Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Images
[1,0] => [1] => [1] => [1]
[1,0,1,0] => [2,1] => [2,1] => [2,1]
[1,1,0,0] => [1,2] => [1,2] => [1,2]
[1,0,1,0,1,0] => [3,2,1] => [3,2,1] => [2,3,1]
[1,0,1,1,0,0] => [2,3,1] => [2,3,1] => [3,2,1]
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => [1,3,2]
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [2,1,3]
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,2,3]
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1] => [2,3,4,1]
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [3,4,2,1] => [2,4,3,1]
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [2,4,3,1] => [3,2,4,1]
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [4,3,2,1]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => [4,2,3,1]
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,4,3,2] => [1,3,4,2]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [1,3,4,2] => [1,4,3,2]
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [2,4,1,3] => [4,2,1,3]
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1,4] => [2,3,1,4]
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [2,3,1,4] => [3,2,1,4]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,2,4,3] => [1,2,4,3]
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,3,2,4] => [1,3,2,4]
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1] => [2,3,4,5,1]
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [4,5,3,2,1] => [2,3,5,4,1]
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [3,5,4,2,1] => [2,4,3,5,1]
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [4,3,5,2,1] => [2,5,4,3,1]
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,4,5,2,1] => [2,5,3,4,1]
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [2,5,4,3,1] => [3,2,4,5,1]
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [2,4,5,3,1] => [3,2,5,4,1]
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [3,5,2,4,1] => [4,5,3,2,1]
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [5,3,4,2,1]
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,4,2,5,1] => [5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [2,3,5,4,1] => [4,2,3,5,1]
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,5,1] => [5,2,4,3,1]
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => [5,3,2,4,1]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => [5,2,3,4,1]
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,5,4,3,2] => [1,3,4,5,2]
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [1,4,5,3,2] => [1,3,5,4,2]
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,3,5,4,2] => [1,4,3,5,2]
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [1,4,3,5,2] => [1,5,4,3,2]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,3,4,5,2] => [1,5,3,4,2]
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [2,5,4,1,3] => [4,2,1,5,3]
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [2,4,5,1,3] => [5,2,1,4,3]
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4]
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [4,3,2,1,5] => [2,3,4,1,5]
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,4,2,1,5] => [2,4,3,1,5]
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [2,3,5,1,4] => [5,2,3,1,4]
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [2,4,3,1,5] => [3,2,4,1,5]
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,2,4,1,5] => [4,3,2,1,5]
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [2,3,4,1,5] => [4,2,3,1,5]
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,5,4,3] => [1,2,4,5,3]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [1,2,4,5,3] => [1,2,5,4,3]
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,3,5,2,4] => [1,5,3,2,4]
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,4,3,2,5] => [1,3,4,2,5]
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [1,3,4,2,5] => [1,4,3,2,5]
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [2,1,5,3,4] => [2,1,5,3,4]
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [2,4,1,3,5] => [4,2,1,3,5]
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5]
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [2,3,1,4,5] => [3,2,1,4,5]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,2,3,5,4] => [1,2,3,5,4]
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5]
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5]
[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]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5]
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [2,3,4,6,5,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => [2,3,5,4,6,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [2,3,6,5,4,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [2,3,6,4,5,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => [2,4,3,5,6,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [3,5,6,4,2,1] => [2,4,3,6,5,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => [2,5,6,4,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [2,6,4,5,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [2,6,5,4,3,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [3,4,6,5,2,1] => [2,5,3,4,6,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [3,5,4,6,2,1] => [2,6,3,5,4,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [2,6,4,3,5,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [2,6,3,4,5,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [2,6,5,4,3,1] => [3,2,4,5,6,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [2,5,6,4,3,1] => [3,2,4,6,5,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [2,4,6,5,3,1] => [3,2,5,4,6,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [2,5,4,6,3,1] => [3,2,6,5,4,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [2,4,5,6,3,1] => [3,2,6,4,5,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [3,6,5,2,4,1] => [4,5,3,2,6,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [3,5,6,2,4,1] => [4,6,3,2,5,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => [5,3,6,4,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [6,3,4,5,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [6,3,5,4,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [3,4,6,2,5,1] => [5,6,3,4,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => [6,4,3,5,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [6,5,4,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [6,5,3,4,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [2,3,6,5,4,1] => [4,2,3,5,6,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [2,3,5,6,4,1] => [4,2,3,6,5,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [2,4,6,3,5,1] => [5,2,6,4,3,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [2,5,4,3,6,1] => [6,2,4,5,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [2,4,5,3,6,1] => [6,2,5,4,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [3,2,6,4,5,1] => [5,3,2,6,4,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => [6,5,3,2,4,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [6,3,4,2,5,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,4,3,2,5,1]
>>> Load all 2295 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] => [5,2,3,4,6,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,5,4,6,1] => [6,2,3,5,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => [6,2,4,3,5,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [6,3,2,4,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [6,2,3,4,5,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => [1,3,4,5,6,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [1,5,6,4,3,2] => [1,3,4,6,5,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,4,6,5,3,2] => [1,3,5,4,6,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [1,5,4,6,3,2] => [1,3,6,5,4,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [1,4,5,6,3,2] => [1,3,6,4,5,2]
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,3,6,5,4,2] => [1,4,3,5,6,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [1,3,5,6,4,2] => [1,4,3,6,5,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,4,6,3,5,2] => [1,5,6,4,3,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [1,5,4,3,6,2] => [1,6,4,5,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [1,4,5,3,6,2] => [1,6,5,4,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,3,4,6,5,2] => [1,5,3,4,6,2]
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [1,3,5,4,6,2] => [1,6,3,5,4,2]
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [1,4,3,5,6,2] => [1,6,4,3,5,2]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [1,3,4,5,6,2] => [1,6,3,4,5,2]
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [2,6,5,4,1,3] => [4,2,1,5,6,3]
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [2,5,6,4,1,3] => [4,2,1,6,5,3]
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [2,4,6,5,1,3] => [5,2,1,4,6,3]
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [2,5,4,6,1,3] => [6,2,1,5,4,3]
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [2,4,5,6,1,3] => [6,2,1,4,5,3]
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [3,6,5,2,1,4] => [2,5,3,1,6,4]
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [3,5,6,2,1,4] => [2,6,3,1,5,4]
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [4,6,3,2,1,5] => [2,3,6,4,1,5]
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [2,3,4,5,1,6]
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [2,3,5,4,1,6]
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [3,4,6,2,1,5] => [2,6,3,4,1,5]
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => [2,4,3,5,1,6]
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [2,5,4,3,1,6]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [2,5,3,4,1,6]
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [2,3,6,5,1,4] => [5,2,3,1,6,4]
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [2,3,5,6,1,4] => [6,2,3,1,5,4]
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [2,4,6,3,1,5] => [3,2,6,4,1,5]
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [2,5,4,3,1,6] => [3,2,4,5,1,6]
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [2,4,5,3,1,6] => [3,2,5,4,1,6]
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [3,2,6,4,1,5] => [4,3,2,6,1,5]
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => [4,5,3,2,1,6]
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [5,3,4,2,1,6]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [5,4,3,2,1,6]
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => [6,2,3,4,1,5]
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,3,5,4,1,6] => [4,2,3,5,1,6]
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => [5,2,4,3,1,6]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [5,3,2,4,1,6]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [5,2,3,4,1,6]
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => [1,2,4,5,6,3]
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [1,2,5,6,4,3] => [1,2,4,6,5,3]
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,2,4,6,5,3] => [1,2,5,4,6,3]
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [1,2,5,4,6,3] => [1,2,6,5,4,3]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [1,2,4,5,6,3] => [1,2,6,4,5,3]
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,3,6,5,2,4] => [1,5,3,2,6,4]
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [1,3,5,6,2,4] => [1,6,3,2,5,4]
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,4,6,3,2,5] => [1,3,6,4,2,5]
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [1,5,4,3,2,6] => [1,3,4,5,2,6]
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [1,4,5,3,2,6] => [1,3,5,4,2,6]
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,3,4,6,2,5] => [1,6,3,4,2,5]
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [1,3,5,4,2,6] => [1,4,3,5,2,6]
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [1,4,3,5,2,6] => [1,5,4,3,2,6]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [1,3,4,5,2,6] => [1,5,3,4,2,6]
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [2,1,6,5,3,4] => [2,1,5,3,6,4]
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [2,1,5,6,3,4] => [2,1,6,3,5,4]
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [2,4,6,1,3,5] => [6,2,1,4,3,5]
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [2,5,4,1,3,6] => [4,2,1,5,3,6]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [2,4,5,1,3,6] => [5,2,1,4,3,6]
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [3,2,6,1,4,5] => [6,3,2,1,4,5]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [3,5,2,1,4,6] => [2,5,3,1,4,6]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [2,3,4,1,5,6]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [2,4,3,1,5,6]
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,3,1,6,4,5] => [3,2,1,6,4,5]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,3,5,1,4,6] => [5,2,3,1,4,6]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => [3,2,4,1,5,6]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [4,3,2,1,5,6]
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [4,2,3,1,5,6]
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,3,6,5,4] => [1,2,3,5,6,4]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [1,2,3,5,6,4] => [1,2,3,6,5,4]
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,2,4,6,3,5] => [1,2,6,4,3,5]
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [1,2,4,5,3,6] => [1,2,5,4,3,6]
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,3,2,6,4,5] => [1,3,2,6,4,5]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [1,3,5,2,4,6] => [1,5,3,2,4,6]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6]
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [1,3,4,2,5,6] => [1,4,3,2,5,6]
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,1,3,6,4,5] => [2,1,3,6,4,5]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,1,5,3,4,6] => [2,1,5,3,4,6]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => [4,2,1,3,5,6]
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6]
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [3,2,1,4,5,6]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6]
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6]
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6]
[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]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6]
[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] => [2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => [2,3,4,5,7,6,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [5,7,6,4,3,2,1] => [2,3,4,6,5,7,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => [2,3,4,7,6,5,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1] => [2,3,4,7,5,6,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [4,7,6,5,3,2,1] => [2,3,5,4,6,7,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [4,6,7,5,3,2,1] => [2,3,5,4,7,6,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [5,7,4,6,3,2,1] => [2,3,6,7,5,4,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => [2,3,7,5,6,4,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [5,6,4,7,3,2,1] => [2,3,7,6,5,4,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [4,5,7,6,3,2,1] => [2,3,6,4,5,7,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [4,6,5,7,3,2,1] => [2,3,7,4,6,5,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1] => [2,3,7,5,4,6,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1] => [2,3,7,4,5,6,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [3,7,6,5,4,2,1] => [2,4,3,5,6,7,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [3,6,7,5,4,2,1] => [2,4,3,5,7,6,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [3,5,7,6,4,2,1] => [2,4,3,6,5,7,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [3,6,5,7,4,2,1] => [2,4,3,7,6,5,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [3,5,6,7,4,2,1] => [2,4,3,7,5,6,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => [2,5,6,4,3,7,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [4,6,7,3,5,2,1] => [2,5,7,4,3,6,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [5,7,4,3,6,2,1] => [2,6,4,7,5,3,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => [2,7,4,5,6,3,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [5,6,4,3,7,2,1] => [2,7,4,6,5,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [4,5,7,3,6,2,1] => [2,6,7,4,5,3,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [4,6,5,3,7,2,1] => [2,7,5,4,6,3,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [5,4,6,3,7,2,1] => [2,7,6,5,4,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1] => [2,7,6,4,5,3,1]
[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] => [2,5,3,4,6,7,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [3,4,6,7,5,2,1] => [2,5,3,4,7,6,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [3,5,7,4,6,2,1] => [2,6,3,7,5,4,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [3,6,5,4,7,2,1] => [2,7,3,5,6,4,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [3,5,6,4,7,2,1] => [2,7,3,6,5,4,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [4,3,7,5,6,2,1] => [2,6,4,3,7,5,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [4,6,3,5,7,2,1] => [2,7,6,4,3,5,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1] => [2,7,4,5,3,6,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1] => [2,7,5,4,3,6,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [3,4,5,7,6,2,1] => [2,6,3,4,5,7,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [3,4,6,5,7,2,1] => [2,7,3,4,6,5,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [3,5,4,6,7,2,1] => [2,7,3,5,4,6,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1] => [2,7,4,3,5,6,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => [2,7,3,4,5,6,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [2,7,6,5,4,3,1] => [3,2,4,5,6,7,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [2,6,7,5,4,3,1] => [3,2,4,5,7,6,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [2,5,7,6,4,3,1] => [3,2,4,6,5,7,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [2,6,5,7,4,3,1] => [3,2,4,7,6,5,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [2,5,6,7,4,3,1] => [3,2,4,7,5,6,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [2,4,7,6,5,3,1] => [3,2,5,4,6,7,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [2,4,6,7,5,3,1] => [3,2,5,4,7,6,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [2,5,7,4,6,3,1] => [3,2,6,7,5,4,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [2,6,5,4,7,3,1] => [3,2,7,5,6,4,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [2,5,6,4,7,3,1] => [3,2,7,6,5,4,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [2,4,5,7,6,3,1] => [3,2,6,4,5,7,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [2,4,6,5,7,3,1] => [3,2,7,4,6,5,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [2,5,4,6,7,3,1] => [3,2,7,5,4,6,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [2,4,5,6,7,3,1] => [3,2,7,4,5,6,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [3,7,6,5,2,4,1] => [4,5,3,2,6,7,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [3,6,7,5,2,4,1] => [4,5,3,2,7,6,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [3,5,7,6,2,4,1] => [4,6,3,2,5,7,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [3,6,5,7,2,4,1] => [4,7,3,2,6,5,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [3,5,6,7,2,4,1] => [4,7,3,2,5,6,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [4,7,6,3,2,5,1] => [5,3,6,4,2,7,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [4,6,7,3,2,5,1] => [5,3,7,4,2,6,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [5,7,4,3,2,6,1] => [6,3,4,7,5,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [7,3,4,5,6,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [5,6,4,3,2,7,1] => [7,3,4,6,5,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [4,5,7,3,2,6,1] => [6,3,7,4,5,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [4,6,5,3,2,7,1] => [7,3,5,4,6,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [5,4,6,3,2,7,1] => [7,3,6,5,4,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1] => [7,3,6,4,5,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [3,4,7,6,2,5,1] => [5,6,3,4,2,7,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [3,4,6,7,2,5,1] => [5,7,3,4,2,6,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [3,5,7,4,2,6,1] => [6,4,3,7,5,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [3,6,5,4,2,7,1] => [7,4,3,5,6,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [3,5,6,4,2,7,1] => [7,4,3,6,5,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [4,3,7,5,2,6,1] => [6,5,4,3,7,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [4,6,3,5,2,7,1] => [7,5,6,4,3,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [5,4,3,6,2,7,1] => [7,6,4,5,3,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [3,4,5,7,2,6,1] => [6,7,3,4,5,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [3,4,6,5,2,7,1] => [7,5,3,4,6,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [2,3,7,6,5,4,1] => [4,2,3,5,6,7,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [2,3,6,7,5,4,1] => [4,2,3,5,7,6,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [2,3,5,7,6,4,1] => [4,2,3,6,5,7,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [2,3,6,5,7,4,1] => [4,2,3,7,6,5,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [2,3,5,6,7,4,1] => [4,2,3,7,5,6,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [2,4,7,6,3,5,1] => [5,2,6,4,3,7,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [2,4,6,7,3,5,1] => [5,2,7,4,3,6,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [2,5,7,4,3,6,1] => [6,2,4,7,5,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [2,6,5,4,3,7,1] => [7,2,4,5,6,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [2,5,6,4,3,7,1] => [7,2,4,6,5,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [2,4,5,7,3,6,1] => [6,2,7,4,5,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [2,4,6,5,3,7,1] => [7,2,5,4,6,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [2,5,4,6,3,7,1] => [7,2,6,5,4,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [2,4,5,6,3,7,1] => [7,2,6,4,5,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [3,2,7,6,4,5,1] => [5,3,2,6,4,7,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [3,2,6,7,4,5,1] => [5,3,2,7,4,6,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [3,5,7,2,4,6,1] => [6,7,3,2,5,4,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [3,6,5,2,4,7,1] => [7,5,3,2,6,4,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [3,5,6,2,4,7,1] => [7,6,3,2,5,4,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [4,3,7,2,5,6,1] => [6,7,4,3,2,5,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,6,3,2,5,7,1] => [7,3,6,4,2,5,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [7,3,4,5,2,6,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1] => [7,3,5,4,2,6,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [3,4,2,7,5,6,1] => [6,4,3,2,7,5,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,4,6,2,5,7,1] => [7,6,3,4,2,5,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [3,5,4,2,6,7,1] => [7,4,3,5,2,6,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [2,3,4,7,6,5,1] => [5,2,3,4,6,7,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [2,3,4,6,7,5,1] => [5,2,3,4,7,6,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [2,3,5,7,4,6,1] => [6,2,3,7,5,4,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [2,3,6,5,4,7,1] => [7,2,3,5,6,4,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [2,3,5,6,4,7,1] => [7,2,3,6,5,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [2,4,3,7,5,6,1] => [6,2,4,3,7,5,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [2,4,6,3,5,7,1] => [7,2,6,4,3,5,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [2,5,4,3,6,7,1] => [7,2,4,5,3,6,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [2,4,5,3,6,7,1] => [7,2,5,4,3,6,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [3,2,4,7,5,6,1] => [6,3,2,4,7,5,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,6,4,5,7,1] => [7,3,2,6,4,5,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => [7,5,3,2,4,6,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [7,3,4,2,5,6,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1]
[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] => [6,2,3,4,5,7,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => [1,3,4,5,6,7,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [1,6,7,5,4,3,2] => [1,3,4,5,7,6,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,5,7,6,4,3,2] => [1,3,4,6,5,7,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [1,6,5,7,4,3,2] => [1,3,4,7,6,5,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [1,5,6,7,4,3,2] => [1,3,4,7,5,6,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,4,7,6,5,3,2] => [1,3,5,4,6,7,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [1,4,6,7,5,3,2] => [1,3,5,4,7,6,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,5,7,4,6,3,2] => [1,3,6,7,5,4,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [1,6,5,4,7,3,2] => [1,3,7,5,6,4,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [1,5,6,4,7,3,2] => [1,3,7,6,5,4,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,4,5,7,6,3,2] => [1,3,6,4,5,7,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [1,4,6,5,7,3,2] => [1,3,7,4,6,5,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [1,5,4,6,7,3,2] => [1,3,7,5,4,6,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [1,4,5,6,7,3,2] => [1,3,7,4,5,6,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,3,7,6,5,4,2] => [1,4,3,5,6,7,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [1,3,6,7,5,4,2] => [1,4,3,5,7,6,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,3,5,7,6,4,2] => [1,4,3,6,5,7,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [1,3,6,5,7,4,2] => [1,4,3,7,6,5,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [1,3,5,6,7,4,2] => [1,4,3,7,5,6,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,4,7,6,3,5,2] => [1,5,6,4,3,7,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [1,4,6,7,3,5,2] => [1,5,7,4,3,6,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,5,7,4,3,6,2] => [1,6,4,7,5,3,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [1,6,5,4,3,7,2] => [1,7,4,5,6,3,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [1,5,6,4,3,7,2] => [1,7,4,6,5,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,4,5,7,3,6,2] => [1,6,7,4,5,3,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [1,4,6,5,3,7,2] => [1,7,5,4,6,3,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,3,4,7,6,5,2] => [1,5,3,4,6,7,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [1,3,4,6,7,5,2] => [1,5,3,4,7,6,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,3,5,7,4,6,2] => [1,6,3,7,5,4,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [1,3,6,5,4,7,2] => [1,7,3,5,6,4,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,4,3,7,5,6,2] => [1,6,4,3,7,5,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [1,4,6,3,5,7,2] => [1,7,6,4,3,5,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [1,5,4,3,6,7,2] => [1,7,4,5,3,6,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,3,4,5,7,6,2] => [1,6,3,4,5,7,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [2,7,6,5,4,1,3] => [4,2,1,5,6,7,3]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [2,6,7,5,4,1,3] => [4,2,1,5,7,6,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [2,5,7,6,4,1,3] => [4,2,1,6,5,7,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [2,6,5,7,4,1,3] => [4,2,1,7,6,5,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [2,5,6,7,4,1,3] => [4,2,1,7,5,6,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [2,4,7,6,5,1,3] => [5,2,1,4,6,7,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [2,4,6,7,5,1,3] => [5,2,1,4,7,6,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [2,5,7,4,6,1,3] => [6,2,1,7,5,4,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [2,6,5,4,7,1,3] => [7,2,1,5,6,4,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [2,5,6,4,7,1,3] => [7,2,1,6,5,4,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [2,4,5,7,6,1,3] => [6,2,1,4,5,7,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [2,4,6,5,7,1,3] => [7,2,1,4,6,5,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [2,5,4,6,7,1,3] => [7,2,1,5,4,6,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [2,4,5,6,7,1,3] => [7,2,1,4,5,6,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [3,7,6,5,2,1,4] => [2,5,3,1,6,7,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [3,6,7,5,2,1,4] => [2,5,3,1,7,6,4]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [3,5,7,6,2,1,4] => [2,6,3,1,5,7,4]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [3,6,5,7,2,1,4] => [2,7,3,1,6,5,4]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [3,5,6,7,2,1,4] => [2,7,3,1,5,6,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [4,7,6,3,2,1,5] => [2,3,6,4,1,7,5]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [4,6,7,3,2,1,5] => [2,3,7,4,1,6,5]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [5,7,4,3,2,1,6] => [2,3,4,7,5,1,6]
[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] => [2,3,4,5,6,1,7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => [2,3,4,6,5,1,7]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [4,5,7,3,2,1,6] => [2,3,7,4,5,1,6]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [4,6,5,3,2,1,7] => [2,3,5,4,6,1,7]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => [2,3,6,5,4,1,7]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => [2,3,6,4,5,1,7]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [3,4,7,6,2,1,5] => [2,6,3,4,1,7,5]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [3,4,6,7,2,1,5] => [2,7,3,4,1,6,5]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [3,5,7,4,2,1,6] => [2,4,3,7,5,1,6]
[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] => [2,4,3,5,6,1,7]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [3,5,6,4,2,1,7] => [2,4,3,6,5,1,7]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [4,3,7,5,2,1,6] => [2,5,4,3,7,1,6]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => [2,5,6,4,3,1,7]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => [2,6,4,5,3,1,7]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => [2,6,5,4,3,1,7]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [3,4,5,7,2,1,6] => [2,7,3,4,5,1,6]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [3,4,6,5,2,1,7] => [2,5,3,4,6,1,7]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [3,5,4,6,2,1,7] => [2,6,3,5,4,1,7]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7] => [2,6,4,3,5,1,7]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => [2,6,3,4,5,1,7]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [2,3,7,6,5,1,4] => [5,2,3,1,6,7,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [2,3,6,7,5,1,4] => [5,2,3,1,7,6,4]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [2,3,5,7,6,1,4] => [6,2,3,1,5,7,4]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [2,3,6,5,7,1,4] => [7,2,3,1,6,5,4]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [2,3,5,6,7,1,4] => [7,2,3,1,5,6,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [2,4,7,6,3,1,5] => [3,2,6,4,1,7,5]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [2,4,6,7,3,1,5] => [3,2,7,4,1,6,5]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [2,5,7,4,3,1,6] => [3,2,4,7,5,1,6]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [2,6,5,4,3,1,7] => [3,2,4,5,6,1,7]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [2,5,6,4,3,1,7] => [3,2,4,6,5,1,7]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [2,4,5,7,3,1,6] => [3,2,7,4,5,1,6]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [2,4,6,5,3,1,7] => [3,2,5,4,6,1,7]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [2,5,4,6,3,1,7] => [3,2,6,5,4,1,7]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [2,4,5,6,3,1,7] => [3,2,6,4,5,1,7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [3,2,7,6,4,1,5] => [4,3,2,6,1,7,5]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [3,2,6,7,4,1,5] => [4,3,2,7,1,6,5]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [3,5,7,2,4,1,6] => [4,7,3,2,5,1,6]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [3,6,5,2,4,1,7] => [4,5,3,2,6,1,7]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [3,5,6,2,4,1,7] => [4,6,3,2,5,1,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [4,3,7,2,5,1,6] => [5,7,4,3,2,1,6]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [4,6,3,2,5,1,7] => [5,3,6,4,2,1,7]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [6,3,4,5,2,1,7]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1,7] => [6,3,5,4,2,1,7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [3,4,2,7,5,1,6] => [5,4,3,2,7,1,6]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [3,4,6,2,5,1,7] => [5,6,3,4,2,1,7]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [3,5,4,2,6,1,7] => [6,4,3,5,2,1,7]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [2,3,4,7,6,1,5] => [6,2,3,4,1,7,5]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [2,3,4,6,7,1,5] => [7,2,3,4,1,6,5]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [2,3,5,7,4,1,6] => [4,2,3,7,5,1,6]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [2,3,6,5,4,1,7] => [4,2,3,5,6,1,7]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [2,3,5,6,4,1,7] => [4,2,3,6,5,1,7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [2,4,3,7,5,1,6] => [5,2,4,3,7,1,6]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [2,4,6,3,5,1,7] => [5,2,6,4,3,1,7]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [2,5,4,3,6,1,7] => [6,2,4,5,3,1,7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [3,2,4,7,5,1,6] => [5,3,2,4,7,1,6]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [3,2,6,4,5,1,7] => [5,3,2,6,4,1,7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [3,5,2,4,6,1,7] => [6,5,3,2,4,1,7]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [6,3,4,2,5,1,7]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [2,3,4,5,7,1,6] => [7,2,3,4,5,1,6]
[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] => [5,2,3,4,6,1,7]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => [1,2,4,5,6,7,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [1,2,6,7,5,4,3] => [1,2,4,5,7,6,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,2,5,7,6,4,3] => [1,2,4,6,5,7,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [1,2,6,5,7,4,3] => [1,2,4,7,6,5,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [1,2,5,6,7,4,3] => [1,2,4,7,5,6,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,4,7,6,5,3] => [1,2,5,4,6,7,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [1,2,4,6,7,5,3] => [1,2,5,4,7,6,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,2,5,7,4,6,3] => [1,2,6,7,5,4,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [1,2,6,5,4,7,3] => [1,2,7,5,6,4,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,3,7,6,5,2,4] => [1,5,3,2,6,7,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [1,3,6,7,5,2,4] => [1,5,3,2,7,6,4]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,3,5,7,6,2,4] => [1,6,3,2,5,7,4]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [1,3,6,5,7,2,4] => [1,7,3,2,6,5,4]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [1,3,5,6,7,2,4] => [1,7,3,2,5,6,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,4,7,6,3,2,5] => [1,3,6,4,2,7,5]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [1,4,6,7,3,2,5] => [1,3,7,4,2,6,5]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,5,7,4,3,2,6] => [1,3,4,7,5,2,6]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => [1,3,4,5,6,2,7]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [1,5,6,4,3,2,7] => [1,3,4,6,5,2,7]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,4,5,7,3,2,6] => [1,3,7,4,5,2,6]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [1,4,6,5,3,2,7] => [1,3,5,4,6,2,7]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [1,5,4,6,3,2,7] => [1,3,6,5,4,2,7]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [1,4,5,6,3,2,7] => [1,3,6,4,5,2,7]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,3,4,7,6,2,5] => [1,6,3,4,2,7,5]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [1,3,4,6,7,2,5] => [1,7,3,4,2,6,5]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,3,5,7,4,2,6] => [1,4,3,7,5,2,6]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [1,3,6,5,4,2,7] => [1,4,3,5,6,2,7]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [1,3,5,6,4,2,7] => [1,4,3,6,5,2,7]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,4,3,7,5,2,6] => [1,5,4,3,7,2,6]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [1,4,6,3,5,2,7] => [1,5,6,4,3,2,7]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [1,5,4,3,6,2,7] => [1,6,4,5,3,2,7]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,3,4,5,7,2,6] => [1,7,3,4,5,2,6]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [1,3,4,6,5,2,7] => [1,5,3,4,6,2,7]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [2,1,7,6,5,3,4] => [2,1,5,3,6,7,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [2,1,6,7,5,3,4] => [2,1,5,3,7,6,4]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [2,1,5,7,6,3,4] => [2,1,6,3,5,7,4]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [2,1,6,5,7,3,4] => [2,1,7,3,6,5,4]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [2,1,5,6,7,3,4] => [2,1,7,3,5,6,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [2,4,7,6,1,3,5] => [6,2,1,4,3,7,5]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [2,4,6,7,1,3,5] => [7,2,1,4,3,6,5]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [2,5,7,4,1,3,6] => [4,2,1,7,5,3,6]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [2,6,5,4,1,3,7] => [4,2,1,5,6,3,7]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [2,5,6,4,1,3,7] => [4,2,1,6,5,3,7]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [2,4,5,7,1,3,6] => [7,2,1,4,5,3,6]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [2,4,6,5,1,3,7] => [5,2,1,4,6,3,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [2,5,4,6,1,3,7] => [6,2,1,5,4,3,7]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [2,4,5,6,1,3,7] => [6,2,1,4,5,3,7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [3,2,7,6,1,4,5] => [6,3,2,1,4,7,5]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [3,2,6,7,1,4,5] => [7,3,2,1,4,6,5]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [3,5,7,2,1,4,6] => [2,7,3,1,5,4,6]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [3,6,5,2,1,4,7] => [2,5,3,1,6,4,7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [3,5,6,2,1,4,7] => [2,6,3,1,5,4,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [4,3,7,2,1,5,6] => [2,7,4,3,1,5,6]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [4,6,3,2,1,5,7] => [2,3,6,4,1,5,7]
[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] => [2,3,4,5,1,6,7]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7] => [2,3,5,4,1,6,7]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [3,4,2,7,1,5,6] => [7,4,3,2,1,5,6]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [3,4,6,2,1,5,7] => [2,6,3,4,1,5,7]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [3,5,4,2,1,6,7] => [2,4,3,5,1,6,7]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7] => [2,5,4,3,1,6,7]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => [2,5,3,4,1,6,7]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [2,3,1,7,6,4,5] => [3,2,1,6,4,7,5]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [2,3,1,6,7,4,5] => [3,2,1,7,4,6,5]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [2,3,5,7,1,4,6] => [7,2,3,1,5,4,6]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [2,3,6,5,1,4,7] => [5,2,3,1,6,4,7]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [2,3,5,6,1,4,7] => [6,2,3,1,5,4,7]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [2,4,3,7,1,5,6] => [7,2,4,3,1,5,6]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [2,4,6,3,1,5,7] => [3,2,6,4,1,5,7]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [2,5,4,3,1,6,7] => [3,2,4,5,1,6,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [2,4,5,3,1,6,7] => [3,2,5,4,1,6,7]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [3,2,4,7,1,5,6] => [7,3,2,4,1,5,6]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [3,2,6,4,1,5,7] => [4,3,2,6,1,5,7]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [3,5,2,4,1,6,7] => [4,5,3,2,1,6,7]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [5,3,4,2,1,6,7]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [2,3,4,1,7,5,6] => [4,2,3,1,7,5,6]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [2,3,4,6,1,5,7] => [6,2,3,4,1,5,7]
[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] => [4,2,3,5,1,6,7]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => [1,2,3,5,6,7,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [1,2,3,6,7,5,4] => [1,2,3,5,7,6,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,4,7,6,3,5] => [1,2,6,4,3,7,5]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [1,2,4,6,7,3,5] => [1,2,7,4,3,6,5]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,2,5,7,4,3,6] => [1,2,4,7,5,3,6]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7] => [1,2,4,5,6,3,7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [1,2,5,6,4,3,7] => [1,2,4,6,5,3,7]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,2,4,5,7,3,6] => [1,2,7,4,5,3,6]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,3,2,7,6,4,5] => [1,3,2,6,4,7,5]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [1,3,2,6,7,4,5] => [1,3,2,7,4,6,5]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,3,5,7,2,4,6] => [1,7,3,2,5,4,6]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [1,3,6,5,2,4,7] => [1,5,3,2,6,4,7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [1,3,5,6,2,4,7] => [1,6,3,2,5,4,7]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,4,3,7,2,5,6] => [1,7,4,3,2,5,6]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [1,4,6,3,2,5,7] => [1,3,6,4,2,5,7]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [1,5,4,3,2,6,7] => [1,3,4,5,2,6,7]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [1,4,5,3,2,6,7] => [1,3,5,4,2,6,7]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,3,4,2,7,5,6] => [1,4,3,2,7,5,6]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [1,3,4,6,2,5,7] => [1,6,3,4,2,5,7]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [2,1,3,7,6,4,5] => [2,1,3,6,4,7,5]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [2,1,3,6,7,4,5] => [2,1,3,7,4,6,5]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [2,1,5,7,3,4,6] => [2,1,7,3,5,4,6]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [2,1,6,5,3,4,7] => [2,1,5,3,6,4,7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [2,1,5,6,3,4,7] => [2,1,6,3,5,4,7]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [2,4,1,7,3,5,6] => [4,2,7,1,3,5,6]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [2,4,6,1,3,5,7] => [6,2,1,4,3,5,7]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [2,5,4,1,3,6,7] => [4,2,1,5,3,6,7]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [2,4,5,1,3,6,7] => [5,2,1,4,3,6,7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [3,2,1,7,4,5,6] => [2,3,1,7,4,5,6]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [3,2,6,1,4,5,7] => [6,3,2,1,4,5,7]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [3,5,2,1,4,6,7] => [2,5,3,1,4,6,7]
[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] => [2,3,4,1,5,6,7]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => [2,4,3,1,5,6,7]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [2,3,1,4,7,5,6] => [3,2,1,4,7,5,6]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [2,3,1,6,4,5,7] => [3,2,1,6,4,5,7]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [2,3,5,1,4,6,7] => [5,2,3,1,4,6,7]
[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] => [3,2,4,1,5,6,7]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,2,3,5,7,4,6] => [1,2,3,7,5,4,6]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,2,4,3,7,5,6] => [1,2,4,3,7,5,6]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [1,2,4,6,3,5,7] => [1,2,6,4,3,5,7]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,3,2,4,7,5,6] => [1,3,2,4,7,5,6]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [1,3,2,6,4,5,7] => [1,3,2,6,4,5,7]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [1,3,5,2,4,6,7] => [1,5,3,2,4,6,7]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [2,1,3,4,7,5,6] => [2,1,3,4,7,5,6]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [2,1,3,6,4,5,7] => [2,1,3,6,4,5,7]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [2,1,5,3,4,6,7] => [2,1,5,3,4,6,7]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7]
[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] => [2,3,1,4,5,6,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7]
[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]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[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] => [2,3,4,5,6,7,8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [6,8,7,5,4,3,2,1] => [2,3,4,5,7,6,8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [7,6,8,5,4,3,2,1] => [2,3,4,5,8,7,6,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [6,7,8,5,4,3,2,1] => [2,3,4,5,8,6,7,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [5,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [5,7,8,6,4,3,2,1] => [2,3,4,6,5,8,7,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [6,8,5,7,4,3,2,1] => [2,3,4,7,8,6,5,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [7,6,5,8,4,3,2,1] => [2,3,4,8,6,7,5,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [6,7,5,8,4,3,2,1] => [2,3,4,8,7,6,5,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [5,6,8,7,4,3,2,1] => [2,3,4,7,5,6,8,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [5,7,6,8,4,3,2,1] => [2,3,4,8,5,7,6,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [6,5,7,8,4,3,2,1] => [2,3,4,8,6,5,7,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [5,6,7,8,4,3,2,1] => [2,3,4,8,5,6,7,1]
[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] => [2,3,5,4,6,7,8,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [4,7,8,6,5,3,2,1] => [2,3,5,4,6,8,7,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [4,6,8,7,5,3,2,1] => [2,3,5,4,7,6,8,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [4,7,6,8,5,3,2,1] => [2,3,5,4,8,7,6,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [4,6,7,8,5,3,2,1] => [2,3,5,4,8,6,7,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [5,8,7,4,6,3,2,1] => [2,3,6,7,5,4,8,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,3,2,1] => [5,7,8,4,6,3,2,1] => [2,3,6,8,5,4,7,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [6,8,5,4,7,3,2,1] => [2,3,7,5,8,6,4,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1] => [2,3,8,5,6,7,4,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [6,7,5,4,8,3,2,1] => [2,3,8,5,7,6,4,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [5,6,8,4,7,3,2,1] => [2,3,7,8,5,6,4,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [5,7,6,4,8,3,2,1] => [2,3,8,6,5,7,4,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [6,5,7,4,8,3,2,1] => [2,3,8,7,6,5,4,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [5,6,7,4,8,3,2,1] => [2,3,8,7,5,6,4,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [4,5,8,7,6,3,2,1] => [2,3,6,4,5,7,8,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,2,1] => [4,5,7,8,6,3,2,1] => [2,3,6,4,5,8,7,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [4,6,8,5,7,3,2,1] => [2,3,7,4,8,6,5,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [4,7,6,5,8,3,2,1] => [2,3,8,4,6,7,5,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [4,6,7,5,8,3,2,1] => [2,3,8,4,7,6,5,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,2,1] => [5,4,8,6,7,3,2,1] => [2,3,7,5,4,8,6,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [5,7,4,6,8,3,2,1] => [2,3,8,7,5,4,6,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [6,5,4,7,8,3,2,1] => [2,3,8,5,6,4,7,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [5,6,4,7,8,3,2,1] => [2,3,8,6,5,4,7,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [4,5,6,8,7,3,2,1] => [2,3,7,4,5,6,8,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [4,5,7,6,8,3,2,1] => [2,3,8,4,5,7,6,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [4,6,5,7,8,3,2,1] => [2,3,8,4,6,5,7,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [5,4,6,7,8,3,2,1] => [2,3,8,5,4,6,7,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [4,5,6,7,8,3,2,1] => [2,3,8,4,5,6,7,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [3,8,7,6,5,4,2,1] => [2,4,3,5,6,7,8,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [3,7,8,6,5,4,2,1] => [2,4,3,5,6,8,7,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [3,6,8,7,5,4,2,1] => [2,4,3,5,7,6,8,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [3,7,6,8,5,4,2,1] => [2,4,3,5,8,7,6,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,2,1] => [3,6,7,8,5,4,2,1] => [2,4,3,5,8,6,7,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [3,5,8,7,6,4,2,1] => [2,4,3,6,5,7,8,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [3,5,7,8,6,4,2,1] => [2,4,3,6,5,8,7,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,2,1] => [3,6,8,5,7,4,2,1] => [2,4,3,7,8,6,5,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [3,7,6,5,8,4,2,1] => [2,4,3,8,6,7,5,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [3,5,6,8,7,4,2,1] => [2,4,3,7,5,6,8,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,2,1] => [3,5,7,6,8,4,2,1] => [2,4,3,8,5,7,6,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [3,6,5,7,8,4,2,1] => [2,4,3,8,6,5,7,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [3,5,6,7,8,4,2,1] => [2,4,3,8,5,6,7,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [4,8,7,6,3,5,2,1] => [2,5,6,4,3,7,8,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [4,7,8,6,3,5,2,1] => [2,5,6,4,3,8,7,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [4,6,8,7,3,5,2,1] => [2,5,7,4,3,6,8,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [4,7,6,8,3,5,2,1] => [2,5,8,4,3,7,6,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [4,6,7,8,3,5,2,1] => [2,5,8,4,3,6,7,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [5,8,7,4,3,6,2,1] => [2,6,4,7,5,3,8,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [5,7,8,4,3,6,2,1] => [2,6,4,8,5,3,7,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [6,8,5,4,3,7,2,1] => [2,7,4,5,8,6,3,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,3,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [6,7,5,4,3,8,2,1] => [2,8,4,5,7,6,3,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,7,2,1] => [5,6,8,4,3,7,2,1] => [2,7,4,8,5,6,3,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [5,7,6,4,3,8,2,1] => [2,8,4,6,5,7,3,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [6,5,7,4,3,8,2,1] => [2,8,4,7,6,5,3,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [5,6,7,4,3,8,2,1] => [2,8,4,7,5,6,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [4,5,8,7,3,6,2,1] => [2,6,7,4,5,3,8,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,7,2,1] => [4,6,8,5,3,7,2,1] => [2,7,5,4,8,6,3,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [4,7,6,5,3,8,2,1] => [2,8,5,4,6,7,3,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [4,6,7,5,3,8,2,1] => [2,8,5,4,7,6,3,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [5,4,8,6,3,7,2,1] => [2,7,6,5,4,8,3,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [5,7,4,6,3,8,2,1] => [2,8,6,7,5,4,3,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [6,5,4,7,3,8,2,1] => [2,8,7,5,6,4,3,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,2,1] => [5,6,4,7,3,8,2,1] => [2,8,7,6,5,4,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [4,5,7,6,3,8,2,1] => [2,8,6,4,5,7,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [4,6,5,7,3,8,2,1] => [2,8,7,4,6,5,3,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,8,2,1] => [2,8,7,5,4,6,3,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [4,5,6,7,3,8,2,1] => [2,8,7,4,5,6,3,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [3,4,8,7,6,5,2,1] => [2,5,3,4,6,7,8,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [3,4,7,8,6,5,2,1] => [2,5,3,4,6,8,7,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [3,4,6,8,7,5,2,1] => [2,5,3,4,7,6,8,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [3,4,7,6,8,5,2,1] => [2,5,3,4,8,7,6,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [3,4,6,7,8,5,2,1] => [2,5,3,4,8,6,7,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [3,5,7,8,4,6,2,1] => [2,6,3,8,5,4,7,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [3,7,6,5,4,8,2,1] => [2,8,3,5,6,7,4,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,8,2,1] => [3,6,7,5,4,8,2,1] => [2,8,3,5,7,6,4,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,7,2,1] => [3,5,6,8,4,7,2,1] => [2,7,3,8,5,6,4,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,8,2,1] => [3,6,5,7,4,8,2,1] => [2,8,3,7,6,5,4,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,2,1] => [3,5,6,7,4,8,2,1] => [2,8,3,7,5,6,4,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [4,3,8,7,5,6,2,1] => [2,6,4,3,7,5,8,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,2,1] => [4,3,7,8,5,6,2,1] => [2,6,4,3,8,5,7,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [4,6,8,3,5,7,2,1] => [2,7,8,4,3,6,5,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [4,7,6,3,5,8,2,1] => [2,8,6,4,3,7,5,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [5,4,8,3,6,7,2,1] => [2,7,8,5,4,3,6,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [5,7,4,3,6,8,2,1] => [2,8,4,7,5,3,6,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [6,5,4,3,7,8,2,1] => [2,8,4,5,6,3,7,1]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,2,1] => [5,6,4,3,7,8,2,1] => [2,8,4,6,5,3,7,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,2,1] => [4,5,7,3,6,8,2,1] => [2,8,7,4,5,3,6,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,2,1] => [5,4,6,3,7,8,2,1] => [2,8,6,5,4,3,7,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,2,1] => [4,5,6,3,7,8,2,1] => [2,8,6,4,5,3,7,1]
[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] => [2,6,3,4,5,7,8,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [3,4,5,7,8,6,2,1] => [2,6,3,4,5,8,7,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,7,2,1] => [3,4,6,8,5,7,2,1] => [2,7,3,4,8,6,5,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [3,4,7,6,5,8,2,1] => [2,8,3,4,6,7,5,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [3,5,4,8,6,7,2,1] => [2,7,3,5,4,8,6,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [3,5,7,4,6,8,2,1] => [2,8,3,7,5,4,6,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [3,6,5,4,7,8,2,1] => [2,8,3,5,6,4,7,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [4,3,5,8,6,7,2,1] => [2,7,4,3,5,8,6,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,8,2,1] => [4,3,7,5,6,8,2,1] => [2,8,4,3,7,5,6,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,2,1] => [4,6,3,5,7,8,2,1] => [2,8,6,4,3,5,7,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [5,4,3,6,7,8,2,1] => [2,8,4,5,3,6,7,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,2,1] => [4,5,3,6,7,8,2,1] => [2,8,5,4,3,6,7,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [3,4,5,6,8,7,2,1] => [2,7,3,4,5,6,8,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [3,4,5,7,6,8,2,1] => [2,8,3,4,5,7,6,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [3,4,6,5,7,8,2,1] => [2,8,3,4,6,5,7,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [3,5,4,6,7,8,2,1] => [2,8,3,5,4,6,7,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,8,2,1] => [2,8,4,3,5,6,7,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [3,4,5,6,7,8,2,1] => [2,8,3,4,5,6,7,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [2,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [2,7,8,6,5,4,3,1] => [3,2,4,5,6,8,7,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [2,6,8,7,5,4,3,1] => [3,2,4,5,7,6,8,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [2,7,6,8,5,4,3,1] => [3,2,4,5,8,7,6,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [2,5,8,7,6,4,3,1] => [3,2,4,6,5,7,8,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,3,1] => [2,5,7,8,6,4,3,1] => [3,2,4,6,5,8,7,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [2,6,8,5,7,4,3,1] => [3,2,4,7,8,6,5,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [2,7,6,5,8,4,3,1] => [3,2,4,8,6,7,5,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [2,6,7,5,8,4,3,1] => [3,2,4,8,7,6,5,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [2,5,6,8,7,4,3,1] => [3,2,4,7,5,6,8,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [2,5,7,6,8,4,3,1] => [3,2,4,8,5,7,6,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,3,1] => [2,6,5,7,8,4,3,1] => [3,2,4,8,6,5,7,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [2,5,6,7,8,4,3,1] => [3,2,4,8,5,6,7,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [2,4,8,7,6,5,3,1] => [3,2,5,4,6,7,8,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,2,3,1] => [2,4,7,8,6,5,3,1] => [3,2,5,4,6,8,7,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [2,4,6,8,7,5,3,1] => [3,2,5,4,7,6,8,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [2,4,6,7,8,5,3,1] => [3,2,5,4,8,6,7,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [2,5,8,7,4,6,3,1] => [3,2,6,7,5,4,8,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [2,6,8,5,4,7,3,1] => [3,2,7,5,8,6,4,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [2,7,6,5,4,8,3,1] => [3,2,8,5,6,7,4,1]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,3,1] => [2,6,7,5,4,8,3,1] => [3,2,8,5,7,6,4,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [2,5,7,6,4,8,3,1] => [3,2,8,6,5,7,4,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [2,6,5,7,4,8,3,1] => [3,2,8,7,6,5,4,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,3,1] => [2,5,6,7,4,8,3,1] => [3,2,8,7,5,6,4,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [2,4,5,7,8,6,3,1] => [3,2,6,4,5,8,7,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [2,4,6,8,5,7,3,1] => [3,2,7,4,8,6,5,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [2,4,7,6,5,8,3,1] => [3,2,8,4,6,7,5,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [2,4,6,7,5,8,3,1] => [3,2,8,4,7,6,5,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,3,1] => [2,5,7,4,6,8,3,1] => [3,2,8,7,5,4,6,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,2,3,1] => [2,6,5,4,7,8,3,1] => [3,2,8,5,6,4,7,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,2,3,1] => [2,5,6,4,7,8,3,1] => [3,2,8,6,5,4,7,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [2,4,5,6,8,7,3,1] => [3,2,7,4,5,6,8,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,2,3,1] => [2,4,6,5,7,8,3,1] => [3,2,8,4,6,5,7,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,3,1] => [2,5,4,6,7,8,3,1] => [3,2,8,5,4,6,7,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [2,4,5,6,7,8,3,1] => [3,2,8,4,5,6,7,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [3,8,7,6,5,2,4,1] => [4,5,3,2,6,7,8,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [3,7,8,6,5,2,4,1] => [4,5,3,2,6,8,7,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [3,6,8,7,5,2,4,1] => [4,5,3,2,7,6,8,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [3,7,6,8,5,2,4,1] => [4,5,3,2,8,7,6,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [3,6,7,8,5,2,4,1] => [4,5,3,2,8,6,7,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [3,5,8,7,6,2,4,1] => [4,6,3,2,5,7,8,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,4,1] => [3,5,7,8,6,2,4,1] => [4,6,3,2,5,8,7,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [3,6,8,5,7,2,4,1] => [4,7,3,2,8,6,5,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [3,7,6,5,8,2,4,1] => [4,8,3,2,6,7,5,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [3,6,7,5,8,2,4,1] => [4,8,3,2,7,6,5,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [3,5,6,8,7,2,4,1] => [4,7,3,2,5,6,8,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,4,1] => [3,5,7,6,8,2,4,1] => [4,8,3,2,5,7,6,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,4,1] => [3,6,5,7,8,2,4,1] => [4,8,3,2,6,5,7,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [3,5,6,7,8,2,4,1] => [4,8,3,2,5,6,7,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [4,8,7,6,3,2,5,1] => [5,3,6,4,2,7,8,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [4,7,8,6,3,2,5,1] => [5,3,6,4,2,8,7,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [4,7,6,8,3,2,5,1] => [5,3,8,4,2,7,6,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [4,6,7,8,3,2,5,1] => [5,3,8,4,2,6,7,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [5,8,7,4,3,2,6,1] => [6,3,4,7,5,2,8,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [5,7,8,4,3,2,6,1] => [6,3,4,8,5,2,7,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [6,8,5,4,3,2,7,1] => [7,3,4,5,8,6,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => [8,3,4,5,6,7,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,8,1] => [8,3,4,5,7,6,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [5,6,8,4,3,2,7,1] => [7,3,4,8,5,6,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => [5,7,6,4,3,2,8,1] => [8,3,4,6,5,7,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,8,1] => [8,3,4,7,6,5,2,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [5,6,7,4,3,2,8,1] => [8,3,4,7,5,6,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [4,6,8,5,3,2,7,1] => [7,3,5,4,8,6,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [4,7,6,5,3,2,8,1] => [8,3,5,4,6,7,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [4,6,7,5,3,2,8,1] => [8,3,5,4,7,6,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,8,1] => [5,7,4,6,3,2,8,1] => [8,3,6,7,5,4,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [6,5,4,7,3,2,8,1] => [8,3,7,5,6,4,2,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,8,1] => [5,6,4,7,3,2,8,1] => [8,3,7,6,5,4,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [4,5,7,6,3,2,8,1] => [8,3,6,4,5,7,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [4,6,5,7,3,2,8,1] => [8,3,7,4,6,5,2,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,8,1] => [5,4,6,7,3,2,8,1] => [8,3,7,5,4,6,2,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [4,5,6,7,3,2,8,1] => [8,3,7,4,5,6,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [3,4,8,7,6,2,5,1] => [5,6,3,4,2,7,8,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [3,4,7,8,6,2,5,1] => [5,6,3,4,2,8,7,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [3,4,6,8,7,2,5,1] => [5,7,3,4,2,6,8,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [3,4,7,6,8,2,5,1] => [5,8,3,4,2,7,6,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [3,4,6,7,8,2,5,1] => [5,8,3,4,2,6,7,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [3,5,8,7,4,2,6,1] => [6,4,3,7,5,2,8,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [3,5,7,8,4,2,6,1] => [6,4,3,8,5,2,7,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [3,6,8,5,4,2,7,1] => [7,4,3,5,8,6,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [3,7,6,5,4,2,8,1] => [8,4,3,5,6,7,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [3,5,6,8,4,2,7,1] => [7,4,3,8,5,6,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [3,5,7,6,4,2,8,1] => [8,4,3,6,5,7,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [3,6,5,7,4,2,8,1] => [8,4,3,7,6,5,2,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,8,1] => [3,5,6,7,4,2,8,1] => [8,4,3,7,5,6,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [4,3,8,7,5,2,6,1] => [6,5,4,3,7,2,8,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [4,3,7,8,5,2,6,1] => [6,5,4,3,8,2,7,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [4,6,8,3,5,2,7,1] => [7,5,8,4,3,6,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [4,7,6,3,5,2,8,1] => [8,5,6,4,3,7,2,1]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,8,1] => [4,6,7,3,5,2,8,1] => [8,5,7,4,3,6,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [5,4,8,3,6,2,7,1] => [7,6,8,5,4,3,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [5,7,4,3,6,2,8,1] => [8,6,4,7,5,3,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,8,1] => [8,7,4,5,6,3,2,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,8,1] => [5,6,4,3,7,2,8,1] => [8,7,4,6,5,3,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [4,5,3,8,6,2,7,1] => [7,6,5,4,3,8,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [4,5,7,3,6,2,8,1] => [8,6,7,4,5,3,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [4,6,5,3,7,2,8,1] => [8,7,5,4,6,3,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,6,1] => [3,4,5,7,8,2,6,1] => [6,8,3,4,5,2,7,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [3,4,6,8,5,2,7,1] => [7,5,3,4,8,6,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [3,4,7,6,5,2,8,1] => [8,5,3,4,6,7,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,2,7,1] => [3,5,4,8,6,2,7,1] => [7,6,3,5,4,8,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [3,5,7,4,6,2,8,1] => [8,6,3,7,5,4,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [3,6,5,4,7,2,8,1] => [8,7,3,5,6,4,2,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [3,5,6,4,7,2,8,1] => [8,7,3,6,5,4,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [4,3,5,8,6,2,7,1] => [7,6,4,3,5,8,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [4,6,3,5,7,2,8,1] => [8,7,6,4,3,5,2,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [5,4,3,6,7,2,8,1] => [8,7,4,5,3,6,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [3,4,5,6,8,2,7,1] => [7,8,3,4,5,6,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [3,4,5,7,6,2,8,1] => [8,6,3,4,5,7,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [3,4,6,5,7,2,8,1] => [8,7,3,4,6,5,2,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,2,8,1] => [3,5,4,6,7,2,8,1] => [8,7,3,5,4,6,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [4,3,5,6,7,2,8,1] => [8,7,4,3,5,6,2,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [3,4,5,6,7,2,8,1] => [8,7,3,4,5,6,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [2,3,8,7,6,5,4,1] => [4,2,3,5,6,7,8,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [2,3,6,8,7,5,4,1] => [4,2,3,5,7,6,8,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [2,3,7,6,8,5,4,1] => [4,2,3,5,8,7,6,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [2,3,6,7,8,5,4,1] => [4,2,3,5,8,6,7,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [2,3,5,8,7,6,4,1] => [4,2,3,6,5,7,8,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [2,3,5,7,8,6,4,1] => [4,2,3,6,5,8,7,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [2,3,6,8,5,7,4,1] => [4,2,3,7,8,6,5,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [2,3,7,6,5,8,4,1] => [4,2,3,8,6,7,5,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [2,3,6,7,5,8,4,1] => [4,2,3,8,7,6,5,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [2,3,5,6,8,7,4,1] => [4,2,3,7,5,6,8,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [2,3,6,5,7,8,4,1] => [4,2,3,8,6,5,7,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [2,3,5,6,7,8,4,1] => [4,2,3,8,5,6,7,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [2,4,8,7,6,3,5,1] => [5,2,6,4,3,7,8,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,3,5,1] => [2,4,7,8,6,3,5,1] => [5,2,6,4,3,8,7,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => [2,4,6,8,7,3,5,1] => [5,2,7,4,3,6,8,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => [2,4,7,6,8,3,5,1] => [5,2,8,4,3,7,6,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [2,4,6,7,8,3,5,1] => [5,2,8,4,3,6,7,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [2,5,8,7,4,3,6,1] => [6,2,4,7,5,3,8,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,3,6,1] => [2,5,7,8,4,3,6,1] => [6,2,4,8,5,3,7,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [2,6,8,5,4,3,7,1] => [7,2,4,5,8,6,3,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [2,7,6,5,4,3,8,1] => [8,2,4,5,6,7,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [2,5,6,8,4,3,7,1] => [7,2,4,8,5,6,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [2,5,7,6,4,3,8,1] => [8,2,4,6,5,7,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [2,6,5,7,4,3,8,1] => [8,2,4,7,6,5,3,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [2,5,6,7,4,3,8,1] => [8,2,4,7,5,6,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,7,1] => [2,4,6,8,5,3,7,1] => [7,2,5,4,8,6,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [2,4,7,6,5,3,8,1] => [8,2,5,4,6,7,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [2,4,6,7,5,3,8,1] => [8,2,5,4,7,6,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,2,3,7,1] => [2,5,4,8,6,3,7,1] => [7,2,6,5,4,8,3,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [2,5,7,4,6,3,8,1] => [8,2,6,7,5,4,3,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [2,5,6,4,7,3,8,1] => [8,2,7,6,5,4,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [2,4,5,7,6,3,8,1] => [8,2,6,4,5,7,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [2,4,6,5,7,3,8,1] => [8,2,7,4,6,5,3,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [2,5,4,6,7,3,8,1] => [8,2,7,5,4,6,3,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [2,4,5,6,7,3,8,1] => [8,2,7,4,5,6,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [3,2,8,7,6,4,5,1] => [5,3,2,6,4,7,8,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [3,2,7,8,6,4,5,1] => [5,3,2,6,4,8,7,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [3,2,6,8,7,4,5,1] => [5,3,2,7,4,6,8,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [3,2,6,7,8,4,5,1] => [5,3,2,8,4,6,7,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [3,5,8,7,2,4,6,1] => [6,7,3,2,5,4,8,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [3,6,8,5,2,4,7,1] => [7,5,3,2,8,6,4,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [3,7,6,5,2,4,8,1] => [8,5,3,2,6,7,4,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [3,6,7,5,2,4,8,1] => [8,5,3,2,7,6,4,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,4,8,1] => [3,5,7,6,2,4,8,1] => [8,6,3,2,5,7,4,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [4,3,8,7,2,5,6,1] => [6,7,4,3,2,5,8,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [4,3,7,8,2,5,6,1] => [6,8,4,3,2,5,7,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [4,6,8,3,2,5,7,1] => [7,3,8,4,2,6,5,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,8,1] => [4,7,6,3,2,5,8,1] => [8,3,6,4,2,7,5,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [4,6,7,3,2,5,8,1] => [8,3,7,4,2,6,5,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [5,4,8,3,2,6,7,1] => [7,3,8,5,4,2,6,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,7,8,1] => [8,3,4,5,6,2,7,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,8,1] => [4,5,7,3,2,6,8,1] => [8,3,7,4,5,2,6,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,2,7,8,1] => [4,6,5,3,2,7,8,1] => [8,3,5,4,6,2,7,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [5,4,6,3,2,7,8,1] => [8,3,6,5,4,2,7,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [4,5,6,3,2,7,8,1] => [8,3,6,4,5,2,7,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [3,4,2,7,8,5,6,1] => [6,4,3,2,8,5,7,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,5,7,1] => [3,4,6,8,2,5,7,1] => [7,8,3,4,2,6,5,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,5,8,1] => [3,4,7,6,2,5,8,1] => [8,6,3,4,2,7,5,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [3,5,4,8,2,6,7,1] => [7,8,3,5,4,2,6,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,8,1] => [3,5,7,4,2,6,8,1] => [8,4,3,7,5,2,6,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [3,6,5,4,2,7,8,1] => [8,4,3,5,6,2,7,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,8,1] => [3,5,6,4,2,7,8,1] => [8,4,3,6,5,2,7,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,8,1] => [4,6,3,5,2,7,8,1] => [8,5,6,4,3,2,7,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [5,4,3,6,2,7,8,1] => [8,6,4,5,3,2,7,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,8,1] => [4,5,3,6,2,7,8,1] => [8,6,5,4,3,2,7,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [3,4,5,2,8,6,7,1] => [7,5,3,4,2,8,6,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,6,8,1] => [3,4,5,7,2,6,8,1] => [8,7,3,4,5,2,6,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [3,4,6,5,2,7,8,1] => [8,5,3,4,6,2,7,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,8,1] => [3,5,4,6,2,7,8,1] => [8,6,3,5,4,2,7,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [4,3,5,6,2,7,8,1] => [8,6,4,3,5,2,7,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [3,4,5,6,2,7,8,1] => [8,6,3,4,5,2,7,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [2,3,4,8,7,6,5,1] => [5,2,3,4,6,7,8,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [2,3,4,7,8,6,5,1] => [5,2,3,4,6,8,7,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [2,3,4,6,8,7,5,1] => [5,2,3,4,7,6,8,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [2,3,4,7,6,8,5,1] => [5,2,3,4,8,7,6,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [2,3,4,6,7,8,5,1] => [5,2,3,4,8,6,7,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,6,1] => [2,3,5,7,8,4,6,1] => [6,2,3,8,5,4,7,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [2,3,7,6,5,4,8,1] => [8,2,3,5,6,7,4,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [2,3,5,7,6,4,8,1] => [8,2,3,6,5,7,4,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [2,3,5,6,7,4,8,1] => [8,2,3,7,5,6,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [2,4,3,7,8,5,6,1] => [6,2,4,3,8,5,7,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [2,4,6,8,3,5,7,1] => [7,2,8,4,3,6,5,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [2,4,7,6,3,5,8,1] => [8,2,6,4,3,7,5,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [2,5,4,8,3,6,7,1] => [7,2,8,5,4,3,6,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [2,5,7,4,3,6,8,1] => [8,2,4,7,5,3,6,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [2,6,5,4,3,7,8,1] => [8,2,4,5,6,3,7,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => [2,5,6,4,3,7,8,1] => [8,2,4,6,5,3,7,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [2,4,5,3,8,6,7,1] => [7,2,5,4,3,8,6,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [2,4,5,7,3,6,8,1] => [8,2,7,4,5,3,6,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [2,4,6,5,3,7,8,1] => [8,2,5,4,6,3,7,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => [2,5,4,6,3,7,8,1] => [8,2,6,5,4,3,7,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [2,4,5,6,3,7,8,1] => [8,2,6,4,5,3,7,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [3,2,4,7,8,5,6,1] => [6,3,2,4,8,5,7,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [3,2,7,6,4,5,8,1] => [8,3,2,6,4,7,5,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [3,2,6,7,4,5,8,1] => [8,3,2,7,4,6,5,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [3,5,7,2,4,6,8,1] => [8,7,3,2,5,4,6,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [3,6,5,2,4,7,8,1] => [8,5,3,2,6,4,7,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [4,3,2,8,5,6,7,1] => [7,3,4,2,8,5,6,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [4,3,7,2,5,6,8,1] => [8,7,4,3,2,5,6,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,8,1] => [8,3,4,5,2,6,7,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [4,5,3,2,6,7,8,1] => [8,3,5,4,2,6,7,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [3,4,2,5,8,6,7,1] => [7,4,3,2,5,8,6,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,2,5,6,8,1] => [3,4,2,7,5,6,8,1] => [8,4,3,2,7,5,6,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [3,5,4,2,6,7,8,1] => [8,4,3,5,2,6,7,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [4,3,5,2,6,7,8,1] => [8,5,4,3,2,6,7,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,8,1] => [8,5,3,4,2,6,7,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [2,3,4,5,8,7,6,1] => [6,2,3,4,5,7,8,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [2,3,4,5,7,8,6,1] => [6,2,3,4,5,8,7,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [2,3,4,6,8,5,7,1] => [7,2,3,4,8,6,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [2,3,4,7,6,5,8,1] => [8,2,3,4,6,7,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [2,3,4,6,7,5,8,1] => [8,2,3,4,7,6,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,7,1] => [2,3,5,4,8,6,7,1] => [7,2,3,5,4,8,6,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [2,3,5,7,4,6,8,1] => [8,2,3,7,5,4,6,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [2,3,6,5,4,7,8,1] => [8,2,3,5,6,4,7,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,8,1] => [2,3,5,6,4,7,8,1] => [8,2,3,6,5,4,7,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [2,4,3,5,8,6,7,1] => [7,2,4,3,5,8,6,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => [2,4,3,7,5,6,8,1] => [8,2,4,3,7,5,6,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,8,1] => [2,4,6,3,5,7,8,1] => [8,2,6,4,3,5,7,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [2,5,4,3,6,7,8,1] => [8,2,4,5,3,6,7,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [2,4,5,3,6,7,8,1] => [8,2,5,4,3,6,7,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [3,2,4,5,8,6,7,1] => [7,3,2,4,5,8,6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [3,2,4,7,5,6,8,1] => [8,3,2,4,7,5,6,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [3,5,2,4,6,7,8,1] => [8,5,3,2,4,6,7,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,8,1] => [8,3,4,2,5,6,7,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,8,1] => [8,4,3,2,5,6,7,1]
[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] => [7,2,3,4,5,6,8,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,7,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [2,3,4,6,5,7,8,1] => [8,2,3,4,6,5,7,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [2,3,5,4,6,7,8,1] => [8,2,3,5,4,6,7,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [2,4,3,5,6,7,8,1] => [8,2,4,3,5,6,7,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => [8,3,2,4,5,6,7,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [1,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [1,7,8,6,5,4,3,2] => [1,3,4,5,6,8,7,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [1,6,8,7,5,4,3,2] => [1,3,4,5,7,6,8,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [1,7,6,8,5,4,3,2] => [1,3,4,5,8,7,6,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [1,6,7,8,5,4,3,2] => [1,3,4,5,8,6,7,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [1,5,8,7,6,4,3,2] => [1,3,4,6,5,7,8,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [1,5,7,8,6,4,3,2] => [1,3,4,6,5,8,7,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [1,6,8,5,7,4,3,2] => [1,3,4,7,8,6,5,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [1,7,6,5,8,4,3,2] => [1,3,4,8,6,7,5,2]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [1,6,7,5,8,4,3,2] => [1,3,4,8,7,6,5,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,1,2] => [1,5,6,8,7,4,3,2] => [1,3,4,7,5,6,8,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [1,5,7,6,8,4,3,2] => [1,3,4,8,5,7,6,2]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [1,6,5,7,8,4,3,2] => [1,3,4,8,6,5,7,2]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [1,5,6,7,8,4,3,2] => [1,3,4,8,5,6,7,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [1,4,8,7,6,5,3,2] => [1,3,5,4,6,7,8,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [1,4,7,8,6,5,3,2] => [1,3,5,4,6,8,7,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [1,4,6,8,7,5,3,2] => [1,3,5,4,7,6,8,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,1,2] => [1,4,7,6,8,5,3,2] => [1,3,5,4,8,7,6,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [1,4,6,7,8,5,3,2] => [1,3,5,4,8,6,7,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [1,5,8,7,4,6,3,2] => [1,3,6,7,5,4,8,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [1,7,6,5,4,8,3,2] => [1,3,8,5,6,7,4,2]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,1,2] => [1,6,7,5,4,8,3,2] => [1,3,8,5,7,6,4,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [1,5,6,8,4,7,3,2] => [1,3,7,8,5,6,4,2]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [1,6,5,7,4,8,3,2] => [1,3,8,7,6,5,4,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,1,2] => [1,4,5,8,7,6,3,2] => [1,3,6,4,5,7,8,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [1,4,5,7,8,6,3,2] => [1,3,6,4,5,8,7,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [1,4,6,8,5,7,3,2] => [1,3,7,4,8,6,5,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [1,4,7,6,5,8,3,2] => [1,3,8,4,6,7,5,2]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [1,4,6,7,5,8,3,2] => [1,3,8,4,7,6,5,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,1,2] => [1,5,7,4,6,8,3,2] => [1,3,8,7,5,4,6,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [1,6,5,4,7,8,3,2] => [1,3,8,5,6,4,7,2]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [1,5,6,4,7,8,3,2] => [1,3,8,6,5,4,7,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,1,2] => [1,4,5,7,6,8,3,2] => [1,3,8,4,5,7,6,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [1,5,4,6,7,8,3,2] => [1,3,8,5,4,6,7,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [1,4,5,6,7,8,3,2] => [1,3,8,4,5,6,7,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [1,3,8,7,6,5,4,2] => [1,4,3,5,6,7,8,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [1,3,7,8,6,5,4,2] => [1,4,3,5,6,8,7,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,1,2] => [1,3,6,8,7,5,4,2] => [1,4,3,5,7,6,8,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [1,3,7,6,8,5,4,2] => [1,4,3,5,8,7,6,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [1,3,6,7,8,5,4,2] => [1,4,3,5,8,6,7,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [1,3,5,8,7,6,4,2] => [1,4,3,6,5,7,8,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [1,3,5,7,8,6,4,2] => [1,4,3,6,5,8,7,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [1,3,6,8,5,7,4,2] => [1,4,3,7,8,6,5,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [1,3,7,6,5,8,4,2] => [1,4,3,8,6,7,5,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [1,3,6,7,5,8,4,2] => [1,4,3,8,7,6,5,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [1,3,5,6,8,7,4,2] => [1,4,3,7,5,6,8,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [1,3,5,7,6,8,4,2] => [1,4,3,8,5,7,6,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [1,3,6,5,7,8,4,2] => [1,4,3,8,6,5,7,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [1,3,5,6,7,8,4,2] => [1,4,3,8,5,6,7,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,1,2] => [1,4,8,7,6,3,5,2] => [1,5,6,4,3,7,8,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,1,2] => [1,4,7,8,6,3,5,2] => [1,5,6,4,3,8,7,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,1,2] => [1,4,6,8,7,3,5,2] => [1,5,7,4,3,6,8,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,1,2] => [1,4,7,6,8,3,5,2] => [1,5,8,4,3,7,6,2]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => [1,4,6,7,8,3,5,2] => [1,5,8,4,3,6,7,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,1,2] => [1,5,8,7,4,3,6,2] => [1,6,4,7,5,3,8,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [1,5,7,8,4,3,6,2] => [1,6,4,8,5,3,7,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [1,6,8,5,4,3,7,2] => [1,7,4,5,8,6,3,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [1,7,6,5,4,3,8,2] => [1,8,4,5,6,7,3,2]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,1,2] => [1,6,7,5,4,3,8,2] => [1,8,4,5,7,6,3,2]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [1,6,5,7,4,3,8,2] => [1,8,4,7,6,5,3,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [1,5,6,7,4,3,8,2] => [1,8,4,7,5,6,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [1,4,5,8,7,3,6,2] => [1,6,7,4,5,3,8,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [1,4,5,7,8,3,6,2] => [1,6,8,4,5,3,7,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,1,2] => [1,4,7,6,5,3,8,2] => [1,8,5,4,6,7,3,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [1,4,6,7,5,3,8,2] => [1,8,5,4,7,6,3,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [1,5,4,8,6,3,7,2] => [1,7,6,5,4,8,3,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [1,5,7,4,6,3,8,2] => [1,8,6,7,5,4,3,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,1,2] => [1,4,5,7,6,3,8,2] => [1,8,6,4,5,7,3,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [1,5,4,6,7,3,8,2] => [1,8,7,5,4,6,3,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [1,4,5,6,7,3,8,2] => [1,8,7,4,5,6,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [1,3,4,8,7,6,5,2] => [1,5,3,4,6,7,8,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [1,3,4,7,8,6,5,2] => [1,5,3,4,6,8,7,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [1,3,4,6,8,7,5,2] => [1,5,3,4,7,6,8,2]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [1,3,4,6,7,8,5,2] => [1,5,3,4,8,6,7,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [1,3,5,7,8,4,6,2] => [1,6,3,8,5,4,7,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,7,1,2] => [1,3,5,6,8,4,7,2] => [1,7,3,8,5,6,4,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => [1,3,5,7,6,4,8,2] => [1,8,3,6,5,7,4,2]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,8,1,2] => [1,3,6,5,7,4,8,2] => [1,8,3,7,6,5,4,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => [1,3,5,6,7,4,8,2] => [1,8,3,7,5,6,4,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [1,4,3,8,7,5,6,2] => [1,6,4,3,7,5,8,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [1,4,3,7,8,5,6,2] => [1,6,4,3,8,5,7,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,1,2] => [1,4,6,8,3,5,7,2] => [1,7,8,4,3,6,5,2]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,8,1,2] => [1,4,6,7,3,5,8,2] => [1,8,7,4,3,6,5,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [1,5,4,8,3,6,7,2] => [1,7,8,5,4,3,6,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [1,6,5,4,3,7,8,2] => [1,8,4,5,6,3,7,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => [1,4,5,7,3,6,8,2] => [1,8,7,4,5,3,6,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,8,1,2] => [1,4,6,5,3,7,8,2] => [1,8,5,4,6,3,7,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [1,5,4,6,3,7,8,2] => [1,8,6,5,4,3,7,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [1,4,5,6,3,7,8,2] => [1,8,6,4,5,3,7,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [1,3,4,5,8,7,6,2] => [1,6,3,4,5,7,8,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [1,3,4,5,7,8,6,2] => [1,6,3,4,5,8,7,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,7,1,2] => [1,3,4,6,8,5,7,2] => [1,7,3,4,8,6,5,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [1,3,4,7,6,5,8,2] => [1,8,3,4,6,7,5,2]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,8,1,2] => [1,3,4,6,7,5,8,2] => [1,8,3,4,7,6,5,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [1,3,5,7,4,6,8,2] => [1,8,3,7,5,4,6,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [1,3,5,6,4,7,8,2] => [1,8,3,6,5,4,7,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [1,4,3,5,8,6,7,2] => [1,7,4,3,5,8,6,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [1,4,6,3,5,7,8,2] => [1,8,6,4,3,5,7,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [1,5,4,3,6,7,8,2] => [1,8,4,5,3,6,7,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [1,4,5,3,6,7,8,2] => [1,8,5,4,3,6,7,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [1,3,4,5,6,8,7,2] => [1,7,3,4,5,6,8,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [1,3,4,5,7,6,8,2] => [1,8,3,4,5,7,6,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [1,3,4,6,5,7,8,2] => [1,8,3,4,6,5,7,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [1,3,5,4,6,7,8,2] => [1,8,3,5,4,6,7,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [1,4,3,5,6,7,8,2] => [1,8,4,3,5,6,7,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [2,8,7,6,5,4,1,3] => [4,2,1,5,6,7,8,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [2,7,8,6,5,4,1,3] => [4,2,1,5,6,8,7,3]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [2,6,8,7,5,4,1,3] => [4,2,1,5,7,6,8,3]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [2,7,6,8,5,4,1,3] => [4,2,1,5,8,7,6,3]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [2,6,7,8,5,4,1,3] => [4,2,1,5,8,6,7,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [2,5,8,7,6,4,1,3] => [4,2,1,6,5,7,8,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [2,5,7,8,6,4,1,3] => [4,2,1,6,5,8,7,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [2,6,8,5,7,4,1,3] => [4,2,1,7,8,6,5,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [2,7,6,5,8,4,1,3] => [4,2,1,8,6,7,5,3]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [2,6,7,5,8,4,1,3] => [4,2,1,8,7,6,5,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,1,3] => [2,5,6,8,7,4,1,3] => [4,2,1,7,5,6,8,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [2,5,7,6,8,4,1,3] => [4,2,1,8,5,7,6,3]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [2,6,5,7,8,4,1,3] => [4,2,1,8,6,5,7,3]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [2,5,6,7,8,4,1,3] => [4,2,1,8,5,6,7,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [2,4,8,7,6,5,1,3] => [5,2,1,4,6,7,8,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,2,1,3] => [2,4,7,8,6,5,1,3] => [5,2,1,4,6,8,7,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => [2,4,6,8,7,5,1,3] => [5,2,1,4,7,6,8,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => [2,4,7,6,8,5,1,3] => [5,2,1,4,8,7,6,3]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,1,3] => [2,4,6,7,8,5,1,3] => [5,2,1,4,8,6,7,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,1,3] => [2,5,8,7,4,6,1,3] => [6,2,1,7,5,4,8,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,2,1,3] => [2,5,7,8,4,6,1,3] => [6,2,1,8,5,4,7,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => [2,6,8,5,4,7,1,3] => [7,2,1,5,8,6,4,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [2,7,6,5,4,8,1,3] => [8,2,1,5,6,7,4,3]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [2,6,7,5,4,8,1,3] => [8,2,1,5,7,6,4,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,1,3] => [2,5,7,6,4,8,1,3] => [8,2,1,6,5,7,4,3]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [2,6,5,7,4,8,1,3] => [8,2,1,7,6,5,4,3]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [2,5,6,7,4,8,1,3] => [8,2,1,7,5,6,4,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => [2,4,5,8,7,6,1,3] => [6,2,1,4,5,7,8,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => [2,4,6,8,5,7,1,3] => [7,2,1,4,8,6,5,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [2,4,7,6,5,8,1,3] => [8,2,1,4,6,7,5,3]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,1,3] => [2,4,6,7,5,8,1,3] => [8,2,1,4,7,6,5,3]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [2,5,7,4,6,8,1,3] => [8,2,1,7,5,4,6,3]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,2,1,3] => [2,6,5,4,7,8,1,3] => [8,2,1,5,6,4,7,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,2,1,3] => [2,5,6,4,7,8,1,3] => [8,2,1,6,5,4,7,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [2,4,5,6,8,7,1,3] => [7,2,1,4,5,6,8,3]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [2,4,5,7,6,8,1,3] => [8,2,1,4,5,7,6,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [2,5,4,6,7,8,1,3] => [8,2,1,5,4,6,7,3]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [2,4,5,6,7,8,1,3] => [8,2,1,4,5,6,7,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [3,8,7,6,5,2,1,4] => [2,5,3,1,6,7,8,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [3,7,8,6,5,2,1,4] => [2,5,3,1,6,8,7,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [3,6,8,7,5,2,1,4] => [2,5,3,1,7,6,8,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [3,7,6,8,5,2,1,4] => [2,5,3,1,8,7,6,4]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [3,6,7,8,5,2,1,4] => [2,5,3,1,8,6,7,4]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [3,5,7,8,6,2,1,4] => [2,6,3,1,5,8,7,4]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [3,6,8,5,7,2,1,4] => [2,7,3,1,8,6,5,4]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [3,7,6,5,8,2,1,4] => [2,8,3,1,6,7,5,4]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [3,6,7,5,8,2,1,4] => [2,8,3,1,7,6,5,4]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [3,5,6,8,7,2,1,4] => [2,7,3,1,5,6,8,4]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [3,5,7,6,8,2,1,4] => [2,8,3,1,5,7,6,4]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [3,6,5,7,8,2,1,4] => [2,8,3,1,6,5,7,4]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [3,5,6,7,8,2,1,4] => [2,8,3,1,5,6,7,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [4,8,7,6,3,2,1,5] => [2,3,6,4,1,7,8,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [4,7,8,6,3,2,1,5] => [2,3,6,4,1,8,7,5]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [4,6,8,7,3,2,1,5] => [2,3,7,4,1,6,8,5]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [4,7,6,8,3,2,1,5] => [2,3,8,4,1,7,6,5]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [4,6,7,8,3,2,1,5] => [2,3,8,4,1,6,7,5]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [5,8,7,4,3,2,1,6] => [2,3,4,7,5,1,8,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [5,7,8,4,3,2,1,6] => [2,3,4,8,5,1,7,6]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [6,8,5,4,3,2,1,7] => [2,3,4,5,8,6,1,7]
[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] => [2,3,4,5,6,7,1,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1,8] => [2,3,4,5,7,6,1,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [5,6,8,4,3,2,1,7] => [2,3,4,8,5,6,1,7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [5,7,6,4,3,2,1,8] => [2,3,4,6,5,7,1,8]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1,8] => [2,3,4,7,6,5,1,8]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1,8] => [2,3,4,7,5,6,1,8]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [4,5,8,7,3,2,1,6] => [2,3,7,4,5,1,8,6]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [4,5,7,8,3,2,1,6] => [2,3,8,4,5,1,7,6]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [4,6,8,5,3,2,1,7] => [2,3,5,4,8,6,1,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [4,7,6,5,3,2,1,8] => [2,3,5,4,6,7,1,8]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [4,6,7,5,3,2,1,8] => [2,3,5,4,7,6,1,8]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => [5,4,8,6,3,2,1,7] => [2,3,6,5,4,8,1,7]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [5,7,4,6,3,2,1,8] => [2,3,6,7,5,4,1,8]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1,8] => [2,3,7,5,6,4,1,8]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [5,6,4,7,3,2,1,8] => [2,3,7,6,5,4,1,8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [4,5,6,8,3,2,1,7] => [2,3,8,4,5,6,1,7]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [4,5,7,6,3,2,1,8] => [2,3,6,4,5,7,1,8]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,1,8] => [4,6,5,7,3,2,1,8] => [2,3,7,4,6,5,1,8]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [5,4,6,7,3,2,1,8] => [2,3,7,5,4,6,1,8]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [4,5,6,7,3,2,1,8] => [2,3,7,4,5,6,1,8]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [3,4,8,7,6,2,1,5] => [2,6,3,4,1,7,8,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [3,4,7,8,6,2,1,5] => [2,6,3,4,1,8,7,5]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,1,5] => [3,4,6,8,7,2,1,5] => [2,7,3,4,1,6,8,5]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [3,4,6,7,8,2,1,5] => [2,8,3,4,1,6,7,5]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [3,6,8,5,4,2,1,7] => [2,4,3,5,8,6,1,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [3,7,6,5,4,2,1,8] => [2,4,3,5,6,7,1,8]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [3,5,6,8,4,2,1,7] => [2,4,3,8,5,6,1,7]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [3,5,7,6,4,2,1,8] => [2,4,3,6,5,7,1,8]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [3,5,6,7,4,2,1,8] => [2,4,3,7,5,6,1,8]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,1,6] => [4,3,8,7,5,2,1,6] => [2,5,4,3,7,1,8,6]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,1,6] => [4,3,7,8,5,2,1,6] => [2,5,4,3,8,1,7,6]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,1,7] => [4,6,8,3,5,2,1,7] => [2,5,8,4,3,6,1,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [4,7,6,3,5,2,1,8] => [2,5,6,4,3,7,1,8]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [4,6,7,3,5,2,1,8] => [2,5,7,4,3,6,1,8]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,1,7] => [5,4,8,3,6,2,1,7] => [2,6,8,5,4,3,1,7]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [5,7,4,3,6,2,1,8] => [2,6,4,7,5,3,1,8]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [6,5,4,3,7,2,1,8] => [2,7,4,5,6,3,1,8]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [5,6,4,3,7,2,1,8] => [2,7,4,6,5,3,1,8]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [4,5,3,8,6,2,1,7] => [2,6,5,4,3,8,1,7]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,1,8] => [4,6,5,3,7,2,1,8] => [2,7,5,4,6,3,1,8]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [5,4,6,3,7,2,1,8] => [2,7,6,5,4,3,1,8]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,1,8] => [4,5,6,3,7,2,1,8] => [2,7,6,4,5,3,1,8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [3,4,5,8,7,2,1,6] => [2,7,3,4,5,1,8,6]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [3,4,5,7,8,2,1,6] => [2,8,3,4,5,1,7,6]
[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] => [2,5,3,4,6,7,1,8]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,1,8] => [3,6,5,4,7,2,1,8] => [2,7,3,5,6,4,1,8]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,1,8] => [3,5,6,4,7,2,1,8] => [2,7,3,6,5,4,1,8]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [4,3,5,8,6,2,1,7] => [2,6,4,3,5,8,1,7]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,1,8] => [4,6,3,5,7,2,1,8] => [2,7,6,4,3,5,1,8]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [5,4,3,6,7,2,1,8] => [2,7,4,5,3,6,1,8]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,1,8] => [4,5,3,6,7,2,1,8] => [2,7,5,4,3,6,1,8]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [3,4,5,6,8,2,1,7] => [2,8,3,4,5,6,1,7]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,1,8] => [4,3,5,6,7,2,1,8] => [2,7,4,3,5,6,1,8]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [3,4,5,6,7,2,1,8] => [2,7,3,4,5,6,1,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [2,3,8,7,6,5,1,4] => [5,2,3,1,6,7,8,4]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [2,3,7,8,6,5,1,4] => [5,2,3,1,6,8,7,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [2,3,6,8,7,5,1,4] => [5,2,3,1,7,6,8,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [2,3,7,6,8,5,1,4] => [5,2,3,1,8,7,6,4]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [2,3,6,7,8,5,1,4] => [5,2,3,1,8,6,7,4]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [2,3,5,8,7,6,1,4] => [6,2,3,1,5,7,8,4]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [2,3,5,7,8,6,1,4] => [6,2,3,1,5,8,7,4]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [2,3,6,8,5,7,1,4] => [7,2,3,1,8,6,5,4]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [2,3,7,6,5,8,1,4] => [8,2,3,1,6,7,5,4]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [2,3,6,7,5,8,1,4] => [8,2,3,1,7,6,5,4]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [2,3,5,6,8,7,1,4] => [7,2,3,1,5,6,8,4]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [2,3,5,7,6,8,1,4] => [8,2,3,1,5,7,6,4]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [2,3,6,5,7,8,1,4] => [8,2,3,1,6,5,7,4]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [2,3,5,6,7,8,1,4] => [8,2,3,1,5,6,7,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [2,4,8,7,6,3,1,5] => [3,2,6,4,1,7,8,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,3,1,5] => [2,4,7,8,6,3,1,5] => [3,2,6,4,1,8,7,5]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,1,5] => [2,4,6,8,7,3,1,5] => [3,2,7,4,1,6,8,5]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [2,4,7,6,8,3,1,5] => [3,2,8,4,1,7,6,5]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [2,4,6,7,8,3,1,5] => [3,2,8,4,1,6,7,5]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [2,6,8,5,4,3,1,7] => [3,2,4,5,8,6,1,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [2,7,6,5,4,3,1,8] => [3,2,4,5,6,7,1,8]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [2,6,7,5,4,3,1,8] => [3,2,4,5,7,6,1,8]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [2,5,6,8,4,3,1,7] => [3,2,4,8,5,6,1,7]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [2,5,7,6,4,3,1,8] => [3,2,4,6,5,7,1,8]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [2,5,6,7,4,3,1,8] => [3,2,4,7,5,6,1,8]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [2,4,5,8,7,3,1,6] => [3,2,7,4,5,1,8,6]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [2,4,5,7,8,3,1,6] => [3,2,8,4,5,1,7,6]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => [2,4,6,8,5,3,1,7] => [3,2,5,4,8,6,1,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [2,4,7,6,5,3,1,8] => [3,2,5,4,6,7,1,8]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [2,4,6,7,5,3,1,8] => [3,2,5,4,7,6,1,8]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [2,5,7,4,6,3,1,8] => [3,2,6,7,5,4,1,8]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [2,5,6,4,7,3,1,8] => [3,2,7,6,5,4,1,8]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [2,4,5,6,8,3,1,7] => [3,2,8,4,5,6,1,7]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [2,4,5,7,6,3,1,8] => [3,2,6,4,5,7,1,8]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [2,5,4,6,7,3,1,8] => [3,2,7,5,4,6,1,8]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [2,4,5,6,7,3,1,8] => [3,2,7,4,5,6,1,8]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [3,2,8,7,6,4,1,5] => [4,3,2,6,1,7,8,5]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [3,2,6,8,7,4,1,5] => [4,3,2,7,1,6,8,5]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,4,1,5] => [3,2,7,6,8,4,1,5] => [4,3,2,8,1,7,6,5]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [3,2,6,7,8,4,1,5] => [4,3,2,8,1,6,7,5]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [3,5,8,7,2,4,1,6] => [4,7,3,2,5,1,8,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,4,1,6] => [3,5,7,8,2,4,1,6] => [4,8,3,2,5,1,7,6]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [3,6,8,5,2,4,1,7] => [4,5,3,2,8,6,1,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [3,7,6,5,2,4,1,8] => [4,5,3,2,6,7,1,8]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,4,1,8] => [3,5,7,6,2,4,1,8] => [4,6,3,2,5,7,1,8]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [3,6,5,7,2,4,1,8] => [4,7,3,2,6,5,1,8]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [3,5,6,7,2,4,1,8] => [4,7,3,2,5,6,1,8]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [4,3,8,7,2,5,1,6] => [5,7,4,3,2,1,8,6]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [4,3,7,8,2,5,1,6] => [5,8,4,3,2,1,7,6]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [4,6,8,3,2,5,1,7] => [5,3,8,4,2,6,1,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [4,7,6,3,2,5,1,8] => [5,3,6,4,2,7,1,8]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [4,6,7,3,2,5,1,8] => [5,3,7,4,2,6,1,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [5,4,8,3,2,6,1,7] => [6,3,8,5,4,2,1,7]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [5,7,4,3,2,6,1,8] => [6,3,4,7,5,2,1,8]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,7,1,8] => [7,3,4,5,6,2,1,8]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [5,6,4,3,2,7,1,8] => [7,3,4,6,5,2,1,8]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,1,7] => [4,5,3,8,2,6,1,7] => [6,8,5,4,3,2,1,7]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [4,5,7,3,2,6,1,8] => [6,3,7,4,5,2,1,8]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [5,4,6,3,2,7,1,8] => [7,3,6,5,4,2,1,8]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [3,4,2,8,7,5,1,6] => [5,4,3,2,7,1,8,6]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [3,4,2,7,8,5,1,6] => [5,4,3,2,8,1,7,6]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,5,1,7] => [3,4,6,8,2,5,1,7] => [5,8,3,4,2,6,1,7]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [3,4,6,7,2,5,1,8] => [5,7,3,4,2,6,1,8]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,1,7] => [3,5,4,8,2,6,1,7] => [6,8,3,5,4,2,1,7]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [3,5,7,4,2,6,1,8] => [6,4,3,7,5,2,1,8]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [3,5,6,4,2,7,1,8] => [7,4,3,6,5,2,1,8]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [4,3,5,8,2,6,1,7] => [6,8,4,3,5,2,1,7]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [4,3,7,5,2,6,1,8] => [6,5,4,3,7,2,1,8]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,1,8] => [4,6,3,5,2,7,1,8] => [7,5,6,4,3,2,1,8]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [5,4,3,6,2,7,1,8] => [7,6,4,5,3,2,1,8]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,1,7] => [3,4,5,2,8,6,1,7] => [6,5,3,4,2,8,1,7]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [3,4,6,5,2,7,1,8] => [7,5,3,4,6,2,1,8]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [3,5,4,6,2,7,1,8] => [7,6,3,5,4,2,1,8]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [2,3,4,8,7,6,1,5] => [6,2,3,4,1,7,8,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,1,5] => [2,3,4,7,8,6,1,5] => [6,2,3,4,1,8,7,5]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [2,3,4,6,8,7,1,5] => [7,2,3,4,1,6,8,5]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [2,3,4,7,6,8,1,5] => [8,2,3,4,1,7,6,5]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [2,3,4,6,7,8,1,5] => [8,2,3,4,1,6,7,5]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,4,1,6] => [2,3,5,8,7,4,1,6] => [4,2,3,7,5,1,8,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [2,3,5,7,8,4,1,6] => [4,2,3,8,5,1,7,6]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [2,3,7,6,5,4,1,8] => [4,2,3,5,6,7,1,8]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [2,3,6,7,5,4,1,8] => [4,2,3,5,7,6,1,8]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [2,3,5,6,8,4,1,7] => [4,2,3,8,5,6,1,7]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [2,3,5,7,6,4,1,8] => [4,2,3,6,5,7,1,8]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [2,3,6,5,7,4,1,8] => [4,2,3,7,6,5,1,8]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [2,3,5,6,7,4,1,8] => [4,2,3,7,5,6,1,8]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,3,5,1,6] => [2,4,3,8,7,5,1,6] => [5,2,4,3,7,1,8,6]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,1,6] => [2,4,3,7,8,5,1,6] => [5,2,4,3,8,1,7,6]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [2,4,6,8,3,5,1,7] => [5,2,8,4,3,6,1,7]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [2,4,6,7,3,5,1,8] => [5,2,7,4,3,6,1,8]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [2,5,4,8,3,6,1,7] => [6,2,8,5,4,3,1,7]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,1,8] => [2,6,5,4,3,7,1,8] => [7,2,4,5,6,3,1,8]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [2,4,5,3,8,6,1,7] => [6,2,5,4,3,8,1,7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [2,4,5,7,3,6,1,8] => [6,2,7,4,5,3,1,8]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,1,8] => [2,4,6,5,3,7,1,8] => [7,2,5,4,6,3,1,8]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [2,5,4,6,3,7,1,8] => [7,2,6,5,4,3,1,8]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,1,8] => [2,4,5,6,3,7,1,8] => [7,2,6,4,5,3,1,8]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [3,2,7,6,4,5,1,8] => [5,3,2,6,4,7,1,8]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [3,2,6,7,4,5,1,8] => [5,3,2,7,4,6,1,8]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [3,5,2,8,4,6,1,7] => [6,5,3,8,2,4,1,7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [3,5,7,2,4,6,1,8] => [6,7,3,2,5,4,1,8]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [3,6,5,2,4,7,1,8] => [7,5,3,2,6,4,1,8]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,7,1,8] => [3,5,6,2,4,7,1,8] => [7,6,3,2,5,4,1,8]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,1,7] => [4,3,2,8,5,6,1,7] => [6,3,4,2,8,5,1,7]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,1,8] => [4,3,7,2,5,6,1,8] => [6,7,4,3,2,5,1,8]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1,8] => [7,3,4,5,2,6,1,8]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,1,8] => [4,5,3,2,6,7,1,8] => [7,3,5,4,2,6,1,8]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [3,4,2,5,8,6,1,7] => [6,4,3,2,5,8,1,7]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,5,7,1,8] => [3,4,6,2,5,7,1,8] => [7,6,3,4,2,5,1,8]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,1,8] => [3,5,4,2,6,7,1,8] => [7,4,3,5,2,6,1,8]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,1,8] => [4,3,5,2,6,7,1,8] => [7,5,4,3,2,6,1,8]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [3,4,5,2,6,7,1,8] => [7,5,3,4,2,6,1,8]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [2,3,4,5,8,7,1,6] => [7,2,3,4,5,1,8,6]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [2,3,4,5,7,8,1,6] => [8,2,3,4,5,1,7,6]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [2,3,4,7,6,5,1,8] => [5,2,3,4,6,7,1,8]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [2,3,4,6,7,5,1,8] => [5,2,3,4,7,6,1,8]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [2,3,5,4,8,6,1,7] => [6,2,3,5,4,8,1,7]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,1,8] => [2,3,5,7,4,6,1,8] => [6,2,3,7,5,4,1,8]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,1,8] => [2,3,5,6,4,7,1,8] => [7,2,3,6,5,4,1,8]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,1,7] => [2,4,3,5,8,6,1,7] => [6,2,4,3,5,8,1,7]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [2,4,3,7,5,6,1,8] => [6,2,4,3,7,5,1,8]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [2,4,6,3,5,7,1,8] => [7,2,6,4,3,5,1,8]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [2,5,4,3,6,7,1,8] => [7,2,4,5,3,6,1,8]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [2,4,5,3,6,7,1,8] => [7,2,5,4,3,6,1,8]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [3,2,4,5,8,6,1,7] => [6,3,2,4,5,8,1,7]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,1,8] => [3,2,4,7,5,6,1,8] => [6,3,2,4,7,5,1,8]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [3,2,6,4,5,7,1,8] => [7,3,2,6,4,5,1,8]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [4,3,2,5,6,7,1,8] => [7,3,4,2,5,6,1,8]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [3,4,2,5,6,7,1,8] => [7,4,3,2,5,6,1,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [2,3,4,5,6,8,1,7] => [8,2,3,4,5,6,1,7]
[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] => [6,2,3,4,5,7,1,8]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [2,3,5,4,6,7,1,8] => [7,2,3,5,4,6,1,8]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [2,4,3,5,6,7,1,8] => [7,2,4,3,5,6,1,8]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1,8] => [7,3,2,4,5,6,1,8]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [1,2,8,7,6,5,4,3] => [1,2,4,5,6,7,8,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [1,2,7,8,6,5,4,3] => [1,2,4,5,6,8,7,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => [1,2,7,6,8,5,4,3] => [1,2,4,5,8,7,6,3]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [1,2,6,7,8,5,4,3] => [1,2,4,5,8,6,7,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [1,2,5,7,8,6,4,3] => [1,2,4,6,5,8,7,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [1,2,6,8,5,7,4,3] => [1,2,4,7,8,6,5,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [1,2,7,6,5,8,4,3] => [1,2,4,8,6,7,5,3]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [1,2,6,7,5,8,4,3] => [1,2,4,8,7,6,5,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [1,2,5,6,8,7,4,3] => [1,2,4,7,5,6,8,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [1,2,5,7,6,8,4,3] => [1,2,4,8,5,7,6,3]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [1,2,6,5,7,8,4,3] => [1,2,4,8,6,5,7,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [1,2,5,6,7,8,4,3] => [1,2,4,8,5,6,7,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [1,2,4,8,7,6,5,3] => [1,2,5,4,6,7,8,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,1,2,3] => [1,2,4,7,8,6,5,3] => [1,2,5,4,6,8,7,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [1,2,4,6,8,7,5,3] => [1,2,5,4,7,6,8,3]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [1,2,4,6,7,8,5,3] => [1,2,5,4,8,6,7,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [1,2,5,8,7,4,6,3] => [1,2,6,7,5,4,8,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [1,2,5,7,8,4,6,3] => [1,2,6,8,5,4,7,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [1,2,6,8,5,4,7,3] => [1,2,7,5,8,6,4,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [1,2,7,6,5,4,8,3] => [1,2,8,5,6,7,4,3]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [1,2,6,7,5,4,8,3] => [1,2,8,5,7,6,4,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => [1,2,5,6,8,4,7,3] => [1,2,7,8,5,6,4,3]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [1,2,6,5,7,4,8,3] => [1,2,8,7,6,5,4,3]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [1,2,5,6,7,4,8,3] => [1,2,8,7,5,6,4,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [1,2,4,5,8,7,6,3] => [1,2,6,4,5,7,8,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [1,2,4,5,7,8,6,3] => [1,2,6,4,5,8,7,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => [1,2,4,6,8,5,7,3] => [1,2,7,4,8,6,5,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [1,2,4,7,6,5,8,3] => [1,2,8,4,6,7,5,3]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [1,2,4,6,7,5,8,3] => [1,2,8,4,7,6,5,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => [1,2,5,4,8,6,7,3] => [1,2,7,5,4,8,6,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [1,2,5,7,4,6,8,3] => [1,2,8,7,5,4,6,3]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [1,2,6,5,4,7,8,3] => [1,2,8,5,6,4,7,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [1,2,5,6,4,7,8,3] => [1,2,8,6,5,4,7,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [1,2,4,5,6,8,7,3] => [1,2,7,4,5,6,8,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [1,2,5,4,6,7,8,3] => [1,2,8,5,4,6,7,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [1,3,8,7,6,5,2,4] => [1,5,3,2,6,7,8,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [1,3,7,8,6,5,2,4] => [1,5,3,2,6,8,7,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [1,3,6,8,7,5,2,4] => [1,5,3,2,7,6,8,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [1,3,7,6,8,5,2,4] => [1,5,3,2,8,7,6,4]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,1,2,4] => [1,3,6,7,8,5,2,4] => [1,5,3,2,8,6,7,4]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [1,3,5,8,7,6,2,4] => [1,6,3,2,5,7,8,4]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [1,3,5,7,8,6,2,4] => [1,6,3,2,5,8,7,4]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => [1,3,6,8,5,7,2,4] => [1,7,3,2,8,6,5,4]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [1,3,7,6,5,8,2,4] => [1,8,3,2,6,7,5,4]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [1,3,6,7,5,8,2,4] => [1,8,3,2,7,6,5,4]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,1,2,4] => [1,3,5,6,8,7,2,4] => [1,7,3,2,5,6,8,4]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [1,3,5,7,6,8,2,4] => [1,8,3,2,5,7,6,4]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [1,3,6,5,7,8,2,4] => [1,8,3,2,6,5,7,4]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [1,3,5,6,7,8,2,4] => [1,8,3,2,5,6,7,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [1,4,8,7,6,3,2,5] => [1,3,6,4,2,7,8,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,1,2,5] => [1,4,7,8,6,3,2,5] => [1,3,6,4,2,8,7,5]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,1,2,5] => [1,4,6,8,7,3,2,5] => [1,3,7,4,2,6,8,5]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,1,2,5] => [1,4,7,6,8,3,2,5] => [1,3,8,4,2,7,6,5]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [1,4,6,7,8,3,2,5] => [1,3,8,4,2,6,7,5]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [1,5,8,7,4,3,2,6] => [1,3,4,7,5,2,8,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [1,5,7,8,4,3,2,6] => [1,3,4,8,5,2,7,6]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [1,6,8,5,4,3,2,7] => [1,3,4,5,8,6,2,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [1,7,6,5,4,3,2,8] => [1,3,4,5,6,7,2,8]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [1,6,7,5,4,3,2,8] => [1,3,4,5,7,6,2,8]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [1,5,7,6,4,3,2,8] => [1,3,4,6,5,7,2,8]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,1,2,8] => [1,6,5,7,4,3,2,8] => [1,3,4,7,6,5,2,8]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,1,2,8] => [1,5,6,7,4,3,2,8] => [1,3,4,7,5,6,2,8]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [1,4,6,8,5,3,2,7] => [1,3,5,4,8,6,2,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [1,4,7,6,5,3,2,8] => [1,3,5,4,6,7,2,8]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,1,2,7] => [1,5,4,8,6,3,2,7] => [1,3,6,5,4,8,2,7]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,1,2,8] => [1,5,7,4,6,3,2,8] => [1,3,6,7,5,4,2,8]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [1,4,5,7,6,3,2,8] => [1,3,6,4,5,7,2,8]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [1,5,4,6,7,3,2,8] => [1,3,7,5,4,6,2,8]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [1,4,5,6,7,3,2,8] => [1,3,7,4,5,6,2,8]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [1,3,4,8,7,6,2,5] => [1,6,3,4,2,7,8,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [1,3,4,7,8,6,2,5] => [1,6,3,4,2,8,7,5]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,1,2,5] => [1,3,4,7,6,8,2,5] => [1,8,3,4,2,7,6,5]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [1,3,4,6,7,8,2,5] => [1,8,3,4,2,6,7,5]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => [1,3,5,7,8,4,2,6] => [1,4,3,8,5,2,7,6]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [1,3,6,8,5,4,2,7] => [1,4,3,5,8,6,2,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [1,3,7,6,5,4,2,8] => [1,4,3,5,6,7,2,8]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,1,2,8] => [1,3,6,7,5,4,2,8] => [1,4,3,5,7,6,2,8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [1,3,5,6,8,4,2,7] => [1,4,3,8,5,6,2,7]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => [1,3,5,7,6,4,2,8] => [1,4,3,6,5,7,2,8]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [1,3,6,5,7,4,2,8] => [1,4,3,7,6,5,2,8]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,1,2,8] => [1,3,5,6,7,4,2,8] => [1,4,3,7,5,6,2,8]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,1,2,6] => [1,4,3,7,8,5,2,6] => [1,5,4,3,8,2,7,6]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,1,2,7] => [1,4,6,8,3,5,2,7] => [1,5,8,4,3,6,2,7]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,1,2,8] => [1,4,6,7,3,5,2,8] => [1,5,7,4,3,6,2,8]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [1,5,4,8,3,6,2,7] => [1,6,8,5,4,3,2,7]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,1,2,8] => [1,5,7,4,3,6,2,8] => [1,6,4,7,5,3,2,8]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [1,6,5,4,3,7,2,8] => [1,7,4,5,6,3,2,8]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,1,2,8] => [1,5,6,4,3,7,2,8] => [1,7,4,6,5,3,2,8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [1,4,5,3,8,6,2,7] => [1,6,5,4,3,8,2,7]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,1,2,8] => [1,4,5,7,3,6,2,8] => [1,6,7,4,5,3,2,8]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [1,4,6,5,3,7,2,8] => [1,7,5,4,6,3,2,8]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [1,3,4,5,8,7,2,6] => [1,7,3,4,5,2,8,6]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [1,3,4,5,7,8,2,6] => [1,8,3,4,5,2,7,6]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [1,3,4,6,8,5,2,7] => [1,5,3,4,8,6,2,7]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [1,3,4,6,7,5,2,8] => [1,5,3,4,7,6,2,8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [1,3,5,4,8,6,2,7] => [1,6,3,5,4,8,2,7]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => [1,3,5,7,4,6,2,8] => [1,6,3,7,5,4,2,8]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,1,2,8] => [1,3,6,5,4,7,2,8] => [1,7,3,5,6,4,2,8]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [1,3,5,6,4,7,2,8] => [1,7,3,6,5,4,2,8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [1,4,3,5,8,6,2,7] => [1,6,4,3,5,8,2,7]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,1,2,8] => [1,4,3,7,5,6,2,8] => [1,6,4,3,7,5,2,8]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,1,2,8] => [1,4,5,3,6,7,2,8] => [1,7,5,4,3,6,2,8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,3,4,5,6,8,2,7] => [1,8,3,4,5,6,2,7]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,1,2,8] => [1,3,4,5,7,6,2,8] => [1,6,3,4,5,7,2,8]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [1,3,4,6,5,7,2,8] => [1,7,3,4,6,5,2,8]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,1,2,8] => [1,3,5,4,6,7,2,8] => [1,7,3,5,4,6,2,8]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [1,4,3,5,6,7,2,8] => [1,7,4,3,5,6,2,8]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [2,1,8,7,6,5,3,4] => [2,1,5,3,6,7,8,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [2,1,7,8,6,5,3,4] => [2,1,5,3,6,8,7,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,1,3,4] => [2,1,6,8,7,5,3,4] => [2,1,5,3,7,6,8,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [2,1,7,6,8,5,3,4] => [2,1,5,3,8,7,6,4]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [2,1,6,7,8,5,3,4] => [2,1,5,3,8,6,7,4]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [2,1,5,8,7,6,3,4] => [2,1,6,3,5,7,8,4]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [2,1,5,7,8,6,3,4] => [2,1,6,3,5,8,7,4]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [2,1,6,8,5,7,3,4] => [2,1,7,3,8,6,5,4]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [2,1,7,6,5,8,3,4] => [2,1,8,3,6,7,5,4]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [2,1,6,7,5,8,3,4] => [2,1,8,3,7,6,5,4]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [2,1,5,6,8,7,3,4] => [2,1,7,3,5,6,8,4]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [2,1,5,7,6,8,3,4] => [2,1,8,3,5,7,6,4]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [2,1,6,5,7,8,3,4] => [2,1,8,3,6,5,7,4]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [2,1,5,6,7,8,3,4] => [2,1,8,3,5,6,7,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [2,4,8,7,6,1,3,5] => [6,2,1,4,3,7,8,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [2,4,7,8,6,1,3,5] => [6,2,1,4,3,8,7,5]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [2,4,6,8,7,1,3,5] => [7,2,1,4,3,6,8,5]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,1,3,5] => [2,4,7,6,8,1,3,5] => [8,2,1,4,3,7,6,5]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [2,4,6,7,8,1,3,5] => [8,2,1,4,3,6,7,5]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,1,3,6] => [2,5,8,7,4,1,3,6] => [4,2,1,7,5,3,8,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [2,5,7,8,4,1,3,6] => [4,2,1,8,5,3,7,6]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [2,6,8,5,4,1,3,7] => [4,2,1,5,8,6,3,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [2,7,6,5,4,1,3,8] => [4,2,1,5,6,7,3,8]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,1,3,8] => [2,6,7,5,4,1,3,8] => [4,2,1,5,7,6,3,8]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [2,6,5,7,4,1,3,8] => [4,2,1,7,6,5,3,8]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,1,3,8] => [2,5,6,7,4,1,3,8] => [4,2,1,7,5,6,3,8]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,1,3,6] => [2,4,5,7,8,1,3,6] => [8,2,1,4,5,3,7,6]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,1,3,7] => [2,4,6,8,5,1,3,7] => [5,2,1,4,8,6,3,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,2,1,3,7] => [2,5,4,8,6,1,3,7] => [6,2,1,5,4,8,3,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [2,5,7,4,6,1,3,8] => [6,2,1,7,5,4,3,8]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,1,3,8] => [2,6,5,4,7,1,3,8] => [7,2,1,5,6,4,3,8]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,1,3,8] => [2,5,6,4,7,1,3,8] => [7,2,1,6,5,4,3,8]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [2,4,5,6,8,1,3,7] => [8,2,1,4,5,6,3,7]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [2,4,5,7,6,1,3,8] => [6,2,1,4,5,7,3,8]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [2,5,4,6,7,1,3,8] => [7,2,1,5,4,6,3,8]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [2,4,5,6,7,1,3,8] => [7,2,1,4,5,6,3,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [3,2,8,7,6,1,4,5] => [6,3,2,1,4,7,8,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [3,2,7,8,6,1,4,5] => [6,3,2,1,4,8,7,5]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [3,2,6,8,7,1,4,5] => [7,3,2,1,4,6,8,5]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [3,2,7,6,8,1,4,5] => [8,3,2,1,4,7,6,5]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [3,2,6,7,8,1,4,5] => [8,3,2,1,4,6,7,5]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [3,5,8,7,2,1,4,6] => [2,7,3,1,5,4,8,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [3,5,7,8,2,1,4,6] => [2,8,3,1,5,4,7,6]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [3,6,8,5,2,1,4,7] => [2,5,3,1,8,6,4,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [3,7,6,5,2,1,4,8] => [2,5,3,1,6,7,4,8]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,1,4,8] => [3,6,7,5,2,1,4,8] => [2,5,3,1,7,6,4,8]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [3,5,6,8,2,1,4,7] => [2,8,3,1,5,6,4,7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,1,4,8] => [3,5,7,6,2,1,4,8] => [2,6,3,1,5,7,4,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [4,3,8,7,2,1,5,6] => [2,7,4,3,1,5,8,6]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [4,3,7,8,2,1,5,6] => [2,8,4,3,1,5,7,6]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [4,6,8,3,2,1,5,7] => [2,3,8,4,1,6,5,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [4,7,6,3,2,1,5,8] => [2,3,6,4,1,7,5,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [5,4,8,3,2,1,6,7] => [2,3,8,5,4,1,6,7]
[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] => [2,3,4,5,6,1,7,8]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [5,6,4,3,2,1,7,8] => [2,3,4,6,5,1,7,8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [4,5,3,8,2,1,6,7] => [2,8,5,4,3,1,6,7]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [4,5,7,3,2,1,6,8] => [2,3,7,4,5,1,6,8]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [5,4,6,3,2,1,7,8] => [2,3,6,5,4,1,7,8]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [4,5,6,3,2,1,7,8] => [2,3,6,4,5,1,7,8]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [3,4,2,8,7,1,5,6] => [7,4,3,2,1,5,8,6]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [3,4,2,7,8,1,5,6] => [8,4,3,2,1,5,7,6]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [3,4,6,8,2,1,5,7] => [2,8,3,4,1,6,5,7]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [3,4,6,7,2,1,5,8] => [2,7,3,4,1,6,5,8]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,1,6,8] => [3,5,7,4,2,1,6,8] => [2,4,3,7,5,1,6,8]
[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] => [2,4,3,5,6,1,7,8]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [3,5,6,4,2,1,7,8] => [2,4,3,6,5,1,7,8]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [4,3,5,8,2,1,6,7] => [2,8,4,3,5,1,6,7]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [4,3,7,5,2,1,6,8] => [2,5,4,3,7,1,6,8]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [5,4,3,6,2,1,7,8] => [2,6,4,5,3,1,7,8]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,1,7,8] => [4,5,3,6,2,1,7,8] => [2,6,5,4,3,1,7,8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [3,4,5,2,8,1,6,7] => [8,5,3,4,2,1,6,7]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [3,4,5,7,2,1,6,8] => [2,7,3,4,5,1,6,8]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,1,7,8] => [3,5,4,6,2,1,7,8] => [2,6,3,5,4,1,7,8]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,1,7,8] => [4,3,5,6,2,1,7,8] => [2,6,4,3,5,1,7,8]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [3,4,5,6,2,1,7,8] => [2,6,3,4,5,1,7,8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [2,3,1,8,7,6,4,5] => [3,2,1,6,4,7,8,5]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [2,3,1,7,8,6,4,5] => [3,2,1,6,4,8,7,5]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [2,3,1,6,8,7,4,5] => [3,2,1,7,4,6,8,5]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [2,3,1,6,7,8,4,5] => [3,2,1,8,4,6,7,5]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,1,4,6] => [2,3,5,8,7,1,4,6] => [7,2,3,1,5,4,8,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,1,4,6] => [2,3,5,7,8,1,4,6] => [8,2,3,1,5,4,7,6]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [2,3,6,8,5,1,4,7] => [5,2,3,1,8,6,4,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [2,3,7,6,5,1,4,8] => [5,2,3,1,6,7,4,8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [2,3,5,6,8,1,4,7] => [8,2,3,1,5,6,4,7]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [2,3,5,7,6,1,4,8] => [6,2,3,1,5,7,4,8]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [2,3,6,5,7,1,4,8] => [7,2,3,1,6,5,4,8]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [2,3,5,6,7,1,4,8] => [7,2,3,1,5,6,4,8]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [2,4,3,7,8,1,5,6] => [8,2,4,3,1,5,7,6]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [2,4,6,8,3,1,5,7] => [3,2,8,4,1,6,5,7]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,1,6,7] => [2,5,4,8,3,1,6,7] => [3,2,8,5,4,1,6,7]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [2,5,7,4,3,1,6,8] => [3,2,4,7,5,1,6,8]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [2,4,5,3,8,1,6,7] => [8,2,5,4,3,1,6,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,1,6,8] => [2,4,5,7,3,1,6,8] => [3,2,7,4,5,1,6,8]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,1,7,8] => [2,4,6,5,3,1,7,8] => [3,2,5,4,6,1,7,8]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [2,5,4,6,3,1,7,8] => [3,2,6,5,4,1,7,8]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,1,7,8] => [2,4,5,6,3,1,7,8] => [3,2,6,4,5,1,7,8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [3,2,4,8,7,1,5,6] => [7,3,2,4,1,5,8,6]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [3,2,4,7,8,1,5,6] => [8,3,2,4,1,5,7,6]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [3,2,6,8,4,1,5,7] => [4,3,2,8,1,6,5,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [3,2,7,6,4,1,5,8] => [4,3,2,6,1,7,5,8]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [3,2,6,7,4,1,5,8] => [4,3,2,7,1,6,5,8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,1,6,7] => [3,5,2,8,4,1,6,7] => [4,8,3,5,1,2,6,7]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [3,5,7,2,4,1,6,8] => [4,7,3,2,5,1,6,8]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,1,7,8] => [3,6,5,2,4,1,7,8] => [4,5,3,2,6,1,7,8]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [3,5,6,2,4,1,7,8] => [4,6,3,2,5,1,7,8]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,1,6,8] => [4,3,7,2,5,1,6,8] => [5,7,4,3,2,1,6,8]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [4,6,3,2,5,1,7,8] => [5,3,6,4,2,1,7,8]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7,8] => [6,3,4,5,2,1,7,8]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7,8] => [6,3,5,4,2,1,7,8]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,5,1,7,8] => [3,4,6,2,5,1,7,8] => [5,6,3,4,2,1,7,8]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,1,7,8] => [3,5,4,2,6,1,7,8] => [6,4,3,5,2,1,7,8]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [3,4,5,2,6,1,7,8] => [6,5,3,4,2,1,7,8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [2,3,4,1,8,7,5,6] => [4,2,3,1,7,5,8,6]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [2,3,4,1,7,8,5,6] => [4,2,3,1,8,5,7,6]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [2,3,4,6,8,1,5,7] => [8,2,3,4,1,6,5,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [2,3,4,7,6,1,5,8] => [6,2,3,4,1,7,5,8]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [2,3,4,6,7,1,5,8] => [7,2,3,4,1,6,5,8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [2,3,5,4,8,1,6,7] => [8,2,3,5,4,1,6,7]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [2,3,6,5,4,1,7,8] => [4,2,3,5,6,1,7,8]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [2,3,5,6,4,1,7,8] => [4,2,3,6,5,1,7,8]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [2,4,3,5,8,1,6,7] => [8,2,4,3,5,1,6,7]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,1,7,8] => [2,4,6,3,5,1,7,8] => [5,2,6,4,3,1,7,8]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,1,7,8] => [2,5,4,3,6,1,7,8] => [6,2,4,5,3,1,7,8]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,1,6,7] => [3,2,4,5,8,1,6,7] => [8,3,2,4,5,1,6,7]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,1,7,8] => [3,2,6,4,5,1,7,8] => [5,3,2,6,4,1,7,8]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8] => [6,3,4,2,5,1,7,8]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [3,4,2,5,6,1,7,8] => [6,4,3,2,5,1,7,8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [2,3,4,5,1,8,6,7] => [5,2,3,4,1,8,6,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [2,3,4,5,7,1,6,8] => [7,2,3,4,5,1,6,8]
[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] => [5,2,3,4,6,1,7,8]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [2,3,5,4,6,1,7,8] => [6,2,3,5,4,1,7,8]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [2,4,3,5,6,1,7,8] => [6,2,4,3,5,1,7,8]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8] => [6,3,2,4,5,1,7,8]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,8,7,6,5,4] => [1,2,3,5,6,7,8,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [1,2,3,7,8,6,5,4] => [1,2,3,5,6,8,7,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [1,2,3,6,8,7,5,4] => [1,2,3,5,7,6,8,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [1,2,3,7,6,8,5,4] => [1,2,3,5,8,7,6,4]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [1,2,3,6,7,8,5,4] => [1,2,3,5,8,6,7,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [1,2,3,5,8,7,6,4] => [1,2,3,6,5,7,8,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [1,2,3,5,7,8,6,4] => [1,2,3,6,5,8,7,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [1,2,3,6,8,5,7,4] => [1,2,3,7,8,6,5,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [1,2,3,7,6,5,8,4] => [1,2,3,8,6,7,5,4]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [1,2,3,6,7,5,8,4] => [1,2,3,8,7,6,5,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [1,2,3,5,6,8,7,4] => [1,2,3,7,5,6,8,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [1,2,3,5,7,6,8,4] => [1,2,3,8,5,7,6,4]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [1,2,3,6,5,7,8,4] => [1,2,3,8,6,5,7,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [1,2,4,8,7,6,3,5] => [1,2,6,4,3,7,8,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [1,2,4,7,8,6,3,5] => [1,2,6,4,3,8,7,5]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,1,2,3,5] => [1,2,4,6,8,7,3,5] => [1,2,7,4,3,6,8,5]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => [1,2,4,7,6,8,3,5] => [1,2,8,4,3,7,6,5]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [1,2,4,6,7,8,3,5] => [1,2,8,4,3,6,7,5]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [1,2,5,8,7,4,3,6] => [1,2,4,7,5,3,8,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [1,2,5,7,8,4,3,6] => [1,2,4,8,5,3,7,6]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [1,2,6,8,5,4,3,7] => [1,2,4,5,8,6,3,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [1,2,7,6,5,4,3,8] => [1,2,4,5,6,7,3,8]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,1,2,3,8] => [1,2,6,7,5,4,3,8] => [1,2,4,5,7,6,3,8]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [1,2,5,6,8,4,3,7] => [1,2,4,8,5,6,3,7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,1,2,3,8] => [1,2,5,7,6,4,3,8] => [1,2,4,6,5,7,3,8]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [1,2,5,6,7,4,3,8] => [1,2,4,7,5,6,3,8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [1,2,4,5,8,7,3,6] => [1,2,7,4,5,3,8,6]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [1,2,4,5,7,8,3,6] => [1,2,8,4,5,3,7,6]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [1,2,4,6,8,5,3,7] => [1,2,5,4,8,6,3,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => [1,2,4,7,6,5,3,8] => [1,2,5,4,6,7,3,8]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,1,2,3,8] => [1,2,4,6,7,5,3,8] => [1,2,5,4,7,6,3,8]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,1,2,3,7] => [1,2,5,4,8,6,3,7] => [1,2,6,5,4,8,3,7]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => [1,2,5,7,4,6,3,8] => [1,2,6,7,5,4,3,8]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [1,2,5,6,4,7,3,8] => [1,2,7,6,5,4,3,8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [1,2,4,5,6,8,3,7] => [1,2,8,4,5,6,3,7]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [1,2,4,5,7,6,3,8] => [1,2,6,4,5,7,3,8]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,1,2,3,8] => [1,2,4,6,5,7,3,8] => [1,2,7,4,6,5,3,8]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [1,2,5,4,6,7,3,8] => [1,2,7,5,4,6,3,8]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [1,2,4,5,6,7,3,8] => [1,2,7,4,5,6,3,8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [1,3,2,8,7,6,4,5] => [1,3,2,6,4,7,8,5]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [1,3,2,6,8,7,4,5] => [1,3,2,7,4,6,8,5]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [1,3,2,7,6,8,4,5] => [1,3,2,8,4,7,6,5]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [1,3,2,6,7,8,4,5] => [1,3,2,8,4,6,7,5]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [1,3,5,8,7,2,4,6] => [1,7,3,2,5,4,8,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [1,3,5,7,8,2,4,6] => [1,8,3,2,5,4,7,6]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,1,2,4,7] => [1,3,6,8,5,2,4,7] => [1,5,3,2,8,6,4,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,1,2,4,8] => [1,3,7,6,5,2,4,8] => [1,5,3,2,6,7,4,8]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,1,2,4,8] => [1,3,6,7,5,2,4,8] => [1,5,3,2,7,6,4,8]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [1,3,5,6,8,2,4,7] => [1,8,3,2,5,6,4,7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => [1,3,5,7,6,2,4,8] => [1,6,3,2,5,7,4,8]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [1,3,5,6,7,2,4,8] => [1,7,3,2,5,6,4,8]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,1,2,5,6] => [1,4,3,8,7,2,5,6] => [1,7,4,3,2,5,8,6]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [1,4,3,7,8,2,5,6] => [1,8,4,3,2,5,7,6]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [1,4,6,8,3,2,5,7] => [1,3,8,4,2,6,5,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [1,4,7,6,3,2,5,8] => [1,3,6,4,2,7,5,8]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,1,2,5,8] => [1,4,6,7,3,2,5,8] => [1,3,7,4,2,6,5,8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,1,2,6,7] => [1,5,4,8,3,2,6,7] => [1,3,8,5,4,2,6,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [1,6,5,4,3,2,7,8] => [1,3,4,5,6,2,7,8]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [1,5,6,4,3,2,7,8] => [1,3,4,6,5,2,7,8]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,1,2,6,8] => [1,4,5,7,3,2,6,8] => [1,3,7,4,5,2,6,8]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [1,4,6,5,3,2,7,8] => [1,3,5,4,6,2,7,8]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [1,5,4,6,3,2,7,8] => [1,3,6,5,4,2,7,8]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,1,2,7,8] => [1,4,5,6,3,2,7,8] => [1,3,6,4,5,2,7,8]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [1,3,4,2,7,8,5,6] => [1,4,3,2,8,5,7,6]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [1,3,4,6,8,2,5,7] => [1,8,3,4,2,6,5,7]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [1,3,4,6,7,2,5,8] => [1,7,3,4,2,6,5,8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [1,3,5,4,8,2,6,7] => [1,8,3,5,4,2,6,7]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => [1,3,5,7,4,2,6,8] => [1,4,3,7,5,2,6,8]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,1,2,7,8] => [1,3,6,5,4,2,7,8] => [1,4,3,5,6,2,7,8]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [1,3,5,6,4,2,7,8] => [1,4,3,6,5,2,7,8]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,1,2,6,7] => [1,4,3,5,8,2,6,7] => [1,8,4,3,5,2,6,7]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [1,5,4,3,6,2,7,8] => [1,6,4,5,3,2,7,8]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,1,2,7,8] => [1,4,5,3,6,2,7,8] => [1,6,5,4,3,2,7,8]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [1,3,4,5,2,8,6,7] => [1,5,3,4,2,8,6,7]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,1,2,6,8] => [1,3,4,5,7,2,6,8] => [1,7,3,4,5,2,6,8]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,1,2,7,8] => [1,3,4,6,5,2,7,8] => [1,5,3,4,6,2,7,8]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,1,2,7,8] => [1,3,5,4,6,2,7,8] => [1,6,3,5,4,2,7,8]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [1,4,3,5,6,2,7,8] => [1,6,4,3,5,2,7,8]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [2,1,3,8,7,6,4,5] => [2,1,3,6,4,7,8,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [2,1,3,7,8,6,4,5] => [2,1,3,6,4,8,7,5]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [2,1,3,6,8,7,4,5] => [2,1,3,7,4,6,8,5]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [2,1,3,6,7,8,4,5] => [2,1,3,8,4,6,7,5]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [2,1,5,8,7,3,4,6] => [2,1,7,3,5,4,8,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [2,1,5,7,8,3,4,6] => [2,1,8,3,5,4,7,6]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [2,1,6,8,5,3,4,7] => [2,1,5,3,8,6,4,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [2,1,7,6,5,3,4,8] => [2,1,5,3,6,7,4,8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [2,1,5,6,8,3,4,7] => [2,1,8,3,5,6,4,7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [2,1,5,7,6,3,4,8] => [2,1,6,3,5,7,4,8]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [2,1,5,6,7,3,4,8] => [2,1,7,3,5,6,4,8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [2,4,1,8,7,3,5,6] => [4,2,7,1,3,5,8,6]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [2,4,1,7,8,3,5,6] => [4,2,8,1,3,5,7,6]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [2,4,6,8,1,3,5,7] => [8,2,1,4,3,6,5,7]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [2,5,4,8,1,3,6,7] => [8,2,1,5,4,3,6,7]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [2,6,5,4,1,3,7,8] => [4,2,1,5,6,3,7,8]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [2,5,6,4,1,3,7,8] => [4,2,1,6,5,3,7,8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,1,3,6,7] => [2,4,5,1,8,3,6,7] => [5,2,8,4,1,3,6,7]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [2,5,4,6,1,3,7,8] => [6,2,1,5,4,3,7,8]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [2,4,5,6,1,3,7,8] => [6,2,1,4,5,3,7,8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [3,2,1,8,7,4,5,6] => [2,3,1,7,4,5,8,6]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [3,2,1,7,8,4,5,6] => [2,3,1,8,4,5,7,6]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [3,2,6,8,1,4,5,7] => [8,3,2,1,4,6,5,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [3,2,7,6,1,4,5,8] => [6,3,2,1,4,7,5,8]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [3,2,6,7,1,4,5,8] => [7,3,2,1,4,6,5,8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [3,5,7,2,1,4,6,8] => [2,7,3,1,5,4,6,8]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [3,6,5,2,1,4,7,8] => [2,5,3,1,6,4,7,8]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [3,5,6,2,1,4,7,8] => [2,6,3,1,5,4,7,8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [4,3,2,8,1,5,6,7] => [8,3,4,2,1,5,6,7]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [4,3,7,2,1,5,6,8] => [2,7,4,3,1,5,6,8]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [4,6,3,2,1,5,7,8] => [2,3,6,4,1,5,7,8]
[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] => [2,3,4,5,1,6,7,8]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [4,5,3,2,1,6,7,8] => [2,3,5,4,1,6,7,8]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [3,4,2,1,8,5,6,7] => [2,4,3,1,8,5,6,7]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,2,1,5,6,8] => [3,4,2,7,1,5,6,8] => [7,4,3,2,1,5,6,8]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [3,4,6,2,1,5,7,8] => [2,6,3,4,1,5,7,8]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [3,5,4,2,1,6,7,8] => [2,4,3,5,1,6,7,8]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [4,3,5,2,1,6,7,8] => [2,5,4,3,1,6,7,8]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [3,4,5,2,1,6,7,8] => [2,5,3,4,1,6,7,8]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [2,3,1,4,8,7,5,6] => [3,2,1,4,7,5,8,6]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [2,3,1,4,7,8,5,6] => [3,2,1,4,8,5,7,6]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,1,4,5,7] => [2,3,1,6,8,4,5,7] => [3,2,1,8,4,6,5,7]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [2,3,1,6,7,4,5,8] => [3,2,1,7,4,6,5,8]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,1,4,6,7] => [2,3,5,1,8,4,6,7] => [5,2,3,8,1,4,6,7]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [2,3,5,7,1,4,6,8] => [7,2,3,1,5,4,6,8]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,1,4,7,8] => [2,3,5,6,1,4,7,8] => [6,2,3,1,5,4,7,8]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [2,4,3,1,8,5,6,7] => [3,2,4,1,8,5,6,7]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,1,5,6,8] => [2,4,3,7,1,5,6,8] => [7,2,4,3,1,5,6,8]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [2,5,4,3,1,6,7,8] => [3,2,4,5,1,6,7,8]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [2,4,5,3,1,6,7,8] => [3,2,5,4,1,6,7,8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,1,5,6,7] => [3,2,4,1,8,5,6,7] => [4,3,2,1,8,5,6,7]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,1,5,6,8] => [3,2,4,7,1,5,6,8] => [7,3,2,4,1,5,6,8]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,1,5,7,8] => [3,2,6,4,1,5,7,8] => [4,3,2,6,1,5,7,8]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [3,5,2,4,1,6,7,8] => [4,5,3,2,1,6,7,8]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [4,3,2,5,1,6,7,8] => [5,3,4,2,1,6,7,8]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [2,3,4,1,5,8,6,7] => [4,2,3,1,5,8,6,7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [2,3,4,1,7,5,6,8] => [4,2,3,1,7,5,6,8]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,1,5,7,8] => [2,3,4,6,1,5,7,8] => [6,2,3,4,1,5,7,8]
[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] => [4,2,3,5,1,6,7,8]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [2,4,3,5,1,6,7,8] => [5,2,4,3,1,6,7,8]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [3,2,4,5,1,6,7,8] => [5,3,2,4,1,6,7,8]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [1,2,3,4,8,7,6,5] => [1,2,3,4,6,7,8,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [1,2,3,4,7,8,6,5] => [1,2,3,4,6,8,7,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,6,8,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,7,6,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [1,2,3,5,8,7,4,6] => [1,2,3,7,5,4,8,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [1,2,3,5,7,8,4,6] => [1,2,3,8,5,4,7,6]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [1,2,3,6,8,5,4,7] => [1,2,3,5,8,6,4,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [1,2,3,7,6,5,4,8] => [1,2,3,5,6,7,4,8]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [1,2,3,6,7,5,4,8] => [1,2,3,5,7,6,4,8]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,2,3,5,6,8,4,7] => [1,2,3,8,5,6,4,7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [1,2,3,5,7,6,4,8] => [1,2,3,6,5,7,4,8]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [1,2,3,6,5,7,4,8] => [1,2,3,7,6,5,4,8]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [1,2,4,3,8,7,5,6] => [1,2,4,3,7,5,8,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => [1,2,4,3,7,8,5,6] => [1,2,4,3,8,5,7,6]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [1,2,4,6,8,3,5,7] => [1,2,8,4,3,6,5,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4,1,2,3,5,8] => [1,2,4,7,6,3,5,8] => [1,2,6,4,3,7,5,8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [1,2,5,4,8,3,6,7] => [1,2,8,5,4,3,6,7]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,5,4,1,2,3,6,8] => [1,2,5,7,4,3,6,8] => [1,2,4,7,5,3,6,8]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [1,2,6,5,4,3,7,8] => [1,2,4,5,6,3,7,8]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,6,4,1,2,3,7,8] => [1,2,5,6,4,3,7,8] => [1,2,4,6,5,3,7,8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [1,2,4,5,3,8,6,7] => [1,2,5,4,3,8,6,7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [1,2,4,5,7,3,6,8] => [1,2,7,4,5,3,6,8]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [6,4,5,1,2,3,7,8] => [1,2,4,6,5,3,7,8] => [1,2,5,4,6,3,7,8]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,6,1,2,3,7,8] => [1,2,5,4,6,3,7,8] => [1,2,6,5,4,3,7,8]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [1,2,4,5,6,3,7,8] => [1,2,6,4,5,3,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [1,3,2,4,7,8,5,6] => [1,3,2,4,8,5,7,6]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [7,6,3,1,2,4,5,8] => [1,3,2,7,6,4,5,8] => [1,3,2,6,4,7,5,8]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [1,3,2,6,7,4,5,8] => [1,3,2,7,4,6,5,8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [1,3,5,2,8,4,6,7] => [1,5,3,8,2,4,6,7]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [1,3,5,7,2,4,6,8] => [1,7,3,2,5,4,6,8]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1,2,4,7,8] => [1,3,6,5,2,4,7,8] => [1,5,3,2,6,4,7,8]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,6,3,1,2,4,7,8] => [1,3,5,6,2,4,7,8] => [1,6,3,2,5,4,7,8]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [8,4,3,1,2,5,6,7] => [1,4,3,2,8,5,6,7] => [1,3,4,2,8,5,6,7]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [1,4,3,7,2,5,6,8] => [1,7,4,3,2,5,6,8]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [1,4,6,3,2,5,7,8] => [1,3,6,4,2,5,7,8]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [1,5,4,3,2,6,7,8] => [1,3,4,5,2,6,7,8]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,5,3,1,2,6,7,8] => [1,4,5,3,2,6,7,8] => [1,3,5,4,2,6,7,8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [1,3,4,2,5,8,6,7] => [1,4,3,2,5,8,6,7]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [1,3,4,2,7,5,6,8] => [1,4,3,2,7,5,6,8]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,4,1,2,5,7,8] => [1,3,4,6,2,5,7,8] => [1,6,3,4,2,5,7,8]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [1,3,5,4,2,6,7,8] => [1,4,3,5,2,6,7,8]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [1,4,3,5,2,6,7,8] => [1,5,4,3,2,6,7,8]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [2,1,3,4,8,7,5,6] => [2,1,3,4,7,5,8,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [2,1,3,4,7,8,5,6] => [2,1,3,4,8,5,7,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [2,1,5,3,8,4,6,7] => [2,1,5,8,3,4,6,7]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1,3,4,6,8] => [2,1,5,7,3,4,6,8] => [2,1,7,3,5,4,6,8]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,3,4,7,8] => [2,1,6,5,3,4,7,8] => [2,1,5,3,6,4,7,8]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [2,1,5,6,3,4,7,8] => [2,1,6,3,5,4,7,8]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [2,4,1,3,8,5,6,7] => [4,2,1,3,8,5,6,7]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [2,4,6,1,3,5,7,8] => [6,2,1,4,3,5,7,8]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [2,5,4,1,3,6,7,8] => [4,2,1,5,3,6,7,8]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [2,4,5,1,3,6,7,8] => [5,2,1,4,3,6,7,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [3,2,1,4,8,5,6,7] => [2,3,1,4,8,5,6,7]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [3,2,1,7,4,5,6,8] => [2,3,1,7,4,5,6,8]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => [3,2,6,1,4,5,7,8] => [6,3,2,1,4,5,7,8]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [3,5,2,1,4,6,7,8] => [2,5,3,1,4,6,7,8]
[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] => [2,3,4,1,5,6,7,8]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [3,4,2,1,5,6,7,8] => [2,4,3,1,5,6,7,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [2,3,1,4,5,8,6,7] => [3,2,1,4,5,8,6,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [2,3,1,4,7,5,6,8] => [3,2,1,4,7,5,6,8]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [2,3,1,6,4,5,7,8] => [3,2,1,6,4,5,7,8]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [2,3,5,1,4,6,7,8] => [5,2,3,1,4,6,7,8]
[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] => [3,2,4,1,5,6,7,8]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [1,2,3,4,6,8,5,7] => [1,2,3,4,8,6,5,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [1,2,3,4,7,6,5,8] => [1,2,3,4,6,7,5,8]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,8,6,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [1,2,3,5,7,4,6,8] => [1,2,3,7,5,4,6,8]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [1,2,3,6,5,4,7,8] => [1,2,3,5,6,4,7,8]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,6,1,2,3,4,7,8] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,8,6,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [1,2,4,3,7,5,6,8] => [1,2,4,3,7,5,6,8]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [1,2,4,6,3,5,7,8] => [1,2,6,4,3,5,7,8]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [1,2,5,4,3,6,7,8] => [1,2,4,5,3,6,7,8]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [1,3,2,4,7,5,6,8] => [1,3,2,4,7,5,6,8]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [1,3,2,6,4,5,7,8] => [1,3,2,6,4,5,7,8]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [1,3,5,2,4,6,7,8] => [1,5,3,2,4,6,7,8]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [1,3,4,2,5,6,7,8]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,8,6,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [2,1,3,4,7,5,6,8] => [2,1,3,4,7,5,6,8]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => [2,1,3,6,4,5,7,8] => [2,1,3,6,4,5,7,8]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => [2,1,5,3,4,6,7,8]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [2,4,1,3,5,6,7,8] => [4,2,1,3,5,6,7,8]
[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] => [2,3,1,4,5,6,7,8]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8]
[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]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8]
[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] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8]
[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] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1]
[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] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9]
[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] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,9,7,8]
[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] => [3,2,4,5,6,7,8,9,1] => [9,3,2,4,5,6,7,8,1]
[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] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1]
[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] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10]
[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] => [2,1,3,4,5,6,7,10,8,9] => [2,1,3,4,5,6,7,10,8,9]
[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] => [1,3,2,4,5,6,9,7,8] => [1,3,2,4,5,6,9,7,8]
[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] => [2,3,1,4,5,6,9,7,8] => [3,2,1,4,5,6,9,7,8]
[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] => [2,4,3,5,6,7,8,9,1] => [9,2,4,3,5,6,7,8,1]
[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] => [3,4,2,5,6,7,8,9,1] => [9,4,3,2,5,6,7,8,1]
[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] => [3,2,4,5,6,7,8,9,10,1] => [10,3,2,4,5,6,7,8,9,1]
[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] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1]
[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] => [1,2,3,4,5,6,7,8,9,10,12,11] => [1,2,3,4,5,6,7,8,9,10,12,11]
[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] => [1,3,2,4,5,6,7,10,8,9] => [1,3,2,4,5,6,7,10,8,9]
[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] => [4,3,2,5,6,7,8,9,1] => [9,3,4,2,5,6,7,8,1]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,1] => [3,4,5,2,6,7,8,9,1] => [9,5,3,4,2,6,7,8,1]
[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] => [3,4,2,5,6,7,8,9,10,1] => [10,4,3,2,5,6,7,8,9,1]
[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] => [3,2,4,5,6,7,8,9,10,11,1] => [11,3,2,4,5,6,7,8,9,10,1]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => [4,3,2,5,6,7,8,9,10,1] => [10,3,4,2,5,6,7,8,9,1]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,10,1] => [3,4,5,2,6,7,8,9,10,1] => [10,5,3,4,2,6,7,8,9,1]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,10,11,1] => [3,4,2,5,6,7,8,9,10,11,1] => [11,4,3,2,5,6,7,8,9,10,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,9,7,8] => [6,2,3,4,5,1,9,7,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => [2,3,4,6,5,7,8,9,10,1] => [10,2,3,4,6,5,7,8,9,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,1] => [3,4,5,6,7,2,8,9,1] => [9,7,3,4,5,6,2,8,1]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,2,7,8,9,10,1] => [3,4,5,6,2,7,8,9,10,1] => [10,6,3,4,5,2,7,8,9,1]
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,10,11,1] => [3,4,5,2,6,7,8,9,10,11,1] => [11,5,3,4,2,6,7,8,9,10,1]
[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] => [1,2,3,4,5,7,9,6,8] => [1,2,3,4,5,9,7,6,8]
[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] => [2,3,4,5,6,7,9,1,8] => [9,2,3,4,5,6,7,1,8]
[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] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7]
[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] => [2,3,4,5,6,8,7,9,1] => [9,2,3,4,5,6,8,7,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => [5,4,3,2,6,7,8,9,1] => [9,3,4,5,2,6,7,8,1]
[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] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2]
[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] => [3,4,5,6,7,8,2,9,1] => [9,8,3,4,5,6,7,2,1]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,10,1] => [3,4,5,6,7,2,8,9,10,1] => [10,7,3,4,5,6,2,8,9,1]
[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] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7]
[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] => [8,2,3,4,5,6,7,9,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,6,7,8,9,10,1] => [5,4,3,2,6,7,8,9,10,1] => [10,3,4,5,2,6,7,8,9,1]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => [1,4,3,5,6,7,8,9,2] => [1,9,4,3,5,6,7,8,2]
[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] => [3,4,5,6,7,8,9,2,1] => [2,9,3,4,5,6,7,8,1]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,10,1] => [3,4,5,6,7,8,2,9,10,1] => [10,8,3,4,5,6,7,2,9,1]
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,10,11,1] => [3,4,5,6,7,2,8,9,10,11,1] => [11,7,3,4,5,6,2,8,9,10,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,10,1,9] => [10,2,3,4,5,6,7,8,1,9]
[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] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,1,3,4,5,6,7] => [2,1,3,4,5,9,8,6,7] => [2,1,3,4,5,8,6,9,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,1,4,5,6,7] => [2,3,1,4,5,8,9,6,7] => [3,2,1,4,5,9,6,8,7]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,1,2] => [1,4,5,3,6,7,8,9,2] => [1,9,5,4,3,6,7,8,2]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,2,1] => [4,3,5,6,7,8,9,2,1] => [2,9,4,3,5,6,7,8,1]
[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] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2]
[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] => [3,4,5,6,7,8,9,2,10,1] => [10,9,3,4,5,6,7,8,2,1]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,10,11,1] => [3,4,5,6,7,8,2,9,10,11,1] => [11,8,3,4,5,6,7,2,9,10,1]
[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] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8]
[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] => [9,2,3,4,5,6,7,8,10,1]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,6,7,2,3,4,8,9,1] => [2,3,5,6,7,4,8,9,1] => [9,2,3,7,5,6,4,8,1]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,2,1] => [4,5,3,6,7,8,9,2,1] => [2,9,5,4,3,6,7,8,1]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,1,2] => [1,4,3,5,6,7,8,9,10,2] => [1,10,4,3,5,6,7,8,9,2]
[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] => [3,4,5,6,7,8,9,10,2,1] => [2,10,3,4,5,6,7,8,9,1]
[] => [] => [] => []
[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] => [2,3,4,5,6,7,8,1,9]
[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] => [7,8,6,5,4,3,2,1,9] => [2,3,4,5,6,8,7,1,9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => [6,8,7,5,4,3,2,1,9] => [2,3,4,5,7,6,8,1,9]
[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] => [7,6,8,5,4,3,2,1,9] => [2,3,4,5,8,7,6,1,9]
[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] => [6,7,8,5,4,3,2,1,9] => [2,3,4,5,8,6,7,1,9]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,7,5,6,4,3,2,1,9] => [5,8,7,6,4,3,2,1,9] => [2,3,4,6,5,7,8,1,9]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,8,4,3,2,1,9] => [7,6,5,8,4,3,2,1,9] => [2,3,4,8,6,7,5,1,9]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [6,7,5,8,4,3,2,1,9] => [6,7,5,8,4,3,2,1,9] => [2,3,4,8,7,6,5,1,9]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [6,5,7,8,4,3,2,1,9] => [6,5,7,8,4,3,2,1,9] => [2,3,4,8,6,5,7,1,9]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1,9] => [5,6,7,8,4,3,2,1,9] => [2,3,4,8,5,6,7,1,9]
[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] => [2,3,5,4,6,7,8,1,9]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [5,8,7,4,6,3,2,1,9] => [2,3,6,7,5,4,8,1,9]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,8,3,2,1,9] => [7,6,5,4,8,3,2,1,9] => [2,3,8,5,6,7,4,1,9]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1,9] => [6,5,4,7,8,3,2,1,9] => [2,3,8,5,6,4,7,1,9]
[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] => [7,6,5,4,3,8,2,1,9] => [2,8,4,5,6,7,3,1,9]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,8,2,1,9] => [6,5,4,3,7,8,2,1,9] => [2,8,4,5,6,3,7,1,9]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => [3,4,5,6,7,8,2,1,9] => [2,8,3,4,5,6,7,1,9]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => [2,8,7,6,5,4,3,1,9] => [3,2,4,5,6,7,8,1,9]
[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] => [7,6,5,4,3,2,8,1,9] => [8,3,4,5,6,7,2,1,9]
[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] => [5,4,6,3,7,2,8,1,9] => [8,7,6,5,4,3,2,1,9]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,1,9] => [6,5,4,3,2,7,8,1,9] => [8,3,4,5,6,2,7,1,9]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1,9] => [3,4,5,2,6,7,8,1,9] => [8,5,3,4,2,6,7,1,9]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8,7,2,3,4,5,6,1,9] => [2,3,4,5,8,7,6,1,9] => [6,2,3,4,5,7,8,1,9]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,1,9] => [4,3,2,5,6,7,8,1,9] => [8,3,4,2,5,6,7,1,9]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1,9] => [3,4,2,5,6,7,8,1,9] => [8,4,3,2,5,6,7,1,9]
[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] => [7,2,3,4,5,6,8,1,9]
[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] => [3,2,4,5,6,7,8,1,9] => [8,3,2,4,5,6,7,1,9]
[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] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9]
[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] => [1,8,7,6,5,4,3,2,9] => [1,3,4,5,6,7,8,2,9]
[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] => [1,3,5,7,8,6,4,2,9] => [1,4,3,6,5,8,7,2,9]
[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] => [1,3,4,5,6,7,8,2,9] => [1,8,3,4,5,6,7,2,9]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,2,1,3,9] => [2,4,5,6,7,8,1,3,9] => [8,2,1,4,5,6,7,3,9]
[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] => [2,3,4,5,6,7,1,8,9]
[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] => [6,7,5,4,3,2,1,8,9] => [2,3,4,5,7,6,1,8,9]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8,9] => [3,4,5,6,7,2,1,8,9] => [2,7,3,4,5,6,1,8,9]
[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] => [6,5,4,3,2,7,1,8,9] => [7,3,4,5,6,2,1,8,9]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,7,1,8,9] => [5,6,4,3,2,7,1,8,9] => [7,3,4,6,5,2,1,8,9]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => [2,3,4,5,7,6,1,8,9] => [6,2,3,4,5,7,1,8,9]
[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] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9]
[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] => [1,2,8,7,6,5,4,3,9] => [1,2,4,5,6,7,8,3,9]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,1,2,8,9] => [1,7,6,5,4,3,2,8,9] => [1,3,4,5,6,7,2,8,9]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => [1,3,4,5,6,7,2,8,9] => [1,7,3,4,5,6,2,8,9]
[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] => [2,3,4,5,6,1,7,8,9]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9] => [5,6,4,3,2,1,7,8,9] => [2,3,4,6,5,1,7,8,9]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,2,1,7,8,9] => [4,3,5,6,2,1,7,8,9] => [2,6,4,3,5,1,7,8,9]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8,9] => [3,4,5,6,2,1,7,8,9] => [2,6,3,4,5,1,7,8,9]
[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] => [5,4,3,2,6,1,7,8,9] => [6,3,4,5,2,1,7,8,9]
[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] => [4,3,5,2,6,1,7,8,9] => [6,5,4,3,2,1,7,8,9]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,1,7,8,9] => [2,3,4,6,5,1,7,8,9] => [5,2,3,4,6,1,7,8,9]
[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] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9]
[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] => [1,2,3,5,6,7,8,4,9] => [1,2,3,8,5,6,7,4,9]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [6,7,4,5,1,2,3,8,9] => [1,2,4,6,7,5,3,8,9] => [1,2,5,4,7,6,3,8,9]
[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] => [1,3,5,6,4,2,7,8,9] => [1,4,3,6,5,2,7,8,9]
[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] => [2,4,6,8,1,3,5,7,9] => [8,2,1,4,3,6,5,7,9]
[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] => [2,3,4,5,1,6,7,8,9]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,1,6,7,8,9] => [4,5,3,2,1,6,7,8,9] => [2,3,5,4,1,6,7,8,9]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9] => [3,4,5,2,1,6,7,8,9] => [2,5,3,4,1,6,7,8,9]
[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] => [4,3,2,5,1,6,7,8,9] => [5,3,4,2,1,6,7,8,9]
[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] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,1,6,7,8,9] => [2,3,5,4,1,6,7,8,9] => [4,2,3,5,1,6,7,8,9]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8,9] => [3,2,4,5,1,6,7,8,9] => [5,3,2,4,1,6,7,8,9]
[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] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => [1,2,3,4,6,7,8,5,9] => [1,2,3,4,8,6,7,5,9]
[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] => [1,2,4,5,6,3,7,8,9] => [1,2,6,4,5,3,7,8,9]
[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] => [1,3,4,5,2,6,7,8,9] => [1,5,3,4,2,6,7,8,9]
[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] => [2,3,4,1,5,6,7,8,9]
[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] => [3,4,2,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9]
[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] => [3,2,4,1,5,6,7,8,9]
[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] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9]
[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] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9]
[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] => [1,2,3,4,5,7,8,6,9] => [1,2,3,4,5,8,7,6,9]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8,9] => [1,2,4,5,3,6,7,8,9] => [1,2,5,4,3,6,7,8,9]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => [1,3,5,2,4,6,7,8,9] => [1,5,3,2,4,6,7,8,9]
[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] => [1,4,3,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9]
[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] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9]
[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] => [2,1,3,4,5,8,6,7,9] => [2,1,3,4,5,8,6,7,9]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [4,2,1,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [4,2,1,3,5,6,7,8,9]
[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] => [2,3,1,4,5,6,7,8,9]
[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] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9]
[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] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9]
[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] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9]
[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] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9]
[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] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9]
[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] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9]
[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] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9]
[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]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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]
[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] => [2,3,4,5,6,7,8,9,1]
[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] => [8,9,7,6,5,4,3,2,1] => [2,3,4,5,6,7,9,8,1]
[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] => [8,7,9,6,5,4,3,2,1] => [2,3,4,5,6,9,8,7,1]
[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] => [8,7,6,9,5,4,3,2,1] => [2,3,4,5,9,7,8,6,1]
[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] => [8,7,6,5,9,4,3,2,1] => [2,3,4,9,6,7,8,5,1]
[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] => [8,7,6,5,4,9,3,2,1] => [2,3,9,5,6,7,8,4,1]
[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] => [8,7,6,5,4,3,9,2,1] => [2,9,4,5,6,7,8,3,1]
[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] => [8,7,6,5,4,3,2,9,1] => [9,3,4,5,6,7,8,2,1]
[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] => [2,3,4,5,6,7,8,9,10,1]
[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] => [9,10,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,10,9,1]
[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] => [7,8,9,6,5,4,3,2,1] => [2,3,4,5,6,9,7,8,1]
[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] => [9,8,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,9,8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [6,8,7,9,5,4,3,2,1] => [2,3,4,5,9,6,8,7,1]
[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] => [9,8,7,10,6,5,4,3,2,1] => [2,3,4,5,6,10,8,9,7,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => [5,8,7,6,9,4,3,2,1] => [2,3,4,9,5,7,8,6,1]
[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] => [9,8,7,6,10,5,4,3,2,1] => [2,3,4,5,10,7,8,9,6,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => [4,8,7,6,5,9,3,2,1] => [2,3,9,4,6,7,8,5,1]
[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] => [9,8,7,6,5,10,4,3,2,1] => [2,3,4,10,6,7,8,9,5,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => [3,8,7,6,5,4,9,2,1] => [2,9,3,5,6,7,8,4,1]
[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] => [9,8,7,6,5,4,10,3,2,1] => [2,3,10,5,6,7,8,9,4,1]
[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] => [2,8,7,6,5,4,3,9,1] => [9,2,4,5,6,7,8,3,1]
[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] => [9,8,7,6,5,4,3,10,2,1] => [2,10,4,5,6,7,8,9,3,1]
[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] => [9,8,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,8,9,2,1]
[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] => [2,3,4,5,6,7,8,9,1,10]
[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] => [2,3,4,5,6,7,8,9,10,11,1]
[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] => [10,11,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,11,10,1]
[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] => [8,9,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,8,9,1]
[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] => [10,9,11,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,11,10,9,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [7,6,8,9,5,4,3,2,1] => [7,6,8,9,5,4,3,2,1] => [2,3,4,5,9,7,6,8,1]
[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] => [6,7,8,9,5,4,3,2,1] => [2,3,4,5,9,6,7,8,1]
[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] => [1,9,8,7,6,5,4,3,2,10] => [1,3,4,5,6,7,8,9,2,10]
[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] => [10,9,8,7,6,5,4,3,2,11,1] => [11,3,4,5,6,7,8,9,10,2,1]
[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] => [2,3,4,5,6,7,8,9,10,1,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [11,10,12,9,8,7,6,5,4,3,2,1] => [11,10,12,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,12,11,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => [8,7,9,10,6,5,4,3,2,1] => [2,3,4,5,6,10,8,7,9,1]
[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] => [7,8,9,10,6,5,4,3,2,1] => [2,3,4,5,6,10,7,8,9,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [6,5,7,8,9,4,3,2,1] => [2,3,4,9,6,5,7,8,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,10,9,8,7,6,5,4,3,2,12,1] => [11,10,9,8,7,6,5,4,3,2,12,1] => [12,3,4,5,6,7,8,9,10,11,2,1]
[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] => [5,6,7,8,9,4,3,2,1] => [2,3,4,9,5,6,7,8,1]
[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] => [6,7,8,9,10,5,4,3,2,1] => [2,3,4,5,10,6,7,8,9,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => [7,6,5,4,3,2,8,9,1] => [9,3,4,5,6,7,2,8,1]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [5,4,6,7,8,9,3,2,1] => [2,3,9,5,4,6,7,8,1]
[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] => [4,5,6,7,8,9,3,2,1] => [2,3,9,4,5,6,7,8,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,9,1] => [6,5,4,3,2,7,8,9,1] => [9,3,4,5,6,2,7,8,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,4,3,2,1] => [6,5,7,8,9,10,4,3,2,1] => [2,3,4,10,6,5,7,8,9,1]
[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] => [5,6,7,8,9,10,4,3,2,1] => [2,3,4,10,5,6,7,8,9,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,10,1] => [8,7,6,5,4,3,2,9,10,1] => [10,3,4,5,6,7,8,2,9,1]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,4,3,6,7,8,9,2,1] => [5,4,3,6,7,8,9,2,1] => [2,9,4,5,3,6,7,8,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,10,1] => [7,6,5,4,3,2,8,9,10,1] => [10,3,4,5,6,7,2,8,9,1]
[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] => [7,9,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,9,1]
[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] => [6,8,9,7,5,4,3,2,1] => [2,3,4,5,7,6,9,8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [9,6,7,8,5,4,3,2,1] => [6,7,9,8,5,4,3,2,1] => [2,3,4,5,8,6,7,9,1]
[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] => [5,9,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,9,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,4,3,2,1] => [5,7,8,9,6,4,3,2,1] => [2,3,4,6,5,9,7,8,1]
[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] => [4,9,8,7,6,5,3,2,1] => [2,3,5,4,6,7,8,9,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,3,2,1] => [4,6,7,8,9,5,3,2,1] => [2,3,5,4,9,6,7,8,1]
[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] => [3,9,8,7,6,5,4,2,1] => [2,4,3,5,6,7,8,9,1]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,2,1] => [3,5,6,7,8,9,4,2,1] => [2,4,3,9,5,6,7,8,1]
[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] => [2,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,1]
[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] => [2,8,9,7,6,5,4,3,1] => [3,2,4,5,6,7,9,8,1]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [2,4,5,6,7,8,9,3,1] => [3,2,9,4,5,6,7,8,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,4,1] => [2,3,9,8,7,6,5,4,1] => [4,2,3,5,6,7,8,9,1]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,4,1] => [2,3,5,6,7,8,9,4,1] => [4,2,3,9,5,6,7,8,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => [2,3,4,6,7,8,9,5,1] => [5,2,3,4,9,6,7,8,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,5,6,1] => [2,3,4,5,7,8,9,6,1] => [6,2,3,4,5,9,7,8,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => [2,3,4,5,6,9,8,7,1] => [7,2,3,4,5,6,8,9,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [2,3,4,5,6,8,9,7,1] => [7,2,3,4,5,6,9,8,1]
[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] => [1,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,2]
[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] => [1,8,9,7,6,5,4,3,2] => [1,3,4,5,6,7,9,8,2]
[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] => [1,7,9,8,6,5,4,3,2] => [1,3,4,5,6,8,7,9,2]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,1,2] => [1,4,5,6,7,8,9,3,2] => [1,3,9,4,5,6,7,8,2]
[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] => [1,3,9,8,7,6,5,4,2] => [1,4,3,5,6,7,8,9,2]
[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] => [1,3,5,9,8,7,6,4,2] => [1,4,3,6,5,7,8,9,2]
[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] => [1,3,5,7,9,8,6,4,2] => [1,4,3,6,5,8,7,9,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [9,8,3,4,5,6,7,1,2] => [1,3,4,5,6,9,8,7,2] => [1,7,3,4,5,6,8,9,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [1,3,4,5,6,7,9,8,2] => [1,8,3,4,5,6,7,9,2]
[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] => [1,2,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [1,2,4,9,8,7,6,5,3] => [1,2,5,4,6,7,8,9,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [1,2,4,6,8,9,7,5,3] => [1,2,5,4,7,6,9,8,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [1,2,4,5,9,8,7,6,3] => [1,2,6,4,5,7,8,9,3]
[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] => [1,2,4,5,7,8,9,6,3] => [1,2,6,4,5,9,7,8,3]
[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] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3]
[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] => [1,2,3,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [1,2,3,5,9,8,7,6,4] => [1,2,3,6,5,7,8,9,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [1,2,3,5,7,9,8,6,4] => [1,2,3,6,5,8,7,9,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [1,2,3,5,6,9,8,7,4] => [1,2,3,7,5,6,8,9,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [1,2,3,5,6,8,9,7,4] => [1,2,3,7,5,6,9,8,4]
[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] => [1,2,3,5,6,7,9,8,4] => [1,2,3,8,5,6,7,9,4]
[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] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4]
[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] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,6,7,8,9,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [1,2,3,4,6,9,8,7,5] => [1,2,3,4,7,6,8,9,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [1,2,3,4,6,7,9,8,5] => [1,2,3,4,8,6,7,9,5]
[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] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5]
[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] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,7,8,9,6]
[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] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,8,7,9,6]
[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] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6]
[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] => [8,10,9,7,6,5,4,3,2,1] => [2,3,4,5,6,7,9,8,10,1]
[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] => [7,9,10,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,10,9,1]
[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] => [6,10,9,8,7,5,4,3,2,1] => [2,3,4,5,7,6,8,9,10,1]
[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] => [2,3,4,6,5,7,8,9,10,1]
[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] => [4,5,6,7,8,9,10,3,2,1] => [2,3,10,4,5,6,7,8,9,1]
[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] => [2,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,1]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [2,4,5,6,7,8,9,10,3,1] => [3,2,10,4,5,6,7,8,9,1]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,2,3,4,1] => [2,3,5,6,7,8,9,10,4,1] => [4,2,3,10,5,6,7,8,9,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,2,3,4,5,1] => [2,3,4,6,7,8,9,10,5,1] => [5,2,3,4,10,6,7,8,9,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,10,9,8,1] => [8,2,3,4,5,6,7,9,10,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [9,10,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,9,10,8,1] => [8,2,3,4,5,6,7,10,9,1]
[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] => [1,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,2]
[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] => [1,9,10,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,10,9,2]
[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] => [1,3,10,9,8,7,6,5,4,2] => [1,4,3,5,6,7,8,9,10,2]
[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] => [1,3,5,10,9,8,7,6,4,2] => [1,4,3,6,5,7,8,9,10,2]
[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] => [1,3,5,7,10,9,8,6,4,2] => [1,4,3,6,5,8,7,9,10,2]
[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] => [1,3,5,7,9,10,8,6,4,2] => [1,4,3,6,5,8,7,10,9,2]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,1,2] => [1,3,4,5,6,7,8,10,9,2] => [1,9,3,4,5,6,7,8,10,2]
[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] => [1,2,10,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,10,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [1,2,4,10,9,8,7,6,5,3] => [1,2,5,4,6,7,8,9,10,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [1,2,4,6,8,10,9,7,5,3] => [1,2,5,4,7,6,9,8,10,3]
[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] => [1,2,4,5,7,9,10,8,6,3] => [1,2,6,4,5,8,7,10,9,3]
[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] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3]
[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] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,10,4]
[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] => [1,2,3,5,7,9,10,8,6,4] => [1,2,3,6,5,8,7,10,9,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [1,2,3,5,6,8,9,10,7,4] => [1,2,3,7,5,6,10,8,9,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,10,9,8,4] => [1,2,3,8,5,6,7,9,10,4]
[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] => [1,2,3,5,6,7,9,10,8,4] => [1,2,3,8,5,6,7,10,9,4]
[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] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4]
[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] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,6,7,8,9,10,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [1,2,3,4,6,8,10,9,7,5] => [1,2,3,4,7,6,9,8,10,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [1,2,3,4,6,7,8,10,9,5] => [1,2,3,4,9,6,7,8,10,5]
[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] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5]
[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] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,7,8,9,10,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,7,8,10,9,6] => [1,2,3,4,5,9,7,8,10,6]
[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] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6]
[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] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,8,9,10,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,10,9,7] => [1,2,3,4,5,6,9,8,10,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7]
[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]
[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] => [2,9,8,7,6,5,4,1,3] => [4,2,1,5,6,7,8,9,3]
[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] => [3,9,8,7,6,5,2,1,4] => [2,5,3,1,6,7,8,9,4]
[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] => [4,9,8,7,6,3,2,1,5] => [2,3,6,4,1,7,8,9,5]
[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] => [5,9,8,7,4,3,2,1,6] => [2,3,4,7,5,1,8,9,6]
[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] => [6,9,8,5,4,3,2,1,7] => [2,3,4,5,8,6,1,9,7]
[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] => [7,9,6,5,4,3,2,1,8] => [2,3,4,5,6,9,7,1,8]
[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] => [2,10,9,8,7,6,5,4,1,3] => [4,2,1,5,6,7,8,9,10,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,1,4] => [2,3,9,8,7,6,5,1,4] => [5,2,3,1,6,7,8,9,4]
[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] => [3,10,9,8,7,6,5,2,1,4] => [2,5,3,1,6,7,8,9,10,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,4,2,1,5] => [3,4,9,8,7,6,2,1,5] => [2,6,3,4,1,7,8,9,5]
[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] => [7,10,9,6,5,4,3,2,1,8] => [2,3,4,5,6,9,7,1,10,8]
[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] => [8,10,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,10,8,1,9]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9,10] => [5,6,4,3,2,1,7,8,9,10] => [2,3,4,6,5,1,7,8,9,10]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10,11] => [6,7,5,4,3,2,1,8,9,10,11] => [2,3,4,5,7,6,1,8,9,10,11]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,7,5,4,3,2,1,8,9,10] => [6,7,5,4,3,2,1,8,9,10] => [2,3,4,5,7,6,1,8,9,10]
[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] => [1,11,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,11,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,1,2] => [1,8,7,9,6,5,4,3,2] => [1,3,4,5,6,9,8,7,2]
[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] => [8,9,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,9,8,1,10]
[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] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10]
[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] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10]
[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] => [2,3,1,4,5,6,7,8,9,10,11] => [3,2,1,4,5,6,7,8,9,10,11]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9,10] => [3,4,2,1,5,6,7,8,9,10] => [2,4,3,1,5,6,7,8,9,10]
[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] => [1,3,2,4,5,6,7,8,9,10,11] => [1,3,2,4,5,6,7,8,9,10,11]
[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] => [1,9,8,10,7,6,5,4,3,2] => [1,3,4,5,6,7,10,9,8,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,3,1] => [2,8,7,9,6,5,4,3,1] => [3,2,4,5,6,9,8,7,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => [2,1,9,8,7,6,5,3,4] => [2,1,5,3,6,7,8,9,4]
[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] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10]
[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] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10]
[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] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11]
[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]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [4,2,3,1,5,6,7,8,9,10]
[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] => [2,3,4,5,1,6,7,8,9,10] => [5,2,3,4,1,6,7,8,9,10]
[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] => [2,3,4,5,6,1,7,8,9,10] => [6,2,3,4,5,1,7,8,9,10]
[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] => [2,3,4,5,6,7,1,8,9,10] => [7,2,3,4,5,6,1,8,9,10]
[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] => [2,3,4,5,6,7,8,1,9,10] => [8,2,3,4,5,6,7,1,9,10]
[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] => [8,7,6,5,4,3,2,9,1,10] => [9,3,4,5,6,7,8,2,1,10]
[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]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,1,3] => [2,4,5,6,7,8,9,1,3] => [9,2,1,4,5,6,7,8,3]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,1,3,4] => [2,1,5,6,7,8,9,3,4] => [2,1,9,3,5,6,7,8,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,2,1] => [4,9,8,7,6,3,5,2,1] => [2,5,6,4,3,7,8,9,1]
[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] => [4,9,8,7,6,5,3,2,1,10] => [2,3,5,4,6,7,8,9,1,10]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,7,8,9,10,1] => [6,5,4,3,2,7,8,9,10,1] => [10,3,4,5,6,2,7,8,9,1]
[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] => [7,8,6,5,4,3,2,9,1] => [9,3,4,5,6,8,7,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,1,10] => [7,8,9,6,5,4,3,2,1,10] => [2,3,4,5,6,9,7,8,1,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7,6,8,9,5,4,3,2,1,10] => [7,6,8,9,5,4,3,2,1,10] => [2,3,4,5,9,7,6,8,1,10]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,6,5,8,9,4,3,2,1,10] => [7,6,5,8,9,4,3,2,1,10] => [2,3,4,9,6,7,5,8,1,10]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,8,9,3,2,1,10] => [7,6,5,4,8,9,3,2,1,10] => [2,3,9,5,6,7,4,8,1,10]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,8,9,2,1,10] => [7,6,5,4,3,8,9,2,1,10] => [2,9,4,5,6,7,3,8,1,10]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,1,10] => [7,6,5,4,3,2,8,9,1,10] => [9,3,4,5,6,7,2,8,1,10]
[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] => [2,3,4,5,6,7,1,8,9,10]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,3,9,1,2] => [1,4,5,6,7,8,3,9,2] => [1,9,8,4,5,6,7,3,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,1,6,7] => [2,3,4,5,1,8,9,6,7] => [5,2,3,4,1,9,6,8,7]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [5,6,7,4,8,9,1,2,3] => [1,2,5,6,7,4,8,9,3] => [1,2,9,7,5,6,4,8,3]
[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] => [1,2,3,6,5,7,8,9,4] => [1,2,3,9,6,5,7,8,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,8,7,6]
[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] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [7,6,8,9,1,2,3,4,5] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,9,7,6,8,5]
[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] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10]
[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] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,1,2,3] => [1,2,5,4,6,7,8,9,3] => [1,2,9,5,4,6,7,8,3]
[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] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10]
[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] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [9,8,6,5,7,4,3,2,1] => [6,9,8,5,7,4,3,2,1] => [2,3,4,7,8,6,5,9,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,9,4,3,2,1,10] => [8,7,6,5,9,4,3,2,1,10] => [2,3,4,9,6,7,8,5,1,10]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [5,9,8,7,6,4,3,2,1,10] => [2,3,4,6,5,7,8,9,1,10]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1,10] => [4,3,2,5,6,7,8,9,1,10] => [9,3,4,2,5,6,7,8,1,10]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1,11] => [3,2,4,5,6,7,8,9,10,1,11] => [10,3,2,4,5,6,7,8,9,1,11]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,1,10] => [2,4,6,8,9,7,5,3,1,10] => [3,2,5,4,7,6,9,8,1,10]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1,10] => [3,4,5,6,7,8,9,2,1,10] => [2,9,3,4,5,6,7,8,1,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1,10] => [6,7,8,9,5,4,3,2,1,10] => [2,3,4,5,9,6,7,8,1,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,7,9,6,5,4,3,2,1,10] => [8,7,9,6,5,4,3,2,1,10] => [2,3,4,5,6,9,8,7,1,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,6,9,5,4,3,2,1,10] => [8,7,6,9,5,4,3,2,1,10] => [2,3,4,5,9,7,8,6,1,10]
[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] => [8,7,6,5,4,9,3,2,1,10] => [2,3,9,5,6,7,8,4,1,10]
[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] => [8,7,6,5,4,3,9,2,1,10] => [2,9,4,5,6,7,8,3,1,10]
[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] => [2,3,4,5,6,7,8,1,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9,10,8,7,6,5,4,3,2,1,11] => [9,10,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,10,9,1,11]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,8,10,7,6,5,4,3,2,1,11] => [9,8,10,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,10,9,8,1,11]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,7,10,6,5,4,3,2,1,11] => [9,8,7,10,6,5,4,3,2,1,11] => [2,3,4,5,6,10,8,9,7,1,11]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,10,5,4,3,2,1,11] => [9,8,7,6,10,5,4,3,2,1,11] => [2,3,4,5,10,7,8,9,6,1,11]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,10,4,3,2,1,11] => [9,8,7,6,5,10,4,3,2,1,11] => [2,3,4,10,6,7,8,9,5,1,11]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,10,3,2,1,11] => [9,8,7,6,5,4,10,3,2,1,11] => [2,3,10,5,6,7,8,9,4,1,11]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1,11] => [9,8,7,6,5,4,3,10,2,1,11] => [2,10,4,5,6,7,8,9,3,1,11]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,10,1,11] => [9,8,7,6,5,4,3,2,10,1,11] => [10,3,4,5,6,7,8,9,2,1,11]
[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] => [2,3,4,5,6,7,8,9,1,10,11]
[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] => [1,3,4,2,5,6,7,8,9,10] => [1,4,3,2,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8,9,10] => [1,2,4,5,3,6,7,8,9,10] => [1,2,5,4,3,6,7,8,9,10]
[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] => [1,2,4,5,6,3,7,8,9,10] => [1,2,6,4,5,3,7,8,9,10]
[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] => [1,2,3,5,6,7,8,4,9,10] => [1,2,3,8,5,6,7,4,9,10]
[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] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1]
[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] => [2,4,6,8,10,1,3,5,7,9] => [10,2,1,4,3,6,5,8,7,9]
[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] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1]
[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]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [1,3,4,5,6,7,8,9,10,11,2] => [1,11,3,4,5,6,7,8,9,10,2]
[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] => [3,2,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1,10] => [3,2,4,5,6,7,8,9,1,10] => [9,3,2,4,5,6,7,8,1,10]
[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] => [2,3,4,5,6,7,8,9,10,1,11] => [10,2,3,4,5,6,7,8,9,1,11]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [11,1,2,3,4,5,6,7,8,9,10,12] => [1,2,3,4,5,6,7,8,9,11,10,12] => [1,2,3,4,5,6,7,8,9,11,10,12]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1,10] => [3,4,2,5,6,7,8,9,1,10] => [9,4,3,2,5,6,7,8,1,10]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1,12] => [2,3,4,5,6,7,8,9,10,11,1,12] => [11,2,3,4,5,6,7,8,9,10,1,12]
[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] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9]
[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] => [2,3,4,5,6,1,7,8,9,10]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [4,2,1,3,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => [4,2,1,3,5,6,7,8,9,10]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,2,1] => [4,3,5,6,7,8,9,10,2,1] => [2,10,4,3,5,6,7,8,9,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [5,4,6,7,8,9,10,3,2,1] => [5,4,6,7,8,9,10,3,2,1] => [2,3,10,5,4,6,7,8,9,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [7,8,9,1,2,3,4,5,6,10] => [1,2,3,4,5,7,8,9,6,10] => [1,2,3,4,5,9,7,8,6,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [7,8,1,2,3,4,5,6,9,10] => [1,2,3,4,5,7,8,6,9,10] => [1,2,3,4,5,8,7,6,9,10]
[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] => [3,9,8,7,6,5,2,4,1] => [4,5,3,2,6,7,8,9,1]
[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] => [2,3,1,4,5,6,7,8,9,10]
[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] => [9,11,10,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,10,9,11,1]
[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] => [2,3,4,5,1,6,7,8,9,10]
[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] => [2,3,4,1,5,6,7,8,9,10]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,11,1,10] => [11,2,3,4,5,6,7,8,9,1,10]
[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] => [9,11,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,11,9,1,10]
[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] => [7,9,6,5,4,3,2,8,1] => [8,3,4,5,6,9,7,2,1]
[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] => [1,2,3,4,5,6,8,9,7,10] => [1,2,3,4,5,6,9,8,7,10]
[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] => [1,3,4,5,6,7,8,9,2,10] => [1,9,3,4,5,6,7,8,2,10]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,5,7,8,9,10,11,4,3,2,1] => [6,5,7,8,9,10,11,4,3,2,1] => [2,3,4,11,6,5,7,8,9,10,1]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,3,9,2,1] => [5,4,6,7,8,3,9,2,1] => [2,9,8,5,4,6,7,3,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [7,6,8,5,9,4,3,2,1] => [7,6,8,5,9,4,3,2,1] => [2,3,4,9,8,7,6,5,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,2,1,3,4] => [2,1,10,9,8,7,6,5,3,4] => [2,1,5,3,6,7,8,9,10,4]
[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] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,10,11,9]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,6,3,2,1] => [5,9,8,7,4,6,3,2,1] => [2,3,6,7,5,4,8,9,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,9,1] => [7,6,8,5,4,3,2,9,1] => [9,3,4,5,8,7,6,2,1]
[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] => [10,2,3,4,5,6,7,8,9,11,1]
[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] => [2,3,4,5,7,8,6,9,1] => [9,2,3,4,5,8,7,6,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,2,1,8] => [3,4,5,6,7,9,2,1,8] => [2,9,3,4,5,6,7,1,8]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [1,3,4,5,6,7,9,2,8] => [1,9,3,4,5,6,7,2,8]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => [1,3,4,5,6,7,8,2,9,10] => [1,8,3,4,5,6,7,2,9,10]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,1,5] => [2,3,4,6,7,8,9,1,5] => [9,2,3,4,1,6,7,8,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,10,1] => [8,9,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,9,8,2,1]
[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] => [5,6,4,7,3,8,2,9,1] => [9,8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [6,7,5,8,4,9,3,10,1,2] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2]
[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] => [5,4,6,3,7,2,8,1,9,10] => [8,7,6,5,4,3,2,1,9,10]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,1,4] => [2,3,5,6,7,8,9,1,4] => [9,2,3,1,5,6,7,8,4]
[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] => [8,2,3,4,5,6,7,9,1,10]
[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] => [1,3,5,7,9,2,4,6,8,10] => [1,9,3,2,5,4,7,6,8,10]
[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] => [1,3,5,7,9,11,12,10,8,6,4,2] => [1,4,3,6,5,8,7,10,9,12,11,2]
[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] => [1,3,5,7,8,6,4,2,9,10] => [1,4,3,6,5,8,7,2,9,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,11,12,10] => [1,2,3,4,5,6,7,8,9,12,11,10]
[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] => [3,4,5,6,7,8,9,10,11,2,1] => [2,11,3,4,5,6,7,8,9,10,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11,12] => [1,3,2,4,5,6,7,8,9,10,11,12] => [1,3,2,4,5,6,7,8,9,10,11,12]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [7,5,6,4,8,3,9,2,10,1] => [5,7,6,4,8,3,9,2,10,1] => [10,9,8,6,5,7,4,3,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,6,7,5,9,4,10,3,11,2,12,1] => [6,8,7,5,9,4,10,3,11,2,12,1] => [12,11,10,9,7,6,8,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,9,1] => [6,7,8,5,4,3,2,9,1] => [9,3,4,5,8,6,7,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,8,4,3,2,9,1] => [7,6,5,8,4,3,2,9,1] => [9,3,4,8,6,7,5,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,7,9,6,5,4,3,2,10,1] => [8,7,9,6,5,4,3,2,10,1] => [10,3,4,5,6,9,8,7,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9,10,8,7,6,5,4,3,2,11,1] => [9,10,8,7,6,5,4,3,2,11,1] => [11,3,4,5,6,7,8,10,9,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [8,9,7,10,5,6,3,4,1,2] => [1,3,5,8,9,7,10,6,4,2] => [1,4,3,6,5,10,9,8,7,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,5,1,6] => [2,3,4,5,7,8,9,1,6] => [9,2,3,4,5,1,7,8,6]
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2,11] => [1,3,4,5,6,7,8,9,10,2,11] => [1,10,3,4,5,6,7,8,9,2,11]
[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] => [3,4,2,5,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,5,10,3,4,1,2] => [1,3,6,8,9,7,5,10,4,2] => [1,4,3,10,7,6,9,8,5,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,3,10,1,2] => [1,4,6,8,9,7,5,3,10,2] => [1,10,5,4,7,6,9,8,3,2]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,11,1] => [3,4,5,6,7,8,9,10,2,11,1] => [11,10,3,4,5,6,7,8,9,2,1]
[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] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,7,5,8,4,9,3,10,2,11,1,12] => [6,7,5,8,4,9,3,10,2,11,1,12] => [11,10,9,8,7,6,5,4,3,2,1,12]
[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] => [1,2,4,5,7,8,9,6,3,10] => [1,2,6,4,5,9,7,8,3,10]
[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] => [2,12,11,10,9,8,7,6,5,4,1,3] => [4,2,1,5,6,7,8,9,10,11,12,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,10,1] => [7,8,9,6,5,4,3,2,10,1] => [10,3,4,5,6,9,7,8,2,1]
[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] => [1,3,5,7,9,2,4,6,8] => [1,9,3,2,5,4,7,6,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,10,11,9,1] => [9,2,3,4,5,6,7,8,11,10,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,11,10,9,8,7,6,5,4,3,1,2] => [1,12,11,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,11,12,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,7,9,6,10,5,4,3,2,1] => [8,7,9,6,10,5,4,3,2,1] => [2,3,4,5,10,9,8,7,6,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [7,8,9,10,11,2,3,4,5,6,1] => [2,3,4,5,7,8,9,10,11,6,1] => [6,2,3,4,5,11,7,8,9,10,1]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9,10] => [3,4,5,2,1,6,7,8,9,10] => [2,5,3,4,1,6,7,8,9,10]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,1,2,4] => [1,3,5,6,7,8,9,2,4] => [1,9,3,2,5,6,7,8,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [9,7,5,2,3,1,4,6,8] => [2,3,5,7,9,1,4,6,8] => [9,2,3,1,5,4,7,6,8]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,2,3,1,4,6,8,10] => [2,3,5,7,9,1,4,6,8,10] => [9,2,3,1,5,4,7,6,8,10]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,9,2,10,1] => [8,7,6,5,4,3,9,2,10,1] => [10,9,4,5,6,7,8,3,2,1]
[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] => [10,12,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,12,10,1,11]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
searching the database
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