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Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
[1,0] => [1] => [1] => [1] => [1]
[1,0,1,0] => [2,1] => [2,1] => [2,1] => [1,1]
[1,1,0,0] => [1,2] => [1,2] => [1,2] => [2]
[1,0,1,0,1,0] => [3,2,1] => [3,2,1] => [3,2,1] => [1,1,1]
[1,0,1,1,0,0] => [2,3,1] => [1,3,2] => [1,3,2] => [2,1]
[1,1,0,0,1,0] => [3,1,2] => [2,3,1] => [3,1,2] => [1,2]
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [2,1,3] => [1,2]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,2,3] => [3]
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1]
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [1,4,3,2] => [1,4,3,2] => [2,1,1]
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [2,4,3,1] => [4,1,3,2] => [1,2,1]
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [2,1,4,3] => [2,1,4,3] => [1,2,1]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,2,4,3] => [1,2,4,3] => [3,1]
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [3,4,2,1] => [4,3,1,2] => [1,1,2]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [3,1,4,2] => [2,4,1,3] => [2,2]
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [3,2,4,1] => [4,2,1,3] => [1,1,2]
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [1,1,2]
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [1,3,2,4] => [1,3,2,4] => [2,2]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [2,3,4,1] => [4,1,2,3] => [1,3]
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [2,3,1,4] => [3,1,2,4] => [1,3]
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,3]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [4]
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [1,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [2,5,4,3,1] => [5,1,4,3,2] => [1,2,1,1]
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [2,1,5,4,3] => [2,1,5,4,3] => [1,2,1,1]
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,2,5,4,3] => [1,2,5,4,3] => [3,1,1]
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [3,5,4,2,1] => [5,4,1,3,2] => [1,1,2,1]
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [3,1,5,4,2] => [2,5,1,4,3] => [2,2,1]
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [3,2,5,4,1] => [5,2,1,4,3] => [1,1,2,1]
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [3,2,1,5,4] => [3,2,1,5,4] => [1,1,2,1]
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,3,2,5,4] => [1,3,2,5,4] => [2,2,1]
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [2,3,5,4,1] => [5,1,2,4,3] => [1,3,1]
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [2,3,1,5,4] => [3,1,2,5,4] => [1,3,1]
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => [1,3,1]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,5,4] => [1,2,3,5,4] => [4,1]
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [4,5,3,2,1] => [5,4,3,1,2] => [1,1,1,2]
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [4,1,5,3,2] => [2,5,4,1,3] => [2,1,2]
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [4,2,5,3,1] => [5,2,4,1,3] => [1,2,2]
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [4,2,1,5,3] => [3,2,5,1,4] => [1,2,2]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,4,2,5,3] => [1,3,5,2,4] => [3,2]
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [4,3,5,2,1] => [5,4,2,1,3] => [1,1,1,2]
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [4,3,1,5,2] => [3,5,2,1,4] => [2,1,2]
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [4,3,2,5,1] => [5,3,2,1,4] => [1,1,1,2]
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,2]
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [1,4,3,2,5] => [1,4,3,2,5] => [2,1,2]
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [2,4,3,5,1] => [5,1,3,2,4] => [1,2,2]
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [2,4,3,1,5] => [4,1,3,2,5] => [1,2,2]
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => [1,2,2]
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => [3,2]
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [3,4,5,2,1] => [5,4,1,2,3] => [1,1,3]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [3,4,1,5,2] => [3,5,1,2,4] => [2,3]
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [3,4,2,5,1] => [5,3,1,2,4] => [1,1,3]
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [3,4,2,1,5] => [4,3,1,2,5] => [1,1,3]
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [3,1,4,2,5] => [2,4,1,3,5] => [2,3]
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [3,2,4,5,1] => [5,2,1,3,4] => [1,1,3]
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [3,2,4,1,5] => [4,2,1,3,5] => [1,1,3]
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [1,1,3]
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [2,3]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1] => [5,1,2,3,4] => [1,4]
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [2,3,4,1,5] => [4,1,2,3,5] => [1,4]
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => [1,4]
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,4]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [5]
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [2,6,5,4,3,1] => [6,1,5,4,3,2] => [1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [3,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [6,5,1,4,3,2] => [1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [3,1,6,5,4,2] => [2,6,1,5,4,3] => [2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [3,2,6,5,4,1] => [6,2,1,5,4,3] => [1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [2,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [2,3,6,5,4,1] => [6,1,2,5,4,3] => [1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [2,3,1,6,5,4] => [3,1,2,6,5,4] => [1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [1,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [4,6,5,3,2,1] => [6,5,4,1,3,2] => [1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [4,1,6,5,3,2] => [2,6,5,1,4,3] => [2,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [4,2,6,5,3,1] => [6,2,5,1,4,3] => [1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [4,2,1,6,5,3] => [3,2,6,1,5,4] => [1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,4,2,6,5,3] => [1,3,6,2,5,4] => [3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [4,3,6,5,2,1] => [6,5,2,1,4,3] => [1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [4,3,1,6,5,2] => [3,6,2,1,5,4] => [2,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [4,3,2,6,5,1] => [6,3,2,1,5,4] => [1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [2,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [2,4,3,6,5,1] => [6,1,3,2,5,4] => [1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [2,4,3,1,6,5] => [4,1,3,2,6,5] => [1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [3,4,6,5,2,1] => [6,5,1,2,4,3] => [1,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [3,4,1,6,5,2] => [3,6,1,2,5,4] => [2,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [3,4,2,6,5,1] => [6,3,1,2,5,4] => [1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [3,4,2,1,6,5] => [4,3,1,2,6,5] => [1,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,1,4,2,6,5] => [2,4,1,3,6,5] => [2,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [3,2,4,6,5,1] => [6,2,1,3,5,4] => [1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,4,1,6,5] => [4,2,1,3,6,5] => [1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [1,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,3,1]
>>> Load all 1905 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [2,3,4,6,5,1] => [6,1,2,3,5,4] => [1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [5,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => [1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [5,1,6,4,3,2] => [2,6,5,4,1,3] => [2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [5,2,6,4,3,1] => [6,2,5,4,1,3] => [1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [5,2,1,6,4,3] => [3,2,6,5,1,4] => [1,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [1,5,2,6,4,3] => [1,3,6,5,2,4] => [3,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [5,3,6,4,2,1] => [6,5,2,4,1,3] => [1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [3,6,2,5,1,4] => [2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [5,3,2,6,4,1] => [6,3,2,5,1,4] => [1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [5,3,2,1,6,4] => [4,3,2,6,1,5] => [1,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [1,5,3,2,6,4] => [1,4,3,6,2,5] => [2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [2,5,3,6,4,1] => [6,1,3,5,2,4] => [1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [2,5,3,1,6,4] => [4,1,3,6,2,5] => [1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [2,1,5,3,6,4] => [2,1,4,6,3,5] => [1,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [1,2,5,3,6,4] => [1,2,4,6,3,5] => [4,2]
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => [1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [5,4,1,6,3,2] => [3,6,5,2,1,4] => [2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [5,4,2,6,3,1] => [6,3,5,2,1,4] => [1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [5,4,2,1,6,3] => [4,3,6,2,1,5] => [1,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [1,5,4,2,6,3] => [1,4,6,3,2,5] => [3,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => [1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [5,4,3,1,6,2] => [4,6,3,2,1,5] => [2,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => [1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [2,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [2,5,4,3,6,1] => [6,1,4,3,2,5] => [1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [2,5,4,3,1,6] => [5,1,4,3,2,6] => [1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [1,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [3,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [3,5,4,6,2,1] => [6,5,1,3,2,4] => [1,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [3,5,4,1,6,2] => [4,6,1,3,2,5] => [2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [3,5,4,2,6,1] => [6,4,1,3,2,5] => [1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [3,5,4,2,1,6] => [5,4,1,3,2,6] => [1,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,1,5,4,2,6] => [2,5,1,4,3,6] => [2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [3,2,5,4,6,1] => [6,2,1,4,3,5] => [1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [3,2,5,4,1,6] => [5,2,1,4,3,6] => [1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [1,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,5,4,6,1] => [6,1,2,4,3,5] => [1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => [5,1,2,4,3,6] => [1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [4,2]
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => [1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [4,5,1,6,3,2] => [3,6,5,1,2,4] => [2,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [6,3,5,1,2,4] => [1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,3,6,1,2,5] => [1,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [2,4,6,1,3,5] => [3,3]
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => [1,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [4,5,3,1,6,2] => [4,6,3,1,2,5] => [2,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => [1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => [1,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [4,1,5,3,2,6] => [2,5,4,1,3,6] => [2,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [6,2,4,1,3,5] => [1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [5,2,4,1,3,6] => [1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [3,2,5,1,4,6] => [1,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [1,4,2,5,3,6] => [1,3,5,2,4,6] => [3,3]
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => [1,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [4,3,5,1,6,2] => [4,6,2,1,3,5] => [2,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => [1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => [1,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [4,3,1,5,2,6] => [3,5,2,1,4,6] => [2,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => [1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => [1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [2,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,4,3,5,6,1] => [6,1,3,2,4,5] => [1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,4,3,5,1,6] => [5,1,3,2,4,6] => [1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => [4,1,3,2,5,6] => [1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [3,3]
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => [1,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [4,6,1,2,3,5] => [2,4]
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => [1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => [1,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,5,1,2,4,6] => [2,4]
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => [1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => [1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => [1,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [2,4,1,3,5,6] => [2,4]
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => [1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => [1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => [1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,4]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,5]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,5]
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,5]
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,5]
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,5]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [2,7,6,5,4,3,1] => [7,1,6,5,4,3,2] => [1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [3,7,6,5,4,2,1] => [7,6,1,5,4,3,2] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [3,1,7,6,5,4,2] => [2,7,1,6,5,4,3] => [2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [3,2,7,6,5,4,1] => [7,2,1,6,5,4,3] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [2,3,7,6,5,4,1] => [7,1,2,6,5,4,3] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [2,3,1,7,6,5,4] => [3,1,2,7,6,5,4] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4] => [1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [4,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [4,7,6,5,3,2,1] => [7,6,5,1,4,3,2] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [4,1,7,6,5,3,2] => [2,7,6,1,5,4,3] => [2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [4,2,7,6,5,3,1] => [7,2,6,1,5,4,3] => [1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [4,2,1,7,6,5,3] => [3,2,7,1,6,5,4] => [1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [1,4,2,7,6,5,3] => [1,3,7,2,6,5,4] => [3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [4,3,7,6,5,2,1] => [7,6,2,1,5,4,3] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [4,3,1,7,6,5,2] => [3,7,2,1,6,5,4] => [2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [4,3,2,7,6,5,1] => [7,3,2,1,6,5,4] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [2,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [2,4,3,7,6,5,1] => [7,1,3,2,6,5,4] => [1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [2,4,3,1,7,6,5] => [4,1,3,2,7,6,5] => [1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5] => [1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [3,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [3,4,7,6,5,2,1] => [7,6,1,2,5,4,3] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [3,4,1,7,6,5,2] => [3,7,1,2,6,5,4] => [2,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [3,4,2,7,6,5,1] => [7,3,1,2,6,5,4] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [3,4,2,1,7,6,5] => [4,3,1,2,7,6,5] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [3,1,4,2,7,6,5] => [2,4,1,3,7,6,5] => [2,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [3,2,4,7,6,5,1] => [7,2,1,3,6,5,4] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [3,2,4,1,7,6,5] => [4,2,1,3,7,6,5] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5] => [1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [2,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [2,3,4,7,6,5,1] => [7,1,2,3,6,5,4] => [1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [2,3,4,1,7,6,5] => [4,1,2,3,7,6,5] => [1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [2,3,1,4,7,6,5] => [3,1,2,4,7,6,5] => [1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5] => [1,4,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [5,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [5,7,6,4,3,2,1] => [7,6,5,4,1,3,2] => [1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [5,1,7,6,4,3,2] => [2,7,6,5,1,4,3] => [2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [5,2,7,6,4,3,1] => [7,2,6,5,1,4,3] => [1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [5,2,1,7,6,4,3] => [3,2,7,6,1,5,4] => [1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [1,5,2,7,6,4,3] => [1,3,7,6,2,5,4] => [3,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [5,3,7,6,4,2,1] => [7,6,2,5,1,4,3] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [5,3,1,7,6,4,2] => [3,7,2,6,1,5,4] => [2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [5,3,2,7,6,4,1] => [7,3,2,6,1,5,4] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [5,3,2,1,7,6,4] => [4,3,2,7,1,6,5] => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [1,5,3,2,7,6,4] => [1,4,3,7,2,6,5] => [2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [2,5,3,7,6,4,1] => [7,1,3,6,2,5,4] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [2,5,3,1,7,6,4] => [4,1,3,7,2,6,5] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [2,1,5,3,7,6,4] => [2,1,4,7,3,6,5] => [1,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [1,2,5,3,7,6,4] => [1,2,4,7,3,6,5] => [4,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [5,4,7,6,3,2,1] => [7,6,5,2,1,4,3] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [5,4,1,7,6,3,2] => [3,7,6,2,1,5,4] => [2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [5,4,2,7,6,3,1] => [7,3,6,2,1,5,4] => [1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [5,4,2,1,7,6,3] => [4,3,7,2,1,6,5] => [1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [1,5,4,2,7,6,3] => [1,4,7,3,2,6,5] => [3,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [5,4,3,7,6,2,1] => [7,6,3,2,1,5,4] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [5,4,3,1,7,6,2] => [4,7,3,2,1,6,5] => [2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [5,4,3,2,7,6,1] => [7,4,3,2,1,6,5] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6] => [2,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [2,5,4,3,7,6,1] => [7,1,4,3,2,6,5] => [1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [2,5,4,3,1,7,6] => [5,1,4,3,2,7,6] => [1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6] => [1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [3,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [3,5,4,7,6,2,1] => [7,6,1,3,2,5,4] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [3,5,4,1,7,6,2] => [4,7,1,3,2,6,5] => [2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [3,5,4,2,7,6,1] => [7,4,1,3,2,6,5] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [3,5,4,2,1,7,6] => [5,4,1,3,2,7,6] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [3,1,5,4,2,7,6] => [2,5,1,4,3,7,6] => [2,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [3,2,5,4,7,6,1] => [7,2,1,4,3,6,5] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,2,5,4,1,7,6] => [5,2,1,4,3,7,6] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6] => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [2,3,5,4,7,6,1] => [7,1,2,4,3,6,5] => [1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [2,3,5,4,1,7,6] => [5,1,2,4,3,7,6] => [1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [1,3,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [4,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [4,5,7,6,3,2,1] => [7,6,5,1,2,4,3] => [1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [4,5,1,7,6,3,2] => [3,7,6,1,2,5,4] => [2,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [4,5,2,7,6,3,1] => [7,3,6,1,2,5,4] => [1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [4,5,2,1,7,6,3] => [4,3,7,1,2,6,5] => [1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [4,1,5,2,7,6,3] => [2,4,7,1,3,6,5] => [3,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [4,5,3,7,6,2,1] => [7,6,3,1,2,5,4] => [1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [4,5,3,1,7,6,2] => [4,7,3,1,2,6,5] => [2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [4,5,3,2,7,6,1] => [7,4,3,1,2,6,5] => [1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [4,5,3,2,1,7,6] => [5,4,3,1,2,7,6] => [1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [4,1,5,3,2,7,6] => [2,5,4,1,3,7,6] => [2,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [4,2,5,3,7,6,1] => [7,2,4,1,3,6,5] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [4,2,5,3,1,7,6] => [5,2,4,1,3,7,6] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [4,2,1,5,3,7,6] => [3,2,5,1,4,7,6] => [1,2,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [1,4,2,5,3,7,6] => [1,3,5,2,4,7,6] => [3,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [4,3,5,7,6,2,1] => [7,6,2,1,3,5,4] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [4,3,5,1,7,6,2] => [4,7,2,1,3,6,5] => [2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [4,3,5,2,7,6,1] => [7,4,2,1,3,6,5] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [4,3,5,2,1,7,6] => [5,4,2,1,3,7,6] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [4,3,1,5,2,7,6] => [3,5,2,1,4,7,6] => [2,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [4,3,2,5,7,6,1] => [7,3,2,1,4,6,5] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,3,2,5,1,7,6] => [5,3,2,1,4,7,6] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6] => [1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [2,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [2,4,3,5,7,6,1] => [7,1,3,2,4,6,5] => [1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [2,4,3,5,1,7,6] => [5,1,3,2,4,7,6] => [1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [2,4,3,1,5,7,6] => [4,1,3,2,5,7,6] => [1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [1,2,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [3,3,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [3,4,5,7,6,2,1] => [7,6,1,2,3,5,4] => [1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [3,4,5,1,7,6,2] => [4,7,1,2,3,6,5] => [2,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [3,4,5,2,7,6,1] => [7,4,1,2,3,6,5] => [1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [3,4,5,2,1,7,6] => [5,4,1,2,3,7,6] => [1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [3,4,1,5,2,7,6] => [3,5,1,2,4,7,6] => [2,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [3,4,2,5,7,6,1] => [7,3,1,2,4,6,5] => [1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [3,4,2,5,1,7,6] => [5,3,1,2,4,7,6] => [1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [3,4,2,1,5,7,6] => [4,3,1,2,5,7,6] => [1,1,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [3,1,4,2,5,7,6] => [2,4,1,3,5,7,6] => [2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [3,2,4,5,7,6,1] => [7,2,1,3,4,6,5] => [1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,4,5,1,7,6] => [5,2,1,3,4,7,6] => [1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [3,2,4,1,5,7,6] => [4,2,1,3,5,7,6] => [1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6] => [1,1,4,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [2,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [2,3,4,5,7,6,1] => [7,1,2,3,4,6,5] => [1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [6,1,7,5,4,3,2] => [2,7,6,5,4,1,3] => [2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [6,2,7,5,4,3,1] => [7,2,6,5,4,1,3] => [1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [6,2,1,7,5,4,3] => [3,2,7,6,5,1,4] => [1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [1,6,2,7,5,4,3] => [1,3,7,6,5,2,4] => [3,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [6,3,7,5,4,2,1] => [7,6,2,5,4,1,3] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [6,3,1,7,5,4,2] => [3,7,2,6,5,1,4] => [2,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [6,3,2,7,5,4,1] => [7,3,2,6,5,1,4] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [6,3,2,1,7,5,4] => [4,3,2,7,6,1,5] => [1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [1,6,3,2,7,5,4] => [1,4,3,7,6,2,5] => [2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [2,6,3,7,5,4,1] => [7,1,3,6,5,2,4] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [2,6,3,1,7,5,4] => [4,1,3,7,6,2,5] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [2,1,6,3,7,5,4] => [2,1,4,7,6,3,5] => [1,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [1,2,6,3,7,5,4] => [1,2,4,7,6,3,5] => [4,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [6,4,7,5,3,2,1] => [7,6,5,2,4,1,3] => [1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [6,4,1,7,5,3,2] => [3,7,6,2,5,1,4] => [2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [6,4,2,7,5,3,1] => [7,3,6,2,5,1,4] => [1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [6,4,2,1,7,5,3] => [4,3,7,2,6,1,5] => [1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [1,6,4,2,7,5,3] => [1,4,7,3,6,2,5] => [3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [6,4,3,7,5,2,1] => [7,6,3,2,5,1,4] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [6,4,3,1,7,5,2] => [4,7,3,2,6,1,5] => [2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [6,4,3,2,7,5,1] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [6,4,3,2,1,7,5] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [1,6,4,3,2,7,5] => [1,5,4,3,7,2,6] => [2,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [2,6,4,3,7,5,1] => [7,1,4,3,6,2,5] => [1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [2,6,4,3,1,7,5] => [5,1,4,3,7,2,6] => [1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [2,1,6,4,3,7,5] => [2,1,5,4,7,3,6] => [1,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [1,2,6,4,3,7,5] => [1,2,5,4,7,3,6] => [3,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [3,6,4,7,5,2,1] => [7,6,1,3,5,2,4] => [1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [3,6,4,1,7,5,2] => [4,7,1,3,6,2,5] => [2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [3,6,4,2,7,5,1] => [7,4,1,3,6,2,5] => [1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [3,6,4,2,1,7,5] => [5,4,1,3,7,2,6] => [1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [3,1,6,4,2,7,5] => [2,5,1,4,7,3,6] => [2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [3,2,6,4,7,5,1] => [7,2,1,4,6,3,5] => [1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [3,2,6,4,1,7,5] => [5,2,1,4,7,3,6] => [1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [3,2,1,6,4,7,5] => [3,2,1,5,7,4,6] => [1,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [1,3,2,6,4,7,5] => [1,3,2,5,7,4,6] => [2,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [2,3,6,4,7,5,1] => [7,1,2,4,6,3,5] => [1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [2,3,6,4,1,7,5] => [5,1,2,4,7,3,6] => [1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [2,3,1,6,4,7,5] => [3,1,2,5,7,4,6] => [1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [2,1,3,6,4,7,5] => [2,1,3,5,7,4,6] => [1,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [1,2,3,6,4,7,5] => [1,2,3,5,7,4,6] => [5,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [6,5,7,4,3,2,1] => [7,6,5,4,2,1,3] => [1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [6,5,1,7,4,3,2] => [3,7,6,5,2,1,4] => [2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [6,5,2,7,4,3,1] => [7,3,6,5,2,1,4] => [1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [6,5,2,1,7,4,3] => [4,3,7,6,2,1,5] => [1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [1,6,5,2,7,4,3] => [1,4,7,6,3,2,5] => [3,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [6,5,3,7,4,2,1] => [7,6,3,5,2,1,4] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [6,5,3,1,7,4,2] => [4,7,3,6,2,1,5] => [2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [6,5,3,2,7,4,1] => [7,4,3,6,2,1,5] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [6,5,3,2,1,7,4] => [5,4,3,7,2,1,6] => [1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [1,6,5,3,2,7,4] => [1,5,4,7,3,2,6] => [2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [2,6,5,3,7,4,1] => [7,1,4,6,3,2,5] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [2,6,5,3,1,7,4] => [5,1,4,7,3,2,6] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [2,1,6,5,3,7,4] => [2,1,5,7,4,3,6] => [1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [1,2,6,5,3,7,4] => [1,2,5,7,4,3,6] => [4,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [6,5,4,7,3,2,1] => [7,6,5,3,2,1,4] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [6,5,4,1,7,3,2] => [4,7,6,3,2,1,5] => [2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [6,5,4,2,7,3,1] => [7,4,6,3,2,1,5] => [1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [6,5,4,2,1,7,3] => [5,4,7,3,2,1,6] => [1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [1,6,5,4,2,7,3] => [1,5,7,4,3,2,6] => [3,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [6,5,4,3,7,2,1] => [7,6,4,3,2,1,5] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [6,5,4,3,1,7,2] => [5,7,4,3,2,1,6] => [2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [6,5,4,3,2,7,1] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7] => [2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [2,6,5,4,3,7,1] => [7,1,5,4,3,2,6] => [1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [2,6,5,4,3,1,7] => [6,1,5,4,3,2,7] => [1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7] => [1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [3,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [3,6,5,4,7,2,1] => [7,6,1,4,3,2,5] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [3,6,5,4,1,7,2] => [5,7,1,4,3,2,6] => [2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [3,6,5,4,2,7,1] => [7,5,1,4,3,2,6] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => [6,5,1,4,3,2,7] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [3,1,6,5,4,2,7] => [2,6,1,5,4,3,7] => [2,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [3,2,6,5,4,7,1] => [7,2,1,5,4,3,6] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [3,2,6,5,4,1,7] => [6,2,1,5,4,3,7] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7] => [1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [2,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [2,3,6,5,4,7,1] => [7,1,2,5,4,3,6] => [1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [2,3,6,5,4,1,7] => [6,1,2,5,4,3,7] => [1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [2,3,1,6,5,4,7] => [3,1,2,6,5,4,7] => [1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7] => [1,3,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [4,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [4,6,5,7,3,2,1] => [7,6,5,1,3,2,4] => [1,1,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [4,6,5,1,7,3,2] => [4,7,6,1,3,2,5] => [2,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [4,6,5,2,7,3,1] => [7,4,6,1,3,2,5] => [1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [4,6,5,2,1,7,3] => [5,4,7,1,3,2,6] => [1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [4,1,6,5,2,7,3] => [2,5,7,1,4,3,6] => [3,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [4,6,5,3,7,2,1] => [7,6,4,1,3,2,5] => [1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [4,6,5,3,1,7,2] => [5,7,4,1,3,2,6] => [2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [4,6,5,3,2,7,1] => [7,5,4,1,3,2,6] => [1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [4,6,5,3,2,1,7] => [6,5,4,1,3,2,7] => [1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [4,1,6,5,3,2,7] => [2,6,5,1,4,3,7] => [2,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [4,2,6,5,3,7,1] => [7,2,5,1,4,3,6] => [1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [4,2,6,5,3,1,7] => [6,2,5,1,4,3,7] => [1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [4,2,1,6,5,3,7] => [3,2,6,1,5,4,7] => [1,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [1,4,2,6,5,3,7] => [1,3,6,2,5,4,7] => [3,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [4,3,6,5,7,2,1] => [7,6,2,1,4,3,5] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [4,3,6,5,1,7,2] => [5,7,2,1,4,3,6] => [2,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [4,3,6,5,2,7,1] => [7,5,2,1,4,3,6] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [4,3,6,5,2,1,7] => [6,5,2,1,4,3,7] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [4,3,1,6,5,2,7] => [3,6,2,1,5,4,7] => [2,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [4,3,2,6,5,7,1] => [7,3,2,1,5,4,6] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [4,3,2,6,5,1,7] => [6,3,2,1,5,4,7] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7] => [1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [2,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [2,4,3,6,5,7,1] => [7,1,3,2,5,4,6] => [1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [2,4,3,6,5,1,7] => [6,1,3,2,5,4,7] => [1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [2,4,3,1,6,5,7] => [4,1,3,2,6,5,7] => [1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [1,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [3,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [3,4,6,5,7,2,1] => [7,6,1,2,4,3,5] => [1,1,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [3,4,6,5,1,7,2] => [5,7,1,2,4,3,6] => [2,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [3,4,6,5,2,7,1] => [7,5,1,2,4,3,6] => [1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [3,4,6,5,2,1,7] => [6,5,1,2,4,3,7] => [1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [3,4,1,6,5,2,7] => [3,6,1,2,5,4,7] => [2,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [3,4,2,6,5,7,1] => [7,3,1,2,5,4,6] => [1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [3,4,2,6,5,1,7] => [6,3,1,2,5,4,7] => [1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [3,4,2,1,6,5,7] => [4,3,1,2,6,5,7] => [1,1,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [3,1,4,2,6,5,7] => [2,4,1,3,6,5,7] => [2,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [3,2,4,6,5,7,1] => [7,2,1,3,5,4,6] => [1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [3,2,4,6,5,1,7] => [6,2,1,3,5,4,7] => [1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [3,2,4,1,6,5,7] => [4,2,1,3,6,5,7] => [1,1,3,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7] => [1,1,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [2,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [2,3,4,6,5,7,1] => [7,1,2,3,5,4,6] => [1,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [2,3,4,6,5,1,7] => [6,1,2,3,5,4,7] => [1,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [1,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [1,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [1,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [5,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3] => [1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [5,6,1,7,4,3,2] => [3,7,6,5,1,2,4] => [2,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [5,6,2,7,4,3,1] => [7,3,6,5,1,2,4] => [1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [5,6,2,1,7,4,3] => [4,3,7,6,1,2,5] => [1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [5,1,6,2,7,4,3] => [2,4,7,6,1,3,5] => [3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [5,6,3,7,4,2,1] => [7,6,3,5,1,2,4] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [5,6,3,1,7,4,2] => [4,7,3,6,1,2,5] => [2,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [5,6,3,2,7,4,1] => [7,4,3,6,1,2,5] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [5,6,3,2,1,7,4] => [5,4,3,7,1,2,6] => [1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [5,1,6,3,2,7,4] => [2,5,4,7,1,3,6] => [2,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [5,2,6,3,7,4,1] => [7,2,4,6,1,3,5] => [1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [5,2,6,3,1,7,4] => [5,2,4,7,1,3,6] => [1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [5,2,1,6,3,7,4] => [3,2,5,7,1,4,6] => [1,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [1,5,2,6,3,7,4] => [1,3,5,7,2,4,6] => [4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => [1,1,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [5,6,4,1,7,3,2] => [4,7,6,3,1,2,5] => [2,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [5,6,4,2,7,3,1] => [7,4,6,3,1,2,5] => [1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [5,6,4,2,1,7,3] => [5,4,7,3,1,2,6] => [1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [5,1,6,4,2,7,3] => [2,5,7,4,1,3,6] => [3,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [5,6,4,3,7,2,1] => [7,6,4,3,1,2,5] => [1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [5,6,4,3,1,7,2] => [5,7,4,3,1,2,6] => [2,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [5,6,4,3,2,7,1] => [7,5,4,3,1,2,6] => [1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [5,6,4,3,2,1,7] => [6,5,4,3,1,2,7] => [1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [5,1,6,4,3,2,7] => [2,6,5,4,1,3,7] => [2,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [5,2,6,4,3,7,1] => [7,2,5,4,1,3,6] => [1,2,1,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [5,2,6,4,3,1,7] => [6,2,5,4,1,3,7] => [1,2,1,3]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [5,2,1,6,4,3,7] => [3,2,6,5,1,4,7] => [1,2,1,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [1,5,2,6,4,3,7] => [1,3,6,5,2,4,7] => [3,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [5,3,6,4,7,2,1] => [7,6,2,4,1,3,5] => [1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [5,3,6,4,1,7,2] => [5,7,2,4,1,3,6] => [2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [5,3,6,4,2,7,1] => [7,5,2,4,1,3,6] => [1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [5,3,6,4,2,1,7] => [6,5,2,4,1,3,7] => [1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [5,3,1,6,4,2,7] => [3,6,2,5,1,4,7] => [2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [5,3,2,6,4,7,1] => [7,3,2,5,1,4,6] => [1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [5,3,2,6,4,1,7] => [6,3,2,5,1,4,7] => [1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [5,3,2,1,6,4,7] => [4,3,2,6,1,5,7] => [1,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [1,5,3,2,6,4,7] => [1,4,3,6,2,5,7] => [2,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [2,5,3,6,4,7,1] => [7,1,3,5,2,4,6] => [1,3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [2,5,3,6,4,1,7] => [6,1,3,5,2,4,7] => [1,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [2,5,3,1,6,4,7] => [4,1,3,6,2,5,7] => [1,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [2,1,5,3,6,4,7] => [2,1,4,6,3,5,7] => [1,3,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [1,2,5,3,6,4,7] => [1,2,4,6,3,5,7] => [4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [5,4,6,7,3,2,1] => [7,6,5,2,1,3,4] => [1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [5,4,6,1,7,3,2] => [4,7,6,2,1,3,5] => [2,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [5,4,6,2,7,3,1] => [7,4,6,2,1,3,5] => [1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [5,4,6,2,1,7,3] => [5,4,7,2,1,3,6] => [1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [5,4,1,6,2,7,3] => [3,5,7,2,1,4,6] => [3,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [5,4,6,3,7,2,1] => [7,6,4,2,1,3,5] => [1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [5,4,6,3,1,7,2] => [5,7,4,2,1,3,6] => [2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [5,4,6,3,2,7,1] => [7,5,4,2,1,3,6] => [1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [5,4,6,3,2,1,7] => [6,5,4,2,1,3,7] => [1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [5,4,1,6,3,2,7] => [3,6,5,2,1,4,7] => [2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [5,4,2,6,3,7,1] => [7,3,5,2,1,4,6] => [1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [5,4,2,6,3,1,7] => [6,3,5,2,1,4,7] => [1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [5,4,2,1,6,3,7] => [4,3,6,2,1,5,7] => [1,2,1,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [1,5,4,2,6,3,7] => [1,4,6,3,2,5,7] => [3,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [5,4,3,6,7,2,1] => [7,6,3,2,1,4,5] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [5,4,3,6,1,7,2] => [5,7,3,2,1,4,6] => [2,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [5,4,3,6,2,7,1] => [7,5,3,2,1,4,6] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [5,4,3,6,2,1,7] => [6,5,3,2,1,4,7] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [5,4,3,1,6,2,7] => [4,6,3,2,1,5,7] => [2,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [5,4,3,2,6,7,1] => [7,4,3,2,1,5,6] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [5,4,3,2,6,1,7] => [6,4,3,2,1,5,7] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7] => [2,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [2,5,4,3,6,7,1] => [7,1,4,3,2,5,6] => [1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [2,5,4,3,6,1,7] => [6,1,4,3,2,5,7] => [1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [2,5,4,3,1,6,7] => [5,1,4,3,2,6,7] => [1,2,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7] => [1,2,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [3,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [3,5,4,6,7,2,1] => [7,6,1,3,2,4,5] => [1,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [3,5,4,6,1,7,2] => [5,7,1,3,2,4,6] => [2,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [3,5,4,6,2,7,1] => [7,5,1,3,2,4,6] => [1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [3,5,4,6,2,1,7] => [6,5,1,3,2,4,7] => [1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [3,5,4,1,6,2,7] => [4,6,1,3,2,5,7] => [2,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [3,5,4,2,6,7,1] => [7,4,1,3,2,5,6] => [1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [3,5,4,2,6,1,7] => [6,4,1,3,2,5,7] => [1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [3,5,4,2,1,6,7] => [5,4,1,3,2,6,7] => [1,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [3,1,5,4,2,6,7] => [2,5,1,4,3,6,7] => [2,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [3,2,5,4,6,7,1] => [7,2,1,4,3,5,6] => [1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [3,2,5,4,6,1,7] => [6,2,1,4,3,5,7] => [1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [3,2,5,4,1,6,7] => [5,2,1,4,3,6,7] => [1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7] => [1,1,2,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [2,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [2,3,5,4,6,7,1] => [7,1,2,4,3,5,6] => [1,3,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [2,3,5,4,6,1,7] => [6,1,2,4,3,5,7] => [1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [2,3,5,4,1,6,7] => [5,1,2,4,3,6,7] => [1,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [1,3,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [4,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [4,5,6,7,3,2,1] => [7,6,5,1,2,3,4] => [1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [4,5,6,1,7,3,2] => [4,7,6,1,2,3,5] => [2,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [4,5,6,2,7,3,1] => [7,4,6,1,2,3,5] => [1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [4,5,6,2,1,7,3] => [5,4,7,1,2,3,6] => [1,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [3,5,7,1,2,4,6] => [3,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [4,5,6,3,7,2,1] => [7,6,4,1,2,3,5] => [1,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [4,5,6,3,1,7,2] => [5,7,4,1,2,3,6] => [2,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [4,5,6,3,2,7,1] => [7,5,4,1,2,3,6] => [1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [4,5,6,3,2,1,7] => [6,5,4,1,2,3,7] => [1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [4,5,1,6,3,2,7] => [3,6,5,1,2,4,7] => [2,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [4,5,2,6,3,7,1] => [7,3,5,1,2,4,6] => [1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [4,5,2,6,3,1,7] => [6,3,5,1,2,4,7] => [1,2,4]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [4,5,2,1,6,3,7] => [4,3,6,1,2,5,7] => [1,2,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [2,4,6,1,3,5,7] => [3,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [4,5,3,6,7,2,1] => [7,6,3,1,2,4,5] => [1,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [4,5,3,6,1,7,2] => [5,7,3,1,2,4,6] => [2,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [4,5,3,6,2,7,1] => [7,5,3,1,2,4,6] => [1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [4,5,3,6,2,1,7] => [6,5,3,1,2,4,7] => [1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [4,5,3,1,6,2,7] => [4,6,3,1,2,5,7] => [2,1,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [4,5,3,2,6,7,1] => [7,4,3,1,2,5,6] => [1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [4,5,3,2,6,1,7] => [6,4,3,1,2,5,7] => [1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [4,5,3,2,1,6,7] => [5,4,3,1,2,6,7] => [1,1,1,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [4,1,5,3,2,6,7] => [2,5,4,1,3,6,7] => [2,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [4,2,5,3,6,7,1] => [7,2,4,1,3,5,6] => [1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [4,2,5,3,6,1,7] => [6,2,4,1,3,5,7] => [1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [4,2,5,3,1,6,7] => [5,2,4,1,3,6,7] => [1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [4,2,1,5,3,6,7] => [3,2,5,1,4,6,7] => [1,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [1,4,2,5,3,6,7] => [1,3,5,2,4,6,7] => [3,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [4,3,5,6,7,2,1] => [7,6,2,1,3,4,5] => [1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [4,3,5,6,1,7,2] => [5,7,2,1,3,4,6] => [2,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [4,3,5,6,2,7,1] => [7,5,2,1,3,4,6] => [1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [4,3,5,6,2,1,7] => [6,5,2,1,3,4,7] => [1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [4,3,5,1,6,2,7] => [4,6,2,1,3,5,7] => [2,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [4,3,5,2,6,7,1] => [7,4,2,1,3,5,6] => [1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [4,3,5,2,6,1,7] => [6,4,2,1,3,5,7] => [1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [4,3,5,2,1,6,7] => [5,4,2,1,3,6,7] => [1,1,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [4,3,1,5,2,6,7] => [3,5,2,1,4,6,7] => [2,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [4,3,2,5,6,7,1] => [7,3,2,1,4,5,6] => [1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [4,3,2,5,6,1,7] => [6,3,2,1,4,5,7] => [1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [4,3,2,5,1,6,7] => [5,3,2,1,4,6,7] => [1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [2,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [2,4,3,5,6,7,1] => [7,1,3,2,4,5,6] => [1,2,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [2,4,3,5,6,1,7] => [6,1,3,2,4,5,7] => [1,2,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [2,4,3,5,1,6,7] => [5,1,3,2,4,6,7] => [1,2,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [2,4,3,1,5,6,7] => [4,1,3,2,5,6,7] => [1,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [1,2,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [3,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5] => [1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [5,7,1,2,3,4,6] => [2,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [3,4,5,6,2,7,1] => [7,5,1,2,3,4,6] => [1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [3,4,5,6,2,1,7] => [6,5,1,2,3,4,7] => [1,1,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [4,6,1,2,3,5,7] => [2,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [3,4,5,2,6,7,1] => [7,4,1,2,3,5,6] => [1,1,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [3,4,5,2,6,1,7] => [6,4,1,2,3,5,7] => [1,1,5]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [3,4,5,2,1,6,7] => [5,4,1,2,3,6,7] => [1,1,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,5,1,2,4,6,7] => [2,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [3,4,2,5,6,7,1] => [7,3,1,2,4,5,6] => [1,1,5]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [3,4,2,5,6,1,7] => [6,3,1,2,4,5,7] => [1,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [3,4,2,5,1,6,7] => [5,3,1,2,4,6,7] => [1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [3,4,2,1,5,6,7] => [4,3,1,2,5,6,7] => [1,1,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [2,4,1,3,5,6,7] => [2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [3,2,4,5,6,7,1] => [7,2,1,3,4,5,6] => [1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [3,2,4,5,6,1,7] => [6,2,1,3,4,5,7] => [1,1,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [3,2,4,5,1,6,7] => [5,2,1,3,4,6,7] => [1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [3,2,4,1,5,6,7] => [4,2,1,3,5,6,7] => [1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [2,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [1,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [1,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [2,8,7,6,5,4,3,1] => [8,1,7,6,5,4,3,2] => [1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => [1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [1,2,8,7,6,5,4,3] => [1,2,8,7,6,5,4,3] => [3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [3,8,7,6,5,4,2,1] => [8,7,1,6,5,4,3,2] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [3,1,8,7,6,5,4,2] => [2,8,1,7,6,5,4,3] => [2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [3,2,8,7,6,5,4,1] => [8,2,1,7,6,5,4,3] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => [1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [1,3,2,8,7,6,5,4] => [1,3,2,8,7,6,5,4] => [2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [2,3,8,7,6,5,4,1] => [8,1,2,7,6,5,4,3] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [2,3,1,8,7,6,5,4] => [3,1,2,8,7,6,5,4] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [2,1,3,8,7,6,5,4] => [2,1,3,8,7,6,5,4] => [1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [1,2,3,8,7,6,5,4] => [1,2,3,8,7,6,5,4] => [4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [4,8,7,6,5,3,2,1] => [8,7,6,1,5,4,3,2] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [4,1,8,7,6,5,3,2] => [2,8,7,1,6,5,4,3] => [2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [4,2,8,7,6,5,3,1] => [8,2,7,1,6,5,4,3] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [4,2,1,8,7,6,5,3] => [3,2,8,1,7,6,5,4] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [1,4,2,8,7,6,5,3] => [1,3,8,2,7,6,5,4] => [3,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [4,3,8,7,6,5,2,1] => [8,7,2,1,6,5,4,3] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [4,3,2,8,7,6,5,1] => [8,3,2,1,7,6,5,4] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [1,4,3,2,8,7,6,5] => [1,4,3,2,8,7,6,5] => [2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [2,4,3,8,7,6,5,1] => [8,1,3,2,7,6,5,4] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [2,4,3,1,8,7,6,5] => [4,1,3,2,8,7,6,5] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => [1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,7,6,5] => [3,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [3,4,8,7,6,5,2,1] => [8,7,1,2,6,5,4,3] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [3,4,2,8,7,6,5,1] => [8,3,1,2,7,6,5,4] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [3,4,2,1,8,7,6,5] => [4,3,1,2,8,7,6,5] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [3,1,4,2,8,7,6,5] => [2,4,1,3,8,7,6,5] => [2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,2,1] => [3,2,4,8,7,6,5,1] => [8,2,1,3,7,6,5,4] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [3,2,4,1,8,7,6,5] => [4,2,1,3,8,7,6,5] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [3,2,1,4,8,7,6,5] => [3,2,1,4,8,7,6,5] => [1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,7,6,5] => [2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [2,3,4,8,7,6,5,1] => [8,1,2,3,7,6,5,4] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [2,3,4,1,8,7,6,5] => [4,1,2,3,8,7,6,5] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [2,3,1,4,8,7,6,5] => [3,1,2,4,8,7,6,5] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,7,6,5] => [1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,7,6,5] => [5,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [5,8,7,6,4,3,2,1] => [8,7,6,5,1,4,3,2] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [5,1,8,7,6,4,3,2] => [2,8,7,6,1,5,4,3] => [2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [5,2,8,7,6,4,3,1] => [8,2,7,6,1,5,4,3] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [5,2,1,8,7,6,4,3] => [3,2,8,7,1,6,5,4] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [5,3,8,7,6,4,2,1] => [8,7,2,6,1,5,4,3] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [5,3,1,8,7,6,4,2] => [3,8,2,7,1,6,5,4] => [2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [5,3,2,1,8,7,6,4] => [4,3,2,8,1,7,6,5] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [2,5,3,8,7,6,4,1] => [8,1,3,7,2,6,5,4] => [1,3,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [2,1,5,3,8,7,6,4] => [2,1,4,8,3,7,6,5] => [1,3,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [1,2,5,3,8,7,6,4] => [1,2,4,8,3,7,6,5] => [4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [5,4,1,8,7,6,3,2] => [3,8,7,2,1,6,5,4] => [2,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [5,4,2,8,7,6,3,1] => [8,3,7,2,1,6,5,4] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [5,4,2,1,8,7,6,3] => [4,3,8,2,1,7,6,5] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [5,4,3,8,7,6,2,1] => [8,7,3,2,1,6,5,4] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [5,4,3,1,8,7,6,2] => [4,8,3,2,1,7,6,5] => [2,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [5,4,3,2,8,7,6,1] => [8,4,3,2,1,7,6,5] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => [1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [1,5,4,3,2,8,7,6] => [1,5,4,3,2,8,7,6] => [2,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [2,5,4,3,1,8,7,6] => [5,1,4,3,2,8,7,6] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [2,1,5,4,3,8,7,6] => [2,1,5,4,3,8,7,6] => [1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [1,2,5,4,3,8,7,6] => [1,2,5,4,3,8,7,6] => [3,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [3,5,4,8,7,6,2,1] => [8,7,1,3,2,6,5,4] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,7,2,1] => [3,5,4,2,8,7,6,1] => [8,4,1,3,2,7,6,5] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [3,5,4,2,1,8,7,6] => [5,4,1,3,2,8,7,6] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [3,1,5,4,2,8,7,6] => [2,5,1,4,3,8,7,6] => [2,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [3,2,5,4,8,7,6,1] => [8,2,1,4,3,7,6,5] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [3,2,5,4,1,8,7,6] => [5,2,1,4,3,8,7,6] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [3,2,1,5,4,8,7,6] => [3,2,1,5,4,8,7,6] => [1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [2,3,5,4,1,8,7,6] => [5,1,2,4,3,8,7,6] => [1,3,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [2,1,3,5,4,8,7,6] => [2,1,3,5,4,8,7,6] => [1,3,2,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,8,7,6] => [4,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [4,5,8,7,6,3,2,1] => [8,7,6,1,2,5,4,3] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [4,5,2,1,8,7,6,3] => [4,3,8,1,2,7,6,5] => [1,2,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [4,1,5,2,8,7,6,3] => [2,4,8,1,3,7,6,5] => [3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [4,5,3,1,8,7,6,2] => [4,8,3,1,2,7,6,5] => [2,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [4,5,3,2,1,8,7,6] => [5,4,3,1,2,8,7,6] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [4,3,5,2,8,7,6,1] => [8,4,2,1,3,7,6,5] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [4,3,5,2,1,8,7,6] => [5,4,2,1,3,8,7,6] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [4,3,2,5,8,7,6,1] => [8,3,2,1,4,7,6,5] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [4,3,2,5,1,8,7,6] => [5,3,2,1,4,8,7,6] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,8,7,6] => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,2,1] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,8,7,6] => [3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [3,4,5,8,7,6,2,1] => [8,7,1,2,3,6,5,4] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [3,4,5,1,8,7,6,2] => [4,8,1,2,3,7,6,5] => [2,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [3,4,5,2,1,8,7,6] => [5,4,1,2,3,8,7,6] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [3,4,2,5,8,7,6,1] => [8,3,1,2,4,7,6,5] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [3,4,2,5,1,8,7,6] => [5,3,1,2,4,8,7,6] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [3,4,2,1,5,8,7,6] => [4,3,1,2,5,8,7,6] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [3,2,4,5,8,7,6,1] => [8,2,1,3,4,7,6,5] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => [1,1,4,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [2,3,4,5,8,7,6,1] => [8,1,2,3,4,7,6,5] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [2,3,4,5,1,8,7,6] => [5,1,2,3,4,8,7,6] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [2,3,4,1,5,8,7,6] => [4,1,2,3,5,8,7,6] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,8,7,6] => [1,5,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,8,7,6] => [6,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [6,8,7,5,4,3,2,1] => [8,7,6,5,4,1,3,2] => [1,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [6,1,8,7,5,4,3,2] => [2,8,7,6,5,1,4,3] => [2,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [6,2,8,7,5,4,3,1] => [8,2,7,6,5,1,4,3] => [1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [6,2,1,8,7,5,4,3] => [3,2,8,7,6,1,5,4] => [1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [6,3,8,7,5,4,2,1] => [8,7,2,6,5,1,4,3] => [1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [6,3,2,8,7,5,4,1] => [8,3,2,7,6,1,5,4] => [1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [6,3,2,1,8,7,5,4] => [4,3,2,8,7,1,6,5] => [1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [1,6,3,2,8,7,5,4] => [1,4,3,8,7,2,6,5] => [2,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [2,6,3,8,7,5,4,1] => [8,1,3,7,6,2,5,4] => [1,3,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [2,6,3,1,8,7,5,4] => [4,1,3,8,7,2,6,5] => [1,3,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [1,2,6,3,8,7,5,4] => [1,2,4,8,7,3,6,5] => [4,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [6,4,8,7,5,3,2,1] => [8,7,6,2,5,1,4,3] => [1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [6,4,2,8,7,5,3,1] => [8,3,7,2,6,1,5,4] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [6,4,2,1,8,7,5,3] => [4,3,8,2,7,1,6,5] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [1,6,4,2,8,7,5,3] => [1,4,8,3,7,2,6,5] => [3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [6,4,3,8,7,5,2,1] => [8,7,3,2,6,1,5,4] => [1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [6,4,3,2,8,7,5,1] => [8,4,3,2,7,1,6,5] => [1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [6,4,3,2,1,8,7,5] => [5,4,3,2,8,1,7,6] => [1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [2,6,4,3,8,7,5,1] => [8,1,4,3,7,2,6,5] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [2,6,4,3,1,8,7,5] => [5,1,4,3,8,2,7,6] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [2,1,6,4,3,8,7,5] => [2,1,5,4,8,3,7,6] => [1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [3,6,4,8,7,5,2,1] => [8,7,1,3,6,2,5,4] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [3,6,4,2,8,7,5,1] => [8,4,1,3,7,2,6,5] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [3,6,4,2,1,8,7,5] => [5,4,1,3,8,2,7,6] => [1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [3,1,6,4,2,8,7,5] => [2,5,1,4,8,3,7,6] => [2,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [2,3,6,4,8,7,5,1] => [8,1,2,4,7,3,6,5] => [1,4,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [1,2,3,6,4,8,7,5] => [1,2,3,5,8,4,7,6] => [5,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [6,5,8,7,4,3,2,1] => [8,7,6,5,2,1,4,3] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [6,5,1,8,7,4,3,2] => [3,8,7,6,2,1,5,4] => [2,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [6,5,2,8,7,4,3,1] => [8,3,7,6,2,1,5,4] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [6,5,2,1,8,7,4,3] => [4,3,8,7,2,1,6,5] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [1,6,5,2,8,7,4,3] => [1,4,8,7,3,2,6,5] => [3,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [6,5,3,8,7,4,2,1] => [8,7,3,6,2,1,5,4] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [6,5,3,2,8,7,4,1] => [8,4,3,7,2,1,6,5] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [6,5,3,2,1,8,7,4] => [5,4,3,8,2,1,7,6] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [1,6,5,3,2,8,7,4] => [1,5,4,8,3,2,7,6] => [2,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [2,6,5,3,8,7,4,1] => [8,1,4,7,3,2,6,5] => [1,3,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [1,2,6,5,3,8,7,4] => [1,2,5,8,4,3,7,6] => [4,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [6,5,4,8,7,3,2,1] => [8,7,6,3,2,1,5,4] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [6,5,4,1,8,7,3,2] => [4,8,7,3,2,1,6,5] => [2,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [6,5,4,2,1,8,7,3] => [5,4,8,3,2,1,7,6] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [1,6,5,4,2,8,7,3] => [1,5,8,4,3,2,7,6] => [3,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [6,5,4,3,8,7,2,1] => [8,7,4,3,2,1,6,5] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [6,5,4,3,1,8,7,2] => [5,8,4,3,2,1,7,6] => [2,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [6,5,4,3,2,8,7,1] => [8,5,4,3,2,1,7,6] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => [1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [1,6,5,4,3,2,8,7] => [1,6,5,4,3,2,8,7] => [2,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [2,6,5,4,3,8,7,1] => [8,1,5,4,3,2,7,6] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => [2,6,5,4,3,1,8,7] => [6,1,5,4,3,2,8,7] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => [1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [1,2,6,5,4,3,8,7] => [1,2,6,5,4,3,8,7] => [3,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [3,6,5,4,2,8,7,1] => [8,5,1,4,3,2,7,6] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [3,6,5,4,2,1,8,7] => [6,5,1,4,3,2,8,7] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [3,2,6,5,4,8,7,1] => [8,2,1,5,4,3,7,6] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [3,2,1,6,5,4,8,7] => [3,2,1,6,5,4,8,7] => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [2,3,6,5,4,1,8,7] => [6,1,2,5,4,3,8,7] => [1,3,1,2,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [1,2,3,6,5,4,8,7] => [1,2,3,6,5,4,8,7] => [4,1,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [4,6,5,8,7,3,2,1] => [8,7,6,1,3,2,5,4] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [4,6,5,1,8,7,3,2] => [4,8,7,1,3,2,6,5] => [2,1,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [4,6,5,2,8,7,3,1] => [8,4,7,1,3,2,6,5] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [4,6,5,2,1,8,7,3] => [5,4,8,1,3,2,7,6] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [4,1,6,5,2,8,7,3] => [2,5,8,1,4,3,7,6] => [3,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [4,6,5,3,8,7,2,1] => [8,7,4,1,3,2,6,5] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [4,6,5,3,1,8,7,2] => [5,8,4,1,3,2,7,6] => [2,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [4,6,5,3,2,8,7,1] => [8,5,4,1,3,2,7,6] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [4,6,5,3,2,1,8,7] => [6,5,4,1,3,2,8,7] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [4,2,6,5,3,8,7,1] => [8,2,5,1,4,3,7,6] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [4,2,6,5,3,1,8,7] => [6,2,5,1,4,3,8,7] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [4,2,1,6,5,3,8,7] => [3,2,6,1,5,4,8,7] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,8,1] => [1,4,2,6,5,3,8,7] => [1,3,6,2,5,4,8,7] => [3,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [4,3,6,5,8,7,2,1] => [8,7,2,1,4,3,6,5] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [4,3,6,5,1,8,7,2] => [5,8,2,1,4,3,7,6] => [2,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [4,3,6,5,2,8,7,1] => [8,5,2,1,4,3,7,6] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [4,3,6,5,2,1,8,7] => [6,5,2,1,4,3,8,7] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [4,3,2,6,5,8,7,1] => [8,3,2,1,5,4,7,6] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [4,3,2,6,5,1,8,7] => [6,3,2,1,5,4,8,7] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [1,1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [2,4,3,6,5,8,7,1] => [8,1,3,2,5,4,7,6] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [2,4,3,6,5,1,8,7] => [6,1,3,2,5,4,8,7] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [2,4,3,1,6,5,8,7] => [4,1,3,2,6,5,8,7] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [3,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [3,4,6,5,2,8,7,1] => [8,5,1,2,4,3,7,6] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [3,4,6,5,2,1,8,7] => [6,5,1,2,4,3,8,7] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [3,4,2,6,5,1,8,7] => [6,3,1,2,5,4,8,7] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [3,4,2,1,6,5,8,7] => [4,3,1,2,6,5,8,7] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [3,1,4,2,6,5,8,7] => [2,4,1,3,6,5,8,7] => [2,3,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [3,2,4,6,5,8,7,1] => [8,2,1,3,5,4,7,6] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [3,2,4,1,6,5,8,7] => [4,2,1,3,6,5,8,7] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [3,2,1,4,6,5,8,7] => [3,2,1,4,6,5,8,7] => [1,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [2,3,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [2,3,4,6,5,8,7,1] => [8,1,2,3,5,4,7,6] => [1,4,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [2,3,4,6,5,1,8,7] => [6,1,2,3,5,4,8,7] => [1,4,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [1,4,2,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [5,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [5,6,8,7,4,3,2,1] => [8,7,6,5,1,2,4,3] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [5,6,2,8,7,4,3,1] => [8,3,7,6,1,2,5,4] => [1,2,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [5,6,2,1,8,7,4,3] => [4,3,8,7,1,2,6,5] => [1,2,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [5,1,6,2,8,7,4,3] => [2,4,8,7,1,3,6,5] => [3,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [5,6,3,8,7,4,2,1] => [8,7,3,6,1,2,5,4] => [1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [5,6,3,2,8,7,4,1] => [8,4,3,7,1,2,6,5] => [1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [5,6,3,2,1,8,7,4] => [5,4,3,8,1,2,7,6] => [1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [5,1,6,3,2,8,7,4] => [2,5,4,8,1,3,7,6] => [2,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [5,2,6,3,8,7,4,1] => [8,2,4,7,1,3,6,5] => [1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [1,5,2,6,3,8,7,4] => [1,3,5,8,2,4,7,6] => [4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [5,6,4,8,7,3,2,1] => [8,7,6,3,1,2,5,4] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => [5,6,4,2,8,7,3,1] => [8,4,7,3,1,2,6,5] => [1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => [5,6,4,2,1,8,7,3] => [5,4,8,3,1,2,7,6] => [1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [5,1,6,4,2,8,7,3] => [2,5,8,4,1,3,7,6] => [3,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [5,6,4,3,8,7,2,1] => [8,7,4,3,1,2,6,5] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [5,6,4,3,2,8,7,1] => [8,5,4,3,1,2,7,6] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [5,6,4,3,2,1,8,7] => [6,5,4,3,1,2,8,7] => [1,1,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [5,1,6,4,3,2,8,7] => [2,6,5,4,1,3,8,7] => [2,1,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [5,2,6,4,3,8,7,1] => [8,2,5,4,1,3,7,6] => [1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [5,2,6,4,3,1,8,7] => [6,2,5,4,1,3,8,7] => [1,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [5,2,1,6,4,3,8,7] => [3,2,6,5,1,4,8,7] => [1,2,1,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,7,1] => [5,3,6,4,2,8,7,1] => [8,5,2,4,1,3,7,6] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [5,3,1,6,4,2,8,7] => [3,6,2,5,1,4,8,7] => [2,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [5,3,2,6,4,1,8,7] => [6,3,2,5,1,4,8,7] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [5,3,2,1,6,4,8,7] => [4,3,2,6,1,5,8,7] => [1,1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [1,5,3,2,6,4,8,7] => [1,4,3,6,2,5,8,7] => [2,2,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [2,5,3,6,4,1,8,7] => [6,1,3,5,2,4,8,7] => [1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [2,5,3,1,6,4,8,7] => [4,1,3,6,2,5,8,7] => [1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [2,1,5,3,6,4,8,7] => [2,1,4,6,3,5,8,7] => [1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [1,2,5,3,6,4,8,7] => [1,2,4,6,3,5,8,7] => [4,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [5,4,6,8,7,3,2,1] => [8,7,6,2,1,3,5,4] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [5,4,6,1,8,7,3,2] => [4,8,7,2,1,3,6,5] => [2,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [5,4,6,2,8,7,3,1] => [8,4,7,2,1,3,6,5] => [1,2,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [5,4,1,6,2,8,7,3] => [3,5,8,2,1,4,7,6] => [3,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [5,4,6,3,8,7,2,1] => [8,7,4,2,1,3,6,5] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [5,4,6,3,2,8,7,1] => [8,5,4,2,1,3,7,6] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [5,4,6,3,2,1,8,7] => [6,5,4,2,1,3,8,7] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [5,4,1,6,3,2,8,7] => [3,6,5,2,1,4,8,7] => [2,1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [5,4,2,1,6,3,8,7] => [4,3,6,2,1,5,8,7] => [1,2,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [5,4,3,6,8,7,2,1] => [8,7,3,2,1,4,6,5] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [5,4,3,6,1,8,7,2] => [5,8,3,2,1,4,7,6] => [2,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [5,4,3,6,2,8,7,1] => [8,5,3,2,1,4,7,6] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [5,4,3,1,6,2,8,7] => [4,6,3,2,1,5,8,7] => [2,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [5,4,3,2,6,8,7,1] => [8,4,3,2,1,5,7,6] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [5,4,3,2,6,1,8,7] => [6,4,3,2,1,5,8,7] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,6,8,7] => [1,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [2,5,4,3,6,8,7,1] => [8,1,4,3,2,5,7,6] => [1,2,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [2,1,5,4,3,6,8,7] => [2,1,5,4,3,6,8,7] => [1,2,1,3,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [1,2,5,4,3,6,8,7] => [1,2,5,4,3,6,8,7] => [3,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [3,5,4,6,1,8,7,2] => [5,8,1,3,2,4,7,6] => [2,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [3,5,4,2,6,8,7,1] => [8,4,1,3,2,5,7,6] => [1,1,2,3,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [3,5,4,2,1,6,8,7] => [5,4,1,3,2,6,8,7] => [1,1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [3,2,5,4,6,1,8,7] => [6,2,1,4,3,5,8,7] => [1,1,2,3,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [3,2,1,5,4,6,8,7] => [3,2,1,5,4,6,8,7] => [1,1,2,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [2,3,5,4,6,8,7,1] => [8,1,2,4,3,5,7,6] => [1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [2,3,5,4,1,6,8,7] => [5,1,2,4,3,6,8,7] => [1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [1,3,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [4,3,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [4,5,6,8,7,3,2,1] => [8,7,6,1,2,3,5,4] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [4,5,6,1,8,7,3,2] => [4,8,7,1,2,3,6,5] => [2,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [4,5,6,2,8,7,3,1] => [8,4,7,1,2,3,6,5] => [1,2,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [4,5,6,2,1,8,7,3] => [5,4,8,1,2,3,7,6] => [1,2,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [4,5,1,6,2,8,7,3] => [3,5,8,1,2,4,7,6] => [3,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [4,5,6,3,2,1,8,7] => [6,5,4,1,2,3,8,7] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [4,1,5,2,6,3,8,7] => [2,4,6,1,3,5,8,7] => [3,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [4,5,3,6,1,8,7,2] => [5,8,3,1,2,4,7,6] => [2,1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [4,5,3,6,2,8,7,1] => [8,5,3,1,2,4,7,6] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [4,5,3,2,6,8,7,1] => [8,4,3,1,2,5,7,6] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [4,5,3,2,6,1,8,7] => [6,4,3,1,2,5,8,7] => [1,1,1,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [4,2,5,3,6,8,7,1] => [8,2,4,1,3,5,7,6] => [1,2,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [4,2,5,3,6,1,8,7] => [6,2,4,1,3,5,8,7] => [1,2,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [4,2,5,3,1,6,8,7] => [5,2,4,1,3,6,8,7] => [1,2,4,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => [4,2,1,5,3,6,8,7] => [3,2,5,1,4,6,8,7] => [1,2,4,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [1,4,2,5,3,6,8,7] => [1,3,5,2,4,6,8,7] => [3,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [4,3,5,6,1,8,7,2] => [5,8,2,1,3,4,7,6] => [2,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [4,3,5,6,2,1,8,7] => [6,5,2,1,3,4,8,7] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [4,3,5,1,6,2,8,7] => [4,6,2,1,3,5,8,7] => [2,1,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [4,3,5,2,6,1,8,7] => [6,4,2,1,3,5,8,7] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [4,3,5,2,1,6,8,7] => [5,4,2,1,3,6,8,7] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [4,3,2,5,6,8,7,1] => [8,3,2,1,4,5,7,6] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [4,3,2,5,6,1,8,7] => [6,3,2,1,4,5,8,7] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [1,1,1,4,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [1,4,3,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [2,1,4,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [2,4,3,5,6,8,7,1] => [8,1,3,2,4,5,7,6] => [1,2,4,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [2,4,3,1,5,6,8,7] => [4,1,3,2,5,6,8,7] => [1,2,4,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [1,2,4,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [3,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [3,4,5,6,8,7,2,1] => [8,7,1,2,3,4,6,5] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [3,4,5,6,1,8,7,2] => [5,8,1,2,3,4,7,6] => [2,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [3,4,5,6,2,8,7,1] => [8,5,1,2,3,4,7,6] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [3,4,5,6,2,1,8,7] => [6,5,1,2,3,4,8,7] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [3,4,5,1,6,2,8,7] => [4,6,1,2,3,5,8,7] => [2,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [3,4,5,2,6,1,8,7] => [6,4,1,2,3,5,8,7] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [3,4,5,2,1,6,8,7] => [5,4,1,2,3,6,8,7] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,8,1] => [3,4,1,5,2,6,8,7] => [3,5,1,2,4,6,8,7] => [2,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [3,4,2,5,6,8,7,1] => [8,3,1,2,4,5,7,6] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => [3,4,2,5,6,1,8,7] => [6,3,1,2,4,5,8,7] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [3,4,2,1,5,6,8,7] => [4,3,1,2,5,6,8,7] => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [3,1,4,2,5,6,8,7] => [2,4,1,3,5,6,8,7] => [2,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [3,2,4,5,6,8,7,1] => [8,2,1,3,4,5,7,6] => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [3,2,4,1,5,6,8,7] => [4,2,1,3,5,6,8,7] => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [3,2,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [2,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,8,7,1] => [8,1,2,3,4,5,7,6] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,6,1,8,7] => [6,1,2,3,4,5,8,7] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [2,3,4,5,1,6,8,7] => [5,1,2,3,4,6,8,7] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [2,3,4,1,5,6,8,7] => [4,1,2,3,5,6,8,7] => [1,6,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [2,3,1,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => [1,6,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [1,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [7,8,6,5,4,3,2,1] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [7,1,8,6,5,4,3,2] => [2,8,7,6,5,4,1,3] => [2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [7,2,8,6,5,4,3,1] => [8,2,7,6,5,4,1,3] => [1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [7,2,1,8,6,5,4,3] => [3,2,8,7,6,5,1,4] => [1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [1,7,2,8,6,5,4,3] => [1,3,8,7,6,5,2,4] => [3,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [7,3,8,6,5,4,2,1] => [8,7,2,6,5,4,1,3] => [1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [7,3,1,8,6,5,4,2] => [3,8,2,7,6,5,1,4] => [2,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [7,3,2,8,6,5,4,1] => [8,3,2,7,6,5,1,4] => [1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [7,3,2,1,8,6,5,4] => [4,3,2,8,7,6,1,5] => [1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [1,7,3,2,8,6,5,4] => [1,4,3,8,7,6,2,5] => [2,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [2,1,7,3,8,6,5,4] => [2,1,4,8,7,6,3,5] => [1,3,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [1,2,7,3,8,6,5,4] => [1,2,4,8,7,6,3,5] => [4,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [7,4,8,6,5,3,2,1] => [8,7,6,2,5,4,1,3] => [1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [7,4,1,8,6,5,3,2] => [3,8,7,2,6,5,1,4] => [2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [7,4,2,8,6,5,3,1] => [8,3,7,2,6,5,1,4] => [1,2,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [1,7,4,2,8,6,5,3] => [1,4,8,3,7,6,2,5] => [3,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [7,4,3,8,6,5,2,1] => [8,7,3,2,6,5,1,4] => [1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [7,4,3,2,1,8,6,5] => [5,4,3,2,8,7,1,6] => [1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [2,7,4,3,1,8,6,5] => [5,1,4,3,8,7,2,6] => [1,2,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [2,1,7,4,3,8,6,5] => [2,1,5,4,8,7,3,6] => [1,2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [3,7,4,1,8,6,5,2] => [4,8,1,3,7,6,2,5] => [2,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [3,1,7,4,2,8,6,5] => [2,5,1,4,8,7,3,6] => [2,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [3,2,7,4,8,6,5,1] => [8,2,1,4,7,6,3,5] => [1,1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [3,2,1,7,4,8,6,5] => [3,2,1,5,8,7,4,6] => [1,1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [1,3,2,7,4,8,6,5] => [1,3,2,5,8,7,4,6] => [2,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [2,1,3,7,4,8,6,5] => [2,1,3,5,8,7,4,6] => [1,4,1,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [1,2,3,7,4,8,6,5] => [1,2,3,5,8,7,4,6] => [5,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [7,5,8,6,4,3,2,1] => [8,7,6,5,2,4,1,3] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [7,5,1,8,6,4,3,2] => [3,8,7,6,2,5,1,4] => [2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [7,5,2,1,8,6,4,3] => [4,3,8,7,2,6,1,5] => [1,2,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [1,7,5,2,8,6,4,3] => [1,4,8,7,3,6,2,5] => [3,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [7,5,3,8,6,4,2,1] => [8,7,3,6,2,5,1,4] => [1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [7,5,3,1,8,6,4,2] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [7,5,3,2,8,6,4,1] => [8,4,3,7,2,6,1,5] => [1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [7,5,3,2,1,8,6,4] => [5,4,3,8,2,7,1,6] => [1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [1,7,5,3,2,8,6,4] => [1,5,4,8,3,7,2,6] => [2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [2,7,5,3,8,6,4,1] => [8,1,4,7,3,6,2,5] => [1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [2,7,5,3,1,8,6,4] => [5,1,4,8,3,7,2,6] => [1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [2,1,7,5,3,8,6,4] => [2,1,5,8,4,7,3,6] => [1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [1,2,7,5,3,8,6,4] => [1,2,5,8,4,7,3,6] => [4,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [7,5,4,3,1,8,6,2] => [5,8,4,3,2,7,1,6] => [2,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [7,5,4,3,2,8,6,1] => [8,5,4,3,2,7,1,6] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [7,5,4,3,2,1,8,6] => [6,5,4,3,2,8,1,7] => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [2,7,5,4,3,1,8,6] => [6,1,5,4,3,8,2,7] => [1,2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [2,1,7,5,4,3,8,6] => [2,1,6,5,4,8,3,7] => [1,2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [1,2,7,5,4,3,8,6] => [1,2,6,5,4,8,3,7] => [3,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [3,7,5,4,8,6,2,1] => [8,7,1,4,3,6,2,5] => [1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [3,7,5,4,1,8,6,2] => [5,8,1,4,3,7,2,6] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [3,1,7,5,4,2,8,6] => [2,6,1,5,4,8,3,7] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [3,2,7,5,4,8,6,1] => [8,2,1,5,4,7,3,6] => [1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [3,2,7,5,4,1,8,6] => [6,2,1,5,4,8,3,7] => [1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [3,2,1,7,5,4,8,6] => [3,2,1,6,5,8,4,7] => [1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [1,3,2,7,5,4,8,6] => [1,3,2,6,5,8,4,7] => [2,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [2,1,3,7,5,4,8,6] => [2,1,3,6,5,8,4,7] => [1,3,2,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [1,2,3,7,5,4,8,6] => [1,2,3,6,5,8,4,7] => [4,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [4,7,5,8,6,3,2,1] => [8,7,6,1,3,5,2,4] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [4,7,5,1,8,6,3,2] => [4,8,7,1,3,6,2,5] => [2,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [4,7,5,2,8,6,3,1] => [8,4,7,1,3,6,2,5] => [1,2,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [4,1,7,5,2,8,6,3] => [2,5,8,1,4,7,3,6] => [3,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [4,7,5,3,1,8,6,2] => [5,8,4,1,3,7,2,6] => [2,1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [4,7,5,3,2,1,8,6] => [6,5,4,1,3,8,2,7] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => [4,2,7,5,3,1,8,6] => [6,2,5,1,4,8,3,7] => [1,2,3,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => [1,4,2,7,5,3,8,6] => [1,3,6,2,5,8,4,7] => [3,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [4,3,7,5,1,8,6,2] => [5,8,2,1,4,7,3,6] => [2,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [4,3,7,5,2,1,8,6] => [6,5,2,1,4,8,3,7] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [4,3,2,7,5,8,6,1] => [8,3,2,1,5,7,4,6] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [4,3,2,7,5,1,8,6] => [6,3,2,1,5,8,4,7] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [4,3,2,1,7,5,8,6] => [4,3,2,1,6,8,5,7] => [1,1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [1,4,3,2,7,5,8,6] => [1,4,3,2,6,8,5,7] => [2,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [2,1,4,3,7,5,8,6] => [2,1,4,3,6,8,5,7] => [1,2,3,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [1,2,4,3,7,5,8,6] => [1,2,4,3,6,8,5,7] => [3,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [3,4,7,5,8,6,2,1] => [8,7,1,2,4,6,3,5] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [3,4,7,5,1,8,6,2] => [5,8,1,2,4,7,3,6] => [2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [3,4,7,5,2,1,8,6] => [6,5,1,2,4,8,3,7] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [3,4,2,7,5,8,6,1] => [8,3,1,2,5,7,4,6] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [3,4,2,7,5,1,8,6] => [6,3,1,2,5,8,4,7] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,1,2] => [3,4,2,1,7,5,8,6] => [4,3,1,2,6,8,5,7] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [3,1,4,2,7,5,8,6] => [2,4,1,3,6,8,5,7] => [2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [3,2,4,7,5,8,6,1] => [8,2,1,3,5,7,4,6] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [3,2,4,1,7,5,8,6] => [4,2,1,3,6,8,5,7] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [3,2,1,4,7,5,8,6] => [3,2,1,4,6,8,5,7] => [1,1,4,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [1,3,2,4,7,5,8,6] => [1,3,2,4,6,8,5,7] => [2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [2,3,4,7,5,8,6,1] => [8,1,2,3,5,7,4,6] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [2,3,4,7,5,1,8,6] => [6,1,2,3,5,8,4,7] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [2,3,4,1,7,5,8,6] => [4,1,2,3,6,8,5,7] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [2,3,1,4,7,5,8,6] => [3,1,2,4,6,8,5,7] => [1,5,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [2,1,3,4,7,5,8,6] => [2,1,3,4,6,8,5,7] => [1,5,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [1,2,3,4,7,5,8,6] => [1,2,3,4,6,8,5,7] => [6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [7,6,8,5,4,3,2,1] => [8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [7,6,1,8,5,4,3,2] => [3,8,7,6,5,2,1,4] => [2,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [7,6,2,8,5,4,3,1] => [8,3,7,6,5,2,1,4] => [1,2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [7,6,2,1,8,5,4,3] => [4,3,8,7,6,2,1,5] => [1,2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [1,7,6,2,8,5,4,3] => [1,4,8,7,6,3,2,5] => [3,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [7,6,3,8,5,4,2,1] => [8,7,3,6,5,2,1,4] => [1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [7,6,3,1,8,5,4,2] => [4,8,3,7,6,2,1,5] => [2,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [7,6,3,2,8,5,4,1] => [8,4,3,7,6,2,1,5] => [1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [7,6,3,2,1,8,5,4] => [5,4,3,8,7,2,1,6] => [1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [1,7,6,3,2,8,5,4] => [1,5,4,8,7,3,2,6] => [2,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [2,7,6,3,1,8,5,4] => [5,1,4,8,7,3,2,6] => [1,3,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [2,1,7,6,3,8,5,4] => [2,1,5,8,7,4,3,6] => [1,3,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [1,2,7,6,3,8,5,4] => [1,2,5,8,7,4,3,6] => [4,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [7,6,4,8,5,3,2,1] => [8,7,6,3,5,2,1,4] => [1,1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => [7,6,4,2,8,5,3,1] => [8,4,7,3,6,2,1,5] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => [7,6,4,2,1,8,5,3] => [5,4,8,3,7,2,1,6] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => [7,6,4,3,2,8,5,1] => [8,5,4,3,7,2,1,6] => [1,1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [7,6,4,3,2,1,8,5] => [6,5,4,3,8,2,1,7] => [1,1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [1,7,6,4,3,2,8,5] => [1,6,5,4,8,3,2,7] => [2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,1,3] => [2,7,6,4,3,1,8,5] => [6,1,5,4,8,3,2,7] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [2,1,7,6,4,3,8,5] => [2,1,6,5,8,4,3,7] => [1,2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [1,2,7,6,4,3,8,5] => [1,2,6,5,8,4,3,7] => [3,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => [3,7,6,4,8,5,2,1] => [8,7,1,4,6,3,2,5] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => [3,7,6,4,2,8,5,1] => [8,5,1,4,7,3,2,6] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [3,7,6,4,2,1,8,5] => [6,5,1,4,8,3,2,7] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [3,2,7,6,4,1,8,5] => [6,2,1,5,8,4,3,7] => [1,1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [2,3,7,6,4,8,5,1] => [8,1,2,5,7,4,3,6] => [1,4,1,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [2,1,3,7,6,4,8,5] => [2,1,3,6,8,5,4,7] => [1,4,1,2]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [1,2,3,7,6,4,8,5] => [1,2,3,6,8,5,4,7] => [5,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [7,6,5,8,4,3,2,1] => [8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [7,6,5,1,8,4,3,2] => [4,8,7,6,3,2,1,5] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [7,6,5,2,8,4,3,1] => [8,4,7,6,3,2,1,5] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [7,6,5,2,1,8,4,3] => [5,4,8,7,3,2,1,6] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [1,7,6,5,2,8,4,3] => [1,5,8,7,4,3,2,6] => [3,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [7,6,5,3,8,4,2,1] => [8,7,4,6,3,2,1,5] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [7,6,5,3,1,8,4,2] => [5,8,4,7,3,2,1,6] => [2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [7,6,5,3,2,8,4,1] => [8,5,4,7,3,2,1,6] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [7,6,5,3,2,1,8,4] => [6,5,4,8,3,2,1,7] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [1,7,6,5,3,2,8,4] => [1,6,5,8,4,3,2,7] => [2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [2,7,6,5,3,8,4,1] => [8,1,5,7,4,3,2,6] => [1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [2,7,6,5,3,1,8,4] => [6,1,5,8,4,3,2,7] => [1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [2,1,7,6,5,3,8,4] => [2,1,6,8,5,4,3,7] => [1,3,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [1,2,7,6,5,3,8,4] => [1,2,6,8,5,4,3,7] => [4,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [7,6,5,4,8,3,2,1] => [8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [7,6,5,4,1,8,3,2] => [5,8,7,4,3,2,1,6] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [7,6,5,4,2,8,3,1] => [8,5,7,4,3,2,1,6] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [7,6,5,4,2,1,8,3] => [6,5,8,4,3,2,1,7] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [1,7,6,5,4,2,8,3] => [1,6,8,5,4,3,2,7] => [3,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [7,6,5,4,3,8,2,1] => [8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [7,6,5,4,3,1,8,2] => [6,8,5,4,3,2,1,7] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [7,6,5,4,3,2,8,1] => [8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [1,7,6,5,4,3,2,8] => [1,7,6,5,4,3,2,8] => [2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [2,7,6,5,4,3,8,1] => [8,1,6,5,4,3,2,7] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [2,7,6,5,4,3,1,8] => [7,1,6,5,4,3,2,8] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [2,1,7,6,5,4,3,8] => [2,1,7,6,5,4,3,8] => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [1,2,7,6,5,4,3,8] => [1,2,7,6,5,4,3,8] => [3,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [3,7,6,5,4,8,2,1] => [8,7,1,5,4,3,2,6] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [3,7,6,5,4,2,8,1] => [8,6,1,5,4,3,2,7] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [3,7,6,5,4,2,1,8] => [7,6,1,5,4,3,2,8] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [3,1,7,6,5,4,2,8] => [2,7,1,6,5,4,3,8] => [2,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [3,2,1,7,6,5,4,8] => [3,2,1,7,6,5,4,8] => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [1,3,2,7,6,5,4,8] => [1,3,2,7,6,5,4,8] => [2,2,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [2,3,7,6,5,4,8,1] => [8,1,2,6,5,4,3,7] => [1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [2,3,7,6,5,4,1,8] => [7,1,2,6,5,4,3,8] => [1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [2,1,3,7,6,5,4,8] => [2,1,3,7,6,5,4,8] => [1,3,1,1,2]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [1,2,3,7,6,5,4,8] => [1,2,3,7,6,5,4,8] => [4,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [4,7,6,5,8,3,2,1] => [8,7,6,1,4,3,2,5] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [4,7,6,5,1,8,3,2] => [5,8,7,1,4,3,2,6] => [2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [4,1,7,6,5,2,8,3] => [2,6,8,1,5,4,3,7] => [3,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [4,7,6,5,3,8,2,1] => [8,7,5,1,4,3,2,6] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [4,7,6,5,3,2,8,1] => [8,6,5,1,4,3,2,7] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [4,7,6,5,3,2,1,8] => [7,6,5,1,4,3,2,8] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [4,1,7,6,5,3,2,8] => [2,7,6,1,5,4,3,8] => [2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [4,2,7,6,5,3,8,1] => [8,2,6,1,5,4,3,7] => [1,2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [4,2,7,6,5,3,1,8] => [7,2,6,1,5,4,3,8] => [1,2,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [1,4,2,7,6,5,3,8] => [1,3,7,2,6,5,4,8] => [3,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,1,7] => [4,3,7,6,5,2,8,1] => [8,6,2,1,5,4,3,7] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [4,3,7,6,5,2,1,8] => [7,6,2,1,5,4,3,8] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [4,3,2,7,6,5,1,8] => [7,3,2,1,6,5,4,8] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5,8] => [1,1,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => [2,1,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [2,4,3,7,6,5,8,1] => [8,1,3,2,6,5,4,7] => [1,2,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,1,8] => [2,4,3,7,6,5,1,8] => [7,1,3,2,6,5,4,8] => [1,2,2,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [3,4,7,6,5,8,2,1] => [8,7,1,2,5,4,3,6] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [3,4,7,6,5,2,1,8] => [7,6,1,2,5,4,3,8] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [3,2,4,7,6,5,8,1] => [8,2,1,3,6,5,4,7] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [3,2,1,4,7,6,5,8] => [3,2,1,4,7,6,5,8] => [1,1,3,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [2,3,4,7,6,5,8,1] => [8,1,2,3,6,5,4,7] => [1,4,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [2,3,4,7,6,5,1,8] => [7,1,2,3,6,5,4,8] => [1,4,1,2]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [1,2,3,4,7,6,5,8] => [1,2,3,4,7,6,5,8] => [5,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [5,7,6,8,4,3,2,1] => [8,7,6,5,1,3,2,4] => [1,1,1,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [5,7,6,1,8,4,3,2] => [4,8,7,6,1,3,2,5] => [2,1,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [5,7,6,2,8,4,3,1] => [8,4,7,6,1,3,2,5] => [1,2,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [5,7,6,2,1,8,4,3] => [5,4,8,7,1,3,2,6] => [1,2,1,2,2]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [5,1,7,6,2,8,4,3] => [2,5,8,7,1,4,3,6] => [3,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [5,7,6,3,8,4,2,1] => [8,7,4,6,1,3,2,5] => [1,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [5,7,6,3,1,8,4,2] => [5,8,4,7,1,3,2,6] => [2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [5,7,6,3,2,8,4,1] => [8,5,4,7,1,3,2,6] => [1,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [5,7,6,3,2,1,8,4] => [6,5,4,8,1,3,2,7] => [1,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [5,1,7,6,3,2,8,4] => [2,6,5,8,1,4,3,7] => [2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [5,2,7,6,3,1,8,4] => [6,2,5,8,1,4,3,7] => [1,3,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [5,2,1,7,6,3,8,4] => [3,2,6,8,1,5,4,7] => [1,3,2,2]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [1,5,2,7,6,3,8,4] => [1,3,6,8,2,5,4,7] => [4,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [5,7,6,4,8,3,2,1] => [8,7,6,4,1,3,2,5] => [1,1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [5,7,6,4,2,1,8,3] => [6,5,8,4,1,3,2,7] => [1,2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [5,7,6,4,3,2,8,1] => [8,6,5,4,1,3,2,7] => [1,1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [5,7,6,4,3,2,1,8] => [7,6,5,4,1,3,2,8] => [1,1,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [5,1,7,6,4,3,2,8] => [2,7,6,5,1,4,3,8] => [2,1,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [5,2,7,6,4,3,8,1] => [8,2,6,5,1,4,3,7] => [1,2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [5,2,7,6,4,3,1,8] => [7,2,6,5,1,4,3,8] => [1,2,1,2,2]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [1,5,2,7,6,4,3,8] => [1,3,7,6,2,5,4,8] => [3,1,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [5,3,7,6,4,8,2,1] => [8,7,2,5,1,4,3,6] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [5,3,7,6,4,1,8,2] => [6,8,2,5,1,4,3,7] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => [5,3,7,6,4,2,8,1] => [8,6,2,5,1,4,3,7] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [5,3,7,6,4,2,1,8] => [7,6,2,5,1,4,3,8] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [5,3,1,7,6,4,2,8] => [3,7,2,6,1,5,4,8] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [5,3,2,7,6,4,1,8] => [7,3,2,6,1,5,4,8] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [5,3,2,1,7,6,4,8] => [4,3,2,7,1,6,5,8] => [1,1,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [1,5,3,2,7,6,4,8] => [1,4,3,7,2,6,5,8] => [2,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [2,5,3,7,6,4,8,1] => [8,1,3,6,2,5,4,7] => [1,3,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [2,5,3,7,6,4,1,8] => [7,1,3,6,2,5,4,8] => [1,3,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [5,4,7,6,8,3,2,1] => [8,7,6,2,1,4,3,5] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [5,4,7,6,2,8,3,1] => [8,5,7,2,1,4,3,6] => [1,2,1,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [5,4,1,7,6,2,8,3] => [3,6,8,2,1,5,4,7] => [3,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [5,4,7,6,3,8,2,1] => [8,7,5,2,1,4,3,6] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [5,4,7,6,3,2,8,1] => [8,6,5,2,1,4,3,7] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [5,4,7,6,3,2,1,8] => [7,6,5,2,1,4,3,8] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [5,4,2,1,7,6,3,8] => [4,3,7,2,1,6,5,8] => [1,2,1,2,2]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [1,5,4,2,7,6,3,8] => [1,4,7,3,2,6,5,8] => [3,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [5,4,3,7,6,8,2,1] => [8,7,3,2,1,5,4,6] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [5,4,3,7,6,1,8,2] => [6,8,3,2,1,5,4,7] => [2,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [5,4,3,7,6,2,8,1] => [8,6,3,2,1,5,4,7] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [5,4,3,7,6,2,1,8] => [7,6,3,2,1,5,4,8] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [5,4,3,1,7,6,2,8] => [4,7,3,2,1,6,5,8] => [2,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [5,4,3,2,7,6,8,1] => [8,4,3,2,1,6,5,7] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [5,4,3,2,7,6,1,8] => [7,4,3,2,1,6,5,8] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,7,6,8] => [1,1,1,1,2,2]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [1,5,4,3,2,7,6,8] => [1,5,4,3,2,7,6,8] => [2,1,1,2,2]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [2,1,5,4,3,7,6,8] => [2,1,5,4,3,7,6,8] => [1,2,1,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [3,5,4,7,6,8,2,1] => [8,7,1,3,2,5,4,6] => [1,1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [3,5,4,7,6,1,8,2] => [6,8,1,3,2,5,4,7] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [3,5,4,1,7,6,2,8] => [4,7,1,3,2,6,5,8] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [3,5,4,2,7,6,1,8] => [7,4,1,3,2,6,5,8] => [1,1,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [3,1,5,4,2,7,6,8] => [2,5,1,4,3,7,6,8] => [2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [3,2,5,4,7,6,8,1] => [8,2,1,4,3,6,5,7] => [1,1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [3,2,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [1,1,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [2,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [2,3,5,4,1,7,6,8] => [5,1,2,4,3,7,6,8] => [1,3,2,2]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [2,3,1,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [1,3,2,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [2,1,3,5,4,7,6,8] => [2,1,3,5,4,7,6,8] => [1,3,2,2]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [4,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [4,5,7,6,8,3,2,1] => [8,7,6,1,2,4,3,5] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [4,5,7,6,2,1,8,3] => [6,5,8,1,2,4,3,7] => [1,2,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [4,5,1,7,6,2,8,3] => [3,6,8,1,2,5,4,7] => [3,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [4,5,7,6,3,1,8,2] => [6,8,5,1,2,4,3,7] => [2,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [4,5,7,6,3,2,8,1] => [8,6,5,1,2,4,3,7] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [4,5,7,6,3,2,1,8] => [7,6,5,1,2,4,3,8] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [4,5,1,7,6,3,2,8] => [3,7,6,1,2,5,4,8] => [2,1,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [4,5,2,7,6,3,8,1] => [8,3,6,1,2,5,4,7] => [1,2,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [4,5,2,7,6,3,1,8] => [7,3,6,1,2,5,4,8] => [1,2,3,2]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [4,1,5,2,7,6,3,8] => [2,4,7,1,3,6,5,8] => [3,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [4,5,3,7,6,2,8,1] => [8,6,3,1,2,5,4,7] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [4,5,3,7,6,2,1,8] => [7,6,3,1,2,5,4,8] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [4,5,3,1,7,6,2,8] => [4,7,3,1,2,6,5,8] => [2,1,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [4,5,3,2,7,6,8,1] => [8,4,3,1,2,6,5,7] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,1,8] => [4,5,3,2,7,6,1,8] => [7,4,3,1,2,6,5,8] => [1,1,1,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [4,2,5,3,7,6,8,1] => [8,2,4,1,3,6,5,7] => [1,2,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [4,2,5,3,7,6,1,8] => [7,2,4,1,3,6,5,8] => [1,2,3,2]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [4,2,1,5,3,7,6,8] => [3,2,5,1,4,7,6,8] => [1,2,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [4,3,5,7,6,2,8,1] => [8,6,2,1,3,5,4,7] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [4,3,5,1,7,6,2,8] => [4,7,2,1,3,6,5,8] => [2,1,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [4,3,5,2,7,6,8,1] => [8,4,2,1,3,6,5,7] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [4,3,5,2,7,6,1,8] => [7,4,2,1,3,6,5,8] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [4,3,5,2,1,7,6,8] => [5,4,2,1,3,7,6,8] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [1,1,1,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [2,4,3,5,7,6,8,1] => [8,1,3,2,4,6,5,7] => [1,2,3,2]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [3,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [3,4,5,7,6,8,2,1] => [8,7,1,2,3,5,4,6] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [3,4,5,7,6,1,8,2] => [6,8,1,2,3,5,4,7] => [2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [3,4,5,7,6,2,1,8] => [7,6,1,2,3,5,4,8] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [3,4,5,2,7,6,8,1] => [8,4,1,2,3,6,5,7] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [3,4,2,5,7,6,1,8] => [7,3,1,2,4,6,5,8] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [3,4,2,5,1,7,6,8] => [5,3,1,2,4,7,6,8] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [3,4,2,1,5,7,6,8] => [4,3,1,2,5,7,6,8] => [1,1,4,2]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [3,1,4,2,5,7,6,8] => [2,4,1,3,5,7,6,8] => [2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [3,2,4,5,7,6,8,1] => [8,2,1,3,4,6,5,7] => [1,1,4,2]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [3,2,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [1,1,4,2]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [2,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [2,3,4,5,7,6,8,1] => [8,1,2,3,4,6,5,7] => [1,5,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [2,3,4,5,7,6,1,8] => [7,1,2,3,4,6,5,8] => [1,5,2]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [2,3,4,5,1,7,6,8] => [5,1,2,3,4,7,6,8] => [1,5,2]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [2,3,4,1,5,7,6,8] => [4,1,2,3,5,7,6,8] => [1,5,2]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [2,3,1,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => [1,5,2]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [1,5,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [6,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [6,7,8,5,4,3,2,1] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [6,7,1,8,5,4,3,2] => [3,8,7,6,5,1,2,4] => [2,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => [6,7,2,1,8,5,4,3] => [4,3,8,7,6,1,2,5] => [1,2,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [6,1,7,2,8,5,4,3] => [2,4,8,7,6,1,3,5] => [3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [6,7,3,1,8,5,4,2] => [4,8,3,7,6,1,2,5] => [2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [6,7,3,2,8,5,4,1] => [8,4,3,7,6,1,2,5] => [1,1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [6,7,3,2,1,8,5,4] => [5,4,3,8,7,1,2,6] => [1,1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [6,1,7,3,2,8,5,4] => [2,5,4,8,7,1,3,6] => [2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [6,2,7,3,8,5,4,1] => [8,2,4,7,6,1,3,5] => [1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [6,2,7,3,1,8,5,4] => [5,2,4,8,7,1,3,6] => [1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [6,2,1,7,3,8,5,4] => [3,2,5,8,7,1,4,6] => [1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [1,6,2,7,3,8,5,4] => [1,3,5,8,7,2,4,6] => [4,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [6,7,4,8,5,3,2,1] => [8,7,6,3,5,1,2,4] => [1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [6,7,4,2,8,5,3,1] => [8,4,7,3,6,1,2,5] => [1,2,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [6,1,7,4,2,8,5,3] => [2,5,8,4,7,1,3,6] => [3,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [6,7,4,3,8,5,2,1] => [8,7,4,3,6,1,2,5] => [1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [6,7,4,3,1,8,5,2] => [5,8,4,3,7,1,2,6] => [2,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [6,7,4,3,2,1,8,5] => [6,5,4,3,8,1,2,7] => [1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [6,1,7,4,3,2,8,5] => [2,6,5,4,8,1,3,7] => [2,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [6,2,7,4,3,1,8,5] => [6,2,5,4,8,1,3,7] => [1,2,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [6,2,1,7,4,3,8,5] => [3,2,6,5,8,1,4,7] => [1,2,2,3]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [1,6,2,7,4,3,8,5] => [1,3,6,5,8,2,4,7] => [3,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [6,3,7,4,8,5,2,1] => [8,7,2,4,6,1,3,5] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [6,3,7,4,1,8,5,2] => [5,8,2,4,7,1,3,6] => [2,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => [6,3,7,4,2,8,5,1] => [8,5,2,4,7,1,3,6] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [6,3,7,4,2,1,8,5] => [6,5,2,4,8,1,3,7] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [6,3,1,7,4,2,8,5] => [3,6,2,5,8,1,4,7] => [2,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => [6,3,2,7,4,8,5,1] => [8,3,2,5,7,1,4,6] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [6,3,2,7,4,1,8,5] => [6,3,2,5,8,1,4,7] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [6,3,2,1,7,4,8,5] => [4,3,2,6,8,1,5,7] => [1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [1,6,3,2,7,4,8,5] => [1,4,3,6,8,2,5,7] => [2,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [2,6,3,7,4,8,5,1] => [8,1,3,5,7,2,4,6] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [2,6,3,7,4,1,8,5] => [6,1,3,5,8,2,4,7] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [2,6,3,1,7,4,8,5] => [4,1,3,6,8,2,5,7] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [2,1,6,3,7,4,8,5] => [2,1,4,6,8,3,5,7] => [1,4,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [1,2,6,3,7,4,8,5] => [1,2,4,6,8,3,5,7] => [5,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [6,7,5,8,4,3,2,1] => [8,7,6,5,3,1,2,4] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [6,7,5,1,8,4,3,2] => [4,8,7,6,3,1,2,5] => [2,1,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [6,7,5,2,8,4,3,1] => [8,4,7,6,3,1,2,5] => [1,2,1,1,3]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [6,7,5,2,1,8,4,3] => [5,4,8,7,3,1,2,6] => [1,2,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [6,7,5,3,1,8,4,2] => [5,8,4,7,3,1,2,6] => [2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => [6,7,5,3,2,8,4,1] => [8,5,4,7,3,1,2,6] => [1,1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [6,7,5,3,2,1,8,4] => [6,5,4,8,3,1,2,7] => [1,1,2,1,3]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [6,1,7,5,3,2,8,4] => [2,6,5,8,4,1,3,7] => [2,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [6,2,7,5,3,1,8,4] => [6,2,5,8,4,1,3,7] => [1,3,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [6,2,1,7,5,3,8,4] => [3,2,6,8,5,1,4,7] => [1,3,1,3]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [1,6,2,7,5,3,8,4] => [1,3,6,8,5,2,4,7] => [4,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [6,7,5,4,8,3,2,1] => [8,7,6,4,3,1,2,5] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [6,1,7,5,4,2,8,3] => [2,6,8,5,4,1,3,7] => [3,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [6,7,5,4,3,8,2,1] => [8,7,5,4,3,1,2,6] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [6,7,5,4,3,1,8,2] => [6,8,5,4,3,1,2,7] => [2,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [6,7,5,4,3,2,8,1] => [8,6,5,4,3,1,2,7] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [6,7,5,4,3,2,1,8] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [6,1,7,5,4,3,2,8] => [2,7,6,5,4,1,3,8] => [2,1,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [6,3,7,5,4,2,8,1] => [8,6,2,5,4,1,3,7] => [1,1,2,1,3]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [2,1,6,3,7,5,4,8] => [2,1,4,7,6,3,5,8] => [1,3,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [6,4,7,5,8,3,2,1] => [8,7,6,2,4,1,3,5] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [6,4,7,5,1,8,3,2] => [5,8,7,2,4,1,3,6] => [2,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [6,4,7,5,2,8,3,1] => [8,5,7,2,4,1,3,6] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [6,4,1,7,5,2,8,3] => [3,6,8,2,5,1,4,7] => [3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [6,4,7,5,3,8,2,1] => [8,7,5,2,4,1,3,6] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [6,4,7,5,3,2,8,1] => [8,6,5,2,4,1,3,7] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [6,4,7,5,3,2,1,8] => [7,6,5,2,4,1,3,8] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [6,4,2,7,5,3,8,1] => [8,3,6,2,5,1,4,7] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => [6,4,2,7,5,3,1,8] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [6,4,2,1,7,5,3,8] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [6,4,3,2,1,7,5,8] => [5,4,3,2,7,1,6,8] => [1,1,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [2,6,4,3,7,5,8,1] => [8,1,4,3,6,2,5,7] => [1,2,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [2,6,4,3,1,7,5,8] => [5,1,4,3,7,2,6,8] => [1,2,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [3,6,4,7,5,1,8,2] => [6,8,1,3,5,2,4,7] => [2,3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [3,6,4,7,5,2,8,1] => [8,6,1,3,5,2,4,7] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [3,6,4,1,7,5,2,8] => [4,7,1,3,6,2,5,8] => [2,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [3,6,4,2,7,5,8,1] => [8,4,1,3,6,2,5,7] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => [3,6,4,2,7,5,1,8] => [7,4,1,3,6,2,5,8] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [3,1,6,4,2,7,5,8] => [2,5,1,4,7,3,6,8] => [2,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [3,2,6,4,7,5,8,1] => [8,2,1,4,6,3,5,7] => [1,1,3,3]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,1,2,8] => [3,2,6,4,1,7,5,8] => [5,2,1,4,7,3,6,8] => [1,1,3,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [2,3,6,4,7,5,8,1] => [8,1,2,4,6,3,5,7] => [1,4,3]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [2,3,6,4,1,7,5,8] => [5,1,2,4,7,3,6,8] => [1,4,3]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [1,2,3,6,4,7,5,8] => [1,2,3,5,7,4,6,8] => [5,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [6,5,7,8,4,3,2,1] => [8,7,6,5,2,1,3,4] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [6,5,7,1,8,4,3,2] => [4,8,7,6,2,1,3,5] => [2,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [6,5,7,2,1,8,4,3] => [5,4,8,7,2,1,3,6] => [1,2,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [6,5,1,7,2,8,4,3] => [3,5,8,7,2,1,4,6] => [3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [6,5,7,3,8,4,2,1] => [8,7,4,6,2,1,3,5] => [1,1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [6,5,7,3,1,8,4,2] => [5,8,4,7,2,1,3,6] => [2,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [6,5,7,3,2,8,4,1] => [8,5,4,7,2,1,3,6] => [1,1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [6,5,7,3,2,1,8,4] => [6,5,4,8,2,1,3,7] => [1,1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [6,5,2,7,3,8,4,1] => [8,3,5,7,2,1,4,6] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [6,5,2,7,3,1,8,4] => [6,3,5,8,2,1,4,7] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [6,5,2,1,7,3,8,4] => [4,3,6,8,2,1,5,7] => [1,3,1,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [1,6,5,2,7,3,8,4] => [1,4,6,8,3,2,5,7] => [4,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [6,5,7,4,8,3,2,1] => [8,7,6,4,2,1,3,5] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [6,5,7,4,1,8,3,2] => [5,8,7,4,2,1,3,6] => [2,1,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [6,5,7,4,2,8,3,1] => [8,5,7,4,2,1,3,6] => [1,2,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [6,5,1,7,4,2,8,3] => [3,6,8,5,2,1,4,7] => [3,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [6,5,7,4,3,1,8,2] => [6,8,5,4,2,1,3,7] => [2,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [6,5,7,4,3,2,8,1] => [8,6,5,4,2,1,3,7] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [6,5,7,4,3,2,1,8] => [7,6,5,4,2,1,3,8] => [1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [6,5,2,7,4,3,8,1] => [8,3,6,5,2,1,4,7] => [1,2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [6,5,2,1,7,4,3,8] => [4,3,7,6,2,1,5,8] => [1,2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,1,3,7] => [6,5,3,7,4,2,8,1] => [8,6,3,5,2,1,4,7] => [1,1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [6,5,3,7,4,2,1,8] => [7,6,3,5,2,1,4,8] => [1,1,2,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [6,5,3,2,7,4,1,8] => [7,4,3,6,2,1,5,8] => [1,1,2,1,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [2,6,5,3,7,4,8,1] => [8,1,4,6,3,2,5,7] => [1,3,1,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [2,6,5,3,7,4,1,8] => [7,1,4,6,3,2,5,8] => [1,3,1,3]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [1,2,6,5,3,7,4,8] => [1,2,5,7,4,3,6,8] => [4,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [6,5,4,7,8,3,2,1] => [8,7,6,3,2,1,4,5] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [6,5,4,7,1,8,3,2] => [5,8,7,3,2,1,4,6] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [6,5,4,7,2,8,3,1] => [8,5,7,3,2,1,4,6] => [1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [6,5,4,7,2,1,8,3] => [6,5,8,3,2,1,4,7] => [1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [6,5,4,1,7,2,8,3] => [4,6,8,3,2,1,5,7] => [3,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [6,5,4,7,3,8,2,1] => [8,7,5,3,2,1,4,6] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [6,5,4,7,3,1,8,2] => [6,8,5,3,2,1,4,7] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [6,5,4,7,3,2,8,1] => [8,6,5,3,2,1,4,7] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [6,5,4,7,3,2,1,8] => [7,6,5,3,2,1,4,8] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [6,5,4,2,7,3,8,1] => [8,4,6,3,2,1,5,7] => [1,2,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [6,5,4,3,7,8,2,1] => [8,7,4,3,2,1,5,6] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [6,5,4,3,7,1,8,2] => [6,8,4,3,2,1,5,7] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [6,5,4,3,7,2,8,1] => [8,6,4,3,2,1,5,7] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [6,5,4,3,7,2,1,8] => [7,6,4,3,2,1,5,8] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [6,5,4,3,2,7,8,1] => [8,5,4,3,2,1,6,7] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [6,5,4,3,2,7,1,8] => [7,5,4,3,2,1,6,8] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [1,6,5,4,3,2,7,8] => [1,6,5,4,3,2,7,8] => [2,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [2,6,5,4,3,7,8,1] => [8,1,5,4,3,2,6,7] => [1,2,1,1,3]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [1,2,6,5,4,3,7,8] => [1,2,6,5,4,3,7,8] => [3,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [3,6,5,4,7,8,2,1] => [8,7,1,4,3,2,5,6] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [3,6,5,4,7,1,8,2] => [6,8,1,4,3,2,5,7] => [2,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [3,6,5,4,7,2,8,1] => [8,6,1,4,3,2,5,7] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [3,6,5,4,7,2,1,8] => [7,6,1,4,3,2,5,8] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [3,6,5,4,1,7,2,8] => [5,7,1,4,3,2,6,8] => [2,2,1,3]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [3,6,5,4,2,1,7,8] => [6,5,1,4,3,2,7,8] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [3,1,6,5,4,2,7,8] => [2,6,1,5,4,3,7,8] => [2,2,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [3,2,6,5,4,7,1,8] => [7,2,1,5,4,3,6,8] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [3,2,1,6,5,4,7,8] => [3,2,1,6,5,4,7,8] => [1,1,2,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [2,3,6,5,4,7,8,1] => [8,1,2,5,4,3,6,7] => [1,3,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [2,3,6,5,4,1,7,8] => [6,1,2,5,4,3,7,8] => [1,3,1,3]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [1,2,3,6,5,4,7,8] => [1,2,3,6,5,4,7,8] => [4,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [4,6,5,7,8,3,2,1] => [8,7,6,1,3,2,4,5] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [4,6,5,7,2,1,8,3] => [6,5,8,1,3,2,4,7] => [1,2,2,3]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [4,6,5,1,7,2,8,3] => [4,6,8,1,3,2,5,7] => [3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [4,6,5,7,3,2,8,1] => [8,6,5,1,3,2,4,7] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [4,6,5,7,3,2,1,8] => [7,6,5,1,3,2,4,8] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [4,6,5,1,7,3,2,8] => [4,7,6,1,3,2,5,8] => [2,1,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [4,6,5,2,7,3,8,1] => [8,4,6,1,3,2,5,7] => [1,2,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [4,6,5,2,7,3,1,8] => [7,4,6,1,3,2,5,8] => [1,2,2,3]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [4,6,5,2,1,7,3,8] => [5,4,7,1,3,2,6,8] => [1,2,2,3]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [4,1,6,5,2,7,3,8] => [2,5,7,1,4,3,6,8] => [3,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [4,6,5,3,7,1,8,2] => [6,8,4,1,3,2,5,7] => [2,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [4,6,5,3,7,2,8,1] => [8,6,4,1,3,2,5,7] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [4,6,5,3,7,2,1,8] => [7,6,4,1,3,2,5,8] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [4,6,5,3,1,7,2,8] => [5,7,4,1,3,2,6,8] => [2,1,2,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [4,6,5,3,2,7,1,8] => [7,5,4,1,3,2,6,8] => [1,1,1,2,3]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [4,2,1,6,5,3,7,8] => [3,2,6,1,5,4,7,8] => [1,2,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [4,3,6,5,7,8,2,1] => [8,7,2,1,4,3,5,6] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [4,3,6,5,7,1,8,2] => [6,8,2,1,4,3,5,7] => [2,1,2,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [4,3,6,5,7,2,8,1] => [8,6,2,1,4,3,5,7] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [4,3,6,5,2,7,1,8] => [7,5,2,1,4,3,6,8] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [4,3,1,6,5,2,7,8] => [3,6,2,1,5,4,7,8] => [2,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [4,3,2,6,5,1,7,8] => [6,3,2,1,5,4,7,8] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [1,1,1,2,3]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [1,4,3,2,6,5,7,8] => [1,4,3,2,6,5,7,8] => [2,1,2,3]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [1,2,2,3]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [3,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [3,4,6,5,7,8,2,1] => [8,7,1,2,4,3,5,6] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [3,4,6,5,7,1,8,2] => [6,8,1,2,4,3,5,7] => [2,3,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [3,4,6,5,7,2,8,1] => [8,6,1,2,4,3,5,7] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [3,4,6,5,7,2,1,8] => [7,6,1,2,4,3,5,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [3,4,6,5,2,7,8,1] => [8,5,1,2,4,3,6,7] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [3,4,6,5,2,7,1,8] => [7,5,1,2,4,3,6,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [3,4,6,5,2,1,7,8] => [6,5,1,2,4,3,7,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [3,4,1,6,5,2,7,8] => [3,6,1,2,5,4,7,8] => [2,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [3,4,2,6,5,7,8,1] => [8,3,1,2,5,4,6,7] => [1,1,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [3,4,2,6,5,7,1,8] => [7,3,1,2,5,4,6,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [3,2,4,1,6,5,7,8] => [4,2,1,3,6,5,7,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [3,2,1,4,6,5,7,8] => [3,2,1,4,6,5,7,8] => [1,1,3,3]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [2,3,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [2,3,4,6,5,7,8,1] => [8,1,2,3,5,4,6,7] => [1,4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [2,3,4,6,5,7,1,8] => [7,1,2,3,5,4,6,8] => [1,4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [2,3,4,6,5,1,7,8] => [6,1,2,3,5,4,7,8] => [1,4,3]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [2,3,4,1,6,5,7,8] => [4,1,2,3,6,5,7,8] => [1,4,3]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [1,4,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [5,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4] => [1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [5,6,7,1,8,4,3,2] => [4,8,7,6,1,2,3,5] => [2,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [5,6,7,2,8,4,3,1] => [8,4,7,6,1,2,3,5] => [1,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [5,6,7,2,1,8,4,3] => [5,4,8,7,1,2,3,6] => [1,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [5,6,1,7,2,8,4,3] => [3,5,8,7,1,2,4,6] => [3,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [5,6,7,3,8,4,2,1] => [8,7,4,6,1,2,3,5] => [1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [5,6,7,3,1,8,4,2] => [5,8,4,7,1,2,3,6] => [2,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [5,6,7,3,2,8,4,1] => [8,5,4,7,1,2,3,6] => [1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [5,6,7,3,2,1,8,4] => [6,5,4,8,1,2,3,7] => [1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [5,6,1,7,3,2,8,4] => [3,6,5,8,1,2,4,7] => [2,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [5,6,2,7,3,8,4,1] => [8,3,5,7,1,2,4,6] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [5,6,2,7,3,1,8,4] => [6,3,5,8,1,2,4,7] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [5,6,2,1,7,3,8,4] => [4,3,6,8,1,2,5,7] => [1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [5,1,6,2,7,3,8,4] => [2,4,6,8,1,3,5,7] => [4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [5,6,7,4,8,3,2,1] => [8,7,6,4,1,2,3,5] => [1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [5,6,7,4,1,8,3,2] => [5,8,7,4,1,2,3,6] => [2,1,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => [5,6,7,4,2,1,8,3] => [6,5,8,4,1,2,3,7] => [1,2,1,4]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [5,6,1,7,4,2,8,3] => [3,6,8,5,1,2,4,7] => [3,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [5,6,7,4,3,8,2,1] => [8,7,5,4,1,2,3,6] => [1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [5,6,7,4,3,1,8,2] => [6,8,5,4,1,2,3,7] => [2,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [5,6,7,4,3,2,8,1] => [8,6,5,4,1,2,3,7] => [1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [5,6,7,4,3,2,1,8] => [7,6,5,4,1,2,3,8] => [1,1,1,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [5,6,2,7,4,3,8,1] => [8,3,6,5,1,2,4,7] => [1,2,1,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,1,2,3,8] => [5,6,2,7,4,3,1,8] => [7,3,6,5,1,2,4,8] => [1,2,1,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [5,6,3,7,4,8,2,1] => [8,7,3,5,1,2,4,6] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [5,6,3,7,4,1,8,2] => [6,8,3,5,1,2,4,7] => [2,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [5,6,3,7,4,2,8,1] => [8,6,3,5,1,2,4,7] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => [5,6,3,7,4,2,1,8] => [7,6,3,5,1,2,4,8] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => [5,6,3,2,7,4,1,8] => [7,4,3,6,1,2,5,8] => [1,1,2,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [5,2,6,3,7,4,8,1] => [8,2,4,6,1,3,5,7] => [1,3,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [5,2,6,3,7,4,1,8] => [7,2,4,6,1,3,5,8] => [1,3,4]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [5,2,1,6,3,7,4,8] => [3,2,5,7,1,4,6,8] => [1,3,4]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [1,5,2,6,3,7,4,8] => [1,3,5,7,2,4,6,8] => [4,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [5,6,4,7,8,3,2,1] => [8,7,6,3,1,2,4,5] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [5,6,4,7,1,8,3,2] => [5,8,7,3,1,2,4,6] => [2,1,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [5,6,4,7,2,8,3,1] => [8,5,7,3,1,2,4,6] => [1,2,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [5,6,4,7,2,1,8,3] => [6,5,8,3,1,2,4,7] => [1,2,1,4]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [5,6,4,1,7,2,8,3] => [4,6,8,3,1,2,5,7] => [3,1,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [5,6,4,7,3,8,2,1] => [8,7,5,3,1,2,4,6] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [5,6,4,2,7,3,8,1] => [8,4,6,3,1,2,5,7] => [1,2,1,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => [5,6,4,2,7,3,1,8] => [7,4,6,3,1,2,5,8] => [1,2,1,4]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [5,1,6,4,2,7,3,8] => [2,5,7,4,1,3,6,8] => [3,1,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [5,6,4,3,7,1,8,2] => [6,8,4,3,1,2,5,7] => [2,1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [5,6,4,3,7,2,8,1] => [8,6,4,3,1,2,5,7] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [5,6,4,3,7,2,1,8] => [7,6,4,3,1,2,5,8] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [5,6,4,3,2,1,7,8] => [6,5,4,3,1,2,7,8] => [1,1,1,1,4]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [5,1,6,4,3,2,7,8] => [2,6,5,4,1,3,7,8] => [2,1,1,4]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [5,2,1,6,4,3,7,8] => [3,2,6,5,1,4,7,8] => [1,2,1,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [5,3,6,4,7,8,2,1] => [8,7,2,4,1,3,5,6] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [5,3,6,4,7,1,8,2] => [6,8,2,4,1,3,5,7] => [2,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [5,3,6,4,7,2,8,1] => [8,6,2,4,1,3,5,7] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [5,3,6,4,1,7,2,8] => [5,7,2,4,1,3,6,8] => [2,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [5,3,6,4,2,7,8,1] => [8,5,2,4,1,3,6,7] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => [5,3,6,4,2,7,1,8] => [7,5,2,4,1,3,6,8] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [5,3,1,6,4,2,7,8] => [3,6,2,5,1,4,7,8] => [2,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => [5,3,2,6,4,1,7,8] => [6,3,2,5,1,4,7,8] => [1,1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [5,3,2,1,6,4,7,8] => [4,3,2,6,1,5,7,8] => [1,1,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [2,5,3,6,4,7,8,1] => [8,1,3,5,2,4,6,7] => [1,3,4]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [2,1,5,3,6,4,7,8] => [2,1,4,6,3,5,7,8] => [1,3,4]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [1,2,5,3,6,4,7,8] => [1,2,4,6,3,5,7,8] => [4,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [5,4,6,7,8,3,2,1] => [8,7,6,2,1,3,4,5] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [5,4,6,7,1,8,3,2] => [5,8,7,2,1,3,4,6] => [2,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [5,4,6,7,2,8,3,1] => [8,5,7,2,1,3,4,6] => [1,2,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [5,4,6,1,7,2,8,3] => [4,6,8,2,1,3,5,7] => [3,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [5,4,6,7,3,8,2,1] => [8,7,5,2,1,3,4,6] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [5,4,6,7,3,1,8,2] => [6,8,5,2,1,3,4,7] => [2,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [5,4,6,7,3,2,8,1] => [8,6,5,2,1,3,4,7] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [5,4,6,7,3,2,1,8] => [7,6,5,2,1,3,4,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [5,4,6,2,7,3,8,1] => [8,4,6,2,1,3,5,7] => [1,2,1,4]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [5,4,1,6,2,7,3,8] => [3,5,7,2,1,4,6,8] => [3,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [5,4,6,3,7,8,2,1] => [8,7,4,2,1,3,5,6] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [5,4,6,3,7,1,8,2] => [6,8,4,2,1,3,5,7] => [2,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [5,4,6,3,7,2,8,1] => [8,6,4,2,1,3,5,7] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [5,4,6,3,7,2,1,8] => [7,6,4,2,1,3,5,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [5,4,6,3,2,7,8,1] => [8,5,4,2,1,3,6,7] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [5,4,6,3,2,1,7,8] => [6,5,4,2,1,3,7,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [5,4,1,6,3,2,7,8] => [3,6,5,2,1,4,7,8] => [2,1,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [5,4,2,6,3,7,1,8] => [7,3,5,2,1,4,6,8] => [1,2,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [5,4,2,6,3,1,7,8] => [6,3,5,2,1,4,7,8] => [1,2,1,4]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [5,4,2,1,6,3,7,8] => [4,3,6,2,1,5,7,8] => [1,2,1,4]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [1,5,4,2,6,3,7,8] => [1,4,6,3,2,5,7,8] => [3,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [5,4,3,6,7,8,2,1] => [8,7,3,2,1,4,5,6] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [5,4,3,6,7,1,8,2] => [6,8,3,2,1,4,5,7] => [2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [5,4,3,6,7,2,8,1] => [8,6,3,2,1,4,5,7] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [5,4,3,6,7,2,1,8] => [7,6,3,2,1,4,5,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [5,4,3,6,1,7,2,8] => [5,7,3,2,1,4,6,8] => [2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [5,4,3,6,2,7,8,1] => [8,5,3,2,1,4,6,7] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [5,4,3,6,2,7,1,8] => [7,5,3,2,1,4,6,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [5,4,3,6,2,1,7,8] => [6,5,3,2,1,4,7,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [5,4,3,1,6,2,7,8] => [4,6,3,2,1,5,7,8] => [2,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [5,4,3,2,6,7,8,1] => [8,4,3,2,1,5,6,7] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [5,4,3,2,6,7,1,8] => [7,4,3,2,1,5,6,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [5,4,3,2,6,1,7,8] => [6,4,3,2,1,5,7,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [1,5,4,3,2,6,7,8] => [1,5,4,3,2,6,7,8] => [2,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [2,5,4,3,6,7,8,1] => [8,1,4,3,2,5,6,7] => [1,2,1,4]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [2,5,4,3,1,6,7,8] => [5,1,4,3,2,6,7,8] => [1,2,1,4]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [2,1,5,4,3,6,7,8] => [2,1,5,4,3,6,7,8] => [1,2,1,4]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [1,2,5,4,3,6,7,8] => [1,2,5,4,3,6,7,8] => [3,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [3,5,4,6,7,8,2,1] => [8,7,1,3,2,4,5,6] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [3,5,4,6,7,1,8,2] => [6,8,1,3,2,4,5,7] => [2,2,4]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [3,5,4,6,1,7,2,8] => [5,7,1,3,2,4,6,8] => [2,2,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [3,5,4,6,2,7,1,8] => [7,5,1,3,2,4,6,8] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [3,5,4,2,6,7,8,1] => [8,4,1,3,2,5,6,7] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [3,5,4,2,1,6,7,8] => [5,4,1,3,2,6,7,8] => [1,1,2,4]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [3,1,5,4,2,6,7,8] => [2,5,1,4,3,6,7,8] => [2,2,4]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [3,2,5,4,1,6,7,8] => [5,2,1,4,3,6,7,8] => [1,1,2,4]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [3,2,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => [1,1,2,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [2,2,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [2,3,5,4,6,7,8,1] => [8,1,2,4,3,5,6,7] => [1,3,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [2,3,5,4,6,7,1,8] => [7,1,2,4,3,5,6,8] => [1,3,4]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [2,3,5,4,1,6,7,8] => [5,1,2,4,3,6,7,8] => [1,3,4]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [2,3,1,5,4,6,7,8] => [3,1,2,5,4,6,7,8] => [1,3,4]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [1,3,4]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [4,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [4,5,6,7,8,3,2,1] => [8,7,6,1,2,3,4,5] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [4,5,6,7,1,8,3,2] => [5,8,7,1,2,3,4,6] => [2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [4,5,6,7,2,8,3,1] => [8,5,7,1,2,3,4,6] => [1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [4,5,6,7,2,1,8,3] => [6,5,8,1,2,3,4,7] => [1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [4,5,6,1,7,2,8,3] => [4,6,8,1,2,3,5,7] => [3,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [4,5,6,7,3,8,2,1] => [8,7,5,1,2,3,4,6] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [4,5,6,7,3,1,8,2] => [6,8,5,1,2,3,4,7] => [2,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [4,5,6,7,3,2,8,1] => [8,6,5,1,2,3,4,7] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [4,5,6,7,3,2,1,8] => [7,6,5,1,2,3,4,8] => [1,1,1,5]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [4,5,6,1,7,3,2,8] => [4,7,6,1,2,3,5,8] => [2,1,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [4,5,6,2,7,3,8,1] => [8,4,6,1,2,3,5,7] => [1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [4,5,6,2,7,3,1,8] => [7,4,6,1,2,3,5,8] => [1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [4,5,6,2,1,7,3,8] => [5,4,7,1,2,3,6,8] => [1,2,5]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [4,5,1,6,2,7,3,8] => [3,5,7,1,2,4,6,8] => [3,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [4,5,6,3,7,8,2,1] => [8,7,4,1,2,3,5,6] => [1,1,1,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => [4,5,6,3,7,1,8,2] => [6,8,4,1,2,3,5,7] => [2,1,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [4,5,6,3,7,2,8,1] => [8,6,4,1,2,3,5,7] => [1,1,1,5]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [4,5,6,3,2,7,8,1] => [8,5,4,1,2,3,6,7] => [1,1,1,5]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [4,5,6,3,2,1,7,8] => [6,5,4,1,2,3,7,8] => [1,1,1,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [4,5,2,6,3,7,8,1] => [8,3,5,1,2,4,6,7] => [1,2,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [4,5,2,6,3,7,1,8] => [7,3,5,1,2,4,6,8] => [1,2,5]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [4,1,5,2,6,3,7,8] => [2,4,6,1,3,5,7,8] => [3,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [4,5,3,6,7,1,8,2] => [6,8,3,1,2,4,5,7] => [2,1,5]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [4,5,3,6,1,7,2,8] => [5,7,3,1,2,4,6,8] => [2,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [4,5,3,6,2,7,8,1] => [8,5,3,1,2,4,6,7] => [1,1,1,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [4,5,3,6,2,7,1,8] => [7,5,3,1,2,4,6,8] => [1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [4,5,3,2,6,7,1,8] => [7,4,3,1,2,5,6,8] => [1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [4,5,3,2,6,1,7,8] => [6,4,3,1,2,5,7,8] => [1,1,1,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [4,5,3,2,1,6,7,8] => [5,4,3,1,2,6,7,8] => [1,1,1,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [4,2,5,3,6,7,8,1] => [8,2,4,1,3,5,6,7] => [1,2,5]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [4,2,5,3,1,6,7,8] => [5,2,4,1,3,6,7,8] => [1,2,5]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [4,2,1,5,3,6,7,8] => [3,2,5,1,4,6,7,8] => [1,2,5]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [1,4,2,5,3,6,7,8] => [1,3,5,2,4,6,7,8] => [3,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [4,3,5,6,7,8,2,1] => [8,7,2,1,3,4,5,6] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [4,3,5,6,7,1,8,2] => [6,8,2,1,3,4,5,7] => [2,1,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [4,3,5,6,2,7,8,1] => [8,5,2,1,3,4,6,7] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [4,3,5,1,6,2,7,8] => [4,6,2,1,3,5,7,8] => [2,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [4,3,5,2,6,7,8,1] => [8,4,2,1,3,5,6,7] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [4,3,5,2,6,1,7,8] => [6,4,2,1,3,5,7,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [4,3,5,2,1,6,7,8] => [5,4,2,1,3,6,7,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [4,3,1,5,2,6,7,8] => [3,5,2,1,4,6,7,8] => [2,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [4,3,2,5,6,7,8,1] => [8,3,2,1,4,5,6,7] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [4,3,2,5,6,7,1,8] => [7,3,2,1,4,5,6,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => [4,3,2,5,6,1,7,8] => [6,3,2,1,4,5,7,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [4,3,2,5,1,6,7,8] => [5,3,2,1,4,6,7,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [1,1,1,5]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [1,4,3,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [2,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [2,4,3,5,6,7,8,1] => [8,1,3,2,4,5,6,7] => [1,2,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [2,4,3,5,6,7,1,8] => [7,1,3,2,4,5,6,8] => [1,2,5]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [2,4,3,5,1,6,7,8] => [5,1,3,2,4,6,7,8] => [1,2,5]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => [4,1,3,2,5,6,7,8] => [1,2,5]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [1,2,5]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [3,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [3,4,5,6,7,8,2,1] => [8,7,1,2,3,4,5,6] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [3,4,5,6,7,1,8,2] => [6,8,1,2,3,4,5,7] => [2,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [3,4,5,6,7,2,8,1] => [8,6,1,2,3,4,5,7] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [3,4,5,6,7,2,1,8] => [7,6,1,2,3,4,5,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [3,4,5,6,1,7,2,8] => [5,7,1,2,3,4,6,8] => [2,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [3,4,5,6,2,7,8,1] => [8,5,1,2,3,4,6,7] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [3,4,5,6,2,7,1,8] => [7,5,1,2,3,4,6,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [3,4,5,6,2,1,7,8] => [6,5,1,2,3,4,7,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,6,1,2,3,4,7,8] => [3,4,5,1,6,2,7,8] => [4,6,1,2,3,5,7,8] => [2,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [3,4,5,2,6,7,8,1] => [8,4,1,2,3,5,6,7] => [1,1,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [3,4,5,2,6,7,1,8] => [7,4,1,2,3,5,6,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [3,4,5,2,6,1,7,8] => [6,4,1,2,3,5,7,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [3,4,5,2,1,6,7,8] => [5,4,1,2,3,6,7,8] => [1,1,6]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [3,4,1,5,2,6,7,8] => [3,5,1,2,4,6,7,8] => [2,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [3,4,2,5,6,7,8,1] => [8,3,1,2,4,5,6,7] => [1,1,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [3,4,2,5,6,7,1,8] => [7,3,1,2,4,5,6,8] => [1,1,6]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [3,4,2,5,6,1,7,8] => [6,3,1,2,4,5,7,8] => [1,1,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [3,4,2,5,1,6,7,8] => [5,3,1,2,4,6,7,8] => [1,1,6]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [3,4,2,1,5,6,7,8] => [4,3,1,2,5,6,7,8] => [1,1,6]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => [2,4,1,3,5,6,7,8] => [2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [3,2,4,5,6,7,8,1] => [8,2,1,3,4,5,6,7] => [1,1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [3,2,4,5,6,7,1,8] => [7,2,1,3,4,5,6,8] => [1,1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => [3,2,4,5,6,1,7,8] => [6,2,1,3,4,5,7,8] => [1,1,6]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [3,2,4,5,1,6,7,8] => [5,2,1,3,4,6,7,8] => [1,1,6]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [3,2,4,1,5,6,7,8] => [4,2,1,3,5,6,7,8] => [1,1,6]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [1,1,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [2,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => [1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => [1,7]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => [1,7]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [1,7]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [1,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [1,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => [3,2,4,5,6,7,8,9,1] => [9,2,1,3,4,5,6,7,8] => [1,1,7]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [1,7,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [9,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [1,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [3,2,4,5,6,7,8,9,10,1] => [10,2,1,3,4,5,6,7,8,9] => [1,1,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => [3,4,2,5,6,7,8,9,1] => [9,3,1,2,4,5,6,7,8] => [1,1,7]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => [2,4,3,5,6,7,8,9,1] => [9,1,3,2,4,5,6,7,8] => [1,2,6]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [2,3,1,4,5,6,7,9,8] => [3,1,2,4,5,6,7,9,8] => [1,7,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [2,6,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [1,8,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [10,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [2,3,4,5,6,7,8,9,10,11,12,1] => [12,1,2,3,4,5,6,7,8,9,10,11] => [1,11]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,1,3,4,5,6,7,8,9,10] => [3,2,4,5,6,7,8,9,10,11,1] => [11,2,1,3,4,5,6,7,8,9,10] => [1,1,9]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [3,4,2,5,6,7,8,9,10,1] => [10,3,1,2,4,5,6,7,8,9] => [1,1,8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [9,4,1,2,3,5,6,7,8] => [3,4,5,2,6,7,8,9,1] => [9,4,1,2,3,5,6,7,8] => [1,1,7]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [3,2,1,4,5,6,7,9,8] => [3,2,1,4,5,6,7,9,8] => [1,1,6,1]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,10,1] => [1,3,2,4,5,6,7,8,10,9] => [1,3,2,4,5,6,7,8,10,9] => [2,7,1]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => [2,1,3,4,5,6,7,8,9,11,10] => [2,1,3,4,5,6,7,8,9,11,10] => [1,9,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [12,2,1,3,4,5,6,7,8,9,10,11] => [3,2,4,5,6,7,8,9,10,11,12,1] => [12,2,1,3,4,5,6,7,8,9,10,11] => [1,1,10]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,1,2,4,5,6,7,8,9,10] => [3,4,2,5,6,7,8,9,10,11,1] => [11,3,1,2,4,5,6,7,8,9,10] => [1,1,9]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => [3,4,5,2,6,7,8,9,10,1] => [10,4,1,2,3,5,6,7,8,9] => [1,1,8]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,1,6,7,8] => [2,3,4,6,5,7,8,9,1] => [9,1,2,3,5,4,6,7,8] => [1,4,4]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,1,6,7,8,9] => [2,3,4,6,5,7,8,9,10,1] => [10,1,2,3,5,4,6,7,8,9] => [1,4,5]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => [3,4,5,6,7,2,8,9,1] => [9,6,1,2,3,4,5,7,8] => [1,1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => [3,4,5,6,7,2,8,9,10,1] => [10,6,1,2,3,4,5,7,8,9] => [1,1,8]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,1,7,8,9] => [2,3,4,5,7,6,8,9,10,1] => [10,1,2,3,4,6,5,7,8,9] => [1,5,4]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [3,4,5,6,7,8,2,9,1] => [9,7,1,2,3,4,5,6,8] => [1,1,7]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => [2,3,4,5,6,8,7,9,1] => [9,1,2,3,4,5,7,6,8] => [1,6,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [3,4,5,6,7,8,1,9,2] => [7,9,1,2,3,4,5,6,8] => [2,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,7,1,9,8] => [7,1,2,3,4,5,6,9,8] => [1,7,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,7,9,6,8] => [7,2]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [6,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => [3,4,5,6,7,8,2,9,10,1] => [10,7,1,2,3,4,5,6,8,9] => [1,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [3,4,5,6,7,8,9,2,1] => [9,8,1,2,3,4,5,6,7] => [1,1,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,9,8,1] => [9,1,2,3,4,5,6,8,7] => [1,7,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,9,8,7] => [7,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [3,4,5,6,7,8,9,1,10,2] => [8,10,1,2,3,4,5,6,7,9] => [2,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [2,3,4,5,6,7,8,1,10,9] => [8,1,2,3,4,5,6,7,10,9] => [1,8,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [1,2,3,4,5,6,9,7,10,8] => [1,2,3,4,5,6,8,10,7,9] => [8,2]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,10,1] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [7,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [3,4,5,6,7,8,9,10,2,1] => [10,9,1,2,3,4,5,6,7,8] => [1,1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,10,9,1] => [10,1,2,3,4,5,6,7,9,8] => [1,8,1]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,10,9,8] => [8,1,1]
[] => [] => [] => [] => []
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [1,8,7,6,5,4,3,2,9] => [1,8,7,6,5,4,3,2,9] => [2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [2,1,8,7,6,5,4,3,9] => [2,1,8,7,6,5,4,3,9] => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,1,9] => [1,2,8,7,6,5,4,3,9] => [1,2,8,7,6,5,4,3,9] => [3,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [4,8,7,6,5,3,2,1,9] => [8,7,6,1,5,4,3,2,9] => [1,1,1,2,1,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,2,1,9] => [5,4,3,2,1,8,7,6,9] => [5,4,3,2,1,8,7,6,9] => [1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => [6,5,4,3,2,1,8,7,9] => [6,5,4,3,2,1,8,7,9] => [1,1,1,1,1,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [1,2,2,2,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,8,7,1,9] => [8,1,2,3,4,5,7,6,9] => [1,6,2]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [1,6,2]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [7,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [7,8,6,5,4,3,2,1,9] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [7,5,3,1,8,6,4,2,9] => [4,8,3,7,2,6,1,5,9] => [2,2,2,3]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [1,2,3,4,7,5,8,6,9] => [1,2,3,4,6,8,5,7,9] => [6,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => [7,6,8,5,4,3,2,1,9] => [8,7,6,5,4,2,1,3,9] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => [7,6,5,8,4,3,2,1,9] => [8,7,6,5,3,2,1,4,9] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1,5,9] => [7,6,5,4,8,3,2,1,9] => [8,7,6,4,3,2,1,5,9] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1,6,9] => [7,6,5,4,3,8,2,1,9] => [8,7,5,4,3,2,1,6,9] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => [7,6,5,4,3,2,8,1,9] => [8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,4,3,2,1,8,9] => [1,7,6,5,4,3,2,8,9] => [1,7,6,5,4,3,2,8,9] => [2,1,1,1,1,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,1,8,9] => [5,4,3,2,1,7,6,8,9] => [5,4,3,2,1,7,6,8,9] => [1,1,1,1,2,3]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [6,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => [6,7,8,5,4,3,2,1,9] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,4]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,1,2,8,9] => [6,4,3,2,1,7,5,8,9] => [5,4,3,2,7,1,6,8,9] => [1,1,1,2,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [1,1,1,1,1,4]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,1,7,8,9] => [4,3,2,1,6,5,7,8,9] => [4,3,2,1,6,5,7,8,9] => [1,1,1,2,4]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,2,6,1,7,8,9] => [2,1,4,3,6,5,7,8,9] => [2,1,4,3,6,5,7,8,9] => [1,2,2,4]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [5,4]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [5,1,6,2,7,3,8,4,9] => [2,4,6,8,1,3,5,7,9] => [4,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => [5,6,4,3,2,1,7,8,9] => [6,5,4,3,1,2,7,8,9] => [1,1,1,1,5]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => [5,3,1,6,4,2,7,8,9] => [3,6,2,5,1,4,7,8,9] => [2,2,5]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => [5,4,6,3,7,2,8,1,9] => [8,6,4,2,1,3,5,7,9] => [1,1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [1,1,1,1,5]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => [1,1,2,5]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [2,2,5]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [4,5]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [4,1,5,2,6,3,7,8,9] => [2,4,6,1,3,5,7,8,9] => [3,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1,2,4,6,8,9] => [4,5,3,6,2,7,1,8,9] => [7,5,3,1,2,4,6,8,9] => [1,1,1,6]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1,2,6,7,8,9] => [4,5,3,2,1,6,7,8,9] => [5,4,3,1,2,6,7,8,9] => [1,1,1,6]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,1,2,6,7,8,9] => [4,2,1,5,3,6,7,8,9] => [3,2,5,1,4,6,7,8,9] => [1,2,6]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => [1,4,2,5,3,6,7,8,9] => [1,3,5,2,4,6,7,8,9] => [3,6]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [1,1,1,6]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [2,1,6]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [4,1,3,2,5,6,7,8,9] => [1,2,6]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [1,2,6]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [3,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [3,4,5,6,7,1,8,2,9] => [6,8,1,2,3,4,5,7,9] => [2,7]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => [1,1,7]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [2,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [3,2,4,5,6,7,8,1,9] => [8,2,1,3,4,5,6,7,9] => [1,1,7]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [1,1,7]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [2,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [2,3,4,5,6,1,7,8,9] => [6,1,2,3,4,5,7,8,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [1,8]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [1,8]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [1,8]
[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] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [2,1,9,8,7,6,5,4,3] => [2,1,9,8,7,6,5,4,3] => [1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [3,2,1,9,8,7,6,5,4] => [3,2,1,9,8,7,6,5,4] => [1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [4,3,2,1,9,8,7,6,5] => [4,3,2,1,9,8,7,6,5] => [1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [5,4,3,2,1,9,8,7,6] => [5,4,3,2,1,9,8,7,6] => [1,1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [6,5,4,3,2,1,9,8,7] => [6,5,4,3,2,1,9,8,7] => [1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [7,6,5,4,3,2,1,9,8] => [7,6,5,4,3,2,1,9,8] => [1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [1,2,9,8,7,6,5,4,3] => [1,2,9,8,7,6,5,4,3] => [3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => [1,2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [3,2,1,10,9,8,7,6,5,4] => [3,2,1,10,9,8,7,6,5,4] => [1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,10,9,8,7,6,5] => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [5,4,3,2,1,10,9,8,7,6] => [5,4,3,2,1,10,9,8,7,6] => [1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7] => [1,1,1,1,1,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [6,7,5,4,3,2,1,9,8] => [7,6,5,4,3,1,2,9,8] => [1,1,1,1,1,3,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [7,6,5,4,3,2,1,10,9,8] => [7,6,5,4,3,2,1,10,9,8] => [1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [1,1,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,10,9,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [1,2,10,9,8,7,6,5,4,3] => [1,2,10,9,8,7,6,5,4,3] => [3,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [2,1,11,10,9,8,7,6,5,4,3] => [2,1,11,10,9,8,7,6,5,4,3] => [1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [1,2,3,9,8,7,6,5,4] => [1,2,3,9,8,7,6,5,4] => [4,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => [8,9,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,1,2,10] => [1,1,1,1,1,1,1,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [9,8,7,6,5,4,3,2,1,11,10] => [9,8,7,6,5,4,3,2,1,11,10] => [1,1,1,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [1,1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,10,9,8,7,6,5,4] => [4,1,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => [8,7,9,6,5,4,3,2,1,10] => [9,8,7,6,5,4,2,1,3,10] => [1,1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,9,8,7,6,5] => [5,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => [8,7,6,9,5,4,3,2,1,10] => [9,8,7,6,5,3,2,1,4,10] => [1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,2,1,3,11] => [9,8,10,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,2,1,3,11] => [1,1,1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,10,9,8,7,6,5] => [5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,3,2,1,4,11] => [9,8,7,10,6,5,4,3,2,1,11] => [10,9,8,7,6,5,3,2,1,4,11] => [1,1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => [8,7,6,5,4,9,3,2,1,10] => [9,8,7,5,4,3,2,1,6,10] => [1,1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,9,8,7,6] => [6,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => [8,7,6,5,4,3,9,2,1,10] => [9,8,6,5,4,3,2,1,7,10] => [1,1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,10,9,8,7,6] => [6,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,5,4,3,2,1,6,11] => [9,8,7,6,5,10,4,3,2,1,11] => [10,9,8,7,5,4,3,2,1,6,11] => [1,1,1,1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,1,2,3,4,5,10] => [5,6,7,8,9,4,3,2,1,10] => [9,8,7,6,1,2,3,4,5,10] => [1,1,1,1,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => [8,7,6,5,4,3,2,9,1,10] => [9,7,6,5,4,3,2,1,8,10] => [1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [10,9,8,6,5,4,3,2,1,7,11] => [9,8,7,6,5,4,10,3,2,1,11] => [10,9,8,6,5,4,3,2,1,7,11] => [1,1,1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,2,1] => [2,9,8,7,6,5,4,3,1] => [9,1,8,7,6,5,4,3,2] => [1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => [3,1,9,8,7,6,5,4,2] => [2,9,1,8,7,6,5,4,3] => [2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,4,3,2,1] => [4,9,8,7,6,5,3,2,1] => [9,8,7,1,6,5,4,3,2] => [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] => [9,8,7,6,4,5,3,2,1] => [5,9,8,7,6,4,3,2,1] => [9,8,7,6,1,5,4,3,2] => [1,1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,2,1] => [6,9,8,7,5,4,3,2,1] => [9,8,7,6,5,1,4,3,2] => [1,1,1,1,1,2,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => [2,3,4,5,6,9,8,7,1] => [9,1,2,3,4,5,8,7,6] => [1,6,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => [7,9,8,6,5,4,3,2,1] => [9,8,7,6,5,4,1,3,2] => [1,1,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,3,1] => [7,1,9,8,6,5,4,3,2] => [2,9,8,7,6,5,1,4,3] => [2,1,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [8,9,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,1,2] => [8,1,9,7,6,5,4,3,2] => [2,9,8,7,6,5,4,1,3] => [2,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => [8,2,9,7,6,5,4,3,1] => [9,2,8,7,6,5,4,1,3] => [1,2,1,1,1,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [8,6,9,7,5,4,3,2,1] => [9,8,7,6,5,2,4,1,3] => [1,1,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [8,6,4,9,7,5,3,2,1] => [9,8,7,3,6,2,5,1,4] => [1,1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [8,6,4,2,9,7,5,3,1] => [9,4,8,3,7,2,6,1,5] => [1,2,2,2,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [7,8,9,6,5,4,3,2,1] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [7,4,1,8,5,2,9,6,3] => [3,6,9,2,5,8,1,4,7] => [3,3,3]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [1,2,3,7,4,8,5,9,6] => [1,2,3,5,7,9,4,6,8] => [6,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [6,7,8,9,5,4,3,2,1] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [6,2,7,3,8,4,9,5,1] => [9,2,4,6,8,1,3,5,7] => [1,4,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [1,6,2,7,3,8,4,9,5] => [1,3,5,7,9,2,4,6,8] => [5,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [5,6,7,8,9,4,3,2,1] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [5,6,1,7,2,8,3,9,4] => [3,5,7,9,1,2,4,6,8] => [4,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [4,5,6,7,8,9,3,2,1] => [9,8,7,1,2,3,4,5,6] => [1,1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [4,5,6,7,8,2,9,3,1] => [9,6,8,1,2,3,4,5,7] => [1,2,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [4,5,6,7,1,8,2,9,3] => [5,7,9,1,2,3,4,6,8] => [3,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [10,8,9,7,6,5,4,3,2,1] => [2,10,9,8,7,6,5,4,3,1] => [10,1,9,8,7,6,5,4,3,2] => [1,2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [9,10,7,8,6,5,4,3,2,1] => [3,1,10,9,8,7,6,5,4,2] => [2,10,1,9,8,7,6,5,4,3] => [2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,5,4,3,2,1] => [4,10,9,8,7,6,5,3,2,1] => [10,9,8,1,7,6,5,4,3,2] => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,4,3,2,1] => [5,10,9,8,7,6,4,3,2,1] => [10,9,8,7,1,6,5,4,3,2] => [1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,10,9,8,7] => [7,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => [2,3,4,5,6,7,10,9,8,1] => [10,1,2,3,4,5,6,9,8,7] => [1,7,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,3,1] => [8,10,9,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,1,3,2] => [1,1,1,1,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [9,10,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,1,2] => [9,1,10,8,7,6,5,4,3,2] => [2,10,9,8,7,6,5,4,1,3] => [2,1,1,1,1,1,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [9,7,10,8,6,5,4,3,2,1] => [10,9,8,7,6,5,2,4,1,3] => [1,1,1,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [9,7,5,10,8,6,4,3,2,1] => [10,9,8,7,3,6,2,5,1,4] => [1,1,1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [9,7,5,3,10,8,6,4,2,1] => [10,9,4,8,3,7,2,6,1,5] => [1,1,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [9,7,5,3,1,10,8,6,4,2] => [5,10,4,9,3,8,2,7,1,6] => [2,2,2,2,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [8,9,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [8,5,9,6,3,1,10,7,4,2] => [6,10,5,9,2,4,8,1,3,7] => [2,2,3,3]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [1,2,3,4,8,5,9,6,10,7] => [1,2,3,4,6,8,10,5,7,9] => [7,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [7,8,9,10,6,5,4,3,2,1] => [10,9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [7,8,9,5,3,1,10,6,4,2] => [6,10,5,9,4,8,1,2,3,7] => [2,2,2,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [7,3,8,4,9,5,1,10,6,2] => [7,10,2,4,6,9,1,3,5,8] => [2,4,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [1,2,7,3,8,4,9,5,10,6] => [1,2,4,6,8,10,3,5,7,9] => [6,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [6,7,8,9,10,5,4,3,2,1] => [10,9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [6,1,7,2,8,3,9,4,10,5] => [2,4,6,8,10,1,3,5,7,9] => [5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [5,6,7,8,9,10,4,3,2,1] => [10,9,8,7,1,2,3,4,5,6] => [1,1,1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [5,6,7,1,8,2,9,3,10,4] => [4,6,8,10,1,2,3,5,7,9] => [4,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [4,5,6,7,8,9,10,3,2,1] => [10,9,8,1,2,3,4,5,6,7] => [1,1,1,7]
[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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => [8,7,9,6,5,4,3,2,1] => [9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,1,4] => [8,7,6,9,5,4,3,2,1] => [9,8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,1,5] => [8,7,6,5,9,4,3,2,1] => [9,8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,3,2,1,6] => [8,7,6,5,4,9,3,2,1] => [9,8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => [8,7,6,5,4,3,9,2,1] => [9,8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => [8,7,6,5,4,3,2,9,1] => [9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,1,3] => [9,8,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => [9,8,7,10,6,5,4,3,2,1] => [10,9,8,7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => [9,8,7,6,10,5,4,3,2,1] => [10,9,8,7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => [9,8,7,6,5,10,4,3,2,1] => [10,9,8,7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => [9,8,7,6,5,4,10,3,2,1] => [10,9,8,6,5,4,3,2,1,7] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => [9,8,7,6,5,4,3,10,2,1] => [10,9,7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => [9,8,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,1,2] => [10,11,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [1,9,8,7,6,5,4,3,2,10] => [1,9,8,7,6,5,4,3,2,10] => [2,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [2,8]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => [1,3,2,4,5,6,7,8,9,10,11] => [1,3,2,4,5,6,7,8,9,10,11] => [2,9]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [2,3,1,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => [1,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,1,2] => [9,2,1,10,8,7,6,5,4,3] => [3,2,10,9,8,7,6,5,1,4] => [1,2,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,1,3] => [8,7,1,9,6,5,4,3,2] => [3,9,8,7,6,5,2,1,4] => [2,1,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [7,6,5,4,3,2,8,9,1] => [9,6,5,4,3,2,1,7,8] => [1,1,1,1,1,1,3]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [8,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => [1,9]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,3,4,5,6,7,8,9,10,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => [1,10]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [1,9]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [3,7]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [4,6]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [5,5]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [6,4]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [7,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,1,10] => [7,6,5,4,3,2,1,9,8,10] => [7,6,5,4,3,2,1,9,8,10] => [1,1,1,1,1,1,2,2]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [1,10]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,9,7,6,4,3,2,1,5] => [8,7,6,5,1,9,4,3,2] => [5,9,8,7,4,3,2,1,6] => [2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,5,3,2,1,10] => [5,9,8,7,6,4,3,2,1,10] => [9,8,7,6,1,5,4,3,2,10] => [1,1,1,1,2,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => [7,8,6,5,4,3,2,9,1] => [9,7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,9,1] => [1,7,6,5,4,3,2,9,8] => [1,7,6,5,4,3,2,9,8] => [2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,1,7] => [8,7,6,5,4,3,1,9,2] => [7,9,6,5,4,3,2,1,8] => [2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,1,2] => [8,6,5,4,3,2,1,9,7] => [7,6,5,4,3,2,9,1,8] => [1,1,1,1,1,2,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [1,1,1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,1,2,3,4] => [6,2,1,7,3,8,4,9,5] => [3,2,5,7,9,1,4,6,8] => [1,4,4]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [2,3,4,5,6,7,8,1,9,10] => [8,1,2,3,4,5,6,7,9,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [1,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [9,7,8,5,4,3,2,1,6] => [8,7,6,5,4,2,9,3,1] => [9,6,8,5,4,3,2,1,7] => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,9,3,2,1,10] => [5,4,3,2,1,9,8,7,6,10] => [5,4,3,2,1,9,8,7,6,10] => [1,1,1,1,2,1,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1,10] => [6,5,4,3,2,1,9,8,7,10] => [6,5,4,3,2,1,9,8,7,10] => [1,1,1,1,1,2,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,1,10,11] => [9,8,7,6,5,4,3,2,1,10,11] => [9,8,7,6,5,4,3,2,1,10,11] => [1,1,1,1,1,1,1,1,3]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [3,1,4,2,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => [2,8]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [4,1,5,2,6,3,7,8,9,10] => [2,4,6,1,3,5,7,8,9,10] => [3,7]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [5,1,6,2,7,3,8,4,9,10] => [2,4,6,8,1,3,5,7,9,10] => [4,6]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => [5,6,1,7,2,8,3,9,4,10] => [3,5,7,9,1,2,4,6,8,10] => [4,6]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [6,5,7,4,8,3,9,2,10,1] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [1,2,2,2,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [6,5,7,4,8,3,9,2,10,1] => [10,8,6,4,2,1,3,5,7,9] => [1,1,1,1,1,5]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [1,2,2,2,2,2,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [11]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => [8,7,6,5,4,3,2,9,10,1] => [10,7,6,5,4,3,2,1,8,9] => [1,1,1,1,1,1,1,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,5,4,3,2,1,6,7,8] => [6,5,4,3,2,7,8,9,1] => [9,5,4,3,2,1,6,7,8] => [1,1,1,1,1,4]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [1,2,7]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [9,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [3,4,5,6,7,8,9,10,1,11,2] => [9,11,1,2,3,4,5,6,7,8,10] => [2,9]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [1,1,1,1,1,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,4,1] => [7,6,9,8,5,4,3,2,1] => [9,8,7,6,5,2,1,4,3] => [1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [1,1,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [11,9,10,8,7,6,5,4,3,2,1] => [2,11,10,9,8,7,6,5,4,3,1] => [11,1,10,9,8,7,6,5,4,3,2] => [1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,9,2,1] => [7,6,5,4,3,2,10,9,8,1] => [10,6,5,4,3,2,1,9,8,7] => [1,1,1,1,1,1,2,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [1,1,1,1,6]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [1,1,1,7]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [2,3,4,5,6,7,8,9,1,11,10] => [9,1,2,3,4,5,6,7,8,11,10] => [1,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => [10,9,8,7,6,5,4,3,2,11,1] => [11,9,8,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,9,8,1] => [9,6,5,4,3,2,1,8,7] => [1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [3,4,5,6,7,8,1,9,2,10] => [7,9,1,2,3,4,5,6,8,10] => [2,8]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => [1,6,2,7,3,8,4,9,5,10] => [1,3,5,7,9,2,4,6,8,10] => [5,5]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [1,2,3,4,5,8,6,9,7,10] => [1,2,3,4,5,7,9,6,8,10] => [7,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,4,3,2,1,5,9] => [8,7,6,5,9,4,3,2,10,1] => [10,8,7,6,4,3,2,1,5,9] => [1,1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => [9,8,7,6,5,4,3,1,10,2] => [8,10,7,6,5,4,3,2,1,9] => [2,1,1,1,1,1,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [8,7,9,5,6,3,4,1,2] => [8,6,4,2,1,9,7,5,3] => [5,4,9,3,8,2,7,1,6] => [1,2,2,2,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => [3,4,5,6,7,8,9,10,11,2,1] => [11,10,1,2,3,4,5,6,7,8,9] => [1,1,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,8,7,6,5,4,3,2,1,9,11] => [9,8,7,6,5,4,3,2,10,1,11] => [10,8,7,6,5,4,3,2,1,9,11] => [1,1,1,1,1,1,1,1,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,2,1,3,4,5,6] => [6,5,7,1,8,2,9,3,10,4] => [4,6,8,10,2,1,3,5,7,9] => [4,1,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,10,9,1] => [10,7,6,5,4,3,2,1,9,8] => [1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,8,3,2,1] => [6,5,4,3,10,9,8,7,2,1] => [10,9,4,3,2,1,8,7,6,5] => [1,1,1,1,1,2,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,11,10,1] => [11,1,2,3,4,5,6,7,8,10,9] => [1,9,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [7,8,2,3,4,5,6,9,1] => [3,4,5,6,1,7,2,9,8] => [5,7,1,2,3,4,6,9,8] => [2,6,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => [8,9,7,6,5,4,3,2,10,1] => [10,8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,2,1] => [6,5,4,3,2,9,8,7,1] => [9,5,4,3,2,1,8,7,6] => [1,1,1,1,1,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [9,8,10,6,7,4,5,2,3,1] => [8,6,4,2,1,10,9,7,5,3] => [5,4,10,3,9,2,8,1,7,6] => [1,2,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [2,2,2,2,1]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9,10] => [2,1,4,3,6,5,8,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => [1,2,2,2,3]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,1,10] => [2,3,4,5,6,7,9,8,1,10] => [9,1,2,3,4,5,6,8,7,10] => [1,7,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => [5,6,4,7,3,8,2,9,1,10] => [9,7,5,3,1,2,4,6,8,10] => [1,1,1,1,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => [11,9,7,5,3,1,12,10,8,6,4,2] => [6,12,5,11,4,10,3,9,2,8,1,7] => [2,2,2,2,2,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => [7,5,3,1,8,6,4,2,9,10] => [4,8,3,7,2,6,1,5,9,10] => [2,2,2,4]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,11,10,9] => [9,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,10,9,1] => [10,2,1,3,4,5,6,7,9,8] => [1,1,7,1]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9,10] => [1,3,2,5,4,6,7,8,9,10] => [1,3,2,5,4,6,7,8,9,10] => [2,2,6]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [2,2,2,2,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [7,4,1,8,5,2,9,6,3,10] => [3,6,9,2,5,8,1,4,7,10] => [3,3,4]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,2,1,3,9] => [8,7,9,6,5,4,3,2,10,1] => [10,8,7,6,5,4,2,1,3,9] => [1,1,1,1,1,1,1,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,11,10,9,8,7,6,5,4,2,1,3] => [11,10,12,9,8,7,6,5,4,3,2,1] => [12,11,10,9,8,7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [5,6,4,7,3,8,2,9,1] => [9,7,5,3,1,2,4,6,8] => [1,1,1,1,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [10,8,6,5,4,3,2,1,7,9] => [8,7,6,5,4,3,9,2,10,1] => [10,8,6,5,4,3,2,1,7,9] => [1,1,1,1,1,1,1,3]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [6,4,5,7,3,8,2,9,1,10] => [2,3,1,5,4,7,6,9,8,10] => [3,1,2,5,4,7,6,9,8,10] => [1,3,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [12,10,9,8,7,6,5,4,3,2,1,11] => [11,10,9,8,7,6,5,4,3,2,12,1] => [12,10,9,8,7,6,5,4,3,2,1,11] => [1,1,1,1,1,1,1,1,1,1,2]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation σ is given by L(σ)=l1…ln with li=#{j>i:σj<σi}. In particular, li is the number of boxes in the i-th column of the Rothe diagram. For example, the Lehmer code of σ=[4,3,1,5,2] is 32010. The Lehmer code L:Sn ˜⟶ Sn is a bijection between permutations of size n and sequences l1…ln∈Nn with li≤i.
* The major code M(σ) of a permutation σ∈Sn is a way to encode a permutation as a sequence m1m2…mn with mi≥i. To define mi, let deli(σ) be the normalized permutation obtained by removing all σj<i from the one-line notation of σ. The i-th index is then given by
mi=maj(deli(σ))−maj(deli−1(σ)).
For example, the permutation [9,3,5,7,2,1,4,6,8] has major code [5,0,1,0,1,2,0,1,0] since
maj([8,2,4,6,1,3,5,7])=5,maj([7,1,3,5,2,4,6])=5,maj([6,2,4,1,3,5])=4,
maj([5,1,3,2,4])=4,maj([4,2,1,3])=3,maj([3,1,2])=1,maj([2,1])=1.
Observe that the sum of the major code of σ equals the major index of σ.
Map
inverse
Description
Sends a permutation to its inverse.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.