Identifier
-
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
St000326: Binary words ⟶ ℤ
Values
[1,0,1,0] => [2,1] => [2,1] => 1 => 1
[1,1,0,0] => [1,2] => [1,2] => 0 => 2
[1,0,1,0,1,0] => [2,1,3] => [2,1,3] => 10 => 1
[1,0,1,1,0,0] => [2,3,1] => [2,3,1] => 10 => 1
[1,1,0,0,1,0] => [3,1,2] => [3,1,2] => 10 => 1
[1,1,0,1,0,0] => [1,3,2] => [1,3,2] => 01 => 2
[1,1,1,0,0,0] => [1,2,3] => [1,3,2] => 01 => 2
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [2,1,4,3] => 101 => 1
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [2,4,1,3] => 100 => 1
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [2,1,4,3] => 101 => 1
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [2,4,1,3] => 100 => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,4,3,1] => 101 => 1
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [3,1,4,2] => 110 => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [3,4,1,2] => 100 => 1
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [3,1,4,2] => 110 => 1
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [1,4,3,2] => 011 => 2
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [1,4,3,2] => 011 => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [4,1,3,2] => 110 => 1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,3,2] => 011 => 2
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [1,4,3,2] => 011 => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,4,3,2] => 011 => 2
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [2,1,5,4,3] => 1011 => 1
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [2,5,1,4,3] => 1010 => 1
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => 1011 => 1
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [2,5,1,4,3] => 1010 => 1
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [2,5,4,1,3] => 1001 => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [2,1,5,4,3] => 1011 => 1
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [2,5,1,4,3] => 1010 => 1
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [2,1,5,4,3] => 1011 => 1
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [2,5,1,4,3] => 1010 => 1
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [2,5,4,1,3] => 1001 => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [2,1,5,4,3] => 1011 => 1
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [2,5,1,4,3] => 1010 => 1
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [2,5,4,1,3] => 1001 => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [2,5,4,3,1] => 1011 => 1
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [3,1,5,4,2] => 1101 => 1
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [3,5,1,4,2] => 1100 => 1
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [3,1,5,4,2] => 1101 => 1
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [3,5,1,4,2] => 1100 => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [3,5,4,1,2] => 1001 => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [3,1,5,4,2] => 1101 => 1
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [3,5,1,4,2] => 1100 => 1
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [3,1,5,4,2] => 1101 => 1
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [1,5,4,3,2] => 0111 => 2
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,5,4,3,2] => 0111 => 2
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [3,1,5,4,2] => 1101 => 1
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [1,5,4,3,2] => 0111 => 2
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [1,5,4,3,2] => 0111 => 2
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [1,5,4,3,2] => 0111 => 2
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [4,1,5,3,2] => 1110 => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [4,5,1,3,2] => 1100 => 1
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [4,1,5,3,2] => 1110 => 1
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [1,5,4,3,2] => 0111 => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [1,5,4,3,2] => 0111 => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [4,1,5,3,2] => 1110 => 1
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [1,5,4,3,2] => 0111 => 2
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [1,5,4,3,2] => 0111 => 2
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [1,5,4,3,2] => 0111 => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [5,1,4,3,2] => 1110 => 1
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [1,5,4,3,2] => 0111 => 2
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [1,5,4,3,2] => 0111 => 2
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [1,5,4,3,2] => 0111 => 2
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,5,4,3,2] => 0111 => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [2,6,5,4,1,3] => 10011 => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [2,6,5,4,1,3] => 10011 => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 10111 => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [2,6,5,4,1,3] => 10011 => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [2,1,6,5,4,3] => 10111 => 1
>>> Load all 2328 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 10110 => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 10101 => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 10011 => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 10111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [3,6,5,1,4,2] => 11001 => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [3,6,5,1,4,2] => 11001 => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [3,6,5,1,4,2] => 11001 => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 10011 => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [3,6,5,1,4,2] => 11001 => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [3,6,1,5,4,2] => 11010 => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [3,1,6,5,4,2] => 11011 => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [4,6,1,5,3,2] => 11100 => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [4,6,1,5,3,2] => 11100 => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [4,6,5,1,3,2] => 11001 => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [4,6,1,5,3,2] => 11100 => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [4,6,1,5,3,2] => 11100 => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [4,1,6,5,3,2] => 11101 => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [5,1,6,4,3,2] => 11110 => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [5,6,1,4,3,2] => 11100 => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [5,1,6,4,3,2] => 11110 => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [5,1,6,4,3,2] => 11110 => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [5,1,6,4,3,2] => 11110 => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [6,1,5,4,3,2] => 11110 => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [1,6,5,4,3,2] => 01111 => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 01111 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => [2,7,6,5,4,1,3] => 100111 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => [2,7,6,5,4,1,3] => 100111 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => [2,7,6,5,4,1,3] => 100111 => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => [2,7,6,5,4,1,3] => 100111 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => [2,1,7,6,5,4,3] => 101111 => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => [2,7,1,6,5,4,3] => 101110 => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => [2,7,6,1,5,4,3] => 101101 => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => [2,7,6,5,1,4,3] => 101011 => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => [2,7,6,5,4,1,3] => 100111 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [2,7,6,5,4,3,1] => 101111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => [3,7,6,5,1,4,2] => 110011 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [3,7,6,5,1,4,2] => 110011 => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => [3,7,6,5,1,4,2] => 110011 => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => [3,7,6,5,1,4,2] => 110011 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [3,7,6,5,4,1,2] => 100111 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => [3,7,6,5,1,4,2] => 110011 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => [3,7,6,1,5,4,2] => 110101 => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => [3,7,1,6,5,4,2] => 110110 => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => [3,1,7,6,5,4,2] => 110111 => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => [4,7,6,1,5,3,2] => 111001 => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => [4,7,6,1,5,3,2] => 111001 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => [4,7,6,1,5,3,2] => 111001 => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [4,7,6,5,1,3,2] => 110011 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => [4,7,6,1,5,3,2] => 111001 => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => [4,7,6,1,5,3,2] => 111001 => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => [4,7,1,6,5,3,2] => 111010 => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => [4,1,7,6,5,3,2] => 111011 => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => [5,7,1,6,4,3,2] => 111100 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => [5,7,1,6,4,3,2] => 111100 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [5,7,6,1,4,3,2] => 111001 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => [5,7,1,6,4,3,2] => 111100 => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => [5,7,1,6,4,3,2] => 111100 => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => [5,7,1,6,4,3,2] => 111100 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => [5,1,7,6,4,3,2] => 111101 => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => [6,1,7,5,4,3,2] => 111110 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [6,7,1,5,4,3,2] => 111100 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => [6,1,7,5,4,3,2] => 111110 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => [6,1,7,5,4,3,2] => 111110 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [6,1,7,5,4,3,2] => 111110 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [6,1,7,5,4,3,2] => 111110 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [7,1,6,5,4,3,2] => 111110 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => [1,7,6,5,4,3,2] => 011111 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,7,6,5,4,3,2] => 011111 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,8,3,5,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,7,8,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,6,3,7,8,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,6,1,3,7,8,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,6,1,7,3,8,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,8,5] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,6,7,8,3,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,6,7,8,3,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,6,1,7,8,3,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,6,7,1,8,3,5] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,7,8,1,3,5] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,7,3,5,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,7,3,5,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,4,7,1,3,5,8,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,7,8,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,7,8,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,7,1,3,8,5,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,7,8,3,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,8,3,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,7,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,7,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,7,8,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,5,7,3,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,1,5,7,3,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,1,7,3,8,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,8,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,5,7,8,3,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,7,8,3,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,5,7,1,8,3,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,7,8,1,3,6] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,8,5,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,8,5,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,4,8,3,5,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,8,3,5,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,4,8,1,3,5,6,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,4,3,5,8,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,4,5,8,3,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,5,8,3,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,4,5,8,1,3,6,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,8,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,8,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,4,5,6,8,3,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,4,1,5,6,8,3,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,4,5,1,6,8,3,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,4,5,6,1,8,3,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,4,5,6,8,1,3,7] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3,8] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,7,8,3] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,4,5,1,6,7,8,3] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,4,5,6,1,7,8,3] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3] => [2,8,7,6,5,4,1,3] => 1001111 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,8,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,8,4,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,8,4,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,8,4,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,5,6,8,3,4,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,6,8,3,4,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,5,1,3,6,7,8,4] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5,1,6,3,7,8,4] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5,6,1,3,7,8,4] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,7,3,8,4] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,7,3,8,4] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5,6,7,1,3,8,4] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,5,6,7,8,3,4] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5,1,6,7,8,3,4] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5,6,1,7,8,3,4] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5,6,7,1,8,3,4] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5,6,7,8,1,3,4] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,7,3,4,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,5,7,1,3,4,8,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,7,8,4,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,8,4,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,7,3,8,4,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,7,3,8,4,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,5,7,1,3,8,4,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,7,8,3,4,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,7,8,3,4,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,7,4,8,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,8,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,7,8,4,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,7,1,8,4,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,7,8,1,4,6] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,8,4,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,5,1,3,8,4,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,8,3,4,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,5,1,8,3,4,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,5,8,1,3,4,6,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,3,5,1,4,8,6,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,5,8,4,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,8,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,8,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,5,6,8,4,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,5,6,8,4,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,1,6,8,4,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,6,1,8,4,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,6,8,1,4,7] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4,8] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,5,6,7,8,4] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,4] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,5,1,6,7,8,4] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,5,6,1,7,8,4] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,5,6,7,1,8,4] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,6,7,8,1,4] => [2,8,7,6,5,4,1,3] => 1001111 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,7,4,8,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,6,1,7,3,4,8,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,6,3,7,8,4,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,6,1,3,7,8,4,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,1,6,7,3,8,4,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,6,1,7,3,8,4,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,6,7,1,3,8,4,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,6,7,8,3,4,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,6,1,7,8,3,4,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,7,8,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,4,8,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,3,6,7,1,4,8,5] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,3,6,7,8,4,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,3,1,6,7,8,4,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,8,4,5] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,3,6,7,8,1,4,5] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,8,4,5,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,8,4,5,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,1,6,8,3,4,5,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,6,1,8,3,4,5,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,6,8,1,3,4,5,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,8,5,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,8,5,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,8,5,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,8,5,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,8,5,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,8,4,5,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,8,4,5,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,3,6,8,1,4,5,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,8,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,8,5,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,8,5,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,8,1,5,7] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5,8] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,6,7,8,5] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,3,4,6,1,7,8,5] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,7,8,1,5] => [2,8,7,6,5,4,1,3] => 1001111 => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,7,3,8,4,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,7,1,3,8,4,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,7,8,3,4,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,7,8,1,3,4,5,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,1,7,3,4,8,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,7,1,3,4,8,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,1,3,7,4,8,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,7,4,8,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,1,4,8,5,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,1,3,7,8,4,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,1,7,8,4,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,7,3,4,5,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,7,4,5,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,7,1,4,5,8,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,8,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,3,4,7,8,5,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,1,4,7,8,5,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,4,7,1,8,5,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,4,7,8,1,5,6] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6,8] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,7,8,6] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,6] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,4,5,7,1,8,6] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,6] => [2,8,7,6,5,4,1,3] => 1001111 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,8,4,5,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,8,4,5,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,8,1,4,5,6,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,4,8,5,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,1,4,8,5,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,3,4,5,8,6,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,3,4,1,5,8,6,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,3,4,5,8,1,6,7] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,8,7] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,8,7] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,8,7] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7] => [2,8,7,6,5,4,1,3] => 1001111 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,8,7,6,5,4,3] => 1011111 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8] => [2,8,1,7,6,5,4,3] => 1011110 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8] => [2,8,7,1,6,5,4,3] => 1011101 => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [2,8,7,6,1,5,4,3] => 1011011 => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [2,8,7,6,5,1,4,3] => 1010111 => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [2,8,7,6,5,4,1,3] => 1001111 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [2,8,7,6,5,4,3,1] => 1011111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,8,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,8,5,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,8,5,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,8,2,5,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,8,2,5,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,7,8,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,6,2,7,8,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,6,2,7,8,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [3,4,6,1,2,7,8,5] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,6,7,2,8,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,6,7,2,8,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [3,4,6,1,7,2,8,5] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,8,5] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,6,7,8,2,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,6,7,8,2,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [3,4,6,1,7,8,2,5] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,4,6,7,1,8,2,5] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,6,7,8,1,2,5] => [3,8,7,6,5,1,4,2] => 1100111 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,7,5,8,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,7,2,5,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,7,2,5,8,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,7,1,2,5,8,6] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,7,8,5,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,7,2,8,5,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,7,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,7,8,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,7,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,7,8,6] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,4,5,7,2,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [3,4,1,5,7,2,8,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,8,6] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,8,2,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,5,7,8,2,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [3,4,5,1,7,8,2,6] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,7,1,8,2,6] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,7,8,1,2,6] => [3,8,7,6,5,1,4,2] => 1100111 => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,2,8,5,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,8,5,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,8,2,5,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,4,1,8,2,5,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,4,8,1,2,5,6,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,8,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,1,2,5,8,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,2,8,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,4,5,1,2,8,6,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,4,5,8,2,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,4,1,5,8,2,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,8,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,8,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,8,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,8,7] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [3,4,1,5,6,8,2,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,4,5,6,1,8,2,7] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,6,8,1,2,7] => [3,8,7,6,5,1,4,2] => 1100111 => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [3,8,7,6,5,1,4,2] => 1100111 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,5,6,7,8,2] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,4,5,1,6,7,8,2] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,4,5,6,1,7,8,2] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,2] => [3,8,7,6,5,1,4,2] => 1100111 => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [3,8,7,6,5,4,1,2] => 1001111 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,8,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,8,4,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,8,4,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,8,4,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,8,4,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,5,6,8,2,4,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,5,1,6,8,2,4,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,5,1,2,6,7,8,4] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,5,6,2,7,8,4] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5,1,6,2,7,8,4] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5,6,1,2,7,8,4] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,5,6,7,2,8,4] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5,1,6,7,2,8,4] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5,6,1,7,2,8,4] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,8,4] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,5,6,7,8,2,4] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5,1,6,7,8,2,4] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5,6,1,7,8,2,4] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5,6,7,1,8,2,4] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5,6,7,8,1,2,4] => [3,8,7,6,5,1,4,2] => 1100111 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,7,4,8,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,7,2,4,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,7,2,4,8,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,7,1,2,4,8,6] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,7,8,4,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,7,8,4,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,7,2,8,4,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,7,2,8,4,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,7,1,2,8,4,6] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,7,8,2,4,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,7,8,2,4,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,7,8,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,7,4,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,7,4,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,7,8,4,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,7,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,8,2,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,8,4,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,5,8,2,4,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,5,1,8,2,4,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,4,8,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,5,1,2,4,8,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,5,8,4,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,8,4,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,8,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,5,6,8,4,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,2,6,8,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,6,2,8,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,6,8,2,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,4] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,5,2,6,7,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,5,6,2,7,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,5,6,7,2,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,6,7,8,2,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,6,1,2,7,4,8,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,6,1,7,2,4,8,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,6,7,1,2,4,8,5] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,6,1,2,7,8,4,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,6,7,2,8,4,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,6,1,7,2,8,4,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,6,7,1,2,8,4,5] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,6,1,7,8,2,4,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [3,8,7,6,1,5,4,2] => 1101011 => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5,8] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,7,8,5] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,7,8,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,6,7,4,8,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,6,2,7,4,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,2,6,7,8,4,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,2,6,7,8,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,6,7,8,2,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,8,4,5,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,8,4,5,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,6,8,2,4,5,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,6,1,8,2,4,5,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,6,8,1,2,4,5,7] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,8,5,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,8,5,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,8,4,5,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,8,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,8,5,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,8,2,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,6,7,8,5] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,6,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,4,6,7,2,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4,6,7,8,2,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,7,2,8,4,5,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [3,7,1,2,8,4,5,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,7,8,2,4,5,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,7,1,8,2,4,5,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,7,8,1,2,4,5,6] => [3,8,7,1,6,5,4,2] => 1101101 => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [3,7,1,2,4,8,5,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [3,1,2,7,4,8,5,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,3,7,2,4,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,7,8,4,5,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,7,2,4,5,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,7,1,2,4,5,8,6] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,3,7,2,4,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [3,1,2,4,7,5,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,3,4,2,7,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,2,4,7,8,5,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,3,4,7,8,2,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6,8] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,8,6] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,4,5,7,8,2,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,8,1,2,4,5,6,7] => [3,8,1,7,6,5,4,2] => 1101110 => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,8,4,5,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,2,8,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,8,2,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,4,8,5,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,3,2,4,8,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,3,4,2,5,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,3,4,5,2,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,3,4,5,8,2,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,3,4,5,6,8,2,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8] => [3,1,8,7,6,5,4,2] => 1101111 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,8,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,8,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,8,7] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,8,3,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,8,3,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,8,3,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,8,3,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,5,6,8,2,3,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [4,5,1,6,8,2,3,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [4,8,7,6,1,5,3,2] => 1110011 => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7,8] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3,8] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3,8] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [4,8,7,6,1,5,3,2] => 1110011 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,6,7,8,3] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [4,5,1,6,2,7,8,3] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [4,5,6,1,2,7,8,3] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [4,1,5,6,7,2,8,3] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5,1,6,7,2,8,3] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5,6,1,7,2,8,3] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,8,3] => [4,8,7,6,1,5,3,2] => 1110011 => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,5,6,7,8,2,3] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5,1,6,7,8,2,3] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,3] => [4,8,7,6,1,5,3,2] => 1110011 => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [4,8,7,6,5,1,3,2] => 1100111 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,7,3,8,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,5,1,7,2,3,8,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,5,7,1,2,3,8,6] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,7,8,3,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,7,8,3,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,1,5,7,2,8,3,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,5,1,7,2,8,3,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,5,7,1,2,8,3,6] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,5,1,7,8,2,3,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [4,8,7,6,1,5,3,2] => 1110011 => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,7,8,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,7,8,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,7,3,8,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,7,3,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,7,8,3,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,7,8,3,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,7,8,2,3,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,8,3,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,8,3,6,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,8,2,3,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,8,2,3,6,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,5,8,1,2,3,6,7] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,8,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,8,6,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,8,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,8,3,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,8,3,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,8,2,3,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,8,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,8,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,5,2,6,8,3,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,5,6,8,2,3,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,3] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,3] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,5,2,6,7,8,3] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,5,6,2,7,8,3] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,3] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,6,7,2,3,8,5] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,6,1,7,2,3,8,5] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,6,7,1,2,3,8,5] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,6,1,2,7,8,3,5] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,6,7,2,8,3,5] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,6,1,7,2,8,3,5] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,6,7,1,2,8,3,5] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,6,7,8,2,3,5] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,6,1,7,8,2,3,5] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [4,8,7,6,1,5,3,2] => 1110011 => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5,8] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,6,2,3,7,8,5] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,6,3,7,8,5] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,6,2,3,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,6,7,3,8,5] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,2,7,3,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,6,7,2,8,3,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,6,7,8,2,3,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,8,3,5,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,8,3,5,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,8,2,3,5,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,8,2,3,5,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,8,1,2,3,5,7] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,8,5,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,8,5,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,8,3,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,8,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,8,5,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,8,3,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,6,7,8,5] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,6,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,6,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,6,3,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,6,7,8,3,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,7,2,8,3,5,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,7,1,2,8,3,5,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,7,8,2,3,5,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [4,7,1,8,2,3,5,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,7,8,1,2,3,5,6] => [4,8,7,1,6,5,3,2] => 1110101 => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,7,2,3,8,5,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [4,7,1,2,3,8,5,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,7,2,3,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,7,8,3,5,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,7,8,3,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,7,2,3,5,8,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,7,1,2,3,5,8,6] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,2,7,3,5,8,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,2,7,3,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,7,2,3,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,3,7,5,8,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,4,3,7,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,3,7,8,5,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,4,7,3,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,4,7,8,3,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6,8] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,8,6] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,4,5,7,3,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,4,5,7,8,3,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,8,2,3,5,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,8,1,2,3,5,6,7] => [4,8,1,7,6,5,3,2] => 1110110 => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,4,2,8,3,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,4,8,2,3,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,4,2,3,8,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,2,3,5,8,6,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,3,5,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,4,5,8,3,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,4,5,6,8,3,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8] => [4,1,8,7,6,5,3,2] => 1110111 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,3] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,6,1,2,7,3,8,4] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,6,7,2,3,8,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,1,2,3,8,4] => [5,8,7,1,6,4,3,2] => 1111001 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [5,1,6,2,7,8,3,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,6,1,2,7,8,3,4] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [5,1,6,7,2,8,3,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,6,1,7,2,8,3,4] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,6,7,1,2,8,3,4] => [5,8,7,1,6,4,3,2] => 1111001 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,6,7,8,2,3,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [5,6,1,7,8,2,3,4] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [5,8,7,1,6,4,3,2] => 1111001 => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [5,8,7,6,1,4,3,2] => 1110011 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4,8] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4,8] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4,8] => [5,8,7,1,6,4,3,2] => 1111001 => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [5,1,6,2,3,7,8,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [5,6,1,2,3,7,8,4] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [5,1,2,6,3,7,8,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,5,6,2,3,7,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,8,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [5,1,2,6,7,8,3,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,5,2,6,7,8,3,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,5,6,7,2,8,3,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,6,7,8,2,3,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,6,2,8,3,4,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,6,1,2,8,3,4,7] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,6,1,8,2,3,4,7] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,6,8,1,2,3,4,7] => [5,8,7,1,6,4,3,2] => 1111001 => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,8,4,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,8,4,7] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,8,4,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,1,2,6,8,3,4,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,8,3,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,8,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,8,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,8,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,8,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,2,5,6,8,3,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7,8] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,6,7,8,4] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,6,7,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,2,5,3,6,7,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,2,5,6,3,7,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,5,6,7,8,3,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,8,3,4,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,7,1,2,8,3,4,6] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,7,8,2,3,4,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,7,1,8,2,3,4,6] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,8,1,2,3,4,6] => [5,8,7,1,6,4,3,2] => 1111001 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,7,2,3,8,4,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,7,1,2,3,8,4,6] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,7,3,8,4,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,5,7,2,3,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,7,8,3,4,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,7,8,3,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,7,2,3,4,8,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,7,3,4,8,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,5,7,2,3,4,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,7,4,8,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,7,4,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,7,8,4,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,7,3,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,7,8,3,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,8,6] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,7,4,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,7,8,4,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,8,2,3,4,6,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,8,1,2,3,4,6,7] => [5,8,1,7,6,4,3,2] => 1111010 => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,5,2,8,3,4,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,5,8,2,3,4,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,3,8,4,6,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,5,2,3,8,4,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,8,6,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,5,8,4,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,5,6,8,4,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => [5,1,8,7,6,4,3,2] => 1111011 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,7,1,2,8,3,4,5] => [6,8,1,7,5,4,3,2] => 1111100 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,4,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,7,1,8,2,3,4,5] => [6,8,1,7,5,4,3,2] => 1111100 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [6,8,7,1,5,4,3,2] => 1111001 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,7,2,3,8,4,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,7,1,2,3,8,4,5] => [6,8,1,7,5,4,3,2] => 1111100 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [6,1,2,7,3,8,4,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,6,7,2,3,8,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [6,1,2,7,8,3,4,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,6,2,7,8,3,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,7,2,3,4,8,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,5] => [6,8,1,7,5,4,3,2] => 1111100 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [6,1,2,7,3,4,8,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,6,2,7,3,4,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,6,7,2,3,4,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [6,1,2,3,7,4,8,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,3,7,4,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [6,1,2,3,7,8,4,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,6,2,3,7,8,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,7,3,8,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,7,8,3,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,8] => [6,8,1,7,5,4,3,2] => 1111100 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5,8] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5,8] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,8,5] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,2,3,6,7,4,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,6,7,8,4,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,8,1,2,3,4,5,7] => [6,8,1,7,5,4,3,2] => 1111100 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,8,3,4,5,7] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,8,4,5,7] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,8,4,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,8,5,7] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,8,4,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8] => [6,1,8,7,5,4,3,2] => 1111101 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,5] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6] => [7,1,8,6,5,4,3,2] => 1111110 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [7,8,1,6,5,4,3,2] => 1111100 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,8,3,4,5,6] => [7,1,8,6,5,4,3,2] => 1111110 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,8,2,3,4,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1,2,3,8,4,5,6] => [7,1,8,6,5,4,3,2] => 1111110 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,7,2,3,8,4,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1,2,3,4,8,5,6] => [7,1,8,6,5,4,3,2] => 1111110 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,7,8,4,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [7,1,8,6,5,4,3,2] => 1111110 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,7,3,4,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [7,1,8,6,5,4,3,2] => 1111110 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [8,1,7,6,5,4,3,2] => 1111110 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,8,7,6,5,4,3,2] => 0111111 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [9,1,8,7,6,5,4,3,2] => 11111110 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [2,9,8,7,6,5,4,3,1] => 10111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [10,1,9,8,7,6,5,4,3,2] => 111111110 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => [8,1,9,7,6,5,4,3,2] => 11111110 => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [2,9,8,7,6,5,4,1,3] => 10011111 => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,10,9,8,7,6,5,4,3,1] => 101111111 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11,1,10,9,8,7,6,5,4,3,2] => 1111111110 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => [9,1,10,8,7,6,5,4,3,2] => 111111110 => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [8,1,9,7,6,5,4,3,2] => 11111110 => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,8] => [2,9,8,7,6,5,4,1,3] => 10011111 => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [2,10,9,8,7,6,5,4,1,3] => 100111111 => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1,11,9,8,7,6,5,4,3,2] => 1111111110 => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [9,1,10,8,7,6,5,4,3,2] => 111111110 => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => [8,1,10,9,7,6,5,4,3,2] => 111111101 => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1,2,3,4,5,9,6,7] => [8,1,9,7,6,5,4,3,2] => 11111110 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9] => [6,1,9,8,7,5,4,3,2] => 11111011 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,9,8] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [2,10,9,8,7,6,5,1,4,3] => 101011111 => 1
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,8,9,1,7] => [2,9,8,7,6,5,4,1,3] => 10011111 => 1
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,10,1,9] => [2,10,9,8,7,6,5,4,1,3] => 100111111 => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,11,9] => [10,1,11,9,8,7,6,5,4,3,2] => 1111111110 => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,10,7,8] => [9,1,10,8,7,6,5,4,3,2] => 111111110 => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [8,1,10,9,7,6,5,4,3,2] => 111111101 => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => [7,1,10,9,8,6,5,4,3,2] => 111111011 => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1,2,3,4,9,5,6,7] => [8,1,9,7,6,5,4,3,2] => 11111110 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,9,6] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9] => [5,1,9,8,7,6,4,3,2] => 11110111 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [2,10,9,8,7,6,1,5,4,3] => 101101111 => 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,9,1,7,8] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,9,7] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,10,9] => [2,10,9,8,7,6,5,1,4,3] => 101011111 => 1
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,7,8,9,1,6] => [2,9,8,7,6,5,4,1,3] => 10011111 => 1
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,10,1,8] => [2,10,9,8,7,6,5,4,1,3] => 100111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,1,2,3,4,5,10,6,7,8] => [9,1,10,8,7,6,5,4,3,2] => 111111110 => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => [6,1,10,9,8,7,5,4,3,2] => 111110111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1,2,3,9,4,5,6,7] => [8,1,9,7,6,5,4,3,2] => 11111110 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6,9] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,9,7,8] => [6,1,9,8,7,5,4,3,2] => 11111011 => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,9,7] => [6,1,9,8,7,5,4,3,2] => 11111011 => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,9,8] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [2,10,9,8,7,1,6,5,4,3] => 101110111 => 1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,9,7,8] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,9,7] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7,9] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [2,10,9,8,7,6,5,1,4,3] => 101011111 => 1
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,9,6] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,10,8] => [2,10,9,8,7,6,5,1,4,3] => 101011111 => 1
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,6,7,8,9,1,5] => [2,9,8,7,6,5,4,1,3] => 10011111 => 1
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,8,9,10,1,7] => [2,10,9,8,7,6,5,4,1,3] => 100111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1,2,3,4,10,5,6,7,8] => [9,1,10,8,7,6,5,4,3,2] => 111111110 => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => [5,1,10,9,8,7,6,4,3,2] => 111101111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,9,3,4,5,6,7] => [8,1,9,7,6,5,4,3,2] => 11111110 => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [8,9,1,7,6,5,4,3,2] => 11111100 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [2,10,9,8,1,7,6,5,4,3] => 101111011 => 1
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [2,3,4,5,9,1,6,7,8] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7,9] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,9,10,8] => [2,10,9,8,7,6,1,5,4,3] => 101101111 => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [3,9,8,7,6,5,4,1,2] => 10011111 => 1
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,6,7,8,9,1,4] => [2,9,8,7,6,5,4,1,3] => 10011111 => 1
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,7,8,9,10,1,6] => [2,10,9,8,7,6,5,4,1,3] => 100111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,1,2,3,10,4,5,6,7,8] => [9,1,10,8,7,6,5,4,3,2] => 111111110 => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,9,10,6] => [7,1,10,9,8,6,5,4,3,2] => 111111011 => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,9,2,3,4,5,6,7] => [8,1,9,7,6,5,4,3,2] => 11111110 => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,9,6,7,8] => [5,1,9,8,7,6,4,3,2] => 11110111 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,9,8] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [2,10,9,1,8,7,6,5,4,3] => 101111101 => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,9,6,7,8] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,9,6] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,10,1,7,8,9] => [2,10,9,8,7,6,1,5,4,3] => 101101111 => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,9,8,10] => [2,10,9,8,7,6,1,5,4,3] => 101101111 => 1
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,9,1,6,8] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,1,3] => [2,9,8,7,6,5,4,1,3] => 10011111 => 1
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,6,7,8,9,10,1,5] => [2,10,9,8,7,6,5,4,1,3] => 100111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,1,2,10,3,4,5,6,7,8] => [9,1,10,8,7,6,5,4,3,2] => 111111110 => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9,10] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [9,10,1,8,7,6,5,4,3,2] => 111111100 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,9,2,3,4,5,6,8] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9,10] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,9,10,7] => [2,10,9,8,7,1,6,5,4,3] => 101110111 => 1
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6,8,9] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,9,3] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,5,6,7,8,9,10,1,4] => [2,10,9,8,7,6,5,4,1,3] => 100111111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,1,10,2,3,4,5,6,7,8] => [9,1,10,8,7,6,5,4,3,2] => 111111110 => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6,9] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [4,1,2,3,9,5,6,7,8] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,9,7,8] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,9,7] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,9,5] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,9,7] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,8,9] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,5,6,7,1,8,4,9] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3,9] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,10,1,3] => [2,10,9,8,7,6,5,4,1,3] => 100111111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,9,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,7,4,9,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,9,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,9,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,7,9,4,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,9,4,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,9,6] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5,6,7,8,9,2,4] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,6,7,8,9,2,4,5] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,8,9,2,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,9,2,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,9,3] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,5,6,7,8,9,2,3] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,3] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,5,2,6,7,8,9,3,4] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,5,6,7,8,9,2,3,4] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,9,4] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,7,8,9,2,3,4,6] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,7,4,9,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,4] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,9,5] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,6,7,8,2,9,3,4,5] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,9,5,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,9,5,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,5] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,7,8,9,2,3,4,5,6] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,9,6] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,7,8,9,4,5,6] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,9,6] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,9,6] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,7,9,2,3,4,5,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,9,5,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,9,6,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,6] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,8,2,9,3,4,5,6,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [1,8,2,3,4,5,9,6,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,8,5,9,6,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,8,9,5,6,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,9,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,9,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,9,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,8,9,6,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,7] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => 01111111 => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7,9] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,8,9,5,7] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7,10] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,9,7] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8,10] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,9,8] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7,9] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,8,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,4,6,1,8,3,9,5,10,7] => [2,10,9,1,8,7,6,5,4,3] => 101111101 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [2,10,9,8,7,1,6,5,4,3] => 101110111 => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,8,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,10,7,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7,9] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,6,7,8,9,1,3,5] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,3,1,9,4,5,6,7,8] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,9,8] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,7,2,8,3,9,4,10,5,6] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7,10,9] => [2,10,9,1,8,7,6,5,4,3] => 101111101 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,9,8,10] => [2,10,9,8,1,7,6,5,4,3] => 101111011 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,9,7,8] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7,8,9] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,9,7,8] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,6,7,8,9,3,4] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,5,6,7,8,9,1,3,4] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,7,8,9,4,5] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,6,7,8,9,1,3,4,5] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,7,8,9,1,3,4,5,6] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,8,9,1,3,4,5,6,7] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,1,9,3,4,5,6,7,8] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,9,1,3,4,5,6,7,8] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,4,8,9,2,5,6,7] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,2] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7,8,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,1,5,6,7,8,9,2,3] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,9] => [5,1,9,8,7,6,4,3,2] => 11110111 => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,1,6,7,8,9,2,3,4] => [5,1,9,8,7,6,4,3,2] => 11110111 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,5] => [6,1,9,8,7,5,4,3,2] => 11111011 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,1,7,8,9,2,3,4,5] => [6,1,9,8,7,5,4,3,2] => 11111011 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,8,2,9,3,4,5,6] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [7,1,8,9,2,3,4,5,6] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,10,7,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,9,10,7] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,9,7,10,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,9,10,7,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,10,7,8,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6,10,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,8,5,9,6,10,7] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,1,4,3,10,5,6,7,8,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7,8,9,10] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,9,10,3] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,9,7,10,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,5,6,7,8,9,10,1,3,4] => [2,10,9,8,7,6,5,1,4,3] => 101011111 => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5,10,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,9,10,5] => [2,10,9,1,8,7,6,5,4,3] => 101111101 => 1
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6,7,8,9,10,1,3,4,5] => [2,10,9,8,7,6,1,5,4,3] => 101101111 => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,7,3,8,4,9,5,10,6] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [2,10,9,8,7,1,6,5,4,3] => 101110111 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,8,9,10,1,3,4,5,6,7] => [2,10,9,8,1,7,6,5,4,3] => 101111011 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,1,10,3,4,5,6,7,8,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,10,1,3,4,5,6,7,8,9] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,9,7,10,8] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6,10,9] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,8,5,9,6,10,7] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7,8,9,10] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,10,9] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,9,7,10,8] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,5,6,7,8,9,10,2,3] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,10,9] => [5,1,10,9,8,7,6,4,3,2] => 111101111 => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,6,7,8,9,10,2,3,4] => [5,1,10,9,8,7,6,4,3,2] => 111101111 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [6,1,10,9,8,7,5,4,3,2] => 111110111 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [6,1,7,8,9,2,3,4,10,5] => [6,1,10,9,8,7,5,4,3,2] => 111110111 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,9,10,4,5] => [6,1,10,9,8,7,5,4,3,2] => 111110111 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [6,1,7,8,9,10,2,3,4,5] => [6,1,10,9,8,7,5,4,3,2] => 111110111 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [7,1,8,2,9,3,10,4,5,6] => [7,1,10,9,8,6,5,4,3,2] => 111111011 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [7,1,8,9,2,3,10,4,5,6] => [7,1,10,9,8,6,5,4,3,2] => 111111011 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [7,1,8,9,10,2,3,4,5,6] => [7,1,10,9,8,6,5,4,3,2] => 111111011 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [8,1,9,2,10,3,4,5,6,7] => [8,1,10,9,7,6,5,4,3,2] => 111111101 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [8,1,9,10,2,3,4,5,6,7] => [8,1,10,9,7,6,5,4,3,2] => 111111101 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,8] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,9,8] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,9,8] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7,10,9] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6,10,9] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,8,4,9,6,7] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,10,8] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,9,6,8,10] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,7,9,6,8] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,9,8,10] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6,9,8] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,9,8,10] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7,10,9,11] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,10,9,11] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,10,7,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,10,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,8,3,5,7,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,9,5,7] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,8,2,3,9,4,5,6] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,9,5] => [6,1,9,8,7,5,4,3,2] => 11111011 => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,9,4,8] => [5,1,9,8,7,6,4,3,2] => 11110111 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6,9] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,9,6,8] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,9,6,8] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,10,7,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,10,7,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,9,6,8] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,8,5,10,7,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,10,7,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7,10,9] => [2,10,9,8,7,1,6,5,4,3] => 101110111 => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6,9] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,9,8] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6,9,8] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,9,4,6,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,7,2,9,4,10,6,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,9,6,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,9,6,10,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,9,6,10,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,10,7,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,8,9,10,5,6,7] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,7,8,9,10,3,4,5,6] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,7,8,9,10,2,3,4,5,6] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7,10,9] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7,10,9] => [6,1,10,9,8,7,5,4,3,2] => 111110111 => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,7,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,10,2,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [1,12,11,10,9,8,7,6,5,4,3,2] => 01111111111 => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,9,7,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [2,6,1,7,3,8,4,9,5] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,1,10,3] => [2,10,9,8,7,6,5,1,4,3] => 101011111 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,8,9,10,2,3,4,5,6,7] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,6,7,8,9,1,4,5] => [2,9,8,7,6,5,1,4,3] => 10101111 => 1
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2,9] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,6,7,8,9,10,2,3,4,5] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,5,6,7,8,9,10,2,3,4] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,5,6,7,8,9,10,2,3] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,10,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,10,5,7,9] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,9,5,10,7] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5,10,9] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,6,7,8,1,9,3,4] => [2,9,8,7,6,1,5,4,3] => 10110111 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [10,1,11,2,3,4,5,6,7,8,9] => [10,1,11,9,8,7,6,5,4,3,2] => 1111111110 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,9,6] => [7,1,9,8,6,5,4,3,2] => 11111101 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,8,6,10,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,9,6,10,8] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,3,9,1,4,5,6,7,8] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,5,6,7,8,9,4] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,10,2,3,4,5,6,7,9] => [8,1,10,9,7,6,5,4,3,2] => 111111101 => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,9,4] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [2,3,4,10,1,5,6,7,8,9] => [2,10,9,8,1,7,6,5,4,3] => 101111011 => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,9,3] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,6,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,9,2,10,3,4,5,6,7,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5,10,9] => [3,1,10,9,8,7,6,5,4,2] => 110111111 => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4,8,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6,10,9] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7,8,9] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8,9] => [2,9,8,7,1,6,5,4,3] => 10111011 => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7,9] => [2,1,9,8,7,6,5,4,3] => 10111111 => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,12,10,11] => [1,12,11,10,9,8,7,6,5,4,3,2] => 01111111111 => 2
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,5,6,7,8,9,2,4] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,6,7,8,9,2,3,5] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,8,9,2,3,4,5,7] => [6,1,9,8,7,5,4,3,2] => 11111011 => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7,8,9,10,11,2,3,4,5,6] => [1,11,10,9,8,7,6,5,4,3,2] => 0111111111 => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => 101111111 => 1
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6,9,11,12,10] => [1,12,11,10,9,8,7,6,5,4,3,2] => 01111111111 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,7,8,9,2,10,3,4,5,6] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,5,1,6,7,9,4,8] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,7,2,9,3,4,6,8] => [5,1,9,8,7,6,4,3,2] => 11110111 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,9,7] => [4,1,9,8,7,6,5,3,2] => 11101111 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [3,1,2,9,4,5,6,7,8] => [3,1,9,8,7,6,5,4,2] => 11011111 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,9,10,6] => [2,10,9,8,1,7,6,5,4,3] => 101111011 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7,8,9] => [2,9,8,1,7,6,5,4,3] => 10111101 => 1
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,9,10,5] => [2,10,9,1,8,7,6,5,4,3] => 101111101 => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7,8,9] => [2,9,1,8,7,6,5,4,3] => 10111110 => 1
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,9,10,4] => [2,10,1,9,8,7,6,5,4,3] => 101111110 => 1
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,9,10,11,12,8] => [1,12,11,10,9,8,7,6,5,4,3,2] => 01111111111 => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,10,8] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,7,2,8,3,9,5,10,6] => [4,1,10,9,8,7,6,5,3,2] => 111011111 => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => 011111111 => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,2 9,5 28,14 90,42 297,132
$F_{2} = q + q^{2}$
$F_{3} = 3\ q + 2\ q^{2}$
$F_{4} = 9\ q + 5\ q^{2}$
$F_{5} = 28\ q + 14\ q^{2}$
$F_{6} = 90\ q + 42\ q^{2}$
$F_{7} = 297\ q + 132\ q^{2}$
Description
The position of the first one in a binary word after appending a 1 at the end.
Regarding the binary word as a subset of $\{1,\dots,n,n+1\}$ that contains $n+1$, this is the minimal element of the set.
Regarding the binary word as a subset of $\{1,\dots,n,n+1\}$ that contains $n+1$, this is the minimal element of the set.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
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