Identifier
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Images
[1,0] => [1] => [1] => [1]
[1,0,1,0] => [1,2] => [1,2] => [1,2]
[1,1,0,0] => [2,1] => [2,1] => [2,1]
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3]
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [1,3,2]
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1,3]
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => [3,2,1]
[1,1,1,0,0,0] => [3,2,1] => [2,3,1] => [3,1,2]
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3]
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4]
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2]
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,3,4,2] => [1,4,2,3]
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4]
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3]
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4]
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,3,2,1] => [4,3,2,1]
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,4,2,1] => [4,2,1,3]
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4]
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [2,4,3,1] => [4,3,1,2]
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,3,4,1] => [4,1,2,3]
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [3,2,4,1] => [4,1,3,2]
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4]
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5]
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3]
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,5,3,4]
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5]
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4]
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5]
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,4,3,2] => [1,5,4,3,2]
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,4,5,3,2] => [1,5,3,2,4]
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,3,4,2,5] => [1,4,2,3,5]
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,3,5,4,2] => [1,5,4,2,3]
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,3,4,5,2] => [1,5,2,3,4]
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,4,3,5,2] => [1,5,2,4,3]
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5]
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4]
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5]
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3]
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,4,5,3] => [2,1,5,3,4]
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5]
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4]
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,3,2,1,5] => [4,3,2,1,5]
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,4,3,2,1] => [5,4,3,2,1]
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,5,3,2,1] => [5,3,2,1,4]
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,4,2,1,5] => [4,2,1,3,5]
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,5,4,2,1] => [5,4,2,1,3]
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,4,5,2,1] => [5,2,1,3,4]
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [4,3,5,2,1] => [5,2,1,4,3]
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5]
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,3,1,5,4] => [3,1,2,5,4]
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [2,4,3,1,5] => [4,3,1,2,5]
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [2,5,4,3,1] => [5,4,3,1,2]
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [2,4,5,3,1] => [5,3,1,2,4]
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,3,4,1,5] => [4,1,2,3,5]
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,3,5,4,1] => [5,4,1,2,3]
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,3,4,5,1] => [5,1,2,3,4]
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,4,3,5,1] => [5,1,2,4,3]
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [3,2,4,1,5] => [4,1,3,2,5]
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,2,5,4,1] => [5,4,1,3,2]
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,2,4,5,1] => [5,1,3,2,4]
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [4,3,2,5,1] => [5,1,4,3,2]
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [3,4,2,5,1] => [5,1,4,2,3]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [1,2,3,6,4,5]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,5,6,4,3] => [1,2,6,4,3,5]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [1,2,5,3,4,6]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,4,6,5,3] => [1,2,6,5,3,4]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [1,2,6,3,4,5]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,5,4,6,3] => [1,2,6,3,5,4]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [1,3,2,6,4,5]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,5,6,4,3,2] => [1,6,4,3,2,5]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,4,5,3,2,6] => [1,5,3,2,4,6]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,4,6,5,3,2] => [1,6,5,3,2,4]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,4,5,6,3,2] => [1,6,3,2,4,5]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,5,4,6,3,2] => [1,6,3,2,5,4]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [1,4,2,3,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [1,4,2,3,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,3,5,4,2,6] => [1,5,4,2,3,6]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,3,6,5,4,2] => [1,6,5,4,2,3]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,3,5,6,4,2] => [1,6,4,2,3,5]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [1,5,2,3,4,6]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,3,4,6,5,2] => [1,6,5,2,3,4]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [1,6,2,3,4,5]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,3,5,4,6,2] => [1,6,2,3,5,4]
>>> Load all 1043 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,4,3,5,2,6] => [1,5,2,4,3,6]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,4,3,6,5,2] => [1,6,5,2,4,3]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,4,3,5,6,2] => [1,6,2,4,3,5]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,5,4,3,6,2] => [1,6,2,5,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,4,5,3,6,2] => [1,6,2,5,3,4]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [2,1,3,6,4,5]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,5,6,4,3] => [2,1,6,4,3,5]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [2,1,5,3,4,6]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,4,6,5,3] => [2,1,6,5,3,4]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [2,1,6,3,4,5]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [2,1,6,3,5,4]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => [3,2,1,6,4,5]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,6,4,3,2,1] => [6,4,3,2,1,5]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,5,3,2,1,6] => [5,3,2,1,4,6]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [4,6,5,3,2,1] => [6,5,3,2,1,4]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [4,5,6,3,2,1] => [6,3,2,1,4,5]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [5,4,6,3,2,1] => [6,3,2,1,5,4]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,4,2,1,5,6] => [4,2,1,3,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,4,2,1,6,5] => [4,2,1,3,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [3,5,4,2,1,6] => [5,4,2,1,3,6]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [3,6,5,4,2,1] => [6,5,4,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [3,5,6,4,2,1] => [6,4,2,1,3,5]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,4,5,2,1,6] => [5,2,1,3,4,6]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [3,4,6,5,2,1] => [6,5,2,1,3,4]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,4,5,6,2,1] => [6,2,1,3,4,5]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [3,5,4,6,2,1] => [6,2,1,3,5,4]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [4,3,5,2,1,6] => [5,2,1,4,3,6]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,3,6,5,2,1] => [6,5,2,1,4,3]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,3,5,6,2,1] => [6,2,1,4,3,5]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [5,4,3,6,2,1] => [6,2,1,5,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [4,5,3,6,2,1] => [6,2,1,5,3,4]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [3,1,2,4,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [3,1,2,5,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => [3,1,2,6,5,4]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [3,1,2,6,4,5]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [2,4,3,1,5,6] => [4,3,1,2,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [2,4,3,1,6,5] => [4,3,1,2,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [2,5,4,3,1,6] => [5,4,3,1,2,6]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [2,6,5,4,3,1] => [6,5,4,3,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [2,5,6,4,3,1] => [6,4,3,1,2,5]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [2,4,5,3,1,6] => [5,3,1,2,4,6]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [2,4,6,5,3,1] => [6,5,3,1,2,4]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [2,4,5,6,3,1] => [6,3,1,2,4,5]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [2,5,4,6,3,1] => [6,3,1,2,5,4]
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [4,1,2,3,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,3,5,4,1,6] => [5,4,1,2,3,6]
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,3,6,5,4,1] => [6,5,4,1,2,3]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [2,3,5,6,4,1] => [6,4,1,2,3,5]
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [5,1,2,3,4,6]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,6,5,1] => [6,5,1,2,3,4]
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [6,1,2,3,4,5]
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [2,3,5,4,6,1] => [6,1,2,3,5,4]
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [2,4,3,5,1,6] => [5,1,2,4,3,6]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [2,4,3,6,5,1] => [6,5,1,2,4,3]
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,4,3,5,6,1] => [6,1,2,4,3,5]
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [2,5,4,3,6,1] => [6,1,2,5,4,3]
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,4,5,3,6,1] => [6,1,2,5,3,4]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [3,2,4,1,5,6] => [4,1,3,2,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [4,1,3,2,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,2,5,4,1,6] => [5,4,1,3,2,6]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [3,2,6,5,4,1] => [6,5,4,1,3,2]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [3,2,5,6,4,1] => [6,4,1,3,2,5]
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,2,4,5,1,6] => [5,1,3,2,4,6]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,4,6,5,1] => [6,5,1,3,2,4]
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,2,4,5,6,1] => [6,1,3,2,4,5]
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [3,2,5,4,6,1] => [6,1,3,2,5,4]
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [4,3,2,5,1,6] => [5,1,4,3,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [4,3,2,6,5,1] => [6,5,1,4,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [4,3,2,5,6,1] => [6,1,4,3,2,5]
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [5,4,3,2,6,1] => [6,1,5,4,3,2]
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [4,5,3,2,6,1] => [6,1,5,3,2,4]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => [5,1,4,2,3,6]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [3,4,2,6,5,1] => [6,5,1,4,2,3]
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [3,4,2,5,6,1] => [6,1,4,2,3,5]
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [3,5,4,2,6,1] => [6,1,5,4,2,3]
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [3,4,5,2,6,1] => [6,1,5,2,3,4]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [6,1,5,2,4,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,6,7,5,4] => [1,2,3,7,5,4,6]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,5,7,6,4] => [1,2,3,7,6,4,5]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,6,5,7,4] => [1,2,3,7,4,6,5]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,6,7,5,4,3] => [1,2,7,5,4,3,6]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,5,6,4,3,7] => [1,2,6,4,3,5,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,5,7,6,4,3] => [1,2,7,6,4,3,5]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [1,2,5,6,7,4,3] => [1,2,7,4,3,5,6]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,6,5,7,4,3] => [1,2,7,4,3,6,5]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,4,6,5,3,7] => [1,2,6,5,3,4,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,4,7,6,5,3] => [1,2,7,6,5,3,4]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,4,6,7,5,3] => [1,2,7,5,3,4,6]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [1,2,4,5,7,6,3] => [1,2,7,6,3,4,5]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [1,2,4,6,5,7,3] => [1,2,7,3,4,6,5]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,5,4,6,3,7] => [1,2,6,3,5,4,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,5,4,7,6,3] => [1,2,7,6,3,5,4]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [1,2,5,4,6,7,3] => [1,2,7,3,5,4,6]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [1,2,6,5,4,7,3] => [1,2,7,3,6,5,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,5,6,4,7,3] => [1,2,7,3,6,4,5]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,6,7,5,4] => [1,3,2,7,5,4,6]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,5,7,6,4] => [1,3,2,7,6,4,5]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,6,5,7,4] => [1,3,2,7,4,6,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,3,2,6,7,5] => [1,4,3,2,7,5,6]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,6,7,5,4,3,2] => [1,7,5,4,3,2,6]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,5,6,4,3,2,7] => [1,6,4,3,2,5,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,5,7,6,4,3,2] => [1,7,6,4,3,2,5]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [1,5,6,7,4,3,2] => [1,7,4,3,2,5,6]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,6,5,7,4,3,2] => [1,7,4,3,2,6,5]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,4,5,3,2,6,7] => [1,5,3,2,4,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,4,5,3,2,7,6] => [1,5,3,2,4,7,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,4,6,5,3,2,7] => [1,6,5,3,2,4,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,4,7,6,5,3,2] => [1,7,6,5,3,2,4]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,4,6,7,5,3,2] => [1,7,5,3,2,4,6]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [1,4,5,6,3,2,7] => [1,6,3,2,4,5,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [1,4,5,7,6,3,2] => [1,7,6,3,2,4,5]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [1,4,5,6,7,3,2] => [1,7,3,2,4,5,6]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [1,4,6,5,7,3,2] => [1,7,3,2,4,6,5]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,5,4,6,3,2,7] => [1,6,3,2,5,4,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,5,4,7,6,3,2] => [1,7,6,3,2,5,4]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [1,5,4,6,7,3,2] => [1,7,3,2,5,4,6]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [1,6,5,4,7,3,2] => [1,7,3,2,6,5,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,5,6,4,7,3,2] => [1,7,3,2,6,4,5]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,3,4,2,7,6,5] => [1,4,2,3,7,6,5]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,3,5,4,2,6,7] => [1,5,4,2,3,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,3,5,4,2,7,6] => [1,5,4,2,3,7,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,3,6,5,4,2,7] => [1,6,5,4,2,3,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,3,7,6,5,4,2] => [1,7,6,5,4,2,3]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,3,6,7,5,4,2] => [1,7,5,4,2,3,6]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,3,5,6,4,2,7] => [1,6,4,2,3,5,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,3,5,7,6,4,2] => [1,7,6,4,2,3,5]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [1,3,5,6,7,4,2] => [1,7,4,2,3,5,6]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,3,6,5,7,4,2] => [1,7,4,2,3,6,5]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [1,3,4,6,5,2,7] => [1,6,5,2,3,4,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [1,3,4,7,6,5,2] => [1,7,6,5,2,3,4]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [1,3,4,6,7,5,2] => [1,7,5,2,3,4,6]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [1,3,4,5,7,6,2] => [1,7,6,2,3,4,5]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [1,3,4,6,5,7,2] => [1,7,2,3,4,6,5]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [1,3,5,4,6,2,7] => [1,6,2,3,5,4,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [1,3,5,4,7,6,2] => [1,7,6,2,3,5,4]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [1,3,5,4,6,7,2] => [1,7,2,3,5,4,6]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [1,3,6,5,4,7,2] => [1,7,2,3,6,5,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [1,3,5,6,4,7,2] => [1,7,2,3,6,4,5]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,4,3,5,2,6,7] => [1,5,2,4,3,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,4,3,5,2,7,6] => [1,5,2,4,3,7,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,4,3,6,5,2,7] => [1,6,5,2,4,3,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,4,3,7,6,5,2] => [1,7,6,5,2,4,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,4,3,6,7,5,2] => [1,7,5,2,4,3,6]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [1,4,3,5,6,2,7] => [1,6,2,4,3,5,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [1,4,3,5,7,6,2] => [1,7,6,2,4,3,5]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [1,4,3,5,6,7,2] => [1,7,2,4,3,5,6]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [1,4,3,6,5,7,2] => [1,7,2,4,3,6,5]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [1,5,4,3,6,2,7] => [1,6,2,5,4,3,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [1,5,4,3,7,6,2] => [1,7,6,2,5,4,3]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [1,5,4,3,6,7,2] => [1,7,2,5,4,3,6]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [1,6,5,4,3,7,2] => [1,7,2,6,5,4,3]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [1,5,6,4,3,7,2] => [1,7,2,6,4,3,5]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,4,5,3,6,2,7] => [1,6,2,5,3,4,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,4,5,3,7,6,2] => [1,7,6,2,5,3,4]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [1,4,5,3,6,7,2] => [1,7,2,5,3,4,6]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [1,4,6,5,3,7,2] => [1,7,2,6,5,3,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [1,4,5,6,3,7,2] => [1,7,2,6,3,4,5]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,5,4,6,3,7,2] => [1,7,2,6,3,5,4]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,6,7,5,4] => [2,1,3,7,5,4,6]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,5,7,6,4] => [2,1,3,7,6,4,5]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,6,5,7,4] => [2,1,3,7,4,6,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,6,7,5,4,3] => [2,1,7,5,4,3,6]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,5,6,4,3,7] => [2,1,6,4,3,5,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,5,7,6,4,3] => [2,1,7,6,4,3,5]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [2,1,5,6,7,4,3] => [2,1,7,4,3,5,6]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,6,5,7,4,3] => [2,1,7,4,3,6,5]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,4,6,5,3,7] => [2,1,6,5,3,4,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,4,7,6,5,3] => [2,1,7,6,5,3,4]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,4,6,7,5,3] => [2,1,7,5,3,4,6]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [2,1,4,5,7,6,3] => [2,1,7,6,3,4,5]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [2,1,4,6,5,7,3] => [2,1,7,3,4,6,5]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,5,4,6,3,7] => [2,1,6,3,5,4,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,5,4,7,6,3] => [2,1,7,6,3,5,4]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [2,1,5,4,6,7,3] => [2,1,7,3,5,4,6]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [2,1,6,5,4,7,3] => [2,1,7,3,6,5,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,5,6,4,7,3] => [2,1,7,3,6,4,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,4,6,7,5] => [3,2,1,4,7,5,6]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,2,1,6,7,5,4] => [3,2,1,7,5,4,6]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,5,6,4,7] => [3,2,1,6,4,5,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,2,1,5,7,6,4] => [3,2,1,7,6,4,5]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [3,2,1,5,6,7,4] => [3,2,1,7,4,5,6]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,1,6,5,7,4] => [3,2,1,7,4,6,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,3,2,1,6,7,5] => [4,3,2,1,7,5,6]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [6,7,5,4,3,2,1] => [7,5,4,3,2,1,6]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,6,4,3,2,1,7] => [6,4,3,2,1,5,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [5,7,6,4,3,2,1] => [7,6,4,3,2,1,5]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [5,6,7,4,3,2,1] => [7,4,3,2,1,5,6]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [6,5,7,4,3,2,1] => [7,4,3,2,1,6,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,5,3,2,1,6,7] => [5,3,2,1,4,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,5,3,2,1,7,6] => [5,3,2,1,4,7,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [4,6,5,3,2,1,7] => [6,5,3,2,1,4,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [4,7,6,5,3,2,1] => [7,6,5,3,2,1,4]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [4,6,7,5,3,2,1] => [7,5,3,2,1,4,6]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [4,5,6,3,2,1,7] => [6,3,2,1,4,5,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [4,5,7,6,3,2,1] => [7,6,3,2,1,4,5]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [4,5,6,7,3,2,1] => [7,3,2,1,4,5,6]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,6,5,7,3,2,1] => [7,3,2,1,4,6,5]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [5,4,6,3,2,1,7] => [6,3,2,1,5,4,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [5,4,7,6,3,2,1] => [7,6,3,2,1,5,4]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [5,4,6,7,3,2,1] => [7,3,2,1,5,4,6]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [6,5,4,7,3,2,1] => [7,3,2,1,6,5,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [5,6,4,7,3,2,1] => [7,3,2,1,6,4,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,4,2,1,5,6,7] => [4,2,1,3,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,4,2,1,5,7,6] => [4,2,1,3,5,7,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,4,2,1,6,5,7] => [4,2,1,3,6,5,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,4,2,1,7,6,5] => [4,2,1,3,7,6,5]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,4,2,1,6,7,5] => [4,2,1,3,7,5,6]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [3,5,4,2,1,6,7] => [5,4,2,1,3,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [3,5,4,2,1,7,6] => [5,4,2,1,3,7,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [3,6,5,4,2,1,7] => [6,5,4,2,1,3,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [3,7,6,5,4,2,1] => [7,6,5,4,2,1,3]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [3,6,7,5,4,2,1] => [7,5,4,2,1,3,6]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [3,5,6,4,2,1,7] => [6,4,2,1,3,5,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [3,5,7,6,4,2,1] => [7,6,4,2,1,3,5]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [3,5,6,7,4,2,1] => [7,4,2,1,3,5,6]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [3,6,5,7,4,2,1] => [7,4,2,1,3,6,5]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [3,4,5,2,1,6,7] => [5,2,1,3,4,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [3,4,5,2,1,7,6] => [5,2,1,3,4,7,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [3,4,6,5,2,1,7] => [6,5,2,1,3,4,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [3,4,7,6,5,2,1] => [7,6,5,2,1,3,4]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [3,4,6,7,5,2,1] => [7,5,2,1,3,4,6]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [3,4,5,6,2,1,7] => [6,2,1,3,4,5,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [3,4,5,7,6,2,1] => [7,6,2,1,3,4,5]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [3,4,5,6,7,2,1] => [7,2,1,3,4,5,6]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [3,4,6,5,7,2,1] => [7,2,1,3,4,6,5]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [3,5,4,6,2,1,7] => [6,2,1,3,5,4,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [3,5,4,7,6,2,1] => [7,6,2,1,3,5,4]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [3,5,4,6,7,2,1] => [7,2,1,3,5,4,6]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [3,6,5,4,7,2,1] => [7,2,1,3,6,5,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [3,5,6,4,7,2,1] => [7,2,1,3,6,4,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [4,3,5,2,1,6,7] => [5,2,1,4,3,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [4,3,5,2,1,7,6] => [5,2,1,4,3,7,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,3,6,5,2,1,7] => [6,5,2,1,4,3,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [4,3,7,6,5,2,1] => [7,6,5,2,1,4,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [4,3,6,7,5,2,1] => [7,5,2,1,4,3,6]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,3,5,6,2,1,7] => [6,2,1,4,3,5,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,3,5,7,6,2,1] => [7,6,2,1,4,3,5]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,3,5,6,7,2,1] => [7,2,1,4,3,5,6]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [4,3,6,5,7,2,1] => [7,2,1,4,3,6,5]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [5,4,3,6,2,1,7] => [6,2,1,5,4,3,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [5,4,3,7,6,2,1] => [7,6,2,1,5,4,3]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [5,4,3,6,7,2,1] => [7,2,1,5,4,3,6]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [6,5,4,3,7,2,1] => [7,2,1,6,5,4,3]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [5,6,4,3,7,2,1] => [7,2,1,6,4,3,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [4,5,3,6,2,1,7] => [6,2,1,5,3,4,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [4,5,3,7,6,2,1] => [7,6,2,1,5,3,4]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [4,5,3,6,7,2,1] => [7,2,1,5,3,4,6]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [4,6,5,3,7,2,1] => [7,2,1,6,5,3,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [4,5,6,3,7,2,1] => [7,2,1,6,3,4,5]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [5,4,6,3,7,2,1] => [7,2,1,6,3,5,4]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [2,3,1,4,7,6,5] => [3,1,2,4,7,6,5]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [2,3,1,6,5,4,7] => [3,1,2,6,5,4,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [2,3,1,7,6,5,4] => [3,1,2,7,6,5,4]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [2,3,1,6,7,5,4] => [3,1,2,7,5,4,6]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [2,3,1,5,7,6,4] => [3,1,2,7,6,4,5]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,3,1,6,5,7,4] => [3,1,2,7,4,6,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [2,4,3,1,5,6,7] => [4,3,1,2,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [2,4,3,1,5,7,6] => [4,3,1,2,5,7,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [2,4,3,1,6,5,7] => [4,3,1,2,6,5,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [2,4,3,1,7,6,5] => [4,3,1,2,7,6,5]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [2,4,3,1,6,7,5] => [4,3,1,2,7,5,6]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [2,5,4,3,1,6,7] => [5,4,3,1,2,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [2,5,4,3,1,7,6] => [5,4,3,1,2,7,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [2,6,5,4,3,1,7] => [6,5,4,3,1,2,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [2,7,6,5,4,3,1] => [7,6,5,4,3,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [2,6,7,5,4,3,1] => [7,5,4,3,1,2,6]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [2,5,6,4,3,1,7] => [6,4,3,1,2,5,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [2,5,7,6,4,3,1] => [7,6,4,3,1,2,5]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [2,5,6,7,4,3,1] => [7,4,3,1,2,5,6]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [2,6,5,7,4,3,1] => [7,4,3,1,2,6,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [2,4,5,3,1,6,7] => [5,3,1,2,4,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [2,4,5,3,1,7,6] => [5,3,1,2,4,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [2,4,6,5,3,1,7] => [6,5,3,1,2,4,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [2,4,7,6,5,3,1] => [7,6,5,3,1,2,4]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [2,4,6,7,5,3,1] => [7,5,3,1,2,4,6]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [2,4,5,6,3,1,7] => [6,3,1,2,4,5,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [2,4,5,7,6,3,1] => [7,6,3,1,2,4,5]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [2,4,5,6,7,3,1] => [7,3,1,2,4,5,6]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [2,4,6,5,7,3,1] => [7,3,1,2,4,6,5]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [2,5,4,6,3,1,7] => [6,3,1,2,5,4,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [2,5,4,7,6,3,1] => [7,6,3,1,2,5,4]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [2,5,4,6,7,3,1] => [7,3,1,2,5,4,6]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [2,6,5,4,7,3,1] => [7,3,1,2,6,5,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [2,5,6,4,7,3,1] => [7,3,1,2,6,4,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [2,3,4,1,7,6,5] => [4,1,2,3,7,6,5]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [2,3,5,4,1,6,7] => [5,4,1,2,3,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [2,3,5,4,1,7,6] => [5,4,1,2,3,7,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [2,3,6,5,4,1,7] => [6,5,4,1,2,3,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [2,3,7,6,5,4,1] => [7,6,5,4,1,2,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [2,3,6,7,5,4,1] => [7,5,4,1,2,3,6]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [2,3,5,6,4,1,7] => [6,4,1,2,3,5,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [2,3,5,7,6,4,1] => [7,6,4,1,2,3,5]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [2,3,5,6,7,4,1] => [7,4,1,2,3,5,6]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [2,3,6,5,7,4,1] => [7,4,1,2,3,6,5]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [2,3,4,6,5,1,7] => [6,5,1,2,3,4,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [2,3,4,7,6,5,1] => [7,6,5,1,2,3,4]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [2,3,4,6,7,5,1] => [7,5,1,2,3,4,6]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,5,7,6,1] => [7,6,1,2,3,4,5]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [2,3,4,6,5,7,1] => [7,1,2,3,4,6,5]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [2,3,5,4,6,1,7] => [6,1,2,3,5,4,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [2,3,5,4,7,6,1] => [7,6,1,2,3,5,4]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,3,5,4,6,7,1] => [7,1,2,3,5,4,6]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [2,3,6,5,4,7,1] => [7,1,2,3,6,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [2,3,5,6,4,7,1] => [7,1,2,3,6,4,5]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [2,4,3,5,1,6,7] => [5,1,2,4,3,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [2,4,3,5,1,7,6] => [5,1,2,4,3,7,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [2,4,3,6,5,1,7] => [6,5,1,2,4,3,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [2,4,3,7,6,5,1] => [7,6,5,1,2,4,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [2,4,3,6,7,5,1] => [7,5,1,2,4,3,6]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,4,3,5,6,1,7] => [6,1,2,4,3,5,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [2,4,3,5,7,6,1] => [7,6,1,2,4,3,5]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,4,3,5,6,7,1] => [7,1,2,4,3,5,6]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [2,4,3,6,5,7,1] => [7,1,2,4,3,6,5]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [2,5,4,3,6,1,7] => [6,1,2,5,4,3,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [2,5,4,3,7,6,1] => [7,6,1,2,5,4,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [2,5,4,3,6,7,1] => [7,1,2,5,4,3,6]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [2,6,5,4,3,7,1] => [7,1,2,6,5,4,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [2,5,6,4,3,7,1] => [7,1,2,6,4,3,5]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [2,4,5,3,6,1,7] => [6,1,2,5,3,4,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [2,4,5,3,7,6,1] => [7,6,1,2,5,3,4]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [2,4,5,3,6,7,1] => [7,1,2,5,3,4,6]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [2,4,6,5,3,7,1] => [7,1,2,6,5,3,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [2,4,5,6,3,7,1] => [7,1,2,6,3,4,5]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [2,5,4,6,3,7,1] => [7,1,2,6,3,5,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [3,2,4,1,5,6,7] => [4,1,3,2,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [3,2,4,1,5,7,6] => [4,1,3,2,5,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [3,2,4,1,6,5,7] => [4,1,3,2,6,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,4,1,7,6,5] => [4,1,3,2,7,6,5]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [3,2,4,1,6,7,5] => [4,1,3,2,7,5,6]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [3,2,5,4,1,6,7] => [5,4,1,3,2,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,5,4,1,7,6] => [5,4,1,3,2,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [3,2,6,5,4,1,7] => [6,5,4,1,3,2,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [3,2,7,6,5,4,1] => [7,6,5,4,1,3,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [3,2,6,7,5,4,1] => [7,5,4,1,3,2,6]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [3,2,5,6,4,1,7] => [6,4,1,3,2,5,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [3,2,5,7,6,4,1] => [7,6,4,1,3,2,5]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [3,2,5,6,7,4,1] => [7,4,1,3,2,5,6]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [3,2,6,5,7,4,1] => [7,4,1,3,2,6,5]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [3,2,4,5,1,6,7] => [5,1,3,2,4,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [3,2,4,5,1,7,6] => [5,1,3,2,4,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,2,4,6,5,1,7] => [6,5,1,3,2,4,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [3,2,4,7,6,5,1] => [7,6,5,1,3,2,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [3,2,4,6,7,5,1] => [7,5,1,3,2,4,6]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [3,2,4,5,6,1,7] => [6,1,3,2,4,5,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,4,5,7,6,1] => [7,6,1,3,2,4,5]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [3,2,4,5,6,7,1] => [7,1,3,2,4,5,6]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [3,2,4,6,5,7,1] => [7,1,3,2,4,6,5]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [3,2,5,4,6,1,7] => [6,1,3,2,5,4,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [3,2,5,4,7,6,1] => [7,6,1,3,2,5,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,2,5,4,6,7,1] => [7,1,3,2,5,4,6]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [3,2,6,5,4,7,1] => [7,1,3,2,6,5,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [3,2,5,6,4,7,1] => [7,1,3,2,6,4,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [4,3,2,5,1,6,7] => [5,1,4,3,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [4,3,2,5,1,7,6] => [5,1,4,3,2,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [4,3,2,6,5,1,7] => [6,5,1,4,3,2,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,3,2,7,6,5,1] => [7,6,5,1,4,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [4,3,2,6,7,5,1] => [7,5,1,4,3,2,6]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [4,3,2,5,6,1,7] => [6,1,4,3,2,5,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [4,3,2,5,7,6,1] => [7,6,1,4,3,2,5]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [4,3,2,5,6,7,1] => [7,1,4,3,2,5,6]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [4,3,2,6,5,7,1] => [7,1,4,3,2,6,5]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [5,4,3,2,6,1,7] => [6,1,5,4,3,2,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [5,4,3,2,7,6,1] => [7,6,1,5,4,3,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [5,4,3,2,6,7,1] => [7,1,5,4,3,2,6]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [6,5,4,3,2,7,1] => [7,1,6,5,4,3,2]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [5,6,4,3,2,7,1] => [7,1,6,4,3,2,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [4,5,3,2,6,1,7] => [6,1,5,3,2,4,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [4,5,3,2,7,6,1] => [7,6,1,5,3,2,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [4,5,3,2,6,7,1] => [7,1,5,3,2,4,6]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [4,6,5,3,2,7,1] => [7,1,6,5,3,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [4,5,6,3,2,7,1] => [7,1,6,3,2,4,5]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [5,4,6,3,2,7,1] => [7,1,6,3,2,5,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [3,4,2,5,1,6,7] => [5,1,4,2,3,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [3,4,2,5,1,7,6] => [5,1,4,2,3,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [3,4,2,6,5,1,7] => [6,5,1,4,2,3,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [3,4,2,7,6,5,1] => [7,6,5,1,4,2,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [3,4,2,6,7,5,1] => [7,5,1,4,2,3,6]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [3,4,2,5,6,1,7] => [6,1,4,2,3,5,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [3,4,2,5,7,6,1] => [7,6,1,4,2,3,5]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [3,4,2,5,6,7,1] => [7,1,4,2,3,5,6]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [3,4,2,6,5,7,1] => [7,1,4,2,3,6,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [3,5,4,2,6,1,7] => [6,1,5,4,2,3,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,5,4,2,7,6,1] => [7,6,1,5,4,2,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [3,5,4,2,6,7,1] => [7,1,5,4,2,3,6]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [3,6,5,4,2,7,1] => [7,1,6,5,4,2,3]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [3,5,6,4,2,7,1] => [7,1,6,4,2,3,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,4,5,2,6,1,7] => [6,1,5,2,3,4,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,4,5,2,7,6,1] => [7,6,1,5,2,3,4]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,4,5,2,6,7,1] => [7,1,5,2,3,4,6]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,4,6,5,2,7,1] => [7,1,6,5,2,3,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,4,5,6,2,7,1] => [7,1,6,2,3,4,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [3,5,4,6,2,7,1] => [7,1,6,2,3,5,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [4,3,5,2,6,1,7] => [6,1,5,2,4,3,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [4,3,5,2,7,6,1] => [7,6,1,5,2,4,3]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [4,3,5,2,6,7,1] => [7,1,5,2,4,3,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [4,3,6,5,2,7,1] => [7,1,6,5,2,4,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [4,3,5,6,2,7,1] => [7,1,6,2,4,3,5]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [5,4,3,6,2,7,1] => [7,1,6,2,5,4,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [4,5,3,6,2,7,1] => [7,1,6,2,5,3,4]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,8,7,6]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,7,6,5]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,8,6,5] => [1,2,3,4,8,6,5,7]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,5,7,6]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,7,6,5,4] => [1,2,3,8,7,6,5,4]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,7,8,6,5,4] => [1,2,3,8,6,5,4,7]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,6,8,7,5,4] => [1,2,3,8,7,5,4,6]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [1,2,3,6,7,8,5,4] => [1,2,3,8,5,4,6,7]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,7,6,8,5,4] => [1,2,3,8,5,4,7,6]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,2,3,5,8,7,6,4] => [1,2,3,8,7,6,4,5]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,2,3,5,7,8,6,4] => [1,2,3,8,6,4,5,7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [1,2,3,5,6,8,7,4] => [1,2,3,8,7,4,5,6]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [1,2,3,5,7,6,8,4] => [1,2,3,8,4,5,7,6]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,2,3,6,5,8,7,4] => [1,2,3,8,7,4,6,5]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [1,2,3,6,5,7,8,4] => [1,2,3,8,4,6,5,7]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [1,2,3,7,6,5,8,4] => [1,2,3,8,4,7,6,5]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,2,3,6,7,5,8,4] => [1,2,3,8,4,7,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,7,6,5]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,5,7,6]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [1,2,6,7,8,5,4,3] => [1,2,8,5,4,3,6,7]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [1,2,5,6,7,8,4,3] => [1,2,8,4,3,5,6,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,2,4,8,7,6,5,3] => [1,2,8,7,6,5,3,4]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [1,2,4,7,8,6,5,3] => [1,2,8,6,5,3,4,7]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [1,2,4,6,7,8,5,3] => [1,2,8,5,3,4,6,7]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [1,2,5,4,6,7,8,3] => [1,2,8,3,5,4,6,7]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [1,2,6,5,4,7,8,3] => [1,2,8,3,6,5,4,7]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [1,2,5,6,4,7,8,3] => [1,2,8,3,6,4,5,7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,7,6,5]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,5,7,6]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [1,3,2,8,7,6,5,4] => [1,3,2,8,7,6,5,4]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,7,6,5] => [1,4,3,2,8,7,6,5]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [1,4,3,2,6,7,8,5] => [1,4,3,2,8,5,6,7]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,4,3,2,7,6,8,5] => [1,4,3,2,8,5,7,6]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,7,8,6,5,4,3,2] => [1,8,6,5,4,3,2,7]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [1,6,8,7,5,4,3,2] => [1,8,7,5,4,3,2,6]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [1,6,7,8,5,4,3,2] => [1,8,5,4,3,2,6,7]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [1,7,6,8,5,4,3,2] => [1,8,5,4,3,2,7,6]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [1,5,8,7,6,4,3,2] => [1,8,7,6,4,3,2,5]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [1,5,6,7,8,4,3,2] => [1,8,4,3,2,5,6,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [1,4,8,7,6,5,3,2] => [1,8,7,6,5,3,2,4]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,7,6,5] => [1,4,2,3,8,7,6,5]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => [1,4,2,3,7,5,6,8]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [1,3,4,2,6,7,8,5] => [1,4,2,3,8,5,6,7]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,3,4,2,7,6,8,5] => [1,4,2,3,8,5,7,6]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,3,5,7,8,6,4,2] => [1,8,6,4,2,3,5,7]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [1,3,5,6,7,8,4,2] => [1,8,4,2,3,5,6,7]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [1,3,6,5,7,8,4,2] => [1,8,4,2,3,6,5,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [1,3,4,8,7,6,5,2] => [1,8,7,6,5,2,3,4]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,5,3,4,7,6,2,8] => [1,3,4,6,7,5,2,8] => [1,7,5,2,3,4,6,8]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [1,3,4,5,7,8,6,2] => [1,8,6,2,3,4,5,7]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [1,3,4,5,6,8,7,2] => [1,8,7,2,3,4,5,6]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,4,3,8,7,6,5,2] => [1,8,7,6,5,2,4,3]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,4,3,7,8,6,5,2] => [1,8,6,5,2,4,3,7]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [1,4,3,7,6,8,5,2] => [1,8,5,2,4,3,7,6]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [1,4,3,5,6,7,8,2] => [1,8,2,4,3,5,6,7]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [1,4,3,6,5,8,7,2] => [1,8,7,2,4,3,6,5]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [1,5,4,3,6,7,8,2] => [1,8,2,5,4,3,6,7]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [1,6,5,4,3,8,7,2] => [1,8,7,2,6,5,4,3]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [1,4,5,3,6,7,8,2] => [1,8,2,5,3,4,6,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,7,6,5]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,5,6,7]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,5,7,6]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,7,6,5,4] => [2,1,3,8,7,6,5,4]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,6,5,7]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,6,8,7,5] => [2,1,4,3,8,7,5,6]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,5,7,6]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [2,1,5,4,3,6,8,7]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [2,1,6,7,8,5,4,3] => [2,1,8,5,4,3,6,7]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,5,6,4,3,8,7] => [2,1,6,4,3,5,8,7]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [2,1,5,6,7,8,4,3] => [2,1,8,4,3,5,6,7]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [2,1,6,5,8,7,4,3] => [2,1,8,7,4,3,6,5]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [2,1,6,5,7,8,4,3] => [2,1,8,4,3,6,5,7]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [2,1,7,6,5,8,4,3] => [2,1,8,4,3,7,6,5]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,6,7,5,8,4,3] => [2,1,8,4,3,7,5,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,4,6,5,3,8,7] => [2,1,6,5,3,4,8,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [2,1,4,8,7,6,5,3] => [2,1,8,7,6,5,3,4]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [2,1,4,7,8,6,5,3] => [2,1,8,6,5,3,4,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [2,1,4,5,8,7,6,3] => [2,1,8,7,6,3,4,5]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [2,1,4,5,7,8,6,3] => [2,1,8,6,3,4,5,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [2,1,4,6,5,8,7,3] => [2,1,8,7,3,4,6,5]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7] => [2,1,6,3,5,4,8,7]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3] => [2,1,8,3,5,4,7,6]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3] => [2,1,8,3,7,4,6,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [3,2,1,4,7,6,5,8]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,7,6,5] => [3,2,1,4,8,7,6,5]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,1,4,7,6,8,5] => [3,2,1,4,8,5,7,6]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,2,1,6,8,7,5,4] => [3,2,1,8,7,5,4,6]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [3,2,1,6,7,8,5,4] => [3,2,1,8,5,4,6,7]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,2,1,5,7,8,6,4] => [3,2,1,8,6,4,5,7]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [3,2,1,5,6,7,8,4] => [3,2,1,8,4,5,6,7]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,2,1,6,5,8,7,4] => [3,2,1,8,7,4,6,5]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [3,2,1,7,6,5,8,4] => [3,2,1,8,4,7,6,5]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,1,6,7,5,8,4] => [3,2,1,8,4,7,5,6]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,8,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,8,7,6]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,3,2,1,5,7,8,6] => [4,3,2,1,5,8,6,7]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7,8]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,3,2,1,7,8,6,5] => [4,3,2,1,8,6,5,7]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [4,3,2,1,6,7,5,8] => [4,3,2,1,7,5,6,8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,3,2,1,6,8,7,5] => [4,3,2,1,8,7,5,6]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [4,3,2,1,6,7,8,5] => [4,3,2,1,8,5,6,7]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,3,2,1,7,6,8,5] => [4,3,2,1,8,5,7,6]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,6,8,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,7,6,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,4,3,2,1,7,8,6] => [5,4,3,2,1,8,6,7]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [7,8,6,5,4,3,2,1] => [8,6,5,4,3,2,1,7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [6,7,5,4,3,2,1,8] => [7,5,4,3,2,1,6,8]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [6,7,8,5,4,3,2,1] => [8,5,4,3,2,1,6,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [7,6,8,5,4,3,2,1] => [8,5,4,3,2,1,7,6]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [5,7,6,4,3,2,1,8] => [7,6,4,3,2,1,5,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [5,8,7,6,4,3,2,1] => [8,7,6,4,3,2,1,5]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [5,6,7,4,3,2,1,8] => [7,4,3,2,1,5,6,8]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [5,6,7,8,4,3,2,1] => [8,4,3,2,1,5,6,7]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [6,5,7,4,3,2,1,8] => [7,4,3,2,1,6,5,8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [6,5,8,7,4,3,2,1] => [8,7,4,3,2,1,6,5]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [6,5,7,8,4,3,2,1] => [8,4,3,2,1,6,5,7]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [7,6,5,8,4,3,2,1] => [8,4,3,2,1,7,6,5]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [4,7,6,5,3,2,1,8] => [7,6,5,3,2,1,4,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [4,8,7,6,5,3,2,1] => [8,7,6,5,3,2,1,4]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [4,5,6,3,2,1,8,7] => [6,3,2,1,4,5,8,7]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [4,5,6,7,8,3,2,1] => [8,3,2,1,4,5,6,7]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [4,7,6,5,8,3,2,1] => [8,3,2,1,4,7,6,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [6,5,4,7,3,2,1,8] => [7,3,2,1,6,5,4,8]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [7,6,5,4,8,3,2,1] => [8,3,2,1,7,6,5,4]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [6,5,7,4,8,3,2,1] => [8,3,2,1,7,4,6,5]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,4,2,1,6,5,8,7] => [4,2,1,3,6,5,8,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [3,4,2,1,8,7,6,5] => [4,2,1,3,8,7,6,5]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,4,2,1,7,8,6,5] => [4,2,1,3,8,6,5,7]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,4,2,1,6,8,7,5] => [4,2,1,3,8,7,5,6]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [3,4,2,1,6,7,8,5] => [4,2,1,3,8,5,6,7]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,4,2,1,7,6,8,5] => [4,2,1,3,8,5,7,6]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [3,5,4,2,1,8,7,6] => [5,4,2,1,3,8,7,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [3,6,5,4,2,1,8,7] => [6,5,4,2,1,3,8,7]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => [3,7,6,8,5,4,2,1] => [8,5,4,2,1,3,7,6]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [3,5,8,7,6,4,2,1] => [8,7,6,4,2,1,3,5]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [3,5,6,8,7,4,2,1] => [8,7,4,2,1,3,5,6]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [3,5,6,7,8,4,2,1] => [8,4,2,1,3,5,6,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [3,4,7,6,5,2,1,8] => [7,6,5,2,1,3,4,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [3,4,8,7,6,5,2,1] => [8,7,6,5,2,1,3,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [3,4,5,8,7,6,2,1] => [8,7,6,2,1,3,4,5]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [4,3,5,2,1,8,7,6] => [5,2,1,4,3,8,7,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [4,3,6,5,2,1,8,7] => [6,5,2,1,4,3,8,7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [4,3,5,6,2,1,8,7] => [6,2,1,4,3,5,8,7]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [4,3,5,6,7,8,2,1] => [8,2,1,4,3,5,6,7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [4,3,6,5,8,7,2,1] => [8,7,2,1,4,3,6,5]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [5,4,3,6,2,1,8,7] => [6,2,1,5,4,3,8,7]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [7,6,5,4,3,8,2,1] => [8,2,1,7,6,5,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [4,5,3,6,2,1,8,7] => [6,2,1,5,3,4,8,7]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [4,5,6,7,3,8,2,1] => [8,2,1,7,3,4,5,6]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [5,4,6,7,3,8,2,1] => [8,2,1,7,3,5,4,6]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => [3,1,2,4,5,8,6,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [2,3,1,4,8,7,6,5] => [3,1,2,4,8,7,6,5]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [2,3,1,4,6,7,8,5] => [3,1,2,4,8,5,6,7]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,3,1,4,7,6,8,5] => [3,1,2,4,8,5,7,6]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [3,1,2,5,4,7,6,8]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [2,3,1,8,7,6,5,4] => [3,1,2,8,7,6,5,4]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [2,3,1,5,6,7,4,8] => [3,1,2,7,4,5,6,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => [4,3,1,2,6,5,8,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [2,4,3,1,8,7,6,5] => [4,3,1,2,8,7,6,5]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [2,4,3,1,7,8,6,5] => [4,3,1,2,8,6,5,7]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [2,4,3,1,6,8,7,5] => [4,3,1,2,8,7,5,6]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [2,4,3,1,6,7,8,5] => [4,3,1,2,8,5,6,7]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [2,4,3,1,7,6,8,5] => [4,3,1,2,8,5,7,6]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [2,7,8,6,5,4,3,1] => [8,6,5,4,3,1,2,7]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [2,6,8,7,5,4,3,1] => [8,7,5,4,3,1,2,6]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [2,5,6,7,8,4,3,1] => [8,4,3,1,2,5,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [2,4,5,3,1,8,7,6] => [5,3,1,2,4,8,7,6]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [2,4,8,7,6,5,3,1] => [8,7,6,5,3,1,2,4]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [2,4,6,8,7,5,3,1] => [8,7,5,3,1,2,4,6]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => [4,1,2,3,5,7,6,8]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [2,3,4,1,5,8,7,6] => [4,1,2,3,5,8,7,6]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => [4,1,2,3,5,8,6,7]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => [4,1,2,3,6,5,7,8]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [4,1,2,3,6,5,8,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [2,3,4,1,8,7,6,5] => [4,1,2,3,8,7,6,5]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [2,3,4,1,7,8,6,5] => [4,1,2,3,8,6,5,7]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => [4,1,2,3,7,5,6,8]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [2,3,4,1,6,8,7,5] => [4,1,2,3,8,7,5,6]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [2,3,4,1,6,7,8,5] => [4,1,2,3,8,5,6,7]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [2,3,4,1,7,6,8,5] => [4,1,2,3,8,5,7,6]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [2,3,5,4,1,8,7,6] => [5,4,1,2,3,8,7,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [2,3,6,5,4,1,8,7] => [6,5,4,1,2,3,8,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [2,3,5,6,8,7,4,1] => [8,7,4,1,2,3,5,6]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [2,3,5,6,7,8,4,1] => [8,4,1,2,3,5,6,7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [2,3,4,5,1,8,7,6] => [5,1,2,3,4,8,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [2,3,4,6,5,1,7,8] => [6,5,1,2,3,4,7,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [2,3,4,8,7,6,5,1] => [8,7,6,5,1,2,3,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [2,3,4,5,6,1,8,7] => [6,1,2,3,4,5,8,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [2,3,4,5,7,6,1,8] => [7,6,1,2,3,4,5,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,6,8,7,1] => [8,7,1,2,3,4,5,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [2,3,5,4,7,6,8,1] => [8,1,2,3,5,4,7,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [2,4,3,6,5,1,8,7] => [6,5,1,2,4,3,8,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [2,4,3,6,5,8,7,1] => [8,7,1,2,4,3,6,5]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [2,4,3,6,5,7,8,1] => [8,1,2,4,3,6,5,7]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [2,4,3,7,6,5,8,1] => [8,1,2,4,3,7,6,5]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,2,4,5,3,8,7,1] => [2,5,4,3,7,8,6,1] => [8,6,1,2,5,4,3,7]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [2,5,4,3,6,8,7,1] => [8,7,1,2,5,4,3,6]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [2,5,4,3,7,6,8,1] => [8,1,2,5,4,3,7,6]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [2,5,4,7,6,3,8,1] => [8,1,2,7,6,3,5,4]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [2,5,4,6,7,3,8,1] => [8,1,2,7,3,5,4,6]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [4,1,3,2,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => [4,1,3,2,5,6,8,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => [4,1,3,2,5,7,6,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [3,2,4,1,5,8,7,6] => [4,1,3,2,5,8,7,6]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => [4,1,3,2,5,8,6,7]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => [4,1,3,2,6,5,7,8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => [4,1,3,2,6,5,8,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [3,2,4,1,7,6,5,8] => [4,1,3,2,7,6,5,8]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [3,2,4,1,8,7,6,5] => [4,1,3,2,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [3,2,4,1,7,8,6,5] => [4,1,3,2,8,6,5,7]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [3,2,4,1,6,7,5,8] => [4,1,3,2,7,5,6,8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [3,2,4,1,6,8,7,5] => [4,1,3,2,8,7,5,6]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [3,2,4,1,6,7,8,5] => [4,1,3,2,8,5,6,7]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [3,2,4,1,7,6,8,5] => [4,1,3,2,8,5,7,6]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [3,2,5,4,1,6,7,8] => [5,4,1,3,2,6,7,8]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [3,2,5,4,1,8,7,6] => [5,4,1,3,2,8,7,6]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [3,2,7,6,5,4,1,8] => [7,6,5,4,1,3,2,8]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [3,2,6,7,5,4,1,8] => [7,5,4,1,3,2,6,8]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [3,2,4,8,7,6,5,1] => [8,7,6,5,1,3,2,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [3,2,4,5,6,7,8,1] => [8,1,3,2,4,5,6,7]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [3,2,4,7,6,5,8,1] => [8,1,3,2,4,7,6,5]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [3,2,5,4,6,1,8,7] => [6,1,3,2,5,4,8,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [3,2,5,4,7,6,1,8] => [7,6,1,3,2,5,4,8]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,8,1] => [8,1,3,2,5,4,7,6]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [3,2,6,5,4,8,7,1] => [8,7,1,3,2,6,5,4]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [3,2,6,5,7,4,8,1] => [8,1,3,2,7,4,6,5]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [4,3,2,5,1,8,7,6] => [5,1,4,3,2,8,7,6]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [4,3,2,8,7,6,5,1] => [8,7,6,5,1,4,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [4,3,2,5,6,1,8,7] => [6,1,4,3,2,5,8,7]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [4,3,2,5,6,7,8,1] => [8,1,4,3,2,5,6,7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,3,4,5,2,1,7,8] => [5,4,3,2,6,1,7,8] => [6,1,5,4,3,2,7,8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [5,4,3,2,6,1,8,7] => [6,1,5,4,3,2,8,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [5,4,3,2,7,6,1,8] => [7,6,1,5,4,3,2,8]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [5,4,3,2,8,7,6,1] => [8,7,6,1,5,4,3,2]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [5,4,3,2,7,8,6,1] => [8,6,1,5,4,3,2,7]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [5,4,3,2,6,7,8,1] => [8,1,5,4,3,2,6,7]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [5,4,3,2,7,6,8,1] => [8,1,5,4,3,2,7,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [7,6,5,4,3,2,8,1] => [8,1,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [6,7,5,4,3,2,8,1] => [8,1,7,5,4,3,2,6]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [6,5,7,4,3,2,8,1] => [8,1,7,4,3,2,6,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [4,5,3,2,6,1,8,7] => [6,1,5,3,2,4,8,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [4,5,3,2,7,6,1,8] => [7,6,1,5,3,2,4,8]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [4,5,6,7,3,2,8,1] => [8,1,7,3,2,4,5,6]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [3,4,2,5,1,8,7,6] => [5,1,4,2,3,8,7,6]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [3,4,2,8,7,6,5,1] => [8,7,6,5,1,4,2,3]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [3,4,2,5,7,8,6,1] => [8,6,1,4,2,3,5,7]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [3,4,2,5,6,7,8,1] => [8,1,4,2,3,5,6,7]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [3,4,2,7,6,5,8,1] => [8,1,4,2,3,7,6,5]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [3,4,2,6,7,5,8,1] => [8,1,4,2,3,7,5,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [3,5,4,2,6,7,1,8] => [7,1,5,4,2,3,6,8]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [3,4,5,2,6,7,8,1] => [8,1,5,2,3,4,6,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [4,3,5,2,6,1,8,7] => [6,1,5,2,4,3,8,7]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [4,3,5,2,7,6,8,1] => [8,1,5,2,4,3,7,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [4,3,6,5,2,8,7,1] => [8,7,1,6,5,2,4,3]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [4,3,6,5,7,2,8,1] => [8,1,7,2,4,3,6,5]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [6,5,4,3,7,2,8,1] => [8,1,7,2,6,5,4,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [4,5,3,6,2,7,1,8] => [7,1,6,2,5,3,4,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => [8,1,7,2,6,3,5,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [8,9,7,6,5,4,3,2,1] => [9,7,6,5,4,3,2,1,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => [7,8,9,6,5,4,3,2,1] => [9,6,5,4,3,2,1,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [8,7,9,6,5,4,3,2,1] => [9,6,5,4,3,2,1,8,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,9,7,8,6,1] => [8,7,6,9,5,4,3,2,1] => [9,5,4,3,2,1,8,7,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,9,6,7,8,5,1] => [8,7,6,5,9,4,3,2,1] => [9,4,3,2,1,8,7,6,5]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,9,5,6,7,8,4,1] => [8,7,6,5,4,9,3,2,1] => [9,3,2,1,8,7,6,5,4]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,9,4,5,6,7,8,3,1] => [8,7,6,5,4,3,9,2,1] => [9,2,1,8,7,6,5,4,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,9,1] => [9,1,3,2,4,5,6,7,8]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [8,7,6,5,4,3,2,9,1] => [9,1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9,4,3,2,5,6,7,8,1] => [3,4,2,5,6,7,8,9,1] => [9,1,4,2,3,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,9,8,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,7,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,6,8,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,10,8,9,7] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,7,8,9]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,9,6,7,8,5] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,5,10,7,8,9,6] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,6,7,8,9]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,9,5,6,7,8,4] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,4,10,6,7,8,9,5] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,5,6,7,8,9]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,9,4,5,6,7,8,3] => [1,2,4,5,6,7,8,9,3] => [1,2,9,3,4,5,6,7,8]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,3,10,5,6,7,8,9,4] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,4,5,6,7,8,9]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,10,4,5,6,7,8,9,3] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,3,4,5,6,7,8,9]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10,3,4,5,6,7,8,9,2] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => [3,1,2,5,4,7,6,9,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => [3,1,2,5,4,7,6,9,8,10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [7,8,6,5,4,3,2,1,9] => [8,6,5,4,3,2,1,7,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [9,10,8,7,6,5,4,3,2,1] => [10,8,7,6,5,4,3,2,1,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,2,3,4,5,6,1,8,9] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,9,4,3,5,6,7,8,2] => [1,4,3,5,6,7,8,9,2] => [1,9,2,4,3,5,6,7,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [1,8,9,7,6,5,4,3,2] => [1,9,7,6,5,4,3,2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [9,8,10,7,6,5,4,3,2,1] => [10,7,6,5,4,3,2,1,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,10,8,9,7,1] => [9,8,7,10,6,5,4,3,2,1] => [10,6,5,4,3,2,1,9,8,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,6,1] => [9,8,7,6,10,5,4,3,2,1] => [10,5,4,3,2,1,9,8,7,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,10,6,7,8,9,5,1] => [9,8,7,6,5,10,4,3,2,1] => [10,4,3,2,1,9,8,7,6,5]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,10,5,6,7,8,9,4,1] => [9,8,7,6,5,4,10,3,2,1] => [10,3,2,1,9,8,7,6,5,4]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,10,4,5,6,7,8,9,3,1] => [9,8,7,6,5,4,3,10,2,1] => [10,2,1,9,8,7,6,5,4,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => [9,8,7,6,5,4,3,2,10,1] => [10,1,9,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,10,6,7,8,9,1] => [6,7,8,9,10,5,4,3,2,1] => [10,5,4,3,2,1,6,7,8,9]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [3,4,2,1,6,5,8,7,10,9] => [4,2,1,3,6,5,8,7,10,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,10,1] => [10,1,3,2,4,5,6,7,8,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1,10] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,5,7,6,8,1,9] => [6,8,7,5,4,3,2,1,9] => [8,7,5,4,3,2,1,6,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,9,5,4,6,7,8,3] => [1,2,5,4,6,7,8,9,3] => [1,2,9,3,5,4,6,7,8]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => [1,7,9,8,6,5,4,3,2] => [1,9,8,6,5,4,3,2,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [1,9,10,8,7,6,5,4,3,2] => [1,10,8,7,6,5,4,3,2,9]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,4,9,7,6,8,5] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,9,5,7,6,8]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,9,6,5,7,8,4] => [1,2,3,6,5,7,8,9,4] => [1,2,3,9,4,6,5,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [8,9,7,6,5,4,3,2,1,10] => [9,7,6,5,4,3,2,1,8,10]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [2,1,5,6,4,3,8,7,10,9] => [2,1,6,4,3,5,8,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [2,1,4,3,7,8,6,5,10,9] => [2,1,4,3,8,6,5,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [2,1,4,3,6,5,9,10,8,7] => [2,1,4,3,6,5,10,8,7,9]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,10,9,7] => [2,1,5,6,4,3,9,10,8,7] => [2,1,6,4,3,5,10,8,7,9]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,10,9,7] => [3,4,2,1,6,5,9,10,8,7] => [4,2,1,3,6,5,10,8,7,9]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9] => [3,4,2,1,7,8,6,5,10,9] => [4,2,1,3,8,6,5,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,7,10,12,11,9] => [2,1,4,3,6,5,8,7,11,12,10,9] => [2,1,4,3,6,5,8,7,12,10,9,11]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,5,8,10,9,7,12,11] => [2,1,4,3,6,5,9,10,8,7,12,11] => [2,1,4,3,6,5,10,8,7,9,12,11]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9,12,11] => [2,1,4,3,7,8,6,5,10,9,12,11] => [2,1,4,3,8,6,5,7,10,9,12,11]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5,10,12,11,9] => [2,1,4,3,7,8,6,5,11,12,10,9] => [2,1,4,3,8,6,5,7,12,10,9,11]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9,12,11] => [2,1,5,6,4,3,8,7,10,9,12,11] => [2,1,6,4,3,5,8,7,10,9,12,11]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,7,10,12,11,9] => [2,1,5,6,4,3,8,7,11,12,10,9] => [2,1,6,4,3,5,8,7,12,10,9,11]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,10,9,7,12,11] => [2,1,5,6,4,3,9,10,8,7,12,11] => [2,1,6,4,3,5,10,8,7,9,12,11]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9,12,11] => [3,4,2,1,6,5,8,7,10,9,12,11] => [4,2,1,3,6,5,8,7,10,9,12,11]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,7,10,12,11,9] => [3,4,2,1,6,5,8,7,11,12,10,9] => [4,2,1,3,6,5,8,7,12,10,9,11]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5,8,10,9,7,12,11] => [3,4,2,1,6,5,9,10,8,7,12,11] => [4,2,1,3,6,5,10,8,7,9,12,11]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9,12,11] => [3,4,2,1,7,8,6,5,10,9,12,11] => [4,2,1,3,8,6,5,7,10,9,12,11]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5,10,12,11,9] => [3,4,2,1,7,8,6,5,11,12,10,9] => [4,2,1,3,8,6,5,7,12,10,9,11]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => [4,3,2,1,6,5,10,9,8,7] => [4,3,2,1,6,5,10,9,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,10,9,8,7,6,5]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,10,9,8,7]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9]
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].
This is the inverse of the map $\Phi$ in [1, sec.3].
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
searching the database
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