Processing math: 100%

Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
[1,0] => [1] => [1] => [1] =>
[1,0,1,0] => [1,2] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3] => 00
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [1,3,2] => 01
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1,3] => 10
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => [2,3,1] => 01
[1,1,1,0,0,0] => [3,2,1] => [2,3,1] => [3,1,2] => 10
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 000
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 001
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 010
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [1,3,4,2] => 001
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,3,4,2] => [1,4,2,3] => 010
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 100
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 101
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => [2,3,1,4] => 010
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,2,3,1] => [2,3,4,1] => 001
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,2,4,1] => [2,4,1,3] => 010
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => 100
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,3,2,1] => [3,2,4,1] => 101
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [2,4,3,1] => [3,4,1,2] => 010
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => 100
[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] => 0000
[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] => 0001
[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] => 0010
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => 0001
[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] => 0010
[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] => 0100
[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] => 0101
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => 0010
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => 0001
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,4,3,5,2] => [1,3,5,2,4] => 0010
[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] => 0100
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,4,3,2] => [1,4,3,5,2] => 0101
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,3,5,4,2] => [1,4,5,2,3] => 0010
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,3,4,5,2] => [1,5,2,3,4] => 0100
[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] => 1000
[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] => 1001
[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] => 1010
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,5,3] => 1001
[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] => 1010
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => 0100
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [2,3,1,5,4] => 0101
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,2,3,1,5] => [2,3,4,1,5] => 0010
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [2,3,4,5,1] => 0001
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,2,3,5,1] => [2,3,5,1,4] => 0010
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,2,4,1,5] => [2,4,1,3,5] => 0100
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,2,4,3,1] => [2,4,3,5,1] => 0101
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [3,2,5,4,1] => [2,4,5,1,3] => 0010
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [3,2,4,5,1] => [2,5,1,3,4] => 0100
[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] => 1000
[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] => 1001
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,3,2,1,5] => [3,2,4,1,5] => 1010
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,3,2,4,1] => [3,2,4,5,1] => 1001
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [4,3,2,5,1] => [3,2,5,1,4] => 1010
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [2,4,3,1,5] => [3,4,1,2,5] => 0100
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,4,3,2,1] => [3,4,2,5,1] => 0101
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [2,5,3,4,1] => [3,4,5,1,2] => 0010
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [2,4,3,5,1] => [3,5,1,2,4] => 0100
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => 1000
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,3,4,2,1] => [4,2,3,5,1] => 1001
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [2,5,4,3,1] => [4,3,5,1,2] => 1010
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [2,3,5,4,1] => [4,5,1,2,3] => 0100
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [2,3,4,5,1] => [5,1,2,3,4] => 1000
[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] => 00000
[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] => 00001
[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] => 00010
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => 00001
[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] => 00010
[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] => 00100
[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] => 00101
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => 00010
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => 00001
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => [1,2,4,6,3,5] => 00010
[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] => 00100
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => [1,2,5,4,6,3] => 00101
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,4,6,5,3] => [1,2,5,6,3,4] => 00010
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 00100
[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] => 01000
[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] => 01001
[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] => 01010
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => 01001
[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] => 01010
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => 00100
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => 00101
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => 00010
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => 00001
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => [1,3,4,6,2,5] => 00010
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => [1,3,5,2,4,6] => 00100
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => [1,3,5,4,6,2] => 00101
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,4,3,6,5,2] => [1,3,5,6,2,4] => 00010
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,4,3,5,6,2] => [1,3,6,2,4,5] => 00100
[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] => 01000
[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] => 01001
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => [1,4,3,5,2,6] => 01010
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => [1,4,3,5,6,2] => 01001
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,5,4,3,6,2] => [1,4,3,6,2,5] => 01010
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,3,5,4,2,6] => [1,4,5,2,3,6] => 00100
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [1,4,5,3,6,2] => 00101
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,3,6,4,5,2] => [1,4,5,6,2,3] => 00010
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,3,5,4,6,2] => [1,4,6,2,3,5] => 00100
>>> Load all 1841 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 01000
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,4,5,3,2] => [1,5,3,4,6,2] => 01001
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,3,6,5,4,2] => [1,5,4,6,2,3] => 01010
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,3,4,6,5,2] => [1,5,6,2,3,4] => 00100
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 01000
[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] => 10000
[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] => 10001
[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] => 10010
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => 10001
[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] => 10010
[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] => 10100
[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] => 10101
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => 10010
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => 10001
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => [2,1,4,6,3,5] => 10010
[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] => 10100
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [2,1,5,4,6,3] => 10101
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,4,6,5,3] => [2,1,5,6,3,4] => 10010
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => 10100
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 01000
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => 01001
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => 01010
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => 01001
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => [2,3,1,6,4,5] => 01010
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => 00100
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => 00101
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => 00010
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => 00001
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => [2,3,4,6,1,5] => 00010
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => [2,3,5,1,4,6] => 00100
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => [2,3,5,4,6,1] => 00101
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [4,2,3,6,5,1] => [2,3,5,6,1,4] => 00010
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,2,3,5,6,1] => [2,3,6,1,4,5] => 00100
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => [2,4,1,3,5,6] => 01000
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => [2,4,1,3,6,5] => 01001
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => [2,4,3,5,1,6] => 01010
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => [2,4,3,5,6,1] => 01001
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [5,2,4,3,6,1] => [2,4,3,6,1,5] => 01010
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [3,2,5,4,1,6] => [2,4,5,1,3,6] => 00100
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => [2,4,5,3,6,1] => 00101
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [3,2,6,4,5,1] => [2,4,5,6,1,3] => 00010
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [3,2,5,4,6,1] => [2,4,6,1,3,5] => 00100
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,2,4,5,1,6] => [2,5,1,3,4,6] => 01000
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,2,4,5,3,1] => [2,5,3,4,6,1] => 01001
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [3,2,6,5,4,1] => [2,5,4,6,1,3] => 01010
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [3,2,4,6,5,1] => [2,5,6,1,3,4] => 00100
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [3,2,4,5,6,1] => [2,6,1,3,4,5] => 01000
[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] => 10000
[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] => 10001
[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] => 10010
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => [3,1,2,5,6,4] => 10001
[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] => 10010
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [3,2,4,1,5,6] => 10100
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => [3,2,4,1,6,5] => 10101
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [3,2,4,5,1,6] => 10010
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [3,2,4,5,6,1] => 10001
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [5,3,2,4,6,1] => [3,2,4,6,1,5] => 10010
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [4,3,2,5,1,6] => [3,2,5,1,4,6] => 10100
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => [3,2,5,4,6,1] => 10101
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [4,3,2,6,5,1] => [3,2,5,6,1,4] => 10010
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [4,3,2,5,6,1] => [3,2,6,1,4,5] => 10100
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [2,4,3,1,5,6] => [3,4,1,2,5,6] => 01000
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [2,4,3,1,6,5] => [3,4,1,2,6,5] => 01001
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => 01010
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [3,4,2,5,6,1] => 01001
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [5,4,3,2,6,1] => [3,4,2,6,1,5] => 01010
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [2,5,3,4,1,6] => [3,4,5,1,2,6] => 00100
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [3,4,5,2,6,1] => 00101
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [2,6,3,4,5,1] => [3,4,5,6,1,2] => 00010
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [2,5,3,4,6,1] => [3,4,6,1,2,5] => 00100
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [2,4,3,5,1,6] => [3,5,1,2,4,6] => 01000
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [6,4,3,5,2,1] => [3,5,2,4,6,1] => 01001
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [2,6,3,5,4,1] => [3,5,4,6,1,2] => 01010
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [2,4,3,6,5,1] => [3,5,6,1,2,4] => 00100
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [2,4,3,5,6,1] => [3,6,1,2,4,5] => 01000
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 10000
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => 10001
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => [4,2,3,5,1,6] => 10010
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => [4,2,3,5,6,1] => 10001
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [5,3,4,2,6,1] => [4,2,3,6,1,5] => 10010
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [2,5,4,3,1,6] => [4,3,5,1,2,6] => 10100
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 10101
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [2,6,4,3,5,1] => [4,3,5,6,1,2] => 10010
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [2,5,4,3,6,1] => [4,3,6,1,2,5] => 10100
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [2,3,5,4,1,6] => [4,5,1,2,3,6] => 01000
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [6,3,5,4,2,1] => [4,5,2,3,6,1] => 01001
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [2,6,5,4,3,1] => [4,5,3,6,1,2] => 01010
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [2,3,6,4,5,1] => [4,5,6,1,2,3] => 00100
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [2,3,5,4,6,1] => [4,6,1,2,3,5] => 01000
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 10000
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => [5,2,3,4,6,1] => 10001
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [2,6,4,5,3,1] => [5,3,4,6,1,2] => 10010
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [2,3,6,5,4,1] => [5,4,6,1,2,3] => 10100
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [2,3,4,6,5,1] => [5,6,1,2,3,4] => 01000
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 10000
[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] => 000000
[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] => 000001
[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] => 000010
[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] => [1,2,3,4,6,7,5] => 000001
[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] => 000010
[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] => 000100
[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] => 000101
[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] => [1,2,3,5,6,4,7] => 000010
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,5,6,7,4] => 000001
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4] => [1,2,3,5,7,4,6] => 000010
[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] => 000100
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => [1,2,3,6,5,7,4] => 000101
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [1,2,3,5,7,6,4] => [1,2,3,6,7,4,5] => 000010
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => 000100
[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] => 001000
[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] => 001001
[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] => 001010
[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] => [1,2,4,3,6,7,5] => 001001
[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] => 001010
[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] => [1,2,4,5,3,6,7] => 000100
[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] => [1,2,4,5,3,7,6] => 000101
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => 000010
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,4,5,6,7,3] => 000001
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3] => [1,2,4,5,7,3,6] => 000010
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7] => [1,2,4,6,3,5,7] => 000100
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => [1,2,4,6,5,7,3] => 000101
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [1,2,5,4,7,6,3] => [1,2,4,6,7,3,5] => 000010
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,5,4,6,7,3] => [1,2,4,7,3,5,6] => 000100
[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] => 001000
[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] => 001001
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => [1,2,5,4,6,3,7] => 001010
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => [1,2,5,4,6,7,3] => 001001
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,6,5,4,7,3] => [1,2,5,4,7,3,6] => 001010
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [1,2,4,6,5,3,7] => [1,2,5,6,3,4,7] => 000100
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => [1,2,5,6,4,7,3] => 000101
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [1,2,4,7,5,6,3] => [1,2,5,6,7,3,4] => 000010
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [1,2,4,6,5,7,3] => [1,2,5,7,3,4,6] => 000100
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => 001000
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,7,5,6,4,3] => [1,2,6,4,5,7,3] => 001001
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [1,2,4,7,6,5,3] => [1,2,6,5,7,3,4] => 001010
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [1,2,4,5,7,6,3] => [1,2,6,7,3,4,5] => 000100
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => 001000
[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] => 010000
[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] => 010001
[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] => 010010
[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] => [1,3,2,4,6,7,5] => 010001
[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] => 010010
[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] => 010100
[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] => 010101
[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] => [1,3,2,5,6,4,7] => 010010
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [1,3,2,5,6,7,4] => 010001
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,6,5,7,4] => [1,3,2,5,7,4,6] => 010010
[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] => 010100
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => [1,3,2,6,5,7,4] => 010101
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [1,3,2,5,7,6,4] => [1,3,2,6,7,4,5] => 010010
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => 010100
[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] => [1,3,4,2,5,6,7] => 001000
[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] => [1,3,4,2,5,7,6] => 001001
[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] => [1,3,4,2,6,5,7] => 001010
[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] => [1,3,4,2,6,7,5] => 001001
[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] => [1,3,4,2,7,5,6] => 001010
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [1,3,4,5,2,6,7] => 000100
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [1,3,4,5,2,7,6] => 000101
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [1,3,4,5,6,2,7] => 000010
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [1,3,4,5,6,7,2] => 000001
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,6,3,4,5,7,2] => [1,3,4,5,7,2,6] => 000010
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,5,3,4,6,2,7] => [1,3,4,6,2,5,7] => 000100
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => [1,3,4,6,5,7,2] => 000101
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [1,5,3,4,7,6,2] => [1,3,4,6,7,2,5] => 000010
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,5,3,4,6,7,2] => [1,3,4,7,2,5,6] => 000100
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => [1,3,5,2,4,6,7] => 001000
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,4,3,5,2,7,6] => [1,3,5,2,4,7,6] => 001001
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => [1,3,5,4,6,2,7] => 001010
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => [1,3,5,4,6,7,2] => 001001
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,6,3,5,4,7,2] => [1,3,5,4,7,2,6] => 001010
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [1,4,3,6,5,2,7] => [1,3,5,6,2,4,7] => 000100
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => [1,3,5,6,4,7,2] => 000101
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [1,4,3,7,5,6,2] => [1,3,5,6,7,2,4] => 000010
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [1,4,3,6,5,7,2] => [1,3,5,7,2,4,6] => 000100
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,4,3,5,6,2,7] => [1,3,6,2,4,5,7] => 001000
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,3,5,6,4,2] => [1,3,6,4,5,7,2] => 001001
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [1,4,3,7,6,5,2] => [1,3,6,5,7,2,4] => 001010
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [1,4,3,5,7,6,2] => [1,3,6,7,2,4,5] => 000100
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,4,3,5,6,7,2] => [1,3,7,2,4,5,6] => 001000
[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] => 010000
[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] => 010001
[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] => 010010
[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] => [1,4,2,3,6,7,5] => 010001
[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] => 010010
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => [1,4,3,5,2,6,7] => 010100
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => [1,4,3,5,2,7,6] => 010101
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => [1,4,3,5,6,2,7] => 010010
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => [1,4,3,5,6,7,2] => 010001
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,6,4,3,5,7,2] => [1,4,3,5,7,2,6] => 010010
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,5,4,3,6,2,7] => [1,4,3,6,2,5,7] => 010100
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => [1,4,3,6,5,7,2] => 010101
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [1,5,4,3,7,6,2] => [1,4,3,6,7,2,5] => 010010
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,5,4,3,6,7,2] => [1,4,3,7,2,5,6] => 010100
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [1,3,5,4,2,6,7] => [1,4,5,2,3,6,7] => 001000
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [1,3,5,4,2,7,6] => [1,4,5,2,3,7,6] => 001001
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7] => [1,4,5,3,6,2,7] => 001010
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => [1,4,5,3,6,7,2] => 001001
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [1,6,5,4,3,7,2] => [1,4,5,3,7,2,6] => 001010
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [1,3,6,4,5,2,7] => [1,4,5,6,2,3,7] => 000100
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => [1,4,5,6,3,7,2] => 000101
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [1,3,7,4,5,6,2] => [1,4,5,6,7,2,3] => 000010
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [1,3,6,4,5,7,2] => [1,4,5,7,2,3,6] => 000100
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [1,3,5,4,6,2,7] => [1,4,6,2,3,5,7] => 001000
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [1,7,5,4,6,3,2] => [1,4,6,3,5,7,2] => 001001
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [1,3,7,4,6,5,2] => [1,4,6,5,7,2,3] => 001010
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [1,3,5,4,7,6,2] => [1,4,6,7,2,3,5] => 000100
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [1,3,5,4,6,7,2] => [1,4,7,2,3,5,6] => 001000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => 010000
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => 010001
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,6,4,5,3,2,7] => [1,5,3,4,6,2,7] => 010010
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,4,5,3,6,2] => [1,5,3,4,6,7,2] => 010001
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,6,4,5,3,7,2] => [1,5,3,4,7,2,6] => 010010
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [1,3,6,5,4,2,7] => [1,5,4,6,2,3,7] => 010100
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [1,5,4,6,3,7,2] => 010101
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [1,3,7,5,4,6,2] => [1,5,4,6,7,2,3] => 010010
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [1,3,6,5,4,7,2] => [1,5,4,7,2,3,6] => 010100
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [1,3,4,6,5,2,7] => [1,5,6,2,3,4,7] => 001000
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [1,7,4,6,5,3,2] => [1,5,6,3,4,7,2] => 001001
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [1,3,7,6,5,4,2] => [1,5,6,4,7,2,3] => 001010
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [1,3,4,7,5,6,2] => [1,5,6,7,2,3,4] => 000100
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [1,3,4,6,5,7,2] => [1,5,7,2,3,4,6] => 001000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => 010000
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,4,5,6,3,2] => [1,6,3,4,5,7,2] => 010001
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [1,3,7,5,6,4,2] => [1,6,4,5,7,2,3] => 010010
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [1,3,4,7,6,5,2] => [1,6,5,7,2,3,4] => 010100
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [1,3,4,5,7,6,2] => [1,6,7,2,3,4,5] => 001000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => 010000
[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] => 100000
[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] => 100001
[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] => 100010
[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] => [2,1,3,4,6,7,5] => 100001
[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] => 100010
[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] => 100100
[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] => 100101
[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] => [2,1,3,5,6,4,7] => 100010
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [2,1,3,5,6,7,4] => 100001
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,6,5,7,4] => [2,1,3,5,7,4,6] => 100010
[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] => 100100
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,7,6,5,4] => [2,1,3,6,5,7,4] => 100101
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [2,1,3,5,7,6,4] => [2,1,3,6,7,4,5] => 100010
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => 100100
[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] => 101000
[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] => 101001
[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] => 101010
[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] => [2,1,4,3,6,7,5] => 101001
[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] => 101010
[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] => [2,1,4,5,3,6,7] => 100100
[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] => [2,1,4,5,3,7,6] => 100101
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [2,1,4,5,6,3,7] => 100010
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [2,1,4,5,6,7,3] => 100001
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,6,4,5,7,3] => [2,1,4,5,7,3,6] => 100010
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,5,4,6,3,7] => [2,1,4,6,3,5,7] => 100100
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,7,4,6,5,3] => [2,1,4,6,5,7,3] => 100101
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [2,1,5,4,7,6,3] => [2,1,4,6,7,3,5] => 100010
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,5,4,6,7,3] => [2,1,4,7,3,5,6] => 100100
[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] => 101000
[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] => 101001
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,6,5,4,3,7] => [2,1,5,4,6,3,7] => 101010
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,7,5,4,6,3] => [2,1,5,4,6,7,3] => 101001
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,6,5,4,7,3] => [2,1,5,4,7,3,6] => 101010
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [2,1,4,6,5,3,7] => [2,1,5,6,3,4,7] => 100100
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [2,1,5,6,4,7,3] => 100101
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [2,1,4,7,5,6,3] => [2,1,5,6,7,3,4] => 100010
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [2,1,4,6,5,7,3] => [2,1,5,7,3,4,6] => 100100
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => 101000
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,7,5,6,4,3] => [2,1,6,4,5,7,3] => 101001
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [2,1,4,7,6,5,3] => [2,1,6,5,7,3,4] => 101010
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [2,1,4,5,7,6,3] => [2,1,6,7,3,4,5] => 100100
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => 101000
[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] => [2,3,1,4,5,6,7] => 010000
[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] => [2,3,1,4,5,7,6] => 010001
[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] => [2,3,1,4,6,5,7] => 010010
[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] => [2,3,1,4,6,7,5] => 010001
[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] => [2,3,1,4,7,5,6] => 010010
[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] => [2,3,1,5,4,6,7] => 010100
[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] => [2,3,1,5,4,7,6] => 010101
[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] => [2,3,1,5,6,4,7] => 010010
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [2,3,1,5,6,7,4] => 010001
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,2,1,6,5,7,4] => [2,3,1,5,7,4,6] => 010010
[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] => [2,3,1,6,4,5,7] => 010100
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,2,1,7,6,5,4] => [2,3,1,6,5,7,4] => 010101
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [3,2,1,5,7,6,4] => [2,3,1,6,7,4,5] => 010010
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,1,5,6,7,4] => [2,3,1,7,4,5,6] => 010100
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [2,3,4,1,5,6,7] => 001000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [2,3,4,1,5,7,6] => 001001
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [2,3,4,1,6,5,7] => 001010
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [2,3,4,1,6,7,5] => 001001
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,3,1,6,7,5] => [2,3,4,1,7,5,6] => 001010
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [2,3,4,5,1,6,7] => 000100
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [2,3,4,5,1,7,6] => 000101
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [2,3,4,5,6,1,7] => 000010
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [2,3,4,5,6,7,1] => 000001
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [6,2,3,4,5,7,1] => [2,3,4,5,7,1,6] => 000010
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,2,3,4,6,1,7] => [2,3,4,6,1,5,7] => 000100
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1] => [2,3,4,6,5,7,1] => 000101
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [5,2,3,4,7,6,1] => [2,3,4,6,7,1,5] => 000010
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [5,2,3,4,6,7,1] => [2,3,4,7,1,5,6] => 000100
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,2,3,5,1,6,7] => [2,3,5,1,4,6,7] => 001000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,3,5,1,7,6] => [2,3,5,1,4,7,6] => 001001
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7] => [2,3,5,4,6,1,7] => 001010
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1] => [2,3,5,4,6,7,1] => 001001
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [6,2,3,5,4,7,1] => [2,3,5,4,7,1,6] => 001010
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [4,2,3,6,5,1,7] => [2,3,5,6,1,4,7] => 000100
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [7,2,3,6,5,4,1] => [2,3,5,6,4,7,1] => 000101
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [4,2,3,7,5,6,1] => [2,3,5,6,7,1,4] => 000010
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [4,2,3,6,5,7,1] => [2,3,5,7,1,4,6] => 000100
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,2,3,5,6,1,7] => [2,3,6,1,4,5,7] => 001000
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,2,3,5,6,4,1] => [2,3,6,4,5,7,1] => 001001
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [4,2,3,7,6,5,1] => [2,3,6,5,7,1,4] => 001010
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [4,2,3,5,7,6,1] => [2,3,6,7,1,4,5] => 000100
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [4,2,3,5,6,7,1] => [2,3,7,1,4,5,6] => 001000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,2,4,1,5,6,7] => [2,4,1,3,5,6,7] => 010000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,2,4,1,5,7,6] => [2,4,1,3,5,7,6] => 010001
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,2,4,1,6,5,7] => [2,4,1,3,6,5,7] => 010010
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,2,4,1,7,6,5] => [2,4,1,3,6,7,5] => 010001
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,4,1,6,7,5] => [2,4,1,3,7,5,6] => 010010
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7] => [2,4,3,5,1,6,7] => 010100
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [5,2,4,3,1,7,6] => [2,4,3,5,1,7,6] => 010101
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7] => [2,4,3,5,6,1,7] => 010010
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1] => [2,4,3,5,6,7,1] => 010001
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [6,2,4,3,5,7,1] => [2,4,3,5,7,1,6] => 010010
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [5,2,4,3,6,1,7] => [2,4,3,6,1,5,7] => 010100
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [7,2,4,3,6,5,1] => [2,4,3,6,5,7,1] => 010101
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [5,2,4,3,7,6,1] => [2,4,3,6,7,1,5] => 010010
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [5,2,4,3,6,7,1] => [2,4,3,7,1,5,6] => 010100
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [3,2,5,4,1,6,7] => [2,4,5,1,3,6,7] => 001000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [3,2,5,4,1,7,6] => [2,4,5,1,3,7,6] => 001001
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7] => [2,4,5,3,6,1,7] => 001010
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [7,2,5,4,3,6,1] => [2,4,5,3,6,7,1] => 001001
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [6,2,5,4,3,7,1] => [2,4,5,3,7,1,6] => 001010
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [3,2,6,4,5,1,7] => [2,4,5,6,1,3,7] => 000100
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [7,2,6,4,5,3,1] => [2,4,5,6,3,7,1] => 000101
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [3,2,7,4,5,6,1] => [2,4,5,6,7,1,3] => 000010
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [3,2,6,4,5,7,1] => [2,4,5,7,1,3,6] => 000100
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [3,2,5,4,6,1,7] => [2,4,6,1,3,5,7] => 001000
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [7,2,5,4,6,3,1] => [2,4,6,3,5,7,1] => 001001
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [3,2,7,4,6,5,1] => [2,4,6,5,7,1,3] => 001010
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [3,2,5,4,7,6,1] => [2,4,6,7,1,3,5] => 000100
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [3,2,5,4,6,7,1] => [2,4,7,1,3,5,6] => 001000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [3,2,4,5,1,6,7] => [2,5,1,3,4,6,7] => 010000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,4,5,1,7,6] => [2,5,1,3,4,7,6] => 010001
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,2,4,5,3,1,7] => [2,5,3,4,6,1,7] => 010010
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [7,2,4,5,3,6,1] => [2,5,3,4,6,7,1] => 010001
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [6,2,4,5,3,7,1] => [2,5,3,4,7,1,6] => 010010
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [3,2,6,5,4,1,7] => [2,5,4,6,1,3,7] => 010100
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [7,2,6,5,4,3,1] => [2,5,4,6,3,7,1] => 010101
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [3,2,7,5,4,6,1] => [2,5,4,6,7,1,3] => 010010
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [3,2,6,5,4,7,1] => [2,5,4,7,1,3,6] => 010100
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [3,2,4,6,5,1,7] => [2,5,6,1,3,4,7] => 001000
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [7,2,4,6,5,3,1] => [2,5,6,3,4,7,1] => 001001
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [3,2,7,6,5,4,1] => [2,5,6,4,7,1,3] => 001010
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [3,2,4,7,5,6,1] => [2,5,6,7,1,3,4] => 000100
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [3,2,4,6,5,7,1] => [2,5,7,1,3,4,6] => 001000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,2,4,5,6,1,7] => [2,6,1,3,4,5,7] => 010000
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,2,4,5,6,3,1] => [2,6,3,4,5,7,1] => 010001
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [3,2,7,5,6,4,1] => [2,6,4,5,7,1,3] => 010010
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [3,2,4,7,6,5,1] => [2,6,5,7,1,3,4] => 010100
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [3,2,4,5,7,6,1] => [2,6,7,1,3,4,5] => 001000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [3,2,4,5,6,7,1] => [2,7,1,3,4,5,6] => 010000
[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] => 100000
[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] => 100001
[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] => 100010
[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] => [3,1,2,4,6,7,5] => 100001
[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] => 100010
[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] => 100100
[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] => 100101
[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] => [3,1,2,5,6,4,7] => 100010
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [2,3,1,7,5,6,4] => [3,1,2,5,6,7,4] => 100001
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [2,3,1,6,5,7,4] => [3,1,2,5,7,4,6] => 100010
[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] => 100100
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [2,3,1,7,6,5,4] => [3,1,2,6,5,7,4] => 100101
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [2,3,1,5,7,6,4] => [3,1,2,6,7,4,5] => 100010
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => 100100
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [3,2,4,1,5,6,7] => 101000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [4,3,2,1,5,7,6] => [3,2,4,1,5,7,6] => 101001
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [4,3,2,1,6,5,7] => [3,2,4,1,6,5,7] => 101010
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [4,3,2,1,7,6,5] => [3,2,4,1,6,7,5] => 101001
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [4,3,2,1,6,7,5] => [3,2,4,1,7,5,6] => 101010
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [3,2,4,5,1,6,7] => 100100
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [5,3,2,4,1,7,6] => [3,2,4,5,1,7,6] => 100101
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [3,2,4,5,6,1,7] => 100010
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [3,2,4,5,6,7,1] => 100001
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [6,3,2,4,5,7,1] => [3,2,4,5,7,1,6] => 100010
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [5,3,2,4,6,1,7] => [3,2,4,6,1,5,7] => 100100
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [7,3,2,4,6,5,1] => [3,2,4,6,5,7,1] => 100101
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [5,3,2,4,7,6,1] => [3,2,4,6,7,1,5] => 100010
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [5,3,2,4,6,7,1] => [3,2,4,7,1,5,6] => 100100
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [4,3,2,5,1,6,7] => [3,2,5,1,4,6,7] => 101000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [4,3,2,5,1,7,6] => [3,2,5,1,4,7,6] => 101001
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => [3,2,5,4,6,1,7] => 101010
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [7,3,2,5,4,6,1] => [3,2,5,4,6,7,1] => 101001
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [6,3,2,5,4,7,1] => [3,2,5,4,7,1,6] => 101010
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [4,3,2,6,5,1,7] => [3,2,5,6,1,4,7] => 100100
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [7,3,2,6,5,4,1] => [3,2,5,6,4,7,1] => 100101
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [4,3,2,7,5,6,1] => [3,2,5,6,7,1,4] => 100010
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [4,3,2,6,5,7,1] => [3,2,5,7,1,4,6] => 100100
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [4,3,2,5,6,1,7] => [3,2,6,1,4,5,7] => 101000
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,3,2,5,6,4,1] => [3,2,6,4,5,7,1] => 101001
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [4,3,2,7,6,5,1] => [3,2,6,5,7,1,4] => 101010
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [4,3,2,5,7,6,1] => [3,2,6,7,1,4,5] => 100100
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [4,3,2,5,6,7,1] => [3,2,7,1,4,5,6] => 101000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [2,4,3,1,5,6,7] => [3,4,1,2,5,6,7] => 010000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [2,4,3,1,5,7,6] => [3,4,1,2,5,7,6] => 010001
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [2,4,3,1,6,5,7] => [3,4,1,2,6,5,7] => 010010
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [2,4,3,1,7,6,5] => [3,4,1,2,6,7,5] => 010001
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [2,4,3,1,6,7,5] => [3,4,1,2,7,5,6] => 010010
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [3,4,2,5,1,6,7] => 010100
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [5,4,3,2,1,7,6] => [3,4,2,5,1,7,6] => 010101
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [3,4,2,5,6,1,7] => 010010
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [3,4,2,5,6,7,1] => 010001
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [6,4,3,2,5,7,1] => [3,4,2,5,7,1,6] => 010010
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [5,4,3,2,6,1,7] => [3,4,2,6,1,5,7] => 010100
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [7,4,3,2,6,5,1] => [3,4,2,6,5,7,1] => 010101
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [5,4,3,2,7,6,1] => [3,4,2,6,7,1,5] => 010010
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [5,4,3,2,6,7,1] => [3,4,2,7,1,5,6] => 010100
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [2,5,3,4,1,6,7] => [3,4,5,1,2,6,7] => 001000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [2,5,3,4,1,7,6] => [3,4,5,1,2,7,6] => 001001
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [3,4,5,2,6,1,7] => 001010
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [3,4,5,2,6,7,1] => 001001
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [6,5,3,4,2,7,1] => [3,4,5,2,7,1,6] => 001010
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [2,6,3,4,5,1,7] => [3,4,5,6,1,2,7] => 000100
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [3,4,5,6,2,7,1] => 000101
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [2,7,3,4,5,6,1] => [3,4,5,6,7,1,2] => 000010
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [2,6,3,4,5,7,1] => [3,4,5,7,1,2,6] => 000100
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [2,5,3,4,6,1,7] => [3,4,6,1,2,5,7] => 001000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [7,5,3,4,6,2,1] => [3,4,6,2,5,7,1] => 001001
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [2,7,3,4,6,5,1] => [3,4,6,5,7,1,2] => 001010
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [2,5,3,4,7,6,1] => [3,4,6,7,1,2,5] => 000100
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [2,5,3,4,6,7,1] => [3,4,7,1,2,5,6] => 001000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [2,4,3,5,1,6,7] => [3,5,1,2,4,6,7] => 010000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [2,4,3,5,1,7,6] => [3,5,1,2,4,7,6] => 010001
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [6,4,3,5,2,1,7] => [3,5,2,4,6,1,7] => 010010
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [7,4,3,5,2,6,1] => [3,5,2,4,6,7,1] => 010001
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [6,4,3,5,2,7,1] => [3,5,2,4,7,1,6] => 010010
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [2,6,3,5,4,1,7] => [3,5,4,6,1,2,7] => 010100
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1] => [3,5,4,6,2,7,1] => 010101
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [2,7,3,5,4,6,1] => [3,5,4,6,7,1,2] => 010010
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [2,6,3,5,4,7,1] => [3,5,4,7,1,2,6] => 010100
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [2,4,3,6,5,1,7] => [3,5,6,1,2,4,7] => 001000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [7,4,3,6,5,2,1] => [3,5,6,2,4,7,1] => 001001
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [2,7,3,6,5,4,1] => [3,5,6,4,7,1,2] => 001010
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [2,4,3,7,5,6,1] => [3,5,6,7,1,2,4] => 000100
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [2,4,3,6,5,7,1] => [3,5,7,1,2,4,6] => 001000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [2,4,3,5,6,1,7] => [3,6,1,2,4,5,7] => 010000
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [7,4,3,5,6,2,1] => [3,6,2,4,5,7,1] => 010001
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [2,7,3,5,6,4,1] => [3,6,4,5,7,1,2] => 010010
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [2,4,3,7,6,5,1] => [3,6,5,7,1,2,4] => 010100
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [2,4,3,5,7,6,1] => [3,6,7,1,2,4,5] => 001000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [2,4,3,5,6,7,1] => [3,7,1,2,4,5,6] => 010000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => 100000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => 100001
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => 100010
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [2,3,4,1,7,6,5] => [4,1,2,3,6,7,5] => 100001
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => 100010
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,3,4,2,1,6,7] => [4,2,3,5,1,6,7] => 100100
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [5,3,4,2,1,7,6] => [4,2,3,5,1,7,6] => 100101
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,3,4,2,5,1,7] => [4,2,3,5,6,1,7] => 100010
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [7,3,4,2,5,6,1] => [4,2,3,5,6,7,1] => 100001
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [6,3,4,2,5,7,1] => [4,2,3,5,7,1,6] => 100010
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [5,3,4,2,6,1,7] => [4,2,3,6,1,5,7] => 100100
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [7,3,4,2,6,5,1] => [4,2,3,6,5,7,1] => 100101
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [5,3,4,2,7,6,1] => [4,2,3,6,7,1,5] => 100010
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [5,3,4,2,6,7,1] => [4,2,3,7,1,5,6] => 100100
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [2,5,4,3,1,6,7] => [4,3,5,1,2,6,7] => 101000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [2,5,4,3,1,7,6] => [4,3,5,1,2,7,6] => 101001
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [4,3,5,2,6,1,7] => 101010
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [4,3,5,2,6,7,1] => 101001
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [6,5,4,3,2,7,1] => [4,3,5,2,7,1,6] => 101010
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [2,6,4,3,5,1,7] => [4,3,5,6,1,2,7] => 100100
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [4,3,5,6,2,7,1] => 100101
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [2,7,4,3,5,6,1] => [4,3,5,6,7,1,2] => 100010
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [2,6,4,3,5,7,1] => [4,3,5,7,1,2,6] => 100100
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [2,5,4,3,6,1,7] => [4,3,6,1,2,5,7] => 101000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [7,5,4,3,6,2,1] => [4,3,6,2,5,7,1] => 101001
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [2,7,4,3,6,5,1] => [4,3,6,5,7,1,2] => 101010
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [2,5,4,3,7,6,1] => [4,3,6,7,1,2,5] => 100100
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [2,5,4,3,6,7,1] => [4,3,7,1,2,5,6] => 101000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [2,3,5,4,1,6,7] => [4,5,1,2,3,6,7] => 010000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [2,3,5,4,1,7,6] => [4,5,1,2,3,7,6] => 010001
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [6,3,5,4,2,1,7] => [4,5,2,3,6,1,7] => 010010
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [7,3,5,4,2,6,1] => [4,5,2,3,6,7,1] => 010001
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [6,3,5,4,2,7,1] => [4,5,2,3,7,1,6] => 010010
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [2,6,5,4,3,1,7] => [4,5,3,6,1,2,7] => 010100
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [4,5,3,6,2,7,1] => 010101
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [2,7,5,4,3,6,1] => [4,5,3,6,7,1,2] => 010010
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [2,6,5,4,3,7,1] => [4,5,3,7,1,2,6] => 010100
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [2,3,6,4,5,1,7] => [4,5,6,1,2,3,7] => 001000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [7,3,6,4,5,2,1] => [4,5,6,2,3,7,1] => 001001
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [2,7,6,4,5,3,1] => [4,5,6,3,7,1,2] => 001010
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [2,3,7,4,5,6,1] => [4,5,6,7,1,2,3] => 000100
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [2,3,6,4,5,7,1] => [4,5,7,1,2,3,6] => 001000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [2,3,5,4,6,1,7] => [4,6,1,2,3,5,7] => 010000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [7,3,5,4,6,2,1] => [4,6,2,3,5,7,1] => 010001
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [2,7,5,4,6,3,1] => [4,6,3,5,7,1,2] => 010010
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [2,3,7,4,6,5,1] => [4,6,5,7,1,2,3] => 010100
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [2,3,5,4,7,6,1] => [4,6,7,1,2,3,5] => 001000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [2,3,5,4,6,7,1] => [4,7,1,2,3,5,6] => 010000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => 100000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => 100001
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,3,4,5,2,1,7] => [5,2,3,4,6,1,7] => 100010
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [7,3,4,5,2,6,1] => [5,2,3,4,6,7,1] => 100001
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [6,3,4,5,2,7,1] => [5,2,3,4,7,1,6] => 100010
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [2,6,4,5,3,1,7] => [5,3,4,6,1,2,7] => 100100
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [7,6,4,5,3,2,1] => [5,3,4,6,2,7,1] => 100101
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [2,7,4,5,3,6,1] => [5,3,4,6,7,1,2] => 100010
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [2,6,4,5,3,7,1] => [5,3,4,7,1,2,6] => 100100
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [2,3,6,5,4,1,7] => [5,4,6,1,2,3,7] => 101000
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [7,3,6,5,4,2,1] => [5,4,6,2,3,7,1] => 101001
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [2,7,6,5,4,3,1] => [5,4,6,3,7,1,2] => 101010
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [2,3,7,5,4,6,1] => [5,4,6,7,1,2,3] => 100100
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [2,3,6,5,4,7,1] => [5,4,7,1,2,3,6] => 101000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [2,3,4,6,5,1,7] => [5,6,1,2,3,4,7] => 010000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [7,3,4,6,5,2,1] => [5,6,2,3,4,7,1] => 010001
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [2,7,4,6,5,3,1] => [5,6,3,4,7,1,2] => 010010
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [2,3,7,6,5,4,1] => [5,6,4,7,1,2,3] => 010100
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [2,3,4,7,5,6,1] => [5,6,7,1,2,3,4] => 001000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [2,3,4,6,5,7,1] => [5,7,1,2,3,4,6] => 010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => 100000
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [7,3,4,5,6,2,1] => [6,2,3,4,5,7,1] => 100001
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [2,7,4,5,6,3,1] => [6,3,4,5,7,1,2] => 100010
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [2,3,7,5,6,4,1] => [6,4,5,7,1,2,3] => 100100
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [2,3,4,7,6,5,1] => [6,5,7,1,2,3,4] => 101000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [2,3,4,5,7,6,1] => [6,7,1,2,3,4,5] => 010000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => 100000
[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] => 0000000
[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] => 0000001
[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] => 0000010
[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] => [1,2,3,4,5,7,8,6] => 0000001
[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] => 0000010
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => 0000100
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => 0000101
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [1,2,3,4,6,7,5,8] => 0000010
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [1,2,3,4,6,7,8,5] => 0000001
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,6,8,5] => [1,2,3,4,6,8,5,7] => 0000010
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,5,6,8] => 0000100
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,8,5] => 0000101
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,8,5,6] => 0000010
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => 0000100
[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] => 0001000
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => 0001001
[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] => 0001010
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,7,8,6] => 0001001
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,6,7] => 0001010
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,5,4,7,8] => [1,2,3,5,6,4,7,8] => 0000100
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,5,4,8,7] => [1,2,3,5,6,4,8,7] => 0000101
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,5,6,4,8] => [1,2,3,5,6,7,4,8] => 0000010
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [1,2,3,5,6,7,8,4] => 0000001
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,7,5,6,8,4] => [1,2,3,5,6,8,4,7] => 0000010
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [1,2,3,6,5,7,4,8] => [1,2,3,5,7,4,6,8] => 0000100
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,8,5,7,6,4] => [1,2,3,5,7,6,8,4] => 0000101
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [1,2,3,6,5,8,7,4] => [1,2,3,5,7,8,4,6] => 0000010
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,6,5,7,8,4] => [1,2,3,5,8,4,6,7] => 0000100
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [1,2,3,5,6,4,7,8] => [1,2,3,6,4,5,7,8] => 0001000
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [1,2,3,5,6,4,8,7] => [1,2,3,6,4,5,8,7] => 0001001
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [1,2,3,7,6,5,4,8] => [1,2,3,6,5,7,4,8] => 0001010
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,2,3,8,6,5,7,4] => [1,2,3,6,5,7,8,4] => 0001001
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,2,3,7,6,5,8,4] => [1,2,3,6,5,8,4,7] => 0001010
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [1,2,3,5,7,6,4,8] => [1,2,3,6,7,4,5,8] => 0000100
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [1,2,3,8,7,6,5,4] => [1,2,3,6,7,5,8,4] => 0000101
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [1,2,3,5,8,6,7,4] => [1,2,3,6,7,8,4,5] => 0000010
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [1,2,3,5,7,6,8,4] => [1,2,3,6,8,4,5,7] => 0000100
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [1,2,3,5,6,7,4,8] => [1,2,3,7,4,5,6,8] => 0001000
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,2,3,8,6,7,5,4] => [1,2,3,7,5,6,8,4] => 0001001
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [1,2,3,5,8,7,6,4] => [1,2,3,7,6,8,4,5] => 0001010
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [1,2,3,5,6,8,7,4] => [1,2,3,7,8,4,5,6] => 0000100
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => 0001000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => 0010000
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => 0010001
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => 0010010
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,7,8,6] => 0010001
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,6,7] => 0010010
[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] => 0010100
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => 0010101
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [1,2,4,3,7,6,5,8] => [1,2,4,3,6,7,5,8] => 0010010
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => [1,2,4,3,6,7,8,5] => 0010001
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [1,2,4,3,7,6,8,5] => [1,2,4,3,6,8,5,7] => 0010010
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [1,2,4,3,6,7,5,8] => [1,2,4,3,7,5,6,8] => 0010100
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,8,5] => 0010101
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [1,2,4,3,6,8,7,5] => [1,2,4,3,7,8,5,6] => 0010010
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7] => 0010100
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [1,2,5,4,3,7,6,8] => [1,2,4,5,3,7,6,8] => 0001010
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [1,2,5,4,3,8,7,6] => [1,2,4,5,3,7,8,6] => 0001001
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [1,2,5,4,3,7,8,6] => [1,2,4,5,3,8,6,7] => 0001010
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [1,2,6,4,5,3,7,8] => [1,2,4,5,6,3,7,8] => 0000100
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [1,2,7,4,5,6,3,8] => [1,2,4,5,6,7,3,8] => 0000010
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [1,2,4,5,6,7,8,3] => 0000001
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [1,2,7,4,5,6,8,3] => [1,2,4,5,6,8,3,7] => 0000010
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [1,2,6,4,5,8,7,3] => [1,2,4,5,7,8,3,6] => 0000010
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [1,2,6,4,5,7,8,3] => [1,2,4,5,8,3,6,7] => 0000100
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [1,2,5,4,6,3,7,8] => [1,2,4,6,3,5,7,8] => 0001000
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,5,3,8,7] => [1,2,5,4,6,3,8,7] => [1,2,4,6,3,5,8,7] => 0001001
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [1,2,7,4,6,5,8,3] => [1,2,4,6,5,8,3,7] => 0001010
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => [1,2,5,4,7,6,3,8] => [1,2,4,6,7,3,5,8] => 0000100
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [1,2,5,4,8,6,7,3] => [1,2,4,6,7,8,3,5] => 0000010
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [1,2,5,4,7,6,8,3] => [1,2,4,6,8,3,5,7] => 0000100
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [1,2,5,4,6,7,3,8] => [1,2,4,7,3,5,6,8] => 0001000
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [1,2,8,4,6,7,5,3] => [1,2,4,7,5,6,8,3] => 0001001
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [1,2,5,4,6,8,7,3] => [1,2,4,7,8,3,5,6] => 0000100
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [1,2,5,4,6,7,8,3] => [1,2,4,8,3,5,6,7] => 0001000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [1,2,4,5,3,6,7,8] => [1,2,5,3,4,6,7,8] => 0010000
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [1,2,4,5,3,6,8,7] => [1,2,5,3,4,6,8,7] => 0010001
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [1,2,4,5,3,7,6,8] => [1,2,5,3,4,7,6,8] => 0010010
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [1,2,4,5,3,8,7,6] => [1,2,5,3,4,7,8,6] => 0010001
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [1,2,4,5,3,7,8,6] => [1,2,5,3,4,8,6,7] => 0010010
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [1,2,7,5,4,6,3,8] => [1,2,5,4,6,7,3,8] => 0010010
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,2,8,5,4,6,7,3] => [1,2,5,4,6,7,8,3] => 0010001
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [1,2,8,5,4,7,6,3] => [1,2,5,4,7,6,8,3] => 0010101
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,7,8,6,3] => [1,2,6,5,4,8,7,3] => [1,2,5,4,7,8,3,6] => 0010010
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [1,2,6,5,4,7,8,3] => [1,2,5,4,8,3,6,7] => 0010100
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [1,2,4,6,5,3,7,8] => [1,2,5,6,3,4,7,8] => 0001000
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,2,5,6,4,3,8,7] => [1,2,4,6,5,3,8,7] => [1,2,5,6,3,4,8,7] => 0001001
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [1,2,7,6,5,4,3,8] => [1,2,5,6,4,7,3,8] => 0001010
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [1,2,8,6,5,4,7,3] => [1,2,5,6,4,7,8,3] => 0001001
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [1,2,8,7,5,6,4,3] => [1,2,5,6,7,4,8,3] => 0000101
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [1,2,4,8,5,6,7,3] => [1,2,5,6,7,8,3,4] => 0000010
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [1,2,4,6,5,7,3,8] => [1,2,5,7,3,4,6,8] => 0001000
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [1,2,8,6,5,7,4,3] => [1,2,5,7,4,6,8,3] => 0001001
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,6,4,3] => [1,2,4,6,5,8,7,3] => [1,2,5,7,8,3,4,6] => 0000100
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [1,2,4,6,5,7,8,3] => [1,2,5,8,3,4,6,7] => 0001000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [1,2,4,5,6,3,7,8] => [1,2,6,3,4,5,7,8] => 0010000
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [1,2,4,5,6,3,8,7] => [1,2,6,3,4,5,8,7] => 0010001
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [1,2,8,5,6,4,7,3] => [1,2,6,4,5,7,8,3] => 0010001
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [1,2,7,5,6,4,8,3] => [1,2,6,4,5,8,3,7] => 0010010
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [1,2,4,7,6,5,8,3] => [1,2,6,5,8,3,4,7] => 0010100
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [1,2,4,5,7,6,3,8] => [1,2,6,7,3,4,5,8] => 0001000
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,5,4,8,3] => [1,2,8,5,7,6,4,3] => [1,2,6,7,4,5,8,3] => 0001001
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,5,8,4,3] => [1,2,4,8,7,6,5,3] => [1,2,6,7,5,8,3,4] => 0001010
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [1,2,4,5,8,6,7,3] => [1,2,6,7,8,3,4,5] => 0000100
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [1,2,4,5,6,7,3,8] => [1,2,7,3,4,5,6,8] => 0010000
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [1,2,8,5,6,7,4,3] => [1,2,7,4,5,6,8,3] => 0010001
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [1,2,4,8,6,7,5,3] => [1,2,7,5,6,8,3,4] => 0010010
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [1,2,4,5,8,7,6,3] => [1,2,7,6,8,3,4,5] => 0010100
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [1,2,4,5,6,8,7,3] => [1,2,7,8,3,4,5,6] => 0001000
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => 0010000
[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] => 0100000
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => 0100001
[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] => 0100010
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,7,8,6] => 0100001
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,6,7] => 0100010
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => 0100100
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => 0100101
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,6,7,5] => [1,3,2,4,6,7,8,5] => 0100001
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [1,3,2,4,7,6,8,5] => [1,3,2,4,6,8,5,7] => 0100010
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,8,5] => 0100101
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,6,5] => [1,3,2,4,6,8,7,5] => [1,3,2,4,7,8,5,6] => 0100010
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7] => 0100100
[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] => 0101000
[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] => 0101010
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,7,8,6] => 0101001
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,6,7] => 0101010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,5,4,7,8] => [1,3,2,5,6,4,7,8] => 0100100
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [1,3,2,6,5,4,8,7] => [1,3,2,5,6,4,8,7] => 0100101
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [1,3,2,7,5,6,4,8] => [1,3,2,5,6,7,4,8] => 0100010
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [1,3,2,8,5,6,7,4] => [1,3,2,5,6,7,8,4] => 0100001
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [1,3,2,6,5,7,4,8] => [1,3,2,5,7,4,6,8] => 0100100
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [1,3,2,8,5,7,6,4] => [1,3,2,5,7,6,8,4] => 0100101
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [1,3,2,6,5,8,7,4] => [1,3,2,5,7,8,4,6] => 0100010
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [1,3,2,6,5,7,8,4] => [1,3,2,5,8,4,6,7] => 0100100
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [1,3,2,5,6,4,7,8] => [1,3,2,6,4,5,7,8] => 0101000
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [1,3,2,7,6,5,4,8] => [1,3,2,6,5,7,4,8] => 0101010
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [1,3,2,8,6,5,7,4] => [1,3,2,6,5,7,8,4] => 0101001
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [1,3,2,7,6,5,8,4] => [1,3,2,6,5,8,4,7] => 0101010
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [1,3,2,5,7,6,4,8] => [1,3,2,6,7,4,5,8] => 0100100
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [1,3,2,8,7,6,5,4] => [1,3,2,6,7,5,8,4] => 0100101
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [1,3,2,5,8,6,7,4] => [1,3,2,6,7,8,4,5] => 0100010
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [1,3,2,5,7,6,8,4] => [1,3,2,6,8,4,5,7] => 0100100
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [1,3,2,5,6,7,4,8] => [1,3,2,7,4,5,6,8] => 0101000
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [1,3,2,8,6,7,5,4] => [1,3,2,7,5,6,8,4] => 0101001
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [1,3,2,5,8,7,6,4] => [1,3,2,7,6,8,4,5] => 0101010
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [1,3,2,5,6,7,8,4] => [1,3,2,8,4,5,6,7] => 0101000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => 0010000
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [1,4,3,2,5,6,8,7] => [1,3,4,2,5,6,8,7] => 0010001
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [1,4,3,2,5,7,6,8] => [1,3,4,2,5,7,6,8] => 0010010
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [1,4,3,2,5,8,7,6] => [1,3,4,2,5,7,8,6] => 0010001
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [1,4,3,2,5,7,8,6] => [1,3,4,2,5,8,6,7] => 0010010
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [1,4,3,2,6,5,8,7] => [1,3,4,2,6,5,8,7] => 0010101
[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] => [1,3,4,2,6,7,5,8] => 0010010
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,4,3,2,8,6,7,5] => [1,3,4,2,6,7,8,5] => 0010001
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [1,4,3,2,8,7,6,5] => [1,3,4,2,7,6,8,5] => 0010101
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [1,4,3,2,6,8,7,5] => [1,3,4,2,7,8,5,6] => 0010010
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,5,6,7] => 0010100
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [1,5,3,4,2,6,7,8] => [1,3,4,5,2,6,7,8] => 0001000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [1,5,3,4,2,7,6,8] => [1,3,4,5,2,7,6,8] => 0001010
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [1,5,3,4,2,8,7,6] => [1,3,4,5,2,7,8,6] => 0001001
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [1,5,3,4,2,7,8,6] => [1,3,4,5,2,8,6,7] => 0001010
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [1,6,3,4,5,2,7,8] => [1,3,4,5,6,2,7,8] => 0000100
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [1,7,3,4,5,6,2,8] => [1,3,4,5,6,7,2,8] => 0000010
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,3,4,5,6,7,2] => [1,3,4,5,6,7,8,2] => 0000001
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,7,3,4,5,6,8,2] => [1,3,4,5,6,8,2,7] => 0000010
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [1,6,3,4,5,7,2,8] => [1,3,4,5,7,2,6,8] => 0000100
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [1,8,3,4,5,7,6,2] => [1,3,4,5,7,6,8,2] => 0000101
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [1,6,3,4,5,8,7,2] => [1,3,4,5,7,8,2,6] => 0000010
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [1,6,3,4,5,7,8,2] => [1,3,4,5,8,2,6,7] => 0000100
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,5,2,7,8] => [1,5,3,4,6,2,7,8] => [1,3,4,6,2,5,7,8] => 0001000
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,5,2,8,7] => [1,5,3,4,6,2,8,7] => [1,3,4,6,2,5,8,7] => 0001001
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [1,7,3,4,6,5,2,8] => [1,3,4,6,5,7,2,8] => 0001010
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [1,8,3,4,6,5,7,2] => [1,3,4,6,5,7,8,2] => 0001001
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,5,8,7,2] => [1,7,3,4,6,5,8,2] => [1,3,4,6,5,8,2,7] => 0001010
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [1,5,3,4,7,6,2,8] => [1,3,4,6,7,2,5,8] => 0000100
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [1,8,3,4,7,6,5,2] => [1,3,4,6,7,5,8,2] => 0000101
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [1,5,3,4,8,6,7,2] => [1,3,4,6,7,8,2,5] => 0000010
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,7,5,2] => [1,5,3,4,7,6,8,2] => [1,3,4,6,8,2,5,7] => 0000100
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [1,5,3,4,8,7,6,2] => [1,3,4,7,6,8,2,5] => 0001010
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,5,3,4,6,7,8,2] => [1,3,4,8,2,5,6,7] => 0001000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [1,4,3,5,2,6,7,8] => [1,3,5,2,4,6,7,8] => 0010000
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [1,4,3,5,2,6,8,7] => [1,3,5,2,4,6,8,7] => 0010001
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [1,4,3,5,2,7,6,8] => [1,3,5,2,4,7,6,8] => 0010010
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [1,4,3,5,2,8,7,6] => [1,3,5,2,4,7,8,6] => 0010001
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,4,2,8,7,6] => [1,4,3,5,2,7,8,6] => [1,3,5,2,4,8,6,7] => 0010010
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [1,6,3,5,4,2,7,8] => [1,3,5,4,6,2,7,8] => 0010100
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => [1,7,3,5,4,6,2,8] => [1,3,5,4,6,7,2,8] => 0010010
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [1,8,3,5,4,6,7,2] => [1,3,5,4,6,7,8,2] => 0010001
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [1,6,3,5,4,7,2,8] => [1,3,5,4,7,2,6,8] => 0010100
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [1,8,3,5,4,7,6,2] => [1,3,5,4,7,6,8,2] => 0010101
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [1,6,3,5,4,8,7,2] => [1,3,5,4,7,8,2,6] => 0010010
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [1,6,3,5,4,7,8,2] => [1,3,5,4,8,2,6,7] => 0010100
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [1,4,3,6,5,2,7,8] => [1,3,5,6,2,4,7,8] => 0001000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [1,7,3,6,5,4,2,8] => [1,3,5,6,4,7,2,8] => 0001010
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,4,7,8,2] => [1,8,3,6,5,4,7,2] => [1,3,5,6,4,7,8,2] => 0001001
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,4,8,7,2] => [1,7,3,6,5,4,8,2] => [1,3,5,6,4,8,2,7] => 0001010
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [1,4,3,7,5,6,2,8] => [1,3,5,6,7,2,4,8] => 0000100
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [1,8,3,7,5,6,4,2] => [1,3,5,6,7,4,8,2] => 0000101
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [1,4,3,8,5,6,7,2] => [1,3,5,6,7,8,2,4] => 0000010
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [1,4,3,6,5,7,2,8] => [1,3,5,7,2,4,6,8] => 0001000
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,6,4,8,2] => [1,8,3,6,5,7,4,2] => [1,3,5,7,4,6,8,2] => 0001001
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [1,4,3,8,5,7,6,2] => [1,3,5,7,6,8,2,4] => 0001010
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [1,4,3,6,5,8,7,2] => [1,3,5,7,8,2,4,6] => 0000100
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [1,4,3,6,5,7,8,2] => [1,3,5,8,2,4,6,7] => 0001000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [1,4,3,5,6,2,7,8] => [1,3,6,2,4,5,7,8] => 0010000
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [1,7,3,5,6,4,8,2] => [1,3,6,4,5,8,2,7] => 0010010
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [1,4,3,7,6,5,2,8] => [1,3,6,5,7,2,4,8] => 0010100
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [1,8,3,7,6,5,4,2] => [1,3,6,5,7,4,8,2] => 0010101
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [1,4,3,8,6,5,7,2] => [1,3,6,5,7,8,2,4] => 0010010
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [1,4,3,8,7,6,5,2] => [1,3,6,7,5,8,2,4] => 0001010
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [1,4,3,5,8,6,7,2] => [1,3,6,7,8,2,4,5] => 0000100
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [1,4,3,5,6,7,2,8] => [1,3,7,2,4,5,6,8] => 0010000
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,6,5,8,4,2] => [1,4,3,8,6,7,5,2] => [1,3,7,5,6,8,2,4] => 0010010
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [1,4,3,5,6,8,7,2] => [1,3,7,8,2,4,5,6] => 0001000
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [1,4,3,5,6,7,8,2] => [1,3,8,2,4,5,6,7] => 0010000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => 0100000
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [1,3,4,2,5,6,8,7] => [1,4,2,3,5,6,8,7] => 0100001
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [1,3,4,2,5,7,6,8] => [1,4,2,3,5,7,6,8] => 0100010
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [1,3,4,2,5,8,7,6] => [1,4,2,3,5,7,8,6] => 0100001
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [1,3,4,2,5,7,8,6] => [1,4,2,3,5,8,6,7] => 0100010
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [1,3,4,2,6,5,8,7] => [1,4,2,3,6,5,8,7] => 0100101
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [1,3,4,2,7,6,5,8] => [1,4,2,3,6,7,5,8] => 0100010
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,6,7,5] => [1,4,2,3,6,7,8,5] => 0100001
[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] => 0100100
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [1,3,4,2,8,7,6,5] => [1,4,2,3,7,6,8,5] => 0100101
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,7,8,6,5] => [1,3,4,2,6,8,7,5] => [1,4,2,3,7,8,5,6] => 0100010
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,3,4,2,6,7,8,5] => [1,4,2,3,8,5,6,7] => 0100100
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [1,5,4,3,2,7,6,8] => [1,4,3,5,2,7,6,8] => 0101010
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [1,5,4,3,2,8,7,6] => [1,4,3,5,2,7,8,6] => 0101001
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [1,5,4,3,2,7,8,6] => [1,4,3,5,2,8,6,7] => 0101010
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [1,6,4,3,5,2,7,8] => [1,4,3,5,6,2,7,8] => 0100100
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,8,4,3,5,6,7,2] => [1,4,3,5,6,7,8,2] => 0100001
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [1,6,4,3,5,8,7,2] => [1,4,3,5,7,8,2,6] => 0100010
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [1,5,4,3,6,2,7,8] => [1,4,3,6,2,5,7,8] => 0101000
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [1,7,4,3,6,5,2,8] => [1,4,3,6,5,7,2,8] => 0101010
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [1,8,4,3,6,5,7,2] => [1,4,3,6,5,7,8,2] => 0101001
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,7,4,3,6,5,8,2] => [1,4,3,6,5,8,2,7] => 0101010
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,3,6,7,5,8,2] => [1,8,4,3,7,6,5,2] => [1,4,3,6,7,5,8,2] => 0100101
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [1,5,4,3,7,6,8,2] => [1,4,3,6,8,2,5,7] => 0100100
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [1,5,4,3,8,7,6,2] => [1,4,3,7,6,8,2,5] => 0101010
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,5,4,3,6,7,8,2] => [1,4,3,8,2,5,6,7] => 0101000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [1,3,5,4,2,6,7,8] => [1,4,5,2,3,6,7,8] => 0010000
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [1,3,5,4,2,7,6,8] => [1,4,5,2,3,7,6,8] => 0010010
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [1,3,5,4,2,8,7,6] => [1,4,5,2,3,7,8,6] => 0010001
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [1,3,5,4,2,7,8,6] => [1,4,5,2,3,8,6,7] => 0010010
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [1,6,5,4,3,2,7,8] => [1,4,5,3,6,2,7,8] => 0010100
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [1,7,5,4,3,6,2,8] => [1,4,5,3,6,7,2,8] => 0010010
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [1,8,5,4,3,6,7,2] => [1,4,5,3,6,7,8,2] => 0010001
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,3,7,6,2,8] => [1,6,5,4,3,7,2,8] => [1,4,5,3,7,2,6,8] => 0010100
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [1,6,5,4,3,8,7,2] => [1,4,5,3,7,8,2,6] => 0010010
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [1,6,5,4,3,7,8,2] => [1,4,5,3,8,2,6,7] => 0010100
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,4,5,6,3,2,8,7] => [1,3,6,4,5,2,8,7] => [1,4,5,6,2,3,8,7] => 0001001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [1,7,6,4,5,3,2,8] => [1,4,5,6,3,7,2,8] => 0001010
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [1,3,7,4,5,6,2,8] => [1,4,5,6,7,2,3,8] => 0000100
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [1,8,7,4,5,6,3,2] => [1,4,5,6,7,3,8,2] => 0000101
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [1,3,8,4,5,6,7,2] => [1,4,5,6,7,8,2,3] => 0000010
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,6,3,2,8] => [1,3,6,4,5,7,2,8] => [1,4,5,7,2,3,6,8] => 0001000
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,6,3,8,2] => [1,8,6,4,5,7,3,2] => [1,4,5,7,3,6,8,2] => 0001001
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,6,3,2] => [1,3,6,4,5,8,7,2] => [1,4,5,7,8,2,3,6] => 0000100
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [1,3,6,4,5,7,8,2] => [1,4,5,8,2,3,6,7] => 0001000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [1,3,5,4,6,2,7,8] => [1,4,6,2,3,5,7,8] => 0010000
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,5,3,7,8,2] => [1,8,5,4,6,3,7,2] => [1,4,6,3,5,7,8,2] => 0010001
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [1,3,7,4,6,5,2,8] => [1,4,6,5,7,2,3,8] => 0010100
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [1,3,5,4,7,6,2,8] => [1,4,6,7,2,3,5,8] => 0001000
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [1,8,5,4,7,6,3,2] => [1,4,6,7,3,5,8,2] => 0001001
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [1,3,5,4,7,6,8,2] => [1,4,6,8,2,3,5,7] => 0001000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [1,3,5,4,6,7,2,8] => [1,4,7,2,3,5,6,8] => 0010000
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,6,5,3,8,2] => [1,8,5,4,6,7,3,2] => [1,4,7,3,5,6,8,2] => 0010001
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [1,3,8,4,6,7,5,2] => [1,4,7,5,6,8,2,3] => 0010010
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,6,8,5,3,2] => [1,3,5,4,8,7,6,2] => [1,4,7,6,8,2,3,5] => 0010100
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [1,3,5,4,6,8,7,2] => [1,4,7,8,2,3,5,6] => 0001000
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [1,3,5,4,6,7,8,2] => [1,4,8,2,3,5,6,7] => 0010000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [1,3,4,5,2,6,7,8] => [1,5,2,3,4,6,7,8] => 0100000
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,4,3,2,6,8,7] => [1,3,4,5,2,6,8,7] => [1,5,2,3,4,6,8,7] => 0100001
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [1,3,4,5,2,7,6,8] => [1,5,2,3,4,7,6,8] => 0100010
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [1,3,4,5,2,8,7,6] => [1,5,2,3,4,7,8,6] => 0100001
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [1,3,4,5,2,7,8,6] => [1,5,2,3,4,8,6,7] => 0100010
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [1,6,4,5,3,2,7,8] => [1,5,3,4,6,2,7,8] => 0100100
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,8,4,5,3,6,7,2] => [1,5,3,4,6,7,8,2] => 0100001
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,7,4,5,3,6,8,2] => [1,5,3,4,6,8,2,7] => 0100010
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,4,3,7,8,6,2] => [1,6,4,5,3,8,7,2] => [1,5,3,4,7,8,2,6] => 0100010
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [1,3,6,5,4,2,7,8] => [1,5,4,6,2,3,7,8] => 0101000
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [1,7,6,5,4,3,2,8] => [1,5,4,6,3,7,2,8] => 0101010
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [1,8,6,5,4,3,7,2] => [1,5,4,6,3,7,8,2] => 0101001
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,4,6,3,8,7,2] => [1,7,6,5,4,3,8,2] => [1,5,4,6,3,8,2,7] => 0101010
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [1,8,7,5,4,6,3,2] => [1,5,4,6,7,3,8,2] => 0100101
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [1,3,8,5,4,6,7,2] => [1,5,4,6,7,8,2,3] => 0100010
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,4,6,8,7,3,2] => [1,3,7,5,4,6,8,2] => [1,5,4,6,8,2,3,7] => 0100100
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,4,7,6,3,8,2] => [1,8,6,5,4,7,3,2] => [1,5,4,7,3,6,8,2] => 0101001
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,4,7,6,8,3,2] => [1,3,8,5,4,7,6,2] => [1,5,4,7,6,8,2,3] => 0101010
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [1,3,4,6,5,2,7,8] => [1,5,6,2,3,4,7,8] => 0010000
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [1,3,4,6,5,2,8,7] => [1,5,6,2,3,4,8,7] => 0010001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,5,6,4,3,7,2,8] => [1,7,4,6,5,3,2,8] => [1,5,6,3,4,7,2,8] => 0010010
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [1,7,4,6,5,3,8,2] => [1,5,6,3,4,8,2,7] => 0010010
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => [1,3,7,6,5,4,2,8] => [1,5,6,4,7,2,3,8] => 0010100
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => [1,5,6,4,7,3,8,2] => 0010101
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [1,8,4,7,5,6,3,2] => [1,5,6,7,3,4,8,2] => 0001001
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,4,8,3,2] => [1,3,8,7,5,6,4,2] => [1,5,6,7,4,8,2,3] => 0001010
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [1,3,4,8,5,6,7,2] => [1,5,6,7,8,2,3,4] => 0000100
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,5,6,8,7,4,3,2] => [1,3,4,7,5,6,8,2] => [1,5,6,8,2,3,4,7] => 0001000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,6,4,3,2,8] => [1,3,4,6,5,7,2,8] => [1,5,7,2,3,4,6,8] => 0010000
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,6,4,3,8,2] => [1,8,4,6,5,7,3,2] => [1,5,7,3,4,6,8,2] => 0010001
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,6,4,3,2] => [1,3,4,6,5,8,7,2] => [1,5,7,8,2,3,4,6] => 0001000
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [1,3,4,6,5,7,8,2] => [1,5,8,2,3,4,6,7] => 0010000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [1,3,4,5,6,2,7,8] => [1,6,2,3,4,5,7,8] => 0100000
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [1,3,4,5,6,2,8,7] => [1,6,2,3,4,5,8,7] => 0100001
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,7,4,5,6,3,8,2] => [1,6,3,4,5,8,2,7] => 0100010
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [1,8,4,7,6,5,3,2] => [1,6,5,7,3,4,8,2] => 0101001
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [1,3,4,8,6,5,7,2] => [1,6,5,7,8,2,3,4] => 0100100
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [1,3,4,7,6,5,8,2] => [1,6,5,8,2,3,4,7] => 0101000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [1,3,4,5,7,6,2,8] => [1,6,7,2,3,4,5,8] => 0010000
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [1,8,4,5,7,6,3,2] => [1,6,7,3,4,5,8,2] => 0010001
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [1,3,4,8,7,6,5,2] => [1,6,7,5,8,2,3,4] => 0010100
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [1,3,4,5,8,6,7,2] => [1,6,7,8,2,3,4,5] => 0001000
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [1,3,4,5,7,6,8,2] => [1,6,8,2,3,4,5,7] => 0010000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [1,3,4,5,6,7,2,8] => [1,7,2,3,4,5,6,8] => 0100000
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [1,8,4,5,6,7,3,2] => [1,7,3,4,5,6,8,2] => 0100001
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [1,3,8,5,6,7,4,2] => [1,7,4,5,6,8,2,3] => 0100010
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [1,3,4,5,8,7,6,2] => [1,7,6,8,2,3,4,5] => 0101000
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [1,3,4,5,6,8,7,2] => [1,7,8,2,3,4,5,6] => 0010000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => 0100000
[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] => 1000000
[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] => 1000001
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => 1000010
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,7,8,6] => 1000001
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,6,7] => 1000010
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => 1000100
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => 1000101
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [2,1,3,4,6,7,8,5] => 1000001
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,7,6,5] => [2,1,3,4,7,6,8,5] => 1000101
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [2,1,3,4,6,8,7,5] => [2,1,3,4,7,8,5,6] => 1000010
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,5,6,7] => 1000100
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => 1001001
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [2,1,3,5,4,7,8,6] => 1001001
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => [2,1,3,5,6,4,8,7] => 1000101
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => [2,1,3,5,6,7,8,4] => 1000001
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [2,1,3,8,5,7,6,4] => [2,1,3,5,7,6,8,4] => 1000101
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,7,6,4] => [2,1,3,6,5,7,8,4] => [2,1,3,5,8,4,6,7] => 1000100
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,5,4,7,8] => [2,1,3,5,6,4,7,8] => [2,1,3,6,4,5,7,8] => 1001000
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [2,1,3,5,6,4,8,7] => [2,1,3,6,4,5,8,7] => 1001001
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [2,1,3,7,6,5,8,4] => [2,1,3,6,5,8,4,7] => 1001010
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [2,1,3,5,8,6,7,4] => [2,1,3,6,7,8,4,5] => 1000010
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [2,1,3,5,6,8,7,4] => [2,1,3,7,8,4,5,6] => 1000100
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,1,3,5,6,7,8,4] => [2,1,3,8,4,5,6,7] => 1001000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => 1010000
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => 1010001
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,7,8,6] => 1010001
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,6,7] => 1010010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => 1010100
[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] => 1010101
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [2,1,4,3,6,7,8,5] => 1010001
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,6,8,5] => [2,1,4,3,6,8,5,7] => 1010010
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5] => 1010101
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,8,5,6] => 1010010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7] => 1010100
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [2,1,4,5,3,6,7,8] => 1001000
[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] => [2,1,4,5,3,6,8,7] => 1001001
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [2,1,4,5,6,3,8,7] => 1000101
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,1,7,4,5,6,3,8] => [2,1,4,5,6,7,3,8] => 1000010
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [2,1,4,5,6,7,8,3] => 1000001
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [2,1,7,4,5,6,8,3] => [2,1,4,5,6,8,3,7] => 1000010
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [2,1,6,4,5,8,7,3] => [2,1,4,5,7,8,3,6] => 1000010
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,6,4,5,7,8,3] => [2,1,4,5,8,3,6,7] => 1000100
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [2,1,5,4,6,3,7,8] => [2,1,4,6,3,5,7,8] => 1001000
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,5,4,6,3,8,7] => [2,1,4,6,3,5,8,7] => 1001001
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [2,1,7,4,6,5,8,3] => [2,1,4,6,5,8,3,7] => 1001010
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [2,1,8,4,7,6,5,3] => [2,1,4,6,7,5,8,3] => 1000101
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [2,1,5,4,8,6,7,3] => [2,1,4,6,7,8,3,5] => 1000010
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [2,1,5,4,7,6,8,3] => [2,1,4,6,8,3,5,7] => 1000100
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [2,1,5,4,6,8,7,3] => [2,1,4,7,8,3,5,6] => 1000100
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,5,4,6,7,8,3] => [2,1,4,8,3,5,6,7] => 1001000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,1,4,5,3,6,7,8] => [2,1,5,3,4,6,7,8] => 1010000
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,4,5,3,6,8,7] => [2,1,5,3,4,6,8,7] => 1010001
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7] => 1010101
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [2,1,8,5,4,6,7,3] => [2,1,5,4,6,7,8,3] => 1010001
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3] => 1010101
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [2,1,6,5,4,7,8,3] => [2,1,5,4,8,3,6,7] => 1010100
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [2,1,4,6,5,3,7,8] => [2,1,5,6,3,4,7,8] => 1001000
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [2,1,4,6,5,3,8,7] => [2,1,5,6,3,4,8,7] => 1001001
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [2,1,8,6,5,4,7,3] => [2,1,5,6,4,7,8,3] => 1001001
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [2,1,7,6,5,4,8,3] => [2,1,5,6,4,8,3,7] => 1001010
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [2,1,8,7,5,6,4,3] => [2,1,5,6,7,4,8,3] => 1000101
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [2,1,4,8,5,6,7,3] => [2,1,5,6,7,8,3,4] => 1000010
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [2,1,4,7,5,6,8,3] => [2,1,5,6,8,3,4,7] => 1000100
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [2,1,8,6,5,7,4,3] => [2,1,5,7,4,6,8,3] => 1001001
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [2,1,4,6,5,8,7,3] => [2,1,5,7,8,3,4,6] => 1000100
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [2,1,4,6,5,7,8,3] => [2,1,5,8,3,4,6,7] => 1001000
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7] => 1010001
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [2,1,8,5,6,4,7,3] => [2,1,6,4,5,7,8,3] => 1010001
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [2,1,7,5,6,4,8,3] => [2,1,6,4,5,8,3,7] => 1010010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3] => 1010101
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [2,1,4,8,6,5,7,3] => [2,1,6,5,7,8,3,4] => 1010010
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [2,1,4,8,7,6,5,3] => [2,1,6,7,5,8,3,4] => 1001010
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [2,1,4,5,8,6,7,3] => [2,1,6,7,8,3,4,5] => 1000100
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [2,1,4,5,7,6,8,3] => [2,1,6,8,3,4,5,7] => 1001000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,1,4,5,6,7,3,8] => [2,1,7,3,4,5,6,8] => 1010000
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [2,1,4,8,6,7,5,3] => [2,1,7,5,6,8,3,4] => 1010010
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [2,1,4,5,8,7,6,3] => [2,1,7,6,8,3,4,5] => 1010100
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [2,1,4,5,6,8,7,3] => [2,1,7,8,3,4,5,6] => 1001000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7] => 1010000
[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] => [2,3,1,4,5,6,7,8] => 0100000
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => 0100001
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => 0100010
[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] => [2,3,1,4,5,7,8,6] => 0100001
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [3,2,1,4,5,7,8,6] => [2,3,1,4,5,8,6,7] => 0100010
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [3,2,1,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => 0100101
[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] => [2,3,1,4,6,7,5,8] => 0100010
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [2,3,1,4,6,7,8,5] => 0100001
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,2,1,4,8,7,6,5] => [2,3,1,4,7,6,8,5] => 0100101
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [3,2,1,4,6,8,7,5] => [2,3,1,4,7,8,5,6] => 0100010
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,1,4,6,7,8,5] => [2,3,1,4,8,5,6,7] => 0100100
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => 0101000
[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] => [2,3,1,5,4,7,6,8] => 0101010
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => [2,3,1,5,6,4,7,8] => 0100100
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => [2,3,1,5,6,7,4,8] => 0100010
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [2,3,1,5,6,7,8,4] => 0100001
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [3,2,1,7,5,6,8,4] => [2,3,1,5,6,8,4,7] => 0100010
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,2,1,8,5,7,6,4] => [2,3,1,5,7,6,8,4] => 0100101
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [3,2,1,6,5,8,7,4] => [2,3,1,5,7,8,4,6] => 0100010
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,2,1,5,6,4,7,8] => [2,3,1,6,4,5,7,8] => 0101000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,2,1,7,6,5,4,8] => [2,3,1,6,5,7,4,8] => 0101010
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => [2,3,1,6,7,5,8,4] => 0100101
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [3,2,1,5,8,6,7,4] => [2,3,1,6,7,8,4,5] => 0100010
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [3,2,1,5,7,6,8,4] => [2,3,1,6,8,4,5,7] => 0100100
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [3,2,1,5,8,7,6,4] => [2,3,1,7,6,8,4,5] => 0101010
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [3,2,1,5,6,8,7,4] => [2,3,1,7,8,4,5,6] => 0100100
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,1,5,6,7,8,4] => [2,3,1,8,4,5,6,7] => 0101000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => 0010000
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [4,2,3,1,5,6,8,7] => [2,3,4,1,5,6,8,7] => 0010001
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => 0010010
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => 0010001
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,2,3,1,5,7,8,6] => [2,3,4,1,5,8,6,7] => 0010010
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => 0010100
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => 0010101
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => 0010010
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [2,3,4,1,6,7,8,5] => 0010001
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,2,3,1,7,6,8,5] => [2,3,4,1,6,8,5,7] => 0010010
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [4,2,3,1,6,7,5,8] => [2,3,4,1,7,5,6,8] => 0010100
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,2,3,1,8,7,6,5] => [2,3,4,1,7,6,8,5] => 0010101
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [4,2,3,1,6,8,7,5] => [2,3,4,1,7,8,5,6] => 0010010
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,3,1,6,7,8,5] => [2,3,4,1,8,5,6,7] => 0010100
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [2,3,4,5,1,6,7,8] => 0001000
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [2,3,4,5,1,6,8,7] => 0001001
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [5,2,3,4,1,7,6,8] => [2,3,4,5,1,7,6,8] => 0001010
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [2,3,4,5,1,7,8,6] => 0001001
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,3,4,1,7,8,6] => [2,3,4,5,1,8,6,7] => 0001010
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [2,3,4,5,6,1,7,8] => 0000100
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [2,3,4,5,6,1,8,7] => 0000101
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [2,3,4,5,6,7,1,8] => 0000010
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,8,1] => 0000001
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [7,2,3,4,5,6,8,1] => [2,3,4,5,6,8,1,7] => 0000010
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [6,2,3,4,5,7,1,8] => [2,3,4,5,7,1,6,8] => 0000100
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,7,6,1] => [2,3,4,5,7,6,8,1] => 0000101
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [6,2,3,4,5,8,7,1] => [2,3,4,5,7,8,1,6] => 0000010
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [6,2,3,4,5,7,8,1] => [2,3,4,5,8,1,6,7] => 0000100
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [5,2,3,4,6,1,7,8] => [2,3,4,6,1,5,7,8] => 0001000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8] => [2,3,4,6,5,7,1,8] => 0001010
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [8,2,3,4,6,5,7,1] => [2,3,4,6,5,7,8,1] => 0001001
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [7,2,3,4,6,5,8,1] => [2,3,4,6,5,8,1,7] => 0001010
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [5,2,3,4,7,6,1,8] => [2,3,4,6,7,1,5,8] => 0000100
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [8,2,3,4,7,6,5,1] => [2,3,4,6,7,5,8,1] => 0000101
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [5,2,3,4,8,6,7,1] => [2,3,4,6,7,8,1,5] => 0000010
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [5,2,3,4,7,6,8,1] => [2,3,4,6,8,1,5,7] => 0000100
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [5,2,3,4,6,7,1,8] => [2,3,4,7,1,5,6,8] => 0001000
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [8,2,3,4,6,7,5,1] => [2,3,4,7,5,6,8,1] => 0001001
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [5,2,3,4,8,7,6,1] => [2,3,4,7,6,8,1,5] => 0001010
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [5,2,3,4,6,8,7,1] => [2,3,4,7,8,1,5,6] => 0000100
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [5,2,3,4,6,7,8,1] => [2,3,4,8,1,5,6,7] => 0001000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [4,2,3,5,1,6,7,8] => [2,3,5,1,4,6,7,8] => 0010000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [4,2,3,5,1,7,6,8] => [2,3,5,1,4,7,6,8] => 0010010
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [4,2,3,5,1,7,8,6] => [2,3,5,1,4,8,6,7] => 0010010
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [6,2,3,5,4,1,7,8] => [2,3,5,4,6,1,7,8] => 0010100
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [7,2,3,5,4,6,1,8] => [2,3,5,4,6,7,1,8] => 0010010
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [8,2,3,5,4,6,7,1] => [2,3,5,4,6,7,8,1] => 0010001
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [8,2,3,5,4,7,6,1] => [2,3,5,4,7,6,8,1] => 0010101
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [4,2,3,6,5,1,7,8] => [2,3,5,6,1,4,7,8] => 0001000
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => [4,2,3,6,5,1,8,7] => [2,3,5,6,1,4,8,7] => 0001001
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [7,2,3,6,5,4,1,8] => [2,3,5,6,4,7,1,8] => 0001010
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [8,2,3,6,5,4,7,1] => [2,3,5,6,4,7,8,1] => 0001001
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [4,2,3,7,5,6,1,8] => [2,3,5,6,7,1,4,8] => 0000100
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [8,2,3,7,5,6,4,1] => [2,3,5,6,7,4,8,1] => 0000101
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [4,2,3,8,5,6,7,1] => [2,3,5,6,7,8,1,4] => 0000010
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [4,2,3,7,5,6,8,1] => [2,3,5,6,8,1,4,7] => 0000100
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [8,2,3,6,5,7,4,1] => [2,3,5,7,4,6,8,1] => 0001001
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [4,2,3,8,5,7,6,1] => [2,3,5,7,6,8,1,4] => 0001010
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [4,2,3,6,5,8,7,1] => [2,3,5,7,8,1,4,6] => 0000100
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [4,2,3,5,6,1,7,8] => [2,3,6,1,4,5,7,8] => 0010000
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,3,5,6,1,8,7] => [2,3,6,1,4,5,8,7] => 0010001
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [8,2,3,5,6,4,7,1] => [2,3,6,4,5,7,8,1] => 0010001
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,5,7,8,4,1] => [4,2,3,8,6,5,7,1] => [2,3,6,5,7,8,1,4] => 0010010
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [4,2,3,7,6,5,8,1] => [2,3,6,5,8,1,4,7] => 0010100
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [4,2,3,5,7,6,1,8] => [2,3,6,7,1,4,5,8] => 0001000
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,6,7,5,4,8,1] => [8,2,3,5,7,6,4,1] => [2,3,6,7,4,5,8,1] => 0001001
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,5,8,4,1] => [4,2,3,8,7,6,5,1] => [2,3,6,7,5,8,1,4] => 0001010
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,6,8,7,5,4,1] => [4,2,3,5,7,6,8,1] => [2,3,6,8,1,4,5,7] => 0001000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [4,2,3,5,6,7,1,8] => [2,3,7,1,4,5,6,8] => 0010000
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [8,2,3,5,6,7,4,1] => [2,3,7,4,5,6,8,1] => 0010001
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [4,2,3,8,6,7,5,1] => [2,3,7,5,6,8,1,4] => 0010010
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,6,5,4,1] => [4,2,3,5,6,8,7,1] => [2,3,7,8,1,4,5,6] => 0001000
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [4,2,3,5,6,7,8,1] => [2,3,8,1,4,5,6,7] => 0010000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [2,4,1,3,5,6,7,8] => 0100000
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,3,1,5,7,8,6] => [3,2,4,1,5,8,7,6] => [2,4,1,3,5,7,8,6] => 0100001
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => [2,4,1,3,6,5,7,8] => 0100100
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => [2,4,1,3,6,5,8,7] => 0100101
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [3,2,4,1,8,6,7,5] => [2,4,1,3,6,7,8,5] => 0100001
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,2,4,1,7,6,8,5] => [2,4,1,3,6,8,5,7] => 0100010
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,2,4,1,8,7,6,5] => [2,4,1,3,7,6,8,5] => 0100101
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [3,2,4,1,6,8,7,5] => [2,4,1,3,7,8,5,6] => 0100010
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,2,4,1,6,7,8,5] => [2,4,1,3,8,5,6,7] => 0100100
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [5,2,4,3,1,6,7,8] => [2,4,3,5,1,6,7,8] => 0101000
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [5,2,4,3,1,6,8,7] => [2,4,3,5,1,6,8,7] => 0101001
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [5,2,4,3,1,7,6,8] => [2,4,3,5,1,7,6,8] => 0101010
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [5,2,4,3,1,8,7,6] => [2,4,3,5,1,7,8,6] => 0101001
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [5,2,4,3,1,7,8,6] => [2,4,3,5,1,8,6,7] => 0101010
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [6,2,4,3,5,1,8,7] => [2,4,3,5,6,1,8,7] => 0100101
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [8,2,4,3,5,6,7,1] => [2,4,3,5,6,7,8,1] => 0100001
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [7,2,4,3,5,6,8,1] => [2,4,3,5,6,8,1,7] => 0100010
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [8,2,4,3,5,7,6,1] => [2,4,3,5,7,6,8,1] => 0100101
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,7,8,6,1] => [6,2,4,3,5,8,7,1] => [2,4,3,5,7,8,1,6] => 0100010
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [5,2,4,3,6,1,8,7] => [2,4,3,6,1,5,8,7] => 0101001
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [7,2,4,3,6,5,1,8] => [2,4,3,6,5,7,1,8] => 0101010
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [8,2,4,3,6,5,7,1] => [2,4,3,6,5,7,8,1] => 0101001
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [7,2,4,3,6,5,8,1] => [2,4,3,6,5,8,1,7] => 0101010
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [8,2,4,3,7,6,5,1] => [2,4,3,6,7,5,8,1] => 0100101
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [5,2,4,3,7,6,8,1] => [2,4,3,6,8,1,5,7] => 0100100
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [8,2,4,3,6,7,5,1] => [2,4,3,7,5,6,8,1] => 0101001
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [5,2,4,3,6,7,8,1] => [2,4,3,8,1,5,6,7] => 0101000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [3,2,5,4,1,6,7,8] => [2,4,5,1,3,6,7,8] => 0010000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [3,2,5,4,1,7,6,8] => [2,4,5,1,3,7,6,8] => 0010010
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [3,2,5,4,1,8,7,6] => [2,4,5,1,3,7,8,6] => 0010001
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [6,2,5,4,3,1,8,7] => [2,4,5,3,6,1,8,7] => 0010101
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,3,6,7,1,8] => [7,2,5,4,3,6,1,8] => [2,4,5,3,6,7,1,8] => 0010010
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [8,2,5,4,3,6,7,1] => [2,4,5,3,6,7,8,1] => 0010001
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [7,2,5,4,3,6,8,1] => [2,4,5,3,6,8,1,7] => 0010010
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [3,2,6,4,5,1,7,8] => [2,4,5,6,1,3,7,8] => 0001000
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,3,1,8,7] => [3,2,6,4,5,1,8,7] => [2,4,5,6,1,3,8,7] => 0001001
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [8,2,6,4,5,3,7,1] => [2,4,5,6,3,7,8,1] => 0001001
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [7,2,6,4,5,3,8,1] => [2,4,5,6,3,8,1,7] => 0001010
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [3,2,7,4,5,6,1,8] => [2,4,5,6,7,1,3,8] => 0000100
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [8,2,7,4,5,6,3,1] => [2,4,5,6,7,3,8,1] => 0000101
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [3,2,8,4,5,6,7,1] => [2,4,5,6,7,8,1,3] => 0000010
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,6,3,8,1] => [8,2,6,4,5,7,3,1] => [2,4,5,7,3,6,8,1] => 0001001
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [3,2,5,4,6,1,7,8] => [2,4,6,1,3,5,7,8] => 0010000
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [3,2,5,4,6,1,8,7] => [2,4,6,1,3,5,8,7] => 0010001
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,4,6,5,3,7,1,8] => [7,2,5,4,6,3,1,8] => [2,4,6,3,5,7,1,8] => 0010010
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [8,2,5,4,6,3,7,1] => [2,4,6,3,5,7,8,1] => 0010001
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [7,2,5,4,6,3,8,1] => [2,4,6,3,5,8,1,7] => 0010010
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [8,2,7,4,6,5,3,1] => [2,4,6,5,7,3,8,1] => 0010101
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [3,2,8,4,6,5,7,1] => [2,4,6,5,7,8,1,3] => 0010010
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [3,2,7,4,6,5,8,1] => [2,4,6,5,8,1,3,7] => 0010100
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [3,2,5,4,7,6,1,8] => [2,4,6,7,1,3,5,8] => 0001000
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [8,2,5,4,7,6,3,1] => [2,4,6,7,3,5,8,1] => 0001001
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [3,2,5,4,8,6,7,1] => [2,4,6,7,8,1,3,5] => 0000100
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [3,2,5,4,7,6,8,1] => [2,4,6,8,1,3,5,7] => 0001000
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,4,7,6,5,3,8,1] => [8,2,5,4,6,7,3,1] => [2,4,7,3,5,6,8,1] => 0010001
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [3,2,5,4,6,8,7,1] => [2,4,7,8,1,3,5,6] => 0001000
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [3,2,5,4,6,7,8,1] => [2,4,8,1,3,5,6,7] => 0010000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [3,2,4,5,1,6,7,8] => [2,5,1,3,4,6,7,8] => 0100000
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [7,2,4,5,3,6,1,8] => [2,5,3,4,6,7,1,8] => 0100010
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [8,2,4,5,3,6,7,1] => [2,5,3,4,6,7,8,1] => 0100001
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [7,2,4,5,3,6,8,1] => [2,5,3,4,6,8,1,7] => 0100010
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [8,2,4,5,3,7,6,1] => [2,5,3,4,7,6,8,1] => 0100101
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [7,2,6,5,4,3,1,8] => [2,5,4,6,3,7,1,8] => 0101010
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => [8,2,6,5,4,3,7,1] => [2,5,4,6,3,7,8,1] => 0101001
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [3,2,7,5,4,6,1,8] => [2,5,4,6,7,1,3,8] => 0100100
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [8,2,7,5,4,6,3,1] => [2,5,4,6,7,3,8,1] => 0100101
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [3,2,8,5,4,7,6,1] => [2,5,4,7,6,8,1,3] => 0101010
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [3,2,6,5,4,8,7,1] => [2,5,4,7,8,1,3,6] => 0100100
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => [3,2,4,6,5,1,8,7] => [2,5,6,1,3,4,8,7] => 0010001
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => [8,2,4,6,5,3,7,1] => [2,5,6,3,4,7,8,1] => 0010001
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [3,2,7,6,5,4,1,8] => [2,5,6,4,7,1,3,8] => 0010100
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [3,2,7,6,5,4,8,1] => [2,5,6,4,8,1,3,7] => 0010100
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [3,2,8,7,5,6,4,1] => [2,5,6,7,4,8,1,3] => 0001010
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [3,2,4,8,5,6,7,1] => [2,5,6,7,8,1,3,4] => 0000100
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,6,4,8,3,1] => [3,2,8,6,5,7,4,1] => [2,5,7,4,6,8,1,3] => 0010010
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [8,2,4,5,6,3,7,1] => [2,6,3,4,5,7,8,1] => 0100001
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [7,2,4,5,6,3,8,1] => [2,6,3,4,5,8,1,7] => 0100010
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [3,2,8,5,6,4,7,1] => [2,6,4,5,7,8,1,3] => 0100010
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [3,2,7,5,6,4,8,1] => [2,6,4,5,8,1,3,7] => 0100100
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,6,5,7,4,3,1,8] => [3,2,4,7,6,5,1,8] => [2,6,5,7,1,3,4,8] => 0101000
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [8,2,4,7,6,5,3,1] => [2,6,5,7,3,4,8,1] => 0101001
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,5,8,7,4,3,1] => [3,2,4,7,6,5,8,1] => [2,6,5,8,1,3,4,7] => 0101000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [3,2,4,5,7,6,1,8] => [2,6,7,1,3,4,5,8] => 0010000
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,5,4,8,3,1] => [3,2,8,5,7,6,4,1] => [2,6,7,4,5,8,1,3] => 0010010
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [3,2,4,8,7,6,5,1] => [2,6,7,5,8,1,3,4] => 0010100
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [3,2,4,5,8,6,7,1] => [2,6,7,8,1,3,4,5] => 0001000
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [3,2,4,5,7,6,8,1] => [2,6,8,1,3,4,5,7] => 0010000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [3,2,4,5,6,7,1,8] => [2,7,1,3,4,5,6,8] => 0100000
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [3,2,8,5,6,7,4,1] => [2,7,4,5,6,8,1,3] => 0100010
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,6,5,8,4,3,1] => [3,2,4,8,6,7,5,1] => [2,7,5,6,8,1,3,4] => 0100100
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [3,2,4,5,6,8,7,1] => [2,7,8,1,3,4,5,6] => 0010000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,1] => [2,8,1,3,4,5,6,7] => 0100000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => 1000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => 1000001
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => 1000010
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [2,3,1,4,5,8,7,6] => [3,1,2,4,5,7,8,6] => 1000001
[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] => 1000010
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => 1000101
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [2,3,1,4,8,6,7,5] => [3,1,2,4,6,7,8,5] => 1000001
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [2,3,1,4,7,6,8,5] => [3,1,2,4,6,8,5,7] => 1000010
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [2,3,1,4,6,7,5,8] => [3,1,2,4,7,5,6,8] => 1000100
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [2,3,1,4,8,7,6,5] => [3,1,2,4,7,6,8,5] => 1000101
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [2,3,1,4,6,8,7,5] => [3,1,2,4,7,8,5,6] => 1000010
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,3,1,4,6,7,8,5] => [3,1,2,4,8,5,6,7] => 1000100
[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] => 1001010
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [2,3,1,6,5,4,7,8] => [3,1,2,5,6,4,7,8] => 1000100
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [2,3,1,7,5,6,4,8] => [3,1,2,5,6,7,4,8] => 1000010
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [2,3,1,8,5,6,7,4] => [3,1,2,5,6,7,8,4] => 1000001
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [2,3,1,7,5,6,8,4] => [3,1,2,5,6,8,4,7] => 1000010
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [2,3,1,6,5,7,4,8] => [3,1,2,5,7,4,6,8] => 1000100
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [2,3,1,8,5,7,6,4] => [3,1,2,5,7,6,8,4] => 1000101
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [2,3,1,6,5,8,7,4] => [3,1,2,5,7,8,4,6] => 1000010
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [2,3,1,6,5,7,8,4] => [3,1,2,5,8,4,6,7] => 1000100
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [2,3,1,5,6,4,8,7] => [3,1,2,6,4,5,8,7] => 1001001
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [2,3,1,8,6,5,7,4] => [3,1,2,6,5,7,8,4] => 1001001
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [2,3,1,8,7,6,5,4] => [3,1,2,6,7,5,8,4] => 1000101
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [2,3,1,5,8,6,7,4] => [3,1,2,6,7,8,4,5] => 1000010
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [2,3,1,5,7,6,8,4] => [3,1,2,6,8,4,5,7] => 1000100
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [2,3,1,8,6,7,5,4] => [3,1,2,7,5,6,8,4] => 1001001
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [2,3,1,5,6,8,7,4] => [3,1,2,7,8,4,5,6] => 1000100
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,3,1,5,6,7,8,4] => [3,1,2,8,4,5,6,7] => 1001000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => 1010000
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => 1010001
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => 1010010
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => 1010001
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,7,8,6] => [3,2,4,1,5,8,6,7] => 1010010
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => 1010100
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => 1010101
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => [3,2,4,1,6,7,5,8] => 1010010
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [3,2,4,1,6,7,8,5] => 1010001
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [4,3,2,1,7,6,8,5] => [3,2,4,1,6,8,5,7] => 1010010
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [4,3,2,1,6,7,5,8] => [3,2,4,1,7,5,6,8] => 1010100
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [3,2,4,1,7,6,8,5] => 1010101
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [4,3,2,1,6,8,7,5] => [3,2,4,1,7,8,5,6] => 1010010
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,3,2,1,6,7,8,5] => [3,2,4,1,8,5,6,7] => 1010100
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => [3,2,4,5,1,6,7,8] => 1001000
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [6,3,2,4,5,1,7,8] => [3,2,4,5,6,1,7,8] => 1000100
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [7,3,2,4,5,6,1,8] => [3,2,4,5,6,7,1,8] => 1000010
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [8,3,2,4,5,6,7,1] => [3,2,4,5,6,7,8,1] => 1000001
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [7,3,2,4,5,6,8,1] => [3,2,4,5,6,8,1,7] => 1000010
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [8,3,2,4,5,7,6,1] => [3,2,4,5,7,6,8,1] => 1000101
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [6,3,2,4,5,8,7,1] => [3,2,4,5,7,8,1,6] => 1000010
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,2,4,6,5,1,8,7] => [5,3,2,4,6,1,8,7] => [3,2,4,6,1,5,8,7] => 1001001
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,6,7,8,5,1] => [5,3,2,4,8,6,7,1] => [3,2,4,6,7,8,1,5] => 1000010
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [8,3,2,4,6,7,5,1] => [3,2,4,7,5,6,8,1] => 1001001
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,7,8,6,5,1] => [5,3,2,4,6,8,7,1] => [3,2,4,7,8,1,5,6] => 1000100
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [5,3,2,4,6,7,8,1] => [3,2,4,8,1,5,6,7] => 1001000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [4,3,2,5,1,6,7,8] => [3,2,5,1,4,6,7,8] => 1010000
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [4,3,2,5,1,6,8,7] => [3,2,5,1,4,6,8,7] => 1010001
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [4,3,2,5,1,7,6,8] => [3,2,5,1,4,7,6,8] => 1010010
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [4,3,2,5,1,8,7,6] => [3,2,5,1,4,7,8,6] => 1010001
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => [3,2,5,4,6,1,8,7] => 1010101
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [8,3,2,5,4,6,7,1] => [3,2,5,4,6,7,8,1] => 1010001
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [6,3,2,5,4,7,1,8] => [3,2,5,4,7,1,6,8] => 1010100
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,8,1] => 1010101
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [6,3,2,5,4,8,7,1] => [3,2,5,4,7,8,1,6] => 1010010
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [8,3,2,6,5,4,7,1] => [3,2,5,6,4,7,8,1] => 1001001
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [8,3,2,7,5,6,4,1] => [3,2,5,6,7,4,8,1] => 1000101
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [4,3,2,8,5,6,7,1] => [3,2,5,6,7,8,1,4] => 1000010
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,5,6,8,7,4,1] => [4,3,2,7,5,6,8,1] => [3,2,5,6,8,1,4,7] => 1000100
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [4,3,2,6,5,7,1,8] => [3,2,5,7,1,4,6,8] => 1001000
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [8,3,2,6,5,7,4,1] => [3,2,5,7,4,6,8,1] => 1001001
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [4,3,2,8,5,7,6,1] => [3,2,5,7,6,8,1,4] => 1001010
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,5,8,7,6,4,1] => [4,3,2,6,5,7,8,1] => [3,2,5,8,1,4,6,7] => 1001000
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [4,3,2,5,6,1,8,7] => [3,2,6,1,4,5,8,7] => 1010001
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [7,3,2,5,6,4,8,1] => [3,2,6,4,5,8,1,7] => 1010010
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [4,3,2,7,6,5,1,8] => [3,2,6,5,7,1,4,8] => 1010100
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => [3,2,6,5,7,4,8,1] => 1010101
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,6,5,7,8,4,1] => [4,3,2,8,6,5,7,1] => [3,2,6,5,7,8,1,4] => 1010010
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [4,3,2,8,7,6,5,1] => [3,2,6,7,5,8,1,4] => 1001010
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [4,3,2,5,7,6,8,1] => [3,2,6,8,1,4,5,7] => 1001000
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,2,7,6,5,8,4,1] => [4,3,2,8,6,7,5,1] => [3,2,7,5,6,8,1,4] => 1010010
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,7,6,8,5,4,1] => [4,3,2,5,8,7,6,1] => [3,2,7,6,8,1,4,5] => 1010100
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [4,3,2,5,6,8,7,1] => [3,2,7,8,1,4,5,6] => 1001000
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [4,3,2,5,6,7,8,1] => [3,2,8,1,4,5,6,7] => 1010000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => [3,4,1,2,5,6,7,8] => 0100000
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,2,1,5,6,8,7] => [2,4,3,1,5,6,8,7] => [3,4,1,2,5,6,8,7] => 0100001
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,2,1,5,7,6,8] => [2,4,3,1,5,7,6,8] => [3,4,1,2,5,7,6,8] => 0100010
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,2,1,5,7,8,6] => [2,4,3,1,5,8,7,6] => [3,4,1,2,5,7,8,6] => 0100001
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,2,1,5,8,7,6] => [2,4,3,1,5,7,8,6] => [3,4,1,2,5,8,6,7] => 0100010
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,2,1,6,5,7,8] => [2,4,3,1,6,5,7,8] => [3,4,1,2,6,5,7,8] => 0100100
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => [3,4,1,2,6,5,8,7] => 0100101
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [2,4,3,1,8,6,7,5] => [3,4,1,2,6,7,8,5] => 0100001
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [2,4,3,1,7,6,8,5] => [3,4,1,2,6,8,5,7] => 0100010
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [2,4,3,1,8,7,6,5] => [3,4,1,2,7,6,8,5] => 0100101
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [2,4,3,1,6,8,7,5] => [3,4,1,2,7,8,5,6] => 0100010
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [2,4,3,1,6,7,8,5] => [3,4,1,2,8,5,6,7] => 0100100
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [3,4,2,5,1,6,7,8] => 0101000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [5,4,3,2,1,7,6,8] => [3,4,2,5,1,7,6,8] => 0101010
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => [3,4,2,5,1,7,8,6] => 0101001
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [5,4,3,2,1,7,8,6] => [3,4,2,5,1,8,6,7] => 0101010
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [6,4,3,2,5,1,7,8] => [3,4,2,5,6,1,7,8] => 0100100
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [6,4,3,2,5,1,8,7] => [3,4,2,5,6,1,8,7] => 0100101
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [7,4,3,2,5,6,1,8] => [3,4,2,5,6,7,1,8] => 0100010
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [8,4,3,2,5,6,7,1] => [3,4,2,5,6,7,8,1] => 0100001
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [7,4,3,2,5,6,8,1] => [3,4,2,5,6,8,1,7] => 0100010
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [8,4,3,2,5,7,6,1] => [3,4,2,5,7,6,8,1] => 0100101
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [7,4,3,2,6,5,1,8] => [3,4,2,6,5,7,1,8] => 0101010
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [8,4,3,2,6,5,7,1] => [3,4,2,6,5,7,8,1] => 0101001
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => [7,4,3,2,6,5,8,1] => [3,4,2,6,5,8,1,7] => 0101010
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [5,4,3,2,7,6,1,8] => [3,4,2,6,7,1,5,8] => 0100100
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [8,4,3,2,7,6,5,1] => [3,4,2,6,7,5,8,1] => 0100101
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,2,6,7,8,5,1] => [5,4,3,2,8,6,7,1] => [3,4,2,6,7,8,1,5] => 0100010
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,2,6,8,7,5,1] => [5,4,3,2,7,6,8,1] => [3,4,2,6,8,1,5,7] => 0100100
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [5,4,3,2,6,8,7,1] => [3,4,2,7,8,1,5,6] => 0100100
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [5,4,3,2,6,7,8,1] => [3,4,2,8,1,5,6,7] => 0101000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [2,5,3,4,1,6,7,8] => [3,4,5,1,2,6,7,8] => 0010000
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => [2,5,3,4,1,8,7,6] => [3,4,5,1,2,7,8,6] => 0010001
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [2,5,3,4,1,7,8,6] => [3,4,5,1,2,8,6,7] => 0010010
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [6,5,3,4,2,1,7,8] => [3,4,5,2,6,1,7,8] => 0010100
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [6,5,3,4,2,1,8,7] => [3,4,5,2,6,1,8,7] => 0010101
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [7,5,3,4,2,6,1,8] => [3,4,5,2,6,7,1,8] => 0010010
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [8,5,3,4,2,6,7,1] => [3,4,5,2,6,7,8,1] => 0010001
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [8,5,3,4,2,7,6,1] => [3,4,5,2,7,6,8,1] => 0010101
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [2,6,3,4,5,1,7,8] => [3,4,5,6,1,2,7,8] => 0001000
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [2,6,3,4,5,1,8,7] => [3,4,5,6,1,2,8,7] => 0001001
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8] => [3,4,5,6,2,7,1,8] => 0001010
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [8,6,3,4,5,2,7,1] => [3,4,5,6,2,7,8,1] => 0001001
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [7,6,3,4,5,2,8,1] => [3,4,5,6,2,8,1,7] => 0001010
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [2,7,3,4,5,6,1,8] => [3,4,5,6,7,1,2,8] => 0000100
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [8,7,3,4,5,6,2,1] => [3,4,5,6,7,2,8,1] => 0000101
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [2,8,3,4,5,6,7,1] => [3,4,5,6,7,8,1,2] => 0000010
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [2,7,3,4,5,6,8,1] => [3,4,5,6,8,1,2,7] => 0000100
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [8,6,3,4,5,7,2,1] => [3,4,5,7,2,6,8,1] => 0001001
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [2,8,3,4,5,7,6,1] => [3,4,5,7,6,8,1,2] => 0001010
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [2,6,3,4,5,8,7,1] => [3,4,5,7,8,1,2,6] => 0000100
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [2,6,3,4,5,7,8,1] => [3,4,5,8,1,2,6,7] => 0001000
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [2,5,3,4,6,1,8,7] => [3,4,6,1,2,5,8,7] => 0010001
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [8,7,3,4,6,5,2,1] => [3,4,6,5,7,2,8,1] => 0010101
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [8,5,3,4,7,6,2,1] => [3,4,6,7,2,5,8,1] => 0001001
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [2,5,3,4,8,6,7,1] => [3,4,6,7,8,1,2,5] => 0000100
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [8,5,3,4,6,7,2,1] => [3,4,7,2,5,6,8,1] => 0010001
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,6,8,5,2,1] => [2,5,3,4,8,7,6,1] => [3,4,7,6,8,1,2,5] => 0010100
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,6,5,2,1] => [2,5,3,4,6,8,7,1] => [3,4,7,8,1,2,5,6] => 0001000
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [2,5,3,4,6,7,8,1] => [3,4,8,1,2,5,6,7] => 0010000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [2,4,3,5,1,6,7,8] => [3,5,1,2,4,6,7,8] => 0100000
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [2,4,3,5,1,6,8,7] => [3,5,1,2,4,6,8,7] => 0100001
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [2,4,3,5,1,7,6,8] => [3,5,1,2,4,7,6,8] => 0100010
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [2,4,3,5,1,8,7,6] => [3,5,1,2,4,7,8,6] => 0100001
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [2,4,3,5,1,7,8,6] => [3,5,1,2,4,8,6,7] => 0100010
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [6,4,3,5,2,1,8,7] => [3,5,2,4,6,1,8,7] => 0100101
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [8,4,3,5,2,6,7,1] => [3,5,2,4,6,7,8,1] => 0100001
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,4,2,6,8,7,1] => [7,4,3,5,2,6,8,1] => [3,5,2,4,6,8,1,7] => 0100010
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [6,4,3,5,2,7,1,8] => [3,5,2,4,7,1,6,8] => 0100100
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [8,4,3,5,2,7,6,1] => [3,5,2,4,7,6,8,1] => 0100101
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,4,6,2,1,8,7] => [2,6,3,5,4,1,8,7] => [3,5,4,6,1,2,8,7] => 0101001
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [7,6,3,5,4,2,1,8] => [3,5,4,6,2,7,1,8] => 0101010
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [8,6,3,5,4,2,7,1] => [3,5,4,6,2,7,8,1] => 0101001
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,4,6,2,8,7,1] => [7,6,3,5,4,2,8,1] => [3,5,4,6,2,8,1,7] => 0101010
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [8,7,3,5,4,6,2,1] => [3,5,4,6,7,2,8,1] => 0100101
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [2,8,3,5,4,6,7,1] => [3,5,4,6,7,8,1,2] => 0100010
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,4,6,8,7,2,1] => [2,7,3,5,4,6,8,1] => [3,5,4,6,8,1,2,7] => 0100100
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [8,6,3,5,4,7,2,1] => [3,5,4,7,2,6,8,1] => 0101001
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [2,8,3,5,4,7,6,1] => [3,5,4,7,6,8,1,2] => 0101010
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [2,6,3,5,4,8,7,1] => [3,5,4,7,8,1,2,6] => 0100100
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,4,2,1,7,8] => [2,4,3,6,5,1,7,8] => [3,5,6,1,2,4,7,8] => 0010000
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [2,4,3,6,5,1,8,7] => [3,5,6,1,2,4,8,7] => 0010001
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [7,4,3,6,5,2,1,8] => [3,5,6,2,4,7,1,8] => 0010010
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [8,4,3,6,5,2,7,1] => [3,5,6,2,4,7,8,1] => 0010001
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [7,4,3,6,5,2,8,1] => [3,5,6,2,4,8,1,7] => 0010010
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [8,7,3,6,5,4,2,1] => [3,5,6,4,7,2,8,1] => 0010101
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [2,8,3,6,5,4,7,1] => [3,5,6,4,7,8,1,2] => 0010010
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [2,4,3,7,5,6,1,8] => [3,5,6,7,1,2,4,8] => 0001000
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [8,4,3,7,5,6,2,1] => [3,5,6,7,2,4,8,1] => 0001001
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [2,4,3,8,5,6,7,1] => [3,5,6,7,8,1,2,4] => 0000100
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [2,4,3,7,5,6,8,1] => [3,5,6,8,1,2,4,7] => 0001000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [2,4,3,6,5,7,1,8] => [3,5,7,1,2,4,6,8] => 0010000
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [8,4,3,6,5,7,2,1] => [3,5,7,2,4,6,8,1] => 0010001
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [2,8,3,6,5,7,4,1] => [3,5,7,4,6,8,1,2] => 0010010
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [2,4,3,6,5,8,7,1] => [3,5,7,8,1,2,4,6] => 0001000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [2,4,3,5,6,1,7,8] => [3,6,1,2,4,5,7,8] => 0100000
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [2,4,3,5,6,1,8,7] => [3,6,1,2,4,5,8,7] => 0100001
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => [7,4,3,5,6,2,1,8] => [3,6,2,4,5,7,1,8] => 0100010
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [8,7,3,5,6,4,2,1] => [3,6,4,5,7,2,8,1] => 0100101
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,5,7,4,8,2,1] => [2,8,3,7,6,5,4,1] => [3,6,5,7,4,8,1,2] => 0101010
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,5,8,7,4,2,1] => [2,4,3,7,6,5,8,1] => [3,6,5,8,1,2,4,7] => 0101000
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,5,4,2,8,1] => [8,4,3,5,7,6,2,1] => [3,6,7,2,4,5,8,1] => 0010001
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,5,4,8,2,1] => [2,8,3,5,7,6,4,1] => [3,6,7,4,5,8,1,2] => 0010010
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,5,8,4,2,1] => [2,4,3,8,7,6,5,1] => [3,6,7,5,8,1,2,4] => 0010100
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,5,4,2,1] => [2,4,3,5,8,6,7,1] => [3,6,7,8,1,2,4,5] => 0001000
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [2,4,3,5,7,6,8,1] => [3,6,8,1,2,4,5,7] => 0010000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,6,5,4,2,1,8] => [2,4,3,5,6,7,1,8] => [3,7,1,2,4,5,6,8] => 0100000
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [2,8,3,5,6,7,4,1] => [3,7,4,5,6,8,1,2] => 0100010
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [2,4,3,8,6,7,5,1] => [3,7,5,6,8,1,2,4] => 0100100
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [2,4,3,5,6,8,7,1] => [3,7,8,1,2,4,5,6] => 0010000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [2,4,3,5,6,7,8,1] => [3,8,1,2,4,5,6,7] => 0100000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => 1000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [2,3,4,1,5,6,8,7] => [4,1,2,3,5,6,8,7] => 1000001
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => [4,1,2,3,5,7,6,8] => 1000010
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [2,3,4,1,5,8,7,6] => [4,1,2,3,5,7,8,6] => 1000001
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => [4,1,2,3,5,8,6,7] => 1000010
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => [4,1,2,3,6,5,7,8] => 1000100
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => 1000101
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [2,3,4,1,7,6,5,8] => [4,1,2,3,6,7,5,8] => 1000010
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [2,3,4,1,8,6,7,5] => [4,1,2,3,6,7,8,5] => 1000001
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [2,3,4,1,7,6,8,5] => [4,1,2,3,6,8,5,7] => 1000010
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => [4,1,2,3,7,5,6,8] => 1000100
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [2,3,4,1,8,7,6,5] => [4,1,2,3,7,6,8,5] => 1000101
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [2,3,4,1,6,8,7,5] => [4,1,2,3,7,8,5,6] => 1000010
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => [4,1,2,3,8,5,6,7] => 1000100
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,3,4,2,1,6,7,8] => [4,2,3,5,1,6,7,8] => 1001000
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [5,3,4,2,1,6,8,7] => [4,2,3,5,1,6,8,7] => 1001001
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [5,3,4,2,1,8,7,6] => [4,2,3,5,1,7,8,6] => 1001001
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [5,3,4,2,1,7,8,6] => [4,2,3,5,1,8,6,7] => 1001010
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [6,3,4,2,5,1,7,8] => [4,2,3,5,6,1,7,8] => 1000100
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [6,3,4,2,5,1,8,7] => [4,2,3,5,6,1,8,7] => 1000101
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [8,3,4,2,5,6,7,1] => [4,2,3,5,6,7,8,1] => 1000001
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [7,3,4,2,5,6,8,1] => [4,2,3,5,6,8,1,7] => 1000010
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [5,3,4,2,6,1,8,7] => [4,2,3,6,1,5,8,7] => 1001001
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,6,7,8,5,1] => [5,3,4,2,8,6,7,1] => [4,2,3,6,7,8,1,5] => 1000010
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [5,3,4,2,7,6,8,1] => [4,2,3,6,8,1,5,7] => 1000100
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [8,3,4,2,6,7,5,1] => [4,2,3,7,5,6,8,1] => 1001001
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [5,3,4,2,6,7,8,1] => [4,2,3,8,1,5,6,7] => 1001000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [2,5,4,3,1,6,7,8] => [4,3,5,1,2,6,7,8] => 1010000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,3,5,2,1,7,6,8] => [2,5,4,3,1,7,6,8] => [4,3,5,1,2,7,6,8] => 1010010
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [4,3,5,2,6,1,7,8] => 1010100
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => [4,3,5,2,6,1,8,7] => 1010101
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [8,5,4,3,2,6,7,1] => [4,3,5,2,6,7,8,1] => 1010001
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,3,5,2,6,8,7,1] => [7,5,4,3,2,6,8,1] => [4,3,5,2,6,8,1,7] => 1010010
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [6,5,4,3,2,7,1,8] => [4,3,5,2,7,1,6,8] => 1010100
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => [4,3,5,2,7,6,8,1] => 1010101
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [6,5,4,3,2,7,8,1] => [4,3,5,2,8,1,6,7] => 1010100
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,3,5,6,2,1,7,8] => [2,6,4,3,5,1,7,8] => [4,3,5,6,1,2,7,8] => 1001000
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [2,6,4,3,5,1,8,7] => [4,3,5,6,1,2,8,7] => 1001001
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8] => [4,3,5,6,2,7,1,8] => 1001010
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [8,6,4,3,5,2,7,1] => [4,3,5,6,2,7,8,1] => 1001001
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [8,7,4,3,5,6,2,1] => [4,3,5,6,7,2,8,1] => 1000101
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [2,8,4,3,5,6,7,1] => [4,3,5,6,7,8,1,2] => 1000010
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,3,5,7,6,2,8,1] => [8,6,4,3,5,7,2,1] => [4,3,5,7,2,6,8,1] => 1001001
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [2,8,4,3,5,7,6,1] => [4,3,5,7,6,8,1,2] => 1001010
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,3,5,8,7,6,2,1] => [2,6,4,3,5,7,8,1] => [4,3,5,8,1,2,6,7] => 1001000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,3,6,5,2,7,1,8] => [7,5,4,3,6,2,1,8] => [4,3,6,2,5,7,1,8] => 1010010
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,3,6,5,2,7,8,1] => [8,5,4,3,6,2,7,1] => [4,3,6,2,5,7,8,1] => 1010001
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [2,7,4,3,6,5,1,8] => [4,3,6,5,7,1,2,8] => 1010100
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => [4,3,6,5,7,2,8,1] => 1010101
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [2,8,4,3,6,5,7,1] => [4,3,6,5,7,8,1,2] => 1010010
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,3,6,7,5,8,2,1] => [2,8,4,3,7,6,5,1] => [4,3,6,7,5,8,1,2] => 1001010
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [2,5,4,3,8,6,7,1] => [4,3,6,7,8,1,2,5] => 1000100
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,3,6,8,7,5,2,1] => [2,5,4,3,7,6,8,1] => [4,3,6,8,1,2,5,7] => 1001000
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [8,5,4,3,6,7,2,1] => [4,3,7,2,5,6,8,1] => 1010001
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [2,8,4,3,6,7,5,1] => [4,3,7,5,6,8,1,2] => 1010010
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,7,6,8,5,2,1] => [2,5,4,3,8,7,6,1] => [4,3,7,6,8,1,2,5] => 1010100
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [2,5,4,3,6,8,7,1] => [4,3,7,8,1,2,5,6] => 1001000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [2,3,5,4,1,6,7,8] => [4,5,1,2,3,6,7,8] => 0100000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => [2,3,5,4,1,7,6,8] => [4,5,1,2,3,7,6,8] => 0100010
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [2,3,5,4,1,7,8,6] => [4,5,1,2,3,8,6,7] => 0100010
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,3,2,6,7,1,8] => [7,3,5,4,2,6,1,8] => [4,5,2,3,6,7,1,8] => 0100010
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [8,3,5,4,2,6,7,1] => [4,5,2,3,6,7,8,1] => 0100001
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [6,3,5,4,2,7,8,1] => [4,5,2,3,8,1,6,7] => 0100100
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [2,6,5,4,3,1,8,7] => [4,5,3,6,1,2,8,7] => 0101001
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [4,5,3,6,2,7,1,8] => 0101010
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [7,6,5,4,3,2,8,1] => [4,5,3,6,2,8,1,7] => 0101010
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1] => [4,5,3,6,7,2,8,1] => 0100101
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,3,6,7,8,2,1] => [2,8,5,4,3,6,7,1] => [4,5,3,6,7,8,1,2] => 0100010
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [2,7,5,4,3,6,8,1] => [4,5,3,6,8,1,2,7] => 0100100
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,3,7,6,2,1,8] => [2,6,5,4,3,7,1,8] => [4,5,3,7,1,2,6,8] => 0101000
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [2,8,5,4,3,7,6,1] => [4,5,3,7,6,8,1,2] => 0101010
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [2,6,5,4,3,8,7,1] => [4,5,3,7,8,1,2,6] => 0100100
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [2,3,6,4,5,1,7,8] => [4,5,6,1,2,3,7,8] => 0010000
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [2,3,6,4,5,1,8,7] => [4,5,6,1,2,3,8,7] => 0010001
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [8,3,6,4,5,2,7,1] => [4,5,6,2,3,7,8,1] => 0010001
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [7,3,6,4,5,2,8,1] => [4,5,6,2,3,8,1,7] => 0010010
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1] => [4,5,6,3,7,2,8,1] => 0010101
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,3,7,8,2,1] => [2,8,6,4,5,3,7,1] => [4,5,6,3,7,8,1,2] => 0010010
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [2,7,6,4,5,3,8,1] => [4,5,6,3,8,1,2,7] => 0010100
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [2,3,7,4,5,6,1,8] => [4,5,6,7,1,2,3,8] => 0001000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [8,3,7,4,5,6,2,1] => [4,5,6,7,2,3,8,1] => 0001001
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [2,8,7,4,5,6,3,1] => [4,5,6,7,3,8,1,2] => 0001010
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [2,3,8,4,5,6,7,1] => [4,5,6,7,8,1,2,3] => 0000100
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [2,3,7,4,5,6,8,1] => [4,5,6,8,1,2,3,7] => 0001000
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,5,7,6,3,2,8,1] => [8,3,6,4,5,7,2,1] => [4,5,7,2,3,6,8,1] => 0010001
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,6,3,8,2,1] => [2,8,6,4,5,7,3,1] => [4,5,7,3,6,8,1,2] => 0010010
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [2,3,8,4,5,7,6,1] => [4,5,7,6,8,1,2,3] => 0010100
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => [2,3,6,4,5,8,7,1] => [4,5,7,8,1,2,3,6] => 0001000
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [2,3,6,4,5,7,8,1] => [4,5,8,1,2,3,6,7] => 0010000
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [7,3,5,4,6,2,8,1] => [4,6,2,3,5,8,1,7] => 0100010
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [8,7,5,4,6,3,2,1] => [4,6,3,5,7,2,8,1] => 0100101
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,6,5,3,7,8,2,1] => [2,8,5,4,6,3,7,1] => [4,6,3,5,7,8,1,2] => 0100010
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,5,3,8,7,2,1] => [2,7,5,4,6,3,8,1] => [4,6,3,5,8,1,2,7] => 0100100
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [2,3,7,4,6,5,1,8] => [4,6,5,7,1,2,3,8] => 0101000
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [8,3,7,4,6,5,2,1] => [4,6,5,7,2,3,8,1] => 0101001
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,5,7,3,8,2,1] => [2,8,7,4,6,5,3,1] => [4,6,5,7,3,8,1,2] => 0101010
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [2,3,8,4,6,5,7,1] => [4,6,5,7,8,1,2,3] => 0100100
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [2,3,5,4,7,6,1,8] => [4,6,7,1,2,3,5,8] => 0010000
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [8,3,5,4,7,6,2,1] => [4,6,7,2,3,5,8,1] => 0010001
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,5,3,8,2,1] => [2,8,5,4,7,6,3,1] => [4,6,7,3,5,8,1,2] => 0010010
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [2,3,8,4,7,6,5,1] => [4,6,7,5,8,1,2,3] => 0010100
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [2,3,5,4,7,6,8,1] => [4,6,8,1,2,3,5,7] => 0010000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [2,3,5,4,6,7,1,8] => [4,7,1,2,3,5,6,8] => 0100000
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [2,3,8,4,6,7,5,1] => [4,7,5,6,8,1,2,3] => 0100100
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [2,3,5,4,6,7,8,1] => [4,8,1,2,3,5,6,7] => 0100000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => 1000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [2,3,4,5,1,6,8,7] => [5,1,2,3,4,6,8,7] => 1000001
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [2,3,4,5,1,8,7,6] => [5,1,2,3,4,7,8,6] => 1000001
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [2,3,4,5,1,7,8,6] => [5,1,2,3,4,8,6,7] => 1000010
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [6,3,4,5,2,1,7,8] => [5,2,3,4,6,1,7,8] => 1000100
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [6,3,4,5,2,1,8,7] => [5,2,3,4,6,1,8,7] => 1000101
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [7,3,4,5,2,6,1,8] => [5,2,3,4,6,7,1,8] => 1000010
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [8,3,4,5,2,6,7,1] => [5,2,3,4,6,7,8,1] => 1000001
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [7,3,4,5,2,6,8,1] => [5,2,3,4,6,8,1,7] => 1000010
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [6,3,4,5,2,7,1,8] => [5,2,3,4,7,1,6,8] => 1000100
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [6,3,4,5,2,7,8,1] => [5,2,3,4,8,1,6,7] => 1000100
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [7,6,4,5,3,2,1,8] => [5,3,4,6,2,7,1,8] => 1001010
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [7,6,4,5,3,2,8,1] => [5,3,4,6,2,8,1,7] => 1001010
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [2,8,4,5,3,6,7,1] => [5,3,4,6,7,8,1,2] => 1000010
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [2,6,4,5,3,8,7,1] => [5,3,4,7,8,1,2,6] => 1000100
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [2,3,6,5,4,1,8,7] => [5,4,6,1,2,3,8,7] => 1010001
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [7,3,6,5,4,2,1,8] => [5,4,6,2,3,7,1,8] => 1010010
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [8,3,6,5,4,2,7,1] => [5,4,6,2,3,7,8,1] => 1010001
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [7,3,6,5,4,2,8,1] => [5,4,6,2,3,8,1,7] => 1010010
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 1010101
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,6,3,7,8,2,1] => [2,8,6,5,4,3,7,1] => [5,4,6,3,7,8,1,2] => 1010010
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [2,3,7,5,4,6,1,8] => [5,4,6,7,1,2,3,8] => 1001000
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,4,6,7,3,2,8,1] => [8,3,7,5,4,6,2,1] => [5,4,6,7,2,3,8,1] => 1001001
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [2,8,7,5,4,6,3,1] => [5,4,6,7,3,8,1,2] => 1001010
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [2,3,8,5,4,6,7,1] => [5,4,6,7,8,1,2,3] => 1000100
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,4,7,6,3,2,8,1] => [8,3,6,5,4,7,2,1] => [5,4,7,2,3,6,8,1] => 1010001
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [2,8,6,5,4,7,3,1] => [5,4,7,3,6,8,1,2] => 1010010
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [2,3,8,5,4,7,6,1] => [5,4,7,6,8,1,2,3] => 1010100
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,4,8,7,6,3,2,1] => [2,3,6,5,4,7,8,1] => [5,4,8,1,2,3,6,7] => 1010000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [2,3,4,6,5,1,8,7] => [5,6,1,2,3,4,8,7] => 0100001
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [2,7,4,6,5,3,1,8] => [5,6,3,4,7,1,2,8] => 0100100
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,4,3,7,2,8,1] => [8,7,4,6,5,3,2,1] => [5,6,3,4,7,2,8,1] => 0100101
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,4,3,7,8,2,1] => [2,8,4,6,5,3,7,1] => [5,6,3,4,7,8,1,2] => 0100010
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,4,7,3,2,8,1] => [8,3,7,6,5,4,2,1] => [5,6,4,7,2,3,8,1] => 0101001
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,4,7,3,8,2,1] => [2,8,7,6,5,4,3,1] => [5,6,4,7,3,8,1,2] => 0101010
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [2,3,8,6,5,4,7,1] => [5,6,4,7,8,1,2,3] => 0100100
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [2,3,4,7,5,6,1,8] => [5,6,7,1,2,3,4,8] => 0010000
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [8,3,4,7,5,6,2,1] => [5,6,7,2,3,4,8,1] => 0010001
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [2,8,4,7,5,6,3,1] => [5,6,7,3,4,8,1,2] => 0010010
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [2,3,8,7,5,6,4,1] => [5,6,7,4,8,1,2,3] => 0010100
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [2,3,4,8,5,6,7,1] => [5,6,7,8,1,2,3,4] => 0001000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [2,3,4,7,5,6,8,1] => [5,6,8,1,2,3,4,7] => 0010000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [2,3,4,6,5,7,1,8] => [5,7,1,2,3,4,6,8] => 0100000
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [8,3,4,6,5,7,2,1] => [5,7,2,3,4,6,8,1] => 0100001
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [2,8,4,6,5,7,3,1] => [5,7,3,4,6,8,1,2] => 0100010
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [2,3,8,6,5,7,4,1] => [5,7,4,6,8,1,2,3] => 0100100
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [2,3,4,8,5,7,6,1] => [5,7,6,8,1,2,3,4] => 0101000
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [2,3,4,6,5,8,7,1] => [5,7,8,1,2,3,4,6] => 0010000
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,1] => [5,8,1,2,3,4,6,7] => 0100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => 1000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => [6,1,2,3,4,5,8,7] => 1000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [7,3,4,5,6,2,1,8] => [6,2,3,4,5,7,1,8] => 1000010
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [8,3,4,5,6,2,7,1] => [6,2,3,4,5,7,8,1] => 1000001
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [7,3,4,5,6,2,8,1] => [6,2,3,4,5,8,1,7] => 1000010
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [2,7,4,5,6,3,1,8] => [6,3,4,5,7,1,2,8] => 1000100
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [8,7,4,5,6,3,2,1] => [6,3,4,5,7,2,8,1] => 1000101
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [2,8,4,5,6,3,7,1] => [6,3,4,5,7,8,1,2] => 1000010
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [2,7,4,5,6,3,8,1] => [6,3,4,5,8,1,2,7] => 1000100
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [8,3,7,5,6,4,2,1] => [6,4,5,7,2,3,8,1] => 1001001
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [2,3,8,5,6,4,7,1] => [6,4,5,7,8,1,2,3] => 1000100
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [2,3,7,5,6,4,8,1] => [6,4,5,8,1,2,3,7] => 1001000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [2,3,4,7,6,5,1,8] => [6,5,7,1,2,3,4,8] => 1010000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [2,3,8,7,6,5,4,1] => [6,5,7,4,8,1,2,3] => 1010100
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [2,3,4,8,6,5,7,1] => [6,5,7,8,1,2,3,4] => 1001000
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [2,3,4,7,6,5,8,1] => [6,5,8,1,2,3,4,7] => 1010000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [2,3,4,5,7,6,1,8] => [6,7,1,2,3,4,5,8] => 0100000
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [8,3,4,5,7,6,2,1] => [6,7,2,3,4,5,8,1] => 0100001
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [2,3,8,5,7,6,4,1] => [6,7,4,5,8,1,2,3] => 0100100
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [2,3,4,8,7,6,5,1] => [6,7,5,8,1,2,3,4] => 0101000
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [2,3,4,5,8,6,7,1] => [6,7,8,1,2,3,4,5] => 0010000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [2,3,4,5,7,6,8,1] => [6,8,1,2,3,4,5,7] => 0100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => 1000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,3,4,5,6,7,2,1] => [7,2,3,4,5,6,8,1] => 1000001
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,3,1] => [7,3,4,5,6,8,1,2] => 1000010
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [2,3,8,5,6,7,4,1] => [7,4,5,6,8,1,2,3] => 1000100
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [2,3,4,8,6,7,5,1] => [7,5,6,8,1,2,3,4] => 1001000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [2,3,4,5,8,7,6,1] => [7,6,8,1,2,3,4,5] => 1010000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,1] => [7,8,1,2,3,4,5,6] => 0100000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => 1000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => 10000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => 01000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => 100000000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [2,3,4,5,6,8,7,1,9] => [7,8,1,2,3,4,5,6,9] => 01000000
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [1,3,4,5,6,7,9,8,2] => [1,8,9,2,3,4,5,6,7] => 00100000
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => 010000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => 1000000000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,9,8,1,10] => [8,9,1,2,3,4,5,6,7,10] => 010000000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [2,3,4,5,7,6,8,1,9] => [6,8,1,2,3,4,5,7,9] => 01000000
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [1,3,4,5,6,8,7,9,2] => [1,7,9,2,3,4,5,6,8] => 00100000
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,10,9,2] => [1,9,10,2,3,4,5,6,7,8] => 001000000
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,11,2] => [1,11,2,3,4,5,6,7,8,9,10] => 0100000000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [3,2,4,5,6,7,8,1,9] => [2,8,1,3,4,5,6,7,9] => 01000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [2,3,4,5,6,7,1,9,8] => [7,1,2,3,4,5,6,9,8] => 10000001
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,3] => [2,1,9,3,4,5,6,7,8] => 10100000
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [1,4,3,5,6,7,8,9,2] => [1,3,9,2,4,5,6,7,8] => 00100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => 10000000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [1,3,4,5,6,7,8,2,9] => [1,8,2,3,4,5,6,7,9] => 01000000
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,3] => [1,2,9,3,4,5,6,7,8] => 00100000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9] => [8,1,2,3,4,5,6,7,10,9] => 100000001
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3] => [2,1,10,3,4,5,6,7,8,9] => 101000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => [8,1,2,3,4,5,6,7,9,10] => 100000000
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [1,3,4,5,6,7,8,9,2,10] => [1,9,2,3,4,5,6,7,8,10] => 010000000
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,3,4,5,6,7,8,9] => 001000000
[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] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,9,1] => 00000001
[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] => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,7,9,1,8] => 00000010
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [9,2,3,4,5,6,8,7,1] => [2,3,4,5,6,8,7,9,1] => 00000101
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,7,8,6,9,1] => [9,2,3,4,5,8,7,6,1] => [2,3,4,5,7,8,6,9,1] => 00000101
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [4,2,3,5,6,7,8,9,1] => [2,3,9,1,4,5,6,7,8] => 00100000
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,1] => [2,9,1,3,4,5,6,7,8] => 01000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [9,3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,9,1] => 10000001
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [4,3,2,5,6,7,8,9,1] => [3,2,9,1,4,5,6,7,8] => 10100000
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [9,4,3,2,5,6,7,8,1] => [3,4,2,5,6,7,8,9,1] => 01000001
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => [9,8,3,4,5,6,7,2,1] => [3,4,5,6,7,8,2,9,1] => 00000101
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [2,9,3,4,5,6,7,8,1] => [3,4,5,6,7,8,9,1,2] => 00000010
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [2,4,3,5,6,7,8,9,1] => [3,9,1,2,4,5,6,7,8] => 01000000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [9,3,4,2,5,6,7,8,1] => [4,2,3,5,6,7,8,9,1] => 10000001
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,9,2,1] => [2,9,4,3,5,6,7,8,1] => [4,3,5,6,7,8,9,1,2] => 10000010
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,5,3,6,7,8,9,2,1] => [2,9,5,4,3,6,7,8,1] => [4,5,3,6,7,8,9,1,2] => 01000010
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [2,3,9,4,5,6,7,8,1] => [4,5,6,7,8,9,1,2,3] => 00000100
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,9,2,1] => [2,9,4,5,3,6,7,8,1] => [5,3,4,6,7,8,9,1,2] => 10000010
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [2,3,9,5,4,6,7,8,1] => [5,4,6,7,8,9,1,2,3] => 10000100
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [9,8,7,6,5,4,3,2,1] => [5,6,4,7,3,8,2,9,1] => 01010101
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [2,3,4,9,5,6,7,8,1] => [5,6,7,8,9,1,2,3,4] => 00001000
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,9,1] => [5,9,1,2,3,4,6,7,8] => 01000000
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [2,3,4,9,6,5,7,8,1] => [6,5,7,8,9,1,2,3,4] => 10001000
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [2,3,4,5,9,6,7,8,1] => [6,7,8,9,1,2,3,4,5] => 00010000
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [2,3,4,5,8,6,7,9,1] => [6,7,9,1,2,3,4,5,8] => 00100000
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [2,3,4,5,9,7,6,8,1] => [7,6,8,9,1,2,3,4,5] => 10010000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => [9,3,4,5,6,8,7,2,1] => [7,8,2,3,4,5,6,9,1] => 01000001
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [2,3,4,5,6,9,7,8,1] => [7,8,9,1,2,3,4,5,6] => 00100000
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,9,1] => [7,9,1,2,3,4,5,6,8] => 01000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,3,4,5,6,7,8,2,1] => [8,2,3,4,5,6,7,9,1] => 10000001
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [2,3,4,5,6,9,8,7,1] => [8,7,9,1,2,3,4,5,6] => 10100000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [2,3,4,5,6,7,9,8,1] => [8,9,1,2,3,4,5,6,7] => 01000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => 10000000
[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] => 00000000
[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] => 00000001
[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] => [1,2,3,4,5,6,8,9,7] => 00000001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => [1,2,3,4,5,7,8,9,6] => 00000001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => [1,2,3,4,6,7,8,9,5] => 00000001
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => [1,2,3,5,6,7,8,9,4] => 00000001
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => [1,2,4,5,6,7,8,9,3] => 00000001
[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] => [1,9,3,4,5,6,7,8,2] => [1,3,4,5,6,7,8,9,2] => 00000001
[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] => 000000000
[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] => 000000001
[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] => 00000010
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => 000000001
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,8,7,9,6] => 00000101
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => [1,2,3,4,5,6,8,9,10,7] => 000000001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,9,7,6,8,5] => [1,2,3,4,7,6,8,9,5] => 00001001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => [1,2,3,4,5,7,8,9,10,6] => 000000001
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [1,2,3,9,6,5,7,8,4] => [1,2,3,6,5,7,8,9,4] => 00010001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => [1,2,3,4,6,7,8,9,10,5] => 000000001
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [1,2,9,5,4,6,7,8,3] => [1,2,5,4,6,7,8,9,3] => 00100001
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => [1,2,3,5,6,7,8,9,10,4] => 000000001
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [1,9,4,3,5,6,7,8,2] => [1,4,3,5,6,7,8,9,2] => 01000001
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => [1,2,4,5,6,7,8,9,10,3] => 000000001
[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] => [1,10,3,4,5,6,7,8,9,2] => [1,3,4,5,6,7,8,9,10,2] => 000000001
[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] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,10,1] => 000000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000
[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] => 0000000001
[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] => 000000010
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,10,11,9] => 0000000001
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,8,9,6,7] => 00000010
[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] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,6,7,8] => 00000100
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,10,1] => 100000001
[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] => [1,11,3,4,5,6,7,8,9,10,2] => [1,3,4,5,6,7,8,9,10,11,2] => 0000000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,9,10] => 0000000010
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,7,8,9] => 000000100
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,5,6,7,8] => 00001000
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,6,7,8,9] => 000001000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,8,3,9,2] => [1,9,8,4,5,6,7,3,2] => [1,4,5,6,7,8,3,9,2] => 00000101
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => [1,3,9,4,5,6,7,8,2] => [1,4,5,6,7,8,9,2,3] => 00000010
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,4,5,6,7,8] => 00010000
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,4,3,2] => [1,3,4,9,5,6,7,8,2] => [1,5,6,7,8,9,2,3,4] => 00000100
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,5,6,7,8,9] => 000010000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,10,3,2] => [1,3,10,4,5,6,7,8,9,2] => [1,4,5,6,7,8,9,10,2,3] => 000000010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,2,10,1] => [10,9,3,4,5,6,7,8,2,1] => [3,4,5,6,7,8,9,2,10,1] => 000000101
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => 00000010
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => 00000100
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => 00000101
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => 00001000
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => 00001010
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => 00010000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => 00010101
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => 00100000
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => 00101010
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => 01000000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => 01000001
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,7,8] => 01000010
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => 01010000
[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] => 01010101
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => 01000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,7,6,5,4,3,2,8,9] => [1,3,4,5,6,7,2,8,9] => [1,7,2,3,4,5,6,8,9] => 01000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [1,3,4,5,6,7,2,9,8] => [1,7,2,3,4,5,6,9,8] => 01000001
[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] => 10000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => 10000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => 10000010
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,8,7] => [2,1,3,4,5,6,8,9,7] => [2,1,3,4,5,6,9,7,8] => 10000010
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => 10100000
[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] => 10101010
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [2,1,4,5,6,7,8,3,9] => [2,1,8,3,4,5,6,7,9] => 10100000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => 10000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => [3,1,2,4,5,6,7,9,8] => 10000001
[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] => 10010101
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [2,3,1,5,6,7,8,9,4] => [3,1,2,9,4,5,6,7,8] => 10010000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => 10000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [2,3,4,1,6,5,8,7,9] => [4,1,2,3,6,5,8,7,9] => 10001010
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [2,3,4,1,6,7,8,9,5] => [4,1,2,3,9,5,6,7,8] => 10001000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => 10000000
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [2,3,4,5,1,7,6,8,9] => [5,1,2,3,4,7,6,8,9] => 10000100
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [2,3,4,5,1,7,8,9,6] => [5,1,2,3,4,9,6,7,8] => 10000100
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => [6,1,2,3,4,5,7,8,9] => 10000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [2,3,4,5,6,1,8,9,7] => [6,1,2,3,4,5,9,7,8] => 10000010
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => 000000010
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => 000000100
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => 000000101
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => 000001000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => 000010000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => 000100000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => 000101010
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,4,5,6,7,8,9] => 000100000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => 001000000
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => 001010101
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => 010000000
[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] => 010101010
[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] => 100000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => 100000001
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => 101000000
[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] => 101010101
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7] => [2,1,6,3,4,5,10,7,8,9] => 101000100
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9] => [2,1,8,3,4,5,6,7,10,9] => 101000001
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => 100000000
[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] => 100101010
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [2,3,1,5,6,7,8,9,10,4] => [3,1,2,10,4,5,6,7,8,9] => 100100000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => 100000000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => [4,1,2,3,6,5,8,7,10,9] => 100010101
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7] => [4,1,2,3,6,5,10,7,8,9] => 100010100
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9] => [4,1,2,3,8,5,6,7,10,9] => 100010001
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5] => [4,1,2,3,10,5,6,7,8,9] => 100010000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => 100000000
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [2,3,4,5,1,7,8,9,10,6] => [5,1,2,3,4,10,6,7,8,9] => 100001000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => 100000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7] => [6,1,2,3,4,5,10,7,8,9] => 100000100
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => 100000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [2,3,4,5,6,7,1,9,10,8] => [7,1,2,3,4,5,6,10,8,9] => 100000010
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => 100000000
[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] => [2,3,1,4,5,6,7,8,9] => 01000000
[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] => [4,2,3,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => 00100000
[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] => [5,2,3,4,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => 00010000
[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] => [6,2,3,4,5,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => 00001000
[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] => [7,2,3,4,5,6,1,8,9] => [2,3,4,5,6,7,1,8,9] => 00000100
[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] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,7,8,1,9] => 00000010
[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] => [2,3,1,4,5,6,7,8,9,10] => 010000000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => 01000000
[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] => [9,2,3,4,5,6,7,8,1,10] => [2,3,4,5,6,7,8,9,1,10] => 000000010
[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] => 1000000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [2,1,3,4,5,6,9,8,7] => [2,1,3,4,5,6,8,9,7] => 10000001
[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] => [9,2,3,4,5,6,7,8,10,1] => [2,3,4,5,6,7,8,10,1,9] => 000000010
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => [1,3,2,4,5,6,8,9,7] => 01000001
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [3,2,1,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => 01000001
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => [2,8,3,4,5,6,7,1,9] => [3,4,5,6,7,8,1,2,9] => 00000100
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => 01000000
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,1] => [2,10,1,3,4,5,6,7,8,9] => 010000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,8,9,2,1] => [9,2,3,4,5,6,7,8,10,1] => 100000001
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,3,4,5,6,7,8,9,10,2,1] => [10,2,3,4,5,6,7,8,9,11,1] => 1000000001
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,9,8,2,1] => [8,9,2,3,4,5,6,7,10,1] => 010000001
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => 10100000
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,10,9,1] => [9,10,1,2,3,4,5,6,7,8] => 010000000
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [2,3,4,6,5,7,8,9,10,1] => [5,10,1,2,3,4,6,7,8,9] => 010000000
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,11,10,1] => [10,11,1,2,3,4,5,6,7,8,9] => 0100000000
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [3,2,1,5,6,7,8,9,4] => [2,3,1,9,4,5,6,7,8] => 01010000
[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] => [1,8,3,4,5,6,7,9,2] => [1,3,4,5,6,7,9,2,8] => 00000010
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => [2,3,4,5,6,7,1,9,8] => 00000101
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => [2,1,4,5,6,7,8,9,3] => 10000001
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [2,3,10,4,5,6,7,8,9,1] => [4,5,6,7,8,9,10,1,2,3] => 000000100
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [2,3,4,5,6,1,9,8,7] => [6,1,2,3,4,5,8,9,7] => 10000001
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [2,10,4,5,6,7,8,9,3,1] => [9,3,4,5,6,7,8,10,1,2] => 100000010
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8,9] => [3,2,1,5,4,6,7,8,9] => [2,3,1,5,4,6,7,8,9] => 01010000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => 01010101
[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] => [3,2,4,1,6,5,8,7,10,9] => [2,4,1,3,6,5,8,7,10,9] => 010010101
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => 010101010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [2,10,3,4,5,6,7,8,9,1] => [3,4,5,6,7,8,9,10,1,2] => 000000010
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,9,10,2,1] => [2,10,4,3,5,6,7,8,9,1] => [4,3,5,6,7,8,9,10,1,2] => 100000010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [2,11,3,4,5,6,7,8,9,10,1] => [3,4,5,6,7,8,9,10,11,1,2] => 0000000010
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2] => [1,6,7,5,8,4,9,3,10,2] => 001010101
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [5,6,4,7,3,8,2,9,1,10] => 010101010
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => 1000000000
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,11,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,11,1] => [2,11,1,3,4,5,6,7,8,9,10] => 0100000000
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [1,2,5,4,6,7,8,9,3] => [1,2,4,9,3,5,6,7,8] => 00010000
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [1,2,3,6,5,7,8,9,4] => [1,2,3,5,9,4,6,7,8] => 00001000
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,6,9,5,7,8] => 00000100
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,7,9,6,8] => 00000010
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [2,3,4,10,5,6,7,8,9,1] => [5,6,7,8,9,10,1,2,3,4] => 000001000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => 00100000
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [2,3,4,5,6,7,10,8,9,1] => [8,9,10,1,2,3,4,5,6,7] => 001000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => 0000000010
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [3,4,2,5,1,6,7,8,9] => 01010000
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [2,3,4,5,10,6,7,8,9,1] => [6,7,8,9,10,1,2,3,4,5] => 000010000
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [2,3,4,5,6,10,7,8,9,1] => [7,8,9,10,1,2,3,4,5,6] => 000100000
[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] => [10,2,3,4,5,6,7,8,9,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => 0000000010
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [6,2,3,4,5,1,9,8,7] => [2,3,4,5,6,1,8,9,7] => 00001001
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => 0101010101
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7,10,9] => [2,4,3,1,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => 010010101
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,8,7,9] => [4,3,2,1,6,5,8,7,9] => [3,2,4,1,6,5,8,7,9] => 10101010
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => 101010101
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => [10,3,2,5,4,7,6,9,8,1] => [3,2,5,4,7,6,9,8,10,1] => 101010101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [1,3,2,5,4,7,6,9,10,8] => 010101001
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => 010000000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => 101000000
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => [6,5,7,4,8,3,9,2,10,1] => 101010101
[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] => 10101010101
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,11,10,12,1] => [12,3,2,5,4,7,6,9,8,11,10,1] => [3,2,5,4,7,6,9,8,11,10,12,1] => 10101010101
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11] => [10,1,2,3,4,5,6,7,8,9,12,11] => 10000000001
[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] => [4,2,3,1,6,5,10,8,9,7] => [2,3,4,1,6,5,8,9,10,7] => 001010001
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [8,7,6,5,4,3,2,1,9] => [5,4,6,3,7,2,8,1,9] => 10101010
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,5,7,4,8,3,9,2] => [1,9,8,7,6,5,4,3,2] => [1,6,5,7,4,8,3,9,2] => 01010101
[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] => [2,1,4,3,6,5,10,8,9,7] => [2,1,4,3,6,5,8,9,10,7] => 101010001
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,1,7,8,9,10,6,5,4,3] => [2,1,4,5,6,10,7,8,9,3] => [2,1,7,8,9,10,3,4,5,6] => 100001000
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,6,5,9,10,8,7] => [2,4,3,1,6,5,8,10,9,7] => [3,4,1,2,6,5,9,10,7,8] => 010010010
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => [1,5,3,4,2,7,6,9,8] => [1,3,4,5,2,7,6,9,8] => 00010101
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [5,6,4,7,3,8,2,10,9,1] => [9,8,7,6,5,4,3,2,10,1] => [5,6,4,7,3,8,2,10,1,9] => 010101010
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [7,6,5,4,3,2,1,8,9] => [4,5,3,6,2,7,1,8,9] => 01010100
[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] => [4,2,3,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => 001010101
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation σ is a pair i<j such that i<σ(j)<σ(i). The element σ(j) is then an invisible inversion bottom.
A descent view in a permutation π is an element π(j) such that π(i+1)<π(j)<π(i), and additionally the smallest element in the decreasing run containing π(i) is smaller than the smallest element in the decreasing run containing π(j).
This map is a bijection χ:Sn→Sn, such that
  • the multiset of descent views in π is the multiset of invisible inversion bottoms in χ(π),
  • the set of left-to-right maxima of π is the set of maximal elements in the cycles of χ(π),
  • the set of global ascent of π is the set of global ascent of χ(π),
  • the set of maximal elements in the decreasing runs of π is the set of weak deficiency positions of χ(π), and
  • the set of minimal elements in the decreasing runs of π is the set of weak deficiency values of χ(π).
Map
inverse first fundamental transformation
Description
Let σ=(i11⋯i1k1)⋯(iℓ1⋯iℓkℓ) be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps σ to the permutation [i11,…,i1k1,…,iℓ1,…,iℓkℓ] in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation π of n letters and each 1≤i≤n−1 such that π(i)>π(i+1) we set wi=1, otherwise wi=0.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.