdbacadabccacbababadbcbabbddabcccddcbbadbbccccaabcaddbacabbabacaddcaddddbadbabbcaabacdbadcddbdababbdccacdabbadcabdaadbaaadccbacaaacabacbbddbdaccccbaacbccadbdcbdcbcdcbdadbaabaccdcdcdddbbcbadbbdcbccadbcaabbabcaaccbddabccdadacdcaccbadcccdbbcbabacbbabbcbdbccacdcbbdbcabbabacccddcbbdabdccaccbbcdcabbbadcbaaacdbacddbccdbdccdbabaadaadcdbdcacabcbddcddabbbddaabccaccbcdcddbcbbaaabaddbacabbdcddbacdbbadccbadbdababbcdbabcdcccdbbddddcaadcaccdbcbcbadddaaacddcdcdbbdccadcacdabdccbdddabbabcdbdddccbbcacadacdcbbddbbbccbccacbcddbcdbbababadacdccacdacbbdbcdcbbacdcbbcccddaacbdbaabbdcbdbdcdabbbdcacbacdaaadcddadcddadbabdabdcaababdbacaabacddadbccccdadbdcaaddbdcadbacdbdcdadbabbdccacdbbcbdacddbcadccabcdacbccabbbaaadabbddbddabcdddaddbaddbaadbcbcdbbcbabcdcbbdcdccdcdbaddaccdbccdddabbbbdcbcadadacbdbdbdbbbcbccdbbaaaddbaabbdddcdabbcabbcdabbadbdadbabbcbaadcabcdaaaaacdcbdbbbadcaaadddaacdddbdbcbdbdcdcbcbaadcdcabdbdbbacdbcbbcbdbddaadadaaaabccdbadcaaacdaabdabbdabaccaccddbbbadbadbcabdcdbddccdcdcccdbcbdbcbaabdaddcadcacbdabbcbbcdabcdcdcdaabbcdadbcdadacbdcaabbccbaabccbdaddcbbabcacabbbacaadcdcacbacdbabccacacaccdcabbccccbbcacdacbdbbacddacbdabdbbddbadcddddbcdadccdbcccbaccbcbbdbdbccabdabbaababcccdcbcabbabbcacddcdacaaddacddadbbacddcbbacaabccdcdcadccdbbaabdcdaddccbdadbbdacccbbdcdcdbddabbcdadcbdbacacddcacabbdbcaacbbaadcdcdaacdbadcddbacddcacdccdaadddbaccbabacababadcdbbdbacbcabdcbcbcccacddbbadcdadcacadacccbbbcdcdcddacdabddddcdbdadcbacbccabbccbcabddbbcacdcbcbdadccdcabdddcdabacdbcbbdddbdacddcbbcacdaaabbabcdabacacaaccaaabadbadccddccddddddadbddadbccbbcabdbaacadbacdbdcaaaaaabbccadadddaadaabcddaccdccdcdbabacdbbccabbcababcacbbbadaacbbacbdaccbdaabadaddcaacdcaacaababcbdbdcbadcadaaddacdcaaacdcdaaddccbacdadcdddbbbaadbaadbbbdbcccdaddcbbbccdaaaabcbddbcbbbaccccdaaabddacaccdaccdcddcddddbbbcadbbadaccdbcccdcabbdadbbbbadbdbddbadcabcaacddbabbcbdcdccaaddcbaacdbdabbddadadbbdcbdaccabbdaccdbbbcbaccdcbbbddcabdbbccdcbcbbcdcaaadaccbcabcaadaadaacdbaadddcdbcdaadabadddbadbbacbdcaacdcaccaaddbdaaacbacbdbacddddbbbccbbaadccccbadbccbaadbbbcbacdbcbbccdcadacaabdbbacddbcccabbbcccbccaabadabccbbbbabaacaabbcddccbacdbdacbabbddbcbbdacdddabcbaadcddcddcadccddcacddacbbcdbcdaadbadbcabbccbbadbbaacaaabcacdcbadbbdddacdabdaadadccdaccbcabaabcacdadbabbabbaadddcaabcccbbaaaaababadbcaaabcdadbddaaabbbdddbbbcbdccadcdcdcdbbdaaaaccbcaacdbbcbbadccbabbadadbdddddbddabbaabaadacaabaabdcdcbaacbcddadcbbdaddcdbcacbcacbddbbcaaabbdadcbcdccaaaabbaaccababdbbcddcbdcdbcbaaddaabddabcaaaababdcccdcabacaadbdacddbcccadbbdbbdcbaddcadaaadbacdadabbcaacdadcdbbdcadcbcaaaabcbbaddacacdaadcbaabbaaaacaaaabcadaabcdcdbcbbddabacacbabcbadaaabaacbdcadccbabdaddcbdbdaddbdbadccddaddadbbddbdabcbbcbaabbbcbaddabbbdbdbbcccbbacdabdaaadcbadaabcaddcdadcbdbdbcbaadbcccadbbbcdcddcaababdcbbdabddcaaddcadacadbddcddbabaaaadbcbbbcadbbaddcabdcdbaccbddaaadbadbaacccabddbdddaaacdaaddcddbbbcccdabddcababaabbbbcadababababadcaaaddaccdbadaaaabdcabdacbcaddaabaadabddacccbddadaddabbcbbccaabbdcaddaddadcbddcbadcdbddcccdbbbcaccbabacdddcccbbdbdbccbdddacccbbbddbacaadabcbaabcbcbdbaabbaabaaadaccdaddddcdcdaadaaabdccbaadcaaacaaadcddbabbcdcdadcdaadbdaabadaacbacdbbabcbdcaccbccbdbdabdddacacadbadbbcbaaaadcbdabcdadadadbddddbcadcbaaacbcbcdbbaccbcdadbabccdcbddaddcbadacababbbccbcaabbdabcbbcdbdbcaddcdcdaaaddcbdbbaccbabbdcbaaabbcccbdcdbbadbabdbbaddcacbcbbcadccadbabcdcacbdbbacdaabbcabcbaccbcccadbdbcbdbbdbcbddbacbcacbdcbcbcbdacbbaacdcbcddbabbaccdabaaccabaddbddabaccabaadddacdabbabcabcbdbdcccddcddbabdbbabbcaaddbacccaacadbabbdbbdbcaaccccbbdbdcabdbadadcadbcbabdaadabbbcccabdaacbaaccddccbbdadccadcbaccdcbcddbbadcdbbacddddbccbcacdbaacbbdabddbddbaabcbcbaddaccccdababdbbdcbacabccdbabbbabcabddaabbcadabbcdcaadcabdbaddabdcbddaabdddcdbabbdbccdacccaabbcacbadcabbcaccbbcdaccdcbbdbaaabcbaaaacadcbddbdaadaabdcbbadcdbdcacabbdbaaadbcacdbdbadbaadcdaadcbcdbbbddbbaaadcbccbcdadaaacdcabadcbdcdccbdbcdacccccaaabcacaacdddcbdcaddcbbdbcbcdaacaabbbabacbdacddbbdaabbacadadcbbbdbbcbcbadbcbcccdbdddcbcadbadcdabcbcadabbaadadbdacbcbdbbcbddcdcccccaaaabdcdabbbbdbadbadbcaacddcacdbacbdbddabccdddcacdaaccdcbaacabdbacbbabcabcbcadbadbabaadbccccbbbcdbdccddbbdcbadccbabacdabbacbbacdadcbbdcbbbbbcbdcbacacadbbaaddabbdbacbaabdababbbadccddaddabccdddddccbdccabadbddcbbbdcdcdaaaddacccdbbabbcdabcdbcdbabbdadaacbabbaaacabbcddcdbbabbbaaadacdabddbbccccbacacacacaddaccaccdabbbcbbcbbbaccdcddacbbaaabaccddddacccdbcdabaaddbcaadccbbcdbbaaabccbdddbbddcbbabcddaaddbabdacbbadacacdbbcbcddbcbdbacbccdacdcababaadcbdddbdddccabbcbacaaaacbcdccdddaabdbddcdbdddbdaaccdddcdacdbcbbcadcdabccabbcbaddcaccabdbaccddadaaacacadbbaddbaaddaaacbcbbcddcbacadcbbabbdabadaddacadabcbddccabdcaaccbdabcdcabccbccabdbaddccbcdaaadbccbbdbddacbcddacaddacadcdbababdabddabadccaaddcbadcdbbccbddbbdbabbdaccacaaabbacaaaddabcabbbdbabdaaccaaabbcaadacdddaacbddbdcbccdbcacacadcbddcbccbcaacaddbdadadabadcdccabbdadcccdbcccbadaabccaccccadbbbcdccabababcbcccbacccdcabbccccabbdaaaaacacbcdcdcabbabacbdcdaabaddaccdbbacabadddcdaadcdbdcbcdcdcdcbdbbbdcccbabbcaaadcbdadcccbaadbbccccccaccdbdaabcbccbdcaadacacdbdbdcbcbaaabbacbacddcbdbdbaddabdcccbccbbacbbacacabcbadadaccbcdadcddbbbbaabdadcbdabbbbbaddddcacbcddbbaacbacbdcdcdbaddcdbccdbaacbbbdccadcbcddcdbbdacdcdaadccbaadbdaadcddcbdbcbdddbccccdadcacdcddabbdbcabbbdbadbcdacaaccbdbcbdabcdbacdcbdcddcbababdbaadbdcbaccadbaabdccaddbcbccbcbbdddddcaadcdcbdbcbbcaddadcdccbbcbacacacddbccbbbadbdadcbdacdcaadabdaadbbbdddbdcaaaaadcbbbcbdbdaddbabcbabacbadbcbbcaaddcbbccdcdaadcadcddccdbbdbcacbcadccbcbbbacbcabadababacdcbaaabbdddccdbdadabcdcdcddcddbabbcbccacbbcaaabaadaddbddaadbbcabcbcbccddcdddacdcdcdcbdaaacddbcabbbddcbcadccddacdcbcaaadcccdaabaaababaabaddadbbbcbdaccdccdbbcdaddaacbddcccdaccbcccddacaaaaaaabbdacbaccdbbbdddbbdddbddddcbacaadbccabbbbdbadbbabcbcbdaacbbdbabbadddadcababadbcccdcbdcdacaababbdbddddabdabdbcdbabccdbdbadacbaadcdabaaadccdaadadcadcbcdbbdbbbcacbaadcdcccaaccabbcbdbacccabadbccbacbdadaaabadbaadbcbcabdaacbddababbadacdccddddddbacabadabbabbbaabbccdbcacacbbdbadbcdcccdcdbdddbabcdcbbcadbabddbbdbaaaaaadacddbdbbabdccdcdcbcdddcbaccddacbcadabbacdddaddbbcaabacddabddcaadcaccdcbaacabbaaacdabccbdaccdaacadbaadaaaabccdcbbddcbccaccabccbcbabdaabacabcadbcbaabbdbacbbbadbbddddaaaadadabcdcaaabbddcbbdbdcdcdbbaccbbdddcdcccddaaccaccccdadddbabcbddddcbbdadcbbcbaabddbbabcbcdddcaabcdbdbddbacdbddaabaabccabcbbaabdcbdcbcbdccdddcbbcdbcdbabaabbbcaddabcaabadbabbdbdccccdabbbdccadadaabcacadcbaaacdddcbbbbbdddabbcdaabaddbdaabbdcbdacadbccbdcaccccaacabbcbbdbcdabdbdcaddccbadabdbddbdbddadddbacbaabdcabbccdcddcdacaadddbcbbacacdcaaaaddabbcbcbcccdcdddaddccacbdccdbbdbdbdccaaaddcbddddbabbdbabaccacabbdbcdddcdabcddcdcbddbcbcabcbcdaddbcdbdcdabdcabdbaacbbaabbbaaddcbbcaabbcdaddbdddacbdbbcacbacdcacadbacdddbdabbcabdddcdaaaacbccbdcbaabccaccaacaaabdccaaadcdbacadbadcbaccdcabcddbaacddbbddbdcdcbcbcbdcdbdbddcddccadddbdabcabcbdccbccaaadbbacacccddacdcaccdacbbdbdbbcddbcbacbbcabdcddbcbaddcccabadacaabaabaadacdabccaabacacbcdcdacbdbbcadbcaabcaddabddbdcdbdaacdbdacddddbdbcccdbadadacdbdbdabdcdbbaacabcdabddcaaaadaaddacabdcdaadcbddcbdbbcdcacdaacdbbcccccababddbccbadababbaccbbaacbdbbdbcacabdaddddcabbdaaccbcdbbbbccdbabacdaaccbacacaabdccdaddadcdabaddcbbbdcdaadcaabacddbdadabcdcbccbaaadcaccabadaacdcdadabbaadbccadddaacadbdbdccdddcdaccbdbdcddaabdbcdbcdabdbcbbcbdabccaacccbcdbccbdcdcdcddddccacbbcbbbddacdadadaabadaacadbbdcbbbcdadbcdbaacddadbdaddbcaddbcdabcabcddadaacaddcbbddccddbdcbcdbdddddcdcbabbcdadacbabdcdbadbbcbcbaaadcbdbbbcabccbdabaccdaadcabcccdcacaacbdcdbaadbcacbbccdbcbbcacbdddacbbcdbcaadaaddcadddcaaddbcbadabbcacadcbddadacabdcdacaccbbbdadabdbdbdcdcbddaaccabccbcbcbdadbaadabcdbabbdccdaaabddbbdccaacababcdabaabaabcaabbaacaacddacadadcdccddacbcdbccbddcaddbbcbbabdcbddaacaacaadbbbcaccadbcbaaaaacabadbbbdbadccbadbdccaddadabcbdcbabddcbddddbbccbbdcccdaccbdcbbbccabcbcbbdbdbaabacadcaacdbcdbcadcbbbdcbabddadbadcdcddaaabcdadcaabccaacbcccaacdadbccdbbcacbccbdbabccbaabbbadacbadbbbaaabccaaacaaabcbdadaaaabbacbbacdcccbaabdcaababbbbaaadabbddcbccabbbbaccbbcccacbcdbdcaddbdbdccabdcddcdbdabbdaacaccdcadbbbbcccddccddacacddbbacadbddabbdccbdcdacdbbbadddbaabbcadbbbaddbbcddbadacbbbdcddabcdcbcbbabddadccadccaabacbcadcddcaabaacdbcbbbdcdaaaabddacabbaddacdcadaccdabcdccaadadbddaacddabddbcdaaacbccdcbbcdbcddcacaaaadababbcccbbbbccabaadbabacaadabdbcdbdaaacddbbbdadaadbcbacbbaadaacbcbabddcbcbdbcabadadccacccababdbaccbbbaaabcdddcbddbcaacbddaabaaacbcbbbadcdcddacdcdbdbcbadbcdadaabcbbcddaaabdccddabbbbacdccbccccbdacabaadbbacadbccabcabcdadddbbbadabbdaabadabbacddccdbccababcdbcccccddababacaabcbadbaacacdbdaadaabbcdacdacbaccccdbcaaccdddcbaaacddadcbbccadbcabcaabbabbbccacabcaabbdccdcdcdbabaadbdcadbbbacabdcadbcdbbccbccdbdcddcbbdcddbcaddbbbdabccbcbcddbcdcdcadbadadddabacaadadbadbbcdbddcbbbadcbbcbdbcbddcdcaccdbcccdaacacbbdbcccaacdcaadbcddabccccaabdadabadabcbccdaadbaacddddaddcddabcbaddaccdbabcabdcabacaababacbddaccabbbacdcbdccacbddbbcbabaaadacdddadbacacbbcabccadbbbbacacddccbdcbcaabdbbdbcbcdbbbdddbacdbcbbdabaacadcbadbdccabbabbccdaacaabcacaabccddddbaabdbaddcdaabbadbcdbccdbbcbacdacabbcddbcbbcbcccaaaabccbdaddccadbcdcdaddcbbbbabbacbcacadadabbbbcdbcdcbbbbababddacacbccacaadadcbaaadccbdcdcbbacbbdcabddcbccddadcdcbddcbddaadddcbacdabdddaccbadbdabbabcbdbadcccbabcccaddabdaacacbcdabdbbbbabdbadabbddcaabbabcaaccdbcddcbdabcbbadbdbbaddcdabcdcdacdbabbacaacadabccbabdbbbcacbbcddacbcabcdddddadcadbbddaadbabbdddadcaacbdccacacdacdddaaddaacbdcddadacddaaccadacdabcbbcccabbddbcabcccbacaabbacbcdcdacdaadacabccbaadcdcbddbbbaadbbccbdcadbdbaabaacbcaccddcdaacddcbaaddabdcadcabaabbbaaadcdcbadbacdababccadbbcbcacddcdbaddddaacabdbcbbaaadcbaddaacbdacdddaccdbbcbdbbaaccaccabdbcabddbaaddcccdadcdbbcdbdadaccaabbcacdddcdabdcbdcadddaacabbcbbbdbdcdbaabadcbdbcbdcdbdcacadcccbbddaaccdcabaaaddcddcbdbbcaabadbcdcccddcbcacadcaaddaabacdadbdbbdcadcbddabaabbbcacdaaaddcdcadcdbdacbaaadbdadcccddbcaddcbccddadaadaabbaabbddbadbcbcdacddcaacbbadbdcdcadaacdacddabccadccaabccdbaaaadbabdabaddcaadcdaacacddcdcadccbcbaacbcacabaaddabdbcbabbcddcadcbcacccbadcaddbadbdaddbdccaddabdbadbadbbcccdcdbaddbbdbabcbbcbcdabbdbbaadadbabadcbcdcbdbcdababaaddacbcaaacdbbbabcbbcbcbccbabbdaadcaaaaaddaacbbcbabcbdaccbbbcbabcbbccbbccbacdbabccdbdabdbccbcaccbbaccacbbacbdcbdcbdccdcbcdaccadddadddcabbabccccbaabdaddbcccaabcbdaaccabbabadcdbcdadaddcdbadcdbacadbabaacadbbbddbcbcbccdcaadcabbbdbbdbcccabcbdbcccaaaababaddbacbcbdcadaabacabcabdaccbcbcabcdaadccbdadbbbacabcbcbacbdcacbacbcbaacaaadbdcaaaabbdadcdcccacccbbaccdabdaccbcdcacbdbdcadbadabbccbbdbcadbccddbbdcbbbcbdcdbddbdacdcaddcadcbccdddbddbbbcabbcaabbdabbaddccdcbaddacdacaaddbcbdcaacbbcabccbcbbcdcbcbbdbabaacaaddcdadcaccbccaacababbbdbcccabdbccaabdaaaacbbcdacdcccdbdbbaacdbcabddbcabbbcccaadccddacacbddcbbdbcbcdbcbadaccacbcaacbddcbdbcdcddbabcaaaacdaccdcacdaddbccdabacdacbdbbdababbbdbbbacacccddccbbdaadcadddcdbbcadaabadaadccbbbdbcbcbbcdcdbadcbcbcacbcabcadbdaabccdcbaaccdbdccdbbddcbcccbcbadbbcccbbabdacaadacaccddabcbaaabacddaaddbdcacaabadcdcdddabcdaacbdccbcacadadabbaccabdbbbccddacccacdcacadaccbcabcdbbbbaacdcbccccaacbdacaddbbaaaadcbaabddaaabbcbddddbdadcbcbbdabadabbbdbdbbccdadbcadaccbdbabbdabdbbbbdcaabccadbaabbcdabcdcaaacdcdbdacccdbabbbacbaadadabdbdbdbcdaadcbbaaaacbcdddcbbacdccdcccaccdcadcbabaadaaddabddaddbbbbabddbdaacaddbbbccbbcdcdcccccccbbdddaaadbabbbcbdbabbdbdabacdccdcaaaabbabcbacacdadccbddadcddddbcaacdaadccaaadaadddbaabddcbdadadaaacbbcbccabbabcbadddaccbabbbaddadddcbbdbaacbacbddabadccdbbbdbbbbdbadabcdbbdbabddacbbddcababaabbbcbbcabddaaabdcccddcdbbccccaddbcdddbccacdccaadaacbaacabccddbaadbdabddadcdcaacaacdadbabaaaadcbaddcbcbbbaddbbccadcdcbaaabbccbcddcbcddbcbaaaacdaacdcdbdccadcacadbacbcdbcdaadbadbbbadaacbcbdcaaacccbadbdbaacddbacccadcbcccdcbcccdcbbadcbabddbbdadbdcddadbcdabdbadcabdacdabbbbbbabbaddaacabaadcdbccdbcbdcbbcdaaddbdcadabddacacbbcbcdcbddacbcbbdababdccaabcdaadbadbacabddcbaccdabdcdcbdbbdbabdaabdadccaacdacbdcbcbdbabdcbcdcdcacbbaaacbcddcacbdcbddbaccadddddbabddbddbddcbdcbdbcabddbaacaccbbaddbdabbdbdccccadbcbacccbccdcaaccbccbdcbccbbbabcbbdbdbcdcdcbddabbddcdbbbbbddddddabbbccaacdadddcdababdbcdbabbdaaacaaacbabdaddaaccddabbabccaabdacdbcaddccaccacaadbcbccddddbacaabcddbccdbcadacddaadbbbcaaabbdadbcbdbbabdbccccaddbccdbcddcaadbbdcdcbcbbcdbccdcdbcdaddadbddaccbabcabccabccbaddacabdabdaabacbacdccdddcacbacdaacbbacdbbabddabcddaabdcacccbbbaabddcbbccccbbddbcccabddbdccaaabddbbacdbbbacaacdaddadcbcbdaabaadacbbdbdacbababcddbbcbcdcdaacdaacddbcdabdadbacddbbdadaaadcadbbddbdacacaddcdbcccadabdcdadcacbacbbbcabbcdaabbabccdddccbdbacaadbbaabbaaccabddcbaddabcbdaddabcbcddbdddccaacdacbabbacdadabdbadbcdbdbcaadbadcaacaacccbbdcdbccabadcabcbdaccdcbcdbcdabcbbbadbdabcbbacdcbbccdddbbdbadbdccdcdcdbcccdabbbacaddbbbaabccaddadbabdbbaabbdbcccaabcbdcaddcddabababaaabacbcbdbcbdbdadbaccaacaadcdcdbdadadbcaccdabaaccadcbcaaacbcddcccbdcbbbcddcbdacdbdaabaabbaccbaaccaddacddcbccdaabadbdbccddbcaadbcccacdabbdbbddcbacaddcbbbbaaadbcadbacbdbddcccddbbdcbccdaddbaddcdaddbddacddaaabadadacccdcaacadbcddddbbddadcaabddccabcabccbbbaaaadacaaadcaadabaaccaccdcdcbdbcbcbdaadbdcdcbbcbcdaccbdcbbbcbdacdbaabdaabbabbbdadbdbadbaaacdacddabcdcdbbacadbdadccbabcacddddbabcacbcdcbccababbabbbddabbbdddacbacdabbbbcdbaadcccdcbbdcbbdaddbdccaccdadcccdbdbcaaccababcbdcdbddddaabcbababadaababbaadbcccbdddabbbbbcabddadbcddabbdbdccaddaadbdcdcdccdbacabaacdddacacbdabbabdbaddbdddaadadbddbcddccbdadbbacabddddcaabbdddcdbdbcdadbcbdddcdbdcdcaccadababaadacccddccddbbccddcdabcaadababcbdbbbabdddddbddcdacadbabdbbaacbdddacddddcdaabcabccbbbdccdddadacaacbcdaccdaabccacccbddcbadacabacbcddccbadacbcadddcccdcdacccdcaaadbadcdbbbabcbdbbdccabbacccdabdabcccccddaabababbcdcbbbbddbcabaadcbabadcdcbbabbbdbddcbabcbbadaddaadcbccdddadbccdbbbbddcaaabdbbabadccacaddbbcddbacdbcabddccbbabbadbdaccbacababacccdabbabcbcddcbdccddbdcbdacbdcbddcdbcbcadabcdadbdddcaaacdaccdddbcaaabdabcbbcbcabadccacacbdcbdbcdccabadaaacaaaddccaabadddbbdddcccbbccbaacaacbbdcaabccccccaaaacdbdcdcdaabbaacbbacdbabaaabddddadddbcdddaadaadbbbababdbcaacbdbabbdbcbaddbbbbdbdcbbbddabdcdbccbcacbddcbbcccabddcbcbabccbccbbcdcdbcbacbbabdbaadbdbcbddbdcbcaaacbcadcbabdacbdcacddcacbbccccbcdbddccbdbccbaccccdbbdabdcbaaadcccacaccbddcdbddadcdbcdddcabbaadabadddbdcabaabcdbabbbbabbcdcdbdabbaaacbdddbbccadaadbbcbacaadadcbbaabacdbddcddbbacadbabdccbbacabcabaaddbdbacadbaaadbcbbdbbccabddbcddbcdbbbccbaaadbbbbcccdbbadddaadaabbaddbddddccaddbddbdcbbdacdcbddddcdbabcddddcbbbdadbbbbabcacbdabdcaabbddadaabababbdbcddbbbdbacbdcbcbbbddbdaaddabbacbbacbcbdbbbdacbdbdccabccdaabadbbccdcbcbbdbcababaabaaaddcbbcabdcbbadbaccccddbbdbdcadbccaaaddacbacbbdaddbdcccbacbcdcaaaaaddaabaacbcaccbcbacbcaabcdbdbcaacacdcdcabbdcdacbaccbaadcbabdcabbaacddcaaaaabbdcbdddadcbcbdacddbdcabbaacdbdcdaccabdcbaabacbcddbcdacbbddadbbaaccbdadccbddbbbbbacadaabacaabaaacacbbdabbabcabbbbaaddabbbdcddaadbbbaacbcbccdbacabdaacabccdccaadcaccbdbcddbadcdcbdbacccabdabaabaacdadaacbacbdcdaacbbadcadbbcddddadbcdbabacbddbcccddbbdcccabcaddcbcdbcbcabadabdddbdababacbdbdcbbabbcaaaaabccddbcdadbbcadbddbbbbbbaaabbdcabbdcdbbcaccbcdddbcdacbcbaaadccbaadbcdbcacbbbbbbaddcbcaabadaccbaacacccbaaacbbdbbbcabcbccadaaadbccbdbadbbaabdbcadaddbbddacdaadcdacccaabccabccbaaacdcccabcdaadaadbbadadaaabdbbbacaaaababdcdbdbdddcccbdabcddcdadbacddacddadddaacaacdaaabbdcadbdcddcddcaccbcbbbcbddaddcabbdddabdabdbcbaddcddbddbddbacbcaacdcabcacdbcadbbcbbddbbcbdccaccdbbbcddbabacadbccbabdbbacdcacbcdddcbabbbabcbcdadbccddabaadccaccaaaccacbacbaccbccabbdbcacaccabcccacadadabbdccbbdbbccabbdbbbcabcbaadccadcacbbbcbaacdabbdadddabdbdbcaacaddbbcdcabacddccaaadbbdddbcabcaddccdbaaaaacacdddacdbddaccdaaaaaccccabcdbdbacaabdabdbcacbbaabcbcccbbbbbaacddddcaaacbabbbdabaaaddabbcbcacddcacaabddcaabbdcdcaaabdaccdabcdcbacacadabaabaabdbbcdabcdddcbdcbabadbdcbadccdabccbaddddbaaabbcbcddbacdcabcdcdabdcbbcaacbdccabcdbbcdbacabbaadcbbbbccbddaadccbdcddcdccabaacbdddbcabcdaccdaabcdbbbdbcdcccbbbaaddaacbbbbbbcdaaadbdadcdccbccdcbcbccdcbaaabacbbaadbccddbcaadcaaacbabdcdabcbdbaaaacdcddcddabdadaacddaaaabaadbdbccdbadbdddbbccccabcccddaaddaaaccabcddbdddabaacdaadbacaabababccddaabdbcbcbdccdadddcaacbcdcbadbdaabccdcbcbcacaddbcddbcbadccbabdccbbaaadccddabcdabbccabcdadacbdbdcaaacbaddaadadddddccbbbdababdcccacdadcdaddbabbabdaccdbacdaaabdcacdcababbbbdbdddbadcacdbbdbcacbcdbbaadbbaabdbaabdbbcddabaabddbbbbcdaaadccdbbcdbdabcbcadcadbabbbaccbdbddbbcdaccabdbddbaccbcbbdccdcbdadbbbdcbdadbbabdabaadadbcbabaabcbbadbccddcccdbabcdccaaaccbbcacaaadaccaaccbccacaddbddccacabccdbdaabacabccacdcabbcbaddccbdaacddaaaabacdcbccbcbdcbbbadbdadcddaccabbcbdddbcbdccdbbacddbdcdabddbaacbaacdaacdbbaacabdddddadcddababdbabdbbaacdcbcdbaadccccdbcaaaccdcbdddbacdbaccddcacddddddcbacdddcbbbccddabcabacbdcaaabcaddadcaddcaabcbcacbbcbdbcacabadaccdadcbbdbdaaccacadcaddcacdaadababddacbcdaadadacdaccbadbaabdbbcbacbacbdcdbacaadacbacaaccaacbbcbbdaaddaacdcbaddcbabbadcadbcdabbadddbcbbdbaaaccbdadbbbaacbccdcbabbcbbbdaddddacadddbaaaacdddbabccbcccdbcbacdaacbdcccbbabdaaaadcabcabcdbcabcbbdbddbbcaaacdaabdddacaccbbbcaabaaddbacddbbdcdbbdddcdbaaadbcdbaacaaacddabaabbadbaacadababcabbcccacbbaabadcbadcccccaadbcaabdcaaadcbadababccbbdaccdaacaccbdacabcdadacbcaabadbadbbdccbdbacadbbdaabbcacbadcabdccabddcdcdabaadbaddadcbcdaabbbcaaccaabbddcabaaddabcadcdddcdcbcbdbadcdaddbdbabcdcccdcdaccdcbcaaacbadbacbaccccbacdaaaaadbcdadcdbaccaabcdbaaccaacababaadbbbbaacbddcdbaaadacbcadaacabdccdcdbaaaabbbbdababcddaccabcbddabaadddaadbcabbcdccbaddcabbdaccdcccbcacaadbdcddaddaabcbddddbcdbababdbaddcbdbadbcbdaccbcdbcabadbccddadbdabbbcaacadddadcdbcdcbcdacccbbcdaaaaaadbdcaaabcacbcbaddbdcdaddadccabcddaaaabbaababddbdacabbcabdccbaccdccbbbaaadcdaaacbaadddcdadccabdbadadbbbcbcdabdddcbdcbaccbccdcabaacbbbbadcacadaaabcccdcacaabacbbcaddcdbdcddabcdbdaabdaaadabdabcaacbbddbbabcddadaddbdbdddadccdaadbdddbdaadddcadadbaabbbdaccaadcbaddababcdccdbbbabaadabcaaaaccaacdddccbcacadacabdaccbdaaabdcbdbddccbcadccaabddbbbddacddabadcaccacdcbacdaaabcdbadcbddcbbcaabcddcacbaaababbabcdaaaabdacdddcabddaddccaabcaabbabbbcbdabddbdacabcacdadcbccbdbccabdcbbccbbbaaddabdcddabccdcbaabcaacacbbababccbacaadcaddabbacbbddabccabcdaacaadcbdccaabbaaabdadcacddccdbaabaccccccaaaddcdacddcaacaaacccaacdaccadbcdbcdcdaaabcabbdddcbdaccaddbaaabccbbbcbdbddcdabdaccbdbaabcdbdddcaccdabcacabacabbdadccdcbabdbcbcbaadddabcaccdcbbdabbcaaccdddccaacdcdcbcdaacccabddadbddacacdddbbbadaddbddbbcbbbcdcdadcdccbbddcdadbdaaacbaaccccaaaabdddddbbadcdaaabbcdbaddbdabddcccaabddabbccabdabddadbddacadadadaaabbcbdbcbbabacbbbddddccbdaacacdbcadcbdaadcddbbdddcdaaaabdccbbccbdadababbbbcccdbacdbcbbbcaabdbdaaccadbbadcddaadaacbacddddccbadbbcadbaddabcbcdcabacbbabddccdddbbadcbabacaddbbbcddbcdccdcbabbddabbdbccabcdaccdaacacadaacdbdaacbacccbdadcdaaabbadbabcdccadaacbbcddaabdbcccddadbcdabaaabaddadaaccbccbbbadbaddddbabaccddddbbbcdbdbabdbabdbacaaccacdabbabaadabaccdaaabcabbcaaacbadbbbdcbaddabbabadadcadaaaadbbbbccacbbabcaddbddcaddbcdbddbaaadabbccabacbcacdbbccabaadbadbdbabbaabdbadabbbcbccdddddcabaaababdabbbbaccacbcccbacaacbacdbdbabdddacdcbdadddddcacadbcbadbaacddbdbdbaaabbaabdabcbcacdddbaaaacaaabdddadcacabbacbbdbbcbcadbccaacabdbaddcabadcababbbcbdaadccdbdacbddcacdbacbbcbcbabdcbcadbcbbcdaddacdaaddbdbbaddacbaaccddbdabcdbabbbbbaaaddaacccbdabbdcadcdcddcadccacdbdabcbccbbbdcabbdaaaadaddccdccbbccaddddabccbcacdadbacaacdbacadbdacbcdadcdcbcbdbbdccddadacadabcdaddbcabdaddbdcccabdddadcbdcaadddcdbdccbabbbbbddbdbbbdcbbcabbccdcbcbaacabadccdbacaadaddbcababdadabcbdbadcaddacbdcdacaacbaccbabccabbaaaacbbacadabbbdabbdcdcbbdabdbddbaabdcdbadcbdbabcbcaccbdddcccccdbccbdbbddcdddbcbbdddcadcaadcacaabcaddcdaabcbcbcddbacddbcaadbcddddcdcbbcaccddbddcbdaacdddaccccdabbbdacccbbadbabdcdbabccccdaaabcbbddbcadbdbbddbdaddbadbaccbccdbbbaabccbabcabcbccbdccbcbbbccaadbdcdbddabadaaababbdcaccdbabbabbacddabbbbbddadbbdddaadbbaddbcadcabbabaaccbabdcaaadabddbccdbcadbaaaadcaabcaaccaaacbbddacbbdbaacadaccdddcaabdbcababbbacadacddadcaadacbdbdbbadbdcabaabcccbcbbbbcdcacacddaacdacbbabacabcbaddcdbadccdcaadacbdbccacbddbcbcddbbdaddbcdadbdcccdddcdbdacbccdbaddabddddbabcacaddabaadadabdabdbdacaaaaaababaabcdcacbabdcdbacbaaccadbdddaabdbbcdddccbbaabdcdadaadcaacaacdaccddcdaaccdcdabbbbcbbbbdacadaaabdcdddbcdcbbabdbaddaddcaddbbdbbcabcbccaddbccbacdbdbdabbcdcadddcaddcbcbdbdaaacbcbcdaaaddccacccdbcdcbccaaccaddabbbbbdbadabbacdccccdddbbabcadaacbadddbabbabacadabdcdddcbccabdddbbdadcaddcccddacbbbdbaddaadcdddacdbddaabaabbbdaacbadbdadbdbdddcdbbdcadabddcbbaaadcdbddaadcbacadddcdbdbdddccbdcaadcbadabbabcccbdbddadabddcadbacacbcbddcaadddddaacabbccbdbddaaadaacbbcddaabadabadcaabbbbacdcdccbcbdaaccabcbcadccddacbdaabdbcbdbbadabdbabacdcdadabadbacbbddacbddccabdbcccccabacbbabcdcacacccbddaaabaccacddaccdbaccddbbdcacaddbcdccdaddcbbbabddddccaacbdbdadcbccdccacaaaccabdacdcaaddddbddcdababbacdcbddcbcbbbcdcdcbacacaacdacadaadcccbaabcadabdbbaabdbbbdadabacbcaababdcddbcbbabccdbbcbcaabbdbcdcbaddaabbababbdccdbdcabcabacadccbaababbacacbddbccdabcbcabbcbaddaabcdcbdcdcacaacdcbdbddbdcaadbbcaddcabbaaaaddccbdcdadaacdbcbcbcbaabdbbddcbbacabbaaddbdddbccdddaaccdbbaaadadcbcaabbcccdccdcbaadcaaddcabbdbababdddbaabbcddcdbcadbcabcdbcbdcbdaadbcdcdaddaaaaadcdcbbabadcbbbbccbcadaabbbdcdcdcccaddaaacbdaadaccaccdcdcbcababacdbdacccabcaadcdbdabcbadbdddaddbaaacaadbdcacbbccdddcddcacbbababddbccabaaadcdabcccbadabcabcdadadacddddabcccdcaabdaacacddabdccccdabcacadcbaaadbcbaddcbddaddaddbdbdabdbccaacabaabcbabbbbbcabaccaaacbccaddbbabdacbabaddadabbaabbbdabbdbbcbdcbbbcdddacadcbbccddddddcbabdbacacbbbabababcdababbcaadbdbbdcdabdbcaabdddddbbccdabddadbacbdbbccdcdbabcddcdcdbbdacbddddbaddaadbbbabbdbdccdcdbacbdabcaadbbaadbdabddaaaccdccaadabccbdbacaccbbacdcdccbdaccddbbddbdcabccbacdbbbddbddabcabacdcbacdbdabdbcbacbbabadacbcadddcbbddacbaabaabbcabcadbbcdadaaadcbbbbabcbcddcaaadbacbbdcbbcdacbaaccbbdcdbbcaacbbccbccabdacadbabaddcbbaadddadcabdabcacacadddbbdadbddcabbdcaaabdadbaccbcbbadaccbacbdacbdaccbcbabbcadacdcacdbaabdcaabbcacbcaaaccbccbbdadbbaaabbcdcbcdcdccbcbcbdadbacacddbadbbcccddbcabbaccddcbddbdbcdcbacbdacbbbccddadbbcbabadbacacbdaacaddbdaaccaadcbddabbababbbcdbcdcaacddcacbaacbbbbbadaadbdcbdcdddddaacccbbbcbcbbaaacbcdcccccbaacacdbddbbadbbcacdadacddaaddccacdbbbcccdaadbcddcabadbcabcdbccbccbabadbcabdccbdbcdcdddabcabdccdcbbbadbaadcadcccdbcaaaabcdbacbadadcaabbaadacddacbabcdabbcabbcdbaccbdaaddcbddcdcbdacdbcdbbcabbbcddccddabbcbbdabbacbbbaaccaaddbacabdbddbaacaddbcacabbbaacdcaccbddbadcdddbacabdcadcbadcdcbdbbbbaabbcdaccabaccaddcacabbdacdbdbaccbbacabdbcaabbadbbbcaddbdcddaaddcbdcbdcabacabbdabcacbddbccdddbdccbadbadbbcbcadacbaccdadabdaacdcdbdcdabcadbbbcbabbddbcbabdcbddbadbdaccacaddabbcdcdabacbdcdcacbcdaddccdaabccdcbbddcbdcadcacacbacadaccbbccabcacdaacacdaacccbccadabddabbcaadbdbddcadadcbcbadcadaaccccbcbdcbbcdbcdcbbadccdbacadbacbabaabdcacdddaccdabdabbcabbbbcaadcabbbbdddcccdabaacadccabddadddccbcadbcabbadcbaddccddacdbbdbcabdbaadadbaccddadbdddbdcabcdadcbacccacbadaaaccccdbdbdaaacdbdaadbddbabddaabcbbcccbccabbbacadacbdbabdcadcccadcdcadabdbdcbabaababddbcadaadcdcabdbdccbdcdccbcbcbddbdccaccbcdacbcaaaadbadccccdcdbbcabaccbbaabcbdaaacbbbabdcbadababaddbcaaaacccbdddaddcdddbacbcacdbbcdacbcddcddcbadbbddaabdcbaabadacdaccaacbcdababaddaaacbabbcacacdcbbadbbdabacbdccbaccbdacaacdcddccadbcbcdcbcaabdcacaacdcbbadcdabcbaddacaccbcbcdbabadbadbabbadcdaacbadadbacaadcdbbbabdcdddacbaacbddcccbbcbacdabccaabdadcdcaadbdbcbcdaababbbdaddbbdddddabcdadabddbcbdabdadabbdbcabacadbdbbbcdacbcadbddcdbaaadbddccbdacccdadcaaadbccddddbddaddbdccaccbcacbdaaaccbbaabcdbbcccacdccabbddcdabcacbadcddcddcbdadbdcbacdcccbacaddbcacccadbbddcbabbdcccddadbcbbcdaaadccddddadabdbacdadaadbbadacdaabbdddbddcbddbbbdcccbddddbcddacdccadacaabaabbbcbdabcbacacdbcccdaaaadbdbdbcbddaddaabadcadbcadbbcaabcccbcdabdbddddbdcacddbdaabdbdccabbbbaadcadacaadbcdbbcccccdbabdcabddcdacacddbadbadbcdccdbccdacdbadabbcdbdbaabcbcadcbcdaabbabdcadaaccbacbdbcaaaaabadcdacdbbbabbcbccadadacccdcdaadddaadaaabcadbaccabdbbdbbacbdbdbabaabadcabcbbbdbdcacbadbddacdbbddcbbdaacccdaddcdbcbdcbacaacbadcaccccccdbaadabaacabcbbadcddcadbbbccadbdbabcdddabddbabacbbaacaadbbbacdbcabaacabcbadadaaadaadddddadcaaabcdddcaccacbbcbddaaccbbddbaaaddadbdbdabbdccbcdabbbabaadabcccddaadabbbdbabbaaacbbadaddbabbbbbabddbccccacbaacccacaadcddadcbdabacaabdabdcaaacbdddddbcabbdcddbcdacbdadcdbbcacdcbdbdbcabdbdddccacccbabaaabbbbaddbcccdbdcacbdbcacaaabbbdcdddbdcaadabcccbddcadcbdbbaddabccbadadabcdcadcbaabccccaaacdabbcbcdabdbbdbbdddadbadbdadcaadabbddccdbccaabacdbdbcadbbdaccaabcabdbaaddddaccbdbbbdaacbdcabdbdcabccccababadaabdddacbcbcbbcdcaddaadcabcbcdcacdadadcdddcaccadbccddaaadcaaababdcddacbaadcccabdbdcdbabcccdcaadbcaacabacccabcbaaaadabcbcbcdabbcacdcbbdcdbabbcabbbacccdcaddaaacdcacabccdaacbbcaabccaaaccaadcabbcdbadbaacdbaaddbbabdbbabcddacbdacbacdaddaccbdbbdadcdcbaddbdbbdbcacddcbaadcdbddbdbadaaaacabbbddbbdcacacbdcdaaacdbccadcaccbcdbacabdacadcbaadadcddabbdcbbbddadabbabababacaaacbcddaabaabbbacbcdcabccdcdbbdbbcdccccadacdbaabbacdbdacbdaddabdbdccdbbdabdbccddaabddbbcdccbbbbadadabbddaabccadddacdddaddaaaaadaacdcddccccbcadddbaaababaaababcdaaacbbaddccdcddcdcdbaadbbdabacdadbccddddcabbdabcabacadcabddbcbbddbacaccdbcbbabdbbadcdbcbcddbcadcbdaacbbabcaabcddccacdcdccbbbccbabaabdbbaaaddaaccbcbcaddabbaadbbdbadabcbccbccbddcbbbacdccdddbadacbaaacabcdddcabaabbcdcbdcdccbcbcbaccdcacbbcdaacadbbddcacadccdccccacdacbdccdbcdbaadacaaccdcadccabbbdddccbbdccadbccababbbabbadcadacdcaadbdcddbaaacbcacdcabcdccabacbddabcdaddaabadaabccddcbcdcdbbacadcaccbdbdbabaccaadbadbbbbdcbdbccbdcccbaddadcdbbcadbdaadcddcbdbccdcccdbccdbccadadcbabcabbddababdaaccbbcccdacbbbabcdcdbaabcddbbbccbabcddcbdbccadbacaadbdbdaccbdbdabddadaccaabbbadcdcabaababddbbacbbcbbbdccaccbbbdccdacdcdcdcacdccbdbdaccabbaccacacdaabdcccccabbacbacaddbbcaabcccdaabbbcbddccaccadacaabaadcdacbaadbdadcbccacbdaabcddcacbbbbbadbbcdcdbcadbcabacbadcccabadddcdbaaaabdadbaccaccdddbcdddbccacdccbbddababdacddcdbcdaacacccbbdbddcacbbbccdcdbcdcbcdccdcacbbadaadddbbdaccbbaacdaddaacbdccbaacbddacabbbadbbdbdbcdbdcaaddcddaadacabaadcababbdaabacdabadcdadccbbbdaabbbbdaaadddcadabddbcddaccbadaaddcdaabcdbcbbcbdcdcabacadbbbdadadaacbbbbdcadcacdcadbcadbabcaacdbacdabbdbdcccadbdcccddccaccdccbdbcddacabddbcbcbcdccdcbbcadcddaddbccaacaadbddadaadbddadcdaadabddbaaaabccadbdadaacdbadcbddcbcbbbdcbaadddcddddbadadcbdaabacbcacbcccadabcdcabadbaadbadbcabdbbdabcbcbbbadcbbbbadbbcbabcdbbdbccdbbaabbacdadacdcdaabdabcadcbcbbbcbcbadcbbddaccaabbbccaadaaccadcbcbcdcacdccbccdbcaacabbcccabdbabbaaadadbbdaabaacdaacdaaaacbabccaabaccbbaaccaccbdddadababadadaacdacccdbdbdcbcdacccabccabcbbdbcddabdbaccaacddbacadadcbaddbdcaadabcdbdabdddcddbacadaaccbacadbabcdcddbdadbdcccabadbdbcccbabdcbbdabcacadadadacdccdcdddccdadcbaaccbdbbdbddccccaabaadbbaabccdabdbdcdbbcbbbabbcaddbbcbdbddddcdcabbcdbdcdcadddcddcdbdccbbbbbbddadabdcbddabababcbbbbdaddcdbadabdcbadacddbddaababccdaccaacdddcabcbbbadbdbbddccaabadadcddabcdadbabaacdbccbaaadabdcacbdacdabcabbbcddcddadcddcbabadabccdcddcbbcdbbadbcabcbaabdaddabddcbcacddbccbadabddacddbdccaadcbbaacadbadaadbabbabcadddacdccadddbaccccbbbdaadcbccabdacdccacdbcdcbaacdabcabdbcddbbbaacdadbadcdbdabdbddadcdccdcacdddcacdcbbaddbaacaabcbcdbdabcaabacbadbaacbbdbcbdabddcdbadbaaaddbbaadbbccbdddbcbcbcdcadddcccabdaccdcccbbacbbbcbdcccdbdddaadccdabadacbbcccddacacbcccadbaaaabdbcbaadaccccababbdadbcccabaaabcbccdaacdaaadabdacdadcddabadcbcbacbbdcbabbcbdcabbabbbbbaccccacdcaaabacbcacdbcdbdaaacacbaddccacaaacdbbcddabaabcabdcadabaaacdddabbdbacbcddbacccacadbccddcbdcdbcbbadbdccbdcdcccbdabddacdddbcdaadbcccaababdcadcbcbbbabbcaacaabddcdccadbabbbdbcccaacbddabddbbdbddaabdacdabbbaddabbabcbaabddbabdacbccbbcabccadaadbcabadddadcdcbabdaaacaaaddacaddacaaadcbadadcdabaaabacabdcbcdacdbcdbddccaabdaadcdcbdbbdabdacaaadcadbddcbccbadcbbdbcdbdbcddabdcdbdaddccadaadadabcacaacccdccccccccdabaccbacbccbcdaadcbcabdbdcdbdaabaacdcdcabdcbbdacdadbacaddcabdaccadbaaaadbdbdddbddbbcbabbabcacdcadaacbaaacbabbdbccdaddadcbacababacddabdbdaccdacacbacccbaccbdcbddbdcccccdcdbcbcddbdabbccbcddbbbdacdccdcbbdbbddcccbdbaaaadbcbacbccbbadbbcaaccdccadbdccadccbbbaaadbdccccabacdcdbdaacdddbcdbcdcbbdbadbcdbaacbbcbdacbacbbbabcbccbaabdbabddcdbdddcdbbddaaacdccdbdbaaddccdbdbbccadbcbaaadacdbccbcbabcaacbababbdaaadacbcbbacbdbbacacbacddbbccbabbccddbdbacbdbcdbbbadbddbdbacccdbbccdbacbaaadcdcbccdbadabadcaccccddcbcdbabcbcbadcbbbbdbaddaaccbbadcddcbbdcdadaacbdddcdadadbccdabcacaacdcbdadcddbbcbdcacddbdacbccccababaaccabcaddbdcadccbbbbacdddddbbdbdbccacdabbcbcdbaaacccabbddacaaaadbdabcbcaababbbdadacaaddacbdbccbacbacbdabbabbaccddabdddbdcdbadbaccccdbdcddbdcabaacdbcccacaabdcacbcacdbcbaadddbcabcdcabaadccbaabdbadcdabddbcacbaacbbdaddcdaadbccbbabcaacdbbcaadccddbbabdbaccabdcddcbacaacbbbcdcdadaccccddccbabbcbdacbccaaacadbdbabbddcdcbadbddbacbbbbcaddbcbcacdbbcbabaabcabbaadbddbbacdddddcbcadaacaccdaacdddcbadbcabdabbaaadacdcabaacdadaccdcbbacaacbaaddbdaabcccbbcbbddbacccadccacadcdcbcddadcdbbabcacbaabdbcaabcadbaaabcccaacdcbaaabacaaaddbccbccdadcbbcaccacdbccccbaaabcbcbabaacddaaaadbbcabdcaabbddaabdddaddcccabdacddaadaccbdddabacbbaccdacaacaabbdbdabcaddabcbdbbacdbcddbdccdbccdacaccacacdbdbcdacbbdccaacdbbcaadddbddaaabccaadcdadbacbaaadcbcdaaadddbdbabdddadcdacdaddcccadddcbbdacbaabccbbacdabcbdaabaacaabaaabbcacdcdbbdabcddbcacabddadddacbaccdabadabcacbacbdbabbcdabbadbdbadabcbbcadbbcddadbcabcddcbadcccbcacddbcbdcdddddbcbbdabccbadabdbccdacaabcbdaaccacdddddbdcddaddbcabcaddcdabcaccdddbddaddaddaccbbbddadadcbbdadbdccbbdcbbccabbddbbaacaadcbbdcccbcbaabacddcddcccdcbbcadddddcbaacbabddbacacadacdadcccdbadcdaaadabaabbdcbcddcdacbdbbbddcaddaaacdbbaaaabbdcaacbbddadbadcdcccacdccccabdbdaabacabbabcbdcbcbbbdbddacdadcaaadabdadaaaabcaddcdacbcbddccacacbcdcabbddadbdcdacdacbcaaddcbdcadabadbcbadabaabcadadbaadaddddcbadcaadbcaaabdbcbccdbccccdacbaacabaadbdbdbbbcadcccadaddbcdcbcaaacbbccaadbcbdccadcddbcbccbadaaabbaccdacddbdbdcacbcbdadddcddcaacadbccbcccbbadabcbdaabbdcaadaccbadcdcbdbcaddaabacbcdcddbaddbabccbcbdbdccdbbbdcdacbdacdcbcbbdbdbdabbccdacddaaaabcaadaadacbcbbabccbbbdbcabaaacabcccbbbbdabacadbabdbdcdccdbbdabcaacbddcbacddbdcadbaabaabbacdddabcbbabadcadccdadcbdadddddddcaabbacbddbbddddaaacaadabddcbccdcaaadcdbdbabddbcbbddccdccddbdaddbbdcdbacdadaadcbbdbabcccaccbacbbdbaababddccbcabdcdbccaaadccbadbcbabcccabbaacbcacabbdaddcacaaaabdabcbdcbaabdbddadacdaaabababcabcaabadbcacbabcbbdaddbdbabcbcacaaadddbdcddcaadacaaadadacddaadbabcacdaadcbccacddadabadbbbdbdbbcaaabdbdccacccdabdbacddbcdcdaabdcbabcbadaddcaddacacdbddbabdddcadddddaaccacbcadbabbacccdabacdbcadacbdaaccaadcddcbccbdaccdcdcdcabadcddddabacadbbabcddcbdcbcbcccbcdbbcbdbbccaddbdcddaacdbbcdbbddacccccccadddbbddaccbbdbacbbdabcdcaaddccbbabbbaaacbaaadcdbbdccbccbdaaccdaacabdbbdddabdcaadbdbdaaadcccdbcbccbaaadaaabdddcbcaacaacbcaadabcccbbddaadcccbadcbdcadcbbacbddcbcbadbadaaddcbbbcdaacbacbabcddbcdcddabadaadadaaadbdbaacddbddcbbdbdaaabbdadbdababccdbabbcbdbdddabbbcdcbdbacbadcbdbaadaabcdcabaadbcaddbaddcdcbdbacddbacddbcbddadbbcabadbbbccdbbbccbcbacadabaaccdacdccdbabdcbacbbccbcdbdcabacaadcbcddcccddcbbaaaaacacaacbccbbabcaacbdaadbbacbbccdaaccddcbccdaaabbcbbbdbabbacdabaadbdaaddbbaddbccdcccccdabaabcccaadbbdaaadbddcdbdadbaddbabbbbabdbcabddbdcbbdddcabacbcbcadacbbacccdcadddcacbcbbcbddabddcdbcaddbdcbdccddddcdbdcacccbaacccaacaddadbcdcabdbbadbcdcbaaccccdcadcbcacbacdddccabbddbbbbaabacbacbdccacddcddbbbaaaacacacbadcddcdadddbadadddacaccccadcaacdbddbcbadcacdbbababadabcdabbcbbccbbbccadadabbbbccbcdbadaadcddddcabbadccdcaabadacbdcabcbddaccccbabbbdaabaaadcdbddddbdccdaacdcdbddabbbcbdbabbaacdcbdbccaccbdcabbbcccdaacaadcdacaabacccccaabdddbdbccbdabcbabcbdddadbbbdddccccdcdadbcdccaddaadcacadcdbbcddddabbbbabcddcacbadacbcddcdbcccabdbbdbbbcbadaaccadcbacaadcabaabbadabcbcdccacbbddbbbdcabbadbabcbadddcabccdabbdcbccbaaddddabaacadbcbacaccaaccacabccdabdaacadbbcdbcaaaacbdcddddacdbbcdbcbdcaacadaaddabaacbaaaadacccabcdcdadaaadccdcadbacaacadabccdbadddddbcbbbbcdabadacbcaacacddcdddabbddcacaaabccccbbdbdddbcbcaaacbabadbbcadaaacdccadabdbabdbcbcacbbbbacacbbdaadaddbcacdbdbbcabacdccdbbbcaccdbaadbdbaabbadbccdacccddaabccbdbabdbbcdcccdaacbbdacbddcbdaaadaccdccbcbaaddcbbbadacdabadcdcadaabdaadccbbbdbabbbdaddcbacddbcaaddcdbaddadcbccbdccdabadcaccdbcabadcaadbbdcbcdacaacccccbccacdaddbcbccbdacacdadcadddcbabacbcadcbdcdacccdcddabacdccbbdbbccbabcbbbdcddddacbbdadbdbcccbbadbaaccaccbadcaddbdaabbcbadccddccacbdbaaabaaccddcbbabcbdbcbddabaaaccdcbccbabbadaaadbaacbbdacccbdcbcabaccacdacdbadcbcddbabdbbadcacddcdadabdbdabdbbacbbcdababdddacdbaacccacdbdddccababdbdbbccbcdadddbbdbbbaabbcacbaabcbcbcacdbaaaccbbdbdccabccdbcadddcbcdbbaddbbbcacbdacbaaabbbdbcdcccbbcccacbccbbaabcabcddbdbcaaababcdbbabdcaacccdcaccdbcccbdccdacdcadddddbbdddddbadcaadaadaaadcadcdddcacabadaaadddcababdacbacbbddcadbacdbacdbabcbdacbbcadcdbbcbdadacbbdbbbcadacacccadbcddcbdddcbcddbcacabccabdcddbdddabacccacddadcacaabcbcbddbabbdacbaabcdcdbabdcbbcdadaaadadddbbacdddabddcddbbdababccdbcbcddcaccdaabbadbbabbbabdacdccbdddddadbddaaadabdcdacccdcbadccacbdddbcbbddaaddababdbccdbacccacbdbaddabacddadcdbcacbbbccbddcbdcbbbdcbcaaccbdaaadbcccababbacadcbcaddbddbdaabaddbbcadddacacadccabdbdbadbdacbbaddabddabcbbdaaaabbbcaaccacddabbcbdaddcbabdbaccbcbcbbdabdbadbbcdbcccddcbbbdaacadbacbbdcadabcdadaabcaaabbcaaaccacddbcadacbdcaaccccbbbcdabdcdcbbabadbabacadaacbaabaccbbdbbcdbabcacacbaabcdcbaaadcbdbddbbbaacadbddcabaadcdabaabadacdcbcbabacabbcddcaabaaabbcdbccbbbcadaaabaadacddddaacacacacaddadaaddbadbbcbcdabbacbdacbcbadadacbbdadacbbddbaacbddccddcbbbbddbbcabcacabbdabdcbbdabbbcdbbddcdaddbcdbbbcacddcdddabcbdaabcbdcbbbadbdcdabbacbadabccbbbaaabbabbdabbabaabbdbbdabdcaddcdccccabdcaaddaaddacaaacbbbdaaaaacacddacdcabbbacdbcaacaddcacddbacdbccdbaacaaabcdbdabaaacbcbdaaadaacbdbaacbdddabcaacbdccaaadcbdadcbbcbdbcaddbcaddddaabbbbcaaacddcbadbcdbcaabcccbaaadaadadadcbbbaccabadcbdacdabbdadcbcbdacbcdcdbccddbaccbacbbcadacadadbcabbabbcdbbbbcaccbccdacbdddcaccdbbbbbadcbbddcbbbdbaaddcacbabccdaddaddbcadcadcbbbcbaadbbccadadadbbbbaabdbcdabcabcbabaddcadbbdaaacbdcbacbbbdccccddacbacddbdcbbcaaccbabddbdccddcbdbdbcaddadccddbdccacccccaabccbbcccbbcbbcdabccdcbdbbccaccdabaadbababdccbcddbdcbcccacabcdbbdcabadbcaaaabcbbcddccacdaadcaddbaaccadbbacccabccbadcabdccadaaddabdabdccabcbbcbbcddddacadbdcbacabacaacaadadccabcdcaacbddbbdaabbcababdabbaccccabcbdadbacccabdbaaccbdabccacdabbcddccbacadbbdbabdbbaacdacccddbaaddabbaaaaadbadadddcbbdddccbdcaccacbdadbdbcabacbccbacddbbdccdcdbacbbdcdbbacccbbcabaacabbdcbbadbdbbddbccdacbdaadcbccccaddabaddaacdadbbacdcbcacbccaadadadcadaddcabdccaaaababaacadddbabccccacadbacbaaaacbcbaabacbdacbdacbaacdcdbadcdabacbcaaabccbaaddbacaacacbbbbdcddacdcbdacabadcbdccabdcbdcdaabccdcdccdbccbcacabbbdbbdcdbabbccdaabcddbddcbbaabdbaadbdabadaaadddbcaddabcdbdadabbcbbbdabdaacaadbdbadcccbcddabcdcdccabdaabbccdbcdcdbdddcbdccdaabdccadacabdddcbaacaccccacaabdcacdaddcacbdacdddadcacadbbcdbbdcbadcbdaddddcbbdabacbdaccabdccdbdcababadbddddbdaabcdadaaaabcbacaccdabcdbbccbbdaaabdabacdbabadddbbacadcbdcccbdbccbabaddbbdadbdbdcbdbdaaaaddcdddbacddbaccdbbbadbbbcbbbccdcaababcadbbdbdabbbddadbbdcddaddcdcacdbdbcbabacaadcdacacabdbaaaddabbccccaaaacddbabdbdbacabadcccbabcaabddddaacadbcdbbacdcdacdcaaaabbbcbcdcbbdcbddcaacbbdddcdacabadbdcadababaabcbcdcdabdaccabadcabbcabbccbbabbdbbdcabbcadcdcdbacccdbabadadacbaaadbdaadabddcadbddacdaaccddcaababcadaadbcdccabcbbbacadcbadbdbddcabdcbbbdadaadcbcbacbdbbbbdbbbabaccbcdccbdbbbdbcbbdccdaddbcadcadacacacabbbaacacaddaaacdcbbcacaccccbaabbdacdcccccacabdcbbabdbdbdcbaadcccddaabaabcbaacbdcbbdadbaccadcbdbabbdbabddbbbdadcbcaccddabdbbaadabaadcbadaddabbcbdbdcdadbcddcadccbaccbbcbaaabdaadcabaaadccdadaddabdbcaacbadbddbdbbadbdccddddbdcabbcbddddccbbacddbcdacaccabcadbbbadabadadadcabacbaadcdbcddacccadbbbcdbcdadacaadbabdbbdcaaacacbcdababaddabdcccbccccdcacaaaadccbdddadcddcdcdcbadaabdcadaddaddddcbdbcaddcbdccbbbaacbdacadcdcdbabbacbdccabbccdcbcbbcacbaaccaccadadcaccbabacdaaccdbdbdcdabcbccadbbbccdddbaabbddacbcccbbbccacadabdddddaabcacbddaababacbccddccadabddacabadddbbbabcbacdbaccaaacbccdcadadabbdcddbcacacabaacdbccabcddbcacdadacadacdbccccbddccaadcbcdbddadaadcdccaacdbbacdabdcccacababccbcaaacbcbdacadcdacabbbaddcaabcddbcddabbcdbcaabcdaccbdcbccabdcbcbccdcdacbccdbdbaacbaccdbbadcadaaaadccdbcdaaacadcdbcdbaccbbdddbcbbcbdacbcabcaacacbdadadccabbddcbddbaabababdcacaccabcdabacdabddaccbddcabdbabbcadaacddbbbadaacbabdabcaccadccdcbabddcbcdcdbccdbbddcbcadbabccdbacaccbbccadcdccddabcbbcdcccabaddddbcccabbdaabbbcdcaaabacbbdabcbacdcaccdbabcddadbbacaabcdacdacadacabcccddbdccbdaddddadcdbabdcbcbadaadacbbdadabbddadcdcababbbcbdddbccadcddbacbccdccadcdbdaabdccccbabdacadddcddcbdcadbccacbbadcbdbcbdacaadccabbcdccdcddbdddaaabcaabdbbdcdbacacadcbdacdddcdddbdbacbcbadbccacbdacdbabdccabcadabadbadcbdadaabbcbbcacbbbbcbbbddcadadcbcbbbaccbabcabbcccbdcacaacddcdbabdbbdbbddcdbaddaadaddcbdacacddadaabdaddccaacadaacddbdacbadbcdcbcddaadbaaddddcbadbaacdbabddbdcadadbbadbabcadcadbdcacddcbddcdadaddbdddacdbaacabaacbdbdcdddbbacddacdcbdccddbddcdbadaabdabbcbcaccadaccababaabdbbacddadddcbcaaaacdbcdccbdbbcabbddccabadbcbccddcdacccbbcaabaddbcacbadccaaadbcbdaddcbccabcabcbabdcbbcbddabdbbcdcdbaccccacaaacabbdacbdcbabaaddbbbbaabcabdaabcabdcbbdcdaacbdadadbcdacaaaacadabdcdacbaccdbcaacbbbcbabbbbabadbbbbbcbcbacbabcbcbbddcdadcddbbaadbcacbcccadbbbadabccaadbcaccbcccccbbaabbbcaaadcbabcdadacddacdbdbddcbaadaaaacbccacbbddcdabdacddddbabbcbcccbbbaddcccddddacdddadaadbdcbddacdbababbbbdbcadbadddddcdcdddbcacddaddcddcbcabdccbdcacdbdbddcaccbacbbcbcabdaabbdbcbacbaadcaaccdcaddcdaadababcdbddcbcccaaaaccdcbaadcbdbbcdaaaaaacadabbaadcacdbdbdbdadddadcbaadabdcdbbbcbccaaabcadbdadcaabadbcbdccbcccbdaacccccdcacadddaabbcbcbdcaaaddabdaadaddabdcacdbcaccabaaaabbbddcabadaddbbbccbbdacbcdcdcbbbcbcddbcdadccdabacbcdbbcdcdabccacccbdbadbabbadadcbabdcccaaaaabacaabbbcadbbccaccdbddbabccddddcbbccccdadbacbbabcaaaddcdabbccdbdbadaccadbcbabcabaddbcaaddaddbbcadacabddcbadcccadbcacbdacdabdbaacdbccbabadbbcbdddcabdcccabacacdabdcabddabcabacdccaccdacbbdabdbaababbaaacdbbabacbbdacacaaaabdddccbcbcdcabbcbdccdacccadaccabaccacdcdcaddbbdacddcddddccccabcaadcadcddaabadbbcbcabacacabaaccdcdcbdcbdcdabcdabbacddbddbcaaaadddccabbcdccabddcadbbccbaaddadcbbddbdddadcacdddccddddbdadaccaaabdabdaacddcaddbcabcdbbdaadcaaaccacaaccacbaabdcabbcaabaaddaaaadccdadbbaccbdddccbacadbaddbcbcccdacccadbbdadbabdaddbdddbbdacdbcadacddadacbbdabaadbcabadcbccacbacbaacccdabcaabbcbcdddcaacadbdadcbabadbdacaadabcacaccccdcbdaddbcbdbacabbdabadbcdcabdabacabbabcbddcdcdaadabcdaadabcddccbbadabbdccabdabacccdbadbcbaccabbcdbaadbbadaaadbdabccccbadcabcdaddcdcdcbbbbcacbdababbcadadbbbcdbddaabccaacccabdbddbccadcbdcdcbcadaacbdadcbbaddaabdbbaabcdcaacbdddcbdaacbbbabbccdbbcdbaccdcdacddadddcabcdbaaddcbaabacdddbdbbdcbbacdbaabdddcbaccabcadbbbadccacdbaaaaccbbdcdbbcdaaddbbbccdbcbcbdbddcbddacaaddbccbdcbdbbdcdacdcbcbaddabbcdcaabbababbccadaaddbbccbcccdbbbbaddabcdbadabdcaaadbdadabbadbacbdadbcbdbabcccadddcbbdabdaacdacadbcaadadbbbddaaddacbadbbcaacdacbaadcabadcdacbdddbabdcaccddaabddcaabcbaabbabdbcbcbacadbaddabcacbaabbdddddcdbbbaaadbdabadcbacccdcdaacdbbadacbdbdacddddddbbccabadabccbdbbcdddcbdaddddacbacbacbdadddbbdccdadddbdabbcbbdccddbcccabcadabbdadcbccbddcbbbdcacdcbaaaadddcadddddbabcdbdaaddcabbcbccbbdbacbabbbbcbaaacacdabdcbdbaccdbbdadddaaddacadcbbaacbdcbdaaddcbbcbcddbabcbdbddcbdabaabccdbdabacbcadcdbcccbbadadaddcccbadaadbcaabddaabcbdcddbbbdbcbcacabacaacdaccaddcbcaabcaadabdcbbbbbddbaacccbccccbdbdcdcdcacacbccdcaccdaabcabacddabcbbaddcaacddabcccadaaaccdbabccdbbcddcdbbcacbddacabcddbdcdcdcbadcadcaaacccacddbabbbcacabadaabdddadcddbbddabdbdbbbbbbddbbbdabddcaddddbdbcadcccdbdacbbcbbddabcbcbdadbabdccacbbbacadcdcdbbccbcddddcddbcaccadbacaabcbbcadcddcbbacbadacadddcadabcccadbaccbdcbacddbbaabadabaccbcaabacdbdccbbbdacdabdccbbaaccddacdccbadbddddbbbacabccadaaaacdaccabcbcdabddcaacaddbdbdbccadcaabbbbbacacbbdcacddbcbcccdcadcacaacabbadcdbdbacaccadcaaabacccccbddacbbccbddcbddcdadcbcdcdabdabddadbbddbabdcbdacccdababcdadacccabadccbbaadadbbdaddabcddacdadacabdaccdcdcdbbcaadadcbacdbcbdccccccdacbbaddabcdaabccdbccbadbbabdbbdbbaddccbbbcacbaabcaacdccccadcbbdcbdcbbbdbbacbdabcbbbbaabbabccbaacacbddabadbcbdadabcdacdbcccccdacdbabbabbcadaabaddccdbdbccadbacdcdcdaacaccbdcbdbbcaaadbbdaddacacabcaccddbdbbdaabbbbbabaadcbcdbdaaaadbaaabdbbacabaabccddcddaadbdbdddabbcbabaadbaccbccababcbdacdabcdbdcbbacdcdddaaaacabbabadcbcbccaaddadadbbaacdadaaaccbdbddacddbcbaabadbadbdbcdbcbdcaabdabdaddbabaacdaaacadbdaabbcddcdcbbbcdacdcacbacdcaaaadcaddbbcbabdcaccadcaabbdadcdabcddcddababbadbbbdcbcbdabcdbcacacaaabccacabcdacaacddadbbbdbdcabaacbacacddabaccbbdbcbddbadcddcaacccccadbbdcbdbabaddbdbacadaabdbbbbdbcddbcadbddcbbbdcbcaaccbcadaddabbbacaadbccbcdcacccabaccbdbcbcabbadcbdbdcdcccdcdcabcbdcddcbcbbdaabdadccbdcbabcccddbadcaabbbbaaabdbdbbdcbdbccabadcaddacadcccdcacacaaaadaccadcadaadcccbbaddcbaaacabbbdbdbaacbbbadddadddbcbcbddbaddadccdaaabccadccaadbbdddbcccbbbccbbbcccadddababbabdbadcadaabcdccddaadaaccddcdcaacdbdbdddabdccabccbaadbbbaddabdabcadaccbcabaaacdbacbaaaabddabcbcddacbadcdaabacbabcbaadbadbcbdbdbaaacddcabddabadbdccdcdbcbccadbdadccdbbcacbbaaabcddbbbbdbcbbaabaddccaababcdcadbacbbbaccccbccdcacdbdbcaddadcdabaabcbbadaabaadbdaabcbdacbbabbccdbabbdbcbbbadbbdbbcdacaccddadaaaadaccdabdddcbabdddcdccacbbacddbddbbcadacbdcdbbdcbcadbbbaaadaaaadaacabcabbbcdbdcadbdacdcbaddbdcdccbaabdacbddddcccacacacbabbbbabcbccbabcadaaccbdaddbddbcdbbacccababaddddccbaaccabccbaadcaadbbbcadcbdabcdcbbcbcbaaadbcbcdcccdadddbdcabcacbbdadbdadbcacabadcabcacdcdbdcdbbcbaacaccbbccaadbbbccbdbdcddcdbadbddcacadbabdabccbdbdaddddbccaadadadaccbbbdbacdcadaddccabaaddcdcdcbabbcbadbaaabcdaddcbabcddcadbaaddadbacdddabcacdadbcbbbbbcbbdcbbbbabdadbccabdbbabadadbddbaaaadccccddbacbaaaabdbdadbabdbabcbbbdcadbadbcbbaacbadcabdddcadddbccccccddccabbbadbabaacdcbcdccacbdddcabcaadabbbadccdbcbcdbbdbcbacdbdadadbbcbcacbaaabbbcadcbbdabddacdcbbcbdaacdddccadccbbbabbbacbabbdddbacbcadadbadccccbbaddddbdcbbbcdbbbcabcddccbcdadcaddcbbbaccdddbcccdbadbaacdacabddbdbacdadcdbbbbbdaaaccabbbbdbbbcdcccbadcdcadddcaddcadccadcaabbdbaccabdbdbcdcadbcbbbdacbaaabaacdcadbccbaabdcababdddacbbdcacbcbcacbadaababdcccbbbbabdbcacabbaaabaacdaddbaacbaaaaaadadddbccddbdcbcaabdbcadbaccdccabacabcdcbccdaacddddccabbacbdabbcabcaabbcdbadbbbbaccbdbdcacddabcbcbacdbdadbcdccabbcadcbbbdabbbadbadabaccabbbddabacbdbbdbcbbaabcacbaddaabbcaacacbcdaabbcddbcacddbacdbcbababddcbdaddbdcadcaccdbbcdbdbbbdccadbcbabadcaaacdbbbbdbcdacaddcdccbacbcbdbddbbccbadbaabbddcbaaccabbcdabadacbdaaadccddaaababbdadadabdabccdabaadcadccdcaabacbcbaadcacbcdcbaacbcaaaadddadbdabcdbdaaccccadbacbcdddcadbbdbbcadddabdbcbabcdadddadccadacdaacccbdbdabcadacaabdbabbcccadadccdbadaddacbdaaccbddccdddcbacdcbabddbccbdbcaabdbbcaaddcadbdbdbabdcabccadcaadabdcbcbacaccbcbdacdcacbbabddbaacbdbbcadaacbdcaabacbacabbcddbacbccdccdacccbabcadacaaccdbddccdbbbbbdddbacdadbccbbdcacbbacabbaccccacdcdbaacabbbccadccbbbaccaaccddcddbdbddddcbaccbdbbddcacbacadbaacbbbdaaadbcacdddcbaadddddbcdacbbbdcbbdbccbdabbdaacdadbbdbadacbbbdbdacbadadbadbbccddbacbaadcdbbddcddbbbacbdcaaccdcbaacaccccddcddbbcaacadbbcdbdddbccddcbcacbcabdcabbaaddcbdbcccdaccacbbcbcddaabbabaadbcdcddbdadcaacaddddcddaacadcdbcaccaddbcccddccbcaacccccbdadcbcddcbdcbaaccababacaadbabbcdddadcbacdcbaaaddcbbacbdaabdaacbacbadccbcaabacbbbbcddcabdcaacaadcdddaabddaabbdcbcaacdbcadbdcddadcaadaabcbdbadccbdabcbcbacbdddddbdcccddabbddaaacccbcdcddbcabcbadaaaddddaaccbacdabbdababbcdaccddbbadcdcbcbbccccddbbccbbddcaaccbccabdbbaabcacbddbabccadccdadcabcacbaaadcccbaccbbccacabadccdbdbadcccbcaccaddcddbcdbbbbbbdaaaacaaacaabddbcdacacadbbbbcbcdbcabbdadacdadcadcabdcadbabccdbcaadcdcbdcbddacdddadcbadcbbbdbdccbaacacbcacabbbdabbcadcdadadbaaaaaaccabcbaabaacdaababbbacbaacbaaadadacadcaddbacddaacdababcdabcadbdddccbdbcabadbdbcbcbccabbdcdddcbddacbaaadcddbcacdcdacadbcbabdaadbacddaaddbddbacbddabccacbaaaadbbcdcdcbdbcbcbbcbbdbacabcbbbacbcbdacbdcbaacbbbcaadbbbbaaabbabcdadacddbbadddadddbaabddbbcaaacdccaaabacbdddbccacbbadbcbbbbadcabadbbdadaaacbdcdaabbdcacccacadbacbbdddbdddaaddcdccdacaacbbcccbcdddbbcaabcdbdaccabccdcccdccdcdacaccbbdabcacdaacbacccbbadaccaadbbabddadbabcddbadbbcbccadddbbcbacaccbacbbdbdcbbbbbcaaacbcadcaacacbcacdacbbdacaaccbcdccdbaddcabcbaabbadcbadcacdaccbbccdadadcdbcbaddacddbddbdbdccbcbddaadcacbdcbdaaadccdbbdadcdbbdbaaaaccabacbdddaabcccdbababaaabdbbadcbdabcabacccaabdaacbbdcaadacaabbdccccaaddacacbaccbcccccbcbdabcbddadabdbdbcddabcacdbabddabddaadcadadbbaaaddbcdbabaabbdbabddcccdcdbcbdbddbdbcbaaacbddcbdbbabbcadacadbbabcaacbbbbbdaacabacdccbabdadbddbbdcbbbbacdaccdacdaccddcdcdadcaabdbdbbcdcbadacadadabcbaaaabcdcacddbbaacaaccccabcadcaabccddacadadbdaddcbadddcbdcbbaddaabdcbbcdaaadcbcaabddbcaddbabbccdbaccdbbbbbddaddacbbabadcdbbcadbcddbddaacbcaadacaccbabddbcbbaabaccabdbcbdbdbdddadacdccdacbcbbddacacaccbbaaaadaadcbbdbcbddbbbbabcddbbdbcccabdacadccbbbaabcbccbbbaaaacabbdddbdadccdadadadaadacbddaababaacadddadcdbacdabddbcccdbacdbabbcbbacbacadacabddbcbbbbcaaddbaadddddabdcacacdbcbaabcabccaaabcbcdbbabcbaabdaaaddcabcabdacbacdbbbcadbbcdacbbbaabababadacabdadcaabbadadcbcaadbcdbdcadabcabbbabaddccabddabcacacbccdccbcaacccdbacadbbcaaabbadcbbcbacbcdbddacccbabaccbbddacccabcabacbadbbbccadbaaccbdcdbdbcbdadbbdbaadbbadaaddaabbabacbbdabbbbcbcbcbbbbcbbddbdcacdcaacccccadbcdcccbcaaababbacadcdcacdddaddcbaddacadacabbbbdaabacababbadaabcbabddadccaacaaadbbaccdddaacddbbaddacdbababcaabcddbbdbcccddcabbabccbaaadddbbcdbbcbaacccabadbbaadcdcabcbbbaccbbdcbdbdbdcbbdddcbbbdbacdddbdbdcddcadddbacaacdccccdccdabcbdcbddaccdcbbbaccdbbacccbacbcdcccacbcbaabbcdcadbdbaadacdcdbbbbdacbacacaacbccabadcabbaccccabbcbbacccadacbabdacadabdbddcaabbbcbbdadbbbdccadabcaadbbbdbccdabcadabcdcaadccbbbddbbacddadccbaaaababacaabcbcbabcccdaadcbaaccaabccbddcaadcbbaaddbddbacccababcbbbccdcaadcbdabbacddbdbadbbaccdababccbaaccbabcbbcaaaadcacadcdcbcabbccaddddbbadcaabbddbbacddbdbacacddbaadddbacccbcacccdbadbcbdbdcbdbccddbbdddcdbacdaccbddbccaaacbcdbddccaccddbcbadcdbbdbbacacabdcababacaabcadbdbbbdcaaaabdcbdadbccbadbabcabbcabbabbccdabacccbbcacdcdaadcbcadbdbcddadcacbaccadacacadddddbbdcbcccdbaaaacaadcdbcabbdaaaadabbbbdbcbccdabcdcbabbbbcdabacdcdccdcababcddbccbcddbcdddabdcdccaadadadbddbdbabcbaaadbcbcabbaacadbadababbccaaddcadcaddbcdacadbabcbacbdcacbbdddacacabbdbddacdcdcdaaaaabaacdcccbdbdabbcabdbaacdadbacccadcbdbcaaacddbcdbccadaadacbbdaacaacddcadaabddbddababaabdcccbadadbacdbdaacbcacddccddacbbdaaabcaaccbcddccaaadbdcdbaadbaadbdbccccbbcadddabddadcaadbbaaccaaacbaddbabbadcadbddddaacbbcadacdbaadaabcaacacdbdbabbbabadbadcbddaccdcbbdbabddcccbbbabdacacddddaabbaccddaccbdbdabdcddcbcccaadbdddaacbbddbccddacbadcdbabbddabaacdadbcdbadcdaddaccacbcbbababadbcacdbcbcccacaadcacdbdcbacaacddcdbbddaacbbacbcbaaccdbccabbbaaacbbcbbccacaadbbcdacacadcaacdabacaddccbcabbcbdccaddbcbdddabddcbbadaabdacadbcacdbbddbdccbbcbcdadabbccdcbabdbaabcdadabbcccccbcbbbcdbbbaaccccdbbdcccaccbcacaddcbbddacbadaacbccbbdcaaddbdaacabcaccaccaabdcbaccacdbddbcddccacabdaadabdbbbccdddadcaabcababdbacabdbacdcddbbcadcdbabddcbacdabcdbdcddcddabccadabbabbbbbdbdbbbdddabdbdcabcadacbcbdcdcdadddaacdaccabcdcbcccadacabcbaccbccaaabddbadbbcbaadabcabccddaabbbdacadcbddbcccbdbbbbbaacdabccaacbddbabbabbaabdaddddbabbdcadabddcdbbacbcbaccbbacabbadcbccdaaddbbcbcdbdbcadacbdbbdcdccaabdcdaabbdcdcaacccdccaaaaabdcbccacbacbadcadabaaccaccacaadacbdcbacadcdcccdbaccbbaacccdcadadbaaadddacddbbbdaccdbcddcacccbbdbaaccbacacbcabbcaacdccaaaabdbbbddbdaaacabdddbcadcadbcdcccbbbbbdcddcadcacdabbacbccaaddbccaadbbdbaaccddcacccacadaaaccbaaddcbacdacdcbabddcabbcadbdaccccddacacbdbbccaadacbacaababdadacbdddbdcabbcbcaccdacbdcabcbadabacaadcbcacccadbccbccccdcacbacaddbdbbbdbcdcabdababbbabaadcdabdbbaaadccbbddcbcccddadcbccabcdbaddcdbcdbccbabddabddaabdbaacbbbadccabaaaaaadbbbadcbbacdabadcbadabcddcdadccaacbbadbacaddabdbcccbbadbdabddbddabdbcbaaaaaabdaadadabcdbbccbbbdbaddabdaabadbabddbacadcddbcdbbbdbaadcbcababbdddcabaddbdadddbdaaabdcbddbbadaadadcbaccdbacacadddabcddcadacbddbcaddcbdabcdcadcdbaaaacbdcddaadcadbbbaccbddaabbaacdbaaadaacdcccbcdaccaabcbbabcabbbbddbccacccbdabdadbdbcbdcadcacdbbabacbccccadabdabcbdaadbabdaacbbcdbddddacdcbdbddbddcbbbbdcdbdcdddadacbaccbccdcbccdcabcbccbcccdaadaaabbadbcbdbcbaabdbadcbcaadaccbbcbacbacbaadadcaabbdacbdaaaacabbadccddaabbddbcabacaacbaaccabbababbcccbcabcbdabccdacdadacaaddbbcbbcacbcdccadcaabadababacdcaacddabdcbdccbaccacdccdacccdadddbacaccccdababddcdbacccabcadcbdacadcadbdbcadcacaadbccbdddcaccbbbadcddcbacccddabcaadaaaacadaabdacbdcdacadbdabdaccbdbaaabdcdccdcdabbcbbdbdacabdcaddccccbacdddbabdbdcabdcdbbcaadacdbbdccbcdacaccbcabdddaaabdcbabcbdaabadbbcbbdcbdbdabaaadccabcabcdbdacdccaccaadabcbbaaaadcdbbbdcccadabccaccaaaccacbabaabaadcbdbddaacbcaccdbccccddcbaaadabbaddddcadababddbcbddabbdbaaccaacaadcadcbbbbddaaadddbcbcbdbcadccadccccbdbdcddccbcbdccdcddbadbbdddbbbcabddbbcccacccbcabaadbdbbdccddaaddcbcaddddabaccbcabacabbadbccccaaccacacbaadcdaccdcabacddacaccbdbabcbadadbbacdadabccbcbcddadbcdbbcacaadbbccbdacccbabacdacdbacaacdaaaddaabadaaddcababdcbacbacccdadbdccacbcaddcddbbcddddbcbacbddddbbbaadadbcabcdbbdddabbbababcbbbbbcbdadaadbcddbdbaddadabcaacdcacbdcbccdabcbabbdbddbcbdaccdcadbacacbcadbdaccadddcdccdbadacdbddadbabbcdcaadadacadcbbbdcbbbadbcaddabbadbabdbacbbdbbdcbdcbabcdccbabdddcabaccaaadcddccdbdadcdacdadacddbaabdbabbcbccbbabccadbbaddcbdbdbdaaacbcabbaddaadddcbbadcdbcddddcddbadbaadddccdbaccbbaaabadbdddbcdaaadaaadcdbbbddddddbabaababdabdbcabcbccdccbccdaabacbaacbbadcaacacbaaadabcbcccadaaaacbaddcdcacddccacadadbacbadddcaabbabbdccabdadacdadccbacbbbdaabdcbbcbbddbacacbdbddddbcbbcdccbcaacddbbaccbcdcdcdbddabcccabbaadbbbababddcdbbaaabbabbabbbcdccaaacaabdacdcdadacdcaabcdbdabdaddaaccbcdbaadbadcaaccbbbaddacdbdbccdaacdcdbbbdcaadcccdcaccdabcdcdbbbbdbcdabaacdacccbdacddacbcdccdadbcabcdbcbdbdbacddbbaddbbbaaacbccccbcdccbbbabdbddcbaaddabcdacacbcbbcbadccaabbccdcaacbabbdbcaccccacbdaaacdbcbdcdcaacbbadbadaddddccddbcdbdbdbabdcacdbbcabcdccbbdaadcaacabacababccbaabddddcccacaaacdbaaabccadbadacacacbabbccdddbcddcdcdbbdacbabacdaaaababacadcdddabadbacbcaabcaaccbadbacadbdcababbbcacbbbdbbaadddcdddaacbcddcbadbdadadcacbacbacdcbbbcbdcdaddddadbddaadcbaacabdcababcdcdcaabdbddaacdbdcbbddacdacdcaaacccacacababcdbbbcbdbddadcdcbdaaaadcdbdacaccbdcdacaabbdcdbcbadadaadacacbbcbaaddbbbaaaaacdabbbccccccbdcaaabddabbbccbcdacdcbccaaabdccbaacaabadaaddccabcbcdaddbbbddccbdcbccdacccdcaaaddbddcaacdbaacdddbabbddcbcaaccdbdcdcacdababaccacabbdcaddbbbabadbbddabaaaabdaaccbacdcadbdaacdbdabcdcccdbbabdabbccabcbdaaabddccddccdabcccbcccdbcadcbcaabcdadddaddbbaaddcdcacbbacadacbcadadcbbcbbbdcabcbaccbbcabddbbbcdadabdbdbcaaccdccbdbdacdddbbbdaccabcbdcdaccbcdccdabcdabcacdcaccbdaaccbccacbdabacacdcbabbdaccadacddacbacbcdcdddaacbabadbdddbdacaaaabdccbadcaadbcbbabcbcacdabdccccdcaccbcadbcbbcbaadbdddbbbbbadacaabcbaccdabddbacbbbbbccbccacadbdabacbcbdacadccbdbbdccbddbabcdaddbadbcaabdddbbbcccccbcaaadacbcadbcaaaddbdcbacbbbbcaccacabbdccaccdbbbbddacbcbabbcadbaadadcaadadbdcccaabcbcddbdacabcbddacadcddabbacabacddcbdcadbbbbcbadcbbcbdcbcbcbcddbacccbbcdcbdddcbbabdacacacddbdbcabadccbbadcacbbdcccbdbadcbbddccadcbbddbddbbacccacbcbacaabacadbbbcdcddcbdacaccaaddcacdddcdcacccbbccbbdacbaccdcdbdbbddbbbdcddaabbdadbaaaadcdaadcabbaaddbbaadaabcaabbcddbaabdddddaabcbbcacbbaccbbcdcbadcdcadcccdbdaaadaddcdbaacabaacbccbdaacddabcdadbddcdbacbaacbaadacdabcbbbcadcddddddbdaddacbbdcdbdcaddacaddbaabcbbccdaacacacbcbdcbdadddcccabdcdcbdbaaddddcbdcbcaaaabdbdadacdbdaddabbdabdaddbdaabddacdddbccaccddbbbddcacccadabaddacdbbbbdcddddaaccabbadccacddbbcabacdccccbbcabddaacbccddababbdcbaaadccbcbcdddadaabbadbdacabcbabdbadccacabcddabdababcbbabaabbababdddaaddcbbdabbacbdcdbdaddbcbcbbcddcbaadaabcbcbcbcdbcdbbbdaacaccacaabadbcbcbccbddabaaaadbddcbbbccccbacccdaadbdbcddcdbdccabcbbddbbcbbadcddcddcbcaccbaadccabcbdcacbcdbbdaacbbbbdbbcbddaaadbccadabdcadadcbabcbdbdacddcabdbcaaccaccadccbbabcbdcbdaddacdabccccccbdabbdbccbbddbbabbacaacabcddcdddcdbdbdcdcbcdddbbcccbaaadbdadbddbbdabddbddccbdacdbbcaabcdbabcbacbabdadadacdcabdaaacbdbbbcbddbaaabcccacabbcbddbbaacbbacbbcabbcdabdccbabbccccccdbcbcadddcacbabacbaabcbccacccdabdbacbaadbbaaabaaccdcbabbbdcbdadddabcdddadabddccbcabdcbcabadacacddacbcbdbdabacbacbadbadcbccaaadcdcddbcbdadaabbbaacccccbacddbdabadbadaacddcbaacdbcdabbabadbddcbbaacdddacdcbcbdcbdacbabcdacabcdcabddaabdabaddaccbadcdcbcbbacadaaabdcbcabbabccdcaabbbcdcbacdbaccbdababacddbdccabacadadbaaadcddddccbdcdbcdddccdcadddcbabbbbadacaddddcabaaabcaddcdadcaabcaabcdcdbbdaabbcddbbbdcabbdacccbabadabdaddbbaddbbbcadadccdaaaaacdbbccdccbadbaadddbccbbadccbbadbbacdcdcabdcdbaaaccbcdbddbcaddbadcacdcccaadaddbbcccacadddcccccdaccdadaddcbabaadcbbacaddaacbaacccbdbbcaabcccbbabcbdbcaabbdcbccbdbdddadbcbbcbbbbadbacdbacadcaabadbbacbacbcacdadcccbdaabaabdcddaabbcbcbbbcbbcbaddcdbabccaaadddbadcdddabbcbcbaadadabcdbddaadcaadababdbcacbaadacdddcbcdacbbdcdbaaacbccdbadcaadaadbdddcabacaadbcddadaabbcbadaabacaccbbbcdcaaddcaccaabdacccccbdbccdbcdbadbddaadcbadababbbadcdabdaddaaabdaabcdcdcdcaddbddbcddcdddbdbcdbdbcaaadadcbbabcbcccdcadaddbcbdbddbccbcbdacdadbbcddadbcdabbabccbdcadcabcaabdadcabaadbcaadbadaacccbabccbcdbcbcdaccbaaddabdbcdbcccadbaababcddacabdddbbccbbccbabbdbaadbdbbcadddcdcbacdbdcbdbccbbddbcaacdbdccadbbabaabccabcdabccbcddcddbdcacaadcddbaadbbcaabbbbccbaddcbcbbdbacdabaccdcbbcacacccbaadadddacdabcbccacdaccadbaabcbadcdccdabcadcdcbbdccccccdbddccbdbaddccadbcdddbcabbbdcbcccaabaadddaaccdadbcbbbcbbcabbaddddaaacdaaabdaddcacdbbcdbdbcbbdcdcacabbbdbbccbbdcaccbbddccdbbcccccdcbddccdbdccbccbdbbaacdadbbddaddabccdacbbabaccaacbddbacaababcacdbcadabdadbbdaaabbbcaabdcbdadadcabdbdaadddbdbcabacadcddcbdadacbbbacccbdaaaadddacacaacadbdcdccdddaaccdabccaaadbbdadbdabbccbbadbadccabcaaaaadadcbdaacdcdbabcdddadabbdbddbbccaaddcdacdaabccbbdcccabbccbbdddcddddcaccdaabddddbcaaacbaaddbcbcdadbadcdcaaccdaccccbcdcddbdcddbabacadccdaccccccbdabbbddbbbabbbbcccbbbbdcdccdbabcbabcaccbdbaabbcabaadccbadbdbbcdbcccbcabbdbcbbcacccacaddcdabcbbbdbadcabaccdbcdadcdbcacbdcabbcadbdabdcddaacddcdaabdbadabbdcdbdbacacdbdcddcaadaaaaaacddddacacccdabddbdccbddbbcdaacacccabddbcadbabdcddcadbcaadbccacbccbadddcccdccadabcaccbdddbcbbdbddbacdbbbbadcadccccaccbdcbdcaacdbccbaddbadacbbbbcbdbbbcdbccddddbdbccadbcccaabcaabbcbcacdbbbbadabcadbabdccddcdaabddddaabccbbbcbacddcccacdbcaddccdacaaabdccdbcbcbdbccdbadaddbabaacabaacbbbaabddbbbbcbcdbbddbcddbadcbbbadbcccadaabbccccddadbcbcdcabbbbccddbadcddbdcacdaaaaabbcbcbddabbaddbacdbbaacdadbcbddcaadbdcbacccbcbbacbacdcdcadaabbadcbbdadbdbacbcdbcdaadbbbcbccdbbcbbacbacddcbbdcdcdbcbccccdbacddaaaccccaccaaccadcacdccaabaadcbbcdaacbdcdaacbabcddcdccbabbacbccaacdaddbaadaabdaaccdddaadccbcbccaaadadcbcbadcadacbbcbabdbaabbcbcbdbbbcadcaabddcbdcdcaaaaccbbbaddacdacdbcbaaccbdbaabbccddccdcadbaaacddaaadbbaaddacccccaaadbbdadcabbbccacbbaaaaccacbcbacbddccdccbcbddaabdaaaacddcacbbbcccbabcdddabadcdcdbccccbaddaabdacaddadbadbcadabacaabcbbadabaadbbdcadcabdbdccbbabbcdbbdcddcddccbdcaaddaaccbbbddccdbdaabacabcdbdacddabadabacdccaccabdbaabbbdcbbdbcbadadcddbccabdccbbdaddaadcdcbdadccdccabacbacdabaabbbabadbdbcddbbcacaabcbbbcbcabcdcbddbcdcccbdbbcbbbddababbcdadaddbdadabcdbacdcabdbbababcaaadcdcabbcadaacbcdadbdcbddacbbdbcacbbaddcdcbbcaccbabdcbbaadbcbabcddcdcbbbadccccdbcddababbcbacccadacbabadddaacacbdcddacccdcdaacdcccbaddacabdbdadddddbccaaabcdaabbabddcdcdcaabdadbdddaddacbacdbabdcdabdccadaccbdacbacadbccdbabdaadacbbaababdccacadbccaacaadcacbcabbacddcccacaadadcbddcabaadbadcccddbbaadbaccabcacabcccbdcbcacbccabaaacdbcccbcbccddcbabcdbdccadbdbcdbdddbadcddcaddcaccaaaccddacabcddcdcdbdcaabdbdbdbcdbaaccbbccaccbdbcdccdabccccabbbdbdbbbcadcdcddddabddaccaccbbddadbbaccadaadacadadbccbddababcacdacdbcacbbdabbcbabdcabcddbddbbcddbacbcdaaaccadacccbbddbbbadcdaacdbcacdcadccdddacaacabacadcdbbbabdadcdbcaabdbdcdbcddddabbacdccabbddccbcddaddbccbcadbcdcabbdbcbdaadbbabdadcbdccbcadbbdcdbcabaaaacbcdddbbdaaaadaacccadbcadbaacabdabdccdcdddaabcbdbdccaaabababdaacddcddbcccdcccddcadacbdaaddcadacbdbddbccbcdcbacadacabcaaddcdcbcbdbbaabaacbccacbbbbbddaadbbadbbdacbbbcadbbbddadcccadbdcaddaaadaccbdddbabcddcbbccbcbdcbccabdbbdbdabbdbbddcbaddcabddbacccddccacaaabababcddddababbaacdbaabbaaaaabddbadcdadadbccbabcdddacadbdbddaabcadadcddbbcbdcacbbcadabcbdbcadcbdbadddcdcdbbaababbbdabbdaccccadbccccdabbdaabbabbdbcabbcdbacbcdbdcbdccadbacbcabbdcdbbcadadcbdddaddcbdcdaddbcdbdbdcbdaabaacdadadccdbdcbabdcabbabdbcdddcdbcccdacdbabcdcdcaddddbadbbadccccbdcabdddadaabcbdcbaddcddacdacbcbcbbcacddaadddbaabccbabccbaaddaddcacdadcadabdbbbdcbdbdbbbbbdacdbdababaadcbbcbcadaabcbbddababaabadddaabbbbcdaccbdaaabdccdabbabddbcaccaadcadbadcdddaddaaaaadbddbaacbaadbadcddcaaddcacdcbaccbcdaacbddbadcbacdcddcacababdbacccbcaccacdccdbaddcacccabdbccbdcacbdcccccaccbcbbddabdacabbcbcbddcacdcbdbabadcabbddaddcdabcddbccdddadadaacbaccbabbcbddbbbccabadadcabbacacdabdbdcddbdadacadcbbbaddddcbdbccddccdaaccdadabaccbdbdbaaacdbdadbcbaacdddcbbcabbcdbbcdadadbcdbddbbcddacbccbddaadcbdcaabdaccdbacbcbacbbdbccacacbdccdbdadcacdacadcbbacbcabcdbaadabdacbaacccdcdaaddddddbaaccbdbbcaccddbbdbaadccbacdbacadcbbdcacbadbbbcccaabccbcccbcdbcccacbdccdbdcaddacdacbbaadcdaadaaaccdbcdcdadabbbbaabacbbcbabbdcdbcdbadbdddbcadcaadcbbdbcbdcddbbbbbbdcccbcdbdcdbbadbcacacabaddacbdbabccabacacaabdbcaacdbddababddcdbacbaccdddbdbddbbdadbcbdbbddcdbcabdddbadcdadbbddabbacadcdabaaadbcbbbabacbdacadccaabdddcbacdcccbbaabbadbccbaacdccaddbbddccbcdbadabbcaabcbdddacbcdccdcaabcaabbdccbaababcccdabbaadbabacadbcacdccbcdccbaaddbdcabcddbcbcccbcbdadaccbdaabcdabaaccacaadabaccddbdcbdcacdcddaadbacbcadccacccdbabbbccaddbcbcaacdcccdcacbcadbcabdbbbdcccbaadccbadbadcdccacdaaccaabbbbbdaaaaaaadacdaddcdbdcddbdaddaabcacabcbbbadbabbbbbbaacadbcadcbaabbacccabdbdcbadaaaaadabbdabdcdccadcdcccbdaccbdacbcdbddcbdccccbcadccabbcabddbababacbaacaaadcdcaccdcdcaaabcabdacacdbbaacdcaacbbadbadccccaaabddbaaccccbdacdacacbcbcbaacaadbcbbdcadaddadabcbbcbacadaddaacaaacccaddbacdcccbbbcccddcdcaccadcbbbdacabadaadcddaacaaadbabdbccdcacbbddbcaddcadaccbaaacbaacdcbababbabcacdcccbadcbdddbbcaacbdaadbbdddbbacabcaacbccdbdbcccdcacbacbbaadcdbddbaabadcbbbddcdaacdccbacaccaadcdbaaddcabaadaaadabaadccbcbbabaadbbaadaccddacdbdadaaadadddcbdbabcddaaababcacabcacdcccbddabdcdbcaadbabcacaaddcdacaadadbbdaadcbdbabbcabcdcdbddbaacdcdbacdcabcbdcaaccabdbdcddabdcaddbcadbaaabbbcabaddacbbcdbbaddacacbcbcdddabbcababbdbaabcccabacbcbcbcccccbcacbcdaabadadadbddabdbcdddadaabdbdbaaadddcdcbaabdaacdaddbacdaabaaaacccddacbdccadbcbbbbacdadacbadbdaacdaaccbcbdddababcdaacabacdabadcdcddcbdbaabaabbbdcabdbbabddaadadaaacdaadacdddabadbddadbcbbbbabacbbbdbcadcabcabcacabacbdbacacaaaabaddaaababbbcacaaababcdccabadcaacbcdbaabaaaabcdbcaacbaacbaabbdacbaaaddbdcbccddbdbbaabbdbadabbccaabdddcdabccaddbbcdadcdaddddbbbdcaacdcabcabbcbdaababbabdcbbacbbdabcdbbcaccaabacaadcdbabcaaccdcbcabbbcaacabcccbddaacccadbccabaccbadcabadbdbbcacaabacdabdcccadbccdbcddadabbdddddccbcdccaccaccdaabddacccdbaacacbaddadcadbabccccbcddcadaaaaaaacbacadabcdbacdbcadabacbaadccdacacdacdbcbdcbbddccbdbbcbdbadbabdacacbaadccdaccabcacdbcddcabdadbbbcdbbcacbdaaacdcdbcababcababbbbcaccccbbabddbddcaaddcabaabbdaaddaddbbcacbdabbbcccccaccbbdacdddbccadbcccbcbacddaddbdddbccabadcbbacdccdbbdbadccbcddcacdaccaabcbcbdacaaccbabcacdcdaddcbaccdddbddccabcbcdbaaabbdbbccddabbbcbccdadcccdadacbcdddacabbbcdccaabbdbcdadbdcdbcbaaacbcbaddabaabcbddadbbdbdacdaacabccbbaaabbdaccaababdabadcdacbcbcddbbadacbacbdddcbbbdadabcddcaddccdacdbccddbdacbcdbcbbbdaabdacdccdddcdaddccabaaabdddcbbadbabcaabdcdacdcbcacadabbddcaaaabbbadbbdbdbacbbadacddaadadbdcacbacacdcbbaaadaacdcabbcdadbddadbbbcaaddbbbadabccabdcbcbbabccdbbcdccacbdcdcbdacbaacadcaabbdbdcbbbccabccabadabbddddbaacadbbdabacbbabccbaaacbbaaddddbccdddcdcbccdbbdadcccbdabcccdcbcdcbbbcacaaadaddbbabccddbcbdaccacaacbacdbddbaddcdbcccbdaccadcadaabcccadabacddabaddacaacbabacdbaacddccbcdcacadaabdbacaadbacbdbbbdabcabcdbcbccbbcbacbdcdaaccaaabcbcdaaaabdaaadcbbcabdadbcbcbcbadbdbdcbadbdccdcbcdcdbcbdbcdbaabbbbbcdaddbbabdcdcaccaccabcaddbaadbbbbcadaadbcbdcbddbbbdcdcadcacaabdcaadaaaadbbbbbcdcbdacadbaaccacdaaadcacdbcbaaaacbccabaadbcbbdbcdbbaabdacdcdccbadadadddababcaacbccdabbcddbcadcabbccabbbccabbaaadccdcbdbbadbdddbadaabacbbcddaaccdabddadddccaacdadadcbbcddbacbcdccacbabacdadcaccadbadbbaaabacbabacdcacccabbabcadcdbccaacaadccdddccddaccbdbabbababbcadccbdcaaaaccacdddaaabbaaccbadcdbbcccabaabdabdacdccbdabccccccddbccdadcadbadaccdacdcbcadddbddbcacdabcbbbddddacadddaddccdcdbdbabddddbacddcdcdbcddbdbcbdabdaaddccdddcddcabcbcdaaadddbdcabbbdcbddacdbbbaaaaddcabccbcddcadbbbbbbbddddbcddadcdadddacadbbbbdaabdabdcabacbacbbdcacbcaccadadcaddacbdbbaaaadccbacbabccacccaccdbbcbbdcbcdbbbbddacdbcacbcadabcacbdaaadbababdadccddaaadcacaacadccbbbbdbdbacddddcbdcacadacadbadbdaccaabddddbccbdaddbddbbddaaaaacabddbbdbcacbbabbabcaaadccbddccccbadbacbbdddacdccdaacddbacadcdccdcbdacdadabcccbdacaacddcbdaabbddbccacddcbcbbabbdabbacadbbbacadcaabdacdabcbaaadabaacadaccbdbcabcbabbdbbcccadbcaaacdcbbbddabaacdcdaaaaacababbadbdaddcbbccbdbdaddccdbbaabcbdbbdbcaccdbadbddcadcbcdaabdbaaccdcccdcdadcbdaabbbdcdcdccabdbaddcccdcccddbdbccdbddabbcbaccddcbdbcdcccdddcdaaadacdddacbccadbbcbaddbabcbadcdcaadaacaaacbddcaccacddcacbdcabbdbdbbadbbbadaadacdaabdaaadbdbbddadbcdcbddacdcdacddcbaacbbcbddabdccddddcbbcdbaddaacddbcbddbaccbcddadacdabdcaadbcaaadddbabdacadabbdbadbacddcbadbdabdbaacbdaccdadbcbadddaabaabbbbdbacbacdcbbacdcddccacadbcddcacacdcdacddabdcaccbabadacbbccadcaddabccdcbaabcbdddbccbabccdddaadacacbdcdcbdadcccbaacbacdaccbcdcccbbddbbdbccababcbababddccdacaabcbdbdaaccaaabcdadaabddaccbacbabaabcbaabbcacabcabdcabbbdadabddbabaabdaddbdcdacababdabdadbdacabcacdddabbbccdbababacadbdbabbacdcddacbccbcbbdcbabacbacdbbdadaaadcaabacaaccdbbaadcbdcccbcdbacdadcbaadcadbbacabbbddbcaadacaabacdadcccddaacacbdcdddddaaaaabacbcababdabdbaaacacacbddccadbaabbdbacadcaddabcbcbdabbbdddabddccaddcdbdcdccbbabacabdccbbbabadcbacabbbbcbdbabbadcdababcadabaaabcbabdddbbabcaccdadaabacdbbabacbadbdbaccdddcaccbbdcabdaabccadbbbcaaaccadccdcbbcbddcddcdbaaccdbbccbacacbcadcddddabdbacbdcdcacbaacdaccdcccaadbcbdbcccaabbdcbadddcbcacdbdadddbcdaacaadbadddaabbdcbcdbaacbbbacbacdccbbdadbdacadaadcbcdabaaadaabbddcbabcdadcacadcbddbcbbcccddacabbbacabacddcdadacdadbcdcbcbbdcadaababbcbbabadbbabbbbccbadbaccdcbbddccacdacdcdbdcdcbabcadbacdcccbccaaabddaadbaaacbccbdabcadbcacbaacbaaddcbaabccbdbabbadabcbdbcdbcdaadbbbdddcaddcbbbaccbcbadcbcbcdabdcdabcaaabdbdacaaabcdaabdacacaddcdcbdadcdddcacaccdcdadcbabbdddbadaaacbdbadbdccbaadaaadaccddabacbbcbcbbadccddcdccbaadcdddaaddbdcdaabbdbbcacaacccacbaabddaabccdbdadddddccdcdaccacbbacadabddadaaacdcccccdacdabaccaaacbbdacdbbbaccbdcacaaddcccccccddabbaadddadadaaacddaabcbacdacbbcbaacaabbddccddcbccaaccadcdcbdaabaabadcadddadbcabcdaadabaaccbbaabdbdaaadbbccaaadcbdbabcdbbbbcadaadcaccccaabdacabbaaaccacddbccadcbccbbaacddbbbdbadbabbdaacdaaccbaacbcaabcacbbdbbdddcbadbadcdcdabcbbddacbbabdbbbddaaddadbaddbbccadabcdddcadaaaaabcbaacbbccadddbaaaadacbacbdcabdbabbccbbbddbdcaaaadaacbbdbddabddcbbcbbbddbbbdbccacadaaccdabbabadabbdaddcddaacbdbaabbbaadabcaabaacdacabcdcbbccbddbdbdcdccaadcdbbaddacdbadddbccdcddddbbbccddccbbbccdaccccabddaaaababbaabcbdbcbcbacbbcabbcbcdbcccbacbcbdccbaabcccbcdaaccaaaaaabdbacddbbdaadcbaaacbdadcccdbbdacdbcaadcababbacadbbbdcdcdbbbaddacadbbdaabbdabbcdcddaaabcacdcccbabaaadccccbcbcaccdcddbadbcdbcbadaacccdddbcddcabbabcbcbaadbddabccadccdbcbbddddbccccdacdcaadabacaddacacbbabdcbbcdbcdccbbaacbdcbdbbbbcbcddabcccbdcdacabaacacddbbabcccdddcaaabccacbdcadbabdccacbaacaadddccaadbdaaccbaacbaccddacacdcbaacaadbbabdbcbbacdcbadabdbadcbaabddaababaaddbbccaaadbbabbbaaaacddddaccabbcddcbcddcdccbdbabaddbcccddacaaadbabccaaabbccdccddbaacdbbbbbbaacccdaddddbbbdbaddaababbdcdadacabdbbbacaacabcaacaadcddbaabbbbbdbabcdbcdadaaacacbddaadabcdcddaaddabcabcdcabadcaddddcddcacdcbcdcdccbabbaabbaaddcccbabcabdbcadcdbccbcccbdcabcaddcadcbcccccabbbbbbadbdacbacbacabaabbcdbabccddcdbaacdcaddabcddaacbabdbbabccacddddbbdacaaddbdcbbdcddddbbbadcadddbdaabdadcababcbccdbbbbcbbdcccacbabbadbddccccacdcadcccaddaccdadcbadccacacadbacbdccdbbbdcacdbcbdacdbdbccbcdccbbcbbacbadabacadccccccbbaabddbcdabacaccbddabcbdabccbbcabbddadaabcdbaaadaacdbbaacaddcdabddbcdbdcdccabdccadcbdadccbdbbcaccbcdddacdcdcdddbbbabcdcdbcaadcdccacbacbcdaaaabaddabdabbcabdddcdcdcadbcaacddcdbdcacccbbacdbabbabcabdbbaabbbccdadcdbddcdbdcabdccdddacbbdbcabaaddacbcaacadddabbbadcddbdadccbccccaacdddcdcaccdccdbbbdbacbadbcadbbabdcaabdcadcccdababaadbddadbdbdabacdabdcbadbdcccbdbabcddbdbcaacaadbadddcadacddcbadbccabcadbbacabcbbacbdcdcdddbdbcadddcadacadbbcaaaabbddcdddcabcccddcdadccadbdcdcdbdcacbcadabdcacbaabddbddbddcabddccbdbcadbbdbcaaddbdcdaaadadaacdcacaabcabbddbdacbbddbbbbbcaadcdaaccadabdbccbcbdacaacbadcaacaabcbcccdbdababcccbccdabcdbccacbadabaaddddcdaddbbbbaddadbbcaaddcaccbacdbbadacaabaabaadadbdbdcdcdcccdcaaaadccbcdcbcadbdddbcbddacadccdadcccddcabdbdcdccdaaabcacdbbcbdadbaadacdcbbbacdbdbcccaacbbdcacacbaaaccdccccacabbdbddabdbabdaabcadbccdcaaacddbcbbacbdcbaadcdddddcbaaadcbdaaacababbbdddccccdccacbaadadadcdddaccdababacaccbcacdcdbcdabbbbcdcccbdcbbdcbcdccadaccdbabadbccdcdabcdbbbbdcbadabccbabcbbaaacaacadabbbbbcdcbbcabdbbacdbddaacbddcbdcaacdacddddcdcacabaabcdbcbbacabcdbbbcbbbcbcbaccddabaadabaadcddcacbbdbaadcbbdaccacbcdbdbcdccbdabddcbaccbbbcbcaaaaadcaabcadbaccbddbbcbadaccbacddccdabbcbacbdddddbddcacadbabdbcdcaadbbcdcabacdbbabcdbdaadbbbdacbcaaaaccdcacdddcbbbdbadbcddcdddbbbbcaacabcdacddbabbcbcadbdcbbccdddabbccccaddcacbabddcbadacadbccddbcabaccccdddacbddcccdaacbdabbdbcccbdcdaabbdcbababdacbbababacbdadcbbadcdddbaddddaaddacbbcdbdddabacbddaabbcbacddacbdbacdbbbaaabdbcaababcabdcddacaddcddbccccbbbddbdadcbabcbaddacaaaaddcbcdaadaddccddaabdadadcaabadbdccbdcabddcdbabbcacddbbccadacaadbbccbadcacaaddcdbdaccbaccccadcaccbacabcbbacadcbddcdadaaabcbdbbabbccabadddccdcbbdadbcddaadbdabcadcbdbdbdddcabaaddcddbcdcbcccabacddbbbcaaccbdcccdbcadcbdaccbbaccabaadcacadddbbacdbdccddadbcccbcddabbddbabadcaabdacbbcdbcadcaaddcdadcdaaabdabbbcdcaadaabdbdcacababbdddcbcbacbcdcbdbdaddadcacdadcdadcbbadbbacdbcadaabdbbccccaddbacdcdcbcbdcbcdbbdadbdadccacdbdbcaabddbcbdadcbcbdbcbbdbcbdbcacbccdbccadabadcccbadabbbbaaaaccbadacbcbadbdaccbdbcadbcbdbaaaacbacbbbdbbbabbdcadbbacccaacaaaddcaabddabdcbcabbdaabddacbccdaddcacaaaaddadbaacaddaccaadbabcdddacbdbacbddbcacccbaabdabaabbcbaccaabddddacdbbbdabbddbaaaccbaabadababadacbbbbcccbabbdaabdddcdcaadcbacbddbccaacacdcddddcbaaaccadbbabaddacbadacbdadcbaabcaaddcdaddcbacabdadadbbdbdaaabdbacacdbdbacbcacadacbcdadcccadcacbbcdbadcbddbbdcadabbaaabaacaaccbacbddabcabdddcdabdaddcdabccaacbbcbbccdabadcabccabcbcdbabdddbbcacddaaaccaabaacacdbbadcbbcbbcbdbdabbbbaabdaacaaddbcdcadbcaaddbbdccdbcdabdcbaadabbcbbcdddabcbbcccdddacdcdbccabcbdabdcccddbbddbccbbdbabcdaadabdbadadcbacaddbdaabaabcabcbccabddaabdbcaddddababbacdbddbcdbdcaadcabcbacbbddddbcdbccadbbccadbcadaaccbcbcacacbdbdbacbdcadddcdbccbbabcbdbbabbadcaabbaaacdcbbdcbdbcdaadaadcccabbcacdaadbbccabdbdddbbaaddcbcbcabddbbdbddacdbcaacbbbdaadcdbdcaadddbccdbddcccbdcaddbdaaadcbdaddaabbcadcdbbbbbdbaabdabbccbdcbbbadcdabdbccabccacccabdaadacbadcabcddbbababcbacccabbcadcddbbcdccabacabbabdcaacddbaabddcdcbcbaaccbcabddcbdccacbcbabddcbddcccbaadbcbddaabbbaacabccbababbaccdbcbdbacdcbbbcdadcdabccbdcbbbadbdcdcadaaacddcddbccbabbcdbdbcadabcaabdbaabcacaaccacadddccaccdddcccbbbdbbadaaddddabbacaadbbacaacbaaddbacdbccbbbbddbdccadaabacabacacbbaacbdcbccdadaacacadbcacdcbaccdbdddbdaaccacbccccbdbbaacdaadaddcbbcabcaddabcabbadccacaaabddbbaabbaaaabdccadcbcabacacaaaaabbdadcccbbaacbbddccbcdadbabddddacadbcabbcbcdcaabbdbabbabdbaaaaaacdcdcabacbbddabcbccddddcdccaaabaaddbbccdbaddbbccdbdadbaaabbbddacdadbbdbaaacabaabaccccccddddcdbbadcdcbadcccdbbbcdcddabdaaadaadcdddbccbbadadbabbddbbadcabbcdcabadaddaacdccaaadcdbccdbdcdddcdddccaabbbaadbcdbbabcaabdcbaadbdadcbcacbacdcdaabdcaaccdcddabbdddddbadcacbbaabacaabbabbacbcdbbdadcadccbcaaacacdabacdbcbabdcbbabddddccabacabdcbcadddcabbcdbbcbaabbdcbdbabcdbacadabdaccaabdacbdaddacbcaabbbdacbdbcdcbbadaacdabbdcddcbbbddbdcdbdbcbdababcaabaadaddddbdbbdddccacbcdabbcaccddcbbdabbaadcccbaabdbaaaddddcbbbbdbdaabbdaccccddadadadccbbbbcbaaddbabcbabdbdcaaddcdbacdcbdabbaabacbabdbddcdcacddbccabbccdaacdddbdaaccacbcdcacdbdcbdcdaacddbbddaabcbaadaccdccdddbcbbbbaaaacabccccaabdddadbadbacdddcbddccbacabacaddddcbadbaababaadaaddaadcdbbbbabbacabcadacdbbddcaccccdabaadcdcacbddcdaaabcddcdccbbccbcacbbbcccdacbdbdadbbcbbaddcdacadadaadbccacddddbaacbdabaabaaddcbbcdaaddbaccccbdbccaaacdcbadbacbbcccabcccabcaccbbcadaadbdbadccddbcaacbcbbbddbdaabbbaaccbcdccbdddbcacdbdddacaccbcddadaadccabdbabccbaaaddcaddddacbddddbbbbbaabdacdabbddddaadcadbadcccaccdcadcbbdbddacbacbdaddbdacdddbbdbadbcaddaaaaacccdcaaaaadbbacadadcbdcacddaabcbcbccaabadcccbdaabacaacbbdabdadadbdbabccdabdbbaaacbbbcabcbbbabddaccbaaacccbcaccbbaadacbadddcbddbdadcdbcdbdbabaccdbdacbddbddcccadaaaacbcbbbcaacccdccdbbbddddcaccdddbabcbaddaadadbbbbbacadcdadcdcddbddabbaaaaabcbcdbcbbcaacdcccdadabbbcdbccdabadadccaababccdcacbdbdbddbadcabcbdcaddbbbccababcaabacbacdcbcbabcbbcbacadadbdbabcbccbcbdadbaddcbaaddddbdadacaccadbdaadcabbccabcadabdcaacdaacbcbabbcaaaaccaadadadcbccbdddbbabdcccdcdcbddbcbbdccbaacdadbabcdadcababbacaabcbcdadbbdbdcdabccbaaacacbabbdcbbdadaacdddaaccdcdbadcbacbccaddcbcdbcccdabcdbcbaacdbdbbccdbdcdddcdddbbddbadccdaaaadddbacacccbaadcacccbdcdbcdaaaccadcadbdcabbadcacdcbdadbddddbaccadaadcadcccabbdbbbaabadacdcacbabbdcdcccdcbcaabaccabdddbbadbdccbdacbaadabcaadcadaccccdadbabcbaacadcddccdcadbbccccbdbcddbbdbdbbcaacadabcaaadabcbcbdcaaccdcadccacdacadbbabbbddbbabadcaabccbbaaccddbadbbdadcbabdbdcddcacbbcacadcaacdcbdbaadcacacadbdcbabccdccddcddbdcadccddddccadcbddabdccadabdadccacbdcaaaaabbdaaadcaadabdabdcdadcbbbddacbbbacadbaadbacabdbdcdaacbbadaaaacaddccacaaddacbdcdaddadabaaccbaabbddcdcdcddddaacdbbbadabcdbcdcbbcaadacccdadcaadcccaaacabacccadbacdbdbbaaaddbbbcabcacbccddadbcddbcdbcddddddaadaddabdddbcbbcaacbddadaacaadcdcddcbbdccacddabacaaccdaadbcbababbaacbdbbcbacacbbcadbdaddddcdcacadadcbdbccddbdcbccacddbabcdcbccccccccaabddbbaadbccdbddcbcaaccbabcdddbbcadcbdacababcaccadcbdbccdbabacaaadccdadcddbdcdbdbdbacdcaaaddcccdcdbaacccaadadabbabccbbabdbccddccadbacccdbacccdbbbccacbdbdadddbdbbdabbdbaccdccbbddcdabadadbcbbdcabcdabcdcccdbaccbdaccbaacaadccbcdccabccbcdddcdbaccabdccbabacadbbccadacbdcabcdbbbdabacabacdbddadbcddbcbcbbdbbcddcaccbbbbcdcbcbcbaddddcacbcbabbbdacaadaccdcccdaadacbcaaadcbdabbcbddaabccbccdacbccbdaccdbadaddadccbbdcbbbccbaabcabddbdccaadbacacdaabccaabadabbbbaadddcbcabcdcacabbbacbaaaadacccadddadaaaadbbddcabccbdabdacbbdddbaddacbabcdabbcccdadbdcaabbacbaabbdabbccdadbbaabacccaadbacacbcacccacdaaadbcbbcadbdddcdadddcbabdbabbccbccabdbabbbcdbabbabbbbdbdadbcaabcbdabbcbaaacdcbbbacdaacabadcdbbddcbacddbbddadaaddbdcddccdacbdbaccabdcabcacabacbcdacdacbccbbabbcadbbccabdcacbbbcabddbadbcddccadaddbbcabbdcbdaddabcbabcabbdbacaaacddbdbbbbbaacbdcdccdbdcddbbaaaccacdbbcccacddabbcacaadbdadcbbdacbacbddcaccabacbdbaddcdbabdbadcbbacddabcabbcacbdcdcbdbcbbcddadcabaadccbabcdaaaddccbbcbcdbabacbdabbdcdcbcbbccbcdbdbbcccbdadadbcddbcabcaaddbadcccbcaddbdbbaadaccdacccddccdbbbbdacbbabdabbcbcadbcabbcbdccbbbaabacacbdddadbbdcbcbaccaadcccbdbcbcaaaaaababcdbcbcbacddddbabdcacbcaaadabbcbabdbdbbabcbcbcadababbaaabbcbdacabaabbabcdbadcbcaadbcccbbddcbabdabcdbccabcbaccbddaacbbbdbbdddacbcbdbaddcdbbaababaccddaacdbaabbaacbbbaadacaddddadaddcbbaddaccbbadacccabcbcadabbcabacacabacdccdcbababccabdacaddcdcaccbdaadcacbbddcdaddacdccddddbbacbabadccdabbaddddccacaabbdcbabddcddabadaabcbaaddcbddbacacbccdcaacbcdabdbddcdcadbcdbcbdbbabdcbaccdbcbacabcdadccaacbaacdbdabbcacaddcddcaaaacbbadcabcbdcbabbaaadcddacbaaabddabdabacbcdbcabbccddcacbbbdbbbbabaddadacddccacbacdbddbadacbbddbacbaabaacdcbbcacacbcdcbcddbabcacdbadaadbdcccacababcdcdaddadbdaaccbcacdddbacbbddcbabaaabadabacbdcbabdadcdcdabacbabbdbacbaadbcdcaadbccbadbbadabaaddbcaddcbbccabdcaadccadcccdcbcdabccbbbdcbdccabdcbdcdddccbcadcabbcdadadcadbaaaaabdcadbadabcdccdccadbdbacddbcccacacbbcaccbbbadbaccaadbdababdbccbacbbdabddbaccbacdddddbccdddbdccdcbbababbccacadbcdabdbdadcbacacdadbacbacdaddbaaaabccbcaccaccabdbacadbbdddcdddacbadbddbbcadcbbdbcadcccdaabbdbabbbdcbddbdaaadcddbadcbdabcbaabbaadcbdcbdabbcadbcddbcbbbdccadacbdacacbaddbcadbabdadbbacdaadcaaaaabbdbbcdacadddabacaacccdcdaaacdabaccddcacbcdddbcacbadcbcdbdbbabbddcadacccdbcacbbaaadacaabdcdbdbcbabbdaadbcacbcddadcaaaaaddcabbadcabcdcadabdbbadaaabdbcbadadcdcdbadcbcbdadacbbdcacbbdcabbcdcacdbbaddddabdabbaccddbddcbacdddcadbccccbbadbccaadadbbcbbcbccaccabacdbcdaadbbbbcacaabddcccdcbbaabbccbbcbadcbcdacadadbdcddadabbdabdadcdbddbabdadaadccccbccbbdcbbbcaddadabdbadabbdcdcdbdbbcdcddaadcbcbdccbdbdddcbdaabdccddbcbcdabacaacdbaddcddccdccbadccddaacadbacaabaccaabcccbcdccdaddcacdddccaaddacdcdbddbabddabbaabdbadcaddbababcdbcbaabcacbabcaccaaaddadddbadcdcaadbbaacbbadabbbcdcdbadbababcdddadadabcccccacdbbabaaccbbadbbbdbdcdbcadcaccccdccddabbaadbbbacacabcdddbdbbaccadcaaacbacbaccdbbaaaabaddcdbbbadacaadbcdbccaabbbbaddbdbccadcabbdabddaaccbbaacdbbacbcdabbdddacbadbbbcddacadbaddddabccccbbababacaaaccdaaddaabcbbaabaadcadacbbdcbdbbcadbbaacdcdbdabdacccabbbcbbabbbbbdcbbdacabbcbdcdaadbcaacaccdacdcadaaacaacbccbcddcaabdabdcdcaabbdbdadbabcdbadbbdcacbbabcdadbcccbadabddcaccabcbdbdddcbdbbadcccdcdcdbdbcbbdddbabcdacdabcbbbcddacdaaaaddcacccadcaddddadadabbcbbdccabbddcacaadcdbdcbdadaccdbdccaddccccbcddacdadddadbbcaadbdabcacbabbadbacdccbcbdcdcdcbbbccaddcacdccbbcddcaddcdbccdccaadbcdaaabcbadcdbcadcdddaabdbdcddcddbbbaacbdaddabdbacccbcadcdbddcbdddcbdbcddabbcadddaabadaabbaacadaabadcacccbbdcbadddcabcdcbdacbcadaaabdbabaadddcadbdcccdadacccccbdcdbbdbaddbbbdbdaabadbbbabcbccabdaabbdcabdcddcddcaaacbbadcbbddbcbcccbbbadbcbdddcabbddbdbabadcacddaddcdbcbcadabbaacaacdabbbccdacbdacbbddcddbbabccbbddabddbccbacabccbbbbcddaaadcbabacaadddadbaccdabaaabddbacabbcbbbbadbcadddabcadcbcdabadadbbcabadbcacadbbcaaddacacdcaabccadabbacbbabcdbacdccabcbbaddabcadccdbdbadbcbabaadbcdaadcbddacaccbdcdbdddbddcddadabdbbaddbbbbacababcdbacaddccbbbcccccbabaabddacbdacbadcacaacdcdcbbbbcbbdcdbadacbcbadcbdaabbdcababbacabbbaadadabbdbaadcadbbbddaadbbddaccadbcadcbcbadaddbbcccdbaacabdbdccbaacbacbdcadbaadcdacdabcabbdbdaccbcdaccaaddccbbddbabddbbdbdabcadacbbbdddbccbbdabadcbcdbbacdcbcdcbbcbacdddabcbdcaddacbcbccbbbaccbaabdbdccacabbabadcdbdcdccdbabbcdccbdaadcadbcbcaabbbddccdcbcbaadddaddbdacccbbbbdbbacacdbbdddabacaabbaaaccdcbcdbacddbabbbbbadcbcaadaddbadbacbdaaaaadcbadddadcaabbbabddabcccadbdbcaaccbbcbccccdaabacbaabcbaaaccbbcacdbbbcbbbbcaaddccababccaddbcbaaccaadbcbadadadaabaabaddadaabbbcdabdcabadaddabdacdcddcbcdbcbdbdbaaccaddbcdabcabacaccccccdcbbcdcccbdcaaadcaaaacbacacdddccdaadbddbbdccbbabcabbbcabbcaccbbdcbdaaddccbcbdabbabdabdabbcbdbbbdbcbbbaadbdcbcdbcddbcddcbdcdbddacddabddadbcacdcbbcdadaaccabbddcbcbbacddadddabaacbdccbadcadbbcadcaaadbbccabaabadacdbadacbcccbbddbcbbdcdadaadadbaacccadabbcdacdacdddcbcbbabbacddaccaaabdabdadbabbbdabdbbbabdacbdddcadacabacaabbadbdbadbbbcbccccbcadadadaccacbdcbbddaaddaddadaacbbddddbaababddcbcdcccbcaabdadacccdccbddcdbcccdccbcdcbaacaddcbcadcadbbdccbdadcadbcdbabaacbabcdbccaabbbccaadcabcdcadbcdbabbcdaaaaabadabcdccacbbaababbcdcbdcbccbcdcddcabbaabaaabddbdbabbcdbabbddbacadbdaadccbcbccddcdbbcadbaacabcbbbbabdcccabcbbbcbcbacbdabbbadbdacacaddbbadccbddabaaabdadcddbabdbabcabdbbcccbccccbcddaabdbcaadacbdadaddadabdcbcbbaacaccabcaaacadbcacbcaaccdcdaccbddadcadcbbaaaddbdaacbbaabaadcbbaaabcbabdbcbaaaacccbbacbdccdcdbdddabbddcdddabdbabbdccadddabaabcdadbcadbdbbcdcbabbbdbbcbdcadbbdbcbbdbbdcdbccdddcbaaccbbbacacbccbabddaddbbcdbdaacccdaaacaddcbcadacaaabbdbcbbbbddcadaccbacbcdbbddadcabbcdcabdbababbbbcdabdcdbcdaadaddadbdadbabbddbaccdbaaadcdcdcabcbcddbacdddcbaabbbdabcdccbdaabdbcacadbcbdcaccbbacabcbaacaaabcacadcaadadacdabcccaababaccaaadccbdadcbcdabbabbcbdabbaacaccbcbbdbadadadbbabdccbbbcccbdbaccbbdacdcbcadbdbbcdddbdbccbaddbbcdbbababdcaadabccaacabacdccacbbaccdbbcaadbddabbdaccbaaccdabbcbdcacacaacabbabadccdacdddcbdcabbbaabcbcbcddcdcbbbdbddbdbcddaddaddbdacacdaccaaaacdbadabaaabdbbdbccbabccbdcdcacdddbcddbaabaddddbcaccabdbddccdcabbbadadcdbcddaaddcadccacbaadbdadbdacbacbbcccbddaccababdaabbabdcbdbccdbcbabdcaddbaddcaddaddcbabbcacbbdddaacdacbadbcadddaaccbddddcdcbadcdcbcadadbacddbcadcbdbbdbbcdbdcabcccdccabbddbabaacbbdaabaaccccacdbdcbabdcaccddccacccbddbacadbbabcbdcbdbddacdcdbcabdbdcdaadbbcbabccbdbacbcdcbddcadddbccaacabbbbaadcbdbdbaadabbabaabcddcccacababcccacbbabdacbcbdcddbcbbdcbdbdddcdbacaddcdcaabbcdcaabbccccdccbddbbddcdbbababbabcdabbdcbacadddbcadccaccbcdcadbbcdaccdbcaaddccdbdbcccadbbaacaacbacdbaadbccbadadabadccdddccdbcdcccbdbbdbddcdacabcdbadbcadabcccdcdbdacaadabbbbdddbbbacadbcbcabbbababbbaadbbbaccabdccabaadaddacbabcbacaabbccbbdcbcadbdabbcacdbbcabbddbbdccbccbdbbdadaacbcadaadcdccddaadbdbdabaadcbbabbbbbdbdbcbbbbaaccbccadcdaaaacaddbdcbaddacadcaabbacbababbaadcccbaddcabbdbbaaabbbcaaccddcbdadacbccdbbadcdacaadccacdcdbbdadabdcadbbcdcaaccacbcddbcddcadccbaadcdbdcdccdaaaccdabcccbdbccbbcbdbbddcddacabdbdddabccacaabbcbbddacbdbbdaccabddaccdbdbcadbacaadccdabbcddbdbabcdddcbbcccbaccbdccccbadccddcdbdaaaaacadaadcadcbccabbbacbacadbdaaacabacbcbcccbbddabbaabacaaacabaadbcadacacbdcabcccbdcaddcbababacbdbbccbbcadbcacabccbadbdacaacbcdcccabcacacbaadcdcbcbccdbcdaadccccaaabaabaaaaadbbcadbbdcbbaaacaddcacbcbccbbdbcddaadbcbdcbbbdbdaccddcdbdacacbdbbabdaadbaaddcadbcbcabcddbcdbabcbaabbcbcaaaabdddacbdbcaccabacbbadcadbbcbcaccdddaaccdbccdabaaccdccacbcaadaabcbaacabcddcbccacccdddbabacdddbcdbcdddccddbdadddcbabbcadcccbdbcccbbbbcbacdaabccccdadcdadadcbbadbacbaacbdabdacdcbccaabbcccbcbabbacbddabbbcbcdcccaabdcaabbdccdbdbdbadacdccaaabadccaccccaadbdbccdaacaaddabaaabaddaddabccacdbbdccaacabccdbbdcbbdccccdadbcaadbbccbdabddaaddcbbacbcadbbaabdaaaaaacadddbcccbdaadbaadcadcbadcdddbccabccdbccdabdbcccbbbbcdbabcdbbdcddcccaabbabbddacbdcdcabccbaacaabadacaacadaabbccbdcbbaccbadcdcccbcbddabcdaacdccbadbdccdcccabadabaaddbcbbdcacdacddbdcbaabccdabcabdbabbddbacbddccdbddadccdddacdbccaaadbadadddddbccdcbcdadaacdbcbcaaccbcaccdcacdbaacaabaccabaaacdbaadabbddcadccdabacabadaabddddbbaacdbdbddaccdbbcdbdacbabcdcbbccabcbacacccbddabcccaaaacccdbaccadcadbddacdabdacbaabaacddddbabacabcddbbbbadbadbbddbabadbbabacdbbdacdcdbbacaaddcadabacccacdbaaadddbbcbbadbbcadddbbbabdccaccacbcaadcdcdbacaaaadbdcdadcdcabdcbcacbacaddcbbaddbaddacabcdccbaabbaddcddbdbbbadcaaddcddaaaccbccaccaccddcbbaaaabadcabdcccbcbababcadcbabbbbdcbcdabdcabdcddaaccadbdaccbdbbaabcdccbabccdbaaabdbadaadbdaddbccbbdacdaabcbccbbadddcaccbdcdcbcbcadbccbcdaacccabbbdddabbddddbcddaddbababacdcddbbbdaabbbbacdbbabaabbadbdbcdbaacacccdcadbbcdabcbdabcbbbaddbbadadbcdcddccdbacadbcacdcdbbbacddcdbadacbbcbadcdcdcabaaabaadccabaacbcdcbcbbdcaadacdcdddcddacbcacbbdaaaacaaaaacbbdadbaaaccacdababbbdcbadadbbcacaccddcacdbcdaccbdddacdaabdcbdcddaaccabcbddbadcadbccbcccccaddaccadcdbdddccadabadcbadccdcccdddccbdbdbddcaabbcddaacbcbdbcdcdcbdcdbaabcbbaabdaddbbdbbbdcbabcaccdbdcccbdacacdccbccccacbadbcdcdddbdccdbccdcddaaabcbcacbbdccbdbbbdbbdcdcccaabaddbabbbcaacbaaadabbcccdcdbbdcbbbbdbaacaadcbdacbdbaabdbdcdcdabcbacddaaadddabbdbbadcddbbdbccbbaacdccabadcbdcdddcadabccdacacdabadaddabddbbcabcadbbcdabbdbcbabdddaabcbdbbabdbcacadcdabbcbdbcbaadcacdcdbccbbddcccccdcddddbcacaaaabcbaabcaaadabdaadcdcaaacbdabcacbdbccdacccbbdbacddadbdcdaccddaababcaccacaadccbdacaaaabcadbcbddadaaaddbcababadaccdddbaaacabccaddccacbbcddaabdddacadcbbbbcdbdcccdddbcccdaabdcacdbcdcdccbabcdadbabcbaacbddadbdbdabcdbccbdcdaccdddcaaadccdbddddcdbaccaacdbaddabddcbddcdbcaccabdadcddbbabcdbadddcccddcbbdbbcacbadddcaadacddbbccacbbcadbdbcaadabbbcdccbdcccabcaabdabcdbcbbbabdabccbbcbaaaacacabadabcbadabdcbabaccccbacbbcadcaaaabbbbcdddddbcaccdaaaccdbddccdccbaddcbcdaaccbbcccdaaaaaabdbacdbabcaaadaabcbabbaabcccdbbaaccdcacdcbcadcddaadddcbcaddbdbadcbaddcadccccbbadbaabdacbadddcadcdabbabadddcbddadadabdaccdcddcaaaaadbaccabbbcaadbbdcdbbdadbdbbccbabccddbaadcbabbcabcccadccddbdaddbabbbcbbdccdcbbadbdaaaadabcdccabdcaddcbdbbadcdccbabddddccbdcbcabbddbcdabaaacacabcbbbccaadbccbadcbabadbcddcadddbcbccbccbadacbbcacbdbdbcddcaaabacababdbacdddcadbbcabddacdcdacbddbaabccbddbbbabcadbaccdbbccbbdbacbabbadddbbbabaddbdbabcbdbaabdabcdcccacacdccddddcacccadaaaddcccacccdddcdbcdbaacdddbdcbcbbdcadbbdddbccadbbdddcbdccdacbdcbdbbcdbdbcaccaccacbbaddacacbdaadacccadadccbddadddcbdcbddcadcbccbdbdadbcdcaaabccaaddaabbacaacccbdcbbdbcbcbadbbaadadbbdaccabadbacdaabbdbdbaadbcacbcaccacbabcccddadccdbacaacbddcdbdacadcabadababacaabdbdbbabacabddadbaacbaccacbcdcccbadabacddddbaabacbdabacbadcdddbcbbcacaddcbbacaadadccbddcdcacabdadadaacbaaddbabbacdbdddbdacdacdcbbdcabcdbdbccccdcbaacbcbcadbbcdbadacabadbdbdcdbdcdccdcdaaddcbbcdbddaaccbacabbcbcdddcaddcaccbdbccacbabcadccbccbddaacbabcbbdaaacbbbdabbabdacdcaaccdbdaccbdddddccaabaacdcabbbbaddcbadbddcaabccdbbaacbbdaccbabddcdddbdaccbcbbcbcaadccaadcadadbdddddbbdcdccbcbcdabbbabbcacbcbdaabbdaaccddacbdaabdacbbdaaadbabaabaccaabbabdcbcdabcbacaddcdbdababccbaccbcaabdbbbbdddaaabcdaaabcacabbaccdaacbabaabbaccddcbccacbdbbadabacbdbdabdddbdbacabbbacccbcadbcababaaabbbdbcbcabbaabadbdbaaaadcdbcabddbbaacbbacdcacdddabbdadbbddaadcbdabdcdbdabadaaccbaccbaacccbababcbdabcbdacbddcbdcdcdacabdcdcadacbbacbacbdaabcbbdacacccaaacacadbdcdcdbabdaccbdccdcaaabdaadddcccddadbcdbcbcbdadaddbcdaddacddcbbacadcdaaadcddabaddabdaabddccbcdddbcdcdaabdcacaabdbdbcccddbcdcaddbddabbbaaacddacaacbccaccabaaacdbbdccbbbaadbbdaddccbdacdcddbdaddbaabacdbbccdccabdcaacaadccadcbcdccccadcaaabaababcbbdcaabbddbbddcabdbaccbcdbcdadccddddbaaadbdacdbdbcdddddcbdbdddabaadadbadbdabdcddcbbbbddccbdddaaaacbabbaacbcadcdaadbbcbbacdabcbdbcbaddbcadcdbaaaccbabbbabdbdbadccdaaaabacabdabbcadddaadbabcdcdbaddbddddbacbbaaaacaadbccaaaabcdddacaaaabdcabdcbbbcbbcbdabcdacbcadaadbdabdadacbdccdcadddbdacdbabcabdddacababcddadcacddaacabdcbdcacccaacdcbbaaadcdbccbdddadaddadadbaadcddaaabbcbbccbbddcdcbacccdcddcacbcadbcdccdacdbcddbdbdbabbdcbabbcaaadbcaaadddcddbdabaccdadcdddaccabcdbdcdbcdacdbaccabcdbdacabcdbaaaadcbccabcddadccbacaccbabbacdbdbdcaabcadcdbaaabdccbbbcddcddabbdddaaddaabaccacaabdacbbbadbdaadccdaababcdaccbaccadcbbbbdbcaaaadacdcdbadcdcccbbbaadbddbcbaacaaaccdcdccaacadbdbccbaadacbacbcbcbbbbacdbaaaccdcdabbcaabbaabdabbcababacbddababcadbbadcaaaacdccccbbdddadcddcdbcdabaacadabcacabadbdaadadbcabbcabdaadccbabbacdbdaacdcaadcaabbcdaabccaacdacbbcadddbbbbdbdadbcbdaabbbbaadbcdadddaabcccbcbcdccbaaabddddbdbdbcabcccbbcdbaacddbdbcdacbdcdacacccaddbaccbdabbbcdddabdcccadabbabcdbbccdbbaaccdbbcadcdbbbbbccabcbccdbbdcbbbccadccddbabddcadccccbdccaccaadccbabcadbccbbbaddcaabcdcddbabbdbbdcdbaccaaadbcdcbacabaccabbbbccacadbdddddcadaddcaadadadadcacbdadbbdcaddbbccdcaaccababdaadbcbadaacbcacdadbddbacddacacbbdbccbbbaadbccdcbdcabaadccdadccdadbbbdaadbbdadcbcdaccccccccbbbbdadadaaaddcaccbdaddcdcbacbcbabaadaaddabddbddcdadcddbadaddaacbaddcacddbaadadabaabadabadacadabaacacdddaccccddcbcabbacadadabcdcdccbccdbcdaacbcbabaaaccdbbdddddadabacbadcbabcbbbcdabccbcdbbabcdbcbadcbbcbdacaaccccccccababbcaaabccbacdccddbcbbadacbaaccbcddbccababbbccbcdbcdcccadbcbcaddacccaaddcbabbcddaacabaccbaddbaadbbcadcdbdadadabbaccaccbaababccdcabaababbbcbbbaaacbdbcddcacdccbbddcbdacdbbabcaabcbcbdabcdbdaaadabbccacdabcaadcddbcdbbbccddcadbcababbcbbadcccadcaabdacacaddbdadcaabaacdacaabddadcbdddaaadccddaddbbcdbddccabaaddbdadaddbdbbdaaccaaabddcbdbcddbabacacbbbbdcddccdccbbddccabbcdabcddbbbcbcadbaadababcbcababcddaccdcbcbdabaccabcacaddadaacbbccdabdbabdabdbacbadcadccbcbdcabcddadbdbaadbddacbadadbcccaccbaccbbaabbbacbbcaccdacabbbddadcbbabcdaddbaabacdcbcacadcadcbabcaaacbababcdbccbccbaabbccccbcdccabddbabcaccabdbbdcbddccaddacbdbcbbacdbaacddcdcccbbabaacadaaaaddbcbbcdbdbcabcbcbbaabaabcddbaacbbaaddbdacddcbbbccadbbabdcbadadbabaaabbcdcdbadcbaddbadababbcccdadccadacdcbdcbbacbadcbdcdcabbcbadcbcbbbdacdcbadbdaddcdddabccabddacaacccadccddcdaddcdbdaadbccbdaccccdbabcdcbaabdcddccaccdbabbdbbdbacbdcbdbbdadcacdcdbcbcdbacccbaaabbdbdacdcdbcaddaadadbbacdaaaacbccddcbcdcacabaacccbcbdcbcdaddbbbbcdacbdadbcdabadcadbcddcacddccacacbcadcaadcbcbbddacbccabbcddcdcabdaacaddcdacdcaddbabdddddddbacabbaaaddcbcdbdcdbdbcbcdbcdacbccbdcabbbaddaadddaccababdaabcddbbacbccddddcaccdbdadbcaccddaccdcbbdaccbdbaacaadaccdcbbbcdbacccbccaacbbcbddcbabdadbccbbadbccdadaddddbaacbcccdaaadbdaaccbbdaadadbdbccabcbadbdcdaadbacadcbcdbcbaaccbbaadddcdcbdaacdaacbcdbcbdcacbccbcddcaadcabddcdacbbaaabaacbcabaadbbadaaabcdaaccaadddcdbbddcacdadbbdcddbbacbbaadaddcadbcbacaaacbadcbcbacccddccabccacaabdcabcdbbbddcdbcadcbbdcdbbbdcdababbccaabdaaddaaaacbdcaccabcaadbcacbcacbaddbdacbdbbcadcaabadadabccccdbddacdaabcaabdbabcbadacbaabddbcdbccbaabddcbdbcddaadacaaddbabddbcabdcdcabbbdaaccdacaccbdaddcbaddcdddadddbbcdcdddbdbcccccdacdbcdbaccacaadddbddbaacbadbcacccaacaacdcabbbccccbadacdabddcdbababbcbaccacbbcbdadadbacbababbcacccdabdaddbcccabccacddbbabbcaddbbbaacccdcbbcbaddcbbdbdddbddbcdabdccaadbabdcbbcdbaccacadacabadbaaadaaccbbcabbbdaadaabaaccbacdbbabdbabacdadacbdabccdcabadbdcbbbacdacbacbbccaaccdbdddccaabaacddcadcaabdbddccddaacbbcbbbbcbbbbdcadccdabdadcdbacccdaaaddaaaacddddcadccdcacdbcbbbcabdacdcbbccadaacddcdccddbacbbcdbbcacbbdbbbaccbaabbdcbbddadccbcddcaaabcdcacdacbdccabaddbabcaaabacccbcabcacbbcdadbdbaccbdcdaacbaccbdbbbdbddddccdbadaacbcdddbabcbdbdcdddcabadddacdbccbcaabbadddaacdcdbcdabccbdaabbdddddabddccdbaacbadcadcbccbcaacaacacddacacbccccbcadacddacadddabcbabbbcbadccdccabbdccabdbadccdbccbdcbbbdacbbdcacbadddcabdbaaabbccccbbbcdddadccccdacdbabdddcacdddddaacababcdbaadccacdcbcdaddcdbddbaadadccbdcdbcbddabdcabcbdacadcabaadabdcacadbdbcbccaacbcbcbcacbcccadcdbccacbcacbbcbddccccddaaacbbbadbcdbcbdcacaabdcaaddcdaaacabcabbbadbdadcbbcdaaccbdadccddcababbacaaddbdcbddbdaabcacaccabbcbaacbbbaddbdcbcbbdcaacccaaccabddabbddaacdbbbbdddddbabadcaadcbaadacccdbccdbcaccbdacdbbabbcdddbcccccdcdadadcaabcccbaacdcccabbcddcdccddcaadaaaabcdabcbcdddcbbbbccdcddbdbbcabdcdbaaaadadbdddbdbbbabbaadccddabccdbaccdaabbbacbdddaaccdcccbcdaabbdcdccdaabbbaaabcdddbbabdbbabbaababdaaaaddcaabddaaddbddababcdbaacddbdcadcccccbcdcdaacabbdacbbbabcabbbacabdccacabbbdbdaabadccbaccdcbcdabccdaacbdadaccbabadccbdacabcbdbcadabccddcbbdabddbdddadbacdcdababdbdccdcdbcbdbbbbbcdbbbcdbbddbcbbdbcdccbcbdcbcaaddabcbcdadcbdcbbabadccdabcbdbbbabdcadccdaadcdaacbcbccbdcacdcdcccbdcabdcdadaaaddaccacbcabcddcddbcdabdcdbadcddaabbccabbddcaaaadbaacdcbbcdbcbbcbcbcdadcbddbdcdcbdaddbccbdacadcaddcdbaadbddbadbaddcdcdbabbddcbdcddaaaabcbdacdbdbcbacbbdcdcaccdccdcadadbacbbaaacbabbcbbaadddccabdaccdcbcdbdbdcbcddcdabbbbcbbdbcbdbaadbabcadddbbdcdacccacabbdbcdaaacbabcabdabacdbadddbbbacccddcbbcabcbbcbddccbbdcdaadddbdcbdacaabccbaccddcacbbdaadbaacadaabdaabbabdabacdcdaaabbdbcdcabdddbddacbdbaabaccdbadbbabbacdccccddcadcbdaccbaccababbdbabdacbaaaadababdadcdadabdcbaddddccaacacddaabbcadbccddbcdaaabaddbcddadbcddbcdadbbddabbacbdddccddadacadbacbcbdbbbddccabccbabddbbdbcbcbdaabcddbdbcddccbabdacbcbcaaaadbbddbacaabadbdbbbcccacaadccdcccaccabdaacbbbbcadbadabdadbbbdcbdaadddaadaacadadadcadbddbaaaabbbbccacbbaabbdcdbcdcbdbabdacabdccdbcdcdcadbbdbcbcdacdaddbabcbcdcbdccacbbcbdabbccacccccadabdbabdccccccdbbdcddbabaaaadbdaacbcaaddddbbdcdadbabddbddcccddacbcdadddadaaaaccddaddacbccacdacabcdaabdcccbcdabdcdbbbaddbdbadbbdcadbadccadcabdbbabadbdbbcdaaadbcccdccccabbadadcacdbaddacaccbabdadddaaacbccdcbdbadddcbabcbccdaabaddcddbbbabbdbabcbbbbddddbaaacabcacdaacbdabbdbdbdaadbaddcadaaaabcacdaccddbdabbbdbdcdcbabadbbbdbaccbcdbccdbddababcbbabacdccaaabcccbbcabbcbdddcdaadbbdccaabbdcdcdbdadaabcdbabbabcdbddccadddabcdcdadbbcbacbadbcbaaccbbbdadbdcdabcabcadadaddbbbbddbaaddddcabaababcbaabccadbddddcacbcdbdacaddcccccabccddbabcabdbaaddbcccabbbdaabdbaacadadbcabdccbaadccdaddddbadbdbabdabddadababccdabdcabaccaaaadcabcbcacbbaadbcaccdbabbbaddbdabccccababcbbdacaacddcdcdbccbaddcdaccbabacaabcbdadcbabcdacadddabbaaddaadccadadaadcbcabdcabbbbccbbbcdbcbbccbabcbddcadbbabaccbdacacacbbcaccddabbcdbcabcccaabcaacdbbdccdddaabdaaacbaccdaacbacaabaadcddbcababbabadddcbddaddabdcbbcddbcbadabaaabaacccbcaaaadbcddbadadcbdbababcadacbbcddbcdbdaadbdacdccbbababbccbacbaccccbababbacbbacaacbbdbccdbcadaccddcdbabaddacacdccbbddbcacabbaddbcddddcccaacbcdbcccbcabbadadbdbbbcdaadcddddabddadccabacdcbbcadabcbbbccdadadacbacccdddaacdbadaddbbadcdabcababcdaabacbdddcbccdabbdaccbabcacbdabcccdbaabdddcdcccdababbcdbdccbcbadbdabadbcbacdcdaabcdabacbabbcdbccddcbabaacccaadaabbbbdabdadddbaddbadcdbbcacdbdcdbbabadbdcdbddabdaddacdcaddccdadddddbbdcddcbccdbaacaacdbcdabcaabbcacbdcbcddaccdcddcaaddbbaccccbbbbcdddabdcbdddbdacddabacdcbcaaacbdddcabbdacccddbdabcbbcbcacdbaadbdbbdadcddcbacbcbbbdaacccacccccdbcdcbbcccbddacccbababbbdcbdcbbddacccddcbadcabcbdbdbabbcdbcdbbdbbcdcccdbabbddcbbababaacccbcccadacbbaabdabaacccacdcabbbabcbcddcabdbaccdbbabcadacbcddcbddacdbbddcbaccdbcbccdccabbbcdcddbaddabdabbadbdaccdadddbaccaadcbbdccbddcbbacadbaadaabacbcacabacdcdadbddcbdbdbaaacabddadbcccdbcaacbbabbdadabcdaddadbaddccdacccaddbbdadabcadbcdddababbbbcdbbbbdcddaacdabddaadacbcccccbcaabbdbbdbbadbcdbaacbaaddbdccbbcaadbcbddccadbaabddbccbdacbcbbacadccccbdaddadccbbadcbcbdccddcbccaaaacbbcdbdcabdadbcdcbdcacbabdccdbacddadcbccccadadbddbcbddddbbdcabccbdddddbbbdddcdcddcdabbacaccbbbabcddaccdbdadabbaddaddbcbddaaaaaadaaacccdaabcddabaabdbbccabbcbabadbaaaccacacabbdcbcaddcdacbdcbbdcdcacdabdbddcbabbacdccdaacddcaddaaababaddbadbdabbbdccababdcdccdccacbdbccaccacabdcabbaddccabdaccaaddaaaabccaacadbcbbbacbbddbbdbdcacdbdabcdccabaaccacddaccbcdaddaadbadacaadaaaadcdccbcacddbabdbaccdbcbbbdcacdaaaccbcbbacababaaddcaccacbcdadddbabdabacbbababdbabaacbbddacddcdbdadcccccbbaabbcbbbccdbacbdaadadbacbcdcbccbbbabcddadabdcdadaddcddcaccbdaaacbccbbaaaaccbdadddccababbaaabacadabdddccadccbbaddbdccadddbbcaaaabdcdababcddbddabcabcbbabacaacdbbabadaaaaaaacbaddcdcbbccdacbcaacaccddbacbbadbbbbacabbbaddbdabadcadacadadadcbbaccbbdadcddcbbcaababcaddcbbbccabcddddcabdababdccababdbdacbcbbbdabcddccccdcaddacddbaabcdcdccabcdcbcdcbbadddddbddaabbcdbddbcbccbcbaccddcaacccaaadcaadabaaadacaabcbbbadbadbadabcbdddbdabccdcaacaadaccccbcdccbbadccdbcbdcbccddcaadaccbbaaaaabcaacbbbcdccdcdbbccabbcdcddbddddcbbdccdacbaadddddcdcbbbddbcadaccdaddccbaddddddbdbcddcddadbcccddaaadacbccadddabbcadbbcbabdacaccabcdcacadaccdaccbcdaadbbabccccdcdaadbaaaabbdcdcbbccccacacacddbabbcbcabdcbbaaccbcaabbacddbadadcdbaddcdddadaaaadbcabbdcadbbbabbdaccddadbbcddaacdbbdccaabbcadcdccadbcdaadabcbcbabadccbccccccddaacabbbdabccbabcdbbdbbbcbdaacdbacaabdaabccaacdcaabbcabccbaaccdcdbbadcaacdbbbadcbdadddccdaddbdaccdbbbadcbacaacbcbadadabcabcabdcaadadbacacadbcbbbdbcdddbbbbddadcdabaabddcbbaaaddaacdbacaabcbbcdbbcbbcdbcdccdacbacdacbdbadcbdbcbacdddcbaaaccbddccabddcaadddabaacdaaaddacdbcaaaacccaccccacddddaabdcbddadadabaddbbaabaccbbaabaddcbdabaabdbdcccadbadbbcdabbbbcadcdccbabddbccbadaaaacdacddcabbdbdccadaabddaccdccdddcbcdbacaddbcbddacbdadbacbacbacbbacaacbbcbbdbbbdcaaaabdccbcaacbabbacbbaddbbdaacbbbdcccbdbdbdadccadacabbacaabddcbdcbaabcadcccabdcacdbacbadabbcbbdadcdbaabdabcdccdcdacbcdcdababcacdcadcdccaccaabadcaaccbacdddcadddaccddcadaabbbcdaacccadcdccdbdcbdaccddcdbcadaaccaaccdddcdbcbdcacadbddadabbabccccbadcdccddcabdacabbadcaddcbbdddcbcacaacbaccaaaddcddbbabadcbabcccdbcdbbabcbccbbccbdaccddbbadbbcabbdcacbcccadbadcdbdbcdbdbdaadcbbbadbaccbccbadbcdbaddaaadbadccdabbabddacbbccacaabcdbdddbdbaaaaaacdbbcdacddcbaaccddabbcddbcabacdcacacaabdbdbdcddcbcbcddbcdbabacabdabbbbaadbbacbbdddcdcadcbbdddddcdabdbadddbdccdcaaabdccbbdccdbbdcddccccaadbbcccbbddacadadccaaadcaabdacbbacdcdbbdbcdbbcbdcbcdccbacccadabbbdaccbbccabccbcdaccaaaddbaacaababdcaabdccbccdabcbccdabacdadacccbbbcbabcacdbdcbcacddccaccadcbccacabdadcccdababdbacccbaddaacdcccdccacadaabcacddcdddadacaadcaccbbaababbcdddcbddabbdadcdabbbbdcbccbcdbaabcbaddbcaaaabbccbabccdcdaacccaabbdcaadacbacdccbadababababcbddcbbdcccaccbaaaddadbbbbacabcbbacddbaacadacadadadcddcaacaaaccccdbdbbbcaacccaabaaaddaddbbacdccdabbbbdbadbdcacdcdcbbadbabaabaababadcdddcdbbacaccdbcbaddcdbbdbcadcbaadadcabbccbdaaccddddaacdbabbcdcadbbcccdbddbdbaccddbabcdbbbbccdbcadabbbcacdbdbcbddabcadbabaaadcaacaddbcaaaadaacbcbacdbdbbdaadcdbcbcccbcadbcaccabcdacadbadbcaaddcdcacddbddabcabaddbccabdcbdabadbbdbaacddabadcacbcabdbdcbbbacbacbacaaadddcaaabacbdbdbababcaccdcbccadabdadcdddcbadbdbaabcbaaadcaadbadabaabcbbdabdddacbadddbddccabbddccaaaaabadbbaccabaaacbaabcbacaabdadcbabcbbcbcacabadcbdccacddbacbabdcaacadcabbbbbdaaddcbbbbbccadacaccadbdabdacddcabdcddbbcddadccacddadbaadabbcccccbaddcadadadaaaccabdccddaddccddaacdbbacdbbbaaacdccaaabdadbbddbbbdcbdddccabccadabaddccdccbcbabcdbdcadcacbaaadbcbdcacabbadbcccaaccadbcadbdaddccaabdadccbdcddbbbbbbaadabdbaaadaaddddcdbadcddccbbaaacabaaadbadbdaabdacdbdbaacccabddcaaadaabbddbcddddcabbdcddbcabacbbadddcddcadaadaddcdadadbabcdbcdccbbdabbcbdbddaabcbcbdbcddbcbbbacaabbbccbccdbacaddbbbdbbcbbcddcbadcddddbcbdbbcbdbcabcbabcccaaabbbbdbcddbbddbaabbabddaadbcdccadbbdadcdadbbdbaaaccacabdbdabbbbcdbaabdaaccdbabbbbaadbcccbbdbaaacdddcaddbdbbbddabdbabdaaddbacbabcbcbdbdaacbccaabbcdcbdabcaaccaaaabadcbdabdacdbdddadbbbaabaddadbbaabaaccdaddcdcdbacacaaabcaccabbdaadbcdddbdccdaadbaadcbabadaddbaacbbcbdbdbdabddcddccdbaacaacbbaadbadccadabcbdcdcccccdcacaaacbddcabcdacaddbabdabbcdbddccababbbcacbaadbdcbcbadddcadcaabbcbbabaadcccdbbbddcaaccddbdaccdcdbacbcbdaaabbddbdbdaacddcdddddbacccccbcbadbdabdabbacadcbcbaabbadadacddbbccbacdcdbdcbabdacccbadabbaddcabdacdabccadacbcddbdcacdbbbdabbccdbcbbbdddcddabdbabcbddabbbaacaadddacccbbdcbadaabcaddcadcddabaadabbcaccaccbbcbdbacbccdbaccacdccaccadbccadbbdabaacacaddddcaaababcbaccaababaacabdbcaaabacbcdadcacdccbcadbabbdbaabcaabcabbacdbbddacdabdddcabbdaabdcbacbcadbaadbdcdcaabbbbddaabacccdccdcdddcddbcbaacccaabdcdccaddcbddbcbaadaadbcdbaddabbcddddddccaccdcdccababdbaccacadcdddbcdbdbadaabdcdaaadbadbadabdbbacacaabdabbcdbdacbdddbddcdbddddabccdcddcdcdbccccbbdccadcbbaaacbadaabdaddcadbcadcaacbbcbccdaaacdcdbcbdadcdbaacabccdbccaccddbcbbaddadcccbdabacdabbbadaccdbddbbabbacacdaabdbaddbcbcaddaabbbcdbcddddaddbacddbddccbbadbdabdcddaaddaadbdbdbbdbbcddddccdbdbcaabdccbbaaccbbadabcdaacdaaaccbccccddadbbbaabdddcaadadbccabbbababadcbdcdcccbaadabaccdadcbcbddaacccddadbcdbcadcacbddbccbabacbbbcacabaabccbddadcadddbdbddcddcbbabbbabdbbcdabdccbdbbbcabcaadcabdbcccddbabbabaaacdacbdbdcdcdbcccdcaacaccadabdbaadcaacdbacadcdabddadcacdacdddcbaaacdbabbcaccadaccdacdbccabddcdcbcbabbdbbadcddccaaadbacacbaccbdadacbdbddbdccbbbcaaabcccbacdccaddcdbbabcbddabbadcbaadbacadaaccabcbdcbbcbcabbacadaabbccbbbacadbbbdbdadcdbacdbcdbbabdccdcabddbdbccbddaadadaaacaacbbbcccddccdcacabacbccdcaddbacdabcccbbbbbaaaacddcdccddcabdabaabbcaccdbadddabccbabcacdddccdaabcddadaddbaaabbbddccadcdcbddcdbbdcbccdccaacdbaaacdbddabcddbddbddccbdcbdadaacbcddbabcdacdccbddbdcacbabdabcdacadbbacdbadabbdaaadbcaabbddcadabdcddaddcdddbcbcdbaaacbbaddcddbcaadbbddadbaacdddbccbdabdaabccacbcbaadccbdaddadaccddccaaccabdaadccdcbaadcacdcbaaccabbbdadcdbdcbbcbbcaadbacccbbcadabdcdbdcbabbbbbbaabdddadccdcddcddcadadbcadcbbdcccbacadcbbdbcdbdaabdbaaaddaccdcdbcabdcaaabaaacacbccbdbdcdddbcbbaddddacbccbcbadcbcaccdccaaabbcbcbbcdcbbdcacbaaaacddddbbcaaccbcacbacdabbbaaacdaabdbbbdacadcdbbabcadbbdcccacdbdddaadcdbacbabddbccbcabbcdddccbdadabaabcaaaaddabacdbbabbcdbbcababbdcbccddabbdbbdcccdcaacababbdabaadbbdddaccbbbbadbbdabbcbdccddccbababaacbbdcccddbacbcbbaaccadccbccdcabcbcadbabdcdcdabaaddccbacdccdbaaabcdadadcdaadbcabbbabdbdadcdbcbcddbdddbdbbdddbbaacdcdadacbbcacdbdddddcdbdacbaaaaddbadaaacdcdacccaddbddcddacdddabdcdaaacabbbaccbaacdccabcddcddcdbbbcdcccaddacdabcccaaaadddcaaabcbdcaadcbcbcaababbaacdcbddbcadbdaccbdbdbbbcbdaddbadbdabadababbbcacdccacabbdaadbbcccccbbdabacacdddabdaaddcbbdacadacbabbdbabbbddacbdaadaddabbbbcacaadbdbbddaaadcdbdbccaaadacbbacadddbcccaaababbbbdaabbdaaddcbbdbcdcbcaabbccccdcaadbaacdadbddaddadcbdadcadcddaddabccbbbbbaaaddbcaaacabccddbddbabcbcccbacdbabcdbaacaadcddcbacaabdddaababaabcacccbccbdcdaaaadaccdadbbdabaadadaadbcddcdaabdddcdbaaabcbcdcaacbdcddaccccbcacddbaaacdbccbdaabadbdabbabadcdbccaabddaddbadabdccbcdadacbacddbdcabddacdabcbbcdcacdcbdacbdbcadcbbadddaaadbddacdaccccbdcaadaacbabcddcbaabdbbaabdcbdbbddccaabacbddcbaadcabbacddcdccbbadbbacabccdaddbdcdadaabacbdbcbacbacbadabaadbbcbabdccabddbcbcddaacacddcbbddcdbdcccbacaaccabccdbabdcbcbcdbdbabcddddadaabbdcaacbbdcdddbcbddbbcadacdadcbbbccacbbbadcbbdbcddbdddaddaddbcccddbabdadddcddddadccccaddcaacdbacacbcacaccabbbaadadccaaabbccbcddbdbaddcaacccdccbadccbbaacbdaaacdadcdbddacdacbbbddaadccccacadadbabbcabcabbbabddcbdcbcaccbbbadccbbbdcacccbaadbaacbdcaaabdbbbaacbddccbdddcbddccddaaddccaacdcacaddbacdcddcbdbcadcadbcdbdcbdddaabcaacbadacdabacaadccbaaccabdaaabcdacbcccbddbadaaadadbcbdddddabaaadcbaabbaacdbdccabcbbdacabddabadcabdadcbdcbbadcdbdbabcadcaacbaaaddaabcbadccaccbabadcdabcbbccdbaaacddbbbacadbcbbbbacdbcbcbadccbdbbdcbdacadccbbddddbdababcdbdbbdccaaaccabdbbdabdacaacbdaabbaddbbaddaabbccbbaabdabdcccbcdbcdbadaaadcdaaabadddcacacaacaacccbabccdadccdbbccaccdcdbccddddcbbbddbaddbadbaccadadcbbdbddccdddbdbbcdcabadbbbcdacddacbacadaacbcabcdaddadcdcabaabcbcdaabbcbcbbcadcbabdbadbbbcaaacdbccddbbabbbaadadbbdcaaabaccddaababccacadcabbdcaabacadddacadbdcbdccddbadcdbbaaacaabbcabcbdccddddcbacbdcbdadabacaabbbbbcabbdbccbbacddcabbbddddddcaaadcdadcacacabdcadcbaacccbbbbbacbdcdcacadaabaabbcacccdabccbbbcccbadbadbaddbcaadaadbabcbcdbbccabadabdabcdddcbadadaddabdbaaabdbbcdabadabdbcccdbabddcbbbadcbbdaacddaaaadcccdcdbddaccbbababacdddaadcbcadbabcaacdacdcabccdbbaaabbccdaadbacbadaddcdaadcdccbbcdbbdadccdcdbccacaccaddcdaabdcabdbaddddcaaacbbbbdcddabdbdaddadbcacbdadcaabccdbcbdbaacdcdcdadbddccdbcaaacaddbdbccdbbaccddbbdabddbabbcabcdddabacdbbbbbbdcbdddbacaddbbabccadccdacbcbccbcaddcdbbbacbabcbabbabddbcaccdadcbdaabdcadccadadaabcbdcddbbccdcadbbadddaaaccdbcdcccadbcdcdabbbcddbcddadbcadbcaaddcbdcdaddcccaddbacdaddcddbadcdddcddbbdcdcadabdddbbddccdcdcbbcbcdadbabcdccbabcadbdabdadbcddbcaccdacbdbbddbbddccbaccacbbddbbbbdbbbbcbbdbadccbacaacbcabdbdbcdabdcddcbaabbddbacadddddbaddbabbbbdaadaababaaccabcaaddcdcbbdddbdbbccaabddadabccbcacdcddcabcabcdbccbadacdddacacccdcaadbcbcbbadbbabbcccddbaaddbbdcaacddaddacdccbbddcadabdcbbcbcdcddacabccadbbbdcadcdbbbadcaaacddabbbcaaadaccdcccbdbacaddcdcdbbcdbddccaabddbbdadaaacabdadcccddbbadbdabcbaddacdbbaaaaaadbaccadabababdadcacaacadcbddbddccbddcdbdabbbdacadddaabddddcdbaddcccbacdcbacbddbacaddabadcdcaccdcdbbdddbddcbbbcddddbcacdadcadacdbaadbaabbacdaddacaadccddccabdccdaddbbaddadbbaccdcdcbdbaadcdaddbcdaacadaaaabdaadcbbdcabbccdadcbcddaacabaacddadaddadabccccdccacbbcacbcbadaccdcaabaccbabbccabcbcacaabcbbbddacdabababadababdcbdacacbacaddcccdcdbaccdbbdccabcababcabdbadabdccdacddacdcbcaddadcbcbddbadbcccbdcdbdccbdacbbbcaccbabdcdaaabcccbcabaacadbaaaabbccbccbbaadcaaadbabcdccadbcbdadaabddbccdcdabbbabacbabaaddccaacbbcbcdaccacdbabccdccadcabdabbcdbabcababcbaadddbdbabbccbbbccadcbbcbdbcbabcbddcadddbdbdbbbdbcbbacdaccddddacbacbacbcdccddcdacaadcdccbaddaacaadadbbbddddaddacbbcabcdabcdacadbcacdcdddcaacdadccabcaacccdcbbddabdbadaddbcdacdcadbbadcbdbdbdcbaabdabdadbcddbcaaccaadadddbdbbdddaabbbaccbdbadbddabcbcbacdcbdcacbbbaccacddcbababdcccaabcbcbaabdbcdaddccccabbaddbaabccddddcbcdaaabaacbcbddbbdcddbdcaaabbbcbaddcdbbccbacbaddddabddddcbccacdbddaaacaaccdbdbdcadcdaddabbdacbaddacdcbcddadcabbbbdadcacaddacbcccbcaaccccaaccadcaccbbcbcdbbacdcddcddbbbcbdaacddccdacdcbbaadcdabbddbcbdcadaacbcaabbcdabdadcbbdbddcbbbbbadddddccdcaddcabdbaabcdddcadacadaacddccbdadcdccddcacbdccabcbaaddbacddcbdccccbdbdbaddcbdcabbcabcbaccbadccbadcacdcbbaadbcdbcbaabbbbbddbdbadaabcddddaabadcacddbdccacbddcbadbacdbacaccbabaabdbccbcadddaadcabaadcbddddbbacdcdcccbddbdcaccbdaadabdbdbdbdcccddcbbcaccbdbaabccdcbddbdcbccadddbdddaccadccababcdddbcdbdbdccccacacabbcdaadcaaadbdbbbcadccdccabbbcdcbbcccddcaddaaacdaccbdcadddaccddccccbcbaadacccbabcddababcaddcdadbbacabdaccddbcbddcbccacaccbcacadcbbdccdcbdaabcadabcdbdbdbbddcabdbbccccddcccaaabbaccadcdbbdaadbbaacbaddbdadcaccdbcabbababdcacbcbaacaddbbbbdadababaaddbacabcadbcaaaadbbaaaddacaacbcbcdcaacbbabbbaddaabcadacababbdacaccddddbdacbaccbcdcdbcbccaabaddadcabcaaadcbbccbbaabcacccdaddbbddccacbaccbbcbcdddbcaaaaabbddacadcbbcddacbadaddccdacaddbdbccccbaacbbbdbcacdcbddddadddbabbaabbbccdadadccaccbabdaabdacacccbccdaccbccdcaaaadacaccaccaaacaddcabaaddcddbccbdcdcacadcaccbbbbcdabdbdbdcdcddadcbcaaadddaacaaabdabbbdccdcbaadaddbaaaacabdaaccbcaabcdbcabccacdcccdddcbbbadaadcbacacaacabdbdbbccadccabaccdbabbccddcaadaacbdabcbbdcbbbbdcdbccdbccabbbbcabddaaabbadacaddbabbcddbbccdccabcaccabbcabbbacddbcdaabccbbdaaaccacbddacbcbdcccacabcbdaddaadcddbcbdaadbacacbbccaadbddbacadaaaabacbdbcbcaabdbbbddbaacaddbcadbabddacccbbcbcdadcabbbbabdbbbabcacaaadcbacdbcdcaccccadcddccaadddbbcbbbcbbcdbbddddabbbccbdabbcadaadcadbccdbabcacadcdbbabbbddcbaabbddcddbbccdabdbbbcbbdcccacddccddbbbccaaddabdddbaadcaaadcbaacddcdbccdbdadbcddcaccdbacdaccdabbdcbaacdadaabaaacccddcacdcacabdddbbaaaaccabdcbcabcabbcaabdccdcdabdcabbccdacaaaaadcadbdbabddbacabcdabbcdbadaabcddddccbcbdbabcccbccdccbaaabccddacacbbabdaddcbadcdaabbdccaababdabddadacbcaabcbbdbacdbbdacaadabbcdaabbddbbbbbacbaadbacbdacabacccadbbaaacabcddaacbbdaabcadddaadacdbcdaaacbcdaabdcbcacbcdacaaacaccabdabdbbbbabcbddbddbdabcbcdccbaacbbcaaaccbcdaccddbcadddbdccaccccbdcacadbccaacdadbbcdbdcdbcbdaccaaccabdccadccdbabbdcadcbcddbccadabcaaaacbdababbcbbaabbddbdaadbcdaaddbacdccbbcbdacabcccdcbbbdacdccddcdcbdcbcabdcaabbadabbdacbdadbbbbcccddbddbcabbaadccadbaaccbcddaacaaadbbadcbbcdbbdbacadbdbbabaaddaccbaacbdcbcabbbcddbbcddacdccdcddbcaaddcdbbbcbbdcdcccacbdacadbccdccacdbcdaabdbccdcbadabcaacabdcbadaccddadbddddbccbaaaaabcaacdcbdcacabdbbdcdbbcdadaabcbbadddcbccdbdbcbdadaadbcbacdcddbccdbbabcbabddaaababcacdddbbbbcbddbbdaaadbdbbabbbcbadacaacabbbaaaadaaacdbcadcdacdcdadabaabaddbbbacbcbdadcddbabddddcdacabdbbdbcccbddbddcdbdbbbcdccbcabccbbacbabdbbbbccddbbcadbcdcdcccbdaccbdbcbbbdcbdaabbcbabbcbabdcabadddbcdcbdbdcdddbbbbdaddbbcaabdbbaaadcbcabdbdbdbcbabcddaaddaadacdcddaccabbbccbabddaccbabdbbddaadacbacacbdccbbdbdbcbadcbdaccdddbddaddbbabbabacbbdacaaaacdddccaaacbcdbcddbaddbcacbccccdabcaaccbaccdcddaddbbbbabbaccdcdbcbabdbbcdcbacbbbdcadbabadaabaaabaccabaddacdbdacbbbabdbcdabdaaddbbcbdcaacaddcacbddbbbcbdcbddbcadcbabaabdadbdbcbbcaadbbdbdaabcaabcabdadabcbbbbadacbddbdbbdbdbcdadbcbccbddadacbacbdcbdabddadbadcdcbabcbacacbcabacaabcabbdddadacdccdcabccddbcbbaadcccdcacbcddacbaccbcaaaabbdcdccbcbbbbbdacdbabbbaccdbadbcabbbadabcacbaccbabdbbcddacadaacaaaabcabcbcddcdbcbabbbddbbadbdacccdaacbbdddbbbbcddcdbbcddaabbbcccacdbacaaddcabbaaddadcdccadbdddaabaddaacbccbdbdcbaaabcacbcbccdacbbbacadbcddadbadbcbcabadacacdcbbcaacddabcbbccabbaadabadddbdbabcbdddbbbccbbbbddaaaadbababcbcaacacdcacdcabaaaaadbdcddacdcddbdcabccaaacabcdcadaaaabaccadbbcdaaadddccabdacbbdbbcdcbbabbdacdddccaabdcccbbadcdbacdccbbbcdcdcabccbbbcbdbbdccdcbbbdabddabcdaddbccbdabdbbdddadaadcdaacdcbbdadaaadabcaabddabaddcbbdcddaaddccbcccdbddbaddacaadaadbddbdabbabbaaacdaccddbbaabccbbccdbaccabaddcdadacadbabbcdcbdcbdbdabadaacdbaccacccabbdcdbabadcdacbacdbcaabdcddcdbaadacccbdbdabbadccaabcadbbdbbaaabdaababdadadccaadcadccbadabaacbccaccdabbdbdbbbccbaababadcadcdddcaacbddcbcbbacbcdacdaacaacbacbcdacbdbaacdacbbacaaccbccbbbddbbbcababaccbdabdabdcbdacbbddbcaabaabcaddcaaccccbcabcbdaadcaddbdbaacabbcdbabcacacababadccdcdcbbcacdacdcddadbacbcdabaabccbbaaadcbddbdccdcacdacbaabaccaadbdaacddcdcaccbadbcacaaadddbbabdbbadccacaddcacacdbbaaccabdcbacdbcdabcbaccbcbcdaacccbbadbcdaacbccbbbddbccadabbbacbbcdcbaabbabcdbcabcdadccabbadcbcccadadaadbaddbdccddadacbdbddbdddcdbccadccbabbcbbbadbbabadbdbdabbcdddcbbaccdcdbddccbbcddaacccbdcccbbacdccaddcbdacccaaabcbbddabbabdcbcddbcbcbcdbcaaadbaddcaddabcbdcbacddaaaadbcdddbadddabcabddcdbbdababbbacccddcbadbcacbdbbaabdccdcddcdadcadaccbcbaabbccccbdacbcaaddccaacddbcaababcaddacbabcbbddaaaddcbaaaaadcbbdcadddadcdacdabbdcdccdcacccaaccaddaacddbdcadcdcaaaaabbdddbaccaabcdcacaacbddacbaadabcddaacccdacccbbbbcabdbaaadbdcddbcdabcabdcddcadccccbabddcbcbbcaaccddccdbbcbaabacbdcaabcdcdacccaaccdbddbdddbacccabbccbccbbaabacaddcaccaccddbdaccbaadcdbdbccbcaaacbcbcbcbabcdcbbccbccdadccdbdabccddadcddbbddadabdacaaacdddabcdadaaccbcdacccccccdabadbdbacdbcdcdbbbbdaabacdacabcacadadbbccaaabbdbcbdcaaadbcbcbcbccaadbbbabdccdabdcaccacdcbccbcbacbbbccdbbdcabbdbcadbbdccbdbbdcaaadacacaccbbbcdbaaaabbabdcdcabcdbcddcacbadbbbbddbadbabddbbdacbdcdccdcacabdbbcdddacddabcdbcccbacdccbabcaaacdbbcdcbdbbccdbdbbcdccddcbbadbdcabddbbddbccdacbbacdddabcabdbdddbaabaaddabcbacddbbbcadcacbaabbbbbccbbddcbdbddddbacbdaabbaaadcbadbbaacccbcbcaccccdaabacdacccabbbdcaddacaacddadcddadaaacbacccbbaccdcddbadabddbbaaabbdcccbaaadbbbadacdbddaacccacccdacbbbddcbacaabcabdddcbccbaabadabbbaccbbaaabbbbdddbdbbbbabcdcaabadcdbdcdadaacbaddcdbbacdabcddddddccacacbdacbcadcacadadadbdadbdcbdccdddccabacaadbcbbaababacabdcaacbcaacdabdddbdaacabdadaabccdccddbaccabbbddbddaaccaddacddabbbddccdabdbcddabbbddccabbbcacacccbabdacdadbdcaccdcdacadaaddcacdcbbbabcdddcdccdbcbadbdabdbacbcabdaaadadcccddcdcdabcaaddadcbbaaaddacbdddbadaccacdacacadcbcbddbcdbdddaabdbdadbccbddbbdadacdbcdcbdadcabbccdbccadcbaabadbabaccdaacacdcbabddcccabdbcdcbaabddddabccdccbbccccacadbdbdbddadcabaababaaadbdcbbcbdcacddabcddbcabadadbdbcdcdacdccdddccccbbddbaabbbcaccadabacbbcacaddbaabdddbacbcdddccacabdddbbbccbcbbadbbbdcadadaccacaabdbddadbcaadaaadcacaaaacbaaabaadcabccccddadbbddcabbddddadaacdacabcabdbccdabdbbbaabacbbddbdcdcbbadccbdaccdbddcadabcdabbbcaadadcbdccddacabbbdadaabcabdcacccdacacdcbbccaabcbabbbddadcaadcbdddaccadabdcddbdccabbdcbdbdaddccdadaadbaccdabccadbbbbadbcabbcdbacabcaaabddabccabcbbcacaddaddbbbadaddbacbcbdaddbdbcbcbadbcdaddabdadccdcabbdcccadbadacaddabdaddbbccdbcabcdcccccbcbccccbbcaacbddbddbdacacccaddcaddcaccbacaddcccbbdbbadcdbbbbadbcbdcdcacbccddbcadcbbddbbcdddaadacabbccbabddcbbcccbccaacabccbbccddaddadddabbbdabdcacdadaaacbbcaabadbcbaacbabaacbaacbdcbbadbbcccbdabdadbdbdabbabdbccbdbaababdcabadabbabdbdbcccbbccccccadacabcccdbcbbbacacdbcdbdaaccbddadbdaaccbbbbcbacacdccdddbabbcddcdbbbacbcdaaacbabcbbddbddcbbddbbcdaddbdbabdacabdbaadddbdddcddcaccdabacaacbcddbdcdcaaaabaacdcbabdabbcddbcbdcbaababbaddcdccdadbcdbcaabcbabcabbcaaadbcbcbcccabaacddaabccbdddccabcbbccbcbbcbdbdddaabadcdaaacaccdbacabcbcacddacbdbbcadadbdaddddbcbcbabccccabddbbadcbdabdccadababcccbdcdbdcccdbccaaadbabcdabcaabdabaaabcdbdbbddbadbacaadbaadccddbdaabadbcacdcbbddcaccdcdbdccbdbcdaddcbcbddabddbcdbaccdcbaaadcbdcbbdbabdbdcddbdaaaabddabccdacbdadabdacddacdccacaabbbadbcdcadbcbbbddbdcbcabadacdbbaacddbadbddadcacbdbddacaacdbdbbbacacacdbaabbdbdcdcbababaaabbbdadaadbcddacbdabddadaacddbaccbcdabccbaccbbdacabbddddcabbdbbbcbcbdbcdbdcacacdbbddcbbbbccaddacdbacccaaadbddcbbaacddbabaccbcbccbdadaacdaaccddbddddcadcbadabbdacbcadbcbacbacddddbcaacdddaacabaaababcbadadcbcbdccbadccaccaaacadccdcbaaacbdbacccaccdbdddccdbcdddcdcbdaaacccabccdcdcdbccadaddccbbbddacbacaabadababddbadcacbadcbabadddcaabbbddacbcabaddacdcaddaaabbdadbdacaadbcdbacccbcbcccadbccaadbbbddaccbbdcdcbaadbbcaddadadbbdaddacaaaddcbbcdbdbbbabaaabdadcabcbadddcaccdcbbbdbabbbaabbcaccdddbaaaddcabdadbcdbbadddbadddbacdbbaddabdaccadddcbdbccdbddbdcaddcabccddababbcdbddacaccaadcddcaababcbcbbadabcaaaacdcbbbddcdcdbdbabcadaacadcabdbcdbbbacaaddcddbcdcbdabdabbdbddbbacccddabdbbadabadcdbbcbabbadacacabbdccddccabadbccabbcaaaccbabcddabcbaabbbaabbdacdaddcbdaccbbcdbcdacbdddddacadcbaadbbcdaacccbcdacaaacabccdabdcacbdaabbddabbcccdbcbddcdcaabcbbbddadccbdccbbbacdbcaaddcbdabdcabadbcdbabacdabaaacbaccaaacacbaadbddcdaaadaccbbdabdbacbacdacdaadbbdaaabaaccdbaacdbcabaaabdcdaccbabcabbaacadaacacabdaddcadbdbacbcbbbcbbdbbdccbdadbdabbadababacbaaaacbaddcaacacabdbadcaaabcdcaddadbcaacdbadbdddacabccddbcbdbaadaccdcabbbdccadbaaadadaccdccadadadbbaadcabacbdcaccaacdbacbaabaadacdaacdbaadaddbcbdabddabbaadbcadcbabbdbcaabaaddccdcacbdadccdccdcbdacbabbdaaacbcadddbdbacadacbbbbcabacdbadaaabddbcaccdbbcacbbaadabdbaacdcaabbccaabcabdccacdccadbccbacaababbcdbbdcbaacaacacdabdcbcccacbcbbdcdaddabdacdadbbdbdcccbbabddbdcccbccaacaadaacdcbdbaacdaadbcbddbbbcadadadaddcddbcccadbdbccbddddabdcbdbacdbccdccbbcbddcddacacccaddaccdcbacbadcddbaabbccccacdcdaccdcadaacccabbabdabbcdcadbbbaabcddbdadadbadbbdbcabdbbaaabddbdcaaddcbbadbdbabccdbdddacdbababdcbcccbcabdbccdacbadcddabadaadddaddbdcbddaaddbdcdbbadddadadbbdcbdbccacddabacddbbccacdcdbdaaccbcbbabcaaddddcbdbddddbacbdbbcbdddbccdcdcddbcaccaadbbabcdddddadcdbccabdddcdabadbdacdbdadabbddddadbccbbbcdbccbcabddaabcbbcbcdadcddccbdddbbbcbcdbbdbddbabaaaccdbdccadaabadbcbdababccaccdcccdbcbddabbdadabbddcdcacddbcbaacbcbccacbbccbcbcdabdcabbdabdcbacbaaaccbbbcaccbaabcacbcbdaddcbcccddbdadacbdcbdaabddbadbbcaacabdabcadacdcbcdcabccabcaaabacbccbbcabccaddcabdaccdabadcdbcadadccccccbbdadddabccdaadccccbcadddbcbcaadccaabbdbccbadddddaaaaccacaabcdbbcdacccbcbbadcaaaaaadbccdcbadbbdacdabbcbcbacddbaacaddbdacdbbddadadbbdbcdadcaddbababbdccdbcbadabbadacbadcbcbcabccdccdcbbccbbacccadadcbbcdbaaaababccaababcccbdbadadcccccdcdbdcaaabbabcbaccbaabdcbcdbcbabbadabcacdcccbdbaadacccdcababcdddccbadaddcbdccadbadcaaaabaadbbabdbccdbadccbddcbddabbcabdaadbbddcababccdcabbdcdcbcbbaccdaddbbbbbcccdccdcddcbccddbbcdbbcbacaccabcbccadccacdbaddaddcbdabcbcdaabccadbbadddacbcadcbdaddbacababdbcbabbbadcbacabcdbbdadabdbccabdaaacbbcddbaddbdbddbddadccbcbaccadbcdacdaadbadcdacccdabddadcadbbddababbadddbbbcacadadbdacbcacdbdcbcadacabccdcaadbadcacccadbabadddadaaabdcddddaadbaddaaccbdcaadaadcabacccdacdcdccbcbcddadabadbdddababddbabbbbcbccbcbaaddcdbbcbaaddaacbcdcdbddddcdabddbcbbdcbdadadabdcabaaabbaddcccacaabccdabcacccbacccdbcaddcddcdabaddcaddbbaaadbcdcbccababddbdcbddadcadabadbaacaadbcabbbadcbccaadcacbbccbbbddddbdbaccddacdaabcbdbccaacbdddcadbabaadaabdbabadbbbdaaadcbbabaaaacacccbabcdcabdadccccabbbcccabbaaadccaccbdcbbbacaaaadababcbbbaabacdadddabddacbdadabadbdadcbccababadbbcdcbacbbccbdcadaacbbdbccabbbacdbaacbdddbbbbdabdcaabbbddcdbddadcacacbbbdddadbdbddcadddcddcdcbbaaddbabddadaccbadcbabcadaabcdadadadaacaabacabcbcbbdabaccdddcbadccacbdadabbdaabaaccdccddabddbdbbadaccdabccbcccbaabadbdbbcdcddbacaaabccbdccddbabbabbdaccadabdbccaddcaadcacaadcdccaabcddddcabdaaaaccccbaddaaccccaabbbbdadabcabbcddbcacdbaaddbddbccdccadbbccdbdcaaabdcacccdcabbccdbbdaacbcdadadbddacdcdbcdcaddabbcddabadcdcbbdbcacdcacabdbdababdcbaabdbbbcddbddbdaaaacdaabbbccdbdadacbabbbabbdcccdacdccabcaaadbbaddcaabcdcbcdcacdbbcbddcdabdddaddccbbaabbdaaadbcdadcadabdbbbddbabbbcddadcabaccdbccbbcaaaadcbadcdadacdacbcbcbcdaabcadcbacabddbdcddbbdbbcbccdcacbdaabdcdcaadbaabadcbcddcccccaddcdccbadcbbacdabdcbcaacbabddbaddadbdddbdcddddacbcadbcadbcbbcaddcddadcdaccabbdcbccbbcbadcdddaadbbbcaddbbddcbaddbddbacacbbdbcdcccdbddbabaaacbabbacdcbcdaaaadbdaddcddaaddcbdbcdcdbcacaddcbbcbcbabbddacadabdbbbbdacdababcbbacabccdddabccbcbccadbdcbddddadcddbaaadbdaadbcbdadaccdbacadaaabbadaabbdccadccdbccadccaaabcaacabddbdbabbddabbdbdbdaadcdcabcbabaadabbadddbbbadcaabbdcabdcacbbbcbdddcaacdbdddcadccabbccdbcddadbcdcaadcabcddcdcabbccdbabddbbaccababccbbadbbbabbbaaacbcbbcabbdacdcabddcdacabacacdbcaaddcabaacddcccdcbabdbababddbcabadadabbdccaacbbcbacccbaabbbbdadaadbbbadabcaadcbaabcbdccacacacdbcccdadcbaddcbacacddbacdbadbddaaabaaaaadbdadbcdcdddbdabbdbcbcaccccdbcbbbbdcbddcddbdabbabcabddcbccdccaadbbaadaacabbadadcdbddacdcacadbbbcbbadadccabbbdbbdbdbcbaccaddbbcccbdadddbaccbbabbdadbcccbccdccadbaadcdbdabcbdadcdadcbcbaabcacacaaaaaabcdbadbaacdcccbdddbdabbbddddacdbdcadbcddddbcaadbbcbcddbdcbcabbbddcdddddbdbdbcdadbdaaaddaacbdddbdaabdbabcbbadbabbaaabbbadddbdadcbbccddccbabcdbcaddccddcbbabcadccbadabddcbcbacdacaaadbacacccbbacadcddcadcdbadaccdbadbaaababddababdabbcdadbcbbaaacabdbbabaabdccaccbaccdccbdaccabcdacacbbbadbccbabccccbbaddadbabadacaabcbcdaddcbacbdddbbcbbaccddcdadbbbdbadddcabbadbbbacbdbcdaabaddaadaaadcdcdadbadbbbdadbdcdbbbaabcbaabcbdbcbbbabbbddbadccbdaaaacdcdccbaabaaacbadddacbbbadaacabddaabdbadcbbacadbdcbabcadabcacddcacbdcbadadbadaddbdaadcabdabbcbbbabcadbabdaacadaaaaacdccacdbdabccabdcbacdccacdadddccbccccdcdabcbbdbcbbcccbdbadccdbdcdaadacddacdbdcdaacdabbcbdcabcadcabacabcdaabbcbbdcbaadbcaddabbcccaddababadcbcbcacdacbcdcadcbcbaccabdcdaacdcbbdccbdabbacbdaacddcbbccdcccddbacbdbddbabcdbdacacdcdbacabcbcbaccdddcaacccacdcddacccdbdbcdcdccdadaabddcdcadcaddddaccadbcddcacbddbddadaabdaacacadcdccdabaaabacacdccaccdbbbcabadcbacccaacaccaabbabbcbbabddbddbdadacbdccdbbacbabbbccdbbcbdcaccbbbadaacdadabaddddbbadcadbacadadcbcaacdadcdcaaacdbbccabaacdbadcbdbbacaddddadabacacaaddccdabacddbbbcdcbcabbbcaaaaddccdbdbdcdacdcccccdbbcddbcdbbadccabbbdbbaaabbcdaccbadaacccddbbacbbadaacdcbccbccbdccacbacdabdacdadccaaacdadbabbccacbdacdcbbcacccbcdbcbddbcbbdabddabaadbacbcbadadabcdccdbcdbbadaabcbbbacbdaccabddbaaacaddbccacaadcbabaadbabbbcddcbccaddbccabbbbdacacbcbaddaccddddacadbbdbaacccabdbacadbaadddcbdcddbccdabaadabcdbddbaacdddbaddbdadbdcacaabbaadbdbcccaabacdcddccaaadddacadacdcddddabcbdbacbbbadaacccbdadbcacadacbadbcddaaadcadcbacbdddbadacdccddaccdcdbbbcbbacddddcdcdddbbbaabcaaddaddbacacadbcddaadcddacdadacddbaadddbaaddbcabcaccaabbdaabdccdabaaccdacbbadacbcacdbcbcbadacbdabdcbcababcaadadacbbbbbcbcabaabcdcadbacaacbdababbcdbacbbbcddccdbcbbdddbbcbcadacbbaaccaaddddcbdcbadadbadcabbaddbcdcddcddcbcbccddacadabbacbcacbadcbdccdcaacdcaacbdbbcaccdbdbacadcdddddabcdbcbcadcabccddcacaddcaddacdaabdadcbddaaccdabcabaaabcdccbbbdcddcbdadcbaaddcdadddcbadabcdccaacdcddacaacbddabacdbbaabaacdbcbbdcbcddbadbcdcddacadbdcccdcabdbababcdcbcbbcaacbacbaacdcadaabacbdacccbcdadbddcdbdacbccdcacacabdcbdaccbccbadcadcbaacddddcdcddcbcbadbcababbdbbdaacbbdaadcaaaddbaabdadabbcddbbccabcbcacbcdaabcbbacddcdadbdcccaccdcdadaaddcabaadacdcbcdaadabaadddcbadcddcbdcacadbdacdbbababacdbacbbabaddcbbcadccaabaaaaaacbbbdcaddaadcadbadbdabbabaaccacbabababccdcacdbaaacbaaabacacadbaccbccbcabadaabadcadcabbcdcaddaaacaccadbdbcbdacbcccbdababddccccccdcdccbcddbcacddcdaccdcdbaccbddaddbadbbbcbacddbbdaacdaadddccdbdabcdcdabbcbaabbdddbdcdbaaacccdaccccdaacdbdbdaacdcbdcadcddabbcdadcacdcacdddccccbdadbdbddbccbdabaccbdcbcdacbcaaacaabaaacbdcddaacaadbbbddaccacbddccabdddaddacddbddccbdabdcdcbbccdcbaddbdaadcccaaaabcabdaddadbcabdaccbdcababbdcdabacbdadcccbcababbaabdadaabcaabacabdcdabdbbdddddbcdcbaaabdbadbccbcdadddbbdccdcababbbbcbccdadaaacaaaccdbabdcbdcbaacdccbcdbadcbddcaaccacaaacadcadbbdcbccaccccadcccbbdadcdcbbcbaccbbadaacabcdacdbdcacdbbaccbadbbbabccdbabacadaaadbcccbcdacadbddbbddcaadbdcadccbaaaccacabbadbabaaadabccabcaacdbbbbccbbaacbaadddacdababbacdcdbaadbacacbbbbbcbddcccddabcccbddabbdcdbbddcbcddcbadbccbddaddaccdccdcdaacbbbaabdaaabadcaadccbbbbbdddaaccdbcaaccbacdaaadbcadcbdbbbcbbddbbcacadcadcaacdcbbbaaaaddbbccacddbacdbccabbacdbcbdbbcdbdadbaddbcbcaadbbddbcabbcadbabacbddcbacccaadcdbbbdbcaccbdabdaddbcaababaaadcaacbcaaabdbbbcccbcbcaddcbbababdbccbddaaabdcddbabddaacccddcaadbaaacdacaacdddbcbdddbadbdbaaaddcaacaabaaddddaddbdcdbacadbbaadadababdbaaabccdacccdaacbbbddcbccaaccdbcbddbadbabaabbccaabbdbadaabcdbaacdaccbaacdcbddcdcacaaaaccccbcccaacbbaababbacaacccdabbdaaadabbddcbbbbabdabadbccbcdaaabaadbcdaaacddcbacddabbbdbdabccbdacacdbdcdbaddadaaddbbcdaccbcbbdcccbcccaabcbaaadddbdacdadcabcbcacdbdcbcacdcbbbaadaaaabcaadbcbbacbadaddbcadacbaddbddddabdcadbcbcbdccbdcbcadadbdabcddccdddadbdaacbcccccadbdcbdacbbacccccccacbccaadbcccabadacdcadaabdadabdbabbbaadddddbaddadacdcabcddddcdacdccdbdcbcacaccbabadccabaaaabadbaaaabccacdcbbbbbccdacbadbcbdcadcddaddbabbdbdadaaddcdaabadcdabdbcbacdbacabbcdbbabcbcaddaddcbadadbbddadcaddcbcbbacddbcdcaaaccbccccabaccabddabddbccbbaaccdacbaaadacdbcbadcbaddadabcadcacbddddcbaacadcdbadbcddadcacdabbacdbadadacacbabcbdbcbccbbbbacdccbaadaaadcacababbcadbccbbbadbdadbdbdbdbcacdacdaccacdbccbaaccdabadaacbacabdcacddbdbbaaabbdccdbdcacbbabdaadcaaddbdccbadadccadcddddccabccdabddddbbaaabdaabaddcaccdabcdaaacdacbccdadabbcaaccccbadcaacabdbdbbdbaaaccddbcbacbdbabacabcadbcdcdbcdadaccadaacdbdbaccbdadcccbccbdcacdddbcbbcdbaddadbbddcaabddbbbddbccaccddbdabbbdcccbcbadcabbadaacdbcabdbbaacadabbbcbaabdddcabbabdbcdbbbaabbacbbdbacdcbcbaccccccccbbdbbabdadbcbdaacacbacbbcaacbcaaaabdbbbcbdbbdacddcbacbaacacbcbacddcbadbadacdadbddaaddcacdbadbbbcddcbabbaaaaabbabcadcbbaaaaacaacadaabacbbdbabcdadcbcccbaccdccacaadabacdddbddcadabdaccbbbcdabdaaccddabacbbabbbacbaabbdcddbddcdccadacbcdbcdbcacbdacbabaadccabddabcdadbdbcdcabaabcdcabccdcacbcabccbbccbaddaadbabcaabbcacaabdcbcacbcdcadbccaabaddccdccbabbbdcaccccabccbcbaaddacdabdbaddcaddbbbacdbbdacaaabcaaadadabbbdcdadabddccaccaabdbdaddddccabddacdbbcadbdacbcabadaccaaacdabcaccdbbacbbdadcccddaadabdadbdddcdacdcacbdbcddbbbacdbddcaabbacaccaccabcbdccaadadacaadcbdcbdccaddcadaaacdacadbaddbacdddcdcdabccabdbbcbdcdbdcadccdccdcbdcbbcbcaacacbaccadadcdadbabcbcacdccaaaacacadccdabaacbadbbaadacabbabccabbbacadbbcdaaabdcccdcadcbbccccdacdcabdbdbdadbdbbdbdbddbcabbdadcddcdcacdbbbbcbcdcadbcbbddbccacacaccdbdbdacdcacdcdddcbcdcadacdbccbdaccccdabadbabaacdababccdccccbcccddbbddbaaddbaadabcacadbcadbbadbcbadbbcaacacadabacddbdbcccbcaabdcddcccbdbdcccadaababbcbbdadadabbdccacabdbbadbdbccbadadbdbbcbcbcbaccdbbbadbdcdaaadddcbabbcbbbbadacdaaacbaabbdbcdaaadcdacadbddcabccbccacdbbcdbdcdbcacabbabccdacccccbbadbcbbdaaadbdcccccddbccabacaaadacacddaddcadbadabacbabbcccaaaacccaabcacbbdcbbbddaccdbbccaaabcbccababcdcacccadcdcbbaacddbddbbabacbdadcdadababadcdaccccdcccadcbbbdadbaccbcbcadcabccdccabaccbdcaccbbbbcdcddadccdcdbbbaabbaabacdbcbdaabcbcabdccbbabbbcbcaccdcbcbadbbbaabdacbccacbacadbcaacaaabbbdcbcddcaddabcccbccbbcbaadacadbcdacaccddbddabdbcbbcaadcbaacccacaacdcabcbddcbaacbcabadccbddaabacdabacdcaddbbcbcbdbcdbcbbdcaacbacdcbbdbbcccabbcbaacbdadaacacdabcdbddaacdaabdcbcddaccdcacdbaababadaddaadbbcaddbcbbadbcbbbdaabbcaaabdacabaddcabcccabaadcadddcbaabcdddaaacbcbdbabadcaaabdbacbdddbbccdcacbbaabbcdadccacaabaaaaabaacdacbaabbcddcaaaadcbdbdbdccccaaadcdbbccdbaaabdcaacabdbdccbbcbcdbdcbccbcbbcbcccacacdbacbdbcdddbbcabbdbcdcbdaaabcbaccdadacbabacbcaaaaadbccbaadbdcabdbcdcaddaccccbdcddcbcdcdcabcddcaacaacaccabcabcdacdbadaadddabbaacbdcacddbdbaaacadbdbccabacbacbcccbaabcaaabbacabbbaddddbabaacbcdaaabbcdbcccbcbcdbbbcadbadacabadddacdbadcccabadcbabdaacbbbbdaddccbcbdcbaacaddcdabdbdadbddbadcbabcbbdbccdccacdbcdadcadaddddadbadaccbcbcddaadccbcadadbaadcacdcdadacdbaddddadbdbbdbdaabdbdbbdcddacdaaaccaabdacbddbbbcaaddbcaacbdadddadcddbaccbcabdcbabddcbdbaaddcbccdccbacbcbbcbcbddcbdbaaddaabcabbcbacdcbacadaccccababbbcdacbaddcbbbaccaacdbaaaacbddabdadbccdbbdddccbdbdddaabbdbbbcacbcddaddcdcacdaabcacbcbbcccddabacbdbbadadcdcdbbabbbaaaddccbcdadaddacdbdbbcadccdbbdacbccdabdcbccabbcaaadbbccababdbadbccdbdbaaadbaccdaacabcccdacabbbdcbcbdacbbaaabbabcccaacabaaccbacdbbbababacdaddbcadcddacadcdcacaababacaddaadbcbabaabcbcbccaccadaacaaabcabdcaabbbdbdbdddbbddcdbcadbacbdccdaddcaaccbbbadddcccbaccababdbcccaddcdcdadbbcbacdbcbccaadbbcdcdccacadccaabbababbccdacaadaccbadbacbdddadcaccbddaabaaccbcaaccdacbdddabcbaadcbbabadbbadabcbacaaaaadacccdddacccdacccaccccaaabcdbbbbbacdcddbcbbddcdacabaaabbabdccdbcabcdccdabcdbadbaabaddaaadabdabbbacbdbdccdcdadadababdbcabddcaaaadccccddcadadcbcdbaaccacaaaccaacbdcbbbbadccacbcddbcbbdcbccdbadbcdabbbadaacaaacbbcbbcbccaabbdbdcabbbcdacabddcdcdaddcaddbdcabdccbdcdcbdbbabaacbddcbdddcbadadbcbabdcddaabdbaccaaacccabacacaccccbccdccbcbbdadccabbbabaadbbcbbdaddaadadcabdcaadbccaacadadbabdddcbbccbbaccadbcdaddccaaacdadbdbbabdababcbccbbccbddaabbbccbbdcaaddbcdcdcdcbddcabcdacddcbddbdbdbacbdcddbacacddddbbacbbdbdcccbbcbdaacaadabddbdbcabcbdcbdccdddbabaabbabacadcbaddcadbaddcabcccabdbdbaaaacadaddbcdbcbbdaabcdaaccdbcadacccbbdadbaabaabaccabddacbdaddbcdaadbdadcbabddbdbcddaacadbbdadadcdddaddacacdbddbccadcbcdcacadcaaabbccadacddbcccddbcacabcbbcccdbbaadcaacbcaadbcadcdcbdacbabcddbcadcabbcbbbcaacbccaacbbbdbcdcaacdabbcbbdaabbaaacdccaccbbcdddbdadcdacdabbbbadcbaaaacdabadcdbbdcdaaccbdabcbabccaaddbcccbcdaaaccdbaddadbddbbadddbaccddacabdbdcccabcadbaaabbbcdbddbdcacabbcdabcbbcbdbbcbbbacdbdadcbbbadababbbbcaadadcbadcdbcabdbbcbadcaaabbbbcdddacabbdaddbadcabbbcaaadddacbddbccaabcbbbdbadbbddaddccddcdaccccdbacbcbdaadcacabccdaabdaddabbcbbaacbbcbcccbcaabdccabbcaabdbcccbaabdbaccacccdbcdddaccdbaabcabcddcdacdccdccbcbcddabcdccabaddbacdaacddcbacccaaacbbddbbddaaabadaabaabbdadbadaaaaadadcbbdccbbcbcbddabcaddacddcbdadabbccadabccadbcbcdadadbadcdbddadbcaaabcbccaabdddccbcacddbcaaadbcbbdadbdcbbbaddcbdadadcdbabdcacdabacabadbdbdadcacbbdddcbaccbddddcdaaadcbcbbcccbdaadaaadadccacbddcdbdcacabcddccacacacbbdbbdddbcccbbacbabaccddcdbcdadbccbaacbadccccdccdaabdbdbdbbbbadcbcaadbbddbbcbbaddbcdabaacbbdbbabbdcaccaddcaabaadcaaadadbabbacbddacdddcddcccaaacdcccdccabddbdaccddadaaabbababcbabddbabdccccaacdccddcadcabcdbadbcdbbcbbcacdaabccacdddcacddadbbacadbadbdbbcdcbbabbddddaccadcddddacaaabadcbbcdbaabdbccddbccdcbcaaccbbdbddacaaddcbddabcdbabdbdaaacbccbcadbbcabccccdddcdddbadccbcbcdbbcaadbaadddbddcbbbbbcdbdaacdcccbabddbcacacdbaccabdbabcaadcacccdcdcbddbbcbdcddaacabbdabbbdccadcbaccccaacdcddcdbdbcdcbaabcdaccddbcabbdacdbdbbddcbccabbabbbbbcbdacacdddacbbccdbbcdacddabdbadcdddadcdccccabbdaaaacbacdbbadaacddaddbbbcbcaccbacaaddccbdbabaababcdcdacddcdbbccaccbdbacdbbcdddcbccabadbadaadcbdabbbccbdbbcbccbbdbcaaacbdaccdaccaaababadaabdbdccadcbcdccbdadddacabacadbcdbcbcaddcadaacaadcdccdbdcdcbaccabccbdbcdcbbaddbacbbbcaabddbdccccccbdcacdbbbabbdcaacccdaaaacacbbcbddacaabbaabacbddacddcaaaaacadaddbbbbcacabbccddbcccdddaabaccbababbddbbdbbccdddcdacabccdcddacccdbbcbadcddaadcdabacbdbdbdaddbcaccdaddbbaccdbacbaddacdbaccddbacbbdcaddbcddabaaaddbdacdbaacbabcccabaaadccbccaaabdbdacdcbddacacdcccdbdcbdccbdbbaaccddbccdcdcbabaacdabaabbcaaaccbadbbdbdbcbcbaccdbbacdcbbcbcccbacaddcbaadbababddaacbbbabcddacacdaaabdaabdddcbdbcbbacbcacccdabbbcabadaaccbbbcdacdbbdacadcabbcdbadbbcccccdaacbbaacbaaaaadbcacddcdadadcccdbbbbbbaaadcdaddbbdccdddddccacaacacbacbcadbadddadaacaddcdbdbbcdcdbbdddcaacabbbcbcdcdcccdababcccaabaabbcddddddbddbddaaddcabdcdbacbdccabcbcdadbcaccadcdbbabcbdbddacdabddaabcadabacbdcdacacddcbcccacbcbaddaabbdddadabdabaacdbacccbccbddacabbaaaacbcdacaacdcccaaacdbbcabbbddbbbcdbdbbcbccdaddadcbaacabccdbabbcacbccadbddbadcddbaddbdcbdbabaadbcbbbcabbbcdadcadbcadadbaaacbccdbaaacbdcabdbdcbcbdacacdaaacccbbacabacabcbddaabdbadababadaadacddadccacaabdcbadddbdcccacbddcababbdcdbcddcadbbadacadddaadbcacdcccccdccbdbbcbcdccbaaabdbcdcacdcadbcdccdcddaadabdadadadcbdccbcabdadcaddadaadbdcaccadaaaaacacbddabacadcbadbcaaabaddadbddabdabcabcbdbbadbbbbcdcdbcbccbccaccddcdcdcabdccccccabaddcbbccbabbbdcabdacdacaadadadddbcbbadbbddaccdbadbbddbdbdbdcddbccbccabacadcccbdcbdccddaadaaacdbabcabccccdcdacaadaaccabcdaacadbddcbcdddddbbbabcbdabdcbaacdaddcbbcacbbcddcdbdcbabacdcbbcddcacbcddbbbbcabbdcddcbcdcddddcaadbbabcdbadcacccdbaaddbcddbdcbbddccbbcabbaacbbabcccbdbbbdbacadbddaabbbaaadadbcabcdccddbccacaabcdcbbbabbababcaadccbcabdcdbbaaabacdcadddcbcabbbdcaaddbcbdabccbbdcdaccdbbbcacbabbbcccaadabbdddbccbadacdbbbbacaccadadabbdcdbcccdacddccacaccacdabcddbaaabdccacbbdababbaacbddaadacabbbbdbbbaabaadcdbaaadacabbcadbabaddacbbbadbadadbdbaabccbdcabcabccadcdaadcbdcbdcdaddccccbbcaccccbaadccabadbccadcadaddacadcaddcdcaadbbabcdddbaababdabcdddbbacbbbdcdaacbcbccdbdbabcbdabbbbddabddcbdaababcacaabbacbaadcdacadccbbbabbcdbbdabddcdcbadabaaacdcabaadcbdbbdabbdddcaacacbdbabacccdaccbdbdcbdacacacdaacaaabbacacadddddbcaddaabadcbdccbdbabcadddbcdacbaacccbdbdadacbcbdbbddbbddadcdcbaacbaabacbadacaadabbdabacddaaabddcbadacddbbdbbdcbaadddababccbdaacabdbcdaacaccacaabdbccdbbdaddbddbdcbdacabcdcddadbcccaaccbdddacabdddbcbbdcdcadbbaccddddaaadbabdbcabccdaacabdcdabbbbdaabcababbdccbadbdbcccbcabdbccdcdababccbbcbacaabacacbcdddbccbddadacacadcccacdccccadabddddccadaddaabbabcacadbddddcdbcdcbdaabcbdacaaaacccdaddbbacdaaadccaaccadccaabdacdbdaaddbbcbdbddccbaaacabdcdcddadacdcccbbbbcdacacabdbcadadbadbcbababbdddddccdabacccbaadaccbdbdbaababacbccbbddcccadccdbbabaddadcdbabbddbbacabdccaadaadaaabdbdaadbbacdabadbaccdadcaaabbcadabcbdcbcadabaccdcdaccabdcbacacdacbdadadcdbcbaabbccbccbccbdaabcbbacacdcbbccacbbdaaabddbccaadbadbddbcdaddcadacbdcadbbaacacbdbaaddbaadddcdcbbadbabbddbbbabbdcaadcdbccaaacdadbadccddddcaacbbaabcdcddbdcdcbbcdcacadaccccccaadacccccbdcabdbcbabcdcdbabaabaaaadbdadaacbddadaaccabcabbabdccdaccbdccacabbbcaadcdddbacbaabdbdbccbbabacbbadbbbcbcbaadcdccacbdcbabccbbcadddbdbdcaccbdbbbbbaadacbddadaaccdcaacdabcbbbdcbcbccbbaddddbbdaddbccddbdddbccdccabababdcbdabbdcabcbdaddcdadbdcadbcdacabcbbcadcabbacbcdcccdabaabcbccdadcdcdcaacdbacabaaccaabdacadcbbcabcacbabccddbbdbcdabacbcbdaadcaacccdbbcdaaaaacbdbddacdccbabdcacccdacddabbdddbbacbddbcddccddabdcbdbbdbbadaadbddbbbadaddbbdbbabbdddccbacabccdbcddabacbaccaabababcddbdadbbbadbddcbbbbccccacdbadabbbababbdcccdbaccadbbbbccbdbaadadadaaccbdddacbaacacbbbccacbaaadcadacbdacddcacadacbacbaaddcdaaadbdabbcaddbacccaddddccbbdcacadacddbabbdddcabbbcacdbcbbaabaccabdddabaddaacbadbaddcbbaaaaccccbbabcddacdcdddbbdbaaccdabbcccaddcbcbbcacdacdaccdacbcaabdddccbcddbbbdbaddacbbdcadbacddaabcabdcbdcabaacacdcaadabbadcabbbbaccdaaaadddbbbcaadccbaaadbcdddbcaabcdddddcbcbabcaabacbcdccddaabbcdaaacccacbdccdcbbabdccbbbcbdbdcdaacaadbadbadcdcaaccdddacadababbdcbbadadddcbcddaacacdccabaacaaccdccacacdaaaaaadcdddbacbdadaabccdacaddccbdabcbbdccbbbbbdcbbddbddbbacdcbaabdaabaddaaaacdbcccdcbababbbdbaadccbbdcbcbdabccccbcacadaddcaaaaacdacddddacaabaccdcaddbacacabdaaadaccacccdccddcdcacdcbadbcadbdabddbbaaaccadbccddbaaaaadccbdbbaccdbbdaaaadddddcacaaaacdccabbdcdcddbcbbaabcbbbbadcbdccaddddacdcccbcccccbbcacbccaaaddbbaabbcccdadcdddbdddccdcabdcacabadbcbadbaacaddbdaabbdddcadadbbccccdbdaabbacabaaadacbdddcccdadbacbdbbddaaddbdbdabcccbccdbaaacabacbcdbcbcdbabdccdbabddccdbcdbdabddabbcabcccabbbcddaadabcbaacadaabcabbccbcbcabbcaadccdadcbccaabddaabcbbadacacbdbddadbbdabcbdabdbcaccdcdbacdaddddbddcdbadbaacabadbbbaddabacbacdbcabddabdddacdbabcaacbbaaadcaabbccbdccdcbacadaadadbdbbcdbdbaaaaccbbbababddadddbbcbcacddaaadcabbcddbbadadaccdadbbabbccaaddcdaaddbdcdcdababbbdbdabdcacabbdbdadccacdcaabcabbacadcdbbbbdccaddacbbdcabaccdcdddbbbaddadccccccadcdbdabcbabcbabbdddcbacbadadcbabdcabaadabaabadbcdbbbdccdaadabdbbcababababdadddbdaccbaabdbbdabddcddbdbbbdbccaddcbabdcccbaaacdaaddadccdcbdbcabdabcdbadabdaddacacaddcdaddacadbadbbdcdbadabaaabccccbbbcbcdbcdbccdddbcdcacdbaadcbcabbbadbbcdbbbddabacbcbcaabacadbadaadaccbddabddbbaaaadbbcdbbccdadbccbdacaccbabbbdbabbdbccbddacbdacdbaadcbdbbcacdbcbdbcdcadcdadcacabbdababadaaadacbddcdbacacbaadccbdacadaacbcbbbcbcdbaacbabcacdcdcacaadbcbabbddacadccbdcbbbdddacddcbadbcadacbbabadaacadabaccdddaabcacbacbdbaaaaabbabaacdaccdadadbbabbababcdcdadccbccdacbbabbadbaaadaccacaaadaaaacdddbdaaacdbaccbcbdabdaabaadacaadcdbbbbbcabdbcaabddaadacadbaacadabbccadabdcdbdccbddbccbbabdcaaacbcbaadaccdbabcabdaabdaddaadbbdcdacddcbbbbccbdaaaddbaadccbbcaabdbadbdabbadcbbbbcadadcccbadccdacacaabdadaccbabaadaabcbadcdcbdccdabdadcbcadddacdcdcbabcddcbcbdccbdadbdbbdcacaccdcdbacbddbcbdbddadcccabdabaacdaccbcbabdaacbadaccccadbbabdcccaadccbbaabacdacaacdccccddcbbdadabbbaccabaabdcbcccaaadccbbbbbccaacbaaddaddaaacaaddaaadbdcdbabaabcbbadbbbcbdaaddbccbcbadcdcabdccabbdddcbcdbcdbddacabbcaccdbdcdaacbcababbddddcbcddbcddbcddadadbdbdaabdcdaadbacdbaddbacddcddadabbccadddadabbbbbdbcbabbcbbbabacbbcaacccbdabbcacdcbbacdcaadbdbacbdcbddabddadcadbacdbcbbdbdadacacabcdaddadbddcbaccbbccbdbbabcdadabdaaabccaccdbdcbcbddcccadddccdcacaabccacdddbcacaabddcbddabdbbdcadddbdadacdacdcbbbbbbdcaacbdcccacbdbbcbdbaccbadcbbcacdcbcccbdbaacaacbcccccdacdabbbbdbabcbcddbabadcddaadccbadbdcbcacdbdcbabbdcbcdbbbdcabdbbdbcaabdbbbbcdcddacbdcddbdcddddabccabcadabddbdcccccacaadaccadcabbcaaabbdbaacccadbbaccadbacccaccbbbccacdccacdcdbccddcccaadabbcdcbabdbbadacbadabbcdadaacbbbcbcbbccacaadabbacbabdacabbcdadddacbaacbaacacccbcbddbdcbbdcbdbcccdbdbabbdbcdbbaababbcdacccdacadcccadcdcdbdddcbddadacbdcbbcdcbcaaaadaadcddcdbdacbadcadaccadcbdbbbdabcbacbcbbadbaaadcbccaaacaaddddbddccbdddcbcbadbaccdbcdccadbdaabdabbabbaadaddadacababcaacbcdcbbcdbcbbcacccbcbbaabbaddcbbcabacadddbbaaadcbcbdcbcccddacbabbdbcbaaacdcadbbdccacbdbaacbbbbdaaccccccaaabdbacbdbddbabcdabdbbbdbccbacdcdcbbcabacbbcdccadbdddbbdadacdaaaaadacbbddadbcbdddbbbbdadaabdbdcccdbabbdcadbddbcbddcaaccacdbaadadcaddddcbaacabdbdbdbcdccaaabccbdbbaddccaddccaacaccababbccbabcccdccadbccbabbdacddddbbcbabbadabdcabcdbabbdcbabdcaadaacaaaddcabbbdacdacadcbdcabadbbccabdabadbdbdbaaaccccbbaaaddbbabaddbbccdddacacbaadabadbacadcccdcaaadcbaddaccdcdadcdcdcadacabdbcacdccadcadddbccabdaccccabbcaddadacddbbaacbdabdababdbdcaaabdabdcbaacadadbabacaadaaddcdbacccdbcbabbbbdbbbabcdcdbbdcdccbadacdbabbddddbbcccccbcadcaaaadbcbdadabcbdcadaaddcddcdababaddaababbcdbddaccbaabdcbbddbcaacaacbaddcbccaccbcbcccdadababbbbacddaabdbbccadbbcaadadccbdbbcacbcbddcabcadbacaaddcdcaabacadcbdacaadccbaabdbcdccaacccbcbdbdcbdbbabbdcdcbaacaaacacccabccbbbabbdabbbdaccdccbcbcbccbdbdbbccacbbaaacabdcbbaccddadbbddabdabcbcccbbdcabbbbbbcabdbbdbdccbcccabcdcbbcbaacbbaaacdaccbbcbcdbccdcbcccaacddacaddbbbacccdbadadddbccabbcccbbdacaabaacadddadcaadbbbccccbaaddacdadcacbcbaacdadddddabbddbcbdacccccabbabccbabbaabccdcddbdabcaaadadbdcacbbacdccbacbbdcbddcddbcdcdcbbacabdcababaadbdddbcddbadadaabcdcacacaaaacdadcdbacdccccdcbdbbdcdddbdbcbcbcbddddbaddbdacbcbcbcdadbaabcbdabacadddbcbdbbadbcdbacdccaaadcaddacbcbcbcdacdcabacaddacbabcbabdcdccbdbabbdcdcbdcddaaabacbabcbdccabadadaabbadddcdcaabdbaaddcaaadccdabdbdbdbabbabddaaadbdbdcbbdcddbddddbdaabbdcddbccbdaaadbaabaacdbcabdabbacbcddbbbacabaddbbdadacbbbabbbbccacccadacdccaccbabadbccdbbdacaadcccccddcccdbbccdacaacbacaccabbbcadcdddddcaaadccdbbaaacbbabacbbbdcaadcbbaadbcdbabdabcbcacbdacabbaddadcbdcadbccdabaddabbcdcbdcddbabcbdcbdcccbbbacbddbcbddcbdcaaccdbcbabccbdbbcaaaaddcdacbabdbaabcbdabaaccbabcabdaddcbbdcdcdcadabdcbdcabbddacdddbaacdcabbdacaabdbcaaaacdabbdabababddbbdabbaaccacbabcbdadacabcadaabadcbbcdbabbcdadacadadbcbcbddcdcbbaabcdcdcabbaacbcdaccaddbdbbddbcbddcddbbcaabcdadbbdccdcaddddcadacbccabbbdbbadaabacbcbbdcdbcddcccbbccbbbaddbbddbabbdabdbabaabdddbdabbcabaadcabccbdacadccbbadabcdbbbcddccabcaddbaccbccbbcaabaaccacdcbadccdcbbccdcbcdadcbbadddbbabacbaaabbddcbabdcbbacadadbbdacacbdabcdadcacbaccbdbcaadccdcdddcabccbadaabddddacabbaaccbcadccadaddabdbacbdcddbcdadbdbddadbbddbdcccdadacbaabcacbdcdcdacadcdbdacccdbacacabaabbadbdacadccdabaccddcddbadcbcbbacadccdbcdbbcabdcdcdccdacacaaacbcddaadbbacbcdcdddacaacdbdcacbdbcdadccdcadddadabcadcdcbcaccbccabccbcbcbdabbabcbccdcbcabccbbdbdacacbadcabdbdcccdbcbcbbcdccbcaaabcdabcbdbcdbbbcabbcdbacbbddbbdddbaccaabbacbcaddbabaaaaddccadcbbacbbaaaaabacdcdadbcaaabbccccbbddccaddbdaadbddabbcddddcbdddcbacdcdbbababaaaddaaaaaabddccddcabdabadbaddbaabacacabbaaccabdbaadbdbbaccdbddacadbcbcbaaacbbaabacdddbacacdacdabacdcccdbbdbdccadcdadababaddadcdccbddabcaaaccdbacbadcaaabbacdcddababccabbacadbadcacabaccbdbadccdbbadddcadccccaabaddddcdbaabcbaabbcacadacdbadbcadacbccbddbaddbccaddccbddcabdaadaccbadabddbbcbdadbdcbdbbbccdcdadaddbcbdbddbbbaddcacbbbbdbcadadaddadddcbccaacdabcccaadadaadddbbabbdcbdacaacdcdaabdaaadbcbacbadaacbcbcbcdcabdccacbbccbcacdbaabcccccddbacdaaddddcbabccacaadcddaacaddbdbbadbbdadddaadbbcbbaadadbccabbadcaddcdddadcaacaacadabaacbdbacbcabaaacacdadbaaaaabacabdaccbcbdbaadbbaaabdabdbbdbabdaaabbcddcbbcacaccbdcbccccccaddadcbbaacdaccacbcbcababdddcacabcbbbdcbdbdadabdbbbdbcbdacabbaadcdaccabbdbbbabaabcaaacbcaabdbabdddcccbabcadcdcaaddcbdadcbcdcdacadbdcdcdacbbcacbacaaccdabdadbaddaacbabcadaacaabdbabaddcbddcbdbbbbacacabcaadabdaacbcaaddccadbbdaacbdddbddbbabbcadadccdbdddccddcabbccdaccdbdbddaabbbbbdaaccbddaadadbbdadbcaddcabbccdbbcdbdabbddbccddadcdcdbbcdccbbbddabcdacddaabacaadcddacdbbdcbaaddccadbbdddbcbdbdcadbaddacacbabdacbadaacbbcabcaddddcadccacbcccaacdadabcccdcaacccaadcddbadadccdbccacbddaaccbcabdabdbbcbbacbaaaaaacccccdbcaaccaccaddaacaababdccbabbdadacaacbbbcbabaacddbbcccbbbbbdcacbdacacbcabdcddadaacbbbdbbdabcddbdaacddbdcbbcccdabbdcccaaadcabaaadcccdaacbaadbabbcbacabadddbddddaadcbbbadcabacaddccdacbabaadaaadbcccaccddcddaadcdcadbbadbabcbcabbccadcbcdbcadaddbccbbdddcccabadbdadcadccbbdcbccdbacbabbdddbaccddadbadbaabcabcaabbbbddcabcbcdcbbbaddadddcacbbbcdddaccacbabddadbababdbddbccaaaaacacaabdbdadacabbacaaacaccdbcbaadbdbcdbdaccacbbbbbdaabdcaadadaabcbaacacbbaddadcbabddadddccbacadccbbbaacbcdcdcdbdabcaaaacbcdbabadbaaddbdcabdcbbdcccdbbbbcccdcccddcacddbdccdbcabbaccbbcbdcbbcdcaacdacacdbcabaddcccdccbdaccaccacdabdbaadddbbdcacbaabbaddbdadacdabcacaabdcdbaddbdccdcddcacbdcccacaaaaadbaaacacbddddccdbbdcbbadcdccaaddbabdbacbdbdacaacccaddaacdcdbacbbabcdbcbdccdbcdbaddcabcbdbacbcdbccbaccccdccddcdbdacaccdbdadbacbcbdccacbaadccbbbbbdccdccdbcacaccbaacbbbaaabdbcccdbabcdbdadbabbcbabdaccbbbbacadaacacdcbcdadcbbdbbabcabdbddaadacdcbdacacdacbaacdcdddcbbaaaccabcdbcacaabbbccbdaadcdbdccdcbcacdcdbddbccddaadaccbddcadbbbdbacdabaabaabdadcadaaccbccccbdadaddddcbcbddbcdbbbcdbccaadbdcaadaacadbdcaccdbbbcacaaadadbdcddbbadcacabcccacabcdddaaaacdbadcdadadacbbddcadaabbbcdadbcdddabaadcaadcbbdadbdddcdcabcbacaddccbabcacbbbdcbdabcdabcaddbdcacabcdccbabbbccdaddadcddaddaaabbaaacabcbcaaaccbdadbaccbdcbabacbaacaacbabdabcacddddddddaaaacabcdaaddbbacabcadbabdbaacadacbcaaadbdaadcbaaddabddbbcacbcbdacbdabacabcbcaacbabcadcdbadccaccdbacbccaddadbddaddbaacccbddbdcddbddaadccaaaadcdabdcbbadddacadadccdaacdbcdcabbcbccadccadbbccbbbcabcaddcbbcaccdcccadcbadaabadabdcdcbcacdbdddcbdcadbbcaddadbadbddddbdccbacacdcdddacaadbabcbaababaaadccccbabbaccbdcadadcbccaddadcdbdbbbbcddbabdcdaadddbcbcdbccadaddacbdbaabcddddacadbddbccbbcbacdbabcccbdadcaadabbacabbdcbbdccbbbccbcbcadabbbddcddbbcbaccaabcbbabddcadcdacdcdbbccdbbddcbdbcaddbdabbcdccccccdbbacbbbaddcbdabdbaadadaaaccadbaacccbbcddcaadddadbdbbbdadbbadccabdacdbbcdcbbadbcaacccbbbbcaacdbdcbbbdadbccaccabccadacbdcacdddcbddbdcbbdacbdcdccdbcbbdddaccdcbbbdadaabdcaccaadbdaaccabcaaaabaacbdcddcaddbcdbdbdabbdbadbbdbbcddcacadaabbabdbccabbddbdaccdcdcaabccbbacbddbdcdccabddddacabccbddbcaddcccdcabdddcbadabbcbabddcbbcbacaccbcacbadcadabbabbbababcdccdccbabbcdcdaadcbbcadaccabbbacccbdcddbaacdcadadccdadaacbcaccaacdcbccbddcbcadadcdacacdddbdbccbdbaccbabcacaabccadbcaaaabadabbdbbdccdcccadaabacbcaacdcbacdbacdcbcddcdabdaccbbccaacdcdaadcacadbbcbaaddbbadbaadbaccaccbbddcbbdaaaaabdccacbdcaacdadcbcdabcaacdcbccbbdcdadaaaabbdddcadccbcddcdcbabbdcaaaccbbdbdbdccbbbcdaaabddabccacbbdbcbadadcbcdddddccdbaddbcbaaadddcabcccdddbbacbccddacaadcddcddbadbbbcbadcaabacabcbacbdbabaacdabcbaccbbcdbbccddadaabcbbcccbdbddacdcacacaabadbbddddcdbbabbdbdcbddddbbaabdadbbacbdccbcbdacaadccddcbbcccdddcbdbdadacdaddbdadbdabbbadcacdabdabacbccddaaccacddcbcadbacdbdadddacbbdcdacccacaabaccabbdbacaaddbabdcddaaacdcacbcddadbcbbbccadadcbbacdaddcdadacbcdbabcdbddcddccbdacacccadcacbccccbccbdbaccadabdbbdcaacadbadccadaddccdacbdcbabaccdbbbdcbcdbaddccaccbcdbacadbbbcabbbdbbccbdbcaddadcbbbccbdbbcabaccbaaadbbbddbcaccbcdaadbbabcbddbbaccccaadbbaddaadaaddddcaddbbcdcabaaccacdadcdcdcaadaaadddcbbdcdabaabcababbcacbcbddaccdbccbaccaddcdacbbadbbdcbadacbaaddadabbaaaababdbcbbadcdbbbcaddddbabcbdddccbbadcdaccadbcdabdabaaacddbbbbdbdcbcdbdacbbcbccccadababbabcaaaddacbabdcdabdcbccbbbbdbaddbbcccdabbcbddcdadaacabbccbbbdacababaaaaddacdcdbcaacbcbbbbccbbbbbdbcacbdcdcdccdddaacdaddaadaaabbccbabaabacaccdacdacdabcdaacdcdbacbaaddbdddaaaadbacaddbbdddadddbabcaabbabdccacdadaddcbdaaacdcaccbcddbcbdbbabdadcdccdaadcdbddbcddacbaacacaaddbcdcbbdbdacdccaacdcaaccbaddbcdabadaaaabddcaabdabacacddaabdccccabaadacdccaabdbbdacbcadadddddbbcdddbacddacacbbdccdacccccaababdbcdcddbcdbbbaddcabdbababdababcdcadddcbcbaddcdacbdaabaaadcdbdbbbcabcaadbcabaacdbaccdacadadcadcdbcbccdcdcadcbddacbdcadcaadadcdacbbcadbaccdaaadaddadbccaabddcbcacabdbcadaaacbdcdaababdaacbadbbddcdcabbddccbdbcadddabbcabcdaaabacbacabcadcacbcadabbadcbadaacbdadaadaddbbccdbaacacbdcacaabccabdcdadbabcaddbdababaaaacdbcdcbbcdbbdddbdcabccacdccbddccabbadbbdacccaaabaacadabacbcccbcdddcdcdddbddaaaacddddcaccdbdacbdbaadcbbddddabdbadbbddcdadbcaccbabacabbbdabbccbabbadbcaaddbdacdaadcbccdccdccdccacdbbccaddddadddadababcaaddabaaddbcdccdbcddccbbbccbabddbbabcabbdcabbcdadccbbbdcbcbbcaabbabadcdbbaaddbabdccccbcbbbbacdbaaaccabdbdcbccbdabdbcddababbcdbdbcdaacacabbbbbbdcacaacccbbcaabbcddabdbdadaadddbbbacdbdcabccdbbdbbcaacdabbcbaadcbbacbccdaaaaddcaabacbdcdbacbddadcbdbbccaabadddbcdbcadcabbddcabdcdcabdaacccdccabbdcbdacbdbddadadcbdccdbbccabddcdaaadbaacbdadbcaccacaddbcbbbababbabbbbdcddccdcaadadbbdcbcdcdcdbcbbacbbcdbababdbdcaccccbccbcdaadbaddcacbaddaccbaddbdcaaaadcdbdcbabbcacdcdcdcacdbbddbddccccaacdddcaacdbccbdcccdcbdcadccbbdccdbadbbdbadaddadadcddcdccddddbdadcbabdadbaabdcddaabaabdbcabbabdcaabccabccadacdaabdabbadaadcaddaddabddabdcccaabddbdacbbbcdaabdaddadabccbaccbcbaddadaddaaaacadcccadcdabaadddaabadccbdddbabdacdccacdcaaabaccdccaddcaacacbcbdccbadbcdabdbccadacaabdcacabdaaddcdbdbaabcdaacddacaadbadbbcadccdddcbcadadadabccdccadadccccbcaaabcdbabdbababccbadabdaabadcccadcbcddcababdbbddcbccccbbddaaadbdcbbadbbdaacacdcaccbccacddcabccbcacdacdcadcbdabadbbddabdaabcbddacabbddcbadbacdccacbbdabbbadcbcccdbadacdadcdccddaaaacbabcdcbabbcdbbdbbabbcbcaabbacbddbcbdcdcbcbcddccbbbcbbbadacadbccdcbdbbddbdddddbcadccbcbdcaacaaddbbabcbcdcdcbdcabdbcdccbabbaccccbbadacbdcddaddabaddcaaadbbddabcaaadaacbcadcbbddcbabcbbbacdbbcdbbccbabddbcdcddcbdbaadbadccbbcbdddbacbbbaadacbddbccacddbcbbbbabaddddacbcdacbabdbaacdcbcccabbdacaaadbbbcbabbbacbaddcbdbbcbadcdabbbcbcdddcdbaccdbdcbcabacdabbabddbcdabdadddccaadddbbddacdddbcccadabcccbabdbcccaadaccbcabacdabcdcbccacacbcbcbaacbacddbabacdbccccacbbdabdccccddbadcbbddcdbaabddcdbdbccdcabbaddcbdbdbdababaabdabcbbbcdbcadccdbdcbacdababadbbddbaabcddbdcbacabaabcdaaabaacbaacccabbbccdabbadccbbbbdbadadadabbaacacdddabaaaabcbcbabbabadcacadbbdcabddcccdcccccaaababacbbddadccdaddabcdabdcbdbbaccdbbaabaacdadbaaaaacaddcbbacdcdaacbccacadcdcdbaacdcccbcccbdccbcdcbbccdaccdcbabbaabcacdcddaccdaaacbdbdbadaadcdaccdabcbdcbbadddbdbbcbcdcaabadcbaadcabbadccdbcdddabdaddcdcbcaccbdddbcdbcabbcdcdccbaabdaaacadddbdabbaddbdcabbcacbacdcacdacabacbddbddaccdbacccaacdacbabddaccacbcbcbbbcabdadbaaadddbdbddcaacbdcbaabacbcbbaddbdbbaaaacacbbccdacbbcccacbcdbcadadbdbcaabbdababbbaaacabacddcdadaacbdaddbcbcbbcabbcbddcaaccadbcddaaacaabcadadcbaccadbcbbabcbbcbcbcbccadacbbcbcdbddddbaccacaabcbccbbbabdbcddddacbaddbcdbbcdbbbdadabaadaabbccccabcbbaacadacdbbadcddbbccccddbcbbabadbbcbdabccabdccddcaaadcbabdadbcdaaabadadccdaabddaabdadddaabbbbdaadaaabbabdbddcaddbccacadccbcdcdcdcbcbbdbdacbbcdcbaaabcbcabbabccdddabbdaabcabdccbccbbcdccadcdbaccbdadcbdcadccdbacaacbabcbddacbadaabcaccdbcaabcbcdbaacadadddcdcbccccccdccaadcdcdbcaacadbabdadcbcdacbabddddadcbccbdabddbbcaaccaadcadddbcbabdaaaaacaabcdccadddbcaaaabcbdadddccccdabcbdadbdbdaadbbdcbbbcddcacacaccadacbcbbbcdbbccbcbacdcadbcadcabbdccddddbbcccdbabcabbdbbacdcccbdbaaccccdacbccaaaddcbdccaaccdbdcdccbcdcccdcdcadabbccbcccacdcbdacaabbddbaacccbdbdacbbdbcbdcdacbcbcadddbddcdcbaabdcaacdabcbbbddcacacbdcaacbddcdbbbdbaacadcadabdcbdccdaccddbcdcdbadcddcdcddacdbbabacdbadbadaadccabcbcbcbdabbdacdbbacccccbababbaddbcddacbdabcdcbdabcdacaccadacddbabcadccaacbbddccdcdabdadadcbbdbddbaacdbbbbdcbbcbddbccccbacabcbddbdabaddccbcdbbdbacddcdccbcbcbbcbcdaccdcbadbabdbdaaddcadccbcbcdcbddbdcdaadbdaabcadadbcdcaddabccccdaadcddadbdaadcbcbdcbabcacadadccbbbbddcdcabccdaabcbabdaadbdcdaddadbacccbaaabdbbdcaabccdabdacbadabacabcdcadabbdbbdacdcadcddabdabadccaaabbbbdaacbdadbdaccdabccbbdadcccaabcddcddbbaaacdbbadcacadbcdbdacdcbbdbcaacddcaabaadcaddabaacdabbbdbcccacdcccbcaddacbbdbaadcaccbacdcabccbdbabacdadcacbcdabbdbdddacdadabbccbbaccaadbaaacabdabbbaaccaddadbbbacabacaaabdbcaacdcdcbddbdbbccbbaacaccbbacaabacdadddccbcccaabcbdbbcadadcaaaacccdacccdcdddccbbbdcaaaddcabbcbadbaaabbacacdcdcaacddacaaadbcccbddbbaababdadbaabcccadabbbbbadbadccddacaaaccbcdccaabdcbcacddadcdbccbbcdcbdbdbabacbdcbbabaabbcbcbdcdbcabbcacbddbccccccddcaaadcabbbbacbdcbbaacadbcacaacaadacdbddacadacdcccaddcbbccaaaddcdcdccaddacaadccccdadcacadccbcddcbbbacccacabdbcbadccabbccccaadababaddddabdbbdcdbacabbbcbbbcbcccccdbcaaccbacccdbcaabdcdccbcdbdbbddababbccbbcbbdccbadddbcabddccacaadbabdabdabdaddcaddadbcccbcccbbdbadaadacbccabaadbaadcacabadcbbabaaadcdccdaddccbcaddcbbbaddadaacacbcbccbabcabddcdcccddcaddacdadabccdbdbddbbaaacbbccccccaaabaddabdcacadbddbbcbabccdaddbcadcdabcbabadbcbdadcccbdbbddbaabcabbbabdcccbaddaabacacbabcbdcddbadcbabdbcddccacbdbbabdbbcbbdbbabcdaddacdcadbadbdbdddacacabcbbbdacdbbbdcaaaabcccdcdadbdcbbacabdbbdbcabdaaacbdbbdbbaacaabbdbbdacdbcabcbbbdbbbcadaadddcbddcbbdcaddbcacbcacdbcbdddbaaabdbdabccddcdacaabcabcaabdccacbaacdcdddabddabdcaddcdabcdbdadcbccdabbcdbbccdcbdcbccdcaaaabddcbddcbdbcbbaaacaaaddbcacdbcbdcbccbbacddcbbccbdaabccdbacdcbbacdacadcbadcadadbbdabddbdadbadccdcbdabacbbdddcdddcaddccbadaadbbcdbccbabccdbbaabbbdbdadbacbccbcbdabddcddbddaaacddabbcacadcbbdcbcacdacaacbcdaccccaaaddbbbaaabadadacdbbdcdcaddddbacccabcbdcdacddcbcbdbcacaabdccdbbcbdbdccbabcdbdacccacbbbaccaacbbbddbccddabdbccdbcbddadddddcaadcddadaccadcaddacbababaadaabbddcccbbdbdacddcacdcadbdbbaabbaaadbbbdacccdcacacddcbdadcadcaadcdcdabcaacadaabbcacccababddadbccdacdacdbabbbdbbcccaabaddcadcbdcaadccaaabbccdacacdcadcbccaacbabbababaababbdaacddaaaccddcbacdabdcbacbbaaddaddbaaabbbbdbdcdbddcdcdccdccbccaabcabacbdbbcbabddbbacdabbcbbabcadddbccababdaabbddccbcdcbbbccccbabbdbcbdcdacddaddcaabddbdbdbbdacccbcadccdbdbdaabdcabdddcbdddcbcdaabacaabdaddddaabbabacbdbbbcdbbaadcbdaccdcbaaccabacddbadcdcaabdddaacadcdcdbacbddadbcaacbadbcdcbabcbaadbbcadccdcbacbbbabbcacacacdcddcbbddbdbbcbabdccacabaabcdaabababcadaaaabcaaabcbacddadddccdcddbbbbacaabccddadabbdbbddbdabaaaababccbdaacdbcadbaacacaccbcddabaababbaddcdabbdaabccdbdbabddcacabdaacddabadcddaadcbbbccccdaabacbcabcbcbdacbbbbcdddbdadcabdbbccccccbcddabcbdcabdbbdcddcaddcdbbdbbadbdbdbadcdcbbcbccbaaddddadcdcddbcbabcbacdddddcccadbcadcccbdbcdacddccbbddddadbdccaddbdbbbcbdccdbdcddadacdddbbbdaccaacddacacbdbdaacbdaccaccdacbbdadbbbabbbcbadccccddcbdbadcbccaddbcacddabdddbccadcccbcaabcddbccdcbbcdcbbcdbddbddcdaacbcdbacbcaacdaabcccbadccbdcbabbdcddcaaabddddaadacbdbdcdcbadababbadacbcbdcccabadcccbbcdbddaacacbacaadcdaaabacbaccdddcdcdaaabcbabaddabdacdbddadacbcbcccbaadddadcaadacaabdbdbbdadbbcdaacbabbbadbdccbdadcdcdbccaacaaabadccbcaaacbccbcaabddcaacdaabaccddddadddadabdadacacdacbdbcbadcabcccbdddcbbcdcbccbbacddaabadadacdcabbdbaadbdaddabacdddcbaccdcbabaddcbdabcaccbacccadadaababaababbdbbdcdaabcdbdadccccabbccbdabddcaacbcdddbadadadacdcbccddaabbaccdbcbdacdbadaddbbccbdbbcaacbaccdbbabbbddbabccddcabcaacccccabaddcbaddabcdacaabdcbcdddcccaabdabccdababcabbcbaadbabcccbdaccacbccaacbaadbcdbbcbcbabccbcbcbbdddcddbccdcbdacdbddbbacccbbaadacdabaabbbdccaccdcaddcdadadbdbbadbddccaabdabadcacabdaaacbacabaacacacadccadabbcbaacbcabaddcbacacacbbdaddcdcdaaaaaaaccbddacbddcdcdbbdadaacddbabadbdbcdcdacdcdcbbccbcccbcacadcdcabaddbdadbdadaaccbcdacbacbbbdbdcbdaadddaadbbbabbcbaadadabbadbbccdabcbccacdccbaddbabcdddacbadbdadbbcadcabcbbaabcbadabcbbcdbcbbcbdcbacbabbcacacbdaabbbcdcdaaacabbadabbdbbbdccccdcdacdadbcdbbbaabdbdbabaadcbcdaccbbcbbcdbbcbdabcaddbdabbdddacabcacaaababdccddaaacccbcbcccdbbacdbdabcdcccbbcbbdaaabbaaabadacbaddbddccbaaaccabcadbabddcddadddacdacddbcbbdbcacbdccbcddcbcbccbdbdbcbcabbbdddddbacdbbaabadbbbbaddacbbbaabcacadbcadabdbaddddadccbcaaaabcacbbdbbcaacdaccbddbccbbbccaabbdacdaaccbaabbcdbbddabacaddadababaabdbcbbdddddbdcdbbcbdadaaabccababbcdacccbbcadcaacdccdbccbdabacdbbcddbcddabddacbccbbadacbbaddacbcbccbaaacdbcbbabbcdadaaddddaadaabdcdbaadddbcdbadabbadaabccacccadbcbacbcdbdccbbabccdccccadcbdaddcbbdbccaccaaaadcadaadcdcdccdbccdacdcaacbcacaadabdcbacdcbbdaabbadccaabbdabaddbdcbabcadaacababccaccdbbabacdcdccddbacccbdbccaaadbbdbacbbabcccacccbddbcccacbacbdabacdcbcaaddccdddaccbaaacdcdcdbdcbdcdacadababadccdaddabbadbdbcdadccaaaacaccaacccccbbacbdcaadccbdbcdadcbcbbdddabcacaaccadcbbbdbbcdbaabbdcbdbbacbbdbbadccdbacbcdcacbbacbbcddcaadcdaddbcddadcadaacdbacdbdaddcddabadaaddaadbbcaddddbcaddbccbccdcadbaccaabbbcccbacdbccdaadbadbadacabcbcdccaddcabbbdddaabccccbaddcbddbdbabbcadbbabbaabbadccdabdabdadbbccabbdbddaabddcbabbbcadacddaccdbbdcdbcacbcbdadbaddabcaadccadaacaccaaddbdbcbcdccddddccdcaccbaadadbbcccaddadbccdbcbbbdbcaabccacccccdcadbaabadaaddaabdacbaacdaabdbccdaccabcbbbcdbadcccdbbdcddcaaccccadccbaabbccaaabbacdccbdcaccdbaaabdbcccadcaabaddaabddbacddcccddbaddcabddbcaddbddccaddbccbaababaabdcddcabbacbcdbccddcbadbabbdbbdbdcbaadadbaccaabcbbdabdccaaadaaddbdcccbddabcbdabbccdaadcadaabaaaaacdabdcaccadbccdcdcadccbcaaabdddcdadadcbbbdaadbaabddcdaabcdaacabccaaacdccbcbbbaabbaccabdcccdbaddcdbaddaddcdbbaadaabddbcdccacbcbacdaacbddacdcccbbdddccababadbbdcabcbaacadaaddcdcbadccdcbddaabddadadacdbbdcbdbadbaababccaababdabcbcbbdccbaaccddadcbdaacccdbcdcaaaacccddcaabddbbdadaadbbdbbcbbcbdbddaaadabbbdabbbdacdbdadbbddbbcddaddbcdbcdcddbcacccaadacdbbcaddabdaddcaaddbacbacdbaaddccaccbdadcadbccdbccaacdbbcddabacccbacbbbadcacdcddcdccbacddaabbbaadabbbaaccbcbabaadbadddbcaaabbbbcabbbdcdcdcddcdcadccaddddababdbbcbdaaccaabbbbbbdadacbaabbdadcadcdbddcbadccabaadaaabdbabddccdcdccbbbcacdddddddcabddadacbdcccccbcbaacbcacdadbadadbbdaaabbdbddbbcbccaaabbaabddabacccacdbbabccdadbadabcdccbddbddbbdbaabccacbdcbbdbdbbacbbcbdaabbdaadbabddabaaadbcddcbcadaabbbcdcacddcdcbcccdabababaaddcdacaaadbaaadccbacdababaaaabaaabcdbccdccbbdaadbbddcbcbbbbcabaabdbbbcbcbccdadccbccdaacdddbdbabcaabcadcdbaddadcacdcacacbacaccddaacbdddbaacadccbadddbcbcbaddbadbbddccdbcdcaaacddbdaccaacbaabcbbdcabaacbcdaabbaddbbdccbcdcbbadbdccccabacbbabbbdbdcbabcabaabbdabdcaddaabdcdbbbccbbdacbbbabdcadccdbbabadaddbcacbdacbddcccccdbaacdbbcabdaadcbbddddcbdabbcbaabbdbbacdccdbbbdaaddbdaacbbcdcacccabbcbbdddbcabaaaadbcdabacadbaaacdaadadabdacbbddcdcabbbdbabcbcdbdbcaacababbccbdacdbcbcbadbbacccdbbbdccdaadbabacabbdccbabbabbdcbddddaccdbbcdcdcdddcacbcdcccdbbcdbcdcdbccdddcadcdacddcaaadbcabaaaaabcadbccadbccacbbcaaadcdcaddbabdcbddaddbdccdbdcbbaacbaddccbcdbabbccabdbbbdadcdcdbcababaaadccaaddcdcdadacbabcbdacdccabbcaabcaadaadbdccdddbbadcccbdddaddcbcddddbddbbbdbaacadddcacdbabacdbcdcdddbcabcbbdbabdcabadaadaaccadccadabadccdabaacbbaadcdaacadcdbdbbabcadbbaacadcdccbaddcaaacccabacbbacaabbaadaabaabcbbdbccbdddbcbcdaddbabaadbbaadccccbbbaddbdbbadbddadbcbcbbcaddabddabcadcacaabdcbddacbbaddccaccaabbbddbbdcbabbdcaadcbbbadaaadabadbdbdacdabcdbcdabbbdaadcccdabbbccbaccbcccabdbadbaadbbbbdcabdbbbdadcbbcaabddcbabacacbbddacaadcbdbaabdaddcbddcbaddbcdaabacdaadccbcbbacabbaadbabbabdaddadbcbacbdbdcaadadbcdbbbdddbcdcdccccbbbdcaadcbbcbdbaccabcbbbaacacabaaacccbadbabbadaabaaaaaadbdcababbcbbcadbcbbbcbbaddccaddbccbcaaaddcabbddaddbadabadadbaabbaaabadcbbacdccdaccdabadddaddabdcbabcacbaccdcbdcdddbacdcccbccdcdbcabdadadcaacdababdddadaccbacbcbddbbabadccadbbbaabbcdcabcadcbbcdbabccacbbabcdcabbbabdcdcdcdddcbdbbbdacdbdadbaddadcdaaadaadbbabdbcbcbbcdaadbdaacabcddddcbdbaadcbbcdcbcdbdabcbcbcacbddbbadbaabcbcbdbacdbaacddcaaccddbdadcbacdbbcaadcbacbaabddacdaacaabcbabbbabbcccdcdadbbcbabcdcaaadbcabbabddccdbbbcddcbcbdabbcaaddcccaabbcbccbabddbabacaadcbbdddddddcccbcbbccacbacddbcaacadaabcbddadbcadcaabcdadddacdbbdccdbdccdbcaadadabdabdbbbaabcdcbaaabdbdcaccddabcaadadcacdddaaaadbacadddccccbbadcaadacddbbbacbacacdcaacaccbdcbacbbccdabddbcabcbcadadbcaaaddbcccbbdbbdbcdcaccabbbccabcaaadaabbccabcacabaadcbbdbdaaadabddbadcbbadabdabcdcaadbbdddadbccbbccbddbabddbbdacdcbccdcccdabadaadcdddddbadbccddbaaddbbdcaadddbdcadcdacabbbabbbcbadaabdccbbddbbbcddcdbddccbdbbdddaaccbdaccdcabdadbadcabbacbccadbdbaacbdbdaacaaddaacbdbaacbdcbabdaaddaccccdabaccabaaabaabbccddbcbcdbdbdbbdcabcacaacbbbbddcbcaccccadacdddcacbdaaccbbccabcabdaabaadabccacadcbaadccbabdbbabdbaacaccaacacbcccbcddbadaaaccaaaddbaadbcbbddcdcabbcadbcbcadaabadcaabbdbaccbcbdadaabdcbcdabadddddabcbcbbbccddaadcbdcddabbbaaadbdbdababdbcbcdaddaadccaaccdcbbaddabdbcdcdaabcbacbaaabbbdbccbdacccabadbddcacbabddadcdccdbcbbcccbadbdaaddcbbacbdcdcacddcbbbdccaccbaacbdddbaadaaccbabacdccaabadadbbcbaddcbbdacaddbabcaddbcdcaadcabddcbccadddcdaaaddcccaddadbdbababcababcaadbbcaabdbbddabdcbbcaaaabccbcccdddccbcdccdacbdcacdbbbddbccbbbdabccbbdcbabaccbcdbddbbdaaabcdaddbacddaadadbbacbdbbcbcbcdbcdbbacbaddddcabbbcabcdaabbbcdabbcaabddcdbcddccaaacdaaabbbabdcaaddcccdbbccdddbddabdcacbcbcbcbdcdbbadbbabbbdaaadcadbcbaccdcadadbcbdddddaccbbbbcacaabcabaadcbdaadcbcbbcdddcabbaaccadddbbadabcdadaaaaadbbcbbdbbadccbbacddadcadcccccadcdbdcccaacbbbbdabdaaadbdcadbdbaadcbadaaddbdbccacadaddaaaabaadcccbadadadcaccddadccdcbbadddbcbcbddbbabddddadaadbccbcbdabddbbcdacdaaddbadbbbdcbdadbdabccabaddccbcbbdadacccacddadcbdbadaccdcadaabdbbccbababdacbcdddddaccdbadcbabadbadddccabbadbdadbbbbcbcaaacabcacabcbccccbbcccadbddabcadbabbabcbbbabcbcdaabdadadcbcaababaaabbbbccadcdaabdddcaacaccaaaabbdcaaaacbbacdcdcdbdbdadbaabaacaccbdcdbcdabccdcdbcdacbdcaadbdbbcabbccaadbdcdbadcdbdbaacbdaaccaaddaabcddaadddabcbdbacadbccbaadacbdabbadacccacadcbddccaddabadddbacbabbdbbbcbbbbddcacdcddabddddababcccadbaaadccbbdcbdabadbcadcdccacbdbbdbaacdcaddacddcbbdddabacdcadddbbcdacdadabdabadadcaabccacdcadccdbdcdaaabcbacacbbcbbddddcababcbcbddbdcbadcbdaddbcbcdcdaabcbbabcbcbdaccbcbbcbcbbabcccabbaaacbdccccadababbbadadabdbbcbcbbbddbabcccbcddbadaddacddcbabadcacbacaaabdaacdbacbcaddcbdddbdcdccbbcadccbbbabacadadadabdbcdddbbcccbbcbaddcccabdaaadadbbcacbaacbabbacbcabdcaabcacacaadacaabdbbddbaaaccabbbaddcbabbdcacaadbbcabdbdbddbcddbdbdcaccdbdbddadaddcaabbdaadbdccccabbcdddaccbabcdbdcdbddabdcbacbaaacaadbcbdbdcdddaaadddcabdcbabbbdabaaabcabdcbaddaadcaaabcdacbadabbbbbcadcadabbbbcbdccbdddbcbcbacdddcaaabcaabbadbadbddbdbaadcccaadbbcccadacdcacdaccdbcdbcabddbabacccbdcbdaadbccddcddabbdbabbdcabbbddcaacabcaddadcbcbdacdaaddcdcccbcacadbadcdbdabdbaacbdddbbdabccbaaaadbbdbadadcbdbdccbabbcabbdbdbcdddaaabacdbababbaccaacbcdabcbaccaacbcbadcabdbcddadbcacabbcbcacdaaddaaaaddcabcacdcaaaacbbdadbbbbbcbbbdccaccaaabcabdbbabbbdcddbcaddbabcacadbabbbadbdbcdddaacadbdccccdacdcabbdddbccabcccacabbcacbcbabcbdcdbacccaaccccddbdbdabbcbadccabadcdcddabcabababcbdbacddbaddcbacacbcaabccbdccddddaadacabdacdbabbabbddcadaabcccbacadbbcdcbcdbcddacabcdacbacdabadcacacabddcbabcadcbbbdddbcacacbbbbbdaabcadabbabdddaddcdbacbaadbdabbbbaadaacabdccdbddbacaccddcacadcbbddcbabbcaacdacdcdddaddccbadadcbdabbccadadcccbdcabccccadddcacbacabcdbaadacdabccdcbadadbcaadaaaccbcaccdadadadcaaaaababbdcaabcaacccbbbddcdcbabdcbbddcadabddbbcdbdbddbaccbaddbaadacdbbabaccbadbacbbbaddadaaadbabbbddcdacdaabddccaddcdbcaccbaccdadcddbcabbccacdccdadabddaaccdcdacbabaaabdddbdababdabdbbabcbbbaacbbbdbdacddbdbbbdacadacaaadbcddbbabdbaabcdbcdadcdbdcabcdbbdabddcdbbcadbccbdcbacbcbaaabcdaccbbddcaacadaadcbbcaadbdcacdadddbaaadbbaddbcaacbdccababbadcdadabbbbcacddcbdccdbcbdacbbabacdccaadcbcbaccbbacaddcbaaacdcadabbbbcdacadbbdacbbaadacbbaaacbdabbddaadbadaaadcdacaabacdbabcbddbbcbdbdcddabbccbbdcbdbccbbbcdadcdcdcbdabcbaadbdbdcccaaccbadcdcdcacacbbadcdbbcbcccbbcacaccadccaaacacbdaabadbcdbabccdcbbdadcbaadcbbcbacbbbaabacdacadcdacdbcddcabcabddbccbbcacccbbaadaddabbccacdaaaaacdbdacacdbbcdbcbdccbdddaaabbdcddacbdaadbcaabacddadaabcbbdcbcbccaabcaadcbcddbccbadbdacdcabadbbbacaaabbcbdcdbbabadcbccbbddaadcbcbddbcacbddaccddaabbcaaaadcabbaabaddacadcdddabcdbddcaabbcdbbcddbdaddbbcddcbcabcbadddaccabadccabbcdbbadaabcaabcacbdcbddcbdbdabcccdbbabcacabdddcaccdccabdcbaccbaabcaccccaadadabccdbbabaaaadbccbbdcbacbdbdabbddccdaadbabaaadbdbbbbbaabddccacaaddddaaadaabbbbaccbbbdadcadbdbbbacbaaabbacddcabbcdcbbbabdddacaaaabcdcadcdaddbdabbadbcadcbbdadadcacccacaaacbaacbdacabcabcdcbaddcacdadbbcdacaaadbdcddcabbadcbabcdddbdaccccdccbbbcacaaccccadabcbdbcdacbccccdccacdbdaddaadddcdbdabdddadacdbbadaccdcadbaddabcbacbbbcacddddadbcbcdadddbdacbbadbcdcbcbcddbdbaabcbbcbdabbcbaaadaaddcccacacdcabbcbbdabaababcdbdbaaadbadaabcbdabcdcdbaaadddaccbabdacabdccdccccaacabbaddccbbcbabbbabbbbaadbbdddccdcdaababdcbcaddcaddbbabcccdaaadbcabdcacaaacadacdbdabbbadddbcbbdaccdbcbacaacdbccaaacbaadcdacbcbaddbcacacbcdcccdaddacccdccdbccaadadddbcccaccadabbdbabacdaddbdbcddaadacadaadcdabaadcabcddabdcadbbaadbabbbacbdbcdbdbaaaacadcdabaabcbccbcdbadadbacdbacdcbbababbddbbabcbaaaddcacdaacdadbbcbcbdbbcdbcbcbcdcbdbaddaadbddbdbacababdababdacdcbabbdabbdbbabacccccbcabdaaaccdadbccccdbbddddaabbbcdabdaddddcbbcacabadbccdcccadbbbdcbacbbcbabcdbdcabadabcacdabaacccbaccacddcaccdaadbacddacdbcbddadcacccadccbcabbbbdbadcdccdcdbddadaacaccbacaddcbddabacdbdacbabccadaadadcabdacddacbccdbdaddabdccbdddbdaadaddcbaddcacbcbabcbbadabcbddaaabdacadbdcbaaaccccabacbdbcdbcabddcaaadaacdaabcabcccaaaaaaadddacddabdbaddcaddbaaddadbbccbcaabdcdbaccbbcaccbaacdcddcbbadacbdaccabbdaabddcdbdcdaacbababacdbaccbbbdaaadcdbcdddbccbdacaddacbbacdbbaacdcbabaccdadadaadbdcccacbacaaadbcdabacabcaaabccdcbacddabdccdcbacddbcbdabddbdddadddaccadddaaadbaccaaddccdcaccdbddaaaadaaabdccbccdbdcbabcbddabdbdcadbdbccbaddcddccccdbddccccbbabddbcadaccdcaabdcabdcccbbacaabbcbdbcadbcdbdccabdaabdcabaddacbcbacbadccbbcddcdaacdcbcddaaabcacdaaccdcccdcdbadbbbbcabdacabbbdbcabdcdcddcabcbabbcacbbddcdadbbbcbadbddcadaaaaabadcaacbbbdcbadabacbdadadddbdadbbcdccdcddbbcaabadbccacbdbdbcdbbcaadbdcacdccabbccacccbdacdbadaaaaddbbacdcbdbbcacaabbbdadbcabadbbbcbcbdacaccdbcbccccddcdbacddccaddaabddcababaddabbddadaddccaadddcabbcddaddddcaaddadcabdbaacdaaacdbadacddbbcacdccdbabcabbdcddbabbacddadaabcadbacacdbdabaacdcbbdccbbdbdadcdbccbbdacbbadacddabddabbabdbccdbaadddaacccdddcabaabaddcabbadadadcadabbbbacbdacaabcddbddbbdbcddcdbcaccbabcadadcadaddabbddbccbccbdcbddccddbabddadcdbbbcdcbccccaabbdbacaaacaddbbbbccccbccdbaddaabcbbadcdaddadddbddaaadbcbadbcbbaccaabdbbddcdbabddacabadabcbcddcdbbaadabccaccdbacdcdcccdacabdabdaacdbcabdcdcaccdaacbabbbcaabddacbdbbddbbbbbddbbccdcbccbcdccbdaadbbdcdbbdaabbcbcdacbbcddcbabdcdcddabacaaadaaaadaacadbddbcadcbadbcdcbbacdadbbaadbbacaadbddbabcdcbccbddbccabcadddcacbccbabababcacddacaccacddbdbbdbccccdcddaaaaacaadadbdababbdcaadcbcdbcadbdcdbbbacaaddaacddaaaaddbaabadddcabdabdbacdbbdaddaadbbccdabcdabbcbcabbcddadccdacdabadcddabdcdbdadbaacbdbccabbaacdcacccbcaacbdacabadcbdbaaaaadacdabacbbcdcacbcbbbcbdbcbcdbcddcdbbccbdbdcdcdcabdbbcbcaaaaabddcaaadcbdbabcddbbbaabdcabbaadabdaccbdaccccadaddcdccddaabdddcddbdacbcbbdbdcdddccaabddbdbabbbbaaaddcaabbaaccbadacdaacacacabdddcbdaacddabddddaacbbcacabdaaccbacbcbcacdacbcadbacbbaadddddcadcddbcdacbcdaccddadaaabbbacddbbdbaacbbaacacdcbcddcdbcddbdbdabddaddbdaaaccdbdacbacddaddadabcdcdddaddbcadabaaddcccccccacbabddcbdaadaaaadccabccdcddacdaccadbbbdadcddadacadaacbdbcbdddccdbadcddaddbbdabbcacbdddacdbacbcdcabcadccbdbcdcdbdbabbddcadbbcbddaacabbadbbdbbbdcadcbbcbbaddbbcdaddcaadbccacdbdcaccabccbdacccadcaddbbbdadcbcacbdadbacdbdbdabdbcccadcaaabaabdbabddabbadcbdcbbacdbbaacdbcdbbcccaaaadbccabbbbdbddadcddcbabcbadcdabdbccdabbbdbadbabaadacddcccbcbdddcddaabcbbacdaccbbccdccababcddcdbcbbadbaccbbacabccdadcdaaaadacaacaaccaccabaaccdddacdadabccbcbacacaadcdaadaacdcbaacaacccadbbccabdacaaadbbcadbcaaabbccadacbacacadcadccaaccccbabbdadaababccbddcdcbddadccddabcabaacbbbbcccdcccadacdbdcddcbabaddccdbcbcbbbadddacdadbdbddaacdccccdcdcacdccaabccaadbaaadadcadcbccacaabbcdbcdcdaddadbcbccbddcacdddaddbcdaadcbcdcbdddbbddbaabdcadaaccacbcdaabdcbbacaacdadcddddddbaaabcadccdadbcdddaddbccbaccabcbdbababbaccacdbbdbbcbaacadbacdbabbbbccaabaabbbacbbbaabbdccbcdcbabdabcbdcadbaaaacdaacbbacabbcabdcbabbcadcbbbaabddabcbbdbdacabacbcabccbbdadbbbabcdddababccbcdacbdaccccbbcdacbdccbacbbbaaddacddcbaabcbcaababdcddadacbdccaabacdccacbbbcacccbdbcdddcddadcccdcbadadccadbdadcacaaddcacdccdbcaddbddababbdcbabadcaccdcbbcacddbcbcaadcddacddbcdbadcdaabaaaacaccacacdbacdddaddacbbaddddaabdaadacacbdccbdbabbcabaddcbdbbbbabccdcccbbbacbacddbdbcccccbaaacdacbbdbccabdaabbacaddabcddbbacababcccbddadbcababbcccdcdbcdadbcdbacbcdaabdbaabadbccdcdcaadaddbddcadbcaaadbadacacccaddccadbbcdbdbdbdacdbdaabcbacbdadacbcbaabdbabaacbddcddcdbbbbbadacbcabdcdbdabcababcbadbccaabacdbbabcccaddcbbddacabbccbbbcdcdaaaccdcdccadbddcbddddadcccccbabdccadcbbddaacacddaccccbcadddbcadaaccaaabcbadccbccadccacbbdadbbcbcaabaaaacdbbbbbbddddcacbdacaaacddcacbdcabcbcccaabcbcdabdbcddbdbcbcccdbdcbacddbdacccadddbdababdaabbdaabaadadadbdcadbbaabcaaabbacacadaabccbacadbcabaccbaddcabcdbcaaddabdcdcadacbbcdabdbccdbcaccbddcdaadccbcdbdabcdaabbbbadcddbacbcbdbdaaaaacaabbcabcdbaaacdaabaaacaabbadbdccbaccacccaacaabaabaccabacbaccdbcaaadbadadacbbabccdbacacdccddacbaaaaaddbcdbaadbbacbaaaaddcaabdccacbadbdbccadacbdbdddcbadaabccdcaadacddcacdbabacbbdbabbaddcdcbbabcbdcaabbcdcddadddbabcbabbbaddbdcbbdcdbadbcbcddbabcbacddadbdaabdcabdbbaddbdcbacacccdacbcbabadccadacaacbbadbbbabcbbcbbdadcbbaaacddaaabcaccaabaabbdadbdcadbdabbdddadbbbbbccbdcadbddbddddbcabddadbdbcdddbcbcbaaaaaadcabdacddaccccbccbacabbaadaadccccaaadbacacaacbbaabdddaaccbdccdbccabacbcaadaddadbabaccdccabbcccaadcbdbbcbcaabcbbcbbdcaababdbbdddddbabccadcdbccbacdabbbdaabcdaabbacdcccadababacaddcdcbaccccccaabbcbacbcdbdddacdcccbddbbcdaabdcdddcbbcbcbbddccaccaaacddccdaabcbccdacddbacadccdcddbcddbaaddbbbbbabacddadddddddddabdabbcbbcabbadaddddadbadaadbcabbbdccbacbddbbdcaadacbdabddddadadbdaabdcbdabcdbdbaddccdcccaaaabbdacdbdcbdcbdccbcadddaadddbbabbcadcadabbaddaaabbacbcbbddcadaadddadcbacdcdcbccacddcdaaabbbadbdabdbbddddabcbbdddadbabdcbadabcabaaccaacdcbcabcbcabcbbacbdaaddbbdccddbadaaddacabcadacbdaddcdbdadadabcbcabaddacaabaccdddbaabacbcbadcdccabaadaacbcbcdacdbddaacacdbcddacdccdbcaaaddbcbacdcdcabbcabcdccbbdbaccbddacddbddadddbdcdddaabbcddacccbcdcbcdcacbdabdabaadaccbcadbdbacbcdcbbbcdcdcdbcbdbbaacacbcabaacdcaddaabbdcbdbbaacabcbcaabadacdcbccbdcadbbdadbaacdbacccbdcccaadbdadadadaccdbbbcbbacbcacacdcdccbacbcccdcccaadacbbdabcddcddbdddbbcbdcaadbabbcbaaddacabcccbbabaccbbaddcbaacaddcabdaacdccbbcaddcdcacddbbaccbaabaabdccacbcbdddacadcaaccbdbcaaaaddcaaadaaacccccddcacddadddbcdadabacacbcddcaabbadddaaaacdcaabdccddabbacdaddcddbbcbbcbbbbcbabaaaccdbbbacaabdbdbdbbaabadbacdbabcdcbddabcbcbbbaccddabbadcdaaadbcadacdbaccbbacdabbaddbacbbacbdccacddddaabadbcdbcdacaccbaddcbddcaaadddadaaadadbdcaaaccacbcddacabbccbddcbaaabccabdaabbcdbaabbcbabadadcdabbaacacdababdcacadcddaaabccdccbbdddcdaabbdbacccdbbcccdaaacddaadbbbddcccccadddccccadbbbbdaacdadabbdbcdbdadabbbdddccdbacdccddbccaccaccaadbcdbaddabbbbcbdccdbdbadabcbbcadccadbacdabbbabcbcbbccbdbbddaabdccdadacbbcbbaabddbaaccaacdbcdbaacbdddcbdabcacdddbacdbcdbcbddabacdaddbcccbcadbbdcbbabdbdcdbdbccbbcdcadaadbdcadabdaddcccccacdabccabdbccadcadcdabcbaabdacbdabccdbbbcbbcdbaacdbcabcddbaccddadaadbcbdcdacbbccbacdcaadcccdbacdbddadbdbbdbdaacdbaadbababdadaddbaaddaabdcddbcabdbacdcddadddccdadacdbbdcdacabcdccdabddccbccbabbdbcabbdcdcdaaadacaddddaddadbddaccbcbabbbcdbaddddbaccbcbbaaaabbcbdcbacbaaabaddcdddcbdcddcabcbdadbbacbacaaabdaacbbacaadcaaacdbcdcaadcbdcddddcbbdcbddacdbddbabaddbbabdbddbbcbbdadbbcddbcdbddaaaddcdabdbbcacaccbddbbdaddcbcdaacddbacbbbddbcdcdddbddcddbbcdabcbbaaccacbacdbadcbbaaabdbadcbaccdaddbacaaadcadadbadbcccacacbbdcdbdbbdbabaabcabbaccabbdacabaadbdccddadadadaaccaabbaddbbbccadccaadccaaaaababddbbbbbbcdacaddabacbabcadcabcbbaabccbddbdcaadcbcbabdbbaacdbddbcbbacabbcccacabbbacddcbddaccdcadaadababddcaaaccaddacbaaadddacaaaaaadbdaccbaaaacacaacbabbbaacbbdabdddababbcbadacccaabcabdccddcdabdaddadabacbabcbdccccbbaadacccadadabddbbcbbadcbcdbbbbbccaddcdaacdaabaabaadddbdabbcacdbaaacbcaaacccdbcbdaacadbcccbabaaadddabacaacdacadbacddcabbbabcbabbdacbbabaadbbddbccacddbdcbaabbbdcdcbabcdbbddccdbdcadcccbbacaaaadcdabadbdbadabbbbccbacbdcadabbccccdbbbdccbdaadbabbabdbccabaabdccbacabcacdacacdbbbacdcbbcdccbccabcaaaadbabbdcbbcadbdcbcabbdcbadddaaabcdddccbbacbcaaabbdcadbdbacdcadbcbcbbaddaccbaabddaadccdacadaccacaaccacbabddbcbbbadbdccaabccbbdbcdcddcdbbacddbabbbdccadcbcdccdbbdccaccdabdcbbcbaabbdaddccbabcdcdcdbddcccbcbcadcdcbdccdacbdaccbbdaacccdacddcadadbadbaadbbdacbcdadbacdbacbadadcdddbccbbccdaadbcdbcbdccbacbdddcbccabaabcbaabcaccaddacadcddccbddaacdbdabaccbcacadbccccacacdaccddcacadcabbabccaacdbccccddaabbccbabbbbddacbbdabadaaaadaabdcddbdaadcbccaacdcdacadcbacadddbdbbbbaacccabccaadddabbabdcaadcaaddbbcabbababbbacdcdabdcbbcaadcbdaddaadcbdabbdbdcbaabbbbbcacdbcbaabbcbccdbaccaddccaddbdbcaabdbbdabcdabcadaaddcdadaabbbccdadbdababccadbddcdadccbbabbaacabcdbcdbbbbdbbbaaaacdabacacadcdadcdcbdcbdbbdbdacbbaabaabcdcbdcbabbbddbbdbaddbadabacdaadbdaacadbbaddacbabbacccabaacaadbdabcabddacbbbcdcccddbcabbdcaccccdbcbaacbddadcbabdbddcddacbcacbdccdbcccbcabcdcbcbddadddbbbcacdbccbcaccbbadbddcbbcddadaadbadddbaaaddbccdbbddbddbcdabcbacacabdbcacdccbdadabaaacaaaacdaccccacddacaddbbdacabdbbaadacabbcbacbdbdbadaadbcdacbdaabdaabacdabdbbacdddacbadacadacdbdbaccbacdcabdbcddadbdaaaaacdbcccbbbaacacbbadccbbbccdbcdccddacdcdcbbdddadbaabbcbbccadddcabcdbcdbdabddacdadcccacadbabcbdcbbbbdadddbbbdcdccdaccccbbbdcdadcbacdcdddaddaaddbbaccbcabbbdaacddcbbdbcbdaccbaaaabaacdcabbabaaddbbdacbddbbbcabbbdadacabdbddcbcddcccaadddadaaabcdcdabbbaccaddbaabbbbaabbadabdbccdadacbddbcaddcaabddbbcabaccadbaacbcadaddbacbdaadbbadcbcccbbcbbcaabcaaadcdcddcbacaddbbdbccccbacadbbccdcbddbbcaaaccbcdadacaaabbadccddccadbbabdababcccddbaaacbacdcdcabcaabbabcdddbdbbcbababcacbaabcbbbaddcdbbaacbbbcccbaaaabaabdcddadbddddddaaadcccccaadbbcacacdcbdbcaaadcaaddbbbacbabdbbcaccccddbdbddbbacccacacaabacbdcbdcbcababcbabcaaaddbbcdaaaccabdccadacacdacbbdabacabddadccbbabcbbccddcdcadbdbbbdbdacdabdbddcdadbacadbdcabddcccbaacdadbcaabacddadcabcddccaadcacaacdddcdddaaaccdababacddbbabbaabbbdcabdcadaaadcdadcaccbdbabdacccccaabcbcbadbcbbcbbcdddcacbdcbacdddadacdcdadadcbdbdadabbaaacdacaadaaacddcaabaaddcdcdaaaadcccdddcabbbdbbaadabaaadbdcbcddbcbdabcacbbcbdcbdcdbcaddbacbbbbbabcccbbacbcdbcbacaaabccbacdaaaddadadddcdbbdcdcadcdbbbdcccdacabdaddcdbddcaaaaabbaddbdaaddaabbdcdbdcccbcccaddddacbabadabacdcdcbdabbddabdbdaaccbaddcbacaddbddaddccacdbbadbcbaccaacbbdcacbbcbbadabbbccbabcacccdabaacdbccdaadcabdddbbddaadcccadbbcdbadaccbdaaddadcbcbdccdbbdbbaaaabdcaadadcdbadabbcabacccddddcbdbbcbcabbbcdabacbdbdabbbabdcadcabccaababdacabbbbdbcccabdcddaccacadddaabdacacbbbacbbaddddcadcdaaccbacdbabdacacdbaaabcdacbaacadcbaacdaabcbdbccabccbacaaaddbddbbdccacaabbdcbbbdcccadacacdacdbdbadcdbaabcacbccbccbbddadbcaadbbbbbccddbdcddccbbbbcdccdacbccdbadbabcbadddbdaacbadbccadccabaacaabcacdaabaddadcbcbccdacddcccdcacdddbbbcbdcdadabbdddbabbbaabbcbaacdcacabddbdbbabddcbdcdbdbdaabbccdccdcbcbdaabcadbcaccdabacdcbbadbddabbcdbdccbccbaaacdddcbdaabcbcbabdccabbcbabcdbbcabcaadadaddddcddbaadcbcacbbbbabaccdadabdbaaabbbadaadadabccdbcabbbbcccbddcbbbccababddacabaabaacacbdbacaaadcdcdaabdbdccaadcdddbdbcaddccddbdbcccbbcbacbdcaabbdadcdacdbaabbbbbaabdbbbbadcbcdcaadbadcabdcbadccaababcacacdadaccaadaadcbcacaacaccdadddacbbbbbbdcddbbbbddbbbbddbbacbcadbbbdcddaadadbbadcbbaacbcdbcbadababbbbccdcbdacccadaaaddcbaabcdbdbdbcdabddccdbbbcacacbadbbdadcacdddaadacdbdddaddcadccdbbcdccdcccbdbcabbcdddaabdcbbadbadacadbbbdcccccdbddbdabbdcbabdcabababdddddabcdabcbdddddbcaaacacdbcbbbbdddbabbacbdbdddaadaabbccacbdcabdabadbdadbdbbdabdbbdaddbbdcccacdcaadbdbdddcbabdaabcddbaadcacbaaddcbdbdcbcabbbbdcbcdbccacbbcadcbdbdabcbbdcbbccdacdbbacabcddbbcdddbacdadccbdccabdccbddcdcbacdacccbccadbcdacadcacdaabcdaaabdddabaccacacadabcdbdaccdcbdcddccccdbbcbcddabbbdbbcdcaacccaddcdaddcaccbbaabcbddcbbbaaabaaccbddcbddabcbabaddcddaacabdbaabaccdbddabddcbcbabccbddccdbdbdabcacabbbbdbddbacbdaadbbccbbdadabcddbaaadacaaddaadcdaabccdcbbdcadabbbacaccccbddadabbcadbcaacbcbdcaacdbccdddccdaadabcdcacabacabacdcbbbadcabccacbbacabcdcabacadddddbddadbbdaddbbddadabdbbcbbddddabdbdaddaaaadccacaaddbdcccabadbbcccabccabbddbdccabddcbbabcadcdcdbbddbddbbbbaacaacabbddbbaccdbcdacaabdbaccccbcdaccdabacccccabcaaaccdccdbbacbacbcbaddccdcdcdaaabacdabdadbacdabccbcabaabdbccaadcabdbbddcbbbcdccacabbbbbdcddcdacabadcaadbdcbbbaacbaabaacaaadccdbabdadccbcdaadaabdcaabdbabdbcbbcacabaccabcdcaadadcacbdaabdbaddddadcaacaddddcaaccbadabbdddcbdabcacbacbbaababacdcbddcdcccabcabccdcdbccbcadcbbcaacbbcadcddcdccbbcbcbbcdbbccbcbdaadaaabcbccabbaddabdcddabbaccdddadadcabdbcdbacdbcaadadbdccaccdbdbabcdadddcabacabcaaabcdcddaabaabadaacdbaccbccccddddbbbcaddbbaaaadbbddcbababdaddcddddacaddacbdddadcaabdacadccacdbbcdadbddbabadabaacdcbabcbaccdcbcdcabcadcbdbbdcbcdbcdcdabbcbacaaaccdacacddcbccdbcbacdabcabaadbacdbdcbadccbbbdadabbbbbadccabcbcdbcbaacbacabcdcdcbcdcbddabbccaadbcddaabbcbcaaacbcdbadaddbdabadbdcbdaacdadbcadaaccbacaddabdcdcbcdaaaaabdccccdaaacbbdbbcacadbaadababdcabdabbadcbaacbbbaaacabcaadcadaacaddbcbadaaaadccaccadcbdbbcdbddbcccbadadccdbddcbcdaccaadabdcbdbdbdabcaddccdcdabbdbbbbccddcccabbaddaabdbbddccaabccbcaadcbdadbdabdabccdcbdbdbcbdaaaaddaaacbbaccbaadddadcdbccadadddacbcabbcccbcddcbddabcdbaadcaddbbabcacdcdaacbbcdbadbbcddacbdcbddaabbbabcbabaadaccaaccbbbadcdabbcacbddaddcadbaacbdcddcddcbbbbcbbbaccabdbbcdaaacdaadbaaccbccacbadadcadcbdcabcacbbdcdbbcbddcabcdabcdbbccdbbccadbabcadbdabccadaddbcbbdbbbaadcaacacadbcabcabdaccdbcdcccabadccddccaacdadbdacdaddcbdadddaabccaddddcbcadddbdbbdcbcdacabdcdaaccbbbbbcccccadacbacdaddbbdabadaaabbddcdbbadbbdbdaaadcdadadcabcabddabaaaccddcaabcbbbcaccaabdbadcddaccbcacddaabddddbbadaaadbcdadcabbabadadacbdcccbcdaaabbadabdddcabadadcdbbcadaacbbccacbdaaddcacbdaccdacaaaaaadacccbbaacbbabdcaddcddbbcdcccadabdcbbcdbcbdccdbcacbdaadbddccaddbcdacacdcababdadddbcbdadbbdaacabacbdadcddbcadccadbccbbbdddccddacbbababdbacccadbcddcccbacbaacddadbdcdabbddbaacdddacacdcdcdcabcbdabdcbaccdddcacbbaaabacddbbdbddabcdcbccccbadbcacdbdccdcdbcbbbdbdccbbaaccdcabacbbaaaabdccbbddcbbaabbcbdbddbcddbcccbaccaacaabbbcdadadbbbcddcacacbccdcacadbcbddcbadabdcacacbcbabccacccddcbcaacdadbabdbcacdcabaccabbbcbdbcbbdbcdcaccddcbaddaacacabdcabbbbcbcaacbcbadabadbcdcbcdbdbaabacbaddabbccdddcdcdadcbbdbbdccbcbcbdcbdbbbcbdabadcabaadbabadbdcccaadbcccaabadcdcaababcbbbddbabcbbdddcdabddcadcaaaccaabcaabbbbdadbcdccddcdacdabdaabaccbbdadbcdabdcaaaadbbaacdbdaacacaaaacdccccabaabdcabdbcacbadbbcacacdacdcbadcdadadddcabcdbcbcbdcabcdddcabcaabdcabbdcccdaaacdbbbdccbcbccdabadabcbcbdccaadbdbaacaddddaadcabbccdbdcbcbadaccbbacaddcaaacbabcbacdbdccadcdbbcccbacbabacbacaadadabaadcbccbdabdbcdcbabcddbcbcbccdacadddddbabcabccdbbabaaabcacabdcadcbccbdabbcdacbacadbcbdbdaadbadddbccdaccbdabcdcdcdaddcccbdacbbcdbdbbadacccbdaddcbcacccbbcddccacbaadbaaadadadabdabdadbcaacbaacdabaadcddcbcaddccbbcdadbaccabaabdcabacdadaaccaadabbadbdcaccacdbcbaaacdaacabaaaaaadabdacababddcdadacdacdbddccdbdbbaadcccbcaadaacbdbbbbcdddbbbcccaaabbddaaadbbbbdbcbdabbccaddaccbdabbdacbaabbacdbcaaabcddcccddccbaaddcbbbbdcdcbbbdcababccdaabaaaaacccabadbcdbadbdbcaaaddacbacddcbbdaaaabcdcaabbdccaaaacbccdcdaaaacacbdbcaccbdbaadaabddcdbbdddaccccaabbcddbbadbcddacdcccdcbaddaababadbacdaddcbdcbcdaddbbddbcbabddabbdaadabadabddcaddccbddcdadcccbabdcdabdaccababddbcbbbbdababdcbbaaaacabbcadbdacccbdbbccccaadbddcdadaabbaddcbdbbdadcdadcdcbaccaccdacbcbbababbdbaacbacbbbdadaaabddcbdbbbacaaabbbaaddccbbdbdbcdbcddbddcdcdbcbddcabbcbccccabcacbdddacdddabcbcdabbbdcbcddddcbacaabaadddacbdcccabcaddbdadabbadbadcdbdccadcaccbdccdcdacdcdaddccccdbddaddbbbaacddcccbccdbabbbbcacbcaccbbadabddcddcbddaabcdbcdcabdcabbdaacdbabccbadcdccdacdadaabcbdbccbddabdabdcddbdbddabddbbcdcdacdcdbcddcccacdcdccbadacaacdcdcbdcbdbdaacddaaabcccbaadddddddddcdbcbccbadacacdaababaadadddccbddcaddcccabddadcabbcddbbcdbabbddbadcabaacccdbbaaadcacaaaddddbcaaacaaabccacdbcccccaaaccdddcacbbdddacaaacbcdbdcabbcdddcbdacccaccccdacccaacdabdbcbbbbdcddcbcdaabadcccadadddabdaaddbccdcadcdabdcdacabbdaaabaccaddbadcaaabbcbccabbcacccaddcccdbcbdaccbbababbccaacacdabbcccacaaaacdadbcbbbdbcaabadababbbccbadcdcaccbcbccbcbbaaabddbcbcbbadcddabdabcddbbacccbbbccdbcdbabcabacbdaddbdbadadbaccbdbcbdaacddaddaddcbacbdbbdbbbcbdcbcdacabaabdddcdadcdcdccdbddbcddcddadbbadbcbcbccdbccbbcbadabcdbccbabdadcbcdcbabddbccdcdaacdbbbadcadaccbadddcddadaaccadcbdbbaabcbabddaccbbdaccddbcbaabcbbacdabbbbcdcccddabcddddbabbcdddadccbabbadcadaabdcabaccbbcdccaabadaacadbadcdddbabbbaacbbdcccdbcdbdaccbbdcdbaadcdabbcccddddbcdbdddcccdcbabdcacddbbddccabdbcccacbbdbbabdbbbbacacbccdadacdccabcdbbdbacaddcbbbabbccdbddaaadbdabdbcddadcbdcdbdcbcdaacbcacdabccddaddaccbdcccbddadaabcbdabcdbcbdcbdccdabdcaddcabdaabddcddbcdcbabcbadabbababbacabddbddcacbdcacbcccabbcdcddccbdcbcdbcccabcbcbadabcdadcabbdaacadcbacabccddcaaddbaaccccabacdadcbcdccaccbabcbbabdbacdaddcbaaaacdccaabcabcbaccbddcddbbaadcbdcbdbcbbccccdacaccacccbadaabddaaaabddababdcdabcddacabacbcdaccdaadbccbbbbcabcbbdbaacddbbbdccadcddbdddacbcdbbdcbacadbdbcbcabcdbbaddbddabdbdbaabcbabdbbddaabccaabbaacddbbbcadddccdcbdddcaddadcbcdadbbbbbdabcacdacdaacbcbbabdcadbccbbdadbdacabaccacbcbbdadbdcacaaadbdccaaadbbadbdbaaacacbcdbcaacdbdcdaccabbbddcbaabdbabacbcacbccadbaaaaadcacdddbbdbccbacdbbaaaadbcbbcabbabcdbbaabcdacbbdbcdacbdbcaccbcbddaaacbbdbcbaabdbddaaddacacdbdabbadabcddcbbbcdddadaddacdaacbbdbadddbdabccacdaccccaaddcdbbbaacdcabbdbdadadccaadcbadddbbaabbaadcddcbacbcaaccaaaaacdcabadadcdcdabcdacbabbaacddbddacaacdbdababbcbcccaccbcccdddcdcaccdcccbaadaacadbcacccbdbdbcbaccdcdcabbcdccddadbdaaababacaccbbdcdcaabbbaaaddbbdaabacccbdccbbbcdadabbbbcbadabdbbcdddadbbdaccaddddddbabbcdbddddbbababaddacbbdddacbcbadaadbaaabbcaadbadcddbaaaaccbbcccbdbddccdbbbaabcdbabcdbddbbadccdbcdaabbbabdcddaaaabbdcbdbbaacddcbdaccdaddbaddabdcaadaccadccacabdcccadddaccdbcadabadcbdaaaadadcadbdcdcacdbcacdadcdabdccdcaabbcbddcbbaaddcdadacadaabdbcbcbbcdadbaccbadcdaaabdaddaaadabacacdababadbabccadbdddbaddbccabcaacdddcadcbcacabbdaddcbdcabdabdbbbbbbccabcaadbabcdbaadadadbcdbbaaaabbdcdddbacbbcbabaadcbdbddaccdcadadacddaadbdbcbacccbadaddcbcaabdbcacdbdcccddcacccaadaddbcaccbddbadbbbbdbaddacdaaddcbbddcdaabbaacbaabccdadddcabcddcbcaaaddbdcccbabcdcdbacbaddcdbdbadbdccdbacbbaabcccdbadccccbdddaacadccbcbdcabcdbcadabadbdccdcbadbbcaaacbddbcbdcabdbcdccdbdabbadcbabcbdcaccaabcaabbdcddcbdbdaacdabdbdcaddbcacdacbcababcdbbdcadcdcbaadbcdbbcabadacddbabdcbdccdcbcacccdbcbcbabccdcdabdccdccbbaabbbaaacbcaababdabdbabbadaabadaacdabdcaadabcbbabdbcbdcccbddaaacaabbcbddbccbbdaabcbcaccddcaddacbddbabcbdbcabdcddddbdccbadbcabbddbdbabccabcabbdbcbabddcddbbacccdacddbcdddbcacdaacabdabccadccabcbdcbaddbccaababdaacdadbbcbbadaadbbddddaacdadaaadbccbdbbbdcdbcbdbccbbdaabccadcabdbadcaabcbbcbbbbdbcdabdbabdcdcdcdbaddacccbdcbcbacbabcaccdbaddccacbddcadacccacdddbcabbddccbdacdcadabdbbcdbdcdadbadaadddcccdbccabbacdcbaadbbbbcadcaacdccbacdbccacaabaddaacdbbabddabbcdcdcbcaddbcacddcdcdbbbdadbdabccabccaadddcbdddcabbcdddbcccdacadcaadabbccccaacadcbbbadabadbaadbaacddcbabcbcccabaaabdaaaaddbbdbcaadbbdbabaacbaddddbddddcaaddddaccccaccadadaadaaadccbabddcbcadccbababcbbaccbdddacdadabbccbcddddcdaacdcbaddccccdbbcbccbcbddbdaaddcaacbadcdcddadccbdcacadccabdddcdbcaadbcbcabcbccbabbbabddabbccdbbcadccdcdddbdbbcabcccddacccabccdaabacabadabbaaaccadbcbcacadccdddddcadbabacabbcadbaddabadcaccdddbbccbdccbccdbacbdcddcadabdadcccddcbcbcdbabccaadddddaddadadbcbadcddabdbddabbdcbdcddabbddbbabacabadbcbbaabddbbbbcacbdbdbbaadddcbbdcddaadababcbddbbaccabcadbddbadcdcbdddcabddbbbadbdccdccabcccaddaadddbaadcccabbbcbababdaadbcabbbddbcadbacaaabacabdadcabbcabbddddadabcdaddcbbcaddbdbaddabbbbcbdcaddbaaacbdcddbccdaacacaabbdcdcbaadbbbcdaaddccbdcdabcddbcdbddbbcaddddabcbbcddbabbcdcbaadbcdbdaccbacabbbbabbabdaaaaaacccabcadabbbbaddbdbddaddabacdababdbaabdadabbadcccaddabacadcbddcdbadaaabaacabaabbbabcddbcabbaaabcdaccdcdcacddbcbbcddadadcaabbabdcdbccdcbacbcacdaddcbabdcbbcbaddacaabbdcdbabccdccabbbbccbddabdbaaabddaddcdacbdabbdbbcabdcaaaaadccdadbcabcabbacccaddccadbcbbcdbcaaabbbcbdccbbcbdcbdacacddabcccbdaadaabbdcbbaddddbdbccbdccaabccacacccdccddaacdacabdaaaccbbcdbbcabcbaddcdddacccabbbbabadadcbccdadbabccdcacdaaadcaabacddadbdcdcdadccaddabddbdabbcdcccbdcabccadcabddbcabcaacbaadbbbadddccbbdabaabccbcddbccbdbbadcbadcdbaccbbcaaaacbdbcaacbdadbcbadbcbdbaacadccacdbbaccbaababadacddbccdadbbaacabcdadadadcdacbccaabbbdabadcacbdbacaaacabaccdbdbaccdaabdaccccccaccababdaadbbdbdacdadbaacbdbcabbcabcbdacdcdacbcacdabdcababddacbcabbdabccdacadabcabaddbcaaacccaabbccacabbcaabbbacbacabddbcbabcacdbacbabdbddcddccabdccdccbaddcadcbcbbcbdbacdaacdcacdbacdbaddbcbbdadaacdacdadbdcdcdabbdbaadcdddddbdacbbdbaddcdbbaabbbcbbdcaacababacaaaccdddddcdcdddcbaacdadbcdbbdccadbcbaaabccbdbdbcaacadadabdaccccabcbbcbdcbcbacdbdadabbcbcabccdbbdbdbaacadbccbacbbbbccddcadccddaaddbcdbcdaacbddbccdddaaddbcbddadddaaabbdaaabaaacdbabbccadcbccdaabcacabddacabaddacdbcaacbdabcccbdcbdacbabddccbccdbaabcacddcbddcabbcddccbddbbcccddaaccadbbdddacbbdcbdbcccbcadddaccaadacbacdcdbcbaaccdadaadcdadbdcbadcbccdbcbbbcabdaaacbbdcabcadccbdcccdbcbbabcaadbcbcbcdcccbcccbdcbadadadcdabcbaacbccbbcaccaddaabcabcaaddaabbcadbddddabbdbbacaddaaaabaddbcbddaaaccbbbdbabbdadbacabadabbcabdacbdadbcbabccbcabaaacccbabbbddaddcbcdaabdbbbccabaccaabbcdbcdadcbdcacbdbdcccacdcbabbdadddbdacadcccdabcccadbbacdadacbdbbdbbadbdbdddaaaddbcdcabacdaadabcaaddacbaacdcbaccbaddacdaaadcbacaaddaccaacdccaaadaacdddbbdbcdadaadacddacdacbadcbbccbcadbbbbdcabbbcbdcdbbdabaacbacccdbadabacbcdcaaabdabdacdaaadbcadcacdbbaacdccaadddcdbabbcddcadddbdcbdbdbdabdabddacddbbaabcdbbcacbcacabaddaaabbaadccbdccdacccbdccddccccabdacdbbdcbdbadaccbccdacbdaadbdabdbdbbccdadbddaddbdccacbacdacdbccddbccbcdacabaccbaccaabbdbaadcccdcbccaabbdadcddbabaadbbadbbbacabacaccbadddbcaabcbcaccabcaaaccdcabcbcabacbcdbababdabbbcdcdbaadcabbdcabcadcddcbcddabcabcbbbddcadbcbbbcdcaccdabbccdcdcabcddaaababcbcadbadaabddbddacdccdcbcadbacddcbdcddaadddddbcacbacabadabacdaacbacaccbccddcadcadbdcadcbcbadcdaabbbcddacbdcdbdaddacacababadaddaacdaaadcaaabcdadcbcccddddabdbddacdbbdadbcabdaabacccadadbccddaacbddaadbdcaabcacddddcddaaccaaacbcaccbbcdacddccdbadbdbccadbaaccccbdcaababcbabbbcbbacddddbccbbacdcdddabbcdcdaabbabddccadbbbadaacdbccabccdbdcacacabdccabbdccadcaacddcbcccbabbbdbbabadaabddbdbdbbababacdbcbbaadabdbadacaaacbdbdcbdbaaabacbcddbaaccacadadcbcabcbcbbdabdccdadddaaacbbabbbdbbdccccadbbcbdddccdccbcccaadabdddaaddbabbbbbcdccabdcbbaacabdabbaccdcaababaccdcbadbdbcaaddadbabaabddddcbdbaddbacaadaaababadbadbddbdbdadcdaccdbbcbbdbccdcdbadaabaadcbdbacdaaacbacdcbcbdabacaaacddacbcabbabbabbaadaadcdaddabccdbbacbdccddadcadbdcbbccbcaadacabacccdbcabadbbacdaccacdbdadbdaacbccbaddccbdbdbabdaaabadcaadbaddabbdcaaccbcabccabcbcdaabccdaddcbbcbaddccabcdbbcadaddacdadcccbcdbcaddcbdabbcbccbddbbcbbadbaddcaadbacacaaadacddddcacddbcaabdbbbcadbddbcbdaddaadaabddcbcdccaaaabcadacddacadaccadbababadaadacaaacbbdcdbccccbaaadcaaacdabdddbdcbbacabacbabaddcdababbadcbcbadcdbdabccddddcbdaadcaaaccaadccbbcbacaaabddcdcbacbcdccddcdccddbbccbcbcbdbbccadcdcbbddabdbccdbcbbcbcbbcdcbccdbcbccdcbcdccdcdcabdcdccaddbbcabaacbddbbbcbccaaacbbbadacbaaacdcddbbcadcbbbdbddaabbdaddddbbabacbacdbcbccccabaccbddbdbcdbcaacbcccbcddccadbbcbdacbcbdadcbcdbdbbcaaddddbcbaaccaaaccaaadaaadcbabccaadadbbdcaaacbaccbbcddddbdcdadacdadcadbcaaccbdcdaaddcdacccdaadbaababdaabccadbbbacadbdddcdbbaddcaaccdbaaddbcbbaabdbdacbbbcaaaaaddddacdaadadacacdcbaaadbcdadacbbdcdaadbbcdcdcacbdbcdaaccbddcddcaaadabbdbadacabbbccaabddaddabbbbdabbbbdbccbcbdcdaadbbbdaaabdcbcccbdabbdaccbacbccabbdcbccdaadcacdbdcaddabcdbbdddbdddbaddcbdbcacaddccbcbdcdbbbabadbbbdbadcacabbaabdbbdaadbaccbbbbcabdacbdaabbabddbbdcccdabaabdcbbbdbbbcbcccccdbbbcbdddbacddbbabdcdddbcbdaaccbbaddabccbbacdbcdabadbdbbcddbbacbacdbbbcdcbacbdaacaccbdaacdbcdbadadbbdcdcddbbbcaaabaddcbdabdaddcbccadaccddbbddcabddacabbbacdcadcbbddbbccabdcaadbcdccbabddbddbdcadddabdcdbbbbdadaccccdacbbdbaccbadcccacbaddacccaacbabdcaacbaadbcbdbdcabadacaadcddacadaddadabcbbbdabacbcabdaaabcdbccdaccbbbaddddaabdddbaababbbbcdccbdcaccbabcdabbcdacadcacadbcbcddbdcaacccacbddabbadbcacbbbbccacdddcacacbcccbbabbbaddadccbdbacbcdcbdaacdcaabbbcbbdcacbbabbdbdcdabcbadbbabbbbbacbddacbabbdddbbbacdaacbadcaccbadcaabdccacbabdabbdbbdbdbcbbbcacabcbaadbacbcaddcccbaaabaabbbadbadcaccaddcacbcbddacbcdbccbaaaadacbaddadacbcdaadcdbbcbcbacddbbdcaaabbcdbaabaddaddbcddccdcccbdccaddbcdbaccbcadcbacacaddadbcacabcbbccbadaacabddbcbbdbbacacadcdaaccaddcacbabcaccbcbcdbbccbaddbbadccbbababaacbbbabadaccabbbadcbbdabcbcbcacdcacbbccacaaadccacaaaabddaadbcabaddcaddcdbdccddabbbccccadbcdcdccdcbcccbbaacddddcbcadbdacadcbadccadbcbbbacaccdabcbcaacaaadccbaacbbbddbdcddbddccddcbababadacdbcddbdaccdadabbcccaadbcacacadabdcdbcabbcaadbdabbdadccacdbdccadcbcaaaaddddbdabadabbbdabacdadadabddabddacacbbcbbbcacacbadaabdabdacadcddbcddcdbcababbadbdbddadbbbaddcdbadbabbcbdaaddccddccbdcdacadbaaaadcbddcbbbbddcbccbbdddbccabacdbbdcbccaaadcacadccdccbaacdcaddaddcacdddcdbbcccbbadcdabbdbccddcbdbbabacbabaddabdcdaabbdbdcccabdbbabdcddccbcbabddccdcaccbccbaabbaacdddbcdbcbbccdcdaacdacabcbbadccbdacdbccaadabbabbdbadbacbbaaadbbcaadcababdabbbdcbbaadaacdccacbacaccbccbaddcbdbdbcdbaabddbaaadadacbdabbccadacbbbabcaddaadbaddbbaddcdbbbaababcdbdcbbaabcdccbcbdcdddaabdbcdacdbddccabccaaadcdccbacccadcabdddaaaaddccbaaccbccdbdadadacbbcbdcddbcbbdbbcbdacbbcdbccdbddcaccaaddccadcbcacbadbddbbdddbaabcccdcadadddddcacbdbddddaababbcdabdabccbdadbacabccadbbcccabdbcadaddcdadddbbdcadbbadaabadaabcdbcadddccdabccaccbbbacaabdcccbadabbdcdbbbcdcbababcbdcbbaabcaadbdcdcdccdcbdaccdcdcdbadddccdcbaabdcccaacaddcdabcbacabddadcbdcaacadadbbcdbdaccacbdbcddbacabaddaadddadcdabadcbabccadabcbadcabdcdcddbcdcdbadbdddcaacacccbbbcbdddcabccaacdabbbddcddabbcbbcdcccbcabcdcaaabccacbddbbccbdacdbacbccbabaddbdddddadabaabdadcadadbbacccddaaaabadbdcdadddacbbccdbdbbdaadbcdbddcabdcadaccbcabccbdacdbacaccbddbabaacadabdbacbbbdbcbcaccddacacdbbddddabbccbcbcdccaaccabcccdacabbbadcbdaacdbacbcadcaccdaddcaabcdbccdabacbcaabcddacbcabbbbdacadbdddbccbbdaabbbaddaadbccadaadbbbbacabdadbbddddacbbcacaddddadcdbbbcbbcbdadcaddbdcbddddcabcddbcdbccdcddddaaadccccbccccddcadaacbccbacdddabbdcbcadabacbbcabaacadbcabdbdcdcddbcbbacabbdabcbadcaacadbdcaadccabbddcccacaaccabadbbdbdbcacdbcbdbbacdccaabccbabccabacdcbcbbaaacdabcadcadbbcdabddbccccabbaaaaaababadcbdabcabadacbddbcaadcadbccaaacdcababbadacdacacdacacacaccdbddbcbdbccdcbaacbccbbcbcdcdbdadbcabddcbabbccaddcccaabadcbaaddcacbccccdcdbaadcdaacdaddbaacacacbdbbcbdcddbaadbdccbbbcccbadbdbaacdbabccddcaabbbadabdaadccdcbbcbcaddaddbadbdbdabddcbccaaacdbbadcbcbccbcbbbbddbacddaaaaacdaccacdaddddcaacabcdbbbcaacdddcaaccbdddabdbbccaddbcdadacbdaadbcabcaaaacabddabaaaabacaaddcabcdcdbddbdadaaacacdcadbaacdcaaacdcbdddbcdcdbaacaabdacbbaaddcbbbbcacbcbaaadaadbbdcddcadcaacbcdcbaccacaadaccdbabaddccacaccddacccacdbacabbddccddddabadadddbcccccdcccdadaabbbccbadcadcabdcacdadadbbdcdbdaccbaabdacdcdbbcbcdabcbccacbadcbacabcaaccacdaabadcadabababdcbaabddcadbabdbccbcbdcabacaaaacddcdbdcaaabcaadbbddacaabdababdcddadbadcdadabcadacaaccacdbddabcdccacdaaaaddcccabcdbbbdcacaadaaddbbcaccbbbcbbdddabbcaccbcaacddaccacbcccbbdcbabacbdccdadbcabdaaacdaddbccabadbbbaabacdcbdaaabcdbdadccadcbcaddbddacaaabbdadbacadccbbdccabcdacacaacadacbbbcdcaababcdcddaccdddbaabaacacdabcaadbbabccdadacacadddacbdcabcacdddbabdcbabcaabdacbdcabdbacccccaddcaddbcbbdcabdcbcadacbacdacabdaacbacdabcdcdadcddadaabcddbaaddadcacdabbaccaaaddbaadbccbbadccaddacacadacdbabcbdbadcbbadcddbcddbadbbacaacdcdcaddbabaccbcdbdaabcabcacddcdddbddbcbcbadbcdabcbbaddddbbcddbdcdbdcaacddbcbdccddbcbcbbdcbabdacdbbcccacbabdaaddbbaaccacacbadbbaabccddccabbcaadcbabcddbbadcbcadadbacdbaadddcbcbaddcadbdaabccabcddbcbcabbbcbadadabcdbbbbacdbbddadccbabacbbdbbaadbbacaaabbcddbbcbbdbaaacabbdbcbbdbbdaacaadbccabcddbbdaddbabaddbcaccaacacaaadaabcaacbdcabcaabadbbcccaaaaaadadddddbdccdcadcdcaddbaadcdcdcdddacbcaddadccacaddabbbabadaacbdbcbbdaaddaacbddccbccacddbbbbaddbdbccbddddaddabadabccadccddaadcddcbbddabdcacaaaaccbbdbbddbbdbdcdcdcdcadddaaadaabadbcbcabacdaccdbbdbdbbdcddcccabdccaddadccdbdcbcadcbcdadcdadcdcccaaadacbadbcbdacbabddbcddadcddbddbbcdaacddbacbdcdbaaaccccaadadcbccaadbcbdadaabdddabbadcadaaccddaacdacdcbdadabbdbacadcacddaccdcadbbcccbcaabbbbbabbbbcbcacbcccbdaacbaaacdcbaccadcdaabbccbcacbaddadbddbdaaacdaaabadccdadcccdbcddaabaaccaacbadcaabbcdbaabbdccbbdcadddcacbbaaaacdacbbdccadbcaacbcadcaabdcddcdabccaccdbbaddddcbbccabddabdcdccaacaddbddacdddbbcccaacbbaccbccbcaabcdcbcdddbbcbdbbaacaacbdacbcdbbcdbcccbbbdcdcdaaabddcdbbcaaabdccbdccdcbbdcdbccaabcbacabdadddcaaabbdadbdbbcabadbbdacabaaaacbbcbcbacadbaddbbbaadadbdcbadbacccbdbbcabddaadbabcabdccdcacbdccbccadcbcdbabcdcdcaccaababccbdbcbacbbabbbbadbcbdcddbddbcbbbdcbccadabaabddcbbaaccddaadbccdbcabbddabbaadaabcddcdbdadddacccdaaadbabdddbaccaacdddaabbcddacbdbabbbbadbdadabdabcaaaaabbbcbcaaadcbdcbdaaadabbcbdaddcdbcdaacbcdabacaccdacddcbdcddccacbbcaccdbadbbcdaaaaccabaccbbbcbaddcddbddcdcabcdbcbdddcbcbcbccbdbaaddaddcdcbbddbaacabccdaddaabcdbccadcdbadccacddcccbbcdabdbdcdbacddbdddbabcbbbcddcdcaacbbbbbdadbdccaadaccabbbdaaacbcddbbacaccbbbcaccdbdddcddddbabbabcbccbbbddaadacbbbdcdcccdddaddaabbcbadabdadadacbdbddcaadbcadabbacbadcdadadbbaccbdcbcbaccbbbbcaaacdcbabbaaabcccadbabdadadbcbdbbadcdddbbccbacbabaddcbccababbdadbdabcdcccdabaddccadacacaaddaddbccaaabaabadacbaacdddacdcacabbdcbacabbbcabdddbccacadbdcbaacaabbdadccdcabcaacacddccddbcaccccadabbbccbcccccbacaabbbbaaddaadabbacdbadbcbccbcccdaacaccdcdcbcaacbbabbadadcacbcbcbccbcabdaacdccbcadbdbccbbccdacccacabbdcccdddbcbdbbadaddcabaddcaddccdbcbbcbcbdbcaccbacbcbbdcacaabdadbcccdabdbdcddbcdcaccdccaddcdbaddacdaabbccaaabdddaadbcbadadacbddddcabbadacaabaacaaabdbccaddbbbbccdccccadbaccbccbadaabddabcadbadacaccacacbbdaadaaabdcabcaabaacbadcabccbaddcbbdaaddddacbaccaabbaddacdbdbbcdbacbdddabcdabadbadacaddabccacdaaadabcaaadaaccddaaabcaddccadccdcddcacabbddcdadbcacdacdadcdcddbdcadcddbbcddcdbcdabacdcadbdadacbadabcbccddcbcccbbdbbbbaacacbabcdaacbbcbadbbbbbdcbbcadbdacddabdbbdbdccdabaaabcaaddcdcaacadaadbbcbdcdacacaddacdbbcacbcbbaadbbbdccbacdccdbaccadaabdbcdddddaddcdabbaabdbbabbcccbdabbdacbbddabcccbddcabdacdcabcbacaababbaddbccabbddccbacabddadcaaadccbbdaabbdabbdbbacbdadcdbcabcacbbccdcbdaabbdbcadccadbccddbbadcadcbabbbbadcbaadacdcbcccbadaacccbbdaabbccdcdddaaabbbbbbdadaaadabcbadcccaabbcddbacbcdbdaadbcdddbabaaacdadbbcbabdbbadbbaccacbcbbcdbdcadaadcdcbbcbaabadcadabadbccbaddadabbdadddcdaccbcbabccabbcbcadbdaadbadaaddbcddbdbbbbabbaadcccdcabcabddcdbdcccbaabbcbcdbabbdaaabccbbdbbdcdabccddddbbdbdbabbcbadadcdbbcdcadbdbbcbbcdaabadbcdabbabaddabdbcdbacdaacacccbcbddccdcbbdbcacccbabcbdadcbadacaaadadbbadcdadcdddaccbdcbaadcabccaaccaccbdbacdaaadacbaaaccdbaacacddaadaaacbddadccdaadbcaababdcbbdaddaccaaadddddccdcacaacaddccdadccbcacdacbbdabbdcaabbbcacbacdadddbbadbcdaadaacacaadcbabadddddccdbcdbbaccbbdadacccbbadbbbacbadcacbdbccdddcdbddacbdbccbbddacdbbcabbacdddcdbcdbdbbacbadcadabbbbbadacddcddaadadadddabbccaddbdcccaccccadaaadacdddbddbdcdbadbadcbdbcbdbbbacbdadabaabdcbdbbdcbdcbddcbccdcbcccbbdddcccaccadcddabdabdccbaddbbbdbabbaddbddddaacdbccacdaadaccdbabcbababccadbccbdacbdbacbcbcdcbdddadcabcbbacacdabdadbbcbdcbaabdbcdbdacbbdaaaaaaabcdcbacababaadcacacdddddcaccadcaaacabdaddcdabccdbaddbcdccbbabaabbbdddbadcbdcbbbaadabdbcdbbacaaacacdbdccaacbaddbabcddcabdccbbbbdaaddacbadabcaacbddddcbbdaabbadbcbcbbccdccabadcdaadbaadaddbabcdbabaddbadbdcaccdcdccaacddabcddabaadbcbcaadddbdbcaabccccacdacdabbaaabbbcdccacbcbdddbbbdabdabbaaaabadbbbdbbbbbdddabacdbbadbacdaacaaacddcbddaddcabaaabaabccdcaabbabcdbaddabcccbddabbacbbccacabcbcddaddaddcdccabdaacadbaacddcbadbccaacddccbddaabadaaadbcacdcadbcacbacdbdaaccdacbbbdbbbbbccdcdbbcaddbdcbaddaababaccbacdccadccdacacadbabddacccadbbdbccadbcaabdaaabcabbbaddccbadaaacccccbdccbdacddbacadbcddadabadbaaaacdacabbdcccbabacbcddbaacadbddacdaabbcccabbcbdcdaccbbbaacbdbddabbaabccbcadbbccbadcdaaccadbcdbaacdbdcdacbabdaccdccbabcdbbcadaacacdadadbabcdaadbccdbcacdbcabadabcaacadbacccaacdcccddabbbcabadaccccaabddbabbcacadaccbaabbadbabcbcdabbdccdcddddadadadabdbccdbcbddbabaaacbdabbaaabcdbbadadccbabcdbddbabaaadaadddcaacabcbbbdcccaadbbacacaabaabdbadcabbdbbadbbbdaaabccccbacadbacbbbadbbddadcdaabddbddabcdcdaddbcdabbaaadaabbcdabbdaacacdbdcdbddbaacdbaddabacccdcbccccbbdcbacdcabacabcabaabbadaabcbccadaacbbdbdbbacccbcadcbbddbcbbcddaaadcbcccdcabacacddacaaabcabdaabdbabdcadbcbcbcddcabadacabdddabdaacadddccdcaacbcbbcdccccbbdbabdcdbdacabbbadaababcaccbabccccdacbbcaabacadabaddabdacbbacddbbcabcccccbdcdaddadadbbacbbddcbbbcabdddddbbacdcbabdccccaabcaccbacaaabbaabacaddcabbcddcadccadaccddaacaadddbcaddcdaadbbcbabbbddabadbabbddbccddddcabccabcccaccbbacdbbaaccacbdacbacabadabcdacadabcadbaccdaaabcacaaabddabbcbcdbbcadaabaacdabdcabbacdddabcacbddbdcdbbbaddbdabdaaabdbdbccbbcaadadccbdaacabcbccdbccadbaadcaaacaddccdbddbaddcbaabccbabbaddbcddabdadadbddabcbcddabbddcbccaccabcccddbabbbabcadcadddaadabaccdcdcccacbbdabcadcbbbdadcadcbddacbbcdbadaccbbdbabbcccbdcadaccbadbcdbabcdbadbadcdcadbbcccaabcacbbadcaddbdcdbdbdbaddadadbcbbbbbbbcdadddacabccccbcdaccadbacbcaabaabcaaabadabdddbadbadcbdacbdbacaabbbbdacdddcdcdbcdcacadababddbdadbddaabcacdcbccadbacddbcadbccacdaccbadccbbabcadabdbacacbbbcadcbaccabbcaaaababcdbbdccbcababbdbcddacbcdbadacbdccdccabbbbaacbacdbaccddaabccbdcabbadddddcdcbdbbddaadaccaabbaddcbcaccadcccacaacabcdccacddadbddcccdcdbcaaadaabaaaacbbcbdabdcabbacadcbbaacbcadbdcddaadcaabbdacbabbcdcaacdacbaabcaccdddadbcaccaddadcccabdadcccbbdcdbbdcbcbbbbdddbaabccacddddbdadaaacdcdcaccdcddddbcabdaddddddbcaddbbcaccbdacbadbcbbccabddcacbcbbaaddabaabdbcbbdabdbabacadabdccaadddaabdbacbcbdddcccbbababdcdddccccaddcbabbabddccaacbdbaaccdbdbdbbdcbddaaccbcbcddacccdaabadbdaaddabacbcbcddccdcadbacacdbdccbdcbdabcdcdddbdbaddabbaacbbacbaccbdbdacadbdbbabbcddccdbabcbdadbcbbcccaacdccbadcbbddadcabddbdbdcbcadcdadcbacadbcbaacabcbcacbdadbcbaaddcdaacddcadcadadcbacccbdccadbbdcaacabbdacdcdcbddacadbdacbccadbaccdcccbcadcbcaaddbdaabddddbbacdbcaaabacbcabbcaabdacbbcabbcbbdbcdcaccdaaadadccadadbadbcccdbbababaaabbacbddbddbcaabbbbabbabacdaaabbdcaabdcdabaadabdaabcabdaddacaadacaadddccbcbacaadbbcacbdbbbbbccccadcdddacaacccddbbdadabdcddbcbcdaacbbdcdacdcdadbdabddacdabaddcaabdacbacccdabccdbdddcdbbadbdcdcccabccabbbdabbbdcdbcccbbabdcdbabbcbdbbabaadacabbbadbaaabbddccaccadddbbddccadcaacabddcacccbcbdbacccbbadbbddccbadcbddaccdabdbbbdabaacbbadaadbcdbabaacaabbdabcdddbdcdbccbcbbdcddccbbddbbbcbcbabbadcacddbbbabaddbbaaababbbccbcbccdaabdacaadbabbaddcbbcabdadbdabdbbabccbbcabccadbdaaaabbdbdccacabcbabdcbbbbbdccdabbaaacbaacabdbdbddddddbdaaadbcaadbdcbadcbddbaadcdccabdabdaacaaaabddabcddbbcddbabaddcabdbcadaaabcdaaddddbccbccdadcccbadadcdbbaccdabbbdaccacabbbcaaccacdbbccdcccbcbdbacbbaccadabcdccbbacacaabdccaadcdbcadbdbaadbcbaccacaadcbccbacbdbcacddbdcbdbbcbdbbdacdcacdadaabaccbcdbcbaacabdaacbbdaddadbccacdbadbdadcaddbddbacabbabbddaccddabbacdbacacdbdbddaacbcaddcbbacccbcccbbaaabbcaacaabacbaaabddbcabaaabcdccbadcaababdccabcaacccbaadbcccccbbcdaacbdccacbacbdbcabadcdaacddccddddacddcdddddcddadbbcbcaddbbbbadcbbdadacacdaddcbbcccbcdcdbbbbdaaccbcaadadcbbadcadbdbadaaaabbdbcdaabadaaaccacccdbabaddcbcdbdacacacdcabacddaabdbaadaaddbdbcdadcccadadcbcddddcdaabdacbadabcdbdbbddacbbbbddccabbaddcbcadcabdacbcabaddbdaaacadabaccdcdadbdcbbbaadbcccccbcdaccbcbbdadddcdddddabdbdbaddaccbcdacbbacbcadacacbcdbadbdcddbcacbccabbacdcaabcccbddacdbaddaccddbdaddbdbdbadccbadbbdbbbbaddbabbcacdcdbaccbcbaacbbbdaaddadaaacaddcdbdaccabaabccbbaddcdddadadbdadadcaacccddabdbabbbbabcdaacdaaddcbdaaddddadcbadbbcbcbddaccdbaaadcdabdababddaaabccbdadadadbadcddacbbbdcdaaadccaacbbccdaacadccbbdcddaaaacbaaadddcabadbdacbcbdbddcccbabbdbcbbbcaddbddccadbbbbcddbcbaddbaacdbaacdcaaddcdcaacadcadcadaddabdddbbcaadbdadbbbadacaacbcbdbcaacbdbbdcadabcdcacbddadcaddddcbddcbadbcdbddcbcbdbbdaaadccacdcacbddcbabbddabdcbdbbaabbbabbcdacccabcbbccddbbbddddbdaadcddabadccdcaabaadddaaabadcbaccdaabbbbddcabdaacdacacccdadacadcbddabddaadadbcbbacdbacdabbaaabcabdcdbdddccdcddbabcaacaabdbcbbbbaddabbcccacdcbbbbbcabadaccccbadadaccaaddbcdbdddcabcaadbbcccdbcaddacdaaccacdcbabdcdbbbaccabdaacadabdcaabbdacabccadbdcababadbcbaaadabbacadaddcacabacaacbcadabccdcbdacacabcdccddaaadcdabcbdcbcbdbdcdddcdacabdbcdaccaaaddaacbddbbdadabcaccbbdabdbddbadabbbbbdcdbdcdabaddbddaadcdbadacccaabccaabdbddddbaaccbdcdadaacccbdcccaabaddcdabcabacbbacbcddbccbcbbbddbdddbcdbcdcaccccbacbbacadcbbabadaabaccabbbcadcbcdddcabcbacadacccdddadcacccadcadacbddccbcbabdcbcdccccccddadcacdaaaaaaaaddaaddccdacddddbcbbdbcdddbbcacbcabdcdbadadbcaaadadcdacbaccbbdddccaddaaacbadadcbdcbbadacbcdddcacaacddbdabacccadcbcbaacbdcddcdadcdcbcdacdacbadaaaccadaadddcadbddacccbcdcccbcaddbadadccccdddbabbbddbbddbdcdbdaabccdaccccabdacababdaaadddbbdbcbddbccaabdcbadcdcdabbcdcbcdbbabbbcabcccadddbacdccbadadaccbacbadccbbccaadabddbabdadbbdbadccaddccbaacdbaabccdcabbbcdcbabbdbacabaaacadbdcdddddacaccacdcbbabcadcbaadcdcadcccaaababdddccdbcaaabbaadddadaaaddcdcccccacccabccbbcddbdadabdddaabacdbbdcdabbdabdbbcaadcabbccabaaaaabaabaaccdbabcbccbbdccbbddcabacbdbddcaacbbdbacbabcccbabbacbbaacbbadacdbcbaaaabdbdbbdaadcbabdababcadabbaaccccddccccacdabcaaccddbbdbbcadccacdbdaadddaddcdbdaadbbcccbcaabcaabdacbabbacdcbcbacbccbadcdddcccdccadcadccbdddbcdaaabcadcdbdbabdcddbbbcaddbccbcdbbcbddaacaccaabacdcaddbadacbdadcabcbdacbcddacdbdabdcadccdadcbdcbdacabbdacccbacaccbbaddccbddabcbbaccbccdddacdcdbcdbdccbcbccbbbcdbdbcdcccbcacadadbbdbabbdcaaabcccabbdbbbddccacdcdbabbdcaccdccddccbcbcdbacbaccbbbbbdcadcdacdadcbcdaacbcdbdbdbbadbacaacbbcccbdcbccccadbabacacdcdaaccabcbdbdcabbcdcabdcdbdcccacdbcdbbcdcadddddabaaacbbabddbdcdbaabbaccaaaaccccdbbababbdcccddcaadbabdbacbdcbadabadcddbdcdbbcacbadccbbdbdbbcdabbbababdcacababadabbcdbccacccbdadbbdbcdabcaabcaabdcddcdaacddacbdccbaaabdadcddadaababdcdaaccadacaacbaacbabbdacddbadbcddcbcadacacccdcbccdddbaccacdccadbdabcbbddacdddcbcdcaacbcabdbdcdbdacadcaaddbaaacacbbbaaaccccbacdadaababbddcdbadddaadbdccbddaaddccdccbaacdabccadbaacdddcbaadacaaadabcccbbddcbcbcdadabbabaabccbdaabbdcdadabcdaabbaabbdadaabcabaaacaadadcacadccdbdacbabdbcacbaccabcccdaadccddaaccdbdcdcabbbcdaabdabacabacbcdcccaadcccbaddacdbbcadbacddababbbdddddccdbdbbbabdaadcabcbaabacdccbacddacdccbbbccbcacdaddcadddbadbdabbbbbccdcddbccbccaaaacdacbaacbccdbbbdcdcdddddbdcabadcaabdadcccdaaccccbdcaadccccbacdaaacaabdcaacbbcddccaadabddbddcabbbaddcbadbbbabaddbbdcdcdbbdaacddcbaadacbcdaccaabbabddaacabadbcbcdcddddbcaaabddbcdbbcbacaadccdbcbbbaabaccdbbacdcdbdcdbdddcbcdccbbddcdccddcbdbddbacaababddaddbbccdbdbcddcabdcbcdbacaaaccadadbbccdbcccbaabccdaddbbabcabbcdaadabbbcdbddaccabcabcbcbbaccdbadbbaddbbabdcacaddabaddcdcacccbadadadcacbbcacccdddaddacbbacbdbcccccdcdbcddabdacabaaaacbabbaaaababccddbddabcaddcdccbcacbdabbcbbadccabbdadcddbaabaacdadddabdadbccbadadbbddadbcdabaddcbcaddddadbadcbaaccaadcddccdcacdaaddaaadaabddbddcccddadbbdadcbbabcbbcdabcddddcdccdacbcccdccbddddaaddadbbddabcbccbabcbdcdbccadcbaccadbdcabbaaacaddabbbcdccaccdccadaaddbadccabababbbbdbaabccccdbcddcbcccacdcaacdadadcabcaabbaacaccccdbdddadcdbcbddacbcaabcdbddccbaaabdcdcdaadddadccdbbaacbbbdcccaccbaacbbccccabdcabadbaaaaabaaabbabbdadddadbbbccccabddaabdbdbbabbddccbcbcddbdaabdcdcadaacdddbdabbccabaccbddabddcdcbbacddcddcbdaccaadbdbcbcaacbacbdabccbbcdcabacbddbcdbbaacabddbcadbaadbbacdbdcccddbaacdddabdccbcbbbbabdbabadaaadabdcccccdacadcdbbabbaababdccaccaaddacddcdcbadadccacddacbacddddbcabadcbbcbaaaccdbcbcaabbcaccacbddabbdbcaccacbdddcabbbddadabaaddbdddadbccacbccacbaabbdddbabdacaaabddbbcababaabdbcaaaccdadbbccbbccdcaadabcdbbdbdddbccdbbddaddbbbaadcaadbcdadcdccdacbabdcbcabcbaaaaacccaccaabcccdaabcadccccbdaccadacaabcccaadacadcdaccadcbdaabaaccabccaacdcbdbabcdcdcbdcadabdaccaccbbdbbbdbacbabcccdbdadbccadbdbccbdaccbabbdddbddababdccbdaabaaadabdaccdddabcbccbbcacaabbcbabccdadcdcbdbcaccdbcaabbddabaaabaaabbbcdadcbdddadabacddbdadbbcabcddbaabacbcbbdbdcdcadaddbabbbdbcbdacabdcdabccccacdbdbddbcaccbadbdcbdbcbcdcabccbbcadccaadaddbdcdcbbddadabdaacdaabcddddacadabbcacdbbbdddbbadbbdcacddbcbabbabbacbaacbcaccdabbccdbbbbbdcdbbdcdccdaccbaabadabbdacaadccdaabaddcdbcdaaccbcabbbdcabcaacaccbabdaaadadcbcacdbdbacdabbdabbbacabdddbacbccabacaccabacabbbdcaaddaacbcdddbddbcbacbdadcdcdaacbcabaddbbbdbbcaadadccdbdadcbbbcbbdbaaadaadabbbcdbcccdbdbbcaaccccdcdacccbbcbddacadbcbbaabbadbbcdbdcbcadccdbdbbabbabacbaacccccbadadbacaadccaacdcccccaabaccaaaaaabacddaddbabcacaadaaacdcdccaabbcabcabadacbabbdacacaaacaacacbdadcbdbdbcbbabbddccacbbaabbccabcbabbbdbbabcdabbddbcabbbbccabdadaccaabbdcacccdaadddcacddacbbbbaccbdaaaccdccbabcaaabadacdbcbbcacddabbdcddadccdbacacdbdbaaccbbabcacdcaacbbbcbddaaadabadcdbbdbdacccaccbccbdcbaaacbdacacdcdbadcbbcddcaadbaccadaddaaadaadccdaaadcddccbbbadcadbcadbddbdaadadcdcddadacdadabdacdaabcaabbccbccacbbbaacdcaacaddbaccabbdcdcdaccbdcabdbccdccbbbbcbaccdaadabdadbbaadadcabbcbabcdcadccbdbaabdddbdbabbdbdbcaddbcdcabadddbaaccdadbdcdbdcbcdbaadcccdcbbcadcddacdaabbbdabbdbaaacbbdddcadcbddbcdbddacdbcdbcabcadbcdaacddcdaccddabcadcddbbcccbcbadbcacaaabbdadacabdcbcbbacbbcbacadbddbbabbcacdbcabadbcccbadbcaacdbcdbbdbaddbbdaacaadcddaccadccaccaaadbdbccbbddbbbdaddbcdbdcdaaddaddbcaacaabbdcaaaabccaadabccbdbbabbabcdaadccadcbdbbcdbbbdcabbadbcdbadaaaadcdddddcacabcaddcadacdcbcbcccbbcaaadcdcddcddbddabcaaacbabadbadabcdbcbddabddcaaddcbccbcaacdabaabbdacadbcddcdddbddacaaadcbbdabdcdcccabdbadcdacaabdbdaabcbcdbdbaaddddabacddcaccaabcacbcacddaabbbccdbcdccaadadddaddbbaadbbddcdadaddaadaabcabbbbabddbababbbdcabdbcbdacdccdcacaabddabbcccdcacbbbaaaaddabbabacbbbbbacbbaaccdddbcbaccddbaccabccddaabacbadacdacacaddccdddcacbdabdabcbcacabbcccdabadbdaccacdacaabaadcaacbbdadbadcdabaddbbacdaaabbdbddcdaadbbdcccccdbadbcaaadcbccdbdbcdddacabbabbbaaaadbadcbcabbbcaadcbbbbdaccadcdcbbaabdbabcdadaabcbadcacacccbaaaaddacacabccbcddadbbcdcbdccdcddccaacbcacadabdccdccbbddbddcbadbdbbbdbdcbacdbdbcadcbbbabddbdbccbcddaadcdcbccdbaccdcccdabdcaccdccaabcdaddacaacdccdddadbaababbccacaccbaccbcdaccabbcabdddddddcadbaddccdacbdbcddbaabdddcdcdcadbcccdaadbbaabacbdcccadacccadcacadbdbbabccbcdbcddcaaaccdadaabacbdddbadcadcadaaadacadddccbccbacdbccddbdbdbbabdadcbadbbadcacbbdbbbabdadddcbabbddbbdaabcbaacaabbbadacacdadadbcaccdbbcbdbdbdbcbacabddacacdcadbacdddadcdcacbccccdddcdcdababddbaacdaccdbbbdbcadaccdadaccddbaacbacdaadbdcdddabcccdacddbbacadcadabbcdaacaaabbdabbcadabbbbdcdddacabacbcbcbccbbabbcddccaaabcadcdabdbbcaaaadccbaaaabdacccacdcacacbbadaaddacbabcbacabdddcacadbadacaacbadacbddbdddbcddacbcddcdabbaaaccacadbccacccddbdbdcbcbdacddacacabadaabacdcdadaabccdaddacbddcbacdbcadbdcbaacbbbbadcbaddcdaaadbaddbbcdbdaabacbdccabadaabcdbabbcadcbdbddddabddbdcaadbcacdbbadbaaacabaabbdbdbcbbdbaacbbccbabbcbdddcccabbcdacbbcdacabbccdbaacdccddbdacdbcbbbbbabbcaaaaabbaadadcbdddadcaccdccabddcaadbbddbdcababadbbbbccadbbcbaddadbaaabbabbccbdddcabddbccabaaccdbdabcabacccdaababbdaadabcbabaccadadabdcacbbdbcbbddbabaaaacabddddbdccabccbcdddcdaddbdcdbcdbcccbcadccddbbbacdcdabdbdacdccadcdcddbadaadbccccbadbacdcabddabccbcabbcaadddcadadcbadbdcccbdababccaacccbacbbdccbbadcabaaacddbbdbdbbbacabdaacbcabcdbcadaccacaadbabddcbccdddacdacdcddadccdcbdcddcbcbcbbacbcbccbacdbccbbbcaacbbcadaacddaababbcdbcbbdcddcbcdacbaaabdccaabadacbcbdbaadbaccabbaaabccadccccadacbdcddcabddcbbccadcdbdbabddbbabbddabbdcdabacddddabccbddbadbcccaacdadbddabbacbcabbaacacbdcbbabbcdaabcccaabddcbdbbcdcbdbaacbbcacbabaccbbdcbddabdccbbaccddbcddacbcbabbbdbaacbbddddddcdabdbddbbdbdcbbbbcaaabdcdddddbccbbbdabcbcdcddacdcccbdcbbbcbbbadcdbdcadcbbaacabdbdcabaacdbacbbdcccbdcdbdcabddbcadaacaacbddbdadaddbbddbaaadbabbbdacbbbbaaaacaaabcabadbabbbacacacdcaadbddaddacdbdbabddcddbcbbcdcaacdcdabbcbccbacdbcacbccaadddbbaacbcacbdddacbccabdaadddccaaaaadbcddcadaacbcaddbcbddccbdadacacbcdacdddacdcdbaaaaadbdcbdbaabcdccadbbddbddaddbddcdbddadbbcdbcbcdcdbaccdaaddcacabbacdcaabbaacdcacdddcdbcdcbdaccaabbdadabbdabaddaadaddabbaacbabccbdcbaccdbcbabdbcbabcdadabbabaaacabcbadabbcbaddacbddcbcaddbdccabbdddbadadaaadcdaacbcbadcaadaccddaaccbcaabddbddbdacbacacdcccbabdbcbdbacddccbdcacdcaacdcaaaddaddaacaacabaaaddbdbaddddbddadadbaadadacddddbabddacdbbccababbcbcbaaacacaabdacbaacbcbccbdcaabdcaabacbdcaabbbababbbcdacbbdccdbcdbdabadacbccdabcbbdadccdadccdbdbdaababbcacacdbbdbaccbdaabacbcdabdbbbcdcccddcdcccbcdadaacccbbbcbddaabdbcbacacccadcbaadcbcaabaacdaaccdbddaadabbadccabcdbbaadaacaaaabbdddcabccbbbbcddcdcbbaccabaacbddddbdcbbdbbaddcdabcdbadbadaccadcacbbaadddadccadadbbddbabcdbbabbcbbadbddadadadddbaadaabdddbbaacbcbadcbadcbabcbcccbbddabdacaccdcddddaacdccaaddaccdbbbbbabcbaccabcdbaacbcaabaaccbbccbdcaadcacbcdcdadbdbcaaadcadcacddcdabdcaabbcbabdabaabdbdddcddddcacabddbcaaadaadcbcdbbadbbdaabcbdbcbbcbbcaacbdbcdadcbcadbbdcbcabcacbacdcadcadaaddcaabccadbbdbadacaccbdbccbcdabaddcacbbacbacbbaaaacccaadcdbdcddddcacbbbddbccadbddddbcbdcbdacdcbbdbadbadabddcabdbddbbaababdccbabbbdbdddbabbdcdbbcbaddcddaaacaccbdabaabbdbcbbbbbccdabbccbdbccbcbcccdccabbdcbdcabcadccbdbcdcddddcaddadccccccadcaacaccbcbcdbaccccbbcdadccbbdbddddbcbddaddbbdcdaabbacbccddbdcaaadccabccdbdcbdabadbacbabcdaccaaadcaacabccadaddabcbbbaadcdddabcbabcacabdbdccccaaadcacbdcacbbdadabdbcaabbdabadbabaaadacacdddcdcdbabdbaaacdccbbcddcbcdbdacaabbabddbdbcadcabcbbbacdddcbbadcddbabcccdaaddabcdcbbdcbbbcbccbcacbddddacacddcccacaddccccccbadacdcbcbccbdadddbbbbcabbcccabcccdcacacdbbcbcdcddacbddbdadcacbabddbddbbcbadbabbcbadbcdadccbbcbcacdaccabaabcbabdcdbaabcbadbdaaaccddbdaadbddbacaacbcbdabbbacaacabddacabbddacbacdaccccacbacddacdbcddcbcadababbcccccdcbacdcdbabaaacaabccdabaddccbddbadaddbadadcadbcacdbccaaddddbbdaabbdaccbbbcbdddcbabcacaadcbdddcbaacadccbbcbaccacddccbcccaacddabdbbddcbcbbaddcaaacbbdaaadddabaacacaabdddadcbcdbacbcccdbbdaaaadbcdacabdccbcbdcabbadaabcbcabaacbccadcccaddabdbaccacbaccbbcdaadbcdbacdbaccabdcabdcbdbbbaaabdbbabbbdbbabdacdcabaadaacccbcaacccdaaabbcaadadbadcdbdcdbcadacdcadbdacdbccdabbcaccabbacdabbdbddbbcababbbbbdcccccdbbcdccdabcacaddacaaacddadccabadbdabccaaddacdbbacaddabdacbcbcaacbdaacdaccbbccccabcdccbcccdbbdabccadabcbaddcdababadabdabdddddbadccbbcdacbbdadbcbaabdbbddbdabbbdcccaaadcadcdddcbabaadddbacbdcbabdddabacaacdcbcbbbbcdbacadadcaabbaadaabdcccdcacdbaddccbbadaddbacdcccbdccacdbbacbabdcbaacddaacacacdbcacbbdbbccdaaccccaccdacadaddadbacdddaaadacccddbccdddaddaadbacaaaacccdcaaddcdccabccdbcdbbcadccabcbdccadcdabbccbbbaccaadcbdcdbaddcaccbcaabbcabcaacbcbcbdcadadabdbcbadacbdbcdcacaacdacacbbcbabcdbaadcacddcddaccddccaaacacdbcdbbcaddcddadbabadbdddcacabdcbdaccbdabccbabaacbccddbadadaabbbcddbcaddaddbdbbcdbccbdaabaaddaddaccdddcaabbbbbcbaacabaccccadacddaacdbaacdddadbbaaaabccbbabacccddddcccbaaaabccbbbbacaaadadbcdcbacaaacadaacacddcadcbadabbdcbdacaccdcaacaacccdbbcbabdaadcbbaacadbacccbbaccbacaaccdbdddaacdbbbdbbbbddaaabcdcdaddbaadbbadbddcccbdddaadabdabbcacaccdcdbdbdcbadacdddbbbbaccbdcddaddbadcbbaadaadaacbaaaddcdaaabaccacdccadadabbbacdaabbcddadabccbbbbcbacdbbdccccdbbabcbddaabaadadcbacdadbdaadbcdbdbaadabbccaaadbbacbbddbcddcbcdadcdacabcbdcbbdbcaadccdbdabdcdabbccacdacbdcbaabdbbbbbbacabadcacbbbdbcadabbcbadcdabcdabbabbbdaccccaddddbadabbcbaaaacaddbcbbcbccbcabbcdacdbddbdacbabdabdddabdbbdbaacbcddcddbcaccbdccbdaddcdaaddcdbddcdcbdabbcabccccbcadcccacccdbdcbadcaaccdbcbccaccdabcabaccabbadcadbadadabbddbdbdaacabbbaaadacbcdbddbcbcddadddbbaadddbabbbddadabbadbbdbaabbcbcdbcaacdbcbbbcddddccbbbddaddadbdccabbdaccacbbcaccbdabaadbbddbacdbabdcbcbbdbdbadbbdbaadccbcccccabcbccbbdccbcbabdbacbcbccbcbdabdddcaaddbccaabbdabcdacbdcdbddbadddddcacaddcacadaccbdbcdbddcababcbcdaccacdbbbadaddddbbcadaacbcacbdcacdbaaaaabbbbdabbbbbadcadbbcbababbbcdacabacdbbdcdcaaadbadaccdcabcccbdbadabdbcddcbacacaccbacadadccdaadabcbbdbadaaaccdcbddddcccdcdabcbacabadcbccabaacdbadadacabbbabaccadbcbcbaddcadbabdadbaaadcdbaabdacadaacdcdbbcdcbcaadddadcddbabdbdcacabaabbdbcddcbcadadccbdacbacbcaacbadacbdbacdddaaccdbbcbbdcddbaddcbbaaabdaacdcabbbdccddababdcbdbcbbacabddcbdadbacaabdbdcdacbabbdcbbdcbddddcccaadacbbcadbacdbdcbcdcddadcadadcacbbbccbadcaaddabddadaddccccdbcdacaadbbccdcabbbadbdbacdbcaaacdccbadcdaadacdcdbdcbcaddaadbaacdcbabbacbbccacabcdbbbbbabaabccccbcdcbbccaabcdbcaadcbbddbacdaccdbbcccccbbccbbcdcbbaabdbacbdabaabddabacdbaccdbdcacadbdcaadcbddacddacadcdcaadaccbcaccbdcbbddcddaadcbaccadaaddddadcbbcaacabbdaccbdbadbcdaaccbaddbdadbabbddcacdccbddbdbdadbaadccbccbacddbbaabacddacdcaadbdcabadcbccdbccdbcadcadcaabcaaddcddadcddcbdcbcaadddcaddcddbcababddcbcadddaacadaabbaaaddcdadbbabacddcdadddccbdcbdcbbdacdbaabddabdcacbcbcaccabdabccdbcbaacddcacaadcbaabcdaaddddcdcddcadccadadbdbdcabdabddabcbbbbcadbbdbadaddbbcdbcbcaaddbbaabbbcaabcccadaaddbabbddcdacababcbdacbddcaacbbbccdcdbadabdbccababbcdadaddcdbddcbcaacddcdabcdabccddcaddcdabddbbcbabbcccbbcdcaaabacdccaccbccacbdbbabbbaadcbdcccbcccdcbdadacaddcdbbbcbdaccadbbccdbcbdddadabcbaabcbabbbbcdabaaacdcbacaaadaaacaabbacdcbcbadddcbbdcdacbbbcdddbbdcdadcbabadbabcabbbbaadcadcbdaaacbbaddaadbdcabddbaaaddbdbaddadcaccdbacbaacccacbcdcabbabcbccdcbcccbcadcbddddaddaddcacbbabdcadabaacabbbabadaccadddbbaddbaccaadbccdaddcbbbddbabbabcacbcadaaacdcbccaaacdcbbbccaaadbadaddcbdccbccdadccbcddccacaacdbacccaaaabbcaaddcabdbabbacdbbdadcbbdbbabddaddcadbdcabadaccbbbacadddbaddbacdbbdababdacadbbcbcccddaabadaabaaabadacaaaadcacdabadaccaccdccbbdcaabcabaacbabaacbdaadbdcbbdcbdbbccaaadadcdadacbababdbddadaadacbdaccdbdcdabcbcdbbccabcacaaababbccbbdaddcccaddaddbdabcddadbbbcadbbdcbbdbadcbdbbbdcccaddcabdabcbacbcdcaadacbdaacdbcaaacddcdbaadcadbaabcbbcbcaddbcbddbcbbdccbccdbdcaccacaabbbdcdabbbdadccbcabccbbbbbbdbdadccabbadcccaacbdbcbadddadacdbbabadbdbbcdbcaddacbabadcdcddcdacdbcaccadadbcabcdcbbbbbcaccccdcbbcbcccdacdbcbdcdcbcabcbbbadcdcdcadbbdadbabddcccaccdcadbcdbbaacdbadcacacbadacdacbcabacbcdcbddccdaddbabadbdbabbadcacdbadbcaaaabdaadabbbcbabbdadcddacbbaacadacaaccaaabacabcdbbddaabdbbdcaddcddbccbcbadbdbdcdbdbaccdcbdadacbcacaadcccdcbcbcbdcabaaacbdcaadadbbbbccbdacaaabbcaccbbbcacddbdadccbadddbcabcaadabbccbdbbddababddcdbddacbadabacdddddacddaadaddbabaaacdacddcdadaddccbacadcdcdadbbbdcadbdbddbccdacccadaadcccaabdcadbcbcbcbdbdadcdadaaccaaaadcbddadaccccbaadddaddadbacbbbcadcadbbadcbbcabacdcacdbadabbaaadcaadaaadabdbaabcdbbbbbbcaddbaacbaabddcdcbcabcdaabcaabaadddadcdccbbacdcdbaacdabadcdbcaaaadcdabcbdcbddcdccdaacbbcccdbbdbdcadcaadcbaadccdddcacbcdbaadbbabddabadbcaacaddccadadcbdacacbcbbcaaaddacdcbadccbdcaadacbaabbbaadcaadbbcdbacaacaccdcacdacaddaddbaacdcbdabacbbbccdbacdcbdacdbdbbcdaadbcbabaabaabccbbcdadbabacddaacdccddcadbdcbcdcdddcabdddb