Identifier
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Images
[1] => [1] => [1,0] => [1]
[1,1] => [2] => [1,1,0,0] => [1,2]
[2] => [1,1] => [1,0,1,0] => [2,1]
[1,1,1] => [3] => [1,1,1,0,0,0] => [1,2,3]
[1,2] => [2,1] => [1,1,0,0,1,0] => [1,3,2]
[2,1] => [1,2] => [1,0,1,1,0,0] => [2,1,3]
[3] => [1,1,1] => [1,0,1,0,1,0] => [2,3,1]
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => [1,2,3,4]
[1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => [1,2,4,3]
[1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,3,2,4]
[1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,3,4,2]
[2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [2,1,3,4]
[2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [2,1,4,3]
[3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [2,3,1,4]
[4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1]
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5]
[1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4]
[1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5]
[1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3]
[1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5]
[1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4]
[1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5]
[1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2]
[2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5]
[2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4]
[2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5]
[2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3]
[3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5]
[3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4]
[4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5]
[5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1]
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6]
[1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5]
[1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6]
[1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4]
[1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6]
[1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5]
[1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6]
[1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3]
[1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6]
[1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5]
[1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6]
[1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4]
[1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6]
[1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5]
[1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6]
[1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2]
[2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6]
[2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5]
[2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6]
[2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4]
[2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6]
[2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5]
[2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6]
[2,4] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3]
[3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6]
[3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5]
[3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6]
[3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4]
[4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6]
[4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5]
[5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6]
[6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1]
[1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7]
[1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6]
[1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7]
[1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5]
[1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7]
[1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6]
[1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7]
[1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4]
[1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7]
[1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6]
[1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7]
[1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5]
[1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7]
[1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6]
[1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7]
[1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3]
[1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7]
[1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6]
[1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7]
[1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5]
[1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7]
[1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6]
[1,2,3,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7]
[1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4]
[1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7]
[1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6]
[1,3,2,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7]
[1,3,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5]
[1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7]
[1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6]
[1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7]
[1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2]
[2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7]
[2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6]
[2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7]
[2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5]
[2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7]
[2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6]
>>> Load all 552 entries. <<<
[2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7]
[2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4]
[2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7]
[2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6]
[2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7]
[2,2,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5]
[2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7]
[2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6]
[2,4,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7]
[2,5] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3]
[3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7]
[3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6]
[3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7]
[3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5]
[3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7]
[3,2,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6]
[3,3,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7]
[3,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4]
[4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7]
[4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6]
[4,2,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7]
[4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5]
[5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7]
[5,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6]
[6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7]
[7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1]
[1,1,1,1,1,1,1,1] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,2] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7]
[1,1,1,1,1,2,1] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8]
[1,1,1,1,1,3] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6]
[1,1,1,1,2,1,1] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8]
[1,1,1,1,2,2] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7]
[1,1,1,1,3,1] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8]
[1,1,1,1,4] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5]
[1,1,1,2,1,1,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8]
[1,1,1,2,1,2] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7]
[1,1,1,2,2,1] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8]
[1,1,1,2,3] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6]
[1,1,1,3,1,1] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,4,7,8]
[1,1,1,3,2] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,5,6,4,8,7]
[1,1,1,4,1] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,4,8]
[1,1,1,5] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4]
[1,1,2,1,1,1,1] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8]
[1,1,2,1,1,2] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7]
[1,1,2,1,2,1] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8]
[1,1,2,1,3] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6]
[1,1,2,2,1,1] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8]
[1,1,2,2,2] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7]
[1,1,2,3,1] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,6,7,5,8]
[1,1,2,4] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5]
[1,1,3,1,1,1] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8]
[1,1,3,1,2] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,4,5,3,6,8,7]
[1,1,3,2,1] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6,8]
[1,1,3,3] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,5,3,7,8,6]
[1,1,4,1,1] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8]
[1,1,4,2] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,4,5,6,3,8,7]
[1,1,5,1] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,7,3,8]
[1,1,6] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3]
[1,2,1,1,1,1,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8]
[1,2,1,1,1,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7]
[1,2,1,1,2,1] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8]
[1,2,1,1,3] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6]
[1,2,1,2,1,1] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8]
[1,2,1,2,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7]
[1,2,1,3,1] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,2,4,6,7,5,8]
[1,2,1,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5]
[1,2,2,1,1,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8]
[1,2,2,1,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,5,4,6,8,7]
[1,2,2,2,1] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8]
[1,2,2,3] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6]
[1,2,3,1,1] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,5,6,4,7,8]
[1,2,3,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,6,4,8,7]
[1,2,4,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,5,6,7,4,8]
[1,2,5] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,4]
[1,3,1,1,1,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8]
[1,3,1,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7]
[1,3,1,2,1] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,4,2,5,7,6,8]
[1,3,1,3] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,4,2,5,7,8,6]
[1,3,2,1,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,4,2,6,5,7,8]
[1,3,2,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7]
[1,3,3,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,6,7,5,8]
[1,3,4] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,5]
[1,4,1,1,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8]
[1,4,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,5,2,6,8,7]
[1,4,2,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,8]
[1,4,3] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,2,7,8,6]
[1,5,1,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,2,7,8]
[1,5,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,2,8,7]
[1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,2,8]
[1,7] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2]
[2,1,1,1,1,1,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8]
[2,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7]
[2,1,1,1,2,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8]
[2,1,1,1,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6]
[2,1,1,2,1,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8]
[2,1,1,2,2] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7]
[2,1,1,3,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,1,3,4,6,7,5,8]
[2,1,1,4] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5]
[2,1,2,1,1,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8]
[2,1,2,1,2] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7]
[2,1,2,2,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6,8]
[2,1,2,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6]
[2,1,3,1,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,1,3,5,6,4,7,8]
[2,1,3,2] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,6,4,8,7]
[2,1,4,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,1,3,5,6,7,4,8]
[2,1,5] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,4]
[2,2,1,1,1,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8]
[2,2,1,1,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7]
[2,2,1,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,4,3,5,7,6,8]
[2,2,1,3] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6]
[2,2,2,1,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8]
[2,2,2,2] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7]
[2,2,3,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,6,7,5,8]
[2,2,4] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5]
[2,3,1,1,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8]
[2,3,1,2] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7]
[2,3,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6,8]
[2,3,3] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3,7,8,6]
[2,4,1,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,4,5,6,3,7,8]
[2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7]
[2,5,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,3,8]
[2,6] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3]
[3,1,1,1,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8]
[3,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7]
[3,1,1,2,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8]
[3,1,1,3] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,4,5,7,8,6]
[3,1,2,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,1,4,6,5,7,8]
[3,1,2,2] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7]
[3,1,3,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8]
[3,1,4] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5]
[3,2,1,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8]
[3,2,1,2] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,5,4,6,8,7]
[3,2,2,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8]
[3,2,3] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,7,8,6]
[3,3,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8]
[3,3,2] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,5,6,4,8,7]
[3,4,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,4,8]
[3,5] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,4]
[4,1,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8]
[4,1,1,2] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,1,5,6,8,7]
[4,1,2,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8]
[4,1,3] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6]
[4,2,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8]
[4,2,2] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7]
[4,3,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8]
[4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5]
[5,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8]
[5,1,2] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7]
[5,2,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,8]
[5,3] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6]
[6,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8]
[6,2] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7]
[7,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8]
[8] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1]
[1,1,1,1,1,1,1,1,1] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,2] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8]
[1,1,1,1,1,1,2,1] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9]
[1,1,1,1,1,1,3] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7]
[1,1,1,1,1,2,1,1] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9]
[1,1,1,1,1,2,2] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8]
[1,1,1,1,1,3,1] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,5,7,8,6,9]
[1,1,1,1,1,4] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,6]
[1,1,1,1,2,1,1,1] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9]
[1,1,1,1,2,1,2] => [5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,4,6,5,7,9,8]
[1,1,1,1,2,3] => [5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,8,9,7]
[1,1,1,1,3,1,1] => [5,1,3] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,4,6,7,5,8,9]
[1,1,1,1,3,2] => [5,1,2,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,7,5,9,8]
[1,1,1,1,4,1] => [5,1,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,7,8,5,9]
[1,1,1,1,5] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,5]
[1,1,1,2,1,1,1,1] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9]
[1,1,1,2,1,1,2] => [4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4,6,7,9,8]
[1,1,1,2,1,2,1] => [4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,5,4,6,8,7,9]
[1,1,1,2,1,3] => [4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,5,4,6,8,9,7]
[1,1,1,2,2,1,1] => [4,2,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,7,6,8,9]
[1,1,1,2,2,2] => [4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8]
[1,1,1,2,4] => [4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,7,8,9,6]
[1,1,1,3,1,1,1] => [4,1,4] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,5,6,4,7,8,9]
[1,1,1,3,1,2] => [4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,5,6,4,7,9,8]
[1,1,1,4,1,1] => [4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,5,6,7,4,8,9]
[1,1,1,5,1] => [4,1,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,8,4,9]
[1,1,1,6] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,4]
[1,1,2,1,1,1,1,1] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9]
[1,1,2,1,1,1,2] => [3,5,1] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,3,5,6,7,9,8]
[1,1,2,1,1,2,1] => [3,4,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,4,3,5,6,8,7,9]
[1,1,2,1,2,1,1] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,7,6,8,9]
[1,1,2,1,4] => [3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,3,5,7,8,9,6]
[1,1,2,2,2,1] => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9]
[1,1,2,5] => [3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,9,5]
[1,1,3,1,1,1,1] => [3,1,5] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,5,3,6,7,8,9]
[1,1,3,1,1,2] => [3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,5,3,6,7,9,8]
[1,1,3,2,2] => [3,1,2,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,9,8]
[1,1,3,3,1] => [3,1,2,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,7,8,6,9]
[1,1,5,1,1] => [3,1,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,7,3,8,9]
[1,1,5,2] => [3,1,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,4,5,6,7,3,9,8]
[1,1,6,1] => [3,1,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,7,8,3,9]
[1,1,7] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,3]
[1,2,1,1,1,1,1,1] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9]
[1,2,1,1,1,1,2] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8]
[1,2,1,1,1,2,1] => [2,5,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,3,2,4,5,6,8,7,9]
[1,2,1,1,1,3] => [2,5,1,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7]
[1,2,1,1,2,1,1] => [2,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,3,2,4,5,7,6,8,9]
[1,2,1,1,4] => [2,4,1,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,3,2,4,5,7,8,9,6]
[1,2,1,2,1,1,1] => [2,3,4] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,6,5,7,8,9]
[1,2,1,2,1,2] => [2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5,7,9,8]
[1,2,1,5] => [2,3,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,9,5]
[1,2,2,1,1,1,1] => [2,2,5] => [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,5,4,6,7,8,9]
[1,2,2,1,2,1] => [2,2,3,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,5,4,6,8,7,9]
[1,2,2,1,3] => [2,2,3,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,5,4,6,8,9,7]
[1,2,2,2,1,1] => [2,2,2,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,8,9]
[1,2,2,2,2] => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8]
[1,2,2,3,1] => [2,2,2,1,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,4,7,8,6,9]
[1,2,2,4] => [2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,7,8,9,6]
[1,2,3,1,1,1] => [2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,5,6,4,7,8,9]
[1,2,5,1] => [2,2,1,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,5,6,7,8,4,9]
[1,2,6] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,9,4]
[1,3,1,1,1,1,1] => [2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9]
[1,3,1,1,1,2] => [2,1,5,1] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,4,2,5,6,7,9,8]
[1,3,1,2,1,1] => [2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,4,2,5,7,6,8,9]
[1,3,2,2,1] => [2,1,2,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,9]
[1,3,5] => [2,1,2,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,9,5]
[1,4,1,1,1,1] => [2,1,1,5] => [1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,5,2,6,7,8,9]
[1,4,1,1,2] => [2,1,1,4,1] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,5,2,6,7,9,8]
[1,4,2,1,1] => [2,1,1,2,3] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,7,6,8,9]
[1,4,4] => [2,1,1,2,1,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,7,8,9,6]
[1,5,1,1,1] => [2,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,6,2,7,8,9]
[1,5,1,2] => [2,1,1,1,3,1] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,5,6,2,7,9,8]
[1,5,2,1] => [2,1,1,1,2,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7,9]
[1,5,3] => [2,1,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,6,2,8,9,7]
[1,6,1,1] => [2,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,7,2,8,9]
[1,6,2] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,7,2,9,8]
[1,7,1] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,2,9]
[1,8] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2]
[2,1,1,1,1,1,1,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9]
[2,1,1,1,1,1,2] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8]
[2,1,1,1,1,2,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9]
[2,1,1,1,1,3] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,8,9,7]
[2,1,1,1,2,1,1] => [1,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,5,7,6,8,9]
[2,1,1,1,4] => [1,5,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,5,7,8,9,6]
[2,1,1,2,1,1,1] => [1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,4,6,5,7,8,9]
[2,1,1,2,3] => [1,4,2,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,8,9,7]
[2,1,1,3,1,1] => [1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [2,1,3,4,6,7,5,8,9]
[2,1,1,5] => [1,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,9,5]
[2,1,2,1,1,1,1] => [1,3,5] => [1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,5,4,6,7,8,9]
[2,1,2,1,2,1] => [1,3,3,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6,8,7,9]
[2,1,2,1,3] => [1,3,3,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,4,6,8,9,7]
[2,1,2,2,2] => [1,3,2,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6,9,8]
[2,1,6] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,9,4]
[2,2,1,1,1,1,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9]
[2,2,1,1,1,2] => [1,2,5,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,3,5,6,7,9,8]
[2,2,1,2,1,1] => [1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,4,3,5,7,6,8,9]
[2,2,1,4] => [1,2,3,1,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,5,7,8,9,6]
[2,2,2,1,1,1] => [1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,7,8,9]
[2,2,2,1,2] => [1,2,2,3,1] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,6,5,7,9,8]
[2,2,2,2,1] => [1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9]
[2,2,2,3] => [1,2,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,9,7]
[2,2,4,1] => [1,2,2,1,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,6,7,8,5,9]
[2,2,5] => [1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,9,5]
[2,3,1,1,1,1] => [1,2,1,5] => [1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,5,3,6,7,8,9]
[2,3,4] => [1,2,1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,7,8,9,6]
[2,4,3] => [1,2,1,1,2,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,6,3,8,9,7]
[2,5,1,1] => [1,2,1,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,4,5,6,7,3,8,9]
[2,5,2] => [1,2,1,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,7,3,9,8]
[2,6,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,8,3,9]
[2,7] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,3]
[3,1,1,1,1,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9]
[3,1,1,1,1,2] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,1,4,5,6,7,9,8]
[3,1,1,1,2,1] => [1,1,5,2] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,1,4,5,6,8,7,9]
[3,1,1,1,3] => [1,1,5,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,1,4,5,6,8,9,7]
[3,1,1,2,1,1] => [1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,1,4,5,7,6,8,9]
[3,1,1,4] => [1,1,4,1,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,4,5,7,8,9,6]
[3,1,2,2,1] => [1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7,9]
[3,1,5] => [1,1,3,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,9,5]
[3,2,1,1,1,1] => [1,1,2,5] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,5,4,6,7,8,9]
[3,2,1,1,2] => [1,1,2,4,1] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,5,4,6,7,9,8]
[3,2,1,2,1] => [1,1,2,3,2] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,5,4,6,8,7,9]
[3,2,2,1,1] => [1,1,2,2,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,7,6,8,9]
[3,2,2,2] => [1,1,2,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8]
[3,2,4] => [1,1,2,2,1,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,7,8,9,6]
[3,3,2,1] => [1,1,2,1,2,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7,9]
[3,4,1,1] => [1,1,2,1,1,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,7,4,8,9]
[3,4,2] => [1,1,2,1,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,6,7,4,9,8]
[3,5,1] => [1,1,2,1,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,5,6,7,8,4,9]
[3,6] => [1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,9,4]
[4,1,1,1,1,1] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9]
[4,1,1,1,2] => [1,1,1,5,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,1,5,6,7,9,8]
[4,1,2,1,1] => [1,1,1,3,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,4,1,5,7,6,8,9]
[4,1,2,2] => [1,1,1,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,9,8]
[4,1,4] => [1,1,1,3,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,1,5,7,8,9,6]
[4,2,1,1,1] => [1,1,1,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,6,5,7,8,9]
[4,2,2,1] => [1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,9]
[4,2,3] => [1,1,1,2,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,8,9,7]
[4,3,2] => [1,1,1,2,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,7,5,9,8]
[4,5] => [1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,9,5]
[5,1,1,1,1] => [1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9]
[5,1,1,2] => [1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,5,1,6,7,9,8]
[5,1,2,1] => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,5,1,6,8,7,9]
[5,1,3] => [1,1,1,1,3,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,5,1,6,8,9,7]
[5,2,1,1] => [1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,7,6,8,9]
[5,2,2] => [1,1,1,1,2,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8]
[5,3,1] => [1,1,1,1,2,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,7,8,6,9]
[5,4] => [1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,7,8,9,6]
[6,1,1,1] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,1,7,8,9]
[6,1,2] => [1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,6,1,7,9,8]
[6,2,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,9]
[6,3] => [1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,6,1,8,9,7]
[7,1,1] => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9]
[7,2] => [1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8]
[8,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9]
[9] => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1]
[1,1,1,1,1,1,1,1,1,1] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,2] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9]
[1,1,1,1,1,1,1,2,1] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10]
[1,1,1,1,1,1,1,3] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8]
[1,1,1,1,1,1,2,1,1] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,1,2,2] => [7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,10,9]
[1,1,1,1,1,1,3,1] => [7,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,9,7,10]
[1,1,1,1,1,1,4] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,5,6,8,9,10,7]
[1,1,1,1,1,2,1,1,1] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,2,1,2] => [6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,4,5,7,6,8,10,9]
[1,1,1,1,1,3,1,1] => [6,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,7,8,6,9,10]
[1,1,1,1,1,3,2] => [6,1,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,8,6,10,9]
[1,1,1,1,1,4,1] => [6,1,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,8,9,6,10]
[1,1,1,1,1,5] => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,7,8,9,10,6]
[1,1,1,1,2,1,1,1,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,2,1,1,2] => [5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,4,6,5,7,8,10,9]
[1,1,1,1,2,2,2] => [5,2,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,10,9]
[1,1,1,1,3,1,1,1] => [5,1,4] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,7,5,8,9,10]
[1,1,1,1,3,1,2] => [5,1,3,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,6,7,5,8,10,9]
[1,1,1,1,5,1] => [5,1,1,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,7,8,9,5,10]
[1,1,1,1,6] => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,9,10,5]
[1,1,1,2,1,1,1,1,1] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10]
[1,1,1,2,1,1,1,2] => [4,5,1] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,5,4,6,7,8,10,9]
[1,1,1,2,1,1,2,1] => [4,4,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6,7,9,8,10]
[1,1,1,2,1,1,3] => [4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,4,6,7,9,10,8]
[1,1,1,2,1,2,1,1] => [4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,8,7,9,10]
[1,1,1,2,2,1,1,1] => [4,2,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,7,6,8,9,10]
[1,1,1,2,2,2,1] => [4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10]
[1,1,1,3,1,1,2] => [4,1,4,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,6,4,7,8,10,9]
[1,1,1,4,1,1,1] => [4,1,1,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,5,6,7,4,8,9,10]
[1,1,1,6,1] => [4,1,1,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,6,7,8,9,4,10]
[1,1,1,7] => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,9,10,4]
[1,1,2,1,1,1,1,1,1] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10]
[1,1,2,1,1,1,1,2] => [3,6,1] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,4,3,5,6,7,8,10,9]
[1,1,2,1,1,2,1,1] => [3,4,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6,8,7,9,10]
[1,1,2,1,2,1,1,1] => [3,3,4] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,7,6,8,9,10]
[1,1,2,1,2,2,1] => [3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,5,7,6,9,8,10]
[1,1,2,2,2,1,1] => [3,2,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,8,7,9,10]
[1,1,2,2,2,2] => [3,2,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,10,9]
[1,1,2,6] => [3,2,1,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,9,10,5]
[1,1,3,1,1,1,2] => [3,1,5,1] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,5,3,6,7,8,10,9]
[1,1,6,2] => [3,1,1,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,4,5,6,7,8,3,10,9]
[1,1,7,1] => [3,1,1,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,7,8,9,3,10]
[1,1,8] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,9,10,3]
[1,2,1,1,1,1,1,1,1] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10]
[1,2,1,1,1,1,1,2] => [2,7,1] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,8,10,9]
[1,2,1,1,1,1,2,1] => [2,6,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8,10]
[1,2,1,1,1,1,3] => [2,6,1,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,7,9,10,8]
[1,2,1,1,2,1,1,1] => [2,4,4] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,7,6,8,9,10]
[1,2,1,1,2,1,2] => [2,4,3,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,5,7,6,8,10,9]
[1,2,1,2,1,2,1] => [2,3,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7,9,8,10]
[1,2,1,6] => [2,3,1,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,9,10,5]
[1,2,2,1,2,1,1] => [2,2,3,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,8,7,9,10]
[1,2,2,1,4] => [2,2,3,1,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,8,9,10,7]
[1,2,2,2,1,1,1] => [2,2,2,4] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,7,6,8,9,10]
[1,2,2,2,1,2] => [2,2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,5,4,7,6,8,10,9]
[1,2,2,2,2,1] => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10]
[1,2,2,2,3] => [2,2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8]
[1,2,2,3,2] => [2,2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,5,4,7,8,6,10,9]
[1,2,2,5] => [2,2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,7,8,9,10,6]
[1,2,4,2,1] => [2,2,1,1,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,6,7,4,9,8,10]
[1,2,7] => [2,2,1,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,5,6,7,8,9,10,4]
[1,3,1,1,1,1,1,1] => [2,1,7] => [1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,2,5,6,7,8,9,10]
[1,3,1,1,1,1,2] => [2,1,6,1] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,4,2,5,6,7,8,10,9]
[1,3,1,1,3,1] => [2,1,4,1,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,9,7,10]
[1,3,6] => [2,1,2,1,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,6,7,8,9,10,5]
[1,5,1,1,1,1] => [2,1,1,1,5] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8,9,10]
[1,6,1,1,1] => [2,1,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,6,7,2,8,9,10]
[1,6,1,2] => [2,1,1,1,1,3,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,5,6,7,2,8,10,9]
[1,6,3] => [2,1,1,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,9,10,8]
[1,7,1,1] => [2,1,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,6,7,8,2,9,10]
[1,7,2] => [2,1,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,6,7,8,2,10,9]
[1,8,1] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,7,8,9,2,10]
[1,9] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2]
[2,1,1,1,1,1,1,1,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10]
[2,1,1,1,1,1,1,2] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9]
[2,1,1,1,1,1,2,1] => [1,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8,10]
[2,1,1,1,1,1,3] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,6,7,9,10,8]
[2,1,1,1,1,4] => [1,6,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,5,6,8,9,10,7]
[2,1,1,1,2,1,1,1] => [1,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5,7,6,8,9,10]
[2,1,1,1,5] => [1,5,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,7,8,9,10,6]
[2,1,1,2,1,1,1,1] => [1,4,5] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,6,5,7,8,9,10]
[2,1,1,6] => [1,4,1,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,9,10,5]
[2,1,2,1,1,1,1,1] => [1,3,6] => [1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,5,4,6,7,8,9,10]
[2,1,2,1,2,1,1] => [1,3,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,8,7,9,10]
[2,1,2,2,2,1] => [1,3,2,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6,9,8,10]
[2,1,7] => [1,3,1,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,5,6,7,8,9,10,4]
[2,2,1,1,1,1,1,1] => [1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9,10]
[2,2,1,1,4] => [1,2,4,1,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,8,9,10,7]
[2,2,1,2,1,1,1] => [1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,7,6,8,9,10]
[2,2,1,2,2,1] => [1,2,3,2,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5,7,6,9,8,10]
[2,2,2,2,1,1] => [1,2,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,8,7,9,10]
[2,2,2,2,2] => [1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9]
[2,2,2,4] => [1,2,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,9,10,7]
[2,2,6] => [1,2,2,1,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,9,10,5]
[2,3,1,3,1] => [1,2,1,3,1,2] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,9,7,10]
[2,6,1,1] => [1,2,1,1,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,4,5,6,7,8,3,9,10]
[2,6,2] => [1,2,1,1,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,7,8,3,10,9]
[2,7,1] => [1,2,1,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,8,9,3,10]
[2,8] => [1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,9,10,3]
[3,1,1,1,1,1,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10]
[3,1,1,1,1,1,2] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,1,4,5,6,7,8,10,9]
[3,1,1,1,1,2,1] => [1,1,6,2] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8,10]
[3,1,1,1,4] => [1,1,5,1,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6,8,9,10,7]
[3,1,1,2,1,1,1] => [1,1,4,4] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,7,6,8,9,10]
[3,1,1,5] => [1,1,4,1,1,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,7,8,9,10,6]
[3,1,6] => [1,1,3,1,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,9,10,5]
[3,2,2,2,1] => [1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8,10]
[3,2,5] => [1,1,2,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,7,8,9,10,6]
[3,7] => [1,1,2,1,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,5,6,7,8,9,10,4]
[4,1,1,1,1,1,1] => [1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10]
[4,1,1,1,1,2] => [1,1,1,6,1] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,1,5,6,7,8,10,9]
[4,1,1,2,2] => [1,1,1,4,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,1,5,6,8,7,10,9]
[4,1,5] => [1,1,1,3,1,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,7,8,9,10,6]
[4,2,2,2] => [1,1,1,2,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,10,9]
[4,2,4] => [1,1,1,2,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,5,8,9,10,7]
[4,5,1] => [1,1,1,2,1,1,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,6,7,8,9,5,10]
[4,6] => [1,1,1,2,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,9,10,5]
[5,1,1,1,1,1] => [1,1,1,1,6] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10]
[5,1,1,1,2] => [1,1,1,1,5,1] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,1,6,7,8,10,9]
[5,1,4] => [1,1,1,1,3,1,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,8,9,10,7]
[5,2,2,1] => [1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8,10]
[5,5] => [1,1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,7,8,9,10,6]
[6,1,1,1,1] => [1,1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10]
[6,1,1,2] => [1,1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,5,6,1,7,8,10,9]
[6,2,2] => [1,1,1,1,1,2,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,10,9]
[6,4] => [1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,8,9,10,7]
[7,1,1,1] => [1,1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10]
[7,1,2] => [1,1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,6,7,1,8,10,9]
[7,2,1] => [1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8,10]
[7,3] => [1,1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,9,10,8]
[8,1,1] => [1,1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,8,1,9,10]
[8,2] => [1,1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,1,10,9]
[9,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10]
[10] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1]
[10,1] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,10,1,11]
[2,2,2,2,2,2] => [1,2,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9,12,11]
[1,2,2,2,2,2,1] => [2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10,12]
[1,1,1,1,1,1,1,1,1,2] => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10]
[2,1,1,1,1,1,1,1,1,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11]
[2,8,1] => [1,2,1,1,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,7,8,9,10,3,11]
[2,1,1,1,1,1,1,2,1] => [1,8,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9,11]
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.