This page contains the first discovered set of permutation-fair 5d60 configurations of Go First Dice. After developing an improved search algorithm, many millions more have been discovered since. Die-wise permutations and trivial substitutions (e.g. "abba" -> "baab") are pruned for conciseness. Note that all solutions thus far have been found by constructing an "[[induction_chart|induced]]" 5th die around a fair 4d60. The induced die is represented by 'e' in the following solutions. ''abcddcbacbaddabcedbaccabdeeeeeeeeeeeeabcddcbaecbaddabcdbaccabdedbaccabdabcddcbaecbaddabceedbaccabdcbaddabcdbaccabdeabcddcbaeeeeecbaddabceabcddcbaeeeeeeeeeecbaddabceabcddcbaeeeeecbaddabcedbaccabdabcddcbadbaccabdeeabcddcbaecbaddabcdbaccabdedbaccabdabcddcbaecbaddabceeeeeeeeeeeedbaccabdeabcddcbacbaddabc'' ''abcddcbacbaddabcedbaccabdeeeeeeeeeeeeabcddcbaecbaddabcdbaccabdedbaccabdcbaddabceabcddcbaeedbaccabdcbaddabcdbaccabdeabcddcbaeeeeeabcddcbaecbaddabceeeeeeeeeeabcddcbaecbaddabceeeeecbaddabcedbaccabdabcddcbadbaccabdeecbaddabceabcddcbadbaccabdedbaccabdabcddcbaecbaddabceeeeeeeeeeeedbaccabdeabcddcbacbaddabc'' ''abcddcbacbaddabcedbaccabdeeeeeeeeeeeecbaddabceabcddcbadbaccabdedbaccabdabcddcbaecbaddabceedbaccabdcbaddabcdbaccabdeabcddcbaeeeeeabcddcbaecbaddabceeeeeeeeeeabcddcbaecbaddabceeeeecbaddabcedbaccabdabcddcbadbaccabdeeabcddcbaecbaddabcdbaccabdedbaccabdcbaddabceabcddcbaeeeeeeeeeeeedbaccabdeabcddcbacbaddabc'' ''abcddcbacbaddabceedbaccabdeeeeeeeeeedbaccabdeabcddcbaeecbaddabcdbaccabdabcddcbaecbaddabcecbaddabcdbaccabdeeecbaddabceeabcddcbadbaccabdabcddcbaeeeeeeeeeeeeeeeeabcddcbacbaddabcabcddcbaeedbaccabdeeecbaddabcdbaccabdedbaccabdeabcddcbacbaddabcdbaccabdeeabcddcbaecbaddabceeeeeeeeeecbaddabceedbaccabdabcddcba'' ''abcddcbacbaddabceeecbaddabceeeeeeeeedbaccabddbaccabdeabcddcbaeedbaccabdeabcddcbaecbaddabcecbaddabcdbaccabdeeabcddcbadbaccabdeabcddcbadbaccabdeeeeeeeeeeeeeeeeeecbaddabcabcddcbaecbaddabcabcddcbaeecbaddabcdbaccabdedbaccabdeabcddcbaecbaddabceeabcddcbaecbaddabccbaddabceeeeeeeeedbaccabdeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeabcddcbaeeedbaccabdeeeeeecbaddabcdbaccabdecbaddabcabcddcbadbaccabdeeedbaccabddbaccabdcbaddabceeeeeabcddcbaeecbaddabceeeeeabcddcbadbaccabdeeeeecbaddabceedbaccabdeeeeecbaddabcabcddcbaabcddcbaeeeabcddcbadbaccabdcbaddabceabcddcbacbaddabceeeeeeabcddcbaeeedbaccabdeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeecbaddabceeecbaddabceeeeeeabcddcbadbaccabdedbaccabddbaccabdabcddcbaeeedbaccabddbaccabdabcddcbaeeeeedbaccabdeeabcddcbaeeeeecbaddabcdbaccabdeeeeeabcddcbaeecbaddabceeeeeabcddcbacbaddabccbaddabceeeabcddcbacbaddabccbaddabcecbaddabcabcddcbaeeeeeedbaccabdeeedbaccabdeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeedbaccabdeeeeabcddcbaeeeeedbaccabdcbaddabccbaddabcabcddcbadbaccabdedbaccabdeeeecbaddabceeabcddcbaeeeeeecbaddabcdbaccabdeedbaccabdeeabcddcbaeeabcddcbacbaddabceeeeeedbaccabdeecbaddabceeeeabcddcbaeabcddcbadbaccabdcbaddabccbaddabcabcddcbaeeeeedbaccabdeeeeabcddcbaeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeedbaccabdeeeeeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabcdbaccabdeabcddcbaeeeeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeabcddcbaeedbaccabdeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeeeeedbaccabdeabcddcbaabcddcbacbaddabccbaddabcabcddcbaeedbaccabdeeeeeeabcddcbaeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeedbaccabdeeeeeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabcdbaccabdeabcddcbaeeeeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeabcddcbaeedbaccabdeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeeeeedbaccabdeabcddcbacbaddabcabcddcbaabcddcbacbaddabceedbaccabdeeeeeeabcddcbaeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeedbaccabdeeeeeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabddbaccabdeabcddcbaeeeeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeabcddcbaeedbaccabdeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeeeeedbaccabdeabcddcbaabcddcbacbaddabccbaddabcabcddcbaeedbaccabdeeeeeeabcddcbaeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeedbaccabdeeeeeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabddbaccabdeabcddcbaeeeeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeabcddcbaeedbaccabdeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeeeeedbaccabdeabcddcbacbaddabcabcddcbaabcddcbacbaddabceedbaccabdeeeeeeabcddcbaeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeedbaccabdeeeeeedbaccabdeabcddcbaecbaddabccbaddabcedbaccabdeeabcddcbadbaccabdeeeecbaddabcabcddcbaeeeeeecbaddabcdbaccabdeeeeabcddcbaabcddcbaeeeecbaddabcdbaccabdeeeeeeabcddcbadbaccabdeeeecbaddabcabcddcbaeecbaddabcedbaccabddbaccabdeabcddcbaecbaddabceeeeeecbaddabceeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeabcddcbadbaccabdeeeeeeeecbaddabccbaddabceedbaccabddbaccabdabcddcbaedbaccabdabcddcbaeeedbaccabdcbaddabceeeedbaccabdeeeeeecbaddabccbaddabceeeeeeabcddcbaeeeecbaddabcabcddcbaeeedbaccabdabcddcbaedbaccabdabcddcbaabcddcbaeecbaddabccbaddabceeeeeeeeabcddcbadbaccabdeeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeeecbaddabceeeedbaccabdeeabcddcbacbaddabcedbaccabdedbaccabdeeedbaccabdeabcddcbaabcddcbaeedbaccabdeeeeeecbaddabcabcddcbaeeeedbaccabdcbaddabceeeeabcddcbadbaccabdeeeeeecbaddabceeabcddcbaabcddcbaecbaddabceeecbaddabcecbaddabcedbaccabdabcddcbaeecbaddabceeeedbaccabdeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeecbaddabceeeedbaccabdeeabcddcbadbaccabdeecbaddabcdbaccabdeabcddcbaedbaccabdeeeedbaccabdeeabcddcbaeeeecbaddabccbaddabceeeabcddcbaeeabcddcbaeeedbaccabddbaccabdeeeeabcddcbaeecbaddabceeeecbaddabceabcddcbaecbaddabcdbaccabdeecbaddabcabcddcbaeecbaddabceeeedbaccabdeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeedbaccabdabcddcbaeeeeeeeecbaddabccbaddabceedbaccabdabcddcbadbaccabdedbaccabdabcddcbaeeedbaccabdcbaddabceeeedbaccabdeeeeeecbaddabccbaddabceeeeeeabcddcbaeeeecbaddabcabcddcbaeeedbaccabdabcddcbaeabcddcbadbaccabdabcddcbaeecbaddabccbaddabceeeeeeeedbaccabdabcddcbaeeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeeedbaccabdabcddcbaeeeeeeeecbaddabccbaddabceedbaccabddbaccabdabcddcbaeabcddcbadbaccabdeeedbaccabdcbaddabceeeedbaccabdeeeeeecbaddabccbaddabceeeeeeabcddcbaeeeecbaddabcabcddcbaeeeabcddcbadbaccabdedbaccabdabcddcbaabcddcbaeecbaddabccbaddabceeeeeeeedbaccabdabcddcbaeeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeeedbaccabdecbaddabceeeeeeecbaddabcdbaccabdabcddcbaeabcddcbaedbaccabdedbaccabdeabcddcbaedbaccabdeeeeeeabcddcbacbaddabcecbaddabceeeeeeeedbaccabdedbaccabdabcddcbaeeeeeecbaddabceabcddcbaecbaddabcecbaddabceabcddcbaeabcddcbacbaddabcdbaccabdeeeeeeedbaccabdecbaddabceeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeedbaccabdedbaccabdeeeeeeecbaddabcdbaccabdabcddcbaeabcddcbaecbaddabcecbaddabceabcddcbaedbaccabdeeeeeeabcddcbacbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdabcddcbaeeeeeecbaddabceabcddcbaedbaccabdedbaccabdeabcddcbaeabcddcbacbaddabcdbaccabdeeeeeeecbaddabcecbaddabceeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeedbaccabdeedbaccabdeeeeabcddcbaecbaddabceedbaccabdeecbaddabccbaddabcabcddcbaeabcddcbadbaccabdeeeeeabcddcbadbaccabdeeeecbaddabceeeeeecbaddabceeeeabcddcbadbaccabdeeeeeabcddcbadbaccabdedbaccabdcbaddabccbaddabceeabcddcbaeecbaddabcedbaccabdeeeeabcddcbaeeabcddcbaeeeeeecbaddabcdbaccabd'' ''abcddcbacbaddabceeeeeedbaccabdeeeedbaccabdeeabcddcbacbaddabceecbaddabcdbaccabdeabcddcbaedbaccabdeeeecbaddabceeabcddcbaeeeecbaddabcdbaccabdeeeabcddcbaeeabcddcbaeeecbaddabcdbaccabdeeeeabcddcbaeedbaccabdeeeecbaddabceabcddcbaecbaddabcdbaccabdeedbaccabdabcddcbaeecbaddabceeeecbaddabceeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeabcddcbaecbaddabcdbaccabdeeedbaccabdeeecbaddabcdbaccabdedbaccabdcbaddabceedbaccabdeeabcddcbaeeeeeeeeabcddcbaeeabcddcbadbaccabdcbaddabcabcddcbaeeabcddcbaeeeeeeeeabcddcbaeecbaddabceedbaccabdcbaddabcecbaddabcdbaccabdeeecbaddabceeecbaddabcdbaccabdeabcddcbaeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeabcddcbaecbaddabcdbaccabdeeedbaccabdeeedbaccabdcbaddabcecbaddabcdbaccabdeedbaccabdeeabcddcbaeeeeeeeeabcddcbaeeabcddcbadbaccabdcbaddabcabcddcbaeeabcddcbaeeeeeeeeabcddcbaeecbaddabceecbaddabcdbaccabdedbaccabdcbaddabceeecbaddabceeecbaddabcdbaccabdeabcddcbaeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeabcddcbaecbaddabcdbaccabdeeedbaccabdeeedbaccabdcbaddabcedbaccabdcbaddabceedbaccabdeeabcddcbaeeeeeeeeabcddcbaeecbaddabcabcddcbaabcddcbadbaccabdeeabcddcbaeeeeeeeeabcddcbaeecbaddabceedbaccabdcbaddabcedbaccabdcbaddabceeecbaddabceeecbaddabcdbaccabdeabcddcbaeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeabcddcbaedbaccabdcbaddabceeedbaccabdeeecbaddabcdbaccabdecbaddabcdbaccabdeedbaccabdeeabcddcbaeeeeeeeeabcddcbaeeabcddcbadbaccabdcbaddabcabcddcbaeeabcddcbaeeeeeeeeabcddcbaeecbaddabceecbaddabcdbaccabdecbaddabcdbaccabdeeecbaddabceeedbaccabdcbaddabceabcddcbaeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeabcddcbaedbaccabdcbaddabceeedbaccabdeeecbaddabcdbaccabdedbaccabdcbaddabceedbaccabdeeabcddcbaeeeeeeeeabcddcbaeecbaddabcabcddcbaabcddcbadbaccabdeeabcddcbaeeeeeeeeabcddcbaeecbaddabceedbaccabdcbaddabcecbaddabcdbaccabdeeecbaddabceeedbaccabdcbaddabceabcddcbaeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeabcddcbaedbaccabdcbaddabceeedbaccabdeeedbaccabdcbaddabcecbaddabcdbaccabdeedbaccabdeeabcddcbaeeeeeeeeabcddcbaeecbaddabcabcddcbaabcddcbadbaccabdeeabcddcbaeeeeeeeeabcddcbaeecbaddabceecbaddabcdbaccabdedbaccabdcbaddabceeecbaddabceeedbaccabdcbaddabceabcddcbaeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeecbaddabcabcddcbaeeeedbaccabddbaccabddbaccabdeecbaddabcedbaccabdeeeeabcddcbadbaccabdecbaddabceeeeeeeecbaddabceabcddcbaeabcddcbaabcddcbaeabcddcbaedbaccabdeeeeeeeedbaccabdecbaddabcabcddcbaeeeecbaddabcedbaccabdeecbaddabccbaddabccbaddabceeeeabcddcbadbaccabdeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeecbaddabcabcddcbaeeeedbaccabddbaccabddbaccabdeedbaccabdecbaddabceeeeabcddcbacbaddabcedbaccabdeeeeeeeecbaddabceabcddcbaeabcddcbaabcddcbaeabcddcbaedbaccabdeeeeeeeecbaddabcedbaccabdabcddcbaeeeedbaccabdecbaddabceecbaddabccbaddabccbaddabceeeeabcddcbadbaccabdeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeecbaddabcedbaccabdcbaddabceeeabcddcbaeedbaccabddbaccabdeeeeabcddcbaabcddcbaeedbaccabdeedbaccabddbaccabdeecbaddabceeeeeeabcddcbaabcddcbaeeeeeedbaccabdeecbaddabccbaddabceecbaddabceeabcddcbaabcddcbaeeeecbaddabccbaddabceeabcddcbaeeedbaccabdcbaddabcedbaccabdeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeedbaccabdecbaddabceecbaddabcabcddcbadbaccabdeedbaccabdeeeeeeabcddcbaeedbaccabdabcddcbadbaccabdabcddcbaeeecbaddabceeeeeecbaddabcdbaccabdeeeeeedbaccabdeeeabcddcbacbaddabcabcddcbacbaddabceeabcddcbaeeeeeecbaddabceecbaddabcabcddcbadbaccabdeedbaccabdecbaddabceeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeecbaddabcedbaccabddbaccabdabcddcbacbaddabcedbaccabdeeeeeeeeabcddcbadbaccabdeeeabcddcbaeeeabcddcbacbaddabcedbaccabdeedbaccabdeeeecbaddabceecbaddabcedbaccabdabcddcbaeeeabcddcbaeeecbaddabcabcddcbaeeeeeeeecbaddabcedbaccabdabcddcbacbaddabccbaddabcedbaccabdeeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabcedbaccabdeeabcddcbaeedbaccabdeeeeeeeeecbaddabcedbaccabdabcddcbaeeeabcddcbacbaddabceedbaccabdabcddcbaeeeabcddcbacbaddabcedbaccabdeeeeeeeeecbaddabceeabcddcbaeecbaddabcedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeedbaccabddbaccabdecbaddabceabcddcbadbaccabdeeeeabcddcbacbaddabcdbaccabdeeeeeeeecbaddabceeabcddcbaeecbaddabcabcddcbaeecbaddabceedbaccabdeeabcddcbadbaccabdeeabcddcbaeedbaccabdeeeeeeeecbaddabcdbaccabdabcddcbaeeeecbaddabcabcddcbaedbaccabdecbaddabccbaddabceeeeeeeeedbaccabdabcddcba'' ''abcddcbacbaddabceeeeeeeeedbaccabddbaccabdeeabcddcbacbaddabcdbaccabdecbaddabceeabcddcbaeedbaccabdeeeeeeeeecbaddabcecbaddabcabcddcbaeeeabcddcbadbaccabdeecbaddabcabcddcbaeeeabcddcbadbaccabdedbaccabdeeeeeeeeecbaddabceeabcddcbaeedbaccabdecbaddabcdbaccabdabcddcbaeecbaddabccbaddabceeeeeeeeedbaccabdabcddcba'' ''abcddcbadbaccabdecbaddabceeeeeeeeeeeeabcddcbaedbaccabdcbaddabcecbaddabcabcddcbaedbaccabdeecbaddabcdbaccabdcbaddabceabcddcbaeeeeedbaccabdeabcddcbaeeeeeeeeeedbaccabdeabcddcbaeeeeedbaccabdecbaddabcabcddcbacbaddabceeabcddcbaedbaccabdcbaddabcecbaddabcabcddcbaedbaccabdeeeeeeeeeeeecbaddabceabcddcbadbaccabd'' ''abcddcbadbaccabdecbaddabceeeeeeeeeeeeabcddcbaedbaccabdcbaddabcecbaddabcdbaccabdeabcddcbaeecbaddabcdbaccabdcbaddabceabcddcbaeeeeeabcddcbaedbaccabdeeeeeeeeeeabcddcbaedbaccabdeeeeedbaccabdecbaddabcabcddcbacbaddabceedbaccabdeabcddcbacbaddabcecbaddabcabcddcbaedbaccabdeeeeeeeeeeeecbaddabceabcddcbadbaccabd'' ''abcddcbadbaccabdecbaddabceeeeeeeeeeeedbaccabdeabcddcbacbaddabcecbaddabcabcddcbaedbaccabdeecbaddabcdbaccabdcbaddabceabcddcbaeeeeeabcddcbaedbaccabdeeeeeeeeeeabcddcbaedbaccabdeeeeedbaccabdecbaddabcabcddcbacbaddabceeabcddcbaedbaccabdcbaddabcecbaddabcdbaccabdeabcddcbaeeeeeeeeeeeecbaddabceabcddcbadbaccabd'' ''abcddcbadbaccabdeecbaddabceeeeeeeeeecbaddabceabcddcbaeedbaccabdcbaddabcabcddcbaedbaccabdedbaccabdcbaddabceeedbaccabdeeabcddcbacbaddabcabcddcbaeeeeeeeeeeeeeeeeabcddcbadbaccabdabcddcbaeecbaddabceeedbaccabdcbaddabcecbaddabceabcddcbadbaccabdcbaddabceeabcddcbaedbaccabdeeeeeeeeeedbaccabdeecbaddabcabcddcba'' ''abcddcbadbaccabdeeedbaccabdeeeeeeeeecbaddabccbaddabceabcddcbaeecbaddabceabcddcbaedbaccabdedbaccabdcbaddabceeabcddcbacbaddabceabcddcbacbaddabceeeeeeeeeeeeeeeeeedbaccabdabcddcbaedbaccabdabcddcbaeedbaccabdcbaddabcecbaddabceabcddcbaedbaccabdeeabcddcbaedbaccabddbaccabdeeeeeeeeecbaddabceeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeabcddcbaeeecbaddabceeeeeedbaccabdcbaddabcedbaccabdabcddcbacbaddabceeecbaddabccbaddabcdbaccabdeeeeeabcddcbaeedbaccabdeeeeeabcddcbacbaddabceeeeedbaccabdeecbaddabceeeeedbaccabdabcddcbaabcddcbaeeeabcddcbacbaddabcdbaccabdeabcddcbadbaccabdeeeeeeabcddcbaeeecbaddabceeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeecbaddabceeeeabcddcbaeeeeecbaddabcdbaccabddbaccabdabcddcbacbaddabcecbaddabceeeedbaccabdeeabcddcbaeeeeeedbaccabdcbaddabceecbaddabceeabcddcbaeeabcddcbadbaccabdeeeeeecbaddabceedbaccabdeeeeabcddcbaeabcddcbacbaddabcdbaccabddbaccabdabcddcbaeeeeecbaddabceeeeabcddcbaeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeecbaddabceeeeeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabccbaddabceabcddcbaeeeeeeeeedbaccabdabcddcbaeeeedbaccabdabcddcbaeeabcddcbaeecbaddabceecbaddabcdbaccabdeeeecbaddabcdbaccabdeeeeeeeeecbaddabceabcddcbaabcddcbadbaccabddbaccabdabcddcbaeecbaddabceeeeeeabcddcbaeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeecbaddabceeeeeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabccbaddabceabcddcbaeeeeeeeeedbaccabdabcddcbaeeeedbaccabdabcddcbaeeabcddcbaeecbaddabceecbaddabcdbaccabdeeeecbaddabcdbaccabdeeeeeeeeecbaddabceabcddcbadbaccabdabcddcbaabcddcbadbaccabdeecbaddabceeeeeeabcddcbaeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeecbaddabceeeeeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabdcbaddabceabcddcbaeeeeeeeeedbaccabdabcddcbaeeeedbaccabdabcddcbaeeabcddcbaeecbaddabceecbaddabcdbaccabdeeeecbaddabcdbaccabdeeeeeeeeecbaddabceabcddcbaabcddcbadbaccabddbaccabdabcddcbaeecbaddabceeeeeeabcddcbaeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeecbaddabceeeeeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabdcbaddabceabcddcbaeeeeeeeeedbaccabdabcddcbaeeeedbaccabdabcddcbaeeabcddcbaeecbaddabceecbaddabcdbaccabdeeeecbaddabcdbaccabdeeeeeeeeecbaddabceabcddcbadbaccabdabcddcbaabcddcbadbaccabdeecbaddabceeeeeeabcddcbaeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeecbaddabceeeeeecbaddabceabcddcbaedbaccabddbaccabdecbaddabceeabcddcbacbaddabceeeedbaccabdabcddcbaeeeeeedbaccabdcbaddabceeeeabcddcbaabcddcbaeeeedbaccabdcbaddabceeeeeeabcddcbacbaddabceeeedbaccabdabcddcbaeedbaccabdecbaddabccbaddabceabcddcbaedbaccabdeeeeeedbaccabdeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeedbaccabdeeedbaccabdeeeeeeabcddcbacbaddabcecbaddabccbaddabcabcddcbaeeecbaddabccbaddabcabcddcbaeeeeecbaddabceeabcddcbaeeeeedbaccabdcbaddabceeeeeabcddcbaeedbaccabdeeeeeabcddcbadbaccabddbaccabdeeeabcddcbadbaccabddbaccabdedbaccabdabcddcbaeeeeeecbaddabceeecbaddabceeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeabcddcbacbaddabceeeeeeeedbaccabddbaccabdeecbaddabccbaddabcabcddcbaecbaddabcabcddcbaeeecbaddabcdbaccabdeeeecbaddabceeeeeedbaccabddbaccabdeeeeeeabcddcbaeeeedbaccabdabcddcbaeeecbaddabcabcddcbaecbaddabcabcddcbaabcddcbaeedbaccabddbaccabdeeeeeeeeabcddcbacbaddabceeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeeecbaddabcabcddcbaeeeeeeeedbaccabddbaccabdeecbaddabcabcddcbacbaddabcecbaddabcabcddcbaeeecbaddabcdbaccabdeeeecbaddabceeeeeedbaccabddbaccabdeeeeeeabcddcbaeeeedbaccabdabcddcbaeeecbaddabcabcddcbaeabcddcbacbaddabcabcddcbaeedbaccabddbaccabdeeeeeeeecbaddabcabcddcbaeeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeeecbaddabcabcddcbaeeeeeeeedbaccabddbaccabdeecbaddabccbaddabcabcddcbaeabcddcbacbaddabceeecbaddabcdbaccabdeeeecbaddabceeeeeedbaccabddbaccabdeeeeeeabcddcbaeeeedbaccabdabcddcbaeeeabcddcbacbaddabcecbaddabcabcddcbaabcddcbaeedbaccabddbaccabdeeeeeeeecbaddabcabcddcbaeeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeeecbaddabcecbaddabceeeeeeedbaccabdcbaddabcabcddcbaeabcddcbaedbaccabdedbaccabdeabcddcbaecbaddabceeeeeeabcddcbadbaccabdecbaddabceeeeeeeedbaccabdecbaddabcabcddcbaeeeeeedbaccabdeabcddcbaecbaddabcecbaddabceabcddcbaeabcddcbadbaccabdcbaddabceeeeeeedbaccabdedbaccabdeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeecbaddabcedbaccabdeeeeeeedbaccabdcbaddabcabcddcbaeabcddcbaecbaddabcecbaddabceabcddcbaecbaddabceeeeeeabcddcbadbaccabdedbaccabdeeeeeeeecbaddabcecbaddabcabcddcbaeeeeeedbaccabdeabcddcbaedbaccabdedbaccabdeabcddcbaeabcddcbadbaccabdcbaddabceeeeeeecbaddabcedbaccabdeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeecbaddabceecbaddabceeeeabcddcbaedbaccabdeecbaddabceedbaccabddbaccabdabcddcbaeabcddcbacbaddabceeeeeabcddcbacbaddabceeeedbaccabdeeeeeedbaccabdeeeeabcddcbacbaddabceeeeeabcddcbacbaddabcecbaddabcdbaccabddbaccabdeeabcddcbaeedbaccabdecbaddabceeeeabcddcbaeeabcddcbaeeeeeedbaccabdcbaddabc'' ''abcddcbadbaccabdeeeeeecbaddabceeeecbaddabceeabcddcbadbaccabdeedbaccabdcbaddabceabcddcbaecbaddabceeeedbaccabdeeabcddcbaeeeedbaccabdcbaddabceeeabcddcbaeeabcddcbaeeedbaccabdcbaddabceeeeabcddcbaeecbaddabceeeedbaccabdeabcddcbaedbaccabdcbaddabceecbaddabcabcddcbaeedbaccabdeeeedbaccabdeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeedbaccabdeeeecbaddabceeabcddcbacbaddabceedbaccabdcbaddabceabcddcbaecbaddabceeeecbaddabceeabcddcbaeeeedbaccabddbaccabdeeeabcddcbaeeabcddcbaeeecbaddabccbaddabceeeeabcddcbaeedbaccabdeeeedbaccabdeabcddcbaedbaccabdcbaddabceedbaccabdabcddcbaeedbaccabdeeeecbaddabceeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeedbaccabdeeeecbaddabceeabcddcbadbaccabdecbaddabcecbaddabceeecbaddabceabcddcbaabcddcbaeecbaddabceeeeeedbaccabdabcddcbaeeeecbaddabcdbaccabdeeeeabcddcbacbaddabceeeeeedbaccabdeeabcddcbaabcddcbaedbaccabdeeedbaccabdedbaccabdecbaddabcabcddcbaeedbaccabdeeeecbaddabceeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeabcddcbaecbaddabcdbaccabdeeecbaddabceeecbaddabcdbaccabdedbaccabdcbaddabceecbaddabceeabcddcbaeeeeeeeeabcddcbaeedbaccabdabcddcbaabcddcbacbaddabceeabcddcbaeeeeeeeeabcddcbaeedbaccabdeedbaccabdcbaddabcecbaddabcdbaccabdeeedbaccabdeeecbaddabcdbaccabdeabcddcbaeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeabcddcbaecbaddabcdbaccabdeeecbaddabceeedbaccabdcbaddabcecbaddabcdbaccabdeecbaddabceeabcddcbaeeeeeeeeabcddcbaeedbaccabdabcddcbaabcddcbacbaddabceeabcddcbaeeeeeeeeabcddcbaeedbaccabdeecbaddabcdbaccabdedbaccabdcbaddabceeedbaccabdeeecbaddabcdbaccabdeabcddcbaeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeabcddcbaecbaddabcdbaccabdeeecbaddabceeedbaccabdcbaddabcedbaccabdcbaddabceecbaddabceeabcddcbaeeeeeeeeabcddcbaeeabcddcbacbaddabcdbaccabdabcddcbaeeabcddcbaeeeeeeeeabcddcbaeedbaccabdeedbaccabdcbaddabcedbaccabdcbaddabceeedbaccabdeeecbaddabcdbaccabdeabcddcbaeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeabcddcbaedbaccabdcbaddabceeecbaddabceeecbaddabcdbaccabdecbaddabcdbaccabdeecbaddabceeabcddcbaeeeeeeeeabcddcbaeedbaccabdabcddcbaabcddcbacbaddabceeabcddcbaeeeeeeeeabcddcbaeedbaccabdeecbaddabcdbaccabdecbaddabcdbaccabdeeedbaccabdeeedbaccabdcbaddabceabcddcbaeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeabcddcbaedbaccabdcbaddabceeecbaddabceeecbaddabcdbaccabdedbaccabdcbaddabceecbaddabceeabcddcbaeeeeeeeeabcddcbaeeabcddcbacbaddabcdbaccabdabcddcbaeeabcddcbaeeeeeeeeabcddcbaeedbaccabdeedbaccabdcbaddabcecbaddabcdbaccabdeeedbaccabdeeedbaccabdcbaddabceabcddcbaeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeabcddcbaedbaccabdcbaddabceeecbaddabceeedbaccabdcbaddabcecbaddabcdbaccabdeecbaddabceeabcddcbaeeeeeeeeabcddcbaeeabcddcbacbaddabcdbaccabdabcddcbaeeabcddcbaeeeeeeeeabcddcbaeedbaccabdeecbaddabcdbaccabdedbaccabdcbaddabceeedbaccabdeeedbaccabdcbaddabceabcddcbaeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeecbaddabcedbaccabdeedbaccabdabcddcbacbaddabceecbaddabceeeeeeabcddcbaeecbaddabcabcddcbacbaddabcabcddcbaeeedbaccabdeeeeeedbaccabdcbaddabceeeeeecbaddabceeeabcddcbadbaccabdabcddcbadbaccabdeeabcddcbaeeeeeedbaccabdeedbaccabdabcddcbacbaddabceecbaddabcedbaccabdeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeedbaccabdabcddcbaeeeecbaddabccbaddabccbaddabceecbaddabcedbaccabdeeeeabcddcbadbaccabdecbaddabceeeeeeeedbaccabdeabcddcbaeabcddcbaabcddcbaeabcddcbaecbaddabceeeeeeeedbaccabdecbaddabcabcddcbaeeeecbaddabcedbaccabdeedbaccabddbaccabddbaccabdeeeeabcddcbacbaddabceeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeedbaccabdabcddcbaeeeecbaddabccbaddabccbaddabceedbaccabdecbaddabceeeeabcddcbacbaddabcedbaccabdeeeeeeeedbaccabdeabcddcbaeabcddcbaabcddcbaeabcddcbaecbaddabceeeeeeeecbaddabcedbaccabdabcddcbaeeeedbaccabdecbaddabceedbaccabddbaccabddbaccabdeeeeabcddcbacbaddabceeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeedbaccabdecbaddabcdbaccabdeeeabcddcbaeecbaddabccbaddabceeeeabcddcbaabcddcbaeecbaddabceecbaddabccbaddabceedbaccabdeeeeeeabcddcbaabcddcbaeeeeeecbaddabceedbaccabddbaccabdeedbaccabdeeabcddcbaabcddcbaeeeedbaccabddbaccabdeeabcddcbaeeecbaddabcdbaccabdecbaddabceeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeecbaddabccbaddabcedbaccabdeabcddcbacbaddabceeeeabcddcbadbaccabdcbaddabceeeeeeeedbaccabdeeabcddcbaeedbaccabdabcddcbaeedbaccabdeecbaddabceeabcddcbacbaddabceeabcddcbaeecbaddabceeeeeeeedbaccabdcbaddabcabcddcbaeeeedbaccabdabcddcbaecbaddabcedbaccabddbaccabdeeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeecbaddabccbaddabceeabcddcbadbaccabdcbaddabcedbaccabdeeabcddcbaeecbaddabceeeeeeeeedbaccabdedbaccabdabcddcbaeeeabcddcbacbaddabceedbaccabdabcddcbaeeeabcddcbacbaddabcecbaddabceeeeeeeeedbaccabdeeabcddcbaeecbaddabcedbaccabdcbaddabcabcddcbaeedbaccabddbaccabdeeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeecbaddabcdbaccabdeeabcddcbacbaddabcdbaccabdecbaddabceeabcddcbaeecbaddabceeeeeeeeedbaccabdecbaddabcabcddcbaeeeabcddcbadbaccabdeecbaddabcabcddcbaeeeabcddcbadbaccabdecbaddabceeeeeeeeedbaccabdeeabcddcbaeedbaccabdecbaddabcdbaccabdabcddcbaeecbaddabcdbaccabdeeeeeeeeecbaddabcabcddcba'' ''abcddcbadbaccabdeeeeeeeeedbaccabdecbaddabccbaddabcabcddcbadbaccabdecbaddabceeeeeeeeabcddcbacbaddabceeeabcddcbaeeeabcddcbadbaccabdecbaddabceecbaddabceeeedbaccabdeedbaccabdecbaddabcabcddcbaeeeabcddcbaeeedbaccabdabcddcbaeeeeeeeedbaccabdecbaddabcabcddcbadbaccabddbaccabdecbaddabceeeeeeeeecbaddabcabcddcba'' ''abcddcbaecbaddabcdbaccabdeeeeeeeeeeeedbaccabdcbaddabccbaddabcabcddcbaeeedbaccabdeabcddcbaeabcddcbadbaccabdecbaddabceeeabcddcbaedbaccabdeecbaddabceeeeeeeeeedbaccabdeecbaddabceabcddcbaeeedbaccabdecbaddabcabcddcbaeabcddcbaecbaddabceeeabcddcbadbaccabddbaccabdcbaddabceeeeeeeeeeeecbaddabcdbaccabdeabcddcba'' ''abcddcbaecbaddabcdbaccabdeeeeeeeeeeeedbaccabdcbaddabcdbaccabdabcddcbaeeecbaddabceabcddcbaeabcddcbacbaddabcedbaccabdeeeabcddcbaecbaddabceedbaccabdeeeeeeeeeecbaddabceedbaccabdeabcddcbaeeecbaddabcedbaccabdabcddcbaeabcddcbaedbaccabdeeeabcddcbacbaddabcdbaccabdcbaddabceeeeeeeeeeeecbaddabcdbaccabdeabcddcba'' ''abcddcbaecbaddabcedbaccabdeeeeeeeeeeabcddcbacbaddabceedbaccabddbaccabdecbaddabcabcddcbaeeedbaccabdeecbaddabcdbaccabdeeabcddcbaecbaddabceabcddcbaeeeeeeeeeeeeabcddcbaecbaddabcedbaccabdeeabcddcbacbaddabceedbaccabdeeecbaddabcabcddcbaedbaccabdabcddcbaeedbaccabdcbaddabceeeeeeeeeedbaccabdecbaddabceabcddcba'' 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''abcddcbaecbaddabceeeeedbaccabddbaccabdeeeeeeecbaddabcabcddcbaeabcddcbaeeedbaccabdcbaddabcdbaccabdcbaddabceeeecbaddabceeabcddcbadbaccabdeeeeeeeabcddcbaabcddcbaeeeeeeecbaddabcabcddcbaeedbaccabdeeeedbaccabdcbaddabcdbaccabdcbaddabceeeabcddcbaeabcddcbadbaccabdeeeeeeecbaddabccbaddabceeeeedbaccabdeabcddcba'' ''abcddcbaecbaddabceeeeedbaccabdecbaddabceeeecbaddabceeabcddcbaeeedbaccabddbaccabdeabcddcbadbaccabdeabcddcbadbaccabdeeeeeeabcddcbaeecbaddabceecbaddabceeeedbaccabdeedbaccabdeeabcddcbaeeeeeecbaddabcabcddcbaecbaddabcabcddcbaecbaddabccbaddabceeeabcddcbaeedbaccabdeeeedbaccabdecbaddabceeeeedbaccabdeabcddcba'' ''abcddcbaecbaddabceeeeedbaccabdedbaccabdeeeecbaddabceeabcddcbaeeedbaccabdcbaddabceabcddcbacbaddabceabcddcbadbaccabdeeeeeeabcddcbaeedbaccabdeecbaddabceeeedbaccabdeecbaddabceeabcddcbaeeeeeecbaddabcabcddcbaedbaccabdabcddcbaedbaccabdcbaddabceeeabcddcbaeedbaccabdeeeecbaddabcecbaddabceeeeedbaccabdeabcddcba'' 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''abcddcbaecbaddabceeeeeedbaccabdcbaddabceeeecbaddabcdbaccabdeeeeeabcddcbadbaccabdabcddcbaabcddcbaeedbaccabdeeeeabcddcbaeeeedbaccabdcbaddabcedbaccabdeeeeeecbaddabcedbaccabdcbaddabceeeeabcddcbaeeeecbaddabceeabcddcbaabcddcbacbaddabcabcddcbaeeeeecbaddabcdbaccabdeeeedbaccabdcbaddabceeeeeedbaccabdeabcddcba'' ''abcddcbaecbaddabceeeeeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeabcddcbadbaccabdabcddcbaabcddcbaeedbaccabdeeeeabcddcbaeeeecbaddabcdbaccabdedbaccabdeeeeeecbaddabcecbaddabcdbaccabdeeeeabcddcbaeeeecbaddabceeabcddcbaabcddcbacbaddabcabcddcbaeeeeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeedbaccabdeabcddcba'' ''abcddcbaecbaddabceeeeeedbaccabddbaccabdeeeeabcddcbaecbaddabceeecbaddabcdbaccabdeabcddcbadbaccabdeeeecbaddabceeeabcddcbacbaddabceeedbaccabdeeeeabcddcbaabcddcbaeeeecbaddabceeedbaccabdabcddcbaeeedbaccabdeeeecbaddabcabcddcbaecbaddabcdbaccabdeeedbaccabdeabcddcbaeeeecbaddabccbaddabceeeeeedbaccabdeabcddcba'' 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''abcddcbaecbaddabceeeeeedbaccabdeedbaccabdecbaddabceeeabcddcbacbaddabcdbaccabdabcddcbadbaccabdeeeeeeeeeeeeabcddcbaecbaddabceabcddcbaecbaddabceedbaccabddbaccabdeeabcddcbaecbaddabceabcddcbaecbaddabceeeeeeeeeeeedbaccabdcbaddabcdbaccabdabcddcbacbaddabceeeabcddcbaedbaccabdeedbaccabdeeeeeeabcddcbaecbaddabc'' ''abcddcbaecbaddabceeeeeeeabcddcbacbaddabcedbaccabddbaccabdeeeeeeedbaccabdcbaddabcedbaccabddbaccabdeeabcddcbaeeeeabcddcbaeecbaddabcabcddcbaeecbaddabceeeeeecbaddabceecbaddabcabcddcbaeedbaccabdeeeedbaccabdeeabcddcbaabcddcbaeabcddcbadbaccabdeeeeeeecbaddabcdbaccabdecbaddabccbaddabceeeeeeedbaccabdeabcddcba'' ''abcddcbaecbaddabceeeeeeecbaddabcdbaccabdedbaccabdeeeabcddcbaedbaccabddbaccabdeeeeeabcddcbaabcddcbaeecbaddabceeecbaddabceecbaddabcecbaddabceeeeabcddcbaabcddcbaeeeedbaccabdedbaccabdeedbaccabdeeedbaccabdeeabcddcbaabcddcbaeeeeecbaddabccbaddabceabcddcbaeeecbaddabcecbaddabcdbaccabdeeeeeeedbaccabdeabcddcba'' ''abcddcbaecbaddabceeeeeeedbaccabdcbaddabcecbaddabceeeabcddcbaedbaccabddbaccabdeeeeeabcddcbaabcddcbaeedbaccabdeeedbaccabdeecbaddabcedbaccabdeeeeabcddcbaabcddcbaeeeecbaddabcedbaccabdeecbaddabceeecbaddabceeabcddcbaabcddcbaeeeeecbaddabccbaddabceabcddcbaeeedbaccabdedbaccabdcbaddabceeeeeeedbaccabdeabcddcba'' ''abcddcbaecbaddabceeeeeeedbaccabddbaccabdecbaddabcdbaccabdeeeeeeecbaddabcabcddcbaeabcddcbaabcddcbaeecbaddabceeeecbaddabceeabcddcbadbaccabdeedbaccabdeeeeeedbaccabdeeabcddcbadbaccabdeeabcddcbaeeeeabcddcbaeecbaddabccbaddabcedbaccabdcbaddabceeeeeeecbaddabccbaddabcedbaccabdabcddcbaeeeeeeedbaccabdeabcddcba'' ''abcddcbaecbaddabceeeeeeedbaccabdecbaddabcdbaccabdedbaccabdeeeabcddcbaeecbaddabcdbaccabdeeeabcddcbaeeeeabcddcbaabcddcbaeeeeeabcddcbacbaddabceeecbaddabccbaddabceeecbaddabcdbaccabdeeeeedbaccabddbaccabdeeeedbaccabdeeeabcddcbacbaddabceedbaccabdeeeabcddcbaeabcddcbacbaddabceabcddcbaeeeeeeecbaddabcedbaccabd'' 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''abcddcbaeedbaccabdeeecbaddabceeabcddcbaeeeeecbaddabcdbaccabdeeecbaddabcabcddcbaedbaccabdeeedbaccabddbaccabdecbaddabceeeeabcddcbacbaddabceeeeeeabcddcbacbaddabceeeeeeabcddcbacbaddabceeeeabcddcbaedbaccabddbaccabdeeedbaccabdecbaddabcabcddcbaeeedbaccabdabcddcbaeeeeecbaddabceeabcddcbaeeedbaccabdeecbaddabc'' ''abcddcbaeedbaccabdeeecbaddabceeeeedbaccabdabcddcbaecbaddabcecbaddabceeeeabcddcbadbaccabdeeabcddcbaedbaccabdeeeeecbaddabcecbaddabceecbaddabcdbaccabdeeeeeedbaccabdabcddcbaeeabcddcbaeabcddcbaeeeeedbaccabdecbaddabceedbaccabdcbaddabceeeeabcddcbaeabcddcbaecbaddabcdbaccabdeeeeeabcddcbaeeedbaccabdeecbaddabc'' ''abcddcbaeedbaccabdeeecbaddabceeeeedbaccabdabcddcbaecbaddabcecbaddabceeeecbaddabcdbaccabdeeabcddcbaedbaccabdeeeeeabcddcbaeabcddcbaeeabcddcbadbaccabdeeeeeedbaccabdcbaddabceecbaddabcecbaddabceeeeedbaccabdecbaddabceedbaccabdabcddcbaeeeeabcddcbaeabcddcbaecbaddabcdbaccabdeeeeeabcddcbaeeedbaccabdeecbaddabc'' 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''abcddcbaeeedbaccabdedbaccabdeeecbaddabceeeeeabcddcbacbaddabceedbaccabdabcddcbaeeeecbaddabcecbaddabcdbaccabdcbaddabceeeeeecbaddabceabcddcbaeeeeabcddcbaabcddcbaeeeeabcddcbaedbaccabdeeeeeedbaccabdcbaddabcdbaccabdedbaccabdeeeeabcddcbacbaddabceedbaccabdabcddcbaeeeeedbaccabdeeecbaddabcecbaddabceeeabcddcba'' ''abcddcbaeeedbaccabdedbaccabdeeeeeabcddcbacbaddabceeeecbaddabcecbaddabccbaddabcedbaccabdeeeeedbaccabdeabcddcbaabcddcbaecbaddabceeeeeeeabcddcbaedbaccabdcbaddabceabcddcbaeeeeeeedbaccabdeabcddcbaabcddcbaecbaddabceeeeecbaddabcedbaccabddbaccabdedbaccabdeeeedbaccabdabcddcbaeeeeecbaddabcecbaddabceeeabcddcba'' ''abcddcbaeeedbaccabdedbaccabdeeeeeabcddcbacbaddabceeeedbaccabdecbaddabccbaddabcecbaddabceeeeecbaddabceabcddcbaabcddcbaedbaccabdeeeeeeeabcddcbaedbaccabdcbaddabceabcddcbaeeeeeeecbaddabceabcddcbaabcddcbaedbaccabdeeeeedbaccabdedbaccabddbaccabdecbaddabceeeedbaccabdabcddcbaeeeeecbaddabcecbaddabceeeabcddcba'' 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''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcabcddcbacbaddabcdbaccabddbaccabdabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaedbaccabdabcddcbacbaddabcabcddcbacbaddabcdbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' ''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcabcddcbadbaccabdcbaddabcdbaccabdabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbacbaddabcdbaccabdcbaddabcabcddcbadbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' ''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcabcddcbadbaccabdcbaddabcdbaccabdabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaecbaddabcabcddcbadbaccabdabcddcbacbaddabcdbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' ''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcdbaccabdabcddcbacbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbacbaddabcdbaccabdcbaddabcabcddcbadbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' ''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcdbaccabdabcddcbacbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbaecbaddabcabcddcbadbaccabdabcddcbacbaddabcdbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' ''eeeabcddcbaedbaccabdcbaddabcecbaddabcabcddcbaeeeedbaccabdeeeeeedbaccabdecbaddabceeabcddcbadbaccabdeeeeeeecbaddabcabcddcbaecbaddabcabcddcbaeeeabcddcbaeedbaccabdeeedbaccabdcbaddabcedbaccabdcbaddabceeeeeeeabcddcbadbaccabdeecbaddabceabcddcbaeeeeeeabcddcbaeeeedbaccabdcbaddabcecbaddabcabcddcbaedbaccabdeee'' ''eeeabcddcbaedbaccabdcbaddabcecbaddabcdbaccabdeabcddcbaeeeeeeeeeeeabcddcbaeecbaddabcdbaccabdedbaccabdeabcddcbacbaddabceeeeedbaccabdeecbaddabceecbaddabcabcddcbaeeabcddcbaeedbaccabdeeeeeabcddcbacbaddabcedbaccabdedbaccabdabcddcbaeecbaddabceeeeeeeeeeecbaddabcedbaccabdabcddcbaeabcddcbadbaccabdecbaddabceee'' ''eeeabcddcbaedbaccabdcbaddabcecbaddabcdbaccabdeabcddcbaeeeeeeeeeeecbaddabceeabcddcbadbaccabdedbaccabdecbaddabcabcddcbaeeeeedbaccabdeeabcddcbaeeabcddcbacbaddabceecbaddabceedbaccabdeeeeecbaddabcabcddcbaedbaccabdedbaccabdcbaddabceeabcddcbaeeeeeeeeeeecbaddabcedbaccabdabcddcbaeabcddcbadbaccabdecbaddabceee'' ''eeeabcddcbaedbaccabdcbaddabcecbaddabceabcddcbaeedbaccabdeeeeeeecbaddabcabcddcbaeeedbaccabdedbaccabdeeeeeabcddcbaeedbaccabdcbaddabceabcddcbaeeecbaddabccbaddabceeedbaccabdecbaddabcabcddcbaeedbaccabdeeeeeabcddcbaeabcddcbaeeedbaccabdcbaddabceeeeeeeabcddcbaeedbaccabdecbaddabcecbaddabcabcddcbaedbaccabdeee'' ''eeeabcddcbaedbaccabdcbaddabceeabcddcbadbaccabdeeecbaddabceeecbaddabcabcddcbaeeeeeeeedbaccabddbaccabdeeeedbaccabdecbaddabceeeeabcddcbaecbaddabccbaddabcabcddcbaabcddcbaecbaddabceeeeabcddcbaedbaccabdeeeedbaccabddbaccabdeeeeeeeecbaddabcabcddcbaeeeabcddcbaeeedbaccabdcbaddabceeabcddcbadbaccabdecbaddabceee'' ''eeeabcddcbaedbaccabdcbaddabceecbaddabcabcddcbadbaccabdeeeeeeeabcddcbaeeecbaddabceeeeedbaccabddbaccabdeecbaddabceeabcddcbacbaddabcdbaccabdeeeeedbaccabdabcddcbaeeeeeabcddcbacbaddabcdbaccabdeecbaddabceeabcddcbaabcddcbaeeeeecbaddabceeedbaccabdeeeeeeeabcddcbadbaccabdcbaddabceecbaddabcabcddcbaedbaccabdeee'' ''eeeabcddcbaedbaccabddbaccabdcbaddabceeeecbaddabcabcddcbaeeeeeabcddcbaedbaccabdeeeeeecbaddabceedbaccabdecbaddabcecbaddabcecbaddabceeabcddcbaeeabcddcbaeeabcddcbaeeabcddcbaeedbaccabdedbaccabdedbaccabdecbaddabceedbaccabdeeeeeecbaddabceabcddcbaeeeeeabcddcbadbaccabdeeeedbaccabdcbaddabccbaddabceabcddcbaeee'' ''eeeeabcddcbacbaddabcabcddcbadbaccabdeecbaddabcedbaccabdeeeeeabcddcbaeeecbaddabceeeeeedbaccabddbaccabdeeecbaddabceedbaccabdecbaddabcabcddcbaedbaccabdeeeeabcddcbaedbaccabdcbaddabceabcddcbaeecbaddabceeeabcddcbaabcddcbaeeeeeecbaddabceeedbaccabdeeeeeabcddcbaecbaddabceeabcddcbadbaccabdcbaddabcdbaccabdeeee'' ''eeeeabcddcbacbaddabcdbaccabdedbaccabdabcddcbaecbaddabceeeeeeabcddcbaeeeedbaccabdeeeeecbaddabccbaddabceeeedbaccabdeabcddcbadbaccabdcbaddabceeecbaddabceeabcddcbaeeeabcddcbadbaccabdcbaddabcedbaccabdeeeeabcddcbaabcddcbaeeeeedbaccabdeeeecbaddabceeeeeeabcddcbaecbaddabcdbaccabdedbaccabdabcddcbacbaddabceeee'' ''eeeeabcddcbacbaddabcedbaccabdcbaddabcdbaccabdabcddcbaeeeeeecbaddabceeeeabcddcbaeeeeedbaccabdedbaccabdeeeeeabcddcbaeecbaddabcabcddcbadbaccabdedbaccabdeecbaddabcecbaddabcabcddcbadbaccabdeeabcddcbaeeeeecbaddabcecbaddabceeeeeabcddcbaeeeedbaccabdeeeeeeabcddcbacbaddabcdbaccabdcbaddabcedbaccabdabcddcbaeeee'' ''eeeeabcddcbadbaccabdabcddcbacbaddabceedbaccabdecbaddabceeeeeabcddcbaeeedbaccabdeeeeeecbaddabccbaddabceeedbaccabdeecbaddabcedbaccabdabcddcbaecbaddabceeeeabcddcbaecbaddabcdbaccabdeabcddcbaeedbaccabdeeeabcddcbaabcddcbaeeeeeedbaccabdeeecbaddabceeeeeabcddcbaedbaccabdeeabcddcbacbaddabcdbaccabdcbaddabceeee'' ''eeeeabcddcbadbaccabdcbaddabcecbaddabcabcddcbaedbaccabdeeeeeeabcddcbaeeeecbaddabceeeeedbaccabddbaccabdeeeecbaddabceabcddcbacbaddabcdbaccabdeeedbaccabdeeabcddcbaeeeabcddcbacbaddabcdbaccabdecbaddabceeeeabcddcbaabcddcbaeeeeecbaddabceeeedbaccabdeeeeeeabcddcbaedbaccabdcbaddabcecbaddabcabcddcbadbaccabdeeee'' ''eeeeabcddcbadbaccabdecbaddabcdbaccabdcbaddabcabcddcbaeeeeeedbaccabdeeeeabcddcbaeeeeecbaddabcecbaddabceeeeeabcddcbaeedbaccabdabcddcbacbaddabcecbaddabceedbaccabdedbaccabdabcddcbacbaddabceeabcddcbaeeeeedbaccabdedbaccabdeeeeeabcddcbaeeeecbaddabceeeeeeabcddcbadbaccabdcbaddabcdbaccabdecbaddabcabcddcbaeeee'' Some of these configurations were found using the high performance computing cluster at the Alabama Supercompter Authority (this work was made possible in part by a grant of high performance computing resources and technical support from the Alabama Supercomputer Authority).