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- # ref: combos seq for my ai game...
- ['abaddcba', 'cacabdda', 'bccadcbd', 'acdbcabb', 'abaddcda', 'adcbccdd', 'cababcda', 'dbdbbacb', 'ddbaccdb', 'bcdaddbd', 'cbcbddaa', 'bdacddbd', 'bdccacdb', 'cabadbdd', 'dcbbddba', 'ccababdd', 'abbabdcc', 'dadabdcc', 'adcadbcd', 'dacbadbb', 'bcddadac', 'cddbadda', 'ddcacbca', 'daccbdbc', 'dadcabab', 'acacdbdc', 'ccbaadcd', 'acbccbdd', 'acadbabd', 'adccbbac', 'bbcbcabd', 'cdadacab', 'bdcbcaac', 'daacbcbc', 'dbccdcac', 'baccddbb', 'ccbbcdba', 'caadbdbd', 'adbdbacb', 'caccdbcd', 'bbadbcba', 'dcdacbac', 'adbcbccb', 'ccabbdad', 'adbdadcd', 'accabddb', 'dabcdabb', 'dccddcba', 'dbadbcda', 'cadbcbcc', 'ccbccdba', 'cbddbbab', 'dbcbccab', 'abbddbdc', 'bbdabccd', 'dbacdbad', 'adcdcddb', 'acdcbbad', 'bbdacacc', 'acbcdbcb', 'ddbadcda', 'abbcadcd', 'dbadacda', 'cbadcadb', 'cbadbdba', 'dccaccbb', 'dabcdcba', 'bddadacd', 'bddcadcc', 'dccdbdca', 'cdaddbab', 'daddbbcb', 'bdabccbd', 'bacdabcb', 'bbabcada', 'bcdccbad', 'bbdcdadc', 'cabbadbc', 'ddbacdad', 'dbcddadc', 'acddbcbb', 'abccadcb', 'accadbdc', 'bbddccac', 'dadbddbc', 'cddadadb', 'ddacbdda', 'adcacbdc', 'ccabdabd', 'bddbdabc', 'dcaddcab', 'dcadacbc', 'bdaddcad', 'ddccdbab', 'dcadddab', 'cbcdaddd', 'dbcacadb', 'acdddbbc', 'bbdcdadd', 'bddcbaba', 'dbddacda', 'dbadcdcc', 'acdbbddc', 'dcbbccaa', 'cbaabaad', 'cabcdcdd', 'bdcdcaac', 'dcadcbab', 'bcbadbac', 'dddcabda', 'acdccabc', 'baadaacb', 'cababdcd', 'ddbccada', 'adcdabcd', 'dbbcbacd', 'dcabcbbc', 'cdbcddac', 'cbdadadb', 'babccbad', 'adbdcdda', 'dbccdbad', 'ddabccad', 'dbabdcac', 'cdaadcbc', 'bbddcaca', 'cdacacbd', 'bacbdacb', 'abbadadc', 'ddaacbbc', 'dabcadcc', 'bcdaccbd', 'cadccbcd', 'adbccbdd', 'bdcacada', 'ddaacabd', 'bddabdac', 'ddbbdaac', 'caccabdc', 'cabbabbd', 'ddcdcadb', 'acdccdbd', 'bcadbcac', 'dbcbabdc', 'cbbcbcad', 'dacbacac', 'dbcadadd', 'ddbcacda', 'cdcdbbac', 'aacbbccd', 'abcdbdcc', 'abdbcbab', 'cbddaddd', 'ddcdabbd', 'adbdbbcb', 'abbcabad', 'bacbbdab', 'abdcabcd', 'acbadaba', 'bcdacddc', 'addaccab', 'ddacbbdd', 'cbdacbcd', 'bacbdbcc', 'dadcbdcd', 'dabacadb', 'ababddac', 'bddcdbac', 'cdccadbc', 'cdabccba', 'cbdbcbac', 'dbbcdacd', 'cabcdadc', 'bbcdbdda', 'ccaadcbd', 'acabbdba', 'acbbdbdd', 'bbadcddd', 'aabaabdc', 'bbddacad', 'abcdacdb', 'cdacbabd', 'abcdcdca', 'acddbcbc', 'dcdbabad', 'dcadbbca', 'dcbcbabc', 'bcbbadbb', 'bcdacacb', 'dcaabcbc', 'dadcabcc', 'dabcabdb', 'abddcbaa', 'ddaccbcb', 'dbccabca', 'abdddcad', 'cbccabcd', 'bbdacbcb', 'dcbbadcd', 'ccbcadbb', 'abadcbda', 'baacaabd', 'cbadcdad', 'bcbbcdba', 'baccbbdb', 'babcdbdb', 'ccacbddb', 'dcaccbdc', 'bbdcaacd', 'bdbcdabd', 'bcbddbab', 'dabcbdba', 'ccdabdbd', 'caccdabd', 'acbbdaba', 'acacdbac', 'cabcbdca', 'bdadcbda', 'dacdccbd', 'cddaccbc', 'abddbcbc', 'addbcadd', 'bdcdadbb', 'bdddaccb', 'cbcdbdca', 'adccabcb', 'bdbccbab', 'bbddccda', 'adadcabd', 'bbcdcacb', 'dbdadadc', 'acbbdcca', 'cdabcbdc', 'bbddacba', 'abcddaca', 'dbbadcac', 'adccdbcd', 'bdadbdac', 'cacadccb', 'dabcbcda', 'dddcdaba', 'bddadddc', 'cbccadcd', 'cadcbbab', 'ddcbdcda', 'adbcbdda', 'abccadbd', 'accddccb', 'cbbddaac', 'acadadbd', 'dcbdddba', 'adddaccb', 'dcbbadca', 'adcacbdb', 'cbdabbac', 'cadcabda', 'abcbacda', 'abcacabd', 'bcabbdcb', 'bcbdcada', 'bcdccbac', 'acbadbad', 'bdddcacc', 'cbadbbdb', 'dbdcabac', 'cbabdcad', 'baabdbcc', 'dcbbcdda', 'aacbbaad', 'cbbdbcda', 'abcbddca', 'bbddaacd', 'dabbacdd', 'acbcbdab', 'dbbdccad', 'bdcbbadc', 'bccbabad', 'ccbdcaad', 'bccddadb', 'acbdabca', 'bdccadbd', 'dcbcdcca', 'cbaacdcb', 'adbbdcbc', 'cddadabd', 'badcacdb', 'bbaccadd', 'abcadabc', 'cabbacda', 'abddacdc', 'cadcabdc', 'cdababbc', 'bccddaad', 'dccdccba', 'ddcadadb', 'ccbcdcaa', 'daddcbac', 'aabcdaad', 'ccbbcaad', 'bacbddda', 'dabdcddb', 'bbcbcadb', 'dabccddb', 'bbdbacbb', 'dbdacdbb', 'dacadadb', 'dbaacdcd', 'bdbcadcc', 'daabaadc', 'adcbacdb', 'dbcbacdb', 'bbdbbaca', 'bccaadcb', 'abadcdda', 'cdbcabdb', 'ccbcbadc', 'addbdccd', 'bacbdcac', 'bacdccdd', 'abbcdcca', 'bdcdadac', 'adbabdcc', 'cdababad', 'bccdbcaa', 'dccabbca', 'acddbdba', 'bcdcadcc', 'dcaacbcc', 'cdabdcdd', 'abcabdcb', 'daccbdba', 'ccdbcadc', 'dccdcbad', 'abcdcdba', 'dbadacca', 'dbcddcba', 'bddcdbba', 'adbcdbcb', 'bbacbbdb', 'dbddcaca', 'cacdbcda', 'bdcdacdb', 'adcababb', 'cacbdcdd', 'dabbadbc', 'aadcbaac', 'abcbadda', 'bcbbdadb', 'cddbabdc', 'cbabbdcb', 'dcbdbcad', 'cbbaccdd', 'bbdbbaac', 'cdbacaba', 'abcbccdb', 'dbcadbac', 'dcabcbad', 'dbdbbadc', 'ccdabada', 'bbaccddc', 'cdbccacb', 'dddbcaad', 'ddabbabc', 'cbcdabbd', 'abdcadcb', 'dabccbba', 'acbcdbba', 'bdbaccdd', 'bacbddcd', 'bcbbaddc', 'bbdabcab', 'bcbdbacc', 'ccabcbdc', 'badbcadc', 'bcaddacc', 'acdbcacb', 'dacdddbc', 'abbacdcc', 'bdbbcadd', 'badbdcab', 'cdddccab', 'ddbbaacd', 'cbbcaacd', 'addbcdda', 'dcdcbadc', 'bbcdcabc', 'adcdadcb', 'dbbcdabc', 'cdcdcbad', 'acbdaccb', 'bbdbdacc', 'babcddab', 'bcdadcca', 'acdbcdbc', 'ccbdbcba', 'bddadbac', 'dadcbdcb', 'acddbddb', 'cbddbabb', 'accbdcdd', 'ddcbcadd', 'daddbbca', 'baccbdbc', 'acbbdadc', 'bacbbcad', 'acddbadb', 'abcaccdd', 'ddcddabc', 'bcacbbdd', 'cbacdcab', 'adacbacd', 'babdcabb', 'cdadadbc', 'bbcdbacc', 'ccbaadbd', 'ddadcddb', 'dadbcdca', 'abaccdab', 'dcddcdab', 'cbcdccac', 'cbadbcdc', 'ccabbadd', 'dddbbcaa', 'cadcbcdc', 'babbcdcc', 'abdcdbcc', 'cdbccbab', 'adbbddcd', 'cadadbab', 'bdcaaccb', 'cbadddbd', 'dbcaadcb', 'cdbcadba', 'bdddadcc', 'abbcbdda', 'addacbac', 'ccdabbad', 'dbcdcacb', 'dcbcdbac', 'abacabdb', 'ccabacda', 'cdbaadcd', 'dbddcbaa', 'ddcbaccb', 'bdadacdb', 'ababadca', 'bdacdabd', 'babcdcbc', 'accadbcd', 'cbdabadd', 'bdbcadba', 'cabaddab', 'dacbbddc', 'cadbddcc', 'dbdbabbc', 'ccdbdaab', 'dbabadcd', 'adaccbda', 'dadacbbc', 'bbcadddd', 'cddaccdb', 'cbdacdcb', 'ccacbacd', 'bcdadbcd', 'abddcdac', 'adabacbd', 'ddacbaac', 'bcddadab', 'bccdcbab', 'bbccddca', 'ccadbdab', 'daddcdbb', 'cdcacbcb', 'badcdacb', 'dcdaacbd', 'cdacbdcd', 'dabcabdd', 'acddadbd', 'aacdaabd', 'dbdadaca', 'bbadcdbb', 'dbcbadac', 'dbacabdd', 'bcddadca', 'bbccddac', 'dabdccbd', 'ddabaacc', 'bacbadca', 'bdccbaca', 'cdcbabbc', 'acdcabad', 'bdcaddbb', 'bddccacd', 'cdacdbda', 'badcadcb', 'cddbddba', 'bcacadcc', 'bddaacaa', 'ccbddaba', 'accbadab', 'bbadbcdd', 'cbadcbdb', 'adbbcdcd', 'babbadcb', 'cdacdbdc', 'ccbdacbb', 'bbdddcaa', 'cbabadbc', 'cadbcddd', 'acdbcdca', 'bcdcddac', 'bcddadad', 'cbbdbacd', 'acbcbcdb', 'babcddba', 'dabccddd', 'ccdcdcab', 'ccacbbdc', 'cbdadccb', 'cdcddbba', 'bcdbcaba', 'ddbddaac', 'babdabca', 'bccdacdc', 'dadabbca', 'caccddba', 'bdbdbdca', 'bbcdcdba', 'cddcbadd', 'cdaccbbd', 'abccbddd', 'daacdaab', 'ccadbdac', 'bcbbadcc', 'daadbdcc', 'aabcbbcd', 'cdcbbaba', 'ccdaddcb', 'dcbaaaad', 'aaccdaab', 'abdcbdac', 'bbadcbad', 'dadccbbd', 'ddcddbaa', 'addbdacc', 'abbcdcda', 'caabcdcc', 'ccbdaccd', 'ddcdbbac', 'bddcabab', 'ccdbdcac', 'dbacdaca', 'adbdbcda', 'cdcdacba', 'bcacdabd', 'ccdcdbac', 'daddbacc', 'adbdbbdc', 'ddaadcbc', 'adddbcbd', 'bbcbdcab', 'cbdcdadd', 'cdabcada', 'acbbcdbc', 'acddaacb', 'ccadabad', 'cabdcadd', 'baacaadb', 'aaccbbdc', 'ddcbdadc', 'dacddaab', 'bcbdbadd', 'bdacbacd', 'acdbbdbc', 'dcabbadd', 'adbddcdb', 'ccbbdaba', 'ccaadcbb', 'dbbdcaac', 'acddabbd', 'dbbcbaad', 'ccbbadad', 'cacbcdcc', 'dccadcba', 'cabbcabd', 'bcdcdbad', 'bababacd', 'bcbaccda', 'dbcbcacc', 'cabccdda', 'cdadabac', 'bbcdccad', 'dccbacab', 'abddbcdb', 'adcbacbb', 'ababcadb', 'ccadccab', 'ababcdcb', 'cacdcadb', 'babddcca', 'dbdaccba', 'bdababac', 'bbacdbdb', 'bddcacbd', 'dabdacdd', 'dccabdab', 'badbddcd', 'cadcabba', 'bdbdbcba', 'baddbdcd', 'bcddccac', 'dbbadabc', 'bcadcabc', 'addcbbac', 'abcdabbd', 'bdccaddb', 'dcddabcc', 'dabadcdd', 'cddbcbca', 'acdbcacc', 'dcddacbb', 'bddabcaa', 'cbdbadcd', 'dbdcadbd', 'dbbadacc', 'dccbcada', 'acacadbb', 'cbbacadb', 'dbdabbac', 'ddcbbaad', 'bcdacaca', 'ddadbacb', 'bcadbbcb', 'dddaccba', 'acdccaba', 'dadcabbd', 'dcabbdca', 'cbcbacad', 'bdddcaca', 'ddcbbadb', 'dacbbdba', 'dbcdcaca', 'ddcabaab', 'dcbabcca', 'daadbaac', 'dbddbcda', 'abdabcdd', 'cabacbdb', 'bdddacaa', 'cbbdbbca', 'dcddbdba', 'abdcaddb', 'bbacdbdd', 'ddaabdcd', 'acabadcc', 'bdddbdac', 'ccabcdca', 'baacdcaa', 'dcadbdcd', 'bcadbabd', 'daccdbbd', 'dcaabdcc', 'cddbbcab', 'bdaacdaa', 'caddbaca', 'cdadbcbd', 'dcabdcab', 'cdacbaca', 'cdbdcaad', 'dbbdbaac', 'abdcaddd', 'cdbdabcb', 'abccbada', 'cbaadbdb', 'dabcbcdd', 'dbabdcba', 'bacbddaa', 'cacbabdc', 'dcdabbad', 'cdbcadca', 'dadbcbcd', 'acbcadac', 'abccbadb', 'cbdbadca', 'aacbaabd', 'acaccdab', 'ababcddd', 'cbaacbdc', 'dbaacdcc', 'adabcbcb', 'dabddaca', 'dbddaaca', 'acbddabc', 'dccbdaba', 'ddccabac', 'ccdddaba', 'dcbabbab', 'abdcdcac', 'ddccbdda', 'cddacabb', 'cbdbadbb', 'cadcdccb', 'babcabad', 'ddadbdac', 'ccbcdcad', 'ddabccba', 'dbaadbbc', 'dcbcbcca', 'dcddbcad', 'bcbddcba', 'abdbacdc', 'abdbcadd', 'bbacdbab', 'babbcdba', 'cbbddacc', 'dcadadbb', 'bdaccdda', 'cdbbcacd', 'dcadccbd', 'cdcbddad', 'bbacadda', 'cdcddbaa', 'ddabcbcc', 'cadabbdb', 'acbbddad', 'cababddd', 'dcabddcc', 'acbdbdbc', 'dcadccba', 'dcdccbac', 'ccaddaba', 'ddcbabda', 'bbddacca', 'caddccbc', 'acacacbd', 'dcbbacca', 'babcddaa', 'daccdbac', 'cababdbc', 'cbaddaab', 'bcbacadc', 'abacddca', 'adcbabcc', 'adcbdaba', 'bbcddaca', 'aacbdbbd', 'abadacac', 'bdccbdda', 'ddadbcbd', 'dbdcbadb', 'accdbcab', 'badbdbca', 'cabccadd', 'cdcbddaa', 'cbddabbc', 'dbacdadb', 'ccadbddd', 'dbdbacca', 'abadcdcc', 'dcbdcaca', 'bdaaaacc', 'cabcdccb', 'dbddbaca', 'bcdbcbda', 'cddbaada', 'bbdacddc', 'ddabddac', 'bdabdacc', 'ddccbaca', 'dcabcacd', 'abacbcda', 'acbdbdab', 'dcabacdc', 'bbcddacc', 'acdccbac', 'dacdbadd', 'abccdbdb', 'bccddadd', 'addccbca', 'aaccbccd', 'dbbcdacc', 'abcddcbc', 'babbcdac', 'cbbdbbad', 'bdbcabdb', 'bccbcadc', 'bcddcaca', 'ababddcb', 'acbadbcc', 'cbacbdcd', 'caccadab', 'abbaccbd', 'bcaadbcd', 'badaddcc', 'cddbbdba', 'ddbdadcb', 'bddabcba', 'bdbababc', 'dcdcbbad', 'abcbcddb', 'bcbcadbc', 'bddadbbc', 'badadbbc', 'ddadbcdd', 'abdbacdd', 'bddbbadc', 'cacbcbdc', 'bacddcda', 'ddacadba', 'dabbcbba', 'acbddccb', 'abacdbca', 'dadcbaba', 'bddbdcaa', 'addcbcdc', 'cacddaba', 'dccbdaab', 'bcdcbdba', 'ddbaadac', 'bdbccacd', 'bdcaddac', 'cddbccac', 'adcdbadc', 'cbdcaacc', 'cdcaabcb', 'badbbccb', 'bbcaddac', 'dddbccac', 'cbcbbdab', 'bdaddadc', 'cbdddbac', 'cdabbcda', 'acbdabdb', 'babaccad', 'cacdabcc', 'bddccadc', 'adbcbdbd', 'cadaccbd', 'acddcadb', 'dbcddadb', 'acdacbca', 'acbdacbc', 'cadbdbbc', 'bcdbadcc', 'ddcddacb', 'babdcddd', 'dadbacdd', 'bdcdcacd', 'acbbcbcd', 'dabcdadc', 'dccdbbab', 'accaddab', 'babbadcc', 'dcdabbda', 'cbdccbaa', 'bbdcdcac', 'abdacabd', 'abddcbcc', 'bcdadadd', 'bcacdcba', 'aadbccbc', 'bdcbcaba', 'bdadcbcc', 'dacbbdad', 'daddcbcd', 'ccdcddab', 'bcbbcdac', 'aaaabcdc', 'dcbbccba', 'daabbccb', 'acbdacac', 'dcacbddd', 'cdbcbbad', 'bcbdabdc', 'ddbcaccb', 'dbdabbcd', 'caddcbaa', 'bacddccb', 'baccdcad', 'cddbcada', 'dbdabcbd', 'bbdddcab', 'cbcadbba', 'adcabdbd', 'cddcabbc', 'cdacdbcd', 'bccbdbad', 'acbdcbad', 'cdbcabab', 'ddbccdda', 'cdabcbac', 'cabdbadc', 'adbdabdc', 'bbadabbc', 'acbadbab', 'bdadcaca', 'cacbcbdb', 'dcbdcbca', 'ccbabada', 'bbddabdc', 'cddabdda', 'dbacacac', 'adbcadcd', 'baadbcaa', 'caacdbcb', 'bdabcddb', 'dbcbacdd', 'accdcdba', 'dadbccbb', 'badbbcab', 'abcabcdc', 'cbadcada', 'aabdcaab', 'dcdacdbd', 'bacdbdba', 'cacdbacc', 'dabddacd', 'abcddbbd', 'cdbcadac', 'bcacabda', 'dcbcdcda', 'cadbabdd', 'accddddb', 'abcdbdbc', 'abccddca', 'bcdcbabb', 'bbcdabcc', 'ddcdaabb', 'accabdbb', 'adbcadad', 'cdbcadbc', 'dbbccada', 'cdccacdb', 'ccddbaab', 'bccdbcad', 'caccbdab', 'acbdbaba', 'babbdccb', 'abdadcab', 'badbcbda', 'bddcadaa', 'dbadcdcd', 'dbcdccaa', 'cbdacdab', 'cbcacabd', 'dccacbcb', 'dbaadcdb', 'ccdaabdc', 'aabbdccb', 'bdaccdad', 'dbccdaca', 'cdbbaabc', 'cacadbdd', 'bddcaaab', 'cadcdbcb', 'dbdcadda', 'caacdbcd', 'bdcadbdc', 'ddcbdbaa', 'cbcbacdd', 'dcbdbada', 'ccbbdaca', 'dadacaba', 'bdcdcdad', 'ccabddad', 'cddaacab', 'ccdaabbd', 'addbcdaa', 'dbcadbbc', 'cbcaddca', 'cbcbcacd', 'bdbbacab', 'adcdabdc', 'dbdccacd', 'bdbdcadb', 'ddcbaabb', 'cddcacbb', 'acbadcba', 'acdccbdb', 'accdabdd', 'bddbcada', 'dbdcabcb', 'cadcdcbb', 'acddcbaa', 'cbdabdba', 'cdacdbbd', 'cdbacdab', 'addcbdba', 'badcdccb', 'dacadbab', 'dddbacda', 'dbbcbada', 'bdacbada', 'adbbdcac', 'dcbbacdc', 'bcbbaadc', 'ddccaacb', 'adccbbdb', 'cdddacbb', 'bddcdbad', 'ddcabcbb', 'bdbabbca', 'dcdbbacc', 'ddacbddc', 'adabcdba', 'cbadccbb', 'cbbcacdb', 'adaccacb', 'bbccddda', 'bdccbacd', 'accddbdc', 'dcdaadbd', 'ccdccabd', 'acddabaa', 'caccbdac', 'bccddcab', 'dcdbddaa', 'cadcabab', 'aacbbdcb', 'bbaabccd', 'ddaadbcb', 'acdabbdd', 'bacbddca', 'cbcdabca', 'addbbccd', 'addbcdcc', 'abdcdbbd', 'bacddacc', 'acdddccb', 'cdaabdbd', 'dacdddcb', 'acdbbabd', 'cabdbddd', 'abbccbbd', 'bbaadccd', 'ccacdacb', 'bdcacdba', 'bcbbabcd', 'cadcbdbc', 'ccabacdc', 'addaaacb', 'bcdbdada', 'cdbbacbb', 'abddccdd', 'adcbdbab', 'bccdcdad', 'bcdbadbc', 'dabdcbca', 'adadbcdc', 'dcacbcbc', 'acddcdbc', 'bbacdcca', 'abdcdccb', 'addbdcbc', 'bddacaba', 'cbddadca', 'bbadcaba', 'dacbdadb', 'badccdab', 'dabddcac', 'cbdadbdb', 'cadabada', 'accbbdcc', 'bbaacdaa', 'dabbdcdc', 'cabbddbb', 'dbcdadcb', 'babdadcd', 'adcaccdb', 'bcacdadd', 'bbcadbad', 'bacbabbd', 'bcbcabad', 'dadcbbda', 'bbdcabbc', 'bcdabbab', 'dcdcdadb', 'acdadbdd', 'ccaddcba', 'dbaccdda', 'cbaddbdc', 'addcbbdd', 'accbbabd', 'cddbdcaa', 'dddbcacb', 'dddcbadc', 'acbcadbb', 'ccdbacdd', 'bbabdbca', 'dcbddaac', 'babdbadc', 'adabccab', 'bcbbdbad', 'addbdcaa', 'cdccbbda', 'dbbddacc', 'ddcacbab', 'dabccdbb', 'badcdcad', 'dccbaadc', 'bccdcbaa', 'adabbcba', 'cbbacbad', 'dcbbcadd', 'cbcdadbb', 'baddcbda', 'bcaccdbb', 'adcbddda', 'abadbcab', 'dabdbcba', 'dabcbcba', 'cbccdaac', 'dbdcbabb', 'abbccdab', 'abcbcdbd', 'dcbbdaab', 'bcbacddd', 'bcadbbdd', 'bdcdadad', 'acbdadad', 'baddbaac', 'bcdbbcda', 'ccdbbcaa', 'cdbbcbba', 'abcddcac', 'bbcddacd', 'cdabdbbd', 'acadabad', 'dabbcbdd', 'cbbdcabc', 'bdddcaba', 'ccbdcadb', 'acdcadba', 'bdbcaddc', 'dcbcbada', 'dddaabbc', 'dbcbadca', 'abdbddca', 'cbbaccdc', 'bdbbacda', 'bbadbacb', 'bdddabdc', 'adcadadb', 'caddbabb', 'bbccddba', 'bdbadcdb', 'bdacabbc', 'baddcbab', 'bdddcabd', 'bdabcacc', 'acbacdbd', 'abcabcda', 'addadccb', 'aadbcdcb', 'ddbcbdba', 'cbdcdaba', 'baacbbcd', 'cdadbdab', 'dbcdcacc', 'cdbcaaaa', 'cdbacadb', 'ddbcdadc', 'bbacbccd', 'ccbdabcd', 'badbcadd', 'dcbaacbc', 'dbcadabb', 'adcbbcdc', 'cbbadbdb', 'cbbcadcd', 'adcdcbba', 'acdbdabd', 'bccaddca', 'bcaccdca', 'dcacbbcb', 'bacacada', 'cacbcdbb', 'abcadacc', 'cbbaacdb', 'cbcadaca', 'dbbdaacb', 'cbdbdada', 'cbdbabad', 'dbbccbda', 'bbcddabd', 'bdcabdca', 'cbdbacbb', 'cbdccadb', 'babddbdc', 'abdbacbd', 'dabdcdbc', 'ccbbabda', 'addbddac', 'bcdadccb', 'bccbcabd', 'cadbaccd', 'dadabcdb', 'cdcddcba', 'adacbccb', 'bacbacdd', 'baddbbca', 'cadddddb', 'dccabdbb', 'bcaccbdd', 'cbacddca', 'cadbccbc', 'baccadda', 'cdcadaba', 'cabdbcba', 'bdadbbcd', 'ccbaddad', 'daabcbcc', 'ddabacbc', 'cacbbccd', 'ddabaaac', 'cbddccab', 'bbdbadbc', 'adacdbac', 'acbccbcd', 'bdadbdca', 'dcbdccba', 'bbcadadd', 'dacbbabd', 'adbdcbcd', 'caabcbcd', 'dadccdbd', 'bbacdbba', 'babdcbba', 'accbdccd', 'dbcdadcd', 'caabaabd', 'cbcdaabd', 'cabadbcb', 'cdacabbc', 'dcddaabd', 'aabdcdcc', 'bacbbdca', 'cabbddaa', 'dcabddbb', 'dcaddabd', 'daccdacb', 'ddbbcadb', 'cabacbdd', 'badbbdcc', 'cabdabac', 'ddacaacb', 'dcddabac', 'ccbaccdd', 'cadddcdb', 'bdcaadbb', 'bdccdcda', 'bcbddcaa', 'dbdacbcb', 'bcabdbad', 'ddadabac', 'bbdaddbc', 'acbbaddd', 'cbdbaddc', 'dbcbabda', 'dccaaaab', 'bdbdaacc', 'ddbcadcc', 'babbcdda', 'cdcdadba', 'abdacddd', 'bbcabdda', 'dcdabcad', 'ccabaddd', 'bbddacdd', 'bdaccbca', 'cbcaddad', 'caddbddb', 'bcaddccd', 'cababdab', 'bcdbcabb', 'acdbdabc', 'aadbcbcd', 'addbcbcb', 'ccbbcdca', 'ccdddbca', 'adbacdad', 'ccabdadb', 'cabdabcb', 'ddabcdca', 'bccaddda', 'dadaccbc', 'abacdccb', 'ddaddbac', 'bbcbdaba', 'cbcdccab', 'ddadcabc', 'abddcdca', 'dcbadacd', 'dddcadba', 'cbddacda', 'accbdbbc', 'addcbbdb', 'accdddbd', 'bbabcdcb', 'ccadcddb', 'ddcbdbca', 'cddacdba', 'badcbddd', 'ccdccabb', 'dccbdaac', 'abdbbacb', 'abdddcaa', 'bbabacda', 'dadbdbbc', 'cbdcacbb', 'dccaadcb', 'adbbabcb', 'dbadabcb', 'cbdadacb', 'cadaddba', 'cbcddadc', 'cdaddbdc', 'adbadacd', 'bacdcadd', 'dbabbccd', 'cdbdcdab', 'dcbbcbaa', 'dddcacbc', 'ddbdacba', 'cabdcddc', 'cbcaddba', 'bcaddbaa', 'abbcbdbb', 'badbccad', 'dcdcdabb', 'caccbbdc', 'bcbabdca', 'cabdccdb', 'abdbaccb', 'dababdac', 'bcddbacb', 'ddcabadc', 'acbdadbb', 'dbcdcbda', 'acabddac', 'cadbdbdd', 'acdabadb', 'bcddbadd', 'bbacadcb', 'adacbcba', 'bbcabcdd', 'bdadcadb', 'dacacdba', 'dadbacab', 'cbcbccad', 'accbadda', 'acacdcbd', 'cdababcd', 'bddddcac', 'bacadccb', 'abadcbdb', 'accbdadb', 'cdacacab', 'acdabacd', 'dbccbcba', 'dbddcdda', 'adcbbccd', 'caccbadd', 'ccbacdda', 'badbcbbc', 'daaaaccb', 'bddcbbca', 'dacabddb', 'dadcacbc', 'acabcabd', 'ccbddabb', 'adcbdddc', 'cbdbbaac', 'bcdabdcd', 'acdcbdca', 'bccacbcd', 'dacddcab', 'bdbcadbb', 'bcdbcbca', 'acbadccb', 'dabdcbba', 'cbdbdbba', 'cabadccd', 'dddbacba', 'dadbbdcc', 'bdcbdadc', 'addcdabc', 'dccadbad', 'bccadcac', 'cdddabdb', 'cdaccdbc', 'ccbabcda', 'adddbacc', 'badcacbd', 'ccdbadab', 'acbcddaa', 'cbddadcd', 'dcaadaab', 'dbabccbb', 'abcdbdba', 'accdbbca', 'ddadadcb', 'dbacbddd', 'abacdacc', 'ccadbbad', 'daabcbdc', 'cadacbba', 'dbcdbacb', 'dcbbcdba', 'dccabbcc', 'dcadcbda', 'abdcacdb', 'cdcbadcd', 'adcdccbc', 'dcdbbabc', 'adabdbbc', 'bdcabccd', 'dcddbcba', 'ddbacbba', 'dadcbcab', 'bccbbcda', 'dacbcabc', 'bdcadada', 'dcadcdcb', 'ccabcdab', 'aabcdbcb', 'dcbaddda', 'ccbcadcc', 'cabcdbba', 'bcacaddd', 'abcbcddc', 'dcbaddcd', 'addcacbb', 'adcddbcc', 'abbcacad', 'dcdaaaab', 'cacdbabb', 'ccbaadbb', 'bacbdbdd', 'adabbccb', 'cdccbcba', 'bcdbddad', 'cbacdadd', 'ddaaccba', 'accddabb', 'dcbcaaaa', 'bccbdabd', 'ddababcc', 'adcdbcac', 'addcdcba', 'aabbaadc', 'adbacbdb', 'ccbbadcb', 'cadbdbbd', 'addbbadc', 'adacbcdd', 'bddcdbca', 'bcdcacdd', 'cdcabcac', 'cbbcadcc', 'caabbcdb', 'bddbacad', 'bdcdbacc', 'badbcdcb', 'cdbababa', 'babcdccd', 'dbdaacaa', 'ccabbcdc', 'bdaccbac', 'bdbbadca', 'dadbdcba', 'adbcdaba', 'ddcbccaa', 'bcadcabb', 'bdbdcbba', 'cddacacb', 'ccabbcbd', 'ddcaacba', 'adbacddd', 'adacabad', 'dbccddab', 'cbaccdac', 'dddcabaa', 'caabcaad', 'ccdcbbda', 'acdcdcba', 'cabcaddb', 'bacdbdab', 'cbcdadcb', 'dcbdacba', 'cadbdcba', 'cbccabbd', 'adbccacc', 'bbcaadcd', 'cdbbcbaa', 'dacddbad', 'bccbdaca', 'dadbcadb', 'cdcdbabc', 'badbcdad', 'dbacacad', 'dbcddada', 'adccdbda', 'adaccbcb', 'ccdcbabd', 'ccddaddb', 'bddcbacc', 'dbadadcd', 'bdbacbcc', 'dbcddbaa', 'cbcbdbad', 'bdaaaacb', 'cbaabdcb', 'dccadaba', 'cadbdddc', 'babccabd', 'abadabac', 'cdcbdabc', 'bbcdbdad', 'dbbdcbad', 'acabddda', 'bccbddba', 'bddcbabb', 'aadbcdcc', 'bcdcbbda', 'cdcbadba', 'dcbbabac', 'bccacbda', 'ddcddbca', 'bacbdadc', 'cacabdac', 'dddacabd', 'ddaddabc', 'bcabbdbb', 'addcbcaa', 'abcddbca', 'abbacdcb', 'bbddbcaa', 'badabcad', 'bdbddcca', 'dbdbabcb', 'dcbaccdd', 'bcadbbcd', 'acbddaba', 'ddacdbda', 'dcbacbbc', 'bcadbadb', 'dacadbcc', 'dbbcacda', 'cdabacbc', 'bdcdcabb', 'abbacacd', 'bbcbacbd', 'adcbcbdb', 'ccadbabd', 'dcabbcdd', 'cacbddac', 'cddaaccb', 'ccadbdba', 'accabcad', 'bbddaaca', 'dcabaccd', 'bacdbbcc', 'bccbdacb', 'bbabcdad', 'dacdabdb', 'bdbbcdba', 'addcbacd', 'bdccaabd', 'ddaacbca', 'accddbbd', 'aabdcaac', 'adbabdcd', 'dcbacbcd', 'cacbdcdb', 'cbbdaccb', 'cbaccddc', 'ddbdcdac', 'ccbabddd', 'dacbbcab', 'dcdbbadb', 'dccbabca', 'bcacacda', 'dbbacdad', 'dcabbcba', 'cddabaca', 'dcddbcda', 'dccacbac', 'bddccbca', 'accbdaca', 'bdacabdb', 'ccbdddba', 'bdbcbaab', 'dbdcadcb', 'cacddcba', 'cdbdcbba', 'bdbcdbaa', 'addabacb', 'cdcacdbb', 'adabdcdd', 'cbacacdc', 'abcabdbd', 'dbdacbbc', 'acdcbcbc', 'cbdcabdc', 'badacbba', 'cacddbcb', 'ccbacdca', 'bdadccda', 'ccacbdbb', 'ddbacbda', 'ddcaacdb', 'bcdbcacc', 'dbdaccda', 'bcadbccb', 'bcddbdda', 'adcdbacc', 'bccaddcd', 'cbadabcb', 'abbccdbb', 'bdacddca', 'bcadcadd', 'bacdbdad', 'cdcabadc', 'ddbabcbb', 'dabbacdc', 'bbdabdcc', 'acacbdcb', 'babdcbac', 'bcdaacbb', 'cbadcadc', 'acbdcddc', 'bcadabca', 'badbdcdc', 'ddbdaabc', 'daabcdcb', 'cbabcdcc', 'cddababb', 'dcacbacd', 'adbdbdcb', 'dacbcaca', 'cbcdccba', 'cbcbdbda', 'dcabbcab', 'cbddbcda', 'abddbcbd', 'babdccdc', 'cbcdbaac', 'dbacdadc', 'dbcbadba', 'cddbddac', 'ddccdaab', 'dbcabcdc', 'ddcaaadb', 'dbacaccb', 'daddacbc', 'bacacddd', 'ddcbaacb', 'ddabcaab', 'cbdbdaac', 'dacdcabc', 'acadbdbd', 'daccabdc', 'bbdddaac', 'aacbdcbc', 'abdbccab', 'cdacbbcd', 'abcbcabd', 'bdbdcadc', 'baddadca', 'cadacbca', 'dcdbdbad', 'cabdacac', 'babdbddc', 'bbcacada', 'bcdadadb', 'babdbcca', 'dadbbacc', 'acbdcadd', 'bbdcbcca', 'dbbcddad', 'dabbcddb', 'dccddabc', 'ddadcbdc', 'dbbdbcaa', 'accadcbd', 'dbdbbdac', 'bdbdcaba', 'accdcbcb', 'dadabdac', 'dbcbbcca', 'dcdaabdb', 'bcdbddda', 'baadcdbc', 'cdadabba', 'ddcdadbc', 'baccbcbd', 'bdacaccb', 'cbdcadab', 'cdbcaddb', 'badccabd', 'bcdabbdc', 'bacdcdcc', 'bcdcbacc', 'cdbbcaba', 'ddacbdcd', 'bdabacdb', 'ccacabda', 'baccdbac', 'cbaddaca', 'abbddacd', 'bcadbccd', 'daaccbdb', 'cdcbdaad', 'bdacddba', 'bdbadaca', 'ccdabcab', 'bcddaaba', 'cacdbaca', 'cddabcbc', 'dbbccbab', 'caacdbaa', 'cbcdbbca', 'ddaabbcd', 'cdaddbda', 'dabdbccd', 'ccbaddcb', 'bbdcadbd', 'babdbcac', 'daccbcba', 'cbacadbc', 'bacdbbab', 'cbddacab', 'cbbddaaa', 'cbddaabd', 'adcbbcdb', 'dccbadbd', 'accbccda', 'cbadbaca', 'bdddadca', 'bddacabc', 'abacacdb', 'dddacaba', 'cbcacbda', 'bccbbacd', 'cdbbdabd', 'ddbaddcb', 'ddacbcad', 'dccbcbaa', 'bcbabdac', 'dcdcaabb', 'abcdbabb', 'adccdbcb', 'acacbdbb', 'acabdccb', 'cacdcbda', 'adcbadba', 'cddbbabc', 'dbbaacaa', 'cbabbdcd', 'cabbdadc', 'acbcabcd', 'ddbdbcaa', 'dcbdddda', 'dabcbcad', 'bdcacacc', 'dccdbbda', 'cbdaacdc', 'dbccdcba', 'ccaadbdc', 'bdcdaddd', 'acbadcad', 'baaaacdb', 'bddccaab', 'bddcabca', 'cbcbcabd', 'acbcbada', 'dcabdadc', 'acbabdba', 'ddbbadcb', 'ddabcbac', 'ddaccaab', 'bdccdbac', 'cdbabcdb', 'cdbcbdaa', 'babdcacb', 'bcaacdcb', 'ccbabcdc', 'abddddac', 'ddabdccd', 'bcdaacdc', 'dccbbacb', 'ccabdbcd', 'cdbdcadb', 'cdddcdba', 'ddacdbdc', 'abbdadac', 'baabbcbd', 'baabdccb', 'bcacbbcd', 'bbaddadc', 'bbabadac', 'cbddaaca', 'bbdbbdac', 'cddacbad', 'cbdadcbd', 'baacdcbd', 'ddabddcc', 'accdcdbd', 'cacbcdab', 'bccaddbb', 'daddccdb', 'adbbdacc', 'dcabdcbd', 'bcbdcadc', 'cababdcb', 'caddbdac', 'abacdcdd', 'cbbdadbc', 'cbacdacb', 'bcdacbcc', 'dabaccab', 'bcdbdacc', 'ddabacdd', 'dabcbcbc', 'dbcbdadd', 'cadbadcd', 'ddddcbac', 'ddcbdacc', 'ccbbabdc', 'bcdddcca', 'bbcbacda', 'dabbdddc', 'acacddab', 'cbdaddad', 'dadbcabc', 'caddddba', 'ababcdcd', 'dadaccdb', 'cbbdacab', 'adabcabd', 'bdabbccb', 'dadcbadc', 'dbdbcaab', 'abdadcdd', 'dcabccab', 'bbdbbcda', 'bccadbdc', 'dccacbba', 'acdabcab', 'ddccadbc', 'ddbaacba', 'bddbcdca', 'bdbacaca', 'dbbdcada', 'cacdadcb', 'dbdddcda', 'adacbbdc', 'baddaacb', 'cacabadc', 'badabccb', 'babccdab', 'abcbddaa', 'bdbdacab', 'ddcbabca', 'dabddcba', 'bcdcddca', 'dcdcbbac', 'bcbcddac', 'cdcadcbb', 'cdcbcadb', 'bbccabad', 'bccdadcd', 'dcbcdbba', 'bddcaabb', 'ccbbcdda', 'cabbdacd', 'dcabbccb', 'cadabacb', 'cadcbdca', 'ddacbdbd', 'bdaddcdd', 'dbaddcdd', 'dbbabcda', 'bcaadbbc', 'dcbacbba', 'cdcabddb', 'cdbbacdb', 'abdabacb', 'dccbcacd', 'cbbabada', 'bcdbbdaa', 'bdaddbcb', 'cbcdbcda', 'cabbccbd', 'ccabacdb', 'acbbddbb', 'bcadbacc', 'dacbccab', 'dcaddabc', 'ccddaaab', 'cabbdadb', 'cdbcaabc', 'bbadcbdd', 'ddaaacab', 'addabcdc', 'dcaddaab', 'bcadbdcb', 'accdbddd', 'dbcbbadd', 'addccabb', 'aabdbcdb', 'dcabbdba', 'dddccbab', 'baccdbcb', 'cabddbba', 'badcdbdc', 'accbadbb', 'bacbadbd', 'acbbadbd', 'ccadddab', 'dadccbca', 'dabdccbc', 'abbccdda', 'ccbcaadb', 'cbdacbad', 'ddcdcacb', 'ddcdbcaa', 'dacaccab', 'bccabdac', 'cddcbaaa', 'bdbdabcc', 'abdabbca', 'ddabcdcc', 'cdcbacbb', 'acdabcca', 'abacdddd', 'abbcadca', 'abdbadac', 'bdddcacb', 'dcdbcbba', 'cbadbbcc', 'bbadcdcb', 'adccbdcc', 'cdbddaad', 'bdcbadac', 'abdbcaca', 'dcdbabbc', 'cacbdcda', 'dabdbcbd', 'dacbabac', 'ccbdbabd', 'bdabcadb', 'dcaacbdc', 'daacbbcd', 'bcddabca', 'abcbdbcd', 'cdbdaabc', 'cbdacacb', 'caadbbcb', 'dbbadbcd', 'addcadab', 'cdbddcba', 'cbadcddb', 'aacdaacb', 'dbbdcbab', 'dddccbaa', 'bccdcdda', 'ccadbdcb', 'abcbcdcb', 'baadcbdb', 'badbccdd', 'acdcbdcd', 'addcaaab', 'adddcaba', 'dcacbddb', 'cdccdacb', 'badbabdc', 'daddbadc', 'dacdabcd', 'abcdccba', 'ccacdcbd', 'bbddabac', 'ddacaddb', 'ddadcabd', 'cbbdbabb', 'dbbddbca', 'bbcdbbaa', 'ddcbcdab', 'dacddcbd', 'abadadbc', 'adadbcbc', 'acbdbbca', 'bdaacbdc', 'cbdabada', 'acabadad', 'bbdabcca', 'cbddbdab', 'bbcddaab', 'cbbaabdb', 'dbbadbca', 'acabdacc', 'daddbbac', 'dddbacca', 'cabcdbcb', 'ccdccaba', 'ccabbdca', 'bcabcbdb', 'dbabaccb', 'caccbcdd', 'bbdadacc', 'baddccaa', 'acdabdcc', 'dcddbaab', 'bbcbcaad', 'cbcbdbba', 'cbabaccd', 'abacaccd', 'dbbcadca', 'cdabbdcb', 'cadbddcd', 'cbbdcadb', 'cabdcaca', 'dcdcacab', 'acbdcbda', 'cbdacacd', 'bbabcbbd', 'accdaccb', 'dcdadbba', 'cacbbddd', 'dbaadaac', 'bdbcddda', 'dbcdabdb', 'dcdccabc', 'dbdccaac', 'adadbcbb', 'daadbbcd', 'abdadbdc', 'abccbbdd', 'abcddcaa', 'dadbaccb', 'dabcdbab', 'dbbcddda', 'bbadacba', 'cdbbabcd', 'dcddaabc', 'dcddaabb', 'bcdabadc', 'ccbcdacc', 'cbacbdab', 'dcdccbad', 'bdcddabd', 'cadaddcb', 'cdbaddca', 'bacbbacd', 'acdbaddd', 'dbcdcadb', 'ababcadd', 'cdcbdcda', 'bdcbbdba', 'dcababca', 'ccabaddc', 'abadcada', 'dbcdcaac', 'babadcad', 'dbddadbc', 'ccadabdc', 'bddbddca', 'aabcbdbb', 'adadcddb', 'cabbdcdd', 'cbbdacdd', 'babdcadd', 'adbbccbc', 'dbcaabdc', 'bcdccdaa', 'bcbadcdd', 'daccbdab', 'adccdabd', 'bbdbcbba', 'dcabcabc', 'dacacbcc', 'cabadcdc', 'dacbabba', 'ddbddacc', 'cdabcadd', 'adccbbad', 'dabccaba', 'dbbcbabc', 'cbbdcaad', 'bbabdcac', 'adbdbaca', 'dbcdcbaa', 'bbcdcaca', 'ccbbadba', 'abcdcbad', 'cbdcaacb', 'acbcbcdc', 'acaddbba', 'ababacdc', 'acbabdbd', 'dbdcadac', 'badcdacc', 'dbbccacd', 'ddbbaaca', 'bbcadbcc', 'adcaddba', 'bacbdada', 'badcbcbb', 'adacbcda', 'dabbcdcb', 'cddadbad', 'dccababc', 'bccacacd', 'adcdadbd', 'acabcadc', 'dccbdbba', 'cdcacacb', 'adccbdca', 'cbcadcdb', 'abaccdda', 'bcbacbcd', 'bdddcadc', 'bdbacabb', 'dccbabda', 'abcabcbd', 'badcacbc', 'bddbbcca', 'ccaabcdb', 'ddbaccab', 'abdcbbca', 'abadccda', 'daaccbbd', 'baddcddc', 'bdbbabcd', 'adbbacdc', 'cadbdbdc', 'abdbcadb', 'bbabbcdb', 'acadbdab', 'dcbcbaad', 'cabddbca', 'abdacbca', 'cdbaacbc', 'bcdcbabd', 'bbabdcbd', 'cdbaccdb', 'dbdcbabd', 'dcbcabda', 'dcabbcac', 'ddddcacb', 'acddcbdc', 'bbcdadcb', 'dcdbcbad', 'cdccabcd', 'cdaccdbb', 'acbdcddb', 'dcacdbcd', 'aadbbcdc', 'bbcadacd', 'babbabcd', 'dacbbcca', 'dacabdcc', 'bbabccdb', 'dbacbdda', 'cbdadbcb', 'bcadbadd', 'abdddacc', 'acbbdacd', 'cabdaccd', 'daddbabc', 'dbcdaddc', 'dacbbaca', 'ddaabcaa', 'baccdbab', 'cbbcdbaa', 'cdcabada', 'dadbdaca', 'dbcdaccb', 'babadcbc', 'ccddadba', 'cddbbaac', 'dccbaadb', 'bbacadba', 'cbaddddb', 'adaccbba', 'dbccacda', 'ccdbcacb', 'abbadddc', 'acacabcd', 'adacbdab', 'adcbabda', 'dcdabbdd', 'dbbdbaca', 'bbccdcba', 'ddadbdcd', 'acbdbddc', 'dbbcacbc', 'cdbcaacc', 'ccacbdcb', 'ddbaacbc', 'dabadbcc', 'abbcbdbd', 'adbdbcbc', 'bacaddbc', 'acdaddab', 'daddcddb', 'cadddbca', 'dbbcbcda', 'dacbcbab', 'bdadccbc', 'dabcbdcb', 'cdbdcadc', 'bbcbbadb', 'adccdbab', 'addccbbd', 'bddacdcb', 'ddcacbbc', 'aabbccbd', 'dadabdcd', 'cadbcddb', 'ccbdabdd', 'bcdccaab', 'dcabcdad', 'bbdacacb', 'cbbccadd', 'ddcbabcd', 'cbdaaaad', 'badbdccb', 'cdabddbb', 'cabbdcab', 'cbcbbdac', 'bcdbccba', 'dbbcabac', 'dabbcbcc', 'adbbcddb', 'cbbdbabd', 'dacbbacb', 'bdacddcd', 'aacbcdbb', 'dacdacbb', 'babcadba', 'ddccbadb', 'cdcabacc', 'bbccbdab', 'dbcbdcab', 'acdbccab', 'cbdadcab', 'bccdbbaa', 'bbcbabbd', 'dcaadccb', 'cbbdbadd', 'dbcdccab', 'dcbaccbb', 'ababbccd', 'dadbacbb', 'dbcdcaba', 'bdddbdca', 'addcbcca', 'aacbdcaa', 'dadddbac', 'dbcbdbda', 'abccdaba', 'cdcbddca', 'bcdadacd', 'bddbdaca', 'bbdaaaac', 'ccabcddd', 'acddbaad', 'ccddbbab', 'dadcabcd', 'bdbdaabc', 'dccbcdca', 'ddccabdb', 'cbddaaba', 'dcdabadc', 'cbaacbdb', 'daacbbcc', 'accadadb', 'dcbdadac', 'ddaacbda', 'dacbacca', 'bcadabdb', 'dbabcddc', 'bdabadcb', 'dccddbca', 'cbdbccda', 'cbdbdbab', 'daddbcad', 'bcbcbdab', 'bcbdabca', 'abdadaca', 'bcdcdaab', 'cbcbcdca', 'cdbbdcac', 'dbacddbb', 'dcdcadcb', 'bcadcabd', 'cbcacdda', 'ddabdabc', 'adbddacb', 'cdacbacc', 'cababadc', 'cacdcbcb', 'dadadcba', 'cddbacab', 'dcacdccb', 'cbdabcca', 'dccbabcb', 'adadabcc', 'acacdbcd', 'adddcdab', 'baddcdcc', 'ccbadddd', 'dabcbcbb', 'bdbccabb', 'dbcabcbc', 'acdcdbdd', 'daccbdcb', 'cbbcadbd', 'abacbadc', 'aadcdcdb', 'bacbabda', 'adacbdba', 'cddcbaba', 'dacdbbad', 'cdccdaab', 'dadccdba', 'dbacadbb', 'acadbada', 'bcabcacd', 'cdcbcdaa', 'adcabdbc', 'bacbcdca', 'accdcbbd', 'cdbcddab', 'ccadbaba', 'adbbccda', 'bdbccdaa', 'abcacdac', 'abdccbac', 'cdbcacab', 'abadacab', 'baaaadcb', 'bdcdbbaa', 'ccbdbacb', 'abaccbda', 'cdadccba', 'dcaacbcd', 'dcacbdbc', 'cdbcdaac', 'dadabbdc', 'acddcbcc', 'ddbbacba', 'dbabdcad', 'bacabdbb', 'dbabcbad', 'aaccdbcb', 'abbddcdc', 'bacabbcd', 'dbabccdc', 'badabcca', 'ddcbadda', 'acbddcba', 'abbdacbb', 'adccabdd', 'dcbdabba', 'cadadcba', 'dbacbcdc', 'adcbbdbb', 'cabcbdab', 'bbddcdca', 'dbcdccac', 'adddcabc', 'bdcbabad', 'badacdcd', 'dacadabc', 'bdcacabb', 'adbddbcc', 'cdabdccb', 'dcadbcac', 'dbacabad', 'abaccbbd', 'abddbcab', 'cbddadda', 'abdadbcc', 'badccbad', 'bbabdcad', 'baccacdb', 'cadabdbd', 'acbdcdad', 'adbcbdcc', 'bbddabcb', 'cbcdbaad', 'cbadbacc', 'bcbbadac', 'dbdbcdac', 'adbcadac', 'aadccdbd', 'dabaccbb', 'ccdccadb', 'adabdcac', 'cbbcadcb', 'bdcdcdda', 'cabdacab', 'bcdbaabc', 'ddaacacb', 'dbcdabba', 'dcddabcb', 'dcbbccab', 'bdcbacdb', 'cbbcdbda', 'baabdbcd', 'dcaddddb', 'abdcabad', 'dcbcdbad', 'bcaddbba', 'bddcdabd', 'adadbdcd', 'dbadddca', 'adbddcbb', 'bacbcabd', 'dbdadddc', 'accabdcb', 'dcbddcda', 'abcbadcc', 'dbacddda', 'abbaccdc', 'ccdadddb', 'acbcadcc', 'cddaaaba', 'cadabcdc', 'cdcbaddb', 'baddbdbc', 'daadcaab', 'bbabacad', 'accddbdd', 'acddbadc', 'caabcdbc', 'ccddacba', 'cdabcacd', 'acacdaba', 'bcdadaca', 'bddabcda', 'ddababca', 'cbddaaac', 'bbdbdbca', 'dcbabcac', 'bcabdbcb', 'ccbbdcba', 'dbacdabb', 'ddcbbaab', 'dadbcddb', 'bbccddaa', 'bdbddcba', 'abadcddc', 'bbcbbcad', 'bdadadbc', 'cadcbbdb', 'ccadbabc', 'bdacabcc', 'ddcabcaa', 'accbacdb', 'adccacbd', 'adbbacda', 'dacdabda', 'bcacddbd', 'bdbaccad', 'bcdacdbc', 'ccabcdcd', 'cdbadbcd', 'acbcdbbd', 'bcadcdcc', 'cdccdbad', 'acbdbbdd', 'cddbaddc', 'cbcddaaa', 'cbdadbac', 'baccbddc', 'ddcdbaac', 'dadadabc', 'dcdbdbca', 'acabdacb', 'acdbcdad', 'cbccaddd', 'bcbdcbca', 'dacdbbdc', 'dabbabbc', 'accddabd', 'bdccbbac', 'cbaabdcd', 'dcabbdbd', 'dabacada', 'dacbcada', 'dbdbccba', 'ccbbaacd', 'abbcbdab', 'addcbabb', 'bdabcbbd', 'daabbaac', 'cabadbba', 'bacdabcd', 'acbcabdb', 'abbddacb', 'dabbcadd', 'cbacabcd', 'ccddbdab', 'dcacabcd', 'abcaddac', 'dbdacdad', 'bbdacbbd', 'adadbcda', 'ccdbcabb', 'dcbabada', 'abcbbcda', 'cbdbabbd', 'dcaddbad', 'cabcdbcd', 'abdbcdbb', 'dddbdabc', 'abacbdba', 'bacbddbd', 'ddabbaac', 'bcdadccd', 'dadbacdc', 'accdbbab', 'cdacbcdb', 'acadcbcc', 'dbdcdcba', 'cdbcdacd', 'cbadbdca', 'bddbcacc', 'ddbcdabb', 'cdcbccaa', 'bcdcbbac', 'bbcdbaba', 'bdaddacd', 'ccbdacdc', 'bdabbcca', 'cdddbbad', 'adbcbcca', 'dbcbdbad', 'adbbdccd', 'acabdaca', 'dbdaacdb', 'abcbcdac', 'cadcdbcc', 'ddabcadd', 'bcbcdacc', 'dbadcddb', 'abadcadd', 'abbccbdd', 'abcacddc', 'bddcddab', 'bbdaacdc', 'cadacbac', 'ddadabcb', 'accbadcd', 'bddacdca', 'cdabccdd', 'cadbbaca', 'bdbcbadd', 'ddcdcbad', 'dcddcbda', 'ddccdbba', 'bdcacdac', 'cdcbcabb', 'ddbdacdd', 'dabbcacc', 'bdcdbbad', 'ccdccbda', 'bdabbcdc', 'cacdbadc', 'cdcacdab', 'bcdbcdab', 'daccbadb', 'ddcacadb', 'dabcddab', 'abadcacb', 'dccadabd', 'bbcadabd', 'baddcbaa', 'dcbdddca', 'cdcdcbda', 'cddbdadc', 'ccacdbdb', 'dcadbcdc', 'dbbcdadc', 'bacbcbcd', 'cdadbddd', 'bcdacbcb', 'abcabcad', 'bbccbdba', 'dabbcabc', 'bacbdabb', 'dccbabdd', 'cddaacbd', 'bcbdaabd', 'dcaddbcb', 'ccdccdab', 'caddbbac', 'cbddabdc', 'cbabcbdc', 'bbdacbda', 'dbdadcbd', 'bdbaccbc', 'acbccbdb', 'cbbcaddd', 'dcabbaca', 'babdccbd', 'bdbcadcb', 'bddadbcd', 'babddbac', 'dcabcabd', 'bcddccaa', 'bcabcdcc', 'bcadcdbc', 'bdbaaccd', 'babcdcca', 'abcbbdbc', 'ddaddcbb', 'aabccbdc', 'ccddadab', 'ccadacdb', 'bddbdcda', 'cdcbbacb', 'daddbcac', 'adbcbbdd', 'dcdbbcaa', 'cbdacaca', 'dbdaccdc', 'dccbacdb', 'baddcaaa', 'bcaabdcb', 'cdbadcdc', 'bbcbdcac', 'cddabdcb', 'dddcbdad', 'dbabbdac', 'bcabcbda', 'dcbadcca', 'abcabbda', 'daabdbcc', 'ddbcaaba', 'caabaadb', 'dcdccabb', 'ddabbcaa', 'baccbadb', 'dbccdaad', 'cabddbbd', 'cdabdbbc', 'cbcbadbd', 'dbbddcad', 'dcbadcad', 'acddabad', 'cbbdabcc', 'dcabadad', 'cbdbbacb', 'dcdbdadc', 'dcacbdda', 'dbabdacd', 'acacbdab', 'adbdacdc', 'dbdcaabc', 'dbbccabb', 'cbacdbad', 'bbdcbacc', 'dabdbacd', 'daadbcaa', 'dbbadcca', 'dcddbaca', 'bdcadabc', 'ddbbcaac', 'ccabadbc', 'dcddbadc', 'abcbdbcb', 'ddabcaaa', 'bcdbcdaa', 'ddcdbaca', 'abdcacbd', 'adcadcba', 'ccdbdcca', 'cdbddcca', 'adccabdc', 'bbdabddc', 'caabcdbd', 'bcdccabd', 'aaaaccbd', 'bdacdbdd', 'cdabdabc', 'bcddaddc', 'daabbccd', 'ccdbacba', 'addcdbcb', 'dacbdcac', 'ccdcbdad', 'adabccdc', 'bbcbddab', 'dbacdadd', 'bccadddc', 'dddabcbb', 'daaaabcc', 'acdbddda', 'bcacdabb', 'adbdccdd', 'dcadddbd', 'dccadcbc', 'acddbcdc', 'cadabcad', 'babdbbcd', 'dadccacb', 'caccbdbb', 'accbadcc', 'dcdbabac', 'cdbcbabb', 'ddbbdcac', 'dadcdcbc', 'dcbbcacc', 'bddcbdda', 'bdbbdabc', 'cdbdcabc', 'abccbbdc', 'bdcbcdac', 'accdabcb', 'acdcbbdc', 'dadbacbd', 'cdadabad', 'dbacdabd', 'cbdbabcd', 'bbdcacdb', 'dbbdacca', 'ddcaccba', 'cacbdbbc', 'bbdcabcc', 'baacdbdb', 'bcbacdbc', 'bdcadbcb', 'ddcacabc', 'dacadcbb', 'ddbbcdca', 'ccbdbaad', 'bdbbcadb', 'babdbcdd', 'ddccbaad', 'ddbcdabd', 'acbadcda', 'abddccbc', 'ccabdacc', 'bdaccaca', 'bbcdabac', 'cdbbadad', 'cbabccdc', 'bacddbca', 'cddccbda', 'ddbabcad', 'acabdddc', 'cddabcac', 'ddabdcab', 'dbacbdcc', 'cadacdab', 'bcdbaadc', 'abdabcca', 'dbcddacd', 'bacadabc', 'dcbabcda', 'bcacabcd', 'abccacdc', 'bdcbdbaa', 'cbcbdaad', 'cdcdabba', 'bdcacbcd', 'bdadbcdd', 'cbccbcda', 'dbdcbaad', 'bbadcddc', 'dcbcacca', 'dabaddbc', 'dddbbcda', 'ddccadba', 'bdaabcdb', 'cacdddcb', 'cacbadcd', 'bcdbabcb', 'cadbbdbb', 'addabcac', 'accbbdcd', 'cbcaabdc', 'aacbcdcd', 'dabccdba', 'cabbcdbd', 'cddbbaab', 'dcacdcbd', 'cddddadb', 'badacacc', 'dbccadba', 'aacbcbcd', 'cdcaabdb', 'badccbcd', 'acbdacdd', 'dbccacab', 'cdcdbbda', 'bcbccdac', 'aabcbbdc', 'dabdaddc', 'cabbddad', 'dabbdbcc', 'babbdcbb', 'bacdccda', 'bdbbccda', 'bddacbca', 'ddbcbadc', 'bccdcaac', 'bbcbdadb', 'bacbadab', 'bdcdcacb', 'cbbdbbda', 'acdbdddd', 'abacbbdb', 'bddcacaa', 'ddbdcbca', 'cdabdabd', 'abdbbdac', 'ccadcabc', 'ddbadddc', 'dabaccbc', 'cbbacdab', 'abadadcb', 'adadacab', 'cbbacddc', 'badccaca', 'dbcdcdad', 'ccadadbd', 'dcbbaaaa', 'bcabbdab', 'baabcdcd', 'dbcdbcba', 'adccbadb', 'dabbacdb', 'acadbcad', 'cddbadba', 'babdadcb', 'ccdcbdaa', 'abcdddbc', 'dcbbacdd', 'acddbacc', 'abddbcad', 'dbabbdcd', 'cbdaacaa', 'bdabdbbc', 'bddcdabb', 'bdcbacbb', 'bacddcab', 'bcbacadb', 'caccabbd', 'dcacbdab', 'dcbccdac', 'caddbbdb', 'babdbbcb', 'bdbadadc', 'adadcbda', 'bcdddada', 'cabadcac', 'abdcbcba', 'bacacbbd', 'ddbddacb', 'bdababcc', 'ccdddadb', 'bbaccdbc', 'addbbcdd', 'caddbabc', 'dbabacba', 'abbdccdb', 'ddbcaabc', 'dbcdbadc', 'dadadbcb', 'bbacdbca', 'cbdbbcca', 'dbacaddb', 'bdcdbdda', 'acaccbad', 'babccada', 'dbcaccdb', 'cbdbaabd', 'cddbbacc', 'cbcaacdc', 'bddcddca', 'acbbadab', 'cdacbbcc', 'cabacdcc', 'dddabbcc', 'dabcacca', 'cdabdbba', 'ddcbaadc', 'acadbacd', 'adbcdddd', 'adacbcbd', 'aabdcaad', 'adbbcbdb', 'bbdabacb', 'bccdadca', 'adabbcca', 'cdbacddc', 'acaccbcd', 'cabdabcd', 'dbacdcad', 'dbacabba', 'abdcbacb', 'adbdccbb', 'badbdbdc', 'dbccdacc', 'ccbdbacc', 'abadddca', 'dcbcacbb', 'dadcbddc', 'aaccbdaa', 'accabdca', 'acdbcdac', 'ccbdadac', 'ccaddabd', 'aadcdbdc', 'dacdbada', 'cbaddbcb', 'bccdabcb', 'acdcdacb', 'bacbabdb', 'bccdbcda', 'dbacddcd', 'abddacac', 'bdaccddb', 'dbcbdbca', 'bccdacbc', 'bbadccbb', 'bdcbcabc', 'dcbddbba', 'acbacbda', 'accdcdcb', 'cabdcbab', 'acdacdab', 'adbacabb', 'bcadddcd', 'dbaaccbb', 'cdadcacb', 'bdaacbdb', 'ddbccbaa', 'cabdcbda', 'cbdadddd', 'bbcbadab', 'cdccbbad', 'cbbabacd', 'cdbbaaaa', 'dbaccbcd', 'bdcdcbab', 'acddcbcd', 'dbabdccb', 'dbaccdba', 'adacdbbc', 'dbaacdcb', 'abccdacc', 'cbaddbcc', 'caaccbcd', 'adccdbbc', 'ccadcdbd', 'abdcbada', 'addcdabb', 'adccddcb', 'cadbbddd', 'dddbbadc', 'acabcdac', 'bdcbabbc', 'dbdbabcd', 'acbccadd', 'cbcabdac', 'adacbbcb', 'bbabdacc', 'dbcbcabd', 'cbadcdcd', 'dbacbbcd', 'cbcbbadb', 'acbbccbd', 'dcacbdcb', 'adbcdabd', 'acdbbada', 'bbadbcac', 'addbbcba', 'accbdbdb', 'acabbdab', 'abddcbac', 'dbaccbcc', 'baccdbca', 'dadcacbb', 'ccbacdab', 'cdccbcda', 'aadbcaab', 'cdbadbba', 'dbbcddba', 'dadcbcbb', 'babcdcbb', 'cddcbabb', 'acabdcca', 'ccbcdcac', 'cdcbadbc', 'cdaccbcd', 'acacdbba', 'cadcbaba', 'bdccabcd', 'adcdbbab', 'cbcbcdab', 'dcabdbdb', 'cadadbdb', 'bccbddaa', 'cababada', 'bcbacada', 'adcdbbcc', 'cddabbaa', 'cdbbabdc', 'acbbdabb', 'dcadbacd', 'abbdabcc', 'bdabbcbd', 'bcbaadbd', 'ddcabbdd', 'ddabdbcb', 'dddcdaab', 'badccdba', 'dbbcbadb', 'babdabbc', 'dabbdcda', 'bbcdacba', 'bcacdbab', 'addbbdcb', 'bbaabdcb', 'abcbdadb', 'adbadcbd', 'cdbacddd', 'adbcbbcc', 'bacdcabc', 'cabcbdba', 'cddcacdb', 'dcddaaba', 'bcaccdcb', 'adbcbadc', 'bdaddddc', 'bcacbadb', 'cabcdbdb', 'bbacbddc', 'cbddadac', 'cdbdaddb', 'cbbadcab', 'cdbabaca', 'ddcbcbca', 'bdcadaca', 'bbadadbc', 'bcdabbda', 'bdcbbadd', 'bcbdacac', 'cbcbabdd', 'bdaaaabc', 'bbcdaadc', 'bdbddcab', 'ddcbcacc', 'cdbdcdba', 'ccbccbda', 'cadadacb', 'dbbcabda', 'bccadccd', 'ddbdaacc', 'bdadabdc', 'dcdbadbd', 'bbdabcbb', 'bddabdcb', 'badcdcbd', 'bdaddcda', 'ccddbdac', 'badbbcbc', 'dadddbdc', 'ccbabdac', 'daccdabb', 'bbdccacb', 'bcddabdb', 'cdacbcdc', 'dabadcda', 'adbdddac', 'dbcadcbc', 'cacdcbbc', 'bdbcbcad', 'bbdabdac', 'bacddaba', 'ababcadc', 'cddadabc', 'bbccbacd', 'addabdbc', 'cabcbddd', 'ccacdadb', 'bdbcadad', 'abdcddad', 'ccbdacda', 'ddcaaabc', 'dbcbcdca', 'bbdbcaac', 'bdabbacb', 'adcddabb', 'bccbdaab', 'dccdbacc', 'cabdacdd', 'bcbcdbda', 'bcbacdbd', 'addcbcba', 'ddacbdaa', 'cabdabdb', 'dacdcbcb', 'ccbdabba', 'acbdbacc', 'adbdbcac', 'adcdadbc', 'dbdacbda', 'cbddbcab', 'dcdbddab', 'dbbccbad', 'bdaccbbc', 'bacdddbb', 'cbdbadba', 'ababbcda', 'accbdcdb', 'adcdbdcb', 'dcbadcdb', 'ddcaddcb', 'babdccac', 'cadbacca', 'dabbccdc', 'cdbdadda', 'cabadbac', 'dbabbcdc', 'cbadcbdd', 'dbcabbcb', 'cdccdadb', 'dabdcbda', 'dadcdcdb', 'dbccbadc', 'dabbcbcb', 'bbcabbcd', 'caddcbab', 'daddccbc', 'cbacacda', 'bddbabdc', 'adadcbbd', 'bddadbdc', 'dccdabab', 'cbbdbbab', 'bbadabcb', 'dbaccdad', 'dcadbdca', 'acbcbdbc', 'dbcbdbaa', 'bcabadcd', 'cbbcdcaa', 'bdcaadcc', 'cbaaccdc', 'acdabcdc', 'bdabadcc', 'cbdddcca', 'aadcdbaa', 'cdbaadcb', 'abdcdbba', 'bbaabbcd', 'babdcbcb', 'bcbdabab', 'ddccabda', 'bccdaadb', 'cabcacda', 'cbcadcdc', 'bcababdc', 'cdadcbba', 'bdacabbd', 'dcbcbabd', 'dacbbcad', 'adcdbdda', 'cdccdbaa', 'dccddaab', 'dccbacdc', 'adabcdda', 'dbdbcdab', 'abdbccdc', 'dbcbadbd', 'dcadacbd', 'abddcbdc', 'bdcababd', 'cabadadb', 'bdccabab', 'ddabddca', 'cdbdbcad', 'bcbcbada', 'bccacbbd', 'dcadbccd', 'dacbabdc', 'cbdddaac', 'dbbaaaac', 'abbdcdba', 'dbccaccb', 'badbddcb', 'dbadcbda', 'adbbdacd', 'ddcaabca', 'ddcadcbc', 'ccdbdbac', 'cabbcdbb', 'acdbacdd', 'abdbbcad', 'abacbdab', 'bcbaddbd', 'dadbcaca', 'bdcbdaca', 'bccabdcb', 'dcabcddd', 'cbbabddd', 'badbccbb', 'bcddadaa', 'cdabbaca', 'addbbdcc', 'cbcabacd', 'abbacdba', 'dcddbabb', 'bcbbdcab', 'cbaabbdb', 'dcaadbcd', 'bbaadbbc', 'bdbacbdb', 'cbcadcad', 'cdabdddb', 'cdcbbaac', 'dcbcbcac', 'dcbdcabd', 'cddbcaab', 'dbacdbdb', 'ccdbcbca', 'dddcabbc', 'dbcacdbd', 'bdcabdbb', 'dccaabdb', 'adabddca', 'cadddaab', 'ddacbaab', 'cbacbbad', 'dcddbbca', 'adabbddc', 'dbdbcaca', 'cacdbcbb', 'dccaccdb', 'dbcbbacb', 'acabdaba', 'ccacadcb', 'dbcdbdac', 'aacdbbcb', 'addacbdb', 'adcbcdda', 'cdddadba', 'ddbdadca', 'aaaacdbb', 'bbcabccd', 'dbaccbdc', 'abccdbbc', 'ddbbcacb', 'ddabdbca', 'bddddacd', 'dacbdbcd', 'abdbbcbb', 'ddacdcba', 'ccbbabdd', 'abbcbada', 'cdcdccba', 'cbdaddbd', 'cbdccacd', 'acdcdbdc', 'daddcaab', 'cdbadcbd', 'bcacdcbb', 'ddaaaabc', 'adbdcacd', 'dcbdabcb', 'bcbbadda', 'acddbdaa', 'cdaddbcc', 'cabccadb', 'ccdababb', 'baccdabc', 'dbccabdc', 'dcbcbadc', 'bcddccab', 'dacabcdb', 'adcabdcd', 'acadbcbd', 'adbbdabc', 'bdcbadcc', 'bbacdcba', 'bbdcdabd', 'abacbbad', 'dcdbdaba', 'badddbca', 'bcdbdadd', 'dcddcbba', 'bbabccad', 'dbddbadc', 'addacdbb', 'bcddbdab', 'bdddacdc', 'ccadbaca', 'bacabdcb', 'bddbaaac', 'adbbdcba', 'cddbacdc', 'bbacbada', 'bacabccd', 'cdddbacc', 'abdcbcdb', 'dbdbacda', 'dabccabc', 'ddbaaadc', 'bbacdbac', 'dccdbcad', 'aadbbccd', 'caddcdab', 'dcddabdd', 'adcbdcdd', 'caccddcb', 'cbdbcbab', 'dddacbad', 'ccbcdbca', 'dacbbddd', 'babdbcdb', 'bcdbddac', 'addacbab', 'cdbacbcb', 'ddddbaac', 'ccddbbda', 'dcdacabb', 'dccbacad', 'bdcbdabc', 'adbcdccd', 'babadbbc', 'adcdabbd', 'acddbaab', 'cacbddad', 'bcbbdaac', 'abcddaba', 'dbdabbdc', 'dbdcbaba', 'bcbabbad', 'ddccddab', 'dbcacbad', 'abbcbcdc', 'bcbdbaad', 'dacbcbcc', 'badabbcd', 'bbadabcd', 'abbcbadb', 'cacdbbcb', 'dcdbaacc', 'dddcbadd', 'cacbdbbd', 'cdbdbadd', 'dcbaddcc', 'adccbccd', 'bddadcbc', 'bccadddb', 'bdacaccd', 'bbcddcaa', 'cbcadada', 'cdcbcbda', 'acbddada', 'cbcddabd', 'abcbbcdd', 'adcdcdbb', 'bbacbdcb', 'dadababc', 'adcbccac', 'abbadcda', 'badbdcbb', 'cdabdcac', 'cdbababc', 'bcacadbd', 'bbcaddaa', 'ccaabdbd', 'dbacbabd', 'dbdacbcd', 'adbdccad', 'dbcbcdba', 'bccdacac', 'aacdbcbc', 'dcbaccbd', 'adddcbcb', 'bbddbbca', 'bcacdabc', 'abdcbabb', 'baccdacc', 'cdcbacbc', 'dbcbcabc', 'cdccaadb', 'cdcaddbd', 'ccabbcdb', 'addcbbcb', 'caccbcda', 'accbccbd', 'adabacba', 'dabdcdcc', 'cdcbdcca', 'bccbadcc', 'ddbcbadd', 'aaccdcdb', 'bccaaaad', 'dbbcbdba', 'cabbcbad', 'bbabcbcd', 'cbcdcabd', 'bddaadac', 'cddbdadb', 'dbbdddca', 'cdaccbbc', 'cdaddccb', 'abcdcbac', 'ddcdabba', 'cdcbbcaa', 'cdaccacb', 'cbaddcab', 'bbdddcac', 'baddcddd', 'dcdbccba', 'babcdadb', 'caacdbcc', 'dbcacdbb', 'bdabdbdc', 'bddbdbac', 'babcddca', 'bacbacdb', 'bdabbcda', 'ddcaaabd', 'bddaccbc', 'ccdcbabb', 'cdababdc', 'bdacbcbc', 'cbcddacd', 'bbabbcda', 'ddaacbba', 'bdabcabb', 'bdcbdabd', 'abddcddb', 'bdadbcda', 'dbdbbacc', 'abdbdcac', 'abdcdacb', 'dbbcabbc', 'bbabcbad', 'dddcdabc', 'daddbcaa', 'abcaddbc', 'dcabcada', 'dabbdadc', 'ddcbcaba', 'bddbadcc', 'dddbabdc', 'abbadcca', 'cdbccbda', 'cbabdbbd', 'bbccbcda', 'bdccaacd', 'dbcbccba', 'bdcacabc', 'cabacdad', 'accbdaba', 'ababbdca', 'dcdbdadb', 'bbcdbcab', 'acbadada', 'bcabdbda', 'cabcdcdc', 'cdbaadcc', 'bdbcdaac', 'dcbddbca', 'cadcabdb', 'accbcbda', 'abbdccda', 'cbdcbcca', 'dacdabbd', 'addbcaba', 'cadccabc', 'acbcacbd', 'bbadccdc', 'daddcbab', 'abdabcda', 'badacdad', 'caccdbac', 'adbcaddc', 'baccddaa', 'cdbdcdca', 'ddbdcacc', 'abdbcabd', 'daccbacd', 'cddacdbc', 'cabcadcb', 'ddbdcada', 'dcbdadad', 'bdbabddc', 'dccabdca', 'adccdddb', 'bcacdcbd', 'dbbcaadc', 'abcadcbb', 'cbabbcdb', 'abccbcda', 'accadbba', 'caddbcaa', 'accbaccd', 'bbdadcbb', 'bacabdab', 'acbadcdd', 'dddddbca', 'bcacdccd', 'dddcbbda', 'cdbdcacb', 'cabcdbcc', 'bdbcbbda', 'ccaabbcd', 'bdababcb', 'dacbdddd', 'aacbdbcc', 'ccdbadba', 'bbdccabd', 'cbcdddca', 'dbcddcad', 'cdaadcdb', 'daabdbcd', 'bccacadc', 'dbadcbca', 'bccbacdd', 'bbcdcbac', 'dddbccaa', 'ddcdaaab', 'adcddbab', 'adddabca', 'acdcdcbd', 'bccbcdba', 'bddbcaca', 'caccdbba', 'bbdcacca', 'bbadabca', 'badcdcca', 'ddadcbdd', 'dcdaabdc', 'bcdacbca', 'bbddaadc', 'adddcbaa', 'addaadbc', 'dcadddbc', 'ddcbcacb', 'cbdcdcab', 'abdcacab', 'aacdcbcc', 'cddcbdaa', 'dabcbccb', 'adabcaca', 'dbccadcc', 'ccabcdbd', 'bcddcdba', 'bcaddaba', 'bdaccdba', 'abcdbdcb', 'baccbddd', 'adaddccb', 'bcbbddac', 'bbdccbda', 'bddaacbd', 'dbacdbdc', 'bcddacca', 'bdabdaca', 'bdccdcab', 'bbaccddb', 'dbacabca', 'adcabcba', 'adbcbdcb', 'babdbcda', 'ddaccbca', 'ddcbcada', 'cdcbadca', 'cbdddacb', 'dacddbcc', 'daccabbd', 'dcabaddb', 'cdcbdacc', 'bdbcbcab', 'cdbbcbab', 'adcbbaba', 'ddaccbdb', 'ddbacdca', 'bbcaddcd', 'dccabdcb', 'accabadd', 'aacdbdbc', 'cbddabcc', 'cabddbab', 'acddcbcb', 'cbddacac', 'adbbadac', 'bdacadbb', 'bcdcbbaa', 'dcadbacb', 'cdcacdbc', 'dcbadccd', 'bcdaacbc', 'acdbcdda', 'baddabcb', 'dddcbbca', 'babdbbdc', 'cdaacbcc', 'dacdbddc', 'bcbadcbd', 'cbbaadbd', 'ddcabbdc', 'bcadbbad', 'ccdcadbc', 'dcadbada', 'acdabcba', 'caccdcdb', 'ccbcbdda', 'cddbdacd', 'bdcaccda', 'dbcabcca', 'dcaccbcc', 'abddcbda', 'cbacdcba', 'bcaacdaa', 'bccdbdba', 'adcddbdd', 'cbdadcdd', 'ccababdc', 'acdaddcb', 'bcacbbdc', 'adcbcddb', 'bdbbadcc', 'cbbdccad', 'abdcabbc', 'bcbabdab', 'adacbadd', 'cdadcbcb', 'adddcbdb', 'bdbacbac', 'dbacdbcd', 'bddabbcd', 'bbcddacb', 'acbbdbca', 'dccabaca', 'cdabbdbc', 'cadbbaba', 'accbbdbb', 'bbdccadd', 'dbdbaccd', 'dcbcdabb', 'dccdbdaa', 'daabccdb', 'bcaabbcd', 'abbaddac', 'abbcadac', 'bbaadcaa', 'dabcbbdd', 'dcdbaccb', 'dacdbcab', 'baccbadc', 'bcbcdaba', 'caddbbcb', 'adbacbdc', 'cddcbada', 'acdcdddb', 'dcaaccbd', 'bdbbcbca', 'cddbabad', 'cbdddbca', 'dbddaabc', 'ccbdddca', 'dabcdada', 'acdbbdbb', 'acabbadc', 'acadbbac', 'cbcdbabc', 'cdbccabc', 'cbabcdcd', 'dbadbdcc', 'cdbdadbc', 'acddbbcc', 'abcbcdab', 'ddcbadcb', 'abcbdcda', 'caadcbdb', 'bacdabab', 'acacbcbd', 'dacbbcda', 'dccbbcab', 'bccaacbd', 'ddcdcdba', 'acacbbdd', 'abddaacc', 'dacbcadb', 'cbcdcadc', 'abccaddb', 'bdcddadd', 'cdccbdad', 'acabcdcd', 'bcadbddd', 'acddbcab', 'addcbdca', 'baccbacd', 'cbacadca', 'abbdcadd', 'cadadbcb', 'bcacdbda', 'cbcdbbac', 'cdadbabc', 'cdcbdbba', 'cbcaddcb', 'acbdacdb', 'dbaabccb', 'bbdadcbc', 'aadcbbdc', 'acabcddb', 'ccddcbad', 'dcbabcdd', 'bdbacdac', 'bcbdcaab', 'adddaacb', 'cacdbdba', 'cbdabcdb', 'ddadabca', 'bcdbabac', 'abccdbca', 'abcbbadd', 'cbadcdbd', 'adddccbc', 'cadcbbdc', 'accdabdc', 'bcbcdcad', 'bcddacda', 'bbabddca', 'bcbabbdb', 'ccbdbaba', 'bcbacbdb', 'aadbbcbc', 'dcbccaab', 'dbcabbdc', 'acbadbac', 'abcadbab', 'cbdacadb', 'bcdbaacb', 'dbcdcdca', 'cabadabc', 'dbadcabc', 'addddabc', 'cddbabaa', 'cdbdabbc', 'dbcdbcad', 'bdbbabcb', 'dbcabacd', 'abdaccbc', 'dacdcbad', 'dcadabca', 'caddcbca', 'cddcbacd', 'bcdaddba', 'ddbadacb', 'daadcdcb', 'baddcacb', 'dcaccadb', 'bcdaccdc', 'dacadbbd', 'adddbbcd', 'adbcbcdd', 'bbcdcabb', 'abddcaad', 'bcabddab', 'aabcdcbb', 'ccacbddc', 'cbbddbac', 'abdcdadb', 'dcadaccb', 'dcbaccac', 'dccdaddb', 'bdbcdacc', 'adbccdab', 'baddbdca', 'dbdcdbac', 'acdabdad', 'adbcbcdc', 'ccdcbcaa', 'bdccbabd', 'cdcaddcb', 'abbadbac', 'adadabdc', 'dcdcabab', 'dbcbbdda', 'baabcdcc', 'cdcdabcd', 'ccacbabd', 'cacdbcac', 'ddcbcdad', 'dbacdcbb', 'acbbcacd', 'aacdbdaa', 'dcadbdcb', 'dcabccdc', 'ccdadbcb', 'cbaadccb', 'adabdadc', 'ddbccdac', 'bacabcdb', 'cdababba', 'ccdbcdba', 'cbdbcdad', 'acbdbdcb', 'caacbdcc', 'dbdaabcc', 'dcdbcdba', 'daddbcdd', 'cacdbccb', 'dcddadcb', 'cddbcabd', 'cddababa', 'cddacbcb', 'bcbbddad', 'accabadc', 'ccacabbd', 'adbdcbab', 'abcbdaba', 'dcababad', 'dcbbabca', 'bbccdcda', 'addcaacb', 'bcbcbcad', 'adcddcbb', 'baccadab', 'bdcbdcca', 'dbcdacca', 'cdaabdbc', 'dcdacbca', 'adccbcad', 'dbcaacbb', 'cdbdcabb', 'cddadbda', 'bdcdbabc', 'acbadaca', 'dbcbdaac', 'bdbaadcb', 'abbddccb', 'adddacab', 'cdbcaacd', 'dbccadbb', 'dccdcdba', 'cabcdcdb', 'ddbabbca', 'adbdcddd', 'cbbcbdba', 'acdacbbd', 'abcdcbcd', 'cdcdbbaa', 'ccdcbbaa', 'abcbdacb', 'abcddbda', 'abcabbcd', 'ccbabdda', 'dcbcbdaa', 'cbcadcda', 'dcdbccab', 'dbabccab', 'baadbccd', 'dcbabdcc', 'adcdbcda', 'acbbacdc', 'cbcaddbb', 'cadbccdc', 'ccbdcaab', 'bbdcbaca', 'acbbdbcb', 'bcabbddb', 'cddddbda', 'dabacbcc', 'adcabbcd', 'bccabbdc', 'acbabdab', 'bddccaaa', 'dababbcc', 'dcbbcabd', 'dcbdacbb', 'cbdaccbc', 'bdbdbcac', 'daabcbaa', 'dacdbdca', 'cbcdabda', 'bdcddbab', 'bcddbdac', 'dccbdcca', 'bcbadada', 'ddaddbcb', 'caabcbdb', 'dcabcddc', 'cbcacddd', 'ccadcacb', 'bccbadda', 'dabcabbd', 'cabaccad', 'acabcdbd', 'dcddabad', 'bddcabda', 'bdaabcbc', 'bdbcddad', 'abcadbca', 'cdacdabb', 'daccadbd', 'bdadbcac', 'dcbbadad', 'bbdbaddc', 'dccaddba', 'cdbdadab', 'dbbcbabd', 'cadbbacd', 'ddbcadab', 'adddcbda', 'bdacbabd', 'ccddbacc', 'dbcaddba', 'cacbcabd', 'bbdbbacd', 'bdabdccd', 'dbcbbcab', 'acacbcdd', 'cbcabdcc', 'accbccad', 'dbcbacba', 'ababacdb', 'ccdcabbd', 'bdcbabac', 'cbdccaca', 'ddacbbda', 'dcbcabcb', 'bcddcaab', 'dcdbbada', 'dabddadc', 'dbccabab', 'babccdbd', 'cbccdaad', 'ccbacbdb', 'bbcabdcd', 'adadddcb', 'daacbdaa', 'ddbadbbc', 'ccdaabcc', 'dcddabdc', 'dbdbdaac', 'dadabdca', 'dbcdabda', 'ccdbacda', 'dabadbbc', 'bcbacdac', 'bcacddda', 'dbdccdda', 'dcbdddab', 'addacbdd', 'ddcbcbaa', 'ddacddbb', 'dbccadab', 'bccadadd', 'adcbccbd', 'dccbbadd', 'ccdbbdaa', 'dbdcacda', 'bddacdbb', 'bcddabad', 'cadbccba', 'aadccaab', 'dabcdbdd', 'babdcddc', 'cdcabbcb', 'bacacbda', 'dcdbabcc', 'bcadabdc', 'baadbdcc', 'dbadcbab', 'cabbcddd', 'dccbadcd', 'addbccdb', 'badacadc', 'bbadacad', 'abdacbcc', 'bacabbdd', 'bcadcbdc', 'bcddcbac', 'dbccadad', 'addbbdac', 'dbdacacc', 'bacddddd', 'bdddacab', 'bdcdbabd', 'abdabaca', 'bcaddadc', 'cdbabbdb', 'bbcabbad', 'adbbabcd', 'dcdbaacd', 'abbacdcd', 'addaaccb', 'dbddbcaa', 'accdbabc', 'cbddddda', 'adbabddc', 'dcbacacb', 'babbcada', 'cddabaad', 'cdbcabbd', 'bcddcadb', 'bdabcdda', 'badacbac', 'ccbbdbac', 'ccdadbcc', 'cdbadbcc', 'bcacdbad', 'bccdcdca', 'dbbcbbaa', 'dbacbdad', 'bcdbccaa', 'ddbcbcda', 'bcadddcc', 'adcadcbd', 'dcbccabd', 'caccbdcb', 'bcaccddd', 'dacdcdcb', 'bdbacddc', 'adbbcbac', 'dabdcacb', 'adcbcacc', 'bccdaadc', 'acbcdcab', 'dcbcbbac', 'cbcbcada', 'bccbdabc', 'abdccadc', 'bdcddacb', 'cdcabdac', 'bcaabccd', 'babcadbc', 'dcacdbbd', 'badcbbdd', 'addbddcb', 'bddbbcda', 'caadcbbc', 'bcbadabd', 'abadcbbc', 'bccadcbc', 'abcbddab', 'dcbdbcca', 'bcdcdada', 'dccdbbac', 'acbddddc', 'ccbbaadc', 'cbdacabb', 'ddcadbbd', 'acacbdad', 'adbbcdbd', 'babdbcba', 'bdabdddc', 'dbdbdbca', 'cbcdbcba', 'dcaaaabd', 'cbbdcada', 'bacdddcd', 'ccddcbaa', 'ccbcdbba', 'acbdcada', 'babccadb', 'cddbdada', 'adbbcdad', 'ccabcbda', 'bbcdacbb', 'acadacbd', 'dacacdbd', 'dcdacbbc', 'ccbabdbd', 'cbcaddaa', 'bdcaccbd', 'cdcdbdba', 'bcabdddd', 'dccadddb', 'acdbcddc', 'accbdacc', 'baabbdcc', 'badadaca', 'badcbdbb', 'dacbdcab', 'ccbbcadd', 'dbdcaadc', 'ddabdcba', 'dcdbcdab', 'dabddbcd', 'dadbccbd', 'aabaabcd', 'cbbacdcc', 'adaddcba', 'dbbdcabc', 'adbbadcd', 'bacdcaca', 'cbaddaaa', 'bacadbbc', 'ccbbdcda', 'dbaadcaa', 'acbacdcd', 'dcbbaabd', 'bcdbacbb', 'acabbdbd', 'acbacadc', 'cabbcdcd', 'badacddd', 'abadcaca', 'ccadabcd', 'bcdabbcd', 'dccadccb', 'ccbcbbda', 'dbacbadc', 'abbacdbc', 'bdccddca', 'ccbccaad', 'cdddddab', 'cbdacbba', 'dcdbcadd', 'daddcbca', 'dcababbc', 'bbaacdcd', 'bbabadcd', 'cabbccda', 'caddcdbb', 'adacdbdb', 'cbadddcc', 'abcaddbb', 'ccdaadbd', 'baddbacd', 'cacdcabb', 'dcaabcbd', 'bcdadbcc', 'bdccabda', 'ddcdabca', 'aabdcdcd', 'bacdcbdd', 'bcbaacdc', 'bdbdcbad', 'adbdcdad', 'acdcacbb', 'bdadbbac', 'cadccdbc', 'adcbbdcd', 'dbcdcacd', 'dbdbbaca', 'acbbcddd', 'acbcdaca', 'cdcbdaac', 'ddacdbab', 'abdacdad', 'bacdbdda', 'dcbbadbb', 'adaddcbd', 'bdcabcca', 'accaccbd', 'dcbbcaab', 'bcadabba', 'ddbbdcad', 'babdcdab', 'dcbabcbc', 'abbdccab', 'bdacdbcb', 'aabbcdbc', 'abcbdbbc', 'dabbcdbc', 'dcbcbcab', 'bbadbbcc', 'dacdadbc', 'cabdcddb', 'cacabcad', 'ddacbadd', 'abccadac', 'bdddbaca', 'dacdcdba', 'dadabacd', 'cdbcbdba', 'bbdcdcaa', 'cdcadcab', 'cbadbcac', 'dcadabdd', 'baddaaac', 'abbcbdbc', 'abbdacdc', 'cacdabbd', 'adcdbcdd', 'babdcddb', 'cbbabcda', 'babcbdcc', 'cadababa', 'cdadddcb', 'ddadbcab', 'adabcacd', 'dbdbaddc', 'cbbdacad', 'dbdbacdc', 'cabcdacc', 'dcadbcbc', 'dbabdcca', 'cabdcabd', 'dbddcbda', 'dcdbdcab', 'cacdacab', 'acbdcdbd', 'dcbacdbd', 'dbaabccd', 'babbddbc', 'daccddbd', 'bdbadbdc', 'adcdadab', 'ccbcabbd', 'cbdbaacc', 'cbabadcb', 'cdbcdadd', 'bdccdaad', 'badcabad', 'ccabadac', 'baabdcbc', 'babcdaca', 'cdbdabca', 'dccbdbad', 'bbabccbd', 'badddbac', 'adacbcdb', 'dcababdd', 'bbdacbbc', 'cdcdadbd', 'abbadbcb', 'bdbdbcaa', 'bcdddaca', 'badcaccb', 'ddaccbad', 'acdbbacd', 'dddbddca', 'bbcdbada', 'acbbdbdb', 'dcdcaccb', 'addcbdac', 'cdcdabca', 'bbdbcabd', 'dddbadbc', 'dbaccddb', 'dbabdbcc', 'bacbcddb', 'dcabddaa', 'aacbbcdb', 'bacddbbd', 'cddbcadc', 'badcbddc', 'bbacdcdb', 'bacacdba', 'addcbcdd', 'dcdcbbca', 'dabbacba', 'ddcdabda', 'abbdcaca', 'acddcbac', 'dabcddad', 'bcabddbb', 'acdbcbdb', 'ddbbdcda', 'cdabadcc', 'acacddcb', 'cdabadda', 'bbaccadb', 'ccbcbcad', 'dabcbaca', 'accbdadd', 'acdacbad', 'cadcbbac', 'dacdabbc', 'ddbaccbd', 'ddcdaccb', 'bbdcbcda', 'ddbacaca', 'adddbabc', 'abdacaba', 'acacdcbc', 'acabbacd', 'acdcdbac', 'dbcabcbd', 'cbadadcd', 'baccaddd', 'ddcbaadb', 'acabdcbb', 'bcdddacb', 'dcbdccac', 'cadbccad', 'cbdbadbd', 'bbadacda', 'ccbdcabc', 'bdadbccb', 'cbaabdcc', 'dbabcabc', 'cdbdccad', 'adcbcadd', 'dcdabdbc', 'ddcbabba', 'cbabddcb', 'ccbcdabb', 'dbabcdda', 'cbabdddc', 'baddbcad', 'dbaccdcb', 'cadcdaba', 'ccaabcdc', 'abdddccd', 'dbdcbcca', 'cadacdcb', 'abcbcdca', 'dcabbabb', 'abacddbd', 'abcdccbb', 'badddbcc', 'acbcdadd', 'bbcadaba', 'bcbadaba', 'cbbcddad', 'bbdbcbda', 'cbaddcca', 'badddaca', 'cddaddba', 'bdaddcbb', 'bcbabdcd', 'cbdacbca', 'ababcbcd', 'cdadcbdd', 'dbdadbac', 'bcdbcaad', 'dabcdcad', 'bdddaaca', 'bdcadbbd', 'adabcddc', 'acbdbcca', 'bdcaabbd', 'ccdabcac', 'ccdababa', 'dbbdcacb', 'cbbdbcab', 'acbbdcbc', 'baddbacc', 'cabcdaba', 'ccdacadb', 'acdbccdc', 'cbddcadb', 'dccaabcc', 'daadbbcb', 'cbccddaa', 'bdcdcbad', 'babadcab', 'cbcbcadd', 'cdaccbca', 'bcacdbdd', 'cbcddcac', 'acdbdadb', 'cacbddaa', 'cacbccda', 'cabdbaba', 'bdbbadcb', 'accbcabd', 'bbcacdba', 'acddbddd', 'ccbaccdc', 'cdababcb', 'cbbdbdac', 'badcaddd', 'babbcdcb', 'bcadbabc', 'abdcddab', 'ccbccdaa', 'cabbacbd', 'bacdcdcb', 'dabbcbab', 'bdbabcbc', 'bcaaaacd', 'abdccdda', 'abbddcca', 'bdccdabc', 'ccdbdbad', 'babbccda', 'ddcabcbc', 'acddddba', 'aadccbbc', 'adadacba', 'dcddadbc', 'bdbacbab', 'bdadacdd', 'abdacabb', 'cbdacadc', 'acbcdaba', 'bddaadbc', 'adaccdbc', 'acabdada', 'bcddcada', 'cdcbdacd', 'cbbadabb', 'acadcbcd', 'ccbadcab', 'aadcaabc', 'dbaaaabc', 'cadbacdc', 'ddacbabd', 'cdcbdadd', 'babcdbdd', 'dccbcbca', 'ddbcbbac', 'adbddacc', 'cdaabccb', 'ddbcaacd', 'ccbbcbda', 'adbbdcab', 'dcbcbacb', 'cddbdcca', 'dbddbacb', 'daabaabc', 'abbdacad', 'adbcadcc', 'adbbaccd', 'bdbbccaa', 'daccbcda', 'abdbacdb', 'cacdbddd', 'bdbaccda', 'abcacbdd', 'bdbdcbac', 'bdabbabc', 'caccdbbc', 'cdcdbcda', 'dcdaccbb', 'babdacbc', 'bacaddbb', 'abbacbdc', 'bddccabc', 'badacada', 'acacdadb', 'acdabcad', 'adbccbad', 'abccaddd', 'dcabdcbc', 'dbadccbd', 'dcbdcadd', 'adcddcba', 'dbccdaac', 'cbcadcab', 'cdacbdbc', 'cabbdbcb', 'ddabcbcd', 'abcddcda', 'daccadbc', 'bdbcbbaa', 'cdbaccdc', 'dbdaabbc', 'dbddbcba', 'dacbabcd', 'dacbbdcc', 'adbddbbc', 'cdaadbdb', 'dddbbcca', 'daccabcd', 'bcabdcac', 'dddabadc', 'abddabcc', 'accaddcb', 'dddabdcc', 'dbccbdda', 'cbdcdaca', 'aaaadbcd', 'abccbcad', 'acbddaac', 'ccbdcbba', 'adabbdca', 'cdbbacdd', 'cdbdabda', 'cbdbcaab', 'adabcbdd', 'accdcbdb', 'dcadcbdc', 'cadbcbda', 'ccddadbc', 'dcdcabbd', 'ddadcaab', 'bcdccbaa', 'ccabddaa', 'cbdcabdd', 'bdbcbcda', 'ddbcaddc', 'bcdaaccd', 'baacdaad', 'bddadcbb', 'ccbdddac', 'cddbcbda', 'dbbadaca', 'cbdbacba', 'cddbcbad', 'acaddabd', 'ccbcdcca', 'ddcdbacb', 'acdacbcb', 'ccddcdab', 'dcbbadac', 'dcabdcdc', 'bddcbdca', 'dbadcaca', 'cbaaccbd', 'cbabbcdd', 'cbbcbcda', 'adacdadb', 'ccbcadca', 'bdbcadab', 'bcadacba', 'adbbcbab', 'ddacbcbb', 'dbddabcc', 'dbdbacba', 'dacddbbd', 'cdacadbc', 'abacadad', 'abcdccab', 'dddbdaca', 'cadabcca', 'bcadadba', 'ccdddbba', 'cdcadbcc', 'cadabccd', 'cdcdbaad', 'bdabddcc', 'bcacdbba', 'dbdacadb', 'dabdadcb', 'cdbddabc', 'dabcbdca', 'adddbacd', 'acababbd', 'baddbcab', 'dbcbbcaa', 'abddbcda', 'cabcabcd', 'dbcdadcc', 'bdacbadc', 'ddcbadca', 'bbdaabcd', 'adabddcb', 'aadbcbaa', 'aabccdbc', 'adabdcad', 'ccdcbdca', 'addadcbb', 'dcbadcdd', 'bdcabbcd', 'bddbdcca', 'cbcdacbc', 'abdcbdbc', 'abbddcbc', 'ccbbcdac', 'cabdcbbc', 'bacbdacc', 'babccadc', 'bccabcdc', 'cacabdcc', 'dbcddaaa', 'badbcdbd', 'ddbaacab', 'bcbbdbca', 'bbcddcca', 'ccadbdad', 'addaccbd', 'cbcddcda', 'abddbdcc', 'abbcddad', 'acdcdbcc', 'cdcdadbc', 'ddbcdada', 'cacdcaba', 'adbcaccb', 'bcddcbca', 'dbabcdbd', 'dbcadadb', 'acbdbdcc', 'abadccba', 'acdbdbdd', 'ccadbcad', 'ccdbabca', 'dbcbccaa', 'bdbcabbd', 'bddacaab', 'abadadcc', 'cdbdbabc', 'cbacddbb', 'cacadcbc', 'abccbcbd', 'abcdadbd', 'addbdccb', 'bdacbaba', 'ccaddddb', 'bcdcacbd', 'adabcdca', 'cdcbadac', 'ccdbcbab', 'bbdcdaab', 'dcbbdacc', 'ddadcbdb', 'cdcadbbd', 'adccabbd', 'dcbcbcaa', 'cddbbdac', 'adccddab', 'addcbbdc', 'cbcbdbaa', 'ddabaacb', 'aabcbdcd', 'cddcdbab', 'bacbbadd', 'accadcab', 'cbcacdbc', 'cbbaadcb', 'bcacbdba', 'cbdcdbca', 'aabbdcbb', 'ddbdadac', 'cdbdacbc', 'cdbdadbd', 'adadcabb', 'cbdbccba', 'bdabdcda', 'cdbaddbb', 'bbaddccd', 'dbdcaabd', 'cbdbbcab', 'bcdcadad', 'addcbcda', 'badacddb', 'cdbacbca', 'bcbdaaaa', 'dcdcbadd', 'bccabbdb', 'abdcdccd', 'bacdadcb', 'cbccdbaa', 'dbbdadcc', 'babcadcc', 'cddddabd', 'abdccddd', 'caddcbcb', 'ccaccabd', 'bbdbcdca', 'abcadcba', 'cbddbdda', 'bacdbaba', 'ccbdbabc', 'bbcaddca', 'cbddcaca', 'bdabccbc', 'cacbdcca', 'dabbccbd', 'bdcbbcac', 'dcdabbdc', 'dcdadadb', 'babddcda', 'bdadacac', 'badcddad', 'cdbcadcc', 'abbcdabc', 'cbdbcabc', 'cdbddadc', 'babdacca', 'acbbddaa', 'bbcbdcaa', 'acadbabc', 'cdabdcdc', 'babdbdbc', 'baabcbdc', 'cbdccdca', 'bcadcdbb', 'abcbdbbd', 'bcbbacdc', 'dccabdda', 'acaddaba', 'cadbdcbb', 'acbcdbdc', 'bdcdccad', 'dbbccadb', 'cabdacbb', 'dbadacbc', 'bdaccadd', 'cbabcadc', 'adbacacd', 'acdbbcdc', 'cacdccdb', 'cbcabcdb', 'bcdbacca', 'dbddacbb', 'cbcabadc', 'cbbdabab', 'cbadbdac', 'bdaddaca', 'babddacd', 'cdaccaba', 'ddcabacc', 'acbabdac', 'dadbcdba', 'dbbabdca', 'bcaddbac', 'abdabcac', 'cbbcabcd', 'caacdbbc', 'acbaddad', 'ddabbdcc', 'abacabcd', 'ababccdc', 'cdddbabc', 'bcaccbbd', 'dcadcbbd', 'bbcbabad', 'dbddaddc', 'bddacaca', 'bcbdabda', 'ccacdbba', 'addabaac', 'dbadbdcd', 'abdacbbc', 'bcdadbab', 'dbbcbdda', 'cdacabcc', 'dddcbaca', 'babcdcdd', 'cadabbda', 'ccacbcdc', 'acddbbcd', 'ddabccdd', 'ccadddba', 'bddaabcd', 'daccddba', 'adccdcab', 'dacbcdbc', 'badcdbdd', 'dacbccdd', 'bcabddbd', 'addaabcd', 'abcbddad', 'bcacbdda', 'dccadbca', 'bcdcacbc', 'bbcabcad', 'cbcadbdb', 'acadbdbb', 'cabddcdb', 'bcbaaaad', 'dcdbbcca', 'aadcbccb', 'abadadac', 'addcdddb', 'dacbcacb', 'bacdbccb', 'ddcacbbd', 'caabccdb', 'dbdaaccb', 'dcdbdbac', 'acadcbba', 'bdccaaaa', 'bbccbada', 'badbadcb', 'dcbdacad', 'cdaddbdb', 'baacbaad', 'dbbcdaca', 'dcaccdcb', 'ddbaabcd', 'cbcbabcd', 'bbddbcca', 'abddbabc', 'babcdcdc', 'ccabddac', 'ddadcbad', 'bcacacdb', 'baccbdba', 'ddbaaacb', 'baccdbdd', 'dcabdbcd', 'daccddcb', 'cbdabcbd', 'ababaccd', 'cadbbcca', 'ccdcddba', 'ccbbddab', 'abcdbacb', 'acadbcdb', 'dcabaccb', 'bdbcdbad', 'dabccdda', 'dadddbbc', 'dacbdadc', 'dbdcbdac', 'bbcbdbca', 'bbdabbca', 'addacabb', 'dbbaabdc', 'ddcbdbda', 'dadbbaca', 'ccdbbabb', 'cbdbdcad', 'dabacdca', 'dcbccbda', 'ccadabca', 'cdabbadb', 'cdbbccda', 'cabcbdbd', 'cdcacbdc', 'badbcbcc', 'bcacbccd', 'cabadbca', 'dbdcaaaa', 'bcdbabba', 'dbdbdacd', 'ddcbddda', 'cbdbacac', 'ccddcabd', 'cbddabdd', 'abdacadb', 'acbdbdcd', 'ccabdcdd', 'cbadaccb', 'cbcabcdd', 'cadbabba', 'addcdbbd', 'dadbacbc', 'acdaccdb', 'cbdcdacb', 'ccdbabcd', 'dcddabab', 'aaaacdbd', 'cdcbddba', 'adccbabd', 'ccbbabdb', 'bddbabcb', 'abdddcbc', 'cadccbba', 'dbcacacc', 'dacbcbcb', 'adbcdcdd', 'dabaccad', 'cdbabdba', 'acdbbdab', 'abdabacc', 'adabacbb', 'aaaadbcb', 'bcadbdcd', 'ddacbcaa', 'cdcdbaba', 'dbbddaac', 'dacdbcad', 'cddddcab', 'bcddcaba', 'cdbacdad', 'daabcdbd', 'dcbabbda', 'adbcdadd', 'acbdabda', 'dadcabac', 'cdcdbaab', 'daacbaad', 'adcdbdad', 'cabdadcc', 'cdbabbdd', 'cddcadcb', 'cbbdabda', 'caddbbda', 'bcdacdcb', 'cdbabbcc', 'dcdbbadc', 'adabbccd', 'dabacdbd', 'cdbdbcba', 'cabcddbd', 'cbabccdd', 'bdaccddd', 'dacabcbd', 'dcbdcbad', 'dcdbacbb', 'ddaabcda', 'badcdbdb', 'cdcbdadc', 'dbcdcabb', 'dbcbacda', 'bbdadaca', 'ddcbdbab', 'cacdabba', 'bbcdacad', 'abdccdab', 'cdbcdbaa', 'acdbcbba', 'dcdbddac', 'dacdacdb', 'babcdbcd', 'dddcbabd', 'cbcaddcc', 'bcdbacbc', 'acdbbcad', 'dacbbabb', 'cdcadcba', 'accddcbd', 'ddcbbaac', 'cdcbbaad', 'abbdccad', 'cdbadabd', 'daccbcdc', 'bababdca', 'acbddacd', 'bdbbacdc', 'cdbccadd', 'dcbbcbba', 'abcdbbcd', 'bcaadaab', 'abcdccdb', 'dccadbdd', 'babdccab', 'cbdcbadc', 'bbcbdacd', 'ddadcbba', 'dabcdacd', 'cdcbddda', 'dacadbbc', 'cadbbacb', 'acdacaba', 'bbaacdcc', 'dbaccdca', 'acbadadd', 'abcdabca', 'babacdbb', 'bcdcacad', 'addadbcb', 'bcbbdbda', 'abbcddda', 'cbdcdabb', 'baadaabc', 'cabdbdcc', 'ccacbdcc', 'cdbbacac', 'ddbdaacb', 'ccabdadd', 'adcdbbac', 'adbbcada', 'dbccbdad', 'cdccaddb', 'cbccbdad', 'caacbcdb', 'dadbbcba', 'bdaacdbc', 'caddbcad', 'cbdccdac', 'cbdabcad', 'cdbbaadb', 'bdcabbad', 'cacbdabb', 'acbadddd', 'bbabcdbb', 'bcaccdad', 'bbcddbad', 'cdaccddb', 'abbccddd', 'adbcdbcd', 'dacbdbdb', 'babdddca', 'ccbddadb', 'aabdbcaa', 'cbddacdc', 'dcdbadcd', 'ccbacdcc', 'adccbbcd', 'bcaddddd', 'dabdddbc', 'ddbbadca', 'aacdcdcb', 'acdbcdcc', 'dbadbbdc', 'babdbcdc', 'dbcddbba', 'babbdbcd', 'dacdbacd', 'dddbaddc', 'dcbddcac', 'ccddcbda', 'bbdcdacb', 'adcbdbba', 'dcdbbadd', 'aabccdaa', 'bdbbdcaa', 'ccadabba', 'cdbdbcda', 'acbdcdbb', 'cababacd', 'cdcacbdd', 'addcbaba', 'bacdcbda', 'bccdabdc', 'cacbddba', 'ddcdaabd', 'dbbccbac', 'bddbbcaa', 'dabdbadc', 'dccbcdac', 'dbbadbbc', 'daadccbc', 'cacbdbca', 'bccddacc', 'adbcabcb', 'abbdbbdc', 'dabaccac', 'dcdcbbaa', 'acdccabb', 'ddaccadb', 'dbdcdadc', 'bcbdbdba', 'ccaccbdc', 'bdbcbbab', 'cbbcbdaa', 'badbddac', 'adcdbacb', 'cabacddc', 'adacdbad', 'acabbddd', 'ccbabddc', 'cbbdcaac', 'babcdadd', 'adabcabc', 'dadacbdb', 'cadcacdb', 'ccddbbac', 'bbcdddda', 'dcdcdabc', 'abbcdadc', 'ccdbaadc', 'cbabdbcb', 'bcdcdacc', 'dbccdbca', 'baadbcbd', 'ccaddbcb', 'ccabcbbd', 'cbabbdac', 'acdddbdc', 'cabdccad', 'aacdbaac', 'adbccddb', 'acdbbcdd', 'ccadcdab', 'cbacbdcb', 'dddaacbc', 'adbdcadc', 'cbaadbdc', 'bbddacbd', 'abacaddb', 'dbdbbcab', 'cdacbdca', 'aadcdaab', 'ccdcacbb', 'dbcbdbac', 'baccabcd', 'bcacbcda', 'acbcbadb', 'cadabdab', 'cddabccb', 'abcbcdcc', 'acbcddba', 'cddbacda', 'dadbdcdd', 'caacdbbd', 'cddacbdb', 'dcbbaabc', 'dcdbcacc', 'abadbbcd', 'bccacadb', 'abcdddbd', 'cabdbcbd', 'abcbdbba', 'bddacaad', 'cdccacab', 'abcdcabb', 'ddbcbadb', 'bacdddac', 'dccaccbd', 'adbdadca', 'ddccaddb', 'bbcdccba', 'ddccbdad', 'bdbaabdc', 'abcbccda', 'aadcbdcc', 'adadcbdc', 'bdadbcad', 'badcbbdb', 'bbcddada', 'cadabbcc', 'cdcdabcc', 'addcadbd', 'ddabcacd', 'abbcdcdb', 'acaccabd', 'cadcbacc', 'cbbacddb', 'dacadcba', 'abbccadc', 'abdbbcbd', 'acadbdac', 'cabdbdbb', 'abddccbd', 'bbcadccd', 'ccdbdaac', 'bbcadbdb', 'cabccbbd', 'dabbccbc', 'adadcbad', 'adbdabcd', 'bdbdcada', 'dacaccbb', 'dcdbcdca', 'ddcababc', 'bcbcbdca', 'cbbacdbc', 'dbdcdaac', 'badddbcd', 'cbdcdacd', 'cabbdddd', 'dacdbbcb', 'dbcbcacb', 'accdabda', 'bddaaddc', 'cabacadb', 'ccbdbdad', 'daddacab', 'cbbadbdd', 'ababcdba', 'daadccbd', 'bcdaddbc', 'dbaccbab', 'dbaddbca', 'accdabac', 'dbbddcca', 'abadbcdb', 'ddbabcab', 'abbcadda', 'cbaadbbc', 'baccdaca', 'ccbadbcb', 'dbcaccda', 'dbcdabbc', 'bcaadbcb', 'cbdbaacd', 'cdabbccd', 'cdcaadbc', 'babcbccd', 'dabbacac', 'ddacdbcb', 'dcdabdcb', 'cdcacdcb', 'cbbdabcb', 'bccabddc', 'cbcddbaa', 'acadbbdd', 'ccbdcaca', 'cdbbacbd', 'abddcdbc', 'dbacbddc', 'dddaaabc', 'cdaccbab', 'bcdaddad', 'dcabccdd', 'adbdbbac', 'acbcbcbd', 'cdbcbaca', 'acbbadda', 'cacbccdc', 'abcdadab', 'dcbcbadb', 'cacabdab', 'ccdbdadb', 'cdbcdabc', 'cbcbddab', 'cdbdabdd', 'bcacbdcd', 'dcdcaabd', 'cbbcaadc', 'bdbbaadc', 'adcdbbcd', 'aacdbdbd', 'dcabdcad', 'adabdaca', 'bcadddca', 'acbbaccd', 'daccbbdc', 'bbddbadc', 'bcabbadb', 'cbadacba', 'dadbabcd', 'badbacda', 'ccdbbadc', 'dbdacadd', 'dacbdaba', 'bcdcbada', 'cddaadbb', 'abbcbbda', 'acbdddab', 'bcdcacac', 'dcbbdaba', 'cbbadbbd', 'dcbacdda', 'dddbaaca', 'dadabcbc', 'cdcbacba', 'ddcbacdd', 'adcbcdab', 'cdbabcda', 'bcdcdcba', 'cbddabbd', 'adddabdc', 'dbbabdbc', 'cbccbdda', 'ccdaccbc', 'cdacbbac', 'abddbbcb', 'addcbaab', 'bdacbccb', 'adbadacc', 'cbbdadbd', 'acbbadcc', 'adddadbc', 'bcbcacad', 'adcdbdbc', 'ccbababd', 'abcdbbdc', 'cbcadadd', 'daccabda', 'badcdddc', 'abdddcdc', 'ddabbcbc', 'dcadcadb', 'bacadcbc', 'dbbddcba', 'abbcdbbd', 'bdaabcaa', 'daddbcbc', 'ccabbdab', 'ddcaacbb', 'cbdacbbd', 'dcbcdabc', 'dabdacba', 'aabcbdcc', 'abccddbd', 'abdacdcb', 'ddcddbad', 'bbaddaca', 'bacadbdc', 'aaaadbbc', 'cadcbccd', 'cbdcbbad', 'ccbccada', 'dcabbaba', 'babbadac', 'dcbcbcad', 'ddabccbd', 'bdcaddba', 'bbdcacab', 'cbccdadd', 'dabccbab', 'bdccaabc', 'daddacbd', 'cadaddbb', 'cbbdcbca', 'abcbccdd', 'bcadaccd', 'ddbdacad', 'baccdabb', 'bddadcbd', 'baddccba', 'bcbdccda', 'dbccddad', 'bdaadbdc', 'cddaabaa', 'dbbdacda', 'ccadbdca', 'bcbbdaca', 'cbcbdcab', 'ccaadbcd', 'cbdcaccb', 'adcdbdbd', 'acacadba', 'ddddbcab', 'bcacdbdb', 'dbaacbcc', 'adcadabd', 'adbacbba', 'cdadcdab', 'babbacdc', 'abcdcbca', 'bdacacdd', 'acddbacd', 'cacbcadd', 'bddcadbd', 'adccdabc', 'bdacadcc', 'bdcabada', 'bdbdacdc', 'cbbadcbc', 'abcbbadb', 'bbacacbd', 'acdacabc', 'acbdbdbd', 'bdbcadcd', 'cbdddaca', 'adabcbda', 'abccbccd', 'bdaddccb', 'bcdbadab', 'bcbcdaab', 'bdbbdacd', 'dbbccacb', 'bdbbcada', 'dbddcdba', 'bcdbdabd', 'badacabc', 'daadcbbc', 'accbccdc', 'dadcdbdb', 'ddcdbada', 'ddcaabda', 'cbbadccb', 'dbdabcac', 'dcaccdbd', 'cdcdacbb', 'abdcabda', 'bcdcdcad', 'bbcdbbca', 'babacbdc', 'adaccbca', 'daccdadb', 'abdcdacc', 'adabccda', 'bcddddad', 'cabddcba', 'cbddbaac', 'bdacadbc', 'babcabdc', 'abcdbcac', 'bacdbdca', 'ccbbdcaa', 'adbcddca', 'bbadacbb', 'acabaddd', 'ddbcbcac', 'dabbccda', 'cacbddcc', 'dddcbcca', 'ccbaddba', 'cdcdbdad', 'bdcbdada', 'cdcacddb', 'cbdccbac', 'cadbabab', 'cbadbcad', 'cdabcbcb', 'acdcdabb', 'baddddcb', 'ccdbcdaa', 'cadbbdca', 'adcbabab', 'ddbcbcaa', 'dbdaabcb', 'daccdcbd', 'adcdabac', 'ccababdb', 'babdbcbb', 'cbbabdbd', 'cdcbcbba', 'cbacbcdc', 'dadcdabc', 'cdbbcdac', 'ccbadcdc', 'cbccadbc', 'cdaacaab', 'bcdcadcb', 'dbbcbacc', 'abcdacda', 'abbccdbd', 'addbdbbc', 'abdadcba', 'bccadbdb', 'dabcdccb', 'dbcdaabb', 'acacaddb', 'babbdcbd', 'abccddcb', 'acbcbbad', 'bbaddacb', 'cbbcdbab', 'cbcadbbc', 'dbddabcd', 'dabacddd', 'cdbdbada', 'dacababc', 'addcbbad', 'bcdcbcaa', 'cabcbbdb', 'adbcacca', 'dccbdbaa', 'dadacbdd', 'bccdccac', 'bdbcabdc', 'dbbcaaaa', 'dbdabcad', 'cacacbbd', 'bacbcadc', 'cadbadda', 'ccdacaba', 'cbcddabb', 'acbbdadb', 'dcdaccbc', 'badcdcda', 'bbdbacca', 'dabdcdca', 'badadcac', 'bacddbcb', 'bbddaabc', 'ccdbcaca', 'bcbcacda', 'abcdabba', 'aaaacdbc', 'badbbacd', 'dcdcbdac', 'ddbabdcd', 'acadddbc', 'bddbcdba', 'ccddacdb', 'cbdcabbd', 'bdacbacb', 'badacddc', 'dbabdbac', 'bdddddac', 'bdbccabd', 'bdbccadd', 'cadccdcb', 'addcabda', 'dadabbcc', 'cdbaacaa', 'abadccac', 'bddccadb', 'daaaadbc', 'bdacdcdc', 'dbdbbabc', 'cacdaccb', 'caacaadb', 'dbadccda', 'ddadddcb', 'cdaccdcb', 'bacbdcbb', 'bcbcbadc', 'ddaabcba', 'dccdbadd', 'daabdcaa', 'cacdbcad', 'dbccbbab', 'cdadaccb', 'daccdcbc', 'cbbdcacd', 'dbcabbac', 'bacabdba', 'cbcbbada', 'dadabbcd', 'acdaddbc', 'aadccbcd', 'cddbaccd', 'accbccdd', 'dcaccdbc', 'cdbaccbb', 'bcbcabdc', 'cabccddb', 'aadbccdb', 'cbccbadb', 'dcbcdbda', 'bacadbad', 'dbdadccd', 'adbadcda', 'bddbcadc', 'cbdccbba', 'addcbcbb', 'cabbdcba', 'babccbcd', 'dbaccaca', 'dcdcbaab', 'cddcbcaa', 'bddacaaa', 'dccabccb', 'cbcaadcb', 'bddabddc', 'adbacdba', 'abdbccdb', 'acbbadac', 'dcdaccab', 'ddbcaabd', 'bccacbdc', 'adabaccd', 'ccdcabab', 'addcbada', 'cbbadcbb', 'abdddbdc', 'dbacbdca', 'bcdcaacd', 'adbdcdcb', 'accdbaca', 'bbcabddc', 'ccdbbaab', 'ccacbadc', 'cbbcaddb', 'dcbddcca', 'bccbcaad', 'cbacdccb', 'daacdcbc', 'acdadabd', 'dbdcbcac', 'bbcdbaab', 'bcbaddbb', 'bdbbcabd', 'acdacabb', 'acacddbd', 'bccdbcab', 'dbdcbcaa', 'dcadcdbd', 'bbcadbda', 'cabccbda', 'cabcbddb', 'addcabbd', 'cadbcbba', 'adabdcdb', 'bbababdc', 'bcddacbd', 'daabdbdc', 'bdabcdbb', 'dabcdadd', 'dddccaba', 'cdbacabd', 'cddbcaba', 'dbdbbcac', 'bccacdcb', 'dbddcdca', 'bbadabcc', 'cbcdbadc', 'bcdcdbac', 'adbacdcb', 'bcdcabcb', 'cdcbadda', 'abbdcdcd', 'dabddcbc', 'dbdccaca', 'bdbbcdad', 'abbacadb', 'bdcacdbc', 'ddcacbdb', 'dbcbabbc', 'cdddbadb', 'cadbbcab', 'dabdbcbc', 'acbdbddd', 'cdabcbbd', 'cdacdcbb', 'dddcbaac', 'acbacddc', 'abddcdbd', 'abcdccac', 'dcbcbacc', 'ccbdacbc', 'caddcacb', 'cdbbdacc', 'baddbccd', 'accdabdb', 'badddcba', 'abdcbbdc', 'cacadadb', 'cbccbabd', 'babadcbd', 'bbacdaba', 'cbcbbcad', 'aadbdbcd', 'badddcac', 'dcdddabc', 'abadccab', 'cbacbdcc', 'dcabbabc', 'cadabbdd', 'dbadcbac', 'bcddabbd', 'dabddbcc', 'abcbdaca', 'babbabdc', 'bbdaadcb', 'cbdacddc', 'bddcdadc', 'cabbabcd', 'ababcbbd', 'adadabcb', 'bdacddbc', 'bdddacdb', 'adbabccb', 'dabdccdc', 'ccdacbcb', 'ddadbddc', 'cacdcdbd', 'badadcbd', 'bcbdacba', 'bbcdbdca', 'cddaabba', 'badbabcd', 'cdccaccb', 'acbdabbd', 'dddabcad', 'bacbbdcd', 'adcaccba', 'cdabbabc', 'cadabacc', 'cdccdcab', 'abacdbdc', 'ccdcaacb', 'dcbddbaa', 'addacbbc', 'acdccdbc', 'dcbadcbb', 'badbccbc', 'cabccbdc', 'adcabadd', 'ccacdbac', 'cddbcbab', 'bcbdcaba', 'bccdabab', 'bddcacba', 'dbbadbcb', 'caccdbdc', 'abbdbcdb', 'cdbbadbd', 'cdbdcdad', 'cabdbbcd', 'adbdcbcb', 'ccbbccda', 'caadbbdc', 'ccdcbdab', 'cabdcadb', 'dcbcdbaa', 'acadabdd', 'bccdadac', 'ddacdbba', 'bcabdcab', 'bbdaddca', 'daccbcbb', 'dcbababd', 'bdadcbba', 'baabbdcb', 'dcbcaacd', 'cadacbbc', 'dccdabba', 'dcacddbb', 'bcabdccd', 'cbdadbdd', 'cdbabdca', 'cdbdccba', 'abadcbdd', 'ddbbcdad', 'bcbaccdd', 'acbcdbdd', 'ddccabcd', 'bcdbbaba', 'cadadaba', 'bbaddcdc', 'bccadbdd', 'abadcbad', 'cabaddcc', 'cdcababd', 'ddabcdcd', 'ccbcaadc', 'ddcdaaba', 'acbdbabc', 'adacbaca', 'dddbcbda', 'cbbdbcba', 'abbdabac', 'caabcdcd', 'bbcbdabb', 'dccdabcc', 'dcbaadbd', 'bcacacbd', 'dbdcddba', 'bcbadcab', 'cbcdbbad', 'bddcacad', 'dacddadb', 'acdbdaba', 'bdcbdcba', 'cbccbacd', 'bcdbcbba', 'cadbdbca', 'cdacdbac', 'addbcdcd', 'ddcdabcc', 'adcdcbbc', 'cdacdaba', 'bbaddabc', 'baddacbb', 'dccacddb', 'bdabcbcc', 'cadcabdd', 'addbddbc', 'ccbdbdba', 'bcdacbdb', 'bddacdcc', 'cdaddcdb', 'ddcbbdac', 'baabcdbb', 'bbcabcdc', 'bbdcacbb', 'bddacbcb', 'adcddaba', 'dddbbacb', 'cacdbcbd', 'adbddcda', 'bbcbccda', 'abcdadbb', 'addcbadd', 'bdbadbcb', 'acddadab', 'cbdbacdb', 'dadddcdb', 'bababcad', 'dbccadcb', 'dadcdbda', 'cabbacdb', 'bccdccad', 'cacddabb', 'bdccadac', 'cbcabdcd', 'ddbacadd', 'cdbcbcad', 'bdcbacab', 'bcdbaaaa', 'bacabdca', 'dacabadd', 'cdaacdbd', 'acbacadb', 'cdabcdcc', 'dbddcadc', 'cdcbadbd', 'bdcacdcb', 'adbbcdda', 'bbdccabc', 'cdcadddb', 'cbadbadb', 'aaccbdcc', 'dbbcaabb', 'cdbcabbc', 'abdbacac', 'dbbabcdb', 'cddddacb', 'bacddcdd', 'bddcbadc', 'cababbad', 'cbbadbba', 'aacdbdcd', 'cddabdcd', 'bbdaabbc', 'bbdacaba', 'baccbdad', 'dabdcabd', 'dcbbcada', 'bccadacd', 'adbbccbb', 'cddbcadb', 'ccaabaad', 'dcbcbabb', 'bccbdabb', 'adbdabcc', 'cabddcda', 'dbcacdab', 'addadcbc', 'bdcdacdc', 'bcddaaaa', 'cadbbadb', 'cabadbad', 'acdabcbd', 'bacdbada', 'cdadbdbb', 'dcdabbdb', 'bdadaddc', 'addbbcac', 'bdacbbda', 'adadbbdc', 'bdbdbabc', 'dadcddcb', 'abccddda', 'abdcbcdc', 'aadbdcdc', 'daddbdcb', 'bcdcdaad', 'cdaabcbd', 'adadcdbc', 'acbddcac', 'acdddabb', 'cadbcbdd', 'dbcbaddc', 'bcabcdbd', 'bcdaacbd', 'ddaadcbb', 'bacababd', 'aacdcbaa', 'ddcabcad', 'ccdbddad', 'ddcabdcd', 'bccddcad', 'dcacdbdc', 'dcadbadb', 'acbcbddb', 'abbadcdd', 'abcdcaca', 'bdbcacbc', 'dccdcbca', 'bddddcda', 'dabbcdcd', 'acdcdbcb', 'adabacad', 'bcadcacb', 'cddbaabd', 'aabaadcb', 'dbcadbcb', 'ddbdcbda', 'dcdaccba', 'bdcdabba', 'dcdadabc', 'bdbabbcc', 'dbcddadd', 'adcbaccb', 'dcbaccda', 'bccbadac', 'bccbdcaa', 'ccdadabc', 'bcdbbaab', 'cddabddc', 'cbbaadcc', 'cacddccb', 'dbcbbabb', 'cbdabccb', 'bcbcacdd', 'bbcdbabb', 'cbaacdbc', 'cddadcdb', 'dcdddbda', 'cdacbbda', 'dabdcadb', 'dcacbdcd', 'cdabdadd', 'addbabac', 'ddabdacd', 'dabcabcd', 'accbbada', 'daadbccb', 'cbdddcba', 'bcacddad', 'cabddaca', 'bbdaacbc', 'badcabcb', 'dcadcbdd', 'bdbdadcd', 'bbdbacab', 'cdbadbcb', 'dbbdbabc', 'dbddadcd', 'cbcaadbd', 'adcddddb', 'ddbadbca', 'dcaabdcb', 'ddacadbb', 'baccabdd', 'cdbbcabb', 'acdbcbcc', 'addbdaac', 'dbbdacba', 'bacddcba', 'adcbbadb', 'bdcbabbd', 'abddcabd', 'cdbcaadc', 'dacbcadd', 'dadacbbd', 'bdbdabbc', 'bdadccdd', 'adabdcda', 'bbdacddb', 'cbaccbdc', 'bdabddac', 'cababcdc', 'acbdddbd', 'accadabb', 'cdabacbd', 'bbddadbc', 'adcddbad', 'bbdcdbad', 'cddbabba', 'ddccacba', 'abddcada', 'bbdcabab', 'cabdacba', 'adbbabca', 'caadcaab', 'cbacdadc', 'dabcdadb', 'cabcadcc', 'ddcbbcaa', 'acdaddbb', 'dacdcbbd', 'bcdcbaad', 'bcbdbacb', 'acbdbcac', 'adacdddb', 'dbddadcb', 'bbcacadc', 'dcbddaaa', 'adbddbca', 'ccbbcdaa', 'cbbadddc', 'cacadbdc', 'abcbacdd', 'dcdbcdad', 'dddcaddb', 'bacdcbca', 'bdcbabcb', 'cdcbbcad', 'bddbcdda', 'dccbbaba', 'dcbadbcd', 'accbddbc', 'cabdcdda', 'bcadadbd', 'bdcddbaa', 'abddcdad', 'bddbacbc', 'dbdabcda', 'ccabdddc', 'badccddc', 'abccdbab', 'dcacddbd', 'dddcadbb', 'ccbddacb', 'ddcdcbaa', 'abbdbcca', 'dadbcdbd', 'bdaacdbb', 'cbaccacd', 'cbddcdab', 'cbcddcad', 'cbcbdcda', 'acdbddbd', 'bcacdbdc', 'abadaddc', 'cbacdcbb', 'dbdddbac', 'bdcabbab', 'acacabbd', 'bdcdbbac', 'dcdbacbd', 'bccadccb', 'dcbcdcaa', 'ddbcbdaa', 'bcdddcda', 'bbcdddca', 'daddddbc', 'bbdacdbd', 'bbcaddbd', 'abdcddcd', 'adbddadc', 'bbaccdad', 'bbcabdad', 'adcdbbcb', 'ccdabcca', 'badcacbb', 'abacbccd', 'ccdabbac', 'baccbcda', 'bdcadabd', 'cacdabda', 'cdcaabbc', 'acadbbdc', 'dbacdcdc', 'cbabdcbb', 'abcbbdca', 'abcbddda', 'ccabbada', 'dcacabba', 'acbddaab', 'adbcbabc', 'cdddabdc', 'cdacadbd', 'baddacdc', 'ddaacddb', 'dcdacdcb', 'bcddcadc', 'bdaacbcc', 'baadbdbc', 'dabbabac', 'abcdcadc', 'acdbdcba', 'cbdaabcd', 'cdbaccda', 'dbabbdcb', 'acdadaba', 'badaccbc', 'cbadbdcc', 'cddbbaca', 'acbacdda', 'adacadbb', 'adcdadbb', 'bbaccdcc', 'babdddcc', 'cbabadac', 'cbdcaccd', 'abbcacdb', 'cadcbcdb', 'dacbacba', 'acddddbb', 'bccbadcb', 'ddabacaa', 'bacbdabd', 'abbdbacc', 'cabcdbac', 'abacdaca', 'bccdddca', 'ddbbacda', 'bddbcaaa', 'dbcbddac', 'cadcbddd', 'ccabadca', 'bcdadacc', 'bacdabcc', 'cabbdcbd', 'caddbaaa', 'addadcbd', 'bdcacdcc', 'cbaccbbd', 'abdbdcbd', 'bddcbcab', 'addbddca', 'bbdcabdb', 'dabddaac', 'aacaadcb', 'babcbdba', 'bdccaacb', 'bcdbdcba', 'dbddabbc', 'cdbbddaa', 'badbabcc', 'ccdbabdb', 'dbacbada', 'dbdaccbc', 'dadadbac', 'dbaaccaa', 'bdabbdac', 'cbcadcdd', 'bcdcacca', 'cdbdadba', 'addbabcd', 'bcbddbac', 'acbbddda', 'ccadacbb', 'cabcdddd', 'dbadcbbd', 'cdcdbada', 'cacddcbc', 'bcddadbc', 'ddccdbca', 'cacdacdb', 'cbabcadb', 'ccdcabbc', 'bcbcbdac', 'dbddbdca', 'baadbbdc', 'cbbacabd', 'bdabcadd', 'ddadcdba', 'abcdcadd', 'cbabbdbc', 'caccbcad', 'cacaddcb', 'dacabadc', 'bbdddacb', 'bbdabcdb', 'cadadabb', 'ccdccbad', 'ccbabacd', 'dacbcbdc', 'cbaccdbc', 'cddbaaba', 'cbcbcdac', 'dcabcdcb', 'abddbcdd', 'dddcaabd', 'bbdcdaac', 'acbddcab', 'dbcbbada', 'bbdbcaab', 'addbbdbc', 'acdbccad', 'ddabccbc', 'bbadddbc', 'bdcddcba', 'adadcabc', 'dccbbdad', 'adcbbada', 'adbadbbc', 'ddadbacc', 'dddcdbba', 'acbcddbd', 'bbacbddb', 'bbddcada', 'bcddbaad', 'dbaabcdc', 'cacdbbab', 'dbdadcdb', 'bdbbcaac', 'bdbddaac', 'cbabdcbc', 'abdacdac', 'daccbcbd', 'bdcbbaba', 'bbcaaccd', 'cacbbdca', 'acabdadd', 'cdbdddad', 'cbabcdbc', 'dbaccacc', 'ddabccdc', 'ddacddba', 'acaddccb', 'abaccbdb', 'ccdbadca', 'ccbadccd', 'cbacbccd', 'cbabbdcc', 'acdbcbac', 'bdcabcbd', 'bbaabbdc', 'dbbaddbc', 'bdcddaca', 'bdaaccbb', 'bdcbbaac', 'bdddbcab', 'babddcba', 'dacddacb', 'bcacdbbc', 'cdcdadcb', 'acbabdbc', 'adcbccad', 'dbddccda', 'adcadcdb', 'cdcdcdba', 'bbdaccbb', 'bcbdddca', 'cddaadbd', 'abdcadba', 'accdabab', 'bcbddacc', 'bdbacbbd', 'dbbadcdc', 'ccddcdba', 'dcaabbcd', 'acbaccdc', 'accdcbad', 'bcddbbad', 'cbadbbad', 'dbdcbbda', 'bbadddca', 'ccdaddbc', 'ccacbadb', 'bcdcabcc', 'dabbcbac', 'dbbcaccb', 'bdcadcbc', 'adccadcb', 'bacadbcc', 'dbcddcac', 'cadbabdc', 'acddccbb', 'caccbbdd', 'ddbcaadb', 'ccadbcda', 'bddcaddc', 'bacacabd', 'bdcacbcb', 'bbddcbba', 'dbacddac', 'bcdacbba', 'cadcbdda', 'dabbcbad', 'cbcdadab', 'bcabdbbd', 'bddadbcb', 'acbacbdd', 'ccbacddb', 'ddcaabdc', 'bcdaadbc', 'bcdadbdd', 'cdccabca', 'bacbcdac', 'acdbbabb', 'dacddcbc', 'dabdcbcc', 'cacdbdcd', 'cdccbbaa', 'abbadbcc', 'adadbcad', 'bddabadc', 'cabcbacd', 'addbdbcc', 'cdbabbda', 'cdabdcba', 'dabcbbcc', 'cddbdaaa', 'dccdbcda', 'dbddacca', 'adacbdbc', 'accbadca', 'adabdbcb', 'dbdabccb', 'dbbddacb', 'cdbdcacd', 'cbdbdcda', 'abadcdab', 'dbdbccad', 'cdbbaddd', 'bcacbcbd', 'ddbbacab', 'dddaabcd', 'ccabdbdd', 'bdbacadb', 'bcbcbaad', 'abdabddc', 'acdbabba', 'dadbdbcc', 'cbdcbcab', 'cadbdbba', 'caacdbdc', 'cbcdcaab', 'caddcdba', 'ccbdacac', 'acdbddcd', 'baacdcdb', 'bbdcacac', 'cdddbdda', 'dcabadab', 'dbadacdd', 'acdcdbca', 'bcbabcbd', 'bcadddcb', 'cbacdbba', 'dbbabdcd', 'acbbcdad', 'dacdbcac', 'ddcbbdab', 'adabccbd', 'dcadabad', 'bdbcdabb', 'cbcdadda', 'baddacab', 'baadccbb', 'adabdbdc', 'cbaaaadc', 'cdbdbacb', 'dadcbaca', 'abaddbac', 'cbdabbdc', 'bbdccdac', 'cddbacaa', 'bcbdaadb', 'dbcaadcd', 'cdbcabac', 'dacdbbca', 'baccbbcd', 'bbcadccb', 'dcdcbabd', 'dbccdaba', 'ccddabcd', 'abccddba', 'bddabdca', 'abbdbdca', 'bccddaca', 'dabdcdab', 'dccdbabd', 'abdcabba', 'adbdabac', 'dbcaddad', 'bbcadddc', 'adcbabad', 'cdabddbc', 'acdbadcc', 'cdabdbad', 'dadccbdb', 'dbbccdac', 'aacdcbcb', 'dcabbddb', 'ccbdabda', 'bcbadcda', 'dbabcadb', 'bdabbdbc', 'abdccbdd', 'abcacdbb', 'cbcbdabc', 'bccbaadb', 'bccdcbca', 'baddbcac', 'cddddabb', 'bcbadcbc', 'cadcadbc', 'ccabcdad', 'ccdbddca', 'bccacadd', 'cadacbcc', 'dacacdbb', 'addadbcc', 'aacaadbb', 'bcddabcd', 'ccbacbdd', 'cbdaddab', 'abdcbcad', 'cdacbbcb', 'ccacbdba', 'dadcbccb', 'cdabacab', 'dcbbcaac', 'bddadccd', 'cbcaadcd', 'abcddacc', 'bdbccabc', 'dbbdccda', 'acbbdddb', 'bacbdbca', 'ddbdaacd', 'bcaabcdc', 'cdbbcdad', 'accddbaa', 'dccaccab', 'bbadacca', 'badaccac', 'ccbcbdac', 'bdbbcabb', 'adcddcdb', 'bdcdacda', 'cbabdcbd', 'ababcbdd', 'acbabcda', 'abcadadb', 'dccabddc', 'cddddbca', 'cbadbcdd', 'bcbcdcac', 'cdddbaca', 'cbddbcca', 'bbcbbdca', 'dddcbcba', 'cbbddcba', 'aadcbaad', 'bdcdbdba', 'ddbcdabc', 'bacddaac', 'ddadcbac', 'cabbddba', 'ddaaccdb', 'daacbdcb', 'daaccbcc', 'daabbcbc', 'ddacbabc', 'addadacb', 'addbaadc', 'babcbadd', 'abacbdad', 'bcbcbdaa', 'bbcbadcc', 'cbccbdab', 'bbcbabdc', 'cabddcab', 'bdcdcbaa', 'cabdbccd', 'cdabcbab', 'dcacbada', 'aabaacdb', 'ddccbcab', 'dabdcdbb', 'caddccba', 'cbddaada', 'cbdadabb', 'bdbdccac', 'cabdddad', 'addabbcb', 'acaccadb', 'bddadccb', 'accabccd', 'abcabddb', 'cbaccdcc', 'cadaccbc', 'dadbdcda', 'aadcbcbc', 'dcbabddd', 'dcacdcdb', 'dabbccad', 'ddaabbac', 'daadbcdb', 'bcacdada', 'dbccabcb', 'addbdbca', 'abdcdcbd', 'ccdcbcab', 'cbdddadd', 'dbacdddd', 'cadbabcc', 'aadbcdcd', 'ccadcabd', 'dcaabdbc', 'acdbbcbc', 'bdaddcbc', 'cdbadcba', 'badccacd', 'adcdccbb', 'dbbdcaba', 'cadadddb', 'bdddacdd', 'bdbccdca', 'ddbdbcab', 'bcabdacd', 'bdadcdcb', 'adabbcdb', 'adbcdbca', 'bbddabca', 'dccdcbab', 'bdbdacac', 'aabccdcb', 'cbabddab', 'cdbcddda', 'bdadbcba', 'ccdabcdb', 'cbddbacc', 'adcdcbdb', 'badacdbc', 'cabbdacb', 'bbcacbad', 'bcbacdba', 'cdaddbdd', 'cdaabcbb', 'ddacbdba', 'dcaabcdb', 'bbdcbbaa', 'bdcddbba', 'bcacbcdc', 'bddacddb', 'acacbdbd', 'abcbddcd', 'baddcbad', 'ccbbdadd', 'dcaadbdc', 'cdddcbba', 'cbabbacd', 'dcbadbdc', 'dcbcacac', 'cbcbabad', 'cdbbcbca', 'abdccbcd', 'babcbdcd', 'accdabba', 'bdbbdcda', 'bcbdcbad', 'cdccdabb', 'ddcabdcb', 'bacabcda', 'acbddcad', 'bdabaccd', 'ddbabbcb', 'acabadba', 'abdacabc', 'dcabdcca', 'cdaddabb', 'aaccaabd', 'bcbdaadc', 'dccacdbc', 'baacaacd', 'bacbdcba', 'bbadbbac', 'bcdacbdd', 'adbabdca', 'dcabdbca', 'bbcbdaca', 'abccdaca', 'ababacda', 'addabcad', 'bcdbcacd', 'acabcbda', 'babbddac', 'bcbdcabd', 'adcbddbd', 'ddcbbadd', 'badbbabc', 'ccdcbdba', 'bcdadabc', 'bdabacdd', 'abddabac', 'cdbbabcb', 'adbacdcc', 'bddacadb', 'dcbabcba', 'cbdcaadb', 'bbddbcda', 'cbcdabcb', 'dbccacad', 'cbbcdbad', 'cbabdbac', 'bcdbadcd', 'bacadada', 'bddcaaaa', 'bddbaddc', 'abacabbd', 'abcdbdca', 'aacdccdb', 'cabddcbb', 'bacbdddc', 'cdabbada', 'dbccbbca', 'dcacbcab', 'cacbdbdc', 'ccabccdb', 'bcddcacc', 'addaacbc', 'dbdddaca', 'abdccbbc', 'baccbddb', 'bacbddad', 'dcbadcda', 'cbdacadd', 'adabcadb', 'adbddaac', 'cabbacad', 'cdddaabb', 'babddaac', 'cacbacda', 'bcabcdbb', 'addcbcad', 'cabaddaa', 'ddacbbaa', 'dcaddbcc', 'baadcdbb', 'bdcabbdd', 'dacbdbda', 'adacbada', 'abbcdbba', 'cbbdbcad', 'ccbbddba', 'ccdaabdb', 'dbaddabc', 'bddaadca', 'dddcabcd', 'dabdcadd', 'acddcddb', 'dbbcaddc', 'adccbcdb', 'aadbbcbb', 'dcbdadba', 'acbdccac', 'ccdbdabd', 'dbdbdbac', 'bdcabddd', 'bdabdcbb', 'acabdbdb', 'bddaabac', 'dbadbcad', 'badbbcad', 'bccbabdc', 'ddaabaca', 'babbdddc', 'dcbaccad', 'ccdbdadd', 'dcbdacdb', 'acdadabb', 'cbbadcdc', 'adabbacd', 'acbdccbd', 'cadabcac', 'acddbbdc', 'bccbadbd', 'caaaacbd', 'dcdaddbc', 'babdacad', 'bcdbbadd', 'dccbcdab', 'bddcacdc', 'cbdccbda', 'bbdbcacb', 'bacdadcc', 'bdbaaaac', 'adbacbbd', 'dddabcdd', 'dcdadbab', 'ccdbabbc', 'dcbbacda', 'acbdadcc', 'cdbacddb', 'dcabdbda', 'adbdacdb', 'dbbdacbd', 'ccbdaddd', 'dadaccbb', 'cdbdaddc', 'acddbaba', 'bdccacbb', 'bbcadbbc', 'adbbcbca', 'cbdbacda', 'dcbcdcad', 'cdacdcbc', 'ddaabadc', 'dccddaba', 'bdcbacca', 'bddadabc', 'bcbdbcba', 'cdbdadcb', 'ababadac', 'ddbadcaa', 'dbdddacb', 'cbddaabb', 'acababad', 'abcdcbcc', 'bddacbba', 'cdbacadd', 'dcbabbca', 'baddacdd', 'bcadacdb', 'cadbdccb', 'cabbcbdd', 'aabdbaac', 'cbbdcadc', 'cddccbac', 'acddbdac', 'dbbababc', 'dcdcddab', 'dbdacbba', 'acdcbada', 'dbcacbcc', 'bccadbda', 'ddccbcad', 'dcbbccac', 'cbbaddac', 'abdbacbb', 'cbdadacc', 'dbadabbc', 'bdcbccad', 'dacacaba', 'cadabcab', 'acadbbca', 'cabdbdca', 'cdbbaacb', 'cdbaadbc', 'abcdddad', 'adcaddbb', 'bcdaabcc', 'ccbadbda', 'dddadbcc', 'cabccadc', 'dbbaccda', 'acddabdb', 'dadddcbc', 'bcbcbbda', 'ccadbbca', 'bcddaadb', 'ddcaccbc', 'bcbccadb', 'bbdccdba', 'bccadcab', 'dbbacbdc', 'caccbada', 'baddacba', 'badacbda', 'bdabccab', 'acbacddd', 'adcbbabd', 'cbbccaad', 'bcdabdbd', 'ddcabdca', 'dbbdcacc', 'dcdddaba', 'bacacdcd', 'dccadbab', 'adcacbbd', 'bcacdbcb', 'cbacdaba', 'bddcdadd', 'bbccdabc', 'cdadbdcb', 'dcbbaddd', 'cabbdcca', 'cdbabbca', 'babbcbdb', 'bddcaadd', 'cbbccdab', 'dacdabcc', 'cbcadcba', 'bacbabad', 'cdabcadc', 'cdadabcb', 'dbcbdabd', 'abacadbc', 'bcbaddac', 'aabdcdbd', 'cbadbcab', 'cacbdcbb', 'dbbddcac', 'ddbbadbc', 'ababbcbd', 'cdadbcba', 'dcbbdbca', 'badcabab', 'bdabccbb', 'cbdacbcc', 'cadbddda', 'bacadaba', 'ddcbcdac', 'acdcabca', 'bdbcacdc', 'abcbdadd', 'dbcabdab', 'acbadcab', 'dcbdaabd', 'dacabacc', 'cabbadba', 'dacabdcb', 'acddcbad', 'ddcaaabb', 'abcdddaa', 'bacacdcc', 'baacdbdc', 'abbdcbbd', 'caddabba', 'dabacbdc', 'ddccddba', 'ddaadbdc', 'dbacbbdc', 'cddbcaac', 'dacacbba', 'ddbacdba', 'bdcdcbda', 'adcbdbcd', 'dbcdacdc', 'dbdcaadb', 'cddbacdd', 'aabbcbdc', 'adcdcaba', 'cdadbcdd', 'acdadbca', 'abcdaddb', 'adccbbcc', 'bacacdbc', 'bbddccba', 'cabdabcc', 'dbabcadd', 'bcbdcdba', 'bbddcdba', 'ddacabaa', 'acbddbaa', 'cabcddcd', 'bbaadbdc', 'cdcbaddc', 'cacbacbd', 'dcaddadb', 'dcbacdad', 'dccdbaad', 'dbbaaccb', 'dababaca', 'dabcbacb', 'cbddddac', 'ddadbdcc', 'cbdcadac', 'adcbbadc', 'accbcbdc', 'bbddadac', 'ddcbbdad', 'bbabbdcd', 'adcbcacb', 'ccbdcaac', 'bbccbcad', 'ccadcbcb', 'bbdbcbad', 'cacacbdb', 'dadbbadc', 'cddbbacb', 'cdddbcad', 'cabdbada', 'cbdbbaba', 'cbcbddac', 'dbdacaba', 'dcbdcbba', 'abcdbbac', 'cdccbabd', 'baabdcdb', 'bcbaabdc', 'cbcdbdba', 'adaccdcb', 'bbabacdb', 'bcbbadbc', 'baddcbbd', 'bcbbabda', 'abbabcad', 'cdcacadb', 'badbbdca', 'cbdbbcaa', 'accbddab', 'adbdcdbd', 'caddaabd', 'abcddada', 'abddbaca', 'bacdadca', 'cacadacb', 'ccdabbca', 'baccaccd', 'cddadbcc', 'dbacbbcc', 'cddacdcb', 'acdcbdcb', 'acddabcb', 'cdcbcdac', 'adddbcaa', 'bcdaddab', 'dccbaddd', 'cabcdbca', 'bdaadcdb', 'ddbcaaac', 'ccddacbc', 'acdaddbd', 'ddbcdadd', 'abdcadca', 'acbbabda', 'dcddcbab', 'adacdcba', 'abacaddd', 'ddbbcaba', 'dbadcacc', 'bbdabacd', 'dbbcacdd', 'abadbcca', 'ddddcdba', 'cdabbdad', 'dacbbdac', 'dcbdbdba', 'cddcdbba', 'cbbdacdb', 'acdcacab', 'dddcbaad', 'caddcdbd', 'dbadabcc', 'bdbaabcd', 'cdadbcad', 'dbdadcda', 'baddcdbd', 'adcabdac', 'bdcdacba', 'caddbcda', 'cbabbadd', 'dbaabcdb', 'abdabcbb', 'dccbadad', 'acabadca', 'cdcddacb', 'dbcbdabb', 'bdcdbaac', 'cabadadd', 'abadaccb', 'cbcadabb', 'acabcdcb', 'abcbcddd', 'bacdaddc', 'bcddcadd', 'acbacbdb', 'ddbdabca', 'cbababdc', 'cbdabcab', 'dbccabdb', 'daabcdaa', 'ccacdbab', 'bdacacbc', 'bbdcdcab', 'dbacbbdd', 'ccddcbca', 'bdbcabac', 'cdabadad', 'ddbccacc', 'dabddbbc', 'abcdcdbb', 'adcbbdbc', 'dddbaaac', 'abacadcb', 'bcdbadbd', 'dbcabacb', 'cbadcddc', 'dcbbaccb', 'dbbacaba', 'bdabbcbb', 'bcddccba', 'cdacabbd', 'cbdccdda', 'accbddbd', 'adccdcba', 'abadcdac', 'bdbdadac', 'dbadbccb', 'bbcdbdaa', 'dabcacda', 'bcabcadc', 'acdddbda', 'cadabdcc', 'babadcdd', 'dcbdadca', 'dabbdbca', 'bcadbbab', 'cadbbdcd', 'abadcbcc', 'adbabacd', 'babddacb', 'dccbdcab', 'ddadabcc', 'bbcacbda', 'bacbadcd', 'ddacdaba', 'abdbabcc', 'ccbbdbad', 'adaddcab', 'bddcdcac', 'caddbcdc', 'daadbdcb', 'cbacbcdb', 'cabdcbdd', 'bcdacbad', 'dcabbacb', 'bbcabbdc', 'dddcabad', 'dbcbadbc', 'cbadbacb', 'daddccbb', 'bcbcdadb', 'bbdbdaca', 'bdaccbab', 'dbabcdcd', 'caacbdaa', 'bccbaddd', 'cdcacabb', 'babdbdcd', 'adbbcabd', 'acacdabc', 'acdbacbd', 'dadcadbb', 'bacabbad', 'cabdccda', 'abadabcc', 'dcbaadcd', 'bacdacab', 'ddcbcadc', 'cbbdaadc', 'bbabbccd', 'cabbdcda', 'bacddbba', 'cabdbcac', 'babdcbbc', 'babcdbab', 'bcadabad', 'dcbcaabd', 'cdbdbbca', 'dabdacac', 'baccdccb', 'bdbbadbc', 'bbddcabd', 'dbcaabbc', 'bddbbaac', 'bccaabdb', 'dadcbbdb', 'cdcdabdd', 'cbdcbdac', 'bcbdcaad', 'aabccbdb', 'acddbbcb', 'ddabbacc', 'cadddbba', 'abcdbdbd', 'cbacdbac', 'dadabddc', 'bdaabcdc', 'ccdabbab', 'ccadcbba', 'ddabadbc', 'adcbcbcd', 'dacadbcd', 'bbcddadc', 'cbaadbaa', 'bdcabdba', 'dbcdcbad', 'adbdbcbd', 'dabcddcb', 'cacadbab', 'cdbbabac', 'abdbcddb', 'bdccbcba', 'cbabdabb', 'ababcada', 'dccbdacd', 'cbcdcbda', 'dadaddbc', 'dcbadcab', 'ccbcdbda', 'ddbccacd', 'abcacbda', 'dabdcdbd', 'dccdbaab', 'dbacabdb', 'bbdccbab', 'acdbaccb', 'ddcddbac', 'bbacbcda', 'bbacdcac', 'bacbadad', 'cbacdcdd', 'ccdddcba', 'caccbbdb', 'dbccabbc', 'cdadcbcc', 'dcadacab', 'cbbcdcac', 'bcaabaad', 'dcbbcaad', 'dbccabba', 'dbabbcad', 'dcbdbcaa', 'abcddaad', 'abadccdc', 'baddcdbc', 'abacadac', 'cdbcabdd', 'cadadbda', 'bbcddbab', 'adbcdacd', 'bdabdacd', 'adcacbba', 'adacadbc', 'acddbdbd', 'bbaabcbd', 'adddadcb', 'acbabddc', 'dddaabca', 'abcdbcba', 'badadcab', 'badbcdcc', 'acacadcb', 'dbbdabcc', 'bcaddaaa', 'abcbcdbb', 'dbcdddaa', 'bdcadabb', 'bcdaadcb', 'dabcbbcb', 'bacddddb', 'bdbadbcc', 'dddcabdb', 'cdccbadb', 'dddbaacc', 'cbadaddc', 'addddacb', 'ccdabcdc', 'bdcdaacd', 'cdbdcaba', 'dacbabab', 'bbcbbdaa', 'bdbdbcab', 'bcbacacd', 'adcaddbc', 'acbcdcdc', 'abbdbabc', 'acddddbc', 'cddbcabb', 'babacbbd', 'ccbcbdba', 'ddaadbac', 'bdacbdbb', 'dbdcadba', 'cadcbacb', 'dddddcab', 'acddbaca', 'cddcabad', 'bcbcdabc', 'baccdcab', 'accbbdbc', 'cbcabcbd', 'cbadacdd', 'bcdcacab', 'cbdddbba', 'acadbdad', 'addcbbcc', 'bbdcbbad', 'bdbcdcac', 'abdacdbb', 'bcddacdd', 'bdaadaac', 'dacdbacc', 'dbddacba', 'cbdcaddc', 'ccdcbbab', 'abacadbd', 'ababcdad', 'ddbcdaba', 'ccbdcdaa', 'dddcacab', 'ddabcaca', 'badacacb', 'cacbdbcb', 'cbdccabd', 'cbcdadca', 'abdcbdba', 'cabcdadd', 'daddabdc', 'bdcbabcd', 'ddcbdacb', 'ddcbcbad', 'dbccbbac', 'cacbaddc', 'dadcacba', 'bcaadbaa', 'dbccbaba', 'abcdcddc', 'baddacbd', 'cddbadca', 'cbaddacc', 'babacbad', 'bbdbacba', 'cabaddbb', 'abcdbcdd', 'dcdaddba', 'accbbccd', 'cdadcabd', 'caddabda', 'babdcbab', 'ccaddadb', 'dadcdcbd', 'dadadcbd', 'cdabddba', 'cbcdbacb', 'dbacdcab', 'cacadcdb', 'caccdbdd', 'abdccbab', 'bccadacc', 'dcababba', 'daabdbcb', 'dbcbbdba', 'bccdbcac', 'bcdabcbd', 'cdcddadb', 'accadabc', 'acddcbca', 'ddaddacb', 'dcbcacba', 'cacdbbdc', 'cbdabacd', 'aabbdbcc', 'cabcadac', 'dbadacad', 'bacadacb', 'dcbccadd', 'abcabdbc', 'abbddcdb', 'cacdabad', 'babdacab', 'bccbcacd', 'dccddbaa', 'babcddbc', 'dadbdcdc', 'dabdccac', 'acddbcdd', 'cbcdbcac', 'cdacbdab', 'dbdcabcd', 'baadbbcd', 'bbcdbbac', 'cbaddbcd', 'bbcacdad', 'bdbdbcad', 'dbabcdac', 'bacbabdd', 'badbdbcd', 'ddcdbaba', 'bdcbbcba', 'bccdddda', 'ccbabbdb', 'dbabddcb', 'aaccbcdc', 'bcabcbbd', 'acdddbaa', 'ccddaacb', 'abacdcdc', 'abdbdacc', 'bbdaabcb', 'bbdacbab', 'caadcbcd', 'cadcbdcd', 'aacbdbcd', 'aadcbcdb', 'bcdcaabb', 'dbdcabdd', 'dcdbabdc', 'ddacdbdd', 'adadbadc', 'ddbccadc', 'ccadbbdc', 'bcadddaa', 'bccdabac', 'babdccda', 'ddccbcca', 'adadccbc', 'dcbaddbb', 'bcbbcadc', 'dbcbabcb', 'abcabbdb', 'bccbabdd', 'dccdbaac', 'bcdbcabd', 'dccbcadb', 'acbddbdc', 'bdbddcaa', 'cbbddcac', 'bcdabcba', 'dbcdaacd', 'abbcdada', 'aabdbbcc', 'daabdbbc', 'accdbcbb', 'adbdaccb', 'dcdbadcc', 'dcbbdadd', 'cbbdbacc', 'badbbacb', 'cbdbdadd', 'cddaaabb', 'cbdadcda', 'bddbcaba', 'bcadcbba', 'bccdcabb', 'bdcbbcad', 'ccbdaabd', 'acbdddad', 'dabacdbb', 'dabccdca', 'dbdcaddc', 'dcaddcbb', 'cbdbabac', 'cbcabcdc', 'caddcadb', 'bdcbccaa', 'caddcabb', 'dbcacdda', 'bccaadaa', 'bcadcbcc', 'dcddaddb', 'bcdbbadb', 'daccbcad', 'cadcbbcd', 'bddacbdc', 'bbabdabc', 'abcbadba', 'bcacdaba', 'accabcbd', 'adbcbcda', 'dadcbabb', 'cddcaabc', 'dcbbaacd', 'bcacdcdc', 'abcbbadc', 'acbacdcc', 'bbcdcbad', 'dbadcaba', 'dadcaccb', 'abccbbad', 'dcdcbdda', 'adbdcddc', 'cdbcacca', 'acdcdccb', 'cbcacdba', 'ddccbabb', 'dccbacda', 'abcddcbd', 'accbdbcb', 'bcaccbad', 'addadcdb', 'babdccba', 'dbadaccb', 'dcbdabdd', 'ddccbabc', 'bbcbcdaa', 'accdbdcd', 'bbdbabac', 'bdcdaabb', 'bcbacdbb', 'bdabdbcc', 'bccadbbd', 'ddbddacd', 'bdadadcc', 'bcabddda', 'acdccdbb', 'acacddbb', 'caccdbad', 'aabccdcc', 'bbacacdb', 'dacabadb', 'dddcadab', 'bccaddaa', 'cdcabdda', 'abdbcbdb', 'cbcdadbd', 'bbccdadb', 'adbcbbca', 'abcdbcca', 'bcbddaaa', 'acdddcbc', 'bcadcbbc', 'bcadddba', 'dadcbccd', 'dbadcddc', 'caaaadbc', 'dcbacdbb', 'bcacbddb', 'cbbdbbac', 'cdcaddbc', 'dbcacdcd', 'cbabbddd', 'cdbbccba', 'dcdcbacc', 'dcadabac', 'bdcdabcd', 'bbaadbcc', 'bdaabdcb', 'adcbdadc', 'accbadba', 'cbacdabb', 'badccaba', 'abdbabca', 'dcaddbba', 'abcdcacb', 'dcdddbca', 'addbaaac', 'baccdbcd', 'dacbbcac', 'ccbaaccd', 'dcddaaab', 'addbcadc', 'cacbdbcd', 'bdadcbca', 'abcbbcdb', 'addbccbb', 'bbcdbcca', 'dccacdbd', 'dbcbcaac', 'dbbcdaad', 'abdcddbd', 'bcaacdbd', 'dccddbda', 'dadbdacd', 'badbbcdc', 'cbcdcdaa', 'caacbaad', 'abdacbba', 'accbdcca', 'acbabadb', 'acdabdca', 'dcadddcb', 'ddabddcd', 'bdcadbac', 'babcdcbd', 'cdaadaab', 'cbcdcadb', 'aabbcdbb', 'dcdacbba', 'bdbccbda', 'cdabdbcd', 'abdadbcb', 'dadcdbcd', 'cbcdbdad', 'dabcddcd', 'cdccbaad', 'adbdcbda', 'dbacbbac', 'cdbcdcda', 'bcbdbabb', 'ccbdcadc', 'cbddccba', 'bcacbdad', 'accdddbb', 'dcdbbacb', 'adbbdccb', 'cbaddbbd', 'adcbadda', 'abbabcda', 'cbabacdc', 'bdccacdc', 'dcdacabc', 'bcaccbda', 'bbccadca', 'bcbbcacd', 'dbcabcac', 'dbccaacc', 'bbcbbabd', 'ddbcacdb', 'bbcdddaa', 'cbdacbdd', 'bdbcdadc', 'acababda', 'bcbbdabc', 'abcdacab', 'abaddbca', 'acdabccd', 'dccacdcb', 'cdcbbdab', 'cabddbbc', 'cadbccdd', 'dbbcdaab', 'bdcacdca', 'cdcbacdd', 'abcbabdd', 'ccbdcbab', 'bcaabcbd', 'bcbcbabd', 'ddacbcca', 'dacbccbd', 'ddabaccb', 'daaccdbb', 'badcdabb', 'dccacbcc', 'cdbaadbb', 'badaccbd', 'adbcbccd', 'bdccddba', 'dabadcab', 'dbcadaca', 'cbabcdab', 'ccbbdacb', 'bbcdabcb', 'bcbadcba', 'abcababd', 'bcadccba', 'cacbbdad', 'ddbaabcb', 'cbccdcca', 'cbcacadb', 'bbcdaabb', 'dacbdacd', 'bbdcdaad', 'ddddcbad', 'bdadddbc', 'aabdcbcd', 'ccbbacdc', 'abcadbdc', 'dabaccbd', 'acddbdad', 'bdacdcab', 'bcdbccab', 'dadbcbca', 'ddccabcc', 'dcbadcba', 'ccbacacd', 'ccabbadb', 'acaddbac', 'cbbadbab', 'cadbbacc', 'ddabdcac', 'acbdbabb', 'acddccab', 'ddabdbac', 'cbcbbacd', 'babcdbdc', 'caabdcdb', 'babdcdbb', 'ccdbadcd', 'dabbaddc', 'dcdbacad', 'bcabadbd', 'dcacadcb', 'dbcacbca', 'bbdbabcb', 'bbddcbab', 'bdabcaba', 'dbdacbad', 'bacbbdbd', 'acbbcdbb', 'adadbabc', 'abdcbabc', 'dddcdacb', 'adbdbabc', 'cbdabbcd', 'bcdcbcac', 'ddcabddb', 'dcddabda', 'accadbdd', 'ababdaca', 'ddccabbd', 'cdbdcdda', 'cbcbabdb', 'ddbdaccd', 'ddddbbca', 'adcdbbdc', 'dbaccacb', 'baaaabdc', 'caacdcdb', 'bcaacdbb', 'cabbdbdb', 'badcddbc', 'ccdaddab', 'acabccdc', 'caabdaab', 'cdccadab', 'dbbaccdb', 'bdcadbcc', 'dabdddcc', 'ddccabdd', 'badacdbb', 'acdddbcd', 'abdbacad', 'bcdadcba', 'cddbcaca', 'dbcababa', 'cdbccdab', 'dcabccda', 'abccdccb', 'abbcdadd', 'ddacbaca', 'ccdbaddc', 'bddbabac', 'abddccaa', 'cadadadb', 'bdcaabcd', 'abbcaddb', 'bbabccdd', 'dccdbcaa', 'badbabca', 'bcdabcca', 'bbaccdba', 'cabadcbc', 'abadacbd', 'daddbacb', 'cdcbdcaa', 'addabdcd', 'bdabbcad', 'cadbddad', 'badaddcb', 'adddbcdd', 'ccabdacd', 'cbacadcd', 'addddbcd', 'caadaabc', 'cbddcada', 'acbdcdac', 'bcdddbaa', 'cabdbacc', 'bdbcbdad', 'dcdcaadb', 'dbbcacab', 'ccbdbadd', 'ddddcbda', 'cbacadcb', 'bcabadad', 'addbccda', 'cdbabdbd', 'dbdbcadd', 'dcadbadc', 'cdbbacdc', 'cdcdabda', 'acddaabd', 'cdabadab', 'cbbadadc', 'dccbcaac', 'ccbdadbd', 'acbcadab', 'baddadbc', 'badcabca', 'dabccddc', 'bdaccbbd', 'cddacbbc', 'ddddacab', 'adcdbcca', 'dddacddb', 'bacadcdd', 'bbdabcdc', 'acabacdd', 'bbcabacd', 'cadddaba', 'babacdbc', 'abcbbcdc', 'bcbabcda', 'bbcbdacb', 'dcbcadca', 'bcabcdba', 'cbaaccdb', 'abbacbad', 'dabcdbcb', 'cdbdbbda', 'acadabba', 'baadccdb', 'adddcadb', 'bcabcdbc', 'dcbacdcc', 'ccbbaadb', 'ccdcbadb', 'acdbabcc', 'ccabdccb', 'bcdacdca', 'bcdddcba', 'acadbbda', 'bbcddcda', 'cadcbaca', 'cddbabac', 'cbacdbcc', 'ccbabdca', 'ddbadcbd', 'cbcbabdc', 'cdbdbdac', 'abdcbcca', 'cdacdbdd', 'bcbcdcab', 'ccdbdbaa', 'acbbcbad', 'adddbacb', 'dccbcaba', 'dabcdbdc', 'cbaabbcd', 'bbdabcdd', 'bbcbadba', 'dcabaddd', 'babcdabd', 'bbdcbdaa', 'dabcadac', 'dccaabbd', 'dbddcdaa', 'cacddbdb', 'baddccda', 'bddbadbc', 'bdcabdcb', 'abacbbda', 'bcbddacb', 'dcbadacc', 'cbbdaddc', 'ddabaaca', 'caacbbdb', 'abadbbcc', 'bcdcbdda', 'ddacdbcd', 'dabccdbc', 'addbcabd', 'daaccdbd', 'dadbcbda', 'cbacbcda', 'dabacadc', 'cbdbcaac', 'cdacbccd', 'abddbdac', 'dcaddbcd', 'dbaccdbc', 'dbabddcd', 'dadbdcbd', 'ddbdcbac', 'bcbdacca', 'abcadaca', 'cabcbbdc', 'dcacdaba', 'dbdbabdc', 'dbabcddb', 'cdaabdcb', 'accdbcdb', 'cbacbcbd', 'ccbbabcd', 'bcadbdba', 'caaaadcb', 'bacddabd', 'cbdacdbd', 'cdccdbba', 'bdbdcadd', 'cbacabda', 'abdacbda', 'ccbdaaaa', 'bacddaab', 'accbaddb', 'dddacbbd', 'bdacacbb', 'dbabaccd', 'ddcddbba', 'dccbbabd', 'acbddcaa', 'dacbbcdc', 'daabcaac', 'dcbdcdaa', 'cdccabbc', 'addacbca', 'addcbbab', 'dcdabada', 'bbadcdca', 'ddcaabab', 'dacbbdda', 'dcbadadc', 'dbcabddc', 'dcbabacc', 'cbbdaacd', 'bacdbdbd', 'ccbacddc', 'dbbcbbad', 'ddbdcacb', 'daccdbda', 'aabbccdc', 'bdaccabb', 'bacdccba', 'dcbaddaa', 'cbcdacac', 'dcbcaacb', 'dcabbdcc', 'daccdddb', 'ddcbabcc', 'ddcbbcca', 'daddbcdb', 'abdcaddc', 'caccbadc', 'bbcaadbd', 'dbadccbc', 'dccdbbaa', 'ccddabdd', 'addadbca', 'ccbcaccd', 'ddbacdcb', 'dabacabc', 'cdabcddd', 'bddadacb', 'ddcbccac', 'adabccdd', 'abcdabac', 'bdabcbdd', 'dcbdccab', 'abddaadc', 'dbdcbcab', 'abdccabb', 'acbddbcc', 'bdcdbaca', 'dcbbacbd', 'acdbcbad', 'caccbdbc', 'bcabbdbc', 'cdcadccb', 'dcabbdda', 'bcbaddad', 'bdbcdada', 'bbadcdbd', 'cbbacddd', 'adcbacdd', 'dbddcabc', 'dcadbaba', 'bacdddda', 'dccabdad', 'cbdbbdad', 'badacdbd', 'ddbdcbad', 'dcddacdb', 'ddabadcc', 'bcdbacda', 'cdcbdbac', 'bbacdddd', 'acbccacd', 'ddcbabdb', 'acbabccd', 'abacabdd', 'bdaccbcc', 'adcbcaba', 'bbdadcdb', 'cdbbdadb', 'ccdacdbb', 'cbcacdbb', 'cacbccad', 'cbacdbdb', 'caddccbd', 'abddaacb', 'bdcabdbd', 'dbcaaaad', 'adcacdcb', 'dcbdcaac', 'dcbcddad', 'babcddcd', 'bccadcbb', 'bdadcddb', 'acbdddbb', 'bbdcbabd', 'adabadcb', 'ccdcabda', 'bcbadbdd', 'ddcdacbc', 'ddcaabdb', 'abbcbbcd', 'abadacca', 'bbcdacdd', 'abdcdcdb', 'aabbcdcb', 'dcbbcdaa', 'dbbacddd', 'dbdbcabb', 'bdcaccdc', 'abadcabd', 'dcadbbad', 'dbcaccdc', 'bdaacbbc', 'adbcaddd', 'babacdbd', 'adcbacbd', 'cdabadcb', 'caddcbda', 'dcdacadb', 'dbddacdc', 'dacbcdad', 'ddadacbc', 'ddaccbba', 'cadabddc', 'caddabdb', 'cadbadca', 'dacbbccd', 'bdaddcaa', 'cdcdbaac', 'cbcdbcaa', 'bcabbccd', 'bcdacdbd', 'cbdacdda', 'bbacdddc', 'dbcabbdd', 'bbdbcacc', 'bbacdbda', 'adacbbdb', 'babadbcc', 'dddbacbd', 'dbbdacdc', 'dbdacbca', 'dcbcacab', 'abdccddc', 'acdbdbab', 'cbdcddab', 'aadaadbc', 'badccacb', 'dacddabc', 'bcbcadbd', 'abbdddca', 'adbbddac', 'bbcabadb', 'abbadabc', 'dacdabac', 'bbccdada', 'cadddcbb', 'bdcdcaab', 'dcddbdaa', 'bacbabcd', 'dddcdcab', 'adbacdbb', 'daddabac', 'adbacacb', 'dadbbcbc', 'dcabdbdd', 'aabdcdaa', 'acdcdbda', 'abcadabd', 'acbaddbc', 'bbcbddda', 'bbadcaca', 'dbabadcb', 'adbcddad', 'bcbdbcaa', 'acbccdac', 'cdcbcacb', 'daddbacd', 'bdabccda', 'dcbdacdc', 'cadbdadd', 'cabbccdd', 'bcbdaacc', 'bacddcbb', 'ddbbacaa', 'dadbdcac', 'dbdcdbca', 'adcdbccd', 'addcbbaa', 'dcbadadb', 'acaddbca', 'cddbbcaa', 'dabdccab', 'cadbbabd', 'acabcbbd', 'cbadddbb', 'adccbaba', 'adcbbcbd', 'aadcbbcc', 'bdacbacc', 'bacdbabd', 'dacbadbc', 'badcabbc', 'dcddabca', 'addcbdad', 'bbabcdda', 'bdbabbac', 'bcadadca', 'dccbddaa', 'accdcbca', 'bdcaacbc', 'ccaddbdb', 'bcbadacb', 'accaddba', 'dadbcbba', 'ddcacbcb', 'dbdbcadb', 'bbaacbdc', 'cbddbacb', 'bcadabda', 'bddbcbba', 'cabbdccb', 'dbcdcbac', 'aabdccbb', 'cddaabcc', 'ddaaccbd', 'abdadccd', 'dadbacac', 'cbacbddc', 'bcacdadc', 'bcdccdad', 'cbbacada', 'adcbbdda', 'dcddbcaa', 'baccdcbc', 'bcdbacab', 'cdccadbb', 'babaddac', 'addcbccb', 'ddabadca', 'dcbdbcda', 'cabdbdda', 'dbccabdd', 'dadaddcb', 'bdadbbcb', 'dabbabcc', 'ccdaabcd', 'dcacdbab', 'bcdcdabc', 'dbbccacc', 'dcdcbdad', 'cbbcdaca', 'cabdccab', 'accdccdb', 'acacadbc', 'bbdacabc', 'accabdad', 'bdcbaabd', 'dabcdbbd', 'bdbbadcd', 'bcbcadcd', 'dbcadcad', 'ccbdbbaa', 'abdabcdb', 'dddbcbaa', 'acdcabcd', 'dbddcacc', 'cddcdabd', 'bdbcadac', 'dbadccad', 'dbadbcca', 'adadcaba', 'abdcbaca', 'abbddddc', 'bdbdacdb', 'acbdbcbc', 'ddbdbcad', 'acddbdcb', 'bbccdaac', 'dbaacbaa', 'dbddacad', 'dbbadcbc', 'cbccbbda', 'cddbdcba', 'bccacddd', 'dcdaccbd', 'cddcbcda', 'ddbccbac', 'bddabccb', 'baaccbbd', 'bccdbdab', 'cbdcbacb', 'cbbccada', 'cddcabba', 'cbcbdacd', 'dadcabad', 'bcadcbac', 'dddabdac', 'acdabcdd', 'caddbdcd', 'bbcbdbab', 'bcbabdcc', 'cdbdccab', 'dbacbcbc', 'cdacbadc', 'dbabcbba', 'aaaadcbb', 'cdbddaaa', 'cabbcdcc', 'abcddadd', 'cbddadbc', 'adcddbdb', 'cacbbdcc', 'cbaccdab', 'bbdccbaa', 'dbcbabcd', 'bccdaccd', 'bcdacddd', 'cbbdcbad', 'cbdcadbb', 'cabddaac', 'cdacbdcb', 'ddabbcac', 'cbadbdbb', 'cadbbcdd', 'acddbdab', 'caddbcdb', 'bbcaddda', 'dbcdadac', 'caddddbd', 'bccdabda', 'cddabadc', 'acaddcbd', 'bdbbabca', 'bbacddab', 'bbadaccb', 'dadabcdd', 'bababcda', 'ababbcdb', 'dbcbbacc', 'cabdabab', 'bacdddcb', 'babadcac', 'bdcbacbd', 'ccbcadac', 'ddabbcdc', 'dbacbcad', 'abcbabdc', 'bcdcddda', 'bdcdadcd', 'abdcdada', 'dababcdb', 'dcdcabcd', 'ddbddbac', 'bcbccada', 'abcdacba', 'dbccbadd', 'dacdbdad', 'bcbacabd', 'bdccabbc', 'dadcdcab', 'adcbadbd', 'cdbcdaab', 'bdcaccdd', 'adcbbabb', 'dbacadcd', 'ccdbaddd', 'dbdaacbb', 'bcddbcaa', 'ddccabca', 'cacdadbc', 'cabcdaca', 'ddaabdcb', 'bababdcd', 'caadbccd', 'dddcdbaa', 'dcbdabbd', 'bbdaacbd', 'adbdccbc', 'ddcbabbd', 'dbdadbcc', 'cbcbddad', 'cadcdbbc', 'ddabdbdc', 'abdadbac', 'dbdcbbca', 'adbdadcb', 'dbcaaaab', 'bbadcadb', 'bdcdadcc', 'dddaccbb', 'dcabdcac', 'cdacbbdc', 'ddadbccb', 'dcbadcbc', 'dbdabcdc', 'dcdbbcba', 'caaccdbb', 'acbabdcb', 'dcbccbab', 'adcbdabc', 'bbdacada', 'dccabbac', 'cdcbcdba', 'caddbbaa', 'adcaddcb', 'ccdbcadb', 'ccbadddb', 'baadcdaa', 'bdbccacc', 'bbaddcac', 'bdbbdcac', 'dcadbbcd', 'cabdcdbb', 'cbddcdba', 'cabbddca', 'bdcacbac', 'bcaddbdc', 'acdababd', 'abbdcacb', 'ccdbacab', 'acdbbdba', 'dbcbabab', 'aadcbdbd', 'adacbcca', 'dbcdcdaa', 'dbccadac', 'cddaaddb', 'dbdcdacb', 'dadbcbdc', 'accbdcac', 'adcbaddd', 'dadbcdac', 'adadbacc', 'dcbaabcd', 'bcadccad', 'dabdcacd', 'cdaacbaa', 'dbddbaac', 'bbacadbc', 'abdbacba', 'abcadcab', 'abbcdbdc', 'bdadcbab', 'bbadbdcb', 'cdadccab', 'dddaccbd', 'cdaadbcb', 'adccbcdc', 'cdcabdab', 'bdbadcac', 'abacddac', 'dcbcbaca', 'bcbaadcc', 'bccacabd', 'cdcddabc', 'abbacadc', 'ddaaadbc', 'ccadacbd', 'cabddbad', 'cddcadbb', 'bdcdaddc', 'bbadcbdb', 'bcadbacd', 'dddbcbad', 'daccdcdb', 'bacddaad', 'bbdabcba', 'addacacb', 'bdbbacba', 'aadcaabd', 'abbcddbb', 'dcadadba', 'ddbcbacc', 'bbacdadd', 'abdabcdc', 'ddbcbcad', 'dbcdabcd', 'bcaddddb', 'bbcdadcc', 'dabccbcc', 'bcbccdab', 'dbccabbd', 'ddcbdbac', 'cddbddaa', 'dabdcaba', 'adcabdba', 'bdbacacc', 'ddcdaddb', 'dccdcadb', 'dbcabbab', 'dbdbacdb', 'bcbaabdb', 'cdabaddd', 'dbdbcbda', 'cabadbcd', 'ddbacabd', 'dbdbcdad', 'abacbdac', 'bbcadcbc', 'bcaddcba', 'dcbddadd', 'cbddbaba', 'bdbcdabc', 'dcabcbba', 'badacdcb', 'cacdbdcb', 'acabcdad', 'dbadbcdd', 'cabbabad', 'abdbabdc', 'babcbcbd', 'bccdadba', 'cdbdcbda', 'dacbbdcd', 'cbbabbcd', 'dcacdcbb', 'dacdcbac', 'bdcbddca', 'acddabbc', 'bccbdadd', 'bccdddaa', 'acdccabd', 'bbcdddab', 'bcbdccaa', 'dbdadbcd', 'dbccabcc', 'bdbbdcca', 'badcabdc', 'acdddcbb', 'ccaccbdd', 'bcbdbcab', 'ddbcbbad', 'dcdbacdc', 'dcbacaca', 'accacdbd', 'cbccbbad', 'adaddcdb', 'dcbadbda', 'dbaddcab', 'acbacada', 'abdaddcb', 'bbabbacd', 'abbdcdbc', 'dadccbba', 'bddccdaa', 'caddbaab', 'cabdcacd', 'bdaaccdc', 'cbcdcabb', 'adccaccb', 'cbadddad', 'dccbbabb', 'bbdcaddb', 'cbabdddd', 'bcabbcdb', 'acbbabdc', 'cbccacdb', 'babddddc', 'bdadcbdc', 'ccdadbac', 'abdcabbd', 'dcaabaab', 'bdcacbab', 'dbabddcc', 'dcabdadb', 'ddcdacbd', 'cabcbcad', 'dadcbbcb', 'abdcadab', 'accbddcc', 'cdbabadb', 'bbdaadbc', 'abbdaddc', 'cabbdbca', 'bbcbabcd', 'cbdccbad', 'dcbcadbc', 'bbdadcad', 'ccbbdaac', 'badaddbc', 'ddbacbaa', 'adbbdbcc', 'dccadadb', 'acadacab', 'ddadcdbd', 'bbaaccdc', 'bdacdadc', 'dbcbacbb', 'ddcbddca', 'acbdbdac', 'adcadbac', 'cdabbcad', 'bdaddbdc', 'abbdbdbc', 'bacdbadc', 'aadcdbcd', 'ccddddba', 'dcbccdda', 'cbddcabb', 'dacbdcbd', 'abdbdcdc', 'baacdcbc', 'bdadacbc', 'bbcdbdba', 'ddcbcbda', 'daacdbcc', 'cdcabbdd', 'ccabcbdb', 'ccbdaacd', 'badabcab', 'ddbadbcd', 'cbbdbdad', 'dcbcdaca', 'accabada', 'cdabadcd', 'bcddacbc', 'bccddaaa', 'cdbcdbac', 'bbcadcab', 'bddbacac', 'dbccdbaa', 'acbcdabc', 'acbadabd', 'bdcbcadb', 'cbccdadc', 'cbacdabc', 'dcdccacb', 'ddbacacb', 'abccacdb', 'baccddab', 'cacdbbcd', 'cbbdcaab', 'cabdbcad', 'caddcbbc', 'cdcaddbb', 'cabadbab', 'cbcaabdb', 'abbdccba', 'cbbdcabb', 'dcbcabbd', 'cbdabcbc', 'caadbcbc', 'ccbbcadc', 'acbddadc', 'dbbcddab', 'dbbcadda', 'dabdaccb', 'cdaddcba', 'abddbaac', 'ccbabdcd', 'dccdbaca', 'dbddaacc', 'bdbadbac', 'ccbadbdd', 'adbdacac', 'dcdabacd', 'acbdbbab', 'cbacddaa', 'cdabadbb', 'dbaabcbc', 'baddcdaa', 'cdabddcc', 'ddcbbacb', 'dbdacabb', 'cabcadba', 'ddacabab', 'cadabbac', 'cacbabdd', 'bcaaccdc', 'dacdbacb', 'dbcbabdd', 'bcaddccb', 'adccadab', 'accabbdb', 'bcbbdcaa', 'bbcdabdb', 'ddabcdda', 'dadbcdcc', 'abcabddd', 'bcaddabb', 'ddacacdb', 'bbaccdcb', 'cddccabd', 'bbdadddc', 'cdddcabb', 'ddabadac', 'dbcadbab', 'bdacbbad', 'abbacada', 'ddabacca', 'badbbacc', 'cdddbaad', 'dabdbacc', 'addabcbd', 'dbcaddcc', 'dbbddcda', 'bbdccaca', 'bbcbcdab', 'dbcddaba', 'bccabdbd', 'ddbdacbc', 'adbbaddc', 'babbccdc', 'ccbdacbd', 'dbcdabad', 'abbdacbc', 'cdcdbdac', 'dbaabcbd', 'adaccabd', 'cdaabbcb', 'cbcddbca', 'dbcaaaac', 'adadacbc', 'dbdcadad', 'bcbbcdca', 'ddbacada', 'ccacdabb', 'cbcdbadb', 'ccbacadc', 'dcdcadab', 'bcacaddb', 'addbcbbd', 'abdbcdad', 'daccacdb', 'bbccacbd', 'dcbbddac', 'cbaddcbb', 'cddababc', 'cdbacbda', 'dabbdcbd', 'ccadbacc', 'addbcdca', 'abcbabbd', 'bbdabbac', 'dbaddacd', 'dbadbcac', 'dcdacacb', 'bbdbacbd', 'cadabcda', 'bacdcbcd', 'babcbddb', 'dddabcac', 'acbadcac', 'ccddcabc', 'accddaba', 'abcacdab', 'cabacbcd', 'abdadcbc', 'cdabcdca', 'cacdcdcb', 'baddcbdd', 'cbdbddca', 'dcdabbcc', 'dcbacbab', 'bccabadd', 'dbcdaadb', 'bcdcdacd', 'dbadabca', 'bbdcaaaa', 'dbdacaca', 'dabbacca', 'abccabdc', 'ddbbdabc', 'cbbcdbca', 'adbbcacd', 'bdabdcdc', 'acdbcadb', 'bcdcbdab', 'dcbcaddc', 'bacdcbac', 'ccddcaab', 'cbdadbdc', 'bdadcabd', 'ccadabbd', 'adcbadcb', 'dbdacdac', 'bddddcba', 'bddbcbac', 'bbdcaabd', 'cadabdbb', 'bddcdacc', 'bdccdaab', 'badcbdcb', 'bdaccbdd', 'dbcbaddd', 'cbcbdbca', 'cbdddbda', 'bbabadcb', 'bccdbaca', 'bbddabbc', 'badacdba', 'bacbcbad', 'adbbcdcb', 'dabddbcb', 'accadbab', 'cbcdbaab', 'ccddbcca', 'caddaaab', 'bcddcdca', 'dcbcdada', 'dccbbadb', 'dccbbabc', 'cddbbada', 'caabbdbd', 'dcbddacd', 'bcdaddcc', 'bddbdaac', 'bcdbdbac', 'ccdbdcaa', 'bbacbacd', 'babccdcc', 'bdddcada', 'aacdcbdb', 'abbabadc', 'bbacabdb', 'bcbadadc', 'badaccdd', 'ddbbabbc', 'acbdbabd', 'baccbdda', 'dcdbcbaa', 'dccdcabb', 'adcdbdac', 'bdddcaad', 'cdcdccab', 'dccabbab', 'bacbdbba', 'cbcbadcc', 'ddbabcaa', 'aaccbdbd', 'cabdcbdb', 'bccacddb', 'adabcddd', 'cbabcdac', 'dcbaacdc', 'dccbadab', 'abdacdbc', 'acbdddba', 'abbcdbcd', 'cddcdacb', 'ccdbaaaa', 'aacbcdcc', 'cdabdddd', 'ccacadbc', 'ddddbdac', 'acbcbdca', 'bdbacdcc', 'cacbbdba', 'caccbdcc', 'bcdbcbab', 'dbcbdaca', 'cbccdcaa', 'ccdccbaa', 'adbbcbcd', 'cabadaca', 'adcdbabd', 'cabdddcb', 'ddcacdbb', 'dcdacdba', 'cdaadbdc', 'bddbaccb', 'adabcacb', 'ccbcadda', 'dcbdbabc', 'abddadca', 'dbcdacbb', 'dbcbbaab', 'cddcbadc', 'babccbdb', 'acdacbbc', 'abdcbddd', 'ccbbadbd', 'cabcdcca', 'caaccbdb', 'ddcbdada', 'bdccaadc', 'bddddaca', 'caddacbb', 'bdabcdcd', 'ccdbcacd', 'dbbcaddb', 'addabcaa', 'abcdadbc', 'accadcbc', 'adcdadba', 'ccdaadbb', 'dddbbcad', 'badbbddc', 'acddbbdd', 'dbcaabcd', 'acddcabc', 'adcacdbd', 'cbacddda', 'dadcadba', 'ccdbadbc', 'dbcbacad', 'cdadccdb', 'caddacbd', 'cbccdacb', 'bdccbdac', 'bdbabcda', 'bddcaadc', 'ddcbacbd', 'badacdda', 'dcddbabd', 'bcdabdad', 'ddbcaaad', 'adacdbbd', 'acbbabad', 'aacbcbdc', 'cbbdaabb', 'abacdacb', 'abbaddcd', 'cbbacbda', 'dccbdacb', 'abacdddc', 'bdcdccda', 'bccdcdac', 'accdbbcb', 'bdacbbcb', 'dddbbcac', 'badcdbad', 'adbcdbac', 'cbcabddd', 'bddcabdb', 'adbabacc', 'cdabccdb', 'dacbcdcd', 'dcbacdab', 'ddbcbabb', 'dcddbdad', 'daddccab', 'cddaabbd', 'adaccaba', 'bbdbacdb', 'cadbadcb', 'adcddabc', 'abbabbdc', 'bdadcadc', 'bcdbbcac', 'ddadcdab', 'ddabbdac', 'bdaccdcd', 'badcdccd', 'dabdbdac', 'cbdabbab', 'dabbddcd', 'addddcbb', 'acabbccd', 'bbadbdbc', 'cddcabac', 'dcdbbdac', 'ccbdbdca', 'acbdacdc', 'abdbabbc', 'caccbbad', 'cbdadbbc', 'aadcdcbc', 'adbdcacb', 'abccdabb', 'cdcbacdc', 'bbcbadcb', 'cabbadca', 'cbcaddac', 'baccddcc', 'dbbacbda', 'dabbadcd', 'acdbdbac', 'bdaacdcd', 'ababdcbb', 'cdccdbab', 'bcdadcab', 'dcdababc', 'bbcdaabd', 'cacbbadd', 'ddaacdab', 'badcdabd', 'bdbbcdaa', 'dbaccdac', 'dddcaaba', 'bddbccad', 'cacacbdd', 'cdccbacc', 'ddbccdca', 'cabddabb', 'cdcadbcb', 'ddacdabc', 'abcbccad', 'dbababbc', 'aacbbdbd', 'dbbccbba', 'dbadacbd', 'bccadbca', 'bacddacd', 'cdbcbaba', 'adcabdca', 'cbdbabab', 'cddbcbaa', 'dabacbda', 'bcdbcbaa', 'aabccaad', 'abccdadd', 'dccabcdc', 'baacdaac', 'ccdcaabc', 'abacadcc', 'dacadcab', 'bccbadcd', 'adccbdab', 'ddadcaba', 'dcdaddbd', 'abddcabc', 'acbddcbb', 'bdacdccd', 'accacadb', 'dcbabadd', 'dcdbaaaa', 'abdccaca', 'dbadcbad', 'cabccdac', 'adacbcab', 'cbbcddba', 'acabcdbc', 'adbacbcc', 'bddacdba', 'bdcaacaa', 'dcbcadac', 'babdbccd', 'dcdbdaac', 'bdcbabcc', 'addbdbcd', 'ddbcbaad', 'dcdcdabd', 'bbabcdba', 'dbdccdba', 'ddbdcdba', 'bbcadcdb', 'dbccbcca', 'ddbcaaaa', 'cdcbadad', 'ccbaddcd', 'addcabdc', 'cbabccad', 'ddacbcda', 'dbacbaca', 'cbdbcbda', 'abddcdba', 'caddbdca', 'dbabdabc', 'dcdacbdc', 'bbdcddda', 'abadbcdd', 'cabadaba', 'dcbcadab', 'bbcdabdd', 'cdccbadc', 'dcbdaddc', 'ccbdbabb', 'bccdaacd', 'adcbdbdc', 'dadbbdcb', 'dcbaacaa', 'acdcdcbb', 'bcadbdac', 'cdddabcb', 'dcdcabca', 'dbabcacc', 'dbbaddcd', 'ddcbddba', 'cabdbbda', 'bbdbbabc', 'adbcddab', 'adbdcacc', 'abdcbacd', 'abcaddcd', 'adddbcac', 'cbccddba', 'cbbdabbc', 'dabadabc', 'caddabad', 'dacbadad', 'cbcbcdda', 'dccdbdda', 'dccdcaab', 'ddadcdbb', 'baadcaab', 'cababcad', 'dcbbacbb', 'dabdcdcb', 'ddaccdba', 'dbdabdcb', 'cbccabdd', 'cbcacddb', 'bdbcbadb', 'addbbcca', 'adcbbcbc', 'accdbdbb', 'bcabdbcc', 'aadbcbbd', 'bbdbadcd', 'abdadcbd', 'bdbddbca', 'bddbcbad', 'bdddccad', 'aabdcbaa', 'bdbccaac', 'ccbadddc', 'cdbaccab', 'baccdcdc', 'cdadabdd', 'bbacdabc', 'ddcdcabd', 'bbacddcb', 'abcdbbdb', 'cacacdcb', 'acbacabd', 'dbaddbac', 'bdbbccab', 'bcdaddca', 'bdbbdaca', 'cabbccdc', 'bddabacb', 'cbdadabc', 'daabccaa', 'ddddbaca', 'cbdcaabc', 'cbabcbad', 'acbaddda', 'cabadddb', 'adcbcdbc', 'cabcadbd', 'ccabcdcb', 'ddacddcb', 'cdddbaac', 'cbdbbcac', 'acbddabd', 'ccdcdbba', 'cabbcbcd', 'dccabbda', 'cbdcbadd', 'adcbddcd', 'acdcdbbc', 'bdbccaca', 'abbdcabb', 'cabcdbad', 'bddddcca', 'dacacabd', 'cacbdddb', 'baddbdcb', 'adbadcac', 'bbcbdabc', 'bcaaaabd', 'bbdcdabc', 'cdcbcbaa', 'dbaccada', 'abbdaccd', 'dabcbddb', 'bdbacbcb', 'dcabadac', 'bddddbac', 'cbdbacca', 'dbadccac', 'cabbcdba', 'bccacdab', 'bbabbdca', 'acbcabbd', 'ccbdabca', 'acbadddc', 'bacdcacd', 'bcbcdaca', 'ddbcbaba', 'bddadcad', 'addaacba', 'bdbcdadd', 'abadacda', 'cadabadc', 'dbabaddc', 'bddbacdd', 'abbcddbc', 'acdcabab', 'aadbdccd', 'adbccadd', 'bdaccbcd', 'adbacddb', 'babbcbad', 'cbaccdbd', 'bbddacda', 'bbadcbbd', 'cdbacbab', 'badbcacc', 'dacddbac', 'bccbaddb', 'ababbdcb', 'bcadacad', 'ddcabadb', 'dbbdaabc', 'bdcadcbb', 'adbddcba', 'ccbbacda', 'bccbbadc', 'dbcbabdb', 'cacdcabc', 'bdaccbad', 'dcabcacc', 'cadacbda', 'cadadabd', 'bbdadcdd', 'ddcdabaa', 'acadbadb', 'cadddabd', 'ddcdbaab', 'ddbaabbc', 'cdddabda', 'dadcbdac', 'accddcab', 'dacabccd', 'bcbcadad', 'cadabdda', 'cddabbab', 'abbadacc', 'cddbccab', 'cbcdabac', 'ddcbaddc', 'abdcacdd', 'baabcdaa', 'abbddcbb', 'dcabcdcd', 'bddcadca', 'dddabacd', 'cacbcadc', 'ccbdddad', 'aabcbdbc', 'abbadccd', 'bdcbbacd', 'acbbccdc', 'abdcbbdd', 'bdbaadcc', 'caddbcbb', 'bcbcadca', 'bacadbda', 'baddcaac', 'abbcdacd', 'bbdbcbaa', 'cbdbaadc', 'caacbdcb', 'adbdcbdb', 'ddbadcbb', 'ddabacbb', 'acdbadba', 'dbbdaddc', 'bcdddadb', 'dabdcdda', 'bcdcacdb', 'ddadccdb', 'dbacdcdd', 'bbaccdca', 'adababcc', 'cbbccabd', 'accbdcad', 'aabccbcd', 'daabcbdb', 'acbbcadb', 'dbcbaacb', 'cbbddaba', 'acbdcbcc', 'bcdcabab', 'adcbbdad', 'cdcbbdba', 'acbabddd', 'bacddbdd', 'cbdadbca', 'cbddabca', 'acdddcbd', 'ccdbaccd', 'acbbacdd', 'dbdbadbc', 'dcbaaaab', 'acdcbacb', 'dbbdbbca', 'ddbaacaa', 'acacbbad', 'ddcabddd', 'bdcddaab', 'cdcdabac', 'dbaddbbc', 'accdccbc', 'dacbbcba', 'cacbddbc', 'cbddaadd', 'ddbcdcab', 'aacdbcbb', 'ccabcbdd', 'bbcdaacd', 'dcddadab', 'dbcaacdb', 'ddabcddc', 'abcdddda', 'aadbbaac', 'bbcdbbad', 'baddcdba', 'cdabbcdb', 'ccdccacb', 'ddbcacab', 'bcaadcdc', 'ccaccddb', 'dbbacddb', 'bcabacdd', 'abddaacd', 'addbddcc', 'cbbdabcd', 'bcabcbcd', 'bacdccbb', 'dabadccd', 'dccbdcac', 'badddcab', 'ddbcaadc', 'bbdaccda', 'adbbcbad', 'cadadbbc', 'bbdcacad', 'cddacbab', 'bddadaca', 'dadcbadb', 'bbadbcda', 'cbcdacdd', 'bccdcdba', 'bdcabcbc', 'acdbccbc', 'dadbdccd', 'dcdaaccb', 'bbcbaddb', 'cdcabdbd', 'cbcddbac', 'dbcaccad', 'adcbcdcc', 'dcbacada', 'adbbabac', 'cbbadddb', 'cbdcbaba', 'acbdaddb', 'cacbadbc', 'dacddbba', 'accbdbdd', 'cdaccbda', 'cdbdddaa', 'cacdcbdc', 'abdacbbd', 'ddbacdbc', 'dbdbcdaa', 'abdbcbbc', 'cbbcabda', 'bacdadbc', 'bcdbdbda', 'ccbddcca', 'bbcdbadb', 'dababadc', 'cdbcabcc', 'abdadcbb', 'abcdddbb', 'dddcacba', 'dbdddacd', 'dbdaadcc', 'adcbaddc', 'cdcdabdc', 'ccaaccdb', 'daacbccb', 'bdadcbdd', 'dddcbdac', 'ccadabdb', 'cabdbdbd', 'badbdcca', 'dbbcbaab', 'dcaccdbb', 'cddcabcd', 'dcbaccdb', 'ddbaadca', 'adcbadcc', 'cadbadbd', 'dbdbcdba', 'bccadbad', 'dcdbaddd', 'abdcddbc', 'bacbcbdc', 'caddabdc', 'cddacbba', 'dabcacac', 'ccabbcad', 'aadaabcc', 'cacacbad', 'abccdbdd', 'dcbcabdc', 'cacbcddb', 'bcaccada', 'cacbbcda', 'ddbadcdc', 'cddbddda', 'acdadbdb', 'ccadcdba', 'ddcdbdda', 'daccbbdb', 'cacbbadb', 'adbbcbbc', 'ddcbabaa', 'aabbcaad', 'bbdccadb', 'ddbabcba', 'bdbbddca', 'dccbddba', 'cdacddab', 'caddccdb', 'adcdcdbc', 'dddabcdc', 'ddadcacb', 'dcdacaba', 'bdbdccad', 'bcdcacda', 'cdabdacd', 'bbccdaba', 'dcddacbc', 'bbcbaabd', 'ddcacbcc', 'dcbbddda', 'ddaabdac', 'bddbaacd', 'adbcabad', 'bbcbcbda', 'bbcaacdb', 'dcabcbcd', 'dacbccad', 'cbdcabac', 'dbdaadcb', 'adbabcba', 'cadadbac', 'cadcdcab', 'dacdbccd', 'dabdbcdc', 'cbcbdada', 'adddcbcc', 'cabadcca', 'ddacbacd', 'abbdadbc', 'dccbbaad', 'abdcddcb', 'adbcddbb', 'cbcbdbab', 'cabddcbd', 'bcdbabad', 'addaabca', 'bcbabdbb', 'babcbadb', 'adbabcca', 'dadcbbac', 'adccbaca', 'dbcbaaaa', 'ababcdac', 'ddcbacdb', 'dbddcbab', 'acabddbd', 'adcddbdc', 'bacddbaa', 'acadbddd', 'cbabacdd', 'bdcadbcd', 'bdacabdc', 'cacabbdb', 'cadcbdcc', 'abcacdcb', 'caabaacd', 'adddbccb', 'acbccdcc', 'bccdcacd', 'ccacddbc', 'dbcabbdb', 'dcadbaca', 'acacdbda', 'dadbcaba', 'abdbbcbc', 'bcaddaab', 'cbdcadcb', 'aaaabdbc', 'cbdbdabc', 'dacdccba', 'cacadbcc', 'addaacab', 'abdaccac', 'cababbdc', 'daabbdcc', 'accdbdba', 'bcbdbdaa', 'dabdadbc', 'dcbacbcc', 'adcbdbac', 'ccaddbbd', 'cbccadcc', 'acbccdbb', 'cdbcdabd', 'ddbbcbab', 'bbcbacad', 'bacdcadc', 'adcadbbc', 'adcdbaca', 'bcaaccbd', 'bdcabacc', 'bccabada', 'babcadcd', 'cdacbdba', 'cdcbbacd', 'bbcddbba', 'bddbdcac', 'adaccabb', 'ddaabcbc', 'abdabdca', 'ccbccabd', 'abcbdcbb', 'dbbcacdb', 'bcabbabd', 'acadcbac', 'dddadbca', 'dbbaacdb', 'cbabdbbc', 'dbcddaad', 'cdbcddaa', 'abcabcdd', 'adacabac', 'dadbcbcc', 'abcbcadd', 'cacdddbc', 'dbddccab', 'dcdaadbc', 'adcbabba', 'addccbad', 'bbdcbaad', 'cdddabcd', 'daddcdba', 'cdddcabd', 'cdcbabba', 'dbddacbc', 'dbcaccdd', 'cdcbbcda', 'dabbddcc', 'ccbbadda', 'dacbbdcb', 'acbdddbc', 'ddacacbc', 'badbacac', 'bdccbcda', 'bdadbcca', 'baccbdbb', 'acbcbdcc', 'dcbaabbd', 'cdcbabcb', 'bcacdccb', 'cbdbdcca', 'acdcdabd', 'accadbca', 'baaccbdb', 'bacbcbbd', 'cacddcab', 'dddbaacd', 'bddcdcca', 'bbcdadbc', 'cadbadbc', 'dcbbddaa', 'ddbccaab', 'abcdacbb', 'abcbbdcc', 'bbcddcba', 'bdacbdac', 'bbcdcbda', 'dabccbac', 'ddbbcbaa', 'badddccb', 'bacdacbb', 'cdcadbad', 'ccbbdabd', 'cbadabad', 'ababbcad', 'bdaabdcc', 'ccaddcbd', 'dbcadccd', 'bbcbacdc', 'dbccaddd', 'ddbbaacb', 'bcdbaacd', 'bcacadab', 'badccbdc', 'caabcdbb', 'bddbcacd', 'bcaabdcc', 'abcbaddb', 'dccbcbac', 'baadcbbc', 'cdbddbba', 'aaccdbdb', 'dbcaccab', 'cdaddadb', 'acbabbdc', 'acbbdbbc', 'cddbaddd', 'bdccdcca', 'dcbcdadc', 'ddbdadbc', 'adabcdbb', 'dccbabad', 'cdadaddb', 'dcddaacb', 'bcdbddca', 'cbdbbdac', 'abdbbccb', 'cdbbcabd', 'bacaccdb', 'cdaccabb', 'addcdbda', 'bbcddbac', 'abbadcdc', 'bdcabcba', 'cbadddba', 'dcababdc', 'bcbdbcca', 'dbcbcbba', 'adcdcacb', 'adbdbdcc', 'cdbcbacd', 'cdadbaca', 'dadbccab', 'bacbcddc', 'ccbaddbb', 'dabddcbd', 'dcadbcdd', 'bcbdcbaa', 'cabbcacd', 'bcdcdcac', 'adccdbba', 'ccddbabb', 'cacbdabd', 'dabaddcb', 'adbdcbad', 'addccaba', 'dbabccdd', 'addcdbbc', 'ccadbdda', 'adbddcdc', 'acadbdcd', 'abbdcdad', 'bdbdacbd', 'cddbabca', 'dbadcbba', 'dbdcdaad', 'abadacba', 'ccbcaddd', 'acddbdcc', 'adbcddbc', 'badaddac', 'cbcbaacd', 'cbbdaaaa', 'cddadacb', 'abddccac', 'dbabacdb', 'bacabbdc', 'cbcdbabb', 'adbcdacc', 'bdadbcdc', 'ddacabbc', 'bdabcdcc', 'dacabacd', 'cabbcdda', 'accbdacd', 'bcbdaabc', 'bcdbaacc', 'bcdbddba', 'dbabcdcc', 'badcbadd', 'bcbcadbb', 'bdcddaaa', 'abcbcadb', 'bcddbcad', 'dcbcdaba', 'cdadadbb', 'dcacdbac', 'cdcabdcc', 'cadbbcdb', 'acbdbdba', 'cbdacabc', 'acaddbbd', 'bdddbcaa', 'bbccadbb', 'dabddcad', 'adbcddda', 'cacabdbc', 'caccadbc', 'dcdabcbd', 'bbacadca', 'bdcbbacb', 'dcbbdaac', 'dccdbcba', 'dadadbca', 'cbacaddd', 'ccddabca', 'cdbdacca', 'bdbdbcca', 'ddaabdca', 'acbdccba', 'aacbbdcc', 'ddaadacb', 'adbdadcc', 'ccacdbbc', 'dbdacacd', 'cacbddcd', 'cbddacba', 'bcaddada', 'accdbbda', 'dadcddbb', 'cacdabdb', 'cbcdcbad', 'baabcaad', 'bcddbdaa', 'abdcacbb', 'badcacda', 'dacadbdc', 'ccddccba', 'dcdadbbd', 'bbccbadc', 'ccbdadda', 'ccbaadaa', 'ddbabdca', 'cdabdcab', 'cdabbabd', 'bcdadbca', 'adcadcab', 'cddabcdd', 'bdbcacab', 'dabbccab', 'dbaacbbd', 'bacdabca', 'abcdacac', 'cabbcadd', 'ddabcaac', 'acdbacdb', 'bdaabcbb', 'dbcbdadb', 'acdababa', 'ccbbddad', 'cbaacaad', 'bbcaddba', 'bcabbddd', 'bcbdcbba', 'bddadcab', 'adbbacab', 'dcaccabc', 'bdccabca', 'bcacadbc', 'cddabaaa', 'abcbcdba', 'babbdcab', 'cadcbddb', 'ddccdabd', 'dbaccbbd', 'dcaccbca', 'ccabcdac', 'bdabdcab', 'cbdabddb', 'bdbcdbab', 'bcdddaad', 'dbacbaba', 'bcdabada', 'bddcadad', 'adabaccb', 'cbbdbaad', 'ddbcacdc', 'badcacdc', 'bbcbadbb', 'cdabcddc', 'cbadadab', 'bcababdd', 'dbacabda', 'ddabdcbc', 'bdaadccb', 'adccabca', 'dccacbca', 'cadccdab', 'abaddcdd', 'aabdccdb', 'bacbdcdd', 'adabbacc', 'acddbabb', 'acbabdca', 'cdaabdcc', 'dddcdabd', 'bbdcabca', 'bcabadbb', 'addbacca', 'adbbabdc', 'daddcbcb', 'bcababad', 'bccbdacc', 'adbcdada', 'ddcdbaad', 'acdbdddc', 'aabdbbcd', 'daddaabc', 'abadddac', 'acaccdcb', 'dbdcaccb', 'cbbddaca', 'dddbcadc', 'ddadbcdc', 'cdadddba', 'cbbcdbba', 'adcacadb', 'aaaadcbd', 'acbddbdb', 'ddacdcdb', 'dccacabc', 'dcbbacba', 'dcbaddcb', 'daccbbcd', 'bccbbdad', 'cdbcdcab', 'dcbbaccd', 'bcbabddb', 'dacddaba', 'dbcbccda', 'ddbadcdd', 'dbabccac', 'dbdcbdaa', 'aaccdcbb', 'dcbdddad', 'daaaacbb', 'dcdddabb', 'ccdcaccb', 'dbaaaacc', 'abbcadab', 'bacdbdbc', 'cacaddbc', 'dbadbdac', 'accabdcc', 'cdabacac', 'bdabbdcd', 'bcdcadbd', 'adccbdbd', 'bdbbabac', 'ccbacdba', 'bcddaccd', 'bcabccad', 'bcddcdac', 'dbaddacc', 'bbabcdbc', 'ccdacbdc', 'dbccadda', 'cdbddcaa', 'ccacadbd', 'bbabcadc', 'abccacbd', 'accbcbbd', 'abdcdcbc', 'ddbbacbc', 'dbbccdba', 'addbbcbc', 'ccaccdab', 'bcbdabba', 'dbadcdad', 'acbbadbb', 'bacadacd', 'bdbdbacd', 'aabbcdcc', 'bdbadacc', 'dbbcdcca', 'ddabcacb', 'dbacacba', 'cacbadca', 'ccacbbcd', 'baadcbbd', 'bbcacbdb', 'bacbbada', 'cbcaccbd', 'dbcddabc', 'dcbdbabb', 'dcdbadbb', 'cbabaddb', 'caacbbcd', 'badccabb', 'dddaabac', 'ddddcaba', 'ddccaccb', 'acbdcbcd', 'abacbdbb', 'cbaccadc', 'cadcddbb', 'ddbacdaa', 'bdbdadcc', 'dbabcbab', 'cdcbdbda', 'cdcabacd', 'ddbadcbc', 'ccdcabdc', 'dacdabcb', 'ddbadaac', 'ccdbbadb', 'cbbaccda', 'bacadcca', 'dcbdabda', 'cdadbbdc', 'acadbbab', 'cdbcadbb', 'abcddccb', 'babbccdb', 'dadadbcd', 'bdaaaacd', 'dcbcadcb', 'dddabdca', 'babdcbcd', 'cbddaaad', 'bcabdbbc', 'cbdacabd', 'ddadcbcd', 'bdaccbdb', 'adadacdb', 'dadccdab', 'acdbdbca', 'abcddddc', 'cbadbccd', 'ddaddccb', 'badcaddc', 'dbdcdbba', 'ccdabaca', 'cbadddcb', 'aacdaadb', 'acbdccda', 'dbbcdcda', 'dbacbbad', 'aadcbaab', 'cdcdbdda', 'bbcbbdab', 'bcdabcab', 'cdababab', 'dcbccdca', 'dadcbbca', 'bddccdac', 'bcacbbda', 'cbadacab', 'dbacbdba', 'ddbcacba', 'ccdbabac', 'cbdcdadc', 'daccdccb', 'abbcdcad', 'cbacdbca', 'adbabbcb', 'dcbaddbd', 'dbcdacad', 'dabcbdda', 'babadbca', 'addbdcdc', 'cdcaabcc', 'dabdacbc', 'cabdbbab', 'acdabcac', 'abcaddca', 'bdbabcba', 'bbcbcdac', 'cdbacacc', 'bbdcbbda', 'dbbcabdd', 'abcddadc', 'adbbdcda', 'bdcdabdd', 'adcdbcba', 'cacbbdab', 'bbdcbdad', 'adcbcadb', 'cbadbdbd', 'daccbdda', 'acbcbcda', 'dbbacdca', 'adcddbcb', 'dbaddbcc', 'adacbddb', 'ccdacbcc', 'cabdbdcd', 'ccdddcab', 'dabccdac', 'bcdaabaa', 'abbaccda', 'ccbadaca', 'cbabccbd', 'ddbcabbc', 'babcacbd', 'bcdadddc', 'bdcacbba', 'bbcbdbac', 'adcababa', 'cbddacdb', 'bdddcaab', 'adacbbad', 'abcdbcbc', 'acdadccb', 'bbdcdbaa', 'ddcaadab', 'acbdcacd', 'bddbbcad', 'dadccabb', 'aaaadbdc', 'ccbcbdab', 'daacbcbd', 'ccdbadbb', 'dacddbcb', 'dbcdbaca', 'cbacbbdc', 'abddcbba', 'dbdccdac', 'bbcbdcda', 'adcacdab', 'acabadbd', 'bddacabd', 'addbcdac', 'bcaccadb', 'ddbacbcb', 'dabcacbd', 'dbcddcca', 'ccdadcba', 'adccadba', 'ccaabccd', 'bbabdcca', 'caadbcbb', 'acabaddc', 'addccadb', 'dadabacc', 'cddbdbaa', 'adcdabad', 'ddabccab', 'accbcbdb', 'abadccdd', 'ccbbaabd', 'dccbbcac', 'accbbcdc', 'dccaabdc', 'dbbacabb', 'bbcdbabd', 'cabdcadc', 'dabadacd', 'adbcdbba', 'dabcbcdb', 'bccbdbab', 'abdadddc', 'abcddcdd', 'bdccdcac', 'bbaacbbd', 'addbdbac', 'ddcdbacd', 'cbbcadad', 'ababcdbd', 'ddbbaaac', 'dccabadc', 'dcabcdbd', 'bcbadcad', 'dacbdcdb', 'aabbccdb', 'cacddbba', 'ddaddcdb', 'dabbacbb', 'cbabddcd', 'abbabccd', 'bdacbbdb', 'ddbbaccd', 'acabdcdd', 'adbddccb', 'ccdaddbb', 'dbcdacdd', 'bbaddbdc', 'cbddabab', 'cabcdabd', 'dddbccad', 'ccdadabd', 'ddaabcad', 'adbdcbba', 'dbdcaacd', 'cacbdadb', 'cdababdd', 'bdbcadbd', 'abcdcdab', 'ccaadcbc', 'dccbaddc', 'adcacdbc', 'acddaabb', 'acbdbbdb', 'cbddcdad', 'ccacbdac', 'dbcaccbb', 'dbcacddd', 'cbddccad', 'dacddcba', 'badbcabb', 'bdddabbc', 'dcbbdcab', 'cbbacbcd', 'bcbaabbd', 'cabdbdac', 'dcabdacd', 'dbbddaca', 'acacdabb', 'aabcdcdb', 'bbdacdbb', 'cabbcbda', 'dcadcddb', 'dbbacbbc', 'dcbdcdab', 'adbadbac', 'acbdbbcd', 'abbdbdcc', 'accdadba', 'adacbdcb', 'cbcabdbd', 'bacadddd', 'dbdcbada', 'dbcacbdd', 'ddcbbdba', 'bbdabdbc', 'bdcdabcc', 'dcbdabad', 'bbccdbab', 'dbbadcba', 'abcbccdc', 'dbcaaccd', 'dbbcdcba', 'dddacacb', 'dabbcdcc', 'acacbbdb', 'dbddcdac', 'bacaccdc', 'ddadbcac', 'dbbadcdb', 'baacbcdb', 'cbadbabb', 'bdabcdbc', 'bbdcacdd', 'ddcababb', 'acaddcbc', 'abcddddb', 'cdacbcac', 'dadccbcc', 'babcddcc', 'bcbcabdb', 'bbaddcca', 'cddbcdac', 'abbadacd', 'dcbbadbd', 'babadcbb', 'acdadbbd', 'dcabddda', 'acdbcbbd', 'bcbcdabd', 'adcdabcc', 'dbabddca', 'dccbdcad', 'bacdccdb', 'bdadccba', 'ddcbdabd', 'dabcdabc', 'aabbcbdb', 'ccbbddaa', 'cadabcba', 'cbcadadb', 'aabcdbcd', 'dbccbabc', 'dabdcbad', 'acddbcad', 'abbcdcac', 'adaddbcc', 'bddcdaaa', 'ddcbacca', 'dcdadbdb', 'ccbadbba', 'dbaddddc', 'daddbbcc', 'badcbcca', 'dccadbcb', 'addbbcdb', 'abacbbcd', 'cddddbab', 'bbadbddc', 'acbdabcb', 'abbcadad', 'bcacbadc', 'dabcabcc', 'acbdbacb', 'abcbbada', 'dbacbdab', 'daccdcab', 'cadcbcdd', 'dacaddab', 'addcacab', 'bacdbcba', 'ccdbcadd', 'cbddadbb', 'cbdabdcc', 'dcabcdbb', 'bacdabba', 'abdbcbad', 'bacbdaba', 'bbddacdb', 'cabadcba', 'dbbcbacb', 'ccadbada', 'cdabccbb', 'cdbabdcd', 'adbacbda', 'ababcacd', 'ddbcaddd', 'cddcabbd', 'bccdacca', 'abadbcbc', 'bcbdacab', 'bcdccaba', 'ccdddabc', 'cbdbadad', 'cbbdacac', 'bacdcddb', 'bbdccada', 'acbdbcad', 'bbddddac', 'dcdababb', 'cacabdca', 'dbabcbca', 'ddaabdbc', 'bcdccacd', 'bbdcaddc', 'bddcdaba', 'dbcadccb', 'bdcdcacc', 'bbcbdaac', 'cbadcabc', 'adbcdcda', 'bbacdcdd', 'abdcaccd', 'bcabcdab', 'bccbacbd', 'cabcdcda', 'abcbddbb', 'babddbcd', 'cdabbddb', 'cbbcddca', 'ccbdcdba', 'bcdaccbc', 'cbcbbdda', 'bccdabcd', 'bacdbabb', 'dbcdbdab', 'acdbcbdc', 'ddcacbdc', 'bdddaacd', 'dbccabad', 'bcdbbdca', 'cbabcbdb', 'adbcdcbd', 'bdcaadbd', 'bdacdddd', 'daadcdbd', 'cbccaadc', 'bcddcabd', 'bccbbadb', 'dddbcacc', 'dcbccadc', 'aabcbdcb', 'bdccdaca', 'bbcdcdca', 'cadcabac', 'dcadacdb', 'accbdadc', 'cbbcdada', 'ddcbacdc', 'ddaabcac', 'bcdacadb', 'bacbdacd', 'cddaaabc', 'cbabdbca', 'accbaddc', 'cbdcacba', 'dabcdcda', 'ddadcbab', 'abcadbac', 'cbabacbd', 'ddcdcbda', 'bddaddcc', 'ccdcbadc', 'adcddacb', 'babcbcdd', 'caddaabb', 'dcbcacdd', 'dbcdadbd', 'adcbbccb', 'abdcacca', 'babcbdca', 'abadcdba', 'cdaddbbc', 'bddabdcc', 'acbcadba', 'cadcdbab', 'acbdabad', 'bbaaaadc', 'cbccdbda', 'addddbcb', 'bcdccdca', 'bccdbadb', 'abccbdcb', 'bbabbcad', 'dcabacdb', 'addcddcb', 'abadacbb', 'acbbdbac', 'cadcdcdb', 'bccbadab', 'dcadaddb', 'acdcadab', 'bddbadcb', 'ddccbaaa', 'ddbcabda', 'cbbdadcc', 'bbcaadcc', 'abbabdbc', 'dbcbccad', 'abdccbcc', 'ddaacdcb', 'ccbcacad', 'bcabadca', 'cddbdacb', 'dcdcbaad', 'cababbda', 'daddbccd', 'acabdbdd', 'dccdbbca', 'dadccbcb', 'cdbbadca', 'dbcaabaa', 'cdabacdc', 'ccbdacdd', 'addbdcba', 'adddbdca', 'ddbbccab', 'cbdcabcc', 'dbbcadad', 'dcaadbcc', 'abcadbba', 'dabccbcb', 'dcbbaadc', 'cdcbbacc', 'dabccaca', 'dbbadcbd', 'dbdbadcc', 'dbdabbcc', 'acadbddb', 'adbbcaca', 'dbabacdc', 'aaccdbbd', 'acdacacb', 'adbbccba', 'abdcbcbb', 'badcbacc', 'bbdbdacd', 'badbdacb', 'cbdacbbc', 'bccadcad', 'bccdccab', 'cddcdadb', 'dbaaaadc', 'accbdbdc', 'dbddadca', 'dabbdcdd', 'cdbadcca', 'abbdcbbc', 'cadddbab', 'abacabdc', 'bddaacdd', 'daccdbca', 'dcaccabb', 'dababcda', 'abbcddaa', 'dbbccadd', 'dabccdcc', 'cbcaaccd', 'bdcbddac', 'dacbbacc', 'dbdbcbac', 'accabcdd', 'adccbddc', 'dcabadcd', 'bdcddcab', 'baccacdc', 'bddbabca', 'bcbcdaad', 'bcbbdcca', 'cbbdcdca', 'cbaddabc', 'dbdbdacc', 'cbabdabd', 'ccdddabd', 'bcdcabdb', 'bbcdaabc', 'aabdccbc', 'daccbcac', 'dcbacbca', 'dbbcabad', 'bdacdadd', 'bdaacaab', 'cadbcada', 'cabddacb', 'cbbcbdca', 'dbaabdcc', 'cbcbadab', 'dbabddac', 'babdbacc', 'cbaddadc', 'bdadacdc', 'dbdaccad', 'bbddaacb', 'cdcaabbd', 'cdcabbcd', 'aabdcdbb', 'ccddbcac', 'cdbbcbac', 'cbddccda', 'accbcdcc', 'bacddcbc', 'acbcdcba', 'cbddaccb', 'aadcdcbb', 'ccbcbcda', 'ddbbccba', 'baddbcba', 'adacddab', 'dbddacac', 'dcabddcd', 'dbcdbabb', 'bacdcdda', 'ddccabba', 'bbdbdaac', 'bdcabbdb', 'dbbdcdba', 'dacababd', 'bcabdadd', 'ddcddaab', 'ccdbbaac', 'cddaacbb', 'bbcdaddc', 'cbcadadc', 'dcdadcbb', 'adadacbb', 'adcbdddd', 'bdacacab', 'bcdbacdc', 'bdadadcd', 'dbadcdda', 'acddadbc', 'dacadcbd', 'dadacdcb', 'cdbddada', 'adddbcbb', 'cadcdadb', 'acbddbcd', 'abcabacd', 'ccabbdcb', 'bdddccba', 'cbadcbcb', 'cdbdaadc', 'bdcdbadc', 'cbacbdad', 'bdbcaccb', 'bdbbcacd', 'ccadbdcd', 'bacbacda', 'bdacabcd', 'dcdcaacb', 'cbcdaddb', 'caddcbba', 'bcadcaba', 'cabdcdab', 'adccbbcb', 'acbbcbdc', 'dbbdbcab', 'adaccbad', 'cadaccab', 'bbccaacd', 'accadbac', 'dabdcbbd', 'cadbdaba', 'caddadbb', 'bbdcdbba', 'bccdcbda', 'cbadcbca', 'bcacddcd', 'dbbdcadc', 'aadaacbc', 'cbaddbdb', 'dbbcabbd', 'aabbdbdc', 'bcdabdac', 'adacbcac', 'babbdcdd', 'dcbddcba', 'ddabcbbc', 'abdcbdcd', 'dbdbcada', 'accdbbad', 'cacdaddb', 'bcdbaabb', 'ababdacc', 'ddabaabc', 'bbdcbdab', 'adcdacbb', 'bacdaddd', 'adadabbc', 'ddcadddb', 'bbdaccac', 'cdacbdbd', 'ddcacaba', 'dadbdbdc', 'adcbdcbd', 'ddcbadad', 'cdccaabd', 'acdcddbd', 'cbadcdca', 'cdbccdba', 'bdacadab', 'dbdacddd', 'cbacbbda', 'bdccabba', 'caaccbdc', 'dccbaccb', 'badbdbcc', 'cbcdaccd', 'ddaccbdc', 'dcbccaac', 'dbdbabac', 'dcaddccb', 'abcacdcc', 'ccaccbda', 'cdabddaa', 'bcdbdacb', 'cbaabcdb', 'ccdcdbca', 'cdbcadad', 'bcddaacb', 'addcbcdb', 'bdcacbbd', 'dcdcacba', 'bccadadc', 'bacbdaca', 'cadbcdcc', 'addcbdab', 'cbccadba', 'bdbacbda', 'cdaaccdb', 'bacabdda', 'bacdddcc', 'dcacacbc', 'adbcdcad', 'cbbcbdab', 'bdacbbac', 'cbcdacdb', 'adbacacc', 'bdcdbcad', 'cdcbccab', 'bbabdcdc', 'bcddadda', 'cbdcdabd', 'addcabba', 'ccdcbacb', 'dcbddabd', 'cadcaddb', 'dabdabcb', 'dcbdbacd', 'acdacdbd', 'bccaddbd', 'cdcadbcd', 'ccdbbacd', 'bdaabdcd', 'bdcbaabb', 'dcababcc', 'dabbabdc', 'baacdcdc', 'badbdacc', 'cabaddda', 'bdddbabc', 'abcddbdb', 'cabbddbd', 'bbdbacad', 'ddcddaba', 'addacbdc', 'badbdcac', 'bacacbdd', 'ccaacdbc', 'baccddac', 'bdabbddc', 'cbdbbdaa', 'cbcdaacc', 'dbdacbab', 'cbcddbad', 'addbbcda', 'ccbbcdab', 'ddabbcad', 'ddbadccd', 'bacddcac', 'acbccadb', 'bbdcbacb', 'bcdcdaac', 'bccddcca', 'caddbbab', 'cacdcabd', 'abacacbd', 'dcbcabad', 'dabcdbbc', 'bddaccbd', 'bacbdccd', 'adbacbdd', 'ddcbdaba', 'cacdbcab', 'dadcdbab', 'bbcaacbd', 'accbacdd', 'dabaddac', 'dcdbaddc', 'dcacabca', 'bbadbacd', 'bcbdddac', 'adcbdddb', 'cbadddcd', 'bcbbdbac', 'bcdccada', 'caddabcd', 'baccbcdd', 'dabdbdca', 'bbcbcdca', 'badacaca', 'adcdbdab', 'cacbcdda', 'adddbbdc', 'adabdbac', 'ddbcddad', 'dddccdba', 'cdbcaddc', 'cbabdcac', 'babcdabc', 'ddbaaaac', 'cdcbcabd', 'babdadac', 'ccdadbca', 'bcbddabc', 'bdcdddab', 'badcabdb', 'ddcdcabb', 'baccdbba', 'ddadbcca', 'cbbadcad', 'cdbddbad', 'acadbcda', 'cdbcabba', 'dbccdacb', 'accacdba', 'bcdcdaba', 'caddddab', 'dbacddab', 'adbadccb', 'caddabcc', 'adddbdcb', 'ddcbaabd', 'cdbacdcc', 'baadbcbc', 'daacdbaa', 'dcdbccda', 'bacbdcbd', 'dcbccbad', 'dcdcbcaa', 'ddacacbb', 'abdcddaa', 'adbaddcd', 'dbdccadd', 'dbacbdbc', 'abaddbcb', 'adbacbcd', 'dbcddbab', 'cdbccaab', 'ddcbaaad', 'cadccbad', 'ddcabdcc', 'dbccbcaa', 'bcbadbcd', 'bbddcaba', 'acbcbdcb', 'bcabacad', 'dbcdbadd', 'daacdbcd', 'adcdaddb', 'abbadbcd', 'cadbabac', 'addbcacb', 'dcdcbbab', 'addabbcd', 'dabcadbb', 'daccdabd', 'aabbdbbc', 'bcadabab', 'bbcadcdc', 'bccabdba', 'bdaddbac', 'addbcbca', 'cbadbdcd', 'cabcbadd', 'bdabcdcb', 'bcbaadaa', 'cbdadcbb', 'cdbccdda', 'accabbda', 'bccabadc', 'cbaaaabd', 'ccdaacbd', 'bacadcba', 'cdabccdc', 'cadddcab', 'cdccabac', 'accdcbdd', 'adcddbbd', 'abdabccb', 'baddaadc', 'addbabdc', 'addbabbc', 'dbacbdcb', 'dbadadca', 'cdabaccd', 'aabcdbdb', 'cadacacb', 'dbbcdcad', 'cabdabdc', 'bbdbcabb', 'adcabdbb', 'ccacdcdb', 'bdacdbba', 'ddccacbc', 'abccddcd', 'bbcdadda', 'abdccaba', 'dabcbcbd', 'dadbbabc', 'daabdccd', 'bacdbbcd', 'acbabdcd', 'bdcacbda', 'bccdadbc', 'dadadccb', 'dbbaadcb', 'cabddbda', 'cddcdabc', 'adbdcdcd', 'dbacbbdb', 'caddbadd', 'cbcadbda', 'adbbacdb', 'adabdbca', 'addccdba', 'ddcbbdca', 'bbaacdbc', 'cabcdddc', 'badbcbac', 'bcacdcda', 'bbadadcc', 'acabaddb', 'cadacabd', 'bdcabcdd', 'acabdcac', 'cdbdcada', 'ddbbdcab', 'cbccddab', 'daccabba', 'accbcdda', 'addbcbdb', 'dcdabddc', 'adabbabc', 'cddabdbd', 'abdccbbd', 'ccbdadcd', 'adcdbddc', 'cbadcddd', 'cdddacbd', 'babcdbac', 'abdbcdbc', 'aadbcaad', 'bbadddac', 'dbacaddc', 'bdcdbdab', 'babcadad', 'abdbadcb', 'ddbacbca', 'bacddcdc', 'bdadabac', 'addcbadc', 'ddadbcaa', 'cbadbbac', 'acdbabdd', 'babccdbc', 'bccdcadc', 'cbabcbbd', 'bdddcdad', 'acbbdabd', 'cbabdbdd', 'cbadddda', 'ddbcbada', 'dbcdaacb', 'aadbdcdb', 'bdaccadc', 'ddadadbc', 'ccdbacbc', 'cdccdbda', 'adadbbca', 'cacbabda', 'acadcabb', 'acabbcdb', 'acdccacb', 'aabbaacd', 'adbaccab', 'cacbdaba', 'dbacaddd', 'acdbddbb', 'dacbcbcd', 'adbccbcd', 'cdbbdadc', 'bdbadbbc', 'ccbcdcba', 'dcdaacdb', 'bdbdcaac', 'dacdbcdd', 'bccdbcba', 'acbaccda', 'bacbcbda', 'cabbaddb', 'ccadbadc', 'accbdccb', 'cddbaadd', 'dbbcdabd', 'dbddabdc', 'dbdbdadc', 'dbcddbad', 'dacbbadc', 'dacacbad', 'bdddcdac', 'bdacdcda', 'adbcacbb', 'baccbbda', 'bbcbbdba', 'cbcabbad', 'dcbacddb', 'cbcdcaca', 'daddabcd', 'dcababdb', 'bdccadcb', 'bbdcbaab', 'addccbac', 'accbcdad', 'daddcbad', 'acadcabd', 'cbaacdcc', 'dabbdbdc', 'acdbbcdb', 'dddbcdad', 'abddcdcc', 'cadbccbb', 'bcbbabdc', 'dadbbdac', 'bddaccdc', 'abcddaab', 'cdacbbdb', 'bdadacad', 'bcbdadcc', 'accdcadb', 'dbbdbacd', 'cbcadbcd', 'ccabdcab', 'addddcdb', 'ddbabdbc', 'bbacdbbc', 'babdcabd', 'dccdbcca', 'bdadacba', 'cbcbacdc', 'cacacdbc', 'addabcda', 'dddccbad', 'dbdbdcaa', 'abdbddcc', 'ccdacbda', 'daddccbd', 'dcbdbacb', 'ccbdddab', 'ddacbdcb', 'adcbddbb', 'bbcdbadc', 'bdcbddaa', 'abcdcaba', 'bdbabdcb', 'ddbabbdc', 'adcbddab', 'bcdcbcca', 'dcbdbacc', 'bdcbdaad', 'cbdbbdca', 'dbdaccbb', 'ccbcdaca', 'dddbacaa', 'dbdccdab', 'babcdaba', 'cacdabab', 'daddabcb', 'cdbaaccb', 'cabbdabd', 'cabcbcdb', 'bacbbcbd', 'bbcdabbd', 'cacbbcdc', 'acddadcb', 'babbcdca', 'cbbddbda', 'dabcbdbb', 'adcddadb', 'bacdbcac', 'bbccdabd', 'cbcbaadc', 'bddabcca', 'adbbadbc', 'dcdbdabc', 'cacdbdda', 'adbcbacd', 'dbabccbd', 'cddcdbac', 'dcdccbca', 'bcdadcbd', 'dcadabba', 'cbdcdbaa', 'cdbccbca', 'cbadbcca', 'bcdddaab', 'badcddbd', 'badbccba', 'cdbbcabc', 'cabadabd', 'bbcbdbad', 'cdabcbda', 'cbabccda', 'ccdbbaba', 'dacdcacb', 'aaaabdcb', 'dbddacdb', 'ccadaddb', 'adbadcba', 'bbdacbcd', 'dacbcbbc', 'abccddad', 'accdcabc', 'cdbdacbb', 'caddddbc', 'cdcabbda', 'dadbdbac', 'bacbccdd', 'abbdbbcd', 'bdcbbdac', 'bddacbdd', 'bcbbadab', 'dbacbcdb', 'dbdabaca', 'bcdbabbd', 'addcbcac', 'bbddbdac', 'cadbdbcc', 'dcabccbc', 'dbddcabd', 'dcaacbbd', 'ddabddcb', 'adabdcca', 'bacadbca', 'cacabbad', 'adbcacdb', 'dcbbaddc', 'aacbdccb', 'bccabdda', 'bbdbdbac', 'dccdbbad', 'ddacabcb', 'abdccbdb', 'dabbacab', 'bddaacbb', 'ddabcdac', 'caaaabdc', 'ddccbdac', 'caddbcba', 'dbcdacba', 'cbdcdcad', 'acddaabc', 'acbdbcda', 'ddbabcbc', 'addcaabc', 'bacbdbbc', 'abbdcdcb', 'cdabcdbd', 'cabdbddb', 'bcadbacb', 'accdbbcc', 'cacdadba', 'acdbccbb', 'cbcdcacc', 'ccbbdaad', 'bcddacad', 'daacdccb', 'dbcadcab', 'cdcdcacb', 'cddddcba', 'cbadccad', 'bdcadbab', 'bacadaca', 'abcddabb', 'bccddbba', 'dbdccacc', 'cabddadb', 'cbdcacdb', 'dadcbcbc', 'ddadbbdc', 'ddaccdab', 'dbbdabdc', 'babddcad', 'bbddccad', 'cabddaab', 'bcdacdbb', 'ddbcadcd', 'bbabcddb', 'dcdabdba', 'bcddddab', 'ddcabccb', 'dcdacbcb', 'adbacdab', 'dabdbcac', 'dacacbdd', 'bbdbbcac', 'dabccbdc', 'cabaccdd', 'dcbddbad', 'cdbcabdc', 'dbbccdad', 'baabcbcd', 'dcdcadbc', 'ddcbcbba', 'cdcdbacd', 'ddcaaaba', 'cdabdadb', 'bcddcdab', 'bacabdac', 'bddbcadb', 'cbdaccbb', 'baddaccd', 'cddbabab', 'baadbccb', 'cbbddacb', 'addacaab', 'accbdada', 'dacddabd', 'bcdbacbd', 'adacabdb', 'caccbadb', 'acbcbbdd', 'bccabccd', 'abbddccd', 'bdabdcca', 'bcababbd', 'dabcadcb', 'dacbdcad', 'bdcababa', 'aadcbdcd', 'badadbcd', 'aadcdbbd', 'bdbcdcaa', 'cbabbdda', 'bdbacada', 'bcacbdac', 'dacbbcbb', 'dacdbdbb', 'cadadbdc', 'adaccbdc', 'baddcdad', 'dadcabcb', 'dbdadcbc', 'acbcdbad', 'cbaadcaa', 'badddacc', 'cacdbaba', 'cadabcdd', 'dbcacabc', 'dbadccdc', 'ddaababc', 'caabdcbd', 'cbccadad', 'cddabcdc', 'cdbbabca', 'cbcdddab', 'dbadbccd', 'bbdddacd', 'abdbcbcb', 'bbddcacd', 'ccdabbdc', 'cbccdabb', 'bdadcbad', 'dbdbacbc', 'cdabddca', 'ccbadbbc', 'bcbadbdc', 'dcbaccba', 'cabcdbdd', 'ccdcbacc', 'ddadbbcb', 'cdcbdbaa', 'aaaabdcc', 'cddbbcda', 'bdcbddad', 'aacdbcdb', 'bddcbcac', 'ccbacddd', 'adbdcdca', 'bdccdcaa', 'bcdadaba', 'dcbbcdab', 'bbccadad', 'caccabad', 'abbadcbb', 'bcdbaddc', 'badccdca', 'bddcdcab', 'ccaacbdc', 'badabdcc', 'adccddba', 'ddacdadb', 'abcbbdac', 'dbbadccd', 'dbcdcbca', 'acbbcdbd', 'bccdabad', 'bdabbcab', 'dcabddbc', 'cbaddbdd', 'badbcbba', 'bdaccbda', 'dadcacdb', 'bcdbcadb', 'dcabaddc', 'abaddccd', 'dadabadc', 'bcadbddc', 'abcbcbad', 'bcbcddad', 'accdbdab', 'ccaadccb', 'daabcdcd', 'dcadadbd', 'bacacdad', 'ccdabbdb', 'dbbacdbd', 'addbacbb', 'ddaaadcb', 'cabddcdd', 'acbbadca', 'cdbdaabb', 'dbdbadac', 'dbbdcbac', 'acbdcbcb', 'bccbddab', 'bcbabacd', 'badccdda', 'bcaabcdb', 'ddacaaba', 'ccbabcbd', 'bdcdacdd', 'aacbdcdb', 'cdcababc', 'cbadacbb', 'dcabbadc', 'dcbcabdd', 'dccbbdac', 'adcdbbdb', 'abbdccbc', 'cbddbcba', 'bdabdbac', 'bbcacbcd', 'cdccbdaa', 'acdbdccb', 'bddacabb', 'ddcbabcb', 'cbddabda', 'cbdcdcba', 'cdbccbad', 'cabdcacb', 'dbdcbbaa', 'bcacabdb', 'ccddbdaa', 'dcdbadac', 'dabcacab', 'abacdbda', 'acbdabdd', 'cbaadaad', 'abacdbdb', 'dacaddbc', 'abcadcdd', 'adabcdbd', 'dacbddad', 'acddddab', 'ccdbccab', 'bcbdbbda', 'bbacdabd', 'adddbadc', 'bdabbccd', 'bbcbdcba', 'ccbbcadb', 'cbbdcaba', 'abdddcda', 'cabbcbbd', 'cdcabbdb', 'cdccaabb', 'acbaddbd', 'dcbccaca', 'bbcdcdaa', 'cabcdadb', 'bdcaabbc', 'ddcadbcc', 'bcbddabb', 'cbcaddda', 'bbddadca', 'ccadbcbc', 'dcbcddab', 'ddacabcd', 'bbcdabca', 'abacddbb', 'adbcbbdc', 'bdbcbdab', 'dbacabab', 'dbababac', 'acdbacad', 'dccdaadb', 'bcabdaca', 'dadabcad', 'babcdbba', 'bcadbbdc', 'abbdcadb', 'dbccbdaa', 'adbbdaca', 'acbcdccd', 'ddcabadd', 'dcbacdbc', 'bdacbadd', 'ccabdcbd', 'bcddaaab', 'cabdcdad', 'cdbbadbc', 'dacaccdb', 'ddacbacc', 'ccaabdcd', 'bbacbdcc', 'cbbcbadc', 'addbcbaa', 'cdacabac', 'dcdbabba', 'cdadbbcc', 'ccdbabdc', 'dabadddc', 'badabcda', 'bcabaccd', 'badccadb', 'acddcdbb', 'badacbcb', 'cadbcdbb', 'dcbcddaa', 'cbadadbc', 'cabbdacc', 'ddcabdaa', 'bcaadbdb', 'addcaabb', 'cdcababa', 'caddbbca', 'badcbadc', 'abcdcdac', 'ddcbbcad', 'abbcbbdb', 'accbacad', 'accaccdb', 'ccacacbd', 'bbaacdcb', 'ddbadacd', 'cdcbdaca', 'bbcbdbaa', 'caddaccb', 'dbddcaba', 'adbcdabb', 'badbbdac', 'adccbcbd', 'acdabbac', 'daaccbdc', 'dadcbcdd', 'dabdacda', 'abbdcdca', 'bbcdabbc', 'cbddbdca', 'ddbacbbd', 'bcbaddda', 'aacdbbdc', 'ddacdbaa', 'baacbccd', 'adabccbc', 'addbacab', 'bbdaccbc', 'babcddad', 'dababbcd', 'acbbacad', 'bbcacdab', 'cbaadbbd', 'bcbacadd', 'bbacabcd', 'bddacbaa', 'bcdbaadb', 'abbdacdd', 'ddbcabcb', 'aadbcdaa', 'addabcab', 'cbdbaddb', 'baccdddd', 'adbddaca', 'bcdacacd', 'dbbaacbd', 'cddbacac', 'babaccdc', 'bcbdabac', 'dbbacdbb', 'accacbcd', 'badcbbac', 'addaccbc', 'bacadcab', 'dcadddbb', 'abcadddd', 'bcadcbcd', 'dbdbcdca', 'ccdbbdac', 'acbcddbc', 'ccaadaab', 'dddcbdaa', 'bcadcddc', 'bdabcddc', 'bcdbacdb', 'cddccbaa', 'cbcadacb', 'acbababd', 'cacdbbad', 'bdcdbcca', 'dbdcddca', 'adbcbdbb', 'abdcdacd', 'dddcdbca', 'bccdcada', 'ccabdada', 'cdcdcabb', 'cacdbada', 'bccdaabb', 'bbccaadb', 'acbbabdb', 'abccacdd', 'abdcbdca', 'babdddbc', 'dbabacda', 'acdbacab', 'abacbbdd', 'dabddddc', 'cdbadacb', 'bbddcacb', 'cbbdcbda', 'abbdacab', 'cdbcabad', 'bdccaddc', 'bdbcaacc', 'ddbbabca', 'ddbcaacc', 'cddbdabc', 'dadbcbcb', 'dbaacaad', 'dbcdbdaa', 'abadbdcb', 'caaccdcb', 'abcabccd', 'adacdbca', 'bbaddbbc', 'ccaccdbc', 'bcdbbcca', 'acdbdabb', 'cdbcbcca', 'daccacab', 'abcbadad', 'ddbdaadc', 'badddcbd', 'addacbcc', 'cadadbbd', 'dbacddcc', 'dbbdbbac', 'cacabcda', 'bccbbada', 'bbddacac', 'dbadbbcb', 'adccaddb', 'badddbbc', 'dadbcbbd', 'aadcbbcb', 'badbdacd', 'cbacddcd', 'dcdbcacd', 'badbbdbc', 'baccddca', 'abdabcbd', 'bdcdbbab', 'acdbcbcd', 'cbcbadda', 'dddcbabc', 'bdbabaca', 'dcabcbdb', 'adbbdcbd', 'dbcadcdb', 'dabdbcdd', 'abccdbdc', 'dacdbccb', 'cbcacbdb', 'bcacdddb', 'cddcddab', 'bdabacba', 'bbcbadad', 'badccdad', 'bdcbdbba', 'cababbcd', 'bbdbcacd', 'acaddbdb', 'bcacadad', 'acdcbcdc', 'bdbcbbac', 'ddccabbc', 'badadcba', 'adbbcdbb', 'bababdbc', 'adabccba', 'cbabddbc', 'abbcadcc', 'addbdddc', 'cbcaccdd', 'bcbadcca', 'dadcbcdb', 'ababacad', 'acacbdcc', 'acacbbcd', 'caccdcba', 'dbcdadab', 'abadacdd', 'abddbadc', 'bbdacaca', 'bcdccaad', 'bbadcdcd', 'cabcddcc', 'adddcbac', 'cbbcdabc', 'badcacba', 'acacabda', 'aabbdcaa', 'adcbbadd', 'cdaccdab', 'bdccbdca', 'daccdaba', 'dbababca', 'bdbaccab', 'adaccbab', 'bccddcac', 'caabbdbb', 'daccbccd', 'baddcdca', 'babacdab', 'dacbdabb', 'abcbabcd', 'dabdcbdc', 'ccabcdbc', 'accdccba', 'dccabcdd', 'badbdbbc', 'ddbdcbab', 'cabaddac', 'dbbacdcb', 'adcbcbdd', 'cddbaaab', 'dcdbbdda', 'bbdcdacc', 'bbadccad', 'dbaddcbd', 'acbabbda', 'bbabdccd', 'cbabddad', 'dcbbabcd', 'cbbabadb', 'cbdccada', 'ccbbadac', 'cbbdddda', 'abdcabcc', 'badbdabc', 'cddbbabb', 'cadccbab', 'bdacacbd', 'adbdacad', 'dacadbdd', 'cadbdcdb', 'baddabca', 'bacaddcc', 'abdacbcd', 'dabbdbcb', 'bddcaaad', 'cdbbdaad', 'bbcacdcb', 'dacbbccb', 'badbddcc', 'ddbbacac', 'bbcabdca', 'cdbccaad', 'bdbdcaab', 'acabddbb', 'cbcbabda', 'daccbada', 'bdaddcba', 'babdaddc', 'ddbcadda', 'dacbdbca', 'dcadbdbc', 'ccabdcbb', 'cbacdddc', 'bdcabddb', 'cbdabdca', 'acdadabc', 'ccbccadb', 'bbaddbcc', 'caadbcaa', 'acbddacb', 'dbcaacbc', 'dccbbacd', 'dbbcacad', 'bcddbacc', 'dabddacc', 'cbdbcdac', 'badbcbad', 'aabcbcdb', 'dbcbaddb', 'adabcabb', 'abacdcdb', 'dbdddcca', 'bdbacdcd', 'bdadcbbd', 'bddbcaac', 'bbacacda', 'ddaaabcc', 'bbccbadd', 'dbdcbcad', 'ddcacbac', 'adccacba', 'bacdabac', 'bdcacbad', 'bdaacbcd', 'accbcadc', 'accaddbd', 'dbaccaba', 'dcaabcbb', 'cabdcbad', 'dddaabdc', 'abddcdcd', 'acabadbb', 'dcbccaba', 'baabcdcb', 'ccabdbdb', 'bddcbacd', 'acdbdbdc', 'dcadcabb', 'cabdcbdc', 'acbbcdca', 'ccdcacbc', 'abdbccdd', 'cacbbdac', 'cdbddacc', 'cabdbdab', 'babccdca', 'baccdcbd', 'ccbacbdc', 'bcadccda', 'abccdcad', 'acadbbad', 'cadcdbca', 'bbdccabb', 'dbccaacd', 'cbcaadcc', 'baadaacc', 'badcdcbc', 'caddccab', 'ccbacdad', 'badabdcb', 'cddcbadb', 'dbbdbcca', 'cbdaddda', 'dabbdccb', 'ccddabad', 'adabdccd', 'dacbcabd', 'dbddccac', 'abadbccb', 'abacdcbb', 'bdaadbcb', 'bdadbdcd', 'dccdabda', 'acddaaba', 'baccdadb', 'ddbcadac', 'bcbadcac', 'bccbdaad', 'cabccddd', 'cbdcdcca', 'bacbddcc', 'bdbabcca', 'cdbadacd', 'bacbcddd', 'cbacabbd', 'cbbdacba', 'acbcadbd', 'daccacbd', 'bdbccaad', 'bddcaaba', 'cacbbdda', 'adcbcdcb', 'cadccbbc', 'caabdbbc', 'cbadacdb', 'cbadacca', 'dcdbaabb', 'baccbabd', 'bccabdbb', 'ccadbcdc', 'dacddabb', 'bddbadcd', 'cbcacbad', 'ddbcbdac', 'adbbccab', 'addbcaad', 'cdbccaca', 'ccbcbdaa', 'abbccddc', 'cdabcbdd', 'bdcdadab', 'bdadcdda', 'ccadabac', 'cbabcacd', 'dcaabbcb', 'dcabdbbd', 'ccddbbca', 'dcddbcac', 'cbbcabdc', 'adbcadda', 'bcbabccd', 'abcadcdc', 'bcbddcda', 'cddaadab', 'adcbccda', 'cdddccba', 'dbbcaabc', 'acddbcbd', 'bacbbddd', 'ddddacdb', 'aabdbbcb', 'baddacad', 'dcdcacdb', 'abbcdcba', 'cadbbddb', 'ccbdbadb', 'cbcbcadc', 'cdcabcca', 'adcbccbb', 'cacdbdab', 'baccdddc', 'daadcbbd', 'cdcaaaab', 'dbbcbadc', 'ddddacbc', 'cdbddaac', 'caddaaba', 'dabdcbac', 'acabacad', 'addccbdc', 'babdadbc', 'ddbdbcac', 'ddadddbc', 'bacbddba', 'ddccbcba', 'addcacdb', 'ccdabddd', 'bcddaabc', 'bacbddbb', 'dccdadbb', 'cdccddab', 'adcddbcd', 'aadccdbc', 'bcadadad', 'bdcdaccd', 'aadcdccb', 'cbadcacc', 'bbdbbcca', 'bcdababb', 'bdccacdd', 'acdababc', 'dccbbcad', 'cdbabcbc', 'cbacacdb', 'ccdccabc', 'bcadabbc', 'bbaadbcb', 'cacbbdcb', 'dddacbbc', 'dcacbcca', 'cabacdca', 'daadbcbc', 'bdcdabda', 'aabcdbbc', 'ddccaabd', 'cddcbbda', 'baadbcbb', 'cbccddad', 'ccbaabbd', 'dccbacbb', 'badcbabc', 'cdcbaccd', 'cabaddad', 'adcabdcc', 'ccbdbcac', 'dcbdabac', 'cbdadada', 'dcdbabbd', 'abdddadc', 'cbacaddb', 'dcaabbdb', 'accbcdcb', 'daddcbdd', 'dbabadca', 'bbdacdac', 'dcaabccd', 'babcdacc', 'cacbacdb', 'adbcacdc', 'bbdaccab', 'bcddadcb', 'dcaddbbc', 'abbdcdbd', 'dabadcac', 'baddbcca', 'ddbccdad', 'bacdbddd', 'cabdbdad', 'bcaddbcc', 'adbbcdcc', 'dbaccbca', 'dacbddab', 'babbdcba', 'ddcdbadc', 'dbbadacb', 'cbaabcbd', 'cbdddaad', 'cddabddb', 'bdddbacd', 'abdbccba', 'dbcbadab', 'dbcdadbb', 'dbaddcca', 'babccddc', 'dacbdcba', 'cdbaabcb', 'dbacacbd', 'abbdddcb', 'ddccbada', 'caddbdcc', 'adcadbba', 'dcbccdba', 'baaaaccd', 'acacdbdb', 'abbddcab', 'dccabbcb', 'cddcabca', 'dccbdaca', 'bbccadcb', 'dacbabbc', 'cdcadabb', 'aaaabccd', 'cdabccab', 'ccacbdda', 'acdbadda', 'baccbdcd', 'adccdbca', 'dddcddba', 'dcacbcac', 'cbddbaab', 'caccbbcd', 'abbdabcb', 'abdddcbb', 'ddaabacb', 'abbcdcbc', 'cbcacdcd', 'bdddddca', 'acdabdbb', 'cbdbacab', 'ccbabddb', 'cdabcddb', 'cacdcdbc', 'caabcbbd', 'acbbaddb', 'dabadcdb', 'dcbbaabb', 'abbccadd', 'dcadadbc', 'dadbdddc', 'abcbbddb', 'ddddcbca', 'cababcdd', 'dbadcdca', 'babcdadc', 'abdbcbca', 'bcdcbaac', 'aabcbccd', 'acbcdcbd', 'babcdccb', 'acdabaca', 'badbcddd', 'dddcdbac', 'bddccdad', 'ddaadbca', 'bcbdaccd', 'adbdddcd', 'bdbacbba', 'acadaddb', 'ddccaaba', 'abacbadb', 'babcaddc', 'cdaccbcb', 'dabacacd', 'ddcbdaca', 'dcbdadcd', 'ccbadacb', 'cbadbabc', 'abbcacdd', 'dddbdcba', 'bbacaddc', 'ddccbdba', 'dcbcdcba', 'bcddacdc', 'bddadcaa', 'cacddbad', 'bcbbaccd', 'ddbbcdba', 'acdbbadc', 'daccbabc', 'ccabdcca', 'aaaadbcc', 'babbaccd', 'cbbadcbd', 'aacbdbaa', 'dbcbacca', 'accbbdab', 'dbacabcb', 'caccabdb', 'dabdcbab', 'dbcdccda', 'dabbdaca', 'badacbad', 'bcdcbaab', 'badabadc', 'bbabcadd', 'dbbcbcab', 'dbdbacbd', 'aabdaadc', 'cbdacbdc', 'babadbac', 'cacbbdbc', 'caadcbcb', 'bacabadb', 'dddaacab', 'abddacba', 'cbbabadd', 'cbccdaab', 'addabcbc', 'acadbaba', 'acdbabad', 'dbbdcdac', 'bbcaddcc', 'dcbcbaac', 'cbbdbcca', 'cbcbdaab', 'dcdcbdab', 'addacdbd', 'ddddacbd', 'dddadacb', 'cddcadbc', 'cbcbacdb', 'dbbcacdc', 'badbbcca', 'cadbaddd', 'dabdcaca', 'cdadcddb', 'dccbaabd', 'dabccadb', 'dcaccdba', 'bdbcdbca', 'bcddabcb', 'bcbbadad', 'dcdadbda', 'adadcadb', 'babbcadd', 'accacbdb', 'cbcbddba', 'aabdbdcb', 'abbcdacb', 'accbbdcb', 'bbacddbb', 'babcbbad', 'dddcabdc', 'badbbcbd', 'ccbcdbaa', 'cabddabc', 'cdcbcadc', 'adddabcd', 'bccdbaba', 'dcdaabbc', 'cdbaccdd', 'baddcadb', 'dacdbdac', 'cadcbcba', 'bbcdabdc', 'adddccdb', 'dabadcbc', 'cbdccdab', 'bbcdcaba', 'ccdcbaac', 'bdccbaac', 'dbbcdadb', 'cadcbdcb', 'bdbaccdb', 'dcdadccb', 'cbcbadca', 'bccddaac', 'dbabcaba', 'bdccdbab', 'ddbccaac', 'dcacadbb', 'abbdccbb', 'adbccadb', 'abacdccd', 'abdaccda', 'dbccbcad', 'cdbadcbc', 'ddccbbac', 'acbcdacb', 'adabcbca', 'cbdaaccd', 'ccaddbba', 'bdcaccac', 'dadbdcca', 'aadaabdc', 'dbabdcab', 'abdadcac', 'cbddcbda', 'dcadbcbb', 'bbdcdabb', 'cabcabdc', 'abaccddd', 'ddcdcdab', 'ccacdabd', 'acbadbca', 'bdcacaba', 'addbbabc', 'ccbdabac', 'adacbbab', 'aadbccaa', 'dcbdadab', 'cdbbacbc', 'bbdcbabb', 'ddcaabba', 'cababdad', 'bdcacdad', 'abdabcab', 'dbabdcdb', 'dbdacabc', 'dacdbbdb', 'adbbcaba', 'abcadadd', 'bdacbdca', 'dbaadbdc', 'cdababca', 'dcdddabd', 'cdbaaaab', 'cbbcdacd', 'bbccbdad', 'dcabdcdd', 'ddacdbad', 'bcabdcbc', 'ababdbbc', 'aadcbdcb', 'dadcabdc', 'acbdbcbb', 'abcbabad', 'dacbddcb', 'bdcadbda', 'bacdcdad', 'cddcadba', 'acdaccbb', 'cdaccabd', 'abdcdcad', 'cbdacdcc', 'acacadab', 'acbaddaa', 'ddabacbd', 'babcbbdb', 'adcdcdcb', 'acdabdbd', 'cabccddc', 'bacaddad', 'dbdbcabc', 'cbaddadd', 'bcabddcc', 'ddcadabb', 'bdddaadc', 'bacbdcca', 'dbbcdbca', 'ccaacbcd', 'cbabddcc', 'bdccadba', 'dbcdadbc', 'badabacc', 'cbdaccdc', 'bcdbacdd', 'cbadcdcc', 'adbdacbb', 'bdcacbca', 'dccbbdab', 'dbcabdac', 'cdcaaccb', 'dbadbabc', 'acbccdad', 'abdcabdb', 'babdcdcb', 'dcbddcad', 'bdbbdacb', 'ddabdcdd', 'ddcbddac', 'abacdabb', 'cdbbcacb', 'bcadcdba', 'babccdbb', 'acacbbdc', 'bcbcabda', 'abbdcdcc', 'dabcdbac', 'adbadcbc', 'cacbadba', 'dcddabdb', 'abbdbbcc', 'cadacdbc', 'addbbcad', 'adccdbbd', 'daabcdcc', 'dadbbcbb', 'addabddc', 'bddbacca', 'cbddbadc', 'cdbdacdd', 'abdcabdd', 'bcbdaddd', 'acbcddcc', 'babdcacc', 'baddacac', 'bdbdcbab', 'ccadccba', 'bcbcdbad', 'cdacadba', 'abacddda', 'acabddca', 'dcdbaadb', 'cbababdd', 'cdbdcbac', 'adabadbc', 'adacabba', 'bbdcaadb', 'abddbcca', 'cbbadbca', 'babbcbbd', 'baacbdbb', 'dbdbcbca', 'ccdcaabd', 'dbddbdac', 'abadcabc', 'acadbbcb', 'ddcabbcb', 'addbacac', 'dadbbcac', 'acbdcaba', 'bdadcdbc', 'bbcadacb', 'cddcbacc', 'accbdbad', 'bddbdcab', 'dcadabbc', 'daddbcab', 'adccbddb', 'dbabdcdc', 'bbcdadbb', 'dcabcddb', 'dacacabc', 'abddccad', 'aacdbccd', 'ccdabdac', 'aabaadbc', 'ccdbdaca', 'cbdddabd', 'cabdabda', 'bcacbbad', 'dbababcd', 'ccdadcdb', 'cdbdabac', 'dbdccbac', 'cadbcacc', 'dcdbacbc', 'dcbabbdd', 'dddcaccb', 'cdabcdbc', 'bcadacbb', 'ccbaddbd', 'bcbaddaa', 'dacbaccb', 'badadacd', 'dbbcbaac', 'cdbbcbda', 'aadcbbcd', 'cdbdccac', 'acdadbbc', 'ccbbdcab', 'cdcacbab', 'babadcdb', 'dbdbcbad', 'bdadcacb', 'ccbcaacd', 'bcdbaddd', 'daabbdcb', 'baddcbac', 'dbddccaa', 'adcbcbca', 'abccddcc', 'cdbcdbca', 'bcdcabda', 'cdbaddac', 'badaccbb', 'cbadbadc', 'bdacdcba', 'bdbbcdab', 'dbadcadd', 'bdaccbdc', 'cddcbbaa', 'abacbada', 'bcbbdabd', 'bdccddad', 'bcbcdbba', 'dbbcabba', 'ddcbcaab', 'adababca', 'ccdbbabd', 'bcbdbbac', 'dcbababc', 'bcaaaadc', 'bdaabbcd', 'bcadbdbd', 'ddadbaac', 'abcadccb', 'aabdaacb', 'dbcadbdc', 'ddabccdb', 'bdbcacdb', 'abadcbac', 'cadacdba', 'bdbddacd', 'cbabdcba', 'cddbdcab', 'cdbacdca', 'bccddaab', 'bcbbdacc', 'dbddcbba', 'ccacadab', 'dbdaccac', 'cbcdabbc', 'ccdcabca', 'dcbdabcd', 'ddcabcdc', 'abadabdc', 'bddcdada', 'dbabbcdb', 'bcbbabdb', 'bdccacad', 'accdbddb', 'acdacbdd', 'cbdaddac', 'bcbabbcd', 'dacaddbb', 'acdbaddb', 'caddadbc', 'adcbcacd', 'cadadccb', 'cdcdacdb', 'dcbbdacb', 'cbcbdcaa', 'bccaaccd', 'daddbdca', 'cdbabddb', 'abcbadac', 'acbaccbd', 'dcabbdac', 'ccaddbaa', 'cdadcbbc', 'ccbadabb', 'ddbdccda', 'cdbabadd', 'bbadcdad', 'bcdaadcc', 'bdcbadbc', 'ccbabadd', 'abacdcbc', 'adabbcab', 'dabcddda', 'bcdbbcab', 'bddcdacd', 'dcbbdcad', 'dcbaadaa', 'adcbdadd', 'bddcaccd', 'dcdbbaba', 'bbccaddb', 'cadbacbd', 'ddabccac', 'dddbacbc', 'ccbbdbaa', 'bdaacbbd', 'dbacacdb', 'bcacdcca', 'cdbcdadb', 'bcdddacc', 'cbbcaddc', 'bccacdac', 'dcddccab', 'dbcbbcba', 'cababdbd', 'ddbdccaa', 'cbabddca', 'bbacacad', 'bdacbcbb', 'ababccdb', 'bdabadac', 'accbdcba', 'aaccbcdb', 'ccabcabd', 'aadcdcbd', 'dddbdacc', 'bdacacdc', 'cadbbabc', 'dacdcbca', 'cbbdaacc', 'dcbcadba', 'bbadacdb', 'baddbcdb', 'bbcbaddd', 'bcdcbdad', 'acbadbbc', 'ccdcacab', 'babddbcb', 'bcabcdda', 'cdadbdac', 'ccbdcadd', 'abdabacd', 'acacdcba', 'ccbbdbda', 'daccdbdb', 'dcdadbcd', 'adcadcbb', 'bdacbccd', 'cbabdcdc', 'abadacdb', 'cabbdbda', 'abdcadad', 'cabbddab', 'acadacba', 'cbddddaa', 'aabbdbcb', 'abdccabd', 'bdacdbcc', 'badcdabc', 'bacdbcbc', 'baddbbcb', 'daadbdcd', 'bcaadccd', 'ddadabcd', 'acacdcab', 'ccbabadb', 'cacbdbda', 'cadcdbdd', 'adbacbab', 'ddcdccab', 'bdddccda', 'bcdbabdb', 'bddcaada', 'bdcbdbca', 'bbdaccbd', 'cbcadbbd', 'caccdbcb', 'bbcdbcad', 'cbadbaba', 'cdbdbbaa', 'cbababcd', 'dbadabdc', 'adbddcad', 'dcddbbaa', 'caccbdcd', 'cdbccbba', 'dacdcbbc', 'cbdcabba', 'cddbdbda', 'cdacbdac', 'cbddaddb', 'bccdbacc', 'cbacabdd', 'cabcbbad', 'bbccbdda', 'dbcababd', 'dcaaaabc', 'cadbbdcb', 'accaddbc', 'bccaddac', 'bbcdcbca', 'ccbccbad', 'ccabbabd', 'cbccaabd', 'badcbbca', 'bbdabacc', 'dabcbdcd', 'accdbacc', 'ccddacab', 'bdbcacbb', 'bdbcddab', 'dbbadbdc', 'daddadbc', 'adcdbbda', 'dbbaadcc', 'cbdbdcba', 'bdabbdcc', 'bdcbdbda', 'cdadbbda', 'dccbaacb', 'bbddabcc', 'dadcbabd', 'dacbdada', 'cdbacbdd', 'acdcdbdb', 'ddacacbd', 'bdbdadbc', 'bcabdadc', 'adccbbda', 'ccbbadcc', 'dcdbacca', 'adbacdca', 'badaddcd', 'ddaabacd', 'badcbdcc', 'adbbcacb', 'bbddbaca', 'bbcbacdd', 'aabdbccb', 'acdcdaba', 'bddabbcc', 'dabaddca', 'ccaddbab', 'ddcdcbab', 'dccacbda', 'cbabbdab', 'cdddaabc', 'cadcbadb', 'cadcacbd', 'bccddabd', 'cbbadacb', 'cdbaddaa', 'cbdbacbc', 'bdcabcdb', 'ccbcaddc', 'bcabbdba', 'cabdabbc', 'dbcbabcc', 'aabbcdcd', 'bcacddcb', 'dababbdc', 'cbcadcbc', 'adddbbac', 'bccbcdca', 'bcbacdcd', 'dccaabcb', 'abbccddb', 'badcabdd', 'adababac', 'acbdbbad', 'bcdcaddc', 'dbcabdad', 'abacdbcb', 'ddaaddbc', 'cdbabdad', 'cbaddada', 'cddadcab', 'bcacbdbd', 'dabadacc', 'ccbddbba', 'dddcaaab', 'acdbcada', 'bdcdcdac', 'ccaddcbc', 'bccadbcd', 'bdbbaccb', 'dddcabbd', 'cbcdabad', 'acdbabbc', 'acbbdaca', 'cacabadb', 'acbcdbcd', 'cdbbaccd', 'abacddbc', 'baddabcc', 'acdadadb', 'bcaadcdb', 'bbccadac', 'babcddbd', 'cadccdba', 'adbbcddc', 'cacdccbb', 'abdbcdcd', 'bdbbcbba', 'cabcdcba', 'caabbdcd', 'baadbbcc', 'ababcdbb', 'cdbabddc', 'dacabcbb', 'dabacbac', 'adbbddcb', 'cbaddcdc', 'adccbbab', 'baddcaba', 'addbadac', 'bdbadcad', 'bdcbbcab', 'adcbadca', 'cdddabba', 'cdbddbaa', 'daabccbb', 'cddacddb', 'accbbcbd', 'dcabacdd', 'dbaccddc', 'cacbcdba', 'dbacadbc', 'ddbcadbc', 'cabcabda', 'bbdacbad', 'badbacdb', 'dadbdcad', 'dabbacbc', 'cbbdddad', 'cdbbacca', 'daabbdcd', 'dacdadcb', 'ddcadbdb', 'abaccadc', 'dbaabcaa', 'baddccbc', 'addabccd', 'ddbacbab', 'ddbaccda', 'abbabdcd', 'abbdcbab', 'babbacad', 'dbaddcba', 'dabccabb', 'ddbcadaa', 'dadacbab', 'cbaadbcd', 'ccaccbcd', 'dcdacbcd', 'cdadcbda', 'ddaabbca', 'bbdbadac', 'cdabdabb', 'cdacbabc', 'bcabddcd', 'bddaabcc', 'cabdadcb', 'acbddbda', 'cbccdcac', 'addcddbc', 'acbbdccb', 'bbcddaad', 'bdcaabcc', 'ddacbbdb', 'cabadbbc', 'dcbabcbd', 'addadcba', 'cabadacd', 'bddccdda', 'dadbcbad', 'cdabcdda', 'cdcaadbb', 'abaddcbb', 'dbdabdca', 'addcadbb', 'bdcadddd', 'dabdccba', 'cadaddbc', 'dcaccbdd', 'cbacdabd', 'bcabddba', 'cbbdacbc', 'cdbadcdd', 'ddbacbbc', 'dabdacdb', 'cacacdbb', 'bbccdbca', 'bcdccbda', 'cbcdbbab', 'aacbdaad', 'dbcabcba', 'abadacdc', 'adcbbcba', 'cbddcaab', 'dacbdbac', 'bcddcbba', 'dabbccdb', 'daccbbcb', 'cbaccdda', 'bdcabcac', 'baadcaad', 'babdcdad', 'adddacbd', 'bcbadbad', 'cabdbadb', 'cbdbdaba', 'baddbcbd', 'cdacbcca', 'badacbcc', 'cadbdbda', 'acabddad', 'bbdcadda', 'adddbcab', 'abadcacd', 'acabddba', 'bcaacbbd', 'acbbdacc', 'dcdbcabb', 'acbdbbcc', 'cadbdbcb', 'aacdcaab', 'ccdbbdca', 'bbdbadca', 'adbccbda', 'ccbbdadc', 'adbcbacc', 'cbbddacd', 'dadbbdcd', 'ccbbccad', 'bdadcacd', 'dacdbcbc', 'bacabcad', 'bcdddcad', 'cdccacbc', 'bddadcda', 'bddcabdc', 'cdbadaca', 'ccddabba', 'bbadcbac', 'bcdbadda', 'bbaadccb', 'bcdbdcaa', 'adcbdacc', 'bbccdcaa', 'ccddbacb', 'dcdacbad', 'ccdddbac', 'acbdabac', 'abcddbcb', 'bdcbacdc', 'bcabdabb', 'ddcbbacc', 'accaddbb', 'abcabbdd', 'bacbbdbb', 'cbdaacbc', 'ccaabbdc', 'acbbddab', 'dadabcda', 'dbdcbcda', 'abbdcdbb', 'dcddcacb', 'adacbdcd', 'abdbddcd', 'dcbdbdac', 'cacbdcab', 'ccacdbca', 'bccaddbc', 'cacabddd', 'abcbdabb', 'dbcbbabc', 'cdabbdca', 'dbcadabc', 'baccdabd', 'bcacabbd', 'abcdbddd', 'dabcdcdb', 'cbcadcca', 'dbddcadb', 'cadccacb', 'dcdadacb', 'abdbdabc', 'bcbdaabb', 'bcdacdab', 'bbcdbacd', 'bddccabd', 'bddbacbb', 'dbddcaad', 'dbacbabc', 'cbacdcdc', 'ddcabccd', 'bddcbbad', 'bbcbadda', 'acbdbbac', 'bbadbbcb', 'accbbddc', 'accdbccb', 'dbaddbdc', 'ccbcdaba', 'addbcaab', 'babcbdbd', 'bddbdbca', 'ccdbacad', 'bcabbcdd', 'acacabdb', 'ddcbdcac', 'cdadbbcd', 'bacdbdcd', 'cdcbcdab', 'bdcdcdab', 'accadbcb', 'bbdddaca', 'dacbdbbd', 'cadbdadc', 'dacacbab', 'abaddccb', 'acdadbab', 'dcbdbaad', 'cbbdadcb', 'cddbcacd', 'dbbcdcab', 'bbcbadca', 'bdbcaacb', 'bdddacbb', 'adbcbcad', 'dabcbbcd', 'ccdbdadc', 'bddaaadc', 'bdcdaadb', 'abdbcdca', 'bcdddcac', 'bdacdadb', 'ddaddcbc', 'babbacda', 'dddbadca', 'bbdbcdda', 'cdadbccb', 'bcabccdd', 'adcbdcab', 'abadbadc', 'cbadcaba', 'addcabcd', 'cdacbdda', 'abbaddcc', 'bdbcbabc', 'ddccdcba', 'dbcabaca', 'ccbabdbc', 'bddbbacd', 'bbdbdcad', 'daccdcba', 'accbcbcd', 'baccbdab', 'ccabbdcc', 'cddababd', 'bdcbdbad', 'cdbbabba', 'cdbbaabb', 'cabcbcdd', 'cacbabcd', 'dadcbdad', 'abadcdcd', 'bdddbcba', 'ddddbacc', 'adccabba', 'bccaadbd', 'ccadacbc', 'cbbdccba', 'dcacadba', 'bcbdbcac', 'dbbdaccb', 'ccbbaddc', 'dcabcbdd', 'bcbadddb', 'abbdccdc', 'daacbdcd', 'baccddba', 'accbbadc', 'acdbdcdd', 'ddacbbab', 'cdcadbdc', 'bdccddac', 'cdbadaba', 'bcddbada', 'bdbccadc', 'dacdacbc', 'caddcabc', 'bcacadda', 'acdbcdbd', 'acdcbbcc', 'cadddbcb', 'bcddcacd', 'ababcbdb', 'abbabdcb', 'cbddadcb', 'bcbcdcba', 'abbdddbc', 'bcadabbd', 'acbdccdb', 'ccacbcbd', 'dbcdbdba', 'bbadaccd', 'acadacdb', 'dabcdabd', 'cbccaddc', 'cabdaddb', 'dcdacabd', 'cdadadbd', 'acdacbdc', 'ddccdbad', 'bcbadddc', 'bcdadbba', 'dcbcabbc', 'bddccdba', 'bdbbcaab', 'bdbbccba', 'abcdbbcc', 'dbccaabd', 'bbccdacd', 'dbcadbcc', 'dccdcbba', 'cabbaccd', 'dcabbcdc', 'bddccabb', 'addbaddc', 'abcbdcca', 'bcacdcdd', 'cbccdada', 'dcaccbba', 'ccadbcca', 'daddcbdc', 'abddddbc', 'bccabbda', 'cdcadabd', 'bbcbdadc', 'badcbccb', 'cdabdaba', 'bcadddac', 'ccbdaadc', 'abcaddaa', 'bcaccbdc', 'aadbbcaa', 'cbaaaadb', 'cdbbadbb', 'dbdaccdd', 'cdbabdab', 'bcbddada', 'cabddbdc', 'cbdaaccb', 'babbcadc', 'dadbcabb', 'dacbbadb', 'ccabaddb', 'ddbcadbd', 'adbdccdb', 'cdbddabb', 'badacbdd', 'abdcacac', 'bacdbcca', 'aabdccbd', 'bdcddacc', 'aadccbdb', 'acadcddb', 'cacbdadd', 'adcdabca', 'dbbcbadd', 'babbdbdc', 'bacbadbb', 'cbccacda', 'bdbccbac', 'bbcacdca', 'caddcdcb', 'dbcdbcca', 'bbacdbdc', 'abbdcbcd', 'bcdddbab', 'adbdadbc', 'acacabdd', 'dddcadcb', 'ddccbbda', 'bcabbada', 'acdbdcac', 'dacbaddc', 'cbdabbcb', 'dbadacba', 'caadbcdc', 'accbdbbd', 'bbacabda', 'abdddcdd', 'cbcbaadb', 'dcdabcdb', 'accdbcda', 'acabddab', 'aadcdbbc', 'ccdcbcca', 'dcdbdaca', 'cddaadba', 'baccadcd', 'bcdcddaa', 'adabcdcc', 'bdabacac', 'cdacbccb', 'acbcacdd', 'acbcbdbb', 'acabddbc', 'bdcdbabb', 'dccabddb', 'aacaadbc', 'ccacdcbc', 'cadbbcbc', 'adbcdbbc', 'dbaddacb', 'bdacacdb', 'acababcd', 'cbbcdcba', 'adbaccdd', 'dbcbdbab', 'cadbabcd', 'baddcabd', 'bdbdbaca', 'cbbadacd', 'acdccbdc', 'cdcbaadb', 'adcdbcdc', 'abcdccdc', 'ddabcbdc', 'dacdaddb', 'acdcdbab', 'dcacacab', 'cabacbdc', 'abbdbdcb', 'abadcadb', 'ddccabcb', 'dcdbcaac', 'abbcbdca', 'dccdbdac', 'babdcdcc', 'bcadbaca', 'cdadcbdb', 'adabacda', 'cbadadda', 'cabdbcca', 'dadddbca', 'cbdcacca', 'dcacdbda', 'abcacdbc', 'ddccabdc', 'dbbcbcad', 'cacbdbad', 'abcdabbc', 'cdcbbabb', 'cbdadcac', 'cdbcbbab', 'daddcabd', 'cbbadbcd', 'bcacddac', 'dabdbddc', 'aabbdaac', 'cddbdbab', 'addddbdc', 'bacdadad', 'abaccdcc', 'cdbbdbad', 'ddbabcdb', 'ddbdadcc', 'ccbdbbac', 'bdcbdcab', 'ccdacbca', 'dbcbabbd', 'ddbabacd', 'ddcaabcd', 'acbcbbcd', 'caddcbdc', 'bcdabacc', 'adbcdadc', 'abddcbca', 'dcaabdbd', 'cabbdadd', 'acbdcacb', 'adaccadb', 'bdcabddc', 'bbabbcdd', 'caddabab', 'daccabcc', 'ccdabcbd', 'baacbdbd', 'daddcbdb', 'cdddbabd', 'cabdbabd', 'bacbbddc', 'cbdcbadb', 'dbaddaca', 'bcbaccbd', 'cacbdddc', 'bacbdcdc', 'cbabadda', 'dcbadbdd', 'adcbcada', 'dacbaddb', 'badbdbac', 'bbdbcadb', 'bdbaabcc', 'cbcacadd', 'cbccacbd', 'cdcddaba', 'acddbbac', 'ccbadcca', 'cdcdabbc', 'cbdadadc', 'dddaaacb', 'addacbba', 'badacbcd', 'bccdabbc', 'cdabadbc', 'bbadcacc', 'cbcdcdba', 'bcabdbdc', 'cdbdbcaa', 'bbdbccab', 'cbdadccd', 'bccaddab', 'bdbbabcc', 'abdcddba', 'bbabdbcd', 'babdcdbc', 'cacddcdb', 'bcaccdac', 'dbcabdcb', 'adcabddd', 'addbccbd', 'dbbaacbc', 'cbadadcb', 'bdbcacba', 'baabcdbc', 'dbacbabb', 'cbaddaac', 'adbdbbca', 'badbadcc', 'dadcdbbc', 'adbabbdc', 'cabcbccd', 'ccbccdca', 'bddcdcba', 'bacdcbcc', 'dbadbdcb', 'bdabdcdb', 'dbcacdca', 'dcbcbbda', 'adcdacba', 'dabbcbbd', 'cbddacad', 'abcadacb', 'acabbdcd', 'bdcbcbab', 'babbacdb', 'badadcda', 'daaaabcb', 'cdcddbad', 'bcdbbdac', 'bcabddcb', 'ddbddcab', 'cacabcdd', 'acdbdbdb', 'cadcdbdb', 'dacbabad', 'baddcacd', 'accbdabc', 'accadbbc', 'abccbddb', 'dcbabdca', 'adcdbbad', 'dcbabacd', 'dcdcaddb', 'cdcadbca', 'dbccdcaa', 'cabbdbdd', 'cddbdbba', 'bbdcddab', 'cdacabcb', 'cdcddbca', 'ccdcbabc', 'dbaddcac', 'abcdcdcb', 'cbcdacdc', 'ddabdcdb', 'cbccdaca', 'acadabdb', 'ddccaabc', 'bbddcaac', 'caccdabc', 'bacddcdb', 'cabddccd', 'babddbcc', 'ccabdbdc', 'bbdddcca', 'dcabcbca', 'abaddbdc', 'cdcbbadb', 'cabcbcda', 'adcdcbda', 'ddabaccd', 'cbcadddc', 'acdababb', 'bdcaccab', 'bbadbccd', 'acbddbac', 'dbcbdcac', 'cababccd', 'aabbdcdb', 'dabddcaa', 'cbbdddaa', 'acbdcbac', 'bbccdcab', 'aadbcbdc', 'dbccbada', 'ddaacdba', 'ddddbcba', 'cddacaba', 'dcbbdaca', 'dbaddaac', 'bddcbcda', 'ccadabcb', 'bbcdcadd', 'ccabbcdd', 'cbabddba', 'ddadbcbc', 'bdcbcabd', 'adacddbd', 'adacbbcc', 'ddcbbdaa', 'cbbcdadd', 'baddccdb', 'bdbadabc', 'ccbabdcb', 'abbdbdcd', 'abbdbdac', 'bdbdcabd', 'bcbdcbac', 'cbcabbda', 'dcdcdacb', 'bccaabbd', 'ddbbcbac', 'badcdbca', 'bccbcdaa', 'cadbddca', 'dccbcdda', 'dabcbadb', 'bcddacac', 'cbddcadc', 'ccadcbda', 'bdbbcdca', 'bacddbac', 'cbcabdbc', 'daddbddc', 'cbdcddba', 'cabdacdb', 'bdbdbbca', 'dadacacb', 'bcacabdc', 'cbadcbad', 'baccadad', 'cbdddcab', 'dbaccadb', 'ddcbdbba', 'abdcadac', 'baddbaca', 'caccaddb', 'ccdbcdda', 'dababcbb', 'bacbbdba', 'dbbabcab', 'babbacbd', 'cabcddac', 'bcbcaacd', 'bdddadac', 'adabdacc', 'dbadbacb', 'ccacdcbb', 'dacbcdab', 'acaddbbc', 'daabcbbd', 'bdbacddb', 'bbcacacd', 'dacbccdc', 'dbdcdabc', 'cdcabbdc', 'dadcdddb', 'cadcdbdc', 'ccdbcbda', 'dcbaacbd', 'aaccdbcc', 'caadbdcc', 'adddacba', 'badabdca', 'cadabdba', 'ccdbcdac', 'cbbabdbc', 'accdcbda', 'abdccacc', 'abcbdccd', 'cabddada', 'cdadbbca', 'dadbcdbb', 'abbcdbdd', 'bddccbba', 'bcddccda', 'dcdaccdb', 'ddcbdadd', 'daabcbcd', 'bddddacb', 'dabccacc', 'bdcbadba', 'ddbddadc', 'addbadca', 'dcdbaadc', 'badbcdba', 'abdbcadc', 'cadbbccd', 'bdabccdd', 'dabdbccb', 'cdadacbd', 'acbbcdda', 'acdbcaca', 'abdbbdca', 'abccadcd', 'bdbdacba', 'dcbabacb', 'dcddcbac', 'dbccdacd', 'cdddadcb', 'dbadbcdc', 'cdddacdb', 'dadcbdbb', 'abcbccbd', 'dcdbdbab', 'bdcbddba', 'dbbdcdab', 'abdcdcbb', 'dcabadca', 'adbabadc', 'abbacbdb', 'acabdabb', 'bcdaccba', 'bcaddcdc', 'bccaadcd', 'badabdcd', 'acdcbdad', 'ddcaccbb', 'ddccdacb', 'dadbacdb', 'dbcbadcb', 'cbbcbadd', 'cdabdccd', 'dcbbabda', 'bbcadabb', 'badddcbc', 'bccbdbaa', 'dddabcda', 'bcbdcbab', 'cbddaccd', 'dbdbabca', 'cabdaddd', 'cdcbbabd', 'bbcbabdb', 'dcdbadba', 'cacddaab', 'dccdacba', 'cdddcabc', 'dbcbabca', 'bdabdccb', 'dcacbbac', 'ccbdabad', 'ccdbaabd', 'ccdbccba', 'bdbadbcd', 'cbadbcbd', 'dbbcbdca', 'dcdbacba', 'bdacdcbb', 'baddabcd', 'acbbdabc', 'bdcdcbac', 'dbacddaa', 'bccbdadb', 'adccacab', 'dcbcbaab', 'ccdbcacc', 'bdacbdab', 'ddcdbacc', 'dadbdcbc', 'bdbbacad', 'accbbcdd', 'bccdabdd', 'ccbdbcab', 'acbdccad', 'bbcdccab', 'acabadda', 'dcbaddac', 'bdbdbacb', 'ddcbdadb', 'ccddadbb', 'bdddcbac', 'cbbadbcb', 'cbabcdca', 'ddbcdaad', 'bcdbdcad', 'acbcdacc', 'adcdbddb', 'acabdbdc', 'bacadddb', 'cacbdcbd', 'cdbdabdc', 'cbcdbabd', 'ddcbadba', 'bcaccadd', 'cdcdaccb', 'abdcdbbc', 'addabbcc', 'caddacdb', 'dbacbcba', 'abddccba', 'dcbddcaa', 'bdbcbaad', 'acdddbca', 'dddacdbd', 'acdabada', 'dbdcdcad', 'cadcdcbd', 'cbbabdcc', 'ccbcdabd', 'cdabdadc', 'daabcbcb', 'bdcdabac', 'bdadcdcd', 'ccdadbdc', 'dccdcbda', 'cacabccd', 'abadddbc', 'cbdcbcac', 'cdbaabaa', 'ccdcbdda', 'bacbbdac', 'ccaaaadb', 'bdccabad', 'dcdddbac', 'dcddbabc', 'abcdadcd', 'cdcbabdb', 'bdadbbdc', 'cdadbdcc', 'bbccabbd', 'ddbbcada', 'ccbdcbad', 'bcbddaac', 'acbadabc', 'dddabdcb', 'bdcbabdb', 'acddbdbc', 'dacdcdbd', 'ccabacdd', 'dcdccbda', 'baabdbbc', 'bcdabdbb', 'baccdcdd', 'bacdcdcd', 'cadbccab', 'baccddbd', 'ddbdabcc', 'bbdccaba', 'cdadcbab', 'addcbcbc', 'ddcbcabc', 'adcbacac', 'baadbaac', 'bbcadadc', 'cdcbabac', 'ddcdbadd', 'cdbbcdba', 'bcbdbabd', 'cdcbcadd', 'caacbcdc', 'cadacaba', 'bbcbdcad', 'daccbddb', 'cdacdbca', 'daacdbdb', 'cddccbba', 'cbdcaabd', 'bdadcacc', 'cdadbcca', 'acbcadcd', 'ddcbbaaa', 'ddbacaad', 'ddcacdbd', 'dacabdcd', 'dccacdab', 'acdddbba', 'abcaccda', 'abbacadd', 'bdcbcdba', 'dabacdba', 'adabaddc', 'ccbabccd', 'cabdbbdb', 'caddbaac', 'cbbdcdda', 'cbcbdcba', 'dcddbbda', 'cadbdbdb', 'bacbddbc', 'bacdacac', 'dcbbdcda', 'dcdcabda', 'badadacc', 'cdbbabda', 'abccdabd', 'cbdbdbad', 'ddadaacb', 'ccbabadc', 'dabcaddb', 'abcabdca', 'bcaacdcd', 'dcdabadd', 'adabdcab', 'bdadbcbb', 'ddbddcba', 'babbccdd', 'dbadccdb', 'aacdbccb', 'cbdbbabc', 'adabdddc', 'babccbda', 'bcaddbdb', 'cabbcdca', 'bdddbacb', 'dbbacbdd', 'bcbbaadb', 'dabcadca', 'cbabcada', 'bddcdcda', 'bdadacbb', 'dbcdbcaa', 'bddabbdc', 'bdbacbdc', 'adcdbada', 'baadccaa', 'aacdbbdb', 'badabcbd', 'baccdcba', 'bdcbaacd', 'ddcbbacd', 'ddaccabc', 'adbcbcdb', 'cdabccac', 'dcbacabc', 'badbdcdd', 'bdacbcca', 'dacddbda', 'bdcbaabc', 'bcacaccd', 'dacbcabb', 'baabdcaa', 'dcdcacbb', 'cdcbaaaa', 'adcbcbab', 'dbcbcadd', 'bdcacdcd', 'cddbccda', 'dadccbcd', 'dcbbddad', 'baccbcad', 'adcadbdb', 'acbcdbcc', 'cbacbdda', 'dbacbbca', 'bcacdcbc', 'bdcbcacb', 'ddcaabdd', 'abdccada', 'abbaccdb', 'adacaddb', 'ddddaccb', 'dddacbdb', 'ccacbddd', 'bcdbdadb', 'bbabcdcd', 'cdcbbcac', 'ddacaabd', 'bbccacdc', 'dbcacbba', 'dcbdbaca', 'cbaddcdd', 'dabcdcbc', 'ddabbaca', 'bdcdcaad', 'adcdbdbb', 'cacdacbb', 'adbdbdac', 'adcdbadd', 'cbcbacda', 'bcbddaad', 'bbdaadcc', 'bacacbcd', 'bbadbacc', 'acbdbcab', 'dcbdcdca', 'cbdbabbc', 'dbddbabc', 'dcdbddba', 'cbbadcca', 'dadbcacd', 'acabccda', 'bbcddadb', 'cbbcbaad', 'cbbdabca', 'addabadc', 'aaaabdcd', 'cdacbddd', 'daabccbc', 'bddabaca', 'cadddadb', 'bcdabcbc', 'adbbdadc', 'cddcbcab', 'dcbdbadb', 'dccdabcd', 'abdccabc', 'dbdcbbad', 'abdabdcb', 'adabbcbb', 'dbccbaad', 'acbabbdb', 'babadbcb', 'ccdbabab', 'dacabcda', 'cddadbdd', 'cabcdacb', 'acacdbbd', 'bdbdbcda', 'cbacddad', 'adbaddcb', 'cddbaacb', 'bbdaaccb', 'acdcadbc', 'abbcdadb', 'bacdddaa', 'bcbcdbca', 'addadbbc', 'cdacddba', 'dcdabcbb', 'bbddcbac', 'cbdccdaa', 'abdcadbc', 'dcbabdcb', 'adcacaba', 'abdcabca', 'dcadcbbc', 'abcbddbd', 'acdcabba', 'bdccdadb', 'acadddbb', 'bbdacadd', 'dbabccad', 'cadcdabb', 'cddcabdd', 'bcddaaca', 'ccbcdabc', 'bcbaacbd', 'ddbadacc', 'bdbbcdda', 'adbdccbd', 'badcaddb', 'dbbacbca', 'dbbcdbda', 'bacabbdb', 'cbdaccab', 'dbdcbdca', 'daccacbb', 'bdcdddda', 'dbaaccbc', 'abdbbacc', 'cdbcadda', 'dabcadcd', 'adbccdac', 'dcddcabc', 'dccbdbda', 'bcacbcdb', 'dcdbcdda', 'bbcadbcd', 'cbdabdcd', 'cdabddcd', 'ccdcabad', 'bacaccad', 'caddbcbd', 'cbdccaab', 'cbdbccaa', 'cddcabdc', 'cddccbad', 'ddbaabac', 'adbbccad', 'accbcdca', 'cbdabcda', 'bbcbdaad', 'dcdccbaa', 'dabdbbcb', 'cdbcdacb', 'bcababcd', 'cddaadcb', 'abcbcbdd', 'addabbac', 'adcbacca', 'bdbabcdd', 'cacdddbd', 'cbbdbdda', 'dacbdccd', 'dcddbdab', 'cbaccddd', 'ababacdd', 'bdcaacbb', 'addcbbca', 'dacbdbba', 'dddbdcab', 'dbcabbcc', 'cacdcbdd', 'bdbcacca', 'dadbdcab', 'aadbdccb', 'bdbdcdac', 'cabdcdcc', 'bcdadcdc', 'daabbcaa', 'dabbdcbc', 'dadcbcba', 'cddbacca', 'cabdcbcb', 'abcbdbdd', 'cbadcdac', 'dcbdbcab', 'cbdbabcb', 'ccbdaccb', 'ddcbcdda', 'bcacbada', 'dddbdcca', 'bddaacca', 'bbdcacba', 'bcbadbbd', 'acbccddb', 'abacacdc', 'bdbccbaa', 'bcbadbdb', 'ccdacbcd', 'dadbaccd', 'cdccbadd', 'caadbcdb', 'adabacdd', 'adacbabd', 'ddcdabdd', 'dabacdab', 'ddbabcac', 'cacdbacd', 'dbcdaabc', 'dbcaabcc', 'daabdcbc', 'cbadcdcb', 'dacdcbab', 'bbadcadc', 'cdccbbca', 'baaaacdc', 'dadbccbc', 'bdcdacab', 'abadcdca', 'cdcbcaab', 'cbdabdbd', 'bcdcdbaa', 'dabbddac', 'cbdadaca', 'dddbadcb', 'dbccdabd', 'dcabdcdb', 'dbdadcdc', 'abbcbddc', 'bcadcdda', 'dbbacbac', 'bcacadca', 'adbdaccd', 'cbbdccac', 'bacdabbc', 'ababcabd', 'dccdbcac', 'bbdaddcb', 'dcdbcaab', 'cdadccbc', 'badcabbd', 'cdbdabad', 'ccbcddba', 'dbbabcad', 'daabbcbb', 'bddaacac', 'dcaabcaa', 'babdcdcd', 'dacbcdac', 'bbacbcdd', 'baacbdcd', 'bdadcbcd', 'bccbdcab', 'cbbacbdb', 'aabaadcc', 'ccbbcacd', 'dbadbbca', 'abacadda', 'bddacaac', 'bcbbdbab', 'babdbcad', 'acdcbbdd', 'acaddacb', 'bddacdda', 'bdcbaadb', 'dbbcdada', 'cadbdabd', 'cdaabcbc', 'acdcbbda', 'bbdacddd', 'cbcdbbda', 'dabddccd', 'cdbcdcaa', 'bcaddaac', 'dcacbadc', 'abcbabdb', 'bdabddbc', 'abdadacb', 'cddbddab', 'adbacaca', 'dabcbbda', 'bcbdaddb', 'dccbdcaa', 'cabbadcd', 'dccaacbb', 'bdbdaccd', 'aacbcdbc', 'cbadccdd', 'dcbacacd', 'cddacbac', 'babdbacb', 'ddbadbcc', 'cbaadcbd', 'addccbcb', 'accddadb', 'ddbdcdda', 'cdaabdbb', 'aaccbdcb', 'acbcabad', 'cacbbddb', 'addadbac', 'bcdccabc', 'ddbadaca', 'bcbbdcba', 'cdcdbadd', 'dacddbdc', 'acddbabd', 'bbaaccbd', 'abdacdcd', 'bacbdbac', 'cadcdabc', 'cadbcdca', 'bdcacacb', 'cbabdbad', 'cdabddda', 'bcdcbdca', 'aabcdbdc', 'adcaccbb', 'bccdadcc', 'bacddbda', 'dadcbabc', 'badccabc', 'cdbadbbd', 'ddbcdbac', 'abdddaca', 'ccbbabbd', 'dcbdcbac', 'cbbdddba', 'dbdbddac', 'acbdbadc', 'acdddacb', 'ccbcbabd', 'dddbbdac', 'cdccbdab', 'cbdbcdab', 'babbcbda', 'cadadcbc', 'bbdbadcb', 'babacada', 'ddcbcaac', 'cabbacdc', 'dcabbccd', 'bdcaaaac', 'dbdcbdda', 'cbdcbaac', 'cddbbaaa', 'bdcbadad', 'abcdaccd', 'abcddbba', 'abacdcad', 'adcdcabd', 'cbcbaccd', 'abccdccd', 'cadabaca', 'adcdbadb', 'abcbcdbc', 'ddddaacb', 'cacbbcad', 'abdcdcdc', 'ccdabdbc', 'dbabcbda', 'dccaabcd', 'ccabbccd', 'dbaacdbc', 'dbcbcacd', 'dacabdad', 'dcbccabb', 'acdbccdb', 'cabababd', 'dcabcadd', 'ccabddcd', 'ddcdaacb', 'bcbcdada', 'abddbddc', 'bdccaccd', 'bbdaddac', 'ddbcdcaa', 'cdbcbadb', 'abdbdbbc', 'dbadbcba', 'dbbadadc', 'babcbada', 'dbddcbad', 'bdccadcd', 'dbbcdbad', 'abbcbddd', 'bbdacbca', 'adcbdabb', 'babcadbb', 'cdaabbdc', 'bdcddabb', 'cbacdbbc', 'bbacddaa', 'dadcdbcb', 'bdadccdb', 'ddccdaba', 'ccbaccdb', 'addcaaba', 'ccdbabbd', 'acacadbd', 'badcbcdd', 'dcbacabb', 'acbbccdd', 'ababbdbc', 'dbbcacba', 'cbbcdadc', 'acdcbdcc', 'bcdacbab', 'cdacacbc', 'acbcddab', 'acdbbaca', 'ccdbbcad', 'cbddacbc', 'cbbdadab', 'dcdbcdaa', 'acdacbdb', 'acbcabdc', 'bcdbadba', 'adcabbab', 'cabdbcda', 'badbacbd', 'cabcacbd', 'badcbcbd', 'bddccbab', 'dabbccdd', 'bdabccba', 'acbbccda', 'daddcdbd', 'ddacdabb', 'ddcabdad', 'dcacdacb', 'cdbbacba', 'cbadbbab', 'dddbcbab', 'abdcbcdd', 'adcabcac', 'dacabdab', 'bcdbbdad', 'bdacbcdd', 'ccacbcad', 'cabcbcbd', 'dcabacbc', 'cacacbdc', 'bcdacadd', 'bcadbdca', 'abdacdba', 'adadbdcc', 'bcbccdba', 'dabcacbb', 'acdcddbb', 'cabddaad', 'bdbcaddb', 'babcdcad', 'dbaacdaa', 'bdabcbda', 'ccbdabbc', 'bcaddaad', 'dddbcadd', 'dbabacad', 'dddcbacd', 'cdbcadbd', 'bbaccdbb', 'dddddcba', 'adcdccba', 'ccbacabd', 'adccdacb', 'dcdbcdac', 'adacacdb', 'cdcacbba', 'adbacdac', 'bdbddcad', 'bcbbdabb', 'dcacbccb', 'dcdadbca', 'cddddbba', 'ddbbadcd', 'bbcddaac', 'bbdcdbca', 'cdcbabad', 'accadaba', 'dabddcdb', 'dacddbdb', 'ddbbdacc', 'aacbdccd', 'bdbcaccd', 'cbcdcadd', 'acaddddb', 'dccbdabd', 'ddddbadc', 'dbaacbcd', 'cdadccbd', 'caddcbbd', 'cabbadcb', 'cbabdddb', 'acdabadc', 'dacdbdda', 'cdcddcab', 'bbdadbac', 'cbbdacca', 'dcbbacbc', 'ddccbcac', 'abbcabda', 'ddadbadc', 'dccbcbad', 'bbacdcad', 'bcdbadbb', 'ccdbadbd', 'cddcbdda', 'badacbbc', 'dddcdbad', 'dcdbacac', 'bdcddaba', 'cddbaabc', 'dababbca', 'cadaccba', 'acbbdacb', 'acbbcdac', 'daaccbcb', 'dbcadbca', 'cdcddaab', 'addcabad', 'dbcbbcac', 'adcdcbdc', 'ccdaccdb', 'abdcbadc', 'dcbcbbad', 'badbdcdb', 'baccbccd', 'bbabdcbb', 'ccacbbdb', 'bcbbaacd', 'abcacdda', 'adbabdcb', 'ddbadabc', 'dbbddadc', 'dccdacbc', 'adcdbcad', 'abbccabd', 'cdbabacc', 'dabcadbc', 'cbbaccdb', 'dcbbcadc', 'cbcbcaad', 'abdbddcb', 'cdbaadaa', 'bcadbdab', 'dabcabbc', 'dbccdcab', 'adbcbcba', 'bccdaddb', 'acdbbcbb', 'dcaddcba', 'bcbabdbd', 'adccacdb', 'cddcdbad', 'addccbdd', 'bcbdacdd', 'cdadbacd', 'dbcadcca', 'bbdacadb', 'bcdaacdb', 'cadbabcb', 'ccddbaad', 'bdbccacb', 'ddadbcda', 'bbaadcbc', 'abdabbdc', 'ddbddcac', 'dacdacbd', 'bbcadbab', 'acbbacda', 'caddccbb', 'dbbdcaca', 'dbccadca', 'ddaccdbd', 'bbabdcdb', 'aabdccaa', 'ddbadcdb', 'addcacba', 'dbacdbcc', 'bdabadcd', 'dacbadca', 'dcbbadbc', 'addacadb', 'abbddcdd', 'bdbccdab', 'dabcbaba', 'dbadbcbc', 'badadccb', 'dddbcaaa', 'dababcac', 'ccbbacbd', 'cdaaccbb', 'bdaddbbc', 'bacbadcc', 'adababcb', 'aabdbccd', 'adacdbba', 'abdcdbad', 'ddccacab', 'cdcdbbca', 'bcbdadcb', 'cdddbdaa', 'bcbdcabc', 'dccbacca', 'abadccad', 'bdacabad', 'cdaccabc', 'ccbdbaab', 'dcdbdcba', 'dcbddabc', 'ddbdabdc', 'bcadacac', 'cabdadca', 'bbaacaad', 'bdacabca', 'cadddbcd', 'dabddbac', 'dabcdcbd', 'ddbcbbda', 'abdcbdcb', 'dccdbdab', 'bacbbadb', 'accdcdbb', 'dabdcddc', 'cbbdddab', 'bcdabbac', 'bcabdaba', 'bdcdadbc', 'cacbcadb', 'cbbdacbb', 'babcddbb', 'acacbcda', 'ddacbdca', 'babccdda', 'dccbaddb', 'acbdbacd', 'ccdcdaba', 'cadccaba', 'dabdcdba', 'dcdcbadb', 'cdcabbac', 'ccabccdd', 'dacdddab', 'bcddbbab', 'cadbcbac', 'adcabbcb', 'bbccdbaa', 'adcbccbc', 'ddbbcacd', 'addcabcc', 'accddbbc', 'cbabdbcc', 'adcacddb', 'cadbdaca', 'dcbcaddd', 'bddcbdac', 'cdadacbc', 'dcaadcbb', 'cbabdbda', 'bbcaddbc', 'cbdbabda', 'acbcdadb', 'bcddbacd', 'cdadabdc', 'badddacb', 'cdbadddd', 'bcdbbcaa', 'abadbcbd', 'bccabddd', 'cababddb', 'abddacda', 'bacdacdb', 'dacadbda', 'bbdccdda', 'dababacb', 'abbcbcdb', 'abcbbccd', 'acacbccd', 'bcdbcdac', 'ccaabdcc', 'dcabccbd', 'abdcadcc', 'bddccbad', 'bacaddbd', 'abbdddac', 'ddcddcba', 'bbadcada', 'daccbddc', 'bbabdacd', 'cbabadab', 'dcacdabb', 'bdcdabbd', 'adbcadca', 'abbabdca', 'abdadcad', 'cbddcbab', 'dcbdcbab', 'cddbaaad', 'adddbdbc', 'bbdccdaa', 'adbdcbca', 'acbbadad', 'caddadba', 'bbacbabd', 'ddaccabb', 'cbcbcbda', 'aaccbdbc', 'cabddddc', 'cbcaddab', 'cbdcdaab', 'ddcbacbb', 'bacdbbda', 'dacbbabc', 'bbabbddc', 'bacddadb', 'bdbcabcb', 'cbdcdbba', 'cbccdabd', 'bddaccdb', 'bdadccac', 'bbaddcba', 'acbadbdb', 'ccaddacb', 'dcbcaabb', 'dadddcbd', 'bbcbcdba', 'bacbcdab', 'dcbdadbc', 'bacdbdcc', 'bacdddad', 'cdadbdca', 'acbbadbc', 'dabcbdbd', 'dbcbbdca', 'cabbccad', 'bccbbabd', 'dabadcca', 'abdcddbb', 'babacdcd', 'bdddbaac', 'bdcddbac', 'ddbaadcb', 'adacacbc', 'caadcdbb', 'caddbddd', 'cbdbbcda', 'cbdddadc', 'bddabccd', 'bdadccbb', 'abddabca', 'dcbccadb', 'abbabcbd', 'abbccdca', 'dacbcacc', 'abbdcacc', 'cdbababd', 'cbcadbab', 'ddbdcaba', 'acddabdd', 'badcdcdd', 'dbadccab', 'ddcddabb', 'acacbcad', 'acdbcdab', 'bdcadcda', 'abbccbdb', 'bcdddabb', 'caddbaad', 'addcdadb', 'dcbbcaba', 'adbbacca', 'bacbaddd', 'aadccbbd', 'cabacdbd', 'cbcaddcd', 'bbcabdcb', 'dbdadcad', 'cdcbdbca', 'ccdaaaab', 'dcacbcbd', 'ddbdcadb', 'dddbdacb', 'dccbacbd', 'dacbacdb', 'cbdaabaa', 'bbadcadd', 'acbddadb', 'bcdddadc', 'dcacabcb', 'ddaddcab', 'cabaccdb', 'bcdaddac', 'bcbdabcc', 'bbcddcac', 'aabccdbb', 'bccdacda', 'bddadcca', 'dababbac', 'cdccbdca', 'abdacadc', 'dacabada', 'cbabcbda', 'ddadccbd', 'dcabccbb', 'dddbcbba', 'dabcdcdd', 'babbdbca', 'cbccabda', 'ccacadba', 'cddbbcba', 'bcaddcbc', 'abcbbdab', 'bcbcadda', 'bccdbaab', 'dcddbacc', 'cbbdcaca', 'ccdaadcb', 'acdbcdba', 'bcbdadab', 'bbcdaacc', 'acdbcaba', 'dabbccba', 'ccdadbdd', 'bccdaacc', 'dddbcada', 'dcdcbbda', 'bdcababc', 'cbcdacbd', 'ddbcabca', 'bcadbcda', 'dbbadcda', 'ddccadbd', 'cadcbdbb', 'ababdcbd', 'acbdadab', 'cdbdbaac', 'acdcbabc', 'bdcbddab', 'bdaacaac', 'adaccbac', 'adbccacb', 'bbddbcba', 'dcbdaccb', 'abdbdadc', 'abdbccbd', 'cdddacab', 'cacadbcb', 'acdbacdc', 'bdcdaabc', 'ddbaccbc', 'cdddcbad', 'abaddcab', 'cdabcabb', 'bbdadbbc', 'bdccdaba', 'aadbcdbc', 'ddaaabca', 'cbcabbdd', 'ccabcbcd', 'cdcabadd', 'babbdadc', 'cdbddbda', 'ccdbbcca', 'dababdca', 'cdabbcab', 'dcbcabac', 'caacdcbb', 'dbdacada', 'bbdaccba', 'dcadabbd', 'dbadbcbb', 'bbdadadc', 'bcabdcad', 'dadcbbdc', 'dbabbcbc', 'cbbddabc', 'abddaabc', 'bdacbcba', 'acbdabba', 'bdcbadcd', 'dcdbcabd', 'bdaccdcc', 'acacdccb', 'dccabacc', 'adabddcd', 'adbccbab', 'dbdabccd', 'cbdacdca', 'cdadbadc', 'cdbbaddb', 'bbdabbcc', 'abcdcddb', 'adabcbac', 'ccbcadbc', 'adccddbd', 'dcbacadd', 'dbabbdbc', 'dbbaacdc', 'acabbddb', 'abacdabc', 'adbcdddb', 'cbbaabdc', 'bcabbdcd', 'cadbcdbc', 'aabaadcd', 'cadbbcbb', 'adddcddb', 'dbcbcbac', 'dbbcadcd', 'cdbdbacc', 'accdcbdc', 'ccbbdaab', 'ddcadbba', 'cbcacdcc', 'dcadbdac', 'cdcbbcca', 'dcabbacd', 'ccdbdcab', 'bcdabbad', 'ccbaabcd', 'bcadddda', 'cabbdccd', 'bdcddcca', 'dabccdbd', 'bbcaccdc', 'aaaabbcd', 'abaddcad', 'badddcdc', 'ddbbcaab', 'acdbbdca', 'dcbcaacc', 'bdaccdab', 'bcbacbbd', 'ccacbbda', 'abccbcdd', 'adddbcdc', 'abcbdbcc', 'dcbdccaa', 'dbcbcdad', 'dcbdadbd', 'dccbdcba', 'acbadbcb', 'cadabdca', 'babacdba', 'dbabcacb', 'acbdcdab', 'cdcacbad', 'bccbadba', 'adacdabd', 'bacddbcd', 'cadcbabd', 'cbababda', 'cbadadbd', 'abcdbacd', 'cbbcdaac', 'accddacb', 'cacdcdbb', 'abadbacb', 'dbdddabc', 'dcbccaad', 'bcacdbbd', 'bcabdbab', 'dabbacad', 'dbbaadcd', 'bbaddcbc', 'badbaccd', 'cdcabdba', 'cbbccdaa', 'abbcaccd', 'cabcdada', 'bbdddabc', 'baadcdcc', 'cdacbddb', 'abcacdba', 'acbdcbdc', 'adcadddb', 'dadcdbac', 'dddacdcb', 'abcdcbab', 'bbdddcad', 'abdbdbdc', 'ccdbbdba', 'adbbacbb', 'cbddadbd', 'babcbddd', 'bacbadda', 'abcabdac', 'acbdddcd', 'abdccdbc', 'bbdaacdb', 'acdadbad', 'dacbdbbc', 'acdabadd', 'ccddbdda', 'bccbbdba', 'bacaddba', 'baddccac', 'cabacacd', 'daccbccb', 'bbccacdb', 'acadacbb', 'ddaddbdc', 'bccddbab', 'cbdaddcd', 'abddcaba', 'dbbdacac', 'dcbccada', 'bcdadddb', 'dadcdabb', 'bcbbabbd', 'ddcbddab', 'cdcdabdb', 'ccacbdad', 'acbadbba', 'cddcadab', 'bcbbcaad', 'cdbcdbab', 'bbadcacd', 'dbbacaca', 'adadcbcd', 'bbacdacc', 'abcbadab', 'bacdbddb', 'adadbcdb', 'bdaacdcc', 'ddcbccda', 'abbcbacd', 'dabacbab', 'acabccdd', 'abbddcda', 'bddccdab', 'bcdccbca', 'dcbabcdc', 'dadbabcc', 'bdbdacda', 'ddcbcabd', 'adbaddbc', 'acdabcbc', 'dacdbadb', 'ddbabdcc', 'dbcdadba', 'cacbcacd', 'accbcdbc', 'bbacacdd', 'bbacdbbd', 'bdbcaddd', 'bacdadba', 'bbdbaadc', 'bddbaadc', 'cdcaddba', 'bbacdcda', 'cadabccb', 'bdcaadaa', 'dabadbdc', 'cabccbdd', 'cbaddbba', 'aadbcbcb', 'cadcadcb', 'babcaddd', 'bcadbdbb', 'bccdcacb', 'bbaccbcd', 'ddbbcabb', 'dabdabac', 'cbdaccbd', 'bdcacabd', 'adadcbca', 'aabcdccb', 'accabacd', 'bbdadabc', 'adcbdbdd', 'bddcabcd', 'ccdcdcba', 'adcabcdb', 'abacddad', 'cbddaaaa', 'cdabcbca', 'cddabacc', 'cdbddbca', 'cbcbadbc', 'cbbddadd', 'bbdccdab', 'cdbbdaba', 'cdbadada', 'bcabbdad', 'acdcbadd', 'abcadcdb', 'ccbadbcd', 'ccdbcbac', 'bddbccab', 'dcdbabdb', 'ccbddbad', 'dddcadbc', 'abbdccbd', 'aabcbdaa', 'bbdcdadb', 'baaccdbc', 'cbadccdc', 'ccbabcdb', 'adbccdba', 'cbbacdbd', 'cbdbcbaa', 'bddbacab', 'adabcbad', 'dbdbcaba', 'ccdbbdab', 'abcdacdc', 'cdaaaabd', 'dbcadacb', 'ccdcdaab', 'cabdbbcb', 'babacdcc', 'bbacadbd', 'aadbccbb', 'abdcdddb', 'bddbbcac', 'ddadccab', 'dbddadcc', 'dcdbabda', 'cdbdaacc', 'acacbadb', 'aacdcdbd', 'bcacbbdb', 'cabdddcc', 'cbacdbcd', 'acbcbacd', 'bddabacd', 'bbdbaacd', 'bccdaaaa', 'abaddcac', 'dbccbbaa', 'acadadab', 'cbadabbd', 'adbccbbc', 'ddbbaadc', 'cacacbcd', 'cdadcbdc', 'ccadabbc', 'ccbddcad', 'bacacddc', 'bbdccdad', 'cbacadad', 'ddcabcbd', 'abddbcdc', 'cddadabb', 'dbcacbbd', 'cdbddaca', 'dcbcdadb', 'cddbabbd', 'cdacbadd', 'bdcacddb', 'abdabadc', 'addcacbc', 'cabccdba', 'accbcddd', 'cbdacbda', 'bdcbacbc', 'cdccaabc', 'cdabbddc', 'ccdbaadb', 'abbcacdc', 'abddcaca', 'ccbacada', 'dddabccb', 'ccddbbad', 'cacbcdbc', 'cabdcbcc', 'cdcbbadd', 'abcabbad', 'bbdcdaba', 'badcacac', 'dbcdcabd', 'adbdcbcc', 'ccddaccb', 'abbdcaba', 'ccddbcda', 'abdcdaba', 'abbcdabd', 'babddcac', 'dccacbab', 'dcdbadab', 'acaccbdb', 'cbcdbacd', 'dacdbbcd', 'cadbccac', 'bcadaccb', 'aaccbcbd', 'adcbcbad', 'bdacdbab', 'bbdacdcc', 'acaddcba', 'dbcdddad', 'adcddabd', 'cdabacba', 'cadddbac', 'cdabdbdd', 'ddddabac', 'bcdcbacb', 'dccaddbb', 'baaccdaa', 'adcaddab', 'bdbcdaab', 'dadcadcb', 'bdadcdac', 'dcbbacab', 'ddbcacbb', 'cabddcca', 'cbcdbada', 'ccaccbbd', 'cacbdbdd', 'cdbccaba', 'bacbddab', 'bbacbbad', 'dcbbabcb', 'dbbdadcb', 'cadbcddc', 'bcadcbdd', 'bcdaadbd', 'ddacddab', 'cbcdbdab', 'cdbbdcca', 'ddbacbcc', 'dacadcdb', 'cbcbcdaa', 'cbbdbdca', 'ddbdbcca', 'cdcbbcab', 'abcdabcc', 'ccabccbd', 'caddbdba', 'abcdcdbc', 'cadcabca', 'badabbca', 'dcdaabcd', 'ddccbbab', 'acdbbcbd', 'bcabddbc', 'adacbbdd', 'babdacdc', 'bacdcbba', 'bdbadccd', 'cbabadca', 'dcbabbad', 'caadbaab', 'dabcdccd', 'dcdcbcac', 'ddababac', 'dbcabdbc', 'dabbdbac', 'cbdcadbd', 'adaddabc', 'ddaabbcc', 'aacdbcdc', 'bcadcbda', 'baccbdcc', 'dacbdcda', 'ccabdddb', 'dbbdbcda', 'acbaddca', 'bdacdddb', 'dacabbdb', 'adcacbac', 'bcdbabdc', 'dbadcbcb', 'bbadcbba', 'cbccadda', 'cddaddbd', 'addbbcdc', 'ddbdcabb', 'dacdcadb', 'cdbcbdda', 'acadccab', 'baccacdd', 'cbccbdaa', 'abccdbcd', 'caddbbdd', 'baccbcdc', 'dbacbcac', 'dacbddaa', 'cacabcdb', 'accbdbac', 'adbabcad', 'cdbdcabd', 'ccbacdbc', 'cbadabda', 'dcbddadc', 'dcadcbcc', 'ccbadabd', 'acadcbda', 'adbcbbad', 'bcadddbb', 'adbaccad', 'bacddabb', 'cddcdaba', 'badcdcdc', 'bcdbbadc', 'dabadadc', 'abbcbabd', 'bdddaacb', 'accdacbc', 'addbbddc', 'cadcacbb', 'caacbbdc', 'bcbcddca', 'dbdacdcb', 'babddcdc', 'bddbdadc', 'bcdcdbca', 'badddcbb', 'ddabbddc', 'dddbadcc', 'bbcaadbb', 'bbadbcbb', 'baabdbdc', 'dcabdcba', 'dcacbaba', 'dbdcdcaa', 'dadabacb', 'cbaacdcd', 'bdaddcdc', 'bbdbdacb', 'badabbcb', 'dbbdccba', 'abbcddcd', 'dbcbbadb', 'dcbbacac', 'ddbbccad', 'adabcacc', 'abcabbdc', 'bcdaccdb', 'daddcacb', 'adbdcdcc', 'dcbdbaab', 'ddcabbca', 'bbdbdcba', 'bbcbccad', 'dccbcabb', 'dabaccdb', 'ddbdcaad', 'cacbcdbd', 'dbdcdadb', 'bdbddaca', 'cabcbadb', 'bcbcaddb', 'dcacbcbb', 'abcddbcd', 'ccbcadcb', 'cdbdccaa', 'dacbddba', 'addccbab', 'bdacdabc', 'cbcdbaca', 'adbcbaba', 'bbdcabdc', 'badacdcc', 'dbbabdcb', 'bcdbdaac', 'dcadbcca', 'daddbcdc', 'dbdcbdab', 'abaccada', 'dccabbad', 'dccbcacc', 'abadccbc', 'dcdabcdc', 'dcbdddaa', 'dbcbdacc', 'dccdabac', 'abbccacd', 'bcabdcca', 'ccaccdbd', 'aacbdbcb', 'cdaabccd', 'baccacda', 'dbacadad', 'ddccbdca', 'bcaddbda', 'adcbddac', 'cdbbddab', 'cbcadabc', 'babcadcb', 'bbcbadac', 'acdbccbd', 'cdbaacbd', 'acddddcb', 'cdccbaab', 'dacdcaba', 'cdcdbabb', 'dcaddbdd', 'ababdcbc', 'bdcacddc', 'abbdadca', 'accabdda', 'ccbcdaac', 'addcaccb', 'adabcadd', 'cdbdbabd', 'bcdbadca', 'cddbacad', 'baacbdcc', 'accbbcad', 'cabcdabc', 'dacdccbc', 'cbbacacd', 'dcdabbca', 'abadbdcc', 'dbadacbb', 'bbdbbcad', 'bcaccabd', 'dcbcacad', 'dbdbccda', 'bdcadbdb', 'accddbdb', 'acdabbcd', 'dbbdaacd', 'badcdcab', 'baabbcdc', 'ddabdcbd', 'bdadacab', 'acabbcdd', 'bacdacba', 'ddbacdab', 'cdbaabbd', 'cadbcbcb', 'dbabcabb', 'adbcacac', 'accdaddb', 'adccbabc', 'baccadcb', 'bdcadcdd', 'cddabdab', 'dbbacada', 'bcbcadcc', 'ababbdcc', 'cdcbabda', 'cbdabcba', 'ddaabcdb', 'cddcabdb', 'dddbccda', 'ccbdcbac', 'abadabca', 'dcabdbab', 'ccbcdacb', 'dccabbdd', 'dccbdadc', 'ccbaddaa', 'dcbcdaab', 'acdddbdd', 'abcbdbdc', 'adadcdba', 'adabadca', 'ccabcddb', 'bdcabbdc', 'cbbabcdb', 'cacacdba', 'cddadbac', 'bacacdab', 'adcbacab', 'acdbcbbc', 'daacbccd', 'ddbacadb', 'bddcabaa', 'bbdbcaba', 'bdababca', 'acdcbcac', 'bcbabdcb', 'dccabacb', 'dabdccad', 'cdbdabdb', 'ccdddbad', 'aadbdbbc', 'acdcbcda', 'dcabbcad', 'ccbcabcd', 'cddadbbd', 'caaccdbc', 'bcaddcab', 'bcdaaaac', 'dbbcdabb', 'ddbaacca', 'dadcbacd', 'adcdbcab', 'cacbdbac', 'badcdcba', 'bcdcadab', 'cabccdcb', 'addbdacb', 'dbacdcda', 'bdaadbbc', 'abaccadd', 'ccdddbab', 'cddcbdab', 'dacdcdbb', 'cbcdddad', 'dcadbbcb', 'bcbcddda', 'bcbabbdd', 'dcbacdba', 'cdadcabb', 'aacbdbdc', 'cbdaadaa', 'bbddcdab', 'cdabbdbb', 'bcaddcdb', 'cdbaddab', 'bcadacdc', 'bcdcabba', 'ddaadcbd', 'dbcdaddb', 'bacddadc', 'dbbdacab', 'dbddaacb', 'bccbdbca', 'acadcadb', 'bdacbdbc', 'dbbdbacc', 'adddbbca', 'dacdbdcc', 'cdbddadb', 'cdbdabba', 'dbacdddc', 'adcddbda', 'bbaddaac', 'ccadcdcb', 'acdcacba', 'dbaabdbc', 'acbbdcdc', 'ccaadcdb', 'abdbcbcc', 'abcdccbc', 'ddbbabcc', 'dcadbcab', 'ddbdcadd', 'abdcbcda', 'cbddcabc', 'bccacdad', 'dcbdadcc', 'cbabcdbd', 'bddbadac', 'bcdadcbc', 'dcbcdcac', 'bbddcacc', 'ddcadaab', 'baaccdcd', 'ddbbacdc', 'bcddabda', 'cbdbdbda', 'dccabdbc', 'badbcdca', 'bdacbcab', 'dcddbada', 'cddaddbb', 'ccabddcb', 'badbcabd', 'cbcdaacb', 'babcdddc', 'cbbddadb', 'dbbddabc', 'acadbdca', 'adbccbbd', 'abcddabc', 'acbcbdcd', 'daccaddb', 'daddabbc', 'abcddbdc', 'ccdabcbb', 'dbcabadc', 'acbdddcb', 'ccdbccaa', 'dabdcdcd', 'baddadcd', 'bdacbbdd', 'ddcadcab', 'bdbbacac', 'ccdacabb', 'adcbacad', 'cacbbcdb', 'abddacdb', 'dacddbcd', 'cbadabcd', 'dcbccacc', 'bddadacc', 'dcbadada', 'dabdbabc', 'cdacdadb', 'ddbbdcca', 'cdbadbdc', 'dbacdbba', 'abcadadc', 'dbbcbcca', 'ccacabdb', 'daabcaad', 'cacbadcc', 'cacdbdbd', 'badbbdcd', 'acdabdda', 'dddabaac', 'dbacadcc', 'cddabdca', 'ccdaddba', 'cbaadaab', 'dbdbbcca', 'addddccb', 'addcbcab', 'bbdaccdc', 'bcabdcdb', 'ccbdcacb', 'cdadadba', 'dddbacbb', 'acddbccb', 'ccdabdda', 'ddbccadb', 'abdddbcb', 'dbaccbbc', 'cdacadbb', 'cbdccaad', 'addcadba', 'badcdbcb', 'ccbaabdc', 'cdbddcad', 'accdccab', 'ccbddaab', 'adddacdb', 'aadbaadc', 'bcbcbdba', 'cadccbcc', 'dcbcacdc', 'cbbcaabd', 'cdbcbabc', 'ddbabcdc', 'bccadddd', 'cadddabc', 'dbcacddb', 'ccbbdadb', 'cababdba', 'cabcaddc', 'ccbddcaa', 'dcbbadba', 'acadcabc', 'cbaabbdc', 'cabdddcd', 'dabadcba', 'accddcdb', 'cdbaccba', 'bbcdaddd', 'dbabccdb', 'cabbadbb', 'bddcadbb', 'bccadbab', 'adacbdda', 'bacdbbdb', 'cbdddada', 'adbaccbc', 'bcacdcac', 'bcbaadcb', 'bddcaadb', 'acbaddcc', 'bddcdaac', 'bddbacba', 'cbabcdba', 'ddbccaca', 'acbddbbc', 'abcddbab', 'dcbcbdca', 'addbcdba', 'baadcbdc', 'acabcddd', 'bdabcabc', 'bdbbcabc', 'adcbcdcd', 'acbadacb', 'dacabcca', 'ccdcbdac', 'acdcaddb', 'aabbdccd', 'dcddacba', 'cacabdcd', 'badcddcc', 'dddbacab', 'dcadabab', 'cbccadca', 'acbbdcba', 'baaaabcd', 'cbcadabd', 'bcadbcab', 'ddbdcdaa', 'cdbbadcb', 'dbbacbcc', 'babadabc', 'cdbdbbad', 'bdddacda', 'cabddccb', 'bcabdbdb', 'dddabcbc', 'bbdadcda', 'dcdcdbca', 'bbdcbdca', 'cbabbcda', 'cadadcdb', 'dcadcbcb', 'ddbbacdd', 'cabbddcd', 'bcaddadb', 'ccdaabcb', 'abacbdca', 'abdddcba', 'cabddadd', 'dadadbbc', 'cbbcddda', 'ddcacabd', 'babcaddb', 'babccddd', 'ddcdddba', 'accdcacb', 'cbaddabb', 'bdcbccda', 'dacbddca', 'dccbccac', 'bddcbbac', 'abcadbcb', 'ccdcbaad', 'bacbcdbb', 'ddbacdbd', 'bddbbdac', 'ddaacbdd', 'acabcdda', 'bbcddbda', 'dbbdacad', 'cadddabb', 'bbababcd', 'dbaabdcb', 'badbbaca', 'acbddbab', 'cadbaccb', 'cbdabdac', 'aadbdbdc', 'cdcabcda', 'bdaddcdb', 'ccababda', 'cabccdcd', 'bacbaddc', 'abdbcdda', 'dabacabd', 'cadbcadc', 'bccddbad', 'ccdabddc', 'cdaadccb', 'dbacabac', 'bddcbadd', 'dcdbccad', 'dddbbdca', 'dbcadbad', 'dcbaadcc', 'badacbab', 'bbdccbba', 'bbdcbbab', 'abadddcd', 'adcabacb', 'bcdabdca', 'dacdbaca', 'cbcbccda', 'adbcdacb', 'bdddacac', 'bcbdcacc', 'cbdddacd', 'addbdbdc', 'abdddcca', 'ddcadbca', 'ccadbbda', 'cbacdcad', 'ddccbcda', 'dbabcbcd', 'badcacab', 'bcabcadb', 'adccbcda', 'badccbbd', 'ddacabac', 'bcdcaadc', 'dadbcdcb', 'bacdbccd', 'acdbbaba', 'dcdcbaac', 'ddcadbaa', 'badcdcbb', 'ddacdbcc', 'ccabddba', 'ccdccbba', 'cbaadcbc', 'bdaabccb', 'bdccdabd', 'bbaabcdb', 'dcdbbabd', 'bacdcbdc', 'cdcadbdb', 'cdbabcab', 'dddbdadc', 'bccbdcad', 'badcbbcd', 'ccdbaacc', 'dccacaba', 'adcacabb', 'dadbddcc', 'aabbcbbd', 'accdbcdd', 'addacdcb', 'cabdbcdb', 'dacdcbcc', 'bbccdabb', 'cdbddacb', 'dddacbab', 'cbdbddab', 'cacdbddb', 'cdbacdbb', 'ccabbdbb', 'ddacbdac', 'adccbbdc', 'badbbcbb', 'dccbbcca', 'dcadcbcd', 'dbcabadd', 'acdddcdb', 'abdcdddc', 'babadbcd', 'cbacddbc', 'accdbcad', 'acbccbdc', 'bdacabcb', 'cbddccac', 'abbdcddd', 'dadbcadd', 'dacdcdbc', 'bdbcdcca', 'cabbdbac', 'cabbcada', 'abdbcacb', 'bacdbcdd', 'cadadbad', 'abddadcb', 'addccabd', 'cdacdbab', 'bbacbdcd', 'bbdbdcab', 'bdadaccb', 'dcadbadd', 'dbbccabc', 'dcadadab', 'dadbacda', 'dbcbdcba', 'cdbbcbad', 'abccdcba', 'ddbddbca', 'adcacbcb', 'acdbcdbb', 'addaacbb', 'ddccadcb', 'cbdcabbc', 'ddbdacaa', 'cdcacbca', 'cadababb', 'bcabbacd', 'bdabcbac', 'cdbcdadc', 'dbccabac', 'adbacbac', 'cbdbabba', 'abadcdad', 'cacacddb', 'addbcbdc', 'dbcababc', 'badaccab', 'bccdbbab', 'cabdcbcd', 'badadbdc', 'ccabdbda', 'bbdbcaad', 'bbcdabad', 'cabdcabb', 'dcacabab', 'abccbdac', 'bdbaadbc', 'bcddcabc', 'ddaadbcc', 'bccbcbad', 'bcdabcad', 'bdccbbda', 'dabcbadc', 'dcacbcdb', 'badccbbc', 'cbbcdadb', 'bcddbaab', 'bbcdcdda', 'dacacdcb', 'adbcdadb', 'caddaddb', 'ddadbacd', 'bdccadcc', 'abcaccad', 'abdbccad', 'cadcbcad', 'cdaadcbd', 'cbcdccaa', 'cacbadad', 'badadbca', 'dddcbdab', 'cbacbcad', 'ddbabdac', 'ccdacdcb', 'dabacdbc', 'dbcabdca', 'dabcdaba', 'dbdddcba', 'ccbdcdca', 'bdbbcaba', 'acbabdda', 'badcdcdb', 'bddbcadd', 'cdbdcdac', 'abcdadcb', 'bcdddabd', 'ddddabca', 'dcbcaadb', 'bacbdbdb', 'cbccdaba', 'dcbdcdac', 'abbddcac', 'cdccabba', 'babacadb', 'ccbbdbba', 'bdbcadca', 'abcdddba', 'badbaccb', 'ddbcabab', 'cbaddbda', 'dacbddbd', 'ddabbccb', 'ccbddbca', 'cabdacca', 'cabdadad', 'cabbdaca', 'dccbabcd', 'ddcbcabb', 'dddcabdd', 'bcdadbdb', 'aabcbcbd', 'cabcddab', 'cdabadca', 'abdddddc', 'ddacddbc', 'dacbcbbd', 'adcabbdc', 'dcbacdac', 'bcdbaccb', 'dbadbdbc', 'dccaccbc', 'acadbcac', 'abcbaccd', 'addabcbb', 'dddacabc', 'caddbdda', 'dddbdcda', 'bdddadcb', 'bdbcbacd', 'dcbcdadd', 'bacabcbd', 'cbbdcbac', 'dbbcdadd', 'ccabcadc', 'dddadcba', 'dabdacad', 'bbddadcd', 'bbdababc', 'dbddddac', 'bdcdabcb', 'cbbabdcb', 'dcbdbdab', 'babcddcb', 'cdbacbbd', 'adbbdacb', 'badadcdc', 'abdbcbba', 'daabbcdc', 'acddccba', 'bdadacda', 'dcaccbdb', 'dadbacad', 'ddadbdcb', 'dccacbdd', 'cbcabdab', 'cbdcdbab', 'daaaacbd', 'bdcbaccd', 'bdadcadd', 'ccbddbab', 'bddabcdb', 'bdadabca', 'acdddddb', 'bacdbcad', 'adcdbdcd', 'bdadbacd', 'bbcdccaa', 'abbcdaca', 'bbabcdca', 'ddbaabca', 'cdbbabbc', 'ccbcddad', 'cbbdbcac', 'adcabbdd', 'cadbcacb', 'abacacda', 'addbccad', 'ccadabda', 'cbbabbad', 'bacbdcda', 'ccdbdaba', 'aacbbcdc', 'dabdcabc', 'dccdacdb', 'abdabdcd', 'dcddbbad', 'bdacdcbd', 'cdabaccb', 'adcdcbad', 'aabcdccd', 'daccabac', 'bacdcddd', 'cddacdbb', 'dacddbaa', 'bcdddbad', 'adadddbc', 'accbddba', 'bdbabcad', 'cabdbbdd', 'dbcbcdab', 'bdcbaacc', 'adacdabc', 'ddbcdbca', 'abddbbdc', 'badbbcdd', 'ddccbabd', 'ddaacbaa', 'accacbbd', 'dddadbcb', 'cddbdacc', 'dccbcaca', 'bdbcddac', 'bcbddaca', 'ccadabab', 'dcaadcbd', 'bccabdbc', 'bacbddcb', 'cbcbdacc', 'caadcbcc', 'aacbdbdb', 'acdccbbc', 'dadbdbca', 'abbdabbc', 'adcbbaca', 'ddaaddcb', 'ccbddbda', 'cbcadcac', 'abddacaa', 'dcdadaba', 'dccbbacc', 'dcabcdab', 'accabdac', 'cabbabdd', 'adbaddca', 'bdcbcaca', 'adbacdbc', 'ccaabdcb', 'bddaaccd', 'daddcaba', 'ccddabac', 'ccadbadb', 'cbddaadc', 'dccbabba', 'adbcdbad', 'adbbabcc', 'babbddca', 'dbdcbadc', 'adadbdbc', 'ddbacbad', 'addccbaa', 'abcadcda', 'badcbacd', 'dcbaacbb', 'dbdabdbc', 'cdbccabd', 'acbaddab', 'acbdbcdb', 'cdcabcbc', 'cbdaadbd', 'acadbccb', 'bcbacbad', 'bdcacbdb', 'badccacc', 'cbbdaabd', 'adaccbcd', 'acbcddac', 'bdadcdad', 'cdaabbaa', 'baddcabb', 'dcbcadcc', 'bdadbabc', 'dbcdbaab', 'dcbdcbaa', 'abacbdbd', 'abcadcbd', 'dccacacb', 'dabbcbcd', 'bdcbaacb', 'accbddbb', 'bdcdcadd', 'ddacadbc', 'acabadbc', 'dadbdadc', 'caabcdcb', 'ddcadbac', 'ddadbccd', 'acbcaddd', 'cacacbda', 'dcabbddd', 'abbddbac', 'cdbcbada', 'dcbbabbd', 'ccdadbba', 'dbccaaaa', 'acdbdbbc', 'adbbcadd', 'dabababc', 'bccdbadd', 'ccbaccbd', 'ddbccabc', 'dcbabbdc', 'cddabdbb', 'bbdaacbb', 'abdccddb', 'dccbacac', 'cadbbdac', 'adbcdbda', 'dadbccba', 'aacaabdb', 'dccadbbc', 'badcadbc', 'acbbabcd', 'ddbcdadb', 'dbcacdba', 'cdbbcaad', 'cabdcacc', 'acbbccdb', 'cdabbddd', 'addcabca', 'dcbabdad', 'dbcacaba', 'bbccbdaa', 'dabdacca', 'acbcdcad', 'bcbdacdc', 'bacdbcbb', 'dacdbbdd', 'dbaaccbd', 'cdabcbad', 'dbdddcac', 'bdabdcac', 'cddbbdad', 'bdcbbdca', 'dbdadcbb', 'dcddabaa', 'bdbbcadc', 'cabcbada', 'bcbdbcad', 'bdbccaab', 'accdcbab', 'dacacbdc', 'cbabaddc', 'cbbacbdd', 'dabcbcca', 'bcadbddb', 'ddbbcdac', 'bddaaabc', 'cddddabc', 'dbcdbdda', 'bbdadbdc', 'dccdcbac', 'dbcadabd', 'aacdbcaa', 'bdabccdb', 'bcddbcca', 'cbdbccad', 'adacacba', 'aacdcbcd', 'badccada', 'dddcaabb', 'dcbccbca', 'acddabcd', 'acdadcbb', 'cacbacad', 'bdccdbba', 'ddbcbbab', 'cacdabac', 'cdccbabc', 'acbbdcab', 'adacbccd', 'bcbdcdca', 'cadbddab', 'abdcddcc', 'adcdccab', 'adcbddcc', 'bcaccdcd', 'babbcddc', 'acabbdca', 'cdabdbdc', 'acdcacbd', 'babadbdc', 'babccadd', 'baddabdc', 'caacdbdb', 'dcbcabab', 'bdacdaba', 'badcbbab', 'cdbacbdb', 'bacbcdcc', 'abbdacca', 'ccbdcada', 'bbddcaad', 'abdbbadc', 'bacdbcbd', 'acdcbaba', 'acbdccbc', 'babdbdcc', 'acdccddb', 'bcbadbbc', 'aacbcdcb', 'adccabac', 'baadaacd', 'acabcdbb', 'adbdcdbb', 'ccadcbbd', 'abcdddac', 'ccdcadbb', 'adabcdbc', 'cdddbbca', 'dbbabcdd', 'abadcbbd', 'cddbdcad', 'cdbcacbb', 'bcabdbba', 'acabbada', 'acbabcad', 'cbdbaabb', 'ddbdbdca', 'bbcbdacc', 'acabaccd', 'bdcdadda', 'cbacdccd', 'dbacbbda', 'cbbaddbb', 'adbccdcb', 'ddbcdbda', 'abdaccbb', 'bcacbdab', 'dcdcadbb', 'bcadaddd', 'cbbddbca', 'bacbadcb', 'cbdbdacb', 'cbddddca', 'cbdabbdb', 'dbddcada', 'cbcaadbc', 'cdabcdbb', 'dddacbca', 'dccadabc', 'dacbabdb', 'cbddabcd', 'cbddcbaa', 'ddbcdcba', 'bcddadbb', 'cdabbcbb', 'acddccbd', 'dcbdacbd', 'bacdcbcb', 'bbcdabba', 'abadbbdc', 'adddcabb', 'dcbbacdb', 'bcbbdaad', 'dabdbbdc', 'bcdddbca', 'abaccbad', 'dcaacaab', 'cacddabd', 'bdbbcdac', 'cdacacdb', 'dbdbacac', 'abcbcbcd', 'dbbdcadb', 'abdbdbcd', 'daddcbcc', 'abbdbcbb', 'cbdbbcba', 'abccdadb', 'ccddcabb', 'abacdbac', 'adcbacbc', 'dbadbaca', 'ddacdcbb', 'cabdcbac', 'accdbcdc', 'adccbdcb', 'cabadcab', 'dacdccab', 'accbcbdd', 'bddbdcad', 'dbcdadda', 'dccbcbab', 'cbabcddd', 'bcadccbb', 'dadbdccb', 'ccadcdbb', 'baadcdbd', 'bddcabcc', 'dcabacbd', 'cadcbdbd', 'dadbbcad', 'adbbdcca', 'adccabda', 'dacacbda', 'bccabcda', 'bacaddab', 'addbcaac', 'accdbcba', 'bbdabdcd', 'cadbdbab', 'abccbdda', 'cadddbaa', 'abccabbd', 'acdcbddc', 'adbccddd', 'dbddddca', 'abbaccdd', 'bccadada', 'cdaadbcc', 'addabcdd', 'cabdbccb', 'cdaccbdb', 'daabaacc', 'babbadcd', 'addbacdd', 'daccabad', 'bdacdcdd', 'cbcddacb', 'dbbadddc', 'acbbdcad', 'abcadbdb', 'bdcbaddd', 'dbabcada', 'cdbdcaac', 'adcbdadb', 'ccdacbdb', 'caddabcb', 'babcdbcb', 'bdabdcba', 'ccabadcc', 'adcbcbcb', 'acbbabbd', 'cdccbaba', 'dabcadad', 'cdbdbbab', 'adbcabab', 'cddaaadb', 'acaddbcc', 'adcadbda', 'dacabbcd', 'adccbcdd', 'bacadddc', 'ccbdcbaa', 'cbbaddda', 'dccbbdaa', 'ddcdbdaa', 'bddcbdba', 'ddddabcd', 'ddcbacac', 'dadabcab', 'caccbdbd', 'cabcddad', 'cbbdadda', 'aadaabcb', 'dadcadbd', 'cdcdbadb', 'adddbcba', 'dabacdad', 'ddbcdaab', 'baccddcd', 'addcdbdd', 'bdbacdad', 'accbdddb', 'adcdbccb', 'adbdcaba', 'badcdada', 'bbccadba', 'cbdddbab', 'bbdabbcb', 'dbdcabcc', 'ddcbcaaa', 'bbddaddc', 'abcadddb', 'bcbabadb', 'caacbdcd', 'dbdcdadd', 'ddcabbdb', 'bcbdbaac', 'cdddbabb', 'acdabdac', 'dcabddab', 'cdddbbda', 'adbdddcb', 'cabdddca', 'abddaaac', 'abacbddb', 'bbcdadac', 'bbdbabbc', 'cddabbca', 'bbaddbac', 'caabdcaa', 'adadbdac', 'dccbacdd', 'dbaddcdb', 'cbbadcdb', 'bcbcadab', 'dbadbacd', 'dccaccba', 'cddbdaba', 'bbcdadab', 'dabdbbac', 'cbabbabd', 'cbacbddb', 'bdbcaadb', 'dcdddadb', 'bccdcabd', 'dbdcaddb', 'cdbbdcba', 'cabdadac', 'addcbdcb', 'bcabadab', 'dacbccdb', 'dcdbadad', 'adbdddca', 'cbdacada', 'dabbcdab', 'dbccdabc', 'aadbaacc', 'ccdbdbab', 'cabcbdcb', 'dbcadddd', 'acddbcdb', 'ddadacba', 'ddabcbad', 'daadcbaa', 'bbdbacac', 'bdcdbacd', 'abcbdcba', 'bddbbabc', 'bdddcbba', 'dbaadcbb', 'ddacbcab', 'dddcaabc', 'ccacdbbd', 'bdbdccaa', 'ccbddbaa', 'bccdbabb', 'cdbacbac', 'cbabdcdb', 'aadbdbcb', 'adbbddbc', 'abbdabdc', 'dbbdacbb', 'ccadabdd', 'bdcacdbb', 'ccbddabd', 'bcbbacda', 'adbdacab', 'daddbdac', 'dadddcab', 'bcacdacc', 'cbcaddbd', 'ccbcdbad', 'ccddadcb', 'cddbccaa', 'dccadbac', 'dcdccaab', 'bdadbcab', 'adbccacd', 'cbaddaba', 'acbdacab', 'accbdcbc', 'dcabccba', 'bcdababa', 'daccbcdd', 'adbaccdc', 'bddcacda', 'cdadabda', 'adccabab', 'cdcbcbab', 'dabbcbca', 'bbcdddac', 'dbbacadc', 'cacddbcc', 'ccbdaacc', 'bccddbca', 'adcadbcb', 'bbcddadd', 'bbcddcad', 'badcbbad', 'cbadbdab', 'abcddcbb', 'bcaadcbc', 'abddadbc', 'cbbabdab', 'babcbcdc', 'dcaadbbc', 'cadbcbdb', 'bdcabacd', 'ddcabaaa', 'dabbaccb', 'babdabcd', 'abdbddbc', 'dbccbacc', 'dbabbccb', 'acdacbac', 'dcacadbc', 'bdacbcda', 'cadacbbd', 'cbadcbba', 'bccdaddc', 'dacbcddd', 'cadcbadc', 'abbacabd', 'abcacdcd', 'dcadbdad', 'bbacaccd', 'cddacbbd', 'bbcabdac', 'cddabbcd', 'cdbbdbba', 'acdcabbc', 'cacabddb', 'dcdcbaca', 'dabbcacd', 'dbbcabdc', 'daddcbda', 'cdbadabb', 'cbcdddda', 'bdcadaba', 'cdbcaacb', 'dcabbadb', 'ccdabdcb', 'babcacdd', 'cdddabac', 'caabbaad', 'dabbdbbc', 'cbcacbdd', 'cdbdcadd', 'ccdbbdad', 'adbaccbb', 'cdabcdcb', 'bdcbbcca', 'babcdbbd', 'adcdabba', 'cbbdbaba', 'dddabbac', 'cacdabcb', 'abcabadc', 'ccaaaabd', 'dbdacdbc', 'cbbdacdc', 'bbdbabdc', 'cacabdbb', 'adabcaba', 'cbcbbcda', 'bbdaccad', 'dbdcdada', 'abccaccd', 'addccbdb', 'abdcbbcd', 'abadcbdc', 'cacbdbcc', 'babdcbdd', 'cbabdbab', 'cbaddcda', 'cdacdabd', 'bacbbabd', 'cadbbdda', 'acbddadd', 'babbadca', 'ccacbdcd', 'ddaaabac', 'bdcbcbac', 'acbcadbc', 'dccdcaba', 'cabbcadc', 'bcabdacc', 'ddbabaac', 'cbbcbacd', 'dbcdbacd', 'ddaccbbc', 'ddadbdca', 'dddbadac', 'cddbaaac', 'bbaccdda', 'ddbbccac', 'abbcdddb', 'acbdcbdb', 'ddabbdbc', 'addbbcbb', 'dcbbadda', 'bbcbbdad', 'dcdbcadb', 'ccdcabdb', 'ccbbdabc', 'adacbdca', 'bbdcadbc', 'adbcdcab', 'dcdaddcb', 'ddbbcaca', 'adccdcbc', 'bcdbadad', 'daadccbb', 'bbdcddad', 'abcaddda', 'abcdbcad', 'dbcabada', 'dcabbddc', 'ababdddc', 'bcabacdb', 'bbcabcda', 'bbdbcadc', 'acbddcbc', 'dbbdccaa', 'bddcbaab', 'bbdadacb', 'accddbca', 'dbcbbabd', 'cdbbadcc', 'dbdabddc', 'adbccdad', 'bdbcabcc', 'caabdbcb', 'adbdbcdc', 'caddaadb', 'dbcdcbab', 'cbbdabad', 'acdcbacd', 'adccabdb', 'badabcac', 'cdddabdd', 'daddcdcb', 'acdcbdbc', 'acadbabb', 'bddbaccd', 'bdbbdadc', 'cacdabdc', 'cddbaddb', 'cdaddcbc', 'bbcaddcb', 'bbcdabda', 'dacadccb', 'abaddcdc', 'adacddba', 'adadabca', 'aabdbdbc', 'caadccbc', 'abcdcbba', 'bdcdccaa', 'dbccbabb', 'babcabbd', 'cdababbd', 'dacadbcb', 'bdcadcad', 'acaddbdd', 'adbcbaca', 'daccbcbc', 'dabcabca', 'aabcdcaa', 'abbcdbdb', 'acbdaccd', 'ccdccbab', 'ccbaddac', 'bbccacda', 'bbdbccad', 'dccababa', 'abadcddb', 'adddbcdb', 'bacdcadb', 'badbadac', 'dacabaca', 'ccdabcba', 'acbcaddc', 'bacbbdcc', 'ccdabccd', 'abddbccd', 'caddbdcb', 'abcadbdd', 'adcacabd', 'cddadbcd', 'bdbcabab', 'cddbaccb', 'bbdacbdd', 'bbcdcadc', 'cacabcdc', 'ccacdbdd', 'bcbabcdc', 'dbcdbada', 'babdbbac', 'dcbbabbc', 'dcabdacc', 'cadbdacd', 'bdcbbadb', 'daddaacb', 'cdbccacc', 'bbadaddc', 'baabcbdb', 'bdcadadc', 'babdcaba', 'bacadcad', 'bccdddad', 'cbadbdcb', 'cadabbcd', 'dabcddbd', 'cacdbcba', 'acaccddb', 'bdbacbca', 'dbabacbb', 'acabccad', 'dcbabadc', 'ddbbabac', 'abcbbdbb', 'dadbabbc', 'dadcbbcc', 'dacbacdc', 'adbcdccb', 'acbbdddc', 'addbdcbb', 'adacbbac', 'cbccddca', 'adcbbdac', 'cdaacdbc', 'dcdabddd', 'dadaccab', 'dcbdbbda', 'acacdbcc', 'dcacbadd', 'bcbcaadc', 'dababcad', 'cbcbacbd', 'caadccbd', 'adcadbca', 'dbaaccdb', 'dbcadbdd', 'cbbdcdba', 'bdadadac', 'cdccabbd', 'abdbcbdc', 'baacdbbc', 'ccbcdadd', 'cddaddab', 'bbdbbacc', 'ccacdccb', 'adddbdac', 'ccadabcc', 'dadccdbc', 'cdacdccb', 'cdabadbd', 'dabccabd', 'adcdcdab', 'ccddbada', 'ddbdbdac', 'bcdccdba', 'bcbbaddd', 'aadaaccb', 'abdbddac', 'adbcbdab', 'badaccdc', 'dacdddba', 'cbdaacbd', 'acbbcadc', 'bccabcdb', 'caadbcbd', 'accacbdd', 'adbddbac', 'adbadbcd', 'dcbcacda', 'cabbaddd', 'adbadcad', 'dcbbabab', 'bcacbddc', 'bddcddac', 'dcdbdaab', 'bddbadca', 'adbabcbd', 'abcdbdab', 'cbadabdc', 'bddbcabd', 'dccacabb', 'bdbccdac', 'dcbaaccb', 'dabbadcc', 'bdbcabda', 'babaddcb', 'dddabccd', 'dddbcabc', 'accbdbda', 'dcacbccd', 'ccbacdbd', 'cddbabda', 'ddbccbca', 'dcadabcb', 'dbacacbb', 'bcbacdcb', 'bdcbabdd', 'dbdccabb', 'cbcaccad', 'dacdbdba', 'acbdbbcb', 'cddacbaa', 'acbcbcdd', 'dbacbadd', 'bcaabdbb', 'cadbcdda', 'cbabdbba', 'abdbdbcc', 'cdacdcab', 'cbcdacad', 'cbdcaadc', 'abdaccdd', 'ababdcdb', 'adbadcdb', 'ccdacabc', 'adcabcdc', 'bccbbaad', 'cddcbcca', 'cdbbaacc', 'aadcdbcc', 'dabdbdcd', 'adbcbadd', 'abcdbadd', 'acdcbcbb', 'bdbaadcd', 'bbdcacbd', 'cbdcbbda', 'adadcbdd', 'cbcdaddc', 'dcbddaab', 'abdbccac', 'bbdadcac', 'daccbbad', 'dbcddaac', 'dbaabbcb', 'cbaddbac', 'bcdaddcb', 'cacbdddd', 'ddaabcca', 'dabcacdc', 'adcbcddd', 'dcdcbada', 'bccdbdaa', 'ddabcbdb', 'dadbcddd', 'adabacca', 'ccabcdda', 'bbaddacc', 'cbbaddab', 'dcbaddab', 'dbacddba', 'bddacada', 'acbccdbd', 'dadcdcba', 'cbcdbcab', 'cbbcbbad', 'bcdcbabc', 'cbdccabb', 'dbacddbd', 'bbcbacdb', 'dbacbacb', 'ddbcacbd', 'bcdbddab', 'bdcbadcb', 'bbcbdcca', 'bdbcdadb', 'bcadcbdb', 'bcadabcb', 'ccdcbacd', 'cdadabdb', 'bcabbadc', 'bcabdddc', 'bdcaddab', 'abacdcda', 'bdbabbcb', 'ddccdbaa', 'adbacdda', 'ccabddca', 'cadccabb', 'ccdcbaca', 'acadacbc', 'accdbdca', 'abddcaab', 'bcdcdbab', 'daaccbcd', 'cdacabdc', 'cbabcdcb', 'acbbddbd', 'daaaacdb', 'ddacdcbc', 'cbcddabc', 'accbabdd', 'bcadbdcc', 'acdbbccb', 'ccdacabd', 'bbdaddcd', 'dacbcbdb', 'cbcabcda', 'dcbcddba', 'dababcca', 'acdcbdbb', 'babdddcb', 'bdbbcbac', 'bccdacba', 'bbdbdcaa', 'babdccbc', 'adadcbac', 'acddacbb', 'cddccadb', 'bcdcabcd', 'acbccbbd', 'adadbacb', 'bcdaadaa', 'adcbbcac', 'acabbdcb', 'ccaabbdb', 'ccacdddb', 'dbadddcc', 'bddabdbc', 'adccbbdd', 'cdcaccba', 'dacdabab', 'cabdbbad', 'ddbdcaaa', 'bcbaabcd', 'cdddabbd', 'acbccbad', 'cdbbaddc', 'bbdbbcba', 'dabacadd', 'cdbaacdc', 'dbcddabb', 'dbbdcacd', 'dcadbcba', 'cacdddab', 'ccabddab', 'badccdcc', 'bcbcaddd', 'abddbbcc', 'abbdbbca', 'cbddbada', 'cadacadb', 'cbaddcad', 'bdababdc', 'bdccaacc', 'bcddaadc', 'abbcabdb', 'bacacadd', 'cbcdacab', 'abdbbccd', 'adbdbdcd', 'bdcbcaad', 'aaccbaad', 'cdccbbab', 'cbabbdbb', 'acbddcdd', 'adcabcdd', 'bacdabdd', 'cacdddba', 'dcbdacda', 'badcddbb', 'bcabdcba', 'dcadbcda', 'acddbaac', 'ddbacddb', 'ccacbccd', 'badcacdd', 'cadddcbc', 'ddbacaac', 'daccbcab', 'babdabcb', 'dacacbcb', 'abdcbbcb', 'ccdbcdad', 'bbcaccda', 'cabbccdb', 'cbbddada', 'bdadcbac', 'cddaabad', 'abbcdcab', 'accbcddb', 'ddcaadbb', 'dacbabcc', 'bbcdbabc', 'dbdcbacb', 'acbbdbdc', 'adbbddcc', 'cbbabbdc', 'ccbdadbb', 'bcacdbca', 'adadbaca', 'dcdadbac', 'ddcbaaca', 'dbadcbdb', 'cdaabdcd', 'bbdabcac', 'cadcaccb', 'cddcdbca', 'cddcbaac', 'bacbdbad', 'bccabdcc', 'daccdbcc', 'bbcdcaad', 'dbcbadcc', 'aadbdcaa', 'cbdacbcb', 'cadcbcbc', 'bcdadadc', 'dacbbdca', 'abdcddac', 'cbdcaaaa', 'dacbadbd', 'abdbbcda', 'daacdbbc', 'dabcdcab', 'acdbdcab', 'cacbbada', 'bacbcdcd', 'bdaccbcb', 'dbcbdcca', 'bcbdbbab', 'babdccad', 'cbbdccda', 'cbcabdad', 'adcdacdb', 'cbcaadbb', 'abacbcdd', 'ccbabbad', 'abacdadb', 'cdcdbcad', 'ccadcabb', 'ccddbdca', 'cdbdbacd', 'abdbdcda', 'bdcabccb', 'ddacaabc', 'dabcabda', 'caccddbd', 'cdbadcdb', 'dacbccba', 'ddccacdb', 'ddadcbcb', 'cadcbbcb', 'acdadcbd', 'dcabddac', 'cadcbadd', 'abdbcbcd', 'cbbcbdad', 'cbcabdba', 'cdddaaba', 'bbcdadad', 'abcdddcc', 'dbadacdc', 'ddbcadcb', 'dcdcbcad', 'bacddcca', 'dcadbddd', 'dacdcddb', 'dbdbdabc', 'dccabbcd', 'acaddcab', 'dbcdbdca', 'cabadbdb', 'bacddbab', 'bccdbabc', 'cbdbabca', 'bddcbcaa', 'bcaabbdb', 'dcbcddda', 'acbcdabd', 'abddcdbb', 'acdbdada', 'bacbbdbc', 'dbcdbbda', 'accdbadd', 'bcdaabdb', 'acdadbda', 'ccbdabdc', 'addcdcbc', 'dcbdaacd', 'dddddbac', 'adcbdaca', 'babdabcc', 'cddcaaab', 'dbaacaab', 'ccbdccab', 'adccbbca', 'dabcbcac', 'cababadb', 'babadcdc', 'babddcdb', 'bcdcaccd', 'aaccbdbb', 'dcbabbcd', 'dacbadcc', 'daadbbdc', 'dbbdbcac', 'accbadcb', 'ddcbadbd', 'babcdbcc', 'dcacbdca', 'acbdbaca', 'bbacbbcd', 'adbdcabd', 'ddcdabcb', 'cdbcddad', 'dbaacdbd', 'cddbcdda', 'bddcacbc', 'bdadcaba', 'ddcdbdad', 'dccdbdba', 'cddcbabd', 'abddabcd', 'acbdbdbb', 'abcdbccd', 'adbbcbdd', 'bcadbbdb', 'dccadbdb', 'dcbacadc', 'dcbdaddd', 'cacbbdbd', 'abacbddd', 'bbacadab', 'ccdbaccb', 'cbcaadaa', 'acdbcdcb', 'dbbcdbac', 'ddaccbda', 'bbdbcdad', 'acacbcdb', 'dbbcaacd', 'abbdcddb', 'abaddbbc', 'ddcadcbd', 'accdcddb', 'bcbbcada', 'cadcbbad', 'bbadcdac', 'dbccacbb', 'dcacacbb', 'ddacbcdd', 'cbccaacd', 'abbcbdcb', 'dadcbcbd', 'cdcaccab', 'baabbdcd', 'cdaccbcc', 'caaccbbd', 'ddcaabbc', 'ddcbaaba', 'bdbacdda', 'adbbccdd', 'cacdbcdb', 'accbbacd', 'cbadadad', 'dacdbdab', 'adbcbddd', 'ddacbabb', 'bdcacbdd', 'cbacdcda', 'aacbdbbc', 'dbadbdca', 'ccdddaab', 'abbddcaa', 'bcdaccbb', 'adaddbdc', 'dbcacbcb', 'bdadddca', 'dcdabacb', 'bcadcacc', 'cdbbdbab', 'ddacbacb', 'bccdabcc', 'bdadcddd', 'abdadbcd', 'adddacbb', 'bddabbca', 'adaccdab', 'ddabbcba', 'abdbcbdd', 'cacdacbc', 'dbbcbdab', 'ccadbddb', 'ccbdadba', 'abbdbcac', 'dbbdccac', 'bdadbacb', 'dcbdcaad', 'cbdbbadb', 'cdcdbdca', 'bbacbdad', 'bcdbcadd', 'cbdaacbb', 'acdccdba', 'cbddadab', 'ddcbcadb', 'dcabdddd', 'accbdcbb', 'acadbcbc', 'dddccaab', 'cdbadddb', 'cdcbabab', 'bdcabadb', 'dbacbdbd', 'ddcaddba', 'cbdbbadc', 'abaccbdd', 'dcbababb', 'cddbbacd', 'bacacacd', 'dacbadac', 'cbaccdcb', 'caccbddb', 'abbddcbd', 'cbbcdaba', 'cdbadbad', 'ddddadbc', 'babcdbbc', 'bcabdcdc', 'dcbcaccd', 'bbacdddb', 'abbacdbb', 'acdccdcb', 'abccadcc', 'abdcdcab', 'cacbdacd', 'acdbbdcc', 'caccadcb', 'acbbdcda', 'cadbcabd', 'acabdacd', 'accddaab', 'bdcdcabc', 'accbbdba', 'abbcaddd', 'daadbdbc', 'bacbdcbc', 'cacddbaa', 'addbbdca', 'bdbdadcb', 'bdbbdaac', 'acabcbdc', 'adcbddbc', 'adacadab', 'cbcddadd', 'dddacdba', 'adadbcab', 'adaccbbd', 'dcaadbaa', 'ccdbdcad', 'ddcdbcad', 'ccdbbcda', 'bccbcdad', 'cbdddadb', 'dadcdbad', 'aadbbdcc', 'ddbabccd', 'bbaddcdb', 'addccabc', 'cadabadd', 'cacabbdc', 'cabdbcdc', 'bdbabadc', 'bbcdcaac', 'ddcdbabd', 'aabdaacc', 'bccbdbba', 'bdacbbca', 'bdcbaddb', 'dabccbda', 'dabacabb', 'ddcabaad', 'dacddbca', 'bbccabdb', 'ddddabbc', 'bcdcaacc', 'bdaddcbd', 'cabccdbd', 'ddadbabc', 'bcbdbaca', 'babcbbdd', 'abacabad', 'addcbaaa', 'cbdcacac', 'cbdbacdd', 'dbaadcbd', 'bddbcacb', 'ddabbcbd', 'abadcddd', 'dcabdccb', 'cdcbdabb', 'ddbcaccd', 'bcbcacdc', 'babcdcba', 'cdadbddc', 'adddcbdc', 'bcddadcd', 'cdbbdacd', 'cbdbcdca', 'dddabacb', 'dcddbdda', 'cdacdcbd', 'dcbcaabc', 'ccdabcbc', 'cabdbabc', 'bacdcacb', 'bcddbaca', 'dbcbcadc', 'cbddadaa', 'bbadccdb', 'bddacdbc', 'bbddbabc', 'cabcdbbd', 'dcacadab', 'baabccdc', 'dbacdbda', 'adbbdcdd', 'cdcdabbd', 'cddaabcb', 'badccddd', 'babbccbd', 'abbdcdac', 'dcacbbca', 'acbcbccd', 'bacdbacb', 'bbaccbbd', 'adbcacad', 'dcbdcada', 'cbbacdac', 'cdbadabc', 'ccadbbcb', 'cadbbcda', 'bddcbbaa', 'dbadccba', 'dabdcbbc', 'babbdcbc', 'cbccabdc', 'dbbddcaa', 'adcbcabd', 'daccbbac', 'cdbcdaca', 'bddaccad', 'abdbcddc', 'bbaccacd', 'abccbdbb', 'dadcbdca', 'bcadddad', 'bddbacbd', 'abbdacdb', 'bccacdba', 'babccdcb', 'cdccacbb', 'bdbcaabc', 'bbddadcb', 'abacdacd', 'cbbdccaa', 'cddbbadc', 'ddddadcb', 'adcbddcb', 'abacdbbc', 'acbbdada', 'ddabcbdd', 'ddbdcaab', 'bddbacdc', 'bbddacbc', 'dcdbcbca', 'dcbddacc', 'abacadba', 'abadcbcd', 'abbacbda', 'cababdcc', 'dbaadccd', 'bcbbabdd', 'cddcabcb', 'bacdaddb', 'cdbcacdd', 'ccdbdacb', 'cdacdcba', 'cabcdcad', 'abdaddca', 'ccaccdcb', 'ddcbdcad', 'bccbbcad', 'acdbddaa', 'ddacadab', 'babbdbbc', 'ddbaccaa', 'ddcaaaab', 'dccaadbb', 'bdcdaddb', 'cabdadab', 'ccdbcaad', 'dadcbbcd', 'dacaccbd', 'caccdbab', 'dbcbdaab', 'adacdcab', 'bcbbacbd', 'cbdbabdd', 'dcdccdba', 'ddabcddb', 'bbdcaddd', 'ccacbadd', 'ccabbdcd', 'dcdbacda', 'bdcabadc', 'cbddbdac', 'dabdbbcc', 'bcddbaaa', 'babcdacd', 'ddadbcad', 'cddbdabd', 'dcaabbdc', 'cbccddda', 'ccabcada', 'dcacdbca', 'bcabddac', 'adacbbda', 'ddadabdc', 'cbdaddba', 'abaddbcd', 'dbdcadca', 'bbacbdbc', 'dacbcaba', 'dbcbacdc', 'cbdacdac', 'bacbbcdc', 'bcadddab', 'bcbdadac', 'bccdaddd', 'dbdcdbad', 'dabbabcb', 'cbadacbc', 'dbdccdad', 'dddccacb', 'dcbaabdb', 'bcdcabbc', 'baddddcd', 'ccabddbb', 'cadcddbd', 'ccadbdbb', 'acdcddab', 'dcbabdda', 'abdaccad', 'baccadac', 'dbacdcbd', 'cdbdbaba', 'adcbdcad', 'bdaacaad', 'badccdac', 'adadcdcb', 'badbacdc', 'cbcbadcb', 'ddacbdad', 'aabcdcbd', 'abacacad', 'babadddc', 'ddcaccdb', 'cadabcbb', 'bcbdabdd', 'dadccbab', 'dbacdbab', 'bcacacad', 'bddcbabc', 'addcbdbd', 'acaddbcb', 'bcbccadc', 'bbcddaaa', 'abdbdcab', 'cdcbaabc', 'cbcdacda', 'acabcbdd', 'acdbccdd', 'dccddabd', 'ababbacd', 'bdbcbacc', 'adabbcad', 'cdaacbcb', 'adcbacda', 'bbaccdcd', 'bccdbabd', 'daadcbdb', 'cadbcbad', 'abbcdccd', 'cdabbcbd', 'abccbdcc', 'dbbcadbb', 'adabdacd', 'adbccbdc', 'babdccdb', 'acacbabd', 'bbacbdab', 'cdddaabd', 'cacdbbdb', 'cbdcbaad', 'acbddcca', 'daacbbcb', 'accdbacd', 'cbccbadd', 'bdcdaaaa', 'dbacdaba', 'adbcddac', 'baacbdbc', 'dacbabcb', 'dcdcdcab', 'bddbcabb', 'adcbdcac', 'abaddacd', 'dccdabbd', 'abcadcbc', 'bcaccdbc', 'abddcbcd', 'dacdabca', 'dabbcbbc', 'bdacdaca', 'babbdcac', 'dacbdabd', 'acdbdcbd', 'bcabadda', 'baadcdcd', 'ddcbdcab', 'dacdbdcd', 'acbadacc', 'cbddabaa', 'adbcddcb', 'abcbcdad', 'ddcacabb', 'acdbddab', 'daccacbc', 'accddcba', 'cbdbacdc', 'babcddda', 'bcdadcbb', 'dddcdbab', 'bbdadacd', 'daaccdbc', 'cacadcbb', 'dccddbab', 'cbacdddb', 'dcbaabbc', 'bdacacba', 'cdccbbac', 'bccdacbd', 'ddbcadca', 'badabcbb', 'badbcddb', 'dccdacab', 'abddcdda', 'cbcbdbac', 'bcdbdaca', 'bacbcada', 'bcbdcbda', 'caddbcdd', 'adbbcdab', 'baccadcc', 'bddcbbab', 'abcbbcbd', 'abbdcbca', 'abdadabc', 'adadbbcc', 'bdcddcaa', 'dabcddac', 'cdbcbaac', 'dabbcabd', 'bdcdabab', 'bbcdcbab', 'accdbadb', 'acbacdab', 'abadbdca', 'abcdcdbd', 'dcdabcca', 'acabbdbc', 'abadcdbd', 'dcdbbdca', 'bccdabdb', 'cbdcabad', 'daccadba', 'abdbadbc', 'abccbadd', 'abdcdadc', 'bdbdcdaa', 'cddbcacb', 'dbccdaab', 'cdbbdacb', 'caddbdbd', 'daccddbc', 'cacaddbd', 'cabdcbca', 'cacbdada', 'daddcabc', 'adcddaab', 'cddbadbc', 'bdcbbdab', 'cddaddbc', 'cdbdbdaa', 'bcadbabb', 'cbdbdaab', 'bdadbadc', 'bbdbacda', 'cddcbcba', 'cacddbac', 'ddcdacdb', 'bdabacab', 'bbaacbdb', 'bacadcac', 'cbdbdbaa', 'ddcbacbc', 'cbdbdbca', 'adddccbb', 'bdddcbca', 'ccbcabdc', 'abcdbabd', 'dadbbccb', 'dadbccdd', 'bccaccda', 'adbdbcdd', 'baabaacd', 'accdabcd', 'bbacbdda', 'bdabcbcd', 'adccbacd', 'dccdaabd', 'bdaaccaa', 'bdcddcac', 'cdcbcbca', 'badcbdca', 'bcdabcac', 'cabbdcbb', 'daccacba', 'abddadcd', 'cadcadbd', 'ddbcbdca', 'dcbcdbca', 'adcabdad', 'bcbbcadd', 'ddabdcdc', 'badbcacb', 'dadcabca', 'addbdabc', 'baadbdcd', 'aadcbdbb', 'cabadcbd', 'dcddacab', 'cdaddbac', 'adbccdcc', 'abdacacb', 'dadbcbdd', 'daacbdbb', 'bbacdcab', 'abdcacdc', 'bacbcadd', 'abcbdacc', 'adbdccdc', 'dcadbcad', 'bbccacdd', 'bcbddcac', 'acdacbba', 'ddacdabd', 'dccbbdca', 'bbdcbdda', 'ccadacba', 'bbacddbc', 'adccacbb', 'ccdadccb', 'dabcbabc', 'bacddacb', 'dccbddac', 'cbdaddcc', 'dbccbacd', 'cbdbcbad', 'cbadbccb', 'accdadcb', 'acdcddbc', 'ddbcaabb', 'abbdcdda', 'dbacacbc', 'daacbcdc', 'ccbcacbd', 'bdcaabdb', 'dabddcdd', 'bcadcddb', 'cadccbda', 'ddbcddda', 'baccdaba', 'bcaadbcc', 'ccdabcda', 'cbbadbac', 'dbcadbda', 'bcbadabc', 'acbcbadd', 'bdadadca', 'cbabdbcd', 'ddbbaddc', 'addbdcdd', 'cdcbcdca', 'abdcdbab', 'bddcacbb', 'cbbddcad', 'acbbcada', 'dcbcbaba', 'cbabcbdd', 'dabbdacc', 'dbcbadcd', 'cbadbcda', 'bdadcdbb', 'cadbbdba', 'accdbccd', 'dabbcada', 'dcdbdaad', 'dccabcbc', 'badcabac', 'bddcaabc', 'acddabab', 'abdbbacd', 'dbdcdbab', 'cabbcdad', 'bcaacbdb', 'bacbcdad', 'caccdbda', 'dccaadbd', 'acddacdb', 'cadbadad', 'dbbdacbc', 'dbadcdbb', 'bdbdaddc', 'ccbcddaa', 'adcabcbd', 'bcbcabdd', 'acaddaab', 'bcdddaac', 'ccabcadd', 'ddaabcbb', 'bbcacddc', 'cdddbaab', 'abbcbcdd', 'ccddabaa', 'badbcacd', 'ababccbd', 'dbccacdb', 'bdaccdca', 'bcbbaabd', 'adadbdcb', 'bdaddcac', 'bdbccbad', 'cacbbddc', 'ddaabccd', 'badcbadb', 'acdcbadc', 'ddbadbcb', 'badacbbd', 'ddadcbcc', 'abcbadcb', 'dcbbcbca', 'addcdbca', 'dabccacd', 'cdddbdab', 'acdddbbd', 'bcdacdcd', 'babbcdbc', 'dcdbdabd', 'cbdcbbab', 'dbccdbab', 'ccdbdcda', 'daaaabbc', 'bbdbcdaa', 'bddcadbc', 'acabacda', 'caacdcbc', 'dbbcdcac', 'cacbbadc', 'dbcbadbb', 'bccababd', 'ddacaabb', 'dcbdaabb', 'ddbbacbb', 'dddbcbca', 'bdccdcba', 'babaddbc', 'cadbbcac', 'dbabbcba', 'abbcacda', 'cdbbacda', 'badbcdda', 'babadcda', 'cabdccdc', 'cbccadab', 'cdacadcb', 'dcdabccd', 'adcabadc', 'abdadadc', 'dbddabac', 'abdacdab', 'cadaccdb', 'ccbccdac', 'cbddacaa', 'cadcbdab', 'dcaddbdb', 'daadcdbc', 'dcbdcacd', 'adbcacdd', 'ccadcbdb', 'addcdacb', 'cdaddbad', 'bcdcbbab', 'acadddab', 'caadaabd', 'cdbacbba', 'ddbcabba', 'cabcbddc', 'dbbadacd', 'cdadbdbd', 'abbadcac', 'aaaaccdb', 'cdabdddc', 'acdadcba', 'dbacdcbc', 'cbacdadb', 'dbadcdba', 'bdadabcb', 'bacaddda', 'ccdadbbd', 'ddbdabcd', 'aadaacbd', 'bbcaadcb', 'bbdacacd', 'dcbbabdb', 'bcdacadc', 'dcdcaabc', 'dabcacbc', 'bddbcdab', 'cdadbdda', 'adbccddc', 'badcddca', 'baddaddc', 'cbcaccdb', 'bcddddda', 'bdbdccba', 'bcaadcbd', 'bcadacdd', 'daddbbcd', 'bddacbdb', 'dddacdbb', 'addbacad', 'dbabcbbd', 'adcacbcd', 'bcbbadca', 'bbadccdd', 'acbccdcb', 'cdadcbad', 'bdbcacac', 'bdccbcab', 'adabbcdc', 'dbcacbcd', 'cbdbbdda', 'dabdacdc', 'bacdcbdb', 'ccdadbcd', 'abbddabc', 'cadddacb', 'dcbdbbab', 'ccacdbcd', 'abcdbddc', 'cabbdbba', 'cdcbaddd', 'bcbdbdca', 'adbdacba', 'cadbacac', 'dabadcbb', 'bbacddcd', 'ddbaccbb', 'dcdcabad', 'dabdabca', 'abddbcbb', 'abbdcbcc', 'acbabcdd', 'acabcdba', 'dcaccbda', 'ccdbacac', 'ccbdcbda', 'bbcddabc', 'acdcbcca', 'cadccbdb', 'cadabcbd', 'cdcbccba', 'ddccaabb', 'dcdabdbb', 'dcddbaac', 'bbcadbca', 'abcbadbc', 'cabbddcb', 'badcbbdc', 'bcbaddbc', 'cdadcbbd', 'bbcadabc', 'adcbddaa', 'cdbcabda', 'cdddbcda', 'dcbadabc', 'abadcbcb', 'bbacddca', 'bcdabcbb', 'cbccbdca', 'dabacaba', 'baddbadc', 'dcdcbacd', 'dacddcdb', 'bbadcbcb', 'daccbbda', 'aabbdcdc', 'accacbad', 'cbcdaacd', 'bbcadcad', 'dcbcaccb', 'baccdcbb', 'ccdaacbb', 'cdabbcac', 'cacdcddb', 'dbcbdacb', 'addbbacb', 'cddaddcb', 'adcbcddc', 'ccbddaac', 'babadccb', 'dcacbdbd', 'bdacdbca', 'dbcaddcb', 'bbcdcdac', 'bcdbdcac', 'adbcbddc', 'addcbddd', 'ccaddcdb', 'abbacbdd', 'adcbbabc', 'dccbaccd', 'bbadabac', 'cadcadba', 'addccdbb', 'acadadbb', 'dcbcacdb', 'acacdbad', 'adddaabc', 'bcbabcad', 'bdbcbdca', 'dacacbcd', 'dcbbdada', 'ddabaacd', 'addcaabd', 'bdccbcaa', 'dddccabd', 'cbaccdcd', 'acbddaca', 'dacadbac', 'aabcbcdc', 'ababdcba', 'ddddcbab', 'cbacdbbd', 'dbaccdbb', 'cdbbaabd', 'dccbdadb', 'dacbccbb', 'ccdabbcb', 'dddabacc', 'dbbcadbd', 'bcbaccdc', 'cabbadbd', 'cbddcacc', 'adaccdbd', 'bbdbcaca', 'bdbbaacd', 'cacadabb', 'adbcacda', 'aadcaacb', 'bbacddad', 'dadcabbc', 'babcabdd', 'ccabadba', 'aacdcdbb', 'abdddbbc', 'dcbdacdd', 'dcbbdbac', 'cbcadbac', 'bbdadcca', 'bdacbbcd', 'dadcabdd', 'dbbcadab', 'bbadcdcc', 'dbdabdcc', 'caadbdcd', 'acbabdad', 'adccbada', 'cdadacba', 'bbccbadb', 'cbcddaba', 'accbdcda', 'dcbbaadb', 'bdcaccbc', 'ddabcabc', 'caccdacb', 'cbcdbdaa', 'ddcabddc', 'bbcadbcb', 'cdabbadc', 'bbcacdda', 'bcdabadb', 'acdacdbb', 'dcddcbca', 'cddccabc', 'cdbbadba', 'bbdadccd', 'dcbadaba', 'acbbdddd', 'adbbadcb', 'bcaddacd', 'ddabbcdb', 'cbcddadb', 'abadadcd', 'dbacadab', 'cdabcdcd', 'bbcdabcd', 'addcbaca', 'abdccdac', 'dbcacacb', 'baccdada', 'cbcbbabd', 'acbddbca', 'cacdbdac', 'dcabbdcd', 'ccacbcda', 'bdadcdca', 'ddbddcda', 'babcdbda', 'dddbbaac', 'cdbcabcd', 'cbbaacdc', 'bddadcba', 'bacdbbdc', 'aacdbbaa', 'adbcbdcd', 'accddcbc', 'dadbaddc', 'cbcaacdb', 'dcabdadd', 'bdabcdad', 'babddcbb', 'dcabbdab', 'dadabbac', 'abccdbac', 'baccabdc', 'ddbcabcd', 'bdbcacad', 'adccbacc', 'cacdbbda', 'bcbbdada', 'cbdabbad', 'abcddabd', 'abccadbb', 'dbcaccba', 'bdabcbca', 'cdbbdbca', 'ccbadcdd', 'dadacabd', 'bbadccda', 'cadbbadd', 'cadadcbb', 'cdbacacd', 'babcdada', 'dccdaabb', 'ddccbaac', 'ddabdaca', 'caabbcdc', 'dddabcca', 'bdacbcac', 'bcbacdcc', 'cdaaccbd', 'abdddccb', 'abdbdcad', 'bcbdccad', 'abddabdc', 'dcbacbcb', 'ccddbadc', 'dabcdcdc', 'bdccaadb', 'cbdbddba', 'bacdabbd', 'ddcabcda', 'bcacbdbb', 'abacddcb', 'daccbadc', 'daccdcbb', 'dddabbcd', 'bdabccad', 'addcbdcd', 'ccdbcbba', 'cbccdadb', 'abbadbca', 'bcbadccb', 'ddcaaddb', 'ccbacbbd', 'adbbcddd', 'bbadccab', 'bacadbdd', 'cdbadacc', 'ddbccbba', 'cdadbcbc', 'bccbaabd', 'ddddbcaa', 'ddcddcab', 'cabccabd', 'dddacbdd', 'acddcbdb', 'dbabcdbc', 'bdabdcdd', 'bdacdbac', 'dadbddca', 'adbcdcac', 'bcaddbab', 'bbcdbcaa', 'caddbabd', 'cbdbabdc', 'abcdccdd', 'bcdcdadb', 'babcbdda', 'cddbdaab', 'babcdbad', 'cabbdbad', 'dacacadb', 'bbcdacdc', 'ababcddb', 'dbdadcab', 'ddcddadb', 'acabdabd', 'ccabdaca', 'bcabbddc', 'ccdddabb', 'dbdbdcca', 'bdddcdba', 'cbcdddac', 'dadadbdc', 'baddccdc', 'adabcdad', 'bcdbbabc', 'cdbbabcc', 'ccbddada', 'cbccdbba', 'bdaccacd', 'abbcbddb', 'adacdcdb', 'adbaccac', 'bbabdaca', 'dbcdbabc', 'abdccdcb', 'cabbcbdb', 'ddcabcdb', 'dadcbacc', 'bdabccac', 'dbbabacd', 'bddddcad', 'dacdbcca', 'cbadabca', 'cdabddab', 'cacaccbd', 'cbddaadb', 'bdbddacb', 'ccbabbcd', 'cadbadab', 'dbaacbdb', 'cacddabc', 'cadabbcb', 'dccddcab', 'dcbcdacc', 'abbccbda', 'bcabddca', 'cbddbaaa', 'adadccdb', 'adbaddcc', 'acbcbddc', 'cbbdaccd', 'acacdbca', 'cabbcddc', 'dbcabbca', 'bdacddaa', 'ddbcddab', 'abdddabc', 'bdccadca', 'adccbdbc', 'badbbcac', 'dacbabca', 'dccdabdc', 'abcbdcbc', 'cddadbca', 'cadbcdcd', 'bdcdccba', 'dcbccabc', 'dbcdcadd', 'bdabcbad', 'bbaccdac', 'badccbdd', 'cbcbbdca', 'ddacbaad', 'cacdabca', 'dadcddbd', 'dacbdacc', 'cddadbbc', 'dcdabcbc', 'dcddbbab', 'dcdcabac', 'bdcdddad', 'cabcbabd', 'badcadcd', 'bdcadcdb', 'abacbcbd', 'baccadbd', 'bdcadcab', 'ccadbabb', 'bdbdddca', 'ccbcdaad', 'ababdcdd', 'bbdaacaa', 'ddabcdad', 'badbccdb', 'bcbdcacb', 'adccbadc', 'bcabdbdd', 'babbcdab', 'ccbcabdb', 'dbccbaac', 'bacadbbd', 'ccddabda', 'bcdadbda', 'ccabcdbb', 'adadbdca', 'dddcbada', 'acabadcb', 'ddddcabd', 'cdbdabab', 'dacabdca', 'bcdacdda', 'bcdadada', 'bdacbddd', 'bddababc', 'adcdddba', 'dcaccbbd', 'ddbcdaac', 'dbcbcaab', 'acdbadab', 'dbcaabcb', 'dabcbabb', 'daacbaac', 'bdadbdcb', 'dbdddbca', 'daacbaab', 'aadcdbcb', 'cdbcbcac', 'dbccaddc', 'acacbddb', 'dbbcaacc', 'bcacdbcd', 'cabdbacb', 'dabacbba', 'ccbbadca', 'cbbdddca', 'aacbbdcd', 'cadddccb', 'dcbabdbc', 'accbdddc', 'ccdadcbd', 'cacadbad', 'accdcbcd', 'bdcdbacb', 'dccabcac', 'bacadadd', 'bdbaabcb', 'dadcbbab', 'dbcacdad', 'dbbacbab', 'bdacddad', 'cdbacbdc', 'bccdcabc', 'cdbbabdb', 'cbaabdaa', 'cabadddc', 'acabacdb', 'bcbbdbba', 'bbcacdcc', 'ddddcdab', 'bcbbcbad', 'acdbdbbd', 'adccabcc', 'dbacacca', 'abdbadcc', 'bdddbcca', 'bddccada', 'cdcbbcba', 'bcabbcad', 'ccddbbaa', 'acbbdadd', 'abdacbdb', 'acababdc', 'dcdaacbc', 'dbaadbcd', 'bddcddad', 'cbcadbcb', 'bdcbccba', 'badbdcda', 'dddcbcaa', 'bbdcbbca', 'abdbcacc', 'dccbbcba', 'ddaaccbb', 'dcddcadb', 'ccabdccd', 'adbcadbd', 'adcadccb', 'cbbdadad', 'adcabccd', 'ddaaccab', 'aacbcdaa', 'dccdbada', 'bbabddcd', 'babadacb', 'ddbddcaa', 'dddbdcac', 'dddbacdb', 'acadddba', 'caccbcbd', 'bbdcdbac', 'cbddadba', 'dbddcaaa', 'cadbcdba', 'ddcddabd', 'ccdbacbd', 'dadadcbb', 'cbabbcdc', 'bcbcdadc', 'dbabdbca', 'cddcacba', 'ababbcdd', 'cadcdbac', 'bbdcbcab', 'dacbdbdd', 'cbbadbdc', 'abcabdad', 'bcabcdac', 'cdbadbbc', 'bcdcaabd', 'dadacddb', 'bcacadba', 'aadcbcaa', 'abadaccd', 'abbabacd', 'aadcbdbc', 'dbdaddbc', 'cdabcdac', 'cbbdcbab', 'dbbacbbd', 'ddbccdaa', 'ccadcbca', 'dddadbac', 'adcacbda', 'ddabdacb', 'dabcddcc', 'cbccadbd', 'acdcdbad', 'ddadacbb', 'bbadcbda', 'ababdacb', 'bbdaabdc', 'cabadcdd', 'cdbcbbca', 'acbdadda', 'adadcacb', 'cdaadcbb', 'bcbdabcd', 'ddddccab', 'cbdadbbd', 'bcbdbdac', 'bddacadd', 'dadcacab', 'bacdbacc', 'abacdbba', 'dcbabaca', 'addcdaab', 'bbddaccd', 'acbddaad', 'ccaccbad', 'dcbbdbab', 'bcbddbca', 'dcbcbbaa', 'cdaccbdd', 'dbcddcda', 'addddcbc', 'bdcbbdda', 'bdcdbaad', 'cadcabad', 'badacdac', 'dbadabcd', 'cbadaccd', 'bacdccad', 'acaddbad', 'cbdbbabb', 'baddbdac', 'dbccddac', 'cadbddac', 'bdacbbcc', 'baacbcdc', 'dcaadbdb', 'bcbcbadb', 'adbbdcbb', 'bcdbcaca', 'ababdcac', 'cbdacddd', 'aabdbcbb', 'dbcaadbd', 'cdcbadcb', 'ddcdbdca', 'dbdacbcc', 'dcbbcbad', 'ccddabbc', 'ccbcacdc', 'adabacab', 'cbbccdba', 'adabcdcb', 'cbabbdba', 'bcdccbab', 'dabbacbd', 'dcbbcdad', 'adbddabc', 'dcadabdc', 'dbddaadc', 'badcbada', 'acdbadac', 'cdcbbdda', 'cdbdcdaa', 'bdddabac', 'bddcabac', 'dacabcab', 'cacbcddc', 'abbcdbcb', 'cbadcbcc', 'dbaddcbb', 'cbaccdca', 'cbddbadb', 'dbacdcdb', 'caabbcbd', 'cdaccbba', 'adcaccab', 'bbabbdcc', 'dacbabda', 'ccdadbda', 'adaddbac', 'bccadbcb', 'cbaadcdc', 'baddbbcc', 'cacabbcd', 'bddcaccb', 'cdaddbbd', 'abcbcbbd', 'bcbddcca', 'ccdbaabc', 'adccdbac', 'bbcadbdd', 'dcaddcdb', 'dddccabc', 'cdbccadb', 'bddacbbc', 'abadbdcd', 'adbabcdb', 'acbdabdc', 'dcadbbdd', 'dacbadcd', 'abdbbdcc', 'badbdbcb', 'abddbdcb', 'cbdaadcb', 'cbdabbca', 'abbadcba', 'aabbdbcd', 'accacdbc', 'cdadbcdc', 'cabdacdc', 'adbbacbc', 'bddadbca', 'dacdcbdb', 'cabbcdbc', 'bddacbcd', 'babcabda', 'cbabcdbb', 'bddccacb', 'bbcdabab', 'addcabaa', 'ccdabdcd', 'dcdbddca', 'cdabacdd', 'bccabacd', 'dcbdcdda', 'adcbbacd', 'dbbaddcb', 'baddbcda', 'caadbdcb', 'cabbddac', 'cddcaadb', 'abbcbbdc', 'badcbacb', 'adbbabbc', 'dacdbbcc', 'ccacabad', 'ccabacad', 'abbdcbdd', 'dcacbcad', 'dcbdaccd', 'bcbadadd', 'ddcaadcb', 'ccbcddca', 'acbdcacc', 'ddddbcad', 'bcbbacdb', 'cbcbaabd', 'bddadcdb', 'ddcbabac', 'abbddbcd', 'dcdadbcb', 'cbddcaaa', 'addaacbd', 'cdbbcadb', 'bcbaadbb', 'dccbdbab', 'dcbdcabc', 'adcbcdbb', 'dbabbdca', 'bbcdacdb', 'acadbadd', 'cacadcab', 'cabbdcdb', 'abacadcd', 'bacdbbcb', 'abcbddbc', 'acbdaddc', 'bdcaddcc', 'bddacdac', 'dbcaccbd', 'cbacdada', 'acdbbadb', 'dabbcdad', 'adddddcb', 'cacababd', 'cbdbbaca', 'cdbdaaaa', 'dbbdabcb', 'bbddacdc', 'cdbcaddd', 'addcddbb', 'cdadbbac', 'acbcdddb', 'accabadb', 'bbacdadc', 'cdcbdcab', 'bbddcbaa', 'ccdcbadd', 'cbcbcadb', 'dccbabac', 'cbadddab', 'dadcdcbb', 'adabcdac', 'cdddbaaa', 'bdcacaca', 'abdbccda', 'aabcdbbd', 'bcaadbbd', 'bcdccdac', 'cbddcacd', 'abbdcabd', 'bcdacada', 'dbdaaccd', 'ccadbbab', 'adbabcdd', 'cdcabbca', 'ddbdcacd', 'cdcabbad', 'adacbadb', 'daabdcbd', 'cbbcacad', 'cacadbba', 'dbbacadd', 'ddaccbab', 'bbabdcdd', 'dccdddab', 'babbcdad', 'ddbdcbaa', 'bdacacad', 'acabcdab', 'dcdcbabb', 'cacdbabd', 'badcbbcc', 'abccdcac', 'abdcdbdd', 'abaccacd', 'badbcdcd', 'adbccdbd', 'abcdadda', 'badabacb', 'cbaacdbd', 'bcdbdadc', 'daccdbcd', 'ababbddc', 'ccbbdbab', 'bcbdcacd', 'ddacaccb', 'bcdcadca', 'cabbdcdc', 'dadabcdc', 'ddbbcbca', 'bcdabbcb', 'bcacdacb', 'bccbabdb', 'bdabbdcb', 'dbbcabab', 'cdacabcd', 'bcadcbbd', 'bcdadcad', 'dbcbacac', 'bdcadccd', 'cbccdbac', 'ccacbdca', 'cbcabdca', 'bcddbdca', 'cbcdcacb', 'aabccbbd', 'bdddcadd', 'adbacbca', 'cdcabcab', 'cacbbdcd', 'cdcacbac', 'bcadccbc', 'acdbcabd', 'acddbbca', 'cdacbbad', 'aaaadccb', 'bdbacdab', 'bcadacbc', 'bcbdddaa', 'ddbbcbad', 'cdcdcaab', 'cbbabbda', 'ccaacdbd', 'acbdcbba', 'bcbdaacd', 'accdcbbc', 'bcdccbba', 'cdcbdcac', 'cadbdabb', 'abbcabbd', 'bcaadbdc', 'ccbcdcda', 'cbbacdad', 'dbbccdca', 'bdccbbad', 'abcdcabd', 'cbbcadca', 'daccddab', 'dbdcbabc', 'dcdddbaa', 'adbabccd', 'ddcdadab', 'dacdcbdd', 'babcadab', 'bdccbdad', 'bdbacacd', 'bdbbabdc', 'bacdccbc', 'acadddcb', 'caadaabb', 'abccabda', 'abcacbad', 'dacdbcdc', 'acdcbcad', 'dccaabaa', 'dccbcbda', 'dbdbabcc', 'bbacabdc', 'dacbcadc', 'bbdcbadc', 'bbdcbdba', 'bdacabda', 'adadbcdd', 'cbcddaac', 'bddadcac', 'dbccaadb', 'abddacad', 'cbbdabba', 'bcacddaa', 'cdddbcab', 'cbccddac', 'ccababad', 'cddbadaa', 'abbdbbcb', 'bbcdddad', 'adbadcca', 'dbcbcaca', 'cbacadab', 'cacabbda', 'ccbaddab', 'babddcaa', 'cbbddaab', 'acdbabcd', 'cddcbaad', 'acdddbcc', 'cbcdbcca', 'bdbacabc', 'addccacb', 'cdcbaadc', 'bdacbcbd', 'baccacad', 'adbdbacd', 'abcbdbac', 'dbbdaacc', 'dcdabaca', 'ccaacdbb', 'ddcadbdd', 'cbadbddb', 'abbcdddc', 'acaddbab', 'adbacadb', 'acdbdacc', 'bccacdda', 'dbcabdbb', 'badadadc', 'dbcacadc', 'bdccbada', 'badbbadc', 'ccabddcc', 'abdabcbc', 'bcdaaaad', 'acdbddcc', 'adcacbca', 'bbcbddac', 'dbbdabbc', 'bcddabac', 'abacdcac', 'cddabcdb', 'babccbdd', 'abbdbcda', 'dccbcdad', 'dcbdbdca', 'babdadcc', 'cdcdabab', 'adbdddcc', 'bbdabadc', 'dbcbdcda', 'bcadbcca', 'cdbcbcda', 'cbaddbbc', 'adadacbd', 'badcacad', 'bdacbcdb', 'acbdbada', 'adacbddc', 'dcdcabcc', 'ababdbcd', 'bcbacdad', 'acadbacc', 'cbdcbacd', 'bdaadcbd', 'ccdabdbb', 'abdbbdcb', 'accadabd', 'dacabbda', 'dacbadcb', 'cdabbcdd', 'cbabbddb', 'accbbdda', 'dcacabdc', 'bbdadccb', 'ccabcddc', 'dcdbbaca', 'adbddbcb', 'aabaaccd', 'ddbabcda', 'accbdcab', 'bddbabbc', 'adadbccd', 'addadbdc', 'cacbbcbd', 'caddaacb', 'ddbcbacb', 'ccadbddc', 'cdabdbdb', 'dcdacbdd', 'abdbbcac', 'dadacdbb', 'ccaddccb', 'bdacdddc', 'ddcdbbab', 'bbcadcac', 'dcddcabb', 'cabbdcac', 'dacabddc', 'bbdcbada', 'ccaddbcd', 'cdbbcdab', 'cadbcadd', 'cdcdbdaa', 'abcdcbbc', 'dcbcadbd', 'abbabcdb', 'bcdccacc', 'adbdcaca', 'bcdbddaa', 'cadccadb', 'dbcbcaba', 'bddaacad', 'ddbcbaac', 'dcdcabba', 'acabcacd', 'dacdddbd', 'acbccddd', 'addbcbbc', 'bccabcdd', 'dabaccdd', 'bddcabdd', 'abaccbcd', 'dcbdaacc', 'acdbabdc', 'abcbaddd', 'acddabac', 'acdddaab', 'dadcddbc', 'bbdaadcd', 'daadbccd', 'cbbacdcd', 'ccadbdcc', 'caddddcb', 'ddddabdc', 'dbdccdaa', 'acbdccbb', 'cbdabcbb', 'abddacbb', 'bcddcbab', 'cbdadcdc', 'bdbcbada', 'adcbbddb', 'bdccadad', 'dbcacbdb', 'cdbabccd', 'bcababda', 'dbabacca', 'abacadab', 'badbddbc', 'accbcdab', 'bbcabbdb', 'bcabacdc', 'cbaadbcb', 'cadacbab', 'accbabdc', 'dadcbddd', 'cdacdbdb', 'ccabadab', 'ccbadcad', 'cadbddba', 'ccdbbada', 'ddcdbdac', 'bababcdd', 'ddaccbac', 'abddcaac', 'bbabbdcb', 'cdacbacb', 'dbddabcb', 'bbabbcdc', 'ccdaacdb', 'bbcdacac', 'babcbdbb', 'cadbbadc', 'dadcbddb', 'bdbdcbda', 'cdbcbcaa', 'dabbcdda', 'cbdcdbda', 'cddaabbc', 'cddccdba', 'abdddcdb', 'cbdcacdd', 'ccddcbac', 'dccbbcaa', 'bacddabc', 'dcacddab', 'dbdbccaa', 'daacaacb', 'dcdbdcac', 'cdbacbcc', 'dbcacacd', 'dddbdcad', 'bcaccbcd', 'cdbdaabd', 'cdacdbad', 'bccdcaca', 'ccbdabbd', 'cacacdab', 'bdbbcbaa', 'cdadbabd', 'dacdbabc', 'cacdbcdd', 'acdcadcb', 'adcdcdba', 'dcabdbad', 'abcddccd', 'accddbcd', 'ddcadbcb', 'cdabccbc', 'dbacdcba', 'cdbabddd', 'accbbdad', 'acacbdac', 'dcddbacb', 'ccaabcbd', 'ccbdabdb', 'cddaccbb', 'bbabdbdc', 'ddbabbcc', 'cdaddddb', 'ddcdbabb', 'ddbcaaab', 'dcdbdabb', 'ddabacda', 'acdcbbac', 'cbacbdbd', 'dcdabacc', 'dcaaccbb', 'abcbdcab', 'acaddabb', 'adabcbba', 'ddacacab', 'cdacdbcb', 'dbdabcdd', 'cbdaacdb', 'bdadbaca', 'dccbaabb', 'bddccbaa', 'badcabcc', 'dbcabcdb', 'dcbbcadb', 'dbbcaadb', 'dcaccbcd', 'baddacdb', 'bbdcddaa', 'dcadbddc', 'dcabbdbc', 'dcadbbac', 'ccbdcdac', 'cdbbccad', 'adccadbd', 'cabcdcac', 'cbddabad', 'abddbccb', 'bbabccdc', 'cdcacbdb', 'bcadcdab', 'cbbdbadb', 'bdabbcac', 'bbcdcadb', 'badcbabb', 'aacdbaad', 'dbacbacd', 'dbabbddc', 'badbdcbc', 'cdcadbda', 'dcbbdbaa', 'cbcaaaad', 'dadbabcb', 'acdbcadc', 'dadacbad', 'abbddbbc', 'bddaccbb', 'cdbddcda', 'badcbabd', 'adbcdcca', 'cadbbcbd', 'babdbcbc', 'cbddcbca', 'dbcdbbad', 'bbdbcdac', 'caabdbcd', 'dbcdabca', 'cacdbadd', 'adccbccb', 'ddbacbdd', 'dbdcacdb', 'ddaacbcb', 'cdbdbdba', 'cdbcadcb', 'dbabdddc', 'daadbcbd', 'acbddccd', 'ddcbaacd', 'dbbcdbaa', 'dacacdab', 'bcbdacad', 'bbacabdd', 'ddbcdbab', 'cdbccadc', 'ddadccbc', 'addacbda', 'acabcbcd', 'dbacdcac', 'aadbaacb', 'abcdabdb', 'babaccdb', 'cabdcddd', 'bcddaaad', 'dcdbacdd', 'accbcadb', 'cbdddcaa', 'adccadbb', 'dbacaccd', 'adcddccb', 'dadcbbad', 'cadbdbad', 'cdcdbadc', 'acdbbacc', 'adcabddc', 'cdababdb', 'dcdabbcb', 'bcacdddc', 'bcdcbadc', 'accdcbac', 'cdaacdbb', 'cbabacda', 'cacddbcd', 'dbabccba', 'caccbdda', 'dbaccacd', 'adbcbacb', 'aabcaabd', 'cabcabad', 'bdaadbcd', 'adcadcbc', 'dacbddcc', 'ccbcacdb', 'bbacdaca', 'abcacdca', 'cdabbdab', 'ccadbbdd', 'dababacc', 'cdddadab', 'adcbdbad', 'dbbacddc', 'acabdadc', 'abdccacb', 'dcacbdad', 'dbacdccd', 'acbcdcbc', 'abdbdbca', 'bacbadba', 'abddcbab', 'adbcabdb', 'adabcadc', 'ddbcaddb', 'abcdadba', 'cbcdaabb', 'aaccaadb', 'bacadbac', 'abbdcadc', 'bbcdaccd', 'cabdadba', 'dabbdcba', 'dacacbdb', 'bacddadd', 'babbdacb', 'bdcadbba', 'bdbcdaba', 'cacadabc', 'cbacdcbc', 'babaddca', 'cbccabad', 'acbdadba', 'cdcdbcaa', 'bbabddac', 'bddbabcd', 'cadccbdc', 'bcaddcbb', 'adacdbdd', 'bcacadcb', 'cddaabda', 'dcabcaba', 'acabdcdb', 'adcdbcbd', 'cbccdcad', 'dcdaacbb', 'abdbcdbd', 'bddaadcb', 'dccabcca', 'accbbdca', 'abcbacbd', 'aadbccdc', 'ddbbdcba', 'dcdabdab', 'babacbdb', 'badacacd', 'abcdacca', 'ddacbbac', 'cdcbdbab', 'dbccdabb', 'cddccbca', 'caddbbdc', 'dbcacdac', 'badbcdab', 'acdbdacd', 'acdabddd', 'babbcdcd', 'abcdbadb', 'bdcaddcd', 'bcdbabca', 'cbdbabdb', 'bacbcdba', 'cbacabdc', 'bdabcbba', 'cbacbbdb', 'bdbaaccb', 'dddbcdca', 'bccadbbc', 'bbabcdcc', 'bdacbdba', 'daccabca', 'cbcaabcd', 'dadbacca', 'cbbcabbd', 'cdccbcca', 'abdcbacc', 'bcaadcbb', 'dbcabcad', 'aaccdbbc', 'dacabcad', 'dcbadcbd', 'cddadbab', 'acdcabcb', 'bcbcaadb', 'ccdadcbb', 'bcabddaa', 'ccdbdbba', 'cabdabad', 'abbdbcbc', 'dbcdbdad', 'bcdcbcab', 'dccabcab', 'dcdcdbad', 'bdacbdcd', 'bcbdabdb', 'cdddadbb', 'dabdcbcd', 'cbbdcabd', 'dbdccbda', 'bcadcbca', 'acdacdba', 'bcaaccdb', 'bcbbdaab', 'ddaadbbc', 'bddacacc', 'baddbbac', 'cddbadab', 'dcdabbab', 'ddcbcbac', 'dddbcaba', 'ddbcaacb', 'cbdddcad', 'badabbdc', 'abcdbacc', 'bacdadbb', 'cdaddbca', 'dbcaacdc', 'abbddaca', 'cdcabccb', 'dbcbbaca', 'dbbacabc', 'ccdabccb', 'abdccdcd', 'cddadbcb', 'caccbdad', 'ddadcdbc', 'addaabcc', 'cacacabd', 'abcbdbab', 'ddccbacb', 'cbdcaddb', 'bcdbabcd', 'cddabaac', 'babcbadc', 'aabcdcbc', 'cbbdbcaa', 'cddccdab', 'ddbbacca', 'dcacdcba', 'baddcbdb', 'cbddbcad', 'caaaadbb', 'bcacdbac', 'ddabbacd', 'cacdbbcc', 'adcabacc', 'ddcbabab', 'bbcaddab', 'cbabdadc', 'dacacabb', 'adbacbbc', 'dbacbdbb', 'bbaddbcd', 'bcdccacb', 'cdddbadc', 'badcbdbd', 'daddbcda', 'cdccabab', 'cdcdcbab', 'bbdbaccb', 'dbdadbcb', 'ccdbddab', 'ccbbcada', 'bcddcbad', 'ddabcbcb', 'dbcbabac', 'acbabddb', 'cddabada', 'acdacdcb', 'cabccdca', 'dddabcab', 'cbcdbcad', 'bbcbdadd', 'cadbbdad', 'cadcbccb', 'cbdbdcaa', 'ccdaccbd', 'adadbcca', 'adacbabb', 'ddabbcbb', 'dadadcab', 'ddcbaaaa', 'cdbabdcb', 'bcddcabb', 'bcaddacb', 'bccddaba', 'bccbaddc', 'dababbcb', 'acbddbba', 'bacbddac', 'cbbdacbd', 'ccdabbcc', 'bddcdcaa', 'cdbabacb', 'dccabcbd', 'accbbddb', 'ccadbcdb', 'dabacdda', 'bdaddbcd', 'abadddcb', 'aabcaadb', 'cabdddbb', 'bddcadcd', 'dbbcddac', 'ccbcdbab', 'acdbbdcb', 'bccdbada', 'adacdbcc', 'cdbadccb', 'dbcbbdad', 'dccbabbd', 'dadbdcdb', 'ccdabacc', 'ababcdbc', 'abcbcdda', 'bdbdbadc', 'bcbccdda', 'ababcbdc', 'daacbcdb', 'dbadddcd', 'dbdcdcac', 'adcbcabb', 'cbcddaab', 'adcdddcb', 'adddcbbd', 'bcaddaca', 'adcbbdcb', 'cbdddcac', 'ddbcbaab', 'cdbbcdda', 'addaddcb', 'dbcdcada', 'cacdddbb', 'adcacacb', 'bbaaccdb', 'dcbccdab', 'acbabbdd', 'badadcdb', 'baccdcdb', 'cadbccdb', 'addcbaac', 'badcadab', 'bddcbdad', 'acbdabab', 'cbccabdb', 'cdbccabb', 'adcabbdb', 'bdbadcda', 'dbcbcdac', 'cbcabadd', 'adababdc', 'abcdbccb', 'cdcadbdd', 'adcacbbc', 'bccacdcc', 'abbcdbca', 'caccbabd', 'ddabcbbd', 'dbacdcca', 'bdcaabcb', 'dbbadcdd', 'dcbabbcc', 'bbdcabad', 'dacbcbac', 'dbabbcbb', 'accacbdc', 'dbadccdd', 'ddaccbcd', 'bdccbdba', 'bdabcdca', 'bbddcabc', 'cabacadd', 'dadddbcc', 'dcbbabad', 'dcbdabdc', 'cbdbbada', 'ccdbccda', 'dccdbabc', 'bdbcddca', 'adcbbdca', 'cacdbbac', 'cbdccaac', 'ddadaccb', 'bbdbadcc', 'bddbbacc', 'cbbddabd', 'dddbcacd', 'abcbdccb', 'dacabdbb', 'dcbadddb', 'acabccdb', 'cdcbbdca', 'acbcdddd', 'cddbabdd', 'cadccbdd', 'cddcbdac', 'bddcbdab', 'accdbbdd', 'bddcdabc', 'cbdaabcb', 'bdbdcaca', 'dccabbdb', 'ddababcb', 'ccbabbda', 'bcabbadd', 'cbdbdaca', 'dcbdaddb', 'bccaccdd', 'cddbdaad', 'bbadbbcd', 'abdbacab', 'bcddbabd', 'dbdbaacd', 'cadacdbd', 'baccdadc', 'bcddaabd', 'addbcaca', 'bdbadcdc', 'bcdaabbd', 'acbcdbda', 'dcbaadbb', 'dbbaccab', 'bdcdddaa', 'cabcddca', 'bccbcada', 'bdbaccac', 'badcbaba', 'babacbda', 'cadbaddc', 'bdabdbca', 'dadccbda', 'adbcabac', 'cabcabdd', 'bddcadac', 'ccdaabbc', 'bbaccbad', 'cddccacb', 'bdddcadb', 'acdaccbc', 'cdacbcdd', 'dcabdaba', 'dadcbcda', 'dbcbbaad', 'cacdccbc', 'dadddcba', 'ddacadcb', 'cbbccadb', 'dbcadcac', 'ddbbabdc', 'acadccbd', 'cbbabddb', 'addcbaad', 'acbaccdb', 'acbacdbc', 'dcbbcabc', 'dcbdaacb', 'acabbdad', 'ccbddacd', 'ccdcacdb', 'cadbcbdc', 'cdabcbba', 'adbdcbdd', 'bdcdaccb', 'bcddbbca', 'addcbadb', 'dbbaabcd', 'acbdccdd', 'cabbadda', 'dddbdbca', 'dcdacdbb', 'cadaddbd', 'cadabadb', 'bddabcac', 'ddbbcadd', 'bcadccdd', 'dbbdacdb', 'bcddaccb', 'bddaccaa', 'cbdcbdba', 'cbcacdcb', 'bddacdab', 'dacdadbd', 'cacbccdb', 'dbbabcba', 'ccbcadcd', 'acddaddb', 'bcddabdd', 'ccbcddab', 'cabcdcbb', 'ababdcca', 'baddcdab', 'adccdadb', 'dbbcacca', 'ddcabbcc', 'adadadcb', 'ccddbaac', 'bcdbdaab', 'cbdabdcb', 'bddacddd', 'badcdadc', 'cbbddaad', 'cdbdaddd', 'bdbcdacb', 'dbbccaca', 'abcddbbc', 'abcdcbdb', 'aadaabcd', 'ddaaacba', 'dadabdbc', 'acbacdbb', 'dbcdabab', 'cbaddabd', 'dacdbabb', 'dbdcadcc', 'ddcaabcc', 'abbcdddd', 'dcabdacb', 'accdbddc', 'cdbcbaad', 'dadcbdbd', 'bdcdbbca', 'bdcadacb', 'dcabdddc', 'dadccabd', 'ccddbabc', 'ddcabdac', 'abcabdda', 'cddabbdb', 'cdabddcb', 'dddbcaab', 'dcbbccda', 'dccdacbb', 'dbccacca', 'abbacdad', 'dbddbbac', 'aacaadbd', 'bdbaccba', 'dccabcda', 'addcbabc', 'dbcbacbc', 'addccdbc', 'dadbdbcb', 'ccdaccab', 'dccbcaab', 'ccddacbd', 'dbcabdba', 'dcbcadad', 'bccdccba', 'addcbddb', 'babdbabc', 'bbccdadd', 'acbdbccd', 'bcdcaacb', 'bcadabcc', 'dabdcbdd', 'cdddcadb', 'cacabcbd', 'cddcbbad', 'abcbdbca', 'bdacadac', 'abccdadc', 'bbdcabac', 'cbcddaca', 'dcbbadcc', 'dacababb', 'bdbacdbc', 'baccdbbc', 'abbcdcbb', 'acbdccdc', 'bcacadac', 'abdcacad', 'bbcabadd', 'bdbdaacb', 'bdbbacbb', 'abddddcb', 'daccabab', 'dccbabab', 'dcbbdcca', 'badddacd', 'cabdbbcc', 'bdcacdab', 'cbddbabd', 'abcbaddc', 'dbdadcba', 'dbcadcdd', 'cadbcbca', 'ccbccadd', 'ccdcdabd', 'cbddccaa', 'daabbcdb', 'dcdcacbc', 'dbdcacac', 'ddababcd', 'cbababdb', 'dbdbccac', 'ccddcaba', 'cabcadbc', 'cddcacab', 'cdaddbba', 'ccaccdbb', 'dcaccbac', 'acbabcbd', 'ccddcbba', 'baddddca', 'dbccadcd', 'abacbcdb', 'dacbddac', 'dbcaabdb', 'ddbaacdb', 'dddccabb', 'bccdaacb', 'dbdacacb', 'ddbaaacd', 'dacbbacd', 'bbcdacbd', 'abccbdad', 'bddcddaa', 'adcdcbcb', 'bdaadccd', 'bcabacda', 'bcabcabd', 'babcdddd', 'bacdacbd', 'cbbacadc', 'cddabdcc', 'dcbdacab', 'accadcdb', 'dccadbba', 'bdadccdc', 'badabbcc', 'adacbacb', 'ddbdbacb', 'cadbacda', 'bdccbadd', 'abcbdabd', 'bcdadbcb', 'dbbdbcba', 'dcdbadda', 'cadccabd', 'bdcacddd', 'dadbacba', 'bacbccda', 'dadbadca', 'baccbadd', 'cadddbad', 'bcbadacc', 'bbdcbaba', 'bcdaaaab', 'cdccabad', 'bbacadbb', 'dddbcdda', 'bcdddbda', 'dddadabc', 'abdaccbd', 'ddcabdbc', 'bcbcdbac', 'dcabbabd', 'cadbadbb', 'ddbcbabd', 'bdaabdbc', 'dbbddacd', 'ddcdddab', 'cdabccda', 'daabcdbb', 'dbbdabac', 'acadabcd', 'dababccd', 'ddbcdacd', 'bcbbabad', 'accbdcbd', 'cbbcadac', 'bdabcadc', 'bcbabdad', 'dcacbcdc', 'dadbadcb', 'bacdacca', 'cadbbcba', 'cabddacd', 'dbcdabac', 'bcaddcbd', 'adbabbcc', 'cdccbcac', 'bddaccdd', 'bacdbcab', 'accabdbd', 'bdbcbdba', 'cdabddbd', 'bccbacad', 'cbadaddb', 'caacdaab', 'dadcabba', 'dcbddbac', 'dbabacab', 'dbbccaac', 'bbddbacb', 'abacdcca', 'cddbdcac', 'bcbbdacd', 'abcdaddc', 'cddbdadd', 'dccdcbaa', 'bcdcaccb', 'bbacbbdd', 'ccdacbab', 'aadbdcbb', 'badcbdda', 'cdadbcdb', 'bbacdada', 'ccdbacca', 'cdaccbac', 'acadbdda', 'abdcabcb', 'dddbaadc', 'dabcbdad', 'ccbaadcc', 'dbdbdaca', 'ccdaacbc', 'cbcddcca', 'ddbcdaca', 'cdddbacd', 'dadbdbcd', 'bbadacdc', 'ccbdabcc', 'bcdcabca', 'daccbbab', 'adddcaab', 'cbdadbcc', 'caddcbdb', 'bcbdadba', 'bcadbcbb', 'dbadadbc', 'ddcbddaa', 'caadcdcb', 'abddcbad', 'ddabcadb', 'bccadcba', 'dabdbacb', 'abdcdbdb', 'abbcdabb', 'bcbdcdad', 'bdbacacb', 'bbcaccdb', 'caaccdbd', 'ccbabdab', 'bcbadcdb', 'bdabadbc', 'bdbabcac', 'cdbbdcda', 'cdbddaab', 'cbdababc', 'caabbdcc', 'adbbdbac', 'bdcadadb', 'cdbdcbca', 'dacddbab', 'bcaacdbc', 'ddacbbcc', 'cbdacaba', 'dacbdbdc', 'acddadba', 'bbdcacdc', 'cbdaccac', 'ccdacddb', 'aadbbccb', 'cbacdbab', 'cdcbaabb', 'bddbcaab', 'bcddbadc', 'badcabcd', 'dcbdabbc', 'caccdccb', 'bcdadcdb', 'daacdbbd', 'baacbdaa', 'cbcdbadd', 'adcbbcab', 'accdbada', 'dcacacba', 'bccdabba', 'dddcbabb', 'dbddcacd', 'ccabbdac', 'cbbdaacb', 'cdcbbdac', 'dddcbdda', 'daddaccb', 'ddcbcdaa', 'abdadbca', 'bdacdacd', 'baddcacc', 'cbbdbdab', 'cabccacd', 'bcadcdad', 'ccdbbdda', 'bcbaacdb', 'adddabcc', 'dbcbcbad', 'bcaccdba', 'ccdbbcac', 'ddaaacbc', 'cdcabdbb', 'ccdacbbd', 'dbddacab', 'aadbaabc', 'cbcadcbd', 'cddaabab', 'dcbbadab', 'ccabbadc', 'adcdcbcc', 'dbbabcca', 'bacacadb', 'bcdddbac', 'acbabbcd', 'adcacbdd', 'abbdbacd', 'dcbdbaba', 'dcbccdaa', 'bbcacdbc', 'dcbadabd', 'ababccdd', 'dcadbbcc', 'abcacbcd', 'abadcaba', 'bdacbbab', 'dcdabbac', 'acacbdda', 'cbbccbda', 'bcbdacbb', 'cdcbddac', 'dabbdcbb', 'bccaacdc', 'acddacab', 'cbdbadcb', 'cadbcdbd', 'dcaddbaa', 'cdcbabdc', 'cadcabcb', 'adbadaca', 'acbcdbac', 'cdbabbab', 'adadcdbd', 'cbdbddda', 'dddacbac', 'aabdbcbd', 'cabcacdc', 'bdbccadb', 'ddaaabcd', 'accdccbd', 'ddabbdcd', 'abcddbcc', 'baabbcdb', 'acbdbbdc', 'dcdcbcca', 'addaabdc', 'dbbacdbc', 'bbcaadbc', 'abbdcabc', 'bacbdbcd', 'cacbddbd', 'bdccdacd', 'baccbdca', 'adadabcd', 'bcddcbaa', 'bddaabca', 'cbcabdcb', 'badacaba', 'bccabcad', 'cdccabcc', 'ddbbacad', 'bcaddcda', 'dacbadab', 'dabcdbdb', 'dadbddac', 'babcabcd', 'dcdadcbc', 'caabdaac', 'cdbdcbab', 'badbccab', 'accdcbcc', 'ddcabaca', 'adddbcbc', 'abdacacd', 'ccbddcac', 'acbdcdcb', 'adbcdaca', 'dadcbdcc', 'caccdcab', 'abaddadc', 'ababdbdc', 'acbcdcac', 'cdbdbadc', 'dbacddca', 'dacbcdbb', 'ccdabcad', 'cacadcba', 'cbdaadcd', 'bbdacbdb', 'ddaacbad', 'bcdbcadc', 'daadbcdc', 'cdccbcad', 'bcdbcacb', 'abccbdab', 'abcdbaba', 'bbdccaab', 'cbcabcad', 'bdddbcac', 'dcbdcaab', 'ddaacdbb', 'bcdbdbba', 'dcddbaba', 'bbadacac', 'badcdbac', 'cabaccdc', 'bdabacbc', 'acdadbdc', 'cbdcdacc', 'badbcbbd', 'cddadaba', 'bcdcaaaa', 'abbdccac', 'adcdbcbc', 'adccdbdd', 'aacbdcdc', 'cbdcbabb', 'bdcabbcc', 'dbcddaca', 'abdcdabc', 'cdcbccda', 'abcddcdc', 'abdbdaca', 'cabddddd', 'dcbcdacb', 'abdcbbac', 'cddcbbac', 'bdcdabdc', 'dadccadb', 'ddabbcab', 'bdcababb', 'bdbcbcba', 'ccababbd', 'cacbdcbc', 'dbacadbd', 'bdcddada', 'bbdbbcaa', 'bdacacac', 'cdabdbda', 'bbdcdada', 'cdacbbca', 'cbadddaa', 'aadccbdc', 'bdadbddc', 'bdcbcacd', 'cddabdaa', 'ddcacddb', 'bbdcaabc', 'dddcbdba', 'acbacbcd', 'ddadacdb', 'ddcbabdd', 'acdabbad', 'dcadabdb', 'dccdbadb', 'ababadcc', 'dbdaddcb', 'cbbdaadb', 'adbcdcdc', 'cbdabadc', 'ddcdacbb', 'bcdbcdca', 'bbcdddba', 'ccabacbd', 'dbddaacd', 'cdadbcab', 'dbaacbbc', 'bcbabdba', 'bcaddbca', 'bbccdbad', 'caccbcdb', 'ddcacdbc', 'dbcadbdb', 'bbabdcab', 'ddcdbcba', 'aaccdbdc', 'dcdbddda', 'dabcbabd', 'bccdaccb', 'bacabdad', 'bdadccab', 'dacdcdab', 'cdcdbcac', 'caddcbcd', 'abddcdcb', 'ddacbccb', 'abddcadb', 'badbbccd', 'baddcaca', 'dccbdabb', 'cadcddcb', 'dadcbbdd', 'acbdcbbd', 'cadcbdba', 'cddbcbba', 'cdcbabcc', 'ccbdaabc', 'cdbbddba', 'abdccbcb', 'cdbbdaca', 'dacbcdba', 'cdbcdcca', 'adbbacba', 'dbacbccb', 'dbacbacc', 'badcbdbc', 'dcbadddd', 'bbccddad', 'cbadbcba', 'adcdabda', 'adadabac', 'abcbadbd', 'bcabdbcd', 'adccabbc', 'bddacbcc', 'ccbbdcac', 'cdaddacb', 'cabddaba', 'dddcdcba', 'cbcabbdc', 'adcbdcbb', 'cbdadbad', 'daabaacb', 'dcdabcba', 'bacacadc', 'bbdcdaca', 'dccacbbc', 'bdababcd', 'bcddddba', 'dbcddabd', 'cdcabacb', 'acddcbdd', 'dbdbbcaa', 'adbdcabc', 'cadbdcdd', 'dacabdba', 'bbccdbba', 'abccdddd', 'abdbacbc', 'baddacca', 'abaddcbd', 'bdcacadc', 'dbdcaacc', 'dccbaabc', 'bbcdbadd', 'dcdabdca', 'ccabccad', 'accacdab', 'bacdadcd', 'dbababcc', 'adcddcbc', 'dbbdacdd', 'dacdbadc', 'ddccdbda', 'addcabbc', 'bddaddcd', 'abccdbad', 'cddbacbd', 'acddbbab', 'cbdadddb', 'cdbcaadb', 'bacacdac', 'dabcbdcc', 'dccdabcb', 'bcbdabad', 'bdcbbaad', 'bdbbacdd', 'acbccdba', 'bcadbcdd', 'cbdadcca', 'ddadbdbc', 'bdcdbdca', 'daccbadd', 'abccdcbc', 'bccaccad', 'cdbabcdd', 'dbaadbcc', 'bbdbcdba', 'dccbacbc', 'bccaacdb', 'cdbbabdd', 'ddddbcca', 'bacacdbd', 'cadcbbcc', 'dccacadb', 'dddbaacb', 'acdabdcb', 'ddcabbac', 'dabbcbdc', 'cdadcabc', 'dbdbbcad', 'dcbcbcda', 'cadbdddb', 'dadacbdc', 'cbdccacc', 'abcaddbd', 'abcbddba', 'cbacddbd', 'dadcdbbd', 'bbcdbbda', 'cdacbcda', 'dbcdbcda', 'cbcbadcd', 'bbcbcada', 'bddbacda', 'ccbcacdd', 'aacbdaab', 'cadcbdac', 'ccaddbac', 'abaddcbc', 'cdadbaba', 'ddbdccab', 'cadacbdc', 'abddabcb', 'dadabcbd', 'dbddaaac', 'cbadcbac', 'cadabdcd', 'dbaddccb', 'bdcdbcba', 'bcdbabda', 'bbdcbadb', 'dabcdddd', 'bdbdabcd', 'bbccdcad', 'accdcabb', 'bdcbddda', 'cbaaaacd', 'dcbdcacc', 'badabcdd', 'bcaadccb', 'cbddcdac', 'cdcabcba', 'dabdbcdb', 'ccabdcba', 'ccbadbac', 'dadcddba', 'cdcdcabd', 'cdaccbad', 'adcddbaa', 'bbdccacd', 'bccbabcd', 'bcbccdca', 'accddbad', 'cbabddaa', 'abadbcda', 'dcdbbcad', 'bacabbda', 'adbcadcb', 'cacbbdbb', 'bcababdb', 'bccddcaa', 'dccabada', 'badcbcda', 'bcdacdcc', 'cabddbcb', 'dadddabc', 'dabdcbdb', 'adcbcbdc', 'bbaacdbd', 'acbbcbdb', 'cbcdaadb', 'bdbdabcb', 'bccabcbd', 'abcbbdbd', 'bbaccada', 'bdbabdcc', 'bbcadaca', 'cbabdcda', 'cdabcacb', 'adcbbdab', 'dbcdacda', 'cadccbac', 'adacabcd', 'ddcbbaca', 'accbdbcc', 'bdabbadc', 'addccbba', 'bdaaccbc', 'dccbabdb', 'dbdcdcca', 'acdcabbd', 'bbadccbd', 'aabdbcbc', 'bccabdab', 'dbdbadcb', 'accdabad', 'acbbcadd', 'cdddcacb', 'bdacacca', 'acbbdbba', 'dacdaccb', 'bbdbcabc', 'baccdbdc', 'cddaccbd', 'babadacd', 'dcbbdadc', 'dbdcabbc', 'adadbbcb', 'abccddab', 'adcdddbd', 'dbcadcda', 'bdaabbcc', 'bcbbadcd', 'cbbcabdb', 'dabbdacd', 'dcdaabaa', 'acadadbc', 'bdabbcba', 'daddbcbb', 'babbcdbb', 'adcdcdbd', 'dcaadbbd', 'ccabdbab', 'cabdccac', 'ddcbdacd', 'accdbabd', 'bacadbcb', 'adbdaddc', 'cadacdbb', 'bbcabada', 'cbcdadac', 'cbdbcaca', 'ddbdccac', 'ccbcbadb', 'ddccbdaa', 'bdacabba', 'dddcdabb', 'cdccabcb', 'bcdbdbca', 'cbbadadb', 'acdaccab', 'dccbbaca', 'dcddacbd', 'bdcdcaca', 'abddaddc', 'caddcbad', 'cdcaddab', 'dadbcacc', 'abcabdcc', 'daddabca', 'bccacdbb', 'cdddbdac', 'aaccbdcd', 'abdabcad', 'bdaccdac', 'addaccba', 'adbcacba', 'dbbdcabd', 'adcbbdcc', 'baccdcca', 'dabcacdb', 'dcdccaba', 'dbdadcca', 'cacbadcb', 'bdcadacd', 'babccbbd', 'bdcaddad', 'bacbadac', 'ababcdca', 'daaaacbc', 'ccdabddb', 'ddcaddbb', 'dbacbbcb', 'dadcdabd', 'cbbaccad', 'acbcbdac', 'dcdbabcd', 'abdddaac', 'cdacacbb', 'baacbbdc', 'cbbccbad', 'bddcaabd', 'bbacbbda', 'dadcbdab', 'bbabcbdb', 'ccdbdacd', 'bdbdaadc', 'bdccacbd', 'cbbdaabc', 'abcdaddd', 'acbdcabb', 'acdbdcca', 'bcdcabbd', 'abcacddd', 'abcdcbdd', 'ccbcbaad', 'cbdbbdba', 'bcdcbbad', 'dabbcbdb', 'dcddcaab', 'ddadcbbd', 'acabdccd', 'cadccbcb', 'dbcddbca', 'ccadcbac', 'acdabbda', 'cdbdacab', 'ddaddbcc', 'dcacbbda', 'bdbddacc', 'accabddc', 'dcbadaca', 'acdbdcbc', 'cddbdaac', 'addbcdbc', 'dbaccadd', 'ddccabad', 'ccaacbdb', 'bccbddad', 'aacdbcbd', 'cbadbdad', 'bccbcdda', 'acadbbdb', 'bacabadd', 'ccaddbdc', 'abbccada', 'bbdcdcba', 'acbabacd', 'abddcbbd', 'bcbdcaca', 'cbdaccda', 'ddccadab', 'adbacdcd', 'bbadbcdb', 'bacabdbd', 'cadadbcd', 'acddabda', 'cdbbdadd', 'cbabdbdb', 'bdbdabca', 'ccbdacca', 'bbabcdab', 'bddcdbab', 'dbdbacbb', 'cdbbadab', 'cadcbabb', 'dcddadbb', 'bcdacddb', 'adbddcac', 'dccabcad', 'dccbcabc', 'bdadcdba', 'badaccad', 'dcacbbcd', 'dbbcbcaa', 'abdbbaca', 'dcabcaca', 'cdbabcad', 'dbccaadc', 'bcaddadd', 'cadabbad', 'ddddbbac', 'cadacbcb', 'acdcbaca', 'cbdcbada', 'babacadc', 'cdaadbaa', 'dabccbbc', 'abbccdac', 'dddcacbd', 'bbdbbacb', 'abbdbccd', 'cdacaddb', 'cadccbbd', 'cbdacdad', 'cbadacbd', 'cacbcdca', 'acdcbbdb', 'bdcaddbd', 'cddbaaca', 'cddabaab', 'cbdbaaaa', 'ababacbd', 'acdbbcab', 'badbdadc', 'adbadbcb', 'ccdcadab', 'cbcaccda', 'dbdcacab', 'cabbabda', 'ccdbbabc', 'dbabcdab', 'aaccdcbc', 'abccbadc', 'bacddbdc', 'bbddcaaa', 'bbadacbc', 'ddbcdcad', 'ddaacaba', 'acbcdccb', 'cbdbbdab', 'dbbacdda', 'badcddac', 'acdbacac', 'dcbdbadc', 'dacdbcdb', 'acadcbcb', 'dabdadcd', 'dcbcabcd', 'adabdcdc', 'dcdddcba', 'aabcbbdb', 'ddddcadb', 'dddacbaa', 'dcdbcbac', 'cabcabbd', 'abcbdddb', 'cbcbabbd', 'accdabbd', 'dddababc', 'abcddbac', 'badcbdcd', 'ddabdcda', 'babcbacd', 'ddaccbcc', 'acdcbcbd', 'dbdcbdba', 'bbacbcbd', 'bbacdcbb', 'adbcbcac', 'ddbdabbc', 'badddddc', 'abdbdbac', 'bdbcaaaa', 'bbcbaadc', 'bdcdadbd', 'bdddacbd', 'addbbccb', 'bcbacddc', 'ddcaaccb', 'ddcdabdb', 'acbdccab', 'badbcaca', 'cacdcbac', 'dcbbdcac', 'dbdccbab', 'abdabcba', 'dcadabda', 'cdcabcbd', 'dccaacdb', 'dcacacbd', 'dcdbcada', 'ddbbcbda', 'bddbccda', 'cdddabca', 'caccabda', 'ddacdaab', 'ddcaabac', 'dcdacbda', 'ccdabdca', 'ccbadcbd', 'cbbacbdc', 'cbcaabbd', 'bcdbbabb', 'bcbccabd', 'addabbdc', 'acacbadd', 'badddcdd', 'bdcbacda', 'cabbcdac', 'abacbddc', 'dbcabdcd', 'dabcbbac', 'acbcacad', 'adcbcbcc', 'abccddac', 'badcddda', 'cdbdaacd', 'badbccac', 'abcdacbd', 'accadacb', 'cdbaadbd', 'bcadabcd', 'bacbbccd', 'dadccbdd', 'acbadbcd', 'addcddba', 'bacacbdc', 'dadbcdcd', 'dbdcddab', 'abdcbccd', 'abdccbca', 'daadaacb', 'bcadbbda', 'bdabcada', 'cddaabcd', 'bdacadda', 'cacbacdc', 'dcdbdcda', 'acdbbddd', 'bdccdbad', 'dcbcacbc', 'badababc', 'babddcbd', 'dcddcbaa', 'acdcabdd', 'addbacba', 'abcdabdd', 'cdaabcdc', 'dccaaccb', 'ccbaacbd', 'cbddbabc', 'dbcacadd', 'abbddbcb', 'badabacd', 'bacdcddc', 'cabaccda', 'abddcacc', 'abcdabcb', 'acadcbab', 'bcadcacd', 'ddbccaba', 'bdcbcadc', 'abdacdca', 'cdcdcadb', 'cdbdcaca', 'ddcaccbd', 'cbbcabdd', 'dcbacbad', 'cdcdaabd', 'ddbdcaca', 'bdddcabb', 'cacbcbda', 'dcabdbba', 'adacadbd', 'daddacdb', 'badabcba', 'ccdacbba', 'cabdcdac', 'bcabccda', 'bcadbbac', 'dcddcdba', 'bcdaccab', 'acdcdbbd', 'abaccdbd', 'dadbccda', 'acdbabda', 'dcdcbabc', 'cddaabdb', 'cababbdd', 'dcdacbcc', 'cbdadbda', 'daccdbba', 'ababdadc', 'cbdaabdc', 'dabbcacb', 'ddcbadcc', 'dbabadcc', 'cadadcbd', 'dabccbca', 'cdadcaba', 'cacadbac', 'cacadbcd', 'acabdadb', 'cacbadbb', 'abadbbac', 'cbdbcacb', 'aabcbaad', 'bbdbdcac', 'cbdabaca', 'cdddadbc', 'cbdaddaa', 'bdadccbd', 'cacdcbab', 'bbcadcbb', 'bcdacdac', 'dcbddadb', 'bdbabacc', 'abcdbdda', 'bbacddbd', 'bcdadbdc', 'dcdbbdba', 'bcbabddd', 'cdadcbca', 'cdbabbad', 'dbabacdd', 'cdbcacda', 'badcaccd', 'abcbbdad', 'cbddacdd', 'abbcbcda', 'cbcadbcc', 'bdcdcadc', 'adacbdcc', 'bcbacdca', 'cdddbcca', 'abdddcbd', 'dbadbacc', 'cdbddadd', 'abacbdda', 'dccbcbba', 'cbbcdaab', 'baddcdbb', 'dabadcad', 'ccbcabda', 'bdbaacaa', 'adbcacbd', 'acbbddba', 'cbbabdcd', 'dbddadac', 'abddacdd', 'dcabdabd', 'dcbcbbab', 'bddcddba', 'bacaccbd', 'dacacbac', 'dcacabbd', 'ddcbadcd', 'bbdcbdac', 'abcdddcd', 'cbbaddaa', 'ccacdbcb', 'dccbcadc', 'bbdcbcaa', 'acdcadbd', 'bccddabc', 'dadbcddc', 'dbdacadc', 'acdcddba', 'bcbdadbd', 'dacbcdcc', 'ddbdccad', 'cacbbabd', 'bdbbaddc', 'bcdccadd', 'babdacda', 'abacadca', 'badbcbca', 'ddbcdcac', 'ddcabcdd', 'dcdcacbd', 'cbddcacb', 'ddaaacbb', 'bdccdadd', 'bccdcaba', 'badcadbb', 'accacdbb', 'cacadbbc', 'cabddbac', 'abadbdac', 'bdbdcdad', 'babccacd', 'acabccbd', 'cbcdadcc', 'baddabbc', 'cadbacba', 'bccdcbad', 'bdbadacd', 'bccdbbca', 'bacddada', 'adabadcc', 'adacbadc', 'bccaadbc', 'bdacddac', 'abbccbcd', 'dccacbdc', 'bdbcaacd', 'adadbbcd', 'dbcbddab', 'cbacdbdc', 'bbdbcbca', 'dcdbccaa', 'dccdabbc', 'abbcddba', 'acbcdacd', 'dacbbcdb', 'dbaabaac', 'cdcabddd', 'ccdaabaa', 'ddbabaca', 'cddadbdb', 'bcdcacbb', 'cdddabaa', 'ccbbdacd', 'dabcadab', 'dadbcdbc', 'cadddbcc', 'dcadadcb', 'abdadcca', 'dbbabacb', 'ddaadabc', 'abcddbaa', 'dbdacdbd', 'acbbddcd', 'bbacdcbd', 'cddddbad', 'dbdadabc', 'abbdbcbd', 'caabcbdc', 'bcdcabdd', 'bdbabacd', 'dbddbacc', 'ccbabdad', 'abbcadcb', 'bcddbbac', 'dddddacb', 'dcbcdabd', 'acadbcab', 'ddaaaccb', 'bbcdbcda', 'dadacabc', 'bbcbcdad', 'abdadcdb', 'bccddacd', 'bdbcdacd', 'ccabbdbc', 'dadbbacb', 'accdbcbd', 'adcbdbdb', 'baddcdda', 'dbdabbca', 'accdbdac', 'bdbaddac', 'bbcdadca', 'daddcbba', 'ccadcbcd', 'addaabbc', 'acbadcbc', 'abcaddab', 'acadccba', 'ccbbdcca', 'cadabddd', 'bdcadccb', 'dddadcab', 'abbcbbdd', 'dbabacbc', 'bbdcbcad', 'bacbcdbd', 'bdacbdad', 'bdcddbad', 'bccdacab', 'dadcbada', 'cbabdadb', 'bababcdb', 'dcdddaab', 'dabbcaca', 'bddbccba', 'caccddbc', 'ccbadbab', 'dbbcbbac', 'baccdadd', 'adabbaca', 'aacdaabb', 'dacbdccb', 'dacbdcdd', 'badcdbcd', 'dcabdcbb', 'ccaccbdb', 'ccabdabb', 'dbcabdcc', 'bccacdbd', 'bdcaccba', 'dcbddacb', 'ddbcbdad', 'abadabbc', 'abdcdcca', 'cbdcdcda', 'acadabbd', 'accbadbc', 'dcaddabb', 'baccabda', 'bbdabdcb', 'cdccbacb', 'badbcabc', 'dddcaacb', 'ccaadbbc', 'cbbcdabb', 'ddbadcab', 'acaddcbb', 'cadcdddb', 'bdacddcc', 'ddcaabcb', 'bbdcbcac', 'cabdabca', 'dacaddba', 'acdcbcab', 'cbbabdca', 'acbddacc', 'cddcbbab', 'acadabcc', 'cbadccac', 'cbbaddbc', 'bcabcddc', 'abbacdca', 'dbbcdcaa', 'bbdcadab', 'dcbadadd', 'cabdaddc', 'cdabbdda', 'dcbaaaac', 'dcacdabd', 'addcbdda', 'dbcacada', 'bcdabdcb', 'cbadcacb', 'abdcadda', 'dbabcbdd', 'cbdcadda', 'adcabdda', 'adbccbcb', 'ccbdbdac', 'bcadccbd', 'cbcbdabd', 'cbadbabd', 'abdcdbcb', 'cdadbddb', 'acabbdda', 'bcbddcab', 'bbacddcc', 'bdccbbaa', 'dccbadca', 'bacadcbd', 'abdadacd', 'acdbacda', 'bbadbabc', 'dddccbac', 'bdcabdbc', 'cdccbaac', 'badcbcab', 'dcabbcbd', 'accbcdcd', 'ddcbacda', 'ccbadacd', 'cbbcbada', 'bbcaccad', 'adcabcbb', 'cdadddbc', 'dccbdabc', 'addbdacd', 'adbadbca', 'cacbdacc', 'bbdadbca', 'badacabd', 'cdbcdaba', 'dddabaca', 'cdaacbdb', 'dbccbbad', 'bccdbdad', 'caacaabd', 'bcaacbdc', 'adcaddbd', 'cbddbacd', 'addcbbda', 'badaccdb', 'baacbdcb', 'cddbdabb', 'dddabdbc', 'cabadacb', 'bcdbacba', 'cabbadac', 'dcabadda', 'dbbcbbab', 'bcabcadd', 'ccbbddca', 'ccacbbdd', 'bddcadba', 'caccdadb', 'bcbbccad', 'bcaccddb', 'baaaadcc', 'dbaccbba', 'adbabdac', 'badddcaa', 'abdbabcb', 'bcbdcdaa', 'dbccddda', 'bcabdbca', 'dcacadbd', 'ccddabdc', 'adcabccb', 'baaccdcc', 'cbacdddd', 'badadbcb', 'dbabcbcc', 'bcbadbba', 'dcbbdcaa', 'dddacadb', 'dbdbcaad', 'dccbcdba', 'cdddaacb', 'ccbdaabb', 'adabcdcd', 'bcadccdb', 'caddabbd', 'aabdcdcb', 'acadabbc', 'bbabacdd', 'abadbcac', 'addbdadc', 'adbcddaa', 'ddacbcba', 'dcaccbcb', 'abacdadc', 'dabbdcca', 'dabadbca', 'addcddbd', 'cadcdcbc', 'bbcdadbd', 'bacbccbd', 'cbcadacc', 'dacaccbc', 'bdccacba', 'cdcbacab', 'dcaacbcb', 'bdddcbab', 'acbadcdb', 'adbdbacc', 'cbcdabcd', 'abbcddca', 'adabbdcc', 'babdcbad', 'dabbddca', 'cbcacacd', 'dbaacbcb', 'aacbbdaa', 'acabdbac', 'bbcaabdc', 'bdabacdc', 'dcbaabcb', 'cbacbabd', 'ccadbccb', 'cbcdadcd', 'cddbcadd', 'ddabbacb', 'ccdbcabd', 'bdcbcdca', 'baddadac', 'adbdacbc', 'cbcacada', 'accabbdd', 'bcaccddc', 'cabadada', 'dcdbccac', 'bdcbbada', 'adbdccda', 'ccdbddda', 'dabdbdcb', 'bdbdcbca', 'adcbcbda', 'dccdabad', 'dbbcadcb', 'dcbbcacd', 'dabccbbd', 'acadbccd', 'cbacbdbb', 'dbaacbdc', 'bdbacaba', 'bdaacdcb', 'cbdddbaa', 'bdcdacac', 'ddacabbd', 'bacddbcc', 'dbabbcac', 'cdcdaadb', 'bdcabbda', 'bdcbbacc', 'cdbcadcd', 'adddcabd', 'dbccdadc', 'cadcbcbb', 'bacbbcdb', 'cacdbacb', 'ccabddbd', 'bcbbdcad', 'abdcdcdd', 'acdbdaca', 'bbddacab', 'dcdabdad', 'cbbadacc', 'ddaacbdc', 'ccaddcbb', 'bbadcdab', 'cbacbacd', 'abddadcc', 'ccbacdcb', 'cdbcaccb', 'dcabcbac', 'ccbadbad', 'bccabbcd', 'bdddcdab', 'cbbcdaad', 'baacbcbd', 'abcdabcd', 'ddaacadb', 'bdcbcdab', 'ddbbcdab', 'cabdccbb', 'dbddcaab', 'ddddbacb', 'bcdbdaad', 'abcacbdb', 'bcbaaccd', 'addbcbba', 'ddacadbd', 'dadcbadd', 'bcacddbb', 'dbcbcaad', 'bdcbbcda', 'ddabcacc', 'ccaabdbc', 'daadcbcd', 'bccdddab', 'cdbddacd', 'cdcadbbc', 'cdddbadd', 'dddabbca', 'cabdddba', 'adbbcabc', 'bacaddca', 'dbabcddd', 'cabbddcc', 'daadcbcc', 'bcbcdcca', 'abcbacad', 'acbcdcda', 'ddabcada', 'adabdcbc', 'babddabc', 'cdbacdbc', 'bcbccacd', 'acbcdcbb', 'addaacdb', 'dabcbbdb', 'ddaddbca', 'dcbccbaa', 'bababccd', 'bdbaddca', 'bcbccadd', 'cbdcbabd', 'dacbbcbc', 'bcacbdbc', 'bcddbdba', 'cbacacdd', 'bcbbacdd', 'cadcdbda', 'dadddcbb', 'acbadbdc', 'dcbbabcc', 'bcadcdca', 'cdbdadcd', 'ccdcadbd', 'ddcbadaa', 'bdcaadbc', 'addabdcc', 'cbaabdbb', 'cbaccddb', 'dcdcbcab', 'acbbcbda', 'cbbcddab', 'cdadadcb', 'bdbcaabd', 'cdbcaccd', 'cdbabbac', 'dbcbccac', 'dcdbaabd', 'cbadcbdc', 'ababdacd', 'dabccacb', 'bbdabdca', 'bbaadcdb', 'ddabbadc', 'bddbacaa', 'abdacdcc', 'abacdcbd', 'abdddcac', 'dabcbbca', 'adddcdbb', 'adccbcac', 'aabdcbdc', 'aadccbcb', 'cbdcdaac', 'bacbdbdc', 'acbcddda', 'adcadaba', 'cabcadab', 'cdbbcadd', 'ccabdcdb', 'accdbdad', 'dcbcaadc', 'adbadcbb', 'cbabdacb', 'cdbddcac', 'bcdbbacc', 'dbdcaccd', 'ccacadbb', 'dddaadcb', 'dbcddbac', 'bdaccabc', 'bacbcbdd', 'acbccadc', 'dcbadacb', 'dbdcbbab', 'bdadaccd', 'cacbcbdd', 'cddaabdc', 'cbdacdbb', 'ddcdacba', 'babbdaca', 'acbdcbca', 'adbdcabb', 'ccbddadc', 'badbcbcb', 'bdcbccac', 'cbcdacbb', 'abcdabad', 'dddbcdaa', 'adccadbc', 'adccddbc', 'bdcbdadd', 'acadcbad', 'bdabcaca', 'ddbacddd', 'dbabcbcb', 'babdadca', 'ccbdddda', 'abadccbd', 'ddadbaca', 'bbdbabca', 'adcbcbba', 'cabbdabb', 'daacbcbb', 'ccbddcba', 'cbadadac', 'ddaccdbc', 'bdccbcad', 'bcadddbc', 'ddcbddad', 'bdbcabba', 'cbdcaabb', 'badabcdc', 'ddbdbabc', 'cbddaacb', 'abdcadcd', 'cbbabdda', 'daccbdca', 'ccbbcabd', 'bccdbbac', 'acbdabbc', 'dabdadca', 'cbadccdb', 'cdcadbab', 'bdcaabdc', 'cdbabbcb', 'badcbcbc', 'adcabbac', 'cdcabaca', 'bbdbcada', 'bddaaccb', 'ddbcddca', 'addcdccb', 'cddadcba', 'cddbdbac', 'acbacdca', 'dbbabcac', 'bdcdddac', 'dddccbda', 'dadcbdda', 'cabacddd', 'bcdddbba', 'dbaccdbd', 'dbaddcaa', 'badddbdc', 'cabadabb', 'bddbdacb', 'ccbdacad', 'dbaccabd', 'dcbbdadb', 'cabdcdba', 'dcbabdcd', 'bbcacddb', 'bccdcaab', 'bcdabcdd', 'ccadcbcc', 'acbdbdad', 'adacdabb', 'bdadcada', 'bdcddacd', 'dddacdbc', 'cbccdbca', 'bbdcdbda', 'bbddaccb', 'dadbadbc', 'dcddbbac', 'adbcbabd', 'dbacbccd', 'ddabdddc', 'acacddba', 'baddadcc', 'ccdcbbca', 'bddcbabd', 'bdbdbdac', 'cbbcbadb', 'cdbcacba', 'dbcacddc', 'bacdacad', 'acaddbda', 'ccdacdbd', 'bbaadcbd', 'bdbcdbda', 'abcdabda', 'ddacbdab', 'cddabcbb', 'dddbcdab', 'abcabdba', 'acbddcda', 'bcddddac', 'bbadbaca', 'dcbdacac', 'dabdaccd', 'dddcadbd', 'cbdaccad', 'cbbdcacb', 'ddbaddbc', 'cbaccada', 'dabdbbca', 'ccbcdbac', 'badcadca', 'acabbabd', 'dbbdadac', 'dadcbdbc', 'acdddabc', 'bccbcdac', 'adabbdac', 'ccabdbbd', 'cbcabadb', 'dbbcbdad', 'bdaccaba', 'abdccbdc', 'ccdabbda', 'addcabdb', 'ddbdddac', 'bbdacdab', 'bbacdccb', 'cacddadb', 'adcdddab', 'ababccad', 'cdcababb', 'bdadcbbc', 'dadcdaba', 'acabcbad', 'ccaadbcb', 'adbdcdbc', 'cddabacd', 'bcaccdbd', 'dbaddbcb', 'cabdacbd', 'cdcadabc', 'ddcacbdd', 'bdddccaa', 'dabddbca', 'acdddbac', 'bcdcbcba', 'babcbcad', 'adcbacdc', 'aacbaadc', 'bdccbabc', 'dcdbaacb', 'dacbcacd', 'bcacddba', 'baddacda', 'ddbbaccb', 'cbddddab', 'cabdadbc', 'babacdac', 'dadbcbbc', 'ddcbaaac', 'dcddbcab', 'bdbaacbd', 'cabdabbd', 'baadbcdc', 'dbdbdcad', 'cdddaddb', 'dbadcacd', 'acdcbcdb', 'babdbdcb', 'acbdbcba', 'dbaccbcb', 'bdacaddc', 'bdabcbdc', 'ddbcadba', 'cdcbacad', 'bbcdcacd', 'dddcabcc', 'bdabacda', 'dcabbcbc', 'dacbcddc', 'bcbcacbd', 'dadccabc', 'bbdbbcab', 'daccdbdc', 'cabbcdab', 'cbacbdbc', 'adadbddc', 'dcbdbcba', 'cbdbbabd', 'ddbbcabd', 'dcabcbbd', 'cdcabddc', 'cacadbca', 'cdbbddac', 'addccdcb', 'acdbabac', 'abdaddbc', 'cbcadbdc', 'addcdbdb', 'dcdbdadd', 'bdddaaac', 'cbbddcaa', 'cdbcadab', 'ababdbcc', 'acdddcba', 'cbdccbca', 'bcbcadcb', 'dccababb', 'bcbcdadd', 'abacdbcc', 'dbcdacab', 'cbcddada', 'badcdadd', 'adcacabc', 'dbabcabd', 'dcabbdcb', 'cdadacbb', 'adbcdbbd', 'dabacbcd', 'dacabcdc', 'bccadbba', 'abcadbcd', 'dbcabcdd', 'adcabcca', 'baaaacbd', 'bdacbaca', 'dbdbbcda', 'cddacbda', 'bdbdcabb', 'bbaddbcb', 'acbcbdad', 'adcbddba', 'cbdbdcab', 'adccabad', 'acabdbbd', 'dbbaddac', 'cbadacda', 'caddbdaa', 'baccbada', 'cababdca', 'ddbdacda', 'dbcdbaad', 'abdcbdda', 'dabcbdbc', 'bdcbdaab', 'bcdbadcb', 'abccdada', 'dacddbdd', 'cdbdddac', 'ccdaddbd', 'aadaacdb', 'bcaabdbc', 'abcdcacc', 'abcbadca', 'bacdacdc', 'dcbdcacb', 'badbacab', 'bcabacbd', 'cabdcabc', 'addbbacc', 'daccbdad', 'cbbdbadc', 'acddcdcb', 'bbadacdd', 'dbdadcac', 'addaccdb', 'dcbdbaac', 'ccbdacdb', 'bbddadcc', 'bcbdabbd', 'bdcadbdd', 'ccdacdab', 'abbacdac', 'bbacbdbb', 'accdadab', 'babacdad', 'addbcadb', 'ccabadad', 'ccadcdbc', 'cdabbdac', 'bcdadbac', 'bcabddad', 'cdbcddca', 'bddddacc', 'adadbccb', 'dcbddaba', 'cadcbbca', 'dbddbbca', 'cbdbaabc', 'abcdcbdc', 'dbdbbaac', 'adbccdbc', 'cbadcabd', 'ddbdbcba', 'bcbadadb', 'abadbcbb', 'bbabccda', 'bdabbcdd', 'dcadbacc', 'acdccbdd', 'dbcbbdac', 'cabacdba', 'dabcbada', 'cdcbbaca', 'cbadadcc', 'acbadccd', 'aabdcbcb', 'dcacaccb', 'ddabdcbb', 'dabcbcdc', 'abddbdcd', 'ddabcabd', 'acddbdcd', 'cddbabdb', 'dbadabac', 'cdccdbca', 'bdbdabac', 'daccaccb', 'ccdcbaab', 'abcdcbcb', 'acdbbdda', 'dabcabdc', 'cabcaccd', 'dbbdbacb', 'dbcbaabd', 'acbadbdd', 'dabaccda', 'bcbacddb', 'ddbcbbca', 'bbacdcdc', 'bcabbdca', 'bcadccac', 'ddbaccdc', 'addbadcd', 'ccdccbca', 'cdacaccb', 'dadbadac', 'caadbdaa', 'accdabca', 'adddcdcb', 'accbbadd', 'cadddbbd', 'addbcdcb', 'caddabca', 'baddcaab', 'bcabadbc', 'abbacdab', 'dbabbcbd', 'bdabbdca', 'bdbcabad', 'adbbcabb', 'bcdddaba', 'cbaadcbb', 'bcadccab', 'dbcdadca', 'cbcdadbc', 'dbbccaba', 'dacdbddb', 'cdbadadb', 'cabdbaca', 'bccdadbd', 'ddaaaacb', 'ccbdaadb', 'caddabdd', 'bcbdcdab', 'ddbdcbba', 'cadbacad', 'dddacbcb', 'acbdbddb', 'bccdddba', 'dbaccdab', 'acdbacbb', 'bbcacdcd', 'adddbaca', 'cbbabcdd', 'ababcbda', 'acdabacc', 'baddbbdc', 'dbdbdcda', 'dcabbcbb', 'cadbdbac', 'cdbccdaa', 'bcdacbcd', 'cadddcba', 'accdbcac', 'dbcaadaa', 'abcddddd', 'babcacad', 'ddacbaba', 'abbdacda', 'bcbbcbda', 'ddaacdbc', 'cbdcacab', 'dcbaabdc', 'adacbcdc', 'cabcabdb', 'cdcabccd', 'bcbcaccd', 'abdbcada', 'addcbabd', 'bacbbcdd', 'cdcbacdb', 'bbadabdc', 'bbcacadd', 'cddacbcd', 'bdccdaac', 'adabbcbd', 'ccacdcba', 'cabddddb', 'abdbadcd', 'cacdadbb', 'bcdacbdc', 'bbabdbcb', 'cdcbcaba', 'ccabdddd', 'aacbbcbd', 'dababdbc', 'ddacbddb', 'bbdcadac', 'cddabcca', 'bdbcdcda', 'bddaadcd', 'caddbcca', 'badcadba', 'cabdbcbc', 'bcadbaba', 'bdabdcbc', 'dcadacbb', 'acadcdbb', 'abdacacc', 'dccdaabc', 'bcddbaba', 'cdadcbac', 'bcbdadca', 'cbcacbbd', 'addacdbc', 'dbacdacb', 'bccadacb', 'cabcddbb', 'baacaadc', 'cdacddbd', 'acdbbddb', 'ddbcabad', 'cbcdbaba', 'adabbacb', 'cbabddac', 'cbcdddaa', 'cabaddca', 'dabaddcc', 'ddbbaabc', 'bacdcdbd', 'bacdcdba', 'cbbabcbd', 'dcbabcdb', 'adbcdcbc', 'abdbacda', 'cabacada', 'cbabadba', 'acdacbda', 'cadcbada', 'cbbdadbb', 'daabcaab', 'bcddbcba', 'cdddbbab', 'dcbdacca', 'bcdcaddd', 'cdddbada', 'bdbdccda', 'dcddbaaa', 'bdcaccad', 'bbcbaddc', 'cadabbca', 'cbabbcbd', 'bdcabdab', 'cddabcab', 'abdaccdb', 'cbaccbdb', 'adcabbca', 'babcdcac', 'aabdbcdc', 'addcdcab', 'cdbbdabc', 'dacbcbca', 'bcbbdacb', 'ddbccabd', 'bcadcaca', 'acbdcdcd', 'ddbccbad', 'bbdaccdd', 'bcabdccb', 'cdccbdda', 'dcdbbdaa', 'ddadabbc', 'ccaadbdb', 'cabddaaa', 'bcbabadc', 'bbabadca', 'cbacdacc', 'dddbdaac', 'dabdacbb', 'dbacdbcb', 'cbdcbbac', 'dbdacabd', 'bcbadbab', 'dbacbdac', 'cdcdacbd', 'bababbdc', 'bddacbab', 'bcddcdaa', 'acdbccda', 'bcdccdda', 'ddaabcdd', 'dbdabcdb', 'dabcabcb', 'acadabcb', 'cdadccbb', 'bbaccbdd', 'adacabca', 'daccbabb', 'cacbabad', 'dabccada', 'ddaadcab', 'cddcabcc', 'abddddca', 'cdbabcbd', 'cbdababa', 'accbcdac', 'cdbaabdb', 'bdcbabdc', 'dccaddcb', 'aadbdcbd', 'caddcddb', 'dbdbcbaa', 'bdaabccd', 'bcdcdadd', 'dbdbcdda', 'bdbccbba', 'abccbbdb', 'adabbdbc', 'acadbdcb', 'acbdacad', 'dbdbacab', 'adcbdada', 'ddbacdda', 'bacadabb', 'adbbcdca', 'abadbcdc', 'bcdddacd', 'adbcbcbd', 'badddcda', 'dbbacdcc', 'ddbacadc', 'badccbda', 'babcbdab', 'dadbbcdd', 'dbdddacc', 'abcdbabc', 'babdcdda', 'bcdbaabd', 'dbdcaacb', 'abaddcca', 'bdaddbca', 'cdacdbcc', 'baccabad', 'acddbddc', 'cacbdccb', 'aacbcdbd', 'acbacacd', 'badbcada', 'acbdcabd', 'dbccdadb', 'acdccbda', 'bbaadbcd', 'addbccba', 'dbbacbcd', 'bcdbdacd', 'acdddaba', 'dcadacba', 'bcbdcabb', 'acdadbcc', 'ccdbcaba', 'bbacdccd', 'cbabcadd', 'babddacc', 'acacbadc', 'cddddaab', 'dddbbcba', 'dbcdbaba', 'bbcbbadc', 'acbcadca', 'dcbaddad', 'bdbadccb', 'ccacddab', 'ddadbbac', 'cabddbdb', 'abacdddb', 'cadccdbb', 'bcddbcda', 'dbbcdaba', 'dacdbdbc', 'bcdbdcab', 'caccdddb', 'bbacbcdb', 'bdcbbdad', 'bdcdbcac', 'dddadccb', 'cdbcbacc', 'cdbaccad', 'bbcabcdb', 'dbcbbdaa', 'addcbccd', 'dbcabddb', 'cbcdbdda', 'bccadabb', 'cdcdabcb', 'adcbbacb', 'accbbcdb', 'ddccacbb', 'acdcacbc', 'ddbaabcc', 'bdbbcaca', 'bcdaddbb', 'dccdabdd', 'badbacbc', 'dabacbca', 'cdbadbac', 'adbddcca', 'adbbdbcd', 'cddcacbd', 'babcacda', 'cabcdbda', 'bcdccdab', 'bddaacdb', 'bcdadabd', 'badccdcd', 'abaccbdc', 'bbddbbac', 'cdcddabd', 'addbadbc', 'daddddcb', 'abbcdbad', 'ddbccbab', 'abcadbbd', 'babcaccd', 'ddbbaacc', 'dabcddca', 'cdcbdcba', 'ccddabbd', 'dccbaacc', 'aacbaacd', 'cbdcddda', 'acbdcadb', 'bbddbcab', 'cdcdddab', 'adcababc', 'bbacaddb', 'cadbcbcd', 'cbaddadb', 'ccabadcb', 'daacbdbc', 'abdcdabd', 'bdcbcbad', 'bcddadcc', 'adacbcbb', 'adcadbcc', 'cbbacdba', 'cbddabdb', 'dcdaabcb', 'dccdbacd', 'babdacdd', 'dacbccbc', 'bcdcadba', 'abdcdddd', 'cadbabbd', 'cbcdabab', 'dcadcbdb', 'cabcdcbd', 'bdccbcac', 'caddcdbc', 'cadcddbc', 'cdabacbb', 'cdabcacc', 'bbaaaacd', 'bdbbdcad', 'dcabadcc', 'dacdbbab', 'bbdabbdc', 'ddcbbada', 'cdbdddab', 'dddabcbd', 'bacadbba', 'bcaddcca', 'bcabdabc', 'bdcacacd', 'bddacbbd', 'addcabab', 'bbddddca', 'ccabbdda', 'addabdcb', 'baadcbcb', 'abacbacd', 'abccdcbd', 'cdbaacdb', 'dacabdac', 'cacddbda', 'cababdac', 'bccdbbda', 'dbcbaccb', 'bdccabbd', 'ddcacbaa', 'dbacbcbd', 'bdadcddc', 'bbcdacca', 'abdcacba', 'abdcdbac', 'addbaccb', 'acbddaaa', 'caddbaba', 'dbbcaccd', 'bddacbda', 'dadcdadb', 'bdacbabc', 'bbccdacc', 'abdcdbcd', 'bdcbadbd', 'abcddcdb', 'cbabdcdd', 'adccbcbc', 'ddcbabad', 'ddbabadc', 'dbccdada', 'bdcdadca', 'cddbcdca', 'dcdaddab', 'badbcadb', 'bdbccdba', 'cddcbcac', 'aabdcbdb', 'bdccabcc', 'abadabcd', 'cdbbacad', 'dbbcabca', 'bccbadbc', 'abbcbdba', 'ccdbdabc', 'cacbcbcd', 'dabbdccd', 'cabdddbc', 'adcdabab', 'cdddabad', 'cbbdaddb', 'dbabcbac', 'dcabcbda', 'dacbaccd', 'dbbacdcd', 'ddbdacdc', 'dbdaaaac', 'bdbcacdd', 'daadcdbb', 'abddbacb', 'bddacddc', 'dbabccda', 'dabcbbdc', 'ccbcabad', 'cbdcadba', 'dcbddabb', 'cdabbadd', 'bdddbbac', 'dbccbdac', 'dccbdbca', 'cadbcbab', 'cacddbbd', 'adacddbb', 'cdcbdada', 'bcdcbbca', 'baadccbc', 'bcbadabb', 'dcbbdacd', 'bdadddcc', 'abcadcca', 'abddbbcd', 'dabaddcd', 'cdacbada', 'ddbcddba', 'cdbadcda', 'babcacdb', 'dacbcddb', 'ddbdbaca', 'dbbaccdc', 'cbbcdabd', 'bcacbdcc', 'dbbabdac', 'dbdcacbb', 'bbcdacda', 'adbcbabb', 'aacbbdbc', 'adabdabc', 'dbcbbcad', 'dcdaddbb', 'abcdddcb', 'dbdaabcd', 'cdadbacc', 'ddaabcdc', 'ccbadbdb', 'addbccdc', 'bbcbadcd', 'abbadcdb', 'babadcba', 'ccbaccda', 'bbdcaadc', 'bcdbcbad', 'adcbdbbd', 'bdcbcacc', 'babdbdca', 'bdcdcada', 'aaaabbdc', 'cababcdb', 'cacdbdad', 'dcdcadbd', 'cadabdcb', 'ddbabbac', 'acbacadd', 'dadccbad', 'cbcbdcac', 'ddabcabb', 'cdbcacad', 'cdbbadcd', 'dabbadcb', 'cdbcbbac', 'accbdcdc', 'adcabdab', 'bbadddcb', 'cddbbadd', 'dcdabcdd', 'dddcaadb', 'ccabbddc', 'bccdacad', 'acaccdbd', 'adcabbcc', 'acabdbcd', 'cdbcbdac', 'cbabdacc', 'cdcabcbb', 'bbaabdcd', 'dacadabd', 'dbaddccd', 'adddcdbc', 'ccacacdb', 'bbacdacb', 'abccdcda', 'dcbdccda', 'badcdbab', 'cbdcdada', 'dddaacbd', 'bdbaddcc', 'ddcaadbd', 'bbadcdda', 'acbddabb', 'cbaacbbd', 'adacabda', 'bccddadc', 'cbbadcac', 'adacbcad', 'bdcbcada', 'bbdadbcb', 'bdbacbdd', 'dccadabb', 'baacdccd', 'dacdbdbd', 'cbadcacd', 'cdbacadc', 'cadabbdc', 'bbacddac', 'ddccbbad', 'acdccbcc', 'dadcdbdd', 'baddcbbc', 'abcaddba', 'dacbadda', 'dcacdcbc', 'bcdacaba', 'ababbdcd', 'dacdcbda', 'ccdcadcb', 'dddacbdc', 'adcbdccd', 'aacdbdcc', 'ddacbcdb', 'ccadccbb', 'ddcbbcac', 'ccbadcba', 'acdcdcab', 'abbcbcbd', 'acbacddb', 'bdacadad', 'addbccac', 'cdaccdbd', 'ccddaabc', 'bdbdcdca', 'bdcbabab', 'dcdababd', 'acdbccac', 'aadbcaac', 'abbdcbba', 'dabbcadb', 'babbacdd', 'cbdababb', 'acbbadba', 'bddabcbd', 'cabcddcb', 'bcabdcbb', 'adbcabcd', 'abdcacbc', 'bdaddacc', 'bcdcddad', 'cdbbccac', 'cbddbbca', 'cdcadadb', 'badcadad', 'dbcdacbd', 'bcbddbba', 'dabacdcb', 'dcabdbcc', 'dcdbdcaa', 'addccdab', 'cbcddbda', 'ddabcbba', 'bbadadac', 'accbcada', 'bcbaadbc', 'acdabbcb', 'adbadabc', 'cabdbdcb', 'bbadcabb', 'bdcddcda', 'cbbddabb', 'dddbabca', 'dddccbba', 'daabdcdb', 'acddbcaa', 'dacdbbda', 'cadacbcd', 'cadcbcda', 'caccdbdb', 'cacdcbad', 'dbdbadca', 'cbacacbd', 'abcabdab', 'dbadddcb', 'acdcbadb', 'badbcbdb', 'dbacbadb', 'cbcdcada', 'aadbcbbc', 'cadbccda', 'addbcddb', 'dabbdcab', 'bbccdaad', 'bbcbdbda', 'dbadcbcc', 'accadbad', 'dabacbbd', 'adabbdcd', 'cdbadcbb', 'baddccbd', 'dcbacbbd', 'bcdbabdd', 'accddabc', 'dabcbddd', 'acadbbcc', 'dccadbbd', 'acabdbbc', 'cadacbdd', 'baccdacb', 'bcacbdcb', 'ddcbccba', 'bcacddbc', 'bddcaacc', 'dcdcdcba', 'cabddcaa', 'dbcdbbaa', 'daccdbab', 'dcacbcda', 'accdddcb', 'bacabada', 'accdadbb', 'babdbacd', 'cdbbaccb', 'acbcadcb', 'babcdddb', 'ddcdaadb', 'cdcadbba', 'bdccbacb', 'dbccbcab', 'cbbabdba', 'cbdbadab', 'accbddaa', 'bcbabbdc', 'bcdcacdc', 'ccdcbaba', 'dbacdacd', 'adcbdacb', 'acbdacba', 'abcadbbc', 'ddbdcabc', 'ddcabcba', 'acbdddac', 'dddbaabc', 'ddcbbabd', 'badadacb', 'cadbacdd', 'acadadba', 'dcbdacbc', 'ddbdacbb', 'cabdbadd', 'bcbbddab', 'adaccbbc', 'acbbaddc', 'baddcbcb', 'dbbcadbc', 'adddccab', 'acbabadc', 'bbacdbcb', 'dcbdadcb', 'dcacdbcc', 'bbcddcab', 'bccdbacb', 'dcacdbba', 'cdadbabb', 'bcabbdac', 'acbacbad', 'acabdcbd', 'ddbcdcda', 'bcdadabb', 'abcdbddb', 'adacbdbb', 'acbadabb', 'cbabadcc', 'dbddacaa', 'bdaddbcc', 'ddbdcaac', 'abccddaa', 'adbabdbc', 'caadbbcc', 'dcdadabb', 'cbacbcdd', 'bccddbac', 'cbbddcda', 'cbdbccac', 'cdccddba', 'ccadbbcd', 'adbdccba', 'aaaabcbd', 'dadcdbdc', 'daabbcbd', 'bbddcdac', 'babadaca', 'cabdddaa', 'bbcaabbd', 'cbcddcba', 'dbccddaa', 'bddacacd', 'bcadabdd', 'ddcaddbd', 'acadabdc', 'cbdccdad', 'ddbbcbba', 'dcbcbdac', 'abacbdcd', 'dbbdcbaa', 'abaccdbb', 'dbdccabc', 'dbcabcab', 'bccddbaa', 'ddbdacbd', 'acadbbcd', 'dcbadabb', 'dcbcbdad', 'caccbcdc', 'ddccacbd', 'bbadcdba', 'ccabddda', 'abdacbdd', 'bdcdadba', 'dadabaca', 'ddcacdab', 'dbdcdabd', 'cbacdacd', 'dbcdccba', 'dbcddcaa', 'baabcdbd', 'dbadbadc', 'ddbcaadd', 'cacbdacb', 'bcadacbd', 'bccdcbba', 'caacbdbb', 'bdbbdcba', 'cdccbdac', 'cbaddcac', 'cabcddaa', 'acdbdbcd', 'cddadbba', 'bccdccaa', 'dbccbaab', 'dcadbcdb', 'dbdbccab', 'adcbadbb', 'abdcbadb', 'bcbbcdab', 'addbbacd', 'cdbdacad', 'acacabdc', 'acdcdbcd', 'ddabcadc', 'abcbddcc', 'abdacbab', 'bdabadca', 'bacadbcd', 'ccbddaad', 'dbbcadcc', 'bdccdbca', 'acdcdcbc', 'dbdddaac', 'accbddad', 'cbccbcad', 'adbbcbbd', 'adbdccab', 'accbdabd', 'bdbcdcba', 'abccadda', 'acdabdcd', 'abddddcd', 'dbddcdab', 'cdbbcdaa', 'bcdcbaba', 'dcbbaacc', 'abaddacb', 'ddaccbaa', 'cdbadbda', 'cdbcacbc', 'bcbcdcaa', 'dbddacdd', 'caddbddc', 'accbcacd', 'cdbaaaad', 'adacdcbd', 'dcadbbda', 'cbbadbcc', 'acbdcddd', 'abcdccbd', 'accdccbb', 'dcdcbdca', 'cdcdddba', 'baddbccb', 'bbccdcac', 'ccdcabac', 'cbabbadc', 'dcbbabba', 'cbddcaad', 'cbaacbcd', 'ddbdbbca', 'cddcadbd', 'caddadcb', 'abdbbdcd', 'acdcabda', 'cbadbbcb', 'cadbadac', 'cadcabcd', 'dccbbdba', 'abdcbaba', 'dccdadba', 'ddddcabb', 'cdbbadda', 'cbddabcb', 'adaddbcd', 'accdabcc', 'bdacdcac', 'accdcdbc', 'addabacd', 'dbabdbbc', 'abdacbcb', 'dcbabdbd', 'accdbbdb', 'ccddbcba', 'addbcbda', 'caacbccd', 'dbcabdbd', 'abadcbab', 'ddddcaab', 'cbacdbda', 'adabadcd', 'bccbacdb', 'bcbbdadc', 'bdccabdb', 'ddabdbcd', 'bbcaacdc', 'ccdbcdca', 'acadabac', 'cddbbdda', 'dbacdbca', 'acdabcda', 'acdbbdad', 'adbbcbcc', 'bcbcaabd', 'baddbacb', 'bbdcaacc', 'cddaabca', 'cdcdabad', 'bdcaccbb', 'bccdcdab', 'abbddbca', 'dccbadcc', 'ddbaddcc', 'dacbbdbc', 'abbdacba', 'abcacbdc', 'dcadbdcc', 'cacddcbd', 'cbddacbb', 'ccabdbbc', 'dccdddba', 'bbdddcda', 'acbdbdda', 'cddbaadc', 'acbbcdcb', 'ababdcad', 'bacadccd', 'adabbcda', 'cacdccba', 'cddbcdba', 'cbdaabbd', 'bcdbabcc', 'cdbccdad', 'cbadadbb', 'bcacacdd', 'cbcdaccb', 'caabbccd', 'dbbdcabb', 'abbcadba', 'dbccaabc', 'adaccabc', 'bcddcaad', 'bcdbaccd', 'dbdcbdad', 'aadbdcbc', 'abadacad', 'ccbbdada', 'dacbcdcb', 'acbdcdda', 'dcaadcbc', 'dbddacbd', 'cbdcabab', 'badcabda', 'dcabcadb', 'abdccdbb', 'adbdbcca', 'aabbcbcd', 'dbcadcbb', 'cbbaddcd', 'bdcbbdaa', 'ccbdbdaa', 'daabdcbb', 'ddcdabab', 'abacdbbd', 'dbaabbdc', 'baddadcb', 'dabccadc', 'dbdababc', 'dababdcd', 'accbabbd', 'caddbbcc', 'dcbdadbb', 'acdbdcad', 'bccdcadb', 'bbccdcca', 'dacbdcbb', 'dbcacdbc', 'abadcadc', 'addabcdb', 'ddcdcbac', 'cdcddbda', 'ccdbabad', 'cdabbdcc', 'ccabbdba', 'bbcdcdad', 'dbdaacdc', 'dcadbdbb', 'cbadbada', 'accddbda', 'adbbcdba', 'cbcdadba', 'ddacabdd', 'bdcbcdda', 'dbcdccad', 'dddadbdc', 'adcabcbc', 'cbadabcc', 'dccddbac', 'cdccbabb', 'ccabcbad', 'dabcacdd', 'caabdaad', 'cdcbbadc', 'bbdccbca', 'bccbacda', 'abccdcdb', 'adcacbad', 'abacddcc', 'cadbbdcc', 'dcbdbcac', 'ddadccbb', 'babbdcdb', 'cddabbdd', 'adbcdbdb', 'cdabdcad', 'dabcdacc', 'dcdbdbaa', 'cbccdacd', 'cadddcbd', 'ccbdbcda', 'cdababda', 'ccdabacb', 'badbcbdd', 'cdbabdac', 'bcadadcc', 'dabcadbd', 'dbabbcab', 'abdcdbdc', 'cdcacdba', 'dddadcbc', 'dcbdaadc', 'cbdcadcd', 'bcbcadba', 'cdaabbdb', 'accdbaba', 'cbcacbdc', 'dccbadbc', 'ccbacdac', 'acdcbabb', 'cdbdaccb', 'dbcadcba', 'dcabcbcc', 'daccabdd', 'abcacdbd', 'dabdddac', 'abddccab', 'dbddccad', 'caddbacb', 'ddcbaddb', 'dbdacbdc', 'cbbddbab', 'abcdacad', 'caddbbad', 'bcadcbad', 'bacbbddb', 'ccbaabdb', 'cbdcddad', 'adcdcbdd', 'bbddcadb', 'bcaadcaa', 'dbccabcd', 'ccadadab', 'bcddcaac', 'dacbdbcb', 'bbdbcbab', 'ccdbdacc', 'bbdacadc', 'aabbdcbc', 'cbdcdadb', 'adbbdcdb', 'cbdbcaba', 'cddcbaab', 'bdcabbac', 'bbaccddd', 'bbccdadc', 'ccbdaacb', 'ddabcaba', 'cbbadbda', 'dbadbcbd', 'cbcbbdba', 'abbdbcad', 'dacdbbac', 'dabcbbad', 'bcdabddc', 'addadbcd', 'cddbcacc', 'adcacdba', 'dbabbaca', 'dbbabcbd', 'aabaacbd', 'cabadbdc', 'acabbadb', 'ccdadbad', 'daccbcca', 'cbccdcab', 'ddcabbaa', 'cbbdabac', 'badbcdbc', 'dccacdba', 'bdddaabc', 'dbbcddca', 'acbcaccd', 'dbdddcab', 'bcadadda', 'abbcbdcd', 'ddbdbadc', 'dabdbbcd', 'dcdcabdb', 'addaaabc', 'dddcacbb', 'ccdbadda', 'adddbcca', 'bdcdaacc', 'bcabcdcb', 'bcdbdbab', 'cdbdadbb', 'caccddbb', 'adddbbcc', 'cbbdbdba', 'cabbdddc', 'bdbbdacc', 'cdaabaab', 'bcaddabd', 'acdabbdc', 'acbccdca', 'ccbdbbab', 'ccddbadb', 'acbdbdca', 'aacbcbdb', 'dbcacabb', 'cdbcbbda', 'dbcacbac', 'acddcabb', 'acbdcbdd', 'cbbadcba', 'dacdadab', 'cacdbcca', 'cacdabdd', 'adabdbcc', 'dccbccda', 'bbdccaad', 'dcacbabb', 'dbddbacd', 'ddccdadb', 'accabddd', 'bbdcdcad', 'abdacaca', 'cbbadabc', 'bcddbcac', 'accdbacb', 'bbdbdcda', 'ddcdacab', 'adbcadba', 'acabadcd', 'bcdbbdab', 'acddcbda', 'bdadcdbd', 'bdaacbaa', 'dddaabcc', 'bababcdc', 'cdaddcab', 'bbcdadba', 'bdbcdaad', 'adccdbad', 'abababcd', 'cadadbcc', 'bdbdccab', 'ddabaadc', 'cbcadacd', 'bddddcaa', 'bcadcbcb', 'abddcabb', 'aacdcbdc', 'acdbddac', 'abbcdcdc', 'aaccdbaa', 'dcbddaca', 'cbadcdbb', 'bdccadda', 'cddbabbc', 'cdcdcbac', 'dcdcdbda', 'ccdcabcd', 'dccabcdb', 'abddbcba', 'adbccbcc', 'cbdaaaab', 'acacbacd', 'dcbdabab', 'abddcdab', 'caccadba', 'addbcddc', 'bdccdada', 'dccacbdb', 'cbdbcdaa', 'daaaabcd', 'abdcbcab', 'cddcbdba', 'bdbcbbad', 'cddabbcb', 'addddbbc', 'bbdabcbd', 'bcacddca', 'acabdbda', 'bcdabccd', 'abadbccd', 'bbcbadbd', 'badbdcbd', 'cbccdcba', 'acabdcba', 'acdbadbb', 'dbdbadcd', 'cbaddcbc', 'aadcbbdb', 'ccbdccaa', 'bbdcdbab', 'bcdabccb', 'babcdcab', 'cacbabdb', 'accdadbc', 'dadddccb', 'addbcbcc', 'abcdbcbb', 'cbcaacbd', 'ccaddabb', 'dbacbcab', 'acbcadda', 'dccabdba', 'dcddddba', 'baabbdbc', 'bbdbabcd', 'dcdddbab', 'caddcaab', 'ddbaacbd', 'caabccdc', 'ddcaadbc', 'acdcdadb', 'adddabcb', 'dbcdaacc', 'abaccdcd', 'cbaadbcc', 'cbdacddb', 'bdaabaac', 'cacdbdbc', 'bbcabdcc', 'addcdbad', 'cdddaadb', 'dbccbadb', 'bdaccadb', 'abbcdbda', 'bbdacbba', 'cdacbbab', 'dddaacba', 'bdbbdbac', 'cbbadbad', 'ccbdcacd', 'cdcabdca', 'abccdcca', 'bacddcbd', 'dbcdbaac', 'abcabada', 'daddbaac', 'dbcabccb', 'accabdcd', 'dbccdbba', 'adacdacb', 'cadcadab', 'abbdcdab', 'cacdbdbb', 'acdbbcca', 'bdbaacbc', 'bbcbdada', 'ddabcddd', 'dbbabacc', 'bdcbadca', 'cdcacbcc', 'cbdbccab', 'ccbacbad', 'cdabbcca', 'ababcddc', 'cdaaaabb', 'ddbdcdad', 'aadccbaa', 'bbcacadb', 'ddcaddab', 'bdddacba', 'ddcacacb', 'bccadaca', 'badadcad', 'bacdbadb', 'bddcabcb', 'cdcbdbad', 'cbdbcdba', 'dccabdcc', 'bdccaccb', 'cbdabcdc', 'acbdadbd', 'abbdbcab', 'cdaacbdc', 'dcbacbda', 'cbdaadcc', 'abadadca', 'cdbcdaad', 'adcddbca', 'bdbabcdb', 'adbdccac', 'abbacddd', 'dbbabbca', 'bcddbbaa', 'cbdaddbc', 'addcbdbb', 'adcdcadb', 'dbcdcadc', 'ddaabaac', 'bcaddcdd', 'dabbdacb', 'ccbdbdab', 'bbdcabcd', 'adbacaba', 'adbdbcba', 'dddaccab', 'bdcdbadd', 'dbdaabdc', 'acabadab', 'bcdbcdda', 'cadbadcc', 'bbcdacab', 'ccbdbcad', 'cdcbcbac', 'daadcbdc', 'bdbcbdda', 'bccbdada', 'acabdcbc', 'aacbccbd', 'cacbddab', 'bcadcdac', 'ddaacbbd', 'bbadcbdc', 'cddacbdc', 'cdbabcdc', 'adbddcdd', 'cdabcdab', 'ccdcdbaa', 'aabcdbcc', 'abbdcbac', 'acdabbcc', 'aaccdcbd', 'ccddbaca', 'dbdacdcc', 'bcabcada', 'dcdbbcda', 'dacdbabd', 'dbaddcdc', 'adcbabcd', 'badccbac', 'bdcadcbd', 'bdbbadac', 'cdabcabd', 'dcacdbad', 'bcddacaa', 'bbabdcba', 'adcbadac', 'bcdbbaca', 'daacdcdb', 'dbbddbac', 'bbabdcbc', 'dcaaccbc', 'ddabacad', 'cdbaccbc', 'abccadca', 'abbdadcc', 'bcbcdcda', 'bdbdacbc', 'cdadcbcd', 'dbdacdca', 'badccdbd', 'ddacdbca', 'bcbcaddc', 'bdabcdab', 'dbbadccb', 'adccdccb', 'bdaacdbd', 'bbcacbdc', 'aadcbcbd', 'accdacba', 'cbadcdda', 'daacbbdb', 'cabacdcb', 'cdcdcbba', 'bacbdcad', 'bdadabcc', 'accdbadc', 'dbddcacb', 'dbccddca', 'baccdbcc', 'dcaacbaa', 'baaccdbd', 'adbcabda', 'cdbabdcc', 'bcdacbac', 'cdbbabbd', 'bccacddc', 'dcdadbad', 'accbddca', 'cdadcdcb', 'acaccdbb', 'cdccadbd', 'ddcbabdc', 'bcdcabad', 'ccbadcdb', 'dcbbabdd', 'acdbdccd', 'dabbcadc', 'bccbabbd', 'ccadccbd', 'dacdcbcd', 'bdcadddb', 'babcbabd', 'cddbddad', 'bddccaac', 'dbbaddcc', 'dbadbcdb', 'dcbbdabd', 'cabdddac', 'bbdcadbb', 'abdbbcca', 'dacacbbc', 'dccabccd', 'abdbcacd', 'ddacdcab', 'ccacdbdc', 'dacddbbc', 'bcdacbbc', 'cdadacdb', 'dabddcca', 'dbdbcbba', 'cbbdcdab', 'cdabdacc', 'dbdccbaa', 'ddaaabbc', 'bbadadcb', 'bbdadbcc', 'cbdaabbc', 'dacabdbd', 'badcbcba', 'dbdbcacb', 'adbacabd', 'cabdadbb', 'cdddcbca', 'badddcdb', 'dbdcdbaa', 'aacdbaab', 'cbadbcdb', 'bcbaccdb', 'adcabbad', 'abcdbbad', 'addbacdc', 'aabccdcd', 'acdcdcdb', 'adddbddc', 'cdbaddda', 'bacdadab', 'ababbadc', 'dabacddb', 'bacdbbac', 'bcbdadad', 'cbacddcc', 'adbabcbb', 'dbcbdaad', 'bddaccba', 'cddcaabb', 'bcbddbad', 'caadcbdc', 'adcbcaca', 'cbccacdc', 'acdbcbab', 'dbdccaab', 'ddacabad', 'abadacbc', 'cbacbadc', 'bccdadbb', 'cdbddcab', 'dbbaccac', 'bbcadcdd', 'babbdacd', 'adbabaca', 'badddadc', 'ccdbdabb', 'ddcddbda', 'cdcdbabd', 'acbbdcbd', 'cadcbcac', 'bdacdacb', 'abbdbcdd', 'bdbcacbd', 'adadcbab', 'cabbdcad', 'bbdabcbc', 'bdcaddcb', 'abcadcad', 'bcdaadcd', 'addccbcd', 'bccdbdac', 'cbdadacd', 'cdcaabaa', 'ccddcbab', 'aaaadcbc', 'ddcbbdda', 'acdcbdab', 'bacacdca', 'dbdbdacb', 'daccddbb', 'accdddab', 'bdaadcbc', 'bbadcbbc', 'cdbddbab', 'adbccdda', 'abbccdba', 'bcdcbadb', 'acbbcbbd', 'cacdcacb', 'cbacdcbd', 'bccbbdaa', 'bcabdcbd', 'acdadcab', 'bbabdacb', 'cdcbabbd', 'bacacdda', 'dbcdbacc', 'aaccbbcd', 'dcabdada', 'dbccdbda', 'adcabaca', 'cddcdabb', 'bdcbdacc', 'bcbabdda', 'adbccdcd', 'dcadbcbd', 'bbdaddcc', 'dbcdabbd', 'dabacdcc', 'abbdbacb', 'cbacdbdd', 'bcbcadac', 'dacbcdbd', 'dccbbcda', 'ccbacadb', 'ddcacbba', 'ddbdbbac', 'bababdcc', 'bcbcdbab', 'acddacba', 'aabbcdaa', 'bcdcbcda', 'ccabdaba', 'dbcdbcac', 'dbbaccad', 'badbadcd', 'acdbdbad', 'bcddaddb', 'dcabdbdc', 'baccadbc', 'bddcbdaa', 'abcbddac', 'acabdddb', 'aacdcdbc', 'abaccdba', 'cbabadcd', 'acbaddcb', 'bcadbcbc', 'ddcadbdc', 'dcabcdac', 'abcaccbd', 'abdacddb', 'cbbaddbd', 'cbdcadcc', 'dcbddada', 'bbdcbbac', 'bcdcbacd', 'acddbdbb', 'cadbacdb', 'acaddabc', 'cbcbbdaa', 'ccdcdabc', 'cdbbdaac', 'cbddbbaa', 'badbcddc', 'dbcadcdc', 'cadbabca', 'ccdbabba', 'acbbcbdd', 'bcadadbc', 'cdcbacac', 'dcbdcbda', 'cbaccadd', 'ddbbacdb', 'acadcbdb', 'abacacdd', 'aacaacdb', 'dddbbabc', 'addbabcb', 'accacddb', 'caadccbb', 'bcdaddaa', 'ddacbada', 'bddcdaab', 'dcbbaacb', 'dbcbddaa', 'dbbcaacb', 'acacbcdc', 'bacdbcdb', 'dcabdcda', 'abbcdaba', 'dbcaaccb', 'cdcacdbd', 'dacdadba', 'baccddbc', 'bbaabcdc', 'adcbbcbb', 'adcbabdc', 'acdbdbcb', 'bcaabbdc', 'acdbbdac', 'cbcdcabc', 'dadcdbcc', 'dadbdcbb', 'adbcdbab', 'cbbaabcd', 'dadadcbc', 'aaccdbcd', 'cbbcdacb', 'babbcacd', 'ccdbdcba', 'daccdbbc', 'ddbabcdd', 'bcdacabb', 'addbaacb', 'dabcddaa', 'acaccbda', 'cdabacdb', 'dcbdbbaa', 'bddcdbda', 'cadcbbda', 'bdbbcacb', 'aabaacdc', 'bccdaabc', 'dbcddcab', 'cabdadcd', 'cbabddbd', 'dbbccabd', 'addbaaca', 'bdacdbdc', 'dddcbcac', 'bcbadbca', 'ddcabbcd', 'aacbdcbb', 'dbdadccb', 'ddabccbb', 'cdbbaadc', 'babbcddd', 'bbdcbadd', 'acdddadb', 'aabccdbd', 'abdacbac', 'dacabbab', 'dbdcacba', 'cabadcda', 'accbcadd', 'acdcabdb', 'abcdcacd', 'cdddabab', 'acadbdcc', 'dcacbdcc', 'adacdbcd', 'cddbaabb', 'acbbddca', 'cdbacdcb', 'cbcbdabb', 'accbbdac', 'bbaddacd', 'adcdabdb', 'cbccbada', 'cdddacba', 'cadddbdd', 'dbccbdba', 'ddbbdcaa', 'abcbbddd', 'cddbbadb', 'cdadabbd', 'abccdbba', 'cbbcbdac', 'bacdcabd', 'adcdbabb', 'daaccdcb', 'bdddccac', 'dcabbcda', 'bddbcabc', 'daddbdcc', 'aabcbdbd', 'cdbdadad', 'dbdcabad', 'bdbdbacc', 'ddcadbda', 'cddaadbc', 'bbcbddad', 'cbddcabd', 'dbacdbbc', 'cdbccbac', 'cdbaabdc', 'dbdadacc', 'daadccdb', 'babdabdc', 'acbddbbd', 'dbabbcda', 'ccadddbd', 'bddaaacb', 'ccbabdba', 'dcbaadcb', 'dddabcaa', 'cadbddbd', 'dbdbcbab', 'dbcbadad', 'bcbbdcda', 'bcabdabd', 'ccacbada', 'dabacacb', 'cdcaabcd', 'dbdbaacc', 'bbacbdca', 'acbcdcca', 'abbcbdad', 'adccdaba', 'ddbbdbac', 'dcbacbdd', 'bbccabda', 'cbbaddca', 'cdacabba', 'bbacbdbd', 'acbcddad', 'cadacddb', 'cbdbddaa', 'bbdbacdd', 'badcdbbd', 'adcbcbbc', 'dbbcdbba', 'dcbcbcba', 'cbbabdad', 'bdcbcadd', 'cddbcdaa', 'bdadbcbc', 'ddddaabc', 'dcdabcda', 'ddacabcc', 'bacddbad', 'dbddbcca', 'bbdacabd', 'cbccaadb', 'cbdcbaca', 'dbdcddda', 'cbbdcbaa', 'cbdcadad', 'ddabacba', 'baddcddb', 'dddabdcd', 'dcabdaca', 'ddabbcdd', 'babcbdad', 'cdbbcaab', 'caddadbd', 'ccbbadcd', 'cddbbaad', 'bdbaacdc', 'bdbbddac', 'acdbcbdd', 'cbdabcdd', 'abacdada', 'adbccbac', 'baaccbcd', 'dbbcadba', 'adabbdcb', 'ddccabab', 'cdbabada', 'babcacdc', 'abadbdbc', 'dacdbcba', 'cadbdacc', 'dddaddcb', 'bddaabdc', 'cdbcabcb', 'ccbdbacd', 'cbabadbb', 'cbdacdba', 'dcbabdac', 'bdcdbadb', 'daddbcca', 'bbdddadc', 'cddadcbd', 'acbcdbab', 'adbbddca', 'cdcacbcd', 'dccabdbd', 'dbbabccd', 'bdddcdda', 'addbccaa', 'acdabdba', 'ccbdcacc', 'ccdbabdd', 'cddacbdd', 'acbbdbcc', 'bababddc', 'cbabbdbd', 'cdbddbac', 'ccadbcdd', 'dbdacdba', 'baaccdbb', 'bdbadcbb', 'acadcaba', 'bccdcaad', 'dddadcdb', 'cbddbaad', 'dbdabdcd', 'bddaddca', 'bcdaaccb', 'cbbccdca', 'dcdbdbda', 'dbddcdad', 'cbaddccb', 'adabcbdc', 'bcbcbdda', 'adabcdab', 'ddcdcabc', 'bacdddca', 'bbadacbd', 'dcabdbac', 'bbdbacdc', 'ccdbadcc', 'bdcabdac', 'abdbccbb', 'dbcbddba', 'bdbabdca', 'bbaddbca', 'bcdabbdb', 'bcbddadc', 'acdbddcb', 'ddddbcda', 'cbbacdcb', 'cdbdabbd', 'dcabccac', 'ababcdcc', 'dcabbada', 'dbcbdbba', 'cbadabbc', 'adcbadbc', 'bdbadcbc', 'dddacbcc', 'dcbbadcb', 'badcddcd', 'dbacdbdd', 'cbbccadc', 'cbdcabdb', 'bbdacdad', 'bcdbdabb', 'dbcdbbca', 'adacabbc', 'cabcbdbb', 'dacacbca', 'cabcbdcd', 'dbdcabba', 'ccbddcda', 'ddcabcab', 'acacbada', 'cddddaba', 'dbdcacdc', 'ddddbcac', 'acddbabc', 'bdcdcbba', 'cdaacdcb', 'cdbccacd', 'dbcacbbc', 'abbadcad', 'bcacddab', 'bcacadcd', 'cdbcddba', 'accbacbd', 'dbabdbcd', 'bddabcdc', 'ccaabdbb', 'ccbaddca', 'dabdbaca', 'dbcbcdda', 'bacdcaba', 'ccbdccac', 'adbacadc', 'ddcabada', 'bacdbdcb', 'cbbdabdd', 'cdcbaacb', 'bbcdccac', 'ddabdbcc', 'cbcbdaba', 'dbabcbbc', 'bdbdcbaa', 'cacddbbc', 'aacdbdbb', 'cbabdccd', 'adcbbdbd', 'bbaadcbb', 'abcadaba', 'daccbabd', 'accabdba', 'dbccbcac', 'acbdcbbc', 'badccddb', 'bbadccbc', 'dcdccdab', 'ccdbadad', 'ddbacbac', 'caaaabcd', 'ccbadadc', 'cabbcddb', 'bddcbaaa', 'acbcbbdb', 'cdabbcbc', 'dabbacda', 'bbdaccdb', 'bccabddb', 'cdddcbaa', 'badbccdc', 'bacdccab', 'abcdccda', 'ccdacacb', 'adcbdbca', 'acddabca', 'cdcdbbad', 'dcadddba', 'ccdbbacc', 'acdbaccd', 'dbdabcbc', 'bccadabd', 'dabdddcd', 'cdcacbda', 'acabddcc', 'bcdbadac', 'acbbcabd', 'abadbaca', 'acbabadd', 'dbcbbaac', 'dbdacdda', 'bacbdadd', 'cbdcabcd', 'bbdabcda', 'addbdcbd', 'abdcbadd', 'caccdcbc', 'babdcdbd', 'babacdcb', 'caacbcbd', 'baccabdb', 'bdbbcacc', 'adbbcadc', 'bcbdddba', 'ddcdadbd', 'dcbddaad', 'ccaabdaa', 'acabdcad', 'bdabbacd', 'dabcabab', 'caacbdbd', 'ccdabbcd', 'bdbacabd', 'bddacacb', 'caddacab', 'cddbacbb', 'cdcdadbb', 'bcaabdbd', 'dabbddcb', 'ddbdcdca', 'cacdccab', 'dbbccbca', 'dbdacddc', 'adabcbdb', 'dcdadbbc', 'bacdaccd', 'bdbcdcad', 'dcadbbdb', 'cddcacbc', 'dcbccacb', 'bdadacca', 'dcdbbaac', 'bcdcadbb', 'dadacbcc', 'abbadcbc', 'bacdddbc', 'ddacdcbd', 'bacabadc', 'dbbccdaa', 'baddbcbc', 'bcaddbbd', 'abcdbdbb', 'dacbacad', 'bcbbdadd', 'ccbcbada', 'bdcadacc', 'accdcdab', 'ccadccbc', 'ddccadbb', 'ccdacdba', 'ccacdbad', 'ddbbadac', 'cbbdddac', 'abcaccdc', 'ddbadccb', 'abacddaa', 'abccddbc', 'dcabddad', 'dcbcadda', 'dbadcada', 'bacbdbcb', 'bdcddbda', 'bcbbadbd', 'bdbabcbd', 'bcabaddc', 'bdbacdca', 'ccbbaddd', 'ccabddbc', 'bdbacadc', 'abdcdbca', 'ccabbdbd', 'cacbdbba', 'dbaaaacb', 'ccbbdabb', 'cadadbdd', 'cbadacdc', 'dcadcdbb', 'bbdcddac', 'ababbdac', 'bbacdbad', 'acbadbbd', 'bbcdbdab', 'bbcdacbc', 'cabcdcbc', 'addabcca', 'adadcdbb', 'cddacabd', 'dcabcdba', 'adbcbdca', 'bcacdacd', 'abdbcabc', 'dabcbcab', 'abcddcad', 'cbaadccd', 'cdbacada', 'dbadcddd', 'cbcabbcd', 'dccbdacc', 'cbcacdac', 'bdbdcacd', 'caadbdbc', 'acbbdccd', 'caabcdaa', 'bccaadcc', 'cbadbdbc', 'accddbcb', 'cbdcadca', 'acddbcca', 'abdbcbbd', 'addbddcd', 'dcadccbc', 'dcdaadbb', 'cbcdccda', 'cadbabbc', 'dbcbdadc', 'cbacbdac', 'dbdccabd', 'dabcdbcd', 'cdddacbc', 'bcaccacd', 'dcadcabd', 'ccadbcbb', 'dcdbdada', 'cabcdbab', 'ddcabbad', 'baddddbc', 'ccadbcba', 'cacadbbd', 'cbabccdb', 'accbddcb', 'caccacdb', 'baadcaac', 'ababadbc', 'bdbcadda', 'dbcbcbab', 'bbaabdbc', 'dcaddbda', 'cbccbdba', 'ababdccd', 'dcdbacab', 'cacbdabc', 'bdcbbabd', 'cbbcaadb', 'cadabcbc', 'cdcabbcc', 'cdaccadb', 'ccadbccd', 'adbbacdd', 'bbcadada', 'bdcadcca', 'ddabcdbb', 'bdccdacc', 'adcbccdb', 'accdbabb', 'bcbadcbb', 'ccdcbcac', 'cabdcbba', 'acabbcad', 'abbcbdac', 'ddcaabad', 'cbababad', 'bdddabcb', 'bdcaadcd', 'ddcbbabb', 'cdacbcba', 'abbacbcd', 'dcabadbc', 'acabdcab', 'cadabddb', 'adcbbcdd', 'acadcbca', 'cdccacba', 'ccdababc', 'dbacbcda', 'cbaacdbb', 'dccdbabb', 'cbdbadda', 'cdabdbcb', 'abadcdcb', 'cbccadbb', 'dabcdbcc', 'ccdccbac', 'cddbadcb', 'bdaccdcb', 'dbcadbba', 'baddcabc', 'dcdbcadc', 'bccdacdd', 'dacdabdc', 'abadbacd', 'bdbcbaca', 'dbbabbdc', 'ddcbbcba', 'dacbdcbc', 'dcabbcca', 'acdcbccb', 'daccbdcc', 'bdaccada', 'bbdacdba', 'cdcdadab', 'abcbdada', 'dcadbdbd', 'bdbabbdc', 'bacbdadb', 'baddbddc', 'ddacbcdc', 'cbdabdad', 'ddbacaab', 'dbadacac', 'bddacadc', 'babbccad', 'abdcbcbd', 'abdccbba', 'abddcacb', 'abdcabdc', 'bcadaddb', 'baddbcbb', 'aadbbdcd', 'cadabdad', 'bccdbcca', 'dcbdbdda', 'accbabcd', 'ccabbcda', 'bdcbabba', 'cdacbdad', 'bbccabdc', 'dbcbdabc', 'badabaca', 'cddadbdc', 'dadcabdb', 'cacbddca', 'adcbdbbc', 'cbdacbab', 'ddccbdab', 'dddcabba', 'dacbacda', 'cbadacac', 'cbdbbaad', 'acacbdca', 'cdcabdcd', 'dccbbdda', 'ddcabcac', 'cbababbd', 'ddddcabc', 'abdbbcab', 'ddbabacc', 'ccbcaabd', 'dacbcbda', 'bcdbcdad', 'abbabbcd', 'bdadbccd', 'acadbcbb', 'ccaacdcb', 'ddcdabad', 'abacdbad', 'acdbacca', 'babccdba', 'bcbdbadc', 'bbdcacda', 'aabbdcbd', 'acadbaca', 'dccddbad', 'bdcdcdca', 'bbacadac', 'cdbadcab', 'acabdbba', 'bbcbbada', 'dabdacab', 'dddacdab', 'ccbbadbb', 'ddccbadc', 'adcbbdba', 'bbacadcd', 'abdcdabb', 'cbcbdcad', 'dabddcbb', 'bcabcbdd', 'cbbadcda', 'bdcaadcb', 'cbdabcac', 'dbdaacbd', 'abcbacdb', 'dbdaddcc', 'bdabccdc', 'dbcdcdba', 'bbcabbdd', 'ddbcadbb', 'ddbdabcb', 'bbadbccb', 'cddaaabd', 'bdaaaadc', 'dddaacbb', 'bdabcbab', 'abddcbcb', 'dcddcbad', 'adccdcbd', 'bcddbbda', 'ccbdccad', 'bccbdbda', 'adcbdcca', 'caddbccb', 'badbbcda', 'acddcaab', 'dacbbcbd', 'babccdad', 'dabacbdd', 'dbabbdcc', 'ddacdbdb', 'dcaadcdb', 'abcbacdc', 'babbdccd', 'badcddaa', 'cdacbbdd', 'bcabbcbd', 'aacaacbd', 'cddcdbda', 'cdabbacd', 'ddcbdcba', 'dcbbcabb', 'dadbbcdb', 'bbccadbc', 'dbdaccab', 'adcabddb', 'babacbdd', 'cbaddbaa', 'aadcbcdc', 'bbabadcc', 'bddddadc', 'dabcbdab', 'dadbbcdc', 'cadbdcbd', 'bbabcacd', 'cadbbcdc', 'ccbdccda', 'dbbacdab', 'acbadcdc', 'bcaccadc', 'cdbbccab', 'dcaccdab', 'dbabacbd', 'abdbabac', 'cdabbacc', 'bdccbdaa', 'acbdcdba', 'dcaabaac', 'bcdcddba', 'badcdacd', 'ddacbdcc', 'addabcba', 'bdadcdcc', 'adbcbddb', 'dcbadbca', 'bcbbdcac', 'bdbcbaac', 'cacddddb', 'dacbbadd', 'bddcaddd', 'babdacac', 'ddbaacdd', 'bcbabadd', 'ddbdaaca', 'badabcdb', 'dbbaabcb', 'dbaddbcd', 'adcbbacc', 'accacabd', 'dabccdad', 'cbbcadba', 'adbcbbac', 'bcabadcb', 'adccbcbb', 'ccdcacba', 'bdbbdbca', 'dcacacdb', 'acbddcdc', 'dabdcdac', 'dccaddab', 'cdddaaab', 'babdcadb', 'bdacbcad', 'bdcaacbd', 'cdaadbbd', 'bdcadbbc', 'dccbddab', 'dcabacab', 'adabddcc', 'cdbabadc', 'adabacac', 'bbdcbaac', 'adbdbcad', 'cbddcdaa', 'bdbabccb', 'baadcbaa', 'bbccadcd', 'bbdccdca', 'baadcbcc', 'acbdaddd', 'acbdbcdd', 'cdcdaabb', 'abbddcba', 'adbcabdd', 'dabdddcb', 'bbcacabd', 'ddadcabb', 'dccdadbd', 'abbcadbc', 'cbddcbad', 'cbdcddaa', 'daccadcb', 'bccdadcb', 'dadacbca', 'acdadbac', 'dbabdaca', 'cabaddcb', 'bdacdbdb', 'bdadddac', 'cbddcbba', 'bcabadac', 'bdcbdadb', 'dccbddca', 'cbaadaac', 'cdaddbcd', 'ccbadcbb', 'cbabdccb', 'aaaacbcd', 'bababbcd', 'ddbdaccb', 'cbccaccd', 'ddbabccb', 'dcaacdcb', 'cbdabadb', 'ddabddbc', 'dbbacbad', 'cbabddda', 'dcbbcbab', 'cddadbaa', 'dbabdadc', 'abcbdcdd', 'bdacdbda', 'ddabdcaa', 'badcbdac', 'abdbdcca', 'ddabbdca', 'dacbccac', 'dcabddba', 'bbcbddaa', 'cabcacdd', 'dbadccbb', 'aabbcdbd', 'acddcacb', 'acdbbccd', 'ccadadbc', 'bdcbcbba', 'bdccddaa', 'bacbadbc', 'addbdcda', 'adccdbdc', 'cabdccba', 'abcdadcc', 'cbcdcbba', 'addbdaca', 'bcadbadc', 'acdbbcba', 'dddbabac', 'adbadacb', 'adbdbbcc', 'bacdccac', 'acbcdddc', 'adcbadab', 'cbbddbba', 'abdbdcbb', 'bcdabbdd', 'abdcdcba', 'ddbbcadc', 'ccdcabdd', 'dddaccbc', 'bcabcbad', 'daddacbb', 'abccbbcd', 'bbcbdabd', 'adabdbcd', 'bbacbadc', 'bbacdcbc', 'dababcbd', 'cdadabcc', 'bcbdadbb', 'bdcdbaba', 'cbbdccab', 'dbcaddbb', 'bdacdcad', 'ddbdabac', 'cbdbcadb', 'dccdbcab', 'bcbaccad', 'cdbabcca', 'adcdacbd', 'acddaccb', 'bbdddcba', 'badcddba', 'ccacddba', 'bdbdbbac', 'bbabadbc', 'dcacbbcc', 'abacbcdc', 'abacdabd', 'addabbca', 'cacbcdcd', 'bddadadc', 'dabcbadd', 'dcbaabcc', 'dabacacc', 'cdcdbcca', 'aadbcbcc', 'babcbcdb', 'abdabdbc', 'acddcbba', 'abbcabdc', 'dcacbdac', 'accbdbba', 'dbdbaacb', 'cabcadcd', 'cbddbbad', 'ddbcdbba', 'badadcdd', 'ababadcd', 'ddbbccaa', 'cdaddaab', 'bddcacac', 'dbbdcaab', 'cadabcdb', 'ccacddbb', 'ccaadbaa', 'cabccdbb', 'addcbddc', 'bdddaccd', 'dccbcaad', 'bcddacdb', 'adccbdac', 'bdaadcaa', 'dbccbbda', 'adacbddd', 'daddbbdc', 'bdaabcbd', 'dacdcabd', 'bdcdcbca', 'bccdadab', 'dddbcdba', 'cadbabda', 'cdcbdabd', 'bdbaacdb', 'dbbcacbb', 'badcadac', 'cdbadbab', 'dcaabccb', 'cbabacad', 'cddbbaba', 'cdbdabcc', 'adabcbab', 'cdbcdbda', 'ddaccbdd', 'dbdcbacd', 'abcbdcac', 'cbacaddc', 'dcadbdba', 'ddbabcca', 'baddbdcc', 'acdcdbba', 'ddaaacbd', 'cabacdcd', 'bcbccaad', 'cdbcbadc', 'cddcabab', 'ccaccdba', 'dcdbddad', 'bbdcdacd', 'dacbdacb', 'cbcbdadb', 'dcbbcbac', 'bcadccdc', 'cddbabcd', 'abdabbcc', 'cdcbabdd', 'cbadcbab', 'cdcbacda', 'cabbaddc', 'baabcbbd', 'abdababc', 'cbabdada', 'cadcdbcd', 'adabbadc', 'bacadabd', 'dbcdcbba', 'cbcdaaaa', 'cbadaddd', 'dcabddbd', 'ccdcbcad', 'adabdcba', 'ddaabddc', 'cddabcda', 'bccacbdd', 'bacdbdbb', 'dabdcdad', 'abcaddad', 'ddbacbdb', 'bcdcacba', 'bdcbdcda', 'cdabaddb', 'cdddbdba', 'dbcbdada', 'bbcdcdab', 'bdaabbdc', 'bdbaddbc', 'dccdadab', 'bdadbcbd', 'bdcacdda', 'ccbdacba', 'aadccdcb', 'adcdabdd', 'addbdcca', 'cdabdcda', 'addcbdcc', 'abccdbcb', 'cddacbcc', 'acbacdad', 'acddabdc', 'cbbcaccd', 'cbcdbbaa', 'abbadbdc', 'baddaaca', 'cddabadb', 'bdcdbcab', 'dcdcbaba', 'dbdacddb', 'accdbdbd', 'ccddaabb', 'bcacdcdb', 'cdadddab', 'ddcbacab', 'dbccaacb', 'ddaccaba', 'adcdbbca', 'bbcbabda', 'abacbdcc', 'cdacbcad', 'aacbdaac', 'cdbbdcad', 'ddbaadbc', 'bbddcdda', 'dbdadbdc', 'ddcbdabb', 'cadacbad', 'bdacdbad', 'addcaadb', 'ddaadcba', 'dbdcadbc', 'adbabacb', 'bbdbcbac', 'babbdabc', 'abbcdacc', 'ddcbdaac', 'badbabac', 'bbaddcdd', 'abcbdcdb', 'abdddbca', 'bdbbcbad', 'ccbcacda', 'acbcbcad', 'bcaabdcd', 'acbbcdba', 'bdccdabb', 'abdbdccb', 'bbcdcbba', 'dadbbcda', 'aadbaacd', 'bbccbdac', 'adbacbad', 'bcdddabc', 'ddbbddac', 'ddbbdacd', 'abdacbdc', 'bccddada', 'baacdbcd', 'bbcddaba', 'dbcaadbb', 'adddcbcd', 'adcdbdcc', 'accbdbcd', 'cadbcdad', 'bdcbdcaa', 'abaccdca', 'bcbddacd', 'bcbaddba', 'dcdbadcb', 'acaccbdd', 'cdbabcba', 'cddcdbaa', 'ccbadbcc', 'cbddbadd', 'cbbcdcad', 'bdcdccac', 'bbdcaccb', 'adbccabc', 'abcbdbad', 'bbaccbdb', 'abccbbda', 'baadbcdb', 'cacbdadc', 'baccbdac', 'dacbddcd', 'bbadcdbc', 'bdabcddd', 'abcddcab', 'dddabcdb', 'bcacacdc', 'acbdbcbd', 'ababccda', 'abbaccad', 'ababdcda', 'bdcaacdb', 'bcddaacc', 'cddbddca', 'acbcbabd', 'daabdccb', 'dbbcbabb', 'abcabcdb', 'bddbcdac', 'bcbcbdad', 'adbdcddb', 'bbcdbdac', 'dbabdcbb', 'aaccbbdb', 'ccadcbad', 'cadcddab', 'dbdcaabb', 'cbacadbd', 'adbbccdc', 'dadabbcb', 'cacddacb', 'dbdcabab', 'abdbcbac', 'ddcaacbc', 'bcdcdbba', 'abadbacc', 'adadbcba', 'bccbbdca', 'bdcbacdd', 'ddcacaab', 'ccdabdba', 'bddddabc', 'acbaddcd', 'abcabddc', 'ddbadbac', 'abcdbbab', 'ababcdab', 'abcaddcc', 'bdccdbaa', 'adbdbcdb', 'cdbacaca', 'cbbcadab', 'adbdcadb', 'dbbcadac', 'bacabdcc', 'cacdcbca', 'babaddcd', 'cadcbddc', 'dddbabcd', 'ddacacba', 'acadccbc', 'ddbaacac', 'dcdcabcb', 'bddaabcb', 'cbddcaac', 'dccadcdb', 'ddbadbdc', 'addbccdd', 'cbbdbacb', 'bacaccdd', 'adabbcac', 'bcbdaddc', 'bdbaddcb', 'bddccacc', 'bcbbaddb', 'dcaddcbc', 'bacbcadb', 'aadbcdbb', 'cdcdcbaa', 'dccbccaa', 'adbddccd', 'cbdcddac', 'aadcbdaa', 'acbdddaa', 'acdadddb', 'cbaddddc', 'ddbacdcc', 'ccdbdaad', 'badbadca', 'cabcdcab', 'bbdabbcd', 'cacbcada', 'abccddbb', 'daddcabb', 'adcbbddd', 'cdabdcdb', 'dacadacb', 'dbbdcbda', 'dcadccab', 'caabdbaa', 'addbcbcd', 'dcbaadbc', 'dabbcdca', 'cbdaccdb', 'dacdbcbb', 'cbdabbda', 'babbcabd', 'cbcabddb', 'cbcdbacc', 'acdaccba', 'ccddbadd', 'dcdccbab', 'cbcdcacd', 'bbacabad', 'cadcdacb', 'cadbddbc', 'cddbadbd', 'badadcbb', 'dcbadcdc', 'bacbdddd', 'acddabba', 'dbbcbdac', 'bbcbadbc', 'dadacbcd', 'daccabdb', 'abacdaba', 'cdbcbdca', 'acacdabd', 'acbdcabc', 'cbaccbad', 'ddadccba', 'dbdbacad', 'dcdadddb', 'bdbdddac', 'bcbdddab', 'ababdabc', 'bbdcadca', 'cadbdcca', 'bcacddcc', 'ccbbaddb', 'bddbccaa', 'dcbacdcb', 'bdadddcb', 'adbcabba', 'dbbcabcc', 'cabdddda', 'dbdabacd', 'bbdcddca', 'bacacddb', 'babdddcd', 'bddccaba', 'dbddbcac', 'bdcaaccd', 'acbbccad', 'bcdccadc', 'acabbdcc', 'cdcbcabc', 'bcaccdda', 'bcadbada', 'addbccbc', 'bacbcdbc', 'cdabbcba', 'dadcbcca', 'bdacabdd', 'ddaabbcb', 'bdbcbcca', 'cdddabcc', 'dadcdccb', 'ccddabcb', 'bddbcbda', 'ddcdcaab', 'abddcddd', 'dbadcabb', 'bbdcadba', 'dcdbdcad', 'bccadbac', 'bbdbcdab', 'babbdacc', 'bcbddabd', 'cddbaacc', 'adddcbad', 'dcbadbab', 'adbdacdd', 'cacbdbab', 'dbccdcda', 'cdcaacdb', 'cbdbcada', 'ddaacabc', 'cbdadbba', 'ccbdadbc', 'ccddabab', 'acddbacb', 'bcadadac', 'acabacbd', 'cdaddabd', 'ddaccddb', 'adcdbcbb', 'ccaaccbd', 'babacacd', 'abbddcad', 'cddbcaaa', 'cdddbbac', 'baabbccd', 'ddbadadc', 'bdbdcdda', 'abdcbcbc', 'abdabdcc', 'dccbadcb', 'cdcbcacd', 'ddbadcca', 'ddaddbcd', 'abbddbcc', 'abddaccb', 'acadbdbc', 'cbdcbabc', 'dadabccb', 'cbaddcaa', 'baadaadc', 'bcabdcdd', 'cbadbbdd', 'bcddadba', 'bbdbdabc', 'cdccdbac', 'dcbabcbb', 'bacddbdb', 'bdadadcb', 'acacdbcb', 'abddbcaa', 'cadbabdb', 'abccdcdd', 'ddcaccab', 'dddcbcad', 'cdababcc', 'bddacdaa', 'adacabcb', 'adacbdbd', 'cabdbdba', 'dbbaddca', 'bdaadcbb', 'bcdadacb', 'bacdddba', 'bcdcbadd', 'dababcba', 'adbddcaa', 'cbaddccd', 'dcadbbab', 'bcdadbad', 'dbabcdcb', 'cdabccad', 'dbcadbcd', 'acdabdbc', 'dcaacbbc', 'bdddccab', 'cbcbcbad', 'bcadcbab', 'dcddccba', 'dacabcdd', 'abcdcdad', 'adacbacc', 'bddcadda', 'ccdabbdd', 'ccdbbacb', 'dddacabb', 'dadacdba', 'ddadcdcb', 'abdccacd', 'adadaccb', 'abcdcbda', 'ccbadabc', 'bcdddcab', 'badabccd', 'bcdcaadb', 'adadbcac', 'bcabdddb', 'cabacdab', 'cbdccabc', 'cbabbada', 'dcabacba', 'bacbbcda', 'cddabbda', 'dcddbdac', 'cbdbaccb', 'cdaaaacb', 'acbcdbdb', 'bacdcbbd', 'cadbdcac', 'dccbbadc', 'cbcbadac', 'dcbdadda', 'ccbccdab', 'bcadbdda', 'abdbdbcb', 'dababcab', 'acbdcdbc', 'bbabdddc', 'dccddadb', 'bbabdccb', 'cddabcaa', 'cbadddca', 'ddbbcdaa', 'dccacbad', 'dccacbcd', 'bacadcdc', 'dabcadba', 'bbcddbca', 'bdbdcacb', 'adddacbc', 'dbdaadbc', 'cbabcdda', 'abcdddab', 'bddcacdb', 'bdacbabb', 'adbcaddb', 'cbdaabdb', 'cbbaddad', 'ccdcabcc', 'dcdbbdab', 'babccdcd', 'bccabdad', 'ccdcacbd', 'cbabddbb', 'adcabbda', 'bdddcbaa', 'cbaccbdd', 'badcbdba', 'dcababab', 'dcabddcb', 'abbccadb', 'acabcdca', 'dabdccbb', 'cadbdcdc', 'cabadbda', 'bdcaddda', 'addbbcbd', 'adddddbc', 'dbccbabd', 'cadbacab', 'acdcacdb', 'cdbcbaab', 'dcdabdbd', 'cddcdcab', 'bcadbcba', 'acadbacb', 'bccabbdd', 'adbbacbd', 'cdbabbdc', 'bdbddcac', 'ddabdadc', 'cacaddab', 'ddbcbcca', 'ababdbcb', 'bbacadcc', 'caddbbcd', 'ccbdadcb', 'dcabcbab', 'abbcbdcc', 'ddbaadcd', 'acdbcabc', 'ccbabdbb', 'cacdabbc', 'abdbcbda', 'dbcdbabd', 'dcadabcd', 'ddcbaacc', 'cbacabad', 'daadaabc', 'bdcabbca', 'ddbaaabc', 'adcbcadc', 'bdbabacb', 'ccadbbac', 'ccdbccac', 'cddcaddb', 'badbcbab', 'cddabccd', 'cdbccada', 'cbdaaaac', 'badcddcb', 'dbdcdacc', 'abddcadc', 'abbcbadc', 'dbadadcb', 'baacdaab', 'dbadbbcd', 'abccdddb', 'cabdcada', 'cbddaabc', 'bdcdcdaa', 'bbcacdac', 'ababdcdc', 'acddcdbd', 'caccadbb', 'ddbcddaa', 'cabadadc', 'bcbababd', 'acdcbccd', 'dbdcacca', 'dcaaccdb', 'bbdadcba', 'cddabbcc', 'ddcababd', 'addbacbc', 'ddbacacd', 'bddcacca', 'ddbabcbd', 'bdbdcdba', 'adcbdbcc', 'bacaddac', 'bcdcadcd', 'adbcdcba', 'bccadabc', 'bddcbada', 'bcbcbbad', 'bddcaacd', 'abcadccd', 'cabdabdd', 'badcbcac', 'cbcabbdb', 'daddabcc', 'ccdcdacb', 'bcacdaca', 'cabadbcc', 'cbbdbaca', 'bcddaaac', 'bbdccbad', 'acadcdab', 'bdcabcdc', 'cdcdcdab', 'aacdbbcc', 'bdabacbd', 'acadcdcb', 'bbcdbaca', 'bacadcdb', 'abbdbddc', 'dcbddcab', 'ccdadacb', 'adcadbdd', 'cdbcdcac', 'ccbbacad', 'dcacabad', 'cacdadab', 'bbadbcbd', 'dcbbdcba', 'dabbdcad', 'cdadcdbc', 'cbbdaddd', 'dabddabc', 'bbaddcbd', 'abdbbcdd', 'abcadacd', 'aaaacbdc', 'dadbcdda', 'badbcbdc', 'cadcddba', 'abdcdcda', 'bbabcbdc', 'babccbdc', 'dbdabadc', 'bddcdacb', 'dbdcdaba', 'cacdbdca', 'bdbadbca', 'bcbdacbd', 'cabdccbd', 'dbccaccd', 'bddcddda', 'dcbdccad', 'cbbacdbb', 'caccdbcc', 'caddbadb', 'dcbabadb', 'acbacdba', 'dddabbcb', 'caadbaac', 'bbddbdca', 'dccaddbd', 'adbadadc', 'adcdcabc', 'dbdcacbc', 'cddbbdaa', 'dbcadaba', 'abddccdc', 'babbcadb', 'dcabcdcc', 'dadcacbd', 'cacbccbd', 'cdbcbdab', 'dbadcadc', 'cadbcdcb', 'bcaddabc', 'cbbdabdb', 'cadbabad', 'cdcdbbab', 'bacadbab', 'cbaabdbd', 'bdcdacad', 'dbcdddab', 'acbdcbab', 'bbcbbdda', 'cdbaacbb', 'dcdabcac', 'ccaddbda', 'cabddcad', 'cadadcab', 'dbdccadb', 'dbbccdab', 'abbcddcb', 'cdaabbcc', 'ccdddbaa', 'bdcbbaca', 'dccdbaba', 'abbddacc', 'abcaccdb', 'bdccadab', 'cadbdadb', 'acdbabdb', 'dcacbbdd', 'abcaddcb', 'dbabdcbd', 'bdacbadb', 'bacbaddb', 'dacabccb', 'badbabbc', 'acbccabd', 'dbcdddac', 'addcdcdb', 'abcdcdda', 'ccadbbcc', 'ccbbabad', 'bdacdcbc', 'adbddbcd', 'ddbaaacc', 'ddbacddc', 'cdbadbca', 'cdbdacbd', 'ccbcdcab', 'cbacddac', 'bcdabcda', 'cbabdbdc', 'dadaccbd', 'cbdadcad', 'bcbacdab', 'cdbcacdb', 'bddacdcd', 'acdddbad', 'dddbdacd', 'bbadcabd', 'acabddaa', 'cabbdada', 'bdddcacd', 'bcdcabac', 'dbcdcdab', 'bdcdaadc', 'ccbdcabb', 'bcdbdcda', 'cbaddaad', 'cbdcbcad', 'bacbdccb', 'cabcbbcd', 'ccdadadb', 'dcdadbdc', 'dbcbcbca', 'ccabdbcc', 'ddcbaddd', 'cbbdcdaa', 'bccbdaac', 'abcbbdda', 'cacddcbb', 'cbbadada', 'acdbdcda', 'acadbcdd', 'cbadadba', 'daabcbbc', 'cbbacdca', 'dbadcabd', 'accadbda', 'acbccdda', 'bcbddaab', 'acdccbbd', 'bcdccaca', 'dadbccac', 'cbbcdcab', 'ccdcabcb', 'bddbaabc', 'bcbcddab', 'dcaabbcc', 'ddbacbdc', 'dbbaccba', 'cbdadaba', 'aacdccbc', 'bbccacad', 'cdacbabb', 'dcdadbdd', 'adbdbbcd', 'dbccdbac', 'acbaddbb', 'cbcbdacb', 'cdccabda', 'bbccbbda', 'adbbadcc', 'dbabdacc', 'dcbadbcb', 'cacdbdcc', 'dbcabacc', 'ddaaabdc', 'bbacbbdc', 'ccadbcac', 'cbdbadac', 'dcabadba', 'bdadbbcc', 'cdaaaabc', 'cddcabaa', 'cacabdad', 'bcadbbcc', 'dccbddda', 'abcbbdcd', 'cddcaacb', 'dcadcaba', 'cdbdcacc', 'dbcddaab', 'ccdabadc', 'badacbca', 'dddaccdb', 'bdcabaca', 'abcacacd', 'accdddba', 'ddbcaaca', 'badbccda', 'bbcdbcba', 'dacbdcdc', 'dbbcbaca', 'adbcabbc', 'acdacabd', 'ddababdc', 'bdddcdca', 'acacabad', 'bddcaaca', 'dbdbcaac', 'ccabadda', 'dadadacb', 'cbcdabdc', 'accbabdb', 'ccdadcab', 'cdaddaba', 'cbcdcbaa', 'cdbdddda', 'dccbdada', 'accbddac', 'ddddabcb', 'ddddabcc', 'dcdbadca', 'abdbdacd', 'cbccbaad', 'bacdabad', 'cbaabdbc', 'abccbdbd', 'bdcbadab', 'bddbaacb', 'abcbdcad', 'cdcbabca', 'bdbacbbc', 'cddaabac', 'bacabddc', 'cdcbcacc', 'addbcbad', 'dbaccadc', 'acbabbad', 'bcdbabbc', 'adbbcbba', 'bdacacda', 'cbbddbaa', 'bddabacc', 'acddacbc', 'adbddddc', 'bdacdbcd', 'cbdbbadd', 'bdccabac', 'bcadbcbd', 'accbcdbd', 'dbdcddaa', 'bcdcdabb', 'addabdac', 'ccbdbaac', 'ddbdacdb', 'dabdacbd', 'acddcaba', 'abcdabdc', 'cdcdaacb', 'ddbacacc', 'bcabbcda', 'dcabccad', 'bccbcbda', 'dbbdabcd', 'acabcdcc', 'acbcddca', 'daacbdcc', 'bbccaccd', 'ddacabdc', 'dbacdbbd', 'caadccdb', 'bbcbaadb', 'bbabbadc', 'adbcabdc', 'bccdbacd', 'ccacabdd', 'badccbcc', 'dacabbca', 'bdacdccb', 'cbaacdaa', 'dbdcbadd', 'abdbcabb', 'dbbdadcd', 'cabbddda', 'acacdcdb', 'bbabacbd', 'bcbbdaba', 'abaccddc', 'acdacbcd', 'caddcabd', 'bbccaddd', 'dddbcbac', 'baabdcbd', 'cdbbdbac', 'cdabacca', 'bacdbbad', 'cbadbddc', 'ababbcdc', 'adbcbbcd', 'cbbabbdd', 'acdddcab', 'aabdbdcc', 'adcbbcca', 'cadabdbc', 'aacdccbd', 'dcacbddc', 'dcdbbdad', 'bbdbccda', 'babcdabb', 'adbcacbc', 'cddbadcd', 'adacabcc', 'bbabbdbc', 'dacaccba', 'cdaabaac', 'adbdcdba', 'bcacbacd', 'cbdcaacd', 'bdbcacda', 'cdbcacbd', 'bcdbcaab', 'bccabdcd', 'bcddbaac', 'babdcbdb', 'cbdcdbad', 'dacadbba', 'cbcadbca', 'ddcadccb', 'cadbbddc', 'abdddbac', 'dacabbcc', 'adcddbba', 'dcaddbdc', 'cdabcbbc', 'cbadccbd', 'bababcbd', 'bacadacc', 'daccadab', 'cdbdadac', 'abbdcada', 'dbdcbbac', 'accdbcbc', 'cdaacbbc', 'cbddaaab', 'bccacdcd', 'daccdbcb', 'ddcbcdba', 'cdacbdbb', 'cdacdbba', 'ccaddbbc', 'baacdbcb', 'bacdcdca', 'bccbbdab', 'adbdbdca', 'cdacdbbc', 'ddabcdaa', 'cbbcacbd', 'adbdcbbc', 'dddaabcb', 'cdbbdaab', 'bdccbacc', 'dadcbcdc', 'adbadcdc', 'caabdbbd', 'bdddcbda', 'bcdcadac', 'babdbccb', 'bdccbbab', 'cdbaccbd', 'cddadccb', 'adbbccbd', 'bbccadda', 'dadbcabd', 'abaddddc', 'cdbbdcaa', 'dcbdcaba', 'ddacbccd', 'cadcbcbd', 'bcbccdad', 'bcddbabc', 'daddbcba', 'abdddcab', 'ccbcbdca', 'cbdaccba', 'ccdbbcab', 'cdbbdbaa', 'bdcbbaab', 'cacbcdcb', 'ddcdabac', 'dabdadac', 'aabdbdcd', 'dbaacdbb', 'adcbdbda', 'abdcdbda', 'dccbadac', 'acdcadbb', 'dcdbaccd', 'dbbcabdb', 'cdbcdcad', 'bdadbdcc', 'daacaabb', 'addbccab', 'dccbabcc', 'cbaddacb', 'ccbcabdd', 'cbdadbab', 'dbacadac', 'adacdbda', 'caddbacd', 'cabdadbd', 'ddacabca', 'cacadcbd', 'bccdabca', 'bdcdacca', 'adacbabc', 'dacdabad', 'bdbabdac', 'bccadaba', 'cdbadcad', 'dbcbddda', 'dbbdddac', 'cabccbcd', 'bdabdabc', 'addcdcbd', 'bdbcbaba', 'bcadbcdb', 'daabaacd', 'bcaadaad', 'cddabddd', 'ccbdcdab', 'ddbadcba', 'bdddcbad', 'ddcdbbad', 'adcbabdb', 'bbcdaaaa', 'dcbbdabc', 'bcdabdbc', 'cabdbbac', 'bccaddcc', 'caddadab', 'abadcbca', 'ccdadaba', 'addacaba', 'cadbcaba', 'ddaaacdb', 'cdacacba', 'daacaabc', 'abadbbcb', 'dcbcabba', 'cdbcacac', 'baccaddb', 'cddbbdca', 'bccbcadd', 'adacabbd', 'daddcdab', 'abcdbcab', 'ddabcdab', 'adbadcab', 'dbacabcd', 'ccdabdcc', 'cadbddbb', 'adddcdbd', 'bdcdbdad', 'bdacdacc', 'bdaacbcb', 'bbddccab', 'babbcbdd', 'adbdcada', 'bdacdbbc', 'bbaccdab', 'ddcabdda', 'adcbdccb', 'bbdcadcd', 'bbdabccb', 'accadbbd', 'dabcdbba', 'abacdadd', 'cbbccdad', 'acadbcba', 'ccbddacc', 'bcdabadd', 'ccbdcdad', 'cadbcadb', 'cadcadbb', 'cbbadaba', 'acdcbabd', 'cabccbdb', 'badacbdc', 'aacbdcbd', 'dcdadcba', 'baccdacd', 'dbdcacad', 'cbbaadbc', 'abababdc', 'dccddacb', 'cbdbdacd', 'accdacbb', 'bbcabcbd', 'cddaacba', 'cbdcbcaa', 'babadcca', 'bdccdadc', 'dbcdabcb', 'cadbddaa', 'cadcbdad', 'dbdcabca', 'ddacdccb', 'ddaabcab', 'cdccabdc', 'ddcdbcac', 'adcdcabb', 'caddbdbb', 'ccadccdb', 'cbbcacdc', 'bddcbaac', 'bbacdbcd', 'abddbdbc', 'acddbbaa', 'cbbaadbb', 'ddacbaaa', 'abbdccdd', 'cabdacbc', 'bcbddaba', 'dbdcdabb', 'acddbaaa', 'cbdabdda', 'dcadbddb', 'dabadbac', 'caabaadc', 'cbadcabb', 'bdcbdbab', 'accddbac', 'cbcacdbd', 'acddadbb', 'bbdbaacb', 'acdacadb', 'bbaddcab', 'ddacbbca', 'cabddcac', 'dbdccada', 'accacbda', 'dbababcb', 'bccacada', 'caabbdcb', 'acdbbdbd', 'addcdbaa', 'accabcdb', 'ccbcdaab', 'abbdddcd', 'abdbbcdb', 'addbbdcd', 'dcacbdbb', 'bacdbdac', 'bdbdacbb', 'cbdcabca', 'acdddbab', 'dbadcdbd', 'bbdcaabb', 'caadbdbb', 'badbdddc', 'adbdacda', 'bcdacacc', 'dbdbcacd', 'dbcaddbd', 'dbacdabc', 'adbabcda', 'dabdadcc', 'abdbcdcb', 'caddcaba', 'adbcabca', 'cadbbdbd', 'ccacbcdd', 'cbabadbd', 'bdbccada', 'bcddbabb', 'bdadbcdb', 'bacbdcab', 'cbcbdaac', 'cbbdcbba', 'abcddacb', 'badacabb', 'dbcaabbd', 'cbcbdadd', 'bddaaacd', 'dcbabddb', 'ddcadbbc', 'cabadcdb', 'bcddabdc', 'cadcabbd', 'ccadbcbd', 'caccddab', 'abdcddda', 'cdbdacdc', 'dbcbdcad', 'dcabdbcb', 'dbcabbcd', 'adcbdbcb', 'ababadcb', 'dcbcbdba', 'abadcacc', 'dadbcbab', 'bcddacbb', 'dcbabccb', 'ddcaadba', 'bddcbacb', 'dcbbdbba', 'bcdabdab', 'ddaabbdc', 'cdcadbac', 'cdbdacac', 'badcbcad', 'bcbddadd', 'dabadcdc', 'bacbdbbd', 'abcbbacd', 'cddcbdca', 'aabcdaab', 'bacabcdc', 'ccdbadac', 'cdabccbd', 'bbccdacb', 'cdbdcbaa', 'addbdcac', 'cdadabca', 'dacabcac', 'cddabcba', 'cdbccaac', 'cacbadac', 'ccdabdad', 'cadddbbc', 'adbdcdac', 'abbdacbd', 'caacdccb', 'daadcbcb', 'dcdbbaad', 'cbbdcadd', 'bbaddccb', 'ababdbac', 'bbccabdd', 'cdbcdacc', 'dccaddbc', 'accbabda', 'dbabcaca', 'ccdbcabc', 'dddcbacc', 'abacbabd', 'acbaddac', 'bacdcdbb', 'acdbcadd', 'ddababbc', 'ddbbcabc', 'bccaddad', 'badcadda', 'addadcab', 'bdccbadc', 'acdbdcbb', 'cabddcbc', 'bdadabbc', 'caabdcbb', 'addbcbdd', 'abbcdccb', 'abbcbadd', 'dcadccdb', 'bddabbcb', 'dbbacacd', 'cbabcabd', 'dacbbcdd', 'cbbdcacc', 'cadcacbc', 'adabdacb', 'baccacbd', 'cbbcacda', 'acabcddc', 'bbcbaacd', 'bbabcdbd', 'bdadbdbc', 'babdccbb', 'dacababa', 'bcbdadda', 'dacabbdc', 'dadcadbc', 'acbdadbc', 'bccdbadc', 'adacdbcb', 'abdcaccb', 'cdbdacba', 'adcdacab', 'cbdabddc', 'ccdbacdc', 'ddcabdba', 'cdcaacbb', 'adadccba', 'cdcdbaca', 'dadccaba', 'babddaca', 'cadbddcb', 'adcdcbcd', 'bcabbdbd', 'dabcdacb', 'cbaddbab', 'ddbccaaa', 'dcbbccad', 'cacbaccd', 'cbdcddca', 'bdbacbad', 'ddcadcba', 'bcdbbacb', 'bddcdbaa', 'ccbddabc', 'cacdbabc', 'abddaccd', 'adccdcdb', 'abdabdac', 'bccbadca', 'abbcddcc', 'abdddacd', 'cbacdbcb', 'cabbadcc', 'cbdcdabc', 'acdbddca', 'dcaadbcb', 'bbccadab', 'ddbaddca', 'bbabcdac', 'baccbbad', 'abcdbada', 'cdbcbdad', 'cbcdabcc', 'bdbabcab', 'dcbabddc', 'daddbdbc', 'ccdbacdb', 'dccbacba', 'babaddcc', 'dddccbca', 'dbbadcad', 'acaccdba', 'bcddddaa', 'ccabdcda', 'dbccabda', 'abcbbcad', 'adcaccbd', 'cacdbcdc', 'dabbabca', 'dabacddc', 'dcbacbdc', 'caabdbdc', 'dabcabba', 'bcacdcab', 'bccdbaad', 'baccadca', 'bdccbadb', 'ccdacbdd', 'dccdaacb', 'dbadcbcd', 'dacbbdab', 'dccdbadc', 'cdabcbcd', 'ccdaccba', 'ccabcacd', 'acbbddcb', 'acadcbdd', 'babacdca', 'ddcabbda', 'ddbcdbaa', 'bddcaacb', 'cabdaccb', 'bbadbcab', 'cbddcdca', 'ddbadcac', 'adabddbc', 'abdcadbb', 'adcdccdb', 'bbacbcad', 'ddaabdcc', 'ccbbcdad', 'cddaccab', 'abdddacb', 'dbabccbc', 'bdbabdbc', 'bcabcdad', 'bdcbaaaa', 'badcdddd', 'cdbbdcab', 'caddbdab', 'dbcdcdda', 'ccdbadcb', 'dcbbcacb', 'cbdbaddd', 'abbcddac', 'adccbacb', 'acadcbbc', 'cddbbcca', 'ccabdcbc', 'acdddbdb', 'adacaccb', 'dbacacdc', 'ddadaabc', 'bcabdcda', 'dbabdccd', 'abdcabac', 'dbbccaad', 'babdaccd', 'cbcabddc', 'accdbbac', 'cdcddbab', 'acaccbdc', 'bdbbaacb', 'dbdadbca', 'abbdabca', 'dcacabdd', 'dcabcdbc', 'cdadabbc', 'ddbccabb', 'cdbadbdb', 'acdccbab', 'adabcbbc', 'cabdbdbc', 'ddbaddcd', 'abcddcca', 'dbbdcdda', 'ccbadaba', 'baddddac', 'bdcbcbaa', 'bcacdadb', 'cbcbcdad', 'abbcdcbd', 'dbdccdca', 'acabdcda', 'bacdbaca', 'abccbddc', 'ddcbdcca', 'dbdaadcd', 'bdbacddd', 'dabbcdac', 'dddbaccd', 'dcabdccd', 'babdddac', 'cbbaddcb', 'bcdaccad', 'cbcddbab', 'dbdbaccb', 'accadccb', 'dbcbddca', 'ddadbcdb', 'dbcdbbab', 'bbadcbca', 'cdbacdcd', 'bccbcdab', 'ccaccadb', 'addcbbcd', 'addbcaaa', 'bacbccad', 'bccbdbac', 'abcddadb', 'cbdbdcac', 'ccabadbb', 'bbdbacbc', 'bbcabddb', 'bcabccdb', 'bcddabbc', 'adccbdbb', 'bcbccdaa', 'dccadcbd', 'cdbbacab', 'bbdccadc', 'dccadacb', 'abdcbabd', 'bddcbcca', 'dcdbdacc', 'cbcadddd', 'abccdddc', 'cdbabcbb', 'dbcacaca', 'daabdcdc', 'baddccbb', 'ccdcbcda', 'adbdddbc', 'cdacbaba', 'ccbadadd', 'cbcdadad', 'dcadcdbc', 'cdcbdcad', 'dcbadbac', 'bdccdacb', 'bdbdaacd', 'bcabcddb', 'bcbadbcb', 'ddbdccba', 'bcdabaca', 'cdacddcb', 'dbaddadc', 'dababdcc', 'cdbcacdc', 'bdcabdda', 'ccaddbcc', 'cacdcbcd', 'adacbbcd', 'aadcdbdb', 'cbadabab', 'acdbdadc', 'badcbcdc', 'cddadcbc', 'dcaddbca', 'dbacddcb', 'dacbacab', 'dbcadacd', 'ccabbddd', 'cdabdbab', 'cdadabab', 'ddcabdbb', 'dadcbcad', 'cbdabdbb', 'bcdaccac', 'adabccbb', 'abccacda', 'bbacbadd', 'abdbbcdc', 'dbaaccdc', 'bcacabdd', 'ccdbbcba', 'badbdcad', 'bbacadad', 'cdbdaccd', 'bcacabad', 'dabdcacc', 'bdbdcabc', 'bddcbcba', 'dccbdcda', 'acbbddac', 'bccbdaba', 'cabdbcdd', 'bbacbddd', 'bdaaccbd', 'bccddacb', 'cbbaddcc', 'dbbdcbca', 'cbacacad', 'cdadbdba', 'dbcaddac', 'dcdbabab', 'cabdccdd', 'cbcabdda', 'baadccbd', 'bcbddadb', 'cbacbadb', 'acbcdcdd', 'cbacddba', 'dbacdccb', 'abccadbc', 'cbbabbdb', 'cbcabada', 'dbcbaabb', 'ccddbdad', 'cbdacbdb', 'bcadcdbd', 'cdcabcdb', 'babddbbc', 'dacbcdda', 'bcdadcda', 'addcdaba', 'ccbddbac', 'bdaccdbc', 'bbdcabcb', 'dacdcbdc', 'bbddabcd', 'adbbdbdc', 'dbbcaddd', 'dbadcacb', 'bcdbccac', 'bdacbdcb', 'dbabcadc', 'cdccaacb', 'dacabddd', 'adbbaccb', 'dbdabcba', 'bacacdcb', 'bddaccac', 'cbcdabba', 'abcbabda', 'adcdbabc', 'bacdaccb', 'dbdcdcab', 'bcbdadbc', 'adacacab', 'cdcabadb', 'cdacdcdb', 'dcadabcc', 'ddbaacda', 'dbcabadb', 'bbdadbcd', 'bbcbbcda', 'dbdcbcba', 'cdbaddad', 'ccdcbada', 'caccacbd', 'bacdadac', 'dbabbacc', 'bcaabdaa', 'bdccacda', 'dbbcacbd', 'bbcdccda', 'cdbdadca', 'ddcdcaba', 'ddddacbb', 'acbddddd', 'baacdbcc', 'cacdbbdd', 'ddddbacd', 'bcbbddba', 'adaccbdb', 'bacdbddc', 'cddbabcc', 'abdadacc', 'caccabcd', 'bddcaaac', 'ddadbbcc', 'cbcacdab', 'cbabadad', 'cbbaacbd', 'baadbdcb', 'dbabdacb', 'bddabcab', 'dbaccdcd', 'ddcbabbc', 'dcdacddb', 'bcbcdbaa', 'acabddcd', 'abbacdbd', 'cabcacdb', 'dbbabdcc', 'dbbccaab', 'aadbbcbd', 'cabaccbd', 'adbbccdb', 'addbcabb', 'bacadbdb', 'cdbcbcab', 'bcadadcb', 'cacbabbd', 'adbbdcad', 'bbcaddbb', 'ccbbadab', 'daacaabd', 'accbacdc', 'cacbcbad', 'caaaabbd', 'dddabbdc', 'cbacadda', 'dbcabccd', 'cbabbadb', 'acbbdcac', 'cbdaddbb', 'dcadcbad', 'acabbdac', 'dababddc', 'caddcbcc', 'cbbabdac', 'baddccab', 'abccbdba', 'acbcacdc', 'cacbcddd', 'ddaadcdb', 'adcadbbd', 'cdbadddc', 'cadbcbbc', 'bbdacbac', 'dabcacba', 'badbddca', 'bdddacbc', 'bdcdcaba', 'bcadaddc', 'dadccddb', 'acbcbdba', 'aadbcdbd', 'ddaccdcb', 'addabaca', 'adbbccac', 'cddbdbca', 'ccadbdbc', 'aadccbcc', 'bbccddab', 'caddbadc', 'acadabca', 'abdbcaba', 'cdbaccac', 'bccadbcc', 'ddccbaab', 'abadabcb', 'bdcacdbd', 'addbdcad', 'ddcabdab', 'abdcddca', 'babbcbcd', 'abcbdadc', 'bbabaccd', 'baccbbdd', 'dcbdbdad', 'cbabdaba', 'acdabcbb', 'dabdabcc', 'ccbcbadd', 'abccabad', 'cbcdcaac', 'ddbbcaaa', 'bcabbdda', 'cbddaacd', 'dcdcbdba', 'ccbaddcc', 'bacdcbbc', 'dcdbcacb', 'baddbbcd', 'cddcdaab', 'ddcadacb', 'cbabdaca', 'bccadcdd', 'adbadddc', 'cdcaacbc', 'cbbdbada', 'cbdbadcc', 'bdacbdcc', 'ccdcbbac', 'abbcadbb', 'accabbdc', 'adcbddad', 'cabccbad', 'abadbcba', 'acdcbbcb', 'bdbcabca', 'ccdbcbaa', 'dacbcbdd', 'dbcbabad', 'bcaadaac', 'cadcdabd', 'dbbcddaa', 'babadccd', 'bccdbaac', 'cadcdbba', 'ddbacdbb', 'ccabdacb', 'cbcabccd', 'ccddbabd', 'addcdbba', 'abcddbad', 'bdcbabda', 'cdcbaacd', 'cdadbada', 'bdbdcdab', 'ddbdbcda', 'bbcabdbc', 'cdcabbab', 'adcbcdca', 'cadbcbbd', 'dbadddac', 'daccbdac', 'dcdababa', 'bcacbadd', 'acddaaab', 'bbdcaacb', 'dddadbbc', 'abccabdd', 'cddbacba', 'acdbadca', 'cdcbbaab', 'dbacacda', 'ccdabcdd', 'cbaddbca', 'acadcbdc', 'abcacada', 'addbacaa', 'dadabccd', 'bdcaccdb', 'ccabdabc', 'dadacbac', 'abccbdbc', 'adccddbb', 'cbbdabbd', 'dcdbadbc', 'adccacbc', 'cdcabcad', 'cbddadad', 'babdaccb', 'ddabccaa', 'acacdbbc', 'cdcbbada', 'babbcbdc', 'bdabacad', 'cdcbcada', 'bcdcdcda', 'cbaccbcd', 'cddadddb', 'adddbcad', 'ccdadbdb', 'abcacadc', 'adbaccda', 'addbcddd', 'cddaaaab', 'acdccbad', 'dbcdabdd', 'abdcbddb', 'adadadbc', 'cdabaddc', 'bdbadacb', 'bccaabcd', 'ccdcdbab', 'dbabbabc', 'baacdbaa', 'bcbdcdda', 'bcddbcab', 'bbadcddb', 'acdabbca', 'bdcbaccb', 'acbaccdd', 'babbdbcc', 'babdcdba', 'abaddaca', 'addbcbab', 'dcddbadd', 'ddbaccad', 'cdaabdaa', 'bdabacbb', 'ccddbcad', 'dadbadcc', 'dbdcbaab', 'cdacbacd', 'bccdadad', 'adbdbadc', 'dadbabac', 'baacdbbd', 'bdacaddd', 'cbbababd', 'cbadcbcd', 'badadbac', 'cadcbbdd', 'cdddcbac', 'bcadddbd', 'cbdcaddd', 'abcbcdcd', 'bcbdcaac', 'cbbabccd', 'abacbdbc', 'dcdbabca', 'abacadbb', 'cabccada', 'cbbccdac', 'abadccbb', 'cdacabda', 'acadbcca', 'cdacdddb', 'dcdbdacb', 'bbccdbda', 'dcbaddbc', 'ccdacdbc', 'ccdbcaac', 'dcbdaaaa', 'dbcbbdab', 'cdcdacab', 'cdddbdca', 'dcbdbadd', 'dcabcabb', 'dadbcbac', 'badcdadb', 'abacdcab', 'bcbdbadb', 'cbcbdadc', 'dcbadbbd', 'bcddcdda', 'ddbccacb', 'cddcaabd', 'cbdccadc', 'addcdcbb', 'accbadac', 'dccbbaab', 'cddcbdad', 'cdaaccbc', 'abddcacd', 'cabdabba', 'dbcbcabb', 'adccbdba', 'dacdadbb', 'dcacbacb', 'cddacbca', 'dbbcdaac', 'cdabdcbd', 'bdcaddbc', 'ccabdcdc', 'bdcadcac', 'dccbabdc', 'cdadbbab', 'cbdbacbd', 'cacdbddc', 'adacadcb', 'cabcbcdc', 'dabbcddc', 'dbaabbcd', 'dcabcdda', 'ddabbccd', 'dcdddbba', 'dbcbbaba', 'abacdbdd', 'acdbdadd', 'ccddadbd', 'dbdcdaab', 'dcbcbbca', 'bbdacabb', 'bddcabad', 'baccdbad', 'dacacbbd', 'dadcdbba', 'cdbdbbac', 'bbaddcad', 'abddbcac', 'cdbbdbda', 'daacbcaa', 'abbdabcd', 'dcdacdbc', 'daddbcbd', 'badbbdcb', 'caadbaad', 'abbdbbac', 'cbdddabc', 'dbcbdacd', 'dcadbabd', 'bcabcbdc', 'bccaadbb', 'cdcadcdb', 'abaccadb', 'cacabddc', 'cbcbbadc', 'abbacbbd', 'bcdbbdba', 'cbdaccdd', 'bcdaddda', 'daddacba', 'ddcbaabc', 'acbdadcd', 'cddbbcac', 'dbcdcabc', 'cdbbccaa', 'dddcbcab', 'ddcdadbb', 'dacdcbba', 'bdcdddca', 'abdcbdab', 'addbbcab', 'bdbccdad', 'addacabd', 'cbbccdda', 'cbcdacca', 'ccacabdc', 'dbaabcbb', 'cbbaaccd', 'babdcbbd', 'adcdbdca', 'abcbdbda', 'cacbddda', 'bcddcbda', 'abbccdcb', 'acdadacb', 'cddccaba', 'acdbcbcb', 'dcabbacc', 'ddcacdcb', 'dbdacbdd', 'dbcabddd', 'dcacbadb', 'ddaabacc', 'dccadbdc', 'bababadc', 'cbaddbad', 'dacabbdd', 'badcbdad', 'bdccbaba', 'addcacbd', 'dddcabac', 'bddcacab', 'dadbbccd', 'dcadbbdc', 'dddccdab', 'dadcbdba', 'cdcddbac', 'adacdccb', 'addccbbc', 'adcdcbbd', 'bddcdaca', 'dbddaccd', 'bddddaac', 'bbadbcad', 'acbcdbca', 'cdbddabd', 'cdbdccda', 'adcbcdbd', 'babdcaca', 'bdbabdcd', 'addbadcc', 'ccabccda', 'bcaddbcb', 'dabbadca', 'bbdaaccd', 'bcadacab', 'bbdcadcb', 'abbddadc', 'adcdabbc', 'abdcadbd', 'dbcddbda', 'dbcaddda', 'cbdcadbc', 'dddadcbd', 'bbcadddb', 'cabcddbc', 'babbddcd', 'cadddbdc', 'bdccabcb', 'ddbcbdab', 'dbcdaadc', 'adacadba', 'acacdbab', 'bcbbddda', 'bddbcbca', 'ddaaccbc', 'bccadcdb', 'cbdddacc', 'dbaccabb', 'abddcbdb', 'dbdabcab', 'ddaabccb', 'aabdaacd', 'dbaccabc', 'cddcaaba', 'abbdcacd', 'ddbbcdda', 'ddcbacba', 'cdbacabb', 'acdbabcb', 'bdbadcdd', 'ccbddcab', 'acdbdbda', 'cdcadcbc', 'dcdbaddb', 'adacdaba', 'bccabadb', 'bcbdbdad', 'bacdabda', 'babdbaca', 'cdbbddad', 'bcbacbdc', 'cacddbdc', 'cbaddcbd', 'dcbbcaca', 'ccbcdada', 'acdcaccb', 'bcacbcdd', 'bbcadadb', 'cbbcadda', 'dccbaaaa', 'badccbdb', 'bcadcada', 'adcdbacd', 'bdddabcc', 'acacbbda', 'cdbaabcd', 'dbabbcca', 'ccdababd', 'ddddcbba', 'ccbcdadc', 'cbdcacad', 'bbddcbda', 'adbccaca', 'cbcdabdb', 'adcbdacd', 'ddcadbab', 'dbcaddab', 'babdcbdc', 'dbabcbdc', 'abdcbbdb', 'dcadcbac', 'acabacdc', 'cadabacd', 'dcaddcbd', 'dabdbcad', 'cddddbaa', 'cdacabad', 'abadcbba', 'bacdacbc', 'dbaadccb', 'ddcbadbb', 'cdabbdbd', 'bacdbcda', 'ccddcadb', 'cadccddb', 'ddcdbbaa', 'bddcdcad', 'ccbddaaa', 'ddbcdbad', 'cddbacbc', 'dddcbbaa', 'bdcabbcb', 'dbdccbba', 'bcabccbd', 'ddbcbcba', 'adbadccd', 'dcadcbba', 'acbdcaca', 'cddabcbd', 'badbabcb', 'cbdadabd', 'cbddddad', 'caadcdbc', 'bddcadcb', 'ccaddbad', 'ccbadadb', 'bcbddbaa', 'ccabdbad', 'badcdbda', 'bbcabdbd', 'ccdbabcc', 'cdabbdcd', 'ccdacbbc', 'bdccbcca', 'cacabdbd', 'dcbcaddb', 'bdccacbc', 'dccdaccb', 'addaabcb', 'bdddabca', 'cadbacbc', 'dcaccbad', 'dbbacabd', 'bccbddda', 'ccbdbaca', 'acdbdbcc', 'babadacc', 'abccbcdc', 'dcdadcbd', 'babdcbcc', 'bbcbcacd', 'caccdcbd', 'dccaacbc', 'bbabbcbd', 'bccdcdaa', 'cabcadbb', 'dcddbcca', 'cbdccacb', 'cbdcabcb', 'bacbacad', 'daccbdbb', 'aacaabcd', 'babaccdd', 'cddabdbc', 'cbcacadc', 'bcdbcbac', 'cdadabcd', 'dccbcdaa', 'ddbabacb', 'abdbdcdd', 'adccbcca', 'abddacbd', 'ccbccdad', 'cbdbdbac', 'cbdcdcaa', 'bdbbcaad', 'bbdcabbd', 'acacbddd', 'adcbcbac', 'dbbdadca', 'acbccddc', 'acbadacd', 'dbbabaca', 'dacabdbc', 'dbdbcadc', 'abdbdccd', 'dcabdddb', 'dcbabcab', 'acbacbbd', 'baddcbca', 'acabbdbb', 'dddbdcaa', 'acbcacdb', 'ccacddbd', 'cdaddabc', 'ddaddbbc', 'abaccdcb', 'dacadaba', 'dabcaddc', 'babbdcdc', 'dccacbbd', 'adbccbdb', 'dadaccba', 'dadacbcb', 'bbcbbaad', 'dccadcab', 'bccddcda', 'dbcaadcc', 'bbcaaaad', 'cdbadadc', 'dcbcdcab', 'bcbdaccb', 'bbadccac', 'babdbbcc', 'bacddbbc', 'acbccdcd', 'dabbaccd', 'dabccbdb', 'ccdcbcba', 'cacbcdac', 'ddcbbabc', 'dcddbadb', 'acbddcdb', 'cbccdcda', 'bccaabdc', 'cdcdcbca', 'bcddaacd', 'ddadacab', 'dcabadbd', 'cbcbaddb', 'abdccadd', 'addbdcdb', 'ccabdbca', 'cbadcaca', 'cbdbdabd', 'cddbdaca', 'babddccb', 'dccabdcd', 'cdadbadd', 'dbbdcaad', 'cddbccad', 'cbacaccd', 'dadbccad', 'ddbcabdc', 'acdabdab', 'abbccdbc', 'dacdbdcb', 'dcddadbd', 'cbdababd', 'badbbcdb', 'bddccbda', 'daccabcb', 'ccdbbadd', 'ccbdcbca', 'dbdbdcba', 'acddbcac', 'cadababc', 'acdbcddd', 'bcaacaad', 'dbacabbd', 'bacbdabc', 'badcdcac', 'cbdadcbc', 'bdcbacad', 'dcacdadb', 'dcbadccb', 'cdcbadcc', 'bbcdaccb', 'dabcadda', 'caadcbaa', 'aaaadcdb', 'ccbcadba', 'bdabacca', 'abdddbcc', 'cbdabdbc', 'dcbacddc', 'dcabdabb', 'bcddbadb', 'acbcddbb', 'cddbaaaa', 'ccaddaab', 'ccddccab', 'abcadabb', 'cdbadcac', 'bccddbda', 'bdaccabd', 'bbdaabcc', 'bcbdcadb', 'abbcbbad', 'ddbcacaa', 'abcadddc', 'bcddabba', 'dbdadacb', 'bcaccdab', 'acbdcadc', 'cdbcaabb', 'badabbac', 'abccacad', 'adacddbc', 'bacabcdd', 'bdcddaad', 'dcbabdba', 'ddaaabcb', 'acbdacbd', 'dabdddca', 'cddaccba', 'ccdbdbda', 'bbddbcad', 'bbacbadb', 'addbadcb', 'ccbcbbad', 'cbadbbca', 'adddbcda', 'cbacddcb', 'dcddbdca', 'adbcbbab', 'cbadbdda', 'bcbdaacb', 'acacbddc', 'bcbdbbaa', 'dbbaadbc', 'cadcdcba', 'ddcbaadd', 'adabcbcd', 'dacddcbb', 'ddacdbbd', 'dacdbcbd', 'ddcbbaba', 'bacdacda', 'ccbbddac', 'bdcaabaa', 'cbdcbbaa', 'dabcaccb', 'acadbdba', 'dccbadba', 'ddbcadad', 'adbcdbcc', 'babacddd', 'cbcacdca', 'addcadbc', 'ababddca', 'ccdadcbc', 'dcaddbac', 'daadbbcc', 'ddcdbbda', 'bbadbcca', 'dbcdacac', 'cacbdcdc', 'acdadbba', 'dbaabbcc', 'dcdadbcc', 'bccdadda', 'dadbcacb', 'ccbdacab', 'acbadadc', 'dccabadd', 'dbcabbad', 'dbcbcbaa', 'ccdcdbda', 'cbbaccbd', 'dbadcdcb', 'badcdddb', 'acadadcb', 'cbddbdba', 'ccbbcbad', 'badddccd', 'cbcbadba', 'dacadddb', 'cbbacbbd', 'badccdbc', 'ddadcbaa', 'adbcdabc', 'cdabddad', 'badadabc', 'dddadcbb', 'acdbdacb', 'addabdca', 'cddabbdc', 'bcbccbad', 'bcdccadb', 'cdbdbcac', 'bbabddbc', 'abdbcdcc', 'cadcacba', 'adbccdca', 'dcdcdbab', 'acddbdca', 'cabcdbdc', 'cdadbbdb', 'abddcddc', 'dbcadada', 'daddcbaa', 'ddacdbbc', 'cabacdbb', 'adbabbac', 'babcbbda', 'baddaacd', 'cbddbdad', 'badccbba', 'accddbba', 'acbbcdcc', 'adcbcdba', 'cdcabcdc', 'babddccd', 'bcdcddab', 'acbabdbb', 'acabdabc', 'cabaddcd', 'bbaacdbb', 'bdacdcca', 'acddbbad', 'adddbccd', 'cdadddbd', 'acacdbdd', 'bbcaadaa', 'dababacd', 'cdacbadb', 'bbcdbcac', 'adababcd', 'dbcacbdc', 'bdcbcabb', 'baccabbd', 'baddccad', 'cddabdba', 'baddaabc', 'aaaacbdb', 'bbdbcadd', 'bcbdacdb', 'accdbdbc', 'bbabdcda', 'dacdccdb', 'addccaab', 'dbbdccab', 'cdbabdda', 'bdcbacac', 'bddcabba', 'cabbabdc', 'babddcab', 'bbadbcbc', 'ccabaccd', 'bcbdbdda', 'ccbacadd', 'ddbcbdda', 'ddacaadb', 'adbabcbc', 'acbbdbab', 'ddbbadcc', 'cbcaddbc', 'accbdacb', 'bcbadddd', 'bcddaada', 'dcaddbbd', 'bdcbbcaa', 'bbdbccac', 'cbadadca', 'adcbcdac', 'cadbdabc', 'adabccdb', 'dbbcbcac', 'cdbacdac', 'cbdbaadb', 'dabbdcdb', 'dddbccab', 'adbacdbd', 'ccdddacb', 'adbadcdd', 'dccdcdab', 'bdcbccab', 'ccacdcab', 'bcacbddd', 'dccdabdb', 'dabacdcd', 'adababbc', 'acddcabd', 'bbabcbda', 'dcadcacb', 'addaadcb', 'cadcacab', 'bbcbaccd', 'cdadbcda', 'dabacbcb', 'dcdabdac', 'dacbcdca', 'bdccacab', 'cdbbabab', 'dbcadcbd', 'adcbbddc', 'dccadcbb', 'cbdcbcba', 'cabbdabc', 'dbdacbbd', 'bcabdada', 'dbabacac', 'bdcbabca', 'baaccaad', 'dcbadbbc', 'addaabac', 'ababcbad', 'cacbacdd', 'adcdacbc', 'bdbdabdc', 'aabdcdbc', 'dccbaacd', 'dcacabac', 'ddcbdabc', 'bddabcbb', 'acdcbdba', 'dbddcadd', 'ddbcbaaa', 'cbddcadd', 'bbdacdcb', 'bdbcadbc', 'bddbbcab', 'bbcbcadd', 'cddabcad', 'cbadcdbc', 'adabacdb', 'dbddbcab', 'bdaddcab', 'ddabdaac', 'dbbcabcb', 'ababdbca', 'bcabdadb', 'dcabddca', 'bdbbccad', 'dddbabcb', 'dccbdbac', 'acbccdab', 'baddcada', 'ccbcadbd', 'cdbdaacb', 'abbcdbac', 'adadccbd', 'acbcaddb', 'acacbdba', 'bdbbacca', 'bdabddcb', 'ccbabdcc', 'acdbadcb', 'ddacdbac', 'cadbcabc', 'baccdccd', 'dcdbcbda', 'ddaacaab', 'ddcadbad', 'dddddabc', 'ddaadccb', 'bdadcbdb', 'cdaaaadb', 'bbabdbac', 'ddacbbcb', 'bccbabda', 'bdccabdd', 'bbccdaca', 'acbdabcd', 'cbcadccb', 'adddcacb', 'bdacadca', 'cabbabdb', 'dcaacbdb', 'dbaccbac', 'cdcaabdc', 'bdadabcd', 'bdcdbdac', 'acdabbdb', 'dcababac', 'ccacbdbc', 'bbdbccba', 'dacaddbd', 'adbcbada', 'cdacddbb', 'bdbadcbd', 'abccbcdb', 'dabddacb', 'ccadbadd', 'bdabdcad', 'bdcabcda', 'abcabadd', 'bcbabddc', 'bddcbadb', 'cdabadac', 'cbbacdda', 'addcbdaa', 'dcadccbb', 'cbdccadd', 'dadccbbc', 'dcbabbdb', 'bacdabdc', 'dcabcdca', 'bdbdacca', 'cdddcbab', 'ddddccba', 'baddcbdc', 'bdacadcb', 'dbdacbac', 'cbcddcaa', 'cbabdacd', 'abcddbdd', 'cdbbaacd', 'ccabcadb', 'bbadadca', 'cacbdccd', 'ddacabdb', 'cabcdacd', 'dabbcddd', 'abdcacda', 'dcdcdbaa', 'cdcdbcab', 'bacacdbb', 'cddbcbac', 'dbbdbadc', 'bacadadc', 'abddbbac', 'cdcdaddb', 'cabadccb', 'cdbbcaca', 'dcdcbcda', 'adccbdad', 'babacbcd', 'bbadcabc', 'adcddcab', 'dcabacda', 'babacddc', 'ddbaccac', 'bbdbaacc', 'cbadabdd', 'cbddadcc', 'dccbddad', 'bdccbbca', 'dadbbdca', 'cbdabbdd', 'dddbcabb', 'dbcbcdaa', 'cadbdddd', 'acbdcdcc', 'baddcbcd', 'cabcadda', 'dbbabcbb', 'cbbcdcca', 'cdabdbcc', 'ddcdbcca', 'cabddbaa', 'dcbbdbad', 'cdabacad', 'baccdbbd', 'bddacdad', 'ddcbccad', 'bbaccbda', 'baddcdcd', 'ccbcbacd', 'cacadddb', 'bdcbadbb', 'ddcdadcb', 'adacbdac', 'ddcbaccd', 'dbdbdcab', 'bbcadbba', 'cdcbbabc', 'cdabdbac', 'adabddac', 'ddbddcad', 'adddcdba', 'bbacbcdc', 'cdcbbdaa', 'acdcbdda', 'adcdbcdb', 'dacadbdb', 'adbabcab', 'dbbaccbd', 'cacdacba', 'cdcabdad', 'cbddbaca', 'abbccdad', 'acdcbcdd', 'cdddcbda', 'bdbddadc', 'abdbcdab', 'abcdbdad', 'bbacdabb', 'cbaccdbb', 'acacdcbb', 'dccdcacb', 'bdabbcbc', 'bdbacadd', 'cacddbca', 'bcddcaaa', 'bdacddcb', 'dabdbcbb', 'bcbadbcc', 'dcabccdb', 'dabcddbb', 'abcdcdcd', 'bdddacad', 'dbadbcab', 'bbcbddba', 'cdacbcab', 'bdddcaac', 'dbdcadbb', 'ddabacac', 'dbacbdcd', 'ccbaadbc', 'ddcadaba', 'ccbddaca', 'acbcbdda', 'accdcaba', 'dbdddcaa', 'dadbccdc', 'addadabc', 'cbaddacd', 'badbccbd', 'bbabaddc', 'cbacbdba', 'addddcab', 'bdabaccb', 'cbdddabb', 'adbdabcb', 'ddacabba', 'bacacbdb', 'dabcdbca', 'bdcdcabd', 'abcbdcbd', 'bbacacdc', 'baabccbd', 'cbdbcadd', 'dbbdaccd', 'acdbaddc', 'dbadcbdc', 'cdbadccd', 'ccacdbda', 'cabcdddb', 'abbdadcd', 'ccadbacb', 'abbdadcb', 'dcbaaccd', 'daacdcbd', 'adcbdcdb', 'cbdadcdb', 'addcdbab', 'cbbadadd', 'dbbaccbb', 'cabcbdac', 'dbddaccb', 'cbadbcbc', 'ddabcdbc', 'dcacdbdd', 'cdadbbcb', 'abdacadd', 'bcdbabab', 'acddbada', 'badcbccd', 'adbdacca', 'ccbbdacc', 'cdababac', 'bcddacba', 'accbcddc', 'bdacdbbd', 'bccaccdb', 'dccabcba', 'cdbcdbad', 'adbdcadd', 'cbbdbdaa', 'dacbcbad', 'dddaacdb', 'adccbabb', 'abdcbbab', 'bcbdbcda', 'badabdac', 'ccdcdbad', 'adcbdcda', 'bdcabacb', 'acdabddc', 'adccbdcd', 'dabadbcd', 'dbbcdacb', 'bdcdcadb', 'bccaccbd', 'adabccad', 'ddcacbcd', 'dcdcadba', 'cbdbacad', 'dbbadcab', 'bccdacbb', 'caccdaba', 'cbdadbcd', 'bacbacbd', 'dabacdac', 'dbbaabbc', 'adabccac', 'adbcbbcb', 'adcdccbd', 'dadbddcb', 'bdcbdbac', 'dbbcacac', 'ccbadbdc', 'bccdaabd', 'acaccdbc', 'adbaccdb', 'dcbcbdab', 'dabadcbd', 'cdabbccb', 'cdddbcaa', 'bacadcbb', 'adbabbca', 'daacdcbb', 'acbcdada', 'bdcadcba', 'ddbdbacc', 'bdacadbd', 'ddaccacb', 'ddbcbcab', 'caacdcbd', 'acbccdbc', 'babbdcda', 'dcdabccb', 'bcbcdaac', 'abdbdcbc', 'dbabcdbb', 'cadbadba', 'ddcbcacd', 'abccadab', 'bacbbdda', 'bdbbaacc', 'adacacbd', 'cbadbbdc', 'dbadacdb', 'dbaabdcd', 'acbbcddc', 'caccbbda', 'bdbcbadc', 'cadddbdb', 'daddbaca', 'cdbdbdca', 'dbcbbadc', 'bcdababc', 'dbccacba', 'caddabbc', 'bacdcabb', 'bcbddcad', 'ddacbdbc', 'ccaddbdd', 'cbadbddd', 'acdaccbd', 'dcbacddd', 'cacadaba', 'addbcacc', 'bcadcdcd', 'cbbabcdc', 'adabacdc', 'cbbdbaac', 'acadccbb', 'cbdabacc', 'abcdbdac', 'cabddabd', 'caccadbd', 'bcdaacaa', 'adbcddbd', 'cabacadc', 'dacbdaca', 'bdaddcca', 'ddadcbda', 'cabcbadc', 'dbdccaad', 'bddabaac', 'bcdabacb', 'dbcbaadc', 'bdababbc', 'bdaccdbd', 'cdddddba', 'abdbbddc', 'cdccdcba', 'dcbcbdda', 'cdbdbdad', 'bcbadacd', 'cdbdbabb', 'abcdccad', 'ddabaddc', 'bdddbacc', 'cbacadcc', 'cdcdcaba', 'cdaddbcb', 'ccddabcc', 'dadacbba', 'abcbbdba', 'ddacbbdc', 'ccadadcb', 'accbdabb', 'bddaddbc', 'adcbabac', 'abdccadb', 'bacbacdc', 'dccbcadd', 'dbccddba', 'addcdabd', 'cdbbdada', 'ccadadbb', 'bccdddac', 'bbcbbdac', 'cadcabcc', 'accabdbc', 'dbbccbaa', 'caccbdba', 'bbadbdcd', 'dcbcabca', 'cdbdbadb', 'cdccbacd', 'addbacdb', 'dcdadcab', 'dbadbbcc', 'dbccbaca', 'bdcddaac', 'baccadba', 'dbaccbda', 'adadbacd', 'abcbcbdc', 'abacddab', 'bccbdcac', 'dadbdacc', 'bbcdaacb', 'dddcdbda', 'aadccdbb', 'dcddaccb', 'acbdadca', 'cbbadaca', 'baccdbda', 'dbabcacd', 'abdccdba', 'acdccbba', 'cbccdbad', 'dabbabcd', 'cbddacbd', 'cdbaddbc', 'ccadddbb', 'dcbaacdb', 'cddcbbca', 'bccbacdc', 'bccadadb', 'cbdbdacc', 'ddacbadc', 'badadcca', 'dcacabbc', 'dddbccba', 'dacabdda', 'dabdcabb', 'abcdbbcb', 'dcbadddc', 'babacddb', 'abaddbcc', 'abdcbbda', 'dbcaccac', 'adabdccb', 'bcdbbabd', 'dcadbabc', 'dcbabbac', 'dcaabcdc', 'babcbdcb', 'cacbddbb', 'bacdacdd', 'acdbabca', 'adacdbdc', 'cdbccdca', 'adddbdcd', 'adcabcda', 'dcabcadc', 'abbccdcd', 'bccdacdb', 'bbcdcada', 'dcabadbb', 'dddcabca', 'dacbdbcc', 'ccabdcac', 'cbabcddb', 'dadbadcd', 'ccbbacdb', 'cdddbacb', 'cdaacbcd', 'cbbadabd', 'baabdcbb', 'dacaddcb', 'ccbcdadb', 'accdddbc', 'dddacbcd', 'adcdabcb', 'dadacdbd', 'bccabbad', 'acddddbd', 'addccbda', 'caddcbac', 'bbaddcbb', 'acbcacda', 'acbbabdd', 'cbdacdcd', 'dbccbcda', 'ddcdaabc', 'ddbaccdd', 'abbcddab', 'cdcbcdad', 'cdccacbd', 'dbacddbc', 'adbcbadb', 'bcbacbda', 'dbdabacc', 'cddcddba', 'aacbcaad', 'bbaddddc', 'dcdaabbd', 'bdcbdcad', 'badacdca', 'cdbbcadc', 'dbbabccb', 'dddbacad', 'ccdcabba', 'dcdbcbab', 'bacdcacc', 'ccdbaacb', 'dbcbaacc', 'acbbdbda', 'cdbaddcb', 'adbcddba', 'adbcbcab', 'dcacdcab', 'bccacdca', 'bbcadcbd', 'cadacabc', 'dcacdbdb', 'ccbdaddb', 'cadbacbb', 'dbcdadad', 'caddabaa', 'dcdbabcb', 'bdccacca', 'bbddcbad', 'accdabbc', 'bbdbbdca', 'dcbbdaad', 'dbadddbc', 'adcddbac', 'daddcbbc', 'bbabdbcc', 'bddaacab', 'bbaccabd', 'badcabba', 'abdddbcd', 'abbdaccb', 'cdcacabd', 'acdbcbca', 'dbcaacbd', 'dbdadcdd', 'adacbcbc', 'acddcdab', 'ccbdaddc', 'ddbdaddc', 'cdadcdbd', 'bacdccdc', 'adaddbca', 'ddabacab', 'cbacbbdd', 'bcdbaddb', 'cbadcbbd', 'dacddddb', 'dcabdbbc', 'dbcdacdb', 'bacdbadd', 'dcaddacb', 'baccadbb', 'ddbdcdab', 'bacdccbd', 'dbbdbcad', 'bdbabcdc', 'acddbadd', 'bdcbbabb', 'dddbcaca', 'abacbadd', 'acddcbbd', 'ccabccdc', 'abbdbcba', 'adbdbccd', 'ccadbdbd', 'cacdbadb', 'cbbddadc', 'cbbadbbc', 'ddcdbaaa', 'adbccada', 'abacddba', 'bcadcadc', 'cbadbbda', 'dccadbcc', 'dadbdabc', 'cdcdacbc', 'bbddbcac', 'dddabddc', 'dbbabcdc', 'daabdaac', 'abccdacd', 'bcdabbcc', 'dbbcbdaa', 'ddacbddd', 'cbbcbdda', 'bacdcdac', 'dbadcdac', 'ccaddabc', 'acbbacdb', 'dcdbacdb', 'badacadb', 'dabcbddc', 'bddabdcd', 'dbbadbac', 'dabccadd', 'cbcbbaad', 'dbbdaadc', 'dbddcaac', 'cdacbcbd', 'cbcdcdac', 'bdacbdda', 'cbdabbcc', 'babcdcda', 'accbdbab', 'adcbabbd', 'ddbacaaa', 'acbddcbd', 'abaccddb', 'ccdcaddb', 'cabdddbd', 'cbddaddc', 'cdadbcbb', 'bcadabac', 'addcdbcc', 'dcbccbac', 'cacbdcad', 'adbdabbc', 'cacaccdb', 'cabbddbc', 'cacbbcdd', 'abdccdbd', 'cabdbcbb', 'dbcdaaaa', 'cadccbca', 'dcddabcd', 'cdacbdcc', 'cabcaddd', 'bcabadcc', 'accbbcda', 'acdccbca', 'cacdadbd', 'acddccdb', 'bdcdbdaa', 'dbcbabba', 'dadbcbdb', 'bcdccaac', 'dbbcbbca', 'cbaddddd', 'ddacabda', 'dbcdddda', 'bacbcacd', 'ccdbddba', 'dbadadcc', 'bddbcaad', 'bbdbdadc', 'dbcacbab', 'ddaacbac', 'baddcdac', 'dacadcbc', 'caaaabdb', 'bcbdbaab', 'dcbadbcc', 'bcddacab', 'cddbbdab', 'ddbaabdc', 'bacdddbd', 'dabcabad', 'dddcbaab', 'cacbadab', 'acdbcacd', 'dcbcadcd', 'bbdcabba', 'bcdcdcab', 'cbadbbcd', 'dbcbdcaa', 'cabdcdcd', 'adaddacb', 'cdabcaca', 'babbdcad', 'baddccdd', 'cbadabba', 'cdbcdabb', 'dccdbdad', 'dbaccbdb', 'bcdbdaba', 'cdaabaad', 'ababddcc', 'dbabadac', 'dcbdbbca', 'bddabbac', 'ddbacabc', 'baacdccb', 'dcbbcbda', 'bccbccda', 'cabcddda', 'adcbaccd', 'bccbbadd', 'bcbadcdc', 'dcdcbdaa', 'addbcdbd', 'ccdcaadb', 'ccabdbba', 'dbcabdda', 'cbbdbabc', 'bddaacbc', 'cdadbcac', 'ccadcbbc', 'adcbdcdc', 'badccdcb', 'bbcbabdd', 'bdcdaabd', 'bcdbbaac', 'dddcbbac', 'ababddcd', 'ddbccdba', 'babcadda', 'dbbaccbc', 'bbcdbacb', 'dacbddda', 'ddaccabd', 'dcacbcdd', 'abbcdbcc', 'dcaabdbb', 'abdcabab', 'babdbcab', 'abccadba', 'dabbcdbb', 'bdccbabb', 'babdacbd', 'abbaddcb', 'bacacbad', 'cdddbdad', 'adbabcdc', 'bcbccbda', 'babbddcb', 'bbdacbcc', 'cdabdacb', 'bdbdacdd', 'daccbcdb', 'ccdcdabb', 'bddaaaac', 'bdbaddcd', 'dbdcabbd', 'cdcdbdab', 'dbdacdcd', 'dbacdada', 'abccdbcc', 'cadaddab', 'babcdacb', 'dbaccddd', 'cbadcbbc', 'bcbaddcd', 'cdbaaccd', 'bdbddabc', 'dcabcbcb', 'acdbacba', 'daccbbdd', 'acababdd', 'dadacdab', 'badbcdac', 'bddcadab', 'dbcaccbc', 'bdabcdba', 'abdcbddc', 'cacdbccd', 'cbdbcabb', 'dcdabdcc', 'dbdccbad', 'ccbbacdd', 'ccdbabda', 'adbddcbc', 'ddbaaddc', 'baccbdbd', 'abbacdda', 'bdccadbb', 'ccbadcda', 'dddcbbad', 'ddcdabcd', 'ccbdadad', 'dbacbddb', 'bcbbcdaa', 'cadbdacb', 'bdbcaabb', 'bcdcaddb', 'bbcbcbad', 'ddaacbab', 'bccdccda', 'dbdcacbd', 'dccdadbc', 'cdaabcdb', 'dddcdadb', 'cbadabdb', 'abccbdcd', 'ccdabdab', 'ddbcbacd', 'dbbabddc', 'dacdacab', 'dbcdbbac', 'ddbaacbb', 'daabccdc', 'cddcbacb', 'bcdaabdc', 'bbdccacc', 'acabbcdc', 'dcdbcaca', 'dacbdcca', 'dabcbbab', 'bbccaabd', 'dbacdacc', 'bcdcbdac', 'bdbcabcd', 'ddaacbcc', 'abdbcdba', 'accadcba', 'adabcddb', 'dadcddab', 'bbcbbacd', 'bdacddda', 'ccbdbada', 'bbacbdba', 'dcdadcdb', 'cbabcdad', 'dbbcbaba', 'cbbcdacc', 'bdddcaaa', 'cdcadacb', 'acbcdadc', 'abdacbad', 'cbddddba', 'cdaadbbc', 'bdacadba', 'bcdbbcad', 'acddbbdb', 'ccdbdbca', 'ddbcdcca', 'dbdbbcba', 'dabadaca', 'abdbaccd', 'dbbabadc', 'bdccaabb', 'badddabc', 'bcabadba', 'baddaccb', 'dbdacdab', 'cbdcdaad', 'ddccdabc', 'ddcabacd', 'caddbada', 'bcbdbada', 'ccaadbbd', 'aadaabbc', 'acadabda', 'dddaddbc', 'dcbacaba', 'aacaabbd', 'bdcbdacb', 'dcbdddac', 'acbacdcb', 'cddcaccb', 'cadcdbad', 'cddabbad', 'acdabddb', 'caabdccb', 'ddbcdacc', 'addbbcaa', 'dbdaccbd', 'cbadddac', 'bacdabdb', 'abdcbdcc', 'aabdcbbd', 'ccdcbbad', 'dcabadcb', 'cdcacbbd', 'bbabbdac', 'abbdcbad', 'dacbbaba', 'cbadccda', 'cabaddbd', 'abdcbdbd', 'cddbadbb', 'dabcdaca', 'cdcdbacc', 'cdcaccbc', 'dcaddaba', 'cddcbcad', 'bdaddaac', 'dacdbddd', 'bbadcacb', 'cdddcdab', 'ddbdcabd', 'cabddbcc', 'cddbcaad', 'dbadaccd', 'bdacabac', 'adcbddca', 'adbccdbb', 'bbcabbda', 'ccbbdcad', 'abcabadb', 'adbabcac', 'cbcadcbb', 'bacbabdc', 'bdddadbc', 'dbdddcad', 'abdbadca', 'bdcadddc', 'ccadacab', 'babddadc', 'cadacbdb', 'abdaddac', 'bbdcbacd', 'abdacada', 'acddcbab', 'acaddbdc', 'ddcadabd', 'dabcabac', 'cdbcbabd', 'cbcbadbb', 'dbabdcda', 'bacaccda', 'baddbcdc', 'dcdddacb', 'cdbaddbd', 'dabcddbc', 'bbdcbabc', 'adabcada', 'abdccbda', 'bddcdadb', 'cdbcdbba', 'bbabddcc', 'cdcbadab', 'cdbdcaab', 'adbababc', 'acdbcbda', 'dbcadacc', 'badcacca', 'cdacabdb', 'bcdabddd', 'bcdacabd', 'ddaabcbd', 'abccbabd', 'dacbdadd', 'bccbdadc', 'bbaadaac', 'adaccdbb', 'abbacddc', 'ddcdbcda', 'bddbbacb', 'adcbccab', 'adbcabbd', 'dbacacdd', 'dcabacad', 'cabcbbda', 'bbddcadd', 'cdcbcdda', 'bacbcdda', 'dabdcada', 'dbdcabdb', 'bbabacdc', 'bcdddadd', 'bacdddab', 'bcdddaaa', 'dcacabdb', 'ccacaddb', 'dbacbcdd', 'dabcdcbb', 'badddcca', 'dcdacbab', 'bbcddbaa', 'dcacbcba', 'bbccadbd', 'abddaaca', 'adddbaac', 'cdbcabca', 'dadbcada', 'bacbdbab', 'dbbabbcc', 'dbbcdbab', 'caddcbdd', 'daabccbd', 'ddbaadcc', 'dcbdbabd', 'bdcabdad', 'ccabdcad', 'bcddaddd', 'dcbaccdc', 'cdbaabcc', 'bacaddcb', 'dadddbcd', 'abdbbdbc', 'dbabdbcb', 'dcacbbad', 'ababaddc', 'dbadcdab', 'abdadcdc', 'cdabcbcc', 'dabcdddc', 'bcdcdabd', 'ccabadbd', 'dccdcabd', 'bcbdacda', 'abbcadbd', 'adacacbb', 'addabccb', 'cbabaddd', 'bbcacdbd', 'bdbacbcd', 'dbabcdca', 'acdadcdb', 'dcbcbadd', 'cbcddbba', 'bbadbdcc', 'acddcbbc', 'adadbcbd', 'cddbdcda', 'dabcacad', 'ddbbabcb', 'addcdbcd', 'dcdbabdd', 'dccbcacb', 'cababcbd', 'ddcdcbca', 'ddbacdac', 'badcbbcb', 'adadccbb', 'babbcdbd', 'cdcbccad', 'bcddadbd', 'abddddcc', 'caddddbb', 'ccbdddaa', 'abcadbcc', 'dbcddacc', 'acabbadd', 'addcabcb', 'cabacbbd', 'dbdcbacc', 'bacddcaa', 'bdcbcbda', 'accbcdba', 'ababddbc', 'bacabacd', 'dcbcddac', 'badbacad', 'ccbabcad', 'ddbcabac', 'abccdbda', 'ddbdacca', 'dccdabca', 'badbacdd', 'dcdcbcba', 'ddbcbbaa', 'bbadcbcd', 'cbccadac', 'acddbcba', 'dccabacd', 'bbaabdcc', 'bcdccabb', 'dcbbddca', 'dddbbaca', 'daccbacc', 'dabcdddb', 'dabddcda', 'abbcacbd', 'dbdcadcd', 'bcabaddb', 'aabdccdc', 'bcacdddd', 'ccdbaacd', 'ccdadbbc', 'acdbdcdb', 'bdcdadcb', 'bdadddcd', 'cbacadac', 'bcdddcaa', 'adcbbcad', 'adbccbba', 'acbdacca', 'ccdadabb', 'dbcdddba', 'abdabccd', 'ccbadacc', 'abcdadac', 'acadcbbd', 'bbadddcc', 'bcdbacac', 'daccabbc', 'acadcdba', 'bdddadcd', 'bcadcddd', 'cabaddba', 'dbdadacd', 'bacdbbdd', 'bdcbcdaa', 'caddacba', 'badcadbd', 'adadcbdb', 'ddbccaad', 'ccbccadc', 'cdbbcacc', 'bbcdcbaa', 'bddacdbd', 'acaddbaa', 'adbcbdbc', 'ddcdabdc', 'acbbcddb', 'bababdac', 'bcabcddd', 'ccacbbad', 'bdacbddc', 'bcdaabbc', 'cbdbbcad', 'badbacba', 'ddbacaba', 'abccbdca', 'bccbcadb', 'bbaccadc', 'acabdcdc', 'cddaaacb', 'bbcdcabd', 'bddccdca', 'cbdccdba', 'bccbbdac', 'abdbbabc', 'adddcbdd', 'bbcbbadd', 'daadbcbb', 'bdbacdcb', 'bcbdabbc', 'abadcabb', 'bcdaabcb', 'abddacbc', 'bcadacca', 'dadbbcca', 'ccdabacd', 'dccabdac', 'ccdcadba', 'dacadbca', 'adbbadca', 'accbaddd', 'dabdbcda', 'caccabdd', 'ccbcddac', 'bcaddcad', 'dabcbacc', 'ddcbcaca', 'aadcbcbb', 'dbccdcca', 'cbcadbdd', 'cabdbbdc', 'abcdbadc', 'bbcaabcd', 'bdcbdaba', 'dcdcabdd', 'adcadabb', 'adaddbcb', 'baaccbdc', 'ccabcdba', 'abcbcada', 'cbdbdadb', 'adbcdcdb', 'abcbddcb', 'cdabddac', 'dcddcaba', 'ddbdddca', 'bcbdbacd', 'cbadddbc', 'ccbdadcc', 'dcaccbab', 'babcabdb', 'cddcdcba', 'bbcadacc', 'bcbbcdda', 'adbccadc', 'bdcadadd', 'abddcbdd', 'acdccbcd', 'dbbacdac', 'dcbcdaac', 'babdcada', 'bcaddcac', 'dcabcacb', 'accbbddd', 'caabdcbc', 'accadcbb', 'bddadbcc', 'ddabcaad', 'accbddcd', 'accddbcc', 'ddbaacdc', 'dcaaaabb', 'dacabbcb', 'cbddabac', 'aadbdbcc', 'bcbcabbd', 'ccabbacd', 'cdbaddcc', 'cbdcabda', 'bacddaaa', 'abcddcba', 'ccdbacbb', 'abbdcbdc', 'addbcada', 'adcadabc', 'dcbdbbad', 'bddabcdd', 'dbaddcda', 'bbddacbb', 'cbcababd', 'ddbabdcb', 'ddacddbd', 'bbacaddd', 'bdabcabd', 'cacabadd', 'dccdbacb', 'dbcdbcab', 'ccdbddac', 'dbddcbac', 'dcbdbbac', 'bacdbabc', 'ddcdbdab', 'abcacddb', 'badccadd', 'acbabcdc', 'dbdbddca', 'acabdbab', 'dacadbad', 'bdaaccdb', 'ddccbaba', 'dbaadcbc', 'bcbdabcb', 'adccbddd', 'cacbaddd', 'cdadbdad', 'dabacbbc', 'abccdacb', 'addbdcab', 'bcbcacdb', 'cdbbadac', 'abcbbddc', 'bbdbccaa', 'acbbadcd', 'dbcdcaab', 'cbabcbcd', 'cbaabccd', 'cadddbda', 'bacabdbc', 'cbdddaaa', 'dbdbcabd', 'bbdbaccd', 'bacadcda', 'dcdcdaba', 'adacddcb', 'cdbdacda', 'dabdabcd', 'caddbccd', 'ccbacbcd', 'bcbabcdb', 'bdccbaad', 'babdcbca', 'cbdcbdca', 'accacdcb', 'bcdbbada', 'acddccbc', 'dbabcbdb', 'babdccdd', 'acabbddc', 'aadcaadb', 'caccbccd', 'dddcbaba', 'dbcdabdc', 'ccbddadd', 'dadcdbca', 'acbacbdc', 'ccdaaccb', 'caddbacc', 'ddcbdaaa', 'bcbacdda', 'babcbbdc', 'cdbbcada', 'accbbdbd', 'dadbdacb', 'addaddbc', 'ddcdadba', 'bcdaadbb', 'bdcabadd', 'caccbdca', 'cddabdac', 'ddbdbacd', 'ddccdabb', 'ddbddcca', 'adabbcdd', 'cabbdbbd', 'cabbdbab', 'abdccdad', 'bcdcdcca', 'cbbddbad', 'badadcbc', 'cbdaabcc', 'bbadadcd', 'bdbaabbc', 'cdabacda', 'dbcdcdac', 'bbdcdcca', 'aabcdaac', 'bcddabaa', 'abbdcbcb', 'dcdbbcab', 'ddcbbadc', 'dababcbc', 'dacbddbb', 'accdbcca', 'ccdbdada', 'cbadccba', 'bcabdbac', 'bcaddbcd', 'acaccbbd', 'dbdabdac', 'dcbaabaa', 'babcadca', 'bbcaddad', 'bddadcdc', 'dabcbacd', 'bcdacdba', 'adcbdabd', 'caddacbc', 'cbcdcbac', 'acdcabdc', 'bbcbdaab', 'bdbcbabb', 'adbdcbac', 'bbccaadc', 'ddacbcbd', 'bddbcbab', 'ccacbdab', 'dcddbacd', 'badbbcba', 'bdcdacbb', 'bccbddac', 'dccaacbd', 'bdbdbaac', 'ccddbaaa', 'abbdbadc', 'acaddbcd', 'cdadcdba', 'acdcbdac', 'abbadcab', 'abbaddca', 'bddcaddb', 'bacdadda', 'cdabcdba', 'abaddacc', 'cbbdadba', 'abdaccdc', 'ddacaaab', 'addacbcb', 'bcdcdbda', 'acbdddcc', 'acddbdda', 'bacddaca', 'cabacdda', 'baccdcda', 'dbccdadd', 'cbbdacda', 'bddbacdb', 'ddbccadd', 'babcdcdb', 'badbdccd', 'ddcdccba', 'adcbcabc', 'babcbddc', 'ddbaaccb', 'cbbadcdd', 'abccdabc', 'dbdbacdd', 'cacdacbd', 'cadbcacd', 'dbcaadbc', 'caadbbdb', 'ddcbcdca', 'adbbdbcb', 'accdbdcc', 'bcbbcabd', 'dbbdadbc', 'ddbbdadc', 'dabcdcca', 'ccdacbac', 'ccadddcb', 'dcadcdba', 'bccbaadc', 'ddabcdcb', 'adcdaccb', 'babddcdd', 'bddaabbc', 'bcabcdca', 'adccdbdb', 'ccbdadab', 'dbabddbc', 'cdccdaba', 'ddbabbcd', 'ddcbadbc', 'dbadcbdd', 'adbcdcbb', 'ccbdccba', 'cbbadddd', 'dbcbdaba', 'aadcaabb', 'cacdabcd', 'abacdcba', 'adcdddbc', 'abddbacd', 'dacbaddd', 'dabbccbb', 'dddbcabd', 'acabdbad', 'cacbcdad', 'dcdbbaab', 'adbaccba', 'dcaccabd', 'ddcdbbca', 'dcacbbdb', 'dddbadcd', 'acdadbcb', 'babcdbca', 'cbbcddac', 'daddcbbd', 'ddcadabc', 'acbccada', 'ddcbadab', 'bcdbcabc', 'bccbccad', 'bdbcbacb', 'adbcaccd', 'dbbdabca', 'dbbdbdca', 'addacdab', 'dacdbcda', 'cddbadad', 'cbcdcdca', 'dcddaadb', 'ddbcacca', 'acbcbddd', 'bbabcddc', 'dddadbcd', 'ddcacdba', 'daacdbdc', 'cdbacbbc', 'dacabbac', 'adbbcbdc', 'bdcbbabc', 'dbaccbad', 'dacdddbb', 'dbbdcbba', 'cacbadda', 'cbccbadc', 'accddbab', 'dddbabbc', 'cabcbbdd', 'abdaddcc', 'abddccda', 'dadccdcb', 'ddaacbcd', 'dcdbcaad', 'cbdacdbc', 'badcbddb', 'cadccdbd', 'bdadbacc', 'dbabcdba', 'cddaacdb', 'bcbcbadd', 'baddaacc', 'dbacbbab', 'ddbcdacb', 'dbacdddb', 'adbbcadb', 'cdccdabc', 'abdbcddd', 'adddbbcb', 'adaddcbb', 'cabcdbbc', 'dbdacbdb', 'dbbacbdb', 'dacbabbd', 'dbdbbacd', 'dadacabb', 'dcaacdbd', 'badddaac', 'adcdcbac', 'cbbabddc', 'dddcbaaa', 'abcabdbb', 'cdcbadbb', 'babdcadc', 'acacdddb', 'cddaabdd', 'bcbbddca', 'bdadccad', 'acadcdbd', 'bdcbdabb', 'abcacbbd', 'adccdcbb', 'bdbadcba', 'dbcdbadb', 'addccdbd', 'baabaadc', 'bdbcbdaa', 'cacbccdd', 'cddacaab', 'cddacdbd', 'ddbbcacc', 'dcdddbad', 'ddbcacad', 'cdbacdbd', 'bdcacadb', 'dcdbbcac', 'adbcbdac', 'bcdacbbd', 'dcdbbacd', 'ccadcbdd', 'badaccba', 'ddcadbcd', 'dadcbacb', 'babbadbc', 'cbacdaca', 'acbdacda', 'bbcaabdb', 'dcaddbab', 'bddbbdca', 'ddcadcbb', 'acbdabcc', 'ccbacbda', 'badacbdb', 'dababcdd', 'bbcdcacc', 'cbcdabdd', 'abcdbcdb', 'adbacadd', 'bcdcbaca', 'ddcbbcab', 'adbcadbc', 'abbabddc', 'baddddcc', 'bcadbbca', 'dbdcddad', 'badddcad', 'abacdbab', 'babdcacd', 'dabddcab', 'bdcdabdb', 'dabccdcb', 'dbbaccdd', 'bdaccddc', 'bdbdaccb', 'cdddbcac', 'dcbabbcb', 'dcabdabc', 'acdacdbc', 'bdbbaabc', 'bbccbbad', 'ccabadcd', 'cabcbdad', 'abcdcdcc', 'adbdbcbb', 'bdcdacbd', 'aacdbdcb', 'cdaccbdc', 'dbcbddad', 'bddcdaad', 'dacddccb', 'dccbbada', 'cadbcdab', 'cbdbddad', 'bcbbcadb', 'adcadbad', 'bdabcbcb', 'addcaddb', 'dcadbdab', 'addacddb', 'abdadccb', 'bbadbdca', 'ddbdcadc', 'ccdbcdab', 'bcbdddda', 'badbaddc', 'adbccabd', 'acabcada', 'bcbbadcb', 'bbabdadc', 'cdcdbcba', 'ddddacba', 'badddbcb', 'adbcbdad', 'bccadcdc', 'abcbadcd', 'cadadbba', 'acbadcbd', 'bcbdccab', 'dacbacdd', 'dbabdcbc', 'cdcbacca', 'adcdddbb', 'cdabcabc', 'acdbabab', 'dadcdacb', 'badccbcb', 'acacbdcd', 'adadccab', 'cdadbadb', 'cdadbbad', 'adddcbba', 'cbddaacc', 'bacabddd', 'bdacdada', 'ddbddaca', 'bbadbbdc', 'dbcacdcb', 'bacdadbd', 'cbdbdaad', 'cbbcadbc', 'dabacbad', 'bdcaacdc', 'ddcbdcaa', 'acdcbbab', 'dabdccdb', 'addcabdd', 'daccdbad', 'bddcabbd', 'dcacdbcb', 'dabdbcab', 'cababbdb', 'bcbdccac', 'cdadcadb', 'dcdabbcd', 'addabacc', 'dbddcabb', 'dbdaddca', 'baddacbc', 'cddadaab', 'cabbdbdc', 'ddbcabbd', 'dcbcabcc', 'ddadbcbb', 'dbcabbda', 'bccbdcba', 'bdcddadc', 'caccdbca', 'bdcaaaab', 'cbcdddba', 'acddabcc', 'abcacadd', 'bdaccacb', 'bdcadbca', 'bccaccdc', 'dcbcdbab', 'caabdcdc', 'abcdbbca', 'acbdcdca', 'dabdbdcc', 'dddacaab', 'cbcadaba', 'ddabccda', 'bdbbaccd', 'bbacdadb', 'cacadbdb', 'abdcbbad', 'dcbacacc', 'cabddadc', 'adadbbac', 'bbddaacc', 'cbdabacb', 'addccddb', 'abddbdca', 'abddcbbc', 'dcbdcdba', 'cddbaacd', 'cabddbdd', 'badcbaca', 'babaccda', 'dacadabb', 'babdbbca', 'adbcdbdc', 'acbbdbad', 'dcaabbaa', 'ddabdcca', 'cddabdad', 'bdadcbcb', 'abdcbdbb', 'abdbdddc', 'bccabdca', 'ccacbdbd', 'bcdadbbd', 'bbcabddd', 'bcdcabdc', 'cadcbabc', 'dbcaddcd', 'abbdcbdb', 'cbcbddda', 'bcaddbad', 'dbccbdab', 'dabcdbda', 'cacbcbbd', 'cbbabdbb', 'acbbdcdd', 'cdcbaabd', 'abddcdaa', 'dabcdcac', 'cbdbadbc', 'bdbbcbab', 'dabbccac', 'bdccbaab', 'ddbcbabc', 'ccbdadca', 'cababdbb', 'bddcbcad', 'bdbdcaad', 'cddabacb', 'dadbccdb', 'adaccbdd', 'cadbdada', 'dcdacbdb', 'bcdcdacb', 'dcbcddca', 'abbabdac', 'dcbddbda', 'dccbccba', 'abadbabc', 'adcdbddd', 'bdcdabad', 'ddabadcb', 'cbdbaccd', 'bbdbddca', 'cbbabcad', 'cacdcdab', 'adacbdad', 'ccadadba', 'cabdbabb', 'bdabbacc', 'accdcbba', 'bccdbbad', 'cacabada', 'abcbcbdb', 'bdcadcdc', 'cbbcdcda', 'cbdcbacc', 'acadcacb', 'badaccda', 'ddabadcd', 'ddcbaada', 'cbbcadbb', 'daaaadcb', 'dcadcbca', 'abcdcabc', 'dbddccba', 'cbdbbaab', 'bdabdbcd', 'dacdacba', 'baabdcdc', 'cdaddcbb', 'bddaacdc', 'cacdcbdb', 'bcbdbabc', 'cbcbddca', 'ddbadcad', 'bddaacba', 'baddcaad', 'adadcbcb', 'bcdbbcba', 'bcbbdbaa', 'addacbad', 'ccabdbcb', 'badcbcdb', 'cbdcbbca', 'dddbcadb', 'bacabddb', 'bacbaccd', 'ddadcbbc', 'bdddbadc', 'bdbcabdd', 'abaccdad', 'bcdaabcd', 'ddccabaa', 'dadacdbc', 'ddabcbab', 'dbadcadb', 'aadbcbdb', 'cdaabbcd', 'ccacdaba', 'bbcbdbba', 'abdcbdad', 'ccddacbb', 'dcabbdad', 'bcdabdba', 'bcdcdcaa', 'cacdcbbd', 'abddcaaa', 'bcabbdcc', 'dccaabbc', 'ccbadcbc', 'dcbdabca', 'bbabcbdd', 'bacbbadc', 'bacddddc', 'dbbdcdaa', 'babddcbc', 'ddbcabdd', 'bcbaddab', 'dddcacdb', 'adaccbcc', 'dbadbddc', 'bcabaddd', 'adbdabca', 'cacbddcb', 'cbbacadd', 'ddabcbda', 'aacbccdc', 'adbcacab', 'dcacabcc', 'abcdddca', 'dcabbcdb', 'abdaccba', 'cacbbacd', 'dcdaadcb', 'acdcddcb', 'cbacbbcd', 'abcbdcdc', 'dadbbdbc', 'dbccaddb', 'cdacabab', 'dcacaddb', 'cdcbcaac', 'bcaddcaa', 'badacdab', 'cdbcbcba', 'dcacdbbc', 'dcadcabc', 'bdcddadb', 'dcbbabdc', 'acbbcdab', 'dbdbaabc', 'acbadddb', 'dbdbcacc', 'dbacddad', 'accdbbcd', 'acbabdcc', 'bcaddddc', 'bdabdacb', 'cabdbbca', 'cbdbaacb', 'dcabacca', 'bbcadbbd', 'acabbcda', 'bbdbbadc', 'aaaabcdb', 'dbdccacb', 'ccadbacd', 'dccdacbd', 'bacbdcdb', 'cbdbcaad', 'cddcbaca', 'bcaccbdb', 'ccdabadb', 'bdbccdda', 'ddabbdcb', 'dbaaaacd', 'addddcbd', 'badcdbcc', 'bdcabcad', 'acbcdcdb', 'adadcdab', 'ccbdbcaa', 'abaddcdb', 'bccdcacc', 'bcbabdbc', 'ccbbadbc', 'daddbccb', 'cdddcaab', 'addbbaac', 'badbdaca', 'abcabdcd', 'bcdaddcd', 'bdcbcbca', 'cdabcadb', 'cdbacacb', 'accbddda', 'cdbdbaca', 'bbadbcdc', 'adaccddb', 'badccdbb', 'daccdbdd', 'bdcbdaac', 'dbbacacc', 'dacdccbb', 'dbabbcdd', 'cabdddab', 'ccbcadab', 'cbacdcac', 'cbbdcdac', 'bdccabdc', 'cdcadcbd', 'bbddaaac', 'bdabddca', 'caadaacb', 'acbddbdd', 'babccdac', 'cdcbcaad', 'cabddcdc', 'cabdcdbc', 'cbcacbcd', 'cbcdbdac', 'cbabdcca', 'dbccacdc', 'bbcaccdd', 'cdccabdb', 'bddaadcc', 'cddacadb', 'abccadad', 'cbcdcaba', 'cbacbadd', 'ddcddbab', 'dababcdc', 'abccaddc', 'ccdbddaa', 'dbdcdacd', 'ddaddcbd', 'dccabbdc', 'dccabadb', 'adcabcad', 'cbcbbadd', 'dbabcdad', 'bacaddcd', 'daddadcb', 'abcddacd', 'acadddbd', 'dcaabdaa', 'dbddbcad', 'cbadcdba', 'abadbddc', 'adbcbbda', 'cbdcbdab', 'cabdadda', 'abadccdb', 'cadbdcad', 'cbbdabdc', 'acdbabbd', 'cbbcbbda', 'ddadcbca', 'dccacabd', 'adbcadab', 'cbdaadbb', 'addbcacd', 'dadcadab', 'acdbbcda', 'ddabcbaa', 'bacdbacd', 'caadcdbd', 'baddacaa', 'dbcbaadb', 'bdcaddaa', 'dbccadbd', 'baddabac', 'acdddbcb', 'ccbdabab', 'cbccaddb', 'acacddbc', 'dbbcbcba', 'abdaccab', 'abcbdabc', 'cbccdabc', 'dbcadbbd', 'cbcdcdda', 'ccbdbadc', 'dccbbaac', 'bbdcdcda', 'ddadcadb', 'baabccdb', 'cbcddcab', 'babddbca', 'cbdabdab', 'bdbaccbb', 'bbdabcad', 'bcdbcada', 'ccdadbab', 'dcbbacad', 'acabcbdb', 'dddbdbac', 'dbdcadab', 'daaccbaa', 'badadddc', 'bdcbdacd', 'acbcddcb', 'bdbbabbc', 'dbcdabcc', 'cabadcad', 'abcddaaa', 'cbdcbaab', 'cababddc', 'aadbbcdb', 'bdbacdbd', 'acdddabd', 'abbabcdd', 'cdbcdada', 'abdccdcc', 'dabdcadc', 'dcbacbac', 'abdcbcac', 'abddbacc', 'cadbbdbc', 'bcdbcaac', 'ddacbcbc', 'adbddacd', 'dadbbcab', 'dddbbacd', 'cbabbdad', 'dbccacdd', 'acadccdb', 'bddcbbda', 'acbcddcd', 'baacbbdb', 'cbcddacc', 'dbdaccdb', 'cdabdcbb', 'bbacddda', 'dcdabcab', 'cddabbac', 'bcdabbca', 'bcbcabcd', 'cbdacbac', 'babcbcda', 'bbdbdcca', 'ddbaacad', 'bdccadbc', 'dbcddacb', 'bbccbaad', 'bdddbcad', 'cabacdbc', 'dddaaccb', 'caddbcac', 'bdddacca', 'bacdbcdc', 'acdccbcb', 'abbdbaca', 'bddbdcba', 'cadbcdac', 'ddbccbda', 'bbccdaab', 'dacbdddc', 'bbdacdcd', 'dacdabdd', 'abbadccb', 'baabdbcb', 'abcbdddc', 'ccbaddda', 'adcababd', 'bddcbaca', 'caccbddd', 'ccbadbca', 'cdacdabc', 'cdbdddca', 'bccacbdb', 'bdbcbbca', 'bddacbad', 'bddccaca', 'bcdbbaad', 'cdabdcbc', 'dbabbacb', 'acdadbcd', 'cbdbbacd', 'ddbacbcd', 'bdabcbdb', 'cddbcdad', 'acbdadcb', 'cbabdabc', 'cdcdcabc', 'dacbbada', 'adddccbd', 'cdcbdaba', 'cdbdabcd', 'dbcaddbc', 'ddccbadd', 'adccbdda', 'bcdaccda', 'ddabdacc', 'dcddddab', 'ccaacbbd', 'cbacdcca', 'bddaddcb', 'adbadbcc', 'bdbcddba', 'abcdbcdc', 'bddcacdd', 'bbccabcd', 'cdcaccbb', 'ddaacdbd', 'dcacbacc', 'aacaabdc', 'aacdcbbd', 'ddaddcba', 'ddbdacac', 'cbacddab', 'cdcbacbd', 'ddccdbac', 'abddabbc', 'bccbadbb', 'addccbcc', 'bddacbac', 'cdbabccb', 'dbbadcbb', 'bcddaabb', 'dcdabdcd', 'adcbacba', 'bcbdccba', 'bdbcaadc', 'cdabbaba', 'ddbacabb', 'cdaacbbd', 'dbdaacbc', 'dbaccdcc', 'dcaccacb', 'bbabcabd', 'abbcdcdd', 'dcddadba', 'aacbbdbb', 'cdabdcca', 'cadacabb', 'cbadccab', 'bdcdbcda', 'adcabacd', 'cbdbabcc', 'cabcbdda', 'adabcbcc', 'cabcdccd', 'adacabab', 'cadadbca', 'cdcbddab', 'dadcaddb', 'dcabbdbb', 'adbacbcb', 'ccdccaab', 'dcacbabc', 'dccbadbb', 'dddbcdac', 'bcadbdbc', 'accabbcd', 'ddbabddc', 'cdabbacb', 'ccadbcab', 'cdbdaadb', 'addacbbd', 'dacbddbc', 'dbacbcbb', 'acadcdbc', 'bdbacdba', 'aabcdcdc', 'ddcaaacb', 'acbdacbb', 'dcbadbdb', 'cdbabcac', 'abbabcdc', 'bdacbbdc', 'abadbcad', 'adccbadd', 'adcabadb', 'cadbbabb', 'acbabcdb', 'cdabdada', 'dbbccadc', 'bbdadcdc', 'abdcdaca', 'cabdbddc', 'dbbdcdad', 'ddaacabb', 'bcbbddaa', 'abadcdbb', 'acdbddba', 'adbbacad', 'cabacdac', 'cbdbcbba', 'cdccadba', 'adccdabb', 'dbccbacb', 'bcdcbcad', 'dadacadb', 'bdbadcca', 'dcdbdacd', 'dcacbabd', 'bdacaddb', 'aacbcbbd', 'dbdcddac', 'bcaacbcd', 'adbdcdab', 'bddbddac', 'dbcdaccd', 'dcadcdab', 'ddcdabbc', 'cbaddcdb', 'ccbacdbb', 'cdacbcbb', 'cbbddcca', 'aabcaadc', 'bbacdacd', 'accdadbd', 'acdbadbc', 'cabdcdca', 'adbbacac', 'bacbdddb', 'dcddcabd', 'dcbcabdb', 'bdbcbdac', 'acdcdabc', 'abcdbbda', 'adddccba', 'daccbbca', 'cbdbddac', 'ccbcddda', 'adcbabbc', 'bdbaacbb', 'bccddcba', 'adbcdddc', 'aadbdaac', 'cdaccdba', 'dbbcaabd', 'abcdcada', 'ddcaabbd', 'dacbccda', 'cbdcbdaa', 'dacbacbd', 'cdddbaba', 'dadddbcb', 'babdacba', 'acbbdcdb', 'dcbbcdac', 'bbcababd', 'dbadcbbc', 'dcbaddca', 'bccbdcda', 'baccdbdb', 'cbcdacba', 'bdcbadda', 'cdadcdbb', 'cdddadbd', 'ddbbdacb', 'dbdcdaca', 'addcdbac', 'dbddcbca', 'adbcbbdb', 'abcbdbdb', 'dccbabbc', 'aadbbdcb', 'dbcbbacd', 'dbaacaac', 'bbaacbcd', 'bcddaadd', 'dbcaacaa', 'ddcdbabc', 'ccacabcd', 'cdbcaabd', 'cbcaccdc', 'caaaacdb', 'dacdcabb', 'adbacabc', 'dbacadba', 'dadadbcc', 'dacbadba', 'caadcbbd', 'cddbacdb', 'dbaddcbc', 'dbacabdc', 'dddbacdc', 'ddccbbca', 'cdbbcdca', 'cabcdabb', 'aacbaadb', 'ddabacdb', 'adccdbcc', 'bbcdbaad', 'ddabdccb', 'dddccadb', 'ddaacbdb', 'abddacca', 'acdabccb', 'dcadbabb', 'cadababd', 'cacdbbca', 'dccaadbc', 'dadbcadc', 'ccdbbaca', 'dabccbcd', 'abdbbcba', 'bbadbadc', 'bbadcbab', 'adbdbccb', 'cadbdcab', 'caddbdbc', 'dcdabddb', 'cdcbdaab', 'dddacbba', 'dababdcb', 'cabacbad', 'cddbccba', 'bdccacac', 'bdbcbabd', 'cdcabdbc', 'abcbbabd', 'adbccbca', 'caabbdaa', 'ccdbccad', 'ddcababa', 'bcbdbaba', 'cadcbcab', 'cdccbcab', 'bcabccdc', 'ddddbabc', 'adbbdbbc', 'bbcabadc', 'abdbacca', 'dbdcbaca', 'dbacadcb', 'ccbaccad', 'daccbbcc', 'bdabbaca', 'bdadbbca', 'bdbbacbc', 'acbddbad', 'dbbaabcc', 'dcddabbd', 'adbddcab', 'cbbccacd', 'cacabdcb', 'cbdccbab', 'cddbbabd', 'ccdccdba', 'bdcddcad', 'cadbbcad', 'badcddab', 'dbcabcbb', 'bcacadbb', 'acadabab', 'dadadcdb', 'bdbbacbd', 'acadbddc', 'bcadcdcb', 'dcadbccb', 'bcdbcdba', 'abdaddcd', 'dcbadbba', 'dcdbbabb', 'dbacbcca', 'adbcddcc', 'bacdbbca', 'bdcaddca', 'cdbacbad', 'ddcdbdba', 'cdccbdba', 'bbcabdbb', 'bbaccbdc', 'dddbbcab', 'bacdcbad', 'cdabbcdc', 'bcdcadda', 'cbcdcdab', 'ccbdabcb', 'bdabdadc', 'bcacdcad', 'accdacdb', 'bcacaddc', 'cbccacad', 'dadbabca', 'adacbbca', 'cbbdadac', 'aabcaacd', 'bdbbdcab', 'cdcbccac', 'abbcaddc', 'bdbadddc', 'babdbdac', 'bddbdacd', 'cacadabd', 'bcbcddba', 'addcbacb', 'cbadcadd', 'cbcacddc', 'adcbbcda', 'bdcdbcaa', 'bcbbcdad', 'cbaccbda', 'cadbccbd', 'caacbdbc', 'bddbcdaa', 'addcadcb', 'acbadbda', 'babdcbda', 'bcabdacb', 'cbdcbdad', 'dcddabbc', 'cdadbdcd', 'bbddcdad', 'cbdabddd', 'acbadadb', 'bccaddcb', 'bdabcdac', 'dcbdcadb', 'ddccaaab', 'ddcbcaad', 'cbadacad', 'cbdbbacc', 'accabbad', 'cddacdab', 'bcbacbdd', 'dbcacabd', 'dbbacdba', 'bcdabacd', 'ccbadbbd', 'ccdbaddb', 'caddbcab', 'cddcabda', 'dbacadca', 'cabdcdcb', 'ddbdbaac', 'babacabd', 'dcdadabd', 'badcdbbc', 'dddbacac', 'caaaadbd', 'dacacacb', 'aaaacdcb', 'abdbdcba', 'dddbabcc', 'acbddddb', 'daddbdcd', 'bbdabaca', 'acabdbcc', 'cdbadbdd', 'acacacdb', 'ddacdddb', 'dbbacacb', 'dabcaccd', 'ababcdda', 'bdcbaadc', 'dcacdddb', 'dcbbdabb', 'dbbabbac', 'abddacab', 'cbdbcacd', 'adbcadbb', 'bccaddba', 'bdcadbad', 'ddbcacdd', 'adacdbab', 'bbacbdac', 'cdcacabc', 'ddcacbad', 'bbacdbcc', 'ccdcdadb', 'cbccadcb', 'dcacbbdc', 'adcacbab', 'accbccdb', 'cdcacaba', 'dcdccbba', 'addddcba', 'abdccbad', 'adbbdddc', 'cdcddabb', 'bbcacddd', 'cbabdadd', 'daacdbcb', 'dbabdcdd', 'dabccdab', 'bbcdbbab', 'cdddcaba', 'dcdbaabc', 'dabbddbc', 'acbdbbda', 'dbccadbc', 'dcdcdaab', 'bdaccacc', 'bdcdbbda', 'caabbdbc', 'abddcadd', 'abbcabdd', 'baabdaac', 'bcddcdad', 'ddabcbca', 'ddbcdaaa', 'bdbabbcd', 'adcbcdad', 'abcdabab', 'addddbac', 'aabcdbaa', 'cdcaacbd', 'dcbdaabc', 'dbdcdbda', 'acddcdba', 'dbabbadc', 'cdbccbaa', 'dbdabbcb', 'dddcbdca', 'babbdbac', 'cadbcaca', 'cbcadddb', 'adccbcab', 'bcddabab', 'cbaabcdc', 'bdcbcaab', 'bcdcbdaa', 'bddddcab', 'ccdbcbad', 'cdbacabc', 'acdcbddb', 'ddcdcbba', 'bdcdbaab', 'dcbbddab', 'bdccddda', 'bacbcdcb', 'abccabdb', 'cbddabba', 'badabddc', 'baccbbdc', 'adbcddcd', 'daacbbdc', 'adcbccdc', 'bdcabdcc', 'dbdccadc', 'cdbdddba', 'abaddcaa', 'cbdaddcb', 'cbacadba', 'acdbadcd', 'bdddbcda', 'acbdbadb', 'cbadbacd', 'acdbdbba', 'ccaddcab', 'bcdadcac', 'adcdbbdd', 'bacabdcd', 'abcdaccb', 'ccadcaba', 'addacdba', 'abcdbdcd', 'cadbaddb', 'ddbbccda', 'cddccaab', 'acdbccba', 'dbdcdcda', 'dbcbaabc', 'addbabca', 'cbbcbabd', 'acdbcdcd', 'ddabbcda', 'bacddcad', 'abdbabcd', 'aaaacbbd', 'ccddbdba', 'dbbaaccd', 'cacacadb', 'cacdbcbc', 'dbbcbbda', 'bdbcdcab', 'acacbdbc', 'cbcbdcca', 'cbdbcadc', 'ddbbdaca', 'bcbaddca', 'dccbcabd', 'acdbbcac', 'accbacda', 'cabbcadb', 'addcdbdc', 'dbababdc', 'ddbbabcd', 'aadcbccd', 'bddbdacc', 'aadcbbaa', 'addbcabc', 'dccadbda', 'dabaccdc', 'cbdbdadc', 'badbcaba', 'abddadac', 'adcacbcc', 'cadadabc', 'accbcdbb', 'bcbcdacb', 'bcdcaabc', 'dabbcdba', 'bdacdcdb', 'cbaadcdb', 'ccbdcabd', 'badcbbda', 'dbadaddc', 'dcbacadb', 'abacabda', 'dabddbdc', 'bbdacdca', 'dcacabda', 'accbadad', 'ccbcaddb', 'adddcbab', 'bbdccaac', 'acdbbdcd', 'dcbabdbb', 'cacdcbba', 'dbacadda', 'dacbcbba', 'bcdcdadc', 'adcacdbb', 'dcbdcdad', 'bcddbdad', 'acabdddd', 'baadcdcb', 'cdcaadcb', 'addbcdab', 'ddacbcac', 'dabdcddd', 'baddcbba', 'bdaccbba', 'bdbdadca', 'babacdda', 'cddbbcad', 'cbbaabbd', 'dbacabcc', 'addbdbcb', 'dccdccab', 'cabbdcbc', 'cdacadab', 'bbdcacbc', 'dadbddcd', 'adcdbdba', 'cdaabcaa', 'abcdcadb', 'bccacbad', 'ababdccb', 'ccbcdacd', 'daccbaca', 'dcdcdbac', 'cabadddd', 'dcacddcb', 'bdbdcacc', 'bcaddbbc', 'ccbcbdad', 'bbacabbd', 'ddacbdbb', 'bacbdbda', 'dcdcabbc', 'abaccabd', 'dbbabbcd', 'ccbabbdd', 'bddccaad', 'bdcbdcac', 'adbaddac', 'cbdabccd', 'dbadcdbc', 'cabbadad', 'babccddb', 'dbbaacbb', 'dacabbad', 'dcaccddb', 'dbdccaba', 'cbadbcbb', 'daaaabdc', 'cdabdbca', 'dabdccdd', 'dcaabaad', 'cdbabbcd', 'bbcadcca', 'bdabaddc', 'baccddad', 'adcbdcba', 'bdcdddba', 'dbdcabda', 'ccddabdb', 'adddcbca', 'dbadbbac', 'ccbacdcd', 'ccadbbdb', 'dbccbdca', 'cbdcacdc', 'cadaccbb', 'cbbddcab', 'cabbdbcc', 'cdbdbcca', 'bbdcadad', 'abcdbcbd', 'bdbcbcaa', 'cbdccaba', 'daabbdbc', 'cdcaccdb', 'acabdbca', 'dddabcba', 'daccbdcd', 'abdacdda', 'cbabbcad', 'bcdadddd', 'bddbabcc', 'ccbaddbc', 'bcdaccdd', 'dcbacdcd', 'baccddcb', 'dacbacbc', 'cabbadab', 'bccbddca', 'bcacbcad', 'bbddcbca', 'bbccadcc', 'acbcabda', 'babdcdca', 'cbdacacc', 'cacbdbdb', 'bdcabdcd', 'dbcbaacd', 'abddccdb', 'acbcabdd', 'bacdcbab', 'daccbdbd', 'cdacddbc', 'bcbddbda', 'acdacbab', 'abcddaac', 'babbdbcb', 'dddcabcb', 'ccbaadcb', 'cabadcbb', 'accdbbdc', 'bbadcbcc', 'bcdcadbc', 'ccacddcb', 'ddccbacc', 'acadbcdc', 'addbcbac', 'abdbcdac', 'dbdaddcd', 'cddbcabc', 'babcddac', 'bcbcddaa', 'abbccdcc', 'dbbdcdca', 'dcdccadb', 'ddcbaaab', 'dcbccacd', 'ccbdcaba', 'dbdcbaac', 'adccbcba', 'acbdbccb', 'bdccdbda', 'caadbbcd', 'cbcbbdad', 'dbbacbba', 'bbccbabd', 'abacddcd', 'cadbdcda', 'cbaccdad', 'cbbaaaad', 'bacbccdc', 'bccadcda', 'abdbdcdb', 'cdbababb', 'dccabcbb', 'bbcddabb', 'dbcbacab', 'adcdcbca', 'ccbbdbca', 'acdbddad', 'ddcbdaab', 'abdadbbc', 'bbdbaabc', 'cdadadab', 'cadcdbbd', 'bcdacbda', 'dbcbcada', 'acddaadb', 'bcbaddcc', 'ddaccdbb', 'cacabacd', 'bcdbdbaa', 'bbddcaab', 'cbcbadad', 'adddabbc', 'cddacabc', 'ccbdbbad', 'cbcdaabc', 'ddacdacb', 'bacdcdbc', 'abcadbda', 'bccacdbc', 'cdacabca', 'adacabdd', 'cdcaadbd', 'accbbadb', 'baccddda', 'dbdabcca', 'abbcabcd', 'bddabcbc', 'daccbacb', 'baadbbcb', 'dacbbdbb', 'addcbacc', 'babbcddb', 'bccbaacd', 'accdcabd', 'abcdacdd', 'dabacaca', 'ccddcacb', 'caccdbbd', 'dcabacac', 'dcbcacbd', 'ddbbdbca', 'ddddcbaa', 'bbdcadcc', 'ddbccdab', 'cbacbddd', 'ddadbcba', 'bdadcabc', 'ababdcab', 'acbbdbcd', 'cbdadddc', 'bdbadcab', 'baccaddc', 'cbbabadc', 'adabbcbc', 'bddabcad', 'ccbccdda', 'bcdabcdb', 'acbdddca', 'acabcadd', 'dddbbacc', 'bdaddabc', 'babcadac', 'bcbcbcda', 'dabaccba', 'bdbabccd', 'dcbadbad', 'cbcbaddd', 'ccbbddda', 'adcabcab', 'dbcdddca', 'acddacbd', 'cdbaabbc', 'adcabdcb', 'adcbccba', 'aabdcbbc', 'adabdcbb', 'dcaaaacb', 'accbcbad', 'dbdadbbc', 'bcadadab', 'cdcbabcd', 'ddcabacb', 'bcacdbcc', 'bbcbcdda', 'adcbaddb', 'bdddcdaa', 'bddddbca', 'bccadcca', 'ccbdcdda', 'abbcbcad', 'ccababcd', 'cbabdcab', 'cabbdddb', 'dababccb', 'dacabcbc', 'bdddbbca', 'cbccdacc', 'abbcdbab', 'dbcaddca', 'caccbacd', 'ddadacbd', 'bddccbac', 'bcdbdbad', 'acdbbadd', 'ccadaccb', 'cabadacc', 'bdcdccab', 'cabcbdcc', 'bcddddca', 'bcadcadb', 'cbdddbad', 'adadcbba', 'bdadacbd', 'adcbadad', 'bcdabdcc', 'babacadd', 'cdaadbcd', 'acabdbcb', 'cdbcbadd', 'aacbccdb', 'daaccaab', 'bcadbcdc', 'dacbdabc', 'bcdadbbc', 'aadbccbd', 'ccabdadc', 'dcabacbb', 'ddcaacab', 'ddbaaccd', 'abacaddc', 'cdbdadcc', 'dcbdcabb', 'bbcadcda', 'dcdbdbba', 'ddbcabaa', 'bcadacda', 'bacdcada', 'dacabacb', 'dcababbd', 'cdbadadd', 'ddcbbcda', 'cabddacc', 'bdaddccd', 'cdacdacb', 'abcbdddd', 'bcadadbb', 'dadbcdab', 'dcdabdda', 'bdabcacd', 'cdcbbdad', 'abacbcad', 'dddcbacb', 'cbdadadd', 'acddbccd', 'bdccddab', 'dbadadac', 'dadbbcbd', 'bcacbdca', 'bdcdcdba', 'bbdbddac', 'caadaadb', 'dccdcabc', 'dabcddba', 'dcaacdbb', 'dcacddbc', 'cdbacdda', 'cadbbada', 'cdbdbdab', 'acdbdddb', 'addcddab', 'bccdbdca', 'bcabbcdc', 'cdbbcaac', 'ddacbadb', 'cabacddb', 'bbddcdaa', 'adabacbc', 'dbbddcab', 'bdacddab', 'cdadbacb', 'cbacabdb', 'ccdaccbb', 'dadddacb', 'dabadccb', 'bbddbacd', 'cdddabbc', 'cbdcacbd', 'dbdcaddd', 'bdacbcdc', 'cabaddbc', 'abdcbccb', 'bdbabcbb', 'bddaaacc', 'dbaddcad', 'dcacbdba', 'cbdcbdda', 'bbdadcab', 'daabcdbc', 'dadacbda', 'adcadbdc', 'badbacca', 'cbcadbad', 'caabccbd', 'dabadacb', 'abdacdbd', 'acbcbbda', 'bcbdcdac', 'abcadcac', 'dddbacdd', 'cadcbcca', 'cdadbccd', 'badbacbb', 'daddccba', 'bdddabcd', 'acdbbacb', 'cadbbccb', 'cddbabcb', 'abbdddcc', 'acdcbcba', 'cbdbcabd', 'cabdbacd', 'abadbbca', 'accdacab', 'ccbabcdd', 'dcbdaadb', 'adbccaba', 'dcbaddba', 'accdacbd', 'cacbdcac', 'cddaacbc', 'bcbadbda', 'ccadcadb', 'dccddabb', 'bcadbdad', 'babdcdac', 'adbbdbca', 'babcbdac', 'caddbdad', 'cdddaccb', 'dabbadac', 'dcbacbdb', 'bcbaadcd', 'cbdaddca', 'abbadaca', 'dcbdbdaa', 'abdabbcd', 'acabcadb', 'cdabcbdb', 'cabacabd', 'bddcabbc', 'abbdacac', 'bdabcdbd', 'dccdadcb', 'adcbdcbc', 'bbcacdbb', 'aadaacbb', 'abddbbca', 'caddbcbc', 'dabdbdbc', 'ddcaddbc', 'dadabcbb', 'abdacddc', 'dcaccaba', 'dccbdaad', 'bbccaddc', 'abcdcddd', 'cadbbdab', 'bbccbdca', 'cadcbacd', 'bacbcbdb', 'cbccacdd', 'bbdddbca', 'bbaadcdc', 'cacabbdd', 'dabccbad', 'abbccbdc', 'cddbadac', 'bdbcabbc', 'adbbcbda', 'dabcaddd', 'dbcbadda', 'ddccbcaa', 'cbdbcbca', 'ccddbaba', 'dcbadcac', 'cbbaadaa', 'cdadbbdd', 'caddabac', 'badccadc', 'ccbdbbca', 'babbaddc', 'cbacdcdb', 'ccbadada', 'adbdbddc', 'acbbdcbb', 'accddcbb', 'bcbabcdd', 'acdacddb', 'acadbadc', 'cbdddcda', 'ccdabadd', 'bdccbdab', 'bbabdbbc', 'abbcddbd', 'bcdacabc', 'dbcdacbc', 'abccdbbd', 'bddbcdad', 'bdbccaba', 'cacbdcba', 'cdcbdacb', 'cdcaccbd', 'bcdbbdda', 'cbdcdbac', 'abdcdadd', 'addbaacd', 'bdddaddc', 'cabcacad', 'bddbbaca', 'bdcbaddc', 'bdddaacc', 'abcdcbbd', 'badcdbba', 'acdbdcdc', 'cdcbcbad', 'dcbabcad', 'dddcabab', 'bbddcabb', 'cdccbaca', 'dbbadbcc', 'cbadcdab', 'adbcbdba', 'ddbcacac', 'bdbcdaca', 'babadadc', 'acdccdab', 'cbddcaba', 'cadbdbcd', 'cabddbcd', 'baccbdcb', 'badcdaca', 'dbaccbdd', 'dabccdcd', 'abbaddbc', 'addbcdad', 'bbadccba', 'baadccdc', 'acababdb', 'bddccadd', 'bcadadcd', 'cbcddaad', 'acdadcbc', 'adacdcbb', 'bdadcdab', 'acdbadad', 'cddbcdab', 'bbcdadcd', 'adbcdbdd', 'ccdaadbc', 'ddcbccab', 'adaddbbc', 'dbcadddb', 'bccdabbd', 'adbcbcbb', 'dcdcdbba', 'dcdbcaba', 'cabbdbbc', 'bcdadcdd', 'dabbdbcd', 'dcbccdad', 'dabadbcb', 'bddcbaad', 'dccababd', 'ddbaaaca', 'bbadacab', 'cbdcacbc', 'dbbccdda', 'accadbcc', 'bdcdaacb', 'bcaacdcc', 'dbdcacdd', 'dbccaabb', 'cababdda', 'abcbcadc', 'cbaccdba', 'cbddcbac', 'bccbdcca', 'acabbcbd', 'ccdbbaad', 'badccbab', 'bbdacbdc', 'babdbcbd', 'abbcdbbc', 'bdcacadd', 'cabcadca', 'dcabcbdc', 'baaaadbc', 'acbbdbbd', 'acbaddba', 'addbacbd', 'abcdbbdd', 'acbaccad', 'acbdbcdc', 'caddaabc', 'abcbbdcb', 'dcdddcab', 'cdbacdba', 'cdbaddba', 'acbdadac', 'dbdcabdc', 'cabbdaba', 'aadbbdbc', 'badcadcc', 'cdbaddcd', 'ccddbacd', 'cdccbada', 'cdbdbaab', 'bcbdddad', 'addbacda', 'ddbbacbd', 'bdcacbbc', 'cdabcaba', 'dccabddd', 'cabccdbc', 'ccbdbdda', 'dbdabacb', 'cddabadd', 'adcbcbbd', 'accdbdcb', 'caabdbdb', 'bbdacdbc', 'adcbabcb', 'bbcacbdd', 'abbdbccb', 'cbbcacdd', 'bcbdcadd', 'dcbdabcc', 'bdbcbcac', 'abdbccbc', 'babdacdb', 'cdacbddc', 'cdbabacd', 'bdcddabc', 'dacacddb', 'cbcdcbab', 'cdcbaccb', 'adbacddc', 'addcbcbd', 'bababdcb', 'dcacbbab', 'cdbdbaad', 'bbabcddd', 'ccbaacdb', 'ddbdadcd', 'dcdaabcc', 'addddbca', 'dccbdadd', 'cabbdbcd', 'ddcbacad', 'acdcabac', 'bbcdaddb', 'ccabcdcc', 'dcaccbbc', 'cbbdbaab', 'cababadd', 'ddbcabdb', 'aacdcbbc', 'ccbdbbda', 'cbabbddc', 'addbbaca', 'dccbccab', 'ddadbbca', 'adbbcbcb', 'adbadbdc', 'acbbddcc', 'dbdbbdca', 'abcbcbda', 'dabdbcca', 'badbadbc', 'bbaddcaa', 'badcdaba', 'bbcbcadc', 'bcbadccd', 'cbcdcbca', 'acdcbbca', 'dbacdbac', 'cbdbcacc', 'ccddaabd', 'ddabcdbd', 'cabcadad', 'bdcdabbc', 'bdabddcd', 'ccddddab', 'bdbaccbd', 'acabddcb', 'ddabdbbc', 'dacbacbb', 'bccbdacd', 'abccdcbb', 'bcdacdad', 'ccacdbcc', 'bcbadaca', 'adbccabb', 'bbddcadc', 'badcbdab', 'bccdbdda', 'ddcacbda', 'dccbccad', 'dcbaccab', 'cddddbac', 'ddbbcaad', 'adbdbcab', 'ddabcdba', 'ddbcddac', 'acbddbcb', 'aaccdccb', 'cbaccadb', 'dcacbaca', 'ccbadccb', 'ddacbbcd', 'bcbabbda', 'dbdccbca', 'ddcdbadb', 'acbcdabb', 'dbdbaadc', 'bacdcdab', 'acdcabcc', 'cbdddaab', 'acbbcdcd', 'bdbcdbac', 'ccbaacdc', 'cdbbddca', 'aabdaabc', 'baaaadcd', 'ddbaccba', 'abadddcc', 'acbdbadd', 'bdaddacb', 'cdbaaaac', 'bbcadcba', 'daddcdbc', 'bdbcdbba', 'cbaccabd', 'adcdbaba', 'dacdbaba', 'dbcbcbda', 'ccbbaccd', 'cacdcbcc', 'cbddcdda', 'dccadbcd', 'bbdcabda', 'dcbacabd', 'adbdcbdc', 'cdabcdad', 'bcddcacb', 'abcdbcda', 'addababc', 'bbcdcaab', 'ddbdacab', 'dadccbac', 'acdabcdb', 'bdacddbb', 'ddaccbbd', 'dbbcabcd', 'dcbddbab', 'cadabbab', 'ccaadbcc', 'dcbccbba', 'cdcacbbc', 'bbaddcda', 'bbadddcd', 'dacbbdbd', 'badadbcc', 'ccdbaabb', 'bbcaccbd', 'dcaacdbc', 'dcaabdcd', 'cabadbbd', 'dabbcaba', 'bdabcacb', 'bbabddcb', 'acbcbdbd', 'cbbcddaa', 'abcbcacd', 'dbccacbd', 'bcdbacad', 'dbbacadb', 'babbddcc', 'baccdddb', 'cbcbaddc', 'cdbcbbaa', 'bcdbdabc', 'accadddb', 'ddcaacbd', 'adbcbcbc', 'bbccdbac', 'abcdbaca', 'dadbbddc', 'cdadddbb', 'adabadac', 'babaccbd', 'dbcaddaa', 'bdccaddd', 'dacdabba', 'bdaabbcb', 'daacbbaa', 'adcddbbc', 'bbcadbdc', 'bcbcdacd', 'dbcbcadb', 'baddbabc', 'cabdcbbd', 'ccbdbcca', 'cabbcbdc', 'adcadbab', 'dcdcabdc', 'daacbdbd', 'acdacbcc', 'dbabadbc', 'dbaadbcb', 'bdabcbbc', 'bbdcbcba', 'cbddacca', 'bbdcaccd', 'abdcbbcc', 'cacabdba', 'ddccaadb', 'bcbbccda', 'ccdcaabb', 'cbcdcaad', 'badbdcba', 'cabdcdbd', 'ddbacdcd', 'cbabbccd', 'cadbcabb', 'adcabada', 'dbdaddac', 'bddbcbaa', 'acdccadb', 'bbcbddca', 'dabacbdb', 'ccddbcab', 'bdabbcdb', 'adcdcbab', 'bacbbdcb', 'adbbcdbc', 'babcbbcd', 'abddccbb', 'bccdcbac', 'bcdabdda', 'cbdcacda', 'bcdabcdc', 'bcbdbbad', 'bccbaccd', 'badbcbcd', 'cacdcdba', 'badadccd', 'accadbdb', 'baddcadc', 'bdbbacdb', 'adabdcbd', 'cbdcbcda', 'cbccdbab', 'ccacbcdb', 'dddcbcda', 'ccdbabcb', 'caabdccd', 'bcdbdcca', 'dbcbaccd', 'cdcabcdd', 'abbadbbc', 'badbcdbb', 'cbdbdabb', 'adbdcbbd', 'cbacbada', 'abbadcbd', 'cabdcaba', 'adcaccbc', 'acdbacbc', 'bdacbddb', 'cddcbabc', 'dddcbbab', 'dbabdbdc', 'ccbadcac', 'bcbdbdab', 'cacdccbd', 'bbddbacc', 'babbdcca', 'cbddbcac', 'aadaadcb', 'cbbaadcd', 'cbbcdbac', 'ddddbdca', 'caadbccb', 'ccdbcaab', 'cacbadbd', 'cdbdacdb', 'bdcaaaad', 'cacbdaca', 'dcababcd', 'abcacdad', 'baccbcdb', 'abccbacd', 'bddbaaca', 'badaddca', 'dcbabdab', 'addbaacc', 'dcbcadbb', 'cddbaadb', 'ccadcbab', 'bdcabcbb', 'bacadadb', 'adaccdba', 'cacddbdd', 'bddaddac', 'abcacadb', 'addacbcd', 'baabdccd', 'bbddacaa', 'dabdabdc', 'bdbaccdc', 'cdddbbaa', 'bddbccac', 'cddadcbb', 'dbabbacd', 'adbdacbd', 'bdaadbcc', 'bcdabddb', 'aabdcbcc', 'cbbdbbaa', 'dbbabcbc', 'dddcbadb', 'badabdbc', 'dabdcbcb', 'cdccadcb', 'dcbabccd', 'cbdbcdda', 'bdabdcbd', 'dcbababa', 'abcdadca', 'acbcbadc', 'dcacdabc', 'cdbabdbc', 'dbccacbc', 'cbcacdad', 'addbcdbb', 'ccadcbdc', 'abcadada', 'acacdacb', 'cbbadccd', 'bbcdbaac', 'bcbabada', 'adbbdcdc', 'babdabac', 'dbdddadc', 'abcdacbc', 'acbbadcb', 'daaccbbc', 'bcdababd', 'addacabc', 'abbccbad', 'ddbbddca', 'baddcdcb', 'dbccacac', 'cabccdad', 'aabdbbdc', 'bbadbbca', 'bbddbaac', 'ddadbbcd', 'baccdcac', 'bdcabcab', 'dadcabda', 'dabdabbc', 'dbcababb', 'bdbddcda', 'abccdcdc', 'accababd', 'adacbaba', 'bdacdabb', 'badccbca', 'bbcdaadb', 'ccbcadad', 'adaddcbc', 'bbdacdda', 'cdbcdcba', 'acdabacb', 'bacaddaa', 'dbcdaddd', 'acdbbabc', 'cabdacad', 'dcdcddba', 'ddbababc', 'bcbdadcd', 'cddccbab', 'acaddadb', 'acbcbbdc', 'bdcbcdad', 'cbdadcba', 'dadabcac', 'cadbdccd', 'caccdabb', 'dacbbddb', 'baddbcaa', 'bbdcabdd', 'cbbdadcd', 'bcbcdabb', 'cacbaddb', 'caabdbcc', 'dddbcaac', 'daccbaba', 'bcdcdaca', 'cbdcdcac', 'cbddbbda', 'adbddbdc', 'dabbcbda', 'dcacddba', 'dcaaaadb', 'ccdbcada', 'ddabbcca', 'bdbddbac', 'cbdaadbc', 'bcbdacbc', 'ddcbacaa', 'dabbdabc', 'cdabdaca', 'cbdddaba', 'cbadbadd', 'adacdcbc', 'bddbbcba', 'bdcddbca', 'adcddcbd', 'abcbdacd', 'ddaadbcd', 'dabccbdd', 'bcaccdcc', 'bbadbdac', 'dbcdcaad', 'cbcabdbb', 'dbbdcadd', 'aacdccbb', 'aacdbbcd', 'adbbcdac', 'acbbddbc', 'addbaabc', 'acbcdbbc', 'cdbbddda', 'ddbddabc', 'acbbacbd', 'dbddabca', 'accabcdc', 'cdccbcaa', 'acadaccb', 'cabcbdbc', 'dcbcbacd', 'cdbbabad', 'adcbadcd', 'abadcdbc', 'babcbdbc', 'dbcacbda', 'abdabbcb', 'dcdbcabc', 'addcbdbc', 'cacadbda', 'dbdabcbb', 'acddbcda', 'caccdcbb', 'adddabac', 'cdcdbacb', 'bccbadad', 'dcdbdcca', 'dcddabba', 'bdcdbada', 'dcdccabd', 'dacabcba', 'ddcbdbad', 'dabddccb', 'bdacadcd', 'bdbbcbda', 'bddaccab', 'cdacbcbc', 'cdcabdcb', 'acbdddda', 'adadcbcc', 'cdbbdabb', 'cdaddbaa', 'cdbdcbad', 'ccabbddb', 'abdbdacb', 'bcbdbbca', 'bcbbacad', 'cbaddcba', 'abaddaac', 'cddbadcc', 'dcdacdab', 'dabdccda', 'cdbdbdda', 'bddbaacc', 'dabbcabb', 'bcadbcad', 'bbdbabcc', 'bddadaac', 'abbadacb', 'bcdbbacd', 'dadcbcac', 'dcbbaddb', 'abbddaac', 'abbdcddc', 'acaddcdb', 'ddabacdc', 'cdbcbacb', 'cbadcbda', 'bdacabab', 'cdcbdadb', 'abaddabc', 'dddacbda', 'ddbcabcc', 'bcbaddcb', 'dcbdcadc', 'cadbdcbc', 'dabcbccd', 'cdccabdd', 'acbadcca', 'abbdcbda', 'ccbaaaad', 'acbacdac', 'dcbdabdb', 'badacadd', 'dacacdbc', 'dbcbbcda', 'dcbaccbc', 'cbcdaadc', 'abaccdbc', 'dacbabdd', 'ddbcaada', 'accbdbca', 'dcbacdca', 'dccbadda', 'bcabcdcd', 'dddaadbc', 'adbdbdbc', 'addddbcc', 'cddbdbad', 'cbacadbb', 'acabadac', 'bdcacbcc', 'accabdab', 'daacaadb', 'dcdacbbd', 'dadabcca', 'bdbdacad', 'ccadddbc', 'baadcbcd', 'bcdbccda', 'cdabadba', 'adbdadac', 'adddbdcc', 'acdcbacc', 'dcdcbacb', 'ddbcacbc', 'dcbcdacd', 'bdcdabca', 'dcababda', 'accbadbd', 'abccdcab', 'bcddccad', 'acdbddbc', 'cdcdaabc', 'cdabbabb', 'ccbccacd', 'adbaccbd', 'bdaadcdc', 'bacbbdad', 'dadccdbb', 'acbabada', 'dbcadddc', 'dccddbba', 'baddcbcc', 'dacbdbab', 'abacdbcd', 'cadabdac', 'bbdadcbd', 'accbdddd', 'ccdddbda', 'abdccdca', 'adbbcacc', 'bbdddbac', 'dadccbdc', 'cdabbdba', 'baaccdcb', 'abacbdcb', 'cdadbdbc', 'dbacabbc', 'ddccbacd', 'acbccbda', 'acdbadbd', 'cdaddcbd', 'cacacdbd', 'cdcbcaca', 'bcacbabd', 'dcbcdaad', 'dbadacab', 'cbbdcdad', 'bbdddacc', 'dbaadcdc', 'ccddaadb', 'ccaddbca', 'cabcddba', 'bbcadbac', 'abbcbccd', 'acdbcddb', 'dbcacdcc', 'bdbcddaa', 'abcadbad', 'adcadacb', 'ddbcbaca', 'accdbdda', 'dddbaccb', 'dabcbdac', 'cbcdccad', 'bacddccd', 'abdbaddc', 'cdbccdac', 'acddbbda', 'cdbdbcab', 'acdabbab', 'abbdbcdc', 'cdcbaacc', 'ddabdcad', 'bccbbdda', 'cdbacbcd', 'bdbbccac', 'cbddbbac', 'bcbbadba', 'dadabcba', 'cabbacdd', 'addbaccd', 'abbacddb', 'dadbabdc', 'bddaaaca', 'bbdccbac', 'bbcacbbd', 'dbccdcad', 'bbabcadb', 'dbdbdcac', 'ddccbbaa', 'ddcbdaad', 'adcbabdd', 'bcddabcc', 'daddcadb', 'cabccdab', 'acbcadad', 'dcbbdbda', 'dbbabbcb', 'cbccbdac', 'ccabdbac', 'ddcbadac', 'cadcabbc', 'cdbabdbb', 'cbacbdca', 'bbacddba', 'cddccabb', 'dbcbacbd', 'bdddcabc', 'dbcdaabd', 'dcddbaad', 'ccddbcaa', 'bccdcadd', 'dcbbcdca', 'dabcdbad', 'bacbccdb', 'ddcdbcab', 'ddccdcab', 'dcdabadb', 'bbddccaa', 'adadcbbc', 'dabbdcac', 'adcbabca', 'addbabcc', 'addaccbb', 'acdcbddd', 'bdadcabb', 'dbbdbdac', 'daccbddd', 'ddcabdbd', 'cbabcddc', 'bcdbccad', 'bccddabb', 'bddadcdd', 'ccddaaba', 'ccdacbad', 'cacddbab', 'cabdbcab', 'dbacacab', 'bdbccbca', 'acdaddba', 'ddacbbad', 'cbcadccd', 'bdcacbdc', 'cabacbda', 'adccabcd', 'badabcbc', 'accabcda', 'adbddcbd', 'adddcbbc', 'dddbddac', 'abcbadbb', 'bdcdacbc', 'cdddbcba', 'cbabbdca', 'bdbacdbb', 'abccabcd', 'cabbcdcb', 'dacbdddb', 'acdcbdbd', 'bddaccda', 'babcadbd', 'abaccdac', 'cabdccbc', 'dbcadadc', 'cbddbcaa', 'bdabdbcb', 'abacbbdc', 'bbcabdab', 'ddbaddac', 'ddcabaac', 'caccbddc', 'cbddbdaa', 'caadbbaa', 'baacdcbb', 'cabccdcc', 'cbbaddba', 'ccbabbdc', 'bbdcddba', 'bbcabdba', 'bdccdcad', 'dbcabcda', 'cbcdcdad', 'addacbaa', 'dabddcdc', 'ddbdaaac', 'bdacbdbd', 'cabdacda', 'adacabdc', 'accbabad', 'bdaccdbb', 'cdbddaba', 'bcaaaadb', 'adbcabcc', 'cbcbdaca', 'abdadcda', 'bbaccdbd', 'baddcadd', 'cdacabdd', 'dcadbdda', 'acdcbbcd', 'aacdaabc', 'dbbacbcb', 'bcbcbacd', 'bdcbacba', 'adbabbcd', 'ddcbcbab', 'cdccdabd', 'cbabacdb', 'dadbbacd', 'daccadbb', 'dacbdbad', 'cacaddbb', 'cbbcabad', 'dadabdcb', 'ddcabbab', 'cbcbcdba', 'dadbcdad', 'ccacdabc', 'abdabbac', 'bddaacda', 'ddcadcdb', 'ddcaabaa', 'acbadcbb', 'abcdadad', 'daccdabc', 'baddbcdd', 'cbadccbc', 'dddcddab', 'babdcabc', 'cbbdadca', 'adbacada', 'ddcabcca', 'dccacdbb', 'addcabac', 'bcaddbdd', 'cbadabac', 'cacaddba', 'dabbcdbd', 'babdacbb', 'adabcbbd', 'dcababcb']
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