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5d60 [2023/09/18 01:43]
paulmeyer
5d60 [2024/09/12 18:40] (current)
paulmeyer
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-This page contains all of the unique permutation-fair 5d60 configurations of Go First Dice that have been discovered so far. Die-wise permutations and trivial substitutions (e.g. "abba" -> "baab") are pruned for conciseness.+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 4d30. The induced die is represented by 'e' in the following solutions.+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.
  
  
-''abcddcbacbaddabceeeeedbaccabdeeeeeedbaccabdeabdccdbaecbdaadbccbdaadbcedbcaacbdeeabcddcbadbcaacbdeeeecbdaadbcabdccdbaeeeeeecbdaadbcdbcaacbdeeeeabcddcbaabcddcbaeeeecbaddabcdbaccabdeeeeeeabdccdbadbaccabdeeeecbaddabcabcddcbaeecbaddabcedbaccabddbaccabdeabdccdbaecbdaadbceeeeeecbdaadbceeeeedbcaacbdabcddcba''+''abcddcbacbaddabcedbaccabdeeeeeeeeeeeeabcddcbaecbaddabcdbaccabdedbaccabdabcddcbaecbaddabceedbaccabdcbaddabcdbaccabdeabcddcbaeeeeecbaddabceabcddcbaeeeeeeeeeecbaddabceabcddcbaeeeeecbaddabcedbaccabdabcddcbadbaccabdeeabcddcbaecbaddabcdbaccabdedbaccabdabcddcbaecbaddabceeeeeeeeeeeedbaccabdeabcddcbacbaddabc''
  
-''abcddcbacbaddabceeeeeedbaccabdeeeedbaccabdeeabdccdbacbdaadbceecbdaadbcdbcaacbdeabcddcbaedbcaacbdeeeecbdaadbceeabdccdbaeeeecbdaadbcdbcaacbdeeeabcddcbaeeabcddcbaeeecbaddabcdbaccabdeeeeabdccdbaeedbaccabdeeeecbaddabceabcddcbaecbaddabcdbaccabdeedbaccabdabdccdbaeecbdaadbceeeecbdaadbceeeeeedbcaacbdabcddcba''+''abcddcbacbaddabcedbaccabdeeeeeeeeeeeeabcddcbaecbaddabcdbaccabdedbaccabdcbaddabceabcddcbaeedbaccabdcbaddabcdbaccabdeabcddcbaeeeeeabcddcbaecbaddabceeeeeeeeeeabcddcbaecbaddabceeeeecbaddabcedbaccabdabcddcbadbaccabdeecbaddabceabcddcbadbaccabdedbaccabdabcddcbaecbaddabceeeeeeeeeeeedbaccabdeabcddcbacbaddabc''
  
-''abcddcbaecbaddabcedbaccabdeeeeeeeeeedbaccabdabdccdbaecbdaadbceecbaddabcabcddcbaedbcaacbdeecbdaadbceedbcaacbdabcddcbadbaccabdeeeabdccdbacbdaadbceeeeeeeeeeeeeecbdaadbcdbcaacbdeeeabcddcbadbaccabdabdccdbaeecbdaadbceeabdccdbaedbaccabdcbaddabceecbdaadbcedbcaacbdabcddcbaeeeeeeeeeeabcddcbaecbaddabcedbaccabd''+''abcddcbacbaddabcedbaccabdeeeeeeeeeeeecbaddabceabcddcbadbaccabdedbaccabdabcddcbaecbaddabceedbaccabdcbaddabcdbaccabdeabcddcbaeeeeeabcddcbaecbaddabceeeeeeeeeeabcddcbaecbaddabceeeeecbaddabcedbaccabdabcddcbadbaccabdeeabcddcbaecbaddabcdbaccabdedbaccabdcbaddabceabcddcbaeeeeeeeeeeeedbaccabdeabcddcbacbaddabc''
  
-''abcddcbaecbaddabceeeedbaccabdeeeabcddcbaeeeecbaddabcdbaccabdeeeecbdaadbcdbcaacbdabcddcbaeeedbaccabdabdccdbacbdaadbceedbcaacbdecbdaadbceeeeeeeeabdccdbadbcaacbdeeeeeeeecbdaadbceabdccdbaeecbdaadbcdbcaacbdabcddcbaeeedbaccabdabdccdbacbdaadbceeeeabcddcbacbaddabceeeedbaccabdeeeabcddcbaeeeecbaddabcedbaccabd''+''abcddcbacbaddabceedbaccabdeeeeeeeeeedbaccabdeabcddcbaeecbaddabcdbaccabdabcddcbaecbaddabcecbaddabcdbaccabdeeecbaddabceeabcddcbadbaccabdabcddcbaeeeeeeeeeeeeeeeeabcddcbacbaddabcabcddcbaeedbaccabdeeecbaddabcdbaccabdedbaccabdeabcddcbacbaddabcdbaccabdeeabcddcbaecbaddabceeeeeeeeeecbaddabceedbaccabdabcddcba''
  
-''abcddcbaecbaddabceeeeedbaccabdedbcaacbdeeeecbdaadbceeabdccdbaeeedbcaacbdcbdaadbceabdccdbacbaddabceabcddcbadbcaacbdeeeeeeabdccdbaeedbaccabdeecbaddabceeeedbcaacbdeecbdaadbceeabdccdbaeeeeeecbaddabcabcddcbaedbcaacbdabdccdbaedbaccabdcbaddabceeeabdccdbaeedbaccabdeeeecbaddabcecbdaadbceeeeedbcaacbdeabcddcba''+''abcddcbacbaddabceeecbaddabceeeeeeeeedbaccabddbaccabdeabcddcbaeedbaccabdeabcddcbaecbaddabcecbaddabcdbaccabdeeabcddcbadbaccabdeabcddcbadbaccabdeeeeeeeeeeeeeeeeeecbaddabcabcddcbaecbaddabcabcddcbaeecbaddabcdbaccabdedbaccabdeabcddcbaecbaddabceeabcddcbaecbaddabccbaddabceeeeeeeeedbaccabdeeedbaccabdabcddcba''
  
-''abcddcbaecbaddabceeeeeedbaccabddbaccabdeeeeabdccdbaecbdaadbceeecbdaadbcdbcaacbdeabcddcbadbcaacbdeeeecbdaadbceeeabdccdbacbdaadbceeedbcaacbdeeeeabcddcbaabcddcbaeeeecbaddabceeedbaccabdabdccdbaeeedbaccabdeeeecbaddabcabcddcbaecbaddabcdbaccabdeeedbaccabdeabdccdbaeeeecbdaadbccbdaadbceeeeeedbcaacbdeabcddcba''+''abcddcbacbaddabceeeeeabcddcbaeeedbaccabdeeeeeecbaddabcdbaccabdecbaddabcabcddcbadbaccabdeeedbaccabddbaccabdcbaddabceeeeeabcddcbaeecbaddabceeeeeabcddcbadbaccabdeeeeecbaddabceedbaccabdeeeeecbaddabcabcddcbaabcddcbaeeeabcddcbadbaccabdcbaddabceabcddcbacbaddabceeeeeeabcddcbaeeedbaccabdeeeeecbaddabcdbaccabd''
  
-''abcddcbaecbaddabceeeeeedbaccabdeedbcaacbdecbdaadbceeeabdccdbacbdaadbcdbcaacbdabcddcbadbaccabdeeeeeeeeeeeeabdccdbaecbdaadbceabcddcbaecbaddabceedbaccabddbaccabdeeabdccdbaecbdaadbceabcddcbaecbaddabceeeeeeeeeeeedbaccabdcbdaadbcdbcaacbdabcddcbacbaddabceeeabcddcbaedbcaacbdeedbaccabdeeeeeeabdccdbaecbdaadbc''+''abcddcbacbaddabceeeeecbaddabceeecbaddabceeeeeeabcddcbadbaccabdedbaccabddbaccabdabcddcbaeeedbaccabddbaccabdabcddcbaeeeeedbaccabdeeabcddcbaeeeeecbaddabcdbaccabdeeeeeabcddcbaeecbaddabceeeeeabcddcbacbaddabccbaddabceeeabcddcbacbaddabccbaddabcecbaddabcabcddcbaeeeeeedbaccabdeeedbaccabdeeeeedbaccabdabcddcba''
  
-''abcddcbaeecbaddabcedbaccabdeeeeeeabcddcbaecbaddabceeeeedbaccabdecbdaadbcdbcaacbdabcddcbaedbaccabdeeabdccdbacbdaadbcedbcaacbdeeeeeeecbdaadbcabdccdbaeeeeeedbcaacbdcbdaadbceeeeeeeabdccdbaecbdaadbcdbcaacbdeeabcddcbaedbaccabdabdccdbacbdaadbceabcddcbaeeeeecbaddabcedbaccabdeeeeeeabcddcbaecbaddabceedbaccabd''+''abcddcbacbaddabceeeeedbaccabdeeeeabcddcbaeeeeedbaccabdcbaddabccbaddabcabcddcbadbaccabdedbaccabdeeeecbaddabceeabcddcbaeeeeeecbaddabcdbaccabdeedbaccabdeeabcddcbaeeabcddcbacbaddabceeeeeedbaccabdeecbaddabceeeeabcddcbaeabcddcbadbaccabdcbaddabccbaddabcabcddcbaeeeeedbaccabdeeeeabcddcbaeeeeecbaddabcdbaccabd''
  
-''abcddcbaeecbaddabceedbaccabdeeedbcaacbdeeeeeecbdaadbcabdccdbaeecbdaadbcdbcaacbdeeabcddcbaedbaccabdabdccdbacbdaadbceeeeeeabcddcbaeecbaddabceeeedbaccabdcbdaadbceeeedbcaacbdeeabcddcbaeeeeeedbaccabdabdccdbacbdaadbceabcddcbaeecbaddabcdbaccabdeeabdccdbadbaccabdeeeeeecbaddabceeecbdaadbceedbcaacbdeeabcddcba''+''abcddcbacbaddabceeeeedbaccabdeeeeeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabcdbaccabdeabcddcbaeeeeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeabcddcbaeedbaccabdeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeeeeedbaccabdeabcddcbaabcddcbacbaddabccbaddabcabcddcbaeedbaccabdeeeeeeabcddcbaeeeeecbaddabcdbaccabd''
  
-''abcddcbaeecbaddabceedbaccabdeeeeecbdaadbcedbcaacbdeeeeabcddcbaabdccdbaeedbaccabdcbaddabcedbaccabdeabdccdbaeeeeecbdaadbcecbdaadbcdbcaacbdeabcddcbaeeeeeeeeeedbaccabdeabdccdbacbdaadbcecbdaadbceeeeedbcaacbdeabcddcbaecbaddabcabcddcbaeedbcaacbddbaccabdeeeeabdccdbaecbdaadbceeeeeabcddcbaeecbaddabceedbaccabd''+''abcddcbacbaddabceeeeedbaccabdeeeeeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabcdbaccabdeabcddcbaeeeeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeabcddcbaeedbaccabdeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeeeeedbaccabdeabcddcbacbaddabcabcddcbaabcddcbacbaddabceedbaccabdeeeeeeabcddcbaeeeeecbaddabcdbaccabd''
  
-''abcddcbaeecbaddabceeeedbaccabddbaccabdeeeeeeabdccdbacbdaadbceeecbdaadbcdbcaacbdeabcddcbaedbcaacbdcbdaadbceeeabdccdbaeeeeeeeecbdaadbceedbcaacbdabcddcbaabcddcbacbaddabceedbaccabdeeeeeeeeabdccdbaeeedbaccabdcbaddabceabcddcbaecbaddabcdbaccabdeeedbaccabdabdccdbaeeeeeecbdaadbccbdaadbceeeedbcaacbdeeabcddcba''+''abcddcbacbaddabceeeeedbaccabdeeeeeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabddbaccabdeabcddcbaeeeeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeabcddcbaeedbaccabdeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeeeeedbaccabdeabcddcbaabcddcbacbaddabccbaddabcabcddcbaeedbaccabdeeeeeeabcddcbaeeeeecbaddabcdbaccabd''
  
-''abcddcbaeecbaddabceeeedbaccabddbaccabdeeeeeeabdccdbacbdaadbceeedbcaacbdcbdaadbceabdccdbaecbdaadbcdbcaacbdeeeabcddcbaeeeeeeeecbdaadbceedbcaacbdabcddcbaabcddcbacbaddabceedbaccabdeeeeeeeeabcddcbaeeecbaddabcdbaccabdeabdccdbaedbaccabdcbaddabceeedbaccabdabdccdbaeeeeeecbdaadbccbdaadbceeeedbcaacbdeeabcddcba''+''abcddcbacbaddabceeeeedbaccabdeeeeeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabddbaccabdeabcddcbaeeeeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeabcddcbaeedbaccabdeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeeeeedbaccabdeabcddcbacbaddabcabcddcbaabcddcbacbaddabceedbaccabdeeeeeeabcddcbaeeeeecbaddabcdbaccabd''
  
-''abcddcbaeeecbaddabcedbaccabdeeedbaccabdeeeeeabdccdbaecbdaadbcedbcaacbdcbdaadbceeabdccdbacbdaadbceeeedbcaacbdabcddcbaeeeeeeeecbdaadbcedbcaacbdeabcddcbaabcddcbaecbaddabcedbaccabdeeeeeeeeabcddcbacbaddabceeeedbaccabdabdccdbaeedbaccabdcbaddabcedbaccabdeabdccdbaeeeeecbdaadbceeecbdaadbcedbcaacbdeeeabcddcba''+''abcddcbacbaddabceeeeedbaccabdeeeeeedbaccabdeabcddcbaecbaddabccbaddabcedbaccabdeeabcddcbadbaccabdeeeecbaddabcabcddcbaeeeeeecbaddabcdbaccabdeeeeabcddcbaabcddcbaeeeecbaddabcdbaccabdeeeeeeabcddcbadbaccabdeeeecbaddabcabcddcbaeecbaddabcedbaccabddbaccabdeabcddcbaecbaddabceeeeeecbaddabceeeeedbaccabdabcddcba''
  
-''abcddcbaeeecbaddabcedbaccabdeeeedbcaacbdeecbdaadbceeabdccdbaeeedbaccabdabdccdbacbdaadbceeeeeecbdaadbcdbcaacbdeabcddcbaabcddcbacbaddabcdbaccabdeeeeeeeeeeeeeeeedbaccabdabdccdbacbdaadbccbdaadbcedbcaacbdabcddcbaeeeeeeabcddcbacbaddabcdbaccabdeeecbaddabceeabcddcbaeedbcaacbdeeeedbaccabdeabdccdbaeeecbdaadbc''+''abcddcbacbaddabceeeeeeabcddcbadbaccabdeeeeeeeecbaddabccbaddabceedbaccabddbaccabdabcddcbaedbaccabdabcddcbaeeedbaccabdcbaddabceeeedbaccabdeeeeeecbaddabccbaddabceeeeeeabcddcbaeeeecbaddabcabcddcbaeeedbaccabdabcddcbaedbaccabdabcddcbaabcddcbaeecbaddabccbaddabceeeeeeeeabcddcbadbaccabdeeeeeecbaddabcdbaccabd''
  
-''abcddcbaeeecbaddabceedbaccabdeeeabcddcbaecbaddabceeedbaccabddbcaacbdeeeeecbdaadbceabdccdbadbcaacbdeecbdaadbceabdccdbacbaddabceeeeeeeeeabcddcbadbcaacbddbaccabdabdccdbaeeeeeeeeecbdaadbcdbcaacbdecbdaadbceeabdccdbadbcaacbdecbdaadbceeeeeabdccdbaabcddcbaeeecbaddabcedbaccabdeeeabcddcbaeecbaddabceeedbaccabd''+''abcddcbacbaddabceeeeeecbaddabceeeedbaccabdeeabcddcbacbaddabcedbaccabdedbaccabdeeedbaccabdeabcddcbaabcddcbaeedbaccabdeeeeeecbaddabcabcddcbaeeeedbaccabdcbaddabceeeeabcddcbadbaccabdeeeeeecbaddabceeabcddcbaabcddcbaecbaddabceeecbaddabcecbaddabcedbaccabdabcddcbaeecbaddabceeeedbaccabdeeeeeedbaccabdabcddcba''
  
-''abcddcbaeeecbaddabceedbaccabdeeeabcddcbaecbaddabceeedbaccabddbcaacbdeeeeecbdaadbceabdccdbadbcaacbdeecbdaadbceabdccdbacbdaadbceeeeeeeeedbcaacbdabcddcbaabdccdbadbaccabdeeeeeeeeecbaddabcdbcaacbdecbdaadbceeabdccdbadbcaacbdecbdaadbceeeeeabdccdbaabcddcbaeeecbaddabcedbaccabdeeeabcddcbaeecbaddabceeedbaccabd''+''abcddcbacbaddabceeeeeecbaddabceeeedbaccabdeeabcddcbadbaccabdeecbaddabcdbaccabdeabcddcbaedbaccabdeeeedbaccabdeeabcddcbaeeeecbaddabccbaddabceeeabcddcbaeeabcddcbaeeedbaccabddbaccabdeeeeabcddcbaeecbaddabceeeecbaddabceabcddcbaecbaddabcdbaccabdeecbaddabcabcddcbaeecbaddabceeeedbaccabdeeeeeedbaccabdabcddcba''
  
-''abcddcbaeeecbaddabceeedbaccabdcbaddabceeeeeabcddcbaedbcaacbdedbcaacbdecbdaadbceabdccdbaedbcaacbdeeeeeeeecbdaadbceabdccdbadbcaacbdcbdaadbceeeeabdccdbaeeabdccdbaeeeedbaccabdcbaddabcabdccdbaedbaccabdeeeeeeeecbaddabceabdccdbaedbaccabdecbaddabcecbaddabceabcddcbaeeeeedbcaacbdcbdaadbceeedbcaacbdeeeabcddcba''+''abcddcbacbaddabceeeeeedbaccabdabcddcbaeeeeeeeecbaddabccbaddabceedbaccabdabcddcbadbaccabdedbaccabdabcddcbaeeedbaccabdcbaddabceeeedbaccabdeeeeeecbaddabccbaddabceeeeeeabcddcbaeeeecbaddabcabcddcbaeeedbaccabdabcddcbaeabcddcbadbaccabdabcddcbaeecbaddabccbaddabceeeeeeeedbaccabdabcddcbaeeeeeecbaddabcdbaccabd''
  
-''abcddcbaeeeecbaddabcdbaccabdeeeeeabcddcbacbaddabceedbaccabdcbdaadbceeeedbcaacbdeeabcddcbaeeedbaccabdeabdccdbaeecbdaadbceedbcaacbdeecbdaadbceabdccdbaeeeedbcaacbdecbdaadbceeabdccdbaeedbcaacbdeecbdaadbceabdccdbaeeeabdccdbaeedbaccabdeeeecbaddabccbaddabceeabcddcbadbcaacbdeeeeeabcddcbacbaddabceeeedbaccabd''+''abcddcbacbaddabceeeeeedbaccabdabcddcbaeeeeeeeecbaddabccbaddabceedbaccabddbaccabdabcddcbaeabcddcbadbaccabdeeedbaccabdcbaddabceeeedbaccabdeeeeeecbaddabccbaddabceeeeeeabcddcbaeeeecbaddabcabcddcbaeeeabcddcbadbaccabdedbaccabdabcddcbaabcddcbaeecbaddabccbaddabceeeeeeeedbaccabdabcddcbaeeeeeecbaddabcdbaccabd''
  
-''abcddcbaeeeecbaddabcdbaccabdeeeeeabdccdbadbaccabdeecbaddabccbaddabceeeeabcddcbaeedbcaacbdeeedbcaacbdecbdaadbceeabdccdbaeedbcaacbdeecbdaadbceabdccdbaeeeedbcaacbdecbdaadbceeabdccdbaeecbdaadbceedbcaacbdeabcddcbaeeedbaccabdeeabdccdbaeeeecbdaadbcabcddcbaeecbaddabcdbaccabdeeeeeabcddcbacbaddabceeeedbaccabd''+''abcddcbacbaddabceeeeeedbaccabdecbaddabceeeeeeecbaddabcdbaccabdabcddcbaeabcddcbaedbaccabdedbaccabdeabcddcbaedbaccabdeeeeeeabcddcbacbaddabcecbaddabceeeeeeeedbaccabdedbaccabdabcddcbaeeeeeecbaddabceabcddcbaecbaddabcecbaddabceabcddcbaeabcddcbacbaddabcdbaccabdeeeeeeedbaccabdecbaddabceeeeeedbaccabdabcddcba''
  
-''abcddcbaeeeecbaddabcedbaccabdecbdaadbceeeeeedbcaacbdabcddcbadbaccabdabdccdbaeecbdaadbcdbaccabdeeeeeeeeeeeeeabdccdbacbdaadbcdbcaacbdecbdaadbcabdccdbaeeeecbaddabcabcddcbaedbcaacbdabcddcbacbaddabceeeeeeeeeeeeedbaccabdabcddcbaeecbaddabcdbaccabdcbdaadbcdbcaacbdeeeeeeabcddcbaedbaccabdeabdccdbaeeeecbdaadbc''+''abcddcbacbaddabceeeeeedbaccabdedbaccabdeeeeeeecbaddabcdbaccabdabcddcbaeabcddcbaecbaddabcecbaddabceabcddcbaedbaccabdeeeeeeabcddcbacbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdabcddcbaeeeeeecbaddabceabcddcbaedbaccabdedbaccabdeabcddcbaeabcddcbacbaddabcdbaccabdeeeeeeecbaddabcecbaddabceeeeeedbaccabdabcddcba''
  
-''abcddcbaeeeecbaddabcedbaccabdecbdaadbceeeeeedbcaacbdabcddcbadbaccabdabdccdbaeecbdaadbcdbcaacbdeeeeeeeeeeeeecbdaadbcabdccdbadbaccabdeabdccdbacbdaadbceeeeabcddcbacbaddabcedbaccabdcbaddabcabcddcbaeeeeeeeeeeeeedbcaacbdabcddcbaeecbaddabcdbaccabdcbdaadbcdbcaacbdeeeeeeabcddcbaedbaccabdeabdccdbaeeeecbdaadbc''+''abcddcbacbaddabceeeeeedbaccabdeedbaccabdeeeeabcddcbaecbaddabceedbaccabdeecbaddabccbaddabcabcddcbaeabcddcbadbaccabdeeeeeabcddcbadbaccabdeeeecbaddabceeeeeecbaddabceeeeabcddcbadbaccabdeeeeeabcddcbadbaccabdedbaccabdcbaddabccbaddabceeabcddcbaeecbaddabcedbaccabdeeeeabcddcbaeeabcddcbaeeeeeecbaddabcdbaccabd''
  
-''abcddcbaeeeecbaddabcedbaccabdeecbdaadbceedbcaacbdeeeabcddcbadbaccabdeeeabdccdbacbdaadbceeeeeedbaccabdabdccdbaeecbdaadbceecbaddabceeabcddcbaedbcaacbdeeeeabdccdbaedbaccabdeecbaddabceecbdaadbceedbcaacbdabcddcbaeeeeeecbdaadbcdbcaacbdeeeabcddcbadbaccabdeeeabdccdbaeecbdaadbceeabcddcbaecbaddabceeeedbaccabd''+''abcddcbacbaddabceeeeeedbaccabdeeeedbaccabdeeabcddcbacbaddabceecbaddabcdbaccabdeabcddcbaedbaccabdeeeecbaddabceeabcddcbaeeeecbaddabcdbaccabdeeeabcddcbaeeabcddcbaeeecbaddabcdbaccabdeeeeabcddcbaeedbaccabdeeeecbaddabceabcddcbaecbaddabcdbaccabdeedbaccabdabcddcbaeecbaddabceeeecbaddabceeeeeedbaccabdabcddcba''
  
-''abcddcbaeeeecbaddabcedbaccabdeedbcaacbdecbdaadbceeeeabdccdbaeeabcddcbaecbaddabcdbaccabdeeeeeedbcaacbdcbdaadbceabdccdbaecbdaadbceeeeedbcaacbdeabcddcbaeeabdccdbaedbaccabdeeeeecbaddabcedbcaacbdecbdaadbcabdccdbaeeeeeeabcddcbacbaddabcedbaccabdeedbaccabdeeeeabdccdbaecbdaadbceecbaddabceabcddcbaeeeedbcaacbd''+''abcddcbacbaddabceeeeeeeeabcddcbaecbaddabcdbaccabdeeedbaccabdeeecbaddabcdbaccabdedbaccabdcbaddabceedbaccabdeeabcddcbaeeeeeeeeabcddcbaeeabcddcbadbaccabdcbaddabcabcddcbaeeabcddcbaeeeeeeeeabcddcbaeecbaddabceedbaccabdcbaddabcecbaddabcdbaccabdeeecbaddabceeecbaddabcdbaccabdeabcddcbaeeeeeeeedbaccabdabcddcba''
  
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-''eeeabcddcbacbaddabcdbaccabdecbdaadbceeeeedbcaacbdeeabcddcbaeeeedbaccabdabdccdbaeeecbdaadbceeedbcaacbdcbdaadbceeabdccdbaedbaccabdabdccdbaeeeeeecbdaadbcabcddcbaeeeeeecbaddabcdbaccabdecbaddabceeabcddcbadbcaacbdeeeabcddcbaeeecbaddabcdbaccabdeeeecbdaadbceedbcaacbdeeeeeabcddcbaedbaccabdabdccdbacbdaadbceee''+''abcddcbaecbaddabceeeeedbaccabdecbaddabceeeecbaddabceeabcddcbaeeedbaccabddbaccabdeabcddcbadbaccabdeabcddcbadbaccabdeeeeeeabcddcbaeecbaddabceecbaddabceeeedbaccabdeedbaccabdeeabcddcbaeeeeeecbaddabcabcddcbaecbaddabcabcddcbaecbaddabccbaddabceeeabcddcbaeedbaccabdeeeedbaccabdecbaddabceeeeedbaccabdeabcddcba''
  
-''eeeabcddcbacbaddabcdbaccabdeeecbdaadbceedbcaacbdabcddcbaeeeeeeeabdccdbaeeedbaccabdcbaddabcdbaccabdeeabdccdbaecbdaadbceeeeeeeedbaccabdeabdccdbacbdaadbccbdaadbcdbcaacbdeabcddcbaeeeeeeeecbdaadbcedbcaacbdeeabcddcbacbaddabcabcddcbaeeedbcaacbdeeeeeeedbaccabdabdccdbaeecbdaadbceeeabcddcbacbaddabcdbaccabdeee''+''abcddcbaecbaddabceeeeedbaccabdedbaccabdeeeecbaddabceeabcddcbaeeedbaccabdcbaddabceabcddcbacbaddabceabcddcbadbaccabdeeeeeeabcddcbaeedbaccabdeecbaddabceeeedbaccabdeecbaddabceeabcddcbaeeeeeecbaddabcabcddcbaedbaccabdabcddcbaedbaccabdcbaddabceeeabcddcbaeedbaccabdeeeecbaddabcecbaddabceeeeedbaccabdeabcddcba''
  
-''eeeabcddcbacbaddabcdbaccabdeeeedbcaacbdcbdaadbcabdccdbaeeeeeeeeedbaccabdeabdccdbaecbdaadbceabcddcbaeecbaddabceedbaccabdeeeecbdaadbcdbcaacbdeeeabcddcbacbdaadbceeedbcaacbdabcddcbaeeeedbaccabdeeabdccdbaeecbdaadbceabcddcbaecbaddabcedbaccabdeeeeeeeeecbaddabcabcddcbadbcaacbdeeeedbaccabdabdccdbacbdaadbceee''+''abcddcbaecbaddabceeeeeeabcddcbadbaccabdeeeeedbaccabdecbaddabcabcddcbadbaccabdeedbaccabdeedbaccabdeeeecbaddabceeecbaddabcecbaddabcecbaddabceeeecbaddabcabcddcbaeeeeabcddcbaeabcddcbaeabcddcbaeeeabcddcbaeeeedbaccabdeedbaccabdeedbaccabdcbaddabcabcddcbaedbaccabdeeeeedbaccabdcbaddabceeeeeeabcddcbaecbaddabc''
  
-''eeeabcddcbacbaddabcdbaccabdeeeedbcaacbdcbdaadbcabdccdbaeeeeeeeeedbcaacbdecbdaadbceabdccdbaecbaddabceeabcddcbaeedbcaacbdeeeeabdccdbadbaccabdeeecbaddabcabdccdbaeeedbaccabdcbaddabceeeedbcaacbdeecbdaadbceeabdccdbaecbaddabceabcddcbaedbcaacbdeeeeeeeeecbaddabcabcddcbadbcaacbdeeeedbaccabdabdccdbacbdaadbceee''+''abcddcbaecbaddabceeeeeecbaddabcdbaccabdeeecbaddabceedbaccabdeeeedbaccabdabcddcbaeabcddcbaabcddcbaeabcddcbaedbaccabdeeeeeedbaccabdeedbaccabdecbaddabceeeedbaccabdecbaddabceecbaddabceeeeeecbaddabceabcddcbaeabcddcbaabcddcbaeabcddcbacbaddabceeeecbaddabceedbaccabdeeecbaddabcdbaccabdeeeeeedbaccabdeabcddcba''
  
-''eeeabcddcbacbaddabcedbaccabddbcaacbdeeeeecbdaadbcabdccdbaeeeeeecbdaadbcedbcaacbdeabcddcbaabcddcbaeeeeecbaddabceeeedbaccabdedbaccabdeabdccdbacbdaadbceeeedbaccabdabdccdbaecbdaadbcecbdaadbceeeedbcaacbdeeeeeabcddcbaabcddcbaecbaddabcedbaccabdeeeeeeabdccdbadbaccabdeeeeecbaddabccbdaadbcedbcaacbdabcddcbaeee''+''abcddcbaecbaddabceeeeeecbaddabcdbaccabdeeeedbaccabdcbaddabceeeeeabcddcbadbaccabdabcddcbaabcddcbaeedbaccabdeeeeabcddcbaeeeedbaccabdcbaddabcedbaccabdeeeeeecbaddabcedbaccabdcbaddabceeeeabcddcbaeeeecbaddabceeabcddcbaabcddcbacbaddabcabcddcbaeeeeedbaccabdcbaddabceeeecbaddabcdbaccabdeeeeeedbaccabdeabcddcba''
  
-''eeeabcddcbacbaddabceedbaccabdcbaddabcabcddcbaedbcaacbdeeeeeeeeeeeedbaccabdeabdccdbacbdaadbcdbaccabdeeabdccdbaeecbdaadbceedbaccabdabdccdbaecbdaadbceeeeeeeecbdaadbcedbcaacbdabcddcbaeecbdaadbceedbcaacbdeeabcddcbacbdaadbcdbcaacbdeabcddcbaeeeeeeeeeeeeabdccdbaedbaccabdcbaddabcabcddcbaeecbaddabcdbaccabdeee''+''abcddcbaecbaddabceeeeeedbaccabdcbaddabceeeecbaddabcdbaccabdeeeeeabcddcbadbaccabdabcddcbaabcddcbaeedbaccabdeeeeabcddcbaeeeedbaccabdcbaddabcedbaccabdeeeeeecbaddabcedbaccabdcbaddabceeeeabcddcbaeeeecbaddabceeabcddcbaabcddcbacbaddabcabcddcbaeeeeecbaddabcdbaccabdeeeedbaccabdcbaddabceeeeeedbaccabdeabcddcba''
  
-''eeeabcddcbacbaddabceedbaccabdcbaddabcabcddcbaedbcaacbdeeeeeeeeeeeedbaccabdeabdccdbacbdaadbcdbcaacbdeecbdaadbceeabdccdbaeedbaccabdabdccdbaecbdaadbceeeeeeeecbdaadbcedbcaacbdabcddcbaeeabdccdbaeedbaccabdeecbaddabccbdaadbcdbcaacbdeabcddcbaeeeeeeeeeeeeabdccdbaedbaccabdcbaddabccbaddabceeabcddcbadbcaacbdeee''+''abcddcbaecbaddabceeeeeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeabcddcbadbaccabdabcddcbaabcddcbaeedbaccabdeeeeabcddcbaeeeecbaddabcdbaccabdedbaccabdeeeeeecbaddabcecbaddabcdbaccabdeeeeabcddcbaeeeecbaddabceeabcddcbaabcddcbacbaddabcabcddcbaeeeeedbaccabdcbaddabceeeedbaccabdcbaddabceeeeeedbaccabdeabcddcba''
  
-''eeeabcddcbacbaddabceedbaccabdcbdaadbcdbcaacbdeabcddcbaeeeeeeeeeeeeabdccdbaedbaccabdcbaddabcdbaccabdeeabdccdbaeecbdaadbceedbaccabdabdccdbaecbdaadbceeeeeeeecbdaadbcedbcaacbdabcddcbaeecbdaadbceedbcaacbdeeabcddcbacbaddabcabcddcbaedbcaacbdeeeeeeeeeeeedbaccabdeabdccdbacbdaadbcabcddcbaeecbaddabcdbaccabdeee''+''abcddcbaecbaddabceeeeeedbaccabddbaccabdeeeeabcddcbaecbaddabceeecbaddabcdbaccabdeabcddcbadbaccabdeeeecbaddabceeeabcddcbacbaddabceeedbaccabdeeeeabcddcbaabcddcbaeeeecbaddabceeedbaccabdabcddcbaeeedbaccabdeeeecbaddabcabcddcbaecbaddabcdbaccabdeeedbaccabdeabcddcbaeeeecbaddabccbaddabceeeeeedbaccabdeabcddcba''
  
-''eeeabcddcbacbaddabceedbaccabdcbdaadbcdbcaacbdeabcddcbaeeeeeeeeeeeeabdccdbaedbaccabdcbaddabcdbcaacbdeecbdaadbceeabdccdbaeedbaccabdabdccdbaecbdaadbceeeeeeeecbdaadbcedbcaacbdabcddcbaeeabdccdbaeedbaccabdeecbaddabccbaddabcabcddcbaedbcaacbdeeeeeeeeeeeedbaccabdeabdccdbacbdaadbccbaddabceeabcddcbadbcaacbdeee''+''abcddcbaecbaddabceeeeeedbaccabdecbaddabceecbaddabceeabcddcbaedbaccabdeedbaccabdeeeabcddcbaabcddcbaeeedbaccabddbaccabdecbaddabceedbaccabdeeeeeeabcddcbaabcddcbaeeeeeecbaddabceedbaccabdecbaddabccbaddabceeeabcddcbaabcddcbaeeecbaddabceecbaddabceabcddcbaeedbaccabdeedbaccabdecbaddabceeeeeedbaccabdeabcddcba''
  
-''eeeabcddcbacbaddabceedbaccabddbaccabdabdccdbaecbdaadbceeeeeeeeeeeecbaddabceabcddcbadbcaacbddbaccabdeeabdccdbaeecbdaadbceecbaddabcabcddcbaedbcaacbdeeeeeeeedbcaacbdecbdaadbcabdccdbaeecbdaadbceedbcaacbdeeabcddcbadbcaacbdcbdaadbceabdccdbaeeeeeeeeeeeeabcddcbaecbaddabcdbaccabdabdccdbaeedbaccabdcbaddabceee''+''abcddcbaecbaddabceeeeeedbaccabdedbaccabdeeeecbaddabcabcddcbacbaddabcdbaccabdeeeeabcddcbaedbaccabdeeeeecbaddabceeabcddcbaeabcddcbaeeedbaccabdeeabcddcbacbaddabceedbaccabdeeecbaddabcecbaddabceeabcddcbaeeeeedbaccabdecbaddabceeeedbaccabdabcddcbacbaddabcabcddcbaeeeedbaccabdedbaccabdeeeeeeabcddcbaecbaddabc''
  
-''eeeabcddcbacbaddabceedbaccabddbcaacbdcbdaadbceabdccdbaeeeeeeeeeeeeabcddcbaecbaddabcdbaccabddbaccabdeeabdccdbaeecbdaadbceecbaddabcabcddcbaedbcaacbdeeeeeeeedbcaacbdecbdaadbcabdccdbaeecbdaadbceedbcaacbdeeabcddcbadbaccabdabdccdbaecbdaadbceeeeeeeeeeeecbaddabceabcddcbadbcaacbdabdccdbaeedbaccabdcbaddabceee''+''abcddcbaecbaddabceeeeeedbaccabdeedbaccabdeabcddcbaeeecbaddabcabcddcbadbaccabdcbaddabcdbaccabdeeeeeeeeeeeecbaddabcecbaddabceabcddcbaeabcddcbaeedbaccabddbaccabdeecbaddabcecbaddabceabcddcbaeabcddcbaeeeeeeeeeeeedbaccabdabcddcbadbaccabdcbaddabcabcddcbaeeecbaddabcedbaccabdeedbaccabdeeeeeeabcddcbaecbaddabc''
  
-''eeeabcddcbacbaddabceedbaccabdecbdaadbcdbcaacbdabcddcbaeeeeeeecbaddabceeeeeabcddcbaeedbcaacbdedbaccabdeeabdccdbaecbdaadbcdbaccabdabdccdbaeeeeeecbdaadbcdbaccabdeeeeeeabdccdbacbdaadbcdbaccabdeabdccdbaeecbdaadbcecbaddabceeabcddcbaeeeeedbcaacbdeeeeeeeabcddcbacbaddabcdbaccabdecbdaadbceedbcaacbdabcddcbaeee''+''abcddcbaecbaddabceeeeeedbaccabdeedbaccabdecbaddabceeeabcddcbacbaddabcdbaccabdabcddcbadbaccabdeeeeeeeeeeeeabcddcbaecbaddabceabcddcbaecbaddabceedbaccabddbaccabdeeabcddcbaecbaddabceabcddcbaecbaddabceeeeeeeeeeeedbaccabdcbaddabcdbaccabdabcddcbacbaddabceeeabcddcbaedbaccabdeedbaccabdeeeeeeabcddcbaecbaddabc''
  
-''eeeabcddcbacbaddabceeedbaccabdcbdaadbcdbcaacbdabcddcbaeeeeeecbaddabceeeeabcddcbaeedbcaacbdedbaccabdeeeeeeabdccdbaeecbdaadbcedbaccabdabdccdbaecbdaadbceedbaccabdeabdccdbacbdaadbcedbaccabdeeabdccdbaeeeeeecbdaadbcecbaddabceeabcddcbaeeeedbcaacbdeeeeeeabcddcbacbaddabcdbaccabdcbdaadbceeedbcaacbdabcddcbaeee''+''abcddcbaecbaddabceeeeeeeabcddcbacbaddabcedbaccabddbaccabdeeeeeeedbaccabdcbaddabcedbaccabddbaccabdeeabcddcbaeeeeabcddcbaeecbaddabcabcddcbaeecbaddabceeeeeecbaddabceecbaddabcabcddcbaeedbaccabdeeeedbaccabdeeabcddcbaabcddcbaeabcddcbadbaccabdeeeeeeecbaddabcdbaccabdecbaddabccbaddabceeeeeeedbaccabdeabcddcba'' 
 + 
 +''abcddcbaecbaddabceeeeeeecbaddabcdbaccabdedbaccabdeeeabcddcbaedbaccabddbaccabdeeeeeabcddcbaabcddcbaeecbaddabceeecbaddabceecbaddabcecbaddabceeeeabcddcbaabcddcbaeeeedbaccabdedbaccabdeedbaccabdeeedbaccabdeeabcddcbaabcddcbaeeeeecbaddabccbaddabceabcddcbaeeecbaddabcecbaddabcdbaccabdeeeeeeedbaccabdeabcddcba'' 
 + 
 +''abcddcbaecbaddabceeeeeeedbaccabdcbaddabcecbaddabceeeabcddcbaedbaccabddbaccabdeeeeeabcddcbaabcddcbaeedbaccabdeeedbaccabdeecbaddabcedbaccabdeeeeabcddcbaabcddcbaeeeecbaddabcedbaccabdeecbaddabceeecbaddabceeabcddcbaabcddcbaeeeeecbaddabccbaddabceabcddcbaeeedbaccabdedbaccabdcbaddabceeeeeeedbaccabdeabcddcba'' 
 + 
 +''abcddcbaecbaddabceeeeeeedbaccabddbaccabdecbaddabcdbaccabdeeeeeeecbaddabcabcddcbaeabcddcbaabcddcbaeecbaddabceeeecbaddabceeabcddcbadbaccabdeedbaccabdeeeeeedbaccabdeeabcddcbadbaccabdeeabcddcbaeeeeabcddcbaeecbaddabccbaddabcedbaccabdcbaddabceeeeeeecbaddabccbaddabcedbaccabdabcddcbaeeeeeeedbaccabdeabcddcba'' 
 + 
 +''abcddcbaecbaddabceeeeeeedbaccabdecbaddabcdbaccabdedbaccabdeeeabcddcbaeecbaddabcdbaccabdeeeabcddcbaeeeeabcddcbaabcddcbaeeeeeabcddcbacbaddabceeecbaddabccbaddabceeecbaddabcdbaccabdeeeeedbaccabddbaccabdeeeedbaccabdeeeabcddcbacbaddabceedbaccabdeeeabcddcbaeabcddcbacbaddabceabcddcbaeeeeeeecbaddabcedbaccabd'' 
 + 
 +''abcddcbaecbaddabceeeeeeedbaccabdedbaccabdeabcddcbaecbaddabcedbaccabdcbaddabceeeabcddcbadbaccabdeeeeeeeeecbaddabceecbaddabceabcddcbaeeeabcddcbadbaccabdcbaddabcabcddcbaeeeabcddcbaedbaccabdeedbaccabdeeeeeeeeecbaddabcabcddcbaeeedbaccabdcbaddabcedbaccabdeabcddcbaecbaddabcecbaddabceeeeeeedbaccabdeabcddcba'' 
 + 
 +''abcddcbaedbaccabdcbaddabceeeeeeeeeeeecbaddabcdbaccabdcbaddabcabcddcbaeeedbaccabdeabcddcbaeabcddcbadbaccabdecbaddabceeeabcddcbaedbaccabdeecbaddabceeeeeeeeeedbaccabdeecbaddabceabcddcbaeeedbaccabdecbaddabcabcddcbaeabcddcbaecbaddabceeeabcddcbadbaccabdcbaddabcdbaccabdeeeeeeeeeeeedbaccabdcbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdcbaddabceeeeeeeeeeeecbaddabcdbaccabddbaccabdabcddcbaeeecbaddabceabcddcbaeabcddcbacbaddabcedbaccabdeeeabcddcbaecbaddabceedbaccabdeeeeeeeeeecbaddabceedbaccabdeabcddcbaeeecbaddabcedbaccabdabcddcbaeabcddcbaedbaccabdeeeabcddcbacbaddabccbaddabcdbaccabdeeeeeeeeeeeedbaccabdcbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdecbaddabceeeeeeeeeeabcddcbacbaddabcedbaccabdeedbaccabdabcddcbaecbaddabceedbaccabdeecbaddabccbaddabcabcddcbaeeeabcddcbadbaccabdeeeeeeeeeeeeeedbaccabdcbaddabceeecbaddabcabcddcbaabcddcbaeedbaccabdeeabcddcbaecbaddabcdbaccabdeedbaccabdeabcddcbacbaddabceeeeeeeeeeabcddcbaedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdecbaddabceeeeeeeeeeabcddcbadbaccabdeecbaddabccbaddabcedbaccabdabcddcbaeeecbaddabceedbaccabdcbaddabceeabcddcbaedbaccabdeabcddcbaeeeeeeeeeeeeabcddcbaedbaccabdecbaddabceeabcddcbadbaccabdeecbaddabceeedbaccabdabcddcbaecbaddabcabcddcbaeecbaddabcdbaccabdeeeeeeeeeecbaddabcedbaccabdeabcddcba'' 
 + 
 +''abcddcbaedbaccabdecbaddabceeeeeeeeeecbaddabcabcddcbaedbaccabdeedbaccabdabcddcbaecbaddabceedbaccabdeecbaddabcabcddcbacbaddabceeeabcddcbadbaccabdeeeeeeeeeeeeeedbaccabdcbaddabceeeabcddcbacbaddabcabcddcbaeedbaccabdeeabcddcbaecbaddabcdbaccabdeedbaccabdecbaddabcabcddcbaeeeeeeeeeeabcddcbaedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdecbaddabceeeeeeeeeedbaccabdcbaddabceeabcddcbacbaddabceabcddcbadbaccabdeeecbaddabceedbaccabdabcddcbaeecbaddabcedbaccabdeabcddcbaeeeeeeeeeeeeabcddcbaedbaccabdeabcddcbaeecbaddabcdbaccabdeecbaddabceeeabcddcbadbaccabdecbaddabccbaddabceedbaccabdabcddcbaeeeeeeeeeecbaddabcedbaccabdeabcddcba'' 
 + 
 +''abcddcbaedbaccabdecbaddabceeeeeeeeeedbaccabdcbaddabceecbaddabceabcddcbaabcddcbadbaccabdcbaddabceeedbaccabdeeeabcddcbaeabcddcbaeeeeeeeeabcddcbadbaccabddbaccabdcbaddabceeeeeeeecbaddabcecbaddabceeedbaccabdeeeabcddcbadbaccabdcbaddabccbaddabceabcddcbaeeabcddcbadbaccabdeeeeeeeeeeabcddcbaedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeecbaddabceeeeeeecbaddabceeedbaccabdeabcddcbaabcddcbadbaccabdecbaddabceeeeedbaccabdcbaddabcecbaddabcabcddcbadbaccabdabcddcbaeeeeeeeeeeeeeeeeeeabcddcbacbaddabcabcddcbadbaccabdedbaccabdcbaddabceeeeedbaccabdecbaddabcabcddcbaabcddcbaecbaddabceeedbaccabdeeeeeeedbaccabdeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeecbaddabceeeeeeeecbaddabcdbaccabdeeedbaccabdeabcddcbaeabcddcbacbaddabccbaddabcabcddcbaeeeeeeabcddcbaecbaddabceeedbaccabdeedbaccabdeeeedbaccabdeedbaccabdeeeabcddcbaecbaddabceeeeeeabcddcbacbaddabccbaddabcabcddcbaecbaddabcedbaccabdeeedbaccabdabcddcbaeeeeeeeeabcddcbaeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeecbaddabceeeeeeeecbaddabcdbaccabdeeedbaccabdeabcddcbaeabcddcbacbaddabccbaddabcabcddcbaeeeeeeabcddcbaecbaddabceeedbaccabdeedbaccabdeeeedbaccabdeedbaccabdeeeabcddcbaecbaddabceeeeeecbaddabcabcddcbaabcddcbacbaddabcecbaddabcedbaccabdeeedbaccabdabcddcbaeeeeeeeeabcddcbaeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeecbaddabceeeeeeeecbaddabcdbaccabdeeedbaccabdeabcddcbaecbaddabcabcddcbaabcddcbacbaddabceeeeeeabcddcbaecbaddabceeedbaccabdeedbaccabdeeeedbaccabdeedbaccabdeeeabcddcbaecbaddabceeeeeeabcddcbacbaddabccbaddabcabcddcbaecbaddabcedbaccabdeeedbaccabdabcddcbaeeeeeeeeabcddcbaeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeecbaddabceeeeeeeecbaddabcdbaccabdeeedbaccabdeabcddcbaecbaddabcabcddcbaabcddcbacbaddabceeeeeeabcddcbaecbaddabceeedbaccabdeedbaccabdeeeedbaccabdeedbaccabdeeeabcddcbaecbaddabceeeeeecbaddabcabcddcbaabcddcbacbaddabcecbaddabcedbaccabdeeedbaccabdabcddcbaeeeeeeeeabcddcbaeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeeeabcddcbaeeeeeeedbaccabdcbaddabcecbaddabcecbaddabceeeeabcddcbadbaccabdcbaddabcedbaccabdeeeabcddcbaecbaddabceeeeecbaddabcdbaccabdeeeeeedbaccabdabcddcbaeeeeeabcddcbaecbaddabceeedbaccabdeabcddcbadbaccabdcbaddabceeeeabcddcbaeabcddcbaeabcddcbadbaccabdeeeeeeecbaddabceeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeeecbaddabceeeeeeecbaddabcdbaccabdedbaccabdeabcddcbaeeeeabcddcbacbaddabcabcddcbaedbaccabdeeecbaddabcecbaddabceeeeecbaddabcabcddcbaeeeeeeabcddcbadbaccabdeeeeedbaccabdedbaccabdeeecbaddabceabcddcbadbaccabdabcddcbaeeeeabcddcbaecbaddabcecbaddabcdbaccabdeeeeeeedbaccabdeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeecbaddabceeeeeeedbaccabdcbaddabceabcddcbaeabcddcbaeeeecbaddabcdbaccabdabcddcbaedbaccabdeeecbaddabcecbaddabceeeeecbaddabcdbaccabdeeeeeedbaccabdabcddcbaeeeeeabcddcbaeabcddcbaeeedbaccabdecbaddabcdbaccabdabcddcbaeeeecbaddabcecbaddabceabcddcbadbaccabdeeeeeeeabcddcbaeeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeeeeabcddcbaeeecbaddabceeeedbaccabdcbaddabceeeedbaccabdcbaddabccbaddabceeeabcddcbaabcddcbadbaccabdeecbaddabcedbaccabdeeeeeeeeabcddcbacbaddabceeeeeeeedbaccabdeabcddcbaeedbaccabdcbaddabccbaddabceeeabcddcbaabcddcbadbaccabdeeeeabcddcbadbaccabdeeeeabcddcbaeeecbaddabceeeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeeeecbaddabceeeabcddcbaeeeedbaccabdcbaddabceeeedbaccabdcbaddabcabcddcbaeeecbaddabcabcddcbadbaccabdeecbaddabcedbaccabdeeeeeeeeabcddcbacbaddabceeeeeeeedbaccabdeabcddcbaeedbaccabdcbaddabcabcddcbaeeecbaddabcabcddcbadbaccabdeeeeabcddcbadbaccabdeeeecbaddabceeeabcddcbaeeeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeeeedbaccabdeeeeecbaddabccbaddabceeeabcddcbacbaddabceeedbaccabdeabcddcbaeabcddcbaedbaccabdeeecbaddabccbaddabceecbaddabcabcddcbaeeeeeeeeeeeeabcddcbadbaccabdeedbaccabddbaccabdeeecbaddabceabcddcbaeabcddcbaecbaddabceeedbaccabdabcddcbaeeedbaccabddbaccabdeeeeecbaddabceeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeedbaccabdeeeeecbaddabccbaddabceeeabcddcbadbaccabdeeecbaddabceabcddcbaeabcddcbaecbaddabceeedbaccabdcbaddabceecbaddabcabcddcbaeeeeeeeeeeeeabcddcbadbaccabdeedbaccabdcbaddabceeedbaccabdeabcddcbaeabcddcbaedbaccabdeeecbaddabcabcddcbaeeedbaccabddbaccabdeeeeecbaddabceeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeabcddcbaeeeecbaddabcedbaccabdcbaddabceecbaddabcedbaccabdeabcddcbacbaddabceeeeeeeedbaccabdabcddcbaeeeedbaccabdcbaddabcecbaddabceeeeabcddcbaeabcddcbadbaccabdeeeecbaddabcdbaccabdeeeeeeeeabcddcbacbaddabcedbaccabdeabcddcbaeeabcddcbadbaccabdeabcddcbaeeeecbaddabceeeeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeeeeecbaddabccbaddabceeeeeeabcddcbaeeedbaccabdcbaddabcdbaccabdeabcddcbaabcddcbaeedbaccabdeeecbaddabceeecbaddabcedbaccabdeeeeedbaccabdabcddcbaeeeeeabcddcbaecbaddabceeecbaddabceeeabcddcbaeedbaccabddbaccabdeabcddcbacbaddabcabcddcbaeeedbaccabdeeeeeecbaddabccbaddabceeeeeabcddcbaedbaccabd'' 
 + 
 +''abcddcbaedbaccabdeeeeecbaddabccbaddabceeeeeedbaccabdeeeabcddcbacbaddabcdbaccabdeabcddcbadbaccabdeeabcddcbaeeecbaddabceeecbaddabceabcddcbaeeeeeabcddcbadbaccabdeeeeedbaccabdecbaddabceeecbaddabceeedbaccabdeeabcddcbadbaccabdeabcddcbacbaddabcdbaccabdeeeabcddcbaeeeeeecbaddabccbaddabceeeeeabcddcbaedbaccabd'' 
 + 
 +''abcddcbaedbaccabdeeeeecbaddabccbaddabceeeeeeedbaccabdabcddcbaeabcddcbaeeecbaddabcdbaccabdcbaddabcdbaccabdeeeedbaccabdeeabcddcbacbaddabceeeeeeeabcddcbaabcddcbaeeeeeeedbaccabdabcddcbaeecbaddabceeeecbaddabcdbaccabdcbaddabcdbaccabdeeeabcddcbaeabcddcbacbaddabceeeeeeedbaccabddbaccabdeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeecbaddabcecbaddabceeeedbaccabdeeabcddcbaeeecbaddabcdbaccabdeabcddcbadbaccabdeabcddcbacbaddabceeeeeeabcddcbaeecbaddabceedbaccabdeeeecbaddabceedbaccabdeeabcddcbaeeeeeedbaccabdabcddcbaecbaddabcabcddcbaecbaddabcdbaccabdeeeabcddcbaeecbaddabceeeedbaccabdedbaccabdeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeecbaddabcedbaccabdeeeedbaccabdeeabcddcbaeeecbaddabccbaddabceabcddcbacbaddabceabcddcbacbaddabceeeeeeabcddcbaeedbaccabdeedbaccabdeeeecbaddabceecbaddabceeabcddcbaeeeeeedbaccabdabcddcbaedbaccabdabcddcbaedbaccabddbaccabdeeeabcddcbaeecbaddabceeeecbaddabcedbaccabdeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeedbaccabdecbaddabceeeeeecbaddabcabcddcbacbaddabceedbaccabdabcddcbaeecbaddabceeeeeabcddcbadbaccabdabcddcbaeecbaddabceeeeeedbaccabdcbaddabceeeeeedbaccabdeeabcddcbacbaddabcabcddcbaeeeeedbaccabdeeabcddcbacbaddabceedbaccabdabcddcbadbaccabdeeeeeedbaccabdecbaddabceeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeedbaccabdedbaccabdeeeeeecbaddabcabcddcbacbaddabceecbaddabcabcddcbaeecbaddabceeeeeabcddcbacbaddabcabcddcbaeecbaddabceeeeeecbaddabcdbaccabdeeeeeedbaccabdeeabcddcbadbaccabdabcddcbaeeeeedbaccabdeeabcddcbadbaccabdeedbaccabdabcddcbadbaccabdeeeeeecbaddabcecbaddabceeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeeabcddcbacbaddabceeeeecbaddabcedbaccabdabcddcbacbaddabceecbaddabceecbaddabceeeedbaccabdeeedbaccabdedbaccabdedbaccabdeeeedbaccabdabcddcbaeeeeabcddcbaeabcddcbaeabcddcbaeeeabcddcbaeeeecbaddabceecbaddabceecbaddabcdbaccabdabcddcbaecbaddabceeeeecbaddabcdbaccabdeeeeeeabcddcbaedbaccabd'' 
 + 
 +''abcddcbaedbaccabdeeeeeecbaddabccbaddabceeeeabcddcbaedbaccabdeeedbaccabdcbaddabceabcddcbacbaddabceeeedbaccabdeeeabcddcbadbaccabdeeecbaddabceeeeabcddcbaabcddcbaeeeedbaccabdeeecbaddabcabcddcbaeeecbaddabceeeedbaccabdabcddcbaedbaccabdcbaddabceeecbaddabceabcddcbaeeeedbaccabddbaccabdeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeecbaddabcdbaccabdeeeecbaddabcdbaccabdeeeeeabcddcbacbaddabcabcddcbaabcddcbaeecbaddabceeeeabcddcbaeeeedbaccabdcbaddabcecbaddabceeeeeedbaccabdedbaccabdcbaddabceeeeabcddcbaeeeedbaccabdeeabcddcbaabcddcbadbaccabdabcddcbaeeeeecbaddabcdbaccabdeeeecbaddabcdbaccabdeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeecbaddabcdbaccabdeeeedbaccabdcbaddabceeeeeabcddcbacbaddabcabcddcbaabcddcbaeecbaddabceeeeabcddcbaeeeecbaddabcdbaccabdecbaddabceeeeeedbaccabdecbaddabcdbaccabdeeeeabcddcbaeeeedbaccabdeeabcddcbaabcddcbadbaccabdabcddcbaeeeeedbaccabdcbaddabceeeecbaddabcdbaccabdeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeecbaddabcecbaddabceeeedbaccabdabcddcbadbaccabdcbaddabceeeeabcddcbaecbaddabceeeeedbaccabdeeabcddcbaeabcddcbaeeecbaddabceeabcddcbadbaccabdeecbaddabceeedbaccabdedbaccabdeeabcddcbaeeeeecbaddabcedbaccabdeeeecbaddabcabcddcbadbaccabdabcddcbaeeeecbaddabcecbaddabceeeeeeabcddcbaedbaccabd'' 
 + 
 +''abcddcbaedbaccabdeeeeeecbaddabcedbaccabdeedbaccabdeeabcddcbaecbaddabceecbaddabceeeabcddcbaabcddcbaeeecbaddabccbaddabcedbaccabdeecbaddabceeeeeeabcddcbaabcddcbaeeeeeedbaccabdeecbaddabcedbaccabddbaccabdeeeabcddcbaabcddcbaeeedbaccabdeedbaccabdeabcddcbaeecbaddabceecbaddabcedbaccabdeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeecbaddabceecbaddabceabcddcbaeeedbaccabdabcddcbacbaddabcdbaccabdcbaddabceeeeeeeeeeeedbaccabdedbaccabdeabcddcbaeabcddcbaeecbaddabccbaddabceedbaccabdedbaccabdeabcddcbaeabcddcbaeeeeeeeeeeeecbaddabcabcddcbacbaddabcdbaccabdabcddcbaeeedbaccabdecbaddabceecbaddabceeeeeeabcddcbaedbaccabd'' 
 + 
 +''abcddcbaedbaccabdeeeeeecbaddabceecbaddabcedbaccabdeeeabcddcbadbaccabdcbaddabcabcddcbacbaddabceeeeeeeeeeeeabcddcbaedbaccabdeabcddcbaedbaccabdeecbaddabccbaddabceeabcddcbaedbaccabdeabcddcbaedbaccabdeeeeeeeeeeeecbaddabcdbaccabdcbaddabcabcddcbadbaccabdeeeabcddcbaecbaddabceecbaddabceeeeeeabcddcbaedbaccabd'' 
 + 
 +''abcddcbaedbaccabdeeeeeedbaccabdcbaddabceeedbaccabdeecbaddabceeeecbaddabcabcddcbaeabcddcbaabcddcbaeabcddcbaecbaddabceeeeeecbaddabceecbaddabcedbaccabdeeeecbaddabcedbaccabdeedbaccabdeeeeeedbaccabdeabcddcbaeabcddcbaabcddcbaeabcddcbadbaccabdeeeedbaccabdeecbaddabceeedbaccabdcbaddabceeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeedbaccabdcbaddabceeeecbaddabcdbaccabdeeeeeabcddcbacbaddabcabcddcbaabcddcbaeecbaddabceeeeabcddcbaeeeecbaddabcdbaccabdecbaddabceeeeeedbaccabdecbaddabcdbaccabdeeeeabcddcbaeeeedbaccabdeeabcddcbaabcddcbadbaccabdabcddcbaeeeeecbaddabcdbaccabdeeeedbaccabdcbaddabceeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeeeabcddcbadbaccabdecbaddabccbaddabceeeeeeecbaddabcdbaccabdecbaddabccbaddabceeabcddcbaeeeeabcddcbaeedbaccabdabcddcbaeedbaccabdeeeeeedbaccabdeedbaccabdabcddcbaeecbaddabceeeecbaddabceeabcddcbaabcddcbaeabcddcbacbaddabceeeeeeedbaccabdcbaddabcedbaccabddbaccabdeeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeeecbaddabccbaddabcedbaccabdcbaddabceeeeeeedbaccabdabcddcbaeabcddcbaabcddcbaeedbaccabdeeeedbaccabdeeabcddcbacbaddabceecbaddabceeeeeecbaddabceeabcddcbacbaddabceeabcddcbaeeeeabcddcbaeedbaccabddbaccabdecbaddabcdbaccabdeeeeeeedbaccabddbaccabdecbaddabcabcddcbaeeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeeecbaddabcdbaccabdedbaccabdeeeabcddcbaecbaddabccbaddabceeeeeabcddcbaabcddcbaeecbaddabceeecbaddabceedbaccabdecbaddabceeeeabcddcbaabcddcbaeeeedbaccabdecbaddabceedbaccabdeeedbaccabdeeabcddcbaabcddcbaeeeeedbaccabddbaccabdeabcddcbaeeecbaddabcecbaddabcdbaccabdeeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeeecbaddabcecbaddabceabcddcbaedbaccabdecbaddabcdbaccabdeeeabcddcbacbaddabceeeeeeeeedbaccabdeedbaccabdeabcddcbaeeeabcddcbacbaddabcdbaccabdabcddcbaeeeabcddcbaecbaddabceecbaddabceeeeeeeeedbaccabdabcddcbaeeecbaddabcdbaccabdecbaddabceabcddcbaedbaccabdedbaccabdeeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaedbaccabdeeeeeeecbaddabcedbaccabdcbaddabcecbaddabceeeabcddcbaeedbaccabdcbaddabceeeabcddcbaeeeeabcddcbaabcddcbaeeeeeabcddcbadbaccabdeeedbaccabddbaccabdeeedbaccabdcbaddabceeeeecbaddabccbaddabceeeecbaddabceeeabcddcbadbaccabdeecbaddabceeeabcddcbaeabcddcbadbaccabdeabcddcbaeeeeeeedbaccabdecbaddabc'' 
 + 
 +''abcddcbaedbaccabdeeeeeeedbaccabdcbaddabcecbaddabceeeabcddcbaecbaddabccbaddabceeeeeabcddcbaabcddcbaeedbaccabdeeedbaccabdeedbaccabdedbaccabdeeeeabcddcbaabcddcbaeeeecbaddabcecbaddabceecbaddabceeecbaddabceeabcddcbaabcddcbaeeeeedbaccabddbaccabdeabcddcbaeeedbaccabdedbaccabdcbaddabceeeeeeecbaddabceabcddcba'' 
 + 
 +''abcddcbaeeabcddcbacbaddabceeeeeeeeeecbaddabcdbaccabddbaccabdeabcddcbaecbaddabceeedbaccabdcbaddabcdbaccabdeeeeeedbaccabdedbaccabdeeeeecbaddabceabcddcbadbaccabdecbaddabceeeeeabcddcbaeabcddcbaeeeeeeabcddcbacbaddabcabcddcbaeeecbaddabcedbaccabdeabcddcbaabcddcbacbaddabceeeeeeeeeecbaddabcdbaccabdeedbaccabd'' 
 + 
 +''abcddcbaeeabcddcbadbaccabdeeeeeeeeeedbaccabdcbaddabccbaddabceabcddcbaedbaccabdeeecbaddabcdbaccabdcbaddabceeeeeecbaddabcecbaddabceeeeedbaccabdeabcddcbacbaddabcedbaccabdeeeeeabcddcbaeabcddcbaeeeeeeabcddcbadbaccabdabcddcbaeeedbaccabdecbaddabceabcddcbaabcddcbadbaccabdeeeeeeeeeedbaccabdcbaddabceecbaddabc'' 
 + 
 +''abcddcbaeeabcddcbaeecbaddabceeeecbaddabcedbaccabdeeeeeedbaccabdeabcddcbaecbaddabcdbaccabddbaccabdeecbaddabcedbaccabdcbaddabceeedbaccabdabcddcbaeeeeeeeeeeeeeedbaccabdabcddcbaeeecbaddabcabcddcbaecbaddabceeabcddcbaabcddcbacbaddabcedbaccabdeabcddcbaeeeeeeabcddcbaecbaddabceeeecbaddabceedbaccabdeedbaccabd'' 
 + 
 +''abcddcbaeeabcddcbaeecbaddabceeeeeecbaddabcdbaccabdeecbaddabceabcddcbaeeedbaccabdeedbaccabdedbaccabddbaccabdedbaccabdecbaddabceeeeeeabcddcbacbaddabceeeeeecbaddabcdbaccabdeeeeeecbaddabceabcddcbaeabcddcbaabcddcbaeabcddcbaeeabcddcbaeeedbaccabdecbaddabceeabcddcbacbaddabceeeeeecbaddabceedbaccabdeedbaccabd'' 
 + 
 +''abcddcbaeeabcddcbaeedbaccabdeeeedbaccabdecbaddabceeeeeecbaddabceabcddcbaedbaccabdcbaddabccbaddabceedbaccabdecbaddabcdbaccabdeeecbaddabcabcddcbaeeeeeeeeeeeeeecbaddabcabcddcbaeeedbaccabdabcddcbaedbaccabdeeabcddcbaabcddcbadbaccabdecbaddabceabcddcbaeeeeeeabcddcbaedbaccabdeeeedbaccabdeecbaddabceecbaddabc'' 
 + 
 +''abcddcbaeeabcddcbaeedbaccabdeeeeeedbaccabdcbaddabceedbaccabdeabcddcbaeeecbaddabceecbaddabcecbaddabccbaddabcecbaddabcedbaccabdeeeeeeabcddcbadbaccabdeeeeeedbaccabdcbaddabceeeeeedbaccabdeabcddcbaeabcddcbaabcddcbaeabcddcbaeeabcddcbaeeecbaddabcedbaccabdeeabcddcbadbaccabdeeeeeedbaccabdeecbaddabceecbaddabc'' 
 + 
 +''abcddcbaeeabcddcbaeeecbaddabceeeeedbaccabddbaccabdecbaddabccbaddabceeeeedbaccabdeabcddcbaeeecbaddabcecbaddabcdbaccabdedbaccabdeeeeeabcddcbadbaccabdeeeeeeabcddcbadbaccabdeeeeeabcddcbaeabcddcbacbaddabcecbaddabceeedbaccabdeabcddcbaeeeeecbaddabccbaddabceabcddcbaabcddcbaeeeeecbaddabceeedbaccabdeedbaccabd'' 
 + 
 +''abcddcbaeeabcddcbaeeedbaccabdeeeeecbaddabccbaddabcedbaccabddbaccabdeeeeecbaddabceabcddcbaeeedbaccabdedbaccabdcbaddabcecbaddabceeeeeabcddcbacbaddabceeeeeeabcddcbacbaddabceeeeeabcddcbaeabcddcbadbaccabdedbaccabdeeecbaddabceabcddcbaeeeeedbaccabddbaccabdeabcddcbaabcddcbaeeeeedbaccabdeeecbaddabceecbaddabc'' 
 + 
 +''abcddcbaeecbaddabccbaddabceeeeeeeedbaccabdeedbaccabdeabcddcbaeedbaccabdeabcddcbacbaddabceeecbaddabcedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdeeeeeeeeeeeeeeeecbaddabceabcddcbaecbaddabcabcddcbacbaddabcedbaccabdeeedbaccabdabcddcbaecbaddabceeabcddcbaecbaddabceecbaddabceeeeeeeedbaccabddbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabcdbaccabdeeeeeeeecbaddabceeabcddcbaeedbaccabdcbaddabcedbaccabdeeeabcddcbadbaccabdabcddcbaedbaccabdeabcddcbaeeeeeeecbaddabccbaddabceeeeeecbaddabccbaddabceeeeeeedbaccabdeabcddcbaedbaccabdabcddcbadbaccabdeeeabcddcbaecbaddabcabcddcbaeedbaccabdeecbaddabceeeeeeeeabcddcbacbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabcdbaccabdeeeeeeeecbaddabceeedbaccabddbaccabdeeabcddcbaabcddcbacbaddabceecbaddabcdbaccabdeeeeeabcddcbaabcddcbaeeeeeeedbaccabdeabcddcbacbaddabcedbaccabdeeeeeeecbaddabccbaddabceeeeedbaccabdabcddcbaeeabcddcbacbaddabccbaddabceedbaccabddbaccabdeeeabcddcbaeeeeeeeedbaccabdabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabcdbaccabdeeeeeeeeedbaccabdabcddcbaeecbaddabcecbaddabceeedbaccabdabcddcbaabcddcbaeecbaddabcdbaccabdecbaddabceeeeeeedbaccabdeedbaccabdeeabcddcbaeeabcddcbaeeeeeeecbaddabceabcddcbacbaddabceedbaccabddbaccabdabcddcbaeeecbaddabcecbaddabceedbaccabdabcddcbaeeeeeeeeeabcddcbacbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeabcddcbaecbaddabceeeeedbaccabdecbaddabcdbaccabdabcddcbaedbaccabdeeabcddcbacbaddabcedbaccabdeeeeeeecbaddabcabcddcbaeeeeeedbaccabdcbaddabceeeeeeeabcddcbaecbaddabcdbaccabdeeabcddcbaedbaccabdabcddcbacbaddabceabcddcbaeeeeecbaddabcedbaccabdeeeeeeabcddcbaecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeabcddcbaeeedbaccabdeecbaddabccbaddabcedbaccabdedbaccabdeeabcddcbacbaddabceeeabcddcbaedbaccabdeeeeeabcddcbacbaddabceeeeeeabcddcbacbaddabceeeeedbaccabdecbaddabceeeabcddcbacbaddabceedbaccabdedbaccabdeabcddcbaabcddcbaeedbaccabdeeecbaddabceeeeeedbaccabdeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeeabcddcbaeecbaddabcedbaccabdedbaccabdecbaddabcdbaccabdabcddcbaecbaddabceeeeeeeeeeabcddcbaecbaddabcabcddcbaabcddcbaeeeeeedbaccabddbaccabdcbaddabcedbaccabdeeeeeeeeeecbaddabcedbaccabdabcddcbacbaddabceabcddcbaeabcddcbaecbaddabceedbaccabdeeeeeeeabcddcbaecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeecbaddabcabcddcbaeeeedbaccabdedbaccabdeabcddcbacbaddabcabcddcbaeeecbaddabceedbaccabdedbaccabdeeeeedbaccabdcbaddabceeeeeecbaddabcabcddcbaeeeeeabcddcbaeabcddcbaeecbaddabceeedbaccabdcbaddabcdbaccabdeabcddcbaeabcddcbaeeeedbaccabdcbaddabceeeeeeeabcddcbaecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeeeabcddcbacbaddabceedbaccabddbaccabdecbaddabceabcddcbaeeedbaccabdeeedbaccabdcbaddabceabcddcbaeeeeeeeeabcddcbacbaddabccbaddabcabcddcbaeeeeeeeecbaddabceabcddcbadbaccabdeeedbaccabdeeecbaddabceabcddcbaedbaccabddbaccabdeeabcddcbacbaddabceeeeeeeedbaccabdeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeeeabcddcbacbaddabceedbaccabddbaccabdecbaddabceabcddcbaeeedbaccabdeeedbaccabdcbaddabceabcddcbaeeeeeeeecbaddabcabcddcbaabcddcbacbaddabceeeeeeeecbaddabceabcddcbadbaccabdeeedbaccabdeeecbaddabceabcddcbaedbaccabddbaccabdeeabcddcbacbaddabceeeeeeeedbaccabdeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeeecbaddabcabcddcbaeedbaccabddbaccabdecbaddabceabcddcbaeeedbaccabdeeedbaccabdcbaddabceabcddcbaeeeeeeeeabcddcbaabcddcbacbaddabccbaddabceeeeeeeecbaddabceabcddcbadbaccabdeeedbaccabdeeecbaddabceabcddcbaedbaccabddbaccabdeecbaddabcabcddcbaeeeeeeeedbaccabdeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeeecbaddabcdbaccabdeabcddcbadbaccabdeeeeabcddcbaeedbaccabdcbaddabcecbaddabceeabcddcbaecbaddabceeeeabcddcbaedbaccabdeeeeeeabcddcbaecbaddabceeeedbaccabdecbaddabceedbaccabdeabcddcbaabcddcbaeedbaccabdeeeecbaddabcabcddcbaecbaddabcdbaccabdeeeeeeeedbaccabdecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeecbaddabcedbaccabdeeeeeeeedbaccabdcbaddabceabcddcbacbaddabceeeedbaccabdeeabcddcbaabcddcbaedbaccabdeecbaddabcedbaccabdeeeecbaddabceabcddcbaeeeeeedbaccabdeabcddcbaeeeecbaddabceabcddcbaeecbaddabcecbaddabcdbaccabdeeabcddcbaeeeedbaccabdabcddcbaedbaccabdcbaddabceeeeeeeedbaccabdecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeedbaccabdeeeeeecbaddabcabcddcbaeecbaddabcdbaccabdeeabcddcbaedbaccabdabcddcbacbaddabceeeeeeabcddcbaeecbaddabceeeedbaccabdcbaddabceeeedbaccabdeeabcddcbaeeeeeedbaccabdabcddcbacbaddabceabcddcbaeecbaddabcdbaccabdeeabcddcbadbaccabdeeeeeecbaddabceeecbaddabceedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeedbaccabdeeecbaddabceeedbaccabdabcddcbaeeabcddcbaecbaddabcecbaddabcabcddcbaeeeedbaccabdabcddcbaecbaddabcdbaccabdeeeeeeeeeeeeeecbaddabcdbaccabdeabcddcbacbaddabceeeeabcddcbadbaccabdedbaccabdeabcddcbaeeabcddcbacbaddabceeedbaccabdeeecbaddabceeeecbaddabceedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeecbaddabcedbaccabdeeeeabcddcbaabcddcbaeedbaccabdcbaddabcedbaccabdeabcddcbaeeeeecbaddabcecbaddabcdbaccabdeabcddcbaeeeeeeeeeedbaccabdeabcddcbacbaddabcecbaddabceeeeedbaccabdeabcddcbaecbaddabcabcddcbaeedbaccabddbaccabdeeeeabcddcbaecbaddabceeeeeabcddcbaeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeecbaddabcedbaccabdeeeedbaccabdabcddcbaeeabcddcbacbaddabceabcddcbaedbaccabdeeeeecbaddabcecbaddabcabcddcbaedbaccabdeeeeeeeeeeabcddcbaedbaccabdcbaddabcecbaddabceeeeeabcddcbaedbaccabdecbaddabcdbaccabdeedbaccabdabcddcbaeeeeabcddcbaecbaddabceeeeeabcddcbaeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeecbaddabceedbaccabdeeabcddcbadbaccabdeeecbaddabcabcddcbaeeeabcddcbadbaccabdeedbaccabdecbaddabceeeecbaddabceabcddcbaeeeeeecbaddabceabcddcbaeeeeabcddcbaedbaccabdeedbaccabdcbaddabceeecbaddabcabcddcbaeeedbaccabdcbaddabceedbaccabdeeabcddcbaeeeeedbaccabdeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeedbaccabdeeabcddcbaeedbaccabdcbaddabceeecbaddabccbaddabceeeabcddcbaabcddcbaeecbaddabcedbaccabdeeeeabcddcbaedbaccabdeeeeeeabcddcbaedbaccabdeeeeabcddcbaecbaddabceedbaccabddbaccabdeeecbaddabccbaddabceeecbaddabcabcddcbaeedbaccabdeeabcddcbaeeeeeabcddcbaeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeeeabcddcbadbaccabdeecbaddabcedbaccabdeeeeabcddcbacbaddabccbaddabceeecbaddabceedbaccabdabcddcbaeeedbaccabdabcddcbaeeeeeeeeeedbaccabdabcddcbaeeedbaccabdabcddcbaeecbaddabceeecbaddabccbaddabcdbaccabdeeeeabcddcbaecbaddabceeabcddcbadbaccabdeeeeeeabcddcbaeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeeedbaccabdabcddcbaeecbaddabcedbaccabdeeeeabcddcbacbaddabccbaddabceeecbaddabceeabcddcbadbaccabdeeedbaccabdabcddcbaeeeeeeeeeedbaccabdabcddcbaeeeabcddcbadbaccabdeecbaddabceeecbaddabccbaddabcdbaccabdeeeeabcddcbaecbaddabceedbaccabdabcddcbaeeeeeeabcddcbaeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeeedbaccabdabcddcbaeecbaddabcedbaccabdeeeeabcddcbacbaddabccbaddabceeecbaddabceedbaccabdabcddcbaeeeabcddcbadbaccabdeeeeeeeeeeabcddcbadbaccabdeeedbaccabdabcddcbaeecbaddabceeecbaddabccbaddabcdbaccabdeeeeabcddcbaecbaddabceedbaccabdabcddcbaeeeeeeabcddcbaeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeeedbaccabdabcddcbaeedbaccabdeabcddcbaeeecbaddabceecbaddabcecbaddabcabcddcbaecbaddabcedbaccabdeeeeeecbaddabcdbaccabdeeeeeedbaccabdabcddcbaeeeeeedbaccabdeabcddcbaecbaddabcabcddcbaeabcddcbaeeabcddcbaeeecbaddabcedbaccabdeecbaddabcdbaccabdeeeeeedbaccabdeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeeedbaccabddbaccabdeecbaddabceabcddcbaeeeeabcddcbacbaddabccbaddabceeecbaddabceeabcddcbaabcddcbaeeedbaccabddbaccabdeeeeeeeeeeabcddcbaabcddcbaeeedbaccabddbaccabdeecbaddabceeecbaddabccbaddabcdbaccabdeeeedbaccabdecbaddabceeabcddcbaabcddcbaeeeeeeabcddcbaeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceedbaccabdeeeeeeeabcddcbadbaccabdcbaddabcdbaccabdeeeeabcddcbaecbaddabceeecbaddabceeedbaccabddbaccabdabcddcbaeeeeeecbaddabcabcddcbaeeeecbaddabcabcddcbaeeeeeecbaddabcdbaccabddbaccabdeeeabcddcbaeeeabcddcbaecbaddabceeeedbaccabdabcddcbadbaccabdcbaddabceeeeeeedbaccabdeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeabcddcbaeeedbaccabdedbaccabdeeeecbaddabcecbaddabceeeedbaccabdabcddcbaedbaccabdcbaddabcabcddcbaecbaddabceeeedbaccabddbaccabdeeeeeeeeeeeeabcddcbaabcddcbaeeeecbaddabcedbaccabdcbaddabcabcddcbaedbaccabdabcddcbaeeeecbaddabcecbaddabceeeeabcddcbaeabcddcbaeeedbaccabdeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeabcddcbaeeedbaccabdeecbaddabceeeabcddcbadbaccabdeeeedbaccabdcbaddabceedbaccabdcbaddabceeecbaddabcdbaccabddbaccabdeabcddcbaeeeeeeeeeeeeeedbaccabdeabcddcbaabcddcbacbaddabceeecbaddabcabcddcbaeecbaddabcabcddcbaeeeeabcddcbadbaccabdeeecbaddabceeabcddcbaeeedbaccabdeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeabcddcbaeeeecbaddabcdbaccabdeeeabcddcbaedbaccabdeeeeedbaccabdcbaddabcdbaccabdecbaddabceedbaccabdedbaccabdeeabcddcbacbaddabceeeeeeeeeeeecbaddabcdbaccabdeeabcddcbaeabcddcbaeecbaddabceabcddcbacbaddabcabcddcbaeeeeeabcddcbaedbaccabdeeeabcddcbacbaddabceeeedbaccabdeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeedbaccabdeeabcddcbaeeeeedbaccabdcbaddabceeeabcddcbadbaccabdecbaddabceeecbaddabccbaddabcedbaccabdeeeedbaccabdabcddcbaeeeeeeabcddcbadbaccabdeeeeeedbaccabdabcddcbaeeeeabcddcbaecbaddabccbaddabceeecbaddabceabcddcbadbaccabdeeecbaddabcabcddcbaeeeeedbaccabdeeabcddcbaeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeedbaccabdeeabcddcbaeeeeedbaccabdcbaddabceeedbaccabdabcddcbaecbaddabceeecbaddabccbaddabcedbaccabdeeeeabcddcbadbaccabdeeeeeeabcddcbadbaccabdeeeeeeabcddcbadbaccabdeeeeabcddcbaecbaddabccbaddabceeecbaddabcedbaccabdabcddcbaeeecbaddabcabcddcbaeeeeedbaccabdeeabcddcbaeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeedbaccabdeeeeecbaddabcabcddcbaedbaccabdedbaccabdeeeeabcddcbacbaddabceeabcddcbaecbaddabceeeeedbaccabdedbaccabdeedbaccabdcbaddabceeeeeecbaddabcabcddcbaeeabcddcbaeabcddcbaeeeeecbaddabcedbaccabdeecbaddabcdbaccabdeeeeabcddcbaeabcddcbaedbaccabdcbaddabceeeeeabcddcbaeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeedbaccabdeeeeecbaddabcabcddcbaedbaccabdedbaccabdeeeedbaccabdcbaddabceeabcddcbaecbaddabceeeeeabcddcbaeabcddcbaeeabcddcbacbaddabceeeeeecbaddabcdbaccabdeedbaccabdedbaccabdeeeeecbaddabcedbaccabdeecbaddabcabcddcbaeeeeabcddcbaeabcddcbaedbaccabdcbaddabceeeeeabcddcbaeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeedbaccabdeeeeecbaddabcdbaccabdedbaccabdeabcddcbaeeeeabcddcbacbaddabceedbaccabdecbaddabceeeeeabcddcbaeabcddcbaeeabcddcbacbaddabceeeeeecbaddabcdbaccabdeedbaccabdedbaccabdeeeeecbaddabceabcddcbaeecbaddabcdbaccabdeeeedbaccabdeabcddcbaeabcddcbacbaddabceeeeeabcddcbaeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeeabcddcbaedbaccabdeeeecbaddabceabcddcbaecbaddabceedbaccabdeedbaccabdedbaccabdeeeedbaccabdcbaddabcdbaccabdeabcddcbaeeeeeeecbaddabccbaddabceeeeeeedbaccabdeabcddcbacbaddabcabcddcbaeeeeabcddcbaeabcddcbaeeabcddcbaeecbaddabcedbaccabdecbaddabceeeeabcddcbaedbaccabdeeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeeabcddcbaedbaccabdeeeeecbaddabcabcddcbaedbaccabddbaccabdeeecbaddabceeecbaddabcdbaccabdeecbaddabceeeeeeedbaccabddbaccabdeedbaccabdabcddcbaeeabcddcbaabcddcbaeeeeeeecbaddabceeabcddcbacbaddabceeecbaddabceeeabcddcbaabcddcbaedbaccabdcbaddabceeeeeabcddcbaedbaccabdeeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeeabcddcbaeeedbaccabdcbaddabcabcddcbaeeeeeedbaccabddbaccabdeeeecbaddabcedbaccabdcbaddabccbaddabceedbaccabdeedbaccabdeeeeeeabcddcbadbaccabdeeeeeeabcddcbaeeabcddcbaeecbaddabccbaddabcabcddcbaecbaddabceeeeabcddcbaabcddcbaeeeeeedbaccabdcbaddabcabcddcbaeeedbaccabdeeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeeabcddcbaeeedbaccabdcbaddabcdbaccabdeeeeeeabcddcbadbaccabdeeeecbaddabcedbaccabdcbaddabccbaddabceedbaccabdeeabcddcbaeeeeeedbaccabdabcddcbaeeeeeedbaccabdeeabcddcbaeecbaddabccbaddabcabcddcbaecbaddabceeeeabcddcbadbaccabdeeeeeeabcddcbacbaddabcabcddcbaeeedbaccabdeeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeecbaddabccbaddabceeeeeeabcddcbadbaccabdeeedbaccabddbaccabdeabcddcbaedbaccabddbaccabdeeeabcddcbaeeeeeeeedbaccabdeeabcddcbacbaddabcdbaccabdabcddcbaeecbaddabceeeeeeeeabcddcbaeeecbaddabccbaddabceabcddcbaecbaddabccbaddabceeecbaddabcabcddcbaeeeeeedbaccabddbaccabdeeeedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceeeecbaddabceedbaccabddbaccabdeeeabcddcbaeeeeeeabcddcbadbaccabdcbaddabccbaddabceedbaccabdedbaccabdeeeeabcddcbaabcddcbaeeeeeedbaccabdcbaddabceeeeeeabcddcbaabcddcbaeeeecbaddabcecbaddabceedbaccabddbaccabdcbaddabcabcddcbaeeeeeeabcddcbaeeecbaddabccbaddabceedbaccabdeeeedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabddbaccabdeeeeeeabcddcbacbaddabceeecbaddabcdbaccabdeabcddcbaedbaccabdcbaddabceeeabcddcbaeeeeeeeecbaddabceedbaccabdabcddcbaabcddcbacbaddabceedbaccabdeeeeeeeeabcddcbaeeedbaccabdcbaddabceabcddcbaecbaddabcdbaccabdeeedbaccabdabcddcbaeeeeeecbaddabccbaddabceeeedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabddbaccabdeeeeeeabcddcbacbaddabceeedbaccabdcbaddabceabcddcbaecbaddabcdbaccabdeeeabcddcbaeeeeeeeecbaddabceedbaccabdabcddcbaabcddcbacbaddabceedbaccabdeeeeeeeeabcddcbaeeecbaddabcdbaccabdeabcddcbaedbaccabdcbaddabceeedbaccabdabcddcbaeeeeeecbaddabccbaddabceeeedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabddbaccabdeeeeeeabcddcbacbaddabceeedbaccabdcbaddabceabcddcbaedbaccabdcbaddabceeeabcddcbaeeeeeeeecbaddabceeabcddcbacbaddabcdbaccabdabcddcbaeedbaccabdeeeeeeeeabcddcbaeeedbaccabdcbaddabceabcddcbaedbaccabdcbaddabceeedbaccabdabcddcbaeeeeeecbaddabccbaddabceeeedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabdeabcddcbaeeeecbaddabceabcddcbaecbaddabceedbaccabdeedbaccabdedbaccabdeeeedbaccabdcbaddabcabcddcbaedbaccabdeeeeeeecbaddabccbaddabceeeeeeeabcddcbaedbaccabdcbaddabcabcddcbaeeeeabcddcbaeabcddcbaeeabcddcbaeecbaddabcedbaccabdecbaddabceeeedbaccabdeabcddcbaeeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabdeabcddcbaeeeeecbaddabcdbaccabdeabcddcbadbaccabdeeecbaddabceeecbaddabcdbaccabdeecbaddabceeeeeeedbaccabdabcddcbaeeabcddcbadbaccabdeedbaccabdabcddcbaeeeeeeecbaddabceeabcddcbacbaddabceeecbaddabceeeabcddcbadbaccabdeabcddcbacbaddabceeeeedbaccabdeabcddcbaeeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabdeabcddcbaeeeeecbaddabcdbaccabdedbaccabdabcddcbaeeecbaddabceeecbaddabcdbaccabdeecbaddabceeeeeeeabcddcbadbaccabdeeabcddcbadbaccabdeeabcddcbadbaccabdeeeeeeecbaddabceeabcddcbacbaddabceeecbaddabceeedbaccabdabcddcbaeabcddcbacbaddabceeeeedbaccabdeabcddcbaeeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabdeedbaccabddbaccabdeeeabcddcbaeeeeeeabcddcbacbaddabccbaddabccbaddabceecbaddabcedbaccabdeeeeabcddcbaabcddcbaeeeeeecbaddabcdbaccabdeeeeeeabcddcbaabcddcbaeeeecbaddabcedbaccabdeedbaccabddbaccabddbaccabdabcddcbaeeeeeeabcddcbaeeecbaddabccbaddabceecbaddabceeeedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabdeeeabcddcbacbaddabceedbaccabddbaccabdeeeeeedbaccabdecbaddabceeabcddcbaeabcddcbaecbaddabccbaddabcedbaccabdabcddcbaeeeeeeeeeeeeeecbaddabcdbaccabdeabcddcbaabcddcbaecbaddabcecbaddabceeabcddcbaedbaccabdeeeeeedbaccabddbaccabdeeabcddcbacbaddabceeedbaccabdeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeedbaccabdeeecbaddabcabcddcbaeedbaccabddbaccabdeeeeeedbaccabdecbaddabceeabcddcbaecbaddabceabcddcbaabcddcbaedbaccabdcbaddabceeeeeeeeeeeeeeabcddcbadbaccabdecbaddabccbaddabceabcddcbaecbaddabceeabcddcbaedbaccabdeeeeeedbaccabddbaccabdeecbaddabcabcddcbaeeedbaccabdeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeecbaddabcdbaccabdeedbaccabdeeeabcddcbaeedbaccabddbaccabdeeeeabcddcbacbaddabceecbaddabceeeabcddcbaeabcddcbadbaccabdeeeeeecbaddabcabcddcbaeeeeeedbaccabdcbaddabcecbaddabceeeabcddcbaeeabcddcbacbaddabceeeedbaccabddbaccabdeecbaddabceeedbaccabdeedbaccabdabcddcbaeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeecbaddabcdbaccabdeeedbaccabdeeabcddcbacbaddabceedbaccabdeeeeabcddcbaabcddcbaeeedbaccabdecbaddabceeedbaccabdedbaccabdeeeeabcddcbaabcddcbaeeeecbaddabcecbaddabceeedbaccabdecbaddabceeeabcddcbaabcddcbaeeeecbaddabceedbaccabdabcddcbaeecbaddabceeecbaddabcdbaccabdeeeeedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceeeeecbaddabcdbaccabdeeedbaccabdeeabcddcbadbaccabdeedbaccabdeeeeabcddcbaabcddcbaeeecbaddabcecbaddabceeecbaddabcecbaddabceeeeabcddcbaabcddcbaeeeedbaccabdedbaccabdeeedbaccabdedbaccabdeeeabcddcbaabcddcbaeeeecbaddabceecbaddabcabcddcbaeecbaddabceeecbaddabcdbaccabdeeeeedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabddbaccabdeeabcddcbacbaddabceeeeeeeabcddcbaeecbaddabccbaddabcdbaccabddbaccabdeabcddcbaeeeeedbaccabdeeecbaddabceeedbaccabdabcddcbaeeecbaddabceeeabcddcbaeeeeedbaccabdeabcddcbaabcddcbacbaddabccbaddabceedbaccabdeeeeeeecbaddabcdbaccabdeeabcddcbaabcddcbaeeeeecbaddabceedbaccabd'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabdeabcddcbaeecbaddabcdbaccabdeeecbaddabcdbaccabdeeeedbaccabdeedbaccabdeeeabcddcbaabcddcbaeeeecbaddabceabcddcbaecbaddabceeeeabcddcbaecbaddabceabcddcbaeeeecbaddabccbaddabceeedbaccabdeedbaccabdeeeedbaccabdabcddcbaeeedbaccabdabcddcbaeecbaddabcedbaccabdeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabdedbaccabdeabcddcbadbaccabdeeeeeecbaddabccbaddabceecbaddabceeabcddcbaeeeabcddcbaabcddcbaecbaddabcedbaccabdeeeedbaccabdeeeedbaccabdeeeedbaccabdeabcddcbaecbaddabccbaddabceeecbaddabceeabcddcbaeeabcddcbaabcddcbaeeeeeedbaccabdcbaddabcedbaccabdedbaccabdeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabdedbaccabdecbaddabcdbaccabdeeeeeeabcddcbaabcddcbaeecbaddabceeabcddcbaeeecbaddabccbaddabceabcddcbaedbaccabdeeeedbaccabdeeeedbaccabdeeeedbaccabdecbaddabceabcddcbaabcddcbaeeecbaddabceeabcddcbaeecbaddabccbaddabceeeeeedbaccabdabcddcbaedbaccabdedbaccabdeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabdeeabcddcbaedbaccabdecbaddabceabcddcbadbaccabdedbaccabdcbaddabceeeeeeeeeeeeeecbaddabcedbaccabdcbaddabceeabcddcbacbaddabcabcddcbacbaddabceeabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbadbaccabdedbaccabdcbaddabceabcddcbaedbaccabdecbaddabceedbaccabdeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabdeecbaddabcedbaccabdeabcddcbaeabcddcbadbaccabdedbaccabdcbaddabceeeeeeeeeeeeeecbaddabcedbaccabdabcddcbaeeabcddcbacbaddabccbaddabcabcddcbaeecbaddabcdbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbadbaccabdedbaccabdcbaddabcecbaddabcedbaccabdeabcddcbaeedbaccabdeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabdeecbaddabcedbaccabdeabcddcbaeabcddcbadbaccabdedbaccabdcbaddabceeeeeeeeeeeeeecbaddabcedbaccabdabcddcbaeecbaddabcabcddcbaabcddcbacbaddabceecbaddabcdbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbadbaccabdedbaccabdcbaddabcecbaddabcedbaccabdeabcddcbaeedbaccabdeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabdeecbaddabcedbaccabdeabcddcbaecbaddabcdbaccabdedbaccabdabcddcbaeeeeeeeeeeeeeeabcddcbaedbaccabdcbaddabceeabcddcbaabcddcbacbaddabccbaddabceeabcddcbadbaccabdecbaddabceeeeeeeeeeeeeecbaddabcdbaccabdedbaccabdabcddcbaecbaddabcedbaccabdeabcddcbaeedbaccabdeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeecbaddabceeeeedbaccabdeedbaccabdecbaddabcecbaddabcabcddcbadbaccabdeeeeeabcddcbadbaccabdeeeeeeeeeabcddcbaecbaddabceabcddcbaeedbaccabdeabcddcbacbaddabcedbaccabdeecbaddabceabcddcbaecbaddabceeeeeeeeedbaccabdcbaddabceeeeedbaccabdcbaddabcabcddcbaeabcddcbaedbaccabdeedbaccabdeeeeeabcddcbaeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdcbaddabceeeeeeeedbaccabdeeabcddcbaeecbaddabcdbaccabdecbaddabceeeabcddcbacbaddabcabcddcbaecbaddabceabcddcbaeeeeeeedbaccabddbaccabdeeeeeedbaccabddbaccabdeeeeeeecbaddabceabcddcbaecbaddabcabcddcbacbaddabceeeabcddcbaedbaccabdabcddcbaeecbaddabceedbaccabdeeeeeeeeabcddcbadbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdcbaddabceeeeeeeedbaccabdeeecbaddabccbaddabceeabcddcbaabcddcbadbaccabdeedbaccabdcbaddabceeeeeabcddcbaabcddcbaeeeeeeecbaddabceabcddcbadbaccabdecbaddabceeeeeeedbaccabddbaccabdeeeeecbaddabcabcddcbaeeabcddcbadbaccabddbaccabdeecbaddabccbaddabceeeabcddcbaeeeeeeeecbaddabcabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdcbaddabceeeeeeeeecbaddabcabcddcbaeedbaccabdedbaccabdeeecbaddabcabcddcbaabcddcbaeedbaccabdcbaddabcedbaccabdeeeeeeecbaddabceecbaddabceeabcddcbaeeabcddcbaeeeeeeedbaccabdeabcddcbadbaccabdeecbaddabccbaddabcabcddcbaeeedbaccabdedbaccabdeecbaddabcabcddcbaeeeeeeeeeabcddcbadbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabddbaccabdeeeeeeeecbaddabceecbaddabceabcddcbaeecbaddabceabcddcbadbaccabdeeedbaccabdecbaddabcabcddcbacbaddabceabcddcbaecbaddabceeeeeeeeeeeeeeeedbaccabdeabcddcbaedbaccabdabcddcbadbaccabdecbaddabceeecbaddabcabcddcbaedbaccabdeeabcddcbaedbaccabdeedbaccabdeeeeeeeecbaddabccbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeabcddcbaedbaccabdeeeeecbaddabcedbaccabdcbaddabcabcddcbaecbaddabceeabcddcbadbaccabdecbaddabceeeeeeedbaccabdabcddcbaeeeeeecbaddabcdbaccabdeeeeeeeabcddcbaedbaccabdcbaddabceeabcddcbaecbaddabcabcddcbadbaccabdeabcddcbaeeeeedbaccabdecbaddabceeeeeeabcddcbaedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeabcddcbaeeecbaddabceedbaccabddbaccabdecbaddabcecbaddabceeabcddcbadbaccabdeeeabcddcbaecbaddabceeeeeabcddcbadbaccabdeeeeeeabcddcbadbaccabdeeeeecbaddabcedbaccabdeeeabcddcbadbaccabdeecbaddabcecbaddabceabcddcbaabcddcbaeecbaddabceeedbaccabdeeeeeecbaddabceabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeeabcddcbaeedbaccabdecbaddabcecbaddabcedbaccabdcbaddabcabcddcbaedbaccabdeeeeeeeeeeabcddcbaedbaccabdabcddcbaabcddcbaeeeeeecbaddabccbaddabcdbaccabdecbaddabceeeeeeeeeedbaccabdecbaddabcabcddcbadbaccabdeabcddcbaeabcddcbaedbaccabdeecbaddabceeeeeeeabcddcbaedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeedbaccabdabcddcbaeeeecbaddabcecbaddabceabcddcbadbaccabdabcddcbaeeedbaccabdeecbaddabcecbaddabceeeeecbaddabcdbaccabdeeeeeedbaccabdabcddcbaeeeeeabcddcbaeabcddcbaeedbaccabdeeecbaddabcdbaccabdcbaddabceabcddcbaeabcddcbaeeeecbaddabcdbaccabdeeeeeeeabcddcbaedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeeeabcddcbadbaccabdeecbaddabccbaddabcedbaccabdeabcddcbaeeecbaddabceeecbaddabcdbaccabdeabcddcbaeeeeeeeeabcddcbadbaccabddbaccabdabcddcbaeeeeeeeedbaccabdeabcddcbacbaddabceeecbaddabceeedbaccabdeabcddcbaecbaddabccbaddabceeabcddcbadbaccabdeeeeeeeecbaddabceabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeeeabcddcbadbaccabdeecbaddabccbaddabcedbaccabdeabcddcbaeeecbaddabceeecbaddabcdbaccabdeabcddcbaeeeeeeeedbaccabdabcddcbaabcddcbadbaccabdeeeeeeeedbaccabdeabcddcbacbaddabceeecbaddabceeedbaccabdeabcddcbaecbaddabccbaddabceeabcddcbadbaccabdeeeeeeeecbaddabceabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeeecbaddabcdbaccabdeabcddcbadbaccabdeeeecbaddabceeabcddcbaabcddcbaecbaddabceedbaccabdecbaddabceeeedbaccabdeabcddcbaeeeeeecbaddabceabcddcbaeeeedbaccabdeabcddcbaeedbaccabdedbaccabdcbaddabceeabcddcbaeeeecbaddabcabcddcbaecbaddabcdbaccabdeeeeeeeecbaddabcedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeeedbaccabdabcddcbaeecbaddabccbaddabcedbaccabdeabcddcbaeeecbaddabceeecbaddabcdbaccabdeabcddcbaeeeeeeeeabcddcbaabcddcbadbaccabddbaccabdeeeeeeeedbaccabdeabcddcbacbaddabceeecbaddabceeedbaccabdeabcddcbaecbaddabccbaddabceedbaccabdabcddcbaeeeeeeeecbaddabceabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdecbaddabceeeeeeeedbaccabdcbaddabceabcddcbacbaddabceeeeabcddcbaeecbaddabcdbaccabdedbaccabdeeabcddcbaedbaccabdeeeeabcddcbaecbaddabceeeeeeabcddcbaedbaccabdeeeecbaddabcedbaccabdeecbaddabceabcddcbaabcddcbaeecbaddabceeeedbaccabdabcddcbaedbaccabdcbaddabceeeeeeeecbaddabcedbaccabdeeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeecbaddabceeeeeedbaccabdabcddcbaeedbaccabdcbaddabceeabcddcbaecbaddabcabcddcbadbaccabdeeeeeeabcddcbaeedbaccabdeeeecbaddabcdbaccabdeeeecbaddabceeabcddcbaeeeeeecbaddabcabcddcbadbaccabdeabcddcbaeedbaccabdcbaddabceeabcddcbacbaddabceeeeeedbaccabdeeedbaccabdeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeecbaddabceeedbaccabdeeecbaddabcabcddcbaeeabcddcbaedbaccabdedbaccabdabcddcbaeeeecbaddabcabcddcbaedbaccabdcbaddabceeeeeeeeeeeeeedbaccabdcbaddabceabcddcbadbaccabdeeeeabcddcbacbaddabcecbaddabceabcddcbaeeabcddcbadbaccabdeeecbaddabceeedbaccabdeeeedbaccabdeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeecbaddabceeabcddcbaeecbaddabcdbaccabdeeedbaccabddbaccabdeeeabcddcbaabcddcbaeedbaccabdecbaddabceeeeabcddcbaecbaddabceeeeeeabcddcbaecbaddabceeeeabcddcbaedbaccabdeecbaddabccbaddabceeedbaccabddbaccabdeeedbaccabdabcddcbaeecbaddabceeabcddcbaeeeeeabcddcbaeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeedbaccabdecbaddabceeeeabcddcbaabcddcbaeecbaddabcdbaccabdecbaddabceabcddcbaeeeeedbaccabdedbaccabdcbaddabceabcddcbaeeeeeeeeeecbaddabceabcddcbadbaccabdedbaccabdeeeeecbaddabceabcddcbaedbaccabdabcddcbaeecbaddabccbaddabceeeeabcddcbaedbaccabdeeeeeabcddcbaeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeedbaccabdecbaddabceeeecbaddabcabcddcbaeeabcddcbadbaccabdeabcddcbaecbaddabceeeeedbaccabdedbaccabdabcddcbaecbaddabceeeeeeeeeeabcddcbaecbaddabcdbaccabdedbaccabdeeeeeabcddcbaecbaddabcedbaccabdcbaddabceecbaddabcabcddcbaeeeeabcddcbaedbaccabdeeeeeabcddcbaeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeedbaccabdeecbaddabceeabcddcbacbaddabceeedbaccabdabcddcbaeeeabcddcbacbaddabceecbaddabcedbaccabdeeeedbaccabdeabcddcbaeeeeeedbaccabdeabcddcbaeeeeabcddcbaecbaddabceecbaddabcdbaccabdeeedbaccabdabcddcbaeeecbaddabcdbaccabdeecbaddabceeabcddcbaeeeeecbaddabceeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeeeabcddcbacbaddabceedbaccabdecbaddabceeeeabcddcbadbaccabddbaccabdeeedbaccabdeecbaddabcabcddcbaeeecbaddabcabcddcbaeeeeeeeeeecbaddabcabcddcbaeeecbaddabcabcddcbaeedbaccabdeeedbaccabddbaccabdcbaddabceeeeabcddcbaedbaccabdeeabcddcbacbaddabceeeeeeabcddcbaeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeeecbaddabcabcddcbaeecbaddabceabcddcbaeeedbaccabdeedbaccabdedbaccabdabcddcbaedbaccabdecbaddabceeeeeedbaccabdcbaddabceeeeeecbaddabcabcddcbaeeeeeecbaddabceabcddcbaedbaccabdabcddcbaeabcddcbaeeabcddcbaeeedbaccabdecbaddabceedbaccabdcbaddabceeeeeecbaddabceeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeeecbaddabcabcddcbaeedbaccabdecbaddabceeeeabcddcbadbaccabddbaccabdeeedbaccabdeeabcddcbacbaddabceeecbaddabcabcddcbaeeeeeeeeeecbaddabcabcddcbaeeeabcddcbacbaddabceedbaccabdeeedbaccabddbaccabdcbaddabceeeeabcddcbaedbaccabdeecbaddabcabcddcbaeeeeeeabcddcbaeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeeecbaddabcabcddcbaeedbaccabdecbaddabceeeeabcddcbadbaccabddbaccabdeeedbaccabdeecbaddabcabcddcbaeeeabcddcbacbaddabceeeeeeeeeeabcddcbacbaddabceeecbaddabcabcddcbaeedbaccabdeeedbaccabddbaccabdcbaddabceeeeabcddcbaedbaccabdeecbaddabcabcddcbaeeeeeeabcddcbaeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeeecbaddabccbaddabceedbaccabdeabcddcbaeeeeabcddcbadbaccabddbaccabdeeedbaccabdeeabcddcbaabcddcbaeeecbaddabccbaddabceeeeeeeeeeabcddcbaabcddcbaeeecbaddabccbaddabceedbaccabdeeedbaccabddbaccabdcbaddabceeeecbaddabcedbaccabdeeabcddcbaabcddcbaeeeeeeabcddcbaeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeecbaddabceeeeeeeabcddcbacbaddabcdbaccabdcbaddabceeeeabcddcbaedbaccabdeeedbaccabdeeecbaddabccbaddabcabcddcbaeeeeeedbaccabdabcddcbaeeeedbaccabdabcddcbaeeeeeedbaccabdcbaddabccbaddabceeeabcddcbaeeeabcddcbaedbaccabdeeeecbaddabcabcddcbacbaddabcdbaccabdeeeeeeecbaddabceeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeabcddcbaeeecbaddabcecbaddabceeeedbaccabdedbaccabdeeeecbaddabcabcddcbaecbaddabcdbaccabdabcddcbaedbaccabdeeeecbaddabccbaddabceeeeeeeeeeeeabcddcbaabcddcbaeeeedbaccabdecbaddabcdbaccabdabcddcbaecbaddabcabcddcbaeeeedbaccabdedbaccabdeeeeabcddcbaeabcddcbaeeecbaddabceeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeabcddcbaeeecbaddabceedbaccabdeeeabcddcbacbaddabceeeecbaddabcdbaccabdeecbaddabcdbaccabdeeedbaccabdcbaddabccbaddabceabcddcbaeeeeeeeeeeeeeecbaddabceabcddcbaabcddcbadbaccabdeeedbaccabdabcddcbaeedbaccabdabcddcbaeeeeabcddcbacbaddabceeedbaccabdeeabcddcbaeeecbaddabceeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeabcddcbaeeeedbaccabdcbaddabceeeabcddcbaecbaddabceeeeecbaddabcdbaccabdcbaddabcedbaccabdeecbaddabcecbaddabceeabcddcbadbaccabdeeeeeeeeeeeedbaccabdcbaddabceeabcddcbaeabcddcbaeedbaccabdeabcddcbadbaccabdabcddcbaeeeeeabcddcbaecbaddabceeeabcddcbadbaccabdeeeecbaddabceeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeecbaddabceeabcddcbaeeeeecbaddabcdbaccabdeeeabcddcbacbaddabcedbaccabdeeedbaccabddbaccabdecbaddabceeeecbaddabcabcddcbaeeeeeeabcddcbacbaddabceeeeeecbaddabcabcddcbaeeeeabcddcbaedbaccabddbaccabdeeedbaccabdeabcddcbacbaddabceeedbaccabdabcddcbaeeeeecbaddabceeabcddcbaeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeecbaddabceeabcddcbaeeeeecbaddabcdbaccabdeeecbaddabcabcddcbaedbaccabdeeedbaccabddbaccabdecbaddabceeeeabcddcbacbaddabceeeeeeabcddcbacbaddabceeeeeeabcddcbacbaddabceeeeabcddcbaedbaccabddbaccabdeeedbaccabdecbaddabcabcddcbaeeedbaccabdabcddcbaeeeeecbaddabceeabcddcbaeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeecbaddabceeeeedbaccabdabcddcbaecbaddabcecbaddabceeeeabcddcbadbaccabdeeabcddcbaedbaccabdeeeeecbaddabcecbaddabceecbaddabcdbaccabdeeeeeedbaccabdabcddcbaeeabcddcbaeabcddcbaeeeeedbaccabdecbaddabceedbaccabdcbaddabceeeeabcddcbaeabcddcbaecbaddabcdbaccabdeeeeeabcddcbaeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeecbaddabceeeeedbaccabdabcddcbaecbaddabcecbaddabceeeecbaddabcdbaccabdeeabcddcbaedbaccabdeeeeeabcddcbaeabcddcbaeeabcddcbadbaccabdeeeeeedbaccabdcbaddabceecbaddabcecbaddabceeeeedbaccabdecbaddabceedbaccabdabcddcbaeeeeabcddcbaeabcddcbaecbaddabcdbaccabdeeeeeabcddcbaeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeecbaddabceeeeedbaccabdcbaddabcecbaddabceabcddcbaeeeeabcddcbadbaccabdeecbaddabcedbaccabdeeeeeabcddcbaeabcddcbaeeabcddcbadbaccabdeeeeeedbaccabdcbaddabceecbaddabcecbaddabceeeeedbaccabdeabcddcbaeedbaccabdcbaddabceeeecbaddabceabcddcbaeabcddcbadbaccabdeeeeeabcddcbaeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeeabcddcbaecbaddabceeeedbaccabdeabcddcbaedbaccabdeecbaddabceecbaddabcecbaddabceeeecbaddabcdbaccabdcbaddabceabcddcbaeeeeeeedbaccabddbaccabdeeeeeeecbaddabceabcddcbadbaccabdabcddcbaeeeeabcddcbaeabcddcbaeeabcddcbaeedbaccabdecbaddabcedbaccabdeeeeabcddcbaecbaddabceeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeeabcddcbaecbaddabceeeeedbaccabdabcddcbaecbaddabccbaddabceeedbaccabdeeedbaccabdcbaddabceedbaccabdeeeeeeecbaddabccbaddabceecbaddabcabcddcbaeeabcddcbaabcddcbaeeeeeeedbaccabdeeabcddcbadbaccabdeeedbaccabdeeeabcddcbaabcddcbaecbaddabcdbaccabdeeeeeabcddcbaecbaddabceeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeeabcddcbaeeecbaddabcdbaccabdabcddcbaeeeeeecbaddabccbaddabceeeedbaccabdecbaddabcdbaccabddbaccabdeecbaddabceecbaddabceeeeeeabcddcbacbaddabceeeeeeabcddcbaeeabcddcbaeedbaccabddbaccabdabcddcbaedbaccabdeeeeabcddcbaabcddcbaeeeeeecbaddabcdbaccabdabcddcbaeeecbaddabceeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeeabcddcbaeeecbaddabcdbaccabdcbaddabceeeeeeabcddcbacbaddabceeeedbaccabdecbaddabcdbaccabddbaccabdeecbaddabceeabcddcbaeeeeeecbaddabcabcddcbaeeeeeecbaddabceeabcddcbaeedbaccabddbaccabdabcddcbaedbaccabdeeeeabcddcbacbaddabceeeeeeabcddcbadbaccabdabcddcbaeeecbaddabceeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabccbaddabceeeeeeabcddcbadbaccabdeeecbaddabcdbaccabdeabcddcbaecbaddabcdbaccabdeeeabcddcbaeeeeeeeedbaccabdeeabcddcbadbaccabdcbaddabcabcddcbaeecbaddabceeeeeeeeabcddcbaeeecbaddabcdbaccabdeabcddcbaecbaddabcdbaccabdeeecbaddabcabcddcbaeeeeeedbaccabddbaccabdeeeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabccbaddabceeeeeeabcddcbadbaccabdeeecbaddabcdbaccabdeabcddcbaedbaccabdcbaddabceeeabcddcbaeeeeeeeedbaccabdeecbaddabcabcddcbaabcddcbadbaccabdeecbaddabceeeeeeeeabcddcbaeeedbaccabdcbaddabceabcddcbaecbaddabcdbaccabdeeecbaddabcabcddcbaeeeeeedbaccabddbaccabdeeeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabccbaddabceeeeeeabcddcbadbaccabdeeedbaccabdcbaddabceabcddcbaecbaddabcdbaccabdeeeabcddcbaeeeeeeeedbaccabdeecbaddabcabcddcbaabcddcbadbaccabdeecbaddabceeeeeeeeabcddcbaeeecbaddabcdbaccabdeabcddcbaedbaccabdcbaddabceeecbaddabcabcddcbaeeeeeedbaccabddbaccabdeeeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabceabcddcbaeeeedbaccabdeabcddcbaedbaccabdeecbaddabceecbaddabcecbaddabceeeecbaddabcdbaccabdabcddcbaecbaddabceeeeeeedbaccabddbaccabdeeeeeeeabcddcbaecbaddabcdbaccabdabcddcbaeeeeabcddcbaeabcddcbaeeabcddcbaeedbaccabdecbaddabcedbaccabdeeeecbaddabceabcddcbaeeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabceabcddcbaeeeeedbaccabdcbaddabceabcddcbacbaddabceeedbaccabdeeedbaccabdcbaddabceedbaccabdeeeeeeecbaddabcabcddcbaeeabcddcbacbaddabceecbaddabcabcddcbaeeeeeeedbaccabdeeabcddcbadbaccabdeeedbaccabdeeeabcddcbacbaddabceabcddcbadbaccabdeeeeecbaddabceabcddcbaeeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabceabcddcbaeeeeedbaccabdcbaddabcecbaddabcabcddcbaeeedbaccabdeeedbaccabdcbaddabceedbaccabdeeeeeeeabcddcbacbaddabceeabcddcbacbaddabceeabcddcbacbaddabceeeeeeedbaccabdeeabcddcbadbaccabdeeedbaccabdeeecbaddabcabcddcbaeabcddcbadbaccabdeeeeecbaddabceabcddcbaeeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabceecbaddabccbaddabceeeabcddcbaeeeeeeabcddcbadbaccabddbaccabddbaccabdeedbaccabdecbaddabceeeeabcddcbaabcddcbaeeeeeedbaccabdcbaddabceeeeeeabcddcbaabcddcbaeeeedbaccabdecbaddabceecbaddabccbaddabccbaddabcabcddcbaeeeeeeabcddcbaeeedbaccabddbaccabdeedbaccabdeeeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabceeeabcddcbadbaccabdeecbaddabccbaddabceeeeeecbaddabcedbaccabdeeabcddcbaeabcddcbaedbaccabddbaccabdecbaddabcabcddcbaeeeeeeeeeeeeeedbaccabdcbaddabceabcddcbaabcddcbaedbaccabdedbaccabdeeabcddcbaecbaddabceeeeeecbaddabccbaddabceeabcddcbadbaccabdeeecbaddabceeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeecbaddabceeedbaccabdabcddcbaeecbaddabccbaddabceeeeeecbaddabcedbaccabdeeabcddcbaedbaccabdeabcddcbaabcddcbaecbaddabcdbaccabdeeeeeeeeeeeeeeabcddcbacbaddabcedbaccabddbaccabdeabcddcbaedbaccabdeeabcddcbaecbaddabceeeeeecbaddabccbaddabceedbaccabdabcddcbaeeecbaddabceeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeedbaccabddbaccabdeeeeeeabcddcbacbaddabceeecbaddabccbaddabceabcddcbaecbaddabccbaddabceeeabcddcbaeeeeeeeecbaddabceeabcddcbadbaccabdcbaddabcabcddcbaeedbaccabdeeeeeeeeabcddcbaeeedbaccabddbaccabdeabcddcbaedbaccabddbaccabdeeedbaccabdabcddcbaeeeeeecbaddabccbaddabceeeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeeeedbaccabdeecbaddabccbaddabceeeabcddcbaeeeeeeabcddcbacbaddabcdbaccabddbaccabdeecbaddabcecbaddabceeeeabcddcbaabcddcbaeeeeeecbaddabcdbaccabdeeeeeeabcddcbaabcddcbaeeeedbaccabdedbaccabdeecbaddabccbaddabcdbaccabdabcddcbaeeeeeeabcddcbaeeedbaccabddbaccabdeecbaddabceeeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabccbaddabceeabcddcbadbaccabdeeeeeeeabcddcbaeedbaccabddbaccabdcbaddabccbaddabceabcddcbaeeeeecbaddabceeedbaccabdeeecbaddabcabcddcbaeeedbaccabdeeeabcddcbaeeeeecbaddabceabcddcbaabcddcbadbaccabddbaccabdeecbaddabceeeeeeedbaccabdcbaddabceeabcddcbaabcddcbaeeeeedbaccabdeecbaddabc'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabceabcddcbaeedbaccabdcbaddabceeedbaccabdcbaddabceeeecbaddabceecbaddabceeeabcddcbaabcddcbaeeeedbaccabdeabcddcbaedbaccabdeeeeabcddcbaedbaccabdeabcddcbaeeeedbaccabddbaccabdeeecbaddabceecbaddabceeeecbaddabcabcddcbaeeecbaddabcabcddcbaeedbaccabdecbaddabceeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabcecbaddabceabcddcbacbaddabceeeeeedbaccabddbaccabdeedbaccabdeeabcddcbaeeeabcddcbaabcddcbaedbaccabdecbaddabceeeecbaddabceeeecbaddabceeeecbaddabceabcddcbaedbaccabddbaccabdeeedbaccabdeeabcddcbaeeabcddcbaabcddcbaeeeeeecbaddabcdbaccabdecbaddabcecbaddabceeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabcecbaddabcedbaccabdcbaddabceeeeeeabcddcbaabcddcbaeedbaccabdeeabcddcbaeeedbaccabddbaccabdeabcddcbaecbaddabceeeecbaddabceeeecbaddabceeeecbaddabcedbaccabdeabcddcbaabcddcbaeeedbaccabdeeabcddcbaeedbaccabddbaccabdeeeeeecbaddabcabcddcbaecbaddabcecbaddabceeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabceeabcddcbaecbaddabcedbaccabdeabcddcbacbaddabcecbaddabcdbaccabdeeeeeeeeeeeeeedbaccabdecbaddabcdbaccabdeeabcddcbadbaccabdabcddcbadbaccabdeeabcddcbacbaddabceabcddcbaeeeeeeeeeeeeeeabcddcbacbaddabcecbaddabcdbaccabdeabcddcbaecbaddabcedbaccabdeecbaddabceeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabceecbaddabcedbaccabdedbaccabdabcddcbacbaddabceeeeeabcddcbacbaddabceeeeeeeeeabcddcbaedbaccabdeabcddcbaeecbaddabceabcddcbadbaccabdecbaddabceedbaccabdeabcddcbaedbaccabdeeeeeeeeecbaddabcdbaccabdeeeeecbaddabcdbaccabdabcddcbaeabcddcbaecbaddabceecbaddabceeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabceedbaccabdecbaddabceabcddcbaeabcddcbacbaddabcecbaddabcdbaccabdeeeeeeeeeeeeeedbaccabdecbaddabcabcddcbaeeabcddcbadbaccabddbaccabdabcddcbaeedbaccabdcbaddabceabcddcbaeeeeeeeeeeeeeeabcddcbacbaddabcecbaddabcdbaccabdedbaccabdecbaddabceabcddcbaeecbaddabceeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabceedbaccabdecbaddabceabcddcbaeabcddcbacbaddabcecbaddabcdbaccabdeeeeeeeeeeeeeedbaccabdecbaddabcabcddcbaeedbaccabdabcddcbaabcddcbadbaccabdeedbaccabdcbaddabceabcddcbaeeeeeeeeeeeeeeabcddcbacbaddabcecbaddabcdbaccabdedbaccabdecbaddabceabcddcbaeecbaddabceeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeecbaddabceedbaccabdecbaddabceabcddcbaedbaccabdcbaddabcecbaddabcabcddcbaeeeeeeeeeeeeeeabcddcbaecbaddabcdbaccabdeeabcddcbaabcddcbadbaccabddbaccabdeeabcddcbacbaddabcedbaccabdeeeeeeeeeeeeeedbaccabdcbaddabcecbaddabcabcddcbaedbaccabdecbaddabceabcddcbaeecbaddabceeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeedbaccabdcbaddabceecbaddabceeeabcddcbaeecbaddabccbaddabceeeeabcddcbadbaccabdeedbaccabdeeeabcddcbaeabcddcbacbaddabceeeeeedbaccabdabcddcbaeeeeeecbaddabcdbaccabdedbaccabdeeeabcddcbaeeabcddcbadbaccabdeeeecbaddabccbaddabceedbaccabdeeecbaddabceecbaddabcabcddcbaeeeeeabcddcbaeedbaccabd'' 
 + 
 +''abcddcbaeedbaccabdeeeeedbaccabdcbaddabceeecbaddabceeabcddcbacbaddabceecbaddabceeeeabcddcbaabcddcbaeeedbaccabdedbaccabdeeedbaccabdedbaccabdeeeeabcddcbaabcddcbaeeeecbaddabcecbaddabceeecbaddabcecbaddabceeeabcddcbaabcddcbaeeeedbaccabdeedbaccabdabcddcbaeedbaccabdeeedbaccabdcbaddabceeeeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeedbaccabdeeeeedbaccabdcbaddabceeecbaddabceeabcddcbadbaccabdeecbaddabceeeeabcddcbaabcddcbaeeecbaddabcedbaccabdeeecbaddabcecbaddabceeeeabcddcbaabcddcbaeeeedbaccabdedbaccabdeeecbaddabcedbaccabdeeeabcddcbaabcddcbaeeeedbaccabdeecbaddabcabcddcbaeedbaccabdeeedbaccabdcbaddabceeeeecbaddabceeabcddcba'' 
 + 
 +''abcddcbaeeeabcddcbacbaddabceeeeecbaddabceedbaccabdeeeeecbaddabcdbaccabddbaccabdeabcddcbaedbaccabdedbaccabdeeeeabcddcbaeecbaddabceedbaccabdcbaddabceeeeeeeecbaddabcabcddcbaeecbaddabceedbaccabdeeeeabcddcbaeabcddcbaedbaccabdeabcddcbaabcddcbacbaddabceeeeeabcddcbaeecbaddabceeeeecbaddabcdbaccabdeeedbaccabd'' 
 + 
 +''abcddcbaeeeabcddcbacbaddabceeeeedbaccabdeecbaddabceeeeecbaddabcdbaccabddbaccabdeabcddcbaedbaccabdecbaddabceeeedbaccabdeeabcddcbaeecbaddabcdbaccabdeeeeeeeeabcddcbacbaddabceedbaccabdeeabcddcbaeeeecbaddabceabcddcbaedbaccabdeabcddcbaabcddcbacbaddabceeeeecbaddabceeabcddcbaeeeeecbaddabcdbaccabdeeedbaccabd'' 
 + 
 +''abcddcbaeeeabcddcbacbaddabceeeeeecbaddabcdbaccabdeeeeecbaddabcedbaccabdedbaccabdabcddcbaedbaccabdeedbaccabdeeeabcddcbaecbaddabceedbaccabdeecbaddabceeeeeecbaddabceeabcddcbaeecbaddabcedbaccabdeeeabcddcbaeeabcddcbaedbaccabdabcddcbaeabcddcbaecbaddabceeeeeabcddcbacbaddabceeeeeecbaddabcdbaccabdeeedbaccabd'' 
 + 
 +''abcddcbaeeeabcddcbacbaddabceeeeeeedbaccabdecbaddabcecbaddabcedbaccabdeabcddcbadbaccabdeeeedbaccabdeeeedbaccabdecbaddabccbaddabceeeeeeeabcddcbadbaccabdabcddcbadbaccabdeeeeeeecbaddabccbaddabceabcddcbaeeeeabcddcbaeeeeabcddcbadbaccabdeabcddcbaecbaddabcecbaddabceabcddcbaeeeeeeecbaddabcdbaccabdeeedbaccabd'' 
 + 
 +''abcddcbaeeeabcddcbadbaccabdeeeeecbaddabceedbaccabdeeeeedbaccabdcbaddabccbaddabceabcddcbaecbaddabcedbaccabdeeeecbaddabceeabcddcbaeedbaccabdcbaddabceeeeeeeeabcddcbadbaccabdeecbaddabceeabcddcbaeeeedbaccabdeabcddcbaecbaddabceabcddcbaabcddcbadbaccabdeeeeedbaccabdeeabcddcbaeeeeedbaccabdcbaddabceeecbaddabc'' 
 + 
 +''abcddcbaeeeabcddcbadbaccabdeeeeedbaccabdeecbaddabceeeeedbaccabdcbaddabccbaddabceabcddcbaecbaddabcecbaddabceeeeabcddcbaeedbaccabdeecbaddabcdbaccabdeeeeeeeedbaccabdabcddcbaeedbaccabdeecbaddabceeeeabcddcbaeabcddcbaecbaddabceabcddcbaabcddcbadbaccabdeeeeeabcddcbaeedbaccabdeeeeedbaccabdcbaddabceeecbaddabc'' 
 + 
 +''abcddcbaeeeabcddcbadbaccabdeeeeeedbaccabdcbaddabceeeeedbaccabdecbaddabcecbaddabcabcddcbaecbaddabceecbaddabceeeabcddcbaedbaccabdeecbaddabceedbaccabdeeeeeedbaccabdeeabcddcbaeedbaccabdecbaddabceeeabcddcbaeeabcddcbaecbaddabcabcddcbaeabcddcbaedbaccabdeeeeeabcddcbadbaccabdeeeeeedbaccabdcbaddabceeecbaddabc'' 
 + 
 +''abcddcbaeeeabcddcbadbaccabdeeeeeeecbaddabcedbaccabdedbaccabdecbaddabceabcddcbacbaddabceeeecbaddabceeeecbaddabcedbaccabddbaccabdeeeeeeeabcddcbacbaddabcabcddcbacbaddabceeeeeeedbaccabddbaccabdeabcddcbaeeeeabcddcbaeeeeabcddcbacbaddabceabcddcbaedbaccabdedbaccabdeabcddcbaeeeeeeedbaccabdcbaddabceeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabcabcddcbaeeeeeedbaccabdeeedbaccabdcbaddabcdbaccabdeeecbaddabccbaddabceeeeeeabcddcbaabcddcbadbaccabddbaccabdeeeeeecbaddabceeedbaccabdabcddcbaeeecbaddabceeeeeeabcddcbaabcddcbadbaccabddbaccabdeeeeeecbaddabccbaddabceeeabcddcbacbaddabcabcddcbaeeeabcddcbaeeeeeedbaccabdcbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeedbaccabdeedbaccabdeeabcddcbaabcddcbaeecbaddabcecbaddabceecbaddabcdbaccabdeeeeeecbaddabcecbaddabcabcddcbaeeabcddcbaeeeeeeabcddcbaeeabcddcbadbaccabdedbaccabdeeeeeecbaddabcdbaccabdeedbaccabdedbaccabdeeabcddcbaabcddcbaeecbaddabceecbaddabceeeeeecbaddabcdbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeedbaccabdeeeabcddcbacbaddabcabcddcbaeeecbaddabccbaddabceeeeeedbaccabddbaccabdabcddcbadbaccabdeeeeeecbaddabceeedbaccabdabcddcbaeeecbaddabceeeeeeabcddcbadbaccabdabcddcbaabcddcbaeeeeeecbaddabccbaddabceeedbaccabdcbaddabcdbaccabdeeeabcddcbaeeeeeeabcddcbacbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeedbaccabdeeeabcddcbacbaddabcdbaccabdeeecbaddabccbaddabceeeeeeabcddcbadbaccabdabcddcbaabcddcbaeeeeeecbaddabceeeabcddcbadbaccabdeeecbaddabceeeeeedbaccabddbaccabdabcddcbadbaccabdeeeeeecbaddabccbaddabceeeabcddcbacbaddabcdbaccabdeeeabcddcbaeeeeeeabcddcbacbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeedbaccabdeeedbaccabdcbaddabcabcddcbaeeecbaddabccbaddabceeeeeeabcddcbaabcddcbaabcddcbadbaccabdeeeeeecbaddabceeeabcddcbadbaccabdeeecbaddabceeeeeeabcddcbadbaccabddbaccabddbaccabdeeeeeecbaddabccbaddabceeedbaccabdcbaddabcabcddcbaeeeabcddcbaeeeeeeabcddcbacbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeeeabcddcbacbaddabcedbaccabdeecbaddabceeeedbaccabdedbaccabdcbaddabceabcddcbaeeeabcddcbadbaccabdeeeabcddcbaeecbaddabceeeeeedbaccabdeeabcddcbaeeecbaddabcabcddcbaeeeabcddcbaedbaccabdcbaddabcecbaddabceeeedbaccabdeecbaddabcedbaccabdabcddcbaeeeeeeecbaddabcdbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeeeabcddcbacbaddabcedbaccabdeedbaccabdeeeedbaccabdecbaddabccbaddabceabcddcbaeeeabcddcbacbaddabceeeabcddcbaeedbaccabdeeeeeecbaddabceeabcddcbaeeedbaccabdabcddcbaeeeabcddcbaedbaccabddbaccabdecbaddabceeeecbaddabceecbaddabcedbaccabdabcddcbaeeeeeeecbaddabcdbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeeeabcddcbadbaccabdecbaddabceedbaccabdeeeecbaddabcedbaccabdcbaddabceabcddcbaeeeabcddcbacbaddabceeeabcddcbaeedbaccabdeeeeeecbaddabceeabcddcbaeeedbaccabdabcddcbaeeeabcddcbaedbaccabdcbaddabcedbaccabdeeeecbaddabceedbaccabdecbaddabcabcddcbaeeeeeeecbaddabcdbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeeeabcddcbacbaddabcedbaccabdeecbaddabcecbaddabceeedbaccabdeeeeedbaccabdcbaddabcabcddcbaeabcddcbaeeeeeeeecbaddabcecbaddabcabcddcbadbaccabdeeeeedbaccabdeeeabcddcbaeabcddcbaeedbaccabdeabcddcbacbaddabceeecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeeecbaddabcabcddcbaedbaccabdeecbaddabcecbaddabceeedbaccabdeeeeedbaccabdabcddcbacbaddabceabcddcbaeeeeeeeecbaddabceabcddcbacbaddabcdbaccabdeeeeedbaccabdeeeabcddcbaeabcddcbaeedbaccabdecbaddabcabcddcbaeeecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceabcddcbaeeeecbaddabcdbaccabdeeeeeedbaccabdeabcddcbaeedbaccabdcbaddabcdbaccabdeeecbaddabcedbaccabdeabcddcbaeedbaccabdcbaddabceeeeeeeeeeeecbaddabcabcddcbaeedbaccabdeabcddcbaecbaddabceeeabcddcbacbaddabcabcddcbaeedbaccabdeabcddcbaeeeeeeabcddcbacbaddabceeeedbaccabdecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceabcddcbaeeeeecbaddabcdbaccabdeeeeabcddcbaedbaccabdedbaccabdcbaddabceedbaccabdeeecbaddabceeeedbaccabdedbaccabdeeabcddcbacbaddabceeeeeecbaddabcdbaccabdeeabcddcbaeabcddcbaeeeecbaddabceeeabcddcbaeecbaddabcabcddcbaeabcddcbaedbaccabdeeeeabcddcbacbaddabceeeeedbaccabdecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcecbaddabceeedbaccabdeeeeeabcddcbadbaccabdeecbaddabcabcddcbaeeeedbaccabdedbaccabdcbaddabcdbaccabdeeeeeedbaccabdeabcddcbaeeeeabcddcbaabcddcbaeeeeabcddcbaecbaddabceeeeeecbaddabcdbaccabdcbaddabcecbaddabceeeeabcddcbadbaccabdeecbaddabcabcddcbaeeeeecbaddabceeedbaccabdedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcecbaddabceeeeeabcddcbadbaccabdeeeecbaddabcedbaccabddbaccabdedbaccabdeeeeedbaccabdeabcddcbaabcddcbaecbaddabceeeeeeeabcddcbaecbaddabcdbaccabdeabcddcbaeeeeeeedbaccabdeabcddcbaabcddcbaecbaddabceeeeecbaddabcecbaddabccbaddabcedbaccabdeeeecbaddabcabcddcbaeeeeedbaccabdedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcecbaddabceeeeeabcddcbadbaccabdeeeedbaccabdedbaccabddbaccabdecbaddabceeeeecbaddabceabcddcbaabcddcbaedbaccabdeeeeeeeabcddcbaecbaddabcdbaccabdeabcddcbaeeeeeeecbaddabceabcddcbaabcddcbaedbaccabdeeeeedbaccabdecbaddabccbaddabcecbaddabceeeecbaddabcabcddcbaeeeeedbaccabdedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcecbaddabceeeeedbaccabdeeeabcddcbadbaccabddbaccabddbaccabdeabcddcbaeeeeeecbaddabcdbaccabdeeeeeeeecbaddabceabcddcbaeeabcddcbacbaddabcabcddcbacbaddabceecbaddabceabcddcbaeeeeeeeedbaccabdabcddcbaeeeeeecbaddabcedbaccabddbaccabddbaccabdcbaddabceeedbaccabdeeeeeabcddcbaeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeedbaccabdeeeeeabcddcbaecbaddabcedbaccabdcbaddabceeabcddcbacbaddabceeeedbaccabdabcddcbaeeeeeeeecbaddabcedbaccabdeabcddcbaabcddcbaecbaddabcedbaccabdeeeeeeeeabcddcbacbaddabceeeedbaccabdabcddcbaeedbaccabdcbaddabcedbaccabdeabcddcbaeeeeecbaddabceeecbaddabcedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeedbaccabdeecbaddabceeabcddcbaeeedbaccabdabcddcbacbaddabceeeeeecbaddabcdbaccabdeabcddcbaabcddcbacbaddabcdbaccabdeeeeeeeeeeeeeeeedbaccabdabcddcbacbaddabccbaddabcedbaccabdabcddcbaeeeeeeabcddcbacbaddabcdbaccabdeeecbaddabceeabcddcbaeedbaccabdeeeedbaccabdeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeedbaccabdeecbaddabceeecbaddabcdbaccabdeeabcddcbaeeeabcddcbaeabcddcbaabcddcbaeeeedbaccabddbaccabdcbaddabccbaddabceeeeeeeeeeeeeecbaddabccbaddabcabcddcbaabcddcbaeeeedbaccabddbaccabdedbaccabdeeedbaccabdeeabcddcbacbaddabceeecbaddabceeabcddcbaeeeeabcddcbaecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeeabcddcbacbaddabceeedbaccabdeecbaddabceeabcddcbaedbaccabdedbaccabdabcddcbaeeeecbaddabceedbaccabdeeeedbaccabdcbaddabceeeecbaddabcabcddcbaeeeeabcddcbaeecbaddabceeeedbaccabdabcddcbaeabcddcbaedbaccabdeecbaddabceeabcddcbaeeecbaddabcdbaccabdeeeeeabcddcbaecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeeabcddcbadbaccabdeeeecbaddabcedbaccabdcbaddabcedbaccabdeeeeecbaddabceabcddcbaabcddcbaecbaddabceeeeeeeabcddcbaedbaccabdcbaddabceabcddcbaeeeeeeedbaccabdeabcddcbaabcddcbaedbaccabdeeeeecbaddabcedbaccabdcbaddabcedbaccabdeeeecbaddabcabcddcbaeeeeecbaddabcedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeeabcddcbaecbaddabceeedbaccabddbaccabdabcddcbaeecbaddabceeeecbaddabcdbaccabdeeeeeecbaddabceabcddcbaedbaccabdeabcddcbaeeeedbaccabdeabcddcbaedbaccabdecbaddabceeeeeeabcddcbacbaddabceeeecbaddabceedbaccabdabcddcbaabcddcbaeeecbaddabcedbaccabdeeeeeabcddcbaecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeecbaddabcdbaccabdeeeeabcddcbaeabcddcbaedbaccabdcbaddabceeabcddcbaeeecbaddabceeeedbaccabdedbaccabdeedbaccabdcbaddabceeeeeecbaddabcabcddcbaeeabcddcbaeabcddcbaeeeecbaddabceeedbaccabdeecbaddabcabcddcbaedbaccabdedbaccabdeeeeabcddcbacbaddabceeeeeabcddcbaecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeedbaccabdcbaddabceeedbaccabdeecbaddabceeabcddcbaeabcddcbaeabcddcbadbaccabdeeeecbaddabceeabcddcbaeeeeabcddcbacbaddabceeeecbaddabcdbaccabdeeeedbaccabdeecbaddabceeeeabcddcbadbaccabdedbaccabdedbaccabdeecbaddabceeabcddcbaeeecbaddabcabcddcbaeeeeeabcddcbaecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeedbaccabdcbaddabceeeedbaccabdeabcddcbaeabcddcbacbaddabceeeabcddcbadbaccabdeeeeeecbaddabceecbaddabcecbaddabceeabcddcbaeeabcddcbaeedbaccabdedbaccabdeedbaccabdeeeeeecbaddabcabcddcbaeeedbaccabdabcddcbaeabcddcbaecbaddabceeeedbaccabdcbaddabceeeeecbaddabcedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeedbaccabdeabcddcbaeeabcddcbacbaddabceeeedbaccabdecbaddabcecbaddabcdbaccabdeeeeedbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeecbaddabccbaddabceabcddcbaeeedbaccabdeeeeedbaccabdabcddcbaeabcddcbaedbaccabdeeeeabcddcbacbaddabceecbaddabcedbaccabdeeeeedbaccabdeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeeecbaddabcabcddcbaeedbaccabdedbaccabdabcddcbacbaddabceeeedbaccabdeeecbaddabceeeeeeedbaccabdeabcddcbaeeabcddcbacbaddabccbaddabcdbaccabdeeabcddcbaeabcddcbaeeeeeeecbaddabceeedbaccabdeeeecbaddabcabcddcbaabcddcbaedbaccabdeedbaccabdcbaddabceeeeeedbaccabdecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabcedbaccabdeeeeeecbaddabcdbaccabdeedbaccabdeabcddcbaabcddcbacbaddabceeeedbaccabdeeecbaddabceeeeeeeabcddcbaeabcddcbaeedbaccabdcbaddabccbaddabcabcddcbaeeabcddcbaedbaccabdeeeeeeecbaddabceeedbaccabdeeeecbaddabcabcddcbadbaccabdedbaccabdeeabcddcbacbaddabceeeeeedbaccabdecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceeabcddcbaeecbaddabceeeeedbaccabddbaccabddbaccabddbaccabdeeeeeecbaddabcecbaddabcdbaccabdecbaddabceeeeeeeeeabcddcbaeabcddcbaabcddcbaabcddcbaabcddcbaeabcddcbaeeeeeeeeedbaccabdecbaddabcdbaccabdedbaccabdeeeeeecbaddabccbaddabccbaddabccbaddabceeeeedbaccabdeeabcddcbaeedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceeabcddcbaeedbaccabdeeeedbaccabdedbaccabdeecbaddabccbaddabceecbaddabcdbaccabdeeeecbaddabcedbaccabdeeeeeeeeabcddcbaeabcddcbaabcddcbaabcddcbaabcddcbaeabcddcbaeeeeeeeecbaddabcedbaccabdeeeecbaddabcdbaccabdeedbaccabddbaccabdeecbaddabcecbaddabceeeecbaddabceeabcddcbaeedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceeabcddcbaeeedbaccabdecbaddabceeeabcddcbadbaccabdeeeeecbaddabcedbaccabddbaccabdeecbaddabcedbaccabdcbaddabceeeeeeeeedbaccabdabcddcbadbaccabdabcddcbaeeeeeeeeecbaddabcabcddcbaecbaddabceeabcddcbaabcddcbaecbaddabceeeeeabcddcbadbaccabdeeecbaddabceabcddcbaeeedbaccabdeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeabcddcbaeeedbaccabdecbaddabceeedbaccabdabcddcbaeeeeecbaddabcedbaccabddbaccabdeecbaddabcedbaccabdcbaddabceeeeeeeeeabcddcbadbaccabdabcddcbadbaccabdeeeeeeeeecbaddabcabcddcbaecbaddabceeabcddcbaabcddcbaecbaddabceeeeedbaccabdabcddcbaeeecbaddabceabcddcbaeeedbaccabdeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeabcddcbaeeedbaccabdedbaccabdcbaddabceeeeeeecbaddabcdbaccabdeeeabcddcbaecbaddabcdbaccabdabcddcbaedbaccabdecbaddabceeeeeeeedbaccabdabcddcbaeeeeeeeecbaddabceabcddcbaedbaccabdabcddcbacbaddabcedbaccabdeeeabcddcbacbaddabceeeeeeecbaddabcabcddcbaeabcddcbaeeedbaccabdeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeabcddcbaeeedbaccabdedbaccabdeeecbaddabceedbaccabdecbaddabccbaddabceeeeeabcddcbaabcddcbaeeedbaccabddbaccabdeeeecbaddabcedbaccabdeeeeabcddcbaecbaddabceeeeabcddcbaabcddcbaeeedbaccabddbaccabdeeeeecbaddabccbaddabceabcddcbaeecbaddabceeeabcddcbaeabcddcbaeeedbaccabdeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceecbaddabccbaddabceeeeeedbaccabdeeabcddcbaeeedbaccabdabcddcbaedbaccabddbaccabdedbaccabdeabcddcbaeeeeeeeabcddcbadbaccabdeedbaccabdeeeecbaddabceecbaddabcabcddcbaeeeeeeeabcddcbaecbaddabcecbaddabccbaddabceabcddcbacbaddabceeeabcddcbaeecbaddabceeeeeedbaccabddbaccabdeedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceecbaddabceedbaccabdedbaccabdeeeeeeedbaccabdabcddcbaabcddcbaecbaddabcdbaccabdeeabcddcbaeeeeeeabcddcbacbaddabceeeeecbaddabccbaddabceedbaccabddbaccabdeeeeedbaccabdabcddcbaeeeeeeabcddcbaeecbaddabcdbaccabdeabcddcbaabcddcbacbaddabceeeeeeecbaddabcecbaddabceedbaccabdeedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceecbaddabceeeeabcddcbadbaccabdedbaccabdedbaccabdeeeeeeedbaccabdabcddcbaeabcddcbaeeecbaddabccbaddabcdbaccabdeecbaddabcabcddcbaeeeeeeeeeeeedbaccabdcbaddabceeabcddcbacbaddabccbaddabceeedbaccabdedbaccabdabcddcbaeeeeeeeabcddcbaeabcddcbaeabcddcbadbaccabdeeeecbaddabceecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceecbaddabceeeedbaccabdabcddcbaedbaccabdedbaccabdeeeeeeeabcddcbadbaccabdeabcddcbaeeecbaddabccbaddabcdbaccabdeecbaddabcabcddcbaeeeeeeeeeeeedbaccabdcbaddabceeabcddcbacbaddabccbaddabceeedbaccabdeabcddcbadbaccabdeeeeeeeabcddcbaeabcddcbaedbaccabdabcddcbaeeeecbaddabceecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceecbaddabceeeedbaccabddbaccabdeabcddcbaedbaccabdeeeeeeeabcddcbaabcddcbaedbaccabdeeecbaddabccbaddabcdbaccabdeecbaddabcabcddcbaeeeeeeeeeeeedbaccabdcbaddabceeabcddcbacbaddabccbaddabceeeabcddcbaedbaccabddbaccabdeeeeeeeabcddcbaedbaccabdeabcddcbaabcddcbaeeeecbaddabceecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceecbaddabceeeedbaccabddbaccabdedbaccabdeabcddcbaeeeeeeeabcddcbadbaccabdeabcddcbaeeecbaddabccbaddabcabcddcbaeecbaddabcdbaccabdeeeeeeeeeeeeabcddcbacbaddabceedbaccabdcbaddabccbaddabceeedbaccabdeabcddcbadbaccabdeeeeeeedbaccabdeabcddcbaeabcddcbaabcddcbaeeeecbaddabceecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabdcbaddabceeeeeecbaddabceeabcddcbaeeedbaccabdabcddcbaedbaccabddbaccabdedbaccabdeabcddcbaeeeeeeeabcddcbacbaddabceecbaddabceeeedbaccabdeedbaccabdabcddcbaeeeeeeeabcddcbaecbaddabcecbaddabccbaddabceabcddcbacbaddabceeeabcddcbaeedbaccabdeeeeeedbaccabdcbaddabceedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabddbaccabdeeeeeecbaddabceecbaddabceeedbaccabdabcddcbaeabcddcbaabcddcbaeabcddcbaecbaddabceeeeeeedbaccabddbaccabdeedbaccabdeeeecbaddabceecbaddabccbaddabceeeeeeedbaccabdeabcddcbaeabcddcbaabcddcbaeabcddcbacbaddabceeedbaccabdeedbaccabdeeeeeecbaddabccbaddabceedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabdeeeabcddcbaeabcddcbaeeecbaddabceedbaccabdecbaddabccbaddabceeeeedbaccabddbaccabdeeedbaccabddbaccabdeeeecbaddabceabcddcbaeeeedbaccabdecbaddabceeeeabcddcbaabcddcbaeeeabcddcbaabcddcbaeeeeecbaddabccbaddabceabcddcbaeecbaddabceeedbaccabdedbaccabdeeeabcddcbaeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabdeeeabcddcbaecbaddabceeedbaccabddbaccabdeeeeecbaddabceabcddcbadbaccabdeecbaddabceabcddcbacbaddabceeeeeeeeeabcddcbadbaccabddbaccabdabcddcbaeeeeeeeeecbaddabcdbaccabdecbaddabceeabcddcbadbaccabdecbaddabceeeeeabcddcbaabcddcbaeeecbaddabcedbaccabdeeeabcddcbaeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabdeeeabcddcbaecbaddabceeedbaccabddbaccabdeeeeecbaddabceabcddcbadbaccabdeecbaddabceabcddcbacbaddabceeeeeeeeedbaccabdabcddcbaabcddcbadbaccabdeeeeeeeeecbaddabcdbaccabdecbaddabceeabcddcbadbaccabdecbaddabceeeeeabcddcbaabcddcbaeeecbaddabcedbaccabdeeeabcddcbaeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabdeeeabcddcbaecbaddabceeedbaccabddbaccabdeeeeecbaddabcedbaccabdabcddcbaeecbaddabceabcddcbacbaddabceeeeeeeeeabcddcbaabcddcbadbaccabddbaccabdeeeeeeeeecbaddabcdbaccabdecbaddabceedbaccabdabcddcbaecbaddabceeeeeabcddcbaabcddcbaeeecbaddabcedbaccabdeeeabcddcbaeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabdeeeabcddcbaedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeeedbaccabdecbaddabcdbaccabdabcddcbaedbaccabdecbaddabceeeeeeeedbaccabdabcddcbaeeeeeeeecbaddabceabcddcbaedbaccabdabcddcbacbaddabceabcddcbaeeedbaccabdcbaddabceeeeeeecbaddabcabcddcbaedbaccabdeeeabcddcbaeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabdeeeabcddcbaedbaccabdeeecbaddabceeabcddcbaecbaddabccbaddabceeeeedbaccabddbaccabdeeedbaccabdabcddcbaeeeecbaddabcedbaccabdeeeeabcddcbaecbaddabceeeedbaccabdabcddcbaeeeabcddcbaabcddcbaeeeeecbaddabccbaddabcedbaccabdeecbaddabceeeabcddcbaedbaccabdeeeabcddcbaeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceedbaccabdeeedbaccabdedbaccabdeeecbaddabceeabcddcbaecbaddabccbaddabceeeeeabcddcbaabcddcbaeeeabcddcbadbaccabdeeeecbaddabceabcddcbaeeeedbaccabdecbaddabceeeeabcddcbadbaccabdeeedbaccabddbaccabdeeeeecbaddabccbaddabcedbaccabdeecbaddabceeeabcddcbaeabcddcbaeeeabcddcbaeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeeabcddcbadbaccabdeeeeedbaccabddbaccabdeeeabcddcbacbaddabceecbaddabceedbaccabdeeecbaddabcedbaccabdeeeeecbaddabccbaddabceabcddcbaeeeecbaddabceabcddcbaabcddcbaeeeeedbaccabdeabcddcbaeeedbaccabdeeabcddcbaeeabcddcbacbaddabceeedbaccabddbaccabdeeeeedbaccabdcbaddabceeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceeeabcddcbaedbaccabdeeecbaddabceabcddcbaeedbaccabdcbaddabceeeeedbaccabdedbaccabdeecbaddabcdbaccabdeeeeeecbaddabcdbaccabdeabcddcbaeeeedbaccabdeabcddcbacbaddabceeeeeeabcddcbacbaddabceeabcddcbaeabcddcbaeeeeecbaddabcabcddcbaeedbaccabdecbaddabceeeabcddcbaedbaccabdeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeeabcddcbaedbaccabdeeecbaddabcedbaccabdeedbaccabdcbaddabceeeeeabcddcbaedbaccabdeecbaddabcabcddcbaeeeeeecbaddabcdbaccabdedbaccabdeeeeabcddcbaeabcddcbacbaddabceeeeeedbaccabdcbaddabceeabcddcbaedbaccabdeeeeecbaddabcabcddcbaeeabcddcbaecbaddabceeeabcddcbaedbaccabdeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeeabcddcbaedbaccabdeeedbaccabddbaccabdeeeeabcddcbacbaddabceeedbaccabdeecbaddabceeecbaddabccbaddabceeecbaddabcabcddcbaeeedbaccabdeeeedbaccabdeeecbaddabcabcddcbaeeeabcddcbaabcddcbaeeeabcddcbaeedbaccabdeeeabcddcbacbaddabceeeedbaccabddbaccabdeeedbaccabdecbaddabceeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceeeabcddcbaedbaccabdeeedbaccabddbaccabdeeeecbaddabcabcddcbaeeedbaccabdeecbaddabceeecbaddabccbaddabceeeabcddcbacbaddabceeedbaccabdeeeedbaccabdeeeabcddcbacbaddabceeeabcddcbaabcddcbaeeeabcddcbaeedbaccabdeeecbaddabcabcddcbaeeeedbaccabddbaccabdeeedbaccabdecbaddabceeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceeeabcddcbaeecbaddabcedbaccabddbaccabdeeeeedbaccabdcbaddabceeeeeabcddcbaedbaccabddbaccabdeabcddcbaeeeecbaddabceabcddcbaeeeecbaddabccbaddabceeeedbaccabdecbaddabceeeedbaccabdeabcddcbaabcddcbaedbaccabdeeeeecbaddabcabcddcbaeeeeeabcddcbaabcddcbaecbaddabceedbaccabdeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeeabcddcbaeecbaddabcedbaccabddbaccabdeeeeedbaccabdcbaddabceeeeedbaccabdeabcddcbaabcddcbaedbaccabdeeeecbaddabceabcddcbaeeeecbaddabccbaddabceeeedbaccabdecbaddabceeeeabcddcbaedbaccabddbaccabdeabcddcbaeeeeecbaddabcabcddcbaeeeeeabcddcbaabcddcbaecbaddabceedbaccabdeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeecbaddabcdbaccabdeeeeeabcddcbaedbaccabdecbaddabcedbaccabdeabcddcbaedbaccabdeeeeeeeedbaccabdeabcddcbacbaddabccbaddabceeeeabcddcbaeeabcddcbaeeeedbaccabddbaccabdabcddcbaecbaddabceeeeeeeecbaddabceabcddcbaecbaddabcedbaccabdecbaddabceabcddcbaeeeeecbaddabcdbaccabdeeedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceeecbaddabceabcddcbaedbaccabdedbaccabdeeeeeeeedbaccabddbaccabdeabcddcbaeabcddcbaeecbaddabccbaddabcdbaccabdcbaddabceeeeeeeabcddcbaeeeedbaccabdeeeeeeecbaddabcabcddcbacbaddabccbaddabceedbaccabdedbaccabdeabcddcbaabcddcbaeeeeeeeeabcddcbaeabcddcbaedbaccabdecbaddabceeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeecbaddabcedbaccabdeabcddcbaedbaccabdeeeeeeeedbaccabdabcddcbaedbaccabdeabcddcbaeecbaddabccbaddabcdbaccabdcbaddabceeeeeeeabcddcbaeeeedbaccabdeeeeeeecbaddabcabcddcbacbaddabccbaddabceedbaccabdeabcddcbaedbaccabdabcddcbaeeeeeeeeabcddcbaedbaccabdeabcddcbaecbaddabceeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeecbaddabcedbaccabdedbaccabdeabcddcbaeeeeeeeedbaccabdabcddcbaeabcddcbaedbaccabdeecbaddabccbaddabcdbaccabdcbaddabceeeeeeeabcddcbaeeeedbaccabdeeeeeeecbaddabcabcddcbacbaddabccbaddabceeabcddcbaedbaccabdedbaccabdabcddcbaeeeeeeeedbaccabdeabcddcbaeabcddcbaecbaddabceeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeecbaddabcedbaccabdeeedbaccabddbaccabdeeeeabcddcbacbaddabceeedbaccabdeeabcddcbaeeeabcddcbacbaddabceeeabcddcbaabcddcbaeeedbaccabdeeeedbaccabdeeecbaddabccbaddabceeeabcddcbacbaddabceeecbaddabceedbaccabdeeeabcddcbacbaddabceeeedbaccabddbaccabdeeedbaccabdeabcddcbaeeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceeecbaddabceeedbaccabddbaccabddbaccabdeeecbaddabceeeabcddcbaabcddcbaeeeeeeabcddcbacbaddabceeedbaccabddbaccabdeeeeeeabcddcbaabcddcbadbaccabdabcddcbaeeeeeecbaddabccbaddabceeecbaddabcdbaccabdeeeeeedbaccabdcbaddabceeecbaddabceeeabcddcbadbaccabdabcddcbaeeecbaddabceeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeedbaccabdcbaddabceeeeeabcddcbaedbaccabdedbaccabdecbaddabceabcddcbaedbaccabdeeeeeeeecbaddabceabcddcbadbaccabdcbaddabceeeeabcddcbaeeabcddcbaeeeedbaccabdcbaddabcabcddcbaedbaccabdeeeeeeeecbaddabceabcddcbaedbaccabdecbaddabcecbaddabceabcddcbaeeeeedbaccabdcbaddabceeedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeecbaddabceeedbaccabdeabcddcbaeecbaddabceeabcddcbaeeedbaccabdecbaddabceeedbaccabddbaccabdeecbaddabcdbaccabdeeeeeeecbaddabcabcddcbaeedbaccabdeeabcddcbaeedbaccabdcbaddabceeeeeeeabcddcbacbaddabceeabcddcbaabcddcbaeeecbaddabceabcddcbaeeedbaccabdeecbaddabceedbaccabdeabcddcbaeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeedbaccabdeabcddcbaeeecbaddabceabcddcbaeedbaccabdcbaddabceeeeedbaccabdedbaccabdeecbaddabcdbaccabdeeeeeecbaddabcabcddcbaedbaccabdeeeeabcddcbaedbaccabdcbaddabceeeeeeabcddcbacbaddabceeabcddcbaeabcddcbaeeeeecbaddabcabcddcbaeedbaccabdecbaddabceeedbaccabdeabcddcbaeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeedbaccabdedbaccabdeeecbaddabcedbaccabdeeabcddcbacbaddabceeeeeabcddcbaeabcddcbaeecbaddabcdbaccabdeeeeeecbaddabcabcddcbaeabcddcbaeeeedbaccabdedbaccabdcbaddabceeeeeeabcddcbacbaddabceedbaccabdedbaccabdeeeeecbaddabcdbaccabdeeabcddcbaecbaddabceeeabcddcbaeabcddcbaeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeedbaccabdeeecbaddabcabcddcbacbaddabceeedbaccabdeeedbaccabdabcddcbaeeeeeeabcddcbadbaccabdeeedbaccabddbaccabdeeeeeecbaddabcabcddcbacbaddabccbaddabceeeeeeabcddcbaabcddcbaeeedbaccabdcbaddabceeeeeecbaddabccbaddabceeedbaccabdeeeabcddcbaabcddcbaabcddcbaeeedbaccabdeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceeedbaccabdeeecbaddabcdbaccabdcbaddabceeedbaccabdeeeabcddcbaabcddcbaeeeeeeabcddcbadbaccabdeeecbaddabcdbaccabdeeeeeeabcddcbaabcddcbadbaccabdabcddcbaeeeeeecbaddabccbaddabceeecbaddabccbaddabceeeeeedbaccabdcbaddabceeedbaccabdeeeabcddcbadbaccabdabcddcbaeeedbaccabdeeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceeedbaccabdeeecbaddabcdbaccabdcbaddabceeedbaccabdeeeabcddcbadbaccabdeeeeeeabcddcbaabcddcbaeeeabcddcbaabcddcbaeeeeeecbaddabcdbaccabdcbaddabccbaddabceeeeeedbaccabdabcddcbaeeedbaccabdcbaddabceeeeeecbaddabccbaddabceeedbaccabdeeeabcddcbadbaccabdabcddcbaeeedbaccabdeeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceeeeabcddcbadbaccabdeecbaddabcabcddcbaeeeedbaccabdeecbaddabceeedbaccabdeedbaccabdcbaddabcedbaccabdeeeeeecbaddabcdbaccabdeeeabcddcbadbaccabdeeeabcddcbacbaddabceeeeeeabcddcbaecbaddabcabcddcbaeeabcddcbaeeecbaddabceeabcddcbaeeeedbaccabdcbaddabceeabcddcbadbaccabdeeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeeeabcddcbadbaccabdeecbaddabcdbaccabdeeeedbaccabdeecbaddabceeeabcddcbaeedbaccabdcbaddabceabcddcbaeeeeeecbaddabcdbaccabdeeedbaccabdabcddcbaeeeabcddcbacbaddabceeeeeedbaccabdecbaddabcabcddcbaeedbaccabdeeecbaddabceeabcddcbaeeeeabcddcbacbaddabceeabcddcbadbaccabdeeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeeeabcddcbaecbaddabcdbaccabdeedbaccabdeeabcddcbaedbaccabdeeeeeedbaccabdcbaddabceecbaddabccbaddabceeeeeeeedbaccabdabcddcbadbaccabdeeabcddcbadbaccabdabcddcbaeeeeeeeecbaddabccbaddabceecbaddabcabcddcbaeeeeeeabcddcbaedbaccabdeeabcddcbaeeabcddcbacbaddabcedbaccabdeeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeeecbaddabcdbaccabdeeedbaccabdecbaddabcdbaccabdabcddcbaeeeeeeedbaccabdabcddcbaeeeedbaccabdeeeabcddcbaeeeabcddcbaeabcddcbaeabcddcbacbaddabcecbaddabcecbaddabceeecbaddabceeedbaccabdeeeecbaddabcdbaccabdeeeeeeecbaddabcdbaccabdabcddcbaedbaccabdeeedbaccabdabcddcbaeeeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeecbaddabceeeedbaccabdecbaddabcabcddcbaeedbaccabdeedbaccabdeabcddcbaeeeeeedbaccabdcbaddabceecbaddabccbaddabceeeeeeeeabcddcbaabcddcbaabcddcbaeedbaccabddbaccabddbaccabdeeeeeeeecbaddabccbaddabceecbaddabcabcddcbaeeeeeedbaccabdeabcddcbaeeabcddcbaeedbaccabdcbaddabceabcddcbaeeeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeecbaddabceeeeedbaccabdcbaddabcdbaccabdeecbaddabcdbaccabdeeabcddcbaeeeeeabcddcbadbaccabdeeeeeeeeabcddcbaeabcddcbaeeedbaccabdcbaddabcecbaddabcabcddcbaeabcddcbadbaccabdeeecbaddabcecbaddabceeeeeeeedbaccabdcbaddabceeeeecbaddabceedbaccabdabcddcbaeedbaccabdabcddcbadbaccabdeeeeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdabcddcbaeeeeeecbaddabceeecbaddabcdbaccabdcbaddabceeedbaccabddbaccabdeeeeeeabcddcbaabcddcbacbaddabccbaddabceeeeeedbaccabdeeecbaddabcabcddcbaeeedbaccabdeeeeeeabcddcbaabcddcbacbaddabccbaddabceeeeeedbaccabddbaccabdeeeabcddcbadbaccabdabcddcbaeeeabcddcbaeeeeeecbaddabcdbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeecbaddabceecbaddabceeabcddcbaabcddcbaeedbaccabdedbaccabdeedbaccabdcbaddabceeeeeedbaccabdedbaccabdabcddcbaeeabcddcbaeeeeeeabcddcbaeeabcddcbacbaddabcecbaddabceeeeeedbaccabdcbaddabceecbaddabcecbaddabceeabcddcbaabcddcbaeedbaccabdeedbaccabdeeeeeedbaccabdcbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeecbaddabceeeabcddcbadbaccabdabcddcbaeeedbaccabddbaccabdeeeeeecbaddabccbaddabcabcddcbacbaddabceeeeeedbaccabdeeecbaddabcabcddcbaeeedbaccabdeeeeeeabcddcbacbaddabcabcddcbaabcddcbaeeeeeedbaccabddbaccabdeeecbaddabcdbaccabdcbaddabceeeabcddcbaeeeeeeabcddcbadbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeecbaddabceeeabcddcbadbaccabdcbaddabceeedbaccabddbaccabdeeeeeeabcddcbacbaddabcabcddcbaabcddcbaeeeeeedbaccabdeeeabcddcbacbaddabceeedbaccabdeeeeeecbaddabccbaddabcabcddcbacbaddabceeeeeedbaccabddbaccabdeeeabcddcbadbaccabdcbaddabceeeabcddcbaeeeeeeabcddcbadbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeecbaddabceeecbaddabcdbaccabdabcddcbaeeedbaccabddbaccabdeeeeeeabcddcbaabcddcbaabcddcbacbaddabceeeeeedbaccabdeeeabcddcbacbaddabceeedbaccabdeeeeeeabcddcbacbaddabccbaddabccbaddabceeeeeedbaccabddbaccabdeeecbaddabcdbaccabdabcddcbaeeeabcddcbaeeeeeeabcddcbadbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeeeabcddcbacbaddabcedbaccabdeecbaddabceeeedbaccabdecbaddabcdbaccabdeabcddcbaeeeabcddcbadbaccabdeeeabcddcbaeecbaddabceeeeeedbaccabdeeabcddcbaeeecbaddabcabcddcbaeeeabcddcbaecbaddabcdbaccabdecbaddabceeeedbaccabdeecbaddabcedbaccabdabcddcbaeeeeeeedbaccabdcbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeeeabcddcbadbaccabdecbaddabceecbaddabceeeecbaddabcedbaccabddbaccabdeabcddcbaeeeabcddcbadbaccabdeeeabcddcbaeecbaddabceeeeeedbaccabdeeabcddcbaeeecbaddabcabcddcbaeeeabcddcbaecbaddabccbaddabcedbaccabdeeeedbaccabdeedbaccabdecbaddabcabcddcbaeeeeeeedbaccabdcbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeeeabcddcbadbaccabdecbaddabceedbaccabdeeeecbaddabcecbaddabcdbaccabdeabcddcbaeeeabcddcbacbaddabceeeabcddcbaeedbaccabdeeeeeecbaddabceeabcddcbaeeedbaccabdabcddcbaeeeabcddcbaecbaddabcdbaccabdedbaccabdeeeecbaddabceedbaccabdecbaddabcabcddcbaeeeeeeedbaccabdcbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeeeabcddcbadbaccabdecbaddabceedbaccabdedbaccabdeeecbaddabceeeeecbaddabcdbaccabdabcddcbaeabcddcbaeeeeeeeedbaccabdedbaccabdabcddcbacbaddabceeeeecbaddabceeeabcddcbaeabcddcbaeecbaddabceabcddcbadbaccabdeeedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeeedbaccabdabcddcbaecbaddabceedbaccabdedbaccabdeeecbaddabceeeeecbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeedbaccabdeabcddcbadbaccabdcbaddabceeeeecbaddabceeeabcddcbaeabcddcbaeecbaddabcedbaccabdabcddcbaeeedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeabcddcbaeeeedbaccabdcbaddabceeeeeecbaddabceabcddcbaeecbaddabcdbaccabdcbaddabceeedbaccabdecbaddabceabcddcbaeecbaddabcdbaccabdeeeeeeeeeeeedbaccabdabcddcbaeecbaddabceabcddcbaedbaccabdeeeabcddcbadbaccabdabcddcbaeecbaddabceabcddcbaeeeeeeabcddcbadbaccabdeeeecbaddabcedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeabcddcbaeeeeedbaccabdcbaddabceeeeabcddcbaecbaddabcecbaddabcdbaccabdeecbaddabceeedbaccabdeeeecbaddabcecbaddabceeabcddcbadbaccabdeeeeeedbaccabdcbaddabceeabcddcbaeabcddcbaeeeedbaccabdeeeabcddcbaeedbaccabdabcddcbaeabcddcbaecbaddabceeeeabcddcbadbaccabdeeeeecbaddabcedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeecbaddabceeeeeabcddcbaedbaccabdecbaddabcdbaccabdeeabcddcbadbaccabdeeeecbaddabcabcddcbaeeeeeeeedbaccabdecbaddabceabcddcbaabcddcbaedbaccabdecbaddabceeeeeeeeabcddcbadbaccabdeeeecbaddabcabcddcbaeecbaddabcdbaccabdecbaddabceabcddcbaeeeeedbaccabdeeedbaccabdecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeecbaddabceedbaccabdeeabcddcbaeeecbaddabcabcddcbadbaccabdeeeeeedbaccabdcbaddabceabcddcbaabcddcbadbaccabdcbaddabceeeeeeeeeeeeeeeecbaddabcabcddcbadbaccabddbaccabdecbaddabcabcddcbaeeeeeeabcddcbadbaccabdcbaddabceeedbaccabdeeabcddcbaeecbaddabceeeecbaddabceabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeecbaddabceedbaccabdeeedbaccabdcbaddabceeabcddcbaeeeabcddcbaeabcddcbaabcddcbaeeeecbaddabccbaddabcdbaccabddbaccabdeeeeeeeeeeeeeedbaccabddbaccabdabcddcbaabcddcbaeeeecbaddabccbaddabcecbaddabceeecbaddabceeabcddcbadbaccabdeeedbaccabdeeabcddcbaeeeeabcddcbaedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeeabcddcbacbaddabceeeedbaccabdecbaddabcdbaccabdecbaddabceeeeedbaccabdeabcddcbaabcddcbaedbaccabdeeeeeeeabcddcbaecbaddabcdbaccabdeabcddcbaeeeeeeecbaddabceabcddcbaabcddcbaecbaddabceeeeedbaccabdecbaddabcdbaccabdecbaddabceeeedbaccabdabcddcbaeeeeedbaccabdecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeeabcddcbadbaccabdeeecbaddabceedbaccabdeeabcddcbaecbaddabcecbaddabcabcddcbaeeeedbaccabdeecbaddabceeeecbaddabcdbaccabdeeeedbaccabdabcddcbaeeeeabcddcbaeedbaccabdeeeecbaddabcabcddcbaeabcddcbaecbaddabceedbaccabdeeabcddcbaeeedbaccabdcbaddabceeeeeabcddcbaedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeeabcddcbaedbaccabdeeecbaddabccbaddabcabcddcbaeedbaccabdeeeedbaccabdcbaddabceeeeeedbaccabdeabcddcbaecbaddabceabcddcbaeeeecbaddabceabcddcbaecbaddabcedbaccabdeeeeeeabcddcbadbaccabdeeeedbaccabdeecbaddabcabcddcbaabcddcbaeeedbaccabdecbaddabceeeeeabcddcbaedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeecbaddabcdbaccabdeeecbaddabceedbaccabdeeabcddcbaeabcddcbaeabcddcbacbaddabceeeedbaccabdeeabcddcbaeeeeabcddcbadbaccabdeeeedbaccabdcbaddabceeeecbaddabceedbaccabdeeeeabcddcbacbaddabcecbaddabcecbaddabceedbaccabdeeabcddcbaeeedbaccabdabcddcbaeeeeeabcddcbaedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeecbaddabcdbaccabdeeeecbaddabceabcddcbaeabcddcbadbaccabdeeeabcddcbacbaddabceeeeeedbaccabdeedbaccabdedbaccabdeeabcddcbaeeabcddcbaeecbaddabcecbaddabceecbaddabceeeeeedbaccabdabcddcbaeeecbaddabcabcddcbaeabcddcbaedbaccabdeeeecbaddabcdbaccabdeeeeedbaccabdecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeecbaddabceabcddcbaeeabcddcbadbaccabdeeeecbaddabcedbaccabdedbaccabdcbaddabceeeeecbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeedbaccabddbaccabdeabcddcbaeeecbaddabceeeeecbaddabcabcddcbaeabcddcbaecbaddabceeeeabcddcbadbaccabdeedbaccabdecbaddabceeeeecbaddabceabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeedbaccabdcbaddabceeeeabcddcbaeabcddcbaecbaddabcdbaccabdeeabcddcbaeeedbaccabdeeeecbaddabcecbaddabceecbaddabcdbaccabdeeeeeedbaccabdabcddcbaeeabcddcbaeabcddcbaeeeedbaccabdeeecbaddabceedbaccabdabcddcbaecbaddabcecbaddabceeeeabcddcbadbaccabdeeeeeabcddcbaedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeeedbaccabdabcddcbaeecbaddabcecbaddabcabcddcbadbaccabdeeeecbaddabceeedbaccabdeeeeeeecbaddabceabcddcbaeeabcddcbadbaccabddbaccabdcbaddabceeabcddcbaeabcddcbaeeeeeeedbaccabdeeecbaddabceeeedbaccabdabcddcbaabcddcbaecbaddabceecbaddabcdbaccabdeeeeeecbaddabcedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdecbaddabceeeeeedbaccabdcbaddabceecbaddabceabcddcbaabcddcbadbaccabdeeeecbaddabceeedbaccabdeeeeeeeabcddcbaeabcddcbaeecbaddabcdbaccabddbaccabdabcddcbaeeabcddcbaecbaddabceeeeeeedbaccabdeeecbaddabceeeedbaccabdabcddcbacbaddabcecbaddabceeabcddcbadbaccabdeeeeeecbaddabcedbaccabdeeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdedbaccabdeeecbaddabceeeeeabcddcbacbaddabceedbaccabdabcddcbaeeeecbaddabcecbaddabcdbaccabdcbaddabceeeeeecbaddabceabcddcbaeeeeabcddcbaabcddcbaeeeeabcddcbaedbaccabdeeeeeedbaccabdcbaddabcdbaccabdedbaccabdeeeeabcddcbacbaddabceedbaccabdabcddcbaeeeeedbaccabdeeecbaddabcecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdedbaccabdeeeeeabcddcbacbaddabceeeecbaddabcecbaddabccbaddabcedbaccabdeeeeedbaccabdeabcddcbaabcddcbaecbaddabceeeeeeeabcddcbaedbaccabdcbaddabceabcddcbaeeeeeeedbaccabdeabcddcbaabcddcbaecbaddabceeeeecbaddabcedbaccabddbaccabdedbaccabdeeeedbaccabdabcddcbaeeeeecbaddabcecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdedbaccabdeeeeeabcddcbacbaddabceeeedbaccabdecbaddabccbaddabcecbaddabceeeeecbaddabceabcddcbaabcddcbaedbaccabdeeeeeeeabcddcbaedbaccabdcbaddabceabcddcbaeeeeeeecbaddabceabcddcbaabcddcbaedbaccabdeeeeedbaccabdedbaccabddbaccabdecbaddabceeeedbaccabdabcddcbaeeeeecbaddabcecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdedbaccabdeeeeecbaddabceeeabcddcbacbaddabccbaddabccbaddabceabcddcbaeeeeeedbaccabdcbaddabceeeeeeeedbaccabdeabcddcbaeeabcddcbadbaccabdabcddcbadbaccabdeedbaccabdeabcddcbaeeeeeeeecbaddabcabcddcbaeeeeeedbaccabdecbaddabccbaddabccbaddabcdbaccabdeeecbaddabceeeeeabcddcbaeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeabcddcbaeecbaddabceeeecbaddabcecbaddabceedbaccabddbaccabdeedbaccabdcbaddabceeeedbaccabdecbaddabceeeeeeeeabcddcbaeabcddcbaabcddcbaabcddcbaabcddcbaeabcddcbaeeeeeeeedbaccabdecbaddabceeeedbaccabdcbaddabceecbaddabccbaddabceedbaccabdedbaccabdeeeedbaccabdeeabcddcbaeecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdeeabcddcbaeedbaccabdeeeeecbaddabccbaddabccbaddabccbaddabceeeeeedbaccabdedbaccabdcbaddabcedbaccabdeeeeeeeeeabcddcbaeabcddcbaabcddcbaabcddcbaabcddcbaeabcddcbaeeeeeeeeecbaddabcedbaccabdcbaddabcecbaddabceeeeeedbaccabddbaccabddbaccabddbaccabdeeeeecbaddabceeabcddcbaeecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdeeabcddcbaeeecbaddabcecbaddabcdbaccabdeeeeeeedbaccabdcbaddabceeeabcddcbaedbaccabdcbaddabcabcddcbaecbaddabcedbaccabdeeeeeeeecbaddabcabcddcbaeeeeeeeedbaccabdeabcddcbaecbaddabcabcddcbadbaccabdecbaddabceeeabcddcbadbaccabdeeeeeeedbaccabdabcddcbaeabcddcbaeeecbaddabceedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeabcddcbaeeecbaddabcecbaddabceeedbaccabdeecbaddabcedbaccabddbaccabdeeeeeabcddcbaabcddcbaeeecbaddabccbaddabceeeedbaccabdecbaddabceeeeabcddcbaedbaccabdeeeeabcddcbaabcddcbaeeecbaddabccbaddabceeeeedbaccabddbaccabdeabcddcbaeedbaccabdeeeabcddcbaeabcddcbaeeecbaddabceedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeabcddcbaeeecbaddabcedbaccabdeeeabcddcbacbaddabceeeeedbaccabdecbaddabccbaddabceedbaccabdecbaddabcdbaccabdeeeeeeeeecbaddabcabcddcbacbaddabcabcddcbaeeeeeeeeedbaccabdabcddcbaedbaccabdeeabcddcbaabcddcbaedbaccabdeeeeeabcddcbacbaddabceeedbaccabdeabcddcbaeeecbaddabceedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeabcddcbaeeecbaddabcedbaccabdeeecbaddabcabcddcbaeeeeedbaccabdecbaddabccbaddabceedbaccabdecbaddabcdbaccabdeeeeeeeeeabcddcbacbaddabcabcddcbacbaddabceeeeeeeeedbaccabdabcddcbaedbaccabdeeabcddcbaabcddcbaedbaccabdeeeeecbaddabcabcddcbaeeedbaccabdeabcddcbaeeecbaddabceedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabccbaddabceeeeeedbaccabdeedbaccabdeeecbaddabcabcddcbaeabcddcbaabcddcbaeabcddcbaedbaccabdeeeeeeecbaddabccbaddabceecbaddabceeeedbaccabdeedbaccabddbaccabdeeeeeeecbaddabceabcddcbaeabcddcbaabcddcbaeabcddcbadbaccabdeeecbaddabceecbaddabceeeeeedbaccabddbaccabdeecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabcdbaccabdeeeeeedbaccabdeeabcddcbaeeecbaddabcabcddcbaecbaddabccbaddabcecbaddabceabcddcbaeeeeeeeabcddcbadbaccabdeedbaccabdeeeecbaddabceecbaddabcabcddcbaeeeeeeeabcddcbaedbaccabdedbaccabddbaccabdeabcddcbadbaccabdeeeabcddcbaeecbaddabceeeeeecbaddabcdbaccabdeecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabceeeabcddcbaeabcddcbaeeedbaccabdeecbaddabcedbaccabddbaccabdeeeeecbaddabccbaddabceeecbaddabccbaddabceeeedbaccabdeabcddcbaeeeecbaddabcedbaccabdeeeeabcddcbaabcddcbaeeeabcddcbaabcddcbaeeeeedbaccabddbaccabdeabcddcbaeedbaccabdeeecbaddabcecbaddabceeeabcddcbaeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabceeeabcddcbaecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeeecbaddabcedbaccabdcbaddabcabcddcbaecbaddabcedbaccabdeeeeeeeecbaddabcabcddcbaeeeeeeeedbaccabdeabcddcbaecbaddabcabcddcbadbaccabdeabcddcbaeeecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaecbaddabceeeabcddcbaeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabceeeabcddcbaecbaddabceeedbaccabdeeabcddcbaedbaccabddbaccabdeeeeecbaddabccbaddabceeecbaddabcabcddcbaeeeedbaccabdecbaddabceeeeabcddcbaedbaccabdeeeecbaddabcabcddcbaeeeabcddcbaabcddcbaeeeeedbaccabddbaccabdecbaddabceedbaccabdeeeabcddcbaecbaddabceeeabcddcbaeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabceeeabcddcbaedbaccabdeeecbaddabccbaddabceeeeedbaccabdeabcddcbacbaddabceedbaccabdeabcddcbadbaccabdeeeeeeeeeabcddcbacbaddabccbaddabcabcddcbaeeeeeeeeedbaccabdcbaddabcedbaccabdeeabcddcbacbaddabcedbaccabdeeeeeabcddcbaabcddcbaeeedbaccabdecbaddabceeeabcddcbaeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabceeeabcddcbaedbaccabdeeecbaddabccbaddabceeeeedbaccabdeabcddcbacbaddabceedbaccabdeabcddcbadbaccabdeeeeeeeeecbaddabcabcddcbaabcddcbacbaddabceeeeeeeeedbaccabdcbaddabcedbaccabdeeabcddcbacbaddabcedbaccabdeeeeeabcddcbaabcddcbaeeedbaccabdecbaddabceeeabcddcbaeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabceeeabcddcbaedbaccabdeeecbaddabccbaddabceeeeedbaccabdecbaddabcabcddcbaeedbaccabdeabcddcbadbaccabdeeeeeeeeeabcddcbaabcddcbacbaddabccbaddabceeeeeeeeedbaccabdcbaddabcedbaccabdeecbaddabcabcddcbaedbaccabdeeeeeabcddcbaabcddcbaeeedbaccabdecbaddabceeeabcddcbaeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeecbaddabceeecbaddabcecbaddabceeedbaccabdeeabcddcbaedbaccabddbaccabdeeeeeabcddcbaabcddcbaeeeabcddcbacbaddabceeeedbaccabdeabcddcbaeeeecbaddabcedbaccabdeeeeabcddcbacbaddabceeecbaddabccbaddabceeeeedbaccabddbaccabdecbaddabceedbaccabdeeeabcddcbaeabcddcbaeeeabcddcbaeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeedbaccabddbaccabdeeeeeecbaddabceeabcddcbaeeecbaddabcabcddcbaecbaddabccbaddabcecbaddabceabcddcbaeeeeeeeabcddcbacbaddabceecbaddabceeeedbaccabdeedbaccabdabcddcbaeeeeeeeabcddcbaedbaccabdedbaccabddbaccabdeabcddcbadbaccabdeeeabcddcbaeedbaccabdeeeeeecbaddabccbaddabceecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdeedbaccabdeecbaddabcecbaddabceeeeeeecbaddabcabcddcbaabcddcbaedbaccabdcbaddabceeabcddcbaeeeeeeabcddcbadbaccabdeeeeedbaccabddbaccabdeecbaddabccbaddabceeeeecbaddabcabcddcbaeeeeeeabcddcbaeedbaccabdcbaddabceabcddcbaabcddcbadbaccabdeeeeeeedbaccabdedbaccabdeecbaddabceecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdeedbaccabdeeeeabcddcbacbaddabcecbaddabcecbaddabceeeeeeecbaddabcabcddcbaeabcddcbaeeedbaccabddbaccabdcbaddabceedbaccabdabcddcbaeeeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabddbaccabdeeecbaddabcecbaddabcabcddcbaeeeeeeeabcddcbaeabcddcbaeabcddcbacbaddabceeeedbaccabdeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeedbaccabdeeeecbaddabcabcddcbaecbaddabcecbaddabceeeeeeeabcddcbacbaddabceabcddcbaeeedbaccabddbaccabdcbaddabceedbaccabdabcddcbaeeeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabddbaccabdeeecbaddabceabcddcbacbaddabceeeeeeeabcddcbaeabcddcbaecbaddabcabcddcbaeeeedbaccabdeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeedbaccabdeeeecbaddabccbaddabceabcddcbaecbaddabceeeeeeeabcddcbaabcddcbaecbaddabceeedbaccabddbaccabdcbaddabceedbaccabdabcddcbaeeeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabddbaccabdeeeabcddcbaecbaddabccbaddabceeeeeeeabcddcbaecbaddabceabcddcbaabcddcbaeeeedbaccabdeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeedbaccabdeeeecbaddabccbaddabcecbaddabceabcddcbaeeeeeeeabcddcbacbaddabceabcddcbaeeedbaccabddbaccabdabcddcbaeedbaccabdcbaddabceeeeeeeeeeeeabcddcbadbaccabdeecbaddabcdbaccabddbaccabdeeecbaddabceabcddcbacbaddabceeeeeeecbaddabceabcddcbaeabcddcbaabcddcbaeeeedbaccabdeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeabcddcbacbaddabceeeeecbaddabccbaddabceeeabcddcbadbaccabdeedbaccabdeecbaddabceeedbaccabdecbaddabceeeeedbaccabddbaccabdeabcddcbaeeeedbaccabdeabcddcbaabcddcbaeeeeecbaddabceabcddcbaeeecbaddabceeabcddcbaeeabcddcbadbaccabdeeecbaddabccbaddabceeeeecbaddabcdbaccabdeeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeeabcddcbaecbaddabceeecbaddabccbaddabceeeeabcddcbadbaccabdeeecbaddabceedbaccabdeeedbaccabddbaccabdeeedbaccabdabcddcbaeeecbaddabceeeecbaddabceeedbaccabdabcddcbaeeeabcddcbaabcddcbaeeeabcddcbaeecbaddabceeeabcddcbadbaccabdeeeecbaddabccbaddabceeecbaddabcedbaccabdeeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeeabcddcbaecbaddabceeecbaddabccbaddabceeeedbaccabdabcddcbaeeecbaddabceedbaccabdeeedbaccabddbaccabdeeeabcddcbadbaccabdeeecbaddabceeeecbaddabceeeabcddcbadbaccabdeeeabcddcbaabcddcbaeeeabcddcbaeecbaddabceeedbaccabdabcddcbaeeeecbaddabccbaddabceeecbaddabcedbaccabdeeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeeabcddcbaecbaddabceeedbaccabdeabcddcbaeecbaddabcdbaccabdeeeeecbaddabcecbaddabceedbaccabdcbaddabceeeeeedbaccabdcbaddabceabcddcbaeeeecbaddabceabcddcbadbaccabdeeeeeeabcddcbadbaccabdeeabcddcbaeabcddcbaeeeeedbaccabdabcddcbaeecbaddabcedbaccabdeeeabcddcbaecbaddabceeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeabcddcbaecbaddabceeedbaccabdecbaddabceecbaddabcdbaccabdeeeeeabcddcbaecbaddabceedbaccabdabcddcbaeeeeeedbaccabdcbaddabcecbaddabceeeeabcddcbaeabcddcbadbaccabdeeeeeecbaddabcdbaccabdeeabcddcbaecbaddabceeeeedbaccabdabcddcbaeeabcddcbaedbaccabdeeeabcddcbaecbaddabceeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeabcddcbaeedbaccabdecbaddabccbaddabceeeeecbaddabcdbaccabdeeeeeabcddcbaecbaddabccbaddabceabcddcbaeeeedbaccabdeabcddcbaeeeedbaccabddbaccabdeeeecbaddabcedbaccabdeeeecbaddabceabcddcbaabcddcbaecbaddabceeeeedbaccabdabcddcbaeeeeeabcddcbaabcddcbaedbaccabdeecbaddabceeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeabcddcbaeedbaccabdecbaddabccbaddabceeeeecbaddabcdbaccabdeeeeecbaddabceabcddcbaabcddcbaecbaddabceeeedbaccabdeabcddcbaeeeedbaccabddbaccabdeeeecbaddabcedbaccabdeeeeabcddcbaecbaddabccbaddabceabcddcbaeeeeedbaccabdabcddcbaeeeeeabcddcbaabcddcbaedbaccabdeecbaddabceeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeecbaddabcdbaccabdeeeeeabcddcbaecbaddabcecbaddabcedbaccabdeabcddcbaecbaddabceeeeeeeedbaccabdeabcddcbacbaddabcdbaccabdeeeeabcddcbaeeabcddcbaeeeecbaddabcdbaccabdabcddcbaecbaddabceeeeeeeedbaccabdeabcddcbaecbaddabcedbaccabdedbaccabdeabcddcbaeeeeecbaddabcdbaccabdeeecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdeeecbaddabceabcddcbaeedbaccabdeeabcddcbaeeecbaddabcedbaccabdeeecbaddabccbaddabceedbaccabdcbaddabceeeeeeedbaccabdabcddcbaeecbaddabceeabcddcbaeecbaddabcdbaccabdeeeeeeeabcddcbadbaccabdeeabcddcbaabcddcbaeeedbaccabdeabcddcbaeeecbaddabceedbaccabdeecbaddabceabcddcbaeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeecbaddabceabcddcbaeeedbaccabdeabcddcbaeecbaddabcdbaccabdeeeeecbaddabcecbaddabceedbaccabdcbaddabceeeeeedbaccabdabcddcbaecbaddabceeeeabcddcbaecbaddabcdbaccabdeeeeeeabcddcbadbaccabdeeabcddcbaeabcddcbaeeeeedbaccabdabcddcbaeecbaddabcedbaccabdeeecbaddabceabcddcbaeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeecbaddabcecbaddabceeedbaccabdecbaddabceeabcddcbadbaccabdeeeeeabcddcbaeabcddcbaeedbaccabdcbaddabceeeeeedbaccabdabcddcbaeabcddcbaeeeecbaddabcecbaddabcdbaccabdeeeeeeabcddcbadbaccabdeecbaddabcecbaddabceeeeedbaccabdcbaddabceeabcddcbaedbaccabdeeeabcddcbaeabcddcbaeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeecbaddabceeedbaccabdabcddcbadbaccabdeeecbaddabceeecbaddabcabcddcbaeeeeeeabcddcbacbaddabceeecbaddabccbaddabceeeeeedbaccabdabcddcbadbaccabddbaccabdeeeeeeabcddcbaabcddcbaeeecbaddabcdbaccabdeeeeeedbaccabddbaccabdeeecbaddabceeeabcddcbaabcddcbaabcddcbaeeecbaddabceeecbaddabceeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeecbaddabceeedbaccabdcbaddabcdbaccabdeeecbaddabceeeabcddcbaabcddcbaeeeeeeabcddcbacbaddabceeedbaccabdcbaddabceeeeeeabcddcbaabcddcbacbaddabcabcddcbaeeeeeedbaccabddbaccabdeeedbaccabddbaccabdeeeeeecbaddabcdbaccabdeeecbaddabceeeabcddcbacbaddabcabcddcbaeeecbaddabceeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeecbaddabceeedbaccabdcbaddabcdbaccabdeeecbaddabceeeabcddcbacbaddabceeeeeeabcddcbaabcddcbaeeeabcddcbaabcddcbaeeeeeedbaccabdcbaddabcdbaccabddbaccabdeeeeeecbaddabcabcddcbaeeecbaddabcdbaccabdeeeeeedbaccabddbaccabdeeecbaddabceeeabcddcbacbaddabcabcddcbaeeecbaddabceeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeedbaccabdcbaddabceeeeeabcddcbaecbaddabcedbaccabdecbaddabceabcddcbaecbaddabceeeeeeeecbaddabceabcddcbadbaccabddbaccabdeeeeabcddcbaeeabcddcbaeeeecbaddabccbaddabcabcddcbaedbaccabdeeeeeeeedbaccabdeabcddcbaedbaccabdecbaddabcedbaccabdeabcddcbaeeeeedbaccabdcbaddabceeecbaddabceeeabcddcba'' 
 + 
 +''abcddcbaeeedbaccabdeeedbaccabdeabcddcbaecbaddabcecbaddabceeeeeeeecbaddabccbaddabceabcddcbaeabcddcbaeedbaccabddbaccabdcbaddabcdbaccabdeeeeeeeabcddcbaeeeecbaddabceeeeeeedbaccabdabcddcbadbaccabddbaccabdeecbaddabcecbaddabceabcddcbaabcddcbaeeeeeeeeabcddcbaeabcddcbaecbaddabcedbaccabdeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeedbaccabdecbaddabceabcddcbaecbaddabceeeeeeeecbaddabcabcddcbaecbaddabceabcddcbaeedbaccabddbaccabdcbaddabcdbaccabdeeeeeeeabcddcbaeeeecbaddabceeeeeeedbaccabdabcddcbadbaccabddbaccabdeecbaddabceabcddcbaecbaddabcabcddcbaeeeeeeeeabcddcbaecbaddabceabcddcbaedbaccabdeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeedbaccabdecbaddabcecbaddabceabcddcbaeeeeeeeecbaddabcabcddcbaeabcddcbaecbaddabceedbaccabddbaccabdcbaddabcdbaccabdeeeeeeeabcddcbaeeeecbaddabceeeeeeedbaccabdabcddcbadbaccabddbaccabdeeabcddcbaecbaddabcecbaddabcabcddcbaeeeeeeeecbaddabceabcddcbaeabcddcbaedbaccabdeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeedbaccabdecbaddabceeecbaddabccbaddabceeeeabcddcbadbaccabdeeecbaddabceeabcddcbaeeeabcddcbadbaccabdeeeabcddcbaabcddcbaeeecbaddabceeeecbaddabceeedbaccabddbaccabdeeeabcddcbadbaccabdeeedbaccabdeecbaddabceeeabcddcbadbaccabdeeeecbaddabccbaddabceeecbaddabceabcddcbaeeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeedbaccabdeeecbaddabccbaddabccbaddabceeedbaccabdeeeabcddcbaabcddcbaeeeeeeabcddcbadbaccabdeeecbaddabccbaddabceeeeeeabcddcbaabcddcbacbaddabcabcddcbaeeeeeedbaccabddbaccabdeeedbaccabdcbaddabceeeeeecbaddabcdbaccabdeeedbaccabdeeeabcddcbacbaddabcabcddcbaeeedbaccabdeeeabcddcbaeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeeabcddcbacbaddabceedbaccabdabcddcbaeeeecbaddabceedbaccabdeeecbaddabceecbaddabcdbaccabdecbaddabceeeeeedbaccabdcbaddabceeeabcddcbacbaddabceeeabcddcbadbaccabdeeeeeeabcddcbaedbaccabdabcddcbaeeabcddcbaeeedbaccabdeeabcddcbaeeeecbaddabcdbaccabdeeabcddcbacbaddabceeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeeabcddcbacbaddabceedbaccabdcbaddabceeeecbaddabceedbaccabdeeeabcddcbaeecbaddabcdbaccabdeabcddcbaeeeeeedbaccabdcbaddabceeecbaddabcabcddcbaeeeabcddcbadbaccabdeeeeeecbaddabcedbaccabdabcddcbaeecbaddabceeedbaccabdeeabcddcbaeeeeabcddcbadbaccabdeeabcddcbacbaddabceeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeeabcddcbaedbaccabdcbaddabceecbaddabceeabcddcbaecbaddabceeeeeecbaddabcdbaccabdeedbaccabddbaccabdeeeeeeeecbaddabcabcddcbacbaddabceeabcddcbacbaddabcabcddcbaeeeeeeeedbaccabddbaccabdeedbaccabdabcddcbaeeeeeeabcddcbaecbaddabceeabcddcbaeeabcddcbadbaccabdecbaddabceeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeecbaddabcedbaccabdabcddcbaeecbaddabceecbaddabceabcddcbaeeeeeecbaddabcdbaccabdeedbaccabddbaccabdeeeeeeeeabcddcbaabcddcbaabcddcbaeecbaddabccbaddabccbaddabceeeeeeeedbaccabddbaccabdeedbaccabdabcddcbaeeeeeecbaddabceabcddcbaeeabcddcbaeecbaddabcdbaccabdeabcddcbaeeeedbaccabdeeecbaddabc'' 
 + 
 +''abcddcbaeeedbaccabdeeeedbaccabdcbaddabceeecbaddabcedbaccabdcbaddabcabcddcbaeeeeeeecbaddabcabcddcbaeeeecbaddabceeeabcddcbaeeeabcddcbaeabcddcbaeabcddcbadbaccabdedbaccabdedbaccabdeeedbaccabdeeecbaddabceeeedbaccabdcbaddabceeeeeeedbaccabdcbaddabcabcddcbaecbaddabceeecbaddabcabcddcbaeeeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeedbaccabdeeeeecbaddabcdbaccabdcbaddabceedbaccabdcbaddabceeabcddcbaeeeeeabcddcbacbaddabceeeeeeeeabcddcbaeabcddcbaeeecbaddabcdbaccabdedbaccabdabcddcbaeabcddcbacbaddabceeedbaccabdedbaccabdeeeeeeeecbaddabcdbaccabdeeeeedbaccabdeecbaddabcabcddcbaeecbaddabcabcddcbacbaddabceeeeeabcddcbaeeedbaccabd'' 
 + 
 +''abcddcbaeeeeabcddcbacbaddabceeeedbaccabddbaccabdeeedbaccabdeeeecbaddabceecbaddabcdbaccabdeabcddcbacbaddabceeeeeabcddcbaecbaddabceeecbaddabcedbaccabdeeeedbaccabdeabcddcbaeeeabcddcbaecbaddabceeeeeabcddcbacbaddabcedbaccabdabcddcbaeeabcddcbaeeeedbaccabdeeedbaccabddbaccabdeeeeabcddcbacbaddabceeeecbaddabc'' 
 + 
 +''abcddcbaeeeeabcddcbacbaddabceeeeedbaccabddbaccabdeecbaddabcdbaccabdeeeecbaddabceeabcddcbaeeecbaddabcedbaccabdeedbaccabdeecbaddabceeabcddcbaedbaccabdeeeecbaddabceabcddcbaeeabcddcbaeecbaddabceeabcddcbaeabcddcbaeeedbaccabdeecbaddabceeeeabcddcbadbaccabdeedbaccabdcbaddabceeeeedbaccabdabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeabcddcbadbaccabdeeeecbaddabccbaddabceeecbaddabceeeedbaccabdeedbaccabdcbaddabceabcddcbadbaccabdeeeeeabcddcbaedbaccabdeeedbaccabdecbaddabceeeecbaddabceabcddcbaeeeabcddcbaedbaccabdeeeeeabcddcbadbaccabdecbaddabcabcddcbaeeabcddcbaeeeecbaddabceeecbaddabccbaddabceeeeabcddcbadbaccabdeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeabcddcbadbaccabdeeeeecbaddabccbaddabceedbaccabdcbaddabceeeedbaccabdeeabcddcbaeeedbaccabdecbaddabceecbaddabceedbaccabdeeabcddcbaecbaddabceeeedbaccabdeabcddcbaeeabcddcbaeedbaccabdeeabcddcbaeabcddcbaeeecbaddabceedbaccabdeeeeabcddcbacbaddabceecbaddabcdbaccabdeeeeecbaddabcabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeabcddcbaecbaddabceedbaccabdeeecbaddabcdbaccabdeeedbaccabdcbaddabceeeeeedbaccabdecbaddabccbaddabceabcddcbaeeeeeeabcddcbaabcddcbaeeeabcddcbadbaccabdeeedbaccabddbaccabdeeeeeedbaccabdecbaddabccbaddabceabcddcbaeeeeeecbaddabcabcddcbaeeeabcddcbacbaddabceeeabcddcbaeecbaddabcedbaccabdeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeabcddcbaecbaddabceedbaccabdeeeecbaddabcdbaccabddbaccabdcbaddabceeeeeeecbaddabceabcddcbaeeeeedbaccabdecbaddabcabcddcbadbaccabdeeeeedbaccabdabcddcbaeeeeeabcddcbadbaccabdcbaddabceabcddcbaeeeeedbaccabdecbaddabceeeeeeeabcddcbacbaddabccbaddabcabcddcbaeeeeabcddcbaeecbaddabcedbaccabdeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeabcddcbaecbaddabceedbaccabdeeeecbaddabcdbaccabddbaccabdcbaddabceeeeeeecbaddabceabcddcbaeeeeedbaccabdecbaddabcabcddcbadbaccabdeeeeedbaccabdabcddcbaeeeeeabcddcbadbaccabdcbaddabceabcddcbaeeeeedbaccabdecbaddabceeeeeeecbaddabcabcddcbaabcddcbacbaddabceeeeabcddcbaeecbaddabcedbaccabdeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeabcddcbaecbaddabceedbaccabdeeeedbaccabdcbaddabccbaddabcdbaccabdeeeeeeecbaddabceabcddcbaeeeeedbaccabdecbaddabcabcddcbadbaccabdeeeeedbaccabdabcddcbaeeeeeabcddcbadbaccabdcbaddabceabcddcbaeeeeedbaccabdecbaddabceeeeeeeabcddcbacbaddabccbaddabcabcddcbaeeeeabcddcbaeecbaddabcedbaccabdeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeabcddcbaecbaddabceedbaccabdeeeedbaccabdcbaddabccbaddabcdbaccabdeeeeeeecbaddabceabcddcbaeeeeedbaccabdecbaddabcabcddcbadbaccabdeeeeedbaccabdabcddcbaeeeeeabcddcbadbaccabdcbaddabceabcddcbaeeeeedbaccabdecbaddabceeeeeeecbaddabcabcddcbaabcddcbacbaddabceeeeabcddcbaeecbaddabcedbaccabdeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeabcddcbaedbaccabdeecbaddabceeedbaccabdcbaddabceeecbaddabcdbaccabdeeeeeecbaddabcedbaccabddbaccabdeabcddcbaeeeeeeabcddcbaabcddcbaeeeabcddcbacbaddabceeecbaddabccbaddabceeeeeecbaddabcedbaccabddbaccabdeabcddcbaeeeeeedbaccabdabcddcbaeeeabcddcbadbaccabdeeeabcddcbaeedbaccabdecbaddabceeeecbaddabc'' 
 + 
 +''abcddcbaeeeeabcddcbaedbaccabdeecbaddabceeeecbaddabcdbaccabddbaccabdcbaddabceeeeeeedbaccabdeabcddcbaeeeeecbaddabcedbaccabdabcddcbacbaddabceeeeecbaddabcabcddcbaeeeeeabcddcbacbaddabcdbaccabdeabcddcbaeeeeecbaddabcedbaccabdeeeeeeeabcddcbadbaccabddbaccabdabcddcbaeeeeabcddcbaeedbaccabdecbaddabceeeecbaddabc'' 
 + 
 +''abcddcbaeeeeabcddcbaedbaccabdeecbaddabceeeecbaddabcdbaccabddbaccabdcbaddabceeeeeeedbaccabdeabcddcbaeeeeecbaddabcedbaccabdabcddcbacbaddabceeeeecbaddabcabcddcbaeeeeeabcddcbacbaddabcdbaccabdeabcddcbaeeeeecbaddabcedbaccabdeeeeeeedbaccabdabcddcbaabcddcbadbaccabdeeeeabcddcbaeedbaccabdecbaddabceeeecbaddabc'' 
 + 
 +''abcddcbaeeeeabcddcbaedbaccabdeecbaddabceeeedbaccabdcbaddabccbaddabcdbaccabdeeeeeeedbaccabdeabcddcbaeeeeecbaddabcedbaccabdabcddcbacbaddabceeeeecbaddabcabcddcbaeeeeeabcddcbacbaddabcdbaccabdeabcddcbaeeeeecbaddabcedbaccabdeeeeeeeabcddcbadbaccabddbaccabdabcddcbaeeeeabcddcbaeedbaccabdecbaddabceeeecbaddabc'' 
 + 
 +''abcddcbaeeeeabcddcbaedbaccabdeecbaddabceeeedbaccabdcbaddabccbaddabcdbaccabdeeeeeeedbaccabdeabcddcbaeeeeecbaddabcedbaccabdabcddcbacbaddabceeeeecbaddabcabcddcbaeeeeeabcddcbacbaddabcdbaccabdeabcddcbaeeeeecbaddabcedbaccabdeeeeeeedbaccabdabcddcbaabcddcbadbaccabdeeeeabcddcbaeedbaccabdecbaddabceeeecbaddabc'' 
 + 
 +''abcddcbaeeeeabcddcbaeecbaddabcdbaccabdeeeedbaccabdedbaccabdecbaddabccbaddabceeeeeeabcddcbadbaccabdeeeecbaddabceeedbaccabdeecbaddabcabcddcbaeeecbaddabcabcddcbaeeecbaddabcabcddcbaeedbaccabdeeeabcddcbaeeeedbaccabdcbaddabceeeeeeabcddcbaabcddcbaedbaccabdedbaccabdeeeedbaccabdabcddcbaeecbaddabceeeecbaddabc'' 
 + 
 +''abcddcbaeeeeabcddcbaeedbaccabdcbaddabceeeecbaddabcecbaddabcedbaccabddbaccabdeeeeeeabcddcbacbaddabceeeedbaccabdeeecbaddabceedbaccabdabcddcbaeeedbaccabdabcddcbaeeedbaccabdabcddcbaeecbaddabceeeabcddcbaeeeecbaddabcdbaccabdeeeeeeabcddcbaabcddcbaecbaddabcecbaddabceeeecbaddabcabcddcbaeedbaccabdeeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcabcddcbaeeeedbaccabddbaccabdeeedbaccabdeeeecbaddabceeabcddcbadbaccabdecbaddabccbaddabceeeeecbaddabceabcddcbaeeecbaddabcedbaccabdeeeedbaccabdeabcddcbaeeecbaddabceabcddcbaeeeeeabcddcbaabcddcbaedbaccabdcbaddabceeabcddcbaeeeedbaccabdeeedbaccabddbaccabdeeeecbaddabcabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcabcddcbaeeeedbaccabdecbaddabceedbaccabdeeeeabcddcbacbaddabcedbaccabdedbaccabdcbaddabceeeeeeeeeedbaccabdcbaddabcabcddcbadbaccabdeeeeeeabcddcbadbaccabdcbaddabcabcddcbaeeeeeeeeeecbaddabcabcddcbaeabcddcbaecbaddabcdbaccabdeeeeabcddcbaeecbaddabceabcddcbaeeeedbaccabdcbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabccbaddabceeedbaccabdeeeedbaccabdeabcddcbaeabcddcbadbaccabdeeeeabcddcbacbaddabceeeedbaccabddbaccabdeeeeeeeecbaddabcdbaccabdecbaddabccbaddabceabcddcbacbaddabceeeeeeeeabcddcbaabcddcbaeeeecbaddabcdbaccabdeeeeabcddcbadbaccabdedbaccabdeabcddcbaeeeeabcddcbaeeecbaddabccbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeecbaddabcedbaccabdeeeeeeeeedbaccabdcbaddabcabcddcbaeabcddcbaabcddcbaeabcddcbaeeecbaddabcedbaccabdeeeeeedbaccabdeedbaccabdcbaddabceecbaddabceeeeeecbaddabcedbaccabdeeeabcddcbaeabcddcbaabcddcbaeabcddcbadbaccabdcbaddabceeeeeeeeecbaddabcedbaccabdeecbaddabcdbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeedbaccabdecbaddabceeeeeeeeedbaccabdcbaddabcabcddcbaeabcddcbaabcddcbaeabcddcbaeeedbaccabdecbaddabceeeeeecbaddabceecbaddabcdbaccabdeedbaccabdeeeeeedbaccabdecbaddabceeeabcddcbaeabcddcbaabcddcbaeabcddcbadbaccabdcbaddabceeeeeeeeedbaccabdecbaddabceecbaddabcdbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeabcddcbaeeeedbaccabddbaccabdeecbaddabccbaddabceeeeeeabcddcbaecbaddabcabcddcbadbaccabdeeeeeedbaccabdcbaddabceeeecbaddabcabcddcbaeeeeabcddcbadbaccabdeeeeeedbaccabdcbaddabcabcddcbaecbaddabceeeeeeabcddcbaabcddcbaeedbaccabddbaccabdeeeecbaddabceeedbaccabdabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeecbaddabceeeabcddcbaeeedbaccabddbaccabddbaccabdeecbaddabceeeeeeeabcddcbacbaddabcabcddcbaabcddcbaeeeeeabcddcbaecbaddabceeeecbaddabcedbaccabdeeeeedbaccabddbaccabdcbaddabcdbaccabdeeeeeeecbaddabceeabcddcbaabcddcbaabcddcbaeeedbaccabdeeecbaddabceeeabcddcbacbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeabcddcbaecbaddabceeabcddcbaeeeedbaccabdcbaddabcedbaccabdedbaccabdcbaddabceeeeeeeeeedbaccabdcbaddabcabcddcbadbaccabdeeeeeeabcddcbadbaccabdcbaddabcabcddcbaeeeeeeeeeecbaddabcabcddcbaeabcddcbaecbaddabcabcddcbaeeeedbaccabdeecbaddabcedbaccabdeeeeabcddcbacbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeabcddcbaecbaddabceedbaccabdeeeedbaccabdcbaddabcedbaccabdeabcddcbacbaddabceeeeeeeeeeabcddcbacbaddabcabcddcbaabcddcbaeeeeeedbaccabddbaccabdcbaddabcdbaccabdeeeeeeeeeecbaddabcdbaccabdeabcddcbaecbaddabcabcddcbaeeeeabcddcbaeecbaddabcedbaccabdeeeeabcddcbacbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeeabcddcbacbaddabceedbaccabdcbaddabceeeedbaccabdeeabcddcbaeeedbaccabdeabcddcbaeecbaddabceedbaccabdeecbaddabceabcddcbaeeeedbaccabdecbaddabceeabcddcbaeedbaccabdeecbaddabceabcddcbaeeeabcddcbaeedbaccabdeeeecbaddabccbaddabceeabcddcbadbaccabdeeeeeabcddcbacbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeeabcddcbadbaccabdeecbaddabccbaddabceeeeabcddcbaeedbaccabdeeedbaccabdecbaddabceeabcddcbaeedbaccabdeecbaddabceabcddcbaeeeedbaccabdecbaddabceeabcddcbaeecbaddabceedbaccabdeabcddcbaeeedbaccabdeeabcddcbaeeeecbaddabcabcddcbaeecbaddabcdbaccabdeeeeeabcddcbacbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeeabcddcbadbaccabdeedbaccabdcbaddabceeeeabcddcbaeedbaccabdeeecbaddabcecbaddabceeabcddcbaeecbaddabceecbaddabceabcddcbaeeeedbaccabdecbaddabceeabcddcbaeedbaccabdeedbaccabdeabcddcbaeeecbaddabceeabcddcbaeeeedbaccabdabcddcbaeedbaccabddbaccabdeeeeeabcddcbacbaddabceeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeeabcddcbaedbaccabdabcddcbaeecbaddabceedbaccabdecbaddabceeeeedbaccabdcbaddabceeeeeecbaddabcdbaccabdeeabcddcbaeecbaddabcdbaccabdeeabcddcbaeecbaddabcabcddcbaeeeeeeabcddcbadbaccabdeeeeeabcddcbaeabcddcbaeecbaddabceedbaccabddbaccabdecbaddabceeeeedbaccabdabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeeabcddcbaedbaccabddbaccabdeeabcddcbaeecbaddabcecbaddabceeeeedbaccabdcbaddabceeeeeecbaddabcabcddcbaeecbaddabceedbaccabdabcddcbaeecbaddabceedbaccabdabcddcbaeeeeeeabcddcbadbaccabdeeeeeabcddcbaedbaccabdeeabcddcbaeecbaddabcdbaccabdecbaddabceeeeedbaccabdabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeecbaddabceabcddcbadbaccabdcbaddabceeeeeeabcddcbaedbaccabdeeedbaccabdcbaddabceedbaccabdeeeeabcddcbaeeeedbaccabdabcddcbacbaddabcabcddcbaeeeeabcddcbaeeeecbaddabceecbaddabcdbaccabdeeecbaddabceabcddcbaeeeeeedbaccabdabcddcbacbaddabcedbaccabdeeeeecbaddabcdbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeecbaddabcedbaccabdabcddcbacbaddabceeeeeeabcddcbaedbaccabdeeecbaddabcdbaccabdeedbaccabdeeeeabcddcbaeeeeabcddcbadbaccabdabcddcbacbaddabceeeeabcddcbaeeeecbaddabceedbaccabdcbaddabceeecbaddabceabcddcbaeeeeeedbaccabdcbaddabcabcddcbaedbaccabdeeeeecbaddabcdbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeedbaccabdeabcddcbacbaddabcdbaccabdeeeeeeabcddcbaecbaddabceeecbaddabcdbaccabdeecbaddabceeeeabcddcbaeeeedbaccabdabcddcbacbaddabcabcddcbaeeeeabcddcbaeeeedbaccabdeedbaccabdcbaddabceeedbaccabdeabcddcbaeeeeeecbaddabcabcddcbadbaccabdecbaddabceeeeecbaddabcdbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcdbaccabdeeeeedbaccabdecbaddabcabcddcbadbaccabdeeeeeeabcddcbaecbaddabceeedbaccabdcbaddabceecbaddabceeeeabcddcbaeeeeabcddcbadbaccabdabcddcbacbaddabceeeeabcddcbaeeeedbaccabdeecbaddabcdbaccabdeeedbaccabdeabcddcbaeeeeeecbaddabcdbaccabdabcddcbaecbaddabceeeeecbaddabcdbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceabcddcbaeecbaddabceedbaccabdeeedbaccabddbaccabdeeedbaccabdcbaddabceeeeeeabcddcbaabcddcbaeecbaddabceecbaddabceedbaccabdeabcddcbaeeeedbaccabdeabcddcbaeecbaddabceecbaddabceedbaccabddbaccabdeeeeeecbaddabcabcddcbaeeeabcddcbaabcddcbaeeeabcddcbaeecbaddabceedbaccabdecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabcdbaccabdeeeeeabcddcbacbaddabceeeeeeedbaccabdabcddcbadbaccabdedbaccabddbaccabdeeecbaddabceeeedbaccabdabcddcbaeeeeeabcddcbaabcddcbaeeeeeabcddcbacbaddabceeeedbaccabdeeecbaddabccbaddabcecbaddabcabcddcbacbaddabceeeeeeedbaccabdabcddcbaeeeeecbaddabcdbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabcecbaddabceeedbaccabdeeeabcddcbadbaccabdeeeeeeabcddcbadbaccabdedbaccabdedbaccabdeabcddcbaabcddcbaeeeeeeedbaccabdedbaccabdeecbaddabcecbaddabceeeeeeeabcddcbaabcddcbaecbaddabcecbaddabcecbaddabcabcddcbaeeeeeecbaddabcabcddcbaeeecbaddabceeedbaccabdedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabcedbaccabdedbaccabdeeeeeeeeabcddcbadbaccabddbaccabdeabcddcbaecbaddabceeabcddcbaeeeeabcddcbaecbaddabceeeeeecbaddabcdbaccabdabcddcbacbaddabceeeeeecbaddabcedbaccabdeeeedbaccabdeecbaddabcedbaccabdeabcddcbaabcddcbadbaccabdeeeeeeeeabcddcbaeabcddcbaecbaddabcecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabcedbaccabdedbaccabdeeeeeeeedbaccabdabcddcbadbaccabdeabcddcbaecbaddabceeabcddcbaeeeeabcddcbaecbaddabceeeeeeabcddcbacbaddabccbaddabcdbaccabdeeeeeecbaddabcedbaccabdeeeedbaccabdeecbaddabcedbaccabdeabcddcbadbaccabdabcddcbaeeeeeeeeabcddcbaeabcddcbaecbaddabcecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabceeedbaccabdcbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaedbaccabdeeabcddcbadbaccabddbaccabdabcddcbaeeeedbaccabdecbaddabceeeeeeeedbaccabdecbaddabceeeeabcddcbacbaddabccbaddabcabcddcbaeecbaddabceabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabdcbaddabceeedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabceeedbaccabdcbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaedbaccabdeeabcddcbadbaccabddbaccabdabcddcbaeeeedbaccabdecbaddabceeeeeeeedbaccabdecbaddabceeeecbaddabcabcddcbaabcddcbacbaddabceecbaddabceabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabdcbaddabceeedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabceeedbaccabdcbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaedbaccabdeedbaccabdabcddcbaabcddcbadbaccabdeeeedbaccabdecbaddabceeeeeeeedbaccabdecbaddabceeeeabcddcbacbaddabccbaddabcabcddcbaeecbaddabceabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabdcbaddabceeedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabceeedbaccabdcbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaedbaccabdeedbaccabdabcddcbaabcddcbadbaccabdeeeedbaccabdecbaddabceeeeeeeedbaccabdecbaddabceeeecbaddabcabcddcbaabcddcbacbaddabceecbaddabceabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabdcbaddabceeedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabceeedbaccabddbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaedbaccabdeeabcddcbadbaccabddbaccabdabcddcbaeeeecbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdeeeeabcddcbacbaddabccbaddabcabcddcbaeecbaddabceabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabccbaddabceeedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabceeedbaccabddbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaedbaccabdeeabcddcbadbaccabddbaccabdabcddcbaeeeecbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdeeeecbaddabcabcddcbaabcddcbacbaddabceecbaddabceabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabccbaddabceeedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabceeedbaccabddbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaedbaccabdeedbaccabdabcddcbaabcddcbadbaccabdeeeecbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdeeeeabcddcbacbaddabccbaddabcabcddcbaeecbaddabceabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabccbaddabceeedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcecbaddabceeedbaccabddbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaedbaccabdeedbaccabdabcddcbaabcddcbadbaccabdeeeecbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdeeeecbaddabcabcddcbaabcddcbacbaddabceecbaddabceabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabccbaddabceeedbaccabdedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdecbaddabcedbaccabdeeeeeeeabcddcbaedbaccabdecbaddabcabcddcbaeeeabcddcbaeedbaccabdedbaccabdecbaddabcecbaddabcabcddcbaeeeeeeeeeeeecbaddabcabcddcbaeabcddcbaedbaccabdedbaccabdeecbaddabceeecbaddabcabcddcbaedbaccabdecbaddabceeeeeeedbaccabdeabcddcbaedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdecbaddabceeeeeedbaccabdabcddcbadbaccabdabcddcbaeecbaddabcdbaccabdeeeeeeeeeeeeeabcddcbacbaddabcdbaccabdecbaddabcabcddcbaeeeecbaddabcabcddcbaedbaccabdabcddcbacbaddabceeeeeeeeeeeeedbaccabdabcddcbaeecbaddabcdbaccabdcbaddabcdbaccabdeeeeeeabcddcbaedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdecbaddabceeeeeedbaccabdabcddcbadbaccabdabcddcbaeecbaddabcdbaccabdeeeeeeeeeeeeecbaddabcabcddcbadbaccabdeabcddcbacbaddabceeeeabcddcbacbaddabcedbaccabdcbaddabcabcddcbaeeeeeeeeeeeeedbaccabdabcddcbaeecbaddabcdbaccabdcbaddabcdbaccabdeeeeeeabcddcbaedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeeabcddcbaeecbaddabceeedbaccabdedbaccabdcbaddabceedbaccabdeeeeeeeabcddcbacbaddabcedbaccabdabcddcbaeeeeeabcddcbaabcddcbaeeeecbaddabccbaddabceeeeecbaddabcdbaccabdeabcddcbacbaddabceeeeeeedbaccabdeeabcddcbadbaccabdedbaccabdeeeabcddcbaeecbaddabceedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeeabcddcbaeeeedbaccabdabcddcbacbaddabcdbaccabdeeeeeeedbaccabdecbaddabceeeeecbaddabcedbaccabdcbaddabccbaddabceeeeeabcddcbacbaddabceeeeeabcddcbaabcddcbadbaccabdeabcddcbaeeeeeabcddcbaedbaccabdeeeeeeedbaccabdabcddcbacbaddabcdbaccabdeeeecbaddabceedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeecbaddabceecbaddabceeedbaccabdedbaccabdabcddcbaeedbaccabdeeeeeeeabcddcbaabcddcbaedbaccabdabcddcbaeeeeeabcddcbacbaddabceeeeabcddcbacbaddabceeeeecbaddabcdbaccabdecbaddabccbaddabceeeeeeedbaccabdeecbaddabcdbaccabdedbaccabdeeeabcddcbaeeabcddcbaeedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeecbaddabceedbaccabdeeeabcddcbadbaccabdeeeabcddcbacbaddabceeeeeedbaccabdabcddcbaeecbaddabceecbaddabceeabcddcbaedbaccabdeeeeabcddcbaedbaccabdeecbaddabceecbaddabceedbaccabdabcddcbaeeeeeecbaddabcdbaccabdeeeabcddcbadbaccabdeeeabcddcbaeecbaddabceeabcddcbaecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeecbaddabceedbaccabdeeedbaccabdabcddcbaeeeabcddcbacbaddabceeeeeeabcddcbadbaccabdeecbaddabceecbaddabceeabcddcbaedbaccabdeeeeabcddcbaedbaccabdeecbaddabceecbaddabceeabcddcbadbaccabdeeeeeecbaddabcdbaccabdeeedbaccabdabcddcbaeeeabcddcbaeecbaddabceeabcddcbaecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeedbaccabdecbaddabceeeeabcddcbaeeabcddcbaecbaddabcdbaccabdeeeeeedbaccabdcbaddabceabcddcbaecbaddabceeeeedbaccabdeabcddcbaeeabcddcbaedbaccabdeeeeecbaddabcedbaccabdecbaddabcabcddcbaeeeeeeabcddcbacbaddabcedbaccabdeedbaccabdeeeeabcddcbaecbaddabceecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeedbaccabdecbaddabceeeeabcddcbaeeabcddcbaedbaccabdcbaddabceeeeeecbaddabcdbaccabdeabcddcbaedbaccabdeeeeeabcddcbaecbaddabceecbaddabceabcddcbaeeeeedbaccabdecbaddabcedbaccabdabcddcbaeeeeeeabcddcbadbaccabdecbaddabceecbaddabceeeedbaccabdeabcddcbaeeabcddcbaedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeedbaccabdecbaddabceeeeabcddcbaeecbaddabcedbaccabdabcddcbaeeeeeeabcddcbadbaccabdecbaddabcedbaccabdeeeeeabcddcbaecbaddabceecbaddabceabcddcbaeeeeedbaccabdeabcddcbaedbaccabdcbaddabceeeeeecbaddabcdbaccabdeabcddcbaeecbaddabceeeedbaccabdeabcddcbaeeabcddcbaedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeedbaccabdecbaddabceeeeabcddcbaeedbaccabdecbaddabcabcddcbaeeeeeeabcddcbacbaddabcedbaccabdecbaddabceeeeedbaccabdeabcddcbaeeabcddcbaedbaccabdeeeeecbaddabceabcddcbaecbaddabcdbaccabdeeeeeedbaccabdcbaddabceabcddcbaeedbaccabdeeeeabcddcbaecbaddabceecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeeeabcddcbaecbaddabceeeabcddcbadbaccabdcbaddabcedbaccabdeeeeeeeedbaccabdecbaddabceeeeedbaccabdcbaddabcabcddcbaeedbaccabdeeabcddcbaeedbaccabdcbaddabcabcddcbaeeeeecbaddabceabcddcbaeeeeeeeeabcddcbaecbaddabcabcddcbadbaccabdeeecbaddabcedbaccabdeeeabcddcbaecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeeeabcddcbaeedbaccabdcbaddabceecbaddabcabcddcbaeeeeedbaccabdedbaccabdeeeeecbaddabccbaddabceeeeeeabcddcbadbaccabdeabcddcbadbaccabdeabcddcbadbaccabdeeeeeecbaddabccbaddabceeeeeabcddcbaeabcddcbaeeeeedbaccabdcbaddabceecbaddabcabcddcbaeedbaccabdeeeabcddcbaecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeeecbaddabcdbaccabdedbaccabdeeeabcddcbaeeeeeeabcddcbaecbaddabceeabcddcbadbaccabdcbaddabcabcddcbaeeeecbaddabcecbaddabceeeeeeeedbaccabdedbaccabdeeeeabcddcbadbaccabdcbaddabcabcddcbaeedbaccabdeabcddcbaeeeeeeabcddcbaeeecbaddabcecbaddabcdbaccabdeeecbaddabcedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeeecbaddabcdbaccabdeeeeabcddcbaedbaccabdabcddcbaecbaddabceeeeeeedbaccabdecbaddabceeabcddcbaedbaccabdeeeeabcddcbaecbaddabcabcddcbaecbaddabceeeedbaccabdecbaddabceeabcddcbaedbaccabdeeeeeeeabcddcbaecbaddabcdbaccabdecbaddabceeeedbaccabdabcddcbaeeedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeeedbaccabdcbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaecbaddabceeabcddcbacbaddabcdbaccabdabcddcbaeeeecbaddabcecbaddabceeeeeeeedbaccabdedbaccabdeeeeabcddcbacbaddabcdbaccabdabcddcbaeedbaccabdeabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabdcbaddabceeecbaddabcedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabcedbaccabdeeeecbaddabcdbaccabdabcddcbaecbaddabceeeeeedbaccabddbaccabdeeeeeabcddcbaabcddcbaeeedbaccabdeecbaddabceeabcddcbaeeabcddcbacbaddabceecbaddabceeabcddcbaeedbaccabdeeecbaddabccbaddabceeeeedbaccabddbaccabdeeeeeeabcddcbaecbaddabcdbaccabdabcddcbaeeeedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceeabcddcbadbaccabdeeedbaccabdcbaddabceeeeeecbaddabcedbaccabdedbaccabdcbaddabceeeeabcddcbaeabcddcbaeeeeeabcddcbaedbaccabdecbaddabceecbaddabceabcddcbaedbaccabdeeeeedbaccabdedbaccabdeeeecbaddabcabcddcbaeabcddcbaecbaddabceeeeeecbaddabcabcddcbaeeeabcddcbadbaccabdeecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabceeabcddcbaedbaccabdedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeeeedbaccabdecbaddabcdbaccabdeedbaccabdeeeabcddcbacbaddabceeeeedbaccabdabcddcbaeeeeecbaddabcdbaccabdeeeabcddcbaeeabcddcbacbaddabceabcddcbaeeeedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeabcddcbaedbaccabdeecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabceecbaddabcdbaccabdecbaddabceeeeedbaccabdabcddcbaeeeeeeabcddcbaedbaccabddbaccabdeeabcddcbaabcddcbadbaccabdeeeeeedbaccabdcbaddabceeeeeedbaccabdcbaddabceeeeeecbaddabcabcddcbaabcddcbaeecbaddabccbaddabceabcddcbaeeeeeeabcddcbacbaddabceeeeedbaccabdecbaddabcdbaccabdeedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceecbaddabcdbaccabdedbaccabdeeeeedbaccabdabcddcbaeeeeeeabcddcbaecbaddabcdbaccabdeeabcddcbaabcddcbacbaddabceeeeeecbaddabccbaddabceeeeeedbaccabddbaccabdeeeeeedbaccabdabcddcbaabcddcbaeecbaddabcdbaccabdeabcddcbaeeeeeeabcddcbacbaddabceeeeecbaddabcecbaddabcdbaccabdeedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceecbaddabcdbaccabdeeeedbaccabdedbaccabdeabcddcbacbaddabceeeeeeabcddcbadbaccabdeeeeabcddcbaeeedbaccabdeecbaddabcabcddcbaeeeabcddcbacbaddabceeecbaddabcabcddcbaeedbaccabdeeecbaddabceeeedbaccabdcbaddabceeeeeeabcddcbacbaddabcedbaccabdedbaccabdeeeedbaccabdabcddcbaeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceecbaddabcdbaccabdeeeedbaccabdedbaccabdecbaddabcabcddcbaeeeeeeabcddcbadbaccabdeeeeabcddcbaeeedbaccabdeeabcddcbacbaddabceeeabcddcbacbaddabceeeabcddcbacbaddabceedbaccabdeeecbaddabceeeedbaccabdcbaddabceeeeeecbaddabcabcddcbaedbaccabdedbaccabdeeeedbaccabdabcddcbaeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceecbaddabcedbaccabdeedbaccabdcbaddabceeeedbaccabdedbaccabdeeeeabcddcbaabcddcbaeeeeabcddcbaabcddcbaeeeeeeabcddcbaecbaddabcdbaccabdeedbaccabdabcddcbaecbaddabceeeeeecbaddabccbaddabceeeecbaddabccbaddabceeeedbaccabdedbaccabdeeeeabcddcbadbaccabdeedbaccabdeabcddcbaeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdabcddcbaeeeeecbaddabcdbaccabddbaccabdeecbaddabceecbaddabcdbaccabdeeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaedbaccabddbaccabdcbaddabccbaddabceabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeecbaddabcdbaccabdeedbaccabdeecbaddabccbaddabcdbaccabdeeeeeabcddcbacbaddabceedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdabcddcbaeeeeecbaddabcdbaccabddbaccabdeecbaddabceedbaccabdcbaddabceeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaecbaddabcdbaccabddbaccabdcbaddabceabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeedbaccabdcbaddabceedbaccabdeecbaddabccbaddabcdbaccabdeeeeeabcddcbacbaddabceedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdabcddcbaeeeeecbaddabcdbaccabddbaccabdeecbaddabceedbaccabdcbaddabceeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaedbaccabdcbaddabccbaddabcdbaccabdeabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeedbaccabdcbaddabceedbaccabdeecbaddabccbaddabcdbaccabdeeeeeabcddcbacbaddabceedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdabcddcbaeeeeedbaccabdcbaddabcdbaccabdeecbaddabceecbaddabcdbaccabdeeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaecbaddabcdbaccabddbaccabdcbaddabceabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeecbaddabcdbaccabdeedbaccabdeecbaddabcdbaccabdcbaddabceeeeeabcddcbacbaddabceedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdabcddcbaeeeeedbaccabdcbaddabcdbaccabdeecbaddabceecbaddabcdbaccabdeeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaedbaccabdcbaddabccbaddabcdbaccabdeabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeecbaddabcdbaccabdeedbaccabdeecbaddabcdbaccabdcbaddabceeeeeabcddcbacbaddabceedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdabcddcbaeeeeedbaccabdcbaddabcdbaccabdeecbaddabceedbaccabdcbaddabceeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaecbaddabccbaddabcdbaccabddbaccabdeabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeedbaccabdcbaddabceedbaccabdeecbaddabcdbaccabdcbaddabceeeeeabcddcbacbaddabceedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdabcddcbaeeeeedbaccabddbaccabdcbaddabceecbaddabceecbaddabcdbaccabdeeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaecbaddabccbaddabcdbaccabddbaccabdeabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeecbaddabcdbaccabdeedbaccabdeedbaccabdcbaddabccbaddabceeeeeabcddcbacbaddabceedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdcbaddabcecbaddabceeeeedbaccabdabcddcbaeeeeeeabcddcbaedbaccabddbaccabdeeabcddcbaabcddcbadbaccabdeeeeeecbaddabcdbaccabdeeeeeecbaddabcdbaccabdeeeeeecbaddabcabcddcbaabcddcbaeecbaddabccbaddabceabcddcbaeeeeeeabcddcbacbaddabceeeeedbaccabdedbaccabdcbaddabceedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdcbaddabcedbaccabdeeeeeedbaccabdeabcddcbaeabcddcbacbaddabceeeeeabcddcbadbaccabdeeeecbaddabceecbaddabcabcddcbadbaccabdeeeeeeeedbaccabdcbaddabcabcddcbaeeabcddcbaeeeedbaccabdcbaddabceeeeeabcddcbacbaddabcecbaddabcedbaccabdeeeeeedbaccabdeabcddcbadbaccabdeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdcbaddabcedbaccabdeeeeeedbaccabdeabcddcbaecbaddabcabcddcbaeeeeeabcddcbadbaccabdeeeecbaddabceeabcddcbacbaddabcdbaccabdeeeeeeeedbaccabdabcddcbacbaddabceeabcddcbaeeeedbaccabdcbaddabceeeeecbaddabcabcddcbaecbaddabcedbaccabdeeeeeedbaccabdeabcddcbadbaccabdeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdcbaddabceedbaccabdeeeedbaccabdabcddcbaeeeeabcddcbaecbaddabceeeabcddcbaecbaddabcedbaccabddbaccabdeeeeeeeeabcddcbacbaddabccbaddabcabcddcbaeeeeeeeedbaccabddbaccabdeabcddcbaecbaddabceeeabcddcbaecbaddabceeeecbaddabcdbaccabdeeeedbaccabdeeabcddcbadbaccabdeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdcbaddabceedbaccabdeeeedbaccabdabcddcbaeeeeabcddcbaecbaddabceeeabcddcbaecbaddabcedbaccabddbaccabdeeeeeeeecbaddabcabcddcbaabcddcbacbaddabceeeeeeeedbaccabddbaccabdeabcddcbaecbaddabceeeabcddcbaecbaddabceeeecbaddabcdbaccabdeeeedbaccabdeeabcddcbadbaccabdeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabddbaccabdeeabcddcbaeeeeecbaddabcabcddcbadbaccabdecbaddabceeeeeeeecbaddabcedbaccabdeabcddcbadbaccabdeecbaddabccbaddabceeeeeeeeabcddcbaabcddcbaeedbaccabdcbaddabcedbaccabdeabcddcbaeeeeeeeeabcddcbaedbaccabdcbaddabcabcddcbaeeeeecbaddabceedbaccabddbaccabdeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabddbaccabdeeeeabcddcbacbaddabceedbaccabdabcddcbaeeeeeeeecbaddabceabcddcbacbaddabceeedbaccabdcbaddabccbaddabceeeeeedbaccabddbaccabdeeeeeeabcddcbaabcddcbadbaccabdeeeabcddcbacbaddabceabcddcbaeeeeeeeecbaddabcdbaccabdeeabcddcbacbaddabceeeedbaccabddbaccabdeeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdeabcddcbaedbaccabdcbaddabceeeeeeecbaddabcdbaccabdeeeeabcddcbaecbaddabcabcddcbaeedbaccabdeeedbaccabdcbaddabceeeeedbaccabdabcddcbaeeeeecbaddabcabcddcbaeeeabcddcbaeedbaccabdcbaddabcedbaccabdeeeeabcddcbacbaddabceeeeeeecbaddabcabcddcbaedbaccabdeabcddcbaeecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdedbaccabdedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeeeeabcddcbaecbaddabcabcddcbaeeabcddcbaeeedbaccabdcbaddabceeeeeabcddcbadbaccabdeeeeecbaddabcabcddcbaeeedbaccabdeedbaccabdcbaddabcedbaccabdeeeedbaccabdcbaddabceeeeeeecbaddabcabcddcbaeabcddcbaeabcddcbaeecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabceedbaccabdedbaccabdeeabcddcbacbaddabceeeedbaccabdeecbaddabceecbaddabcabcddcbaeeeeeabcddcbadbaccabdeeeeeeecbaddabceabcddcbadbaccabdabcddcbadbaccabdecbaddabceeeeeeeabcddcbadbaccabdeeeeedbaccabdcbaddabceecbaddabceeabcddcbaeeeecbaddabcdbaccabdeeabcddcbaeabcddcbaeecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeecbaddabceeedbaccabdabcddcbadbaccabdcbaddabceeeeeeeecbaddabcecbaddabceedbaccabddbaccabdeeeeabcddcbaedbaccabdeeeabcddcbaeabcddcbaeedbaccabdeecbaddabceeabcddcbaeabcddcbaeeecbaddabceabcddcbaeeeecbaddabccbaddabceedbaccabdedbaccabdeeeeeeeedbaccabdcbaddabcabcddcbacbaddabceeedbaccabdeeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdabcddcbaeeeecbaddabccbaddabceeecbaddabceeeedbaccabdeeabcddcbacbaddabcedbaccabddbaccabdeeeeedbaccabdeabcddcbaeeedbaccabdecbaddabceeeecbaddabceabcddcbaeeedbaccabdeabcddcbaeeeeeabcddcbaabcddcbaecbaddabcdbaccabdeeabcddcbaeeeecbaddabceeecbaddabccbaddabceeeedbaccabdabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdabcddcbaeeeecbaddabcedbaccabdeecbaddabceeeeabcddcbadbaccabdecbaddabcecbaddabcdbaccabdeeeeeeeeeecbaddabcdbaccabdabcddcbacbaddabceeeeeeabcddcbacbaddabcdbaccabdabcddcbaeeeeeeeeeedbaccabdabcddcbaeabcddcbaedbaccabdcbaddabceeeeabcddcbaeedbaccabdeabcddcbaeeeecbaddabcdbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceecbaddabcedbaccabdeeeeeeeeecbaddabcdbaccabdabcddcbaeabcddcbaabcddcbaeabcddcbaeeecbaddabcedbaccabdeeeeeedbaccabdeedbaccabdcbaddabceecbaddabceeeeeecbaddabcedbaccabdeeeabcddcbaeabcddcbaabcddcbaeabcddcbacbaddabcdbaccabdeeeeeeeeecbaddabcedbaccabdeedbaccabdcbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceedbaccabdecbaddabceeeeeeeeecbaddabcdbaccabdabcddcbaeabcddcbaabcddcbaeabcddcbaeeedbaccabdecbaddabceeeeeecbaddabceecbaddabcdbaccabdeedbaccabdeeeeeedbaccabdecbaddabceeeabcddcbaeabcddcbaabcddcbaeabcddcbacbaddabcdbaccabdeeeeeeeeedbaccabdecbaddabceedbaccabdcbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeabcddcbaeeeecbaddabccbaddabceedbaccabddbaccabdeeeeeeabcddcbaedbaccabdabcddcbacbaddabceeeeeecbaddabcdbaccabdeeeedbaccabdabcddcbaeeeeabcddcbacbaddabceeeeeecbaddabcdbaccabdabcddcbaedbaccabdeeeeeeabcddcbaabcddcbaeecbaddabccbaddabceeeedbaccabdeeecbaddabcabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeedbaccabdeeeabcddcbaeeecbaddabccbaddabccbaddabceedbaccabdeeeeeeeabcddcbadbaccabdabcddcbaabcddcbaeeeeeabcddcbaedbaccabdeeeedbaccabdecbaddabceeeeecbaddabccbaddabcdbaccabdcbaddabceeeeeeedbaccabdeeabcddcbaabcddcbaabcddcbaeeecbaddabceeedbaccabdeeeabcddcbadbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeabcddcbaedbaccabdeeabcddcbaeeeecbaddabcdbaccabdecbaddabcecbaddabcdbaccabdeeeeeeeeeecbaddabcdbaccabdabcddcbacbaddabceeeeeeabcddcbacbaddabcdbaccabdabcddcbaeeeeeeeeeedbaccabdabcddcbaeabcddcbaedbaccabdabcddcbaeeeecbaddabceedbaccabdecbaddabceeeeabcddcbadbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeabcddcbaedbaccabdeecbaddabceeeecbaddabcdbaccabdecbaddabceabcddcbadbaccabdeeeeeeeeeeabcddcbadbaccabdabcddcbaabcddcbaeeeeeecbaddabccbaddabcdbaccabdcbaddabceeeeeeeeeedbaccabdcbaddabceabcddcbaedbaccabdabcddcbaeeeeabcddcbaeedbaccabdecbaddabceeeeabcddcbadbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeeabcddcbacbaddabceecbaddabcdbaccabdeeeeabcddcbaeecbaddabceeedbaccabdedbaccabdeeabcddcbaeedbaccabdeedbaccabdeabcddcbaeeeecbaddabcedbaccabdeeabcddcbaeecbaddabceecbaddabceabcddcbaeeedbaccabdeeabcddcbaeeeecbaddabcabcddcbaeecbaddabccbaddabceeeeeabcddcbadbaccabdeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeeabcddcbacbaddabceedbaccabddbaccabdeeeeabcddcbaeecbaddabceeecbaddabcedbaccabdeeabcddcbaeecbaddabceedbaccabdeabcddcbaeeeecbaddabcedbaccabdeeabcddcbaeedbaccabdeecbaddabceabcddcbaeeecbaddabceeabcddcbaeeeedbaccabdabcddcbaeedbaccabdcbaddabceeeeeabcddcbadbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeeabcddcbadbaccabdeecbaddabcdbaccabdeeeecbaddabceeabcddcbaeeecbaddabceabcddcbaeedbaccabdeecbaddabceedbaccabdeabcddcbaeeeecbaddabcedbaccabdeeabcddcbaeecbaddabceedbaccabdeabcddcbaeeeabcddcbaeecbaddabceeeedbaccabddbaccabdeeabcddcbacbaddabceeeeeabcddcbadbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeeabcddcbaecbaddabcabcddcbaeedbaccabdeecbaddabcedbaccabdeeeeecbaddabcdbaccabdeeeeeedbaccabdcbaddabceeabcddcbaeedbaccabdcbaddabceeabcddcbaeedbaccabdabcddcbaeeeeeeabcddcbacbaddabceeeeeabcddcbaeabcddcbaeedbaccabdeecbaddabccbaddabcedbaccabdeeeeecbaddabcabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeeabcddcbaecbaddabccbaddabceeabcddcbaeedbaccabdedbaccabdeeeeecbaddabcdbaccabdeeeeeedbaccabdabcddcbaeedbaccabdeecbaddabcabcddcbaeedbaccabdeecbaddabcabcddcbaeeeeeeabcddcbacbaddabceeeeeabcddcbaecbaddabceeabcddcbaeedbaccabdcbaddabcedbaccabdeeeeecbaddabcabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeecbaddabceabcddcbadbaccabdcbaddabceeeeeeabcddcbaedbaccabdeeedbaccabdcbaddabceedbaccabdeeeeabcddcbaeeeecbaddabcabcddcbadbaccabdabcddcbaeeeeabcddcbaeeeecbaddabceecbaddabcdbaccabdeeecbaddabceabcddcbaeeeeeedbaccabdabcddcbacbaddabcedbaccabdeeeeedbaccabdcbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeecbaddabcedbaccabdabcddcbacbaddabceeeeeeabcddcbaedbaccabdeeecbaddabcdbaccabdeedbaccabdeeeeabcddcbaeeeeabcddcbacbaddabcabcddcbadbaccabdeeeeabcddcbaeeeecbaddabceedbaccabdcbaddabceeecbaddabceabcddcbaeeeeeedbaccabdcbaddabcabcddcbaedbaccabdeeeeedbaccabdcbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeedbaccabdeabcddcbacbaddabcdbaccabdeeeeeeabcddcbaecbaddabceeecbaddabcdbaccabdeecbaddabceeeeabcddcbaeeeecbaddabcabcddcbadbaccabdabcddcbaeeeeabcddcbaeeeedbaccabdeedbaccabdcbaddabceeedbaccabdeabcddcbaeeeeeecbaddabcabcddcbadbaccabdecbaddabceeeeedbaccabdcbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdcbaddabceeeeedbaccabdecbaddabcabcddcbadbaccabdeeeeeeabcddcbaecbaddabceeedbaccabdcbaddabceecbaddabceeeeabcddcbaeeeeabcddcbacbaddabcabcddcbadbaccabdeeeeabcddcbaeeeedbaccabdeecbaddabcdbaccabdeeedbaccabdeabcddcbaeeeeeecbaddabcdbaccabdabcddcbaecbaddabceeeeedbaccabdcbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabddbaccabdeeecbaddabceeeecbaddabceabcddcbaeabcddcbacbaddabceeeeabcddcbadbaccabdeeeecbaddabccbaddabceeeeeeeedbaccabdcbaddabcedbaccabddbaccabdeabcddcbadbaccabdeeeeeeeeabcddcbaabcddcbaeeeedbaccabdcbaddabceeeeabcddcbacbaddabcecbaddabceabcddcbaeeeeabcddcbaeeedbaccabddbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdeabcddcbaeedbaccabdeecbaddabceeecbaddabccbaddabceeecbaddabcdbaccabdeeeeeeabcddcbaabcddcbaeedbaccabdeedbaccabdeecbaddabceabcddcbaeeeecbaddabceabcddcbaeedbaccabdeedbaccabdeecbaddabccbaddabceeeeeedbaccabdabcddcbaeeeabcddcbaabcddcbaeeeabcddcbaeedbaccabdeecbaddabcedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabcedbaccabdecbaddabceeeeeeeabcddcbaecbaddabcedbaccabdabcddcbaeeeabcddcbaeecbaddabcecbaddabcedbaccabdedbaccabdabcddcbaeeeeeeeeeeeedbaccabdabcddcbaeabcddcbaecbaddabcecbaddabceedbaccabdeeedbaccabdabcddcbaecbaddabcedbaccabdeeeeeeecbaddabceabcddcbaecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabcedbaccabdeeeeeecbaddabcabcddcbacbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeeeeabcddcbadbaccabdcbaddabcedbaccabdabcddcbaeeeedbaccabdabcddcbaecbaddabcabcddcbadbaccabdeeeeeeeeeeeeecbaddabcabcddcbaeedbaccabdcbaddabcdbaccabdcbaddabceeeeeeabcddcbaecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabcedbaccabdeeeeeecbaddabcabcddcbacbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeeeedbaccabdabcddcbacbaddabceabcddcbadbaccabdeeeeabcddcbadbaccabdecbaddabcdbaccabdabcddcbaeeeeeeeeeeeeecbaddabcabcddcbaeedbaccabdcbaddabcdbaccabdcbaddabceeeeeeabcddcbaecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceeabcddcbaeedbaccabdeeecbaddabcecbaddabcdbaccabdeecbaddabceeeeeeeabcddcbadbaccabdecbaddabcabcddcbaeeeeeabcddcbaabcddcbaeeeedbaccabddbaccabdeeeeedbaccabdcbaddabceabcddcbadbaccabdeeeeeeecbaddabceeabcddcbacbaddabcecbaddabceeeabcddcbaeedbaccabdeecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceeabcddcbaeeeecbaddabcabcddcbadbaccabdcbaddabceeeeeeecbaddabcedbaccabdeeeeedbaccabdecbaddabcdbaccabddbaccabdeeeeeabcddcbadbaccabdeeeeeabcddcbaabcddcbacbaddabceabcddcbaeeeeeabcddcbaecbaddabceeeeeeecbaddabcabcddcbadbaccabdcbaddabceeeedbaccabdeecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceecbaddabcedbaccabdeeeeabcddcbaeeabcddcbaecbaddabcdbaccabdeeeeeedbaccabdcbaddabceabcddcbaecbaddabceeeeeabcddcbaedbaccabdeedbaccabdeabcddcbaeeeeecbaddabcedbaccabdecbaddabcabcddcbaeeeeeeabcddcbacbaddabcedbaccabdeedbaccabdeeeecbaddabceabcddcbaeeabcddcbaecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceecbaddabcedbaccabdeeeeabcddcbaeeabcddcbaedbaccabdcbaddabceeeeeecbaddabcdbaccabdeabcddcbaedbaccabdeeeeecbaddabceabcddcbaeeabcddcbaecbaddabceeeeedbaccabdecbaddabcedbaccabdabcddcbaeeeeeeabcddcbadbaccabdecbaddabceecbaddabceeeeabcddcbaedbaccabdeedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceecbaddabcedbaccabdeeeeabcddcbaeecbaddabcedbaccabdabcddcbaeeeeeeabcddcbadbaccabdecbaddabcedbaccabdeeeeecbaddabceabcddcbaeeabcddcbaecbaddabceeeeedbaccabdeabcddcbaedbaccabdcbaddabceeeeeecbaddabcdbaccabdeabcddcbaeecbaddabceeeeabcddcbaedbaccabdeedbaccabdeabcddcbaeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceecbaddabcedbaccabdeeeeabcddcbaeedbaccabdecbaddabcabcddcbaeeeeeeabcddcbacbaddabcedbaccabdecbaddabceeeeeabcddcbaedbaccabdeedbaccabdeabcddcbaeeeeecbaddabceabcddcbaecbaddabcdbaccabdeeeeeedbaccabdcbaddabceabcddcbaeedbaccabdeeeecbaddabceabcddcbaeeabcddcbaecbaddabceeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceedbaccabdeecbaddabceeeabcddcbacbaddabceeeabcddcbadbaccabdeeeeeecbaddabcabcddcbaeedbaccabdeedbaccabdeeabcddcbaecbaddabceeeeabcddcbaecbaddabceedbaccabdeedbaccabdeecbaddabcabcddcbaeeeeeedbaccabdcbaddabceeeabcddcbacbaddabceeeabcddcbaeedbaccabdeeabcddcbaedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceedbaccabdeecbaddabceeecbaddabcabcddcbaeeeabcddcbadbaccabdeeeeeeabcddcbacbaddabceedbaccabdeedbaccabdeeabcddcbaecbaddabceeeeabcddcbaecbaddabceedbaccabdeedbaccabdeeabcddcbacbaddabceeeeeedbaccabdcbaddabceeecbaddabcabcddcbaeeeabcddcbaeedbaccabdeeabcddcbaedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceedbaccabdeedbaccabdeeecbaddabcecbaddabcabcddcbaeecbaddabceeeeeeeabcddcbaabcddcbaecbaddabcabcddcbaeeeeeabcddcbadbaccabdeeeeabcddcbadbaccabdeeeeedbaccabdcbaddabcedbaccabddbaccabdeeeeeeecbaddabceedbaccabdcbaddabcecbaddabceeeabcddcbaeeabcddcbaeecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceeeabcddcbaedbaccabdeeeabcddcbacbaddabcdbaccabdecbaddabceeeeeeeecbaddabcedbaccabdeeeeecbaddabcdbaccabdabcddcbaeecbaddabceeabcddcbaeecbaddabcdbaccabdabcddcbaeeeeedbaccabdeabcddcbaeeeeeeeeabcddcbaedbaccabdabcddcbacbaddabceeedbaccabdecbaddabceeeabcddcbaedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceeeabcddcbaeecbaddabcdbaccabdeedbaccabdabcddcbaeeeeecbaddabcecbaddabceeeeedbaccabddbaccabdeeeeeeabcddcbacbaddabceabcddcbacbaddabceabcddcbacbaddabceeeeeedbaccabddbaccabdeeeeeabcddcbaeabcddcbaeeeeecbaddabcdbaccabdeedbaccabdabcddcbaeecbaddabceeeabcddcbaedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceeecbaddabcdbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaedbaccabdeeabcddcbadbaccabdcbaddabcabcddcbaeeeedbaccabdedbaccabdeeeeeeeecbaddabcecbaddabceeeeabcddcbadbaccabdcbaddabcabcddcbaeecbaddabceabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabcdbaccabdeeedbaccabdecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceeedbaccabdcbaddabcecbaddabceeeabcddcbaeeeeeeabcddcbaedbaccabdeeabcddcbacbaddabcdbaccabdabcddcbaeeeedbaccabdedbaccabdeeeeeeeecbaddabcecbaddabceeeeabcddcbacbaddabcdbaccabdabcddcbaeecbaddabceabcddcbaeeeeeeabcddcbaeeedbaccabdedbaccabdcbaddabceeedbaccabdecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceeedbaccabdcbaddabceeeeabcddcbaecbaddabcabcddcbaedbaccabdeeeeeeecbaddabcedbaccabdeeabcddcbaecbaddabceeeeabcddcbaedbaccabdabcddcbaedbaccabdeeeecbaddabcedbaccabdeeabcddcbaecbaddabceeeeeeeabcddcbaedbaccabdcbaddabcedbaccabdeeeecbaddabcabcddcbaeeecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdecbaddabceeeedbaccabdcbaddabcabcddcbaedbaccabdeeeeeecbaddabccbaddabceeeeeabcddcbaabcddcbaeeecbaddabceedbaccabdeeabcddcbaeeabcddcbadbaccabdeedbaccabdeeabcddcbaeecbaddabceeedbaccabddbaccabdeeeeecbaddabccbaddabceeeeeeabcddcbaedbaccabdcbaddabcabcddcbaeeeecbaddabceabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdcbaddabceeeeeabcddcbadbaccabdeeeeeeecbaddabcabcddcbacbaddabcecbaddabccbaddabceeedbaccabdeeeecbaddabcabcddcbaeeeeeabcddcbaabcddcbaeeeeeabcddcbadbaccabdeeeecbaddabceeedbaccabddbaccabdedbaccabdabcddcbadbaccabdeeeeeeecbaddabcabcddcbaeeeeedbaccabdcbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdecbaddabcecbaddabceeeeeeeeabcddcbacbaddabccbaddabceabcddcbaedbaccabdeeabcddcbaeeeeabcddcbaedbaccabdeeeeeedbaccabdcbaddabcabcddcbadbaccabdeeeeeedbaccabdecbaddabceeeecbaddabceedbaccabdecbaddabceabcddcbaabcddcbacbaddabceeeeeeeeabcddcbaeabcddcbaedbaccabdedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdecbaddabcecbaddabceeeeeeeecbaddabcabcddcbacbaddabceabcddcbaedbaccabdeeabcddcbaeeeeabcddcbaedbaccabdeeeeeeabcddcbadbaccabddbaccabdcbaddabceeeeeedbaccabdecbaddabceeeecbaddabceedbaccabdecbaddabceabcddcbacbaddabcabcddcbaeeeeeeeeabcddcbaeabcddcbaedbaccabdedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdedbaccabdeeecbaddabceeeabcddcbacbaddabceeeeeeabcddcbacbaddabcecbaddabcecbaddabceabcddcbaabcddcbaeeeeeeecbaddabcecbaddabceedbaccabdedbaccabdeeeeeeeabcddcbaabcddcbaedbaccabdedbaccabdedbaccabdabcddcbaeeeeeedbaccabdabcddcbaeeedbaccabdeeecbaddabcecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdeeecbaddabccbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaecbaddabceeabcddcbacbaddabccbaddabcabcddcbaeeeedbaccabdecbaddabceeeeeeeedbaccabdecbaddabceeeeabcddcbadbaccabddbaccabdabcddcbaeedbaccabdeabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabddbaccabdeeecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdeeecbaddabccbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaecbaddabceeabcddcbacbaddabccbaddabcabcddcbaeeeedbaccabdecbaddabceeeeeeeedbaccabdecbaddabceeeedbaccabdabcddcbaabcddcbadbaccabdeedbaccabdeabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabddbaccabdeeecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdeeecbaddabccbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaecbaddabceecbaddabcabcddcbaabcddcbacbaddabceeeedbaccabdecbaddabceeeeeeeedbaccabdecbaddabceeeeabcddcbadbaccabddbaccabdabcddcbaeedbaccabdeabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabddbaccabdeeecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdeeecbaddabccbaddabcedbaccabdeeeabcddcbaeeeeeeabcddcbaecbaddabceecbaddabcabcddcbaabcddcbacbaddabceeeedbaccabdecbaddabceeeeeeeedbaccabdecbaddabceeeedbaccabdabcddcbaabcddcbadbaccabdeedbaccabdeabcddcbaeeeeeeabcddcbaeeecbaddabcedbaccabddbaccabdeeecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdeeecbaddabcdbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaecbaddabceeabcddcbacbaddabccbaddabcabcddcbaeeeecbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdeeeeabcddcbadbaccabddbaccabdabcddcbaeedbaccabdeabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabcdbaccabdeeecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdeeecbaddabcdbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaecbaddabceeabcddcbacbaddabccbaddabcabcddcbaeeeecbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdeeeedbaccabdabcddcbaabcddcbadbaccabdeedbaccabdeabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabcdbaccabdeeecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdeeecbaddabcdbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaecbaddabceecbaddabcabcddcbaabcddcbacbaddabceeeecbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdeeeeabcddcbadbaccabddbaccabdabcddcbaeedbaccabdeabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabcdbaccabdeeecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdedbaccabdeeecbaddabcdbaccabdecbaddabceeeabcddcbaeeeeeeabcddcbaecbaddabceecbaddabcabcddcbaabcddcbacbaddabceeeecbaddabcedbaccabdeeeeeeeecbaddabcedbaccabdeeeedbaccabdabcddcbaabcddcbadbaccabdeedbaccabdeabcddcbaeeeeeeabcddcbaeeedbaccabdecbaddabcdbaccabdeeecbaddabcecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeeabcddcbacbaddabceeecbaddabcdbaccabdeeeeeedbaccabdecbaddabcecbaddabcdbaccabdeeeeabcddcbaeabcddcbaeeeeeabcddcbaecbaddabcedbaccabdeedbaccabdeabcddcbaecbaddabceeeeecbaddabcecbaddabceeeedbaccabdabcddcbaeabcddcbaedbaccabdeeeeeedbaccabdabcddcbaeeeabcddcbacbaddabceedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdeeabcddcbaecbaddabcecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeeeecbaddabcedbaccabdcbaddabceecbaddabceeeabcddcbadbaccabdeeeeecbaddabcabcddcbaeeeeedbaccabdcbaddabceeeabcddcbaeeabcddcbadbaccabdeabcddcbaeeeecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeabcddcbaecbaddabceedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcabcddcbaeeeeecbaddabccbaddabcdbaccabdeedbaccabdeedbaccabdcbaddabceeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaedbaccabddbaccabdcbaddabccbaddabceabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeedbaccabdcbaddabceecbaddabceecbaddabcdbaccabddbaccabdeeeeeabcddcbadbaccabdeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcabcddcbaeeeeecbaddabcdbaccabdcbaddabceedbaccabdeecbaddabcdbaccabdeeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaedbaccabddbaccabdcbaddabccbaddabceabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeecbaddabcdbaccabdeecbaddabceedbaccabdcbaddabcdbaccabdeeeeeabcddcbadbaccabdeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcabcddcbaeeeeecbaddabcdbaccabdcbaddabceedbaccabdeedbaccabdcbaddabceeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaecbaddabcdbaccabddbaccabdcbaddabceabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeedbaccabdcbaddabceecbaddabceedbaccabdcbaddabcdbaccabdeeeeeabcddcbadbaccabdeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcabcddcbaeeeeecbaddabcdbaccabdcbaddabceedbaccabdeedbaccabdcbaddabceeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaedbaccabdcbaddabccbaddabcdbaccabdeabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeedbaccabdcbaddabceecbaddabceedbaccabdcbaddabcdbaccabdeeeeeabcddcbadbaccabdeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcabcddcbaeeeeedbaccabdcbaddabccbaddabceedbaccabdeecbaddabcdbaccabdeeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaecbaddabcdbaccabddbaccabdcbaddabceabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeecbaddabcdbaccabdeecbaddabceedbaccabddbaccabdcbaddabceeeeeabcddcbadbaccabdeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcabcddcbaeeeeedbaccabdcbaddabccbaddabceedbaccabdeecbaddabcdbaccabdeeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaedbaccabdcbaddabccbaddabcdbaccabdeabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeecbaddabcdbaccabdeecbaddabceedbaccabddbaccabdcbaddabceeeeeabcddcbadbaccabdeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcabcddcbaeeeeedbaccabdcbaddabccbaddabceedbaccabdeedbaccabdcbaddabceeeeeeeeeeabcddcbaeabcddcbaeeeabcddcbaecbaddabccbaddabcdbaccabddbaccabdeabcddcbaeeeabcddcbaeabcddcbaeeeeeeeeeedbaccabdcbaddabceecbaddabceedbaccabddbaccabdcbaddabceeeeeabcddcbadbaccabdeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabccbaddabceeabcddcbaeeeeedbaccabdabcddcbacbaddabcedbaccabdeeeeeeeedbaccabdecbaddabceabcddcbacbaddabceedbaccabddbaccabdeeeeeeeeabcddcbaabcddcbaeecbaddabcdbaccabdecbaddabceabcddcbaeeeeeeeeabcddcbaecbaddabcdbaccabdabcddcbaeeeeedbaccabdeecbaddabccbaddabceeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabccbaddabceeeeabcddcbadbaccabdeecbaddabcabcddcbaeeeeeeeedbaccabdeabcddcbadbaccabdeeecbaddabcdbaccabddbaccabdeeeeeecbaddabccbaddabceeeeeeabcddcbaabcddcbacbaddabceeeabcddcbadbaccabdeabcddcbaeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdeeeecbaddabccbaddabceeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcdbaccabdecbaddabceeeeeecbaddabceabcddcbaeabcddcbadbaccabdeeeeeabcddcbacbaddabceeeedbaccabdeedbaccabdabcddcbacbaddabceeeeeeeecbaddabcdbaccabdabcddcbaeeabcddcbaeeeecbaddabcdbaccabdeeeeeabcddcbadbaccabdedbaccabdecbaddabceeeeeecbaddabceabcddcbacbaddabceeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcdbaccabdecbaddabceeeeeecbaddabceabcddcbaedbaccabdabcddcbaeeeeeabcddcbacbaddabceeeedbaccabdeeabcddcbadbaccabdcbaddabceeeeeeeecbaddabcabcddcbadbaccabdeeabcddcbaeeeecbaddabcdbaccabdeeeeedbaccabdabcddcbaedbaccabdecbaddabceeeeeecbaddabceabcddcbacbaddabceeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcdbaccabdedbaccabdeeeeecbaddabcabcddcbaeeeeeeabcddcbaecbaddabccbaddabceeabcddcbaabcddcbacbaddabceeeeeedbaccabdcbaddabceeeeeedbaccabdcbaddabceeeeeedbaccabdabcddcbaabcddcbaeedbaccabddbaccabdeabcddcbaeeeeeeabcddcbadbaccabdeeeeecbaddabcecbaddabcdbaccabdeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcdbaccabdeecbaddabceeeecbaddabcabcddcbaeeeeabcddcbaedbaccabdeeeabcddcbaedbaccabdecbaddabccbaddabceeeeeeeeabcddcbadbaccabddbaccabdabcddcbaeeeeeeeecbaddabccbaddabceabcddcbaedbaccabdeeeabcddcbaedbaccabdeeeedbaccabdcbaddabceeeecbaddabceeabcddcbacbaddabceeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcdbaccabdeecbaddabceeeecbaddabcabcddcbaeeeeabcddcbaedbaccabdeeeabcddcbaedbaccabdecbaddabccbaddabceeeeeeeedbaccabdabcddcbaabcddcbadbaccabdeeeeeeeecbaddabccbaddabceabcddcbaedbaccabdeeeabcddcbaedbaccabdeeeedbaccabdcbaddabceeeecbaddabceeabcddcbacbaddabceeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabceabcddcbaecbaddabcdbaccabdeeeeeeedbaccabdcbaddabceeeeabcddcbaedbaccabdabcddcbaeecbaddabceeecbaddabcdbaccabdeeeeecbaddabcabcddcbaeeeeedbaccabdabcddcbaeeeabcddcbaeecbaddabcdbaccabdecbaddabceeeeabcddcbadbaccabdeeeeeeedbaccabdabcddcbaecbaddabceabcddcbaeedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcecbaddabcecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeeeeabcddcbaedbaccabdabcddcbaeeabcddcbaeeecbaddabcdbaccabdeeeeeabcddcbacbaddabceeeeedbaccabdabcddcbaeeecbaddabceecbaddabcdbaccabdecbaddabceeeecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaeabcddcbaeabcddcbaeedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdeecbaddabcecbaddabceeabcddcbadbaccabdeeeecbaddabceedbaccabdeedbaccabdabcddcbaeeeeeabcddcbacbaddabceeeeeeedbaccabdeabcddcbacbaddabcabcddcbacbaddabcedbaccabdeeeeeeeabcddcbacbaddabceeeeecbaddabcdbaccabdeedbaccabdeeabcddcbaeeeedbaccabdcbaddabceeabcddcbaeabcddcbaeedbaccabdeeeecbaddabc'' 
 + 
 +''abcddcbaeeeedbaccabdeedbaccabdcbaddabcecbaddabceeeeecbaddabcabcddcbaeeeeeeabcddcbaedbaccabdcbaddabceeabcddcbaabcddcbadbaccabdeeeeeedbaccabddbaccabdeeeeeecbaddabccbaddabceeeeeecbaddabcabcddcbaabcddcbaeedbaccabdcbaddabceabcddcbaeeeeeeabcddcbadbaccabdeeeeedbaccabdedbaccabdcbaddabceecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeedbaccabdcbaddabcedbaccabdeeeeecbaddabcabcddcbaeeeeeeabcddcbaecbaddabccbaddabceeabcddcbaabcddcbacbaddabceeeeeecbaddabcdbaccabdeeeeeecbaddabcdbaccabdeeeeeedbaccabdabcddcbaabcddcbaeedbaccabddbaccabdeabcddcbaeeeeeeabcddcbadbaccabdeeeeecbaddabcedbaccabdcbaddabceecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeedbaccabdeedbaccabdcbaddabceeeecbaddabcecbaddabceabcddcbadbaccabdeeeeeeabcddcbacbaddabceeeeabcddcbaeeecbaddabceedbaccabdabcddcbaeeeabcddcbadbaccabdeeedbaccabdabcddcbaeecbaddabceeedbaccabdeeeecbaddabcdbaccabdeeeeeeabcddcbadbaccabdecbaddabcecbaddabceeeecbaddabcabcddcbaeeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeedbaccabdcbaddabceeeecbaddabcecbaddabcedbaccabdabcddcbaeeeeeeabcddcbacbaddabceeeeabcddcbaeeecbaddabceeabcddcbadbaccabdeeeabcddcbadbaccabdeeeabcddcbadbaccabdeecbaddabceeedbaccabdeeeecbaddabcdbaccabdeeeeeedbaccabdabcddcbaecbaddabcecbaddabceeeecbaddabcabcddcbaeeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeedbaccabdecbaddabceecbaddabcdbaccabdeeeecbaddabcecbaddabceeeeabcddcbaabcddcbaeeeeabcddcbaabcddcbaeeeeeeabcddcbaedbaccabdcbaddabceecbaddabcabcddcbaedbaccabdeeeeeedbaccabddbaccabdeeeedbaccabddbaccabdeeeecbaddabcecbaddabceeeeabcddcbacbaddabceecbaddabceabcddcbaeeabcddcbaeeeedbaccabd'' 
 + 
 +''abcddcbaeeeedbaccabdeeecbaddabcabcddcbacbaddabcdbaccabdeeeeeeeedbaccabdedbaccabdeecbaddabccbaddabceeeeabcddcbaecbaddabceeeabcddcbaeabcddcbaeecbaddabceedbaccabdeeabcddcbaeabcddcbaeeedbaccabdeabcddcbaeeeedbaccabddbaccabdeecbaddabcecbaddabceeeeeeeecbaddabcdbaccabdabcddcbadbaccabdeeecbaddabceeeeabcddcba'' 
 + 
 +''abcddcbaeeeeeabcddcbacbaddabcdbaccabdeecbaddabceeeeeedbaccabdeecbaddabcdbaccabdedbaccabdeeeeeabcddcbacbaddabcecbaddabceabcddcbaeeedbaccabdabcddcbaeeeeeeeedbaccabdabcddcbaeeedbaccabdecbaddabcecbaddabcdbaccabdeeeeeabcddcbaeabcddcbacbaddabceeabcddcbaeeeeeecbaddabceeabcddcbacbaddabcdbaccabdeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeabcddcbacbaddabcecbaddabcedbaccabdeeeeedbaccabdeedbaccabdedbaccabdeeecbaddabccbaddabcabcddcbaeeeeeeecbaddabcabcddcbaeeeeeabcddcbadbaccabdabcddcbadbaccabdeeeeedbaccabdcbaddabceeeeeeedbaccabdcbaddabccbaddabceeeabcddcbaeabcddcbaeeabcddcbaeeeeeabcddcbaecbaddabcecbaddabcdbaccabdeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeabcddcbacbaddabcedbaccabdeedbaccabdeeeedbaccabdcbaddabceeecbaddabcabcddcbaeeeeeeedbaccabdcbaddabcdbaccabdeeecbaddabceeeabcddcbaecbaddabceeabcddcbaecbaddabceeeabcddcbaeeedbaccabdabcddcbadbaccabdeeeeeeecbaddabcabcddcbaeeeabcddcbadbaccabdeeeedbaccabdeedbaccabdeabcddcbacbaddabceeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeabcddcbadbaccabdcbaddabceedbaccabdeeeeeecbaddabceedbaccabdcbaddabcecbaddabceeeeeabcddcbadbaccabdedbaccabdeabcddcbaeeecbaddabcabcddcbaeeeeeeeecbaddabcabcddcbaeeecbaddabcedbaccabdedbaccabdcbaddabceeeeeabcddcbaeabcddcbadbaccabdeeabcddcbaeeeeeedbaccabdeeabcddcbadbaccabdcbaddabceeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeabcddcbadbaccabdecbaddabceecbaddabceeeecbaddabcdbaccabdeeedbaccabdabcddcbaeeeeeeecbaddabcdbaccabdcbaddabceeedbaccabdeeeabcddcbaedbaccabdeeabcddcbaedbaccabdeeeabcddcbaeeecbaddabcabcddcbacbaddabceeeeeeedbaccabdabcddcbaeeeabcddcbacbaddabceeeecbaddabceecbaddabceabcddcbadbaccabdeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeabcddcbadbaccabdedbaccabdecbaddabceeeeecbaddabceecbaddabcecbaddabceeedbaccabddbaccabdabcddcbaeeeeeeedbaccabdabcddcbaeeeeeabcddcbacbaddabcabcddcbacbaddabceeeeecbaddabcdbaccabdeeeeeeecbaddabcdbaccabddbaccabdeeeabcddcbaeabcddcbaeeabcddcbaeeeeeabcddcbaedbaccabdedbaccabdcbaddabceeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbacbaddabcdbaccabdeeeeeeeeeedbaccabddbaccabdecbaddabceeeabcddcbadbaccabdabcddcbadbaccabdeeecbaddabceeeeeeeecbaddabcdbaccabdabcddcbacbaddabceeeeeeeecbaddabceeeabcddcbadbaccabdabcddcbadbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeeeeeeabcddcbacbaddabcdbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbacbaddabcdbaccabdeeeeeeeeeedbaccabddbaccabdecbaddabceeeabcddcbadbaccabddbaccabdabcddcbaeeecbaddabceeeeeeeeabcddcbacbaddabccbaddabcdbaccabdeeeeeeeecbaddabceeeabcddcbadbaccabddbaccabdabcddcbaeeecbaddabceabcddcbaabcddcbaeeeeeeeeeeabcddcbacbaddabcdbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbacbaddabcdbaccabdeeeeeeeeeedbaccabddbaccabdecbaddabceeeabcddcbadbaccabddbaccabdabcddcbaeeecbaddabceeeeeeeeabcddcbacbaddabccbaddabcdbaccabdeeeeeeeecbaddabceeedbaccabdabcddcbaabcddcbadbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeeeeeeabcddcbacbaddabcdbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbacbaddabcdbaccabdeeeeeeeeeedbaccabddbaccabdecbaddabceeedbaccabdabcddcbaabcddcbadbaccabdeeecbaddabceeeeeeeeabcddcbacbaddabccbaddabcdbaccabdeeeeeeeecbaddabceeeabcddcbadbaccabddbaccabdabcddcbaeeecbaddabceabcddcbaabcddcbaeeeeeeeeeeabcddcbacbaddabcdbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbacbaddabcdbaccabdeeeeeeeeeedbaccabddbaccabdecbaddabceeedbaccabdabcddcbaabcddcbadbaccabdeeecbaddabceeeeeeeeabcddcbacbaddabccbaddabcdbaccabdeeeeeeeecbaddabceeedbaccabdabcddcbaabcddcbadbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeeeeeeabcddcbacbaddabcdbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbadbaccabdcbaddabceeeeeeeeeedbaccabddbaccabdecbaddabceeeabcddcbadbaccabdabcddcbadbaccabdeeecbaddabceeeeeeeecbaddabccbaddabcabcddcbadbaccabdeeeeeeeecbaddabceeeabcddcbadbaccabdabcddcbadbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeeeeeeabcddcbadbaccabdcbaddabccbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbaedbaccabdecbaddabceeeeedbaccabdecbaddabceeedbaccabdabcddcbaeeeeedbaccabdeabcddcbaecbaddabcedbaccabddbaccabdeecbaddabceeeeeeeecbaddabceeabcddcbaabcddcbaecbaddabcedbaccabdeabcddcbaeeeeedbaccabdabcddcbaeeecbaddabceabcddcbaeeeeecbaddabceabcddcbaedbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbaedbaccabdecbaddabceeeeeedbaccabdcbaddabcdbaccabdeeeabcddcbaeeeeeeedbaccabdabcddcbadbaccabdcbaddabcecbaddabceedbaccabdeeeeeeeeabcddcbaeecbaddabcecbaddabcabcddcbadbaccabdabcddcbaeeeeeeedbaccabdeeeabcddcbacbaddabcabcddcbaeeeeeecbaddabceabcddcbaedbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbaedbaccabdeedbaccabdeeeedbaccabdcbaddabceeeabcddcbacbaddabceeeeeeedbaccabdcbaddabcdbaccabdeeecbaddabceeeabcddcbaecbaddabceeabcddcbaecbaddabceeeabcddcbaeeedbaccabdabcddcbadbaccabdeeeeeeeabcddcbacbaddabceeeabcddcbadbaccabdeeeedbaccabdeedbaccabdecbaddabcabcddcbaeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbaeedbaccabdcbaddabceeeeedbaccabdedbaccabdcbaddabceeabcddcbaeeeeedbaccabdeecbaddabceeeeabcddcbaecbaddabcdbaccabddbaccabdeeeeeeabcddcbaabcddcbacbaddabcedbaccabdeeeecbaddabceeabcddcbaeeeeedbaccabdeecbaddabcabcddcbaeabcddcbaeeeeecbaddabcabcddcbaeedbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbaeedbaccabddbaccabdeeeeecbaddabcedbaccabdcbaddabcecbaddabceeeeeeeedbaccabdabcddcbaeeeabcddcbaecbaddabceabcddcbaeeedbaccabdabcddcbaeeedbaccabdecbaddabcedbaccabdeeedbaccabdabcddcbaeeeeeeeecbaddabcecbaddabcabcddcbaecbaddabceeeeeabcddcbaabcddcbaeedbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcabcddcbaeedbaccabdeedbaccabddbaccabdeeecbaddabceeecbaddabccbaddabceeeeeecbaddabcabcddcbaeeeeabcddcbaedbaccabdeeeedbaccabdabcddcbadbaccabdabcddcbaeeeeabcddcbaedbaccabdeeeedbaccabdcbaddabceeeeeecbaddabccbaddabceeecbaddabceeeabcddcbaabcddcbaeeabcddcbaeedbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabccbaddabcabcddcbadbaccabdeeeeeeeeeedbaccabddbaccabdecbaddabceeeabcddcbadbaccabdabcddcbadbaccabdeeecbaddabceeeeeeeeabcddcbadbaccabdcbaddabccbaddabceeeeeeeecbaddabceeeabcddcbadbaccabdabcddcbadbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeeeeeecbaddabcabcddcbadbaccabdcbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabccbaddabcdbaccabdabcddcbaeeeeeeeeeedbaccabddbaccabdecbaddabceeeabcddcbaabcddcbadbaccabddbaccabdeeecbaddabceeeeeeeeabcddcbadbaccabdcbaddabccbaddabceeeeeeeecbaddabceeeabcddcbaabcddcbadbaccabddbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeeeeeecbaddabcdbaccabdabcddcbacbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabccbaddabcdbaccabdeecbaddabceeeeeedbaccabdabcddcbaeeeeabcddcbaeedbaccabddbaccabdeabcddcbaeeabcddcbadbaccabdeeeedbaccabdecbaddabceeeeeedbaccabdecbaddabceeeecbaddabcabcddcbaeeabcddcbaecbaddabccbaddabceeabcddcbaeeeeabcddcbacbaddabceeeeeedbaccabdeecbaddabcdbaccabddbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabccbaddabcdbaccabdeecbaddabceeeeeeeabcddcbadbaccabdeedbaccabdabcddcbaeabcddcbaeedbaccabdeeeeeedbaccabdedbaccabdeecbaddabceabcddcbaeeabcddcbaedbaccabdeecbaddabcecbaddabceeeeeecbaddabceeabcddcbaeabcddcbacbaddabceecbaddabcabcddcbaeeeeeeedbaccabdeecbaddabcdbaccabddbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabccbaddabcdbaccabdeedbaccabdeeeeeedbaccabdabcddcbaeeeeabcddcbaeecbaddabcdbaccabdeabcddcbaeeabcddcbacbaddabceeeecbaddabcecbaddabceeeeeedbaccabdedbaccabdeeeedbaccabdabcddcbaeeabcddcbaecbaddabcdbaccabdeeabcddcbaeeeeabcddcbacbaddabceeeeeecbaddabceecbaddabcdbaccabddbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabccbaddabcdbaccabdeedbaccabdeeeeeeeabcddcbadbaccabdeecbaddabcabcddcbaeabcddcbaeecbaddabceeeeeedbaccabdedbaccabdeedbaccabdeabcddcbaeeabcddcbaecbaddabceecbaddabcecbaddabceeeeeedbaccabdeeabcddcbaeabcddcbadbaccabdeecbaddabcabcddcbaeeeeeeecbaddabceecbaddabcdbaccabddbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabccbaddabceedbaccabdcbaddabceeeeeabcddcbadbaccabdeedbaccabdeeeeabcddcbaabcddcbadbaccabdeeeeeeeeedbaccabdedbaccabdecbaddabceabcddcbaabcddcbaedbaccabdecbaddabcecbaddabceeeeeeeeecbaddabcabcddcbaabcddcbaeeeecbaddabceecbaddabcabcddcbaeeeeedbaccabdcbaddabceedbaccabddbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdabcddcbacbaddabceeeeeeeeeedbaccabddbaccabdecbaddabceeeabcddcbaabcddcbadbaccabddbaccabdeeecbaddabceeeeeeeecbaddabccbaddabcabcddcbadbaccabdeeeeeeeecbaddabceeeabcddcbaabcddcbadbaccabddbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeeeeeedbaccabdabcddcbacbaddabccbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdcbaddabcabcddcbaeeeeeeeeeedbaccabddbaccabdecbaddabceeeabcddcbaabcddcbadbaccabddbaccabdeeecbaddabceeeeeeeeabcddcbacbaddabccbaddabcdbaccabdeeeeeeeecbaddabceeeabcddcbaabcddcbadbaccabddbaccabdeeecbaddabceabcddcbaabcddcbaeeeeeeeeeedbaccabdcbaddabcabcddcbacbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdcbaddabceedbaccabdeeeeeecbaddabceedbaccabdabcddcbaeabcddcbaeeeeeabcddcbadbaccabdedbaccabdeabcddcbaeeecbaddabccbaddabceeeeeeeeabcddcbaabcddcbaeeecbaddabcedbaccabdedbaccabdcbaddabceeeeecbaddabcecbaddabcdbaccabdeeabcddcbaeeeeeedbaccabdeeabcddcbadbaccabdabcddcbaeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeabcddcbadbaccabdeeeeeeeedbaccabdcbaddabccbaddabcecbaddabceeeeeabcddcbaeeedbaccabdabcddcbaeeabcddcbaecbaddabcdbaccabdeeeeeeeedbaccabdabcddcbaecbaddabceecbaddabcdbaccabdeeecbaddabceeeeeabcddcbaeabcddcbaabcddcbadbaccabdeeeeeeeedbaccabdcbaddabcedbaccabdabcddcbaeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeabcddcbaecbaddabceeeeedbaccabdecbaddabceeedbaccabdabcddcbaeeeeeabcddcbaedbaccabdecbaddabcedbaccabddbaccabdeecbaddabceeeeeeeecbaddabceeabcddcbaabcddcbaecbaddabceabcddcbaedbaccabdeeeeedbaccabdabcddcbaeeecbaddabceabcddcbaeeeeecbaddabcedbaccabdeabcddcbacbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdecbaddabcdbaccabdeeeeeeeedbaccabdabcddcbaabcddcbaecbaddabceeeeeabcddcbaeeedbaccabdcbaddabceecbaddabceabcddcbadbaccabdeeeeeeeedbaccabdcbaddabceabcddcbaeeabcddcbadbaccabdeeecbaddabceeeeeabcddcbaecbaddabccbaddabcdbaccabdeeeeeeeedbaccabdabcddcbaedbaccabdabcddcbaeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdecbaddabcdbaccabdeeeeeeeedbaccabdabcddcbacbaddabceabcddcbaeeeeeabcddcbaeeedbaccabdcbaddabceeabcddcbaecbaddabcdbaccabdeeeeeeeedbaccabdabcddcbaecbaddabceeabcddcbadbaccabdeeecbaddabceeeeecbaddabceabcddcbacbaddabcdbaccabdeeeeeeeedbaccabdabcddcbaedbaccabdabcddcbaeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdedbaccabdecbaddabceeeeeabcddcbaecbaddabceeedbaccabddbaccabdeeeeeabcddcbaeabcddcbaecbaddabceabcddcbaabcddcbaeecbaddabceeeeeeeecbaddabceedbaccabddbaccabdecbaddabcedbaccabdedbaccabdeeeeeabcddcbaabcddcbaeeecbaddabcedbaccabdeeeeecbaddabceabcddcbaeabcddcbacbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeeabcddcbacbaddabceeeeeabcddcbaedbaccabdcbaddabceedbaccabdeeeeedbaccabdeecbaddabceeeedbaccabdecbaddabcabcddcbadbaccabdeeeeeeabcddcbadbaccabdcbaddabceabcddcbaeeeecbaddabceeabcddcbaeeeeeabcddcbaeecbaddabcabcddcbaedbaccabdeeeeecbaddabcdbaccabdeeabcddcbacbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeeabcddcbadbaccabdeeeeecbaddabcecbaddabccbaddabcedbaccabdeeeeeeeedbaccabdabcddcbaeeedbaccabdeabcddcbaeabcddcbaeeedbaccabdcbaddabceeeabcddcbaeabcddcbaecbaddabceeeabcddcbacbaddabceeeeeeeecbaddabcedbaccabddbaccabdedbaccabdeeeeecbaddabcabcddcbaeecbaddabcdbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeedbaccabddbaccabdeeeeeabcddcbacbaddabceecbaddabceeeeabcddcbaabcddcbacbaddabceeeeeeeeedbaccabdecbaddabcecbaddabceabcddcbaabcddcbaedbaccabdedbaccabdecbaddabceeeeeeeeedbaccabdabcddcbaabcddcbaeeeedbaccabdeedbaccabdabcddcbaeeeeecbaddabccbaddabceecbaddabcdbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeedbaccabdeeabcddcbadbaccabdeeecbaddabceeecbaddabccbaddabceeeeeecbaddabcabcddcbaeeeeabcddcbaeabcddcbaeeeedbaccabddbaccabdabcddcbaabcddcbaeeeedbaccabdedbaccabdeeeedbaccabdcbaddabceeeeeecbaddabccbaddabceeecbaddabceeeabcddcbadbaccabdeeabcddcbaeeabcddcbacbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeedbaccabdeedbaccabdabcddcbaeeecbaddabceeecbaddabccbaddabceeeeeecbaddabcabcddcbaeeeeabcddcbaeabcddcbaeeeeabcddcbadbaccabddbaccabdabcddcbaeeeedbaccabdedbaccabdeeeedbaccabdcbaddabceeeeeecbaddabccbaddabceeecbaddabceeedbaccabdabcddcbaeeabcddcbaeeabcddcbacbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeedbaccabdeedbaccabdabcddcbaeeecbaddabceeecbaddabccbaddabceeeeeecbaddabcabcddcbaeeeeabcddcbaeabcddcbaeeeedbaccabdabcddcbaabcddcbadbaccabdeeeedbaccabdedbaccabdeeeedbaccabdcbaddabceeeeeecbaddabccbaddabceeecbaddabceeedbaccabdabcddcbaeeabcddcbaeeabcddcbacbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcdbaccabdeeecbaddabcdbaccabdeabcddcbacbaddabceeeeeeeedbaccabddbaccabdeeeeabcddcbaeeabcddcbadbaccabdeeecbaddabceabcddcbaeabcddcbaeeeecbaddabcecbaddabceabcddcbaeeedbaccabdcbaddabceecbaddabceeeedbaccabddbaccabdeeeeeeeeabcddcbacbaddabcedbaccabdabcddcbaeeedbaccabdabcddcbaeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabceabcddcbadbaccabdeedbaccabdeedbaccabdcbaddabceeeeeeecbaddabccbaddabceecbaddabceeabcddcbaeeeeedbaccabddbaccabdeeabcddcbaeabcddcbaeeabcddcbaedbaccabdeedbaccabdabcddcbaeeeeeabcddcbaeecbaddabceecbaddabccbaddabceeeeeeecbaddabcdbaccabdeeabcddcbaeedbaccabddbaccabdecbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcecbaddabcdbaccabddbaccabdeeeedbaccabdeabcddcbaeeeeeeeeabcddcbaeabcddcbaedbaccabdcbaddabccbaddabccbaddabceeeeeabcddcbaeeecbaddabceedbaccabdeeeabcddcbaeeeeedbaccabddbaccabddbaccabdcbaddabceabcddcbaeabcddcbaeeeeeeeeabcddcbaecbaddabceeeecbaddabccbaddabcdbaccabdedbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcecbaddabceabcddcbadbaccabddbaccabdeeeeeecbaddabceedbaccabdeeeeeedbaccabddbaccabdabcddcbacbaddabceeeeeabcddcbacbaddabceeeeabcddcbaabcddcbaeeeedbaccabdabcddcbaeeeeedbaccabdabcddcbacbaddabccbaddabceeeeeecbaddabceedbaccabdeeeeeecbaddabccbaddabcabcddcbaedbaccabdedbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabdcbaddabcdbaccabdeeeedbaccabdeabcddcbaeeeeeeeeabcddcbaeabcddcbaecbaddabcdbaccabdcbaddabccbaddabceeeeeabcddcbaeeecbaddabceedbaccabdeeeabcddcbaeeeeedbaccabddbaccabdcbaddabcdbaccabdeabcddcbaeabcddcbaeeeeeeeeabcddcbaecbaddabceeeecbaddabcdbaccabdcbaddabcedbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabdcbaddabcdbaccabdeeeeeedbaccabdeabcddcbaeabcddcbaecbaddabceeeeeeecbaddabceabcddcbaedbaccabdeabcddcbaedbaccabdecbaddabceeeeeeabcddcbaedbaccabdecbaddabcedbaccabdecbaddabceabcddcbaeeeeeeeabcddcbaecbaddabcecbaddabcedbaccabdeeeeeedbaccabdabcddcbadbaccabdeabcddcbaeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabdcbaddabcdbaccabdeeeeeedbaccabdeabcddcbaecbaddabceabcddcbaeeeeeeeabcddcbaecbaddabcedbaccabdeabcddcbaedbaccabdecbaddabceeeeeeabcddcbaedbaccabdecbaddabcedbaccabdeabcddcbaecbaddabceeeeeeecbaddabceabcddcbaecbaddabcedbaccabdeeeeeedbaccabdabcddcbadbaccabdeabcddcbaeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabddbaccabdcbaddabceeeedbaccabdeabcddcbaeeeeeeeeabcddcbaeabcddcbaecbaddabccbaddabcdbaccabdcbaddabceeeeeabcddcbaeeecbaddabceedbaccabdeeeabcddcbaeeeeedbaccabdcbaddabcdbaccabddbaccabdeabcddcbaeabcddcbaeeeeeeeeabcddcbaecbaddabceeeedbaccabdcbaddabccbaddabcedbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabddbaccabdeabcddcbaeeeedbaccabdeecbaddabcecbaddabccbaddabceeeeeeeecbaddabcabcddcbaeeeabcddcbaeabcddcbaeedbaccabdedbaccabdeeabcddcbaeabcddcbaeedbaccabdedbaccabdeeedbaccabdcbaddabceeeeeeeecbaddabccbaddabcecbaddabceeabcddcbaeeeedbaccabdeabcddcbaabcddcbaecbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabddbaccabdeeabcddcbaeedbaccabdcbaddabceeeeeeecbaddabccbaddabceecbaddabceeabcddcbaeeeeeabcddcbadbaccabdeedbaccabdeabcddcbaeeabcddcbaeabcddcbaeedbaccabddbaccabdeeeeeabcddcbaeecbaddabceecbaddabccbaddabceeeeeeecbaddabcdbaccabdeedbaccabdeedbaccabdabcddcbaecbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabdeabcddcbacbaddabceedbaccabdedbaccabdeeeeeeeedbaccabdcbaddabccbaddabceeeabcddcbaeeeecbaddabceabcddcbaeeeedbaccabdabcddcbaabcddcbacbaddabceeeeabcddcbaedbaccabdeeeeabcddcbaeeedbaccabddbaccabdcbaddabceeeeeeeecbaddabcecbaddabceedbaccabdabcddcbaecbaddabcedbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabdeabcddcbaedbaccabdecbaddabcecbaddabceeeeabcddcbaeedbaccabdeeeeeeecbaddabcedbaccabdeabcddcbadbaccabdeecbaddabcdbaccabdeeeeeeabcddcbacbaddabceeabcddcbadbaccabdeabcddcbaecbaddabceeeeeeeabcddcbaeedbaccabdeeeecbaddabcecbaddabceabcddcbaedbaccabdeabcddcbaecbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabdedbaccabdeabcddcbaecbaddabcecbaddabceeeeabcddcbaeedbaccabdeeeeeeecbaddabceabcddcbaedbaccabddbaccabdeecbaddabcdbaccabdeeeeeeabcddcbacbaddabceeabcddcbaabcddcbaedbaccabdecbaddabceeeeeeeabcddcbaeedbaccabdeeeecbaddabcecbaddabcedbaccabdeabcddcbaeabcddcbaecbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeecbaddabcedbaccabdedbaccabdedbaccabdecbaddabcecbaddabceeeeabcddcbaeeabcddcbaeeeeeeecbaddabceabcddcbaeabcddcbadbaccabdeecbaddabcabcddcbaeeeeeedbaccabdcbaddabceeabcddcbadbaccabdedbaccabdecbaddabceeeeeeedbaccabdeedbaccabdeeeecbaddabcecbaddabceabcddcbaeabcddcbaeabcddcbaecbaddabceeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbacbaddabcdbaccabdeeeeeeeeeecbaddabccbaddabcedbaccabdeeeabcddcbacbaddabcabcddcbacbaddabceeedbaccabdeeeeeeeedbaccabddbaccabdabcddcbacbaddabceeeeeeeedbaccabdeeeabcddcbacbaddabcabcddcbacbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeeeeeeabcddcbacbaddabcdbaccabddbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbadbaccabdcbaddabceeeeeeeeeecbaddabccbaddabcedbaccabdeeeabcddcbacbaddabcabcddcbacbaddabceeedbaccabdeeeeeeeedbaccabdcbaddabcabcddcbadbaccabdeeeeeeeedbaccabdeeeabcddcbacbaddabcabcddcbacbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeeeeeeabcddcbadbaccabdcbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbadbaccabdcbaddabceeeeeeeeeecbaddabccbaddabcedbaccabdeeeabcddcbacbaddabccbaddabcabcddcbaeeedbaccabdeeeeeeeeabcddcbadbaccabddbaccabdcbaddabceeeeeeeedbaccabdeeeabcddcbacbaddabccbaddabcabcddcbaeeedbaccabdeabcddcbaabcddcbaeeeeeeeeeeabcddcbadbaccabdcbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbadbaccabdcbaddabceeeeeeeeeecbaddabccbaddabcedbaccabdeeeabcddcbacbaddabccbaddabcabcddcbaeeedbaccabdeeeeeeeeabcddcbadbaccabddbaccabdcbaddabceeeeeeeedbaccabdeeecbaddabcabcddcbaabcddcbacbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeeeeeeabcddcbadbaccabdcbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbadbaccabdcbaddabceeeeeeeeeecbaddabccbaddabcedbaccabdeeecbaddabcabcddcbaabcddcbacbaddabceeedbaccabdeeeeeeeeabcddcbadbaccabddbaccabdcbaddabceeeeeeeedbaccabdeeeabcddcbacbaddabccbaddabcabcddcbaeeedbaccabdeabcddcbaabcddcbaeeeeeeeeeeabcddcbadbaccabdcbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbadbaccabdcbaddabceeeeeeeeeecbaddabccbaddabcedbaccabdeeecbaddabcabcddcbaabcddcbacbaddabceeedbaccabdeeeeeeeeabcddcbadbaccabddbaccabdcbaddabceeeeeeeedbaccabdeeecbaddabcabcddcbaabcddcbacbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeeeeeeabcddcbadbaccabdcbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbaecbaddabcedbaccabdeeeeecbaddabcedbaccabdeeecbaddabcabcddcbaeeeeecbaddabceabcddcbaedbaccabdecbaddabccbaddabceedbaccabdeeeeeeeedbaccabdeeabcddcbaabcddcbaedbaccabdecbaddabceabcddcbaeeeeecbaddabcabcddcbaeeedbaccabdeabcddcbaeeeeedbaccabdeabcddcbaecbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbaecbaddabcedbaccabdeeeeeecbaddabcdbaccabdcbaddabceeeabcddcbaeeeeeeecbaddabcabcddcbacbaddabcdbaccabdedbaccabdeecbaddabceeeeeeeeabcddcbaeedbaccabdedbaccabdabcddcbacbaddabcabcddcbaeeeeeeecbaddabceeeabcddcbadbaccabdabcddcbaeeeeeedbaccabdeabcddcbaecbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbaecbaddabceecbaddabceeeecbaddabcdbaccabdeeeabcddcbadbaccabdeeeeeeecbaddabcdbaccabdcbaddabceeedbaccabdeeeabcddcbaedbaccabdeeabcddcbaedbaccabdeeeabcddcbaeeecbaddabcabcddcbacbaddabceeeeeeeabcddcbadbaccabdeeeabcddcbacbaddabceeeecbaddabceecbaddabcedbaccabdabcddcbaeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbaeecbaddabccbaddabceeeeedbaccabdecbaddabcdbaccabdedbaccabdeeeeeeeecbaddabcabcddcbaeeeabcddcbaedbaccabdeabcddcbaeeecbaddabcabcddcbaeeecbaddabcedbaccabdecbaddabceeecbaddabcabcddcbaeeeeeeeedbaccabdedbaccabdabcddcbaedbaccabdeeeeeabcddcbaabcddcbaeecbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbaeecbaddabcdbaccabdeeeeecbaddabcecbaddabcdbaccabdeeabcddcbaeeeeecbaddabceedbaccabdeeeeabcddcbaedbaccabdcbaddabccbaddabceeeeeeabcddcbaabcddcbadbaccabdecbaddabceeeedbaccabdeeabcddcbaeeeeecbaddabceedbaccabdabcddcbaeabcddcbaeeeeedbaccabdabcddcbaeecbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdabcddcbaeecbaddabceecbaddabccbaddabceeedbaccabdeeedbaccabddbaccabdeeeeeedbaccabdabcddcbaeeeeabcddcbaecbaddabceeeecbaddabcabcddcbacbaddabcabcddcbaeeeeabcddcbaecbaddabceeeecbaddabcdbaccabdeeeeeedbaccabddbaccabdeeedbaccabdeeeabcddcbaabcddcbaeeabcddcbaeecbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabcabcddcbadbaccabdeeeeeeeeeecbaddabccbaddabcedbaccabdeeeabcddcbaabcddcbacbaddabccbaddabceeedbaccabdeeeeeeeedbaccabddbaccabdabcddcbacbaddabceeeeeeeedbaccabdeeeabcddcbaabcddcbacbaddabccbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeeeeeecbaddabcabcddcbadbaccabddbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabcdbaccabdabcddcbaeeeeeeeeeecbaddabccbaddabcedbaccabdeeeabcddcbaabcddcbacbaddabccbaddabceeedbaccabdeeeeeeeeabcddcbadbaccabddbaccabdcbaddabceeeeeeeedbaccabdeeeabcddcbaabcddcbacbaddabccbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeeeeeecbaddabcdbaccabdabcddcbadbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabcdbaccabdeecbaddabceeeeeedbaccabdeecbaddabcabcddcbaeabcddcbaeeeeeabcddcbacbaddabcecbaddabceabcddcbaeeedbaccabddbaccabdeeeeeeeeabcddcbaabcddcbaeeedbaccabdecbaddabcecbaddabcdbaccabdeeeeedbaccabdedbaccabdcbaddabceeabcddcbaeeeeeecbaddabceeabcddcbacbaddabcabcddcbaeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceabcddcbacbaddabceeeeeeeecbaddabcdbaccabddbaccabdedbaccabdeeeeeabcddcbaeeecbaddabcabcddcbaeeabcddcbaedbaccabdcbaddabceeeeeeeecbaddabcabcddcbaedbaccabdeedbaccabdcbaddabceeedbaccabdeeeeeabcddcbaeabcddcbaabcddcbacbaddabceeeeeeeecbaddabcdbaccabdecbaddabcabcddcbaeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceabcddcbaedbaccabdeeeeecbaddabcedbaccabdeeecbaddabcabcddcbaeeeeeabcddcbaecbaddabcedbaccabdecbaddabccbaddabceedbaccabdeeeeeeeedbaccabdeeabcddcbaabcddcbaedbaccabdeabcddcbaecbaddabceeeeecbaddabcabcddcbaeeedbaccabdeabcddcbaeeeeedbaccabdecbaddabceabcddcbadbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabcecbaddabcedbaccabdeeeeeabcddcbaedbaccabdeeecbaddabccbaddabceeeeeabcddcbaeabcddcbaedbaccabdeabcddcbaabcddcbaeedbaccabdeeeeeeeedbaccabdeecbaddabccbaddabcedbaccabdecbaddabcecbaddabceeeeeabcddcbaabcddcbaeeedbaccabdecbaddabceeeeedbaccabdeabcddcbaeabcddcbadbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabcedbaccabdcbaddabceeeeeeeecbaddabcabcddcbaabcddcbaedbaccabdeeeeeabcddcbaeeecbaddabcdbaccabdeedbaccabdeabcddcbacbaddabceeeeeeeecbaddabcdbaccabdeabcddcbaeeabcddcbacbaddabceeedbaccabdeeeeeabcddcbaedbaccabddbaccabdcbaddabceeeeeeeecbaddabcabcddcbaecbaddabcabcddcbaeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabcedbaccabdcbaddabceeeeeeeecbaddabcabcddcbadbaccabdeabcddcbaeeeeeabcddcbaeeecbaddabcdbaccabdeeabcddcbaedbaccabdcbaddabceeeeeeeecbaddabcabcddcbaedbaccabdeeabcddcbacbaddabceeedbaccabdeeeeedbaccabdeabcddcbadbaccabdcbaddabceeeeeeeecbaddabcabcddcbaecbaddabcabcddcbaeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceeabcddcbacbaddabceeeeedbaccabdedbaccabddbaccabdecbaddabceeeeeeeecbaddabcabcddcbaeeecbaddabceabcddcbaeabcddcbaeeecbaddabcdbaccabdeeeabcddcbaeabcddcbaedbaccabdeeeabcddcbadbaccabdeeeeeeeedbaccabdecbaddabccbaddabcecbaddabceeeeedbaccabdabcddcbaeedbaccabdcbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceeabcddcbadbaccabdeeeeeabcddcbaecbaddabcdbaccabdeecbaddabceeeeecbaddabceedbaccabdeeeecbaddabcedbaccabdabcddcbacbaddabceeeeeeabcddcbacbaddabcdbaccabdeabcddcbaeeeedbaccabdeeabcddcbaeeeeeabcddcbaeedbaccabdabcddcbaecbaddabceeeeedbaccabdcbaddabceeabcddcbadbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceecbaddabccbaddabceeeeeabcddcbadbaccabdeedbaccabdeeeeabcddcbaabcddcbadbaccabdeeeeeeeeecbaddabcedbaccabdedbaccabdeabcddcbaabcddcbaecbaddabcecbaddabcedbaccabdeeeeeeeeecbaddabcabcddcbaabcddcbaeeeecbaddabceecbaddabcabcddcbaeeeeedbaccabddbaccabdeedbaccabdcbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceecbaddabceeabcddcbacbaddabceeedbaccabdeeedbaccabddbaccabdeeeeeedbaccabdabcddcbaeeeeabcddcbaeabcddcbaeeeecbaddabccbaddabcabcddcbaabcddcbaeeeecbaddabcecbaddabceeeecbaddabcdbaccabdeeeeeedbaccabddbaccabdeeedbaccabdeeeabcddcbacbaddabceeabcddcbaeeabcddcbadbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceecbaddabceecbaddabcabcddcbaeeedbaccabdeeedbaccabddbaccabdeeeeeedbaccabdabcddcbaeeeeabcddcbaeabcddcbaeeeeabcddcbacbaddabccbaddabcabcddcbaeeeecbaddabcecbaddabceeeecbaddabcdbaccabdeeeeeedbaccabddbaccabdeeedbaccabdeeecbaddabcabcddcbaeeabcddcbaeeabcddcbadbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceecbaddabceecbaddabcabcddcbaeeedbaccabdeeedbaccabddbaccabdeeeeeedbaccabdabcddcbaeeeeabcddcbaeabcddcbaeeeecbaddabcabcddcbaabcddcbacbaddabceeeecbaddabcecbaddabceeeecbaddabcdbaccabdeeeeeedbaccabddbaccabdeeedbaccabdeeecbaddabcabcddcbaeeabcddcbaeeabcddcbadbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdcbaddabceeedbaccabdcbaddabceabcddcbadbaccabdeeeeeeeecbaddabccbaddabceeeeabcddcbaeeabcddcbacbaddabceeedbaccabdeabcddcbaeabcddcbaeeeedbaccabdedbaccabdeabcddcbaeeecbaddabcdbaccabdeedbaccabdeeeecbaddabccbaddabceeeeeeeeabcddcbadbaccabdecbaddabcabcddcbaeeecbaddabcabcddcbaeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabddbaccabdabcddcbacbaddabceeeeeeeeeecbaddabccbaddabcedbaccabdeeeabcddcbacbaddabcabcddcbacbaddabceeedbaccabdeeeeeeeeabcddcbacbaddabcdbaccabddbaccabdeeeeeeeedbaccabdeeeabcddcbacbaddabcabcddcbacbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeeeeeedbaccabdabcddcbacbaddabcdbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabddbaccabdcbaddabcabcddcbaeeeeeeeeeecbaddabccbaddabcedbaccabdeeeabcddcbaabcddcbacbaddabccbaddabceeedbaccabdeeeeeeeeabcddcbacbaddabcdbaccabddbaccabdeeeeeeeedbaccabdeeeabcddcbaabcddcbacbaddabccbaddabceeedbaccabdeabcddcbaabcddcbaeeeeeeeeeedbaccabdcbaddabcabcddcbadbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabddbaccabdcbaddabceecbaddabceeeeeecbaddabcabcddcbaeeeeabcddcbaeedbaccabdcbaddabceabcddcbaeeabcddcbadbaccabdeeeedbaccabdedbaccabdeeeeeecbaddabcecbaddabceeeecbaddabcabcddcbaeeabcddcbaedbaccabdcbaddabceeabcddcbaeeeeabcddcbadbaccabdeeeeeedbaccabdeedbaccabdcbaddabccbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabddbaccabdcbaddabceecbaddabceeeeeeeabcddcbacbaddabceedbaccabdabcddcbaeabcddcbaeedbaccabdeeeeeecbaddabcecbaddabceecbaddabceabcddcbaeeabcddcbaedbaccabdeedbaccabdedbaccabdeeeeeecbaddabceeabcddcbaeabcddcbacbaddabceedbaccabdabcddcbaeeeeeeedbaccabdeedbaccabdcbaddabccbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabddbaccabdcbaddabceedbaccabdeeeeeecbaddabcabcddcbaeeeeabcddcbaeecbaddabccbaddabceabcddcbaeeabcddcbacbaddabceeeecbaddabcedbaccabdeeeeeecbaddabcedbaccabdeeeedbaccabdabcddcbaeeabcddcbaedbaccabddbaccabdeeabcddcbaeeeeabcddcbadbaccabdeeeeeecbaddabceedbaccabdcbaddabccbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabddbaccabdcbaddabceedbaccabdeeeeeeeabcddcbacbaddabceecbaddabcabcddcbaeabcddcbaeecbaddabceeeeeecbaddabcecbaddabceedbaccabdeabcddcbaeeabcddcbaecbaddabceedbaccabdedbaccabdeeeeeedbaccabdeeabcddcbaeabcddcbadbaccabdeedbaccabdabcddcbaeeeeeeecbaddabceedbaccabdcbaddabccbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabddbaccabdeecbaddabcdbaccabdeeeeeabcddcbacbaddabceecbaddabceeeeabcddcbaabcddcbacbaddabceeeeeeeeecbaddabcecbaddabcedbaccabdeabcddcbaabcddcbaecbaddabcedbaccabdedbaccabdeeeeeeeeedbaccabdabcddcbaabcddcbaeeeedbaccabdeedbaccabdabcddcbaeeeeecbaddabcdbaccabdeecbaddabccbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdeabcddcbacbaddabceecbaddabceecbaddabcdbaccabdeeeeeeedbaccabddbaccabdeedbaccabdeeabcddcbaeeeeecbaddabccbaddabceeabcddcbaeabcddcbaeeabcddcbaecbaddabceecbaddabcabcddcbaeeeeeabcddcbaeedbaccabdeedbaccabddbaccabdeeeeeeedbaccabdcbaddabceeabcddcbaeecbaddabccbaddabcedbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabccbaddabcdbaccabdeeeecbaddabceabcddcbaeeeeeeeeabcddcbaeabcddcbaedbaccabddbaccabdcbaddabcdbaccabdeeeeeabcddcbaeeedbaccabdeecbaddabceeeabcddcbaeeeeecbaddabcdbaccabdcbaddabccbaddabceabcddcbaeabcddcbaeeeeeeeeabcddcbaedbaccabdeeeecbaddabcdbaccabddbaccabdecbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabccbaddabceabcddcbaeeeecbaddabceedbaccabdedbaccabddbaccabdeeeeeeeedbaccabdabcddcbaeeeabcddcbaeabcddcbaeecbaddabcecbaddabceeabcddcbaeabcddcbaeecbaddabcecbaddabceeecbaddabcdbaccabdeeeeeeeedbaccabddbaccabdedbaccabdeeabcddcbaeeeecbaddabceabcddcbaabcddcbaedbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabccbaddabceeabcddcbaeecbaddabcdbaccabdeeeeeeedbaccabddbaccabdeedbaccabdeeabcddcbaeeeeeabcddcbacbaddabceecbaddabceabcddcbaeeabcddcbaeabcddcbaeecbaddabccbaddabceeeeeabcddcbaeedbaccabdeedbaccabddbaccabdeeeeeeedbaccabdcbaddabceecbaddabceecbaddabcabcddcbaedbaccabdeeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabcdbaccabdcbaddabceeeecbaddabceabcddcbaeeeeeeeeabcddcbaeabcddcbaedbaccabdcbaddabcdbaccabddbaccabdeeeeeabcddcbaeeedbaccabdeecbaddabceeeabcddcbaeeeeecbaddabccbaddabcdbaccabdcbaddabceabcddcbaeabcddcbaeeeeeeeeabcddcbaedbaccabdeeeedbaccabdcbaddabcdbaccabdecbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabcdbaccabdcbaddabceeeeeecbaddabceabcddcbaeabcddcbaedbaccabdeeeeeeedbaccabdeabcddcbaecbaddabceabcddcbaecbaddabcedbaccabdeeeeeeabcddcbaecbaddabcedbaccabdecbaddabcedbaccabdeabcddcbaeeeeeeeabcddcbaedbaccabdedbaccabdecbaddabceeeeeecbaddabcabcddcbacbaddabceabcddcbaeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabcdbaccabdcbaddabceeeeeecbaddabceabcddcbaedbaccabdeabcddcbaeeeeeeeabcddcbaedbaccabdecbaddabceabcddcbaecbaddabcedbaccabdeeeeeeabcddcbaecbaddabcedbaccabdecbaddabceabcddcbaedbaccabdeeeeeeedbaccabdeabcddcbaedbaccabdecbaddabceeeeeecbaddabcabcddcbacbaddabceabcddcbaeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabceabcddcbadbaccabdeecbaddabcecbaddabceeeeeeeecbaddabcdbaccabddbaccabdeeeabcddcbaeeeedbaccabdeabcddcbaeeeecbaddabcabcddcbaabcddcbadbaccabdeeeeabcddcbaecbaddabceeeeabcddcbaeeecbaddabccbaddabcdbaccabdeeeeeeeedbaccabdedbaccabdeecbaddabcabcddcbaedbaccabdecbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabceabcddcbaecbaddabcedbaccabdedbaccabdeeeeabcddcbaeecbaddabceeeeeeedbaccabdecbaddabceabcddcbacbaddabceedbaccabdcbaddabceeeeeeabcddcbadbaccabdeeabcddcbacbaddabceabcddcbaedbaccabdeeeeeeeabcddcbaeecbaddabceeeedbaccabdedbaccabdeabcddcbaecbaddabceabcddcbaedbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabcecbaddabceabcddcbaedbaccabdedbaccabdeeeeabcddcbaeecbaddabceeeeeeedbaccabdeabcddcbaecbaddabccbaddabceedbaccabdcbaddabceeeeeeabcddcbadbaccabdeeabcddcbaabcddcbaecbaddabcedbaccabdeeeeeeeabcddcbaeecbaddabceeeedbaccabdedbaccabdecbaddabceabcddcbaeabcddcbaedbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdecbaddabcecbaddabcecbaddabcedbaccabdedbaccabdeeeeabcddcbaeeabcddcbaeeeeeeedbaccabdeabcddcbaeabcddcbacbaddabceedbaccabdabcddcbaeeeeeecbaddabcdbaccabdeeabcddcbacbaddabcecbaddabcedbaccabdeeeeeeecbaddabceecbaddabceeeedbaccabdedbaccabdeabcddcbaeabcddcbaeabcddcbaedbaccabdeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeedbaccabdedbaccabdcbaddabccbaddabceeeecbaddabceabcddcbaeeeeeeeeabcddcbaeabcddcbaecbaddabcdbaccabddbaccabddbaccabdeeeeeabcddcbaeeedbaccabdeecbaddabceeeabcddcbaeeeeecbaddabccbaddabccbaddabcdbaccabdeabcddcbaeabcddcbaeeeeeeeeabcddcbaedbaccabdeeeedbaccabddbaccabdcbaddabcecbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeedbaccabdedbaccabdeabcddcbacbaddabccbaddabceeeeeedbaccabdeecbaddabceeeeeecbaddabccbaddabcabcddcbadbaccabdeeeeeabcddcbadbaccabdeeeeabcddcbaabcddcbaeeeecbaddabcabcddcbaeeeeecbaddabcabcddcbadbaccabddbaccabdeeeeeedbaccabdeecbaddabceeeeeedbaccabddbaccabdabcddcbaecbaddabcecbaddabceeeeeabcddcba'' 
 + 
 +''abcddcbaeeeeeeabcddcbacbaddabcdbaccabdcbaddabceeeecbaddabcdbaccabdeeeeedbaccabdeeeedbaccabdeabcddcbaabcddcbaeeeeeeedbaccabdecbaddabccbaddabcedbaccabdeeabcddcbaecbaddabccbaddabceabcddcbaeeeeeeedbaccabddbaccabdeabcddcbaeeeeabcddcbaeeeeeabcddcbacbaddabceeeecbaddabcabcddcbacbaddabcdbaccabdeeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeeabcddcbacbaddabcedbaccabdecbaddabcdbaccabdcbaddabceeeedbaccabdeeeabcddcbaeeeeeeeeeeecbaddabcdbaccabddbaccabdcbaddabceeabcddcbaeeabcddcbadbaccabdeedbaccabdeeabcddcbacbaddabccbaddabcabcddcbaeeeeeeeeeeedbaccabdeeeabcddcbaeeeecbaddabcabcddcbacbaddabceabcddcbaecbaddabcdbaccabdeeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeeabcddcbacbaddabcedbaccabdecbaddabcdbaccabdcbaddabceeeedbaccabdeeeabcddcbaeeeeeeeeeeecbaddabcdbaccabddbaccabdcbaddabceeabcddcbaeeabcddcbadbaccabdeedbaccabdeecbaddabcabcddcbaabcddcbacbaddabceeeeeeeeeeedbaccabdeeeabcddcbaeeeecbaddabcabcddcbacbaddabceabcddcbaecbaddabcdbaccabdeeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeeabcddcbacbaddabcedbaccabdecbaddabcdbaccabdcbaddabceeeedbaccabdeeeabcddcbaeeeeeeeeeeedbaccabdcbaddabccbaddabcdbaccabdeeabcddcbaeeabcddcbadbaccabdeedbaccabdeeabcddcbacbaddabccbaddabcabcddcbaeeeeeeeeeeedbaccabdeeeabcddcbaeeeecbaddabcabcddcbacbaddabceabcddcbaecbaddabcdbaccabdeeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeeabcddcbacbaddabcedbaccabdecbaddabcdbaccabdcbaddabceeeedbaccabdeeeabcddcbaeeeeeeeeeeedbaccabdcbaddabccbaddabcdbaccabdeeabcddcbaeeabcddcbadbaccabdeedbaccabdeecbaddabcabcddcbaabcddcbacbaddabceeeeeeeeeeedbaccabdeeeabcddcbaeeeecbaddabcabcddcbacbaddabceabcddcbaecbaddabcdbaccabdeeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeeabcddcbadbaccabdcbaddabcdbaccabdeeeedbaccabdcbaddabceeeeecbaddabceeeecbaddabceabcddcbaabcddcbaeeeeeeecbaddabcedbaccabddbaccabdecbaddabceeabcddcbaedbaccabddbaccabdeabcddcbaeeeeeeecbaddabccbaddabceabcddcbaeeeeabcddcbaeeeeeabcddcbadbaccabdeeeedbaccabdabcddcbadbaccabdcbaddabceeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeeabcddcbadbaccabdecbaddabcedbaccabdcbaddabcdbaccabdeeeecbaddabceeeabcddcbaeeeeeeeeeeecbaddabcdbaccabddbaccabdcbaddabceeabcddcbaeeabcddcbacbaddabceecbaddabceeabcddcbadbaccabddbaccabdabcddcbaeeeeeeeeeeecbaddabceeeabcddcbaeeeedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdcbaddabceeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeeabcddcbadbaccabdecbaddabcedbaccabdcbaddabcdbaccabdeeeecbaddabceeeabcddcbaeeeeeeeeeeecbaddabcdbaccabddbaccabdcbaddabceeabcddcbaeeabcddcbacbaddabceecbaddabceedbaccabdabcddcbaabcddcbadbaccabdeeeeeeeeeeecbaddabceeeabcddcbaeeeedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdcbaddabceeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeeabcddcbadbaccabdecbaddabcedbaccabdcbaddabcdbaccabdeeeecbaddabceeeabcddcbaeeeeeeeeeeedbaccabdcbaddabccbaddabcdbaccabdeeabcddcbaeeabcddcbacbaddabceecbaddabceeabcddcbadbaccabddbaccabdabcddcbaeeeeeeeeeeecbaddabceeeabcddcbaeeeedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdcbaddabceeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeeabcddcbadbaccabdecbaddabcedbaccabdcbaddabcdbaccabdeeeecbaddabceeeabcddcbaeeeeeeeeeeedbaccabdcbaddabccbaddabcdbaccabdeeabcddcbaeeabcddcbacbaddabceecbaddabceedbaccabdabcddcbaabcddcbadbaccabdeeeeeeeeeeecbaddabceeeabcddcbaeeeedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdcbaddabceeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeecbaddabcabcddcbaedbaccabdcbaddabcdbaccabdeecbaddabceeeeeeeabcddcbaedbaccabdeeeeedbaccabdeeabcddcbaeedbaccabdedbaccabdcbaddabccbaddabceeeeeecbaddabccbaddabcabcddcbaeabcddcbaeedbaccabdeeabcddcbaeeeeeabcddcbaedbaccabdeeeeeeecbaddabceeabcddcbacbaddabcabcddcbaedbaccabdcbaddabceeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeecbaddabcdbaccabdecbaddabcedbaccabdabcddcbadbaccabdeeeecbaddabceeeabcddcbaeeeeeeeeeeeabcddcbadbaccabddbaccabdcbaddabceecbaddabceeabcddcbacbaddabceeabcddcbaeeabcddcbadbaccabddbaccabdcbaddabceeeeeeeeeeecbaddabceeeabcddcbaeeeedbaccabdcbaddabcdbaccabdeabcddcbaedbaccabdabcddcbaeeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeecbaddabcdbaccabdecbaddabcedbaccabdcbaddabcdbaccabdeeeeabcddcbaeeeabcddcbaeeeeeeeeeeeabcddcbadbaccabddbaccabdabcddcbaeecbaddabceecbaddabcabcddcbaeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabceeeeeeeeeeecbaddabceeecbaddabceeeedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdabcddcbaeeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeecbaddabcdbaccabdecbaddabcedbaccabdcbaddabcdbaccabdeeeeabcddcbaeeeabcddcbaeeeeeeeeeeeabcddcbadbaccabddbaccabdabcddcbaeecbaddabceecbaddabcabcddcbaeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabdeeeeeeeeeeecbaddabceeecbaddabceeeedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdabcddcbaeeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeecbaddabcdbaccabdecbaddabcedbaccabdcbaddabcdbaccabdeeeeabcddcbaeeeabcddcbaeeeeeeeeeeedbaccabdabcddcbaabcddcbadbaccabdeecbaddabceecbaddabcabcddcbaeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabceeeeeeeeeeecbaddabceeecbaddabceeeedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdabcddcbaeeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeecbaddabcdbaccabdecbaddabcedbaccabdcbaddabcdbaccabdeeeeabcddcbaeeeabcddcbaeeeeeeeeeeedbaccabdabcddcbaabcddcbadbaccabdeecbaddabceecbaddabcabcddcbaeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabdeeeeeeeeeeecbaddabceeecbaddabceeeedbaccabdabcddcbadbaccabdeabcddcbaedbaccabdabcddcbaeeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeedbaccabdabcddcbaecbaddabcdbaccabdcbaddabceedbaccabdeeeeeeeabcddcbaecbaddabceeeeecbaddabceeabcddcbaeecbaddabcecbaddabcdbaccabddbaccabdeeeeeedbaccabddbaccabdabcddcbaeabcddcbaeecbaddabceeabcddcbaeeeeeabcddcbaecbaddabceeeeeeedbaccabdeeabcddcbadbaccabdabcddcbaecbaddabcdbaccabdeeeeeecbaddabc'' 
 + 
 +''abcddcbaeeeeeedbaccabdcbaddabcedbaccabdecbaddabcabcddcbacbaddabceeeedbaccabdeeeabcddcbaeeeeeeeeeeeabcddcbacbaddabccbaddabcdbaccabdeedbaccabdeeabcddcbadbaccabdeeabcddcbaeeabcddcbacbaddabccbaddabcdbaccabdeeeeeeeeeeedbaccabdeeeabcddcbaeeeecbaddabcdbaccabdcbaddabceabcddcbaecbaddabcabcddcbaeeeeeedbaccabd'' 
 + 
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 + 
 +''abcddcbaeeeeeedbaccabdcbaddabcedbaccabdecbaddabcdbaccabdcbaddabceeeeabcddcbaeeeabcddcbaeeeeeeeeeeeabcddcbacbaddabccbaddabcabcddcbaeedbaccabdeedbaccabdabcddcbaeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabdeeeeeeeeeeedbaccabdeeedbaccabdeeeecbaddabcabcddcbacbaddabceabcddcbaecbaddabcabcddcbaeeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeedbaccabdcbaddabcedbaccabdecbaddabcdbaccabdcbaddabceeeeabcddcbaeeeabcddcbaeeeeeeeeeeecbaddabcabcddcbaabcddcbacbaddabceedbaccabdeedbaccabdabcddcbaeeabcddcbaeecbaddabcdbaccabddbaccabdcbaddabceeeeeeeeeeedbaccabdeeedbaccabdeeeecbaddabcabcddcbacbaddabceabcddcbaecbaddabcabcddcbaeeeeeedbaccabd'' 
 + 
 +''abcddcbaeeeeeedbaccabdcbaddabcedbaccabdecbaddabcdbaccabdcbaddabceeeeabcddcbaeeeabcddcbaeeeeeeeeeeecbaddabcabcddcbaabcddcbacbaddabceedbaccabdeedbaccabdabcddcbaeeabcddcbaeedbaccabdcbaddabccbaddabcdbaccabdeeeeeeeeeeedbaccabdeeedbaccabdeeeecbaddabcabcddcbacbaddabceabcddcbaecbaddabcabcddcbaeeeeeedbaccabd'' 
 + 
 +''eabcddcbaabcddcbaecbaddabceeeeeeedbaccabdeeeecbaddabccbaddabcabcddcbaeeeeedbaccabddbaccabddbaccabdcbaddabcedbaccabddbaccabdeeeeeeecbaddabcabcddcbaeeeeeeeedbaccabdcbaddabceeeeeeeabcddcbaabcddcbaecbaddabcabcddcbaabcddcbaabcddcbaeeeeedbaccabdcbaddabccbaddabceeeeabcddcbaeeeeeeecbaddabcedbaccabddbaccabde'' 
 + 
 +''eabcddcbaabcddcbaecbaddabceeeeeeeeecbaddabcedbaccabddbaccabdeecbaddabceabcddcbadbaccabdeeeedbaccabddbaccabdeeecbaddabcecbaddabceeeabcddcbadbaccabdeeeeeeeeabcddcbadbaccabdeeecbaddabcecbaddabceeeabcddcbaabcddcbaeeeeabcddcbadbaccabdecbaddabceeabcddcbaabcddcbaecbaddabceeeeeeeeecbaddabcedbaccabddbaccabde'' 
 + 
 +''eabcddcbaabcddcbaedbaccabdeeeeeeecbaddabceeeedbaccabddbaccabdabcddcbaeeeeecbaddabccbaddabccbaddabcdbaccabdecbaddabccbaddabceeeeeeedbaccabdabcddcbaeeeeeeeecbaddabcdbaccabdeeeeeeeabcddcbaabcddcbaedbaccabdabcddcbaabcddcbaabcddcbaeeeeecbaddabcdbaccabddbaccabdeeeeabcddcbaeeeeeeedbaccabdecbaddabccbaddabce'' 
 + 
 +''eabcddcbaabcddcbaedbaccabdeeeeeeeeedbaccabdecbaddabccbaddabceedbaccabdeabcddcbacbaddabceeeecbaddabccbaddabceeedbaccabdedbaccabdeeeabcddcbacbaddabceeeeeeeeabcddcbacbaddabceeedbaccabdedbaccabdeeeabcddcbaabcddcbaeeeeabcddcbacbaddabcedbaccabdeeabcddcbaabcddcbaedbaccabdeeeeeeeeedbaccabdecbaddabccbaddabce'' 
 + 
 +''eabcddcbaabcddcbaeeeeecbaddabceeedbaccabddbaccabdeeecbaddabcdbaccabddbaccabdeeeeeeabcddcbaeecbaddabcecbaddabccbaddabceeeeeeabcddcbacbaddabceeedbaccabddbaccabdeeeabcddcbacbaddabceeeeeeabcddcbaabcddcbaeabcddcbaeecbaddabceeeeeedbaccabddbaccabdabcddcbaeeedbaccabddbaccabdeeeabcddcbaeeeeecbaddabccbaddabce'' 
 + 
 +''eabcddcbaabcddcbaeeeeedbaccabdeeecbaddabccbaddabceeedbaccabdcbaddabccbaddabceeeeeeabcddcbaeedbaccabdedbaccabddbaccabdeeeeeeabcddcbadbaccabdeeecbaddabccbaddabceeeabcddcbadbaccabdeeeeeeabcddcbaabcddcbaeabcddcbaeedbaccabdeeeeeecbaddabccbaddabcabcddcbaeeecbaddabccbaddabceeeabcddcbaeeeeedbaccabddbaccabde'' 
 + 
 +''eabcddcbacbaddabcecbaddabceeeeeeeeecbaddabcabcddcbaeedbaccabddbaccabdeeeedbaccabddbaccabdabcddcbaeabcddcbaeeedbaccabdedbaccabdeeeeeabcddcbaeecbaddabceedbaccabdeeabcddcbaeeeeecbaddabcecbaddabceeeabcddcbaeabcddcbacbaddabccbaddabceeeecbaddabccbaddabceeabcddcbadbaccabdeeeeeeeeedbaccabdedbaccabdabcddcbae'' 
 + 
 +''eabcddcbacbaddabcedbaccabdeeeeeeeeecbaddabcabcddcbaeedbaccabddbaccabdeeeabcddcbaeecbaddabcdbaccabdecbaddabcabcddcbaecbaddabceeeeeeeeedbaccabdabcddcbaeedbaccabdabcddcbaeeeeeeeeecbaddabceabcddcbadbaccabdecbaddabccbaddabceeabcddcbaeeedbaccabddbaccabdeeabcddcbacbaddabceeeeeeeeecbaddabceabcddcbadbaccabde'' 
 + 
 +''eabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdcbaddabceeabcddcbaabcddcbaeeecbaddabceedbaccabddbaccabdeabcddcbacbaddabcedbaccabdeeeeeeeeecbaddabcabcddcbaeecbaddabcabcddcbaeeeeeeeeedbaccabdecbaddabcdbaccabdeabcddcbadbaccabdeecbaddabceeeabcddcbaabcddcbaeecbaddabcdbaccabdeeeeeeeeeabcddcbaedbaccabdcbaddabce'' 
 + 
 +''eabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdeabcddcbacbaddabceedbaccabdecbaddabccbaddabceeeeabcddcbaabcddcbaeeedbaccabdedbaccabdeeeabcddcbaabcddcbaeeeeeeeecbaddabccbaddabceeedbaccabdedbaccabdeeecbaddabccbaddabceeeeabcddcbaabcddcbaedbaccabdeeabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdeabcddcbacbaddabce'' 
 + 
 +''eabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdecbaddabcabcddcbaeedbaccabdeabcddcbacbaddabceeeecbaddabcabcddcbaeeedbaccabdedbaccabdeeecbaddabcabcddcbaeeeeeeeeabcddcbacbaddabceeedbaccabdedbaccabdeeeabcddcbacbaddabceeeecbaddabcabcddcbaedbaccabdeecbaddabcabcddcbaedbaccabdeeeeeeeeedbaccabdeabcddcbacbaddabce'' 
 + 
 +''eabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdecbaddabcabcddcbaeedbaccabdeabcddcbacbaddabceeeecbaddabcabcddcbaeeedbaccabdedbaccabdeeecbaddabcabcddcbaeeeeeeeecbaddabcabcddcbaeeedbaccabdedbaccabdeeeabcddcbacbaddabceeeeabcddcbacbaddabcedbaccabdeeabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdecbaddabcabcddcbae'' 
 + 
 +''eabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdecbaddabcabcddcbaeedbaccabdecbaddabcabcddcbaeeeeabcddcbacbaddabceeedbaccabdedbaccabdeeeabcddcbacbaddabceeeeeeeecbaddabcabcddcbaeeedbaccabdedbaccabdeeecbaddabcabcddcbaeeeeabcddcbacbaddabcedbaccabdeecbaddabcabcddcbaedbaccabdeeeeeeeeedbaccabdeabcddcbacbaddabce'' 
 + 
 +''eabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdecbaddabcabcddcbaeedbaccabdecbaddabcabcddcbaeeeecbaddabcabcddcbaeeedbaccabdedbaccabdeeeabcddcbacbaddabceeeeeeeeabcddcbacbaddabceeedbaccabdedbaccabdeeeabcddcbacbaddabceeeecbaddabcabcddcbaedbaccabdeeabcddcbacbaddabcedbaccabdeeeeeeeeedbaccabdecbaddabcabcddcbae'' 
 + 
 +''eabcddcbacbaddabceecbaddabceeeeeecbaddabceeabcddcbaedbaccabdeeeedbaccabdedbaccabddbaccabdabcddcbaeeeabcddcbadbaccabdedbaccabdabcddcbaeeeeeeeeecbaddabcdbaccabdeeeeeeeeeabcddcbacbaddabcecbaddabcabcddcbaeeeabcddcbacbaddabccbaddabcecbaddabceeeecbaddabceabcddcbaeedbaccabdeeeeeedbaccabdeedbaccabdabcddcbae'' 
 + 
 +''eabcddcbacbaddabceedbaccabdeeeeeecbaddabceeeedbaccabdabcddcbacbaddabcabcddcbaeeeedbaccabdedbaccabdeeecbaddabcabcddcbaeeedbaccabdabcddcbaeeeeedbaccabdeecbaddabceeeeeabcddcbacbaddabceeeabcddcbadbaccabdeeecbaddabcecbaddabceeeeabcddcbadbaccabdabcddcbacbaddabceeeedbaccabdeeeeeecbaddabceedbaccabdabcddcbae'' 
 + 
 +''eabcddcbacbaddabceedbaccabdeeeeeeedbaccabdecbaddabceedbaccabdeabcddcbacbaddabcecbaddabceeeeeabcddcbaabcddcbaeeeabcddcbadbaccabdabcddcbadbaccabdeeeeeeeeeeeeeedbaccabdcbaddabcdbaccabdcbaddabceeecbaddabccbaddabceeeeeabcddcbaeabcddcbacbaddabcedbaccabdeeabcddcbaedbaccabdeeeeeeedbaccabdeeabcddcbacbaddabce'' 
 + 
 +''eabcddcbacbaddabceedbaccabdeeeeeeeeabcddcbadbaccabdecbaddabcedbaccabdecbaddabcabcddcbaeeeeeeecbaddabcdbaccabdedbaccabdeabcddcbaeeeabcddcbaecbaddabceeeeeeabcddcbaecbaddabceeecbaddabcedbaccabdedbaccabdabcddcbaeeeeeeecbaddabcabcddcbaedbaccabdeabcddcbaedbaccabdcbaddabceeeeeeeedbaccabdeeabcddcbacbaddabce'' 
 + 
 +''eabcddcbacbaddabceedbaccabdeeeeeeeecbaddabcdbaccabdeabcddcbaedbaccabdecbaddabcabcddcbaeeeeeeeabcddcbadbaccabdedbaccabdecbaddabceeecbaddabceabcddcbaeeeeeecbaddabceabcddcbaeeeabcddcbaedbaccabdedbaccabdcbaddabceeeeeeecbaddabcabcddcbaedbaccabdecbaddabcedbaccabdabcddcbaeeeeeeeedbaccabdeeabcddcbacbaddabce'' 
 + 
 +''eabcddcbacbaddabceedbaccabdeeeeeeeecbaddabcdbaccabdedbaccabdabcddcbaeeeabcddcbacbaddabceeeeeabcddcbaeedbaccabdcbaddabcecbaddabceabcddcbadbaccabdeeeeeeeeeeeecbaddabcabcddcbaedbaccabdedbaccabdcbaddabceeabcddcbaeeeeedbaccabdabcddcbaeeeabcddcbacbaddabcecbaddabcdbaccabdeeeeeeeecbaddabceedbaccabdabcddcbae'' 
 + 
 +''eabcddcbacbaddabceedbaccabdeeeeeeeedbaccabdcbaddabcedbaccabdabcddcbaeeeabcddcbacbaddabceeeeeabcddcbaeecbaddabcdbaccabdecbaddabceabcddcbadbaccabdeeeeeeeeeeeecbaddabcabcddcbaedbaccabdecbaddabcdbaccabdeeabcddcbaeeeeedbaccabdabcddcbaeeeabcddcbacbaddabcedbaccabdcbaddabceeeeeeeecbaddabceedbaccabdabcddcbae'' 
 + 
 +''eabcddcbacbaddabceedbaccabdeeeeeeeedbaccabddbaccabdecbaddabcabcddcbaeeeabcddcbacbaddabceeeeeabcddcbaeecbaddabccbaddabcedbaccabdeabcddcbadbaccabdeeeeeeeeeeeecbaddabcabcddcbaecbaddabcedbaccabddbaccabdeeabcddcbaeeeeedbaccabdabcddcbaeeeabcddcbadbaccabdecbaddabccbaddabceeeeeeeecbaddabceedbaccabdabcddcbae'' 
 + 
 +''eabcddcbacbaddabceeeabcddcbaeeeedbaccabdeeeeecbaddabcdbaccabdabcddcbacbaddabceeedbaccabdedbaccabdeeecbaddabceedbaccabdeeeeecbaddabcabcddcbaeedbaccabdeeabcddcbaeedbaccabdcbaddabceeeeeabcddcbaeecbaddabceeeabcddcbaeabcddcbaeeecbaddabcdbaccabdabcddcbacbaddabceeeeeabcddcbaeeeedbaccabdeeecbaddabcdbaccabde'' 
 + 
 +''eabcddcbacbaddabceeeabcddcbaeeeeeedbaccabdecbaddabcedbaccabdeabcddcbaecbaddabcedbaccabddbaccabdeeeeeeeecbaddabcdbaccabdeeeecbaddabcabcddcbaeeedbaccabdabcddcbaeeedbaccabdcbaddabceeeeabcddcbacbaddabceeeeeeeeabcddcbaabcddcbaecbaddabcedbaccabdeabcddcbaecbaddabceabcddcbaeeeeeedbaccabdeeecbaddabcdbaccabde'' 
 + 
 +''eabcddcbacbaddabceeeabcddcbaeeeeeedbaccabdedbaccabdcbaddabceeecbaddabcdbaccabdeabcddcbaedbaccabdeeeeeeeecbaddabcabcddcbacbaddabcdbaccabdeeeeedbaccabdeeabcddcbaeeeeeabcddcbacbaddabcdbaccabdcbaddabceeeeeeeeabcddcbaedbaccabdeabcddcbacbaddabceeecbaddabcabcddcbaeabcddcbaeeeeeedbaccabdeeecbaddabcdbaccabde'' 
 + 
 +''eabcddcbacbaddabceeecbaddabceeeeecbaddabceedbaccabdabcddcbaeeeedbaccabdedbaccabdabcddcbaedbaccabdeeeeabcddcbaedbaccabdeabcddcbadbaccabdeeeeeeedbaccabdcbaddabceeeeeeecbaddabcabcddcbaecbaddabceabcddcbaeeeecbaddabceabcddcbacbaddabcecbaddabceeeeabcddcbacbaddabceedbaccabdeeeeedbaccabdeeedbaccabdabcddcbae'' 
 + 
 +''eabcddcbacbaddabceeedbaccabdeeeedbaccabdeeeeabcddcbacbaddabceeecbaddabcdbaccabdeabcddcbaedbaccabdeeecbaddabceeabcddcbaeecbaddabcabcddcbaeeeeeabcddcbaeedbaccabdeeeeedbaccabdcbaddabceedbaccabdeecbaddabceeeabcddcbaedbaccabdeabcddcbacbaddabceeecbaddabcdbaccabdeeeeabcddcbaeeeeabcddcbaeeecbaddabcdbaccabde'' 
 + 
 +''eabcddcbacbaddabceeedbaccabdeeeeecbaddabceecbaddabcabcddcbaeeeedbaccabdedbaccabdabcddcbaedbaccabdeeeeabcddcbaedbaccabdeabcddcbacbaddabceeeeeeecbaddabcdbaccabdeeeeeeedbaccabdabcddcbaecbaddabceabcddcbaeeeecbaddabceabcddcbacbaddabcecbaddabceeeeabcddcbadbaccabdeedbaccabdeeeeecbaddabceeedbaccabdabcddcbae'' 
 + 
 +''eabcddcbacbaddabceeedbaccabdeeeeeeabcddcbaedbaccabdcbaddabceeecbaddabcdbaccabdedbaccabdeabcddcbaeeeeeeeecbaddabcabcddcbacbaddabcabcddcbaeeeeeabcddcbaeedbaccabdeeeeedbaccabdcbaddabcdbaccabdcbaddabceeeeeeeedbaccabdeabcddcbaeabcddcbacbaddabceeecbaddabcabcddcbaedbaccabdeeeeeeabcddcbaeeecbaddabcdbaccabde'' 
 + 
 +''eabcddcbacbaddabceeedbaccabdeeeeeedbaccabdeabcddcbacbaddabceeecbaddabcdbaccabdeabcddcbaedbaccabdeeeeeeeecbaddabcabcddcbacbaddabcabcddcbaeeeeeabcddcbaeedbaccabdeeeeedbaccabdcbaddabcdbaccabdcbaddabceeeeeeeeabcddcbaedbaccabdeabcddcbacbaddabceeecbaddabcdbaccabdeabcddcbaeeeeeeabcddcbaeeecbaddabcdbaccabde'' 
 + 
 +''eabcddcbacbaddabceeeeabcddcbaeeeedbaccabdeecbaddabcdbaccabdeeedbaccabdcbaddabcabcddcbaedbaccabdeeeeeeeecbaddabceeabcddcbaeecbaddabcdbaccabdeedbaccabdeeabcddcbaeeabcddcbacbaddabceedbaccabdeecbaddabceeeeeeeeabcddcbaedbaccabdcbaddabcabcddcbaeeeabcddcbacbaddabceeabcddcbaeeeedbaccabdeeeecbaddabcdbaccabde'' 
 + 
 +''eabcddcbacbaddabceeeecbaddabcedbaccabdeeeeeabcddcbaeecbaddabceeedbaccabdedbaccabddbaccabdabcddcbaeabcddcbadbaccabdeeeeeecbaddabceeeabcddcbaeedbaccabdeecbaddabceeabcddcbaeeedbaccabdeeeeeecbaddabcabcddcbaeabcddcbacbaddabccbaddabcecbaddabceeedbaccabdeeabcddcbaeeeeecbaddabcedbaccabdeeeedbaccabdabcddcbae'' 
 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 + 
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 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcabcddcbadbaccabddbaccabdcbaddabcabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbadbaccabdcbaddabccbaddabcabcddcbadbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcabcddcbadbaccabddbaccabdcbaddabcabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaecbaddabcabcddcbadbaccabdabcddcbadbaccabdcbaddabceeeeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcdbaccabdabcddcbadbaccabdabcddcbacbaddabceabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbacbaddabccbaddabcdbaccabdabcddcbadbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeeeedbaccabdabcddcbacbaddabccbaddabcdbaccabdabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbacbaddabccbaddabcdbaccabdabcddcbadbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeeeedbaccabdcbaddabcabcddcbacbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbadbaccabdcbaddabccbaddabcabcddcbadbaccabdeeeeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeeeedbaccabdcbaddabcabcddcbacbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbaecbaddabcabcddcbadbaccabdabcddcbadbaccabdcbaddabceeeeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeeeecbaddabcabcddcbadbaccabdcbaddabcdbaccabdabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbadbaccabdcbaddabcdbaccabdabcddcbacbaddabceeeeecbaddabcdbaccabdeeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeeeecbaddabcabcddcbadbaccabdcbaddabcdbaccabdabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaedbaccabdabcddcbacbaddabcabcddcbadbaccabdcbaddabceeeeecbaddabcdbaccabdeeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeeeecbaddabcabcddcbadbaccabddbaccabdcbaddabcabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbadbaccabdcbaddabccbaddabcabcddcbadbaccabdeeeeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeeeecbaddabcabcddcbadbaccabddbaccabdcbaddabcabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaecbaddabcabcddcbadbaccabdabcddcbadbaccabdcbaddabceeeeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeeeecbaddabcdbaccabdabcddcbacbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbadbaccabdcbaddabcdbaccabdabcddcbacbaddabceeeeecbaddabcdbaccabdeeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeeeecbaddabcdbaccabdabcddcbacbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbaedbaccabdabcddcbacbaddabcabcddcbadbaccabdcbaddabceeeeecbaddabcdbaccabdeeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeeeedbaccabdcbaddabcabcddcbacbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbadbaccabdcbaddabccbaddabcabcddcbadbaccabdeeeeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeeeedbaccabdcbaddabcabcddcbacbaddabcabcddcbadbaccabdeabcddcbaeeeeeeeeeeeeeeabcddcbaecbaddabcabcddcbadbaccabdabcddcbadbaccabdcbaddabceeeeecbaddabcdbaccabdeeeeeeeeeeedbaccabdcbaddabceeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''eeeabcddcbaedbaccabdcbaddabcabcddcbaeedbaccabdcbaddabceeeeeeeeeeedbaccabdcbaddabceeeeecbaddabcabcddcbacbaddabcdbaccabddbaccabdabcddcbaeabcddcbaeeeeeeeeeeeeeeabcddcbaeabcddcbacbaddabcdbaccabddbaccabdabcddcbacbaddabceeeeedbaccabdcbaddabceeeeeeeeeeecbaddabcdbaccabdeeabcddcbadbaccabdcbaddabceabcddcbaeee'' 
 + 
 +''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).  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). 
5d60.1695001405.txt.gz · Last modified: 2023/09/18 01:43 by paulmeyer